LMFDB - Embedded newform 1680.2.bl.d.463.1

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 = [24,0,0,0,0,0,0,0,0,0,0,0,-16] 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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.1
Character	$\chi$	$=$	1680.463
Dual form			1680.2.bl.d.127.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{3} +(2.14388 + 0.635431i) q^{5} +(0.707107 + 0.707107i) q^{7} -1.00000i q^{9} +1.41421i q^{11} +(-4.66562 - 4.66562i) q^{13} +(-1.96527 + 1.06664i) q^{15} +(3.52228 - 3.52228i) q^{17} +7.26583 q^{19} -1.00000 q^{21} +(2.99848 - 2.99848i) q^{23} +(4.19245 + 2.72458i) q^{25} +(0.707107 + 0.707107i) q^{27} -7.18789i q^{29} +7.80968i q^{31} +(-1.00000 - 1.00000i) q^{33} +(1.06664 + 1.96527i) q^{35} +(0.824446 - 0.824446i) q^{37} +6.59818 q^{39} -2.09715 q^{41} +(3.56546 - 3.56546i) q^{43} +(0.635431 - 2.14388i) q^{45} +(1.31286 + 1.31286i) q^{47} +1.00000i q^{49} +4.98125i q^{51} +(6.73055 + 6.73055i) q^{53} +(-0.898635 + 3.03191i) q^{55} +(-5.13772 + 5.13772i) q^{57} -7.63237 q^{59} +8.13210 q^{61} +(0.707107 - 0.707107i) q^{63} +(-7.03785 - 12.9672i) q^{65} +(-4.41495 - 4.41495i) q^{67} +4.24049i q^{69} +9.78861i q^{71} +(0.731281 + 0.731281i) q^{73} +(-4.89108 + 1.03795i) q^{75} +(-1.00000 + 1.00000i) q^{77} -13.6293 q^{79} -1.00000 q^{81} +(-0.102937 + 0.102937i) q^{83} +(9.78951 - 5.31318i) q^{85} +(5.08261 + 5.08261i) q^{87} +8.17829i q^{89} -6.59818i q^{91} +(-5.52228 - 5.52228i) q^{93} +(15.5771 + 4.61694i) q^{95} +(9.35559 - 9.35559i) q^{97} +1.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 16 q^{13} - 8 q^{17} - 24 q^{21} + 8 q^{25} - 24 q^{33} + 24 q^{37} + 32 q^{41} + 8 q^{45} - 16 q^{53} - 8 q^{57} - 32 q^{61} + 32 q^{65} - 48 q^{73} - 24 q^{77} - 24 q^{81} + 72 q^{85} - 40 q^{93}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q - 16 * q^13 - 8 * q^17 - 24 * q^21 + 8 * q^25 - 24 * q^33 + 24 * q^37 + 32 * q^41 + 8 * q^45 - 16 * q^53 - 8 * q^57 - 32 * q^61 + 32 * q^65 - 48 * q^73 - 24 * q^77 - 24 * q^81 + 72 * q^85 - 40 * q^93 - 16 * q^97

Character values

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

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$-1$

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
$5$	2.14388	+	0.635431i	0.958773	+	0.284173i
$5$	2.14388	+	0.635431i	0.958773	+	0.284173i
$6$		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
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$		0			0
$13$	−4.66562	−	4.66562i	−1.29401	−	1.29401i	−0.932285	−	0.361724i	$-0.882188\pi$
$13$	−4.66562	−	4.66562i	−1.29401	−	1.29401i	−0.361724	−	0.932285i	$-0.617812\pi$
$14$		0			0
$15$	−1.96527	+	1.06664i	−0.507431	+	0.275404i
$16$		0			0
$17$	3.52228	−	3.52228i	0.854278	−	0.854278i	−0.136379	−	0.990657i	$-0.543546\pi$
$17$	3.52228	−	3.52228i	0.854278	−	0.854278i	0.990657	+	0.136379i	$0.0435465\pi$
$18$		0			0
$19$	7.26583			1.66690			0.833448	−	0.552598i	$-0.186363\pi$
$19$	7.26583			1.66690			0.833448	+	0.552598i	$0.186363\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	2.99848	−	2.99848i	0.625226	−	0.625226i	−0.321637	−	0.946863i	$-0.604233\pi$
$23$	2.99848	−	2.99848i	0.625226	−	0.625226i	0.946863	+	0.321637i	$0.104233\pi$
$24$		0			0
$25$	4.19245	+	2.72458i	0.838491	+	0.544915i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	7.18789i		−	1.33476i	−0.744718	−	0.667379i	$-0.767416\pi$
$29$		−	7.18789i		−	1.33476i	0.744718	−	0.667379i	$-0.232584\pi$
$30$		0			0
$31$			7.80968i			1.40266i	0.712837	+	0.701330i	$0.247410\pi$
$31$			7.80968i			1.40266i	−0.712837	+	0.701330i	$0.752590\pi$
$32$		0			0
$33$	−1.00000	−	1.00000i	−0.174078	−	0.174078i
$34$		0			0
$35$	1.06664	+	1.96527i	0.180294	+	0.332191i
$36$		0			0
$37$	0.824446	−	0.824446i	0.135538	−	0.135538i	−0.636083	−	0.771621i	$-0.719446\pi$
$37$	0.824446	−	0.824446i	0.135538	−	0.135538i	0.771621	+	0.636083i	$0.219446\pi$
$38$		0			0
$39$	6.59818			1.05655
$40$		0			0
$41$	−2.09715			−0.327519			−0.163760	−	0.986500i	$-0.552362\pi$
$41$	−2.09715			−0.327519			−0.163760	+	0.986500i	$0.552362\pi$
$42$		0			0
$43$	3.56546	−	3.56546i	0.543727	−	0.543727i	−0.380892	−	0.924619i	$-0.624383\pi$
$43$	3.56546	−	3.56546i	0.543727	−	0.543727i	0.924619	+	0.380892i	$0.124383\pi$
$44$		0			0
$45$	0.635431	−	2.14388i	0.0947245	−	0.319591i
$46$		0			0
$47$	1.31286	+	1.31286i	0.191500	+	0.191500i	0.796344	−	0.604844i	$-0.206765\pi$
$47$	1.31286	+	1.31286i	0.191500	+	0.191500i	−0.604844	+	0.796344i	$0.706765\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$			4.98125i			0.697515i
$52$		0			0
$53$	6.73055	+	6.73055i	0.924512	+	0.924512i	0.997344	−	0.0728322i	$-0.0232038\pi$
$53$	6.73055	+	6.73055i	0.924512	+	0.924512i	−0.0728322	+	0.997344i	$0.523204\pi$
$54$		0			0
$55$	−0.898635	+	3.03191i	−0.121172	+	0.408822i
$56$		0			0
$57$	−5.13772	+	5.13772i	−0.680508	+	0.680508i
$58$		0			0
$59$	−7.63237			−0.993649			−0.496825	−	0.867851i	$-0.665501\pi$
$59$	−7.63237			−0.993649			−0.496825	+	0.867851i	$0.665501\pi$
$60$		0			0
$61$	8.13210			1.04121			0.520604	−	0.853798i	$-0.325707\pi$
$61$	8.13210			1.04121			0.520604	+	0.853798i	$0.325707\pi$
$62$		0			0
$63$	0.707107	−	0.707107i	0.0890871	−	0.0890871i
$64$		0			0
$65$	−7.03785	−	12.9672i	−0.872938	−	1.60838i
$66$		0			0
$67$	−4.41495	−	4.41495i	−0.539373	−	0.539373i	0.383972	−	0.923345i	$-0.374556\pi$
$67$	−4.41495	−	4.41495i	−0.539373	−	0.539373i	−0.923345	+	0.383972i	$0.874556\pi$
$68$		0			0
$69$			4.24049i			0.510495i
$70$		0			0
$71$			9.78861i			1.16169i	0.814013	+	0.580847i	$0.197279\pi$
$71$			9.78861i			1.16169i	−0.814013	+	0.580847i	$0.802721\pi$
$72$		0			0
$73$	0.731281	+	0.731281i	0.0855900	+	0.0855900i	0.748606	−	0.663016i	$-0.230724\pi$
$73$	0.731281	+	0.731281i	0.0855900	+	0.0855900i	−0.663016	+	0.748606i	$0.730724\pi$
$74$		0			0
$75$	−4.89108	+	1.03795i	−0.564773	+	0.119852i
$76$		0			0
$77$	−1.00000	+	1.00000i	−0.113961	+	0.113961i
$78$		0			0
$79$	−13.6293			−1.53342			−0.766709	−	0.641995i	$-0.778107\pi$
$79$	−13.6293			−1.53342			−0.766709	+	0.641995i	$0.778107\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−0.102937	+	0.102937i	−0.0112989	+	0.0112989i	−0.712734	−	0.701435i	$-0.752543\pi$
