LMFDB - Embedded newform 592.2.w.b.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(529,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("592.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.w (of order $6$, degree $2$, not 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:	$4.72714379966$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 148)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	592.529
Dual form			592.2.w.b.545.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(1.50000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(1.50000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.50000 + 0.866025i) q^{13} +(1.50000 - 0.866025i) q^{15} +(1.50000 - 0.866025i) q^{17} +(1.50000 + 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{21} +3.46410i q^{23} +(-1.00000 - 1.73205i) q^{25} +5.00000 q^{27} -6.92820i q^{29} +3.46410i q^{31} +(1.50000 - 0.866025i) q^{35} +(-5.00000 + 3.46410i) q^{37} +(1.50000 - 0.866025i) q^{39} +(4.50000 - 7.79423i) q^{41} -3.46410i q^{43} +3.46410i q^{45} +(3.00000 + 5.19615i) q^{49} -1.73205i q^{51} +(-1.50000 - 2.59808i) q^{53} +(1.50000 - 0.866025i) q^{57} +(-1.50000 + 0.866025i) q^{59} +(1.50000 + 0.866025i) q^{61} +2.00000 q^{63} +(1.50000 + 2.59808i) q^{65} +(6.50000 - 11.2583i) q^{67} +(3.00000 + 1.73205i) q^{69} +(-7.50000 + 12.9904i) q^{71} -2.00000 q^{73} -2.00000 q^{75} +(-10.5000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{83} +3.00000 q^{85} +(-6.00000 - 3.46410i) q^{87} +(-4.50000 + 2.59808i) q^{89} +(1.50000 - 0.866025i) q^{91} +(3.00000 + 1.73205i) q^{93} +(1.50000 + 2.59808i) q^{95} +6.92820i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 3 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 + 3 * q^5 + q^7 + 2 * q^9	$ 2 q + q^{3} + 3 q^{5} + q^{7} + 2 q^{9} + 3 q^{13} + 3 q^{15} + 3 q^{17} + 3 q^{19} - q^{21} - 2 q^{25} + 10 q^{27} + 3 q^{35} - 10 q^{37} + 3 q^{39} + 9 q^{41} + 6 q^{49} - 3 q^{53} + 3 q^{57} - 3 q^{59} + 3 q^{61} + 4 q^{63} + 3 q^{65} + 13 q^{67} + 6 q^{69} - 15 q^{71} - 4 q^{73} - 4 q^{75} - 21 q^{79} - q^{81} - 9 q^{83} + 6 q^{85} - 12 q^{87} - 9 q^{89} + 3 q^{91} + 6 q^{93} + 3 q^{95}+O(q^{100}) $ 2 * q + q^3 + 3 * q^5 + q^7 + 2 * q^9 + 3 * q^13 + 3 * q^15 + 3 * q^17 + 3 * q^19 - q^21 - 2 * q^25 + 10 * q^27 + 3 * q^35 - 10 * q^37 + 3 * q^39 + 9 * q^41 + 6 * q^49 - 3 * q^53 + 3 * q^57 - 3 * q^59 + 3 * q^61 + 4 * q^63 + 3 * q^65 + 13 * q^67 + 6 * q^69 - 15 * q^71 - 4 * q^73 - 4 * q^75 - 21 * q^79 - q^81 - 9 * q^83 + 6 * q^85 - 12 * q^87 - 9 * q^89 + 3 * q^91 + 6 * q^93 + 3 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$		0			0
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	−0.125567	+	0.992085i	$0.540075\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	1.50000	+	0.866025i	0.416025	+	0.240192i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	1.50000	+	0.866025i	0.416025	+	0.240192i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$		0			0
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	−0.306944	−	0.951727i	$-0.599307\pi$
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	0.670748	+	0.741685i	$0.265973\pi$
$18$		0			0
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$	−0.500000	−	0.866025i	−0.109109	−	0.188982i
$22$		0			0
$23$			3.46410i			0.722315i	0.932505	+	0.361158i	$0.117618\pi$
$23$			3.46410i			0.722315i	−0.932505	+	0.361158i	$0.882382\pi$
$24$		0			0
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$		−	6.92820i		−	1.28654i	−0.765641	−	0.643268i	$-0.777578\pi$
$29$		−	6.92820i		−	1.28654i	0.765641	−	0.643268i	$-0.222422\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.50000	−	0.866025i	0.253546	−	0.146385i
$36$		0			0
$37$	−5.00000	+	3.46410i	−0.821995	+	0.569495i
$37$	−5.00000	+	3.46410i	−0.821995	+	0.569495i
$38$		0			0
$39$	1.50000	−	0.866025i	0.240192	−	0.138675i
$40$		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
$43$		−	3.46410i		−	0.528271i	−0.964486	−	0.264135i	$-0.914913\pi$
$43$		−	3.46410i		−	0.528271i	0.964486	−	0.264135i	$-0.0850865\pi$
$44$		0			0
$45$			3.46410i			0.516398i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$		−	1.73205i		−	0.242536i
$52$		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
$55$		0			0
$56$		0			0
$57$	1.50000	−	0.866025i	0.198680	−	0.114708i
$58$		0			0
$59$	−1.50000	+	0.866025i	−0.195283	+	0.112747i	−0.594454	−	0.804130i	$-0.702632\pi$
$59$	−1.50000	+	0.866025i	−0.195283	+	0.112747i	0.399170	+	0.916877i	$0.369298\pi$
$60$		0			0
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	0.592944	−	0.805243i	$-0.297965\pi$
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	−0.400889	+	0.916127i	$0.631299\pi$
$62$		0			0
$63$	2.00000			0.251976
$64$		0			0
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$		0			0
$69$	3.00000	+	1.73205i	0.361158	+	0.208514i
$70$		0			0
$71$	−7.50000	+	12.9904i	−0.890086	+	1.54167i	−0.0503155	+	0.998733i	$0.516023\pi$
$71$	−7.50000	+	12.9904i	−0.890086	+	1.54167i	−0.839771	+	0.542941i	$0.817311\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$		0			0
$75$	−2.00000			−0.230940
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−10.5000	−	6.06218i	−1.18134	−	0.682048i	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−10.5000	−	6.06218i	−1.18134	−	0.682048i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		0			0
$85$	3.00000			0.325396
$86$		0			0
$87$	−6.00000	−	3.46410i	−0.643268	−	0.371391i
$88$		0			0
$89$	−4.50000	+	2.59808i	−0.476999	+	0.275396i	−0.719165	−	0.694839i	$-0.755475\pi$
$89$	−4.50000	+	2.59808i	−0.476999	+	0.275396i	0.242166	+	0.970235i	$0.422142\pi$
$90$		0			0
$91$	1.50000	−	0.866025i	0.157243	−	0.0907841i
$92$		0			0
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$		0			0
$95$	1.50000	+	2.59808i	0.153897	+	0.266557i
$96$		0			0
