LMFDB - Embedded newform 1344.2.u.a.1231.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(559,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 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("1344.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.u (of order $4$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1231.1
Character	$\chi$	$=$	1344.1231
Dual form			1344.2.u.a.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(3.13913 - 3.13913i) q^{5} +(-1.14645 - 2.38446i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(3.13913 - 3.13913i) q^{5} +(-1.14645 - 2.38446i) q^{7} -1.00000i q^{9} +(-0.422784 + 0.422784i) q^{11} +(3.06112 + 3.06112i) q^{13} +4.43939i q^{15} +2.56875i q^{17} +(0.955253 - 0.955253i) q^{19} +(2.49673 + 0.875401i) q^{21} +5.93702 q^{23} -14.7082i q^{25} +(0.707107 + 0.707107i) q^{27} +(1.07143 - 1.07143i) q^{29} +5.77245 q^{31} -0.597907i q^{33} +(-11.0840 - 3.88625i) q^{35} +(-3.30963 - 3.30963i) q^{37} -4.32908 q^{39} -6.17767 q^{41} +(3.35840 - 3.35840i) q^{43} +(-3.13913 - 3.13913i) q^{45} -4.38522 q^{47} +(-4.37128 + 5.46735i) q^{49} +(-1.81638 - 1.81638i) q^{51} +(-7.85667 - 7.85667i) q^{53} +2.65434i q^{55} +1.35093i q^{57} +(-5.63360 - 5.63360i) q^{59} +(0.351526 + 0.351526i) q^{61} +(-2.38446 + 1.14645i) q^{63} +19.2185 q^{65} +(-7.37756 - 7.37756i) q^{67} +(-4.19810 + 4.19810i) q^{69} +4.30558 q^{71} +6.71670 q^{73} +(10.4003 + 10.4003i) q^{75} +(1.49281 + 0.523408i) q^{77} -8.39558i q^{79} -1.00000 q^{81} +(6.54381 - 6.54381i) q^{83} +(8.06362 + 8.06362i) q^{85} +1.51523i q^{87} +14.8890 q^{89} +(3.78968 - 10.8086i) q^{91} +(-4.08174 + 4.08174i) q^{93} -5.99732i q^{95} +3.86266i q^{97} +(0.422784 + 0.422784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	3.13913	−	3.13913i	1.40386	−	1.40386i	0.616521	−	0.787339i	$-0.288542\pi$
$5$	3.13913	−	3.13913i	1.40386	−	1.40386i	0.787339	−	0.616521i	$-0.211458\pi$
$6$		0			0
$7$	−1.14645	−	2.38446i	−0.433319	−	0.901241i
$7$	−1.14645	−	2.38446i	−0.433319	−	0.901241i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−0.422784	+	0.422784i	−0.127474	+	0.127474i	−0.767965	−	0.640491i	$-0.778731\pi$
$11$	−0.422784	+	0.422784i	−0.127474	+	0.127474i	0.640491	+	0.767965i	$0.278731\pi$
$12$		0			0
$13$	3.06112	+	3.06112i	0.849002	+	0.849002i	0.990009	−	0.141007i	$-0.0450339\pi$
$13$	3.06112	+	3.06112i	0.849002	+	0.849002i	−0.141007	+	0.990009i	$0.545034\pi$
$14$		0			0
$15$			4.43939i			1.14625i
$16$		0			0
$17$			2.56875i			0.623013i	0.950244	+	0.311506i	$0.100834\pi$
$17$			2.56875i			0.623013i	−0.950244	+	0.311506i	$0.899166\pi$
$18$		0			0
$19$	0.955253	−	0.955253i	0.219150	−	0.219150i	−0.588990	−	0.808140i	$-0.700474\pi$
$19$	0.955253	−	0.955253i	0.219150	−	0.219150i	0.808140	+	0.588990i	$0.200474\pi$
$20$		0			0
$21$	2.49673	+	0.875401i	0.544832	+	0.191028i
$22$		0			0
$23$	5.93702			1.23795			0.618977	−	0.785409i	$-0.287548\pi$
$23$	5.93702			1.23795			0.618977	+	0.785409i	$0.287548\pi$
$24$		0			0
$25$		−	14.7082i		−	2.94164i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	1.07143	−	1.07143i	0.198959	−	0.198959i	−0.600595	−	0.799554i	$-0.705069\pi$
$29$	1.07143	−	1.07143i	0.198959	−	0.198959i	0.799554	+	0.600595i	$0.205069\pi$
$30$		0			0
$31$	5.77245			1.03676			0.518381	−	0.855150i	$-0.326535\pi$
$31$	5.77245			1.03676			0.518381	+	0.855150i	$0.326535\pi$
$32$		0			0
$33$		−	0.597907i		−	0.104082i
$34$		0			0
$35$	−11.0840	−	3.88625i	−1.87353	−	0.656896i
$36$		0			0
$37$	−3.30963	−	3.30963i	−0.544099	−	0.544099i	0.380629	−	0.924728i	$-0.375708\pi$
$37$	−3.30963	−	3.30963i	−0.544099	−	0.544099i	−0.924728	+	0.380629i	$0.875708\pi$
$38$		0			0
$39$	−4.32908			−0.693207
$40$		0			0
$41$	−6.17767			−0.964790			−0.482395	−	0.875954i	$-0.660233\pi$
$41$	−6.17767			−0.964790			−0.482395	+	0.875954i	$0.660233\pi$
$42$		0			0
$43$	3.35840	−	3.35840i	0.512151	−	0.512151i	−0.403034	−	0.915185i	$-0.632044\pi$
$43$	3.35840	−	3.35840i	0.512151	−	0.512151i	0.915185	+	0.403034i	$0.132044\pi$
$44$		0			0
$45$	−3.13913	−	3.13913i	−0.467953	−	0.467953i
$46$		0			0
$47$	−4.38522			−0.639650			−0.319825	−	0.947477i	$-0.603624\pi$
$47$	−4.38522			−0.639650			−0.319825	+	0.947477i	$0.603624\pi$
$48$		0			0
$49$	−4.37128	+	5.46735i	−0.624469	+	0.781050i
$50$		0			0
$51$	−1.81638	−	1.81638i	−0.254344	−	0.254344i
$52$		0			0
$53$	−7.85667	−	7.85667i	−1.07920	−	1.07920i	−0.996582	−	0.0826143i	$-0.973673\pi$
$53$	−7.85667	−	7.85667i	−1.07920	−	1.07920i	−0.0826143	−	0.996582i	$-0.526327\pi$
$54$		0			0
$55$			2.65434i			0.357911i
$56$		0			0
$57$			1.35093i			0.178935i
$58$		0			0
$59$	−5.63360	−	5.63360i	−0.733432	−	0.733432i	0.237866	−	0.971298i	$-0.423552\pi$
$59$	−5.63360	−	5.63360i	−0.733432	−	0.733432i	−0.971298	+	0.237866i	$0.923552\pi$
$60$		0			0
$61$	0.351526	+	0.351526i	0.0450083	+	0.0450083i	0.729253	−	0.684244i	$-0.239868\pi$
$61$	0.351526	+	0.351526i	0.0450083	+	0.0450083i	−0.684244	+	0.729253i	$0.739868\pi$
$62$		0			0
$63$	−2.38446	+	1.14645i	−0.300414	+	0.144440i
$64$		0			0
$65$	19.2185			2.38376
$66$		0			0
$67$	−7.37756	−	7.37756i	−0.901313	−	0.901313i	0.0942371	−	0.995550i	$-0.469959\pi$
$67$	−7.37756	−	7.37756i	−0.901313	−	0.901313i	−0.995550	+	0.0942371i	$0.969959\pi$
$68$		0			0
$69$	−4.19810	+	4.19810i	−0.505392	+	0.505392i
$70$		0			0
$71$	4.30558			0.510978			0.255489	−	0.966812i	$-0.417763\pi$
$71$	4.30558			0.510978			0.255489	+	0.966812i	$0.417763\pi$
$72$		0			0
$73$	6.71670			0.786131			0.393065	−	0.919511i	$-0.371415\pi$
$73$	6.71670			0.786131			0.393065	+	0.919511i	$0.371415\pi$
$74$		0			0
$75$	10.4003	+	10.4003i	1.20092	+	1.20092i
$76$		0			0
$77$	1.49281	+	0.523408i	0.170122	+	0.0596479i
$78$		0			0
$79$		−	8.39558i		−	0.944577i	−0.881444	−	0.472288i	$-0.843428\pi$
$79$		−	8.39558i		−	0.944577i	0.881444	−	0.472288i	$-0.156572\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	6.54381	−	6.54381i	0.718277	−	0.718277i	−0.249975	−	0.968252i	$-0.580423\pi$
$83$	6.54381	−	6.54381i	0.718277	−	0.718277i	0.968252	+	0.249975i	$0.0804225\pi$
$84$		0			0
