LMFDB - Embedded newform 572.2.x.a.25.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(25,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("572.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.x (of order $10$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.8
Character	$\chi$	$=$	572.25
Dual form			572.2.x.a.389.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0444965 - 0.136946i) q^{3} +(1.21904 - 1.67786i) q^{5} +(3.54683 + 1.15243i) q^{7} +(2.41028 - 1.75117i) q^{9} +O(q^{10})$	\(q+(-0.0444965 - 0.136946i) q^{3} +(1.21904 - 1.67786i) q^{5} +(3.54683 + 1.15243i) q^{7} +(2.41028 - 1.75117i) q^{9} +(-3.27866 + 0.500402i) q^{11} +(2.92250 + 2.11163i) q^{13} +(-0.284019 - 0.0922834i) q^{15} +(-4.88065 - 3.54600i) q^{17} +(-5.67834 + 1.84501i) q^{19} -0.537004i q^{21} +9.27407 q^{23} +(0.215924 + 0.664547i) q^{25} +(-0.696545 - 0.506070i) q^{27} +(2.59933 - 7.99990i) q^{29} +(-0.0444393 - 0.0611655i) q^{31} +(0.214417 + 0.426734i) q^{33} +(6.25733 - 4.54622i) q^{35} +(6.84207 + 2.22312i) q^{37} +(0.159139 - 0.494186i) q^{39} +(-1.12720 + 0.366249i) q^{41} -2.80932 q^{43} -6.17884i q^{45} +(4.57778 - 1.48741i) q^{47} +(5.58877 + 4.06048i) q^{49} +(-0.268439 + 0.826172i) q^{51} +(-5.54287 + 4.02713i) q^{53} +(-3.15719 + 6.11113i) q^{55} +(0.505333 + 0.695531i) q^{57} +(-2.50595 - 0.814232i) q^{59} +(-5.78727 - 4.20470i) q^{61} +(10.5669 - 3.43341i) q^{63} +(7.10565 - 2.32938i) q^{65} +7.07902i q^{67} +(-0.412664 - 1.27005i) q^{69} +(-3.31360 + 4.56078i) q^{71} +(-4.21701 - 1.37019i) q^{73} +(0.0813993 - 0.0591401i) q^{75} +(-12.2055 - 2.00360i) q^{77} +(0.128633 - 0.0934571i) q^{79} +(2.72362 - 8.38244i) q^{81} +(-2.82387 + 3.88673i) q^{83} +(-11.8994 + 3.86634i) q^{85} -1.21122 q^{87} +9.89947i q^{89} +(7.93208 + 10.8576i) q^{91} +(-0.00639898 + 0.00880745i) q^{93} +(-3.82644 + 11.7766i) q^{95} +(-8.41519 - 11.5825i) q^{97} +(-7.02618 + 6.94759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^9	$ 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) $ 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.0444965	−	0.136946i	−0.0256901	−	0.0790659i	0.937389	−	0.348283i	$-0.113235\pi$
$3$	−0.0444965	−	0.136946i	−0.0256901	−	0.0790659i	−0.963080	+	0.269217i	$0.913235\pi$
$4$		0			0
$5$	1.21904	−	1.67786i	0.545169	−	0.750361i	−0.444178	−	0.895939i	$-0.646504\pi$
$5$	1.21904	−	1.67786i	0.545169	−	0.750361i	0.989347	+	0.145578i	$0.0465041\pi$
$6$		0			0
$7$	3.54683	+	1.15243i	1.34058	+	0.435579i	0.889512	−	0.456913i	$-0.151045\pi$
$7$	3.54683	+	1.15243i	1.34058	+	0.435579i	0.451064	+	0.892492i	$0.351045\pi$
$8$		0			0
$9$	2.41028	−	1.75117i	0.803426	−	0.583723i
$10$		0			0
$11$	−3.27866	+	0.500402i	−0.988553	+	0.150877i
$11$	−3.27866	+	0.500402i	−0.988553	+	0.150877i
$12$		0			0
$13$	2.92250	+	2.11163i	0.810555	+	0.585662i
$13$	2.92250	+	2.11163i	0.810555	+	0.585662i
$14$		0			0
$15$	−0.284019	−	0.0922834i	−0.0733334	−	0.0238275i
$16$		0			0
$17$	−4.88065	−	3.54600i	−1.18373	−	0.860032i	−0.191144	−	0.981562i	$-0.561220\pi$
$17$	−4.88065	−	3.54600i	−1.18373	−	0.860032i	−0.992588	+	0.121530i	$0.961220\pi$
$18$		0			0
$19$	−5.67834	+	1.84501i	−1.30270	+	0.423273i	−0.876520	−	0.481365i	$-0.840141\pi$
$19$	−5.67834	+	1.84501i	−1.30270	+	0.423273i	−0.426181	+	0.904638i	$0.640141\pi$
$20$		0			0
$21$		−	0.537004i		−	0.117184i
$22$		0			0
$23$	9.27407			1.93378			0.966888	−	0.255199i	$-0.0821411\pi$
$23$	9.27407			1.93378			0.966888	+	0.255199i	$0.0821411\pi$
$24$		0			0
$25$	0.215924	+	0.664547i	0.0431849	+	0.132909i
$26$		0			0
$27$	−0.696545	−	0.506070i	−0.134050	−	0.0973931i
$28$		0			0
$29$	2.59933	−	7.99990i	0.482683	−	1.48554i	−0.352627	−	0.935764i	$-0.614711\pi$
$29$	2.59933	−	7.99990i	0.482683	−	1.48554i	0.835309	−	0.549780i	$-0.185289\pi$
$30$		0			0
$31$	−0.0444393	−	0.0611655i	−0.00798154	−	0.0109856i	0.805008	−	0.593265i	$-0.202161\pi$
$31$	−0.0444393	−	0.0611655i	−0.00798154	−	0.0109856i	−0.812989	+	0.582279i	$0.802161\pi$
$32$		0			0
$33$	0.214417	+	0.426734i	0.0373252	+	0.0742848i
$34$		0			0
$35$	6.25733	−	4.54622i	1.05768	−	0.768451i
$36$		0			0
$37$	6.84207	+	2.22312i	1.12483	+	0.365479i	0.811609	−	0.584201i	$-0.198592\pi$
$37$	6.84207	+	2.22312i	1.12483	+	0.365479i	0.313221	+	0.949680i	$0.398592\pi$
$38$		0			0
$39$	0.159139	−	0.494186i	0.0254827	−	0.0791330i
$40$		0			0
$41$	−1.12720	+	0.366249i	−0.176039	+	0.0571985i	−0.395710	−	0.918375i	$-0.629501\pi$
$41$	−1.12720	+	0.366249i	−0.176039	+	0.0571985i	0.219671	+	0.975574i	$0.429501\pi$
$42$		0			0
$43$	−2.80932			−0.428418			−0.214209	−	0.976788i	$-0.568717\pi$
$43$	−2.80932			−0.428418			−0.214209	+	0.976788i	$0.568717\pi$
$44$		0			0
$45$		−	6.17884i		−	0.921087i
$46$		0			0
$47$	4.57778	−	1.48741i	0.667737	−	0.216961i	0.0445186	−	0.999009i	$-0.485825\pi$
$47$	4.57778	−	1.48741i	0.667737	−	0.216961i	0.623219	+	0.782048i	$0.285825\pi$
$48$		0			0
$49$	5.58877	+	4.06048i	0.798396	+	0.580068i
$50$		0			0
$51$	−0.268439	+	0.826172i	−0.0375890	+	0.115687i
$52$		0			0
$53$	−5.54287	+	4.02713i	−0.761372	+	0.553169i	−0.899331	−	0.437269i	$-0.855946\pi$
$53$	−5.54287	+	4.02713i	−0.761372	+	0.553169i	0.137959	+	0.990438i	$0.455946\pi$
$54$		0			0
$55$	−3.15719	+	6.11113i	−0.425716	+	0.824025i
$56$		0			0
$57$	0.505333	+	0.695531i	0.0669330	+	0.0921254i
$58$		0			0
$59$	−2.50595	−	0.814232i	−0.326247	−	0.106004i	0.141314	−	0.989965i	$-0.454867\pi$
$59$	−2.50595	−	0.814232i	−0.326247	−	0.106004i	−0.467561	+	0.883961i	$0.654867\pi$
$60$		0			0
$61$	−5.78727	−	4.20470i	−0.740984	−	0.538356i	0.152035	−	0.988375i	$-0.451417\pi$
$61$	−5.78727	−	4.20470i	−0.740984	−	0.538356i	−0.893019	+	0.450019i	$0.851417\pi$
$62$		0			0
$63$	10.5669	−	3.43341i	1.33131	−	0.432569i
$64$		0			0
$65$	7.10565	−	2.32938i	0.881348	−	0.288924i
$66$		0			0
$67$			7.07902i			0.864840i	0.901672	+	0.432420i	$0.142340\pi$
$67$			7.07902i			0.864840i	−0.901672	+	0.432420i	$0.857660\pi$
$68$		0			0
$69$	−0.412664	−	1.27005i	−0.0496789	−	0.152896i
$70$		0			0
$71$	−3.31360	+	4.56078i	−0.393252	+	0.541265i	−0.959034	−	0.283290i	$-0.908574\pi$
$71$	−3.31360	+	4.56078i	−0.393252	+	0.541265i	0.565783	+	0.824554i	$0.308574\pi$
$72$		0			0
$73$	−4.21701	−	1.37019i	−0.493564	−	0.160369i	0.0516505	−	0.998665i	$-0.483552\pi$
$73$	−4.21701	−	1.37019i	−0.493564	−	0.160369i	−0.545215	+	0.838297i	$0.683552\pi$
$74$		0			0
$75$	0.0813993	−	0.0591401i	0.00939919	−	0.00682891i
$76$		0			0
$77$	−12.2055	−	2.00360i	−1.39095	−	0.228331i
$78$		0			0
$79$	0.128633	−	0.0934571i	0.0144723	−	0.0105147i	−0.580526	−	0.814242i	$-0.697153\pi$
