LMFDB - Embedded newform 4020.2.q.d.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$2$
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.d.3781.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{9} +(0.500000 - 0.866025i) q^{11} +(1.50000 + 2.59808i) q^{13} -1.00000 q^{15} +(2.50000 + 4.33013i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{21} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.50000 - 6.06218i) q^{29} +(-0.500000 + 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{33} +(0.500000 - 0.866025i) q^{35} +(1.50000 + 2.59808i) q^{37} +(-1.50000 - 2.59808i) q^{39} +(1.50000 - 2.59808i) q^{41} +4.00000 q^{43} +1.00000 q^{45} +(1.50000 - 2.59808i) q^{47} +(3.00000 + 5.19615i) q^{49} +(-2.50000 - 4.33013i) q^{51} +6.00000 q^{53} +(0.500000 - 0.866025i) q^{55} +(3.50000 + 6.06218i) q^{57} -4.00000 q^{59} +(-3.50000 - 6.06218i) q^{61} +(0.500000 - 0.866025i) q^{63} +(1.50000 + 2.59808i) q^{65} +(8.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{69} +(-7.50000 + 12.9904i) q^{71} +(1.50000 + 2.59808i) q^{73} -1.00000 q^{75} +(-0.500000 - 0.866025i) q^{77} +(1.50000 - 2.59808i) q^{79} +1.00000 q^{81} +(-5.50000 - 9.52628i) q^{83} +(2.50000 + 4.33013i) q^{85} +(-3.50000 + 6.06218i) q^{87} -6.00000 q^{89} +3.00000 q^{91} +(0.500000 - 0.866025i) q^{93} +(-3.50000 - 6.06218i) q^{95} +(-6.50000 - 11.2583i) q^{97} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + q^{11} + 3 q^{13} - 2 q^{15} + 5 q^{17} - 7 q^{19} - q^{21} - 3 q^{23} + 2 q^{25} - 2 q^{27} + 7 q^{29} - q^{31} - q^{33} + q^{35} + 3 q^{37} - 3 q^{39} + 3 q^{41} + 8 q^{43} + 2 q^{45} + 3 q^{47} + 6 q^{49} - 5 q^{51} + 12 q^{53} + q^{55} + 7 q^{57} - 8 q^{59} - 7 q^{61} + q^{63} + 3 q^{65} + 16 q^{67} + 3 q^{69} - 15 q^{71} + 3 q^{73} - 2 q^{75} - q^{77} + 3 q^{79} + 2 q^{81} - 11 q^{83} + 5 q^{85} - 7 q^{87} - 12 q^{89} + 6 q^{91} + q^{93} - 7 q^{95} - 13 q^{97} + q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^5 + q^7 + 2 * q^9 + q^11 + 3 * q^13 - 2 * q^15 + 5 * q^17 - 7 * q^19 - q^21 - 3 * q^23 + 2 * q^25 - 2 * q^27 + 7 * q^29 - q^31 - q^33 + q^35 + 3 * q^37 - 3 * q^39 + 3 * q^41 + 8 * q^43 + 2 * q^45 + 3 * q^47 + 6 * q^49 - 5 * q^51 + 12 * q^53 + q^55 + 7 * q^57 - 8 * q^59 - 7 * q^61 + q^63 + 3 * q^65 + 16 * q^67 + 3 * q^69 - 15 * q^71 + 3 * q^73 - 2 * q^75 - q^77 + 3 * q^79 + 2 * q^81 - 11 * q^83 + 5 * q^85 - 7 * q^87 - 12 * q^89 + 6 * q^91 + q^93 - 7 * q^95 - 13 * q^97 + 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
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$		0			0
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	0.995535	−	0.0943882i	$-0.0300895\pi$
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	−0.579510	+	0.814965i	$0.696756\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$		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
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	−0.333205	−	0.942855i	$-0.608130\pi$
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	0.983138	−	0.182864i	$-0.0585367\pi$
$30$		0			0
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	0.817625	+	0.575751i	$0.195290\pi$
$32$		0			0
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$		0			0
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$		0			0
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	0.962580	−	0.270998i	$-0.0873538\pi$
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	−0.715981	+	0.698119i	$0.754020\pi$
$38$		0			0
$39$	−1.50000	−	2.59808i	−0.240192	−	0.416025i
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$	−2.50000	−	4.33013i	−0.350070	−	0.606339i
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	0.500000	−	0.866025i	0.0674200	−	0.116775i
$56$		0			0
$57$	3.50000	+	6.06218i	0.463586	+	0.802955i
$58$		0			0
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		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
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$	8.00000	+	1.73205i	0.977356	+	0.211604i
$67$	8.00000	+	1.73205i	0.977356	+	0.211604i
$68$		0			0
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$		0			0
$71$	−7.50000	+	12.9904i	−0.890086	+	1.54167i	−0.0503155	+	0.998733i	$0.516023\pi$
$71$	−7.50000	+	12.9904i	−0.890086	+	1.54167i	−0.839771	+	0.542941i	$0.817311\pi$
$72$		0			0
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	0.940356	−	0.340193i	$-0.110493\pi$
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	−0.764794	+	0.644275i	$0.777159\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−0.500000	−	0.866025i	−0.0569803	−	0.0986928i
$78$		0			0
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	−0.769222	−	0.638982i	$-0.779356\pi$
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	0.937985	+	0.346675i	$0.112689\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−5.50000	−	9.52628i	−0.603703	−	1.04565i	−0.992255	−	0.124218i	$-0.960358\pi$
$83$	−5.50000	−	9.52628i	−0.603703	−	1.04565i	0.388552	−	0.921427i	$-0.372976\pi$
$84$		0			0
$85$	2.50000	+	4.33013i	0.271163	+	0.469668i
$86$		0			0
$87$	−3.50000	+	6.06218i	−0.375239	+	0.649934i
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	3.00000			0.314485
$92$		0			0
$93$	0.500000	−	0.866025i	0.0518476	−	0.0898027i
$94$		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
$99$	0.500000	−	0.866025i	0.0502519	−	0.0870388i
$100$		0			0
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$		0			0
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	−0.716173	−	0.697923i	$-0.754108\pi$
