LMFDB - Embedded newform 572.2.bq.a.49.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(49,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 12, 25]))

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

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

chi := DirichletCharacter("572.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bq (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.12
Character	$\chi$	$=$	572.49
Dual form			572.2.bq.a.537.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.201901 - 1.92096i) q^{3} +(1.20386 + 0.391159i) q^{5} +(-4.99946 + 0.525464i) q^{7} +(-0.714895 - 0.151956i) q^{9} +O(q^{10})$	\(q+(0.201901 - 1.92096i) q^{3} +(1.20386 + 0.391159i) q^{5} +(-4.99946 + 0.525464i) q^{7} +(-0.714895 - 0.151956i) q^{9} +(-3.16590 - 0.988460i) q^{11} +(-3.55935 + 0.575323i) q^{13} +(0.994464 - 2.23360i) q^{15} +(-2.54988 - 2.83193i) q^{17} +(-2.53820 - 5.70090i) q^{19} +9.70987i q^{21} +(0.896808 + 1.55332i) q^{23} +(-2.74880 - 1.99712i) q^{25} +(1.35440 - 4.16842i) q^{27} +(5.34677 + 2.38054i) q^{29} +(0.723072 - 0.234940i) q^{31} +(-2.53800 + 5.88202i) q^{33} +(-6.22420 - 1.32300i) q^{35} +(-1.37840 + 3.09594i) q^{37} +(0.386535 + 6.95355i) q^{39} +(4.59931 + 0.483407i) q^{41} +(-1.69704 + 2.93936i) q^{43} +(-0.801198 - 0.462572i) q^{45} +(-0.112971 + 0.155492i) q^{47} +(17.8714 - 3.79869i) q^{49} +(-5.95486 + 4.32646i) q^{51} +(-0.565212 - 1.73954i) q^{53} +(-3.42467 - 2.42834i) q^{55} +(-11.4637 + 3.72478i) q^{57} +(-2.25756 + 0.237279i) q^{59} +(-8.08734 - 8.98190i) q^{61} +(3.65394 + 0.384044i) q^{63} +(-4.51002 - 0.699664i) q^{65} +(0.274439 - 0.158447i) q^{67} +(3.16493 - 1.40912i) q^{69} +(3.90224 - 3.51359i) q^{71} +(6.23401 + 8.58037i) q^{73} +(-4.39139 + 4.87713i) q^{75} +(16.3472 + 3.27819i) q^{77} +(2.29072 + 7.05010i) q^{79} +(-9.73696 - 4.33518i) q^{81} +(-10.0218 - 3.25627i) q^{83} +(-1.96197 - 4.40667i) q^{85} +(5.65244 - 9.79032i) q^{87} +(-8.43217 + 4.86832i) q^{89} +(17.4925 - 4.74661i) q^{91} +(-0.305323 - 1.43643i) q^{93} +(-0.825693 - 7.85594i) q^{95} +(1.86500 - 8.77414i) q^{97} +(2.11309 + 1.18772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 20 q^{9}+O(q^{10}) $ 112 * q + 20 * q^9	$ 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) $ 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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
$3$	0.201901	−	1.92096i	0.116568	−	1.10907i	−0.767286	−	0.641305i	$-0.778393\pi$
$3$	0.201901	−	1.92096i	0.116568	−	1.10907i	0.883854	−	0.467764i	$-0.154940\pi$
$4$		0			0
$5$	1.20386	+	0.391159i	0.538384	+	0.174932i	0.565572	−	0.824699i	$-0.308655\pi$
$5$	1.20386	+	0.391159i	0.538384	+	0.174932i	−0.0271882	+	0.999630i	$0.508655\pi$
$6$		0			0
$7$	−4.99946	+	0.525464i	−1.88962	+	0.198607i	−0.977444	−	0.211197i	$-0.932264\pi$
$7$	−4.99946	+	0.525464i	−1.88962	+	0.198607i	−0.912174	+	0.409804i	$0.865597\pi$
$8$		0			0
$9$	−0.714895	−	0.151956i	−0.238298	−	0.0506519i
$10$		0			0
$11$	−3.16590	−	0.988460i	−0.954556	−	0.298032i
$11$	−3.16590	−	0.988460i	−0.954556	−	0.298032i
$12$		0			0
$13$	−3.55935	+	0.575323i	−0.987187	+	0.159566i
$13$	−3.55935	+	0.575323i	−0.987187	+	0.159566i
$14$		0			0
$15$	0.994464	−	2.23360i	0.256769	−	0.576714i
$16$		0			0
$17$	−2.54988	−	2.83193i	−0.618437	−	0.686844i	0.349815	−	0.936819i	$-0.386244\pi$
$17$	−2.54988	−	2.83193i	−0.618437	−	0.686844i	−0.968252	+	0.249975i	$0.919578\pi$
$18$		0			0
$19$	−2.53820	−	5.70090i	−0.582304	−	1.30788i	−0.929063	−	0.369922i	$-0.879385\pi$
$19$	−2.53820	−	5.70090i	−0.582304	−	1.30788i	0.346759	−	0.937954i	$-0.387282\pi$
$20$		0			0
$21$			9.70987i			2.11887i
$22$		0			0
$23$	0.896808	+	1.55332i	0.186997	+	0.323889i	0.944248	−	0.329236i	$-0.106791\pi$
$23$	0.896808	+	1.55332i	0.186997	+	0.323889i	−0.757250	+	0.653125i	$0.773458\pi$
$24$		0			0
$25$	−2.74880	−	1.99712i	−0.549761	−	0.399424i
$26$		0			0
$27$	1.35440	−	4.16842i	0.260655	−	0.802212i
$28$		0			0
$29$	5.34677	+	2.38054i	0.992871	+	0.442054i	0.837876	−	0.545861i	$-0.183797\pi$
$29$	5.34677	+	2.38054i	0.992871	+	0.442054i	0.154995	+	0.987915i	$0.450464\pi$
$30$		0			0
$31$	0.723072	−	0.234940i	0.129868	−	0.0421966i	−0.243362	−	0.969936i	$-0.578250\pi$
$31$	0.723072	−	0.234940i	0.129868	−	0.0421966i	0.373230	+	0.927739i	$0.378250\pi$
$32$		0			0
$33$	−2.53800	+	5.88202i	−0.441808	+	1.02393i
$34$		0			0
$35$	−6.22420	−	1.32300i	−1.05208	−	0.223627i
$36$		0			0
$37$	−1.37840	+	3.09594i	−0.226608	+	0.508970i	−0.990688	−	0.136151i	$-0.956527\pi$
$37$	−1.37840	+	3.09594i	−0.226608	+	0.508970i	0.764080	+	0.645122i	$0.223193\pi$
$38$		0			0
$39$	0.386535	+	6.95355i	0.0618952	+	1.11346i
$40$		0			0
$41$	4.59931	+	0.483407i	0.718292	+	0.0754955i	0.456621	−	0.889662i	$-0.349060\pi$
$41$	4.59931	+	0.483407i	0.718292	+	0.0754955i	0.261671	+	0.965157i	$0.415726\pi$
$42$		0			0
$43$	−1.69704	+	2.93936i	−0.258796	+	0.448249i	−0.965920	−	0.258842i	$-0.916659\pi$
$43$	−1.69704	+	2.93936i	−0.258796	+	0.448249i	0.707123	+	0.707090i	$0.249993\pi$
$44$		0			0
$45$	−0.801198	−	0.462572i	−0.119435	−	0.0689561i
$46$		0			0
$47$	−0.112971	+	0.155492i	−0.0164786	+	0.0226808i	−0.817177	−	0.576387i	$-0.804462\pi$
$47$	−0.112971	+	0.155492i	−0.0164786	+	0.0226808i	0.800698	+	0.599068i	$0.204462\pi$
$48$		0			0
$49$	17.8714	−	3.79869i	2.55306	−	0.542670i
$50$		0			0
$51$	−5.95486	+	4.32646i	−0.833848	+	0.605826i
$52$		0			0
$53$	−0.565212	−	1.73954i	−0.0776378	−	0.238945i	0.904704	−	0.426041i	$-0.140092\pi$
$53$	−0.565212	−	1.73954i	−0.0776378	−	0.238945i	−0.982341	+	0.187097i	$0.940092\pi$
$54$		0			0
$55$	−3.42467	−	2.42834i	−0.461783	−	0.327438i
$56$		0			0
$57$	−11.4637	+	3.72478i	−1.51840	+	0.493359i
$58$		0			0
$59$	−2.25756	+	0.237279i	−0.293910	+	0.0308911i	−0.250336	−	0.968159i	$-0.580541\pi$
$59$	−2.25756	+	0.237279i	−0.293910	+	0.0308911i	−0.0435738	+	0.999050i	$0.513874\pi$
$60$		0			0
$61$	−8.08734	−	8.98190i	−1.03548	−	1.15001i	−0.988516	−	0.151118i	$-0.951713\pi$
$61$	−8.08734	−	8.98190i	−1.03548	−	1.15001i	−0.0469620	−	0.998897i	$-0.514954\pi$
$62$		0			0
$63$	3.65394	+	0.384044i	0.460353	+	0.0483850i
$64$		0			0
$65$	−4.51002	−	0.699664i	−0.559399	−	0.0867826i
$66$		0			0
$67$	0.274439	−	0.158447i	0.0335281	−	0.0193574i	−0.483142	−	0.875542i	$-0.660505\pi$
$67$	0.274439	−	0.158447i	0.0335281	−	0.0193574i	0.516670	+	0.856184i	$0.327171\pi$
$68$		0			0
$69$	3.16493	−	1.40912i	0.381013	−	0.169638i
$70$		0			0
$71$	3.90224	−	3.51359i	0.463111	−	0.416987i	−0.404264	−	0.914642i	$-0.632472\pi$
$71$	3.90224	−	3.51359i	0.463111	−	0.416987i	0.867375	+	0.497656i	$0.165806\pi$
$72$		0			0
$73$	6.23401	+	8.58037i	0.729635	+	1.00426i	0.999148	+	0.0412599i	$0.0131372\pi$
$73$	6.23401	+	8.58037i	0.729635	+	1.00426i	−0.269513	+	0.962997i	$0.586863\pi$
$74$		0			0
$75$	−4.39139	+	4.87713i	−0.507074	+	0.563162i
