LMFDB - Embedded newform 528.2.bn.a.305.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,2,Mod(17,528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))

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

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

chi := DirichletCharacter("528.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	528.bn (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.21610122672$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.185640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			305.2
Root			$-1.52536 + 0.820539i$ of defining polynomial
Character	$\chi$	$=$	528.305
Dual form			528.2.bn.a.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 1.70426i) q^{3} +(-1.56076 + 2.14820i) q^{5} +(-1.56076 - 0.507121i) q^{7} +(-2.80902 + 1.05329i) q^{9} +O(q^{10})$	\(q+(0.309017 + 1.70426i) q^{3} +(-1.56076 + 2.14820i) q^{5} +(-1.56076 - 0.507121i) q^{7} +(-2.80902 + 1.05329i) q^{9} +(-2.77710 - 1.81321i) q^{11} +(0.885446 + 1.21871i) q^{13} +(-4.14339 - 1.99611i) q^{15} +(-5.49344 - 3.99122i) q^{17} +(5.21982 - 1.69602i) q^{19} +(0.381966 - 2.81665i) q^{21} +4.78856i q^{23} +(-0.633706 - 1.95035i) q^{25} +(-2.66312 - 4.46182i) q^{27} +(-0.143392 + 0.441315i) q^{29} +(-4.20067 + 3.05196i) q^{31} +(2.23201 - 5.29321i) q^{33} +(3.52536 - 2.56132i) q^{35} +(0.311168 - 0.957676i) q^{37} +(-1.80339 + 1.88563i) q^{39} +(0.486479 + 1.49723i) q^{41} +3.42500i q^{43} +(2.12151 - 7.67826i) q^{45} +(-9.52285 + 3.09416i) q^{47} +(-3.48433 - 2.53151i) q^{49} +(5.10451 - 10.5956i) q^{51} +(5.77495 + 7.94853i) q^{53} +(8.22951 - 3.13578i) q^{55} +(4.50348 + 8.37184i) q^{57} +(5.81307 + 1.88878i) q^{59} +(-8.17223 + 11.2481i) q^{61} +(4.91834 - 0.219422i) q^{63} -4.00000 q^{65} -11.7972 q^{67} +(-8.16097 + 1.47975i) q^{69} +(-0.527864 + 0.726543i) q^{71} +(-4.40076 - 1.42989i) q^{73} +(3.12808 - 1.68269i) q^{75} +(3.41486 + 4.23830i) q^{77} +(1.86762 + 2.57056i) q^{79} +(6.78115 - 5.91743i) q^{81} +(1.51625 + 1.10162i) q^{83} +(17.1478 - 5.57167i) q^{85} +(-0.796426 - 0.108003i) q^{87} +12.8092i q^{89} +(-0.763932 - 2.35114i) q^{91} +(-6.49942 - 6.21593i) q^{93} +(-4.50348 + 13.8603i) q^{95} +(2.90517 - 2.11073i) q^{97} +(9.71075 + 2.16824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 18 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 18 * q^9	$ 8 q - 2 q^{3} - 18 q^{9} + q^{11} - 9 q^{15} - 10 q^{17} + 15 q^{19} + 12 q^{21} - 6 q^{25} + 10 q^{27} + 23 q^{29} - 13 q^{31} + 17 q^{33} + 13 q^{35} + 6 q^{37} - 18 q^{39} + 2 q^{41} - 8 q^{45} - 10 q^{47} - 18 q^{49} + 30 q^{51} + 15 q^{53} + 14 q^{55} + 20 q^{57} + 25 q^{59} - 10 q^{61} - 16 q^{63} - 32 q^{65} + 2 q^{67} - 26 q^{69} - 40 q^{71} + 5 q^{73} + 34 q^{75} - 12 q^{77} - 10 q^{79} + 14 q^{81} + 21 q^{83} + 30 q^{85} - 42 q^{87} - 24 q^{91} - 53 q^{93} - 20 q^{95} + 9 q^{97} - 34 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 18 * q^9 + q^11 - 9 * q^15 - 10 * q^17 + 15 * q^19 + 12 * q^21 - 6 * q^25 + 10 * q^27 + 23 * q^29 - 13 * q^31 + 17 * q^33 + 13 * q^35 + 6 * q^37 - 18 * q^39 + 2 * q^41 - 8 * q^45 - 10 * q^47 - 18 * q^49 + 30 * q^51 + 15 * q^53 + 14 * q^55 + 20 * q^57 + 25 * q^59 - 10 * q^61 - 16 * q^63 - 32 * q^65 + 2 * q^67 - 26 * q^69 - 40 * q^71 + 5 * q^73 + 34 * q^75 - 12 * q^77 - 10 * q^79 + 14 * q^81 + 21 * q^83 + 30 * q^85 - 42 * q^87 - 24 * q^91 - 53 * q^93 - 20 * q^95 + 9 * q^97 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.309017	+	1.70426i	0.178411	+	0.983956i
$3$	0.309017	+	1.70426i	0.178411	+	0.983956i
$4$		0			0
$5$	−1.56076	+	2.14820i	−0.697992	+	0.960703i	0.301981	+	0.953314i	$0.402352\pi$
$5$	−1.56076	+	2.14820i	−0.697992	+	0.960703i	−0.999973	+	0.00738926i	$0.997648\pi$
$6$		0			0
$7$	−1.56076	−	0.507121i	−0.589911	−	0.191674i	−0.00117514	−	0.999999i	$-0.500374\pi$
$7$	−1.56076	−	0.507121i	−0.589911	−	0.191674i	−0.588736	+	0.808326i	$0.700374\pi$
$8$		0			0
$9$	−2.80902	+	1.05329i	−0.936339	+	0.351097i
$10$		0			0
$11$	−2.77710	−	1.81321i	−0.837327	−	0.546703i
$11$	−2.77710	−	1.81321i	−0.837327	−	0.546703i
$12$		0			0
$13$	0.885446	+	1.21871i	0.245579	+	0.338010i	0.913957	−	0.405812i	$-0.133011\pi$
$13$	0.885446	+	1.21871i	0.245579	+	0.338010i	−0.668378	+	0.743822i	$0.733011\pi$
$14$		0			0
$15$	−4.14339	−	1.99611i	−1.06982	−	0.515393i
$16$		0			0
$17$	−5.49344	−	3.99122i	−1.33235	−	0.968012i	−0.999688	−	0.0249677i	$-0.992052\pi$
$17$	−5.49344	−	3.99122i	−1.33235	−	0.968012i	−0.332666	−	0.943045i	$-0.607948\pi$
$18$		0			0
$19$	5.21982	−	1.69602i	1.19751	−	0.389094i	0.358665	−	0.933466i	$-0.383232\pi$
$19$	5.21982	−	1.69602i	1.19751	−	0.389094i	0.838844	+	0.544372i	$0.183232\pi$
$20$		0			0
$21$	0.381966	−	2.81665i	0.0833518	−	0.614643i
$22$		0			0
$23$			4.78856i			0.998485i	0.866462	+	0.499242i	$0.166388\pi$
$23$			4.78856i			0.998485i	−0.866462	+	0.499242i	$0.833612\pi$
$24$		0			0
$25$	−0.633706	−	1.95035i	−0.126741	−	0.390069i
$26$		0			0
$27$	−2.66312	−	4.46182i	−0.512517	−	0.858677i
$28$		0			0
$29$	−0.143392	+	0.441315i	−0.0266272	+	0.0819501i	−0.963487	−	0.267755i	$-0.913718\pi$
$29$	−0.143392	+	0.441315i	−0.0266272	+	0.0819501i	0.936860	+	0.349705i	$0.113718\pi$
$30$		0			0
$31$	−4.20067	+	3.05196i	−0.754462	+	0.548149i	−0.897207	−	0.441611i	$-0.854407\pi$
$31$	−4.20067	+	3.05196i	−0.754462	+	0.548149i	0.142744	+	0.989760i	$0.454407\pi$
$32$		0			0
$33$	2.23201	−	5.29321i	0.388544	−	0.921430i
$34$		0			0
$35$	3.52536	−	2.56132i	0.595894	−	0.432943i
$36$		0			0
$37$	0.311168	−	0.957676i	0.0511557	−	0.157441i	−0.922215	−	0.386677i	$-0.873623\pi$
$37$	0.311168	−	0.957676i	0.0511557	−	0.157441i	0.973371	+	0.229236i	$0.0736228\pi$
$38$		0			0
$39$	−1.80339	+	1.88563i	−0.288773	+	0.301943i
$40$		0			0
$41$	0.486479	+	1.49723i	0.0759752	+	0.233828i	0.981831	−	0.189759i	$-0.0607708\pi$
$41$	0.486479	+	1.49723i	0.0759752	+	0.233828i	−0.905855	+	0.423587i	$0.860771\pi$
$42$		0			0
$43$			3.42500i			0.522308i	0.965297	+	0.261154i	$0.0841030\pi$
$43$			3.42500i			0.522308i	−0.965297	+	0.261154i	$0.915897\pi$
$44$		0			0
$45$	2.12151	−	7.67826i	0.316257	−	1.14461i
$46$		0			0
$47$	−9.52285	+	3.09416i	−1.38905	+	0.451330i	−0.905634	−	0.424060i	$-0.860604\pi$
$47$	−9.52285	+	3.09416i	−1.38905	+	0.451330i	−0.483417	+	0.875390i	$0.660604\pi$
$48$		0			0
$49$	−3.48433	−	2.53151i	−0.497761	−	0.361645i
$50$		0			0
$51$	5.10451	−	10.5956i	0.714775	−	1.48368i
$52$		0			0
$53$	5.77495	+	7.94853i	0.793250	+	1.09181i	0.993696	+	0.112110i	$0.0357609\pi$
$53$	5.77495	+	7.94853i	0.793250	+	1.09181i	−0.200446	+	0.979705i	$0.564239\pi$
$54$		0			0
$55$	8.22951	−	3.13578i	1.10967	−	0.422828i
$56$		0			0
$57$	4.50348	+	8.37184i	0.596500	+	1.10888i
$58$		0			0
$59$	5.81307	+	1.88878i	0.756798	+	0.245898i	0.661904	−	0.749589i	$-0.269749\pi$
$59$	5.81307	+	1.88878i	0.756798	+	0.245898i	0.0948939	+	0.995487i	$0.469749\pi$
$60$		0			0
$61$	−8.17223	+	11.2481i	−1.04635	+	1.44017i	−0.154413	+	0.988006i	$0.549349\pi$
$61$	−8.17223	+	11.2481i	−1.04635	+	1.44017i	−0.891934	+	0.452166i	$0.850651\pi$
$62$		0			0
$63$	4.91834	−	0.219422i	0.619652	−	0.0276446i
$64$		0			0
