LMFDB - Embedded newform 4020.2.q.a.3781.1

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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.a.841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(-1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(-1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +(-2.50000 - 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(3.50000 - 6.06218i) q^{17} +(2.50000 - 4.33013i) q^{19} +(1.50000 + 2.59808i) q^{21} +(-0.500000 + 0.866025i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(1.50000 + 2.59808i) q^{31} +(2.50000 + 4.33013i) q^{33} +(-1.50000 - 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{37} +(0.500000 - 0.866025i) q^{39} +(2.50000 + 4.33013i) q^{41} -4.00000 q^{43} +1.00000 q^{45} +(-1.50000 - 2.59808i) q^{47} +(-1.00000 + 1.73205i) q^{49} +(-3.50000 + 6.06218i) q^{51} +6.00000 q^{53} +(-2.50000 - 4.33013i) q^{55} +(-2.50000 + 4.33013i) q^{57} +4.00000 q^{59} +(-3.50000 + 6.06218i) q^{61} +(-1.50000 - 2.59808i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(-8.00000 - 1.73205i) q^{67} +(0.500000 - 0.866025i) q^{69} +(-0.500000 - 0.866025i) q^{71} +(-2.50000 + 4.33013i) q^{73} -1.00000 q^{75} +(-7.50000 + 12.9904i) q^{77} +(-4.50000 - 7.79423i) q^{79} +1.00000 q^{81} +(-4.50000 + 7.79423i) q^{83} +(3.50000 - 6.06218i) q^{85} +(1.50000 + 2.59808i) q^{87} -10.0000 q^{89} +3.00000 q^{91} +(-1.50000 - 2.59808i) q^{93} +(2.50000 - 4.33013i) q^{95} +(3.50000 - 6.06218i) q^{97} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{5} - 3 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 2 * q^5 - 3 * q^7 + 2 * q^9	$ 2 q - 2 q^{3} + 2 q^{5} - 3 q^{7} + 2 q^{9} - 5 q^{11} - q^{13} - 2 q^{15} + 7 q^{17} + 5 q^{19} + 3 q^{21} - q^{23} + 2 q^{25} - 2 q^{27} - 3 q^{29} + 3 q^{31} + 5 q^{33} - 3 q^{35} - q^{37} + q^{39} + 5 q^{41} - 8 q^{43} + 2 q^{45} - 3 q^{47} - 2 q^{49} - 7 q^{51} + 12 q^{53} - 5 q^{55} - 5 q^{57} + 8 q^{59} - 7 q^{61} - 3 q^{63} - q^{65} - 16 q^{67} + q^{69} - q^{71} - 5 q^{73} - 2 q^{75} - 15 q^{77} - 9 q^{79} + 2 q^{81} - 9 q^{83} + 7 q^{85} + 3 q^{87} - 20 q^{89} + 6 q^{91} - 3 q^{93} + 5 q^{95} + 7 q^{97} - 5 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^5 - 3 * q^7 + 2 * q^9 - 5 * q^11 - q^13 - 2 * q^15 + 7 * q^17 + 5 * q^19 + 3 * q^21 - q^23 + 2 * q^25 - 2 * q^27 - 3 * q^29 + 3 * q^31 + 5 * q^33 - 3 * q^35 - q^37 + q^39 + 5 * q^41 - 8 * q^43 + 2 * q^45 - 3 * q^47 - 2 * q^49 - 7 * q^51 + 12 * q^53 - 5 * q^55 - 5 * q^57 + 8 * q^59 - 7 * q^61 - 3 * q^63 - q^65 - 16 * q^67 + q^69 - q^71 - 5 * q^73 - 2 * q^75 - 15 * q^77 - 9 * q^79 + 2 * q^81 - 9 * q^83 + 7 * q^85 + 3 * q^87 - 20 * q^89 + 6 * q^91 - 3 * q^93 + 5 * q^95 + 7 * q^97 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	3.50000	−	6.06218i	0.848875	−	1.47029i	−0.0333386	−	0.999444i	$-0.510614\pi$
$17$	3.50000	−	6.06218i	0.848875	−	1.47029i	0.882213	−	0.470850i	$-0.156053\pi$
$18$		0			0
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$		0			0
$21$	1.50000	+	2.59808i	0.327327	+	0.566947i
$22$		0			0
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	0.968709	−	0.248199i	$-0.0798387\pi$
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	−0.699301	+	0.714827i	$0.746505\pi$
$32$		0			0
$33$	2.50000	+	4.33013i	0.435194	+	0.753778i
$34$		0			0
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$		0			0
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	0.992507	−	0.122189i	$-0.0389915\pi$
$41$	2.50000	+	4.33013i	0.390434	+	0.676252i	−0.602072	+	0.798441i	$0.705658\pi$
$42$		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
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	0.735643	−	0.677369i	$-0.236880\pi$
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	−0.954441	+	0.298401i	$0.903547\pi$
$48$		0			0
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$		0			0
$51$	−3.50000	+	6.06218i	−0.490098	+	0.848875i
$52$		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
$55$	−2.50000	−	4.33013i	−0.337100	−	0.583874i
$56$		0			0
$57$	−2.50000	+	4.33013i	−0.331133	+	0.573539i
$58$		0			0
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		0			0
$63$	−1.50000	−	2.59808i	−0.188982	−	0.327327i
$64$		0			0
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	−8.00000	−	1.73205i	−0.977356	−	0.211604i
$67$	−8.00000	−	1.73205i	−0.977356	−	0.211604i
$68$		0			0
$69$	0.500000	−	0.866025i	0.0601929	−	0.104257i
$70$		0			0
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	0.834830	−	0.550508i	$-0.185566\pi$
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	−0.894169	+	0.447730i	$0.852233\pi$
$72$		0			0
$73$	−2.50000	+	4.33013i	−0.292603	+	0.506803i	−0.974424	−	0.224716i	$-0.927855\pi$
$73$	−2.50000	+	4.33013i	−0.292603	+	0.506803i	0.681822	+	0.731519i	$0.261188\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−7.50000	+	12.9904i	−0.854704	+	1.48039i
$78$		0			0
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	−0.999974	−	0.00727784i	$-0.997683\pi$
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	0.493684	−	0.869641i	$-0.335650\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$	3.50000	−	6.06218i	0.379628	−	0.657536i
$86$		0			0
$87$	1.50000	+	2.59808i	0.160817	+	0.278543i
$88$		0			0
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	3.00000			0.314485
$92$		0			0
$93$	−1.50000	−	2.59808i	−0.155543	−	0.269408i
$94$		0			0
$95$	2.50000	−	4.33013i	0.256495	−	0.444262i
$96$		0			0
$97$	3.50000	−	6.06218i	0.355371	−	0.615521i	−0.631810	−	0.775123i	$-0.717688\pi$
$97$	3.50000	−	6.06218i	0.355371	−	0.615521i	0.987181	+	0.159602i	$0.0510211\pi$
$98$		0			0