$83$	−0.102937	+	0.102937i	−0.0112989	+	0.0112989i	0.701435	+	0.712734i	$0.252543\pi$
$84$		0			0
$85$	9.78951	−	5.31318i	1.06182	−	0.576295i
$86$		0			0
$87$	5.08261	+	5.08261i	0.544913	+	0.544913i
$88$		0			0
$89$			8.17829i			0.866897i	0.901178	+	0.433449i	$0.142703\pi$
$89$			8.17829i			0.866897i	−0.901178	+	0.433449i	$0.857297\pi$
$90$		0			0
$91$		−	6.59818i		−	0.691677i
$92$		0			0
$93$	−5.52228	−	5.52228i	−0.572634	−	0.572634i
$94$		0			0
$95$	15.5771	+	4.61694i	1.59818	+	0.473688i
$96$		0			0
$97$	9.35559	−	9.35559i	0.949917	−	0.949917i	−0.0488878	−	0.998804i	$-0.515568\pi$
$97$	9.35559	−	9.35559i	0.949917	−	0.949917i	0.998804	+	0.0488878i	$0.0155677\pi$
$98$		0			0
$99$	1.41421			0.142134
$100$		0			0
$101$	−11.2828			−1.12268			−0.561341	−	0.827585i	$-0.689714\pi$
$101$	−11.2828			−1.12268			−0.561341	+	0.827585i	$0.689714\pi$
$102$		0			0
$103$	9.21278	−	9.21278i	0.907763	−	0.907763i	−0.0883288	−	0.996091i	$-0.528153\pi$
$103$	9.21278	−	9.21278i	0.907763	−	0.907763i	0.996091	+	0.0883288i	$0.0281526\pi$
$104$		0			0
$105$	−2.14388	−	0.635431i	−0.209221	−	0.0620117i
$106$		0			0
$107$	8.81565	+	8.81565i	0.852241	+	0.852241i	0.990409	−	0.138168i	$-0.0441214\pi$
$107$	8.81565	+	8.81565i	0.852241	+	0.852241i	−0.138168	+	0.990409i	$0.544121\pi$
$108$		0			0
$109$			3.71332i			0.355672i	0.984060	+	0.177836i	$0.0569096\pi$
$109$			3.71332i			0.355672i	−0.984060	+	0.177836i	$0.943090\pi$
$110$		0			0
$111$			1.16594i			0.110666i
$112$		0			0
$113$	9.48619	+	9.48619i	0.892386	+	0.892386i	0.994747	−	0.102362i	$-0.0326399\pi$
$113$	9.48619	+	9.48619i	0.892386	+	0.892386i	−0.102362	+	0.994747i	$0.532640\pi$
$114$		0			0
$115$	8.33370	−	4.52305i	0.777122	−	0.421777i
$116$		0			0
$117$	−4.66562	+	4.66562i	−0.431336	+	0.431336i
$118$		0			0
$119$	4.98125			0.456631
$120$		0			0
$121$	9.00000			0.818182
$122$		0			0
$123$	1.48291	−	1.48291i	0.133709	−	0.133709i
$124$		0			0
$125$	7.25684	+	8.50519i	0.649072	+	0.760727i
$126$		0			0
$127$	6.05433	+	6.05433i	0.537235	+	0.537235i	0.922716	−	0.385481i	$-0.125964\pi$
$127$	6.05433	+	6.05433i	0.537235	+	0.537235i	−0.385481	+	0.922716i	$0.625964\pi$
$128$		0			0
$129$			5.04232i			0.443951i
$130$		0			0
$131$			0.295576i			0.0258246i	0.999917	+	0.0129123i	$0.00411022\pi$
$131$			0.295576i			0.0258246i	−0.999917	+	0.0129123i	$0.995890\pi$
$132$		0			0
$133$	5.13772	+	5.13772i	0.445497	+	0.445497i
$134$		0			0
$135$	1.06664	+	1.96527i	0.0918014	+	0.169144i
$136$		0			0
$137$	−5.25598	+	5.25598i	−0.449048	+	0.449048i	−0.895038	−	0.445990i	$-0.852852\pi$
$137$	−5.25598	+	5.25598i	−0.449048	+	0.449048i	0.445990	+	0.895038i	$0.352852\pi$
$138$		0			0
$139$	14.2625			1.20973			0.604866	−	0.796327i	$-0.293227\pi$
$139$	14.2625			1.20973			0.604866	+	0.796327i	$0.293227\pi$
$140$		0			0
$141$	−1.85666			−0.156359
$142$		0			0
$143$	6.59818	−	6.59818i	0.551767	−	0.551767i
$144$		0			0
$145$	4.56741	−	15.4100i	0.379303	−	1.27973i
$146$		0			0
$147$	−0.707107	−	0.707107i	−0.0583212	−	0.0583212i
$148$		0			0
$149$		−	20.7803i		−	1.70239i	−0.524849	−	0.851195i	$-0.675878\pi$
$149$		−	20.7803i		−	1.70239i	0.524849	−	0.851195i	$-0.324122\pi$
$150$		0			0
$151$			9.12096i			0.742253i	0.928582	+	0.371126i	$0.121028\pi$
$151$			9.12096i			0.742253i	−0.928582	+	0.371126i	$0.878972\pi$
$152$		0			0
$153$	−3.52228	−	3.52228i	−0.284759	−	0.284759i
$154$		0			0
$155$	−4.96251	+	16.7430i	−0.398599	+	1.34483i
$156$		0			0
$157$	12.3655	−	12.3655i	0.986871	−	0.986871i	−0.0130435	−	0.999915i	$-0.504152\pi$
$157$	12.3655	−	12.3655i	0.986871	−	0.986871i	0.999915	+	0.0130435i	$0.00415200\pi$
$158$		0			0
$159$	−9.51843			−0.754861
$160$		0			0
$161$	4.24049			0.334197
$162$		0			0
$163$	0.829894	−	0.829894i	0.0650023	−	0.0650023i	−0.673858	−	0.738861i	$-0.735364\pi$
$163$	0.829894	−	0.829894i	0.0650023	−	0.0650023i	0.738861	+	0.673858i	$0.235364\pi$
$164$		0			0
$165$	−1.50845	−	2.77931i	−0.117433	−	0.216369i
$166$		0			0
$167$	−8.74942	−	8.74942i	−0.677051	−	0.677051i	0.282281	−	0.959332i	$-0.408909\pi$
$167$	−8.74942	−	8.74942i	−0.677051	−	0.677051i	−0.959332	+	0.282281i	$0.908909\pi$
$168$		0			0
$169$			30.5360i			2.34892i
$170$		0			0
$171$		−	7.26583i		−	0.555632i
$172$		0			0
$173$	−15.9745	−	15.9745i	−1.21452	−	1.21452i	−0.969524	−	0.244995i	$-0.921214\pi$
$173$	−15.9745	−	15.9745i	−1.21452	−	1.21452i	−0.244995	−	0.969524i	$-0.578786\pi$
$174$		0			0
$175$	1.03795	+	4.89108i	0.0784613	+	0.369731i
$176$		0			0
$177$	5.39690	−	5.39690i	0.405656	−	0.405656i
$178$		0			0
$179$	−7.41117			−0.553937			−0.276968	−	0.960879i	$-0.589330\pi$
$179$	−7.41117			−0.553937			−0.276968	+	0.960879i	$0.589330\pi$
$180$		0			0
$181$	−6.38926			−0.474910			−0.237455	−	0.971399i	$-0.576313\pi$
$181$	−6.38926			−0.474910			−0.237455	+	0.971399i	$0.576313\pi$
$182$		0			0
$183$	−5.75026	+	5.75026i	−0.425072	+	0.425072i
$184$		0			0
$185$	2.29139	−	1.24364i	0.168467	−	0.0914339i
$186$		0			0
$187$	4.98125	+	4.98125i	0.364265	+	0.364265i
$188$		0			0
$189$			1.00000i			0.0727393i
$190$		0			0
$191$			9.38455i			0.679042i	0.940598	+	0.339521i	$0.110265\pi$
$191$			9.38455i			0.679042i	−0.940598	+	0.339521i	$0.889735\pi$
$192$		0			0
$193$	4.60270	+	4.60270i	0.331310	+	0.331310i	0.853084	−	0.521774i	$-0.174730\pi$
$193$	4.60270	+	4.60270i	0.331310	+	0.331310i	−0.521774	+	0.853084i	$0.674730\pi$
$194$		0			0
$195$	14.1457	+	4.19269i	1.01300	+	0.300245i
$196$		0			0
$197$	−12.7328	+	12.7328i	−0.907173	+	0.907173i	−0.996043	−	0.0888699i	$-0.971674\pi$
$197$	−12.7328	+	12.7328i	−0.907173	+	0.907173i	0.0888699	+	0.996043i	$0.471674\pi$
$198$		0			0
$199$	−23.0059			−1.63085			−0.815423	−	0.578865i	$-0.803496\pi$
$199$	−23.0059			−1.63085			−0.815423	+	0.578865i	$0.803496\pi$
$200$		0			0
$201$	6.24369			0.440396
$202$		0			0
$203$	5.08261	−	5.08261i	0.356729	−	0.356729i
$204$		0			0
$205$	−4.49603	−	1.33259i	−0.314017	−	0.0930723i
$206$		0			0
$207$	−2.99848	−	2.99848i	−0.208409	−	0.208409i
$208$		0			0
$209$			10.2754i			0.710767i
$210$		0			0
$211$		−	7.78881i		−	0.536204i	−0.963391	−	0.268102i	$-0.913604\pi$
