LMFDB - Embedded newform 270.2.f.b.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(53,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("270.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	270.53
Dual form			270.2.f.b.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.48356 + 1.67303i) q^{5} +(-0.366025 + 0.366025i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.23205 + 0.133975i) q^{10} +4.76028i q^{11} +(3.46410 + 3.46410i) q^{13} -0.517638 q^{14} -1.00000 q^{16} +(-1.03528 - 1.03528i) q^{17} -7.46410i q^{19} +(-1.67303 - 1.48356i) q^{20} +(-3.36603 + 3.36603i) q^{22} +(-1.41421 + 1.41421i) q^{23} +(-0.598076 - 4.96410i) q^{25} +4.89898i q^{26} +(-0.366025 - 0.366025i) q^{28} +6.31319 q^{29} +6.66025 q^{31} +(-0.707107 - 0.707107i) q^{32} -1.46410i q^{34} +(-0.0693504 - 1.15539i) q^{35} +(-2.19615 + 2.19615i) q^{37} +(5.27792 - 5.27792i) q^{38} +(-0.133975 - 2.23205i) q^{40} -4.62158i q^{41} +(-1.26795 - 1.26795i) q^{43} -4.76028 q^{44} -2.00000 q^{46} +(-4.24264 - 4.24264i) q^{47} +6.73205i q^{49} +(3.08725 - 3.93305i) q^{50} +(-3.46410 + 3.46410i) q^{52} +(5.08845 - 5.08845i) q^{53} +(-7.96410 - 7.06218i) q^{55} -0.517638i q^{56} +(4.46410 + 4.46410i) q^{58} +4.52004 q^{59} +9.46410 q^{61} +(4.70951 + 4.70951i) q^{62} -1.00000i q^{64} +(-10.9348 + 0.656339i) q^{65} +(-6.19615 + 6.19615i) q^{67} +(1.03528 - 1.03528i) q^{68} +(0.767949 - 0.866025i) q^{70} -15.4548i q^{71} +(9.36603 + 9.36603i) q^{73} -3.10583 q^{74} +7.46410 q^{76} +(-1.74238 - 1.74238i) q^{77} -3.46410i q^{79} +(1.48356 - 1.67303i) q^{80} +(3.26795 - 3.26795i) q^{82} +(1.46498 - 1.46498i) q^{83} +(3.26795 - 0.196152i) q^{85} -1.79315i q^{86} +(-3.36603 - 3.36603i) q^{88} +5.93426 q^{89} -2.53590 q^{91} +(-1.41421 - 1.41421i) q^{92} -6.00000i q^{94} +(12.4877 + 11.0735i) q^{95} +(-13.5622 + 13.5622i) q^{97} +(-4.76028 + 4.76028i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7} - 4 q^{10} - 8 q^{16} - 20 q^{22} + 16 q^{25} + 4 q^{28} - 16 q^{31} + 24 q^{37} - 8 q^{40} - 24 q^{43} - 16 q^{46} - 36 q^{55} + 8 q^{58} + 48 q^{61} - 8 q^{67} + 20 q^{70} + 68 q^{73} + 32 q^{76}+ \cdots - 60 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 4 * q^10 - 8 * q^16 - 20 * q^22 + 16 * q^25 + 4 * q^28 - 16 * q^31 + 24 * q^37 - 8 * q^40 - 24 * q^43 - 16 * q^46 - 36 * q^55 + 8 * q^58 + 48 * q^61 - 8 * q^67 + 20 * q^70 + 68 * q^73 + 32 * q^76 + 40 * q^82 + 40 * q^85 - 20 * q^88 - 48 * q^91 - 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−1.48356	+	1.67303i	−0.663470	+	0.748203i
$5$	−1.48356	+	1.67303i	−0.663470	+	0.748203i
$6$		0			0
$7$	−0.366025	+	0.366025i	−0.138345	+	0.138345i	−0.772888	−	0.634543i	$-0.781188\pi$
$7$	−0.366025	+	0.366025i	−0.138345	+	0.138345i	0.634543	+	0.772888i	$0.281188\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−2.23205	+	0.133975i	−0.705836	+	0.0423665i
$11$			4.76028i			1.43528i	0.696415	+	0.717639i	$0.254777\pi$
$11$			4.76028i			1.43528i	−0.696415	+	0.717639i	$0.745223\pi$
$12$		0			0
$13$	3.46410	+	3.46410i	0.960769	+	0.960769i	0.999259	−	0.0384901i	$-0.0122548\pi$
$13$	3.46410	+	3.46410i	0.960769	+	0.960769i	−0.0384901	+	0.999259i	$0.512255\pi$
$14$	−0.517638			−0.138345
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.03528	−	1.03528i	−0.251091	−	0.251091i	0.570327	−	0.821418i	$-0.306817\pi$
$17$	−1.03528	−	1.03528i	−0.251091	−	0.251091i	−0.821418	+	0.570327i	$0.806817\pi$
$18$		0			0
$19$		−	7.46410i		−	1.71238i	−0.516659	−	0.856191i	$-0.672825\pi$
$19$		−	7.46410i		−	1.71238i	0.516659	−	0.856191i	$-0.327175\pi$
$20$	−1.67303	−	1.48356i	−0.374101	−	0.331735i
$21$		0			0
$22$	−3.36603	+	3.36603i	−0.717639	+	0.717639i
$23$	−1.41421	+	1.41421i	−0.294884	+	0.294884i	−0.839006	−	0.544122i	$-0.816863\pi$
$23$	−1.41421	+	1.41421i	−0.294884	+	0.294884i	0.544122	+	0.839006i	$0.316863\pi$
$24$		0			0
$25$	−0.598076	−	4.96410i	−0.119615	−	0.992820i
$26$			4.89898i			0.960769i
$27$		0			0
$28$	−0.366025	−	0.366025i	−0.0691723	−	0.0691723i
$29$	6.31319			1.17233			0.586165	−	0.810192i	$-0.300637\pi$
$29$	6.31319			1.17233			0.586165	+	0.810192i	$0.300637\pi$
$30$		0			0
$31$	6.66025			1.19622			0.598108	−	0.801415i	$-0.295919\pi$
$31$	6.66025			1.19622			0.598108	+	0.801415i	$0.295919\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$		−	1.46410i		−	0.251091i
$35$	−0.0693504	−	1.15539i	−0.0117223	−	0.195297i
$36$		0			0
$37$	−2.19615	+	2.19615i	−0.361045	+	0.361045i	−0.864198	−	0.503152i	$-0.832173\pi$
$37$	−2.19615	+	2.19615i	−0.361045	+	0.361045i	0.503152	+	0.864198i	$0.332173\pi$
$38$	5.27792	−	5.27792i	0.856191	−	0.856191i
$39$		0			0
$40$	−0.133975	−	2.23205i	−0.0211832	−	0.352918i
$41$		−	4.62158i		−	0.721769i	−0.932610	−	0.360885i	$-0.882475\pi$
$41$		−	4.62158i		−	0.721769i	0.932610	−	0.360885i	$-0.117525\pi$
$42$		0			0
$43$	−1.26795	−	1.26795i	−0.193360	−	0.193360i	0.603786	−	0.797146i	$-0.293658\pi$
$43$	−1.26795	−	1.26795i	−0.193360	−	0.193360i	−0.797146	+	0.603786i	$0.793658\pi$
$44$	−4.76028			−0.717639
$45$		0			0
$46$	−2.00000			−0.294884
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	0.326384	−	0.945237i	$-0.394170\pi$
$47$	−4.24264	−	4.24264i	−0.618853	−	0.618853i	−0.945237	+	0.326384i	$0.894170\pi$
$48$		0			0
$49$			6.73205i			0.961722i
$50$	3.08725	−	3.93305i	0.436603	−	0.556218i
$51$		0			0
$52$	−3.46410	+	3.46410i	−0.480384	+	0.480384i
$53$	5.08845	−	5.08845i	0.698952	−	0.698952i	−0.265232	−	0.964185i	$-0.585449\pi$
$53$	5.08845	−	5.08845i	0.698952	−	0.698952i	0.964185	+	0.265232i	$0.0854487\pi$
$54$		0			0
$55$	−7.96410	−	7.06218i	−1.07388	−	0.952264i
$56$		−	0.517638i		−	0.0691723i
$57$		0			0
$58$	4.46410	+	4.46410i	0.586165	+	0.586165i
$59$	4.52004			0.588459			0.294230	−	0.955735i	$-0.404937\pi$
$59$	4.52004			0.588459			0.294230	+	0.955735i	$0.404937\pi$
$60$		0			0
$61$	9.46410			1.21175			0.605877	−	0.795558i	$-0.292822\pi$
$61$	9.46410			1.21175			0.605877	+	0.795558i	$0.292822\pi$
$62$	4.70951	+	4.70951i	0.598108	+	0.598108i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−10.9348	+	0.656339i	−1.35629	+	0.0814088i
$66$		0			0
$67$	−6.19615	+	6.19615i	−0.756980	+	0.756980i	−0.975772	−	0.218791i	$-0.929789\pi$
$67$	−6.19615	+	6.19615i	−0.756980	+	0.756980i	0.218791	+	0.975772i	$0.429789\pi$
$68$	1.03528	−	1.03528i	0.125546	−	0.125546i
$69$		0			0
$70$	0.767949	−	0.866025i	0.0917875	−	0.103510i
$71$		−	15.4548i		−	1.83415i	−0.398716	−	0.917074i	$-0.630544\pi$
$71$		−	15.4548i		−	1.83415i	0.398716	−	0.917074i	$-0.369456\pi$
$72$		0			0
$73$	9.36603	+	9.36603i	1.09621	+	1.09621i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	9.36603	+	9.36603i	1.09621	+	1.09621i	0.101361	+	0.994850i	$0.467680\pi$
$74$	−3.10583			−0.361045
$75$		0			0
$76$	7.46410			0.856191
$77$	−1.74238	−	1.74238i	−0.198563	−	0.198563i
$78$		0			0
$79$		−	3.46410i		−	0.389742i	−0.980829	−	0.194871i	$-0.937571\pi$
$79$		−	3.46410i		−	0.389742i	0.980829	−	0.194871i	$-0.0624288\pi$