$99$	−2.50000	−	4.33013i	−0.251259	−	0.435194i
$100$		0			0
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	4.50000	+	7.79423i	0.443398	+	0.767988i	0.997939	−	0.0641683i	$-0.0204394\pi$
$103$	4.50000	+	7.79423i	0.443398	+	0.767988i	−0.554541	+	0.832156i	$0.687106\pi$
$104$		0			0
$105$	1.50000	+	2.59808i	0.146385	+	0.253546i
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		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
$111$	0.500000	−	0.866025i	0.0474579	−	0.0821995i
$112$		0			0
$113$	−10.5000	−	18.1865i	−0.987757	−	1.71085i	−0.628979	−	0.777422i	$-0.716527\pi$
$113$	−10.5000	−	18.1865i	−0.987757	−	1.71085i	−0.358778	−	0.933423i	$-0.616806\pi$
$114$		0			0
$115$	−0.500000	+	0.866025i	−0.0466252	+	0.0807573i
$116$		0			0
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$		0			0
$119$	−21.0000			−1.92507
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$	−2.50000	−	4.33013i	−0.225417	−	0.390434i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−7.50000	−	12.9904i	−0.665517	−	1.15271i	−0.979145	−	0.203164i	$-0.934878\pi$
$127$	−7.50000	−	12.9904i	−0.665517	−	1.15271i	0.313627	−	0.949546i	$-0.398456\pi$
$128$		0			0
$129$	4.00000			0.352180
$130$		0			0
$131$	−16.0000			−1.39793			−0.698963	−	0.715158i	$-0.746355\pi$
$131$	−16.0000			−1.39793			−0.698963	+	0.715158i	$0.746355\pi$
$132$		0			0
$133$	−15.0000			−1.30066
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	10.0000			0.854358			0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000			0.854358			0.427179	+	0.904167i	$0.359507\pi$
$138$		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
$143$	5.00000			0.418121
$144$		0			0
$145$	−1.50000	−	2.59808i	−0.124568	−	0.215758i
$146$		0			0
$147$	1.00000	−	1.73205i	0.0824786	−	0.142857i
$148$		0			0
$149$	18.0000			1.47462			0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000			1.47462			0.737309	+	0.675556i	$0.236096\pi$
$150$		0			0
$151$	4.50000	−	7.79423i	0.366205	−	0.634285i	−0.622764	−	0.782410i	$-0.713990\pi$
$151$	4.50000	−	7.79423i	0.366205	−	0.634285i	0.988969	+	0.148124i	$0.0473236\pi$
$152$		0			0
$153$	3.50000	−	6.06218i	0.282958	−	0.490098i
$154$		0			0
$155$	1.50000	+	2.59808i	0.120483	+	0.208683i
$156$		0			0
$157$	−6.50000	+	11.2583i	−0.518756	+	0.898513i	0.481006	+	0.876717i	$0.340272\pi$
$157$	−6.50000	+	11.2583i	−0.518756	+	0.898513i	−0.999762	+	0.0217953i	$0.993062\pi$
$158$		0			0
$159$	−6.00000			−0.475831
$160$		0			0
$161$	3.00000			0.236433
$162$		0			0
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$		0			0
$165$	2.50000	+	4.33013i	0.194625	+	0.337100i
$166$		0			0
$167$	8.50000	+	14.7224i	0.657750	+	1.13926i	0.981197	+	0.193010i	$0.0618249\pi$
$167$	8.50000	+	14.7224i	0.657750	+	1.13926i	−0.323447	+	0.946246i	$0.604842\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	2.50000	−	4.33013i	0.191180	−	0.331133i
$172$		0			0
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130287\pi$
$174$		0			0
$175$	−1.50000	−	2.59808i	−0.113389	−	0.196396i
$176$		0			0
$177$	−4.00000			−0.300658
$178$		0			0
$179$	4.00000			0.298974			0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000			0.298974			0.149487	+	0.988764i	$0.452238\pi$
$180$		0			0
$181$	−1.50000	−	2.59808i	−0.111494	−	0.193113i	0.804879	−	0.593439i	$-0.202230\pi$
$181$	−1.50000	−	2.59808i	−0.111494	−	0.193113i	−0.916373	+	0.400326i	$0.868897\pi$
$182$		0			0
$183$	3.50000	−	6.06218i	0.258727	−	0.448129i
$184$		0			0
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$		0			0
$187$	−35.0000			−2.55945
$188$		0			0
$189$	1.50000	+	2.59808i	0.109109	+	0.188982i
$190$		0			0
$191$	2.50000	−	4.33013i	0.180894	−	0.313317i	−0.761291	−	0.648410i	$-0.775434\pi$
$191$	2.50000	−	4.33013i	0.180894	−	0.313317i	0.942185	+	0.335093i	$0.108768\pi$
$192$		0			0
$193$	−18.0000			−1.29567			−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000			−1.29567			−0.647834	+	0.761781i	$0.724325\pi$
$194$		0			0
$195$	0.500000	−	0.866025i	0.0358057	−	0.0620174i
$196$		0			0
$197$	3.50000	+	6.06218i	0.249365	+	0.431912i	0.963350	−	0.268249i	$-0.0864449\pi$
$197$	3.50000	+	6.06218i	0.249365	+	0.431912i	−0.713985	+	0.700161i	$0.753112\pi$
$198$		0			0
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	0.992434	−	0.122782i	$-0.0391815\pi$
$200$		0			0
$201$	8.00000	+	1.73205i	0.564276	+	0.122169i
$202$		0			0
$203$	−4.50000	+	7.79423i	−0.315838	+	0.547048i
$204$		0			0
$205$	2.50000	+	4.33013i	0.174608	+	0.302429i
$206$		0			0
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$		0			0
$209$	−25.0000			−1.72929
$210$		0			0
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$		0			0
$213$	0.500000	+	0.866025i	0.0342594	+	0.0593391i
$214$		0			0
$215$	−4.00000			−0.272798
$216$		0			0
$217$	4.50000	−	7.79423i	0.305480	−	0.529107i
$218$		0			0
$219$	2.50000	−	4.33013i	0.168934	−	0.292603i
$220$		0			0
$221$	3.50000	+	6.06218i	0.235435	+	0.407786i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$		0			0
$229$	2.50000	−	4.33013i	0.165205	−	0.286143i	−0.771523	−	0.636201i	$-0.780505\pi$
$229$	2.50000	−	4.33013i	0.165205	−	0.286143i	0.936728	+	0.350058i	$0.113838\pi$
$230$		0			0
$231$	7.50000	−	12.9904i	0.493464	−	0.854704i
$232$		0			0
$233$	7.50000	+	12.9904i	0.491341	+	0.851028i	0.999950	−	0.00996947i	$-0.00317343\pi$
$233$	7.50000	+	12.9904i	0.491341	+	0.851028i	−0.508609	+	0.860998i	$0.669840\pi$
$234$		0			0
$235$	−1.50000	−	2.59808i	−0.0978492	−	0.169480i
$236$		0			0
$237$	4.50000	+	7.79423i	0.292306	+	0.506290i
$238$		0			0
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	0.999854	−	0.0170808i	$-0.00543724\pi$