$211$		−	7.78881i		−	0.536204i	0.963391	−	0.268102i	$-0.0863964\pi$
$212$		0			0
$213$	−6.92159	−	6.92159i	−0.474260	−	0.474260i
$214$		0			0
$215$	9.90952	−	5.37832i	0.675824	−	0.366798i
$216$		0			0
$217$	−5.52228	+	5.52228i	−0.374877	+	0.374877i
$218$		0			0
$219$	−1.03419			−0.0698839
$220$		0			0
$221$	−32.8672			−2.21089
$222$		0			0
$223$	11.7067	−	11.7067i	0.783942	−	0.783942i	−0.196552	−	0.980493i	$-0.562974\pi$
$223$	11.7067	−	11.7067i	0.783942	−	0.783942i	0.980493	+	0.196552i	$0.0629744\pi$
$224$		0			0
$225$	2.72458	−	4.19245i	0.181638	−	0.279497i
$226$		0			0
$227$	−15.1573	−	15.1573i	−1.00602	−	1.00602i	−0.999982	−	0.00604137i	$-0.998077\pi$
$227$	−15.1573	−	15.1573i	−1.00602	−	1.00602i	−0.00604137	−	0.999982i	$-0.501923\pi$
$228$		0			0
$229$		−	9.03108i		−	0.596791i	−0.954442	−	0.298395i	$-0.903549\pi$
$229$		−	9.03108i		−	0.596791i	0.954442	−	0.298395i	$-0.0964514\pi$
$230$		0			0
$231$		−	1.41421i		−	0.0930484i
$232$		0			0
$233$	1.49966	+	1.49966i	0.0982463	+	0.0982463i	0.754522	−	0.656275i	$-0.227869\pi$
$233$	1.49966	+	1.49966i	0.0982463	+	0.0982463i	−0.656275	+	0.754522i	$0.727869\pi$
$234$		0			0
$235$	1.98038	+	3.64884i	0.129186	+	0.238024i
$236$		0			0
$237$	9.63738	−	9.63738i	0.626015	−	0.626015i
$238$		0			0
$239$	9.11403			0.589538			0.294769	−	0.955569i	$-0.404757\pi$
$239$	9.11403			0.589538			0.294769	+	0.955569i	$0.404757\pi$
$240$		0			0
$241$	24.6527			1.58802			0.794010	−	0.607905i	$-0.207990\pi$
$241$	24.6527			1.58802			0.794010	+	0.607905i	$0.207990\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−0.635431	+	2.14388i	−0.0405962	+	0.136968i
$246$		0			0
$247$	−33.8996	−	33.8996i	−2.15698	−	2.15698i
$248$		0			0
$249$		−	0.145576i		−	0.00922547i
$250$		0			0
$251$			10.9383i			0.690418i	0.938526	+	0.345209i	$0.112192\pi$
$251$			10.9383i			0.690418i	−0.938526	+	0.345209i	$0.887808\pi$
$252$		0			0
$253$	4.24049	+	4.24049i	0.266597	+	0.266597i
$254$		0			0
$255$	−3.16524	+	10.6792i	−0.198215	+	0.668758i
$256$		0			0
$257$	−5.76053	+	5.76053i	−0.359332	+	0.359332i	−0.863567	−	0.504235i	$-0.831775\pi$
$257$	−5.76053	+	5.76053i	−0.359332	+	0.359332i	0.504235	+	0.863567i	$0.331775\pi$
$258$		0			0
$259$	1.16594			0.0724481
$260$		0			0
$261$	−7.18789			−0.444919
$262$		0			0
$263$	−7.74153	+	7.74153i	−0.477363	+	0.477363i	−0.904287	−	0.426924i	$-0.859597\pi$
$263$	−7.74153	+	7.74153i	−0.477363	+	0.477363i	0.426924	+	0.904287i	$0.359597\pi$
$264$		0			0
$265$	10.1527	+	18.7063i	0.623675	+	1.14912i
$266$		0			0
$267$	−5.78293	−	5.78293i	−0.353909	−	0.353909i
$268$		0			0
$269$		−	8.69024i		−	0.529854i	−0.964269	−	0.264927i	$-0.914652\pi$
$269$		−	8.69024i		−	0.529854i	0.964269	−	0.264927i	$-0.0853478\pi$
$270$		0			0
$271$		−	14.2413i		−	0.865100i	−0.901610	−	0.432550i	$-0.857614\pi$
$271$		−	14.2413i		−	0.865100i	0.901610	−	0.432550i	$-0.142386\pi$
$272$		0			0
$273$	4.66562	+	4.66562i	0.282376	+	0.282376i
$274$		0			0
$275$	−3.85313	+	5.92903i	−0.232353	+	0.357534i
$276$		0			0
$277$	3.30542	−	3.30542i	0.198603	−	0.198603i	−0.600798	−	0.799401i	$-0.705150\pi$
$277$	3.30542	−	3.30542i	0.198603	−	0.198603i	0.799401	+	0.600798i	$0.205150\pi$
$278$		0			0
$279$	7.80968			0.467553
$280$		0			0
$281$	6.17106			0.368135			0.184067	−	0.982914i	$-0.441074\pi$
$281$	6.17106			0.368135			0.184067	+	0.982914i	$0.441074\pi$
$282$		0			0
$283$	−6.81200	+	6.81200i	−0.404931	+	0.404931i	−0.879967	−	0.475035i	$-0.842435\pi$
$283$	−6.81200	+	6.81200i	−0.404931	+	0.404931i	0.475035	+	0.879967i	$0.342435\pi$
$284$		0			0
$285$	−14.2793	+	7.75000i	−0.845834	+	0.459070i
$286$		0			0
$287$	−1.48291	−	1.48291i	−0.0875332	−	0.0875332i
$288$		0			0
$289$		−	7.81288i		−	0.459581i
$290$		0			0
$291$			13.2308i			0.775604i
$292$		0			0
$293$	−21.0463	−	21.0463i	−1.22954	−	1.22954i	−0.964139	−	0.265399i	$-0.914496\pi$
$293$	−21.0463	−	21.0463i	−1.22954	−	1.22954i	−0.265399	−	0.964139i	$-0.585504\pi$
$294$		0			0
$295$	−16.3629	−	4.84984i	−0.952684	−	0.282369i
$296$		0			0
$297$	−1.00000	+	1.00000i	−0.0580259	+	0.0580259i
$298$		0			0
$299$	−27.9795			−1.61810
$300$		0			0
$301$	5.04232			0.290634
$302$		0			0
$303$	7.97815	−	7.97815i	0.458333	−	0.458333i
$304$		0			0
$305$	17.4343	+	5.16739i	0.998283	+	0.295884i
$306$		0			0
$307$	−16.6351	−	16.6351i	−0.949413	−	0.949413i	0.0493677	−	0.998781i	$-0.484279\pi$
$307$	−16.6351	−	16.6351i	−0.949413	−	0.949413i	−0.998781	+	0.0493677i	$0.984279\pi$
$308$		0			0
$309$			13.0288i			0.741185i
$310$		0			0
$311$			33.8175i			1.91761i	0.284061	+	0.958806i	$0.408318\pi$
$311$			33.8175i			1.91761i	−0.284061	+	0.958806i	$0.591682\pi$
$312$		0			0
$313$	1.02020	+	1.02020i	0.0576649	+	0.0576649i	0.735351	−	0.677686i	$-0.237017\pi$
$313$	1.02020	+	1.02020i	0.0576649	+	0.0576649i	−0.677686	+	0.735351i	$0.737017\pi$
$314$		0			0
$315$	1.96527	−	1.06664i	0.110730	−	0.0600981i
$316$		0			0
$317$	−17.8732	+	17.8732i	−1.00386	+	1.00386i	−0.00386734	+	0.999993i	$0.501231\pi$
$317$	−17.8732	+	17.8732i	−1.00386	+	1.00386i	−0.999993	+	0.00386734i	$0.998769\pi$
$318$		0			0
$319$	10.1652			0.569143
$320$		0			0
$321$	−12.4672			−0.695852
$322$		0			0
$323$	25.5923	−	25.5923i	1.42399	−	1.42399i
$324$		0			0
$325$	−6.84855	−	32.2722i	−0.379889	−	1.79014i
$326$		0			0
$327$	−2.62571	−	2.62571i	−0.145202	−	0.145202i
$328$		0			0
$329$			1.85666i			0.102361i
$330$		0			0
$331$		−	15.8415i		−	0.870728i	−0.900254	−	0.435364i	$-0.856620\pi$
$331$		−	15.8415i		−	0.870728i	0.900254	−	0.435364i	$-0.143380\pi$
$332$		0			0
$333$	−0.824446	−	0.824446i	−0.0451794	−	0.0451794i
$334$		0			0
$335$	−6.65974	−	12.2705i	−0.363860	−	0.670411i
$336$		0			0
$337$	2.53677	−	2.53677i	0.138186	−	0.138186i	−0.634630	−	0.772816i	$-0.718847\pi$
$337$	2.53677	−	2.53677i	0.138186	−	0.138186i	0.772816	+	0.634630i	$0.218847\pi$
$338$		0			0
$339$	−13.4155			−0.728630
$340$		0			0
$341$	−11.0446			−0.598096
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	−2.69454	+	9.09110i	−0.145069	+	0.489448i
$346$		0			0
$347$	−21.0551	−	21.0551i	−1.13030	−	1.13030i	−0.990127	−	0.140171i	$-0.955235\pi$
$347$	−21.0551	−	21.0551i	−1.13030	−	1.13030i	−0.140171	−	0.990127i	$-0.544765\pi$
