LMFDB - Embedded newform 252.2.i.a.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.i (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:	$2.01223013094$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.121
Dual form			252.2.i.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-2.00000 + 3.46410i) q^{11} +(-1.50000 + 2.59808i) q^{13} +3.46410i q^{15} +(-3.50000 - 6.06218i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(4.50000 + 0.866025i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{29} -3.00000 q^{31} +(6.00000 - 3.46410i) q^{33} +(4.00000 + 3.46410i) q^{35} +(-5.50000 + 9.52628i) q^{37} +(4.50000 - 2.59808i) q^{39} +(4.50000 - 7.79423i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(3.00000 - 5.19615i) q^{45} +3.00000 q^{47} +(5.50000 - 4.33013i) q^{49} +12.1244i q^{51} +(-1.50000 - 2.59808i) q^{53} +8.00000 q^{55} +(7.50000 - 4.33013i) q^{57} -7.00000 q^{59} +3.00000 q^{61} +(-6.00000 - 5.19615i) q^{63} +6.00000 q^{65} +13.0000 q^{67} +6.92820i q^{69} -8.00000 q^{71} +(-3.50000 - 6.06218i) q^{73} +(-1.50000 + 0.866025i) q^{75} +(2.00000 - 10.3923i) q^{77} -9.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} +(-0.500000 - 0.866025i) q^{83} +(-7.00000 + 12.1244i) q^{85} -1.73205i q^{87} +(-7.50000 + 12.9904i) q^{89} +(1.50000 - 7.79423i) q^{91} +(4.50000 + 2.59808i) q^{93} +10.0000 q^{95} +(8.50000 + 14.7224i) q^{97} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} - 2 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 - 2 * q^5 - 5 * q^7 + 3 * q^9	$ 2 q - 3 q^{3} - 2 q^{5} - 5 q^{7} + 3 q^{9} - 4 q^{11} - 3 q^{13} - 7 q^{17} - 5 q^{19} + 9 q^{21} - 4 q^{23} + q^{25} + q^{29} - 6 q^{31} + 12 q^{33} + 8 q^{35} - 11 q^{37} + 9 q^{39} + 9 q^{41} - 5 q^{43} + 6 q^{45} + 6 q^{47} + 11 q^{49} - 3 q^{53} + 16 q^{55} + 15 q^{57} - 14 q^{59} + 6 q^{61} - 12 q^{63} + 12 q^{65} + 26 q^{67} - 16 q^{71} - 7 q^{73} - 3 q^{75} + 4 q^{77} - 18 q^{79} - 9 q^{81} - q^{83} - 14 q^{85} - 15 q^{89} + 3 q^{91} + 9 q^{93} + 20 q^{95} + 17 q^{97} - 24 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 - 2 * q^5 - 5 * q^7 + 3 * q^9 - 4 * q^11 - 3 * q^13 - 7 * q^17 - 5 * q^19 + 9 * q^21 - 4 * q^23 + q^25 + q^29 - 6 * q^31 + 12 * q^33 + 8 * q^35 - 11 * q^37 + 9 * q^39 + 9 * q^41 - 5 * q^43 + 6 * q^45 + 6 * q^47 + 11 * q^49 - 3 * q^53 + 16 * q^55 + 15 * q^57 - 14 * q^59 + 6 * q^61 - 12 * q^63 + 12 * q^65 + 26 * q^67 - 16 * q^71 - 7 * q^73 - 3 * q^75 + 4 * q^77 - 18 * q^79 - 9 * q^81 - q^83 - 14 * q^85 - 15 * q^89 + 3 * q^91 + 9 * q^93 + 20 * q^95 + 17 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$		0			0
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	−0.995535	−	0.0943882i	$-0.969911\pi$
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	0.579510	+	0.814965i	$0.303244\pi$
$14$		0			0
$15$			3.46410i			0.894427i
$16$		0			0
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	−0.882213	−	0.470850i	$-0.843947\pi$
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	0.0333386	−	0.999444i	$-0.489386\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$	4.50000	+	0.866025i	0.981981	+	0.188982i
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		0			0
$31$	−3.00000			−0.538816			−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000			−0.538816			−0.269408	+	0.963026i	$0.586828\pi$
$32$		0			0
$33$	6.00000	−	3.46410i	1.04447	−	0.603023i
$34$		0			0
$35$	4.00000	+	3.46410i	0.676123	+	0.585540i
$36$		0			0
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.0821995	+	0.996616i	$0.526194\pi$
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	4.50000	−	2.59808i	0.720577	−	0.416025i
$40$		0			0
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$		0			0
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	0.609994	−	0.792406i	$-0.291172\pi$
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$	3.00000	−	5.19615i	0.447214	−	0.774597i
$46$		0			0
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$			12.1244i			1.69775i
$52$		0			0
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$		0			0
$57$	7.50000	−	4.33013i	0.993399	−	0.573539i
$58$		0			0
$59$	−7.00000			−0.911322			−0.455661	−	0.890153i	$-0.650597\pi$
$59$	−7.00000			−0.911322			−0.455661	+	0.890153i	$0.650597\pi$
$60$		0			0
$61$	3.00000			0.384111			0.192055	−	0.981384i	$-0.438485\pi$
$61$	3.00000			0.384111			0.192055	+	0.981384i	$0.438485\pi$
$62$		0			0
$63$	−6.00000	−	5.19615i	−0.755929	−	0.654654i
$64$		0			0
$65$	6.00000			0.744208
$66$		0			0
$67$	13.0000			1.58820			0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000			1.58820			0.794101	+	0.607785i	$0.207942\pi$
$68$		0			0
$69$			6.92820i			0.834058i
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$	−1.50000	+	0.866025i	−0.173205	+	0.100000i
$76$		0			0
$77$	2.00000	−	10.3923i	0.227921	−	1.18431i
$78$		0			0
$79$	−9.00000			−1.01258			−0.506290	−	0.862364i	$-0.668983\pi$
$79$	−9.00000			−1.01258			−0.506290	+	0.862364i	$0.668983\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−0.500000	−	0.866025i	−0.0548821	−	0.0950586i	0.837279	−	0.546776i	$-0.184145\pi$
$83$	−0.500000	−	0.866025i	−0.0548821	−	0.0950586i	−0.892161	+	0.451717i	$0.850812\pi$
$84$		0			0
$85$	−7.00000	+	12.1244i	−0.759257	+	1.31507i
$86$		0			0
$87$		−	1.73205i		−	0.185695i
$88$		0			0
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	0.127842	+	0.991795i	$0.459195\pi$
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	−0.922840	+	0.385183i	$0.874138\pi$
$90$		0			0
$91$	1.50000	−	7.79423i	0.157243	−	0.817057i
$92$		0			0
$93$	4.50000	+	2.59808i	0.466628	+	0.269408i
$94$		0			0
$95$	10.0000			1.02598
$96$		0			0
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	0.868976	+	0.494854i	$0.164778\pi$
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	−0.00593185	+	0.999982i	$0.501888\pi$