$79$	0.128633	−	0.0934571i	0.0144723	−	0.0105147i	0.594998	+	0.803727i	$0.297153\pi$
$80$		0			0
$81$	2.72362	−	8.38244i	0.302625	−	0.931383i
$82$		0			0
$83$	−2.82387	+	3.88673i	−0.309960	+	0.426624i	−0.935369	−	0.353674i	$-0.884932\pi$
$83$	−2.82387	+	3.88673i	−0.309960	+	0.426624i	0.625409	+	0.780297i	$0.284932\pi$
$84$		0			0
$85$	−11.8994	+	3.86634i	−1.29067	+	0.419364i
$86$		0			0
$87$	−1.21122			−0.129856
$88$		0			0
$89$			9.89947i			1.04934i	0.851305	+	0.524671i	$0.175812\pi$
$89$			9.89947i			1.04934i	−0.851305	+	0.524671i	$0.824188\pi$
$90$		0			0
$91$	7.93208	+	10.8576i	0.831508	+	1.13819i
$92$		0			0
$93$	−0.00639898	+	0.00880745i	−0.000663544	+	0.000913290i
$94$		0			0
$95$	−3.82644	+	11.7766i	−0.392585	+	1.20825i
$96$		0			0
$97$	−8.41519	−	11.5825i	−0.854433	−	1.17603i	−0.982868	−	0.184309i	$-0.940995\pi$
$97$	−8.41519	−	11.5825i	−0.854433	−	1.17603i	0.128435	−	0.991718i	$-0.459005\pi$
$98$		0			0
$99$	−7.02618	+	6.94759i	−0.706158	+	0.698259i
$100$		0			0
$101$	−11.2913	+	8.20364i	−1.12353	+	0.816293i	−0.984741	−	0.174029i	$-0.944321\pi$
$101$	−11.2913	+	8.20364i	−1.12353	+	0.816293i	−0.138790	+	0.990322i	$0.544321\pi$
$102$		0			0
$103$	−2.15169	+	6.62222i	−0.212012	+	0.652507i	0.787340	+	0.616519i	$0.211458\pi$
$103$	−2.15169	+	6.62222i	−0.212012	+	0.652507i	−0.999352	+	0.0359878i	$0.988542\pi$
$104$		0			0
$105$	−0.901017	−	0.654627i	−0.0879302	−	0.0638850i
$106$		0			0
$107$	2.71233	+	8.34770i	0.262211	+	0.807002i	0.992323	+	0.123675i	$0.0394679\pi$
$107$	2.71233	+	8.34770i	0.262211	+	0.807002i	−0.730112	+	0.683328i	$0.760532\pi$
$108$		0			0
$109$		−	11.2161i		−	1.07431i	−0.843483	−	0.537156i	$-0.819499\pi$
$109$		−	11.2161i		−	1.07431i	0.843483	−	0.537156i	$-0.180501\pi$
$110$		0			0
$111$		−	1.03592i		−	0.0983249i
$112$		0			0
$113$	−3.56478	−	10.9713i	−0.335346	−	1.03209i	−0.966551	−	0.256474i	$-0.917439\pi$
$113$	−3.56478	−	10.9713i	−0.335346	−	1.03209i	0.631205	−	0.775616i	$-0.282561\pi$
$114$		0			0
$115$	11.3054	−	15.5606i	1.05424	−	1.45103i
$116$		0			0
$117$	10.7419	−	0.0281642i	0.993085	−	0.00260378i
$118$		0			0
$119$	−13.2243	−	18.2017i	−1.21227	−	1.66855i
$120$		0			0
$121$	10.4992	−	3.28130i	0.954472	−	0.298300i
$122$		0			0
$123$	0.100313	+	0.138069i	0.00904490	+	0.0124492i
$124$		0			0
$125$	11.2404	+	3.65224i	1.00538	+	0.326666i
$126$		0			0
$127$	4.95270	+	3.59834i	0.439481	+	0.319301i	0.785429	−	0.618952i	$-0.212443\pi$
$127$	4.95270	+	3.59834i	0.439481	+	0.319301i	−0.345948	+	0.938254i	$0.612443\pi$
$128$		0			0
$129$	0.125005	+	0.384726i	0.0110061	+	0.0338733i
$130$		0			0
$131$	3.53499			0.308853			0.154427	−	0.988004i	$-0.450647\pi$
$131$	3.53499			0.308853			0.154427	+	0.988004i	$0.450647\pi$
$132$		0			0
$133$	−22.2664			−1.93074
$134$		0			0
$135$	−1.69823	+	0.551787i	−0.146160	+	0.0474903i
$136$		0			0
$137$	0.329390	−	0.453366i	0.0281417	−	0.0387337i	−0.794714	−	0.606984i	$-0.792379\pi$
$137$	0.329390	−	0.453366i	0.0281417	−	0.0387337i	0.822856	+	0.568250i	$0.192379\pi$
$138$		0			0
$139$	−6.66923	+	20.5258i	−0.565677	+	1.74097i	0.100256	+	0.994962i	$0.468034\pi$
$139$	−6.66923	+	20.5258i	−0.565677	+	1.74097i	−0.665932	+	0.746012i	$0.731966\pi$
$140$		0			0
$141$	−0.407390	−	0.560725i	−0.0343084	−	0.0472215i
$142$		0			0
$143$	−10.6385	−	5.46090i	−0.889639	−	0.456664i
$144$		0			0
$145$	−10.2540	−	14.1135i	−0.851551	−	1.17206i
$146$		0			0
$147$	0.307386	−	0.946038i	0.0253528	−	0.0780279i
$148$		0			0
$149$	−10.0343	+	13.8110i	−0.822041	+	1.13144i	0.167311	+	0.985904i	$0.446491\pi$
$149$	−10.0343	+	13.8110i	−0.822041	+	1.13144i	−0.989353	+	0.145538i	$0.953509\pi$
$150$		0			0
$151$	−14.6391	+	4.75655i	−1.19132	+	0.387082i	−0.836559	−	0.547876i	$-0.815436\pi$
$151$	−14.6391	+	4.75655i	−1.19132	+	0.387082i	−0.354757	+	0.934959i	$0.615436\pi$
$152$		0			0
$153$	−17.9734			−1.45306
$154$		0			0
$155$	−0.156800			−0.0125945
$156$		0			0
$157$	6.24271	+	19.2131i	0.498223	+	1.53337i	0.811874	+	0.583833i	$0.198448\pi$
$157$	6.24271	+	19.2131i	0.498223	+	1.53337i	−0.313651	+	0.949538i	$0.601552\pi$
$158$		0			0
$159$	0.798139	+	0.579882i	0.0632965	+	0.0459876i
$160$		0			0
$161$	32.8935	+	10.6878i	2.59237	+	0.842313i
$162$		0			0
$163$	−7.34436	−	10.1086i	−0.575254	−	0.791770i	0.417911	−	0.908488i	$-0.362762\pi$
$163$	−7.34436	−	10.1086i	−0.575254	−	0.791770i	−0.993165	+	0.116718i	$0.962762\pi$
$164$		0			0
$165$	0.977380	+	0.160442i	0.0760890	+	0.0124904i
$166$		0			0
$167$	3.13442	+	4.31416i	0.242549	+	0.333839i	0.912884	−	0.408219i	$-0.133850\pi$
$167$	3.13442	+	4.31416i	0.242549	+	0.333839i	−0.670336	+	0.742058i	$0.733850\pi$
$168$		0			0
$169$	4.08200	+	12.3425i	0.314000	+	0.949423i
$170$		0			0
$171$	−10.4555	+	14.3907i	−0.799549	+	1.10049i
$172$		0			0
$173$	−1.38870	−	4.27397i	−0.105581	−	0.324944i	0.884286	−	0.466946i	$-0.154646\pi$
$173$	−1.38870	−	4.27397i	−0.105581	−	0.324944i	−0.989866	+	0.142003i	$0.954646\pi$
$174$		0			0
$175$			2.60587i			0.196986i
$176$		0			0
$177$			0.379411i			0.0285182i
$178$		0			0
$179$	−4.85538	−	14.9433i	−0.362908	−	1.11692i	−0.951281	−	0.308326i	$-0.900231\pi$
$179$	−4.85538	−	14.9433i	−0.362908	−	1.11692i	0.588373	−	0.808590i	$-0.299769\pi$
$180$		0			0
$181$	2.18734	+	1.58920i	0.162584	+	0.118124i	0.666102	−	0.745860i	$-0.267961\pi$
$181$	2.18734	+	1.58920i	0.162584	+	0.118124i	−0.503518	+	0.863984i	$0.667961\pi$
$182$		0			0
$183$	−0.318304	+	0.979639i	−0.0235297	+	0.0724170i
$184$		0			0
$185$	12.0708	−	8.76996i	0.887464	−	0.644780i
$186$		0			0
$187$	17.7764	+	9.18384i	1.29994	+	0.671589i
$188$		0			0
$189$	−1.88731	−	2.59766i	−0.137282	−	0.188952i
$190$		0			0
$191$	−1.62821	+	5.01113i	−0.117813	+	0.362593i	−0.992523	−	0.122054i	$-0.961052\pi$
$191$	−1.62821	+	5.01113i	−0.117813	+	0.362593i	0.874710	+	0.484647i	$0.161052\pi$
$192$		0			0
$193$	−6.89554	+	9.49089i	−0.496352	+	0.683169i	−0.981544	−	0.191238i	$-0.938750\pi$
$193$	−6.89554	+	9.49089i	−0.496352	+	0.683169i	0.485192	+	0.874408i	$0.338750\pi$
$194$		0			0
$195$	−0.635177	−	0.869443i	−0.0454859	−	0.0622621i
$196$		0			0
$197$		−	1.22973i		−	0.0876147i	−0.999040	−	0.0438074i	$-0.986051\pi$
$197$		−	1.22973i		−	0.0876147i	0.999040	−	0.0438074i	$-0.0139488\pi$
$198$		0			0
$199$	5.08855			0.360717			0.180359	−	0.983601i	$-0.442274\pi$
$199$	5.08855			0.360717			0.180359	+	0.983601i	$0.442274\pi$
$200$		0			0
$201$	0.969445	−	0.314992i	0.0683794	−	0.0222178i
$202$		0			0
$203$	18.4387	−	25.3787i	1.29414	−	1.78124i
$204$		0			0
$205$	−0.759580	+	2.33775i	−0.0530514	+	0.163275i
$206$		0			0
$207$	22.3531	−	16.2405i	1.55365	−	1.12879i
$208$		0			0
$209$	17.6941	−	8.89060i	1.22393	−	0.614976i
