LMFDB - Embedded newform 572.2.bh.a.57.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, 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 $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.14
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.57936 - 1.87402i) q^{3} +(-2.69008 - 1.37067i) q^{5} +(-3.38722 + 0.536483i) q^{7} +(2.21412 - 6.81437i) q^{9} +O(q^{10})$	\(q+(2.57936 - 1.87402i) q^{3} +(-2.69008 - 1.37067i) q^{5} +(-3.38722 + 0.536483i) q^{7} +(2.21412 - 6.81437i) q^{9} +(-2.34434 - 2.34607i) q^{11} +(-1.68806 + 3.18598i) q^{13} +(-9.50735 + 1.50582i) q^{15} +(-0.258017 - 0.794093i) q^{17} +(4.73114 + 0.749338i) q^{19} +(-7.73148 + 7.73148i) q^{21} -5.87424i q^{23} +(2.41890 + 3.32932i) q^{25} +(-4.10353 - 12.6294i) q^{27} +(3.31526 - 4.56306i) q^{29} +(2.42573 + 4.76077i) q^{31} +(-10.4435 - 1.65803i) q^{33} +(9.84723 + 3.19956i) q^{35} +(-1.66772 - 10.5296i) q^{37} +(1.61645 + 11.3812i) q^{39} +(2.72351 + 0.431362i) q^{41} +0.815096 q^{43} +(-15.2964 + 15.2964i) q^{45} +(8.50101 + 1.34643i) q^{47} +(4.52803 - 1.47125i) q^{49} +(-2.15366 - 1.56473i) q^{51} +(-1.71767 + 5.28645i) q^{53} +(3.09080 + 9.52444i) q^{55} +(13.6076 - 6.93341i) q^{57} +(0.658186 + 4.15562i) q^{59} +(4.27700 - 1.38968i) q^{61} +(-3.84392 + 24.2696i) q^{63} +(8.90794 - 6.25677i) q^{65} +(3.51004 - 3.51004i) q^{67} +(-11.0084 - 15.1518i) q^{69} +(-6.36905 - 3.24519i) q^{71} +(-3.96998 + 0.628784i) q^{73} +(12.4784 + 4.05448i) q^{75} +(9.19943 + 6.68896i) q^{77} +(-12.9482 - 4.20713i) q^{79} +(-16.8622 - 12.2511i) q^{81} +(3.65567 - 7.17466i) q^{83} +(-0.394351 + 2.48983i) q^{85} -17.9826i q^{87} +(1.38938 + 1.38938i) q^{89} +(4.00861 - 11.6972i) q^{91} +(15.1786 + 7.73389i) q^{93} +(-11.7001 - 8.50059i) q^{95} +(-5.00585 - 9.82454i) q^{97} +(-21.1777 + 10.7807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

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
$3$	2.57936	−	1.87402i	1.48920	−	1.08196i	0.514750	−	0.857340i	$-0.327885\pi$
$3$	2.57936	−	1.87402i	1.48920	−	1.08196i	0.974446	−	0.224624i	$-0.0721153\pi$
$4$		0			0
$5$	−2.69008	−	1.37067i	−1.20304	−	0.612980i	−0.266601	−	0.963807i	$-0.585901\pi$
$5$	−2.69008	−	1.37067i	−1.20304	−	0.612980i	−0.936440	+	0.350827i	$0.885901\pi$
$6$		0			0
$7$	−3.38722	+	0.536483i	−1.28025	+	0.202771i	−0.759257	−	0.650791i	$-0.774437\pi$
$7$	−3.38722	+	0.536483i	−1.28025	+	0.202771i	−0.520991	+	0.853562i	$0.674437\pi$
$8$		0			0
$9$	2.21412	−	6.81437i	0.738041	−	2.27146i
$10$		0			0
$11$	−2.34434	−	2.34607i	−0.706846	−	0.707367i
$11$	−2.34434	−	2.34607i	−0.706846	−	0.707367i
$12$		0			0
$13$	−1.68806	+	3.18598i	−0.468184	+	0.883631i
$13$	−1.68806	+	3.18598i	−0.468184	+	0.883631i
$14$		0			0
$15$	−9.50735	+	1.50582i	−2.45479	+	0.388800i
$16$		0			0
$17$	−0.258017	−	0.794093i	−0.0625782	−	0.192596i	0.914880	−	0.403727i	$-0.132285\pi$
$17$	−0.258017	−	0.794093i	−0.0625782	−	0.192596i	−0.977458	+	0.211131i	$0.932285\pi$
$18$		0			0
$19$	4.73114	+	0.749338i	1.08540	+	0.171910i	0.673402	−	0.739276i	$-0.264832\pi$
$19$	4.73114	+	0.749338i	1.08540	+	0.171910i	0.411995	+	0.911186i	$0.364832\pi$
$20$		0			0
$21$	−7.73148	+	7.73148i	−1.68715	+	1.68715i
$22$		0			0
$23$		−	5.87424i		−	1.22486i	−0.790524	−	0.612432i	$-0.790191\pi$
$23$		−	5.87424i		−	1.22486i	0.790524	−	0.612432i	$-0.209809\pi$
$24$		0			0
$25$	2.41890	+	3.32932i	0.483779	+	0.665865i
$26$		0			0
$27$	−4.10353	−	12.6294i	−0.789724	−	2.43052i
$28$		0			0
$29$	3.31526	−	4.56306i	0.615628	−	0.847340i	−0.381397	−	0.924411i	$-0.624557\pi$
$29$	3.31526	−	4.56306i	0.615628	−	0.847340i	0.997026	+	0.0770716i	$0.0245570\pi$
$30$		0			0
$31$	2.42573	+	4.76077i	0.435674	+	0.855059i	0.999573	+	0.0292153i	$0.00930085\pi$
$31$	2.42573	+	4.76077i	0.435674	+	0.855059i	−0.563899	+	0.825844i	$0.690699\pi$
$32$		0			0
$33$	−10.4435	−	1.65803i	−1.81798	−	0.288627i
$34$		0			0
$35$	9.84723	+	3.19956i	1.66449	+	0.540824i
$36$		0			0
$37$	−1.66772	−	10.5296i	−0.274172	−	1.73105i	−0.612892	−	0.790167i	$-0.709994\pi$
$37$	−1.66772	−	10.5296i	−0.274172	−	1.73105i	0.338720	−	0.940887i	$-0.390006\pi$
$38$		0			0
$39$	1.61645	+	11.3812i	0.258839	+	1.82246i
$40$		0			0
$41$	2.72351	+	0.431362i	0.425341	+	0.0673674i	0.365435	−	0.930837i	$-0.380920\pi$
$41$	2.72351	+	0.431362i	0.425341	+	0.0673674i	0.0599054	+	0.998204i	$0.480920\pi$
$42$		0			0
$43$	0.815096			0.124301			0.0621505	−	0.998067i	$-0.480204\pi$
$43$	0.815096			0.124301			0.0621505	+	0.998067i	$0.480204\pi$
$44$		0			0
$45$	−15.2964	+	15.2964i	−2.28025	+	2.28025i
$46$		0			0
$47$	8.50101	+	1.34643i	1.24000	+	0.196397i	0.741774	−	0.670650i	$-0.233985\pi$
$47$	8.50101	+	1.34643i	1.24000	+	0.196397i	0.498226	+	0.867047i	$0.333985\pi$
$48$		0			0
$49$	4.52803	−	1.47125i	0.646862	−	0.210178i
$50$		0			0
$51$	−2.15366	−	1.56473i	−0.301573	−	0.219106i
$52$		0			0
$53$	−1.71767	+	5.28645i	−0.235940	+	0.726149i	0.761055	+	0.648687i	$0.224682\pi$
$53$	−1.71767	+	5.28645i	−0.235940	+	0.726149i	−0.996995	+	0.0774620i	$0.975318\pi$
$54$		0			0
$55$	3.09080	+	9.52444i	0.416763	+	1.28428i
$56$		0			0
$57$	13.6076	−	6.93341i	1.80237	−	0.918353i
$58$		0			0
$59$	0.658186	+	4.15562i	0.0856885	+	0.541016i	0.992767	+	0.120055i	$0.0383071\pi$
$59$	0.658186	+	4.15562i	0.0856885	+	0.541016i	−0.907079	+	0.420961i	$0.861693\pi$
$60$		0			0
$61$	4.27700	−	1.38968i	0.547614	−	0.177931i	−0.0221264	−	0.999755i	$-0.507044\pi$
$61$	4.27700	−	1.38968i	0.547614	−	0.177931i	0.569741	+	0.821825i	$0.307044\pi$
$62$		0			0
$63$	−3.84392	+	24.2696i	−0.484289	+	3.05768i
$64$		0			0
$65$	8.90794	−	6.25677i	1.10489	−	0.776057i
$66$		0			0
$67$	3.51004	−	3.51004i	0.428819	−	0.428819i	−0.459407	−	0.888226i	$-0.651938\pi$
$67$	3.51004	−	3.51004i	0.428819	−	0.428819i	0.888226	+	0.459407i	$0.151938\pi$
$68$		0			0
$69$	−11.0084	−	15.1518i	−1.32526	−	1.82406i
$70$		0			0
$71$	−6.36905	−	3.24519i	−0.755867	−	0.385133i	0.0331937	−	0.999449i	$-0.489432\pi$
$71$	−6.36905	−	3.24519i	−0.755867	−	0.385133i	−0.789060	+	0.614316i	$0.789432\pi$
$72$		0			0
$73$	−3.96998	+	0.628784i	−0.464651	+	0.0735936i	−0.384371	−	0.923179i	$-0.625582\pi$
$73$	−3.96998	+	0.628784i	−0.464651	+	0.0735936i	−0.0802806	+	0.996772i	$0.525582\pi$
$74$		0			0
$75$	12.4784	+	4.05448i	1.44088	+	0.468172i
$76$		0			0
$77$	9.19943	+	6.68896i	1.04837	+	0.762278i
$78$		0			0
$79$	−12.9482	−	4.20713i	−1.45679	−	0.473339i	−0.529700	−	0.848185i	$-0.677695\pi$
$79$	−12.9482	−	4.20713i	−1.45679	−	0.473339i	−0.927087	+	0.374847i	$0.877695\pi$
$80$		0			0
$81$	−16.8622	−	12.2511i	−1.87357	−	1.36123i
$82$		0			0
$83$	3.65567	−	7.17466i	0.401262	−	0.787521i	−0.598647	−	0.801013i	$-0.704295\pi$
