LMFDB - Embedded newform 1680.2.bl.c.127.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(127,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.5
Root			$1.19252 - 0.760198i$ of defining polynomial
Character	$\chi$	$=$	1680.127
Dual form			1680.2.bl.c.463.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(0.432320 + 2.19388i) q^{5} +(-0.707107 + 0.707107i) q^{7} +1.00000i q^{9} -2.82843i q^{11} +(-1.76156 + 1.76156i) q^{13} +(-1.24561 + 1.85700i) q^{15} +(0.896916 + 0.896916i) q^{17} +1.07700 q^{19} -1.00000 q^{21} +(3.29404 + 3.29404i) q^{23} +(-4.62620 + 1.89692i) q^{25} +(-0.707107 + 0.707107i) q^{27} +7.25240i q^{29} +3.52258i q^{31} +(2.00000 - 2.00000i) q^{33} +(-1.85700 - 1.24561i) q^{35} +(1.00000 + 1.00000i) q^{37} -2.49122 q^{39} -9.64015 q^{41} +(4.05121 + 4.05121i) q^{43} +(-2.19388 + 0.432320i) q^{45} +(-1.22279 + 1.22279i) q^{47} -1.00000i q^{49} +1.26843i q^{51} +(-1.49084 + 1.49084i) q^{53} +(6.20522 - 1.22279i) q^{55} +(0.761557 + 0.761557i) q^{57} -10.2564 q^{59} -8.98168 q^{61} +(-0.707107 - 0.707107i) q^{63} +(-4.62620 - 3.10308i) q^{65} +(1.22279 - 1.22279i) q^{67} +4.65847i q^{69} -14.3077i q^{71} +(-3.01395 + 3.01395i) q^{73} +(-4.61254 - 1.92989i) q^{75} +(2.00000 + 2.00000i) q^{77} +10.2564 q^{79} -1.00000 q^{81} +(-3.37680 - 3.37680i) q^{83} +(-1.57997 + 2.35548i) q^{85} +(-5.12822 + 5.12822i) q^{87} +1.40608i q^{89} -2.49122i q^{91} +(-2.49084 + 2.49084i) q^{93} +(0.465611 + 2.36282i) q^{95} +(-1.49084 - 1.49084i) q^{97} +2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{13} - 4 q^{17} - 12 q^{21} - 20 q^{25} + 24 q^{33} + 12 q^{37} + 16 q^{41} + 4 q^{45} + 28 q^{53} - 16 q^{57} - 16 q^{61} - 20 q^{65} + 60 q^{73} + 24 q^{77} - 12 q^{81} - 84 q^{85} + 16 q^{93}+ \cdots + 28 q^{97}+O(q^{100}) $ 12 * q + 4 * q^13 - 4 * q^17 - 12 * q^21 - 20 * q^25 + 24 * q^33 + 12 * q^37 + 16 * q^41 + 4 * q^45 + 28 * q^53 - 16 * q^57 - 16 * q^61 - 20 * q^65 + 60 * q^73 + 24 * q^77 - 12 * q^81 - 84 * q^85 + 16 * q^93 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	0.432320	+	2.19388i	0.193340	+	0.981132i
$5$	0.432320	+	2.19388i	0.193340	+	0.981132i
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	2.82843i		−	0.852803i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$		−	2.82843i		−	0.852803i	0.904534	−	0.426401i	$-0.140219\pi$
$12$		0			0
$13$	−1.76156	+	1.76156i	−0.488568	+	0.488568i	−0.907854	−	0.419286i	$-0.862280\pi$
$13$	−1.76156	+	1.76156i	−0.488568	+	0.488568i	0.419286	+	0.907854i	$0.362280\pi$
$14$		0			0
$15$	−1.24561	+	1.85700i	−0.321615	+	0.479476i
$16$		0			0
$17$	0.896916	+	0.896916i	0.217534	+	0.217534i	0.807459	−	0.589924i	$-0.200842\pi$
$17$	0.896916	+	0.896916i	0.217534	+	0.217534i	−0.589924	+	0.807459i	$0.700842\pi$
$18$		0			0
$19$	1.07700			0.247082			0.123541	−	0.992339i	$-0.460575\pi$
$19$	1.07700			0.247082			0.123541	+	0.992339i	$0.460575\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	3.29404	+	3.29404i	0.686854	+	0.686854i	0.961535	−	0.274681i	$-0.0885722\pi$
$23$	3.29404	+	3.29404i	0.686854	+	0.686854i	−0.274681	+	0.961535i	$0.588572\pi$
$24$		0			0
$25$	−4.62620	+	1.89692i	−0.925240	+	0.379383i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$			7.25240i			1.34674i	0.739307	+	0.673368i	$0.235153\pi$
$29$			7.25240i			1.34674i	−0.739307	+	0.673368i	$0.764847\pi$
$30$		0			0
$31$			3.52258i			0.632674i	0.948647	+	0.316337i	$0.102453\pi$
$31$			3.52258i			0.632674i	−0.948647	+	0.316337i	$0.897547\pi$
$32$		0			0
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$		0			0
$35$	−1.85700	−	1.24561i	−0.313891	−	0.210546i
$36$		0			0
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	0.784512	−	0.620113i	$-0.212913\pi$
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	−0.620113	+	0.784512i	$0.712913\pi$
$38$		0			0
$39$	−2.49122			−0.398914
$40$		0			0
$41$	−9.64015			−1.50554			−0.752769	−	0.658284i	$-0.771282\pi$
$41$	−9.64015			−1.50554			−0.752769	+	0.658284i	$0.771282\pi$
$42$		0			0
$43$	4.05121	+	4.05121i	0.617804	+	0.617804i	0.944968	−	0.327163i	$-0.106093\pi$
$43$	4.05121	+	4.05121i	0.617804	+	0.617804i	−0.327163	+	0.944968i	$0.606093\pi$
$44$		0			0
$45$	−2.19388	+	0.432320i	−0.327044	+	0.0644465i
$46$		0			0
$47$	−1.22279	+	1.22279i	−0.178362	+	0.178362i	−0.790641	−	0.612280i	$-0.790253\pi$
$47$	−1.22279	+	1.22279i	−0.178362	+	0.178362i	0.612280	+	0.790641i	$0.290253\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$			1.26843i			0.177616i
$52$		0			0
$53$	−1.49084	+	1.49084i	−0.204782	+	0.204782i	−0.802045	−	0.597263i	$-0.796255\pi$
$53$	−1.49084	+	1.49084i	−0.204782	+	0.204782i	0.597263	+	0.802045i	$0.296255\pi$
$54$		0			0
$55$	6.20522	−	1.22279i	0.836712	−	0.164881i
$56$		0			0
$57$	0.761557	+	0.761557i	0.100871	+	0.100871i
$58$		0			0
$59$	−10.2564			−1.33527			−0.667637	−	0.744487i	$-0.732694\pi$
$59$	−10.2564			−1.33527			−0.667637	+	0.744487i	$0.732694\pi$
$60$		0			0
$61$	−8.98168			−1.14999			−0.574993	−	0.818158i	$-0.694995\pi$
$61$	−8.98168			−1.14999			−0.574993	+	0.818158i	$0.694995\pi$
$62$		0			0
$63$	−0.707107	−	0.707107i	−0.0890871	−	0.0890871i
$64$		0			0
$65$	−4.62620	−	3.10308i	−0.573809	−	0.384890i
$66$		0			0
$67$	1.22279	−	1.22279i	0.149387	−	0.149387i	−0.628457	−	0.777844i	$-0.716313\pi$
$67$	1.22279	−	1.22279i	0.149387	−	0.149387i	0.777844	+	0.628457i	$0.216313\pi$
$68$		0			0
$69$			4.65847i			0.560814i
$70$		0			0
$71$		−	14.3077i		−	1.69801i	−0.528388	−	0.849003i	$-0.677203\pi$
$71$		−	14.3077i		−	1.69801i	0.528388	−	0.849003i	$-0.322797\pi$
$72$		0			0
$73$	−3.01395	+	3.01395i	−0.352757	+	0.352757i	−0.861134	−	0.508378i	$-0.830245\pi$
$73$	−3.01395	+	3.01395i	−0.352757	+	0.352757i	0.508378	+	0.861134i	$0.330245\pi$
$74$		0			0
$75$	−4.61254	−	1.92989i	−0.532610	−	0.222845i
$76$		0			0
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$		0			0
$79$	10.2564			1.15394			0.576970	−	0.816766i	$-0.304235\pi$
$79$	10.2564			1.15394			0.576970	+	0.816766i	$0.304235\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−3.37680	−	3.37680i	−0.370651	−	0.370651i	0.497063	−	0.867714i	$-0.334412\pi$
