LMFDB - Embedded newform 4020.2.q.c.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.c.3781.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{9} +(-1.50000 + 2.59808i) q^{11} +(-2.50000 - 4.33013i) q^{13} -1.00000 q^{15} +(0.500000 + 0.866025i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{21} +(4.50000 + 7.79423i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-2.50000 + 4.33013i) q^{29} +(3.50000 - 6.06218i) q^{31} +(1.50000 - 2.59808i) q^{33} +(0.500000 - 0.866025i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(2.50000 + 4.33013i) q^{39} +(-0.500000 + 0.866025i) q^{41} -4.00000 q^{43} +1.00000 q^{45} +(-0.500000 + 0.866025i) q^{47} +(3.00000 + 5.19615i) q^{49} +(-0.500000 - 0.866025i) q^{51} -10.0000 q^{53} +(-1.50000 + 2.59808i) q^{55} +(3.50000 + 6.06218i) q^{57} -12.0000 q^{59} +(-3.50000 - 6.06218i) q^{61} +(0.500000 - 0.866025i) q^{63} +(-2.50000 - 4.33013i) q^{65} +(-8.00000 + 1.73205i) q^{67} +(-4.50000 - 7.79423i) q^{69} +(-1.50000 + 2.59808i) q^{71} +(5.50000 + 9.52628i) q^{73} -1.00000 q^{75} +(1.50000 + 2.59808i) q^{77} +(-2.50000 + 4.33013i) q^{79} +1.00000 q^{81} +(4.50000 + 7.79423i) q^{83} +(0.500000 + 0.866025i) q^{85} +(2.50000 - 4.33013i) q^{87} +10.0000 q^{89} -5.00000 q^{91} +(-3.50000 + 6.06218i) q^{93} +(-3.50000 - 6.06218i) q^{95} +(-6.50000 - 11.2583i) q^{97} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 2 * q^5 + q^7 + 2 * q^9	$ 2 q - 2 q^{3} + 2 q^{5} + q^{7} + 2 q^{9} - 3 q^{11} - 5 q^{13} - 2 q^{15} + q^{17} - 7 q^{19} - q^{21} + 9 q^{23} + 2 q^{25} - 2 q^{27} - 5 q^{29} + 7 q^{31} + 3 q^{33} + q^{35} - 5 q^{37} + 5 q^{39} - q^{41} - 8 q^{43} + 2 q^{45} - q^{47} + 6 q^{49} - q^{51} - 20 q^{53} - 3 q^{55} + 7 q^{57} - 24 q^{59} - 7 q^{61} + q^{63} - 5 q^{65} - 16 q^{67} - 9 q^{69} - 3 q^{71} + 11 q^{73} - 2 q^{75} + 3 q^{77} - 5 q^{79} + 2 q^{81} + 9 q^{83} + q^{85} + 5 q^{87} + 20 q^{89} - 10 q^{91} - 7 q^{93} - 7 q^{95} - 13 q^{97} - 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^5 + q^7 + 2 * q^9 - 3 * q^11 - 5 * q^13 - 2 * q^15 + q^17 - 7 * q^19 - q^21 + 9 * q^23 + 2 * q^25 - 2 * q^27 - 5 * q^29 + 7 * q^31 + 3 * q^33 + q^35 - 5 * q^37 + 5 * q^39 - q^41 - 8 * q^43 + 2 * q^45 - q^47 + 6 * q^49 - q^51 - 20 * q^53 - 3 * q^55 + 7 * q^57 - 24 * q^59 - 7 * q^61 + q^63 - 5 * q^65 - 16 * q^67 - 9 * q^69 - 3 * q^71 + 11 * q^73 - 2 * q^75 + 3 * q^77 - 5 * q^79 + 2 * q^81 + 9 * q^83 + q^85 + 5 * q^87 + 20 * q^89 - 10 * q^91 - 7 * q^93 - 7 * q^95 - 13 * q^97 - 3 * 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
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	0.920268	−	0.391289i	$-0.127971\pi$
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	−0.799000	+	0.601331i	$0.794637\pi$
$18$		0			0
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$		0			0
$21$	−0.500000	+	0.866025i	−0.109109	+	0.188982i
$22$		0			0
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.768613	+	0.639713i	$0.220947\pi$
$23$	4.50000	+	7.79423i	0.938315	+	1.62521i	0.169701	+	0.985496i	$0.445720\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	−0.999167	−	0.0408130i	$-0.987005\pi$
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	0.534928	+	0.844897i	$0.320339\pi$
$30$		0			0
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$		0			0
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$		0			0
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$		0			0
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	0.584002	−	0.811752i	$-0.301486\pi$
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	−0.994999	+	0.0998840i	$0.968153\pi$
$38$		0			0
$39$	2.50000	+	4.33013i	0.400320	+	0.693375i
$40$		0			0
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i	−0.902424	−	0.430848i	$-0.858214\pi$
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i	0.824338	+	0.566099i	$0.191548\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	−0.900185	−	0.435507i	$-0.856569\pi$
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	0.827253	+	0.561830i	$0.189902\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$	−0.500000	−	0.866025i	−0.0700140	−	0.121268i
$52$		0			0
$53$	−10.0000			−1.37361			−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000			−1.37361			−0.686803	+	0.726844i	$0.740986\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$		0			0
$57$	3.50000	+	6.06218i	0.463586	+	0.802955i
$58$		0			0
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$		0			0
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$		0			0
$65$	−2.50000	−	4.33013i	−0.310087	−	0.537086i
$66$		0			0
$67$	−8.00000	+	1.73205i	−0.977356	+	0.211604i
$67$	−8.00000	+	1.73205i	−0.977356	+	0.211604i
$68$		0			0
$69$	−4.50000	−	7.79423i	−0.541736	−	0.938315i
$70$		0			0
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	−0.941201	−	0.337846i	$-0.890302\pi$
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	0.763184	+	0.646181i	$0.223635\pi$
$72$		0			0
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	1.50000	+	2.59808i	0.170941	+	0.296078i
$78$		0			0
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$		0			0
$85$	0.500000	+	0.866025i	0.0542326	+	0.0939336i
$86$		0			0
$87$	2.50000	−	4.33013i	0.268028	−	0.464238i
$88$		0			0
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$		0			0
$91$	−5.00000			−0.524142
$92$		0			0
$93$	−3.50000	+	6.06218i	−0.362933	+	0.628619i
$94$		0			0
$95$	−3.50000	−	6.06218i	−0.359092	−	0.621966i
$96$		0			0
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	−0.980622	−	0.195911i	$-0.937234\pi$
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	0.320647	−	0.947199i	$-0.396100\pi$
$98$		0			0
$99$	−1.50000	+	2.59808i	−0.150756	+	0.261116i
$100$		0			0