$80$	1.48356	−	1.67303i	0.165867	−	0.187051i
$81$		0			0
$82$	3.26795	−	3.26795i	0.360885	−	0.360885i
$83$	1.46498	−	1.46498i	0.160803	−	0.160803i	−0.622120	−	0.782922i	$-0.713728\pi$
$83$	1.46498	−	1.46498i	0.160803	−	0.160803i	0.782922	+	0.622120i	$0.213728\pi$
$84$		0			0
$85$	3.26795	−	0.196152i	0.354459	−	0.0212757i
$86$		−	1.79315i		−	0.193360i
$87$		0			0
$88$	−3.36603	−	3.36603i	−0.358820	−	0.358820i
$89$	5.93426			0.629030			0.314515	−	0.949253i	$-0.398158\pi$
$89$	5.93426			0.629030			0.314515	+	0.949253i	$0.398158\pi$
$90$		0			0
$91$	−2.53590			−0.265834
$92$	−1.41421	−	1.41421i	−0.147442	−	0.147442i
$93$		0			0
$94$		−	6.00000i		−	0.618853i
$95$	12.4877	+	11.0735i	1.28121	+	1.13611i
$96$		0			0
$97$	−13.5622	+	13.5622i	−1.37703	+	1.37703i	−0.527435	+	0.849595i	$0.676846\pi$
$97$	−13.5622	+	13.5622i	−1.37703	+	1.37703i	−0.849595	+	0.527435i	$0.823154\pi$
$98$	−4.76028	+	4.76028i	−0.480861	+	0.480861i
$99$		0			0
$100$	4.96410	−	0.598076i	0.496410	−	0.0598076i
$101$			14.6598i			1.45870i	0.684140	+	0.729351i	$0.260178\pi$
$101$			14.6598i			1.45870i	−0.684140	+	0.729351i	$0.739822\pi$
$102$		0			0
$103$	−9.73205	−	9.73205i	−0.958927	−	0.958927i	0.0402617	−	0.999189i	$-0.487181\pi$
$103$	−9.73205	−	9.73205i	−0.958927	−	0.958927i	−0.999189	+	0.0402617i	$0.987181\pi$
$104$	−4.89898			−0.480384
$105$		0			0
$106$	7.19615			0.698952
$107$	−1.36345	−	1.36345i	−0.131809	−	0.131809i	0.638124	−	0.769933i	$-0.279711\pi$
$107$	−1.36345	−	1.36345i	−0.131809	−	0.131809i	−0.769933	+	0.638124i	$0.779711\pi$
$108$		0			0
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$	−0.637756	−	10.6252i	−0.0608077	−	1.01307i
$111$		0			0
$112$	0.366025	−	0.366025i	0.0345861	−	0.0345861i
$113$	−11.9700	+	11.9700i	−1.12605	+	1.12605i	−0.135234	+	0.990814i	$0.543178\pi$
$113$	−11.9700	+	11.9700i	−1.12605	+	1.12605i	−0.990814	+	0.135234i	$0.956822\pi$
$114$		0			0
$115$	−0.267949	−	4.46410i	−0.0249864	−	0.416280i
$116$			6.31319i			0.586165i
$117$		0			0
$118$	3.19615	+	3.19615i	0.294230	+	0.294230i
$119$	0.757875			0.0694743
$120$		0			0
$121$	−11.6603			−1.06002
$122$	6.69213	+	6.69213i	0.605877	+	0.605877i
$123$		0			0
$124$			6.66025i			0.598108i
$125$	9.19239	+	6.36396i	0.822192	+	0.569210i
$126$		0			0
$127$	−1.16987	+	1.16987i	−0.103809	+	0.103809i	−0.757104	−	0.653294i	$-0.773386\pi$
$127$	−1.16987	+	1.16987i	−0.103809	+	0.103809i	0.653294	+	0.757104i	$0.273386\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−8.19615	−	7.26795i	−0.718850	−	0.637441i
$131$		−	14.1793i		−	1.23885i	−0.785055	−	0.619426i	$-0.787366\pi$
$131$		−	14.1793i		−	1.23885i	0.785055	−	0.619426i	$-0.212634\pi$
$132$		0			0
$133$	2.73205	+	2.73205i	0.236899	+	0.236899i
$134$	−8.76268			−0.756980
$135$		0			0
$136$	1.46410			0.125546
$137$	−2.44949	−	2.44949i	−0.209274	−	0.209274i	0.594685	−	0.803959i	$-0.297277\pi$
$137$	−2.44949	−	2.44949i	−0.209274	−	0.209274i	−0.803959	+	0.594685i	$0.797277\pi$
$138$		0			0
$139$		−	9.85641i		−	0.836009i	−0.908445	−	0.418005i	$-0.862730\pi$
$139$		−	9.85641i		−	0.836009i	0.908445	−	0.418005i	$-0.137270\pi$
$140$	1.15539	−	0.0693504i	0.0976487	−	0.00586117i
$141$		0			0
$142$	10.9282	−	10.9282i	0.917074	−	0.917074i
$143$	−16.4901	+	16.4901i	−1.37897	+	1.37897i
$144$		0			0
$145$	−9.36603	+	10.5622i	−0.777806	+	0.877141i
$146$			13.2456i			1.09621i
$147$		0			0
$148$	−2.19615	−	2.19615i	−0.180523	−	0.180523i
$149$	−12.4877			−1.02303			−0.511516	−	0.859274i	$-0.670916\pi$
$149$	−12.4877			−1.02303			−0.511516	+	0.859274i	$0.670916\pi$
$150$		0			0
$151$	−8.46410			−0.688799			−0.344399	−	0.938823i	$-0.611917\pi$
$151$	−8.46410			−0.688799			−0.344399	+	0.938823i	$0.611917\pi$
$152$	5.27792	+	5.27792i	0.428096	+	0.428096i
$153$		0			0
$154$		−	2.46410i		−	0.198563i
$155$	−9.88091	+	11.1428i	−0.793654	+	0.895013i
$156$		0			0
$157$	12.0000	−	12.0000i	0.957704	−	0.957704i	−0.0414369	−	0.999141i	$-0.513194\pi$
$157$	12.0000	−	12.0000i	0.957704	−	0.957704i	0.999141	+	0.0414369i	$0.0131935\pi$
$158$	2.44949	−	2.44949i	0.194871	−	0.194871i
$159$		0			0
$160$	2.23205	−	0.133975i	0.176459	−	0.0105916i
$161$		−	1.03528i		−	0.0815912i
$162$		0			0
$163$	5.46410	+	5.46410i	0.427981	+	0.427981i	0.887940	−	0.459959i	$-0.152136\pi$
$163$	5.46410	+	5.46410i	0.427981	+	0.427981i	−0.459959	+	0.887940i	$0.652136\pi$
$164$	4.62158			0.360885
$165$		0			0
$166$	2.07180			0.160803
$167$	11.9700	+	11.9700i	0.926270	+	0.926270i	0.997463	−	0.0711925i	$-0.0226805\pi$
$167$	11.9700	+	11.9700i	0.926270	+	0.926270i	−0.0711925	+	0.997463i	$0.522680\pi$
$168$		0			0
$169$			11.0000i			0.846154i
$170$	2.44949	+	2.17209i	0.187867	+	0.166592i
$171$		0			0
$172$	1.26795	−	1.26795i	0.0966802	−	0.0966802i
$173$	7.39924	−	7.39924i	0.562554	−	0.562554i	−0.367478	−	0.930032i	$-0.619779\pi$
$173$	7.39924	−	7.39924i	0.562554	−	0.562554i	0.930032	+	0.367478i	$0.119779\pi$
$174$		0			0
$175$	2.03590	+	1.59808i	0.153899	+	0.120803i
$176$		−	4.76028i		−	0.358820i
$177$		0			0
$178$	4.19615	+	4.19615i	0.314515	+	0.314515i
$179$	−5.41662			−0.404857			−0.202429	−	0.979297i	$-0.564883\pi$
$179$	−5.41662			−0.404857			−0.202429	+	0.979297i	$0.564883\pi$
$180$		0			0
$181$	14.9282			1.10960			0.554802	−	0.831982i	$-0.312794\pi$
$181$	14.9282			1.10960			0.554802	+	0.831982i	$0.312794\pi$
$182$	−1.79315	−	1.79315i	−0.132917	−	0.132917i
$183$		0			0
$184$		−	2.00000i		−	0.147442i
$185$	−0.416102	−	6.93237i	−0.0305924	−	0.509678i
$186$		0			0
$187$	4.92820	−	4.92820i	0.360386	−	0.360386i
$188$	4.24264	−	4.24264i	0.309426	−	0.309426i
$189$		0			0
$190$	1.00000	+	16.6603i	0.0725476	+	1.20866i
$191$		−	3.38323i		−	0.244802i	−0.992481	−	0.122401i	$-0.960941\pi$
$191$		−	3.38323i		−	0.244802i	0.992481	−	0.122401i	$-0.0390594\pi$
$192$		0			0
$193$	−8.02628	−	8.02628i	−0.577744	−	0.577744i	0.356537	−	0.934281i	$-0.383957\pi$
$193$	−8.02628	−	8.02628i	−0.577744	−	0.577744i	−0.934281	+	0.356537i	$0.883957\pi$
$194$	−19.1798			−1.37703
$195$		0			0
$196$	−6.73205			−0.480861
$197$	−3.01790	−	3.01790i	−0.215016	−	0.215016i	0.591378	−	0.806394i	$-0.298584\pi$
$197$	−3.01790	−	3.01790i	−0.215016	−	0.215016i	−0.806394	+	0.591378i	$0.798584\pi$
$198$		0			0
$199$			14.3205i			1.01515i	0.861606	+	0.507577i	$0.169459\pi$
$199$			14.3205i			1.01515i	−0.861606	+	0.507577i	$0.830541\pi$
$200$	3.93305	+	3.08725i	0.278109	+	0.218301i
$201$		0			0
$202$	−10.3660	+	10.3660i	−0.729351	+	0.729351i
$203$	−2.31079	+	2.31079i	−0.162186	+	0.162186i
$204$		0			0
$205$	7.73205	+	6.85641i	0.540030	+	0.478872i
$206$		−	13.7632i		−	0.958927i
$207$		0			0
$208$	−3.46410	−	3.46410i	−0.240192	−	0.240192i
$209$	35.5312			2.45774
$210$		0			0
$211$	−21.3205			−1.46776			−0.733882	−	0.679277i	$-0.762294\pi$
$211$	−21.3205			−1.46776			−0.733882	+	0.679277i	$0.762294\pi$
$212$	5.08845	+	5.08845i	0.349476	+	0.349476i
$213$		0			0
$214$		−	1.92820i		−	0.131809i
