LMFDB - Embedded newform 1064.2.q.j.457.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.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:	$8.49608277506$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1064.457
Dual form			1064.2.q.j.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 - 3.46410i) q^{11} +2.00000 q^{13} +2.00000 q^{15} +(3.50000 + 6.06218i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-1.00000 + 5.19615i) q^{21} +(1.50000 - 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} +4.00000 q^{27} +4.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(4.00000 - 6.92820i) q^{33} +(2.50000 - 0.866025i) q^{35} +(-5.00000 + 8.66025i) q^{37} +(2.00000 + 3.46410i) q^{39} -9.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(2.00000 - 3.46410i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-7.00000 + 12.1244i) q^{51} +(-3.00000 - 5.19615i) q^{53} -4.00000 q^{55} +2.00000 q^{57} +(6.00000 + 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(1.00000 - 1.73205i) q^{65} +(-8.00000 - 13.8564i) q^{67} +6.00000 q^{69} +6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{75} +(2.00000 - 10.3923i) q^{77} +(-2.00000 + 3.46410i) q^{79} +(5.50000 + 9.52628i) q^{81} -9.00000 q^{83} +7.00000 q^{85} +(4.00000 + 6.92820i) q^{87} +(2.00000 - 3.46410i) q^{89} +(4.00000 + 3.46410i) q^{91} +(4.00000 - 6.92820i) q^{93} +(-0.500000 - 0.866025i) q^{95} -4.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + q^{5} + 4 q^{7} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + q^5 + 4 * q^7 - q^9	$ 2 q + 2 q^{3} + q^{5} + 4 q^{7} - q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{15} + 7 q^{17} + q^{19} - 2 q^{21} + 3 q^{23} + 4 q^{25} + 8 q^{27} + 8 q^{29} - 4 q^{31} + 8 q^{33} + 5 q^{35} - 10 q^{37} + 4 q^{39} - 18 q^{43} + q^{45} + 4 q^{47} + 2 q^{49} - 14 q^{51} - 6 q^{53} - 8 q^{55} + 4 q^{57} + 12 q^{59} + 2 q^{61} - 5 q^{63} + 2 q^{65} - 16 q^{67} + 12 q^{69} + 12 q^{71} - 2 q^{73} - 8 q^{75} + 4 q^{77} - 4 q^{79} + 11 q^{81} - 18 q^{83} + 14 q^{85} + 8 q^{87} + 4 q^{89} + 8 q^{91} + 8 q^{93} - q^{95} - 8 q^{97} + 8 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + q^5 + 4 * q^7 - q^9 - 4 * q^11 + 4 * q^13 + 4 * q^15 + 7 * q^17 + q^19 - 2 * q^21 + 3 * q^23 + 4 * q^25 + 8 * q^27 + 8 * q^29 - 4 * q^31 + 8 * q^33 + 5 * q^35 - 10 * q^37 + 4 * q^39 - 18 * q^43 + q^45 + 4 * q^47 + 2 * q^49 - 14 * q^51 - 6 * q^53 - 8 * q^55 + 4 * q^57 + 12 * q^59 + 2 * q^61 - 5 * q^63 + 2 * q^65 - 16 * q^67 + 12 * q^69 + 12 * q^71 - 2 * q^73 - 8 * q^75 + 4 * q^77 - 4 * q^79 + 11 * q^81 - 18 * q^83 + 14 * q^85 + 8 * q^87 + 4 * q^89 + 8 * q^91 + 8 * q^93 - q^95 - 8 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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	+	1.73205i	0.577350	+	1.00000i	0.995782	+	0.0917517i	$0.0292466\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	−0.418432	+	0.908248i	$0.637420\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		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
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$		0			0
$21$	−1.00000	+	5.19615i	−0.218218	+	1.13389i
$22$		0			0
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	4.00000	−	6.92820i	0.696311	−	1.20605i
$34$		0			0
$35$	2.50000	−	0.866025i	0.422577	−	0.146385i
$36$		0			0
$37$	−5.00000	+	8.66025i	−0.821995	+	1.42374i	0.0821995	+	0.996616i	$0.473806\pi$
$37$	−5.00000	+	8.66025i	−0.821995	+	1.42374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$		0			0
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−9.00000			−1.37249			−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000			−1.37249			−0.686244	+	0.727372i	$0.740742\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	−0.682489	−	0.730896i	$-0.739102\pi$
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	0.974219	+	0.225605i	$0.0724358\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	−7.00000	+	12.1244i	−0.980196	+	1.69775i
$52$		0			0
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	−4.00000			−0.539360
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$	−2.50000	+	0.866025i	−0.314970	+	0.109109i
$64$		0			0
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$	−8.00000	−	13.8564i	−0.977356	−	1.69283i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−8.00000	−	13.8564i	−0.977356	−	1.69283i	−0.305424	−	0.952217i	$-0.598798\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$		0			0
$75$	−4.00000	+	6.92820i	−0.461880	+	0.800000i
$76$		0			0
$77$	2.00000	−	10.3923i	0.227921	−	1.18431i
$78$		0			0
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	−9.00000			−0.987878			−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000			−0.987878			−0.493939	+	0.869496i	$0.664443\pi$
$84$		0			0
$85$	7.00000			0.759257
$86$		0			0
$87$	4.00000	+	6.92820i	0.428845	+	0.742781i
$88$		0			0
$89$	2.00000	−	3.46410i	0.212000	−	0.367194i	−0.740341	−	0.672232i	$-0.765336\pi$
$89$	2.00000	−	3.46410i	0.212000	−	0.367194i	0.952340	+	0.305038i	$0.0986691\pi$
$90$		0			0
$91$	4.00000	+	3.46410i	0.419314	+	0.363137i
$92$		0			0
$93$	4.00000	−	6.92820i	0.414781	−	0.718421i
$94$		0			0
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	−4.00000			−0.406138			−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000			−0.406138			−0.203069	+	0.979164i	$0.565092\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	−0.999964	−	0.00844953i	$-0.997310\pi$
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	0.507300	+	0.861770i	$0.330644\pi$
