LMFDB - Embedded newform 672.2.bc.b.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(257,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))

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

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

chi := DirichletCharacter("672.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bc (of order $6$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	672.257
Dual form			672.2.bc.b.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-4.33013 + 2.50000i) q^{11} -3.46410i q^{13} +(-0.866025 - 1.50000i) q^{15} +(0.500000 + 0.866025i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(-4.50000 + 0.866025i) q^{21} +(-4.33013 - 2.50000i) q^{23} +(2.00000 + 3.46410i) q^{25} -5.19615 q^{27} -3.46410i q^{29} +(7.79423 - 4.50000i) q^{31} +8.66025i q^{33} +(-2.59808 + 0.500000i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-5.19615 - 3.00000i) q^{39} +8.00000 q^{41} -3.00000 q^{45} +(-0.866025 + 1.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +1.73205 q^{51} +(10.5000 - 6.06218i) q^{53} +5.00000i q^{55} +(-1.50000 + 0.866025i) q^{57} +(-4.33013 - 7.50000i) q^{59} +(-10.5000 - 6.06218i) q^{61} +(-2.59808 + 7.50000i) q^{63} +(-3.00000 - 1.73205i) q^{65} +(-6.06218 - 10.5000i) q^{67} +(-7.50000 + 4.33013i) q^{69} -2.00000i q^{71} +(7.50000 - 4.33013i) q^{73} +6.92820 q^{75} +(12.5000 + 4.33013i) q^{77} +(-0.866025 + 1.50000i) q^{79} +(-4.50000 + 7.79423i) q^{81} +13.8564 q^{83} +1.00000 q^{85} +(-5.19615 - 3.00000i) q^{87} +(-6.50000 + 11.2583i) q^{89} +(-6.92820 + 6.00000i) q^{91} -15.5885i q^{93} +(-0.866025 + 0.500000i) q^{95} +3.46410i q^{97} +(12.9904 + 7.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^5 - 6 * q^9	$ 4 q + 2 q^{5} - 6 q^{9} + 2 q^{17} - 18 q^{21} + 8 q^{25} - 6 q^{37} + 32 q^{41} - 12 q^{45} - 4 q^{49} + 42 q^{53} - 6 q^{57} - 42 q^{61} - 12 q^{65} - 30 q^{69} + 30 q^{73} + 50 q^{77} - 18 q^{81} + 4 q^{85} - 26 q^{89}+O(q^{100}) $ 4 * q + 2 * q^5 - 6 * q^9 + 2 * q^17 - 18 * q^21 + 8 * q^25 - 6 * q^37 + 32 * q^41 - 12 * q^45 - 4 * q^49 + 42 * q^53 - 6 * q^57 - 42 * q^61 - 12 * q^65 - 30 * q^69 + 30 * q^73 + 50 * q^77 - 18 * q^81 + 4 * q^85 - 26 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	−4.33013	+	2.50000i	−1.30558	+	0.753778i	−0.981356	−	0.192201i	$-0.938437\pi$
$11$	−4.33013	+	2.50000i	−1.30558	+	0.753778i	−0.324227	+	0.945979i	$0.605104\pi$
$12$		0			0
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$		0			0
$15$	−0.866025	−	1.50000i	−0.223607	−	0.387298i
$16$		0			0
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	0.920268	−	0.391289i	$-0.127971\pi$
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	−0.799000	+	0.601331i	$0.794637\pi$
$18$		0			0
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	0.397360	−	0.917663i	$-0.369927\pi$
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	−0.596040	+	0.802955i	$0.703260\pi$
$20$		0			0
$21$	−4.50000	+	0.866025i	−0.981981	+	0.188982i
$22$		0			0
$23$	−4.33013	−	2.50000i	−0.902894	−	0.521286i	−0.0247559	−	0.999694i	$-0.507881\pi$
$23$	−4.33013	−	2.50000i	−0.902894	−	0.521286i	−0.878138	+	0.478407i	$0.841214\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$		−	3.46410i		−	0.643268i	−0.946864	−	0.321634i	$-0.895768\pi$
$29$		−	3.46410i		−	0.643268i	0.946864	−	0.321634i	$-0.104232\pi$
$30$		0			0
$31$	7.79423	−	4.50000i	1.39988	−	0.808224i	0.405505	−	0.914093i	$-0.367096\pi$
$31$	7.79423	−	4.50000i	1.39988	−	0.808224i	0.994380	+	0.105869i	$0.0337625\pi$
$32$		0			0
$33$			8.66025i			1.50756i
$34$		0			0
$35$	−2.59808	+	0.500000i	−0.439155	+	0.0845154i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$		0			0
$39$	−5.19615	−	3.00000i	−0.832050	−	0.480384i
$40$		0			0
$41$	8.00000			1.24939			0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000			1.24939			0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$		0			0
$47$	−0.866025	+	1.50000i	−0.126323	+	0.218797i	−0.922249	−	0.386596i	$-0.873651\pi$
$47$	−0.866025	+	1.50000i	−0.126323	+	0.218797i	0.795926	+	0.605393i	$0.206984\pi$
$48$		0			0
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$	1.73205			0.242536
$52$		0			0
$53$	10.5000	−	6.06218i	1.44229	−	0.832704i	0.444284	−	0.895886i	$-0.353458\pi$
$53$	10.5000	−	6.06218i	1.44229	−	0.832704i	0.998002	+	0.0631819i	$0.0201248\pi$
$54$		0			0
$55$			5.00000i			0.674200i
$56$		0			0
$57$	−1.50000	+	0.866025i	−0.198680	+	0.114708i
$58$		0			0
$59$	−4.33013	−	7.50000i	−0.563735	−	0.976417i	−0.997166	−	0.0752304i	$-0.976031\pi$
$59$	−4.33013	−	7.50000i	−0.563735	−	0.976417i	0.433432	−	0.901186i	$-0.357303\pi$
$60$		0			0
$61$	−10.5000	−	6.06218i	−1.34439	−	0.776182i	−0.356939	−	0.934128i	$-0.616180\pi$
$61$	−10.5000	−	6.06218i	−1.34439	−	0.776182i	−0.987448	+	0.157945i	$0.949513\pi$
$62$		0			0
$63$	−2.59808	+	7.50000i	−0.327327	+	0.944911i
$64$		0			0
$65$	−3.00000	−	1.73205i	−0.372104	−	0.214834i
$66$		0			0
$67$	−6.06218	−	10.5000i	−0.740613	−	1.28278i	−0.952217	−	0.305424i	$-0.901202\pi$
$67$	−6.06218	−	10.5000i	−0.740613	−	1.28278i	0.211604	−	0.977356i	$-0.432131\pi$
$68$		0			0
$69$	−7.50000	+	4.33013i	−0.902894	+	0.521286i
$70$		0			0
$71$		−	2.00000i		−	0.237356i	−0.992933	−	0.118678i	$-0.962134\pi$
$71$		−	2.00000i		−	0.237356i	0.992933	−	0.118678i	$-0.0378657\pi$
$72$		0			0
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.00787336	−	0.999969i	$-0.497494\pi$
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.869935	+	0.493166i	$0.164160\pi$
$74$		0			0
$75$	6.92820			0.800000
$76$		0			0
$77$	12.5000	+	4.33013i	1.42451	+	0.493464i
$78$		0			0
$79$	−0.866025	+	1.50000i	−0.0974355	+	0.168763i	−0.910622	−	0.413239i	$-0.864397\pi$
$79$	−0.866025	+	1.50000i	−0.0974355	+	0.168763i	0.813187	+	0.582003i	$0.197731\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	13.8564			1.52094			0.760469	−	0.649374i	$-0.224969\pi$
$83$	13.8564			1.52094			0.760469	+	0.649374i	$0.224969\pi$
$84$		0			0
$85$	1.00000			0.108465
$86$		0			0
$87$	−5.19615	−	3.00000i	−0.557086	−	0.321634i
$88$		0			0
$89$	−6.50000	+	11.2583i	−0.688999	+	1.19338i	0.283164	+	0.959072i	$0.408616\pi$
$89$	−6.50000	+	11.2583i	−0.688999	+	1.19338i	−0.972162	+	0.234309i	$0.924717\pi$