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	−0.451190	−	0.892428i	$-0.649000\pi$
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	0.998460	−	0.0554722i	$-0.0176664\pi$
$102$		0			0
$103$	−9.50000	+	16.4545i	−0.936063	+	1.62131i	−0.163335	+	0.986571i	$0.552225\pi$
$103$	−9.50000	+	16.4545i	−0.936063	+	1.62131i	−0.772728	+	0.634738i	$0.781108\pi$
$104$		0			0
$105$	−0.500000	+	0.866025i	−0.0487950	+	0.0845154i
$106$		0			0
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	2.50000	+	4.33013i	0.237289	+	0.410997i
$112$		0			0
$113$	10.5000	−	18.1865i	0.987757	−	1.71085i	0.358778	−	0.933423i	$-0.383194\pi$
$113$	10.5000	−	18.1865i	0.987757	−	1.71085i	0.628979	−	0.777422i	$-0.283473\pi$
$114$		0			0
$115$	4.50000	+	7.79423i	0.419627	+	0.726816i
$116$		0			0
$117$	−2.50000	−	4.33013i	−0.231125	−	0.400320i
$118$		0			0
$119$	1.00000			0.0916698
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	0.500000	−	0.866025i	0.0450835	−	0.0780869i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−3.50000	+	6.06218i	−0.310575	+	0.537931i	−0.978487	−	0.206309i	$-0.933855\pi$
$127$	−3.50000	+	6.06218i	−0.310575	+	0.537931i	0.667912	+	0.744240i	$0.267188\pi$
$128$		0			0
$129$	4.00000			0.352180
$130$		0			0
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$		0			0
$133$	−7.00000			−0.606977
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−10.0000			−0.854358			−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000			−0.854358			−0.427179	+	0.904167i	$0.640493\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$		0			0
$141$	0.500000	−	0.866025i	0.0421076	−	0.0729325i
$142$		0			0
$143$	15.0000			1.25436
$144$		0			0
$145$	−2.50000	+	4.33013i	−0.207614	+	0.359597i
$146$		0			0
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$		0			0
$149$	−22.0000			−1.80231			−0.901155	−	0.433497i	$-0.857280\pi$
$149$	−22.0000			−1.80231			−0.901155	+	0.433497i	$0.857280\pi$
$150$		0			0
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	0.687741	−	0.725956i	$-0.258602\pi$
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	−0.972567	+	0.232623i	$0.925269\pi$
$152$		0			0
$153$	0.500000	+	0.866025i	0.0404226	+	0.0700140i
$154$		0			0
$155$	3.50000	−	6.06218i	0.281127	−	0.486926i
$156$		0			0
$157$	1.50000	+	2.59808i	0.119713	+	0.207349i	0.919654	−	0.392730i	$-0.128469\pi$
$157$	1.50000	+	2.59808i	0.119713	+	0.207349i	−0.799941	+	0.600079i	$0.795136\pi$
$158$		0			0
$159$	10.0000			0.793052
$160$		0			0
$161$	9.00000			0.709299
$162$		0			0
$163$	−3.50000	+	6.06218i	−0.274141	+	0.474826i	−0.969918	−	0.243432i	$-0.921727\pi$
$163$	−3.50000	+	6.06218i	−0.274141	+	0.474826i	0.695777	+	0.718258i	$0.255060\pi$
$164$		0			0
$165$	1.50000	−	2.59808i	0.116775	−	0.202260i
$166$		0			0
$167$	−2.50000	+	4.33013i	−0.193456	+	0.335075i	−0.946393	−	0.323017i	$-0.895303\pi$
$167$	−2.50000	+	4.33013i	−0.193456	+	0.335075i	0.752937	+	0.658092i	$0.228636\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$	−3.50000	−	6.06218i	−0.267652	−	0.463586i
$172$		0			0
$173$	−11.5000	−	19.9186i	−0.874329	−	1.51438i	−0.857476	−	0.514524i	$-0.827969\pi$
$173$	−11.5000	−	19.9186i	−0.874329	−	1.51438i	−0.0168528	−	0.999858i	$-0.505365\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$		0			0
$177$	12.0000			0.901975
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	−0.355383	−	0.934721i	$-0.615650\pi$
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	0.987184	−	0.159589i	$-0.0510169\pi$
$182$		0			0
$183$	3.50000	+	6.06218i	0.258727	+	0.448129i
$184$		0			0
$185$	−2.50000	−	4.33013i	−0.183804	−	0.318357i
$186$		0			0
$187$	−3.00000			−0.219382
$188$		0			0
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$		0			0
$191$	−4.50000	−	7.79423i	−0.325609	−	0.563971i	0.656027	−	0.754738i	$-0.272236\pi$
$191$	−4.50000	−	7.79423i	−0.325609	−	0.563971i	−0.981635	+	0.190767i	$0.938902\pi$
$192$		0			0
$193$	−22.0000			−1.58359			−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000			−1.58359			−0.791797	+	0.610784i	$0.790854\pi$
$194$		0			0
$195$	2.50000	+	4.33013i	0.179029	+	0.310087i
$196$		0			0
$197$	−7.50000	+	12.9904i	−0.534353	+	0.925526i	0.464841	+	0.885394i	$0.346111\pi$
$197$	−7.50000	+	12.9904i	−0.534353	+	0.925526i	−0.999194	+	0.0401324i	$0.987222\pi$
$198$		0			0
$199$	−7.50000	−	12.9904i	−0.531661	−	0.920864i	−0.999317	−	0.0369532i	$-0.988235\pi$
$199$	−7.50000	−	12.9904i	−0.531661	−	0.920864i	0.467656	−	0.883911i	$-0.345099\pi$
$200$		0			0
$201$	8.00000	−	1.73205i	0.564276	−	0.122169i
$202$		0			0
$203$	2.50000	+	4.33013i	0.175466	+	0.303915i
$204$		0			0
$205$	−0.500000	+	0.866025i	−0.0349215	+	0.0604858i
$206$		0			0
$207$	4.50000	+	7.79423i	0.312772	+	0.541736i
$208$		0			0
$209$	21.0000			1.45260
$210$		0			0
$211$	10.5000	+	18.1865i	0.722850	+	1.25201i	0.959853	+	0.280504i	$0.0905015\pi$
$211$	10.5000	+	18.1865i	0.722850	+	1.25201i	−0.237003	+	0.971509i	$0.576165\pi$
$212$		0			0
$213$	1.50000	−	2.59808i	0.102778	−	0.178017i
$214$		0			0
$215$	−4.00000			−0.272798
$216$		0			0
$217$	−3.50000	−	6.06218i	−0.237595	−	0.411527i
$218$		0			0
$219$	−5.50000	−	9.52628i	−0.371656	−	0.643726i
$220$		0			0
$221$	2.50000	−	4.33013i	0.168168	−	0.291276i
$222$		0			0
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−10.5000	+	18.1865i	−0.696909	+	1.20708i	0.272623	+	0.962121i	$0.412109\pi$
$227$	−10.5000	+	18.1865i	−0.696909	+	1.20708i	−0.969533	+	0.244962i	$0.921225\pi$
$228$		0			0
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	0.996832	−	0.0795401i	$-0.0253452\pi$
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	−0.567300	+	0.823511i	$0.692012\pi$
$230$		0			0
$231$	−1.50000	−	2.59808i	−0.0986928	−	0.170941i
