LMFDB - Embedded newform 4020.2.q.m.3781.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, 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:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.2
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.m.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(-2.09133 - 3.62228i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(-2.09133 - 3.62228i) q^{7} +1.00000 q^{9} +(-1.91804 - 3.32213i) q^{11} +(3.12517 - 5.41296i) q^{13} +1.00000 q^{15} +(-0.293577 + 0.508491i) q^{17} +(-1.03005 + 1.78410i) q^{19} +(-2.09133 - 3.62228i) q^{21} +(-0.208156 + 0.360537i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-2.56059 - 4.43507i) q^{29} +(0.705813 + 1.22250i) q^{31} +(-1.91804 - 3.32213i) q^{33} +(-2.09133 - 3.62228i) q^{35} +(-3.95686 + 6.85348i) q^{37} +(3.12517 - 5.41296i) q^{39} +(-0.442565 - 0.766545i) q^{41} -4.05387 q^{43} +1.00000 q^{45} +(0.533290 + 0.923685i) q^{47} +(-5.24728 + 9.08856i) q^{49} +(-0.293577 + 0.508491i) q^{51} -6.55179 q^{53} +(-1.91804 - 3.32213i) q^{55} +(-1.03005 + 1.78410i) q^{57} +7.65466 q^{59} +(-2.87975 + 4.98787i) q^{61} +(-2.09133 - 3.62228i) q^{63} +(3.12517 - 5.41296i) q^{65} +(8.13155 - 0.936929i) q^{67} +(-0.208156 + 0.360537i) q^{69} +(-7.60355 - 13.1697i) q^{71} +(-5.89026 + 10.2022i) q^{73} +1.00000 q^{75} +(-8.02247 + 13.8953i) q^{77} +(-2.23720 - 3.87494i) q^{79} +1.00000 q^{81} +(-1.17272 + 2.03122i) q^{83} +(-0.293577 + 0.508491i) q^{85} +(-2.56059 - 4.43507i) q^{87} +7.94567 q^{89} -26.1430 q^{91} +(0.705813 + 1.22250i) q^{93} +(-1.03005 + 1.78410i) q^{95} +(-3.07541 + 5.32677i) q^{97} +(-1.91804 - 3.32213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−2.09133	−	3.62228i	−0.790447	−	1.36909i	−0.925691	−	0.378281i	$-0.876515\pi$
$7$	−2.09133	−	3.62228i	−0.790447	−	1.36909i	0.135244	−	0.990812i	$-0.456818\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−1.91804	−	3.32213i	−0.578309	−	1.00166i	−0.995673	−	0.0929218i	$-0.970379\pi$
$11$	−1.91804	−	3.32213i	−0.578309	−	1.00166i	0.417364	−	0.908739i	$-0.362954\pi$
$12$		0			0
$13$	3.12517	−	5.41296i	0.866767	−	1.50129i	0.00148575	−	0.999999i	$-0.499527\pi$
$13$	3.12517	−	5.41296i	0.866767	−	1.50129i	0.865282	−	0.501286i	$-0.167140\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−0.293577	+	0.508491i	−0.0712029	+	0.123327i	−0.899429	−	0.437067i	$-0.856017\pi$
$17$	−0.293577	+	0.508491i	−0.0712029	+	0.123327i	0.828226	+	0.560394i	$0.189350\pi$
$18$		0			0
$19$	−1.03005	+	1.78410i	−0.236310	+	0.409300i	−0.959652	−	0.281189i	$-0.909271\pi$
$19$	−1.03005	+	1.78410i	−0.236310	+	0.409300i	0.723343	+	0.690489i	$0.242605\pi$
$20$		0			0
$21$	−2.09133	−	3.62228i	−0.456365	−	0.790447i
$22$		0			0
$23$	−0.208156	+	0.360537i	−0.0434036	+	0.0751772i	−0.886911	−	0.461940i	$-0.847153\pi$
$23$	−0.208156	+	0.360537i	−0.0434036	+	0.0751772i	0.843507	+	0.537117i	$0.180487\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.56059	−	4.43507i	−0.475489	−	0.823571i	0.524117	−	0.851646i	$-0.324395\pi$
$29$	−2.56059	−	4.43507i	−0.475489	−	0.823571i	−0.999606	+	0.0280754i	$0.991062\pi$
$30$		0			0
$31$	0.705813	+	1.22250i	0.126768	+	0.219568i	0.922423	−	0.386182i	$-0.126206\pi$
$31$	0.705813	+	1.22250i	0.126768	+	0.219568i	−0.795655	+	0.605750i	$0.792873\pi$
$32$		0			0
$33$	−1.91804	−	3.32213i	−0.333887	−	0.578309i
$34$		0			0
$35$	−2.09133	−	3.62228i	−0.353498	−	0.612277i
$36$		0			0
$37$	−3.95686	+	6.85348i	−0.650503	+	1.12670i	0.332498	+	0.943104i	$0.392109\pi$
$37$	−3.95686	+	6.85348i	−0.650503	+	1.12670i	−0.983001	+	0.183601i	$0.941225\pi$
$38$		0			0
$39$	3.12517	−	5.41296i	0.500428	−	0.866767i
$40$		0			0
$41$	−0.442565	−	0.766545i	−0.0691170	−	0.119714i	0.829396	−	0.558661i	$-0.188685\pi$
$41$	−0.442565	−	0.766545i	−0.0691170	−	0.119714i	−0.898513	+	0.438947i	$0.855352\pi$
$42$		0			0
$43$	−4.05387			−0.618209			−0.309104	−	0.951028i	$-0.600029\pi$
$43$	−4.05387			−0.618209			−0.309104	+	0.951028i	$0.600029\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	0.533290	+	0.923685i	0.0777883	+	0.134733i	0.902295	−	0.431118i	$-0.141881\pi$
$47$	0.533290	+	0.923685i	0.0777883	+	0.134733i	−0.824507	+	0.565852i	$0.808548\pi$
$48$		0			0
$49$	−5.24728	+	9.08856i	−0.749612	+	1.29837i
$50$		0			0
$51$	−0.293577	+	0.508491i	−0.0411090	+	0.0712029i
$52$		0			0
$53$	−6.55179			−0.899958			−0.449979	−	0.893039i	$-0.648568\pi$
$53$	−6.55179			−0.899958			−0.449979	+	0.893039i	$0.648568\pi$
$54$		0			0
$55$	−1.91804	−	3.32213i	−0.258628	−	0.447957i
$56$		0			0
$57$	−1.03005	+	1.78410i	−0.136433	+	0.236310i
$58$		0			0
$59$	7.65466			0.996552			0.498276	−	0.867019i	$-0.333967\pi$
$59$	7.65466			0.996552			0.498276	+	0.867019i	$0.333967\pi$
$60$		0			0
$61$	−2.87975	+	4.98787i	−0.368714	+	0.638631i	−0.989365	−	0.145456i	$-0.953535\pi$
$61$	−2.87975	+	4.98787i	−0.368714	+	0.638631i	0.620651	+	0.784087i	$0.286868\pi$
$62$		0			0
$63$	−2.09133	−	3.62228i	−0.263482	−	0.456365i
$64$		0			0
$65$	3.12517	−	5.41296i	0.387630	−	0.671395i
$66$		0			0
$67$	8.13155	−	0.936929i	0.993427	−	0.114464i
$67$	8.13155	−	0.936929i	0.993427	−	0.114464i
$68$		0			0
$69$	−0.208156	+	0.360537i	−0.0250591	+	0.0434036i
$70$		0			0
$71$	−7.60355	−	13.1697i	−0.902376	−	1.56296i	−0.824402	−	0.566005i	$-0.808488\pi$
$71$	−7.60355	−	13.1697i	−0.902376	−	1.56296i	−0.0779736	−	0.996955i	$-0.524845\pi$
$72$		0			0
$73$	−5.89026	+	10.2022i	−0.689403	+	1.19408i	0.282629	+	0.959229i	$0.408794\pi$
$73$	−5.89026	+	10.2022i	−0.689403	+	1.19408i	−0.972031	+	0.234851i	$0.924540\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−8.02247	+	13.8953i	−0.914245	+	1.58352i
$78$		0			0
$79$	−2.23720	−	3.87494i	−0.251704	−	0.435965i	0.712291	−	0.701884i	$-0.247658\pi$
$79$	−2.23720	−	3.87494i	−0.251704	−	0.435965i	−0.963995	+	0.265920i	$0.914324\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−1.17272	+	2.03122i	−0.128723	+	0.222955i	−0.923182	−	0.384363i	$-0.874421\pi$
$83$	−1.17272	+	2.03122i	−0.128723	+	0.222955i	0.794459	+	0.607318i	$0.207755\pi$
$84$		0			0
$85$	−0.293577	+	0.508491i	−0.0318429	+	0.0551535i
$86$		0			0
$87$	−2.56059	−	4.43507i	−0.274524	−	0.475489i
