LMFDB - Embedded newform 4020.2.q.l.841.11

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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.11
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.l.3781.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -1.00000 q^{5} +(2.11433 - 3.66213i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -1.00000 q^{5} +(2.11433 - 3.66213i) q^{7} +1.00000 q^{9} +(-1.59532 + 2.76317i) q^{11} +(-3.28938 - 5.69738i) q^{13} +1.00000 q^{15} +(3.94016 + 6.82456i) q^{17} +(-0.787346 - 1.36372i) q^{19} +(-2.11433 + 3.66213i) q^{21} +(-1.83942 - 3.18598i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.82916 - 6.63231i) q^{29} +(-1.14320 + 1.98007i) q^{31} +(1.59532 - 2.76317i) q^{33} +(-2.11433 + 3.66213i) q^{35} +(-5.16859 - 8.95226i) q^{37} +(3.28938 + 5.69738i) q^{39} +(-2.81544 + 4.87649i) q^{41} +0.735148 q^{43} -1.00000 q^{45} +(2.26378 - 3.92098i) q^{47} +(-5.44080 - 9.42375i) q^{49} +(-3.94016 - 6.82456i) q^{51} -4.70757 q^{53} +(1.59532 - 2.76317i) q^{55} +(0.787346 + 1.36372i) q^{57} +4.74077 q^{59} +(4.83423 + 8.37313i) q^{61} +(2.11433 - 3.66213i) q^{63} +(3.28938 + 5.69738i) q^{65} +(7.48888 - 3.30405i) q^{67} +(1.83942 + 3.18598i) q^{69} +(-3.13699 + 5.43343i) q^{71} +(-5.15891 - 8.93550i) q^{73} -1.00000 q^{75} +(6.74607 + 11.6845i) q^{77} +(-4.63648 + 8.03063i) q^{79} +1.00000 q^{81} +(0.0412902 + 0.0715167i) q^{83} +(-3.94016 - 6.82456i) q^{85} +(-3.82916 + 6.63231i) q^{87} -8.35910 q^{89} -27.8194 q^{91} +(1.14320 - 1.98007i) q^{93} +(0.787346 + 1.36372i) q^{95} +(-3.08777 - 5.34818i) q^{97} +(-1.59532 + 2.76317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

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
$7$	2.11433	−	3.66213i	0.799142	−	1.38416i	−0.121033	−	0.992649i	$-0.538621\pi$
$7$	2.11433	−	3.66213i	0.799142	−	1.38416i	0.920175	−	0.391507i	$-0.128046\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−1.59532	+	2.76317i	−0.481007	+	0.833128i	−0.999762	−	0.0217942i	$-0.993062\pi$
$11$	−1.59532	+	2.76317i	−0.481007	+	0.833128i	0.518756	+	0.854923i	$0.326395\pi$
$12$		0			0
$13$	−3.28938	−	5.69738i	−0.912311	−	1.58017i	−0.810791	−	0.585336i	$-0.800963\pi$
$13$	−3.28938	−	5.69738i	−0.912311	−	1.58017i	−0.101520	−	0.994833i	$-0.532371\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	3.94016	+	6.82456i	0.955629	+	1.65520i	0.732921	+	0.680313i	$0.238156\pi$
$17$	3.94016	+	6.82456i	0.955629	+	1.65520i	0.222708	+	0.974885i	$0.428510\pi$
$18$		0			0
$19$	−0.787346	−	1.36372i	−0.180630	−	0.312860i	0.761465	−	0.648205i	$-0.224480\pi$
$19$	−0.787346	−	1.36372i	−0.180630	−	0.312860i	−0.942095	+	0.335346i	$0.891147\pi$
$20$		0			0
$21$	−2.11433	+	3.66213i	−0.461385	+	0.799142i
$22$		0			0
$23$	−1.83942	−	3.18598i	−0.383546	−	0.664322i	0.608020	−	0.793922i	$-0.291964\pi$
$23$	−1.83942	−	3.18598i	−0.383546	−	0.664322i	−0.991566	+	0.129600i	$0.958631\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.82916	−	6.63231i	0.711058	−	1.23159i	−0.253402	−	0.967361i	$-0.581550\pi$
$29$	3.82916	−	6.63231i	0.711058	−	1.23159i	0.964460	−	0.264228i	$-0.0851171\pi$
$30$		0			0
$31$	−1.14320	+	1.98007i	−0.205324	+	0.355632i	−0.950236	−	0.311531i	$-0.899158\pi$
$31$	−1.14320	+	1.98007i	−0.205324	+	0.355632i	0.744912	+	0.667163i	$0.232491\pi$
$32$		0			0
$33$	1.59532	−	2.76317i	0.277709	−	0.481007i
$34$		0			0
$35$	−2.11433	+	3.66213i	−0.357387	+	0.619013i
$36$		0			0
$37$	−5.16859	−	8.95226i	−0.849711	−	1.47174i	−0.881466	−	0.472247i	$-0.843443\pi$
$37$	−5.16859	−	8.95226i	−0.849711	−	1.47174i	0.0317556	−	0.999496i	$-0.489890\pi$
$38$		0			0
$39$	3.28938	+	5.69738i	0.526723	+	0.912311i
$40$		0			0
$41$	−2.81544	+	4.87649i	−0.439698	+	0.761579i	−0.997666	−	0.0682831i	$-0.978248\pi$
$41$	−2.81544	+	4.87649i	−0.439698	+	0.761579i	0.557968	+	0.829863i	$0.311581\pi$
$42$		0			0
$43$	0.735148			0.112109			0.0560545	−	0.998428i	$-0.482148\pi$
$43$	0.735148			0.112109			0.0560545	+	0.998428i	$0.482148\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	2.26378	−	3.92098i	0.330206	−	0.571933i	−0.652346	−	0.757921i	$-0.726215\pi$
$47$	2.26378	−	3.92098i	0.330206	−	0.571933i	0.982552	+	0.185988i	$0.0595485\pi$
$48$		0			0
$49$	−5.44080	−	9.42375i	−0.777257	−	1.34625i
$50$		0			0
$51$	−3.94016	−	6.82456i	−0.551733	−	0.955629i
$52$		0			0
$53$	−4.70757			−0.646635			−0.323317	−	0.946291i	$-0.604798\pi$
$53$	−4.70757			−0.646635			−0.323317	+	0.946291i	$0.604798\pi$
$54$		0			0
$55$	1.59532	−	2.76317i	0.215113	−	0.372586i
$56$		0			0
$57$	0.787346	+	1.36372i	0.104287	+	0.180630i
$58$		0			0
$59$	4.74077			0.617196			0.308598	−	0.951193i	$-0.400140\pi$
$59$	4.74077			0.617196			0.308598	+	0.951193i	$0.400140\pi$
$60$		0			0
$61$	4.83423	+	8.37313i	0.618960	+	1.07207i	0.989676	+	0.143324i	$0.0457789\pi$
$61$	4.83423	+	8.37313i	0.618960	+	1.07207i	−0.370716	+	0.928746i	$0.620888\pi$
$62$		0			0
$63$	2.11433	−	3.66213i	0.266381	−	0.461385i
$64$		0			0
$65$	3.28938	+	5.69738i	0.407998	+	0.706673i
$66$		0			0
$67$	7.48888	−	3.30405i	0.914912	−	0.403654i
$67$	7.48888	−	3.30405i	0.914912	−	0.403654i
$68$		0			0
$69$	1.83942	+	3.18598i	0.221441	+	0.383546i
$70$		0			0
$71$	−3.13699	+	5.43343i	−0.372292	+	0.644829i	−0.989918	−	0.141643i	$-0.954761\pi$
$71$	−3.13699	+	5.43343i	−0.372292	+	0.644829i	0.617625	+	0.786472i	$0.288095\pi$
$72$		0			0
$73$	−5.15891	−	8.93550i	−0.603805	−	1.04582i	−0.992239	−	0.124344i	$-0.960317\pi$
$73$	−5.15891	−	8.93550i	−0.603805	−	1.04582i	0.388434	−	0.921476i	$-0.373016\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	6.74607	+	11.6845i	0.768786	+	1.33158i
$78$		0			0
$79$	−4.63648	+	8.03063i	−0.521645	+	0.903516i	0.478038	+	0.878339i	$0.341348\pi$
$79$	−4.63648	+	8.03063i	−0.521645	+	0.903516i	−0.999683	+	0.0251768i	$0.991985\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	0.0412902	+	0.0715167i	0.00453219	+	0.00784997i	0.868283	−	0.496070i	$-0.165224\pi$
$83$	0.0412902	+	0.0715167i	0.00453219	+	0.00784997i	−0.863750	+	0.503920i	$0.831891\pi$
$84$		0			0
$85$	−3.94016	−	6.82456i	−0.427370	−	0.740227i
$86$		0			0
$87$	−3.82916	+	6.63231i	−0.410530	+	0.711058i