$85$	8.06362	+	8.06362i	0.874622	+	0.874622i
$86$		0			0
$87$			1.51523i			0.162449i
$88$		0			0
$89$	14.8890			1.57823			0.789115	−	0.614246i	$-0.210540\pi$
$89$	14.8890			1.57823			0.789115	+	0.614246i	$0.210540\pi$
$90$		0			0
$91$	3.78968	−	10.8086i	0.397266	−	1.13304i
$92$		0			0
$93$	−4.08174	+	4.08174i	−0.423256	+	0.423256i
$94$		0			0
$95$		−	5.99732i		−	0.615312i
$96$		0			0
$97$			3.86266i			0.392193i	0.980585	+	0.196097i	$0.0628266\pi$
$97$			3.86266i			0.392193i	−0.980585	+	0.196097i	$0.937173\pi$
$98$		0			0
$99$	0.422784	+	0.422784i	0.0424914	+	0.0424914i
$100$		0			0
$101$	1.63152	−	1.63152i	0.162343	−	0.162343i	−0.621261	−	0.783604i	$-0.713379\pi$
$101$	1.63152	−	1.63152i	0.162343	−	0.162343i	0.783604	+	0.621261i	$0.213379\pi$
$102$		0			0
$103$			9.59390i			0.945315i	0.881246	+	0.472657i	$0.156705\pi$
$103$			9.59390i			0.945315i	−0.881246	+	0.472657i	$0.843295\pi$
$104$		0			0
$105$	10.5855	−	5.08956i	1.03304	−	0.496690i
$106$		0			0
$107$	−10.1696	+	10.1696i	−0.983130	+	0.983130i	−0.999860	−	0.0167296i	$-0.994675\pi$
$107$	−10.1696	+	10.1696i	−0.983130	+	0.983130i	0.0167296	+	0.999860i	$0.494675\pi$
$108$		0			0
$109$	−10.3263	+	10.3263i	−0.989076	+	0.989076i	−0.999941	−	0.0108654i	$-0.996541\pi$
$109$	−10.3263	+	10.3263i	−0.989076	+	0.989076i	0.0108654	+	0.999941i	$0.496541\pi$
$110$		0			0
$111$	4.68052			0.444255
$112$		0			0
$113$	1.12613			0.105937			0.0529686	−	0.998596i	$-0.483132\pi$
$113$	1.12613			0.105937			0.0529686	+	0.998596i	$0.483132\pi$
$114$		0			0
$115$	18.6370	−	18.6370i	1.73791	−	1.73791i
$116$		0			0
$117$	3.06112	−	3.06112i	0.283001	−	0.283001i
$118$		0			0
$119$	6.12507	−	2.94495i	0.561484	−	0.269963i
$120$		0			0
$121$			10.6425i			0.967501i
$122$		0			0
$123$	4.36827	−	4.36827i	0.393874	−	0.393874i
$124$		0			0
$125$	−30.4753	−	30.4753i	−2.72579	−	2.72579i
$126$		0			0
$127$			15.6332i			1.38722i	0.720349	+	0.693612i	$0.243982\pi$
$127$			15.6332i			1.38722i	−0.720349	+	0.693612i	$0.756018\pi$
$128$		0			0
$129$			4.74949i			0.418169i
$130$		0			0
$131$	4.20910	−	4.20910i	0.367751	−	0.367751i	−0.498905	−	0.866656i	$-0.666264\pi$
$131$	4.20910	−	4.20910i	0.367751	−	0.367751i	0.866656	+	0.498905i	$0.166264\pi$
$132$		0			0
$133$	−3.37291	−	1.18261i	−0.292469	−	0.102545i
$134$		0			0
$135$	4.43939			0.382082
$136$		0			0
$137$			0.494682i			0.0422635i	0.999777	+	0.0211318i	$0.00672695\pi$
$137$			0.494682i			0.0422635i	−0.999777	+	0.0211318i	$0.993273\pi$
$138$		0			0
$139$	2.46499	+	2.46499i	0.209078	+	0.209078i	0.803875	−	0.594798i	$-0.202768\pi$
$139$	2.46499	+	2.46499i	0.209078	+	0.209078i	−0.594798	+	0.803875i	$0.702768\pi$
$140$		0			0
$141$	3.10082	−	3.10082i	0.261136	−	0.261136i
$142$		0			0
$143$	−2.58838			−0.216452
$144$		0			0
$145$		−	6.72669i		−	0.558621i
$146$		0			0
$147$	−0.775034	−	6.95696i	−0.0639237	−	0.573801i
$148$		0			0
$149$	−11.5750	−	11.5750i	−0.948265	−	0.948265i	0.0504610	−	0.998726i	$-0.483931\pi$
$149$	−11.5750	−	11.5750i	−0.948265	−	0.948265i	−0.998726	+	0.0504610i	$0.983931\pi$
$150$		0			0
$151$	2.32516			0.189219			0.0946095	−	0.995514i	$-0.469840\pi$
$151$	2.32516			0.189219			0.0946095	+	0.995514i	$0.469840\pi$
$152$		0			0
$153$	2.56875			0.207671
$154$		0			0
$155$	18.1204	−	18.1204i	1.45547	−	1.45547i
$156$		0			0
$157$	15.6617	+	15.6617i	1.24994	+	1.24994i	0.955746	+	0.294192i	$0.0950505\pi$
$157$	15.6617	+	15.6617i	1.24994	+	1.24994i	0.294192	+	0.955746i	$0.404949\pi$
$158$		0			0
$159$	11.1110			0.881160
$160$		0			0
$161$	−6.80652	−	14.1566i	−0.536429	−	1.11569i
$162$		0			0
$163$	15.0401	+	15.0401i	1.17804	+	1.17804i	0.980244	+	0.197791i	$0.0633767\pi$
$163$	15.0401	+	15.0401i	1.17804	+	1.17804i	0.197791	+	0.980244i	$0.436623\pi$
$164$		0			0
$165$	−1.87690	−	1.87690i	−0.146117	−	0.146117i
$166$		0			0
$167$			9.75468i			0.754840i	0.926042	+	0.377420i	$0.123189\pi$
$167$			9.75468i			0.754840i	−0.926042	+	0.377420i	$0.876811\pi$
$168$		0			0
$169$			5.74092i			0.441609i
$170$		0			0
$171$	−0.955253	−	0.955253i	−0.0730500	−	0.0730500i
$172$		0			0
$173$	3.08743	+	3.08743i	0.234733	+	0.234733i	0.814665	−	0.579932i	$-0.196921\pi$
$173$	3.08743	+	3.08743i	0.234733	+	0.234733i	−0.579932	+	0.814665i	$0.696921\pi$
$174$		0			0
$175$	−35.0711	+	16.8623i	−2.65113	+	1.27467i
$176$		0			0
$177$	7.96711			0.598845
$178$		0			0
$179$	−9.33519	−	9.33519i	−0.697745	−	0.697745i	0.266179	−	0.963924i	$-0.414239\pi$
$179$	−9.33519	−	9.33519i	−0.697745	−	0.697745i	−0.963924	+	0.266179i	$0.914239\pi$
$180$		0			0
$181$	5.23801	−	5.23801i	0.389339	−	0.389339i	−0.485113	−	0.874451i	$-0.661222\pi$
$181$	5.23801	−	5.23801i	0.389339	−	0.389339i	0.874451	+	0.485113i	$0.161222\pi$
$182$		0			0
$183$	−0.497133			−0.0367491
$184$		0			0
$185$	−20.7787			−1.52768
$186$		0			0
$187$	−1.08602	−	1.08602i	−0.0794180	−	0.0794180i
$188$		0			0
$189$	0.875401	−	2.49673i	0.0636760	−	0.181611i
$190$		0			0
$191$			1.31624i			0.0952400i	0.998866	+	0.0476200i	$0.0151636\pi$
$191$			1.31624i			0.0952400i	−0.998866	+	0.0476200i	$0.984836\pi$
$192$		0			0
$193$	12.1525			0.874756			0.437378	−	0.899278i	$-0.355907\pi$
$193$	12.1525			0.874756			0.437378	+	0.899278i	$0.355907\pi$
$194$		0			0
$195$	−13.5895	+	13.5895i	−0.973166	+	0.973166i
$196$		0			0
$197$	6.99289	+	6.99289i	0.498223	+	0.498223i	0.910884	−	0.412662i	$-0.135401\pi$
$197$	6.99289	+	6.99289i	0.498223	+	0.498223i	−0.412662	+	0.910884i	$0.635401\pi$
$198$		0			0
$199$			17.9378i			1.27158i	0.771862	+	0.635790i	$0.219325\pi$
$199$			17.9378i			1.27158i	−0.771862	+	0.635790i	$0.780675\pi$
$200$		0			0
$201$	10.4334			0.735919
$202$		0			0
$203$	−3.78312	−	1.32643i	−0.265523	−	0.0930973i
$204$		0			0
$205$	−19.3925	+	19.3925i	−1.35443	+	1.35443i
$206$		0			0
$207$		−	5.93702i		−	0.412651i
$208$		0			0
$209$			0.807731i			0.0558719i
$210$		0			0
$211$	−10.1381	−	10.1381i	−0.697936	−	0.697936i	0.266029	−	0.963965i	$-0.414288\pi$
$211$	−10.1381	−	10.1381i	−0.697936	−	0.697936i	−0.963965	+	0.266029i	$0.914288\pi$
$212$		0			0
$213$	−3.04450	+	3.04450i	−0.208606	+	0.208606i