$65$	−4.00000			−0.496139
$66$		0			0
$67$	−11.7972			−1.44126			−0.720630	−	0.693320i	$-0.756147\pi$
$67$	−11.7972			−1.44126			−0.720630	+	0.693320i	$0.756147\pi$
$68$		0			0
$69$	−8.16097	+	1.47975i	−0.982465	+	0.178141i
$70$		0			0
$71$	−0.527864	+	0.726543i	−0.0626459	+	0.0862247i	−0.839190	−	0.543838i	$-0.816971\pi$
$71$	−0.527864	+	0.726543i	−0.0626459	+	0.0862247i	0.776544	+	0.630062i	$0.216971\pi$
$72$		0			0
$73$	−4.40076	−	1.42989i	−0.515070	−	0.167356i	0.0399366	−	0.999202i	$-0.487284\pi$
$73$	−4.40076	−	1.42989i	−0.515070	−	0.167356i	−0.555007	+	0.831846i	$0.687284\pi$
$74$		0			0
$75$	3.12808	−	1.68269i	0.361199	−	0.194300i
$76$		0			0
$77$	3.41486	+	4.23830i	0.389159	+	0.482999i
$78$		0			0
$79$	1.86762	+	2.57056i	0.210124	+	0.289211i	0.901051	−	0.433714i	$-0.142797\pi$
$79$	1.86762	+	2.57056i	0.210124	+	0.289211i	−0.690927	+	0.722925i	$0.742797\pi$
$80$		0			0
$81$	6.78115	−	5.91743i	0.753461	−	0.657492i
$82$		0			0
$83$	1.51625	+	1.10162i	0.166430	+	0.120918i	0.667882	−	0.744267i	$-0.267201\pi$
$83$	1.51625	+	1.10162i	0.166430	+	0.120918i	−0.501453	+	0.865185i	$0.667201\pi$
$84$		0			0
$85$	17.1478	−	5.57167i	1.85994	−	0.604333i
$86$		0			0
$87$	−0.796426	−	0.108003i	−0.0853859	−	0.0115792i
$88$		0			0
$89$			12.8092i			1.35777i	0.734244	+	0.678886i	$0.237537\pi$
$89$			12.8092i			1.35777i	−0.734244	+	0.678886i	$0.762463\pi$
$90$		0			0
$91$	−0.763932	−	2.35114i	−0.0800818	−	0.246467i
$92$		0			0
$93$	−6.49942	−	6.21593i	−0.673959	−	0.644562i
$94$		0			0
$95$	−4.50348	+	13.8603i	−0.462047	+	1.42204i
$96$		0			0
$97$	2.90517	−	2.11073i	0.294976	−	0.214312i	−0.430447	−	0.902616i	$-0.641644\pi$
$97$	2.90517	−	2.11073i	0.294976	−	0.214312i	0.725423	+	0.688303i	$0.241644\pi$
$98$		0			0
$99$	9.71075	+	2.16824i	0.975967	+	0.217916i
$100$		0			0
$101$	9.84754	−	7.15466i	0.979867	−	0.711915i	0.0221881	−	0.999754i	$-0.492937\pi$
$101$	9.84754	−	7.15466i	0.979867	−	0.711915i	0.957679	+	0.287839i	$0.0929367\pi$
$102$		0			0
$103$	−0.273973	+	0.843203i	−0.0269954	+	0.0830833i	−0.963647	−	0.267180i	$-0.913908\pi$
$103$	−0.273973	+	0.843203i	−0.0269954	+	0.0830833i	0.936651	+	0.350264i	$0.113908\pi$
$104$		0			0
$105$	5.45456	+	5.21664i	0.532311	+	0.509092i
$106$		0			0
$107$	0.689654	+	2.12254i	0.0666713	+	0.205193i	0.978842	−	0.204617i	$-0.0655949\pi$
$107$	0.689654	+	2.12254i	0.0666713	+	0.205193i	−0.912171	+	0.409810i	$0.865595\pi$
$108$		0			0
$109$		−	4.73524i		−	0.453554i	−0.973947	−	0.226777i	$-0.927181\pi$
$109$		−	4.73524i		−	0.453554i	0.973947	−	0.226777i	$-0.0728188\pi$
$110$		0			0
$111$	1.72829	+	0.234373i	0.164042	+	0.0222457i
$112$		0			0
$113$	3.70508	−	1.20385i	0.348545	−	0.113249i	−0.129512	−	0.991578i	$-0.541341\pi$
$113$	3.70508	−	1.20385i	0.348545	−	0.113249i	0.478057	+	0.878329i	$0.341341\pi$
$114$		0			0
$115$	−10.2868	−	7.47379i	−0.959248	−	0.696934i
$116$		0			0
$117$	−3.77089	−	2.49075i	−0.348619	−	0.230270i
$118$		0			0
$119$	6.54989	+	9.01516i	0.600428	+	0.826418i
$120$		0			0
$121$	4.42454	+	10.0709i	0.402231	+	0.915538i
$122$		0			0
$123$	−2.40134	+	1.29176i	−0.216521	+	0.116474i
$124$		0			0
$125$	−7.44800	−	2.42000i	−0.666169	−	0.216451i
$126$		0			0
$127$	0.138938	−	0.191232i	0.0123288	−	0.0169691i	−0.802808	−	0.596237i	$-0.796662\pi$
$127$	0.138938	−	0.191232i	0.0123288	−	0.0169691i	0.815137	+	0.579268i	$0.196662\pi$
$128$		0			0
$129$	−5.83710	+	1.05838i	−0.513928	+	0.0931855i
$130$		0			0
$131$	5.26741			0.460216			0.230108	−	0.973165i	$-0.426092\pi$
$131$	5.26741			0.460216			0.230108	+	0.973165i	$0.426092\pi$
$132$		0			0
$133$	−9.00696			−0.781002
$134$		0			0
$135$	13.7413	+	1.24290i	1.18267	+	0.106972i
$136$		0			0
$137$	0.545331	−	0.750584i	0.0465908	−	0.0641267i	−0.785086	−	0.619387i	$-0.787381\pi$
$137$	0.545331	−	0.750584i	0.0465908	−	0.0641267i	0.831677	+	0.555260i	$0.187381\pi$
$138$		0			0
$139$	8.03945	+	2.61218i	0.681898	+	0.221562i	0.629426	−	0.777060i	$-0.283290\pi$
$139$	8.03945	+	2.61218i	0.681898	+	0.221562i	0.0524716	+	0.998622i	$0.483290\pi$
$140$		0			0
$141$	−8.21599	−	15.2733i	−0.691911	−	1.28624i
$142$		0			0
$143$	−0.249191	−	4.98998i	−0.0208384	−	0.417283i
$144$		0			0
$145$	−0.724231	−	0.996819i	−0.0601441	−	0.0827813i
$146$		0			0
$147$	3.23764	−	6.72049i	0.267036	−	0.554296i
$148$		0			0
$149$	14.6202	+	10.6222i	1.19774	+	0.870206i	0.994060	−	0.108832i	$-0.0347112\pi$
$149$	14.6202	+	10.6222i	1.19774	+	0.870206i	0.203676	+	0.979038i	$0.434711\pi$
$150$		0			0
$151$	12.6775	−	4.11917i	1.03168	−	0.335213i	0.256226	−	0.966617i	$-0.417521\pi$
$151$	12.6775	−	4.11917i	1.03168	−	0.335213i	0.775454	+	0.631403i	$0.217521\pi$
$152$		0			0
$153$	19.6351	+	5.42520i	1.58740	+	0.438602i
$154$		0			0
$155$		−	13.7872i		−	1.10742i
$156$		0			0
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	0.996503	+	0.0835524i	$0.0266266\pi$
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	−0.757077	+	0.653325i	$0.773373\pi$
$158$		0			0
$159$	−11.7618	+	12.2983i	−0.932773	+	0.975315i
$160$		0			0
$161$	2.42838	−	7.47379i	0.191383	−	0.589017i
$162$		0			0
$163$	5.72951	−	4.16273i	0.448770	−	0.326050i	−0.340340	−	0.940302i	$-0.610542\pi$
$163$	5.72951	−	4.16273i	0.448770	−	0.326050i	0.789110	+	0.614252i	$0.210542\pi$
$164$		0			0
$165$	7.88724	+	13.0562i	0.614021	+	1.01643i
$166$		0			0
$167$	−2.05072	+	1.48993i	−0.158689	+	0.115294i	−0.664296	−	0.747470i	$-0.731269\pi$
$167$	−2.05072	+	1.48993i	−0.158689	+	0.115294i	0.505607	+	0.862764i	$0.331269\pi$
$168$		0			0
$169$	3.31598	−	10.2055i	0.255075	−	0.785041i
$170$		0			0
$171$	−12.8762	+	10.2622i	−0.984664	+	0.784766i
$172$		0			0
$173$	0.293345	+	0.902823i	0.0223026	+	0.0686404i	0.961588	−	0.274496i	$-0.0885109\pi$
$173$	0.293345	+	0.902823i	0.0223026	+	0.0686404i	−0.939286	+	0.343136i	$0.888511\pi$
$174$		0			0
$175$			3.36538i			0.254399i
$176$		0			0
$177$	−1.42264	+	10.4907i	−0.106932	+	0.788526i
$178$		0			0
$179$	17.6570	−	5.73709i	1.31974	−	0.428810i	0.437336	−	0.899298i	$-0.355922\pi$
$179$	17.6570	−	5.73709i	1.31974	−	0.428810i	0.882407	+	0.470488i	$0.155922\pi$
$180$		0			0
$181$	−10.4196	−	7.57025i	−0.774480	−	0.562692i	0.128837	−	0.991666i	$-0.458875\pi$
$181$	−10.4196	−	7.57025i	−0.774480	−	0.562692i	−0.903317	+	0.428973i	$0.858875\pi$
$182$		0			0
$183$	−21.6951	−	10.4518i	−1.60375	−	0.772617i
$184$		0			0
$185$	1.57162	+	2.16315i	0.115548	+	0.159038i
$186$		0			0
$187$	8.01891	+	21.0448i	0.586400	+	1.53894i
$188$		0			0
$189$	1.89380	+	8.31433i	0.137754	+	0.604779i
$190$		0			0
$191$	3.07080	+	0.997763i	0.222195	+	0.0721956i	0.417999	−	0.908448i	$-0.362732\pi$
$191$	3.07080	+	0.997763i	0.222195	+	0.0721956i	−0.195804	+	0.980643i	$0.562732\pi$
$192$		0			0
$193$	5.73979	−	7.90015i	0.413159	−	0.568665i	−0.550826	−	0.834620i	$-0.685687\pi$
$193$	5.73979	−	7.90015i	0.413159	−	0.568665i	0.963985	+	0.265955i	$0.0856872\pi$
$194$		0			0
$195$	−1.23607	−	6.81705i	−0.0885167	−	0.488179i
$196$		0			0
$197$	−13.9679			−0.995175			−0.497587	−	0.867414i	$-0.665781\pi$
$197$	−13.9679			−0.995175			−0.497587	+	0.867414i	$0.665781\pi$
$198$		0			0
$199$	−15.9679			−1.13194			−0.565969	−	0.824427i	$-0.691498\pi$