$97$			6.92820i			0.703452i	0.936103	+	0.351726i	$0.114405\pi$
$97$			6.92820i			0.703452i	−0.936103	+	0.351726i	$0.885595\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$			17.3205i			1.70664i	0.521387	+	0.853320i	$0.325415\pi$
$103$			17.3205i			1.70664i	−0.521387	+	0.853320i	$0.674585\pi$
$104$		0			0
$105$		−	1.73205i		−	0.169031i
$106$		0			0
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	−0.562267	−	0.826956i	$-0.690071\pi$
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	0.997298	+	0.0734594i	$0.0234039\pi$
$108$		0			0
$109$	−10.5000	+	6.06218i	−1.00572	+	0.580651i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−10.5000	+	6.06218i	−1.00572	+	0.580651i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	0.500000	+	6.06218i	0.0474579	+	0.575396i
$112$		0			0
$113$	1.50000	−	0.866025i	0.141108	−	0.0814688i	−0.427784	−	0.903881i	$-0.640706\pi$
$113$	1.50000	−	0.866025i	0.141108	−	0.0814688i	0.568892	+	0.822412i	$0.307372\pi$
$114$		0			0
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$		0			0
$117$			3.46410i			0.320256i
$118$		0			0
$119$		−	1.73205i		−	0.158777i
$120$		0			0
$121$	−11.0000			−1.00000
$122$		0			0
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$		0			0
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	0.999905	−	0.0137486i	$-0.00437646\pi$
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	−0.511859	+	0.859069i	$0.671043\pi$
$128$		0			0
$129$	−3.00000	−	1.73205i	−0.264135	−	0.152499i
$130$		0			0
$131$	−13.5000	+	7.79423i	−1.17950	+	0.680985i	−0.955899	−	0.293696i	$-0.905115\pi$
$131$	−13.5000	+	7.79423i	−1.17950	+	0.680985i	−0.223602	+	0.974681i	$0.571781\pi$
$132$		0			0
$133$	1.50000	−	0.866025i	0.130066	−	0.0750939i
$134$		0			0
$135$	7.50000	+	4.33013i	0.645497	+	0.372678i
$136$		0			0
$137$	−18.0000			−1.53784			−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000			−1.53784			−0.768922	+	0.639343i	$0.779207\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	6.00000	−	10.3923i	0.498273	−	0.863034i
$146$		0			0
$147$	6.00000			0.494872
$148$		0			0
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$		0			0
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$		0			0
$153$	3.00000	+	1.73205i	0.242536	+	0.140028i
$154$		0			0
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$		0			0
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	0.948373	−	0.317156i	$-0.102728\pi$
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	−0.748852	+	0.662738i	$0.769394\pi$
$158$		0			0
$159$	−3.00000			−0.237915
$160$		0			0
$161$	3.00000	+	1.73205i	0.236433	+	0.136505i
$162$		0			0
$163$	16.5000	−	9.52628i	1.29238	−	0.746156i	0.313304	−	0.949653i	$-0.398564\pi$
$163$	16.5000	−	9.52628i	1.29238	−	0.746156i	0.979076	+	0.203497i	$0.0652307\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.5000	−	6.06218i	−0.812514	−	0.469105i	0.0353139	−	0.999376i	$-0.488757\pi$
$167$	−10.5000	−	6.06218i	−0.812514	−	0.469105i	−0.847828	+	0.530271i	$0.822090\pi$
$168$		0			0
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$		0			0
$171$			3.46410i			0.264906i
$172$		0			0
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		0			0
$175$	−2.00000			−0.151186
$176$		0			0
$177$			1.73205i			0.130189i
$178$		0			0
$179$		−	17.3205i		−	1.29460i	−0.762237	−	0.647298i	$-0.775899\pi$
$179$		−	17.3205i		−	1.29460i	0.762237	−	0.647298i	$-0.224101\pi$
$180$		0			0
$181$	2.50000	−	4.33013i	0.185824	−	0.321856i	−0.758030	−	0.652219i	$-0.773838\pi$
$181$	2.50000	−	4.33013i	0.185824	−	0.321856i	0.943854	+	0.330364i	$0.107171\pi$
$182$		0			0
$183$	1.50000	−	0.866025i	0.110883	−	0.0640184i
$184$		0			0
$185$	−10.5000	+	0.866025i	−0.771975	+	0.0636715i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.50000	−	4.33013i	0.181848	−	0.314970i
$190$		0			0
$191$		−	10.3923i		−	0.751961i	−0.926628	−	0.375980i	$-0.877306\pi$
$191$		−	10.3923i		−	0.751961i	0.926628	−	0.375980i	$-0.122694\pi$
$192$		0			0
$193$			20.7846i			1.49611i	0.663637	+	0.748054i	$0.269012\pi$
$193$			20.7846i			1.49611i	−0.663637	+	0.748054i	$0.730988\pi$
$194$		0			0
$195$	3.00000			0.214834
$196$		0			0
$197$	10.5000	+	18.1865i	0.748094	+	1.29574i	0.948735	+	0.316072i	$0.102364\pi$
$197$	10.5000	+	18.1865i	0.748094	+	1.29574i	−0.200641	+	0.979665i	$0.564303\pi$
$198$		0			0
$199$		−	10.3923i		−	0.736691i	−0.929689	−	0.368345i	$-0.879924\pi$
$199$		−	10.3923i		−	0.736691i	0.929689	−	0.368345i	$-0.120076\pi$
$200$		0			0
$201$	−6.50000	−	11.2583i	−0.458475	−	0.794101i
$202$		0			0
$203$	−6.00000	−	3.46410i	−0.421117	−	0.243132i
$204$		0			0
$205$	13.5000	−	7.79423i	0.942881	−	0.544373i
$206$		0			0
$207$	−6.00000	+	3.46410i	−0.417029	+	0.240772i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		0			0
$213$	7.50000	+	12.9904i	0.513892	+	0.890086i
$214$		0			0
$215$	3.00000	−	5.19615i	0.204598	−	0.354375i
$216$		0			0
$217$	3.00000	+	1.73205i	0.203653	+	0.117579i
$218$		0			0
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$		0			0
$221$	3.00000			0.201802
$222$		0			0
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$		0			0
$227$	−16.5000	−	9.52628i	−1.09514	−	0.632281i	−0.160202	−	0.987084i	$-0.551215\pi$
$227$	−16.5000	−	9.52628i	−1.09514	−	0.632281i	−0.934941	+	0.354803i	$0.884548\pi$
$228$		0			0
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−10.5000	+	6.06218i	−0.682048	+	0.393781i
$238$		0			0
$239$	10.5000	−	6.06218i	0.679189	−	0.392130i	−0.120361	−	0.992730i	$-0.538405\pi$
$239$	10.5000	−	6.06218i	0.679189	−	0.392130i	0.799549	+	0.600601i	$0.205072\pi$
$240$		0			0
$241$	25.5000	+	14.7224i	1.64260	+	0.948355i	0.979905	+	0.199465i	$0.0639205\pi$
$241$	25.5000	+	14.7224i	1.64260	+	0.948355i	0.662695	+	0.748890i	$0.269413\pi$
$242$		0			0
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$		0			0
