LMFDB - Embedded newform 4020.2.q.m.841.1

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			841.1
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.m.3781.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(-2.18663 + 3.78736i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(-2.18663 + 3.78736i) q^{7} +1.00000 q^{9} +(1.49547 - 2.59023i) q^{11} +(-1.04087 - 1.80283i) q^{13} +1.00000 q^{15} +(-0.454199 - 0.786696i) q^{17} +(3.53072 + 6.11538i) q^{19} +(-2.18663 + 3.78736i) q^{21} +(3.49083 + 6.04630i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(3.93896 - 6.82248i) q^{29} +(-3.83972 + 6.65058i) q^{31} +(1.49547 - 2.59023i) q^{33} +(-2.18663 + 3.78736i) q^{35} +(-0.417228 - 0.722660i) q^{37} +(-1.04087 - 1.80283i) q^{39} +(-1.33572 + 2.31353i) q^{41} -12.0882 q^{43} +1.00000 q^{45} +(0.436600 - 0.756213i) q^{47} +(-6.06274 - 10.5010i) q^{49} +(-0.454199 - 0.786696i) q^{51} +7.39196 q^{53} +(1.49547 - 2.59023i) q^{55} +(3.53072 + 6.11538i) q^{57} -1.81848 q^{59} +(1.99000 + 3.44678i) q^{61} +(-2.18663 + 3.78736i) q^{63} +(-1.04087 - 1.80283i) q^{65} +(2.50950 + 7.79118i) q^{67} +(3.49083 + 6.04630i) q^{69} +(0.0217755 - 0.0377163i) q^{71} +(4.49932 + 7.79305i) q^{73} +1.00000 q^{75} +(6.54008 + 11.3278i) q^{77} +(-0.453494 + 0.785474i) q^{79} +1.00000 q^{81} +(1.41204 + 2.44573i) q^{83} +(-0.454199 - 0.786696i) q^{85} +(3.93896 - 6.82248i) q^{87} +2.76333 q^{89} +9.10397 q^{91} +(-3.83972 + 6.65058i) q^{93} +(3.53072 + 6.11538i) q^{95} +(0.274039 + 0.474649i) q^{97} +(1.49547 - 2.59023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

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

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
$7$	−2.18663	+	3.78736i	−0.826470	+	1.43149i	0.0743207	+	0.997234i	$0.476321\pi$
$7$	−2.18663	+	3.78736i	−0.826470	+	1.43149i	−0.900791	+	0.434254i	$0.857012\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.49547	−	2.59023i	0.450900	−	0.780982i	−0.547542	−	0.836778i	$-0.684436\pi$
$11$	1.49547	−	2.59023i	0.450900	−	0.780982i	0.998442	+	0.0557959i	$0.0177696\pi$
$12$		0			0
$13$	−1.04087	−	1.80283i	−0.288684	−	0.500016i	0.684812	−	0.728720i	$-0.259884\pi$
$13$	−1.04087	−	1.80283i	−0.288684	−	0.500016i	−0.973496	+	0.228704i	$0.926551\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−0.454199	−	0.786696i	−0.110159	−	0.190802i	0.805675	−	0.592358i	$-0.201803\pi$
$17$	−0.454199	−	0.786696i	−0.110159	−	0.190802i	−0.915834	+	0.401556i	$0.868469\pi$
$18$		0			0
$19$	3.53072	+	6.11538i	0.810002	+	1.40297i	0.912862	+	0.408269i	$0.133868\pi$
$19$	3.53072	+	6.11538i	0.810002	+	1.40297i	−0.102859	+	0.994696i	$0.532799\pi$
$20$		0			0
$21$	−2.18663	+	3.78736i	−0.477163	+	0.826470i
$22$		0			0
$23$	3.49083	+	6.04630i	0.727889	+	1.26074i	0.957774	+	0.287523i	$0.0928319\pi$
$23$	3.49083	+	6.04630i	0.727889	+	1.26074i	−0.229884	+	0.973218i	$0.573835\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.93896	−	6.82248i	0.731447	−	1.26690i	−0.224818	−	0.974401i	$-0.572179\pi$
$29$	3.93896	−	6.82248i	0.731447	−	1.26690i	0.956265	−	0.292502i	$-0.0944879\pi$
$30$		0			0
$31$	−3.83972	+	6.65058i	−0.689633	+	1.19448i	0.282323	+	0.959319i	$0.408895\pi$
$31$	−3.83972	+	6.65058i	−0.689633	+	1.19448i	−0.971957	+	0.235161i	$0.924438\pi$
$32$		0			0
$33$	1.49547	−	2.59023i	0.260327	−	0.450900i
$34$		0			0
$35$	−2.18663	+	3.78736i	−0.369609	+	0.640181i
$36$		0			0
$37$	−0.417228	−	0.722660i	−0.0685919	−	0.118805i	0.829690	−	0.558225i	$-0.188517\pi$
$37$	−0.417228	−	0.722660i	−0.0685919	−	0.118805i	−0.898282	+	0.439420i	$0.855184\pi$
$38$		0			0
$39$	−1.04087	−	1.80283i	−0.166672	−	0.288684i
$40$		0			0
$41$	−1.33572	+	2.31353i	−0.208604	+	0.361313i	−0.951275	−	0.308343i	$-0.900225\pi$
$41$	−1.33572	+	2.31353i	−0.208604	+	0.361313i	0.742671	+	0.669657i	$0.233559\pi$
$42$		0			0
$43$	−12.0882			−1.84343			−0.921713	−	0.387872i	$-0.873210\pi$
$43$	−12.0882			−1.84343			−0.921713	+	0.387872i	$0.873210\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	0.436600	−	0.756213i	0.0636846	−	0.110305i	−0.832425	−	0.554138i	$-0.813048\pi$
$47$	0.436600	−	0.756213i	0.0636846	−	0.110305i	0.896110	+	0.443833i	$0.146382\pi$
$48$		0			0
$49$	−6.06274	−	10.5010i	−0.866105	−	1.50014i
$50$		0			0
$51$	−0.454199	−	0.786696i	−0.0636006	−	0.110159i
$52$		0			0
$53$	7.39196			1.01536			0.507682	−	0.861545i	$-0.330502\pi$
$53$	7.39196			1.01536			0.507682	+	0.861545i	$0.330502\pi$
$54$		0			0
$55$	1.49547	−	2.59023i	0.201649	−	0.349266i
$56$		0			0
$57$	3.53072	+	6.11538i	0.467655	+	0.810002i
$58$		0			0
$59$	−1.81848			−0.236746			−0.118373	−	0.992969i	$-0.537768\pi$
$59$	−1.81848			−0.236746			−0.118373	+	0.992969i	$0.537768\pi$
$60$		0			0
$61$	1.99000	+	3.44678i	0.254793	+	0.441315i	0.964839	−	0.262840i	$-0.0846592\pi$
$61$	1.99000	+	3.44678i	0.254793	+	0.441315i	−0.710046	+	0.704155i	$0.751326\pi$
$62$		0			0
$63$	−2.18663	+	3.78736i	−0.275490	+	0.477163i
$64$		0			0
$65$	−1.04087	−	1.80283i	−0.129104	−	0.223614i
$66$		0			0
$67$	2.50950	+	7.79118i	0.306584	+	0.951844i
$67$	2.50950	+	7.79118i	0.306584	+	0.951844i
$68$		0			0
$69$	3.49083	+	6.04630i	0.420247	+	0.727889i
$70$		0			0
$71$	0.0217755	−	0.0377163i	0.00258428	−	0.00447610i	−0.864730	−	0.502236i	$-0.832511\pi$
$71$	0.0217755	−	0.0377163i	0.00258428	−	0.00447610i	0.867315	+	0.497760i	$0.165844\pi$
$72$		0			0
$73$	4.49932	+	7.79305i	0.526606	+	0.912108i	0.999519	+	0.0309989i	$0.00986884\pi$
$73$	4.49932	+	7.79305i	0.526606	+	0.912108i	−0.472914	+	0.881109i	$0.656798\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	6.54008	+	11.3278i	0.745311	+	1.29092i
$78$		0			0
$79$	−0.453494	+	0.785474i	−0.0510221	+	0.0883728i	−0.890408	−	0.455162i	$-0.849581\pi$
$79$	−0.453494	+	0.785474i	−0.0510221	+	0.0883728i	0.839386	+	0.543535i	$0.182915\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	1.41204	+	2.44573i	0.154992	+	0.268454i	0.933056	−	0.359731i	$-0.117132\pi$
$83$	1.41204	+	2.44573i	0.154992	+	0.268454i	−0.778064	+	0.628185i	$0.783798\pi$
$84$		0			0
$85$	−0.454199	−	0.786696i	−0.0492648	−	0.0853291i
$86$		0			0
$87$	3.93896	−	6.82248i	0.422301	−	0.731447i
$88$		0			0