$88$		0			0
$89$	−8.35910			−0.886063			−0.443032	−	0.896506i	$-0.646097\pi$
$89$	−8.35910			−0.886063			−0.443032	+	0.896506i	$0.646097\pi$
$90$		0			0
$91$	−27.8194			−2.91627
$92$		0			0
$93$	1.14320	−	1.98007i	0.118544	−	0.205324i
$94$		0			0
$95$	0.787346	+	1.36372i	0.0807800	+	0.139915i
$96$		0			0
$97$	−3.08777	−	5.34818i	−0.313516	−	0.543025i	0.665605	−	0.746304i	$-0.268173\pi$
$97$	−3.08777	−	5.34818i	−0.313516	−	0.543025i	−0.979121	+	0.203279i	$0.934840\pi$
$98$		0			0
$99$	−1.59532	+	2.76317i	−0.160336	+	0.277709i
$100$		0			0
$101$	3.78402	−	6.55412i	0.376524	−	0.652159i	−0.614030	−	0.789283i	$-0.710452\pi$
$101$	3.78402	−	6.55412i	0.376524	−	0.652159i	0.990554	+	0.137124i	$0.0437858\pi$
$102$		0			0
$103$	−8.50386	+	14.7291i	−0.837910	+	1.45130i	0.0537290	+	0.998556i	$0.482889\pi$
$103$	−8.50386	+	14.7291i	−0.837910	+	1.45130i	−0.891639	+	0.452747i	$0.850444\pi$
$104$		0			0
$105$	2.11433	−	3.66213i	0.206338	−	0.357387i
$106$		0			0
$107$	−1.00359			−0.0970203			−0.0485101	−	0.998823i	$-0.515447\pi$
$107$	−1.00359			−0.0970203			−0.0485101	+	0.998823i	$0.515447\pi$
$108$		0			0
$109$	5.14050			0.492371			0.246185	−	0.969223i	$-0.420823\pi$
$109$	5.14050			0.492371			0.246185	+	0.969223i	$0.420823\pi$
$110$		0			0
$111$	5.16859	+	8.95226i	0.490581	+	0.849711i
$112$		0			0
$113$	−7.08806	+	12.2769i	−0.666788	+	1.15491i	0.312009	+	0.950079i	$0.398998\pi$
$113$	−7.08806	+	12.2769i	−0.666788	+	1.15491i	−0.978797	+	0.204832i	$0.934335\pi$
$114$		0			0
$115$	1.83942	+	3.18598i	0.171527	+	0.297094i
$116$		0			0
$117$	−3.28938	−	5.69738i	−0.304104	−	0.526723i
$118$		0			0
$119$	33.3232			3.05474
$120$		0			0
$121$	0.409911	+	0.709987i	0.0372647	+	0.0645443i
$122$		0			0
$123$	2.81544	−	4.87649i	0.253860	−	0.439698i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.54877	−	4.41460i	0.226167	−	0.391733i	−0.730502	−	0.682911i	$-0.760714\pi$
$127$	2.54877	−	4.41460i	0.226167	−	0.391733i	0.956669	+	0.291178i	$0.0940472\pi$
$128$		0			0
$129$	−0.735148			−0.0647262
$130$		0			0
$131$	−14.5076			−1.26753			−0.633767	−	0.773524i	$-0.718492\pi$
$131$	−14.5076			−1.26753			−0.633767	+	0.773524i	$0.718492\pi$
$132$		0			0
$133$	−6.65885			−0.577395
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−8.42224			−0.719561			−0.359780	−	0.933037i	$-0.617148\pi$
$137$	−8.42224			−0.719561			−0.359780	+	0.933037i	$0.617148\pi$
$138$		0			0
$139$	−6.15512			−0.522070			−0.261035	−	0.965329i	$-0.584064\pi$
$139$	−6.15512			−0.522070			−0.261035	+	0.965329i	$0.584064\pi$
$140$		0			0
$141$	−2.26378	+	3.92098i	−0.190644	+	0.330206i
$142$		0			0
$143$	20.9905			1.75531
$144$		0			0
$145$	−3.82916	+	6.63231i	−0.317995	+	0.550783i
$146$		0			0
$147$	5.44080	+	9.42375i	0.448750	+	0.777257i
$148$		0			0
$149$	9.12652			0.747673			0.373837	−	0.927495i	$-0.378042\pi$
$149$	9.12652			0.747673			0.373837	+	0.927495i	$0.378042\pi$
$150$		0			0
$151$	−0.927106	−	1.60579i	−0.0754468	−	0.130678i	0.825834	−	0.563914i	$-0.190705\pi$
$151$	−0.927106	−	1.60579i	−0.0754468	−	0.130678i	−0.901280	+	0.433236i	$0.857372\pi$
$152$		0			0
$153$	3.94016	+	6.82456i	0.318543	+	0.551733i
$154$		0			0
$155$	1.14320	−	1.98007i	0.0918237	−	0.159043i
$156$		0			0
$157$	−6.04661	−	10.4730i	−0.482572	−	0.835839i	0.517228	−	0.855848i	$-0.326964\pi$
$157$	−6.04661	−	10.4730i	−0.482572	−	0.835839i	−0.999800	+	0.0200086i	$0.993631\pi$
$158$		0			0
$159$	4.70757			0.373335
$160$		0			0
$161$	−15.5566			−1.22603
$162$		0			0
$163$	−3.42745	+	5.93651i	−0.268458	+	0.464983i	−0.968464	−	0.249154i	$-0.919847\pi$
$163$	−3.42745	+	5.93651i	−0.268458	+	0.464983i	0.700006	+	0.714137i	$0.253181\pi$
$164$		0			0
$165$	−1.59532	+	2.76317i	−0.124195	+	0.215113i
$166$		0			0
$167$	3.77235	−	6.53389i	0.291913	−	0.505608i	−0.682349	−	0.731026i	$-0.739042\pi$
$167$	3.77235	−	6.53389i	0.291913	−	0.505608i	0.974262	+	0.225419i	$0.0723749\pi$
$168$		0			0
$169$	−15.1401	+	26.2234i	−1.16462	+	2.01719i
$170$		0			0
$171$	−0.787346	−	1.36372i	−0.0602099	−	0.104287i
$172$		0			0
$173$	−8.60247	−	14.8999i	−0.654034	−	1.13282i	−0.982135	−	0.188177i	$-0.939742\pi$
$173$	−8.60247	−	14.8999i	−0.654034	−	1.13282i	0.328101	−	0.944643i	$-0.393591\pi$
$174$		0			0
$175$	2.11433	−	3.66213i	0.159828	−	0.276831i
$176$		0			0
$177$	−4.74077			−0.356338
$178$		0			0
$179$	−18.7632			−1.40243			−0.701215	−	0.712950i	$-0.747359\pi$
$179$	−18.7632			−1.40243			−0.701215	+	0.712950i	$0.747359\pi$
$180$		0			0
$181$	−8.59287	+	14.8833i	−0.638703	+	1.10627i	0.347015	+	0.937860i	$0.387195\pi$
$181$	−8.59287	+	14.8833i	−0.638703	+	1.10627i	−0.985718	+	0.168406i	$0.946138\pi$
$182$		0			0
$183$	−4.83423	−	8.37313i	−0.357357	−	0.618960i
$184$		0			0
$185$	5.16859	+	8.95226i	0.380002	+	0.658183i
$186$		0			0
$187$	−25.1433			−1.83866
$188$		0			0
$189$	−2.11433	+	3.66213i	−0.153795	+	0.266381i
$190$		0			0
$191$	−3.08061	−	5.33577i	−0.222905	−	0.386082i	0.732784	−	0.680461i	$-0.238221\pi$
$191$	−3.08061	−	5.33577i	−0.222905	−	0.386082i	−0.955689	+	0.294379i	$0.904887\pi$
$192$		0			0
$193$	9.14547			0.658305			0.329153	−	0.944277i	$-0.393237\pi$
$193$	9.14547			0.658305			0.329153	+	0.944277i	$0.393237\pi$
$194$		0			0
$195$	−3.28938	−	5.69738i	−0.235558	−	0.407998i
$196$		0			0
$197$	4.45960	−	7.72426i	0.317733	−	0.550330i	−0.662281	−	0.749255i	$-0.730412\pi$
$197$	4.45960	−	7.72426i	0.317733	−	0.550330i	0.980015	+	0.198925i	$0.0637449\pi$
$198$		0			0
$199$	7.82720	+	13.5571i	0.554855	+	0.961038i	0.997915	+	0.0645455i	$0.0205598\pi$
$199$	7.82720	+	13.5571i	0.554855	+	0.961038i	−0.443059	+	0.896492i	$0.646107\pi$
$200$		0			0
$201$	−7.48888	+	3.30405i	−0.528225	+	0.233050i
$202$		0			0
$203$	−16.1923	−	28.0458i	−1.13647	−	1.96843i
$204$		0			0
$205$	2.81544	−	4.87649i	0.196639	−	0.340589i
$206$		0			0
$207$	−1.83942	−	3.18598i	−0.127849	−	0.221441i
$208$		0			0
$209$	5.02428			0.347536
$210$		0			0
$211$	−9.92677	−	17.1937i	−0.683387	−	1.18366i	−0.973941	−	0.226803i	$-0.927173\pi$
$211$	−9.92677	−	17.1937i	−0.683387	−	1.18366i	0.290553	−	0.956859i	$-0.406161\pi$
$212$		0			0
$213$	3.13699	−	5.43343i	0.214943	−	0.372292i
