LMFDB - Embedded newform 624.2.q.i.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(289,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("624.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.q (of order $3$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-0.651388 + 1.12824i$ of defining polynomial
Character	$\chi$	$=$	624.289
Dual form			624.2.q.i.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} -1.00000 q^{5} +(-1.30278 + 2.25647i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.30278 + 2.25647i) q^{11} +(-1.80278 - 3.12250i) q^{13} +(-0.500000 - 0.866025i) q^{15} +(-0.802776 + 1.39045i) q^{17} +(-3.30278 + 5.72058i) q^{19} -2.60555 q^{21} +(1.30278 + 2.25647i) q^{23} -4.00000 q^{25} -1.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} -5.21110 q^{31} +(-1.30278 + 2.25647i) q^{33} +(1.30278 - 2.25647i) q^{35} +(1.19722 + 2.07365i) q^{37} +(1.80278 - 3.12250i) q^{39} +(5.80278 + 10.0507i) q^{41} +(-1.30278 + 2.25647i) q^{43} +(0.500000 - 0.866025i) q^{45} +1.39445 q^{47} +(0.105551 + 0.182820i) q^{49} -1.60555 q^{51} +3.00000 q^{53} +(-1.30278 - 2.25647i) q^{55} -6.60555 q^{57} +(4.60555 - 7.97705i) q^{59} +(3.80278 - 6.58660i) q^{61} +(-1.30278 - 2.25647i) q^{63} +(1.80278 + 3.12250i) q^{65} +(-5.30278 - 9.18468i) q^{67} +(-1.30278 + 2.25647i) q^{69} +(-4.69722 + 8.13583i) q^{71} +7.00000 q^{73} +(-2.00000 - 3.46410i) q^{75} -6.78890 q^{77} -12.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +11.8167 q^{83} +(0.802776 - 1.39045i) q^{85} +(1.50000 - 2.59808i) q^{87} +(8.21110 + 14.2220i) q^{89} +9.39445 q^{91} +(-2.60555 - 4.51295i) q^{93} +(3.30278 - 5.72058i) q^{95} +(-5.60555 + 9.70910i) q^{97} -2.60555 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{5} + 2 q^{7} - 2 q^{9} - 2 q^{11} - 2 q^{15} + 4 q^{17} - 6 q^{19} + 4 q^{21} - 2 q^{23} - 16 q^{25} - 4 q^{27} - 6 q^{29} + 8 q^{31} + 2 q^{33} - 2 q^{35} + 12 q^{37} + 16 q^{41} + 2 q^{43}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^5 + 2 * q^7 - 2 * q^9 - 2 * q^11 - 2 * q^15 + 4 * q^17 - 6 * q^19 + 4 * q^21 - 2 * q^23 - 16 * q^25 - 4 * q^27 - 6 * q^29 + 8 * q^31 + 2 * q^33 - 2 * q^35 + 12 * q^37 + 16 * q^41 + 2 * q^43 + 2 * q^45 + 20 * q^47 - 14 * q^49 + 8 * q^51 + 12 * q^53 + 2 * q^55 - 12 * q^57 + 4 * q^59 + 8 * q^61 + 2 * q^63 - 14 * q^67 + 2 * q^69 - 26 * q^71 + 28 * q^73 - 8 * q^75 - 56 * q^77 - 48 * q^79 - 2 * q^81 + 4 * q^83 - 4 * q^85 + 6 * q^87 + 4 * q^89 + 52 * q^91 + 4 * q^93 + 6 * q^95 - 8 * q^97 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$		0			0
$7$	−1.30278	+	2.25647i	−0.492403	+	0.852867i	−0.999962	−	0.00875026i	$-0.997215\pi$
$7$	−1.30278	+	2.25647i	−0.492403	+	0.852867i	0.507559	+	0.861617i	$0.330548\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.30278	+	2.25647i	0.392802	+	0.680352i	0.992818	−	0.119635i	$-0.0381726\pi$
$11$	1.30278	+	2.25647i	0.392802	+	0.680352i	−0.600016	+	0.799988i	$0.704839\pi$
$12$		0			0
$13$	−1.80278	−	3.12250i	−0.500000	−	0.866025i
$13$	−1.80278	−	3.12250i	−0.500000	−	0.866025i
$14$		0			0
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$		0			0
$17$	−0.802776	+	1.39045i	−0.194702	+	0.337233i	−0.946803	−	0.321815i	$-0.895707\pi$
$17$	−0.802776	+	1.39045i	−0.194702	+	0.337233i	0.752101	+	0.659048i	$0.229041\pi$
$18$		0			0
$19$	−3.30278	+	5.72058i	−0.757709	+	1.31239i	0.186308	+	0.982491i	$0.440348\pi$
$19$	−3.30278	+	5.72058i	−0.757709	+	1.31239i	−0.944016	+	0.329899i	$0.892985\pi$
$20$		0			0
$21$	−2.60555			−0.568578
$22$		0			0
$23$	1.30278	+	2.25647i	0.271647	+	0.470507i	0.969284	−	0.245945i	$-0.0790982\pi$
$23$	1.30278	+	2.25647i	0.271647	+	0.470507i	−0.697636	+	0.716452i	$0.745765\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	−5.21110			−0.935942			−0.467971	−	0.883744i	$-0.655015\pi$
$31$	−5.21110			−0.935942			−0.467971	+	0.883744i	$0.655015\pi$
$32$		0			0
$33$	−1.30278	+	2.25647i	−0.226784	+	0.392802i
$34$		0			0
$35$	1.30278	−	2.25647i	0.220209	−	0.381414i
$36$		0			0
$37$	1.19722	+	2.07365i	0.196822	+	0.340907i	0.947496	−	0.319766i	$-0.103604\pi$
$37$	1.19722	+	2.07365i	0.196822	+	0.340907i	−0.750674	+	0.660673i	$0.770271\pi$
$38$		0			0
$39$	1.80278	−	3.12250i	0.288675	−	0.500000i
$40$		0			0
$41$	5.80278	+	10.0507i	0.906241	+	1.56966i	0.819242	+	0.573448i	$0.194394\pi$
$41$	5.80278	+	10.0507i	0.906241	+	1.56966i	0.0869990	+	0.996208i	$0.472272\pi$
$42$		0			0
$43$	−1.30278	+	2.25647i	−0.198671	+	0.344109i	−0.948098	−	0.317979i	$-0.896996\pi$
$43$	−1.30278	+	2.25647i	−0.198671	+	0.344109i	0.749426	+	0.662088i	$0.230329\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	1.39445			0.203401			0.101701	−	0.994815i	$-0.467572\pi$
$47$	1.39445			0.203401			0.101701	+	0.994815i	$0.467572\pi$
$48$		0			0
$49$	0.105551	+	0.182820i	0.0150788	+	0.0261172i
$50$		0			0
$51$	−1.60555			−0.224822
$52$		0			0
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		0			0
$55$	−1.30278	−	2.25647i	−0.175666	−	0.304263i
$56$		0			0
$57$	−6.60555			−0.874927
$58$		0			0
$59$	4.60555	−	7.97705i	0.599592	−	1.03852i	−0.393290	−	0.919415i	$-0.628663\pi$
$59$	4.60555	−	7.97705i	0.599592	−	1.03852i	0.992881	−	0.119109i	$-0.0380037\pi$
$60$		0			0
$61$	3.80278	−	6.58660i	0.486896	−	0.843328i	−0.512991	−	0.858394i	$-0.671463\pi$
$61$	3.80278	−	6.58660i	0.486896	−	0.843328i	0.999886	+	0.0150662i	$0.00479591\pi$
$62$		0			0
$63$	−1.30278	−	2.25647i	−0.164134	−	0.284289i
$64$		0			0
$65$	1.80278	+	3.12250i	0.223607	+	0.387298i
$66$		0			0
$67$	−5.30278	−	9.18468i	−0.647837	−	1.12209i	−0.983638	−	0.180154i	$-0.942340\pi$
$67$	−5.30278	−	9.18468i	−0.647837	−	1.12209i	0.335801	−	0.941933i	$-0.390993\pi$
$68$		0			0
$69$	−1.30278	+	2.25647i	−0.156836	+	0.271647i
$70$		0			0
$71$	−4.69722	+	8.13583i	−0.557458	+	0.965546i	0.440250	+	0.897875i	$0.354890\pi$
$71$	−4.69722	+	8.13583i	−0.557458	+	0.965546i	−0.997708	+	0.0676702i	$0.978443\pi$
$72$		0			0
$73$	7.00000			0.819288			0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000			0.819288			0.409644	+	0.912245i	$0.365653\pi$
$74$		0			0
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$		0			0
$77$	−6.78890			−0.773667
$78$		0			0