$104$		0			0
$105$	4.00000	+	3.46410i	0.390360	+	0.338062i
$106$		0			0
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	−0.605308	−	0.795991i	$-0.706950\pi$
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	0.992003	+	0.126217i	$0.0402834\pi$
$108$		0			0
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	0.977769	+	0.209687i	$0.0672444\pi$
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	−0.307290	+	0.951616i	$0.599422\pi$
$110$		0			0
$111$	−20.0000			−1.89832
$112$		0			0
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$		0			0
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$		0			0
$119$	−3.50000	+	18.1865i	−0.320844	+	1.66716i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$	−9.00000	−	15.5885i	−0.792406	−	1.37249i
$130$		0			0
$131$	6.50000	−	11.2583i	0.567908	−	0.983645i	−0.428865	−	0.903369i	$-0.641086\pi$
$131$	6.50000	−	11.2583i	0.567908	−	0.983645i	0.996773	−	0.0802763i	$-0.0255803\pi$
$132$		0			0
$133$	2.50000	−	0.866025i	0.216777	−	0.0750939i
$134$		0			0
$135$	2.00000	−	3.46410i	0.172133	−	0.298142i
$136$		0			0
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$	8.00000			0.673722
$142$		0			0
$143$	−4.00000	−	6.92820i	−0.334497	−	0.579365i
$144$		0			0
$145$	2.00000	−	3.46410i	0.166091	−	0.287678i
$146$		0			0
$147$	−11.0000	+	8.66025i	−0.907265	+	0.714286i
$148$		0			0
$149$	−2.50000	+	4.33013i	−0.204808	+	0.354738i	−0.950072	−	0.312032i	$-0.898990\pi$
$149$	−2.50000	+	4.33013i	−0.204808	+	0.354738i	0.745264	+	0.666770i	$0.232324\pi$
$150$		0			0
$151$	10.0000	+	17.3205i	0.813788	+	1.40952i	0.910195	+	0.414181i	$0.135932\pi$
$151$	10.0000	+	17.3205i	0.813788	+	1.40952i	−0.0964061	+	0.995342i	$0.530735\pi$
$152$		0			0
$153$	−7.00000			−0.565916
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$	−12.5000	−	21.6506i	−0.997609	−	1.72791i	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−12.5000	−	21.6506i	−0.997609	−	1.72791i	−0.438948	−	0.898513i	$-0.644649\pi$
$158$		0			0
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$		0			0
$161$	7.50000	−	2.59808i	0.591083	−	0.204757i
$162$		0			0
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	−0.566149	−	0.824303i	$-0.691567\pi$
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	0.996942	+	0.0781474i	$0.0249005\pi$
$164$		0			0
$165$	−4.00000	−	6.92820i	−0.311400	−	0.539360i
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	−2.00000	+	10.3923i	−0.151186	+	0.785584i
$176$		0			0
$177$	−12.0000	+	20.7846i	−0.901975	+	1.56227i
$178$		0			0
$179$	−7.00000	−	12.1244i	−0.523205	−	0.906217i	−0.999635	−	0.0270049i	$-0.991403\pi$
$179$	−7.00000	−	12.1244i	−0.523205	−	0.906217i	0.476431	−	0.879212i	$-0.341930\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$	4.00000			0.295689
$184$		0			0
$185$	5.00000	+	8.66025i	0.367607	+	0.636715i
$186$		0			0
$187$	14.0000	−	24.2487i	1.02378	−	1.77324i
$188$		0			0
$189$	8.00000	+	6.92820i	0.581914	+	0.503953i
$190$		0			0
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	−0.529101	−	0.848559i	$-0.677471\pi$
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	0.999424	+	0.0339349i	$0.0108039\pi$
$192$		0			0
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	0.628037	−	0.778183i	$-0.283859\pi$
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	−0.987945	+	0.154805i	$0.950525\pi$
$194$		0			0
$195$	4.00000			0.286446
$196$		0			0
$197$	23.0000			1.63868			0.819341	−	0.573306i	$-0.194340\pi$
$197$	23.0000			1.63868			0.819341	+	0.573306i	$0.194340\pi$
$198$		0			0
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	−0.992434	+	0.122782i	$0.960818\pi$
$200$		0			0
$201$	16.0000	−	27.7128i	1.12855	−	1.95471i
$202$		0			0
$203$	8.00000	+	6.92820i	0.561490	+	0.486265i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.50000	+	2.59808i	0.104257	+	0.180579i
$208$		0			0
$209$	−4.00000			−0.276686
$210$		0			0
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$		0			0
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$		0			0
$215$	−4.50000	+	7.79423i	−0.306897	+	0.531562i
$216$		0			0
$217$	2.00000	−	10.3923i	0.135769	−	0.705476i
$218$		0			0
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$		0			0
$221$	7.00000	+	12.1244i	0.470871	+	0.815572i
$222$		0			0
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$	−4.00000			−0.266667
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	11.5000	−	19.9186i	0.759941	−	1.31626i	−0.182939	−	0.983124i	$-0.558561\pi$
$229$	11.5000	−	19.9186i	0.759941	−	1.31626i	0.942880	−	0.333133i	$-0.108106\pi$
$230$		0			0
$231$	20.0000	−	6.92820i	1.31590	−	0.455842i
$232$		0			0
$233$	−13.5000	+	23.3827i	−0.884414	+	1.53185i	−0.0380310	+	0.999277i	$0.512109\pi$
$233$	−13.5000	+	23.3827i	−0.884414	+	1.53185i	−0.846383	+	0.532574i	$0.821225\pi$
$234$		0			0
$235$	−2.00000	−	3.46410i	−0.130466	−	0.225973i
$236$		0			0
$237$	−8.00000			−0.519656
$238$		0			0
$239$	1.00000			0.0646846			0.0323423	−	0.999477i	$-0.489703\pi$
$239$	1.00000			0.0646846			0.0323423	+	0.999477i	$0.489703\pi$
$240$		0			0
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$		0			0
$243$	−5.00000	+	8.66025i	−0.320750	+	0.555556i
$244$		0			0
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$		0			0
$247$	1.00000	−	1.73205i	0.0636285	−	0.110208i
$248$		0			0
$249$	−9.00000	−	15.5885i	−0.570352	−	0.987878i
$250$		0			0
$251$	−31.0000			−1.95670			−0.978351	−	0.206951i	$-0.933646\pi$
$251$	−31.0000			−1.95670			−0.978351	+	0.206951i	$0.933646\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$		0			0