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	−0.514719	+	0.857359i	$0.672104\pi$
$240$		0			0
$241$	−26.0000			−1.67481			−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000			−1.67481			−0.837404	+	0.546585i	$0.815928\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$		0			0
$247$	2.50000	+	4.33013i	0.159071	+	0.275519i
$248$		0			0
$249$	4.50000	−	7.79423i	0.285176	−	0.493939i
$250$		0			0
$251$	6.50000	−	11.2583i	0.410276	−	0.710620i	−0.584643	−	0.811290i	$-0.698766\pi$
$251$	6.50000	−	11.2583i	0.410276	−	0.710620i	0.994920	+	0.100671i	$0.0320989\pi$
$252$		0			0
$253$	5.00000			0.314347
$254$		0			0
$255$	−3.50000	+	6.06218i	−0.219179	+	0.379628i
$256$		0			0
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$		0			0
$259$	3.00000			0.186411
$260$		0			0
$261$	−1.50000	−	2.59808i	−0.0928477	−	0.160817i
$262$		0			0
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	10.0000			0.611990
$268$		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
$271$	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
$273$	−3.00000			−0.181568
$274$		0			0
$275$	−2.50000	−	4.33013i	−0.150756	−	0.261116i
$276$		0			0
$277$	−18.0000			−1.08152			−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000			−1.08152			−0.540758	+	0.841178i	$0.681862\pi$
$278$		0			0
$279$	1.50000	+	2.59808i	0.0898027	+	0.155543i
$280$		0			0
$281$	4.50000	−	7.79423i	0.268447	−	0.464965i	−0.700014	−	0.714130i	$-0.746823\pi$
$281$	4.50000	−	7.79423i	0.268447	−	0.464965i	0.968461	+	0.249165i	$0.0801561\pi$
$282$		0			0
$283$	−28.0000			−1.66443			−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000			−1.66443			−0.832214	+	0.554455i	$0.812927\pi$
$284$		0			0
$285$	−2.50000	+	4.33013i	−0.148087	+	0.256495i
$286$		0			0
$287$	7.50000	−	12.9904i	0.442711	−	0.766798i
$288$		0			0
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$		0			0
$291$	−3.50000	+	6.06218i	−0.205174	+	0.355371i
$292$		0			0
$293$	−22.0000			−1.28525			−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000			−1.28525			−0.642627	+	0.766179i	$0.722155\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$		0			0
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$		0			0
$299$	−0.500000	−	0.866025i	−0.0289157	−	0.0500835i
$300$		0			0
$301$	6.00000	+	10.3923i	0.345834	+	0.599002i
$302$		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
$307$	−0.500000	+	0.866025i	−0.0285365	+	0.0494267i	−0.879941	−	0.475083i	$-0.842418\pi$
$307$	−0.500000	+	0.866025i	−0.0285365	+	0.0494267i	0.851404	+	0.524510i	$0.175751\pi$
$308$		0			0
$309$	−4.50000	−	7.79423i	−0.255996	−	0.443398i
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	−26.0000			−1.46961			−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000			−1.46961			−0.734803	+	0.678280i	$0.762726\pi$
$314$		0			0
$315$	−1.50000	−	2.59808i	−0.0845154	−	0.146385i
$316$		0			0
$317$	15.5000	−	26.8468i	0.870567	−	1.50787i	0.00915525	−	0.999958i	$-0.497086\pi$
$317$	15.5000	−	26.8468i	0.870567	−	1.50787i	0.861411	−	0.507908i	$-0.169581\pi$
$318$		0			0
$319$	−7.50000	+	12.9904i	−0.419919	+	0.727322i
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$	−17.5000	−	30.3109i	−0.973726	−	1.68654i
$324$		0			0
$325$	−0.500000	+	0.866025i	−0.0277350	+	0.0480384i
$326$		0			0
$327$	−10.0000			−0.553001
$328$		0			0
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	1.50000	+	2.59808i	0.0824475	+	0.142803i	0.904301	−	0.426896i	$-0.140393\pi$
$331$	1.50000	+	2.59808i	0.0824475	+	0.142803i	−0.821853	+	0.569699i	$0.807060\pi$
$332$		0			0
$333$	−0.500000	+	0.866025i	−0.0273998	+	0.0474579i
$334$		0			0
$335$	−8.00000	−	1.73205i	−0.437087	−	0.0946320i
$336$		0			0
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	−0.754811	−	0.655942i	$-0.772271\pi$
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	0.945468	+	0.325714i	$0.105605\pi$
$338$		0			0
$339$	10.5000	+	18.1865i	0.570282	+	0.987757i
$340$		0			0
$341$	7.50000	−	12.9904i	0.406148	−	0.703469i
$342$		0			0
$343$	−15.0000			−0.809924
$344$		0			0
$345$	0.500000	−	0.866025i	0.0269191	−	0.0466252i
$346$		0			0
$347$	−3.50000	−	6.06218i	−0.187890	−	0.325435i	0.756657	−	0.653812i	$-0.226831\pi$
$347$	−3.50000	−	6.06218i	−0.187890	−	0.325435i	−0.944547	+	0.328378i	$0.893498\pi$
$348$		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
$351$	0.500000	−	0.866025i	0.0266880	−	0.0462250i
$352$		0			0
$353$	−16.5000	+	28.5788i	−0.878206	+	1.52110i	−0.0248989	+	0.999690i	$0.507926\pi$
$353$	−16.5000	+	28.5788i	−0.878206	+	1.52110i	−0.853307	+	0.521408i	$0.825407\pi$
$354$		0			0
$355$	−0.500000	−	0.866025i	−0.0265372	−	0.0459639i
$356$		0			0
$357$	21.0000			1.11144
$358$		0			0
$359$	4.00000			0.211112			0.105556	−	0.994413i	$-0.466338\pi$
$359$	4.00000			0.211112			0.105556	+	0.994413i	$0.466338\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$	7.00000	−	12.1244i	0.367405	−	0.636364i
$364$		0			0
$365$	−2.50000	+	4.33013i	−0.130856	+	0.226649i
$366$		0			0
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	0.760100	−	0.649806i	$-0.225150\pi$
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	−0.942799	+	0.333363i	$0.891817\pi$
$368$		0			0
$369$	2.50000	+	4.33013i	0.130145	+	0.225417i
$370$		0			0
$371$	−9.00000	−	15.5885i	−0.467257	−	0.809312i
$372$		0			0
$373$	−12.5000	−	21.6506i	−0.647225	−	1.12103i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−12.5000	−	21.6506i	−0.647225	−	1.12103i	0.336557	−	0.941663i	$-0.390737\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	−7.50000	+	12.9904i	−0.385249	+	0.667271i	−0.991804	−	0.127771i	$-0.959218\pi$
$379$	−7.50000	+	12.9904i	−0.385249	+	0.667271i	0.606555	+	0.795042i	$0.292551\pi$
