LMFDB - Embedded newform 572.2.n.b.157.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.6
Character	$\chi$	$=$	572.157
Dual form			572.2.n.b.521.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.955130 + 2.93959i) q^{3} +(-3.52306 - 2.55966i) q^{5} +(0.357931 - 1.10160i) q^{7} +(-5.30186 + 3.85203i) q^{9} +O(q^{10})$	\(q+(0.955130 + 2.93959i) q^{3} +(-3.52306 - 2.55966i) q^{5} +(0.357931 - 1.10160i) q^{7} +(-5.30186 + 3.85203i) q^{9} +(-3.03732 + 1.33217i) q^{11} +(0.809017 - 0.587785i) q^{13} +(4.15935 - 12.8012i) q^{15} +(-6.11202 - 4.44064i) q^{17} +(-1.75118 - 5.38958i) q^{19} +3.58012 q^{21} +0.202818 q^{23} +(4.31506 + 13.2804i) q^{25} +(-8.88565 - 6.45580i) q^{27} +(-1.81115 + 5.57415i) q^{29} +(1.85144 - 1.34515i) q^{31} +(-6.81707 - 7.65608i) q^{33} +(-4.08073 + 2.96482i) q^{35} +(-0.723352 + 2.22625i) q^{37} +(2.50056 + 1.81677i) q^{39} +(-0.719547 - 2.21454i) q^{41} -3.95526 q^{43} +28.5387 q^{45} +(-0.684154 - 2.10561i) q^{47} +(4.57771 + 3.32590i) q^{49} +(7.21589 - 22.2082i) q^{51} +(-0.0852965 + 0.0619716i) q^{53} +(14.1106 + 3.08118i) q^{55} +(14.1705 - 10.2955i) q^{57} +(-2.05086 + 6.31189i) q^{59} +(-8.65038 - 6.28487i) q^{61} +(2.34569 + 7.21928i) q^{63} -4.35475 q^{65} -9.05284 q^{67} +(0.193718 + 0.596203i) q^{69} +(0.100914 + 0.0733180i) q^{71} +(-0.654868 + 2.01548i) q^{73} +(-34.9174 + 25.3690i) q^{75} +(0.380365 + 3.82274i) q^{77} +(10.1959 - 7.40777i) q^{79} +(4.41506 - 13.5882i) q^{81} +(6.63394 + 4.81984i) q^{83} +(10.1665 + 31.2894i) q^{85} -18.1156 q^{87} -14.0653 q^{89} +(-0.357931 - 1.10160i) q^{91} +(5.72257 + 4.15769i) q^{93} +(-7.62594 + 23.4702i) q^{95} +(2.25497 - 1.63833i) q^{97} +(10.9719 - 18.7628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

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
$3$	0.955130	+	2.93959i	0.551445	+	1.69717i	0.705152	+	0.709056i	$0.250879\pi$
$3$	0.955130	+	2.93959i	0.551445	+	1.69717i	−0.153707	+	0.988116i	$0.549121\pi$
$4$		0			0
$5$	−3.52306	−	2.55966i	−1.57556	−	1.14471i	−0.921570	−	0.388212i	$-0.873093\pi$
$5$	−3.52306	−	2.55966i	−1.57556	−	1.14471i	−0.653992	−	0.756501i	$-0.726907\pi$
$6$		0			0
$7$	0.357931	−	1.10160i	0.135285	−	0.416365i	−0.860349	−	0.509705i	$-0.829754\pi$
$7$	0.357931	−	1.10160i	0.135285	−	0.416365i	0.995634	+	0.0933401i	$0.0297544\pi$
$8$		0			0
$9$	−5.30186	+	3.85203i	−1.76729	+	1.28401i
$10$		0			0
$11$	−3.03732	+	1.33217i	−0.915787	+	0.401664i
$11$	−3.03732	+	1.33217i	−0.915787	+	0.401664i
$12$		0			0
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$		0			0
$15$	4.15935	−	12.8012i	1.07394	−	3.30525i
$16$		0			0
$17$	−6.11202	−	4.44064i	−1.48238	−	1.07701i	−0.976779	−	0.214249i	$-0.931270\pi$
$17$	−6.11202	−	4.44064i	−1.48238	−	1.07701i	−0.505604	−	0.862766i	$-0.668730\pi$
$18$		0			0
$19$	−1.75118	−	5.38958i	−0.401748	−	1.23645i	−0.923580	−	0.383405i	$-0.874751\pi$
$19$	−1.75118	−	5.38958i	−0.401748	−	1.23645i	0.521832	−	0.853048i	$-0.325249\pi$
$20$		0			0
$21$	3.58012			0.781246
$22$		0			0
$23$	0.202818			0.0422906			0.0211453	−	0.999776i	$-0.493269\pi$
$23$	0.202818			0.0422906			0.0211453	+	0.999776i	$0.493269\pi$
$24$		0			0
$25$	4.31506	+	13.2804i	0.863012	+	2.65608i
$26$		0			0
$27$	−8.88565	−	6.45580i	−1.71004	−	1.24242i
$28$		0			0
$29$	−1.81115	+	5.57415i	−0.336322	+	1.03509i	0.629744	+	0.776802i	$0.283160\pi$
$29$	−1.81115	+	5.57415i	−0.336322	+	1.03509i	−0.966067	+	0.258292i	$0.916840\pi$
$30$		0			0
$31$	1.85144	−	1.34515i	0.332529	−	0.241597i	−0.408974	−	0.912546i	$-0.634113\pi$
$31$	1.85144	−	1.34515i	0.332529	−	0.241597i	0.741503	+	0.670949i	$0.234113\pi$
$32$		0			0
$33$	−6.81707	−	7.65608i	−1.18670	−	1.33275i
$34$		0			0
$35$	−4.08073	+	2.96482i	−0.689769	+	0.501147i
$36$		0			0
$37$	−0.723352	+	2.22625i	−0.118918	+	0.365993i	−0.992744	−	0.120246i	$-0.961632\pi$
$37$	−0.723352	+	2.22625i	−0.118918	+	0.365993i	0.873826	+	0.486239i	$0.161632\pi$
$38$		0			0
$39$	2.50056	+	1.81677i	0.400411	+	0.290915i
$40$		0			0
$41$	−0.719547	−	2.21454i	−0.112374	−	0.345853i	0.879016	−	0.476792i	$-0.158201\pi$
$41$	−0.719547	−	2.21454i	−0.112374	−	0.345853i	−0.991390	+	0.130940i	$0.958201\pi$
$42$		0			0
$43$	−3.95526			−0.603172			−0.301586	−	0.953439i	$-0.597516\pi$
$43$	−3.95526			−0.603172			−0.301586	+	0.953439i	$0.597516\pi$
$44$		0			0
$45$	28.5387			4.25429
$46$		0			0
$47$	−0.684154	−	2.10561i	−0.0997942	−	0.307135i	0.888679	−	0.458529i	$-0.151624\pi$
$47$	−0.684154	−	2.10561i	−0.0997942	−	0.307135i	−0.988473	+	0.151395i	$0.951624\pi$
$48$		0			0
$49$	4.57771	+	3.32590i	0.653959	+	0.475129i
$50$		0			0
$51$	7.21589	−	22.2082i	1.01043	−	3.10977i
$52$		0			0
$53$	−0.0852965	+	0.0619716i	−0.0117164	+	0.00851245i	−0.593628	−	0.804740i	$-0.702305\pi$
$53$	−0.0852965	+	0.0619716i	−0.0117164	+	0.00851245i	0.581912	+	0.813252i	$0.302305\pi$
$54$		0			0
$55$	14.1106	+	3.08118i	1.90267	+	0.415466i
$56$		0			0
$57$	14.1705	−	10.2955i	1.87693	−	1.36367i
$58$		0			0
$59$	−2.05086	+	6.31189i	−0.266999	+	0.821738i	0.724227	+	0.689561i	$0.242197\pi$
$59$	−2.05086	+	6.31189i	−0.266999	+	0.821738i	−0.991226	+	0.132177i	$0.957803\pi$
$60$		0			0
$61$	−8.65038	−	6.28487i	−1.10757	−	0.804695i	−0.125288	−	0.992120i	$-0.539986\pi$
$61$	−8.65038	−	6.28487i	−1.10757	−	0.804695i	−0.982279	+	0.187426i	$0.939986\pi$
$62$		0			0
$63$	2.34569	+	7.21928i	0.295529	+	0.909544i
$64$		0			0
$65$	−4.35475			−0.540140
$66$		0			0
$67$	−9.05284			−1.10598			−0.552990	−	0.833188i	$-0.686513\pi$
$67$	−9.05284			−1.10598			−0.552990	+	0.833188i	$0.686513\pi$
$68$		0			0
$69$	0.193718	+	0.596203i	0.0233209	+	0.0717744i
$70$		0			0
$71$	0.100914	+	0.0733180i	0.0119762	+	0.00870124i	0.593757	−	0.804644i	$-0.297644\pi$
$71$	0.100914	+	0.0733180i	0.0119762	+	0.00870124i	−0.581781	+	0.813345i	$0.697644\pi$
$72$		0			0
$73$	−0.654868	+	2.01548i	−0.0766465	+	0.235894i	−0.982038	−	0.188685i	$-0.939578\pi$
$73$	−0.654868	+	2.01548i	−0.0766465	+	0.235894i	0.905391	+	0.424578i	$0.139578\pi$
$74$		0			0
$75$	−34.9174	+	25.3690i	−4.03192	+	2.92936i
$76$		0			0
$77$	0.380365	+	3.82274i	0.0433466	+	0.435641i
$78$		0			0
$79$	10.1959	−	7.40777i	1.14713	−	0.833439i	0.159034	−	0.987273i	$-0.449162\pi$
$79$	10.1959	−	7.40777i	1.14713	−	0.833439i	0.988097	+	0.153834i	$0.0491621\pi$
$80$		0			0
$81$	4.41506	−	13.5882i	0.490563	−	1.50980i
$82$		0			0
$83$	6.63394	+	4.81984i	0.728170	+	0.529046i	0.888984	−	0.457938i	$-0.151412\pi$
$83$	6.63394	+	4.81984i	0.728170	+	0.529046i	−0.160814	+	0.986985i	$0.551412\pi$