$90$		0			0
$91$	−6.92820	+	6.00000i	−0.726273	+	0.628971i
$92$		0			0
$93$		−	15.5885i		−	1.61645i
$94$		0			0
$95$	−0.866025	+	0.500000i	−0.0888523	+	0.0512989i
$96$		0			0
$97$			3.46410i			0.351726i	0.984415	+	0.175863i	$0.0562716\pi$
$97$			3.46410i			0.351726i	−0.984415	+	0.175863i	$0.943728\pi$
$98$		0			0
$99$	12.9904	+	7.50000i	1.30558	+	0.753778i
$100$		0			0
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	0.637678	−	0.770303i	$-0.279895\pi$
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	−0.985941	+	0.167094i	$0.946562\pi$
$102$		0			0
$103$	7.79423	+	4.50000i	0.767988	+	0.443398i	0.832156	−	0.554541i	$-0.187106\pi$
$103$	7.79423	+	4.50000i	0.767988	+	0.443398i	−0.0641683	+	0.997939i	$0.520439\pi$
$104$		0			0
$105$	−1.50000	+	4.33013i	−0.146385	+	0.422577i
$106$		0			0
$107$	11.2583	+	6.50000i	1.08838	+	0.628379i	0.933146	−	0.359498i	$-0.117052\pi$
$107$	11.2583	+	6.50000i	1.08838	+	0.628379i	0.155238	+	0.987877i	$0.450386\pi$
$108$		0			0
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	0.721102	−	0.692829i	$-0.243636\pi$
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	−0.960558	+	0.278078i	$0.910303\pi$
$110$		0			0
$111$	2.59808	+	4.50000i	0.246598	+	0.427121i
$112$		0			0
$113$		−	17.3205i		−	1.62938i	−0.579899	−	0.814688i	$-0.696908\pi$
$113$		−	17.3205i		−	1.62938i	0.579899	−	0.814688i	$-0.303092\pi$
$114$		0			0
$115$	−4.33013	+	2.50000i	−0.403786	+	0.233126i
$116$		0			0
$117$	−9.00000	+	5.19615i	−0.832050	+	0.480384i
$118$		0			0
$119$	0.866025	−	2.50000i	0.0793884	−	0.229175i
$120$		0			0
$121$	7.00000	−	12.1244i	0.636364	−	1.10221i
$122$		0			0
$123$	6.92820	−	12.0000i	0.624695	−	1.08200i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	−0.956916	−	0.290365i	$-0.906223\pi$
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	0.729921	+	0.683531i	$0.239557\pi$
$132$		0			0
$133$	0.500000	+	2.59808i	0.0433555	+	0.225282i
$134$		0			0
$135$	−2.59808	+	4.50000i	−0.223607	+	0.387298i
$136$		0			0
$137$	19.5000	−	11.2583i	1.66600	−	0.961864i	0.696235	−	0.717814i	$-0.254857\pi$
$137$	19.5000	−	11.2583i	1.66600	−	0.961864i	0.969763	−	0.244050i	$-0.0784761\pi$
$138$		0			0
$139$			6.00000i			0.508913i	0.967084	+	0.254457i	$0.0818966\pi$
$139$			6.00000i			0.508913i	−0.967084	+	0.254457i	$0.918103\pi$
$140$		0			0
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$		0			0
$143$	8.66025	+	15.0000i	0.724207	+	1.25436i
$144$		0			0
$145$	−3.00000	−	1.73205i	−0.249136	−	0.143839i
$146$		0			0
$147$	9.52628	+	7.50000i	0.785714	+	0.618590i
$148$		0			0
$149$	−16.5000	−	9.52628i	−1.35173	−	0.780423i	−0.363241	−	0.931695i	$-0.618330\pi$
$149$	−16.5000	−	9.52628i	−1.35173	−	0.780423i	−0.988492	+	0.151272i	$0.951663\pi$
$150$		0			0
$151$	9.52628	+	16.5000i	0.775238	+	1.34275i	0.934661	+	0.355541i	$0.115703\pi$
$151$	9.52628	+	16.5000i	0.775238	+	1.34275i	−0.159423	+	0.987210i	$0.550963\pi$
$152$		0			0
$153$	1.50000	−	2.59808i	0.121268	−	0.210042i
$154$		0			0
$155$		−	9.00000i		−	0.722897i
$156$		0			0
$157$	1.50000	−	0.866025i	0.119713	−	0.0691164i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	1.50000	−	0.866025i	0.119713	−	0.0691164i	0.558661	+	0.829396i	$0.311315\pi$
$158$		0			0
$159$		−	21.0000i		−	1.66541i
$160$		0			0
$161$	2.50000	+	12.9904i	0.197028	+	1.02379i
$162$		0			0
$163$	−4.33013	+	7.50000i	−0.339162	+	0.587445i	−0.984275	−	0.176641i	$-0.943477\pi$
$163$	−4.33013	+	7.50000i	−0.339162	+	0.587445i	0.645114	+	0.764087i	$0.276810\pi$
$164$		0			0
$165$	7.50000	+	4.33013i	0.583874	+	0.337100i
$166$		0			0
$167$	10.3923			0.804181			0.402090	−	0.915600i	$-0.368284\pi$
$167$	10.3923			0.804181			0.402090	+	0.915600i	$0.368284\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$			3.00000i			0.229416i
$172$		0			0
$173$	−0.500000	+	0.866025i	−0.0380143	+	0.0658427i	−0.884407	−	0.466717i	$-0.845437\pi$
$173$	−0.500000	+	0.866025i	−0.0380143	+	0.0658427i	0.846392	+	0.532560i	$0.178770\pi$
$174$		0			0
$175$	3.46410	−	10.0000i	0.261861	−	0.755929i
$176$		0			0
$177$	−15.0000			−1.12747
$178$		0			0
$179$	6.06218	−	3.50000i	0.453108	−	0.261602i	−0.256034	−	0.966668i	$-0.582416\pi$
$179$	6.06218	−	3.50000i	0.453108	−	0.261602i	0.709142	+	0.705066i	$0.249082\pi$
$180$		0			0
$181$			20.7846i			1.54491i	0.635071	+	0.772454i	$0.280971\pi$
$181$			20.7846i			1.54491i	−0.635071	+	0.772454i	$0.719029\pi$
$182$		0			0
$183$	−18.1865	+	10.5000i	−1.34439	+	0.776182i
$184$		0			0
$185$	1.50000	+	2.59808i	0.110282	+	0.191014i
$186$		0			0
$187$	−4.33013	−	2.50000i	−0.316650	−	0.182818i
$188$		0			0
$189$	9.00000	+	10.3923i	0.654654	+	0.755929i
$190$		0			0
$191$	11.2583	+	6.50000i	0.814624	+	0.470323i	0.848559	−	0.529101i	$-0.177471\pi$
$191$	11.2583	+	6.50000i	0.814624	+	0.470323i	−0.0339349	+	0.999424i	$0.510804\pi$
$192$		0			0
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	0.998911	+	0.0466572i	$0.0148568\pi$
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	−0.459049	+	0.888411i	$0.651810\pi$
$194$		0			0
$195$	−5.19615	+	3.00000i	−0.372104	+	0.214834i
$196$		0			0
$197$			17.3205i			1.23404i	0.786949	+	0.617018i	$0.211659\pi$
$197$			17.3205i			1.23404i	−0.786949	+	0.617018i	$0.788341\pi$
$198$		0			0
$199$	14.7224	−	8.50000i	1.04365	−	0.602549i	0.122782	−	0.992434i	$-0.460818\pi$
$199$	14.7224	−	8.50000i	1.04365	−	0.602549i	0.920864	+	0.389885i	$0.127485\pi$
$200$		0			0
$201$	−21.0000			−1.48123
$202$		0			0
$203$	−6.92820	+	6.00000i	−0.486265	+	0.421117i
$204$		0			0
$205$	4.00000	−	6.92820i	0.279372	−	0.483887i
$206$		0			0
$207$			15.0000i			1.04257i
$208$		0			0
$209$	5.00000			0.345857
$210$		0			0
$211$	−6.92820			−0.476957			−0.238479	−	0.971148i	$-0.576649\pi$
$211$	−6.92820			−0.476957			−0.238479	+	0.971148i	$0.576649\pi$
$212$		0			0
$213$	−3.00000	−	1.73205i	−0.205557	−	0.118678i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−22.5000	−	7.79423i	−1.52740	−	0.529107i
$218$		0			0
$219$		−	15.0000i		−	1.01361i
$220$		0			0
$221$	3.00000	−	1.73205i	0.201802	−	0.116510i
$222$		0			0
$223$		−	2.00000i		−	0.133930i	−0.997755	−	0.0669650i	$-0.978668\pi$
$223$		−	2.00000i		−	0.133930i	0.997755	−	0.0669650i	$-0.0213316\pi$
$224$		0			0