$348$		0			0
$349$			21.9570i			1.17533i	0.809104	+	0.587666i	$0.199953\pi$
$349$			21.9570i			1.17533i	−0.809104	+	0.587666i	$0.800047\pi$
$350$		0			0
$351$		−	6.59818i		−	0.352185i
$352$		0			0
$353$	−19.1257	−	19.1257i	−1.01796	−	1.01796i	−0.999836	−	0.0181252i	$-0.994230\pi$
$353$	−19.1257	−	19.1257i	−1.01796	−	1.01796i	−0.0181252	−	0.999836i	$-0.505770\pi$
$354$		0			0
$355$	−6.21999	+	20.9856i	−0.330123	+	1.11380i
$356$		0			0
$357$	−3.52228	+	3.52228i	−0.186419	+	0.186419i
$358$		0			0
$359$	−7.02551			−0.370792			−0.185396	−	0.982664i	$-0.559357\pi$
$359$	−7.02551			−0.370792			−0.185396	+	0.982664i	$0.559357\pi$
$360$		0			0
$361$	33.7923			1.77854
$362$		0			0
$363$	−6.36396	+	6.36396i	−0.334021	+	0.334021i
$364$		0			0
$365$	1.10310	+	2.03246i	0.0577390	+	0.106384i
$366$		0			0
$367$	−13.0434	−	13.0434i	−0.680861	−	0.680861i	0.279333	−	0.960194i	$-0.409887\pi$
$367$	−13.0434	−	13.0434i	−0.680861	−	0.680861i	−0.960194	+	0.279333i	$0.909887\pi$
$368$		0			0
$369$			2.09715i			0.109173i
$370$		0			0
$371$			9.51843i			0.494172i
$372$		0			0
$373$	−11.8183	−	11.8183i	−0.611930	−	0.611930i	0.331518	−	0.943449i	$-0.392439\pi$
$373$	−11.8183	−	11.8183i	−0.611930	−	0.611930i	−0.943449	+	0.331518i	$0.892439\pi$
$374$		0			0
$375$	−11.1454	−	0.882711i	−0.575548	−	0.0455830i
$376$		0			0
$377$	−33.5360	+	33.5360i	−1.72719	+	1.72719i
$378$		0			0
$379$	−21.6192			−1.11050			−0.555251	−	0.831683i	$-0.687378\pi$
$379$	−21.6192			−1.11050			−0.555251	+	0.831683i	$0.687378\pi$
$380$		0			0
$381$	−8.56212			−0.438651
$382$		0			0
$383$	−3.71840	+	3.71840i	−0.190001	+	0.190001i	−0.795697	−	0.605695i	$-0.792895\pi$
$383$	−3.71840	+	3.71840i	−0.190001	+	0.190001i	0.605695	+	0.795697i	$0.292895\pi$
$384$		0			0
$385$	−2.77931	+	1.50845i	−0.141647	+	0.0768777i
$386$		0			0
$387$	−3.56546	−	3.56546i	−0.181242	−	0.181242i
$388$		0			0
$389$			36.3278i			1.84189i	0.389687	+	0.920947i	$0.372583\pi$
$389$			36.3278i			1.84189i	−0.389687	+	0.920947i	$0.627417\pi$
$390$		0			0
$391$		−	21.1229i		−	1.06823i
$392$		0			0
$393$	−0.209004	−	0.209004i	−0.0105428	−	0.0105428i
$394$		0			0
$395$	−29.2196	−	8.66049i	−1.47020	−	0.435757i
$396$		0			0
$397$	−1.71017	+	1.71017i	−0.0858311	+	0.0858311i	−0.748719	−	0.662888i	$-0.769331\pi$
$397$	−1.71017	+	1.71017i	−0.0858311	+	0.0858311i	0.662888	+	0.748719i	$0.269331\pi$
$398$		0			0
$399$	−7.26583			−0.363747
$400$		0			0
$401$	30.5962			1.52790			0.763951	−	0.645274i	$-0.223257\pi$
$401$	30.5962			1.52790			0.763951	+	0.645274i	$0.223257\pi$
$402$		0			0
$403$	36.4370	−	36.4370i	1.81505	−	1.81505i
$404$		0			0
$405$	−2.14388	−	0.635431i	−0.106530	−	0.0315748i
$406$		0			0
$407$	1.16594	+	1.16594i	0.0577936	+	0.0577936i
$408$		0			0
$409$		−	21.6519i		−	1.07062i	−0.844656	−	0.535309i	$-0.820195\pi$
$409$		−	21.6519i		−	1.07062i	0.844656	−	0.535309i	$-0.179805\pi$
$410$		0			0
$411$		−	7.43307i		−	0.366646i
$412$		0			0
$413$	−5.39690	−	5.39690i	−0.265564	−	0.265564i
$414$		0			0
$415$	−0.286095	+	0.155276i	−0.0140439	+	0.00762220i
$416$		0			0
$417$	−10.0851	+	10.0851i	−0.493871	+	0.493871i
$418$		0			0
$419$	−18.9270			−0.924645			−0.462323	−	0.886712i	$-0.652984\pi$
$419$	−18.9270			−0.924645			−0.462323	+	0.886712i	$0.652984\pi$
$420$		0			0
$421$	−7.14190			−0.348075			−0.174037	−	0.984739i	$-0.555681\pi$
$421$	−7.14190			−0.348075			−0.174037	+	0.984739i	$0.555681\pi$
$422$		0			0
$423$	1.31286	−	1.31286i	0.0638333	−	0.0638333i
$424$		0			0
$425$	24.3637	−	5.17027i	1.18181	−	0.250795i
$426$		0			0
$427$	5.75026	+	5.75026i	0.278275	+	0.278275i
$428$		0			0
$429$			9.33123i			0.450516i
$430$		0			0
$431$		−	18.2523i		−	0.879182i	−0.898198	−	0.439591i	$-0.855123\pi$
$431$		−	18.2523i		−	0.879182i	0.898198	−	0.439591i	$-0.144877\pi$
$432$		0			0
$433$	19.6445	+	19.6445i	0.944055	+	0.944055i	0.998516	−	0.0544611i	$-0.0173441\pi$
$433$	19.6445	+	19.6445i	0.944055	+	0.944055i	−0.0544611	+	0.998516i	$0.517344\pi$
$434$		0			0
$435$	7.66686	+	14.1262i	0.367598	+	0.677297i
$436$		0			0
$437$	21.7864	−	21.7864i	1.04219	−	1.04219i
$438$		0			0
$439$	−24.4990			−1.16928			−0.584638	−	0.811294i	$-0.698763\pi$
$439$	−24.4990			−1.16928			−0.584638	+	0.811294i	$0.698763\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	10.2108	−	10.2108i	0.485130	−	0.485130i	−0.421635	−	0.906765i	$-0.638544\pi$
$443$	10.2108	−	10.2108i	0.485130	−	0.485130i	0.906765	+	0.421635i	$0.138544\pi$
$444$		0			0
$445$	−5.19674	+	17.5333i	−0.246349	+	0.831158i
$446$		0			0
$447$	14.6939	+	14.6939i	0.694998	+	0.694998i
$448$		0			0
$449$			19.8884i			0.938592i	0.883041	+	0.469296i	$0.155492\pi$
$449$			19.8884i			0.938592i	−0.883041	+	0.469296i	$0.844508\pi$
$450$		0			0
$451$		−	2.96581i		−	0.139655i
$452$		0			0
$453$	−6.44949	−	6.44949i	−0.303023	−	0.303023i
$454$		0			0
$455$	4.19269	−	14.1457i	0.196556	−	0.663161i
$456$		0			0
$457$	−23.9349	+	23.9349i	−1.11963	+	1.11963i	−0.127831	+	0.991796i	$0.540802\pi$
$457$	−23.9349	+	23.9349i	−1.11963	+	1.11963i	−0.991796	+	0.127831i	$0.959198\pi$
$458$		0			0
$459$	4.98125			0.232505
$460$		0			0
$461$	28.9898			1.35019			0.675095	−	0.737730i	$-0.264102\pi$
$461$	28.9898			1.35019			0.675095	+	0.737730i	$0.264102\pi$
$462$		0			0
$463$	9.90687	−	9.90687i	0.460411	−	0.460411i	−0.438379	−	0.898790i	$-0.644447\pi$
$463$	9.90687	−	9.90687i	0.460411	−	0.460411i	0.898790	+	0.438379i	$0.144447\pi$
$464$		0			0
$465$	−8.33008	−	15.3481i	−0.386298	−	0.711753i
$466$		0			0
$467$	25.1847	+	25.1847i	1.16541	+	1.16541i	0.983273	+	0.182136i	$0.0583013\pi$
$467$	25.1847	+	25.1847i	1.16541	+	1.16541i	0.182136	+	0.983273i	$0.441699\pi$
$468$		0			0
$469$		−	6.24369i		−	0.288307i
$470$		0			0
$471$			17.4874i			0.805777i
$472$		0			0
$473$	5.04232	+	5.04232i	0.231846	+	0.231846i
$474$		0			0
$475$	30.4617	+	19.7963i	1.39768	+	0.908318i
$476$		0			0
$477$	6.73055	−	6.73055i	0.308171	−	0.308171i
$478$		0			0
$479$	−15.2716			−0.697776			−0.348888	−	0.937164i	$-0.613441\pi$
$479$	−15.2716			−0.697776			−0.348888	+	0.937164i	$0.613441\pi$
$480$		0			0
$481$	−7.69310			−0.350775
$482$		0			0
$483$	−2.99848	+	2.99848i	−0.136435	+	0.136435i
