LMFDB - Embedded newform 1320.2.bw.h.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 13 x^{10} - 30 x^{9} + 96 x^{8} + 35 x^{7} + 177 x^{6} + 598 x^{5} + 1576 x^{4} + \cdots + 25 $ x^12 - x^11 + 13x^10 - 30x^9 + 96x^8 + 35x^7 + 177x^6 + 598x^5 + 1576x^4 + 450x^3 + 240x^2 + 100x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			961.3
Root			$0.715311 + 2.20150i$ of defining polynomial
Character	$\chi$	$=$	1320.961
Dual form			1320.2.bw.h.1081.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{3} +(0.809017 - 0.587785i) q^{5} +(1.02554 + 3.15630i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{3} +(0.809017 - 0.587785i) q^{5} +(1.02554 + 3.15630i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.09827 - 2.56852i) q^{11} +(-2.68172 - 1.94839i) q^{13} +(0.309017 + 0.951057i) q^{15} +(-3.68688 + 2.67868i) q^{17} +(-1.92550 + 5.92609i) q^{19} -3.31873 q^{21} -8.41210 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.809017 - 0.587785i) q^{27} +(1.40177 + 4.31420i) q^{29} +(7.58969 + 5.51423i) q^{31} +(3.09120 - 1.20185i) q^{33} +(2.68491 + 1.95070i) q^{35} +(-2.21752 - 6.82482i) q^{37} +(2.68172 - 1.94839i) q^{39} +(0.755467 - 2.32509i) q^{41} +0.193787 q^{43} -1.00000 q^{45} +(-0.575908 + 1.77246i) q^{47} +(-3.24738 + 2.35936i) q^{49} +(-1.40826 - 4.33419i) q^{51} +(-10.8408 - 7.87630i) q^{53} +(-3.20727 - 0.844644i) q^{55} +(-5.04104 - 3.66253i) q^{57} +(1.93123 + 5.94371i) q^{59} +(-10.4255 + 7.57460i) q^{61} +(1.02554 - 3.15630i) q^{63} -3.31479 q^{65} -5.68962 q^{67} +(2.59948 - 8.00039i) q^{69} +(7.41890 - 5.39015i) q^{71} +(3.53648 + 10.8842i) q^{73} +(0.809017 + 0.587785i) q^{75} +(5.95515 - 9.25689i) q^{77} +(-0.248985 - 0.180898i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-4.84040 + 3.51676i) q^{83} +(-1.40826 + 4.33419i) q^{85} -4.53622 q^{87} -9.45841 q^{89} +(3.39947 - 10.4625i) q^{91} +(-7.58969 + 5.51423i) q^{93} +(1.92550 + 5.92609i) q^{95} +(-3.01986 - 2.19405i) q^{97} +(0.187796 + 3.31130i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 3 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 3 * q^5 + 5 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} + 3 q^{5} + 5 q^{7} - 3 q^{9} + 6 q^{11} - 2 q^{13} - 3 q^{15} - 13 q^{17} - 12 q^{23} - 3 q^{25} + 3 q^{27} - 15 q^{29} - 3 q^{31} + 9 q^{33} + 5 q^{35} + 11 q^{37} + 2 q^{39} + 13 q^{41} + 10 q^{43} - 12 q^{45} + 14 q^{47} + 12 q^{49} - 12 q^{51} - 21 q^{53} - q^{55} + 5 q^{57} - 31 q^{59} - 39 q^{61} + 5 q^{63} - 8 q^{65} - 40 q^{67} + 7 q^{69} - q^{71} + 9 q^{73} + 3 q^{75} + 79 q^{77} + 39 q^{79} - 3 q^{81} - 17 q^{83} - 12 q^{85} - 40 q^{87} + 36 q^{89} + 17 q^{91} + 3 q^{93} + 3 q^{97} + 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 + 3 * q^5 + 5 * q^7 - 3 * q^9 + 6 * q^11 - 2 * q^13 - 3 * q^15 - 13 * q^17 - 12 * q^23 - 3 * q^25 + 3 * q^27 - 15 * q^29 - 3 * q^31 + 9 * q^33 + 5 * q^35 + 11 * q^37 + 2 * q^39 + 13 * q^41 + 10 * q^43 - 12 * q^45 + 14 * q^47 + 12 * q^49 - 12 * q^51 - 21 * q^53 - q^55 + 5 * q^57 - 31 * q^59 - 39 * q^61 + 5 * q^63 - 8 * q^65 - 40 * q^67 + 7 * q^69 - q^71 + 9 * q^73 + 3 * q^75 + 79 * q^77 + 39 * q^79 - 3 * q^81 - 17 * q^83 - 12 * q^85 - 40 * q^87 + 36 * q^89 + 17 * q^91 + 3 * q^93 + 3 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	1.02554	+	3.15630i	0.387620	+	1.19297i	0.934562	+	0.355800i	$0.115792\pi$
$7$	1.02554	+	3.15630i	0.387620	+	1.19297i	−0.546943	+	0.837170i	$0.684208\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−2.09827	−	2.56852i	−0.632651	−	0.774437i
$11$	−2.09827	−	2.56852i	−0.632651	−	0.774437i
$12$		0			0
$13$	−2.68172	−	1.94839i	−0.743777	−	0.540385i	0.150115	−	0.988669i	$-0.452036\pi$
$13$	−2.68172	−	1.94839i	−0.743777	−	0.540385i	−0.893892	+	0.448283i	$0.852036\pi$
$14$		0			0
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$		0			0
$17$	−3.68688	+	2.67868i	−0.894200	+	0.649674i	−0.936970	−	0.349411i	$-0.886382\pi$
$17$	−3.68688	+	2.67868i	−0.894200	+	0.649674i	0.0427697	+	0.999085i	$0.486382\pi$
$18$		0			0
$19$	−1.92550	+	5.92609i	−0.441741	+	1.35954i	0.444277	+	0.895889i	$0.353461\pi$
$19$	−1.92550	+	5.92609i	−0.441741	+	1.35954i	−0.886018	+	0.463650i	$0.846539\pi$
$20$		0			0
$21$	−3.31873			−0.724207
$22$		0			0
$23$	−8.41210			−1.75404			−0.877022	−	0.480449i	$-0.840474\pi$
$23$	−8.41210			−1.75404			−0.877022	+	0.480449i	$0.840474\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	1.40177	+	4.31420i	0.260302	+	0.801126i	0.992739	+	0.120291i	$0.0383829\pi$
$29$	1.40177	+	4.31420i	0.260302	+	0.801126i	−0.732437	+	0.680835i	$0.761617\pi$
$30$		0			0
$31$	7.58969	+	5.51423i	1.36315	+	0.990386i	0.998238	+	0.0593435i	$0.0189007\pi$
$31$	7.58969	+	5.51423i	1.36315	+	0.990386i	0.364911	+	0.931042i	$0.381099\pi$
$32$		0			0
$33$	3.09120	−	1.20185i	0.538110	−	0.209216i
$34$		0			0
$35$	2.68491	+	1.95070i	0.453833	+	0.329729i
$36$		0			0
$37$	−2.21752	−	6.82482i	−0.364558	−	1.12199i	−0.950258	−	0.311465i	$-0.899180\pi$
$37$	−2.21752	−	6.82482i	−0.364558	−	1.12199i	0.585700	−	0.810528i	$-0.300820\pi$
$38$		0			0
$39$	2.68172	−	1.94839i	0.429420	−	0.311992i
$40$		0			0
$41$	0.755467	−	2.32509i	0.117984	−	0.363118i	−0.874574	−	0.484893i	$-0.838859\pi$
$41$	0.755467	−	2.32509i	0.117984	−	0.363118i	0.992558	+	0.121775i	$0.0388586\pi$
$42$		0			0
$43$	0.193787			0.0295522			0.0147761	−	0.999891i	$-0.495296\pi$
$43$	0.193787			0.0295522			0.0147761	+	0.999891i	$0.495296\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−0.575908	+	1.77246i	−0.0840048	+	0.258540i	−0.984233	−	0.176879i	$-0.943400\pi$
$47$	−0.575908	+	1.77246i	−0.0840048	+	0.258540i	0.900228	+	0.435419i	$0.143400\pi$
$48$		0			0
$49$	−3.24738	+	2.35936i	−0.463912	+	0.337052i
$50$		0			0
$51$	−1.40826	−	4.33419i	−0.197196	−	0.606908i
$52$		0			0
$53$	−10.8408	−	7.87630i	−1.48910	−	1.08189i	−0.974480	−	0.224473i	$-0.927934\pi$
$53$	−10.8408	−	7.87630i	−1.48910	−	1.08189i	−0.514617	−	0.857420i	$-0.672066\pi$
$54$		0			0
$55$	−3.20727	−	0.844644i	−0.432468	−	0.113892i
$56$		0			0
$57$	−5.04104	−	3.66253i	−0.667702	−	0.485114i
$58$		0			0
$59$	1.93123	+	5.94371i	0.251424	+	0.773805i	0.994513	+	0.104612i	$0.0333600\pi$
$59$	1.93123	+	5.94371i	0.251424	+	0.773805i	−0.743089	+	0.669193i	$0.766640\pi$
$60$		0			0
$61$	−10.4255	+	7.57460i	−1.33485	+	0.969828i	−0.335237	+	0.942134i	$0.608816\pi$
$61$	−10.4255	+	7.57460i	−1.33485	+	0.969828i	−0.999616	+	0.0276939i	$0.991184\pi$
$62$		0			0
$63$	1.02554	−	3.15630i	0.129207	−	0.397657i
$64$		0			0
$65$	−3.31479			−0.411150
$66$		0			0
$67$	−5.68962			−0.695098			−0.347549	−	0.937662i	$-0.612986\pi$
$67$	−5.68962			−0.695098			−0.347549	+	0.937662i	$0.612986\pi$
$68$		0			0
$69$	2.59948	−	8.00039i	0.312941	−	0.963133i
$70$		0			0
