LMFDB - Embedded newform 572.2.x.a.25.7

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			25.7
Character	$\chi$	$=$	572.25
Dual form			572.2.x.a.389.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0444965 - 0.136946i) q^{3} +(-1.21904 + 1.67786i) q^{5} +(-3.54683 - 1.15243i) q^{7} +(2.41028 - 1.75117i) q^{9} +O(q^{10})$	\(q+(-0.0444965 - 0.136946i) q^{3} +(-1.21904 + 1.67786i) q^{5} +(-3.54683 - 1.15243i) q^{7} +(2.41028 - 1.75117i) q^{9} +(3.27866 - 0.500402i) q^{11} +(-1.10518 - 3.43199i) q^{13} +(0.284019 + 0.0922834i) q^{15} +(-4.88065 - 3.54600i) q^{17} +(5.67834 - 1.84501i) q^{19} +0.537004i q^{21} +9.27407 q^{23} +(0.215924 + 0.664547i) q^{25} +(-0.696545 - 0.506070i) q^{27} +(2.59933 - 7.99990i) q^{29} +(0.0444393 + 0.0611655i) q^{31} +(-0.214417 - 0.426734i) q^{33} +(6.25733 - 4.54622i) q^{35} +(-6.84207 - 2.22312i) q^{37} +(-0.420822 + 0.304062i) q^{39} +(1.12720 - 0.366249i) q^{41} -2.80932 q^{43} +6.17884i q^{45} +(-4.57778 + 1.48741i) q^{47} +(5.58877 + 4.06048i) q^{49} +(-0.268439 + 0.826172i) q^{51} +(-5.54287 + 4.02713i) q^{53} +(-3.15719 + 6.11113i) q^{55} +(-0.505333 - 0.695531i) q^{57} +(2.50595 + 0.814232i) q^{59} +(-5.78727 - 4.20470i) q^{61} +(-10.5669 + 3.43341i) q^{63} +(7.10565 + 2.32938i) q^{65} -7.07902i q^{67} +(-0.412664 - 1.27005i) q^{69} +(3.31360 - 4.56078i) q^{71} +(4.21701 + 1.37019i) q^{73} +(0.0813993 - 0.0591401i) q^{75} +(-12.2055 - 2.00360i) q^{77} +(0.128633 - 0.0934571i) q^{79} +(2.72362 - 8.38244i) q^{81} +(2.82387 - 3.88673i) q^{83} +(11.8994 - 3.86634i) q^{85} -1.21122 q^{87} -9.89947i q^{89} +(-0.0352550 + 13.4463i) q^{91} +(0.00639898 - 0.00880745i) q^{93} +(-3.82644 + 11.7766i) q^{95} +(8.41519 + 11.5825i) q^{97} +(7.02618 - 6.94759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.989347	−	0.145578i	$-0.953496\pi$
$5$	−1.21904	+	1.67786i	−0.545169	+	0.750361i	0.444178	+	0.895939i	$0.353496\pi$
$6$		0			0
$7$	−3.54683	−	1.15243i	−1.34058	−	0.435579i	−0.451064	−	0.892492i	$-0.648955\pi$
$7$	−3.54683	−	1.15243i	−1.34058	−	0.435579i	−0.889512	+	0.456913i	$0.848955\pi$
$8$		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
$13$	−1.10518	−	3.43199i	−0.306522	−	0.951863i
$13$	−1.10518	−	3.43199i	−0.306522	−	0.951863i
$14$		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	0.426181	−	0.904638i	$-0.359859\pi$
$19$	5.67834	−	1.84501i	1.30270	−	0.423273i	0.876520	+	0.481365i	$0.159859\pi$
$20$		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	0.812989	−	0.582279i	$-0.197839\pi$
$31$	0.0444393	+	0.0611655i	0.00798154	+	0.0109856i	−0.805008	+	0.593265i	$0.797839\pi$
$32$		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	−0.313221	−	0.949680i	$-0.601408\pi$
$37$	−6.84207	−	2.22312i	−1.12483	−	0.365479i	−0.811609	+	0.584201i	$0.801408\pi$
$38$		0			0
$39$	−0.420822	+	0.304062i	−0.0673854	+	0.0486889i
$40$		0			0
$41$	1.12720	−	0.366249i	0.176039	−	0.0571985i	−0.219671	−	0.975574i	$-0.570499\pi$
$41$	1.12720	−	0.366249i	0.176039	−	0.0571985i	0.395710	+	0.918375i	$0.370499\pi$
$42$		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	−0.623219	−	0.782048i	$-0.714175\pi$