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	0.962505	+	0.271263i	$0.0874412\pi$
$104$		0			0
$105$	−0.500000	+	0.866025i	−0.0487950	+	0.0845154i
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		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
$111$	−1.50000	−	2.59808i	−0.142374	−	0.246598i
$112$		0			0
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	−0.572938	−	0.819599i	$-0.694196\pi$
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	0.996262	+	0.0863794i	$0.0275297\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$		0			0
$117$	1.50000	+	2.59808i	0.138675	+	0.240192i
$118$		0			0
$119$	5.00000			0.458349
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$	−1.50000	+	2.59808i	−0.135250	+	0.234261i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	0.887357	+	0.461084i	$0.152539\pi$
$128$		0			0
$129$	−4.00000			−0.352180
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		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
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−1.50000	+	2.59808i	−0.126323	+	0.218797i
$142$		0			0
$143$	3.00000			0.250873
$144$		0			0
$145$	3.50000	−	6.06218i	0.290659	−	0.503436i
$146$		0			0
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$		0			0
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$	−7.50000	−	12.9904i	−0.610341	−	1.05714i	−0.991183	−	0.132502i	$-0.957699\pi$
$151$	−7.50000	−	12.9904i	−0.610341	−	1.05714i	0.380841	−	0.924640i	$-0.375634\pi$
$152$		0			0
$153$	2.50000	+	4.33013i	0.202113	+	0.350070i
$154$		0			0
$155$	−0.500000	+	0.866025i	−0.0401610	+	0.0695608i
$156$		0			0
$157$	−10.5000	−	18.1865i	−0.837991	−	1.45144i	−0.891572	−	0.452880i	$-0.850397\pi$
$157$	−10.5000	−	18.1865i	−0.837991	−	1.45144i	0.0535803	−	0.998564i	$-0.482937\pi$
$158$		0			0
$159$	−6.00000			−0.475831
$160$		0			0
$161$	−3.00000			−0.236433
$162$		0			0
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	0.979076	−	0.203497i	$-0.0652307\pi$
$164$		0			0
$165$	−0.500000	+	0.866025i	−0.0389249	+	0.0674200i
$166$		0			0
$167$	7.50000	−	12.9904i	0.580367	−	1.00523i	−0.415068	−	0.909790i	$-0.636242\pi$
$167$	7.50000	−	12.9904i	0.580367	−	1.00523i	0.995436	−	0.0954356i	$-0.0304244\pi$
$168$		0			0
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$		0			0
$171$	−3.50000	−	6.06218i	−0.267652	−	0.463586i
$172$		0			0
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	0.920722	+	0.390218i	$0.127601\pi$
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	−0.122422	+	0.992478i	$0.539066\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$		0			0
$177$	4.00000			0.300658
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	12.5000	−	21.6506i	0.929118	−	1.60928i	0.144316	−	0.989532i	$-0.453902\pi$
$181$	12.5000	−	21.6506i	0.929118	−	1.60928i	0.784801	−	0.619747i	$-0.212765\pi$
$182$		0			0
$183$	3.50000	+	6.06218i	0.258727	+	0.448129i
$184$		0			0
$185$	1.50000	+	2.59808i	0.110282	+	0.191014i
$186$		0			0
$187$	5.00000			0.365636
$188$		0			0
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$		0			0
$191$	−2.50000	−	4.33013i	−0.180894	−	0.313317i	0.761291	−	0.648410i	$-0.224566\pi$
$191$	−2.50000	−	4.33013i	−0.180894	−	0.313317i	−0.942185	+	0.335093i	$0.891232\pi$
$192$		0			0
$193$	−6.00000			−0.431889			−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000			−0.431889			−0.215945	+	0.976406i	$0.569283\pi$
$194$		0			0
$195$	−1.50000	−	2.59808i	−0.107417	−	0.186052i
$196$		0			0
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	−0.914501	−	0.404584i	$-0.867416\pi$
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	0.807630	+	0.589689i	$0.200750\pi$
$198$		0			0
$199$	12.5000	+	21.6506i	0.886102	+	1.53477i	0.844446	+	0.535641i	$0.179930\pi$
$199$	12.5000	+	21.6506i	0.886102	+	1.53477i	0.0416556	+	0.999132i	$0.486737\pi$
$200$		0			0
$201$	−8.00000	−	1.73205i	−0.564276	−	0.122169i
$202$		0			0
$203$	−3.50000	−	6.06218i	−0.245652	−	0.425481i
$204$		0			0
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$		0			0
$207$	−1.50000	−	2.59808i	−0.104257	−	0.180579i
$208$		0			0
$209$	−7.00000			−0.484200
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$		0			0
$213$	7.50000	−	12.9904i	0.513892	−	0.890086i
$214$		0			0
$215$	4.00000			0.272798
$216$		0			0
$217$	0.500000	+	0.866025i	0.0339422	+	0.0587896i
$218$		0			0
$219$	−1.50000	−	2.59808i	−0.101361	−	0.175562i
$220$		0			0
$221$	−7.50000	+	12.9904i	−0.504505	+	0.873828i
$222$		0			0
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−4.50000	+	7.79423i	−0.298675	+	0.517321i	−0.975833	−	0.218517i	$-0.929878\pi$
$227$	−4.50000	+	7.79423i	−0.298675	+	0.517321i	0.677158	+	0.735838i	$0.263211\pi$
$228$		0			0
$229$	10.5000	+	18.1865i	0.693860	+	1.20180i	0.970564	+	0.240845i	$0.0774245\pi$
$229$	10.5000	+	18.1865i	0.693860	+	1.20180i	−0.276704	+	0.960955i	$0.589242\pi$
$230$		0			0
$231$	0.500000	+	0.866025i	0.0328976	+	0.0569803i
$232$		0			0
$233$	6.50000	−	11.2583i	0.425829	−	0.737558i	−0.570668	−	0.821181i	$-0.693316\pi$
$233$	6.50000	−	11.2583i	0.425829	−	0.737558i	0.996497	+	0.0836229i	$0.0266491\pi$
$234$		0			0
$235$	1.50000	−	2.59808i	0.0978492	−	0.169480i
$236$		0			0
$237$	−1.50000	+	2.59808i	−0.0974355	+	0.168763i
$238$		0			0
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	−0.296037	−	0.955176i	$-0.595665\pi$
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	0.975226	−	0.221213i	$-0.0710015\pi$