$210$		0			0
$211$	−13.3774	+	9.71925i	−0.920938	+	0.669101i	−0.943757	−	0.330639i	$-0.892736\pi$
$211$	−13.3774	+	9.71925i	−0.920938	+	0.669101i	0.0228193	+	0.999740i	$0.492736\pi$
$212$		0			0
$213$	0.772025	+	0.250846i	0.0528983	+	0.0171877i
$214$		0			0
$215$	−3.42466	+	4.71365i	−0.233560	+	0.321468i
$216$		0			0
$217$	−0.0871294	−	0.268157i	−0.00591473	−	0.0182037i
$218$		0			0
$219$			0.638473i			0.0431440i
$220$		0			0
$221$	−6.77584	−	20.6693i	−0.455792	−	1.39037i
$222$		0			0
$223$	−17.9643	+	5.83697i	−1.20298	+	0.390872i	−0.840857	−	0.541257i	$-0.817948\pi$
$223$	−17.9643	+	5.83697i	−1.20298	+	0.390872i	−0.362124	+	0.932130i	$0.617948\pi$
$224$		0			0
$225$	1.68417	+	1.22362i	0.112278	+	0.0815748i
$226$		0			0
$227$	−19.1278	−	6.21500i	−1.26956	−	0.412504i	−0.404666	−	0.914465i	$-0.632612\pi$
$227$	−19.1278	−	6.21500i	−1.26956	−	0.412504i	−0.864890	+	0.501961i	$0.832612\pi$
$228$		0			0
$229$	7.85291	+	10.8086i	0.518935	+	0.714253i	0.985394	−	0.170290i	$-0.0544705\pi$
$229$	7.85291	+	10.8086i	0.518935	+	0.714253i	−0.466459	+	0.884543i	$0.654470\pi$
$230$		0			0
$231$	0.268718	+	1.76065i	0.0176804	+	0.115842i
$232$		0			0
$233$	2.99663	−	2.17718i	0.196316	−	0.142632i	−0.485285	−	0.874356i	$-0.661284\pi$
$233$	2.99663	−	2.17718i	0.196316	−	0.142632i	0.681601	+	0.731724i	$0.261284\pi$
$234$		0			0
$235$	3.08481	−	9.49406i	0.201231	−	0.619324i
$236$		0			0
$237$	−0.0185223	−	0.0134572i	−0.00120315	−	0.000874142i
$238$		0			0
$239$	8.78938	−	2.85584i	0.568538	−	0.184729i	−0.0106216	−	0.999944i	$-0.503381\pi$
$239$	8.78938	−	2.85584i	0.568538	−	0.184729i	0.579159	+	0.815215i	$0.303381\pi$
$240$		0			0
$241$		−	19.1756i		−	1.23521i	−0.786490	−	0.617603i	$-0.788104\pi$
$241$		−	19.1756i		−	1.23521i	0.786490	−	0.617603i	$-0.211896\pi$
$242$		0			0
$243$	−3.85207			−0.247110
$244$		0			0
$245$	13.6258	−	4.42730i	0.870521	−	0.282850i
$246$		0			0
$247$	−20.4909	−	6.59856i	−1.30381	−	0.419856i
$248$		0			0
$249$	0.657925	+	0.213773i	0.0416943	+	0.0135473i
$250$		0			0
$251$	−1.10264	+	0.801115i	−0.0695980	+	0.0505659i	−0.622040	−	0.782985i	$-0.713696\pi$
$251$	−1.10264	+	0.801115i	−0.0695980	+	0.0505659i	0.552442	+	0.833551i	$0.313696\pi$
$252$		0			0
$253$	−30.4065	+	4.64077i	−1.91164	+	0.291763i
$254$		0			0
$255$	1.05896	+	1.45754i	0.0663147	+	0.0912744i
$256$		0			0
$257$	0.0380282	−	0.117039i	0.00237213	−	0.00730068i	−0.949863	−	0.312665i	$-0.898778\pi$
$257$	0.0380282	−	0.117039i	0.00237213	−	0.00730068i	0.952236	+	0.305364i	$0.0987783\pi$
$258$		0			0
$259$	21.7057	+	15.7701i	1.34872	+	0.979905i
$260$		0			0
$261$	−7.74408	−	23.8338i	−0.479347	−	1.47528i
$262$		0			0
$263$	21.2939			1.31304			0.656518	−	0.754311i	$-0.272029\pi$
$263$	21.2939			1.31304			0.656518	+	0.754311i	$0.272029\pi$
$264$		0			0
$265$			14.2094i			0.872875i
$266$		0			0
$267$	1.35569	−	0.440492i	0.0829672	−	0.0269577i
$268$		0			0
$269$	5.28705	+	3.84127i	0.322357	+	0.234206i	0.737181	−	0.675696i	$-0.236157\pi$
$269$	5.28705	+	3.84127i	0.322357	+	0.234206i	−0.414823	+	0.909902i	$0.636157\pi$
$270$		0			0
$271$	26.1951	+	8.51130i	1.59124	+	0.517025i	0.964920	−	0.262543i	$-0.0845611\pi$
$271$	26.1951	+	8.51130i	1.59124	+	0.517025i	0.626318	+	0.779567i	$0.284561\pi$
$272$		0			0
$273$	1.13396	−	1.56939i	0.0686302	−	0.0949840i
$274$		0			0
$275$	−1.04048	−	2.07077i	−0.0627435	−	0.124872i
$276$		0			0
$277$	16.9698	−	12.3293i	1.01962	−	0.740795i	0.0534121	−	0.998573i	$-0.482990\pi$
$277$	16.9698	−	12.3293i	1.01962	−	0.740795i	0.966204	+	0.257778i	$0.0829903\pi$
$278$		0			0
$279$	−0.214222	−	0.0696050i	−0.0128251	−	0.00416714i
$280$		0			0
$281$	1.94634	−	2.67891i	0.116109	−	0.159811i	−0.747007	−	0.664817i	$-0.768510\pi$
$281$	1.94634	−	2.67891i	0.116109	−	0.159811i	0.863116	+	0.505006i	$0.168510\pi$
$282$		0			0
$283$	−8.31385	−	25.5874i	−0.494207	−	1.52101i	−0.818189	−	0.574949i	$-0.805022\pi$
$283$	−8.31385	−	25.5874i	−0.494207	−	1.52101i	0.323982	−	0.946063i	$-0.394978\pi$
$284$		0			0
$285$	1.78302			0.105617
$286$		0			0
$287$	−4.42006			−0.260908
$288$		0			0
$289$	5.99335	+	18.4456i	0.352550	+	1.08504i
$290$		0			0
$291$	−1.21174	+	1.66781i	−0.0710332	+	0.0977688i
$292$		0			0
$293$	0.127234	+	0.0413408i	0.00743308	+	0.00241515i	0.312731	−	0.949842i	$-0.398756\pi$
$293$	0.127234	+	0.0413408i	0.00743308	+	0.00241515i	−0.305298	+	0.952257i	$0.598756\pi$
$294$		0			0
$295$	−4.42100	+	3.21205i	−0.257401	+	0.187013i
$296$		0			0
$297$	2.53697	+	1.31068i	0.147210	+	0.0760531i
$298$		0			0
$299$	27.1035	+	19.5834i	1.56743	+	1.13254i
$300$		0			0
$301$	−9.96419	−	3.23756i	−0.574326	−	0.186610i
$302$		0			0
$303$	1.62588	+	1.18127i	0.0934046	+	0.0678624i
$304$		0			0
$305$	−14.1098	+	4.58454i	−0.807923	+	0.262510i
$306$		0			0
$307$			7.45831i			0.425668i	0.977088	+	0.212834i	$0.0682694\pi$
$307$			7.45831i			0.425668i	−0.977088	+	0.212834i	$0.931731\pi$
$308$		0			0
$309$	1.00263			0.0570377
$310$		0			0
$311$	−8.86235	−	27.2755i	−0.502538	−	1.54665i	−0.804871	−	0.593450i	$-0.797765\pi$
$311$	−8.86235	−	27.2755i	−0.502538	−	1.54665i	0.302333	−	0.953202i	$-0.402235\pi$
$312$		0			0
$313$	7.17272	+	5.21129i	0.405426	+	0.294559i	0.771748	−	0.635929i	$-0.219383\pi$
$313$	7.17272	+	5.21129i	0.405426	+	0.294559i	−0.366321	+	0.930488i	$0.619383\pi$
$314$		0			0
$315$	7.12071	−	21.9153i	0.401206	−	1.23479i
$316$		0			0
$317$	−18.4362	−	25.3753i	−1.03548	−	1.42522i	−0.900750	−	0.434338i	$-0.856983\pi$
$317$	−18.4362	−	25.3753i	−1.03548	−	1.42522i	−0.134732	−	0.990882i	$-0.543017\pi$
$318$		0			0
$319$	−4.51913	+	27.5296i	−0.253023	+	1.54136i
$320$		0			0
$321$	1.02250	−	0.742887i	0.0570702	−	0.0414639i
$322$		0			0
$323$	34.2564	+	11.1306i	1.90608	+	0.619322i
$324$		0			0
$325$	−0.772242	+	2.39809i	−0.0428363	+	0.133022i
$326$		0			0
$327$	−1.53601	+	0.499079i	−0.0849414	+	0.0275991i
$328$		0			0
$329$	17.9507			0.989656
$330$		0			0
$331$		−	18.4511i		−	1.01417i	−0.861897	−	0.507083i	$-0.830724\pi$
$331$		−	18.4511i		−	1.01417i	0.861897	−	0.507083i	$-0.169276\pi$
$332$		0			0
$333$	20.3843	−	6.62328i	1.11706	−	0.362953i
$334$		0			0
$335$	11.8776	+	8.62958i	0.648942	+	0.471484i
$336$		0			0
$337$	0.551477	−	1.69727i	0.0300409	−	0.0924563i	−0.934912	−	0.354880i	$-0.884522\pi$
$337$	0.551477	−	1.69727i	0.0300409	−	0.0924563i	0.964953	+	0.262424i	$0.0845218\pi$
$338$		0			0
$339$	−1.34385	+	0.976367i	−0.0729881	+	0.0530290i
$340$		0			0
$341$	0.176309	+	0.178303i	0.00954765	+	0.00965566i
$342$		0			0
$343$	−0.201452	−	0.277275i	−0.0108774	−	0.0149714i
$344$		0			0
$345$	−2.63401	−	0.855843i	−0.141810	−	0.0460770i