$88$		0			0
$89$	7.94567			0.842239			0.421119	−	0.907005i	$-0.361637\pi$
$89$	7.94567			0.842239			0.421119	+	0.907005i	$0.361637\pi$
$90$		0			0
$91$	−26.1430			−2.74053
$92$		0			0
$93$	0.705813	+	1.22250i	0.0731894	+	0.126768i
$94$		0			0
$95$	−1.03005	+	1.78410i	−0.105681	+	0.183045i
$96$		0			0
$97$	−3.07541	+	5.32677i	−0.312261	+	0.540851i	−0.978851	−	0.204573i	$-0.934420\pi$
$97$	−3.07541	+	5.32677i	−0.312261	+	0.540851i	0.666591	+	0.745424i	$0.267753\pi$
$98$		0			0
$99$	−1.91804	−	3.32213i	−0.192770	−	0.333887i
$100$		0			0
$101$	−2.42548	−	4.20106i	−0.241344	−	0.418021i	0.719753	−	0.694230i	$-0.244255\pi$
$101$	−2.42548	−	4.20106i	−0.241344	−	0.418021i	−0.961098	+	0.276209i	$0.910922\pi$
$102$		0			0
$103$	−4.41679	−	7.65011i	−0.435199	−	0.753787i	0.562113	−	0.827061i	$-0.309989\pi$
$103$	−4.41679	−	7.65011i	−0.435199	−	0.753787i	−0.997312	+	0.0732734i	$0.976655\pi$
$104$		0			0
$105$	−2.09133	−	3.62228i	−0.204092	−	0.353498i
$106$		0			0
$107$	−12.1867			−1.17814			−0.589068	−	0.808084i	$-0.700505\pi$
$107$	−12.1867			−1.17814			−0.589068	+	0.808084i	$0.700505\pi$
$108$		0			0
$109$	0.744063			0.0712683			0.0356342	−	0.999365i	$-0.488655\pi$
$109$	0.744063			0.0712683			0.0356342	+	0.999365i	$0.488655\pi$
$110$		0			0
$111$	−3.95686	+	6.85348i	−0.375568	+	0.650503i
$112$		0			0
$113$	3.78018	+	6.54747i	0.355610	+	0.615934i	0.987222	−	0.159350i	$-0.0509399\pi$
$113$	3.78018	+	6.54747i	0.355610	+	0.615934i	−0.631612	+	0.775284i	$0.717607\pi$
$114$		0			0
$115$	−0.208156	+	0.360537i	−0.0194107	+	0.0336203i
$116$		0			0
$117$	3.12517	−	5.41296i	0.288922	−	0.500428i
$118$		0			0
$119$	2.45586			0.225128
$120$		0			0
$121$	−1.85772	+	3.21766i	−0.168883	+	0.292515i
$122$		0			0
$123$	−0.442565	−	0.766545i	−0.0399047	−	0.0691170i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	2.76879	+	4.79569i	0.245691	+	0.425549i	0.962326	−	0.271900i	$-0.0876519\pi$
$127$	2.76879	+	4.79569i	0.245691	+	0.425549i	−0.716635	+	0.697449i	$0.754319\pi$
$128$		0			0
$129$	−4.05387			−0.356923
$130$		0			0
$131$	−10.0828			−0.880941			−0.440471	−	0.897767i	$-0.645188\pi$
$131$	−10.0828			−0.880941			−0.440471	+	0.897767i	$0.645188\pi$
$132$		0			0
$133$	8.61667			0.747160
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	0.0225579			0.00192725			0.000963627	−	1.00000i	$-0.499693\pi$
$137$	0.0225579			0.00192725			0.000963627		1.00000i	$0.499693\pi$
$138$		0			0
$139$	7.48979			0.635276			0.317638	−	0.948212i	$-0.397110\pi$
$139$	7.48979			0.635276			0.317638	+	0.948212i	$0.397110\pi$
$140$		0			0
$141$	0.533290	+	0.923685i	0.0449111	+	0.0777883i
$142$		0			0
$143$	−23.9768			−2.00504
$144$		0			0
$145$	−2.56059	−	4.43507i	−0.212645	−	0.368312i
$146$		0			0
$147$	−5.24728	+	9.08856i	−0.432788	+	0.749612i
$148$		0			0
$149$	10.1305			0.829925			0.414963	−	0.909838i	$-0.363795\pi$
$149$	10.1305			0.829925			0.414963	+	0.909838i	$0.363795\pi$
$150$		0			0
$151$	0.221117	−	0.382986i	0.0179942	−	0.0311669i	−0.856888	−	0.515503i	$-0.827605\pi$
$151$	0.221117	−	0.382986i	0.0179942	−	0.0311669i	0.874882	+	0.484336i	$0.160939\pi$
$152$		0			0
$153$	−0.293577	+	0.508491i	−0.0237343	+	0.0411090i
$154$		0			0
$155$	0.705813	+	1.22250i	0.0566923	+	0.0981939i
$156$		0			0
$157$	1.00851	−	1.74679i	0.0804880	−	0.139409i	−0.822972	−	0.568082i	$-0.807685\pi$
$157$	1.00851	−	1.74679i	0.0804880	−	0.139409i	0.903460	+	0.428673i	$0.141019\pi$
$158$		0			0
$159$	−6.55179			−0.519591
$160$		0			0
$161$	1.74129			0.137233
$162$		0			0
$163$	−9.70644	−	16.8121i	−0.760267	−	1.31682i	−0.942713	−	0.333606i	$-0.891735\pi$
$163$	−9.70644	−	16.8121i	−0.760267	−	1.31682i	0.182445	−	0.983216i	$-0.441599\pi$
$164$		0			0
$165$	−1.91804	−	3.32213i	−0.149319	−	0.258628i
$166$		0			0
$167$	−8.83490	−	15.3025i	−0.683665	−	1.18414i	−0.973854	−	0.227174i	$-0.927051\pi$
$167$	−8.83490	−	15.3025i	−0.683665	−	1.18414i	0.290189	−	0.956969i	$-0.406282\pi$
$168$		0			0
$169$	−13.0334	−	22.5746i	−1.00257	−	1.73650i
$170$		0			0
$171$	−1.03005	+	1.78410i	−0.0787699	+	0.136433i
$172$		0			0
$173$	4.68892	−	8.12145i	0.356492	−	0.617463i	−0.630880	−	0.775880i	$-0.717306\pi$
$173$	4.68892	−	8.12145i	0.356492	−	0.617463i	0.987372	+	0.158418i	$0.0506393\pi$
$174$		0			0
$175$	−2.09133	−	3.62228i	−0.158089	−	0.273819i
$176$		0			0
$177$	7.65466			0.575359
$178$		0			0
$179$	23.5734			1.76196			0.880979	−	0.473155i	$-0.156885\pi$
$179$	23.5734			1.76196			0.880979	+	0.473155i	$0.156885\pi$
$180$		0			0
$181$	7.62823	+	13.2125i	0.567002	+	0.982076i	0.996860	+	0.0791799i	$0.0252301\pi$
$181$	7.62823	+	13.2125i	0.567002	+	0.982076i	−0.429858	+	0.902896i	$0.641437\pi$
$182$		0			0
$183$	−2.87975	+	4.98787i	−0.212877	+	0.368714i
$184$		0			0
$185$	−3.95686	+	6.85348i	−0.290914	+	0.503878i
$186$		0			0
$187$	2.25237			0.164709
$188$		0			0
$189$	−2.09133	−	3.62228i	−0.152122	−	0.263482i
$190$		0			0
$191$	7.88933	−	13.6647i	0.570852	−	0.988744i	−0.425627	−	0.904899i	$-0.639946\pi$
$191$	7.88933	−	13.6647i	0.570852	−	0.988744i	0.996479	−	0.0838456i	$-0.0267202\pi$
$192$		0			0
$193$	−5.22234			−0.375912			−0.187956	−	0.982177i	$-0.560186\pi$
$193$	−5.22234			−0.375912			−0.187956	+	0.982177i	$0.560186\pi$
$194$		0			0
$195$	3.12517	−	5.41296i	0.223798	−	0.387630i
$196$		0			0
$197$	−5.69980	−	9.87235i	−0.406094	−	0.703376i	0.588354	−	0.808604i	$-0.299776\pi$
$197$	−5.69980	−	9.87235i	−0.406094	−	0.703376i	−0.994448	+	0.105228i	$0.966443\pi$
$198$		0			0
$199$	7.95010	−	13.7700i	0.563568	−	0.976128i	−0.433613	−	0.901099i	$-0.642762\pi$
$199$	7.95010	−	13.7700i	0.563568	−	0.976128i	0.997181	−	0.0750293i	$-0.0239050\pi$
$200$		0			0
$201$	8.13155	−	0.936929i	0.573556	−	0.0660859i
$202$		0			0
$203$	−10.7100	+	18.5503i	−0.751697	+	1.30198i
$204$		0			0
$205$	−0.442565	−	0.766545i	−0.0309101	−	0.0535378i
$206$		0			0
$207$	−0.208156	+	0.360537i	−0.0144679	+	0.0250591i
$208$		0			0
$209$	7.90269			0.546640
$210$		0			0
$211$	9.62480	−	16.6706i	0.662599	−	1.14765i	−0.317332	−	0.948315i	$-0.602787\pi$
$211$	9.62480	−	16.6706i	0.662599	−	1.14765i	0.979930	−	0.199340i	$-0.0638798\pi$
$212$		0			0
$213$	−7.60355	−	13.1697i	−0.520987	−	0.902376i