$215$	4.00240	−	0.240237i	0.272962	−	0.0163840i
$216$		0			0
$217$	−2.43782	+	2.43782i	−0.165490	+	0.165490i
$218$	1.41421	−	1.41421i	0.0957826	−	0.0957826i
$219$		0			0
$220$	7.06218	−	7.96410i	0.476132	−	0.536940i
$221$		−	7.17260i		−	0.482482i
$222$		0			0
$223$	4.26795	+	4.26795i	0.285803	+	0.285803i	0.835418	−	0.549615i	$-0.185226\pi$
$223$	4.26795	+	4.26795i	0.285803	+	0.285803i	−0.549615	+	0.835418i	$0.685226\pi$
$224$	0.517638			0.0345861
$225$		0			0
$226$	−16.9282			−1.12605
$227$	−3.20736	−	3.20736i	−0.212880	−	0.212880i	0.592610	−	0.805490i	$-0.298098\pi$
$227$	−3.20736	−	3.20736i	−0.212880	−	0.212880i	−0.805490	+	0.592610i	$0.798098\pi$
$228$		0			0
$229$		−	1.60770i		−	0.106239i	−0.998588	−	0.0531197i	$-0.983083\pi$
$229$		−	1.60770i		−	0.106239i	0.998588	−	0.0531197i	$-0.0169165\pi$
$230$	2.96713	−	3.34607i	0.195647	−	0.220633i
$231$		0			0
$232$	−4.46410	+	4.46410i	−0.293083	+	0.293083i
$233$	5.55532	−	5.55532i	0.363941	−	0.363941i	−0.501321	−	0.865262i	$-0.667152\pi$
$233$	5.55532	−	5.55532i	0.363941	−	0.363941i	0.865262	+	0.501321i	$0.167152\pi$
$234$		0			0
$235$	13.3923	−	0.803848i	0.873618	−	0.0524372i
$236$			4.52004i			0.294230i
$237$		0			0
$238$	0.535898	+	0.535898i	0.0347371	+	0.0347371i
$239$	−5.37945			−0.347968			−0.173984	−	0.984748i	$-0.555664\pi$
$239$	−5.37945			−0.347968			−0.173984	+	0.984748i	$0.555664\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$	−8.24504	−	8.24504i	−0.530012	−	0.530012i
$243$		0			0
$244$			9.46410i			0.605877i
$245$	−11.2629	−	9.98743i	−0.719563	−	0.638073i
$246$		0			0
$247$	25.8564	−	25.8564i	1.64520	−	1.64520i
$248$	−4.70951	+	4.70951i	−0.299054	+	0.299054i
$249$		0			0
$250$	2.00000	+	11.0000i	0.126491	+	0.695701i
$251$		−	14.5211i		−	0.916562i	−0.888807	−	0.458281i	$-0.848465\pi$
$251$		−	14.5211i		−	0.916562i	0.888807	−	0.458281i	$-0.151535\pi$
$252$		0			0
$253$	−6.73205	−	6.73205i	−0.423240	−	0.423240i
$254$	−1.65445			−0.103809
$255$		0			0
$256$	1.00000			0.0625000
$257$	−20.3538	−	20.3538i	−1.26963	−	1.26963i	−0.946277	−	0.323358i	$-0.895188\pi$
$257$	−20.3538	−	20.3538i	−1.26963	−	1.26963i	−0.323358	−	0.946277i	$-0.604812\pi$
$258$		0			0
$259$		−	1.60770i		−	0.0998973i
$260$	−0.656339	−	10.9348i	−0.0407044	−	0.678146i
$261$		0			0
$262$	10.0263	−	10.0263i	0.619426	−	0.619426i
$263$	9.89949	−	9.89949i	0.610429	−	0.610429i	−0.332629	−	0.943058i	$-0.607936\pi$
$263$	9.89949	−	9.89949i	0.610429	−	0.610429i	0.943058	+	0.332629i	$0.107936\pi$
$264$		0			0
$265$	0.964102	+	16.0622i	0.0592243	+	0.986692i
$266$			3.86370i			0.236899i
$267$		0			0
$268$	−6.19615	−	6.19615i	−0.378490	−	0.378490i
$269$	7.62587			0.464958			0.232479	−	0.972601i	$-0.425316\pi$
$269$	7.62587			0.464958			0.232479	+	0.972601i	$0.425316\pi$
$270$		0			0
$271$	4.60770			0.279898			0.139949	−	0.990159i	$-0.455306\pi$
$271$	4.60770			0.279898			0.139949	+	0.990159i	$0.455306\pi$
$272$	1.03528	+	1.03528i	0.0627728	+	0.0627728i
$273$		0			0
$274$		−	3.46410i		−	0.209274i
$275$	23.6305	−	2.84701i	1.42497	−	0.171681i
$276$		0			0
$277$	19.8564	−	19.8564i	1.19306	−	1.19306i	0.216851	−	0.976205i	$-0.430421\pi$
$277$	19.8564	−	19.8564i	1.19306	−	1.19306i	0.976205	−	0.216851i	$-0.0695786\pi$
$278$	6.96953	−	6.96953i	0.418005	−	0.418005i
$279$		0			0
$280$	0.866025	+	0.767949i	0.0517549	+	0.0458937i
$281$			13.3843i			0.798438i	0.916856	+	0.399219i	$0.130719\pi$
$281$			13.3843i			0.798438i	−0.916856	+	0.399219i	$0.869281\pi$
$282$		0			0
$283$	−8.73205	−	8.73205i	−0.519067	−	0.519067i	0.398222	−	0.917289i	$-0.369627\pi$
$283$	−8.73205	−	8.73205i	−0.519067	−	0.519067i	−0.917289	+	0.398222i	$0.869627\pi$
$284$	15.4548			0.917074
$285$		0			0
$286$	−23.3205			−1.37897
$287$	1.69161	+	1.69161i	0.0998529	+	0.0998529i
$288$		0			0
$289$		−	14.8564i		−	0.873906i
$290$	−14.0914	+	0.845807i	−0.827474	+	0.0496675i
$291$		0			0
$292$	−9.36603	+	9.36603i	−0.548105	+	0.548105i
$293$	8.48528	−	8.48528i	0.495715	−	0.495715i	−0.414386	−	0.910101i	$-0.636004\pi$
$293$	8.48528	−	8.48528i	0.495715	−	0.495715i	0.910101	+	0.414386i	$0.136004\pi$
$294$		0			0
$295$	−6.70577	+	7.56218i	−0.390425	+	0.440287i
$296$		−	3.10583i		−	0.180523i
$297$		0			0
$298$	−8.83013	−	8.83013i	−0.511516	−	0.511516i
$299$	−9.79796			−0.566631
$300$		0			0
$301$	0.928203			0.0535007
$302$	−5.98502	−	5.98502i	−0.344399	−	0.344399i
$303$		0			0
$304$			7.46410i			0.428096i
$305$	−14.0406	+	15.8338i	−0.803962	+	0.906638i
$306$		0			0
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$	1.74238	−	1.74238i	0.0992815	−	0.0992815i
$309$		0			0
$310$	−14.8660	+	0.892305i	−0.844334	+	0.0506795i
$311$		−	3.86370i		−	0.219091i	−0.993982	−	0.109545i	$-0.965061\pi$
$311$		−	3.86370i		−	0.219091i	0.993982	−	0.109545i	$-0.0349395\pi$
$312$		0			0
$313$	−20.0263	−	20.0263i	−1.13195	−	1.13195i	−0.989852	−	0.142100i	$-0.954615\pi$
$313$	−20.0263	−	20.0263i	−1.13195	−	1.13195i	−0.142100	−	0.989852i	$-0.545385\pi$
$314$	16.9706			0.957704
$315$		0			0
$316$	3.46410			0.194871
$317$	−8.81345	−	8.81345i	−0.495013	−	0.495013i	0.414869	−	0.909881i	$-0.363828\pi$
$317$	−8.81345	−	8.81345i	−0.495013	−	0.495013i	−0.909881	+	0.414869i	$0.863828\pi$
$318$		0			0
$319$			30.0526i			1.68262i
$320$	1.67303	+	1.48356i	0.0935254	+	0.0829337i
$321$		0			0
$322$	0.732051	−	0.732051i	0.0407956	−	0.0407956i
$323$	−7.72741	+	7.72741i	−0.429964	+	0.429964i
$324$		0			0
$325$	15.1244	−	19.2679i	0.838948	−	1.06879i
$326$			7.72741i			0.427981i
$327$		0			0
$328$	3.26795	+	3.26795i	0.180442	+	0.180442i
$329$	3.10583			0.171230
$330$		0			0
$331$	7.46410			0.410264			0.205132	−	0.978734i	$-0.434238\pi$
$331$	7.46410			0.410264			0.205132	+	0.978734i	$0.434238\pi$
$332$	1.46498	+	1.46498i	0.0804013	+	0.0804013i
$333$		0			0
$334$			16.9282i			0.926270i
$335$	−1.17398	−	19.5588i	−0.0641412	−	1.06861i
$336$		0			0
$337$	0.464102	−	0.464102i	0.0252812	−	0.0252812i	−0.694353	−	0.719634i	$-0.744309\pi$
$337$	0.464102	−	0.464102i	0.0252812	−	0.0252812i	0.719634	+	0.694353i	$0.244309\pi$
$338$	−7.77817	+	7.77817i	−0.423077	+	0.423077i
$339$		0			0
$340$	0.196152	+	3.26795i	0.0106379	+	0.177229i
$341$			31.7047i			1.71690i
$342$		0			0
$343$	−5.02628	−	5.02628i	−0.271394	−	0.271394i
$344$	1.79315			0.0966802
$345$		0			0
$346$	10.4641			0.562554
$347$	20.2659	+	20.2659i	1.08793	+	1.08793i	0.995742	+	0.0921866i	$0.0293856\pi$
$347$	20.2659	+	20.2659i	1.08793	+	1.08793i	0.0921866	+	0.995742i	$0.470614\pi$
$348$		0			0
$349$		−	5.60770i		−	0.300173i	−0.988673	−	0.150087i	$-0.952045\pi$
$349$		−	5.60770i		−	0.300173i	0.988673	−	0.150087i	$-0.0479552\pi$
$350$	0.309587	+	2.56961i	0.0165481	+	0.137351i
$351$		0			0
$352$	3.36603	−	3.36603i	0.179410	−	0.179410i
$353$	14.0406	−	14.0406i	0.747306	−	0.747306i	−0.226667	−	0.973972i	$-0.572783\pi$
$353$	14.0406	−	14.0406i	0.747306	−	0.747306i	0.973972	+	0.226667i	$0.0727828\pi$
$354$		0			0
$355$	25.8564	+	22.9282i	1.37232	+	1.21690i