$232$		0			0
$233$	−7.50000	+	12.9904i	−0.491341	+	0.851028i	−0.999950	−	0.00996947i	$-0.996827\pi$
$233$	−7.50000	+	12.9904i	−0.491341	+	0.851028i	0.508609	+	0.860998i	$0.330160\pi$
$234$		0			0
$235$	−0.500000	+	0.866025i	−0.0326164	+	0.0564933i
$236$		0			0
$237$	2.50000	−	4.33013i	0.162392	−	0.281272i
$238$		0			0
$239$	−11.5000	+	19.9186i	−0.743873	+	1.28843i	0.206846	+	0.978373i	$0.433680\pi$
$239$	−11.5000	+	19.9186i	−0.743873	+	1.28843i	−0.950719	+	0.310053i	$0.899653\pi$
$240$		0			0
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$		0			0
$247$	−17.5000	+	30.3109i	−1.11350	+	1.92864i
$248$		0			0
$249$	−4.50000	−	7.79423i	−0.285176	−	0.493939i
$250$		0			0
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	0.909475	−	0.415759i	$-0.136484\pi$
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	−0.814795	+	0.579748i	$0.803151\pi$
$252$		0			0
$253$	−27.0000			−1.69748
$254$		0			0
$255$	−0.500000	−	0.866025i	−0.0313112	−	0.0542326i
$256$		0			0
$257$	−13.5000	+	23.3827i	−0.842107	+	1.45857i	0.0460033	+	0.998941i	$0.485352\pi$
$257$	−13.5000	+	23.3827i	−0.842107	+	1.45857i	−0.888110	+	0.459631i	$0.847982\pi$
$258$		0			0
$259$	−5.00000			−0.310685
$260$		0			0
$261$	−2.50000	+	4.33013i	−0.154746	+	0.268028i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	−10.0000			−0.614295
$266$		0			0
$267$	−10.0000			−0.611990
$268$		0			0
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$		0			0
$273$	5.00000			0.302614
$274$		0			0
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$		0			0
$277$	10.0000			0.600842			0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000			0.600842			0.300421	+	0.953807i	$0.402873\pi$
$278$		0			0
$279$	3.50000	−	6.06218i	0.209540	−	0.362933i
$280$		0			0
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	0.907293	−	0.420500i	$-0.138145\pi$
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	−0.817810	+	0.575488i	$0.804812\pi$
$282$		0			0
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$		0			0
$285$	3.50000	+	6.06218i	0.207322	+	0.359092i
$286$		0			0
$287$	0.500000	+	0.866025i	0.0295141	+	0.0511199i
$288$		0			0
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$		0			0
$291$	6.50000	+	11.2583i	0.381037	+	0.659975i
$292$		0			0
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$	−12.0000			−0.698667
$296$		0			0
$297$	1.50000	−	2.59808i	0.0870388	−	0.150756i
$298$		0			0
$299$	22.5000	−	38.9711i	1.30121	−	2.25376i
$300$		0			0
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$		0			0
$303$	−5.50000	+	9.52628i	−0.315967	+	0.547270i
$304$		0			0
$305$	−3.50000	−	6.06218i	−0.200409	−	0.347119i
$306$		0			0
$307$	7.50000	+	12.9904i	0.428048	+	0.741400i	0.996700	−	0.0811780i	$-0.0258682\pi$
$307$	7.50000	+	12.9904i	0.428048	+	0.741400i	−0.568652	+	0.822578i	$0.692535\pi$
$308$		0			0
$309$	9.50000	−	16.4545i	0.540436	−	0.936063i
$310$		0			0
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$		0			0
$313$	−30.0000			−1.69570			−0.847850	−	0.530236i	$-0.822103\pi$
$313$	−30.0000			−1.69570			−0.847850	+	0.530236i	$0.822103\pi$
$314$		0			0
$315$	0.500000	−	0.866025i	0.0281718	−	0.0487950i
$316$		0			0
$317$	−13.5000	−	23.3827i	−0.758236	−	1.31330i	−0.943750	−	0.330661i	$-0.892728\pi$
$317$	−13.5000	−	23.3827i	−0.758236	−	1.31330i	0.185514	−	0.982642i	$-0.440605\pi$
$318$		0			0
$319$	−7.50000	−	12.9904i	−0.419919	−	0.727322i
$320$		0			0
$321$	4.00000			0.223258
$322$		0			0
$323$	3.50000	−	6.06218i	0.194745	−	0.337309i
$324$		0			0
$325$	−2.50000	−	4.33013i	−0.138675	−	0.240192i
$326$		0			0
$327$	−10.0000			−0.553001
$328$		0			0
$329$	0.500000	+	0.866025i	0.0275659	+	0.0477455i
$330$		0			0
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	0.851957	+	0.523612i	$0.175416\pi$
$332$		0			0
$333$	−2.50000	−	4.33013i	−0.136999	−	0.237289i
$334$		0			0
$335$	−8.00000	+	1.73205i	−0.437087	+	0.0946320i
$336$		0			0
$337$	−12.5000	−	21.6506i	−0.680918	−	1.17939i	−0.974701	−	0.223513i	$-0.928247\pi$
$337$	−12.5000	−	21.6506i	−0.680918	−	1.17939i	0.293783	−	0.955872i	$-0.405086\pi$
$338$		0			0
$339$	−10.5000	+	18.1865i	−0.570282	+	0.987757i
$340$		0			0
$341$	10.5000	+	18.1865i	0.568607	+	0.984856i
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$	−4.50000	−	7.79423i	−0.242272	−	0.419627i
$346$		0			0
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	−0.489946	−	0.871753i	$-0.662984\pi$
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	0.999933	−	0.0115703i	$-0.00368303\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	2.50000	+	4.33013i	0.133440	+	0.231125i
$352$		0			0
$353$	−13.5000	−	23.3827i	−0.718532	−	1.24453i	−0.961581	−	0.274521i	$-0.911481\pi$
$353$	−13.5000	−	23.3827i	−0.718532	−	1.24453i	0.243049	−	0.970014i	$-0.421853\pi$
$354$		0			0
$355$	−1.50000	+	2.59808i	−0.0796117	+	0.137892i
$356$		0			0
$357$	−1.00000			−0.0529256
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		0			0
$363$	−1.00000	−	1.73205i	−0.0524864	−	0.0909091i
$364$		0			0
$365$	5.50000	+	9.52628i	0.287883	+	0.498628i
$366$		0			0
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	−0.554264	−	0.832341i	$-0.687000\pi$
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	0.997960	+	0.0638362i	$0.0203335\pi$
$368$		0			0
$369$	−0.500000	+	0.866025i	−0.0260290	+	0.0450835i
$370$		0			0
$371$	−5.00000	+	8.66025i	−0.259587	+	0.449618i
$372$		0			0
$373$	5.50000	−	9.52628i	0.284779	−	0.493252i	−0.687776	−	0.725923i	$-0.741413\pi$
$373$	5.50000	−	9.52628i	0.284779	−	0.493252i	0.972556	+	0.232671i	$0.0747464\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	25.0000			1.28757
$378$		0			0
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	0.878581	−	0.477593i	$-0.158491\pi$