$71$	7.41890	−	5.39015i	0.880462	−	0.639693i	−0.0529120	−	0.998599i	$-0.516850\pi$
$71$	7.41890	−	5.39015i	0.880462	−	0.639693i	0.933374	+	0.358906i	$0.116850\pi$
$72$		0			0
$73$	3.53648	+	10.8842i	0.413913	+	1.27389i	0.913219	+	0.407469i	$0.133588\pi$
$73$	3.53648	+	10.8842i	0.413913	+	1.27389i	−0.499306	+	0.866426i	$0.666412\pi$
$74$		0			0
$75$	0.809017	+	0.587785i	0.0934172	+	0.0678716i
$76$		0			0
$77$	5.95515	−	9.25689i	0.678653	−	1.05492i
$78$		0			0
$79$	−0.248985	−	0.180898i	−0.0280130	−	0.0203526i	0.573691	−	0.819072i	$-0.305511\pi$
$79$	−0.248985	−	0.180898i	−0.0280130	−	0.0203526i	−0.601704	+	0.798719i	$0.705511\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−4.84040	+	3.51676i	−0.531303	+	0.386014i	−0.820845	−	0.571151i	$-0.806497\pi$
$83$	−4.84040	+	3.51676i	−0.531303	+	0.386014i	0.289542	+	0.957165i	$0.406497\pi$
$84$		0			0
$85$	−1.40826	+	4.33419i	−0.152748	+	0.470109i
$86$		0			0
$87$	−4.53622			−0.486333
$88$		0			0
$89$	−9.45841			−1.00259			−0.501294	−	0.865277i	$-0.667143\pi$
$89$	−9.45841			−1.00259			−0.501294	+	0.865277i	$0.667143\pi$
$90$		0			0
$91$	3.39947	−	10.4625i	0.356361	−	1.09677i
$92$		0			0
$93$	−7.58969	+	5.51423i	−0.787014	+	0.571799i
$94$		0			0
$95$	1.92550	+	5.92609i	0.197553	+	0.608004i
$96$		0			0
$97$	−3.01986	−	2.19405i	−0.306620	−	0.222772i	0.423825	−	0.905744i	$-0.360687\pi$
$97$	−3.01986	−	2.19405i	−0.306620	−	0.222772i	−0.730445	+	0.682972i	$0.760687\pi$
$98$		0			0
$99$	0.187796	+	3.31130i	0.0188742	+	0.332799i
$100$		0			0
$101$	5.10650	+	3.71009i	0.508116	+	0.369168i	0.812108	−	0.583507i	$-0.198320\pi$
$101$	5.10650	+	3.71009i	0.508116	+	0.369168i	−0.303992	+	0.952674i	$0.598320\pi$
$102$		0			0
$103$	5.40872	+	16.6463i	0.532937	+	1.64021i	0.748065	+	0.663626i	$0.230983\pi$
$103$	5.40872	+	16.6463i	0.532937	+	1.64021i	−0.215128	+	0.976586i	$0.569017\pi$
$104$		0			0
$105$	−2.68491	+	1.95070i	−0.262021	+	0.190369i
$106$		0			0
$107$	3.27590	−	10.0822i	0.316693	−	0.974680i	−0.658359	−	0.752704i	$-0.728749\pi$
$107$	3.27590	−	10.0822i	0.316693	−	0.974680i	0.975052	−	0.221976i	$-0.0712508\pi$
$108$		0			0
$109$	−1.60439			−0.153672			−0.0768361	−	0.997044i	$-0.524482\pi$
$109$	−1.60439			−0.153672			−0.0768361	+	0.997044i	$0.524482\pi$
$110$		0			0
$111$	7.17604			0.681119
$112$		0			0
$113$	−1.23475	+	3.80017i	−0.116156	+	0.357490i	−0.992186	−	0.124765i	$-0.960182\pi$
$113$	−1.23475	+	3.80017i	−0.116156	+	0.357490i	0.876031	+	0.482255i	$0.160182\pi$
$114$		0			0
$115$	−6.80553	+	4.94451i	−0.634619	+	0.461078i
$116$		0			0
$117$	1.02433	+	3.15256i	0.0946991	+	0.291454i
$118$		0			0
$119$	−12.2358	−	8.88981i	−1.12165	−	0.814927i
$120$		0			0
$121$	−2.19456	+	10.7789i	−0.199506	+	0.979897i
$122$		0			0
$123$	1.97784	+	1.43698i	0.178336	+	0.129568i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−14.9090	+	10.8321i	−1.32296	+	0.961189i	−0.323074	+	0.946374i	$0.604716\pi$
$127$	−14.9090	+	10.8321i	−1.32296	+	0.961189i	−0.999890	+	0.0148157i	$0.995284\pi$
$128$		0			0
$129$	−0.0598834	+	0.184302i	−0.00527244	+	0.0162269i
$130$		0			0
$131$	6.79605			0.593773			0.296887	−	0.954913i	$-0.404052\pi$
$131$	6.79605			0.593773			0.296887	+	0.954913i	$0.404052\pi$
$132$		0			0
$133$	−20.6792			−1.79312
$134$		0			0
$135$	0.309017	−	0.951057i	0.0265959	−	0.0818539i
$136$		0			0
$137$	4.53903	−	3.29780i	0.387795	−	0.281750i	−0.376756	−	0.926312i	$-0.622961\pi$
$137$	4.53903	−	3.29780i	0.387795	−	0.281750i	0.764551	+	0.644563i	$0.222961\pi$
$138$		0			0
$139$	−3.98246	−	12.2568i	−0.337788	−	1.03960i	−0.965332	−	0.261024i	$-0.915940\pi$
$139$	−3.98246	−	12.2568i	−0.337788	−	1.03960i	0.627544	−	0.778581i	$-0.284060\pi$
$140$		0			0
$141$	−1.50775	−	1.09544i	−0.126975	−	0.0922528i
$142$		0			0
$143$	0.622505	+	10.9763i	0.0520565	+	0.917883i
$144$		0			0
$145$	3.66988	+	2.66632i	0.304767	+	0.221426i
$146$		0			0
$147$	−1.24039	−	3.81753i	−0.102306	−	0.314865i
$148$		0			0
$149$	−4.07480	+	2.96051i	−0.333821	+	0.242535i	−0.742050	−	0.670345i	$-0.766146\pi$
$149$	−4.07480	+	2.96051i	−0.333821	+	0.242535i	0.408229	+	0.912879i	$0.366146\pi$
$150$		0			0
$151$	6.99928	−	21.5416i	0.569593	−	1.75303i	−0.0842990	−	0.996441i	$-0.526865\pi$
$151$	6.99928	−	21.5416i	0.569593	−	1.75303i	0.653892	−	0.756588i	$-0.273135\pi$
$152$		0			0
$153$	4.55724			0.368431
$154$		0			0
$155$	9.38138			0.753530
$156$		0			0
$157$	2.21777	−	6.82560i	0.176997	−	0.544742i	−0.822722	−	0.568444i	$-0.807545\pi$
$157$	2.21777	−	6.82560i	0.176997	−	0.544742i	0.999719	+	0.0237025i	$0.00754544\pi$
$158$		0			0
$159$	10.8408	−	7.87630i	0.859731	−	0.624631i
$160$		0			0
$161$	−8.62699	−	26.5511i	−0.679902	−	2.09252i
$162$		0			0
$163$	10.2400	+	7.43981i	0.802060	+	0.582731i	0.911518	−	0.411261i	$-0.134911\pi$
$163$	10.2400	+	7.43981i	0.802060	+	0.582731i	−0.109458	+	0.993991i	$0.534911\pi$
$164$		0			0
$165$	1.79441	−	2.78928i	0.139694	−	0.217146i
$166$		0			0
$167$	4.72041	+	3.42958i	0.365277	+	0.265389i	0.755250	−	0.655437i	$-0.227516\pi$
$167$	4.72041	+	3.42958i	0.365277	+	0.265389i	−0.389973	+	0.920826i	$0.627516\pi$
$168$		0			0
$169$	−0.621787	−	1.91366i	−0.0478297	−	0.147205i
$170$		0			0
$171$	5.04104	−	3.66253i	0.385498	−	0.280081i
$172$		0			0
$173$	3.78005	−	11.6338i	0.287392	−	0.884502i	−0.698280	−	0.715825i	$-0.746051\pi$
$173$	3.78005	−	11.6338i	0.287392	−	0.884502i	0.985671	−	0.168676i	$-0.0539493\pi$
$174$		0			0
$175$	3.31873			0.250873
$176$		0			0
$177$	−6.24958			−0.469747
$178$		0			0
$179$	4.56308	−	14.0437i	0.341060	−	1.04968i	−0.622599	−	0.782541i	$-0.713923\pi$
$179$	4.56308	−	14.0437i	0.341060	−	1.04968i	0.963659	−	0.267135i	$-0.0860769\pi$
$180$		0			0
$181$	2.36049	−	1.71500i	0.175454	−	0.127475i	−0.496592	−	0.867984i	$-0.665416\pi$
$181$	2.36049	−	1.71500i	0.175454	−	0.127475i	0.672046	+	0.740509i	$0.265416\pi$
$182$		0			0
$183$	−3.98220	−	12.2560i	−0.294373	−	0.905986i
$184$		0			0
$185$	−5.80553	−	4.21797i	−0.426831	−	0.310111i
$186$		0			0
$187$	14.6163	+	3.84924i	1.06885	+	0.281485i
$188$		0			0
$189$	2.68491	+	1.95070i	0.195299	+	0.141893i
$190$		0			0
$191$	6.11267	+	18.8129i	0.442298	+	1.36125i	0.885420	+	0.464791i	$0.153871\pi$
$191$	6.11267	+	18.8129i	0.442298	+	1.36125i	−0.443123	+	0.896461i	$0.646129\pi$
$192$		0			0
$193$	−2.38466	+	1.73256i	−0.171652	+	0.124712i	−0.670294	−	0.742095i	$-0.733832\pi$
$193$	−2.38466	+	1.73256i	−0.171652	+	0.124712i	0.498642	+	0.866808i	$0.333832\pi$
$194$		0			0
$195$	1.02433	−	3.15256i	0.0733536	−	0.225759i
$196$		0			0
$197$	24.0588			1.71412			0.857059	−	0.515218i	$-0.172289\pi$
$197$	24.0588			1.71412			0.857059	+	0.515218i	$0.172289\pi$
$198$		0			0
$199$	−14.8355			−1.05166			−0.525829	−	0.850590i	$-0.676245\pi$
