LMFDB - Embedded newform 680.2.bd.b.81.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(81,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bd (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 38 x^{18} + 597 x^{16} + 5004 x^{14} + 24072 x^{12} + 66452 x^{10} + 99328 x^{8} + 70784 x^{6} + \cdots + 16 $ x^20 + 38x^18 + 597x^16 + 5004x^14 + 24072x^12 + 66452x^10 + 99328x^8 + 70784x^6 + 19972x^4 + 1104*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.7
Root			$-0.205791i$ of defining polynomial
Character	$\chi$	$=$	680.81
Dual form			680.2.bd.b.361.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.145516 + 0.145516i) q^{3} +(0.707107 + 0.707107i) q^{5} +(2.63491 - 2.63491i) q^{7} -2.95765i q^{9} +(0.218606 - 0.218606i) q^{11} -0.787596 q^{13} +0.205791i q^{15} +(-2.62024 - 3.18345i) q^{17} +1.28179i q^{19} +0.766846 q^{21} +(2.21824 - 2.21824i) q^{23} +1.00000i q^{25} +(0.866936 - 0.866936i) q^{27} +(-3.63514 - 3.63514i) q^{29} +(2.89651 + 2.89651i) q^{31} +0.0636215 q^{33} +3.72633 q^{35} +(2.44736 + 2.44736i) q^{37} +(-0.114608 - 0.114608i) q^{39} +(6.82926 - 6.82926i) q^{41} +8.35792i q^{43} +(2.09137 - 2.09137i) q^{45} +9.08591 q^{47} -6.88550i q^{49} +(0.0819568 - 0.844532i) q^{51} -3.79803i q^{53} +0.309156 q^{55} +(-0.186522 + 0.186522i) q^{57} +7.49443i q^{59} +(-4.19949 + 4.19949i) q^{61} +(-7.79314 - 7.79314i) q^{63} +(-0.556915 - 0.556915i) q^{65} +8.77184 q^{67} +0.645582 q^{69} +(-1.97955 - 1.97955i) q^{71} +(-1.44255 - 1.44255i) q^{73} +(-0.145516 + 0.145516i) q^{75} -1.15201i q^{77} +(-7.20162 + 7.20162i) q^{79} -8.62064 q^{81} -6.52587i q^{83} +(0.398252 - 4.10383i) q^{85} -1.05795i q^{87} -5.13917 q^{89} +(-2.07525 + 2.07525i) q^{91} +0.842980i q^{93} +(-0.906364 + 0.906364i) q^{95} +(4.75240 + 4.75240i) q^{97} +(-0.646560 - 0.646560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} + 4 q^{7} + 12 q^{11} + 4 q^{13} + 4 q^{17} + 16 q^{21} - 4 q^{23} - 16 q^{27} - 4 q^{29} - 4 q^{31} + 16 q^{33} - 8 q^{35} - 8 q^{37} - 8 q^{39} - 8 q^{41} + 4 q^{47} - 4 q^{51} - 8 q^{55}+ \cdots + 52 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 + 4 * q^7 + 12 * q^11 + 4 * q^13 + 4 * q^17 + 16 * q^21 - 4 * q^23 - 16 * q^27 - 4 * q^29 - 4 * q^31 + 16 * q^33 - 8 * q^35 - 8 * q^37 - 8 * q^39 - 8 * q^41 + 4 * q^47 - 4 * q^51 - 8 * q^55 - 24 * q^57 - 24 * q^61 + 60 * q^63 - 4 * q^65 - 56 * q^67 + 24 * q^69 - 40 * q^71 - 20 * q^73 + 4 * q^75 - 8 * q^79 + 4 * q^81 - 12 * q^85 + 28 * q^89 - 4 * q^95 + 24 * q^97 + 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.145516	+	0.145516i	0.0840140	+	0.0840140i	0.747865	−	0.663851i	$-0.231079\pi$
$3$	0.145516	+	0.145516i	0.0840140	+	0.0840140i	−0.663851	+	0.747865i	$0.731079\pi$
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$	2.63491	−	2.63491i	0.995902	−	0.995902i	−0.00408920	−	0.999992i	$-0.501302\pi$
$7$	2.63491	−	2.63491i	0.995902	−	0.995902i	0.999992	+	0.00408920i	$0.00130164\pi$
$8$		0			0
$9$		−	2.95765i		−	0.985883i
$10$		0			0
$11$	0.218606	−	0.218606i	0.0659122	−	0.0659122i	−0.673382	−	0.739294i	$-0.735159\pi$
$11$	0.218606	−	0.218606i	0.0659122	−	0.0659122i	0.739294	+	0.673382i	$0.235159\pi$
$12$		0			0
$13$	−0.787596			−0.218440			−0.109220	−	0.994018i	$-0.534835\pi$
$13$	−0.787596			−0.218440			−0.109220	+	0.994018i	$0.534835\pi$
$14$		0			0
$15$			0.205791i			0.0531351i
$16$		0			0
$17$	−2.62024	−	3.18345i	−0.635501	−	0.772100i
$17$	−2.62024	−	3.18345i	−0.635501	−	0.772100i
$18$		0			0
$19$			1.28179i			0.294063i	0.989132	+	0.147032i	$0.0469719\pi$
$19$			1.28179i			0.294063i	−0.989132	+	0.147032i	$0.953028\pi$
$20$		0			0
$21$	0.766846			0.167339
$22$		0			0
$23$	2.21824	−	2.21824i	0.462536	−	0.462536i	−0.436950	−	0.899486i	$-0.643941\pi$
$23$	2.21824	−	2.21824i	0.462536	−	0.462536i	0.899486	+	0.436950i	$0.143941\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	0.866936	−	0.866936i	0.166842	−	0.166842i
$28$		0			0
$29$	−3.63514	−	3.63514i	−0.675029	−	0.675029i	0.283842	−	0.958871i	$-0.408391\pi$
$29$	−3.63514	−	3.63514i	−0.675029	−	0.675029i	−0.958871	+	0.283842i	$0.908391\pi$
$30$		0			0
$31$	2.89651	+	2.89651i	0.520228	+	0.520228i	0.917640	−	0.397412i	$-0.130092\pi$
$31$	2.89651	+	2.89651i	0.520228	+	0.520228i	−0.397412	+	0.917640i	$0.630092\pi$
$32$		0			0
$33$	0.0636215			0.0110751
$34$		0			0
$35$	3.72633			0.629864
$36$		0			0
$37$	2.44736	+	2.44736i	0.402343	+	0.402343i	0.879058	−	0.476715i	$-0.158173\pi$
$37$	2.44736	+	2.44736i	0.402343	+	0.402343i	−0.476715	+	0.879058i	$0.658173\pi$
$38$		0			0
$39$	−0.114608	−	0.114608i	−0.0183520	−	0.0183520i
$40$		0			0
$41$	6.82926	−	6.82926i	1.06655	−	1.06655i	0.0689297	−	0.997622i	$-0.478042\pi$
$41$	6.82926	−	6.82926i	1.06655	−	1.06655i	0.997622	−	0.0689297i	$-0.0219584\pi$
$42$		0			0
$43$			8.35792i			1.27457i	0.770628	+	0.637286i	$0.219943\pi$
$43$			8.35792i			1.27457i	−0.770628	+	0.637286i	$0.780057\pi$
$44$		0			0
$45$	2.09137	−	2.09137i	0.311764	−	0.311764i
$46$		0			0
$47$	9.08591			1.32532			0.662658	−	0.748922i	$-0.269428\pi$
$47$	9.08591			1.32532			0.662658	+	0.748922i	$0.269428\pi$
$48$		0			0
$49$		−	6.88550i		−	0.983643i
$50$		0			0
$51$	0.0819568	−	0.844532i	0.0114762	−	0.118258i
$52$		0			0
$53$		−	3.79803i		−	0.521700i	−0.965379	−	0.260850i	$-0.915997\pi$
$53$		−	3.79803i		−	0.521700i	0.965379	−	0.260850i	$-0.0840028\pi$
$54$		0			0
$55$	0.309156			0.0416865
$56$		0			0
$57$	−0.186522	+	0.186522i	−0.0247054	+	0.0247054i
$58$		0			0
$59$			7.49443i			0.975692i	0.872930	+	0.487846i	$0.162217\pi$
$59$			7.49443i			0.975692i	−0.872930	+	0.487846i	$0.837783\pi$
$60$		0			0
$61$	−4.19949	+	4.19949i	−0.537689	+	0.537689i	−0.922850	−	0.385160i	$-0.874146\pi$
$61$	−4.19949	+	4.19949i	−0.537689	+	0.537689i	0.385160	+	0.922850i	$0.374146\pi$
$62$		0			0
$63$	−7.79314	−	7.79314i	−0.981844	−	0.981844i
$64$		0			0
$65$	−0.556915	−	0.556915i	−0.0690768	−	0.0690768i
$66$		0			0
$67$	8.77184			1.07165			0.535825	−	0.844329i	$-0.320001\pi$
$67$	8.77184			1.07165			0.535825	+	0.844329i	$0.320001\pi$
$68$		0			0
$69$	0.645582			0.0777189
$70$		0			0
$71$	−1.97955	−	1.97955i	−0.234929	−	0.234929i	0.579817	−	0.814747i	$-0.303124\pi$