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$		0			0
$227$	0.866025	+	1.50000i	0.0574801	+	0.0995585i	0.893334	−	0.449394i	$-0.148360\pi$
$227$	0.866025	+	1.50000i	0.0574801	+	0.0995585i	−0.835853	+	0.548953i	$0.815027\pi$
$228$		0			0
$229$	−1.50000	−	0.866025i	−0.0991228	−	0.0572286i	0.449619	−	0.893220i	$-0.351560\pi$
$229$	−1.50000	−	0.866025i	−0.0991228	−	0.0572286i	−0.548742	+	0.835992i	$0.684893\pi$
$230$		0			0
$231$	17.3205	−	15.0000i	1.13961	−	0.986928i
$232$		0			0
$233$	−4.50000	−	2.59808i	−0.294805	−	0.170206i	0.345302	−	0.938492i	$-0.387777\pi$
$233$	−4.50000	−	2.59808i	−0.294805	−	0.170206i	−0.640107	+	0.768286i	$0.721110\pi$
$234$		0			0
$235$	0.866025	+	1.50000i	0.0564933	+	0.0978492i
$236$		0			0
$237$	1.50000	+	2.59808i	0.0974355	+	0.168763i
$238$		0			0
$239$		−	28.0000i		−	1.81117i	−0.424165	−	0.905585i	$-0.639432\pi$
$239$		−	28.0000i		−	1.81117i	0.424165	−	0.905585i	$-0.360568\pi$
$240$		0			0
$241$	−22.5000	+	12.9904i	−1.44935	+	0.836784i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−22.5000	+	12.9904i	−1.44935	+	0.836784i	−0.450910	+	0.892570i	$0.648900\pi$
$242$		0			0
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$		0			0
$245$	5.50000	+	4.33013i	0.351382	+	0.276642i
$246$		0			0
$247$	−1.73205	+	3.00000i	−0.110208	+	0.190885i
$248$		0			0
$249$	12.0000	−	20.7846i	0.760469	−	1.31717i
$250$		0			0
$251$	−3.46410			−0.218652			−0.109326	−	0.994006i	$-0.534869\pi$
$251$	−3.46410			−0.218652			−0.109326	+	0.994006i	$0.534869\pi$
$252$		0			0
$253$	25.0000			1.57174
$254$		0			0
$255$	0.866025	−	1.50000i	0.0542326	−	0.0939336i
$256$		0			0
$257$	−5.50000	+	9.52628i	−0.343081	+	0.594233i	−0.985003	−	0.172536i	$-0.944804\pi$
$257$	−5.50000	+	9.52628i	−0.343081	+	0.594233i	0.641923	+	0.766769i	$0.278137\pi$
$258$		0			0
$259$	7.79423	−	1.50000i	0.484310	−	0.0932055i
$260$		0			0
$261$	−9.00000	+	5.19615i	−0.557086	+	0.321634i
$262$		0			0
$263$	−9.52628	+	5.50000i	−0.587416	+	0.339145i	−0.764075	−	0.645128i	$-0.776804\pi$
$263$	−9.52628	+	5.50000i	−0.587416	+	0.339145i	0.176659	+	0.984272i	$0.443471\pi$
$264$		0			0
$265$		−	12.1244i		−	0.744793i
$266$		0			0
$267$	11.2583	+	19.5000i	0.688999	+	1.19338i
$268$		0			0
$269$	−0.500000	−	0.866025i	−0.0304855	−	0.0528025i	0.850380	−	0.526169i	$-0.176372\pi$
$269$	−0.500000	−	0.866025i	−0.0304855	−	0.0528025i	−0.880866	+	0.473366i	$0.843039\pi$
$270$		0			0
$271$	−12.9904	−	7.50000i	−0.789109	−	0.455593i	0.0505395	−	0.998722i	$-0.483906\pi$
$271$	−12.9904	−	7.50000i	−0.789109	−	0.455593i	−0.839649	+	0.543130i	$0.817239\pi$
$272$		0			0
$273$	3.00000	+	15.5885i	0.181568	+	0.943456i
$274$		0			0
$275$	−17.3205	−	10.0000i	−1.04447	−	0.603023i
$276$		0			0
$277$	10.5000	+	18.1865i	0.630884	+	1.09272i	0.987371	+	0.158423i	$0.0506409\pi$
$277$	10.5000	+	18.1865i	0.630884	+	1.09272i	−0.356488	+	0.934300i	$0.616026\pi$
$278$		0			0
$279$	−23.3827	−	13.5000i	−1.39988	−	0.808224i
$280$		0			0
$281$		−	17.3205i		−	1.03325i	−0.856210	−	0.516627i	$-0.827187\pi$
$281$		−	17.3205i		−	1.03325i	0.856210	−	0.516627i	$-0.172813\pi$
$282$		0			0
$283$	−26.8468	+	15.5000i	−1.59588	+	0.921379i	−0.603606	+	0.797283i	$0.706270\pi$
$283$	−26.8468	+	15.5000i	−1.59588	+	0.921379i	−0.992270	+	0.124096i	$0.960397\pi$
$284$		0			0
$285$			1.73205i			0.102598i
$286$		0			0
$287$	−13.8564	−	16.0000i	−0.817918	−	0.944450i
$288$		0			0
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$		0			0
$291$	5.19615	+	3.00000i	0.304604	+	0.175863i
$292$		0			0
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$	−8.66025			−0.504219
$296$		0			0
$297$	22.5000	−	12.9904i	1.30558	−	0.753778i
$298$		0			0
$299$	−8.66025	+	15.0000i	−0.500835	+	0.867472i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−12.1244			−0.696526
$304$		0			0
$305$	−10.5000	+	6.06218i	−0.601228	+	0.347119i
$306$		0			0
$307$		−	26.0000i		−	1.48390i	−0.670456	−	0.741949i	$-0.733902\pi$
$307$		−	26.0000i		−	1.48390i	0.670456	−	0.741949i	$-0.266098\pi$
$308$		0			0
$309$	13.5000	−	7.79423i	0.767988	−	0.443398i
$310$		0			0
$311$	9.52628	+	16.5000i	0.540186	+	0.935629i	0.998893	+	0.0470417i	$0.0149794\pi$
$311$	9.52628	+	16.5000i	0.540186	+	0.935629i	−0.458707	+	0.888587i	$0.651687\pi$
$312$		0			0
$313$	1.50000	+	0.866025i	0.0847850	+	0.0489506i	0.541793	−	0.840512i	$-0.317746\pi$
$313$	1.50000	+	0.866025i	0.0847850	+	0.0489506i	−0.457008	+	0.889463i	$0.651079\pi$
$314$		0			0
$315$	5.19615	+	6.00000i	0.292770	+	0.338062i
$316$		0			0
$317$	−13.5000	−	7.79423i	−0.758236	−	0.437767i	0.0704263	−	0.997517i	$-0.477564\pi$
$317$	−13.5000	−	7.79423i	−0.758236	−	0.437767i	−0.828662	+	0.559749i	$0.810897\pi$
$318$		0			0
$319$	8.66025	+	15.0000i	0.484881	+	0.839839i
$320$		0			0
$321$	19.5000	−	11.2583i	1.08838	−	0.628379i
$322$		0			0
$323$		−	1.00000i		−	0.0556415i
$324$		0			0
$325$	12.0000	−	6.92820i	0.665640	−	0.384308i
$326$		0			0
$327$	−8.66025			−0.478913
$328$		0			0
$329$	4.50000	−	0.866025i	0.248093	−	0.0477455i
$330$		0			0
$331$	12.9904	−	22.5000i	0.714016	−	1.23671i	−0.249322	−	0.968421i	$-0.580208\pi$
$331$	12.9904	−	22.5000i	0.714016	−	1.23671i	0.963338	−	0.268291i	$-0.0864589\pi$
$332$		0			0
$333$	9.00000			0.493197
$334$		0			0
$335$	−12.1244			−0.662424
$336$		0			0
$337$	−16.0000			−0.871576			−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000			−0.871576			−0.435788	+	0.900049i	$0.643530\pi$
$338$		0			0
$339$	−25.9808	−	15.0000i	−1.41108	−	0.814688i
$340$		0			0
$341$	−22.5000	+	38.9711i	−1.21844	+	2.11041i
$342$		0			0
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$		0			0
$345$			8.66025i			0.466252i
$346$		0			0
$347$	11.2583	−	6.50000i	0.604379	−	0.348938i	−0.166383	−	0.986061i	$-0.553209\pi$
$347$	11.2583	−	6.50000i	0.604379	−	0.348938i	0.770762	+	0.637123i	$0.219876\pi$
$348$		0			0
$349$		−	17.3205i		−	0.927146i	−0.886059	−	0.463573i	$-0.846567\pi$
$349$		−	17.3205i		−	0.927146i	0.886059	−	0.463573i	$-0.153433\pi$
$350$		0			0
$351$			18.0000i			0.960769i
$352$		0			0
$353$	−9.50000	−	16.4545i	−0.505634	−	0.875784i	−0.999979	−	0.00651782i	$-0.997925\pi$
$353$	−9.50000	−	16.4545i	−0.505634	−	0.875784i	0.494345	−	0.869266i	$-0.335408\pi$
$354$		0			0
$355$	−1.73205	−	1.00000i	−0.0919277	−	0.0530745i