$76$		0			0
$77$	16.3472	+	3.27819i	1.86294	+	0.373585i
$78$		0			0
$79$	2.29072	+	7.05010i	0.257726	+	0.793198i	0.993280	+	0.115733i	$0.0369216\pi$
$79$	2.29072	+	7.05010i	0.257726	+	0.793198i	−0.735555	+	0.677465i	$0.763078\pi$
$80$		0			0
$81$	−9.73696	−	4.33518i	−1.08188	−	0.481686i
$82$		0			0
$83$	−10.0218	−	3.25627i	−1.10003	−	0.357423i	−0.297918	−	0.954591i	$-0.596292\pi$
$83$	−10.0218	−	3.25627i	−1.10003	−	0.357423i	−0.802116	+	0.597169i	$0.796292\pi$
$84$		0			0
$85$	−1.96197	−	4.40667i	−0.212806	−	0.477970i
$86$		0			0
$87$	5.65244	−	9.79032i	0.606006	−	1.04963i
$88$		0			0
$89$	−8.43217	+	4.86832i	−0.893809	+	0.516041i	−0.875186	−	0.483786i	$-0.839261\pi$
$89$	−8.43217	+	4.86832i	−0.893809	+	0.516041i	−0.0186223	+	0.999827i	$0.505928\pi$
$90$		0			0
$91$	17.4925	−	4.74661i	1.83372	−	0.497580i
$92$		0			0
$93$	−0.305323	−	1.43643i	−0.0316605	−	0.148951i
$94$		0			0
$95$	−0.825693	−	7.85594i	−0.0847143	−	0.806003i
$96$		0			0
$97$	1.86500	−	8.77414i	0.189362	−	0.890879i	−0.776156	−	0.630542i	$-0.782833\pi$
$97$	1.86500	−	8.77414i	0.189362	−	0.890879i	0.965518	−	0.260337i	$-0.0838338\pi$
$98$		0			0
$99$	2.11309	+	1.18772i	0.212373	+	0.119371i
$100$		0			0
$101$	11.9154	−	13.2334i	1.18562	−	1.31677i	0.248148	−	0.968722i	$-0.420178\pi$
$101$	11.9154	−	13.2334i	1.18562	−	1.31677i	0.937477	−	0.348047i	$-0.113155\pi$
$102$		0			0
$103$	−0.0841029	+	0.0611043i	−0.00828690	+	0.00602079i	−0.591921	−	0.805996i	$-0.701630\pi$
$103$	−0.0841029	+	0.0611043i	−0.00828690	+	0.00602079i	0.583634	+	0.812017i	$0.301630\pi$
$104$		0			0
$105$	−3.79810	+	11.6894i	−0.370657	+	1.14076i
$106$		0			0
$107$	1.36107	−	12.9498i	0.131580	−	1.25190i	−0.707036	−	0.707177i	$-0.749968\pi$
$107$	1.36107	−	12.9498i	0.131580	−	1.25190i	0.838616	−	0.544723i	$-0.183365\pi$
$108$		0			0
$109$		−	3.68584i		−	0.353039i	−0.984297	−	0.176520i	$-0.943516\pi$
$109$		−	3.68584i		−	0.353039i	0.984297	−	0.176520i	$-0.0564839\pi$
$110$		0			0
$111$	5.66890	+	3.27294i	0.538068	+	0.310654i
$112$		0			0
$113$	6.05209	−	2.69457i	0.569333	−	0.253483i	−0.101819	−	0.994803i	$-0.532466\pi$
$113$	6.05209	−	2.69457i	0.569333	−	0.253483i	0.671152	+	0.741320i	$0.265800\pi$
$114$		0			0
$115$	0.472041	+	2.22078i	0.0440180	+	0.207088i
$116$		0			0
$117$	2.63199	+	0.129569i	0.243328	+	0.0119786i
$118$		0			0
$119$	14.2361	+	12.8182i	1.30502	+	1.17505i
$120$		0			0
$121$	9.04589	+	6.25874i	0.822354	+	0.568976i
$122$		0			0
$123$	1.85722	−	8.73751i	0.167459	−	0.787835i
$124$		0			0
$125$	−6.24813	−	8.59982i	−0.558850	−	0.769191i
$126$		0			0
$127$	8.27384	−	1.75866i	0.734184	−	0.156056i	0.174378	−	0.984679i	$-0.444209\pi$
$127$	8.27384	−	1.75866i	0.734184	−	0.156056i	0.559807	+	0.828623i	$0.310875\pi$
$128$		0			0
$129$	5.30377	+	3.85342i	0.466971	+	0.339274i
$130$		0			0
$131$	0.441761			0.0385968			0.0192984	−	0.999814i	$-0.493857\pi$
$131$	0.441761			0.0385968			0.0192984	+	0.999814i	$0.493857\pi$
$132$		0			0
$133$	15.6853	+	27.1677i	1.36008	+	2.35574i
$134$		0			0
$135$	3.26103	−	4.48842i	0.280665	−	0.386302i
$136$		0			0
$137$	−15.3417	+	13.8138i	−1.31073	+	1.18019i	−0.339894	+	0.940464i	$0.610391\pi$
$137$	−15.3417	+	13.8138i	−1.31073	+	1.18019i	−0.970840	+	0.239726i	$0.922942\pi$
$138$		0			0
$139$	1.02230	+	9.72651i	0.0867101	+	0.824992i	0.948298	+	0.317383i	$0.102804\pi$
$139$	1.02230	+	9.72651i	0.0867101	+	0.824992i	−0.861587	+	0.507609i	$0.830529\pi$
$140$		0			0
$141$	0.275885	+	0.248408i	0.0232337	+	0.0209197i
$142$		0			0
$143$	11.8373	+	1.69686i	0.989881	+	0.141899i
$144$		0			0
$145$	5.50561	+	4.95728i	0.457216	+	0.411680i
$146$		0			0
$147$	−3.68888	−	35.0973i	−0.304253	−	2.89478i
$148$		0			0
$149$	−10.8845	+	9.80044i	−0.891692	+	0.802883i	−0.981178	−	0.193105i	$-0.938144\pi$
$149$	−10.8845	+	9.80044i	−0.891692	+	0.802883i	0.0894858	+	0.995988i	$0.471478\pi$
$150$		0			0
$151$	5.51313	−	7.58817i	0.448652	−	0.617516i	−0.523455	−	0.852053i	$-0.675357\pi$
$151$	5.51313	−	7.58817i	0.448652	−	0.617516i	0.972107	+	0.234537i	$0.0753573\pi$
$152$		0			0
$153$	1.39257	+	2.41200i	0.112583	+	0.194999i
$154$		0			0
$155$	0.962379			0.0773002
$156$		0			0
$157$	3.06329	+	2.22561i	0.244477	+	0.177623i	0.703275	−	0.710917i	$-0.251720\pi$
$157$	3.06329	+	2.22561i	0.244477	+	0.177623i	−0.458799	+	0.888540i	$0.651720\pi$
$158$		0			0
$159$	−3.45571	+	0.734535i	−0.274056	+	0.0582524i
$160$		0			0
$161$	−5.29977	−	7.29450i	−0.417680	−	0.574887i
$162$		0			0
$163$	−0.241078	+	1.13418i	−0.0188827	+	0.0888360i	−0.986580	−	0.163279i	$-0.947793\pi$
$163$	−0.241078	+	1.13418i	−0.0188827	+	0.0888360i	0.967697	+	0.252115i	$0.0811262\pi$
$164$		0			0
$165$	−5.35620	+	6.08838i	−0.416980	+	0.473980i
$166$		0			0
$167$	−16.8229	−	15.1474i	−1.30179	−	1.17214i	−0.973787	−	0.227462i	$-0.926957\pi$
$167$	−16.8229	−	15.1474i	−1.30179	−	1.17214i	−0.328004	−	0.944676i	$-0.606376\pi$
$168$		0			0
$169$	12.3380	−	4.09555i	0.949078	−	0.315043i
$170$		0			0
$171$	0.948266	+	4.46124i	0.0725157	+	0.341160i
$172$		0			0
$173$	−14.5634	+	6.48405i	−1.10724	+	0.492973i	−0.877159	−	0.480199i	$-0.840564\pi$
$173$	−14.5634	+	6.48405i	−1.10724	+	0.492973i	−0.230077	+	0.973173i	$0.573898\pi$
$174$		0			0
$175$	14.7919	+	8.54013i	1.11817	+	0.645573i
$176$		0			0
$177$			4.38460i			0.329567i
$178$		0			0
$179$	1.16245	−	11.0599i	0.0868853	−	0.826659i	−0.861119	−	0.508403i	$-0.830236\pi$
$179$	1.16245	−	11.0599i	0.0868853	−	0.826659i	0.948005	−	0.318256i	$-0.103097\pi$
$180$		0			0
$181$	4.56216	−	14.0409i	0.339102	−	1.04365i	−0.625563	−	0.780173i	$-0.715131\pi$
$181$	4.56216	−	14.0409i	0.339102	−	1.04365i	0.964666	−	0.263477i	$-0.0848692\pi$
$182$		0			0
$183$	−18.8868	+	13.7220i	−1.39615	+	1.01436i
$184$		0			0
$185$	−2.87042	+	3.18792i	−0.211037	+	0.234381i
$186$		0			0
$187$	5.27343	+	11.4861i	0.385632	+	0.839945i
$188$		0			0
$189$	−4.58092	+	21.5515i	−0.333213	+	1.56764i
$190$		0			0
$191$	1.14309	+	10.8758i	0.0827114	+	0.786946i	0.954730	+	0.297474i	$0.0961440\pi$
$191$	1.14309	+	10.8758i	0.0827114	+	0.786946i	−0.872019	+	0.489473i	$0.837189\pi$
$192$		0			0
$193$	−3.31698	−	15.6052i	−0.238761	−	1.12328i	−0.920212	−	0.391420i	$-0.871984\pi$
$193$	−3.31698	−	15.6052i	−0.238761	−	1.12328i	0.681451	−	0.731864i	$-0.261349\pi$
$194$		0			0
$195$	−2.25461	+	8.52232i	−0.161456	+	0.610296i
$196$		0			0
$197$	−22.9631	+	13.2578i	−1.63605	+	0.944576i	−0.653880	+	0.756598i	$0.726860\pi$
$197$	−22.9631	+	13.2578i	−1.63605	+	0.944576i	−0.982173	+	0.187978i	$0.939807\pi$
$198$		0			0
$199$	−5.73462	+	9.93266i	−0.406517	+	0.704107i	−0.994497	−	0.104768i	$-0.966590\pi$
$199$	−5.73462	+	9.93266i	−0.406517	+	0.704107i	0.587980	+	0.808875i	$0.299923\pi$
$200$		0			0
$201$	−0.248962	−	0.559178i	−0.0175604	−	0.0394414i
$202$		0			0
$203$	−27.9818	−	9.09185i	−1.96394	−	0.638123i