$199$	−14.8355			−1.05166			−0.525829	+	0.850590i	$0.676245\pi$
$200$		0			0
$201$	1.75819	−	5.41115i	0.124013	−	0.381673i
$202$		0			0
$203$	−12.1793	+	8.84881i	−0.854822	+	0.621065i
$204$		0			0
$205$	−0.755467	−	2.32509i	−0.0527641	−	0.162391i
$206$		0			0
$207$	6.80553	+	4.94451i	0.473017	+	0.343667i
$208$		0			0
$209$	19.2615	−	7.48883i	1.33235	−	0.518013i
$210$		0			0
$211$	14.5865	+	10.5977i	1.00417	+	0.729575i	0.962979	−	0.269576i	$-0.0868835\pi$
$211$	14.5865	+	10.5977i	1.00417	+	0.729575i	0.0411951	+	0.999151i	$0.486883\pi$
$212$		0			0
$213$	2.83377	+	8.72144i	0.194167	+	0.597583i
$214$		0			0
$215$	0.156777	−	0.113905i	0.0106921	−	0.00776826i
$216$		0			0
$217$	−9.62102	+	29.6105i	−0.653118	+	2.01009i
$218$		0			0
$219$	−11.4443			−0.773333
$220$		0			0
$221$	15.1063			1.01616
$222$		0			0
$223$	−7.84209	+	24.1355i	−0.525145	+	1.61623i	0.238884	+	0.971048i	$0.423219\pi$
$223$	−7.84209	+	24.1355i	−0.525145	+	1.61623i	−0.764029	+	0.645182i	$0.776781\pi$
$224$		0			0
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$		0			0
$227$	−2.61524	−	8.04887i	−0.173579	−	0.534222i	0.825986	−	0.563690i	$-0.190619\pi$
$227$	−2.61524	−	8.04887i	−0.173579	−	0.534222i	−0.999566	+	0.0294677i	$0.990619\pi$
$228$		0			0
$229$	17.1670	+	12.4725i	1.13443	+	0.824209i	0.986333	−	0.164765i	$-0.0526865\pi$
$229$	17.1670	+	12.4725i	1.13443	+	0.824209i	0.148093	+	0.988973i	$0.452686\pi$
$230$		0			0
$231$	6.96358	+	8.52422i	0.458170	+	0.560853i
$232$		0			0
$233$	−15.5017	−	11.2627i	−1.01555	−	0.737842i	−0.0501857	−	0.998740i	$-0.515981\pi$
$233$	−15.5017	−	11.2627i	−1.01555	−	0.737842i	−0.965366	+	0.260898i	$0.915981\pi$
$234$		0			0
$235$	0.575908	+	1.77246i	0.0375681	+	0.115623i
$236$		0			0
$237$	0.248985	−	0.180898i	0.0161733	−	0.0117506i
$238$		0			0
$239$	−7.04104	+	21.6701i	−0.455447	+	1.40172i	0.415163	+	0.909747i	$0.363725\pi$
$239$	−7.04104	+	21.6701i	−0.455447	+	1.40172i	−0.870610	+	0.491974i	$0.836275\pi$
$240$		0			0
$241$	14.1019			0.908380			0.454190	−	0.890905i	$-0.349929\pi$
$241$	14.1019			0.908380			0.454190	+	0.890905i	$0.349929\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−1.24039	+	3.81753i	−0.0792456	+	0.243893i
$246$		0			0
$247$	16.7100	−	12.1405i	1.06323	−	0.772483i
$248$		0			0
$249$	−1.84887	−	5.69024i	−0.117167	−	0.360604i
$250$		0			0
$251$	−16.0549	−	11.6645i	−1.01337	−	0.736260i	−0.0484604	−	0.998825i	$-0.515431\pi$
$251$	−16.0549	−	11.6645i	−1.01337	−	0.736260i	−0.964914	+	0.262565i	$0.915431\pi$
$252$		0			0
$253$	17.6508	+	21.6066i	1.10970	+	1.35840i
$254$		0			0
$255$	−3.68688	−	2.67868i	−0.230881	−	0.167745i
$256$		0			0
$257$	−7.64966	−	23.5432i	−0.477173	−	1.46859i	−0.843005	−	0.537905i	$-0.819216\pi$
$257$	−7.64966	−	23.5432i	−0.477173	−	1.46859i	0.365833	−	0.930681i	$-0.380784\pi$
$258$		0			0
$259$	19.2670	−	13.9983i	1.19719	−	0.869813i
$260$		0			0
$261$	1.40177	−	4.31420i	0.0867673	−	0.267042i
$262$		0			0
$263$	10.2056			0.629306			0.314653	−	0.949207i	$-0.398112\pi$
$263$	10.2056			0.629306			0.314653	+	0.949207i	$0.398112\pi$
$264$		0			0
$265$	−13.4000			−0.823153
$266$		0			0
$267$	2.92281	−	8.99548i	0.178873	−	0.550514i
$268$		0			0
$269$	14.7997	−	10.7526i	0.902351	−	0.655596i	−0.0367178	−	0.999326i	$-0.511690\pi$
$269$	14.7997	−	10.7526i	0.902351	−	0.655596i	0.939069	+	0.343729i	$0.111690\pi$
$270$		0			0
$271$	2.26583	+	6.97350i	0.137639	+	0.423610i	0.995991	−	0.0894513i	$-0.0285113\pi$
$271$	2.26583	+	6.97350i	0.137639	+	0.423610i	−0.858352	+	0.513061i	$0.828511\pi$
$272$		0			0
$273$	8.89993	+	6.46618i	0.538648	+	0.391351i
$274$		0			0
$275$	−3.09120	+	1.20185i	−0.186407	+	0.0724745i
$276$		0			0
$277$	10.2895	+	7.47577i	0.618237	+	0.449176i	0.852305	−	0.523045i	$-0.175204\pi$
$277$	10.2895	+	7.47577i	0.618237	+	0.449176i	−0.234068	+	0.972220i	$0.575204\pi$
$278$		0			0
$279$	−2.89900	−	8.92222i	−0.173559	−	0.534159i
$280$		0			0
$281$	0.257459	−	0.187055i	0.0153587	−	0.0111588i	−0.580079	−	0.814560i	$-0.696978\pi$
$281$	0.257459	−	0.187055i	0.0153587	−	0.0111588i	0.595438	+	0.803401i	$0.296978\pi$
$282$		0			0
$283$	−0.341245	+	1.05024i	−0.0202849	+	0.0624305i	−0.960687	−	0.277635i	$-0.910449\pi$
$283$	−0.341245	+	1.05024i	−0.0202849	+	0.0624305i	0.940402	+	0.340066i	$0.110449\pi$
$284$		0			0
$285$	−6.23106			−0.369096
$286$		0			0
$287$	8.11345			0.478922
$288$		0			0
$289$	1.16450	−	3.58396i	0.0684999	−	0.210821i
$290$		0			0
$291$	3.01986	−	2.19405i	0.177027	−	0.128618i
$292$		0			0
$293$	7.99119	+	24.5944i	0.466850	+	1.43682i	0.856640	+	0.515914i	$0.172548\pi$
$293$	7.99119	+	24.5944i	0.466850	+	1.43682i	−0.389790	+	0.920904i	$0.627452\pi$
$294$		0			0
$295$	5.05602	+	3.67341i	0.294373	+	0.213874i
$296$		0			0
$297$	−3.20727	−	0.844644i	−0.186105	−	0.0490112i
$298$		0			0
$299$	22.5589	+	16.3900i	1.30462	+	0.947860i
$300$		0			0
$301$	0.198737	+	0.611650i	0.0114550	+	0.0352549i
$302$		0			0
$303$	−5.10650	+	3.71009i	−0.293361	+	0.213139i
$304$		0			0
$305$	−3.98220	+	12.2560i	−0.228020	+	0.701774i
$306$		0			0
$307$	11.2522			0.642195			0.321098	−	0.947046i	$-0.395948\pi$
$307$	11.2522			0.642195			0.321098	+	0.947046i	$0.395948\pi$
$308$		0			0
$309$	−17.5030			−0.995710
$310$		0			0
$311$	−1.51495	+	4.66255i	−0.0859051	+	0.264389i	−0.984777	−	0.173823i	$-0.944388\pi$
$311$	−1.51495	+	4.66255i	−0.0859051	+	0.264389i	0.898872	+	0.438212i	$0.144388\pi$
$312$		0			0
$313$	−8.75038	+	6.35753i	−0.494601	+	0.359349i	−0.806951	−	0.590618i	$-0.798884\pi$
$313$	−8.75038	+	6.35753i	−0.494601	+	0.359349i	0.312350	+	0.949967i	$0.398884\pi$
$314$		0			0
$315$	−1.02554	−	3.15630i	−0.0577829	−	0.177837i
$316$		0			0
$317$	3.16572	+	2.30003i	0.177805	+	0.129183i	0.673128	−	0.739526i	$-0.264950\pi$
$317$	3.16572	+	2.30003i	0.177805	+	0.129183i	−0.495323	+	0.868709i	$0.664950\pi$
$318$		0			0
$319$	8.13981	−	12.6528i	0.455742	−	0.708421i
$320$		0			0
$321$	8.57641	+	6.23112i	0.478688	+	0.347787i
$322$		0			0
$323$	−8.77498	−	27.0066i	−0.488253	−	1.50269i
$324$		0			0
$325$	−2.68172	+	1.94839i	−0.148755	+	0.108077i
$326$		0			0
$327$	0.495783	−	1.52586i	0.0274168	−	0.0843803i
$328$		0			0
$329$	−6.18505			−0.340993
$330$		0			0
$331$	14.9864			0.823729			0.411864	−	0.911245i	$-0.364878\pi$
$331$	14.9864			0.823729			0.411864	+	0.911245i	$0.364878\pi$
$332$		0			0
$333$	−2.21752	+	6.82482i	−0.121519	+	0.373998i
$334$		0			0
$335$	−4.60300	+	3.34427i	−0.251489	+	0.182717i
$336$		0			0
$337$	−2.28227	−	7.02410i	−0.124323	−	0.382627i	0.869454	−	0.494014i	$-0.164471\pi$
$337$	−2.28227	−	7.02410i	−0.124323	−	0.382627i	−0.993777	+	0.111387i	$0.964471\pi$
$338$		0			0
$339$	−3.23262	−	2.34863i	−0.175572	−	0.127560i
$340$		0			0
$341$	−1.76179	−	31.0646i	−0.0954060	−	1.68224i
$342$		0			0
