LMFDB - Embedded newform 4020.2.q.m.3781.7

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			3781.7
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.m.841.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(0.134465 + 0.232901i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(0.134465 + 0.232901i) q^{7} +1.00000 q^{9} +(-3.05941 - 5.29905i) q^{11} +(-1.14872 + 1.98965i) q^{13} +1.00000 q^{15} +(-3.76596 + 6.52284i) q^{17} +(-1.88181 + 3.25939i) q^{19} +(0.134465 + 0.232901i) q^{21} +(2.57707 - 4.46362i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-3.06664 - 5.31157i) q^{29} +(-5.25390 - 9.10002i) q^{31} +(-3.05941 - 5.29905i) q^{33} +(0.134465 + 0.232901i) q^{35} +(2.62278 - 4.54279i) q^{37} +(-1.14872 + 1.98965i) q^{39} +(1.80796 + 3.13148i) q^{41} +10.9631 q^{43} +1.00000 q^{45} +(-6.55135 - 11.3473i) q^{47} +(3.46384 - 5.99954i) q^{49} +(-3.76596 + 6.52284i) q^{51} +12.0675 q^{53} +(-3.05941 - 5.29905i) q^{55} +(-1.88181 + 3.25939i) q^{57} -11.8215 q^{59} +(4.89473 - 8.47792i) q^{61} +(0.134465 + 0.232901i) q^{63} +(-1.14872 + 1.98965i) q^{65} +(4.96860 - 6.50484i) q^{67} +(2.57707 - 4.46362i) q^{69} +(-6.02544 - 10.4364i) q^{71} +(0.167288 - 0.289752i) q^{73} +1.00000 q^{75} +(0.822768 - 1.42508i) q^{77} +(4.90196 + 8.49044i) q^{79} +1.00000 q^{81} +(4.16136 - 7.20768i) q^{83} +(-3.76596 + 6.52284i) q^{85} +(-3.06664 - 5.31157i) q^{87} -1.47751 q^{89} -0.617854 q^{91} +(-5.25390 - 9.10002i) q^{93} +(-1.88181 + 3.25939i) q^{95} +(-2.64816 + 4.58675i) q^{97} +(-3.05941 - 5.29905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	0.134465	+	0.232901i	0.0508231	+	0.0880282i	0.890318	−	0.455340i	$-0.150482\pi$
$7$	0.134465	+	0.232901i	0.0508231	+	0.0880282i	−0.839495	+	0.543368i	$0.817149\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−3.05941	−	5.29905i	−0.922446	−	1.59772i	−0.795617	−	0.605799i	$-0.792853\pi$
$11$	−3.05941	−	5.29905i	−0.922446	−	1.59772i	−0.126829	−	0.991925i	$-0.540480\pi$
$12$		0			0
$13$	−1.14872	+	1.98965i	−0.318599	+	0.551829i	−0.980196	−	0.198030i	$-0.936546\pi$
$13$	−1.14872	+	1.98965i	−0.318599	+	0.551829i	0.661597	+	0.749859i	$0.269879\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−3.76596	+	6.52284i	−0.913380	+	1.58202i	−0.104123	+	0.994564i	$0.533204\pi$
$17$	−3.76596	+	6.52284i	−0.913380	+	1.58202i	−0.809256	+	0.587456i	$0.800130\pi$
$18$		0			0
$19$	−1.88181	+	3.25939i	−0.431716	+	0.747754i	−0.997021	−	0.0771275i	$-0.975425\pi$
$19$	−1.88181	+	3.25939i	−0.431716	+	0.747754i	0.565305	+	0.824882i	$0.308758\pi$
$20$		0			0
$21$	0.134465	+	0.232901i	0.0293427	+	0.0508231i
$22$		0			0
$23$	2.57707	−	4.46362i	0.537356	−	0.930728i	−0.461689	−	0.887042i	$-0.652756\pi$
$23$	2.57707	−	4.46362i	0.537356	−	0.930728i	0.999045	−	0.0436864i	$-0.0139102\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−3.06664	−	5.31157i	−0.569461	−	0.986335i	−0.996619	−	0.0821580i	$-0.973819\pi$
$29$	−3.06664	−	5.31157i	−0.569461	−	0.986335i	0.427159	−	0.904177i	$-0.359515\pi$
$30$		0			0
$31$	−5.25390	−	9.10002i	−0.943629	−	1.63441i	−0.758474	−	0.651703i	$-0.774055\pi$
$31$	−5.25390	−	9.10002i	−0.943629	−	1.63441i	−0.185154	−	0.982709i	$-0.559278\pi$
$32$		0			0
$33$	−3.05941	−	5.29905i	−0.532575	−	0.922446i
$34$		0			0
$35$	0.134465	+	0.232901i	0.0227288	+	0.0393674i
$36$		0			0
$37$	2.62278	−	4.54279i	0.431182	−	0.746830i	−0.565793	−	0.824547i	$-0.691430\pi$
$37$	2.62278	−	4.54279i	0.431182	−	0.746830i	0.996975	+	0.0777176i	$0.0247632\pi$
$38$		0			0
$39$	−1.14872	+	1.98965i	−0.183943	+	0.318599i
$40$		0			0
$41$	1.80796	+	3.13148i	0.282356	+	0.489054i	0.971964	−	0.235128i	$-0.0755508\pi$
$41$	1.80796	+	3.13148i	0.282356	+	0.489054i	−0.689609	+	0.724182i	$0.742218\pi$
$42$		0			0
$43$	10.9631			1.67186			0.835931	−	0.548834i	$-0.184928\pi$
$43$	10.9631			1.67186			0.835931	+	0.548834i	$0.184928\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−6.55135	−	11.3473i	−0.955612	−	1.65517i	−0.732962	−	0.680270i	$-0.761863\pi$
$47$	−6.55135	−	11.3473i	−0.955612	−	1.65517i	−0.222650	−	0.974898i	$-0.571471\pi$
$48$		0			0
$49$	3.46384	−	5.99954i	0.494834	−	0.857078i
$50$		0			0
$51$	−3.76596	+	6.52284i	−0.527340	+	0.913380i
$52$		0			0
$53$	12.0675			1.65760			0.828800	−	0.559545i	$-0.189024\pi$
$53$	12.0675			1.65760			0.828800	+	0.559545i	$0.189024\pi$
$54$		0			0
$55$	−3.05941	−	5.29905i	−0.412531	−	0.714524i
$56$		0			0
$57$	−1.88181	+	3.25939i	−0.249251	+	0.431716i
$58$		0			0
$59$	−11.8215			−1.53903			−0.769515	−	0.638628i	$-0.779502\pi$
$59$	−11.8215			−1.53903			−0.769515	+	0.638628i	$0.779502\pi$
$60$		0			0
$61$	4.89473	−	8.47792i	0.626706	−	1.08549i	−0.361502	−	0.932371i	$-0.617736\pi$
$61$	4.89473	−	8.47792i	0.626706	−	1.08549i	0.988208	−	0.153115i	$-0.0489306\pi$
$62$		0			0
$63$	0.134465	+	0.232901i	0.0169410	+	0.0293427i
$64$		0			0
$65$	−1.14872	+	1.98965i	−0.142482	+	0.246786i
$66$		0			0
$67$	4.96860	−	6.50484i	0.607011	−	0.794693i
$67$	4.96860	−	6.50484i	0.607011	−	0.794693i
$68$		0			0
$69$	2.57707	−	4.46362i	0.310243	−	0.537356i
$70$		0			0
$71$	−6.02544	−	10.4364i	−0.715088	−	1.23857i	−0.962926	−	0.269767i	$-0.913053\pi$
$71$	−6.02544	−	10.4364i	−0.715088	−	1.23857i	0.247837	−	0.968802i	$-0.420280\pi$
$72$		0			0
$73$	0.167288	−	0.289752i	0.0195796	−	0.0339129i	−0.856070	−	0.516861i	$-0.827101\pi$
$73$	0.167288	−	0.289752i	0.0195796	−	0.0339129i	0.875649	+	0.482948i	$0.160434\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	0.822768	−	1.42508i	0.0937631	−	0.162403i
$78$		0			0
$79$	4.90196	+	8.49044i	0.551514	+	0.955250i	0.998166	+	0.0605418i	$0.0192829\pi$
$79$	4.90196	+	8.49044i	0.551514	+	0.955250i	−0.446652	+	0.894708i	$0.647384\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	4.16136	−	7.20768i	0.456768	−	0.791146i	−0.542020	−	0.840366i	$-0.682340\pi$
$83$	4.16136	−	7.20768i	0.456768	−	0.791146i	0.998788	+	0.0492198i	$0.0156735\pi$
$84$		0			0
$85$	−3.76596	+	6.52284i	−0.408476	+	0.707501i
$86$		0			0
$87$	−3.06664	−	5.31157i	−0.328778	−	0.569461i
$88$		0			0
$89$	−1.47751			−0.156616			−0.0783081	−	0.996929i	$-0.524952\pi$