$214$		0			0
$215$	−4.05387			−0.276471
$216$		0			0
$217$	2.95217	−	5.11331i	0.200406	−	0.347114i
$218$		0			0
$219$	−5.89026	+	10.2022i	−0.398027	+	0.689403i
$220$		0			0
$221$	1.83496	+	3.17824i	0.123433	+	0.213792i
$222$		0			0
$223$	2.85543			0.191214			0.0956068	−	0.995419i	$-0.469521\pi$
$223$	2.85543			0.191214			0.0956068	+	0.995419i	$0.469521\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	2.66814	+	4.62136i	0.177091	+	0.306730i	0.940883	−	0.338732i	$-0.109998\pi$
$227$	2.66814	+	4.62136i	0.177091	+	0.306730i	−0.763792	+	0.645462i	$0.776665\pi$
$228$		0			0
$229$	−13.2685	+	22.9818i	−0.876810	+	1.51868i	−0.0219886	+	0.999758i	$0.507000\pi$
$229$	−13.2685	+	22.9818i	−0.876810	+	1.51868i	−0.854822	+	0.518922i	$0.826334\pi$
$230$		0			0
$231$	−8.02247	+	13.8953i	−0.527840	+	0.914245i
$232$		0			0
$233$	0.104139	+	0.180374i	0.00682236	+	0.0118167i	0.869416	−	0.494080i	$-0.164495\pi$
$233$	0.104139	+	0.180374i	0.00682236	+	0.0118167i	−0.862594	+	0.505897i	$0.831162\pi$
$234$		0			0
$235$	0.533290	+	0.923685i	0.0347880	+	0.0602546i
$236$		0			0
$237$	−2.23720	−	3.87494i	−0.145322	−	0.251704i
$238$		0			0
$239$	−13.1875	−	22.8415i	−0.853031	−	1.47749i	−0.878459	−	0.477817i	$-0.841428\pi$
$239$	−13.1875	−	22.8415i	−0.853031	−	1.47749i	0.0254279	−	0.999677i	$-0.491905\pi$
$240$		0			0
$241$	27.2201			1.75340			0.876700	−	0.481037i	$-0.159740\pi$
$241$	27.2201			1.75340			0.876700	+	0.481037i	$0.159740\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−5.24728	+	9.08856i	−0.335237	+	0.580647i
$246$		0			0
$247$	6.43817	+	11.1512i	0.409651	+	0.709536i
$248$		0			0
$249$	−1.17272	+	2.03122i	−0.0743183	+	0.128723i
$250$		0			0
$251$	−3.47938	+	6.02645i	−0.219616	+	0.380386i	−0.954691	−	0.297600i	$-0.903814\pi$
$251$	−3.47938	+	6.02645i	−0.219616	+	0.380386i	0.735074	+	0.677986i	$0.237147\pi$
$252$		0			0
$253$	1.59700			0.100403
$254$		0			0
$255$	−0.293577	+	0.508491i	−0.0183845	+	0.0318429i
$256$		0			0
$257$	1.03907	+	1.79973i	0.0648156	+	0.112264i	0.896612	−	0.442817i	$-0.146021\pi$
$257$	1.03907	+	1.79973i	0.0648156	+	0.112264i	−0.831797	+	0.555081i	$0.812687\pi$
$258$		0			0
$259$	33.1003			2.05675
$260$		0			0
$261$	−2.56059	−	4.43507i	−0.158496	−	0.274524i
$262$		0			0
$263$	−7.94240			−0.489749			−0.244875	−	0.969555i	$-0.578747\pi$
$263$	−7.94240			−0.489749			−0.244875	+	0.969555i	$0.578747\pi$
$264$		0			0
$265$	−6.55179			−0.402473
$266$		0			0
$267$	7.94567			0.486267
$268$		0			0
$269$	5.12283			0.312345			0.156172	−	0.987730i	$-0.450084\pi$
$269$	5.12283			0.312345			0.156172	+	0.987730i	$0.450084\pi$
$270$		0			0
$271$	−10.6311			−0.645791			−0.322895	−	0.946435i	$-0.604656\pi$
$271$	−10.6311			−0.645791			−0.322895	+	0.946435i	$0.604656\pi$
$272$		0			0
$273$	−26.1430			−1.58225
$274$		0			0
$275$	−1.91804	−	3.32213i	−0.115662	−	0.200332i
$276$		0			0
$277$	28.1704			1.69260			0.846298	−	0.532710i	$-0.178826\pi$
$277$	28.1704			1.69260			0.846298	+	0.532710i	$0.178826\pi$
$278$		0			0
$279$	0.705813	+	1.22250i	0.0422559	+	0.0731894i
$280$		0			0
$281$	5.26477	−	9.11885i	0.314070	−	0.543985i	−0.665169	−	0.746692i	$-0.731641\pi$
$281$	5.26477	−	9.11885i	0.314070	−	0.543985i	0.979239	+	0.202707i	$0.0649740\pi$
$282$		0			0
$283$	−0.813007			−0.0483283			−0.0241641	−	0.999708i	$-0.507692\pi$
$283$	−0.813007			−0.0483283			−0.0241641	+	0.999708i	$0.507692\pi$
$284$		0			0
$285$	−1.03005	+	1.78410i	−0.0610149	+	0.105681i
$286$		0			0
$287$	−1.85109	+	3.20619i	−0.109267	+	0.189255i
$288$		0			0
$289$	8.32762	+	14.4239i	0.489860	+	0.848463i
$290$		0			0
$291$	−3.07541	+	5.32677i	−0.180284	+	0.312261i
$292$		0			0
$293$	−15.0523			−0.879362			−0.439681	−	0.898154i	$-0.644909\pi$
$293$	−15.0523			−0.879362			−0.439681	+	0.898154i	$0.644909\pi$
$294$		0			0
$295$	7.65466			0.445671
$296$		0			0
$297$	−1.91804	−	3.32213i	−0.111296	−	0.192770i
$298$		0			0
$299$	1.30105	+	2.25348i	0.0752416	+	0.130322i
$300$		0			0
$301$	8.47795	+	14.6842i	0.488661	+	0.846386i
$302$		0			0
$303$	−2.42548	−	4.20106i	−0.139340	−	0.241344i
$304$		0			0
$305$	−2.87975	+	4.98787i	−0.164894	+	0.285605i
$306$		0			0
$307$	10.9138	−	18.9033i	0.622885	−	1.07887i	−0.366061	−	0.930591i	$-0.619294\pi$
$307$	10.9138	−	18.9033i	0.622885	−	1.07887i	0.988946	−	0.148277i	$-0.0473728\pi$
$308$		0			0
$309$	−4.41679	−	7.65011i	−0.251262	−	0.435199i
$310$		0			0
$311$	3.05958			0.173493			0.0867463	−	0.996230i	$-0.472353\pi$
$311$	3.05958			0.173493			0.0867463	+	0.996230i	$0.472353\pi$
$312$		0			0
$313$	−6.17605			−0.349091			−0.174546	−	0.984649i	$-0.555846\pi$
$313$	−6.17605			−0.349091			−0.174546	+	0.984649i	$0.555846\pi$
$314$		0			0
$315$	−2.09133	−	3.62228i	−0.117833	−	0.204092i
$316$		0			0
$317$	4.57422	−	7.92279i	0.256914	−	0.444988i	−0.708500	−	0.705711i	$-0.750628\pi$
$317$	4.57422	−	7.92279i	0.256914	−	0.444988i	0.965414	+	0.260723i	$0.0839610\pi$
$318$		0			0
$319$	−9.82259	+	17.0132i	−0.549959	+	0.952558i
$320$		0			0
$321$	−12.1867			−0.680197
$322$		0			0
$323$	−0.604798	−	1.04754i	−0.0336519	−	0.0582867i
$324$		0			0
$325$	3.12517	−	5.41296i	0.173353	−	0.300257i
$326$		0			0
$327$	0.744063			0.0411468
$328$		0			0
$329$	2.23057	−	3.86345i	0.122975	−	0.212999i
$330$		0			0
$331$	3.06775	+	5.31350i	0.168619	+	0.292056i	0.937934	−	0.346812i	$-0.112736\pi$
$331$	3.06775	+	5.31350i	0.168619	+	0.292056i	−0.769316	+	0.638869i	$0.779403\pi$
$332$		0			0
$333$	−3.95686	+	6.85348i	−0.216834	+	0.375568i
$334$		0			0
$335$	8.13155	−	0.936929i	0.444274	−	0.0511899i
$336$		0			0
$337$	12.9045	−	22.3512i	0.702952	−	1.21755i	−0.264474	−	0.964393i	$-0.585198\pi$
$337$	12.9045	−	22.3512i	0.702952	−	1.21755i	0.967426	−	0.253155i	$-0.0814683\pi$
$338$		0			0
$339$	3.78018	+	6.54747i	0.205311	+	0.355610i
$340$		0			0
$341$	2.70755	−	4.68961i	0.146622	−	0.253957i
$342$		0			0
$343$	14.6165			0.789219
$344$		0			0
$345$	−0.208156	+	0.360537i	−0.0112068	+	0.0194107i
$346$		0			0
$347$	3.27184	+	5.66699i	0.175642	+	0.304220i	0.940383	−	0.340117i	$-0.110467\pi$
$347$	3.27184	+	5.66699i	0.175642	+	0.304220i	−0.764742	+	0.644337i	$0.777133\pi$
$348$		0			0
$349$	−26.8654			−1.43807			−0.719036	−	0.694973i	$-0.755416\pi$