$346$		0			0
$347$	8.19786	+	5.95610i	0.440084	+	0.319740i	0.785668	−	0.618648i	$-0.212319\pi$
$347$	8.19786	+	5.95610i	0.440084	+	0.319740i	−0.345584	+	0.938388i	$0.612319\pi$
$348$		0			0
$349$	22.8897	−	7.43730i	1.22526	−	0.398110i	0.376262	−	0.926513i	$-0.377209\pi$
$349$	22.8897	−	7.43730i	1.22526	−	0.398110i	0.848993	+	0.528404i	$0.177209\pi$
$350$		0			0
$351$	−0.967018	−	2.94984i	−0.0516156	−	0.157451i
$352$		0			0
$353$			27.7698i			1.47804i	0.673684	+	0.739019i	$0.264711\pi$
$353$			27.7698i			1.47804i	−0.673684	+	0.739019i	$0.735289\pi$
$354$		0			0
$355$	3.61294	+	11.1195i	0.191755	+	0.590162i
$356$		0			0
$357$	−1.90422	+	2.62093i	−0.100782	+	0.138714i
$358$		0			0
$359$	3.90532	+	1.26892i	0.206115	+	0.0669708i	0.410255	−	0.911971i	$-0.365440\pi$
$359$	3.90532	+	1.26892i	0.206115	+	0.0669708i	−0.204140	+	0.978942i	$0.565440\pi$
$360$		0			0
$361$	13.4682	−	9.78523i	0.708853	−	0.515012i
$362$		0			0
$363$	−0.916539	−	1.29182i	−0.0481058	−	0.0678029i
$364$		0			0
$365$	−7.43967	+	5.40524i	−0.389410	+	0.282923i
$366$		0			0
$367$	−5.73156	+	17.6399i	−0.299185	+	0.920796i	0.682599	+	0.730793i	$0.260850\pi$
$367$	−5.73156	+	17.6399i	−0.299185	+	0.920796i	−0.981784	+	0.190003i	$0.939150\pi$
$368$		0			0
$369$	−2.07550	+	2.85667i	−0.108046	+	0.148713i
$370$		0			0
$371$	−24.3006	+	7.89575i	−1.26163	+	0.409927i
$372$		0			0
$373$	−2.53205			−0.131105			−0.0655523	−	0.997849i	$-0.520881\pi$
$373$	−2.53205			−0.131105			−0.0655523	+	0.997849i	$0.520881\pi$
$374$		0			0
$375$		−	1.70185i		−	0.0878830i
$376$		0			0
$377$	24.4894	−	17.8909i	1.26127	−	0.921427i
$378$		0			0
$379$	14.7128	−	20.2505i	0.755747	−	1.04020i	−0.241809	−	0.970324i	$-0.577741\pi$
$379$	14.7128	−	20.2505i	0.755747	−	1.04020i	0.997556	−	0.0698721i	$-0.0222591\pi$
$380$		0			0
$381$	0.272402	−	0.838367i	0.0139556	−	0.0429508i
$382$		0			0
$383$	−15.3026	−	21.0623i	−0.781928	−	1.07623i	−0.995067	−	0.0992093i	$-0.968369\pi$
$383$	−15.3026	−	21.0623i	−0.781928	−	1.07623i	0.213139	−	0.977022i	$-0.431631\pi$
$384$		0			0
$385$	−18.2407	+	18.0367i	−0.929632	+	0.919234i
$386$		0			0
$387$	−6.77125	+	4.91960i	−0.344202	+	0.250077i
$388$		0			0
$389$	−4.04324	+	12.4438i	−0.205000	+	0.630926i	0.794713	+	0.606985i	$0.207621\pi$
$389$	−4.04324	+	12.4438i	−0.205000	+	0.630926i	−0.999713	+	0.0239405i	$0.992379\pi$
$390$		0			0
$391$	−45.2635	−	32.8859i	−2.28907	−	1.66311i
$392$		0			0
$393$	−0.157295	−	0.484103i	−0.00793446	−	0.0244198i
$394$		0			0
$395$		−	0.329755i		−	0.0165918i
$396$		0			0
$397$			1.57385i			0.0789892i	0.999220	+	0.0394946i	$0.0125748\pi$
$397$			1.57385i			0.0789892i	−0.999220	+	0.0394946i	$0.987425\pi$
$398$		0			0
$399$	0.990776	+	3.04929i	0.0496008	+	0.152656i
$400$		0			0
$401$	−2.66989	+	3.67479i	−0.133328	+	0.183510i	−0.870461	−	0.492237i	$-0.836179\pi$
$401$	−2.66989	+	3.67479i	−0.133328	+	0.183510i	0.737133	+	0.675748i	$0.236179\pi$
$402$		0			0
$403$	−0.000714720	−	0.272596i	−3.56028e−5	−	0.0135790i
$404$		0			0
$405$	−10.7444	−	14.7883i	−0.533891	−	0.734839i
$406$		0			0
$407$	−23.5453	−	3.86507i	−1.16710	−	0.191585i
$408$		0			0
$409$	8.49621	+	11.6940i	0.420110	+	0.578232i	0.965648	−	0.259854i	$-0.0836745\pi$
$409$	8.49621	+	11.6940i	0.420110	+	0.578232i	−0.545537	+	0.838086i	$0.683674\pi$
$410$		0			0
$411$	−0.0767434	−	0.0249355i	−0.00378548	−	0.00122998i
$412$		0			0
$413$	−7.94982	−	5.77588i	−0.391185	−	0.284213i
$414$		0			0
$415$	3.07898	+	9.47611i	0.151141	+	0.465164i
$416$		0			0
$417$	3.10768			0.152184
$418$		0			0
$419$	18.8459			0.920682			0.460341	−	0.887742i	$-0.347727\pi$
$419$	18.8459			0.920682			0.460341	+	0.887742i	$0.347727\pi$
$420$		0			0
$421$	23.4792	−	7.62887i	1.14431	−	0.371808i	0.325312	−	0.945607i	$-0.394531\pi$
$421$	23.4792	−	7.62887i	1.14431	−	0.371808i	0.818996	+	0.573799i	$0.194531\pi$
$422$		0			0
$423$	8.42900	−	11.6015i	0.409832	−	0.564086i
$424$		0			0
$425$	1.30263	−	4.00909i	0.0631870	−	0.194470i
$426$		0			0
$427$	−15.6808	−	21.5828i	−0.758848	−	1.04446i
$428$		0			0
$429$	−0.274472	+	1.69990i	−0.0132516	+	0.0820719i
$430$		0			0
$431$	−13.8061	−	19.0025i	−0.665018	−	0.915319i	0.334616	−	0.942354i	$-0.391393\pi$
$431$	−13.8061	−	19.0025i	−0.665018	−	0.915319i	−0.999634	+	0.0270355i	$0.991393\pi$
$432$		0			0
$433$	−4.96556	+	15.2824i	−0.238630	+	0.734427i	0.757989	+	0.652267i	$0.226182\pi$
$433$	−4.96556	+	15.2824i	−0.238630	+	0.734427i	−0.996619	+	0.0821601i	$0.973818\pi$
$434$		0			0
$435$	−1.47652	+	2.03225i	−0.0707935	+	0.0974389i
$436$		0			0
$437$	−52.6613	+	17.1107i	−2.51913	+	0.818516i
$438$		0			0
$439$	27.1530			1.29594			0.647972	−	0.761664i	$-0.275617\pi$
$439$	27.1530			1.29594			0.647972	+	0.761664i	$0.275617\pi$
$440$		0			0
$441$	20.5811			0.980051
$442$		0			0
$443$	−4.23566	−	13.0360i	−0.201242	−	0.619360i	−0.999847	−	0.0175038i	$-0.994428\pi$
$443$	−4.23566	−	13.0360i	−0.201242	−	0.619360i	0.798605	−	0.601856i	$-0.205572\pi$
$444$		0			0
$445$	16.6099	+	12.0678i	0.787385	+	0.572069i
$446$		0			0
$447$	2.33786	+	0.759616i	0.110577	+	0.0359286i
$448$		0			0
$449$	9.91778	+	13.6507i	0.468049	+	0.644214i	0.976154	−	0.217081i	$-0.0696537\pi$
$449$	9.91778	+	13.6507i	0.468049	+	0.644214i	−0.508105	+	0.861295i	$0.669654\pi$
$450$		0			0
$451$	3.51242	−	1.76486i	0.165394	−	0.0831039i
$452$		0			0
$453$	1.30278	+	1.79313i	0.0612100	+	0.0842484i
$454$		0			0
$455$	27.8870	−	0.0731171i	1.30736	−	0.00342778i
$456$		0			0
$457$	−19.1210	+	26.3178i	−0.894444	+	1.23110i	0.0777631	+	0.996972i	$0.475222\pi$
$457$	−19.1210	+	26.3178i	−0.894444	+	1.23110i	−0.972207	+	0.234124i	$0.924778\pi$
$458$		0			0
$459$	1.60507	+	4.93990i	0.0749183	+	0.230575i
$460$		0			0
$461$		−	16.8303i		−	0.783866i	−0.919994	−	0.391933i	$-0.871806\pi$
$461$		−	16.8303i		−	0.783866i	0.919994	−	0.391933i	$-0.128194\pi$
$462$		0			0
$463$		−	37.6534i		−	1.74990i	−0.484210	−	0.874952i	$-0.660893\pi$
$463$		−	37.6534i		−	1.74990i	0.484210	−	0.874952i	$-0.339107\pi$
$464$		0			0
$465$	0.00697706	+	0.0214732i	0.000323553	+	0.000995795i
$466$		0			0
$467$	−16.2531	−	11.8086i	−0.752103	−	0.546435i	0.144375	−	0.989523i	$-0.453883\pi$
$467$	−16.2531	−	11.8086i	−0.752103	−	0.546435i	−0.896478	+	0.443088i	$0.853883\pi$
$468$		0			0
$469$	−8.15811	+	25.1081i	−0.376707	+	1.15938i
$470$		0			0
$471$	2.35338	−	1.70983i	0.108438	−	0.0787849i
$472$		0			0
$473$	9.21081	−	1.40579i	0.423514	−	0.0646384i
$474$		0			0
$475$	−2.45219	−	3.37515i	−0.112514	−	0.154862i
$476$		0			0
$477$	−6.30767	+	19.4130i	−0.288808	+	0.888861i
$478$		0			0
$479$	2.88750	−	3.97430i	0.131933	−	0.181590i	−0.737939	−	0.674867i	$-0.764201\pi$