$89$	2.76333			0.292912			0.146456	−	0.989217i	$-0.453213\pi$
$89$	2.76333			0.292912			0.146456	+	0.989217i	$0.453213\pi$
$90$		0			0
$91$	9.10397			0.954356
$92$		0			0
$93$	−3.83972	+	6.65058i	−0.398160	+	0.689633i
$94$		0			0
$95$	3.53072	+	6.11538i	0.362244	+	0.627425i
$96$		0			0
$97$	0.274039	+	0.474649i	0.0278244	+	0.0481933i	0.879602	−	0.475710i	$-0.157809\pi$
$97$	0.274039	+	0.474649i	0.0278244	+	0.0481933i	−0.851778	+	0.523903i	$0.824475\pi$
$98$		0			0
$99$	1.49547	−	2.59023i	0.150300	−	0.260327i
$100$		0			0
$101$	0.346371	−	0.599931i	0.0344652	−	0.0596954i	−0.848278	−	0.529551i	$-0.822361\pi$
$101$	0.346371	−	0.599931i	0.0344652	−	0.0596954i	0.882743	+	0.469855i	$0.155694\pi$
$102$		0			0
$103$	−7.65401	+	13.2571i	−0.754172	+	1.30626i	0.191613	+	0.981471i	$0.438628\pi$
$103$	−7.65401	+	13.2571i	−0.754172	+	1.30626i	−0.945785	+	0.324794i	$0.894705\pi$
$104$		0			0
$105$	−2.18663	+	3.78736i	−0.213394	+	0.369609i
$106$		0			0
$107$	6.42328			0.620962			0.310481	−	0.950580i	$-0.399510\pi$
$107$	6.42328			0.620962			0.310481	+	0.950580i	$0.399510\pi$
$108$		0			0
$109$	1.66310			0.159296			0.0796481	−	0.996823i	$-0.474620\pi$
$109$	1.66310			0.159296			0.0796481	+	0.996823i	$0.474620\pi$
$110$		0			0
$111$	−0.417228	−	0.722660i	−0.0396015	−	0.0685919i
$112$		0			0
$113$	−7.20189	+	12.4740i	−0.677496	+	1.17346i	0.298236	+	0.954492i	$0.403602\pi$
$113$	−7.20189	+	12.4740i	−0.677496	+	1.17346i	−0.975732	+	0.218966i	$0.929732\pi$
$114$		0			0
$115$	3.49083	+	6.04630i	0.325522	+	0.563821i
$116$		0			0
$117$	−1.04087	−	1.80283i	−0.0962281	−	0.166672i
$118$		0			0
$119$	3.97267			0.364174
$120$		0			0
$121$	1.02715	+	1.77908i	0.0933776	+	0.161735i
$122$		0			0
$123$	−1.33572	+	2.31353i	−0.120438	+	0.208604i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	4.44194	−	7.69366i	0.394158	−	0.682702i	−0.598835	−	0.800872i	$-0.704370\pi$
$127$	4.44194	−	7.69366i	0.394158	−	0.682702i	0.992993	+	0.118171i	$0.0377029\pi$
$128$		0			0
$129$	−12.0882			−1.06430
$130$		0			0
$131$	−3.70567			−0.323766			−0.161883	−	0.986810i	$-0.551757\pi$
$131$	−3.70567			−0.323766			−0.161883	+	0.986810i	$0.551757\pi$
$132$		0			0
$133$	−30.8816			−2.67777
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−17.0338			−1.45530			−0.727648	−	0.685951i	$-0.759386\pi$
$137$	−17.0338			−1.45530			−0.727648	+	0.685951i	$0.759386\pi$
$138$		0			0
$139$	4.20074			0.356302			0.178151	−	0.984003i	$-0.442988\pi$
$139$	4.20074			0.356302			0.178151	+	0.984003i	$0.442988\pi$
$140$		0			0
$141$	0.436600	−	0.756213i	0.0367683	−	0.0636846i
$142$		0			0
$143$	−6.22633			−0.520671
$144$		0			0
$145$	3.93896	−	6.82248i	0.327113	−	0.566576i
$146$		0			0
$147$	−6.06274	−	10.5010i	−0.500046	−	0.866105i
$148$		0			0
$149$	10.5719			0.866084			0.433042	−	0.901374i	$-0.357440\pi$
$149$	10.5719			0.866084			0.433042	+	0.901374i	$0.357440\pi$
$150$		0			0
$151$	7.55070	+	13.0782i	0.614468	+	1.06429i	0.990478	+	0.137673i	$0.0439625\pi$
$151$	7.55070	+	13.0782i	0.614468	+	1.06429i	−0.376010	+	0.926616i	$0.622704\pi$
$152$		0			0
$153$	−0.454199	−	0.786696i	−0.0367198	−	0.0636006i
$154$		0			0
$155$	−3.83972	+	6.65058i	−0.308413	+	0.534188i
$156$		0			0
$157$	5.40208	+	9.35667i	0.431133	+	0.746744i	0.996971	−	0.0777723i	$-0.0247807\pi$
$157$	5.40208	+	9.35667i	0.431133	+	0.746744i	−0.565838	+	0.824516i	$0.691447\pi$
$158$		0			0
$159$	7.39196			0.586221
$160$		0			0
$161$	−30.5327			−2.40631
$162$		0			0
$163$	−6.42050	+	11.1206i	−0.502893	+	0.871036i	0.497102	+	0.867692i	$0.334398\pi$
$163$	−6.42050	+	11.1206i	−0.502893	+	0.871036i	−0.999994	+	0.00334341i	$0.998936\pi$
$164$		0			0
$165$	1.49547	−	2.59023i	0.116422	−	0.201649i
$166$		0			0
$167$	10.1268	−	17.5401i	0.783635	−	1.35730i	−0.146176	−	0.989259i	$-0.546697\pi$
$167$	10.1268	−	17.5401i	0.783635	−	1.35730i	0.929811	−	0.368037i	$-0.119970\pi$
$168$		0			0
$169$	4.33320	−	7.50532i	0.333323	−	0.577332i
$170$		0			0
$171$	3.53072	+	6.11538i	0.270001	+	0.467655i
$172$		0			0
$173$	1.68539	+	2.91918i	0.128138	+	0.221941i	0.922955	−	0.384908i	$-0.125767\pi$
$173$	1.68539	+	2.91918i	0.128138	+	0.221941i	−0.794817	+	0.606849i	$0.792433\pi$
$174$		0			0
$175$	−2.18663	+	3.78736i	−0.165294	+	0.286298i
$176$		0			0
$177$	−1.81848			−0.136685
$178$		0			0
$179$	−8.54970			−0.639035			−0.319517	−	0.947580i	$-0.603521\pi$
$179$	−8.54970			−0.639035			−0.319517	+	0.947580i	$0.603521\pi$
$180$		0			0
$181$	2.30488	−	3.99218i	0.171321	−	0.296736i	−0.767561	−	0.640976i	$-0.778530\pi$
$181$	2.30488	−	3.99218i	0.171321	−	0.296736i	0.938882	+	0.344240i	$0.111863\pi$
$182$		0			0
$183$	1.99000	+	3.44678i	0.147105	+	0.254793i
$184$		0			0
$185$	−0.417228	−	0.722660i	−0.0306752	−	0.0531310i
$186$		0			0
$187$	−2.71696			−0.198684
$188$		0			0
$189$	−2.18663	+	3.78736i	−0.159054	+	0.275490i
$190$		0			0
$191$	−6.49218	−	11.2448i	−0.469758	−	0.813645i	0.529644	−	0.848220i	$-0.322325\pi$
$191$	−6.49218	−	11.2448i	−0.469758	−	0.813645i	−0.999402	+	0.0345753i	$0.988992\pi$
$192$		0			0
$193$	−10.1932			−0.733722			−0.366861	−	0.930276i	$-0.619568\pi$
$193$	−10.1932			−0.733722			−0.366861	+	0.930276i	$0.619568\pi$
$194$		0			0
$195$	−1.04087	−	1.80283i	−0.0745380	−	0.129104i
$196$		0			0
$197$	−9.06345	+	15.6984i	−0.645744	+	1.11846i	0.338385	+	0.941008i	$0.390119\pi$
$197$	−9.06345	+	15.6984i	−0.645744	+	1.11846i	−0.984129	+	0.177454i	$0.943214\pi$
$198$		0			0
$199$	9.84561	+	17.0531i	0.697937	+	1.20886i	0.969181	+	0.246351i	$0.0792317\pi$
$199$	9.84561	+	17.0531i	0.697937	+	1.20886i	−0.271244	+	0.962511i	$0.587435\pi$
$200$		0			0
$201$	2.50950	+	7.79118i	0.177006	+	0.549547i
$202$		0			0
$203$	17.2261	+	29.8365i	1.20904	+	2.09411i
$204$		0			0
$205$	−1.33572	+	2.31353i	−0.0932907	+	0.161584i
$206$		0			0
$207$	3.49083	+	6.04630i	0.242630	+	0.420247i
$208$		0			0
$209$	21.1203			1.46092
$210$		0			0
$211$	−10.5249	−	18.2296i	−0.724563	−	1.25498i	−0.959153	−	0.282886i	$-0.908708\pi$
$211$	−10.5249	−	18.2296i	−0.724563	−	1.25498i	0.234590	−	0.972094i	$-0.424625\pi$
$212$		0			0
$213$	0.0217755	−	0.0377163i	0.00149203	−	0.00258428i
$214$		0			0
$215$	−12.0882			−0.824405