$484$		0			0
$485$	26.0021	−	14.1124i	1.18070	−	0.640813i
$486$		0			0
$487$	19.7521	+	19.7521i	0.895055	+	0.895055i	0.994994	−	0.0999387i	$-0.0318647\pi$
$487$	19.7521	+	19.7521i	0.895055	+	0.895055i	−0.0999387	+	0.994994i	$0.531865\pi$
$488$		0			0
$489$			1.17365i			0.0530742i
$490$		0			0
$491$			12.3239i			0.556168i	0.960557	+	0.278084i	$0.0896994\pi$
$491$			12.3239i			0.556168i	−0.960557	+	0.278084i	$0.910301\pi$
$492$		0			0
$493$	−25.3178	−	25.3178i	−1.14025	−	1.14025i
$494$		0			0
$495$	3.03191	+	0.898635i	0.136274	+	0.0403906i
$496$		0			0
$497$	−6.92159	+	6.92159i	−0.310476	+	0.310476i
$498$		0			0
$499$	−0.784427			−0.0351158			−0.0175579	−	0.999846i	$-0.505589\pi$
$499$	−0.784427			−0.0351158			−0.0175579	+	0.999846i	$0.505589\pi$
$500$		0			0
$501$	12.3736			0.552810
$502$		0			0
$503$	18.9390	−	18.9390i	0.844449	−	0.844449i	−0.144985	−	0.989434i	$-0.546313\pi$
$503$	18.9390	−	18.9390i	0.844449	−	0.844449i	0.989434	+	0.144985i	$0.0463134\pi$
$504$		0			0
$505$	−24.1890	−	7.16944i	−1.07640	−	0.319036i
$506$		0			0
$507$	−21.5922	−	21.5922i	−0.958943	−	0.958943i
$508$		0			0
$509$		−	30.8483i		−	1.36733i	−0.729798	−	0.683663i	$-0.760386\pi$
$509$		−	30.8483i		−	1.36733i	0.729798	−	0.683663i	$-0.239614\pi$
$510$		0			0
$511$			1.03419i			0.0457498i
$512$		0			0
$513$	5.13772	+	5.13772i	0.226836	+	0.226836i
$514$		0			0
$515$	25.6052	−	13.8970i	1.12830	−	0.612376i
$516$		0			0
$517$	−1.85666	+	1.85666i	−0.0816558	+	0.0816558i
$518$		0			0
$519$	22.5914			0.991651
$520$		0			0
$521$	−29.0942			−1.27464			−0.637320	−	0.770599i	$-0.719957\pi$
$521$	−29.0942			−1.27464			−0.637320	+	0.770599i	$0.719957\pi$
$522$		0			0
$523$	−5.29523	+	5.29523i	−0.231544	+	0.231544i	−0.813337	−	0.581793i	$-0.802351\pi$
$523$	−5.29523	+	5.29523i	−0.231544	+	0.231544i	0.581793	+	0.813337i	$0.302351\pi$
$524$		0			0
$525$	−4.19245	−	2.72458i	−0.182974	−	0.118910i
$526$		0			0
$527$	27.5079	+	27.5079i	1.19826	+	1.19826i
$528$		0			0
$529$			5.01828i			0.218186i
$530$		0			0
$531$			7.63237i			0.331216i
$532$		0			0
$533$	9.78448	+	9.78448i	0.423813	+	0.423813i
$534$		0			0
$535$	13.2980	+	24.5014i	0.574921	+	1.05929i
$536$		0			0
$537$	5.24049	−	5.24049i	0.226144	−	0.226144i
$538$		0			0
$539$	−1.41421			−0.0609145
$540$		0			0
$541$	4.65699			0.200220			0.100110	−	0.994976i	$-0.468081\pi$
$541$	4.65699			0.200220			0.100110	+	0.994976i	$0.468081\pi$
$542$		0			0
$543$	4.51789	−	4.51789i	0.193881	−	0.193881i
$544$		0			0
$545$	−2.35956	+	7.96092i	−0.101072	+	0.341008i
$546$		0			0
$547$	−4.33662	−	4.33662i	−0.185420	−	0.185420i	0.608292	−	0.793713i	$-0.291855\pi$
$547$	−4.33662	−	4.33662i	−0.185420	−	0.185420i	−0.793713	+	0.608292i	$0.791855\pi$
$548$		0			0
$549$		−	8.13210i		−	0.347070i
$550$		0			0
$551$		−	52.2260i		−	2.22490i
$552$		0			0
$553$	−9.63738	−	9.63738i	−0.409823	−	0.409823i
$554$		0			0
$555$	−0.740876	+	2.49964i	−0.0314484	+	0.106104i
$556$		0			0
$557$	−11.6175	+	11.6175i	−0.492250	+	0.492250i	−0.909015	−	0.416764i	$-0.863164\pi$
$557$	−11.6175	+	11.6175i	−0.492250	+	0.492250i	0.416764	+	0.909015i	$0.363164\pi$
$558$		0			0
$559$	−33.2701			−1.40718
$560$		0			0
$561$	−7.04456			−0.297421
$562$		0			0
$563$	−31.8323	+	31.8323i	−1.34157	+	1.34157i	−0.447077	+	0.894495i	$0.647535\pi$
$563$	−31.8323	+	31.8323i	−1.34157	+	1.34157i	−0.894495	+	0.447077i	$0.852465\pi$
$564$		0			0
$565$	14.3094	+	26.3651i	0.602003	+	1.10919i
$566$		0			0
$567$	−0.707107	−	0.707107i	−0.0296957	−	0.0296957i
$568$		0			0
$569$		−	29.5035i		−	1.23685i	−0.785843	−	0.618426i	$-0.787771\pi$
$569$		−	29.5035i		−	1.23685i	0.785843	−	0.618426i	$-0.212229\pi$
$570$		0			0
$571$			21.8049i			0.912506i	0.889850	+	0.456253i	$0.150809\pi$
$571$			21.8049i			0.912506i	−0.889850	+	0.456253i	$0.849191\pi$
$572$		0			0
$573$	−6.63588	−	6.63588i	−0.277218	−	0.277218i
$574$		0			0
$575$	20.7406	−	4.40140i	0.864941	−	0.183551i
$576$		0			0
$577$	1.00595	−	1.00595i	0.0418782	−	0.0418782i	−0.685858	−	0.727736i	$-0.740573\pi$
$577$	1.00595	−	1.00595i	0.0418782	−	0.0418782i	0.727736	+	0.685858i	$0.240573\pi$
$578$		0			0
$579$	−6.50920			−0.270513
$580$		0			0
$581$	−0.145576			−0.00603949
$582$		0			0
$583$	−9.51843	+	9.51843i	−0.394213	+	0.394213i
$584$		0			0
$585$	−12.9672	+	7.03785i	−0.536128	+	0.290979i
$586$		0			0
$587$	10.6590	+	10.6590i	0.439943	+	0.439943i	0.891993	−	0.452050i	$-0.149307\pi$
$587$	10.6590	+	10.6590i	0.439943	+	0.439943i	−0.452050	+	0.891993i	$0.649307\pi$
$588$		0			0
$589$			56.7438i			2.33809i
$590$		0			0
$591$		−	18.0069i		−	0.740704i
$592$		0			0
$593$	1.50307	+	1.50307i	0.0617239	+	0.0617239i	0.737295	−	0.675571i	$-0.236103\pi$
$593$	1.50307	+	1.50307i	0.0617239	+	0.0617239i	−0.675571	+	0.737295i	$0.736103\pi$
$594$		0			0
$595$	10.6792	+	3.16524i	0.437805	+	0.129762i
$596$		0			0
$597$	16.2676	−	16.2676i	0.665790	−	0.665790i
$598$		0			0
$599$	−43.0442			−1.75874			−0.879369	−	0.476141i	$-0.842035\pi$
$599$	−43.0442			−1.75874			−0.879369	+	0.476141i	$0.842035\pi$
$600$		0			0
$601$	3.45562			0.140958			0.0704788	−	0.997513i	$-0.477547\pi$
$601$	3.45562			0.140958			0.0704788	+	0.997513i	$0.477547\pi$
$602$		0			0
$603$	−4.41495	+	4.41495i	−0.179791	+	0.179791i
$604$		0			0
$605$	19.2949	+	5.71888i	0.784451	+	0.232506i
$606$		0			0
$607$	−24.0258	−	24.0258i	−0.975178	−	0.975178i	0.0245217	−	0.999699i	$-0.492194\pi$
$607$	−24.0258	−	24.0258i	−0.975178	−	0.975178i	−0.999699	+	0.0245217i	$0.992194\pi$
$608$		0			0
$609$			7.18789i			0.291268i
$610$		0			0
$611$		−	12.2506i		−	0.495605i
$612$		0			0
$613$	−8.82988	−	8.82988i	−0.356636	−	0.356636i	0.505936	−	0.862571i	$-0.331147\pi$
$613$	−8.82988	−	8.82988i	−0.356636	−	0.356636i	−0.862571	+	0.505936i	$0.831147\pi$
$614$		0			0
$615$	4.12146	−	2.23689i	0.166193	−	0.0902002i
$616$		0			0
$617$	−5.08089	+	5.08089i	−0.204549	+	0.204549i	−0.801946	−	0.597397i	$-0.796202\pi$
$617$	−5.08089	+	5.08089i	−0.204549	+	0.204549i	0.597397	+	0.801946i	$0.296202\pi$
$618$		0			0
$619$	37.5701			1.51007			0.755036	−	0.655684i	$-0.227620\pi$
$619$	37.5701			1.51007			0.755036	+	0.655684i	$0.227620\pi$
$620$		0			0