$199$	−15.9679			−1.13194			−0.565969	+	0.824427i	$0.691498\pi$
$200$		0			0
$201$	−3.64554	−	20.1056i	−0.257137	−	1.41814i
$202$		0			0
$203$	0.447600	−	0.616068i	0.0314153	−	0.0432395i
$204$		0			0
$205$	−3.97562	−	1.29176i	−0.277669	−	0.0902201i
$206$		0			0
$207$	−5.04376	−	13.4512i	−0.350565	−	0.934920i
$208$		0			0
$209$	−17.5712	−	4.75461i	−1.21543	−	0.328883i
$210$		0			0
$211$	−1.33315	−	1.83493i	−0.0917782	−	0.126322i	0.760659	−	0.649152i	$-0.224876\pi$
$211$	−1.33315	−	1.83493i	−0.0917782	−	0.126322i	−0.852437	+	0.522830i	$0.824876\pi$
$212$		0			0
$213$	−1.40134	−	0.675105i	−0.0960181	−	0.0462574i
$214$		0			0
$215$	−7.35758	−	5.34560i	−0.501783	−	0.364567i
$216$		0			0
$217$	8.10394	−	2.63313i	0.550131	−	0.178748i
$218$		0			0
$219$	1.07700	−	7.94191i	0.0727772	−	0.536665i
$220$		0			0
$221$		−	10.2289i		−	0.688072i
$222$		0			0
$223$	−1.36009	−	4.18592i	−0.0910782	−	0.280310i	0.895134	−	0.445798i	$-0.147080\pi$
$223$	−1.36009	−	4.18592i	−0.0910782	−	0.280310i	−0.986212	+	0.165488i	$0.947080\pi$
$224$		0			0
$225$	3.83437	+	4.81108i	0.255625	+	0.320739i
$226$		0			0
$227$	−3.93483	+	12.1102i	−0.261164	+	0.803780i	0.731388	+	0.681961i	$0.238873\pi$
$227$	−3.93483	+	12.1102i	−0.261164	+	0.803780i	−0.992552	+	0.121819i	$0.961127\pi$
$228$		0			0
$229$	−5.19661	+	3.77556i	−0.343402	+	0.249496i	−0.746096	−	0.665839i	$-0.768074\pi$
$229$	−5.19661	+	3.77556i	−0.343402	+	0.249496i	0.402694	+	0.915335i	$0.368074\pi$
$230$		0			0
$231$	−6.16793	+	7.12952i	−0.405820	+	0.469088i
$232$		0			0
$233$	−13.5999	+	9.88087i	−0.890956	+	0.647318i	−0.936127	−	0.351662i	$-0.885617\pi$
$233$	−13.5999	+	9.88087i	−0.890956	+	0.647318i	0.0451710	+	0.998979i	$0.485617\pi$
$234$		0			0
$235$	8.21599	−	25.2862i	0.535952	−	1.64949i
$236$		0			0
$237$	−3.80378	+	3.97727i	−0.247082	+	0.258351i
$238$		0			0
$239$	−3.72018	−	11.4495i	−0.240638	−	0.740608i	−0.996323	−	0.0856731i	$-0.972696\pi$
$239$	−3.72018	−	11.4495i	−0.240638	−	0.740608i	0.755685	−	0.654935i	$-0.227304\pi$
$240$		0			0
$241$			20.5642i			1.32466i	0.749214	+	0.662328i	$0.230432\pi$
$241$			20.5642i			1.32466i	−0.749214	+	0.662328i	$0.769568\pi$
$242$		0			0
$243$	12.1803	+	9.72827i	0.781369	+	0.624069i
$244$		0			0
$245$	10.8764	−	3.53395i	0.694866	−	0.225776i
$246$		0			0
$247$	6.68883	+	4.85972i	0.425600	+	0.309217i
$248$		0			0
$249$	−1.40890	+	2.92450i	−0.0892854	+	0.185333i
$250$		0			0
$251$	−9.61958	−	13.2402i	−0.607183	−	0.835715i	0.389159	−	0.921170i	$-0.372766\pi$
$251$	−9.61958	−	13.2402i	−0.607183	−	0.835715i	−0.996342	+	0.0854552i	$0.972766\pi$
$252$		0			0
$253$	8.68267	−	13.2983i	0.545875	−	0.836058i
$254$		0			0
$255$	14.7946	+	27.5027i	0.926472	+	1.72228i
$256$		0			0
$257$	−8.11843	−	2.63784i	−0.506414	−	0.164544i	0.0446568	−	0.999002i	$-0.485781\pi$
$257$	−8.11843	−	2.63784i	−0.506414	−	0.164544i	−0.551071	+	0.834459i	$0.685781\pi$
$258$		0			0
$259$	−0.971314	+	1.33690i	−0.0603545	+	0.0830709i
$260$		0			0
$261$	−0.0620430	−	1.39069i	−0.00384037	−	0.0860818i
$262$		0			0
$263$	−13.5666			−0.836553			−0.418276	−	0.908320i	$-0.637366\pi$
$263$	−13.5666			−0.836553			−0.418276	+	0.908320i	$0.637366\pi$
$264$		0			0
$265$	−26.0883			−1.60259
$266$		0			0
$267$	−21.8302	+	3.95826i	−1.33599	+	0.242242i
$268$		0			0
$269$	6.96435	−	9.58561i	0.424624	−	0.584445i	−0.542085	−	0.840324i	$-0.682365\pi$
$269$	6.96435	−	9.58561i	0.424624	−	0.584445i	0.966709	+	0.255879i	$0.0823648\pi$
$270$		0			0
$271$	−20.5918	−	6.69068i	−1.25086	−	0.406430i	−0.392632	−	0.919696i	$-0.628436\pi$
$271$	−20.5918	−	6.69068i	−1.25086	−	0.406430i	−0.858230	+	0.513266i	$0.828436\pi$
$272$		0			0
$273$	3.77089	−	2.02848i	0.228225	−	0.122769i
$274$		0			0
$275$	−1.77652	+	6.56534i	−0.107128	+	0.395905i
$276$		0			0
$277$	−2.39438	−	3.29558i	−0.143864	−	0.198012i	0.731004	−	0.682373i	$-0.239052\pi$
$277$	−2.39438	−	3.29558i	−0.143864	−	0.198012i	−0.874868	+	0.484361i	$0.839052\pi$
$278$		0			0
$279$	8.58514	−	12.9976i	0.513979	−	0.778143i
$280$		0			0
$281$	−14.4528	−	10.5006i	−0.862182	−	0.626412i	0.0662956	−	0.997800i	$-0.478882\pi$
$281$	−14.4528	−	10.5006i	−0.862182	−	0.626412i	−0.928478	+	0.371388i	$0.878882\pi$
$282$		0			0
$283$	−2.89090	+	0.939310i	−0.171846	+	0.0558362i	−0.393676	−	0.919249i	$-0.628797\pi$
$283$	−2.89090	+	0.939310i	−0.171846	+	0.0558362i	0.221830	+	0.975085i	$0.428797\pi$
$284$		0			0
$285$	−25.0132	−	3.39205i	−1.48165	−	0.200927i
$286$		0			0
$287$		−	2.58351i		−	0.152500i
$288$		0			0
$289$	8.99477	+	27.6830i	0.529104	+	1.62841i
$290$		0			0
$291$	4.49499	+	4.29892i	0.263501	+	0.252007i
$292$		0			0
$293$	−7.21279	+	22.1987i	−0.421376	+	1.29686i	0.485046	+	0.874489i	$0.338803\pi$
$293$	−7.21279	+	22.1987i	−0.421376	+	1.29686i	−0.906422	+	0.422373i	$0.861197\pi$
$294$		0			0
$295$	−13.1303	+	9.53970i	−0.764474	+	0.555423i
$296$		0			0
$297$	−0.694463	+	17.2197i	−0.0402968	+	0.999188i
$298$		0			0
$299$	−5.83588	+	4.24002i	−0.337498	+	0.245206i
$300$		0			0
$301$	1.73689	−	5.34560i	0.100113	−	0.308115i
$302$		0			0
$303$	15.2365	+	14.5719i	0.875312	+	0.837132i
$304$		0			0
$305$	−11.4083	−	35.1111i	−0.653237	−	2.01046i
$306$		0			0
$307$			30.0216i			1.71342i	0.515794	+	0.856712i	$0.327497\pi$
$307$			30.0216i			1.71342i	−0.515794	+	0.856712i	$0.672503\pi$
$308$		0			0
$309$	−1.52170	−	0.206358i	−0.0865666	−	0.0117393i
$310$		0			0
$311$	−0.470986	+	0.153033i	−0.0267071	+	0.00867768i	−0.322340	−	0.946624i	$-0.604469\pi$
$311$	−0.470986	+	0.153033i	−0.0267071	+	0.00867768i	0.295633	+	0.955302i	$0.404469\pi$
$312$		0			0
$313$	22.9590	+	16.6807i	1.29772	+	0.942849i	0.999931	−	0.0117826i	$-0.00375062\pi$
$313$	22.9590	+	16.6807i	1.29772	+	0.942849i	0.297790	+	0.954632i	$0.403751\pi$
$314$		0			0
$315$	−7.20497	+	10.9080i	−0.405954	+	0.614598i
$316$		0			0
$317$	−3.90331	−	5.37244i	−0.219232	−	0.301747i	0.685209	−	0.728347i	$-0.259711\pi$
$317$	−3.90331	−	5.37244i	−0.219232	−	0.301747i	−0.904440	+	0.426600i	$0.859711\pi$
$318$		0			0
$319$	1.19841	−	0.965575i	0.0670980	−	0.0540618i
$320$		0			0
$321$	−3.40424	+	1.83125i	−0.190006	+	0.102210i
$322$		0			0
$323$	−35.4440	−	11.5164i	−1.97215	−	0.640792i
$324$		0			0
$325$	1.81580	−	2.49923i	0.100722	−	0.138632i
$326$		0			0
$327$	8.07009	−	1.46327i	0.446277	−	0.0809190i
$328$		0			0
$329$	16.4320			0.905924
$330$		0			0
$331$	−7.41016			−0.407299			−0.203650	−	0.979044i	$-0.565280\pi$
$331$	−7.41016			−0.407299			−0.203650	+	0.979044i	$0.565280\pi$
$332$		0			0
$333$	0.134637	+	3.01788i	0.00737804	+	0.165379i
$334$		0			0
$335$	18.4126	−	25.3428i	1.00599	−	1.38462i
$336$		0			0
$337$	−32.5392	−	10.5726i	−1.77252	−	0.575927i	−0.774152	−	0.632999i	$-0.781824\pi$
$337$	−32.5392	−	10.5726i	−1.77252	−	0.575927i	−0.998370	+	0.0570720i	$0.981824\pi$
$338$		0			0
$339$	3.19661	+	5.94241i	0.173616	+	0.322748i
$340$		0			0
$341$	17.1995	−	0.858913i	0.931406	−	0.0465127i
$342$		0			0
$343$	10.9066	+	15.0117i	0.588902	+	0.810554i
$344$		0			0
$345$	9.55850	−	19.8409i	0.514612	−	1.06820i
$346$		0			0
$347$	16.9283	+	12.2991i	0.908760	+	0.660252i	0.940701	−	0.339237i	$-0.110169\pi$
