LMFDB - Embedded newform 4020.2.q.g.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.g.3781.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{9} +(2.50000 - 4.33013i) q^{11} +(0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(3.50000 + 6.06218i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{21} +(-4.50000 - 7.79423i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(1.50000 - 2.59808i) q^{29} +(3.50000 - 6.06218i) q^{31} +(2.50000 - 4.33013i) q^{33} +(0.500000 - 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{41} -8.00000 q^{43} -1.00000 q^{45} +(-3.50000 + 6.06218i) q^{47} +(3.00000 + 5.19615i) q^{49} +(3.50000 + 6.06218i) q^{51} +6.00000 q^{53} +(-2.50000 + 4.33013i) q^{55} +(2.50000 + 4.33013i) q^{57} +4.00000 q^{59} +(6.50000 + 11.2583i) q^{61} +(-0.500000 + 0.866025i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-4.50000 - 7.79423i) q^{69} +(-3.50000 + 6.06218i) q^{71} +(2.50000 + 4.33013i) q^{73} +1.00000 q^{75} +(2.50000 + 4.33013i) q^{77} +(-6.50000 + 11.2583i) q^{79} +1.00000 q^{81} +(-8.50000 - 14.7224i) q^{83} +(-3.50000 - 6.06218i) q^{85} +(1.50000 - 2.59808i) q^{87} +18.0000 q^{89} -1.00000 q^{91} +(3.50000 - 6.06218i) q^{93} +(-2.50000 - 4.33013i) q^{95} +(0.500000 + 0.866025i) q^{97} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 5 q^{11} + q^{13} - 2 q^{15} + 7 q^{17} + 5 q^{19} - q^{21} - 9 q^{23} + 2 q^{25} + 2 q^{27} + 3 q^{29} + 7 q^{31} + 5 q^{33} + q^{35} - 7 q^{37} + q^{39} + 3 q^{41} - 16 q^{43} - 2 q^{45} - 7 q^{47} + 6 q^{49} + 7 q^{51} + 12 q^{53} - 5 q^{55} + 5 q^{57} + 8 q^{59} + 13 q^{61} - q^{63} - q^{65} + 16 q^{67} - 9 q^{69} - 7 q^{71} + 5 q^{73} + 2 q^{75} + 5 q^{77} - 13 q^{79} + 2 q^{81} - 17 q^{83} - 7 q^{85} + 3 q^{87} + 36 q^{89} - 2 q^{91} + 7 q^{93} - 5 q^{95} + q^{97} + 5 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 2 * q^5 - q^7 + 2 * q^9 + 5 * q^11 + q^13 - 2 * q^15 + 7 * q^17 + 5 * q^19 - q^21 - 9 * q^23 + 2 * q^25 + 2 * q^27 + 3 * q^29 + 7 * q^31 + 5 * q^33 + q^35 - 7 * q^37 + q^39 + 3 * q^41 - 16 * q^43 - 2 * q^45 - 7 * q^47 + 6 * q^49 + 7 * q^51 + 12 * q^53 - 5 * q^55 + 5 * q^57 + 8 * q^59 + 13 * q^61 - q^63 - q^65 + 16 * q^67 - 9 * q^69 - 7 * q^71 + 5 * q^73 + 2 * q^75 + 5 * q^77 - 13 * q^79 + 2 * q^81 - 17 * q^83 - 7 * q^85 + 3 * q^87 + 36 * q^89 - 2 * q^91 + 7 * q^93 - 5 * q^95 + q^97 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	0.882213	+	0.470850i	$0.156053\pi$
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	−0.0333386	+	0.999444i	$0.510614\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$	−0.500000	+	0.866025i	−0.109109	+	0.188982i
$22$		0			0
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.768613	−	0.639713i	$-0.779053\pi$
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.169701	−	0.985496i	$-0.554280\pi$
$24$		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	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$		0			0
$33$	2.50000	−	4.33013i	0.435194	−	0.753778i
$34$		0			0
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$		0			0
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$		0			0
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		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
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	0.489398	+	0.872060i	$0.337217\pi$
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	−0.999926	+	0.0121990i	$0.996117\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		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
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$		0			0
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$		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
$69$	−4.50000	−	7.79423i	−0.541736	−	0.938315i
$70$		0			0
$71$	−3.50000	+	6.06218i	−0.415374	+	0.719448i	−0.995468	−	0.0951014i	$-0.969682\pi$
$71$	−3.50000	+	6.06218i	−0.415374	+	0.719448i	0.580094	+	0.814550i	$0.303016\pi$
$72$		0			0
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	0.974424	−	0.224716i	$-0.0721453\pi$
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	−0.681822	+	0.731519i	$0.738812\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	2.50000	+	4.33013i	0.284901	+	0.493464i
$78$		0			0
$79$	−6.50000	+	11.2583i	−0.731307	+	1.26666i	0.225018	+	0.974355i	$0.427756\pi$
$79$	−6.50000	+	11.2583i	−0.731307	+	1.26666i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−8.50000	−	14.7224i	−0.932996	−	1.61600i	−0.778169	−	0.628055i	$-0.783851\pi$
$83$	−8.50000	−	14.7224i	−0.932996	−	1.61600i	−0.154828	−	0.987942i	$-0.549482\pi$
$84$		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
$89$	18.0000			1.90800			0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000			1.90800			0.953998	+	0.299813i	$0.0969242\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$		0			0
$93$	3.50000	−	6.06218i	0.362933	−	0.628619i
$94$		0			0
$95$	−2.50000	−	4.33013i	−0.256495	−	0.444262i
$96$		0			0
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	0.890292	−	0.455389i	$-0.150500\pi$
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	−0.839525	+	0.543321i	$0.817167\pi$
$98$		0			0
$99$	2.50000	−	4.33013i	0.251259	−	0.435194i
$100$		0			0
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	−0.451190	−	0.892428i	$-0.649000\pi$
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	0.998460	−	0.0554722i	$-0.0176664\pi$
$102$		0			0
$103$	9.50000	−	16.4545i	0.936063	−	1.62131i	0.163335	−	0.986571i	$-0.447775\pi$
$103$	9.50000	−	16.4545i	0.936063	−	1.62131i	0.772728	−	0.634738i	$-0.218892\pi$
$104$		0			0
$105$	0.500000	−	0.866025i	0.0487950	−	0.0845154i