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	−0.852898	+	0.522077i	$0.825157\pi$
$380$		0			0
$381$	3.50000	−	6.06218i	0.179310	−	0.310575i
$382$		0			0
$383$	−9.50000	−	16.4545i	−0.485427	−	0.840785i	0.514432	−	0.857531i	$-0.328003\pi$
$383$	−9.50000	−	16.4545i	−0.485427	−	0.840785i	−0.999860	+	0.0167461i	$0.994669\pi$
$384$		0			0
$385$	1.50000	+	2.59808i	0.0764471	+	0.132410i
$386$		0			0
$387$	−4.00000			−0.203331
$388$		0			0
$389$	1.50000	+	2.59808i	0.0760530	+	0.131728i	0.901544	−	0.432688i	$-0.142435\pi$
$389$	1.50000	+	2.59808i	0.0760530	+	0.131728i	−0.825491	+	0.564416i	$0.809102\pi$
$390$		0			0
$391$	−4.50000	+	7.79423i	−0.227575	+	0.394171i
$392$		0			0
$393$	−8.00000			−0.403547
$394$		0			0
$395$	−2.50000	+	4.33013i	−0.125789	+	0.217872i
$396$		0			0
$397$	34.0000			1.70641			0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000			1.70641			0.853206	+	0.521575i	$0.174655\pi$
$398$		0			0
$399$	7.00000			0.350438
$400$		0			0
$401$	−22.0000			−1.09863			−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000			−1.09863			−0.549314	+	0.835616i	$0.685111\pi$
$402$		0			0
$403$	−35.0000			−1.74347
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	15.0000			0.743522
$408$		0			0
$409$	16.5000	−	28.5788i	0.815872	−	1.41313i	−0.0928272	−	0.995682i	$-0.529590\pi$
$409$	16.5000	−	28.5788i	0.815872	−	1.41313i	0.908700	−	0.417450i	$-0.137076\pi$
$410$		0			0
$411$	10.0000			0.493264
$412$		0			0
$413$	−6.00000	+	10.3923i	−0.295241	+	0.511372i
$414$		0			0
$415$	4.50000	+	7.79423i	0.220896	+	0.382604i
$416$		0			0
$417$	12.0000			0.587643
$418$		0			0
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	0.989000	−	0.147918i	$-0.0472572\pi$
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	−0.622601	+	0.782540i	$0.713924\pi$
$420$		0			0
$421$	−9.50000	−	16.4545i	−0.463002	−	0.801942i	0.536107	−	0.844150i	$-0.319894\pi$
$421$	−9.50000	−	16.4545i	−0.463002	−	0.801942i	−0.999109	+	0.0422075i	$0.986561\pi$
$422$		0			0
$423$	−0.500000	+	0.866025i	−0.0243108	+	0.0421076i
$424$		0			0
$425$	0.500000	+	0.866025i	0.0242536	+	0.0420084i
$426$		0			0
$427$	−7.00000			−0.338754
$428$		0			0
$429$	−15.0000			−0.724207
$430$		0			0
$431$	−7.50000	+	12.9904i	−0.361262	+	0.625725i	−0.988169	−	0.153370i	$-0.950987\pi$
$431$	−7.50000	+	12.9904i	−0.361262	+	0.625725i	0.626907	+	0.779094i	$0.284321\pi$
$432$		0			0
$433$	3.50000	−	6.06218i	0.168199	−	0.291330i	−0.769588	−	0.638541i	$-0.779538\pi$
$433$	3.50000	−	6.06218i	0.168199	−	0.291330i	0.937787	+	0.347212i	$0.112871\pi$
$434$		0			0
$435$	2.50000	−	4.33013i	0.119866	−	0.207614i
$436$		0			0
$437$	31.5000	−	54.5596i	1.50685	−	2.60994i
$438$		0			0
$439$	10.5000	+	18.1865i	0.501138	+	0.867996i	0.999999	+	0.00131415i	$0.000418308\pi$
$439$	10.5000	+	18.1865i	0.501138	+	0.867996i	−0.498861	+	0.866682i	$0.666248\pi$
$440$		0			0
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$		0			0
$443$	−18.5000	+	32.0429i	−0.878962	+	1.52241i	−0.0264796	+	0.999649i	$0.508430\pi$
$443$	−18.5000	+	32.0429i	−0.878962	+	1.52241i	−0.852482	+	0.522757i	$0.824904\pi$
$444$		0			0
$445$	10.0000			0.474045
$446$		0			0
$447$	22.0000			1.04056
$448$		0			0
$449$	−12.5000	+	21.6506i	−0.589911	+	1.02176i	0.404332	+	0.914612i	$0.367504\pi$
$449$	−12.5000	+	21.6506i	−0.589911	+	1.02176i	−0.994243	+	0.107144i	$0.965829\pi$
$450$		0			0
$451$	−1.50000	−	2.59808i	−0.0706322	−	0.122339i
$452$		0			0
$453$	3.50000	+	6.06218i	0.164444	+	0.284826i
$454$		0			0
$455$	−5.00000			−0.234404
$456$		0			0
$457$	1.50000	−	2.59808i	0.0701670	−	0.121533i	−0.828807	−	0.559534i	$-0.810980\pi$
$457$	1.50000	−	2.59808i	0.0701670	−	0.121533i	0.898974	+	0.438001i	$0.144313\pi$
$458$		0			0
$459$	−0.500000	−	0.866025i	−0.0233380	−	0.0404226i
$460$		0			0
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	−4.50000	−	7.79423i	−0.209133	−	0.362229i	0.742309	−	0.670058i	$-0.233731\pi$
$463$	−4.50000	−	7.79423i	−0.209133	−	0.362229i	−0.951442	+	0.307829i	$0.900397\pi$
$464$		0			0
$465$	−3.50000	+	6.06218i	−0.162309	+	0.281127i
$466$		0			0
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	0.773611	−	0.633661i	$-0.218448\pi$
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	−0.935572	+	0.353137i	$0.885115\pi$
$468$		0			0
$469$	−2.50000	+	7.79423i	−0.115439	+	0.359904i
$470$		0			0
$471$	−1.50000	−	2.59808i	−0.0691164	−	0.119713i
$472$		0			0
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$		0			0
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$	−10.0000			−0.457869
$478$		0			0
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	0.984930	−	0.172953i	$-0.0553307\pi$
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	−0.642246	+	0.766498i	$0.721997\pi$
$480$		0			0
$481$	−12.5000	+	21.6506i	−0.569951	+	0.987184i
$482$		0			0
$483$	−9.00000			−0.409514
$484$		0			0
$485$	−6.50000	−	11.2583i	−0.295150	−	0.511214i
$486$		0			0
$487$	−12.5000	−	21.6506i	−0.566429	−	0.981084i	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$	−12.5000	−	21.6506i	−0.566429	−	0.981084i	0.430486	−	0.902597i	$-0.358342\pi$
$488$		0			0
$489$	3.50000	−	6.06218i	0.158275	−	0.274141i
$490$		0			0
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$		0			0
$493$	−5.00000			−0.225189
$494$		0			0
$495$	−1.50000	+	2.59808i	−0.0674200	+	0.116775i
$496$		0			0
$497$	1.50000	+	2.59808i	0.0672842	+	0.116540i
$498$		0			0
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	0.983336	+	0.181797i	$0.0581915\pi$
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	−0.334227	+	0.942493i	$0.608475\pi$
$500$		0			0
$501$	2.50000	−	4.33013i	0.111692	−	0.193456i
$502$		0			0