$89$	−1.47751			−0.156616			−0.0783081	+	0.996929i	$0.524952\pi$
$90$		0			0
$91$	−0.617854			−0.0647687
$92$		0			0
$93$	−5.25390	−	9.10002i	−0.544804	−	0.943629i
$94$		0			0
$95$	−1.88181	+	3.25939i	−0.193069	+	0.334406i
$96$		0			0
$97$	−2.64816	+	4.58675i	−0.268880	+	0.465714i	−0.968573	−	0.248730i	$-0.919987\pi$
$97$	−2.64816	+	4.58675i	−0.268880	+	0.465714i	0.699693	+	0.714444i	$0.253320\pi$
$98$		0			0
$99$	−3.05941	−	5.29905i	−0.307482	−	0.532575i
$100$		0			0
$101$	5.55036	+	9.61350i	0.552281	+	0.956579i	0.998110	+	0.0614604i	$0.0195758\pi$
$101$	5.55036	+	9.61350i	0.552281	+	0.956579i	−0.445829	+	0.895118i	$0.647091\pi$
$102$		0			0
$103$	1.61545	+	2.79804i	0.159175	+	0.275699i	0.934571	−	0.355776i	$-0.115783\pi$
$103$	1.61545	+	2.79804i	0.159175	+	0.275699i	−0.775396	+	0.631475i	$0.782450\pi$
$104$		0			0
$105$	0.134465	+	0.232901i	0.0131225	+	0.0227288i
$106$		0			0
$107$	−8.58118			−0.829574			−0.414787	−	0.909918i	$-0.636144\pi$
$107$	−8.58118			−0.829574			−0.414787	+	0.909918i	$0.636144\pi$
$108$		0			0
$109$	−18.0243			−1.72642			−0.863208	−	0.504848i	$-0.831548\pi$
$109$	−18.0243			−1.72642			−0.863208	+	0.504848i	$0.831548\pi$
$110$		0			0
$111$	2.62278	−	4.54279i	0.248943	−	0.431182i
$112$		0			0
$113$	−9.83260	−	17.0306i	−0.924973	−	1.60210i	−0.791605	−	0.611033i	$-0.790754\pi$
$113$	−9.83260	−	17.0306i	−0.924973	−	1.60210i	−0.133368	−	0.991067i	$-0.542579\pi$
$114$		0			0
$115$	2.57707	−	4.46362i	0.240313	−	0.416234i
$116$		0			0
$117$	−1.14872	+	1.98965i	−0.106200	+	0.183943i
$118$		0			0
$119$	−2.02556			−0.185683
$120$		0			0
$121$	−13.2200	+	22.8976i	−1.20181	+	2.08160i
$122$		0			0
$123$	1.80796	+	3.13148i	0.163018	+	0.282356i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.27915	−	7.41171i	−0.379713	−	0.657683i	0.611307	−	0.791394i	$-0.290644\pi$
$127$	−4.27915	−	7.41171i	−0.379713	−	0.657683i	−0.991020	+	0.133711i	$0.957311\pi$
$128$		0			0
$129$	10.9631			0.965250
$130$		0			0
$131$	−9.67842			−0.845607			−0.422804	−	0.906221i	$-0.638954\pi$
$131$	−9.67842			−0.845607			−0.422804	+	0.906221i	$0.638954\pi$
$132$		0			0
$133$	−1.01215			−0.0877646
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−5.37712			−0.459398			−0.229699	−	0.973262i	$-0.573774\pi$
$137$	−5.37712			−0.459398			−0.229699	+	0.973262i	$0.573774\pi$
$138$		0			0
$139$	−12.8831			−1.09273			−0.546365	−	0.837547i	$-0.683989\pi$
$139$	−12.8831			−1.09273			−0.546365	+	0.837547i	$0.683989\pi$
$140$		0			0
$141$	−6.55135	−	11.3473i	−0.551723	−	0.955612i
$142$		0			0
$143$	14.0577			1.17556
$144$		0			0
$145$	−3.06664	−	5.31157i	−0.254671	−	0.441102i
$146$		0			0
$147$	3.46384	−	5.99954i	0.285693	−	0.494834i
$148$		0			0
$149$	3.97030			0.325260			0.162630	−	0.986687i	$-0.448002\pi$
$149$	3.97030			0.325260			0.162630	+	0.986687i	$0.448002\pi$
$150$		0			0
$151$	2.43423	−	4.21621i	0.198095	−	0.343110i	−0.749816	−	0.661647i	$-0.769858\pi$
$151$	2.43423	−	4.21621i	0.198095	−	0.343110i	0.947911	+	0.318536i	$0.103191\pi$
$152$		0			0
$153$	−3.76596	+	6.52284i	−0.304460	+	0.527340i
$154$		0			0
$155$	−5.25390	−	9.10002i	−0.422003	−	0.730931i
$156$		0			0
$157$	−0.387721	+	0.671552i	−0.0309435	+	0.0535957i	−0.881082	−	0.472963i	$-0.843185\pi$
$157$	−0.387721	+	0.671552i	−0.0309435	+	0.0535957i	0.850139	+	0.526558i	$0.176518\pi$
$158$		0			0
$159$	12.0675			0.957015
$160$		0			0
$161$	1.38611			0.109240
$162$		0			0
$163$	2.56301	+	4.43926i	0.200750	+	0.347710i	0.948770	−	0.315966i	$-0.102329\pi$
$163$	2.56301	+	4.43926i	0.200750	+	0.347710i	−0.748020	+	0.663676i	$0.768995\pi$
$164$		0			0
$165$	−3.05941	−	5.29905i	−0.238175	−	0.412531i
$166$		0			0
$167$	5.81380	+	10.0698i	0.449885	+	0.779225i	0.998378	−	0.0569309i	$-0.0181315\pi$
$167$	5.81380	+	10.0698i	0.449885	+	0.779225i	−0.548493	+	0.836155i	$0.684798\pi$
$168$		0			0
$169$	3.86087	+	6.68721i	0.296990	+	0.514401i
$170$		0			0
$171$	−1.88181	+	3.25939i	−0.143905	+	0.249251i
$172$		0			0
$173$	−6.10683	+	10.5773i	−0.464294	+	0.804180i	−0.999169	−	0.0407504i	$-0.987025\pi$
$173$	−6.10683	+	10.5773i	−0.464294	+	0.804180i	0.534876	+	0.844931i	$0.320358\pi$
$174$		0			0
$175$	0.134465	+	0.232901i	0.0101646	+	0.0176056i
$176$		0			0
$177$	−11.8215			−0.888560
$178$		0			0
$179$	20.1511			1.50617			0.753083	−	0.657926i	$-0.228566\pi$
$179$	20.1511			1.50617			0.753083	+	0.657926i	$0.228566\pi$
$180$		0			0
$181$	−2.76240	−	4.78462i	−0.205328	−	0.355638i	0.744909	−	0.667166i	$-0.232493\pi$
$181$	−2.76240	−	4.78462i	−0.205328	−	0.355638i	−0.950237	+	0.311527i	$0.899159\pi$
$182$		0			0
$183$	4.89473	−	8.47792i	0.361829	−	0.626706i
$184$		0			0
$185$	2.62278	−	4.54279i	0.192831	−	0.333992i
$186$		0			0
$187$	46.0865			3.37018
$188$		0			0
$189$	0.134465	+	0.232901i	0.00978091	+	0.0169410i
$190$		0			0
$191$	2.25042	−	3.89784i	0.162835	−	0.282038i	−0.773050	−	0.634346i	$-0.781270\pi$
$191$	2.25042	−	3.89784i	0.162835	−	0.282038i	0.935884	+	0.352308i	$0.114603\pi$
$192$		0			0
$193$	0.522022			0.0375760			0.0187880	−	0.999823i	$-0.494019\pi$
$193$	0.522022			0.0375760			0.0187880	+	0.999823i	$0.494019\pi$
$194$		0			0
$195$	−1.14872	+	1.98965i	−0.0822619	+	0.142482i
$196$		0			0
$197$	10.7953	+	18.6980i	0.769131	+	1.33217i	0.938035	+	0.346541i	$0.112644\pi$
$197$	10.7953	+	18.6980i	0.769131	+	1.33217i	−0.168904	+	0.985633i	$0.554023\pi$
$198$		0			0
$199$	−1.46680	+	2.54057i	−0.103979	+	0.180096i	−0.913320	−	0.407242i	$-0.866491\pi$
$199$	−1.46680	+	2.54057i	−0.103979	+	0.180096i	0.809342	+	0.587338i	$0.199824\pi$
$200$		0			0
$201$	4.96860	−	6.50484i	0.350458	−	0.458816i
$202$		0			0
$203$	0.824713	−	1.42844i	0.0578835	−	0.100257i
$204$		0			0
$205$	1.80796	+	3.13148i	0.126273	+	0.218712i
$206$		0			0
$207$	2.57707	−	4.46362i	0.179119	−	0.310243i
$208$		0			0
$209$	23.0289			1.59294
$210$		0			0
$211$	−9.86509	+	17.0868i	−0.679141	+	1.17631i	0.296099	+	0.955157i	$0.404314\pi$
$211$	−9.86509	+	17.0868i	−0.679141	+	1.17631i	−0.975240	+	0.221149i	$0.929019\pi$
$212$		0			0
$213$	−6.02544	−	10.4364i	−0.412856	−	0.715088i
$214$		0			0
$215$	10.9631			0.747680
$216$		0			0
$217$	1.41293	−	2.44727i	0.0959162	−	0.166132i