$621$	4.24049			0.170165
$622$		0			0
$623$	−5.78293	+	5.78293i	−0.231688	+	0.231688i
$624$		0			0
$625$	10.1534	+	22.8453i	0.406134	+	0.913813i
$626$		0			0
$627$	−7.26583	−	7.26583i	−0.290169	−	0.290169i
$628$		0			0
$629$		−	5.80785i		−	0.231574i
$630$		0			0
$631$			17.8121i			0.709089i	0.935039	+	0.354544i	$0.115364\pi$
$631$			17.8121i			0.709089i	−0.935039	+	0.354544i	$0.884636\pi$
$632$		0			0
$633$	5.50752	+	5.50752i	0.218904	+	0.218904i
$634$		0			0
$635$	9.13266	+	16.8269i	0.362419	+	0.667754i
$636$		0			0
$637$	4.66562	−	4.66562i	0.184858	−	0.184858i
$638$		0			0
$639$	9.78861			0.387231
$640$		0			0
$641$	−6.40623			−0.253031			−0.126515	−	0.991965i	$-0.540379\pi$
$641$	−6.40623			−0.253031			−0.126515	+	0.991965i	$0.540379\pi$
$642$		0			0
$643$	−18.1731	+	18.1731i	−0.716676	+	0.716676i	−0.967923	−	0.251247i	$-0.919159\pi$
$643$	−18.1731	+	18.1731i	−0.716676	+	0.716676i	0.251247	+	0.967923i	$0.419159\pi$
$644$		0			0
$645$	−3.20405	+	10.8101i	−0.126159	+	0.425649i
$646$		0			0
$647$	−30.6179	−	30.6179i	−1.20371	−	1.20371i	−0.973029	−	0.230684i	$-0.925903\pi$
$647$	−30.6179	−	30.6179i	−1.20371	−	1.20371i	−0.230684	−	0.973029i	$-0.574097\pi$
$648$		0			0
$649$		−	10.7938i		−	0.423694i
$650$		0			0
$651$		−	7.80968i		−	0.306085i
$652$		0			0
$653$	6.20659	+	6.20659i	0.242882	+	0.242882i	0.818042	−	0.575159i	$-0.195060\pi$
$653$	6.20659	+	6.20659i	0.242882	+	0.242882i	−0.575159	+	0.818042i	$0.695060\pi$
$654$		0			0
$655$	−0.187818	+	0.633679i	−0.00733865	+	0.0247599i
$656$		0			0
$657$	0.731281	−	0.731281i	0.0285300	−	0.0285300i
$658$		0			0
$659$	13.1320			0.511549			0.255775	−	0.966736i	$-0.417669\pi$
$659$	13.1320			0.511549			0.255775	+	0.966736i	$0.417669\pi$
$660$		0			0
$661$	−16.9897			−0.660821			−0.330411	−	0.943837i	$-0.607187\pi$
$661$	−16.9897			−0.660821			−0.330411	+	0.943837i	$0.607187\pi$
$662$		0			0
$663$	23.2406	−	23.2406i	0.902591	−	0.902591i
$664$		0			0
$665$	7.75000	+	14.2793i	0.300532	+	0.553729i
$666$		0			0
$667$	−21.5527	−	21.5527i	−0.834525	−	0.834525i
$668$		0			0
$669$			16.5558i			0.640086i
$670$		0			0
$671$			11.5005i			0.443973i
$672$		0			0
$673$	19.1196	+	19.1196i	0.737006	+	0.737006i	0.971997	−	0.234991i	$-0.0755062\pi$
$673$	19.1196	+	19.1196i	0.737006	+	0.737006i	−0.234991	+	0.971997i	$0.575506\pi$
$674$		0			0
$675$	1.03795	+	4.89108i	0.0399506	+	0.188258i
$676$		0			0
$677$	25.8589	−	25.8589i	0.993838	−	0.993838i	−0.00614329	−	0.999981i	$-0.501955\pi$
$677$	25.8589	−	25.8589i	0.993838	−	0.993838i	0.999981	+	0.00614329i	$0.00195548\pi$
$678$		0			0
$679$	13.2308			0.507752
$680$		0			0
$681$	21.4356			0.821414
$682$		0			0
$683$	−0.748003	+	0.748003i	−0.0286216	+	0.0286216i	−0.721273	−	0.692651i	$-0.756443\pi$
$683$	−0.748003	+	0.748003i	−0.0286216	+	0.0286216i	0.692651	+	0.721273i	$0.256443\pi$
$684$		0			0
$685$	−14.6080	+	7.92838i	−0.558143	+	0.302928i
$686$		0			0
$687$	6.38594	+	6.38594i	0.243639	+	0.243639i
$688$		0			0
$689$		−	62.8043i		−	2.39265i
$690$		0			0
$691$			36.1829i			1.37646i	0.725492	+	0.688231i	$0.241612\pi$
$691$			36.1829i			1.37646i	−0.725492	+	0.688231i	$0.758388\pi$
$692$		0			0
$693$	1.00000	+	1.00000i	0.0379869	+	0.0379869i
$694$		0			0
$695$	30.5772	+	9.06285i	1.15986	+	0.343774i
$696$		0			0
$697$	−7.38673	+	7.38673i	−0.279792	+	0.279792i
$698$		0			0
$699$	−2.12085			−0.0802177
$700$		0			0
$701$	−40.3220			−1.52294			−0.761471	−	0.648199i	$-0.775523\pi$
$701$	−40.3220			−1.52294			−0.761471	+	0.648199i	$0.775523\pi$
$702$		0			0
$703$	5.99029	−	5.99029i	0.225928	−	0.225928i
$704$		0			0
$705$	−3.98046	−	1.17978i	−0.149913	−	0.0444331i
$706$		0			0
$707$	−7.97815	−	7.97815i	−0.300049	−	0.300049i
$708$		0			0
$709$			24.9039i			0.935286i	0.883917	+	0.467643i	$0.154897\pi$
$709$			24.9039i			0.935286i	−0.883917	+	0.467643i	$0.845103\pi$
$710$		0			0
$711$			13.6293i			0.511139i
$712$		0			0
$713$	23.4171	+	23.4171i	0.876979	+	0.876979i
$714$		0			0
$715$	18.3384	−	9.95302i	0.685817	−	0.372222i
$716$		0			0
$717$	−6.44459	+	6.44459i	−0.240678	+	0.240678i
$718$		0			0
$719$	−30.6825			−1.14426			−0.572132	−	0.820161i	$-0.693884\pi$
$719$	−30.6825			−1.14426			−0.572132	+	0.820161i	$0.693884\pi$
$720$		0			0
$721$	13.0288			0.485219
$722$		0			0
$723$	−17.4321	+	17.4321i	−0.648306	+	0.648306i
$724$		0			0
$725$	19.5840	−	30.1349i	0.727331	−	1.11918i
$726$		0			0
$727$	12.2213	+	12.2213i	0.453263	+	0.453263i	0.896436	−	0.443173i	$-0.146147\pi$
$727$	12.2213	+	12.2213i	0.453263	+	0.453263i	−0.443173	+	0.896436i	$0.646147\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	25.1171i		−	0.928988i
$732$		0			0
$733$	−28.5145	−	28.5145i	−1.05321	−	1.05321i	−0.998503	−	0.0547057i	$-0.982578\pi$
$733$	−28.5145	−	28.5145i	−1.05321	−	1.05321i	−0.0547057	−	0.998503i	$-0.517422\pi$
$734$		0			0
$735$	−1.06664	−	1.96527i	−0.0393434	−	0.0724901i
$736$		0			0
$737$	6.24369	−	6.24369i	0.229989	−	0.229989i
$738$		0			0
$739$	25.8507			0.950933			0.475467	−	0.879734i	$-0.342279\pi$
$739$	25.8507			0.950933			0.475467	+	0.879734i	$0.342279\pi$
$740$		0			0
$741$	47.9413			1.76117
$742$		0			0
$743$	35.3809	−	35.3809i	1.29800	−	1.29800i	0.368288	−	0.929712i	$-0.379944\pi$
$743$	35.3809	−	35.3809i	1.29800	−	1.29800i	0.929712	−	0.368288i	$-0.120056\pi$
$744$		0			0
$745$	13.2045	−	44.5505i	0.483774	−	1.63221i
$746$		0			0
$747$	0.102937	+	0.102937i	0.00376628	+	0.00376628i
$748$		0			0
$749$			12.4672i			0.455542i
$750$		0			0
$751$			4.71070i			0.171896i	0.996300	+	0.0859479i	$0.0273918\pi$
$751$			4.71070i			0.171896i	−0.996300	+	0.0859479i	$0.972608\pi$
$752$		0			0
$753$	−7.73453	−	7.73453i	−0.281862	−	0.281862i
$754$		0			0
$755$	−5.79574	+	19.5542i	−0.210929	+	0.711652i
$756$		0			0
$757$	13.7132	−	13.7132i	0.498413	−	0.498413i	−0.412531	−	0.910944i	$-0.635355\pi$
$757$	13.7132	−	13.7132i	0.498413	−	0.498413i	0.910944	+	0.412531i	$0.135355\pi$
$758$		0			0
$759$	−5.99695			−0.217676
$760$		0			0
$761$	−10.2580			−0.371851			−0.185926	−	0.982564i	$-0.559528\pi$
$761$	−10.2580			−0.371851			−0.185926	+	0.982564i	$0.559528\pi$
$762$		0			0
$763$	−2.62571	+	2.62571i	−0.0950573	+	0.0950573i