$255$	7.00000	+	12.1244i	0.438357	+	0.759257i
$256$		0			0
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$		0			0
$259$	−25.0000	+	8.66025i	−1.55342	+	0.538122i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$		0			0
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	0.816066	−	0.577959i	$-0.196151\pi$
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	−0.908560	+	0.417755i	$0.862817\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	8.00000			0.489592
$268$		0			0
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			0
$271$	−3.50000	+	6.06218i	−0.212610	+	0.368251i	−0.952531	−	0.304443i	$-0.901530\pi$
$271$	−3.50000	+	6.06218i	−0.212610	+	0.368251i	0.739921	+	0.672694i	$0.234863\pi$
$272$		0			0
$273$	−2.00000	+	10.3923i	−0.121046	+	0.628971i
$274$		0			0
$275$	8.00000	−	13.8564i	0.482418	−	0.835573i
$276$		0			0
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$		0			0
$279$	4.00000			0.239474
$280$		0			0
$281$	22.0000			1.31241			0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000			1.31241			0.656205	+	0.754583i	$0.272161\pi$
$282$		0			0
$283$	−11.5000	−	19.9186i	−0.683604	−	1.18404i	−0.973873	−	0.227092i	$-0.927078\pi$
$283$	−11.5000	−	19.9186i	−0.683604	−	1.18404i	0.290269	−	0.956945i	$-0.406255\pi$
$284$		0			0
$285$	1.00000	−	1.73205i	0.0592349	−	0.102598i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$		0			0
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$		0			0
$293$	−4.00000			−0.233682			−0.116841	−	0.993151i	$-0.537277\pi$
$293$	−4.00000			−0.233682			−0.116841	+	0.993151i	$0.537277\pi$
$294$		0			0
$295$	12.0000			0.698667
$296$		0			0
$297$	−8.00000	−	13.8564i	−0.464207	−	0.804030i
$298$		0			0
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	−18.0000	−	15.5885i	−1.03750	−	0.898504i
$302$		0			0
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$		0			0
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$		0			0
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$		0			0
$309$	−20.0000			−1.13776
$310$		0			0
$311$	4.50000	+	7.79423i	0.255172	+	0.441970i	0.964942	−	0.262463i	$-0.0845347\pi$
$311$	4.50000	+	7.79423i	0.255172	+	0.441970i	−0.709771	+	0.704433i	$0.751201\pi$
$312$		0			0
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	−0.978553	−	0.205996i	$-0.933957\pi$
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	0.667674	+	0.744453i	$0.267290\pi$
$314$		0			0
$315$	−0.500000	+	2.59808i	−0.0281718	+	0.146385i
$316$		0			0
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$		0			0
$319$	−8.00000	−	13.8564i	−0.447914	−	0.775810i
$320$		0			0
$321$	16.0000			0.893033
$322$		0			0
$323$	7.00000			0.389490
$324$		0			0
$325$	4.00000	+	6.92820i	0.221880	+	0.384308i
$326$		0			0
$327$	−14.0000	+	24.2487i	−0.774202	+	1.34096i
$328$		0			0
$329$	10.0000	−	3.46410i	0.551318	−	0.190982i
$330$		0			0
$331$	−9.00000	+	15.5885i	−0.494685	+	0.856819i	−0.999981	−	0.00612670i	$-0.998050\pi$
$331$	−9.00000	+	15.5885i	−0.494685	+	0.856819i	0.505296	+	0.862946i	$0.331383\pi$
$332$		0			0
$333$	−5.00000	−	8.66025i	−0.273998	−	0.474579i
$334$		0			0
$335$	−16.0000			−0.874173
$336$		0			0
$337$	4.00000			0.217894			0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000			0.217894			0.108947	+	0.994048i	$0.465252\pi$
$338$		0			0
$339$	−10.0000	−	17.3205i	−0.543125	−	0.940721i
$340$		0			0
$341$	−8.00000	+	13.8564i	−0.433224	+	0.750366i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	3.00000	−	5.19615i	0.161515	−	0.279751i
$346$		0			0
$347$	3.50000	+	6.06218i	0.187890	+	0.325435i	0.944547	−	0.328378i	$-0.106502\pi$
$347$	3.50000	+	6.06218i	0.187890	+	0.325435i	−0.756657	+	0.653812i	$0.773169\pi$
$348$		0			0
$349$	−11.0000			−0.588817			−0.294408	−	0.955680i	$-0.595123\pi$
$349$	−11.0000			−0.588817			−0.294408	+	0.955680i	$0.595123\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		0			0
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	−0.920677	−	0.390324i	$-0.872363\pi$
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	0.122308	−	0.992492i	$-0.460970\pi$
$354$		0			0
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$		0			0
$357$	−35.0000	+	12.1244i	−1.85240	+	0.641689i
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$	−10.0000			−0.524864
$364$		0			0
$365$	−2.00000			−0.104685
$366$		0			0
$367$	−12.0000	−	20.7846i	−0.626395	−	1.08495i	−0.988269	−	0.152721i	$-0.951196\pi$
$367$	−12.0000	−	20.7846i	−0.626395	−	1.08495i	0.361874	−	0.932227i	$-0.382137\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.00000	−	15.5885i	0.155752	−	0.809312i
$372$		0			0
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$		0			0
$375$	9.00000	+	15.5885i	0.464758	+	0.804984i
$376$		0			0
$377$	8.00000			0.412021
$378$		0			0
$379$	34.0000			1.74646			0.873231	−	0.487306i	$-0.162020\pi$
$379$	34.0000			1.74646			0.873231	+	0.487306i	$0.162020\pi$
$380$		0			0
$381$	2.00000	+	3.46410i	0.102463	+	0.177471i
$382$		0			0
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	−0.315214	−	0.949021i	$-0.602076\pi$
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	0.979483	−	0.201527i	$-0.0645904\pi$
$384$		0			0
$385$	−8.00000	−	6.92820i	−0.407718	−	0.353094i
$386$		0			0
$387$	4.50000	−	7.79423i	0.228748	−	0.396203i
$388$		0			0
$389$	10.5000	+	18.1865i	0.532371	+	0.922094i	0.999286	+	0.0377914i	$0.0120322\pi$
$389$	10.5000	+	18.1865i	0.532371	+	0.922094i	−0.466915	+	0.884302i	$0.654634\pi$
$390$		0			0