$83$	3.65567	−	7.17466i	0.401262	−	0.787521i	0.999909	+	0.0134917i	$0.00429467\pi$
$84$		0			0
$85$	−0.394351	+	2.48983i	−0.0427733	+	0.270060i
$86$		0			0
$87$		−	17.9826i		−	1.92794i
$88$		0			0
$89$	1.38938	+	1.38938i	0.147274	+	0.147274i	0.776899	−	0.629625i	$-0.216791\pi$
$89$	1.38938	+	1.38938i	0.147274	+	0.147274i	−0.629625	+	0.776899i	$0.716791\pi$
$90$		0			0
$91$	4.00861	−	11.6972i	0.420217	−	1.22620i
$92$		0			0
$93$	15.1786	+	7.73389i	1.57395	+	0.801967i
$94$		0			0
$95$	−11.7001	−	8.50059i	−1.20040	−	0.872142i
$96$		0			0
$97$	−5.00585	−	9.82454i	−0.508267	−	0.997531i	−0.992460	−	0.122569i	$-0.960887\pi$
$97$	−5.00585	−	9.82454i	−0.508267	−	0.997531i	0.484193	−	0.874961i	$-0.339113\pi$
$98$		0			0
$99$	−21.1777	+	10.7807i	−2.12843	+	1.08350i
$100$		0			0
$101$	1.46255	−	4.50126i	0.145529	−	0.447892i	−0.851550	−	0.524274i	$-0.824337\pi$
$101$	1.46255	−	4.50126i	0.145529	−	0.447892i	0.997079	+	0.0763817i	$0.0243367\pi$
$102$		0			0
$103$	−1.30192	+	1.79193i	−0.128282	+	0.176565i	−0.868327	−	0.495993i	$-0.834804\pi$
$103$	−1.30192	+	1.79193i	−0.128282	+	0.176565i	0.740045	+	0.672557i	$0.234804\pi$
$104$		0			0
$105$	31.3956	−	10.2011i	3.06390	−	0.995521i
$106$		0			0
$107$	−3.30890	−	4.55431i	−0.319883	−	0.440282i	0.618548	−	0.785747i	$-0.287721\pi$
$107$	−3.30890	−	4.55431i	−0.319883	−	0.440282i	−0.938432	+	0.345465i	$0.887721\pi$
$108$		0			0
$109$	8.96853	+	8.96853i	0.859030	+	0.859030i	0.991224	−	0.132194i	$-0.0422023\pi$
$109$	8.96853	+	8.96853i	0.859030	+	0.859030i	−0.132194	+	0.991224i	$0.542202\pi$
$110$		0			0
$111$	−24.0343	−	24.0343i	−2.28123	−	2.28123i
$112$		0			0
$113$	12.1974	−	8.86194i	1.14744	−	0.833661i	0.159298	−	0.987231i	$-0.449077\pi$
$113$	12.1974	−	8.86194i	1.14744	−	0.833661i	0.988138	+	0.153570i	$0.0490770\pi$
$114$		0			0
$115$	−8.05162	+	15.8022i	−0.750817	+	1.47356i
$116$		0			0
$117$	17.9728	+	18.5572i	1.66159	+	1.71561i
$118$		0			0
$119$	1.29998	+	2.55135i	0.119169	+	0.233881i
$120$		0			0
$121$	−0.00811308	+	11.0000i	−0.000737553	+	1.00000i
$122$		0			0
$123$	7.83330	−	3.99127i	0.706305	−	0.359880i
$124$		0			0
$125$	0.417856	+	2.63824i	0.0373742	+	0.235972i
$126$		0			0
$127$	6.69370	+	20.6011i	0.593970	+	1.82805i	0.559790	+	0.828635i	$0.310882\pi$
$127$	6.69370	+	20.6011i	0.593970	+	1.82805i	0.0341795	+	0.999416i	$0.489118\pi$
$128$		0			0
$129$	2.10243	−	1.52750i	0.185109	−	0.134489i
$130$		0			0
$131$			19.8226i			1.73191i	0.500123	+	0.865954i	$0.333288\pi$
$131$			19.8226i			1.73191i	−0.500123	+	0.865954i	$0.666712\pi$
$132$		0			0
$133$	−16.4274			−1.42444
$134$		0			0
$135$	−6.27180	+	39.5986i	−0.539791	+	3.40810i
$136$		0			0
$137$	−1.39385	+	2.73558i	−0.119085	+	0.233717i	−0.942852	−	0.333211i	$-0.891868\pi$
$137$	−1.39385	+	2.73558i	−0.119085	+	0.233717i	0.823768	+	0.566927i	$0.191868\pi$
$138$		0			0
$139$	−10.4429	+	14.3734i	−0.885756	+	1.21914i	0.0890367	+	0.996028i	$0.471621\pi$
$139$	−10.4429	+	14.3734i	−0.885756	+	1.21914i	−0.974793	+	0.223111i	$0.928379\pi$
$140$		0			0
$141$	24.4504	−	12.4581i	2.05910	−	1.04916i
$142$		0			0
$143$	11.4319	−	3.50871i	0.955986	−	0.293413i
$144$		0			0
$145$	−15.1728	+	7.73091i	−1.26003	+	0.642017i
$146$		0			0
$147$	8.92230	−	12.2805i	0.735899	−	1.01288i
$148$		0			0
$149$	9.00039	−	17.6643i	0.737341	−	1.44711i	−0.151290	−	0.988489i	$-0.548343\pi$
$149$	9.00039	−	17.6643i	0.737341	−	1.44711i	0.888631	−	0.458623i	$-0.151657\pi$
$150$		0			0
$151$	1.25959	−	7.95276i	0.102504	−	0.647187i	−0.881923	−	0.471394i	$-0.843751\pi$
$151$	1.25959	−	7.95276i	0.102504	−	0.647187i	0.984427	−	0.175793i	$-0.0562489\pi$
$152$		0			0
$153$	−5.98252			−0.483658
$154$		0			0
$155$		−	16.1317i		−	1.29573i
$156$		0			0
$157$	11.7209	−	8.51575i	0.935431	−	0.679631i	−0.0118851	−	0.999929i	$-0.503783\pi$
$157$	11.7209	−	8.51575i	0.935431	−	0.679631i	0.947317	+	0.320299i	$0.103783\pi$
$158$		0			0
$159$	5.47639	+	16.8546i	0.434306	+	1.33666i
$160$		0			0
$161$	3.15143	+	19.8973i	0.248367	+	1.56813i
$162$		0			0
$163$	−14.3134	+	7.29303i	−1.12111	+	0.571234i	−0.913444	−	0.406966i	$-0.866587\pi$
$163$	−14.3134	+	7.29303i	−1.12111	+	0.571234i	−0.207667	+	0.978200i	$0.566587\pi$
$164$		0			0
$165$	25.8212	+	18.7748i	2.01018	+	1.46161i
$166$		0			0
$167$	−9.16527	−	17.9879i	−0.709230	−	1.39194i	−0.910957	−	0.412501i	$-0.864655\pi$
$167$	−9.16527	−	17.9879i	−0.709230	−	1.39194i	0.201727	−	0.979442i	$-0.435345\pi$
$168$		0			0
$169$	−7.30090	−	10.7563i	−0.561607	−	0.827404i
$170$		0			0
$171$	15.5816	−	30.5806i	1.19155	−	2.33855i
$172$		0			0
$173$	−0.921233	+	0.669315i	−0.0700400	+	0.0508871i	−0.622254	−	0.782815i	$-0.713783\pi$
$173$	−0.921233	+	0.669315i	−0.0700400	+	0.0508871i	0.552214	+	0.833702i	$0.313783\pi$
$174$		0			0
$175$	−9.97945	−	9.97945i	−0.754376	−	0.754376i
$176$		0			0
$177$	9.48541	+	9.48541i	0.712967	+	0.712967i
$178$		0			0
$179$	9.30821	+	12.8117i	0.695728	+	0.957588i	0.999988	+	0.00499853i	$0.00159109\pi$
$179$	9.30821	+	12.8117i	0.695728	+	0.957588i	−0.304259	+	0.952589i	$0.598409\pi$
$180$		0			0
$181$	13.0022	−	4.22466i	0.966444	−	0.314017i	0.217064	−	0.976157i	$-0.430352\pi$
$181$	13.0022	−	4.22466i	0.966444	−	0.314017i	0.749379	+	0.662141i	$0.230352\pi$
$182$		0			0
$183$	8.42766	−	11.5997i	0.622990	−	0.857473i
$184$		0			0
$185$	−9.94624	+	30.6114i	−0.731262	+	2.25059i
$186$		0			0
$187$	−1.25812	+	2.46695i	−0.0920029	+	0.180401i
$188$		0			0
$189$	20.6750	+	40.5769i	1.50388	+	2.95154i
$190$		0			0
$191$	−0.492305	−	0.357680i	−0.0356219	−	0.0258808i	0.569832	−	0.821761i	$-0.307008\pi$
$191$	−0.492305	−	0.357680i	−0.0356219	−	0.0258808i	−0.605454	+	0.795880i	$0.707008\pi$
$192$		0			0
$193$	−5.49324	−	2.79895i	−0.395412	−	0.201473i	0.244967	−	0.969531i	$-0.421223\pi$
$193$	−5.49324	−	2.79895i	−0.395412	−	0.201473i	−0.640379	+	0.768059i	$0.721223\pi$
$194$		0			0
$195$	11.2515	−	32.8321i	0.805736	−	2.35116i
$196$		0			0
$197$	13.3591	+	13.3591i	0.951795	+	0.951795i	0.998890	−	0.0470957i	$-0.0149966\pi$
$197$	13.3591	+	13.3591i	0.951795	+	0.951795i	−0.0470957	+	0.998890i	$0.514997\pi$
$198$		0			0
$199$			22.0680i			1.56436i	0.623054	+	0.782179i	$0.285892\pi$
$199$			22.0680i			1.56436i	−0.623054	+	0.782179i	$0.714108\pi$
$200$		0			0
$201$	2.47579	−	15.6315i	0.174629	−	1.10256i
$202$		0			0
$203$	−8.78150	+	17.2347i	−0.616341	+	1.20964i
$204$		0			0
$205$	−6.73522	−	4.89342i	−0.470408	−	0.341771i
$206$		0			0
$207$	−40.0292	−	13.0063i	−2.78222	−	0.903999i
$208$		0			0
$209$	−9.33340	−	12.8563i	−0.645605	−	0.889288i
$210$		0			0
$211$	16.4204	+	5.33531i	1.13043	+	0.367298i	0.813738	−	0.581232i	$-0.197429\pi$
$211$	16.4204	+	5.33531i	1.13043	+	0.367298i	0.316688	+	0.948530i	$0.397429\pi$