$214$		0			0
$215$		−	21.0849i		−	1.43798i
$216$		0			0
$217$	−6.61785	−	13.7642i	−0.449249	−	0.934372i
$218$		0			0
$219$	−4.74943	+	4.74943i	−0.320936	+	0.320936i
$220$		0			0
$221$	−7.86324	+	7.86324i	−0.528939	+	0.528939i
$222$		0			0
$223$	8.91647			0.597091			0.298545	−	0.954395i	$-0.403499\pi$
$223$	8.91647			0.597091			0.298545	+	0.954395i	$0.403499\pi$
$224$		0			0
$225$	−14.7082			−0.980548
$226$		0			0
$227$	−15.4137	+	15.4137i	−1.02304	+	1.02304i	−0.0233148	+	0.999728i	$0.507422\pi$
$227$	−15.4137	+	15.4137i	−1.02304	+	1.02304i	−0.999728	+	0.0233148i	$0.992578\pi$
$228$		0			0
$229$	−9.56042	+	9.56042i	−0.631770	+	0.631770i	−0.948512	−	0.316742i	$-0.897411\pi$
$229$	−9.56042	+	9.56042i	−0.631770	+	0.631770i	0.316742	+	0.948512i	$0.397411\pi$
$230$		0			0
$231$	−1.42568	+	0.685473i	−0.0938031	+	0.0451008i
$232$		0			0
$233$		−	15.3607i		−	1.00631i	−0.864195	−	0.503157i	$-0.832172\pi$
$233$		−	15.3607i		−	1.00631i	0.864195	−	0.503157i	$-0.167828\pi$
$234$		0			0
$235$	−13.7658	+	13.7658i	−0.897979	+	0.897979i
$236$		0			0
$237$	5.93657	+	5.93657i	0.385622	+	0.385622i
$238$		0			0
$239$			2.60913i			0.168771i	0.996433	+	0.0843853i	$0.0268927\pi$
$239$			2.60913i			0.168771i	−0.996433	+	0.0843853i	$0.973107\pi$
$240$		0			0
$241$			20.8007i			1.33989i	0.742411	+	0.669944i	$0.233682\pi$
$241$			20.8007i			1.33989i	−0.742411	+	0.669944i	$0.766318\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	3.44068	+	30.8847i	0.219817	+	1.97315i
$246$		0			0
$247$	5.84829			0.372118
$248$		0			0
$249$			9.25435i			0.586471i
$250$		0			0
$251$	3.34903	+	3.34903i	0.211389	+	0.211389i	0.804857	−	0.593469i	$-0.202242\pi$
$251$	3.34903	+	3.34903i	0.211389	+	0.211389i	−0.593469	+	0.804857i	$0.702242\pi$
$252$		0			0
$253$	−2.51007	+	2.51007i	−0.157807	+	0.157807i
$254$		0			0
$255$	−11.4037			−0.714126
$256$		0			0
$257$		−	4.35968i		−	0.271949i	−0.990712	−	0.135975i	$-0.956583\pi$
$257$		−	4.35968i		−	0.271949i	0.990712	−	0.135975i	$-0.0434166\pi$
$258$		0			0
$259$	−4.09733	+	11.6860i	−0.254596	+	0.726133i
$260$		0			0
$261$	−1.07143	−	1.07143i	−0.0663197	−	0.0663197i
$262$		0			0
$263$	10.9327			0.674140			0.337070	−	0.941480i	$-0.390564\pi$
$263$	10.9327			0.674140			0.337070	+	0.941480i	$0.390564\pi$
$264$		0			0
$265$	−49.3261			−3.03008
$266$		0			0
$267$	−10.5281	+	10.5281i	−0.644310	+	0.644310i
$268$		0			0
$269$	4.06387	+	4.06387i	0.247779	+	0.247779i	0.820058	−	0.572280i	$-0.193941\pi$
$269$	4.06387	+	4.06387i	0.247779	+	0.247779i	−0.572280	+	0.820058i	$0.693941\pi$
$270$		0			0
$271$	4.34285			0.263810			0.131905	−	0.991262i	$-0.457891\pi$
$271$	4.34285			0.263810			0.131905	+	0.991262i	$0.457891\pi$
$272$		0			0
$273$	4.96309	+	10.3225i	0.300380	+	0.624747i
$274$		0			0
$275$	6.21839	+	6.21839i	0.374983	+	0.374983i
$276$		0			0
$277$	4.81640	+	4.81640i	0.289389	+	0.289389i	0.836839	−	0.547449i	$-0.184401\pi$
$277$	4.81640	+	4.81640i	0.289389	+	0.289389i	−0.547449	+	0.836839i	$0.684401\pi$
$278$		0			0
$279$		−	5.77245i		−	0.345587i
$280$		0			0
$281$		−	4.22817i		−	0.252232i	−0.992016	−	0.126116i	$-0.959749\pi$
$281$		−	4.22817i		−	0.252232i	0.992016	−	0.126116i	$-0.0402511\pi$
$282$		0			0
$283$	−4.59280	−	4.59280i	−0.273014	−	0.273014i	0.557298	−	0.830312i	$-0.311838\pi$
$283$	−4.59280	−	4.59280i	−0.273014	−	0.273014i	−0.830312	+	0.557298i	$0.811838\pi$
$284$		0			0
$285$	4.24074	+	4.24074i	0.251200	+	0.251200i
$286$		0			0
$287$	7.08242	+	14.7304i	0.418062	+	0.869508i
$288$		0			0
$289$	10.4015			0.611855
$290$		0			0
$291$	−2.73131	−	2.73131i	−0.160112	−	0.160112i
$292$		0			0
$293$	−11.0062	+	11.0062i	−0.642991	+	0.642991i	−0.951290	−	0.308299i	$-0.900240\pi$
$293$	−11.0062	+	11.0062i	−0.642991	+	0.642991i	0.308299	+	0.951290i	$0.400240\pi$
$294$		0			0
$295$	−35.3691			−2.05927
$296$		0			0
$297$	−0.597907			−0.0346941
$298$		0			0
$299$	18.1739	+	18.1739i	1.05102	+	1.05102i
$300$		0			0
$301$	−11.8582	−	4.15771i	−0.683496	−	0.239646i
$302$		0			0
$303$			2.30732i			0.132552i
$304$		0			0
$305$	2.20697			0.126371
$306$		0			0
$307$	−1.20915	+	1.20915i	−0.0690101	+	0.0690101i	−0.740769	−	0.671759i	$-0.765539\pi$
$307$	−1.20915	+	1.20915i	−0.0690101	+	0.0690101i	0.671759	+	0.740769i	$0.265539\pi$
$308$		0			0
$309$	−6.78391	−	6.78391i	−0.385923	−	0.385923i
$310$		0			0
$311$		−	27.0431i		−	1.53347i	−0.641961	−	0.766737i	$-0.721879\pi$
$311$		−	27.0431i		−	1.53347i	0.641961	−	0.766737i	$-0.278121\pi$
$312$		0			0
$313$	4.07592			0.230385			0.115192	−	0.993343i	$-0.463252\pi$
$313$	4.07592			0.230385			0.115192	+	0.993343i	$0.463252\pi$
$314$		0			0
$315$	−3.88625	+	11.0840i	−0.218965	+	0.624511i
$316$		0			0
$317$	10.2893	−	10.2893i	0.577905	−	0.577905i	−0.356420	−	0.934326i	$-0.616003\pi$
$317$	10.2893	−	10.2893i	0.577905	−	0.577905i	0.934326	+	0.356420i	$0.116003\pi$
$318$		0			0
$319$			0.905965i			0.0507243i
$320$		0			0
$321$		−	14.3820i		−	0.802723i
$322$		0			0
$323$	2.45380	+	2.45380i	0.136533	+	0.136533i
$324$		0			0
$325$	45.0236	−	45.0236i	2.49746	−	2.49746i
$326$		0			0
$327$		−	14.6035i		−	0.807577i
$328$		0			0
$329$	5.02745	+	10.4564i	0.277173	+	0.576479i
$330$		0			0
$331$	−4.51356	+	4.51356i	−0.248088	+	0.248088i	−0.820186	−	0.572098i	$-0.806130\pi$
$331$	−4.51356	+	4.51356i	−0.248088	+	0.248088i	0.572098	+	0.820186i	$0.306130\pi$
$332$		0			0
$333$	−3.30963	+	3.30963i	−0.181366	+	0.181366i
$334$		0			0
$335$	−46.3182			−2.53063
$336$		0			0
$337$	−4.16157			−0.226695			−0.113348	−	0.993555i	$-0.536157\pi$
$337$	−4.16157			−0.226695			−0.113348	+	0.993555i	$0.536157\pi$
$338$		0			0
$339$	−0.796293	+	0.796293i	−0.0432487	+	0.0432487i
$340$		0			0
$341$	−2.44050	+	2.44050i	−0.132160	+	0.132160i
$342$		0			0
$343$	18.0481	+	4.15508i	0.974508	+	0.224353i
$344$		0			0
$345$			26.3567i			1.41900i
$346$		0			0
$347$	−9.38128	+	9.38128i	−0.503613	+	0.503613i	−0.912559	−	0.408945i	$-0.865897\pi$
$347$	−9.38128	+	9.38128i	−0.503613	+	0.503613i	0.408945	+	0.912559i	$0.365897\pi$
$348$		0			0
$349$	9.89989	+	9.89989i	0.529929	+	0.529929i	0.920551	−	0.390622i	$-0.127740\pi$
