LMFDB - Embedded newform 208.2.k.b.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(31,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("208.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 147x^{8} + 662x^{6} + 2233x^{4} + 588x^{2} + 144 $ x^12 + 14x^10 + 147x^8 + 662x^6 + 2233x^4 + 588*x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.4
Root			$-0.257153 - 0.445402i$ of defining polynomial
Character	$\chi$	$=$	208.47
Dual form			208.2.k.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.514306i q^{3} +(-1.42234 - 1.42234i) q^{5} +(2.97788 + 2.97788i) q^{7} +2.73549 q^{9} +(1.73205 + 1.73205i) q^{11} +(1.42234 - 3.31315i) q^{13} +(0.731519 - 0.731519i) q^{15} +3.73549i q^{17} +(1.21774 - 1.21774i) q^{19} +(-1.53154 + 1.53154i) q^{21} -8.39124 q^{23} -0.953882i q^{25} +2.94980i q^{27} -4.62629 q^{29} +(2.24636 - 2.24636i) q^{31} +(-0.890804 + 0.890804i) q^{33} -8.47112i q^{35} +(2.57766 - 2.57766i) q^{37} +(1.70397 + 0.731519i) q^{39} +(2.10920 + 2.10920i) q^{41} -2.94980 q^{43} +(-3.89080 - 3.89080i) q^{45} +(-7.47059 - 7.47059i) q^{47} +10.7355i q^{49} -1.92118 q^{51} +2.84469 q^{53} -4.92714i q^{55} +(0.626293 + 0.626293i) q^{57} +(-4.73801 - 4.73801i) q^{59} -11.6894 q^{61} +(8.14595 + 8.14595i) q^{63} +(-6.73549 + 2.68937i) q^{65} +(-11.1519 + 11.1519i) q^{67} -4.31566i q^{69} +(7.47059 - 7.47059i) q^{71} +(4.73549 - 4.73549i) q^{73} +0.490587 q^{75} +10.3157i q^{77} +13.9126i q^{79} +6.68937 q^{81} +(5.19615 - 5.19615i) q^{83} +(5.31315 - 5.31315i) q^{85} -2.37933i q^{87} +(9.58018 - 9.58018i) q^{89} +(14.1017 - 5.63058i) q^{91} +(1.15531 + 1.15531i) q^{93} -3.46410 q^{95} +(-3.84469 - 3.84469i) q^{97} +(4.73801 + 4.73801i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5} - 20 q^{9} - 4 q^{13} - 8 q^{21} + 8 q^{29} + 52 q^{37} + 36 q^{41} - 36 q^{45} - 8 q^{53} - 56 q^{57} - 56 q^{61} - 28 q^{65} + 4 q^{73} - 4 q^{81} + 32 q^{85} + 20 q^{89} + 56 q^{93} - 4 q^{97}+O(q^{100}) $ 12 * q + 4 * q^5 - 20 * q^9 - 4 * q^13 - 8 * q^21 + 8 * q^29 + 52 * q^37 + 36 * q^41 - 36 * q^45 - 8 * q^53 - 56 * q^57 - 56 * q^61 - 28 * q^65 + 4 * q^73 - 4 * q^81 + 32 * q^85 + 20 * q^89 + 56 * q^93 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			0.514306i			0.296935i	0.988917	+	0.148467i	$0.0474340\pi$
$3$			0.514306i			0.296935i	−0.988917	+	0.148467i	$0.952566\pi$
$4$		0			0
$5$	−1.42234	−	1.42234i	−0.636091	−	0.636091i	0.313498	−	0.949589i	$-0.398499\pi$
$5$	−1.42234	−	1.42234i	−0.636091	−	0.636091i	−0.949589	+	0.313498i	$0.898499\pi$
$6$		0			0
$7$	2.97788	+	2.97788i	1.12553	+	1.12553i	0.990895	+	0.134636i	$0.0429866\pi$
$7$	2.97788	+	2.97788i	1.12553	+	1.12553i	0.134636	+	0.990895i	$0.457013\pi$
$8$		0			0
$9$	2.73549			0.911830
$10$		0			0
$11$	1.73205	+	1.73205i	0.522233	+	0.522233i	0.918245	−	0.396012i	$-0.129606\pi$
$11$	1.73205	+	1.73205i	0.522233	+	0.522233i	−0.396012	+	0.918245i	$0.629606\pi$
$12$		0			0
$13$	1.42234	−	3.31315i	0.394487	−	0.918902i
$13$	1.42234	−	3.31315i	0.394487	−	0.918902i
$14$		0			0
$15$	0.731519	−	0.731519i	0.188877	−	0.188877i
$16$		0			0
$17$			3.73549i			0.905989i	0.891513	+	0.452995i	$0.149644\pi$
$17$			3.73549i			0.905989i	−0.891513	+	0.452995i	$0.850356\pi$
$18$		0			0
$19$	1.21774	−	1.21774i	0.279370	−	0.279370i	−0.553488	−	0.832857i	$-0.686703\pi$
$19$	1.21774	−	1.21774i	0.279370	−	0.279370i	0.832857	+	0.553488i	$0.186703\pi$
$20$		0			0
$21$	−1.53154	+	1.53154i	−0.334209	+	0.334209i
$22$		0			0
$23$	−8.39124			−1.74969			−0.874847	−	0.484399i	$-0.839038\pi$
$23$	−8.39124			−1.74969			−0.874847	+	0.484399i	$0.839038\pi$
$24$		0			0
$25$		−	0.953882i		−	0.190776i
$26$		0			0
$27$			2.94980i			0.567688i
$28$		0			0
$29$	−4.62629			−0.859081			−0.429541	−	0.903048i	$-0.641324\pi$
$29$	−4.62629			−0.859081			−0.429541	+	0.903048i	$0.641324\pi$
$30$		0			0
$31$	2.24636	−	2.24636i	0.403458	−	0.403458i	−0.475992	−	0.879450i	$-0.657911\pi$
$31$	2.24636	−	2.24636i	0.403458	−	0.403458i	0.879450	+	0.475992i	$0.157911\pi$
$32$		0			0
$33$	−0.890804	+	0.890804i	−0.155069	+	0.155069i
$34$		0			0
$35$		−	8.47112i		−	1.43188i
$36$		0			0
$37$	2.57766	−	2.57766i	0.423764	−	0.423764i	−0.462733	−	0.886498i	$-0.653131\pi$
$37$	2.57766	−	2.57766i	0.423764	−	0.423764i	0.886498	+	0.462733i	$0.153131\pi$
$38$		0			0
$39$	1.70397	+	0.731519i	0.272854	+	0.117137i
$40$		0			0
$41$	2.10920	+	2.10920i	0.329401	+	0.329401i	0.852359	−	0.522958i	$-0.175171\pi$
$41$	2.10920	+	2.10920i	0.329401	+	0.329401i	−0.522958	+	0.852359i	$0.675171\pi$
$42$		0			0
$43$	−2.94980			−0.449840			−0.224920	−	0.974377i	$-0.572212\pi$
$43$	−2.94980			−0.449840			−0.224920	+	0.974377i	$0.572212\pi$
$44$		0			0
$45$	−3.89080	−	3.89080i	−0.580007	−	0.580007i
$46$		0			0
$47$	−7.47059	−	7.47059i	−1.08970	−	1.08970i	−0.995559	−	0.0941383i	$-0.969990\pi$
$47$	−7.47059	−	7.47059i	−1.08970	−	1.08970i	−0.0941383	−	0.995559i	$-0.530010\pi$