$240$		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
$247$	10.5000	−	18.1865i	0.668099	−	1.15718i
$248$		0			0
$249$	5.50000	+	9.52628i	0.348548	+	0.603703i
$250$		0			0
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	0.999536	−	0.0304521i	$-0.00969471\pi$
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	−0.526140	+	0.850398i	$0.676361\pi$
$252$		0			0
$253$	−3.00000			−0.188608
$254$		0			0
$255$	−2.50000	−	4.33013i	−0.156556	−	0.271163i
$256$		0			0
$257$	8.50000	−	14.7224i	0.530215	−	0.918360i	−0.469163	−	0.883112i	$-0.655444\pi$
$257$	8.50000	−	14.7224i	0.530215	−	0.918360i	0.999379	−	0.0352486i	$-0.0112223\pi$
$258$		0			0
$259$	3.00000			0.186411
$260$		0			0
$261$	3.50000	−	6.06218i	0.216645	−	0.375239i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	6.00000			0.367194
$268$		0			0
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$		0			0
$273$	−3.00000			−0.181568
$274$		0			0
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		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
$279$	−0.500000	+	0.866025i	−0.0299342	+	0.0518476i
$280$		0			0
$281$	11.5000	+	19.9186i	0.686032	+	1.18824i	0.973111	+	0.230336i	$0.0739826\pi$
$281$	11.5000	+	19.9186i	0.686032	+	1.18824i	−0.287079	+	0.957907i	$0.592684\pi$
$282$		0			0
$283$	20.0000			1.18888			0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000			1.18888			0.594438	+	0.804141i	$0.297374\pi$
$284$		0			0
$285$	3.50000	+	6.06218i	0.207322	+	0.359092i
$286$		0			0
$287$	−1.50000	−	2.59808i	−0.0885422	−	0.153360i
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		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
$295$	−4.00000			−0.232889
$296$		0			0
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$		0			0
$299$	4.50000	−	7.79423i	0.260242	−	0.450752i
$300$		0			0
$301$	2.00000	−	3.46410i	0.115278	−	0.199667i
$302$		0			0
$303$	4.50000	−	7.79423i	0.258518	−	0.447767i
$304$		0			0
$305$	−3.50000	−	6.06218i	−0.200409	−	0.347119i
$306$		0			0
$307$	−4.50000	−	7.79423i	−0.256829	−	0.444840i	0.708562	−	0.705649i	$-0.249344\pi$
$307$	−4.50000	−	7.79423i	−0.256829	−	0.444840i	−0.965391	+	0.260808i	$0.916011\pi$
$308$		0			0
$309$	−2.50000	+	4.33013i	−0.142220	+	0.246332i
$310$		0			0
$311$	−20.0000			−1.13410			−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000			−1.13410			−0.567048	+	0.823685i	$0.691915\pi$
$312$		0			0
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$		0			0
$315$	0.500000	−	0.866025i	0.0281718	−	0.0487950i
$316$		0			0
$317$	0.500000	+	0.866025i	0.0280828	+	0.0486408i	0.879725	−	0.475482i	$-0.157726\pi$
$317$	0.500000	+	0.866025i	0.0280828	+	0.0486408i	−0.851642	+	0.524123i	$0.824393\pi$
$318$		0			0
$319$	−3.50000	−	6.06218i	−0.195962	−	0.339417i
$320$		0			0
$321$	−12.0000			−0.669775
$322$		0			0
$323$	17.5000	−	30.3109i	0.973726	−	1.68654i
$324$		0			0
$325$	1.50000	+	2.59808i	0.0832050	+	0.144115i
$326$		0			0
$327$	−10.0000			−0.553001
$328$		0			0
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$		0			0
$331$	−4.50000	+	7.79423i	−0.247342	+	0.428410i	−0.962788	−	0.270259i	$-0.912891\pi$
$331$	−4.50000	+	7.79423i	−0.247342	+	0.428410i	0.715445	+	0.698669i	$0.246224\pi$
$332$		0			0
$333$	1.50000	+	2.59808i	0.0821995	+	0.142374i
$334$		0			0
$335$	8.00000	+	1.73205i	0.437087	+	0.0946320i
$336$		0			0
$337$	11.5000	+	19.9186i	0.626445	+	1.08503i	0.988260	+	0.152784i	$0.0488240\pi$
$337$	11.5000	+	19.9186i	0.626445	+	1.08503i	−0.361815	+	0.932250i	$0.617843\pi$
$338$		0			0
$339$	−4.50000	+	7.79423i	−0.244406	+	0.423324i
$340$		0			0
$341$	0.500000	+	0.866025i	0.0270765	+	0.0468979i
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$	1.50000	+	2.59808i	0.0807573	+	0.139876i
$346$		0			0
$347$	−8.50000	+	14.7224i	−0.456304	+	0.790342i	−0.998762	−	0.0497412i	$-0.984160\pi$
$347$	−8.50000	+	14.7224i	−0.456304	+	0.790342i	0.542458	+	0.840083i	$0.317494\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	−1.50000	−	2.59808i	−0.0800641	−	0.138675i
$352$		0			0
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	0.594441	−	0.804139i	$-0.297373\pi$
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	−0.993626	+	0.112731i	$0.964040\pi$
$354$		0			0
$355$	−7.50000	+	12.9904i	−0.398059	+	0.689458i
$356$		0			0
$357$	−5.00000			−0.264628
$358$		0			0
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		0			0
$363$	−5.00000	−	8.66025i	−0.262432	−	0.454545i
$364$		0			0
$365$	1.50000	+	2.59808i	0.0785136	+	0.135990i
$366$		0			0
$367$	16.5000	−	28.5788i	0.861293	−	1.49180i	−0.00938849	−	0.999956i	$-0.502988\pi$
$367$	16.5000	−	28.5788i	0.861293	−	1.49180i	0.870681	−	0.491847i	$-0.163678\pi$
$368$		0			0
$369$	1.50000	−	2.59808i	0.0780869	−	0.135250i
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		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
$377$	21.0000			1.08156
$378$		0			0
$379$	−7.50000	−	12.9904i	−0.385249	−	0.667271i	0.606555	−	0.795042i	$-0.292551\pi$
$379$	−7.50000	−	12.9904i	−0.385249	−	0.667271i	−0.991804	+	0.127771i	$0.959218\pi$
$380$		0			0
$381$	−0.500000	+	0.866025i	−0.0256158	+	0.0443678i
$382$		0			0
$383$	−11.5000	−	19.9186i	−0.587623	−	1.01779i	−0.994543	−	0.104328i	$-0.966731\pi$
$383$	−11.5000	−	19.9186i	−0.587623	−	1.01779i	0.406920	−	0.913464i	$-0.366603\pi$
$384$		0			0
$385$	−0.500000	−	0.866025i	−0.0254824	−	0.0441367i
$386$		0			0
$387$	4.00000			0.203331
$388$		0			0
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	0.729103	−	0.684403i	$-0.239937\pi$