$218$		0			0
$219$	0.167288	−	0.289752i	0.0113043	−	0.0195796i
$220$		0			0
$221$	−8.65210	−	14.9859i	−0.582003	−	1.00806i
$222$		0			0
$223$	−1.29322			−0.0866002			−0.0433001	−	0.999062i	$-0.513787\pi$
$223$	−1.29322			−0.0866002			−0.0433001	+	0.999062i	$0.513787\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−0.117554	−	0.203609i	−0.00780233	−	0.0135140i	0.862098	−	0.506742i	$-0.169150\pi$
$227$	−0.117554	−	0.203609i	−0.00780233	−	0.0135140i	−0.869900	+	0.493228i	$0.835817\pi$
$228$		0			0
$229$	4.55100	−	7.88257i	0.300739	−	0.520895i	−0.675565	−	0.737301i	$-0.736100\pi$
$229$	4.55100	−	7.88257i	0.300739	−	0.520895i	0.976303	+	0.216406i	$0.0694334\pi$
$230$		0			0
$231$	0.822768	−	1.42508i	0.0541342	−	0.0937631i
$232$		0			0
$233$	−9.73932	−	16.8690i	−0.638044	−	1.10513i	−0.985861	−	0.167563i	$-0.946410\pi$
$233$	−9.73932	−	16.8690i	−0.638044	−	1.10513i	0.347817	−	0.937562i	$-0.386923\pi$
$234$		0			0
$235$	−6.55135	−	11.3473i	−0.427363	−	0.740214i
$236$		0			0
$237$	4.90196	+	8.49044i	0.318417	+	0.551514i
$238$		0			0
$239$	4.89980	+	8.48670i	0.316942	+	0.548959i	0.979848	−	0.199743i	$-0.0640107\pi$
$239$	4.89980	+	8.48670i	0.316942	+	0.548959i	−0.662907	+	0.748702i	$0.730677\pi$
$240$		0			0
$241$	15.3003			0.985577			0.492788	−	0.870149i	$-0.335978\pi$
$241$	15.3003			0.985577			0.492788	+	0.870149i	$0.335978\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	3.46384	−	5.99954i	0.221297	−	0.383297i
$246$		0			0
$247$	−4.32336	−	7.48827i	−0.275089	−	0.476467i
$248$		0			0
$249$	4.16136	−	7.20768i	0.263715	−	0.456768i
$250$		0			0
$251$	0.00388720	−	0.00673283i	0.000245358	−	0.000424972i	−0.865903	−	0.500212i	$-0.833255\pi$
$251$	0.00388720	−	0.00673283i	0.000245358	−	0.000424972i	0.866148	+	0.499787i	$0.166589\pi$
$252$		0			0
$253$	−31.5372			−1.98273
$254$		0			0
$255$	−3.76596	+	6.52284i	−0.235834	+	0.408476i
$256$		0			0
$257$	0.440192	+	0.762436i	0.0274585	+	0.0475594i	0.879428	−	0.476032i	$-0.157925\pi$
$257$	0.440192	+	0.762436i	0.0274585	+	0.0475594i	−0.851970	+	0.523591i	$0.824592\pi$
$258$		0			0
$259$	1.41069			0.0876561
$260$		0			0
$261$	−3.06664	−	5.31157i	−0.189820	−	0.328778i
$262$		0			0
$263$	−14.2044			−0.875880			−0.437940	−	0.899004i	$-0.644292\pi$
$263$	−14.2044			−0.875880			−0.437940	+	0.899004i	$0.644292\pi$
$264$		0			0
$265$	12.0675			0.741301
$266$		0			0
$267$	−1.47751			−0.0904224
$268$		0			0
$269$	−9.28569			−0.566158			−0.283079	−	0.959097i	$-0.591356\pi$
$269$	−9.28569			−0.566158			−0.283079	+	0.959097i	$0.591356\pi$
$270$		0			0
$271$	25.0251			1.52017			0.760083	−	0.649826i	$-0.225158\pi$
$271$	25.0251			1.52017			0.760083	+	0.649826i	$0.225158\pi$
$272$		0			0
$273$	−0.617854			−0.0373942
$274$		0			0
$275$	−3.05941	−	5.29905i	−0.184489	−	0.319545i
$276$		0			0
$277$	1.55977			0.0937176			0.0468588	−	0.998902i	$-0.485079\pi$
$277$	1.55977			0.0937176			0.0468588	+	0.998902i	$0.485079\pi$
$278$		0			0
$279$	−5.25390	−	9.10002i	−0.314543	−	0.544804i
$280$		0			0
$281$	16.3222	−	28.2709i	0.973703	−	1.68650i	0.289552	−	0.957162i	$-0.406494\pi$
$281$	16.3222	−	28.2709i	0.973703	−	1.68650i	0.684151	−	0.729341i	$-0.260173\pi$
$282$		0			0
$283$	−23.0663			−1.37115			−0.685575	−	0.728002i	$-0.740449\pi$
$283$	−23.0663			−1.37115			−0.685575	+	0.728002i	$0.740449\pi$
$284$		0			0
$285$	−1.88181	+	3.25939i	−0.111469	+	0.193069i
$286$		0			0
$287$	−0.486215	+	0.842149i	−0.0287004	+	0.0497105i
$288$		0			0
$289$	−19.8649	−	34.4071i	−1.16853	−	2.02394i
$290$		0			0
$291$	−2.64816	+	4.58675i	−0.155238	+	0.268880i
$292$		0			0
$293$	−29.7425			−1.73758			−0.868789	−	0.495182i	$-0.835101\pi$
$293$	−29.7425			−1.73758			−0.868789	+	0.495182i	$0.835101\pi$
$294$		0			0
$295$	−11.8215			−0.688275
$296$		0			0
$297$	−3.05941	−	5.29905i	−0.177525	−	0.307482i
$298$		0			0
$299$	5.92069	+	10.2549i	0.342402	+	0.593058i
$300$		0			0
$301$	1.47416	+	2.55332i	0.0849692	+	0.147171i
$302$		0			0
$303$	5.55036	+	9.61350i	0.318860	+	0.552281i
$304$		0			0
$305$	4.89473	−	8.47792i	0.280271	−	0.485444i
$306$		0			0
$307$	−7.69252	+	13.3238i	−0.439036	+	0.760432i	−0.997615	−	0.0690189i	$-0.978013\pi$
$307$	−7.69252	+	13.3238i	−0.439036	+	0.760432i	0.558580	+	0.829451i	$0.311346\pi$
$308$		0			0
$309$	1.61545	+	2.79804i	0.0918997	+	0.159175i
$310$		0			0
$311$	13.6420			0.773568			0.386784	−	0.922170i	$-0.373586\pi$
$311$	13.6420			0.773568			0.386784	+	0.922170i	$0.373586\pi$
$312$		0			0
$313$	24.2528			1.37085			0.685424	−	0.728144i	$-0.259617\pi$
$313$	24.2528			1.37085			0.685424	+	0.728144i	$0.259617\pi$
$314$		0			0
$315$	0.134465	+	0.232901i	0.00757626	+	0.0131225i
$316$		0			0
$317$	−2.84265	+	4.92362i	−0.159659	+	0.276538i	−0.934746	−	0.355317i	$-0.884373\pi$
$317$	−2.84265	+	4.92362i	−0.159659	+	0.276538i	0.775086	+	0.631855i	$0.217706\pi$
$318$		0			0
$319$	−18.7642	+	32.5006i	−1.05059	+	1.81968i
$320$		0			0
$321$	−8.58118			−0.478955
$322$		0			0
$323$	−14.1736	−	24.5494i	−0.788642	−	1.36597i
$324$		0			0
$325$	−1.14872	+	1.98965i	−0.0637198	+	0.110366i
$326$		0			0
$327$	−18.0243			−0.996747
$328$		0			0
$329$	1.76186	−	3.05162i	0.0971343	−	0.168242i
$330$		0			0
$331$	6.80666	+	11.7895i	0.374128	+	0.648008i	0.990196	−	0.139684i	$-0.0446088\pi$
$331$	6.80666	+	11.7895i	0.374128	+	0.648008i	−0.616068	+	0.787693i	$0.711275\pi$
$332$		0			0
$333$	2.62278	−	4.54279i	0.143727	−	0.248943i
$334$		0			0
$335$	4.96860	−	6.50484i	0.271464	−	0.355398i
$336$		0			0
$337$	−17.0893	+	29.5995i	−0.930913	+	1.61239i	−0.149150	+	0.988815i	$0.547654\pi$
$337$	−17.0893	+	29.5995i	−0.930913	+	1.61239i	−0.781764	+	0.623575i	$0.785680\pi$
$338$		0			0
$339$	−9.83260	−	17.0306i	−0.534033	−	0.924973i
$340$		0			0
$341$	−32.1477	+	55.6814i	−1.74089	+	3.01532i
$342$		0			0
$343$	3.74558			0.202242
$344$		0			0
$345$	2.57707	−	4.46362i	0.138745	−	0.240313i
$346$		0			0
$347$	−12.8534	−	22.2628i	−0.690007	−	1.19513i	−0.971835	−	0.235662i	$-0.924274\pi$
$347$	−12.8534	−	22.2628i	−0.690007	−	1.19513i	0.281828	−	0.959465i	$-0.409059\pi$
$348$		0			0
$349$	−20.1244			−1.07724			−0.538618	−	0.842550i	$-0.681053\pi$