$212$		0			0
$213$	−22.5096	+	3.56517i	−1.54233	+	0.244282i
$214$		0			0
$215$	−2.19268	−	1.11722i	−0.149539	−	0.0761941i
$216$		0			0
$217$	−10.7706	−	14.8244i	−0.731153	−	1.00635i
$218$		0			0
$219$	−9.06168	+	9.06168i	−0.612331	+	0.612331i
$220$		0			0
$221$	2.96551	+	0.518444i	0.199482	+	0.0348743i
$222$		0			0
$223$	−2.27798	+	14.3826i	−0.152545	+	0.963131i	0.786063	+	0.618146i	$0.212116\pi$
$223$	−2.27798	+	14.3826i	−0.152545	+	0.963131i	−0.938608	+	0.344985i	$0.887884\pi$
$224$		0			0
$225$	28.0430	−	9.11171i	1.86953	−	0.607448i
$226$		0			0
$227$	−2.21771	−	14.0020i	−0.147194	−	0.929349i	−0.945151	−	0.326634i	$-0.894086\pi$
$227$	−2.21771	−	14.0020i	−0.147194	−	0.929349i	0.797957	−	0.602715i	$-0.205914\pi$
$228$		0			0
$229$	6.99046	−	3.56182i	0.461943	−	0.235371i	−0.207500	−	0.978235i	$-0.566533\pi$
$229$	6.99046	−	3.56182i	0.461943	−	0.235371i	0.669443	+	0.742863i	$0.266533\pi$
$230$		0			0
$231$	36.2639	+	0.0133733i	2.38599	+	0.000879896i
$232$		0			0
$233$	−4.43582	+	13.6520i	−0.290600	+	0.894375i	0.694064	+	0.719913i	$0.255818\pi$
$233$	−4.43582	+	13.6520i	−0.290600	+	0.894375i	−0.984664	+	0.174461i	$0.944182\pi$
$234$		0			0
$235$	−21.0229	−	15.2741i	−1.37138	−	0.996369i
$236$		0			0
$237$	−41.2823	+	13.4134i	−2.68158	+	0.871297i
$238$		0			0
$239$	−18.4920	−	2.92884i	−1.19615	−	0.189451i	−0.473578	−	0.880752i	$-0.657038\pi$
$239$	−18.4920	−	2.92884i	−1.19615	−	0.189451i	−0.722567	+	0.691301i	$0.757038\pi$
$240$		0			0
$241$	3.07688	−	3.07688i	0.198199	−	0.198199i	−0.601028	−	0.799228i	$-0.705242\pi$
$241$	3.07688	−	3.07688i	0.198199	−	0.198199i	0.799228	+	0.601028i	$0.205242\pi$
$242$		0			0
$243$	−26.6145			−1.70732
$244$		0			0
$245$	−14.1974	−	2.24864i	−0.907037	−	0.143661i
$246$		0			0
$247$	−10.3738	+	13.8084i	−0.660071	+	0.878605i
$248$		0			0
$249$	−4.01613	−	25.3568i	−0.254512	−	1.60692i
$250$		0			0
$251$	6.74139	+	2.19041i	0.425513	+	0.138258i	0.513942	−	0.857825i	$-0.328185\pi$
$251$	6.74139	+	2.19041i	0.425513	+	0.138258i	−0.0884290	+	0.996082i	$0.528185\pi$
$252$		0			0
$253$	−13.7814	+	13.7712i	−0.866428	+	0.865790i
$254$		0			0
$255$	3.64881	+	7.16120i	0.228498	+	0.448452i
$256$		0			0
$257$	13.2479	−	18.2341i	0.826380	−	1.13741i	−0.162206	−	0.986757i	$-0.551861\pi$
$257$	13.2479	−	18.2341i	0.826380	−	1.13741i	0.988586	−	0.150658i	$-0.0481391\pi$
$258$		0			0
$259$	11.2979	+	34.7713i	0.702016	+	2.16058i
$260$		0			0
$261$	−23.7540	−	32.6946i	−1.47034	−	2.02374i
$262$		0			0
$263$		−	6.99555i		−	0.431364i	−0.976464	−	0.215682i	$-0.930803\pi$
$263$		−	6.99555i		−	0.431364i	0.976464	−	0.215682i	$-0.0691975\pi$
$264$		0			0
$265$	11.8666	−	11.8666i	0.728961	−	0.728961i
$266$		0			0
$267$	6.18745	+	0.979996i	0.378666	+	0.0599748i
$268$		0			0
$269$	4.50191	+	13.8554i	0.274486	+	0.844782i	0.989355	+	0.145523i	$0.0464864\pi$
$269$	4.50191	+	13.8554i	0.274486	+	0.844782i	−0.714869	+	0.699259i	$0.753514\pi$
$270$		0			0
$271$	13.4244	−	2.12621i	0.815472	−	0.129158i	0.265253	−	0.964179i	$-0.414544\pi$
$271$	13.4244	−	2.12621i	0.815472	−	0.129158i	0.550219	+	0.835021i	$0.314544\pi$
$272$		0			0
$273$	−11.5811	−	37.6836i	−0.700921	−	2.28071i
$274$		0			0
$275$	2.14012	−	13.4800i	0.129054	−	0.812874i
$276$		0			0
$277$	4.04150	−	12.4385i	0.242830	−	0.747355i	−0.753155	−	0.657843i	$-0.771469\pi$
$277$	4.04150	−	12.4385i	0.242830	−	0.747355i	0.995986	−	0.0895125i	$-0.0285309\pi$
$278$		0			0
$279$	37.8125	−	5.98891i	2.26377	−	0.358547i
$280$		0			0
$281$	−2.29495	−	1.16934i	−0.136905	−	0.0697567i	0.384196	−	0.923252i	$-0.374479\pi$
$281$	−2.29495	−	1.16934i	−0.136905	−	0.0697567i	−0.521101	+	0.853495i	$0.674479\pi$
$282$		0			0
$283$	−18.4162	+	13.3802i	−1.09473	+	0.795368i	−0.980192	−	0.198051i	$-0.936539\pi$
$283$	−18.4162	+	13.3802i	−1.09473	+	0.795368i	−0.114539	+	0.993419i	$0.536539\pi$
$284$		0			0
$285$	−46.1089			−2.73126
$286$		0			0
$287$	−9.45654			−0.558202
$288$		0			0
$289$	13.1893	−	9.58257i	0.775840	−	0.563681i
$290$		0			0
$291$	−31.3233	−	15.9600i	−1.83620	−	0.935592i
$292$		0			0
$293$	27.2835	−	4.32129i	1.59392	−	0.252452i	0.704556	−	0.709649i	$-0.251146\pi$
$293$	27.2835	−	4.32129i	1.59392	−	0.252452i	0.889366	+	0.457196i	$0.151146\pi$
$294$		0			0
$295$	3.92540	−	12.0811i	0.228545	−	0.703390i
$296$		0			0
$297$	−20.0093	+	39.2347i	−1.16106	+	2.27663i
$298$		0			0
$299$	18.7152	+	9.91608i	1.08233	+	0.573461i
$300$		0			0
$301$	−2.76091	+	0.437285i	−0.159136	+	0.0252047i
$302$		0			0
$303$	−4.66300	−	14.3512i	−0.267882	−	0.824457i
$304$		0			0
$305$	−13.4103	−	2.12398i	−0.767871	−	0.121619i
$306$		0			0
$307$	5.79472	−	5.79472i	0.330722	−	0.330722i	−0.522138	−	0.852861i	$-0.674866\pi$
$307$	5.79472	−	5.79472i	0.330722	−	0.330722i	0.852861	+	0.522138i	$0.174866\pi$
$308$		0			0
$309$			7.06186i			0.401735i
$310$		0			0
$311$	−15.1162	−	20.8057i	−0.857162	−	1.17978i	−0.982239	−	0.187636i	$-0.939918\pi$
$311$	−15.1162	−	20.8057i	−0.857162	−	1.17978i	0.125076	−	0.992147i	$-0.460082\pi$
$312$		0			0
$313$	−4.26440	−	13.1245i	−0.241038	−	0.741839i	−0.996263	−	0.0863733i	$-0.972472\pi$
$313$	−4.26440	−	13.1245i	−0.241038	−	0.741839i	0.755225	−	0.655466i	$-0.227528\pi$
$314$		0			0
$315$	43.6060	−	60.0185i	2.45692	−	3.38166i
$316$		0			0
$317$	−9.47184	−	18.5895i	−0.531991	−	1.04409i	−0.988049	−	0.154141i	$-0.950739\pi$
$317$	−9.47184	−	18.5895i	−0.531991	−	1.04409i	0.456057	−	0.889950i	$-0.349261\pi$
$318$		0			0
$319$	−18.4774	+	2.91955i	−1.03453	+	0.163463i
$320$		0			0
$321$	−17.0697	−	5.54628i	−0.952738	−	0.309563i
$322$		0			0
$323$	−0.625667	−	3.95031i	−0.0348130	−	0.219801i
$324$		0			0
$325$	−14.6904	+	2.08644i	−0.814877	+	0.115735i
$326$		0			0
$327$	39.9403	+	6.32592i	2.20870	+	0.349824i
$328$		0			0
$329$	−29.5171			−1.62733
$330$		0			0
$331$	−11.5801	+	11.5801i	−0.636501	+	0.636501i	−0.949691	−	0.313189i	$-0.898603\pi$
$331$	−11.5801	+	11.5801i	−0.636501	+	0.636501i	0.313189	+	0.949691i	$0.398603\pi$
$332$		0			0
$333$	−75.4450	−	11.9493i	−4.13436	−	0.654819i
$334$		0			0
$335$	−14.2534	+	4.63120i	−0.778745	+	0.253030i
$336$		0			0
$337$	−8.60286	−	6.25034i	−0.468628	−	0.340478i	0.328279	−	0.944581i	$-0.393532\pi$
$337$	−8.60286	−	6.25034i	−0.468628	−	0.340478i	−0.796906	+	0.604103i	$0.793532\pi$
$338$		0			0
$339$	14.8541	−	45.7163i	0.806765	−	2.48297i
$340$		0			0
$341$	5.48236	−	16.8518i	0.296886	−	0.912577i
$342$		0			0
$343$	6.84144	−	3.48589i	0.369403	−	0.188220i
$344$		0			0
$345$	8.84552	+	55.8484i	0.476227	+	3.00678i
$346$		0			0
$347$	−7.06346	+	2.29506i	−0.379187	+	0.123205i	−0.492408	−	0.870365i	$-0.663883\pi$