$216$		0			0
$217$	−16.7921	−	29.0848i	−1.13992	−	1.97440i
$218$		0			0
$219$	4.49932	+	7.79305i	0.304036	+	0.526606i
$220$		0			0
$221$	−0.945520	+	1.63769i	−0.0636026	+	0.110163i
$222$		0			0
$223$	−12.4616			−0.834488			−0.417244	−	0.908794i	$-0.637004\pi$
$223$	−12.4616			−0.834488			−0.417244	+	0.908794i	$0.637004\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−5.36483	+	9.29216i	−0.356076	+	0.616742i	−0.987302	−	0.158857i	$-0.949219\pi$
$227$	−5.36483	+	9.29216i	−0.356076	+	0.616742i	0.631225	+	0.775600i	$0.282552\pi$
$228$		0			0
$229$	−7.19516	−	12.4624i	−0.475469	−	0.823537i	0.524136	−	0.851635i	$-0.324388\pi$
$229$	−7.19516	−	12.4624i	−0.475469	−	0.823537i	−0.999605	+	0.0280976i	$0.991055\pi$
$230$		0			0
$231$	6.54008	+	11.3278i	0.430306	+	0.745311i
$232$		0			0
$233$	−1.88321	+	3.26182i	−0.123373	+	0.213689i	−0.921096	−	0.389336i	$-0.872705\pi$
$233$	−1.88321	+	3.26182i	−0.123373	+	0.213689i	0.797723	+	0.603025i	$0.206038\pi$
$234$		0			0
$235$	0.436600	−	0.756213i	0.0284806	−	0.0493299i
$236$		0			0
$237$	−0.453494	+	0.785474i	−0.0294576	+	0.0510221i
$238$		0			0
$239$	0.447416	−	0.774947i	0.0289409	−	0.0501272i	−0.851192	−	0.524854i	$-0.824120\pi$
$239$	0.447416	−	0.774947i	0.0289409	−	0.0501272i	0.880133	+	0.474727i	$0.157453\pi$
$240$		0			0
$241$	−20.3244			−1.30921			−0.654603	−	0.755972i	$-0.727164\pi$
$241$	−20.3244			−1.30921			−0.654603	+	0.755972i	$0.727164\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−6.06274	−	10.5010i	−0.387334	−	0.670882i
$246$		0			0
$247$	7.35001	−	12.7306i	0.467670	−	0.810028i
$248$		0			0
$249$	1.41204	+	2.44573i	0.0894845	+	0.154992i
$250$		0			0
$251$	8.24998	+	14.2894i	0.520734	+	0.901938i	0.999709	+	0.0241096i	$0.00767508\pi$
$251$	8.24998	+	14.2894i	0.520734	+	0.901938i	−0.478975	+	0.877828i	$0.658992\pi$
$252$		0			0
$253$	20.8817			1.31282
$254$		0			0
$255$	−0.454199	−	0.786696i	−0.0284430	−	0.0492648i
$256$		0			0
$257$	−9.99116	+	17.3052i	−0.623231	+	1.07947i	0.365649	+	0.930753i	$0.380847\pi$
$257$	−9.99116	+	17.3052i	−0.623231	+	1.07947i	−0.988880	+	0.148715i	$0.952486\pi$
$258$		0			0
$259$	3.64930			0.226757
$260$		0			0
$261$	3.93896	−	6.82248i	0.243816	−	0.422301i
$262$		0			0
$263$	22.0971			1.36257			0.681284	−	0.732019i	$-0.261422\pi$
$263$	22.0971			1.36257			0.681284	+	0.732019i	$0.261422\pi$
$264$		0			0
$265$	7.39196			0.454085
$266$		0			0
$267$	2.76333			0.169113
$268$		0			0
$269$	19.1061			1.16492			0.582459	−	0.812860i	$-0.302091\pi$
$269$	19.1061			1.16492			0.582459	+	0.812860i	$0.302091\pi$
$270$		0			0
$271$	15.1078			0.917736			0.458868	−	0.888504i	$-0.348255\pi$
$271$	15.1078			0.917736			0.458868	+	0.888504i	$0.348255\pi$
$272$		0			0
$273$	9.10397			0.550997
$274$		0			0
$275$	1.49547	−	2.59023i	0.0901801	−	0.156196i
$276$		0			0
$277$	13.5221			0.812465			0.406233	−	0.913770i	$-0.366842\pi$
$277$	13.5221			0.812465			0.406233	+	0.913770i	$0.366842\pi$
$278$		0			0
$279$	−3.83972	+	6.65058i	−0.229878	+	0.398160i
$280$		0			0
$281$	−5.59295	−	9.68728i	−0.333648	−	0.577895i	0.649577	−	0.760296i	$-0.274946\pi$
$281$	−5.59295	−	9.68728i	−0.333648	−	0.577895i	−0.983224	+	0.182402i	$0.941613\pi$
$282$		0			0
$283$	31.3977			1.86640			0.933201	−	0.359356i	$-0.117004\pi$
$283$	31.3977			1.86640			0.933201	+	0.359356i	$0.117004\pi$
$284$		0			0
$285$	3.53072	+	6.11538i	0.209142	+	0.362244i
$286$		0			0
$287$	−5.84146	−	10.1177i	−0.344810	−	0.597229i
$288$		0			0
$289$	8.08741	−	14.0078i	0.475730	−	0.823988i
$290$		0			0
$291$	0.274039	+	0.474649i	0.0160644	+	0.0278244i
$292$		0			0
$293$	0.857561			0.0500992			0.0250496	−	0.999686i	$-0.492026\pi$
$293$	0.857561			0.0500992			0.0250496	+	0.999686i	$0.492026\pi$
$294$		0			0
$295$	−1.81848			−0.105876
$296$		0			0
$297$	1.49547	−	2.59023i	0.0867758	−	0.150300i
$298$		0			0
$299$	7.26698	−	12.5868i	0.420260	−	0.727912i
$300$		0			0
$301$	26.4324	−	45.7822i	1.52354	−	2.63884i
$302$		0			0
$303$	0.346371	−	0.599931i	0.0198985	−	0.0344652i
$304$		0			0
$305$	1.99000	+	3.44678i	0.113947	+	0.197362i
$306$		0			0
$307$	−3.19008	−	5.52538i	−0.182067	−	0.315350i	0.760517	−	0.649318i	$-0.224946\pi$
$307$	−3.19008	−	5.52538i	−0.182067	−	0.315350i	−0.942584	+	0.333968i	$0.891612\pi$
$308$		0			0
$309$	−7.65401	+	13.2571i	−0.435421	+	0.754172i
$310$		0			0
$311$	21.0122			1.19150			0.595748	−	0.803172i	$-0.296856\pi$
$311$	21.0122			1.19150			0.595748	+	0.803172i	$0.296856\pi$
$312$		0			0
$313$	−13.7198			−0.775489			−0.387745	−	0.921767i	$-0.626746\pi$
$313$	−13.7198			−0.775489			−0.387745	+	0.921767i	$0.626746\pi$
$314$		0			0
$315$	−2.18663	+	3.78736i	−0.123203	+	0.213394i
$316$		0			0
$317$	4.53972	+	7.86302i	0.254976	+	0.441631i	0.964889	−	0.262658i	$-0.0845991\pi$
$317$	4.53972	+	7.86302i	0.254976	+	0.441631i	−0.709913	+	0.704289i	$0.751266\pi$
$318$		0			0
$319$	−11.7812	−	20.4056i	−0.659619	−	1.14249i
$320$		0			0
$321$	6.42328			0.358512
$322$		0			0
$323$	3.20730	−	5.55520i	0.178459	−	0.309100i
$324$		0			0
$325$	−1.04087	−	1.80283i	−0.0577369	−	0.100003i
$326$		0			0
$327$	1.66310			0.0919697
$328$		0			0
$329$	1.90937	+	3.30712i	0.105267	+	0.182327i
$330$		0			0
$331$	−4.36593	+	7.56201i	−0.239973	+	0.415646i	−0.960706	−	0.277567i	$-0.910472\pi$
$331$	−4.36593	+	7.56201i	−0.239973	+	0.415646i	0.720733	+	0.693213i	$0.243805\pi$
$332$		0			0
$333$	−0.417228	−	0.722660i	−0.0228640	−	0.0396015i
$334$		0			0
$335$	2.50950	+	7.79118i	0.137109	+	0.425677i
$336$		0			0
$337$	−15.1782	−	26.2894i	−0.826807	−	1.43207i	−0.900530	−	0.434793i	$-0.856821\pi$
$337$	−15.1782	−	26.2894i	−0.826807	−	1.43207i	0.0737229	−	0.997279i	$-0.476512\pi$
$338$		0			0
$339$	−7.20189	+	12.4740i	−0.391153	+	0.677496i
$340$		0			0
$341$	11.4843	+	19.8915i	0.621912	+	1.07718i
$342$		0			0
$343$	22.4151			1.21030
$344$		0			0
$345$	3.49083	+	6.04630i	0.187940	+	0.325522i
$346$		0			0
$347$	−2.79561	+	4.84214i	−0.150076	+	0.259940i	−0.931255	−	0.364367i	$-0.881285\pi$
$347$	−2.79561	+	4.84214i	−0.150076	+	0.259940i	0.781179	+	0.624307i	$0.214619\pi$
$348$		0			0
$349$	36.7337			1.96631			0.983154	−	0.182781i	$-0.0585098\pi$