$349$	−20.1244			−1.07724			−0.538618	+	0.842550i	$0.681053\pi$
$350$		0			0
$351$	−1.14872	+	1.98965i	−0.0613144	+	0.106200i
$352$		0			0
$353$	2.48311	−	4.30088i	0.132163	−	0.228913i	−0.792347	−	0.610070i	$-0.791141\pi$
$353$	2.48311	−	4.30088i	0.132163	−	0.228913i	0.924510	+	0.381158i	$0.124474\pi$
$354$		0			0
$355$	−6.02544	−	10.4364i	−0.319797	−	0.553905i
$356$		0			0
$357$	−2.02556			−0.107204
$358$		0			0
$359$	23.3539			1.23257			0.616286	−	0.787523i	$-0.288637\pi$
$359$	23.3539			1.23257			0.616286	+	0.787523i	$0.288637\pi$
$360$		0			0
$361$	2.41760	+	4.18741i	0.127242	+	0.220390i
$362$		0			0
$363$	−13.2200	+	22.8976i	−0.693868	+	1.20181i
$364$		0			0
$365$	0.167288	−	0.289752i	0.00875627	−	0.0151663i
$366$		0			0
$367$	10.9902	+	19.0356i	0.573685	+	0.993651i	0.996183	+	0.0872874i	$0.0278199\pi$
$367$	10.9902	+	19.0356i	0.573685	+	0.993651i	−0.422498	+	0.906364i	$0.638847\pi$
$368$		0			0
$369$	1.80796	+	3.13148i	0.0941186	+	0.163018i
$370$		0			0
$371$	1.62266	+	2.81053i	0.0842443	+	0.145915i
$372$		0			0
$373$	−2.01096	−	3.48308i	−0.104124	−	0.180347i	0.809256	−	0.587456i	$-0.199870\pi$
$373$	−2.01096	−	3.48308i	−0.104124	−	0.180347i	−0.913380	+	0.407109i	$0.866537\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	14.0909			0.725718
$378$		0			0
$379$	6.03876	−	10.4594i	0.310190	−	0.537265i	−0.668213	−	0.743970i	$-0.732941\pi$
$379$	6.03876	−	10.4594i	0.310190	−	0.537265i	0.978403	+	0.206705i	$0.0662739\pi$
$380$		0			0
$381$	−4.27915	−	7.41171i	−0.219228	−	0.379713i
$382$		0			0
$383$	16.4594	−	28.5084i	0.841034	−	1.45671i	−0.0479881	−	0.998848i	$-0.515281\pi$
$383$	16.4594	−	28.5084i	0.841034	−	1.45671i	0.889022	−	0.457865i	$-0.151386\pi$
$384$		0			0
$385$	0.822768	−	1.42508i	0.0419321	−	0.0726286i
$386$		0			0
$387$	10.9631			0.557288
$388$		0			0
$389$	−8.37688	+	14.5092i	−0.424725	+	0.735645i	−0.996395	−	0.0848387i	$-0.972962\pi$
$389$	−8.37688	+	14.5092i	−0.424725	+	0.735645i	0.571670	+	0.820484i	$0.306296\pi$
$390$		0			0
$391$	19.4103	+	33.6196i	0.981621	+	1.70022i
$392$		0			0
$393$	−9.67842			−0.488212
$394$		0			0
$395$	4.90196	+	8.49044i	0.246644	+	0.427201i
$396$		0			0
$397$	11.9253			0.598515			0.299257	−	0.954172i	$-0.403261\pi$
$397$	11.9253			0.598515			0.299257	+	0.954172i	$0.403261\pi$
$398$		0			0
$399$	−1.01215			−0.0506709
$400$		0			0
$401$	9.48657			0.473737			0.236868	−	0.971542i	$-0.423879\pi$
$401$	9.48657			0.473737			0.236868	+	0.971542i	$0.423879\pi$
$402$		0			0
$403$	24.1411			1.20256
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−32.0966			−1.59097
$408$		0			0
$409$	−6.42013	−	11.1200i	−0.317455	−	0.549848i	0.662501	−	0.749061i	$-0.269495\pi$
$409$	−6.42013	−	11.1200i	−0.317455	−	0.549848i	−0.979956	+	0.199213i	$0.936162\pi$
$410$		0			0
$411$	−5.37712			−0.265234
$412$		0			0
$413$	−1.58958	−	2.75324i	−0.0782183	−	0.135478i
$414$		0			0
$415$	4.16136	−	7.20768i	0.204273	−	0.353811i
$416$		0			0
$417$	−12.8831			−0.630888
$418$		0			0
$419$	3.34364	−	5.79136i	0.163348	−	0.282927i	−0.772720	−	0.634748i	$-0.781104\pi$
$419$	3.34364	−	5.79136i	0.163348	−	0.282927i	0.936067	+	0.351821i	$0.114437\pi$
$420$		0			0
$421$	1.21145	−	2.09829i	0.0590425	−	0.102265i	−0.834993	−	0.550260i	$-0.814529\pi$
$421$	1.21145	−	2.09829i	0.0590425	−	0.102265i	0.894036	+	0.447995i	$0.147862\pi$
$422$		0			0
$423$	−6.55135	−	11.3473i	−0.318537	−	0.551723i
$424$		0			0
$425$	−3.76596	+	6.52284i	−0.182676	+	0.316404i
$426$		0			0
$427$	2.63268			0.127405
$428$		0			0
$429$	14.0577			0.678711
$430$		0			0
$431$	−18.4364	−	31.9327i	−0.888048	−	1.53815i	−0.842179	−	0.539198i	$-0.818728\pi$
$431$	−18.4364	−	31.9327i	−0.888048	−	1.53815i	−0.0458691	−	0.998947i	$-0.514606\pi$
$432$		0			0
$433$	12.5764	+	21.7830i	0.604384	+	1.04682i	0.992149	+	0.125065i	$0.0399139\pi$
$433$	12.5764	+	21.7830i	0.604384	+	1.04682i	−0.387765	+	0.921758i	$0.626753\pi$
$434$		0			0
$435$	−3.06664	−	5.31157i	−0.147034	−	0.254671i
$436$		0			0
$437$	9.69910	+	16.7993i	0.463971	+	0.803621i
$438$		0			0
$439$	−15.2586	+	26.4287i	−0.728255	+	1.26137i	0.229366	+	0.973340i	$0.426335\pi$
$439$	−15.2586	+	26.4287i	−0.728255	+	1.26137i	−0.957620	+	0.288034i	$0.906999\pi$
$440$		0			0
$441$	3.46384	−	5.99954i	0.164945	−	0.285693i
$442$		0			0
$443$	2.85162	+	4.93916i	0.135485	+	0.234666i	0.925783	−	0.378056i	$-0.123407\pi$
$443$	2.85162	+	4.93916i	0.135485	+	0.234666i	−0.790298	+	0.612723i	$0.790074\pi$
$444$		0			0
$445$	−1.47751			−0.0700409
$446$		0			0
$447$	3.97030			0.187789
$448$		0			0
$449$	−2.29779	−	3.97989i	−0.108439	−	0.187823i	0.806699	−	0.590963i	$-0.201252\pi$
$449$	−2.29779	−	3.97989i	−0.108439	−	0.187823i	−0.915138	+	0.403140i	$0.867919\pi$
$450$		0			0
$451$	11.0626	−	19.1609i	0.520916	−	0.902253i
$452$		0			0
$453$	2.43423	−	4.21621i	0.114370	−	0.198095i
$454$		0			0
$455$	−0.617854			−0.0289654
$456$		0			0
$457$	−1.40065	−	2.42600i	−0.0655196	−	0.113483i	0.831405	−	0.555667i	$-0.187537\pi$
$457$	−1.40065	−	2.42600i	−0.0655196	−	0.113483i	−0.896924	+	0.442184i	$0.854204\pi$
$458$		0			0
$459$	−3.76596	+	6.52284i	−0.175780	+	0.304460i
$460$		0			0
$461$	39.4011			1.83509			0.917545	−	0.397631i	$-0.130168\pi$
$461$	39.4011			1.83509			0.917545	+	0.397631i	$0.130168\pi$
$462$		0			0
$463$	−2.78868	+	4.83014i	−0.129601	+	0.224476i	−0.923522	−	0.383545i	$-0.874703\pi$
$463$	−2.78868	+	4.83014i	−0.129601	+	0.224476i	0.793921	+	0.608021i	$0.208036\pi$
$464$		0			0
$465$	−5.25390	−	9.10002i	−0.243644	−	0.422003i
$466$		0			0
$467$	−3.61786	+	6.26632i	−0.167415	+	0.289971i	−0.937510	−	0.347958i	$-0.886875\pi$
$467$	−3.61786	+	6.26632i	−0.167415	+	0.289971i	0.770096	+	0.637929i	$0.220208\pi$
$468$		0			0
$469$	2.18309	+	0.282515i	0.100806	+	0.0130453i
$470$		0			0
$471$	−0.387721	+	0.671552i	−0.0178652	+	0.0309435i
$472$		0			0
$473$	−33.5407	−	58.0942i	−1.54220	−	2.67117i
$474$		0			0
$475$	−1.88181	+	3.25939i	−0.0863432	+	0.149551i
$476$		0			0
$477$	12.0675			0.552533
$478$		0			0
$479$	9.76713	−	16.9172i	0.446272	−	0.772965i	−0.551868	−	0.833931i	$-0.686085\pi$
$479$	9.76713	−	16.9172i	0.446272	−	0.772965i	0.998140	+	0.0609662i	$0.0194182\pi$