$204$		0			0
$205$	5.34785	+	2.38102i	0.373510	+	0.166297i
$206$		0			0
$207$	−0.405089	−	1.24673i	−0.0281556	−	0.0866540i
$208$		0			0
$209$	2.40060	+	20.5574i	0.166053	+	1.42199i
$210$		0			0
$211$	11.1130	−	12.3422i	0.765049	−	0.849673i	−0.227212	−	0.973845i	$-0.572961\pi$
$211$	11.1130	−	12.3422i	0.765049	−	0.849673i	0.992261	+	0.124172i	$0.0396276\pi$
$212$		0			0
$213$	−5.96162	−	8.20546i	−0.408483	−	0.562229i
$214$		0			0
$215$	−3.19276	+	2.87478i	−0.217745	+	0.196058i
$216$		0			0
$217$	−3.49152	+	1.55452i	−0.237020	+	0.105528i
$218$		0			0
$219$	17.7412	−	10.2429i	1.19884	−	0.692152i
$220$		0			0
$221$	10.7052	+	8.61284i	0.720110	+	0.579362i
$222$		0			0
$223$	−9.16953	−	0.963757i	−0.614037	−	0.0645379i	−0.207596	−	0.978215i	$-0.566564\pi$
$223$	−9.16953	−	0.963757i	−0.614037	−	0.0645379i	−0.406442	+	0.913677i	$0.633231\pi$
$224$		0			0
$225$	1.66163	+	1.84543i	0.110775	+	0.123029i
$226$		0			0
$227$	28.0534	−	2.94853i	1.86197	−	0.195701i	0.894223	−	0.447621i	$-0.147729\pi$
$227$	28.0534	−	2.94853i	1.86197	−	0.195701i	0.967748	+	0.251920i	$0.0810621\pi$
$228$		0			0
$229$	25.6296	−	8.32756i	1.69365	−	0.550301i	0.706172	−	0.708041i	$-0.250421\pi$
$229$	25.6296	−	8.32756i	1.69365	−	0.550301i	0.987481	+	0.157740i	$0.0504207\pi$
$230$		0			0
$231$	9.59781	−	30.7405i	0.631490	−	2.02258i
$232$		0			0
$233$	−3.13347	−	9.64382i	−0.205280	−	0.631788i	−0.999702	−	0.0244208i	$-0.992226\pi$
$233$	−3.13347	−	9.64382i	−0.205280	−	0.631788i	0.794422	−	0.607367i	$-0.207774\pi$
$234$		0			0
$235$	−0.196824	+	0.143001i	−0.0128394	+	0.00932837i
$236$		0			0
$237$	14.0055	−	2.97696i	0.909754	−	0.193374i
$238$		0			0
$239$	3.13461	−	4.31441i	0.202761	−	0.279076i	−0.695512	−	0.718514i	$-0.744822\pi$
$239$	3.13461	−	4.31441i	0.202761	−	0.279076i	0.898273	+	0.439438i	$0.144822\pi$
$240$		0			0
$241$	−22.4541	−	12.9639i	−1.44640	−	0.835078i	−0.448133	−	0.893967i	$-0.647911\pi$
$241$	−22.4541	−	12.9639i	−1.44640	−	0.835078i	−0.998265	+	0.0588892i	$0.981244\pi$
$242$		0			0
$243$	−3.71922	+	6.44188i	−0.238588	+	0.413247i
$244$		0			0
$245$	23.0006	+	2.41747i	1.46946	+	0.154446i
$246$		0			0
$247$	12.3142	+	18.8312i	0.783535	+	1.19820i
$248$		0			0
$249$	−8.27860	+	18.5940i	−0.524635	+	1.17835i
$250$		0			0
$251$	−21.5406	−	4.57860i	−1.35963	−	0.288999i	−0.530326	−	0.847794i	$-0.677930\pi$
$251$	−21.5406	−	4.57860i	−1.35963	−	0.288999i	−0.829306	+	0.558795i	$0.811264\pi$
$252$		0			0
$253$	−1.30382	−	5.80411i	−0.0819703	−	0.364901i
$254$		0			0
$255$	−8.86118	+	2.87917i	−0.554908	+	0.180301i
$256$		0			0
$257$	−25.3636	−	11.2926i	−1.58214	−	0.704414i	−0.587636	−	0.809125i	$-0.699941\pi$
$257$	−25.3636	−	11.2926i	−1.58214	−	0.704414i	−0.994503	+	0.104711i	$0.966608\pi$
$258$		0			0
$259$	5.26446	−	16.2023i	0.327118	−	1.00676i
$260$		0			0
$261$	−3.46065	−	2.51431i	−0.214209	−	0.155632i
$262$		0			0
$263$	2.69955	+	4.67576i	0.166461	+	0.288320i	0.937173	−	0.348864i	$-0.113433\pi$
$263$	2.69955	+	4.67576i	0.166461	+	0.288320i	−0.770712	+	0.637184i	$0.780099\pi$
$264$		0			0
$265$		−	2.31526i		−	0.142225i
$266$		0			0
$267$	7.64940	+	17.1808i	0.468135	+	1.05145i
$268$		0			0
$269$	−18.7338	−	20.8059i	−1.14222	−	1.26856i	−0.958346	−	0.285611i	$-0.907804\pi$
$269$	−18.7338	−	20.8059i	−1.14222	−	1.26856i	−0.183872	−	0.982950i	$-0.558863\pi$
$270$		0			0
$271$	−7.43123	+	16.6908i	−0.451415	+	1.01390i	0.534272	+	0.845312i	$0.320586\pi$
$271$	−7.43123	+	16.6908i	−0.451415	+	1.01390i	−0.985688	+	0.168583i	$0.946081\pi$
$272$		0			0
$273$	−5.58631	−	34.5609i	−0.338099	−	2.09172i
$274$		0			0
$275$	6.72837	+	9.03978i	0.405736	+	0.545119i
$276$		0			0
$277$	10.2279	+	2.17401i	0.614535	+	0.130624i	0.504655	−	0.863321i	$-0.331620\pi$
$277$	10.2279	+	2.17401i	0.614535	+	0.130624i	0.109881	+	0.993945i	$0.464953\pi$
$278$		0			0
$279$	−0.552622	+	0.0580829i	−0.0330846	+	0.00347733i
$280$		0			0
$281$	−13.1594	−	4.27574i	−0.785022	−	0.255069i	−0.111039	−	0.993816i	$-0.535418\pi$
$281$	−13.1594	−	4.27574i	−0.785022	−	0.255069i	−0.673983	+	0.738747i	$0.735418\pi$
$282$		0			0
$283$	−3.41315	+	32.4739i	−0.202890	+	1.93037i	0.138321	+	0.990387i	$0.455829\pi$
$283$	−3.41315	+	32.4739i	−0.202890	+	1.93037i	−0.341212	+	0.939986i	$0.610837\pi$
$284$		0			0
$285$	−15.2577			−0.903788
$286$		0			0
$287$	−23.2481			−1.37229
$288$		0			0
$289$	0.259049	−	2.46469i	0.0152382	−	0.144982i
$290$		0			0
$291$	−16.4783	−	5.35411i	−0.965973	−	0.313864i
$292$		0			0
$293$	24.0774	−	2.53064i	1.40662	−	0.147842i	0.629405	−	0.777078i	$-0.283299\pi$
$293$	24.0774	−	2.53064i	1.40662	−	0.147842i	0.777214	+	0.629236i	$0.216632\pi$
$294$		0			0
$295$	−2.81061	−	0.597414i	−0.163640	−	0.0347828i
$296$		0			0
$297$	−8.40822	+	11.8580i	−0.487894	+	0.688073i
$298$		0			0
$299$	−4.08572	−	5.01285i	−0.236283	−	0.289901i
$300$		0			0
$301$	6.93976	−	15.5870i	0.400001	−	0.898417i
$302$		0			0
$303$	−23.0151	−	25.5609i	−1.32218	−	1.46843i
$304$		0			0
$305$	−6.22270	−	13.9764i	−0.356311	−	0.800287i
$306$		0			0
$307$		−	18.6991i		−	1.06721i	−0.845733	−	0.533606i	$-0.820836\pi$
$307$		−	18.6991i		−	1.06721i	0.845733	−	0.533606i	$-0.179164\pi$
$308$		0			0
$309$	0.100399	+	0.173896i	0.00571148	+	0.00989257i
$310$		0			0
$311$	0.243441	+	0.176870i	0.0138043	+	0.0100294i	0.594666	−	0.803973i	$-0.297284\pi$
$311$	0.243441	+	0.176870i	0.0138043	+	0.0100294i	−0.580862	+	0.814002i	$0.697284\pi$
$312$		0			0
$313$	−5.34967	+	16.4646i	−0.302381	+	0.930634i	0.678260	+	0.734822i	$0.262734\pi$
$313$	−5.34967	+	16.4646i	−0.302381	+	0.930634i	−0.980641	+	0.195812i	$0.937266\pi$
$314$		0			0
$315$	4.24862	+	1.89161i	0.239382	+	0.106580i
$316$		0			0
$317$	0.912039	−	0.296339i	0.0512252	−	0.0166441i	−0.283292	−	0.959034i	$-0.591427\pi$
$317$	0.912039	−	0.296339i	0.0512252	−	0.0166441i	0.334518	+	0.942390i	$0.391427\pi$
$318$		0			0
$319$	−14.5743	−	12.8216i	−0.816004	−	0.717873i
$320$		0			0
$321$	−24.6012	−	5.22915i	−1.37311	−	0.291863i
$322$		0			0
$323$	−9.67243	+	21.7246i	−0.538189	+	1.20879i
$324$		0			0
$325$	10.9330	+	5.52702i	0.606451	+	0.306584i
$326$		0			0
$327$	−7.08036	−	0.744176i	−0.391545	−	0.0411530i
$328$		0			0
$329$	0.483091	−	0.836738i	0.0266337	−	0.0461308i
$330$		0			0
$331$	−6.76313	−	3.90470i	−0.371735	−	0.214622i	0.302481	−	0.953155i	$-0.402185\pi$
$331$	−6.76313	−	3.90470i	−0.371735	−	0.214622i	−0.674216	+	0.738534i	$0.735518\pi$
$332$		0			0
$333$	1.45586	−	2.00382i	0.0797807	−	0.109809i
$334$		0			0
$335$	0.392365	−	0.0833998i	0.0214372	−	0.00455662i
$336$		0			0
$337$	0.165207	−	0.120030i	0.00899940	−	0.00653845i	−0.583276	−	0.812274i	$-0.698230\pi$
$337$	0.165207	−	0.120030i	0.00899940	−	0.00653845i	0.592276	+	0.805735i	$0.298230\pi$
$338$		0			0
$339$	−3.95424	−	12.1699i	−0.214765	−	0.660978i
$340$		0			0
$341$	−2.52141	+	0.0290710i	−0.136542	+	0.00157428i