$47$	−4.57778	+	1.48741i	−0.667737	+	0.216961i	−0.0445186	+	0.999009i	$0.514175\pi$
$48$		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	0.467561	−	0.883961i	$-0.345133\pi$
$59$	2.50595	+	0.814232i	0.326247	+	0.106004i	−0.141314	+	0.989965i	$0.545133\pi$
$60$		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	$-0.857660\pi$
$67$		−	7.07902i		−	0.864840i	0.901672	−	0.432420i	$-0.142340\pi$
$68$		0			0
$69$	−0.412664	−	1.27005i	−0.0496789	−	0.152896i
$70$		0			0
$71$	3.31360	−	4.56078i	0.393252	−	0.541265i	−0.565783	−	0.824554i	$-0.691426\pi$
$71$	3.31360	−	4.56078i	0.393252	−	0.541265i	0.959034	+	0.283290i	$0.0914258\pi$
$72$		0			0
$73$	4.21701	+	1.37019i	0.493564	+	0.160369i	0.545215	−	0.838297i	$-0.316448\pi$
$73$	4.21701	+	1.37019i	0.493564	+	0.160369i	−0.0516505	+	0.998665i	$0.516448\pi$
$74$		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	−0.625409	−	0.780297i	$-0.715068\pi$
$83$	2.82387	−	3.88673i	0.309960	−	0.426624i	0.935369	+	0.353674i	$0.115068\pi$
$84$		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	$-0.824188\pi$
$89$		−	9.89947i		−	1.04934i	0.851305	−	0.524671i	$-0.175812\pi$
$90$		0			0
$91$	−0.0352550	+	13.4463i	−0.00369573	+	1.40956i
$92$		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	$0.0590046\pi$
$97$	8.41519	+	11.5825i	0.854433	+	1.17603i	−0.128435	+	0.991718i	$0.540995\pi$
$98$		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	$0.180501\pi$
$109$			11.2161i			1.07431i	−0.843483	+	0.537156i	$0.819499\pi$
$110$		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
$117$	−8.67379	−	6.33669i	−0.801892	−	0.585827i
$118$		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	−0.822856	−	0.568250i	$-0.807621\pi$
$137$	−0.329390	+	0.453366i	−0.0281417	+	0.0387337i	0.794714	+	0.606984i	$0.207621\pi$
$138$		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
$143$	−5.34089	−	10.6993i	−0.446628	−	0.894720i
$144$		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	$-0.553509\pi$
$149$	10.0343	−	13.8110i	0.822041	−	1.13144i	0.989353	−	0.145538i	$-0.0464915\pi$
$150$		0			0
$151$	14.6391	−	4.75655i	1.19132	−	0.387082i	0.354757	−	0.934959i	$-0.384564\pi$
$151$	14.6391	−	4.75655i	1.19132	−	0.387082i	0.836559	+	0.547876i	$0.184564\pi$
$152$		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	0.993165	−	0.116718i	$-0.0372375\pi$
$163$	7.34436	+	10.1086i	0.575254	+	0.791770i	−0.417911	+	0.908488i	$0.637238\pi$
$164$		0			0
$165$	0.977380	+	0.160442i	0.0760890	+	0.0124904i
$166$		0			0
$167$	−3.13442	−	4.31416i	−0.242549	−	0.333839i	0.670336	−	0.742058i	$-0.266150\pi$
$167$	−3.13442	−	4.31416i	−0.242549	−	0.333839i	−0.912884	+	0.408219i	$0.866150\pi$
$168$		0			0
$169$	−10.5571	+	7.58595i	−0.812088	+	0.583535i
$170$		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	−0.485192	−	0.874408i	$-0.661250\pi$
$193$	6.89554	−	9.49089i	0.496352	−	0.683169i	0.981544	+	0.191238i	$0.0612503\pi$
$194$		0			0
$195$	0.00282312	−	1.07674i	0.000202168	−	0.0771071i
$196$		0			0
$197$			1.22973i			0.0876147i	0.999040	+	0.0438074i	$0.0139488\pi$