$764$		0			0
$765$	−5.31318	−	9.78951i	−0.192098	−	0.353940i
$766$		0			0
$767$	35.6097	+	35.6097i	1.28579	+	1.28579i
$768$		0			0
$769$		−	15.5869i		−	0.562080i	−0.959696	−	0.281040i	$-0.909321\pi$
$769$		−	15.5869i		−	0.562080i	0.959696	−	0.281040i	$-0.0906793\pi$
$770$		0			0
$771$		−	8.14662i		−	0.293393i
$772$		0			0
$773$	5.55825	+	5.55825i	0.199916	+	0.199916i	0.799964	−	0.600048i	$-0.204852\pi$
$773$	5.55825	+	5.55825i	0.199916	+	0.199916i	−0.600048	+	0.799964i	$0.704852\pi$
$774$		0			0
$775$	−21.2781	+	32.7417i	−0.764331	+	1.17612i
$776$		0			0
$777$	−0.824446	+	0.824446i	−0.0295768	+	0.0295768i
$778$		0			0
$779$	−15.2375			−0.545941
$780$		0			0
$781$	−13.8432			−0.495348
$782$		0			0
$783$	5.08261	−	5.08261i	0.181638	−	0.181638i
$784$		0			0
$785$	34.3675	−	18.6527i	1.22663	−	0.665743i
$786$		0			0
$787$	14.8693	+	14.8693i	0.530033	+	0.530033i	0.920582	−	0.390549i	$-0.127715\pi$
$787$	14.8693	+	14.8693i	0.530033	+	0.530033i	−0.390549	+	0.920582i	$0.627715\pi$
$788$		0			0
$789$		−	10.9482i		−	0.389766i
$790$		0			0
$791$			13.4155i			0.477000i
$792$		0			0
$793$	−37.9413	−	37.9413i	−1.34733	−	1.34733i
$794$		0			0
$795$	−20.4064	−	6.04831i	−0.723740	−	0.214511i
$796$		0			0
$797$	−14.7614	+	14.7614i	−0.522874	+	0.522874i	−0.918438	−	0.395564i	$-0.870549\pi$
$797$	−14.7614	+	14.7614i	−0.522874	+	0.522874i	0.395564	+	0.918438i	$0.370549\pi$
$798$		0			0
$799$	9.24850			0.327188
$800$		0			0
$801$	8.17829			0.288966
$802$		0			0
$803$	−1.03419	+	1.03419i	−0.0364957	+	0.0364957i
$804$		0			0
$805$	9.09110	+	2.69454i	0.320419	+	0.0949699i
$806$		0			0
$807$	6.14493	+	6.14493i	0.216312	+	0.216312i
$808$		0			0
$809$		−	5.57269i		−	0.195925i	−0.995190	−	0.0979626i	$-0.968767\pi$
$809$		−	5.57269i		−	0.195925i	0.995190	−	0.0979626i	$-0.0312326\pi$
$810$		0			0
$811$		−	28.3259i		−	0.994658i	−0.867562	−	0.497329i	$-0.834314\pi$
$811$		−	28.3259i		−	0.994658i	0.867562	−	0.497329i	$-0.165686\pi$
$812$		0			0
$813$	10.0701	+	10.0701i	0.353176	+	0.353176i
$814$		0			0
$815$	2.30653	−	1.25185i	0.0807944	−	0.0438505i
$816$		0			0
$817$	25.9060	−	25.9060i	0.906337	−	0.906337i
$818$		0			0
$819$	−6.59818			−0.230559
$820$		0			0
$821$	−20.0455			−0.699591			−0.349796	−	0.936826i	$-0.613749\pi$
$821$	−20.0455			−0.699591			−0.349796	+	0.936826i	$0.613749\pi$
$822$		0			0
$823$	−28.0000	+	28.0000i	−0.976020	+	0.976020i	−0.999719	−	0.0236994i	$-0.992456\pi$
$823$	−28.0000	+	28.0000i	−0.976020	+	0.976020i	0.0236994	+	0.999719i	$0.492456\pi$
$824$		0			0
$825$	−1.46788	−	6.91703i	−0.0511049	−	0.240820i
$826$		0			0
$827$	12.3073	+	12.3073i	0.427966	+	0.427966i	0.887935	−	0.459969i	$-0.152139\pi$
$827$	12.3073	+	12.3073i	0.427966	+	0.427966i	−0.459969	+	0.887935i	$0.652139\pi$
$828$		0			0
$829$		−	30.7848i		−	1.06920i	−0.845105	−	0.534600i	$-0.820462\pi$
$829$		−	30.7848i		−	1.06920i	0.845105	−	0.534600i	$-0.179538\pi$
$830$		0			0
$831$			4.67457i			0.162159i
$832$		0			0
$833$	3.52228	+	3.52228i	0.122040	+	0.122040i
$834$		0			0
$835$	−13.1981	−	24.3174i	−0.456738	−	0.841538i
$836$		0			0
$837$	−5.52228	+	5.52228i	−0.190878	+	0.190878i
$838$		0			0
$839$	6.92930			0.239226			0.119613	−	0.992821i	$-0.461835\pi$
$839$	6.92930			0.239226			0.119613	+	0.992821i	$0.461835\pi$
$840$		0			0
$841$	−22.6658			−0.781580
$842$		0			0
$843$	−4.36360	+	4.36360i	−0.150290	+	0.150290i
$844$		0			0
$845$	−19.4035	+	65.4655i	−0.667501	+	2.25208i
$846$		0			0
$847$	6.36396	+	6.36396i	0.218668	+	0.218668i
$848$		0			0
$849$		−	9.63362i		−	0.330625i
$850$		0			0
$851$		−	4.94416i		−	0.169484i
$852$		0			0
$853$	−6.43540	−	6.43540i	−0.220344	−	0.220344i	0.588299	−	0.808643i	$-0.299798\pi$
$853$	−6.43540	−	6.43540i	−0.220344	−	0.220344i	−0.808643	+	0.588299i	$0.799798\pi$
$854$		0			0
$855$	4.61694	−	15.5771i	0.157896	−	0.532725i
$856$		0			0
$857$	−34.6045	+	34.6045i	−1.18207	+	1.18207i	−0.202859	+	0.979208i	$0.565023\pi$
$857$	−34.6045	+	34.6045i	−1.18207	+	1.18207i	−0.979208	+	0.202859i	$0.934977\pi$
$858$		0			0
$859$	41.2139			1.40620			0.703101	−	0.711090i	$-0.251798\pi$
$859$	41.2139			1.40620			0.703101	+	0.711090i	$0.251798\pi$
$860$		0			0
$861$	2.09715			0.0714706
$862$		0			0
$863$	−29.1524	+	29.1524i	−0.992360	+	0.992360i	−0.999971	−	0.00761058i	$-0.997577\pi$
$863$	−29.1524	+	29.1524i	−0.992360	+	0.992360i	0.00761058	+	0.999971i	$0.497577\pi$
$864$		0			0
$865$	−24.0967	−	44.3981i	−0.819314	−	1.50958i
$866$		0			0
$867$	5.52454	+	5.52454i	0.187623	+	0.187623i
$868$		0			0
$869$		−	19.2748i		−	0.653852i
$870$		0			0
$871$			41.1970i			1.39591i
$872$		0			0
$873$	−9.35559	−	9.35559i	−0.316639	−	0.316639i
$874$		0			0
$875$	−0.882711	+	11.1454i	−0.0298411	+	0.376785i
$876$		0			0
$877$	16.1507	−	16.1507i	0.545370	−	0.545370i	−0.379728	−	0.925098i	$-0.623982\pi$
$877$	16.1507	−	16.1507i	0.545370	−	0.545370i	0.925098	+	0.379728i	$0.123982\pi$
$878$		0			0
$879$	29.7640			1.00391
$880$		0			0
$881$	48.8984			1.64743			0.823715	−	0.567004i	$-0.191897\pi$
$881$	48.8984			1.64743			0.823715	+	0.567004i	$0.191897\pi$
$882$		0			0
$883$	31.8940	−	31.8940i	1.07332	−	1.07332i	0.0762280	−	0.997090i	$-0.475712\pi$
$883$	31.8940	−	31.8940i	1.07332	−	1.07332i	0.997090	−	0.0762280i	$-0.0242877\pi$
$884$		0			0
$885$	14.9997	−	8.14095i	0.504208	−	0.273655i
$886$		0			0
$887$	−7.61308	−	7.61308i	−0.255622	−	0.255622i	0.567649	−	0.823271i	$-0.307853\pi$
$887$	−7.61308	−	7.61308i	−0.255622	−	0.255622i	−0.823271	+	0.567649i	$0.807853\pi$
$888$		0			0
$889$			8.56212i			0.287164i
$890$		0			0
$891$		−	1.41421i		−	0.0473779i
$892$		0			0
$893$	9.53900	+	9.53900i	0.319211	+	0.319211i
$894$		0			0
$895$	−15.8887	−	4.70929i	−0.531099	−	0.157414i
$896$		0			0
$897$	19.7845	−	19.7845i	0.660585	−	0.660585i
$898$		0			0
$899$	56.1352			1.87221
$900$		0			0
$901$	47.4137			1.57958
$902$		0			0
$903$	−3.56546	+	3.56546i	−0.118651	+	0.118651i
$904$		0			0
$905$	−13.6978	−	4.05994i	−0.455331	−	0.134957i
$906$		0			0
$907$	4.91362	+	4.91362i	0.163154	+	0.163154i	0.783962	−	0.620808i	$-0.213195\pi$
$907$	4.91362	+	4.91362i	0.163154	+	0.163154i	−0.620808	+	0.783962i	$0.713195\pi$
$908$		0			0