$48$		0			0
$49$			10.7355i			1.53364i
$50$		0			0
$51$	−1.92118			−0.269020
$52$		0			0
$53$	2.84469			0.390748			0.195374	−	0.980729i	$-0.437408\pi$
$53$	2.84469			0.390748			0.195374	+	0.980729i	$0.437408\pi$
$54$		0			0
$55$		−	4.92714i		−	0.664375i
$56$		0			0
$57$	0.626293	+	0.626293i	0.0829546	+	0.0829546i
$58$		0			0
$59$	−4.73801	−	4.73801i	−0.616836	−	0.616836i	0.327883	−	0.944718i	$-0.393665\pi$
$59$	−4.73801	−	4.73801i	−0.616836	−	0.616836i	−0.944718	+	0.327883i	$0.893665\pi$
$60$		0			0
$61$	−11.6894			−1.49667			−0.748335	−	0.663321i	$-0.769147\pi$
$61$	−11.6894			−1.49667			−0.748335	+	0.663321i	$0.769147\pi$
$62$		0			0
$63$	8.14595	+	8.14595i	1.02629	+	1.02629i
$64$		0			0
$65$	−6.73549	+	2.68937i	−0.835435	+	0.333575i
$66$		0			0
$67$	−11.1519	+	11.1519i	−1.36242	+	1.36242i	−0.491602	+	0.870820i	$0.663588\pi$
$67$	−11.1519	+	11.1519i	−1.36242	+	1.36242i	−0.870820	+	0.491602i	$0.836412\pi$
$68$		0			0
$69$		−	4.31566i		−	0.519545i
$70$		0			0
$71$	7.47059	−	7.47059i	0.886596	−	0.886596i	−0.107599	−	0.994194i	$-0.534316\pi$
$71$	7.47059	−	7.47059i	0.886596	−	0.886596i	0.994194	+	0.107599i	$0.0343161\pi$
$72$		0			0
$73$	4.73549	−	4.73549i	0.554247	−	0.554247i	−0.373417	−	0.927664i	$-0.621814\pi$
$73$	4.73549	−	4.73549i	0.554247	−	0.554247i	0.927664	+	0.373417i	$0.121814\pi$
$74$		0			0
$75$	0.490587			0.0566481
$76$		0			0
$77$			10.3157i			1.17558i
$78$		0			0
$79$			13.9126i			1.56529i	0.622471	+	0.782643i	$0.286129\pi$
$79$			13.9126i			1.56529i	−0.622471	+	0.782643i	$0.713871\pi$
$80$		0			0
$81$	6.68937			0.743263
$82$		0			0
$83$	5.19615	−	5.19615i	0.570352	−	0.570352i	−0.361875	−	0.932227i	$-0.617863\pi$
$83$	5.19615	−	5.19615i	0.570352	−	0.570352i	0.932227	+	0.361875i	$0.117863\pi$
$84$		0			0
$85$	5.31315	−	5.31315i	0.576292	−	0.576292i
$86$		0			0
$87$		−	2.37933i		−	0.255091i
$88$		0			0
$89$	9.58018	−	9.58018i	1.01550	−	1.01550i	0.0156185	−	0.999878i	$-0.495028\pi$
$89$	9.58018	−	9.58018i	1.01550	−	1.01550i	0.999878	−	0.0156185i	$-0.00497173\pi$
$90$		0			0
$91$	14.1017	−	5.63058i	1.47826	−	0.590245i
$92$		0			0
$93$	1.15531	+	1.15531i	0.119801	+	0.119801i
$94$		0			0
$95$	−3.46410			−0.355409
$96$		0			0
$97$	−3.84469	−	3.84469i	−0.390369	−	0.390369i	0.484450	−	0.874819i	$-0.339020\pi$
$97$	−3.84469	−	3.84469i	−0.390369	−	0.390369i	−0.874819	+	0.484450i	$0.839020\pi$
$98$		0			0
$99$	4.73801	+	4.73801i	0.476188	+	0.476188i
$100$		0			0
$101$		−	5.68937i		−	0.566114i	−0.959103	−	0.283057i	$-0.908652\pi$
$101$		−	5.68937i		−	0.566114i	0.959103	−	0.283057i	$-0.0913485\pi$
$102$		0			0
$103$	0.434427			0.0428053			0.0214027	−	0.999771i	$-0.493187\pi$
$103$	0.434427			0.0428053			0.0214027	+	0.999771i	$0.493187\pi$
$104$		0			0
$105$	4.35675			0.425175
$106$		0			0
$107$			13.3184i			1.28754i	0.765220	+	0.643768i	$0.222630\pi$
$107$			13.3184i			1.28754i	−0.765220	+	0.643768i	$0.777370\pi$
$108$		0			0
$109$	8.26703	+	8.26703i	0.791838	+	0.791838i	0.981793	−	0.189955i	$-0.0608342\pi$
$109$	8.26703	+	8.26703i	0.791838	+	0.791838i	−0.189955	+	0.981793i	$0.560834\pi$
$110$		0			0
$111$	1.32570	+	1.32570i	0.125830	+	0.125830i
$112$		0			0
$113$	−13.4710			−1.26724			−0.633622	−	0.773643i	$-0.718432\pi$
$113$	−13.4710			−1.26724			−0.633622	+	0.773643i	$0.718432\pi$
$114$		0			0
$115$	11.9352	+	11.9352i	1.11297	+	1.11297i
$116$		0			0
$117$	3.89080	−	9.06308i	0.359705	−	0.837882i
$118$		0			0
$119$	−11.1238	+	11.1238i	−1.01972	+	1.01972i
$120$		0			0
$121$		−	5.00000i		−	0.454545i
$122$		0			0
$123$	−1.08477	+	1.08477i	−0.0978106	+	0.0978106i
$124$		0			0
$125$	−8.46846	+	8.46846i	−0.757442	+	0.757442i
$126$		0			0
$127$	−5.46516			−0.484955			−0.242477	−	0.970157i	$-0.577960\pi$
$127$	−5.46516			−0.484955			−0.242477	+	0.970157i	$0.577960\pi$
$128$		0			0
$129$		−	1.51710i		−	0.133573i
$130$		0			0
$131$		−	4.46899i		−	0.390458i	−0.980758	−	0.195229i	$-0.937455\pi$
$131$		−	4.46899i		−	0.390458i	0.980758	−	0.195229i	$-0.0625450\pi$
$132$		0			0
$133$	7.25259			0.628879
$134$		0			0
$135$	4.19562	−	4.19562i	0.361102	−	0.361102i
$136$		0			0
$137$	−1.21839	+	1.21839i	−0.104094	+	0.104094i	−0.757236	−	0.653142i	$-0.773451\pi$
$137$	−1.21839	+	1.21839i	−0.104094	+	0.104094i	0.653142	+	0.757236i	$0.273451\pi$
$138$		0			0
$139$		−	18.3254i		−	1.55434i	−0.629291	−	0.777170i	$-0.716654\pi$
$139$		−	18.3254i		−	1.55434i	0.629291	−	0.777170i	$-0.283346\pi$
$140$		0			0
$141$	3.84217	−	3.84217i	0.323569	−	0.323569i
$142$		0			0
$143$	8.20211	−	3.27497i	0.685895	−	0.273867i
$144$		0			0
$145$	6.58018	+	6.58018i	0.546454	+	0.546454i
$146$		0			0
$147$	−5.52132			−0.455391
$148$		0			0
$149$	8.20647	+	8.20647i	0.672300	+	0.672300i	0.958246	−	0.285946i	$-0.0923077\pi$
$149$	8.20647	+	8.20647i	0.672300	+	0.672300i	−0.285946	+	0.958246i	$0.592308\pi$
$150$		0			0