$380$		0			0
$381$	7.50000	+	12.9904i	0.384237	+	0.665517i
$382$		0			0
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$		0			0
$385$	−7.50000	+	12.9904i	−0.382235	+	0.662051i
$386$		0			0
$387$	−4.00000			−0.203331
$388$		0			0
$389$	−15.5000	+	26.8468i	−0.785881	+	1.36119i	0.142590	+	0.989782i	$0.454457\pi$
$389$	−15.5000	+	26.8468i	−0.785881	+	1.36119i	−0.928471	+	0.371404i	$0.878876\pi$
$390$		0			0
$391$	3.50000	+	6.06218i	0.177003	+	0.306578i
$392$		0			0
$393$	16.0000			0.807093
$394$		0			0
$395$	−4.50000	−	7.79423i	−0.226420	−	0.392170i
$396$		0			0
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$		0			0
$399$	15.0000			0.750939
$400$		0			0
$401$	14.0000			0.699127			0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000			0.699127			0.349563	+	0.936913i	$0.386330\pi$
$402$		0			0
$403$	−3.00000			−0.149441
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	5.00000			0.247841
$408$		0			0
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	−0.996701	−	0.0811615i	$-0.974137\pi$
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	0.428063	−	0.903749i	$-0.359196\pi$
$410$		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
$417$	−4.00000			−0.195881
$418$		0			0
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	−0.900337	−	0.435194i	$-0.856680\pi$
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	0.827057	+	0.562118i	$0.190013\pi$
$420$		0			0
$421$	−5.50000	+	9.52628i	−0.268054	+	0.464282i	−0.968359	−	0.249561i	$-0.919714\pi$
$421$	−5.50000	+	9.52628i	−0.268054	+	0.464282i	0.700306	+	0.713843i	$0.253047\pi$
$422$		0			0
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$		0			0
$425$	3.50000	−	6.06218i	0.169775	−	0.294059i
$426$		0			0
$427$	21.0000			1.01626
$428$		0			0
$429$	−5.00000			−0.241402
$430$		0			0
$431$	15.5000	+	26.8468i	0.746609	+	1.29316i	0.949439	+	0.313950i	$0.101653\pi$
$431$	15.5000	+	26.8468i	0.746609	+	1.29316i	−0.202831	+	0.979214i	$0.565014\pi$
$432$		0			0
$433$	7.50000	+	12.9904i	0.360427	+	0.624278i	0.988031	−	0.154255i	$-0.0492977\pi$
$433$	7.50000	+	12.9904i	0.360427	+	0.624278i	−0.627604	+	0.778533i	$0.715964\pi$
$434$		0			0
$435$	1.50000	+	2.59808i	0.0719195	+	0.124568i
$436$		0			0
$437$	2.50000	+	4.33013i	0.119591	+	0.207138i
$438$		0			0
$439$	14.5000	−	25.1147i	0.692047	−	1.19866i	−0.279119	−	0.960257i	$-0.590042\pi$
$439$	14.5000	−	25.1147i	0.692047	−	1.19866i	0.971166	−	0.238404i	$-0.0766244\pi$
$440$		0			0
$441$	−1.00000	+	1.73205i	−0.0476190	+	0.0824786i
$442$		0			0
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	0.999999	−	0.00130426i	$-0.000415158\pi$
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	−0.501129	+	0.865373i	$0.667082\pi$
$444$		0			0
$445$	−10.0000			−0.474045
$446$		0			0
$447$	−18.0000			−0.851371
$448$		0			0
$449$	4.50000	+	7.79423i	0.212368	+	0.367832i	0.952455	−	0.304679i	$-0.0985491\pi$
$449$	4.50000	+	7.79423i	0.212368	+	0.367832i	−0.740087	+	0.672511i	$0.765216\pi$
$450$		0			0
$451$	12.5000	−	21.6506i	0.588602	−	1.01949i
$452$		0			0
$453$	−4.50000	+	7.79423i	−0.211428	+	0.366205i
$454$		0			0
$455$	3.00000			0.140642
$456$		0			0
$457$	3.50000	+	6.06218i	0.163723	+	0.283577i	0.936201	−	0.351465i	$-0.114316\pi$
$457$	3.50000	+	6.06218i	0.163723	+	0.283577i	−0.772478	+	0.635042i	$0.780983\pi$
$458$		0			0
$459$	−3.50000	+	6.06218i	−0.163366	+	0.282958i
$460$		0			0
$461$	34.0000			1.58354			0.791769	−	0.610821i	$-0.209160\pi$
$461$	34.0000			1.58354			0.791769	+	0.610821i	$0.209160\pi$
$462$		0			0
$463$	−12.5000	+	21.6506i	−0.580924	+	1.00619i	0.414446	+	0.910074i	$0.363975\pi$
$463$	−12.5000	+	21.6506i	−0.580924	+	1.00619i	−0.995370	+	0.0961164i	$0.969358\pi$
$464$		0			0
$465$	−1.50000	−	2.59808i	−0.0695608	−	0.120483i
$466$		0			0
$467$	21.5000	−	37.2391i	0.994901	−	1.72322i	0.410110	−	0.912036i	$-0.365490\pi$
$467$	21.5000	−	37.2391i	0.994901	−	1.72322i	0.584792	−	0.811183i	$-0.301176\pi$
$468$		0			0
$469$	7.50000	+	23.3827i	0.346318	+	1.07971i
$470$		0			0
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$		0			0
$473$	10.0000	+	17.3205i	0.459800	+	0.796398i
$474$		0			0
$475$	2.50000	−	4.33013i	0.114708	−	0.198680i
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	6.50000	−	11.2583i	0.296993	−	0.514406i	−0.678454	−	0.734643i	$-0.737350\pi$
$479$	6.50000	−	11.2583i	0.296993	−	0.514406i	0.975446	+	0.220237i	$0.0706830\pi$
$480$		0			0
$481$	−0.500000	−	0.866025i	−0.0227980	−	0.0394874i
$482$		0			0
$483$	−3.00000			−0.136505
$484$		0			0
$485$	3.50000	−	6.06218i	0.158927	−	0.275269i
$486$		0			0
$487$	−12.5000	+	21.6506i	−0.566429	+	0.981084i	0.430486	+	0.902597i	$0.358342\pi$
$487$	−12.5000	+	21.6506i	−0.566429	+	0.981084i	−0.996915	+	0.0784867i	$0.974991\pi$
$488$		0			0
$489$	5.50000	+	9.52628i	0.248719	+	0.430793i
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	−21.0000			−0.945792
$494$		0			0
$495$	−2.50000	−	4.33013i	−0.112367	−	0.194625i
$496$		0			0
$497$	−1.50000	+	2.59808i	−0.0672842	+	0.116540i
$498$		0			0
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	−0.804627	−	0.593780i	$-0.797635\pi$
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	0.916542	+	0.399937i	$0.130968\pi$
$500$		0			0
$501$	−8.50000	−	14.7224i	−0.379752	−	0.657750i
$502$		0			0
$503$	0.500000	+	0.866025i	0.0222939	+	0.0386142i	0.876957	−	0.480569i	$-0.159570\pi$
$503$	0.500000	+	0.866025i	0.0222939	+	0.0386142i	−0.854663	+	0.519183i	$0.826236\pi$
$504$		0			0
$505$	4.50000	+	7.79423i	0.200247	+	0.346839i
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$		0			0
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$		0			0