$83$	−3.37680	−	3.37680i	−0.370651	−	0.370651i	−0.867714	+	0.497063i	$0.834412\pi$
$84$		0			0
$85$	−1.57997	+	2.35548i	−0.171372	+	0.255488i
$86$		0			0
$87$	−5.12822	+	5.12822i	−0.549803	+	0.549803i
$88$		0			0
$89$			1.40608i			0.149044i	0.997219	+	0.0745219i	$0.0237431\pi$
$89$			1.40608i			0.149044i	−0.997219	+	0.0745219i	$0.976257\pi$
$90$		0			0
$91$		−	2.49122i		−	0.261151i
$92$		0			0
$93$	−2.49084	+	2.49084i	−0.258288	+	0.258288i
$94$		0			0
$95$	0.465611	+	2.36282i	0.0477707	+	0.242420i
$96$		0			0
$97$	−1.49084	−	1.49084i	−0.151372	−	0.151372i	0.627359	−	0.778730i	$-0.284136\pi$
$97$	−1.49084	−	1.49084i	−0.151372	−	0.151372i	−0.778730	+	0.627359i	$0.784136\pi$
$98$		0			0
$99$	2.82843			0.284268
$100$		0			0
$101$	−3.61224			−0.359432			−0.179716	−	0.983719i	$-0.557518\pi$
$101$	−3.61224			−0.359432			−0.179716	+	0.983719i	$0.557518\pi$
$102$		0			0
$103$	−1.45986	−	1.45986i	−0.143844	−	0.143844i	0.631518	−	0.775362i	$-0.282432\pi$
$103$	−1.45986	−	1.45986i	−0.143844	−	0.143844i	−0.775362	+	0.631518i	$0.782432\pi$
$104$		0			0
$105$	−0.432320	−	2.19388i	−0.0421902	−	0.214101i
$106$		0			0
$107$	2.36282	−	2.36282i	0.228422	−	0.228422i	−0.583611	−	0.812033i	$-0.698361\pi$
$107$	2.36282	−	2.36282i	0.228422	−	0.228422i	0.812033	+	0.583611i	$0.198361\pi$
$108$		0			0
$109$			12.2986i			1.17799i	0.808135	+	0.588997i	$0.200477\pi$
$109$			12.2986i			1.17799i	−0.808135	+	0.588997i	$0.799523\pi$
$110$		0			0
$111$			1.41421i			0.134231i
$112$		0			0
$113$	2.23844	−	2.23844i	0.210575	−	0.210575i	−0.593937	−	0.804512i	$-0.702427\pi$
$113$	2.23844	−	2.23844i	0.210575	−	0.210575i	0.804512	+	0.593937i	$0.202427\pi$
$114$		0			0
$115$	−5.80264	+	8.65080i	−0.541099	+	0.806691i
$116$		0			0
$117$	−1.76156	−	1.76156i	−0.162856	−	0.162856i
$118$		0			0
$119$	−1.26843			−0.116277
$120$		0			0
$121$	3.00000			0.272727
$122$		0			0
$123$	−6.81662	−	6.81662i	−0.614634	−	0.614634i
$124$		0			0
$125$	−6.16160	−	9.32924i	−0.551110	−	0.834432i
$126$		0			0
$127$	9.58202	−	9.58202i	0.850267	−	0.850267i	−0.139899	−	0.990166i	$-0.544678\pi$
$127$	9.58202	−	9.58202i	0.850267	−	0.850267i	0.990166	+	0.139899i	$0.0446778\pi$
$128$		0			0
$129$			5.72928i			0.504435i
$130$		0			0
$131$			4.59958i			0.401867i	0.979605	+	0.200934i	$0.0643976\pi$
$131$			4.59958i			0.401867i	−0.979605	+	0.200934i	$0.935602\pi$
$132$		0			0
$133$	−0.761557	+	0.761557i	−0.0660354	+	0.0660354i
$134$		0			0
$135$	−1.85700	−	1.24561i	−0.159825	−	0.107205i
$136$		0			0
$137$	−1.28467	−	1.28467i	−0.109757	−	0.109757i	0.650096	−	0.759852i	$-0.274729\pi$
$137$	−1.28467	−	1.28467i	−0.109757	−	0.109757i	−0.759852	+	0.650096i	$0.774729\pi$
$138$		0			0
$139$	16.9903			1.44110			0.720549	−	0.693404i	$-0.243890\pi$
$139$	16.9903			1.44110			0.720549	+	0.693404i	$0.243890\pi$
$140$		0			0
$141$	−1.72928			−0.145632
$142$		0			0
$143$	4.98244	+	4.98244i	0.416652	+	0.416652i
$144$		0			0
$145$	−15.9109	+	3.13536i	−1.32133	+	0.260377i
$146$		0			0
$147$	0.707107	−	0.707107i	0.0583212	−	0.0583212i
$148$		0			0
$149$			17.0462i			1.39648i	0.715863	+	0.698241i	$0.246033\pi$
$149$			17.0462i			1.39648i	−0.715863	+	0.698241i	$0.753967\pi$
$150$		0			0
$151$		−	17.7757i		−	1.44657i	−0.690550	−	0.723284i	$-0.742632\pi$
$151$		−	17.7757i		−	1.44657i	0.690550	−	0.723284i	$-0.257368\pi$
$152$		0			0
$153$	−0.896916	+	0.896916i	−0.0725114	+	0.0725114i
$154$		0			0
$155$	−7.72811	+	1.52288i	−0.620736	+	0.122321i
$156$		0			0
$157$	15.0140	+	15.0140i	1.19824	+	1.19824i	0.974692	+	0.223552i	$0.0717652\pi$
$157$	15.0140	+	15.0140i	1.19824	+	1.19824i	0.223552	+	0.974692i	$0.428235\pi$
$158$		0			0
$159$	−2.10836			−0.167204
$160$		0			0
$161$	−4.65847			−0.367139
$162$		0			0
$163$	12.7933	+	12.7933i	1.00205	+	1.00205i	0.999998	+	0.00205064i	$0.000652741\pi$
$163$	12.7933	+	12.7933i	1.00205	+	1.00205i	0.00205064	+	0.999998i	$0.499347\pi$
$164$		0			0
$165$	5.25240	+	3.52311i	0.408898	+	0.274274i
$166$		0			0
$167$	−2.53686	+	2.53686i	−0.196308	+	0.196308i	−0.798415	−	0.602107i	$-0.794328\pi$
$167$	−2.53686	+	2.53686i	−0.196308	+	0.196308i	0.602107	+	0.798415i	$0.294328\pi$
$168$		0			0
$169$			6.79383i			0.522603i
$170$		0			0
$171$			1.07700i			0.0823606i
$172$		0			0
$173$	7.10308	−	7.10308i	0.540037	−	0.540037i	−0.383502	−	0.923540i	$-0.625282\pi$
$173$	7.10308	−	7.10308i	0.540037	−	0.540037i	0.923540	+	0.383502i	$0.125282\pi$
$174$		0			0
$175$	1.92989	−	4.61254i	0.145886	−	0.348675i
$176$		0			0
$177$	−7.25240	−	7.25240i	−0.545123	−	0.545123i
$178$		0			0
$179$	−9.41650			−0.703823			−0.351911	−	0.936033i	$-0.614468\pi$
$179$	−9.41650			−0.703823			−0.351911	+	0.936033i	$0.614468\pi$
$180$		0			0
$181$	14.2341			1.05801			0.529005	−	0.848619i	$-0.322565\pi$
$181$	14.2341			1.05801			0.529005	+	0.848619i	$0.322565\pi$
$182$		0			0
$183$	−6.35101	−	6.35101i	−0.469480	−	0.469480i
$184$		0			0
$185$	−1.76156	+	2.62620i	−0.129512	+	0.193082i
$186$		0			0
$187$	2.53686	−	2.53686i	0.185514	−	0.185514i
$188$		0			0
$189$		−	1.00000i		−	0.0727393i
$190$		0			0
$191$			15.2389i			1.10265i	0.834292	+	0.551323i	$0.185877\pi$
$191$			15.2389i			1.10265i	−0.834292	+	0.551323i	$0.814123\pi$
$192$		0			0
$193$	15.7755	−	15.7755i	1.13555	−	1.13555i	0.146307	−	0.989239i	$-0.453261\pi$
$193$	15.7755	−	15.7755i	1.13555	−	1.13555i	0.989239	−	0.146307i	$-0.0467387\pi$
$194$		0			0
$195$	−1.07700	−	5.46543i	−0.0771259	−	0.391387i
$196$		0			0
$197$	18.5371	+	18.5371i	1.32071	+	1.32071i	0.913200	+	0.407511i	$0.133603\pi$
$197$	18.5371	+	18.5371i	1.32071	+	1.32071i	0.407511	+	0.913200i	$0.366397\pi$
$198$		0			0
$199$	22.3556			1.58475			0.792373	−	0.610037i	$-0.208846\pi$
$199$	22.3556			1.58475			0.792373	+	0.610037i	$0.208846\pi$
$200$		0			0
$201$	1.72928			0.121974
$202$		0			0
$203$	−5.12822	−	5.12822i	−0.359930	−	0.359930i
$204$		0			0
$205$	−4.16763	−	21.1493i	−0.291080	−	1.47713i
$206$		0			0
$207$	−3.29404	+	3.29404i	−0.228951	+	0.228951i
$208$		0			0
$209$		−	3.04623i		−	0.210712i
$210$		0			0
$211$		−	5.65685i		−	0.389434i	−0.980859	−	0.194717i	$-0.937621\pi$
$211$		−	5.65685i		−	0.389434i	0.980859	−	0.194717i	$-0.0623788\pi$
$212$		0			0