$151$	2.97788	+	2.97788i	0.242336	+	0.242336i	0.817816	−	0.575480i	$-0.195185\pi$
$151$	2.97788	+	2.97788i	0.242336	+	0.242336i	−0.575480	+	0.817816i	$0.695185\pi$
$152$		0			0
$153$			10.2184i			0.826108i
$154$		0			0
$155$	−6.39018			−0.513271
$156$		0			0
$157$	1.90776			0.152256			0.0761281	−	0.997098i	$-0.475744\pi$
$157$	1.90776			0.152256			0.0761281	+	0.997098i	$0.475744\pi$
$158$		0			0
$159$			1.46304i			0.116026i
$160$		0			0
$161$	−24.9881	−	24.9881i	−1.96934	−	1.96934i
$162$		0			0
$163$	2.16648	+	2.16648i	0.169692	+	0.169692i	0.786844	−	0.617152i	$-0.211714\pi$
$163$	2.16648	+	2.16648i	0.169692	+	0.169692i	−0.617152	+	0.786844i	$0.711714\pi$
$164$		0			0
$165$	2.53406			0.197276
$166$		0			0
$167$	3.65323	+	3.65323i	0.282696	+	0.282696i	0.834183	−	0.551487i	$-0.185940\pi$
$167$	3.65323	+	3.65323i	0.282696	+	0.282696i	−0.551487	+	0.834183i	$0.685940\pi$
$168$		0			0
$169$	−8.95388	−	9.42486i	−0.688760	−	0.724989i
$170$		0			0
$171$	3.33113	−	3.33113i	0.254738	−	0.254738i
$172$		0			0
$173$			23.7866i			1.80847i	0.427040	+	0.904233i	$0.359556\pi$
$173$			23.7866i			1.80847i	−0.427040	+	0.904233i	$0.640444\pi$
$174$		0			0
$175$	2.84054	−	2.84054i	0.214725	−	0.214725i
$176$		0			0
$177$	2.43678	−	2.43678i	0.183160	−	0.183160i
$178$		0			0
$179$	−17.9471			−1.34143			−0.670716	−	0.741714i	$-0.734013\pi$
$179$	−17.9471			−1.34143			−0.670716	+	0.741714i	$0.734013\pi$
$180$		0			0
$181$		−	6.09727i		−	0.453207i	−0.973987	−	0.226603i	$-0.927238\pi$
$181$		−	6.09727i		−	0.453207i	0.973987	−	0.226603i	$-0.0727621\pi$
$182$		0			0
$183$		−	6.01191i		−	0.444413i
$184$		0			0
$185$	−7.33262			−0.539105
$186$		0			0
$187$	−6.47006	+	6.47006i	−0.473137	+	0.473137i
$188$		0			0
$189$	−8.78413	+	8.78413i	−0.638951	+	0.638951i
$190$		0			0
$191$		−	18.7835i		−	1.35913i	−0.733615	−	0.679565i	$-0.762169\pi$
$191$		−	18.7835i		−	1.35913i	0.733615	−	0.679565i	$-0.237831\pi$
$192$		0			0
$193$	−11.3157	+	11.3157i	−0.814519	+	0.814519i	−0.985308	−	0.170788i	$-0.945369\pi$
$193$	−11.3157	+	11.3157i	−0.814519	+	0.814519i	0.170788	+	0.985308i	$0.445369\pi$
$194$		0			0
$195$	−1.38316	−	3.46410i	−0.0990501	−	0.248069i
$196$		0			0
$197$	9.20395	+	9.20395i	0.655754	+	0.655754i	0.954373	−	0.298618i	$-0.0965257\pi$
$197$	9.20395	+	9.20395i	0.655754	+	0.655754i	−0.298618	+	0.954373i	$0.596526\pi$
$198$		0			0
$199$	−8.39124			−0.594839			−0.297420	−	0.954747i	$-0.596126\pi$
$199$	−8.39124			−0.594839			−0.297420	+	0.954747i	$0.596126\pi$
$200$		0			0
$201$	−5.73549	−	5.73549i	−0.404550	−	0.404550i
$202$		0			0
$203$	−13.7765	−	13.7765i	−0.966923	−	0.966923i
$204$		0			0
$205$		−	6.00000i		−	0.419058i
$206$		0			0
$207$	−22.9542			−1.59542
$208$		0			0
$209$	4.21839			0.291792
$210$		0			0
$211$		−	20.3826i		−	1.40320i	−0.712572	−	0.701599i	$-0.752470\pi$
$211$		−	20.3826i		−	1.40320i	0.712572	−	0.701599i	$-0.247530\pi$
$212$		0			0
$213$	3.84217	+	3.84217i	0.263261	+	0.263261i
$214$		0			0
$215$	4.19562	+	4.19562i	0.286139	+	0.286139i
$216$		0			0
$217$	13.3787			0.908208
$218$		0			0
$219$	2.43549	+	2.43549i	0.164575	+	0.164575i
$220$		0			0
$221$	12.3762	+	5.31315i	0.832515	+	0.357401i
$222$		0			0
$223$	5.41337	−	5.41337i	0.362506	−	0.362506i	−0.502229	−	0.864735i	$-0.667487\pi$
$223$	5.41337	−	5.41337i	0.362506	−	0.362506i	0.864735	+	0.502229i	$0.167487\pi$
$224$		0			0
$225$		−	2.60933i		−	0.173956i
$226$		0			0
$227$	6.20105	−	6.20105i	0.411578	−	0.411578i	−0.470710	−	0.882288i	$-0.656002\pi$
$227$	6.20105	−	6.20105i	0.411578	−	0.411578i	0.882288	+	0.470710i	$0.156002\pi$
$228$		0			0
$229$	−15.5196	+	15.5196i	−1.02557	+	1.02557i	−0.0259005	+	0.999665i	$0.508245\pi$
$229$	−15.5196	+	15.5196i	−1.02557	+	1.02557i	−0.999665	+	0.0259005i	$0.991755\pi$
$230$		0			0
$231$	−5.30541			−0.349070
$232$		0			0
$233$		−	10.0461i		−	0.658143i	−0.944305	−	0.329072i	$-0.893264\pi$
$233$		−	10.0461i		−	0.658143i	0.944305	−	0.329072i	$-0.106736\pi$
$234$		0			0
$235$			21.2515i			1.38629i
$236$		0			0
$237$	−7.15531			−0.464788
$238$		0			0
$239$	2.92172	−	2.92172i	0.188990	−	0.188990i	−0.606269	−	0.795259i	$-0.707335\pi$
$239$	2.92172	−	2.92172i	0.188990	−	0.188990i	0.795259	+	0.606269i	$0.207335\pi$
$240$		0			0
$241$	−0.109196	+	0.109196i	−0.00703394	+	0.00703394i	−0.710615	−	0.703581i	$-0.751583\pi$
$241$	−0.109196	+	0.109196i	−0.00703394	+	0.00703394i	0.703581	+	0.710615i	$0.251583\pi$
$242$		0			0
$243$			12.2898i			0.788389i
$244$		0			0
$245$	15.2695	−	15.2695i	0.975536	−	0.975536i
$246$		0			0
$247$	−2.30252	−	5.76662i	−0.146506	−	0.366921i
$248$		0			0
$249$	2.67241	+	2.67241i	0.169357	+	0.169357i
$250$		0			0
$251$	19.8683			1.25408			0.627039	−	0.778988i	$-0.284267\pi$
$251$	19.8683			1.25408			0.627039	+	0.778988i	$0.284267\pi$
$252$		0			0
$253$	−14.5341	−	14.5341i	−0.913748	−	0.913748i
$254$		0			0
$255$	2.73258	+	2.73258i	0.171121	+	0.171121i