$503$	−2.50000	+	4.33013i	−0.111469	+	0.193071i	−0.916363	−	0.400349i	$-0.868889\pi$
$503$	−2.50000	+	4.33013i	−0.111469	+	0.193071i	0.804893	+	0.593419i	$0.202222\pi$
$504$		0			0
$505$	5.50000	−	9.52628i	0.244747	−	0.423914i
$506$		0			0
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$		0			0
$509$	18.0000			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$510$		0			0
$511$	11.0000			0.486611
$512$		0			0
$513$	3.50000	+	6.06218i	0.154529	+	0.267652i
$514$		0			0
$515$	−9.50000	+	16.4545i	−0.418620	+	0.725071i
$516$		0			0
$517$	−1.50000	−	2.59808i	−0.0659699	−	0.114263i
$518$		0			0
$519$	11.5000	+	19.9186i	0.504794	+	0.874329i
$520$		0			0
$521$	26.0000			1.13908			0.569540	−	0.821963i	$-0.307121\pi$
$521$	26.0000			1.13908			0.569540	+	0.821963i	$0.307121\pi$
$522$		0			0
$523$	−4.50000	−	7.79423i	−0.196771	−	0.340818i	0.750708	−	0.660634i	$-0.229712\pi$
$523$	−4.50000	−	7.79423i	−0.196771	−	0.340818i	−0.947480	+	0.319816i	$0.896379\pi$
$524$		0			0
$525$	−0.500000	+	0.866025i	−0.0218218	+	0.0377964i
$526$		0			0
$527$	7.00000			0.304925
$528$		0			0
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$	5.00000			0.216574
$534$		0			0
$535$	−4.00000			−0.172935
$536$		0			0
$537$	12.0000			0.517838
$538$		0			0
$539$	−18.0000			−0.775315
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$		0			0
$543$	−8.50000	+	14.7224i	−0.364770	+	0.631800i
$544$		0			0
$545$	10.0000			0.428353
$546$		0			0
$547$	−21.5000	+	37.2391i	−0.919274	+	1.59223i	−0.118753	+	0.992924i	$0.537890\pi$
$547$	−21.5000	+	37.2391i	−0.919274	+	1.59223i	−0.800521	+	0.599305i	$0.795444\pi$
$548$		0			0
$549$	−3.50000	−	6.06218i	−0.149376	−	0.258727i
$550$		0			0
$551$	35.0000			1.49105
$552$		0			0
$553$	2.50000	+	4.33013i	0.106311	+	0.184136i
$554$		0			0
$555$	2.50000	+	4.33013i	0.106119	+	0.183804i
$556$		0			0
$557$	14.5000	−	25.1147i	0.614385	−	1.06415i	−0.376107	−	0.926576i	$-0.622738\pi$
$557$	14.5000	−	25.1147i	0.614385	−	1.06415i	0.990492	−	0.137569i	$-0.0439290\pi$
$558$		0			0
$559$	10.0000	+	17.3205i	0.422955	+	0.732579i
$560$		0			0
$561$	3.00000			0.126660
$562$		0			0
$563$	4.00000			0.168580			0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000			0.168580			0.0842900	+	0.996441i	$0.473138\pi$
$564$		0			0
$565$	10.5000	−	18.1865i	0.441738	−	0.765113i
$566$		0			0
$567$	0.500000	−	0.866025i	0.0209980	−	0.0363696i
$568$		0			0
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	−0.664897	−	0.746935i	$-0.731525\pi$
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	0.979313	+	0.202350i	$0.0648579\pi$
$570$		0			0
$571$	17.5000	−	30.3109i	0.732352	−	1.26847i	−0.223523	−	0.974699i	$-0.571756\pi$
$571$	17.5000	−	30.3109i	0.732352	−	1.26847i	0.955875	−	0.293773i	$-0.0949108\pi$
$572$		0			0
$573$	4.50000	+	7.79423i	0.187990	+	0.325609i
$574$		0			0
$575$	4.50000	+	7.79423i	0.187663	+	0.325042i
$576$		0			0
$577$	−18.5000	+	32.0429i	−0.770165	+	1.33397i	0.167307	+	0.985905i	$0.446493\pi$
$577$	−18.5000	+	32.0429i	−0.770165	+	1.33397i	−0.937472	+	0.348060i	$0.886840\pi$
$578$		0			0
$579$	22.0000			0.914289
$580$		0			0
$581$	9.00000			0.373383
$582$		0			0
$583$	15.0000	−	25.9808i	0.621237	−	1.07601i
$584$		0			0
$585$	−2.50000	−	4.33013i	−0.103362	−	0.179029i
$586$		0			0
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$		0			0
$589$	−49.0000			−2.01901
$590$		0			0
$591$	7.50000	−	12.9904i	0.308509	−	0.534353i
$592$		0			0
$593$	2.50000	+	4.33013i	0.102663	+	0.177817i	0.912781	−	0.408450i	$-0.133930\pi$
$593$	2.50000	+	4.33013i	0.102663	+	0.177817i	−0.810118	+	0.586267i	$0.800597\pi$
$594$		0			0
$595$	1.00000			0.0409960
$596$		0			0
$597$	7.50000	+	12.9904i	0.306955	+	0.531661i
$598$		0			0
$599$	16.5000	−	28.5788i	0.674172	−	1.16770i	−0.302539	−	0.953137i	$-0.597834\pi$
$599$	16.5000	−	28.5788i	0.674172	−	1.16770i	0.976710	−	0.214563i	$-0.0688326\pi$
$600$		0			0
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$		0			0
$603$	−8.00000	+	1.73205i	−0.325785	+	0.0705346i
$604$		0			0
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$		0			0
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$		0			0
$609$	−2.50000	−	4.33013i	−0.101305	−	0.175466i
$610$		0			0
$611$	5.00000			0.202278
$612$		0			0
$613$	−4.50000	−	7.79423i	−0.181753	−	0.314806i	0.760724	−	0.649075i	$-0.224844\pi$
$613$	−4.50000	−	7.79423i	−0.181753	−	0.314806i	−0.942478	+	0.334269i	$0.891511\pi$
$614$		0			0
$615$	0.500000	−	0.866025i	0.0201619	−	0.0349215i
$616$		0			0
$617$	38.0000			1.52982			0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000			1.52982			0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	0.734068	−	0.679076i	$-0.237620\pi$
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	−0.955131	+	0.296183i	$0.904286\pi$
$620$		0			0
$621$	−4.50000	−	7.79423i	−0.180579	−	0.312772i
$622$		0			0
$623$	5.00000	−	8.66025i	0.200321	−	0.346966i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−21.0000			−0.838659
$628$		0			0
$629$	2.50000	−	4.33013i	0.0996815	−	0.172653i
$630$		0			0
$631$	14.5000	+	25.1147i	0.577236	+	0.999802i	0.995795	+	0.0916122i	$0.0292020\pi$
$631$	14.5000	+	25.1147i	0.577236	+	0.999802i	−0.418559	+	0.908190i	$0.637465\pi$
$632$		0			0
$633$	−10.5000	−	18.1865i	−0.417338	−	0.722850i
$634$		0			0
$635$	−3.50000	+	6.06218i	−0.138893	+	0.240570i
$636$		0			0
$637$	15.0000	−	25.9808i	0.594322	−	1.02940i
$638$		0			0
$639$	−1.50000	+	2.59808i	−0.0593391	+	0.102778i
$640$		0			0
$641$	−8.50000	+	14.7224i	−0.335730	+	0.581501i	−0.983625	−	0.180229i	$-0.942316\pi$
$641$	−8.50000	+	14.7224i	−0.335730	+	0.581501i	0.647895	+	0.761730i	$0.275650\pi$
$642$		0			0
$643$	−48.0000			−1.89294			−0.946468	−	0.322799i	$-0.895376\pi$