$347$	16.9283	+	12.2991i	0.908760	+	0.660252i	−0.0319413	+	0.999490i	$0.510169\pi$
$348$		0			0
$349$	28.0113	−	9.10144i	1.49941	−	0.487189i	0.559566	−	0.828786i	$-0.310968\pi$
$349$	28.0113	−	9.10144i	1.49941	−	0.487189i	0.939847	+	0.341597i	$0.110968\pi$
$350$		0			0
$351$	3.07962	−	7.19627i	0.164378	−	0.384109i
$352$		0			0
$353$		−	24.3265i		−	1.29477i	−0.762163	−	0.647385i	$-0.775863\pi$
$353$		−	24.3265i		−	1.29477i	0.762163	−	0.647385i	$-0.224137\pi$
$354$		0			0
$355$	−0.736889	−	2.26791i	−0.0391100	−	0.120368i
$356$		0			0
$357$	−13.3402	+	13.9486i	−0.706036	+	0.738237i
$358$		0			0
$359$	10.1134	−	31.1259i	0.533765	−	1.64276i	−0.212537	−	0.977153i	$-0.568173\pi$
$359$	10.1134	−	31.1259i	0.533765	−	1.64276i	0.746302	−	0.665607i	$-0.231827\pi$
$360$		0			0
$361$	8.99871	−	6.53795i	0.473617	−	0.344103i
$362$		0			0
$363$	−15.7962	+	10.6527i	−0.829087	+	0.559120i
$364$		0			0
$365$	9.94022	−	7.22199i	0.520295	−	0.378016i
$366$		0			0
$367$	3.67822	−	11.3204i	0.192001	−	0.590919i	−0.807997	−	0.589186i	$-0.799448\pi$
$367$	3.67822	−	11.3204i	0.192001	−	0.590919i	0.999998	−	0.00173292i	$-0.000551606\pi$
$368$		0			0
$369$	−2.94354	−	3.69333i	−0.153235	−	0.192267i
$370$		0			0
$371$	−4.98242	−	15.3343i	−0.258675	−	0.796118i
$372$		0			0
$373$			27.7804i			1.43841i	0.694796	+	0.719207i	$0.255495\pi$
$373$			27.7804i			1.43841i	−0.694796	+	0.719207i	$0.744505\pi$
$374$		0			0
$375$	1.82276	−	13.4412i	0.0941268	−	0.694099i
$376$		0			0
$377$	−0.664801	+	0.216007i	−0.0342390	+	0.0111249i
$378$		0			0
$379$	−6.36264	−	4.62273i	−0.326827	−	0.237454i	0.412256	−	0.911068i	$-0.364741\pi$
$379$	−6.36264	−	4.62273i	−0.326827	−	0.237454i	−0.739083	+	0.673614i	$0.764741\pi$
$380$		0			0
$381$	0.368843	+	0.177693i	0.0188964	+	0.00910349i
$382$		0			0
$383$	7.61538	+	10.4817i	0.389128	+	0.535588i	0.957974	−	0.286856i	$-0.0926101\pi$
$383$	7.61538	+	10.4817i	0.389128	+	0.535588i	−0.568846	+	0.822444i	$0.692610\pi$
$384$		0			0
$385$	−14.4345	+	0.720832i	−0.735649	+	0.0367370i
$386$		0			0
$387$	−3.60753	−	9.62089i	−0.183381	−	0.489057i
$388$		0			0
$389$	24.6301	+	8.00280i	1.24880	+	0.405758i	0.857489	−	0.514502i	$-0.172023\pi$
$389$	24.6301	+	8.00280i	1.24880	+	0.405758i	0.391306	+	0.920261i	$0.372023\pi$
$390$		0			0
$391$	19.1122	−	26.3057i	0.966546	−	1.33034i
$392$		0			0
$393$	1.62772	+	8.97705i	0.0821076	+	0.452832i
$394$		0			0
$395$	−8.43698			−0.424511
$396$		0			0
$397$	−17.9986			−0.903323			−0.451661	−	0.892189i	$-0.649168\pi$
$397$	−17.9986			−0.903323			−0.451661	+	0.892189i	$0.649168\pi$
$398$		0			0
$399$	−2.78330	−	15.3502i	−0.139339	−	0.768472i
$400$		0			0
$401$	−2.21479	+	3.04840i	−0.110601	+	0.152230i	−0.860729	−	0.509063i	$-0.829992\pi$
$401$	−2.21479	+	3.04840i	−0.110601	+	0.152230i	0.750128	+	0.661293i	$0.229992\pi$
$402$		0			0
$403$	−7.43893	−	2.41706i	−0.370560	−	0.120402i
$404$		0			0
$405$	2.12808	+	23.8029i	0.105745	+	1.18278i
$406$		0			0
$407$	−2.60061	+	2.09535i	−0.128907	+	0.103863i
$408$		0			0
$409$	−8.44886	−	11.6289i	−0.417769	−	0.575010i	0.547323	−	0.836922i	$-0.315647\pi$
$409$	−8.44886	−	11.6289i	−0.417769	−	0.575010i	−0.965092	+	0.261912i	$0.915647\pi$
$410$		0			0
$411$	1.44771	+	0.697444i	0.0714102	+	0.0344024i
$412$		0			0
$413$	−8.11495	−	5.89586i	−0.399311	−	0.290116i
$414$		0			0
$415$	−4.73299	+	1.53784i	−0.232333	+	0.0754896i
$416$		0			0
$417$	−1.96751	+	14.5085i	−0.0963492	+	0.710486i
$418$		0			0
$419$			31.1601i			1.52227i	0.648595	+	0.761134i	$0.275357\pi$
$419$			31.1601i			1.52227i	−0.648595	+	0.761134i	$0.724643\pi$
$420$		0			0
$421$	−3.34251	−	10.2872i	−0.162904	−	0.501367i	0.835972	−	0.548773i	$-0.184905\pi$
$421$	−3.34251	−	10.2872i	−0.162904	−	0.501367i	−0.998876	+	0.0474055i	$0.984905\pi$
$422$		0			0
$423$	23.4908	−	18.7219i	1.14216	−	0.910290i
$424$		0			0
$425$	−4.30303	+	13.2434i	−0.208728	+	0.642398i
$426$		0			0
$427$	18.4590	−	13.4113i	0.893294	−	0.649016i
$428$		0			0
$429$	8.42723	−	1.96667i	0.406870	−	0.0949520i
$430$		0			0
$431$	32.2249	−	23.4128i	1.55222	−	1.12775i	0.610173	−	0.792268i	$-0.291100\pi$
$431$	32.2249	−	23.4128i	1.55222	−	1.12775i	0.942046	−	0.335484i	$-0.108900\pi$
$432$		0			0
$433$	4.99226	−	15.3646i	0.239913	−	0.738376i	−0.756519	−	0.653972i	$-0.773101\pi$
$433$	4.99226	−	15.3646i	0.239913	−	0.738376i	0.996432	−	0.0844037i	$-0.0268985\pi$
$434$		0			0
$435$	1.47504	−	1.54231i	0.0707228	−	0.0739483i
$436$		0			0
$437$	8.12151	+	24.9954i	0.388505	+	1.19569i
$438$		0			0
$439$			6.13994i			0.293043i	0.989207	+	0.146522i	$0.0468078\pi$
$439$			6.13994i			0.293043i	−0.989207	+	0.146522i	$0.953192\pi$
$440$		0			0
$441$	12.4540	+	3.44105i	0.593046	+	0.163859i
$442$		0			0
$443$	1.55768	−	0.506119i	0.0740074	−	0.0240465i	−0.271779	−	0.962360i	$-0.587612\pi$
$443$	1.55768	−	0.506119i	0.0740074	−	0.0240465i	0.345787	+	0.938313i	$0.387612\pi$
$444$		0			0
$445$	−27.5167	−	19.9920i	−1.30442	−	0.947714i
$446$		0			0
$447$	−13.5851	+	28.1991i	−0.642555	+	1.33377i
$448$		0			0
$449$	−10.7458	−	14.7903i	−0.507125	−	0.697997i	0.476306	−	0.879279i	$-0.341975\pi$
$449$	−10.7458	−	14.7903i	−0.507125	−	0.697997i	−0.983431	+	0.181282i	$0.941975\pi$
$450$		0			0
$451$	1.36379	−	5.04004i	0.0642183	−	0.237326i
$452$		0			0
$453$	10.9377	+	20.3329i	0.513898	+	0.955323i
$454$		0			0
$455$	6.24303	+	2.02848i	0.292678	+	0.0950967i
$456$		0			0
$457$	16.4490	−	22.6402i	0.769454	−	1.05906i	−0.226915	−	0.973915i	$-0.572864\pi$
$457$	16.4490	−	22.6402i	0.769454	−	1.05906i	0.996368	−	0.0851474i	$-0.0271361\pi$
$458$		0			0
$459$	−3.17839	+	35.1398i	−0.148355	+	1.64019i
$460$		0			0
$461$	30.3359			1.41288			0.706441	−	0.707772i	$-0.250300\pi$
$461$	30.3359			1.41288			0.706441	+	0.707772i	$0.250300\pi$
$462$		0			0
$463$	10.9632			0.509503			0.254752	−	0.967007i	$-0.418006\pi$
$463$	10.9632			0.509503			0.254752	+	0.967007i	$0.418006\pi$
$464$		0			0
$465$	23.4971	−	4.26049i	1.08965	−	0.197576i
$466$		0			0
$467$	−18.9376	+	26.0653i	−0.876326	+	1.20616i	0.101099	+	0.994876i	$0.467764\pi$
$467$	−18.9376	+	26.0653i	−0.876326	+	1.20616i	−0.977425	+	0.211283i	$0.932236\pi$
$468$		0			0
$469$	18.4126	+	5.98262i	0.850215	+	0.276252i
$470$		0			0
$471$	−14.8085	+	7.96596i	−0.682339	+	0.367052i
$472$		0			0
$473$	6.21025	−	9.51157i	0.285547	−	0.437342i
$474$		0			0
$475$	−6.61566	−	9.10568i	−0.303547	−	0.417797i
$476$		0			0
$477$	−24.5940	−	16.2449i	−1.12608	−	0.743801i
$478$		0			0
$479$	−15.2361	−	11.0697i	−0.696154	−	0.505785i	0.182524	−	0.983201i	$-0.441573\pi$
$479$	−15.2361	−	11.0697i	−0.696154	−	0.505785i	−0.878677	+	0.477416i	$0.841573\pi$
$480$		0			0
$481$	1.44265	−	0.468746i	0.0657793	−	0.0213730i
$482$		0			0
$483$	13.4877	+	1.82907i	0.613712	+	0.0832255i
$484$		0			0
$485$			9.53523i			0.432972i
$486$		0			0
$487$	8.30030	+	25.5457i	0.376123	+	1.15759i	0.942718	+	0.333591i	$0.108260\pi$
$487$	8.30030	+	25.5457i	0.376123	+	1.15759i	−0.566595	+	0.823996i	$0.691740\pi$
$488$		0			0
$489$	8.86490	+	8.47823i	0.400885	+	0.383399i
$490$		0			0
$491$	5.88351	−	18.1076i	0.265519	−	0.817184i	−0.726054	−	0.687638i	$-0.758648\pi$