$349$	36.7337			1.96631			0.983154	+	0.182781i	$0.0585098\pi$
$350$		0			0
$351$	−1.04087	−	1.80283i	−0.0555573	−	0.0962281i
$352$		0			0
$353$	−2.21593	−	3.83811i	−0.117942	−	0.204282i	0.801010	−	0.598651i	$-0.204296\pi$
$353$	−2.21593	−	3.83811i	−0.117942	−	0.204282i	−0.918952	+	0.394369i	$0.870963\pi$
$354$		0			0
$355$	0.0217755	−	0.0377163i	0.00115572	−	0.00200177i
$356$		0			0
$357$	3.97267			0.210256
$358$		0			0
$359$	−8.95476			−0.472614			−0.236307	−	0.971678i	$-0.575937\pi$
$359$	−8.95476			−0.472614			−0.236307	+	0.971678i	$0.575937\pi$
$360$		0			0
$361$	−15.4319	+	26.7289i	−0.812208	+	1.40678i
$362$		0			0
$363$	1.02715	+	1.77908i	0.0539116	+	0.0933776i
$364$		0			0
$365$	4.49932	+	7.79305i	0.235505	+	0.407907i
$366$		0			0
$367$	8.80302	−	15.2473i	0.459514	−	0.795901i	−0.539421	−	0.842036i	$-0.681357\pi$
$367$	8.80302	−	15.2473i	0.459514	−	0.795901i	0.998935	+	0.0461347i	$0.0146903\pi$
$368$		0			0
$369$	−1.33572	+	2.31353i	−0.0695348	+	0.120438i
$370$		0			0
$371$	−16.1635	+	27.9960i	−0.839168	+	1.45348i
$372$		0			0
$373$	4.17950	−	7.23911i	0.216406	−	0.374827i	−0.737300	−	0.675565i	$-0.763900\pi$
$373$	4.17950	−	7.23911i	0.216406	−	0.374827i	0.953707	+	0.300738i	$0.0972331\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−16.3997			−0.844629
$378$		0			0
$379$	−6.77956	−	11.7425i	−0.348243	−	0.603174i	0.637695	−	0.770289i	$-0.279888\pi$
$379$	−6.77956	−	11.7425i	−0.348243	−	0.603174i	−0.985937	+	0.167115i	$0.946555\pi$
$380$		0			0
$381$	4.44194	−	7.69366i	0.227567	−	0.394158i
$382$		0			0
$383$	−5.07543	−	8.79091i	−0.259343	−	0.449195i	0.706723	−	0.707490i	$-0.250173\pi$
$383$	−5.07543	−	8.79091i	−0.259343	−	0.449195i	−0.966066	+	0.258295i	$0.916839\pi$
$384$		0			0
$385$	6.54008	+	11.3278i	0.333313	+	0.577316i
$386$		0			0
$387$	−12.0882			−0.614476
$388$		0			0
$389$	−3.92875	−	6.80480i	−0.199196	−	0.345017i	0.749072	−	0.662488i	$-0.230500\pi$
$389$	−3.92875	−	6.80480i	−0.199196	−	0.345017i	−0.948268	+	0.317471i	$0.897166\pi$
$390$		0			0
$391$	3.17107	−	5.49245i	0.160368	−	0.277765i
$392$		0			0
$393$	−3.70567			−0.186926
$394$		0			0
$395$	−0.453494	+	0.785474i	−0.0228178	+	0.0395215i
$396$		0			0
$397$	10.6770			0.535861			0.267931	−	0.963438i	$-0.413660\pi$
$397$	10.6770			0.535861			0.267931	+	0.963438i	$0.413660\pi$
$398$		0			0
$399$	−30.8816			−1.54601
$400$		0			0
$401$	−23.0544			−1.15128			−0.575641	−	0.817703i	$-0.695247\pi$
$401$	−23.0544			−1.15128			−0.575641	+	0.817703i	$0.695247\pi$
$402$		0			0
$403$	15.9865			0.796345
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−2.49580			−0.123712
$408$		0			0
$409$	−9.74620	+	16.8809i	−0.481918	+	0.834707i	−0.999785	−	0.0207545i	$-0.993393\pi$
$409$	−9.74620	+	16.8809i	−0.481918	+	0.834707i	0.517866	+	0.855462i	$0.326726\pi$
$410$		0			0
$411$	−17.0338			−0.840215
$412$		0			0
$413$	3.97635	−	6.88724i	0.195663	−	0.338899i
$414$		0			0
$415$	1.41204	+	2.44573i	0.0693144	+	0.120056i
$416$		0			0
$417$	4.20074			0.205711
$418$		0			0
$419$	−13.4661	−	23.3240i	−0.657863	−	1.13945i	−0.981168	−	0.193158i	$-0.938127\pi$
$419$	−13.4661	−	23.3240i	−0.657863	−	1.13945i	0.323304	−	0.946295i	$-0.395206\pi$
$420$		0			0
$421$	−11.5808	−	20.0585i	−0.564411	−	0.977589i	−0.997104	−	0.0760477i	$-0.975770\pi$
$421$	−11.5808	−	20.0585i	−0.564411	−	0.977589i	0.432693	−	0.901541i	$-0.357563\pi$
$422$		0			0
$423$	0.436600	−	0.756213i	0.0212282	−	0.0367683i
$424$		0			0
$425$	−0.454199	−	0.786696i	−0.0220319	−	0.0381603i
$426$		0			0
$427$	−17.4056			−0.842316
$428$		0			0
$429$	−6.22633			−0.300610
$430$		0			0
$431$	−5.01576	+	8.68755i	−0.241601	+	0.418465i	−0.961170	−	0.275956i	$-0.911006\pi$
$431$	−5.01576	+	8.68755i	−0.241601	+	0.418465i	0.719570	+	0.694420i	$0.244339\pi$
$432$		0			0
$433$	6.20238	−	10.7428i	0.298067	−	0.516267i	−0.677627	−	0.735406i	$-0.736991\pi$
$433$	6.20238	−	10.7428i	0.298067	−	0.516267i	0.975694	+	0.219139i	$0.0703247\pi$
$434$		0			0
$435$	3.93896	−	6.82248i	0.188859	−	0.327113i
$436$		0			0
$437$	−24.6503	+	42.6956i	−1.17918	+	2.04241i
$438$		0			0
$439$	−4.61849	−	7.99945i	−0.220428	−	0.381793i	0.734510	−	0.678598i	$-0.237412\pi$
$439$	−4.61849	−	7.99945i	−0.220428	−	0.381793i	−0.954938	+	0.296805i	$0.904079\pi$
$440$		0			0
$441$	−6.06274	−	10.5010i	−0.288702	−	0.500046i
$442$		0			0
$443$	−0.837559	+	1.45070i	−0.0397937	+	0.0689246i	−0.885236	−	0.465142i	$-0.846003\pi$
$443$	−0.837559	+	1.45070i	−0.0397937	+	0.0689246i	0.845443	+	0.534066i	$0.179337\pi$
$444$		0			0
$445$	2.76333			0.130994
$446$		0			0
$447$	10.5719			0.500034
$448$		0			0
$449$	−10.4119	+	18.0339i	−0.491366	+	0.851071i	−0.999951	−	0.00994101i	$-0.996836\pi$
$449$	−10.4119	+	18.0339i	−0.491366	+	0.851071i	0.508584	+	0.861012i	$0.330169\pi$
$450$		0			0
$451$	3.99505	+	6.91963i	0.188120	+	0.325833i
$452$		0			0
$453$	7.55070	+	13.0782i	0.354763	+	0.614468i
$454$		0			0
$455$	9.10397			0.426801
$456$		0			0
$457$	17.9737	−	31.1314i	0.840774	−	1.45626i	−0.0484666	−	0.998825i	$-0.515433\pi$
$457$	17.9737	−	31.1314i	0.840774	−	1.45626i	0.889241	−	0.457439i	$-0.151233\pi$
$458$		0			0
$459$	−0.454199	−	0.786696i	−0.0212002	−	0.0367198i
$460$		0			0
$461$	17.9362			0.835370			0.417685	−	0.908592i	$-0.362842\pi$
$461$	17.9362			0.835370			0.417685	+	0.908592i	$0.362842\pi$
$462$		0			0
$463$	1.88693	+	3.26826i	0.0876932	+	0.151889i	0.906536	−	0.422129i	$-0.138717\pi$
$463$	1.88693	+	3.26826i	0.0876932	+	0.151889i	−0.818842	+	0.574018i	$0.805384\pi$
$464$		0			0
$465$	−3.83972	+	6.65058i	−0.178063	+	0.308413i
$466$		0			0
$467$	−14.6753	−	25.4183i	−0.679091	−	1.17622i	−0.975255	−	0.221082i	$-0.929041\pi$
$467$	−14.6753	−	25.4183i	−0.679091	−	1.17622i	0.296165	−	0.955137i	$-0.404292\pi$
$468$		0			0
$469$	−34.9954	−	7.53207i	−1.61594	−	0.347799i
$470$		0			0
$471$	5.40208	+	9.35667i	0.248915	+	0.431133i
$472$		0			0
$473$	−18.0774	+	31.3111i	−0.831202	+	1.43968i
$474$		0			0
$475$	3.53072	+	6.11538i	0.162000	+	0.280593i
$476$		0			0
$477$	7.39196			0.338455
$478$		0			0
$479$	−7.28475	−	12.6176i	−0.332849	−	0.576511i	0.650220	−	0.759746i	$-0.274677\pi$
$479$	−7.28475	−	12.6176i	−0.332849	−	0.576511i	−0.983069	+	0.183234i	$0.941343\pi$