$71$	−1.97955	−	1.97955i	−0.234929	−	0.234929i	−0.814747	+	0.579817i	$0.803124\pi$
$72$		0			0
$73$	−1.44255	−	1.44255i	−0.168837	−	0.168837i	0.617631	−	0.786468i	$-0.288093\pi$
$73$	−1.44255	−	1.44255i	−0.168837	−	0.168837i	−0.786468	+	0.617631i	$0.788093\pi$
$74$		0			0
$75$	−0.145516	+	0.145516i	−0.0168028	+	0.0168028i
$76$		0			0
$77$		−	1.15201i		−	0.131284i
$78$		0			0
$79$	−7.20162	+	7.20162i	−0.810245	+	0.810245i	−0.984670	−	0.174425i	$-0.944193\pi$
$79$	−7.20162	+	7.20162i	−0.810245	+	0.810245i	0.174425	+	0.984670i	$0.444193\pi$
$80$		0			0
$81$	−8.62064			−0.957849
$82$		0			0
$83$		−	6.52587i		−	0.716307i	−0.933663	−	0.358153i	$-0.883406\pi$
$83$		−	6.52587i		−	0.716307i	0.933663	−	0.358153i	$-0.116594\pi$
$84$		0			0
$85$	0.398252	−	4.10383i	0.0431965	−	0.445123i
$86$		0			0
$87$		−	1.05795i		−	0.113424i
$88$		0			0
$89$	−5.13917			−0.544751			−0.272376	−	0.962191i	$-0.587809\pi$
$89$	−5.13917			−0.544751			−0.272376	+	0.962191i	$0.587809\pi$
$90$		0			0
$91$	−2.07525	+	2.07525i	−0.217545	+	0.217545i
$92$		0			0
$93$			0.842980i			0.0874129i
$94$		0			0
$95$	−0.906364	+	0.906364i	−0.0929910	+	0.0929910i
$96$		0			0
$97$	4.75240	+	4.75240i	0.482533	+	0.482533i	0.905940	−	0.423406i	$-0.139166\pi$
$97$	4.75240	+	4.75240i	0.482533	+	0.482533i	−0.423406	+	0.905940i	$0.639166\pi$
$98$		0			0
$99$	−0.646560	−	0.646560i	−0.0649817	−	0.0649817i
$100$		0			0
$101$	−12.8725			−1.28086			−0.640431	−	0.768016i	$-0.721244\pi$
$101$	−12.8725			−1.28086			−0.640431	+	0.768016i	$0.721244\pi$
$102$		0			0
$103$	−0.468663			−0.0461787			−0.0230894	−	0.999733i	$-0.507350\pi$
$103$	−0.468663			−0.0461787			−0.0230894	+	0.999733i	$0.507350\pi$
$104$		0			0
$105$	0.542242	+	0.542242i	0.0529174	+	0.0529174i
$106$		0			0
$107$	11.6043	+	11.6043i	1.12183	+	1.12183i	0.991466	+	0.130368i	$0.0416160\pi$
$107$	11.6043	+	11.6043i	1.12183	+	1.12183i	0.130368	+	0.991466i	$0.458384\pi$
$108$		0			0
$109$	2.28031	−	2.28031i	0.218414	−	0.218414i	−0.589416	−	0.807830i	$-0.700642\pi$
$109$	2.28031	−	2.28031i	0.218414	−	0.218414i	0.807830	+	0.589416i	$0.200642\pi$
$110$		0			0
$111$			0.712262i			0.0676049i
$112$		0			0
$113$	−10.6982	+	10.6982i	−1.00640	+	1.00640i	−0.00642546	+	0.999979i	$0.502045\pi$
$113$	−10.6982	+	10.6982i	−1.00640	+	1.00640i	−0.999979	+	0.00642546i	$0.997955\pi$
$114$		0			0
$115$	3.13707			0.292533
$116$		0			0
$117$			2.32943i			0.215356i
$118$		0			0
$119$	−15.2922	−	1.48402i	−1.40183	−	0.136040i
$120$		0			0
$121$			10.9044i			0.991311i
$122$		0			0
$123$	1.98754			0.179210
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$			10.0472i			0.891546i	0.895146	+	0.445773i	$0.147071\pi$
$127$			10.0472i			0.891546i	−0.895146	+	0.445773i	$0.852929\pi$
$128$		0			0
$129$	−1.21622	+	1.21622i	−0.107082	+	0.107082i
$130$		0			0
$131$	−4.61692	−	4.61692i	−0.403382	−	0.403382i	0.476041	−	0.879423i	$-0.342071\pi$
$131$	−4.61692	−	4.61692i	−0.403382	−	0.403382i	−0.879423	+	0.476041i	$0.842071\pi$
$132$		0			0
$133$	3.37741	+	3.37741i	0.292858	+	0.292858i
$134$		0			0
$135$	1.22603			0.105520
$136$		0			0
$137$	20.3491			1.73854			0.869269	−	0.494340i	$-0.164590\pi$
$137$	20.3491			1.73854			0.869269	+	0.494340i	$0.164590\pi$
$138$		0			0
$139$	4.78213	+	4.78213i	0.405615	+	0.405615i	0.880206	−	0.474591i	$-0.157404\pi$
$139$	4.78213	+	4.78213i	0.405615	+	0.405615i	−0.474591	+	0.880206i	$0.657404\pi$
$140$		0			0
$141$	1.32215	+	1.32215i	0.111345	+	0.111345i
$142$		0			0
$143$	−0.172173	+	0.172173i	−0.0143979	+	0.0143979i
$144$		0			0
$145$		−	5.14087i		−	0.426926i
$146$		0			0
$147$	1.00195	−	1.00195i	0.0826398	−	0.0826398i
$148$		0			0
$149$	−20.2934			−1.66250			−0.831252	−	0.555897i	$-0.812375\pi$
$149$	−20.2934			−1.66250			−0.831252	+	0.555897i	$0.812375\pi$
$150$		0			0
$151$		−	4.63707i		−	0.377360i	−0.982039	−	0.188680i	$-0.939579\pi$
$151$		−	4.63707i		−	0.377360i	0.982039	−	0.188680i	$-0.0604208\pi$
$152$		0			0
$153$	−9.41553	+	7.74974i	−0.761201	+	0.626530i
$154$		0			0
$155$			4.09628i			0.329021i
$156$		0			0
$157$	2.95080			0.235500			0.117750	−	0.993043i	$-0.462432\pi$
$157$	2.95080			0.235500			0.117750	+	0.993043i	$0.462432\pi$
$158$		0			0
$159$	0.552677	−	0.552677i	0.0438301	−	0.0438301i
$160$		0			0
$161$		−	11.6897i		−	0.921281i
$162$		0			0
$163$	1.11213	−	1.11213i	0.0871085	−	0.0871085i	−0.662210	−	0.749318i	$-0.730381\pi$
$163$	1.11213	−	1.11213i	0.0871085	−	0.0871085i	0.749318	+	0.662210i	$0.230381\pi$
$164$		0			0
$165$	0.0449872	+	0.0449872i	0.00350225	+	0.00350225i
$166$		0			0
$167$	−10.2368	−	10.2368i	−0.792149	−	0.792149i	0.189694	−	0.981843i	$-0.439250\pi$
$167$	−10.2368	−	10.2368i	−0.792149	−	0.792149i	−0.981843	+	0.189694i	$0.939250\pi$
$168$		0			0
$169$	−12.3797			−0.952284
$170$		0			0
$171$	3.79109			0.289912
$172$		0			0
$173$	1.78759	+	1.78759i	0.135908	+	0.135908i	0.771788	−	0.635880i	$-0.219363\pi$
$173$	1.78759	+	1.78759i	0.135908	+	0.135908i	−0.635880	+	0.771788i	$0.719363\pi$
$174$		0			0
$175$	2.63491	+	2.63491i	0.199180	+	0.199180i
$176$		0			0
$177$	−1.09056	+	1.09056i	−0.0819718	+	0.0819718i
$178$		0			0
$179$			23.7133i			1.77241i	0.463290	+	0.886207i	$0.346669\pi$
$179$			23.7133i			1.77241i	−0.463290	+	0.886207i	$0.653331\pi$
$180$		0			0
$181$	−1.89581	+	1.89581i	−0.140914	+	0.140914i	−0.774045	−	0.633131i	$-0.781770\pi$
$181$	−1.89581	+	1.89581i	−0.140914	+	0.140914i	0.633131	+	0.774045i	$0.281770\pi$
$182$		0			0
$183$	−1.22219			−0.0903468
$184$		0			0
$185$			3.46109i			0.254464i
$186$		0			0
$187$	−1.26872	−	0.123122i	−0.0927781	−	0.00900356i
$188$		0			0
$189$		−	4.56860i		−	0.332317i
$190$		0			0
$191$	−2.01974			−0.146143			−0.0730716	−	0.997327i	$-0.523280\pi$
$191$	−2.01974			−0.146143			−0.0730716	+	0.997327i	$0.523280\pi$
$192$		0			0
$193$	−12.2369	+	12.2369i	−0.880829	+	0.880829i	−0.993619	−	0.112790i	$-0.964021\pi$
$193$	−12.2369	+	12.2369i	−0.880829	+	0.880829i	0.112790	+	0.993619i	$0.464021\pi$
$194$		0			0
$195$		−	0.162080i		−	0.0116068i
$196$		0			0
$197$	6.13046	−	6.13046i	0.436777	−	0.436777i	−0.454149	−	0.890926i	$-0.650057\pi$
$197$	6.13046	−	6.13046i	0.436777	−	0.436777i	0.890926	+	0.454149i	$0.150057\pi$
$198$		0			0
$199$	−5.92452	−	5.92452i	−0.419978	−	0.419978i	0.465218	−	0.885196i	$-0.345976\pi$