$391$	21.0000			1.06202
$392$		0			0
$393$	26.0000			1.31153
$394$		0			0
$395$	2.00000	+	3.46410i	0.100631	+	0.174298i
$396$		0			0
$397$	−6.50000	+	11.2583i	−0.326226	+	0.565039i	−0.981760	−	0.190126i	$-0.939110\pi$
$397$	−6.50000	+	11.2583i	−0.326226	+	0.565039i	0.655534	+	0.755166i	$0.272444\pi$
$398$		0			0
$399$	4.00000	+	3.46410i	0.200250	+	0.173422i
$400$		0			0
$401$	−14.0000	+	24.2487i	−0.699127	+	1.21092i	0.269643	+	0.962960i	$0.413094\pi$
$401$	−14.0000	+	24.2487i	−0.699127	+	1.21092i	−0.968770	+	0.247962i	$0.920239\pi$
$402$		0			0
$403$	−4.00000	−	6.92820i	−0.199254	−	0.345118i
$404$		0			0
$405$	11.0000			0.546594
$406$		0			0
$407$	40.0000			1.98273
$408$		0			0
$409$	3.00000	+	5.19615i	0.148340	+	0.256933i	0.930614	−	0.366002i	$-0.119274\pi$
$409$	3.00000	+	5.19615i	0.148340	+	0.256933i	−0.782274	+	0.622935i	$0.785940\pi$
$410$		0			0
$411$	18.0000	−	31.1769i	0.887875	−	1.53784i
$412$		0			0
$413$	−6.00000	+	31.1769i	−0.295241	+	1.53412i
$414$		0			0
$415$	−4.50000	+	7.79423i	−0.220896	+	0.382604i
$416$		0			0
$417$	−16.0000	−	27.7128i	−0.783523	−	1.35710i
$418$		0			0
$419$	15.0000			0.732798			0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000			0.732798			0.366399	+	0.930458i	$0.380591\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$	2.00000	+	3.46410i	0.0972433	+	0.168430i
$424$		0			0
$425$	−14.0000	+	24.2487i	−0.679100	+	1.17624i
$426$		0			0
$427$	5.00000	−	1.73205i	0.241967	−	0.0838198i
$428$		0			0
$429$	8.00000	−	13.8564i	0.386244	−	0.668994i
$430$		0			0
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	0.991817	−	0.127666i	$-0.0407486\pi$
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	−0.606471	+	0.795106i	$0.707415\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$		0			0
$435$	8.00000			0.383571
$436$		0			0
$437$	−1.50000	−	2.59808i	−0.0717547	−	0.124283i
$438$		0			0
$439$	−20.0000	+	34.6410i	−0.954548	+	1.65333i	−0.219149	+	0.975691i	$0.570328\pi$
$439$	−20.0000	+	34.6410i	−0.954548	+	1.65333i	−0.735399	+	0.677634i	$0.763005\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	−0.899457	−	0.437009i	$-0.856038\pi$
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	0.828190	+	0.560448i	$0.189371\pi$
$444$		0			0
$445$	−2.00000	−	3.46410i	−0.0948091	−	0.164214i
$446$		0			0
$447$	−10.0000			−0.472984
$448$		0			0
$449$	8.00000			0.377543			0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000			0.377543			0.188772	+	0.982021i	$0.439549\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−20.0000	+	34.6410i	−0.939682	+	1.62758i
$454$		0			0
$455$	5.00000	−	1.73205i	0.234404	−	0.0811998i
$456$		0			0
$457$	1.00000	−	1.73205i	0.0467780	−	0.0810219i	−0.841688	−	0.539964i	$-0.818438\pi$
$457$	1.00000	−	1.73205i	0.0467780	−	0.0810219i	0.888466	+	0.458942i	$0.151771\pi$
$458$		0			0
$459$	14.0000	+	24.2487i	0.653464	+	1.13183i
$460$		0			0
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$		0			0
$465$	−4.00000	−	6.92820i	−0.185496	−	0.321288i
$466$		0			0
$467$	10.0000	−	17.3205i	0.462745	−	0.801498i	−0.536352	−	0.843995i	$-0.680198\pi$
$467$	10.0000	−	17.3205i	0.462745	−	0.801498i	0.999097	+	0.0424970i	$0.0135313\pi$
$468$		0			0
$469$	8.00000	−	41.5692i	0.369406	−	1.91949i
$470$		0			0
$471$	25.0000	−	43.3013i	1.15194	−	1.99522i
$472$		0			0
$473$	18.0000	+	31.1769i	0.827641	+	1.43352i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	−19.5000	−	33.7750i	−0.890978	−	1.54322i	−0.838705	−	0.544586i	$-0.816687\pi$
$479$	−19.5000	−	33.7750i	−0.890978	−	1.54322i	−0.0522726	−	0.998633i	$-0.516646\pi$
$480$		0			0
$481$	−10.0000	+	17.3205i	−0.455961	+	0.789747i
$482$		0			0
$483$	12.0000	+	10.3923i	0.546019	+	0.472866i
$484$		0			0
$485$	−2.00000	+	3.46410i	−0.0908153	+	0.157297i
$486$		0			0
$487$	19.0000	+	32.9090i	0.860972	+	1.49125i	0.870992	+	0.491298i	$0.163477\pi$
$487$	19.0000	+	32.9090i	0.860972	+	1.49125i	−0.0100195	+	0.999950i	$0.503189\pi$
$488$		0			0
$489$	22.0000			0.994874
$490$		0			0
$491$	−5.00000			−0.225647			−0.112823	−	0.993615i	$-0.535989\pi$
$491$	−5.00000			−0.225647			−0.112823	+	0.993615i	$0.535989\pi$
$492$		0			0
$493$	14.0000	+	24.2487i	0.630528	+	1.09211i
$494$		0			0
$495$	2.00000	−	3.46410i	0.0898933	−	0.155700i
$496$		0			0
$497$	12.0000	+	10.3923i	0.538274	+	0.466159i
$498$		0			0
$499$	−6.50000	+	11.2583i	−0.290980	+	0.503992i	−0.974042	−	0.226369i	$-0.927315\pi$
$499$	−6.50000	+	11.2583i	−0.290980	+	0.503992i	0.683062	+	0.730361i	$0.260648\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.0000			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$		0			0
$507$	−9.00000	−	15.5885i	−0.399704	−	0.692308i
$508$		0			0
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$	1.00000	−	5.19615i	0.0442374	−	0.229864i
$512$		0			0
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$		0			0
$515$	5.00000	+	8.66025i	0.220326	+	0.381616i
$516$		0			0
$517$	−16.0000			−0.703679
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	0.954519	−	0.298150i	$-0.0963696\pi$
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	−0.735465	+	0.677563i	$0.763036\pi$
$522$		0			0
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	0.378695	+	0.925521i	$0.376373\pi$
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	−0.990873	+	0.134801i	$0.956961\pi$
$524$		0			0
$525$	−20.0000	+	6.92820i	−0.872872	+	0.302372i
$526$		0			0
$527$	14.0000	−	24.2487i	0.609850	−	1.05629i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−4.00000	−	6.92820i	−0.172935	−	0.299532i