$79$	−12.0000			−1.35011			−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000			−1.35011			−0.675053	+	0.737769i	$0.735879\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	11.8167			1.29705			0.648523	−	0.761195i	$-0.275387\pi$
$83$	11.8167			1.29705			0.648523	+	0.761195i	$0.275387\pi$
$84$		0			0
$85$	0.802776	−	1.39045i	0.0870732	−	0.150815i
$86$		0			0
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	8.21110	+	14.2220i	0.870375	+	1.50753i	0.861609	+	0.507572i	$0.169457\pi$
$89$	8.21110	+	14.2220i	0.870375	+	1.50753i	0.00876600	+	0.999962i	$0.497210\pi$
$90$		0			0
$91$	9.39445			0.984806
$92$		0			0
$93$	−2.60555	−	4.51295i	−0.270183	−	0.467971i
$94$		0			0
$95$	3.30278	−	5.72058i	0.338858	−	0.586919i
$96$		0			0
$97$	−5.60555	+	9.70910i	−0.569157	+	0.985810i	0.427492	+	0.904019i	$0.359397\pi$
$97$	−5.60555	+	9.70910i	−0.569157	+	0.985810i	−0.996650	+	0.0817906i	$0.973936\pi$
$98$		0			0
$99$	−2.60555			−0.261868
$100$		0			0
$101$	−2.10555	−	3.64692i	−0.209510	−	0.362882i	0.742050	−	0.670344i	$-0.233854\pi$
$101$	−2.10555	−	3.64692i	−0.209510	−	0.362882i	−0.951560	+	0.307462i	$0.900520\pi$
$102$		0			0
$103$	15.8167			1.55846			0.779231	−	0.626737i	$-0.215610\pi$
$103$	15.8167			1.55846			0.779231	+	0.626737i	$0.215610\pi$
$104$		0			0
$105$	2.60555			0.254276
$106$		0			0
$107$	3.30278	+	5.72058i	0.319291	+	0.553029i	0.980340	−	0.197314i	$-0.0632218\pi$
$107$	3.30278	+	5.72058i	0.319291	+	0.553029i	−0.661049	+	0.750343i	$0.729888\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	−1.19722	+	2.07365i	−0.113636	+	0.196822i
$112$		0			0
$113$	5.80278	−	10.0507i	0.545879	−	0.945491i	−0.452672	−	0.891677i	$-0.649529\pi$
$113$	5.80278	−	10.0507i	0.545879	−	0.945491i	0.998551	−	0.0538133i	$-0.0171376\pi$
$114$		0			0
$115$	−1.30278	−	2.25647i	−0.121484	−	0.210417i
$116$		0			0
$117$	3.60555			0.333333
$118$		0			0
$119$	−2.09167	−	3.62288i	−0.191743	−	0.332109i
$120$		0			0
$121$	2.10555	−	3.64692i	0.191414	−	0.331538i
$122$		0			0
$123$	−5.80278	+	10.0507i	−0.523219	+	0.906241i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	0.941014	−	0.338368i	$-0.109875\pi$
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	−0.763542	+	0.645758i	$0.776542\pi$
$128$		0			0
$129$	−2.60555			−0.229406
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−8.60555	−	14.9053i	−0.746196	−	1.29245i
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	8.40833	−	14.5636i	0.718372	−	1.24426i	−0.243273	−	0.969958i	$-0.578221\pi$
$137$	8.40833	−	14.5636i	0.718372	−	1.24426i	0.961645	−	0.274299i	$-0.0884457\pi$
$138$		0			0
$139$	−1.39445	+	2.41526i	−0.118276	+	0.204859i	−0.919084	−	0.394061i	$-0.871070\pi$
$139$	−1.39445	+	2.41526i	−0.118276	+	0.204859i	0.800809	+	0.598920i	$0.204403\pi$
$140$		0			0
$141$	0.697224	+	1.20763i	0.0587169	+	0.101701i
$142$		0			0
$143$	4.69722	−	8.13583i	0.392802	−	0.680352i
$144$		0			0
$145$	1.50000	+	2.59808i	0.124568	+	0.215758i
$146$		0			0
$147$	−0.105551	+	0.182820i	−0.00870572	+	0.0150788i
$148$		0			0
$149$	5.10555	−	8.84307i	0.418263	−	0.724453i	−0.577502	−	0.816389i	$-0.695972\pi$
$149$	5.10555	−	8.84307i	0.418263	−	0.724453i	0.995765	+	0.0919365i	$0.0293057\pi$
$150$		0			0
$151$	6.60555			0.537552			0.268776	−	0.963203i	$-0.413381\pi$
$151$	6.60555			0.537552			0.268776	+	0.963203i	$0.413381\pi$
$152$		0			0
$153$	−0.802776	−	1.39045i	−0.0649006	−	0.112411i
$154$		0			0
$155$	5.21110			0.418566
$156$		0			0
$157$	8.39445			0.669950			0.334975	−	0.942227i	$-0.391272\pi$
$157$	8.39445			0.669950			0.334975	+	0.942227i	$0.391272\pi$
$158$		0			0
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$	−6.78890			−0.535040
$162$		0			0
$163$	−2.60555	+	4.51295i	−0.204083	+	0.353481i	−0.949840	−	0.312736i	$-0.898754\pi$
$163$	−2.60555	+	4.51295i	−0.204083	+	0.353481i	0.745757	+	0.666217i	$0.232088\pi$
$164$		0			0
$165$	1.30278	−	2.25647i	0.101421	−	0.175666i
$166$		0			0
$167$	8.60555	+	14.9053i	0.665918	+	1.15340i	0.979036	+	0.203689i	$0.0652931\pi$
$167$	8.60555	+	14.9053i	0.665918	+	1.15340i	−0.313118	+	0.949714i	$0.601374\pi$
$168$		0			0
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$		0			0
$171$	−3.30278	−	5.72058i	−0.252570	−	0.437463i
$172$		0			0
$173$	10.8167	−	18.7350i	0.822375	−	1.42440i	−0.0815341	−	0.996671i	$-0.525982\pi$
$173$	10.8167	−	18.7350i	0.822375	−	1.42440i	0.903909	−	0.427725i	$-0.140685\pi$
$174$		0			0
$175$	5.21110	−	9.02589i	0.393922	−	0.682293i
$176$		0			0
$177$	9.21110			0.692349
$178$		0			0
$179$	−8.51388	−	14.7465i	−0.636357	−	1.10220i	−0.986226	−	0.165404i	$-0.947107\pi$
$179$	−8.51388	−	14.7465i	−0.636357	−	1.10220i	0.349869	−	0.936799i	$-0.386226\pi$
$180$		0			0
$181$	−24.8167			−1.84461			−0.922304	−	0.386466i	$-0.873696\pi$
$181$	−24.8167			−1.84461			−0.922304	+	0.386466i	$0.873696\pi$
$182$		0			0
$183$	7.60555			0.562219
$184$		0			0
$185$	−1.19722	−	2.07365i	−0.0880217	−	0.152458i
$186$		0			0
$187$	−4.18335			−0.305917
$188$		0			0
$189$	1.30278	−	2.25647i	0.0947630	−	0.164134i
$190$		0			0
$191$	−11.8167	+	20.4670i	−0.855023	+	1.48094i	0.0216006	+	0.999767i	$0.493124\pi$
$191$	−11.8167	+	20.4670i	−0.855023	+	1.48094i	−0.876624	+	0.481177i	$0.840210\pi$
$192$		0			0
$193$	3.89445	+	6.74538i	0.280329	+	0.485543i	0.971466	−	0.237180i	$-0.0762233\pi$
$193$	3.89445	+	6.74538i	0.280329	+	0.485543i	−0.691137	+	0.722724i	$0.742890\pi$
$194$		0			0
$195$	−1.80278	+	3.12250i	−0.129099	+	0.223607i
$196$		0			0
$197$	5.00000	+	8.66025i	0.356235	+	0.617018i	0.987329	−	0.158689i	$-0.0507268\pi$
$197$	5.00000	+	8.66025i	0.356235	+	0.617018i	−0.631093	+	0.775707i	$0.717394\pi$
$198$		0			0
$199$	9.90833	−	17.1617i	0.702383	−	1.21656i	−0.265245	−	0.964181i	$-0.585453\pi$
$199$	9.90833	−	17.1617i	0.702383	−	1.21656i	0.967628	−	0.252381i	$-0.0812138\pi$
$200$		0			0
$201$	5.30278	−	9.18468i	0.374029	−	0.647837i
$202$		0			0
$203$	7.81665			0.548622
$204$		0			0
$205$	−5.80278	−	10.0507i	−0.405283	−	0.701971i
$206$		0			0
$207$	−2.60555			−0.181098
$208$		0			0
$209$	−17.2111			−1.19052
$210$		0			0
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$		0			0
$213$	−9.39445			−0.643697
$214$		0			0
$215$	1.30278	−	2.25647i	0.0888486	−	0.153890i
$216$		0			0
$217$	6.78890	−	11.7587i	0.460860	−	0.798234i
$218$		0			0
$219$	3.50000	+	6.06218i	0.236508	+	0.409644i
$220$		0			0