$199$	−5.92452	−	5.92452i	−0.419978	−	0.419978i	−0.885196	+	0.465218i	$0.845976\pi$
$200$		0			0
$201$	1.27645	+	1.27645i	0.0900336	+	0.0900336i
$202$		0			0
$203$	−19.1565			−1.34453
$204$		0			0
$205$	9.65803			0.674546
$206$		0			0
$207$	−6.56079	−	6.56079i	−0.456006	−	0.456006i
$208$		0			0
$209$	0.280208	+	0.280208i	0.0193824	+	0.0193824i
$210$		0			0
$211$	3.65661	−	3.65661i	0.251731	−	0.251731i	−0.569949	−	0.821680i	$-0.693037\pi$
$211$	3.65661	−	3.65661i	0.251731	−	0.251731i	0.821680	+	0.569949i	$0.193037\pi$
$212$		0			0
$213$		−	0.576114i		−	0.0394747i
$214$		0			0
$215$	−5.90995	+	5.90995i	−0.403055	+	0.403055i
$216$		0			0
$217$	15.2641			1.03619
$218$		0			0
$219$		−	0.419828i		−	0.0283694i
$220$		0			0
$221$	2.06369	+	2.50727i	0.138819	+	0.168657i
$222$		0			0
$223$		−	5.66618i		−	0.379436i	−0.981839	−	0.189718i	$-0.939243\pi$
$223$		−	5.66618i		−	0.379436i	0.981839	−	0.189718i	$-0.0607573\pi$
$224$		0			0
$225$	2.95765			0.197177
$226$		0			0
$227$	−11.6771	+	11.6771i	−0.775039	+	0.775039i	−0.978983	−	0.203944i	$-0.934624\pi$
$227$	−11.6771	+	11.6771i	−0.775039	+	0.775039i	0.203944	+	0.978983i	$0.434624\pi$
$228$		0			0
$229$		−	21.8971i		−	1.44700i	−0.690324	−	0.723501i	$-0.742532\pi$
$229$		−	21.8971i		−	1.44700i	0.690324	−	0.723501i	$-0.257468\pi$
$230$		0			0
$231$	0.167637	−	0.167637i	0.0110297	−	0.0110297i
$232$		0			0
$233$	16.8292	+	16.8292i	1.10252	+	1.10252i	0.994106	+	0.108415i	$0.0345774\pi$
$233$	16.8292	+	16.8292i	1.10252	+	1.10252i	0.108415	+	0.994106i	$0.465423\pi$
$234$		0			0
$235$	6.42471	+	6.42471i	0.419102	+	0.419102i
$236$		0			0
$237$	−2.09591			−0.136144
$238$		0			0
$239$	−28.3825			−1.83591			−0.917956	−	0.396683i	$-0.870161\pi$
$239$	−28.3825			−1.83591			−0.917956	+	0.396683i	$0.870161\pi$
$240$		0			0
$241$	10.2423	+	10.2423i	0.659765	+	0.659765i	0.955324	−	0.295560i	$-0.0955061\pi$
$241$	10.2423	+	10.2423i	0.659765	+	0.659765i	−0.295560	+	0.955324i	$0.595506\pi$
$242$		0			0
$243$	−3.85525	−	3.85525i	−0.247315	−	0.247315i
$244$		0			0
$245$	4.86879	−	4.86879i	0.311055	−	0.311055i
$246$		0			0
$247$		−	1.00953i		−	0.0642352i
$248$		0			0
$249$	0.949621	−	0.949621i	0.0601798	−	0.0601798i
$250$		0			0
$251$	16.5272			1.04318			0.521592	−	0.853195i	$-0.325338\pi$
$251$	16.5272			1.04318			0.521592	+	0.853195i	$0.325338\pi$
$252$		0			0
$253$		−	0.969843i		−	0.0609735i
$254$		0			0
$255$	0.655127	−	0.539222i	0.0410256	−	0.0337674i
$256$		0			0
$257$		−	9.26318i		−	0.577822i	−0.957356	−	0.288911i	$-0.906707\pi$
$257$		−	9.26318i		−	0.577822i	0.957356	−	0.288911i	$-0.0932931\pi$
$258$		0			0
$259$	12.8971			0.801389
$260$		0			0
$261$	−10.7515	+	10.7515i	−0.665500	+	0.665500i
$262$		0			0
$263$		−	27.4019i		−	1.68967i	−0.535023	−	0.844837i	$-0.679697\pi$
$263$		−	27.4019i		−	1.68967i	0.535023	−	0.844837i	$-0.320303\pi$
$264$		0			0
$265$	2.68562	−	2.68562i	0.164976	−	0.164976i
$266$		0			0
$267$	−0.747834	−	0.747834i	−0.0457667	−	0.0457667i
$268$		0			0
$269$	2.58696	+	2.58696i	0.157730	+	0.157730i	0.781560	−	0.623830i	$-0.214424\pi$
$269$	2.58696	+	2.58696i	0.157730	+	0.157730i	−0.623830	+	0.781560i	$0.714424\pi$
$270$		0			0
$271$	−13.7714			−0.836550			−0.418275	−	0.908320i	$-0.637365\pi$
$271$	−13.7714			−0.836550			−0.418275	+	0.908320i	$0.637365\pi$
$272$		0			0
$273$	−0.603965			−0.0365536
$274$		0			0
$275$	0.218606	+	0.218606i	0.0131824	+	0.0131824i
$276$		0			0
$277$	18.4646	+	18.4646i	1.10943	+	1.10943i	0.993225	+	0.116206i	$0.0370733\pi$
$277$	18.4646	+	18.4646i	1.10943	+	1.10943i	0.116206	+	0.993225i	$0.462927\pi$
$278$		0			0
$279$	8.56686	−	8.56686i	0.512884	−	0.512884i
$280$		0			0
$281$		−	2.85126i		−	0.170092i	−0.996377	−	0.0850458i	$-0.972896\pi$
$281$		−	2.85126i		−	0.170092i	0.996377	−	0.0850458i	$-0.0271037\pi$
$282$		0			0
$283$	13.9476	−	13.9476i	0.829097	−	0.829097i	−0.158295	−	0.987392i	$-0.550600\pi$
$283$	13.9476	−	13.9476i	0.829097	−	0.829097i	0.987392	+	0.158295i	$0.0505996\pi$
$284$		0			0
$285$	−0.263782			−0.0156251
$286$		0			0
$287$		−	35.9890i		−	2.12436i
$288$		0			0
$289$	−3.26871	+	16.6828i	−0.192277	+	0.981341i
$290$		0			0
$291$			1.38311i			0.0810791i
$292$		0			0
$293$	6.07154			0.354703			0.177352	−	0.984148i	$-0.443247\pi$
$293$	6.07154			0.354703			0.177352	+	0.984148i	$0.443247\pi$
$294$		0			0
$295$	−5.29937	+	5.29937i	−0.308541	+	0.308541i
$296$		0			0
$297$		−	0.379035i		−	0.0219938i
$298$		0			0
$299$	−1.74708	+	1.74708i	−0.101036	+	0.101036i
$300$		0			0
$301$	22.0224	+	22.0224i	1.26935	+	1.26935i
$302$		0			0
$303$	−1.87316	−	1.87316i	−0.107610	−	0.107610i
$304$		0			0
$305$	−5.93897			−0.340065
$306$		0			0
$307$	26.5578			1.51573			0.757867	−	0.652409i	$-0.226242\pi$
$307$	26.5578			1.51573			0.757867	+	0.652409i	$0.226242\pi$
$308$		0			0
$309$	−0.0681981	−	0.0681981i	−0.00387966	−	0.00387966i
$310$		0			0
$311$	0.717230	+	0.717230i	0.0406704	+	0.0406704i	0.727150	−	0.686479i	$-0.240845\pi$
$311$	0.717230	+	0.717230i	0.0406704	+	0.0406704i	−0.686479	+	0.727150i	$0.740845\pi$
$312$		0			0
$313$	−6.54837	+	6.54837i	−0.370136	+	0.370136i	−0.867526	−	0.497391i	$-0.834291\pi$
$313$	−6.54837	+	6.54837i	−0.370136	+	0.370136i	0.497391	+	0.867526i	$0.334291\pi$
$314$		0			0
$315$		−	11.0212i		−	0.620972i
$316$		0			0
$317$	7.10289	−	7.10289i	0.398938	−	0.398938i	−0.478920	−	0.877858i	$-0.658972\pi$
$317$	7.10289	−	7.10289i	0.398938	−	0.398938i	0.877858	+	0.478920i	$0.158972\pi$
$318$		0			0
$319$	−1.58933			−0.0889853
$320$		0			0
$321$			3.37725i			0.188499i
$322$		0			0
$323$	4.08052	−	3.35860i	0.227046	−	0.186878i
$324$		0			0
$325$		−	0.787596i		−	0.0436880i
$326$		0			0
$327$	0.663647			0.0366997
$328$		0			0
$329$	23.9405	−	23.9405i	1.31989	−	1.31989i
$330$		0			0
$331$		−	24.5152i		−	1.34748i	−0.738970	−	0.673738i	$-0.764688\pi$
$331$		−	24.5152i		−	1.34748i	0.738970	−	0.673738i	$-0.235312\pi$
$332$		0			0
$333$	7.23843	−	7.23843i	0.396663	−	0.396663i
$334$		0			0
$335$	6.20263	+	6.20263i	0.338886	+	0.338886i
$336$		0			0
$337$	−18.7248	−	18.7248i	−1.02000	−	1.02000i	−0.999796	−	0.0202089i	$-0.993567\pi$
$337$	−18.7248	−	18.7248i	−1.02000	−	1.02000i	−0.0202089	−	0.999796i	$-0.506433\pi$