$356$		0			0
$357$	−3.00000	−	3.46410i	−0.158777	−	0.183340i
$358$		0			0
$359$	−16.4545	−	9.50000i	−0.868434	−	0.501391i	−0.00160673	−	0.999999i	$-0.500511\pi$
$359$	−16.4545	−	9.50000i	−0.868434	−	0.501391i	−0.866828	+	0.498608i	$0.833845\pi$
$360$		0			0
$361$	−9.00000	−	15.5885i	−0.473684	−	0.820445i
$362$		0			0
$363$	−12.1244	−	21.0000i	−0.636364	−	1.10221i
$364$		0			0
$365$		−	8.66025i		−	0.453298i
$366$		0			0
$367$	6.06218	−	3.50000i	0.316443	−	0.182699i	−0.333363	−	0.942799i	$-0.608183\pi$
$367$	6.06218	−	3.50000i	0.316443	−	0.182699i	0.649806	+	0.760100i	$0.274850\pi$
$368$		0			0
$369$	−12.0000	−	20.7846i	−0.624695	−	1.08200i
$370$		0			0
$371$	−30.3109	−	10.5000i	−1.57366	−	0.545133i
$372$		0			0
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	−0.852791	−	0.522253i	$-0.825092\pi$
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	0.878680	+	0.477412i	$0.158425\pi$
$374$		0			0
$375$	7.79423	−	13.5000i	0.402492	−	0.697137i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	24.2487			1.24557			0.622786	−	0.782392i	$-0.286001\pi$
$379$	24.2487			1.24557			0.622786	+	0.782392i	$0.286001\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.7224	+	25.5000i	−0.752281	+	1.30299i	0.194434	+	0.980916i	$0.437713\pi$
$383$	−14.7224	+	25.5000i	−0.752281	+	1.30299i	−0.946715	+	0.322073i	$0.895620\pi$
$384$		0			0
$385$	10.0000	−	8.66025i	0.509647	−	0.441367i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.50000	−	0.866025i	0.0760530	−	0.0439092i	−0.461491	−	0.887145i	$-0.652685\pi$
$389$	1.50000	−	0.866025i	0.0760530	−	0.0439092i	0.537544	+	0.843236i	$0.319352\pi$
$390$		0			0
$391$		−	5.00000i		−	0.252861i
$392$		0			0
$393$	4.50000	+	7.79423i	0.226995	+	0.393167i
$394$		0			0
$395$	0.866025	+	1.50000i	0.0435745	+	0.0754732i
$396$		0			0
$397$	−7.50000	−	4.33013i	−0.376414	−	0.217323i	0.299843	−	0.953989i	$-0.403066\pi$
$397$	−7.50000	−	4.33013i	−0.376414	−	0.217323i	−0.676257	+	0.736666i	$0.736399\pi$
$398$		0			0
$399$	4.33013	+	1.50000i	0.216777	+	0.0750939i
$400$		0			0
$401$	−16.5000	−	9.52628i	−0.823971	−	0.475720i	0.0278131	−	0.999613i	$-0.491146\pi$
$401$	−16.5000	−	9.52628i	−0.823971	−	0.475720i	−0.851784	+	0.523893i	$0.824479\pi$
$402$		0			0
$403$	−15.5885	−	27.0000i	−0.776516	−	1.34497i
$404$		0			0
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$		0			0
$407$		−	15.0000i		−	0.743522i
$408$		0			0
$409$	−7.50000	+	4.33013i	−0.370851	+	0.214111i	−0.673830	−	0.738886i	$-0.735352\pi$
$409$	−7.50000	+	4.33013i	−0.370851	+	0.214111i	0.302979	+	0.952997i	$0.402019\pi$
$410$		0			0
$411$		−	39.0000i		−	1.92373i
$412$		0			0
$413$	−7.50000	+	21.6506i	−0.369051	+	1.06536i
$414$		0			0
$415$	6.92820	−	12.0000i	0.340092	−	0.589057i
$416$		0			0
$417$	9.00000	+	5.19615i	0.440732	+	0.254457i
$418$		0			0
$419$	13.8564			0.676930			0.338465	−	0.940979i	$-0.390092\pi$
$419$	13.8564			0.676930			0.338465	+	0.940979i	$0.390092\pi$
$420$		0			0
$421$	−12.0000			−0.584844			−0.292422	−	0.956289i	$-0.594461\pi$
$421$	−12.0000			−0.584844			−0.292422	+	0.956289i	$0.594461\pi$
$422$		0			0
$423$	5.19615			0.252646
$424$		0			0
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$		0			0
$427$	6.06218	+	31.5000i	0.293369	+	1.52439i
$428$		0			0
$429$	30.0000			1.44841
$430$		0			0
$431$	−21.6506	+	12.5000i	−1.04287	+	0.602104i	−0.920646	−	0.390398i	$-0.872337\pi$
$431$	−21.6506	+	12.5000i	−1.04287	+	0.602104i	−0.122228	+	0.992502i	$0.539004\pi$
$432$		0			0
$433$			31.1769i			1.49827i	0.662419	+	0.749133i	$0.269530\pi$
$433$			31.1769i			1.49827i	−0.662419	+	0.749133i	$0.730470\pi$
$434$		0			0
$435$	−5.19615	+	3.00000i	−0.249136	+	0.143839i
$436$		0			0
$437$	2.50000	+	4.33013i	0.119591	+	0.207138i
$438$		0			0
$439$	6.06218	+	3.50000i	0.289332	+	0.167046i	0.637641	−	0.770334i	$-0.279911\pi$
$439$	6.06218	+	3.50000i	0.289332	+	0.167046i	−0.348309	+	0.937380i	$0.613244\pi$
$440$		0			0
$441$	19.5000	−	7.79423i	0.928571	−	0.371154i
$442$		0			0
$443$	21.6506	+	12.5000i	1.02865	+	0.593893i	0.916598	−	0.399809i	$-0.130924\pi$
$443$	21.6506	+	12.5000i	1.02865	+	0.593893i	0.112054	+	0.993702i	$0.464257\pi$
$444$		0			0
$445$	6.50000	+	11.2583i	0.308130	+	0.533696i
$446$		0			0
$447$	−28.5788	+	16.5000i	−1.35173	+	0.780423i
$448$		0			0
$449$			31.1769i			1.47133i	0.677346	+	0.735665i	$0.263130\pi$
$449$			31.1769i			1.47133i	−0.677346	+	0.735665i	$0.736870\pi$
$450$		0			0
$451$	−34.6410	+	20.0000i	−1.63118	+	0.941763i
$452$		0			0
$453$	33.0000			1.55048
$454$		0			0
$455$	1.73205	+	9.00000i	0.0811998	+	0.421927i
$456$		0			0
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	−0.672994	−	0.739648i	$-0.734992\pi$
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	0.977051	+	0.213006i	$0.0683253\pi$
$458$		0			0
$459$	−2.59808	−	4.50000i	−0.121268	−	0.210042i
$460$		0			0
$461$	8.00000			0.372597			0.186299	−	0.982493i	$-0.440351\pi$
$461$	8.00000			0.372597			0.186299	+	0.982493i	$0.440351\pi$
$462$		0			0
$463$	−13.8564			−0.643962			−0.321981	−	0.946746i	$-0.604349\pi$
$463$	−13.8564			−0.643962			−0.321981	+	0.946746i	$0.604349\pi$
$464$		0			0
$465$	−13.5000	−	7.79423i	−0.626048	−	0.361449i
$466$		0			0
$467$	−6.06218	+	10.5000i	−0.280524	+	0.485882i	−0.971514	−	0.236982i	$-0.923842\pi$
$467$	−6.06218	+	10.5000i	−0.280524	+	0.485882i	0.690990	+	0.722865i	$0.257175\pi$
$468$		0			0
$469$	−10.5000	+	30.3109i	−0.484845	+	1.39963i
$470$		0			0
$471$		−	3.00000i		−	0.138233i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		−	4.00000i		−	0.183533i
$476$		0			0
$477$	−31.5000	−	18.1865i	−1.44229	−	0.832704i
$478$		0			0
$479$	−7.79423	−	13.5000i	−0.356127	−	0.616831i	0.631183	−	0.775634i	$-0.282570\pi$
$479$	−7.79423	−	13.5000i	−0.356127	−	0.616831i	−0.987310	+	0.158803i	$0.949236\pi$
$480$		0			0
$481$	9.00000	+	5.19615i	0.410365	+	0.236924i
$482$		0			0
$483$	21.6506	+	7.50000i	0.985138	+	0.341262i
$484$		0			0
$485$	3.00000	+	1.73205i	0.136223	+	0.0786484i
$486$		0			0
$487$	7.79423	+	13.5000i	0.353190	+	0.611743i	0.986807	−	0.161904i	$-0.0517635\pi$
$487$	7.79423	+	13.5000i	0.353190	+	0.611743i	−0.633616	+	0.773647i	$0.718430\pi$
$488$		0			0
$489$	7.50000	+	12.9904i	0.339162	+	0.587445i
$490$		0			0