$511$	15.0000			0.663561
$512$		0			0
$513$	−2.50000	+	4.33013i	−0.110378	+	0.191180i
$514$		0			0
$515$	4.50000	+	7.79423i	0.198294	+	0.343455i
$516$		0			0
$517$	−7.50000	+	12.9904i	−0.329850	+	0.571316i
$518$		0			0
$519$	−1.50000	+	2.59808i	−0.0658427	+	0.114043i
$520$		0			0
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$		0			0
$523$	−20.5000	+	35.5070i	−0.896402	+	1.55261i	−0.0643431	+	0.997928i	$0.520495\pi$
$523$	−20.5000	+	35.5070i	−0.896402	+	1.55261i	−0.832059	+	0.554687i	$0.812838\pi$
$524$		0			0
$525$	1.50000	+	2.59808i	0.0654654	+	0.113389i
$526$		0			0
$527$	21.0000			0.914774
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$	4.00000			0.173585
$532$		0			0
$533$	−5.00000			−0.216574
$534$		0			0
$535$	−12.0000			−0.518805
$536$		0			0
$537$	−4.00000			−0.172613
$538$		0			0
$539$	10.0000			0.430730
$540$		0			0
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$		0			0
$543$	1.50000	+	2.59808i	0.0643712	+	0.111494i
$544$		0			0
$545$	10.0000			0.428353
$546$		0			0
$547$	12.5000	+	21.6506i	0.534461	+	0.925714i	0.999189	+	0.0402607i	$0.0128188\pi$
$547$	12.5000	+	21.6506i	0.534461	+	0.925714i	−0.464728	+	0.885454i	$0.653848\pi$
$548$		0			0
$549$	−3.50000	+	6.06218i	−0.149376	+	0.258727i
$550$		0			0
$551$	−15.0000			−0.639021
$552$		0			0
$553$	−13.5000	+	23.3827i	−0.574078	+	0.994333i
$554$		0			0
$555$	0.500000	−	0.866025i	0.0212238	−	0.0367607i
$556$		0			0
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$		0			0
$559$	2.00000	−	3.46410i	0.0845910	−	0.146516i
$560$		0			0
$561$	35.0000			1.47770
$562$		0			0
$563$	36.0000			1.51722			0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000			1.51722			0.758610	+	0.651546i	$0.225879\pi$
$564$		0			0
$565$	−10.5000	−	18.1865i	−0.441738	−	0.765113i
$566$		0			0
$567$	−1.50000	−	2.59808i	−0.0629941	−	0.109109i
$568$		0			0
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$		0			0
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	0.808962	−	0.587861i	$-0.200030\pi$
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	−0.913584	+	0.406651i	$0.866697\pi$
$572$		0			0
$573$	−2.50000	+	4.33013i	−0.104439	+	0.180894i
$574$		0			0
$575$	−0.500000	+	0.866025i	−0.0208514	+	0.0361158i
$576$		0			0
$577$	13.5000	+	23.3827i	0.562012	+	0.973434i	0.997321	+	0.0731526i	$0.0233060\pi$
$577$	13.5000	+	23.3827i	0.562012	+	0.973434i	−0.435308	+	0.900281i	$0.643361\pi$
$578$		0			0
$579$	18.0000			0.748054
$580$		0			0
$581$	27.0000			1.12015
$582$		0			0
$583$	−15.0000	−	25.9808i	−0.621237	−	1.07601i
$584$		0			0
$585$	−0.500000	+	0.866025i	−0.0206725	+	0.0358057i
$586$		0			0
$587$	−8.50000	+	14.7224i	−0.350833	+	0.607660i	−0.986396	−	0.164389i	$-0.947435\pi$
$587$	−8.50000	+	14.7224i	−0.350833	+	0.607660i	0.635563	+	0.772049i	$0.280768\pi$
$588$		0			0
$589$	15.0000			0.618064
$590$		0			0
$591$	−3.50000	−	6.06218i	−0.143971	−	0.249365i
$592$		0			0
$593$	19.5000	−	33.7750i	0.800769	−	1.38697i	−0.118342	−	0.992973i	$-0.537758\pi$
$593$	19.5000	−	33.7750i	0.800769	−	1.38697i	0.919111	−	0.394000i	$-0.128909\pi$
$594$		0			0
$595$	−21.0000			−0.860916
$596$		0			0
$597$	−8.50000	+	14.7224i	−0.347882	+	0.602549i
$598$		0			0
$599$	−10.5000	−	18.1865i	−0.429018	−	0.743082i	0.567768	−	0.823189i	$-0.307807\pi$
$599$	−10.5000	−	18.1865i	−0.429018	−	0.743082i	−0.996786	+	0.0801071i	$0.974474\pi$
$600$		0			0
$601$	−5.50000	+	9.52628i	−0.224350	+	0.388585i	−0.956124	−	0.292962i	$-0.905359\pi$
$601$	−5.50000	+	9.52628i	−0.224350	+	0.388585i	0.731774	+	0.681547i	$0.238692\pi$
$602$		0			0
$603$	−8.00000	−	1.73205i	−0.325785	−	0.0705346i
$604$		0			0
$605$	−7.00000	+	12.1244i	−0.284590	+	0.492925i
$606$		0			0
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$		0			0
$609$	4.50000	−	7.79423i	0.182349	−	0.315838i
$610$		0			0
$611$	3.00000			0.121367
$612$		0			0
$613$	23.5000	−	40.7032i	0.949156	−	1.64399i	0.201948	−	0.979396i	$-0.435273\pi$
$613$	23.5000	−	40.7032i	0.949156	−	1.64399i	0.747208	−	0.664590i	$-0.231394\pi$
$614$		0			0
$615$	−2.50000	−	4.33013i	−0.100810	−	0.174608i
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$		0			0
$619$	−11.5000	+	19.9186i	−0.462224	+	0.800595i	−0.999071	−	0.0430838i	$-0.986282\pi$
$619$	−11.5000	+	19.9186i	−0.462224	+	0.800595i	0.536847	+	0.843679i	$0.319615\pi$
$620$		0			0
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$		0			0
$623$	15.0000	+	25.9808i	0.600962	+	1.04090i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	25.0000			0.998404
$628$		0			0
$629$	3.50000	+	6.06218i	0.139554	+	0.241715i
$630$		0			0
$631$	8.50000	−	14.7224i	0.338380	−	0.586091i	−0.645748	−	0.763550i	$-0.723455\pi$
$631$	8.50000	−	14.7224i	0.338380	−	0.586091i	0.984128	+	0.177459i	$0.0567879\pi$
$632$		0			0
$633$	−2.50000	+	4.33013i	−0.0993661	+	0.172107i
$634$		0			0
$635$	−7.50000	−	12.9904i	−0.297628	−	0.515508i
$636$		0			0
$637$	−1.00000	−	1.73205i	−0.0396214	−	0.0686264i
$638$		0			0
$639$	−0.500000	−	0.866025i	−0.0197797	−	0.0342594i
$640$		0			0
$641$	8.50000	+	14.7224i	0.335730	+	0.581501i	0.983625	−	0.180229i	$-0.0576838\pi$
$641$	8.50000	+	14.7224i	0.335730	+	0.581501i	−0.647895	+	0.761730i	$0.724350\pi$
$642$		0			0
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$		0			0
$645$	4.00000			0.157500
$646$		0			0
$647$	17.5000	−	30.3109i	0.687996	−	1.19164i	−0.284489	−	0.958679i	$-0.591824\pi$
$647$	17.5000	−	30.3109i	0.687996	−	1.19164i	0.972485	−	0.232965i	$-0.0748427\pi$
$648$		0			0
$649$	−10.0000	−	17.3205i	−0.392534	−	0.679889i
$650$		0			0
$651$	−4.50000	+	7.79423i	−0.176369	+	0.305480i
$652$		0			0