$84$		0			0
$85$	10.1665	+	31.2894i	1.10271	+	3.39381i
$86$		0			0
$87$	−18.1156			−1.94220
$88$		0			0
$89$	−14.0653			−1.49092			−0.745461	−	0.666550i	$-0.767770\pi$
$89$	−14.0653			−1.49092			−0.745461	+	0.666550i	$0.767770\pi$
$90$		0			0
$91$	−0.357931	−	1.10160i	−0.0375214	−	0.115479i
$92$		0			0
$93$	5.72257	+	4.15769i	0.593403	+	0.431132i
$94$		0			0
$95$	−7.62594	+	23.4702i	−0.782405	+	2.40800i
$96$		0			0
$97$	2.25497	−	1.63833i	0.228958	−	0.166348i	−0.467392	−	0.884050i	$-0.654806\pi$
$97$	2.25497	−	1.63833i	0.228958	−	0.166348i	0.696350	+	0.717703i	$0.254806\pi$
$98$		0			0
$99$	10.9719	−	18.7628i	1.10272	−	1.88573i
$100$		0			0
$101$	0.179575	−	0.130469i	0.0178684	−	0.0129821i	−0.578815	−	0.815459i	$-0.696485\pi$
$101$	0.179575	−	0.130469i	0.0178684	−	0.0129821i	0.596684	+	0.802477i	$0.296485\pi$
$102$		0			0
$103$	−2.85773	+	8.79518i	−0.281580	+	0.866615i	0.705823	+	0.708389i	$0.250578\pi$
$103$	−2.85773	+	8.79518i	−0.281580	+	0.866615i	−0.987403	+	0.158226i	$0.949422\pi$
$104$		0			0
$105$	−12.6130	−	9.16388i	−1.23090	−	0.894303i
$106$		0			0
$107$	1.59508	+	4.90915i	0.154202	+	0.474585i	0.998079	−	0.0619513i	$-0.0197324\pi$
$107$	1.59508	+	4.90915i	0.154202	+	0.474585i	−0.843877	+	0.536537i	$0.819732\pi$
$108$		0			0
$109$	−6.35660			−0.608852			−0.304426	−	0.952536i	$-0.598465\pi$
$109$	−6.35660			−0.608852			−0.304426	+	0.952536i	$0.598465\pi$
$110$		0			0
$111$	−7.23515			−0.686730
$112$		0			0
$113$	2.13707	+	6.57722i	0.201038	+	0.618733i	0.999853	+	0.0171552i	$0.00546094\pi$
$113$	2.13707	+	6.57722i	0.201038	+	0.618733i	−0.798814	+	0.601578i	$0.794539\pi$
$114$		0			0
$115$	−0.714542	−	0.519145i	−0.0666314	−	0.0484106i
$116$		0			0
$117$	−2.02513	+	6.23271i	−0.187223	+	0.576214i
$118$		0			0
$119$	−7.07949	+	5.14355i	−0.648976	+	0.471509i
$120$		0			0
$121$	7.45065	−	8.09246i	0.677331	−	0.735678i
$122$		0			0
$123$	5.82257	−	4.23035i	0.525004	−	0.381437i
$124$		0			0
$125$	12.0625	−	37.1247i	1.07891	−	3.32053i
$126$		0			0
$127$	−13.6475	−	9.91546i	−1.21102	−	0.879854i	−0.215693	−	0.976461i	$-0.569201\pi$
$127$	−13.6475	−	9.91546i	−1.21102	−	0.879854i	−0.995323	+	0.0966068i	$0.969201\pi$
$128$		0			0
$129$	−3.77779	−	11.6268i	−0.332616	−	1.02369i
$130$		0			0
$131$	−7.23919			−0.632491			−0.316245	−	0.948677i	$-0.602422\pi$
$131$	−7.23919			−0.632491			−0.316245	+	0.948677i	$0.602422\pi$
$132$		0			0
$133$	−6.56395			−0.569167
$134$		0			0
$135$	14.7801	+	45.4884i	1.27207	+	3.91502i
$136$		0			0
$137$	−6.94980	−	5.04932i	−0.593761	−	0.431393i	0.249898	−	0.968272i	$-0.419603\pi$
$137$	−6.94980	−	5.04932i	−0.593761	−	0.431393i	−0.843659	+	0.536879i	$0.819603\pi$
$138$		0			0
$139$	0.742484	−	2.28513i	0.0629767	−	0.193822i	−0.914618	−	0.404320i	$-0.867508\pi$
$139$	0.742484	−	2.28513i	0.0629767	−	0.193822i	0.977594	+	0.210497i	$0.0675083\pi$
$140$		0			0
$141$	5.53617	−	4.02227i	0.466230	−	0.338736i
$142$		0			0
$143$	−1.67421	+	2.86304i	−0.140005	+	0.239420i
$144$		0			0
$145$	20.6487	−	15.0022i	1.71478	−	1.24586i
$146$		0			0
$147$	−5.40448	+	16.6333i	−0.445754	+	1.37189i
$148$		0			0
$149$	5.44837	+	3.95847i	0.446348	+	0.324291i	0.788152	−	0.615480i	$-0.211038\pi$
$149$	5.44837	+	3.95847i	0.446348	+	0.324291i	−0.341804	+	0.939771i	$0.611038\pi$
$150$		0			0
$151$	4.68788	+	14.4278i	0.381495	+	1.17412i	0.938991	+	0.343940i	$0.111762\pi$
$151$	4.68788	+	14.4278i	0.381495	+	1.17412i	−0.557497	+	0.830179i	$0.688238\pi$
$152$		0			0
$153$	49.5106			4.00269
$154$		0			0
$155$	−9.96589			−0.800479
$156$		0			0
$157$	0.800629	+	2.46408i	0.0638972	+	0.196655i	0.977909	−	0.209033i	$-0.0670317\pi$
$157$	0.800629	+	2.46408i	0.0638972	+	0.196655i	−0.914011	+	0.405689i	$0.867032\pi$
$158$		0			0
$159$	−0.263640	−	0.191546i	−0.0209080	−	0.0151906i
$160$		0			0
$161$	0.0725950	−	0.223425i	0.00572129	−	0.0176083i
$162$		0			0
$163$	−5.89167	+	4.28055i	−0.461471	+	0.335279i	−0.794108	−	0.607776i	$-0.792062\pi$
$163$	−5.89167	+	4.28055i	−0.461471	+	0.335279i	0.332637	+	0.943055i	$0.392062\pi$
$164$		0			0
$165$	4.42004	+	44.4222i	0.344100	+	3.45827i
$166$		0			0
$167$	11.6293	−	8.44917i	0.899901	−	0.653817i	−0.0385392	−	0.999257i	$-0.512270\pi$
$167$	11.6293	−	8.44917i	0.899901	−	0.653817i	0.938441	+	0.345440i	$0.112270\pi$
$168$		0			0
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$		0			0
$171$	30.0453	+	21.8292i	2.29762	+	1.66932i
$172$		0			0
$173$	4.66937	+	14.3709i	0.355006	+	1.09260i	0.956006	+	0.293347i	$0.0947691\pi$
$173$	4.66937	+	14.3709i	0.355006	+	1.09260i	−0.601000	+	0.799249i	$0.705231\pi$
$174$		0			0
$175$	16.1742			1.22265
$176$		0			0
$177$	−20.5132			−1.54187
$178$		0			0
$179$	−6.83277	−	21.0291i	−0.510705	−	1.57179i	−0.790963	−	0.611864i	$-0.790420\pi$
$179$	−6.83277	−	21.0291i	−0.510705	−	1.57179i	0.280258	−	0.959925i	$-0.409580\pi$
$180$		0			0
$181$	−9.72075	−	7.06253i	−0.722537	−	0.524954i	0.164657	−	0.986351i	$-0.447348\pi$
$181$	−9.72075	−	7.06253i	−0.722537	−	0.524954i	−0.887194	+	0.461397i	$0.847348\pi$
$182$		0			0
$183$	10.2127	−	31.4314i	0.754944	−	2.32348i
$184$		0			0
$185$	8.24685	−	5.99169i	0.606320	−	0.440518i
$186$		0			0
$187$	24.4799	+	5.34541i	1.79015	+	0.390895i
$188$		0			0
$189$	−10.2922	+	7.47769i	−0.748644	+	0.543922i
$190$		0			0
$191$	1.68795	−	5.19496i	0.122136	−	0.375894i	−0.871233	−	0.490870i	$-0.836679\pi$
$191$	1.68795	−	5.19496i	0.122136	−	0.375894i	0.993368	+	0.114976i	$0.0366790\pi$
$192$		0			0
$193$	2.89095	+	2.10040i	0.208095	+	0.151190i	0.686951	−	0.726703i	$-0.258949\pi$
$193$	2.89095	+	2.10040i	0.208095	+	0.151190i	−0.478856	+	0.877893i	$0.658949\pi$
$194$		0			0
$195$	−4.15935	−	12.8012i	−0.297857	−	0.916711i
$196$		0			0
$197$	4.75850			0.339029			0.169515	−	0.985528i	$-0.445780\pi$
$197$	4.75850			0.339029			0.169515	+	0.985528i	$0.445780\pi$
$198$		0			0
$199$	14.0534			0.996219			0.498109	−	0.867114i	$-0.334028\pi$
$199$	14.0534			0.996219			0.498109	+	0.867114i	$0.334028\pi$
$200$		0			0
$201$	−8.64665	−	26.6116i	−0.609887	−	1.87704i
$202$		0			0
$203$	5.49221	+	3.99033i	0.385478	+	0.280066i
$204$		0			0
$205$	−3.13345	+	9.64375i	−0.218849	+	0.673549i
$206$		0			0
$207$	−1.07531	+	0.781262i	−0.0747395	+	0.0543015i
$208$		0			0
$209$	12.4987	+	14.0370i	0.864555	+	0.970960i
$210$		0			0
$211$	−14.1901	+	10.3097i	−0.976888	+	0.709751i	−0.957011	−	0.290052i	$-0.906328\pi$
$211$	−14.1901	+	10.3097i	−0.976888	+	0.709751i	−0.0198771	+	0.999802i	$0.506328\pi$