$479$	2.88750	−	3.97430i	0.131933	−	0.181590i	0.869872	+	0.493277i	$0.164201\pi$
$480$		0			0
$481$	15.3015	+	20.9450i	0.697689	+	0.955011i
$482$		0			0
$483$		−	4.98021i		−	0.226608i
$484$		0			0
$485$	−29.6922			−1.34825
$486$		0			0
$487$	−24.2146	+	7.86781i	−1.09727	+	0.356525i	−0.801051	−	0.598596i	$-0.795726\pi$
$487$	−24.2146	+	7.86781i	−1.09727	+	0.356525i	−0.296219	+	0.955120i	$0.595726\pi$
$488$		0			0
$489$	−1.05754	+	1.45558i	−0.0478237	+	0.0658236i
$490$		0			0
$491$	3.01998	−	9.29453i	0.136290	−	0.419456i	−0.859499	−	0.511138i	$-0.829224\pi$
$491$	3.01998	−	9.29453i	0.136290	−	0.419456i	0.995788	+	0.0916815i	$0.0292242\pi$
$492$		0			0
$493$	−41.0541	+	29.8275i	−1.84898	+	1.34336i
$494$		0			0
$495$	3.09191	+	20.2583i	0.138971	+	0.910543i
$496$		0			0
$497$	−17.0088	+	12.3576i	−0.762947	+	0.554314i
$498$		0			0
$499$	−2.08115	−	0.676206i	−0.0931650	−	0.0302711i	0.262064	−	0.965051i	$-0.415597\pi$
$499$	−2.08115	−	0.676206i	−0.0931650	−	0.0302711i	−0.355229	+	0.934779i	$0.615597\pi$
$500$		0			0
$501$	0.451337	−	0.621212i	0.0201642	−	0.0277537i
$502$		0			0
$503$	−4.73816	−	14.5825i	−0.211264	−	0.650204i	−0.999398	−	0.0346997i	$-0.988953\pi$
$503$	−4.73816	−	14.5825i	−0.211264	−	0.650204i	0.788134	−	0.615504i	$-0.211047\pi$
$504$		0			0
$505$			28.9458i			1.28807i
$506$		0			0
$507$	1.50862	−	1.10821i	0.0670003	−	0.0492174i
$508$		0			0
$509$	−36.9657	+	12.0109i	−1.63847	+	0.532373i	−0.976197	−	0.216886i	$-0.930410\pi$
$509$	−36.9657	+	12.0109i	−1.63847	+	0.532373i	−0.662278	+	0.749258i	$0.730410\pi$
$510$		0			0
$511$	−13.3780	−	9.71966i	−0.591806	−	0.429973i
$512$		0			0
$513$	4.88892	+	1.58851i	0.215851	+	0.0701343i
$514$		0			0
$515$	8.48816	+	11.6830i	0.374033	+	0.514812i
$516$		0			0
$517$	−14.2647	+	7.16744i	−0.627359	+	0.315224i
$518$		0			0
$519$	−0.523512	+	0.380354i	−0.0229796	+	0.0166957i
$520$		0			0
$521$	2.45522	−	7.55639i	0.107565	−	0.331051i	−0.882759	−	0.469826i	$-0.844317\pi$
$521$	2.45522	−	7.55639i	0.107565	−	0.331051i	0.990324	+	0.138775i	$0.0443165\pi$
$522$		0			0
$523$	−28.1406	−	20.4453i	−1.23050	−	0.894012i	−0.233574	−	0.972339i	$-0.575042\pi$
$523$	−28.1406	−	20.4453i	−1.23050	−	0.894012i	−0.996928	+	0.0783274i	$0.975042\pi$
$524$		0			0
$525$	0.356865	−	0.115952i	0.0155748	−	0.00506057i
$526$		0			0
$527$			0.456109i			0.0198684i
$528$		0			0
$529$	63.0083			2.73949
$530$		0			0
$531$	−7.46589	+	2.42581i	−0.323992	+	0.105271i
$532$		0			0
$533$	−4.06762	−	1.30987i	−0.176188	−	0.0567367i
$534$		0			0
$535$	17.3127	+	5.62523i	0.748492	+	0.243200i
$536$		0			0
$537$	−1.83038	+	1.32985i	−0.0789869	+	0.0573873i
$538$		0			0
$539$	−20.3555	−	10.5163i	−0.876775	−	0.452969i
$540$		0			0
$541$	5.13331	+	7.06540i	0.220698	+	0.303765i	0.904981	−	0.425451i	$-0.139885\pi$
$541$	5.13331	+	7.06540i	0.220698	+	0.303765i	−0.684283	+	0.729217i	$0.739885\pi$
$542$		0			0
$543$	0.120305	−	0.370262i	0.00516280	−	0.0158895i
$544$		0			0
$545$	−18.8191	−	13.6729i	−0.806121	−	0.585681i
$546$		0			0
$547$	7.59093	+	23.3625i	0.324565	+	0.998908i	0.971637	+	0.236479i	$0.0759934\pi$
$547$	7.59093	+	23.3625i	0.324565	+	0.998908i	−0.647072	+	0.762429i	$0.724007\pi$
$548$		0			0
$549$	−21.3121			−0.909576
$550$		0			0
$551$			50.2220i			2.13953i
$552$		0			0
$553$	0.563941	−	0.183236i	0.0239812	−	0.00779197i
$554$		0			0
$555$	−1.73812	−	1.26282i	−0.0737792	−	0.0536037i
$556$		0			0
$557$	11.2455	+	3.65389i	0.476487	+	0.154820i	0.537408	−	0.843322i	$-0.319404\pi$
$557$	11.2455	+	3.65389i	0.476487	+	0.154820i	−0.0609204	+	0.998143i	$0.519404\pi$
$558$		0			0
$559$	−8.21025	−	5.93227i	−0.347256	−	0.250908i
$560$		0			0
$561$	0.466703	−	2.84306i	0.0197042	−	0.120034i
$562$		0			0
$563$	−22.1715	+	16.1086i	−0.934419	+	0.678895i	−0.947071	−	0.321025i	$-0.895973\pi$
$563$	−22.1715	+	16.1086i	−0.934419	+	0.678895i	0.0126517	+	0.999920i	$0.495973\pi$
$564$		0			0
$565$	−22.7538	−	7.39317i	−0.957261	−	0.311033i
$566$		0			0
$567$	19.3204	−	26.5923i	0.811382	−	1.11677i
$568$		0			0
$569$	13.1354	+	40.4267i	0.550665	+	1.69477i	0.707124	+	0.707089i	$0.249992\pi$
$569$	13.1354	+	40.4267i	0.550665	+	1.69477i	−0.156459	+	0.987684i	$0.550008\pi$
$570$		0			0
$571$	−33.4787			−1.40104			−0.700519	−	0.713633i	$-0.747048\pi$
$571$	−33.4787			−1.40104			−0.700519	+	0.713633i	$0.747048\pi$
$572$		0			0
$573$	0.758705			0.0316954
$574$		0			0
$575$	2.00250	+	6.16306i	0.0835100	+	0.257017i
$576$		0			0
$577$	23.6654	−	32.5727i	0.985205	−	1.35602i	0.0512273	−	0.998687i	$-0.483687\pi$
$577$	23.6654	−	32.5727i	0.985205	−	1.35602i	0.933978	−	0.357331i	$-0.116313\pi$
$578$		0			0
$579$	1.60657	+	0.522006i	0.0667667	+	0.0216938i
$580$		0			0
$581$	−14.4950	+	10.5312i	−0.601353	+	0.436909i
$582$		0			0
$583$	16.1580	−	15.9773i	0.669196	−	0.661710i
$584$		0			0
$585$	13.0474	−	18.0576i	0.539446	−	0.746592i
$586$		0			0
$587$	−6.70955	−	2.18007i	−0.276933	−	0.0899809i	0.167258	−	0.985913i	$-0.446509\pi$
$587$	−6.70955	−	2.18007i	−0.276933	−	0.0899809i	−0.444191	+	0.895932i	$0.646509\pi$
$588$		0			0
$589$	0.365192	+	0.265328i	0.0150475	+	0.0109326i
$590$		0			0
$591$	−0.168407	+	0.0547188i	−0.00692734	+	0.00225083i
$592$		0			0
$593$		−	26.1513i		−	1.07391i	−0.843612	−	0.536953i	$-0.819575\pi$
$593$		−	26.1513i		−	1.07391i	0.843612	−	0.536953i	$-0.180425\pi$
$594$		0			0
$595$	−46.6607			−1.91290
$596$		0			0
$597$	−0.226423	−	0.696857i	−0.00926686	−	0.0285205i
$598$		0			0
$599$	35.0231	+	25.4457i	1.43100	+	1.03968i	0.989829	+	0.142264i	$0.0454380\pi$
$599$	35.0231	+	25.4457i	1.43100	+	1.03968i	0.441175	+	0.897421i	$0.354562\pi$
$600$		0			0
$601$	−8.03357	+	24.7248i	−0.327696	+	1.00854i	0.642513	+	0.766275i	$0.277892\pi$
$601$	−8.03357	+	24.7248i	−0.327696	+	1.00854i	−0.970209	+	0.242270i	$0.922108\pi$
$602$		0			0
$603$	12.3966	+	17.0624i	0.504827	+	0.694835i
$604$		0			0
$605$	7.29334	−	21.6162i	0.296516	−	0.878822i
$606$		0			0
$607$	13.5719	−	9.86057i	0.550867	−	0.400228i	−0.277238	−	0.960801i	$-0.589419\pi$
$607$	13.5719	−	9.86057i	0.550867	−	0.400228i	0.828105	+	0.560573i	$0.189419\pi$
$608$		0			0
$609$	−4.29598	−	1.39585i	−0.174082	−	0.0565626i
$610$		0			0
$611$	16.5194	+	5.31964i	0.668304	+	0.215210i
$612$		0			0
$613$	36.1325	−	11.7402i	1.45938	−	0.474181i	0.531499	−	0.847059i	$-0.321629\pi$
$613$	36.1325	−	11.7402i	1.45938	−	0.474181i	0.927880	+	0.372878i	$0.121629\pi$
$614$		0			0
$615$	0.353944			0.0142724
$616$		0			0
$617$		−	38.4841i		−	1.54931i	−0.632383	−	0.774656i	$-0.717923\pi$
$617$		−	38.4841i		−	1.54931i	0.632383	−	0.774656i	$-0.282077\pi$
$618$		0			0