$342$		0			0
$343$	−53.8847	+	17.5082i	−2.90950	+	0.945353i
$344$		0			0
$345$	4.36134	−	0.458395i	0.234807	−	0.0246792i
$346$		0			0
$347$	10.0299	+	11.1393i	0.538434	+	0.597992i	0.949559	−	0.313587i	$-0.101531\pi$
$347$	10.0299	+	11.1393i	0.538434	+	0.597992i	−0.411125	+	0.911579i	$0.634864\pi$
$348$		0			0
$349$	15.5600	+	1.63542i	0.832905	+	0.0875419i	0.511375	−	0.859358i	$-0.329136\pi$
$349$	15.5600	+	1.63542i	0.832905	+	0.0875419i	0.321530	+	0.946899i	$0.395803\pi$
$350$		0			0
$351$	−2.42261	+	15.6161i	−0.129309	+	0.833525i
$352$		0			0
$353$	6.70717	−	3.87239i	0.356987	−	0.206106i	−0.310771	−	0.950485i	$-0.600587\pi$
$353$	6.70717	−	3.87239i	0.356987	−	0.206106i	0.667758	+	0.744378i	$0.267254\pi$
$354$		0			0
$355$	6.07214	−	2.70349i	0.322276	−	0.143486i
$356$		0			0
$357$	27.4977	−	24.7590i	1.45533	−	1.31039i
$358$		0			0
$359$	10.3392	+	14.2308i	0.545685	+	0.751071i	0.989419	−	0.145088i	$-0.0463465\pi$
$359$	10.3392	+	14.2308i	0.545685	+	0.751071i	−0.443734	+	0.896158i	$0.646347\pi$
$360$		0			0
$361$	−13.3443	+	14.8203i	−0.702331	+	0.780018i
$362$		0			0
$363$	13.8492	−	16.1132i	0.726894	−	0.845723i
$364$		0			0
$365$	4.14860	+	12.7681i	0.217148	+	0.668312i
$366$		0			0
$367$	−11.0572	−	4.92297i	−0.577180	−	0.256977i	0.0973184	−	0.995253i	$-0.468973\pi$
$367$	−11.0572	−	4.92297i	−0.577180	−	0.256977i	−0.674499	+	0.738276i	$0.735640\pi$
$368$		0			0
$369$	−3.21457	−	1.04448i	−0.167344	−	0.0543733i
$370$		0			0
$371$	3.73982	+	8.39977i	0.194162	+	0.436094i
$372$		0			0
$373$	−8.83564	+	15.3038i	−0.457492	+	0.792399i	−0.998828	−	0.0484072i	$-0.984585\pi$
$373$	−8.83564	+	15.3038i	−0.457492	+	0.792399i	0.541336	+	0.840807i	$0.317919\pi$
$374$		0			0
$375$	−17.7814	+	10.2661i	−0.918230	+	0.530140i
$376$		0			0
$377$	−20.4006	−	5.39705i	−1.05069	−	0.277962i
$378$		0			0
$379$	4.57296	+	21.5141i	0.234897	+	1.10510i	0.924579	+	0.380991i	$0.124417\pi$
$379$	4.57296	+	21.5141i	0.234897	+	1.10510i	−0.689682	+	0.724113i	$0.742249\pi$
$380$		0			0
$381$	−1.70782	−	16.2488i	−0.0874943	−	0.832452i
$382$		0			0
$383$	−7.63465	+	35.9182i	−0.390112	+	1.83533i	0.143558	+	0.989642i	$0.454146\pi$
$383$	−7.63465	+	35.9182i	−0.390112	+	1.83533i	−0.533670	+	0.845693i	$0.679188\pi$
$384$		0			0
$385$	18.3975	+	10.3409i	0.937624	+	0.527019i
$386$		0			0
$387$	1.65986	−	1.84346i	0.0843754	−	0.0937084i
$388$		0			0
$389$	22.7187	−	16.5061i	1.15188	−	0.836892i	0.163153	−	0.986601i	$-0.447833\pi$
$389$	22.7187	−	16.5061i	1.15188	−	0.836892i	0.988730	+	0.149708i	$0.0478335\pi$
$390$		0			0
$391$	2.11213	−	6.50048i	0.106815	−	0.328743i
$392$		0			0
$393$	0.0891921	−	0.848607i	0.00449915	−	0.0428065i
$394$		0			0
$395$			9.38339i			0.472130i
$396$		0			0
$397$	−20.4515	−	11.8077i	−1.02643	−	0.592612i	−0.110472	−	0.993879i	$-0.535236\pi$
$397$	−20.4515	−	11.8077i	−1.02643	−	0.592612i	−0.915961	+	0.401268i	$0.868570\pi$
$398$		0			0
$399$	55.3550	−	24.6456i	2.77122	−	1.23382i
$400$		0			0
$401$	6.22921	+	29.3061i	0.311072	+	1.46348i	0.804636	+	0.593768i	$0.202360\pi$
$401$	6.22921	+	29.3061i	0.311072	+	1.46348i	−0.493564	+	0.869709i	$0.664306\pi$
$402$		0			0
$403$	−2.43850	+	1.25224i	−0.121471	+	0.0623783i
$404$		0			0
$405$	−10.0262	−	9.02766i	−0.498207	−	0.448588i
$406$		0			0
$407$	7.42411	−	8.43897i	0.367999	−	0.418304i
$408$		0			0
$409$	−1.06723	+	5.02092i	−0.0527711	+	0.248268i	−0.996624	−	0.0820965i	$-0.973838\pi$
$409$	−1.06723	+	5.02092i	−0.0527711	+	0.248268i	0.943853	+	0.330365i	$0.107172\pi$
$410$		0			0
$411$	23.4382	+	32.2600i	1.15612	+	1.59127i
$412$		0			0
$413$	11.1619	−	2.37254i	0.549241	−	0.116745i
$414$		0			0
$415$	−10.7911	−	7.84022i	−0.529716	−	0.384861i
$416$		0			0
$417$	18.8907			0.925081
$418$		0			0
$419$	−10.7234	−	18.5735i	−0.523872	−	0.907374i	−0.999614	−	0.0277885i	$-0.991153\pi$
$419$	−10.7234	−	18.5735i	−0.523872	−	0.907374i	0.475741	−	0.879585i	$-0.342180\pi$
$420$		0			0
$421$	7.99038	−	10.9978i	0.389427	−	0.536001i	−0.568624	−	0.822598i	$-0.692524\pi$
$421$	7.99038	−	10.9978i	0.389427	−	0.536001i	0.958051	+	0.286597i	$0.0925240\pi$
$422$		0			0
$423$	0.104391	−	0.0939938i	0.00507565	−	0.00457013i
$424$		0			0
$425$	1.35341	+	12.8768i	0.0656501	+	0.624619i
$426$		0			0
$427$	45.1520	+	40.6550i	2.18506	+	1.96743i
$428$		0			0
$429$	5.64957	−	22.3963i	0.272764	−	1.08131i
$430$		0			0
$431$	−19.7348	−	17.7693i	−0.950593	−	0.855918i	0.0390834	−	0.999236i	$-0.487556\pi$
$431$	−19.7348	−	17.7693i	−0.950593	−	0.855918i	−0.989677	+	0.143318i	$0.954223\pi$
$432$		0			0
$433$	−2.32717	−	22.1415i	−0.111837	−	1.06405i	−0.896169	−	0.443713i	$-0.853661\pi$
$433$	−2.32717	−	22.1415i	−0.111837	−	1.06405i	0.784332	−	0.620341i	$-0.213006\pi$
$434$		0			0
$435$	10.6343	−	9.57521i	0.509878	−	0.459096i
$436$		0			0
$437$	6.57902	−	9.05525i	0.314717	−	0.433171i
$438$		0			0
$439$	18.2181	+	31.5546i	0.869501	+	1.50602i	0.862507	+	0.506045i	$0.168893\pi$
$439$	18.2181	+	31.5546i	0.869501	+	1.50602i	0.00699433	+	0.999976i	$0.497774\pi$
$440$		0			0
$441$	−13.3534			−0.635878
$442$		0			0
$443$	−18.2738	−	13.2767i	−0.868215	−	0.630795i	0.0618923	−	0.998083i	$-0.480286\pi$
$443$	−18.2738	−	13.2767i	−0.868215	−	0.630795i	−0.930107	+	0.367288i	$0.880286\pi$
$444$		0			0
$445$	−12.0555	+	2.56247i	−0.571484	+	0.121473i
$446$		0			0
$447$	16.6287	+	22.8874i	0.786510	+	1.08254i
$448$		0			0
$449$	−3.39587	+	15.9763i	−0.160261	+	0.753969i	0.822452	+	0.568834i	$0.192605\pi$
$449$	−3.39587	+	15.9763i	−0.160261	+	0.753969i	−0.982713	+	0.185135i	$0.940728\pi$
$450$		0			0
$451$	−14.0831	−	6.07665i	−0.663150	−	0.286138i
$452$		0			0
$453$	−13.4635	−	12.1226i	−0.632570	−	0.569568i
$454$		0			0
$455$	22.9153	+	1.12808i	1.07429	+	0.0528854i
$456$		0			0
$457$	2.71449	+	12.7707i	0.126979	+	0.597388i	0.994916	+	0.100713i	$0.0321124\pi$
$457$	2.71449	+	12.7707i	0.126979	+	0.597388i	−0.867937	+	0.496675i	$0.834554\pi$
$458$		0			0
$459$	−15.2582	+	6.79340i	−0.712193	+	0.317089i
$460$		0			0
$461$	34.6785	+	20.0217i	1.61514	+	0.932501i	0.988153	+	0.153472i	$0.0490454\pi$
$461$	34.6785	+	20.0217i	1.61514	+	0.932501i	0.626987	+	0.779030i	$0.284288\pi$
$462$		0			0
$463$		−	2.52490i		−	0.117342i	−0.998277	−	0.0586710i	$-0.981314\pi$
$463$		−	2.52490i		−	0.117342i	0.998277	−	0.0586710i	$-0.0186863\pi$
$464$		0			0
$465$	0.194306	−	1.84870i	0.00901072	−	0.0857312i
$466$		0			0
$467$	−4.11467	+	12.6637i	−0.190404	+	0.586004i	−1.00000		0.000984579i	$-0.999687\pi$
$467$	−4.11467	+	12.6637i	−0.190404	+	0.586004i	0.809595	+	0.586988i	$0.199687\pi$
$468$		0			0
$469$	−1.28879	+	0.936359i	−0.0595107	+	0.0432370i
$470$		0			0
$471$	4.89379	−	5.43511i	0.225494	−	0.250437i
$472$		0			0
$473$	8.27811	−	7.62828i	0.380628	−	0.350749i
$474$		0			0
$475$	−4.40837	+	20.7398i	−0.202270	+	0.951605i
$476$		0			0
$477$	0.139734	+	1.32948i	0.00639797	+	0.0608726i