$213$	10.1170	−	10.1170i	0.693208	−	0.693208i
$214$		0			0
$215$	−7.13645	+	10.6393i	−0.486702	+	0.725594i
$216$		0			0
$217$	−2.49084	−	2.49084i	−0.169089	−	0.169089i
$218$		0			0
$219$	−4.26237			−0.288025
$220$		0			0
$221$	−3.15994			−0.212560
$222$		0			0
$223$	−9.94514	−	9.94514i	−0.665976	−	0.665976i	0.290806	−	0.956782i	$-0.406077\pi$
$223$	−9.94514	−	9.94514i	−0.665976	−	0.665976i	−0.956782	+	0.290806i	$0.906077\pi$
$224$		0			0
$225$	−1.89692	−	4.62620i	−0.126461	−	0.308413i
$226$		0			0
$227$	−14.8560	+	14.8560i	−0.986029	+	0.986029i	−0.999904	−	0.0138751i	$-0.995583\pi$
$227$	−14.8560	+	14.8560i	−0.986029	+	0.986029i	0.0138751	+	0.999904i	$0.495583\pi$
$228$		0			0
$229$			4.20617i			0.277951i	0.990296	+	0.138976i	$0.0443810\pi$
$229$			4.20617i			0.277951i	−0.990296	+	0.138976i	$0.955619\pi$
$230$		0			0
$231$			2.82843i			0.186097i
$232$		0			0
$233$	−5.55539	+	5.55539i	−0.363946	+	0.363946i	−0.865263	−	0.501318i	$-0.832849\pi$
$233$	−5.55539	+	5.55539i	−0.363946	+	0.363946i	0.501318	+	0.865263i	$0.332849\pi$
$234$		0			0
$235$	−3.21128	−	2.15401i	−0.209481	−	0.140512i
$236$		0			0
$237$	7.25240	+	7.25240i	0.471094	+	0.471094i
$238$		0			0
$239$	−3.92516			−0.253898			−0.126949	−	0.991909i	$-0.540518\pi$
$239$	−3.92516			−0.253898			−0.126949	+	0.991909i	$0.540518\pi$
$240$		0			0
$241$	−19.2524			−1.24016			−0.620078	−	0.784540i	$-0.712899\pi$
$241$	−19.2524			−1.24016			−0.620078	+	0.784540i	$0.712899\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	2.19388	−	0.432320i	0.140162	−	0.0276199i
$246$		0			0
$247$	−1.89721	+	1.89721i	−0.120716	+	0.120716i
$248$		0			0
$249$		−	4.77551i		−	0.302636i
$250$		0			0
$251$		−	22.6669i		−	1.43072i	−0.698756	−	0.715360i	$-0.746263\pi$
$251$		−	22.6669i		−	1.43072i	0.698756	−	0.715360i	$-0.253737\pi$
$252$		0			0
$253$	9.31695	−	9.31695i	0.585751	−	0.585751i
$254$		0			0
$255$	−2.78278	+	0.548369i	−0.174265	+	0.0343402i
$256$		0			0
$257$	−5.28467	−	5.28467i	−0.329649	−	0.329649i	0.522804	−	0.852453i	$-0.324886\pi$
$257$	−5.28467	−	5.28467i	−0.329649	−	0.329649i	−0.852453	+	0.522804i	$0.824886\pi$
$258$		0			0
$259$	−1.41421			−0.0878750
$260$		0			0
$261$	−7.25240			−0.448912
$262$		0			0
$263$	5.19124	+	5.19124i	0.320106	+	0.320106i	0.848808	−	0.528702i	$-0.177321\pi$
$263$	5.19124	+	5.19124i	0.320106	+	0.320106i	−0.528702	+	0.848808i	$0.677321\pi$
$264$		0			0
$265$	−3.91524	−	2.62620i	−0.240511	−	0.161326i
$266$		0			0
$267$	−0.994247	+	0.994247i	−0.0608469	+	0.0608469i
$268$		0			0
$269$		−	11.9754i		−	0.730154i	−0.930977	−	0.365077i	$-0.881043\pi$
$269$		−	11.9754i		−	0.730154i	0.930977	−	0.365077i	$-0.118957\pi$
$270$		0			0
$271$			19.9100i			1.20945i	0.796435	+	0.604724i	$0.206716\pi$
$271$			19.9100i			1.20945i	−0.796435	+	0.604724i	$0.793284\pi$
$272$		0			0
$273$	1.76156	−	1.76156i	0.106614	−	0.106614i
$274$		0			0
$275$	5.36529	+	13.0849i	0.323539	+	0.789047i
$276$		0			0
$277$	14.2524	+	14.2524i	0.856343	+	0.856343i	0.990905	−	0.134562i	$-0.0429627\pi$
$277$	14.2524	+	14.2524i	0.856343	+	0.856343i	−0.134562	+	0.990905i	$0.542963\pi$
$278$		0			0
$279$	−3.52258			−0.210891
$280$		0			0
$281$	3.25240			0.194022			0.0970108	−	0.995283i	$-0.469072\pi$
$281$	3.25240			0.194022			0.0970108	+	0.995283i	$0.469072\pi$
$282$		0			0
$283$	21.2983	+	21.2983i	1.26605	+	1.26605i	0.948110	+	0.317944i	$0.102992\pi$
$283$	21.2983	+	21.2983i	1.26605	+	1.26605i	0.317944	+	0.948110i	$0.397008\pi$
$284$		0			0
$285$	−1.34153	+	2.00000i	−0.0794652	+	0.118470i
$286$		0			0
$287$	6.81662	−	6.81662i	0.402372	−	0.402372i
$288$		0			0
$289$		−	15.3911i		−	0.905358i
$290$		0			0
$291$		−	2.10836i		−	0.123595i
$292$		0			0
$293$	15.0785	−	15.0785i	0.880896	−	0.880896i	−0.112730	−	0.993626i	$-0.535960\pi$
$293$	15.0785	−	15.0785i	0.880896	−	0.880896i	0.993626	+	0.112730i	$0.0359595\pi$
$294$		0			0
$295$	−4.43407	−	22.5014i	−0.258161	−	1.31008i
$296$		0			0
$297$	2.00000	+	2.00000i	0.116052	+	0.116052i
$298$		0			0
$299$	−11.6053			−0.671150
$300$		0			0
$301$	−5.72928			−0.330230
$302$		0			0
$303$	−2.55424	−	2.55424i	−0.146737	−	0.146737i
$304$		0			0
$305$	−3.88296	−	19.7047i	−0.222338	−	1.12829i
$306$		0			0
$307$	7.81086	−	7.81086i	0.445790	−	0.445790i	−0.448163	−	0.893952i	$-0.647921\pi$
$307$	7.81086	−	7.81086i	0.445790	−	0.445790i	0.893952	+	0.448163i	$0.147921\pi$
$308$		0			0
$309$		−	2.06455i		−	0.117448i
$310$		0			0
$311$			23.7636i			1.34751i	0.738954	+	0.673756i	$0.235320\pi$
$311$			23.7636i			1.34751i	−0.738954	+	0.673756i	$0.764680\pi$
$312$		0			0
$313$	14.2384	−	14.2384i	0.804804	−	0.804804i	−0.179038	−	0.983842i	$-0.557298\pi$
$313$	14.2384	−	14.2384i	0.804804	−	0.804804i	0.983842	+	0.179038i	$0.0572984\pi$
$314$		0			0
$315$	1.24561	−	1.85700i	0.0701821	−	0.104630i
$316$		0			0
$317$	11.7616	+	11.7616i	0.660595	+	0.660595i	0.955520	−	0.294925i	$-0.0952948\pi$
$317$	11.7616	+	11.7616i	0.660595	+	0.660595i	−0.294925	+	0.955520i	$0.595295\pi$
$318$		0			0
$319$	20.5129			1.14850
$320$		0			0
$321$	3.34153			0.186506
$322$		0			0
$323$	0.965983	+	0.965983i	0.0537487	+	0.0537487i
$324$		0			0
$325$	4.80779	−	11.4908i	0.266688	−	0.637397i
$326$		0			0
$327$	−8.69644	+	8.69644i	−0.480914	+	0.480914i
$328$		0			0
$329$		−	1.72928i		−	0.0953384i
$330$		0			0
$331$			11.6447i			0.640053i	0.947409	+	0.320026i	$0.103692\pi$
$331$			11.6447i			0.640053i	−0.947409	+	0.320026i	$0.896308\pi$
$332$		0			0
$333$	−1.00000	+	1.00000i	−0.0547997	+	0.0547997i
$334$		0			0
$335$	3.21128	+	2.15401i	0.175451	+	0.117686i
$336$		0			0
$337$	−13.8401	−	13.8401i	−0.753916	−	0.753916i	0.221292	−	0.975208i	$-0.428973\pi$
$337$	−13.8401	−	13.8401i	−0.753916	−	0.753916i	−0.975208	+	0.221292i	$0.928973\pi$
$338$		0			0
$339$	3.16564			0.171934
$340$		0			0
$341$	9.96336			0.539546
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	−10.2201	+	2.01395i	−0.550233	+	0.108428i
$346$		0			0
$347$	8.56804	−	8.56804i	0.459956	−	0.459956i	−0.438685	−	0.898641i	$-0.644555\pi$
$347$	8.56804	−	8.56804i	0.459956	−	0.459956i	0.898641	+	0.438685i	$0.144555\pi$
$348$		0			0
$349$			7.43066i			0.397754i	0.980024	+	0.198877i	$0.0637294\pi$