$212$		0			0
$213$	−0.119139	+	0.366673i	−0.00816328	+	0.0251240i
$214$		0			0
$215$	13.9346	+	10.1241i	0.950335	+	0.690459i
$216$		0			0
$217$	−0.819130	−	2.52102i	−0.0556061	−	0.171138i
$218$		0			0
$219$	−6.55016			−0.442619
$220$		0			0
$221$	−7.55488			−0.508196
$222$		0			0
$223$	−4.19211	−	12.9020i	−0.280724	−	0.863980i	−0.987648	−	0.156690i	$-0.949918\pi$
$223$	−4.19211	−	12.9020i	−0.280724	−	0.863980i	0.706924	−	0.707290i	$-0.250082\pi$
$224$		0			0
$225$	−74.0342	−	53.7890i	−4.93562	−	3.58594i
$226$		0			0
$227$	4.84162	−	14.9010i	0.321349	−	0.989012i	−0.651712	−	0.758466i	$-0.725949\pi$
$227$	4.84162	−	14.9010i	0.321349	−	0.989012i	0.973062	−	0.230545i	$-0.0740510\pi$
$228$		0			0
$229$	−19.7787	+	14.3700i	−1.30701	+	0.949599i	−0.999998	−	0.00210593i	$-0.999330\pi$
$229$	−19.7787	+	14.3700i	−1.30701	+	0.949599i	−0.307013	+	0.951705i	$0.599330\pi$
$230$		0			0
$231$	−10.8740	+	4.76933i	−0.715455	+	0.313799i
$232$		0			0
$233$	10.5875	−	7.69227i	0.693610	−	0.503937i	−0.184235	−	0.982882i	$-0.558981\pi$
$233$	10.5875	−	7.69227i	0.693610	−	0.503937i	0.877845	+	0.478945i	$0.158981\pi$
$234$		0			0
$235$	−2.97932	+	9.16940i	−0.194349	+	0.598146i
$236$		0			0
$237$	31.5142	+	22.8964i	2.04707	+	1.48728i
$238$		0			0
$239$	−7.29858	−	22.4627i	−0.472106	−	1.45299i	−0.849822	−	0.527071i	$-0.823290\pi$
$239$	−7.29858	−	22.4627i	−0.472106	−	1.45299i	0.377716	−	0.925922i	$-0.376710\pi$
$240$		0			0
$241$	16.0365			1.03300			0.516502	−	0.856286i	$-0.327234\pi$
$241$	16.0365			1.03300			0.516502	+	0.856286i	$0.327234\pi$
$242$		0			0
$243$	11.2108			0.719173
$244$		0			0
$245$	−7.61441	−	23.4347i	−0.486467	−	1.49719i
$246$		0			0
$247$	−4.58465	−	3.33094i	−0.291714	−	0.211943i
$248$		0			0
$249$	−7.83207	+	24.1046i	−0.496338	+	1.52757i
$250$		0			0
$251$	−4.35764	+	3.16601i	−0.275052	+	0.199837i	−0.716756	−	0.697324i	$-0.754374\pi$
$251$	−4.35764	+	3.16601i	−0.275052	+	0.199837i	0.441705	+	0.897161i	$0.354374\pi$
$252$		0			0
$253$	−0.616025	+	0.270189i	−0.0387291	+	0.0169866i
$254$		0			0
$255$	−82.2675	+	59.7708i	−5.15179	+	3.74299i
$256$		0			0
$257$	6.26005	−	19.2664i	0.390491	−	1.20181i	−0.541927	−	0.840426i	$-0.682305\pi$
$257$	6.26005	−	19.2664i	0.390491	−	1.20181i	0.932418	−	0.361382i	$-0.117695\pi$
$258$		0			0
$259$	2.19352	+	1.59369i	0.136299	+	0.0990270i
$260$		0			0
$261$	−11.8693	−	36.5300i	−0.734692	−	2.26115i
$262$		0			0
$263$	15.7553			0.971513			0.485757	−	0.874094i	$-0.338544\pi$
$263$	15.7553			0.971513			0.485757	+	0.874094i	$0.338544\pi$
$264$		0			0
$265$	0.459131			0.0282042
$266$		0			0
$267$	−13.4342	−	41.3463i	−0.822161	−	2.53035i
$268$		0			0
$269$	8.43534	+	6.12863i	0.514312	+	0.373669i	0.814457	−	0.580224i	$-0.197035\pi$
$269$	8.43534	+	6.12863i	0.514312	+	0.373669i	−0.300145	+	0.953894i	$0.597035\pi$
$270$		0			0
$271$	7.86893	−	24.2181i	0.478004	−	1.47114i	−0.363860	−	0.931454i	$-0.618541\pi$
$271$	7.86893	−	24.2181i	0.478004	−	1.47114i	0.841864	−	0.539690i	$-0.181459\pi$
$272$		0			0
$273$	2.89638	−	2.10434i	0.175297	−	0.127361i
$274$		0			0
$275$	−30.7980	−	34.5884i	−1.85719	−	2.08576i
$276$		0			0
$277$	20.4632	−	14.8674i	1.22951	−	0.893293i	0.232658	−	0.972558i	$-0.425258\pi$
$277$	20.4632	−	14.8674i	1.22951	−	0.893293i	0.996854	+	0.0792657i	$0.0252576\pi$
$278$		0			0
$279$	−4.63453	+	14.2636i	−0.277462	+	0.853941i
$280$		0			0
$281$	−7.33155	−	5.32668i	−0.437364	−	0.317763i	0.347223	−	0.937783i	$-0.387125\pi$
$281$	−7.33155	−	5.32668i	−0.437364	−	0.317763i	−0.784587	+	0.620019i	$0.787125\pi$
$282$		0			0
$283$	−2.41980	−	7.44737i	−0.143842	−	0.442700i	0.853018	−	0.521881i	$-0.174770\pi$
$283$	−2.41980	−	7.44737i	−0.143842	−	0.442700i	−0.996860	+	0.0791809i	$0.974770\pi$
$284$		0			0
$285$	−76.2767			−4.51824
$286$		0			0
$287$	−2.69708			−0.159204
$288$		0			0
$289$	12.3842	+	38.1147i	0.728483	+	2.24204i
$290$		0			0
$291$	6.96982	+	5.06387i	0.408578	+	0.296849i
$292$		0			0
$293$	−2.26675	+	6.97634i	−0.132425	+	0.407562i	−0.995181	−	0.0980591i	$-0.968737\pi$
$293$	−2.26675	+	6.97634i	−0.132425	+	0.407562i	0.862756	+	0.505621i	$0.168737\pi$
$294$		0			0
$295$	23.3816	−	16.9877i	1.36133	−	0.989063i
$296$		0			0
$297$	35.5888	+	7.77115i	2.06507	+	0.450928i
$298$		0			0
$299$	0.164084	−	0.119214i	0.00948920	−	0.00689430i
$300$		0			0
$301$	−1.41571	+	4.35711i	−0.0816003	+	0.251140i
$302$		0			0
$303$	0.555043	+	0.403262i	0.0318864	+	0.0231668i
$304$		0			0
$305$	14.3887	+	44.2840i	0.823897	+	2.53569i
$306$		0			0
$307$	−0.284283			−0.0162249			−0.00811243	−	0.999967i	$-0.502582\pi$
$307$	−0.284283			−0.0162249			−0.00811243	+	0.999967i	$0.502582\pi$
$308$		0			0
$309$	−28.5837			−1.62607
$310$		0			0
$311$	−4.67943	−	14.4018i	−0.265346	−	0.816652i	−0.991613	−	0.129239i	$-0.958746\pi$
$311$	−4.67943	−	14.4018i	−0.265346	−	0.816652i	0.726267	−	0.687413i	$-0.241254\pi$
$312$		0			0
$313$	0.121385	+	0.0881911i	0.00686107	+	0.00498486i	0.591211	−	0.806517i	$-0.298650\pi$
$313$	0.121385	+	0.0881911i	0.00686107	+	0.00498486i	−0.584349	+	0.811502i	$0.698650\pi$
$314$		0			0
$315$	10.2149	−	31.4382i	0.575543	−	1.77134i
$316$		0			0
$317$	−2.41114	+	1.75179i	−0.135423	+	0.0983905i	−0.653434	−	0.756983i	$-0.726672\pi$
$317$	−2.41114	+	1.75179i	−0.135423	+	0.0983905i	0.518011	+	0.855374i	$0.326672\pi$
$318$		0			0
$319$	−1.92467	−	19.3433i	−0.107761	−	1.08301i
$320$		0			0
$321$	−12.9074	+	9.37775i	−0.720419	+	0.523415i
$322$		0			0
$323$	−13.2299	+	40.7176i	−0.736134	+	2.26559i
$324$		0			0
$325$	11.2970	+	8.20773i	0.626643	+	0.455283i
$326$		0			0
$327$	−6.07138	−	18.6858i	−0.335748	−	1.03333i
$328$		0			0
$329$	−2.56442			−0.141381
$330$		0			0
$331$	−21.8875			−1.20305			−0.601524	−	0.798855i	$-0.705440\pi$
$331$	−21.8875			−1.20305			−0.601524	+	0.798855i	$0.705440\pi$
$332$		0			0
$333$	−4.74046	−	14.5896i	−0.259776	−	0.799507i
$334$		0			0
$335$	31.8938	+	23.1722i	1.74254	+	1.26603i
$336$		0			0
$337$	−9.10886	+	28.0342i	−0.496191	+	1.52712i	0.318900	+	0.947788i	$0.396686\pi$
$337$	−9.10886	+	28.0342i	−0.496191	+	1.52712i	−0.815092	+	0.579332i	$0.803314\pi$
$338$		0			0
$339$	−17.2931	+	12.5642i	−0.939235	+	0.682394i
$340$		0			0
$341$	−3.83146	+	6.55210i	−0.207485	+	0.354816i
$342$		0			0
$343$	11.8619	−	8.61814i	0.640480	−	0.465336i
$344$		0			0
$345$	0.843593	−	2.59631i	0.0454175	−	0.139781i
$346$		0			0
$347$	−10.5848	−	7.69034i	−0.568224	−	0.412839i	0.266236	−	0.963908i	$-0.414220\pi$