$106$		0			0
$107$	8.00000			0.773389			0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000			0.773389			0.386695	+	0.922208i	$0.373617\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	−3.50000	−	6.06218i	−0.332205	−	0.575396i
$112$		0			0
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	−0.888585	−	0.458712i	$-0.848311\pi$
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	0.841549	+	0.540181i	$0.181644\pi$
$114$		0			0
$115$	4.50000	+	7.79423i	0.419627	+	0.726816i
$116$		0			0
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$		0			0
$119$	−7.00000			−0.641689
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$		0			0
$123$	1.50000	−	2.59808i	0.135250	−	0.234261i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	9.50000	−	16.4545i	0.842989	−	1.46010i	−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	9.50000	−	16.4545i	0.842989	−	1.46010i	0.887357	−	0.461084i	$-0.152539\pi$
$128$		0			0
$129$	−8.00000			−0.704361
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	−5.00000			−0.433555
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	2.00000			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$	−3.50000	+	6.06218i	−0.294753	+	0.510527i
$142$		0			0
$143$	5.00000			0.418121
$144$		0			0
$145$	−1.50000	+	2.59808i	−0.124568	+	0.215758i
$146$		0			0
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$		0			0
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	0.885653	−	0.464348i	$-0.153711\pi$
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	−0.844963	+	0.534824i	$0.820378\pi$
$152$		0			0
$153$	3.50000	+	6.06218i	0.282958	+	0.490098i
$154$		0			0
$155$	−3.50000	+	6.06218i	−0.281127	+	0.486926i
$156$		0			0
$157$	−11.5000	−	19.9186i	−0.917800	−	1.58968i	−0.802749	−	0.596316i	$-0.796630\pi$
$157$	−11.5000	−	19.9186i	−0.917800	−	1.58968i	−0.115050	−	0.993360i	$-0.536703\pi$
$158$		0			0
$159$	6.00000			0.475831
$160$		0			0
$161$	9.00000			0.709299
$162$		0			0
$163$	−12.5000	+	21.6506i	−0.979076	+	1.69581i	−0.313304	+	0.949653i	$0.601436\pi$
$163$	−12.5000	+	21.6506i	−0.979076	+	1.69581i	−0.665771	+	0.746156i	$0.731897\pi$
$164$		0			0
$165$	−2.50000	+	4.33013i	−0.194625	+	0.337100i
$166$		0			0
$167$	2.50000	−	4.33013i	0.193456	−	0.335075i	−0.752937	−	0.658092i	$-0.771364\pi$
$167$	2.50000	−	4.33013i	0.193456	−	0.335075i	0.946393	+	0.323017i	$0.104697\pi$
$168$		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
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	0.995754	−	0.0920525i	$-0.0293428\pi$
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	−0.577597	+	0.816322i	$0.696009\pi$
$174$		0			0
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$		0			0
$177$	4.00000			0.300658
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	0.706129	+	0.708083i	$0.250440\pi$
$182$		0			0
$183$	6.50000	+	11.2583i	0.480494	+	0.832240i
$184$		0			0
$185$	3.50000	+	6.06218i	0.257325	+	0.445700i
$186$		0			0
$187$	35.0000			2.55945
$188$		0			0
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$		0			0
$191$	13.5000	+	23.3827i	0.976826	+	1.69191i	0.673774	+	0.738938i	$0.264672\pi$
$191$	13.5000	+	23.3827i	0.976826	+	1.69191i	0.303052	+	0.952974i	$0.401994\pi$
$192$		0			0
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$		0			0
$195$	−0.500000	−	0.866025i	−0.0358057	−	0.0620174i
$196$		0			0
$197$	9.50000	−	16.4545i	0.676847	−	1.17233i	−0.299078	−	0.954229i	$-0.596679\pi$
$197$	9.50000	−	16.4545i	0.676847	−	1.17233i	0.975925	−	0.218105i	$-0.0699875\pi$
$198$		0			0
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	0.807950	−	0.589252i	$-0.200577\pi$
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	−0.914282	+	0.405079i	$0.867244\pi$
$200$		0			0
$201$	8.00000	−	1.73205i	0.564276	−	0.122169i
$202$		0			0
$203$	1.50000	+	2.59808i	0.105279	+	0.182349i
$204$		0			0
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$		0			0
$207$	−4.50000	−	7.79423i	−0.312772	−	0.541736i
$208$		0			0
$209$	25.0000			1.72929
$210$		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
$213$	−3.50000	+	6.06218i	−0.239816	+	0.415374i
$214$		0			0
$215$	8.00000			0.545595
$216$		0			0
$217$	3.50000	+	6.06218i	0.237595	+	0.411527i
$218$		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
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	0.500000	−	0.866025i	0.0331862	−	0.0574801i	−0.848955	−	0.528465i	$-0.822768\pi$
$227$	0.500000	−	0.866025i	0.0331862	−	0.0574801i	0.882141	+	0.470985i	$0.156101\pi$
$228$		0			0
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	0.975533	−	0.219853i	$-0.0705577\pi$
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	−0.678165	+	0.734910i	$0.737224\pi$
$230$		0			0
$231$	2.50000	+	4.33013i	0.164488	+	0.284901i
$232$		0			0
$233$	3.50000	−	6.06218i	0.229293	−	0.397146i	−0.728306	−	0.685252i	$-0.759692\pi$
$233$	3.50000	−	6.06218i	0.229293	−	0.397146i	0.957599	+	0.288106i	$0.0930254\pi$
$234$		0			0
$235$	3.50000	−	6.06218i	0.228315	−	0.395453i
$236$		0			0
$237$	−6.50000	+	11.2583i	−0.422220	+	0.731307i
$238$		0			0
$239$	4.50000	−	7.79423i	0.291081	−	0.504167i	−0.682985	−	0.730433i	$-0.739318\pi$
$239$	4.50000	−	7.79423i	0.291081	−	0.504167i	0.974066	+	0.226266i	$0.0726518\pi$
$240$		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
$247$	−2.50000	+	4.33013i	−0.159071	+	0.275519i
$248$		0			0
$249$	−8.50000	−	14.7224i	−0.538666	−	0.932996i
$250$		0			0
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	0.584643	−	0.811290i	$-0.301234\pi$
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	−0.994920	+	0.100671i	$0.967901\pi$