$349$			7.43066i			0.397754i	−0.980024	+	0.198877i	$0.936271\pi$
$350$		0			0
$351$		−	2.49122i		−	0.132971i
$352$		0			0
$353$	22.0602	−	22.0602i	1.17415	−	1.17415i	0.192933	−	0.981212i	$-0.438200\pi$
$353$	22.0602	−	22.0602i	1.17415	−	1.17415i	0.981212	−	0.192933i	$-0.0618000\pi$
$354$		0			0
$355$	31.3892	−	6.18549i	1.66597	−	0.328292i
$356$		0			0
$357$	−0.896916	−	0.896916i	−0.0474698	−	0.0474698i
$358$		0			0
$359$	−22.2446			−1.17402			−0.587012	−	0.809579i	$-0.699696\pi$
$359$	−22.2446			−1.17402			−0.587012	+	0.809579i	$0.699696\pi$
$360$		0			0
$361$	−17.8401			−0.938951
$362$		0			0
$363$	2.12132	+	2.12132i	0.111340	+	0.111340i
$364$		0			0
$365$	−7.91524	−	5.30925i	−0.414303	−	0.277899i
$366$		0			0
$367$	−19.4359	+	19.4359i	−1.01454	+	1.01454i	−0.0146515	+	0.999893i	$0.504664\pi$
$367$	−19.4359	+	19.4359i	−1.01454	+	1.01454i	−0.999893	+	0.0146515i	$0.995336\pi$
$368$		0			0
$369$		−	9.64015i		−	0.501846i
$370$		0			0
$371$		−	2.10836i		−	0.109461i
$372$		0			0
$373$	25.8034	−	25.8034i	1.33605	−	1.33605i	0.436201	−	0.899849i	$-0.356324\pi$
$373$	25.8034	−	25.8034i	1.33605	−	1.33605i	0.899849	−	0.436201i	$-0.143676\pi$
$374$		0			0
$375$	2.23986	−	10.9537i	0.115666	−	0.565645i
$376$		0			0
$377$	−12.7755	−	12.7755i	−0.657972	−	0.657972i
$378$		0			0
$379$	23.2500			1.19427			0.597136	−	0.802140i	$-0.296305\pi$
$379$	23.2500			1.19427			0.597136	+	0.802140i	$0.296305\pi$
$380$		0			0
$381$	13.5510			0.694240
$382$		0			0
$383$	1.31408	+	1.31408i	0.0671461	+	0.0671461i	0.739882	−	0.672736i	$-0.234881\pi$
$383$	1.31408	+	1.31408i	0.0671461	+	0.0671461i	−0.672736	+	0.739882i	$0.734881\pi$
$384$		0			0
$385$	−3.52311	+	5.25240i	−0.179555	+	0.267687i
$386$		0			0
$387$	−4.05121	+	4.05121i	−0.205935	+	0.205935i
$388$		0			0
$389$		−	10.7755i		−	0.546340i	−0.961966	−	0.273170i	$-0.911928\pi$
$389$		−	10.7755i		−	0.546340i	0.961966	−	0.273170i	$-0.0880722\pi$
$390$		0			0
$391$			5.90895i			0.298829i
$392$		0			0
$393$	−3.25240	+	3.25240i	−0.164062	+	0.164062i
$394$		0			0
$395$	4.43407	+	22.5014i	0.223102	+	1.13217i
$396$		0			0
$397$	−0.173892	−	0.173892i	−0.00872739	−	0.00872739i	0.702730	−	0.711457i	$-0.251964\pi$
$397$	−0.173892	−	0.173892i	−0.00872739	−	0.00872739i	−0.711457	+	0.702730i	$0.751964\pi$
$398$		0			0
$399$	−1.07700			−0.0539177
$400$		0			0
$401$	11.7293			0.585732			0.292866	−	0.956153i	$-0.405391\pi$
$401$	11.7293			0.585732			0.292866	+	0.956153i	$0.405391\pi$
$402$		0			0
$403$	−6.20522	−	6.20522i	−0.309104	−	0.309104i
$404$		0			0
$405$	−0.432320	−	2.19388i	−0.0214822	−	0.109015i
$406$		0			0
$407$	2.82843	−	2.82843i	0.140200	−	0.140200i
$408$		0			0
$409$			18.9046i			0.934773i	0.884053	+	0.467386i	$0.154804\pi$
$409$			18.9046i			0.934773i	−0.884053	+	0.467386i	$0.845196\pi$
$410$		0			0
$411$		−	1.81680i		−	0.0896161i
$412$		0			0
$413$	7.25240	−	7.25240i	0.356867	−	0.356867i
$414$		0			0
$415$	5.94842	−	8.86813i	0.291996	−	0.435320i
$416$		0			0
$417$	12.0140	+	12.0140i	0.588326	+	0.588326i
$418$		0			0
$419$	−25.8387			−1.26230			−0.631151	−	0.775660i	$-0.717417\pi$
$419$	−25.8387			−1.26230			−0.631151	+	0.775660i	$0.717417\pi$
$420$		0			0
$421$	21.2158			1.03399			0.516996	−	0.855988i	$-0.327050\pi$
$421$	21.2158			1.03399			0.516996	+	0.855988i	$0.327050\pi$
$422$		0			0
$423$	−1.22279	−	1.22279i	−0.0594539	−	0.0594539i
$424$		0			0
$425$	−5.85069	−	2.44794i	−0.283800	−	0.118742i
$426$		0			0
$427$	6.35101	−	6.35101i	0.307347	−	0.307347i
$428$		0			0
$429$			7.04623i			0.340195i
$430$		0			0
$431$		−	40.4774i		−	1.94973i	−0.222804	−	0.974863i	$-0.571521\pi$
$431$		−	40.4774i		−	1.94973i	0.222804	−	0.974863i	$-0.428479\pi$
$432$		0			0
$433$	18.9494	−	18.9494i	0.910650	−	0.910650i	−0.0856731	−	0.996323i	$-0.527304\pi$
$433$	18.9494	−	18.9494i	0.910650	−	0.910650i	0.996323	+	0.0856731i	$0.0273041\pi$
$434$		0			0
$435$	−13.4677	−	9.03365i	−0.645728	−	0.433130i
$436$		0			0
$437$	3.54769	+	3.54769i	0.169709	+	0.169709i
$438$		0			0
$439$	−14.5447			−0.694182			−0.347091	−	0.937832i	$-0.612830\pi$
$439$	−14.5447			−0.694182			−0.347091	+	0.937832i	$0.612830\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	−15.1561	−	15.1561i	−0.720089	−	0.720089i	0.248534	−	0.968623i	$-0.420051\pi$
$443$	−15.1561	−	15.1561i	−0.720089	−	0.720089i	−0.968623	+	0.248534i	$0.920051\pi$
$444$		0			0
$445$	−3.08476	+	0.607876i	−0.146232	+	0.0288161i
$446$		0			0
$447$	−12.0535	+	12.0535i	−0.570111	+	0.570111i
$448$		0			0
$449$			18.9538i			0.894484i	0.894413	+	0.447242i	$0.147594\pi$
$449$			18.9538i			0.894484i	−0.894413	+	0.447242i	$0.852406\pi$
$450$		0			0
$451$			27.2665i			1.28393i
$452$		0			0
$453$	12.5693	−	12.5693i	0.590559	−	0.590559i
$454$		0			0
$455$	5.46543	−	1.07700i	0.256223	−	0.0504907i
$456$		0			0
$457$	8.18785	+	8.18785i	0.383011	+	0.383011i	0.872186	−	0.489175i	$-0.162702\pi$
$457$	8.18785	+	8.18785i	0.383011	+	0.383011i	−0.489175	+	0.872186i	$0.662702\pi$
$458$		0			0
$459$	−1.26843			−0.0592053
$460$		0			0
$461$	−18.1170			−0.843795			−0.421897	−	0.906644i	$-0.638636\pi$
$461$	−18.1170			−0.843795			−0.421897	+	0.906644i	$0.638636\pi$
$462$		0			0
$463$	−14.1816	−	14.1816i	−0.659075	−	0.659075i	0.296086	−	0.955161i	$-0.404318\pi$
$463$	−14.1816	−	14.1816i	−0.659075	−	0.659075i	−0.955161	+	0.296086i	$0.904318\pi$
$464$		0			0
$465$	−6.54144	−	4.38776i	−0.303352	−	0.203477i
$466$		0			0
$467$	24.0157	−	24.0157i	1.11131	−	1.11131i	0.118342	−	0.992973i	$-0.462242\pi$
$467$	24.0157	−	24.0157i	1.11131	−	1.11131i	0.992973	−	0.118342i	$-0.0377579\pi$
$468$		0			0
$469$			1.72928i			0.0798508i
$470$		0			0
$471$			21.2329i			0.978362i
$472$		0			0
$473$	11.4586	−	11.4586i	0.526865	−	0.526865i
$474$		0			0
$475$	−4.98244	+	2.04299i	−0.228610	+	0.0937387i
$476$		0			0
$477$	−1.49084	−	1.49084i	−0.0682608	−	0.0682608i
$478$		0			0
$479$	12.8846			0.588712			0.294356	−	0.955696i	$-0.404895\pi$
$479$	12.8846			0.588712			0.294356	+	0.955696i	$0.404895\pi$
$480$		0			0
$481$	−3.52311			−0.160640
$482$		0			0
$483$	−3.29404	−	3.29404i	−0.149884	−	0.149884i
$484$		0			0