$245$			10.3923i			0.663940i
$246$		0			0
$247$	1.50000	+	2.59808i	0.0954427	+	0.165312i
$248$		0			0
$249$	−9.00000			−0.570352
$250$		0			0
$251$			17.3205i			1.09326i	0.837374	+	0.546630i	$0.184090\pi$
$251$			17.3205i			1.09326i	−0.837374	+	0.546630i	$0.815910\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	1.50000	−	2.59808i	0.0939336	−	0.162698i
$256$		0			0
$257$	−4.50000	+	2.59808i	−0.280702	+	0.162064i	−0.633741	−	0.773545i	$-0.718482\pi$
$257$	−4.50000	+	2.59808i	−0.280702	+	0.162064i	0.353039	+	0.935609i	$0.385148\pi$
$258$		0			0
$259$	0.500000	+	6.06218i	0.0310685	+	0.376685i
$260$		0			0
$261$	12.0000	−	6.92820i	0.742781	−	0.428845i
$262$		0			0
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	−0.336270	−	0.941766i	$-0.609166\pi$
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	0.983728	−	0.179664i	$-0.0575011\pi$
$264$		0			0
$265$		−	5.19615i		−	0.319197i
$266$		0			0
$267$			5.19615i			0.317999i
$268$		0			0
$269$	−30.0000			−1.82913			−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000			−1.82913			−0.914566	+	0.404436i	$0.867468\pi$
$270$		0			0
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	0.952531	−	0.304443i	$-0.0984703\pi$
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	−0.739921	+	0.672694i	$0.765137\pi$
$272$		0			0
$273$		−	1.73205i		−	0.104828i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.5000	+	7.79423i	0.811136	+	0.468310i	0.847350	−	0.531034i	$-0.178196\pi$
$277$	13.5000	+	7.79423i	0.811136	+	0.468310i	−0.0362140	+	0.999344i	$0.511530\pi$
$278$		0			0
$279$	−6.00000	+	3.46410i	−0.359211	+	0.207390i
$280$		0			0
$281$	13.5000	−	7.79423i	0.805342	−	0.464965i	−0.0399934	−	0.999200i	$-0.512734\pi$
$281$	13.5000	−	7.79423i	0.805342	−	0.464965i	0.845336	+	0.534235i	$0.179400\pi$
$282$		0			0
$283$	25.5000	+	14.7224i	1.51582	+	0.875158i	0.999828	+	0.0185631i	$0.00590916\pi$
$283$	25.5000	+	14.7224i	1.51582	+	0.875158i	0.515990	+	0.856595i	$0.327424\pi$
$284$		0			0
$285$	3.00000			0.177705
$286$		0			0
$287$	−4.50000	−	7.79423i	−0.265627	−	0.460079i
$288$		0			0
$289$	−7.00000	+	12.1244i	−0.411765	+	0.713197i
$290$		0			0
$291$	6.00000	+	3.46410i	0.351726	+	0.203069i
$292$		0			0
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$		0			0
$295$	−3.00000			−0.174667
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$		0			0
$301$	−3.00000	−	1.73205i	−0.172917	−	0.0998337i
$302$		0			0
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$		0			0
$305$	1.50000	+	2.59808i	0.0858898	+	0.148765i
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$	15.0000	+	8.66025i	0.853320	+	0.492665i
$310$		0			0
$311$	22.5000	−	12.9904i	1.27586	−	0.736617i	0.299774	−	0.954010i	$-0.403089\pi$
$311$	22.5000	−	12.9904i	1.27586	−	0.736617i	0.976084	+	0.217393i	$0.0697554\pi$
$312$		0			0
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.165406	−	0.986226i	$-0.447107\pi$
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.936799	+	0.349867i	$0.113773\pi$
$314$		0			0
$315$	3.00000	+	1.73205i	0.169031	+	0.0975900i
$316$		0			0
$317$	−7.50000	−	12.9904i	−0.421242	−	0.729612i	0.574819	−	0.818280i	$-0.305072\pi$
$317$	−7.50000	−	12.9904i	−0.421242	−	0.729612i	−0.996061	+	0.0886679i	$0.971739\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−4.50000	−	7.79423i	−0.251166	−	0.435031i
$322$		0			0
$323$	3.00000			0.166924
$324$		0			0
$325$		−	3.46410i		−	0.192154i
$326$		0			0
$327$			12.1244i			0.670478i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.50000	−	2.59808i	0.247342	−	0.142803i	−0.371204	−	0.928551i	$-0.621055\pi$
$331$	4.50000	−	2.59808i	0.247342	−	0.142803i	0.618547	+	0.785748i	$0.287722\pi$
$332$		0			0
$333$	−11.0000	−	5.19615i	−0.602796	−	0.284747i
$334$		0			0
$335$	19.5000	−	11.2583i	1.06540	−	0.615108i
$336$		0			0
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	−0.632882	−	0.774248i	$-0.718128\pi$
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	0.986960	+	0.160968i	$0.0514616\pi$
$338$		0			0
$339$		−	1.73205i		−	0.0940721i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$	3.00000	+	5.19615i	0.161515	+	0.279751i
$346$		0			0
$347$		−	17.3205i		−	0.929814i	−0.885360	−	0.464907i	$-0.846088\pi$
$347$		−	17.3205i		−	0.929814i	0.885360	−	0.464907i	$-0.153912\pi$
$348$		0			0
$349$	−9.50000	−	16.4545i	−0.508523	−	0.880788i	−0.999951	−	0.00987003i	$-0.996858\pi$
$349$	−9.50000	−	16.4545i	−0.508523	−	0.880788i	0.491428	−	0.870918i	$-0.336475\pi$
$350$		0			0
$351$	7.50000	+	4.33013i	0.400320	+	0.231125i
$352$		0			0
$353$	7.50000	−	4.33013i	0.399185	−	0.230469i	−0.286947	−	0.957946i	$-0.592641\pi$
$353$	7.50000	−	4.33013i	0.399185	−	0.230469i	0.686132	+	0.727477i	$0.259307\pi$
$354$		0			0
$355$	−22.5000	+	12.9904i	−1.19418	+	0.689458i
$356$		0			0
$357$	−1.50000	−	0.866025i	−0.0793884	−	0.0458349i
$358$		0			0
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$		0			0
$363$	−5.50000	+	9.52628i	−0.288675	+	0.500000i
$364$		0			0
$365$	−3.00000	−	1.73205i	−0.157027	−	0.0906597i
$366$		0			0
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	−0.942799	−	0.333363i	$-0.891817\pi$
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	0.760100	+	0.649806i	$0.225150\pi$
$368$		0			0
$369$	18.0000			0.937043
$370$		0			0
$371$	−3.00000			−0.155752
$372$		0			0
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	−0.999956	−	0.00933789i	$-0.997028\pi$
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	0.508065	+	0.861319i	$0.330361\pi$
$374$		0			0
$375$	−10.5000	−	6.06218i	−0.542218	−	0.313050i
$376$		0			0
$377$	6.00000	−	10.3923i	0.309016	−	0.535231i
$378$		0			0
$379$	3.50000	+	6.06218i	0.179783	+	0.311393i	0.941806	−	0.336157i	$-0.109127\pi$
$379$	3.50000	+	6.06218i	0.179783	+	0.311393i	−0.762023	+	0.647550i	$0.775794\pi$
$380$		0			0