$252$		0			0
$253$	−45.0000			−2.82913
$254$		0			0
$255$	−3.50000	−	6.06218i	−0.219179	−	0.379628i
$256$		0			0
$257$	−6.50000	+	11.2583i	−0.405459	+	0.702275i	−0.994375	−	0.105919i	$-0.966222\pi$
$257$	−6.50000	+	11.2583i	−0.405459	+	0.702275i	0.588916	+	0.808194i	$0.299555\pi$
$258$		0			0
$259$	7.00000			0.434959
$260$		0			0
$261$	1.50000	−	2.59808i	0.0928477	−	0.160817i
$262$		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
$267$	18.0000			1.10158
$268$		0			0
$269$	−2.00000			−0.121942			−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000			−0.121942			−0.0609711	+	0.998140i	$0.519420\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$		0			0
$273$	−1.00000			−0.0605228
$274$		0			0
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$		0			0
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$		0			0
$279$	3.50000	−	6.06218i	0.209540	−	0.362933i
$280$		0			0
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	0.907293	−	0.420500i	$-0.138145\pi$
$281$	1.50000	+	2.59808i	0.0894825	+	0.154988i	−0.817810	+	0.575488i	$0.804812\pi$
$282$		0			0
$283$	−16.0000			−0.951101			−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000			−0.951101			−0.475551	+	0.879688i	$0.657751\pi$
$284$		0			0
$285$	−2.50000	−	4.33013i	−0.148087	−	0.256495i
$286$		0			0
$287$	1.50000	+	2.59808i	0.0885422	+	0.153360i
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$		0			0
$291$	0.500000	+	0.866025i	0.0293105	+	0.0507673i
$292$		0			0
$293$	26.0000			1.51894			0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000			1.51894			0.759468	+	0.650545i	$0.225459\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$		0			0
$297$	2.50000	−	4.33013i	0.145065	−	0.251259i
$298$		0			0
$299$	4.50000	−	7.79423i	0.260242	−	0.450752i
$300$		0			0
$301$	4.00000	−	6.92820i	0.230556	−	0.399335i
$302$		0			0
$303$	5.50000	−	9.52628i	0.315967	−	0.547270i
$304$		0			0
$305$	−6.50000	−	11.2583i	−0.372189	−	0.644650i
$306$		0			0
$307$	−3.50000	−	6.06218i	−0.199756	−	0.345987i	0.748694	−	0.662916i	$-0.230681\pi$
$307$	−3.50000	−	6.06218i	−0.199756	−	0.345987i	−0.948449	+	0.316929i	$0.897348\pi$
$308$		0			0
$309$	9.50000	−	16.4545i	0.540436	−	0.936063i
$310$		0			0
$311$	8.00000			0.453638			0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000			0.453638			0.226819	+	0.973937i	$0.427167\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$		0			0
$315$	0.500000	−	0.866025i	0.0281718	−	0.0487950i
$316$		0			0
$317$	5.50000	+	9.52628i	0.308911	+	0.535049i	0.978124	−	0.208021i	$-0.0667022\pi$
$317$	5.50000	+	9.52628i	0.308911	+	0.535049i	−0.669214	+	0.743070i	$0.733369\pi$
$318$		0			0
$319$	−7.50000	−	12.9904i	−0.419919	−	0.727322i
$320$		0			0
$321$	8.00000			0.446516
$322$		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
$327$	2.00000			0.110600
$328$		0			0
$329$	−3.50000	−	6.06218i	−0.192961	−	0.334219i
$330$		0			0
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	−0.926516	−	0.376254i	$-0.877212\pi$
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	0.789104	+	0.614260i	$0.210545\pi$
$332$		0			0
$333$	−3.50000	−	6.06218i	−0.191799	−	0.332205i
$334$		0			0
$335$	−8.00000	+	1.73205i	−0.437087	+	0.0946320i
$336$		0			0
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	0.879322	−	0.476227i	$-0.157996\pi$
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	−0.852086	+	0.523402i	$0.824663\pi$
$338$		0			0
$339$	−0.500000	+	0.866025i	−0.0271563	+	0.0470360i
$340$		0			0
$341$	−17.5000	−	30.3109i	−0.947678	−	1.64143i
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$	4.50000	+	7.79423i	0.242272	+	0.419627i
$346$		0			0
$347$	14.5000	−	25.1147i	0.778401	−	1.34823i	−0.154462	−	0.987999i	$-0.549365\pi$
$347$	14.5000	−	25.1147i	0.778401	−	1.34823i	0.932863	−	0.360231i	$-0.117302\pi$
$348$		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
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$		0			0
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	0.993626	−	0.112731i	$-0.0359599\pi$
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$354$		0			0
$355$	3.50000	−	6.06218i	0.185761	−	0.321747i
$356$		0			0
$357$	−7.00000			−0.370479
$358$		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
$361$	−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
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	−0.984301	−	0.176500i	$-0.943523\pi$
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	0.645003	+	0.764180i	$0.276856\pi$
$368$		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
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	−0.852791	−	0.522253i	$-0.825092\pi$
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	0.878680	+	0.477412i	$0.158425\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	−11.5000	−	19.9186i	−0.590715	−	1.02315i	−0.994136	−	0.108134i	$-0.965512\pi$
$379$	−11.5000	−	19.9186i	−0.590715	−	1.02315i	0.403421	−	0.915014i	$-0.367821\pi$
$380$		0			0
$381$	9.50000	−	16.4545i	0.486700	−	0.842989i
$382$		0			0
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	0.727851	−	0.685736i	$-0.240519\pi$
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	−0.957790	+	0.287469i	$0.907186\pi$
$384$		0			0
$385$	−2.50000	−	4.33013i	−0.127412	−	0.220684i
$386$		0			0
$387$	−8.00000			−0.406663
$388$		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
$391$	31.5000	−	54.5596i	1.59302	−	2.75920i
$392$		0			0
$393$	12.0000			0.605320
$394$		0			0
$395$	6.50000	−	11.2583i	0.327050	−	0.566468i
$396$		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
$399$	−5.00000			−0.250313