$214$		0			0
$215$	−0.735148			−0.0501367
$216$		0			0
$217$	4.83419	+	8.37306i	0.328166	+	0.568401i
$218$		0			0
$219$	5.15891	+	8.93550i	0.348607	+	0.603805i
$220$		0			0
$221$	25.9214	−	44.8972i	1.74366	−	3.02011i
$222$		0			0
$223$	14.8340			0.993359			0.496680	−	0.867934i	$-0.334552\pi$
$223$	14.8340			0.993359			0.496680	+	0.867934i	$0.334552\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−10.9386	+	18.9462i	−0.726020	+	1.25750i	0.232533	+	0.972588i	$0.425299\pi$
$227$	−10.9386	+	18.9462i	−0.726020	+	1.25750i	−0.958553	+	0.284914i	$0.908035\pi$
$228$		0			0
$229$	−7.09658	−	12.2916i	−0.468955	−	0.812254i	0.530415	−	0.847738i	$-0.322036\pi$
$229$	−7.09658	−	12.2916i	−0.468955	−	0.812254i	−0.999370	+	0.0354841i	$0.988703\pi$
$230$		0			0
$231$	−6.74607	−	11.6845i	−0.443859	−	0.768786i
$232$		0			0
$233$	−1.40282	+	2.42976i	−0.0919021	+	0.159179i	−0.908311	−	0.418294i	$-0.862628\pi$
$233$	−1.40282	+	2.42976i	−0.0919021	+	0.159179i	0.816409	+	0.577474i	$0.195961\pi$
$234$		0			0
$235$	−2.26378	+	3.92098i	−0.147673	+	0.255776i
$236$		0			0
$237$	4.63648	−	8.03063i	0.301172	−	0.521645i
$238$		0			0
$239$	−3.00317	+	5.20164i	−0.194259	+	0.336466i	−0.946657	−	0.322242i	$-0.895564\pi$
$239$	−3.00317	+	5.20164i	−0.194259	+	0.336466i	0.752398	+	0.658708i	$0.228897\pi$
$240$		0			0
$241$	−4.05428			−0.261159			−0.130580	−	0.991438i	$-0.541684\pi$
$241$	−4.05428			−0.261159			−0.130580	+	0.991438i	$0.541684\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	5.44080	+	9.42375i	0.347600	+	0.602061i
$246$		0			0
$247$	−5.17977	+	8.97162i	−0.329581	+	0.570851i
$248$		0			0
$249$	−0.0412902	−	0.0715167i	−0.00261666	−	0.00453219i
$250$		0			0
$251$	−10.4044	−	18.0210i	−0.656723	−	1.13748i	−0.981459	−	0.191672i	$-0.938609\pi$
$251$	−10.4044	−	18.0210i	−0.656723	−	1.13748i	0.324736	−	0.945805i	$-0.394724\pi$
$252$		0			0
$253$	11.7379			0.737954
$254$		0			0
$255$	3.94016	+	6.82456i	0.246742	+	0.427370i
$256$		0			0
$257$	4.18271	−	7.24467i	0.260910	−	0.451910i	−0.705574	−	0.708636i	$-0.749311\pi$
$257$	4.18271	−	7.24467i	0.260910	−	0.451910i	0.966484	+	0.256727i	$0.0826440\pi$
$258$		0			0
$259$	−43.7125			−2.71616
$260$		0			0
$261$	3.82916	−	6.63231i	0.237019	−	0.410530i
$262$		0			0
$263$	−19.2604			−1.18765			−0.593825	−	0.804594i	$-0.702383\pi$
$263$	−19.2604			−1.18765			−0.593825	+	0.804594i	$0.702383\pi$
$264$		0			0
$265$	4.70757			0.289184
$266$		0			0
$267$	8.35910			0.511569
$268$		0			0
$269$	−24.2471			−1.47837			−0.739186	−	0.673501i	$-0.764790\pi$
$269$	−24.2471			−1.47837			−0.739186	+	0.673501i	$0.764790\pi$
$270$		0			0
$271$	−32.6006			−1.98035			−0.990174	−	0.139840i	$-0.955341\pi$
$271$	−32.6006			−1.98035			−0.990174	+	0.139840i	$0.955341\pi$
$272$		0			0
$273$	27.8194			1.68371
$274$		0			0
$275$	−1.59532	+	2.76317i	−0.0962014	+	0.166626i
$276$		0			0
$277$	−18.9645			−1.13947			−0.569734	−	0.821829i	$-0.692954\pi$
$277$	−18.9645			−1.13947			−0.569734	+	0.821829i	$0.692954\pi$
$278$		0			0
$279$	−1.14320	+	1.98007i	−0.0684413	+	0.118544i
$280$		0			0
$281$	−9.13466	−	15.8217i	−0.544928	−	0.943843i	−0.998611	−	0.0526801i	$-0.983224\pi$
$281$	−9.13466	−	15.8217i	−0.544928	−	0.943843i	0.453683	−	0.891163i	$-0.350110\pi$
$282$		0			0
$283$	9.02309			0.536367			0.268184	−	0.963368i	$-0.413577\pi$
$283$	9.02309			0.536367			0.268184	+	0.963368i	$0.413577\pi$
$284$		0			0
$285$	−0.787346	−	1.36372i	−0.0466384	−	0.0807800i
$286$		0			0
$287$	11.9056	+	20.6210i	0.702763	+	1.21722i
$288$		0			0
$289$	−22.5497	+	39.0573i	−1.32645	+	2.29749i
$290$		0			0
$291$	3.08777	+	5.34818i	0.181008	+	0.313516i
$292$		0			0
$293$	3.34271			0.195283			0.0976416	−	0.995222i	$-0.468870\pi$
$293$	3.34271			0.195283			0.0976416	+	0.995222i	$0.468870\pi$
$294$		0			0
$295$	−4.74077			−0.276019
$296$		0			0
$297$	1.59532	−	2.76317i	0.0925698	−	0.160336i
$298$		0			0
$299$	−12.1011	+	20.9598i	−0.699827	+	1.21214i
$300$		0			0
$301$	1.55435	−	2.69221i	0.0895911	−	0.155176i
$302$		0			0
$303$	−3.78402	+	6.55412i	−0.217386	+	0.376524i
$304$		0			0
$305$	−4.83423	−	8.37313i	−0.276807	−	0.479444i
$306$		0			0
$307$	4.21314	+	7.29737i	0.240457	+	0.416483i	0.960844	−	0.277088i	$-0.0893695\pi$
$307$	4.21314	+	7.29737i	0.240457	+	0.416483i	−0.720388	+	0.693571i	$0.756036\pi$
$308$		0			0
$309$	8.50386	−	14.7291i	0.483768	−	0.837910i
$310$		0			0
$311$	5.23109			0.296628			0.148314	−	0.988940i	$-0.452615\pi$
$311$	5.23109			0.296628			0.148314	+	0.988940i	$0.452615\pi$
$312$		0			0
$313$	−4.33056			−0.244778			−0.122389	−	0.992482i	$-0.539056\pi$
$313$	−4.33056			−0.244778			−0.122389	+	0.992482i	$0.539056\pi$
$314$		0			0
$315$	−2.11433	+	3.66213i	−0.119129	+	0.206338i
$316$		0			0
$317$	2.03122	+	3.51817i	0.114085	+	0.197600i	0.917413	−	0.397935i	$-0.130273\pi$
$317$	2.03122	+	3.51817i	0.114085	+	0.197600i	−0.803329	+	0.595536i	$0.796940\pi$
$318$		0			0
$319$	12.2175	+	21.1613i	0.684048	+	1.18481i
$320$		0			0
$321$	1.00359			0.0560147
$322$		0			0
$323$	6.20454	−	10.7466i	0.345230	−	0.597956i
$324$		0			0
$325$	−3.28938	−	5.69738i	−0.182462	−	0.316034i
$326$		0			0
$327$	−5.14050			−0.284270
$328$		0			0
$329$	−9.57276	−	16.5805i	−0.527763	−	0.914113i
$330$		0			0
$331$	−14.6023	+	25.2919i	−0.802614	+	1.39017i	0.115276	+	0.993333i	$0.463225\pi$
$331$	−14.6023	+	25.2919i	−0.802614	+	1.39017i	−0.917890	+	0.396835i	$0.870109\pi$
$332$		0			0
$333$	−5.16859	−	8.95226i	−0.283237	−	0.490581i
$334$		0			0
$335$	−7.48888	+	3.30405i	−0.409161	+	0.180520i
$336$		0			0
$337$	−13.9649	−	24.1879i	−0.760715	−	1.31760i	−0.942482	−	0.334256i	$-0.891515\pi$
$337$	−13.9649	−	24.1879i	−0.760715	−	1.31760i	0.181767	−	0.983342i	$-0.441818\pi$
$338$		0			0
$339$	7.08806	−	12.2769i	0.384970	−	0.666788i
$340$		0			0
$341$	−3.64752	−	6.31770i	−0.197525	−	0.342122i
$342$		0			0
$343$	−16.4140			−0.886273
$344$		0			0
$345$	−1.83942	−	3.18598i	−0.0990313	−	0.171527i
$346$		0			0
$347$	8.41037	−	14.5672i	0.451492	−	0.782008i	−0.546987	−	0.837141i	$-0.684225\pi$
$347$	8.41037	−	14.5672i	0.451492	−	0.782008i	0.998479	+	0.0551335i	$0.0175584\pi$
$348$		0			0