$343$	8.01718	+	5.82482i	0.432887	+	0.314511i
$344$		0			0
$345$	−2.59948	−	8.00039i	−0.139951	−	0.430726i
$346$		0			0
$347$	−9.78508	+	7.10928i	−0.525291	+	0.381646i	−0.818593	−	0.574374i	$-0.805246\pi$
$347$	−9.78508	+	7.10928i	−0.525291	+	0.381646i	0.293303	+	0.956020i	$0.405246\pi$
$348$		0			0
$349$	2.34105	−	7.20500i	0.125313	−	0.385675i	−0.868645	−	0.495435i	$-0.835009\pi$
$349$	2.34105	−	7.20500i	0.125313	−	0.385675i	0.993958	+	0.109761i	$0.0350085\pi$
$350$		0			0
$351$	−3.31479			−0.176931
$352$		0			0
$353$	24.5886			1.30872			0.654361	−	0.756183i	$-0.272938\pi$
$353$	24.5886			1.30872			0.654361	+	0.756183i	$0.272938\pi$
$354$		0			0
$355$	2.83377	−	8.72144i	0.150401	−	0.462886i
$356$		0			0
$357$	12.2358	−	8.88981i	0.647586	−	0.470499i
$358$		0			0
$359$	8.88914	+	27.3580i	0.469151	+	1.44390i	0.853686	+	0.520788i	$0.174362\pi$
$359$	8.88914	+	27.3580i	0.469151	+	1.44390i	−0.384536	+	0.923110i	$0.625638\pi$
$360$		0			0
$361$	−16.0397	−	11.6535i	−0.844195	−	0.613344i
$362$		0			0
$363$	−9.57315	−	5.41800i	−0.502460	−	0.284371i
$364$		0			0
$365$	9.25862	+	6.72678i	0.484618	+	0.352096i
$366$		0			0
$367$	7.02805	+	21.6301i	0.366861	+	1.12908i	0.948807	+	0.315855i	$0.102291\pi$
$367$	7.02805	+	21.6301i	0.366861	+	1.12908i	−0.581946	+	0.813227i	$0.697709\pi$
$368$		0			0
$369$	−1.97784	+	1.43698i	−0.102962	+	0.0748064i
$370$		0			0
$371$	13.7423	−	42.2943i	0.713463	−	2.19581i
$372$		0			0
$373$	−3.64880			−0.188928			−0.0944640	−	0.995528i	$-0.530114\pi$
$373$	−3.64880			−0.188928			−0.0944640	+	0.995528i	$0.530114\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	4.64657	−	14.3007i	0.239311	−	0.736522i
$378$		0			0
$379$	−25.4935	+	18.5221i	−1.30952	+	0.951419i	−0.309516	+	0.950894i	$0.600167\pi$
$379$	−25.4935	+	18.5221i	−1.30952	+	0.951419i	−1.00000		0.000524257i	$0.999833\pi$
$380$		0			0
$381$	−5.69475	−	17.5266i	−0.291751	−	0.897917i
$382$		0			0
$383$	−19.4934	−	14.1628i	−0.996068	−	0.723686i	−0.0348263	−	0.999393i	$-0.511088\pi$
$383$	−19.4934	−	14.1628i	−0.996068	−	0.723686i	−0.961242	+	0.275708i	$0.911088\pi$
$384$		0			0
$385$	−0.623245	−	10.9893i	−0.0317635	−	0.560068i
$386$		0			0
$387$	−0.156777	−	0.113905i	−0.00796941	−	0.00579012i
$388$		0			0
$389$	3.48209	+	10.7168i	0.176549	+	0.543362i	0.999701	−	0.0244595i	$-0.00778647\pi$
$389$	3.48209	+	10.7168i	0.176549	+	0.543362i	−0.823152	+	0.567821i	$0.807786\pi$
$390$		0			0
$391$	31.0144	−	22.5333i	1.56847	−	1.13956i
$392$		0			0
$393$	−2.10009	+	6.46343i	−0.105936	+	0.326037i
$394$		0			0
$395$	−0.307762			−0.0154852
$396$		0			0
$397$	13.3451			0.669772			0.334886	−	0.942259i	$-0.391302\pi$
$397$	13.3451			0.669772			0.334886	+	0.942259i	$0.391302\pi$
$398$		0			0
$399$	6.39024	−	19.6671i	0.319912	−	0.984588i
$400$		0			0
$401$	−29.2922	+	21.2820i	−1.46278	+	1.06277i	−0.480153	+	0.877185i	$0.659419\pi$
$401$	−29.2922	+	21.2820i	−1.46278	+	1.06277i	−0.982628	+	0.185588i	$0.940581\pi$
$402$		0			0
$403$	−9.60960	−	29.5753i	−0.478688	−	1.47325i
$404$		0			0
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$		0			0
$407$	−12.8767	+	20.0160i	−0.638275	+	0.992157i
$408$		0			0
$409$	22.0070	+	15.9890i	1.08818	+	0.790606i	0.979090	−	0.203427i	$-0.0652079\pi$
$409$	22.0070	+	15.9890i	1.08818	+	0.790606i	0.109085	+	0.994032i	$0.465208\pi$
$410$		0			0
$411$	1.73375	+	5.33595i	0.0855198	+	0.263203i
$412$		0			0
$413$	−16.7796	+	12.1911i	−0.825669	+	0.599884i
$414$		0			0
$415$	−1.84887	+	5.69024i	−0.0907574	+	0.279323i
$416$		0			0
$417$	12.8875			0.631105
$418$		0			0
$419$	2.09245			0.102223			0.0511115	−	0.998693i	$-0.483724\pi$
$419$	2.09245			0.102223			0.0511115	+	0.998693i	$0.483724\pi$
$420$		0			0
$421$	2.07383	−	6.38258i	0.101072	−	0.311068i	−0.887716	−	0.460391i	$-0.847709\pi$
$421$	2.07383	−	6.38258i	0.101072	−	0.311068i	0.988789	+	0.149323i	$0.0477093\pi$
$422$		0			0
$423$	1.50775	−	1.09544i	0.0733091	−	0.0532622i
$424$		0			0
$425$	1.40826	+	4.33419i	0.0683108	+	0.210239i
$426$		0			0
$427$	−34.5996	−	25.1381i	−1.67439	−	1.21652i
$428$		0			0
$429$	−10.6314	−	2.79982i	−0.513291	−	0.135177i
$430$		0			0
$431$	16.8390	+	12.2342i	0.811105	+	0.589302i	0.914151	−	0.405375i	$-0.132859\pi$
$431$	16.8390	+	12.2342i	0.811105	+	0.589302i	−0.103046	+	0.994677i	$0.532859\pi$
$432$		0			0
$433$	−7.13851	−	21.9701i	−0.343055	−	1.05581i	−0.962617	−	0.270867i	$-0.912690\pi$
$433$	−7.13851	−	21.9701i	−0.343055	−	1.05581i	0.619562	−	0.784948i	$-0.287310\pi$
$434$		0			0
$435$	−3.66988	+	2.66632i	−0.175957	+	0.127840i
$436$		0			0
$437$	16.1975	−	49.8509i	0.774834	−	2.38469i
$438$		0			0
$439$	−18.2517			−0.871104			−0.435552	−	0.900163i	$-0.643447\pi$
$439$	−18.2517			−0.871104			−0.435552	+	0.900163i	$0.643447\pi$
$440$		0			0
$441$	4.01399			0.191142
$442$		0			0
$443$	6.63717	−	20.4271i	0.315342	−	0.970522i	−0.660272	−	0.751027i	$-0.729559\pi$
$443$	6.63717	−	20.4271i	0.315342	−	0.970522i	0.975614	−	0.219495i	$-0.0704410\pi$
$444$		0			0
$445$	−7.65201	+	5.55951i	−0.362740	+	0.263546i
$446$		0			0
$447$	−1.55643	−	4.79021i	−0.0736168	−	0.226569i
$448$		0			0
$449$	20.3041	+	14.7518i	0.958208	+	0.696179i	0.952734	−	0.303806i	$-0.0982575\pi$
$449$	20.3041	+	14.7518i	0.958208	+	0.696179i	0.00547414	+	0.999985i	$0.498258\pi$
$450$		0			0
$451$	−7.55720	+	2.93822i	−0.355855	+	0.138356i
$452$		0			0
$453$	18.3244	+	13.3134i	0.860953	+	0.625519i
$454$		0			0
$455$	−3.39947	−	10.4625i	−0.159370	−	0.490489i
$456$		0			0
$457$	4.72560	−	3.43335i	0.221054	−	0.160605i	−0.471747	−	0.881734i	$-0.656376\pi$
$457$	4.72560	−	3.43335i	0.221054	−	0.160605i	0.692801	+	0.721129i	$0.256376\pi$
$458$		0			0
$459$	−1.40826	+	4.33419i	−0.0657321	+	0.202303i
$460$		0			0
$461$	10.5406			0.490923			0.245462	−	0.969406i	$-0.421060\pi$
$461$	10.5406			0.490923			0.245462	+	0.969406i	$0.421060\pi$
$462$		0			0
$463$	−33.1984			−1.54286			−0.771430	−	0.636314i	$-0.780458\pi$
$463$	−33.1984			−1.54286			−0.771430	+	0.636314i	$0.780458\pi$
$464$		0			0
$465$	−2.89900	+	8.92222i	−0.134438	+	0.413758i
$466$		0			0
$467$	−27.7175	+	20.1380i	−1.28262	+	0.931874i	−0.999629	−	0.0272494i	$-0.991325\pi$
$467$	−27.7175	+	20.1380i	−1.28262	+	0.931874i	−0.282987	+	0.959124i	$0.591325\pi$
$468$		0			0
$469$	−5.83496	−	17.9582i	−0.269433	−	0.829231i
$470$		0			0
$471$	5.80620	+	4.21845i	0.267536	+	0.194376i
$472$		0			0
$473$	−0.406616	−	0.497745i	−0.0186962	−	0.0228863i
$474$		0			0
$475$	5.04104	+	3.66253i	0.231299	+	0.168048i
$476$		0			0
$477$	4.14082	+	12.7441i	0.189595	+	0.583513i
$478$		0			0
$479$	−9.84309	+	7.15143i	−0.449742	+	0.326757i	−0.789494	−	0.613758i	$-0.789657\pi$
$479$	−9.84309	+	7.15143i	−0.449742	+	0.326757i	0.339752	+	0.940515i	$0.389657\pi$
$480$		0			0