$221$	5.78890			0.389403
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$		0			0
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$		0			0
$227$	−13.3028	+	23.0411i	−0.882936	+	1.52929i	−0.0348753	+	0.999392i	$0.511103\pi$
$227$	−13.3028	+	23.0411i	−0.882936	+	1.52929i	−0.848061	+	0.529899i	$0.822230\pi$
$228$		0			0
$229$	15.2111			1.00518			0.502589	−	0.864525i	$-0.332381\pi$
$229$	15.2111			1.00518			0.502589	+	0.864525i	$0.332381\pi$
$230$		0			0
$231$	−3.39445	−	5.87936i	−0.223338	−	0.386833i
$232$		0			0
$233$	−14.0000			−0.917170			−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000			−0.917170			−0.458585	+	0.888650i	$0.651644\pi$
$234$		0			0
$235$	−1.39445			−0.0909638
$236$		0			0
$237$	−6.00000	−	10.3923i	−0.389742	−	0.675053i
$238$		0			0
$239$	−17.0278			−1.10143			−0.550717	−	0.834692i	$-0.685646\pi$
$239$	−17.0278			−1.10143			−0.550717	+	0.834692i	$0.685646\pi$
$240$		0			0
$241$	−7.31665	+	12.6728i	−0.471307	+	0.816328i	−0.999461	−	0.0328207i	$-0.989551\pi$
$241$	−7.31665	+	12.6728i	−0.471307	+	0.816328i	0.528154	+	0.849149i	$0.322884\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−0.105551	−	0.182820i	−0.00674342	−	0.0116800i
$246$		0			0
$247$	23.8167			1.51542
$248$		0			0
$249$	5.90833	+	10.2335i	0.374425	+	0.648523i
$250$		0			0
$251$	14.6056	−	25.2976i	0.921894	−	1.59677i	0.125413	−	0.992105i	$-0.459974\pi$
$251$	14.6056	−	25.2976i	0.921894	−	1.59677i	0.796481	−	0.604663i	$-0.206692\pi$
$252$		0			0
$253$	−3.39445	+	5.87936i	−0.213407	+	0.369632i
$254$		0			0
$255$	1.60555			0.100544
$256$		0			0
$257$	11.8028	+	20.4430i	0.736237	+	1.27520i	0.954179	+	0.299238i	$0.0967324\pi$
$257$	11.8028	+	20.4430i	0.736237	+	1.27520i	−0.217942	+	0.975962i	$0.569934\pi$
$258$		0			0
$259$	−6.23886			−0.387664
$260$		0			0
$261$	3.00000			0.185695
$262$		0			0
$263$	9.30278	+	16.1129i	0.573634	+	0.993563i	0.996189	+	0.0872254i	$0.0278000\pi$
$263$	9.30278	+	16.1129i	0.573634	+	0.993563i	−0.422555	+	0.906337i	$0.638867\pi$
$264$		0			0
$265$	−3.00000			−0.184289
$266$		0			0
$267$	−8.21110	+	14.2220i	−0.502511	+	0.870375i
$268$		0			0
$269$	−12.8167	+	22.1991i	−0.781445	+	1.35350i	0.149655	+	0.988738i	$0.452184\pi$
$269$	−12.8167	+	22.1991i	−0.781445	+	1.35350i	−0.931100	+	0.364764i	$0.881150\pi$
$270$		0			0
$271$	−0.605551	−	1.04885i	−0.0367846	−	0.0637128i	0.847047	−	0.531518i	$-0.178378\pi$
$271$	−0.605551	−	1.04885i	−0.0367846	−	0.0637128i	−0.883832	+	0.467805i	$0.845045\pi$
$272$		0			0
$273$	4.69722	+	8.13583i	0.284289	+	0.492403i
$274$		0			0
$275$	−5.21110	−	9.02589i	−0.314241	−	0.544282i
$276$		0			0
$277$	−14.6194	+	25.3216i	−0.878396	+	1.52143i	−0.0252962	+	0.999680i	$0.508053\pi$
$277$	−14.6194	+	25.3216i	−0.878396	+	1.52143i	−0.853100	+	0.521747i	$0.825280\pi$
$278$		0			0
$279$	2.60555	−	4.51295i	0.155990	−	0.270183i
$280$		0			0
$281$	0.394449			0.0235308			0.0117654	−	0.999931i	$-0.496255\pi$
$281$	0.394449			0.0235308			0.0117654	+	0.999931i	$0.496255\pi$
$282$		0			0
$283$	7.30278	+	12.6488i	0.434105	+	0.751892i	0.997222	−	0.0744852i	$-0.0237314\pi$
$283$	7.30278	+	12.6488i	0.434105	+	0.751892i	−0.563117	+	0.826377i	$0.690398\pi$
$284$		0			0
$285$	6.60555			0.391279
$286$		0			0
$287$	−30.2389			−1.78494
$288$		0			0
$289$	7.21110	+	12.4900i	0.424183	+	0.734706i
$290$		0			0
$291$	−11.2111			−0.657206
$292$		0			0
$293$	−0.105551	+	0.182820i	−0.00616637	+	0.0106805i	−0.869092	−	0.494650i	$-0.835296\pi$
$293$	−0.105551	+	0.182820i	−0.00616637	+	0.0106805i	0.862926	+	0.505331i	$0.168629\pi$
$294$		0			0
$295$	−4.60555	+	7.97705i	−0.268146	+	0.464442i
$296$		0			0
$297$	−1.30278	−	2.25647i	−0.0755947	−	0.130934i
$298$		0			0
$299$	4.69722	−	8.13583i	0.271647	−	0.470507i
$300$		0			0
$301$	−3.39445	−	5.87936i	−0.195653	−	0.338881i
$302$		0			0
$303$	2.10555	−	3.64692i	0.120961	−	0.209510i
$304$		0			0
$305$	−3.80278	+	6.58660i	−0.217746	+	0.377148i
$306$		0			0
$307$	−5.39445			−0.307877			−0.153939	−	0.988080i	$-0.549196\pi$
$307$	−5.39445			−0.307877			−0.153939	+	0.988080i	$0.549196\pi$
$308$		0			0
$309$	7.90833	+	13.6976i	0.449889	+	0.779231i
$310$		0			0
$311$	−27.8167			−1.57734			−0.788669	−	0.614818i	$-0.789229\pi$
$311$	−27.8167			−1.57734			−0.788669	+	0.614818i	$0.789229\pi$
$312$		0			0
$313$	3.21110			0.181502			0.0907511	−	0.995874i	$-0.471073\pi$
$313$	3.21110			0.181502			0.0907511	+	0.995874i	$0.471073\pi$
$314$		0			0
$315$	1.30278	+	2.25647i	0.0734031	+	0.127138i
$316$		0			0
$317$	−2.21110			−0.124188			−0.0620939	−	0.998070i	$-0.519778\pi$
$317$	−2.21110			−0.124188			−0.0620939	+	0.998070i	$0.519778\pi$
$318$		0			0
$319$	3.90833	−	6.76942i	0.218824	−	0.379015i
$320$		0			0
$321$	−3.30278	+	5.72058i	−0.184343	+	0.319291i
$322$		0			0
$323$	−5.30278	−	9.18468i	−0.295054	−	0.511049i
$324$		0			0
$325$	7.21110	+	12.4900i	0.400000	+	0.692820i
$326$		0			0
$327$	−1.00000	−	1.73205i	−0.0553001	−	0.0957826i
$328$		0			0
$329$	−1.81665	+	3.14654i	−0.100155	+	0.173474i
$330$		0			0
$331$	−7.81665	+	13.5388i	−0.429642	+	0.744162i	−0.996841	−	0.0794186i	$-0.974694\pi$
$331$	−7.81665	+	13.5388i	−0.429642	+	0.744162i	0.567199	+	0.823581i	$0.308027\pi$
$332$		0			0
$333$	−2.39445			−0.131215
$334$		0			0
$335$	5.30278	+	9.18468i	0.289722	+	0.501813i
$336$		0			0
$337$	−2.57779			−0.140421			−0.0702107	−	0.997532i	$-0.522367\pi$
$337$	−2.57779			−0.140421			−0.0702107	+	0.997532i	$0.522367\pi$
$338$		0			0
$339$	11.6056			0.630327
$340$		0			0
$341$	−6.78890	−	11.7587i	−0.367639	−	0.636770i
$342$		0			0
$343$	−18.7889			−1.01451
$344$		0			0
$345$	1.30278	−	2.25647i	0.0701391	−	0.121484i
$346$		0			0
$347$	8.51388	−	14.7465i	0.457049	−	0.791632i	−0.541755	−	0.840537i	$-0.682240\pi$
$347$	8.51388	−	14.7465i	0.457049	−	0.791632i	0.998803	+	0.0489048i	$0.0155731\pi$
$348$		0			0
$349$	18.2111	+	31.5426i	0.974818	+	1.68843i	0.680534	+	0.732716i	$0.261748\pi$
$349$	18.2111	+	31.5426i	0.974818	+	1.68843i	0.294284	+	0.955718i	$0.404919\pi$
$350$		0			0
$351$	1.80278	+	3.12250i	0.0962250	+	0.166667i
$352$		0			0
$353$	−8.01388	−	13.8804i	−0.426536	−	0.738781i	0.570027	−	0.821626i	$-0.306933\pi$
$353$	−8.01388	−	13.8804i	−0.426536	−	0.738781i	−0.996562	+	0.0828446i	$0.973599\pi$
$354$		0			0