$381$	11.0000			0.563547
$382$		0			0
$383$	7.50000	+	4.33013i	0.383232	+	0.221259i	0.679224	−	0.733931i	$-0.262317\pi$
$383$	7.50000	+	4.33013i	0.383232	+	0.221259i	−0.295991	+	0.955191i	$0.595650\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.00000	−	3.46410i	0.304997	−	0.176090i
$388$		0			0
$389$	13.5000	+	7.79423i	0.684477	+	0.395183i	0.801540	−	0.597941i	$-0.204014\pi$
$389$	13.5000	+	7.79423i	0.684477	+	0.395183i	−0.117063	+	0.993125i	$0.537348\pi$
$390$		0			0
$391$	3.00000	+	5.19615i	0.151717	+	0.262781i
$392$		0			0
$393$			15.5885i			0.786334i
$394$		0			0
$395$	−10.5000	−	18.1865i	−0.528312	−	0.915064i
$396$		0			0
$397$	−2.00000			−0.100377			−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000			−0.100377			−0.0501886	+	0.998740i	$0.515982\pi$
$398$		0			0
$399$		−	1.73205i		−	0.0867110i
$400$		0			0
$401$			20.7846i			1.03793i	0.854794	+	0.518967i	$0.173683\pi$
$401$			20.7846i			1.03793i	−0.854794	+	0.518967i	$0.826317\pi$
$402$		0			0
$403$	−3.00000	+	5.19615i	−0.149441	+	0.258839i
$404$		0			0
$405$	−1.50000	+	0.866025i	−0.0745356	+	0.0430331i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.50000	−	0.866025i	0.0741702	−	0.0428222i	−0.462456	−	0.886642i	$-0.653032\pi$
$409$	1.50000	−	0.866025i	0.0741702	−	0.0428222i	0.536626	+	0.843820i	$0.319698\pi$
$410$		0			0
$411$	−9.00000	+	15.5885i	−0.443937	+	0.768922i
$412$		0			0
$413$			1.73205i			0.0852286i
$414$		0			0
$415$		−	15.5885i		−	0.765207i
$416$		0			0
$417$	−5.00000			−0.244851
$418$		0			0
$419$	−16.5000	−	28.5788i	−0.806078	−	1.39617i	−0.915561	−	0.402179i	$-0.868253\pi$
$419$	−16.5000	−	28.5788i	−0.806078	−	1.39617i	0.109483	−	0.993989i	$-0.465080\pi$
$420$		0			0
$421$			13.8564i			0.675320i	0.941268	+	0.337660i	$0.109635\pi$
$421$			13.8564i			0.675320i	−0.941268	+	0.337660i	$0.890365\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.00000	−	1.73205i	−0.145521	−	0.0840168i
$426$		0			0
$427$	1.50000	−	0.866025i	0.0725901	−	0.0419099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.5000	−	6.06218i	−0.505767	−	0.292005i	0.225325	−	0.974284i	$-0.427656\pi$
$431$	−10.5000	−	6.06218i	−0.505767	−	0.292005i	−0.731092	+	0.682279i	$0.760989\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	−6.00000	−	10.3923i	−0.287678	−	0.498273i
$436$		0			0
$437$	−3.00000	+	5.19615i	−0.143509	+	0.248566i
$438$		0			0
$439$	−28.5000	−	16.4545i	−1.36023	−	0.785330i	−0.370576	−	0.928802i	$-0.620840\pi$
$439$	−28.5000	−	16.4545i	−1.36023	−	0.785330i	−0.989654	+	0.143472i	$0.954173\pi$
$440$		0			0
$441$	−6.00000	+	10.3923i	−0.285714	+	0.494872i
$442$		0			0
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$		0			0
$445$	−9.00000			−0.426641
$446$		0			0
$447$	−3.00000	+	5.19615i	−0.141895	+	0.245770i
$448$		0			0
$449$	−16.5000	−	9.52628i	−0.778683	−	0.449573i	0.0572802	−	0.998358i	$-0.481757\pi$
$449$	−16.5000	−	9.52628i	−0.778683	−	0.449573i	−0.835963	+	0.548785i	$0.815090\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	9.50000	+	16.4545i	0.446349	+	0.773099i
$454$		0			0
$455$	3.00000			0.140642
$456$		0			0
$457$	13.5000	+	7.79423i	0.631503	+	0.364599i	0.781334	−	0.624113i	$-0.214540\pi$
$457$	13.5000	+	7.79423i	0.631503	+	0.364599i	−0.149831	+	0.988712i	$0.547873\pi$
$458$		0			0
$459$	7.50000	−	4.33013i	0.350070	−	0.202113i
$460$		0			0
$461$	1.50000	−	0.866025i	0.0698620	−	0.0403348i	−0.464662	−	0.885488i	$-0.653824\pi$
$461$	1.50000	−	0.866025i	0.0698620	−	0.0403348i	0.534524	+	0.845153i	$0.320491\pi$
$462$		0			0
$463$	−4.50000	−	2.59808i	−0.209133	−	0.120743i	0.391776	−	0.920061i	$-0.371861\pi$
$463$	−4.50000	−	2.59808i	−0.209133	−	0.120743i	−0.600908	+	0.799318i	$0.705194\pi$
$464$		0			0
$465$	3.00000	+	5.19615i	0.139122	+	0.240966i
$466$		0			0
$467$			38.1051i			1.76329i	0.471909	+	0.881647i	$0.343565\pi$
$467$			38.1051i			1.76329i	−0.471909	+	0.881647i	$0.656435\pi$
$468$		0			0
$469$	−6.50000	−	11.2583i	−0.300142	−	0.519861i
$470$		0			0
$471$	5.00000			0.230388
$472$		0			0
$473$		0			0
$474$		0			0
$475$		−	3.46410i		−	0.158944i
$476$		0			0
$477$	3.00000	−	5.19615i	0.137361	−	0.237915i
$478$		0			0
$479$	10.5000	−	6.06218i	0.479757	−	0.276988i	−0.240558	−	0.970635i	$-0.577330\pi$
$479$	10.5000	−	6.06218i	0.479757	−	0.276988i	0.720315	+	0.693647i	$0.243997\pi$
$480$		0			0
$481$	−10.5000	+	0.866025i	−0.478759	+	0.0394874i
$482$		0			0
$483$	3.00000	−	1.73205i	0.136505	−	0.0788110i
$484$		0			0
$485$	−6.00000	+	10.3923i	−0.272446	+	0.471890i
$486$		0			0
$487$		−	24.2487i		−	1.09881i	−0.835555	−	0.549407i	$-0.814854\pi$
$487$		−	24.2487i		−	1.09881i	0.835555	−	0.549407i	$-0.185146\pi$
$488$		0			0
$489$		−	19.0526i		−	0.861586i
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.50000	+	12.9904i	0.336421	+	0.582698i
$498$		0			0
$499$	−4.50000	−	2.59808i	−0.201448	−	0.116306i	0.395883	−	0.918301i	$-0.370439\pi$
$499$	−4.50000	−	2.59808i	−0.201448	−	0.116306i	−0.597331	+	0.801995i	$0.703772\pi$
$500$		0			0
$501$	−10.5000	+	6.06218i	−0.469105	+	0.270838i
$502$		0			0
$503$	−13.5000	+	7.79423i	−0.601935	+	0.347527i	−0.769803	−	0.638282i	$-0.779645\pi$
$503$	−13.5000	+	7.79423i	−0.601935	+	0.347527i	0.167867	+	0.985810i	$0.446312\pi$
$504$		0			0
$505$	−9.00000	−	5.19615i	−0.400495	−	0.231226i
$506$		0			0
$507$	−10.0000			−0.444116
$508$		0			0
$509$	−19.5000	−	33.7750i	−0.864322	−	1.49705i	−0.867719	−	0.497056i	$-0.834414\pi$
$509$	−19.5000	−	33.7750i	−0.864322	−	1.49705i	0.00339621	−	0.999994i	$-0.498919\pi$
$510$		0			0
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$		0			0
$513$	7.50000	+	4.33013i	0.331133	+	0.191180i
$514$		0			0
$515$	−15.0000	+	25.9808i	−0.660979	+	1.14485i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−15.0000			−0.658427
$520$		0			0
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	−0.982231	−	0.187678i	$-0.939904\pi$