$349$	9.89989	+	9.89989i	0.529929	+	0.529929i	−0.390622	+	0.920551i	$0.627740\pi$
$350$		0			0
$351$			4.32908i			0.231069i
$352$		0			0
$353$		−	4.23294i		−	0.225297i	−0.993635	−	0.112648i	$-0.964067\pi$
$353$		−	4.23294i		−	0.225297i	0.993635	−	0.112648i	$-0.0359334\pi$
$354$		0			0
$355$	13.5158	−	13.5158i	0.717342	−	0.717342i
$356$		0			0
$357$	−2.24868	+	6.41347i	−0.119013	+	0.339437i
$358$		0			0
$359$	−23.0033			−1.21407			−0.607033	−	0.794677i	$-0.707640\pi$
$359$	−23.0033			−1.21407			−0.607033	+	0.794677i	$0.707640\pi$
$360$		0			0
$361$			17.1750i			0.903947i
$362$		0			0
$363$	−7.52539	−	7.52539i	−0.394981	−	0.394981i
$364$		0			0
$365$	21.0846	−	21.0846i	1.10362	−	1.10362i
$366$		0			0
$367$	21.1825			1.10572			0.552859	−	0.833275i	$-0.313537\pi$
$367$	21.1825			1.10572			0.552859	+	0.833275i	$0.313537\pi$
$368$		0			0
$369$			6.17767i			0.321597i
$370$		0			0
$371$	−9.72658	+	27.7412i	−0.504979	+	1.44025i
$372$		0			0
$373$	7.70573	+	7.70573i	0.398987	+	0.398987i	0.877876	−	0.478888i	$-0.158960\pi$
$373$	7.70573	+	7.70573i	0.398987	+	0.398987i	−0.478888	+	0.877876i	$0.658960\pi$
$374$		0			0
$375$	43.0986			2.22560
$376$		0			0
$377$	6.55954			0.337833
$378$		0			0
$379$	−2.73370	+	2.73370i	−0.140421	+	0.140421i	−0.773823	−	0.633402i	$-0.781658\pi$
$379$	−2.73370	+	2.73370i	−0.140421	+	0.140421i	0.633402	+	0.773823i	$0.281658\pi$
$380$		0			0
$381$	−11.0544	−	11.0544i	−0.566332	−	0.566332i
$382$		0			0
$383$	18.5055			0.945588			0.472794	−	0.881173i	$-0.343246\pi$
$383$	18.5055			0.945588			0.472794	+	0.881173i	$0.343246\pi$
$384$		0			0
$385$	6.32917	−	3.04308i	0.322564	−	0.155090i
$386$		0			0
$387$	−3.35840	−	3.35840i	−0.170717	−	0.170717i
$388$		0			0
$389$	18.4302	+	18.4302i	0.934449	+	0.934449i	0.997980	−	0.0635309i	$-0.0202361\pi$
$389$	18.4302	+	18.4302i	0.934449	+	0.934449i	−0.0635309	+	0.997980i	$0.520236\pi$
$390$		0			0
$391$			15.2507i			0.771260i
$392$		0			0
$393$			5.95257i			0.300268i
$394$		0			0
$395$	−26.3548	−	26.3548i	−1.32605	−	1.32605i
$396$		0			0
$397$	9.65214	+	9.65214i	0.484427	+	0.484427i	0.906542	−	0.422115i	$-0.138712\pi$
$397$	9.65214	+	9.65214i	0.484427	+	0.484427i	−0.422115	+	0.906542i	$0.638712\pi$
$398$		0			0
$399$	3.22124	−	1.54878i	0.161264	−	0.0775360i
$400$		0			0
$401$	−4.76372			−0.237889			−0.118944	−	0.992901i	$-0.537951\pi$
$401$	−4.76372			−0.237889			−0.118944	+	0.992901i	$0.537951\pi$
$402$		0			0
$403$	17.6702	+	17.6702i	0.880213	+	0.880213i
$404$		0			0
$405$	−3.13913	+	3.13913i	−0.155984	+	0.155984i
$406$		0			0
$407$	2.79851			0.138717
$408$		0			0
$409$	11.1720			0.552422			0.276211	−	0.961097i	$-0.410921\pi$
$409$	11.1720			0.552422			0.276211	+	0.961097i	$0.410921\pi$
$410$		0			0
$411$	−0.349793	−	0.349793i	−0.0172540	−	0.0172540i
$412$		0			0
$413$	−6.97441	+	19.8917i	−0.343188	+	0.978809i
$414$		0			0
$415$		−	41.0837i		−	2.01672i
$416$		0			0
$417$	−3.48602			−0.170711
$418$		0			0
$419$	4.99890	−	4.99890i	0.244212	−	0.244212i	−0.574378	−	0.818590i	$-0.694756\pi$
$419$	4.99890	−	4.99890i	0.244212	−	0.244212i	0.818590	+	0.574378i	$0.194756\pi$
$420$		0			0
$421$	−28.0333	−	28.0333i	−1.36626	−	1.36626i	−0.865705	−	0.500554i	$-0.833130\pi$
$421$	−28.0333	−	28.0333i	−1.36626	−	1.36626i	−0.500554	−	0.865705i	$-0.666870\pi$
$422$		0			0
$423$			4.38522i			0.213217i
$424$		0			0
$425$	37.7817			1.83268
$426$		0			0
$427$	0.435191	−	1.24121i	0.0210604	−	0.0600663i
$428$		0			0
$429$	1.83026	−	1.83026i	0.0883660	−	0.0883660i
$430$		0			0
$431$			39.6062i			1.90776i	0.300181	+	0.953882i	$0.402953\pi$
$431$			39.6062i			1.90776i	−0.300181	+	0.953882i	$0.597047\pi$
$432$		0			0
$433$		−	37.9857i		−	1.82548i	−0.408546	−	0.912738i	$-0.633964\pi$
$433$		−	37.9857i		−	1.82548i	0.408546	−	0.912738i	$-0.366036\pi$
$434$		0			0
$435$	4.75649	+	4.75649i	0.228056	+	0.228056i
$436$		0			0
$437$	5.67135	−	5.67135i	0.271297	−	0.271297i
$438$		0			0
$439$			9.40058i			0.448665i	0.974513	+	0.224333i	$0.0720202\pi$
$439$			9.40058i			0.448665i	−0.974513	+	0.224333i	$0.927980\pi$
$440$		0			0
$441$	5.46735	+	4.37128i	0.260350	+	0.208156i
$442$		0			0
$443$	15.1211	−	15.1211i	0.718426	−	0.718426i	−0.249857	−	0.968283i	$-0.580384\pi$
$443$	15.1211	−	15.1211i	0.718426	−	0.718426i	0.968283	+	0.249857i	$0.0803837\pi$
$444$		0			0
$445$	46.7384	−	46.7384i	2.21561	−	2.21561i
$446$		0			0
$447$	16.3696			0.774255
$448$		0			0
$449$	−37.7663			−1.78230			−0.891151	−	0.453707i	$-0.850101\pi$
$449$	−37.7663			−1.78230			−0.891151	+	0.453707i	$0.850101\pi$
$450$		0			0
$451$	2.61182	−	2.61182i	0.122986	−	0.122986i
$452$		0			0
$453$	−1.64414	+	1.64414i	−0.0772484	+	0.0772484i
$454$		0			0
$455$	−22.0331	−	45.8257i	−1.03293	−	2.14834i
$456$		0			0
$457$		−	20.6321i		−	0.965129i	−0.875860	−	0.482564i	$-0.839705\pi$
$457$		−	20.6321i		−	0.965129i	0.875860	−	0.482564i	$-0.160295\pi$
$458$		0			0
$459$	−1.81638	+	1.81638i	−0.0847813	+	0.0847813i
$460$		0			0
$461$	−7.60470	−	7.60470i	−0.354186	−	0.354186i	0.507478	−	0.861665i	$-0.330578\pi$
$461$	−7.60470	−	7.60470i	−0.354186	−	0.354186i	−0.861665	+	0.507478i	$0.830578\pi$
$462$		0			0
$463$			3.46558i			0.161059i	0.996752	+	0.0805297i	$0.0256612\pi$
$463$			3.46558i			0.161059i	−0.996752	+	0.0805297i	$0.974339\pi$
$464$		0			0
$465$			25.6262i			1.18839i
$466$		0			0
$467$	12.3445	−	12.3445i	0.571236	−	0.571236i	−0.361238	−	0.932474i	$-0.617646\pi$
$467$	12.3445	−	12.3445i	0.571236	−	0.571236i	0.932474	+	0.361238i	$0.117646\pi$
$468$		0			0
$469$	−9.13345	+	26.0495i	−0.421744	+	1.20286i
$470$		0			0
$471$	−22.1490			−1.02057
$472$		0			0
$473$			2.83975i			0.130572i
$474$		0			0
$475$	−14.0501	−	14.0501i	−0.644661	−	0.644661i
$476$		0			0
$477$	−7.85667	+	7.85667i	−0.359732	+	0.359732i
$478$		0			0
$479$	24.4302			1.11625			0.558123	−	0.829758i	$-0.311522\pi$
$479$	24.4302			1.11625			0.558123	+	0.829758i	$0.311522\pi$
$480$		0			0
$481$		−	20.2623i		−	0.923883i
$482$		0			0
$483$	14.8231	+	5.19727i	0.674476	+	0.236484i
$484$		0			0