$347$	−7.06346	+	2.29506i	−0.379187	+	0.123205i	0.113221	+	0.993570i	$0.463883\pi$
$348$		0			0
$349$	2.09800	−	13.2463i	0.112304	−	0.709057i	−0.865715	−	0.500538i	$-0.833136\pi$
$349$	2.09800	−	13.2463i	0.112304	−	0.709057i	0.978018	−	0.208519i	$-0.0668644\pi$
$350$		0			0
$351$	47.1638	+	8.24539i	2.51742	+	0.440106i
$352$		0			0
$353$	−10.0314	+	10.0314i	−0.533920	+	0.533920i	−0.921737	−	0.387817i	$-0.873229\pi$
$353$	−10.0314	+	10.0314i	−0.533920	+	0.533920i	0.387817	+	0.921737i	$0.373229\pi$
$354$		0			0
$355$	12.6852	+	17.4597i	0.673260	+	0.926663i
$356$		0			0
$357$	8.13437	+	4.14467i	0.430517	+	0.219359i
$358$		0			0
$359$	6.86090	−	1.08666i	0.362104	−	0.0573517i	0.0272685	−	0.999628i	$-0.491319\pi$
$359$	6.86090	−	1.08666i	0.362104	−	0.0573517i	0.334836	+	0.942276i	$0.391319\pi$
$360$		0			0
$361$	3.75207	+	1.21912i	0.197477	+	0.0641642i
$362$		0			0
$363$	20.5933	+	28.3882i	1.08087	+	1.48999i
$364$		0			0
$365$	11.5414	+	3.75004i	0.604107	+	0.196286i
$366$		0			0
$367$	1.19182	+	0.865907i	0.0622125	+	0.0452000i	0.618457	−	0.785819i	$-0.287758\pi$
$367$	1.19182	+	0.865907i	0.0622125	+	0.0452000i	−0.556244	+	0.831019i	$0.687758\pi$
$368$		0			0
$369$	8.96964	−	17.6039i	0.466941	−	0.916423i
$370$		0			0
$371$	2.98204	−	18.8278i	0.154820	−	0.977493i
$372$		0			0
$373$			16.4565i			0.852085i	0.904703	+	0.426043i	$0.140093\pi$
$373$			16.4565i			0.852085i	−0.904703	+	0.426043i	$0.859907\pi$
$374$		0			0
$375$	6.02191	+	6.02191i	0.310970	+	0.310970i
$376$		0			0
$377$	8.94145	+	18.2651i	0.460508	+	0.940699i
$378$		0			0
$379$	−3.29663	−	1.67972i	−0.169337	−	0.0862813i	0.367268	−	0.930115i	$-0.380293\pi$
$379$	−3.29663	−	1.67972i	−0.169337	−	0.0862813i	−0.536604	+	0.843834i	$0.680293\pi$
$380$		0			0
$381$	55.8722	+	40.5936i	2.86242	+	2.07967i
$382$		0			0
$383$	2.52057	+	4.94689i	0.128795	+	0.252774i	0.946395	−	0.323013i	$-0.104696\pi$
$383$	2.52057	+	4.94689i	0.128795	+	0.252774i	−0.817600	+	0.575787i	$0.804696\pi$
$384$		0			0
$385$	−15.5789	−	30.6032i	−0.793974	−	1.55968i
$386$		0			0
$387$	1.80472	−	5.55437i	0.0917392	−	0.282344i
$388$		0			0
$389$	−12.2946	+	16.9221i	−0.623363	+	0.857985i	−0.997592	−	0.0693508i	$-0.977907\pi$
$389$	−12.2946	+	16.9221i	−0.623363	+	0.857985i	0.374230	+	0.927336i	$0.377907\pi$
$390$		0			0
$391$	−4.66469	+	1.51565i	−0.235904	+	0.0766498i
$392$		0			0
$393$	37.1479	+	51.1297i	1.87386	+	2.57915i
$394$		0			0
$395$	29.0652	+	29.0652i	1.46243	+	1.46243i
$396$		0			0
$397$	−17.2553	−	17.2553i	−0.866021	−	0.866021i	0.126008	−	0.992029i	$-0.459783\pi$
$397$	−17.2553	−	17.2553i	−0.866021	−	0.866021i	−0.992029	+	0.126008i	$0.959783\pi$
$398$		0			0
$399$	−42.3722	+	30.7852i	−2.12126	+	1.54119i
$400$		0			0
$401$	4.75319	−	9.32866i	0.237363	−	0.465851i	−0.741341	−	0.671129i	$-0.765810\pi$
$401$	4.75319	−	9.32866i	0.237363	−	0.465851i	0.978704	+	0.205278i	$0.0658097\pi$
$402$		0			0
$403$	−19.2625	−	0.308142i	−0.959533	−	0.0153497i
$404$		0			0
$405$	28.5685	+	56.0688i	1.41958	+	2.78608i
$406$		0			0
$407$	−20.7935	+	28.5976i	−1.03069	+	1.41753i
$408$		0			0
$409$	−17.7205	+	9.02904i	−0.876221	+	0.446457i	−0.833429	−	0.552627i	$-0.813625\pi$
$409$	−17.7205	+	9.02904i	−0.876221	+	0.446457i	−0.0427926	+	0.999084i	$0.513625\pi$
$410$		0			0
$411$	1.53129	+	9.66816i	0.0755328	+	0.476895i
$412$		0			0
$413$	−4.45884	−	13.7229i	−0.219405	−	0.675259i
$414$		0			0
$415$	−19.6681	+	14.2897i	−0.965470	+	0.701455i
$416$		0			0
$417$			56.6445i			2.77389i
$418$		0			0
$419$	8.61536			0.420888			0.210444	−	0.977606i	$-0.432509\pi$
$419$	8.61536			0.420888			0.210444	+	0.977606i	$0.432509\pi$
$420$		0			0
$421$	−0.805771	+	5.08744i	−0.0392709	+	0.247947i	−0.999512	−	0.0312240i	$-0.990059\pi$
$421$	−0.805771	+	5.08744i	−0.0392709	+	0.247947i	0.960242	+	0.279171i	$0.0900595\pi$
$422$		0			0
$423$	27.9973	−	54.9479i	1.36128	−	2.67166i
$424$		0			0
$425$	2.01968	−	2.77985i	0.0979688	−	0.134843i
$426$		0			0
$427$	−13.7416	+	7.00170i	−0.665003	+	0.338836i
$428$		0			0
$429$	22.9117	−	30.4738i	1.10619	−	1.47129i
$430$		0			0
$431$	−0.864889	+	0.440683i	−0.0416602	+	0.0212269i	−0.474697	−	0.880150i	$-0.657442\pi$
$431$	−0.864889	+	0.440683i	−0.0416602	+	0.0212269i	0.433036	+	0.901376i	$0.357442\pi$
$432$		0			0
$433$	18.3431	−	25.2471i	0.881511	−	1.21330i	−0.0944886	−	0.995526i	$-0.530122\pi$
$433$	18.3431	−	25.2471i	0.881511	−	1.21330i	0.976000	−	0.217770i	$-0.0698784\pi$
$434$		0			0
$435$	−24.6482	+	48.3748i	−1.18179	+	2.31939i
$436$		0			0
$437$	4.40179	−	27.7918i	0.210566	−	1.32946i
$438$		0			0
$439$	11.0809			0.528863			0.264432	−	0.964404i	$-0.414816\pi$
$439$	11.0809			0.528863			0.264432	+	0.964404i	$0.414816\pi$
$440$		0			0
$441$		−	34.1132i		−	1.62444i
$442$		0			0
$443$	−13.1819	+	9.57719i	−0.626290	+	0.455026i	−0.855113	−	0.518442i	$-0.826512\pi$
$443$	−13.1819	+	9.57719i	−0.626290	+	0.455026i	0.228823	+	0.973468i	$0.426512\pi$
$444$		0			0
$445$	−1.83318	−	5.64194i	−0.0869009	−	0.267454i
$446$		0			0
$447$	−9.88785	−	62.4294i	−0.467679	−	2.95281i
$448$		0			0
$449$	22.1289	−	11.2752i	1.04433	−	0.532112i	0.154303	−	0.988024i	$-0.450687\pi$
$449$	22.1289	−	11.2752i	1.04433	−	0.532112i	0.890025	+	0.455912i	$0.150687\pi$
$450$		0			0
$451$	−5.37284	−	7.40081i	−0.252997	−	0.348491i
$452$		0			0
$453$	−11.6547	−	22.8736i	−0.547584	−	1.07469i
$454$		0			0
$455$	−26.8165	+	25.9720i	−1.25718	+	1.21759i
$456$		0			0
$457$	−11.0797	+	21.7452i	−0.518289	+	1.01720i	0.472442	+	0.881362i	$0.343373\pi$
$457$	−11.0797	+	21.7452i	−0.518289	+	1.01720i	−0.990731	+	0.135838i	$0.956627\pi$
$458$		0			0
$459$	−8.97011	+	6.51717i	−0.418689	+	0.304195i
$460$		0			0
$461$	−11.4979	−	11.4979i	−0.535511	−	0.535511i	0.386696	−	0.922207i	$-0.373616\pi$
$461$	−11.4979	−	11.4979i	−0.535511	−	0.535511i	−0.922207	+	0.386696i	$0.873616\pi$
$462$		0			0
$463$	5.57044	+	5.57044i	0.258880	+	0.258880i	0.824599	−	0.565718i	$-0.191401\pi$
$463$	5.57044	+	5.57044i	0.258880	+	0.258880i	−0.565718	+	0.824599i	$0.691401\pi$
$464$		0			0
$465$	−30.2311	−	41.6096i	−1.40194	−	1.92960i
$466$		0			0
$467$	−11.5900	+	3.76582i	−0.536321	+	0.174261i	−0.564639	−	0.825338i	$-0.690985\pi$
$467$	−11.5900	+	3.76582i	−0.536321	+	0.174261i	0.0283185	+	0.999599i	$0.490985\pi$
$468$		0			0
$469$	−10.0062	+	13.7723i	−0.462043	+	0.635947i
$470$		0			0
$471$	14.2739	−	43.9304i	0.657705	−	2.02421i
$472$		0			0
$473$	−1.91087	−	1.91228i	−0.0878617	−	0.0879265i
$474$		0			0
$475$	8.94934	+	17.5641i	0.410624	+	0.805894i
$476$		0			0
$477$	32.2207	+	23.4097i	1.47528	+	1.07186i
$478$		0			0
$479$	−12.1551	−	6.19335i	−0.555383	−	0.282982i	0.153688	−	0.988119i	$-0.450885\pi$
$479$	−12.1551	−	6.19335i	−0.555383	−	0.282982i	−0.709070	+	0.705138i	$0.750885\pi$