$478$		0			0
$479$	−2.35885	−	11.0975i	−0.107778	−	0.507058i	−0.998609	−	0.0527225i	$-0.983210\pi$
$479$	−2.35885	−	11.0975i	−0.107778	−	0.507058i	0.890831	−	0.454335i	$-0.150123\pi$
$480$		0			0
$481$	3.12506	−	11.8126i	0.142490	−	0.538608i
$482$		0			0
$483$	−15.0825	+	8.70789i	−0.686278	+	0.396223i
$484$		0			0
$485$	5.67729	−	9.83335i	0.257792	−	0.446510i
$486$		0			0
$487$	−0.424844	−	0.954215i	−0.0192515	−	0.0432396i	0.903664	−	0.428243i	$-0.140867\pi$
$487$	−0.424844	−	0.954215i	−0.0192515	−	0.0432396i	−0.922915	+	0.385003i	$0.874200\pi$
$488$		0			0
$489$	2.13005	+	0.692095i	0.0963242	+	0.0312976i
$490$		0			0
$491$	24.5740	+	10.9411i	1.10901	+	0.493763i	0.877745	−	0.479128i	$-0.159047\pi$
$491$	24.5740	+	10.9411i	1.10901	+	0.493763i	0.231264	+	0.972891i	$0.425714\pi$
$492$		0			0
$493$	−6.89212	−	21.2118i	−0.310406	−	0.955330i
$494$		0			0
$495$	2.07928	+	2.25641i	0.0934567	+	0.101418i
$496$		0			0
$497$	−17.6628	+	19.6165i	−0.792285	+	0.879922i
$498$		0			0
$499$	5.96115	+	8.20482i	0.266858	+	0.367298i	0.921326	−	0.388791i	$-0.127107\pi$
$499$	5.96115	+	8.20482i	0.266858	+	0.367298i	−0.654468	+	0.756090i	$0.727107\pi$
$500$		0			0
$501$	−32.4941	+	29.2578i	−1.45173	+	1.30714i
$502$		0			0
$503$	17.1894	−	7.65323i	0.766439	−	0.341240i	0.0139993	−	0.999902i	$-0.495544\pi$
$503$	17.1894	−	7.65323i	0.766439	−	0.341240i	0.752439	+	0.658662i	$0.228877\pi$
$504$		0			0
$505$	19.5208	−	11.2704i	0.868666	−	0.501525i
$506$		0			0
$507$	−5.37635	−	24.5278i	−0.238772	−	1.08932i
$508$		0			0
$509$	27.3786	+	2.87761i	1.21354	+	0.127548i	0.689588	−	0.724202i	$-0.257792\pi$
$509$	27.3786	+	2.87761i	1.21354	+	0.127548i	0.523949	+	0.851750i	$0.324458\pi$
$510$		0			0
$511$	−35.6753	−	39.6215i	−1.57818	−	1.75275i
$512$		0			0
$513$	−27.2015	+	2.85899i	−1.20097	+	0.126227i
$514$		0			0
$515$	−0.125150	+	0.0406636i	−0.00551476	+	0.00179185i
$516$		0			0
$517$	0.511354	−	0.380605i	0.0224893	−	0.0167390i
$518$		0			0
$519$	9.51525	+	29.2849i	0.417673	+	1.28547i
$520$		0			0
$521$	23.3341	−	16.9532i	1.02229	−	0.742734i	0.0555356	−	0.998457i	$-0.482313\pi$
$521$	23.3341	−	16.9532i	1.02229	−	0.742734i	0.966750	+	0.255723i	$0.0823134\pi$
$522$		0			0
$523$	23.5912	−	5.01447i	1.03157	−	0.219268i	0.339129	−	0.940740i	$-0.389868\pi$
$523$	23.5912	−	5.01447i	1.03157	−	0.219268i	0.692444	+	0.721472i	$0.256534\pi$
$524$		0			0
$525$	19.3918	−	26.6905i	0.846327	−	1.16487i
$526$		0			0
$527$	−2.50908	−	1.44862i	−0.109297	−	0.0631029i
$528$		0			0
$529$	9.89147	−	17.1325i	0.430064	−	0.744893i
$530$		0			0
$531$	1.64998	+	0.173420i	0.0716029	+	0.00752577i
$532$		0			0
$533$	−16.6487	+	0.925470i	−0.721135	+	0.0400866i
$534$		0			0
$535$	6.70396	−	15.0573i	0.289837	−	0.650985i
$536$		0			0
$537$	−21.0110	−	4.46604i	−0.906694	−	0.192724i
$538$		0			0
$539$	−60.3341	−	5.63890i	−2.59877	−	0.242885i
$540$		0			0
$541$	6.07983	−	1.97546i	0.261392	−	0.0849315i	−0.175389	−	0.984499i	$-0.556118\pi$
$541$	6.07983	−	1.97546i	0.261392	−	0.0849315i	0.436781	+	0.899568i	$0.356118\pi$
$542$		0			0
$543$	−26.0509	−	11.5986i	−1.11795	−	0.497744i
$544$		0			0
$545$	1.44175	−	4.43724i	0.0617577	−	0.190071i
$546$		0			0
$547$	28.5413	+	20.7364i	1.22034	+	0.886626i	0.996128	−	0.0879151i	$-0.0280204\pi$
$547$	28.5413	+	20.7364i	1.22034	+	0.886626i	0.224208	+	0.974541i	$0.428020\pi$
$548$		0			0
$549$	4.41675	+	7.65004i	0.188502	+	0.326496i
$550$		0			0
$551$		−	36.5237i		−	1.55596i
$552$		0			0
$553$	−15.1569	−	34.0430i	−0.644537	−	1.44765i
$554$		0			0
$555$	5.54434	+	6.15761i	0.235344	+	0.261376i
$556$		0			0
$557$	−0.771446	+	1.73270i	−0.0326872	+	0.0734167i	−0.929151	−	0.369700i	$-0.879461\pi$
$557$	−0.771446	+	1.73270i	−0.0326872	+	0.0734167i	0.896464	+	0.443116i	$0.146127\pi$
$558$		0			0
$559$	4.34929	−	11.4386i	0.183955	−	0.483800i
$560$		0			0
$561$	23.1291	−	7.81102i	0.976510	−	0.329781i
$562$		0			0
$563$	3.42697	+	0.728425i	0.144430	+	0.0306994i	0.279559	−	0.960128i	$-0.409812\pi$
$563$	3.42697	+	0.728425i	0.144430	+	0.0306994i	−0.135130	+	0.990828i	$0.543145\pi$
$564$		0			0
$565$	8.33990	−	0.876559i	0.350862	−	0.0368771i
$566$		0			0
$567$	50.9575	+	16.5571i	2.14001	+	0.695333i
$568$		0			0
$569$	−1.92023	+	18.2697i	−0.0805000	+	0.765907i	0.877585	+	0.479422i	$0.159154\pi$
$569$	−1.92023	+	18.2697i	−0.0805000	+	0.765907i	−0.958085	+	0.286485i	$0.907513\pi$
$570$		0			0
$571$	−43.9952			−1.84114			−0.920571	−	0.390574i	$-0.872277\pi$
$571$	−43.9952			−1.84114			−0.920571	+	0.390574i	$0.872277\pi$
$572$		0			0
$573$	21.1228			0.882419
$574$		0			0
$575$	0.637016	−	6.06080i	0.0265654	−	0.252753i
$576$		0			0
$577$	36.0097	+	11.7003i	1.49910	+	0.487088i	0.939756	−	0.341846i	$-0.111052\pi$
$577$	36.0097	+	11.7003i	1.49910	+	0.487088i	0.559346	+	0.828934i	$0.311052\pi$
$578$		0			0
$579$	−30.6466	+	3.22109i	−1.27363	+	0.133864i
$580$		0			0
$581$	51.8145	+	11.0135i	2.14963	+	0.456918i
$582$		0			0
$583$	0.0699380	+	6.06591i	0.00289654	+	0.251224i
$584$		0			0
$585$	3.11787	+	1.18551i	0.128908	+	0.0490148i
$586$		0			0
$587$	15.4629	−	34.7303i	0.638223	−	1.43347i	−0.247329	−	0.968932i	$-0.579553\pi$
$587$	15.4629	−	34.7303i	0.638223	−	1.43347i	0.885552	−	0.464540i	$-0.153780\pi$
$588$		0			0
$589$	−3.17468	−	3.52584i	−0.130810	−	0.145280i
$590$		0			0
$591$	20.8314	+	46.7881i	0.856889	+	1.92460i
$592$		0			0
$593$		−	21.8342i		−	0.896624i	−0.893877	−	0.448312i	$-0.852025\pi$
$593$		−	21.8342i		−	0.896624i	0.893877	−	0.448312i	$-0.147975\pi$
$594$		0			0
$595$	12.1244	+	21.0000i	0.497050	+	0.860916i
$596$		0			0
$597$	17.9224	+	13.0214i	0.733517	+	0.532931i
$598$		0			0
$599$	−1.17387	+	3.61280i	−0.0479630	+	0.147615i	−0.972170	−	0.234278i	$-0.924728\pi$
$599$	−1.17387	+	3.61280i	−0.0479630	+	0.147615i	0.924207	+	0.381892i	$0.124728\pi$
$600$		0			0
$601$	−24.3215	−	10.8286i	−0.992094	−	0.441708i	−0.154494	−	0.987994i	$-0.549375\pi$
$601$	−24.3215	−	10.8286i	−0.992094	−	0.441708i	−0.837599	+	0.546285i	$0.816041\pi$
$602$		0			0
$603$	−0.220272	+	0.0715707i	−0.00897017	+	0.00291459i
$604$		0			0
$605$	8.44186	+	11.0730i	0.343210	+	0.450183i
$606$		0			0
$607$	−16.4629	−	3.49929i	−0.668208	−	0.142032i	−0.138697	−	0.990335i	$-0.544291\pi$
$607$	−16.4629	−	3.49929i	−0.668208	−	0.142032i	−0.529511	+	0.848303i	$0.677625\pi$
$608$		0			0
$609$	−23.1147	+	51.9165i	−0.936655	+	2.10376i
$610$		0			0
$611$	0.312648	−	0.618446i	0.0126484	−	0.0250196i
$612$		0			0
$613$	15.3978	+	1.61837i	0.621911	+	0.0653654i	0.410243	−	0.911976i	$-0.365444\pi$
$613$	15.3978	+	1.61837i	0.621911	+	0.0653654i	0.211668	+	0.977342i	$0.432111\pi$
$614$		0			0
$615$	5.65359	−	9.79230i	0.227975	−	0.394864i
$616$		0			0
$617$	−23.8974	−	13.7972i	−0.962072	−	0.555452i	−0.0652617	−	0.997868i	$-0.520788\pi$
$617$	−23.8974	−	13.7972i	−0.962072	−	0.555452i	−0.896810	+	0.442416i	$0.854122\pi$