$643$	−48.0000			−1.89294			−0.946468	+	0.322799i	$0.895376\pi$
$644$		0			0
$645$	4.00000			0.157500
$646$		0			0
$647$	−3.50000	−	6.06218i	−0.137599	−	0.238329i	0.788988	−	0.614408i	$-0.210605\pi$
$647$	−3.50000	−	6.06218i	−0.137599	−	0.238329i	−0.926587	+	0.376080i	$0.877272\pi$
$648$		0			0
$649$	18.0000	−	31.1769i	0.706562	−	1.22380i
$650$		0			0
$651$	3.50000	+	6.06218i	0.137176	+	0.237595i
$652$		0			0
$653$	16.5000	+	28.5788i	0.645695	+	1.11838i	0.984141	+	0.177390i	$0.0567655\pi$
$653$	16.5000	+	28.5788i	0.645695	+	1.11838i	−0.338446	+	0.940986i	$0.609901\pi$
$654$		0			0
$655$	8.00000			0.312586
$656$		0			0
$657$	5.50000	+	9.52628i	0.214575	+	0.371656i
$658$		0			0
$659$	10.5000	−	18.1865i	0.409022	−	0.708447i	−0.585758	−	0.810486i	$-0.699203\pi$
$659$	10.5000	−	18.1865i	0.409022	−	0.708447i	0.994780	+	0.102039i	$0.0325366\pi$
$660$		0			0
$661$	42.0000			1.63361			0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000			1.63361			0.816805	+	0.576913i	$0.195743\pi$
$662$		0			0
$663$	−2.50000	+	4.33013i	−0.0970920	+	0.168168i
$664$		0			0
$665$	−7.00000			−0.271448
$666$		0			0
$667$	−45.0000			−1.74241
$668$		0			0
$669$	8.00000			0.309298
$670$		0			0
$671$	21.0000			0.810696
$672$		0			0
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−11.5000	+	19.9186i	−0.441981	+	0.765533i	−0.997836	−	0.0657455i	$-0.979057\pi$
$677$	−11.5000	+	19.9186i	−0.441981	+	0.765533i	0.555856	+	0.831279i	$0.312391\pi$
$678$		0			0
$679$	−13.0000			−0.498894
$680$		0			0
$681$	10.5000	−	18.1865i	0.402361	−	0.696909i
$682$		0			0
$683$	4.50000	+	7.79423i	0.172188	+	0.298238i	0.939184	−	0.343413i	$-0.111583\pi$
$683$	4.50000	+	7.79423i	0.172188	+	0.298238i	−0.766997	+	0.641651i	$0.778250\pi$
$684$		0			0
$685$	−10.0000			−0.382080
$686$		0			0
$687$	−6.50000	−	11.2583i	−0.247990	−	0.429532i
$688$		0			0
$689$	25.0000	+	43.3013i	0.952424	+	1.64965i
$690$		0			0
$691$	11.5000	−	19.9186i	0.437481	−	0.757739i	−0.560014	−	0.828483i	$-0.689204\pi$
$691$	11.5000	−	19.9186i	0.437481	−	0.757739i	0.997494	+	0.0707446i	$0.0225375\pi$
$692$		0			0
$693$	1.50000	+	2.59808i	0.0569803	+	0.0986928i
$694$		0			0
$695$	−12.0000			−0.455186
$696$		0			0
$697$	−1.00000			−0.0378777
$698$		0			0
$699$	7.50000	−	12.9904i	0.283676	−	0.491341i
$700$		0			0
$701$	23.5000	−	40.7032i	0.887583	−	1.53734i	0.0448582	−	0.998993i	$-0.485716\pi$
$701$	23.5000	−	40.7032i	0.887583	−	1.53734i	0.842725	−	0.538345i	$-0.180950\pi$
$702$		0			0
$703$	−17.5000	+	30.3109i	−0.660025	+	1.14320i
$704$		0			0
$705$	0.500000	−	0.866025i	0.0188311	−	0.0326164i
$706$		0			0
$707$	−5.50000	−	9.52628i	−0.206849	−	0.358273i
$708$		0			0
$709$	12.5000	+	21.6506i	0.469447	+	0.813107i	0.999390	−	0.0349269i	$-0.0111198\pi$
$709$	12.5000	+	21.6506i	0.469447	+	0.813107i	−0.529943	+	0.848034i	$0.677787\pi$
$710$		0			0
$711$	−2.50000	+	4.33013i	−0.0937573	+	0.162392i
$712$		0			0
$713$	63.0000			2.35937
$714$		0			0
$715$	15.0000			0.560968
$716$		0			0
$717$	11.5000	−	19.9186i	0.429475	−	0.743873i
$718$		0			0
$719$	−4.50000	−	7.79423i	−0.167822	−	0.290676i	0.769832	−	0.638247i	$-0.220340\pi$
$719$	−4.50000	−	7.79423i	−0.167822	−	0.290676i	−0.937654	+	0.347571i	$0.887007\pi$
$720$		0			0
$721$	9.50000	+	16.4545i	0.353798	+	0.612797i
$722$		0			0
$723$	10.0000			0.371904
$724$		0			0
$725$	−2.50000	+	4.33013i	−0.0928477	+	0.160817i
$726$		0			0
$727$	1.50000	+	2.59808i	0.0556319	+	0.0963573i	0.892500	−	0.451047i	$-0.148949\pi$
$727$	1.50000	+	2.59808i	0.0556319	+	0.0963573i	−0.836868	+	0.547404i	$0.815616\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.00000	−	3.46410i	−0.0739727	−	0.128124i
$732$		0			0
$733$	−14.5000	+	25.1147i	−0.535570	+	0.927634i	0.463566	+	0.886062i	$0.346570\pi$
$733$	−14.5000	+	25.1147i	−0.535570	+	0.927634i	−0.999136	+	0.0415715i	$0.986764\pi$
$734$		0			0
$735$	−3.00000	−	5.19615i	−0.110657	−	0.191663i
$736$		0			0
$737$	7.50000	−	23.3827i	0.276266	−	0.861312i
$738$		0			0
$739$	16.5000	+	28.5788i	0.606962	+	1.05129i	0.991738	+	0.128279i	$0.0409454\pi$
$739$	16.5000	+	28.5788i	0.606962	+	1.05129i	−0.384776	+	0.923010i	$0.625721\pi$
$740$		0			0
$741$	17.5000	−	30.3109i	0.642879	−	1.11350i
$742$		0			0
$743$	−1.50000	−	2.59808i	−0.0550297	−	0.0953142i	0.837198	−	0.546899i	$-0.184192\pi$
$743$	−1.50000	−	2.59808i	−0.0550297	−	0.0953142i	−0.892228	+	0.451585i	$0.850859\pi$
$744$		0			0
$745$	−22.0000			−0.806018
$746$		0			0
$747$	4.50000	+	7.79423i	0.164646	+	0.285176i
$748$		0			0
$749$	−2.00000	+	3.46410i	−0.0730784	+	0.126576i
$750$		0			0
$751$	−40.0000			−1.45962			−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000			−1.45962			−0.729810	+	0.683650i	$0.760392\pi$
$752$		0			0
$753$	−1.50000	−	2.59808i	−0.0546630	−	0.0946792i
$754$		0			0
$755$	−3.50000	−	6.06218i	−0.127378	−	0.220625i
$756$		0			0
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	−0.959634	−	0.281251i	$-0.909251\pi$
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	0.723388	+	0.690442i	$0.242584\pi$
$758$		0			0
$759$	27.0000			0.980038
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$	5.00000	−	8.66025i	0.181012	−	0.313522i
$764$		0			0
$765$	0.500000	+	0.866025i	0.0180775	+	0.0313112i
$766$		0			0
$767$	30.0000	+	51.9615i	1.08324	+	1.87622i
$768$		0			0
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	−0.398541	−	0.917151i	$-0.630483\pi$
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	0.993546	−	0.113429i	$-0.0361834\pi$
$770$		0			0
$771$	13.5000	−	23.3827i	0.486191	−	0.842107i
$772$		0			0
$773$	−9.50000	+	16.4545i	−0.341691	+	0.591827i	−0.984747	−	0.173993i	$-0.944333\pi$
$773$	−9.50000	+	16.4545i	−0.341691	+	0.591827i	0.643056	+	0.765819i	$0.277666\pi$
$774$		0			0