$491$	5.88351	−	18.1076i	0.265519	−	0.817184i	0.991573	−	0.129547i	$-0.0413522\pi$
$492$		0			0
$493$	2.54910	−	1.85203i	0.114806	−	0.0834111i
$494$		0			0
$495$	−19.8139	+	17.4765i	−0.890570	+	0.785511i
$496$		0			0
$497$	1.19231	−	0.866266i	0.0534825	−	0.0388573i
$498$		0			0
$499$	−3.28175	+	10.1002i	−0.146912	+	0.452147i	−0.997252	−	0.0740860i	$-0.976396\pi$
$499$	−3.28175	+	10.1002i	−0.146912	+	0.452147i	0.850340	+	0.526233i	$0.176396\pi$
$500$		0			0
$501$	−3.17294	−	3.03454i	−0.141757	−	0.135573i
$502$		0			0
$503$	9.56998	+	29.4534i	0.426704	+	1.31326i	0.901353	+	0.433085i	$0.142575\pi$
$503$	9.56998	+	29.4534i	0.426704	+	1.31326i	−0.474649	+	0.880175i	$0.657425\pi$
$504$		0			0
$505$			32.3211i			1.43827i
$506$		0			0
$507$	18.4176	+	2.49761i	0.817954	+	0.110923i
$508$		0			0
$509$	−19.5685	+	6.35820i	−0.867359	+	0.281822i	−0.708699	−	0.705511i	$-0.750717\pi$
$509$	−19.5685	+	6.35820i	−0.867359	+	0.281822i	−0.158660	+	0.987333i	$0.550717\pi$
$510$		0			0
$511$	6.14339	+	4.46344i	0.271768	+	0.197451i
$512$		0			0
$513$	−21.4683	−	18.7732i	−0.947851	−	0.828856i
$514$		0			0
$515$	−1.38376	−	1.90458i	−0.0609758	−	0.0839260i
$516$		0			0
$517$	32.0563	+	8.67413i	1.40983	+	0.381488i
$518$		0			0
$519$	−1.44800	+	0.778924i	−0.0635601	+	0.0341910i
$520$		0			0
$521$	3.64239	+	1.18348i	0.159576	+	0.0518494i	0.387716	−	0.921779i	$-0.373264\pi$
$521$	3.64239	+	1.18348i	0.159576	+	0.0518494i	−0.228140	+	0.973628i	$0.573264\pi$
$522$		0			0
$523$	−5.66137	+	7.79220i	−0.247554	+	0.340729i	−0.914653	−	0.404240i	$-0.867536\pi$
$523$	−5.66137	+	7.79220i	−0.247554	+	0.340729i	0.667099	+	0.744969i	$0.267536\pi$
$524$		0			0
$525$	−5.73549	+	1.03996i	−0.250317	+	0.0453876i
$526$		0			0
$527$	35.2572			1.53583
$528$		0			0
$529$	0.0696480			0.00302817
$530$		0			0
$531$	−18.3185	+	0.817241i	−0.794953	+	0.0354652i
$532$		0			0
$533$	−1.39394	+	1.91859i	−0.0603782	+	0.0831034i
$534$		0			0
$535$	−5.63601	−	1.83125i	−0.243666	−	0.0791719i
$536$		0			0
$537$	15.2338	+	28.3192i	0.657387	+	1.22206i
$538$		0			0
$539$	5.08616	+	13.3481i	0.219076	+	0.574942i
$540$		0			0
$541$	1.63935	+	2.25638i	0.0704813	+	0.0970092i	0.842802	−	0.538223i	$-0.180904\pi$
$541$	1.63935	+	2.25638i	0.0704813	+	0.0970092i	−0.772321	+	0.635232i	$0.780904\pi$
$542$		0			0
$543$	9.68187	−	20.0970i	0.415489	−	0.862445i
$544$		0			0
$545$	10.1722	+	7.39056i	0.435730	+	0.316577i
$546$		0			0
$547$	31.5016	−	10.2355i	1.34691	−	0.437638i	0.455259	−	0.890359i	$-0.349547\pi$
$547$	31.5016	−	10.2355i	1.34691	−	0.437638i	0.891652	+	0.452721i	$0.149547\pi$
$548$		0			0
$549$	11.1084	−	40.2039i	0.474095	−	1.71586i
$550$		0			0
$551$			2.54678i			0.108496i
$552$		0			0
$553$	−1.61132	−	4.95913i	−0.0685203	−	0.210884i
$554$		0			0
$555$	−3.20092	+	3.34690i	−0.135871	+	0.142068i
$556$		0			0
$557$	8.46752	−	26.0604i	0.358780	−	1.10421i	−0.595004	−	0.803722i	$-0.702850\pi$
$557$	8.46752	−	26.0604i	0.358780	−	1.10421i	0.953785	−	0.300490i	$-0.0971503\pi$
$558$		0			0
$559$	−4.17409	+	3.03265i	−0.176545	+	0.128268i
$560$		0			0
$561$	−33.3878	+	20.1695i	−1.40963	+	0.851557i
$562$		0			0
$563$	−17.1967	+	12.4941i	−0.724753	+	0.526564i	−0.887899	−	0.460038i	$-0.847836\pi$
$563$	−17.1967	+	12.4941i	−0.724753	+	0.526564i	0.163146	+	0.986602i	$0.447836\pi$
$564$		0			0
$565$	−3.19661	+	9.83817i	−0.134483	+	0.413895i
$566$		0			0
$567$	−13.5846	+	5.79681i	−0.570499	+	0.243443i
$568$		0			0
$569$	11.4052	+	35.1015i	0.478130	+	1.47153i	0.841690	+	0.539961i	$0.181561\pi$
$569$	11.4052	+	35.1015i	0.478130	+	1.47153i	−0.363560	+	0.931571i	$0.618439\pi$
$570$		0			0
$571$			26.4505i			1.10692i	0.832876	+	0.553460i	$0.186693\pi$
$571$			26.4505i			1.10692i	−0.832876	+	0.553460i	$0.813307\pi$
$572$		0			0
$573$	−0.751520	+	5.54177i	−0.0313952	+	0.231511i
$574$		0			0
$575$	9.33936	−	3.03454i	0.389478	−	0.126549i
$576$		0			0
$577$	19.8138	+	14.3955i	0.824858	+	0.599294i	0.918100	−	0.396349i	$-0.129723\pi$
$577$	19.8138	+	14.3955i	0.824858	+	0.599294i	−0.0932422	+	0.995643i	$0.529723\pi$
$578$		0			0
$579$	15.2376	+	7.34083i	0.633254	+	0.305075i
$580$		0			0
$581$	−1.80784	−	2.48828i	−0.0750018	−	0.103231i
$582$		0			0
$583$	−1.62524	−	32.5450i	−0.0673106	−	1.34788i
$584$		0			0
$585$	11.2361	−	4.21317i	0.464554	−	0.174193i
$586$		0			0
$587$	39.3939	+	12.7999i	1.62596	+	0.528307i	0.973338	−	0.229375i	$-0.0736683\pi$
$587$	39.3939	+	12.7999i	1.62596	+	0.528307i	0.652624	+	0.757682i	$0.273668\pi$
$588$		0			0
$589$	−16.7505	+	23.0551i	−0.690194	+	0.949970i
$590$		0			0
$591$	−4.31633	−	23.8050i	−0.177550	−	0.979208i
$592$		0			0
$593$	−2.94808			−0.121063			−0.0605316	−	0.998166i	$-0.519280\pi$
$593$	−2.94808			−0.121063			−0.0605316	+	0.998166i	$0.519280\pi$
$594$		0			0
$595$	−29.5891			−1.21304
$596$		0			0
$597$	−4.93437	−	27.2136i	−0.201950	−	1.11378i
$598$		0			0
$599$	−16.3070	+	22.4446i	−0.666284	+	0.917061i	−0.999669	−	0.0257295i	$-0.991809\pi$
$599$	−16.3070	+	22.4446i	−0.666284	+	0.917061i	0.333385	+	0.942791i	$0.391809\pi$
$600$		0			0
$601$	4.22399	+	1.37246i	0.172300	+	0.0559836i	0.393897	−	0.919155i	$-0.371127\pi$
$601$	4.22399	+	1.37246i	0.172300	+	0.0559836i	−0.221597	+	0.975138i	$0.571127\pi$
$602$		0			0
$603$	33.1386	−	12.4259i	1.34951	−	0.506023i
$604$		0			0
$605$	−28.5400	−	6.21346i	−1.16031	−	0.252613i
$606$		0			0
$607$	−23.8874	−	32.8782i	−0.969559	−	1.33448i	−0.942269	−	0.334856i	$-0.891312\pi$
$607$	−23.8874	−	32.8782i	−0.969559	−	1.33448i	−0.0272902	−	0.999628i	$-0.508688\pi$
$608$		0			0
$609$	1.18826	+	0.572451i	0.0481506	+	0.0231969i
$610$		0			0
$611$	−12.2029	−	8.86590i	−0.493675	−	0.358676i
$612$		0			0
$613$	−27.4583	+	8.92174i	−1.10903	+	0.360346i	−0.805571	−	0.592499i	$-0.798142\pi$
$613$	−27.4583	+	8.92174i	−1.10903	+	0.360346i	−0.303459	+	0.952845i	$0.598142\pi$
$614$		0			0
$615$	0.972957	−	7.17467i	0.0392334	−	0.289310i
$616$		0			0
$617$			31.6428i			1.27389i	0.770909	+	0.636946i	$0.219802\pi$
$617$			31.6428i			1.27389i	−0.770909	+	0.636946i	$0.780198\pi$
$618$		0			0
$619$	−0.294921	−	0.907672i	−0.0118539	−	0.0364824i	0.944955	−	0.327201i	$-0.106106\pi$
$619$	−0.294921	−	0.907672i	−0.0118539	−	0.0364824i	−0.956808	+	0.290719i	$0.906106\pi$
$620$		0			0
$621$	21.3657	−	12.7525i	0.857376	−	0.511741i
$622$		0			0
$623$	6.49581	−	19.9920i	0.260249	−	0.800964i
$624$		0			0
$625$	25.1185	−	18.2496i	1.00474	−	0.729986i
$626$		0			0
$627$	2.67330	−	31.4152i	0.106761	−	1.25460i
$628$		0			0
$629$	−5.53167	+	4.01900i	−0.220562	+	0.160248i
$630$		0			0
$631$	−2.19912	+	6.76820i	−0.0875456	+	0.269438i	−0.985239	−	0.171182i	$-0.945241\pi$
$631$	−2.19912	+	6.76820i	−0.0875456	+	0.269438i	0.897694	+	0.440620i	$0.145241\pi$
$632$		0			0
$633$	2.71523	−	2.83907i	0.107921	−	0.112843i
$634$		0			0
$635$	0.193955	+	0.596933i	0.00769688	+	0.0236886i
$636$		0			0
$637$		−	6.48791i		−	0.257060i
$638$		0			0
$639$	0.717518	−	2.59687i	0.0283846	−	0.102730i
$640$		0			0
$641$	−31.2374	+	10.1496i	−1.23380	+	0.400887i	−0.852090	−	0.523395i	$-0.824665\pi$
$641$	−31.2374	+	10.1496i	−1.23380	+	0.400887i	−0.381712	+	0.924281i	$0.624665\pi$
$642$		0			0