$491$			8.00000i			0.361035i	0.983572	+	0.180517i	$0.0577772\pi$
$491$			8.00000i			0.361035i	−0.983572	+	0.180517i	$0.942223\pi$
$492$		0			0
$493$	3.00000	−	1.73205i	0.135113	−	0.0780076i
$494$		0			0
$495$	12.9904	−	7.50000i	0.583874	−	0.337100i
$496$		0			0
$497$	−4.00000	+	3.46410i	−0.179425	+	0.155386i
$498$		0			0
$499$	6.06218	−	10.5000i	0.271380	−	0.470045i	−0.697835	−	0.716258i	$-0.745853\pi$
$499$	6.06218	−	10.5000i	0.271380	−	0.470045i	0.969216	+	0.246214i	$0.0791865\pi$
$500$		0			0
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$		0			0
$503$	34.6410			1.54457			0.772283	−	0.635278i	$-0.219115\pi$
$503$	34.6410			1.54457			0.772283	+	0.635278i	$0.219115\pi$
$504$		0			0
$505$	−7.00000			−0.311496
$506$		0			0
$507$	0.866025	−	1.50000i	0.0384615	−	0.0666173i
$508$		0			0
$509$	2.50000	−	4.33013i	0.110811	−	0.191930i	−0.805287	−	0.592886i	$-0.797989\pi$
$509$	2.50000	−	4.33013i	0.110811	−	0.191930i	0.916097	+	0.400956i	$0.131322\pi$
$510$		0			0
$511$	−21.6506	−	7.50000i	−0.957768	−	0.331780i
$512$		0			0
$513$	4.50000	+	2.59808i	0.198680	+	0.114708i
$514$		0			0
$515$	7.79423	−	4.50000i	0.343455	−	0.198294i
$516$		0			0
$517$		−	8.66025i		−	0.380878i
$518$		0			0
$519$	0.866025	+	1.50000i	0.0380143	+	0.0658427i
$520$		0			0
$521$	17.5000	+	30.3109i	0.766689	+	1.32794i	0.939349	+	0.342963i	$0.111430\pi$
$521$	17.5000	+	30.3109i	0.766689	+	1.32794i	−0.172660	+	0.984981i	$0.555236\pi$
$522$		0			0
$523$	12.9904	+	7.50000i	0.568030	+	0.327952i	0.756362	−	0.654153i	$-0.226975\pi$
$523$	12.9904	+	7.50000i	0.568030	+	0.327952i	−0.188332	+	0.982105i	$0.560308\pi$
$524$		0			0
$525$	−12.0000	−	13.8564i	−0.523723	−	0.604743i
$526$		0			0
$527$	7.79423	+	4.50000i	0.339522	+	0.196023i
$528$		0			0
$529$	1.00000	+	1.73205i	0.0434783	+	0.0753066i
$530$		0			0
$531$	−12.9904	+	22.5000i	−0.563735	+	0.976417i
$532$		0			0
$533$		−	27.7128i		−	1.20038i
$534$		0			0
$535$	11.2583	−	6.50000i	0.486740	−	0.281020i
$536$		0			0
$537$		−	12.1244i		−	0.523205i
$538$		0			0
$539$	−12.9904	−	32.5000i	−0.559535	−	1.39987i
$540$		0			0
$541$	−10.5000	+	18.1865i	−0.451430	+	0.781900i	−0.998475	−	0.0552031i	$-0.982419\pi$
$541$	−10.5000	+	18.1865i	−0.451430	+	0.781900i	0.547045	+	0.837103i	$0.315753\pi$
$542$		0			0
$543$	31.1769	+	18.0000i	1.33793	+	0.772454i
$544$		0			0
$545$	−5.00000			−0.214176
$546$		0			0
$547$	17.3205			0.740571			0.370286	−	0.928918i	$-0.379260\pi$
$547$	17.3205			0.740571			0.370286	+	0.928918i	$0.379260\pi$
$548$		0			0
$549$			36.3731i			1.55236i
$550$		0			0
$551$	−1.73205	+	3.00000i	−0.0737878	+	0.127804i
$552$		0			0
$553$	4.50000	−	0.866025i	0.191359	−	0.0368271i
$554$		0			0
$555$	5.19615			0.220564
$556$		0			0
$557$	−34.5000	+	19.9186i	−1.46181	+	0.843978i	−0.999095	−	0.0425287i	$-0.986459\pi$
$557$	−34.5000	+	19.9186i	−1.46181	+	0.843978i	−0.462717	+	0.886506i	$0.653125\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−7.50000	+	4.33013i	−0.316650	+	0.182818i
$562$		0			0
$563$	12.9904	+	22.5000i	0.547479	+	0.948262i	0.998446	+	0.0557214i	$0.0177458\pi$
$563$	12.9904	+	22.5000i	0.547479	+	0.948262i	−0.450967	+	0.892541i	$0.648921\pi$
$564$		0			0
$565$	−15.0000	−	8.66025i	−0.631055	−	0.364340i
$566$		0			0
$567$	23.3827	−	4.50000i	0.981981	−	0.188982i
$568$		0			0
$569$	−13.5000	−	7.79423i	−0.565949	−	0.326751i	0.189580	−	0.981865i	$-0.439287\pi$
$569$	−13.5000	−	7.79423i	−0.565949	−	0.326751i	−0.755530	+	0.655114i	$0.772621\pi$
$570$		0			0
$571$	6.06218	+	10.5000i	0.253694	+	0.439411i	0.964540	−	0.263937i	$-0.0850210\pi$
$571$	6.06218	+	10.5000i	0.253694	+	0.439411i	−0.710846	+	0.703348i	$0.751688\pi$
$572$		0			0
$573$	19.5000	−	11.2583i	0.814624	−	0.470323i
$574$		0			0
$575$		−	20.0000i		−	0.834058i
$576$		0			0
$577$	25.5000	−	14.7224i	1.06158	−	0.612903i	0.135710	−	0.990749i	$-0.456668\pi$
$577$	25.5000	−	14.7224i	1.06158	−	0.612903i	0.925869	+	0.377846i	$0.123335\pi$
$578$		0			0
$579$	25.9808			1.07972
$580$		0			0
$581$	−24.0000	−	27.7128i	−0.995688	−	1.14972i
$582$		0			0
$583$	−30.3109	+	52.5000i	−1.25535	+	2.17433i
$584$		0			0
$585$			10.3923i			0.429669i
$586$		0			0
$587$	27.7128			1.14383			0.571915	−	0.820313i	$-0.306201\pi$
$587$	27.7128			1.14383			0.571915	+	0.820313i	$0.306201\pi$
$588$		0			0
$589$	−9.00000			−0.370839
$590$		0			0
$591$	25.9808	+	15.0000i	1.06871	+	0.617018i
$592$		0			0
$593$	0.500000	−	0.866025i	0.0205325	−	0.0355634i	−0.855577	−	0.517676i	$-0.826797\pi$
$593$	0.500000	−	0.866025i	0.0205325	−	0.0355634i	0.876109	+	0.482113i	$0.160130\pi$
$594$		0			0
$595$	−1.73205	−	2.00000i	−0.0710072	−	0.0819920i
$596$		0			0
$597$		−	29.4449i		−	1.20510i
$598$		0			0
$599$	0.866025	−	0.500000i	0.0353848	−	0.0204294i	−0.482203	−	0.876059i	$-0.660163\pi$
$599$	0.866025	−	0.500000i	0.0353848	−	0.0204294i	0.517588	+	0.855630i	$0.326830\pi$
$600$		0			0
$601$			3.46410i			0.141304i	0.997501	+	0.0706518i	$0.0225079\pi$
$601$			3.46410i			0.141304i	−0.997501	+	0.0706518i	$0.977492\pi$
$602$		0			0
$603$	−18.1865	+	31.5000i	−0.740613	+	1.28278i
$604$		0			0
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−32.0429	−	18.5000i	−1.30058	−	0.750892i	−0.320079	−	0.947391i	$-0.603709\pi$
$607$	−32.0429	−	18.5000i	−1.30058	−	0.750892i	−0.980504	+	0.196499i	$0.937043\pi$
$608$		0			0
$609$	3.00000	+	15.5885i	0.121566	+	0.631676i
$610$		0			0
$611$	5.19615	+	3.00000i	0.210214	+	0.121367i
$612$		0			0
$613$	−24.5000	−	42.4352i	−0.989546	−	1.71394i	−0.619671	−	0.784862i	$-0.712734\pi$
$613$	−24.5000	−	42.4352i	−0.989546	−	1.71394i	−0.369875	−	0.929082i	$-0.620599\pi$
$614$		0			0
$615$	−6.92820	−	12.0000i	−0.279372	−	0.483887i
$616$		0			0
$617$			24.2487i			0.976216i	0.872783	+	0.488108i	$0.162313\pi$
$617$			24.2487i			0.976216i	−0.872783	+	0.488108i	$0.837687\pi$
$618$		0			0
$619$	23.3827	−	13.5000i	0.939829	−	0.542611i	0.0499226	−	0.998753i	$-0.484103\pi$
$619$	23.3827	−	13.5000i	0.939829	−	0.542611i	0.889907	+	0.456142i	$0.150769\pi$
$620$		0			0
$621$	22.5000	+	12.9904i	0.902894	+	0.521286i
$622$		0			0
$623$	33.7750	−	6.50000i	1.35317	−	0.260417i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$	4.33013	−	7.50000i	0.172929	−	0.299521i
$628$		0			0
$629$	−3.00000			−0.119618