$480$		0			0
$481$	−0.868557	+	1.50439i	−0.0396028	+	0.0685941i
$482$		0			0
$483$	−30.5327			−1.38929
$484$		0			0
$485$	0.274039	+	0.474649i	0.0124435	+	0.0215527i
$486$		0			0
$487$	−2.94405	−	5.09925i	−0.133408	−	0.231069i	0.791580	−	0.611065i	$-0.209259\pi$
$487$	−2.94405	−	5.09925i	−0.133408	−	0.231069i	−0.924988	+	0.379996i	$0.875925\pi$
$488$		0			0
$489$	−6.42050	+	11.1206i	−0.290345	+	0.502893i
$490$		0			0
$491$	19.8188			0.894410			0.447205	−	0.894431i	$-0.352419\pi$
$491$	19.8188			0.894410			0.447205	+	0.894431i	$0.352419\pi$
$492$		0			0
$493$	−7.15629			−0.322303
$494$		0			0
$495$	1.49547	−	2.59023i	0.0672163	−	0.116422i
$496$		0			0
$497$	0.0952302	+	0.164944i	0.00427166	+	0.00739873i
$498$		0			0
$499$	5.09991	+	8.83331i	0.228304	+	0.395433i	0.957305	−	0.289078i	$-0.0933488\pi$
$499$	5.09991	+	8.83331i	0.228304	+	0.395433i	−0.729002	+	0.684512i	$0.760015\pi$
$500$		0			0
$501$	10.1268	−	17.5401i	0.452432	−	0.783635i
$502$		0			0
$503$	−11.2004	+	19.3996i	−0.499401	+	0.864987i	−1.00000		0.000691938i	$-0.999780\pi$
$503$	−11.2004	+	19.3996i	−0.499401	+	0.864987i	0.500599	+	0.865679i	$0.333113\pi$
$504$		0			0
$505$	0.346371	−	0.599931i	0.0154133	−	0.0266966i
$506$		0			0
$507$	4.33320	−	7.50532i	0.192444	−	0.333323i
$508$		0			0
$509$	26.4309			1.17153			0.585765	−	0.810481i	$-0.300794\pi$
$509$	26.4309			1.17153			0.585765	+	0.810481i	$0.300794\pi$
$510$		0			0
$511$	−39.3535			−1.74089
$512$		0			0
$513$	3.53072	+	6.11538i	0.155885	+	0.270001i
$514$		0			0
$515$	−7.65401	+	13.2571i	−0.337276	+	0.584179i
$516$		0			0
$517$	−1.30584	−	2.26178i	−0.0574308	−	0.0994731i
$518$		0			0
$519$	1.68539	+	2.91918i	0.0739803	+	0.128138i
$520$		0			0
$521$	20.0477			0.878304			0.439152	−	0.898413i	$-0.355279\pi$
$521$	20.0477			0.878304			0.439152	+	0.898413i	$0.355279\pi$
$522$		0			0
$523$	−10.3772	−	17.9739i	−0.453764	−	0.785943i	0.544852	−	0.838532i	$-0.316586\pi$
$523$	−10.3772	−	17.9739i	−0.453764	−	0.785943i	−0.998616	+	0.0525894i	$0.983253\pi$
$524$		0			0
$525$	−2.18663	+	3.78736i	−0.0954325	+	0.165294i
$526$		0			0
$527$	6.97598			0.303878
$528$		0			0
$529$	−12.8719	+	22.2947i	−0.559646	+	0.969335i
$530$		0			0
$531$	−1.81848			−0.0789153
$532$		0			0
$533$	5.56122			0.240883
$534$		0			0
$535$	6.42328			0.277702
$536$		0			0
$537$	−8.54970			−0.368947
$538$		0			0
$539$	−36.2665			−1.56211
$540$		0			0
$541$	0.500503			0.0215183			0.0107592	−	0.999942i	$-0.496575\pi$
$541$	0.500503			0.0215183			0.0107592	+	0.999942i	$0.496575\pi$
$542$		0			0
$543$	2.30488	−	3.99218i	0.0989120	−	0.171321i
$544$		0			0
$545$	1.66310			0.0712395
$546$		0			0
$547$	17.1918	−	29.7771i	0.735070	−	1.27318i	−0.219622	−	0.975585i	$-0.570483\pi$
$547$	17.1918	−	29.7771i	0.735070	−	1.27318i	0.954693	−	0.297594i	$-0.0961842\pi$
$548$		0			0
$549$	1.99000	+	3.44678i	0.0849311	+	0.147105i
$550$		0			0
$551$	55.6295			2.36989
$552$		0			0
$553$	−1.98325	−	3.43509i	−0.0843364	−	0.146075i
$554$		0			0
$555$	−0.417228	−	0.722660i	−0.0177103	−	0.0306752i
$556$		0			0
$557$	−11.7577	+	20.3650i	−0.498192	+	0.862894i	−0.999998	−	0.00208665i	$-0.999336\pi$
$557$	−11.7577	+	20.3650i	−0.498192	+	0.862894i	0.501806	+	0.864980i	$0.332669\pi$
$558$		0			0
$559$	12.5822	+	21.7929i	0.532168	+	0.921743i
$560$		0			0
$561$	−2.71696			−0.114710
$562$		0			0
$563$	43.3432			1.82670			0.913350	−	0.407176i	$-0.133487\pi$
$563$	43.3432			1.82670			0.913350	+	0.407176i	$0.133487\pi$
$564$		0			0
$565$	−7.20189	+	12.4740i	−0.302986	+	0.524786i
$566$		0			0
$567$	−2.18663	+	3.78736i	−0.0918300	+	0.159054i
$568$		0			0
$569$	13.3419	−	23.1088i	0.559320	−	0.968770i	−0.438234	−	0.898861i	$-0.644396\pi$
$569$	13.3419	−	23.1088i	0.559320	−	0.968770i	0.997553	−	0.0699088i	$-0.0222708\pi$
$570$		0			0
$571$	−0.527129	+	0.913015i	−0.0220597	+	0.0382085i	−0.876844	−	0.480774i	$-0.840356\pi$
$571$	−0.527129	+	0.913015i	−0.0220597	+	0.0382085i	0.854785	+	0.518983i	$0.173689\pi$
$572$		0			0
$573$	−6.49218	−	11.2448i	−0.271215	−	0.469758i
$574$		0			0
$575$	3.49083	+	6.04630i	0.145578	+	0.252148i
$576$		0			0
$577$	9.28518	−	16.0824i	0.386547	−	0.669519i	−0.605435	−	0.795894i	$-0.707001\pi$
$577$	9.28518	−	16.0824i	0.386547	−	0.669519i	0.991983	+	0.126375i	$0.0403343\pi$
$578$		0			0
$579$	−10.1932			−0.423615
$580$		0			0
$581$	−12.3505			−0.512384
$582$		0			0
$583$	11.0544	−	19.1469i	0.457828	−	0.792982i
$584$		0			0
$585$	−1.04087	−	1.80283i	−0.0430345	−	0.0745380i
$586$		0			0
$587$	−10.8014	−	18.7086i	−0.445821	−	0.772185i	0.552288	−	0.833653i	$-0.313755\pi$
$587$	−10.8014	−	18.7086i	−0.445821	−	0.772185i	−0.998109	+	0.0614687i	$0.980422\pi$
$588$		0			0
$589$	−54.2278			−2.23442
$590$		0			0
$591$	−9.06345	+	15.6984i	−0.372821	+	0.645744i
$592$		0			0
$593$	24.1278	+	41.7906i	0.990811	+	1.71614i	0.612537	+	0.790442i	$0.290149\pi$
$593$	24.1278	+	41.7906i	0.990811	+	1.71614i	0.378275	+	0.925693i	$0.376517\pi$
$594$		0			0
$595$	3.97267			0.162863
$596$		0			0
$597$	9.84561	+	17.0531i	0.402954	+	0.697937i
$598$		0			0
$599$	−13.0066	+	22.5281i	−0.531436	+	0.920474i	0.467891	+	0.883786i	$0.345014\pi$
$599$	−13.0066	+	22.5281i	−0.531436	+	0.920474i	−0.999327	+	0.0366878i	$0.988319\pi$
$600$		0			0
$601$	−10.4264	−	18.0590i	−0.425302	−	0.736644i	0.571147	−	0.820848i	$-0.306499\pi$
$601$	−10.4264	−	18.0590i	−0.425302	−	0.736644i	−0.996449	+	0.0842039i	$0.973165\pi$
$602$		0			0
$603$	2.50950	+	7.79118i	0.102195	+	0.317281i
$604$		0			0
$605$	1.02715	+	1.77908i	0.0417597	+	0.0723300i
$606$		0			0
$607$	−3.02951	+	5.24727i	−0.122964	+	0.212980i	−0.920935	−	0.389715i	$-0.872573\pi$
$607$	−3.02951	+	5.24727i	−0.122964	+	0.212980i	0.797971	+	0.602696i	$0.205907\pi$
$608$		0			0
$609$	17.2261	+	29.8365i	0.698038	+	1.20904i
$610$		0			0
$611$	−1.81777			−0.0735390
$612$		0			0
$613$	13.3261	+	23.0815i	0.538236	+	0.932251i	0.998999	+	0.0447284i	$0.0142423\pi$
$613$	13.3261	+	23.0815i	0.538236	+	0.932251i	−0.460764	+	0.887523i	$0.652424\pi$
$614$		0			0
$615$	−1.33572	+	2.31353i	−0.0538614	+	0.0932907i
$616$		0			0
$617$	−23.4714			−0.944924			−0.472462	−	0.881351i	$-0.656635\pi$