$349$	31.8594			1.70540			0.852698	−	0.522404i	$-0.174965\pi$
$349$	31.8594			1.70540			0.852698	+	0.522404i	$0.174965\pi$
$350$		0			0
$351$	3.28938	+	5.69738i	0.175574	+	0.304104i
$352$		0			0
$353$	14.0038	+	24.2552i	0.745345	+	1.29098i	0.950033	+	0.312148i	$0.101049\pi$
$353$	14.0038	+	24.2552i	0.745345	+	1.29098i	−0.204688	+	0.978827i	$0.565618\pi$
$354$		0			0
$355$	3.13699	−	5.43343i	0.166494	−	0.288376i
$356$		0			0
$357$	−33.3232			−1.76365
$358$		0			0
$359$	−10.9258			−0.576642			−0.288321	−	0.957534i	$-0.593097\pi$
$359$	−10.9258			−0.576642			−0.288321	+	0.957534i	$0.593097\pi$
$360$		0			0
$361$	8.26017	−	14.3070i	0.434746	−	0.753002i
$362$		0			0
$363$	−0.409911	−	0.709987i	−0.0215148	−	0.0372647i
$364$		0			0
$365$	5.15891	+	8.93550i	0.270030	+	0.467705i
$366$		0			0
$367$	−8.20192	+	14.2061i	−0.428137	+	0.741555i	−0.996708	−	0.0810795i	$-0.974163\pi$
$367$	−8.20192	+	14.2061i	−0.428137	+	0.741555i	0.568571	+	0.822634i	$0.307497\pi$
$368$		0			0
$369$	−2.81544	+	4.87649i	−0.146566	+	0.253860i
$370$		0			0
$371$	−9.95337	+	17.2397i	−0.516753	+	0.895043i
$372$		0			0
$373$	−0.740193	+	1.28205i	−0.0383257	+	0.0663821i	−0.884552	−	0.466442i	$-0.845536\pi$
$373$	−0.740193	+	1.28205i	−0.0383257	+	0.0663821i	0.846226	+	0.532824i	$0.178869\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−50.3824			−2.59482
$378$		0			0
$379$	0.0839809	+	0.145459i	0.00431381	+	0.00747173i	0.868174	−	0.496259i	$-0.165294\pi$
$379$	0.0839809	+	0.145459i	0.00431381	+	0.00747173i	−0.863860	+	0.503731i	$0.831960\pi$
$380$		0			0
$381$	−2.54877	+	4.41460i	−0.130578	+	0.226167i
$382$		0			0
$383$	10.7735	+	18.6603i	0.550501	+	0.953496i	0.998238	+	0.0593308i	$0.0188967\pi$
$383$	10.7735	+	18.6603i	0.550501	+	0.953496i	−0.447737	+	0.894165i	$0.647770\pi$
$384$		0			0
$385$	−6.74607	−	11.6845i	−0.343812	−	0.595499i
$386$		0			0
$387$	0.735148			0.0373697
$388$		0			0
$389$	−16.2711	−	28.1825i	−0.824980	−	1.42891i	−0.901935	−	0.431873i	$-0.857853\pi$
$389$	−16.2711	−	28.1825i	−0.824980	−	1.42891i	0.0769546	−	0.997035i	$-0.475480\pi$
$390$		0			0
$391$	14.4953	−	25.1065i	0.733056	−	1.26969i
$392$		0			0
$393$	14.5076			0.731811
$394$		0			0
$395$	4.63648	−	8.03063i	0.233287	−	0.404065i
$396$		0			0
$397$	−16.1812			−0.812112			−0.406056	−	0.913848i	$-0.633096\pi$
$397$	−16.1812			−0.812112			−0.406056	+	0.913848i	$0.633096\pi$
$398$		0			0
$399$	6.65885			0.333359
$400$		0			0
$401$	2.84928			0.142286			0.0711432	−	0.997466i	$-0.477335\pi$
$401$	2.84928			0.142286			0.0711432	+	0.997466i	$0.477335\pi$
$402$		0			0
$403$	15.0416			0.749277
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	32.9822			1.63487
$408$		0			0
$409$	17.7983	−	30.8275i	0.880067	−	1.52432i	0.0288019	−	0.999585i	$-0.490831\pi$
$409$	17.7983	−	30.8275i	0.880067	−	1.52432i	0.851265	−	0.524736i	$-0.175836\pi$
$410$		0			0
$411$	8.42224			0.415438
$412$		0			0
$413$	10.0236	−	17.3613i	0.493228	−	0.854295i
$414$		0			0
$415$	−0.0412902	−	0.0715167i	−0.00202685	−	0.00351062i
$416$		0			0
$417$	6.15512			0.301417
$418$		0			0
$419$	−0.653126	−	1.13125i	−0.0319073	−	0.0552650i	0.849631	−	0.527378i	$-0.176825\pi$
$419$	−0.653126	−	1.13125i	−0.0319073	−	0.0552650i	−0.881538	+	0.472113i	$0.843491\pi$
$420$		0			0
$421$	−5.44316	−	9.42783i	−0.265283	−	0.459484i	0.702354	−	0.711827i	$-0.252132\pi$
$421$	−5.44316	−	9.42783i	−0.265283	−	0.459484i	−0.967638	+	0.252343i	$0.918799\pi$
$422$		0			0
$423$	2.26378	−	3.92098i	0.110069	−	0.190644i
$424$		0			0
$425$	3.94016	+	6.82456i	0.191126	+	0.331040i
$426$		0			0
$427$	40.8847			1.97855
$428$		0			0
$429$	−20.9905			−1.01343
$430$		0			0
$431$	−16.5434	+	28.6540i	−0.796867	+	1.38021i	0.124781	+	0.992184i	$0.460177\pi$
$431$	−16.5434	+	28.6540i	−0.796867	+	1.38021i	−0.921647	+	0.388029i	$0.873156\pi$
$432$		0			0
$433$	4.99633	−	8.65389i	0.240108	−	0.415879i	−0.720637	−	0.693313i	$-0.756150\pi$
$433$	4.99633	−	8.65389i	0.240108	−	0.415879i	0.960745	+	0.277433i	$0.0894838\pi$
$434$		0			0
$435$	3.82916	−	6.63231i	0.183594	−	0.317995i
$436$		0			0
$437$	−2.89653	+	5.01693i	−0.138560	+	0.239992i
$438$		0			0
$439$	−12.6869	−	21.9743i	−0.605511	−	1.04878i	−0.991970	−	0.126470i	$-0.959635\pi$
$439$	−12.6869	−	21.9743i	−0.605511	−	1.04878i	0.386459	−	0.922306i	$-0.373698\pi$
$440$		0			0
$441$	−5.44080	−	9.42375i	−0.259086	−	0.448750i
$442$		0			0
$443$	−15.9948	+	27.7038i	−0.759935	+	1.31625i	0.182948	+	0.983123i	$0.441436\pi$
$443$	−15.9948	+	27.7038i	−0.759935	+	1.31625i	−0.942883	+	0.333123i	$0.891897\pi$
$444$		0			0
$445$	8.35910			0.396259
$446$		0			0
$447$	−9.12652			−0.431669
$448$		0			0
$449$	13.4394	−	23.2776i	0.634242	−	1.09854i	−0.352433	−	0.935837i	$-0.614645\pi$
$449$	13.4394	−	23.2776i	0.634242	−	1.09854i	0.986675	−	0.162703i	$-0.0520212\pi$
$450$		0			0
$451$	−8.98306	−	15.5591i	−0.422996	−	0.732650i
$452$		0			0
$453$	0.927106	+	1.60579i	0.0435592	+	0.0754468i
$454$		0			0
$455$	27.8194			1.30419
$456$		0			0
$457$	10.4916	−	18.1720i	0.490777	−	0.850051i	−0.509167	−	0.860668i	$-0.670046\pi$
$457$	10.4916	−	18.1720i	0.490777	−	0.850051i	0.999944	+	0.0106173i	$0.00337965\pi$
$458$		0			0
$459$	−3.94016	−	6.82456i	−0.183911	−	0.318543i
$460$		0			0
$461$	−3.36778			−0.156853			−0.0784267	−	0.996920i	$-0.524990\pi$
$461$	−3.36778			−0.156853			−0.0784267	+	0.996920i	$0.524990\pi$
$462$		0			0
$463$	4.15688	+	7.19993i	0.193187	+	0.334609i	0.946305	−	0.323276i	$-0.104784\pi$
$463$	4.15688	+	7.19993i	0.193187	+	0.334609i	−0.753118	+	0.657886i	$0.771451\pi$
$464$		0			0
$465$	−1.14320	+	1.98007i	−0.0530144	+	0.0918237i
$466$		0			0
$467$	11.8249	+	20.4814i	0.547193	+	0.947767i	0.998465	+	0.0553802i	$0.0176371\pi$
$467$	11.8249	+	20.4814i	0.547193	+	0.947767i	−0.451272	+	0.892386i	$0.649030\pi$
$468$		0			0
$469$	3.73411	−	34.4111i	0.172425	−	1.58896i
$470$		0			0
$471$	6.04661	+	10.4730i	0.278613	+	0.482572i
$472$		0			0
$473$	−1.17280	+	2.03134i	−0.0539252	+	0.0934013i
$474$		0			0
$475$	−0.787346	−	1.36372i	−0.0361259	−	0.0625719i
$476$		0			0
$477$	−4.70757			−0.215545
$478$		0			0
$479$	16.5293	+	28.6296i	0.755242	+	1.30812i	0.945254	+	0.326336i	$0.105814\pi$