$356$			5.93426i			0.314515i
$357$		0			0
$358$	−3.83013	−	3.83013i	−0.202429	−	0.202429i
$359$	−23.4596			−1.23815			−0.619076	−	0.785331i	$-0.712493\pi$
$359$	−23.4596			−1.23815			−0.619076	+	0.785331i	$0.712493\pi$
$360$		0			0
$361$	−36.7128			−1.93225
$362$	10.5558	+	10.5558i	0.554802	+	0.554802i
$363$		0			0
$364$		−	2.53590i		−	0.132917i
$365$	−29.5648	+	1.77457i	−1.54749	+	0.0928852i
$366$		0			0
$367$	−3.02628	+	3.02628i	−0.157971	+	0.157971i	−0.781667	−	0.623696i	$-0.785630\pi$
$367$	−3.02628	+	3.02628i	−0.157971	+	0.157971i	0.623696	+	0.781667i	$0.285630\pi$
$368$	1.41421	−	1.41421i	0.0737210	−	0.0737210i
$369$		0			0
$370$	4.60770	−	5.19615i	0.239543	−	0.270135i
$371$			3.72500i			0.193392i
$372$		0			0
$373$	8.39230	+	8.39230i	0.434537	+	0.434537i	0.890169	−	0.455631i	$-0.150586\pi$
$373$	8.39230	+	8.39230i	0.434537	+	0.434537i	−0.455631	+	0.890169i	$0.650586\pi$
$374$	6.96953			0.360386
$375$		0			0
$376$	6.00000			0.309426
$377$	21.8695	+	21.8695i	1.12634	+	1.12634i
$378$		0			0
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$	−11.0735	+	12.4877i	−0.568057	+	0.640605i
$381$		0			0
$382$	2.39230	−	2.39230i	0.122401	−	0.122401i
$383$	−0.480473	+	0.480473i	−0.0245510	+	0.0245510i	−0.719276	−	0.694725i	$-0.755526\pi$
$383$	−0.480473	+	0.480473i	−0.0245510	+	0.0245510i	0.694725	+	0.719276i	$0.255526\pi$
$384$		0			0
$385$	5.50000	−	0.330127i	0.280306	−	0.0168248i
$386$		−	11.3509i		−	0.577744i
$387$		0			0
$388$	−13.5622	−	13.5622i	−0.688515	−	0.688515i
$389$	−13.1440			−0.666428			−0.333214	−	0.942851i	$-0.608133\pi$
$389$	−13.1440			−0.666428			−0.333214	+	0.942851i	$0.608133\pi$
$390$		0			0
$391$	2.92820			0.148086
$392$	−4.76028	−	4.76028i	−0.240430	−	0.240430i
$393$		0			0
$394$		−	4.26795i		−	0.215016i
$395$	5.79555	+	5.13922i	0.291606	+	0.258582i
$396$		0			0
$397$	4.92820	−	4.92820i	0.247339	−	0.247339i	−0.572538	−	0.819878i	$-0.694041\pi$
$397$	4.92820	−	4.92820i	0.247339	−	0.247339i	0.819878	+	0.572538i	$0.194041\pi$
$398$	−10.1261	+	10.1261i	−0.507577	+	0.507577i
$399$		0			0
$400$	0.598076	+	4.96410i	0.0299038	+	0.248205i
$401$			18.2832i			0.913021i	0.889718	+	0.456511i	$0.150901\pi$
$401$			18.2832i			0.913021i	−0.889718	+	0.456511i	$0.849099\pi$
$402$		0			0
$403$	23.0718	+	23.0718i	1.14929	+	1.14929i
$404$	−14.6598			−0.729351
$405$		0			0
$406$	−3.26795			−0.162186
$407$	−10.4543	−	10.4543i	−0.518200	−	0.518200i
$408$		0			0
$409$			3.33975i			0.165140i	0.996585	+	0.0825699i	$0.0263128\pi$
$409$			3.33975i			0.165140i	−0.996585	+	0.0825699i	$0.973687\pi$
$410$	0.619174	+	10.3156i	0.0305788	+	0.509451i
$411$		0			0
$412$	9.73205	−	9.73205i	0.479464	−	0.479464i
$413$	−1.65445	+	1.65445i	−0.0814102	+	0.0814102i
$414$		0			0
$415$	0.277568	+	4.62436i	0.0136253	+	0.227001i
$416$		−	4.89898i		−	0.240192i
$417$		0			0
$418$	25.1244	+	25.1244i	1.22887	+	1.22887i
$419$	13.2084			0.645272			0.322636	−	0.946523i	$-0.395431\pi$
$419$	13.2084			0.645272			0.322636	+	0.946523i	$0.395431\pi$
$420$		0			0
$421$	−17.8564			−0.870268			−0.435134	−	0.900366i	$-0.643299\pi$
$421$	−17.8564			−0.870268			−0.435134	+	0.900366i	$0.643299\pi$
$422$	−15.0759	−	15.0759i	−0.733882	−	0.733882i
$423$		0			0
$424$			7.19615i			0.349476i
$425$	−4.52004	+	5.75839i	−0.219254	+	0.279323i
$426$		0			0
$427$	−3.46410	+	3.46410i	−0.167640	+	0.167640i
$428$	1.36345	−	1.36345i	0.0659046	−	0.0659046i
$429$		0			0
$430$	3.00000	+	2.66025i	0.144673	+	0.128289i
$431$			25.7332i			1.23953i	0.784789	+	0.619763i	$0.212771\pi$
$431$			25.7332i			1.23953i	−0.784789	+	0.619763i	$0.787229\pi$
$432$		0			0
$433$	−9.83013	−	9.83013i	−0.472406	−	0.472406i	0.430287	−	0.902692i	$-0.358413\pi$
$433$	−9.83013	−	9.83013i	−0.472406	−	0.472406i	−0.902692	+	0.430287i	$0.858413\pi$
$434$	−3.44760			−0.165490
$435$		0			0
$436$	2.00000			0.0957826
$437$	10.5558	+	10.5558i	0.504954	+	0.504954i
$438$		0			0
$439$		−	29.2487i		−	1.39596i	−0.716115	−	0.697982i	$-0.754081\pi$
$439$		−	29.2487i		−	1.39596i	0.716115	−	0.697982i	$-0.245919\pi$
$440$	10.6252	−	0.637756i	0.506536	−	0.0304038i
$441$		0			0
$442$	5.07180	−	5.07180i	0.241241	−	0.241241i
$443$	−25.6317	+	25.6317i	−1.21780	+	1.21780i	−0.249398	+	0.968401i	$0.580233\pi$
$443$	−25.6317	+	25.6317i	−1.21780	+	1.21780i	−0.968401	+	0.249398i	$0.919767\pi$
$444$		0			0
$445$	−8.80385	+	9.92820i	−0.417342	+	0.470642i
$446$			6.03579i			0.285803i
$447$		0			0
$448$	0.366025	+	0.366025i	0.0172931	+	0.0172931i
$449$	14.9743			0.706683			0.353341	−	0.935494i	$-0.385045\pi$
$449$	14.9743			0.706683			0.353341	+	0.935494i	$0.385045\pi$
$450$		0			0
$451$	22.0000			1.03594
$452$	−11.9700	−	11.9700i	−0.563024	−	0.563024i
$453$		0			0
$454$		−	4.53590i		−	0.212880i
$455$	3.76217	−	4.24264i	0.176373	−	0.198898i
$456$		0			0
$457$	−8.70577	+	8.70577i	−0.407239	+	0.407239i	−0.880775	−	0.473536i	$-0.842977\pi$
$457$	−8.70577	+	8.70577i	−0.407239	+	0.407239i	0.473536	+	0.880775i	$0.342977\pi$
$458$	1.13681	−	1.13681i	0.0531197	−	0.0531197i
$459$		0			0
$460$	4.46410	−	0.267949i	0.208140	−	0.0124932i
$461$			20.7699i			0.967350i	0.875248	+	0.483675i	$0.160698\pi$
$461$			20.7699i			0.967350i	−0.875248	+	0.483675i	$0.839302\pi$
$462$		0			0
$463$	8.29423	+	8.29423i	0.385465	+	0.385465i	0.873067	−	0.487601i	$-0.162128\pi$
$463$	8.29423	+	8.29423i	0.385465	+	0.385465i	−0.487601	+	0.873067i	$0.662128\pi$
$464$	−6.31319			−0.293083
$465$		0			0
$466$	7.85641			0.363941
$467$	−9.19239	−	9.19239i	−0.425373	−	0.425373i	0.461676	−	0.887049i	$-0.347248\pi$
$467$	−9.19239	−	9.19239i	−0.425373	−	0.425373i	−0.887049	+	0.461676i	$0.847248\pi$
$468$		0			0
$469$		−	4.53590i		−	0.209448i
$470$	10.0382	+	8.90138i	0.463027	+	0.410590i
$471$		0			0
$472$	−3.19615	+	3.19615i	−0.147115	+	0.147115i
$473$	6.03579	−	6.03579i	0.277526	−	0.277526i
$474$		0			0
$475$	−37.0526	+	4.46410i	−1.70009	+	0.204827i
$476$			0.757875i			0.0347371i
$477$		0			0
$478$	−3.80385	−	3.80385i	−0.173984	−	0.173984i
$479$	11.0363			0.504262			0.252131	−	0.967693i	$-0.418869\pi$
$479$	11.0363			0.504262			0.252131	+	0.967693i	$0.418869\pi$
$480$		0			0
$481$	−15.2154			−0.693762
$482$	2.82843	+	2.82843i	0.128831	+	0.128831i
$483$		0			0
$484$		−	11.6603i		−	0.530012i
$485$	−2.56961	−	42.8103i	−0.116680	−	1.94392i
$486$		0			0
$487$	−23.1962	+	23.1962i	−1.05112	+	1.05112i	−0.0524969	+	0.998621i	$0.516718\pi$
$487$	−23.1962	+	23.1962i	−1.05112	+	1.05112i	−0.998621	+	0.0524969i	$0.983282\pi$
$488$	−6.69213	+	6.69213i	−0.302939	+	0.302939i
$489$		0			0
$490$	−0.901924	−	15.0263i	−0.0407448	−	0.678818i
$491$		−	22.5630i		−	1.01826i	−0.860691	−	0.509128i	$-0.829968\pi$
$491$		−	22.5630i		−	1.01826i	0.860691	−	0.509128i	$-0.170032\pi$
$492$		0			0
$493$	−6.53590	−	6.53590i	−0.294362	−	0.294362i
$494$	36.5665			1.64520
$495$		0			0
$496$	−6.66025			−0.299054
$497$	5.65685	+	5.65685i	0.253745	+	0.253745i
$498$		0			0