$618$		0			0
$619$	12.3705	−	17.0266i	0.497214	−	0.684357i	−0.484484	−	0.874800i	$-0.660993\pi$
$619$	12.3705	−	17.0266i	0.497214	−	0.684357i	0.981698	+	0.190443i	$0.0609926\pi$
$620$		0			0
$621$	7.68951	−	1.63446i	0.308570	−	0.0655885i
$622$		0			0
$623$	39.5982	−	28.7698i	1.58647	−	1.15264i
$624$		0			0
$625$	1.09174	+	3.36004i	0.0436697	+	0.134402i
$626$		0			0
$627$	39.9747	−	0.460896i	1.59644	−	0.0184064i
$628$		0			0
$629$	12.2823	−	3.99075i	0.489726	−	0.159122i
$630$		0			0
$631$	11.9234	−	1.25320i	0.474665	−	0.0498893i	0.135824	−	0.990733i	$-0.456632\pi$
$631$	11.9234	−	1.25320i	0.474665	−	0.0498893i	0.338841	+	0.940844i	$0.389965\pi$
$632$		0			0
$633$	−21.4652	−	23.8395i	−0.853166	−	0.947537i
$634$		0			0
$635$	10.6485	+	1.11920i	0.422572	+	0.0444141i
$636$		0			0
$637$	−61.4253	+	23.8027i	−2.43376	+	0.943098i
$638$		0			0
$639$	−3.32360	+	1.91888i	−0.131480	+	0.0759098i
$640$		0			0
$641$	−10.5981	+	4.71860i	−0.418602	+	0.186373i	−0.605219	−	0.796059i	$-0.706914\pi$
$641$	−10.5981	+	4.71860i	−0.418602	+	0.186373i	0.186617	+	0.982433i	$0.440248\pi$
$642$		0			0
$643$	13.6355	−	12.2774i	0.537730	−	0.484174i	−0.354937	−	0.934890i	$-0.615498\pi$
$643$	13.6355	−	12.2774i	0.537730	−	0.484174i	0.892668	+	0.450716i	$0.148831\pi$
$644$		0			0
$645$	4.87772	+	6.71361i	0.192060	+	0.264348i
$646$		0			0
$647$	−9.09470	+	10.1007i	−0.357550	+	0.397099i	−0.894905	−	0.446257i	$-0.852757\pi$
$647$	−9.09470	+	10.1007i	−0.357550	+	0.397099i	0.537355	+	0.843356i	$0.319423\pi$
$648$		0			0
$649$	7.38177	+	1.48031i	0.289760	+	0.0581071i
$650$		0			0
$651$	2.28124	+	7.02094i	0.0894089	+	0.275172i
$652$		0			0
$653$	−21.7248	−	9.67251i	−0.850157	−	0.378515i	−0.0650560	−	0.997882i	$-0.520723\pi$
$653$	−21.7248	−	9.67251i	−0.850157	−	0.378515i	−0.785102	+	0.619367i	$0.787389\pi$
$654$		0			0
$655$	0.531820	+	0.172799i	0.0207799	+	0.00675180i
$656$		0			0
$657$	−3.15282	−	7.08136i	−0.123003	−	0.276270i
$658$		0			0
$659$	8.27686	−	14.3359i	0.322421	−	0.558449i	−0.658566	−	0.752523i	$-0.728837\pi$
$659$	8.27686	−	14.3359i	0.322421	−	0.558449i	0.980987	+	0.194074i	$0.0621702\pi$
$660$		0			0
$661$	4.34986	−	2.51139i	0.169190	−	0.0976818i	−0.413014	−	0.910725i	$-0.635524\pi$
$661$	4.34986	−	2.51139i	0.169190	−	0.0976818i	0.582204	+	0.813043i	$0.302191\pi$
$662$		0			0
$663$	18.7064	−	18.8254i	0.726495	−	0.731117i
$664$		0			0
$665$	8.25603	+	38.8416i	0.320155	+	1.50621i
$666$		0			0
$667$	1.09730	+	10.4401i	0.0424877	+	0.404243i
$668$		0			0
$669$	−3.70268	+	17.4198i	−0.143154	+	0.673487i
$670$		0			0
$671$	16.7255	+	36.4298i	0.645681	+	1.40636i
$672$		0			0
$673$	22.0040	−	24.4379i	0.848192	−	0.942012i	−0.150724	−	0.988576i	$-0.548160\pi$
$673$	22.0040	−	24.4379i	0.848192	−	0.942012i	0.998915	+	0.0465636i	$0.0148270\pi$
$674$		0			0
$675$	−12.0478	+	8.75325i	−0.463721	+	0.336913i
$676$		0			0
$677$	1.38876	−	4.27417i	0.0533744	−	0.164270i	−0.920816	−	0.389997i	$-0.872476\pi$
$677$	1.38876	−	4.27417i	0.0533744	−	0.164270i	0.974190	+	0.225728i	$0.0724760\pi$
$678$		0			0
$679$	−4.71350	+	44.8459i	−0.180887	+	1.72103i
$680$		0			0
$681$		−	54.4849i		−	2.08787i
$682$		0			0
$683$	−12.7166	−	7.34192i	−0.486586	−	0.280931i	0.236571	−	0.971614i	$-0.423976\pi$
$683$	−12.7166	−	7.34192i	−0.486586	−	0.280931i	−0.723157	+	0.690684i	$0.757310\pi$
$684$		0			0
$685$	−23.8728	+	10.6288i	−0.912131	+	0.406107i
$686$		0			0
$687$	−10.8223	−	50.9149i	−0.412896	−	1.94252i
$688$		0			0
$689$	3.01259	+	5.86647i	0.114770	+	0.223495i
$690$		0			0
$691$	−27.2043	−	24.4949i	−1.03490	−	0.931829i	−0.0371805	−	0.999309i	$-0.511838\pi$
$691$	−27.2043	−	24.4949i	−1.03490	−	0.931829i	−0.997721	+	0.0674794i	$0.978504\pi$
$692$		0			0
$693$	−11.1884	−	4.82762i	−0.425012	−	0.183386i
$694$		0			0
$695$	−2.57391	+	12.1093i	−0.0976338	+	0.459331i
$696$		0			0
$697$	−10.3587	−	14.2576i	−0.392365	−	0.540044i
$698$		0			0
$699$	−19.1581	+	4.07218i	−0.724625	+	0.154024i
$700$		0			0
$701$	−42.1900	−	30.6528i	−1.59349	−	1.15774i	−0.898732	−	0.438499i	$-0.855510\pi$
$701$	−42.1900	−	30.6528i	−1.59349	−	1.15774i	−0.694761	−	0.719241i	$-0.744490\pi$
$702$		0			0
$703$	21.1483			0.797625
$704$		0			0
$705$	0.234961	+	0.406965i	0.00884915	+	0.0153272i
$706$		0			0
$707$	−52.6168	+	72.4208i	−1.97886	+	2.72366i
$708$		0			0
$709$	16.5654	−	14.9156i	0.622128	−	0.560167i	−0.296627	−	0.954993i	$-0.595862\pi$
$709$	16.5654	−	14.9156i	0.622128	−	0.560167i	0.918756	+	0.394826i	$0.129195\pi$
$710$		0			0
$711$	−0.566319	−	5.38817i	−0.0212386	−	0.202072i
$712$		0			0
$713$	1.01339	+	0.912464i	0.0379519	+	0.0341721i
$714$		0			0
$715$	13.5867	+	6.67304i	0.508114	+	0.249558i
$716$		0			0
$717$	−7.65495	−	6.89255i	−0.285879	−	0.257407i
$718$		0			0
$719$	1.25549	+	11.9452i	0.0468219	+	0.445481i	0.992669	+	0.120867i	$0.0385675\pi$
$719$	1.25549	+	11.9452i	0.0468219	+	0.445481i	−0.945847	+	0.324613i	$0.894766\pi$
$720$		0			0
$721$	0.388360	−	0.349681i	0.0144633	−	0.0130228i
$722$		0			0
$723$	−29.4367	+	40.5161i	−1.09476	+	1.50681i
$724$		0			0
$725$	−9.94300	−	17.2218i	−0.369274	−	0.639601i
$726$		0			0
$727$	36.0777			1.33805			0.669023	−	0.743242i	$-0.266713\pi$
$727$	36.0777			1.33805			0.669023	+	0.743242i	$0.266713\pi$
$728$		0			0
$729$	−14.2449	−	10.3495i	−0.527587	−	0.383315i
$730$		0			0
$731$	12.6513	−	2.68912i	0.467926	−	0.0994608i
$732$		0			0
$733$	1.18040	+	1.62469i	0.0435992	+	0.0600092i	0.830260	−	0.557376i	$-0.188192\pi$
$733$	1.18040	+	1.62469i	0.0435992	+	0.0600092i	−0.786661	+	0.617385i	$0.788192\pi$
$734$		0			0
$735$	9.28773	−	43.6953i	0.342583	−	1.61173i
$736$		0			0
$737$	−1.02547	+	0.230357i	−0.0377735	+	0.00848532i
$738$		0			0
$739$	25.8422	+	23.2685i	0.950622	+	0.855944i	0.989680	−	0.143293i	$-0.0457691\pi$
$739$	25.8422	+	23.2685i	0.950622	+	0.855944i	−0.0390583	+	0.999237i	$0.512436\pi$
$740$		0			0
$741$	38.6604	−	19.8531i	1.42022	−	0.729323i
$742$		0			0
$743$	−3.46195	−	16.2872i	−0.127007	−	0.597520i	−0.994908	−	0.100784i	$-0.967865\pi$
$743$	−3.46195	−	16.2872i	−0.127007	−	0.597520i	0.867902	−	0.496736i	$-0.165468\pi$
$744$		0			0
$745$	−16.9370	+	7.54083i	−0.620523	+	0.276275i
$746$		0			0
$747$	6.66972	+	3.85076i	0.244032	+	0.140892i
$748$		0			0
$749$			65.4569i			2.39174i
$750$		0			0
$751$	−5.50445	+	52.3713i	−0.200860	+	1.91106i	0.175322	+	0.984511i	$0.443903\pi$
$751$	−5.50445	+	52.3713i	−0.200860	+	1.91106i	−0.376182	+	0.926546i	$0.622763\pi$
$752$		0			0
$753$	−13.1444	+	40.4543i	−0.479009	+	1.47424i
$754$		0			0
$755$	9.60523	−	6.97861i	0.349570	−	0.253978i
$756$		0			0
$757$	−29.1696	+	32.3962i	−1.06019	+	1.17746i	−0.0765947	+	0.997062i	$0.524405\pi$
$757$	−29.1696	+	32.3962i	−1.06019	+	1.17746i	−0.983594	+	0.180397i	$0.942262\pi$
$758$		0			0
$759$	−11.4127	+	1.33273i	−0.414256	+	0.0483749i
$760$		0			0