$481$	−7.35061	+	22.6229i	−0.335159	+	1.03151i
$482$		0			0
$483$	27.9175			1.27029
$484$		0			0
$485$	−3.73275			−0.169495
$486$		0			0
$487$	4.58967	−	14.1256i	0.207978	−	0.640090i	−0.791600	−	0.611040i	$-0.790752\pi$
$487$	4.58967	−	14.1256i	0.207978	−	0.640090i	0.999578	−	0.0290506i	$-0.00924840\pi$
$488$		0			0
$489$	−10.2400	+	7.43981i	−0.463069	+	0.336440i
$490$		0			0
$491$	−8.72996	−	26.8681i	−0.393978	−	1.21254i	−0.929755	−	0.368179i	$-0.879981\pi$
$491$	−8.72996	−	26.8681i	−0.393978	−	1.21254i	0.535777	−	0.844360i	$-0.320019\pi$
$492$		0			0
$493$	−16.7245	−	12.1511i	−0.753233	−	0.547256i
$494$		0			0
$495$	2.09827	+	2.56852i	0.0943100	+	0.115446i
$496$		0			0
$497$	24.6214	+	17.8885i	1.10442	+	0.802407i
$498$		0			0
$499$	−3.40061	−	10.4660i	−0.152232	−	0.468523i	0.845638	−	0.533757i	$-0.179220\pi$
$499$	−3.40061	−	10.4660i	−0.152232	−	0.468523i	−0.997870	+	0.0652346i	$0.979220\pi$
$500$		0			0
$501$	−4.72041	+	3.42958i	−0.210892	+	0.153222i
$502$		0			0
$503$	−13.0574	+	40.1866i	−0.582201	+	1.79183i	0.0280306	+	0.999607i	$0.491076\pi$
$503$	−13.0574	+	40.1866i	−0.582201	+	1.79183i	−0.610232	+	0.792223i	$0.708924\pi$
$504$		0			0
$505$	6.31199			0.280880
$506$		0			0
$507$	2.01214			0.0893624
$508$		0			0
$509$	1.05481	−	3.24638i	0.0467538	−	0.143893i	−0.924954	−	0.380078i	$-0.875897\pi$
$509$	1.05481	−	3.24638i	0.0467538	−	0.143893i	0.971708	+	0.236185i	$0.0758971\pi$
$510$		0			0
$511$	−30.7269	+	22.3244i	−1.35928	+	0.987573i
$512$		0			0
$513$	1.92550	+	5.92609i	0.0850131	+	0.261643i
$514$		0			0
$515$	14.1602	+	10.2880i	0.623974	+	0.453343i
$516$		0			0
$517$	5.76101	−	2.23987i	0.253369	−	0.0985092i
$518$		0			0
$519$	9.89630	+	7.19008i	0.434399	+	0.315610i
$520$		0			0
$521$	−2.88796	−	8.88822i	−0.126524	−	0.389400i	0.867652	−	0.497172i	$-0.165628\pi$
$521$	−2.88796	−	8.88822i	−0.126524	−	0.389400i	−0.994176	+	0.107772i	$0.965628\pi$
$522$		0			0
$523$	−13.3912	+	9.72926i	−0.585555	+	0.425431i	−0.840723	−	0.541466i	$-0.817869\pi$
$523$	−13.3912	+	9.72926i	−0.585555	+	0.425431i	0.255167	+	0.966897i	$0.417869\pi$
$524$		0			0
$525$	−1.02554	+	3.15630i	−0.0447584	+	0.137752i
$526$		0			0
$527$	−42.7531			−1.86236
$528$		0			0
$529$	47.7635			2.07667
$530$		0			0
$531$	1.93123	−	5.94371i	0.0838081	−	0.257935i
$532$		0			0
$533$	−6.55613	+	4.76330i	−0.283977	+	0.206322i
$534$		0			0
$535$	−3.27590	−	10.0822i	−0.141629	−	0.435890i
$536$		0			0
$537$	11.9463	+	8.67949i	0.515521	+	0.374548i
$538$		0			0
$539$	12.8739	+	3.39039i	0.554520	+	0.146035i
$540$		0			0
$541$	−27.9869	−	20.3336i	−1.20325	−	0.874212i	−0.208649	−	0.977991i	$-0.566906\pi$
$541$	−27.9869	−	20.3336i	−1.20325	−	0.874212i	−0.994600	+	0.103779i	$0.966906\pi$
$542$		0			0
$543$	0.901627	+	2.77492i	0.0386925	+	0.119083i
$544$		0			0
$545$	−1.29798	+	0.943034i	−0.0555992	+	0.0403952i
$546$		0			0
$547$	3.86490	−	11.8949i	0.165251	−	0.508590i	−0.833804	−	0.552061i	$-0.813842\pi$
$547$	3.86490	−	11.8949i	0.165251	−	0.508590i	0.999055	+	0.0434708i	$0.0138415\pi$
$548$		0			0
$549$	12.8867			0.549990
$550$		0			0
$551$	−28.2655			−1.20415
$552$		0			0
$553$	0.315624	−	0.971391i	0.0134217	−	0.0413077i
$554$		0			0
$555$	5.80553	−	4.21797i	0.246431	−	0.179043i
$556$		0			0
$557$	8.46658	+	26.0575i	0.358740	+	1.10409i	0.953809	+	0.300415i	$0.0971250\pi$
$557$	8.46658	+	26.0575i	0.358740	+	1.10409i	−0.595068	+	0.803675i	$0.702875\pi$
$558$		0			0
$559$	−0.519683	−	0.377572i	−0.0219802	−	0.0159696i
$560$		0			0
$561$	−8.17753	+	12.7114i	−0.345255	+	0.536677i
$562$		0			0
$563$	−15.5705	−	11.3126i	−0.656218	−	0.476771i	0.209165	−	0.977880i	$-0.432925\pi$
$563$	−15.5705	−	11.3126i	−0.656218	−	0.476771i	−0.865384	+	0.501110i	$0.832925\pi$
$564$		0			0
$565$	1.23475	+	3.80017i	0.0519463	+	0.159874i
$566$		0			0
$567$	−2.68491	+	1.95070i	−0.112756	+	0.0819218i
$568$		0			0
$569$	7.80335	−	24.0163i	0.327134	−	1.00681i	−0.643335	−	0.765585i	$-0.722450\pi$
$569$	7.80335	−	24.0163i	0.327134	−	1.00681i	0.970468	−	0.241229i	$-0.0775504\pi$
$570$		0			0
$571$	20.8410			0.872168			0.436084	−	0.899906i	$-0.356365\pi$
$571$	20.8410			0.872168			0.436084	+	0.899906i	$0.356365\pi$
$572$		0			0
$573$	−19.7810			−0.826364
$574$		0			0
$575$	−2.59948	+	8.00039i	−0.108406	+	0.333639i
$576$		0			0
$577$	34.3052	−	24.9242i	1.42814	−	1.03761i	0.437785	−	0.899079i	$-0.355763\pi$
$577$	34.3052	−	24.9242i	1.42814	−	1.03761i	0.990359	−	0.138528i	$-0.0442371\pi$
$578$		0			0
$579$	−0.910861	−	2.80334i	−0.0378541	−	0.116503i
$580$		0			0
$581$	−16.0640	−	11.6712i	−0.666447	−	0.484202i
$582$		0			0
$583$	2.51646	+	44.3713i	0.104221	+	1.83767i
$584$		0			0
$585$	2.68172	+	1.94839i	0.110876	+	0.0805559i
$586$		0			0
$587$	8.02963	+	24.7127i	0.331418	+	1.02000i	0.968459	+	0.249171i	$0.0801582\pi$
$587$	8.02963	+	24.7127i	0.331418	+	1.02000i	−0.637041	+	0.770830i	$0.719842\pi$
$588$		0			0
$589$	−47.2919	+	34.3596i	−1.94863	+	1.41576i
$590$		0			0
$591$	−7.43458	+	22.8813i	−0.305818	+	0.941210i
$592$		0			0
$593$	37.6076			1.54436			0.772179	−	0.635405i	$-0.219167\pi$
$593$	37.6076			1.54436			0.772179	+	0.635405i	$0.219167\pi$
$594$		0			0
$595$	−15.1242			−0.620034
$596$		0			0
$597$	4.58441	−	14.1094i	0.187628	−	0.577458i
$598$		0			0
$599$	−31.1022	+	22.5971i	−1.27080	+	0.923292i	−0.999234	−	0.0391278i	$-0.987542\pi$
$599$	−31.1022	+	22.5971i	−1.27080	+	0.923292i	−0.271568	+	0.962419i	$0.587542\pi$
$600$		0			0
$601$	5.39965	+	16.6184i	0.220256	+	0.677879i	0.998739	+	0.0502124i	$0.0159898\pi$
$601$	5.39965	+	16.6184i	0.220256	+	0.677879i	−0.778482	+	0.627666i	$0.784010\pi$
$602$		0			0
$603$	4.60300	+	3.34427i	0.187449	+	0.136189i
$604$		0			0
$605$	4.56022	+	10.0102i	0.185399	+	0.406973i
$606$		0			0
$607$	19.3958	+	14.0919i	0.787252	+	0.571972i	0.907147	−	0.420815i	$-0.138256\pi$
$607$	19.3958	+	14.0919i	0.787252	+	0.571972i	−0.119895	+	0.992787i	$0.538256\pi$
$608$		0			0
$609$	−4.65209	−	14.3177i	−0.188512	−	0.580181i
$610$		0			0
$611$	4.99787	−	3.63116i	0.202192	−	0.146901i
$612$		0			0
$613$	−5.11216	+	15.7336i	−0.206478	+	0.635475i	0.793171	+	0.608999i	$0.208429\pi$
$613$	−5.11216	+	15.7336i	−0.206478	+	0.635475i	−0.999649	+	0.0264761i	$0.991571\pi$
$614$		0			0
$615$	2.44474			0.0985815
$616$		0			0
$617$	−14.5370			−0.585237			−0.292618	−	0.956229i	$-0.594527\pi$
$617$	−14.5370			−0.585237			−0.292618	+	0.956229i	$0.594527\pi$
$618$		0			0
$619$	6.20675	−	19.1024i	0.249470	−	0.767790i	−0.745399	−	0.666619i	$-0.767741\pi$
$619$	6.20675	−	19.1024i	0.249470	−	0.767790i	0.994869	−	0.101171i	$-0.0322591\pi$
$620$		0			0
$621$	−6.80553	+	4.94451i	−0.273097	+	0.198416i
$622$		0			0
$623$	−9.70002	−	29.8536i	−0.388623	−	1.19606i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	1.17017	+	20.6329i	0.0467321	+	0.824001i