$536$		0			0
$537$	14.0000	−	24.2487i	0.604145	−	1.04641i
$538$		0			0
$539$	22.0000	−	17.3205i	0.947607	−	0.746047i
$540$		0			0
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	−0.980993	−	0.194043i	$-0.937840\pi$
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	0.658543	+	0.752543i	$0.271173\pi$
$542$		0			0
$543$	22.0000	+	38.1051i	0.944110	+	1.63525i
$544$		0			0
$545$	14.0000			0.599694
$546$		0			0
$547$	−40.0000			−1.71028			−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000			−1.71028			−0.855138	+	0.518400i	$0.826528\pi$
$548$		0			0
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$		0			0
$551$	2.00000	−	3.46410i	0.0852029	−	0.147576i
$552$		0			0
$553$	−10.0000	+	3.46410i	−0.425243	+	0.147309i
$554$		0			0
$555$	−10.0000	+	17.3205i	−0.424476	+	0.735215i
$556$		0			0
$557$	−20.5000	−	35.5070i	−0.868613	−	1.50448i	−0.863415	−	0.504495i	$-0.831679\pi$
$557$	−20.5000	−	35.5070i	−0.868613	−	1.50448i	−0.00519835	−	0.999986i	$-0.501655\pi$
$558$		0			0
$559$	−18.0000			−0.761319
$560$		0			0
$561$	56.0000			2.36432
$562$		0			0
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	0.999978	+	0.00664037i	$0.00211371\pi$
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	−0.494238	+	0.869326i	$0.664553\pi$
$564$		0			0
$565$	−5.00000	+	8.66025i	−0.210352	+	0.364340i
$566$		0			0
$567$	−5.50000	+	28.5788i	−0.230978	+	1.20020i
$568$		0			0
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	0.518509	−	0.855072i	$-0.326487\pi$
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	−0.999769	+	0.0215055i	$0.993154\pi$
$572$		0			0
$573$	26.0000			1.08617
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	−3.00000	−	5.19615i	−0.124892	−	0.216319i	0.796799	−	0.604245i	$-0.206525\pi$
$577$	−3.00000	−	5.19615i	−0.124892	−	0.216319i	−0.921691	+	0.387926i	$0.873192\pi$
$578$		0			0
$579$	10.0000	−	17.3205i	0.415586	−	0.719816i
$580$		0			0
$581$	−18.0000	−	15.5885i	−0.746766	−	0.646718i
$582$		0			0
$583$	−12.0000	+	20.7846i	−0.496989	+	0.860811i
$584$		0			0
$585$	1.00000	+	1.73205i	0.0413449	+	0.0716115i
$586$		0			0
$587$	7.00000			0.288921			0.144460	−	0.989511i	$-0.453855\pi$
$587$	7.00000			0.288921			0.144460	+	0.989511i	$0.453855\pi$
$588$		0			0
$589$	−4.00000			−0.164817
$590$		0			0
$591$	23.0000	+	39.8372i	0.946094	+	1.63868i
$592$		0			0
$593$	−1.50000	+	2.59808i	−0.0615976	+	0.106690i	−0.895180	−	0.445705i	$-0.852953\pi$
$593$	−1.50000	+	2.59808i	−0.0615976	+	0.106690i	0.833582	+	0.552396i	$0.186286\pi$
$594$		0			0
$595$	14.0000	+	12.1244i	0.573944	+	0.497050i
$596$		0			0
$597$	11.0000	−	19.0526i	0.450200	−	0.779769i
$598$		0			0
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	0.920783	−	0.390075i	$-0.127551\pi$
$599$	3.00000	+	5.19615i	0.122577	+	0.212309i	−0.798206	+	0.602384i	$0.794218\pi$
$600$		0			0
$601$	16.0000			0.652654			0.326327	−	0.945257i	$-0.394189\pi$
$601$	16.0000			0.652654			0.326327	+	0.945257i	$0.394189\pi$
$602$		0			0
$603$	16.0000			0.651570
$604$		0			0
$605$	2.50000	+	4.33013i	0.101639	+	0.176045i
$606$		0			0
$607$	−14.0000	+	24.2487i	−0.568242	+	0.984225i	0.428497	+	0.903543i	$0.359043\pi$
$607$	−14.0000	+	24.2487i	−0.568242	+	0.984225i	−0.996740	+	0.0806818i	$0.974290\pi$
$608$		0			0
$609$	−4.00000	+	20.7846i	−0.162088	+	0.842235i
$610$		0			0
$611$	4.00000	−	6.92820i	0.161823	−	0.280285i
$612$		0			0
$613$	5.50000	+	9.52628i	0.222143	+	0.384763i	0.955458	−	0.295126i	$-0.0953615\pi$
$613$	5.50000	+	9.52628i	0.222143	+	0.384763i	−0.733316	+	0.679888i	$0.762028\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.0000			0.684394			0.342197	−	0.939628i	$-0.388829\pi$
$617$	17.0000			0.684394			0.342197	+	0.939628i	$0.388829\pi$
$618$		0			0
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	0.999996	+	0.00279365i	$0.000889247\pi$
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	−0.497579	+	0.867419i	$0.665777\pi$
$620$		0			0
$621$	6.00000	−	10.3923i	0.240772	−	0.417029i
$622$		0			0
$623$	10.0000	−	3.46410i	0.400642	−	0.138786i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$	−4.00000	−	6.92820i	−0.159745	−	0.276686i
$628$		0			0
$629$	−70.0000			−2.79108
$630$		0			0
$631$	−25.0000			−0.995234			−0.497617	−	0.867397i	$-0.665792\pi$
$631$	−25.0000			−0.995234			−0.497617	+	0.867397i	$0.665792\pi$
$632$		0			0
$633$	−18.0000	−	31.1769i	−0.715436	−	1.23917i
$634$		0			0
$635$	1.00000	−	1.73205i	0.0396838	−	0.0687343i
$636$		0			0
$637$	2.00000	+	13.8564i	0.0792429	+	0.549011i
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$		0			0
$643$	−19.0000			−0.749287			−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000			−0.749287			−0.374643	+	0.927169i	$0.622235\pi$
$644$		0			0
$645$	−18.0000			−0.708749
$646$		0			0
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	0.835033	−	0.550200i	$-0.185449\pi$
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	−0.894004	+	0.448059i	$0.852115\pi$
$648$		0			0
$649$	24.0000	−	41.5692i	0.942082	−	1.63173i
$650$		0			0
$651$	20.0000	−	6.92820i	0.783862	−	0.271538i
$652$		0			0
$653$	7.50000	−	12.9904i	0.293498	−	0.508353i	−0.681137	−	0.732156i	$-0.738514\pi$
$653$	7.50000	−	12.9904i	0.293498	−	0.508353i	0.974634	+	0.223803i	$0.0718474\pi$
$654$		0			0
$655$	−6.50000	−	11.2583i	−0.253976	−	0.439899i
$656$		0			0
$657$	2.00000			0.0780274
$658$		0			0
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$		0			0
$661$	8.00000	+	13.8564i	0.311164	+	0.538952i	0.978615	−	0.205702i	$-0.0659478\pi$