$643$	2.66685	+	1.93758i	0.105170	+	0.0764106i	0.639127	−	0.769101i	$-0.279296\pi$
$643$	2.66685	+	1.93758i	0.105170	+	0.0764106i	−0.533957	+	0.845511i	$0.679296\pi$
$644$		0			0
$645$	6.83668	−	14.1911i	0.269194	−	0.558775i
$646$		0			0
$647$	−3.42235	−	4.71046i	−0.134547	−	0.185187i	0.736427	−	0.676516i	$-0.236511\pi$
$647$	−3.42235	−	4.71046i	−0.134547	−	0.185187i	−0.870974	+	0.491329i	$0.836511\pi$
$648$		0			0
$649$	−12.7187	−	15.7856i	−0.499253	−	0.619641i
$650$		0			0
$651$	6.99180	+	12.9976i	0.274030	+	0.509414i
$652$		0			0
$653$	4.16347	+	1.35279i	0.162929	+	0.0529390i	0.389346	−	0.921092i	$-0.372701\pi$
$653$	4.16347	+	1.35279i	0.162929	+	0.0529390i	−0.226417	+	0.974031i	$0.572701\pi$
$654$		0			0
$655$	−8.22115	+	11.3154i	−0.321227	+	0.442131i
$656$		0			0
$657$	13.8679	−	0.618689i	0.541039	−	0.0241374i
$658$		0			0
$659$	−15.3805			−0.599141			−0.299570	−	0.954074i	$-0.596843\pi$
$659$	−15.3805			−0.599141			−0.299570	+	0.954074i	$0.596843\pi$
$660$		0			0
$661$	12.6047			0.490266			0.245133	−	0.969489i	$-0.421168\pi$
$661$	12.6047			0.490266			0.245133	+	0.969489i	$0.421168\pi$
$662$		0			0
$663$	17.4328	−	3.16091i	0.677033	−	0.122760i
$664$		0			0
$665$	14.0577	−	19.3487i	0.545133	−	0.750312i
$666$		0			0
$667$	−2.11326	−	0.686641i	−0.0818259	−	0.0265868i
$668$		0			0
$669$	6.71361	−	3.61147i	0.259563	−	0.139627i
$670$		0			0
$671$	43.0903	−	16.4191i	1.66348	−	0.633854i
$672$		0			0
$673$	−18.9461	−	26.0771i	−0.730319	−	1.00520i	−0.999118	−	0.0420013i	$-0.986627\pi$
$673$	−18.9461	−	26.0771i	−0.730319	−	1.00520i	0.268799	−	0.963196i	$-0.413373\pi$
$674$		0			0
$675$	−7.01445	+	8.02148i	−0.269986	+	0.308747i
$676$		0			0
$677$	7.37175	+	5.35589i	0.283319	+	0.205844i	0.720364	−	0.693596i	$-0.243975\pi$
$677$	7.37175	+	5.35589i	0.283319	+	0.205844i	−0.437045	+	0.899440i	$0.643975\pi$
$678$		0			0
$679$	−5.60466	+	1.82107i	−0.215087	+	0.0698861i
$680$		0			0
$681$	−21.8548	−	2.96374i	−0.837479	−	0.113571i
$682$		0			0
$683$		−	28.1535i		−	1.07726i	−0.842541	−	0.538632i	$-0.818941\pi$
$683$		−	28.1535i		−	1.07726i	0.842541	−	0.538632i	$-0.181059\pi$
$684$		0			0
$685$	0.761274	+	2.34296i	0.0290868	+	0.0895199i
$686$		0			0
$687$	−8.04039	−	7.68968i	−0.306760	−	0.293380i
$688$		0			0
$689$	−4.57357	+	14.0760i	−0.174239	+	0.536253i
$690$		0			0
$691$	8.68690	−	6.31140i	0.330465	−	0.240097i	−0.410163	−	0.912012i	$-0.634528\pi$
$691$	8.68690	−	6.31140i	0.330465	−	0.240097i	0.740628	+	0.671915i	$0.234528\pi$
$692$		0			0
$693$	−14.0566	−	8.30862i	−0.533965	−	0.315618i
$694$		0			0
$695$	−18.1591	+	13.1934i	−0.688814	+	0.500453i
$696$		0			0
$697$	3.30332	−	10.1666i	0.125122	−	0.385086i
$698$		0			0
$699$	−21.0422	−	20.1244i	−0.795888	−	0.761173i
$700$		0			0
$701$	−12.8347	−	39.5012i	−0.484761	−	1.49194i	−0.832327	−	0.554285i	$-0.812992\pi$
$701$	−12.8347	−	39.5012i	−0.484761	−	1.49194i	0.347566	−	0.937656i	$-0.387008\pi$
$702$		0			0
$703$		−	5.52664i		−	0.208441i
$704$		0			0
$705$	45.6332	+	6.18832i	1.71865	+	0.233066i
$706$		0			0
$707$	−18.9979	+	6.17279i	−0.714489	+	0.232152i
$708$		0			0
$709$	−24.4440	−	17.7596i	−0.918015	−	0.666977i	0.0250143	−	0.999687i	$-0.492037\pi$
$709$	−24.4440	−	17.7596i	−0.918015	−	0.666977i	−0.943029	+	0.332710i	$0.892037\pi$
$710$		0			0
$711$	−7.95374	−	5.25360i	−0.298288	−	0.197025i
$712$		0			0
$713$	−14.6145	−	20.1152i	−0.547318	−	0.753319i
$714$		0			0
$715$	11.1084	+	7.25284i	0.415430	+	0.271241i
$716$		0			0
$717$	18.3634	−	9.87825i	0.685793	−	0.368910i
$718$		0			0
$719$	−47.7748	−	15.5230i	−1.78170	−	0.578909i	−0.782648	−	0.622465i	$-0.786131\pi$
$719$	−47.7748	−	15.5230i	−1.78170	−	0.578909i	−0.999051	+	0.0435556i	$0.986131\pi$
$720$		0			0
$721$	0.855212	−	1.17710i	0.0318497	−	0.0438374i
$722$		0			0
$723$	−35.0468	+	6.35469i	−1.30340	+	0.236333i
$724$		0			0
$725$	0.951585			0.0353410
$726$		0			0
$727$	−42.9707			−1.59369			−0.796847	−	0.604181i	$-0.793501\pi$
$727$	−42.9707			−1.59369			−0.796847	+	0.604181i	$0.793501\pi$
$728$		0			0
$729$	−12.8156	+	23.7647i	−0.474652	+	0.880174i
$730$		0			0
$731$	13.6699	−	18.8150i	0.505601	−	0.695899i
$732$		0			0
$733$	32.7807	+	10.6511i	1.21078	+	0.393408i	0.843718	−	0.536787i	$-0.180362\pi$
$733$	32.7807	+	10.6511i	1.21078	+	0.393408i	0.367066	+	0.930195i	$0.380362\pi$
$734$		0			0
$735$	9.38376	+	17.4441i	0.346125	+	0.643437i
$736$		0			0
$737$	32.7620	+	21.3908i	1.20681	+	0.787942i
$738$		0			0
$739$	0.669749	+	0.921830i	0.0246371	+	0.0339101i	0.821158	−	0.570701i	$-0.193329\pi$
$739$	0.669749	+	0.921830i	0.0246371	+	0.0339101i	−0.796521	+	0.604611i	$0.793329\pi$
$740$		0			0
$741$	−6.21527	+	12.9013i	−0.228324	+	0.473940i
$742$		0			0
$743$	−11.8635	−	8.61934i	−0.435230	−	0.316213i	0.348507	−	0.937306i	$-0.386689\pi$
$743$	−11.8635	−	8.61934i	−0.435230	−	0.316213i	−0.783737	+	0.621093i	$0.786689\pi$
$744$		0			0
$745$	−45.6372	+	14.8284i	−1.67202	+	0.543272i
$746$		0			0
$747$	−5.41949	−	1.49741i	−0.198289	−	0.0547875i
$748$		0			0
$749$		−	3.66250i		−	0.133825i
$750$		0			0
$751$	9.49151	+	29.2119i	0.346350	+	1.06596i	0.960857	+	0.277044i	$0.0893549\pi$
$751$	9.49151	+	29.2119i	0.346350	+	1.06596i	−0.614507	+	0.788911i	$0.710645\pi$
$752$		0			0
$753$	19.5922	−	20.4857i	0.713979	−	0.746542i
$754$		0			0
$755$	−10.9377	+	33.6628i	−0.398064	+	1.22512i
$756$		0			0
$757$	−29.7783	+	21.6352i	−1.08231	+	0.786345i	−0.978084	−	0.208209i	$-0.933237\pi$
$757$	−29.7783	+	21.6352i	−1.08231	+	0.786345i	−0.104226	+	0.994554i	$0.533237\pi$
$758$		0			0
$759$	25.3469	+	10.6881i	0.920034	+	0.387955i
$760$		0			0
$761$	14.4001	−	10.4623i	0.522004	−	0.379258i	−0.295354	−	0.955388i	$-0.595438\pi$
$761$	14.4001	−	10.4623i	0.522004	−	0.379258i	0.817358	+	0.576130i	$0.195438\pi$
$762$		0			0
$763$	−2.40134	+	7.39056i	−0.0869343	+	0.267556i
$764$		0			0
$765$	−42.3000	+	33.7126i	−1.52936	+	1.21888i
$766$		0			0
$767$	2.84528	+	8.75687i	0.102737	+	0.316192i
$768$		0			0
$769$		−	15.5249i		−	0.559841i	−0.960023	−	0.279920i	$-0.909692\pi$
$769$		−	15.5249i		−	0.559841i	0.960023	−	0.279920i	$-0.0903081\pi$
$770$		0			0
$771$	1.98683	−	14.6511i	0.0715541	−	0.527645i
$772$		0			0
$773$	−33.1016	+	10.7554i	−1.19058	+	0.386843i	−0.836288	−	0.548291i	$-0.815279\pi$
$773$	−33.1016	+	10.7554i	−1.19058	+	0.386843i	−0.354294	+	0.935134i	$0.615279\pi$
$774$		0			0
$775$	8.61438	+	6.25871i	0.309438	+	0.224820i
$776$		0			0
$777$	−2.57858	−	1.24225i	−0.0925060	−	0.0445655i
$778$		0			0
$779$	5.07866	+	6.99018i	0.181962	+	0.250449i
$780$		0			0
$781$	2.78330	−	1.06055i	0.0995944	−	0.0379495i
$782$		0			0
$783$	2.35093	−	0.535486i	0.0840155	−	0.0191367i
$784$		0			0
$785$	−24.5167	−	7.96596i	−0.875038	−	0.284317i
$786$		0			0
$787$	11.1034	−	15.2825i	0.395792	−	0.544761i	−0.563890	−	0.825850i	$-0.690696\pi$
$787$	11.1034	−	15.2825i	0.395792	−	0.544761i	0.959682	+	0.281089i	$0.0906956\pi$
$788$		0			0
$789$	−4.19231	−	23.1211i	−0.149250	−	0.823131i
$790$		0			0
$791$	−6.39323			−0.227317
$792$		0			0
$793$	−20.9443			−0.743753
$794$		0			0
$795$	−8.06173	−	44.4613i	−0.285920	−	1.57688i
$796$		0			0