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	0.653650	+	0.756797i	$0.273237\pi$
$522$		0			0
$523$	1.50000	+	0.866025i	0.0655904	+	0.0378686i	0.532437	−	0.846470i	$-0.321276\pi$
$523$	1.50000	+	0.866025i	0.0655904	+	0.0378686i	−0.466846	+	0.884339i	$0.654610\pi$
$524$		0			0
$525$	−1.00000	+	1.73205i	−0.0436436	+	0.0755929i
$526$		0			0
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$		0			0
$529$	11.0000			0.478261
$530$		0			0
$531$	−3.00000	−	1.73205i	−0.130189	−	0.0751646i
$532$		0			0
$533$	13.5000	−	7.79423i	0.584750	−	0.337606i
$534$		0			0
$535$	13.5000	−	7.79423i	0.583656	−	0.336974i
$536$		0			0
$537$	−15.0000	−	8.66025i	−0.647298	−	0.373718i
$538$		0			0
$539$		0			0
$540$		0			0
$541$			13.8564i			0.595733i	0.954607	+	0.297867i	$0.0962751\pi$
$541$			13.8564i			0.595733i	−0.954607	+	0.297867i	$0.903725\pi$
$542$		0			0
$543$	−2.50000	−	4.33013i	−0.107285	−	0.185824i
$544$		0			0
$545$	−21.0000			−0.899541
$546$		0			0
$547$			38.1051i			1.62926i	0.579983	+	0.814629i	$0.303059\pi$
$547$			38.1051i			1.62926i	−0.579983	+	0.814629i	$0.696941\pi$
$548$		0			0
$549$			3.46410i			0.147844i
$550$		0			0
$551$	6.00000	−	10.3923i	0.255609	−	0.442727i
$552$		0			0
$553$	−10.5000	+	6.06218i	−0.446505	+	0.257790i
$554$		0			0
$555$	−4.50000	+	9.52628i	−0.191014	+	0.404368i
$556$		0			0
$557$	7.50000	−	4.33013i	0.317785	−	0.183473i	−0.332620	−	0.943061i	$-0.607933\pi$
$557$	7.50000	−	4.33013i	0.317785	−	0.183473i	0.650405	+	0.759588i	$0.274599\pi$
$558$		0			0
$559$	3.00000	−	5.19615i	0.126886	−	0.219774i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			31.1769i			1.31395i	0.753912	+	0.656975i	$0.228164\pi$
$563$			31.1769i			1.31395i	−0.753912	+	0.656975i	$0.771836\pi$
$564$		0			0
$565$	3.00000			0.126211
$566$		0			0
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$		0			0
$569$		−	34.6410i		−	1.45223i	−0.687575	−	0.726113i	$-0.741325\pi$
$569$		−	34.6410i		−	1.45223i	0.687575	−	0.726113i	$-0.258675\pi$
$570$		0			0
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	0.808962	−	0.587861i	$-0.200030\pi$
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	−0.913584	+	0.406651i	$0.866697\pi$
$572$		0			0
$573$	−9.00000	−	5.19615i	−0.375980	−	0.217072i
$574$		0			0
$575$	6.00000	−	3.46410i	0.250217	−	0.144463i
$576$		0			0
$577$	−28.5000	+	16.4545i	−1.18647	+	0.685009i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−28.5000	+	16.4545i	−1.18647	+	0.685009i	−0.228968	+	0.973434i	$0.573535\pi$
$578$		0			0
$579$	18.0000	+	10.3923i	0.748054	+	0.431889i
$580$		0			0
$581$	−9.00000			−0.373383
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$		0			0
$587$	7.50000	+	4.33013i	0.309558	+	0.178723i	0.646729	−	0.762720i	$-0.276137\pi$
$587$	7.50000	+	4.33013i	0.309558	+	0.178723i	−0.337171	+	0.941444i	$0.609470\pi$
$588$		0			0
$589$	−3.00000	+	5.19615i	−0.123613	+	0.214104i
$590$		0			0
$591$	21.0000			0.863825
$592$		0			0
$593$	30.0000			1.23195			0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000			1.23195			0.615976	+	0.787765i	$0.288762\pi$
$594$		0			0
$595$	1.50000	−	2.59808i	0.0614940	−	0.106511i
$596$		0			0
$597$	−9.00000	−	5.19615i	−0.368345	−	0.212664i
$598$		0			0
$599$	−1.50000	+	2.59808i	−0.0612883	+	0.106155i	−0.895042	−	0.445983i	$-0.852854\pi$
$599$	−1.50000	+	2.59808i	−0.0612883	+	0.106155i	0.833753	+	0.552137i	$0.186188\pi$
$600$		0			0
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	0.912499	−	0.409079i	$-0.134150\pi$
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	−0.810522	+	0.585708i	$0.800816\pi$
$602$		0			0
$603$	26.0000			1.05880
$604$		0			0
$605$	−16.5000	−	9.52628i	−0.670820	−	0.387298i
$606$		0			0
$607$	−7.50000	+	4.33013i	−0.304416	+	0.175754i	−0.644425	−	0.764668i	$-0.722903\pi$
$607$	−7.50000	+	4.33013i	−0.304416	+	0.175754i	0.340009	+	0.940422i	$0.389570\pi$
$608$		0			0
$609$	−6.00000	+	3.46410i	−0.243132	+	0.140372i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$		0			0
$615$		−	15.5885i		−	0.628587i
$616$		0			0
$617$	−7.50000	−	12.9904i	−0.301939	−	0.522973i	0.674636	−	0.738150i	$-0.264300\pi$
$617$	−7.50000	−	12.9904i	−0.301939	−	0.522973i	−0.976575	+	0.215177i	$0.930967\pi$
$618$		0			0
$619$	−44.0000			−1.76851			−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000			−1.76851			−0.884255	+	0.467005i	$0.845333\pi$
$620$		0			0
$621$			17.3205i			0.695048i
$622$		0			0
$623$			5.19615i			0.208179i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.50000	+	9.52628i	−0.179427	+	0.379838i
$630$		0			0
$631$	22.5000	−	12.9904i	0.895711	−	0.517139i	0.0199047	−	0.999802i	$-0.493664\pi$
$631$	22.5000	−	12.9904i	0.895711	−	0.517139i	0.875806	+	0.482663i	$0.160330\pi$
$632$		0			0
$633$	2.00000	−	3.46410i	0.0794929	−	0.137686i
$634$		0			0
$635$			19.0526i			0.756078i
$636$		0			0
$637$			10.3923i			0.411758i
$638$		0			0
$639$	−30.0000			−1.18678
$640$		0			0
$641$	−1.50000	−	2.59808i	−0.0592464	−	0.102618i	0.834881	−	0.550431i	$-0.185536\pi$
$641$	−1.50000	−	2.59808i	−0.0592464	−	0.102618i	−0.894127	+	0.447813i	$0.852203\pi$
$642$		0			0
$643$		−	17.3205i		−	0.683054i	−0.939872	−	0.341527i	$-0.889056\pi$
$643$		−	17.3205i		−	0.683054i	0.939872	−	0.341527i	$-0.110944\pi$
$644$		0			0
$645$	−3.00000	−	5.19615i	−0.118125	−	0.204598i
$646$		0			0
$647$	19.5000	+	11.2583i	0.766624	+	0.442611i	0.831669	−	0.555272i	$-0.187386\pi$
$647$	19.5000	+	11.2583i	0.766624	+	0.442611i	−0.0650449	+	0.997882i	$0.520719\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	3.00000	−	1.73205i	0.117579	−	0.0678844i
$652$		0			0
$653$	31.5000	+	18.1865i	1.23269	+	0.711694i	0.967590	−	0.252527i	$-0.0812616\pi$
$653$	31.5000	+	18.1865i	1.23269	+	0.711694i	0.265100	+	0.964221i	$0.414595\pi$
$654$		0			0
$655$	−27.0000			−1.05498