$338$		0			0
$339$	−3.11354			−0.169104
$340$		0			0
$341$	1.26639			0.0685788
$342$		0			0
$343$	0.301688	+	0.301688i	0.0162896	+	0.0162896i
$344$		0			0
$345$	0.456495	+	0.456495i	0.0245769	+	0.0245769i
$346$		0			0
$347$	−23.5332	+	23.5332i	−1.26333	+	1.26333i	−0.313857	+	0.949470i	$0.601621\pi$
$347$	−23.5332	+	23.5332i	−1.26333	+	1.26333i	−0.949470	+	0.313857i	$0.898379\pi$
$348$		0			0
$349$			26.1012i			1.39716i	0.715530	+	0.698582i	$0.246185\pi$
$349$			26.1012i			1.39716i	−0.715530	+	0.698582i	$0.753815\pi$
$350$		0			0
$351$	−0.682796	+	0.682796i	−0.0364449	+	0.0364449i
$352$		0			0
$353$	7.37556			0.392562			0.196281	−	0.980548i	$-0.437114\pi$
$353$	7.37556			0.392562			0.196281	+	0.980548i	$0.437114\pi$
$354$		0			0
$355$		−	2.79951i		−	0.148582i
$356$		0			0
$357$	−2.00932	−	2.44122i	−0.106344	−	0.129203i
$358$		0			0
$359$		−	18.1134i		−	0.955987i	−0.878363	−	0.477993i	$-0.841364\pi$
$359$		−	18.1134i		−	0.955987i	0.878363	−	0.477993i	$-0.158636\pi$
$360$		0			0
$361$	17.3570			0.913527
$362$		0			0
$363$	−1.58677	+	1.58677i	−0.0832840	+	0.0832840i
$364$		0			0
$365$		−	2.04007i		−	0.106782i
$366$		0			0
$367$	16.7983	−	16.7983i	0.876865	−	0.876865i	−0.116344	−	0.993209i	$-0.537117\pi$
$367$	16.7983	−	16.7983i	0.876865	−	0.876865i	0.993209	+	0.116344i	$0.0371174\pi$
$368$		0			0
$369$	−20.1986	−	20.1986i	−1.05150	−	1.05150i
$370$		0			0
$371$	−10.0075	−	10.0075i	−0.519562	−	0.519562i
$372$		0			0
$373$	−9.58726			−0.496409			−0.248205	−	0.968708i	$-0.579841\pi$
$373$	−9.58726			−0.496409			−0.248205	+	0.968708i	$0.579841\pi$
$374$		0			0
$375$	−0.205791			−0.0106270
$376$		0			0
$377$	2.86302	+	2.86302i	0.147453	+	0.147453i
$378$		0			0
$379$	12.3147	+	12.3147i	0.632566	+	0.632566i	0.948711	−	0.316145i	$-0.102389\pi$
$379$	12.3147	+	12.3147i	0.632566	+	0.632566i	−0.316145	+	0.948711i	$0.602389\pi$
$380$		0			0
$381$	−1.46203	+	1.46203i	−0.0749023	+	0.0749023i
$382$		0			0
$383$		−	0.106779i		−	0.00545613i	−0.999996	−	0.00272806i	$-0.999132\pi$
$383$		−	0.106779i		−	0.00545613i	0.999996	−	0.00272806i	$-0.000868371\pi$
$384$		0			0
$385$	0.814597	−	0.814597i	0.0415157	−	0.0415157i
$386$		0			0
$387$	24.7198			1.25658
$388$		0			0
$389$		−	17.3747i		−	0.880934i	−0.897769	−	0.440467i	$-0.854813\pi$
$389$		−	17.3747i		−	0.880934i	0.897769	−	0.440467i	$-0.145187\pi$
$390$		0			0
$391$	−12.8740	−	1.24934i	−0.651066	−	0.0631820i
$392$		0			0
$393$		−	1.34368i		−	0.0677795i
$394$		0			0
$395$	−10.1846			−0.512444
$396$		0			0
$397$	−23.0576	+	23.0576i	−1.15723	+	1.15723i	−0.172161	+	0.985069i	$0.555075\pi$
$397$	−23.0576	+	23.0576i	−1.15723	+	1.15723i	−0.985069	+	0.172161i	$0.944925\pi$
$398$		0			0
$399$			0.982937i			0.0492084i
$400$		0			0
$401$	17.9393	−	17.9393i	0.895848	−	0.895848i	−0.0992182	−	0.995066i	$-0.531634\pi$
$401$	17.9393	−	17.9393i	0.895848	−	0.895848i	0.995066	+	0.0992182i	$0.0316342\pi$
$402$		0			0
$403$	−2.28128	−	2.28128i	−0.113639	−	0.113639i
$404$		0			0
$405$	−6.09571	−	6.09571i	−0.302899	−	0.302899i
$406$		0			0
$407$	1.07001			0.0530386
$408$		0			0
$409$	19.8305			0.980554			0.490277	−	0.871567i	$-0.336896\pi$
$409$	19.8305			0.980554			0.490277	+	0.871567i	$0.336896\pi$
$410$		0			0
$411$	2.96112	+	2.96112i	0.146061	+	0.146061i
$412$		0			0
$413$	19.7472	+	19.7472i	0.971694	+	0.971694i
$414$		0			0
$415$	4.61448	−	4.61448i	0.226516	−	0.226516i
$416$		0			0
$417$			1.39176i			0.0681546i
$418$		0			0
$419$	−18.3160	+	18.3160i	−0.894793	+	0.894793i	−0.994970	−	0.100176i	$-0.968059\pi$
$419$	−18.3160	+	18.3160i	−0.894793	+	0.894793i	0.100176	+	0.994970i	$0.468059\pi$
$420$		0			0
$421$	−4.46855			−0.217784			−0.108892	−	0.994054i	$-0.534730\pi$
$421$	−4.46855			−0.217784			−0.108892	+	0.994054i	$0.534730\pi$
$422$		0			0
$423$		−	26.8729i		−	1.30661i
$424$		0			0
$425$	3.18345	−	2.62024i	0.154420	−	0.127100i
$426$		0			0
$427$			22.1305i			1.07097i
$428$		0			0
$429$	−0.0501081			−0.00241924
$430$		0			0
$431$	−7.54183	+	7.54183i	−0.363277	+	0.363277i	−0.865018	−	0.501741i	$-0.832693\pi$
$431$	−7.54183	+	7.54183i	−0.363277	+	0.363277i	0.501741	+	0.865018i	$0.332693\pi$
$432$		0			0
$433$		−	31.3924i		−	1.50862i	−0.656517	−	0.754312i	$-0.727971\pi$
$433$		−	31.3924i		−	1.50862i	0.656517	−	0.754312i	$-0.272029\pi$
$434$		0			0
$435$	0.748081	−	0.748081i	0.0358677	−	0.0358677i
$436$		0			0
$437$	2.84333	+	2.84333i	0.136015	+	0.136015i
$438$		0			0
$439$	22.0920	+	22.0920i	1.05439	+	1.05439i	0.998433	+	0.0559602i	$0.0178220\pi$
$439$	22.0920	+	22.0920i	1.05439	+	1.05439i	0.0559602	+	0.998433i	$0.482178\pi$
$440$		0			0
$441$	−20.3649			−0.969758
$442$		0			0
$443$	2.70863			0.128691			0.0643454	−	0.997928i	$-0.479504\pi$
$443$	2.70863			0.128691			0.0643454	+	0.997928i	$0.479504\pi$
$444$		0			0
$445$	−3.63394	−	3.63394i	−0.172265	−	0.172265i
$446$		0			0
$447$	−2.95303	−	2.95303i	−0.139673	−	0.139673i
$448$		0			0
$449$	13.5378	−	13.5378i	0.638889	−	0.638889i	−0.311392	−	0.950281i	$-0.600795\pi$
$449$	13.5378	−	13.5378i	0.638889	−	0.638889i	0.950281	+	0.311392i	$0.100795\pi$
$450$		0			0
$451$		−	2.98583i		−	0.140597i
$452$		0			0
$453$	0.674770	−	0.674770i	0.0317035	−	0.0317035i
$454$		0			0
$455$	−2.93484			−0.137587
$456$		0			0
$457$			25.1155i			1.17485i	0.809277	+	0.587427i	$0.199859\pi$
$457$			25.1155i			1.17485i	−0.809277	+	0.587427i	$0.800141\pi$
$458$		0			0
$459$	−5.03143	−	0.488270i	−0.234847	−	0.0227905i
$460$		0			0
$461$		−	35.8956i		−	1.67183i	−0.548863	−	0.835913i	$-0.684939\pi$
$461$		−	35.8956i		−	1.67183i	0.548863	−	0.835913i	$-0.315061\pi$
$462$		0			0
$463$	15.7696			0.732874			0.366437	−	0.930443i	$-0.380578\pi$
$463$	15.7696			0.732874			0.366437	+	0.930443i	$0.380578\pi$
$464$		0			0
$465$	−0.596077	+	0.596077i	−0.0276424	+	0.0276424i
$466$		0			0
$467$		−	14.9165i		−	0.690255i	−0.938556	−	0.345127i	$-0.887836\pi$
$467$		−	14.9165i		−	0.690255i	0.938556	−	0.345127i	$-0.112164\pi$
$468$		0			0
$469$	23.1130	−	23.1130i	1.06726	−	1.06726i
$470$		0			0
$471$	0.429391	+	0.429391i	0.0197853	+	0.0197853i
$472$		0			0
$473$	1.82709	+	1.82709i	0.0840098	+	0.0840098i
$474$		0			0
$475$	−1.28179			−0.0588127
$476$		0			0
$477$	−11.2333			−0.514336
$478$		0			0