$797$	−26.6012	+	36.6134i	−0.942261	+	1.29691i	0.0126187	+	0.999920i	$0.495983\pi$
$797$	−26.6012	+	36.6134i	−0.942261	+	1.29691i	−0.954880	+	0.296991i	$0.904017\pi$
$798$		0			0
$799$	64.6627	+	21.0102i	2.28760	+	0.743287i
$800$		0			0
$801$	−13.4918	−	35.9813i	−0.476710	−	1.27134i
$802$		0			0
$803$	9.62865	+	11.9505i	0.339788	+	0.421723i
$804$		0			0
$805$	12.2651	+	16.8814i	0.432286	+	0.594991i
$806$		0			0
$807$	18.4885	+	8.90697i	0.650826	+	0.313540i
$808$		0			0
$809$	19.7941	+	14.3813i	0.695925	+	0.505619i	0.878603	−	0.477554i	$-0.158476\pi$
$809$	19.7941	+	14.3813i	0.695925	+	0.505619i	−0.182678	+	0.983173i	$0.558476\pi$
$810$		0			0
$811$	11.5278	−	3.74561i	0.404796	−	0.131526i	−0.0995405	−	0.995034i	$-0.531737\pi$
$811$	11.5278	−	3.74561i	0.404796	−	0.131526i	0.504336	+	0.863507i	$0.331737\pi$
$812$		0			0
$813$	5.03945	−	37.1613i	0.176741	−	1.30330i
$814$		0			0
$815$			18.8051i			0.658715i
$816$		0			0
$817$	5.80888	+	17.8779i	0.203227	+	0.625468i
$818$		0			0
$819$	4.62234	+	5.79975i	0.161517	+	0.202660i
$820$		0			0
$821$	11.9303	−	36.7177i	0.416371	−	1.28146i	−0.494648	−	0.869093i	$-0.664703\pi$
$821$	11.9303	−	36.7177i	0.416371	−	1.28146i	0.911019	−	0.412364i	$-0.135297\pi$
$822$		0			0
$823$	−5.77674	+	4.19705i	−0.201365	+	0.146300i	−0.683898	−	0.729578i	$-0.739717\pi$
$823$	−5.77674	+	4.19705i	−0.201365	+	0.146300i	0.482533	+	0.875878i	$0.339717\pi$
$824$		0			0
$825$	−11.7380	−	0.998857i	−0.408666	−	0.0347757i
$826$		0			0
$827$	−11.6755	+	8.48277i	−0.405998	+	0.294975i	−0.771980	−	0.635647i	$-0.780733\pi$
$827$	−11.6755	+	8.48277i	−0.405998	+	0.294975i	0.365982	+	0.930622i	$0.380733\pi$
$828$		0			0
$829$	−17.2062	+	52.9553i	−0.597597	+	1.83921i	−0.0562483	+	0.998417i	$0.517914\pi$
$829$	−17.2062	+	52.9553i	−0.597597	+	1.83921i	−0.541349	+	0.840798i	$0.682086\pi$
$830$		0			0
$831$	4.87662	−	5.09904i	0.169168	−	0.176884i
$832$		0			0
$833$	9.03713	+	27.8134i	0.313118	+	0.963678i
$834$		0			0
$835$		−	6.73076i		−	0.232928i
$836$		0			0
$837$	24.8042	+	10.6149i	0.857358	+	0.366903i
$838$		0			0
$839$	−39.3719	+	12.7927i	−1.35927	+	0.441654i	−0.895799	−	0.444458i	$-0.853396\pi$
$839$	−39.3719	+	12.7927i	−1.35927	+	0.441654i	−0.463471	+	0.886112i	$0.653396\pi$
$840$		0			0
$841$	23.2873	+	16.9192i	0.803010	+	0.583421i
$842$		0			0
$843$	13.4296	−	27.8762i	0.462539	−	0.960108i
$844$		0			0
$845$	16.7481	+	23.0517i	0.576151	+	0.793003i
$846$		0			0
$847$	−1.79847	−	17.9620i	−0.0617961	−	0.617183i
$848$		0			0
$849$	−2.49417	−	4.63658i	−0.0855996	−	0.159127i
$850$		0			0
$851$	4.58589	+	1.49005i	0.157202	+	0.0510781i
$852$		0			0
$853$	21.9644	−	30.2313i	0.752045	−	1.03510i	−0.245789	−	0.969323i	$-0.579047\pi$
$853$	21.9644	−	30.2313i	0.752045	−	1.03510i	0.997834	−	0.0657781i	$-0.0209529\pi$
$854$		0			0
$855$	−1.94857	−	43.6773i	−0.0666398	−	1.49373i
$856$		0			0
$857$	−34.9831			−1.19500			−0.597499	−	0.801869i	$-0.703839\pi$
$857$	−34.9831			−1.19500			−0.597499	+	0.801869i	$0.703839\pi$
$858$		0			0
$859$	−3.21505			−0.109696			−0.0548481	−	0.998495i	$-0.517467\pi$
$859$	−3.21505			−0.109696			−0.0548481	+	0.998495i	$0.517467\pi$
$860$		0			0
$861$	4.40298	−	0.798349i	0.150053	−	0.0272077i
$862$		0			0
$863$	−26.6104	+	36.6260i	−0.905827	+	1.24676i	0.0627444	+	0.998030i	$0.480015\pi$
$863$	−26.6104	+	36.6260i	−0.905827	+	1.24676i	−0.968572	+	0.248735i	$0.919985\pi$
$864$		0			0
$865$	−2.39728	−	0.778924i	−0.0815101	−	0.0264842i
$866$		0			0
$867$	−44.3996	+	23.8840i	−1.50789	+	0.811142i
$868$		0			0
$869$	−0.525604	−	10.5251i	−0.0178299	−	0.357039i
$870$		0			0
$871$	−10.4458	−	14.3774i	−0.353943	−	0.487160i
$872$		0			0
$873$	−5.93746	+	8.98908i	−0.200953	+	0.304234i
$874$		0			0
$875$	10.3973	+	7.55407i	0.351492	+	0.255374i
$876$		0			0
$877$	45.4373	−	14.7635i	1.53431	−	0.498527i	0.584509	−	0.811387i	$-0.301287\pi$
$877$	45.4373	−	14.7635i	1.53431	−	0.498527i	0.949799	+	0.312860i	$0.101287\pi$
$878$		0			0
$879$	−40.0613	−	5.43271i	−1.35123	−	0.183241i
$880$		0			0
$881$		−	34.4685i		−	1.16127i	−0.814163	−	0.580636i	$-0.802804\pi$
$881$		−	34.4685i		−	1.16127i	0.814163	−	0.580636i	$-0.197196\pi$
$882$		0			0
$883$	11.4707	+	35.3032i	0.386020	+	1.18805i	0.935738	+	0.352696i	$0.114735\pi$
$883$	11.4707	+	35.3032i	0.386020	+	1.18805i	−0.549718	+	0.835350i	$0.685265\pi$
$884$		0			0
$885$	−20.3156	−	19.4295i	−0.682902	−	0.653115i
$886$		0			0
$887$	−13.2813	+	40.8757i	−0.445943	+	1.37247i	0.435502	+	0.900188i	$0.356571\pi$
$887$	−13.2813	+	40.8757i	−0.445943	+	1.37247i	−0.881446	+	0.472285i	$0.843429\pi$
$888$		0			0
$889$	−0.313826	+	0.228008i	−0.0105254	+	0.00764715i
$890$		0			0
$891$	−29.5615	+	4.13763i	−0.990346	+	0.138616i
$892$		0			0
$893$	−44.4598	+	32.3019i	−1.48779	+	1.08094i
$894$		0			0
$895$	−15.2338	+	46.8848i	−0.509210	+	1.56719i
$896$		0			0
$897$	−9.02948	−	8.63563i	−0.301486	−	0.288335i
$898$		0			0
$899$	−0.744535	−	2.29144i	−0.0248316	−	0.0764239i
$900$		0			0
$901$		−	66.7138i		−	2.22256i
$902$		0			0
$903$	9.64702	+	1.30823i	0.321033	+	0.0435353i
$904$		0			0
$905$	32.5248	−	10.5679i	1.08116	−	0.351290i
$906$		0			0
$907$	−30.6111	−	22.2403i	−1.01642	−	0.738476i	−0.0508777	−	0.998705i	$-0.516202\pi$
$907$	−30.6111	−	22.2403i	−1.01642	−	0.738476i	−0.965547	+	0.260229i	$0.916202\pi$
$908$		0			0
$909$	−20.1260	+	30.4699i	−0.667536	+	1.01062i
$910$		0			0
$911$	−11.9412	−	16.4356i	−0.395629	−	0.544536i	0.564011	−	0.825767i	$-0.309257\pi$
$911$	−11.9412	−	16.4356i	−0.395629	−	0.544536i	−0.959640	+	0.281231i	$0.909257\pi$
$912$		0			0
$913$	−2.21330	−	5.80857i	−0.0732496	−	0.192236i
$914$		0			0
$915$	56.3132	−	30.2927i	1.86166	−	1.00144i
$916$		0			0
$917$	−8.22115	−	2.67121i	−0.271486	−	0.0882112i
$918$		0			0
$919$	19.6230	−	27.0088i	0.647304	−	0.890938i	−0.351674	−	0.936122i	$-0.614388\pi$
$919$	19.6230	−	27.0088i	0.647304	−	0.890938i	0.998979	+	0.0451844i	$0.0143876\pi$
$920$		0			0
$921$	−51.1647	+	9.27719i	−1.68593	+	0.305694i
$922$		0			0
$923$	−1.35284			−0.0445293
$924$		0			0
$925$	−2.06499			−0.0678964
$926$		0			0
$927$	−0.118543	−	2.65715i	−0.00389347	−	0.0872721i
$928$		0			0
$929$	−13.8375	+	19.0457i	−0.453995	+	0.624870i	−0.973250	−	0.229749i	$-0.926210\pi$
$929$	−13.8375	+	19.0457i	−0.453995	+	0.624870i	0.519255	+	0.854619i	$0.326210\pi$
$930$		0			0
$931$	−22.4811	−	7.30454i	−0.736787	−	0.239397i
$932$		0			0
$933$	−0.406350	−	0.755393i	−0.0133033	−	0.0247305i
$934$		0			0
$935$	−57.7239	−	15.6196i	−1.88777	−	0.510814i
$936$		0			0
$937$	14.6111	+	20.1105i	0.477324	+	0.656981i	0.977988	−	0.208661i	$-0.0669106\pi$
$937$	14.6111	+	20.1105i	0.477324	+	0.656981i	−0.500664	+	0.865642i	$0.666911\pi$
$938$		0			0
$939$	−21.3336	+	44.2828i	−0.696194	+	1.44511i
$940$		0			0
$941$	5.71703	+	4.15366i	0.186370	+	0.135406i	0.677058	−	0.735930i	$-0.263255\pi$
$941$	5.71703	+	4.15366i	0.186370	+	0.135406i	−0.490688	+	0.871335i	$0.663255\pi$
$942$		0			0
$943$	−7.16957	+	2.32953i	−0.233473	+	0.0758601i
$944$		0			0
$945$	−20.8166	−	8.90839i	−0.677164	−	0.289790i
$946$		0			0
$947$		−	11.7619i		−	0.382210i	−0.981570	−	0.191105i	$-0.938793\pi$