$775$	3.50000	−	6.06218i	0.125724	−	0.217760i
$776$		0			0
$777$	5.00000			0.179374
$778$		0			0
$779$	7.00000			0.250801
$780$		0			0
$781$	−4.50000	−	7.79423i	−0.161023	−	0.278899i
$782$		0			0
$783$	2.50000	−	4.33013i	0.0893427	−	0.154746i
$784$		0			0
$785$	1.50000	+	2.59808i	0.0535373	+	0.0927293i
$786$		0			0
$787$	25.5000	+	44.1673i	0.908977	+	1.57439i	0.815488	+	0.578774i	$0.196469\pi$
$787$	25.5000	+	44.1673i	0.908977	+	1.57439i	0.0934886	+	0.995620i	$0.470198\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10.5000	−	18.1865i	−0.373337	−	0.646639i
$792$		0			0
$793$	−17.5000	+	30.3109i	−0.621443	+	1.07637i
$794$		0			0
$795$	10.0000			0.354663
$796$		0			0
$797$	24.5000	−	42.4352i	0.867835	−	1.50313i	0.00362965	−	0.999993i	$-0.498845\pi$
$797$	24.5000	−	42.4352i	0.867835	−	1.50313i	0.864205	−	0.503140i	$-0.167822\pi$
$798$		0			0
$799$	−1.00000			−0.0353775
$800$		0			0
$801$	10.0000			0.353333
$802$		0			0
$803$	−33.0000			−1.16454
$804$		0			0
$805$	9.00000			0.317208
$806$		0			0
$807$	10.0000			0.352017
$808$		0			0
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	11.5000	−	19.9186i	0.403820	−	0.699436i	−0.590364	−	0.807137i	$-0.701016\pi$
$811$	11.5000	−	19.9186i	0.403820	−	0.699436i	0.994183	+	0.107701i	$0.0343490\pi$
$812$		0			0
$813$	−8.00000			−0.280572
$814$		0			0
$815$	−3.50000	+	6.06218i	−0.122600	+	0.212349i
$816$		0			0
$817$	14.0000	+	24.2487i	0.489798	+	0.848355i
$818$		0			0
$819$	−5.00000			−0.174714
$820$		0			0
$821$	−4.50000	−	7.79423i	−0.157051	−	0.272020i	0.776753	−	0.629805i	$-0.216865\pi$
$821$	−4.50000	−	7.79423i	−0.157051	−	0.272020i	−0.933804	+	0.357785i	$0.883532\pi$
$822$		0			0
$823$	−24.5000	−	42.4352i	−0.854016	−	1.47920i	−0.877555	−	0.479477i	$-0.840826\pi$
$823$	−24.5000	−	42.4352i	−0.854016	−	1.47920i	0.0235383	−	0.999723i	$-0.492507\pi$
$824$		0			0
$825$	1.50000	−	2.59808i	0.0522233	−	0.0904534i
$826$		0			0
$827$	10.5000	+	18.1865i	0.365121	+	0.632408i	0.988796	−	0.149276i	$-0.0476944\pi$
$827$	10.5000	+	18.1865i	0.365121	+	0.632408i	−0.623675	+	0.781684i	$0.714361\pi$
$828$		0			0
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$		0			0
$831$	−10.0000			−0.346896
$832$		0			0
$833$	−3.00000	+	5.19615i	−0.103944	+	0.180036i
$834$		0			0
$835$	−2.50000	+	4.33013i	−0.0865161	+	0.149850i
$836$		0			0
$837$	−3.50000	+	6.06218i	−0.120978	+	0.209540i
$838$		0			0
$839$	−17.5000	+	30.3109i	−0.604167	+	1.04645i	0.388015	+	0.921653i	$0.373161\pi$
$839$	−17.5000	+	30.3109i	−0.604167	+	1.04645i	−0.992183	+	0.124795i	$0.960173\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$		0			0
$843$	−1.50000	−	2.59808i	−0.0516627	−	0.0894825i
$844$		0			0
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	2.00000			0.0687208
$848$		0			0
$849$	4.00000			0.137280
$850$		0			0
$851$	22.5000	−	38.9711i	0.771290	−	1.33591i
$852$		0			0
$853$	13.5000	+	23.3827i	0.462231	+	0.800608i	0.999072	−	0.0430758i	$-0.0137157\pi$
$853$	13.5000	+	23.3827i	0.462231	+	0.800608i	−0.536841	+	0.843684i	$0.680382\pi$
$854$		0			0
$855$	−3.50000	−	6.06218i	−0.119697	−	0.207322i
$856$		0			0
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$		0			0
$859$	25.5000	−	44.1673i	0.870049	−	1.50697i	0.00810361	−	0.999967i	$-0.497421\pi$
$859$	25.5000	−	44.1673i	0.870049	−	1.50697i	0.861945	−	0.507002i	$-0.169246\pi$
$860$		0			0
$861$	−0.500000	−	0.866025i	−0.0170400	−	0.0295141i
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	−11.5000	−	19.9186i	−0.391012	−	0.677252i
$866$		0			0
$867$	−8.00000	+	13.8564i	−0.271694	+	0.470588i
$868$		0			0
$869$	−7.50000	−	12.9904i	−0.254420	−	0.440668i
$870$		0			0
$871$	27.5000	+	30.3109i	0.931802	+	1.02705i
$872$		0			0
$873$	−6.50000	−	11.2583i	−0.219992	−	0.381037i
$874$		0			0
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$		0			0
$877$	21.5000	+	37.2391i	0.726003	+	1.25747i	0.958560	+	0.284892i	$0.0919577\pi$
$877$	21.5000	+	37.2391i	0.726003	+	1.25747i	−0.232556	+	0.972583i	$0.574709\pi$
$878$		0			0
$879$	14.0000			0.472208
$880$		0			0
$881$	−22.5000	−	38.9711i	−0.758044	−	1.31297i	−0.943847	−	0.330384i	$-0.892822\pi$
$881$	−22.5000	−	38.9711i	−0.758044	−	1.31297i	0.185802	−	0.982587i	$-0.440512\pi$
$882$		0			0
$883$	20.5000	−	35.5070i	0.689880	−	1.19491i	−0.281996	−	0.959415i	$-0.590997\pi$
$883$	20.5000	−	35.5070i	0.689880	−	1.19491i	0.971876	−	0.235492i	$-0.0756700\pi$
$884$		0			0
$885$	12.0000			0.403376
$886$		0			0
$887$	−17.5000	−	30.3109i	−0.587592	−	1.01774i	−0.994547	−	0.104292i	$-0.966743\pi$
$887$	−17.5000	−	30.3109i	−0.587592	−	1.01774i	0.406954	−	0.913449i	$-0.366591\pi$
$888$		0			0
$889$	3.50000	+	6.06218i	0.117386	+	0.203319i
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$		0			0
$893$	7.00000			0.234246
$894$		0			0
$895$	−12.0000			−0.401116
$896$		0			0
$897$	−22.5000	+	38.9711i	−0.751253	+	1.30121i
$898$		0			0
$899$	17.5000	+	30.3109i	0.583658	+	1.01092i
$900$		0			0
$901$	−5.00000	−	8.66025i	−0.166574	−	0.288515i
$902$		0			0
$903$	2.00000	−	3.46410i	0.0665558	−	0.115278i
$904$		0			0
$905$	8.50000	−	14.7224i	0.282550	−	0.489390i
$906$		0			0
$907$	16.5000	−	28.5788i	0.547874	−	0.948945i	−0.450546	−	0.892753i	$-0.648771\pi$
$907$	16.5000	−	28.5788i	0.547874	−	0.948945i	0.998420	−	0.0561918i	$-0.0178958\pi$
$908$		0			0
$909$	5.50000	−	9.52628i	0.182423	−	0.315967i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−27.0000			−0.893570
$914$		0			0
$915$	3.50000	+	6.06218i	0.115706	+	0.200409i
$916$		0			0
$917$	4.00000	−	6.92820i	0.132092	−	0.228789i
$918$		0			0
$919$	0.500000	+	0.866025i	0.0164935	+	0.0285675i	0.874154	−	0.485648i	$-0.161416\pi$
$919$	0.500000	+	0.866025i	0.0164935	+	0.0285675i	−0.857661	+	0.514216i	$0.828083\pi$