$98$		0			0
$99$	−12.0000			−1.20605
$100$		0			0
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$	−3.00000	−	8.66025i	−0.292770	−	0.845154i
$106$		0			0
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	−0.784366	−	0.620298i	$-0.787012\pi$
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	0.929377	+	0.369132i	$0.120345\pi$
$108$		0			0
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	0.648292	−	0.761392i	$-0.275484\pi$
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	−0.983531	+	0.180741i	$0.942150\pi$
$110$		0			0
$111$	16.5000	−	9.52628i	1.56611	−	0.904194i
$112$		0			0
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	−0.841549	−	0.540181i	$-0.818356\pi$
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	0.888585	+	0.458712i	$0.151689\pi$
$114$		0			0
$115$	−4.00000	+	6.92820i	−0.373002	+	0.646058i
$116$		0			0
$117$	−9.00000			−0.832050
$118$		0			0
$119$	14.0000	+	12.1244i	1.28338	+	1.11144i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$	−13.5000	+	7.79423i	−1.21725	+	0.702782i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$			8.66025i			0.762493i
$130$		0			0
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$		0			0
$133$	2.50000	−	12.9904i	0.216777	−	1.12641i
$134$		0			0
$135$	−9.00000	+	5.19615i	−0.774597	+	0.447214i
$136$		0			0
$137$	−7.00000	+	12.1244i	−0.598050	+	1.03585i	0.395058	+	0.918656i	$0.370724\pi$
$137$	−7.00000	+	12.1244i	−0.598050	+	1.03585i	−0.993109	+	0.117198i	$0.962609\pi$
$138$		0			0
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	−0.740308	−	0.672268i	$-0.765320\pi$
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	0.952355	+	0.304991i	$0.0986536\pi$
$140$		0			0
$141$	−4.50000	−	2.59808i	−0.378968	−	0.218797i
$142$		0			0
$143$	−6.00000	−	10.3923i	−0.501745	−	0.869048i
$144$		0			0
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$		0			0
$147$	−12.0000	+	1.73205i	−0.989743	+	0.142857i
$148$		0			0
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$		0			0
$153$	10.5000	−	18.1865i	0.848875	−	1.47029i
$154$		0			0
$155$	3.00000	+	5.19615i	0.240966	+	0.417365i
$156$		0			0
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$		0			0
$159$			5.19615i			0.412082i
$160$		0			0
$161$	8.00000	+	6.92820i	0.630488	+	0.546019i
$162$		0			0
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	−0.206518	−	0.978443i	$-0.566213\pi$
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	0.950615	−	0.310372i	$-0.100454\pi$
$164$		0			0
$165$	−12.0000	−	6.92820i	−0.934199	−	0.539360i
$166$		0			0
$167$	−11.5000	+	19.9186i	−0.889897	+	1.54135i	−0.0499004	+	0.998754i	$0.515890\pi$
$167$	−11.5000	+	19.9186i	−0.889897	+	1.54135i	−0.839996	+	0.542592i	$0.817443\pi$
$168$		0			0
$169$	2.00000	+	3.46410i	0.153846	+	0.266469i
$170$		0			0
$171$	−15.0000			−1.14708
$172$		0			0
$173$	−1.00000			−0.0760286			−0.0380143	−	0.999277i	$-0.512103\pi$
$173$	−1.00000			−0.0760286			−0.0380143	+	0.999277i	$0.512103\pi$
$174$		0			0
$175$	−0.500000	+	2.59808i	−0.0377964	+	0.196396i
$176$		0			0
$177$	10.5000	+	6.06218i	0.789228	+	0.455661i
$178$		0			0
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	0.929114	+	0.369792i	$0.120571\pi$
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	−0.144308	+	0.989533i	$0.546095\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		0			0
$183$	−4.50000	−	2.59808i	−0.332650	−	0.192055i
$184$		0			0
$185$	22.0000			1.61747
$186$		0			0
$187$	28.0000			2.04756
$188$		0			0
$189$	4.50000	+	12.9904i	0.327327	+	0.944911i
$190$		0			0
$191$	15.0000			1.08536			0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000			1.08536			0.542681	+	0.839939i	$0.317409\pi$
$192$		0			0
$193$	−1.00000			−0.0719816			−0.0359908	−	0.999352i	$-0.511459\pi$
$193$	−1.00000			−0.0719816			−0.0359908	+	0.999352i	$0.511459\pi$
$194$		0			0
$195$	−9.00000	−	5.19615i	−0.644503	−	0.372104i
$196$		0			0
$197$	−26.0000			−1.85242			−0.926212	−	0.377004i	$-0.876954\pi$
$197$	−26.0000			−1.85242			−0.926212	+	0.377004i	$0.876954\pi$
$198$		0			0
$199$	6.50000	+	11.2583i	0.460773	+	0.798082i	0.999000	−	0.0447181i	$-0.0142390\pi$
$199$	6.50000	+	11.2583i	0.460773	+	0.798082i	−0.538227	+	0.842800i	$0.680906\pi$
$200$		0			0
$201$	−19.5000	−	11.2583i	−1.37542	−	0.794101i
$202$		0			0
$203$	−2.00000	−	1.73205i	−0.140372	−	0.121566i
$204$		0			0
$205$	−18.0000			−1.25717
$206$		0			0
$207$	6.00000	−	10.3923i	0.417029	−	0.722315i
$208$		0			0
$209$	−10.0000	−	17.3205i	−0.691714	−	1.19808i
$210$		0			0
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	0.998221	+	0.0596196i	$0.0189888\pi$
$212$		0			0
$213$	12.0000	+	6.92820i	0.822226	+	0.474713i
$214$		0			0
$215$	−5.00000	+	8.66025i	−0.340997	+	0.590624i
$216$		0			0
$217$	7.50000	−	2.59808i	0.509133	−	0.176369i
$218$		0			0
$219$			12.1244i			0.819288i
$220$		0			0
$221$	21.0000			1.41261
$222$		0			0
$223$	3.50000	+	6.06218i	0.234377	+	0.405953i	0.959092	−	0.283096i	$-0.0913615\pi$
$223$	3.50000	+	6.06218i	0.234377	+	0.405953i	−0.724714	+	0.689050i	$0.758028\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$		0			0
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$		0			0
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$		0			0
$231$	−12.0000	+	13.8564i	−0.789542	+	0.911685i
$232$		0			0
$233$	14.5000	−	25.1147i	0.949927	−	1.64532i	0.204354	−	0.978897i	$-0.434491\pi$
$233$	14.5000	−	25.1147i	0.949927	−	1.64532i	0.745573	−	0.666424i	$-0.232176\pi$
$234$		0			0
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$		0			0
$237$	13.5000	+	7.79423i	0.876919	+	0.506290i
$238$		0			0
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	−0.296037	−	0.955176i	$-0.595665\pi$