$628$		0			0
$629$	26.4572	+	19.2223i	1.05492	+	0.766442i
$630$		0			0
$631$	−11.3809	−	35.0267i	−0.453065	−	1.39439i	−0.873391	−	0.487019i	$-0.838084\pi$
$631$	−11.3809	−	35.0267i	−0.453065	−	1.39439i	0.420326	−	0.907373i	$-0.361916\pi$
$632$		0			0
$633$	−14.5865	+	10.5977i	−0.579760	+	0.421221i
$634$		0			0
$635$	−5.69475	+	17.5266i	−0.225989	+	0.695523i
$636$		0			0
$637$	13.3055			0.527185
$638$		0			0
$639$	−9.17027			−0.362770
$640$		0			0
$641$	9.79242	−	30.1380i	0.386777	−	1.19038i	−0.548405	−	0.836213i	$-0.684765\pi$
$641$	9.79242	−	30.1380i	0.386777	−	1.19038i	0.935183	−	0.354166i	$-0.115235\pi$
$642$		0			0
$643$	−17.1611	+	12.4682i	−0.676766	+	0.491699i	−0.872283	−	0.489001i	$-0.837361\pi$
$643$	−17.1611	+	12.4682i	−0.676766	+	0.491699i	0.195517	+	0.980700i	$0.437361\pi$
$644$		0			0
$645$	0.0598834	+	0.184302i	0.00235791	+	0.00725689i
$646$		0			0
$647$	−22.0756	−	16.0389i	−0.867883	−	0.630554i	0.0621352	−	0.998068i	$-0.480209\pi$
$647$	−22.0756	−	16.0389i	−0.867883	−	0.630554i	−0.930018	+	0.367514i	$0.880209\pi$
$648$		0			0
$649$	11.2143	−	17.4319i	0.440199	−	0.684261i
$650$		0			0
$651$	−25.1882	−	18.3003i	−0.987202	−	0.717244i
$652$		0			0
$653$	6.84709	+	21.0732i	0.267947	+	0.824657i	0.991000	+	0.133864i	$0.0427385\pi$
$653$	6.84709	+	21.0732i	0.267947	+	0.824657i	−0.723052	+	0.690793i	$0.757262\pi$
$654$		0			0
$655$	5.49812	−	3.99462i	0.214829	−	0.156083i
$656$		0			0
$657$	3.53648	−	10.8842i	0.137971	−	0.424632i
$658$		0			0
$659$	−6.39513			−0.249119			−0.124560	−	0.992212i	$-0.539752\pi$
$659$	−6.39513			−0.249119			−0.124560	+	0.992212i	$0.539752\pi$
$660$		0			0
$661$	−2.76291			−0.107465			−0.0537324	−	0.998555i	$-0.517112\pi$
$661$	−2.76291			−0.107465			−0.0537324	+	0.998555i	$0.517112\pi$
$662$		0			0
$663$	−4.66810	+	14.3669i	−0.181294	+	0.557966i
$664$		0			0
$665$	−16.7299	+	12.1550i	−0.648756	+	0.471349i
$666$		0			0
$667$	−11.7918	−	36.2915i	−0.456581	−	1.40521i
$668$		0			0
$669$	−20.5309	−	14.9165i	−0.793769	−	0.576707i
$670$		0			0
$671$	41.3310	+	10.8847i	1.59557	+	0.420198i
$672$		0			0
$673$	4.23501	+	3.07691i	0.163248	+	0.118606i	0.666410	−	0.745586i	$-0.267830\pi$
$673$	4.23501	+	3.07691i	0.163248	+	0.118606i	−0.503162	+	0.864192i	$0.667830\pi$
$674$		0			0
$675$	−0.309017	−	0.951057i	−0.0118941	−	0.0366062i
$676$		0			0
$677$	−3.86783	+	2.81015i	−0.148653	+	0.108003i	−0.659626	−	0.751594i	$-0.729285\pi$
$677$	−3.86783	+	2.81015i	−0.148653	+	0.108003i	0.510973	+	0.859597i	$0.329285\pi$
$678$		0			0
$679$	3.82810	−	11.7817i	0.146909	−	0.452139i
$680$		0			0
$681$	8.46308			0.324306
$682$		0			0
$683$	−27.9820			−1.07070			−0.535351	−	0.844630i	$-0.679821\pi$
$683$	−27.9820			−1.07070			−0.535351	+	0.844630i	$0.679821\pi$
$684$		0			0
$685$	1.73375	−	5.33595i	0.0662433	−	0.203876i
$686$		0			0
$687$	−17.1670	+	12.4725i	−0.654961	+	0.475857i
$688$		0			0
$689$	13.7259	+	42.2441i	0.522917	+	1.60937i
$690$		0			0
$691$	−2.99906	−	2.17895i	−0.114090	−	0.0828911i	0.529277	−	0.848449i	$-0.322463\pi$
$691$	−2.99906	−	2.17895i	−0.114090	−	0.0828911i	−0.643367	+	0.765558i	$0.722463\pi$
$692$		0			0
$693$	−10.2589	+	3.98863i	−0.389703	+	0.151516i
$694$		0			0
$695$	−10.4262	−	7.57510i	−0.395489	−	0.287340i
$696$		0			0
$697$	3.44284	+	10.5960i	0.130407	+	0.401351i
$698$		0			0
$699$	15.5017	−	11.2627i	0.586329	−	0.425993i
$700$		0			0
$701$	−3.00828	+	9.25854i	−0.113621	+	0.349690i	−0.991657	−	0.128905i	$-0.958854\pi$
$701$	−3.00828	+	9.25854i	−0.113621	+	0.349690i	0.878036	+	0.478595i	$0.158854\pi$
$702$		0			0
$703$	44.7143			1.68643
$704$		0			0
$705$	−1.86368			−0.0701901
$706$		0			0
$707$	−6.47322	+	19.9225i	−0.243451	+	0.749264i
$708$		0			0
$709$	−4.11481	+	2.98959i	−0.154535	+	0.112276i	−0.662366	−	0.749181i	$-0.730448\pi$
$709$	−4.11481	+	2.98959i	−0.154535	+	0.112276i	0.507831	+	0.861457i	$0.330448\pi$
$710$		0			0
$711$	0.0951037	+	0.292699i	0.00356667	+	0.0109771i
$712$		0			0
$713$	−63.8453	−	46.3863i	−2.39102	−	1.73718i
$714$		0			0
$715$	6.95532	+	8.51410i	0.260114	+	0.318409i
$716$		0			0
$717$	−18.4337	−	13.3928i	−0.688418	−	0.500165i
$718$		0			0
$719$	3.62178	+	11.1467i	0.135070	+	0.415702i	0.995601	−	0.0936962i	$-0.0298682\pi$
$719$	3.62178	+	11.1467i	0.135070	+	0.415702i	−0.860531	+	0.509398i	$0.829868\pi$
$720$		0			0
$721$	−46.9940	+	34.1431i	−1.75015	+	1.27156i
$722$		0			0
$723$	−4.35771	+	13.4117i	−0.162065	+	0.498785i
$724$		0			0
$725$	4.53622			0.168471
$726$		0			0
$727$	−45.1243			−1.67357			−0.836785	−	0.547532i	$-0.815567\pi$
$727$	−45.1243			−1.67357			−0.836785	+	0.547532i	$0.815567\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−0.714469	+	0.519092i	−0.0264256	+	0.0191993i
$732$		0			0
$733$	−3.14549	−	9.68082i	−0.116181	−	0.357569i	0.876010	−	0.482292i	$-0.160196\pi$
$733$	−3.14549	−	9.68082i	−0.116181	−	0.357569i	−0.992192	+	0.124723i	$0.960196\pi$
$734$		0			0
$735$	−3.24738	−	2.35936i	−0.119782	−	0.0870264i
$736$		0			0
$737$	11.9383	+	14.6139i	0.439754	+	0.538309i
$738$		0			0
$739$	−25.2780	−	18.3656i	−0.929868	−	0.675589i	0.0160925	−	0.999871i	$-0.494877\pi$
$739$	−25.2780	−	18.3656i	−0.929868	−	0.675589i	−0.945961	+	0.324282i	$0.894877\pi$
$740$		0			0
$741$	6.38265	+	19.6438i	0.234473	+	0.721632i
$742$		0			0
$743$	12.8074	−	9.30511i	0.469857	−	0.341371i	−0.327528	−	0.944841i	$-0.606216\pi$
$743$	12.8074	−	9.30511i	0.469857	−	0.341371i	0.797386	+	0.603470i	$0.206216\pi$
$744$		0			0
$745$	−1.55643	+	4.79021i	−0.0570234	+	0.175500i
$746$		0			0
$747$	5.98307			0.218909
$748$		0			0
$749$	35.1820			1.28552
$750$		0			0
$751$	12.1666	−	37.4448i	0.443964	−	1.36638i	−0.439651	−	0.898169i	$-0.644898\pi$
$751$	12.1666	−	37.4448i	0.443964	−	1.36638i	0.883616	−	0.468213i	$-0.155102\pi$
$752$		0			0
$753$	16.0549	−	11.6645i	0.585072	−	0.425080i
$754$		0			0
$755$	−6.99928	−	21.5416i	−0.254730	−	0.783978i
$756$		0			0
$757$	0.591946	+	0.430074i	0.0215147	+	0.0156313i	0.598491	−	0.801130i	$-0.295767\pi$
$757$	0.591946	+	0.430074i	0.0215147	+	0.0156313i	−0.576976	+	0.816761i	$0.695767\pi$
$758$		0			0
$759$	−26.0035	+	10.1101i	−0.943869	+	0.366974i
$760$		0			0
$761$	8.23440	+	5.98264i	0.298497	+	0.216871i	0.726945	−	0.686696i	$-0.240940\pi$
$761$	8.23440	+	5.98264i	0.298497	+	0.216871i	−0.428448	+	0.903566i	$0.640940\pi$
$762$		0			0
$763$	−1.64537	−	5.06393i	−0.0595664	−	0.183326i
$764$		0			0
$765$	3.68688	−	2.67868i	0.133299	−	0.0968477i
$766$		0			0
$767$	6.40162	−	19.7022i	0.231149	−	0.711404i
$768$		0			0
$769$	−34.9604			−1.26071			−0.630353	−	0.776309i	$-0.717090\pi$
$769$	−34.9604			−1.26071			−0.630353	+	0.776309i	$0.717090\pi$
$770$		0			0
$771$	24.7548			0.891523
$772$		0			0