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	−0.940541	−	0.339680i	$-0.889681\pi$
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	0.764442	+	0.644692i	$0.223014\pi$
$654$		0			0
$655$	−16.0000			−0.625172
$656$		0			0
$657$	−2.50000	+	4.33013i	−0.0975343	+	0.168934i
$658$		0			0
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	0.585758	−	0.810486i	$-0.300797\pi$
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	−0.994780	+	0.102039i	$0.967463\pi$
$660$		0			0
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$		0			0
$663$	−3.50000	−	6.06218i	−0.135929	−	0.235435i
$664$		0			0
$665$	−15.0000			−0.581675
$666$		0			0
$667$	3.00000			0.116160
$668$		0			0
$669$	4.00000			0.154649
$670$		0			0
$671$	35.0000			1.35116
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−2.50000	−	4.33013i	−0.0960828	−	0.166420i	0.813977	−	0.580897i	$-0.197298\pi$
$677$	−2.50000	−	4.33013i	−0.0960828	−	0.166420i	−0.910060	+	0.414477i	$0.863965\pi$
$678$		0			0
$679$	−21.0000			−0.805906
$680$		0			0
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$		0			0
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	−0.939184	−	0.343413i	$-0.888417\pi$
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	0.766997	+	0.641651i	$0.221750\pi$
$684$		0			0
$685$	10.0000			0.382080
$686$		0			0
$687$	−2.50000	+	4.33013i	−0.0953809	+	0.165205i
$688$		0			0
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$		0			0
$691$	15.5000	+	26.8468i	0.589648	+	1.02130i	0.994278	+	0.106820i	$0.0340668\pi$
$691$	15.5000	+	26.8468i	0.589648	+	1.02130i	−0.404631	+	0.914480i	$0.632600\pi$
$692$		0			0
$693$	−7.50000	+	12.9904i	−0.284901	+	0.493464i
$694$		0			0
$695$	4.00000			0.151729
$696$		0			0
$697$	35.0000			1.32572
$698$		0			0
$699$	−7.50000	−	12.9904i	−0.283676	−	0.491341i
$700$		0			0
$701$	16.5000	+	28.5788i	0.623196	+	1.07941i	0.988887	+	0.148671i	$0.0474996\pi$
$701$	16.5000	+	28.5788i	0.623196	+	1.07941i	−0.365690	+	0.930737i	$0.619167\pi$
$702$		0			0
$703$	2.50000	+	4.33013i	0.0942893	+	0.163314i
$704$		0			0
$705$	1.50000	+	2.59808i	0.0564933	+	0.0978492i
$706$		0			0
$707$	13.5000	−	23.3827i	0.507720	−	0.879396i
$708$		0			0
$709$	8.50000	−	14.7224i	0.319224	−	0.552913i	−0.661102	−	0.750296i	$-0.729911\pi$
$709$	8.50000	−	14.7224i	0.319224	−	0.552913i	0.980326	+	0.197383i	$0.0632444\pi$
$710$		0			0
$711$	−4.50000	−	7.79423i	−0.168763	−	0.292306i
$712$		0			0
$713$	−3.00000			−0.112351
$714$		0			0
$715$	5.00000			0.186989
$716$		0			0
$717$	−7.50000	−	12.9904i	−0.280093	−	0.485135i
$718$		0			0
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$720$		0			0
$721$	13.5000	−	23.3827i	0.502766	−	0.870817i
$722$		0			0
$723$	26.0000			0.966950
$724$		0			0
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$		0			0
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	−0.570049	−	0.821611i	$-0.693076\pi$
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	0.996560	+	0.0828714i	$0.0264091\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−14.0000	+	24.2487i	−0.517809	+	0.896871i
$732$		0			0
$733$	−24.5000	−	42.4352i	−0.904928	−	1.56738i	−0.821014	−	0.570909i	$-0.806591\pi$
$733$	−24.5000	−	42.4352i	−0.904928	−	1.56738i	−0.0839145	−	0.996473i	$-0.526742\pi$
$734$		0			0
$735$	1.00000	−	1.73205i	0.0368856	−	0.0638877i
$736$		0			0
$737$	12.5000	+	38.9711i	0.460443	+	1.43552i
$738$		0			0
$739$	−9.50000	+	16.4545i	−0.349463	+	0.605288i	−0.986154	−	0.165831i	$-0.946969\pi$
$739$	−9.50000	+	16.4545i	−0.349463	+	0.605288i	0.636691	+	0.771119i	$0.280303\pi$
$740$		0			0
$741$	−2.50000	−	4.33013i	−0.0918398	−	0.159071i
$742$		0			0
$743$	17.5000	−	30.3109i	0.642013	−	1.11200i	−0.342970	−	0.939346i	$-0.611433\pi$
$743$	17.5000	−	30.3109i	0.642013	−	1.11200i	0.984983	−	0.172652i	$-0.0552337\pi$
$744$		0			0
$745$	18.0000			0.659469
$746$		0			0
$747$	−4.50000	+	7.79423i	−0.164646	+	0.285176i
$748$		0			0
$749$	18.0000	+	31.1769i	0.657706	+	1.13918i
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$		0			0
$753$	−6.50000	+	11.2583i	−0.236873	+	0.410276i
$754$		0			0
$755$	4.50000	−	7.79423i	0.163772	−	0.283661i
$756$		0			0
$757$	−6.50000	−	11.2583i	−0.236247	−	0.409191i	0.723388	−	0.690442i	$-0.242584\pi$
$757$	−6.50000	−	11.2583i	−0.236247	−	0.409191i	−0.959634	+	0.281251i	$0.909251\pi$
$758$		0			0
$759$	−5.00000			−0.181489
$760$		0			0
$761$	54.0000			1.95750			0.978749	−	0.205061i	$-0.0657392\pi$
$761$	54.0000			1.95750			0.978749	+	0.205061i	$0.0657392\pi$
$762$		0			0
$763$	−15.0000	−	25.9808i	−0.543036	−	0.940567i
$764$		0			0
$765$	3.50000	−	6.06218i	0.126543	−	0.219179i
$766$		0			0
$767$	−2.00000	+	3.46410i	−0.0722158	+	0.125081i
$768$		0			0
$769$	−17.5000	−	30.3109i	−0.631066	−	1.09304i	−0.987334	−	0.158655i	$-0.949284\pi$
$769$	−17.5000	−	30.3109i	−0.631066	−	1.09304i	0.356268	−	0.934384i	$-0.384049\pi$
$770$		0			0
$771$	−1.50000	−	2.59808i	−0.0540212	−	0.0935674i
$772$		0			0
$773$	9.50000	+	16.4545i	0.341691	+	0.591827i	0.984747	−	0.173993i	$-0.0556670\pi$
$773$	9.50000	+	16.4545i	0.341691	+	0.591827i	−0.643056	+	0.765819i	$0.722334\pi$
$774$		0			0
$775$	1.50000	+	2.59808i	0.0538816	+	0.0933257i
$776$		0			0
$777$	−3.00000			−0.107624
$778$		0			0
$779$	25.0000			0.895718
$780$		0			0
$781$	−2.50000	+	4.33013i	−0.0894570	+	0.154944i
$782$		0			0
$783$	1.50000	+	2.59808i	0.0536056	+	0.0928477i
$784$		0			0
$785$	−6.50000	+	11.2583i	−0.231995	+	0.401827i
$786$		0			0
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	−0.976812	−	0.214097i	$-0.931319\pi$
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	0.673820	+	0.738896i	$0.264652\pi$
$788$		0			0
$789$	12.0000			0.427211