$480$		0			0
$481$	36.3623	+	12.4613i	1.65798	+	0.568185i
$482$		0			0
$483$	45.4166	+	45.4166i	2.06653	+	2.06653i
$484$		0			0
$485$			33.2902i			1.51163i
$486$		0			0
$487$	0.348250	−	2.19876i	0.0157807	−	0.0996354i	−0.978541	−	0.206053i	$-0.933938\pi$
$487$	0.348250	−	2.19876i	0.0157807	−	0.0996354i	0.994322	+	0.106418i	$0.0339381\pi$
$488$		0			0
$489$	−23.2521	+	45.6349i	−1.05150	+	2.06368i
$490$		0			0
$491$	30.7014	+	22.3059i	1.38554	+	1.00665i	0.996339	+	0.0854959i	$0.0272475\pi$
$491$	30.7014	+	22.3059i	1.38554	+	1.00665i	0.389197	+	0.921155i	$0.372753\pi$
$492$		0			0
$493$	−4.47889	−	1.45528i	−0.201719	−	0.0655425i
$494$		0			0
$495$	71.7464	+	0.0264584i	3.22476	+	0.00118922i
$496$		0			0
$497$	23.3143	+	7.57528i	1.04579	+	0.339798i
$498$		0			0
$499$	30.2837	−	4.79646i	1.35568	−	0.214719i	0.564063	−	0.825732i	$-0.309238\pi$
$499$	30.2837	−	4.79646i	1.35568	−	0.214719i	0.791621	+	0.611013i	$0.209238\pi$
$500$		0			0
$501$	−57.3501	−	29.2213i	−2.56221	−	1.30551i
$502$		0			0
$503$	−16.8065	−	23.1322i	−0.749365	−	1.03141i	−0.998025	−	0.0628212i	$-0.979990\pi$
$503$	−16.8065	−	23.1322i	−0.749365	−	1.03141i	0.248660	−	0.968591i	$-0.420010\pi$
$504$		0			0
$505$	−10.1041	+	10.1041i	−0.449627	+	0.449627i
$506$		0			0
$507$	−38.9890	−	14.0623i	−1.73156	−	0.624527i
$508$		0			0
$509$	1.19975	−	7.57494i	0.0531781	−	0.335753i	−0.946728	−	0.322035i	$-0.895633\pi$
$509$	1.19975	−	7.57494i	0.0531781	−	0.335753i	0.999906	−	0.0137185i	$-0.00436687\pi$
$510$		0			0
$511$	13.1099	−	4.25965i	0.579946	−	0.188436i
$512$		0			0
$513$	−9.95068	−	62.8261i	−0.439333	−	2.77384i
$514$		0			0
$515$	5.95841	−	3.03596i	0.262559	−	0.133780i
$516$		0			0
$517$	−16.7705	−	23.1005i	−0.737564	−	1.01596i
$518$		0			0
$519$	−1.12189	+	3.45281i	−0.0492454	+	0.151562i
$520$		0			0
$521$	−6.99797	−	5.08432i	−0.306587	−	0.222748i	0.423844	−	0.905735i	$-0.360681\pi$
$521$	−6.99797	−	5.08432i	−0.306587	−	0.222748i	−0.730430	+	0.682987i	$0.760681\pi$
$522$		0			0
$523$	−10.3381	+	3.35905i	−0.452053	+	0.146881i	−0.526190	−	0.850367i	$-0.676380\pi$
$523$	−10.3381	+	3.35905i	−0.452053	+	0.146881i	0.0741369	+	0.997248i	$0.476380\pi$
$524$		0			0
$525$	−44.4423	−	7.03897i	−1.93962	−	0.307206i
$526$		0			0
$527$	3.15462	−	3.15462i	0.137417	−	0.137417i
$528$		0			0
$529$	−11.5067			−0.500290
$530$		0			0
$531$	29.7752	+	4.71594i	1.29214	+	0.204654i
$532$		0			0
$533$	−5.97176	+	7.94888i	−0.258666	+	0.344304i
$534$		0			0
$535$	2.65878	+	16.7869i	0.114949	+	0.725760i
$536$		0			0
$537$	48.0185	+	15.6022i	2.07215	+	0.673283i
$538$		0			0
$539$	−14.0669	−	7.17399i	−0.605905	−	0.309005i
$540$		0			0
$541$	11.2198	+	22.0200i	0.482376	+	0.946716i	0.996055	+	0.0887337i	$0.0282820\pi$
$541$	11.2198	+	22.0200i	0.482376	+	0.946716i	−0.513680	+	0.857982i	$0.671718\pi$
$542$		0			0
$543$	25.6202	−	35.2632i	1.09947	−	1.51329i
$544$		0			0
$545$	−11.8332	−	36.4190i	−0.506880	−	1.56002i
$546$		0			0
$547$	−8.96042	−	12.3330i	−0.383120	−	0.527319i	0.573288	−	0.819354i	$-0.305668\pi$
$547$	−8.96042	−	12.3330i	−0.383120	−	0.527319i	−0.956408	+	0.292035i	$0.905668\pi$
$548$		0			0
$549$		−	32.2220i		−	1.37520i
$550$		0			0
$551$	19.1042	−	19.1042i	0.813867	−	0.813867i
$552$		0			0
$553$	46.1154	+	7.30396i	1.96103	+	0.310596i
$554$		0			0
$555$	31.7113	+	97.5972i	1.34607	+	4.14277i
$556$		0			0
$557$	−2.34226	+	0.370977i	−0.0992446	+	0.0157188i	−0.205859	−	0.978582i	$-0.565999\pi$
$557$	−2.34226	+	0.370977i	−0.0992446	+	0.0157188i	0.106615	+	0.994300i	$0.465999\pi$
$558$		0			0
$559$	−1.37593	+	2.59688i	−0.0581958	+	0.109836i
$560$		0			0
$561$	1.37796	+	8.72091i	0.0581775	+	0.368197i
$562$		0			0
$563$	5.41418	−	16.6631i	0.228180	−	0.702267i	−0.769773	−	0.638318i	$-0.779631\pi$
$563$	5.41418	−	16.6631i	0.228180	−	0.702267i	0.997953	−	0.0639489i	$-0.0203695\pi$
$564$		0			0
$565$	−44.9588	+	7.12077i	−1.89143	+	0.299573i
$566$		0			0
$567$	63.6883	+	32.4508i	2.67466	+	1.36281i
$568$		0			0
$569$	2.29586	−	1.66804i	0.0962474	−	0.0699279i	−0.538621	−	0.842548i	$-0.681054\pi$
$569$	2.29586	−	1.66804i	0.0962474	−	0.0699279i	0.634868	+	0.772620i	$0.281054\pi$
$570$		0			0
$571$	−36.3297			−1.52035			−0.760174	−	0.649719i	$-0.774887\pi$
$571$	−36.3297			−1.52035			−0.760174	+	0.649719i	$0.774887\pi$
$572$		0			0
$573$	−1.94013			−0.0810502
$574$		0			0
$575$	19.5572	−	14.2092i	0.815594	−	0.592563i
$576$		0			0
$577$	30.9220	+	15.7556i	1.28730	+	0.655912i	0.957580	−	0.288166i	$-0.0930457\pi$
$577$	30.9220	+	15.7556i	1.28730	+	0.655912i	0.329720	+	0.944079i	$0.393046\pi$
$578$		0			0
$579$	−19.4143	+	3.07493i	−0.806833	+	0.127790i
$580$		0			0
$581$	−8.53348	+	26.2633i	−0.354028	+	1.08959i
$582$		0			0
$583$	16.4292	−	8.36346i	0.680428	−	0.346379i
$584$		0			0
$585$	−22.9127	−	74.5552i	−0.947323	−	3.08248i
$586$		0			0
$587$	15.3166	−	2.42591i	0.632183	−	0.100128i	0.167884	−	0.985807i	$-0.446306\pi$
$587$	15.3166	−	2.42591i	0.632183	−	0.100128i	0.464299	+	0.885679i	$0.346306\pi$
$588$		0			0
$589$	7.90905	+	24.3415i	0.325887	+	1.00298i
$590$		0			0
$591$	59.4930	+	9.42277i	2.44722	+	0.387601i
$592$		0			0
$593$	−5.24585	+	5.24585i	−0.215421	+	0.215421i	−0.806566	−	0.591145i	$-0.798676\pi$
$593$	−5.24585	+	5.24585i	−0.215421	+	0.215421i	0.591145	+	0.806566i	$0.298676\pi$
$594$		0			0
$595$		−	8.64516i		−	0.354417i
$596$		0			0
$597$	41.3558	+	56.9213i	1.69258	+	2.32964i
$598$		0			0
$599$	−3.61652	−	11.1305i	−0.147767	−	0.454780i	0.849589	−	0.527445i	$-0.176850\pi$
$599$	−3.61652	−	11.1305i	−0.147767	−	0.454780i	−0.997356	+	0.0726644i	$0.976850\pi$
$600$		0			0
$601$	4.82832	−	6.64561i	0.196951	−	0.271080i	−0.699107	−	0.715018i	$-0.746419\pi$
$601$	4.82832	−	6.64561i	0.196951	−	0.271080i	0.896058	+	0.443937i	$0.146419\pi$
$602$		0			0
$603$	−16.1470	−	31.6903i	−0.657558	−	1.29053i
$604$		0			0
$605$	15.0991	−	29.5798i	0.613868	−	1.20259i
$606$		0			0
$607$	−16.9010	−	5.49145i	−0.685989	−	0.222891i	−0.0547733	−	0.998499i	$-0.517444\pi$
$607$	−16.9010	−	5.49145i	−0.685989	−	0.222891i	−0.631215	+	0.775608i	$0.717444\pi$
$608$		0			0
$609$	9.64738	+	60.9111i	0.390931	+	2.46824i
$610$		0			0
$611$	−18.6399	+	24.8112i	−0.754091	+	1.00375i
$612$		0			0
$613$	−17.9000	−	2.83509i	−0.722976	−	0.114508i	−0.215907	−	0.976414i	$-0.569271\pi$
$613$	−17.9000	−	2.83509i	−0.722976	−	0.114508i	−0.507069	+	0.861906i	$0.669271\pi$
$614$		0			0
$615$	−26.5429			−1.07031
$616$		0			0
$617$	−4.99800	+	4.99800i	−0.201212	+	0.201212i	−0.800519	−	0.599307i	$-0.795443\pi$
$617$	−4.99800	+	4.99800i	−0.201212	+	0.201212i	0.599307	+	0.800519i	$0.295443\pi$
$618$		0			0