$485$	2.62620	−	3.91524i	0.119250	−	0.177782i
$486$		0			0
$487$	18.9072	−	18.9072i	0.856769	−	0.856769i	−0.134187	−	0.990956i	$-0.542842\pi$
$487$	18.9072	−	18.9072i	0.856769	−	0.856769i	0.990956	+	0.134187i	$0.0428424\pi$
$488$		0			0
$489$			18.0925i			0.818169i
$490$		0			0
$491$		−	33.1407i		−	1.49562i	−0.663915	−	0.747808i	$-0.731106\pi$
$491$		−	33.1407i		−	1.49562i	0.663915	−	0.747808i	$-0.268894\pi$
$492$		0			0
$493$	−6.50479	+	6.50479i	−0.292961	+	0.292961i
$494$		0			0
$495$	1.22279	+	6.20522i	0.0549602	+	0.278904i
$496$		0			0
$497$	10.1170	+	10.1170i	0.453811	+	0.453811i
$498$		0			0
$499$	−28.9069			−1.29405			−0.647025	−	0.762469i	$-0.723987\pi$
$499$	−28.9069			−1.29405			−0.647025	+	0.762469i	$0.723987\pi$
$500$		0			0
$501$	−3.58767			−0.160285
$502$		0			0
$503$	−8.35923	−	8.35923i	−0.372720	−	0.372720i	0.495747	−	0.868467i	$-0.334894\pi$
$503$	−8.35923	−	8.35923i	−0.372720	−	0.372720i	−0.868467	+	0.495747i	$0.834894\pi$
$504$		0			0
$505$	−1.56165	−	7.92482i	−0.0694924	−	0.352650i
$506$		0			0
$507$	−4.80397	+	4.80397i	−0.213352	+	0.213352i
$508$		0			0
$509$			23.3694i			1.03583i	0.855432	+	0.517916i	$0.173292\pi$
$509$			23.3694i			1.03583i	−0.855432	+	0.517916i	$0.826708\pi$
$510$		0			0
$511$		−	4.26237i		−	0.188556i
$512$		0			0
$513$	−0.761557	+	0.761557i	−0.0336236	+	0.0336236i
$514$		0			0
$515$	2.57162	−	3.83388i	0.113319	−	0.168941i
$516$		0			0
$517$	3.45856	+	3.45856i	0.152107	+	0.152107i
$518$		0			0
$519$	10.0453			0.440939
$520$		0			0
$521$	0.566016			0.0247976			0.0123988	−	0.999923i	$-0.496053\pi$
$521$	0.566016			0.0247976			0.0123988	+	0.999923i	$0.496053\pi$
$522$		0			0
$523$	10.6590	+	10.6590i	0.466087	+	0.466087i	0.900644	−	0.434558i	$-0.143095\pi$
$523$	10.6590	+	10.6590i	0.466087	+	0.466087i	−0.434558	+	0.900644i	$0.643095\pi$
$524$		0			0
$525$	4.62620	−	1.89692i	0.201904	−	0.0827882i
$526$		0			0
$527$	−3.15946	+	3.15946i	−0.137628	+	0.137628i
$528$		0			0
$529$		−	1.29862i		−	0.0564620i
$530$		0			0
$531$		−	10.2564i		−	0.445091i
$532$		0			0
$533$	16.9817	−	16.9817i	0.735558	−	0.735558i
$534$		0			0
$535$	6.20522	+	4.16224i	0.268275	+	0.179949i
$536$		0			0
$537$	−6.65847	−	6.65847i	−0.287334	−	0.287334i
$538$		0			0
$539$	−2.82843			−0.121829
$540$		0			0
$541$	2.80342			0.120528			0.0602642	−	0.998182i	$-0.480806\pi$
$541$	2.80342			0.120528			0.0602642	+	0.998182i	$0.480806\pi$
$542$		0			0
$543$	10.0650	+	10.0650i	0.431931	+	0.431931i
$544$		0			0
$545$	−26.9817	+	5.31695i	−1.15577	+	0.227753i
$546$		0			0
$547$	−15.7478	+	15.7478i	−0.673326	+	0.673326i	−0.958481	−	0.285155i	$-0.907955\pi$
$547$	−15.7478	+	15.7478i	−0.673326	+	0.673326i	0.285155	+	0.958481i	$0.407955\pi$
$548$		0			0
$549$		−	8.98168i		−	0.383329i
$550$		0			0
$551$			7.81086i			0.332754i
$552$		0			0
$553$	−7.25240	+	7.25240i	−0.308403	+	0.308403i
$554$		0			0
$555$	−3.10261	+	0.611393i	−0.131699	+	0.0259522i
$556$		0			0
$557$	17.5554	+	17.5554i	0.743846	+	0.743846i	0.973316	−	0.229470i	$-0.0736993\pi$
$557$	17.5554	+	17.5554i	0.743846	+	0.743846i	−0.229470	+	0.973316i	$0.573699\pi$
$558$		0			0
$559$	−14.2729			−0.603679
$560$		0			0
$561$	3.58767			0.151471
$562$		0			0
$563$	29.6378	+	29.6378i	1.24908	+	1.24908i	0.956125	+	0.292960i	$0.0946404\pi$
$563$	29.6378	+	29.6378i	1.24908	+	1.24908i	0.292960	+	0.956125i	$0.405360\pi$
$564$		0			0
$565$	5.87859	+	3.94315i	0.247314	+	0.165889i
$566$		0			0
$567$	0.707107	−	0.707107i	0.0296957	−	0.0296957i
$568$		0			0
$569$			2.36318i			0.0990695i	0.998772	+	0.0495347i	$0.0157739\pi$
$569$			2.36318i			0.0990695i	−0.998772	+	0.0495347i	$0.984226\pi$
$570$		0			0
$571$			3.21128i			0.134388i	0.997740	+	0.0671940i	$0.0214046\pi$
$571$			3.21128i			0.134388i	−0.997740	+	0.0671940i	$0.978595\pi$
$572$		0			0
$573$	−10.7755	+	10.7755i	−0.450153	+	0.450153i
$574$		0			0
$575$	−21.4874	−	8.99036i	−0.896086	−	0.374924i
$576$		0			0
$577$	−6.53707	−	6.53707i	−0.272142	−	0.272142i	0.557820	−	0.829962i	$-0.311638\pi$
$577$	−6.53707	−	6.53707i	−0.272142	−	0.272142i	−0.829962	+	0.557820i	$0.811638\pi$
$578$		0			0
$579$	22.3099			0.927170
$580$		0			0
$581$	4.77551			0.198122
$582$		0			0
$583$	4.21673	+	4.21673i	0.174639	+	0.174639i
$584$		0			0
$585$	3.10308	−	4.62620i	0.128297	−	0.191270i
$586$		0			0
$587$	22.8842	−	22.8842i	0.944533	−	0.944533i	−0.0540076	−	0.998541i	$-0.517200\pi$
$587$	22.8842	−	22.8842i	0.944533	−	0.944533i	0.998541	+	0.0540076i	$0.0171995\pi$
$588$		0			0
$589$			3.79383i			0.156322i
$590$		0			0
$591$			26.2154i			1.07836i
$592$		0			0
$593$	14.1493	−	14.1493i	0.581043	−	0.581043i	−0.354147	−	0.935190i	$-0.615229\pi$
$593$	14.1493	−	14.1493i	0.581043	−	0.581043i	0.935190	+	0.354147i	$0.115229\pi$
$594$		0			0
$595$	−0.548369	−	2.78278i	−0.0224809	−	0.114083i
$596$		0			0
$597$	15.8078	+	15.8078i	0.646970	+	0.646970i
$598$		0			0
$599$	−17.3534			−0.709041			−0.354521	−	0.935048i	$-0.615356\pi$
$599$	−17.3534			−0.709041			−0.354521	+	0.935048i	$0.615356\pi$
$600$		0			0
$601$	20.1570			0.822222			0.411111	−	0.911585i	$-0.365141\pi$
$601$	20.1570			0.822222			0.411111	+	0.911585i	$0.365141\pi$
$602$		0			0
$603$	1.22279	+	1.22279i	0.0497957	+	0.0497957i
$604$		0			0
$605$	1.29696	+	6.58163i	0.0527290	+	0.267581i
$606$		0			0
$607$	−0.785440	+	0.785440i	−0.0318800	+	0.0318800i	−0.722867	−	0.690987i	$-0.757176\pi$
$607$	−0.785440	+	0.785440i	−0.0318800	+	0.0318800i	0.690987	+	0.722867i	$0.257176\pi$
$608$		0			0
$609$		−	7.25240i		−	0.293882i
$610$		0			0
$611$		−	4.30802i		−	0.174284i
$612$		0			0
$613$	−32.0741	+	32.0741i	−1.29546	+	1.29546i	−0.364104	+	0.931358i	$0.618625\pi$
$613$	−32.0741	+	32.0741i	−1.29546	+	1.29546i	−0.931358	+	0.364104i	$0.881375\pi$
$614$		0			0
$615$	12.0079	−	17.9018i	0.484204	−	0.721870i
$616$		0			0
$617$	−15.6970	−	15.6970i	−0.631938	−	0.631938i	0.316616	−	0.948554i	$-0.397453\pi$
$617$	−15.6970	−	15.6970i	−0.631938	−	0.631938i	−0.948554	+	0.316616i	$0.897453\pi$
$618$		0			0
$619$	5.05399			0.203137			0.101569	−	0.994829i	$-0.467614\pi$
$619$	5.05399			0.203137			0.101569	+	0.994829i	$0.467614\pi$
$620$		0			0
$621$	−4.65847			−0.186938