$400$		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
$403$	7.00000			0.348695
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−35.0000			−1.73489
$408$		0			0
$409$	−13.5000	+	23.3827i	−0.667532	+	1.15620i	0.311060	+	0.950390i	$0.399316\pi$
$409$	−13.5000	+	23.3827i	−0.667532	+	1.15620i	−0.978592	+	0.205809i	$0.934017\pi$
$410$		0			0
$411$	2.00000			0.0986527
$412$		0			0
$413$	−2.00000	+	3.46410i	−0.0984136	+	0.170457i
$414$		0			0
$415$	8.50000	+	14.7224i	0.417249	+	0.722696i
$416$		0			0
$417$	12.0000			0.587643
$418$		0			0
$419$	9.50000	+	16.4545i	0.464105	+	0.803854i	0.999161	−	0.0409630i	$-0.0130426\pi$
$419$	9.50000	+	16.4545i	0.464105	+	0.803854i	−0.535055	+	0.844817i	$0.679709\pi$
$420$		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
$423$	−3.50000	+	6.06218i	−0.170176	+	0.294753i
$424$		0			0
$425$	3.50000	+	6.06218i	0.169775	+	0.294059i
$426$		0			0
$427$	−13.0000			−0.629114
$428$		0			0
$429$	5.00000			0.241402
$430$		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
$433$	−1.50000	+	2.59808i	−0.0720854	+	0.124856i	−0.899815	−	0.436271i	$-0.856299\pi$
$433$	−1.50000	+	2.59808i	−0.0720854	+	0.124856i	0.827730	+	0.561127i	$0.189632\pi$
$434$		0			0
$435$	−1.50000	+	2.59808i	−0.0719195	+	0.124568i
$436$		0			0
$437$	22.5000	−	38.9711i	1.07632	−	1.86424i
$438$		0			0
$439$	−7.50000	−	12.9904i	−0.357955	−	0.619997i	0.629664	−	0.776868i	$-0.283193\pi$
$439$	−7.50000	−	12.9904i	−0.357955	−	0.619997i	−0.987619	+	0.156871i	$0.949859\pi$
$440$		0			0
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$		0			0
$443$	−13.5000	+	23.3827i	−0.641404	+	1.11094i	0.343715	+	0.939074i	$0.388315\pi$
$443$	−13.5000	+	23.3827i	−0.641404	+	1.11094i	−0.985119	+	0.171871i	$0.945019\pi$
$444$		0			0
$445$	−18.0000			−0.853282
$446$		0			0
$447$	6.00000			0.283790
$448$		0			0
$449$	−18.5000	+	32.0429i	−0.873069	+	1.51220i	−0.0142633	+	0.999898i	$0.504540\pi$
$449$	−18.5000	+	32.0429i	−0.873069	+	1.51220i	−0.858806	+	0.512302i	$0.828793\pi$
$450$		0			0
$451$	−7.50000	−	12.9904i	−0.353161	−	0.611693i
$452$		0			0
$453$	0.500000	+	0.866025i	0.0234920	+	0.0406894i
$454$		0			0
$455$	1.00000			0.0468807
$456$		0			0
$457$	−19.5000	+	33.7750i	−0.912172	+	1.57993i	−0.101181	+	0.994868i	$0.532262\pi$
$457$	−19.5000	+	33.7750i	−0.912172	+	1.57993i	−0.810990	+	0.585059i	$0.801071\pi$
$458$		0			0
$459$	3.50000	+	6.06218i	0.163366	+	0.282958i
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	4.50000	+	7.79423i	0.209133	+	0.362229i	0.951442	−	0.307829i	$-0.0996026\pi$
$463$	4.50000	+	7.79423i	0.209133	+	0.362229i	−0.742309	+	0.670058i	$0.766269\pi$
$464$		0			0
$465$	−3.50000	+	6.06218i	−0.162309	+	0.281127i
$466$		0			0
$467$	19.5000	+	33.7750i	0.902352	+	1.56292i	0.824432	+	0.565961i	$0.191495\pi$
$467$	19.5000	+	33.7750i	0.902352	+	1.56292i	0.0779201	+	0.996960i	$0.475172\pi$
$468$		0			0
$469$	−2.50000	+	7.79423i	−0.115439	+	0.359904i
$470$		0			0
$471$	−11.5000	−	19.9186i	−0.529892	−	0.917800i
$472$		0			0
$473$	−20.0000	+	34.6410i	−0.919601	+	1.59280i
$474$		0			0
$475$	2.50000	+	4.33013i	0.114708	+	0.198680i
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	−16.5000	−	28.5788i	−0.753904	−	1.30580i	−0.945917	−	0.324408i	$-0.894835\pi$
$479$	−16.5000	−	28.5788i	−0.753904	−	1.30580i	0.192013	−	0.981392i	$-0.438498\pi$
$480$		0			0
$481$	3.50000	−	6.06218i	0.159586	−	0.276412i
$482$		0			0
$483$	9.00000			0.409514
$484$		0			0
$485$	−0.500000	−	0.866025i	−0.0227038	−	0.0393242i
$486$		0			0
$487$	−13.5000	−	23.3827i	−0.611743	−	1.05957i	−0.990947	−	0.134257i	$-0.957135\pi$
$487$	−13.5000	−	23.3827i	−0.611743	−	1.05957i	0.379203	−	0.925313i	$-0.376198\pi$
$488$		0			0
$489$	−12.5000	+	21.6506i	−0.565270	+	0.979076i
$490$		0			0
$491$	20.0000			0.902587			0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000			0.902587			0.451294	+	0.892375i	$0.350963\pi$
$492$		0			0
$493$	21.0000			0.945792
$494$		0			0
$495$	−2.50000	+	4.33013i	−0.112367	+	0.194625i
$496$		0			0
$497$	−3.50000	−	6.06218i	−0.156996	−	0.271926i
$498$		0			0
$499$	−15.5000	−	26.8468i	−0.693875	−	1.20183i	−0.970558	−	0.240866i	$-0.922569\pi$
$499$	−15.5000	−	26.8468i	−0.693875	−	1.20183i	0.276683	−	0.960961i	$-0.410765\pi$
$500$		0			0
$501$	2.50000	−	4.33013i	0.111692	−	0.193456i
$502$		0			0
$503$	−5.50000	+	9.52628i	−0.245233	+	0.424756i	−0.962197	−	0.272354i	$-0.912198\pi$
$503$	−5.50000	+	9.52628i	−0.245233	+	0.424756i	0.716964	+	0.697110i	$0.245531\pi$
$504$		0			0
$505$	−5.50000	+	9.52628i	−0.244747	+	0.423914i
$506$		0			0
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$		0			0
$509$	−10.0000			−0.443242			−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000			−0.443242			−0.221621	+	0.975133i	$0.571135\pi$
$510$		0			0
$511$	−5.00000			−0.221187
$512$		0			0
$513$	2.50000	+	4.33013i	0.110378	+	0.191180i
$514$		0			0
$515$	−9.50000	+	16.4545i	−0.418620	+	0.725071i
$516$		0			0
$517$	17.5000	+	30.3109i	0.769649	+	1.33307i
$518$		0			0
$519$	5.50000	+	9.52628i	0.241423	+	0.418157i
$520$		0			0
$521$	−14.0000			−0.613351			−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000			−0.613351			−0.306676	+	0.951814i	$0.599217\pi$
$522$		0			0
$523$	−5.50000	−	9.52628i	−0.240498	−	0.416555i	0.720358	−	0.693602i	$-0.243977\pi$
$523$	−5.50000	−	9.52628i	−0.240498	−	0.416555i	−0.960856	+	0.277047i	$0.910644\pi$
$524$		0			0
$525$	−0.500000	+	0.866025i	−0.0218218	+	0.0377964i
$526$		0			0
$527$	49.0000			2.13447
$528$		0			0
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$		0			0
$531$	4.00000			0.173585
$532$		0			0