$349$	−26.8654			−1.43807			−0.719036	+	0.694973i	$0.755416\pi$
$350$		0			0
$351$	3.12517	−	5.41296i	0.166809	−	0.288922i
$352$		0			0
$353$	0.470947	−	0.815704i	0.0250660	−	0.0434156i	−0.853220	−	0.521551i	$-0.825354\pi$
$353$	0.470947	−	0.815704i	0.0250660	−	0.0434156i	0.878286	+	0.478135i	$0.158687\pi$
$354$		0			0
$355$	−7.60355	−	13.1697i	−0.403555	−	0.698977i
$356$		0			0
$357$	2.45586			0.129978
$358$		0			0
$359$	−0.0674987			−0.00356245			−0.00178122	−	0.999998i	$-0.500567\pi$
$359$	−0.0674987			−0.00356245			−0.00178122	+	0.999998i	$0.500567\pi$
$360$		0			0
$361$	7.37800	+	12.7791i	0.388316	+	0.672582i
$362$		0			0
$363$	−1.85772	+	3.21766i	−0.0975049	+	0.168883i
$364$		0			0
$365$	−5.89026	+	10.2022i	−0.308310	+	0.534009i
$366$		0			0
$367$	1.39195	+	2.41092i	0.0726590	+	0.125849i	0.900066	−	0.435754i	$-0.143518\pi$
$367$	1.39195	+	2.41092i	0.0726590	+	0.125849i	−0.827407	+	0.561603i	$0.810185\pi$
$368$		0			0
$369$	−0.442565	−	0.766545i	−0.0230390	−	0.0399047i
$370$		0			0
$371$	13.7019	+	23.7324i	0.711368	+	1.23213i
$372$		0			0
$373$	−1.14916	−	1.99040i	−0.0595011	−	0.103059i	0.834740	−	0.550644i	$-0.185618\pi$
$373$	−1.14916	−	1.99040i	−0.0595011	−	0.103059i	−0.894242	+	0.447585i	$0.852284\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−32.0091			−1.64855
$378$		0			0
$379$	−18.2789	+	31.6600i	−0.938925	+	1.62627i	−0.171443	+	0.985194i	$0.554843\pi$
$379$	−18.2789	+	31.6600i	−0.938925	+	1.62627i	−0.767481	+	0.641071i	$0.778490\pi$
$380$		0			0
$381$	2.76879	+	4.79569i	0.141850	+	0.245691i
$382$		0			0
$383$	4.60091	−	7.96901i	0.235096	−	0.407198i	−0.724205	−	0.689585i	$-0.757793\pi$
$383$	4.60091	−	7.96901i	0.235096	−	0.407198i	0.959300	+	0.282387i	$0.0911263\pi$
$384$		0			0
$385$	−8.02247	+	13.8953i	−0.408863	+	0.708171i
$386$		0			0
$387$	−4.05387			−0.206070
$388$		0			0
$389$	13.6961	−	23.7224i	0.694421	−	1.20277i	−0.275954	−	0.961171i	$-0.588994\pi$
$389$	13.6961	−	23.7224i	0.694421	−	1.20277i	0.970375	−	0.241602i	$-0.0776728\pi$
$390$		0			0
$391$	−0.122220	−	0.211691i	−0.00618093	−	0.0107057i
$392$		0			0
$393$	−10.0828			−0.508612
$394$		0			0
$395$	−2.23720	−	3.87494i	−0.112566	−	0.194969i
$396$		0			0
$397$	2.54514			0.127737			0.0638686	−	0.997958i	$-0.479656\pi$
$397$	2.54514			0.127737			0.0638686	+	0.997958i	$0.479656\pi$
$398$		0			0
$399$	8.61667			0.431373
$400$		0			0
$401$	−16.5673			−0.827333			−0.413666	−	0.910429i	$-0.635752\pi$
$401$	−16.5673			−0.827333			−0.413666	+	0.910429i	$0.635752\pi$
$402$		0			0
$403$	8.82316			0.439513
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	30.3576			1.50477
$408$		0			0
$409$	7.28821	+	12.6236i	0.360379	+	0.624195i	0.988023	−	0.154306i	$-0.0493141\pi$
$409$	7.28821	+	12.6236i	0.360379	+	0.624195i	−0.627644	+	0.778500i	$0.715981\pi$
$410$		0			0
$411$	0.0225579			0.00111270
$412$		0			0
$413$	−16.0084	−	27.7273i	−0.787721	−	1.36437i
$414$		0			0
$415$	−1.17272	+	2.03122i	−0.0575667	+	0.0997085i
$416$		0			0
$417$	7.48979			0.366777
$418$		0			0
$419$	−15.1279	+	26.2023i	−0.739047	+	1.28007i	0.213878	+	0.976860i	$0.431391\pi$
$419$	−15.1279	+	26.2023i	−0.739047	+	1.28007i	−0.952925	+	0.303206i	$0.901943\pi$
$420$		0			0
$421$	16.4313	−	28.4599i	0.800814	−	1.38705i	−0.118267	−	0.992982i	$-0.537734\pi$
$421$	16.4313	−	28.4599i	0.800814	−	1.38705i	0.919081	−	0.394068i	$-0.128933\pi$
$422$		0			0
$423$	0.533290	+	0.923685i	0.0259294	+	0.0449111i
$424$		0			0
$425$	−0.293577	+	0.508491i	−0.0142406	+	0.0246654i
$426$		0			0
$427$	24.0900			1.16579
$428$		0			0
$429$	−23.9768			−1.15761
$430$		0			0
$431$	0.0302759	+	0.0524394i	0.00145834	+	0.00252592i	0.866754	−	0.498737i	$-0.166202\pi$
$431$	0.0302759	+	0.0524394i	0.00145834	+	0.00252592i	−0.865295	+	0.501262i	$0.832869\pi$
$432$		0			0
$433$	1.05130	+	1.82090i	0.0505221	+	0.0875069i	0.890181	−	0.455608i	$-0.150578\pi$
$433$	1.05130	+	1.82090i	0.0505221	+	0.0875069i	−0.839658	+	0.543115i	$0.817245\pi$
$434$		0			0
$435$	−2.56059	−	4.43507i	−0.122771	−	0.212645i
$436$		0			0
$437$	−0.428823	−	0.742743i	−0.0205134	−	0.0355302i
$438$		0			0
$439$	11.3130	−	19.5947i	0.539940	−	0.935203i	−0.458967	−	0.888453i	$-0.651780\pi$
$439$	11.3130	−	19.5947i	0.539940	−	0.935203i	0.998907	−	0.0467494i	$-0.0148862\pi$
$440$		0			0
$441$	−5.24728	+	9.08856i	−0.249871	+	0.432788i
$442$		0			0
$443$	−18.0654	−	31.2902i	−0.858314	−	1.48664i	−0.873536	−	0.486760i	$-0.838179\pi$
$443$	−18.0654	−	31.2902i	−0.858314	−	1.48664i	0.0152219	−	0.999884i	$-0.495155\pi$
$444$		0			0
$445$	7.94567			0.376661
$446$		0			0
$447$	10.1305			0.479158
$448$		0			0
$449$	−20.6277	−	35.7282i	−0.973481	−	1.68612i	−0.684859	−	0.728676i	$-0.740136\pi$
$449$	−20.6277	−	35.7282i	−0.973481	−	1.68612i	−0.288622	−	0.957443i	$-0.593197\pi$
$450$		0			0
$451$	−1.69771	+	2.94052i	−0.0799420	+	0.138464i
$452$		0			0
$453$	0.221117	−	0.382986i	0.0103890	−	0.0179942i
$454$		0			0
$455$	−26.1430			−1.22560
$456$		0			0
$457$	0.652530	+	1.13021i	0.0305241	+	0.0528692i	0.880884	−	0.473332i	$-0.156949\pi$
$457$	0.652530	+	1.13021i	0.0305241	+	0.0528692i	−0.850360	+	0.526202i	$0.823616\pi$
$458$		0			0
$459$	−0.293577	+	0.508491i	−0.0137030	+	0.0237343i
$460$		0			0
$461$	−6.02791			−0.280748			−0.140374	−	0.990099i	$-0.544830\pi$
$461$	−6.02791			−0.280748			−0.140374	+	0.990099i	$0.544830\pi$
$462$		0			0
$463$	−0.750824	+	1.30046i	−0.0348937	+	0.0604377i	−0.882945	−	0.469477i	$-0.844443\pi$
$463$	−0.750824	+	1.30046i	−0.0348937	+	0.0604377i	0.848051	+	0.529914i	$0.177776\pi$
$464$		0			0
$465$	0.705813	+	1.22250i	0.0327313	+	0.0566923i
$466$		0			0
$467$	9.50989	−	16.4716i	0.440065	−	0.762215i	−0.557629	−	0.830090i	$-0.688289\pi$
$467$	9.50989	−	16.4716i	0.440065	−	0.762215i	0.997694	+	0.0678754i	$0.0216220\pi$
$468$		0			0
$469$	−20.3995	−	27.4954i	−0.941963	−	1.26962i
$470$		0			0
$471$	1.00851	−	1.74679i	0.0464697	−	0.0804880i
$472$		0			0
$473$	7.77546	+	13.4675i	0.357516	+	0.619236i
$474$		0			0
$475$	−1.03005	+	1.78410i	−0.0472619	+	0.0818600i
$476$		0			0
$477$	−6.55179			−0.299986
$478$		0			0
$479$	5.67894	−	9.83621i	0.259477	−	0.449428i	−0.706625	−	0.707589i	$-0.749783\pi$