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	−0.957263	+	0.289220i	$0.906604\pi$
$390$		0			0
$391$	7.50000	−	12.9904i	0.379291	−	0.656952i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.50000	−	2.59808i	0.0754732	−	0.130723i
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$		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
$403$	−3.00000			−0.149441
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	3.00000			0.148704
$408$		0			0
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	−0.575670	−	0.817682i	$-0.695259\pi$
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	0.995968	+	0.0897044i	$0.0285922\pi$
$410$		0			0
$411$	10.0000			0.493264
$412$		0			0
$413$	−2.00000	+	3.46410i	−0.0984136	+	0.170457i
$414$		0			0
$415$	−5.50000	−	9.52628i	−0.269984	−	0.467627i
$416$		0			0
$417$	−4.00000			−0.195881
$418$		0			0
$419$	−2.50000	−	4.33013i	−0.122133	−	0.211541i	0.798476	−	0.602027i	$-0.205640\pi$
$419$	−2.50000	−	4.33013i	−0.122133	−	0.211541i	−0.920609	+	0.390487i	$0.872307\pi$
$420$		0			0
$421$	6.50000	+	11.2583i	0.316791	+	0.548697i	0.979817	−	0.199899i	$-0.0640614\pi$
$421$	6.50000	+	11.2583i	0.316791	+	0.548697i	−0.663026	+	0.748596i	$0.730728\pi$
$422$		0			0
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$		0			0
$425$	2.50000	+	4.33013i	0.121268	+	0.210042i
$426$		0			0
$427$	−7.00000			−0.338754
$428$		0			0
$429$	−3.00000			−0.144841
$430$		0			0
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	0.332785	+	0.943003i	$0.392012\pi$
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	−0.983057	+	0.183301i	$0.941322\pi$
$432$		0			0
$433$	19.5000	−	33.7750i	0.937110	−	1.62312i	0.166283	−	0.986078i	$-0.446823\pi$
$433$	19.5000	−	33.7750i	0.937110	−	1.62312i	0.770827	−	0.637044i	$-0.219843\pi$
$434$		0			0
$435$	−3.50000	+	6.06218i	−0.167812	+	0.290659i
$436$		0			0
$437$	−10.5000	+	18.1865i	−0.502283	+	0.869980i
$438$		0			0
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$		0			0
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$		0			0
$443$	−8.50000	+	14.7224i	−0.403847	+	0.699484i	−0.994187	−	0.107671i	$-0.965661\pi$
$443$	−8.50000	+	14.7224i	−0.403847	+	0.699484i	0.590339	+	0.807155i	$0.298994\pi$
$444$		0			0
$445$	−6.00000			−0.284427
$446$		0			0
$447$	−10.0000			−0.472984
$448$		0			0
$449$	−10.5000	+	18.1865i	−0.495526	+	0.858276i	−0.999987	−	0.00515887i	$-0.998358\pi$
$449$	−10.5000	+	18.1865i	−0.495526	+	0.858276i	0.504461	+	0.863434i	$0.331691\pi$
$450$		0			0
$451$	−1.50000	−	2.59808i	−0.0706322	−	0.122339i
$452$		0			0
$453$	7.50000	+	12.9904i	0.352381	+	0.610341i
$454$		0			0
$455$	3.00000			0.140642
$456$		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
$459$	−2.50000	−	4.33013i	−0.116690	−	0.202113i
$460$		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
$463$	−8.50000	−	14.7224i	−0.395029	−	0.684209i	0.598076	−	0.801439i	$-0.295932\pi$
$463$	−8.50000	−	14.7224i	−0.395029	−	0.684209i	−0.993105	+	0.117230i	$0.962599\pi$
$464$		0			0
$465$	0.500000	−	0.866025i	0.0231869	−	0.0401610i
$466$		0			0
$467$	−9.50000	−	16.4545i	−0.439608	−	0.761423i	0.558052	−	0.829806i	$-0.311549\pi$
$467$	−9.50000	−	16.4545i	−0.439608	−	0.761423i	−0.997659	+	0.0683836i	$0.978216\pi$
$468$		0			0
$469$	5.50000	−	6.06218i	0.253966	−	0.279925i
$470$		0			0
$471$	10.5000	+	18.1865i	0.483814	+	0.837991i
$472$		0			0
$473$	2.00000	−	3.46410i	0.0919601	−	0.159280i
$474$		0			0
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	−10.5000	−	18.1865i	−0.479757	−	0.830964i	0.519973	−	0.854183i	$-0.325942\pi$
$479$	−10.5000	−	18.1865i	−0.479757	−	0.830964i	−0.999730	+	0.0232187i	$0.992609\pi$
$480$		0			0
$481$	−4.50000	+	7.79423i	−0.205182	+	0.355386i
$482$		0			0
$483$	3.00000			0.136505
$484$		0			0
$485$	−6.50000	−	11.2583i	−0.295150	−	0.511214i
$486$		0			0
$487$	3.50000	+	6.06218i	0.158600	+	0.274703i	0.934364	−	0.356320i	$-0.115969\pi$
$487$	3.50000	+	6.06218i	0.158600	+	0.274703i	−0.775764	+	0.631023i	$0.782635\pi$
$488$		0			0
$489$	−8.50000	+	14.7224i	−0.384383	+	0.665771i
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	35.0000			1.57632
$494$		0			0
$495$	0.500000	−	0.866025i	0.0224733	−	0.0389249i
$496$		0			0
$497$	7.50000	+	12.9904i	0.336421	+	0.582698i
$498$		0			0
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	0.716258	−	0.697835i	$-0.245853\pi$
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	−0.962472	+	0.271380i	$0.912520\pi$
$500$		0			0
$501$	−7.50000	+	12.9904i	−0.335075	+	0.580367i
$502$		0			0
$503$	−20.5000	+	35.5070i	−0.914050	+	1.58318i	−0.105763	+	0.994391i	$0.533729\pi$
$503$	−20.5000	+	35.5070i	−0.914050	+	1.58318i	−0.808286	+	0.588789i	$0.799605\pi$
$504$		0			0
$505$	−4.50000	+	7.79423i	−0.200247	+	0.346839i
$506$		0			0
$507$	−2.00000	+	3.46410i	−0.0888231	+	0.153846i
$508$		0			0
$509$	34.0000			1.50702			0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000			1.50702			0.753512	+	0.657434i	$0.228358\pi$
$510$		0			0
$511$	3.00000			0.132712
$512$		0			0
$513$	3.50000	+	6.06218i	0.154529	+	0.267652i
$514$		0			0
$515$	2.50000	−	4.33013i	0.110163	−	0.190808i
$516$		0			0
$517$	−1.50000	−	2.59808i	−0.0659699	−	0.114263i
$518$		0			0
$519$	−10.5000	−	18.1865i	−0.460899	−	0.798300i
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$		0			0
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	0.854887	−	0.518815i	$-0.173627\pi$
$523$	−0.500000	−	0.866025i	−0.0218635	−	0.0378686i	−0.876750	+	0.480946i	$0.840293\pi$