$619$	14.6205	−	4.75050i	0.587649	−	0.190939i	−7.53944e−5	−	1.00000i	$-0.500024\pi$
$619$	14.6205	−	4.75050i	0.587649	−	0.190939i	0.587724	+	0.809061i	$0.300024\pi$
$620$		0			0
$621$	−6.45981	−	4.69332i	−0.259223	−	0.188337i
$622$		0			0
$623$	−11.4085	+	35.1117i	−0.457071	+	1.40672i
$624$		0			0
$625$	17.0039	−	12.3541i	0.680157	−	0.494163i
$626$		0			0
$627$	−2.00486	−	2.02754i	−0.0800664	−	0.0809721i
$628$		0			0
$629$	−25.5106	−	35.1123i	−1.01717	−	1.40002i
$630$		0			0
$631$	−15.0962	−	4.90504i	−0.600969	−	0.195267i	−0.00729623	−	0.999973i	$-0.502322\pi$
$631$	−15.0962	−	4.90504i	−0.600969	−	0.195267i	−0.593672	+	0.804707i	$0.702322\pi$
$632$		0			0
$633$	1.92626	+	1.39951i	0.0765620	+	0.0556256i
$634$		0			0
$635$	12.0750	−	3.92341i	0.479183	−	0.155696i
$636$		0			0
$637$	7.75892	+	23.6682i	0.307420	+	0.937768i
$638$		0			0
$639$			16.7954i			0.664416i
$640$		0			0
$641$	9.96095	+	30.6567i	0.393434	+	1.21087i	0.930174	+	0.367118i	$0.119655\pi$
$641$	9.96095	+	30.6567i	0.393434	+	1.21087i	−0.536741	+	0.843747i	$0.680345\pi$
$642$		0			0
$643$	−21.0423	+	28.9622i	−0.829826	+	1.14216i	0.158129	+	0.987418i	$0.449454\pi$
$643$	−21.0423	+	28.9622i	−0.829826	+	1.14216i	−0.987955	+	0.154739i	$0.950546\pi$
$644$		0			0
$645$	0.797902	+	0.259254i	0.0314173	+	0.0102081i
$646$		0			0
$647$	9.79189	−	7.11423i	0.384959	−	0.279689i	−0.378428	−	0.925631i	$-0.623535\pi$
$647$	9.79189	−	7.11423i	0.384959	−	0.279689i	0.763387	+	0.645942i	$0.223535\pi$
$648$		0			0
$649$	8.62359	+	1.41561i	0.338506	+	0.0555674i
$650$		0			0
$651$	−0.0328461	+	0.0238641i	−0.00128734	+	0.000935308i
$652$		0			0
$653$	10.0242	−	30.8515i	0.392279	−	1.20731i	−0.538781	−	0.842446i	$-0.681115\pi$
$653$	10.0242	−	30.8515i	0.392279	−	1.20731i	0.931060	−	0.364865i	$-0.118885\pi$
$654$		0			0
$655$	4.30927	−	5.93120i	0.168377	−	0.231751i
$656$		0			0
$657$	−12.5636	+	4.08216i	−0.490153	+	0.159260i
$658$		0			0
$659$	−16.9888			−0.661789			−0.330895	−	0.943668i	$-0.607351\pi$
$659$	−16.9888			−0.661789			−0.330895	+	0.943668i	$0.607351\pi$
$660$		0			0
$661$			10.6026i			0.412395i	0.978510	+	0.206197i	$0.0661089\pi$
$661$			10.6026i			0.412395i	−0.978510	+	0.206197i	$0.933891\pi$
$662$		0			0
$663$	−2.52909	+	1.84764i	−0.0982216	+	0.0717564i
$664$		0			0
$665$	−27.1435	+	37.3598i	−1.05258	+	1.44875i
$666$		0			0
$667$	24.1063	−	74.1916i	0.933401	−	2.87271i
$668$		0			0
$669$	1.59870	+	2.20042i	0.0618094	+	0.0850733i
$670$		0			0
$671$	21.0785	+	10.8898i	0.813727	+	0.420396i
$672$		0			0
$673$	21.4870	−	15.6113i	0.828265	−	0.601770i	−0.0908031	−	0.995869i	$-0.528943\pi$
$673$	21.4870	−	15.6113i	0.828265	−	0.601770i	0.919068	+	0.394099i	$0.128943\pi$
$674$		0			0
$675$	0.185906	−	0.572160i	0.00715553	−	0.0220224i
$676$		0			0
$677$	29.8637	+	21.6973i	1.14776	+	0.833894i	0.988181	−	0.153292i	$-0.0489874\pi$
$677$	29.8637	+	21.6973i	1.14776	+	0.833894i	0.159576	+	0.987186i	$0.448987\pi$
$678$		0			0
$679$	−16.4992	−	50.7792i	−0.633179	−	1.94873i
$680$		0			0
$681$			2.89603i			0.110976i
$682$		0			0
$683$			17.3059i			0.662193i	0.943597	+	0.331097i	$0.107419\pi$
$683$			17.3059i			0.662193i	−0.943597	+	0.331097i	$0.892581\pi$
$684$		0			0
$685$	−0.359146	−	1.10534i	−0.0137223	−	0.0422328i
$686$		0			0
$687$	1.13077	−	1.55637i	0.0431416	−	0.0593793i
$688$		0			0
$689$	−24.7029	+	0.0647686i	−0.941104	+	0.00246749i
$690$		0			0
$691$	−21.4006	−	29.4554i	−0.814117	−	1.12054i	−0.990675	−	0.136245i	$-0.956496\pi$
$691$	−21.4006	−	29.4554i	−0.814117	−	1.12054i	0.176558	−	0.984290i	$-0.443504\pi$
$692$		0			0
$693$	−32.9273	+	16.5447i	−1.25081	+	0.628481i
$694$		0			0
$695$	26.3093	+	36.2117i	0.997969	+	1.37359i
$696$		0			0
$697$	6.80018	+	2.20951i	0.257575	+	0.0836913i
$698$		0			0
$699$	−0.431496	−	0.313500i	−0.0163207	−	0.0118577i
$700$		0			0
$701$	−5.37303	−	16.5365i	−0.202937	−	0.624575i	−0.999792	−	0.0204045i	$-0.993505\pi$
$701$	−5.37303	−	16.5365i	−0.202937	−	0.624575i	0.796855	−	0.604170i	$-0.206495\pi$
$702$		0			0
$703$	−42.9533			−1.62001
$704$		0			0
$705$	−1.43744			−0.0541371
$706$		0			0
$707$	−49.5026	+	16.0844i	−1.86174	+	0.604915i
$708$		0			0
$709$	11.3832	−	15.6677i	0.427506	−	0.588412i	−0.539872	−	0.841747i	$-0.681527\pi$
$709$	11.3832	−	15.6677i	0.427506	−	0.588412i	0.967379	+	0.253335i	$0.0815274\pi$
$710$		0			0
$711$	0.146381	−	0.450515i	0.00548972	−	0.0168956i
$712$		0			0
$713$	−0.412133	−	0.567253i	−0.0154345	−	0.0212438i
$714$		0			0
$715$	−22.1314	+	11.1929i	−0.827666	+	0.418592i
$716$		0			0
$717$	−0.782193	−	1.07660i	−0.0292115	−	0.0402062i
$718$		0			0
$719$	4.70334	−	14.4754i	0.175405	−	0.539841i	−0.824247	−	0.566231i	$-0.808401\pi$
$719$	4.70334	−	14.4754i	0.175405	−	0.539841i	0.999652	+	0.0263897i	$0.00840108\pi$
$720$		0			0
$721$	−15.2634	+	21.0082i	−0.568437	+	0.782387i
$722$		0			0
$723$	−2.62602	+	0.853246i	−0.0976628	+	0.0317326i
$724$		0			0
$725$	5.87757			0.218287
$726$		0			0
$727$	−2.37929			−0.0882432			−0.0441216	−	0.999026i	$-0.514049\pi$
$727$	−2.37929			−0.0882432			−0.0441216	+	0.999026i	$0.514049\pi$
$728$		0			0
$729$	−7.99946	−	24.6198i	−0.296276	−	0.911845i
$730$		0			0
$731$	13.7113	+	9.96187i	0.507132	+	0.368453i
$732$		0			0
$733$	4.13439	+	1.34334i	0.152707	+	0.0496175i	0.384373	−	0.923178i	$-0.374418\pi$
$733$	4.13439	+	1.34334i	0.152707	+	0.0496175i	−0.231666	+	0.972795i	$0.574418\pi$
$734$		0			0
$735$	−1.21260	−	1.66900i	−0.0447275	−	0.0615621i
$736$		0			0
$737$	−3.54236	−	23.2097i	−0.130485	−	0.854940i
$738$		0			0
$739$	10.7484	+	14.7938i	0.395385	+	0.544200i	0.959578	−	0.281442i	$-0.0908128\pi$
$739$	10.7484	+	14.7938i	0.395385	+	0.544200i	−0.564193	+	0.825643i	$0.690813\pi$
$740$		0			0
$741$	0.00812730	+	3.09977i	0.000298564	+	0.113873i
$742$		0			0
$743$	11.8609	−	16.3251i	0.435133	−	0.598910i	−0.533989	−	0.845492i	$-0.679307\pi$
$743$	11.8609	−	16.3251i	0.435133	−	0.598910i	0.969122	+	0.246582i	$0.0793075\pi$
$744$		0			0
$745$	10.9408	+	33.6722i	0.400839	+	1.23366i
$746$		0			0
$747$			14.3132i			0.523691i
$748$		0			0
$749$			32.7336i			1.19606i
$750$		0			0
$751$	14.0841	+	43.3465i	0.513938	+	1.58174i	0.785206	+	0.619234i	$0.212557\pi$
$751$	14.0841	+	43.3465i	0.513938	+	1.58174i	−0.271269	+	0.962504i	$0.587443\pi$
$752$		0			0
$753$	0.158773	+	0.115356i	0.00578602	+	0.00420379i
$754$		0			0
$755$	−9.86482	+	30.3608i	−0.359018	+	1.10494i
$756$		0			0
$757$	3.44867	−	2.50561i	0.125344	−	0.0910678i	−0.523347	−	0.852120i	$-0.675317\pi$
$757$	3.44867	−	2.50561i	0.125344	−	0.0910678i	0.648691	+	0.761052i	$0.275317\pi$
$758$		0			0
$759$	1.98852	+	3.95756i	0.0721787	+	0.143650i