$617$	−23.4714			−0.944924			−0.472462	+	0.881351i	$0.656635\pi$
$618$		0			0
$619$	−3.97219	−	6.88003i	−0.159656	−	0.276532i	0.775089	−	0.631852i	$-0.217705\pi$
$619$	−3.97219	−	6.88003i	−0.159656	−	0.276532i	−0.934745	+	0.355321i	$0.884372\pi$
$620$		0			0
$621$	3.49083	+	6.04630i	0.140082	+	0.242630i
$622$		0			0
$623$	−6.04239	+	10.4657i	−0.242083	+	0.419300i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	21.1203			0.843463
$628$		0			0
$629$	−0.379009	+	0.656463i	−0.0151121	+	0.0261749i
$630$		0			0
$631$	−21.0072	−	36.3856i	−0.836285	−	1.44849i	−0.892980	−	0.450097i	$-0.851389\pi$
$631$	−21.0072	−	36.3856i	−0.836285	−	1.44849i	0.0566945	−	0.998392i	$-0.481944\pi$
$632$		0			0
$633$	−10.5249	−	18.2296i	−0.418327	−	0.724563i
$634$		0			0
$635$	4.44194	−	7.69366i	0.176273	−	0.305313i
$636$		0			0
$637$	−12.6210	+	21.8602i	−0.500062	+	0.866133i
$638$		0			0
$639$	0.0217755	−	0.0377163i	0.000861426	−	0.00149203i
$640$		0			0
$641$	20.1762	−	34.9462i	0.796912	−	1.38029i	−0.124707	−	0.992194i	$-0.539799\pi$
$641$	20.1762	−	34.9462i	0.796912	−	1.38029i	0.921618	−	0.388098i	$-0.126868\pi$
$642$		0			0
$643$	11.4834			0.452862			0.226431	−	0.974027i	$-0.427294\pi$
$643$	11.4834			0.452862			0.226431	+	0.974027i	$0.427294\pi$
$644$		0			0
$645$	−12.0882			−0.475971
$646$		0			0
$647$	−17.0745	−	29.5740i	−0.671270	−	1.16267i	−0.977544	−	0.210730i	$-0.932416\pi$
$647$	−17.0745	−	29.5740i	−0.671270	−	1.16267i	0.306275	−	0.951943i	$-0.400917\pi$
$648$		0			0
$649$	−2.71948	+	4.71027i	−0.106749	+	0.184894i
$650$		0			0
$651$	−16.7921	−	29.0848i	−0.658135	−	1.13992i
$652$		0			0
$653$	−7.30873	−	12.6591i	−0.286013	−	0.495388i	0.686842	−	0.726807i	$-0.258997\pi$
$653$	−7.30873	−	12.6591i	−0.286013	−	0.495388i	−0.972854	+	0.231419i	$0.925663\pi$
$654$		0			0
$655$	−3.70567			−0.144793
$656$		0			0
$657$	4.49932	+	7.79305i	0.175535	+	0.304036i
$658$		0			0
$659$	9.49306	−	16.4425i	0.369797	−	0.640507i	−0.619736	−	0.784810i	$-0.712761\pi$
$659$	9.49306	−	16.4425i	0.369797	−	0.640507i	0.989534	+	0.144303i	$0.0460939\pi$
$660$		0			0
$661$	−8.42342			−0.327633			−0.163817	−	0.986491i	$-0.552381\pi$
$661$	−8.42342			−0.327633			−0.163817	+	0.986491i	$0.552381\pi$
$662$		0			0
$663$	−0.945520	+	1.63769i	−0.0367210	+	0.0636026i
$664$		0			0
$665$	−30.8816			−1.19754
$666$		0			0
$667$	55.0011			2.12965
$668$		0			0
$669$	−12.4616			−0.481792
$670$		0			0
$671$	11.9039			0.459546
$672$		0			0
$673$	22.6687			0.873814			0.436907	−	0.899507i	$-0.356074\pi$
$673$	22.6687			0.873814			0.436907	+	0.899507i	$0.356074\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	18.3304	−	31.7491i	0.704493	−	1.22022i	−0.262381	−	0.964964i	$-0.584508\pi$
$677$	18.3304	−	31.7491i	0.704493	−	1.22022i	0.966874	−	0.255253i	$-0.0821589\pi$
$678$		0			0
$679$	−2.39689			−0.0919842
$680$		0			0
$681$	−5.36483	+	9.29216i	−0.205581	+	0.356076i
$682$		0			0
$683$	16.2991	+	28.2309i	0.623668	+	1.08023i	0.988797	+	0.149268i	$0.0476918\pi$
$683$	16.2991	+	28.2309i	0.623668	+	1.08023i	−0.365128	+	0.930957i	$0.618975\pi$
$684$		0			0
$685$	−17.0338			−0.650828
$686$		0			0
$687$	−7.19516	−	12.4624i	−0.274512	−	0.475469i
$688$		0			0
$689$	−7.69404	−	13.3265i	−0.293120	−	0.507698i
$690$		0			0
$691$	13.9651	−	24.1882i	0.531257	−	0.920164i	−0.468077	−	0.883687i	$-0.655053\pi$
$691$	13.9651	−	24.1882i	0.531257	−	0.920164i	0.999335	−	0.0364767i	$-0.0116135\pi$
$692$		0			0
$693$	6.54008	+	11.3278i	0.248437	+	0.430306i
$694$		0			0
$695$	4.20074			0.159343
$696$		0			0
$697$	2.42673			0.0919189
$698$		0			0
$699$	−1.88321	+	3.26182i	−0.0712297	+	0.123373i
$700$		0			0
$701$	18.4378	−	31.9352i	0.696386	−	1.20618i	−0.273325	−	0.961922i	$-0.588124\pi$
$701$	18.4378	−	31.9352i	0.696386	−	1.20618i	0.969711	−	0.244254i	$-0.0785431\pi$
$702$		0			0
$703$	2.94623	−	5.10302i	0.111119	−	0.192464i
$704$		0			0
$705$	0.436600	−	0.756213i	0.0164433	−	0.0284806i
$706$		0			0
$707$	1.51477	+	2.62366i	0.0569688	+	0.0986729i
$708$		0			0
$709$	−8.62600	−	14.9407i	−0.323956	−	0.561109i	0.657344	−	0.753590i	$-0.271680\pi$
$709$	−8.62600	−	14.9407i	−0.323956	−	0.561109i	−0.981301	+	0.192482i	$0.938346\pi$
$710$		0			0
$711$	−0.453494	+	0.785474i	−0.0170074	+	0.0294576i
$712$		0			0
$713$	−53.6152			−2.00791
$714$		0			0
$715$	−6.22633			−0.232851
$716$		0			0
$717$	0.447416	−	0.774947i	0.0167091	−	0.0289409i
$718$		0			0
$719$	−16.7156	−	28.9523i	−0.623387	−	1.07974i	−0.988850	−	0.148912i	$-0.952423\pi$
$719$	−16.7156	−	28.9523i	−0.623387	−	1.07974i	0.365464	−	0.930825i	$-0.380910\pi$
$720$		0			0
$721$	−33.4730	−	57.9770i	−1.24660	−	2.15918i
$722$		0			0
$723$	−20.3244			−0.755871
$724$		0			0
$725$	3.93896	−	6.82248i	0.146289	−	0.253381i
$726$		0			0
$727$	23.3419	+	40.4294i	0.865703	+	1.49944i	0.866347	+	0.499443i	$0.166462\pi$
$727$	23.3419	+	40.4294i	0.865703	+	1.49944i	−0.000643607		1.00000i	$0.500205\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	5.49043	+	9.50970i	0.203071	+	0.351729i
$732$		0			0
$733$	−7.73972	+	13.4056i	−0.285873	+	0.495147i	−0.972821	−	0.231560i	$-0.925617\pi$
$733$	−7.73972	+	13.4056i	−0.285873	+	0.495147i	0.686947	+	0.726707i	$0.258950\pi$
$734$		0			0
$735$	−6.06274	−	10.5010i	−0.223627	−	0.387334i
$736$		0			0
$737$	23.9338	+	5.15128i	0.881612	+	0.189750i
$738$		0			0
$739$	17.0656	+	29.5585i	0.627769	+	1.08733i	0.987998	+	0.154464i	$0.0493649\pi$
$739$	17.0656	+	29.5585i	0.627769	+	1.08733i	−0.360230	+	0.932864i	$0.617302\pi$
$740$		0			0
$741$	7.35001	−	12.7306i	0.270009	−	0.467670i
$742$		0			0
$743$	17.3705	+	30.0866i	0.637262	+	1.10377i	0.986031	+	0.166561i	$0.0532664\pi$
$743$	17.3705	+	30.0866i	0.637262	+	1.10377i	−0.348769	+	0.937209i	$0.613400\pi$
$744$		0			0
$745$	10.5719			0.387325
$746$		0			0
$747$	1.41204	+	2.44573i	0.0516639	+	0.0894845i
$748$		0			0
$749$	−14.0454	+	24.3273i	−0.513206	+	0.888899i
$750$		0			0
$751$	37.8526			1.38126			0.690630	−	0.723208i	$-0.257333\pi$
$751$	37.8526			1.38126			0.690630	+	0.723208i	$0.257333\pi$
$752$		0			0
$753$	8.24998	+	14.2894i	0.300646	+	0.520734i
$754$		0			0
$755$	7.55070	+	13.0782i	0.274798	+	0.475965i