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	0.975226	−	0.221213i	$-0.0710015\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$		0			0
$245$	−13.0000	−	5.19615i	−0.830540	−	0.331970i
$246$		0			0
$247$	−7.50000	−	12.9904i	−0.477214	−	0.826558i
$248$		0			0
$249$			1.73205i			0.109764i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	16.0000			1.00591
$254$		0			0
$255$	21.0000	−	12.1244i	1.31507	−	0.759257i
$256$		0			0
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$	5.50000	−	28.5788i	0.341753	−	1.77580i
$260$		0			0
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	−3.00000	+	5.19615i	−0.184289	+	0.319197i
$266$		0			0
$267$	22.5000	−	12.9904i	1.37698	−	0.794998i
$268$		0			0
$269$	0.500000	+	0.866025i	0.0304855	+	0.0528025i	0.880866	−	0.473366i	$-0.156961\pi$
$269$	0.500000	+	0.866025i	0.0304855	+	0.0528025i	−0.850380	+	0.526169i	$0.823628\pi$
$270$		0			0
$271$	1.50000	−	2.59808i	0.0911185	−	0.157822i	−0.816864	−	0.576831i	$-0.804289\pi$
$271$	1.50000	−	2.59808i	0.0911185	−	0.157822i	0.907982	+	0.419009i	$0.137622\pi$
$272$		0			0
$273$	−9.00000	+	10.3923i	−0.544705	+	0.628971i
$274$		0			0
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$		0			0
$279$	−4.50000	−	7.79423i	−0.269408	−	0.466628i
$280$		0			0
$281$	8.50000	+	14.7224i	0.507067	+	0.878267i	0.999967	+	0.00818015i	$0.00260385\pi$
$281$	8.50000	+	14.7224i	0.507067	+	0.878267i	−0.492899	+	0.870087i	$0.664063\pi$
$282$		0			0
$283$	1.00000			0.0594438			0.0297219	−	0.999558i	$-0.490538\pi$
$283$	1.00000			0.0594438			0.0297219	+	0.999558i	$0.490538\pi$
$284$		0			0
$285$	−15.0000	−	8.66025i	−0.888523	−	0.512989i
$286$		0			0
$287$	−4.50000	+	23.3827i	−0.265627	+	1.38024i
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$		0			0
$291$		−	29.4449i		−	1.72609i
$292$		0			0
$293$	−13.5000	+	23.3827i	−0.788678	+	1.36603i	0.138098	+	0.990419i	$0.455901\pi$
$293$	−13.5000	+	23.3827i	−0.788678	+	1.36603i	−0.926777	+	0.375613i	$0.877432\pi$
$294$		0			0
$295$	7.00000	+	12.1244i	0.407556	+	0.705907i
$296$		0			0
$297$	18.0000	+	10.3923i	1.04447	+	0.603023i
$298$		0			0
$299$	12.0000			0.693978
$300$		0			0
$301$	10.0000	+	8.66025i	0.576390	+	0.499169i
$302$		0			0
$303$	3.00000	−	1.73205i	0.172345	−	0.0995037i
$304$		0			0
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$			13.8564i			0.788263i
$310$		0			0
$311$	−31.0000			−1.75785			−0.878924	−	0.476961i	$-0.841738\pi$
$311$	−31.0000			−1.75785			−0.878924	+	0.476961i	$0.841738\pi$
$312$		0			0
$313$	−17.0000			−0.960897			−0.480448	−	0.877023i	$-0.659526\pi$
$313$	−17.0000			−0.960897			−0.480448	+	0.877023i	$0.659526\pi$
$314$		0			0
$315$	−3.00000	+	15.5885i	−0.169031	+	0.878310i
$316$		0			0
$317$	−9.00000			−0.505490			−0.252745	−	0.967533i	$-0.581333\pi$
$317$	−9.00000			−0.505490			−0.252745	+	0.967533i	$0.581333\pi$
$318$		0			0
$319$	−4.00000			−0.223957
$320$		0			0
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$		0			0
$323$	35.0000			1.94745
$324$		0			0
$325$	1.50000	+	2.59808i	0.0832050	+	0.144115i
$326$		0			0
$327$			12.1244i			0.670478i
$328$		0			0
$329$	−7.50000	+	2.59808i	−0.413488	+	0.143237i
$330$		0			0
$331$	−25.0000			−1.37412			−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000			−1.37412			−0.687062	+	0.726599i	$0.741100\pi$
$332$		0			0
$333$	−33.0000			−1.80839
$334$		0			0
$335$	−13.0000	−	22.5167i	−0.710266	−	1.23022i
$336$		0			0
$337$	−1.50000	+	2.59808i	−0.0817102	+	0.141526i	−0.903985	−	0.427565i	$-0.859372\pi$
$337$	−1.50000	+	2.59808i	−0.0817102	+	0.141526i	0.822274	+	0.569091i	$0.192705\pi$
$338$		0			0
$339$	−1.50000	+	0.866025i	−0.0814688	+	0.0470360i
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	12.0000	−	6.92820i	0.646058	−	0.373002i
$346$		0			0
$347$	−15.0000			−0.805242			−0.402621	−	0.915367i	$-0.631901\pi$
$347$	−15.0000			−0.805242			−0.402621	+	0.915367i	$0.631901\pi$
$348$		0			0
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$		0			0
$351$	13.5000	+	7.79423i	0.720577	+	0.416025i
$352$		0			0
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$		0			0
$355$	8.00000	+	13.8564i	0.424596	+	0.735422i
$356$		0			0
$357$	−10.5000	−	30.3109i	−0.555719	−	1.60422i
$358$		0			0
$359$	15.5000	−	26.8468i	0.818059	−	1.41692i	−0.0890519	−	0.996027i	$-0.528384\pi$
$359$	15.5000	−	26.8468i	0.818059	−	1.41692i	0.907111	−	0.420892i	$-0.138283\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$			8.66025i			0.454545i
$364$		0			0
$365$	−7.00000	+	12.1244i	−0.366397	+	0.634618i
$366$		0			0
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	0.0586798	+	0.998277i	$0.481311\pi$
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	−0.893873	+	0.448320i	$0.852022\pi$
$368$		0			0
$369$	27.0000			1.40556
$370$		0			0
$371$	6.00000	+	5.19615i	0.311504	+	0.269771i
$372$		0			0
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	−0.996610	−	0.0822766i	$-0.973781\pi$
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	0.427051	−	0.904227i	$-0.359552\pi$
$374$		0			0
$375$	18.0000	+	10.3923i	0.929516	+	0.536656i
$376$		0			0
$377$	−3.00000			−0.154508
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$		0			0
$385$	−20.0000	+	6.92820i	−1.01929	+	0.353094i
$386$		0			0
$387$	7.50000	−	12.9904i	0.381246	−	0.660338i
$388$		0			0
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	0.321716	+	0.946836i	$0.395740\pi$
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	−0.980842	+	0.194804i	$0.937593\pi$
$390$		0			0
$391$	−14.0000	+	24.2487i	−0.708010	+	1.22631i
$392$		0			0
$393$		−	6.92820i		−	0.349482i
$394$		0			0
$395$	9.00000	+	15.5885i	0.452839	+	0.784340i
$396$		0			0
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	−0.472526	−	0.881317i	$-0.656658\pi$
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	0.999506	−	0.0314391i	$-0.0100090\pi$