$760$		0			0
$761$	−15.7035	−	21.6140i	−0.569250	−	0.783505i	0.423216	−	0.906029i	$-0.360901\pi$
$761$	−15.7035	−	21.6140i	−0.569250	−	0.783505i	−0.992466	+	0.122524i	$0.960901\pi$
$762$		0			0
$763$	12.9259	−	39.7817i	0.467948	−	1.44020i
$764$		0			0
$765$	−21.9102	+	30.1568i	−0.792164	+	1.09032i
$766$		0			0
$767$	−5.60427	−	7.67124i	−0.202358	−	0.276992i
$768$		0			0
$769$		−	32.0680i		−	1.15640i	−0.815894	−	0.578201i	$-0.803755\pi$
$769$		−	32.0680i		−	1.15640i	0.815894	−	0.578201i	$-0.196245\pi$
$770$		0			0
$771$	−0.0177201			−0.000638175
$772$		0			0
$773$	33.1722	−	10.7783i	1.19312	−	0.387668i	0.355895	−	0.934526i	$-0.384176\pi$
$773$	33.1722	−	10.7783i	1.19312	−	0.387668i	0.837226	+	0.546858i	$0.184176\pi$
$774$		0			0
$775$	0.0310518	−	0.0427391i	0.00111541	−	0.00153524i
$776$		0			0
$777$	1.19383	−	3.67422i	0.0428283	−	0.131812i
$778$		0			0
$779$	5.72489	−	4.15937i	0.205115	−	0.149025i
$780$		0			0
$781$	8.58193	−	16.6114i	0.307086	−	0.594401i
$782$		0			0
$783$	−5.85905	+	4.25685i	−0.209386	+	0.152127i
$784$		0			0
$785$	39.8469	+	12.9470i	1.42220	+	0.462100i
$786$		0			0
$787$	7.18116	−	9.88401i	0.255981	−	0.352327i	−0.661614	−	0.749845i	$-0.730128\pi$
$787$	7.18116	−	9.88401i	0.255981	−	0.352327i	0.917595	+	0.397518i	$0.130128\pi$
$788$		0			0
$789$	−0.947502	−	2.91611i	−0.0337320	−	0.103816i
$790$		0			0
$791$		−	43.0214i		−	1.52966i
$792$		0			0
$793$	−8.03450	−	24.5088i	−0.285314	−	0.870334i
$794$		0			0
$795$	1.94592	−	0.632267i	0.0690146	−	0.0224242i
$796$		0			0
$797$	−24.1730	−	17.5627i	−0.856253	−	0.622104i	0.0706099	−	0.997504i	$-0.477505\pi$
$797$	−24.1730	−	17.5627i	−0.856253	−	0.622104i	−0.926863	+	0.375400i	$0.877505\pi$
$798$		0			0
$799$	−27.6169	−	8.97327i	−0.977016	−	0.317452i
$800$		0			0
$801$	17.3356	+	23.8605i	0.612525	+	0.843068i
$802$		0			0
$803$	14.5118	+	2.38218i	0.512110	+	0.0840654i
$804$		0			0
$805$	58.0309	−	42.1619i	2.04532	−	1.48601i
$806$		0			0
$807$	0.290792	−	0.894965i	0.0102364	−	0.0315043i
$808$		0			0
$809$	15.0519	+	10.9358i	0.529196	+	0.384483i	0.820057	−	0.572282i	$-0.193942\pi$
$809$	15.0519	+	10.9358i	0.529196	+	0.384483i	−0.290861	+	0.956765i	$0.593942\pi$
$810$		0			0
$811$	25.7864	−	8.37850i	0.905482	−	0.294209i	0.180984	−	0.983486i	$-0.442072\pi$
$811$	25.7864	−	8.37850i	0.905482	−	0.294209i	0.724498	+	0.689277i	$0.242072\pi$
$812$		0			0
$813$		−	3.96604i		−	0.139095i
$814$		0			0
$815$	−25.9139			−0.907724
$816$		0			0
$817$	15.9523	−	5.18322i	0.558100	−	0.181338i
$818$		0			0
$819$	38.1320	+	12.2794i	1.33244	+	0.429077i
$820$		0			0
$821$	3.76634	+	1.22376i	0.131446	+	0.0427094i	0.374001	−	0.927428i	$-0.377986\pi$
$821$	3.76634	+	1.22376i	0.131446	+	0.0427094i	−0.242555	+	0.970138i	$0.577986\pi$
$822$		0			0
$823$	34.7601	−	25.2547i	1.21166	−	0.880324i	0.216281	−	0.976331i	$-0.430607\pi$
$823$	34.7601	−	25.2547i	1.21166	−	0.880324i	0.995381	+	0.0960074i	$0.0306073\pi$
$824$		0			0
$825$	−0.237287	+	0.234633i	−0.00826126	+	0.00816886i
$826$		0			0
$827$	2.96506	+	4.08106i	0.103105	+	0.141912i	0.857452	−	0.514564i	$-0.172046\pi$
$827$	2.96506	+	4.08106i	0.103105	+	0.141912i	−0.754347	+	0.656476i	$0.772046\pi$
$828$		0			0
$829$	10.2177	−	31.4469i	0.354876	−	1.09220i	−0.601206	−	0.799094i	$-0.705313\pi$
$829$	10.2177	−	31.4469i	0.354876	−	1.09220i	0.956081	−	0.293101i	$-0.0946873\pi$
$830$		0			0
$831$	−2.44354	−	1.77534i	−0.0847656	−	0.0615858i
$832$		0			0
$833$	−12.8784	−	39.6356i	−0.446209	−	1.37329i
$834$		0			0
$835$	11.0595			0.382730
$836$		0			0
$837$			0.0650939i			0.00224997i
$838$		0			0
$839$	−16.1383	+	5.24364i	−0.557155	+	0.181031i	−0.574041	−	0.818827i	$-0.694625\pi$
$839$	−16.1383	+	5.24364i	−0.557155	+	0.181031i	0.0168858	+	0.999857i	$0.494625\pi$
$840$		0			0
$841$	−33.7804	−	24.5429i	−1.16484	−	0.846308i
$842$		0			0
$843$	−0.453473	−	0.147342i	−0.0156184	−	0.00507474i
$844$		0			0
$845$	25.6851	+	8.19693i	0.883593	+	0.281983i
$846$		0			0
$847$	41.0203	+	0.461436i	1.40948	+	0.0158551i
$848$		0			0
$849$	−3.13416	+	2.27710i	−0.107564	+	0.0781499i
$850$		0			0
$851$	63.4538	+	20.6174i	2.17517	+	0.706755i
$852$		0			0
$853$	−0.201981	+	0.278004i	−0.00691571	+	0.00951866i	−0.812461	−	0.583016i	$-0.801873\pi$
$853$	−0.201981	+	0.278004i	−0.00691571	+	0.00951866i	0.805545	+	0.592534i	$0.201873\pi$
$854$		0			0
$855$	11.4000	+	35.0856i	0.389871	+	1.19990i
$856$		0			0
$857$	15.8342			0.540885			0.270442	−	0.962736i	$-0.412830\pi$
$857$	15.8342			0.540885			0.270442	+	0.962736i	$0.412830\pi$
$858$		0			0
$859$	47.8488			1.63258			0.816290	−	0.577642i	$-0.196027\pi$
$859$	47.8488			1.63258			0.816290	+	0.577642i	$0.196027\pi$
$860$		0			0
$861$	0.196677	+	0.605310i	0.00670274	+	0.0206289i
$862$		0			0
$863$	0.640535	−	0.881621i	0.0218041	−	0.0300107i	−0.797976	−	0.602690i	$-0.794096\pi$
$863$	0.640535	−	0.881621i	0.0218041	−	0.0300107i	0.819780	+	0.572679i	$0.194096\pi$
$864$		0			0
$865$	−8.86398	−	2.88008i	−0.301384	−	0.0979257i
$866$		0			0
$867$	2.25938	−	1.64153i	0.0767325	−	0.0557494i
$868$		0			0
$869$	−0.374976	+	0.370782i	−0.0127202	+	0.0125779i
$870$		0			0
$871$	−14.9483	+	20.6884i	−0.506504	+	0.701001i
$872$		0			0
$873$	−40.5659	−	13.1807i	−1.37295	−	0.446098i
$874$		0			0
$875$	35.6589	+	25.9077i	1.20549	+	0.875841i
$876$		0			0
$877$	43.3415	−	14.0825i	1.46354	−	0.475533i	0.534390	−	0.845238i	$-0.320542\pi$
$877$	43.3415	−	14.0825i	1.46354	−	0.475533i	0.929149	+	0.369706i	$0.120542\pi$
$878$		0			0
$879$		−	0.0192637i		−	0.000649749i
$880$		0			0
$881$	−10.9772			−0.369832			−0.184916	−	0.982754i	$-0.559201\pi$
$881$	−10.9772			−0.369832			−0.184916	+	0.982754i	$0.559201\pi$
$882$		0			0
$883$	0.899018	+	2.76689i	0.0302544	+	0.0931134i	0.965043	−	0.262090i	$-0.0844117\pi$
$883$	0.899018	+	2.76689i	0.0302544	+	0.0931134i	−0.934789	+	0.355203i	$0.884412\pi$
$884$		0			0
$885$	0.636597	+	0.462515i	0.0213990	+	0.0155473i
$886$		0			0
$887$	11.5704	−	35.6101i	0.388497	−	1.19567i	−0.545415	−	0.838166i	$-0.683628\pi$
$887$	11.5704	−	35.6101i	0.388497	−	1.19567i	0.933912	−	0.357503i	$-0.116372\pi$
$888$		0			0
$889$	13.4195	+	18.4704i	0.450076	+	0.619476i
$890$		0			0
$891$	−4.73523	+	28.8461i	−0.158636	+	0.966380i
$892$		0			0
$893$	−23.2499	+	16.8920i	−0.778028	+	0.565271i
$894$		0			0
$895$	−30.9916	−	10.0698i	−1.03594	−	0.336596i
$896$		0			0
$897$	1.47587	−	4.58311i	0.0492778	−	0.153026i
$898$		0			0
$899$	−0.604830	+	0.196521i	−0.0201722	+	0.00655435i
$900$		0			0
$901$	41.3331			1.37700
$902$		0			0
$903$			1.50862i			0.0502037i
$904$		0			0
$905$	5.33289	−	1.73276i	0.177271	−	0.0575989i
$906$		0			0