$622$		0			0
$623$	−0.994247	−	0.994247i	−0.0398337	−	0.0398337i
$624$		0			0
$625$	17.8034	−	17.5510i	0.712137	−	0.702041i
$626$		0			0
$627$	2.15401	−	2.15401i	0.0860228	−	0.0860228i
$628$		0			0
$629$			1.79383i			0.0715248i
$630$		0			0
$631$		−	48.8366i		−	1.94415i	−0.234660	−	0.972077i	$-0.575398\pi$
$631$		−	48.8366i		−	1.94415i	0.234660	−	0.972077i	$-0.424602\pi$
$632$		0			0
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$		0			0
$635$	25.1643	+	16.8793i	0.998614	+	0.669834i
$636$		0			0
$637$	1.76156	+	1.76156i	0.0697954	+	0.0697954i
$638$		0			0
$639$	14.3077			0.566002
$640$		0			0
$641$	−4.74760			−0.187519			−0.0937595	−	0.995595i	$-0.529888\pi$
$641$	−4.74760			−0.187519			−0.0937595	+	0.995595i	$0.529888\pi$
$642$		0			0
$643$	−32.8839	−	32.8839i	−1.29681	−	1.29681i	−0.930487	−	0.366326i	$-0.880615\pi$
$643$	−32.8839	−	32.8839i	−1.29681	−	1.29681i	−0.366326	−	0.930487i	$-0.619385\pi$
$644$		0			0
$645$	−12.5693	+	2.47689i	−0.494917	+	0.0975273i
$646$		0			0
$647$	10.3477	−	10.3477i	0.406811	−	0.406811i	−0.473814	−	0.880625i	$-0.657123\pi$
$647$	10.3477	−	10.3477i	0.406811	−	0.406811i	0.880625	+	0.473814i	$0.157123\pi$
$648$		0			0
$649$			29.0096i			1.13873i
$650$		0			0
$651$		−	3.52258i		−	0.138061i
$652$		0			0
$653$	−26.5004	+	26.5004i	−1.03704	+	1.03704i	−0.0377547	+	0.999287i	$0.512021\pi$
$653$	−26.5004	+	26.5004i	−1.03704	+	1.03704i	−0.999287	+	0.0377547i	$0.987979\pi$
$654$		0			0
$655$	−10.0909	+	1.98849i	−0.394285	+	0.0776969i
$656$		0			0
$657$	−3.01395	−	3.01395i	−0.117586	−	0.117586i
$658$		0			0
$659$	4.09068			0.159350			0.0796751	−	0.996821i	$-0.474612\pi$
$659$	4.09068			0.159350			0.0796751	+	0.996821i	$0.474612\pi$
$660$		0			0
$661$	−23.4865			−0.913518			−0.456759	−	0.889591i	$-0.650990\pi$
$661$	−23.4865			−0.913518			−0.456759	+	0.889591i	$0.650990\pi$
$662$		0			0
$663$	−2.23441	−	2.23441i	−0.0867775	−	0.0867775i
$664$		0			0
$665$	−2.00000	−	1.34153i	−0.0775567	−	0.0520222i
$666$		0			0
$667$	−23.8897	+	23.8897i	−0.925012	+	0.925012i
$668$		0			0
$669$		−	14.0646i		−	0.543767i
$670$		0			0
$671$			25.4040i			0.980711i
$672$		0			0
$673$	20.4586	−	20.4586i	0.788620	−	0.788620i	−0.192648	−	0.981268i	$-0.561708\pi$
$673$	20.4586	−	20.4586i	0.788620	−	0.788620i	0.981268	+	0.192648i	$0.0617076\pi$
$674$		0			0
$675$	1.92989	−	4.61254i	0.0742816	−	0.177537i
$676$		0			0
$677$	5.60788	+	5.60788i	0.215528	+	0.215528i	0.806611	−	0.591083i	$-0.201299\pi$
$677$	5.60788	+	5.60788i	0.215528	+	0.215528i	−0.591083	+	0.806611i	$0.701299\pi$
$678$		0			0
$679$	2.10836			0.0809116
$680$		0			0
$681$	−21.0096			−0.805089
$682$		0			0
$683$	−25.2865	−	25.2865i	−0.967561	−	0.967561i	0.0319290	−	0.999490i	$-0.489835\pi$
$683$	−25.2865	−	25.2865i	−0.967561	−	0.967561i	−0.999490	+	0.0319290i	$0.989835\pi$
$684$		0			0
$685$	2.26302	−	3.37380i	0.0864656	−	0.128906i
$686$		0			0
$687$	−2.97421	+	2.97421i	−0.113473	+	0.113473i
$688$		0			0
$689$		−	5.25240i		−	0.200100i
$690$		0			0
$691$			31.0411i			1.18086i	0.807089	+	0.590430i	$0.201042\pi$
$691$			31.0411i			1.18086i	−0.807089	+	0.590430i	$0.798958\pi$
$692$		0			0
$693$	−2.00000	+	2.00000i	−0.0759737	+	0.0759737i
$694$		0			0
$695$	7.34525	+	37.2746i	0.278621	+	1.41391i
$696$		0			0
$697$	−8.64641	−	8.64641i	−0.327506	−	0.327506i
$698$		0			0
$699$	−7.85651			−0.297160
$700$		0			0
$701$	−20.2620			−0.765284			−0.382642	−	0.923897i	$-0.624986\pi$
$701$	−20.2620			−0.765284			−0.382642	+	0.923897i	$0.624986\pi$
$702$		0			0
$703$	1.07700	+	1.07700i	0.0406200	+	0.0406200i
$704$		0			0
$705$	−0.747604	−	3.79383i	−0.0281564	−	0.142884i
$706$		0			0
$707$	2.55424	−	2.55424i	0.0960622	−	0.0960622i
$708$		0			0
$709$		−	14.6339i		−	0.549587i	−0.961503	−	0.274794i	$-0.911390\pi$
$709$		−	14.6339i		−	0.549587i	0.961503	−	0.274794i	$-0.0886096\pi$
$710$		0			0
$711$			10.2564i			0.384646i
$712$		0			0
$713$	−11.6035	+	11.6035i	−0.434555	+	0.434555i
$714$		0			0
$715$	−8.77685	+	13.0849i	−0.328235	+	0.489346i
$716$		0			0
$717$	−2.77551	−	2.77551i	−0.103653	−	0.103653i
$718$		0			0
$719$	−26.6439			−0.993649			−0.496824	−	0.867851i	$-0.665501\pi$
$719$	−26.6439			−0.993649			−0.496824	+	0.867851i	$0.665501\pi$
$720$		0			0
$721$	2.06455			0.0768879
$722$		0			0
$723$	−13.6135	−	13.6135i	−0.506292	−	0.506292i
$724$		0			0
$725$	−13.7572	−	33.5510i	−0.510929	−	1.24605i
$726$		0			0
$727$	23.6329	−	23.6329i	0.876494	−	0.876494i	−0.116676	−	0.993170i	$-0.537224\pi$
$727$	23.6329	−	23.6329i	0.876494	−	0.876494i	0.993170	+	0.116676i	$0.0372238\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			7.26720i			0.268787i
$732$		0			0
$733$	−29.3405	+	29.3405i	−1.08372	+	1.08372i	−0.0875559	+	0.996160i	$0.527906\pi$
$733$	−29.3405	+	29.3405i	−1.08372	+	1.08372i	−0.996160	+	0.0875559i	$0.972094\pi$
$734$		0			0
$735$	1.85700	+	1.24561i	0.0684966	+	0.0459450i
$736$		0			0
$737$	−3.45856	−	3.45856i	−0.127398	−	0.127398i
$738$		0			0
$739$	13.4283			0.493966			0.246983	−	0.969020i	$-0.420561\pi$
$739$	13.4283			0.493966			0.246983	+	0.969020i	$0.420561\pi$
$740$		0			0
$741$	−2.68305			−0.0985644
$742$		0			0
$743$	10.2650	+	10.2650i	0.376585	+	0.376585i	0.869869	−	0.493283i	$-0.164203\pi$
$743$	10.2650	+	10.2650i	0.376585	+	0.376585i	−0.493283	+	0.869869i	$0.664203\pi$
$744$		0			0
$745$	−37.3973	+	7.36943i	−1.37013	+	0.269995i
$746$		0			0
$747$	3.37680	−	3.37680i	0.123550	−	0.123550i
$748$		0			0
$749$			3.34153i			0.122097i
$750$		0			0
$751$			20.1818i			0.736446i	0.929738	+	0.368223i	$0.120034\pi$
$751$			20.1818i			0.736446i	−0.929738	+	0.368223i	$0.879966\pi$
$752$		0			0
$753$	16.0279	−	16.0279i	0.584089	−	0.584089i
$754$		0			0
$755$	38.9978	−	7.68481i	1.41927	−	0.279679i
$756$		0			0
$757$	−0.793833	−	0.793833i	−0.0288523	−	0.0288523i	0.692533	−	0.721386i	$-0.256495\pi$
$757$	−0.793833	−	0.793833i	−0.0288523	−	0.0288523i	−0.721386	+	0.692533i	$0.756495\pi$
$758$		0			0
$759$	13.1762			0.478264
$760$		0			0
$761$	35.9754			1.30411			0.652054	−	0.758173i	$-0.273908\pi$
$761$	35.9754			1.30411			0.652054	+	0.758173i	$0.273908\pi$
$762$		0			0