$355$	4.69722	−	8.13583i	0.249303	−	0.431805i
$356$		0			0
$357$	2.09167	−	3.62288i	0.110703	−	0.191743i
$358$		0			0
$359$	−7.81665			−0.412547			−0.206274	−	0.978494i	$-0.566134\pi$
$359$	−7.81665			−0.412547			−0.206274	+	0.978494i	$0.566134\pi$
$360$		0			0
$361$	−12.3167	−	21.3331i	−0.648245	−	1.12279i
$362$		0			0
$363$	4.21110			0.221026
$364$		0			0
$365$	−7.00000			−0.366397
$366$		0			0
$367$	−0.697224	−	1.20763i	−0.0363948	−	0.0630377i	0.847254	−	0.531188i	$-0.178254\pi$
$367$	−0.697224	−	1.20763i	−0.0363948	−	0.0630377i	−0.883649	+	0.468150i	$0.844921\pi$
$368$		0			0
$369$	−11.6056			−0.604161
$370$		0			0
$371$	−3.90833	+	6.76942i	−0.202910	+	0.351451i
$372$		0			0
$373$	15.0139	−	26.0048i	0.777389	−	1.34648i	−0.156053	−	0.987749i	$-0.549877\pi$
$373$	15.0139	−	26.0048i	0.777389	−	1.34648i	0.933442	−	0.358729i	$-0.116790\pi$
$374$		0			0
$375$	4.50000	+	7.79423i	0.232379	+	0.402492i
$376$		0			0
$377$	−5.40833	+	9.36750i	−0.278543	+	0.482451i
$378$		0			0
$379$	3.21110	+	5.56179i	0.164943	+	0.285690i	0.936635	−	0.350306i	$-0.113923\pi$
$379$	3.21110	+	5.56179i	0.164943	+	0.285690i	−0.771692	+	0.635997i	$0.780589\pi$
$380$		0			0
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$		0			0
$383$	−9.21110	+	15.9541i	−0.470665	+	0.815216i	−0.999437	−	0.0335478i	$-0.989319\pi$
$383$	−9.21110	+	15.9541i	−0.470665	+	0.815216i	0.528772	+	0.848764i	$0.322653\pi$
$384$		0			0
$385$	6.78890			0.345994
$386$		0			0
$387$	−1.30278	−	2.25647i	−0.0662238	−	0.114703i
$388$		0			0
$389$	−36.6333			−1.85738			−0.928691	−	0.370854i	$-0.879065\pi$
$389$	−36.6333			−1.85738			−0.928691	+	0.370854i	$0.879065\pi$
$390$		0			0
$391$	−4.18335			−0.211561
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.0000			0.603786
$396$		0			0
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	0.446051	+	0.895008i	$0.352830\pi$
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	−0.998125	+	0.0612128i	$0.980503\pi$
$398$		0			0
$399$	8.60555	−	14.9053i	0.430816	−	0.746196i
$400$		0			0
$401$	−13.2250	−	22.9063i	−0.660424	−	1.14389i	−0.980504	−	0.196498i	$-0.937043\pi$
$401$	−13.2250	−	22.9063i	−0.660424	−	1.14389i	0.320080	−	0.947390i	$-0.396290\pi$
$402$		0			0
$403$	9.39445	+	16.2717i	0.467971	+	0.810549i
$404$		0			0
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$		0			0
$407$	−3.11943	+	5.40301i	−0.154624	+	0.267817i
$408$		0			0
$409$	−2.28890	+	3.96449i	−0.113179	+	0.196031i	−0.917050	−	0.398772i	$-0.869437\pi$
$409$	−2.28890	+	3.96449i	−0.113179	+	0.196031i	0.803872	+	0.594803i	$0.202770\pi$
$410$		0			0
$411$	16.8167			0.829504
$412$		0			0
$413$	12.0000	+	20.7846i	0.590481	+	1.02274i
$414$		0			0
$415$	−11.8167			−0.580057
$416$		0			0
$417$	−2.78890			−0.136573
$418$		0			0
$419$	−9.21110	−	15.9541i	−0.449992	−	0.779409i	0.548393	−	0.836221i	$-0.315240\pi$
$419$	−9.21110	−	15.9541i	−0.449992	−	0.779409i	−0.998385	+	0.0568120i	$0.981906\pi$
$420$		0			0
$421$	24.3944			1.18891			0.594456	−	0.804128i	$-0.297367\pi$
$421$	24.3944			1.18891			0.594456	+	0.804128i	$0.297367\pi$
$422$		0			0
$423$	−0.697224	+	1.20763i	−0.0339002	+	0.0587169i
$424$		0			0
$425$	3.21110	−	5.56179i	0.155761	−	0.269787i
$426$		0			0
$427$	9.90833	+	17.1617i	0.479498	+	0.830514i
$428$		0			0
$429$	9.39445			0.453568
$430$		0			0
$431$	−7.90833	−	13.6976i	−0.380931	−	0.659791i	0.610265	−	0.792197i	$-0.291063\pi$
$431$	−7.90833	−	13.6976i	−0.380931	−	0.659791i	−0.991196	+	0.132406i	$0.957730\pi$
$432$		0			0
$433$	17.7111	−	30.6765i	0.851141	−	1.47422i	−0.0290379	−	0.999578i	$-0.509244\pi$
$433$	17.7111	−	30.6765i	0.851141	−	1.47422i	0.880179	−	0.474642i	$-0.157422\pi$
$434$		0			0
$435$	−1.50000	+	2.59808i	−0.0719195	+	0.124568i
$436$		0			0
$437$	−17.2111			−0.823319
$438$		0			0
$439$	17.9083	+	31.0181i	0.854718	+	1.48041i	0.876907	+	0.480661i	$0.159603\pi$
$439$	17.9083	+	31.0181i	0.854718	+	1.48041i	−0.0221888	+	0.999754i	$0.507063\pi$
$440$		0			0
$441$	−0.211103			−0.0100525
$442$		0			0
$443$	15.6333			0.742761			0.371380	−	0.928481i	$-0.378885\pi$
$443$	15.6333			0.742761			0.371380	+	0.928481i	$0.378885\pi$
$444$		0			0
$445$	−8.21110	−	14.2220i	−0.389244	−	0.674190i
$446$		0			0
$447$	10.2111			0.482969
$448$		0			0
$449$	15.0000	−	25.9808i	0.707894	−	1.22611i	−0.257743	−	0.966213i	$-0.582979\pi$
$449$	15.0000	−	25.9808i	0.707894	−	1.22611i	0.965637	−	0.259895i	$-0.0836878\pi$
$450$		0			0
$451$	−15.1194	+	26.1876i	−0.711946	+	1.23313i
$452$		0			0
$453$	3.30278	+	5.72058i	0.155178	+	0.268776i
$454$		0			0
$455$	−9.39445			−0.440419
$456$		0			0
$457$	−17.3167	−	29.9933i	−0.810039	−	1.40303i	−0.912836	−	0.408326i	$-0.866113\pi$
$457$	−17.3167	−	29.9933i	−0.810039	−	1.40303i	0.102797	−	0.994702i	$-0.467221\pi$
$458$		0			0
$459$	0.802776	−	1.39045i	0.0374704	−	0.0649006i
$460$		0			0
$461$	−9.31665	+	16.1369i	−0.433920	+	0.751571i	−0.997207	−	0.0746901i	$-0.976203\pi$
$461$	−9.31665	+	16.1369i	−0.433920	+	0.751571i	0.563287	+	0.826261i	$0.309537\pi$
$462$		0			0
$463$	4.18335			0.194417			0.0972083	−	0.995264i	$-0.469009\pi$
$463$	4.18335			0.194417			0.0972083	+	0.995264i	$0.469009\pi$
$464$		0			0
$465$	2.60555	+	4.51295i	0.120830	+	0.209283i
$466$		0			0
$467$	−8.18335			−0.378680			−0.189340	−	0.981912i	$-0.560635\pi$
$467$	−8.18335			−0.378680			−0.189340	+	0.981912i	$0.560635\pi$
$468$		0			0
$469$	27.6333			1.27599
$470$		0			0
$471$	4.19722	+	7.26981i	0.193398	+	0.334975i
$472$		0			0
$473$	−6.78890			−0.312154
$474$		0			0
$475$	13.2111	−	22.8823i	0.606167	−	1.04991i
$476$		0			0
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$		0			0
$479$	−1.81665	−	3.14654i	−0.0830050	−	0.143769i	0.821534	−	0.570159i	$-0.193118\pi$
$479$	−1.81665	−	3.14654i	−0.0830050	−	0.143769i	−0.904539	+	0.426390i	$0.859785\pi$
$480$		0			0
$481$	4.31665	−	7.47666i	0.196822	−	0.340907i
$482$		0			0
$483$	−3.39445	−	5.87936i	−0.154453	−	0.267520i
$484$		0			0
$485$	5.60555	−	9.70910i	0.254535	−	0.440868i
$486$		0			0
$487$	15.3028	−	26.5052i	0.693435	−	1.20106i	−0.277270	−	0.960792i	$-0.589430\pi$
$487$	15.3028	−	26.5052i	0.693435	−	1.20106i	0.970705	−	0.240273i	$-0.0772369\pi$
$488$		0			0
$489$	−5.21110			−0.235654
$490$		0			0
$491$	9.90833	+	17.1617i	0.447157	+	0.774498i	0.998200	−	0.0599789i	$-0.0191034\pi$