$524$		0			0
$525$	−0.500000	+	0.866025i	−0.0218218	+	0.0377964i
$526$		0			0
$527$	−5.00000			−0.217803
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$	9.00000			0.389833
$534$		0			0
$535$	12.0000			0.518805
$536$		0			0
$537$	−12.0000			−0.517838
$538$		0			0
$539$	6.00000			0.258438
$540$		0			0
$541$	−30.0000			−1.28980			−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000			−1.28980			−0.644900	+	0.764267i	$0.723101\pi$
$542$		0			0
$543$	−12.5000	+	21.6506i	−0.536426	+	0.929118i
$544$		0			0
$545$	10.0000			0.428353
$546$		0			0
$547$	−13.5000	+	23.3827i	−0.577218	+	0.999771i	0.418578	+	0.908181i	$0.362529\pi$
$547$	−13.5000	+	23.3827i	−0.577218	+	0.999771i	−0.995797	+	0.0915908i	$0.970805\pi$
$548$		0			0
$549$	−3.50000	−	6.06218i	−0.149376	−	0.258727i
$550$		0			0
$551$	−49.0000			−2.08747
$552$		0			0
$553$	−1.50000	−	2.59808i	−0.0637865	−	0.110481i
$554$		0			0
$555$	−1.50000	−	2.59808i	−0.0636715	−	0.110282i
$556$		0			0
$557$	−19.5000	+	33.7750i	−0.826242	+	1.43109i	0.0747252	+	0.997204i	$0.476192\pi$
$557$	−19.5000	+	33.7750i	−0.826242	+	1.43109i	−0.900967	+	0.433888i	$0.857141\pi$
$558$		0			0
$559$	6.00000	+	10.3923i	0.253773	+	0.439548i
$560$		0			0
$561$	−5.00000			−0.211100
$562$		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
$565$	4.50000	−	7.79423i	0.189316	−	0.327906i
$566$		0			0
$567$	0.500000	−	0.866025i	0.0209980	−	0.0363696i
$568$		0			0
$569$	−6.50000	+	11.2583i	−0.272494	+	0.471974i	−0.969500	−	0.245092i	$-0.921182\pi$
$569$	−6.50000	+	11.2583i	−0.272494	+	0.471974i	0.697006	+	0.717066i	$0.254515\pi$
$570$		0			0
$571$	1.50000	−	2.59808i	0.0627730	−	0.108726i	−0.832931	−	0.553377i	$-0.813339\pi$
$571$	1.50000	−	2.59808i	0.0627730	−	0.108726i	0.895704	+	0.444651i	$0.146672\pi$
$572$		0			0
$573$	2.50000	+	4.33013i	0.104439	+	0.180894i
$574$		0			0
$575$	−1.50000	−	2.59808i	−0.0625543	−	0.108347i
$576$		0			0
$577$	−10.5000	+	18.1865i	−0.437121	+	0.757115i	−0.997466	−	0.0711438i	$-0.977335\pi$
$577$	−10.5000	+	18.1865i	−0.437121	+	0.757115i	0.560345	+	0.828259i	$0.310668\pi$
$578$		0			0
$579$	6.00000			0.249351
$580$		0			0
$581$	−11.0000			−0.456357
$582$		0			0
$583$	3.00000	−	5.19615i	0.124247	−	0.215203i
$584$		0			0
$585$	1.50000	+	2.59808i	0.0620174	+	0.107417i
$586$		0			0
$587$	−11.5000	−	19.9186i	−0.474656	−	0.822128i	0.524923	−	0.851150i	$-0.324094\pi$
$587$	−11.5000	−	19.9186i	−0.474656	−	0.822128i	−0.999579	+	0.0290218i	$0.990761\pi$
$588$		0			0
$589$	7.00000			0.288430
$590$		0			0
$591$	1.50000	−	2.59808i	0.0617018	−	0.106871i
$592$		0			0
$593$	4.50000	+	7.79423i	0.184793	+	0.320071i	0.943507	−	0.331353i	$-0.107505\pi$
$593$	4.50000	+	7.79423i	0.184793	+	0.320071i	−0.758714	+	0.651424i	$0.774172\pi$
$594$		0			0
$595$	5.00000			0.204980
$596$		0			0
$597$	−12.5000	−	21.6506i	−0.511591	−	0.886102i
$598$		0			0
$599$	−13.5000	+	23.3827i	−0.551595	+	0.955391i	0.446565	+	0.894751i	$0.352647\pi$
$599$	−13.5000	+	23.3827i	−0.551595	+	0.955391i	−0.998160	+	0.0606393i	$0.980686\pi$
$600$		0			0
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	0.967600	−	0.252486i	$-0.0812483\pi$
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	−0.702460	+	0.711723i	$0.747915\pi$
$602$		0			0
$603$	8.00000	+	1.73205i	0.325785	+	0.0705346i
$604$		0			0
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$		0			0
$607$	−5.50000	+	9.52628i	−0.223238	+	0.386660i	−0.955789	−	0.294052i	$-0.904996\pi$
$607$	−5.50000	+	9.52628i	−0.223238	+	0.386660i	0.732551	+	0.680712i	$0.238329\pi$
$608$		0			0
$609$	3.50000	+	6.06218i	0.141827	+	0.245652i
$610$		0			0
$611$	9.00000			0.364101
$612$		0			0
$613$	−20.5000	−	35.5070i	−0.827987	−	1.43412i	−0.899615	−	0.436684i	$-0.856153\pi$
$613$	−20.5000	−	35.5070i	−0.827987	−	1.43412i	0.0716275	−	0.997431i	$-0.477181\pi$
$614$		0			0
$615$	−1.50000	+	2.59808i	−0.0604858	+	0.104765i
$616$		0			0
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$		0			0
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	−0.967271	−	0.253744i	$-0.918338\pi$
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	0.263887	−	0.964554i	$-0.414995\pi$
$620$		0			0
$621$	1.50000	+	2.59808i	0.0601929	+	0.104257i
$622$		0			0
$623$	−3.00000	+	5.19615i	−0.120192	+	0.208179i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	7.00000			0.279553
$628$		0			0
$629$	−7.50000	+	12.9904i	−0.299045	+	0.517960i
$630$		0			0
$631$	2.50000	+	4.33013i	0.0995234	+	0.172380i	0.911487	−	0.411328i	$-0.134935\pi$
$631$	2.50000	+	4.33013i	0.0995234	+	0.172380i	−0.811964	+	0.583707i	$0.801602\pi$
$632$		0			0
$633$	−2.50000	−	4.33013i	−0.0993661	−	0.172107i
$634$		0			0
$635$	0.500000	−	0.866025i	0.0198419	−	0.0343672i
$636$		0			0
$637$	−9.00000	+	15.5885i	−0.356593	+	0.617637i
$638$		0			0
$639$	−7.50000	+	12.9904i	−0.296695	+	0.513892i
$640$		0			0
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	−0.466029	−	0.884769i	$-0.654316\pi$
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	0.999247	−	0.0387913i	$-0.0123508\pi$
$642$		0			0
$643$	48.0000			1.89294			0.946468	−	0.322799i	$-0.104624\pi$
$643$	48.0000			1.89294			0.946468	+	0.322799i	$0.104624\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$		0			0
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	0.995194	−	0.0979182i	$-0.0312184\pi$
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	−0.582397	+	0.812905i	$0.697885\pi$
$648$		0			0
$649$	−2.00000	+	3.46410i	−0.0785069	+	0.135978i