$656$		0			0
$657$	−2.00000	−	3.46410i	−0.0780274	−	0.135147i
$658$		0			0
$659$	−13.5000	+	23.3827i	−0.525885	+	0.910860i	0.473660	+	0.880708i	$0.342933\pi$
$659$	−13.5000	+	23.3827i	−0.525885	+	0.910860i	−0.999545	+	0.0301523i	$0.990401\pi$
$660$		0			0
$661$	19.5000	+	11.2583i	0.758462	+	0.437898i	0.828743	−	0.559629i	$-0.189056\pi$
$661$	19.5000	+	11.2583i	0.758462	+	0.437898i	−0.0702812	+	0.997527i	$0.522390\pi$
$662$		0			0
$663$	1.50000	−	2.59808i	0.0582552	−	0.100901i
$664$		0			0
$665$	3.00000			0.116335
$666$		0			0
$667$	24.0000			0.929284
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−9.50000	+	16.4545i	−0.366198	+	0.634274i	−0.988968	−	0.148132i	$-0.952674\pi$
$673$	−9.50000	+	16.4545i	−0.366198	+	0.634274i	0.622770	+	0.782405i	$0.286007\pi$
$674$		0			0
$675$	−5.00000	−	8.66025i	−0.192450	−	0.333333i
$676$		0			0
$677$	42.0000			1.61419			0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000			1.61419			0.807096	+	0.590421i	$0.201038\pi$
$678$		0			0
$679$	6.00000	+	3.46410i	0.230259	+	0.132940i
$680$		0			0
$681$	−16.5000	+	9.52628i	−0.632281	+	0.365048i
$682$		0			0
$683$	−25.5000	+	14.7224i	−0.975730	+	0.563338i	−0.900978	−	0.433864i	$-0.857150\pi$
$683$	−25.5000	+	14.7224i	−0.975730	+	0.563338i	−0.0747520	+	0.997202i	$0.523817\pi$
$684$		0			0
$685$	−27.0000	−	15.5885i	−1.03162	−	0.595604i
$686$		0			0
$687$	−6.50000	−	11.2583i	−0.247990	−	0.429532i
$688$		0			0
$689$		−	5.19615i		−	0.197958i
$690$		0			0
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	0.657823	−	0.753173i	$-0.271478\pi$
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	−0.981178	+	0.193105i	$0.938144\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	8.66025i		−	0.328502i
$696$		0			0
$697$		−	15.5885i		−	0.590455i
$698$		0			0
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$		0			0
$701$	19.5000	−	11.2583i	0.736505	−	0.425221i	−0.0842923	−	0.996441i	$-0.526863\pi$
$701$	19.5000	−	11.2583i	0.736505	−	0.425221i	0.820797	+	0.571220i	$0.193530\pi$
$702$		0			0
$703$	−10.5000	+	0.866025i	−0.396015	+	0.0326628i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$		−	6.92820i		−	0.260194i	−0.991501	−	0.130097i	$-0.958471\pi$
$709$		−	6.92820i		−	0.260194i	0.991501	−	0.130097i	$-0.0415289\pi$
$710$		0			0
$711$		−	24.2487i		−	0.909398i
$712$		0			0
$713$	−12.0000			−0.449404
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	12.1244i		−	0.452792i
$718$		0			0
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	0.601075	−	0.799193i	$-0.294739\pi$
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	−0.992659	+	0.120950i	$0.961406\pi$
$720$		0			0
$721$	15.0000	+	8.66025i	0.558629	+	0.322525i
$722$		0			0
$723$	25.5000	−	14.7224i	0.948355	−	0.547533i
$724$		0			0
$725$	−12.0000	+	6.92820i	−0.445669	+	0.257307i
$726$		0			0
$727$	−28.5000	−	16.4545i	−1.05701	−	0.610263i	−0.132404	−	0.991196i	$-0.542270\pi$
$727$	−28.5000	−	16.4545i	−1.05701	−	0.610263i	−0.924603	+	0.380933i	$0.875603\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−3.00000	−	5.19615i	−0.110959	−	0.192187i
$732$		0			0
$733$	−11.5000	+	19.9186i	−0.424762	+	0.735710i	−0.996398	−	0.0847976i	$-0.972976\pi$
$733$	−11.5000	+	19.9186i	−0.424762	+	0.735710i	0.571636	+	0.820507i	$0.306309\pi$
$734$		0			0
$735$	9.00000	+	5.19615i	0.331970	+	0.191663i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	4.00000			0.147142			0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000			0.147142			0.0735712	+	0.997290i	$0.476560\pi$
$740$		0			0
$741$	3.00000			0.110208
$742$		0			0
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	−0.970173	−	0.242415i	$-0.922060\pi$
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	0.695024	+	0.718986i	$0.255394\pi$
$744$		0			0
$745$	−9.00000	−	5.19615i	−0.329734	−	0.190372i
$746$		0			0
$747$	9.00000	−	15.5885i	0.329293	−	0.570352i
$748$		0			0
$749$	−4.50000	−	7.79423i	−0.164426	−	0.284795i
$750$		0			0
$751$	20.0000			0.729810			0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000			0.729810			0.364905	+	0.931045i	$0.381101\pi$
$752$		0			0
$753$	15.0000	+	8.66025i	0.546630	+	0.315597i
$754$		0			0
$755$	−28.5000	+	16.4545i	−1.03722	+	0.598840i
$756$		0			0
$757$	−4.50000	+	2.59808i	−0.163555	+	0.0944287i	−0.579543	−	0.814941i	$-0.696769\pi$
$757$	−4.50000	+	2.59808i	−0.163555	+	0.0944287i	0.415988	+	0.909370i	$0.363436\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	22.5000	+	38.9711i	0.815624	+	1.41270i	0.908879	+	0.417061i	$0.136940\pi$
$761$	22.5000	+	38.9711i	0.815624	+	1.41270i	−0.0932544	+	0.995642i	$0.529727\pi$
$762$		0			0
$763$			12.1244i			0.438931i
$764$		0			0
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$		0			0
$767$	−3.00000			−0.108324
$768$		0			0
$769$			20.7846i			0.749512i	0.927123	+	0.374756i	$0.122274\pi$
$769$			20.7846i			0.749512i	−0.927123	+	0.374756i	$0.877726\pi$
$770$		0			0
$771$			5.19615i			0.187135i
$772$		0			0
$773$	−7.50000	+	12.9904i	−0.269756	+	0.467232i	−0.968799	−	0.247849i	$-0.920276\pi$
$773$	−7.50000	+	12.9904i	−0.269756	+	0.467232i	0.699043	+	0.715080i	$0.253610\pi$
$774$		0			0
$775$	6.00000	−	3.46410i	0.215526	−	0.124434i
$776$		0			0
$777$	5.50000	+	2.59808i	0.197311	+	0.0932055i
$778$		0			0
$779$	13.5000	−	7.79423i	0.483688	−	0.279257i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	34.6410i		−	1.23797i
$784$		0			0
$785$			8.66025i			0.309098i
$786$		0			0
$787$	−32.0000			−1.14068			−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000			−1.14068			−0.570338	+	0.821410i	$0.693188\pi$
$788$		0			0
$789$	−10.5000	−	18.1865i	−0.373810	−	0.647458i
$790$		0			0
$791$		−	1.73205i		−	0.0615846i
$792$		0			0
$793$	1.50000	+	2.59808i	0.0532666	+	0.0922604i
$794$		0			0
$795$	−4.50000	−	2.59808i	−0.159599	−	0.0921443i
$796$		0			0