$479$	16.5293	+	28.6296i	0.755242	+	1.30812i	−0.190011	+	0.981782i	$0.560852\pi$
$480$		0			0
$481$	−34.0030	+	58.8949i	−1.55040	+	2.68537i
$482$		0			0
$483$	15.5566			0.707851
$484$		0			0
$485$	3.08777	+	5.34818i	0.140208	+	0.242848i
$486$		0			0
$487$	3.58559	+	6.21042i	0.162479	+	0.281421i	0.935757	−	0.352645i	$-0.114718\pi$
$487$	3.58559	+	6.21042i	0.162479	+	0.281421i	−0.773278	+	0.634067i	$0.781384\pi$
$488$		0			0
$489$	3.42745	−	5.93651i	0.154994	−	0.268458i
$490$		0			0
$491$	−19.9061			−0.898348			−0.449174	−	0.893444i	$-0.648282\pi$
$491$	−19.9061			−0.898348			−0.449174	+	0.893444i	$0.648282\pi$
$492$		0			0
$493$	60.3501			2.71803
$494$		0			0
$495$	1.59532	−	2.76317i	0.0717043	−	0.124195i
$496$		0			0
$497$	13.2653	+	22.9761i	0.595029	+	1.03062i
$498$		0			0
$499$	−7.47982	−	12.9554i	−0.334843	−	0.579964i	0.648612	−	0.761119i	$-0.275350\pi$
$499$	−7.47982	−	12.9554i	−0.334843	−	0.579964i	−0.983455	+	0.181155i	$0.942016\pi$
$500$		0			0
$501$	−3.77235	+	6.53389i	−0.168536	+	0.291913i
$502$		0			0
$503$	−19.2277	+	33.3033i	−0.857319	+	1.48492i	0.0171580	+	0.999853i	$0.494538\pi$
$503$	−19.2277	+	33.3033i	−0.857319	+	1.48492i	−0.874477	+	0.485067i	$0.838795\pi$
$504$		0			0
$505$	−3.78402	+	6.55412i	−0.168387	+	0.291655i
$506$		0			0
$507$	15.1401	−	26.2234i	0.672396	−	1.16462i
$508$		0			0
$509$	14.9849			0.664196			0.332098	−	0.943245i	$-0.392244\pi$
$509$	14.9849			0.664196			0.332098	+	0.943245i	$0.392244\pi$
$510$		0			0
$511$	−43.6306			−1.93010
$512$		0			0
$513$	0.787346	+	1.36372i	0.0347622	+	0.0602099i
$514$		0			0
$515$	8.50386	−	14.7291i	0.374725	−	0.649042i
$516$		0			0
$517$	7.22290	+	12.5104i	0.317663	+	0.550208i
$518$		0			0
$519$	8.60247	+	14.8999i	0.377607	+	0.654034i
$520$		0			0
$521$	33.2516			1.45678			0.728390	−	0.685163i	$-0.240269\pi$
$521$	33.2516			1.45678			0.728390	+	0.685163i	$0.240269\pi$
$522$		0			0
$523$	6.43841	+	11.1517i	0.281532	+	0.487628i	0.971762	−	0.235962i	$-0.0758240\pi$
$523$	6.43841	+	11.1517i	0.281532	+	0.487628i	−0.690230	+	0.723590i	$0.742491\pi$
$524$		0			0
$525$	−2.11433	+	3.66213i	−0.0922770	+	0.159828i
$526$		0			0
$527$	−18.0175			−0.784854
$528$		0			0
$529$	4.73304	−	8.19786i	0.205784	−	0.356429i
$530$		0			0
$531$	4.74077			0.205732
$532$		0			0
$533$	37.0443			1.60457
$534$		0			0
$535$	1.00359			0.0433888
$536$		0			0
$537$	18.7632			0.809693
$538$		0			0
$539$	34.7193			1.49546
$540$		0			0
$541$	34.3674			1.47757			0.738786	−	0.673940i	$-0.235400\pi$
$541$	34.3674			1.47757			0.738786	+	0.673940i	$0.235400\pi$
$542$		0			0
$543$	8.59287	−	14.8833i	0.368755	−	0.638703i
$544$		0			0
$545$	−5.14050			−0.220195
$546$		0			0
$547$	−9.32931	+	16.1588i	−0.398892	+	0.690902i	−0.993590	−	0.113048i	$-0.963939\pi$
$547$	−9.32931	+	16.1588i	−0.398892	+	0.690902i	0.594697	+	0.803950i	$0.297272\pi$
$548$		0			0
$549$	4.83423	+	8.37313i	0.206320	+	0.357357i
$550$		0			0
$551$	−12.0595			−0.513753
$552$		0			0
$553$	19.6061	+	33.9588i	0.833738	+	1.44408i
$554$		0			0
$555$	−5.16859	−	8.95226i	−0.219394	−	0.380002i
$556$		0			0
$557$	4.81673	−	8.34283i	0.204092	−	0.353497i	−0.745751	−	0.666224i	$-0.767909\pi$
$557$	4.81673	−	8.34283i	0.204092	−	0.353497i	0.949843	+	0.312727i	$0.101243\pi$
$558$		0			0
$559$	−2.41819	−	4.18842i	−0.102278	−	0.177151i
$560$		0			0
$561$	25.1433			1.06155
$562$		0			0
$563$	31.8509			1.34236			0.671178	−	0.741296i	$-0.265789\pi$
$563$	31.8509			1.34236			0.671178	+	0.741296i	$0.265789\pi$
$564$		0			0
$565$	7.08806	−	12.2769i	0.298197	−	0.516492i
$566$		0			0
$567$	2.11433	−	3.66213i	0.0887936	−	0.153795i
$568$		0			0
$569$	4.82224	−	8.35236i	0.202159	−	0.350149i	−0.747065	−	0.664751i	$-0.768538\pi$
$569$	4.82224	−	8.35236i	0.202159	−	0.350149i	0.949224	+	0.314602i	$0.101871\pi$
$570$		0			0
$571$	8.86727	−	15.3586i	0.371084	−	0.642736i	−0.618649	−	0.785668i	$-0.712320\pi$
$571$	8.86727	−	15.3586i	0.371084	−	0.642736i	0.989733	+	0.142932i	$0.0456529\pi$
$572$		0			0
$573$	3.08061	+	5.33577i	0.128694	+	0.222905i
$574$		0			0
$575$	−1.83942	−	3.18598i	−0.0767093	−	0.132864i
$576$		0			0
$577$	−12.1913	+	21.1159i	−0.507530	+	0.879068i	0.492432	+	0.870351i	$0.336108\pi$
$577$	−12.1913	+	21.1159i	−0.507530	+	0.879068i	−0.999962	+	0.00871724i	$0.997225\pi$
$578$		0			0
$579$	−9.14547			−0.380073
$580$		0			0
$581$	0.349205			0.0144874
$582$		0			0
$583$	7.51008	−	13.0078i	0.311036	−	0.538730i
$584$		0			0
$585$	3.28938	+	5.69738i	0.135999	+	0.235558i
$586$		0			0
$587$	21.9063	+	37.9428i	0.904170	+	1.56607i	0.822027	+	0.569448i	$0.192843\pi$
$587$	21.9063	+	37.9428i	0.904170	+	1.56607i	0.0821430	+	0.996621i	$0.473824\pi$
$588$		0			0
$589$	3.60036			0.148350
$590$		0			0
$591$	−4.45960	+	7.72426i	−0.183443	+	0.317733i
$592$		0			0
$593$	−19.3412	−	33.5000i	−0.794249	−	1.37568i	−0.923315	−	0.384044i	$-0.874531\pi$
$593$	−19.3412	−	33.5000i	−0.794249	−	1.37568i	0.129066	−	0.991636i	$-0.458802\pi$
$594$		0			0
$595$	−33.3232			−1.36612
$596$		0			0
$597$	−7.82720	−	13.5571i	−0.320346	−	0.554855i
$598$		0			0
$599$	19.1999	−	33.2551i	0.784485	−	1.35877i	−0.144822	−	0.989458i	$-0.546261\pi$
$599$	19.1999	−	33.2551i	0.784485	−	1.35877i	0.929306	−	0.369310i	$-0.120406\pi$
$600$		0			0
$601$	−17.8572	−	30.9296i	−0.728410	−	1.26164i	−0.957555	−	0.288251i	$-0.906926\pi$
$601$	−17.8572	−	30.9296i	−0.728410	−	1.26164i	0.229145	−	0.973392i	$-0.426407\pi$
$602$		0			0
$603$	7.48888	−	3.30405i	0.304971	−	0.134551i
$604$		0			0
$605$	−0.409911	−	0.709987i	−0.0166653	−	0.0288651i
$606$		0			0
$607$	7.10583	−	12.3077i	0.288417	−	0.499553i	−0.685015	−	0.728529i	$-0.740204\pi$
$607$	7.10583	−	12.3077i	0.288417	−	0.499553i	0.973432	+	0.228976i	$0.0735378\pi$
$608$		0			0
$609$	16.1923	+	28.0458i	0.656143	+	1.13647i
$610$		0			0
$611$	−29.7857			−1.20500
$612$		0			0
$613$	15.3062	+	26.5112i	0.618213	+	1.07078i	0.989812	+	0.142383i	$0.0454764\pi$
$613$	15.3062	+	26.5112i	0.618213	+	1.07078i	−0.371599	+	0.928393i	$0.621190\pi$
$614$		0			0
$615$	−2.81544	+	4.87649i	−0.113530	+	0.196639i
$616$		0			0
$617$	27.8598			1.12159			0.560796	−	0.827954i	$-0.310495\pi$