$197$			1.22973i			0.0876147i	−0.999040	+	0.0438074i	$0.986051\pi$
$198$		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	0.362124	−	0.932130i	$-0.382052\pi$
$223$	17.9643	−	5.83697i	1.20298	−	0.390872i	0.840857	+	0.541257i	$0.182052\pi$
$224$		0			0
$225$	1.68417	+	1.22362i	0.112278	+	0.0815748i
$226$		0			0
$227$	19.1278	+	6.21500i	1.26956	+	0.412504i	0.864890	−	0.501961i	$-0.167388\pi$
$227$	19.1278	+	6.21500i	1.26956	+	0.412504i	0.404666	+	0.914465i	$0.367388\pi$
$228$		0			0
$229$	−7.85291	−	10.8086i	−0.518935	−	0.714253i	0.466459	−	0.884543i	$-0.345530\pi$
$229$	−7.85291	−	10.8086i	−0.518935	−	0.714253i	−0.985394	+	0.170290i	$0.945530\pi$
$230$		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	−0.579159	−	0.815215i	$-0.696619\pi$
$239$	−8.78938	+	2.85584i	−0.568538	+	0.184729i	0.0106216	+	0.999944i	$0.496619\pi$
$240$		0			0
$241$			19.1756i			1.23521i	0.786490	+	0.617603i	$0.211896\pi$
$241$			19.1756i			1.23521i	−0.786490	+	0.617603i	$0.788104\pi$
$242$		0			0
$243$	−3.85207			−0.247110
$244$		0			0
$245$	−13.6258	+	4.42730i	−0.870521	+	0.282850i
$246$		0			0
$247$	−12.6076	−	17.4490i	−0.802205	−	1.11025i
$248$		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	−0.626318	−	0.779567i	$-0.715439\pi$
$271$	−26.1951	−	8.51130i	−1.59124	−	0.517025i	−0.964920	+	0.262543i	$0.915439\pi$
$272$		0			0
$273$	1.84299	−	0.593487i	0.111543	−	0.0359195i
$274$		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	−0.863116	−	0.505006i	$-0.831490\pi$
$281$	−1.94634	+	2.67891i	−0.116109	+	0.159811i	0.747007	+	0.664817i	$0.231490\pi$
$282$		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	0.305298	−	0.952257i	$-0.401244\pi$
$293$	−0.127234	−	0.0413408i	−0.00743308	−	0.00241515i	−0.312731	+	0.949842i	$0.601244\pi$
$294$		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
$299$	−10.2495	−	31.8285i	−0.592746	−	1.84069i
$300$		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	$-0.931731\pi$
$307$		−	7.45831i		−	0.425668i	0.977088	−	0.212834i	$-0.0682694\pi$
$308$		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	$0.143017\pi$
$317$	18.4362	+	25.3753i	1.03548	+	1.42522i	0.134732	+	0.990882i	$0.456983\pi$
$318$		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
$325$	2.04209	−	1.47550i	0.113275	−	0.0818458i
$326$		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	$0.169276\pi$
$331$			18.4511i			1.01417i	−0.861897	+	0.507083i	$0.830724\pi$
$332$		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	−0.848993	−	0.528404i	$-0.822791\pi$
$349$	−22.8897	+	7.43730i	−1.22526	+	0.398110i	−0.376262	+	0.926513i	$0.622791\pi$
$350$		0			0
$351$	−0.967018	+	2.94984i	−0.0516156	+	0.157451i
$352$		0			0
$353$		−	27.7698i		−	1.47804i	−0.673684	−	0.739019i	$-0.735289\pi$
$353$		−	27.7698i		−	1.47804i	0.673684	−	0.739019i	$-0.264711\pi$
$354$		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	0.204140	−	0.978942i	$-0.434560\pi$
$359$	−3.90532	−	1.26892i	−0.206115	−	0.0669708i	−0.410255	+	0.911971i	$0.634560\pi$
$360$		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
$377$	−30.3283	−	0.0795181i	−1.56199	−	0.00409539i
$378$		0			0