$909$			11.2828i			0.374227i
$910$		0			0
$911$			39.0084i			1.29241i	0.763166	+	0.646203i	$0.223644\pi$
$911$			39.0084i			1.29241i	−0.763166	+	0.646203i	$0.776356\pi$
$912$		0			0
$913$	−0.145576	−	0.145576i	−0.00481785	−	0.00481785i
$914$		0			0
$915$	−15.9818	+	8.67399i	−0.528341	+	0.286753i
$916$		0			0
$917$	−0.209004	+	0.209004i	−0.00690190	+	0.00690190i
$918$		0			0
$919$	−1.31347			−0.0433274			−0.0216637	−	0.999765i	$-0.506896\pi$
$919$	−1.31347			−0.0433274			−0.0216637	+	0.999765i	$0.506896\pi$
$920$		0			0
$921$	23.5255			0.775192
$922$		0			0
$923$	45.6699	−	45.6699i	1.50324	−	1.50324i
$924$		0			0
$925$	5.70272	−	1.21019i	0.187504	−	0.0397907i
$926$		0			0
$927$	−9.21278	−	9.21278i	−0.302588	−	0.302588i
$928$		0			0
$929$		−	42.5276i		−	1.39529i	−0.716446	−	0.697643i	$-0.754232\pi$
$929$		−	42.5276i		−	1.39529i	0.716446	−	0.697643i	$-0.245768\pi$
$930$		0			0
$931$			7.26583i			0.238128i
$932$		0			0
$933$	−23.9126	−	23.9126i	−0.782862	−	0.782862i
$934$		0			0
$935$	7.51397	+	13.8445i	0.245733	+	0.452762i
$936$		0			0
$937$	−31.5880	+	31.5880i	−1.03194	+	1.03194i	−0.0324634	+	0.999473i	$0.510335\pi$
$937$	−31.5880	+	31.5880i	−1.03194	+	1.03194i	−0.999473	+	0.0324634i	$0.989665\pi$
$938$		0			0
$939$	−1.44277			−0.0470832
$940$		0			0
$941$	27.2932			0.889733			0.444866	−	0.895597i	$-0.353251\pi$
$941$	27.2932			0.889733			0.444866	+	0.895597i	$0.353251\pi$
$942$		0			0
$943$	−6.28825	+	6.28825i	−0.204773	+	0.204773i
$944$		0			0
$945$	−0.635431	+	2.14388i	−0.0206706	+	0.0697405i
$946$		0			0
$947$	−14.5369	−	14.5369i	−0.472385	−	0.472385i	0.430301	−	0.902686i	$-0.358408\pi$
$947$	−14.5369	−	14.5369i	−0.472385	−	0.472385i	−0.902686	+	0.430301i	$0.858408\pi$
$948$		0			0
$949$		−	6.82375i		−	0.221508i
$950$		0			0
$951$		−	25.2765i		−	0.819648i
$952$		0			0
$953$	8.34701	+	8.34701i	0.270386	+	0.270386i	0.829256	−	0.558869i	$-0.188765\pi$
$953$	8.34701	+	8.34701i	0.270386	+	0.270386i	−0.558869	+	0.829256i	$0.688765\pi$
$954$		0			0
$955$	−5.96324	+	20.1194i	−0.192966	+	0.651047i
$956$		0			0
$957$	−7.18789	+	7.18789i	−0.232352	+	0.232352i
$958$		0			0
$959$	−7.43307			−0.240026
$960$		0			0
$961$	−29.9911			−0.967455
$962$		0			0
$963$	8.81565	−	8.81565i	0.284080	−	0.284080i
$964$		0			0
$965$	6.94294	+	12.7923i	0.223501	+	0.411800i
$966$		0			0
$967$	0.931250	+	0.931250i	0.0299470	+	0.0299470i	0.721922	−	0.691975i	$-0.243259\pi$
$967$	0.931250	+	0.931250i	0.0299470	+	0.0299470i	−0.691975	+	0.721922i	$0.743259\pi$
$968$		0			0
$969$			36.1930i			1.16269i
$970$		0			0
$971$			44.2511i			1.42009i	0.704159	+	0.710043i	$0.251324\pi$
$971$			44.2511i			1.42009i	−0.704159	+	0.710043i	$0.748676\pi$
$972$		0			0
$973$	10.0851	+	10.0851i	0.323314	+	0.323314i
$974$		0			0
$975$	27.6626	+	17.9772i	0.885911	+	0.575733i
$976$		0			0
$977$	−4.80622	+	4.80622i	−0.153765	+	0.153765i	−0.779797	−	0.626032i	$-0.784678\pi$
$977$	−4.80622	+	4.80622i	−0.153765	+	0.153765i	0.626032	+	0.779797i	$0.284678\pi$
$978$		0			0
$979$	−11.5659			−0.369646
$980$		0			0
$981$	3.71332			0.118557
$982$		0			0
$983$	12.7152	−	12.7152i	0.405552	−	0.405552i	−0.474632	−	0.880184i	$-0.657419\pi$
$983$	12.7152	−	12.7152i	0.405552	−	0.405552i	0.880184	+	0.474632i	$0.157419\pi$
$984$		0			0
$985$	−35.3884	+	19.2068i	−1.12757	+	0.611979i
$986$		0			0
$987$	−1.31286	−	1.31286i	−0.0417887	−	0.0417887i
$988$		0			0
$989$		−	21.3819i		−	0.679904i
$990$		0			0
$991$			26.6749i			0.847355i	0.905813	+	0.423678i	$0.139261\pi$
$991$			26.6749i			0.847355i	−0.905813	+	0.423678i	$0.860739\pi$
$992$		0			0
$993$	11.2016	+	11.2016i	0.355473	+	0.355473i
$994$		0			0
$995$	−49.3220	−	14.6187i	−1.56361	−	0.463443i
$996$		0			0
$997$	29.4374	−	29.4374i	0.932292	−	0.932292i	−0.0655565	−	0.997849i	$-0.520882\pi$
$997$	29.4374	−	29.4374i	0.932292	−	0.932292i	0.997849	+	0.0655565i	$0.0208822\pi$
$998$		0			0
$999$	1.16594			0.0368888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bl.d.463.1	yes	24
4.3	odd	2	inner	1680.2.bl.d.463.8	yes	24
5.2	odd	4	inner	1680.2.bl.d.127.8	yes	24
20.7	even	4	inner	1680.2.bl.d.127.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1680.2.bl.d.127.1	✓	24	20.7	even	4	inner
1680.2.bl.d.127.8	yes	24	5.2	odd	4	inner
1680.2.bl.d.463.1	yes	24	1.1	even	1	trivial
1680.2.bl.d.463.8	yes	24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(2.14388 + 0.635431i) q^{5} +(0.707107 + 0.707107i) q^{7} -1.00000i q^{9} +1.41421i q^{11} +(-4.66562 - 4.66562i) q^{13} +(-1.96527 + 1.06664i) q^{15} +(3.52228 - 3.52228i) q^{17} +7.26583 q^{19} -1.00000 q^{21} +(2.99848 - 2.99848i) q^{23} +(4.19245 + 2.72458i) q^{25} +(0.707107 + 0.707107i) q^{27} -7.18789i q^{29} +7.80968i q^{31} +(-1.00000 - 1.00000i) q^{33} +(1.06664 + 1.96527i) q^{35} +(0.824446 - 0.824446i) q^{37} +6.59818 q^{39} -2.09715 q^{41} +(3.56546 - 3.56546i) q^{43} +(0.635431 - 2.14388i) q^{45} +(1.31286 + 1.31286i) q^{47} +1.00000i q^{49} +4.98125i q^{51} +(6.73055 + 6.73055i) q^{53} +(-0.898635 + 3.03191i) q^{55} +(-5.13772 + 5.13772i) q^{57} -7.63237 q^{59} +8.13210 q^{61} +(0.707107 - 0.707107i) q^{63} +(-7.03785 - 12.9672i) q^{65} +(-4.41495 - 4.41495i) q^{67} +4.24049i q^{69} +9.78861i q^{71} +(0.731281 + 0.731281i) q^{73} +(-4.89108 + 1.03795i) q^{75} +(-1.00000 + 1.00000i) q^{77} -13.6293 q^{79} -1.00000 q^{81} +(-0.102937 + 0.102937i) q^{83} +(9.78951 - 5.31318i) q^{85} +(5.08261 + 5.08261i) q^{87} +8.17829i q^{89} -6.59818i q^{91} +(-5.52228 - 5.52228i) q^{93} +(15.5771 + 4.61694i) q^{95} +(9.35559 - 9.35559i) q^{97} +1.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 16 q^{13} - 8 q^{17} - 24 q^{21} + 8 q^{25} - 24 q^{33} + 24 q^{37} + 32 q^{41} + 8 q^{45} - 16 q^{53} - 8 q^{57} - 32 q^{61} + 32 q^{65} - 48 q^{73} - 24 q^{77} - 24 q^{81} + 72 q^{85} - 40 q^{93}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q - 16 * q^13 - 8 * q^17 - 24 * q^21 + 8 * q^25 - 24 * q^33 + 24 * q^37 + 32 * q^41 + 8 * q^45 - 16 * q^53 - 8 * q^57 - 32 * q^61 + 32 * q^65 - 48 * q^73 - 24 * q^77 - 24 * q^81 + 72 * q^85 - 40 * q^93 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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