$256$		0			0
$257$			6.48290i			0.404392i	0.979345	+	0.202196i	$0.0648079\pi$
$257$			6.48290i			0.404392i	−0.979345	+	0.202196i	$0.935192\pi$
$258$		0			0
$259$	15.3519			0.953920
$260$		0			0
$261$	−12.6552			−0.783336
$262$		0			0
$263$			17.3205i			1.06803i	0.845476	+	0.534014i	$0.179317\pi$
$263$			17.3205i			1.06803i	−0.845476	+	0.534014i	$0.820683\pi$
$264$		0			0
$265$	−4.04612	−	4.04612i	−0.248551	−	0.248551i
$266$		0			0
$267$	4.92714	+	4.92714i	0.301536	+	0.301536i
$268$		0			0
$269$	−0.310629			−0.0189394			−0.00946968	−	0.999955i	$-0.503014\pi$
$269$	−0.310629			−0.0189394			−0.00946968	+	0.999955i	$0.503014\pi$
$270$		0			0
$271$	−3.35614	−	3.35614i	−0.203871	−	0.203871i	0.597785	−	0.801656i	$-0.296048\pi$
$271$	−3.35614	−	3.35614i	−0.203871	−	0.203871i	−0.801656	+	0.597785i	$0.796048\pi$
$272$		0			0
$273$	2.89584	+	7.25259i	0.175264	+	0.438947i
$274$		0			0
$275$	1.65217	−	1.65217i	0.0996297	−	0.0996297i
$276$		0			0
$277$			8.09224i			0.486215i	0.969999	+	0.243108i	$0.0781668\pi$
$277$			8.09224i			0.486215i	−0.969999	+	0.243108i	$0.921833\pi$
$278$		0			0
$279$	6.14489	−	6.14489i	0.367885	−	0.367885i
$280$		0			0
$281$	5.67241	−	5.67241i	0.338388	−	0.338388i	−0.517373	−	0.855760i	$-0.673090\pi$
$281$	5.67241	−	5.67241i	0.338388	−	0.338388i	0.855760	+	0.517373i	$0.173090\pi$
$282$		0			0
$283$	−9.85428			−0.585776			−0.292888	−	0.956147i	$-0.594616\pi$
$283$	−9.85428			−0.585776			−0.292888	+	0.956147i	$0.594616\pi$
$284$		0			0
$285$		−	1.78161i		−	0.105533i
$286$		0			0
$287$			12.5618i			0.741502i
$288$		0			0
$289$	3.04612			0.179183
$290$		0			0
$291$	1.97734	−	1.97734i	0.115914	−	0.115914i
$292$		0			0
$293$	18.0486	−	18.0486i	1.05441	−	1.05441i	0.0559807	−	0.998432i	$-0.482171\pi$
$293$	18.0486	−	18.0486i	1.05441	−	1.05441i	0.998432	−	0.0559807i	$-0.0178285\pi$
$294$		0			0
$295$			13.4781i			0.784728i
$296$		0			0
$297$	−5.10920	+	5.10920i	−0.296466	+	0.296466i
$298$		0			0
$299$	−11.9352	+	27.8014i	−0.690232	+	1.60780i
$300$		0			0
$301$	−8.78413	−	8.78413i	−0.506309	−	0.506309i
$302$		0			0
$303$	2.92608			0.168099
$304$		0			0
$305$	16.6263	+	16.6263i	0.952019	+	0.952019i
$306$		0			0
$307$	3.21881	+	3.21881i	0.183707	+	0.183707i	0.792969	−	0.609262i	$-0.208534\pi$
$307$	3.21881	+	3.21881i	0.183707	+	0.183707i	−0.609262	+	0.792969i	$0.708534\pi$
$308$		0			0
$309$			0.223428i			0.0127104i
$310$		0			0
$311$	26.7965			1.51949			0.759746	−	0.650220i	$-0.225323\pi$
$311$	26.7965			1.51949			0.759746	+	0.650220i	$0.225323\pi$
$312$		0			0
$313$	25.6433			1.44944			0.724721	−	0.689042i	$-0.241969\pi$
$313$	25.6433			1.44944			0.724721	+	0.689042i	$0.241969\pi$
$314$		0			0
$315$		−	23.1727i		−	1.30563i
$316$		0			0
$317$	14.5171	+	14.5171i	0.815361	+	0.815361i	0.985432	−	0.170070i	$-0.0543995\pi$
$317$	14.5171	+	14.5171i	0.815361	+	0.815361i	−0.170070	+	0.985432i	$0.554400\pi$
$318$		0			0
$319$	−8.01298	−	8.01298i	−0.448640	−	0.448640i
$320$		0			0
$321$	−6.84972			−0.382314
$322$		0			0
$323$	4.54887	+	4.54887i	0.253106	+	0.253106i
$324$		0			0
$325$	−3.16035	−	1.35675i	−0.175305	−	0.0752588i
$326$		0			0
$327$	−4.25178	+	4.25178i	−0.235124	+	0.235124i
$328$		0			0
$329$		−	44.4930i		−	2.45298i
$330$		0			0
$331$	−2.76066	+	2.76066i	−0.151740	+	0.151740i	−0.778895	−	0.627155i	$-0.784219\pi$
$331$	−2.76066	+	2.76066i	−0.151740	+	0.151740i	0.627155	+	0.778895i	$0.284219\pi$
$332$		0			0
$333$	7.05115	−	7.05115i	0.386401	−	0.386401i
$334$		0			0
$335$	31.7237			1.73325
$336$		0			0
$337$			15.2987i			0.833374i	0.909050	+	0.416687i	$0.136809\pi$
$337$			15.2987i			0.833374i	−0.909050	+	0.416687i	$0.863191\pi$
$338$		0			0
$339$		−	6.92820i		−	0.376288i
$340$		0			0
$341$	7.78161			0.421398
$342$		0			0
$343$	−11.1238	+	11.1238i	−0.600630	+	0.600630i
$344$		0			0
$345$	−6.13835	+	6.13835i	−0.330478	+	0.330478i
$346$		0			0
$347$			24.3373i			1.30650i	0.757144	+	0.653248i	$0.226594\pi$
$347$			24.3373i			1.30650i	−0.757144	+	0.653248i	$0.773406\pi$
$348$		0			0
$349$	5.20395	−	5.20395i	0.278561	−	0.278561i	−0.553973	−	0.832534i	$-0.686889\pi$
$349$	5.20395	−	5.20395i	0.278561	−	0.278561i	0.832534	+	0.553973i	$0.186889\pi$
$350$		0			0
$351$	9.77311	+	4.19562i	0.521650	+	0.223946i
$352$		0			0
$353$	−19.3157	−	19.3157i	−1.02807	−	1.02807i	−0.999595	−	0.0284746i	$-0.990935\pi$
$353$	−19.3157	−	19.3157i	−1.02807	−	1.02807i	−0.0284746	−	0.999595i	$-0.509065\pi$
$354$		0			0
$355$	−21.2515			−1.12791
$356$		0			0
$357$	−5.72105	−	5.72105i	−0.302790	−	0.302790i
$358$		0			0
$359$	2.73694	+	2.73694i	0.144450	+	0.144450i	0.775634	−	0.631183i	$-0.217430\pi$
$359$	2.73694	+	2.73694i	0.144450	+	0.144450i	−0.631183	+	0.775634i	$0.717430\pi$
$360$		0			0
$361$			16.0342i			0.843905i
$362$		0			0
$363$	2.57153			0.134970
$364$		0			0
$365$	−13.4710			−0.705103
$366$		0			0