$379$	−14.7128	+	20.2505i	−0.755747	+	1.04020i	0.241809	+	0.970324i	$0.422259\pi$
$379$	−14.7128	+	20.2505i	−0.755747	+	1.04020i	−0.997556	+	0.0698721i	$0.977741\pi$
$380$		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	$0.0316313\pi$
$383$	15.3026	+	21.0623i	0.781928	+	1.07623i	−0.213139	+	0.977022i	$0.568369\pi$
$384$		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	$-0.987425\pi$
$397$		−	1.57385i		−	0.0789892i	0.999220	−	0.0394946i	$-0.0125748\pi$
$398$		0			0
$399$	0.990776	+	3.04929i	0.0496008	+	0.152656i
$400$		0			0
$401$	2.66989	−	3.67479i	0.133328	−	0.183510i	−0.737133	−	0.675748i	$-0.763821\pi$
$401$	2.66989	−	3.67479i	0.133328	−	0.183510i	0.870461	+	0.492237i	$0.163821\pi$
$402$		0			0
$403$	0.160806	−	0.220114i	0.00801031	−	0.0109647i
$404$		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	0.545537	−	0.838086i	$-0.316326\pi$
$409$	−8.49621	−	11.6940i	−0.420110	−	0.578232i	−0.965648	+	0.259854i	$0.916326\pi$
$410$		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	−0.818996	−	0.573799i	$-0.805469\pi$
$421$	−23.4792	+	7.62887i	−1.14431	+	0.371808i	−0.325312	+	0.945607i	$0.605469\pi$
$422$		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
$429$	−1.22758	+	1.20750i	−0.0592680	+	0.0582985i
$430$		0			0
$431$	13.8061	+	19.0025i	0.665018	+	0.915319i	0.999634	−	0.0270355i	$-0.00860672\pi$
$431$	13.8061	+	19.0025i	0.665018	+	0.915319i	−0.334616	+	0.942354i	$0.608607\pi$
$432$		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	0.508105	−	0.861295i	$-0.330346\pi$
$449$	−9.91778	−	13.6507i	−0.468049	−	0.644214i	−0.976154	+	0.217081i	$0.930346\pi$
$450$		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
$455$	−22.5181	−	16.4507i	−1.05566	−	0.771221i
$456$		0			0
$457$	19.1210	−	26.3178i	0.894444	−	1.23110i	−0.0777631	−	0.996972i	$-0.524778\pi$
$457$	19.1210	−	26.3178i	0.894444	−	1.23110i	0.972207	−	0.234124i	$-0.0752222\pi$
$458$		0			0
$459$	1.60507	+	4.93990i	0.0749183	+	0.230575i
$460$		0			0
$461$			16.8303i			0.783866i	0.919994	+	0.391933i	$0.128194\pi$
$461$			16.8303i			0.783866i	−0.919994	+	0.391933i	$0.871806\pi$
$462$		0			0
$463$			37.6534i			1.74990i	0.484210	+	0.874952i	$0.339107\pi$
$463$			37.6534i			1.74990i	−0.484210	+	0.874952i	$0.660893\pi$
$464$		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	−0.869872	−	0.493277i	$-0.835799\pi$
$479$	−2.88750	+	3.97430i	−0.131933	+	0.181590i	0.737939	+	0.674867i	$0.235799\pi$
$480$		0			0
$481$	−0.0680094	+	25.9389i	−0.00310096	+	1.18271i
$482$		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	0.296219	−	0.955120i	$-0.404274\pi$
$487$	24.2146	−	7.86781i	1.09727	−	0.356525i	0.801051	+	0.598596i	$0.204274\pi$
$488$		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	0.355229	−	0.934779i	$-0.384403\pi$
$499$	2.08115	+	0.676206i	0.0931650	+	0.0302711i	−0.262064	+	0.965051i	$0.584403\pi$
$500$		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	0.662278	−	0.749258i	$-0.269590\pi$
$509$	36.9657	−	12.0109i	1.63847	−	0.532373i	0.976197	+	0.216886i	$0.0695899\pi$
$510$		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