$617$	27.8598			1.12159			0.560796	+	0.827954i	$0.310495\pi$
$618$		0			0
$619$	3.27266	+	5.66841i	0.131539	+	0.227832i	0.924270	−	0.381739i	$-0.124675\pi$
$619$	3.27266	+	5.66841i	0.131539	+	0.227832i	−0.792731	+	0.609572i	$0.791341\pi$
$620$		0			0
$621$	1.83942	+	3.18598i	0.0738136	+	0.127849i
$622$		0			0
$623$	−17.6739	+	30.6121i	−0.708091	+	1.22645i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−5.02428			−0.200650
$628$		0			0
$629$	40.7301	−	70.5467i	1.62402	−	2.81288i
$630$		0			0
$631$	17.9789	+	31.1403i	0.715727	+	1.23968i	0.962678	+	0.270648i	$0.0872380\pi$
$631$	17.9789	+	31.1403i	0.715727	+	1.23968i	−0.246951	+	0.969028i	$0.579429\pi$
$632$		0			0
$633$	9.92677	+	17.1937i	0.394554	+	0.683387i
$634$		0			0
$635$	−2.54877	+	4.41460i	−0.101145	+	0.175188i
$636$		0			0
$637$	−35.7938	+	61.9967i	−1.41820	+	2.45640i
$638$		0			0
$639$	−3.13699	+	5.43343i	−0.124097	+	0.214943i
$640$		0			0
$641$	−6.53682	+	11.3221i	−0.258189	+	0.447196i	−0.965757	−	0.259449i	$-0.916459\pi$
$641$	−6.53682	+	11.3221i	−0.258189	+	0.447196i	0.707568	+	0.706645i	$0.249792\pi$
$642$		0			0
$643$	16.8128			0.663032			0.331516	−	0.943450i	$-0.392440\pi$
$643$	16.8128			0.663032			0.331516	+	0.943450i	$0.392440\pi$
$644$		0			0
$645$	0.735148			0.0289464
$646$		0			0
$647$	−14.9696	−	25.9281i	−0.588516	−	1.01934i	−0.994427	−	0.105427i	$-0.966379\pi$
$647$	−14.9696	−	25.9281i	−0.588516	−	1.01934i	0.405911	−	0.913913i	$-0.366954\pi$
$648$		0			0
$649$	−7.56305	+	13.0996i	−0.296876	+	0.514204i
$650$		0			0
$651$	−4.83419	−	8.37306i	−0.189467	−	0.328166i
$652$		0			0
$653$	18.5598	+	32.1465i	0.726301	+	1.25799i	0.958436	+	0.285307i	$0.0920956\pi$
$653$	18.5598	+	32.1465i	0.726301	+	1.25799i	−0.232135	+	0.972684i	$0.574571\pi$
$654$		0			0
$655$	14.5076			0.566858
$656$		0			0
$657$	−5.15891	−	8.93550i	−0.201268	−	0.348607i
$658$		0			0
$659$	−2.17859	+	3.77343i	−0.0848659	+	0.146992i	−0.905334	−	0.424700i	$-0.860380\pi$
$659$	−2.17859	+	3.77343i	−0.0848659	+	0.146992i	0.820468	+	0.571692i	$0.193713\pi$
$660$		0			0
$661$	23.3052			0.906467			0.453233	−	0.891392i	$-0.350270\pi$
$661$	23.3052			0.906467			0.453233	+	0.891392i	$0.350270\pi$
$662$		0			0
$663$	−25.9214	+	44.8972i	−1.00670	+	1.74366i
$664$		0			0
$665$	6.65885			0.258219
$666$		0			0
$667$	−28.1738			−1.09090
$668$		0			0
$669$	−14.8340			−0.573516
$670$		0			0
$671$	−30.8486			−1.19090
$672$		0			0
$673$	−10.5442			−0.406447			−0.203224	−	0.979132i	$-0.565142\pi$
$673$	−10.5442			−0.406447			−0.203224	+	0.979132i	$0.565142\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	19.5404	−	33.8450i	0.750999	−	1.30077i	−0.196340	−	0.980536i	$-0.562906\pi$
$677$	19.5404	−	33.8450i	0.750999	−	1.30077i	0.947339	−	0.320232i	$-0.103761\pi$
$678$		0			0
$679$	−26.1143			−1.00217
$680$		0			0
$681$	10.9386	−	18.9462i	0.419168	−	0.726020i
$682$		0			0
$683$	−0.0927543	−	0.160655i	−0.00354914	−	0.00614730i	0.864245	−	0.503070i	$-0.167796\pi$
$683$	−0.0927543	−	0.160655i	−0.00354914	−	0.00614730i	−0.867795	+	0.496923i	$0.834463\pi$
$684$		0			0
$685$	8.42224			0.321797
$686$		0			0
$687$	7.09658	+	12.2916i	0.270751	+	0.468955i
$688$		0			0
$689$	15.4850	+	26.8208i	0.589932	+	1.02179i
$690$		0			0
$691$	1.11278	−	1.92740i	0.0423323	−	0.0733217i	−0.844083	−	0.536213i	$-0.819855\pi$
$691$	1.11278	−	1.92740i	0.0423323	−	0.0733217i	0.886415	+	0.462891i	$0.153188\pi$
$692$		0			0
$693$	6.74607	+	11.6845i	0.256262	+	0.443859i
$694$		0			0
$695$	6.15512			0.233477
$696$		0			0
$697$	−44.3732			−1.68075
$698$		0			0
$699$	1.40282	−	2.42976i	0.0530597	−	0.0919021i
$700$		0			0
$701$	−23.3204	+	40.3920i	−0.880798	+	1.52559i	−0.0303418	+	0.999540i	$0.509660\pi$
$701$	−23.3204	+	40.3920i	−0.880798	+	1.52559i	−0.850456	+	0.526047i	$0.823674\pi$
$702$		0			0
$703$	−8.13894	+	14.0971i	−0.306966	+	0.531681i
$704$		0			0
$705$	2.26378	−	3.92098i	0.0852588	−	0.147673i
$706$		0			0
$707$	−16.0014	−	27.7152i	−0.601793	−	1.04234i
$708$		0			0
$709$	−18.4183	−	31.9014i	−0.691713	−	1.19808i	−0.971276	−	0.237955i	$-0.923523\pi$
$709$	−18.4183	−	31.9014i	−0.691713	−	1.19808i	0.279563	−	0.960127i	$-0.409810\pi$
$710$		0			0
$711$	−4.63648	+	8.03063i	−0.173882	+	0.301172i
$712$		0			0
$713$	8.41129			0.315005
$714$		0			0
$715$	−20.9905			−0.784999
$716$		0			0
$717$	3.00317	−	5.20164i	0.112155	−	0.194259i
$718$		0			0
$719$	3.29702	+	5.71060i	0.122958	+	0.212970i	0.920933	−	0.389721i	$-0.127429\pi$
$719$	3.29702	+	5.71060i	0.122958	+	0.212970i	−0.797975	+	0.602691i	$0.794095\pi$
$720$		0			0
$721$	35.9600	+	62.2845i	1.33922	+	2.31960i
$722$		0			0
$723$	4.05428			0.150780
$724$		0			0
$725$	3.82916	−	6.63231i	0.142212	−	0.246318i
$726$		0			0
$727$	−3.69800	−	6.40512i	−0.137151	−	0.237553i	0.789266	−	0.614052i	$-0.210461\pi$
$727$	−3.69800	−	6.40512i	−0.137151	−	0.237553i	−0.926417	+	0.376499i	$0.877128\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.89660	+	5.01706i	0.107135	+	0.185563i
$732$		0			0
$733$	−24.4026	+	42.2665i	−0.901330	+	1.56115i	−0.0755616	+	0.997141i	$0.524075\pi$
$733$	−24.4026	+	42.2665i	−0.901330	+	1.56115i	−0.825769	+	0.564009i	$0.809258\pi$
$734$		0			0
$735$	−5.44080	−	9.42375i	−0.200687	−	0.347600i
$736$		0			0
$737$	−2.81748	+	25.9641i	−0.103783	+	0.956399i
$738$		0			0
$739$	−23.5971	−	40.8714i	−0.868033	−	1.50348i	−0.864004	−	0.503486i	$-0.832051\pi$
$739$	−23.5971	−	40.8714i	−0.868033	−	1.50348i	−0.00402950	−	0.999992i	$-0.501283\pi$
$740$		0			0
$741$	5.17977	−	8.97162i	0.190284	−	0.329581i
$742$		0			0
$743$	−19.2779	−	33.3902i	−0.707236	−	1.22497i	−0.965879	−	0.258995i	$-0.916609\pi$
$743$	−19.2779	−	33.3902i	−0.707236	−	1.22497i	0.258643	−	0.965973i	$-0.416725\pi$
$744$		0			0
$745$	−9.12652			−0.334370
$746$		0			0
$747$	0.0412902	+	0.0715167i	0.00151073	+	0.00261666i
$748$		0			0
$749$	−2.12191	+	3.67526i	−0.0775330	+	0.134291i
$750$		0			0
$751$	−24.9255			−0.909546			−0.454773	−	0.890607i	$-0.650280\pi$
$751$	−24.9255			−0.909546			−0.454773	+	0.890607i	$0.650280\pi$
$752$		0			0
$753$	10.4044	+	18.0210i	0.379159	+	0.656723i
$754$		0			0