$533$	3.00000			0.129944
$534$		0			0
$535$	−8.00000			−0.345870
$536$		0			0
$537$		0			0
$538$		0			0
$539$	30.0000			1.29219
$540$		0			0
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$		0			0
$543$	−3.50000	+	6.06218i	−0.150199	+	0.260153i
$544$		0			0
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−6.50000	+	11.2583i	−0.277920	+	0.481371i	−0.970868	−	0.239616i	$-0.922978\pi$
$547$	−6.50000	+	11.2583i	−0.277920	+	0.481371i	0.692948	+	0.720988i	$0.256312\pi$
$548$		0			0
$549$	6.50000	+	11.2583i	0.277413	+	0.480494i
$550$		0			0
$551$	15.0000			0.639021
$552$		0			0
$553$	−6.50000	−	11.2583i	−0.276408	−	0.478753i
$554$		0			0
$555$	3.50000	+	6.06218i	0.148567	+	0.257325i
$556$		0			0
$557$	−8.50000	+	14.7224i	−0.360157	+	0.623809i	−0.987986	−	0.154541i	$-0.950610\pi$
$557$	−8.50000	+	14.7224i	−0.360157	+	0.623809i	0.627830	+	0.778351i	$0.283943\pi$
$558$		0			0
$559$	−4.00000	−	6.92820i	−0.169182	−	0.293032i
$560$		0			0
$561$	35.0000			1.47770
$562$		0			0
$563$	−16.0000			−0.674320			−0.337160	−	0.941447i	$-0.609466\pi$
$563$	−16.0000			−0.674320			−0.337160	+	0.941447i	$0.609466\pi$
$564$		0			0
$565$	0.500000	−	0.866025i	0.0210352	−	0.0364340i
$566$		0			0
$567$	−0.500000	+	0.866025i	−0.0209980	+	0.0363696i
$568$		0			0
$569$	−10.5000	+	18.1865i	−0.440183	+	0.762419i	−0.997703	−	0.0677445i	$-0.978420\pi$
$569$	−10.5000	+	18.1865i	−0.440183	+	0.762419i	0.557520	+	0.830164i	$0.311753\pi$
$570$		0			0
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	−0.913584	−	0.406651i	$-0.866697\pi$
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	0.808962	+	0.587861i	$0.200030\pi$
$572$		0			0
$573$	13.5000	+	23.3827i	0.563971	+	0.976826i
$574$		0			0
$575$	−4.50000	−	7.79423i	−0.187663	−	0.325042i
$576$		0			0
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	−0.633062	−	0.774101i	$-0.718202\pi$
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	0.986922	+	0.161198i	$0.0515357\pi$
$578$		0			0
$579$	−2.00000			−0.0831172
$580$		0			0
$581$	17.0000			0.705279
$582$		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
$587$	−18.5000	−	32.0429i	−0.763577	−	1.32255i	−0.940996	−	0.338418i	$-0.890108\pi$
$587$	−18.5000	−	32.0429i	−0.763577	−	1.32255i	0.177419	−	0.984135i	$-0.443225\pi$
$588$		0			0
$589$	35.0000			1.44215
$590$		0			0
$591$	9.50000	−	16.4545i	0.390778	−	0.676847i
$592$		0			0
$593$	−16.5000	−	28.5788i	−0.677574	−	1.17359i	−0.975709	−	0.219069i	$-0.929698\pi$
$593$	−16.5000	−	28.5788i	−0.677574	−	1.17359i	0.298136	−	0.954524i	$-0.403635\pi$
$594$		0			0
$595$	7.00000			0.286972
$596$		0			0
$597$	−1.50000	−	2.59808i	−0.0613909	−	0.106332i
$598$		0			0
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	−0.759328	−	0.650708i	$-0.774472\pi$
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	0.943193	+	0.332244i	$0.107806\pi$
$600$		0			0
$601$	20.5000	+	35.5070i	0.836212	+	1.44836i	0.893039	+	0.449978i	$0.148568\pi$
$601$	20.5000	+	35.5070i	0.836212	+	1.44836i	−0.0568270	+	0.998384i	$0.518098\pi$
$602$		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
$607$	−10.5000	+	18.1865i	−0.426182	+	0.738169i	−0.996530	−	0.0832344i	$-0.973475\pi$
$607$	−10.5000	+	18.1865i	−0.426182	+	0.738169i	0.570348	+	0.821403i	$0.306808\pi$
$608$		0			0
$609$	1.50000	+	2.59808i	0.0607831	+	0.105279i
$610$		0			0
$611$	−7.00000			−0.283190
$612$		0			0
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$		0			0
$615$	−1.50000	+	2.59808i	−0.0604858	+	0.104765i
$616$		0			0
$617$	−42.0000			−1.69086			−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000			−1.69086			−0.845428	+	0.534089i	$0.820655\pi$
$618$		0			0
$619$	18.5000	+	32.0429i	0.743578	+	1.28791i	0.950856	+	0.309633i	$0.100206\pi$
$619$	18.5000	+	32.0429i	0.743578	+	1.28791i	−0.207279	+	0.978282i	$0.566461\pi$
$620$		0			0
$621$	−4.50000	−	7.79423i	−0.180579	−	0.312772i
$622$		0			0
$623$	−9.00000	+	15.5885i	−0.360577	+	0.624538i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	25.0000			0.998404
$628$		0			0
$629$	24.5000	−	42.4352i	0.976879	−	1.69200i
$630$		0			0
$631$	−13.5000	−	23.3827i	−0.537427	−	0.930850i	−0.999042	−	0.0437697i	$-0.986063\pi$
$631$	−13.5000	−	23.3827i	−0.537427	−	0.930850i	0.461615	−	0.887080i	$-0.347270\pi$
$632$		0			0
$633$	2.50000	+	4.33013i	0.0993661	+	0.172107i
$634$		0			0
$635$	−9.50000	+	16.4545i	−0.376996	+	0.652976i
$636$		0			0
$637$	−3.00000	+	5.19615i	−0.118864	+	0.205879i
$638$		0			0
$639$	−3.50000	+	6.06218i	−0.138458	+	0.239816i
$640$		0			0
$641$	21.5000	−	37.2391i	0.849199	−	1.47086i	−0.0327252	−	0.999464i	$-0.510419\pi$
$641$	21.5000	−	37.2391i	0.849199	−	1.47086i	0.881924	−	0.471391i	$-0.156248\pi$
$642$		0			0
$643$	−12.0000			−0.473234			−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000			−0.473234			−0.236617	+	0.971603i	$0.576039\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	9.50000	+	16.4545i	0.373484	+	0.646892i	0.990099	−	0.140372i	$-0.0448299\pi$
$647$	9.50000	+	16.4545i	0.373484	+	0.646892i	−0.616615	+	0.787265i	$0.711497\pi$
$648$		0			0
$649$	10.0000	−	17.3205i	0.392534	−	0.679889i
$650$		0			0
$651$	3.50000	+	6.06218i	0.137176	+	0.237595i
$652$		0			0
$653$	−22.5000	−	38.9711i	−0.880493	−	1.52506i	−0.850794	−	0.525500i	$-0.823878\pi$
$653$	−22.5000	−	38.9711i	−0.880493	−	1.52506i	−0.0296993	−	0.999559i	$-0.509455\pi$
$654$		0			0
$655$	−12.0000			−0.468879
$656$		0			0
$657$	2.50000	+	4.33013i	0.0975343	+	0.168934i
$658$		0			0
$659$	22.5000	−	38.9711i	0.876476	−	1.51810i	0.0212930	−	0.999773i	$-0.493222\pi$
$659$	22.5000	−	38.9711i	0.876476	−	1.51810i	0.855183	−	0.518327i	$-0.173445\pi$