$533$	−2.50272	−	3.46376i	−0.108405	−	0.150032i
$534$		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	0.684283	−	0.729217i	$-0.260115\pi$
$541$	−5.13331	−	7.06540i	−0.220698	−	0.303765i	−0.904981	+	0.425451i	$0.860115\pi$
$542$		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	0.0609204	−	0.998143i	$-0.480596\pi$
$557$	−11.2455	−	3.65389i	−0.476487	−	0.154820i	−0.537408	+	0.843322i	$0.680596\pi$
$558$		0			0
$559$	3.10481	+	9.64158i	0.131320	+	0.407795i
$560$		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	$0.516313\pi$
$577$	−23.6654	+	32.5727i	−0.985205	+	1.35602i	−0.933978	+	0.357331i	$0.883687\pi$
$578$		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
$585$	21.2057	−	6.82874i	0.876749	−	0.282334i
$586$		0			0
$587$	6.70955	+	2.18007i	0.276933	+	0.0899809i	0.444191	−	0.895932i	$-0.353491\pi$
$587$	6.70955	+	2.18007i	0.276933	+	0.0899809i	−0.167258	+	0.985913i	$0.553491\pi$
$588$		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	$0.180425\pi$
$593$			26.1513i			1.07391i	−0.843612	+	0.536953i	$0.819575\pi$
$594$		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
$611$	10.1641	+	14.0670i	0.411194	+	0.569091i
$612$		0			0
$613$	−36.1325	+	11.7402i	−1.45938	+	0.474181i	−0.927880	−	0.372878i	$-0.878371\pi$
$613$	−36.1325	+	11.7402i	−1.45938	+	0.474181i	−0.531499	+	0.847059i	$0.678371\pi$
$614$		0			0
$615$	0.353944			0.0142724
$616$		0			0
$617$			38.4841i			1.54931i	0.632383	+	0.774656i	$0.282077\pi$
$617$			38.4841i			1.54931i	−0.632383	+	0.774656i	$0.717923\pi$
$618$		0			0
$619$	−14.6205	+	4.75050i	−0.587649	+	0.190939i	−0.587724	−	0.809061i	$-0.699976\pi$
$619$	−14.6205	+	4.75050i	−0.587649	+	0.190939i	7.53944e−5		1.00000i	$0.499976\pi$
$620$		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	0.593672	−	0.804707i	$-0.297678\pi$
$631$	15.0962	+	4.90504i	0.600969	+	0.195267i	0.00729623	+	0.999973i	$0.497678\pi$
$632$		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	$-0.550546\pi$
$643$	21.0423	−	28.9622i	0.829826	−	1.14216i	0.987955	−	0.154739i	$-0.0494538\pi$
$644$		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	$-0.933891\pi$
$661$		−	10.6026i		−	0.412395i	0.978510	−	0.206197i	$-0.0661089\pi$
$662$		0			0
$663$	3.13209	+	0.00821205i	0.121640	+	0.000318929i
$664$		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	$-0.892581\pi$
$683$		−	17.3059i		−	0.662193i	0.943597	−	0.331097i	$-0.107419\pi$
$684$		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
$689$	19.9470	+	14.5724i	0.759919	+	0.555164i
$690$		0			0
$691$	21.4006	+	29.4554i	0.814117	+	1.12054i	0.990675	+	0.136245i	$0.0435036\pi$
$691$	21.4006	+	29.4554i	0.814117	+	1.12054i	−0.176558	+	0.984290i	$0.556496\pi$
$692$		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	−0.967379	−	0.253335i	$-0.918473\pi$
$709$	−11.3832	+	15.6677i	−0.427506	+	0.588412i	0.539872	+	0.841747i	$0.318473\pi$
$710$		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
$715$	24.4626	+	4.08156i	0.914850	+	0.152642i
$716$		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	0.231666	−	0.972795i	$-0.425582\pi$