$479$	25.5319	+	25.5319i	1.16658	+	1.16658i	0.983006	+	0.183574i	$0.0587668\pi$
$479$	25.5319	+	25.5319i	1.16658	+	1.16658i	0.183574	+	0.983006i	$0.441233\pi$
$480$		0			0
$481$	−1.92753	−	1.92753i	−0.0878878	−	0.0878878i
$482$		0			0
$483$	1.70105	−	1.70105i	0.0774005	−	0.0774005i
$484$		0			0
$485$			6.72091i			0.305181i
$486$		0			0
$487$	−1.59399	+	1.59399i	−0.0722308	+	0.0722308i	−0.742299	−	0.670068i	$-0.766265\pi$
$487$	−1.59399	+	1.59399i	−0.0722308	+	0.0722308i	0.670068	+	0.742299i	$0.266265\pi$
$488$		0			0
$489$	0.323666			0.0146367
$490$		0			0
$491$		−	29.5542i		−	1.33376i	−0.745165	−	0.666880i	$-0.767629\pi$
$491$		−	29.5542i		−	1.33376i	0.745165	−	0.666880i	$-0.232371\pi$
$492$		0			0
$493$	−2.04736	+	21.0972i	−0.0922085	+	0.950172i
$494$		0			0
$495$		−	0.914374i		−	0.0410981i
$496$		0			0
$497$	−10.4319			−0.467933
$498$		0			0
$499$	−13.0094	+	13.0094i	−0.582380	+	0.582380i	−0.935557	−	0.353176i	$-0.885102\pi$
$499$	−13.0094	+	13.0094i	−0.582380	+	0.582380i	0.353176	+	0.935557i	$0.385102\pi$
$500$		0			0
$501$		−	2.97925i		−	0.133103i
$502$		0			0
$503$	−25.8407	+	25.8407i	−1.15218	+	1.15218i	−0.166063	+	0.986115i	$0.553105\pi$
$503$	−25.8407	+	25.8407i	−1.15218	+	1.15218i	−0.986115	+	0.166063i	$0.946895\pi$
$504$		0			0
$505$	−9.10223	−	9.10223i	−0.405044	−	0.405044i
$506$		0			0
$507$	−1.80145	−	1.80145i	−0.0800052	−	0.0800052i
$508$		0			0
$509$	−4.02666			−0.178479			−0.0892394	−	0.996010i	$-0.528444\pi$
$509$	−4.02666			−0.178479			−0.0892394	+	0.996010i	$0.528444\pi$
$510$		0			0
$511$	−7.60195			−0.336291
$512$		0			0
$513$	1.11123	+	1.11123i	0.0490621	+	0.0490621i
$514$		0			0
$515$	−0.331395	−	0.331395i	−0.0146030	−	0.0146030i
$516$		0			0
$517$	1.98623	−	1.98623i	0.0873545	−	0.0873545i
$518$		0			0
$519$			0.520248i			0.0228364i
$520$		0			0
$521$	−23.0572	+	23.0572i	−1.01015	+	1.01015i	−0.0102053	+	0.999948i	$0.503248\pi$
$521$	−23.0572	+	23.0572i	−1.01015	+	1.01015i	−0.999948	+	0.0102053i	$0.996752\pi$
$522$		0			0
$523$	24.2516			1.06045			0.530225	−	0.847857i	$-0.322107\pi$
$523$	24.2516			1.06045			0.530225	+	0.847857i	$0.322107\pi$
$524$		0			0
$525$			0.766846i			0.0334679i
$526$		0			0
$527$	1.63135	−	16.8104i	0.0710628	−	0.732274i
$528$		0			0
$529$			13.1588i			0.572121i
$530$		0			0
$531$	22.1659			0.961919
$532$		0			0
$533$	−5.37870	+	5.37870i	−0.232977	+	0.232977i
$534$		0			0
$535$			16.4110i			0.709510i
$536$		0			0
$537$	−3.45067	+	3.45067i	−0.148907	+	0.148907i
$538$		0			0
$539$	−1.50521	−	1.50521i	−0.0648341	−	0.0648341i
$540$		0			0
$541$	25.6963	+	25.6963i	1.10477	+	1.10477i	0.993827	+	0.110942i	$0.0353868\pi$
$541$	25.6963	+	25.6963i	1.10477	+	1.10477i	0.110942	+	0.993827i	$0.464613\pi$
$542$		0			0
$543$	−0.551743			−0.0236775
$544$		0			0
$545$	3.22485			0.138137
$546$		0			0
$547$	−0.987573	−	0.987573i	−0.0422256	−	0.0422256i	0.685679	−	0.727904i	$-0.259506\pi$
$547$	−0.987573	−	0.987573i	−0.0422256	−	0.0422256i	−0.727904	+	0.685679i	$0.759506\pi$
$548$		0			0
$549$	12.4206	+	12.4206i	0.530099	+	0.530099i
$550$		0			0
$551$	4.65950	−	4.65950i	0.198501	−	0.198501i
$552$		0			0
$553$			37.9512i			1.61385i
$554$		0			0
$555$	−0.503645	+	0.503645i	−0.0213785	+	0.0213785i
$556$		0			0
$557$	−4.66974			−0.197863			−0.0989316	−	0.995094i	$-0.531543\pi$
$557$	−4.66974			−0.197863			−0.0989316	+	0.995094i	$0.531543\pi$
$558$		0			0
$559$		−	6.58267i		−	0.278417i
$560$		0			0
$561$	−0.166704	−	0.202536i	−0.00703823	−	0.00855108i
$562$		0			0
$563$			40.3498i			1.70054i	0.526347	+	0.850270i	$0.323561\pi$
$563$			40.3498i			1.70054i	−0.526347	+	0.850270i	$0.676439\pi$
$564$		0			0
$565$	−15.1296			−0.636506
$566$		0			0
$567$	−22.7146	+	22.7146i	−0.953924	+	0.953924i
$568$		0			0
$569$		−	14.0333i		−	0.588307i	−0.955758	−	0.294154i	$-0.904962\pi$
$569$		−	14.0333i		−	0.588307i	0.955758	−	0.294154i	$-0.0950378\pi$
$570$		0			0
$571$	−19.9923	+	19.9923i	−0.836652	+	0.836652i	−0.988417	−	0.151764i	$-0.951505\pi$
$571$	−19.9923	+	19.9923i	−0.836652	+	0.836652i	0.151764	+	0.988417i	$0.451505\pi$
$572$		0			0
$573$	−0.293905	−	0.293905i	−0.0122781	−	0.0122781i
$574$		0			0
$575$	2.21824	+	2.21824i	0.0925072	+	0.0925072i
$576$		0			0
$577$	−34.5210			−1.43713			−0.718565	−	0.695460i	$-0.755201\pi$
$577$	−34.5210			−1.43713			−0.718565	+	0.695460i	$0.755201\pi$
$578$		0			0
$579$	−3.56133			−0.148004
$580$		0			0
$581$	−17.1951	−	17.1951i	−0.713372	−	0.713372i
$582$		0			0
$583$	−0.830273	−	0.830273i	−0.0343864	−	0.0343864i
$584$		0			0
$585$	−1.64716	+	1.64716i	−0.0681016	+	0.0681016i
$586$		0			0
$587$		−	0.102673i		−	0.00423777i	−0.999998	−	0.00211888i	$-0.999326\pi$
$587$		−	0.102673i		−	0.00423777i	0.999998	−	0.00211888i	$-0.000674462\pi$
$588$		0			0
$589$	−3.71272	+	3.71272i	−0.152980	+	0.152980i
$590$		0			0
$591$	1.78417			0.0733907
$592$		0			0
$593$		−	24.0826i		−	0.988955i	−0.869191	−	0.494477i	$-0.835359\pi$
$593$		−	24.0826i		−	0.988955i	0.869191	−	0.494477i	$-0.164641\pi$
$594$		0			0
$595$	−9.76386	−	11.8626i	−0.400279	−	0.486318i
$596$		0			0
$597$		−	1.72423i		−	0.0705681i
$598$		0			0
$599$	8.44769			0.345163			0.172582	−	0.984995i	$-0.444789\pi$
$599$	8.44769			0.345163			0.172582	+	0.984995i	$0.444789\pi$
$600$		0			0
$601$	−20.4341	+	20.4341i	−0.833526	+	0.833526i	−0.987997	−	0.154471i	$-0.950633\pi$
$601$	−20.4341	+	20.4341i	−0.833526	+	0.833526i	0.154471	+	0.987997i	$0.450633\pi$
$602$		0			0
$603$		−	25.9440i		−	1.05652i
$604$		0			0
$605$	−7.71059	+	7.71059i	−0.313480	+	0.313480i
$606$		0			0
$607$	−27.8178	−	27.8178i	−1.12909	−	1.12909i	−0.990325	−	0.138764i	$-0.955687\pi$
$607$	−27.8178	−	27.8178i	−1.12909	−	1.12909i	−0.138764	−	0.990325i	$-0.544313\pi$
$608$		0			0
$609$	−2.78759	−	2.78759i	−0.112959	−	0.112959i
$610$		0			0
$611$	−7.15603			−0.289502
$612$		0			0
$613$	−24.3227			−0.982386			−0.491193	−	0.871051i	$-0.663439\pi$
$613$	−24.3227			−0.982386			−0.491193	+	0.871051i	$0.663439\pi$
$614$		0			0
$615$	1.40540	+	1.40540i	0.0566713	+	0.0566713i
$616$		0			0
$617$	7.06490	+	7.06490i	0.284422	+	0.284422i	0.834870	−	0.550448i	$-0.185543\pi$
$617$	7.06490	+	7.06490i	0.284422	+	0.284422i	−0.550448	+	0.834870i	$0.685543\pi$
$618$		0			0