$367$		−	5.84343i		−	0.305025i	−0.988302	−	0.152512i	$-0.951264\pi$
$367$		−	5.84343i		−	0.305025i	0.988302	−	0.152512i	$-0.0487364\pi$
$368$		0			0
$369$	5.76968	+	5.76968i	0.300358	+	0.300358i
$370$		0			0
$371$	8.47112	+	8.47112i	0.439799	+	0.439799i
$372$		0			0
$373$	−12.8497			−0.665333			−0.332667	−	0.943044i	$-0.607948\pi$
$373$	−12.8497			−0.665333			−0.332667	+	0.943044i	$0.607948\pi$
$374$		0			0
$375$	−4.35538	−	4.35538i	−0.224911	−	0.224911i
$376$		0			0
$377$	−6.58018	+	15.3276i	−0.338896	+	0.789411i
$378$		0			0
$379$	15.6446	−	15.6446i	0.803610	−	0.803610i	−0.180048	−	0.983658i	$-0.557625\pi$
$379$	15.6446	−	15.6446i	0.803610	−	0.803610i	0.983658	+	0.180048i	$0.0576253\pi$
$380$		0			0
$381$		−	2.81077i		−	0.144000i
$382$		0			0
$383$	−19.3259	+	19.3259i	−0.987509	+	0.987509i	−0.999923	−	0.0124139i	$-0.996048\pi$
$383$	−19.3259	+	19.3259i	−0.987509	+	0.987509i	0.0124139	+	0.999923i	$0.496048\pi$
$384$		0			0
$385$	14.6724	−	14.6724i	0.747775	−	0.747775i
$386$		0			0
$387$	−8.06914			−0.410177
$388$		0			0
$389$		−	2.12616i		−	0.107800i	−0.998546	−	0.0539002i	$-0.982835\pi$
$389$		−	2.12616i		−	0.107800i	0.998546	−	0.0539002i	$-0.0171653\pi$
$390$		0			0
$391$		−	31.3454i		−	1.58520i
$392$		0			0
$393$	2.29843			0.115940
$394$		0			0
$395$	19.7884	−	19.7884i	0.995664	−	0.995664i
$396$		0			0
$397$	4.20647	−	4.20647i	0.211117	−	0.211117i	−0.593625	−	0.804742i	$-0.702304\pi$
$397$	4.20647	−	4.20647i	0.211117	−	0.211117i	0.804742	+	0.593625i	$0.202304\pi$
$398$		0			0
$399$			3.73005i			0.186736i
$400$		0			0
$401$	−22.4710	+	22.4710i	−1.12215	+	1.12215i	−0.130729	+	0.991418i	$0.541732\pi$
$401$	−22.4710	+	22.4710i	−1.12215	+	1.12215i	−0.991418	+	0.130729i	$0.958268\pi$
$402$		0			0
$403$	−4.24742	−	10.6376i	−0.211579	−	0.529897i
$404$		0			0
$405$	−9.51458	−	9.51458i	−0.472783	−	0.472783i
$406$		0			0
$407$	8.92927			0.442607
$408$		0			0
$409$	19.8497	+	19.8497i	0.981506	+	0.981506i	0.999832	−	0.0183265i	$-0.00583383\pi$
$409$	19.8497	+	19.8497i	0.981506	+	0.981506i	−0.0183265	+	0.999832i	$0.505834\pi$
$410$		0			0
$411$	−0.626626	−	0.626626i	−0.0309092	−	0.0309092i
$412$		0			0
$413$		−	28.2184i		−	1.38854i
$414$		0			0
$415$	−14.7814			−0.725591
$416$		0			0
$417$	9.42486			0.461537
$418$		0			0
$419$			25.2536i			1.23372i	0.787073	+	0.616860i	$0.211595\pi$
$419$			25.2536i			1.23372i	−0.787073	+	0.616860i	$0.788405\pi$
$420$		0			0
$421$	15.3301	+	15.3301i	0.747144	+	0.747144i	0.973942	−	0.226798i	$-0.0728258\pi$
$421$	15.3301	+	15.3301i	0.747144	+	0.747144i	−0.226798	+	0.973942i	$0.572826\pi$
$422$		0			0
$423$	−20.4357	−	20.4357i	−0.993619	−	0.993619i
$424$		0			0
$425$	3.56322			0.172841
$426$		0			0
$427$	−34.8095	−	34.8095i	−1.68455	−	1.68455i
$428$		0			0
$429$	1.68434	+	4.21839i	0.0813205	+	0.203666i
$430$		0			0
$431$	−10.9347	+	10.9347i	−0.526706	+	0.526706i	−0.919588	−	0.392883i	$-0.871478\pi$
$431$	−10.9347	+	10.9347i	−0.526706	+	0.526706i	0.392883	+	0.919588i	$0.371478\pi$
$432$		0			0
$433$			24.4591i			1.17543i	0.809069	+	0.587714i	$0.199972\pi$
$433$			24.4591i			1.17543i	−0.809069	+	0.587714i	$0.800028\pi$
$434$		0			0
$435$	−3.38422	+	3.38422i	−0.162261	+	0.162261i
$436$		0			0
$437$	−10.2184	+	10.2184i	−0.488812	+	0.488812i
$438$		0			0
$439$	18.8397			0.899170			0.449585	−	0.893238i	$-0.351572\pi$
$439$	18.8397			0.899170			0.449585	+	0.893238i	$0.351572\pi$
$440$		0			0
$441$			29.3668i			1.39842i
$442$		0			0
$443$		−	18.3254i		−	0.870666i	−0.900269	−	0.435333i	$-0.856631\pi$
$443$		−	18.3254i		−	0.870666i	0.900269	−	0.435333i	$-0.143369\pi$
$444$		0			0
$445$	−27.2526			−1.29190
$446$		0			0
$447$	−4.22063	+	4.22063i	−0.199629	+	0.199629i
$448$		0			0
$449$	1.93692	−	1.93692i	0.0914090	−	0.0914090i	−0.659924	−	0.751333i	$-0.729411\pi$
$449$	1.93692	−	1.93692i	0.0914090	−	0.0914090i	0.751333	+	0.659924i	$0.229411\pi$
$450$		0			0
$451$			7.30647i			0.344048i
$452$		0			0
$453$	−1.53154	+	1.53154i	−0.0719580	+	0.0719580i
$454$		0			0
$455$	−28.0661	−	12.0488i	−1.31576	−	0.564858i
$456$		0			0
$457$	−3.67241	−	3.67241i	−0.171788	−	0.171788i	0.615976	−	0.787765i	$-0.288762\pi$
$457$	−3.67241	−	3.67241i	−0.171788	−	0.171788i	−0.787765	+	0.615976i	$0.788762\pi$
$458$		0			0
$459$	−11.0189			−0.514320
$460$		0			0
$461$	−15.9564	−	15.9564i	−0.743164	−	0.743164i	0.230022	−	0.973185i	$-0.426120\pi$
$461$	−15.9564	−	15.9564i	−0.743164	−	0.743164i	−0.973185	+	0.230022i	$0.926120\pi$
$462$		0			0
$463$	1.59601	+	1.59601i	0.0741729	+	0.0741729i	0.743220	−	0.669047i	$-0.233298\pi$
$463$	1.59601	+	1.59601i	0.0741729	+	0.0741729i	−0.669047	+	0.743220i	$0.733298\pi$
$464$		0			0
$465$		−	3.28651i		−	0.152408i
$466$		0			0
$467$	7.84449			0.363000			0.181500	−	0.983391i	$-0.441905\pi$
$467$	7.84449			0.363000			0.181500	+	0.983391i	$0.441905\pi$
$468$		0			0
$469$	−66.4180			−3.06690
$470$		0			0
$471$			0.981174i			0.0452101i