$479$	5.67894	−	9.83621i	0.259477	−	0.449428i	0.966102	+	0.258161i	$0.0831164\pi$
$480$		0			0
$481$	24.7317	+	42.8366i	1.12767	+	1.95318i
$482$		0			0
$483$	1.74129			0.0792315
$484$		0			0
$485$	−3.07541	+	5.32677i	−0.139647	+	0.241876i
$486$		0			0
$487$	−4.60134	+	7.96976i	−0.208507	+	0.361144i	−0.951244	−	0.308438i	$-0.900194\pi$
$487$	−4.60134	+	7.96976i	−0.208507	+	0.361144i	0.742738	+	0.669583i	$0.233527\pi$
$488$		0			0
$489$	−9.70644	−	16.8121i	−0.438941	−	0.760267i
$490$		0			0
$491$	−22.0779			−0.996361			−0.498180	−	0.867073i	$-0.665998\pi$
$491$	−22.0779			−0.996361			−0.498180	+	0.867073i	$0.665998\pi$
$492$		0			0
$493$	3.00692			0.135425
$494$		0			0
$495$	−1.91804	−	3.32213i	−0.0862093	−	0.149319i
$496$		0			0
$497$	−31.8030	+	55.0844i	−1.42656	+	2.47087i
$498$		0			0
$499$	−2.84273	+	4.92376i	−0.127258	+	0.220418i	−0.922613	−	0.385726i	$-0.873951\pi$
$499$	−2.84273	+	4.92376i	−0.127258	+	0.220418i	0.795355	+	0.606144i	$0.207284\pi$
$500$		0			0
$501$	−8.83490	−	15.3025i	−0.394714	−	0.683665i
$502$		0			0
$503$	−9.52569	−	16.4990i	−0.424730	−	0.735653i	0.571666	−	0.820487i	$-0.306298\pi$
$503$	−9.52569	−	16.4990i	−0.424730	−	0.735653i	−0.996395	+	0.0848335i	$0.972964\pi$
$504$		0			0
$505$	−2.42548	−	4.20106i	−0.107933	−	0.186945i
$506$		0			0
$507$	−13.0334	−	22.5746i	−0.578835	−	1.00257i
$508$		0			0
$509$	−3.48834			−0.154618			−0.0773090	−	0.997007i	$-0.524633\pi$
$509$	−3.48834			−0.154618			−0.0773090	+	0.997007i	$0.524633\pi$
$510$		0			0
$511$	49.2738			2.17974
$512$		0			0
$513$	−1.03005	+	1.78410i	−0.0454778	+	0.0787699i
$514$		0			0
$515$	−4.41679	−	7.65011i	−0.194627	−	0.337104i
$516$		0			0
$517$	2.04574	−	3.54332i	0.0899714	−	0.155835i
$518$		0			0
$519$	4.68892	−	8.12145i	0.205821	−	0.356492i
$520$		0			0
$521$	−33.9529			−1.48751			−0.743753	−	0.668455i	$-0.766956\pi$
$521$	−33.9529			−1.48751			−0.743753	+	0.668455i	$0.766956\pi$
$522$		0			0
$523$	16.9346	−	29.3316i	0.740499	−	1.28258i	−0.211769	−	0.977320i	$-0.567922\pi$
$523$	16.9346	−	29.3316i	0.740499	−	1.28258i	0.952268	−	0.305263i	$-0.0987443\pi$
$524$		0			0
$525$	−2.09133	−	3.62228i	−0.0912729	−	0.158089i
$526$		0			0
$527$	−0.828843			−0.0361050
$528$		0			0
$529$	11.4133	+	19.7685i	0.496232	+	0.859499i
$530$		0			0
$531$	7.65466			0.332184
$532$		0			0
$533$	−5.53237			−0.239633
$534$		0			0
$535$	−12.1867			−0.526878
$536$		0			0
$537$	23.5734			1.01727
$538$		0			0
$539$	40.2579			1.73403
$540$		0			0
$541$	41.2292			1.77258			0.886291	−	0.463129i	$-0.153273\pi$
$541$	41.2292			1.77258			0.886291	+	0.463129i	$0.153273\pi$
$542$		0			0
$543$	7.62823	+	13.2125i	0.327359	+	0.567002i
$544$		0			0
$545$	0.744063			0.0318722
$546$		0			0
$547$	−2.30887	−	3.99908i	−0.0987201	−	0.170988i	0.812435	−	0.583052i	$-0.198142\pi$
$547$	−2.30887	−	3.99908i	−0.0987201	−	0.170988i	−0.911155	+	0.412063i	$0.864808\pi$
$548$		0			0
$549$	−2.87975	+	4.98787i	−0.122905	+	0.212877i
$550$		0			0
$551$	10.5501			0.449450
$552$		0			0
$553$	−9.35741	+	16.2075i	−0.397918	+	0.689213i
$554$		0			0
$555$	−3.95686	+	6.85348i	−0.167959	+	0.290914i
$556$		0			0
$557$	14.7310	+	25.5148i	0.624172	+	1.08110i	0.988700	+	0.149905i	$0.0478967\pi$
$557$	14.7310	+	25.5148i	0.624172	+	1.08110i	−0.364529	+	0.931192i	$0.618770\pi$
$558$		0			0
$559$	−12.6690	+	21.9434i	−0.535843	+	0.928108i
$560$		0			0
$561$	2.25237			0.0950949
$562$		0			0
$563$	−20.4065			−0.860031			−0.430016	−	0.902821i	$-0.641492\pi$
$563$	−20.4065			−0.860031			−0.430016	+	0.902821i	$0.641492\pi$
$564$		0			0
$565$	3.78018	+	6.54747i	0.159034	+	0.275454i
$566$		0			0
$567$	−2.09133	−	3.62228i	−0.0878274	−	0.152122i
$568$		0			0
$569$	−2.88106	−	4.99015i	−0.120780	−	0.209198i	0.799295	−	0.600939i	$-0.205206\pi$
$569$	−2.88106	−	4.99015i	−0.120780	−	0.209198i	−0.920076	+	0.391741i	$0.871873\pi$
$570$		0			0
$571$	−7.94487	−	13.7609i	−0.332482	−	0.575876i	0.650516	−	0.759493i	$-0.274553\pi$
$571$	−7.94487	−	13.7609i	−0.332482	−	0.575876i	−0.982998	+	0.183617i	$0.941220\pi$
$572$		0			0
$573$	7.88933	−	13.6647i	0.329581	−	0.570852i
$574$		0			0
$575$	−0.208156	+	0.360537i	−0.00868072	+	0.0150354i
$576$		0			0
$577$	20.7183	+	35.8852i	0.862515	+	1.49392i	0.869494	+	0.493944i	$0.164445\pi$
$577$	20.7183	+	35.8852i	0.862515	+	1.49392i	−0.00697932	+	0.999976i	$0.502222\pi$
$578$		0			0
$579$	−5.22234			−0.217033
$580$		0			0
$581$	9.81018			0.406995
$582$		0			0
$583$	12.5666	+	21.7659i	0.520454	+	0.901453i
$584$		0			0
$585$	3.12517	−	5.41296i	0.129210	−	0.223798i
$586$		0			0
$587$	−4.06565	+	7.04191i	−0.167807	+	0.290651i	−0.937649	−	0.347584i	$-0.887002\pi$
$587$	−4.06565	+	7.04191i	−0.167807	+	0.290651i	0.769841	+	0.638235i	$0.220335\pi$
$588$		0			0
$589$	−2.90809			−0.119826
$590$		0			0
$591$	−5.69980	−	9.87235i	−0.234459	−	0.406094i
$592$		0			0
$593$	−17.8532	+	30.9226i	−0.733141	+	1.26984i	0.222393	+	0.974957i	$0.428613\pi$
$593$	−17.8532	+	30.9226i	−0.733141	+	1.26984i	−0.955534	+	0.294881i	$0.904720\pi$
$594$		0			0
$595$	2.45586			0.100680
$596$		0			0
$597$	7.95010	−	13.7700i	0.325376	−	0.563568i
$598$		0			0
$599$	10.7368	+	18.5967i	0.438695	+	0.759842i	0.997589	−	0.0693971i	$-0.0221075\pi$
$599$	10.7368	+	18.5967i	0.438695	+	0.759842i	−0.558894	+	0.829239i	$0.688774\pi$
$600$		0			0
$601$	6.34161	−	10.9840i	0.258680	−	0.448047i	−0.707209	−	0.707005i	$-0.750046\pi$
$601$	6.34161	−	10.9840i	0.258680	−	0.448047i	0.965889	+	0.258958i	$0.0833792\pi$
$602$		0			0
$603$	8.13155	−	0.936929i	0.331142	−	0.0381547i
$604$		0			0
$605$	−1.85772	+	3.21766i	−0.0755270	+	0.130817i
$606$		0			0
$607$	1.33478	+	2.31191i	0.0541771	+	0.0938375i	0.891842	−	0.452347i	$-0.149413\pi$
$607$	1.33478	+	2.31191i	0.0541771	+	0.0938375i	−0.837665	+	0.546184i	$0.816080\pi$
$608$		0			0
$609$	−10.7100	+	18.5503i	−0.433993	+	0.751697i
$610$		0			0
$611$	6.66649			0.269698
$612$		0			0
$613$	−4.17094	+	7.22428i	−0.168463	+	0.291786i	−0.937880	−	0.346961i	$-0.887214\pi$
$613$	−4.17094	+	7.22428i	−0.168463	+	0.291786i	0.769417	+	0.638747i	$0.220547\pi$
$614$		0			0
$615$	−0.442565	−	0.766545i	−0.0178459	−	0.0309101i
$616$		0			0