$619$	7.94353	+	1.25813i	0.319277	+	0.0505686i	0.314016	−	0.949418i	$-0.398325\pi$
$619$	7.94353	+	1.25813i	0.319277	+	0.0505686i	0.00526110	+	0.999986i	$0.498325\pi$
$620$		0			0
$621$	−74.1878	+	24.1051i	−2.97706	+	0.967304i
$622$		0			0
$623$	−5.45153	−	3.96076i	−0.218411	−	0.158685i
$624$		0			0
$625$	8.85052	−	27.2391i	0.354021	−	1.08956i
$626$		0			0
$627$	−48.1671	−	15.6701i	−1.92361	−	0.625803i
$628$		0			0
$629$	−7.93118	+	4.04114i	−0.316237	+	0.161131i
$630$		0			0
$631$	5.95776	+	37.6158i	0.237175	+	1.49746i	0.762738	+	0.646707i	$0.223854\pi$
$631$	5.95776	+	37.6158i	0.237175	+	1.49746i	−0.525564	+	0.850754i	$0.676146\pi$
$632$		0			0
$633$	52.3526	−	17.0104i	2.08083	−	0.676102i
$634$		0			0
$635$	10.2306	−	64.5934i	0.405989	−	2.56331i
$636$		0			0
$637$	−2.95624	+	16.9098i	−0.117130	+	0.669989i
$638$		0			0
$639$	−36.2158	+	36.2158i	−1.43267	+	1.43267i
$640$		0			0
$641$	−21.5404	−	29.6478i	−0.850794	−	1.17102i	−0.983687	−	0.179887i	$-0.942427\pi$
$641$	−21.5404	−	29.6478i	−0.850794	−	1.17102i	0.132894	−	0.991130i	$-0.457573\pi$
$642$		0			0
$643$	18.4335	+	9.39231i	0.726944	+	0.370397i	0.777971	−	0.628301i	$-0.216249\pi$
$643$	18.4335	+	9.39231i	0.726944	+	0.370397i	−0.0510262	+	0.998697i	$0.516249\pi$
$644$		0			0
$645$	−7.74941	+	1.22739i	−0.305133	+	0.0483283i
$646$		0			0
$647$	−20.7211	−	6.73269i	−0.814630	−	0.264689i	−0.128072	−	0.991765i	$-0.540879\pi$
$647$	−20.7211	−	6.73269i	−0.814630	−	0.264689i	−0.686557	+	0.727076i	$0.740879\pi$
$648$		0			0
$649$	8.20638	−	11.2864i	0.322129	−	0.443028i
$650$		0			0
$651$	−55.5623	−	18.0533i	−2.17766	−	0.707564i
$652$		0			0
$653$	20.6010	+	14.9675i	0.806180	+	0.585724i	0.912721	−	0.408584i	$-0.133977\pi$
$653$	20.6010	+	14.9675i	0.806180	+	0.585724i	−0.106541	+	0.994308i	$0.533977\pi$
$654$		0			0
$655$	27.1702	−	53.3244i	1.06163	−	2.08356i
$656$		0			0
$657$	−4.50527	+	28.4451i	−0.175767	+	1.10975i
$658$		0			0
$659$			14.9562i			0.582609i	0.956630	+	0.291305i	$0.0940893\pi$
$659$			14.9562i			0.582609i	−0.956630	+	0.291305i	$0.905911\pi$
$660$		0			0
$661$	18.2531	+	18.2531i	0.709965	+	0.709965i	0.966528	−	0.256563i	$-0.0825901\pi$
$661$	18.2531	+	18.2531i	0.709965	+	0.709965i	−0.256563	+	0.966528i	$0.582590\pi$
$662$		0			0
$663$	8.62070	−	4.22016i	0.334800	−	0.163898i
$664$		0			0
$665$	44.1911	+	22.5165i	1.71366	+	0.873151i
$666$		0			0
$667$	−26.8045	−	19.4746i	−1.03788	−	0.754061i
$668$		0			0
$669$	21.0775	+	41.3670i	0.814904	+	1.59934i
$670$		0			0
$671$	−13.2871	−	6.77627i	−0.512941	−	0.261595i
$672$		0			0
$673$	6.63212	−	20.4116i	0.255649	−	0.786808i	−0.738052	−	0.674744i	$-0.764254\pi$
$673$	6.63212	−	20.4116i	0.255649	−	0.786808i	0.993701	−	0.112064i	$-0.0357460\pi$
$674$		0			0
$675$	32.1212	−	44.2111i	1.23635	−	1.70169i
$676$		0			0
$677$	7.45426	−	2.42203i	0.286490	−	0.0930864i	−0.162247	−	0.986750i	$-0.551874\pi$
$677$	7.45426	−	2.42203i	0.286490	−	0.0930864i	0.448737	+	0.893664i	$0.351874\pi$
$678$		0			0
$679$	22.2266	+	30.5923i	0.852979	+	1.17402i
$680$		0			0
$681$	−31.9603	−	31.9603i	−1.22472	−	1.22472i
$682$		0			0
$683$	17.0095	+	17.0095i	0.650852	+	0.650852i	0.953198	−	0.302346i	$-0.0977698\pi$
$683$	17.0095	+	17.0095i	0.650852	+	0.650852i	−0.302346	+	0.953198i	$0.597770\pi$
$684$		0			0
$685$	7.49914	−	5.44845i	0.286528	−	0.208174i
$686$		0			0
$687$	11.3560	−	22.2875i	0.433259	−	0.850319i
$688$		0			0
$689$	−13.9430	−	14.3963i	−0.531185	−	0.548456i
$690$		0			0
$691$	−4.34480	−	8.52715i	−0.165284	−	0.324388i	0.793478	−	0.608599i	$-0.208268\pi$
$691$	−4.34480	−	8.52715i	−0.165284	−	0.324388i	−0.958762	+	0.284211i	$0.908268\pi$
$692$		0			0
$693$	65.9497	−	47.8781i	2.50522	−	1.81874i
$694$		0			0
$695$	47.7935	−	24.3520i	1.81291	−	0.923724i
$696$		0			0
$697$	−0.360169	−	2.27402i	−0.0136424	−	0.0861346i
$698$		0			0
$699$	14.1426	+	43.5263i	0.534921	+	1.64632i
$700$		0			0
$701$	−24.2596	+	17.6257i	−0.916274	+	0.665712i	−0.942594	−	0.333942i	$-0.891621\pi$
$701$	−24.2596	+	17.6257i	−0.916274	+	0.665712i	0.0263200	+	0.999654i	$0.491621\pi$
$702$		0			0
$703$		−	51.0666i		−	1.92601i
$704$		0			0
$705$	−82.8496			−3.12030
$706$		0			0
$707$	−2.53912	+	16.0314i	−0.0954935	+	0.602922i
$708$		0			0
$709$	2.08199	−	4.08613i	0.0781907	−	0.153458i	−0.848601	−	0.529033i	$-0.822555\pi$
$709$	2.08199	−	4.08613i	0.0781907	−	0.153458i	0.926792	+	0.375575i	$0.122555\pi$
$710$		0			0
$711$	−57.3378	+	78.9187i	−2.15034	+	2.95968i
$712$		0			0
$713$	27.9659	−	14.2493i	1.04733	−	0.533642i
$714$		0			0
$715$	−35.5621	−	6.23064i	−1.32995	−	0.233013i
$716$		0			0
$717$	−53.1861	+	27.0997i	−1.98627	+	1.01206i
$718$		0			0
$719$	25.6913	−	35.3611i	0.958124	−	1.31874i	0.0103016	−	0.999947i	$-0.496721\pi$
$719$	25.6913	−	35.3611i	0.958124	−	1.31874i	0.947823	−	0.318798i	$-0.103279\pi$
$720$		0			0
$721$	3.44853	−	6.76813i	0.128430	−	0.252058i
$722$		0			0
$723$	2.17027	−	13.7025i	0.0807131	−	0.509602i
$724$		0			0
$725$	23.2112			0.862042
$726$		0			0
$727$		−	30.6948i		−	1.13841i	−0.822196	−	0.569204i	$-0.807251\pi$
$727$		−	30.6948i		−	1.13841i	0.822196	−	0.569204i	$-0.192749\pi$
$728$		0			0
$729$	−18.0619	+	13.1228i	−0.668961	+	0.486028i
$730$		0			0
$731$	−0.210308	−	0.647263i	−0.00777854	−	0.0239399i
$732$		0			0
$733$	4.70974	+	29.7361i	0.173958	+	1.09833i	0.907922	+	0.419140i	$0.137668\pi$
$733$	4.70974	+	29.7361i	0.173958	+	1.09833i	−0.733963	+	0.679189i	$0.762332\pi$
$734$		0			0
$735$	−40.8342	+	20.8060i	−1.50619	+	0.767442i
$736$		0			0
$737$	−16.4635	−	0.00607136i	−0.606442	−	0.000223641i
$738$		0			0
$739$	16.1376	+	31.6718i	0.593631	+	1.16507i	0.971017	+	0.239010i	$0.0768228\pi$
$739$	16.1376	+	31.6718i	0.593631	+	1.16507i	−0.377387	+	0.926056i	$0.623177\pi$
$740$		0			0
$741$	−0.880756	+	55.0575i	−0.0323554	+	2.02259i
$742$		0			0
$743$	−14.5151	+	28.4875i	−0.532508	+	1.04511i	0.455432	+	0.890271i	$0.349485\pi$
$743$	−14.5151	+	28.4875i	−0.532508	+	1.04511i	−0.987940	+	0.154836i	$0.950515\pi$
$744$		0			0
$745$	−48.4236	+	35.1818i	−1.77410	+	1.28896i
$746$		0			0
$747$	−40.7967	−	40.7967i	−1.49267	−	1.49267i
$748$		0			0
$749$	13.6513	+	13.6513i	0.498807	+	0.498807i
$750$		0			0
$751$	6.60195	+	9.08681i	0.240909	+	0.331582i	0.912301	−	0.409519i	$-0.134304\pi$
$751$	6.60195	+	9.08681i	0.240909	+	0.331582i	−0.671393	+	0.741102i	$0.734304\pi$
$752$		0			0
$753$	21.4934	−	6.98362i	0.783262	−	0.254497i
$754$		0			0
$755$	−14.2890	+	19.6671i	−0.520030	+	0.715759i
$756$		0			0
$757$	−4.30469	+	13.2485i	−0.156457	+	0.481524i	−0.998306	−	0.0581892i	$-0.981467\pi$
$757$	−4.30469	+	13.2485i	−0.156457	+	0.481524i	0.841849	+	0.539713i	$0.181467\pi$
$758$		0			0
$759$	−9.73969	+	61.3475i	−0.353528	+	2.22677i