$630$		0			0
$631$	−20.7846			−0.827422			−0.413711	−	0.910408i	$-0.635768\pi$
$631$	−20.7846			−0.827422			−0.413711	+	0.910408i	$0.635768\pi$
$632$		0			0
$633$	−6.00000	+	10.3923i	−0.238479	+	0.413057i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	24.0000	+	3.46410i	0.950915	+	0.137253i
$638$		0			0
$639$	−5.19615	+	3.00000i	−0.205557	+	0.118678i
$640$		0			0
$641$	−7.50000	+	4.33013i	−0.296232	+	0.171030i	−0.640749	−	0.767750i	$-0.721376\pi$
$641$	−7.50000	+	4.33013i	−0.296232	+	0.171030i	0.344517	+	0.938780i	$0.388043\pi$
$642$		0			0
$643$			26.0000i			1.02534i	0.858586	+	0.512670i	$0.171344\pi$
$643$			26.0000i			1.02534i	−0.858586	+	0.512670i	$0.828656\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.06218	+	10.5000i	0.238329	+	0.412798i	0.960235	−	0.279193i	$-0.0900671\pi$
$647$	6.06218	+	10.5000i	0.238329	+	0.412798i	−0.721906	+	0.691991i	$0.756734\pi$
$648$		0			0
$649$	37.5000	+	21.6506i	1.47200	+	0.849862i
$650$		0			0
$651$	−31.1769	+	27.0000i	−1.22192	+	1.05821i
$652$		0			0
$653$	28.5000	+	16.4545i	1.11529	+	0.643914i	0.940195	−	0.340638i	$-0.110643\pi$
$653$	28.5000	+	16.4545i	1.11529	+	0.643914i	0.175097	+	0.984551i	$0.443976\pi$
$654$		0			0
$655$	2.59808	+	4.50000i	0.101515	+	0.175830i
$656$		0			0
$657$	−22.5000	−	12.9904i	−0.877809	−	0.506803i
$658$		0			0
$659$		−	34.0000i		−	1.32445i	−0.749304	−	0.662226i	$-0.769612\pi$
$659$		−	34.0000i		−	1.32445i	0.749304	−	0.662226i	$-0.230388\pi$
$660$		0			0
$661$	19.5000	−	11.2583i	0.758462	−	0.437898i	−0.0702812	−	0.997527i	$-0.522390\pi$
$661$	19.5000	−	11.2583i	0.758462	−	0.437898i	0.828743	+	0.559629i	$0.189056\pi$
$662$		0			0
$663$		−	6.00000i		−	0.233021i
$664$		0			0
$665$	2.50000	+	0.866025i	0.0969458	+	0.0335830i
$666$		0			0
$667$	−8.66025	+	15.0000i	−0.335326	+	0.580802i
$668$		0			0
$669$	−3.00000	−	1.73205i	−0.115987	−	0.0669650i
$670$		0			0
$671$	60.6218			2.34028
$672$		0			0
$673$	36.0000			1.38770			0.693849	−	0.720121i	$-0.255914\pi$
$673$	36.0000			1.38770			0.693849	+	0.720121i	$0.255914\pi$
$674$		0			0
$675$	−10.3923	−	18.0000i	−0.400000	−	0.692820i
$676$		0			0
$677$	18.5000	−	32.0429i	0.711013	−	1.23151i	−0.253465	−	0.967345i	$-0.581570\pi$
$677$	18.5000	−	32.0429i	0.711013	−	1.23151i	0.964477	−	0.264166i	$-0.0850965\pi$
$678$		0			0
$679$	6.92820	−	6.00000i	0.265880	−	0.230259i
$680$		0			0
$681$	3.00000			0.114960
$682$		0			0
$683$	−11.2583	+	6.50000i	−0.430788	+	0.248716i	−0.699682	−	0.714454i	$-0.746675\pi$
$683$	−11.2583	+	6.50000i	−0.430788	+	0.248716i	0.268894	+	0.963170i	$0.413342\pi$
$684$		0			0
$685$		−	22.5167i		−	0.860317i
$686$		0			0
$687$	−2.59808	+	1.50000i	−0.0991228	+	0.0572286i
$688$		0			0
$689$	−21.0000	−	36.3731i	−0.800036	−	1.38570i
$690$		0			0
$691$	28.5788	+	16.5000i	1.08719	+	0.627690i	0.932827	−	0.360325i	$-0.117334\pi$
$691$	28.5788	+	16.5000i	1.08719	+	0.627690i	0.154363	+	0.988014i	$0.450667\pi$
$692$		0			0
$693$	−7.50000	−	38.9711i	−0.284901	−	1.48039i
$694$		0			0
$695$	5.19615	+	3.00000i	0.197101	+	0.113796i
$696$		0			0
$697$	4.00000	+	6.92820i	0.151511	+	0.262424i
$698$		0			0
$699$	−7.79423	+	4.50000i	−0.294805	+	0.170206i
$700$		0			0
$701$			20.7846i			0.785024i	0.919747	+	0.392512i	$0.128394\pi$
$701$			20.7846i			0.785024i	−0.919747	+	0.392512i	$0.871606\pi$
$702$		0			0
$703$	2.59808	−	1.50000i	0.0979883	−	0.0565736i
$704$		0			0
$705$	3.00000			0.112987
$706$		0			0
$707$	−6.06218	+	17.5000i	−0.227992	+	0.658155i
$708$		0			0
$709$	−15.5000	+	26.8468i	−0.582115	+	1.00825i	0.413114	+	0.910679i	$0.364441\pi$
$709$	−15.5000	+	26.8468i	−0.582115	+	1.00825i	−0.995228	+	0.0975728i	$0.968892\pi$
$710$		0			0
$711$	5.19615			0.194871
$712$		0			0
$713$	−45.0000			−1.68526
$714$		0			0
$715$	17.3205			0.647750
$716$		0			0
$717$	−42.0000	−	24.2487i	−1.56852	−	0.905585i
$718$		0			0
$719$	11.2583	−	19.5000i	0.419865	−	0.727227i	−0.576061	−	0.817407i	$-0.695411\pi$
$719$	11.2583	−	19.5000i	0.419865	−	0.727227i	0.995926	+	0.0901797i	$0.0287441\pi$
$720$		0			0
$721$	−4.50000	−	23.3827i	−0.167589	−	0.870817i
$722$		0			0
$723$			45.0000i			1.67357i
$724$		0			0
$725$	12.0000	−	6.92820i	0.445669	−	0.257307i
$726$		0			0
$727$			30.0000i			1.11264i	0.830969	+	0.556319i	$0.187787\pi$
$727$			30.0000i			1.11264i	−0.830969	+	0.556319i	$0.812213\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−34.5000	−	19.9186i	−1.27429	−	0.735710i	−0.298495	−	0.954411i	$-0.596485\pi$
$733$	−34.5000	−	19.9186i	−1.27429	−	0.735710i	−0.975792	+	0.218702i	$0.929818\pi$
$734$		0			0
$735$	11.2583	−	4.50000i	0.415270	−	0.165985i
$736$		0			0
$737$	52.5000	+	30.3109i	1.93386	+	1.11652i
$738$		0			0
$739$	−18.1865	−	31.5000i	−0.669002	−	1.15875i	−0.978183	−	0.207743i	$-0.933388\pi$
$739$	−18.1865	−	31.5000i	−0.669002	−	1.15875i	0.309181	−	0.951003i	$-0.399945\pi$
$740$		0			0
$741$	3.00000	+	5.19615i	0.110208	+	0.190885i
$742$		0			0
$743$		−	22.0000i		−	0.807102i	−0.914957	−	0.403551i	$-0.867776\pi$
$743$		−	22.0000i		−	0.807102i	0.914957	−	0.403551i	$-0.132224\pi$
$744$		0			0
$745$	−16.5000	+	9.52628i	−0.604513	+	0.349016i
$746$		0			0
$747$	−20.7846	−	36.0000i	−0.760469	−	1.31717i
$748$		0			0
$749$	−6.50000	−	33.7750i	−0.237505	−	1.23411i
$750$		0			0
$751$	21.6506	−	37.5000i	0.790043	−	1.36839i	−0.135897	−	0.990723i	$-0.543392\pi$
$751$	21.6506	−	37.5000i	0.790043	−	1.36839i	0.925940	−	0.377671i	$-0.123275\pi$
$752$		0			0
$753$	−3.00000	+	5.19615i	−0.109326	+	0.189358i
$754$		0			0
$755$	19.0526			0.693394
$756$		0			0
$757$	−8.00000			−0.290765			−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000			−0.290765			−0.145382	+	0.989376i	$0.546441\pi$
$758$		0			0
$759$	21.6506	−	37.5000i	0.785868	−	1.36116i
$760$		0			0
$761$	18.5000	−	32.0429i	0.670624	−	1.16156i	−0.307103	−	0.951676i	$-0.599360\pi$
$761$	18.5000	−	32.0429i	0.670624	−	1.16156i	0.977727	−	0.209879i	$-0.0673071\pi$
$762$		0			0
$763$	−4.33013	+	12.5000i	−0.156761	+	0.452530i
$764$		0			0
$765$	−1.50000	−	2.59808i	−0.0542326	−	0.0939336i
$766$		0			0
$767$	−25.9808	+	15.0000i	−0.938111	+	0.541619i
$768$		0			0
$769$		−	10.3923i		−	0.374756i	−0.982288	−	0.187378i	$-0.940001\pi$
$769$		−	10.3923i		−	0.374756i	0.982288	−	0.187378i	$-0.0599989\pi$