$499$			35.8564i			1.60515i	0.596549	+	0.802577i	$0.296538\pi$
$499$			35.8564i			1.60515i	−0.596549	+	0.802577i	$0.703462\pi$
$500$	−6.36396	+	9.19239i	−0.284605	+	0.411096i
$501$		0			0
$502$	10.2679	−	10.2679i	0.458281	−	0.458281i
$503$	1.13681	−	1.13681i	0.0506879	−	0.0506879i	−0.681308	−	0.731996i	$-0.738589\pi$
$503$	1.13681	−	1.13681i	0.0506879	−	0.0506879i	0.731996	+	0.681308i	$0.238589\pi$
$504$		0			0
$505$	−24.5263	−	21.7487i	−1.09141	−	0.967805i
$506$		−	9.52056i		−	0.423240i
$507$		0			0
$508$	−1.16987	−	1.16987i	−0.0519047	−	0.0519047i
$509$	−30.6694			−1.35940			−0.679698	−	0.733492i	$-0.737889\pi$
$509$	−30.6694			−1.35940			−0.679698	+	0.733492i	$0.737889\pi$
$510$		0			0
$511$	−6.85641			−0.303310
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	28.7846i		−	1.26963i
$515$	30.7202	−	1.84392i	1.35369	−	0.0812528i
$516$		0			0
$517$	20.1962	−	20.1962i	0.888226	−	0.888226i
$518$	1.13681	−	1.13681i	0.0499487	−	0.0499487i
$519$		0			0
$520$	7.26795	−	8.19615i	0.318721	−	0.359425i
$521$		−	3.58630i		−	0.157119i	−0.996909	−	0.0785594i	$-0.974968\pi$
$521$		−	3.58630i		−	0.157119i	0.996909	−	0.0785594i	$-0.0250320\pi$
$522$		0			0
$523$	−21.4641	−	21.4641i	−0.938560	−	0.938560i	0.0596592	−	0.998219i	$-0.480999\pi$
$523$	−21.4641	−	21.4641i	−0.938560	−	0.938560i	−0.998219	+	0.0596592i	$0.980999\pi$
$524$	14.1793			0.619426
$525$		0			0
$526$	14.0000			0.610429
$527$	−6.89520	−	6.89520i	−0.300360	−	0.300360i
$528$		0			0
$529$			19.0000i			0.826087i
$530$	−10.6760	+	12.0394i	−0.463734	+	0.522958i
$531$		0			0
$532$	−2.73205	+	2.73205i	−0.118449	+	0.118449i
$533$	16.0096	−	16.0096i	0.693453	−	0.693453i
$534$		0			0
$535$	4.30385	−	0.258330i	0.186072	−	0.0111686i
$536$		−	8.76268i		−	0.378490i
$537$		0			0
$538$	5.39230	+	5.39230i	0.232479	+	0.232479i
$539$	−32.0464			−1.38034
$540$		0			0
$541$	27.3205			1.17460			0.587300	−	0.809369i	$-0.300191\pi$
$541$	27.3205			1.17460			0.587300	+	0.809369i	$0.300191\pi$
$542$	3.25813	+	3.25813i	0.139949	+	0.139949i
$543$		0			0
$544$			1.46410i			0.0627728i
$545$	3.34607	+	2.96713i	0.143330	+	0.127098i
$546$		0			0
$547$	−0.928203	+	0.928203i	−0.0396871	+	0.0396871i	−0.726672	−	0.686985i	$-0.758934\pi$
$547$	−0.928203	+	0.928203i	−0.0396871	+	0.0396871i	0.686985	+	0.726672i	$0.258934\pi$
$548$	2.44949	−	2.44949i	0.104637	−	0.104637i
$549$		0			0
$550$	18.7224	+	14.6962i	0.798327	+	0.626646i
$551$		−	47.1223i		−	2.00748i
$552$		0			0
$553$	1.26795	+	1.26795i	0.0539187	+	0.0539187i
$554$	28.0812			1.19306
$555$		0			0
$556$	9.85641			0.418005
$557$	1.88108	+	1.88108i	0.0797041	+	0.0797041i	0.745835	−	0.666131i	$-0.232051\pi$
$557$	1.88108	+	1.88108i	0.0797041	+	0.0797041i	−0.666131	+	0.745835i	$0.732051\pi$
$558$		0			0
$559$		−	8.78461i		−	0.371549i
$560$	0.0693504	+	1.15539i	0.00293059	+	0.0488243i
$561$		0			0
$562$	−9.46410	+	9.46410i	−0.399219	+	0.399219i
$563$	4.81105	−	4.81105i	0.202761	−	0.202761i	−0.598421	−	0.801182i	$-0.704205\pi$
$563$	4.81105	−	4.81105i	0.202761	−	0.202761i	0.801182	+	0.598421i	$0.204205\pi$
$564$		0			0
$565$	−2.26795	−	37.7846i	−0.0954133	−	1.58961i
$566$		−	12.3490i		−	0.519067i
$567$		0			0
$568$	10.9282	+	10.9282i	0.458537	+	0.458537i
$569$	−26.2137			−1.09894			−0.549468	−	0.835515i	$-0.685170\pi$
$569$	−26.2137			−1.09894			−0.549468	+	0.835515i	$0.685170\pi$
$570$		0			0
$571$	−1.46410			−0.0612707			−0.0306354	−	0.999531i	$-0.509753\pi$
$571$	−1.46410			−0.0612707			−0.0306354	+	0.999531i	$0.509753\pi$
$572$	−16.4901	−	16.4901i	−0.689485	−	0.689485i
$573$		0			0
$574$			2.39230i			0.0998529i
$575$	7.86611	+	6.17449i	0.328039	+	0.257494i
$576$		0			0
$577$	−15.3923	+	15.3923i	−0.640790	+	0.640790i	−0.950750	−	0.309960i	$-0.899684\pi$
$577$	−15.3923	+	15.3923i	−0.640790	+	0.640790i	0.309960	+	0.950750i	$0.399684\pi$
$578$	10.5051	−	10.5051i	0.436953	−	0.436953i
$579$		0			0
$580$	−10.5622	−	9.36603i	−0.438571	−	0.388903i
$581$			1.07244i			0.0444923i
$582$		0			0
$583$	24.2224	+	24.2224i	1.00319	+	1.00319i
$584$	−13.2456			−0.548105
$585$		0			0
$586$	12.0000			0.495715
$587$	31.5152	+	31.5152i	1.30077	+	1.30077i	0.927872	+	0.372900i	$0.121636\pi$
$587$	31.5152	+	31.5152i	1.30077	+	1.30077i	0.372900	+	0.927872i	$0.378364\pi$
$588$		0			0
$589$		−	49.7128i		−	2.04838i
$590$	−10.0890	+	0.605571i	−0.415356	+	0.0249310i
$591$		0			0
$592$	2.19615	−	2.19615i	0.0902613	−	0.0902613i
$593$	8.86422	−	8.86422i	0.364010	−	0.364010i	−0.501277	−	0.865287i	$-0.667136\pi$
$593$	8.86422	−	8.86422i	0.364010	−	0.364010i	0.865287	+	0.501277i	$0.167136\pi$
$594$		0			0
$595$	−1.12436	+	1.26795i	−0.0460941	+	0.0519808i
$596$		−	12.4877i		−	0.511516i
$597$		0			0
$598$	−6.92820	−	6.92820i	−0.283315	−	0.283315i
$599$	7.45001			0.304399			0.152199	−	0.988350i	$-0.451364\pi$
$599$	7.45001			0.304399			0.152199	+	0.988350i	$0.451364\pi$
$600$		0			0
$601$	−13.0000			−0.530281			−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000			−0.530281			−0.265141	+	0.964210i	$0.585418\pi$
$602$	0.656339	+	0.656339i	0.0267504	+	0.0267504i
$603$		0			0
$604$		−	8.46410i		−	0.344399i
$605$	17.2987	−	19.5080i	0.703293	−	0.793112i
$606$		0			0
$607$	−21.5885	+	21.5885i	−0.876248	+	0.876248i	−0.993144	−	0.116896i	$-0.962706\pi$
$607$	−21.5885	+	21.5885i	−0.876248	+	0.876248i	0.116896	+	0.993144i	$0.462706\pi$
$608$	−5.27792	+	5.27792i	−0.214048	+	0.214048i
$609$		0			0
$610$	−21.1244	+	1.26795i	−0.855300	+	0.0513378i
$611$		−	29.3939i		−	1.18915i
$612$		0			0
$613$	17.6603	+	17.6603i	0.713291	+	0.713291i	0.967222	−	0.253931i	$-0.0817237\pi$
$613$	17.6603	+	17.6603i	0.713291	+	0.713291i	−0.253931	+	0.967222i	$0.581724\pi$
$614$		0			0
$615$		0			0
$616$	2.46410			0.0992815
$617$	−29.2180	−	29.2180i	−1.17627	−	1.17627i	−0.980686	−	0.195586i	$-0.937339\pi$
$617$	−29.2180	−	29.2180i	−1.17627	−	1.17627i	−0.195586	−	0.980686i	$-0.562661\pi$
$618$		0			0
$619$		−	7.60770i		−	0.305779i	−0.988243	−	0.152890i	$-0.951142\pi$
$619$		−	7.60770i		−	0.305779i	0.988243	−	0.152890i	$-0.0488579\pi$
$620$	−11.1428	−	9.88091i	−0.447507	−	0.396827i
$621$		0			0
$622$	2.73205	−	2.73205i	0.109545	−	0.109545i
$623$	−2.17209	+	2.17209i	−0.0870229	+	0.0870229i
$624$		0			0
$625$	−24.2846	+	5.93782i	−0.971384	+	0.237513i
$626$		−	28.3214i		−	1.13195i
$627$		0			0
$628$	12.0000	+	12.0000i	0.478852	+	0.478852i
$629$	4.54725			0.181311
$630$		0			0
$631$	30.9090			1.23047			0.615233	−	0.788345i	$-0.289062\pi$
$631$	30.9090			1.23047			0.615233	+	0.788345i	$0.289062\pi$
$632$	2.44949	+	2.44949i	0.0974355	+	0.0974355i
$633$		0			0
$634$		−	12.4641i		−	0.495013i
$635$	−0.221654	−	3.69282i	−0.00879608	−	0.146545i
$636$		0			0
$637$	−23.3205	+	23.3205i	−0.923992	+	0.923992i
$638$	−21.2504	+	21.2504i	−0.841310	+	0.841310i
$639$		0			0
$640$	0.133975	+	2.23205i	0.00529581	+	0.0882296i
$641$		−	25.7332i		−	1.01640i	−0.861238	−	0.508201i	$-0.830311\pi$
$641$		−	25.7332i		−	1.01640i	0.861238	−	0.508201i	$-0.169689\pi$