$619$	20.9225	−	20.9225i	0.840947	−	0.840947i	−0.148035	−	0.988982i	$-0.547295\pi$
$619$	20.9225	−	20.9225i	0.840947	−	0.840947i	0.988982	+	0.148035i	$0.0472950\pi$
$620$		0			0
$621$		−	3.84615i		−	0.154341i
$622$		0			0
$623$	−13.5413	+	13.5413i	−0.542519	+	0.542519i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$			0.0815496i			0.00325678i
$628$		0			0
$629$	1.37838	−	14.2037i	0.0549598	−	0.566339i
$630$		0			0
$631$			28.7809i			1.14575i	0.819643	+	0.572875i	$0.194172\pi$
$631$			28.7809i			1.14575i	−0.819643	+	0.572875i	$0.805828\pi$
$632$		0			0
$633$	1.06419			0.0422979
$634$		0			0
$635$	−7.10445	+	7.10445i	−0.281931	+	0.281931i
$636$		0			0
$637$			5.42300i			0.214867i
$638$		0			0
$639$	−5.85482	+	5.85482i	−0.231613	+	0.231613i
$640$		0			0
$641$	11.2401	+	11.2401i	0.443958	+	0.443958i	0.893340	−	0.449382i	$-0.148356\pi$
$641$	11.2401	+	11.2401i	0.443958	+	0.443958i	−0.449382	+	0.893340i	$0.648356\pi$
$642$		0			0
$643$	5.77814	+	5.77814i	0.227867	+	0.227867i	0.811801	−	0.583934i	$-0.198487\pi$
$643$	5.77814	+	5.77814i	0.227867	+	0.227867i	−0.583934	+	0.811801i	$0.698487\pi$
$644$		0			0
$645$	−1.71999			−0.0677245
$646$		0			0
$647$	0.927072			0.0364469			0.0182235	−	0.999834i	$-0.494199\pi$
$647$	0.927072			0.0364469			0.0182235	+	0.999834i	$0.494199\pi$
$648$		0			0
$649$	1.63833	+	1.63833i	0.0643100	+	0.0643100i
$650$		0			0
$651$	2.22118	+	2.22118i	0.0870547	+	0.0870547i
$652$		0			0
$653$	−20.2482	+	20.2482i	−0.792373	+	0.792373i	−0.981879	−	0.189507i	$-0.939311\pi$
$653$	−20.2482	+	20.2482i	−0.792373	+	0.792373i	0.189507	+	0.981879i	$0.439311\pi$
$654$		0			0
$655$		−	6.52932i		−	0.255121i
$656$		0			0
$657$	−4.26654	+	4.26654i	−0.166454	+	0.166454i
$658$		0			0
$659$	−3.92658			−0.152958			−0.0764789	−	0.997071i	$-0.524368\pi$
$659$	−3.92658			−0.152958			−0.0764789	+	0.997071i	$0.524368\pi$
$660$		0			0
$661$		−	21.0735i		−	0.819664i	−0.912161	−	0.409832i	$-0.865587\pi$
$661$		−	21.0735i		−	0.819664i	0.912161	−	0.409832i	$-0.134413\pi$
$662$		0			0
$663$	−0.0645488	+	0.665150i	−0.00250687	+	0.0258323i
$664$		0			0
$665$			4.77638i			0.185220i
$666$		0			0
$667$	−16.1273			−0.624450
$668$		0			0
$669$	0.824523	−	0.824523i	0.0318779	−	0.0318779i
$670$		0			0
$671$			1.83607i			0.0708806i
$672$		0			0
$673$	33.6996	−	33.6996i	1.29902	−	1.29902i	0.369985	−	0.929038i	$-0.379363\pi$
$673$	33.6996	−	33.6996i	1.29902	−	1.29902i	0.929038	−	0.369985i	$-0.120637\pi$
$674$		0			0
$675$	0.866936	+	0.866936i	0.0333684	+	0.0333684i
$676$		0			0
$677$	−32.0336	−	32.0336i	−1.23115	−	1.23115i	−0.963522	−	0.267629i	$-0.913760\pi$
$677$	−32.0336	−	32.0336i	−1.23115	−	1.23115i	−0.267629	−	0.963522i	$-0.586240\pi$
$678$		0			0
$679$	25.0443			0.961112
$680$		0			0
$681$	−3.39843			−0.130228
$682$		0			0
$683$	17.2754	+	17.2754i	0.661024	+	0.661024i	0.955621	−	0.294598i	$-0.0951856\pi$
$683$	17.2754	+	17.2754i	0.661024	+	0.661024i	−0.294598	+	0.955621i	$0.595186\pi$
$684$		0			0
$685$	14.3890	+	14.3890i	0.549774	+	0.549774i
$686$		0			0
$687$	3.18639	−	3.18639i	0.121568	−	0.121568i
$688$		0			0
$689$			2.99132i			0.113960i
$690$		0			0
$691$	12.9696	−	12.9696i	0.493385	−	0.493385i	−0.415986	−	0.909371i	$-0.636563\pi$
$691$	12.9696	−	12.9696i	0.493385	−	0.493385i	0.909371	+	0.415986i	$0.136563\pi$
$692$		0			0
$693$	−3.40726			−0.129431
$694$		0			0
$695$			6.76295i			0.256533i
$696$		0			0
$697$	−39.6349	−	3.84633i	−1.50128	−	0.145690i
$698$		0			0
$699$			4.89786i			0.185254i
$700$		0			0
$701$	−6.46378			−0.244134			−0.122067	−	0.992522i	$-0.538952\pi$
$701$	−6.46378			−0.244134			−0.122067	+	0.992522i	$0.538952\pi$
$702$		0			0
$703$	−3.13701	+	3.13701i	−0.118314	+	0.118314i
$704$		0			0
$705$			1.86980i			0.0704208i
$706$		0			0
$707$	−33.9179	+	33.9179i	−1.27561	+	1.27561i
$708$		0			0
$709$	−23.1984	−	23.1984i	−0.871235	−	0.871235i	0.121372	−	0.992607i	$-0.461271\pi$
$709$	−23.1984	−	23.1984i	−0.871235	−	0.871235i	−0.992607	+	0.121372i	$0.961271\pi$
$710$		0			0
$711$	21.2999	+	21.2999i	0.798807	+	0.798807i
$712$		0			0
$713$	12.8503			0.481249
$714$		0			0
$715$	−0.243490			−0.00910600
$716$		0			0
$717$	−4.13012	−	4.13012i	−0.154242	−	0.154242i
$718$		0			0
$719$	13.7918	+	13.7918i	0.514349	+	0.514349i	0.915856	−	0.401507i	$-0.131514\pi$
$719$	13.7918	+	13.7918i	0.514349	+	0.514349i	−0.401507	+	0.915856i	$0.631514\pi$
$720$		0			0
$721$	−1.23488	+	1.23488i	−0.0459895	+	0.0459895i
$722$		0			0
$723$			2.98085i			0.110859i
$724$		0			0
$725$	3.63514	−	3.63514i	0.135006	−	0.135006i
$726$		0			0
$727$	−23.5795			−0.874516			−0.437258	−	0.899336i	$-0.644050\pi$
$727$	−23.5795			−0.874516			−0.437258	+	0.899336i	$0.644050\pi$
$728$		0			0
$729$			24.7399i			0.916293i
$730$		0			0
$731$	26.6070	−	21.8997i	0.984097	−	0.809991i
$732$		0			0
$733$		−	50.3403i		−	1.85936i	−0.368368	−	0.929680i	$-0.620083\pi$
$733$		−	50.3403i		−	1.85936i	0.368368	−	0.929680i	$-0.379917\pi$
$734$		0			0
$735$	1.41698			0.0522660
$736$		0			0
$737$	1.91758	−	1.91758i	0.0706349	−	0.0706349i
$738$		0			0
$739$			47.5180i			1.74798i	0.485947	+	0.873988i	$0.338475\pi$
$739$			47.5180i			1.74798i	−0.485947	+	0.873988i	$0.661525\pi$
$740$		0			0
$741$	0.146904	−	0.146904i	0.00539665	−	0.00539665i
$742$		0			0
$743$	12.8360	+	12.8360i	0.470909	+	0.470909i	0.902209	−	0.431300i	$-0.141945\pi$
$743$	12.8360	+	12.8360i	0.470909	+	0.470909i	−0.431300	+	0.902209i	$0.641945\pi$
$744$		0			0
$745$	−14.3496	−	14.3496i	−0.525730	−	0.525730i
$746$		0			0
$747$	−19.3012			−0.706195
$748$		0			0
$749$	61.1528			2.23447
$750$		0			0
$751$	37.7958	+	37.7958i	1.37919	+	1.37919i	0.845991	+	0.533198i	$0.179010\pi$
$751$	37.7958	+	37.7958i	1.37919	+	1.37919i	0.533198	+	0.845991i	$0.320990\pi$
$752$		0			0
$753$	2.40497	+	2.40497i	0.0876421	+	0.0876421i
$754$		0			0
$755$	3.27891	−	3.27891i	0.119332	−	0.119332i
$756$		0			0
$757$		−	13.8366i		−	0.502899i	−0.967870	−	0.251449i	$-0.919093\pi$
$757$		−	13.8366i		−	0.502899i	0.967870	−	0.251449i	$-0.0809072\pi$
$758$		0			0
$759$	0.141128	−	0.141128i	0.00512263	−	0.00512263i
$760$		0			0
$761$	0.584674			0.0211944			0.0105972	−	0.999944i	$-0.496627\pi$
$761$	0.584674			0.0211944			0.0105972	+	0.999944i	$0.496627\pi$