$485$	12.1254	+	12.1254i	0.550584	+	0.550584i
$486$		0			0
$487$	−36.2898			−1.64445			−0.822224	−	0.569164i	$-0.807267\pi$
$487$	−36.2898			−1.64445			−0.822224	+	0.569164i	$0.807267\pi$
$488$		0			0
$489$	−21.2700			−0.961862
$490$		0			0
$491$	2.77669	−	2.77669i	0.125310	−	0.125310i	−0.641670	−	0.766981i	$-0.721758\pi$
$491$	2.77669	−	2.77669i	0.125310	−	0.125310i	0.766981	+	0.641670i	$0.221758\pi$
$492$		0			0
$493$	2.75223	+	2.75223i	0.123954	+	0.123954i
$494$		0			0
$495$	2.65434			0.119304
$496$		0			0
$497$	−4.93615	−	10.2665i	−0.221417	−	0.460514i
$498$		0			0
$499$	−11.8814	−	11.8814i	−0.531886	−	0.531886i	0.389247	−	0.921133i	$-0.372735\pi$
$499$	−11.8814	−	11.8814i	−0.531886	−	0.531886i	−0.921133	+	0.389247i	$0.872735\pi$
$500$		0			0
$501$	−6.89760	−	6.89760i	−0.308162	−	0.308162i
$502$		0			0
$503$			26.7447i			1.19249i	0.802804	+	0.596243i	$0.203340\pi$
$503$			26.7447i			1.19249i	−0.802804	+	0.596243i	$0.796660\pi$
$504$		0			0
$505$		−	10.2431i		−	0.455813i
$506$		0			0
$507$	−4.05944	−	4.05944i	−0.180286	−	0.180286i
$508$		0			0
$509$	−20.3067	−	20.3067i	−0.900079	−	0.900079i	0.0953637	−	0.995442i	$-0.469599\pi$
$509$	−20.3067	−	20.3067i	−0.900079	−	0.900079i	−0.995442	+	0.0953637i	$0.969599\pi$
$510$		0			0
$511$	−7.70039	−	16.0157i	−0.340645	−	0.708493i
$512$		0			0
$513$	1.35093			0.0596451
$514$		0			0
$515$	30.1164	+	30.1164i	1.32709	+	1.32709i
$516$		0			0
$517$	1.85400	−	1.85400i	0.0815388	−	0.0815388i
$518$		0			0
$519$	−4.36629			−0.191659
$520$		0			0
$521$	−6.58341			−0.288424			−0.144212	−	0.989547i	$-0.546065\pi$
$521$	−6.58341			−0.288424			−0.144212	+	0.989547i	$0.546065\pi$
$522$		0			0
$523$	17.5584	+	17.5584i	0.767775	+	0.767775i	0.977714	−	0.209940i	$-0.0673267\pi$
$523$	17.5584	+	17.5584i	0.767775	+	0.767775i	−0.209940	+	0.977714i	$0.567327\pi$
$524$		0			0
$525$	12.8756	−	36.7225i	0.561936	−	1.60270i
$526$		0			0
$527$			14.8280i			0.645916i
$528$		0			0
$529$	12.2481			0.532528
$530$		0			0
$531$	−5.63360	+	5.63360i	−0.244477	+	0.244477i
$532$		0			0
$533$	−18.9106	−	18.9106i	−0.819108	−	0.819108i
$534$		0			0
$535$			63.8472i			2.76035i
$536$		0			0
$537$	13.2020			0.569706
$538$		0			0
$539$	−0.463398	−	4.15961i	−0.0199600	−	0.179167i
$540$		0			0
$541$	13.1000	−	13.1000i	0.563215	−	0.563215i	−0.367005	−	0.930219i	$-0.619617\pi$
$541$	13.1000	−	13.1000i	0.563215	−	0.563215i	0.930219	+	0.367005i	$0.119617\pi$
$542$		0			0
$543$			7.40767i			0.317894i
$544$		0			0
$545$			64.8308i			2.77705i
$546$		0			0
$547$	24.6751	+	24.6751i	1.05503	+	1.05503i	0.998395	+	0.0566382i	$0.0180381\pi$
$547$	24.6751	+	24.6751i	1.05503	+	1.05503i	0.0566382	+	0.998395i	$0.481962\pi$
$548$		0			0
$549$	0.351526	−	0.351526i	0.0150028	−	0.0150028i
$550$		0			0
$551$		−	2.04697i		−	0.0872038i
$552$		0			0
$553$	−20.0189	+	9.62515i	−0.851291	+	0.409303i
$554$		0			0
$555$	14.6927	−	14.6927i	0.623672	−	0.623672i
$556$		0			0
$557$	−19.0634	+	19.0634i	−0.807740	+	0.807740i	−0.984291	−	0.176551i	$-0.943506\pi$
$557$	−19.0634	+	19.0634i	−0.807740	+	0.807740i	0.176551	+	0.984291i	$0.443506\pi$
$558$		0			0
$559$	20.5609			0.869634
$560$		0			0
$561$	1.53587			0.0648445
$562$		0			0
$563$	−15.4083	+	15.4083i	−0.649380	+	0.649380i	−0.952843	−	0.303463i	$-0.901857\pi$
$563$	−15.4083	+	15.4083i	−0.649380	+	0.649380i	0.303463	+	0.952843i	$0.401857\pi$
$564$		0			0
$565$	3.53506	−	3.53506i	0.148721	−	0.148721i
$566$		0			0
$567$	1.14645	+	2.38446i	0.0481466	+	0.100138i
$568$		0			0
$569$			25.8165i			1.08228i	0.840931	+	0.541142i	$0.182008\pi$
$569$			25.8165i			1.08228i	−0.840931	+	0.541142i	$0.817992\pi$
$570$		0			0
$571$	17.9757	−	17.9757i	0.752258	−	0.752258i	−0.222642	−	0.974900i	$-0.571468\pi$
$571$	17.9757	−	17.9757i	0.752258	−	0.752258i	0.974900	+	0.222642i	$0.0714681\pi$
$572$		0			0
$573$	−0.930724	−	0.930724i	−0.0388816	−	0.0388816i
$574$		0			0
$575$		−	87.3229i		−	3.64162i
$576$		0			0
$577$			2.60870i			0.108602i	0.998525	+	0.0543008i	$0.0172930\pi$
$577$			2.60870i			0.108602i	−0.998525	+	0.0543008i	$0.982707\pi$
$578$		0			0
$579$	−8.59311	+	8.59311i	−0.357117	+	0.357117i
$580$		0			0
$581$	−23.1056	−	8.10126i	−0.958583	−	0.336097i
$582$		0			0
$583$	6.64334			0.275139
$584$		0			0
$585$		−	19.2185i		−	0.794586i
$586$		0			0
$587$	−20.0167	−	20.0167i	−0.826176	−	0.826176i	0.160809	−	0.986986i	$-0.448590\pi$
$587$	−20.0167	−	20.0167i	−0.826176	−	0.826176i	−0.986986	+	0.160809i	$0.948590\pi$
$588$		0			0
$589$	5.51415	−	5.51415i	0.227206	−	0.227206i
$590$		0			0
$591$	−9.88943			−0.406797
$592$		0			0
$593$			11.8075i			0.484877i	0.970167	+	0.242438i	$0.0779472\pi$
$593$			11.8075i			0.484877i	−0.970167	+	0.242438i	$0.922053\pi$
$594$		0			0
$595$	9.98279	−	28.4719i	0.409254	−	1.16724i
$596$		0			0
$597$	−12.6840	−	12.6840i	−0.519120	−	0.519120i
$598$		0			0
$599$	−7.64439			−0.312341			−0.156171	−	0.987730i	$-0.549915\pi$
$599$	−7.64439			−0.312341			−0.156171	+	0.987730i	$0.549915\pi$
$600$		0			0
$601$	−5.46690			−0.222999			−0.111500	−	0.993764i	$-0.535565\pi$
$601$	−5.46690			−0.222999			−0.111500	+	0.993764i	$0.535565\pi$
$602$		0			0
$603$	−7.37756	+	7.37756i	−0.300438	+	0.300438i
$604$		0			0
$605$	33.4082	+	33.4082i	1.35824	+	1.35824i
$606$		0			0
$607$	11.1394			0.452133			0.226066	−	0.974112i	$-0.427413\pi$
$607$	11.1394			0.452133			0.226066	+	0.974112i	$0.427413\pi$
$608$		0			0
$609$	3.61300	−	1.73714i	0.146406	−	0.0703925i
$610$		0			0
$611$	−13.4237	−	13.4237i	−0.543064	−	0.543064i
$612$		0			0
$613$	21.4823	+	21.4823i	0.867664	+	0.867664i	0.992213	−	0.124549i	$-0.0397485\pi$
$613$	21.4823	+	21.4823i	0.867664	+	0.867664i	−0.124549	+	0.992213i	$0.539749\pi$
$614$		0			0
$615$		−	27.4251i		−	1.10589i
$616$		0			0
$617$			16.3658i			0.658862i	0.944180	+	0.329431i	$0.106857\pi$
$617$			16.3658i			0.658862i	−0.944180	+	0.329431i	$0.893143\pi$
$618$		0			0
$619$	−28.3481	−	28.3481i	−1.13941	−	1.13941i	−0.988557	−	0.150851i	$-0.951799\pi$
$619$	−28.3481	−	28.3481i	−1.13941	−	1.13941i	−0.150851	−	0.988557i	$-0.548201\pi$
$620$		0			0