$347$	−10.5848	−	7.69034i	−0.568224	−	0.412839i	−0.834460	+	0.551069i	$0.814220\pi$
$348$		0			0
$349$	5.13718	+	15.8106i	0.274987	+	0.846322i	0.989223	+	0.146417i	$0.0467743\pi$
$349$	5.13718	+	15.8106i	0.274987	+	0.846322i	−0.714236	+	0.699905i	$0.753226\pi$
$350$		0			0
$351$	−10.9833			−0.586244
$352$		0			0
$353$	23.5960			1.25589			0.627945	−	0.778258i	$-0.283896\pi$
$353$	23.5960			1.25589			0.627945	+	0.778258i	$0.283896\pi$
$354$		0			0
$355$	−0.167856	−	0.516608i	−0.00890888	−	0.0274187i
$356$		0			0
$357$	−21.8818	−	15.8980i	−1.15811	−	0.841413i
$358$		0			0
$359$	6.53556	−	20.1144i	0.344934	−	1.06160i	−0.616686	−	0.787209i	$-0.711525\pi$
$359$	6.53556	−	20.1144i	0.344934	−	1.06160i	0.961619	−	0.274387i	$-0.0884749\pi$
$360$		0			0
$361$	−10.6096	+	7.70831i	−0.558399	+	0.405701i
$362$		0			0
$363$	30.9048	+	14.1725i	1.62208	+	0.743863i
$364$		0			0
$365$	7.46607	−	5.42442i	0.390792	−	0.283927i
$366$		0			0
$367$	1.05820	−	3.25680i	0.0552374	−	0.170003i	−0.919632	−	0.392782i	$-0.871513\pi$
$367$	1.05820	−	3.25680i	0.0552374	−	0.170003i	0.974869	+	0.222779i	$0.0715127\pi$
$368$		0			0
$369$	12.3454	+	8.96946i	0.642676	+	0.466931i
$370$		0			0
$371$	0.0377375	+	0.116144i	0.00195923	+	0.00602990i
$372$		0			0
$373$	13.4617			0.697022			0.348511	−	0.937305i	$-0.386687\pi$
$373$	13.4617			0.697022			0.348511	+	0.937305i	$0.386687\pi$
$374$		0			0
$375$	120.653			6.23047
$376$		0			0
$377$	1.81115	+	5.57415i	0.0932791	+	0.287083i
$378$		0			0
$379$	−5.34861	−	3.88599i	−0.274740	−	0.199610i	0.441880	−	0.897074i	$-0.354312\pi$
$379$	−5.34861	−	3.88599i	−0.274740	−	0.199610i	−0.716620	+	0.697464i	$0.754312\pi$
$380$		0			0
$381$	16.1123	−	49.5885i	0.825457	−	2.54049i
$382$		0			0
$383$	9.27312	−	6.73732i	0.473835	−	0.344261i	−0.325099	−	0.945680i	$-0.605398\pi$
$383$	9.27312	−	6.73732i	0.473835	−	0.344261i	0.798934	+	0.601419i	$0.205398\pi$
$384$		0			0
$385$	8.44484	−	14.4413i	0.430389	−	0.735999i
$386$		0			0
$387$	20.9702	−	15.2358i	1.06598	−	0.774478i
$388$		0			0
$389$	−1.25681	+	3.86807i	−0.0637229	+	0.196119i	−0.977849	−	0.209311i	$-0.932878\pi$
$389$	−1.25681	+	3.86807i	−0.0637229	+	0.196119i	0.914126	+	0.405429i	$0.132878\pi$
$390$		0			0
$391$	−1.23963	−	0.900644i	−0.0626908	−	0.0455475i
$392$		0			0
$393$	−6.91437	−	21.2802i	−0.348784	−	1.07345i
$394$		0			0
$395$	−54.8822			−2.76142
$396$		0			0
$397$	9.91030			0.497384			0.248692	−	0.968583i	$-0.419999\pi$
$397$	9.91030			0.497384			0.248692	+	0.968583i	$0.419999\pi$
$398$		0			0
$399$	−6.26943	−	19.2953i	−0.313864	−	0.965975i
$400$		0			0
$401$	9.75343	+	7.08628i	0.487063	+	0.353872i	0.804054	−	0.594557i	$-0.202672\pi$
$401$	9.75343	+	7.08628i	0.487063	+	0.353872i	−0.316991	+	0.948429i	$0.602672\pi$
$402$		0			0
$403$	0.707189	−	2.17650i	0.0352276	−	0.108419i
$404$		0			0
$405$	−50.3356	+	36.5710i	−2.50120	+	1.81723i
$406$		0			0
$407$	−0.768689	−	7.72546i	−0.0381025	−	0.382937i
$408$		0			0
$409$	−22.5450	+	16.3799i	−1.11478	+	0.809934i	−0.983410	−	0.181399i	$-0.941937\pi$
$409$	−22.5450	+	16.3799i	−1.11478	+	0.809934i	−0.131369	+	0.991334i	$0.541937\pi$
$410$		0			0
$411$	8.20498	−	25.2523i	0.404722	−	1.24561i
$412$		0			0
$413$	6.21911	+	4.51845i	0.306022	+	0.222338i
$414$		0			0
$415$	−11.0347	−	33.9612i	−0.541671	−	1.66709i
$416$		0			0
$417$	7.42652			0.363678
$418$		0			0
$419$	−3.83944			−0.187569			−0.0937844	−	0.995593i	$-0.529896\pi$
$419$	−3.83944			−0.187569			−0.0937844	+	0.995593i	$0.529896\pi$
$420$		0			0
$421$	−8.17338	−	25.1551i	−0.398346	−	1.22598i	−0.926325	−	0.376725i	$-0.877050\pi$
$421$	−8.17338	−	25.1551i	−0.398346	−	1.22598i	0.527979	−	0.849257i	$-0.322950\pi$
$422$		0			0
$423$	11.7382	+	8.52827i	0.570729	+	0.414659i
$424$		0			0
$425$	32.5997	−	100.332i	1.58132	−	4.86680i
$426$		0			0
$427$	−10.0196	+	7.27970i	−0.484884	+	0.352289i
$428$		0			0
$429$	−10.0153	−	2.18693i	−0.483541	−	0.105586i
$430$		0			0
$431$	−25.0659	+	18.2115i	−1.20738	+	0.877216i	−0.994991	−	0.0999684i	$-0.968126\pi$
$431$	−25.0659	+	18.2115i	−1.20738	+	0.877216i	−0.212393	+	0.977184i	$0.568126\pi$
$432$		0			0
$433$	−3.57827	+	11.0128i	−0.171961	+	0.529241i	−0.999482	−	0.0321942i	$-0.989751\pi$
$433$	−3.57827	+	11.0128i	−0.171961	+	0.529241i	0.827521	+	0.561435i	$0.189751\pi$
$434$		0			0
$435$	63.8225	+	46.3697i	3.06005	+	2.22326i
$436$		0			0
$437$	−0.355171	−	1.09311i	−0.0169902	−	0.0522903i
$438$		0			0
$439$	20.6685			0.986456			0.493228	−	0.869900i	$-0.335817\pi$
$439$	20.6685			0.986456			0.493228	+	0.869900i	$0.335817\pi$
$440$		0			0
$441$	−37.0819			−1.76580
$442$		0			0
$443$	3.79135	+	11.6686i	0.180133	+	0.554391i	0.999831	−	0.0184047i	$-0.00585874\pi$
$443$	3.79135	+	11.6686i	0.180133	+	0.554391i	−0.819698	+	0.572796i	$0.805859\pi$
$444$		0			0
$445$	49.5530	+	36.0024i	2.34904	+	1.70668i
$446$		0			0
$447$	−6.43238	+	19.7968i	−0.304241	+	0.936358i
$448$		0			0
$449$	−25.2442	+	18.3410i	−1.19135	+	0.865565i	−0.993406	−	0.114649i	$-0.963426\pi$
$449$	−25.2442	+	18.3410i	−1.19135	+	0.865565i	−0.197941	+	0.980214i	$0.563426\pi$
$450$		0			0
$451$	5.13564	+	5.76771i	0.241828	+	0.271591i
$452$		0			0
$453$	−37.9343	+	27.5609i	−1.78231	+	1.29492i
$454$		0			0
$455$	−1.55870	+	4.79719i	−0.0730730	+	0.224896i
$456$		0			0
$457$	−1.64699	−	1.19660i	−0.0770427	−	0.0559748i	0.548597	−	0.836087i	$-0.315162\pi$
$457$	−1.64699	−	1.19660i	−0.0770427	−	0.0559748i	−0.625640	+	0.780112i	$0.715162\pi$
$458$		0			0
$459$	25.6414	+	78.9160i	1.19684	+	3.68349i
$460$		0			0
$461$	−30.0387			−1.39904			−0.699520	−	0.714613i	$-0.746603\pi$
$461$	−30.0387			−1.39904			−0.699520	+	0.714613i	$0.746603\pi$
$462$		0			0
$463$	−22.8590			−1.06235			−0.531174	−	0.847263i	$-0.678249\pi$
$463$	−22.8590			−1.06235			−0.531174	+	0.847263i	$0.678249\pi$
$464$		0			0
$465$	−9.51872	−	29.2956i	−0.441420	−	1.35855i
$466$		0			0
$467$	25.6147	+	18.6101i	1.18531	+	0.861175i	0.992760	−	0.120113i	$-0.0383258\pi$
$467$	25.6147	+	18.6101i	1.18531	+	0.861175i	0.192545	+	0.981288i	$0.438326\pi$
$468$		0			0
$469$	−3.24030	+	9.97260i	−0.149623	+	0.460492i
$470$		0			0
$471$	−6.47869	+	4.70704i	−0.298522	+	0.216889i
$472$		0			0
$473$	12.0134	−	5.26908i	0.552377	−	0.242273i
$474$		0			0
$475$	64.0192	−	46.5127i	2.93740	−	2.13415i
$476$		0			0
$477$	0.213514	−	0.657129i	0.00977614	−	0.0300879i
$478$		0			0
$479$	−20.3486	−	14.7841i	−0.929752	−	0.675504i	0.0161800	−	0.999869i	$-0.494850\pi$
$479$	−20.3486	−	14.7841i	−0.929752	−	0.675504i	−0.945932	+	0.324365i	$0.894850\pi$