$770$		0			0
$771$	9.52628	+	16.5000i	0.343081	+	0.594233i
$772$		0			0
$773$	24.5000	+	42.4352i	0.881204	+	1.52629i	0.850004	+	0.526777i	$0.176600\pi$
$773$	24.5000	+	42.4352i	0.881204	+	1.52629i	0.0311999	+	0.999513i	$0.490067\pi$
$774$		0			0
$775$	31.1769	+	18.0000i	1.11991	+	0.646579i
$776$		0			0
$777$	4.50000	−	12.9904i	0.161437	−	0.466027i
$778$		0			0
$779$	−6.92820	−	4.00000i	−0.248229	−	0.143315i
$780$		0			0
$781$	5.00000	+	8.66025i	0.178914	+	0.309888i
$782$		0			0
$783$			18.0000i			0.643268i
$784$		0			0
$785$		−	1.73205i		−	0.0618195i
$786$		0			0
$787$	23.3827	−	13.5000i	0.833503	−	0.481223i	−0.0215477	−	0.999768i	$-0.506859\pi$
$787$	23.3827	−	13.5000i	0.833503	−	0.481223i	0.855050	+	0.518545i	$0.173526\pi$
$788$		0			0
$789$			19.0526i			0.678289i
$790$		0			0
$791$	−34.6410	+	30.0000i	−1.23169	+	1.06668i
$792$		0			0
$793$	−21.0000	+	36.3731i	−0.745732	+	1.29165i
$794$		0			0
$795$	−18.1865	−	10.5000i	−0.645010	−	0.372397i
$796$		0			0
$797$	32.0000			1.13350			0.566749	−	0.823890i	$-0.308201\pi$
$797$	32.0000			1.13350			0.566749	+	0.823890i	$0.308201\pi$
$798$		0			0
$799$	−1.73205			−0.0612756
$800$		0			0
$801$	39.0000			1.37800
$802$		0			0
$803$	−21.6506	+	37.5000i	−0.764034	+	1.32335i
$804$		0			0
$805$	12.5000	+	4.33013i	0.440567	+	0.152617i
$806$		0			0
$807$	−1.73205			−0.0609711
$808$		0			0
$809$	−25.5000	+	14.7224i	−0.896532	+	0.517613i	−0.876074	−	0.482178i	$-0.839846\pi$
$809$	−25.5000	+	14.7224i	−0.896532	+	0.517613i	−0.0204587	+	0.999791i	$0.506513\pi$
$810$		0			0
$811$			30.0000i			1.05344i	0.850038	+	0.526721i	$0.176579\pi$
$811$			30.0000i			1.05344i	−0.850038	+	0.526721i	$0.823421\pi$
$812$		0			0
$813$	−22.5000	+	12.9904i	−0.789109	+	0.455593i
$814$		0			0
$815$	4.33013	+	7.50000i	0.151678	+	0.262714i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	25.9808	+	9.00000i	0.907841	+	0.314485i
$820$		0			0
$821$	13.5000	+	7.79423i	0.471153	+	0.272020i	0.716722	−	0.697359i	$-0.245641\pi$
$821$	13.5000	+	7.79423i	0.471153	+	0.272020i	−0.245569	+	0.969379i	$0.578975\pi$
$822$		0			0
$823$	−26.8468	−	46.5000i	−0.935820	−	1.62089i	−0.773165	−	0.634205i	$-0.781327\pi$
$823$	−26.8468	−	46.5000i	−0.935820	−	1.62089i	−0.162655	−	0.986683i	$-0.552006\pi$
$824$		0			0
$825$	−30.0000	+	17.3205i	−1.04447	+	0.603023i
$826$		0			0
$827$		−	2.00000i		−	0.0695468i	−0.999395	−	0.0347734i	$-0.988929\pi$
$827$		−	2.00000i		−	0.0695468i	0.999395	−	0.0347734i	$-0.0110710\pi$
$828$		0			0
$829$	−1.50000	+	0.866025i	−0.0520972	+	0.0300783i	−0.525822	−	0.850594i	$-0.676242\pi$
$829$	−1.50000	+	0.866025i	−0.0520972	+	0.0300783i	0.473725	+	0.880673i	$0.342909\pi$
$830$		0			0
$831$	36.3731			1.26177
$832$		0			0
$833$	−6.50000	+	2.59808i	−0.225212	+	0.0900180i
$834$		0			0
$835$	5.19615	−	9.00000i	0.179820	−	0.311458i
$836$		0			0
$837$	−40.5000	+	23.3827i	−1.39988	+	0.808224i
$838$		0			0
$839$	−27.7128			−0.956753			−0.478376	−	0.878155i	$-0.658774\pi$
$839$	−27.7128			−0.956753			−0.478376	+	0.878155i	$0.658774\pi$
$840$		0			0
$841$	17.0000			0.586207
$842$		0			0
$843$	−25.9808	−	15.0000i	−0.894825	−	0.516627i
$844$		0			0
$845$	0.500000	−	0.866025i	0.0172005	−	0.0297922i
$846$		0			0
$847$	−36.3731	+	7.00000i	−1.24979	+	0.240523i
$848$		0			0
$849$			53.6936i			1.84276i
$850$		0			0
$851$	12.9904	−	7.50000i	0.445305	−	0.257097i
$852$		0			0
$853$		−	45.0333i		−	1.54191i	−0.636889	−	0.770956i	$-0.719779\pi$
$853$		−	45.0333i		−	1.54191i	0.636889	−	0.770956i	$-0.280221\pi$
$854$		0			0
$855$	2.59808	+	1.50000i	0.0888523	+	0.0512989i
$856$		0			0
$857$	3.50000	+	6.06218i	0.119558	+	0.207080i	0.919592	−	0.392874i	$-0.128519\pi$
$857$	3.50000	+	6.06218i	0.119558	+	0.207080i	−0.800035	+	0.599954i	$0.795186\pi$
$858$		0			0
$859$	−0.866025	−	0.500000i	−0.0295484	−	0.0170598i	0.485153	−	0.874429i	$-0.338764\pi$
$859$	−0.866025	−	0.500000i	−0.0295484	−	0.0170598i	−0.514701	+	0.857369i	$0.672097\pi$
$860$		0			0
$861$	−36.0000	+	6.92820i	−1.22688	+	0.236113i
$862$		0			0
$863$	16.4545	+	9.50000i	0.560117	+	0.323384i	0.753193	−	0.657800i	$-0.228513\pi$
$863$	16.4545	+	9.50000i	0.560117	+	0.323384i	−0.193075	+	0.981184i	$0.561846\pi$
$864$		0			0
$865$	0.500000	+	0.866025i	0.0170005	+	0.0294457i
$866$		0			0
$867$	−13.8564	−	24.0000i	−0.470588	−	0.815083i
$868$		0			0
$869$		−	8.66025i		−	0.293779i
$870$		0			0
$871$	−36.3731	+	21.0000i	−1.23245	+	0.711558i
$872$		0			0
$873$	9.00000	−	5.19615i	0.304604	−	0.175863i
$874$		0			0
$875$	−15.5885	−	18.0000i	−0.526986	−	0.608511i
$876$		0			0
$877$	−18.5000	+	32.0429i	−0.624701	+	1.08201i	0.363898	+	0.931439i	$0.381446\pi$
$877$	−18.5000	+	32.0429i	−0.624701	+	1.08201i	−0.988599	+	0.150574i	$0.951888\pi$
$878$		0			0
$879$	−12.1244	+	21.0000i	−0.408944	+	0.708312i
$880$		0			0
$881$	10.0000			0.336909			0.168454	−	0.985709i	$-0.446122\pi$
$881$	10.0000			0.336909			0.168454	+	0.985709i	$0.446122\pi$
$882$		0			0
$883$	6.92820			0.233153			0.116576	−	0.993182i	$-0.462808\pi$
$883$	6.92820			0.233153			0.116576	+	0.993182i	$0.462808\pi$
$884$		0			0
$885$	−7.50000	+	12.9904i	−0.252110	+	0.436667i
$886$		0			0
$887$	−7.79423	+	13.5000i	−0.261705	+	0.453286i	−0.966695	−	0.255931i	$-0.917618\pi$
$887$	−7.79423	+	13.5000i	−0.261705	+	0.453286i	0.704990	+	0.709217i	$0.250951\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		−	45.0000i		−	1.50756i
$892$		0			0
$893$	1.50000	−	0.866025i	0.0501956	−	0.0289804i
$894$		0			0
$895$		−	7.00000i		−	0.233984i
$896$		0			0
$897$	15.0000	+	25.9808i	0.500835	+	0.867472i
$898$		0			0
$899$	−15.5885	−	27.0000i	−0.519904	−	0.900500i
$900$		0			0
$901$	10.5000	+	6.06218i	0.349806	+	0.201960i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	18.0000	+	10.3923i	0.598340	+	0.345452i
$906$		0			0
$907$	0.866025	+	1.50000i	0.0287559	+	0.0498067i	0.880045	−	0.474890i	$-0.157512\pi$
$907$	0.866025	+	1.50000i	0.0287559	+	0.0498067i	−0.851289	+	0.524697i	$0.824179\pi$
$908$		0			0
$909$	−10.5000	+	18.1865i	−0.348263	+	0.603209i
$910$		0			0
$911$			22.0000i			0.728893i	0.931224	+	0.364446i	$0.118742\pi$
$911$			22.0000i			0.728893i	−0.931224	+	0.364446i	$0.881258\pi$
$912$		0			0
$913$	−60.0000	+	34.6410i	−1.98571	+	1.14645i
$914$		0			0