$617$	−22.3777			−0.900892			−0.450446	−	0.892804i	$-0.648735\pi$
$617$	−22.3777			−0.900892			−0.450446	+	0.892804i	$0.648735\pi$
$618$		0			0
$619$	−3.37237	+	5.84111i	−0.135547	+	0.234774i	−0.925806	−	0.377998i	$-0.876612\pi$
$619$	−3.37237	+	5.84111i	−0.135547	+	0.234774i	0.790259	+	0.612772i	$0.209946\pi$
$620$		0			0
$621$	−0.208156	+	0.360537i	−0.00835303	+	0.0144679i
$622$		0			0
$623$	−16.6170	−	28.7814i	−0.665745	−	1.15310i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	7.90269			0.315603
$628$		0			0
$629$	−2.32329	−	4.02405i	−0.0926355	−	0.160449i
$630$		0			0
$631$	−16.4631	+	28.5150i	−0.655387	+	1.13516i	0.326410	+	0.945228i	$0.394161\pi$
$631$	−16.4631	+	28.5150i	−0.655387	+	1.13516i	−0.981797	+	0.189935i	$0.939172\pi$
$632$		0			0
$633$	9.62480	−	16.6706i	0.382552	−	0.662599i
$634$		0			0
$635$	2.76879	+	4.79569i	0.109876	+	0.190311i
$636$		0			0
$637$	32.7973	+	56.8067i	1.29948	+	2.25076i
$638$		0			0
$639$	−7.60355	−	13.1697i	−0.300792	−	0.520987i
$640$		0			0
$641$	−6.98943	−	12.1060i	−0.276066	−	0.478160i	0.694338	−	0.719649i	$-0.255697\pi$
$641$	−6.98943	−	12.1060i	−0.276066	−	0.478160i	−0.970403	+	0.241489i	$0.922364\pi$
$642$		0			0
$643$	−6.04228			−0.238284			−0.119142	−	0.992877i	$-0.538014\pi$
$643$	−6.04228			−0.238284			−0.119142	+	0.992877i	$0.538014\pi$
$644$		0			0
$645$	−4.05387			−0.159621
$646$		0			0
$647$	−6.76733	+	11.7214i	−0.266051	+	0.460814i	−0.967839	−	0.251572i	$-0.919052\pi$
$647$	−6.76733	+	11.7214i	−0.266051	+	0.460814i	0.701787	+	0.712387i	$0.252386\pi$
$648$		0			0
$649$	−14.6819	−	25.4298i	−0.576315	−	0.998207i
$650$		0			0
$651$	2.95217	−	5.11331i	0.115705	−	0.200406i
$652$		0			0
$653$	22.1215	−	38.3156i	0.865683	−	1.49941i	−0.000684565	−	1.00000i	$-0.500218\pi$
$653$	22.1215	−	38.3156i	0.865683	−	1.49941i	0.866367	−	0.499407i	$-0.166449\pi$
$654$		0			0
$655$	−10.0828			−0.393969
$656$		0			0
$657$	−5.89026	+	10.2022i	−0.229801	+	0.398027i
$658$		0			0
$659$	8.09426	+	14.0197i	0.315307	+	0.546128i	0.979503	−	0.201431i	$-0.0645590\pi$
$659$	8.09426	+	14.0197i	0.315307	+	0.546128i	−0.664195	+	0.747559i	$0.731226\pi$
$660$		0			0
$661$	41.4544			1.61239			0.806195	−	0.591650i	$-0.201523\pi$
$661$	41.4544			1.61239			0.806195	+	0.591650i	$0.201523\pi$
$662$		0			0
$663$	1.83496	+	3.17824i	0.0712639	+	0.123433i
$664$		0			0
$665$	8.61667			0.334140
$666$		0			0
$667$	2.13201			0.0825517
$668$		0			0
$669$	2.85543			0.110397
$670$		0			0
$671$	22.0938			0.852923
$672$		0			0
$673$	3.62156			0.139601			0.0698004	−	0.997561i	$-0.477764\pi$
$673$	3.62156			0.139601			0.0698004	+	0.997561i	$0.477764\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−6.66510	−	11.5443i	−0.256161	−	0.443683i	0.709049	−	0.705159i	$-0.249124\pi$
$677$	−6.66510	−	11.5443i	−0.256161	−	0.443683i	−0.965210	+	0.261475i	$0.915791\pi$
$678$		0			0
$679$	25.7267			0.987301
$680$		0			0
$681$	2.66814	+	4.62136i	0.102243	+	0.177091i
$682$		0			0
$683$	4.80165	−	8.31670i	0.183730	−	0.318230i	−0.759418	−	0.650603i	$-0.774516\pi$
$683$	4.80165	−	8.31670i	0.183730	−	0.318230i	0.943148	+	0.332374i	$0.107849\pi$
$684$		0			0
$685$	0.0225579			0.000861894
$686$		0			0
$687$	−13.2685	+	22.9818i	−0.506227	+	0.876810i
$688$		0			0
$689$	−20.4755	+	35.4646i	−0.780054	+	1.35109i
$690$		0			0
$691$	−21.4636	−	37.1760i	−0.816512	−	1.41424i	−0.908237	−	0.418456i	$-0.862571\pi$
$691$	−21.4636	−	37.1760i	−0.816512	−	1.41424i	0.0917251	−	0.995784i	$-0.470762\pi$
$692$		0			0
$693$	−8.02247	+	13.8953i	−0.304748	+	0.527840i
$694$		0			0
$695$	7.48979			0.284104
$696$		0			0
$697$	0.519708			0.0196853
$698$		0			0
$699$	0.104139	+	0.180374i	0.00393889	+	0.00682236i
$700$		0			0
$701$	12.1288	+	21.0078i	0.458100	+	0.793452i	0.998861	−	0.0477244i	$-0.0151969\pi$
$701$	12.1288	+	21.0078i	0.458100	+	0.793452i	−0.540761	+	0.841176i	$0.681864\pi$
$702$		0			0
$703$	−8.15152	−	14.1188i	−0.307440	−	0.532502i
$704$		0			0
$705$	0.533290	+	0.923685i	0.0200849	+	0.0347880i
$706$		0			0
$707$	−10.1449	+	17.5716i	−0.381540	+	0.660846i
$708$		0			0
$709$	−0.0842249	+	0.145882i	−0.00316313	+	0.00547871i	−0.867603	−	0.497258i	$-0.834340\pi$
$709$	−0.0842249	+	0.145882i	−0.00316313	+	0.00547871i	0.864440	+	0.502737i	$0.167674\pi$
$710$		0			0
$711$	−2.23720	−	3.87494i	−0.0839014	−	0.145322i
$712$		0			0
$713$	−0.587678			−0.0220087
$714$		0			0
$715$	−23.9768			−0.896681
$716$		0			0
$717$	−13.1875	−	22.8415i	−0.492498	−	0.853031i
$718$		0			0
$719$	−18.6856	+	32.3644i	−0.696856	+	1.20699i	0.272695	+	0.962100i	$0.412085\pi$
$719$	−18.6856	+	32.3644i	−0.696856	+	1.20699i	−0.969551	+	0.244889i	$0.921248\pi$
$720$		0			0
$721$	−18.4739	+	31.9977i	−0.688004	+	1.19166i
$722$		0			0
$723$	27.2201			1.01233
$724$		0			0
$725$	−2.56059	−	4.43507i	−0.0950978	−	0.164714i
$726$		0			0
$727$	−14.2675	+	24.7120i	−0.529152	+	0.916518i	0.470270	+	0.882523i	$0.344157\pi$
$727$	−14.2675	+	24.7120i	−0.529152	+	0.916518i	−0.999422	+	0.0339956i	$0.989177\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	1.19012	−	2.06135i	0.0440183	−	0.0762419i
$732$		0			0
$733$	−8.74666	−	15.1497i	−0.323065	−	0.559565i	0.658054	−	0.752971i	$-0.271380\pi$
$733$	−8.74666	−	15.1497i	−0.323065	−	0.559565i	−0.981119	+	0.193406i	$0.938047\pi$
$734$		0			0
$735$	−5.24728	+	9.08856i	−0.193549	+	0.335237i
$736$		0			0
$737$	−18.7092	−	25.2171i	−0.689163	−	0.928882i
$738$		0			0
$739$	−2.67851	+	4.63931i	−0.0985305	+	0.170660i	−0.911077	−	0.412237i	$-0.864748\pi$
$739$	−2.67851	+	4.63931i	−0.0985305	+	0.170660i	0.812546	+	0.582897i	$0.198081\pi$
$740$		0			0
$741$	6.43817	+	11.1512i	0.236512	+	0.409651i
$742$		0			0
$743$	12.8448	−	22.2478i	0.471229	−	0.816193i	−0.528229	−	0.849102i	$-0.677144\pi$
$743$	12.8448	−	22.2478i	0.471229	−	0.816193i	0.999458	+	0.0329087i	$0.0104771\pi$
$744$		0			0
$745$	10.1305			0.371154
$746$		0			0
$747$	−1.17272	+	2.03122i	−0.0429077	+	0.0743183i
$748$		0			0
$749$	25.4864	+	44.1438i	0.931253	+	1.61298i
$750$		0			0
$751$	13.7536			0.501877			0.250938	−	0.968003i	$-0.419261\pi$
$751$	13.7536			0.501877			0.250938	+	0.968003i	$0.419261\pi$
$752$		0			0
$753$	−3.47938	+	6.02645i	−0.126795	+	0.219616i