$661$	8.00000	+	13.8564i	0.311164	+	0.538952i	−0.667451	+	0.744654i	$0.732615\pi$
$662$		0			0
$663$	−14.0000	+	24.2487i	−0.543715	+	0.941742i
$664$		0			0
$665$	0.500000	−	2.59808i	0.0193892	−	0.100749i
$666$		0			0
$667$	6.00000	−	10.3923i	0.232321	−	0.402392i
$668$		0			0
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$		0			0
$671$	−8.00000			−0.308837
$672$		0			0
$673$	38.0000			1.46479			0.732396	−	0.680879i	$-0.238402\pi$
$673$	38.0000			1.46479			0.732396	+	0.680879i	$0.238402\pi$
$674$		0			0
$675$	8.00000	+	13.8564i	0.307920	+	0.533333i
$676$		0			0
$677$	2.00000	−	3.46410i	0.0768662	−	0.133136i	−0.825030	−	0.565089i	$-0.808842\pi$
$677$	2.00000	−	3.46410i	0.0768662	−	0.133136i	0.901896	+	0.431953i	$0.142175\pi$
$678$		0			0
$679$	−8.00000	−	6.92820i	−0.307012	−	0.265880i
$680$		0			0
$681$	12.0000	−	20.7846i	0.459841	−	0.796468i
$682$		0			0
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	0.825222	−	0.564809i	$-0.191050\pi$
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	−0.901750	+	0.432259i	$0.857717\pi$
$684$		0			0
$685$	−18.0000			−0.687745
$686$		0			0
$687$	46.0000			1.75501
$688$		0			0
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	−11.5000	+	19.9186i	−0.437481	+	0.757739i	−0.997494	−	0.0707446i	$-0.977462\pi$
$691$	−11.5000	+	19.9186i	−0.437481	+	0.757739i	0.560014	+	0.828483i	$0.310796\pi$
$692$		0			0
$693$	8.00000	+	6.92820i	0.303895	+	0.263181i
$694$		0			0
$695$	−8.00000	+	13.8564i	−0.303457	+	0.525603i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−54.0000			−2.04247
$700$		0			0
$701$	17.0000			0.642081			0.321041	−	0.947065i	$-0.395967\pi$
$701$	17.0000			0.642081			0.321041	+	0.947065i	$0.395967\pi$
$702$		0			0
$703$	5.00000	+	8.66025i	0.188579	+	0.326628i
$704$		0			0
$705$	4.00000	−	6.92820i	0.150649	−	0.260931i
$706$		0			0
$707$	−1.50000	+	7.79423i	−0.0564133	+	0.293132i
$708$		0			0
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	−0.980326	−	0.197383i	$-0.936756\pi$
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	0.661102	+	0.750296i	$0.270089\pi$
$710$		0			0
$711$	−2.00000	−	3.46410i	−0.0750059	−	0.129914i
$712$		0			0
$713$	−12.0000			−0.449404
$714$		0			0
$715$	−8.00000			−0.299183
$716$		0			0
$717$	1.00000	+	1.73205i	0.0373457	+	0.0646846i
$718$		0			0
$719$	−24.5000	+	42.4352i	−0.913696	+	1.58257i	−0.104896	+	0.994483i	$0.533451\pi$
$719$	−24.5000	+	42.4352i	−0.913696	+	1.58257i	−0.808800	+	0.588084i	$0.799882\pi$
$720$		0			0
$721$	−25.0000	+	8.66025i	−0.931049	+	0.322525i
$722$		0			0
$723$	8.00000	−	13.8564i	0.297523	−	0.515325i
$724$		0			0
$725$	8.00000	+	13.8564i	0.297113	+	0.514614i
$726$		0			0
$727$	1.00000			0.0370879			0.0185440	−	0.999828i	$-0.494097\pi$
$727$	1.00000			0.0370879			0.0185440	+	0.999828i	$0.494097\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−31.5000	−	54.5596i	−1.16507	−	2.01796i
$732$		0			0
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	−0.707303	−	0.706910i	$-0.750088\pi$
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	0.965854	+	0.259087i	$0.0834217\pi$
$734$		0			0
$735$	2.00000	+	13.8564i	0.0737711	+	0.511101i
$736$		0			0
$737$	−32.0000	+	55.4256i	−1.17874	+	2.04163i
$738$		0			0
$739$	−4.50000	−	7.79423i	−0.165535	−	0.286715i	0.771310	−	0.636460i	$-0.219602\pi$
$739$	−4.50000	−	7.79423i	−0.165535	−	0.286715i	−0.936845	+	0.349744i	$0.886268\pi$
$740$		0			0
$741$	4.00000			0.146944
$742$		0			0
$743$	−8.00000			−0.293492			−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000			−0.293492			−0.146746	+	0.989174i	$0.546880\pi$
$744$		0			0
$745$	2.50000	+	4.33013i	0.0915929	+	0.158644i
$746$		0			0
$747$	4.50000	−	7.79423i	0.164646	−	0.285176i
$748$		0			0
$749$	20.0000	−	6.92820i	0.730784	−	0.253151i
$750$		0			0
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	−0.735542	−	0.677479i	$-0.763072\pi$
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	0.954485	+	0.298259i	$0.0964058\pi$
$752$		0			0
$753$	−31.0000	−	53.6936i	−1.12970	−	1.95670i
$754$		0			0
$755$	20.0000			0.727875
$756$		0			0
$757$	−46.0000			−1.67190			−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000			−1.67190			−0.835949	+	0.548807i	$0.815082\pi$
$758$		0			0
$759$	−12.0000	−	20.7846i	−0.435572	−	0.754434i
$760$		0			0
$761$	−18.5000	+	32.0429i	−0.670624	+	1.16156i	0.307103	+	0.951676i	$0.400640\pi$
$761$	−18.5000	+	32.0429i	−0.670624	+	1.16156i	−0.977727	+	0.209879i	$0.932693\pi$
$762$		0			0
$763$	−7.00000	+	36.3731i	−0.253417	+	1.31679i
$764$		0			0
$765$	−3.50000	+	6.06218i	−0.126543	+	0.219179i
$766$		0			0
$767$	12.0000	+	20.7846i	0.433295	+	0.750489i
$768$		0			0
$769$	39.0000			1.40638			0.703188	−	0.711004i	$-0.251759\pi$
$769$	39.0000			1.40638			0.703188	+	0.711004i	$0.251759\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$		0			0
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	0.998930	+	0.0462427i	$0.0147248\pi$
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	−0.459418	+	0.888220i	$0.651942\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$		0			0
$777$	−40.0000	−	34.6410i	−1.43499	−	1.24274i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−12.0000	−	20.7846i	−0.429394	−	0.743732i
$782$		0			0
$783$	16.0000			0.571793
$784$		0			0
$785$	−25.0000			−0.892288
$786$		0			0
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	0.600620	−	0.799535i	$-0.294921\pi$
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	−0.992727	+	0.120384i	$0.961587\pi$
$788$		0			0