$472$		0			0
$473$	−5.10920	−	5.10920i	−0.234921	−	0.234921i
$474$		0			0
$475$	−1.16158	−	1.16158i	−0.0532972	−	0.0532972i
$476$		0			0
$477$	7.78161			0.356295
$478$		0			0
$479$	−19.7042	−	19.7042i	−0.900308	−	0.900308i	0.0951547	−	0.995463i	$-0.469665\pi$
$479$	−19.7042	−	19.7042i	−0.900308	−	0.900308i	−0.995463	+	0.0951547i	$0.969665\pi$
$480$		0			0
$481$	−4.87384	−	12.2065i	−0.222228	−	0.556567i
$482$		0			0
$483$	12.8515	−	12.8515i	0.584764	−	0.584764i
$484$		0			0
$485$			10.9369i			0.496620i
$486$		0			0
$487$	−7.76768	+	7.76768i	−0.351987	+	0.351987i	−0.860849	−	0.508861i	$-0.830067\pi$
$487$	−7.76768	+	7.76768i	−0.351987	+	0.351987i	0.508861	+	0.860849i	$0.330067\pi$
$488$		0			0
$489$	−1.11423	+	1.11423i	−0.0503873	+	0.0503873i
$490$		0			0
$491$	41.8176			1.88720			0.943600	−	0.331086i	$-0.107415\pi$
$491$	41.8176			1.88720			0.943600	+	0.331086i	$0.107415\pi$
$492$		0			0
$493$		−	17.2815i		−	0.778318i
$494$		0			0
$495$		−	13.4781i		−	0.605797i
$496$		0			0
$497$	44.4930			1.99578
$498$		0			0
$499$	−19.4071	+	19.4071i	−0.868781	+	0.868781i	−0.992338	−	0.123556i	$-0.960570\pi$
$499$	−19.4071	+	19.4071i	−0.868781	+	0.868781i	0.123556	+	0.992338i	$0.460570\pi$
$500$		0			0
$501$	−1.87888	+	1.87888i	−0.0839422	+	0.0839422i
$502$		0			0
$503$			0.538025i			0.0239893i	0.999928	+	0.0119947i	$0.00381811\pi$
$503$			0.538025i			0.0239893i	−0.999928	+	0.0119947i	$0.996182\pi$
$504$		0			0
$505$	−8.09224	+	8.09224i	−0.360100	+	0.360100i
$506$		0			0
$507$	4.84726	−	4.60503i	0.215274	−	0.204517i
$508$		0			0
$509$	22.3326	+	22.3326i	0.989876	+	0.989876i	0.999949	−	0.0100731i	$-0.00320642\pi$
$509$	22.3326	+	22.3326i	0.989876	+	0.989876i	−0.0100731	+	0.999949i	$0.503206\pi$
$510$		0			0
$511$	28.2034			1.24764
$512$		0			0
$513$	3.59210	+	3.59210i	0.158595	+	0.158595i
$514$		0			0
$515$	−0.617904	−	0.617904i	−0.0272281	−	0.0272281i
$516$		0			0
$517$		−	25.8789i		−	1.13815i
$518$		0			0
$519$	−12.2336			−0.536996
$520$		0			0
$521$	11.5171			0.504573			0.252287	−	0.967653i	$-0.418817\pi$
$521$	11.5171			0.504573			0.252287	+	0.967653i	$0.418817\pi$
$522$		0			0
$523$			13.3184i			0.582372i	0.956666	+	0.291186i	$0.0940499\pi$
$523$			13.3184i			0.582372i	−0.956666	+	0.291186i	$0.905950\pi$
$524$		0			0
$525$	1.46091	+	1.46091i	0.0637592	+	0.0637592i
$526$		0			0
$527$	8.39124	+	8.39124i	0.365528	+	0.365528i
$528$		0			0
$529$	47.4129			2.06143
$530$		0			0
$531$	−12.9608	−	12.9608i	−0.562449	−	0.562449i
$532$		0			0
$533$	9.98808	−	3.98808i	0.432632	−	0.172743i
$534$		0			0
$535$	18.9433	−	18.9433i	0.818990	−	0.818990i
$536$		0			0
$537$		−	9.23032i		−	0.398318i
$538$		0			0
$539$	−18.5944	+	18.5944i	−0.800918	+	0.800918i
$540$		0			0
$541$	24.9906	−	24.9906i	1.07443	−	1.07443i	0.0774319	−	0.996998i	$-0.475328\pi$
$541$	24.9906	−	24.9906i	1.07443	−	1.07443i	0.996998	−	0.0774319i	$-0.0246720\pi$
$542$		0			0
$543$	3.13586			0.134573
$544$		0			0
$545$		−	23.5171i		−	1.00736i
$546$		0			0
$547$		−	12.1537i		−	0.519656i	−0.965655	−	0.259828i	$-0.916334\pi$
$547$		−	12.1537i		−	0.519656i	0.965655	−	0.259828i	$-0.0836659\pi$
$548$		0			0
$549$	−31.9762			−1.36471
$550$		0			0
$551$	−5.63365	+	5.63365i	−0.240001	+	0.240001i
$552$		0			0
$553$	−41.4299	+	41.4299i	−1.76178	+	1.76178i
$554$		0			0
$555$		−	3.77121i		−	0.160079i
$556$		0			0
$557$	−14.5827	+	14.5827i	−0.617889	+	0.617889i	−0.944989	−	0.327101i	$-0.893928\pi$
$557$	−14.5827	+	14.5827i	−0.617889	+	0.617889i	0.327101	+	0.944989i	$0.393928\pi$
$558$		0			0
$559$	−4.19562	+	9.77311i	−0.177456	+	0.413358i
$560$		0			0
$561$	−3.32759	−	3.32759i	−0.140491	−	0.140491i
$562$		0			0
$563$	20.8732			0.879701			0.439850	−	0.898071i	$-0.355031\pi$
$563$	20.8732			0.879701			0.439850	+	0.898071i	$0.355031\pi$
$564$		0			0
$565$	19.1604	+	19.1604i	0.806082	+	0.806082i
$566$		0			0
$567$	19.9201	+	19.9201i	0.836566	+	0.836566i
$568$		0			0
$569$			3.73549i			0.156600i	0.996930	+	0.0782999i	$0.0249492\pi$
$569$			3.73549i			0.156600i	−0.996930	+	0.0782999i	$0.975051\pi$
$570$		0			0
$571$	−18.8634			−0.789410			−0.394705	−	0.918808i	$-0.629153\pi$
$571$	−18.8634			−0.789410			−0.394705	+	0.918808i	$0.629153\pi$
$572$		0			0
$573$	9.66049			0.403573
$574$		0			0
$575$			8.00425i			0.333800i
$576$		0			0
$577$	−24.3326	−	24.3326i	−1.01298	−	1.01298i	−0.999915	−	0.0130658i	$-0.995841\pi$
$577$	−24.3326	−	24.3326i	−1.01298	−	1.01298i	−0.0130658	−	0.999915i	$-0.504159\pi$
$578$		0			0
$579$	−5.81971	−	5.81971i	−0.241859	−	0.241859i
$580$		0			0
$581$	30.9470			1.28390
$582$		0			0
$583$	4.92714	+	4.92714i	0.204061	+	0.204061i
$584$		0			0
$585$	−18.4249	+	7.35675i	−0.761774	+	0.304164i
$586$		0			0
$587$	−0.269012	+	0.269012i	−0.0111033	+	0.0111033i	−0.712637	−	0.701533i	$-0.752499\pi$
$587$	−0.269012	+	0.269012i	−0.0111033	+	0.0111033i	0.701533	+	0.712637i	$0.252499\pi$