$480$		0			0
$481$	0.723352	+	2.22625i	0.0329820	+	0.101508i
$482$		0			0
$483$	0.726114			0.0330393
$484$		0			0
$485$	−12.1380			−0.551157
$486$		0			0
$487$	12.3471	+	38.0004i	0.559500	+	1.72196i	0.683753	+	0.729713i	$0.260346\pi$
$487$	12.3471	+	38.0004i	0.559500	+	1.72196i	−0.124253	+	0.992251i	$0.539654\pi$
$488$		0			0
$489$	−18.2104	−	13.2306i	−0.823502	−	0.598309i
$490$		0			0
$491$	−0.981311	+	3.02016i	−0.0442859	+	0.136298i	−0.970755	−	0.240074i	$-0.922828\pi$
$491$	−0.981311	+	3.02016i	−0.0442859	+	0.136298i	0.926469	+	0.376372i	$0.122828\pi$
$492$		0			0
$493$	35.8226	−	26.0267i	1.61337	−	1.17218i
$494$		0			0
$495$	−86.6811	+	38.0183i	−3.89603	+	1.70880i
$496$		0			0
$497$	0.116887	−	0.0849235i	0.00524310	−	0.00380934i
$498$		0			0
$499$	2.29358	−	7.05891i	0.102675	−	0.316000i	−0.886503	−	0.462723i	$-0.846873\pi$
$499$	2.29358	−	7.05891i	0.102675	−	0.316000i	0.989178	+	0.146723i	$0.0468725\pi$
$500$		0			0
$501$	35.9446	+	26.1153i	1.60589	+	1.16674i
$502$		0			0
$503$	−10.1202	−	31.1466i	−0.451236	−	1.38876i	−0.875498	−	0.483221i	$-0.839467\pi$
$503$	−10.1202	−	31.1466i	−0.451236	−	1.38876i	0.424263	−	0.905539i	$-0.360533\pi$
$504$		0			0
$505$	−0.966610			−0.0430136
$506$		0			0
$507$	3.09087			0.137270
$508$		0			0
$509$	−5.48996	−	16.8964i	−0.243338	−	0.748918i	−0.995905	−	0.0904024i	$-0.971185\pi$
$509$	−5.48996	−	16.8964i	−0.243338	−	0.748918i	0.752567	−	0.658516i	$-0.228815\pi$
$510$		0			0
$511$	1.98585	+	1.44280i	0.0878488	+	0.0638259i
$512$		0			0
$513$	−19.2337	+	59.1952i	−0.849188	+	2.61353i
$514$		0			0
$515$	32.5806	−	23.6712i	1.43567	−	1.04308i
$516$		0			0
$517$	4.88303	+	5.48401i	0.214755	+	0.241186i
$518$		0			0
$519$	−37.7845	+	27.4521i	−1.65856	+	1.20501i
$520$		0			0
$521$	−11.8179	+	36.3719i	−0.517753	+	1.59348i	0.260463	+	0.965484i	$0.416125\pi$
$521$	−11.8179	+	36.3719i	−0.517753	+	1.59348i	−0.778216	+	0.627996i	$0.783875\pi$
$522$		0			0
$523$	−10.4671	−	7.60480i	−0.457695	−	0.332535i	0.334932	−	0.942242i	$-0.391287\pi$
$523$	−10.4671	−	7.60480i	−0.457695	−	0.332535i	−0.792626	+	0.609708i	$0.791287\pi$
$524$		0			0
$525$	15.4484	+	47.5454i	0.674225	+	2.07505i
$526$		0			0
$527$	−17.2894			−0.753139
$528$		0			0
$529$	−22.9589			−0.998212
$530$		0			0
$531$	−13.4402	−	41.3647i	−0.583256	−	1.79508i
$532$		0			0
$533$	−1.88380	−	1.36866i	−0.0815964	−	0.0592832i
$534$		0			0
$535$	6.94617	−	21.3781i	0.300309	−	0.924256i
$536$		0			0
$537$	55.2907	−	40.1711i	2.38597	−	1.73351i
$538$		0			0
$539$	−18.3347	−	4.00355i	−0.789730	−	0.172445i
$540$		0			0
$541$	−17.5037	+	12.7172i	−0.752541	+	0.546753i	−0.896613	−	0.442814i	$-0.853980\pi$
$541$	−17.5037	+	12.7172i	−0.752541	+	0.546753i	0.144072	+	0.989567i	$0.453980\pi$
$542$		0			0
$543$	11.4764	−	35.3206i	0.492498	−	1.51575i
$544$		0			0
$545$	22.3947	+	16.2707i	0.959284	+	0.696961i
$546$		0			0
$547$	0.873354	+	2.68791i	0.0373419	+	0.114927i	0.967990	−	0.250989i	$-0.0807558\pi$
$547$	0.873354	+	2.68791i	0.0373419	+	0.114927i	−0.930648	+	0.365916i	$0.880756\pi$
$548$		0			0
$549$	70.0725			2.99062
$550$		0			0
$551$	33.2140			1.41496
$552$		0			0
$553$	−4.51095	−	13.8833i	−0.191825	−	0.590377i
$554$		0			0
$555$	25.4899	+	18.5195i	1.08199	+	0.786109i
$556$		0			0
$557$	−0.924181	+	2.84434i	−0.0391588	+	0.120518i	−0.968725	−	0.248137i	$-0.920182\pi$
$557$	−0.924181	+	2.84434i	−0.0391588	+	0.120518i	0.929566	+	0.368655i	$0.120182\pi$
$558$		0			0
$559$	−3.19987	+	2.32484i	−0.135340	+	0.0983305i
$560$		0			0
$561$	7.66816	+	77.0663i	0.323750	+	3.25374i
$562$		0			0
$563$	−34.0974	+	24.7732i	−1.43703	+	1.04407i	−0.448383	+	0.893842i	$0.648000\pi$
$563$	−34.0974	+	24.7732i	−1.43703	+	1.04407i	−0.988652	+	0.150225i	$0.952000\pi$
$564$		0			0
$565$	9.30639	−	28.6421i	0.391523	−	1.20498i
$566$		0			0
$567$	−13.3884	−	9.72726i	−0.562261	−	0.408507i
$568$		0			0
$569$	6.74740	+	20.7664i	0.282866	+	0.870571i	0.987030	+	0.160534i	$0.0513218\pi$
$569$	6.74740	+	20.7664i	0.282866	+	0.870571i	−0.704164	+	0.710037i	$0.748678\pi$
$570$		0			0
$571$	−0.518018			−0.0216784			−0.0108392	−	0.999941i	$-0.503450\pi$
$571$	−0.518018			−0.0216784			−0.0108392	+	0.999941i	$0.503450\pi$
$572$		0			0
$573$	16.8833			0.705309
$574$		0			0
$575$	0.875173	+	2.69351i	0.0364973	+	0.112327i
$576$		0			0
$577$	−13.0232	−	9.46194i	−0.542165	−	0.393906i	0.282724	−	0.959201i	$-0.408762\pi$
$577$	−13.0232	−	9.46194i	−0.542165	−	0.393906i	−0.824888	+	0.565296i	$0.808762\pi$
$578$		0			0
$579$	−3.41307	+	10.5044i	−0.141842	+	0.436546i
$580$		0			0
$581$	7.68403	−	5.58277i	0.318787	−	0.231612i
$582$		0			0
$583$	0.176516	−	0.301857i	0.00731056	−	0.0125016i
$584$		0			0
$585$	23.0883	−	16.7746i	0.954582	−	0.693544i
$586$		0			0
$587$	−3.58484	+	11.0330i	−0.147962	+	0.455380i	−0.997380	−	0.0723404i	$-0.976953\pi$
$587$	−3.58484	+	11.0330i	−0.147962	+	0.455380i	0.849418	+	0.527721i	$0.176953\pi$
$588$		0			0
$589$	−10.4920	−	7.62290i	−0.432316	−	0.314096i
$590$		0			0
$591$	4.54499	+	13.9880i	0.186956	+	0.575391i
$592$		0			0
$593$	−46.7255			−1.91878			−0.959392	−	0.282075i	$-0.908977\pi$
$593$	−46.7255			−1.91878			−0.959392	+	0.282075i	$0.908977\pi$
$594$		0			0
$595$	38.1072			1.56224
$596$		0			0
$597$	13.4228	+	41.3112i	0.549360	+	1.69076i
$598$		0			0
$599$	−20.1116	−	14.6120i	−0.821739	−	0.597029i	0.0954709	−	0.995432i	$-0.469564\pi$
$599$	−20.1116	−	14.6120i	−0.821739	−	0.597029i	−0.917210	+	0.398404i	$0.869564\pi$
$600$		0			0
$601$	10.0418	−	30.9055i	0.409613	−	1.26066i	−0.507368	−	0.861730i	$-0.669381\pi$
$601$	10.0418	−	30.9055i	0.409613	−	1.26066i	0.916981	−	0.398931i	$-0.130619\pi$
$602$		0			0
$603$	47.9969	−	34.8718i	1.95459	−	1.42009i
$604$		0			0
$605$	−46.9630	+	9.43916i	−1.90932	+	0.383756i
$606$		0			0
$607$	2.88890	−	2.09891i	0.117257	−	0.0851920i	−0.527611	−	0.849486i	$-0.676912\pi$
$607$	2.88890	−	2.09891i	0.117257	−	0.0851920i	0.644868	+	0.764294i	$0.276912\pi$
$608$		0			0
$609$	−6.48414	+	19.9561i	−0.262751	+	0.808663i
$610$		0			0
$611$	−1.79114	−	1.30134i	−0.0724617	−	0.0526465i
$612$		0			0
$613$	−6.78455	−	20.8807i	−0.274025	−	0.843363i	−0.989476	−	0.144699i	$-0.953778\pi$
$613$	−6.78455	−	20.8807i	−0.274025	−	0.843363i	0.715450	−	0.698664i	$-0.246222\pi$
$614$		0			0
$615$	−31.3415			−1.26381
$616$		0			0
$617$	−2.23675			−0.0900483			−0.0450241	−	0.998986i	$-0.514336\pi$
$617$	−2.23675			−0.0900483			−0.0450241	+	0.998986i	$0.514336\pi$
$618$		0			0