$650$		0			0
$651$	−0.500000	−	0.866025i	−0.0195965	−	0.0339422i
$652$		0			0
$653$	22.5000	+	38.9711i	0.880493	+	1.52506i	0.850794	+	0.525500i	$0.176122\pi$
$653$	22.5000	+	38.9711i	0.880493	+	1.52506i	0.0296993	+	0.999559i	$0.490545\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.50000	+	2.59808i	0.0585206	+	0.101361i
$658$		0			0
$659$	−3.50000	+	6.06218i	−0.136341	+	0.236149i	−0.926109	−	0.377257i	$-0.876867\pi$
$659$	−3.50000	+	6.06218i	−0.136341	+	0.236149i	0.789768	+	0.613405i	$0.210201\pi$
$660$		0			0
$661$	10.0000			0.388955			0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000			0.388955			0.194477	+	0.980907i	$0.437699\pi$
$662$		0			0
$663$	7.50000	−	12.9904i	0.291276	−	0.504505i
$664$		0			0
$665$	−7.00000			−0.271448
$666$		0			0
$667$	−21.0000			−0.813123
$668$		0			0
$669$	−24.0000			−0.927894
$670$		0			0
$671$	−7.00000			−0.270232
$672$		0			0
$673$	−22.0000			−0.848038			−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000			−0.848038			−0.424019	+	0.905653i	$0.639381\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−25.5000	+	44.1673i	−0.980045	+	1.69749i	−0.317876	+	0.948132i	$0.602970\pi$
$677$	−25.5000	+	44.1673i	−0.980045	+	1.69749i	−0.662169	+	0.749355i	$0.730364\pi$
$678$		0			0
$679$	−13.0000			−0.498894
$680$		0			0
$681$	4.50000	−	7.79423i	0.172440	−	0.298675i
$682$		0			0
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	0.993940	−	0.109926i	$-0.0350613\pi$
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	−0.592168	+	0.805814i	$0.701728\pi$
$684$		0			0
$685$	−10.0000			−0.382080
$686$		0			0
$687$	−10.5000	−	18.1865i	−0.400600	−	0.693860i
$688$		0			0
$689$	9.00000	+	15.5885i	0.342873	+	0.593873i
$690$		0			0
$691$	−12.5000	+	21.6506i	−0.475522	+	0.823629i	−0.999607	−	0.0280373i	$-0.991074\pi$
$691$	−12.5000	+	21.6506i	−0.475522	+	0.823629i	0.524084	+	0.851666i	$0.324408\pi$
$692$		0			0
$693$	−0.500000	−	0.866025i	−0.0189934	−	0.0328976i
$694$		0			0
$695$	4.00000			0.151729
$696$		0			0
$697$	15.0000			0.568166
$698$		0			0
$699$	−6.50000	+	11.2583i	−0.245853	+	0.425829i
$700$		0			0
$701$	−14.5000	+	25.1147i	−0.547657	+	0.948571i	0.450777	+	0.892637i	$0.351147\pi$
$701$	−14.5000	+	25.1147i	−0.547657	+	0.948571i	−0.998434	+	0.0559339i	$0.982186\pi$
$702$		0			0
$703$	10.5000	−	18.1865i	0.396015	−	0.685918i
$704$		0			0
$705$	−1.50000	+	2.59808i	−0.0564933	+	0.0978492i
$706$		0			0
$707$	4.50000	+	7.79423i	0.169240	+	0.293132i
$708$		0			0
$709$	−7.50000	−	12.9904i	−0.281668	−	0.487864i	0.690127	−	0.723688i	$-0.257554\pi$
$709$	−7.50000	−	12.9904i	−0.281668	−	0.487864i	−0.971796	+	0.235824i	$0.924221\pi$
$710$		0			0
$711$	1.50000	−	2.59808i	0.0562544	−	0.0974355i
$712$		0			0
$713$	3.00000			0.112351
$714$		0			0
$715$	3.00000			0.112194
$716$		0			0
$717$	−10.5000	+	18.1865i	−0.392130	+	0.679189i
$718$		0			0
$719$	−2.50000	−	4.33013i	−0.0932343	−	0.161486i	0.815636	−	0.578565i	$-0.196387\pi$
$719$	−2.50000	−	4.33013i	−0.0932343	−	0.161486i	−0.908870	+	0.417079i	$0.863054\pi$
$720$		0			0
$721$	−2.50000	−	4.33013i	−0.0931049	−	0.161262i
$722$		0			0
$723$	10.0000			0.371904
$724$		0			0
$725$	3.50000	−	6.06218i	0.129987	−	0.225144i
$726$		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
$731$	10.0000	+	17.3205i	0.369863	+	0.640622i
$732$		0			0
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	−0.635515	−	0.772088i	$-0.719212\pi$
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	0.986406	+	0.164328i	$0.0525456\pi$
$734$		0			0
$735$	−3.00000	−	5.19615i	−0.110657	−	0.191663i
$736$		0			0
$737$	5.50000	−	6.06218i	0.202595	−	0.223303i
$738$		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
$741$	−10.5000	+	18.1865i	−0.385727	+	0.668099i
$742$		0			0
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	0.936687	−	0.350168i	$-0.113876\pi$
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	−0.771598	+	0.636111i	$0.780542\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$		0			0
$747$	−5.50000	−	9.52628i	−0.201234	−	0.348548i
$748$		0			0
$749$	6.00000	−	10.3923i	0.219235	−	0.379727i
$750$		0			0
$751$	−48.0000			−1.75154			−0.875772	−	0.482724i	$-0.839647\pi$
$751$	−48.0000			−1.75154			−0.875772	+	0.482724i	$0.839647\pi$
$752$		0			0
$753$	−7.50000	−	12.9904i	−0.273315	−	0.473396i
$754$		0			0
$755$	−7.50000	−	12.9904i	−0.272953	−	0.472768i
$756$		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
$759$	3.00000			0.108893
$760$		0			0
$761$	−54.0000			−1.95750			−0.978749	−	0.205061i	$-0.934261\pi$
$761$	−54.0000			−1.95750			−0.978749	+	0.205061i	$0.934261\pi$
$762$		0			0
$763$	5.00000	−	8.66025i	0.181012	−	0.313522i
$764$		0			0
$765$	2.50000	+	4.33013i	0.0903877	+	0.156556i
$766$		0			0
$767$	−6.00000	−	10.3923i	−0.216647	−	0.375244i
$768$		0			0
$769$	8.50000	−	14.7224i	0.306518	−	0.530904i	−0.671080	−	0.741385i	$-0.734169\pi$
$769$	8.50000	−	14.7224i	0.306518	−	0.530904i	0.977598	+	0.210480i	$0.0675028\pi$
$770$		0			0
$771$	−8.50000	+	14.7224i	−0.306120	+	0.530215i
$772$		0			0
$773$	0.500000	−	0.866025i	0.0179838	−	0.0311488i	−0.856893	−	0.515494i	$-0.827609\pi$
$773$	0.500000	−	0.866025i	0.0179838	−	0.0311488i	0.874877	+	0.484345i	$0.160942\pi$
$774$		0			0
$775$	−0.500000	+	0.866025i	−0.0179605	+	0.0311086i
$776$		0			0
$777$	−3.00000			−0.107624
$778$		0			0
$779$	−21.0000			−0.752403
$780$		0			0
$781$	7.50000	+	12.9904i	0.268371	+	0.464832i
$782$		0			0
$783$	−3.50000	+	6.06218i	−0.125080	+	0.216645i
$784$		0			0