$491$	9.90833	+	17.1617i	0.447157	+	0.774498i	−0.551043	+	0.834477i	$0.685770\pi$
$492$		0			0
$493$	4.81665			0.216931
$494$		0			0
$495$	2.60555			0.117111
$496$		0			0
$497$	−12.2389	−	21.1983i	−0.548988	−	0.950875i
$498$		0			0
$499$	−33.2111			−1.48673			−0.743367	−	0.668884i	$-0.766772\pi$
$499$	−33.2111			−1.48673			−0.743367	+	0.668884i	$0.766772\pi$
$500$		0			0
$501$	−8.60555	+	14.9053i	−0.384468	+	0.665918i
$502$		0			0
$503$	7.90833	−	13.6976i	0.352615	−	0.610747i	−0.634092	−	0.773258i	$-0.718626\pi$
$503$	7.90833	−	13.6976i	0.352615	−	0.610747i	0.986707	+	0.162511i	$0.0519592\pi$
$504$		0			0
$505$	2.10555	+	3.64692i	0.0936958	+	0.162286i
$506$		0			0
$507$	−13.0000			−0.577350
$508$		0			0
$509$	2.31665	+	4.01256i	0.102684	+	0.177854i	0.912790	−	0.408430i	$-0.133924\pi$
$509$	2.31665	+	4.01256i	0.102684	+	0.177854i	−0.810106	+	0.586284i	$0.800590\pi$
$510$		0			0
$511$	−9.11943	+	15.7953i	−0.403420	+	0.698744i
$512$		0			0
$513$	3.30278	−	5.72058i	0.145821	−	0.252570i
$514$		0			0
$515$	−15.8167			−0.696965
$516$		0			0
$517$	1.81665	+	3.14654i	0.0798963	+	0.138385i
$518$		0			0
$519$	21.6333			0.949597
$520$		0			0
$521$	−23.2389			−1.01811			−0.509056	−	0.860733i	$-0.670006\pi$
$521$	−23.2389			−1.01811			−0.509056	+	0.860733i	$0.670006\pi$
$522$		0			0
$523$	0.513878	+	0.890063i	0.0224703	+	0.0389197i	0.877042	−	0.480414i	$-0.159514\pi$
$523$	0.513878	+	0.890063i	0.0224703	+	0.0389197i	−0.854572	+	0.519334i	$0.826180\pi$
$524$		0			0
$525$	10.4222			0.454862
$526$		0			0
$527$	4.18335	−	7.24577i	0.182229	−	0.315631i
$528$		0			0
$529$	8.10555	−	14.0392i	0.352415	−	0.610401i
$530$		0			0
$531$	4.60555	+	7.97705i	0.199864	+	0.346174i
$532$		0			0
$533$	20.9222	−	36.2383i	0.906241	−	1.56966i
$534$		0			0
$535$	−3.30278	−	5.72058i	−0.142791	−	0.247322i
$536$		0			0
$537$	8.51388	−	14.7465i	0.367401	−	0.636357i
$538$		0			0
$539$	−0.275019	+	0.476347i	−0.0118459	+	0.0205177i
$540$		0			0
$541$	−10.3944			−0.446892			−0.223446	−	0.974716i	$-0.571731\pi$
$541$	−10.3944			−0.446892			−0.223446	+	0.974716i	$0.571731\pi$
$542$		0			0
$543$	−12.4083	−	21.4919i	−0.532492	−	0.922304i
$544$		0			0
$545$	2.00000			0.0856706
$546$		0			0
$547$	−17.0278			−0.728054			−0.364027	−	0.931388i	$-0.618598\pi$
$547$	−17.0278			−0.728054			−0.364027	+	0.931388i	$0.618598\pi$
$548$		0			0
$549$	3.80278	+	6.58660i	0.162299	+	0.281109i
$550$		0			0
$551$	19.8167			0.844218
$552$		0			0
$553$	15.6333	−	27.0777i	0.664796	−	1.15146i
$554$		0			0
$555$	1.19722	−	2.07365i	0.0508193	−	0.0880217i
$556$		0			0
$557$	14.9222	+	25.8460i	0.632274	+	1.09513i	0.987086	+	0.160193i	$0.0512117\pi$
$557$	14.9222	+	25.8460i	0.632274	+	1.09513i	−0.354812	+	0.934938i	$0.615455\pi$
$558$		0			0
$559$	9.39445			0.397343
$560$		0			0
$561$	−2.09167	−	3.62288i	−0.0883105	−	0.152958i
$562$		0			0
$563$	13.8167	−	23.9311i	0.582303	−	1.00858i	−0.412903	−	0.910775i	$-0.635485\pi$
$563$	13.8167	−	23.9311i	0.582303	−	1.00858i	0.995206	−	0.0978027i	$-0.0311814\pi$
$564$		0			0
$565$	−5.80278	+	10.0507i	−0.244125	+	0.422836i
$566$		0			0
$567$	2.60555			0.109423
$568$		0			0
$569$	11.6056	+	20.1014i	0.486530	+	0.842695i	0.999880	−	0.0154846i	$-0.00492909\pi$
$569$	11.6056	+	20.1014i	0.486530	+	0.842695i	−0.513350	+	0.858179i	$0.671596\pi$
$570$		0			0
$571$	19.4500			0.813956			0.406978	−	0.913438i	$-0.366583\pi$
$571$	19.4500			0.813956			0.406978	+	0.913438i	$0.366583\pi$
$572$		0			0
$573$	−23.6333			−0.987296
$574$		0			0
$575$	−5.21110	−	9.02589i	−0.217318	−	0.376406i
$576$		0			0
$577$	−26.2111			−1.09118			−0.545591	−	0.838051i	$-0.683695\pi$
$577$	−26.2111			−1.09118			−0.545591	+	0.838051i	$0.683695\pi$
$578$		0			0
$579$	−3.89445	+	6.74538i	−0.161848	+	0.280329i
$580$		0			0
$581$	−15.3944	+	26.6640i	−0.638669	+	1.10621i
$582$		0			0
$583$	3.90833	+	6.76942i	0.161866	+	0.280361i
$584$		0			0
$585$	−3.60555			−0.149071
$586$		0			0
$587$	21.2111	+	36.7387i	0.875476	+	1.51637i	0.856255	+	0.516553i	$0.172785\pi$
$587$	21.2111	+	36.7387i	0.875476	+	1.51637i	0.0192210	+	0.999815i	$0.493881\pi$
$588$		0			0
$589$	17.2111	−	29.8105i	0.709171	−	1.22832i
$590$		0			0
$591$	−5.00000	+	8.66025i	−0.205673	+	0.356235i
$592$		0			0
$593$	16.0278			0.658181			0.329091	−	0.944298i	$-0.393258\pi$
$593$	16.0278			0.658181			0.329091	+	0.944298i	$0.393258\pi$
$594$		0			0
$595$	2.09167	+	3.62288i	0.0857502	+	0.148524i
$596$		0			0
$597$	19.8167			0.811042
$598$		0			0
$599$	26.4222			1.07958			0.539791	−	0.841799i	$-0.318503\pi$
$599$	26.4222			1.07958			0.539791	+	0.841799i	$0.318503\pi$
$600$		0			0
$601$	19.7111	+	34.1406i	0.804033	+	1.39263i	0.916942	+	0.399020i	$0.130650\pi$
$601$	19.7111	+	34.1406i	0.804033	+	1.39263i	−0.112910	+	0.993605i	$0.536017\pi$
$602$		0			0
$603$	10.6056			0.431891
$604$		0			0
$605$	−2.10555	+	3.64692i	−0.0856028	+	0.148268i
$606$		0			0
$607$	15.0278	−	26.0288i	0.609958	−	1.05648i	−0.381289	−	0.924456i	$-0.624520\pi$
$607$	15.0278	−	26.0288i	0.609958	−	1.05648i	0.991247	−	0.132022i	$-0.0421470\pi$
$608$		0			0
$609$	3.90833	+	6.76942i	0.158373	+	0.274311i
$610$		0			0
$611$	−2.51388	−	4.35416i	−0.101701	−	0.176151i
$612$		0			0
$613$	−6.80278	−	11.7828i	−0.274762	−	0.475901i	0.695313	−	0.718707i	$-0.255266\pi$
$613$	−6.80278	−	11.7828i	−0.274762	−	0.475901i	−0.970075	+	0.242806i	$0.921932\pi$
$614$		0			0
$615$	5.80278	−	10.0507i	0.233990	−	0.405283i
$616$		0			0
$617$	−6.19722	+	10.7339i	−0.249491	+	0.432131i	−0.963385	−	0.268123i	$-0.913597\pi$
$617$	−6.19722	+	10.7339i	−0.249491	+	0.432131i	0.713894	+	0.700254i	$0.246930\pi$
$618$		0			0
$619$	−19.6333			−0.789129			−0.394565	−	0.918868i	$-0.629105\pi$
$619$	−19.6333			−0.789129			−0.394565	+	0.918868i	$0.629105\pi$
$620$		0			0
$621$	−1.30278	−	2.25647i	−0.0522786	−	0.0905492i
$622$		0			0
$623$	−42.7889			−1.71430
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$	−8.60555	−	14.9053i	−0.343673	−	0.595258i
$628$		0			0
$629$	−3.84441			−0.153287
$630$		0			0
$631$	−13.3944	+	23.1999i	−0.533225	+	0.923572i	0.466022	+	0.884773i	$0.345687\pi$
$631$	−13.3944	+	23.1999i	−0.533225	+	0.923572i	−0.999247	+	0.0387992i	$0.987647\pi$
$632$		0			0
$633$	4.00000	−	6.92820i	0.158986	−	0.275371i
$634$		0			0