$733$	−4.13439	−	1.34334i	−0.152707	−	0.0496175i	−0.384373	+	0.923178i	$0.625582\pi$
$734$		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	0.564193	−	0.825643i	$-0.309187\pi$
$739$	−10.7484	−	14.7938i	−0.395385	−	0.544200i	−0.959578	+	0.281442i	$0.909187\pi$
$740$		0			0
$741$	−1.82857	+	2.50299i	−0.0671743	+	0.0919496i
$742$		0			0
$743$	−11.8609	+	16.3251i	−0.435133	+	0.598910i	−0.969122	−	0.246582i	$-0.920693\pi$
$743$	−11.8609	+	16.3251i	−0.435133	+	0.598910i	0.533989	+	0.845492i	$0.320693\pi$
$744$		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	0.992466	−	0.122524i	$-0.0390988\pi$
$761$	15.7035	+	21.6140i	0.569250	+	0.783505i	−0.423216	+	0.906029i	$0.639099\pi$
$762$		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
$767$	0.0249088	−	9.50027i	0.000899405	−	0.343035i
$768$		0			0
$769$			32.0680i			1.15640i	0.815894	+	0.578201i	$0.196245\pi$
$769$			32.0680i			1.15640i	−0.815894	+	0.578201i	$0.803755\pi$
$770$		0			0
$771$	−0.0177201			−0.000638175
$772$		0			0
$773$	−33.1722	+	10.7783i	−1.19312	+	0.387668i	−0.837226	−	0.546858i	$-0.815824\pi$
$773$	−33.1722	+	10.7783i	−1.19312	+	0.387668i	−0.355895	+	0.934526i	$0.615824\pi$
$774$		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	−0.917595	−	0.397518i	$-0.869872\pi$
$787$	−7.18116	+	9.88401i	−0.255981	+	0.352327i	0.661614	+	0.749845i	$0.269872\pi$
$788$		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	−0.724498	−	0.689277i	$-0.757928\pi$
$811$	−25.7864	+	8.37850i	−0.905482	+	0.294209i	−0.180984	+	0.983486i	$0.557928\pi$
$812$		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
$819$	23.4618	+	32.4711i	0.819823	+	1.13463i
$820$		0			0
$821$	−3.76634	−	1.22376i	−0.131446	−	0.0427094i	0.242555	−	0.970138i	$-0.422014\pi$
$821$	−3.76634	−	1.22376i	−0.131446	−	0.0427094i	−0.374001	+	0.927428i	$0.622014\pi$
$822$		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	0.754347	−	0.656476i	$-0.227954\pi$
$827$	−2.96506	−	4.08106i	−0.103105	−	0.141912i	−0.857452	+	0.514564i	$0.827954\pi$
$828$		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	−0.0168858	−	0.999857i	$-0.505375\pi$
$839$	16.1383	−	5.24364i	0.557155	−	0.181031i	0.574041	+	0.818827i	$0.305375\pi$
$840$		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
$845$	0.141379	−	26.9609i	0.00486359	−	0.927484i
$846$		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	−0.805545	−	0.592534i	$-0.798127\pi$
$853$	0.201981	−	0.278004i	0.00691571	−	0.00951866i	0.812461	+	0.583016i	$0.198127\pi$
$854$		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	−0.819780	−	0.572679i	$-0.805904\pi$
$863$	−0.640535	+	0.881621i	−0.0218041	+	0.0300107i	0.797976	+	0.602690i	$0.205904\pi$
$864$		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
$871$	−24.2952	+	7.82361i	−0.823210	+	0.265093i
$872$		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	−0.929149	−	0.369706i	$-0.879458\pi$
$877$	−43.3415	+	14.0825i	−1.46354	+	0.475533i	−0.534390	+	0.845238i	$0.679458\pi$
$878$		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
$897$	−3.90273	+	2.81989i	−0.130308	+	0.0941535i