$621$	4.19810	+	4.19810i	0.168464	+	0.168464i
$622$		0			0
$623$	−17.0696	−	35.5022i	−0.683877	−	1.42236i
$624$		0			0
$625$	−117.790			−4.71162
$626$		0			0
$627$	−0.571152	−	0.571152i	−0.0228096	−	0.0228096i
$628$		0			0
$629$	8.50159	−	8.50159i	0.338981	−	0.338981i
$630$		0			0
$631$	−14.8066			−0.589443			−0.294722	−	0.955583i	$-0.595227\pi$
$631$	−14.8066			−0.589443			−0.294722	+	0.955583i	$0.595227\pi$
$632$		0			0
$633$	14.3374			0.569862
$634$		0			0
$635$	49.0746	+	49.0746i	1.94747	+	1.94747i
$636$		0			0
$637$	−30.1172	+	3.35518i	−1.19329	+	0.132937i
$638$		0			0
$639$		−	4.30558i		−	0.170326i
$640$		0			0
$641$	−41.8951			−1.65476			−0.827379	−	0.561644i	$-0.810169\pi$
$641$	−41.8951			−1.65476			−0.827379	+	0.561644i	$0.810169\pi$
$642$		0			0
$643$	−22.2070	+	22.2070i	−0.875757	+	0.875757i	−0.993092	−	0.117335i	$-0.962565\pi$
$643$	−22.2070	+	22.2070i	−0.875757	+	0.875757i	0.117335	+	0.993092i	$0.462565\pi$
$644$		0			0
$645$	14.9092	+	14.9092i	0.587051	+	0.587051i
$646$		0			0
$647$			42.6451i			1.67655i	0.545246	+	0.838276i	$0.316436\pi$
$647$			42.6451i			1.67655i	−0.545246	+	0.838276i	$0.683564\pi$
$648$		0			0
$649$	4.76359			0.186987
$650$		0			0
$651$	14.4123	+	5.05321i	0.564861	+	0.198051i
$652$		0			0
$653$	22.0201	−	22.0201i	0.861714	−	0.861714i	−0.129823	−	0.991537i	$-0.541441\pi$
$653$	22.0201	−	22.0201i	0.861714	−	0.861714i	0.991537	+	0.129823i	$0.0414410\pi$
$654$		0			0
$655$		−	26.4258i		−	1.03254i
$656$		0			0
$657$		−	6.71670i		−	0.262044i
$658$		0			0
$659$	−17.1418	−	17.1418i	−0.667749	−	0.667749i	0.289446	−	0.957194i	$-0.406529\pi$
$659$	−17.1418	−	17.1418i	−0.667749	−	0.667749i	−0.957194	+	0.289446i	$0.906529\pi$
$660$		0			0
$661$	3.64387	−	3.64387i	0.141730	−	0.141730i	−0.632682	−	0.774412i	$-0.718046\pi$
$661$	3.64387	−	3.64387i	0.141730	−	0.141730i	0.774412	+	0.632682i	$0.218046\pi$
$662$		0			0
$663$		−	11.1203i		−	0.431877i
$664$		0			0
$665$	−14.3003	+	6.87565i	−0.554544	+	0.266626i
$666$		0			0
$667$	6.36108	−	6.36108i	0.246302	−	0.246302i
$668$		0			0
$669$	−6.30490	+	6.30490i	−0.243761	+	0.243761i
$670$		0			0
$671$	−0.297239			−0.0114748
$672$		0			0
$673$	24.8436			0.957650			0.478825	−	0.877910i	$-0.341063\pi$
$673$	24.8436			0.957650			0.478825	+	0.877910i	$0.341063\pi$
$674$		0			0
$675$	10.4003	−	10.4003i	0.400307	−	0.400307i
$676$		0			0
$677$	−7.14618	+	7.14618i	−0.274650	+	0.274650i	−0.830969	−	0.556319i	$-0.812213\pi$
$677$	−7.14618	+	7.14618i	−0.274650	+	0.274650i	0.556319	+	0.830969i	$0.312213\pi$
$678$		0			0
$679$	9.21034	−	4.42836i	0.353461	−	0.169945i
$680$		0			0
$681$		−	21.7983i		−	0.835311i
$682$		0			0
$683$	3.09491	−	3.09491i	0.118424	−	0.118424i	−0.645411	−	0.763835i	$-0.723314\pi$
$683$	3.09491	−	3.09491i	0.118424	−	0.118424i	0.763835	+	0.645411i	$0.223314\pi$
$684$		0			0
$685$	1.55287	+	1.55287i	0.0593321	+	0.0593321i
$686$		0			0
$687$		−	13.5205i		−	0.515838i
$688$		0			0
$689$		−	48.1004i		−	1.83248i
$690$		0			0
$691$	−21.8919	+	21.8919i	−0.832807	+	0.832807i	−0.987900	−	0.155093i	$-0.950432\pi$
$691$	−21.8919	+	21.8919i	−0.832807	+	0.832807i	0.155093	+	0.987900i	$0.450432\pi$
$692$		0			0
$693$	0.523408	−	1.49281i	0.0198826	−	0.0567073i
$694$		0			0
$695$	15.4758			0.587031
$696$		0			0
$697$		−	15.8689i		−	0.601076i
$698$		0			0
$699$	10.8617	+	10.8617i	0.410826	+	0.410826i
$700$		0			0
$701$	9.94444	−	9.94444i	0.375596	−	0.375596i	−0.493914	−	0.869511i	$-0.664434\pi$
$701$	9.94444	−	9.94444i	0.375596	−	0.375596i	0.869511	+	0.493914i	$0.164434\pi$
$702$		0			0
$703$	−6.32306			−0.238479
$704$		0			0
$705$		−	19.4677i		−	0.733197i
$706$		0			0
$707$	−5.76077	−	2.01983i	−0.216656	−	0.0759636i
$708$		0			0
$709$	27.3155	+	27.3155i	1.02585	+	1.02585i	0.999657	+	0.0261973i	$0.00833980\pi$
$709$	27.3155	+	27.3155i	1.02585	+	1.02585i	0.0261973	+	0.999657i	$0.491660\pi$
$710$		0			0
$711$	−8.39558			−0.314859
$712$		0			0
$713$	34.2711			1.28346
$714$		0			0
$715$	−8.12526	+	8.12526i	−0.303868	+	0.303868i
$716$		0			0
$717$	−1.84493	−	1.84493i	−0.0689003	−	0.0689003i
$718$		0			0
$719$	25.6353			0.956034			0.478017	−	0.878351i	$-0.341356\pi$
$719$	25.6353			0.956034			0.478017	+	0.878351i	$0.341356\pi$
$720$		0			0
$721$	22.8763	−	10.9990i	0.851956	−	0.409623i
$722$		0			0
$723$	−14.7083	−	14.7083i	−0.547007	−	0.547007i
$724$		0			0
$725$	−15.7588	−	15.7588i	−0.585267	−	0.585267i
$726$		0			0
$727$		−	17.7539i		−	0.658454i	−0.944251	−	0.329227i	$-0.893212\pi$
$727$		−	17.7539i		−	0.658454i	0.944251	−	0.329227i	$-0.106788\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	8.62687	+	8.62687i	0.319076	+	0.319076i
$732$		0			0
$733$	27.9290	+	27.9290i	1.03158	+	1.03158i	0.999485	+	0.0320947i	$0.0102178\pi$
$733$	27.9290	+	27.9290i	1.03158	+	1.03158i	0.0320947	+	0.999485i	$0.489782\pi$
$734$		0			0
$735$	−24.2717	−	19.4058i	−0.895275	−	0.715795i
$736$		0			0
$737$	6.23823			0.229788
$738$		0			0
$739$	−4.89433	−	4.89433i	−0.180041	−	0.180041i	0.611333	−	0.791374i	$-0.290634\pi$
$739$	−4.89433	−	4.89433i	−0.180041	−	0.180041i	−0.791374	+	0.611333i	$0.790634\pi$
$740$		0			0
$741$	−4.13536	+	4.13536i	−0.151916	+	0.151916i
$742$		0			0
$743$	39.5863			1.45228			0.726141	−	0.687546i	$-0.241312\pi$
$743$	39.5863			1.45228			0.726141	+	0.687546i	$0.241312\pi$
$744$		0			0
$745$	−72.6711			−2.66246
$746$		0			0
$747$	−6.54381	−	6.54381i	−0.239426	−	0.239426i
$748$		0			0
$749$	35.9079	+	12.5900i	1.31205	+	0.460028i
$750$		0			0
$751$			35.6555i			1.30109i	0.759468	+	0.650545i	$0.225459\pi$
$751$			35.6555i			1.30109i	−0.759468	+	0.650545i	$0.774541\pi$
$752$		0			0
$753$	−4.73624			−0.172598
$754$		0			0
$755$	7.29898	−	7.29898i	0.265637	−	0.265637i
$756$		0			0
$757$	15.1414	+	15.1414i	0.550324	+	0.550324i	0.926534	−	0.376210i	$-0.122773\pi$
$757$	15.1414	+	15.1414i	0.550324	+	0.550324i	−0.376210	+	0.926534i	$0.622773\pi$
$758$		0			0
$759$		−	3.54978i		−	0.128849i
$760$		0			0
$761$	−4.79478			−0.173811			−0.0869053	−	0.996217i	$-0.527698\pi$
$761$	−4.79478			−0.173811			−0.0869053	+	0.996217i	$0.527698\pi$
$762$		0			0