$754$		0			0
$755$	0.221117	−	0.382986i	0.00804727	−	0.0139383i
$756$		0			0
$757$	12.3053	+	21.3135i	0.447245	+	0.774651i	0.998206	−	0.0598804i	$-0.0190719\pi$
$757$	12.3053	+	21.3135i	0.447245	+	0.774651i	−0.550961	+	0.834531i	$0.685739\pi$
$758$		0			0
$759$	1.59700			0.0579676
$760$		0			0
$761$	23.3821			0.847600			0.423800	−	0.905756i	$-0.360696\pi$
$761$	23.3821			0.847600			0.423800	+	0.905756i	$0.360696\pi$
$762$		0			0
$763$	−1.55608	−	2.69521i	−0.0563338	−	0.0975730i
$764$		0			0
$765$	−0.293577	+	0.508491i	−0.0106143	+	0.0183845i
$766$		0			0
$767$	23.9221	−	41.4344i	0.863778	−	1.49611i
$768$		0			0
$769$	8.11389	+	14.0537i	0.292595	+	0.506789i	0.974422	−	0.224724i	$-0.0721481\pi$
$769$	8.11389	+	14.0537i	0.292595	+	0.506789i	−0.681828	+	0.731513i	$0.738815\pi$
$770$		0			0
$771$	1.03907	+	1.79973i	0.0374213	+	0.0648156i
$772$		0			0
$773$	−23.2113	−	40.2031i	−0.834852	−	1.44601i	−0.894151	−	0.447766i	$-0.852220\pi$
$773$	−23.2113	−	40.2031i	−0.834852	−	1.44601i	0.0592989	−	0.998240i	$-0.481113\pi$
$774$		0			0
$775$	0.705813	+	1.22250i	0.0253536	+	0.0439137i
$776$		0			0
$777$	33.1003			1.18747
$778$		0			0
$779$	1.82345			0.0653320
$780$		0			0
$781$	−29.1678	+	50.5200i	−1.04370	+	1.80775i
$782$		0			0
$783$	−2.56059	−	4.43507i	−0.0915079	−	0.158496i
$784$		0			0
$785$	1.00851	−	1.74679i	0.0359953	−	0.0623457i
$786$		0			0
$787$	25.7633	−	44.6233i	0.918362	−	1.59065i	0.116459	−	0.993195i	$-0.462846\pi$
$787$	25.7633	−	44.6233i	0.918362	−	1.59065i	0.801903	−	0.597454i	$-0.203821\pi$
$788$		0			0
$789$	−7.94240			−0.282757
$790$		0			0
$791$	15.8112	−	27.3858i	0.562181	−	0.973726i
$792$		0			0
$793$	17.9994	+	31.1759i	0.639178	+	1.10709i
$794$		0			0
$795$	−6.55179			−0.232368
$796$		0			0
$797$	17.5950	+	30.4754i	0.623246	+	1.07949i	0.988877	+	0.148734i	$0.0475198\pi$
$797$	17.5950	+	30.4754i	0.623246	+	1.07949i	−0.365631	+	0.930760i	$0.619147\pi$
$798$		0			0
$799$	−0.626247			−0.0221550
$800$		0			0
$801$	7.94567			0.280746
$802$		0			0
$803$	45.1909			1.59475
$804$		0			0
$805$	1.74129			0.0613724
$806$		0			0
$807$	5.12283			0.180332
$808$		0			0
$809$	−7.38600			−0.259678			−0.129839	−	0.991535i	$-0.541446\pi$
$809$	−7.38600			−0.259678			−0.129839	+	0.991535i	$0.541446\pi$
$810$		0			0
$811$	2.76830	+	4.79484i	0.0972082	+	0.168370i	0.910528	−	0.413447i	$-0.135675\pi$
$811$	2.76830	+	4.79484i	0.0972082	+	0.168370i	−0.813320	+	0.581817i	$0.802342\pi$
$812$		0			0
$813$	−10.6311			−0.372847
$814$		0			0
$815$	−9.70644	−	16.8121i	−0.340002	−	0.588901i
$816$		0			0
$817$	4.17568	−	7.23250i	0.146089	−	0.253033i
$818$		0			0
$819$	−26.1430			−0.913511
$820$		0			0
$821$	8.33135	−	14.4303i	0.290766	−	0.503622i	−0.683225	−	0.730208i	$-0.739423\pi$
$821$	8.33135	−	14.4303i	0.290766	−	0.503622i	0.973991	+	0.226586i	$0.0727565\pi$
$822$		0			0
$823$	−3.87700	+	6.71515i	−0.135144	+	0.234076i	−0.925652	−	0.378375i	$-0.876483\pi$
$823$	−3.87700	+	6.71515i	−0.135144	+	0.234076i	0.790509	+	0.612451i	$0.209816\pi$
$824$		0			0
$825$	−1.91804	−	3.32213i	−0.0667774	−	0.115662i
$826$		0			0
$827$	−11.7775	+	20.3992i	−0.409543	+	0.709350i	−0.994839	−	0.101471i	$-0.967645\pi$
$827$	−11.7775	+	20.3992i	−0.409543	+	0.709350i	0.585295	+	0.810820i	$0.300979\pi$
$828$		0			0
$829$	−2.74644			−0.0953878			−0.0476939	−	0.998862i	$-0.515187\pi$
$829$	−2.74644			−0.0953878			−0.0476939	+	0.998862i	$0.515187\pi$
$830$		0			0
$831$	28.1704			0.977220
$832$		0			0
$833$	−3.08096	−	5.33639i	−0.106749	−	0.184895i
$834$		0			0
$835$	−8.83490	−	15.3025i	−0.305744	−	0.529565i
$836$		0			0
$837$	0.705813	+	1.22250i	0.0243965	+	0.0422559i
$838$		0			0
$839$	25.4698	+	44.1150i	0.879314	+	1.52302i	0.852095	+	0.523388i	$0.175332\pi$
$839$	25.4698	+	44.1150i	0.879314	+	1.52302i	0.0272198	+	0.999629i	$0.491335\pi$
$840$		0			0
$841$	1.38680	−	2.40201i	0.0478206	−	0.0828278i
$842$		0			0
$843$	5.26477	−	9.11885i	0.181328	−	0.314070i
$844$		0			0
$845$	−13.0334	−	22.5746i	−0.448363	−	0.776588i
$846$		0			0
$847$	15.5404			0.533974
$848$		0			0
$849$	−0.813007			−0.0279023
$850$		0			0
$851$	−1.64729	−	2.85319i	−0.0564684	−	0.0978061i
$852$		0			0
$853$	11.5429	−	19.9929i	0.395221	−	0.684542i	−0.597909	−	0.801564i	$-0.704001\pi$
$853$	11.5429	−	19.9929i	0.395221	−	0.684542i	0.993129	+	0.117022i	$0.0373348\pi$
$854$		0			0
$855$	−1.03005	+	1.78410i	−0.0352270	+	0.0610149i
$856$		0			0
$857$	−7.64408			−0.261117			−0.130558	−	0.991441i	$-0.541677\pi$
$857$	−7.64408			−0.261117			−0.130558	+	0.991441i	$0.541677\pi$
$858$		0			0
$859$	−7.81966	−	13.5441i	−0.266803	−	0.462117i	0.701231	−	0.712934i	$-0.252634\pi$
$859$	−7.81966	−	13.5441i	−0.266803	−	0.462117i	−0.968035	+	0.250817i	$0.919301\pi$
$860$		0			0
$861$	−1.85109	+	3.20619i	−0.0630851	+	0.109267i
$862$		0			0
$863$	−27.0325			−0.920198			−0.460099	−	0.887868i	$-0.652186\pi$
$863$	−27.0325			−0.920198			−0.460099	+	0.887868i	$0.652186\pi$
$864$		0			0
$865$	4.68892	−	8.12145i	0.159428	−	0.276138i
$866$		0			0
$867$	8.32762	+	14.4239i	0.282821	+	0.489860i
$868$		0			0
$869$	−8.58204	+	14.8645i	−0.291126	+	0.504245i
$870$		0			0
$871$	20.3410	−	46.9438i	0.689227	−	1.59063i
$872$		0			0
$873$	−3.07541	+	5.32677i	−0.104087	+	0.180284i
$874$		0			0
$875$	−2.09133	−	3.62228i	−0.0706997	−	0.122455i
$876$		0			0
$877$	−8.66291	+	15.0046i	−0.292526	+	0.506669i	−0.974406	−	0.224794i	$-0.927829\pi$
$877$	−8.66291	+	15.0046i	−0.292526	+	0.506669i	0.681881	+	0.731464i	$0.261162\pi$
$878$		0			0
$879$	−15.0523			−0.507700
$880$		0			0
$881$	−0.946085	+	1.63867i	−0.0318744	+	0.0552081i	−0.881523	−	0.472142i	$-0.843481\pi$
$881$	−0.946085	+	1.63867i	−0.0318744	+	0.0552081i	0.849648	+	0.527350i	$0.176814\pi$
$882$		0			0
$883$	−0.775911	−	1.34392i	−0.0261115	−	0.0452264i	0.852674	−	0.522443i	$-0.174979\pi$
$883$	−0.775911	−	1.34392i	−0.0261115	−	0.0452264i	−0.878786	+	0.477216i	$0.841646\pi$
$884$		0			0
$885$	7.65466			0.257309
$886$		0			0
$887$	27.3389	−	47.3524i	0.917951	−	1.58994i	0.115428	−	0.993316i	$-0.463176\pi$
$887$	27.3389	−	47.3524i	0.917951	−	1.58994i	0.802523	−	0.596622i	$-0.203491\pi$
$888$		0			0
$889$	11.5809	−	20.0587i	0.388411	−	0.672747i