$635$	−2.00000	−	3.46410i	−0.0793676	−	0.137469i
$636$		0			0
$637$	0.380571	−	0.659168i	0.0150788	−	0.0261172i
$638$		0			0
$639$	−4.69722	−	8.13583i	−0.185819	−	0.321849i
$640$		0			0
$641$	13.1972	−	22.8583i	0.521259	−	0.902847i	−0.478435	−	0.878123i	$-0.658796\pi$
$641$	13.1972	−	22.8583i	0.521259	−	0.902847i	0.999694	−	0.0247243i	$-0.00787079\pi$
$642$		0			0
$643$	21.8167	−	37.7876i	0.860365	−	1.49020i	−0.0112123	−	0.999937i	$-0.503569\pi$
$643$	21.8167	−	37.7876i	0.860365	−	1.49020i	0.871577	−	0.490258i	$-0.163098\pi$
$644$		0			0
$645$	2.60555			0.102593
$646$		0			0
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$		0			0
$649$	24.0000			0.942082
$650$		0			0
$651$	13.5778			0.532156
$652$		0			0
$653$	10.8167	+	18.7350i	0.423288	+	0.733157i	0.996259	−	0.0864190i	$-0.0275424\pi$
$653$	10.8167	+	18.7350i	0.423288	+	0.733157i	−0.572971	+	0.819576i	$0.694209\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.50000	+	6.06218i	−0.136548	+	0.236508i
$658$		0			0
$659$	20.0000	−	34.6410i	0.779089	−	1.34942i	−0.153378	−	0.988168i	$-0.549015\pi$
$659$	20.0000	−	34.6410i	0.779089	−	1.34942i	0.932467	−	0.361255i	$-0.117652\pi$
$660$		0			0
$661$	10.4083	+	18.0278i	0.404837	+	0.701198i	0.994302	−	0.106595i	$-0.0339949\pi$
$661$	10.4083	+	18.0278i	0.404837	+	0.701198i	−0.589465	+	0.807794i	$0.700662\pi$
$662$		0			0
$663$	2.89445	+	5.01333i	0.112411	+	0.194702i
$664$		0			0
$665$	8.60555	+	14.9053i	0.333709	+	0.578001i
$666$		0			0
$667$	3.90833	−	6.76942i	0.151331	−	0.262113i
$668$		0			0
$669$	4.00000	−	6.92820i	0.154649	−	0.267860i
$670$		0			0
$671$	19.8167			0.765013
$672$		0			0
$673$	−7.50000	−	12.9904i	−0.289104	−	0.500742i	0.684492	−	0.729020i	$-0.260024\pi$
$673$	−7.50000	−	12.9904i	−0.289104	−	0.500742i	−0.973596	+	0.228278i	$0.926691\pi$
$674$		0			0
$675$	4.00000			0.153960
$676$		0			0
$677$	28.0555			1.07826			0.539130	−	0.842222i	$-0.318753\pi$
$677$	28.0555			1.07826			0.539130	+	0.842222i	$0.318753\pi$
$678$		0			0
$679$	−14.6056	−	25.2976i	−0.560510	−	0.970831i
$680$		0			0
$681$	−26.6056			−1.01953
$682$		0			0
$683$	9.21110	−	15.9541i	0.352453	−	0.610467i	−0.634226	−	0.773148i	$-0.718681\pi$
$683$	9.21110	−	15.9541i	0.352453	−	0.610467i	0.986679	+	0.162681i	$0.0520143\pi$
$684$		0			0
$685$	−8.40833	+	14.5636i	−0.321266	+	0.556448i
$686$		0			0
$687$	7.60555	+	13.1732i	0.290170	+	0.502589i
$688$		0			0
$689$	−5.40833	−	9.36750i	−0.206041	−	0.356873i
$690$		0			0
$691$	−3.30278	−	5.72058i	−0.125644	−	0.217621i	0.796341	−	0.604848i	$-0.206766\pi$
$691$	−3.30278	−	5.72058i	−0.125644	−	0.217621i	−0.921984	+	0.387227i	$0.873433\pi$
$692$		0			0
$693$	3.39445	−	5.87936i	0.128944	−	0.223338i
$694$		0			0
$695$	1.39445	−	2.41526i	0.0528945	−	0.0916159i
$696$		0			0
$697$	−18.6333			−0.705787
$698$		0			0
$699$	−7.00000	−	12.1244i	−0.264764	−	0.458585i
$700$		0			0
$701$	−6.36669			−0.240467			−0.120233	−	0.992746i	$-0.538364\pi$
$701$	−6.36669			−0.240467			−0.120233	+	0.992746i	$0.538364\pi$
$702$		0			0
$703$	−15.8167			−0.596536
$704$		0			0
$705$	−0.697224	−	1.20763i	−0.0262590	−	0.0454819i
$706$		0			0
$707$	10.9722			0.412654
$708$		0			0
$709$	−16.1972	+	28.0544i	−0.608300	+	1.05361i	0.383221	+	0.923657i	$0.374815\pi$
$709$	−16.1972	+	28.0544i	−0.608300	+	1.05361i	−0.991521	+	0.129949i	$0.958519\pi$
$710$		0			0
$711$	6.00000	−	10.3923i	0.225018	−	0.389742i
$712$		0			0
$713$	−6.78890	−	11.7587i	−0.254246	−	0.440367i
$714$		0			0
$715$	−4.69722	+	8.13583i	−0.175666	+	0.304263i
$716$		0			0
$717$	−8.51388	−	14.7465i	−0.317957	−	0.550717i
$718$		0			0
$719$	−7.39445	+	12.8076i	−0.275766	+	0.477641i	−0.970328	−	0.241792i	$-0.922265\pi$
$719$	−7.39445	+	12.8076i	−0.275766	+	0.477641i	0.694562	+	0.719433i	$0.255598\pi$
$720$		0			0
$721$	−20.6056	+	35.6899i	−0.767391	+	1.32916i
$722$		0			0
$723$	−14.6333			−0.544219
$724$		0			0
$725$	6.00000	+	10.3923i	0.222834	+	0.385961i
$726$		0			0
$727$	15.8167			0.586607			0.293304	−	0.956019i	$-0.405245\pi$
$727$	15.8167			0.586607			0.293304	+	0.956019i	$0.405245\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.09167	−	3.62288i	−0.0773633	−	0.133997i
$732$		0			0
$733$	33.2389			1.22771			0.613853	−	0.789421i	$-0.289619\pi$
$733$	33.2389			1.22771			0.613853	+	0.789421i	$0.289619\pi$
$734$		0			0
$735$	0.105551	−	0.182820i	0.00389332	−	0.00674342i
$736$		0			0
$737$	13.8167	−	23.9311i	0.508943	−	0.881515i
$738$		0			0
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		0			0
$741$	11.9083	+	20.6258i	0.437463	+	0.757709i
$742$		0			0
$743$	5.39445	+	9.34346i	0.197903	+	0.342778i	0.947848	−	0.318722i	$-0.103254\pi$
$743$	5.39445	+	9.34346i	0.197903	+	0.342778i	−0.749945	+	0.661500i	$0.769920\pi$
$744$		0			0
$745$	−5.10555	+	8.84307i	−0.187053	+	0.323985i
$746$		0			0
$747$	−5.90833	+	10.2335i	−0.216174	+	0.374425i
$748$		0			0
$749$	−17.2111			−0.628880
$750$		0			0
$751$	−4.51388	−	7.81827i	−0.164714	−	0.285293i	0.771840	−	0.635817i	$-0.219337\pi$
$751$	−4.51388	−	7.81827i	−0.164714	−	0.285293i	−0.936554	+	0.350524i	$0.886003\pi$
$752$		0			0
$753$	29.2111			1.06451
$754$		0			0
$755$	−6.60555			−0.240401
$756$		0			0
$757$	14.2111	+	24.6144i	0.516511	+	0.894624i	0.999816	+	0.0191717i	$0.00610292\pi$
$757$	14.2111	+	24.6144i	0.516511	+	0.894624i	−0.483305	+	0.875452i	$0.660564\pi$
$758$		0			0
$759$	−6.78890			−0.246421
$760$		0			0
$761$	5.78890	−	10.0267i	0.209847	−	0.363466i	−0.741819	−	0.670600i	$-0.766037\pi$
$761$	5.78890	−	10.0267i	0.209847	−	0.363466i	0.951666	+	0.307134i	$0.0993700\pi$
$762$		0			0
$763$	2.60555	−	4.51295i	0.0943273	−	0.163380i
$764$		0			0
$765$	0.802776	+	1.39045i	0.0290244	+	0.0502718i
$766$		0			0
$767$	−33.2111			−1.19918
$768$		0			0
$769$	−3.18335	−	5.51372i	−0.114794	−	0.198830i	0.802903	−	0.596110i	$-0.203288\pi$
$769$	−3.18335	−	5.51372i	−0.114794	−	0.198830i	−0.917698	+	0.397280i	$0.869954\pi$
$770$		0			0
$771$	−11.8028	+	20.4430i	−0.425067	+	0.736237i
$772$		0			0
$773$	10.8167	−	18.7350i	0.389048	−	0.673851i	−0.603274	−	0.797534i	$-0.706137\pi$
$773$	10.8167	−	18.7350i	0.389048	−	0.673851i	0.992322	+	0.123683i	$0.0394707\pi$
$774$		0			0
$775$	20.8444			0.748753
$776$		0			0
$777$	−3.11943	−	5.40301i	−0.111909	−	0.193832i
$778$		0			0