$762$		0			0
$763$		−	12.0168i		−	0.435039i
$764$		0			0
$765$	−12.1377	−	1.17789i	−0.438839	−	0.0425867i
$766$		0			0
$767$		−	5.90259i		−	0.213130i
$768$		0			0
$769$	−12.9605			−0.467366			−0.233683	−	0.972313i	$-0.575078\pi$
$769$	−12.9605			−0.467366			−0.233683	+	0.972313i	$0.575078\pi$
$770$		0			0
$771$	1.34795	−	1.34795i	0.0485451	−	0.0485451i
$772$		0			0
$773$			22.5429i			0.810811i	0.914137	+	0.405406i	$0.132870\pi$
$773$			22.5429i			0.810811i	−0.914137	+	0.405406i	$0.867130\pi$
$774$		0			0
$775$	−2.89651	+	2.89651i	−0.104046	+	0.104046i
$776$		0			0
$777$	1.87675	+	1.87675i	0.0673279	+	0.0673279i
$778$		0			0
$779$	8.75369	+	8.75369i	0.313634	+	0.313634i
$780$		0			0
$781$	−0.865483			−0.0309694
$782$		0			0
$783$	−6.30287			−0.225246
$784$		0			0
$785$	2.08653	+	2.08653i	0.0744716	+	0.0744716i
$786$		0			0
$787$	0.598097	+	0.598097i	0.0213198	+	0.0213198i	0.717686	−	0.696367i	$-0.245201\pi$
$787$	0.598097	+	0.598097i	0.0213198	+	0.0213198i	−0.696367	+	0.717686i	$0.745201\pi$
$788$		0			0
$789$	3.98743	−	3.98743i	0.141956	−	0.141956i
$790$		0			0
$791$			56.3777i			2.00456i
$792$		0			0
$793$	3.30750	−	3.30750i	0.117453	−	0.117453i
$794$		0			0
$795$	0.781603			0.0277206
$796$		0			0
$797$		−	8.29645i		−	0.293875i	−0.989146	−	0.146938i	$-0.953058\pi$
$797$		−	8.29645i		−	0.293875i	0.989146	−	0.146938i	$-0.0469417\pi$
$798$		0			0
$799$	−23.8072	−	28.9245i	−0.842239	−	1.02328i
$800$		0			0
$801$			15.1999i			0.537061i
$802$		0			0
$803$	−0.630698			−0.0222569
$804$		0			0
$805$	8.26590	−	8.26590i	0.291335	−	0.291335i
$806$		0			0
$807$			0.752891i			0.0265030i
$808$		0			0
$809$	8.18012	−	8.18012i	0.287598	−	0.287598i	−0.548532	−	0.836130i	$-0.684813\pi$
$809$	8.18012	−	8.18012i	0.287598	−	0.287598i	0.836130	+	0.548532i	$0.184813\pi$
$810$		0			0
$811$	−31.5853	−	31.5853i	−1.10911	−	1.10911i	−0.993268	−	0.115841i	$-0.963044\pi$
$811$	−31.5853	−	31.5853i	−1.10911	−	1.10911i	−0.115841	−	0.993268i	$-0.536956\pi$
$812$		0			0
$813$	−2.00396	−	2.00396i	−0.0702819	−	0.0702819i
$814$		0			0
$815$	1.57279			0.0550923
$816$		0			0
$817$	−10.7131			−0.374805
$818$		0			0
$819$	6.13785	+	6.13785i	0.214474	+	0.214474i
$820$		0			0
$821$	15.1168	+	15.1168i	0.527581	+	0.527581i	0.919850	−	0.392270i	$-0.128310\pi$
$821$	15.1168	+	15.1168i	0.527581	+	0.527581i	−0.392270	+	0.919850i	$0.628310\pi$
$822$		0			0
$823$	27.6470	−	27.6470i	0.963712	−	0.963712i	−0.0356520	−	0.999364i	$-0.511351\pi$
$823$	27.6470	−	27.6470i	0.963712	−	0.963712i	0.999364	+	0.0356520i	$0.0113508\pi$
$824$		0			0
$825$			0.0636215i			0.00221502i
$826$		0			0
$827$	−28.7715	+	28.7715i	−1.00048	+	1.00048i	−0.000484580		1.00000i	$0.500154\pi$
$827$	−28.7715	+	28.7715i	−1.00048	+	1.00048i	−1.00000		0.000484580i	$0.999846\pi$
$828$		0			0
$829$	−42.2942			−1.46894			−0.734469	−	0.678642i	$-0.762569\pi$
$829$	−42.2942			−1.46894			−0.734469	+	0.678642i	$0.762569\pi$
$830$		0			0
$831$			5.37381i			0.186415i
$832$		0			0
$833$	−21.9197	+	18.0417i	−0.759471	+	0.625106i
$834$		0			0
$835$		−	14.4771i		−	0.500999i
$836$		0			0
$837$	5.02218			0.173592
$838$		0			0
$839$	21.3426	−	21.3426i	0.736828	−	0.736828i	−0.235135	−	0.971963i	$-0.575553\pi$
$839$	21.3426	−	21.3426i	0.736828	−	0.736828i	0.971963	+	0.235135i	$0.0755533\pi$
$840$		0			0
$841$		−	2.57148i		−	0.0886716i
$842$		0			0
$843$	0.414905	−	0.414905i	0.0142901	−	0.0142901i
$844$		0			0
$845$	−8.75376	−	8.75376i	−0.301139	−	0.301139i
$846$		0			0
$847$	28.7322	+	28.7322i	0.987249	+	0.987249i
$848$		0			0
$849$	4.05920			0.139311
$850$		0			0
$851$	10.8577			0.372196
$852$		0			0
$853$	−12.4572	−	12.4572i	−0.426526	−	0.426526i	0.460917	−	0.887443i	$-0.347520\pi$
$853$	−12.4572	−	12.4572i	−0.426526	−	0.426526i	−0.887443	+	0.460917i	$0.847520\pi$
$854$		0			0
$855$	2.68071	+	2.68071i	0.0916783	+	0.0916783i
$856$		0			0
$857$	8.37477	−	8.37477i	0.286077	−	0.286077i	−0.549450	−	0.835527i	$-0.685163\pi$
$857$	8.37477	−	8.37477i	0.286077	−	0.286077i	0.835527	+	0.549450i	$0.185163\pi$
$858$		0			0
$859$		−	44.2165i		−	1.50865i	−0.656503	−	0.754323i	$-0.727965\pi$
$859$		−	44.2165i		−	1.50865i	0.656503	−	0.754323i	$-0.272035\pi$
$860$		0			0
$861$	5.23699	−	5.23699i	0.178476	−	0.178476i
$862$		0			0
$863$	14.1125			0.480394			0.240197	−	0.970724i	$-0.422788\pi$
$863$	14.1125			0.480394			0.240197	+	0.970724i	$0.422788\pi$
$864$		0			0
$865$			2.52804i			0.0859559i
$866$		0			0
$867$	−2.90327	+	1.95197i	−0.0986003	+	0.0662924i
$868$		0			0
$869$			3.14863i			0.106810i
$870$		0			0
$871$	−6.90867			−0.234091
$872$		0			0
$873$	14.0559	−	14.0559i	0.475722	−	0.475722i
$874$		0			0
$875$			3.72633i			0.125973i
$876$		0			0
$877$	12.5523	−	12.5523i	0.423863	−	0.423863i	−0.462669	−	0.886531i	$-0.653108\pi$
$877$	12.5523	−	12.5523i	0.423863	−	0.423863i	0.886531	+	0.462669i	$0.153108\pi$
$878$		0			0
$879$	0.883510	+	0.883510i	0.0298000	+	0.0298000i
$880$		0			0
$881$	−29.9202	−	29.9202i	−1.00804	−	1.00804i	−0.999967	−	0.00807089i	$-0.997431\pi$
$881$	−29.9202	−	29.9202i	−1.00804	−	1.00804i	−0.00807089	−	0.999967i	$-0.502569\pi$
$882$		0			0
$883$	−20.5506			−0.691583			−0.345791	−	0.938311i	$-0.612390\pi$
$883$	−20.5506			−0.691583			−0.345791	+	0.938311i	$0.612390\pi$
$884$		0			0
$885$	−1.54229			−0.0518435
$886$		0			0
$887$	−2.06591	−	2.06591i	−0.0693666	−	0.0693666i	0.671572	−	0.740939i	$-0.265619\pi$
$887$	−2.06591	−	2.06591i	−0.0693666	−	0.0693666i	−0.740939	+	0.671572i	$0.765619\pi$
$888$		0			0
$889$	26.4735	+	26.4735i	0.887892	+	0.887892i
$890$		0			0
$891$	−1.88452	+	1.88452i	−0.0631339	+	0.0631339i
$892$		0			0
$893$			11.6462i			0.389727i
$894$		0			0
$895$	−16.7678	+	16.7678i	−0.560486	+	0.560486i
$896$		0			0
$897$	−0.508458			−0.0169769
$898$		0			0
$899$		−	21.0584i		−	0.702339i
$900$		0			0
$901$	−12.0909	+	9.95175i	−0.402805	+	0.331541i
$902$		0			0
$903$			6.40924i			0.213286i
$904$		0			0
$905$	−2.68108			−0.0891220
$906$		0			0
$907$	−8.56255	+	8.56255i	−0.284315	+	0.284315i	−0.834827	−	0.550512i	$-0.814432\pi$
$907$	−8.56255	+	8.56255i	−0.284315	+	0.284315i	0.550512	+	0.834827i	$0.314432\pi$
$908$		0			0
$909$			38.0723i			1.26278i
$910$		0			0