$755$	0.927106	+	1.60579i	0.0337408	+	0.0584408i
$756$		0			0
$757$	9.53408	−	16.5135i	0.346522	−	0.600194i	−0.639107	−	0.769118i	$-0.720696\pi$
$757$	9.53408	−	16.5135i	0.346522	−	0.600194i	0.985629	+	0.168924i	$0.0540293\pi$
$758$		0			0
$759$	−11.7379			−0.426058
$760$		0			0
$761$	23.6290			0.856552			0.428276	−	0.903648i	$-0.359121\pi$
$761$	23.6290			0.856552			0.428276	+	0.903648i	$0.359121\pi$
$762$		0			0
$763$	10.8687	−	18.8252i	0.393474	−	0.681517i
$764$		0			0
$765$	−3.94016	−	6.82456i	−0.142457	−	0.246742i
$766$		0			0
$767$	−15.5942	−	27.0100i	−0.563075	−	0.975274i
$768$		0			0
$769$	−9.53444	+	16.5141i	−0.343821	+	0.595515i	−0.985139	−	0.171760i	$-0.945055\pi$
$769$	−9.53444	+	16.5141i	−0.343821	+	0.595515i	0.641318	+	0.767275i	$0.278388\pi$
$770$		0			0
$771$	−4.18271	+	7.24467i	−0.150637	+	0.260910i
$772$		0			0
$773$	15.2264	−	26.3728i	0.547654	−	0.948564i	−0.450781	−	0.892635i	$-0.648854\pi$
$773$	15.2264	−	26.3728i	0.547654	−	0.948564i	0.998435	−	0.0559296i	$-0.0178122\pi$
$774$		0			0
$775$	−1.14320	+	1.98007i	−0.0410648	+	0.0711263i
$776$		0			0
$777$	43.7125			1.56818
$778$		0			0
$779$	8.86691			0.317690
$780$		0			0
$781$	−10.0090	−	17.3361i	−0.358150	−	0.620335i
$782$		0			0
$783$	−3.82916	+	6.63231i	−0.136843	+	0.237019i
$784$		0			0
$785$	6.04661	+	10.4730i	0.215813	+	0.373799i
$786$		0			0
$787$	−22.3373	−	38.6893i	−0.796237	−	1.37912i	−0.922051	−	0.387069i	$-0.873487\pi$
$787$	−22.3373	−	38.6893i	−0.796237	−	1.37912i	0.125814	−	0.992054i	$-0.459846\pi$
$788$		0			0
$789$	19.2604			0.685690
$790$		0			0
$791$	29.9730	+	51.9148i	1.06572	+	1.84588i
$792$		0			0
$793$	31.8033	−	55.0849i	1.12937	−	1.95612i
$794$		0			0
$795$	−4.70757			−0.166960
$796$		0			0
$797$	21.1306	−	36.5993i	0.748485	−	1.29641i	−0.200063	−	0.979783i	$-0.564115\pi$
$797$	21.1306	−	36.5993i	0.748485	−	1.29641i	0.948549	−	0.316632i	$-0.102552\pi$
$798$		0			0
$799$	35.6786			1.26222
$800$		0			0
$801$	−8.35910			−0.295354
$802$		0			0
$803$	32.9204			1.16174
$804$		0			0
$805$	15.5566			0.548299
$806$		0			0
$807$	24.2471			0.853539
$808$		0			0
$809$	−18.2912			−0.643085			−0.321543	−	0.946895i	$-0.604201\pi$
$809$	−18.2912			−0.643085			−0.321543	+	0.946895i	$0.604201\pi$
$810$		0			0
$811$	−11.1428	+	19.2999i	−0.391277	+	0.677712i	−0.992618	−	0.121280i	$-0.961300\pi$
$811$	−11.1428	+	19.2999i	−0.391277	+	0.677712i	0.601341	+	0.798993i	$0.294633\pi$
$812$		0			0
$813$	32.6006			1.14335
$814$		0			0
$815$	3.42745	−	5.93651i	0.120058	−	0.207947i
$816$		0			0
$817$	−0.578816	−	1.00254i	−0.0202502	−	0.0350744i
$818$		0			0
$819$	−27.8194			−0.972089
$820$		0			0
$821$	−11.8602	−	20.5424i	−0.413922	−	0.716934i	0.581392	−	0.813623i	$-0.302508\pi$
$821$	−11.8602	−	20.5424i	−0.413922	−	0.716934i	−0.995315	+	0.0966889i	$0.969175\pi$
$822$		0			0
$823$	−12.9947	−	22.5074i	−0.452965	−	0.784559i	0.545603	−	0.838043i	$-0.316300\pi$
$823$	−12.9947	−	22.5074i	−0.452965	−	0.784559i	−0.998569	+	0.0534848i	$0.982967\pi$
$824$		0			0
$825$	1.59532	−	2.76317i	0.0555419	−	0.0962014i
$826$		0			0
$827$	−1.47161	−	2.54890i	−0.0511728	−	0.0886339i	0.839304	−	0.543662i	$-0.182963\pi$
$827$	−1.47161	−	2.54890i	−0.0511728	−	0.0886339i	−0.890477	+	0.455028i	$0.849629\pi$
$828$		0			0
$829$	42.1637			1.46441			0.732203	−	0.681086i	$-0.238492\pi$
$829$	42.1637			1.46441			0.732203	+	0.681086i	$0.238492\pi$
$830$		0			0
$831$	18.9645			0.657872
$832$		0			0
$833$	42.8753	−	74.2621i	1.48554	−	2.57303i
$834$		0			0
$835$	−3.77235	+	6.53389i	−0.130547	+	0.226115i
$836$		0			0
$837$	1.14320	−	1.98007i	0.0395146	−	0.0684413i
$838$		0			0
$839$	1.59119	−	2.75602i	0.0549340	−	0.0951484i	−0.837251	−	0.546819i	$-0.815839\pi$
$839$	1.59119	−	2.75602i	0.0549340	−	0.0951484i	0.892185	+	0.451671i	$0.149172\pi$
$840$		0			0
$841$	−14.8250	−	25.6777i	−0.511207	−	0.885437i
$842$		0			0
$843$	9.13466	+	15.8217i	0.314614	+	0.544928i
$844$		0			0
$845$	15.1401	−	26.2234i	0.520835	−	0.902113i
$846$		0			0
$847$	3.46676			0.119119
$848$		0			0
$849$	−9.02309			−0.309672
$850$		0			0
$851$	−19.0145	+	32.9340i	−0.651807	+	1.12896i
$852$		0			0
$853$	−26.4136	−	45.7496i	−0.904383	−	1.56644i	−0.821743	−	0.569858i	$-0.806998\pi$
$853$	−26.4136	−	45.7496i	−0.904383	−	1.56644i	−0.0826396	−	0.996579i	$-0.526335\pi$
$854$		0			0
$855$	0.787346	+	1.36372i	0.0269267	+	0.0466384i
$856$		0			0
$857$	34.1729			1.16732			0.583661	−	0.811997i	$-0.301620\pi$
$857$	34.1729			1.16732			0.583661	+	0.811997i	$0.301620\pi$
$858$		0			0
$859$	−15.5160	+	26.8746i	−0.529400	+	0.916948i	0.470012	+	0.882660i	$0.344250\pi$
$859$	−15.5160	+	26.8746i	−0.529400	+	0.916948i	−0.999412	+	0.0342879i	$0.989084\pi$
$860$		0			0
$861$	−11.9056	−	20.6210i	−0.405740	−	0.702763i
$862$		0			0
$863$	13.1702			0.448320			0.224160	−	0.974552i	$-0.428036\pi$
$863$	13.1702			0.448320			0.224160	+	0.974552i	$0.428036\pi$
$864$		0			0
$865$	8.60247	+	14.8999i	0.292493	+	0.506612i
$866$		0			0
$867$	22.5497	−	39.0573i	0.765829	−	1.32645i
$868$		0			0
$869$	−14.7933	−	25.6228i	−0.501830	−	0.869195i
$870$		0			0
$871$	−43.4582	−	31.7987i	−1.47253	−	1.07746i
$872$		0			0
$873$	−3.08777	−	5.34818i	−0.104505	−	0.181008i
$874$		0			0
$875$	−2.11433	+	3.66213i	−0.0714775	+	0.123803i
$876$		0			0
$877$	5.39321	+	9.34132i	0.182116	+	0.315434i	0.942601	−	0.333922i	$-0.108372\pi$
$877$	5.39321	+	9.34132i	0.182116	+	0.315434i	−0.760485	+	0.649356i	$0.775039\pi$
$878$		0			0
$879$	−3.34271			−0.112747
$880$		0			0
$881$	13.1509	+	22.7780i	0.443065	+	0.767412i	0.997915	−	0.0645389i	$-0.0205577\pi$
$881$	13.1509	+	22.7780i	0.443065	+	0.767412i	−0.554850	+	0.831950i	$0.687224\pi$
$882$		0			0
$883$	5.22445	−	9.04901i	0.175817	−	0.304523i	−0.764627	−	0.644473i	$-0.777077\pi$
$883$	5.22445	−	9.04901i	0.175817	−	0.304523i	0.940444	+	0.339950i	$0.110410\pi$
$884$		0			0
$885$	4.74077			0.159359
$886$		0			0
$887$	−1.94869	−	3.37523i	−0.0654306	−	0.113329i	0.831454	−	0.555593i	$-0.187509\pi$
$887$	−1.94869	−	3.37523i	−0.0654306	−	0.113329i	−0.896885	+	0.442264i	$0.854175\pi$
$888$		0			0
$889$	−10.7779	−	18.6679i	−0.361479	−	0.626100i
$890$		0			0