$789$	3.00000	−	5.19615i	0.106803	−	0.184988i
$790$		0			0
$791$	−20.0000	−	17.3205i	−0.711118	−	0.615846i
$792$		0			0
$793$	2.00000	−	3.46410i	0.0710221	−	0.123014i
$794$		0			0
$795$	−6.00000	−	10.3923i	−0.212798	−	0.368577i
$796$		0			0
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		0			0
$799$	28.0000			0.990569
$800$		0			0
$801$	2.00000	+	3.46410i	0.0706665	+	0.122398i
$802$		0			0
$803$	−4.00000	+	6.92820i	−0.141157	+	0.244491i
$804$		0			0
$805$	1.50000	−	7.79423i	0.0528681	−	0.274710i
$806$		0			0
$807$	18.0000	−	31.1769i	0.633630	−	1.09748i
$808$		0			0
$809$	12.5000	+	21.6506i	0.439477	+	0.761196i	0.997649	−	0.0685291i	$-0.0218306\pi$
$809$	12.5000	+	21.6506i	0.439477	+	0.761196i	−0.558173	+	0.829725i	$0.688497\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	−14.0000			−0.491001
$814$		0			0
$815$	−5.50000	−	9.52628i	−0.192657	−	0.333691i
$816$		0			0
$817$	−4.50000	+	7.79423i	−0.157435	+	0.272686i
$818$		0			0
$819$	−5.00000	+	1.73205i	−0.174714	+	0.0605228i
$820$		0			0
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	−0.765487	−	0.643451i	$-0.777502\pi$
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	0.939989	+	0.341206i	$0.110835\pi$
$822$		0			0
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	0.829060	−	0.559159i	$-0.188876\pi$
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	−0.898776	+	0.438408i	$0.855543\pi$
$824$		0			0
$825$	32.0000			1.11410
$826$		0			0
$827$	6.00000			0.208640			0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000			0.208640			0.104320	+	0.994544i	$0.466733\pi$
$828$		0			0
$829$	−14.0000	−	24.2487i	−0.486240	−	0.842193i	0.513635	−	0.858009i	$-0.328299\pi$
$829$	−14.0000	−	24.2487i	−0.486240	−	0.842193i	−0.999875	+	0.0158163i	$0.994965\pi$
$830$		0			0
$831$	22.0000	−	38.1051i	0.763172	−	1.32185i
$832$		0			0
$833$	−38.5000	+	30.3109i	−1.33395	+	1.05021i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.00000	−	13.8564i	−0.276520	−	0.478947i
$838$		0			0
$839$	6.00000			0.207143			0.103572	−	0.994622i	$-0.466973\pi$
$839$	6.00000			0.207143			0.103572	+	0.994622i	$0.466973\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$	22.0000	+	38.1051i	0.757720	+	1.31241i
$844$		0			0
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$	−12.5000	+	4.33013i	−0.429505	+	0.148785i
$848$		0			0
$849$	23.0000	−	39.8372i	0.789358	−	1.36721i
$850$		0			0
$851$	15.0000	+	25.9808i	0.514193	+	0.890609i
$852$		0			0
$853$	43.0000			1.47229			0.736146	−	0.676823i	$-0.236644\pi$
$853$	43.0000			1.47229			0.736146	+	0.676823i	$0.236644\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$		0			0
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	−17.5000	+	30.3109i	−0.597092	+	1.03419i	0.396156	+	0.918183i	$0.370344\pi$
$859$	−17.5000	+	30.3109i	−0.597092	+	1.03419i	−0.993248	+	0.116011i	$0.962989\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.0000	+	27.7128i	−0.544646	+	0.943355i	0.453983	+	0.891010i	$0.350003\pi$
$863$	−16.0000	+	27.7128i	−0.544646	+	0.943355i	−0.998629	+	0.0523446i	$0.983331\pi$
$864$		0			0
$865$	−3.00000	−	5.19615i	−0.102003	−	0.176674i
$866$		0			0
$867$	−64.0000			−2.17355
$868$		0			0
$869$	16.0000			0.542763
$870$		0			0
$871$	−16.0000	−	27.7128i	−0.542139	−	0.939013i
$872$		0			0
$873$	2.00000	−	3.46410i	0.0676897	−	0.117242i
$874$		0			0
$875$	18.0000	+	15.5885i	0.608511	+	0.526986i
$876$		0			0
$877$	−2.00000	+	3.46410i	−0.0675352	+	0.116974i	−0.897816	−	0.440371i	$-0.854847\pi$
$877$	−2.00000	+	3.46410i	−0.0675352	+	0.116974i	0.830281	+	0.557346i	$0.188180\pi$
$878$		0			0
$879$	−4.00000	−	6.92820i	−0.134917	−	0.233682i
$880$		0			0
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$		0			0
$883$	−27.0000			−0.908622			−0.454311	−	0.890843i	$-0.650115\pi$
$883$	−27.0000			−0.908622			−0.454311	+	0.890843i	$0.650115\pi$
$884$		0			0
$885$	12.0000	+	20.7846i	0.403376	+	0.698667i
$886$		0			0
$887$	5.00000	−	8.66025i	0.167884	−	0.290783i	−0.769792	−	0.638295i	$-0.779640\pi$
$887$	5.00000	−	8.66025i	0.167884	−	0.290783i	0.937676	+	0.347512i	$0.112973\pi$
$888$		0			0
$889$	4.00000	+	3.46410i	0.134156	+	0.116182i
$890$		0			0
$891$	22.0000	−	38.1051i	0.737028	−	1.27657i
$892$		0			0
$893$	−2.00000	−	3.46410i	−0.0669274	−	0.115922i
$894$		0			0
$895$	−14.0000			−0.467968
$896$		0			0
$897$	12.0000			0.400668
$898$		0			0
$899$	−8.00000	−	13.8564i	−0.266815	−	0.462137i
$900$		0			0
$901$	21.0000	−	36.3731i	0.699611	−	1.21176i
$902$		0			0
$903$	9.00000	−	46.7654i	0.299501	−	1.55625i
$904$		0			0
$905$	11.0000	−	19.0526i	0.365652	−	0.633328i
$906$		0			0
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$		0			0
$909$	−3.00000			−0.0995037
$910$		0			0
$911$	−58.0000			−1.92163			−0.960813	−	0.277198i	$-0.910594\pi$
$911$	−58.0000			−1.92163			−0.960813	+	0.277198i	$0.910594\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$		0			0
$915$	2.00000	−	3.46410i	0.0661180	−	0.114520i
$916$		0			0
$917$	32.5000	−	11.2583i	1.07324	−	0.371783i
$918$		0			0
$919$	6.50000	−	11.2583i	0.214415	−	0.371378i	−0.738676	−	0.674060i	$-0.764549\pi$
$919$	6.50000	−	11.2583i	0.214415	−	0.371378i	0.953092	+	0.302682i	$0.0978821\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$		0			0
$923$	12.0000			0.394985
$924$		0			0
$925$	−40.0000			−1.31519
$926$		0			0
$927$	−5.00000	−	8.66025i	−0.164222	−	0.284440i
$928$		0			0
$929$	0.500000	−	0.866025i	0.0164045	−	0.0284134i	−0.857707	−	0.514139i	$-0.828111\pi$
$929$	0.500000	−	0.866025i	0.0164045	−	0.0284134i	0.874111	+	0.485726i	$0.161445\pi$