$660$		0			0
$661$	−30.0000			−1.16686			−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000			−1.16686			−0.583432	+	0.812162i	$0.698291\pi$
$662$		0			0
$663$	−3.50000	+	6.06218i	−0.135929	+	0.235435i
$664$		0			0
$665$	5.00000			0.193892
$666$		0			0
$667$	−27.0000			−1.04544
$668$		0			0
$669$	−8.00000			−0.309298
$670$		0			0
$671$	65.0000			2.50930
$672$		0			0
$673$	−2.00000			−0.0770943			−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000			−0.0770943			−0.0385472	+	0.999257i	$0.512273\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	1.50000	−	2.59808i	0.0576497	−	0.0998522i	−0.835760	−	0.549095i	$-0.814973\pi$
$677$	1.50000	−	2.59808i	0.0576497	−	0.0998522i	0.893410	+	0.449242i	$0.148306\pi$
$678$		0			0
$679$	−1.00000			−0.0383765
$680$		0			0
$681$	0.500000	−	0.866025i	0.0191600	−	0.0331862i
$682$		0			0
$683$	1.50000	+	2.59808i	0.0573959	+	0.0994126i	0.893296	−	0.449469i	$-0.148387\pi$
$683$	1.50000	+	2.59808i	0.0573959	+	0.0994126i	−0.835900	+	0.548882i	$0.815054\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$		0			0
$687$	4.50000	+	7.79423i	0.171686	+	0.297368i
$688$		0			0
$689$	3.00000	+	5.19615i	0.114291	+	0.197958i
$690$		0			0
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	−0.981178	−	0.193105i	$-0.938144\pi$
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	0.657823	+	0.753173i	$0.271478\pi$
$692$		0			0
$693$	2.50000	+	4.33013i	0.0949671	+	0.164488i
$694$		0			0
$695$	−12.0000			−0.455186
$696$		0			0
$697$	21.0000			0.795432
$698$		0			0
$699$	3.50000	−	6.06218i	0.132382	−	0.229293i
$700$		0			0
$701$	1.50000	−	2.59808i	0.0566542	−	0.0981280i	−0.836307	−	0.548261i	$-0.815290\pi$
$701$	1.50000	−	2.59808i	0.0566542	−	0.0981280i	0.892962	+	0.450133i	$0.148623\pi$
$702$		0			0
$703$	17.5000	−	30.3109i	0.660025	−	1.14320i
$704$		0			0
$705$	3.50000	−	6.06218i	0.131818	−	0.228315i
$706$		0			0
$707$	5.50000	+	9.52628i	0.206849	+	0.358273i
$708$		0			0
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	0.875262	−	0.483650i	$-0.160689\pi$
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	−0.856484	+	0.516174i	$0.827356\pi$
$710$		0			0
$711$	−6.50000	+	11.2583i	−0.243769	+	0.422220i
$712$		0			0
$713$	−63.0000			−2.35937
$714$		0			0
$715$	−5.00000			−0.186989
$716$		0			0
$717$	4.50000	−	7.79423i	0.168056	−	0.291081i
$718$		0			0
$719$	−0.500000	−	0.866025i	−0.0186469	−	0.0322973i	0.856551	−	0.516062i	$-0.172602\pi$
$719$	−0.500000	−	0.866025i	−0.0186469	−	0.0322973i	−0.875198	+	0.483764i	$0.839269\pi$
$720$		0			0
$721$	9.50000	+	16.4545i	0.353798	+	0.612797i
$722$		0			0
$723$	−10.0000			−0.371904
$724$		0			0
$725$	1.50000	−	2.59808i	0.0557086	−	0.0964901i
$726$		0			0
$727$	0.500000	+	0.866025i	0.0185440	+	0.0321191i	0.875148	−	0.483854i	$-0.160764\pi$
$727$	0.500000	+	0.866025i	0.0185440	+	0.0321191i	−0.856605	+	0.515974i	$0.827430\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−28.0000	−	48.4974i	−1.03562	−	1.79374i
$732$		0			0
$733$	−5.50000	+	9.52628i	−0.203147	+	0.351861i	−0.949541	−	0.313644i	$-0.898450\pi$
$733$	−5.50000	+	9.52628i	−0.203147	+	0.351861i	0.746394	+	0.665505i	$0.231784\pi$
$734$		0			0
$735$	−3.00000	−	5.19615i	−0.110657	−	0.191663i
$736$		0			0
$737$	12.5000	−	38.9711i	0.460443	−	1.43552i
$738$		0			0
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	−0.867581	−	0.497296i	$-0.834326\pi$
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	0.00311943	−	0.999995i	$-0.499007\pi$
$740$		0			0
$741$	−2.50000	+	4.33013i	−0.0918398	+	0.159071i
$742$		0			0
$743$	−20.5000	−	35.5070i	−0.752072	−	1.30263i	−0.946817	−	0.321773i	$-0.895721\pi$
$743$	−20.5000	−	35.5070i	−0.752072	−	1.30263i	0.194745	−	0.980854i	$-0.437612\pi$
$744$		0			0
$745$	−6.00000			−0.219823
$746$		0			0
$747$	−8.50000	−	14.7224i	−0.310999	−	0.538666i
$748$		0			0
$749$	−4.00000	+	6.92820i	−0.146157	+	0.253151i
$750$		0			0
$751$	20.0000			0.729810			0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000			0.729810			0.364905	+	0.931045i	$0.381101\pi$
$752$		0			0
$753$	−6.50000	−	11.2583i	−0.236873	−	0.410276i
$754$		0			0
$755$	−0.500000	−	0.866025i	−0.0181969	−	0.0315179i
$756$		0			0
$757$	−21.5000	+	37.2391i	−0.781431	+	1.35348i	0.149677	+	0.988735i	$0.452176\pi$
$757$	−21.5000	+	37.2391i	−0.781431	+	1.35348i	−0.931108	+	0.364743i	$0.881157\pi$
$758$		0			0
$759$	−45.0000			−1.63340
$760$		0			0
$761$	26.0000			0.942499			0.471250	−	0.882000i	$-0.343803\pi$
$761$	26.0000			0.942499			0.471250	+	0.882000i	$0.343803\pi$
$762$		0			0
$763$	−1.00000	+	1.73205i	−0.0362024	+	0.0627044i
$764$		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
$769$	10.5000	−	18.1865i	0.378640	−	0.655823i	−0.612225	−	0.790684i	$-0.709725\pi$
$769$	10.5000	−	18.1865i	0.378640	−	0.655823i	0.990865	+	0.134860i	$0.0430586\pi$
$770$		0			0
$771$	−6.50000	+	11.2583i	−0.234092	+	0.405459i
$772$		0			0
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	−0.990721	−	0.135910i	$-0.956604\pi$
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	0.613062	+	0.790034i	$0.289937\pi$
$774$		0			0
$775$	3.50000	−	6.06218i	0.125724	−	0.217760i
$776$		0			0
$777$	7.00000			0.251124
$778$		0			0
$779$	15.0000			0.537431
$780$		0			0
$781$	17.5000	+	30.3109i	0.626199	+	1.08461i
$782$		0			0
$783$	1.50000	−	2.59808i	0.0536056	−	0.0928477i
$784$		0			0
$785$	11.5000	+	19.9186i	0.410453	+	0.710925i
$786$		0			0
$787$	20.5000	+	35.5070i	0.730746	+	1.26569i	0.956565	+	0.291520i	$0.0941610\pi$
$787$	20.5000	+	35.5070i	0.730746	+	1.26569i	−0.225819	+	0.974169i	$0.572506\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.500000	−	0.866025i	−0.0177780	−	0.0307923i