$947$		−	11.7619i		−	0.382210i	0.981570	−	0.191105i	$-0.0612071\pi$
$948$		0			0
$949$	−2.15401	−	6.62936i	−0.0699221	−	0.215198i
$950$		0			0
$951$	7.94986	−	8.31244i	0.257792	−	0.269549i
$952$		0			0
$953$	0.840470	−	2.58670i	0.0272255	−	0.0837915i	−0.936521	−	0.350613i	$-0.885973\pi$
$953$	0.840470	−	2.58670i	0.0272255	−	0.0837915i	0.963746	+	0.266821i	$0.0859733\pi$
$954$		0			0
$955$	−6.93616	+	5.03942i	−0.224449	+	0.163072i
$956$		0			0
$957$	2.01592	+	1.74402i	0.0651655	+	0.0563763i
$958$		0			0
$959$	−1.23177	+	0.894931i	−0.0397758	+	0.0288988i
$960$		0			0
$961$	−1.24840	+	3.84217i	−0.0402708	+	0.123941i
$962$		0			0
$963$	−4.17290	−	5.23583i	−0.134470	−	0.168722i
$964$		0			0
$965$	8.01266	+	24.6604i	0.257937	+	0.793847i
$966$		0			0
$967$		−	21.8182i		−	0.701625i	−0.936446	−	0.350812i	$-0.885905\pi$
$967$		−	21.8182i		−	0.701625i	0.936446	−	0.350812i	$-0.114095\pi$
$968$		0			0
$969$	8.67424	−	63.9646i	0.278657	−	2.05484i
$970$		0			0
$971$	42.1986	−	13.7111i	1.35422	−	0.440012i	0.460108	−	0.887863i	$-0.347811\pi$
$971$	42.1986	−	13.7111i	1.35422	−	0.440012i	0.894108	+	0.447851i	$0.147811\pi$
$972$		0			0
$973$	−11.2229	−	8.15395i	−0.359791	−	0.261404i
$974$		0			0
$975$	4.82046	+	2.32229i	0.154378	+	0.0743728i
$976$		0			0
$977$	18.4138	+	25.3445i	0.589111	+	0.810841i	0.994657	−	0.103233i	$-0.0329187\pi$
$977$	18.4138	+	25.3445i	0.589111	+	0.810841i	−0.405546	+	0.914074i	$0.632919\pi$
$978$		0			0
$979$	23.2258	−	35.5724i	0.742298	−	1.13690i
$980$		0			0
$981$	4.98759	+	13.3014i	0.159241	+	0.424680i
$982$		0			0
$983$	36.5417	+	11.8731i	1.16550	+	0.378694i	0.826962	−	0.562259i	$-0.190067\pi$
$983$	36.5417	+	11.8731i	1.16550	+	0.378694i	0.338539	+	0.940952i	$0.390067\pi$
$984$		0			0
$985$	21.8006	−	30.0059i	0.694624	−	0.956068i
$986$		0			0
$987$	5.07776	+	28.0044i	0.161627	+	0.891389i
$988$		0			0
$989$	−16.4008			−0.521517
$990$		0			0
$991$	28.2808			0.898371			0.449185	−	0.893439i	$-0.351714\pi$
$991$	28.2808			0.898371			0.449185	+	0.893439i	$0.351714\pi$
$992$		0			0
$993$	−2.28987	−	12.6289i	−0.0726667	−	0.400764i
$994$		0			0
$995$	24.9221	−	34.3023i	0.790083	−	1.08746i
$996$		0			0
$997$	22.4761	+	7.30292i	0.711825	+	0.231286i	0.642475	−	0.766307i	$-0.277908\pi$
$997$	22.4761	+	7.30292i	0.711825	+	0.231286i	0.0693496	+	0.997592i	$0.477908\pi$
$998$		0			0
$999$	−5.10165	+	1.16203i	−0.161409	+	0.0367651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.bn.a.305.2		8
3.2	odd	2		528.2.bn.b.305.2		8
4.3	odd	2		66.2.h.b.41.1	yes	8
11.7	odd	10		528.2.bn.b.161.2		8
12.11	even	2		66.2.h.a.41.1	yes	8
33.29	even	10	inner	528.2.bn.a.161.1		8
44.3	odd	10		726.2.h.h.215.2		8
44.7	even	10		66.2.h.a.29.1	✓	8
44.15	odd	10		726.2.h.j.161.1		8
44.19	even	10		726.2.h.c.215.2		8
44.27	odd	10		726.2.h.f.233.2		8
44.31	odd	10		726.2.b.c.725.1		8
44.35	even	10		726.2.b.e.725.1		8
44.39	even	10		726.2.h.a.233.2		8
44.43	even	2		726.2.h.d.239.1		8
132.35	odd	10		726.2.b.c.725.2		8
132.47	even	10		726.2.h.a.215.2		8
132.59	even	10		726.2.h.d.161.2		8
132.71	even	10		726.2.h.c.233.2		8
132.83	odd	10		726.2.h.h.233.2		8
132.95	odd	10		66.2.h.b.29.2	yes	8
132.107	odd	10		726.2.h.f.215.2		8
132.119	even	10		726.2.b.e.725.2		8
132.131	odd	2		726.2.h.j.239.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.h.a.29.1	✓	8	44.7	even	10
66.2.h.a.41.1	yes	8	12.11	even	2
66.2.h.b.29.2	yes	8	132.95	odd	10
66.2.h.b.41.1	yes	8	4.3	odd	2
528.2.bn.a.161.1		8	33.29	even	10	inner
528.2.bn.a.305.2		8	1.1	even	1	trivial
528.2.bn.b.161.2		8	11.7	odd	10
528.2.bn.b.305.2		8	3.2	odd	2
726.2.b.c.725.1		8	44.31	odd	10
726.2.b.c.725.2		8	132.35	odd	10
726.2.b.e.725.1		8	44.35	even	10
726.2.b.e.725.2		8	132.119	even	10
726.2.h.a.215.2		8	132.47	even	10
726.2.h.a.233.2		8	44.39	even	10
726.2.h.c.215.2		8	44.19	even	10
726.2.h.c.233.2		8	132.71	even	10
726.2.h.d.161.2		8	132.59	even	10
726.2.h.d.239.1		8	44.43	even	2
726.2.h.f.215.2		8	132.107	odd	10
726.2.h.f.233.2		8	44.27	odd	10
726.2.h.h.215.2		8	44.3	odd	10
726.2.h.h.233.2		8	132.83	odd	10
726.2.h.j.161.1		8	44.15	odd	10
726.2.h.j.239.1		8	132.131	odd	2

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:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.bn (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 1.70426i) q^{3} +(-1.56076 + 2.14820i) q^{5} +(-1.56076 - 0.507121i) q^{7} +(-2.80902 + 1.05329i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 1.70426i) q^{3} +(-1.56076 + 2.14820i) q^{5} +(-1.56076 - 0.507121i) q^{7} +(-2.80902 + 1.05329i) q^{9} +(-2.77710 - 1.81321i) q^{11} +(0.885446 + 1.21871i) q^{13} +(-4.14339 - 1.99611i) q^{15} +(-5.49344 - 3.99122i) q^{17} +(5.21982 - 1.69602i) q^{19} +(0.381966 - 2.81665i) q^{21} +4.78856i q^{23} +(-0.633706 - 1.95035i) q^{25} +(-2.66312 - 4.46182i) q^{27} +(-0.143392 + 0.441315i) q^{29} +(-4.20067 + 3.05196i) q^{31} +(2.23201 - 5.29321i) q^{33} +(3.52536 - 2.56132i) q^{35} +(0.311168 - 0.957676i) q^{37} +(-1.80339 + 1.88563i) q^{39} +(0.486479 + 1.49723i) q^{41} +3.42500i q^{43} +(2.12151 - 7.67826i) q^{45} +(-9.52285 + 3.09416i) q^{47} +(-3.48433 - 2.53151i) q^{49} +(5.10451 - 10.5956i) q^{51} +(5.77495 + 7.94853i) q^{53} +(8.22951 - 3.13578i) q^{55} +(4.50348 + 8.37184i) q^{57} +(5.81307 + 1.88878i) q^{59} +(-8.17223 + 11.2481i) q^{61} +(4.91834 - 0.219422i) q^{63} -4.00000 q^{65} -11.7972 q^{67} +(-8.16097 + 1.47975i) q^{69} +(-0.527864 + 0.726543i) q^{71} +(-4.40076 - 1.42989i) q^{73} +(3.12808 - 1.68269i) q^{75} +(3.41486 + 4.23830i) q^{77} +(1.86762 + 2.57056i) q^{79} +(6.78115 - 5.91743i) q^{81} +(1.51625 + 1.10162i) q^{83} +(17.1478 - 5.57167i) q^{85} +(-0.796426 - 0.108003i) q^{87} +12.8092i q^{89} +(-0.763932 - 2.35114i) q^{91} +(-6.49942 - 6.21593i) q^{93} +(-4.50348 + 13.8603i) q^{95} +(2.90517 - 2.11073i) q^{97} +(9.71075 + 2.16824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 18 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 18 * q^9	\( 8 q - 2 q^{3} - 18 q^{9} + q^{11} - 9 q^{15} - 10 q^{17} + 15 q^{19} + 12 q^{21} - 6 q^{25} + 10 q^{27} + 23 q^{29} - 13 q^{31} + 17 q^{33} + 13 q^{35} + 6 q^{37} - 18 q^{39} + 2 q^{41} - 8 q^{45} - 10 q^{47} - 18 q^{49} + 30 q^{51} + 15 q^{53} + 14 q^{55} + 20 q^{57} + 25 q^{59} - 10 q^{61} - 16 q^{63} - 32 q^{65} + 2 q^{67} - 26 q^{69} - 40 q^{71} + 5 q^{73} + 34 q^{75} - 12 q^{77} - 10 q^{79} + 14 q^{81} + 21 q^{83} + 30 q^{85} - 42 q^{87} - 24 q^{91} - 53 q^{93} - 20 q^{95} + 9 q^{97} - 34 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 18 * q^9 + q^11 - 9 * q^15 - 10 * q^17 + 15 * q^19 + 12 * q^21 - 6 * q^25 + 10 * q^27 + 23 * q^29 - 13 * q^31 + 17 * q^33 + 13 * q^35 + 6 * q^37 - 18 * q^39 + 2 * q^41 - 8 * q^45 - 10 * q^47 - 18 * q^49 + 30 * q^51 + 15 * q^53 + 14 * q^55 + 20 * q^57 + 25 * q^59 - 10 * q^61 - 16 * q^63 - 32 * q^65 + 2 * q^67 - 26 * q^69 - 40 * q^71 + 5 * q^73 + 34 * q^75 - 12 * q^77 - 10 * q^79 + 14 * q^81 + 21 * q^83 + 30 * q^85 - 42 * q^87 - 24 * q^91 - 53 * q^93 - 20 * q^95 + 9 * q^97 - 34 * q^99

Introduction

L-functions

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Database

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