$890$		0			0
$891$	−1.91804	−	3.32213i	−0.0642566	−	0.111296i
$892$		0			0
$893$	−2.19726			−0.0735285
$894$		0			0
$895$	23.5734			0.787972
$896$		0			0
$897$	1.30105	+	2.25348i	0.0434408	+	0.0752416i
$898$		0			0
$899$	3.61459	−	6.26066i	0.120553	−	0.208805i
$900$		0			0
$901$	1.92346	−	3.33152i	0.0640796	−	0.110989i
$902$		0			0
$903$	8.47795	+	14.6842i	0.282129	+	0.488661i
$904$		0			0
$905$	7.62823	+	13.2125i	0.253571	+	0.439198i
$906$		0			0
$907$	12.2153	+	21.1575i	0.405602	+	0.702523i	0.994391	−	0.105764i	$-0.0337287\pi$
$907$	12.2153	+	21.1575i	0.405602	+	0.702523i	−0.588790	+	0.808286i	$0.700395\pi$
$908$		0			0
$909$	−2.42548	−	4.20106i	−0.0804482	−	0.139340i
$910$		0			0
$911$	50.1713			1.66225			0.831125	−	0.556086i	$-0.187697\pi$
$911$	50.1713			1.66225			0.831125	+	0.556086i	$0.187697\pi$
$912$		0			0
$913$	8.99730			0.297767
$914$		0			0
$915$	−2.87975	+	4.98787i	−0.0952015	+	0.164894i
$916$		0			0
$917$	21.0865	+	36.5229i	0.696337	+	1.20609i
$918$		0			0
$919$	4.44549	−	7.69982i	0.146643	−	0.253993i	−0.783342	−	0.621591i	$-0.786486\pi$
$919$	4.44549	−	7.69982i	0.146643	−	0.253993i	0.929985	+	0.367598i	$0.119820\pi$
$920$		0			0
$921$	10.9138	−	18.9033i	0.359623	−	0.622885i
$922$		0			0
$923$	−95.0497			−3.12860
$924$		0			0
$925$	−3.95686	+	6.85348i	−0.130101	+	0.225341i
$926$		0			0
$927$	−4.41679	−	7.65011i	−0.145066	−	0.251262i
$928$		0			0
$929$	59.4509			1.95052			0.975261	−	0.221056i	$-0.0709504\pi$
$929$	59.4509			1.95052			0.975261	+	0.221056i	$0.0709504\pi$
$930$		0			0
$931$	−10.8099	−	18.7233i	−0.354281	−	0.613632i
$932$		0			0
$933$	3.05958			0.100166
$934$		0			0
$935$	2.25237			0.0736602
$936$		0			0
$937$	−9.82384			−0.320931			−0.160465	−	0.987041i	$-0.551300\pi$
$937$	−9.82384			−0.320931			−0.160465	+	0.987041i	$0.551300\pi$
$938$		0			0
$939$	−6.17605			−0.201548
$940$		0			0
$941$	−7.96220			−0.259560			−0.129780	−	0.991543i	$-0.541427\pi$
$941$	−7.96220			−0.259560			−0.129780	+	0.991543i	$0.541427\pi$
$942$		0			0
$943$	0.368491			0.0119997
$944$		0			0
$945$	−2.09133	−	3.62228i	−0.0680308	−	0.117833i
$946$		0			0
$947$	40.7600			1.32452			0.662261	−	0.749273i	$-0.269597\pi$
$947$	40.7600			1.32452			0.662261	+	0.749273i	$0.269597\pi$
$948$		0			0
$949$	36.8162	+	63.7675i	1.19510	+	2.06998i
$950$		0			0
$951$	4.57422	−	7.92279i	0.148329	−	0.256914i
$952$		0			0
$953$	57.2256			1.85372			0.926860	−	0.375407i	$-0.122497\pi$
$953$	57.2256			1.85372			0.926860	+	0.375407i	$0.122497\pi$
$954$		0			0
$955$	7.88933	−	13.6647i	0.255293	−	0.442180i
$956$		0			0
$957$	−9.82259	+	17.0132i	−0.317519	+	0.549959i
$958$		0			0
$959$	−0.0471759	−	0.0817111i	−0.00152339	−	0.00263859i
$960$		0			0
$961$	14.5037	−	25.1211i	0.467860	−	0.810357i
$962$		0			0
$963$	−12.1867			−0.392712
$964$		0			0
$965$	−5.22234			−0.168113
$966$		0			0
$967$	−14.0496	−	24.3346i	−0.451804	−	0.782548i	0.546694	−	0.837333i	$-0.315886\pi$
$967$	−14.0496	−	24.3346i	−0.451804	−	0.782548i	−0.998498	+	0.0547844i	$0.982553\pi$
$968$		0			0
$969$	−0.604798	−	1.04754i	−0.0194289	−	0.0336519i
$970$		0			0
$971$	27.4160	+	47.4860i	0.879822	+	1.52390i	0.851535	+	0.524297i	$0.175672\pi$
$971$	27.4160	+	47.4860i	0.879822	+	1.52390i	0.0282870	+	0.999600i	$0.490995\pi$
$972$		0			0
$973$	−15.6636	−	27.1301i	−0.502151	−	0.869752i
$974$		0			0
$975$	3.12517	−	5.41296i	0.100086	−	0.173353i
$976$		0			0
$977$	11.6988	−	20.2630i	0.374279	−	0.648270i	−0.615940	−	0.787793i	$-0.711224\pi$
$977$	11.6988	−	20.2630i	0.374279	−	0.648270i	0.990219	+	0.139523i	$0.0445570\pi$
$978$		0			0
$979$	−15.2401	−	26.3966i	−0.487075	−	0.843638i
$980$		0			0
$981$	0.744063			0.0237561
$982$		0			0
$983$	34.9382			1.11436			0.557178	−	0.830393i	$-0.311884\pi$
$983$	34.9382			1.11436			0.557178	+	0.830393i	$0.311884\pi$
$984$		0			0
$985$	−5.69980	−	9.87235i	−0.181611	−	0.314559i
$986$		0			0
$987$	2.23057	−	3.86345i	0.0709997	−	0.122975i
$988$		0			0
$989$	0.843838	−	1.46157i	0.0268325	−	0.0464752i
$990$		0			0
$991$	18.8811			0.599779			0.299890	−	0.953974i	$-0.403050\pi$
$991$	18.8811			0.599779			0.299890	+	0.953974i	$0.403050\pi$
$992$		0			0
$993$	3.06775	+	5.31350i	0.0973521	+	0.168619i
$994$		0			0
$995$	7.95010	−	13.7700i	0.252035	−	0.436538i
$996$		0			0
$997$	−32.8376			−1.03998			−0.519988	−	0.854173i	$-0.674064\pi$
$997$	−32.8376			−1.03998			−0.519988	+	0.854173i	$0.674064\pi$
$998$		0			0
$999$	−3.95686	+	6.85348i	−0.125189	+	0.216834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.3781.2	yes	24
67.37	even	3	inner	4020.2.q.m.841.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.2	✓	24	67.37	even	3	inner
4020.2.q.m.3781.2	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-2.09133 - 3.62228i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-2.09133 - 3.62228i) q^{7} +1.00000 q^{9} +(-1.91804 - 3.32213i) q^{11} +(3.12517 - 5.41296i) q^{13} +1.00000 q^{15} +(-0.293577 + 0.508491i) q^{17} +(-1.03005 + 1.78410i) q^{19} +(-2.09133 - 3.62228i) q^{21} +(-0.208156 + 0.360537i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-2.56059 - 4.43507i) q^{29} +(0.705813 + 1.22250i) q^{31} +(-1.91804 - 3.32213i) q^{33} +(-2.09133 - 3.62228i) q^{35} +(-3.95686 + 6.85348i) q^{37} +(3.12517 - 5.41296i) q^{39} +(-0.442565 - 0.766545i) q^{41} -4.05387 q^{43} +1.00000 q^{45} +(0.533290 + 0.923685i) q^{47} +(-5.24728 + 9.08856i) q^{49} +(-0.293577 + 0.508491i) q^{51} -6.55179 q^{53} +(-1.91804 - 3.32213i) q^{55} +(-1.03005 + 1.78410i) q^{57} +7.65466 q^{59} +(-2.87975 + 4.98787i) q^{61} +(-2.09133 - 3.62228i) q^{63} +(3.12517 - 5.41296i) q^{65} +(8.13155 - 0.936929i) q^{67} +(-0.208156 + 0.360537i) q^{69} +(-7.60355 - 13.1697i) q^{71} +(-5.89026 + 10.2022i) q^{73} +1.00000 q^{75} +(-8.02247 + 13.8953i) q^{77} +(-2.23720 - 3.87494i) q^{79} +1.00000 q^{81} +(-1.17272 + 2.03122i) q^{83} +(-0.293577 + 0.508491i) q^{85} +(-2.56059 - 4.43507i) q^{87} +7.94567 q^{89} -26.1430 q^{91} +(0.705813 + 1.22250i) q^{93} +(-1.03005 + 1.78410i) q^{95} +(-3.07541 + 5.32677i) q^{97} +(-1.91804 - 3.32213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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