$773$	−3.46264	+	10.6569i	−0.124542	+	0.383302i	−0.993817	−	0.111027i	$-0.964586\pi$
$773$	−3.46264	+	10.6569i	−0.124542	+	0.383302i	0.869275	+	0.494329i	$0.164586\pi$
$774$		0			0
$775$	7.58969	−	5.51423i	0.272630	−	0.198077i
$776$		0			0
$777$	7.35935	+	22.6497i	0.264015	+	0.812555i
$778$		0			0
$779$	12.3240	+	8.95394i	0.441555	+	0.320808i
$780$		0			0
$781$	−29.4115	−	7.74561i	−1.05243	−	0.277160i
$782$		0			0
$783$	3.66988	+	2.66632i	0.131151	+	0.0952865i
$784$		0			0
$785$	−2.21777	−	6.82560i	−0.0791556	−	0.243616i
$786$		0			0
$787$	4.10201	−	2.98028i	0.146221	−	0.106236i	−0.512270	−	0.858825i	$-0.671195\pi$
$787$	4.10201	−	2.98028i	0.146221	−	0.106236i	0.658491	+	0.752589i	$0.271195\pi$
$788$		0			0
$789$	−3.15371	+	9.70612i	−0.112275	+	0.345547i
$790$		0			0
$791$	−13.2608			−0.471499
$792$		0			0
$793$	42.7167			1.51691
$794$		0			0
$795$	4.14082	−	12.7441i	0.146860	−	0.451987i
$796$		0			0
$797$	−36.6934	+	26.6593i	−1.29975	+	0.944322i	−0.999953	−	0.00968167i	$-0.996918\pi$
$797$	−36.6934	+	26.6593i	−1.29975	+	0.944322i	−0.299795	+	0.954004i	$0.596918\pi$
$798$		0			0
$799$	−2.62455	−	8.07753i	−0.0928498	−	0.285762i
$800$		0			0
$801$	7.65201	+	5.55951i	0.270370	+	0.196436i
$802$		0			0
$803$	20.5357	−	31.9214i	0.724689	−	1.12648i
$804$		0			0
$805$	−22.5858	−	16.4095i	−0.796043	−	0.578359i
$806$		0			0
$807$	5.65297	+	17.3980i	0.198994	+	0.612440i
$808$		0			0
$809$	3.86553	−	2.80847i	0.135905	−	0.0987405i	−0.517756	−	0.855528i	$-0.673232\pi$
$809$	3.86553	−	2.80847i	0.135905	−	0.0987405i	0.653660	+	0.756788i	$0.273232\pi$
$810$		0			0
$811$	10.1252	−	31.1620i	0.355542	−	1.09425i	−0.600152	−	0.799886i	$-0.704893\pi$
$811$	10.1252	−	31.1620i	0.355542	−	1.09425i	0.955694	−	0.294361i	$-0.0951067\pi$
$812$		0			0
$813$	−7.33237			−0.257158
$814$		0			0
$815$	12.6574			0.443368
$816$		0			0
$817$	−0.373137	+	1.14840i	−0.0130544	+	0.0401774i
$818$		0			0
$819$	−8.89993	+	6.46618i	−0.310989	+	0.225946i
$820$		0			0
$821$	5.37278	+	16.5357i	0.187511	+	0.577101i	0.999983	−	0.00590059i	$-0.00187823\pi$
$821$	5.37278	+	16.5357i	0.187511	+	0.577101i	−0.812471	+	0.583001i	$0.801878\pi$
$822$		0			0
$823$	36.3274	+	26.3934i	1.26629	+	0.920015i	0.999048	−	0.0436140i	$-0.0138872\pi$
$823$	36.3274	+	26.3934i	1.26629	+	0.920015i	0.267244	+	0.963629i	$0.413887\pi$
$824$		0			0
$825$	−0.187796	−	3.31130i	−0.00653822	−	0.115285i
$826$		0			0
$827$	−14.3917	−	10.4561i	−0.500447	−	0.363596i	0.308741	−	0.951146i	$-0.400092\pi$
$827$	−14.3917	−	10.4561i	−0.500447	−	0.363596i	−0.809188	+	0.587550i	$0.800092\pi$
$828$		0			0
$829$	−7.17793	−	22.0914i	−0.249300	−	0.767266i	−0.994899	−	0.100872i	$-0.967837\pi$
$829$	−7.17793	−	22.0914i	−0.249300	−	0.767266i	0.745599	−	0.666394i	$-0.232163\pi$
$830$		0			0
$831$	−10.2895	+	7.47577i	−0.356939	+	0.259332i
$832$		0			0
$833$	5.65275	−	17.3974i	0.195856	−	0.602783i
$834$		0			0
$835$	5.83475			0.201920
$836$		0			0
$837$	9.38138			0.324268
$838$		0			0
$839$	11.8705	−	36.5336i	0.409814	−	1.26128i	−0.506993	−	0.861950i	$-0.669243\pi$
$839$	11.8705	−	36.5336i	0.409814	−	1.26128i	0.916808	−	0.399329i	$-0.130757\pi$
$840$		0			0
$841$	6.81414	−	4.95076i	0.234970	−	0.170716i
$842$		0			0
$843$	0.0983408	+	0.302662i	0.00338704	+	0.0104242i
$844$		0			0
$845$	−1.62786	−	1.18271i	−0.0560000	−	0.0406864i
$846$		0			0
$847$	−36.2720	+	4.12751i	−1.24632	+	0.141823i
$848$		0			0
$849$	−0.893391	−	0.649086i	−0.0306611	−	0.0222766i
$850$		0			0
$851$	18.6540	+	57.4111i	0.639450	+	1.96803i
$852$		0			0
$853$	31.7137	−	23.0413i	1.08585	−	0.788920i	0.107160	−	0.994242i	$-0.465824\pi$
$853$	31.7137	−	23.0413i	1.08585	−	0.788920i	0.978694	+	0.205322i	$0.0658242\pi$
$854$		0			0
$855$	1.92550	−	5.92609i	0.0658509	−	0.202668i
$856$		0			0
$857$	−41.8087			−1.42816			−0.714079	−	0.700065i	$-0.753154\pi$
$857$	−41.8087			−1.42816			−0.714079	+	0.700065i	$0.753154\pi$
$858$		0			0
$859$	−39.8824			−1.36077			−0.680385	−	0.732855i	$-0.738187\pi$
$859$	−39.8824			−1.36077			−0.680385	+	0.732855i	$0.738187\pi$
$860$		0			0
$861$	−2.50719	+	7.71635i	−0.0854449	+	0.262972i
$862$		0			0
$863$	10.3681	−	7.53285i	0.352934	−	0.256421i	−0.397165	−	0.917747i	$-0.630006\pi$
$863$	10.3681	−	7.53285i	0.352934	−	0.256421i	0.750099	+	0.661326i	$0.230006\pi$
$864$		0			0
$865$	−3.78005	−	11.6338i	−0.128526	−	0.395561i
$866$		0			0
$867$	3.04870	+	2.21501i	0.103539	+	0.0752256i
$868$		0			0
$869$	0.0577965	+	1.01909i	0.00196061	+	0.0345704i
$870$		0			0
$871$	15.2580	+	11.0856i	0.516997	+	0.375621i
$872$		0			0
$873$	1.15348	+	3.55005i	0.0390395	+	0.120151i
$874$		0			0
$875$	2.68491	−	1.95070i	0.0907666	−	0.0659458i
$876$		0			0
$877$	−12.4771	+	38.4005i	−0.421321	+	1.29669i	0.485153	+	0.874429i	$0.338764\pi$
$877$	−12.4771	+	38.4005i	−0.421321	+	1.29669i	−0.906474	+	0.422262i	$0.861236\pi$
$878$		0			0
$879$	−25.8600			−0.872237
$880$		0			0
$881$	−29.7965			−1.00387			−0.501936	−	0.864905i	$-0.667379\pi$
$881$	−29.7965			−1.00387			−0.501936	+	0.864905i	$0.667379\pi$
$882$		0			0
$883$	3.35039	−	10.3114i	0.112750	−	0.347007i	−0.878721	−	0.477335i	$-0.841603\pi$
$883$	3.35039	−	10.3114i	0.112750	−	0.347007i	0.991471	+	0.130327i	$0.0416029\pi$
$884$		0			0
$885$	−5.05602	+	3.67341i	−0.169956	+	0.123480i
$886$		0			0
$887$	2.78420	+	8.56888i	0.0934842	+	0.287715i	0.986856	−	0.161604i	$-0.0516667\pi$
$887$	2.78420	+	8.56888i	0.0934842	+	0.287715i	−0.893371	+	0.449319i	$0.851667\pi$
$888$		0			0
$889$	−49.4791	−	35.9487i	−1.65948	−	1.20568i
$890$		0			0
$891$	1.79441	−	2.78928i	0.0601148	−	0.0934446i
$892$		0			0
$893$	−9.39486	−	6.82577i	−0.314387	−	0.228416i
$894$		0			0
$895$	−4.56308	−	14.0437i	−0.152527	−	0.469429i
$896$		0			0
$897$	−22.5589	+	16.3900i	−0.753221	+	0.547247i
$898$		0			0
$899$	−13.1505	+	40.4731i	−0.438594	+	1.34985i
$900$		0			0
$901$	61.0668			2.03443
$902$		0			0
$903$	−0.643126			−0.0214019
$904$		0			0
$905$	0.901627	−	2.77492i	0.0299711	−	0.0922415i
$906$		0			0
$907$	24.6205	−	17.8878i	0.817510	−	0.593956i	−0.0984882	−	0.995138i	$-0.531401\pi$
$907$	24.6205	−	17.8878i	0.817510	−	0.593956i	0.915998	+	0.401182i	$0.131401\pi$
$908$		0			0
$909$	−1.95051	−	6.00305i	−0.0646944	−	0.199109i
$910$		0			0
$911$	−2.71744	−	1.97434i	−0.0900328	−	0.0654127i	0.541858	−	0.840470i	$-0.317721\pi$
$911$	−2.71744	−	1.97434i	−0.0900328	−	0.0654127i	−0.631891	+	0.775057i	$0.717721\pi$
$912$		0			0
$913$	19.1893	+	5.05357i	0.635073	+	0.167249i
$914$		0			0
$915$	−10.4255	−	7.57460i	−0.344658	−	0.250408i
$916$		0			0
$917$	6.96965	+	21.4504i	0.230158	+	0.708354i
$918$		0			0
$919$	−35.0472	+	25.4633i	−1.15610	+	0.839957i	−0.989280	−	0.146030i	$-0.953350\pi$
$919$	−35.0472	+	25.4633i	−1.15610	+	0.839957i	−0.166821	+	0.985987i	$0.553350\pi$