$642$		0			0
$643$	3.46410	+	3.46410i	0.136611	+	0.136611i	0.772105	−	0.635495i	$-0.219204\pi$
$643$	3.46410	+	3.46410i	0.136611	+	0.136611i	−0.635495	+	0.772105i	$0.719204\pi$
$644$	1.03528			0.0407956
$645$		0			0
$646$	−10.9282			−0.429964
$647$	15.7322	+	15.7322i	0.618497	+	0.618497i	0.945146	−	0.326649i	$-0.105919\pi$
$647$	15.7322	+	15.7322i	0.618497	+	0.618497i	−0.326649	+	0.945146i	$0.605919\pi$
$648$		0			0
$649$			21.5167i			0.844603i
$650$	24.3190	−	2.92996i	0.953871	−	0.114923i
$651$		0			0
$652$	−5.46410	+	5.46410i	−0.213991	+	0.213991i
$653$	10.1261	−	10.1261i	0.396266	−	0.396266i	−0.480648	−	0.876914i	$-0.659598\pi$
$653$	10.1261	−	10.1261i	0.396266	−	0.396266i	0.876914	+	0.480648i	$0.159598\pi$
$654$		0			0
$655$	23.7224	+	21.0359i	0.926912	+	0.821941i
$656$			4.62158i			0.180442i
$657$		0			0
$658$	2.19615	+	2.19615i	0.0856149	+	0.0856149i
$659$	−48.4994			−1.88927			−0.944633	−	0.328127i	$-0.893582\pi$
$659$	−48.4994			−1.88927			−0.944633	+	0.328127i	$0.893582\pi$
$660$		0			0
$661$	−2.39230			−0.0930499			−0.0465249	−	0.998917i	$-0.514815\pi$
$661$	−2.39230			−0.0930499			−0.0465249	+	0.998917i	$0.514815\pi$
$662$	5.27792	+	5.27792i	0.205132	+	0.205132i
$663$		0			0
$664$			2.07180i			0.0804013i
$665$	−8.62398	+	0.517638i	−0.334424	+	0.0200731i
$666$		0			0
$667$	−8.92820	+	8.92820i	−0.345701	+	0.345701i
$668$	−11.9700	+	11.9700i	−0.463135	+	0.463135i
$669$		0			0
$670$	13.0000	−	14.6603i	0.502234	−	0.566375i
$671$			45.0518i			1.73920i
$672$		0			0
$673$	3.02628	+	3.02628i	0.116654	+	0.116654i	0.763024	−	0.646370i	$-0.223714\pi$
$673$	3.02628	+	3.02628i	0.116654	+	0.116654i	−0.646370	+	0.763024i	$0.723714\pi$
$674$	0.656339			0.0252812
$675$		0			0
$676$	−11.0000			−0.423077
$677$	29.4954	+	29.4954i	1.13360	+	1.13360i	0.989574	+	0.144027i	$0.0460052\pi$
$677$	29.4954	+	29.4954i	1.13360	+	1.13360i	0.144027	+	0.989574i	$0.453995\pi$
$678$		0			0
$679$		−	9.92820i		−	0.381009i
$680$	−2.17209	+	2.44949i	−0.0832958	+	0.0939336i
$681$		0			0
$682$	−22.4186	+	22.4186i	−0.858452	+	0.858452i
$683$	21.8695	−	21.8695i	0.836815	−	0.836815i	−0.151624	−	0.988438i	$-0.548450\pi$
$683$	21.8695	−	21.8695i	0.836815	−	0.836815i	0.988438	+	0.151624i	$0.0484501\pi$
$684$		0			0
$685$	7.73205	−	0.464102i	0.295426	−	0.0177324i
$686$		−	7.10823i		−	0.271394i
$687$		0			0
$688$	1.26795	+	1.26795i	0.0483401	+	0.0483401i
$689$	35.2538			1.34306
$690$		0			0
$691$	34.6410			1.31781			0.658903	−	0.752228i	$-0.271021\pi$
$691$	34.6410			1.31781			0.658903	+	0.752228i	$0.271021\pi$
$692$	7.39924	+	7.39924i	0.281277	+	0.281277i
$693$		0			0
$694$			28.6603i			1.08793i
$695$	16.4901	+	14.6226i	0.625505	+	0.554667i
$696$		0			0
$697$	−4.78461	+	4.78461i	−0.181230	+	0.181230i
$698$	3.96524	−	3.96524i	0.150087	−	0.150087i
$699$		0			0
$700$	−1.59808	+	2.03590i	−0.0604016	+	0.0769497i
$701$			22.8677i			0.863699i	0.901946	+	0.431850i	$0.142139\pi$
$701$			22.8677i			0.863699i	−0.901946	+	0.431850i	$0.857861\pi$
$702$		0			0
$703$	16.3923	+	16.3923i	0.618247	+	0.618247i
$704$	4.76028			0.179410
$705$		0			0
$706$	19.8564			0.747306
$707$	−5.36585	−	5.36585i	−0.201804	−	0.201804i
$708$		0			0
$709$		−	12.7846i		−	0.480136i	−0.970756	−	0.240068i	$-0.922830\pi$
$709$		−	12.7846i		−	0.480136i	0.970756	−	0.240068i	$-0.0771698\pi$
$710$	2.07055	+	34.4959i	0.0777064	+	1.29461i
$711$		0			0
$712$	−4.19615	+	4.19615i	−0.157257	+	0.157257i
$713$	−9.41902	+	9.41902i	−0.352745	+	0.352745i
$714$		0			0
$715$	−3.12436	−	52.0526i	−0.116844	−	1.94666i
$716$		−	5.41662i		−	0.202429i
$717$		0			0
$718$	−16.5885	−	16.5885i	−0.619076	−	0.619076i
$719$	−9.04008			−0.337138			−0.168569	−	0.985690i	$-0.553915\pi$
$719$	−9.04008			−0.337138			−0.168569	+	0.985690i	$0.553915\pi$
$720$		0			0
$721$	7.12436			0.265325
$722$	−25.9599	−	25.9599i	−0.966127	−	0.966127i
$723$		0			0
$724$			14.9282i			0.554802i
$725$	−3.77577	−	31.3393i	−0.140229	−	1.16391i
$726$		0			0
$727$	0.973721	−	0.973721i	0.0361133	−	0.0361133i	−0.688820	−	0.724933i	$-0.741871\pi$
$727$	0.973721	−	0.973721i	0.0361133	−	0.0361133i	0.724933	+	0.688820i	$0.241871\pi$
$728$	1.79315	−	1.79315i	0.0664586	−	0.0664586i
$729$		0			0
$730$	−22.1603	−	19.6506i	−0.820188	−	0.727303i
$731$			2.62536i			0.0971023i
$732$		0			0
$733$	−11.1244	−	11.1244i	−0.410887	−	0.410887i	0.471160	−	0.882048i	$-0.343835\pi$
$733$	−11.1244	−	11.1244i	−0.410887	−	0.410887i	−0.882048	+	0.471160i	$0.843835\pi$
$734$	−4.27981			−0.157971
$735$		0			0
$736$	2.00000			0.0737210
$737$	−29.4954	−	29.4954i	−1.08648	−	1.08648i
$738$		0			0
$739$			9.07180i			0.333711i	0.985981	+	0.166856i	$0.0533614\pi$
$739$			9.07180i			0.333711i	−0.985981	+	0.166856i	$0.946639\pi$
$740$	6.93237	−	0.416102i	0.254839	−	0.0152962i
$741$		0			0
$742$	−2.63397	+	2.63397i	−0.0966962	+	0.0966962i
$743$	−30.4292	+	30.4292i	−1.11634	+	1.11634i	−0.124063	+	0.992274i	$0.539592\pi$
$743$	−30.4292	+	30.4292i	−1.11634	+	1.11634i	−0.992274	+	0.124063i	$0.960408\pi$
$744$		0			0
$745$	18.5263	−	20.8923i	0.678750	−	0.765435i
$746$			11.8685i			0.434537i
$747$		0			0
$748$	4.92820	+	4.92820i	0.180193	+	0.180193i
$749$	0.998111			0.0364702
$750$		0			0
$751$	2.41154			0.0879984			0.0439992	−	0.999032i	$-0.485990\pi$
$751$	2.41154			0.0879984			0.0439992	+	0.999032i	$0.485990\pi$
$752$	4.24264	+	4.24264i	0.154713	+	0.154713i
$753$		0			0
$754$			30.9282i			1.12634i
$755$	12.5570	−	14.1607i	0.456997	−	0.515361i
$756$		0			0
$757$	−2.19615	+	2.19615i	−0.0798205	+	0.0798205i	−0.745890	−	0.666069i	$-0.767975\pi$
$757$	−2.19615	+	2.19615i	−0.0798205	+	0.0798205i	0.666069	+	0.745890i	$0.267975\pi$
$758$	−5.65685	+	5.65685i	−0.205466	+	0.205466i
$759$		0			0
$760$	−16.6603	+	1.00000i	−0.604331	+	0.0362738i
$761$			44.4970i			1.61301i	0.591225	+	0.806507i	$0.298645\pi$
$761$			44.4970i			1.61301i	−0.591225	+	0.806507i	$0.701355\pi$
$762$		0			0
$763$	0.732051	+	0.732051i	0.0265020	+	0.0265020i
$764$	3.38323			0.122401
$765$		0			0
$766$	−0.679492			−0.0245510
$767$	15.6579	+	15.6579i	0.565373	+	0.565373i
$768$		0			0
$769$		−	31.7846i		−	1.14618i	−0.819492	−	0.573091i	$-0.805744\pi$
$769$		−	31.7846i		−	1.14618i	0.819492	−	0.573091i	$-0.194256\pi$
$770$	4.12252	+	3.65565i	0.148565	+	0.131741i
$771$		0			0
$772$	8.02628	−	8.02628i	0.288872	−	0.288872i
$773$	−11.4152	+	11.4152i	−0.410578	+	0.410578i	−0.881940	−	0.471362i	$-0.843763\pi$
$773$	−11.4152	+	11.4152i	−0.410578	+	0.410578i	0.471362	+	0.881940i	$0.343763\pi$
$774$		0			0
$775$	−3.98334	−	33.0622i	−0.143086	−	1.18763i
$776$		−	19.1798i		−	0.688515i
$777$		0			0
$778$	−9.29423	−	9.29423i	−0.333214	−	0.333214i
$779$	−34.4959			−1.23594
$780$		0			0
$781$	73.5692			2.63251
$782$	2.07055	+	2.07055i	0.0740428	+	0.0740428i
$783$		0			0
$784$		−	6.73205i		−	0.240430i
$785$	2.27362	+	37.8792i	0.0811491	+	1.35197i
$786$		0			0
$787$	3.07180	−	3.07180i	0.109498	−	0.109498i	−0.650235	−	0.759733i	$-0.725330\pi$