$898$		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	−0.850338	−	0.526237i	$-0.823602\pi$
$929$	−2.65439	+	3.65345i	−0.0870875	+	0.119866i	0.763250	+	0.646103i	$0.223602\pi$
$930$		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	−0.624339	−	0.781153i	$-0.714632\pi$
$941$	9.55590	−	13.1526i	0.311513	−	0.428761i	0.935852	+	0.352392i	$0.114632\pi$
$942$		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	$0.164686\pi$
$947$			30.4412i			0.989205i	−0.869119	+	0.494602i	$0.835314\pi$
$948$		0			0
$949$	0.0419166	−	15.9871i	0.00136067	−	0.518962i
$950$		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	$-0.790831\pi$
$967$		−	37.9903i		−	1.22168i	0.791752	−	0.610842i	$-0.209169\pi$
$968$		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
$975$	−0.292929	−	0.214001i	−0.00938125	−	0.00685353i
$976$		0			0
$977$	−30.2127	−	41.5843i	−0.966591	−	1.33040i	−0.943750	−	0.330659i	$-0.892729\pi$
$977$	−30.2127	−	41.5843i	−0.966591	−	1.33040i	−0.0228405	−	0.999739i	$-0.507271\pi$
$978$		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	0.942958	−	0.332911i	$-0.108031\pi$
$983$	47.3474	+	15.3841i	1.51015	+	0.490677i	0.567189	+	0.823587i	$0.308031\pi$
$984$		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.25.7	✓	56
11.4	even	5	inner	572.2.x.a.389.8	yes	56
13.12	even	2	inner	572.2.x.a.25.8	yes	56
143.103	even	10	inner	572.2.x.a.389.7	yes	56

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0444965 - 0.136946i) q^{3} +(-1.21904 + 1.67786i) q^{5} +(-3.54683 - 1.15243i) q^{7} +(2.41028 - 1.75117i) q^{9} +O(q^{10})\)	\(q+(-0.0444965 - 0.136946i) q^{3} +(-1.21904 + 1.67786i) q^{5} +(-3.54683 - 1.15243i) q^{7} +(2.41028 - 1.75117i) q^{9} +(3.27866 - 0.500402i) q^{11} +(-1.10518 - 3.43199i) q^{13} +(0.284019 + 0.0922834i) q^{15} +(-4.88065 - 3.54600i) q^{17} +(5.67834 - 1.84501i) q^{19} +0.537004i q^{21} +9.27407 q^{23} +(0.215924 + 0.664547i) q^{25} +(-0.696545 - 0.506070i) q^{27} +(2.59933 - 7.99990i) q^{29} +(0.0444393 + 0.0611655i) q^{31} +(-0.214417 - 0.426734i) q^{33} +(6.25733 - 4.54622i) q^{35} +(-6.84207 - 2.22312i) q^{37} +(-0.420822 + 0.304062i) q^{39} +(1.12720 - 0.366249i) q^{41} -2.80932 q^{43} +6.17884i q^{45} +(-4.57778 + 1.48741i) q^{47} +(5.58877 + 4.06048i) q^{49} +(-0.268439 + 0.826172i) q^{51} +(-5.54287 + 4.02713i) q^{53} +(-3.15719 + 6.11113i) q^{55} +(-0.505333 - 0.695531i) q^{57} +(2.50595 + 0.814232i) q^{59} +(-5.78727 - 4.20470i) q^{61} +(-10.5669 + 3.43341i) q^{63} +(7.10565 + 2.32938i) q^{65} -7.07902i q^{67} +(-0.412664 - 1.27005i) q^{69} +(3.31360 - 4.56078i) q^{71} +(4.21701 + 1.37019i) q^{73} +(0.0813993 - 0.0591401i) q^{75} +(-12.2055 - 2.00360i) q^{77} +(0.128633 - 0.0934571i) q^{79} +(2.72362 - 8.38244i) q^{81} +(2.82387 - 3.88673i) q^{83} +(11.8994 - 3.86634i) q^{85} -1.21122 q^{87} -9.89947i q^{89} +(-0.0352550 + 13.4463i) q^{91} +(0.00639898 - 0.00880745i) q^{93} +(-3.82644 + 11.7766i) q^{95} +(8.41519 + 11.5825i) q^{97} +(7.02618 - 6.94759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{9}+O(q^{10}) \) 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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