$480$		0			0
$481$	6.02570	+	10.4368i	0.274748	+	0.475878i
$482$		0			0
$483$	1.38611			0.0630700
$484$		0			0
$485$	−2.64816	+	4.58675i	−0.120247	+	0.208274i
$486$		0			0
$487$	1.15817	−	2.00601i	0.0524818	−	0.0909012i	−0.838591	−	0.544762i	$-0.816620\pi$
$487$	1.15817	−	2.00601i	0.0524818	−	0.0909012i	0.891073	+	0.453860i	$0.149954\pi$
$488$		0			0
$489$	2.56301	+	4.43926i	0.115903	+	0.200750i
$490$		0			0
$491$	5.42241			0.244710			0.122355	−	0.992486i	$-0.460955\pi$
$491$	5.42241			0.244710			0.122355	+	0.992486i	$0.460955\pi$
$492$		0			0
$493$	46.1954			2.08054
$494$		0			0
$495$	−3.05941	−	5.29905i	−0.137510	−	0.238175i
$496$		0			0
$497$	1.62042	−	2.80666i	0.0726860	−	0.125896i
$498$		0			0
$499$	14.0470	−	24.3301i	0.628830	−	1.08917i	−0.358957	−	0.933354i	$-0.616867\pi$
$499$	14.0470	−	24.3301i	0.628830	−	1.08917i	0.987787	−	0.155811i	$-0.0497992\pi$
$500$		0			0
$501$	5.81380	+	10.0698i	0.259742	+	0.449885i
$502$		0			0
$503$	−19.8880	−	34.4471i	−0.886764	−	1.53592i	−0.843678	−	0.536849i	$-0.819614\pi$
$503$	−19.8880	−	34.4471i	−0.886764	−	1.53592i	−0.0430860	−	0.999071i	$-0.513719\pi$
$504$		0			0
$505$	5.55036	+	9.61350i	0.246988	+	0.427795i
$506$		0			0
$507$	3.86087	+	6.68721i	0.171467	+	0.296990i
$508$		0			0
$509$	−19.9647			−0.884920			−0.442460	−	0.896788i	$-0.645894\pi$
$509$	−19.9647			−0.884920			−0.442460	+	0.896788i	$0.645894\pi$
$510$		0			0
$511$	0.0899779			0.00398039
$512$		0			0
$513$	−1.88181	+	3.25939i	−0.0830838	+	0.143905i
$514$		0			0
$515$	1.61545	+	2.79804i	0.0711852	+	0.123296i
$516$		0			0
$517$	−40.0865	+	69.4318i	−1.76300	+	3.05361i
$518$		0			0
$519$	−6.10683	+	10.5773i	−0.268060	+	0.464294i
$520$		0			0
$521$	−27.7518			−1.21583			−0.607913	−	0.794003i	$-0.707993\pi$
$521$	−27.7518			−1.21583			−0.607913	+	0.794003i	$0.707993\pi$
$522$		0			0
$523$	1.57105	−	2.72113i	0.0686971	−	0.118987i	−0.829631	−	0.558312i	$-0.811449\pi$
$523$	1.57105	−	2.72113i	0.0686971	−	0.118987i	0.898328	+	0.439325i	$0.144782\pi$
$524$		0			0
$525$	0.134465	+	0.232901i	0.00586854	+	0.0101646i
$526$		0			0
$527$	79.1440			3.44756
$528$		0			0
$529$	−1.78258	−	3.08751i	−0.0775034	−	0.134240i
$530$		0			0
$531$	−11.8215			−0.513010
$532$		0			0
$533$	−8.30738			−0.359833
$534$		0			0
$535$	−8.58118			−0.370997
$536$		0			0
$537$	20.1511			0.869585
$538$		0			0
$539$	−42.3892			−1.82583
$540$		0			0
$541$	2.81725			0.121123			0.0605614	−	0.998164i	$-0.480711\pi$
$541$	2.81725			0.121123			0.0605614	+	0.998164i	$0.480711\pi$
$542$		0			0
$543$	−2.76240	−	4.78462i	−0.118546	−	0.205328i
$544$		0			0
$545$	−18.0243			−0.772077
$546$		0			0
$547$	1.77829	+	3.08009i	0.0760342	+	0.131695i	0.901536	−	0.432705i	$-0.142441\pi$
$547$	1.77829	+	3.08009i	0.0760342	+	0.131695i	−0.825501	+	0.564400i	$0.809108\pi$
$548$		0			0
$549$	4.89473	−	8.47792i	0.208902	−	0.361829i
$550$		0			0
$551$	23.0833			0.983381
$552$		0			0
$553$	−1.31829	+	2.28334i	−0.0560592	+	0.0970975i
$554$		0			0
$555$	2.62278	−	4.54279i	0.111331	−	0.192831i
$556$		0			0
$557$	−13.9232	−	24.1156i	−0.589943	−	1.02181i	−0.994239	−	0.107184i	$-0.965817\pi$
$557$	−13.9232	−	24.1156i	−0.589943	−	1.02181i	0.404296	−	0.914628i	$-0.367517\pi$
$558$		0			0
$559$	−12.5936	+	21.8128i	−0.532653	+	0.922583i
$560$		0			0
$561$	46.0865			1.94577
$562$		0			0
$563$	−2.71161			−0.114281			−0.0571403	−	0.998366i	$-0.518198\pi$
$563$	−2.71161			−0.114281			−0.0571403	+	0.998366i	$0.518198\pi$
$564$		0			0
$565$	−9.83260	−	17.0306i	−0.413660	−	0.716481i
$566$		0			0
$567$	0.134465	+	0.232901i	0.00564701	+	0.00978091i
$568$		0			0
$569$	7.92018	+	13.7182i	0.332031	+	0.575095i	0.982910	−	0.184087i	$-0.0589327\pi$
$569$	7.92018	+	13.7182i	0.332031	+	0.575095i	−0.650879	+	0.759182i	$0.725599\pi$
$570$		0			0
$571$	12.0111	+	20.8038i	0.502649	+	0.870614i	0.999995	+	0.00306177i	$0.000974595\pi$
$571$	12.0111	+	20.8038i	0.502649	+	0.870614i	−0.497346	+	0.867552i	$0.665692\pi$
$572$		0			0
$573$	2.25042	−	3.89784i	0.0940127	−	0.162835i
$574$		0			0
$575$	2.57707	−	4.46362i	0.107471	−	0.186146i
$576$		0			0
$577$	4.00330	+	6.93392i	0.166660	+	0.288663i	0.937243	−	0.348676i	$-0.113369\pi$
$577$	4.00330	+	6.93392i	0.166660	+	0.288663i	−0.770584	+	0.637339i	$0.780035\pi$
$578$		0			0
$579$	0.522022			0.0216945
$580$		0			0
$581$	2.23823			0.0928575
$582$		0			0
$583$	−36.9194	−	63.9463i	−1.52905	−	2.64839i
$584$		0			0
$585$	−1.14872	+	1.98965i	−0.0474939	+	0.0822619i
$586$		0			0
$587$	4.39318	−	7.60921i	0.181326	−	0.314066i	−0.761006	−	0.648744i	$-0.775294\pi$
$587$	4.39318	−	7.60921i	0.181326	−	0.314066i	0.942332	+	0.334679i	$0.108628\pi$
$588$		0			0
$589$	39.5473			1.62952
$590$		0			0
$591$	10.7953	+	18.6980i	0.444058	+	0.769131i
$592$		0			0
$593$	5.56163	−	9.63303i	0.228389	−	0.395581i	−0.728942	−	0.684576i	$-0.759988\pi$
$593$	5.56163	−	9.63303i	0.228389	−	0.395581i	0.957331	+	0.288994i	$0.0933209\pi$
$594$		0			0
$595$	−2.02556			−0.0830400
$596$		0			0
$597$	−1.46680	+	2.54057i	−0.0600322	+	0.103979i
$598$		0			0
$599$	24.0600	+	41.6731i	0.983065	+	1.70272i	0.650240	+	0.759729i	$0.274668\pi$
$599$	24.0600	+	41.6731i	0.983065	+	1.70272i	0.332825	+	0.942989i	$0.391998\pi$
$600$		0			0
$601$	−4.46941	+	7.74125i	−0.182311	+	0.315772i	−0.942667	−	0.333734i	$-0.891691\pi$
$601$	−4.46941	+	7.74125i	−0.182311	+	0.315772i	0.760356	+	0.649507i	$0.225025\pi$
$602$		0			0
$603$	4.96860	−	6.50484i	0.202337	−	0.264898i
$604$		0			0
$605$	−13.2200	+	22.8976i	−0.537468	+	0.930922i
$606$		0			0
$607$	19.8664	+	34.4097i	0.806354	+	1.39665i	0.915373	+	0.402607i	$0.131896\pi$
$607$	19.8664	+	34.4097i	0.806354	+	1.39665i	−0.109019	+	0.994040i	$0.534771\pi$
$608$		0			0
$609$	0.824713	−	1.42844i	0.0334190	−	0.0578835i
$610$		0			0
$611$	30.1028			1.21783
$612$		0			0
$613$	−0.726735	+	1.25874i	−0.0293525	+	0.0508401i	−0.880329	−	0.474365i	$-0.842678\pi$
$613$	−0.726735	+	1.25874i	−0.0293525	+	0.0508401i	0.850976	+	0.525205i	$0.176011\pi$
$614$		0			0
$615$	1.80796	+	3.13148i	0.0729039	+	0.126273i
$616$		0			0
$617$	17.4071			0.700782			0.350391	−	0.936604i	$-0.386049\pi$