$619$	8.81411	+	27.1270i	0.354269	+	1.09033i	0.956432	+	0.291955i	$0.0943057\pi$
$619$	8.81411	+	27.1270i	0.354269	+	1.09033i	−0.602163	+	0.798373i	$0.705694\pi$
$620$		0			0
$621$	−1.80217	−	1.30936i	−0.0723187	−	0.0525426i
$622$		0			0
$623$	−5.03442	+	15.4943i	−0.201700	+	0.620768i
$624$		0			0
$625$	−81.0387	+	58.8780i	−3.24155	+	2.35512i
$626$		0			0
$627$	−29.3251	+	50.1483i	−1.17113	+	2.00273i
$628$		0			0
$629$	14.3071	−	10.3947i	0.570462	−	0.414465i
$630$		0			0
$631$	6.11844	−	18.8306i	0.243571	−	0.749636i	−0.752297	−	0.658824i	$-0.771054\pi$
$631$	6.11844	−	18.8306i	0.243571	−	0.749636i	0.995868	−	0.0908112i	$-0.0289460\pi$
$632$		0			0
$633$	−43.8598	−	31.8660i	−1.74327	−	1.26656i
$634$		0			0
$635$	22.7007	+	69.8656i	0.900850	+	2.77253i
$636$		0			0
$637$	5.65836			0.224193
$638$		0			0
$639$	−0.817452			−0.0323379
$640$		0			0
$641$	−9.84615	−	30.3033i	−0.388899	−	1.19691i	−0.933612	−	0.358286i	$-0.883361\pi$
$641$	−9.84615	−	30.3033i	−0.388899	−	1.19691i	0.544712	−	0.838623i	$-0.316639\pi$
$642$		0			0
$643$	−18.3057	−	13.2999i	−0.721906	−	0.524495i	0.165087	−	0.986279i	$-0.447210\pi$
$643$	−18.3057	−	13.2999i	−0.721906	−	0.524495i	−0.886993	+	0.461784i	$0.847210\pi$
$644$		0			0
$645$	−16.4513	+	50.6320i	−0.647770	+	1.99363i
$646$		0			0
$647$	−22.9612	+	16.6823i	−0.902696	+	0.655847i	−0.939157	−	0.343488i	$-0.888392\pi$
$647$	−22.9612	+	16.6823i	−0.902696	+	0.655847i	0.0364609	+	0.999335i	$0.488392\pi$
$648$		0			0
$649$	−2.17940	−	21.9033i	−0.0855489	−	0.859781i
$650$		0			0
$651$	6.62839	−	4.81581i	0.259787	−	0.188746i
$652$		0			0
$653$	13.3694	−	41.1468i	0.523185	−	1.61020i	−0.244693	−	0.969601i	$-0.578687\pi$
$653$	13.3694	−	41.1468i	0.523185	−	1.61020i	0.767878	−	0.640596i	$-0.221313\pi$
$654$		0			0
$655$	25.5041	+	18.5298i	0.996529	+	0.724021i
$656$		0			0
$657$	−4.29165	−	13.2083i	−0.167433	−	0.515307i
$658$		0			0
$659$	14.2138			0.553692			0.276846	−	0.960914i	$-0.410711\pi$
$659$	14.2138			0.553692			0.276846	+	0.960914i	$0.410711\pi$
$660$		0			0
$661$	18.9390			0.736641			0.368320	−	0.929699i	$-0.379933\pi$
$661$	18.9390			0.736641			0.368320	+	0.929699i	$0.379933\pi$
$662$		0			0
$663$	−7.21589	−	22.2082i	−0.280242	−	0.862496i
$664$		0			0
$665$	23.1252	+	16.8015i	0.896758	+	0.651533i
$666$		0			0
$667$	−0.367335	+	1.13054i	−0.0142233	+	0.0437747i
$668$		0			0
$669$	33.9225	−	24.6461i	1.31152	−	0.952875i
$670$		0			0
$671$	34.6465	+	7.56539i	1.33751	+	0.292059i
$672$		0			0
$673$	2.00199	−	1.45453i	0.0771710	−	0.0560680i	−0.548531	−	0.836130i	$-0.684813\pi$
$673$	2.00199	−	1.45453i	0.0771710	−	0.0560680i	0.625702	+	0.780062i	$0.284813\pi$
$674$		0			0
$675$	47.3935	−	145.862i	1.82418	−	5.61423i
$676$		0			0
$677$	−0.371113	−	0.269629i	−0.0142630	−	0.0103627i	0.580631	−	0.814167i	$-0.302806\pi$
$677$	−0.371113	−	0.269629i	−0.0142630	−	0.0103627i	−0.594894	+	0.803804i	$0.702806\pi$
$678$		0			0
$679$	−0.997661	−	3.07049i	−0.0382867	−	0.117834i
$680$		0			0
$681$	48.4271			1.85573
$682$		0			0
$683$	−2.33448			−0.0893263			−0.0446631	−	0.999002i	$-0.514221\pi$
$683$	−2.33448			−0.0893263			−0.0446631	+	0.999002i	$0.514221\pi$
$684$		0			0
$685$	11.5601	+	35.5782i	0.441687	+	1.35937i
$686$		0			0
$687$	−61.1332	−	44.4159i	−2.33238	−	1.69457i
$688$		0			0
$689$	−0.0325804	+	0.100272i	−0.00124121	+	0.00382006i
$690$		0			0
$691$	3.48066	−	2.52885i	0.132410	−	0.0962018i	−0.519609	−	0.854404i	$-0.673922\pi$
$691$	3.48066	−	2.52885i	0.132410	−	0.0962018i	0.652019	+	0.758203i	$0.273922\pi$
$692$		0			0
$693$	−16.7419	−	18.8024i	−0.635973	−	0.714245i
$694$		0			0
$695$	−8.46497	+	6.15016i	−0.321095	+	0.233289i
$696$		0			0
$697$	−5.43609	+	16.7306i	−0.205907	+	0.633715i
$698$		0			0
$699$	32.7246	+	23.7758i	1.23776	+	0.899283i
$700$		0			0
$701$	9.40803	+	28.9549i	0.355336	+	1.09361i	0.955814	+	0.293971i	$0.0949770\pi$
$701$	9.40803	+	28.9549i	0.355336	+	1.09361i	−0.600478	+	0.799641i	$0.705023\pi$
$702$		0			0
$703$	13.2653			0.500309
$704$		0			0
$705$	−29.7999			−1.12233
$706$		0			0
$707$	−0.0794489	−	0.244519i	−0.00298798	−	0.00919607i
$708$		0			0
$709$	−36.8880	−	26.8007i	−1.38536	−	1.00652i	−0.996357	−	0.0852856i	$-0.972820\pi$
$709$	−36.8880	−	26.8007i	−1.38536	−	1.00652i	−0.389002	−	0.921237i	$-0.627180\pi$
$710$		0			0
$711$	−25.5224	+	78.5499i	−0.957165	+	2.94585i
$712$		0			0
$713$	0.375507	−	0.272822i	0.0140628	−	0.0102173i
$714$		0			0
$715$	13.2268	−	5.80126i	0.494653	−	0.216955i
$716$		0			0
$717$	59.0601	−	42.9096i	2.20564	−	1.60249i
$718$		0			0
$719$	0.476254	−	1.46576i	0.0177613	−	0.0546636i	−0.941783	−	0.336221i	$-0.890851\pi$
$719$	0.476254	−	1.46576i	0.0177613	−	0.0546636i	0.959544	+	0.281558i	$0.0908510\pi$
$720$		0			0
$721$	8.66589	+	6.29614i	0.322735	+	0.234481i
$722$		0			0
$723$	15.3170	+	47.1408i	0.569644	+	1.75319i
$724$		0			0
$725$	−81.8421			−3.03954
$726$		0			0
$727$	−40.3503			−1.49651			−0.748255	−	0.663411i	$-0.769108\pi$
$727$	−40.3503			−1.49651			−0.748255	+	0.663411i	$0.769108\pi$
$728$		0			0
$729$	−2.53742	−	7.80938i	−0.0939785	−	0.289236i
$730$		0			0
$731$	24.1747	+	17.5639i	0.894132	+	0.649625i
$732$		0			0
$733$	−11.6988	+	36.0053i	−0.432107	+	1.32989i	0.463916	+	0.885879i	$0.346444\pi$
$733$	−11.6988	+	36.0053i	−0.432107	+	1.32989i	−0.896023	+	0.444008i	$0.853556\pi$
$734$		0			0
$735$	61.6158	−	44.7665i	2.27273	−	1.65124i
$736$		0			0
$737$	27.4964	−	12.0599i	1.01284	−	0.444233i
$738$		0			0
$739$	1.09602	−	0.796302i	0.0403176	−	0.0292924i	−0.567444	−	0.823412i	$-0.692068\pi$
$739$	1.09602	−	0.796302i	0.0403176	−	0.0292924i	0.607762	+	0.794120i	$0.292068\pi$
$740$		0			0
$741$	5.41266	−	16.6585i	0.198839	−	0.611964i
$742$		0			0
$743$	−6.58783	−	4.78634i	−0.241684	−	0.175594i	0.460349	−	0.887738i	$-0.347724\pi$
$743$	−6.58783	−	4.78634i	−0.241684	−	0.175594i	−0.702033	+	0.712144i	$0.747724\pi$
$744$		0			0
$745$	−9.06264	−	27.8919i	−0.332029	−	1.02188i
$746$		0			0
$747$	−53.7384			−1.96618
$748$		0			0
$749$	5.97884			0.218462
$750$		0			0
$751$	2.74427	+	8.44599i	0.100140	+	0.308199i	0.988559	−	0.150834i	$-0.0481960\pi$
$751$	2.74427	+	8.44599i	0.100140	+	0.308199i	−0.888419	+	0.459033i	$0.848196\pi$
$752$		0			0
$753$	−13.4689	−	9.78571i	−0.490833	−	0.356611i
$754$		0			0
$755$	20.4145	−	62.8295i	0.742961	−	2.28660i
$756$		0			0
$757$	−35.8792	+	26.0678i	−1.30405	+	0.947450i	−0.999986	−	0.00520055i	$-0.998345\pi$
$757$	−35.8792	+	26.0678i	−1.30405	+	0.947450i	−0.304067	+	0.952651i	$0.598345\pi$