$756$		0			0
$757$	3.01713	−	5.22582i	0.109659	−	0.189936i	−0.805973	−	0.591952i	$-0.798357\pi$
$757$	3.01713	−	5.22582i	0.109659	−	0.189936i	0.915632	+	0.402017i	$0.131691\pi$
$758$		0			0
$759$	20.8817			0.757958
$760$		0			0
$761$	−17.2286			−0.624535			−0.312267	−	0.949994i	$-0.601088\pi$
$761$	−17.2286			−0.624535			−0.312267	+	0.949994i	$0.601088\pi$
$762$		0			0
$763$	−3.63660	+	6.29877i	−0.131654	+	0.228031i
$764$		0			0
$765$	−0.454199	−	0.786696i	−0.0164216	−	0.0284430i
$766$		0			0
$767$	1.89279	+	3.27841i	0.0683448	+	0.118377i
$768$		0			0
$769$	5.61143	−	9.71929i	0.202353	−	0.350486i	−0.746933	−	0.664900i	$-0.768474\pi$
$769$	5.61143	−	9.71929i	0.202353	−	0.350486i	0.949286	+	0.314413i	$0.101808\pi$
$770$		0			0
$771$	−9.99116	+	17.3052i	−0.359823	+	0.623231i
$772$		0			0
$773$	5.31801	−	9.21106i	0.191275	−	0.331299i	−0.754398	−	0.656418i	$-0.772071\pi$
$773$	5.31801	−	9.21106i	0.191275	−	0.331299i	0.945673	+	0.325119i	$0.105404\pi$
$774$		0			0
$775$	−3.83972	+	6.65058i	−0.137927	+	0.238896i
$776$		0			0
$777$	3.64930			0.130918
$778$		0			0
$779$	−18.8642			−0.675880
$780$		0			0
$781$	−0.0651292	−	0.112807i	−0.00233050	−	0.00403655i
$782$		0			0
$783$	3.93896	−	6.82248i	0.140767	−	0.243816i
$784$		0			0
$785$	5.40208	+	9.35667i	0.192808	+	0.333954i
$786$		0			0
$787$	2.04693	+	3.54538i	0.0729650	+	0.126379i	0.900200	−	0.435478i	$-0.143421\pi$
$787$	2.04693	+	3.54538i	0.0729650	+	0.126379i	−0.827235	+	0.561857i	$0.810087\pi$
$788$		0			0
$789$	22.0971			0.786679
$790$		0			0
$791$	−31.4958	−	54.5523i	−1.11986	−	1.93966i
$792$		0			0
$793$	4.14265	−	7.17528i	0.147110	−	0.254801i
$794$		0			0
$795$	7.39196			0.262166
$796$		0			0
$797$	23.3322	−	40.4126i	0.826470	−	1.43149i	−0.0743202	−	0.997234i	$-0.523679\pi$
$797$	23.3322	−	40.4126i	0.826470	−	1.43149i	0.900790	−	0.434254i	$-0.142988\pi$
$798$		0			0
$799$	−0.793212			−0.0280618
$800$		0			0
$801$	2.76333			0.0976374
$802$		0			0
$803$	26.9143			0.949787
$804$		0			0
$805$	−30.5327			−1.07614
$806$		0			0
$807$	19.1061			0.672565
$808$		0			0
$809$	−23.5590			−0.828291			−0.414145	−	0.910211i	$-0.635919\pi$
$809$	−23.5590			−0.828291			−0.414145	+	0.910211i	$0.635919\pi$
$810$		0			0
$811$	−11.3750	+	19.7020i	−0.399429	+	0.691831i	−0.993655	−	0.112467i	$-0.964125\pi$
$811$	−11.3750	+	19.7020i	−0.399429	+	0.691831i	0.594227	+	0.804297i	$0.297458\pi$
$812$		0			0
$813$	15.1078			0.529855
$814$		0			0
$815$	−6.42050	+	11.1206i	−0.224900	+	0.389539i
$816$		0			0
$817$	−42.6799	−	73.9237i	−1.49318	−	2.58626i
$818$		0			0
$819$	9.10397			0.318119
$820$		0			0
$821$	−6.73838	−	11.6712i	−0.235171	−	0.407328i	0.724151	−	0.689641i	$-0.242232\pi$
$821$	−6.73838	−	11.6712i	−0.235171	−	0.407328i	−0.959322	+	0.282313i	$0.908898\pi$
$822$		0			0
$823$	−4.88421	−	8.45970i	−0.170253	−	0.294886i	0.768255	−	0.640143i	$-0.221125\pi$
$823$	−4.88421	−	8.45970i	−0.170253	−	0.294886i	−0.938508	+	0.345257i	$0.887792\pi$
$824$		0			0
$825$	1.49547	−	2.59023i	0.0520655	−	0.0901801i
$826$		0			0
$827$	−0.467810	−	0.810270i	−0.0162673	−	0.0281759i	0.857777	−	0.514022i	$-0.171845\pi$
$827$	−0.467810	−	0.810270i	−0.0162673	−	0.0281759i	−0.874044	+	0.485846i	$0.838512\pi$
$828$		0			0
$829$	−29.4682			−1.02347			−0.511736	−	0.859143i	$-0.670997\pi$
$829$	−29.4682			−1.02347			−0.511736	+	0.859143i	$0.670997\pi$
$830$		0			0
$831$	13.5221			0.469077
$832$		0			0
$833$	−5.50738	+	9.53906i	−0.190819	+	0.330509i
$834$		0			0
$835$	10.1268	−	17.5401i	0.350452	−	0.607001i
$836$		0			0
$837$	−3.83972	+	6.65058i	−0.132720	+	0.229878i
$838$		0			0
$839$	23.9506	−	41.4837i	0.826867	−	1.43218i	−0.0736164	−	0.997287i	$-0.523454\pi$
$839$	23.9506	−	41.4837i	0.826867	−	1.43218i	0.900484	−	0.434890i	$-0.143213\pi$
$840$		0			0
$841$	−16.5308	−	28.6322i	−0.570029	−	0.987319i
$842$		0			0
$843$	−5.59295	−	9.68728i	−0.192632	−	0.333648i
$844$		0			0
$845$	4.33320	−	7.50532i	0.149066	−	0.258191i
$846$		0			0
$847$	−8.98404			−0.308695
$848$		0			0
$849$	31.3977			1.07757
$850$		0			0
$851$	2.91295	−	5.04538i	0.0998546	−	0.172953i
$852$		0			0
$853$	−4.06418	−	7.03937i	−0.139155	−	0.241024i	0.788022	−	0.615647i	$-0.211105\pi$
$853$	−4.06418	−	7.03937i	−0.139155	−	0.241024i	−0.927177	+	0.374624i	$0.877772\pi$
$854$		0			0
$855$	3.53072	+	6.11538i	0.120748	+	0.209142i
$856$		0			0
$857$	32.6205			1.11430			0.557148	−	0.830413i	$-0.311896\pi$
$857$	32.6205			1.11430			0.557148	+	0.830413i	$0.311896\pi$
$858$		0			0
$859$	15.8967	−	27.5339i	0.542388	−	0.939444i	−0.456378	−	0.889786i	$-0.650854\pi$
$859$	15.8967	−	27.5339i	0.542388	−	0.939444i	0.998766	−	0.0496579i	$-0.0158131\pi$
$860$		0			0
$861$	−5.84146	−	10.1177i	−0.199076	−	0.344810i
$862$		0			0
$863$	−54.7907			−1.86510			−0.932549	−	0.361044i	$-0.882421\pi$
$863$	−54.7907			−1.86510			−0.932549	+	0.361044i	$0.882421\pi$
$864$		0			0
$865$	1.68539	+	2.91918i	0.0573049	+	0.0992550i
$866$		0			0
$867$	8.08741	−	14.0078i	0.274663	−	0.475730i
$868$		0			0
$869$	1.35637	+	2.34930i	0.0460117	+	0.0796946i
$870$		0			0
$871$	11.4341	−	12.6338i	0.387431	−	0.428079i
$872$		0			0
$873$	0.274039	+	0.474649i	0.00927481	+	0.0160644i
$874$		0			0
$875$	−2.18663	+	3.78736i	−0.0739217	+	0.128036i
$876$		0			0
$877$	5.01417	+	8.68480i	0.169317	+	0.293265i	0.938180	−	0.346148i	$-0.112511\pi$
$877$	5.01417	+	8.68480i	0.169317	+	0.293265i	−0.768863	+	0.639413i	$0.779177\pi$
$878$		0			0
$879$	0.857561			0.0289248
$880$		0			0
$881$	−20.9472	−	36.2816i	−0.705729	−	1.22236i	−0.966428	−	0.256938i	$-0.917286\pi$
$881$	−20.9472	−	36.2816i	−0.705729	−	1.22236i	0.260699	−	0.965420i	$-0.416047\pi$
$882$		0			0
$883$	−2.01930	+	3.49752i	−0.0679547	+	0.117701i	−0.898001	−	0.439994i	$-0.854981\pi$
$883$	−2.01930	+	3.49752i	−0.0679547	+	0.117701i	0.830046	+	0.557695i	$0.188314\pi$
$884$		0			0
$885$	−1.81848			−0.0611275
$886$		0			0
$887$	18.3630	+	31.8056i	0.616569	+	1.06793i	0.990107	+	0.140314i	$0.0448112\pi$
$887$	18.3630	+	31.8056i	0.616569	+	1.06793i	−0.373538	+	0.927615i	$0.621855\pi$
$888$		0			0
$889$	19.4258	+	33.6464i	0.651520	+	1.12846i
$890$		0			0
$891$	1.49547	−	2.59023i	0.0501000	−	0.0867758i
$892$		0			0