$930$		0			0
$931$	6.50000	+	2.59808i	0.213029	+	0.0851485i
$932$		0			0
$933$	−9.00000	+	15.5885i	−0.294647	+	0.510343i
$934$		0			0
$935$	−14.0000	−	24.2487i	−0.457849	−	0.793018i
$936$		0			0
$937$	−23.0000			−0.751377			−0.375689	−	0.926746i	$-0.622594\pi$
$937$	−23.0000			−0.751377			−0.375689	+	0.926746i	$0.622594\pi$
$938$		0			0
$939$	−22.0000			−0.717943
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	10.0000	−	3.46410i	0.325300	−	0.112687i
$946$		0			0
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	−0.409964	−	0.912102i	$-0.634459\pi$
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	0.994885	−	0.101012i	$-0.0322080\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$		0			0
$951$	−24.0000			−0.778253
$952$		0			0
$953$	−50.0000			−1.61966			−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000			−1.61966			−0.809829	+	0.586665i	$0.800440\pi$
$954$		0			0
$955$	−6.50000	−	11.2583i	−0.210335	−	0.364311i
$956$		0			0
$957$	16.0000	−	27.7128i	0.517207	−	0.895828i
$958$		0			0
$959$	9.00000	−	46.7654i	0.290625	−	1.51013i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	4.00000	+	6.92820i	0.128898	+	0.223258i
$964$		0			0
$965$	−10.0000			−0.321911
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$		0			0
$969$	7.00000	+	12.1244i	0.224872	+	0.389490i
$970$		0			0
$971$	4.00000	−	6.92820i	0.128366	−	0.222337i	−0.794678	−	0.607032i	$-0.792360\pi$
$971$	4.00000	−	6.92820i	0.128366	−	0.222337i	0.923044	+	0.384695i	$0.125693\pi$
$972$		0			0
$973$	−32.0000	−	27.7128i	−1.02587	−	0.888432i
$974$		0			0
$975$	−8.00000	+	13.8564i	−0.256205	+	0.443760i
$976$		0			0
$977$	−14.0000	−	24.2487i	−0.447900	−	0.775785i	0.550349	−	0.834934i	$-0.314494\pi$
$977$	−14.0000	−	24.2487i	−0.447900	−	0.775785i	−0.998249	+	0.0591494i	$0.981161\pi$
$978$		0			0
$979$	−16.0000			−0.511362
$980$		0			0
$981$	−14.0000			−0.446986
$982$		0			0
$983$	−11.0000	−	19.0526i	−0.350846	−	0.607682i	0.635552	−	0.772058i	$-0.280772\pi$
$983$	−11.0000	−	19.0526i	−0.350846	−	0.607682i	−0.986398	+	0.164376i	$0.947439\pi$
$984$		0			0
$985$	11.5000	−	19.9186i	0.366420	−	0.634659i
$986$		0			0
$987$	16.0000	+	13.8564i	0.509286	+	0.441054i
$988$		0			0
$989$	−13.5000	+	23.3827i	−0.429275	+	0.743526i
$990$		0			0
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$		0			0
$993$	−36.0000			−1.14243
$994$		0			0
$995$	−11.0000			−0.348723
$996$		0			0
$997$	9.50000	+	16.4545i	0.300868	+	0.521119i	0.976333	−	0.216274i	$-0.0693903\pi$
$997$	9.50000	+	16.4545i	0.300868	+	0.521119i	−0.675465	+	0.737392i	$0.736057\pi$
$998$		0			0
$999$	−20.0000	+	34.6410i	−0.632772	+	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.j.457.1	yes	2
7.2	even	3		7448.2.a.c.1.1		1
7.4	even	3	inner	1064.2.q.j.305.1	✓	2
7.5	odd	6		7448.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.j.305.1	✓	2	7.4	even	3	inner
1064.2.q.j.457.1	yes	2	1.1	even	1	trivial
7448.2.a.c.1.1		1	7.2	even	3
7448.2.a.v.1.1		1	7.5	odd	6

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:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 - 3.46410i) q^{11} +2.00000 q^{13} +2.00000 q^{15} +(3.50000 + 6.06218i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-1.00000 + 5.19615i) q^{21} +(1.50000 - 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} +4.00000 q^{27} +4.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(4.00000 - 6.92820i) q^{33} +(2.50000 - 0.866025i) q^{35} +(-5.00000 + 8.66025i) q^{37} +(2.00000 + 3.46410i) q^{39} -9.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(2.00000 - 3.46410i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-7.00000 + 12.1244i) q^{51} +(-3.00000 - 5.19615i) q^{53} -4.00000 q^{55} +2.00000 q^{57} +(6.00000 + 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(1.00000 - 1.73205i) q^{65} +(-8.00000 - 13.8564i) q^{67} +6.00000 q^{69} +6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{75} +(2.00000 - 10.3923i) q^{77} +(-2.00000 + 3.46410i) q^{79} +(5.50000 + 9.52628i) q^{81} -9.00000 q^{83} +7.00000 q^{85} +(4.00000 + 6.92820i) q^{87} +(2.00000 - 3.46410i) q^{89} +(4.00000 + 3.46410i) q^{91} +(4.00000 - 6.92820i) q^{93} +(-0.500000 - 0.866025i) q^{95} -4.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + q^{5} + 4 q^{7} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + q^5 + 4 * q^7 - q^9	\( 2 q + 2 q^{3} + q^{5} + 4 q^{7} - q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{15} + 7 q^{17} + q^{19} - 2 q^{21} + 3 q^{23} + 4 q^{25} + 8 q^{27} + 8 q^{29} - 4 q^{31} + 8 q^{33} + 5 q^{35} - 10 q^{37} + 4 q^{39} - 18 q^{43} + q^{45} + 4 q^{47} + 2 q^{49} - 14 q^{51} - 6 q^{53} - 8 q^{55} + 4 q^{57} + 12 q^{59} + 2 q^{61} - 5 q^{63} + 2 q^{65} - 16 q^{67} + 12 q^{69} + 12 q^{71} - 2 q^{73} - 8 q^{75} + 4 q^{77} - 4 q^{79} + 11 q^{81} - 18 q^{83} + 14 q^{85} + 8 q^{87} + 4 q^{89} + 8 q^{91} + 8 q^{93} - q^{95} - 8 q^{97} + 8 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + q^5 + 4 * q^7 - q^9 - 4 * q^11 + 4 * q^13 + 4 * q^15 + 7 * q^17 + q^19 - 2 * q^21 + 3 * q^23 + 4 * q^25 + 8 * q^27 + 8 * q^29 - 4 * q^31 + 8 * q^33 + 5 * q^35 - 10 * q^37 + 4 * q^39 - 18 * q^43 + q^45 + 4 * q^47 + 2 * q^49 - 14 * q^51 - 6 * q^53 - 8 * q^55 + 4 * q^57 + 12 * q^59 + 2 * q^61 - 5 * q^63 + 2 * q^65 - 16 * q^67 + 12 * q^69 + 12 * q^71 - 2 * q^73 - 8 * q^75 + 4 * q^77 - 4 * q^79 + 11 * q^81 - 18 * q^83 + 14 * q^85 + 8 * q^87 + 4 * q^89 + 8 * q^91 + 8 * q^93 - q^95 - 8 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more