$588$		0			0
$589$		−	5.47098i		−	0.225428i
$590$		0			0
$591$	−4.73365	+	4.73365i	−0.194716	+	0.194716i
$592$		0			0
$593$	5.84469	−	5.84469i	0.240012	−	0.240012i	−0.576843	−	0.816855i	$-0.695715\pi$
$593$	5.84469	−	5.84469i	0.240012	−	0.240012i	0.816855	+	0.576843i	$0.195715\pi$
$594$		0			0
$595$	31.6438			1.29727
$596$		0			0
$597$		−	4.31566i		−	0.176628i
$598$		0			0
$599$			2.54781i			0.104101i	0.998644	+	0.0520504i	$0.0165756\pi$
$599$			2.54781i			0.104101i	−0.998644	+	0.0520504i	$0.983424\pi$
$600$		0			0
$601$	−23.8616			−0.973337			−0.486668	−	0.873587i	$-0.661788\pi$
$601$	−23.8616			−0.973337			−0.486668	+	0.873587i	$0.661788\pi$
$602$		0			0
$603$	−30.5059	+	30.5059i	−1.24230	+	1.24230i
$604$		0			0
$605$	−7.11171	+	7.11171i	−0.289132	+	0.289132i
$606$		0			0
$607$			24.0890i			0.977740i	0.872357	+	0.488870i	$0.162591\pi$
$607$			24.0890i			0.977740i	−0.872357	+	0.488870i	$0.837409\pi$
$608$		0			0
$609$	7.08535	−	7.08535i	0.287113	−	0.287113i
$610$		0			0
$611$	−35.3769	+	14.1254i	−1.43120	+	0.571453i
$612$		0			0
$613$	−2.94885	−	2.94885i	−0.119103	−	0.119103i	0.645043	−	0.764146i	$-0.276839\pi$
$613$	−2.94885	−	2.94885i	−0.119103	−	0.119103i	−0.764146	+	0.645043i	$0.776839\pi$
$614$		0			0
$615$	3.08584			0.124433
$616$		0			0
$617$	−2.20647	−	2.20647i	−0.0888291	−	0.0888291i	0.661296	−	0.750125i	$-0.270007\pi$
$617$	−2.20647	−	2.20647i	−0.0888291	−	0.0888291i	−0.750125	+	0.661296i	$0.770007\pi$
$618$		0			0
$619$	32.5070	+	32.5070i	1.30657	+	1.30657i	0.923878	+	0.382688i	$0.125002\pi$
$619$	32.5070	+	32.5070i	1.30657	+	1.30657i	0.382688	+	0.923878i	$0.374998\pi$
$620$		0			0
$621$		−	24.7524i		−	0.993282i
$622$		0			0
$623$	57.0571			2.28595
$624$		0			0
$625$	19.3207			0.772828
$626$		0			0
$627$			2.16954i			0.0866432i
$628$		0			0
$629$	9.62881	+	9.62881i	0.383926	+	0.383926i
$630$		0			0
$631$	4.32859	+	4.32859i	0.172319	+	0.172319i	0.787997	−	0.615679i	$-0.211118\pi$
$631$	4.32859	+	4.32859i	0.172319	+	0.172319i	−0.615679	+	0.787997i	$0.711118\pi$
$632$		0			0
$633$	10.4829			0.416658
$634$		0			0
$635$	7.77334	+	7.77334i	0.308476	+	0.308476i
$636$		0			0
$637$	35.5683	+	15.2695i	1.40927	+	0.605001i
$638$		0			0
$639$	20.4357	−	20.4357i	0.808425	−	0.808425i
$640$		0			0
$641$		−	9.87384i		−	0.389993i	−0.980804	−	0.194997i	$-0.937530\pi$
$641$		−	9.87384i		−	0.389993i	0.980804	−	0.194997i	$-0.0624696\pi$
$642$		0			0
$643$	11.8022	−	11.8022i	0.465435	−	0.465435i	−0.434997	−	0.900432i	$-0.643250\pi$
$643$	11.8022	−	11.8022i	0.465435	−	0.465435i	0.900432	+	0.434997i	$0.143250\pi$
$644$		0			0
$645$	−2.15783	+	2.15783i	−0.0849646	+	0.0849646i
$646$		0			0
$647$	13.8564			0.544752			0.272376	−	0.962191i	$-0.412191\pi$
$647$	13.8564			0.544752			0.272376	+	0.962191i	$0.412191\pi$
$648$		0			0
$649$		−	16.4129i		−	0.644264i
$650$		0			0
$651$			6.88077i			0.269678i
$652$		0			0
$653$	34.7236			1.35884			0.679419	−	0.733750i	$-0.262232\pi$
$653$	34.7236			1.35884			0.679419	+	0.733750i	$0.262232\pi$
$654$		0			0
$655$	−6.35644	+	6.35644i	−0.248367	+	0.248367i
$656$		0			0
$657$	12.9539	−	12.9539i	0.505379	−	0.505379i
$658$		0			0
$659$		−	6.39018i		−	0.248926i	−0.992224	−	0.124463i	$-0.960279\pi$
$659$		−	6.39018i		−	0.248926i	0.992224	−	0.124463i	$-0.0397208\pi$
$660$		0			0
$661$	−9.45402	+	9.45402i	−0.367719	+	0.367719i	−0.866645	−	0.498926i	$-0.833728\pi$
$661$	−9.45402	+	9.45402i	−0.367719	+	0.367719i	0.498926	+	0.866645i	$0.333728\pi$
$662$		0			0
$663$	−2.73258	+	6.36516i	−0.106125	+	0.247203i
$664$		0			0
$665$	−10.3157	−	10.3157i	−0.400024	−	0.400024i
$666$		0			0
$667$	38.8203			1.50313
$668$		0			0
$669$	2.78413	+	2.78413i	0.107641	+	0.107641i
$670$		0			0
$671$	−20.2466	−	20.2466i	−0.781611	−	0.781611i
$672$		0			0
$673$		−	18.6774i		−	0.719963i	−0.932960	−	0.359981i	$-0.882783\pi$
$673$		−	18.6774i		−	0.719963i	0.932960	−	0.359981i	$-0.117217\pi$
$674$		0			0
$675$	2.81376			0.108302
$676$		0			0
$677$	−32.1895			−1.23714			−0.618572	−	0.785728i	$-0.712288\pi$
$677$	−32.1895			−1.23714			−0.618572	+	0.785728i	$0.712288\pi$
$678$		0			0
$679$		−	22.8980i		−	0.878744i
$680$		0			0
$681$	3.18923	+	3.18923i	0.122212	+	0.122212i
$682$		0			0
$683$	−11.2081	−	11.2081i	−0.428865	−	0.428865i	0.459377	−	0.888241i	$-0.348073\pi$
$683$	−11.2081	−	11.2081i	−0.428865	−	0.428865i	−0.888241	+	0.459377i	$0.848073\pi$
$684$		0			0
$685$	3.46594			0.132427
$686$		0			0
$687$	−7.98183	−	7.98183i	−0.304526	−	0.304526i
$688$		0			0
$689$	4.04612	−	9.42486i	0.154145	−	0.359059i
$690$		0			0
$691$	−13.3452	+	13.3452i	−0.507674	+	0.507674i	−0.913812	−	0.406138i	$-0.866875\pi$
$691$	−13.3452	+	13.3452i	−0.507674	+	0.507674i	0.406138	+	0.913812i	$0.366875\pi$
$692$		0			0
$693$			28.2184i			1.07193i
$694$		0			0
$695$	−26.0650	+	26.0650i	−0.988702	+	0.988702i
$696$		0			0
$697$	−7.87888	+	7.87888i	−0.298434	+	0.298434i