$893$	6.16604			0.206339
$894$		0			0
$895$	−8.54970			−0.285785
$896$		0			0
$897$	7.26698	−	12.5868i	0.242637	−	0.420260i
$898$		0			0
$899$	30.2490	+	52.3928i	1.00886	+	1.74740i
$900$		0			0
$901$	−3.35742	−	5.81522i	−0.111852	−	0.193733i
$902$		0			0
$903$	26.4324	−	45.7822i	0.879614	−	1.52354i
$904$		0			0
$905$	2.30488	−	3.99218i	0.0766169	−	0.132704i
$906$		0			0
$907$	−2.42704	+	4.20376i	−0.0805886	+	0.139583i	−0.903503	−	0.428582i	$-0.859013\pi$
$907$	−2.42704	+	4.20376i	−0.0805886	+	0.139583i	0.822914	+	0.568165i	$0.192347\pi$
$908$		0			0
$909$	0.346371	−	0.599931i	0.0114884	−	0.0198985i
$910$		0			0
$911$	18.1911			0.602697			0.301348	−	0.953514i	$-0.402563\pi$
$911$	18.1911			0.602697			0.301348	+	0.953514i	$0.402563\pi$
$912$		0			0
$913$	8.44665			0.279543
$914$		0			0
$915$	1.99000	+	3.44678i	0.0657874	+	0.113947i
$916$		0			0
$917$	8.10295	−	14.0347i	0.267583	−	0.463467i
$918$		0			0
$919$	−13.8787	−	24.0385i	−0.457815	−	0.792958i	0.541031	−	0.841003i	$-0.318034\pi$
$919$	−13.8787	−	24.0385i	−0.457815	−	0.792958i	−0.998845	+	0.0480449i	$0.984701\pi$
$920$		0			0
$921$	−3.19008	−	5.52538i	−0.105117	−	0.182067i
$922$		0			0
$923$	−0.0906616			−0.00298416
$924$		0			0
$925$	−0.417228	−	0.722660i	−0.0137184	−	0.0237609i
$926$		0			0
$927$	−7.65401	+	13.2571i	−0.251391	+	0.435421i
$928$		0			0
$929$	12.8287			0.420897			0.210449	−	0.977605i	$-0.432508\pi$
$929$	12.8287			0.420897			0.210449	+	0.977605i	$0.432508\pi$
$930$		0			0
$931$	42.8116	−	74.1519i	1.40309	−	2.43023i
$932$		0			0
$933$	21.0122			0.687910
$934$		0			0
$935$	−2.71696			−0.0888540
$936$		0			0
$937$	−52.5470			−1.71664			−0.858318	−	0.513117i	$-0.828491\pi$
$937$	−52.5470			−1.71664			−0.858318	+	0.513117i	$0.828491\pi$
$938$		0			0
$939$	−13.7198			−0.447729
$940$		0			0
$941$	56.7928			1.85139			0.925697	−	0.378266i	$-0.123480\pi$
$941$	56.7928			1.85139			0.925697	+	0.378266i	$0.123480\pi$
$942$		0			0
$943$	−18.6511			−0.607363
$944$		0			0
$945$	−2.18663	+	3.78736i	−0.0711312	+	0.123203i
$946$		0			0
$947$	−53.5181			−1.73910			−0.869551	−	0.493842i	$-0.835592\pi$
$947$	−53.5181			−1.73910			−0.869551	+	0.493842i	$0.835592\pi$
$948$		0			0
$949$	9.36638	−	16.2230i	0.304046	−	0.526622i
$950$		0			0
$951$	4.53972	+	7.86302i	0.147210	+	0.254976i
$952$		0			0
$953$	52.1650			1.68979			0.844894	−	0.534933i	$-0.179663\pi$
$953$	52.1650			1.68979			0.844894	+	0.534933i	$0.179663\pi$
$954$		0			0
$955$	−6.49218	−	11.2448i	−0.210082	−	0.363873i
$956$		0			0
$957$	−11.7812	−	20.4056i	−0.380831	−	0.659619i
$958$		0			0
$959$	37.2467	−	64.5132i	1.20276	−	2.08324i
$960$		0			0
$961$	−13.9868	−	24.2259i	−0.451188	−	0.781481i
$962$		0			0
$963$	6.42328			0.206987
$964$		0			0
$965$	−10.1932			−0.328131
$966$		0			0
$967$	30.3818	−	52.6229i	0.977014	−	1.69224i	0.303892	−	0.952706i	$-0.401714\pi$
$967$	30.3818	−	52.6229i	0.977014	−	1.69224i	0.673122	−	0.739532i	$-0.264953\pi$
$968$		0			0
$969$	3.20730	−	5.55520i	0.103033	−	0.178459i
$970$		0			0
$971$	−26.0672	+	45.1497i	−0.836537	+	1.44892i	0.0562365	+	0.998417i	$0.482090\pi$
$971$	−26.0672	+	45.1497i	−0.836537	+	1.44892i	−0.892773	+	0.450507i	$0.851243\pi$
$972$		0			0
$973$	−9.18547	+	15.9097i	−0.294473	+	0.510042i
$974$		0			0
$975$	−1.04087	−	1.80283i	−0.0333344	−	0.0577369i
$976$		0			0
$977$	−0.462261	−	0.800660i	−0.0147890	−	0.0256154i	0.858536	−	0.512753i	$-0.171374\pi$
$977$	−0.462261	−	0.800660i	−0.0147890	−	0.0256154i	−0.873325	+	0.487138i	$0.838041\pi$
$978$		0			0
$979$	4.13247	−	7.15765i	0.132074	−	0.228759i
$980$		0			0
$981$	1.66310			0.0530988
$982$		0			0
$983$	32.6111			1.04013			0.520067	−	0.854126i	$-0.325907\pi$
$983$	32.6111			1.04013			0.520067	+	0.854126i	$0.325907\pi$
$984$		0			0
$985$	−9.06345	+	15.6984i	−0.288786	+	0.500191i
$986$		0			0
$987$	1.90937	+	3.30712i	0.0607758	+	0.105267i
$988$		0			0
$989$	−42.1978	−	73.0887i	−1.34181	−	2.32408i
$990$		0			0
$991$	−29.1668			−0.926514			−0.463257	−	0.886224i	$-0.653319\pi$
$991$	−29.1668			−0.926514			−0.463257	+	0.886224i	$0.653319\pi$
$992$		0			0
$993$	−4.36593	+	7.56201i	−0.138549	+	0.239973i
$994$		0			0
$995$	9.84561	+	17.0531i	0.312127	+	0.540619i
$996$		0			0
$997$	17.4009			0.551092			0.275546	−	0.961288i	$-0.411141\pi$
$997$	17.4009			0.551092			0.275546	+	0.961288i	$0.411141\pi$
$998$		0			0
$999$	−0.417228	−	0.722660i	−0.0132005	−	0.0228640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.841.1	✓	24
67.29	even	3	inner	4020.2.q.m.3781.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.1	✓	24	1.1	even	1	trivial
4020.2.q.m.3781.1	yes	24	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-2.18663 + 3.78736i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-2.18663 + 3.78736i) q^{7} +1.00000 q^{9} +(1.49547 - 2.59023i) q^{11} +(-1.04087 - 1.80283i) q^{13} +1.00000 q^{15} +(-0.454199 - 0.786696i) q^{17} +(3.53072 + 6.11538i) q^{19} +(-2.18663 + 3.78736i) q^{21} +(3.49083 + 6.04630i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(3.93896 - 6.82248i) q^{29} +(-3.83972 + 6.65058i) q^{31} +(1.49547 - 2.59023i) q^{33} +(-2.18663 + 3.78736i) q^{35} +(-0.417228 - 0.722660i) q^{37} +(-1.04087 - 1.80283i) q^{39} +(-1.33572 + 2.31353i) q^{41} -12.0882 q^{43} +1.00000 q^{45} +(0.436600 - 0.756213i) q^{47} +(-6.06274 - 10.5010i) q^{49} +(-0.454199 - 0.786696i) q^{51} +7.39196 q^{53} +(1.49547 - 2.59023i) q^{55} +(3.53072 + 6.11538i) q^{57} -1.81848 q^{59} +(1.99000 + 3.44678i) q^{61} +(-2.18663 + 3.78736i) q^{63} +(-1.04087 - 1.80283i) q^{65} +(2.50950 + 7.79118i) q^{67} +(3.49083 + 6.04630i) q^{69} +(0.0217755 - 0.0377163i) q^{71} +(4.49932 + 7.79305i) q^{73} +1.00000 q^{75} +(6.54008 + 11.3278i) q^{77} +(-0.453494 + 0.785474i) q^{79} +1.00000 q^{81} +(1.41204 + 2.44573i) q^{83} +(-0.454199 - 0.786696i) q^{85} +(3.93896 - 6.82248i) q^{87} +2.76333 q^{89} +9.10397 q^{91} +(-3.83972 + 6.65058i) q^{93} +(3.53072 + 6.11538i) q^{95} +(0.274039 + 0.474649i) q^{97} +(1.49547 - 2.59023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 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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