$617$	17.4071			0.700782			0.350391	+	0.936604i	$0.386049\pi$
$618$		0			0
$619$	3.15801	−	5.46983i	0.126931	−	0.219851i	−0.795555	−	0.605881i	$-0.792821\pi$
$619$	3.15801	−	5.46983i	0.126931	−	0.219851i	0.922486	+	0.386030i	$0.126154\pi$
$620$		0			0
$621$	2.57707	−	4.46362i	0.103414	−	0.179119i
$622$		0			0
$623$	−0.198674	−	0.344114i	−0.00795972	−	0.0137866i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	23.0289			0.919684
$628$		0			0
$629$	19.7546	+	34.2159i	0.787666	+	1.36428i
$630$		0			0
$631$	−3.45825	+	5.98987i	−0.137671	+	0.238453i	−0.926615	−	0.376013i	$-0.877295\pi$
$631$	−3.45825	+	5.98987i	−0.137671	+	0.238453i	0.788944	+	0.614465i	$0.210628\pi$
$632$		0			0
$633$	−9.86509	+	17.0868i	−0.392102	+	0.679141i
$634$		0			0
$635$	−4.27915	−	7.41171i	−0.169813	−	0.294125i
$636$		0			0
$637$	7.95799	+	13.7836i	0.315307	+	0.546128i
$638$		0			0
$639$	−6.02544	−	10.4364i	−0.238363	−	0.412856i
$640$		0			0
$641$	−5.94521	−	10.2974i	−0.234822	−	0.406723i	0.724399	−	0.689381i	$-0.242117\pi$
$641$	−5.94521	−	10.2974i	−0.234822	−	0.406723i	−0.959221	+	0.282658i	$0.908784\pi$
$642$		0			0
$643$	18.3036			0.721822			0.360911	−	0.932600i	$-0.382466\pi$
$643$	18.3036			0.721822			0.360911	+	0.932600i	$0.382466\pi$
$644$		0			0
$645$	10.9631			0.431673
$646$		0			0
$647$	−14.5162	+	25.1429i	−0.570692	+	0.988468i	0.425803	+	0.904816i	$0.359992\pi$
$647$	−14.5162	+	25.1429i	−0.570692	+	0.988468i	−0.996495	+	0.0836518i	$0.973342\pi$
$648$		0			0
$649$	36.1669	+	62.6428i	1.41967	+	2.45895i
$650$		0			0
$651$	1.41293	−	2.44727i	0.0553773	−	0.0959162i
$652$		0			0
$653$	14.5471	−	25.1963i	0.569273	−	0.986009i	−0.427365	−	0.904079i	$-0.640558\pi$
$653$	14.5471	−	25.1963i	0.569273	−	0.986009i	0.996638	−	0.0819302i	$-0.0261085\pi$
$654$		0			0
$655$	−9.67842			−0.378167
$656$		0			0
$657$	0.167288	−	0.289752i	0.00652654	−	0.0113043i
$658$		0			0
$659$	3.33052	+	5.76863i	0.129739	+	0.224714i	0.923575	−	0.383417i	$-0.125253\pi$
$659$	3.33052	+	5.76863i	0.129739	+	0.224714i	−0.793837	+	0.608131i	$0.791919\pi$
$660$		0			0
$661$	24.1141			0.937931			0.468965	−	0.883217i	$-0.344627\pi$
$661$	24.1141			0.937931			0.468965	+	0.883217i	$0.344627\pi$
$662$		0			0
$663$	−8.65210	−	14.9859i	−0.336020	−	0.582003i
$664$		0			0
$665$	−1.01215			−0.0392495
$666$		0			0
$667$	−31.6118			−1.22401
$668$		0			0
$669$	−1.29322			−0.0499986
$670$		0			0
$671$	−59.8999			−2.31241
$672$		0			0
$673$	−1.74705			−0.0673437			−0.0336719	−	0.999433i	$-0.510720\pi$
$673$	−1.74705			−0.0673437			−0.0336719	+	0.999433i	$0.510720\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	2.43731	+	4.22154i	0.0936733	+	0.162247i	0.909054	−	0.416678i	$-0.136806\pi$
$677$	2.43731	+	4.22154i	0.0936733	+	0.162247i	−0.815381	+	0.578925i	$0.803472\pi$
$678$		0			0
$679$	−1.42434			−0.0546613
$680$		0			0
$681$	−0.117554	−	0.203609i	−0.00450468	−	0.00780233i
$682$		0			0
$683$	−7.05378	+	12.2175i	−0.269905	+	0.467490i	−0.968837	−	0.247699i	$-0.920326\pi$
$683$	−7.05378	+	12.2175i	−0.269905	+	0.467490i	0.698932	+	0.715188i	$0.253659\pi$
$684$		0			0
$685$	−5.37712			−0.205449
$686$		0			0
$687$	4.55100	−	7.88257i	0.173632	−	0.300739i
$688$		0			0
$689$	−13.8622	+	24.0101i	−0.528109	+	0.914712i
$690$		0			0
$691$	−13.7011	−	23.7311i	−0.521215	−	0.902772i	−0.999696	−	0.0246733i	$-0.992145\pi$
$691$	−13.7011	−	23.7311i	−0.521215	−	0.902772i	0.478480	−	0.878098i	$-0.341188\pi$
$692$		0			0
$693$	0.822768	−	1.42508i	0.0312544	−	0.0541342i
$694$		0			0
$695$	−12.8831			−0.488684
$696$		0			0
$697$	−27.2348			−1.03159
$698$		0			0
$699$	−9.73932	−	16.8690i	−0.368375	−	0.638044i
$700$		0			0
$701$	−5.74457	−	9.94989i	−0.216969	−	0.375802i	0.736911	−	0.675990i	$-0.236284\pi$
$701$	−5.74457	−	9.94989i	−0.216969	−	0.375802i	−0.953880	+	0.300188i	$0.902951\pi$
$702$		0			0
$703$	9.87113	+	17.0973i	0.372297	+	0.644837i
$704$		0			0
$705$	−6.55135	−	11.3473i	−0.246738	−	0.427363i
$706$		0			0
$707$	−1.49266	+	2.58536i	−0.0561372	+	0.0972326i
$708$		0			0
$709$	−11.6373	+	20.1564i	−0.437048	+	0.756989i	−0.997460	−	0.0712246i	$-0.977309\pi$
$709$	−11.6373	+	20.1564i	−0.437048	+	0.756989i	0.560412	+	0.828214i	$0.310643\pi$
$710$		0			0
$711$	4.90196	+	8.49044i	0.183838	+	0.318417i
$712$		0			0
$713$	−54.1587			−2.02826
$714$		0			0
$715$	14.0577			0.525727
$716$		0			0
$717$	4.89980	+	8.48670i	0.182986	+	0.316942i
$718$		0			0
$719$	11.1752	−	19.3560i	0.416764	−	0.721857i	−0.578848	−	0.815436i	$-0.696497\pi$
$719$	11.1752	−	19.3560i	0.416764	−	0.721857i	0.995612	+	0.0935790i	$0.0298308\pi$
$720$		0			0
$721$	−0.434444	+	0.752478i	−0.0161795	+	0.0280238i
$722$		0			0
$723$	15.3003			0.569023
$724$		0			0
$725$	−3.06664	−	5.31157i	−0.113892	−	0.197267i
$726$		0			0
$727$	0.885689	−	1.53406i	0.0328484	−	0.0568951i	−0.849134	−	0.528178i	$-0.822875\pi$
$727$	0.885689	−	1.53406i	0.0328484	−	0.0568951i	0.881982	+	0.471283i	$0.156209\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−41.2867	+	71.5107i	−1.52705	+	2.64492i
$732$		0			0
$733$	3.15295	+	5.46108i	0.116457	+	0.201709i	0.918361	−	0.395743i	$-0.129513\pi$
$733$	3.15295	+	5.46108i	0.116457	+	0.201709i	−0.801904	+	0.597453i	$0.796180\pi$
$734$		0			0
$735$	3.46384	−	5.99954i	0.127766	−	0.221297i
$736$		0			0
$737$	−49.6705	−	6.42789i	−1.82964	−	0.236774i
$738$		0			0
$739$	8.04082	−	13.9271i	0.295786	−	0.512317i	−0.679381	−	0.733785i	$-0.737752\pi$
$739$	8.04082	−	13.9271i	0.295786	−	0.512317i	0.975167	+	0.221469i	$0.0710851\pi$
$740$		0			0
$741$	−4.32336	−	7.48827i	−0.158822	−	0.275089i
$742$		0			0
$743$	−13.6661	+	23.6704i	−0.501361	+	0.868383i	0.498637	+	0.866811i	$0.333834\pi$
$743$	−13.6661	+	23.6704i	−0.501361	+	0.868383i	−0.999999	+	0.00157266i	$0.999499\pi$
$744$		0			0
$745$	3.97030			0.145461
$746$		0			0
$747$	4.16136	−	7.20768i	0.152256	−	0.263715i
$748$		0			0
$749$	−1.15387	−	1.99856i	−0.0421615	−	0.0730259i
$750$		0			0
$751$	21.9798			0.802054			0.401027	−	0.916066i	$-0.368653\pi$
$751$	21.9798			0.802054			0.401027	+	0.916066i	$0.368653\pi$
$752$		0			0
$753$	0.00388720	−	0.00673283i	0.000141657	−	0.000245358i