$758$		0			0
$759$	−1.38263	−	1.55279i	−0.0501862	−	0.0563629i
$760$		0			0
$761$	10.2042	−	7.41375i	0.369900	−	0.268748i	−0.387269	−	0.921967i	$-0.626582\pi$
$761$	10.2042	−	7.41375i	0.369900	−	0.268748i	0.757170	+	0.653218i	$0.226582\pi$
$762$		0			0
$763$	−2.27523	+	7.00242i	−0.0823687	+	0.253505i
$764$		0			0
$765$	−174.429	−	126.730i	−6.30649	−	4.58193i
$766$		0			0
$767$	2.05086	+	6.31189i	0.0740522	+	0.227909i
$768$		0			0
$769$	−31.9862			−1.15345			−0.576725	−	0.816938i	$-0.695670\pi$
$769$	−31.9862			−1.15345			−0.576725	+	0.816938i	$0.695670\pi$
$770$		0			0
$771$	62.6146			2.25501
$772$		0			0
$773$	3.72136	+	11.4532i	0.133848	+	0.411942i	0.995409	−	0.0957119i	$-0.0305128\pi$
$773$	3.72136	+	11.4532i	0.133848	+	0.411942i	−0.861561	+	0.507654i	$0.830513\pi$
$774$		0			0
$775$	25.8532	+	18.7835i	0.928676	+	0.674723i
$776$		0			0
$777$	−2.58969	+	7.97024i	−0.0929045	+	0.285931i
$778$		0			0
$779$	−10.6754	+	7.75611i	−0.382485	+	0.277891i
$780$		0			0
$781$	−0.404179	−	0.0882563i	−0.0144627	−	0.00315806i
$782$		0			0
$783$	52.0789	−	37.8375i	1.86115	−	1.35220i
$784$		0			0
$785$	3.48654	−	10.7305i	0.124440	−	0.382987i
$786$		0			0
$787$	17.7102	+	12.8672i	0.631302	+	0.458668i	0.856851	−	0.515564i	$-0.172418\pi$
$787$	17.7102	+	12.8672i	0.631302	+	0.458668i	−0.225549	+	0.974232i	$0.572418\pi$
$788$		0			0
$789$	15.0484	+	46.3141i	0.535736	+	1.64883i
$790$		0			0
$791$	8.01038			0.284816
$792$		0			0
$793$	−10.6925			−0.379700
$794$		0			0
$795$	0.438530	+	1.34966i	0.0155531	+	0.0478674i
$796$		0			0
$797$	23.1094	+	16.7900i	0.818577	+	0.594731i	0.916304	−	0.400482i	$-0.131157\pi$
$797$	23.1094	+	16.7900i	0.818577	+	0.594731i	−0.0977278	+	0.995213i	$0.531157\pi$
$798$		0			0
$799$	−5.16870	+	15.9076i	−0.182855	+	0.562771i
$800$		0			0
$801$	74.5724	−	54.1800i	2.63488	−	1.91436i
$802$		0			0
$803$	−0.695913	−	6.99405i	−0.0245582	−	0.246815i
$804$		0			0
$805$	−0.827647	+	0.601321i	−0.0291707	+	0.0211938i
$806$		0			0
$807$	−9.95881	+	30.6501i	−0.350567	+	1.07893i
$808$		0			0
$809$	−20.1510	−	14.6406i	−0.708472	−	0.514735i	0.174209	−	0.984709i	$-0.444263\pi$
$809$	−20.1510	−	14.6406i	−0.708472	−	0.514735i	−0.882680	+	0.469974i	$0.844263\pi$
$810$		0			0
$811$	−2.48834	−	7.65833i	−0.0873775	−	0.268920i	0.897815	−	0.440373i	$-0.145154\pi$
$811$	−2.48834	−	7.65833i	−0.0873775	−	0.268920i	−0.985192	+	0.171453i	$0.945154\pi$
$812$		0			0
$813$	78.7071			2.76038
$814$		0			0
$815$	31.7135			1.11087
$816$		0			0
$817$	6.92637	+	21.3172i	0.242323	+	0.745794i
$818$		0			0
$819$	6.14109	+	4.46176i	0.214587	+	0.155907i
$820$		0			0
$821$	−10.7501	+	33.0854i	−0.375181	+	1.15469i	0.568176	+	0.822907i	$0.307649\pi$
$821$	−10.7501	+	33.0854i	−0.375181	+	1.15469i	−0.943357	+	0.331780i	$0.892351\pi$
$822$		0			0
$823$	−1.79515	+	1.30425i	−0.0625750	+	0.0454634i	−0.618633	−	0.785680i	$-0.712313\pi$
$823$	−1.79515	+	1.30425i	−0.0625750	+	0.0454634i	0.556058	+	0.831143i	$0.312313\pi$
$824$		0			0
$825$	72.2597	−	123.570i	2.51576	−	4.30215i
$826$		0			0
$827$	29.3220	−	21.3037i	1.01963	−	0.740801i	0.0534196	−	0.998572i	$-0.482988\pi$
$827$	29.3220	−	21.3037i	1.01963	−	0.740801i	0.966206	+	0.257771i	$0.0829879\pi$
$828$		0			0
$829$	−7.32850	+	22.5548i	−0.254529	+	0.783360i	0.739393	+	0.673274i	$0.235113\pi$
$829$	−7.32850	+	22.5548i	−0.254529	+	0.783360i	−0.993922	+	0.110086i	$0.964887\pi$
$830$		0			0
$831$	63.2489	+	45.9530i	2.19408	+	1.59409i
$832$		0			0
$833$	−13.2099	−	40.6560i	−0.457697	−	1.40865i
$834$		0			0
$835$	−62.5977			−2.16628
$836$		0			0
$837$	−25.1353			−0.868804
$838$		0			0
$839$	12.0796	+	37.1772i	0.417035	+	1.28350i	0.910418	+	0.413689i	$0.135760\pi$
$839$	12.0796	+	37.1772i	0.417035	+	1.28350i	−0.493384	+	0.869812i	$0.664240\pi$
$840$		0			0
$841$	−4.32942	−	3.14550i	−0.149290	−	0.108466i
$842$		0			0
$843$	8.65567	−	26.6394i	0.298117	−	0.917511i
$844$		0			0
$845$	−3.52306	+	2.55966i	−0.121197	+	0.0880549i
$846$		0			0
$847$	−6.24783	−	11.1042i	−0.214678	−	0.381544i
$848$		0			0
$849$	19.5810	−	14.2264i	0.672018	−	0.488249i
$850$		0			0
$851$	−0.146709	+	0.451524i	−0.00502912	+	0.0154781i
$852$		0			0
$853$	−31.5856	−	22.9483i	−1.08147	−	0.785734i	−0.103532	−	0.994626i	$-0.533014\pi$
$853$	−31.5856	−	22.9483i	−1.08147	−	0.785734i	−0.977939	+	0.208892i	$0.933014\pi$
$854$		0			0
$855$	−49.9763	−	153.811i	−1.70915	−	5.26024i
$856$		0			0
$857$	56.9547			1.94554			0.972768	−	0.231780i	$-0.0744551\pi$
$857$	56.9547			1.94554			0.972768	+	0.231780i	$0.0744551\pi$
$858$		0			0
$859$	−48.5826			−1.65762			−0.828808	−	0.559533i	$-0.810981\pi$
$859$	−48.5826			−1.65762			−0.828808	+	0.559533i	$0.810981\pi$
$860$		0			0
$861$	−2.57606	−	7.92831i	−0.0877920	−	0.270196i
$862$		0			0
$863$	14.2723	+	10.3694i	0.485834	+	0.352979i	0.803580	−	0.595197i	$-0.202926\pi$
$863$	14.2723	+	10.3694i	0.485834	+	0.352979i	−0.317746	+	0.948176i	$0.602926\pi$
$864$		0			0
$865$	20.3339	−	62.5814i	0.691375	−	2.12783i
$866$		0			0
$867$	−100.213	+	72.8090i	−3.40341	+	2.47272i
$868$		0			0
$869$	−21.0999	+	36.0825i	−0.715764	+	1.22401i
$870$		0			0
$871$	−7.32390	+	5.32113i	−0.248161	+	0.180300i
$872$		0			0
$873$	−5.64464	+	17.3724i	−0.191042	+	0.587967i
$874$		0			0
$875$	−36.5789	−	26.5762i	−1.23659	−	0.898438i
$876$		0			0
$877$	−9.43084	−	29.0252i	−0.318457	−	0.980110i	−0.974308	−	0.225219i	$-0.927690\pi$
$877$	−9.43084	−	29.0252i	−0.318457	−	0.980110i	0.655851	−	0.754890i	$-0.272310\pi$
$878$		0			0
$879$	−22.6726			−0.764728
$880$		0			0
$881$	20.2275			0.681482			0.340741	−	0.940157i	$-0.389322\pi$
$881$	20.2275			0.681482			0.340741	+	0.940157i	$0.389322\pi$
$882$		0			0
$883$	8.34203	+	25.6741i	0.280732	+	0.864004i	0.987646	+	0.156704i	$0.0500869\pi$
$883$	8.34203	+	25.6741i	0.280732	+	0.864004i	−0.706914	+	0.707300i	$0.749913\pi$
$884$		0			0
$885$	72.2694	+	52.5068i	2.42931	+	1.76500i
$886$		0			0
$887$	−1.66474	+	5.12354i	−0.0558964	+	0.172032i	−0.975107	−	0.221735i	$-0.928828\pi$
$887$	−1.66474	+	5.12354i	−0.0558964	+	0.172032i	0.919211	+	0.393766i	$0.128828\pi$
$888$		0			0
$889$	−15.8077	+	11.4850i	−0.530173	+	0.385194i
$890$		0			0
$891$	4.69178	+	47.1533i	0.157181	+	1.57969i
$892$		0			0
$893$	−10.1503	+	7.37460i	−0.339666	+	0.246782i
$894$		0			0
$895$	−29.7550	+	91.5764i	−0.994599	+	3.06106i
$896$		0			0
$897$	0.507160	+	0.368474i	0.0169336	+	0.0123030i
$898$		0			0
$899$	4.14484	+	12.7565i	0.138238	+	0.425453i
$900$		0			0
$901$	0.796528			0.0265362