$398$		0			0
$399$	−15.0000	+	17.3205i	−0.750939	+	0.867110i
$400$		0			0
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$		0			0
$403$	4.50000	−	7.79423i	0.224161	−	0.388258i
$404$		0			0
$405$	18.0000			0.894427
$406$		0			0
$407$	−22.0000	−	38.1051i	−1.09050	−	1.88880i
$408$		0			0
$409$	23.0000			1.13728			0.568638	−	0.822588i	$-0.307470\pi$
$409$	23.0000			1.13728			0.568638	+	0.822588i	$0.307470\pi$
$410$		0			0
$411$	21.0000	−	12.1244i	1.03585	−	0.598050i
$412$		0			0
$413$	17.5000	−	6.06218i	0.861119	−	0.298300i
$414$		0			0
$415$	−1.00000	+	1.73205i	−0.0490881	+	0.0850230i
$416$		0			0
$417$	−7.50000	+	4.33013i	−0.367277	+	0.212047i
$418$		0			0
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	−0.989000	−	0.147918i	$-0.952743\pi$
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	0.622601	+	0.782540i	$0.286076\pi$
$420$		0			0
$421$	4.50000	+	7.79423i	0.219317	+	0.379867i	0.954599	−	0.297893i	$-0.0962839\pi$
$421$	4.50000	+	7.79423i	0.219317	+	0.379867i	−0.735283	+	0.677761i	$0.762951\pi$
$422$		0			0
$423$	4.50000	+	7.79423i	0.218797	+	0.378968i
$424$		0			0
$425$	−7.00000			−0.339550
$426$		0			0
$427$	−7.50000	+	2.59808i	−0.362950	+	0.125730i
$428$		0			0
$429$			20.7846i			1.00349i
$430$		0			0
$431$	−19.5000	−	33.7750i	−0.939282	−	1.62688i	−0.766814	−	0.641869i	$-0.778159\pi$
$431$	−19.5000	−	33.7750i	−0.939282	−	1.62688i	−0.172468	−	0.985015i	$-0.555174\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$	−3.00000	+	1.73205i	−0.143839	+	0.0830455i
$436$		0			0
$437$	20.0000			0.956730
$438$		0			0
$439$	−21.0000			−1.00228			−0.501138	−	0.865368i	$-0.667085\pi$
$439$	−21.0000			−1.00228			−0.501138	+	0.865368i	$0.667085\pi$
$440$		0			0
$441$	19.5000	+	7.79423i	0.928571	+	0.371154i
$442$		0			0
$443$	−29.0000			−1.37783			−0.688916	−	0.724841i	$-0.741913\pi$
$443$	−29.0000			−1.37783			−0.688916	+	0.724841i	$0.741913\pi$
$444$		0			0
$445$	30.0000			1.42214
$446$		0			0
$447$		−	10.3923i		−	0.491539i
$448$		0			0
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$		0			0
$451$	18.0000	+	31.1769i	0.847587	+	1.46806i
$452$		0			0
$453$	−12.0000	+	6.92820i	−0.563809	+	0.325515i
$454$		0			0
$455$	−15.0000	+	5.19615i	−0.703211	+	0.243599i
$456$		0			0
$457$	31.0000			1.45012			0.725059	−	0.688686i	$-0.241812\pi$
$457$	31.0000			1.45012			0.725059	+	0.688686i	$0.241812\pi$
$458$		0			0
$459$	−31.5000	+	18.1865i	−1.47029	+	0.848875i
$460$		0			0
$461$	−11.5000	−	19.9186i	−0.535608	−	0.927701i	−0.999134	−	0.0416172i	$-0.986749\pi$
$461$	−11.5000	−	19.9186i	−0.535608	−	0.927701i	0.463525	−	0.886084i	$-0.346584\pi$
$462$		0			0
$463$	2.50000	−	4.33013i	0.116185	−	0.201238i	−0.802068	−	0.597233i	$-0.796267\pi$
$463$	2.50000	−	4.33013i	0.116185	−	0.201238i	0.918253	+	0.395995i	$0.129600\pi$
$464$		0			0
$465$		−	10.3923i		−	0.481932i
$466$		0			0
$467$	−8.50000	+	14.7224i	−0.393333	+	0.681273i	−0.992887	−	0.119062i	$-0.962011\pi$
$467$	−8.50000	+	14.7224i	−0.393333	+	0.681273i	0.599554	+	0.800334i	$0.295345\pi$
$468$		0			0
$469$	−32.5000	+	11.2583i	−1.50071	+	0.519861i
$470$		0			0
$471$	19.5000	+	11.2583i	0.898513	+	0.518756i
$472$		0			0
$473$	20.0000			0.919601
$474$		0			0
$475$	2.50000	+	4.33013i	0.114708	+	0.198680i
$476$		0			0
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$		0			0
$479$	4.00000	−	6.92820i	0.182765	−	0.316558i	−0.760056	−	0.649857i	$-0.774829\pi$
$479$	4.00000	−	6.92820i	0.182765	−	0.316558i	0.942821	+	0.333300i	$0.108162\pi$
$480$		0			0
$481$	−16.5000	−	28.5788i	−0.752335	−	1.30308i
$482$		0			0
$483$	−6.00000	−	17.3205i	−0.273009	−	0.788110i
$484$		0			0
$485$	17.0000	−	29.4449i	0.771930	−	1.33702i
$486$		0			0
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	0.877132	−	0.480250i	$-0.159454\pi$
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	−0.854475	+	0.519493i	$0.826121\pi$
$488$		0			0
$489$	−28.5000	+	16.4545i	−1.28881	+	0.744097i
$490$		0			0
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	−0.746438	−	0.665455i	$-0.768237\pi$
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	0.949520	+	0.313707i	$0.101571\pi$
$492$		0			0
$493$	3.50000	−	6.06218i	0.157632	−	0.273027i
$494$		0			0
$495$	12.0000	+	20.7846i	0.539360	+	0.934199i
$496$		0			0
$497$	20.0000	−	6.92820i	0.897123	−	0.310772i
$498$		0			0
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$		0			0
$501$	34.5000	−	19.9186i	1.54135	−	0.889897i
$502$		0			0
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	4.00000			0.177998
$506$		0			0
$507$		−	6.92820i		−	0.307692i
$508$		0			0
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	14.0000	+	12.1244i	0.619324	+	0.536350i
$512$		0			0
$513$	22.5000	+	12.9904i	0.993399	+	0.573539i
$514$		0			0
$515$	−8.00000	+	13.8564i	−0.352522	+	0.610586i
$516$		0			0
$517$	−6.00000	+	10.3923i	−0.263880	+	0.457053i
$518$		0			0
$519$	1.50000	+	0.866025i	0.0658427	+	0.0380143i
$520$		0			0
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$		0			0
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$		0			0
$525$	3.00000	−	3.46410i	0.130931	−	0.151186i
$526$		0			0
$527$	10.5000	+	18.1865i	0.457387	+	0.792218i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	−10.5000	−	18.1865i	−0.455661	−	0.789228i
$532$		0			0
$533$	13.5000	+	23.3827i	0.584750	+	1.01282i
$534$		0			0
$535$	−6.00000			−0.259403
$536$		0			0
$537$		−	36.3731i		−	1.56961i
$538$		0			0
$539$	4.00000	+	27.7128i	0.172292	+	1.19368i
$540$		0			0
$541$	16.5000	−	28.5788i	0.709390	−	1.22870i	−0.255693	−	0.966758i	$-0.582304\pi$
$541$	16.5000	−	28.5788i	0.709390	−	1.22870i	0.965084	−	0.261942i	$-0.0843630\pi$
$542$		0			0
$543$	9.00000	+	5.19615i	0.386227	+	0.222988i
$544$		0			0
$545$	−7.00000	+	12.1244i	−0.299847	+	0.519350i
$546$		0			0