$754$		0			0
$755$	2.43423	−	4.21621i	0.0885907	−	0.153444i
$756$		0			0
$757$	−17.1659	−	29.7321i	−0.623904	−	1.08063i	−0.988752	−	0.149566i	$-0.952212\pi$
$757$	−17.1659	−	29.7321i	−0.623904	−	1.08063i	0.364848	−	0.931067i	$-0.381121\pi$
$758$		0			0
$759$	−31.5372			−1.14473
$760$		0			0
$761$	−21.9275			−0.794871			−0.397436	−	0.917630i	$-0.630100\pi$
$761$	−21.9275			−0.794871			−0.397436	+	0.917630i	$0.630100\pi$
$762$		0			0
$763$	−2.42364	−	4.19787i	−0.0877418	−	0.151973i
$764$		0			0
$765$	−3.76596	+	6.52284i	−0.136159	+	0.235834i
$766$		0			0
$767$	13.5797	−	23.5207i	0.490333	−	0.849282i
$768$		0			0
$769$	−7.91490	−	13.7090i	−0.285419	−	0.494360i	0.687292	−	0.726381i	$-0.258799\pi$
$769$	−7.91490	−	13.7090i	−0.285419	−	0.494360i	−0.972711	+	0.232022i	$0.925466\pi$
$770$		0			0
$771$	0.440192	+	0.762436i	0.0158531	+	0.0274585i
$772$		0			0
$773$	−7.02348	−	12.1650i	−0.252617	−	0.437546i	0.711628	−	0.702556i	$-0.247958\pi$
$773$	−7.02348	−	12.1650i	−0.252617	−	0.437546i	−0.964246	+	0.265010i	$0.914625\pi$
$774$		0			0
$775$	−5.25390	−	9.10002i	−0.188726	−	0.326883i
$776$		0			0
$777$	1.41069			0.0506082
$778$		0			0
$779$	−13.6089			−0.487590
$780$		0			0
$781$	−36.8686	+	63.8582i	−1.31926	+	2.28503i
$782$		0			0
$783$	−3.06664	−	5.31157i	−0.109593	−	0.189820i
$784$		0			0
$785$	−0.387721	+	0.671552i	−0.0138384	+	0.0239687i
$786$		0			0
$787$	−1.15172	+	1.99484i	−0.0410544	+	0.0711083i	−0.885822	−	0.464024i	$-0.846405\pi$
$787$	−1.15172	+	1.99484i	−0.0410544	+	0.0711083i	0.844768	+	0.535133i	$0.179738\pi$
$788$		0			0
$789$	−14.2044			−0.505690
$790$		0			0
$791$	2.64428	−	4.58003i	0.0940199	−	0.162847i
$792$		0			0
$793$	11.2454	+	19.4776i	0.399335	+	0.691669i
$794$		0			0
$795$	12.0675			0.427990
$796$		0			0
$797$	−4.64793	−	8.05046i	−0.164638	−	0.285162i	0.771889	−	0.635758i	$-0.219312\pi$
$797$	−4.64793	−	8.05046i	−0.164638	−	0.285162i	−0.936527	+	0.350596i	$0.885979\pi$
$798$		0			0
$799$	98.6884			3.49135
$800$		0			0
$801$	−1.47751			−0.0522054
$802$		0			0
$803$	−2.04721			−0.0722446
$804$		0			0
$805$	1.38611			0.0488538
$806$		0			0
$807$	−9.28569			−0.326872
$808$		0			0
$809$	−37.1029			−1.30447			−0.652235	−	0.758017i	$-0.726168\pi$
$809$	−37.1029			−1.30447			−0.652235	+	0.758017i	$0.726168\pi$
$810$		0			0
$811$	4.31942	+	7.48145i	0.151675	+	0.262709i	0.931843	−	0.362861i	$-0.118200\pi$
$811$	4.31942	+	7.48145i	0.151675	+	0.262709i	−0.780168	+	0.625570i	$0.784867\pi$
$812$		0			0
$813$	25.0251			0.877669
$814$		0			0
$815$	2.56301	+	4.43926i	0.0897783	+	0.155501i
$816$		0			0
$817$	−20.6305	+	35.7331i	−0.721770	+	1.25014i
$818$		0			0
$819$	−0.617854			−0.0215896
$820$		0			0
$821$	−8.11182	+	14.0501i	−0.283105	+	0.490351i	−0.972148	−	0.234369i	$-0.924698\pi$
$821$	−8.11182	+	14.0501i	−0.283105	+	0.490351i	0.689043	+	0.724720i	$0.258031\pi$
$822$		0			0
$823$	16.5546	−	28.6733i	0.577055	−	0.999489i	−0.418760	−	0.908097i	$-0.637535\pi$
$823$	16.5546	−	28.6733i	0.577055	−	0.999489i	0.995815	−	0.0913921i	$-0.0291317\pi$
$824$		0			0
$825$	−3.05941	−	5.29905i	−0.106515	−	0.184489i
$826$		0			0
$827$	20.0811	−	34.7816i	0.698290	−	1.20947i	−0.270769	−	0.962644i	$-0.587278\pi$
$827$	20.0811	−	34.7816i	0.698290	−	1.20947i	0.969059	−	0.246829i	$-0.0793886\pi$
$828$		0			0
$829$	43.5191			1.51148			0.755741	−	0.654871i	$-0.227277\pi$
$829$	43.5191			1.51148			0.755741	+	0.654871i	$0.227277\pi$
$830$		0			0
$831$	1.55977			0.0541079
$832$		0			0
$833$	26.0894	+	45.1881i	0.903943	+	1.56567i
$834$		0			0
$835$	5.81380	+	10.0698i	0.201195	+	0.348480i
$836$		0			0
$837$	−5.25390	−	9.10002i	−0.181601	−	0.314543i
$838$		0			0
$839$	−9.12578	−	15.8063i	−0.315057	−	0.545695i	0.664393	−	0.747384i	$-0.268690\pi$
$839$	−9.12578	−	15.8063i	−0.315057	−	0.545695i	−0.979450	+	0.201689i	$0.935357\pi$
$840$		0			0
$841$	−4.30855	+	7.46263i	−0.148571	+	0.257332i
$842$		0			0
$843$	16.3222	−	28.2709i	0.562168	−	0.973703i
$844$		0			0
$845$	3.86087	+	6.68721i	0.132818	+	0.230047i
$846$		0			0
$847$	−7.11050			−0.244320
$848$		0			0
$849$	−23.0663			−0.791633
$850$		0			0
$851$	−13.5182	−	23.4142i	−0.463397	−	0.802627i
$852$		0			0
$853$	−11.1112	+	19.2451i	−0.380440	+	0.658941i	−0.991125	−	0.132932i	$-0.957561\pi$
$853$	−11.1112	+	19.2451i	−0.380440	+	0.658941i	0.610685	+	0.791873i	$0.290894\pi$
$854$		0			0
$855$	−1.88181	+	3.25939i	−0.0643565	+	0.111469i
$856$		0			0
$857$	23.7509			0.811315			0.405657	−	0.914025i	$-0.367043\pi$
$857$	23.7509			0.811315			0.405657	+	0.914025i	$0.367043\pi$
$858$		0			0
$859$	−15.1911	−	26.3118i	−0.518315	−	0.897748i	−0.999774	−	0.0212788i	$-0.993226\pi$
$859$	−15.1911	−	26.3118i	−0.518315	−	0.897748i	0.481459	−	0.876469i	$-0.340107\pi$
$860$		0			0
$861$	−0.486215	+	0.842149i	−0.0165702	+	0.0287004i
$862$		0			0
$863$	45.1045			1.53537			0.767687	−	0.640825i	$-0.221407\pi$
$863$	45.1045			1.53537			0.767687	+	0.640825i	$0.221407\pi$
$864$		0			0
$865$	−6.10683	+	10.5773i	−0.207638	+	0.359640i
$866$		0			0
$867$	−19.8649	−	34.4071i	−0.674648	−	1.16853i
$868$		0			0
$869$	29.9942	−	51.9515i	1.01748	−	1.76233i
$870$		0			0
$871$	7.23480	+	17.3580i	0.245142	+	0.588155i
$872$		0			0
$873$	−2.64816	+	4.58675i	−0.0896268	+	0.155238i
$874$		0			0
$875$	0.134465	+	0.232901i	0.00454575	+	0.00787348i
$876$		0			0
$877$	3.54078	−	6.13281i	0.119564	−	0.207090i	−0.800031	−	0.599958i	$-0.795184\pi$
$877$	3.54078	−	6.13281i	0.119564	−	0.207090i	0.919595	+	0.392868i	$0.128517\pi$
$878$		0			0
$879$	−29.7425			−1.00319
$880$		0			0
$881$	4.57111	−	7.91740i	0.154005	−	0.266744i	−0.778691	−	0.627407i	$-0.784116\pi$
$881$	4.57111	−	7.91740i	0.154005	−	0.266744i	0.932696	+	0.360663i	$0.117450\pi$
$882$		0			0
$883$	−21.2989	−	36.8907i	−0.716764	−	1.24147i	−0.962275	−	0.272077i	$-0.912289\pi$
$883$	−21.2989	−	36.8907i	−0.716764	−	1.24147i	0.245512	−	0.969394i	$-0.421044\pi$
$884$		0			0
$885$	−11.8215			−0.397376
$886$		0			0
$887$	−10.3149	+	17.8660i	−0.346342	+	0.599881i	−0.985597	−	0.169114i	$-0.945910\pi$
$887$	−10.3149	+	17.8660i	−0.346342	+	0.599881i	0.639255	+	0.768995i	$0.279243\pi$
$888$		0			0