$792$		0			0
$793$	−6.50000	+	11.2583i	−0.230822	+	0.399795i
$794$		0			0
$795$	−6.00000			−0.212798
$796$		0			0
$797$	19.5000	−	33.7750i	0.690725	−	1.19637i	−0.280875	−	0.959744i	$-0.590625\pi$
$797$	19.5000	−	33.7750i	0.690725	−	1.19637i	0.971601	−	0.236627i	$-0.0760420\pi$
$798$		0			0
$799$	−49.0000			−1.73350
$800$		0			0
$801$	18.0000			0.635999
$802$		0			0
$803$	25.0000			0.882231
$804$		0			0
$805$	−9.00000			−0.317208
$806$		0			0
$807$	−2.00000			−0.0704033
$808$		0			0
$809$	−42.0000			−1.47664			−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000			−1.47664			−0.738321	+	0.674450i	$0.764381\pi$
$810$		0			0
$811$	−2.50000	+	4.33013i	−0.0877869	+	0.152051i	−0.906575	−	0.422044i	$-0.861313\pi$
$811$	−2.50000	+	4.33013i	−0.0877869	+	0.152051i	0.818788	+	0.574095i	$0.194646\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$		0			0
$815$	12.5000	−	21.6506i	0.437856	−	0.758389i
$816$		0			0
$817$	−20.0000	−	34.6410i	−0.699711	−	1.21194i
$818$		0			0
$819$	−1.00000			−0.0349428
$820$		0			0
$821$	19.5000	+	33.7750i	0.680555	+	1.17876i	0.974812	+	0.223029i	$0.0715945\pi$
$821$	19.5000	+	33.7750i	0.680555	+	1.17876i	−0.294257	+	0.955726i	$0.595072\pi$
$822$		0			0
$823$	−7.50000	−	12.9904i	−0.261434	−	0.452816i	0.705190	−	0.709019i	$-0.250862\pi$
$823$	−7.50000	−	12.9904i	−0.261434	−	0.452816i	−0.966623	+	0.256203i	$0.917529\pi$
$824$		0			0
$825$	2.50000	−	4.33013i	0.0870388	−	0.150756i
$826$		0			0
$827$	−20.5000	−	35.5070i	−0.712855	−	1.23470i	−0.963781	−	0.266695i	$-0.914068\pi$
$827$	−20.5000	−	35.5070i	−0.712855	−	1.23470i	0.250926	−	0.968006i	$-0.419265\pi$
$828$		0			0
$829$	−46.0000			−1.59765			−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000			−1.59765			−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$	−10.0000			−0.346896
$832$		0			0
$833$	−21.0000	+	36.3731i	−0.727607	+	1.26025i
$834$		0			0
$835$	−2.50000	+	4.33013i	−0.0865161	+	0.149850i
$836$		0			0
$837$	3.50000	−	6.06218i	0.120978	−	0.209540i
$838$		0			0
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	−0.777832	−	0.628473i	$-0.783680\pi$
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	0.933189	+	0.359386i	$0.117014\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	1.50000	+	2.59808i	0.0516627	+	0.0894825i
$844$		0			0
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	14.0000			0.481046
$848$		0			0
$849$	−16.0000			−0.549119
$850$		0			0
$851$	−31.5000	+	54.5596i	−1.07981	+	1.87028i
$852$		0			0
$853$	−19.5000	−	33.7750i	−0.667667	−	1.15643i	−0.978555	−	0.205987i	$-0.933960\pi$
$853$	−19.5000	−	33.7750i	−0.667667	−	1.15643i	0.310887	−	0.950447i	$-0.399374\pi$
$854$		0			0
$855$	−2.50000	−	4.33013i	−0.0854982	−	0.148087i
$856$		0			0
$857$	26.0000			0.888143			0.444072	−	0.895991i	$-0.353534\pi$
$857$	26.0000			0.888143			0.444072	+	0.895991i	$0.353534\pi$
$858$		0			0
$859$	−22.5000	+	38.9711i	−0.767690	+	1.32968i	0.171122	+	0.985250i	$0.445261\pi$
$859$	−22.5000	+	38.9711i	−0.767690	+	1.32968i	−0.938813	+	0.344428i	$0.888073\pi$
$860$		0			0
$861$	1.50000	+	2.59808i	0.0511199	+	0.0885422i
$862$		0			0
$863$	16.0000			0.544646			0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000			0.544646			0.272323	+	0.962206i	$0.412208\pi$
$864$		0			0
$865$	−5.50000	−	9.52628i	−0.187006	−	0.323903i
$866$		0			0
$867$	−16.0000	+	27.7128i	−0.543388	+	0.941176i
$868$		0			0
$869$	32.5000	+	56.2917i	1.10249	+	1.90956i
$870$		0			0
$871$	5.50000	+	6.06218i	0.186360	+	0.205409i
$872$		0			0
$873$	0.500000	+	0.866025i	0.0169224	+	0.0293105i
$874$		0			0
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$		0			0
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	0.954652	−	0.297724i	$-0.0962275\pi$
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	−0.735163	+	0.677891i	$0.762894\pi$
$878$		0			0
$879$	26.0000			0.876958
$880$		0			0
$881$	17.5000	+	30.3109i	0.589590	+	1.02120i	0.994286	+	0.106749i	$0.0340440\pi$
$881$	17.5000	+	30.3109i	0.589590	+	1.02120i	−0.404696	+	0.914451i	$0.632623\pi$
$882$		0			0
$883$	−24.5000	+	42.4352i	−0.824491	+	1.42806i	0.0778173	+	0.996968i	$0.475205\pi$
$883$	−24.5000	+	42.4352i	−0.824491	+	1.42806i	−0.902308	+	0.431092i	$0.858128\pi$
$884$		0			0
$885$	−4.00000			−0.134459
$886$		0			0
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	0.634141	−	0.773217i	$-0.281354\pi$
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	−0.986696	+	0.162573i	$0.948021\pi$
$888$		0			0
$889$	9.50000	+	16.4545i	0.318620	+	0.551866i
$890$		0			0
$891$	2.50000	−	4.33013i	0.0837532	−	0.145065i
$892$		0			0
$893$	−35.0000			−1.17123
$894$		0			0
$895$		0			0
$896$		0			0
$897$	4.50000	−	7.79423i	0.150251	−	0.260242i
$898$		0			0
$899$	−10.5000	−	18.1865i	−0.350195	−	0.606555i
$900$		0			0
$901$	21.0000	+	36.3731i	0.699611	+	1.21176i
$902$		0			0
$903$	4.00000	−	6.92820i	0.133112	−	0.230556i
$904$		0			0
$905$	3.50000	−	6.06218i	0.116344	−	0.201514i
$906$		0			0
$907$	13.5000	−	23.3827i	0.448260	−	0.776409i	−0.550013	−	0.835156i	$-0.685377\pi$
$907$	13.5000	−	23.3827i	0.448260	−	0.776409i	0.998273	+	0.0587469i	$0.0187105\pi$
$908$		0			0
$909$	5.50000	−	9.52628i	0.182423	−	0.315967i
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	−85.0000			−2.81309
$914$		0			0
$915$	−6.50000	−	11.2583i	−0.214883	−	0.372189i
$916$		0			0
$917$	−6.00000	+	10.3923i	−0.198137	+	0.343184i
$918$		0			0
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	−0.965147	−	0.261708i	$-0.915714\pi$
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	0.255927	−	0.966696i	$-0.417619\pi$