$891$	−1.59532	+	2.76317i	−0.0534452	+	0.0925698i
$892$		0			0
$893$	−7.12951			−0.238580
$894$		0			0
$895$	18.7632			0.627185
$896$		0			0
$897$	12.1011	−	20.9598i	0.404046	−	0.699827i
$898$		0			0
$899$	8.75497	+	15.1641i	0.291995	+	0.505749i
$900$		0			0
$901$	−18.5486	−	32.1271i	−0.617943	−	1.07031i
$902$		0			0
$903$	−1.55435	+	2.69221i	−0.0517255	+	0.0895911i
$904$		0			0
$905$	8.59287	−	14.8833i	0.285637	−	0.494737i
$906$		0			0
$907$	16.6252	−	28.7958i	0.552032	−	0.956148i	−0.446095	−	0.894985i	$-0.647186\pi$
$907$	16.6252	−	28.7958i	0.552032	−	0.956148i	0.998128	−	0.0611627i	$-0.0194808\pi$
$908$		0			0
$909$	3.78402	−	6.55412i	0.125508	−	0.217386i
$910$		0			0
$911$	−5.48430			−0.181703			−0.0908514	−	0.995864i	$-0.528959\pi$
$911$	−5.48430			−0.181703			−0.0908514	+	0.995864i	$0.528959\pi$
$912$		0			0
$913$	−0.263484			−0.00872005
$914$		0			0
$915$	4.83423	+	8.37313i	0.159815	+	0.276807i
$916$		0			0
$917$	−30.6738	+	53.1287i	−1.01294	+	1.75446i
$918$		0			0
$919$	−20.7922	−	36.0132i	−0.685872	−	1.18796i	−0.973162	−	0.230121i	$-0.926088\pi$
$919$	−20.7922	−	36.0132i	−0.685872	−	1.18796i	0.287291	−	0.957843i	$-0.407245\pi$
$920$		0			0
$921$	−4.21314	−	7.29737i	−0.138828	−	0.240457i
$922$		0			0
$923$	41.2751			1.35859
$924$		0			0
$925$	−5.16859	−	8.95226i	−0.169942	−	0.294348i
$926$		0			0
$927$	−8.50386	+	14.7291i	−0.279303	+	0.483768i
$928$		0			0
$929$	−2.74791			−0.0901561			−0.0450781	−	0.998983i	$-0.514354\pi$
$929$	−2.74791			−0.0901561			−0.0450781	+	0.998983i	$0.514354\pi$
$930$		0			0
$931$	−8.56759	+	14.8395i	−0.280791	+	0.486345i
$932$		0			0
$933$	−5.23109			−0.171258
$934$		0			0
$935$	25.1433			0.822273
$936$		0			0
$937$	14.9354			0.487918			0.243959	−	0.969786i	$-0.421554\pi$
$937$	14.9354			0.487918			0.243959	+	0.969786i	$0.421554\pi$
$938$		0			0
$939$	4.33056			0.141323
$940$		0			0
$941$	−7.60504			−0.247917			−0.123959	−	0.992287i	$-0.539559\pi$
$941$	−7.60504			−0.247917			−0.123959	+	0.992287i	$0.539559\pi$
$942$		0			0
$943$	20.7152			0.674579
$944$		0			0
$945$	2.11433	−	3.66213i	0.0687792	−	0.119129i
$946$		0			0
$947$	−24.3473			−0.791180			−0.395590	−	0.918427i	$-0.629460\pi$
$947$	−24.3473			−0.791180			−0.395590	+	0.918427i	$0.629460\pi$
$948$		0			0
$949$	−33.9393	+	58.7846i	−1.10172	+	1.90823i
$950$		0			0
$951$	−2.03122	−	3.51817i	−0.0658668	−	0.114085i
$952$		0			0
$953$	30.1226			0.975767			0.487884	−	0.872909i	$-0.337769\pi$
$953$	30.1226			0.975767			0.487884	+	0.872909i	$0.337769\pi$
$954$		0			0
$955$	3.08061	+	5.33577i	0.0996861	+	0.172661i
$956$		0			0
$957$	−12.2175	−	21.1613i	−0.394935	−	0.684048i
$958$		0			0
$959$	−17.8074	+	30.8433i	−0.575031	+	0.995984i
$960$		0			0
$961$	12.8862	+	22.3196i	0.415684	+	0.719986i
$962$		0			0
$963$	−1.00359			−0.0323401
$964$		0			0
$965$	−9.14547			−0.294403
$966$		0			0
$967$	25.2817	−	43.7892i	0.813005	−	1.40817i	−0.0977471	−	0.995211i	$-0.531164\pi$
$967$	25.2817	−	43.7892i	0.813005	−	1.40817i	0.910752	−	0.412954i	$-0.135503\pi$
$968$		0			0
$969$	−6.20454	+	10.7466i	−0.199319	+	0.345230i
$970$		0			0
$971$	9.59561	−	16.6201i	0.307938	−	0.533364i	−0.669973	−	0.742385i	$-0.733695\pi$
$971$	9.59561	−	16.6201i	0.307938	−	0.533364i	0.977911	+	0.209021i	$0.0670278\pi$
$972$		0			0
$973$	−13.0140	+	22.5409i	−0.417209	+	0.722627i
$974$		0			0
$975$	3.28938	+	5.69738i	0.105345	+	0.182462i
$976$		0			0
$977$	12.8232	+	22.2104i	0.410250	+	0.710574i	0.994917	−	0.100699i	$-0.0321080\pi$
$977$	12.8232	+	22.2104i	0.410250	+	0.710574i	−0.584667	+	0.811274i	$0.698775\pi$
$978$		0			0
$979$	13.3354	−	23.0977i	0.426202	−	0.738204i
$980$		0			0
$981$	5.14050			0.164124
$982$		0			0
$983$	45.2356			1.44279			0.721395	−	0.692524i	$-0.243501\pi$
$983$	45.2356			1.44279			0.721395	+	0.692524i	$0.243501\pi$
$984$		0			0
$985$	−4.45960	+	7.72426i	−0.142095	+	0.246115i
$986$		0			0
$987$	9.57276	+	16.5805i	0.304704	+	0.527763i
$988$		0			0
$989$	−1.35225	−	2.34217i	−0.0429990	−	0.0744765i
$990$		0			0
$991$	45.7461			1.45317			0.726586	−	0.687075i	$-0.241106\pi$
$991$	45.7461			1.45317			0.726586	+	0.687075i	$0.241106\pi$
$992$		0			0
$993$	14.6023	−	25.2919i	0.463389	−	0.802614i
$994$		0			0
$995$	−7.82720	−	13.5571i	−0.248139	−	0.429789i
$996$		0			0
$997$	13.9065			0.440423			0.220211	−	0.975452i	$-0.429325\pi$
$997$	13.9065			0.440423			0.220211	+	0.975452i	$0.429325\pi$
$998$		0			0
$999$	5.16859	+	8.95226i	0.163527	+	0.283237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.l.841.11	✓	22
67.29	even	3	inner	4020.2.q.l.3781.11	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.l.841.11	✓	22	1.1	even	1	trivial
4020.2.q.l.3781.11	yes	22	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(2.11433 - 3.66213i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(2.11433 - 3.66213i) q^{7} +1.00000 q^{9} +(-1.59532 + 2.76317i) q^{11} +(-3.28938 - 5.69738i) q^{13} +1.00000 q^{15} +(3.94016 + 6.82456i) q^{17} +(-0.787346 - 1.36372i) q^{19} +(-2.11433 + 3.66213i) q^{21} +(-1.83942 - 3.18598i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.82916 - 6.63231i) q^{29} +(-1.14320 + 1.98007i) q^{31} +(1.59532 - 2.76317i) q^{33} +(-2.11433 + 3.66213i) q^{35} +(-5.16859 - 8.95226i) q^{37} +(3.28938 + 5.69738i) q^{39} +(-2.81544 + 4.87649i) q^{41} +0.735148 q^{43} -1.00000 q^{45} +(2.26378 - 3.92098i) q^{47} +(-5.44080 - 9.42375i) q^{49} +(-3.94016 - 6.82456i) q^{51} -4.70757 q^{53} +(1.59532 - 2.76317i) q^{55} +(0.787346 + 1.36372i) q^{57} +4.74077 q^{59} +(4.83423 + 8.37313i) q^{61} +(2.11433 - 3.66213i) q^{63} +(3.28938 + 5.69738i) q^{65} +(7.48888 - 3.30405i) q^{67} +(1.83942 + 3.18598i) q^{69} +(-3.13699 + 5.43343i) q^{71} +(-5.15891 - 8.93550i) q^{73} -1.00000 q^{75} +(6.74607 + 11.6845i) q^{77} +(-4.63648 + 8.03063i) q^{79} +1.00000 q^{81} +(0.0412902 + 0.0715167i) q^{83} +(-3.94016 - 6.82456i) q^{85} +(-3.82916 + 6.63231i) q^{87} -8.35910 q^{89} -27.8194 q^{91} +(1.14320 - 1.98007i) q^{93} +(0.787346 + 1.36372i) q^{95} +(-3.08777 - 5.34818i) q^{97} +(-1.59532 + 2.76317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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