$760$		0			0
$761$	13.3515	+	26.2037i	0.483990	+	0.949884i	0.995867	+	0.0908254i	$0.0289505\pi$
$761$	13.3515	+	26.2037i	0.483990	+	0.949884i	−0.511877	+	0.859059i	$0.671049\pi$
$762$		0			0
$763$	−35.1898	−	25.5669i	−1.27396	−	0.925584i
$764$		0			0
$765$	16.0935	+	8.20004i	0.581861	+	0.296473i
$766$		0			0
$767$	−14.3508	−	4.91798i	−0.518177	−	0.177578i
$768$		0			0
$769$	15.6742	+	15.6742i	0.565228	+	0.565228i	0.930788	−	0.365560i	$-0.119122\pi$
$769$	15.6742	+	15.6742i	0.565228	+	0.565228i	−0.365560	+	0.930788i	$0.619122\pi$
$770$		0			0
$771$		−	71.8592i		−	2.58795i
$772$		0			0
$773$	0.564543	−	3.56438i	0.0203052	−	0.128202i	−0.975453	−	0.220206i	$-0.929327\pi$
$773$	0.564543	−	3.56438i	0.0203052	−	0.128202i	0.995759	+	0.0920037i	$0.0293272\pi$
$774$		0			0
$775$	−9.98255	+	19.5919i	−0.358584	+	0.703760i
$776$		0			0
$777$	94.3033	+	68.5154i	3.38311	+	2.45798i
$778$		0			0
$779$	12.5621	+	4.08166i	0.450083	+	0.146241i
$780$		0			0
$781$	7.31777	+	22.5501i	0.261851	+	0.806905i
$782$		0			0
$783$	−71.2328	−	23.1449i	−2.54565	−	0.827133i
$784$		0			0
$785$	−43.2025	+	6.84260i	−1.54196	+	0.244223i
$786$		0			0
$787$	−5.36226	−	2.73221i	−0.191144	−	0.0973927i	0.355799	−	0.934562i	$-0.384209\pi$
$787$	−5.36226	−	2.73221i	−0.191144	−	0.0973927i	−0.546943	+	0.837170i	$0.684209\pi$
$788$		0			0
$789$	−13.1098	−	18.0441i	−0.466720	−	0.642385i
$790$		0			0
$791$	−36.5610	+	36.5610i	−1.29996	+	1.29996i
$792$		0			0
$793$	−2.79235	+	15.9723i	−0.0991592	+	0.567193i
$794$		0			0
$795$	8.37008	−	52.8466i	0.296856	−	1.87428i
$796$		0			0
$797$	−1.47830	+	0.480329i	−0.0523641	+	0.0170141i	−0.335082	−	0.942189i	$-0.608764\pi$
$797$	−1.47830	+	0.480329i	−0.0523641	+	0.0170141i	0.282718	+	0.959203i	$0.408764\pi$
$798$		0			0
$799$	−1.12421	−	7.09800i	−0.0397718	−	0.251109i
$800$		0			0
$801$	12.5440	−	6.39151i	0.443222	−	0.225833i
$802$		0			0
$803$	10.7822	+	7.83979i	0.380495	+	0.276660i
$804$		0			0
$805$	18.7950	−	57.8450i	0.662436	−	2.03877i
$806$		0			0
$807$	37.5774	+	27.3016i	1.32279	+	0.961061i
$808$		0			0
$809$	7.55389	−	2.45441i	0.265581	−	0.0862924i	−0.173200	−	0.984887i	$-0.555411\pi$
$809$	7.55389	−	2.45441i	0.265581	−	0.0862924i	0.438780	+	0.898594i	$0.355411\pi$
$810$		0			0
$811$	30.1305	+	4.77221i	1.05803	+	0.167575i	0.661117	−	0.750283i	$-0.270083\pi$
$811$	30.1305	+	4.77221i	1.05803	+	0.167575i	0.396909	+	0.917858i	$0.370083\pi$
$812$		0			0
$813$	30.6417	−	30.6417i	1.07465	−	1.07465i
$814$		0			0
$815$	48.5005			1.69890
$816$		0			0
$817$	3.85633	+	0.610783i	0.134916	+	0.0213686i
$818$		0			0
$819$	−70.8335	−	53.2152i	−2.47512	−	1.85949i
$820$		0			0
$821$	−7.65200	−	48.3128i	−0.267057	−	1.68613i	−0.648086	−	0.761567i	$-0.724430\pi$
$821$	−7.65200	−	48.3128i	−0.267057	−	1.68613i	0.381029	−	0.924563i	$-0.375570\pi$
$822$		0			0
$823$	36.8913	+	11.9867i	1.28595	+	0.417831i	0.870673	−	0.491863i	$-0.163684\pi$
$823$	36.8913	+	11.9867i	1.28595	+	0.417831i	0.415279	+	0.909694i	$0.363684\pi$
$824$		0			0
$825$	−19.7416	−	38.7804i	−0.687314	−	1.35016i
$826$		0			0
$827$	1.07951	+	2.11867i	0.0375384	+	0.0736732i	0.909014	−	0.416766i	$-0.136836\pi$
$827$	1.07951	+	2.11867i	0.0375384	+	0.0736732i	−0.871476	+	0.490439i	$0.836836\pi$
$828$		0			0
$829$	14.9445	−	20.5694i	0.519044	−	0.714403i	−0.466367	−	0.884591i	$-0.654438\pi$
$829$	14.9445	−	20.5694i	0.519044	−	0.714403i	0.985412	+	0.170188i	$0.0544375\pi$
$830$		0			0
$831$	−12.8854	−	39.6572i	−0.446989	−	1.37569i
$832$		0			0
$833$	−2.33661	−	3.21607i	−0.0809589	−	0.111430i
$834$		0			0
$835$			60.9514i			2.10931i
$836$		0			0
$837$	50.1714	−	50.1714i	1.73418	−	1.73418i
$838$		0			0
$839$	14.6595	+	2.32183i	0.506101	+	0.0801585i	0.404263	−	0.914643i	$-0.367528\pi$
$839$	14.6595	+	2.32183i	0.506101	+	0.0801585i	0.101837	+	0.994801i	$0.467528\pi$
$840$		0			0
$841$	−0.869110	−	2.67485i	−0.0299693	−	0.0922361i
$842$		0			0
$843$	−8.11086	+	1.28463i	−0.279353	+	0.0442452i
$844$		0			0
$845$	4.89679	+	38.9423i	0.168455	+	1.33966i
$846$		0			0
$847$	−5.87383	−	37.2637i	−0.201827	−	1.28040i
$848$		0			0
$849$	−22.4275	+	69.0246i	−0.769708	+	2.36892i
$850$		0			0
$851$	−61.8533	+	9.79660i	−2.12030	+	0.335823i
$852$		0			0
$853$	2.54064	+	1.29452i	0.0869897	+	0.0443235i	0.496944	−	0.867783i	$-0.334455\pi$
$853$	2.54064	+	1.29452i	0.0869897	+	0.0443235i	−0.409954	+	0.912106i	$0.634455\pi$
$854$		0			0
$855$	−83.8315	+	60.9071i	−2.86698	+	2.08298i
$856$		0			0
$857$	−7.97041			−0.272264			−0.136132	−	0.990691i	$-0.543467\pi$
$857$	−7.97041			−0.272264			−0.136132	+	0.990691i	$0.543467\pi$
$858$		0			0
$859$	50.9460			1.73826			0.869128	−	0.494587i	$-0.164681\pi$
$859$	50.9460			1.73826			0.869128	+	0.494587i	$0.164681\pi$
$860$		0			0
$861$	−24.3918	+	17.7217i	−0.831272	+	0.603954i
$862$		0			0
$863$	27.9764	+	14.2547i	0.952329	+	0.485236i	0.859888	−	0.510483i	$-0.170533\pi$
$863$	27.9764	+	14.2547i	0.952329	+	0.485236i	0.0924405	+	0.995718i	$0.470533\pi$
$864$		0			0
$865$	3.39560	−	0.537810i	0.115454	−	0.0182861i
$866$		0			0
$867$	16.0620	−	49.4338i	0.545495	−	1.67886i
$868$		0			0
$869$	20.4848	+	40.2404i	0.694899	+	1.36506i
$870$		0			0
$871$	5.25774	+	17.1081i	0.178152	+	0.579684i
$872$		0			0
$873$	−78.0316	+	12.3590i	−2.64097	+	0.418288i
$874$		0			0
$875$	−2.83074	−	8.71213i	−0.0956965	−	0.294524i
$876$		0			0
$877$	21.8306	+	3.45763i	0.737167	+	0.116756i	0.513717	−	0.857960i	$-0.328268\pi$
$877$	21.8306	+	3.45763i	0.737167	+	0.116756i	0.223450	+	0.974715i	$0.428268\pi$
$878$		0			0
$879$	62.2760	−	62.2760i	2.10052	−	2.10052i
$880$		0			0
$881$		−	22.7886i		−	0.767769i	−0.923381	−	0.383884i	$-0.874586\pi$
$881$		−	22.7886i		−	0.767769i	0.923381	−	0.383884i	$-0.125414\pi$
$882$		0			0
$883$	−16.8083	−	23.1347i	−0.565645	−	0.778544i	0.426385	−	0.904542i	$-0.359787\pi$
$883$	−16.8083	−	23.1347i	−0.565645	−	0.778544i	−0.992031	+	0.125998i	$0.959787\pi$
$884$		0			0
$885$	−12.5152	−	38.5179i	−0.420694	−	1.29476i
$886$		0			0
$887$	10.0630	−	13.8506i	0.337883	−	0.465056i	−0.605939	−	0.795511i	$-0.707202\pi$
$887$	10.0630	−	13.8506i	0.337883	−	0.465056i	0.943822	+	0.330455i	$0.107202\pi$
$888$		0			0
$889$	−33.7251	−	66.1893i	−1.13110	−	2.21992i
$890$		0			0
$891$	10.7888	+	68.2806i	0.361438	+	2.28749i
$892$		0			0
$893$	39.2105	+	12.7403i	1.31213	+	0.426337i
$894$		0			0
$895$	−7.47936	−	47.2229i	−0.250008	−	1.57849i
$896$		0			0
$897$	66.8561	−	9.49541i	2.23226	−	0.317043i
$898$		0			0
$899$	29.7656	+	4.71441i	0.992739	+	0.157234i
$900$		0			0
$901$	4.64112			0.154618
$902$		0			0
$903$	−6.30191	+	6.30191i	−0.209714	+	0.209714i
$904$		0			0
$905$	−40.7675	−	6.45694i	−1.35516	−	0.214636i