$790$		0			0
$791$	−31.5000	+	54.5596i	−1.12001	+	1.93992i
$792$		0			0
$793$	−3.50000	−	6.06218i	−0.124289	−	0.215274i
$794$		0			0
$795$	−6.00000			−0.212798
$796$		0			0
$797$	1.50000	+	2.59808i	0.0531327	+	0.0920286i	0.891368	−	0.453279i	$-0.149746\pi$
$797$	1.50000	+	2.59808i	0.0531327	+	0.0920286i	−0.838236	+	0.545308i	$0.816413\pi$
$798$		0			0
$799$	−21.0000			−0.742927
$800$		0			0
$801$	−10.0000			−0.353333
$802$		0			0
$803$	25.0000			0.882231
$804$		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	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$	21.5000	+	37.2391i	0.754967	+	1.30764i	0.945391	+	0.325939i	$0.105681\pi$
$811$	21.5000	+	37.2391i	0.754967	+	1.30764i	−0.190424	+	0.981702i	$0.560986\pi$
$812$		0			0
$813$	−8.00000			−0.280572
$814$		0			0
$815$	−5.50000	−	9.52628i	−0.192657	−	0.333691i
$816$		0			0
$817$	−10.0000	+	17.3205i	−0.349856	+	0.605968i
$818$		0			0
$819$	3.00000			0.104828
$820$		0			0
$821$	8.50000	−	14.7224i	0.296652	−	0.513816i	−0.678716	−	0.734401i	$-0.737463\pi$
$821$	8.50000	−	14.7224i	0.296652	−	0.513816i	0.975368	+	0.220585i	$0.0707965\pi$
$822$		0			0
$823$	15.5000	−	26.8468i	0.540296	−	0.935820i	−0.458591	−	0.888648i	$-0.651646\pi$
$823$	15.5000	−	26.8468i	0.540296	−	0.935820i	0.998887	−	0.0471726i	$-0.0150211\pi$
$824$		0			0
$825$	2.50000	+	4.33013i	0.0870388	+	0.150756i
$826$		0			0
$827$	25.5000	−	44.1673i	0.886722	−	1.53585i	0.0429946	−	0.999075i	$-0.486310\pi$
$827$	25.5000	−	44.1673i	0.886722	−	1.53585i	0.843727	−	0.536772i	$-0.180356\pi$
$828$		0			0
$829$	26.0000			0.903017			0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000			0.903017			0.451509	+	0.892267i	$0.350886\pi$
$830$		0			0
$831$	18.0000			0.624413
$832$		0			0
$833$	7.00000	+	12.1244i	0.242536	+	0.420084i
$834$		0			0
$835$	8.50000	+	14.7224i	0.294155	+	0.509491i
$836$		0			0
$837$	−1.50000	−	2.59808i	−0.0518476	−	0.0898027i
$838$		0			0
$839$	1.50000	+	2.59808i	0.0517858	+	0.0896956i	0.890756	−	0.454481i	$-0.150175\pi$
$839$	1.50000	+	2.59808i	0.0517858	+	0.0896956i	−0.838971	+	0.544177i	$0.816842\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	−4.50000	+	7.79423i	−0.154988	+	0.268447i
$844$		0			0
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$		0			0
$847$	42.0000			1.44314
$848$		0			0
$849$	28.0000			0.960958
$850$		0			0
$851$	−0.500000	−	0.866025i	−0.0171398	−	0.0296870i
$852$		0			0
$853$	19.5000	−	33.7750i	0.667667	−	1.15643i	−0.310887	−	0.950447i	$-0.600626\pi$
$853$	19.5000	−	33.7750i	0.667667	−	1.15643i	0.978555	−	0.205987i	$-0.0660404\pi$
$854$		0			0
$855$	2.50000	−	4.33013i	0.0854982	−	0.148087i
$856$		0			0
$857$	−14.0000			−0.478231			−0.239115	−	0.970991i	$-0.576857\pi$
$857$	−14.0000			−0.478231			−0.239115	+	0.970991i	$0.576857\pi$
$858$		0			0
$859$	19.5000	+	33.7750i	0.665331	+	1.15239i	0.979195	+	0.202920i	$0.0650431\pi$
$859$	19.5000	+	33.7750i	0.665331	+	1.15239i	−0.313864	+	0.949468i	$0.601624\pi$
$860$		0			0
$861$	−7.50000	+	12.9904i	−0.255599	+	0.442711i
$862$		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
$865$	1.50000	−	2.59808i	0.0510015	−	0.0883372i
$866$		0			0
$867$	16.0000	+	27.7128i	0.543388	+	0.941176i
$868$		0			0
$869$	−22.5000	+	38.9711i	−0.763260	+	1.32201i
$870$		0			0
$871$	5.50000	−	6.06218i	0.186360	−	0.205409i
$872$		0			0
$873$	3.50000	−	6.06218i	0.118457	−	0.205174i
$874$		0			0
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$		0			0
$877$	−24.5000	+	42.4352i	−0.827306	+	1.43294i	0.0728377	+	0.997344i	$0.476794\pi$
$877$	−24.5000	+	42.4352i	−0.827306	+	1.43294i	−0.900144	+	0.435593i	$0.856539\pi$
$878$		0			0
$879$	22.0000			0.742042
$880$		0			0
$881$	−5.50000	+	9.52628i	−0.185300	+	0.320949i	−0.943677	−	0.330867i	$-0.892659\pi$
$881$	−5.50000	+	9.52628i	−0.185300	+	0.320949i	0.758378	+	0.651815i	$0.225992\pi$
$882$		0			0
$883$	−3.50000	−	6.06218i	−0.117784	−	0.204009i	0.801105	−	0.598524i	$-0.204246\pi$
$883$	−3.50000	−	6.06218i	−0.117784	−	0.204009i	−0.918889	+	0.394515i	$0.870912\pi$
$884$		0			0
$885$	−4.00000			−0.134459
$886$		0			0
$887$	−28.5000	+	49.3634i	−0.956936	+	1.65746i	−0.227063	+	0.973880i	$0.572912\pi$
$887$	−28.5000	+	49.3634i	−0.956936	+	1.65746i	−0.729873	+	0.683582i	$0.760421\pi$
$888$		0			0
$889$	−22.5000	+	38.9711i	−0.754626	+	1.30705i
$890$		0			0
$891$	−2.50000	−	4.33013i	−0.0837532	−	0.145065i
$892$		0			0
$893$	−15.0000			−0.501956
$894$		0			0
$895$	4.00000			0.133705
$896$		0			0
$897$	0.500000	+	0.866025i	0.0166945	+	0.0289157i
$898$		0			0
$899$	4.50000	−	7.79423i	0.150083	−	0.259952i
$900$		0			0
$901$	21.0000	−	36.3731i	0.699611	−	1.21176i
$902$		0			0
$903$	−6.00000	−	10.3923i	−0.199667	−	0.345834i
$904$		0			0
$905$	−1.50000	−	2.59808i	−0.0498617	−	0.0863630i
$906$		0			0
$907$	0.500000	+	0.866025i	0.0166022	+	0.0287559i	0.874207	−	0.485553i	$-0.161382\pi$
$907$	0.500000	+	0.866025i	0.0166022	+	0.0287559i	−0.857605	+	0.514309i	$0.828048\pi$
$908$		0			0
$909$	4.50000	+	7.79423i	0.149256	+	0.258518i
$910$		0			0
$911$	−56.0000			−1.85536			−0.927681	−	0.373373i	$-0.878201\pi$
$911$	−56.0000			−1.85536			−0.927681	+	0.373373i	$0.878201\pi$
$912$		0			0
$913$	45.0000			1.48928
$914$		0			0
$915$	3.50000	−	6.06218i	0.115706	−	0.200409i
$916$		0			0
$917$	24.0000	+	41.5692i	0.792550	+	1.37274i
$918$		0			0
$919$	18.5000	−	32.0429i	0.610259	−	1.05700i	−0.380938	−	0.924601i	$-0.624399\pi$
$919$	18.5000	−	32.0429i	0.610259	−	1.05700i	0.991197	−	0.132398i	$-0.0422678\pi$
$920$		0			0
$921$	0.500000	−	0.866025i	0.0164756	−	0.0285365i
$922$		0			0
$923$	1.00000			0.0329154
$924$		0			0
$925$	−0.500000	+	0.866025i	−0.0164399	+	0.0284747i