$763$	36.4611	+	12.7839i	1.31998	+	0.462810i
$764$		0			0
$765$	8.06362	−	8.06362i	0.291541	−	0.291541i
$766$		0			0
$767$		−	34.4902i		−	1.24537i
$768$		0			0
$769$		−	4.32933i		−	0.156120i	−0.996949	−	0.0780598i	$-0.975128\pi$
$769$		−	4.32933i		−	0.156120i	0.996949	−	0.0780598i	$-0.0248725\pi$
$770$		0			0
$771$	3.08276	+	3.08276i	0.111023	+	0.111023i
$772$		0			0
$773$	28.7662	−	28.7662i	1.03465	−	1.03465i	0.0352718	−	0.999378i	$-0.488770\pi$
$773$	28.7662	−	28.7662i	1.03465	−	1.03465i	0.999378	−	0.0352718i	$-0.0112297\pi$
$774$		0			0
$775$		−	84.9024i		−	3.04978i
$776$		0			0
$777$	−5.36600	−	11.1605i	−0.192504	−	0.400381i
$778$		0			0
$779$	−5.90123	+	5.90123i	−0.211434	+	0.211434i
$780$		0			0
$781$	−1.82033	+	1.82033i	−0.0651365	+	0.0651365i
$782$		0			0
$783$	1.51523			0.0541498
$784$		0			0
$785$	98.3280			3.50948
$786$		0			0
$787$	20.7135	−	20.7135i	0.738356	−	0.738356i	−0.233904	−	0.972260i	$-0.575150\pi$
$787$	20.7135	−	20.7135i	0.738356	−	0.738356i	0.972260	+	0.233904i	$0.0751500\pi$
$788$		0			0
$789$	−7.73059	+	7.73059i	−0.275216	+	0.275216i
$790$		0			0
$791$	−1.29105	−	2.68521i	−0.0459046	−	0.0954749i
$792$		0			0
$793$			2.15213i			0.0764243i
$794$		0			0
$795$	34.8788	−	34.8788i	1.23702	−	1.23702i
$796$		0			0
$797$	14.7360	+	14.7360i	0.521977	+	0.521977i	0.918168	−	0.396191i	$-0.129668\pi$
$797$	14.7360	+	14.7360i	0.521977	+	0.521977i	−0.396191	+	0.918168i	$0.629668\pi$
$798$		0			0
$799$		−	11.2645i		−	0.398510i
$800$		0			0
$801$		−	14.8890i		−	0.526077i
$802$		0			0
$803$	−2.83971	+	2.83971i	−0.100211	+	0.100211i
$804$		0			0
$805$	−65.8057	−	23.0727i	−2.31935	−	0.813206i
$806$		0			0
$807$	−5.74718			−0.202310
$808$		0			0
$809$			16.1272i			0.567002i	0.958972	+	0.283501i	$0.0914959\pi$
$809$			16.1272i			0.567002i	−0.958972	+	0.283501i	$0.908504\pi$
$810$		0			0
$811$	−27.1830	−	27.1830i	−0.954525	−	0.954525i	0.0444849	−	0.999010i	$-0.485835\pi$
$811$	−27.1830	−	27.1830i	−0.954525	−	0.954525i	−0.999010	+	0.0444849i	$0.985835\pi$
$812$		0			0
$813$	−3.07086	+	3.07086i	−0.107700	+	0.107700i
$814$		0			0
$815$	94.4258			3.30759
$816$		0			0
$817$		−	6.41624i		−	0.224476i
$818$		0			0
$819$	−10.8086	−	3.78968i	−0.377681	−	0.132422i
$820$		0			0
$821$	−28.4565	−	28.4565i	−0.993140	−	0.993140i	0.00683656	−	0.999977i	$-0.497824\pi$
$821$	−28.4565	−	28.4565i	−0.993140	−	0.993140i	−0.999977	+	0.00683656i	$0.997824\pi$
$822$		0			0
$823$	−6.62917			−0.231078			−0.115539	−	0.993303i	$-0.536860\pi$
$823$	−6.62917			−0.231078			−0.115539	+	0.993303i	$0.536860\pi$
$824$		0			0
$825$	−8.79414			−0.306173
$826$		0			0
$827$	−7.69624	+	7.69624i	−0.267625	+	0.267625i	−0.828142	−	0.560518i	$-0.810602\pi$
$827$	−7.69624	+	7.69624i	−0.267625	+	0.267625i	0.560518	+	0.828142i	$0.310602\pi$
$828$		0			0
$829$	−12.2451	−	12.2451i	−0.425288	−	0.425288i	0.461731	−	0.887020i	$-0.347228\pi$
$829$	−12.2451	−	12.2451i	−0.425288	−	0.425288i	−0.887020	+	0.461731i	$0.847228\pi$
$830$		0			0
$831$	−6.81142			−0.236285
$832$		0			0
$833$	−14.0442	−	11.2287i	−0.486604	−	0.389052i
$834$		0			0
$835$	30.6212	+	30.6212i	1.05969	+	1.05969i
$836$		0			0
$837$	4.08174	+	4.08174i	0.141085	+	0.141085i
$838$		0			0
$839$		−	32.2896i		−	1.11476i	−0.830258	−	0.557380i	$-0.811807\pi$
$839$		−	32.2896i		−	1.11476i	0.830258	−	0.557380i	$-0.188193\pi$
$840$		0			0
$841$			26.7041i			0.920831i
$842$		0			0
$843$	2.98977	+	2.98977i	0.102973	+	0.102973i
$844$		0			0
$845$	18.0215	+	18.0215i	0.619957	+	0.619957i
$846$		0			0
$847$	25.3766	−	12.2012i	0.871951	−	0.419237i
$848$		0			0
$849$	6.49520			0.222915
$850$		0			0
$851$	−19.6493	−	19.6493i	−0.673569	−	0.673569i
$852$		0			0
$853$	−14.5661	+	14.5661i	−0.498733	+	0.498733i	−0.911043	−	0.412310i	$-0.864722\pi$
$853$	−14.5661	+	14.5661i	−0.498733	+	0.498733i	0.412310	+	0.911043i	$0.364722\pi$
$854$		0			0
$855$	−5.99732			−0.205104
$856$		0			0
$857$	−14.4706			−0.494307			−0.247153	−	0.968976i	$-0.579495\pi$
$857$	−14.4706			−0.494307			−0.247153	+	0.968976i	$0.579495\pi$
$858$		0			0
$859$	11.7304	+	11.7304i	0.400236	+	0.400236i	0.878316	−	0.478080i	$-0.158667\pi$
$859$	11.7304	+	11.7304i	0.400236	+	0.400236i	−0.478080	+	0.878316i	$0.658667\pi$
$860$		0			0
$861$	−15.4240	−	5.40794i	−0.525648	−	0.184302i
$862$		0			0
$863$			36.3253i			1.23653i	0.785971	+	0.618264i	$0.212164\pi$
$863$			36.3253i			1.23653i	−0.785971	+	0.618264i	$0.787836\pi$
$864$		0			0
$865$	19.3837			0.659065
$866$		0			0
$867$	−7.35500	+	7.35500i	−0.249789	+	0.249789i
$868$		0			0
$869$	3.54951	+	3.54951i	0.120409	+	0.120409i
$870$		0			0
$871$		−	45.1672i		−	1.53043i
$872$		0			0
$873$	3.86266			0.130731
$874$		0			0
$875$	−37.7285	+	107.606i	−1.27546	+	3.63773i
$876$		0			0
$877$	14.8508	−	14.8508i	0.501477	−	0.501477i	−0.410420	−	0.911897i	$-0.634618\pi$
$877$	14.8508	−	14.8508i	0.501477	−	0.501477i	0.911897	+	0.410420i	$0.134618\pi$
$878$		0			0
$879$		−	15.5652i		−	0.525000i
$880$		0			0
$881$			24.9375i			0.840166i	0.907486	+	0.420083i	$0.137999\pi$
$881$			24.9375i			0.840166i	−0.907486	+	0.420083i	$0.862001\pi$
$882$		0			0
$883$	12.3198	+	12.3198i	0.414595	+	0.414595i	0.883336	−	0.468741i	$-0.155292\pi$
$883$	12.3198	+	12.3198i	0.414595	+	0.414595i	−0.468741	+	0.883336i	$0.655292\pi$
$884$		0			0
$885$	25.0098	−	25.0098i	0.840694	−	0.840694i
$886$		0			0
$887$			31.2525i			1.04936i	0.851301	+	0.524678i	$0.175814\pi$
$887$			31.2525i			1.04936i	−0.851301	+	0.524678i	$0.824186\pi$
$888$		0			0
$889$	37.2768	−	17.9228i	1.25022	−	0.601111i
$890$		0			0
$891$	0.422784	−	0.422784i	0.0141638	−	0.0141638i
$892$		0			0
$893$	−4.18899	+	4.18899i	−0.140179	+	0.140179i
$894$		0			0
$895$	−58.6087			−1.95907
$896$		0			0
$897$	−25.7018			−0.858158
$898$		0			0
$899$	6.18476	−	6.18476i	0.206273	−	0.206273i
$900$		0			0
$901$	20.1818	−	20.1818i	0.672353	−	0.672353i
$902$		0			0
$903$	11.3250	−	5.44508i	0.376871	−	0.181201i
$904$		0			0
$905$		−	32.8856i		−	1.09315i
$906$		0			0
$907$	−13.1808	+	13.1808i	−0.437663	+	0.437663i	−0.891225	−	0.453562i	$-0.850153\pi$