$787$	3.07180	−	3.07180i	0.109498	−	0.109498i	0.759733	+	0.650235i	$0.225330\pi$
$788$	3.01790	−	3.01790i	0.107508	−	0.107508i
$789$		0			0
$790$	0.464102	+	7.73205i	0.0165120	+	0.275094i
$791$		−	8.76268i		−	0.311565i
$792$		0			0
$793$	32.7846	+	32.7846i	1.16422	+	1.16422i
$794$	6.96953			0.247339
$795$		0			0
$796$	−14.3205			−0.507577
$797$	23.5104	+	23.5104i	0.832781	+	0.832781i	0.987896	−	0.155116i	$-0.0495750\pi$
$797$	23.5104	+	23.5104i	0.832781	+	0.832781i	−0.155116	+	0.987896i	$0.549575\pi$
$798$		0			0
$799$			8.78461i			0.310777i
$800$	−3.08725	+	3.93305i	−0.109151	+	0.139054i
$801$		0			0
$802$	−12.9282	+	12.9282i	−0.456511	+	0.456511i
$803$	−44.5849	+	44.5849i	−1.57337	+	1.57337i
$804$		0			0
$805$	1.73205	+	1.53590i	0.0610468	+	0.0541333i
$806$			32.6284i			1.14929i
$807$		0			0
$808$	−10.3660	−	10.3660i	−0.364676	−	0.364676i
$809$	19.3185			0.679203			0.339601	−	0.940569i	$-0.389708\pi$
$809$	19.3185			0.679203			0.339601	+	0.940569i	$0.389708\pi$
$810$		0			0
$811$	−28.9282			−1.01581			−0.507903	−	0.861414i	$-0.669579\pi$
$811$	−28.9282			−1.01581			−0.507903	+	0.861414i	$0.669579\pi$
$812$	−2.31079	−	2.31079i	−0.0810928	−	0.0810928i
$813$		0			0
$814$		−	14.7846i		−	0.518200i
$815$	−17.2480	+	1.03528i	−0.604170	+	0.0362641i
$816$		0			0
$817$	−9.46410	+	9.46410i	−0.331107	+	0.331107i
$818$	−2.36156	+	2.36156i	−0.0825699	+	0.0825699i
$819$		0			0
$820$	−6.85641	+	7.73205i	−0.239436	+	0.270015i
$821$			8.93855i			0.311957i	0.987760	+	0.155979i	$0.0498531\pi$
$821$			8.93855i			0.311957i	−0.987760	+	0.155979i	$0.950147\pi$
$822$		0			0
$823$	−31.2942	−	31.2942i	−1.09085	−	1.09085i	−0.995438	−	0.0954102i	$-0.969584\pi$
$823$	−31.2942	−	31.2942i	−1.09085	−	1.09085i	−0.0954102	−	0.995438i	$-0.530416\pi$
$824$	13.7632			0.479464
$825$		0			0
$826$	−2.33975			−0.0814102
$827$	4.72311	+	4.72311i	0.164239	+	0.164239i	0.784442	−	0.620203i	$-0.212950\pi$
$827$	4.72311	+	4.72311i	0.164239	+	0.164239i	−0.620203	+	0.784442i	$0.712950\pi$
$828$		0			0
$829$		−	2.67949i		−	0.0930626i	−0.998917	−	0.0465313i	$-0.985183\pi$
$829$		−	2.67949i		−	0.0930626i	0.998917	−	0.0465313i	$-0.0148167\pi$
$830$	−3.07364	+	3.46618i	−0.106688	+	0.120313i
$831$		0			0
$832$	3.46410	−	3.46410i	0.120096	−	0.120096i
$833$	6.96953	−	6.96953i	0.241480	−	0.241480i
$834$		0			0
$835$	−37.7846	+	2.26795i	−1.30759	+	0.0784856i
$836$			35.5312i			1.22887i
$837$		0			0
$838$	9.33975	+	9.33975i	0.322636	+	0.322636i
$839$	−28.8391			−0.995635			−0.497818	−	0.867282i	$-0.665865\pi$
$839$	−28.8391			−0.995635			−0.497818	+	0.867282i	$0.665865\pi$
$840$		0			0
$841$	10.8564			0.374359
$842$	−12.6264	−	12.6264i	−0.435134	−	0.435134i
$843$		0			0
$844$		−	21.3205i		−	0.733882i
$845$	−18.4034	−	16.3192i	−0.633095	−	0.561398i
$846$		0			0
$847$	4.26795	−	4.26795i	0.146648	−	0.146648i
$848$	−5.08845	+	5.08845i	−0.174738	+	0.174738i
$849$		0			0
$850$	−7.26795	+	0.875644i	−0.249289	+	0.0300344i
$851$		−	6.21166i		−	0.212933i
$852$		0			0
$853$	−10.8756	−	10.8756i	−0.372375	−	0.372375i	0.495967	−	0.868342i	$-0.334814\pi$
$853$	−10.8756	−	10.8756i	−0.372375	−	0.372375i	−0.868342	+	0.495967i	$0.834814\pi$
$854$	−4.89898			−0.167640
$855$		0			0
$856$	1.92820			0.0659046
$857$	−32.9802	−	32.9802i	−1.12658	−	1.12658i	−0.990729	−	0.135852i	$-0.956623\pi$
$857$	−32.9802	−	32.9802i	−1.12658	−	1.12658i	−0.135852	−	0.990729i	$-0.543377\pi$
$858$		0			0
$859$		−	31.3205i		−	1.06864i	−0.845282	−	0.534321i	$-0.820567\pi$
$859$		−	31.3205i		−	1.06864i	0.845282	−	0.534321i	$-0.179433\pi$
$860$	0.240237	+	4.00240i	0.00819200	+	0.136481i
$861$		0			0
$862$	−18.1962	+	18.1962i	−0.619763	+	0.619763i
$863$	19.3185	−	19.3185i	0.657610	−	0.657610i	−0.297204	−	0.954814i	$-0.596054\pi$
$863$	19.3185	−	19.3185i	0.657610	−	0.657610i	0.954814	+	0.297204i	$0.0960542\pi$
$864$		0			0
$865$	1.40192	+	23.3564i	0.0476668	+	0.794142i
$866$		−	13.9019i		−	0.472406i
$867$		0			0
$868$	−2.43782	−	2.43782i	−0.0827451	−	0.0827451i
$869$	16.4901			0.559388
$870$		0			0
$871$	−42.9282			−1.45457
$872$	1.41421	+	1.41421i	0.0478913	+	0.0478913i
$873$		0			0
$874$			14.9282i			0.504954i
$875$	−5.69402	+	1.03528i	−0.192493	+	0.0349987i
$876$		0			0
$877$	−1.26795	+	1.26795i	−0.0428156	+	0.0428156i	−0.728190	−	0.685375i	$-0.759638\pi$
$877$	−1.26795	+	1.26795i	−0.0428156	+	0.0428156i	0.685375	+	0.728190i	$0.259638\pi$
$878$	20.6820	−	20.6820i	0.697982	−	0.697982i
$879$		0			0
$880$	7.96410	+	7.06218i	0.268470	+	0.238066i
$881$		−	6.41473i		−	0.216118i	−0.994144	−	0.108059i	$-0.965537\pi$
$881$		−	6.41473i		−	0.216118i	0.994144	−	0.108059i	$-0.0344635\pi$
$882$		0			0
$883$	19.1244	+	19.1244i	0.643586	+	0.643586i	0.951435	−	0.307849i	$-0.0996093\pi$
$883$	19.1244	+	19.1244i	0.643586	+	0.643586i	−0.307849	+	0.951435i	$0.599609\pi$
$884$	7.17260			0.241241
$885$		0			0
$886$	−36.2487			−1.21780
$887$	29.8744	+	29.8744i	1.00308	+	1.00308i	0.999995	+	0.00308728i	$0.000982712\pi$
$887$	29.8744	+	29.8744i	1.00308	+	1.00308i	0.00308728	+	0.999995i	$0.499017\pi$
$888$		0			0
$889$		−	0.856406i		−	0.0287230i
$890$	−13.2456	+	0.795040i	−0.443992	+	0.0266498i
$891$		0			0
$892$	−4.26795	+	4.26795i	−0.142902	+	0.142902i
$893$	−31.6675	+	31.6675i	−1.05971	+	1.05971i
$894$		0			0
$895$	8.03590	−	9.06218i	0.268610	−	0.302915i
$896$			0.517638i			0.0172931i
$897$		0			0
$898$	10.5885	+	10.5885i	0.353341	+	0.353341i
$899$	42.0475			1.40236
$900$		0			0
$901$	−10.5359			−0.351002
$902$	15.5563	+	15.5563i	0.517970	+	0.517970i
$903$		0			0
$904$		−	16.9282i		−	0.563024i
$905$	−22.1469	+	24.9754i	−0.736189	+	0.830209i
$906$		0			0
$907$	26.9808	−	26.9808i	0.895882	−	0.895882i	−0.0991873	−	0.995069i	$-0.531624\pi$
$907$	26.9808	−	26.9808i	0.895882	−	0.895882i	0.995069	+	0.0991873i	$0.0316243\pi$
$908$	3.20736	−	3.20736i	0.106440	−	0.106440i
$909$		0			0
$910$	5.66025	−	0.339746i	0.187636	−	0.0112625i
$911$		−	51.1891i		−	1.69597i	−0.530020	−	0.847985i	$-0.677816\pi$
$911$		−	51.1891i		−	1.69597i	0.530020	−	0.847985i	$-0.322184\pi$
$912$		0			0
$913$	6.97372	+	6.97372i	0.230796	+	0.230796i
$914$	−12.3118			−0.407239
$915$		0			0
$916$	1.60770			0.0531197
$917$	5.18998	+	5.18998i	0.171388	+	0.171388i
$918$		0			0
$919$		−	41.5885i		−	1.37188i	−0.727660	−	0.685938i	$-0.759392\pi$
$919$		−	41.5885i		−	1.37188i	0.727660	−	0.685938i	$-0.240608\pi$
$920$	3.34607	+	2.96713i	0.110317	+	0.0978233i
$921$		0			0
$922$	−14.6865	+	14.6865i	−0.483675	+	0.483675i
$923$	53.5370	−	53.5370i	1.76219	−	1.76219i
$924$		0			0
$925$	12.2154	+	9.58846i	0.401640	+	0.315267i
$926$			11.7298i			0.385465i
$927$		0			0
$928$	−4.46410	−	4.46410i	−0.146541	−	0.146541i
$929$	−17.1736			−0.563449			−0.281724	−	0.959495i	$-0.590906\pi$
$929$	−17.1736			−0.563449			−0.281724	+	0.959495i	$0.590906\pi$
$930$		0			0
$931$	50.2487			1.64683
$932$	5.55532	+	5.55532i	0.181971	+	0.181971i
$933$		0			0