$785$	−10.5000	−	18.1865i	−0.374761	−	0.649105i
$786$		0			0
$787$	−6.50000	−	11.2583i	−0.231700	−	0.401316i	0.726609	−	0.687052i	$-0.241095\pi$
$787$	−6.50000	−	11.2583i	−0.231700	−	0.401316i	−0.958308	+	0.285736i	$0.907762\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.50000	−	7.79423i	−0.160002	−	0.277131i
$792$		0			0
$793$	10.5000	−	18.1865i	0.372866	−	0.645823i
$794$		0			0
$795$	−6.00000			−0.212798
$796$		0			0
$797$	−25.5000	+	44.1673i	−0.903256	+	1.56449i	−0.0800155	+	0.996794i	$0.525497\pi$
$797$	−25.5000	+	44.1673i	−0.903256	+	1.56449i	−0.823241	+	0.567692i	$0.807836\pi$
$798$		0			0
$799$	15.0000			0.530662
$800$		0			0
$801$	−6.00000			−0.212000
$802$		0			0
$803$	3.00000			0.105868
$804$		0			0
$805$	−3.00000			−0.105736
$806$		0			0
$807$	18.0000			0.633630
$808$		0			0
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$		0			0
$811$	−0.500000	+	0.866025i	−0.0175574	+	0.0304103i	−0.874671	−	0.484718i	$-0.838922\pi$
$811$	−0.500000	+	0.866025i	−0.0175574	+	0.0304103i	0.857113	+	0.515128i	$0.172256\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.50000	−	14.7224i	0.297742	−	0.515704i
$816$		0			0
$817$	−14.0000	−	24.2487i	−0.489798	−	0.848355i
$818$		0			0
$819$	3.00000			0.104828
$820$		0			0
$821$	−14.5000	−	25.1147i	−0.506053	−	0.876510i	−0.999975	−	0.00700413i	$-0.997770\pi$
$821$	−14.5000	−	25.1147i	−0.506053	−	0.876510i	0.493922	−	0.869506i	$-0.335563\pi$
$822$		0			0
$823$	11.5000	+	19.9186i	0.400865	+	0.694318i	0.993831	−	0.110910i	$-0.0353764\pi$
$823$	11.5000	+	19.9186i	0.400865	+	0.694318i	−0.592966	+	0.805228i	$0.702043\pi$
$824$		0			0
$825$	−0.500000	+	0.866025i	−0.0174078	+	0.0301511i
$826$		0			0
$827$	16.5000	+	28.5788i	0.573761	+	0.993784i	0.996175	+	0.0873805i	$0.0278496\pi$
$827$	16.5000	+	28.5788i	0.573761	+	0.993784i	−0.422414	+	0.906403i	$0.638817\pi$
$828$		0			0
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$		0			0
$831$	−10.0000			−0.346896
$832$		0			0
$833$	−15.0000	+	25.9808i	−0.519719	+	0.900180i
$834$		0			0
$835$	7.50000	−	12.9904i	0.259548	−	0.449551i
$836$		0			0
$837$	0.500000	−	0.866025i	0.0172825	−	0.0299342i
$838$		0			0
$839$	16.5000	−	28.5788i	0.569643	−	0.986651i	−0.426958	−	0.904272i	$-0.640415\pi$
$839$	16.5000	−	28.5788i	0.569643	−	0.986651i	0.996601	−	0.0823795i	$-0.0262520\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$		0			0
$843$	−11.5000	−	19.9186i	−0.396081	−	0.686032i
$844$		0			0
$845$	2.00000	−	3.46410i	0.0688021	−	0.119169i
$846$		0			0
$847$	10.0000			0.343604
$848$		0			0
$849$	−20.0000			−0.686398
$850$		0			0
$851$	4.50000	−	7.79423i	0.154258	−	0.267183i
$852$		0			0
$853$	9.50000	+	16.4545i	0.325274	+	0.563391i	0.981568	−	0.191115i	$-0.0612102\pi$
$853$	9.50000	+	16.4545i	0.325274	+	0.563391i	−0.656294	+	0.754505i	$0.727877\pi$
$854$		0			0
$855$	−3.50000	−	6.06218i	−0.119697	−	0.207322i
$856$		0			0
$857$	−10.0000			−0.341593			−0.170797	−	0.985306i	$-0.554634\pi$
$857$	−10.0000			−0.341593			−0.170797	+	0.985306i	$0.554634\pi$
$858$		0			0
$859$	−26.5000	+	45.8993i	−0.904168	+	1.56607i	−0.0821386	+	0.996621i	$0.526175\pi$
$859$	−26.5000	+	45.8993i	−0.904168	+	1.56607i	−0.822030	+	0.569445i	$0.807158\pi$
$860$		0			0
$861$	1.50000	+	2.59808i	0.0511199	+	0.0885422i
$862$		0			0
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$		0			0
$865$	10.5000	+	18.1865i	0.357011	+	0.618361i
$866$		0			0
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$		0			0
$869$	−1.50000	−	2.59808i	−0.0508840	−	0.0881337i
$870$		0			0
$871$	7.50000	+	23.3827i	0.254128	+	0.792292i
$872$		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
$877$	25.5000	+	44.1673i	0.861074	+	1.49142i	0.870893	+	0.491472i	$0.163541\pi$
$877$	25.5000	+	44.1673i	0.861074	+	1.49142i	−0.00981966	+	0.999952i	$0.503126\pi$
$878$		0			0
$879$	14.0000			0.472208
$880$		0			0
$881$	−12.5000	−	21.6506i	−0.421136	−	0.729428i	0.574915	−	0.818213i	$-0.305035\pi$
$881$	−12.5000	−	21.6506i	−0.421136	−	0.729428i	−0.996051	+	0.0887846i	$0.971702\pi$
$882$		0			0
$883$	−7.50000	+	12.9904i	−0.252395	+	0.437161i	−0.964185	−	0.265232i	$-0.914552\pi$
$883$	−7.50000	+	12.9904i	−0.252395	+	0.437161i	0.711790	+	0.702393i	$0.247885\pi$
$884$		0			0
$885$	4.00000			0.134459
$886$		0			0
$887$	−11.5000	−	19.9186i	−0.386132	−	0.668801i	0.605793	−	0.795622i	$-0.292856\pi$
$887$	−11.5000	−	19.9186i	−0.386132	−	0.668801i	−0.991926	+	0.126821i	$0.959522\pi$
$888$		0			0
$889$	−0.500000	−	0.866025i	−0.0167695	−	0.0290456i
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$		0			0
$893$	−21.0000			−0.702738
$894$		0			0
$895$	12.0000			0.401116
$896$		0			0
$897$	−4.50000	+	7.79423i	−0.150251	+	0.260242i
$898$		0			0
$899$	3.50000	+	6.06218i	0.116732	+	0.202185i
$900$		0			0
$901$	15.0000	+	25.9808i	0.499722	+	0.865545i
$902$		0			0
$903$	−2.00000	+	3.46410i	−0.0665558	+	0.115278i
$904$		0			0
$905$	12.5000	−	21.6506i	0.415514	−	0.719691i
$906$		0			0
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$		0			0
$909$	−4.50000	+	7.79423i	−0.149256	+	0.258518i
$910$		0			0
$911$	−32.0000			−1.06021			−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000			−1.06021			−0.530104	+	0.847933i	$0.677847\pi$
$912$		0			0
$913$	−11.0000			−0.364047
$914$		0			0
$915$	3.50000	+	6.06218i	0.115706	+	0.200409i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	20.5000	+	35.5070i	0.676233	+	1.17127i	0.976107	+	0.217291i	$0.0697219\pi$
$919$	20.5000	+	35.5070i	0.676233	+	1.17127i	−0.299874	+	0.953979i	$0.596945\pi$