$907$	−13.1808	+	13.1808i	−0.437663	+	0.437663i	0.453562	+	0.891225i	$0.350153\pi$
$908$		0			0
$909$	−1.63152	−	1.63152i	−0.0541142	−	0.0541142i
$910$		0			0
$911$			23.9885i			0.794773i	0.917651	+	0.397387i	$0.130083\pi$
$911$			23.9885i			0.794773i	−0.917651	+	0.397387i	$0.869917\pi$
$912$		0			0
$913$			5.53324i			0.183123i
$914$		0			0
$915$	−1.56056	+	1.56056i	−0.0515906	+	0.0515906i
$916$		0			0
$917$	−14.8620	−	5.21089i	−0.490786	−	0.172079i
$918$		0			0
$919$	10.4093			0.343373			0.171686	−	0.985152i	$-0.445078\pi$
$919$	10.4093			0.343373			0.171686	+	0.985152i	$0.445078\pi$
$920$		0			0
$921$		−	1.71000i		−	0.0563465i
$922$		0			0
$923$	13.1799	+	13.1799i	0.433822	+	0.433822i
$924$		0			0
$925$	−48.6787	+	48.6787i	−1.60055	+	1.60055i
$926$		0			0
$927$	9.59390			0.315105
$928$		0			0
$929$		−	30.0238i		−	0.985050i	−0.870298	−	0.492525i	$-0.836074\pi$
$929$		−	30.0238i		−	0.985050i	0.870298	−	0.492525i	$-0.163926\pi$
$930$		0			0
$931$	1.04702	+	9.39838i	0.0343146	+	0.308019i
$932$		0			0
$933$	19.1224	+	19.1224i	0.626038	+	0.626038i
$934$		0			0
$935$	−6.81833			−0.222983
$936$		0			0
$937$	32.6745			1.06743			0.533714	−	0.845665i	$-0.320796\pi$
$937$	32.6745			1.06743			0.533714	+	0.845665i	$0.320796\pi$
$938$		0			0
$939$	−2.88211	+	2.88211i	−0.0940542	+	0.0940542i
$940$		0			0
$941$	6.54400	+	6.54400i	0.213328	+	0.213328i	0.805680	−	0.592351i	$-0.201800\pi$
$941$	6.54400	+	6.54400i	0.213328	+	0.213328i	−0.592351	+	0.805680i	$0.701800\pi$
$942$		0			0
$943$	−36.6769			−1.19436
$944$		0			0
$945$	−5.08956	−	10.5855i	−0.165563	−	0.344348i
$946$		0			0
$947$	−28.9233	−	28.9233i	−0.939879	−	0.939879i	0.0584131	−	0.998292i	$-0.481396\pi$
$947$	−28.9233	−	28.9233i	−0.939879	−	0.939879i	−0.998292	+	0.0584131i	$0.981396\pi$
$948$		0			0
$949$	20.5606	+	20.5606i	0.667427	+	0.667427i
$950$		0			0
$951$			14.5513i			0.471858i
$952$		0			0
$953$		−	20.7126i		−	0.670948i	−0.942049	−	0.335474i	$-0.891104\pi$
$953$		−	20.7126i		−	0.670948i	0.942049	−	0.335474i	$-0.108896\pi$
$954$		0			0
$955$	4.13185	+	4.13185i	0.133704	+	0.133704i
$956$		0			0
$957$	−0.640614	−	0.640614i	−0.0207081	−	0.0207081i
$958$		0			0
$959$	1.17955	−	0.567130i	0.0380896	−	0.0183136i
$960$		0			0
$961$	2.32116			0.0748761
$962$		0			0
$963$	10.1696	+	10.1696i	0.327710	+	0.327710i
$964$		0			0
$965$	38.1482	−	38.1482i	1.22803	−	1.22803i
$966$		0			0
$967$	20.3296			0.653757			0.326879	−	0.945066i	$-0.394003\pi$
$967$	20.3296			0.653757			0.326879	+	0.945066i	$0.394003\pi$
$968$		0			0
$969$	−3.47020			−0.111479
$970$		0			0
$971$	−26.0614	−	26.0614i	−0.836352	−	0.836352i	0.152025	−	0.988377i	$-0.451421\pi$
$971$	−26.0614	−	26.0614i	−0.836352	−	0.836352i	−0.988377	+	0.152025i	$0.951421\pi$
$972$		0			0
$973$	3.05167	−	8.70366i	0.0978319	−	0.279027i
$974$		0			0
$975$			63.6730i			2.03917i
$976$		0			0
$977$	−26.1606			−0.836951			−0.418475	−	0.908228i	$-0.637435\pi$
$977$	−26.1606			−0.836951			−0.418475	+	0.908228i	$0.637435\pi$
$978$		0			0
$979$	−6.29482	+	6.29482i	−0.201183	+	0.201183i
$980$		0			0
$981$	10.3263	+	10.3263i	0.329692	+	0.329692i
$982$		0			0
$983$			45.5195i			1.45185i	0.687776	+	0.725923i	$0.258587\pi$
$983$			45.5195i			1.45185i	−0.687776	+	0.725923i	$0.741413\pi$
$984$		0			0
$985$	43.9031			1.39887
$986$		0			0
$987$	−10.9487	−	3.83882i	−0.348502	−	0.122191i
$988$		0			0
$989$	19.9389	−	19.9389i	0.634019	−	0.634019i
$990$		0			0
$991$		−	1.70803i		−	0.0542572i	−0.999632	−	0.0271286i	$-0.991364\pi$
$991$		−	1.70803i		−	0.0542572i	0.999632	−	0.0271286i	$-0.00863637\pi$
$992$		0			0
$993$		−	6.38314i		−	0.202563i
$994$		0			0
$995$	56.3091	+	56.3091i	1.78512	+	1.78512i
$996$		0			0
$997$	−25.4084	+	25.4084i	−0.804691	+	0.804691i	−0.983825	−	0.179134i	$-0.942670\pi$
$997$	−25.4084	+	25.4084i	−0.804691	+	0.804691i	0.179134	+	0.983825i	$0.442670\pi$
$998$		0			0
$999$		−	4.68052i		−	0.148085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.u.a.1231.1		64
4.3	odd	2		336.2.u.a.139.10	yes	64
7.6	odd	2	inner	1344.2.u.a.1231.32		64
16.3	odd	4	inner	1344.2.u.a.559.32		64
16.13	even	4		336.2.u.a.307.9	yes	64
28.27	even	2		336.2.u.a.139.9	✓	64
112.13	odd	4		336.2.u.a.307.10	yes	64
112.83	even	4	inner	1344.2.u.a.559.1		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.9	✓	64	28.27	even	2
336.2.u.a.139.10	yes	64	4.3	odd	2
336.2.u.a.307.9	yes	64	16.13	even	4
336.2.u.a.307.10	yes	64	112.13	odd	4
1344.2.u.a.559.1		64	112.83	even	4	inner
1344.2.u.a.559.32		64	16.3	odd	4	inner
1344.2.u.a.1231.1		64	1.1	even	1	trivial
1344.2.u.a.1231.32		64	7.6	odd	2	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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(3.13913 - 3.13913i) q^{5} +(-1.14645 - 2.38446i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(3.13913 - 3.13913i) q^{5} +(-1.14645 - 2.38446i) q^{7} -1.00000i q^{9} +(-0.422784 + 0.422784i) q^{11} +(3.06112 + 3.06112i) q^{13} +4.43939i q^{15} +2.56875i q^{17} +(0.955253 - 0.955253i) q^{19} +(2.49673 + 0.875401i) q^{21} +5.93702 q^{23} -14.7082i q^{25} +(0.707107 + 0.707107i) q^{27} +(1.07143 - 1.07143i) q^{29} +5.77245 q^{31} -0.597907i q^{33} +(-11.0840 - 3.88625i) q^{35} +(-3.30963 - 3.30963i) q^{37} -4.32908 q^{39} -6.17767 q^{41} +(3.35840 - 3.35840i) q^{43} +(-3.13913 - 3.13913i) q^{45} -4.38522 q^{47} +(-4.37128 + 5.46735i) q^{49} +(-1.81638 - 1.81638i) q^{51} +(-7.85667 - 7.85667i) q^{53} +2.65434i q^{55} +1.35093i q^{57} +(-5.63360 - 5.63360i) q^{59} +(0.351526 + 0.351526i) q^{61} +(-2.38446 + 1.14645i) q^{63} +19.2185 q^{65} +(-7.37756 - 7.37756i) q^{67} +(-4.19810 + 4.19810i) q^{69} +4.30558 q^{71} +6.71670 q^{73} +(10.4003 + 10.4003i) q^{75} +(1.49281 + 0.523408i) q^{77} -8.39558i q^{79} -1.00000 q^{81} +(6.54381 - 6.54381i) q^{83} +(8.06362 + 8.06362i) q^{85} +1.51523i q^{87} +14.8890 q^{89} +(3.78968 - 10.8086i) q^{91} +(-4.08174 + 4.08174i) q^{93} -5.99732i q^{95} +3.86266i q^{97} +(0.422784 + 0.422784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Introduction

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