$547$	−16.5000	−	28.5788i	−0.705489	−	1.22194i	−0.966515	−	0.256611i	$-0.917394\pi$
$547$	−16.5000	−	28.5788i	−0.705489	−	1.22194i	0.261026	−	0.965332i	$-0.415939\pi$
$548$		0			0
$549$	4.50000	+	7.79423i	0.192055	+	0.332650i
$550$		0			0
$551$	−5.00000			−0.213007
$552$		0			0
$553$	22.5000	−	7.79423i	0.956797	−	0.331444i
$554$		0			0
$555$	−33.0000	−	19.0526i	−1.40077	−	0.808736i
$556$		0			0
$557$	−5.50000	−	9.52628i	−0.233042	−	0.403641i	0.725660	−	0.688054i	$-0.241535\pi$
$557$	−5.50000	−	9.52628i	−0.233042	−	0.403641i	−0.958702	+	0.284413i	$0.908201\pi$
$558$		0			0
$559$	15.0000			0.634432
$560$		0			0
$561$	−42.0000	−	24.2487i	−1.77324	−	1.02378i
$562$		0			0
$563$	13.0000			0.547885			0.273942	−	0.961746i	$-0.411672\pi$
$563$	13.0000			0.547885			0.273942	+	0.961746i	$0.411672\pi$
$564$		0			0
$565$	−2.00000			−0.0841406
$566$		0			0
$567$	4.50000	−	23.3827i	0.188982	−	0.981981i
$568$		0			0
$569$	27.0000			1.13190			0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000			1.13190			0.565949	+	0.824440i	$0.308510\pi$
$570$		0			0
$571$	−3.00000			−0.125546			−0.0627730	−	0.998028i	$-0.519994\pi$
$571$	−3.00000			−0.125546			−0.0627730	+	0.998028i	$0.519994\pi$
$572$		0			0
$573$	−22.5000	−	12.9904i	−0.939951	−	0.542681i
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	0.783930	−	0.620850i	$-0.213212\pi$
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	−0.929636	+	0.368478i	$0.879879\pi$
$578$		0			0
$579$	1.50000	+	0.866025i	0.0623379	+	0.0359908i
$580$		0			0
$581$	2.00000	+	1.73205i	0.0829740	+	0.0718576i
$582$		0			0
$583$	12.0000			0.496989
$584$		0			0
$585$	9.00000	+	15.5885i	0.372104	+	0.644503i
$586$		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
$589$	7.50000	−	12.9904i	0.309032	−	0.535259i
$590$		0			0
$591$	39.0000	+	22.5167i	1.60425	+	0.926212i
$592$		0			0
$593$	−13.5000	+	23.3827i	−0.554379	+	0.960212i	0.443573	+	0.896238i	$0.353711\pi$
$593$	−13.5000	+	23.3827i	−0.554379	+	0.960212i	−0.997952	+	0.0639736i	$0.979623\pi$
$594$		0			0
$595$	7.00000	−	36.3731i	0.286972	−	1.49115i
$596$		0			0
$597$		−	22.5167i		−	0.921546i
$598$		0			0
$599$	−3.00000			−0.122577			−0.0612883	−	0.998120i	$-0.519521\pi$
$599$	−3.00000			−0.122577			−0.0612883	+	0.998120i	$0.519521\pi$
$600$		0			0
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$		0			0
$603$	19.5000	+	33.7750i	0.794101	+	1.37542i
$604$		0			0
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		0			0
$607$	24.0000	+	41.5692i	0.974130	+	1.68724i	0.682777	+	0.730627i	$0.260772\pi$
$607$	24.0000	+	41.5692i	0.974130	+	1.68724i	0.291353	+	0.956616i	$0.405895\pi$
$608$		0			0
$609$	1.50000	+	4.33013i	0.0607831	+	0.175466i
$610$		0			0
$611$	−4.50000	+	7.79423i	−0.182051	+	0.315321i
$612$		0			0
$613$	4.50000	+	7.79423i	0.181753	+	0.314806i	0.942478	−	0.334269i	$-0.108489\pi$
$613$	4.50000	+	7.79423i	0.181753	+	0.314806i	−0.760724	+	0.649075i	$0.775156\pi$
$614$		0			0
$615$	27.0000	+	15.5885i	1.08875	+	0.628587i
$616$		0			0
$617$	−21.5000	+	37.2391i	−0.865557	+	1.49919i	0.000935233		1.00000i	$0.499702\pi$
$617$	−21.5000	+	37.2391i	−0.865557	+	1.49919i	−0.866493	+	0.499190i	$0.833631\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$		0			0
$621$	−18.0000	+	10.3923i	−0.722315	+	0.417029i
$622$		0			0
$623$	7.50000	−	38.9711i	0.300481	−	1.56135i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$		0			0
$627$			34.6410i			1.38343i
$628$		0			0
$629$	77.0000			3.07019
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	−19.5000	+	11.2583i	−0.775055	+	0.447478i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.00000	+	20.7846i	0.118864	+	0.823516i
$638$		0			0
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$		0			0
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	−0.845601	−	0.533816i	$-0.820758\pi$
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	0.885098	+	0.465404i	$0.154091\pi$
$642$		0			0
$643$	6.50000	−	11.2583i	0.256335	−	0.443985i	−0.708922	−	0.705287i	$-0.750818\pi$
$643$	6.50000	−	11.2583i	0.256335	−	0.443985i	0.965257	+	0.261301i	$0.0841516\pi$
$644$		0			0
$645$	15.0000	−	8.66025i	0.590624	−	0.340997i
$646$		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
$649$	14.0000	−	24.2487i	0.549548	−	0.951845i
$650$		0			0
$651$	−13.5000	−	2.59808i	−0.529107	−	0.101827i
$652$		0			0
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		0			0
$655$	4.00000	−	6.92820i	0.156293	−	0.270707i
$656$		0			0
$657$	10.5000	−	18.1865i	0.409644	−	0.709524i
$658$		0			0
$659$	−12.5000	−	21.6506i	−0.486931	−	0.843389i	0.512956	−	0.858415i	$-0.328550\pi$
$659$	−12.5000	−	21.6506i	−0.486931	−	0.843389i	−0.999887	+	0.0150258i	$0.995217\pi$
$660$		0			0
$661$	−17.0000			−0.661223			−0.330612	−	0.943767i	$-0.607255\pi$
$661$	−17.0000			−0.661223			−0.330612	+	0.943767i	$0.607255\pi$
$662$		0			0
$663$	−31.5000	−	18.1865i	−1.22336	−	0.706306i
$664$		0			0
$665$	−25.0000	+	8.66025i	−0.969458	+	0.335830i
$666$		0			0
$667$	2.00000	−	3.46410i	0.0774403	−	0.134131i
$668$		0			0
$669$		−	12.1244i		−	0.468755i
$670$		0			0
$671$	−6.00000	+	10.3923i	−0.231627	+	0.401190i
$672$		0			0
$673$	12.5000	+	21.6506i	0.481840	+	0.834571i	0.999783	−	0.0208444i	$-0.00663546\pi$
$673$	12.5000	+	21.6506i	0.481840	+	0.834571i	−0.517943	+	0.855415i	$0.673302\pi$
$674$		0			0
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$		0			0
$677$	27.0000			1.03769			0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000			1.03769			0.518847	+	0.854867i	$0.326361\pi$
$678$		0			0
$679$	−34.0000	−	29.4449i	−1.30480	−	1.12999i
$680$		0			0
$681$	−18.0000	+	10.3923i	−0.689761	+	0.398234i
$682$		0			0
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	0.993940	−	0.109926i	$-0.0350613\pi$
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	−0.592168	+	0.805814i	$0.701728\pi$