$797$	31.5000	−	18.1865i	1.11579	−	0.644200i	0.175465	−	0.984486i	$-0.443857\pi$
$797$	31.5000	−	18.1865i	1.11579	−	0.644200i	0.940322	+	0.340286i	$0.110524\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−9.00000	−	5.19615i	−0.317999	−	0.183597i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	3.00000	+	5.19615i	0.105736	+	0.183140i
$806$		0			0
$807$	−15.0000	+	25.9808i	−0.528025	+	0.914566i
$808$		0			0
$809$	−16.5000	−	9.52628i	−0.580109	−	0.334926i	0.181068	−	0.983471i	$-0.442045\pi$
$809$	−16.5000	−	9.52628i	−0.580109	−	0.334926i	−0.761177	+	0.648544i	$0.775378\pi$
$810$		0			0
$811$	24.5000	−	42.4352i	0.860311	−	1.49010i	−0.0113172	−	0.999936i	$-0.503602\pi$
$811$	24.5000	−	42.4352i	0.860311	−	1.49010i	0.871629	−	0.490167i	$-0.163064\pi$
$812$		0			0
$813$	7.00000			0.245501
$814$		0			0
$815$	33.0000			1.15594
$816$		0			0
$817$	3.00000	−	5.19615i	0.104957	−	0.181790i
$818$		0			0
$819$	3.00000	+	1.73205i	0.104828	+	0.0605228i
$820$		0			0
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	−0.891013	−	0.453978i	$-0.850005\pi$
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	0.838663	+	0.544651i	$0.183338\pi$
$822$		0			0
$823$	23.5000	+	40.7032i	0.819159	+	1.41882i	0.906303	+	0.422628i	$0.138892\pi$
$823$	23.5000	+	40.7032i	0.819159	+	1.41882i	−0.0871445	+	0.996196i	$0.527774\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	25.5000	+	14.7224i	0.886722	+	0.511949i	0.872869	−	0.487955i	$-0.162257\pi$
$827$	25.5000	+	14.7224i	0.886722	+	0.511949i	0.0138531	+	0.999904i	$0.495590\pi$
$828$		0			0
$829$	31.5000	−	18.1865i	1.09404	−	0.631644i	0.159391	−	0.987216i	$-0.449047\pi$
$829$	31.5000	−	18.1865i	1.09404	−	0.631644i	0.934649	+	0.355571i	$0.115714\pi$
$830$		0			0
$831$	13.5000	−	7.79423i	0.468310	−	0.270379i
$832$		0			0
$833$	9.00000	+	5.19615i	0.311832	+	0.180036i
$834$		0			0
$835$	−10.5000	−	18.1865i	−0.363367	−	0.629371i
$836$		0			0
$837$			17.3205i			0.598684i
$838$		0			0
$839$	−4.50000	−	7.79423i	−0.155357	−	0.269087i	0.777832	−	0.628473i	$-0.216320\pi$
$839$	−4.50000	−	7.79423i	−0.155357	−	0.269087i	−0.933189	+	0.359386i	$0.882986\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$		0			0
$843$		−	15.5885i		−	0.536895i
$844$		0			0
$845$		−	17.3205i		−	0.595844i
$846$		0			0
$847$	−5.50000	+	9.52628i	−0.188982	+	0.327327i
$848$		0			0
$849$	25.5000	−	14.7224i	0.875158	−	0.505273i
$850$		0			0
$851$	−12.0000	−	17.3205i	−0.411355	−	0.593739i
$852$		0			0
$853$	37.5000	−	21.6506i	1.28398	−	0.741304i	0.306403	−	0.951902i	$-0.400875\pi$
$853$	37.5000	−	21.6506i	1.28398	−	0.741304i	0.977573	+	0.210598i	$0.0675412\pi$
$854$		0			0
$855$	−3.00000	+	5.19615i	−0.102598	+	0.177705i
$856$		0			0
$857$		−	48.4974i		−	1.65664i	−0.560255	−	0.828320i	$-0.689297\pi$
$857$		−	48.4974i		−	1.65664i	0.560255	−	0.828320i	$-0.310703\pi$
$858$		0			0
$859$			10.3923i			0.354581i	0.984159	+	0.177290i	$0.0567332\pi$
$859$			10.3923i			0.354581i	−0.984159	+	0.177290i	$0.943267\pi$
$860$		0			0
$861$	−9.00000			−0.306719
$862$		0			0
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	0.979612	+	0.200897i	$0.0643855\pi$
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	−0.315825	+	0.948818i	$0.602281\pi$
$864$		0			0
$865$		−	25.9808i		−	0.883372i
$866$		0			0
$867$	7.00000	+	12.1244i	0.237732	+	0.411765i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	19.5000	−	11.2583i	0.660732	−	0.381474i
$872$		0			0
$873$	−12.0000	+	6.92820i	−0.406138	+	0.234484i
$874$		0			0
$875$	−10.5000	−	6.06218i	−0.354965	−	0.204939i
$876$		0			0
$877$	−2.00000			−0.0675352			−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000			−0.0675352			−0.0337676	+	0.999430i	$0.510751\pi$
$878$		0			0
$879$	−4.50000	−	7.79423i	−0.151781	−	0.262893i
$880$		0			0
$881$	−1.50000	+	2.59808i	−0.0505363	+	0.0875314i	−0.890187	−	0.455595i	$-0.849426\pi$
$881$	−1.50000	+	2.59808i	−0.0505363	+	0.0875314i	0.839651	+	0.543127i	$0.182760\pi$
$882$		0			0
$883$	43.5000	+	25.1147i	1.46389	+	0.845178i	0.999188	−	0.0402882i	$-0.0128276\pi$
$883$	43.5000	+	25.1147i	1.46389	+	0.845178i	0.464703	+	0.885466i	$0.346161\pi$
$884$		0			0
$885$	−1.50000	+	2.59808i	−0.0504219	+	0.0873334i
$886$		0			0
$887$	48.0000			1.61168			0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000			1.61168			0.805841	+	0.592132i	$0.201714\pi$
$888$		0			0
$889$	11.0000			0.368928
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	15.0000	−	25.9808i	0.501395	−	0.868441i
$896$		0			0
$897$	3.00000	+	5.19615i	0.100167	+	0.173494i
$898$		0			0
$899$	24.0000			0.800445
$900$		0			0
$901$	−4.50000	−	2.59808i	−0.149917	−	0.0865545i
$902$		0			0
$903$	−3.00000	+	1.73205i	−0.0998337	+	0.0576390i
$904$		0			0
$905$	7.50000	−	4.33013i	0.249308	−	0.143938i
$906$		0			0
$907$	31.5000	+	18.1865i	1.04594	+	0.603874i	0.921510	−	0.388354i	$-0.126956\pi$
$907$	31.5000	+	18.1865i	1.04594	+	0.603874i	0.124430	+	0.992228i	$0.460290\pi$
$908$		0			0
$909$	−6.00000	−	10.3923i	−0.199007	−	0.344691i
$910$		0			0
$911$			58.8897i			1.95110i	0.219769	+	0.975552i	$0.429470\pi$
$911$			58.8897i			1.95110i	−0.219769	+	0.975552i	$0.570530\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	3.00000			0.0991769
$916$		0			0
$917$			15.5885i			0.514776i
$918$		0			0
$919$		−	3.46410i		−	0.114270i	−0.998366	−	0.0571351i	$-0.981803\pi$
$919$		−	3.46410i		−	0.114270i	0.998366	−	0.0571351i	$-0.0181966\pi$
$920$		0			0
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$		0			0
$923$	−22.5000	+	12.9904i	−0.740597	+	0.427584i
$924$		0			0
$925$	11.0000	+	5.19615i	0.361678	+	0.170848i
$926$		0			0
$927$	−30.0000	+	17.3205i	−0.985329	+	0.568880i
$928$		0			0
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	0.345708	+	0.938342i	$0.387639\pi$
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	−0.985482	+	0.169779i	$0.945695\pi$