$920$		0			0
$921$	−7.50000	−	12.9904i	−0.247133	−	0.428048i
$922$		0			0
$923$	15.0000			0.493731
$924$		0			0
$925$	−2.50000	−	4.33013i	−0.0821995	−	0.142374i
$926$		0			0
$927$	−9.50000	+	16.4545i	−0.312021	+	0.540436i
$928$		0			0
$929$	−6.00000			−0.196854			−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000			−0.196854			−0.0984268	+	0.995144i	$0.531381\pi$
$930$		0			0
$931$	21.0000	−	36.3731i	0.688247	−	1.19208i
$932$		0			0
$933$	−20.0000			−0.654771
$934$		0			0
$935$	−3.00000			−0.0981105
$936$		0			0
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$		0			0
$939$	30.0000			0.979013
$940$		0			0
$941$	54.0000			1.76035			0.880175	−	0.474650i	$-0.157425\pi$
$941$	54.0000			1.76035			0.880175	+	0.474650i	$0.157425\pi$
$942$		0			0
$943$	−9.00000			−0.293080
$944$		0			0
$945$	−0.500000	+	0.866025i	−0.0162650	+	0.0281718i
$946$		0			0
$947$	24.0000			0.779895			0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000			0.779895			0.389948	+	0.920837i	$0.372493\pi$
$948$		0			0
$949$	27.5000	−	47.6314i	0.892688	−	1.54618i
$950$		0			0
$951$	13.5000	+	23.3827i	0.437767	+	0.758236i
$952$		0			0
$953$	30.0000			0.971795			0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000			0.971795			0.485898	+	0.874016i	$0.338493\pi$
$954$		0			0
$955$	−4.50000	−	7.79423i	−0.145617	−	0.252215i
$956$		0			0
$957$	7.50000	+	12.9904i	0.242441	+	0.419919i
$958$		0			0
$959$	−5.00000	+	8.66025i	−0.161458	+	0.279654i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$		0			0
$963$	−4.00000			−0.128898
$964$		0			0
$965$	−22.0000			−0.708205
$966$		0			0
$967$	16.5000	−	28.5788i	0.530604	−	0.919033i	−0.468758	−	0.883327i	$-0.655298\pi$
$967$	16.5000	−	28.5788i	0.530604	−	0.919033i	0.999362	−	0.0357069i	$-0.0113683\pi$
$968$		0			0
$969$	−3.50000	+	6.06218i	−0.112436	+	0.194745i
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$		0			0
$973$	−6.00000	+	10.3923i	−0.192351	+	0.333162i
$974$		0			0
$975$	2.50000	+	4.33013i	0.0800641	+	0.138675i
$976$		0			0
$977$	−17.5000	−	30.3109i	−0.559875	−	0.969731i	−0.997506	−	0.0705770i	$-0.977516\pi$
$977$	−17.5000	−	30.3109i	−0.559875	−	0.969731i	0.437632	−	0.899154i	$-0.355817\pi$
$978$		0			0
$979$	−15.0000	+	25.9808i	−0.479402	+	0.830349i
$980$		0			0
$981$	10.0000			0.319275
$982$		0			0
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		0			0
$985$	−7.50000	+	12.9904i	−0.238970	+	0.413908i
$986$		0			0
$987$	−0.500000	−	0.866025i	−0.0159152	−	0.0275659i
$988$		0			0
$989$	−18.0000	−	31.1769i	−0.572367	−	0.991368i
$990$		0			0
$991$	−60.0000			−1.90596			−0.952981	−	0.303029i	$-0.902002\pi$
$991$	−60.0000			−1.90596			−0.952981	+	0.303029i	$0.902002\pi$
$992$		0			0
$993$	0.500000	−	0.866025i	0.0158670	−	0.0274825i
$994$		0			0
$995$	−7.50000	−	12.9904i	−0.237766	−	0.411823i
$996$		0			0
$997$	−18.0000			−0.570066			−0.285033	−	0.958518i	$-0.592005\pi$
$997$	−18.0000			−0.570066			−0.285033	+	0.958518i	$0.592005\pi$
$998$		0			0
$999$	2.50000	+	4.33013i	0.0790965	+	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.c.841.1	✓	2
67.29	even	3	inner	4020.2.q.c.3781.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.c.841.1	✓	2	1.1	even	1	trivial
4020.2.q.c.3781.1	yes	2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{9} +(-1.50000 + 2.59808i) q^{11} +(-2.50000 - 4.33013i) q^{13} -1.00000 q^{15} +(0.500000 + 0.866025i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{21} +(4.50000 + 7.79423i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-2.50000 + 4.33013i) q^{29} +(3.50000 - 6.06218i) q^{31} +(1.50000 - 2.59808i) q^{33} +(0.500000 - 0.866025i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(2.50000 + 4.33013i) q^{39} +(-0.500000 + 0.866025i) q^{41} -4.00000 q^{43} +1.00000 q^{45} +(-0.500000 + 0.866025i) q^{47} +(3.00000 + 5.19615i) q^{49} +(-0.500000 - 0.866025i) q^{51} -10.0000 q^{53} +(-1.50000 + 2.59808i) q^{55} +(3.50000 + 6.06218i) q^{57} -12.0000 q^{59} +(-3.50000 - 6.06218i) q^{61} +(0.500000 - 0.866025i) q^{63} +(-2.50000 - 4.33013i) q^{65} +(-8.00000 + 1.73205i) q^{67} +(-4.50000 - 7.79423i) q^{69} +(-1.50000 + 2.59808i) q^{71} +(5.50000 + 9.52628i) q^{73} -1.00000 q^{75} +(1.50000 + 2.59808i) q^{77} +(-2.50000 + 4.33013i) q^{79} +1.00000 q^{81} +(4.50000 + 7.79423i) q^{83} +(0.500000 + 0.866025i) q^{85} +(2.50000 - 4.33013i) q^{87} +10.0000 q^{89} -5.00000 q^{91} +(-3.50000 + 6.06218i) q^{93} +(-3.50000 - 6.06218i) q^{95} +(-6.50000 - 11.2583i) q^{97} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^5 + q^7 + 2 * q^9	\( 2 q - 2 q^{3} + 2 q^{5} + q^{7} + 2 q^{9} - 3 q^{11} - 5 q^{13} - 2 q^{15} + q^{17} - 7 q^{19} - q^{21} + 9 q^{23} + 2 q^{25} - 2 q^{27} - 5 q^{29} + 7 q^{31} + 3 q^{33} + q^{35} - 5 q^{37} + 5 q^{39} - q^{41} - 8 q^{43} + 2 q^{45} - q^{47} + 6 q^{49} - q^{51} - 20 q^{53} - 3 q^{55} + 7 q^{57} - 24 q^{59} - 7 q^{61} + q^{63} - 5 q^{65} - 16 q^{67} - 9 q^{69} - 3 q^{71} + 11 q^{73} - 2 q^{75} + 3 q^{77} - 5 q^{79} + 2 q^{81} + 9 q^{83} + q^{85} + 5 q^{87} + 20 q^{89} - 10 q^{91} - 7 q^{93} - 7 q^{95} - 13 q^{97} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^5 + q^7 + 2 * q^9 - 3 * q^11 - 5 * q^13 - 2 * q^15 + q^17 - 7 * q^19 - q^21 + 9 * q^23 + 2 * q^25 - 2 * q^27 - 5 * q^29 + 7 * q^31 + 3 * q^33 + q^35 - 5 * q^37 + 5 * q^39 - q^41 - 8 * q^43 + 2 * q^45 - q^47 + 6 * q^49 - q^51 - 20 * q^53 - 3 * q^55 + 7 * q^57 - 24 * q^59 - 7 * q^61 + q^63 - 5 * q^65 - 16 * q^67 - 9 * q^69 - 3 * q^71 + 11 * q^73 - 2 * q^75 + 3 * q^77 - 5 * q^79 + 2 * q^81 + 9 * q^83 + q^85 + 5 * q^87 + 20 * q^89 - 10 * q^91 - 7 * q^93 - 7 * q^95 - 13 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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