$684$		0			0
$685$	28.0000			1.06983
$686$		0			0
$687$		−	24.2487i		−	0.925146i
$688$		0			0
$689$	9.00000			0.342873
$690$		0			0
$691$	11.0000			0.418460			0.209230	−	0.977866i	$-0.432904\pi$
$691$	11.0000			0.418460			0.209230	+	0.977866i	$0.432904\pi$
$692$		0			0
$693$	30.0000	−	10.3923i	1.13961	−	0.394771i
$694$		0			0
$695$	−10.0000			−0.379322
$696$		0			0
$697$	−63.0000			−2.38630
$698$		0			0
$699$	−43.5000	+	25.1147i	−1.64532	+	0.949927i
$700$		0			0
$701$	−22.0000			−0.830929			−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000			−0.830929			−0.415464	+	0.909610i	$0.636381\pi$
$702$		0			0
$703$	−27.5000	−	47.6314i	−1.03718	−	1.79645i
$704$		0			0
$705$			10.3923i			0.391397i
$706$		0			0
$707$	1.00000	−	5.19615i	0.0376089	−	0.195421i
$708$		0			0
$709$	−25.0000			−0.938895			−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000			−0.938895			−0.469447	+	0.882960i	$0.655547\pi$
$710$		0			0
$711$	−13.5000	−	23.3827i	−0.506290	−	0.876919i
$712$		0			0
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$		0			0
$715$	−12.0000	+	20.7846i	−0.448775	+	0.777300i
$716$		0			0
$717$	−31.5000	+	18.1865i	−1.17639	+	0.679189i
$718$		0			0
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	−0.691608	−	0.722273i	$-0.743097\pi$
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	0.971311	+	0.237814i	$0.0764307\pi$
$720$		0			0
$721$	16.0000	+	13.8564i	0.595871	+	0.516040i
$722$		0			0
$723$	−15.0000	+	8.66025i	−0.557856	+	0.322078i
$724$		0			0
$725$	1.00000			0.0371391
$726$		0			0
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.860376	+	0.509661i	$0.170229\pi$
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.0111912	+	0.999937i	$0.496438\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−17.5000	+	30.3109i	−0.647261	+	1.12109i
$732$		0			0
$733$	−15.0000	−	25.9808i	−0.554038	−	0.959621i	−0.997978	−	0.0635649i	$-0.979753\pi$
$733$	−15.0000	−	25.9808i	−0.554038	−	0.959621i	0.443940	−	0.896056i	$-0.353580\pi$
$734$		0			0
$735$	15.0000	+	19.0526i	0.553283	+	0.702764i
$736$		0			0
$737$	−26.0000	+	45.0333i	−0.957722	+	1.65882i
$738$		0			0
$739$	10.5000	+	18.1865i	0.386249	+	0.669002i	0.991942	−	0.126696i	$-0.0404373\pi$
$739$	10.5000	+	18.1865i	0.386249	+	0.669002i	−0.605693	+	0.795699i	$0.707104\pi$
$740$		0			0
$741$			25.9808i			0.954427i
$742$		0			0
$743$	4.50000	−	7.79423i	0.165089	−	0.285943i	−0.771598	−	0.636111i	$-0.780542\pi$
$743$	4.50000	−	7.79423i	0.165089	−	0.285943i	0.936687	+	0.350168i	$0.113876\pi$
$744$		0			0
$745$	6.00000	−	10.3923i	0.219823	−	0.380745i
$746$		0			0
$747$	1.50000	−	2.59808i	0.0548821	−	0.0950586i
$748$		0			0
$749$	−1.50000	+	7.79423i	−0.0548088	+	0.284795i
$750$		0			0
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	0.997526	−	0.0702946i	$-0.0223939\pi$
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	−0.559640	+	0.828736i	$0.689061\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−16.0000			−0.582300
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$		0			0
$759$	−24.0000	−	13.8564i	−0.871145	−	0.502956i
$760$		0			0
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	0.883581	−	0.468278i	$-0.155125\pi$
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	−0.847331	+	0.531065i	$0.821792\pi$
$762$		0			0
$763$	14.0000	+	12.1244i	0.506834	+	0.438931i
$764$		0			0
$765$	−42.0000			−1.51851
$766$		0			0
$767$	10.5000	−	18.1865i	0.379133	−	0.656678i
$768$		0			0
$769$	2.50000	−	4.33013i	0.0901523	−	0.156148i	−0.817423	−	0.576038i	$-0.804598\pi$
$769$	2.50000	−	4.33013i	0.0901523	−	0.156148i	0.907575	+	0.419890i	$0.137931\pi$
$770$		0			0
$771$			31.1769i			1.12281i
$772$		0			0
$773$	−11.5000	−	19.9186i	−0.413626	−	0.716422i	0.581657	−	0.813434i	$-0.302405\pi$
$773$	−11.5000	−	19.9186i	−0.413626	−	0.716422i	−0.995283	+	0.0970125i	$0.969071\pi$
$774$		0			0
$775$	−1.50000	+	2.59808i	−0.0538816	+	0.0933257i
$776$		0			0
$777$	−33.0000	+	38.1051i	−1.18387	+	1.36701i
$778$		0			0
$779$	22.5000	+	38.9711i	0.806146	+	1.39629i
$780$		0			0
$781$	16.0000	−	27.7128i	0.572525	−	0.991642i
$782$		0			0
$783$	4.50000	−	2.59808i	0.160817	−	0.0928477i
$784$		0			0
$785$	13.0000	+	22.5167i	0.463990	+	0.803654i
$786$		0			0
$787$	21.0000			0.748569			0.374285	−	0.927314i	$-0.377888\pi$
$787$	21.0000			0.748569			0.374285	+	0.927314i	$0.377888\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.500000	+	2.59808i	−0.0177780	+	0.0923770i
$792$		0			0
$793$	−4.50000	+	7.79423i	−0.159800	+	0.276781i
$794$		0			0
$795$	9.00000	−	5.19615i	0.319197	−	0.184289i
$796$		0			0
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	−0.967737	−	0.251961i	$-0.918924\pi$
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	0.702074	+	0.712104i	$0.252258\pi$
$798$		0			0
$799$	−10.5000	−	18.1865i	−0.371463	−	0.643393i
$800$		0			0
$801$	−45.0000			−1.59000
$802$		0			0
$803$	28.0000			0.988099
$804$		0			0
$805$	4.00000	−	20.7846i	0.140981	−	0.732561i
$806$		0			0
$807$		−	1.73205i		−	0.0609711i
$808$		0			0
$809$	0.500000	+	0.866025i	0.0175791	+	0.0304478i	0.874681	−	0.484699i	$-0.161071\pi$
$809$	0.500000	+	0.866025i	0.0175791	+	0.0304478i	−0.857102	+	0.515147i	$0.827737\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	−4.50000	+	2.59808i	−0.157822	+	0.0911185i
$814$		0			0
$815$	−38.0000			−1.33108
$816$		0			0
$817$	25.0000			0.874639
$818$		0			0
$819$	22.5000	−	7.79423i	0.786214	−	0.272352i
$820$		0			0
$821$	−53.0000			−1.84971			−0.924856	−	0.380317i	$-0.875815\pi$
$821$	−53.0000			−1.84971			−0.924856	+	0.380317i	$0.875815\pi$
$822$		0			0
$823$	−23.0000			−0.801730			−0.400865	−	0.916137i	$-0.631290\pi$
$823$	−23.0000			−0.801730			−0.400865	+	0.916137i	$0.631290\pi$
$824$		0			0