$930$		0			0
$931$			10.3923i			0.340594i
$932$		0			0
$933$		−	25.9808i		−	0.850572i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−29.5000	−	51.0955i	−0.963723	−	1.66922i	−0.713008	−	0.701156i	$-0.752667\pi$
$937$	−29.5000	−	51.0955i	−0.963723	−	1.66922i	−0.250715	−	0.968061i	$-0.580666\pi$
$938$		0			0
$939$		−	22.5167i		−	0.734803i
$940$		0			0
$941$	22.5000	+	38.9711i	0.733479	+	1.27042i	0.955387	+	0.295355i	$0.0954381\pi$
$941$	22.5000	+	38.9711i	0.733479	+	1.27042i	−0.221908	+	0.975068i	$0.571229\pi$
$942$		0			0
$943$	27.0000	+	15.5885i	0.879241	+	0.507630i
$944$		0			0
$945$	7.50000	−	4.33013i	0.243975	−	0.140859i
$946$		0			0
$947$	22.5000	−	12.9904i	0.731152	−	0.422131i	−0.0876916	−	0.996148i	$-0.527949\pi$
$947$	22.5000	−	12.9904i	0.731152	−	0.422131i	0.818843	+	0.574017i	$0.194616\pi$
$948$		0			0
$949$	−3.00000	−	1.73205i	−0.0973841	−	0.0562247i
$950$		0			0
$951$	−15.0000			−0.486408
$952$		0			0
$953$	4.50000	+	7.79423i	0.145769	+	0.252480i	0.929660	−	0.368419i	$-0.120101\pi$
$953$	4.50000	+	7.79423i	0.145769	+	0.252480i	−0.783890	+	0.620899i	$0.786768\pi$
$954$		0			0
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.00000	+	15.5885i	−0.290625	+	0.503378i
$960$		0			0
$961$	19.0000			0.612903
$962$		0			0
$963$	18.0000			0.580042
$964$		0			0
$965$	−18.0000	+	31.1769i	−0.579441	+	1.00362i
$966$		0			0
$967$	−22.5000	−	12.9904i	−0.723551	−	0.417742i	0.0925071	−	0.995712i	$-0.470512\pi$
$967$	−22.5000	−	12.9904i	−0.723551	−	0.417742i	−0.816058	+	0.577970i	$0.803845\pi$
$968$		0			0
$969$	1.50000	−	2.59808i	0.0481869	−	0.0834622i
$970$		0			0
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	0.889090	−	0.457732i	$-0.151338\pi$
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	−0.840953	+	0.541108i	$0.818005\pi$
$972$		0			0
$973$	−5.00000			−0.160293
$974$		0			0
$975$	−3.00000	−	1.73205i	−0.0960769	−	0.0554700i
$976$		0			0
$977$	37.5000	−	21.6506i	1.19973	−	0.692665i	0.239236	−	0.970961i	$-0.423103\pi$
$977$	37.5000	−	21.6506i	1.19973	−	0.692665i	0.960495	+	0.278296i	$0.0897697\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−21.0000	−	12.1244i	−0.670478	−	0.387101i
$982$		0			0
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	0.888955	−	0.457995i	$-0.151432\pi$
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	−0.841112	+	0.540860i	$0.818099\pi$
$984$		0			0
$985$			36.3731i			1.15894i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.0000			0.381578
$990$		0			0
$991$		−	38.1051i		−	1.21045i	−0.796055	−	0.605224i	$-0.793083\pi$
$991$		−	38.1051i		−	1.21045i	0.796055	−	0.605224i	$-0.206917\pi$
$992$		0			0
$993$		−	5.19615i		−	0.164895i
$994$		0			0
$995$	9.00000	−	15.5885i	0.285319	−	0.494187i
$996$		0			0
$997$	31.5000	−	18.1865i	0.997615	−	0.575973i	0.0900732	−	0.995935i	$-0.471290\pi$
$997$	31.5000	−	18.1865i	0.997615	−	0.575973i	0.907542	+	0.419962i	$0.137957\pi$
$998$		0			0
$999$	−25.0000	+	17.3205i	−0.790965	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.w.b.529.1		2
4.3	odd	2		148.2.h.a.85.1	✓	2
12.11	even	2		1332.2.bi.a.973.1		2
37.27	even	6	inner	592.2.w.b.545.1		2
148.27	odd	6		148.2.h.a.101.1	yes	2
148.103	even	12		5476.2.a.c.1.1		2
148.119	even	12		5476.2.a.c.1.2		2
444.323	even	6		1332.2.bi.a.397.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
148.2.h.a.85.1	✓	2	4.3	odd	2
148.2.h.a.101.1	yes	2	148.27	odd	6
592.2.w.b.529.1		2	1.1	even	1	trivial
592.2.w.b.545.1		2	37.27	even	6	inner
1332.2.bi.a.397.1		2	444.323	even	6
1332.2.bi.a.973.1		2	12.11	even	2
5476.2.a.c.1.1		2	148.103	even	12
5476.2.a.c.1.2		2	148.119	even	12

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.50000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.50000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.50000 + 0.866025i) q^{13} +(1.50000 - 0.866025i) q^{15} +(1.50000 - 0.866025i) q^{17} +(1.50000 + 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{21} +3.46410i q^{23} +(-1.00000 - 1.73205i) q^{25} +5.00000 q^{27} -6.92820i q^{29} +3.46410i q^{31} +(1.50000 - 0.866025i) q^{35} +(-5.00000 + 3.46410i) q^{37} +(1.50000 - 0.866025i) q^{39} +(4.50000 - 7.79423i) q^{41} -3.46410i q^{43} +3.46410i q^{45} +(3.00000 + 5.19615i) q^{49} -1.73205i q^{51} +(-1.50000 - 2.59808i) q^{53} +(1.50000 - 0.866025i) q^{57} +(-1.50000 + 0.866025i) q^{59} +(1.50000 + 0.866025i) q^{61} +2.00000 q^{63} +(1.50000 + 2.59808i) q^{65} +(6.50000 - 11.2583i) q^{67} +(3.00000 + 1.73205i) q^{69} +(-7.50000 + 12.9904i) q^{71} -2.00000 q^{73} -2.00000 q^{75} +(-10.5000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{83} +3.00000 q^{85} +(-6.00000 - 3.46410i) q^{87} +(-4.50000 + 2.59808i) q^{89} +(1.50000 - 0.866025i) q^{91} +(3.00000 + 1.73205i) q^{93} +(1.50000 + 2.59808i) q^{95} +6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 3 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 + 3 * q^5 + q^7 + 2 * q^9	\( 2 q + q^{3} + 3 q^{5} + q^{7} + 2 q^{9} + 3 q^{13} + 3 q^{15} + 3 q^{17} + 3 q^{19} - q^{21} - 2 q^{25} + 10 q^{27} + 3 q^{35} - 10 q^{37} + 3 q^{39} + 9 q^{41} + 6 q^{49} - 3 q^{53} + 3 q^{57} - 3 q^{59} + 3 q^{61} + 4 q^{63} + 3 q^{65} + 13 q^{67} + 6 q^{69} - 15 q^{71} - 4 q^{73} - 4 q^{75} - 21 q^{79} - q^{81} - 9 q^{83} + 6 q^{85} - 12 q^{87} - 9 q^{89} + 3 q^{91} + 6 q^{93} + 3 q^{95}+O(q^{100}) \) 2 * q + q^3 + 3 * q^5 + q^7 + 2 * q^9 + 3 * q^13 + 3 * q^15 + 3 * q^17 + 3 * q^19 - q^21 - 2 * q^25 + 10 * q^27 + 3 * q^35 - 10 * q^37 + 3 * q^39 + 9 * q^41 + 6 * q^49 - 3 * q^53 + 3 * q^57 - 3 * q^59 + 3 * q^61 + 4 * q^63 + 3 * q^65 + 13 * q^67 + 6 * q^69 - 15 * q^71 - 4 * q^73 - 4 * q^75 - 21 * q^79 - q^81 - 9 * q^83 + 6 * q^85 - 12 * q^87 - 9 * q^89 + 3 * q^91 + 6 * q^93 + 3 * q^95

Introduction

L-functions

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