$915$			21.0000i			0.694239i
$916$		0			0
$917$	13.5000	−	2.59808i	0.445809	−	0.0857960i
$918$		0			0
$919$	−9.52628	+	16.5000i	−0.314243	+	0.544285i	−0.979276	−	0.202529i	$-0.935084\pi$
$919$	−9.52628	+	16.5000i	−0.314243	+	0.544285i	0.665033	+	0.746814i	$0.268417\pi$
$920$		0			0
$921$	−39.0000	−	22.5167i	−1.28509	−	0.741949i
$922$		0			0
$923$	−6.92820			−0.228045
$924$		0			0
$925$	−12.0000			−0.394558
$926$		0			0
$927$		−	27.0000i		−	0.886796i
$928$		0			0
$929$	27.5000	−	47.6314i	0.902246	−	1.56274i	0.0776734	−	0.996979i	$-0.475251\pi$
$929$	27.5000	−	47.6314i	0.902246	−	1.56274i	0.824572	−	0.565757i	$-0.191416\pi$
$930$		0			0
$931$	4.33013	−	5.50000i	0.141914	−	0.180255i
$932$		0			0
$933$	33.0000			1.08037
$934$		0			0
$935$	−4.33013	+	2.50000i	−0.141610	+	0.0817587i
$936$		0			0
$937$			27.7128i			0.905338i	0.891679	+	0.452669i	$0.149528\pi$
$937$			27.7128i			0.905338i	−0.891679	+	0.452669i	$0.850472\pi$
$938$		0			0
$939$	2.59808	−	1.50000i	0.0847850	−	0.0489506i
$940$		0			0
$941$	−14.5000	−	25.1147i	−0.472686	−	0.818717i	0.526825	−	0.849974i	$-0.323382\pi$
$941$	−14.5000	−	25.1147i	−0.472686	−	0.818717i	−0.999511	+	0.0312568i	$0.990049\pi$
$942$		0			0
$943$	−34.6410	−	20.0000i	−1.12807	−	0.651290i
$944$		0			0
$945$	13.5000	−	2.59808i	0.439155	−	0.0845154i
$946$		0			0
$947$	9.52628	+	5.50000i	0.309562	+	0.178726i	0.646731	−	0.762718i	$-0.276136\pi$
$947$	9.52628	+	5.50000i	0.309562	+	0.178726i	−0.337168	+	0.941444i	$0.609469\pi$
$948$		0			0
$949$	−15.0000	−	25.9808i	−0.486921	−	0.843371i
$950$		0			0
$951$	−23.3827	+	13.5000i	−0.758236	+	0.437767i
$952$		0			0
$953$			17.3205i			0.561066i	0.959844	+	0.280533i	$0.0905113\pi$
$953$			17.3205i			0.561066i	−0.959844	+	0.280533i	$0.909489\pi$
$954$		0			0
$955$	11.2583	−	6.50000i	0.364311	−	0.210335i
$956$		0			0
$957$	30.0000			0.969762
$958$		0			0
$959$	−56.2917	−	19.5000i	−1.81775	−	0.629688i
$960$		0			0
$961$	25.0000	−	43.3013i	0.806452	−	1.39682i
$962$		0			0
$963$		−	39.0000i		−	1.25676i
$964$		0			0
$965$	15.0000			0.482867
$966$		0			0
$967$	6.92820			0.222796			0.111398	−	0.993776i	$-0.464467\pi$
$967$	6.92820			0.222796			0.111398	+	0.993776i	$0.464467\pi$
$968$		0			0
$969$	−1.50000	−	0.866025i	−0.0481869	−	0.0278207i
$970$		0			0
$971$	4.33013	−	7.50000i	0.138960	−	0.240686i	−0.788143	−	0.615492i	$-0.788957\pi$
$971$	4.33013	−	7.50000i	0.138960	−	0.240686i	0.927103	+	0.374806i	$0.122291\pi$
$972$		0			0
$973$	12.0000	−	10.3923i	0.384702	−	0.333162i
$974$		0			0
$975$		−	24.0000i		−	0.768615i
$976$		0			0
$977$	25.5000	−	14.7224i	0.815817	−	0.471012i	−0.0331547	−	0.999450i	$-0.510555\pi$
$977$	25.5000	−	14.7224i	0.815817	−	0.471012i	0.848972	+	0.528438i	$0.177222\pi$
$978$		0			0
$979$		−	65.0000i		−	2.07741i
$980$		0			0
$981$	−7.50000	+	12.9904i	−0.239457	+	0.414751i
$982$		0			0
$983$	−2.59808	−	4.50000i	−0.0828658	−	0.143528i	0.821614	−	0.570044i	$-0.193074\pi$
$983$	−2.59808	−	4.50000i	−0.0828658	−	0.143528i	−0.904480	+	0.426517i	$0.859741\pi$
$984$		0			0
$985$	15.0000	+	8.66025i	0.477940	+	0.275939i
$986$		0			0
$987$	2.59808	−	7.50000i	0.0826977	−	0.238728i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−9.52628	−	16.5000i	−0.302612	−	0.524140i	0.674115	−	0.738627i	$-0.264525\pi$
$991$	−9.52628	−	16.5000i	−0.302612	−	0.524140i	−0.976727	+	0.214487i	$0.931192\pi$
$992$		0			0
$993$	−22.5000	−	38.9711i	−0.714016	−	1.23671i
$994$		0			0
$995$		−	17.0000i		−	0.538936i
$996$		0			0
$997$	19.5000	−	11.2583i	0.617571	−	0.356555i	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	19.5000	−	11.2583i	0.617571	−	0.356555i	0.775923	+	0.630828i	$0.217285\pi$
$998$		0			0
$999$	7.79423	−	13.5000i	0.246598	−	0.427121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bc.b.257.2	yes	4
3.2	odd	2		672.2.bc.a.257.2	yes	4
4.3	odd	2	inner	672.2.bc.b.257.1	yes	4
7.3	odd	6		672.2.bc.a.353.2	yes	4
12.11	even	2		672.2.bc.a.257.1	✓	4
21.17	even	6	inner	672.2.bc.b.353.2	yes	4
28.3	even	6		672.2.bc.a.353.1	yes	4
84.59	odd	6	inner	672.2.bc.b.353.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bc.a.257.1	✓	4	12.11	even	2
672.2.bc.a.257.2	yes	4	3.2	odd	2
672.2.bc.a.353.1	yes	4	28.3	even	6
672.2.bc.a.353.2	yes	4	7.3	odd	6
672.2.bc.b.257.1	yes	4	4.3	odd	2	inner
672.2.bc.b.257.2	yes	4	1.1	even	1	trivial
672.2.bc.b.353.1	yes	4	84.59	odd	6	inner
672.2.bc.b.353.2	yes	4	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-4.33013 + 2.50000i) q^{11} -3.46410i q^{13} +(-0.866025 - 1.50000i) q^{15} +(0.500000 + 0.866025i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(-4.50000 + 0.866025i) q^{21} +(-4.33013 - 2.50000i) q^{23} +(2.00000 + 3.46410i) q^{25} -5.19615 q^{27} -3.46410i q^{29} +(7.79423 - 4.50000i) q^{31} +8.66025i q^{33} +(-2.59808 + 0.500000i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-5.19615 - 3.00000i) q^{39} +8.00000 q^{41} -3.00000 q^{45} +(-0.866025 + 1.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +1.73205 q^{51} +(10.5000 - 6.06218i) q^{53} +5.00000i q^{55} +(-1.50000 + 0.866025i) q^{57} +(-4.33013 - 7.50000i) q^{59} +(-10.5000 - 6.06218i) q^{61} +(-2.59808 + 7.50000i) q^{63} +(-3.00000 - 1.73205i) q^{65} +(-6.06218 - 10.5000i) q^{67} +(-7.50000 + 4.33013i) q^{69} -2.00000i q^{71} +(7.50000 - 4.33013i) q^{73} +6.92820 q^{75} +(12.5000 + 4.33013i) q^{77} +(-0.866025 + 1.50000i) q^{79} +(-4.50000 + 7.79423i) q^{81} +13.8564 q^{83} +1.00000 q^{85} +(-5.19615 - 3.00000i) q^{87} +(-6.50000 + 11.2583i) q^{89} +(-6.92820 + 6.00000i) q^{91} -15.5885i q^{93} +(-0.866025 + 0.500000i) q^{95} +3.46410i q^{97} +(12.9904 + 7.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^5 - 6 * q^9	\( 4 q + 2 q^{5} - 6 q^{9} + 2 q^{17} - 18 q^{21} + 8 q^{25} - 6 q^{37} + 32 q^{41} - 12 q^{45} - 4 q^{49} + 42 q^{53} - 6 q^{57} - 42 q^{61} - 12 q^{65} - 30 q^{69} + 30 q^{73} + 50 q^{77} - 18 q^{81} + 4 q^{85} - 26 q^{89}+O(q^{100}) \) 4 * q + 2 * q^5 - 6 * q^9 + 2 * q^17 - 18 * q^21 + 8 * q^25 - 6 * q^37 + 32 * q^41 - 12 * q^45 - 4 * q^49 + 42 * q^53 - 6 * q^57 - 42 * q^61 - 12 * q^65 - 30 * q^69 + 30 * q^73 + 50 * q^77 - 18 * q^81 + 4 * q^85 - 26 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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