$779$	−76.6611			−2.74667
$780$		0			0
$781$	−24.4777			−0.875882
$782$		0			0
$783$	1.50000	+	2.59808i	0.0536056	+	0.0928477i
$784$		0			0
$785$	−8.39445			−0.299611
$786$		0			0
$787$	10.6056	−	18.3694i	0.378047	−	0.654797i	−0.612731	−	0.790292i	$-0.709929\pi$
$787$	10.6056	−	18.3694i	0.378047	−	0.654797i	0.990778	+	0.135495i	$0.0432624\pi$
$788$		0			0
$789$	−9.30278	+	16.1129i	−0.331188	+	0.573634i
$790$		0			0
$791$	15.1194	+	26.1876i	0.537585	+	0.931125i
$792$		0			0
$793$	−27.4222			−0.973791
$794$		0			0
$795$	−1.50000	−	2.59808i	−0.0531995	−	0.0921443i
$796$		0			0
$797$	−1.42221	+	2.46333i	−0.0503771	+	0.0872557i	−0.890114	−	0.455737i	$-0.849376\pi$
$797$	−1.42221	+	2.46333i	−0.0503771	+	0.0872557i	0.839737	+	0.542993i	$0.182709\pi$
$798$		0			0
$799$	−1.11943	+	1.93891i	−0.0396026	+	0.0685937i
$800$		0			0
$801$	−16.4222			−0.580250
$802$		0			0
$803$	9.11943	+	15.7953i	0.321818	+	0.557405i
$804$		0			0
$805$	6.78890			0.239277
$806$		0			0
$807$	−25.6333			−0.902335
$808$		0			0
$809$	15.8028	+	27.3712i	0.555596	+	0.962321i	0.997857	+	0.0654341i	$0.0208432\pi$
$809$	15.8028	+	27.3712i	0.555596	+	0.962321i	−0.442261	+	0.896886i	$0.645823\pi$
$810$		0			0
$811$	−23.6333			−0.829878			−0.414939	−	0.909849i	$-0.636197\pi$
$811$	−23.6333			−0.829878			−0.414939	+	0.909849i	$0.636197\pi$
$812$		0			0
$813$	0.605551	−	1.04885i	0.0212376	−	0.0367846i
$814$		0			0
$815$	2.60555	−	4.51295i	0.0912685	−	0.158082i
$816$		0			0
$817$	−8.60555	−	14.9053i	−0.301070	−	0.521469i
$818$		0			0
$819$	−4.69722	+	8.13583i	−0.164134	+	0.284289i
$820$		0			0
$821$	−3.60555	−	6.24500i	−0.125835	−	0.217952i	0.796224	−	0.605002i	$-0.206828\pi$
$821$	−3.60555	−	6.24500i	−0.125835	−	0.217952i	−0.922059	+	0.387050i	$0.873494\pi$
$822$		0			0
$823$	9.81665	−	17.0029i	0.342187	−	0.592685i	−0.642652	−	0.766159i	$-0.722166\pi$
$823$	9.81665	−	17.0029i	0.342187	−	0.592685i	0.984839	+	0.173473i	$0.0554990\pi$
$824$		0			0
$825$	5.21110	−	9.02589i	0.181427	−	0.314241i
$826$		0			0
$827$	1.21110			0.0421142			0.0210571	−	0.999778i	$-0.493297\pi$
$827$	1.21110			0.0421142			0.0210571	+	0.999778i	$0.493297\pi$
$828$		0			0
$829$	−23.4083	−	40.5444i	−0.813005	−	1.40817i	−0.910752	−	0.412954i	$-0.864497\pi$
$829$	−23.4083	−	40.5444i	−0.813005	−	1.40817i	0.0977469	−	0.995211i	$-0.468836\pi$
$830$		0			0
$831$	−29.2389			−1.01428
$832$		0			0
$833$	−0.338936			−0.0117434
$834$		0			0
$835$	−8.60555	−	14.9053i	−0.297807	−	0.515818i
$836$		0			0
$837$	5.21110			0.180122
$838$		0			0
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	0.197224	+	0.341603i	0.00679277	+	0.0117654i
$844$		0			0
$845$	6.50000	−	11.2583i	0.223607	−	0.387298i
$846$		0			0
$847$	5.48612	+	9.50224i	0.188505	+	0.326501i
$848$		0			0
$849$	−7.30278	+	12.6488i	−0.250631	+	0.434105i
$850$		0			0
$851$	−3.11943	+	5.40301i	−0.106933	+	0.185213i
$852$		0			0
$853$	−36.8167			−1.26058			−0.630289	−	0.776361i	$-0.717064\pi$
$853$	−36.8167			−1.26058			−0.630289	+	0.776361i	$0.717064\pi$
$854$		0			0
$855$	3.30278	+	5.72058i	0.112953	+	0.195640i
$856$		0			0
$857$	4.39445			0.150112			0.0750558	−	0.997179i	$-0.476087\pi$
$857$	4.39445			0.150112			0.0750558	+	0.997179i	$0.476087\pi$
$858$		0			0
$859$	47.8167			1.63148			0.815742	−	0.578417i	$-0.196329\pi$
$859$	47.8167			1.63148			0.815742	+	0.578417i	$0.196329\pi$
$860$		0			0
$861$	−15.1194	−	26.1876i	−0.515269	−	0.892472i
$862$		0			0
$863$	33.0278			1.12428			0.562139	−	0.827043i	$-0.309979\pi$
$863$	33.0278			1.12428			0.562139	+	0.827043i	$0.309979\pi$
$864$		0			0
$865$	−10.8167	+	18.7350i	−0.367777	+	0.637009i
$866$		0			0
$867$	−7.21110	+	12.4900i	−0.244902	+	0.424183i
$868$		0			0
$869$	−15.6333	−	27.0777i	−0.530324	−	0.918547i
$870$		0			0
$871$	−19.1194	+	33.1158i	−0.647837	+	1.12209i
$872$		0			0
$873$	−5.60555	−	9.70910i	−0.189719	−	0.328603i
$874$		0			0
$875$	−11.7250	+	20.3083i	−0.396377	+	0.686545i
$876$		0			0
$877$	−9.40833	+	16.2957i	−0.317697	+	0.550267i	−0.980007	−	0.198963i	$-0.936243\pi$
$877$	−9.40833	+	16.2957i	−0.317697	+	0.550267i	0.662310	+	0.749230i	$0.269576\pi$
$878$		0			0
$879$	−0.211103			−0.00712031
$880$		0			0
$881$	14.4083	+	24.9560i	0.485429	+	0.840787i	0.999860	−	0.0167444i	$-0.00533014\pi$
$881$	14.4083	+	24.9560i	0.485429	+	0.840787i	−0.514431	+	0.857532i	$0.671997\pi$
$882$		0			0
$883$	−9.21110			−0.309978			−0.154989	−	0.987916i	$-0.549534\pi$
$883$	−9.21110			−0.309978			−0.154989	+	0.987916i	$0.549534\pi$
$884$		0			0
$885$	−9.21110			−0.309628
$886$		0			0
$887$	1.81665	+	3.14654i	0.0609973	+	0.105650i	0.894911	−	0.446244i	$-0.147239\pi$
$887$	1.81665	+	3.14654i	0.0609973	+	0.105650i	−0.833914	+	0.551894i	$0.813905\pi$
$888$		0			0
$889$	−10.4222			−0.349550
$890$		0			0
$891$	1.30278	−	2.25647i	0.0436446	−	0.0755947i
$892$		0			0
$893$	−4.60555	+	7.97705i	−0.154119	+	0.266942i
$894$		0			0
$895$	8.51388	+	14.7465i	0.284588	+	0.492920i
$896$		0			0
$897$	9.39445			0.313672
$898$		0			0
$899$	7.81665	+	13.5388i	0.260700	+	0.451546i
$900$		0			0
$901$	−2.40833	+	4.17134i	−0.0802330	+	0.138968i
$902$		0			0
$903$	3.39445	−	5.87936i	0.112960	−	0.195653i
$904$		0			0
$905$	24.8167			0.824933
$906$		0			0
$907$	−5.39445	−	9.34346i	−0.179120	−	0.310244i	0.762460	−	0.647036i	$-0.223992\pi$
$907$	−5.39445	−	9.34346i	−0.179120	−	0.310244i	−0.941579	+	0.336791i	$0.890658\pi$
$908$		0			0
$909$	4.21110			0.139673
$910$		0			0
$911$	19.6333			0.650481			0.325240	−	0.945631i	$-0.394555\pi$
$911$	19.6333			0.650481			0.325240	+	0.945631i	$0.394555\pi$
$912$		0			0
$913$	15.3944	+	26.6640i	0.509482	+	0.882449i
$914$		0			0
$915$	−7.60555			−0.251432
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.81665	+	3.14654i	−0.0599259	+	0.103795i	−0.894432	−	0.447204i	$-0.852420\pi$
$919$	−1.81665	+	3.14654i	−0.0599259	+	0.103795i	0.834506	+	0.550999i	$0.185753\pi$
$920$		0			0
$921$	−2.69722	−	4.67173i	−0.0888766	−	0.153939i
$922$		0			0
$923$	33.8722			1.11492
$924$		0			0
$925$	−4.78890	−	8.29461i	−0.157458	−	0.272725i
$926$		0			0
$927$	−7.90833	+	13.6976i	−0.259744	+	0.449889i
$928$		0			0
$929$	−10.1972	+	17.6621i	−0.334560	+	0.579475i	−0.983400	−	0.181450i	$-0.941921\pi$
$929$	−10.1972	+	17.6621i	−0.334560	+	0.579475i	0.648840	+	0.760925i	$0.275254\pi$