$825$		−	6.92820i		−	0.241209i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−9.50000	−	16.4545i	−0.329949	−	0.571488i	0.652553	−	0.757743i	$-0.273698\pi$
$829$	−9.50000	−	16.4545i	−0.329949	−	0.571488i	−0.982501	+	0.186256i	$0.940365\pi$
$830$		0			0
$831$	3.00000	−	1.73205i	0.104069	−	0.0600842i
$832$		0			0
$833$	−45.5000	−	18.1865i	−1.57648	−	0.630126i
$834$		0			0
$835$	46.0000			1.59190
$836$		0			0
$837$			15.5885i			0.538816i
$838$		0			0
$839$	11.5000	+	19.9186i	0.397024	+	0.687666i	0.993357	−	0.115071i	$-0.0367096\pi$
$839$	11.5000	+	19.9186i	0.397024	+	0.687666i	−0.596333	+	0.802737i	$0.703376\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$		0			0
$843$		−	29.4449i		−	1.01413i
$844$		0			0
$845$	4.00000	−	6.92820i	0.137604	−	0.238337i
$846$		0			0
$847$	10.0000	+	8.66025i	0.343604	+	0.297570i
$848$		0			0
$849$	−1.50000	−	0.866025i	−0.0514799	−	0.0297219i
$850$		0			0
$851$	44.0000			1.50830
$852$		0			0
$853$	−17.5000	−	30.3109i	−0.599189	−	1.03783i	−0.992941	−	0.118609i	$-0.962157\pi$
$853$	−17.5000	−	30.3109i	−0.599189	−	1.03783i	0.393753	−	0.919216i	$-0.371177\pi$
$854$		0			0
$855$	15.0000	+	25.9808i	0.512989	+	0.888523i
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	−22.0000	−	38.1051i	−0.750630	−	1.30013i	−0.947518	−	0.319704i	$-0.896417\pi$
$859$	−22.0000	−	38.1051i	−0.750630	−	1.30013i	0.196887	−	0.980426i	$-0.436917\pi$
$860$		0			0
$861$	27.0000	−	31.1769i	0.920158	−	1.06251i
$862$		0			0
$863$	−20.5000	+	35.5070i	−0.697828	+	1.20867i	0.271390	+	0.962470i	$0.412517\pi$
$863$	−20.5000	+	35.5070i	−0.697828	+	1.20867i	−0.969218	+	0.246204i	$0.920817\pi$
$864$		0			0
$865$	1.00000	+	1.73205i	0.0340010	+	0.0588915i
$866$		0			0
$867$	48.0000	−	27.7128i	1.63017	−	0.941176i
$868$		0			0
$869$	18.0000	−	31.1769i	0.610608	−	1.05760i
$870$		0			0
$871$	−19.5000	+	33.7750i	−0.660732	+	1.14442i
$872$		0			0
$873$	−25.5000	+	44.1673i	−0.863044	+	1.49484i
$874$		0			0
$875$	30.0000	−	10.3923i	1.01419	−	0.351324i
$876$		0			0
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	0.985079	+	0.172102i	$0.0550559\pi$
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	−0.343495	+	0.939155i	$0.611611\pi$
$878$		0			0
$879$	40.5000	−	23.3827i	1.36603	−	0.788678i
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$		0			0
$885$		−	24.2487i		−	0.815112i
$886$		0			0
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	0.747539	−	0.664218i	$-0.231235\pi$
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	−0.948999	+	0.315279i	$0.897902\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−18.0000	−	31.1769i	−0.603023	−	1.04447i
$892$		0			0
$893$	−7.50000	+	12.9904i	−0.250978	+	0.434707i
$894$		0			0
$895$	21.0000	−	36.3731i	0.701953	−	1.21582i
$896$		0			0
$897$	−18.0000	−	10.3923i	−0.601003	−	0.346989i
$898$		0			0
$899$	−1.50000	−	2.59808i	−0.0500278	−	0.0866507i
$900$		0			0
$901$	−10.5000	+	18.1865i	−0.349806	+	0.605881i
$902$		0			0
$903$	−7.50000	−	21.6506i	−0.249584	−	0.720488i
$904$		0			0
$905$	6.00000	+	10.3923i	0.199447	+	0.345452i
$906$		0			0
$907$	−18.0000	+	31.1769i	−0.597680	+	1.03521i	0.395482	+	0.918474i	$0.370577\pi$
$907$	−18.0000	+	31.1769i	−0.597680	+	1.03521i	−0.993163	+	0.116739i	$0.962756\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$	19.5000	+	33.7750i	0.646064	+	1.11902i	0.984055	+	0.177866i	$0.0569194\pi$
$911$	19.5000	+	33.7750i	0.646064	+	1.11902i	−0.337991	+	0.941149i	$0.609747\pi$
$912$		0			0
$913$	4.00000			0.132381
$914$		0			0
$915$			10.3923i			0.343559i
$916$		0			0
$917$	−8.00000	−	6.92820i	−0.264183	−	0.228789i
$918$		0			0
$919$	17.5000	−	30.3109i	0.577272	−	0.999864i	−0.418519	−	0.908208i	$-0.637451\pi$
$919$	17.5000	−	30.3109i	0.577272	−	0.999864i	0.995791	−	0.0916559i	$-0.0292160\pi$
$920$		0			0
$921$	12.0000	+	6.92820i	0.395413	+	0.228292i
$922$		0			0
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$		0			0
$925$	5.50000	+	9.52628i	0.180839	+	0.313222i
$926$		0			0
$927$	12.0000	−	20.7846i	0.394132	−	0.682656i
$928$		0			0
$929$	3.00000			0.0984268			0.0492134	−	0.998788i	$-0.484329\pi$
$929$	3.00000			0.0984268			0.0492134	+	0.998788i	$0.484329\pi$
$930$		0			0
$931$	5.00000	+	34.6410i	0.163868	+	1.13531i
$932$		0			0
$933$	46.5000	+	26.8468i	1.52234	+	0.878924i
$934$		0			0
$935$	−28.0000	−	48.4974i	−0.915698	−	1.58604i
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$	25.5000	+	14.7224i	0.832161	+	0.480448i
$940$		0			0
$941$	59.0000			1.92335			0.961673	−	0.274201i	$-0.0884132\pi$
$941$	59.0000			1.92335			0.961673	+	0.274201i	$0.0884132\pi$
$942$		0			0
$943$	−36.0000			−1.17232
$944$		0			0
$945$	18.0000	−	20.7846i	0.585540	−	0.676123i
$946$		0			0
$947$	−25.0000			−0.812391			−0.406195	−	0.913786i	$-0.633145\pi$
$947$	−25.0000			−0.812391			−0.406195	+	0.913786i	$0.633145\pi$
$948$		0			0
$949$	21.0000			0.681689
$950$		0			0
$951$	13.5000	+	7.79423i	0.437767	+	0.252745i
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	−15.0000	−	25.9808i	−0.485389	−	0.840718i
$956$		0			0
$957$	6.00000	+	3.46410i	0.193952	+	0.111979i
$958$		0			0
$959$	7.00000	−	36.3731i	0.226042	−	1.17455i
$960$		0			0
$961$	−22.0000			−0.709677
$962$		0			0
$963$	9.00000			0.290021
$964$		0			0
$965$	1.00000	+	1.73205i	0.0321911	+	0.0557567i
$966$		0			0
$967$	−23.5000	+	40.7032i	−0.755709	+	1.30893i	0.189312	+	0.981917i	$0.439374\pi$
$967$	−23.5000	+	40.7032i	−0.755709	+	1.30893i	−0.945021	+	0.327009i	$0.893959\pi$
$968$		0			0
$969$	−52.5000	−	30.3109i	−1.68654	−	0.973726i
$970$		0			0
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$		0			0
$973$	−2.50000	+	12.9904i	−0.0801463	+	0.416452i
$974$		0			0
$975$		−	5.19615i		−	0.166410i
$976$		0			0
$977$	3.00000			0.0959785			0.0479893	−	0.998848i	$-0.484719\pi$
$977$	3.00000			0.0959785			0.0479893	+	0.998848i	$0.484719\pi$