$763$	−8.69644	−	8.69644i	−0.314832	−	0.314832i
$764$		0			0
$765$	−2.35548	−	1.57997i	−0.0851626	−	0.0571239i
$766$		0			0
$767$	18.0673	−	18.0673i	0.652372	−	0.652372i
$768$		0			0
$769$			4.98168i			0.179644i	0.995958	+	0.0898220i	$0.0286298\pi$
$769$			4.98168i			0.179644i	−0.995958	+	0.0898220i	$0.971370\pi$
$770$		0			0
$771$		−	7.47365i		−	0.269157i
$772$		0			0
$773$	−20.5092	+	20.5092i	−0.737663	+	0.737663i	−0.972125	−	0.234462i	$-0.924667\pi$
$773$	−20.5092	+	20.5092i	−0.737663	+	0.737663i	0.234462	+	0.972125i	$0.424667\pi$
$774$		0			0
$775$	−6.68204	−	16.2961i	−0.240026	−	0.585375i
$776$		0			0
$777$	−1.00000	−	1.00000i	−0.0358748	−	0.0358748i
$778$		0			0
$779$	−10.3825			−0.371991
$780$		0			0
$781$	−40.4681			−1.44806
$782$		0			0
$783$	−5.12822	−	5.12822i	−0.183268	−	0.183268i
$784$		0			0
$785$	−26.4479	+	39.4296i	−0.943967	+	1.40730i
$786$		0			0
$787$	−25.5150	+	25.5150i	−0.909513	+	0.909513i	−0.996233	−	0.0867197i	$-0.972362\pi$
$787$	−25.5150	+	25.5150i	−0.909513	+	0.909513i	0.0867197	+	0.996233i	$0.472362\pi$
$788$		0			0
$789$			7.34153i			0.261365i
$790$		0			0
$791$			3.16564i			0.112557i
$792$		0			0
$793$	15.8217	−	15.8217i	0.561846	−	0.561846i
$794$		0			0
$795$	−0.911489	−	4.62549i	−0.0323272	−	0.164049i
$796$		0			0
$797$	11.9431	+	11.9431i	0.423048	+	0.423048i	0.886252	−	0.463204i	$-0.153300\pi$
$797$	11.9431	+	11.9431i	0.423048	+	0.423048i	−0.463204	+	0.886252i	$0.653300\pi$
$798$		0			0
$799$	−2.19347			−0.0775996
$800$		0			0
$801$	−1.40608			−0.0496813
$802$		0			0
$803$	8.52475	+	8.52475i	0.300832	+	0.300832i
$804$		0			0
$805$	−2.01395	−	10.2201i	−0.0709825	−	0.360212i
$806$		0			0
$807$	8.46790	−	8.46790i	0.298084	−	0.298084i
$808$		0			0
$809$			35.4865i			1.24764i	0.781569	+	0.623819i	$0.214420\pi$
$809$			35.4865i			1.24764i	−0.781569	+	0.623819i	$0.785580\pi$
$810$		0			0
$811$			37.6857i			1.32333i	0.749802	+	0.661663i	$0.230149\pi$
$811$			37.6857i			1.32333i	−0.749802	+	0.661663i	$0.769851\pi$
$812$		0			0
$813$	−14.0785	+	14.0785i	−0.493755	+	0.493755i
$814$		0			0
$815$	−22.5361	+	33.5977i	−0.789406	+	1.17688i
$816$		0			0
$817$	4.36318	+	4.36318i	0.152648	+	0.152648i
$818$		0			0
$819$	2.49122			0.0870502
$820$		0			0
$821$	−50.5327			−1.76360			−0.881802	−	0.471620i	$-0.843669\pi$
$821$	−50.5327			−1.76360			−0.881802	+	0.471620i	$0.843669\pi$
$822$		0			0
$823$	−18.4502	−	18.4502i	−0.643132	−	0.643132i	0.308192	−	0.951324i	$-0.400276\pi$
$823$	−18.4502	−	18.4502i	−0.643132	−	0.643132i	−0.951324	+	0.308192i	$0.900276\pi$
$824$		0			0
$825$	−5.45856	+	13.0462i	−0.190043	+	0.454211i
$826$		0			0
$827$	31.1436	−	31.1436i	1.08297	−	1.08297i	0.0867392	−	0.996231i	$-0.472355\pi$
$827$	31.1436	−	31.1436i	1.08297	−	1.08297i	0.996231	−	0.0867392i	$-0.0276447\pi$
$828$		0			0
$829$			34.4190i			1.19542i	0.801712	+	0.597710i	$0.203923\pi$
$829$			34.4190i			1.19542i	−0.801712	+	0.597710i	$0.796077\pi$
$830$		0			0
$831$			20.1559i			0.699202i
$832$		0			0
$833$	0.896916	−	0.896916i	0.0310763	−	0.0310763i
$834$		0			0
$835$	−6.66230	−	4.46883i	−0.230559	−	0.154650i
$836$		0			0
$837$	−2.49084	−	2.49084i	−0.0860960	−	0.0860960i
$838$		0			0
$839$	−22.6274			−0.781185			−0.390593	−	0.920564i	$-0.627730\pi$
$839$	−22.6274			−0.781185			−0.390593	+	0.920564i	$0.627730\pi$
$840$		0			0
$841$	−23.5972			−0.813698
$842$		0			0
$843$	2.29979	+	2.29979i	0.0792090	+	0.0792090i
$844$		0			0
$845$	−14.9048	+	2.93711i	−0.512742	+	0.101040i
$846$		0			0
$847$	−2.12132	+	2.12132i	−0.0728894	+	0.0728894i
$848$		0			0
$849$			30.1204i			1.03373i
$850$		0			0
$851$			6.58808i			0.225836i
$852$		0			0
$853$	18.0881	−	18.0881i	0.619324	−	0.619324i	−0.326034	−	0.945358i	$-0.605712\pi$
$853$	18.0881	−	18.0881i	0.619324	−	0.619324i	0.945358	+	0.326034i	$0.105712\pi$
$854$		0			0
$855$	−2.36282	+	0.465611i	−0.0808066	+	0.0159236i
$856$		0			0
$857$	−14.1739	−	14.1739i	−0.484171	−	0.484171i	0.422290	−	0.906461i	$-0.361226\pi$
$857$	−14.1739	−	14.1739i	−0.484171	−	0.484171i	−0.906461	+	0.422290i	$0.861226\pi$
$858$		0			0
$859$	4.61932			0.157609			0.0788045	−	0.996890i	$-0.474890\pi$
$859$	4.61932			0.157609			0.0788045	+	0.996890i	$0.474890\pi$
$860$		0			0
$861$	9.64015			0.328535
$862$		0			0
$863$	17.2188	+	17.2188i	0.586136	+	0.586136i	0.936583	−	0.350447i	$-0.113970\pi$
$863$	17.2188	+	17.2188i	0.586136	+	0.586136i	−0.350447	+	0.936583i	$0.613970\pi$
$864$		0			0
$865$	18.6541	+	12.5125i	0.634259	+	0.425437i
$866$		0			0
$867$	10.8831	−	10.8831i	0.369611	−	0.369611i
$868$		0			0
$869$		−	29.0096i		−	0.984083i
$870$		0			0
$871$			4.30802i			0.145972i
$872$		0			0
$873$	1.49084	−	1.49084i	0.0504573	−	0.0504573i
$874$		0			0
$875$	10.9537	+	2.23986i	0.370302	+	0.0757209i
$876$		0			0
$877$	10.9721	+	10.9721i	0.370501	+	0.370501i	0.867660	−	0.497158i	$-0.165623\pi$
$877$	10.9721	+	10.9721i	0.370501	+	0.370501i	−0.497158	+	0.867660i	$0.665623\pi$
$878$		0			0
$879$	21.3242			0.719248
$880$		0			0
$881$	1.81841			0.0612639			0.0306319	−	0.999531i	$-0.490248\pi$
$881$	1.81841			0.0612639			0.0306319	+	0.999531i	$0.490248\pi$
$882$		0			0
$883$	17.2621	+	17.2621i	0.580917	+	0.580917i	0.935155	−	0.354238i	$-0.115260\pi$
$883$	17.2621	+	17.2621i	0.580917	+	0.580917i	−0.354238	+	0.935155i	$0.615260\pi$
$884$		0			0
$885$	12.7755	−	19.0462i	0.429444	−	0.640232i
$886$		0			0
$887$	−22.8324	+	22.8324i	−0.766637	+	0.766637i	−0.977513	−	0.210876i	$-0.932368\pi$
$887$	−22.8324	+	22.8324i	−0.766637	+	0.766637i	0.210876	+	0.977513i	$0.432368\pi$
$888$		0			0
$889$			13.5510i			0.454487i
$890$		0			0
$891$			2.82843i			0.0947559i
$892$		0			0
$893$	−1.31695	+	1.31695i	−0.0440699	+	0.0440699i
$894$		0			0
$895$	−4.07095	−	20.6587i	−0.136077	−	0.690543i
$896$		0			0
$897$	−8.20617	−	8.20617i	−0.273996	−	0.273996i
$898$		0			0
$899$	−25.5471			−0.852045
$900$		0			0
$901$	−2.67432			−0.0890944
$902$		0			0
$903$	−4.05121	−	4.05121i	−0.134816	−	0.134816i
$904$		0			0
$905$	6.15368	+	31.2278i	0.204555	+	1.03805i
$906$		0			0
$907$	−28.6153	+	28.6153i	−0.950156	+	0.950156i	−0.998815	−	0.0486599i	$-0.984505\pi$
$907$	−28.6153	+	28.6153i	−0.950156	+	0.950156i	0.0486599	+	0.998815i	$0.484505\pi$