$907$	−18.9773	−	13.7878i	−0.630132	−	0.457818i	0.226314	−	0.974054i	$-0.427333\pi$
$907$	−18.9773	−	13.7878i	−0.630132	−	0.457818i	−0.856446	+	0.516236i	$0.827333\pi$
$908$		0			0
$909$	−12.8493	+	39.5461i	−0.426185	+	1.31166i
$910$		0			0
$911$	−2.08509	+	1.51491i	−0.0690822	+	0.0501912i	−0.621790	−	0.783184i	$-0.713594\pi$
$911$	−2.08509	+	1.51491i	−0.0690822	+	0.0501912i	0.552708	+	0.833375i	$0.313594\pi$
$912$		0			0
$913$	7.31358	−	14.1563i	0.242044	−	0.468506i
$914$		0			0
$915$	1.25567	+	1.72828i	0.0415112	+	0.0571353i
$916$		0			0
$917$	12.5380	+	4.07384i	0.414041	+	0.134530i
$918$		0			0
$919$	−0.304946	−	0.221556i	−0.0100593	−	0.00730847i	0.582744	−	0.812656i	$-0.301979\pi$
$919$	−0.304946	−	0.221556i	−0.0100593	−	0.00730847i	−0.592804	+	0.805347i	$0.701979\pi$
$920$		0			0
$921$	1.02139	−	0.331869i	0.0336558	−	0.0109354i
$922$		0			0
$923$	−19.3147	+	6.33176i	−0.635751	+	0.208412i
$924$		0			0
$925$			5.02691i			0.165284i
$926$		0			0
$927$	6.41046	+	19.7294i	0.210547	+	0.647997i
$928$		0			0
$929$	2.65439	−	3.65345i	0.0870875	−	0.119866i	−0.763250	−	0.646103i	$-0.776398\pi$
$929$	2.65439	−	3.65345i	0.0870875	−	0.119866i	0.850338	+	0.526237i	$0.176398\pi$
$930$		0			0
$931$	−39.2266	−	12.7455i	−1.28560	−	0.417716i
$932$		0			0
$933$	−3.34093	+	2.42733i	−0.109377	+	0.0794672i
$934$		0			0
$935$	37.0793	−	18.6309i	1.21262	−	0.609295i
$936$		0			0
$937$	−18.5891	+	13.5058i	−0.607279	+	0.441214i	−0.848455	−	0.529268i	$-0.822467\pi$
$937$	−18.5891	+	13.5058i	−0.607279	+	0.441214i	0.241176	+	0.970481i	$0.422467\pi$
$938$		0			0
$939$	0.394505	−	1.21416i	0.0128742	−	0.0396227i
$940$		0			0
$941$	−9.55590	+	13.1526i	−0.311513	+	0.428761i	−0.935852	−	0.352392i	$-0.885368\pi$
$941$	−9.55590	+	13.1526i	−0.311513	+	0.428761i	0.624339	+	0.781153i	$0.285368\pi$
$942$		0			0
$943$	−10.4537	+	3.39662i	−0.340420	+	0.110609i
$944$		0			0
$945$	−6.65921			−0.216624
$946$		0			0
$947$		−	30.4412i		−	0.989205i	−0.869119	−	0.494602i	$-0.835314\pi$
$947$		−	30.4412i		−	0.989205i	0.869119	−	0.494602i	$-0.164686\pi$
$948$		0			0
$949$	−9.43087	−	12.9092i	−0.306139	−	0.419049i
$950$		0			0
$951$	−2.65470	+	3.65389i	−0.0860847	+	0.118485i
$952$		0			0
$953$	16.3472	−	50.3115i	0.529537	−	1.62975i	−0.225627	−	0.974214i	$-0.572443\pi$
$953$	16.3472	−	50.3115i	0.529537	−	1.62975i	0.755165	−	0.655535i	$-0.227557\pi$
$954$		0			0
$955$	6.42311	+	8.84065i	0.207847	+	0.286077i
$956$		0			0
$957$	3.97117	−	0.606096i	0.128370	−	0.0195923i
$958$		0			0
$959$	1.69076	−	1.22841i	0.0545976	−	0.0396675i
$960$		0			0
$961$	9.57776	−	29.4773i	0.308960	−	0.950881i
$962$		0			0
$963$	21.1557	+	15.3705i	0.681733	+	0.495308i
$964$		0			0
$965$	7.51847	+	23.1395i	0.242028	+	0.744886i
$966$		0			0
$967$			37.9903i			1.22168i	0.791752	+	0.610842i	$0.209169\pi$
$967$			37.9903i			1.22168i	−0.791752	+	0.610842i	$0.790831\pi$
$968$		0			0
$969$		−	5.18656i		−	0.166616i
$970$		0			0
$971$	−13.7240	−	42.2381i	−0.440424	−	1.35549i	−0.887425	−	0.460952i	$-0.847508\pi$
$971$	−13.7240	−	42.2381i	−0.440424	−	1.35549i	0.447001	−	0.894533i	$-0.352492\pi$
$972$		0			0
$973$	−47.3092	+	65.1156i	−1.51666	+	2.08751i
$974$		0			0
$975$	0.362772		0.000951154i	0.0116180		3.04613e-5i
$976$		0			0
$977$	30.2127	+	41.5843i	0.966591	+	1.33040i	0.943750	+	0.330659i	$0.107271\pi$
$977$	30.2127	+	41.5843i	0.966591	+	1.33040i	0.0228405	+	0.999739i	$0.492729\pi$
$978$		0			0
$979$	−4.95372	−	32.4570i	−0.158322	−	1.03733i
$980$		0			0
$981$	−19.6413	−	27.0340i	−0.627100	−	0.863129i
$982$		0			0
$983$	−47.3474	−	15.3841i	−1.51015	−	0.490677i	−0.567189	−	0.823587i	$-0.691969\pi$
$983$	−47.3474	−	15.3841i	−1.51015	−	0.490677i	−0.942958	+	0.332911i	$0.891969\pi$
$984$		0			0
$985$	−2.06331	−	1.49909i	−0.0657427	−	0.0477648i
$986$		0			0
$987$	−0.798745	−	2.45828i	−0.0254243	−	0.0782481i
$988$		0			0
$989$	−26.0539			−0.828465
$990$		0			0
$991$	−0.249660			−0.00793072			−0.00396536	−	0.999992i	$-0.501262\pi$
$991$	−0.249660			−0.00793072			−0.00396536	+	0.999992i	$0.501262\pi$
$992$		0			0
$993$	−2.52681	+	0.821012i	−0.0801860	+	0.0260540i
$994$		0			0
$995$	6.20312	−	8.53786i	0.196652	−	0.270668i
$996$		0			0
$997$	−7.45043	+	22.9301i	−0.235958	+	0.726203i	0.761035	+	0.648710i	$0.224691\pi$
$997$	−7.45043	+	22.9301i	−0.235958	+	0.726203i	−0.996993	+	0.0774924i	$0.975309\pi$
$998$		0			0
$999$	−3.64076	−	5.01107i	−0.115188	−	0.158543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.x.a.25.8	yes	56
11.4	even	5	inner	572.2.x.a.389.7	yes	56
13.12	even	2	inner	572.2.x.a.25.7	✓	56
143.103	even	10	inner	572.2.x.a.389.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.x.a.25.7	✓	56	13.12	even	2	inner
572.2.x.a.25.8	yes	56	1.1	even	1	trivial
572.2.x.a.389.7	yes	56	11.4	even	5	inner
572.2.x.a.389.8	yes	56	143.103	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0444965 - 0.136946i) q^{3} +(1.21904 - 1.67786i) q^{5} +(3.54683 + 1.15243i) q^{7} +(2.41028 - 1.75117i) q^{9} +O(q^{10})\)	\(q+(-0.0444965 - 0.136946i) q^{3} +(1.21904 - 1.67786i) q^{5} +(3.54683 + 1.15243i) q^{7} +(2.41028 - 1.75117i) q^{9} +(-3.27866 + 0.500402i) q^{11} +(2.92250 + 2.11163i) q^{13} +(-0.284019 - 0.0922834i) q^{15} +(-4.88065 - 3.54600i) q^{17} +(-5.67834 + 1.84501i) q^{19} -0.537004i q^{21} +9.27407 q^{23} +(0.215924 + 0.664547i) q^{25} +(-0.696545 - 0.506070i) q^{27} +(2.59933 - 7.99990i) q^{29} +(-0.0444393 - 0.0611655i) q^{31} +(0.214417 + 0.426734i) q^{33} +(6.25733 - 4.54622i) q^{35} +(6.84207 + 2.22312i) q^{37} +(0.159139 - 0.494186i) q^{39} +(-1.12720 + 0.366249i) q^{41} -2.80932 q^{43} -6.17884i q^{45} +(4.57778 - 1.48741i) q^{47} +(5.58877 + 4.06048i) q^{49} +(-0.268439 + 0.826172i) q^{51} +(-5.54287 + 4.02713i) q^{53} +(-3.15719 + 6.11113i) q^{55} +(0.505333 + 0.695531i) q^{57} +(-2.50595 - 0.814232i) q^{59} +(-5.78727 - 4.20470i) q^{61} +(10.5669 - 3.43341i) q^{63} +(7.10565 - 2.32938i) q^{65} +7.07902i q^{67} +(-0.412664 - 1.27005i) q^{69} +(-3.31360 + 4.56078i) q^{71} +(-4.21701 - 1.37019i) q^{73} +(0.0813993 - 0.0591401i) q^{75} +(-12.2055 - 2.00360i) q^{77} +(0.128633 - 0.0934571i) q^{79} +(2.72362 - 8.38244i) q^{81} +(-2.82387 + 3.88673i) q^{83} +(-11.8994 + 3.86634i) q^{85} -1.21122 q^{87} +9.89947i q^{89} +(7.93208 + 10.8576i) q^{91} +(-0.00639898 + 0.00880745i) q^{93} +(-3.82644 + 11.7766i) q^{95} +(-8.41519 - 11.5825i) q^{97} +(-7.02618 + 6.94759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^9	\( 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) \) 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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