$911$	12.7588	−	12.7588i	0.422717	−	0.422717i	−0.463421	−	0.886138i	$-0.653378\pi$
$911$	12.7588	−	12.7588i	0.422717	−	0.422717i	0.886138	+	0.463421i	$0.153378\pi$
$912$		0			0
$913$	−1.42659	−	1.42659i	−0.0472134	−	0.0472134i
$914$		0			0
$915$	−0.864218	−	0.864218i	−0.0285702	−	0.0285702i
$916$		0			0
$917$	−24.3304			−0.803459
$918$		0			0
$919$	15.0666			0.497000			0.248500	−	0.968632i	$-0.420062\pi$
$919$	15.0666			0.497000			0.248500	+	0.968632i	$0.420062\pi$
$920$		0			0
$921$	3.86460	+	3.86460i	0.127343	+	0.127343i
$922$		0			0
$923$	1.55909	+	1.55909i	0.0513179	+	0.0513179i
$924$		0			0
$925$	−2.44736	+	2.44736i	−0.0804686	+	0.0804686i
$926$		0			0
$927$			1.38614i			0.0455268i
$928$		0			0
$929$	−19.5976	+	19.5976i	−0.642977	+	0.642977i	−0.951286	−	0.308309i	$-0.900237\pi$
$929$	−19.5976	+	19.5976i	−0.642977	+	0.642977i	0.308309	+	0.951286i	$0.400237\pi$
$930$		0			0
$931$	8.82579			0.289253
$932$		0			0
$933$			0.208738i			0.00683376i
$934$		0			0
$935$	−0.810061	−	0.984181i	−0.0264918	−	0.0321862i
$936$		0			0
$937$		−	12.8130i		−	0.418583i	−0.977853	−	0.209292i	$-0.932884\pi$
$937$		−	12.8130i		−	0.418583i	0.977853	−	0.209292i	$-0.0671158\pi$
$938$		0			0
$939$	−1.90579			−0.0621931
$940$		0			0
$941$	23.2420	−	23.2420i	0.757667	−	0.757667i	−0.218231	−	0.975897i	$-0.570028\pi$
$941$	23.2420	−	23.2420i	0.757667	−	0.757667i	0.975897	+	0.218231i	$0.0700285\pi$
$942$		0			0
$943$		−	30.2979i		−	0.986636i
$944$		0			0
$945$	3.23049	−	3.23049i	0.105088	−	0.105088i
$946$		0			0
$947$	−0.802556	−	0.802556i	−0.0260796	−	0.0260796i	0.693947	−	0.720026i	$-0.255870\pi$
$947$	−0.802556	−	0.802556i	−0.0260796	−	0.0260796i	−0.720026	+	0.693947i	$0.755870\pi$
$948$		0			0
$949$	1.13614	+	1.13614i	0.0368808	+	0.0368808i
$950$		0			0
$951$	2.06718			0.0670328
$952$		0			0
$953$	4.74335			0.153652			0.0768261	−	0.997045i	$-0.475521\pi$
$953$	4.74335			0.153652			0.0768261	+	0.997045i	$0.475521\pi$
$954$		0			0
$955$	−1.42817	−	1.42817i	−0.0462145	−	0.0462145i
$956$		0			0
$957$	−0.231273	−	0.231273i	−0.00747601	−	0.00747601i
$958$		0			0
$959$	53.6179	−	53.6179i	1.73141	−	1.73141i
$960$		0			0
$961$		−	14.2205i		−	0.458725i
$962$		0			0
$963$	34.3216	−	34.3216i	1.10600	−	1.10600i
$964$		0			0
$965$	−17.3055			−0.557085
$966$		0			0
$967$		−	30.0520i		−	0.966407i	−0.875508	−	0.483204i	$-0.839473\pi$
$967$		−	30.0520i		−	0.966407i	0.875508	−	0.483204i	$-0.160527\pi$
$968$		0			0
$969$	1.08251	+	0.105052i	0.0347754	+	0.00337474i
$970$		0			0
$971$		−	18.4225i		−	0.591206i	−0.955311	−	0.295603i	$-0.904480\pi$
$971$		−	18.4225i		−	0.591206i	0.955311	−	0.295603i	$-0.0955205\pi$
$972$		0			0
$973$	25.2010			0.807906
$974$		0			0
$975$	0.114608	−	0.114608i	0.00367040	−	0.00367040i
$976$		0			0
$977$		−	22.2649i		−	0.712317i	−0.934426	−	0.356158i	$-0.884086\pi$
$977$		−	22.2649i		−	0.712317i	0.934426	−	0.356158i	$-0.115914\pi$
$978$		0			0
$979$	−1.12345	+	1.12345i	−0.0359057	+	0.0359057i
$980$		0			0
$981$	−6.74437	−	6.74437i	−0.215331	−	0.215331i
$982$		0			0
$983$	19.0722	+	19.0722i	0.608308	+	0.608308i	0.942504	−	0.334196i	$-0.108465\pi$
$983$	19.0722	+	19.0722i	0.608308	+	0.608308i	−0.334196	+	0.942504i	$0.608465\pi$
$984$		0			0
$985$	8.66978			0.276242
$986$		0			0
$987$	6.96749			0.221778
$988$		0			0
$989$	18.5399	+	18.5399i	0.589535	+	0.589535i
$990$		0			0
$991$	−4.02397	−	4.02397i	−0.127826	−	0.127826i	0.640300	−	0.768125i	$-0.278810\pi$
$991$	−4.02397	−	4.02397i	−0.127826	−	0.127826i	−0.768125	+	0.640300i	$0.778810\pi$
$992$		0			0
$993$	3.56736	−	3.56736i	0.113207	−	0.113207i
$994$		0			0
$995$		−	8.37854i		−	0.265618i
$996$		0			0
$997$	3.32705	−	3.32705i	0.105369	−	0.105369i	−0.652457	−	0.757826i	$-0.726262\pi$
$997$	3.32705	−	3.32705i	0.105369	−	0.105369i	0.757826	+	0.652457i	$0.226262\pi$
$998$		0			0
$999$	4.24341			0.134255

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bd.b.81.7	✓	20
4.3	odd	2		1360.2.bt.f.81.4		20
17.4	even	4	inner	680.2.bd.b.361.7	yes	20
68.55	odd	4		1360.2.bt.f.1041.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bd.b.81.7	✓	20	1.1	even	1	trivial
680.2.bd.b.361.7	yes	20	17.4	even	4	inner
1360.2.bt.f.81.4		20	4.3	odd	2
1360.2.bt.f.1041.4		20	68.55	odd	4

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.145516 + 0.145516i) q^{3} +(0.707107 + 0.707107i) q^{5} +(2.63491 - 2.63491i) q^{7} -2.95765i q^{9} +(0.218606 - 0.218606i) q^{11} -0.787596 q^{13} +0.205791i q^{15} +(-2.62024 - 3.18345i) q^{17} +1.28179i q^{19} +0.766846 q^{21} +(2.21824 - 2.21824i) q^{23} +1.00000i q^{25} +(0.866936 - 0.866936i) q^{27} +(-3.63514 - 3.63514i) q^{29} +(2.89651 + 2.89651i) q^{31} +0.0636215 q^{33} +3.72633 q^{35} +(2.44736 + 2.44736i) q^{37} +(-0.114608 - 0.114608i) q^{39} +(6.82926 - 6.82926i) q^{41} +8.35792i q^{43} +(2.09137 - 2.09137i) q^{45} +9.08591 q^{47} -6.88550i q^{49} +(0.0819568 - 0.844532i) q^{51} -3.79803i q^{53} +0.309156 q^{55} +(-0.186522 + 0.186522i) q^{57} +7.49443i q^{59} +(-4.19949 + 4.19949i) q^{61} +(-7.79314 - 7.79314i) q^{63} +(-0.556915 - 0.556915i) q^{65} +8.77184 q^{67} +0.645582 q^{69} +(-1.97955 - 1.97955i) q^{71} +(-1.44255 - 1.44255i) q^{73} +(-0.145516 + 0.145516i) q^{75} -1.15201i q^{77} +(-7.20162 + 7.20162i) q^{79} -8.62064 q^{81} -6.52587i q^{83} +(0.398252 - 4.10383i) q^{85} -1.05795i q^{87} -5.13917 q^{89} +(-2.07525 + 2.07525i) q^{91} +0.842980i q^{93} +(-0.906364 + 0.906364i) q^{95} +(4.75240 + 4.75240i) q^{97} +(-0.646560 - 0.646560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} + 4 q^{7} + 12 q^{11} + 4 q^{13} + 4 q^{17} + 16 q^{21} - 4 q^{23} - 16 q^{27} - 4 q^{29} - 4 q^{31} + 16 q^{33} - 8 q^{35} - 8 q^{37} - 8 q^{39} - 8 q^{41} + 4 q^{47} - 4 q^{51} - 8 q^{55}+ \cdots + 52 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 + 4 * q^7 + 12 * q^11 + 4 * q^13 + 4 * q^17 + 16 * q^21 - 4 * q^23 - 16 * q^27 - 4 * q^29 - 4 * q^31 + 16 * q^33 - 8 * q^35 - 8 * q^37 - 8 * q^39 - 8 * q^41 + 4 * q^47 - 4 * q^51 - 8 * q^55 - 24 * q^57 - 24 * q^61 + 60 * q^63 - 4 * q^65 - 56 * q^67 + 24 * q^69 - 40 * q^71 - 20 * q^73 + 4 * q^75 - 8 * q^79 + 4 * q^81 - 12 * q^85 + 28 * q^89 - 4 * q^95 + 24 * q^97 + 52 * q^99

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