$902$		0			0
$903$	−14.1603			−0.471226
$904$		0			0
$905$	16.1692	+	49.7635i	0.537481	+	1.65420i
$906$		0			0
$907$	11.9078	+	8.65153i	0.395392	+	0.287269i	0.767661	−	0.640856i	$-0.221420\pi$
$907$	11.9078	+	8.65153i	0.395392	+	0.287269i	−0.372269	+	0.928125i	$0.621420\pi$
$908$		0			0
$909$	−0.449512	+	1.38346i	−0.0149094	+	0.0458863i
$910$		0			0
$911$	−11.2809	+	8.19605i	−0.373753	+	0.271547i	−0.758765	−	0.651364i	$-0.774197\pi$
$911$	−11.2809	+	8.19605i	−0.373753	+	0.271547i	0.385013	+	0.922911i	$0.374197\pi$
$912$		0			0
$913$	−26.5703	−	5.80187i	−0.879347	−	0.192014i
$914$		0			0
$915$	−116.434	+	84.5940i	−3.84918	+	2.79659i
$916$		0			0
$917$	−2.59113	+	7.97468i	−0.0855667	+	0.263347i
$918$		0			0
$919$	−15.7619	−	11.4517i	−0.519936	−	0.377756i	0.296644	−	0.954988i	$-0.404133\pi$
$919$	−15.7619	−	11.4517i	−0.519936	−	0.377756i	−0.816580	+	0.577232i	$0.804133\pi$
$920$		0			0
$921$	−0.271527	−	0.835674i	−0.00894712	−	0.0275364i
$922$		0			0
$923$	0.124736			0.00410574
$924$		0			0
$925$	−32.6868			−1.07473
$926$		0			0
$927$	−18.7280	−	57.6389i	−0.615108	−	1.89311i
$928$		0			0
$929$	48.3113	+	35.1002i	1.58504	+	1.15160i	0.910611	+	0.413264i	$0.135611\pi$
$929$	48.3113	+	35.1002i	1.58504	+	1.15160i	0.674432	+	0.738337i	$0.264389\pi$
$930$		0			0
$931$	9.90881	−	30.4962i	0.324748	−	0.999472i
$932$		0			0
$933$	37.8660	−	27.5112i	1.23968	−	0.900677i
$934$		0			0
$935$	−72.5618	−	81.4923i	−2.37302	−	2.66508i
$936$		0			0
$937$	−21.7027	+	15.7680i	−0.708997	+	0.515117i	−0.882850	−	0.469655i	$-0.844378\pi$
$937$	−21.7027	+	15.7680i	−0.708997	+	0.515117i	0.173853	+	0.984772i	$0.444378\pi$
$938$		0			0
$939$	−0.143307	+	0.441055i	−0.00467666	+	0.0143933i
$940$		0			0
$941$	26.2535	+	19.0743i	0.855838	+	0.621803i	0.926750	−	0.375680i	$-0.122591\pi$
$941$	26.2535	+	19.0743i	0.855838	+	0.621803i	−0.0709111	+	0.997483i	$0.522591\pi$
$942$		0			0
$943$	−0.145937	−	0.449149i	−0.00475237	−	0.0146263i
$944$		0			0
$945$	55.4003			1.80217
$946$		0			0
$947$	47.2247			1.53460			0.767298	−	0.641291i	$-0.221601\pi$
$947$	47.2247			1.53460			0.767298	+	0.641291i	$0.221601\pi$
$948$		0			0
$949$	0.654868	+	2.01548i	0.0212579	+	0.0654252i
$950$		0			0
$951$	−7.45250	−	5.41456i	−0.241664	−	0.175579i
$952$		0			0
$953$	−11.0035	+	33.8653i	−0.356438	+	1.09700i	0.598733	+	0.800949i	$0.295671\pi$
$953$	−11.0035	+	33.8653i	−0.356438	+	1.09700i	−0.955171	+	0.296055i	$0.904329\pi$
$954$		0			0
$955$	−19.2441	+	13.9816i	−0.622723	+	0.452435i
$956$		0			0
$957$	55.0229	−	24.1331i	1.77864	−	0.780111i
$958$		0			0
$959$	−8.04988	+	5.84858i	−0.259944	+	0.188861i
$960$		0			0
$961$	−7.96112	+	24.5018i	−0.256810	+	0.790381i
$962$		0			0
$963$	−27.3671	−	19.8833i	−0.881891	−	0.640731i
$964$		0			0
$965$	−4.80870	−	14.7997i	−0.154798	−	0.476418i
$966$		0			0
$967$	24.6176			0.791649			0.395824	−	0.918326i	$-0.370459\pi$
$967$	24.6176			0.791649			0.395824	+	0.918326i	$0.370459\pi$
$968$		0			0
$969$	−132.329			−4.25103
$970$		0			0
$971$	−15.7082	−	48.3449i	−0.504100	−	1.55146i	−0.802278	−	0.596951i	$-0.796379\pi$
$971$	−15.7082	−	48.3449i	−0.504100	−	1.55146i	0.298178	−	0.954510i	$-0.403621\pi$
$972$		0			0
$973$	−2.25154	−	1.63584i	−0.0721811	−	0.0524426i
$974$		0			0
$975$	−13.3373	+	41.0479i	−0.427135	+	1.31459i
$976$		0			0
$977$	−33.2670	+	24.1699i	−1.06431	+	0.773263i	−0.974880	−	0.222730i	$-0.928503\pi$
$977$	−33.2670	+	24.1699i	−1.06431	+	0.773263i	−0.0894256	+	0.995994i	$0.528503\pi$
$978$		0			0
$979$	42.7209	−	18.7374i	1.36537	−	0.598850i
$980$		0			0
$981$	33.7018	−	24.4858i	1.07602	−	0.781771i
$982$		0			0
$983$	7.16327	−	22.0463i	0.228473	−	0.703167i	−0.769448	−	0.638710i	$-0.779468\pi$
$983$	7.16327	−	22.0463i	0.228473	−	0.703167i	0.997920	−	0.0644570i	$-0.0205315\pi$
$984$		0			0
$985$	−16.7645	−	12.1801i	−0.534161	−	0.388091i
$986$		0			0
$987$	−2.44935	−	7.53834i	−0.0779638	−	0.239948i
$988$		0			0
$989$	−0.802200			−0.0255085
$990$		0			0
$991$	−41.9183			−1.33158			−0.665789	−	0.746140i	$-0.731905\pi$
$991$	−41.9183			−1.33158			−0.665789	+	0.746140i	$0.731905\pi$
$992$		0			0
$993$	−20.9055	−	64.3404i	−0.663415	−	2.04178i
$994$		0			0
$995$	−49.5110	−	35.9719i	−1.56960	−	1.14038i
$996$		0			0
$997$	2.85970	−	8.80124i	0.0905675	−	0.278738i	−0.895506	−	0.445050i	$-0.853186\pi$
$997$	2.85970	−	8.80124i	0.0905675	−	0.278738i	0.986073	+	0.166312i	$0.0531859\pi$
$998$		0			0
$999$	20.7997	−	15.1119i	0.658073	−	0.478118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.157.6	✓	28
11.2	odd	10		6292.2.a.y.1.13		14
11.4	even	5	inner	572.2.n.b.521.6	yes	28
11.9	even	5		6292.2.a.z.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.157.6	✓	28	1.1	even	1	trivial
572.2.n.b.521.6	yes	28	11.4	even	5	inner
6292.2.a.y.1.13		14	11.2	odd	10
6292.2.a.z.1.13		14	11.9	even	5

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.955130 + 2.93959i) q^{3} +(-3.52306 - 2.55966i) q^{5} +(0.357931 - 1.10160i) q^{7} +(-5.30186 + 3.85203i) q^{9} +O(q^{10})\)	\(q+(0.955130 + 2.93959i) q^{3} +(-3.52306 - 2.55966i) q^{5} +(0.357931 - 1.10160i) q^{7} +(-5.30186 + 3.85203i) q^{9} +(-3.03732 + 1.33217i) q^{11} +(0.809017 - 0.587785i) q^{13} +(4.15935 - 12.8012i) q^{15} +(-6.11202 - 4.44064i) q^{17} +(-1.75118 - 5.38958i) q^{19} +3.58012 q^{21} +0.202818 q^{23} +(4.31506 + 13.2804i) q^{25} +(-8.88565 - 6.45580i) q^{27} +(-1.81115 + 5.57415i) q^{29} +(1.85144 - 1.34515i) q^{31} +(-6.81707 - 7.65608i) q^{33} +(-4.08073 + 2.96482i) q^{35} +(-0.723352 + 2.22625i) q^{37} +(2.50056 + 1.81677i) q^{39} +(-0.719547 - 2.21454i) q^{41} -3.95526 q^{43} +28.5387 q^{45} +(-0.684154 - 2.10561i) q^{47} +(4.57771 + 3.32590i) q^{49} +(7.21589 - 22.2082i) q^{51} +(-0.0852965 + 0.0619716i) q^{53} +(14.1106 + 3.08118i) q^{55} +(14.1705 - 10.2955i) q^{57} +(-2.05086 + 6.31189i) q^{59} +(-8.65038 - 6.28487i) q^{61} +(2.34569 + 7.21928i) q^{63} -4.35475 q^{65} -9.05284 q^{67} +(0.193718 + 0.596203i) q^{69} +(0.100914 + 0.0733180i) q^{71} +(-0.654868 + 2.01548i) q^{73} +(-34.9174 + 25.3690i) q^{75} +(0.380365 + 3.82274i) q^{77} +(10.1959 - 7.40777i) q^{79} +(4.41506 - 13.5882i) q^{81} +(6.63394 + 4.81984i) q^{83} +(10.1665 + 31.2894i) q^{85} -18.1156 q^{87} -14.0653 q^{89} +(-0.357931 - 1.10160i) q^{91} +(5.72257 + 4.15769i) q^{93} +(-7.62594 + 23.4702i) q^{95} +(2.25497 - 1.63833i) q^{97} +(10.9719 - 18.7628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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