$934$		−	13.0000i		−	0.425373i
$935$	0.933740	+	15.5563i	0.0305366	+	0.508747i
$936$		0			0
$937$	18.8301	−	18.8301i	0.615153	−	0.615153i	−0.329131	−	0.944284i	$-0.606756\pi$
$937$	18.8301	−	18.8301i	0.615153	−	0.615153i	0.944284	+	0.329131i	$0.106756\pi$
$938$	3.20736	−	3.20736i	0.104724	−	0.104724i
$939$		0			0
$940$	0.803848	+	13.3923i	0.0262186	+	0.436809i
$941$			43.4988i			1.41802i	0.705197	+	0.709011i	$0.250858\pi$
$941$			43.4988i			1.41802i	−0.705197	+	0.709011i	$0.749142\pi$
$942$		0			0
$943$	6.53590	+	6.53590i	0.212838	+	0.212838i
$944$	−4.52004			−0.147115
$945$		0			0
$946$	8.53590			0.277526
$947$	11.5775	+	11.5775i	0.376218	+	0.376218i	0.869736	−	0.493517i	$-0.164289\pi$
$947$	11.5775	+	11.5775i	0.376218	+	0.376218i	−0.493517	+	0.869736i	$0.664289\pi$
$948$		0			0
$949$			64.8897i			2.10641i
$950$	−29.3567	−	23.0435i	−0.952458	−	0.747630i
$951$		0			0
$952$	−0.535898	+	0.535898i	−0.0173686	+	0.0173686i
$953$	10.2784	−	10.2784i	0.332951	−	0.332951i	−0.520755	−	0.853706i	$-0.674350\pi$
$953$	10.2784	−	10.2784i	0.332951	−	0.332951i	0.853706	+	0.520755i	$0.174350\pi$
$954$		0			0
$955$	5.66025	+	5.01924i	0.183162	+	0.162419i
$956$		−	5.37945i		−	0.173984i
$957$		0			0
$958$	7.80385	+	7.80385i	0.252131	+	0.252131i
$959$	1.79315			0.0579039
$960$		0			0
$961$	13.3590			0.430935
$962$	−10.7589	−	10.7589i	−0.346881	−	0.346881i
$963$		0			0
$964$			4.00000i			0.128831i
$965$	25.3357	−	1.52073i	0.815586	−	0.0489540i
$966$		0			0
$967$	−2.50962	+	2.50962i	−0.0807039	+	0.0807039i	−0.746306	−	0.665603i	$-0.768175\pi$
$967$	−2.50962	+	2.50962i	−0.0807039	+	0.0807039i	0.665603	+	0.746306i	$0.268175\pi$
$968$	8.24504	−	8.24504i	0.265006	−	0.265006i
$969$		0			0
$970$	28.4545	−	32.0885i	0.913618	−	1.03030i
$971$			31.6303i			1.01507i	0.861632	+	0.507533i	$0.169442\pi$
$971$			31.6303i			1.01507i	−0.861632	+	0.507533i	$0.830558\pi$
$972$		0			0
$973$	3.60770	+	3.60770i	0.115657	+	0.115657i
$974$	−32.8043			−1.05112
$975$		0			0
$976$	−9.46410			−0.302939
$977$	−2.92996	−	2.92996i	−0.0937378	−	0.0937378i	0.658683	−	0.752421i	$-0.271114\pi$
$977$	−2.92996	−	2.92996i	−0.0937378	−	0.0937378i	−0.752421	+	0.658683i	$0.771114\pi$
$978$		0			0
$979$			28.2487i			0.902833i
$980$	9.98743	−	11.2629i	0.319037	−	0.359781i
$981$		0			0
$982$	15.9545	−	15.9545i	0.509128	−	0.509128i
$983$	31.2886	−	31.2886i	0.997950	−	0.997950i	−0.00204770	−	0.999998i	$-0.500652\pi$
$983$	31.2886	−	31.2886i	0.997950	−	0.997950i	0.999998	+	0.00204770i	$0.000651804\pi$
$984$		0			0
$985$	9.52628	−	0.571797i	0.303533	−	0.0182190i
$986$		−	9.24316i		−	0.294362i
$987$		0			0
$988$	25.8564	+	25.8564i	0.822602	+	0.822602i
$989$	3.58630			0.114038
$990$		0			0
$991$	2.60770			0.0828362			0.0414181	−	0.999142i	$-0.486812\pi$
$991$	2.60770			0.0828362			0.0414181	+	0.999142i	$0.486812\pi$
$992$	−4.70951	−	4.70951i	−0.149527	−	0.149527i
$993$		0			0
$994$			8.00000i			0.253745i
$995$	−23.9587	−	21.2454i	−0.759541	−	0.673524i
$996$		0			0
$997$	−33.8564	+	33.8564i	−1.07224	+	1.07224i	−0.0750645	+	0.997179i	$0.523916\pi$
$997$	−33.8564	+	33.8564i	−1.07224	+	1.07224i	−0.997179	+	0.0750645i	$0.976084\pi$
$998$	−25.3543	+	25.3543i	−0.802577	+	0.802577i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.f.b.53.3	yes	8
3.2	odd	2	inner	270.2.f.b.53.2	✓	8
4.3	odd	2		2160.2.w.b.593.2		8
5.2	odd	4	inner	270.2.f.b.107.2	yes	8
5.3	odd	4		1350.2.f.a.107.4		8
5.4	even	2		1350.2.f.a.593.2		8
9.2	odd	6		810.2.m.e.53.1		8
9.4	even	3		810.2.m.d.593.1		8
9.5	odd	6		810.2.m.d.593.2		8
9.7	even	3		810.2.m.e.53.2		8
12.11	even	2		2160.2.w.b.593.3		8
15.2	even	4	inner	270.2.f.b.107.3	yes	8
15.8	even	4		1350.2.f.a.107.2		8
15.14	odd	2		1350.2.f.a.593.4		8
20.7	even	4		2160.2.w.b.1457.3		8
45.2	even	12		810.2.m.d.377.1		8
45.7	odd	12		810.2.m.d.377.2		8
45.22	odd	12		810.2.m.e.107.1		8
45.32	even	12		810.2.m.e.107.2		8
60.47	odd	4		2160.2.w.b.1457.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.f.b.53.2	✓	8	3.2	odd	2	inner
270.2.f.b.53.3	yes	8	1.1	even	1	trivial
270.2.f.b.107.2	yes	8	5.2	odd	4	inner
270.2.f.b.107.3	yes	8	15.2	even	4	inner
810.2.m.d.377.1		8	45.2	even	12
810.2.m.d.377.2		8	45.7	odd	12
810.2.m.d.593.1		8	9.4	even	3
810.2.m.d.593.2		8	9.5	odd	6
810.2.m.e.53.1		8	9.2	odd	6
810.2.m.e.53.2		8	9.7	even	3
810.2.m.e.107.1		8	45.22	odd	12
810.2.m.e.107.2		8	45.32	even	12
1350.2.f.a.107.2		8	15.8	even	4
1350.2.f.a.107.4		8	5.3	odd	4
1350.2.f.a.593.2		8	5.4	even	2
1350.2.f.a.593.4		8	15.14	odd	2
2160.2.w.b.593.2		8	4.3	odd	2
2160.2.w.b.593.3		8	12.11	even	2
2160.2.w.b.1457.2		8	60.47	odd	4
2160.2.w.b.1457.3		8	20.7	even	4

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.48356 + 1.67303i) q^{5} +(-0.366025 + 0.366025i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.23205 + 0.133975i) q^{10} +4.76028i q^{11} +(3.46410 + 3.46410i) q^{13} -0.517638 q^{14} -1.00000 q^{16} +(-1.03528 - 1.03528i) q^{17} -7.46410i q^{19} +(-1.67303 - 1.48356i) q^{20} +(-3.36603 + 3.36603i) q^{22} +(-1.41421 + 1.41421i) q^{23} +(-0.598076 - 4.96410i) q^{25} +4.89898i q^{26} +(-0.366025 - 0.366025i) q^{28} +6.31319 q^{29} +6.66025 q^{31} +(-0.707107 - 0.707107i) q^{32} -1.46410i q^{34} +(-0.0693504 - 1.15539i) q^{35} +(-2.19615 + 2.19615i) q^{37} +(5.27792 - 5.27792i) q^{38} +(-0.133975 - 2.23205i) q^{40} -4.62158i q^{41} +(-1.26795 - 1.26795i) q^{43} -4.76028 q^{44} -2.00000 q^{46} +(-4.24264 - 4.24264i) q^{47} +6.73205i q^{49} +(3.08725 - 3.93305i) q^{50} +(-3.46410 + 3.46410i) q^{52} +(5.08845 - 5.08845i) q^{53} +(-7.96410 - 7.06218i) q^{55} -0.517638i q^{56} +(4.46410 + 4.46410i) q^{58} +4.52004 q^{59} +9.46410 q^{61} +(4.70951 + 4.70951i) q^{62} -1.00000i q^{64} +(-10.9348 + 0.656339i) q^{65} +(-6.19615 + 6.19615i) q^{67} +(1.03528 - 1.03528i) q^{68} +(0.767949 - 0.866025i) q^{70} -15.4548i q^{71} +(9.36603 + 9.36603i) q^{73} -3.10583 q^{74} +7.46410 q^{76} +(-1.74238 - 1.74238i) q^{77} -3.46410i q^{79} +(1.48356 - 1.67303i) q^{80} +(3.26795 - 3.26795i) q^{82} +(1.46498 - 1.46498i) q^{83} +(3.26795 - 0.196152i) q^{85} -1.79315i q^{86} +(-3.36603 - 3.36603i) q^{88} +5.93426 q^{89} -2.53590 q^{91} +(-1.41421 - 1.41421i) q^{92} -6.00000i q^{94} +(12.4877 + 11.0735i) q^{95} +(-13.5622 + 13.5622i) q^{97} +(-4.76028 + 4.76028i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7} - 4 q^{10} - 8 q^{16} - 20 q^{22} + 16 q^{25} + 4 q^{28} - 16 q^{31} + 24 q^{37} - 8 q^{40} - 24 q^{43} - 16 q^{46} - 36 q^{55} + 8 q^{58} + 48 q^{61} - 8 q^{67} + 20 q^{70} + 68 q^{73} + 32 q^{76}+ \cdots - 60 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 4 * q^10 - 8 * q^16 - 20 * q^22 + 16 * q^25 + 4 * q^28 - 16 * q^31 + 24 * q^37 - 8 * q^40 - 24 * q^43 - 16 * q^46 - 36 * q^55 + 8 * q^58 + 48 * q^61 - 8 * q^67 + 20 * q^70 + 68 * q^73 + 32 * q^76 + 40 * q^82 + 40 * q^85 - 20 * q^88 - 48 * q^91 - 60 * q^97

Introduction

L-functions

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