$920$		0			0
$921$	4.50000	+	7.79423i	0.148280	+	0.256829i
$922$		0			0
$923$	−45.0000			−1.48119
$924$		0			0
$925$	1.50000	+	2.59808i	0.0493197	+	0.0854242i
$926$		0			0
$927$	2.50000	−	4.33013i	0.0821108	−	0.142220i
$928$		0			0
$929$	10.0000			0.328089			0.164045	−	0.986453i	$-0.447546\pi$
$929$	10.0000			0.328089			0.164045	+	0.986453i	$0.447546\pi$
$930$		0			0
$931$	21.0000	−	36.3731i	0.688247	−	1.19208i
$932$		0			0
$933$	20.0000			0.654771
$934$		0			0
$935$	5.00000			0.163517
$936$		0			0
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$		0			0
$939$	−10.0000			−0.326338
$940$		0			0
$941$	−10.0000			−0.325991			−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000			−0.325991			−0.162995	+	0.986627i	$0.552116\pi$
$942$		0			0
$943$	−9.00000			−0.293080
$944$		0			0
$945$	−0.500000	+	0.866025i	−0.0162650	+	0.0281718i
$946$		0			0
$947$	−48.0000			−1.55979			−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000			−1.55979			−0.779895	+	0.625910i	$0.784728\pi$
$948$		0			0
$949$	−4.50000	+	7.79423i	−0.146076	+	0.253011i
$950$		0			0
$951$	−0.500000	−	0.866025i	−0.0162136	−	0.0280828i
$952$		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
$955$	−2.50000	−	4.33013i	−0.0808981	−	0.140120i
$956$		0			0
$957$	3.50000	+	6.06218i	0.113139	+	0.195962i
$958$		0			0
$959$	−5.00000	+	8.66025i	−0.161458	+	0.279654i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$		0			0
$963$	12.0000			0.386695
$964$		0			0
$965$	−6.00000			−0.193147
$966$		0			0
$967$	−11.5000	+	19.9186i	−0.369815	+	0.640538i	−0.989536	−	0.144283i	$-0.953912\pi$
$967$	−11.5000	+	19.9186i	−0.369815	+	0.640538i	0.619721	+	0.784822i	$0.287246\pi$
$968$		0			0
$969$	−17.5000	+	30.3109i	−0.562181	+	0.973726i
$970$		0			0
$971$	−17.5000	+	30.3109i	−0.561602	+	0.972723i	0.435755	+	0.900065i	$0.356481\pi$
$971$	−17.5000	+	30.3109i	−0.561602	+	0.972723i	−0.997357	+	0.0726575i	$0.976852\pi$
$972$		0			0
$973$	2.00000	−	3.46410i	0.0641171	−	0.111054i
$974$		0			0
$975$	−1.50000	−	2.59808i	−0.0480384	−	0.0832050i
$976$		0			0
$977$	8.50000	+	14.7224i	0.271939	+	0.471012i	0.969358	−	0.245651i	$-0.0790017\pi$
$977$	8.50000	+	14.7224i	0.271939	+	0.471012i	−0.697419	+	0.716663i	$0.745668\pi$
$978$		0			0
$979$	−3.00000	+	5.19615i	−0.0958804	+	0.166070i
$980$		0			0
$981$	10.0000			0.319275
$982$		0			0
$983$	16.0000			0.510321			0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000			0.510321			0.255160	+	0.966899i	$0.417872\pi$
$984$		0			0
$985$	−1.50000	+	2.59808i	−0.0477940	+	0.0827816i
$986$		0			0
$987$	1.50000	+	2.59808i	0.0477455	+	0.0826977i
$988$		0			0
$989$	−6.00000	−	10.3923i	−0.190789	−	0.330456i
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$		0			0
$993$	4.50000	−	7.79423i	0.142803	−	0.247342i
$994$		0			0
$995$	12.5000	+	21.6506i	0.396277	+	0.686371i
$996$		0			0
$997$	30.0000			0.950110			0.475055	−	0.879956i	$-0.342428\pi$
$997$	30.0000			0.950110			0.475055	+	0.879956i	$0.342428\pi$
$998$		0			0
$999$	−1.50000	−	2.59808i	−0.0474579	−	0.0821995i

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{9} +(0.500000 - 0.866025i) q^{11} +(1.50000 + 2.59808i) q^{13} -1.00000 q^{15} +(2.50000 + 4.33013i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{21} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.50000 - 6.06218i) q^{29} +(-0.500000 + 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{33} +(0.500000 - 0.866025i) q^{35} +(1.50000 + 2.59808i) q^{37} +(-1.50000 - 2.59808i) q^{39} +(1.50000 - 2.59808i) q^{41} +4.00000 q^{43} +1.00000 q^{45} +(1.50000 - 2.59808i) q^{47} +(3.00000 + 5.19615i) q^{49} +(-2.50000 - 4.33013i) q^{51} +6.00000 q^{53} +(0.500000 - 0.866025i) q^{55} +(3.50000 + 6.06218i) q^{57} -4.00000 q^{59} +(-3.50000 - 6.06218i) q^{61} +(0.500000 - 0.866025i) q^{63} +(1.50000 + 2.59808i) q^{65} +(8.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{69} +(-7.50000 + 12.9904i) q^{71} +(1.50000 + 2.59808i) q^{73} -1.00000 q^{75} +(-0.500000 - 0.866025i) q^{77} +(1.50000 - 2.59808i) q^{79} +1.00000 q^{81} +(-5.50000 - 9.52628i) q^{83} +(2.50000 + 4.33013i) q^{85} +(-3.50000 + 6.06218i) q^{87} -6.00000 q^{89} +3.00000 q^{91} +(0.500000 - 0.866025i) q^{93} +(-3.50000 - 6.06218i) q^{95} +(-6.50000 - 11.2583i) q^{97} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^5 + q^7 + 2 * q^9	\( 2 q - 2 q^{3} + 2 q^{5} + q^{7} + 2 q^{9} + q^{11} + 3 q^{13} - 2 q^{15} + 5 q^{17} - 7 q^{19} - q^{21} - 3 q^{23} + 2 q^{25} - 2 q^{27} + 7 q^{29} - q^{31} - q^{33} + q^{35} + 3 q^{37} - 3 q^{39} + 3 q^{41} + 8 q^{43} + 2 q^{45} + 3 q^{47} + 6 q^{49} - 5 q^{51} + 12 q^{53} + q^{55} + 7 q^{57} - 8 q^{59} - 7 q^{61} + q^{63} + 3 q^{65} + 16 q^{67} + 3 q^{69} - 15 q^{71} + 3 q^{73} - 2 q^{75} - q^{77} + 3 q^{79} + 2 q^{81} - 11 q^{83} + 5 q^{85} - 7 q^{87} - 12 q^{89} + 6 q^{91} + q^{93} - 7 q^{95} - 13 q^{97} + q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^5 + q^7 + 2 * q^9 + q^11 + 3 * q^13 - 2 * q^15 + 5 * q^17 - 7 * q^19 - q^21 - 3 * q^23 + 2 * q^25 - 2 * q^27 + 7 * q^29 - q^31 - q^33 + q^35 + 3 * q^37 - 3 * q^39 + 3 * q^41 + 8 * q^43 + 2 * q^45 + 3 * q^47 + 6 * q^49 - 5 * q^51 + 12 * q^53 + q^55 + 7 * q^57 - 8 * q^59 - 7 * q^61 + q^63 + 3 * q^65 + 16 * q^67 + 3 * q^69 - 15 * q^71 + 3 * q^73 - 2 * q^75 - q^77 + 3 * q^79 + 2 * q^81 - 11 * q^83 + 5 * q^85 - 7 * q^87 - 12 * q^89 + 6 * q^91 + q^93 - 7 * q^95 - 13 * q^97 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more