$908$		0			0
$909$		−	3.61224i		−	0.119811i
$910$		0			0
$911$		−	49.9457i		−	1.65478i	−0.561631	−	0.827388i	$-0.689826\pi$
$911$		−	49.9457i		−	1.65478i	0.561631	−	0.827388i	$-0.310174\pi$
$912$		0			0
$913$	−9.55102	+	9.55102i	−0.316093	+	0.316093i
$914$		0			0
$915$	11.1877	−	16.6790i	0.369853	−	0.551391i
$916$		0			0
$917$	−3.25240	−	3.25240i	−0.107404	−	0.107404i
$918$		0			0
$919$	9.96487			0.328711			0.164355	−	0.986401i	$-0.447446\pi$
$919$	9.96487			0.328711			0.164355	+	0.986401i	$0.447446\pi$
$920$		0			0
$921$	11.0462			0.363986
$922$		0			0
$923$	25.2037	+	25.2037i	0.829591	+	0.829591i
$924$		0			0
$925$	−6.52311	−	2.72928i	−0.214479	−	0.0897382i
$926$		0			0
$927$	1.45986	−	1.45986i	0.0479480	−	0.0479480i
$928$		0			0
$929$		−	13.5756i		−	0.445401i	−0.974887	−	0.222701i	$-0.928513\pi$
$929$		−	13.5756i		−	0.445401i	0.974887	−	0.222701i	$-0.0714872\pi$
$930$		0			0
$931$		−	1.07700i		−	0.0352974i
$932$		0			0
$933$	−16.8034	+	16.8034i	−0.550119	+	0.550119i
$934$		0			0
$935$	6.66230	+	4.46883i	0.217881	+	0.146146i
$936$		0			0
$937$	16.7711	+	16.7711i	0.547889	+	0.547889i	0.925830	−	0.377941i	$-0.123368\pi$
$937$	16.7711	+	16.7711i	0.547889	+	0.547889i	−0.377941	+	0.925830i	$0.623368\pi$
$938$		0			0
$939$	20.1362			0.657120
$940$		0			0
$941$	0.800090			0.0260822			0.0130411	−	0.999915i	$-0.495849\pi$
$941$	0.800090			0.0260822			0.0130411	+	0.999915i	$0.495849\pi$
$942$		0			0
$943$	−31.7550	−	31.7550i	−1.03409	−	1.03409i
$944$		0			0
$945$	2.19388	−	0.432320i	0.0713668	−	0.0140634i
$946$		0			0
$947$	4.26002	−	4.26002i	0.138432	−	0.138432i	−0.634495	−	0.772927i	$-0.718792\pi$
$947$	4.26002	−	4.26002i	0.138432	−	0.138432i	0.772927	+	0.634495i	$0.218792\pi$
$948$		0			0
$949$		−	10.6185i		−	0.344691i
$950$		0			0
$951$			16.6334i			0.539373i
$952$		0			0
$953$	−9.04186	+	9.04186i	−0.292895	+	0.292895i	−0.838223	−	0.545328i	$-0.816405\pi$
$953$	−9.04186	+	9.04186i	−0.292895	+	0.292895i	0.545328	+	0.838223i	$0.316405\pi$
$954$		0			0
$955$	−33.4322	+	6.58808i	−1.08184	+	0.213185i
$956$		0			0
$957$	14.5048	+	14.5048i	0.468873	+	0.468873i
$958$		0			0
$959$	1.81680			0.0586675
$960$		0			0
$961$	18.5914			0.599724
$962$		0			0
$963$	2.36282	+	2.36282i	0.0761407	+	0.0761407i
$964$		0			0
$965$	41.4296	+	27.7895i	1.33367	+	0.894574i
$966$		0			0
$967$	−30.0207	+	30.0207i	−0.965400	+	0.965400i	−0.999421	−	0.0340216i	$-0.989169\pi$
$967$	−30.0207	+	30.0207i	−0.965400	+	0.965400i	0.0340216	+	0.999421i	$0.489169\pi$
$968$		0			0
$969$			1.36611i			0.0438857i
$970$		0			0
$971$			2.69767i			0.0865724i	0.999063	+	0.0432862i	$0.0137827\pi$
$971$			2.69767i			0.0865724i	−0.999063	+	0.0432862i	$0.986217\pi$
$972$		0			0
$973$	−12.0140	+	12.0140i	−0.385150	+	0.385150i
$974$		0			0
$975$	11.5249	−	4.72563i	0.369091	−	0.151341i
$976$		0			0
$977$	3.15557	+	3.15557i	0.100956	+	0.100956i	0.755781	−	0.654825i	$-0.227258\pi$
$977$	3.15557	+	3.15557i	0.100956	+	0.100956i	−0.654825	+	0.755781i	$0.727258\pi$
$978$		0			0
$979$	3.97699			0.127105
$980$		0			0
$981$	−12.2986			−0.392665
$982$		0			0
$983$	42.3746	+	42.3746i	1.35154	+	1.35154i	0.883941	+	0.467598i	$0.154881\pi$
$983$	42.3746	+	42.3746i	1.35154	+	1.35154i	0.467598	+	0.883941i	$0.345119\pi$
$984$		0			0
$985$	−32.6541	+	48.6820i	−1.04045	+	1.55114i
$986$		0			0
$987$	1.22279	−	1.22279i	0.0389217	−	0.0389217i
$988$		0			0
$989$			26.6897i			0.848683i
$990$		0			0
$991$		−	12.4104i		−	0.394231i	−0.980380	−	0.197115i	$-0.936843\pi$
$991$		−	12.4104i		−	0.394231i	0.980380	−	0.197115i	$-0.0631574\pi$
$992$		0			0
$993$	−8.23407	+	8.23407i	−0.261300	+	0.261300i
$994$		0			0
$995$	9.66478	+	49.0454i	0.306394	+	1.55484i
$996$		0			0
$997$	10.5737	+	10.5737i	0.334873	+	0.334873i	0.854434	−	0.519561i	$-0.173904\pi$
$997$	10.5737	+	10.5737i	0.334873	+	0.334873i	−0.519561	+	0.854434i	$0.673904\pi$
$998$		0			0
$999$	−1.41421			−0.0447437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bl.c.127.5	yes	12
4.3	odd	2	inner	1680.2.bl.c.127.2	✓	12
5.3	odd	4	inner	1680.2.bl.c.463.2	yes	12
20.3	even	4	inner	1680.2.bl.c.463.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1680.2.bl.c.127.2	✓	12	4.3	odd	2	inner
1680.2.bl.c.127.5	yes	12	1.1	even	1	trivial
1680.2.bl.c.463.2	yes	12	5.3	odd	4	inner
1680.2.bl.c.463.5	yes	12	20.3	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(0.432320 + 2.19388i) q^{5} +(-0.707107 + 0.707107i) q^{7} +1.00000i q^{9} -2.82843i q^{11} +(-1.76156 + 1.76156i) q^{13} +(-1.24561 + 1.85700i) q^{15} +(0.896916 + 0.896916i) q^{17} +1.07700 q^{19} -1.00000 q^{21} +(3.29404 + 3.29404i) q^{23} +(-4.62620 + 1.89692i) q^{25} +(-0.707107 + 0.707107i) q^{27} +7.25240i q^{29} +3.52258i q^{31} +(2.00000 - 2.00000i) q^{33} +(-1.85700 - 1.24561i) q^{35} +(1.00000 + 1.00000i) q^{37} -2.49122 q^{39} -9.64015 q^{41} +(4.05121 + 4.05121i) q^{43} +(-2.19388 + 0.432320i) q^{45} +(-1.22279 + 1.22279i) q^{47} -1.00000i q^{49} +1.26843i q^{51} +(-1.49084 + 1.49084i) q^{53} +(6.20522 - 1.22279i) q^{55} +(0.761557 + 0.761557i) q^{57} -10.2564 q^{59} -8.98168 q^{61} +(-0.707107 - 0.707107i) q^{63} +(-4.62620 - 3.10308i) q^{65} +(1.22279 - 1.22279i) q^{67} +4.65847i q^{69} -14.3077i q^{71} +(-3.01395 + 3.01395i) q^{73} +(-4.61254 - 1.92989i) q^{75} +(2.00000 + 2.00000i) q^{77} +10.2564 q^{79} -1.00000 q^{81} +(-3.37680 - 3.37680i) q^{83} +(-1.57997 + 2.35548i) q^{85} +(-5.12822 + 5.12822i) q^{87} +1.40608i q^{89} -2.49122i q^{91} +(-2.49084 + 2.49084i) q^{93} +(0.465611 + 2.36282i) q^{95} +(-1.49084 - 1.49084i) q^{97} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{13} - 4 q^{17} - 12 q^{21} - 20 q^{25} + 24 q^{33} + 12 q^{37} + 16 q^{41} + 4 q^{45} + 28 q^{53} - 16 q^{57} - 16 q^{61} - 20 q^{65} + 60 q^{73} + 24 q^{77} - 12 q^{81} - 84 q^{85} + 16 q^{93}+ \cdots + 28 q^{97}+O(q^{100}) \) 12 * q + 4 * q^13 - 4 * q^17 - 12 * q^21 - 20 * q^25 + 24 * q^33 + 12 * q^37 + 16 * q^41 + 4 * q^45 + 28 * q^53 - 16 * q^57 - 16 * q^61 - 20 * q^65 + 60 * q^73 + 24 * q^77 - 12 * q^81 - 84 * q^85 + 16 * q^93 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more