$761$	−0.337300	+	1.58687i	−0.0122271	+	0.0575241i	−0.983838	−	0.179060i	$-0.942694\pi$
$761$	−0.337300	+	1.58687i	−0.0122271	+	0.0575241i	0.971611	+	0.236584i	$0.0760278\pi$
$762$		0			0
$763$	1.93677	+	18.4272i	0.0701159	+	0.667109i
$764$		0			0
$765$	0.732988	+	3.44844i	0.0265013	+	0.124679i
$766$		0			0
$767$	7.89895	−	2.14339i	0.285215	−	0.0773933i
$768$		0			0
$769$	−2.06354	+	1.19138i	−0.0744131	+	0.0429624i	−0.536745	−	0.843745i	$-0.680346\pi$
$769$	−2.06354	+	1.19138i	−0.0744131	+	0.0429624i	0.462332	+	0.886707i	$0.347013\pi$
$770$		0			0
$771$	−26.8136	+	46.4426i	−0.965670	+	1.67259i
$772$		0			0
$773$	−13.6893	−	30.7466i	−0.492369	−	1.10588i	−0.973387	−	0.229169i	$-0.926399\pi$
$773$	−13.6893	−	30.7466i	−0.492369	−	1.10588i	0.481017	−	0.876711i	$-0.340267\pi$
$774$		0			0
$775$	−2.45679	−	0.798259i	−0.0882504	−	0.0286743i
$776$		0			0
$777$	−30.0612	−	13.3841i	−1.07844	−	0.480153i
$778$		0			0
$779$	−8.91813	−	27.4472i	−0.319525	−	0.983398i
$780$		0			0
$781$	−15.8272	+	7.26649i	−0.566340	+	0.260015i
$782$		0			0
$783$	17.1647	−	19.0634i	0.613418	−	0.681270i
$784$		0			0
$785$	2.81721	+	3.87756i	0.100551	+	0.138396i
$786$		0			0
$787$	15.0292	−	13.5323i	0.535732	−	0.482375i	−0.356285	−	0.934377i	$-0.615957\pi$
$787$	15.0292	−	13.5323i	0.535732	−	0.482375i	0.892017	+	0.452002i	$0.149290\pi$
$788$		0			0
$789$	9.52701	−	4.24170i	0.339170	−	0.151008i
$790$		0			0
$791$	−28.8413	+	16.6515i	−1.02548	+	0.592060i
$792$		0			0
$793$	33.9532	+	27.3169i	1.20571	+	0.970053i
$794$		0			0
$795$	−4.44753	−	0.467454i	−0.157738	−	0.0165789i
$796$		0			0
$797$	−29.5941	−	32.8676i	−1.04828	−	1.16423i	−0.986098	−	0.166166i	$-0.946861\pi$
$797$	−29.5941	−	32.8676i	−1.04828	−	1.16423i	−0.0621802	−	0.998065i	$-0.519805\pi$
$798$		0			0
$799$	0.728406	−	0.0765586i	0.0257692	−	0.00270845i
$800$		0			0
$801$	6.76789	−	2.19902i	0.239132	−	0.0776986i
$802$		0			0
$803$	−11.2549	−	33.3267i	−0.397177	−	1.17607i
$804$		0			0
$805$	−3.52689	−	10.8546i	−0.124306	−	0.382576i
$806$		0			0
$807$	−43.7498	+	31.7861i	−1.54007	+	1.11892i
$808$		0			0
$809$	−24.3058	+	5.16636i	−0.854547	+	0.181640i	−0.614300	−	0.789072i	$-0.710562\pi$
$809$	−24.3058	+	5.16636i	−0.854547	+	0.181640i	−0.240247	+	0.970712i	$0.577228\pi$
$810$		0			0
$811$	21.7677	−	29.9607i	0.764369	−	1.05206i	−0.232470	−	0.972604i	$-0.574681\pi$
$811$	21.7677	−	29.9607i	0.764369	−	1.05206i	0.996838	−	0.0794594i	$-0.0253194\pi$
$812$		0			0
$813$	30.5621	+	17.6450i	1.07186	+	0.618838i
$814$		0			0
$815$	−0.733870	+	1.27110i	−0.0257064	+	0.0445247i
$816$		0			0
$817$	21.0644	+	2.21396i	0.736952	+	0.0774567i
$818$		0			0
$819$	−13.2266	+	0.735243i	−0.462175	+	0.0256915i
$820$		0			0
$821$	−10.6073	+	23.8245i	−0.370199	+	0.831480i	0.628366	+	0.777918i	$0.283724\pi$
$821$	−10.6073	+	23.8245i	−0.370199	+	0.831480i	−0.998565	+	0.0535619i	$0.982943\pi$
$822$		0			0
$823$	15.9555	+	3.39144i	0.556173	+	0.118218i	0.477419	−	0.878676i	$-0.341572\pi$
$823$	15.9555	+	3.39144i	0.556173	+	0.118218i	0.0787541	+	0.996894i	$0.474906\pi$
$824$		0			0
$825$	18.7236	−	11.0998i	0.651871	−	0.386446i
$826$		0			0
$827$	14.5363	−	4.72312i	0.505476	−	0.164239i	−0.0451681	−	0.998979i	$-0.514382\pi$
$827$	14.5363	−	4.72312i	0.505476	−	0.164239i	0.550644	+	0.834740i	$0.314382\pi$
$828$		0			0
$829$	−9.74550	−	4.33897i	−0.338475	−	0.150699i	0.230459	−	0.973082i	$-0.425977\pi$
$829$	−9.74550	−	4.33897i	−0.338475	−	0.150699i	−0.568934	+	0.822383i	$0.692644\pi$
$830$		0			0
$831$	6.24122	−	19.2085i	0.216506	−	0.666336i
$832$		0			0
$833$	−56.3277	−	40.9244i	−1.95164	−	1.41795i
$834$		0			0
$835$	−14.3274	−	24.8158i	−0.495820	−	0.858785i
$836$		0			0
$837$		−	3.33227i		−	0.115180i
$838$		0			0
$839$	−4.65973	−	10.4659i	−0.160872	−	0.361324i	0.815068	−	0.579366i	$-0.196700\pi$
$839$	−4.65973	−	10.4659i	−0.160872	−	0.361324i	−0.975939	+	0.218042i	$0.930033\pi$
$840$		0			0
$841$	3.51623	+	3.90517i	0.121249	+	0.134661i
$842$		0			0
$843$	−10.8704	+	24.4154i	−0.374398	+	0.840911i
$844$		0			0
$845$	16.4553	−	0.104365i	0.566079	−	0.00359028i
$846$		0			0
$847$	−48.5133	−	26.5370i	−1.66694	−	0.911822i
$848$		0			0
$849$	61.6921	+	13.1131i	2.11727	+	0.450039i
$850$		0			0
$851$	−6.04515	+	0.635371i	−0.207225	+	0.0217802i
$852$		0			0
$853$	−29.1498	−	9.47134i	−0.998070	−	0.324293i	−0.235976	−	0.971759i	$-0.575829\pi$
$853$	−29.1498	−	9.47134i	−0.998070	−	0.324293i	−0.762094	+	0.647466i	$0.775829\pi$
$854$		0			0
$855$	−0.603471	+	5.74165i	−0.0206383	+	0.196360i
$856$		0			0
$857$	38.1938			1.30468			0.652338	−	0.757928i	$-0.273788\pi$
$857$	38.1938			1.30468			0.652338	+	0.757928i	$0.273788\pi$
$858$		0			0
$859$	−27.1803			−0.927381			−0.463690	−	0.885997i	$-0.653475\pi$
$859$	−27.1803			−0.927381			−0.463690	+	0.885997i	$0.653475\pi$
$860$		0			0
$861$	−4.69382	+	44.6587i	−0.159965	+	1.52196i
$862$		0			0
$863$	−11.8107	−	3.83754i	−0.402042	−	0.130631i	0.101014	−	0.994885i	$-0.467791\pi$
$863$	−11.8107	−	3.83754i	−0.402042	−	0.130631i	−0.503057	+	0.864254i	$0.667791\pi$
$864$		0			0
$865$	−20.0687	+	2.10930i	−0.682355	+	0.0717184i
$866$		0			0
$867$	−4.68227	−	0.995248i	−0.159018	−	0.0338004i
$868$		0			0
$869$	−0.283448	−	24.5842i	−0.00961531	−	0.833962i
$870$		0			0
$871$	−0.885667	+	0.721861i	−0.0300097	+	0.0244593i
$872$		0			0
$873$	−2.66656	+	5.98919i	−0.0902494	+	0.202704i
$874$		0			0
$875$	35.7562	+	39.7113i	1.20878	+	1.34249i
$876$		0			0
$877$	−8.42523	−	18.9234i	−0.284500	−	0.638997i	0.713604	−	0.700549i	$-0.247062\pi$
$877$	−8.42523	−	18.9234i	−0.284500	−	0.638997i	−0.998104	+	0.0615522i	$0.980395\pi$
$878$		0			0
$879$		−	46.7628i		−	1.57727i
$880$		0			0
$881$	15.9957	+	27.7054i	0.538909	+	0.933418i	0.998963	+	0.0455274i	$0.0144968\pi$
$881$	15.9957	+	27.7054i	0.538909	+	0.933418i	−0.460054	+	0.887891i	$0.652170\pi$
$882$		0			0
$883$	−0.142893	−	0.103818i	−0.00480872	−	0.00349374i	0.585378	−	0.810760i	$-0.300946\pi$
$883$	−0.142893	−	0.103818i	−0.00480872	−	0.00349374i	−0.590187	+	0.807267i	$0.700946\pi$
$884$		0			0
$885$	−1.71508	+	5.27846i	−0.0576517	+	0.177434i
$886$		0			0
$887$	1.44601	+	0.643804i	0.0485522	+	0.0216168i	0.430869	−	0.902414i	$-0.358207\pi$
$887$	1.44601	+	0.643804i	0.0485522	+	0.0216168i	−0.382317	+	0.924031i	$0.624874\pi$
$888$		0			0
$889$	−40.4406	+	13.1399i	−1.35633	+	0.440700i
$890$		0			0
$891$	26.5411	+	23.3493i	0.889162	+	0.782233i
$892$		0			0
$893$	1.17319	+	0.249369i	0.0392593	+	0.00834481i
$894$		0			0
$895$	5.72562	−	12.8600i	0.191386	−	0.429861i
$896$		0			0
$897$	−10.4544	+	6.83641i	−0.349063	+	0.228261i
$898$		0			0
$899$	4.42539	+	0.465127i	0.147595	+	0.0155129i
$900$		0			0
$901$	−3.48504	+	6.03627i	−0.116104	+	0.201097i
$902$		0			0
$903$	−28.5408	−	16.4781i	−0.949779	−	0.548355i
$904$		0			0
$905$	10.9844	−	15.1188i	0.365135	−	0.502565i
$906$		0			0