$926$		0			0
$927$	4.50000	+	7.79423i	0.147799	+	0.255996i
$928$		0			0
$929$	14.0000			0.459325			0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000			0.459325			0.229663	+	0.973270i	$0.426238\pi$
$930$		0			0
$931$	5.00000	+	8.66025i	0.163868	+	0.283828i
$932$		0			0
$933$	−24.0000			−0.785725
$934$		0			0
$935$	−35.0000			−1.14462
$936$		0			0
$937$	50.0000			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$938$		0			0
$939$	26.0000			0.848478
$940$		0			0
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$		0			0
$943$	−5.00000			−0.162822
$944$		0			0
$945$	1.50000	+	2.59808i	0.0487950	+	0.0845154i
$946$		0			0
$947$	4.00000			0.129983			0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000			0.129983			0.0649913	+	0.997886i	$0.479298\pi$
$948$		0			0
$949$	−2.50000	−	4.33013i	−0.0811534	−	0.140562i
$950$		0			0
$951$	−15.5000	+	26.8468i	−0.502622	+	0.870567i
$952$		0			0
$953$	−30.0000			−0.971795			−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000			−0.971795			−0.485898	+	0.874016i	$0.661507\pi$
$954$		0			0
$955$	2.50000	−	4.33013i	0.0808981	−	0.140120i
$956$		0			0
$957$	7.50000	−	12.9904i	0.242441	−	0.419919i
$958$		0			0
$959$	−15.0000	−	25.9808i	−0.484375	−	0.838963i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$		0			0
$963$	−12.0000			−0.386695
$964$		0			0
$965$	−18.0000			−0.579441
$966$		0			0
$967$	−15.5000	−	26.8468i	−0.498446	−	0.863334i	0.501552	−	0.865128i	$-0.332763\pi$
$967$	−15.5000	−	26.8468i	−0.498446	−	0.863334i	−0.999998	+	0.00179302i	$0.999429\pi$
$968$		0			0
$969$	17.5000	+	30.3109i	0.562181	+	0.973726i
$970$		0			0
$971$	23.5000	+	40.7032i	0.754151	+	1.30623i	0.945795	+	0.324763i	$0.105285\pi$
$971$	23.5000	+	40.7032i	0.754151	+	1.30623i	−0.191644	+	0.981464i	$0.561382\pi$
$972$		0			0
$973$	−6.00000	−	10.3923i	−0.192351	−	0.333162i
$974$		0			0
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$		0			0
$977$	13.5000	−	23.3827i	0.431903	−	0.748078i	−0.565134	−	0.824999i	$-0.691176\pi$
$977$	13.5000	−	23.3827i	0.431903	−	0.748078i	0.997037	+	0.0769208i	$0.0245089\pi$
$978$		0			0
$979$	25.0000	+	43.3013i	0.799003	+	1.38391i
$980$		0			0
$981$	10.0000			0.319275
$982$		0			0
$983$	56.0000			1.78612			0.893061	−	0.449935i	$-0.148553\pi$
$983$	56.0000			1.78612			0.893061	+	0.449935i	$0.148553\pi$
$984$		0			0
$985$	3.50000	+	6.06218i	0.111519	+	0.193157i
$986$		0			0
$987$	4.50000	−	7.79423i	0.143237	−	0.248093i
$988$		0			0
$989$	2.00000	−	3.46410i	0.0635963	−	0.110152i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	−1.50000	−	2.59808i	−0.0476011	−	0.0824475i
$994$		0			0
$995$	8.50000	−	14.7224i	0.269468	−	0.466732i
$996$		0			0
$997$	6.00000			0.190022			0.0950110	−	0.995476i	$-0.469711\pi$
$997$	6.00000			0.190022			0.0950110	+	0.995476i	$0.469711\pi$
$998$		0			0
$999$	0.500000	−	0.866025i	0.0158193	−	0.0273998i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.a.841.1	✓	2	67.37	even	3	inner
4020.2.q.a.3781.1	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(-1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(-1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +(-2.50000 - 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(3.50000 - 6.06218i) q^{17} +(2.50000 - 4.33013i) q^{19} +(1.50000 + 2.59808i) q^{21} +(-0.500000 + 0.866025i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(1.50000 + 2.59808i) q^{31} +(2.50000 + 4.33013i) q^{33} +(-1.50000 - 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{37} +(0.500000 - 0.866025i) q^{39} +(2.50000 + 4.33013i) q^{41} -4.00000 q^{43} +1.00000 q^{45} +(-1.50000 - 2.59808i) q^{47} +(-1.00000 + 1.73205i) q^{49} +(-3.50000 + 6.06218i) q^{51} +6.00000 q^{53} +(-2.50000 - 4.33013i) q^{55} +(-2.50000 + 4.33013i) q^{57} +4.00000 q^{59} +(-3.50000 + 6.06218i) q^{61} +(-1.50000 - 2.59808i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(-8.00000 - 1.73205i) q^{67} +(0.500000 - 0.866025i) q^{69} +(-0.500000 - 0.866025i) q^{71} +(-2.50000 + 4.33013i) q^{73} -1.00000 q^{75} +(-7.50000 + 12.9904i) q^{77} +(-4.50000 - 7.79423i) q^{79} +1.00000 q^{81} +(-4.50000 + 7.79423i) q^{83} +(3.50000 - 6.06218i) q^{85} +(1.50000 + 2.59808i) q^{87} -10.0000 q^{89} +3.00000 q^{91} +(-1.50000 - 2.59808i) q^{93} +(2.50000 - 4.33013i) q^{95} +(3.50000 - 6.06218i) q^{97} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{5} - 3 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^5 - 3 * q^7 + 2 * q^9	\( 2 q - 2 q^{3} + 2 q^{5} - 3 q^{7} + 2 q^{9} - 5 q^{11} - q^{13} - 2 q^{15} + 7 q^{17} + 5 q^{19} + 3 q^{21} - q^{23} + 2 q^{25} - 2 q^{27} - 3 q^{29} + 3 q^{31} + 5 q^{33} - 3 q^{35} - q^{37} + q^{39} + 5 q^{41} - 8 q^{43} + 2 q^{45} - 3 q^{47} - 2 q^{49} - 7 q^{51} + 12 q^{53} - 5 q^{55} - 5 q^{57} + 8 q^{59} - 7 q^{61} - 3 q^{63} - q^{65} - 16 q^{67} + q^{69} - q^{71} - 5 q^{73} - 2 q^{75} - 15 q^{77} - 9 q^{79} + 2 q^{81} - 9 q^{83} + 7 q^{85} + 3 q^{87} - 20 q^{89} + 6 q^{91} - 3 q^{93} + 5 q^{95} + 7 q^{97} - 5 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^5 - 3 * q^7 + 2 * q^9 - 5 * q^11 - q^13 - 2 * q^15 + 7 * q^17 + 5 * q^19 + 3 * q^21 - q^23 + 2 * q^25 - 2 * q^27 - 3 * q^29 + 3 * q^31 + 5 * q^33 - 3 * q^35 - q^37 + q^39 + 5 * q^41 - 8 * q^43 + 2 * q^45 - 3 * q^47 - 2 * q^49 - 7 * q^51 + 12 * q^53 - 5 * q^55 - 5 * q^57 + 8 * q^59 - 7 * q^61 - 3 * q^63 - q^65 - 16 * q^67 + q^69 - q^71 - 5 * q^73 - 2 * q^75 - 15 * q^77 - 9 * q^79 + 2 * q^81 - 9 * q^83 + 7 * q^85 + 3 * q^87 - 20 * q^89 + 6 * q^91 - 3 * q^93 + 5 * q^95 + 7 * q^97 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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