$889$	1.15079	−	1.99323i	0.0385964	−	0.0668510i
$890$		0			0
$891$	−3.05941	−	5.29905i	−0.102494	−	0.177525i
$892$		0			0
$893$	49.3135			1.65021
$894$		0			0
$895$	20.1511			0.673578
$896$		0			0
$897$	5.92069	+	10.2549i	0.197686	+	0.342402i
$898$		0			0
$899$	−32.2236	+	55.8130i	−1.07472	+	1.86147i
$900$		0			0
$901$	−45.4458	+	78.7144i	−1.51402	+	2.62236i
$902$		0			0
$903$	1.47416	+	2.55332i	0.0490570	+	0.0849692i
$904$		0			0
$905$	−2.76240	−	4.78462i	−0.0918254	−	0.159046i
$906$		0			0
$907$	1.45033	+	2.51205i	0.0481575	+	0.0834112i	0.889099	−	0.457714i	$-0.151332\pi$
$907$	1.45033	+	2.51205i	0.0481575	+	0.0834112i	−0.840942	+	0.541125i	$0.817998\pi$
$908$		0			0
$909$	5.55036	+	9.61350i	0.184094	+	0.318860i
$910$		0			0
$911$	47.0652			1.55934			0.779669	−	0.626192i	$-0.215387\pi$
$911$	47.0652			1.55934			0.779669	+	0.626192i	$0.215387\pi$
$912$		0			0
$913$	−50.9252			−1.68538
$914$		0			0
$915$	4.89473	−	8.47792i	0.161815	−	0.280271i
$916$		0			0
$917$	−1.30141	−	2.25411i	−0.0429764	−	0.0744373i
$918$		0			0
$919$	−10.1149	+	17.5195i	−0.333658	+	0.577913i	−0.983226	−	0.182390i	$-0.941617\pi$
$919$	−10.1149	+	17.5195i	−0.333658	+	0.577913i	0.649568	+	0.760304i	$0.274950\pi$
$920$		0			0
$921$	−7.69252	+	13.3238i	−0.253477	+	0.439036i
$922$		0			0
$923$	27.6863			0.911305
$924$		0			0
$925$	2.62278	−	4.54279i	0.0862365	−	0.149366i
$926$		0			0
$927$	1.61545	+	2.79804i	0.0530583	+	0.0918997i
$928$		0			0
$929$	−5.78842			−0.189912			−0.0949560	−	0.995481i	$-0.530271\pi$
$929$	−5.78842			−0.189912			−0.0949560	+	0.995481i	$0.530271\pi$
$930$		0			0
$931$	13.0366	+	22.5800i	0.427256	+	0.740029i
$932$		0			0
$933$	13.6420			0.446620
$934$		0			0
$935$	46.0865			1.50719
$936$		0			0
$937$	7.62353			0.249050			0.124525	−	0.992216i	$-0.460259\pi$
$937$	7.62353			0.249050			0.124525	+	0.992216i	$0.460259\pi$
$938$		0			0
$939$	24.2528			0.791460
$940$		0			0
$941$	8.02812			0.261709			0.130855	−	0.991402i	$-0.458228\pi$
$941$	8.02812			0.261709			0.130855	+	0.991402i	$0.458228\pi$
$942$		0			0
$943$	18.6369			0.606902
$944$		0			0
$945$	0.134465	+	0.232901i	0.00437415	+	0.00757626i
$946$		0			0
$947$	39.8835			1.29604			0.648021	−	0.761623i	$-0.275597\pi$
$947$	39.8835			1.29604			0.648021	+	0.761623i	$0.275597\pi$
$948$		0			0
$949$	0.384336	+	0.665690i	0.0124761	+	0.0216092i
$950$		0			0
$951$	−2.84265	+	4.92362i	−0.0921794	+	0.159659i
$952$		0			0
$953$	22.8924			0.741557			0.370778	−	0.928721i	$-0.379091\pi$
$953$	22.8924			0.741557			0.370778	+	0.928721i	$0.379091\pi$
$954$		0			0
$955$	2.25042	−	3.89784i	0.0728219	−	0.126131i
$956$		0			0
$957$	−18.7642	+	32.5006i	−0.606561	+	1.05059i
$958$		0			0
$959$	−0.723036	−	1.25233i	−0.0233480	−	0.0404400i
$960$		0			0
$961$	−39.7070	+	68.7745i	−1.28087	+	2.21853i
$962$		0			0
$963$	−8.58118			−0.276525
$964$		0			0
$965$	0.522022			0.0168045
$966$		0			0
$967$	11.2004	+	19.3997i	0.360182	+	0.623854i	0.987991	−	0.154514i	$-0.0493812\pi$
$967$	11.2004	+	19.3997i	0.360182	+	0.623854i	−0.627808	+	0.778368i	$0.716048\pi$
$968$		0			0
$969$	−14.1736	−	24.5494i	−0.455322	−	0.788642i
$970$		0			0
$971$	22.5266	+	39.0173i	0.722914	+	1.25212i	0.959827	+	0.280593i	$0.0905310\pi$
$971$	22.5266	+	39.0173i	0.722914	+	1.25212i	−0.236913	+	0.971531i	$0.576136\pi$
$972$		0			0
$973$	−1.73233	−	3.00048i	−0.0555359	−	0.0961910i
$974$		0			0
$975$	−1.14872	+	1.98965i	−0.0367886	+	0.0637198i
$976$		0			0
$977$	19.2937	−	33.4178i	0.617262	−	1.06913i	−0.372722	−	0.927943i	$-0.621575\pi$
$977$	19.2937	−	33.4178i	0.617262	−	1.06913i	0.989983	−	0.141185i	$-0.0450913\pi$
$978$		0			0
$979$	4.52032	+	7.82942i	0.144470	+	0.250229i
$980$		0			0
$981$	−18.0243			−0.575472
$982$		0			0
$983$	29.0071			0.925182			0.462591	−	0.886572i	$-0.346920\pi$
$983$	29.0071			0.925182			0.462591	+	0.886572i	$0.346920\pi$
$984$		0			0
$985$	10.7953	+	18.6980i	0.343966	+	0.595766i
$986$		0			0
$987$	1.76186	−	3.05162i	0.0560805	−	0.0971343i
$988$		0			0
$989$	28.2528	−	48.9352i	0.898386	−	1.55605i
$990$		0			0
$991$	−8.56394			−0.272043			−0.136021	−	0.990706i	$-0.543432\pi$
$991$	−8.56394			−0.272043			−0.136021	+	0.990706i	$0.543432\pi$
$992$		0			0
$993$	6.80666	+	11.7895i	0.216003	+	0.374128i
$994$		0			0
$995$	−1.46680	+	2.54057i	−0.0465007	+	0.0805416i
$996$		0			0
$997$	49.4074			1.56475			0.782375	−	0.622808i	$-0.214008\pi$
$997$	49.4074			1.56475			0.782375	+	0.622808i	$0.214008\pi$
$998$		0			0
$999$	2.62278	−	4.54279i	0.0829811	−	0.143727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.3781.7	yes	24
67.37	even	3	inner	4020.2.q.m.841.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.7	✓	24	67.37	even	3	inner
4020.2.q.m.3781.7	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(0.134465 + 0.232901i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(0.134465 + 0.232901i) q^{7} +1.00000 q^{9} +(-3.05941 - 5.29905i) q^{11} +(-1.14872 + 1.98965i) q^{13} +1.00000 q^{15} +(-3.76596 + 6.52284i) q^{17} +(-1.88181 + 3.25939i) q^{19} +(0.134465 + 0.232901i) q^{21} +(2.57707 - 4.46362i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-3.06664 - 5.31157i) q^{29} +(-5.25390 - 9.10002i) q^{31} +(-3.05941 - 5.29905i) q^{33} +(0.134465 + 0.232901i) q^{35} +(2.62278 - 4.54279i) q^{37} +(-1.14872 + 1.98965i) q^{39} +(1.80796 + 3.13148i) q^{41} +10.9631 q^{43} +1.00000 q^{45} +(-6.55135 - 11.3473i) q^{47} +(3.46384 - 5.99954i) q^{49} +(-3.76596 + 6.52284i) q^{51} +12.0675 q^{53} +(-3.05941 - 5.29905i) q^{55} +(-1.88181 + 3.25939i) q^{57} -11.8215 q^{59} +(4.89473 - 8.47792i) q^{61} +(0.134465 + 0.232901i) q^{63} +(-1.14872 + 1.98965i) q^{65} +(4.96860 - 6.50484i) q^{67} +(2.57707 - 4.46362i) q^{69} +(-6.02544 - 10.4364i) q^{71} +(0.167288 - 0.289752i) q^{73} +1.00000 q^{75} +(0.822768 - 1.42508i) q^{77} +(4.90196 + 8.49044i) q^{79} +1.00000 q^{81} +(4.16136 - 7.20768i) q^{83} +(-3.76596 + 6.52284i) q^{85} +(-3.06664 - 5.31157i) q^{87} -1.47751 q^{89} -0.617854 q^{91} +(-5.25390 - 9.10002i) q^{93} +(-1.88181 + 3.25939i) q^{95} +(-2.64816 + 4.58675i) q^{97} +(-3.05941 - 5.29905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more