$920$		0			0
$921$	−3.50000	−	6.06218i	−0.115329	−	0.199756i
$922$		0			0
$923$	−7.00000			−0.230408
$924$		0			0
$925$	−3.50000	−	6.06218i	−0.115079	−	0.199323i
$926$		0			0
$927$	9.50000	−	16.4545i	0.312021	−	0.540436i
$928$		0			0
$929$	30.0000			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$930$		0			0
$931$	−15.0000	+	25.9808i	−0.491605	+	0.851485i
$932$		0			0
$933$	8.00000			0.261908
$934$		0			0
$935$	−35.0000			−1.14462
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	6.00000			0.195803
$940$		0			0
$941$	−18.0000			−0.586783			−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000			−0.586783			−0.293392	+	0.955992i	$0.594784\pi$
$942$		0			0
$943$	−27.0000			−0.879241
$944$		0			0
$945$	0.500000	−	0.866025i	0.0162650	−	0.0281718i
$946$		0			0
$947$	36.0000			1.16984			0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000			1.16984			0.584921	+	0.811090i	$0.301125\pi$
$948$		0			0
$949$	−2.50000	+	4.33013i	−0.0811534	+	0.140562i
$950$		0			0
$951$	5.50000	+	9.52628i	0.178350	+	0.308911i
$952$		0			0
$953$	−10.0000			−0.323932			−0.161966	−	0.986796i	$-0.551783\pi$
$953$	−10.0000			−0.323932			−0.161966	+	0.986796i	$0.551783\pi$
$954$		0			0
$955$	−13.5000	−	23.3827i	−0.436850	−	0.756646i
$956$		0			0
$957$	−7.50000	−	12.9904i	−0.242441	−	0.419919i
$958$		0			0
$959$	−1.00000	+	1.73205i	−0.0322917	+	0.0559308i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$		0			0
$963$	8.00000			0.257796
$964$		0			0
$965$	2.00000			0.0643823
$966$		0			0
$967$	−2.50000	+	4.33013i	−0.0803946	+	0.139247i	−0.903419	−	0.428758i	$-0.858951\pi$
$967$	−2.50000	+	4.33013i	−0.0803946	+	0.139247i	0.823025	+	0.568005i	$0.192285\pi$
$968$		0			0
$969$	−17.5000	+	30.3109i	−0.562181	+	0.973726i
$970$		0			0
$971$	10.5000	−	18.1865i	0.336961	−	0.583634i	−0.646899	−	0.762576i	$-0.723934\pi$
$971$	10.5000	−	18.1865i	0.336961	−	0.583634i	0.983860	+	0.178942i	$0.0572676\pi$
$972$		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
$977$	−20.5000	−	35.5070i	−0.655853	−	1.13597i	−0.981679	−	0.190541i	$-0.938976\pi$
$977$	−20.5000	−	35.5070i	−0.655853	−	1.13597i	0.325826	−	0.945430i	$-0.394358\pi$
$978$		0			0
$979$	45.0000	−	77.9423i	1.43821	−	2.49105i
$980$		0			0
$981$	2.00000			0.0638551
$982$		0			0
$983$	−40.0000			−1.27580			−0.637901	−	0.770118i	$-0.720197\pi$
$983$	−40.0000			−1.27580			−0.637901	+	0.770118i	$0.720197\pi$
$984$		0			0
$985$	−9.50000	+	16.4545i	−0.302695	+	0.524283i
$986$		0			0
$987$	−3.50000	−	6.06218i	−0.111406	−	0.192961i
$988$		0			0
$989$	36.0000	+	62.3538i	1.14473	+	1.98274i
$990$		0			0
$991$	48.0000			1.52477			0.762385	−	0.647124i	$-0.224028\pi$
$991$	48.0000			1.52477			0.762385	+	0.647124i	$0.224028\pi$
$992$		0			0
$993$	−2.50000	+	4.33013i	−0.0793351	+	0.137412i
$994$		0			0
$995$	1.50000	+	2.59808i	0.0475532	+	0.0823646i
$996$		0			0
$997$	−6.00000			−0.190022			−0.0950110	−	0.995476i	$-0.530289\pi$
$997$	−6.00000			−0.190022			−0.0950110	+	0.995476i	$0.530289\pi$
$998$		0			0
$999$	−3.50000	−	6.06218i	−0.110735	−	0.191799i

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{9} +(2.50000 - 4.33013i) q^{11} +(0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(3.50000 + 6.06218i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{21} +(-4.50000 - 7.79423i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(1.50000 - 2.59808i) q^{29} +(3.50000 - 6.06218i) q^{31} +(2.50000 - 4.33013i) q^{33} +(0.500000 - 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{41} -8.00000 q^{43} -1.00000 q^{45} +(-3.50000 + 6.06218i) q^{47} +(3.00000 + 5.19615i) q^{49} +(3.50000 + 6.06218i) q^{51} +6.00000 q^{53} +(-2.50000 + 4.33013i) q^{55} +(2.50000 + 4.33013i) q^{57} +4.00000 q^{59} +(6.50000 + 11.2583i) q^{61} +(-0.500000 + 0.866025i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-4.50000 - 7.79423i) q^{69} +(-3.50000 + 6.06218i) q^{71} +(2.50000 + 4.33013i) q^{73} +1.00000 q^{75} +(2.50000 + 4.33013i) q^{77} +(-6.50000 + 11.2583i) q^{79} +1.00000 q^{81} +(-8.50000 - 14.7224i) q^{83} +(-3.50000 - 6.06218i) q^{85} +(1.50000 - 2.59808i) q^{87} +18.0000 q^{89} -1.00000 q^{91} +(3.50000 - 6.06218i) q^{93} +(-2.50000 - 4.33013i) q^{95} +(0.500000 + 0.866025i) q^{97} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 2 q^{5} - q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 - 2 * q^5 - q^7 + 2 * q^9	\( 2 q + 2 q^{3} - 2 q^{5} - q^{7} + 2 q^{9} + 5 q^{11} + q^{13} - 2 q^{15} + 7 q^{17} + 5 q^{19} - q^{21} - 9 q^{23} + 2 q^{25} + 2 q^{27} + 3 q^{29} + 7 q^{31} + 5 q^{33} + q^{35} - 7 q^{37} + q^{39} + 3 q^{41} - 16 q^{43} - 2 q^{45} - 7 q^{47} + 6 q^{49} + 7 q^{51} + 12 q^{53} - 5 q^{55} + 5 q^{57} + 8 q^{59} + 13 q^{61} - q^{63} - q^{65} + 16 q^{67} - 9 q^{69} - 7 q^{71} + 5 q^{73} + 2 q^{75} + 5 q^{77} - 13 q^{79} + 2 q^{81} - 17 q^{83} - 7 q^{85} + 3 q^{87} + 36 q^{89} - 2 q^{91} + 7 q^{93} - 5 q^{95} + q^{97} + 5 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 2 * q^5 - q^7 + 2 * q^9 + 5 * q^11 + q^13 - 2 * q^15 + 7 * q^17 + 5 * q^19 - q^21 - 9 * q^23 + 2 * q^25 + 2 * q^27 + 3 * q^29 + 7 * q^31 + 5 * q^33 + q^35 - 7 * q^37 + q^39 + 3 * q^41 - 16 * q^43 - 2 * q^45 - 7 * q^47 + 6 * q^49 + 7 * q^51 + 12 * q^53 - 5 * q^55 + 5 * q^57 + 8 * q^59 + 13 * q^61 - q^63 - q^65 + 16 * q^67 - 9 * q^69 - 7 * q^71 + 5 * q^73 + 2 * q^75 + 5 * q^77 - 13 * q^79 + 2 * q^81 - 17 * q^83 - 7 * q^85 + 3 * q^87 + 36 * q^89 - 2 * q^91 + 7 * q^93 - 5 * q^95 + q^97 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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