$930$		0			0
$931$	−1.39445			−0.0457012
$932$		0			0
$933$	−13.9083	−	24.0899i	−0.455338	−	0.788669i
$934$		0			0
$935$	4.18335			0.136810
$936$		0			0
$937$	−27.0555			−0.883865			−0.441933	−	0.897048i	$-0.645707\pi$
$937$	−27.0555			−0.883865			−0.441933	+	0.897048i	$0.645707\pi$
$938$		0			0
$939$	1.60555	+	2.78090i	0.0523952	+	0.0907511i
$940$		0			0
$941$	47.2111			1.53904			0.769519	−	0.638624i	$-0.220496\pi$
$941$	47.2111			1.53904			0.769519	+	0.638624i	$0.220496\pi$
$942$		0			0
$943$	−15.1194	+	26.1876i	−0.492356	+	0.852786i
$944$		0			0
$945$	−1.30278	+	2.25647i	−0.0423793	+	0.0734031i
$946$		0			0
$947$	−1.81665	−	3.14654i	−0.0590333	−	0.102249i	0.834998	−	0.550252i	$-0.185468\pi$
$947$	−1.81665	−	3.14654i	−0.0590333	−	0.102249i	−0.894032	+	0.448004i	$0.852135\pi$
$948$		0			0
$949$	−12.6194	−	21.8575i	−0.409644	−	0.709524i
$950$		0			0
$951$	−1.10555	−	1.91487i	−0.0358500	−	0.0620939i
$952$		0			0
$953$	−4.39445	+	7.61141i	−0.142350	+	0.246558i	−0.928381	−	0.371629i	$-0.878799\pi$
$953$	−4.39445	+	7.61141i	−0.142350	+	0.246558i	0.786031	+	0.618187i	$0.212133\pi$
$954$		0			0
$955$	11.8167	−	20.4670i	0.382378	−	0.662298i
$956$		0			0
$957$	7.81665			0.252677
$958$		0			0
$959$	21.9083	+	37.9463i	0.707457	+	1.22535i
$960$		0			0
$961$	−3.84441			−0.124013
$962$		0			0
$963$	−6.60555			−0.212861
$964$		0			0
$965$	−3.89445	−	6.74538i	−0.125367	−	0.217142i
$966$		0			0
$967$	−2.97224			−0.0955809			−0.0477905	−	0.998857i	$-0.515218\pi$
$967$	−2.97224			−0.0955809			−0.0477905	+	0.998857i	$0.515218\pi$
$968$		0			0
$969$	5.30278	−	9.18468i	0.170350	−	0.295054i
$970$		0			0
$971$	−21.6333	+	37.4700i	−0.694246	+	1.20247i	0.276188	+	0.961104i	$0.410929\pi$
$971$	−21.6333	+	37.4700i	−0.694246	+	1.20247i	−0.970434	+	0.241366i	$0.922405\pi$
$972$		0			0
$973$	−3.63331	−	6.29307i	−0.116478	−	0.201747i
$974$		0			0
$975$	−7.21110	+	12.4900i	−0.230940	+	0.400000i
$976$		0			0
$977$	−25.2250	−	43.6909i	−0.807019	−	1.39780i	−0.914920	−	0.403636i	$-0.867746\pi$
$977$	−25.2250	−	43.6909i	−0.807019	−	1.39780i	0.107901	−	0.994162i	$-0.465587\pi$
$978$		0			0
$979$	−21.3944	+	37.0563i	−0.683770	+	1.18432i
$980$		0			0
$981$	1.00000	−	1.73205i	0.0319275	−	0.0553001i
$982$		0			0
$983$	37.2111			1.18685			0.593425	−	0.804889i	$-0.297775\pi$
$983$	37.2111			1.18685			0.593425	+	0.804889i	$0.297775\pi$
$984$		0			0
$985$	−5.00000	−	8.66025i	−0.159313	−	0.275939i
$986$		0			0
$987$	−3.63331			−0.115649
$988$		0			0
$989$	−6.78890			−0.215874
$990$		0			0
$991$	−10.6972	−	18.5281i	−0.339809	−	0.588566i	0.644588	−	0.764530i	$-0.277029\pi$
$991$	−10.6972	−	18.5281i	−0.339809	−	0.588566i	−0.984397	+	0.175964i	$0.943696\pi$
$992$		0			0
$993$	−15.6333			−0.496108
$994$		0			0
$995$	−9.90833	+	17.1617i	−0.314115	+	0.544063i
$996$		0			0
$997$	−29.2250	+	50.6192i	−0.925564	+	1.60312i	−0.134914	+	0.990857i	$0.543076\pi$
$997$	−29.2250	+	50.6192i	−0.925564	+	1.60312i	−0.790651	+	0.612267i	$0.790258\pi$
$998$		0			0
$999$	−1.19722	−	2.07365i	−0.0378785	−	0.0656075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.q.i.289.1		4
3.2	odd	2		1872.2.t.q.289.1		4
4.3	odd	2		312.2.q.d.289.2	yes	4
12.11	even	2		936.2.t.e.289.2		4
13.3	even	3		8112.2.a.bl.1.2		2
13.9	even	3	inner	624.2.q.i.529.1		4
13.10	even	6		8112.2.a.bn.1.1		2
39.35	odd	6		1872.2.t.q.1153.1		4
52.3	odd	6		4056.2.a.v.1.1		2
52.11	even	12		4056.2.c.l.337.2		4
52.15	even	12		4056.2.c.l.337.3		4
52.23	odd	6		4056.2.a.w.1.2		2
52.35	odd	6		312.2.q.d.217.2	✓	4
156.35	even	6		936.2.t.e.217.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.q.d.217.2	✓	4	52.35	odd	6
312.2.q.d.289.2	yes	4	4.3	odd	2
624.2.q.i.289.1		4	1.1	even	1	trivial
624.2.q.i.529.1		4	13.9	even	3	inner
936.2.t.e.217.2		4	156.35	even	6
936.2.t.e.289.2		4	12.11	even	2
1872.2.t.q.289.1		4	3.2	odd	2
1872.2.t.q.1153.1		4	39.35	odd	6
4056.2.a.v.1.1		2	52.3	odd	6
4056.2.a.w.1.2		2	52.23	odd	6
4056.2.c.l.337.2		4	52.11	even	12
4056.2.c.l.337.3		4	52.15	even	12
8112.2.a.bl.1.2		2	13.3	even	3
8112.2.a.bn.1.1		2	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} -1.00000 q^{5} +(-1.30278 + 2.25647i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.30278 + 2.25647i) q^{11} +(-1.80278 - 3.12250i) q^{13} +(-0.500000 - 0.866025i) q^{15} +(-0.802776 + 1.39045i) q^{17} +(-3.30278 + 5.72058i) q^{19} -2.60555 q^{21} +(1.30278 + 2.25647i) q^{23} -4.00000 q^{25} -1.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} -5.21110 q^{31} +(-1.30278 + 2.25647i) q^{33} +(1.30278 - 2.25647i) q^{35} +(1.19722 + 2.07365i) q^{37} +(1.80278 - 3.12250i) q^{39} +(5.80278 + 10.0507i) q^{41} +(-1.30278 + 2.25647i) q^{43} +(0.500000 - 0.866025i) q^{45} +1.39445 q^{47} +(0.105551 + 0.182820i) q^{49} -1.60555 q^{51} +3.00000 q^{53} +(-1.30278 - 2.25647i) q^{55} -6.60555 q^{57} +(4.60555 - 7.97705i) q^{59} +(3.80278 - 6.58660i) q^{61} +(-1.30278 - 2.25647i) q^{63} +(1.80278 + 3.12250i) q^{65} +(-5.30278 - 9.18468i) q^{67} +(-1.30278 + 2.25647i) q^{69} +(-4.69722 + 8.13583i) q^{71} +7.00000 q^{73} +(-2.00000 - 3.46410i) q^{75} -6.78890 q^{77} -12.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +11.8167 q^{83} +(0.802776 - 1.39045i) q^{85} +(1.50000 - 2.59808i) q^{87} +(8.21110 + 14.2220i) q^{89} +9.39445 q^{91} +(-2.60555 - 4.51295i) q^{93} +(3.30278 - 5.72058i) q^{95} +(-5.60555 + 9.70910i) q^{97} -2.60555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{5} + 2 q^{7} - 2 q^{9} - 2 q^{11} - 2 q^{15} + 4 q^{17} - 6 q^{19} + 4 q^{21} - 2 q^{23} - 16 q^{25} - 4 q^{27} - 6 q^{29} + 8 q^{31} + 2 q^{33} - 2 q^{35} + 12 q^{37} + 16 q^{41} + 2 q^{43}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^5 + 2 * q^7 - 2 * q^9 - 2 * q^11 - 2 * q^15 + 4 * q^17 - 6 * q^19 + 4 * q^21 - 2 * q^23 - 16 * q^25 - 4 * q^27 - 6 * q^29 + 8 * q^31 + 2 * q^33 - 2 * q^35 + 12 * q^37 + 16 * q^41 + 2 * q^43 + 2 * q^45 + 20 * q^47 - 14 * q^49 + 8 * q^51 + 12 * q^53 + 2 * q^55 - 12 * q^57 + 4 * q^59 + 8 * q^61 + 2 * q^63 - 14 * q^67 + 2 * q^69 - 26 * q^71 + 28 * q^73 - 8 * q^75 - 56 * q^77 - 48 * q^79 - 2 * q^81 + 4 * q^83 - 4 * q^85 + 6 * q^87 + 4 * q^89 + 52 * q^91 + 4 * q^93 + 6 * q^95 - 8 * q^97 + 4 * q^99

Introduction

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