$920$		0			0
$921$	−3.47711	+	10.7014i	−0.114575	+	0.352625i
$922$		0			0
$923$	−30.3975			−1.00055
$924$		0			0
$925$	−7.17604			−0.235947
$926$		0			0
$927$	5.40872	−	16.6463i	0.177646	−	0.546737i
$928$		0			0
$929$	−1.23544	+	0.897598i	−0.0405334	+	0.0294492i	−0.607867	−	0.794038i	$-0.707975\pi$
$929$	−1.23544	+	0.897598i	−0.0405334	+	0.0294492i	0.567334	+	0.823488i	$0.307975\pi$
$930$		0			0
$931$	−7.72895	−	23.7873i	−0.253306	−	0.779596i
$932$		0			0
$933$	−3.96620	−	2.88161i	−0.129847	−	0.0943397i
$934$		0			0
$935$	14.0873	−	5.47713i	0.460706	−	0.179121i
$936$		0			0
$937$	17.8570	+	12.9739i	0.583364	+	0.423839i	0.839935	−	0.542687i	$-0.182593\pi$
$937$	17.8570	+	12.9739i	0.583364	+	0.423839i	−0.256571	+	0.966525i	$0.582593\pi$
$938$		0			0
$939$	−3.34235	−	10.2867i	−0.109073	−	0.335694i
$940$		0			0
$941$	−29.1974	+	21.2132i	−0.951808	+	0.691529i	−0.951234	−	0.308471i	$-0.900183\pi$
$941$	−29.1974	+	21.2132i	−0.951808	+	0.691529i	−0.000574177		1.00000i	$0.500183\pi$
$942$		0			0
$943$	−6.35507	+	19.5589i	−0.206949	+	0.636925i
$944$		0			0
$945$	3.31873			0.107958
$946$		0			0
$947$	−12.5481			−0.407757			−0.203879	−	0.978996i	$-0.565355\pi$
$947$	−12.5481			−0.407757			−0.203879	+	0.978996i	$0.565355\pi$
$948$		0			0
$949$	11.7227	−	36.0787i	0.380535	−	1.17117i
$950$		0			0
$951$	−3.16572	+	2.30003i	−0.102656	+	0.0745837i
$952$		0			0
$953$	−0.111072	−	0.341845i	−0.00359798	−	0.0110735i	0.949241	−	0.314548i	$-0.101853\pi$
$953$	−0.111072	−	0.341845i	−0.00359798	−	0.0110735i	−0.952839	+	0.303475i	$0.901853\pi$
$954$		0			0
$955$	16.0032	+	11.6270i	0.517851	+	0.376241i
$956$		0			0
$957$	9.51819	+	11.6513i	0.307679	+	0.376635i
$958$		0			0
$959$	15.0638	+	10.9445i	0.486436	+	0.353417i
$960$		0			0
$961$	17.6171	+	54.2199i	0.568294	+	1.74903i
$962$		0			0
$963$	−8.57641	+	6.23112i	−0.276371	+	0.200795i
$964$		0			0
$965$	−0.910861	+	2.80334i	−0.0293216	+	0.0902427i
$966$		0			0
$967$	−41.4974			−1.33447			−0.667233	−	0.744849i	$-0.732521\pi$
$967$	−41.4974			−1.33447			−0.667233	+	0.744849i	$0.732521\pi$
$968$		0			0
$969$	28.3964			0.912225
$970$		0			0
$971$	−5.46346	+	16.8148i	−0.175331	+	0.539613i	−0.999648	−	0.0265149i	$-0.991559\pi$
$971$	−5.46346	+	16.8148i	−0.175331	+	0.539613i	0.824318	+	0.566128i	$0.191559\pi$
$972$		0			0
$973$	34.6019	−	25.1397i	1.10928	−	0.805942i
$974$		0			0
$975$	−1.02433	−	3.15256i	−0.0328047	−	0.100963i
$976$		0			0
$977$	12.0634	+	8.76459i	0.385943	+	0.280404i	0.763791	−	0.645464i	$-0.223336\pi$
$977$	12.0634	+	8.76459i	0.385943	+	0.280404i	−0.377848	+	0.925868i	$0.623336\pi$
$978$		0			0
$979$	19.8462	+	24.2941i	0.634289	+	0.776442i
$980$		0			0
$981$	1.29798	+	0.943034i	0.0414412	+	0.0301088i
$982$		0			0
$983$	−1.96553	−	6.04927i	−0.0626905	−	0.192942i	0.914806	−	0.403894i	$-0.132344\pi$
$983$	−1.96553	−	6.04927i	−0.0626905	−	0.192942i	−0.977496	+	0.210952i	$0.932344\pi$
$984$		0			0
$985$	19.4640	−	14.1414i	0.620174	−	0.450583i
$986$		0			0
$987$	1.91128	−	5.88233i	0.0608368	−	0.187237i
$988$		0			0
$989$	−1.63015			−0.0518359
$990$		0			0
$991$	30.1509			0.957774			0.478887	−	0.877877i	$-0.341040\pi$
$991$	30.1509			0.957774			0.478887	+	0.877877i	$0.341040\pi$
$992$		0			0
$993$	−4.63106	+	14.2529i	−0.146962	+	0.452303i
$994$		0			0
$995$	−12.0022	+	8.72007i	−0.380494	+	0.276445i
$996$		0			0
$997$	−7.15191	−	22.0113i	−0.226503	−	0.697105i	−0.998136	−	0.0610364i	$-0.980559\pi$
$997$	−7.15191	−	22.0113i	−0.226503	−	0.697105i	0.771632	−	0.636069i	$-0.219441\pi$
$998$		0			0
$999$	−5.80553	−	4.21797i	−0.183679	−	0.133451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.h.961.3	✓	12
11.3	even	5	inner	1320.2.bw.h.1081.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.h.961.3	✓	12	1.1	even	1	trivial
1320.2.bw.h.1081.3	yes	12	11.3	even	5	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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(0.809017 - 0.587785i) q^{5} +(1.02554 + 3.15630i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{3} +(0.809017 - 0.587785i) q^{5} +(1.02554 + 3.15630i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.09827 - 2.56852i) q^{11} +(-2.68172 - 1.94839i) q^{13} +(0.309017 + 0.951057i) q^{15} +(-3.68688 + 2.67868i) q^{17} +(-1.92550 + 5.92609i) q^{19} -3.31873 q^{21} -8.41210 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.809017 - 0.587785i) q^{27} +(1.40177 + 4.31420i) q^{29} +(7.58969 + 5.51423i) q^{31} +(3.09120 - 1.20185i) q^{33} +(2.68491 + 1.95070i) q^{35} +(-2.21752 - 6.82482i) q^{37} +(2.68172 - 1.94839i) q^{39} +(0.755467 - 2.32509i) q^{41} +0.193787 q^{43} -1.00000 q^{45} +(-0.575908 + 1.77246i) q^{47} +(-3.24738 + 2.35936i) q^{49} +(-1.40826 - 4.33419i) q^{51} +(-10.8408 - 7.87630i) q^{53} +(-3.20727 - 0.844644i) q^{55} +(-5.04104 - 3.66253i) q^{57} +(1.93123 + 5.94371i) q^{59} +(-10.4255 + 7.57460i) q^{61} +(1.02554 - 3.15630i) q^{63} -3.31479 q^{65} -5.68962 q^{67} +(2.59948 - 8.00039i) q^{69} +(7.41890 - 5.39015i) q^{71} +(3.53648 + 10.8842i) q^{73} +(0.809017 + 0.587785i) q^{75} +(5.95515 - 9.25689i) q^{77} +(-0.248985 - 0.180898i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-4.84040 + 3.51676i) q^{83} +(-1.40826 + 4.33419i) q^{85} -4.53622 q^{87} -9.45841 q^{89} +(3.39947 - 10.4625i) q^{91} +(-7.58969 + 5.51423i) q^{93} +(1.92550 + 5.92609i) q^{95} +(-3.01986 - 2.19405i) q^{97} +(0.187796 + 3.31130i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 3 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 3 * q^5 + 5 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} + 3 q^{5} + 5 q^{7} - 3 q^{9} + 6 q^{11} - 2 q^{13} - 3 q^{15} - 13 q^{17} - 12 q^{23} - 3 q^{25} + 3 q^{27} - 15 q^{29} - 3 q^{31} + 9 q^{33} + 5 q^{35} + 11 q^{37} + 2 q^{39} + 13 q^{41} + 10 q^{43} - 12 q^{45} + 14 q^{47} + 12 q^{49} - 12 q^{51} - 21 q^{53} - q^{55} + 5 q^{57} - 31 q^{59} - 39 q^{61} + 5 q^{63} - 8 q^{65} - 40 q^{67} + 7 q^{69} - q^{71} + 9 q^{73} + 3 q^{75} + 79 q^{77} + 39 q^{79} - 3 q^{81} - 17 q^{83} - 12 q^{85} - 40 q^{87} + 36 q^{89} + 17 q^{91} + 3 q^{93} + 3 q^{97} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 + 3 * q^5 + 5 * q^7 - 3 * q^9 + 6 * q^11 - 2 * q^13 - 3 * q^15 - 13 * q^17 - 12 * q^23 - 3 * q^25 + 3 * q^27 - 15 * q^29 - 3 * q^31 + 9 * q^33 + 5 * q^35 + 11 * q^37 + 2 * q^39 + 13 * q^41 + 10 * q^43 - 12 * q^45 + 14 * q^47 + 12 * q^49 - 12 * q^51 - 21 * q^53 - q^55 + 5 * q^57 - 31 * q^59 - 39 * q^61 + 5 * q^63 - 8 * q^65 - 40 * q^67 + 7 * q^69 - q^71 + 9 * q^73 + 3 * q^75 + 79 * q^77 + 39 * q^79 - 3 * q^81 - 17 * q^83 - 12 * q^85 - 40 * q^87 + 36 * q^89 + 17 * q^91 + 3 * q^93 + 3 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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