$978$		0			0
$979$	−30.0000	−	51.9615i	−0.958804	−	1.66070i
$980$		0			0
$981$	10.5000	−	18.1865i	0.335239	−	0.580651i
$982$		0			0
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$		0			0
$985$	26.0000	+	45.0333i	0.828429	+	1.43488i
$986$		0			0
$987$	13.5000	+	2.59808i	0.429710	+	0.0826977i
$988$		0			0
$989$	−10.0000	+	17.3205i	−0.317982	+	0.550760i
$990$		0			0
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	0.994537	+	0.104389i	$0.0332887\pi$
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	−0.406865	+	0.913488i	$0.633378\pi$
$992$		0			0
$993$	37.5000	+	21.6506i	1.19003	+	0.687062i
$994$		0			0
$995$	13.0000	−	22.5167i	0.412128	−	0.713826i
$996$		0			0
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	−0.637587	−	0.770378i	$-0.720067\pi$
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	0.985961	+	0.166978i	$0.0534008\pi$
$998$		0			0
$999$	49.5000	+	28.5788i	1.56611	+	0.904194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.i.a.121.1	yes	2
3.2	odd	2		756.2.i.a.37.1		2
4.3	odd	2		1008.2.q.f.625.1		2
7.2	even	3		1764.2.j.c.589.1		2
7.3	odd	6		1764.2.l.b.949.1		2
7.4	even	3		252.2.l.a.193.1	yes	2
7.5	odd	6		1764.2.j.a.589.1		2
7.6	odd	2		1764.2.i.b.373.1		2
9.2	odd	6		756.2.l.a.289.1		2
9.4	even	3		2268.2.k.a.1297.1		2
9.5	odd	6		2268.2.k.b.1297.1		2
9.7	even	3		252.2.l.a.205.1	yes	2
12.11	even	2		3024.2.q.e.2305.1		2
21.2	odd	6		5292.2.j.c.1765.1		2
21.5	even	6		5292.2.j.b.1765.1		2
21.11	odd	6		756.2.l.a.361.1		2
21.17	even	6		5292.2.l.b.361.1		2
21.20	even	2		5292.2.i.b.1549.1		2
28.11	odd	6		1008.2.t.b.193.1		2
36.7	odd	6		1008.2.t.b.961.1		2
36.11	even	6		3024.2.t.b.289.1		2
63.2	odd	6		5292.2.j.c.3529.1		2
63.4	even	3		2268.2.k.a.1621.1		2
63.11	odd	6		756.2.i.a.613.1		2
63.16	even	3		1764.2.j.c.1177.1		2
63.20	even	6		5292.2.l.b.3313.1		2
63.25	even	3	inner	252.2.i.a.25.1	✓	2
63.32	odd	6		2268.2.k.b.1621.1		2
63.34	odd	6		1764.2.l.b.961.1		2
63.38	even	6		5292.2.i.b.2125.1		2
63.47	even	6		5292.2.j.b.3529.1		2
63.52	odd	6		1764.2.i.b.1537.1		2
63.61	odd	6		1764.2.j.a.1177.1		2
84.11	even	6		3024.2.t.b.1873.1		2
252.11	even	6		3024.2.q.e.2881.1		2
252.151	odd	6		1008.2.q.f.529.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.a.25.1	✓	2	63.25	even	3	inner
252.2.i.a.121.1	yes	2	1.1	even	1	trivial
252.2.l.a.193.1	yes	2	7.4	even	3
252.2.l.a.205.1	yes	2	9.7	even	3
756.2.i.a.37.1		2	3.2	odd	2
756.2.i.a.613.1		2	63.11	odd	6
756.2.l.a.289.1		2	9.2	odd	6
756.2.l.a.361.1		2	21.11	odd	6
1008.2.q.f.529.1		2	252.151	odd	6
1008.2.q.f.625.1		2	4.3	odd	2
1008.2.t.b.193.1		2	28.11	odd	6
1008.2.t.b.961.1		2	36.7	odd	6
1764.2.i.b.373.1		2	7.6	odd	2
1764.2.i.b.1537.1		2	63.52	odd	6
1764.2.j.a.589.1		2	7.5	odd	6
1764.2.j.a.1177.1		2	63.61	odd	6
1764.2.j.c.589.1		2	7.2	even	3
1764.2.j.c.1177.1		2	63.16	even	3
1764.2.l.b.949.1		2	7.3	odd	6
1764.2.l.b.961.1		2	63.34	odd	6
2268.2.k.a.1297.1		2	9.4	even	3
2268.2.k.a.1621.1		2	63.4	even	3
2268.2.k.b.1297.1		2	9.5	odd	6
2268.2.k.b.1621.1		2	63.32	odd	6
3024.2.q.e.2305.1		2	12.11	even	2
3024.2.q.e.2881.1		2	252.11	even	6
3024.2.t.b.289.1		2	36.11	even	6
3024.2.t.b.1873.1		2	84.11	even	6
5292.2.i.b.1549.1		2	21.20	even	2
5292.2.i.b.2125.1		2	63.38	even	6
5292.2.j.b.1765.1		2	21.5	even	6
5292.2.j.b.3529.1		2	63.47	even	6
5292.2.j.c.1765.1		2	21.2	odd	6
5292.2.j.c.3529.1		2	63.2	odd	6
5292.2.l.b.361.1		2	21.17	even	6
5292.2.l.b.3313.1		2	63.20	even	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-2.00000 + 3.46410i) q^{11} +(-1.50000 + 2.59808i) q^{13} +3.46410i q^{15} +(-3.50000 - 6.06218i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(4.50000 + 0.866025i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{29} -3.00000 q^{31} +(6.00000 - 3.46410i) q^{33} +(4.00000 + 3.46410i) q^{35} +(-5.50000 + 9.52628i) q^{37} +(4.50000 - 2.59808i) q^{39} +(4.50000 - 7.79423i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(3.00000 - 5.19615i) q^{45} +3.00000 q^{47} +(5.50000 - 4.33013i) q^{49} +12.1244i q^{51} +(-1.50000 - 2.59808i) q^{53} +8.00000 q^{55} +(7.50000 - 4.33013i) q^{57} -7.00000 q^{59} +3.00000 q^{61} +(-6.00000 - 5.19615i) q^{63} +6.00000 q^{65} +13.0000 q^{67} +6.92820i q^{69} -8.00000 q^{71} +(-3.50000 - 6.06218i) q^{73} +(-1.50000 + 0.866025i) q^{75} +(2.00000 - 10.3923i) q^{77} -9.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} +(-0.500000 - 0.866025i) q^{83} +(-7.00000 + 12.1244i) q^{85} -1.73205i q^{87} +(-7.50000 + 12.9904i) q^{89} +(1.50000 - 7.79423i) q^{91} +(4.50000 + 2.59808i) q^{93} +10.0000 q^{95} +(8.50000 + 14.7224i) q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} - 2 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 - 2 * q^5 - 5 * q^7 + 3 * q^9	\( 2 q - 3 q^{3} - 2 q^{5} - 5 q^{7} + 3 q^{9} - 4 q^{11} - 3 q^{13} - 7 q^{17} - 5 q^{19} + 9 q^{21} - 4 q^{23} + q^{25} + q^{29} - 6 q^{31} + 12 q^{33} + 8 q^{35} - 11 q^{37} + 9 q^{39} + 9 q^{41} - 5 q^{43} + 6 q^{45} + 6 q^{47} + 11 q^{49} - 3 q^{53} + 16 q^{55} + 15 q^{57} - 14 q^{59} + 6 q^{61} - 12 q^{63} + 12 q^{65} + 26 q^{67} - 16 q^{71} - 7 q^{73} - 3 q^{75} + 4 q^{77} - 18 q^{79} - 9 q^{81} - q^{83} - 14 q^{85} - 15 q^{89} + 3 q^{91} + 9 q^{93} + 20 q^{95} + 17 q^{97} - 24 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 - 2 * q^5 - 5 * q^7 + 3 * q^9 - 4 * q^11 - 3 * q^13 - 7 * q^17 - 5 * q^19 + 9 * q^21 - 4 * q^23 + q^25 + q^29 - 6 * q^31 + 12 * q^33 + 8 * q^35 - 11 * q^37 + 9 * q^39 + 9 * q^41 - 5 * q^43 + 6 * q^45 + 6 * q^47 + 11 * q^49 - 3 * q^53 + 16 * q^55 + 15 * q^57 - 14 * q^59 + 6 * q^61 - 12 * q^63 + 12 * q^65 + 26 * q^67 - 16 * q^71 - 7 * q^73 - 3 * q^75 + 4 * q^77 - 18 * q^79 - 9 * q^81 - q^83 - 14 * q^85 - 15 * q^89 + 3 * q^91 + 9 * q^93 + 20 * q^95 + 17 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more