$907$	−19.4660	+	4.13762i	−0.646357	+	0.137388i	−0.519414	−	0.854522i	$-0.673850\pi$
$907$	−19.4660	+	4.13762i	−0.646357	+	0.137388i	−0.126943	+	0.991910i	$0.540517\pi$
$908$		0			0
$909$	−10.5291	+	7.64987i	−0.349229	+	0.253730i
$910$		0			0
$911$	4.53934	+	13.9707i	0.150395	+	0.462869i	0.997665	−	0.0682937i	$-0.0217555\pi$
$911$	4.53934	+	13.9707i	0.150395	+	0.462869i	−0.847270	+	0.531162i	$0.821755\pi$
$912$		0			0
$913$	28.5093	+	20.2152i	0.943520	+	0.669025i
$914$		0			0
$915$	−28.1046	+	9.13173i	−0.929108	+	0.301886i
$916$		0			0
$917$	−2.20856	+	0.232129i	−0.0729332	+	0.00766559i
$918$		0			0
$919$	−5.85818	−	6.50617i	−0.193243	−	0.214619i	0.638735	−	0.769427i	$-0.279458\pi$
$919$	−5.85818	−	6.50617i	−0.193243	−	0.214619i	−0.831978	+	0.554809i	$0.812792\pi$
$920$		0			0
$921$	−35.9203	−	3.77537i	−1.18361	−	0.124403i
$922$		0			0
$923$	−11.8680	+	14.7512i	−0.390640	+	0.485541i
$924$		0			0
$925$	9.97194	−	5.75730i	0.327875	−	0.189299i
$926$		0			0
$927$	0.0694099	−	0.0309033i	0.00227972	−	0.00101500i
$928$		0			0
$929$	38.0011	−	34.2163i	1.24677	−	1.12260i	0.259137	−	0.965840i	$-0.416562\pi$
$929$	38.0011	−	34.2163i	1.24677	−	1.12260i	0.987637	−	0.156760i	$-0.0501049\pi$
$930$		0			0
$931$	−67.0173	−	92.2413i	−2.19640	−	3.02309i
$932$		0			0
$933$	0.388913	−	0.431932i	0.0127324	−	0.0141408i
$934$		0			0
$935$	1.85561	+	15.8904i	0.0606850	+	0.519672i
$936$		0			0
$937$	−8.36492	−	25.7446i	−0.273270	−	0.841039i	−0.989672	−	0.143351i	$-0.954212\pi$
$937$	−8.36492	−	25.7446i	−0.273270	−	0.841039i	0.716402	−	0.697688i	$-0.245788\pi$
$938$		0			0
$939$	30.5478	+	13.6007i	0.996889	+	0.443844i
$940$		0			0
$941$	40.4045	+	13.1282i	1.31715	+	0.427968i	0.881515	−	0.472155i	$-0.156524\pi$
$941$	40.4045	+	13.1282i	1.31715	+	0.427968i	0.435635	+	0.900123i	$0.356524\pi$
$942$		0			0
$943$	3.37382	+	7.57771i	0.109867	+	0.246764i
$944$		0			0
$945$	−13.9449	+	24.1532i	−0.453626	+	0.785704i
$946$		0			0
$947$	37.2287	−	21.4940i	1.20977	−	0.698462i	0.247062	−	0.969000i	$-0.420535\pi$
$947$	37.2287	−	21.4940i	1.20977	−	0.698462i	0.962709	+	0.270538i	$0.0872015\pi$
$948$		0			0
$949$	−27.1255	−	26.9540i	−0.880531	−	0.874965i
$950$		0			0
$951$	−0.385115	−	1.81183i	−0.0124882	−	0.0587525i
$952$		0			0
$953$	0.208711	+	1.98575i	0.00676081	+	0.0643248i	0.997382	−	0.0723114i	$-0.0230375\pi$
$953$	0.208711	+	1.98575i	0.00676081	+	0.0643248i	−0.990621	+	0.136636i	$0.956371\pi$
$954$		0			0
$955$	−2.87804	+	13.5401i	−0.0931313	+	0.438148i
$956$		0			0
$957$	−27.5724	+	25.4080i	−0.891290	+	0.821324i
$958$		0			0
$959$	69.4418	−	77.1229i	2.24239	−	2.49043i
$960$		0			0
$961$	−24.6119	+	17.8816i	−0.793932	+	0.576825i
$962$		0			0
$963$	−2.94081	+	9.05089i	−0.0947664	+	0.291661i
$964$		0			0
$965$	2.11091	−	20.0839i	0.0679525	−	0.646525i
$966$		0			0
$967$		−	26.4939i		−	0.851986i	−0.904727	−	0.425993i	$-0.859925\pi$
$967$		−	26.4939i		−	0.851986i	0.904727	−	0.425993i	$-0.140075\pi$
$968$		0			0
$969$	39.7794	+	22.9666i	1.27790	+	0.737795i
$970$		0			0
$971$	−23.0874	+	10.2792i	−0.740910	+	0.329874i	−0.742249	−	0.670125i	$-0.766241\pi$
$971$	−23.0874	+	10.2792i	−0.740910	+	0.329874i	0.00133847	+	0.999999i	$0.499574\pi$
$972$		0			0
$973$	−10.2219	−	48.0901i	−0.327698	−	1.54170i
$974$		0			0
$975$	12.8246	−	19.8859i	0.410715	−	0.636858i
$976$		0			0
$977$	−15.2461	−	13.7276i	−0.487765	−	0.439185i	0.388189	−	0.921580i	$-0.373101\pi$
$977$	−15.2461	−	13.7276i	−0.487765	−	0.439185i	−0.875954	+	0.482394i	$0.839767\pi$
$978$		0			0
$979$	31.5076	−	7.07776i	1.00699	−	0.226206i
$980$		0			0
$981$	−0.560084	+	2.63499i	−0.0178821	+	0.0841287i
$982$		0			0
$983$	−17.8957	−	24.6313i	−0.570783	−	0.785615i	0.421864	−	0.906659i	$-0.361376\pi$
$983$	−17.8957	−	24.6313i	−0.570783	−	0.785615i	−0.992647	+	0.121044i	$0.961376\pi$
$984$		0			0
$985$	−32.8303	+	6.97830i	−1.04606	+	0.222347i
$986$		0			0
$987$	−1.50981	−	1.09694i	−0.0480577	−	0.0349159i
$988$		0			0
$989$	−6.08768			−0.193577
$990$		0			0
$991$	−20.1733	−	34.9413i	−0.640827	−	1.10995i	−0.985248	−	0.171130i	$-0.945258\pi$
$991$	−20.1733	−	34.9413i	−0.640827	−	1.10995i	0.344421	−	0.938815i	$-0.388075\pi$
$992$		0			0
$993$	−8.86627	+	12.2034i	−0.281363	+	0.387262i
$994$		0			0
$995$	−10.7889	+	9.71441i	−0.342033	+	0.307968i
$996$		0			0
$997$	−2.72033	−	25.8822i	−0.0861537	−	0.819698i	−0.949221	−	0.314609i	$-0.898127\pi$
$997$	−2.72033	−	25.8822i	−0.0861537	−	0.819698i	0.863068	−	0.505088i	$-0.168540\pi$
$998$		0			0
$999$	11.0383	+	9.93891i	0.349236	+	0.314453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bq.a.49.12	✓	112
11.9	even	5	inner	572.2.bq.a.361.3	yes	112
13.4	even	6	inner	572.2.bq.a.225.3	yes	112
143.108	even	30	inner	572.2.bq.a.537.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bq.a.49.12	✓	112	1.1	even	1	trivial
572.2.bq.a.225.3	yes	112	13.4	even	6	inner
572.2.bq.a.361.3	yes	112	11.9	even	5	inner
572.2.bq.a.537.12	yes	112	143.108	even	30	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.201901 - 1.92096i) q^{3} +(1.20386 + 0.391159i) q^{5} +(-4.99946 + 0.525464i) q^{7} +(-0.714895 - 0.151956i) q^{9} +O(q^{10})\)	\(q+(0.201901 - 1.92096i) q^{3} +(1.20386 + 0.391159i) q^{5} +(-4.99946 + 0.525464i) q^{7} +(-0.714895 - 0.151956i) q^{9} +(-3.16590 - 0.988460i) q^{11} +(-3.55935 + 0.575323i) q^{13} +(0.994464 - 2.23360i) q^{15} +(-2.54988 - 2.83193i) q^{17} +(-2.53820 - 5.70090i) q^{19} +9.70987i q^{21} +(0.896808 + 1.55332i) q^{23} +(-2.74880 - 1.99712i) q^{25} +(1.35440 - 4.16842i) q^{27} +(5.34677 + 2.38054i) q^{29} +(0.723072 - 0.234940i) q^{31} +(-2.53800 + 5.88202i) q^{33} +(-6.22420 - 1.32300i) q^{35} +(-1.37840 + 3.09594i) q^{37} +(0.386535 + 6.95355i) q^{39} +(4.59931 + 0.483407i) q^{41} +(-1.69704 + 2.93936i) q^{43} +(-0.801198 - 0.462572i) q^{45} +(-0.112971 + 0.155492i) q^{47} +(17.8714 - 3.79869i) q^{49} +(-5.95486 + 4.32646i) q^{51} +(-0.565212 - 1.73954i) q^{53} +(-3.42467 - 2.42834i) q^{55} +(-11.4637 + 3.72478i) q^{57} +(-2.25756 + 0.237279i) q^{59} +(-8.08734 - 8.98190i) q^{61} +(3.65394 + 0.384044i) q^{63} +(-4.51002 - 0.699664i) q^{65} +(0.274439 - 0.158447i) q^{67} +(3.16493 - 1.40912i) q^{69} +(3.90224 - 3.51359i) q^{71} +(6.23401 + 8.58037i) q^{73} +(-4.39139 + 4.87713i) q^{75} +(16.3472 + 3.27819i) q^{77} +(2.29072 + 7.05010i) q^{79} +(-9.73696 - 4.33518i) q^{81} +(-10.0218 - 3.25627i) q^{83} +(-1.96197 - 4.40667i) q^{85} +(5.65244 - 9.79032i) q^{87} +(-8.43217 + 4.86832i) q^{89} +(17.4925 - 4.74661i) q^{91} +(-0.305323 - 1.43643i) q^{93} +(-0.825693 - 7.85594i) q^{95} +(1.86500 - 8.77414i) q^{97} +(2.11309 + 1.18772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 20 q^{9}+O(q^{10}) \) 112 * q + 20 * q^9	\( 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) \) 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more