$906$		0			0
$907$	40.6308	−	13.2018i	1.34912	−	0.438357i	0.456727	−	0.889607i	$-0.349022\pi$
$907$	40.6308	−	13.2018i	1.34912	−	0.438357i	0.892398	+	0.451250i	$0.149022\pi$
$908$		0			0
$909$	−27.4350	−	19.9327i	−0.909961	−	0.661126i
$910$		0			0
$911$	−10.5506	+	32.4714i	−0.349557	+	1.07583i	0.609541	+	0.792754i	$0.291354\pi$
$911$	−10.5506	+	32.4714i	−0.349557	+	1.07583i	−0.959099	+	0.283073i	$0.908646\pi$
$912$		0			0
$913$	−25.4024	+	8.24339i	−0.840698	+	0.272817i
$914$		0			0
$915$	−38.5704	+	19.6526i	−1.27510	+	0.649694i
$916$		0			0
$917$	−10.6345	−	67.1434i	−0.351181	−	2.21727i
$918$		0			0
$919$	22.8275	−	7.41712i	0.753011	−	0.244668i	0.0927347	−	0.995691i	$-0.470439\pi$
$919$	22.8275	−	7.41712i	0.753011	−	0.244668i	0.660276	+	0.751023i	$0.270439\pi$
$920$		0			0
$921$	4.08728	−	25.8061i	0.134681	−	0.850340i
$922$		0			0
$923$	21.0904	−	14.8135i	0.694200	−	0.487594i
$924$		0			0
$925$	31.0224	−	31.0224i	1.02001	−	1.02001i
$926$		0			0
$927$	9.32830	+	12.8393i	0.306381	+	0.421698i
$928$		0			0
$929$	−15.8602	−	8.08118i	−0.520356	−	0.265135i	0.174026	−	0.984741i	$-0.444322\pi$
$929$	−15.8602	−	8.08118i	−0.520356	−	0.265135i	−0.694382	+	0.719606i	$0.744322\pi$
$930$		0			0
$931$	22.5252	−	3.56764i	0.738234	−	0.116925i
$932$		0			0
$933$	−77.9804	−	25.3374i	−2.55296	−	0.829509i
$934$		0			0
$935$	6.76582	−	4.91184i	0.221266	−	0.160634i
$936$		0			0
$937$	10.1269	+	3.29043i	0.330831	+	0.107494i	0.469723	−	0.882814i	$-0.344354\pi$
$937$	10.1269	+	3.29043i	0.330831	+	0.107494i	−0.138891	+	0.990308i	$0.544354\pi$
$938$		0			0
$939$	−35.5949	−	25.8612i	−1.16160	−	0.843949i
$940$		0			0
$941$	−16.1172	+	31.6318i	−0.525406	+	1.03117i	0.463978	+	0.885847i	$0.346422\pi$
$941$	−16.1172	+	31.6318i	−0.525406	+	1.03117i	−0.989385	+	0.145321i	$0.953578\pi$
$942$		0			0
$943$	2.53392	−	15.9985i	0.0825158	−	0.520984i
$944$		0			0
$945$		−	137.494i		−	4.47267i
$946$		0			0
$947$	9.82779	+	9.82779i	0.319360	+	0.319360i	0.848521	−	0.529161i	$-0.177493\pi$
$947$	9.82779	+	9.82779i	0.319360	+	0.319360i	−0.529161	+	0.848521i	$0.677493\pi$
$948$		0			0
$949$	4.69829	−	13.7097i	0.152513	−	0.445036i
$950$		0			0
$951$	−59.2684	−	30.1987i	−1.92191	−	0.979261i
$952$		0			0
$953$	−21.2744	−	15.4568i	−0.689145	−	0.500693i	0.187234	−	0.982315i	$-0.440048\pi$
$953$	−21.2744	−	15.4568i	−0.689145	−	0.500693i	−0.876379	+	0.481622i	$0.840048\pi$
$954$		0			0
$955$	0.834081	+	1.63698i	0.0269902	+	0.0529713i
$956$		0			0
$957$	−42.1886	+	42.1575i	−1.36376	+	1.36276i
$958$		0			0
$959$	3.25368	−	10.0138i	0.105067	−	0.323362i
$960$		0			0
$961$	1.44060	−	1.98282i	0.0464710	−	0.0639619i
$962$		0			0
$963$	−38.3610	+	12.4643i	−1.23617	+	0.401655i
$964$		0			0
$965$	10.9409	+	15.0588i	0.352199	+	0.484760i
$966$		0			0
$967$	0.312857	+	0.312857i	0.0100608	+	0.0100608i	0.712119	−	0.702058i	$-0.247736\pi$
$967$	0.312857	+	0.312857i	0.0100608	+	0.0100608i	−0.702058	+	0.712119i	$0.747736\pi$
$968$		0			0
$969$	−9.01676	−	9.01676i	−0.289660	−	0.289660i
$970$		0			0
$971$	−28.3367	+	20.5878i	−0.909369	+	0.660695i	−0.940855	−	0.338809i	$-0.889976\pi$
$971$	−28.3367	+	20.5878i	−0.909369	+	0.660695i	0.0314861	+	0.999504i	$0.489976\pi$
$972$		0			0
$973$	27.6613	−	54.2884i	0.886781	−	1.74041i
$974$		0			0
$975$	−33.9818	+	32.9117i	−1.08829	+	1.05402i
$976$		0			0
$977$	2.61600	+	5.13419i	0.0836932	+	0.164257i	0.929060	−	0.369929i	$-0.120618\pi$
$977$	2.61600	+	5.13419i	0.0836932	+	0.164257i	−0.845367	+	0.534186i	$0.820618\pi$
$978$		0			0
$979$	0.00240324	−	6.51679i	7.68078e−5	−	0.208277i
$980$		0			0
$981$	80.9723	−	41.2574i	2.58525	−	1.31725i
$982$		0			0
$983$	4.50846	+	28.4653i	0.143798	+	0.907902i	0.949086	+	0.315018i	$0.102011\pi$
$983$	4.50846	+	28.4653i	0.143798	+	0.907902i	−0.805288	+	0.592884i	$0.797989\pi$
$984$		0			0
$985$	−17.6262	−	54.2478i	−0.561617	−	1.72848i
$986$		0			0
$987$	−76.1353	+	55.3156i	−2.42341	+	1.76071i
$988$		0			0
$989$		−	4.78807i		−	0.152252i
$990$		0			0
$991$	−3.49282			−0.110953			−0.0554766	−	0.998460i	$-0.517668\pi$
$991$	−3.49282			−0.110953			−0.0554766	+	0.998460i	$0.517668\pi$
$992$		0			0
$993$	−8.16800	+	51.5707i	−0.259204	+	1.63655i
$994$		0			0
$995$	30.2478	−	59.3647i	0.958921	−	1.88199i
$996$		0			0
$997$	−31.7064	+	43.6401i	−1.00415	+	1.38210i	−0.0814082	+	0.996681i	$0.525942\pi$
$997$	−31.7064	+	43.6401i	−1.00415	+	1.38210i	−0.922743	+	0.385415i	$0.874058\pi$
$998$		0			0
$999$	−126.138	+	64.2707i	−3.99084	+	2.03344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.14	✓	112
11.6	odd	10	inner	572.2.bh.a.369.14	yes	112
13.8	odd	4	inner	572.2.bh.a.541.14	yes	112
143.138	even	20	inner	572.2.bh.a.281.14	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.14	✓	112	1.1	even	1	trivial
572.2.bh.a.281.14	yes	112	143.138	even	20	inner
572.2.bh.a.369.14	yes	112	11.6	odd	10	inner
572.2.bh.a.541.14	yes	112	13.8	odd	4	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.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.57936 - 1.87402i) q^{3} +(-2.69008 - 1.37067i) q^{5} +(-3.38722 + 0.536483i) q^{7} +(2.21412 - 6.81437i) q^{9} +O(q^{10})\)	\(q+(2.57936 - 1.87402i) q^{3} +(-2.69008 - 1.37067i) q^{5} +(-3.38722 + 0.536483i) q^{7} +(2.21412 - 6.81437i) q^{9} +(-2.34434 - 2.34607i) q^{11} +(-1.68806 + 3.18598i) q^{13} +(-9.50735 + 1.50582i) q^{15} +(-0.258017 - 0.794093i) q^{17} +(4.73114 + 0.749338i) q^{19} +(-7.73148 + 7.73148i) q^{21} -5.87424i q^{23} +(2.41890 + 3.32932i) q^{25} +(-4.10353 - 12.6294i) q^{27} +(3.31526 - 4.56306i) q^{29} +(2.42573 + 4.76077i) q^{31} +(-10.4435 - 1.65803i) q^{33} +(9.84723 + 3.19956i) q^{35} +(-1.66772 - 10.5296i) q^{37} +(1.61645 + 11.3812i) q^{39} +(2.72351 + 0.431362i) q^{41} +0.815096 q^{43} +(-15.2964 + 15.2964i) q^{45} +(8.50101 + 1.34643i) q^{47} +(4.52803 - 1.47125i) q^{49} +(-2.15366 - 1.56473i) q^{51} +(-1.71767 + 5.28645i) q^{53} +(3.09080 + 9.52444i) q^{55} +(13.6076 - 6.93341i) q^{57} +(0.658186 + 4.15562i) q^{59} +(4.27700 - 1.38968i) q^{61} +(-3.84392 + 24.2696i) q^{63} +(8.90794 - 6.25677i) q^{65} +(3.51004 - 3.51004i) q^{67} +(-11.0084 - 15.1518i) q^{69} +(-6.36905 - 3.24519i) q^{71} +(-3.96998 + 0.628784i) q^{73} +(12.4784 + 4.05448i) q^{75} +(9.19943 + 6.68896i) q^{77} +(-12.9482 - 4.20713i) q^{79} +(-16.8622 - 12.2511i) q^{81} +(3.65567 - 7.17466i) q^{83} +(-0.394351 + 2.48983i) q^{85} -17.9826i q^{87} +(1.38938 + 1.38938i) q^{89} +(4.00861 - 11.6972i) q^{91} +(15.1786 + 7.73389i) q^{93} +(-11.7001 - 8.50059i) q^{95} +(-5.00585 - 9.82454i) q^{97} +(-21.1777 + 10.7807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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