$698$		0			0
$699$	5.16678			0.195425
$700$		0			0
$701$		−	10.0050i		−	0.377885i	−0.981988	−	0.188942i	$-0.939494\pi$
$701$		−	10.0050i		−	0.377885i	0.981988	−	0.188942i	$-0.0605060\pi$
$702$		0			0
$703$		−	6.27786i		−	0.236774i
$704$		0			0
$705$	−10.9298			−0.411639
$706$		0			0
$707$	16.9422	−	16.9422i	0.637179	−	0.637179i
$708$		0			0
$709$	21.8958	−	21.8958i	0.822316	−	0.822316i	−0.164124	−	0.986440i	$-0.552480\pi$
$709$	21.8958	−	21.8958i	0.822316	−	0.822316i	0.986440	+	0.164124i	$0.0524798\pi$
$710$		0			0
$711$			38.0577i			1.42727i
$712$		0			0
$713$	−18.8497	+	18.8497i	−0.705928	+	0.705928i
$714$		0			0
$715$	−16.3243	−	7.00808i	−0.610496	−	0.262087i
$716$		0			0
$717$	1.50266	+	1.50266i	0.0561177	+	0.0561177i
$718$		0			0
$719$	−20.4151			−0.761353			−0.380677	−	0.924708i	$-0.624309\pi$
$719$	−20.4151			−0.761353			−0.380677	+	0.924708i	$0.624309\pi$
$720$		0			0
$721$	1.29367	+	1.29367i	0.0481788	+	0.0481788i
$722$		0			0
$723$	−0.0561602	−	0.0561602i	−0.00208862	−	0.00208862i
$724$		0			0
$725$			4.41294i			0.163892i
$726$		0			0
$727$	−12.2336			−0.453719			−0.226860	−	0.973927i	$-0.572846\pi$
$727$	−12.2336			−0.453719			−0.226860	+	0.973927i	$0.572846\pi$
$728$		0			0
$729$	13.7474			0.509163
$730$		0			0
$731$		−	11.0189i		−	0.407550i
$732$		0			0
$733$	24.2670	+	24.2670i	0.896323	+	0.896323i	0.995109	−	0.0987856i	$-0.0314958\pi$
$733$	24.2670	+	24.2670i	0.896323	+	0.896323i	−0.0987856	+	0.995109i	$0.531496\pi$
$734$		0			0
$735$	7.85322	+	7.85322i	0.289670	+	0.289670i
$736$		0			0
$737$	−38.6313			−1.42300
$738$		0			0
$739$	−21.0861	−	21.0861i	−0.775663	−	0.775663i	0.203427	−	0.979090i	$-0.434792\pi$
$739$	−21.0861	−	21.0861i	−0.775663	−	0.775663i	−0.979090	+	0.203427i	$0.934792\pi$
$740$		0			0
$741$	2.96581	−	1.18420i	0.108952	−	0.0435026i
$742$		0			0
$743$	22.0335	−	22.0335i	0.808331	−	0.808331i	−0.176050	−	0.984381i	$-0.556332\pi$
$743$	22.0335	−	22.0335i	0.808331	−	0.808331i	0.984381	+	0.176050i	$0.0563322\pi$
$744$		0			0
$745$		−	23.3448i		−	0.855288i
$746$		0			0
$747$	14.2140	−	14.2140i	0.520064	−	0.520064i
$748$		0			0
$749$	−39.6605	+	39.6605i	−1.44916	+	1.44916i
$750$		0			0
$751$	−51.4884			−1.87884			−0.939419	−	0.342771i	$-0.888634\pi$
$751$	−51.4884			−1.87884			−0.939419	+	0.342771i	$0.888634\pi$
$752$		0			0
$753$			10.2184i			0.372379i
$754$		0			0
$755$		−	8.47112i		−	0.308296i
$756$		0			0
$757$	−12.0973			−0.439683			−0.219841	−	0.975536i	$-0.570554\pi$
$757$	−12.0973			−0.439683			−0.219841	+	0.975536i	$0.570554\pi$
$758$		0			0
$759$	7.47495	−	7.47495i	0.271324	−	0.271324i
$760$		0			0
$761$	−7.35675	+	7.35675i	−0.266682	+	0.266682i	−0.827762	−	0.561080i	$-0.810386\pi$
$761$	−7.35675	+	7.35675i	−0.266682	+	0.266682i	0.561080	+	0.827762i	$0.310386\pi$
$762$		0			0
$763$			49.2364i			1.78248i
$764$		0			0
$765$	14.5341	−	14.5341i	0.525480	−	0.525480i
$766$		0			0
$767$	−22.4368	+	8.95864i	−0.810145	+	0.323478i
$768$		0			0
$769$	−27.8958	−	27.8958i	−1.00595	−	1.00595i	−0.999982	−	0.00596752i	$-0.998100\pi$
$769$	−27.8958	−	27.8958i	−1.00595	−	1.00595i	−0.00596752	−	0.999982i	$-0.501900\pi$
$770$		0			0
$771$	−3.33419			−0.120078
$772$		0			0
$773$	−2.58269	−	2.58269i	−0.0928930	−	0.0928930i	0.659133	−	0.752026i	$-0.270923\pi$
$773$	−2.58269	−	2.58269i	−0.0928930	−	0.0928930i	−0.752026	+	0.659133i	$0.770923\pi$
$774$		0			0
$775$	−2.14276	−	2.14276i	−0.0769702	−	0.0769702i
$776$		0			0
$777$			7.89556i			0.283252i
$778$		0			0
$779$	5.13693			0.184049
$780$		0			0
$781$	25.8789			0.926019
$782$		0			0
$783$		−	13.6466i		−	0.487690i
$784$		0			0
$785$	−2.71349	−	2.71349i	−0.0968487	−	0.0968487i
$786$		0			0
$787$	−19.0288	−	19.0288i	−0.678305	−	0.678305i	0.281312	−	0.959616i	$-0.409231\pi$
$787$	−19.0288	−	19.0288i	−0.678305	−	0.678305i	−0.959616	+	0.281312i	$0.909231\pi$
$788$		0			0
$789$	−8.90804			−0.317135
$790$		0			0
$791$	−40.1149	−	40.1149i	−1.42632	−	1.42632i
$792$		0			0
$793$	−16.6263	+	38.7286i	−0.590417	+	1.37529i
$794$		0			0
$795$	2.08094	−	2.08094i	0.0738034	−	0.0738034i
$796$		0			0
$797$		−	33.5971i		−	1.19007i	−0.803699	−	0.595036i	$-0.797138\pi$
$797$		−	33.5971i		−	1.19007i	0.803699	−	0.595036i	$-0.202862\pi$
$798$		0			0
$799$	27.9063	−	27.9063i	0.987254	−	0.987254i
$800$		0			0
$801$	26.2065	−	26.2065i	0.925960	−	0.925960i
$802$		0			0
$803$	16.4042			0.578892
$804$		0			0
$805$			71.0832i			2.50535i
$806$		0			0
$807$		−	0.159758i		−	0.00562375i
$808$		0			0
$809$	20.1484			0.708381			0.354190	−	0.935173i	$-0.384756\pi$
$809$	20.1484			0.708381			0.354190	+	0.935173i	$0.384756\pi$
$810$		0			0
$811$	−0.405052	+	0.405052i	−0.0142233	+	0.0142233i	−0.714183	−	0.699959i	$-0.753201\pi$
$811$	−0.405052	+	0.405052i	−0.0142233	+	0.0142233i	0.699959	+	0.714183i	$0.253201\pi$
$812$		0			0
$813$	1.72608	−	1.72608i	0.0605364	−	0.0605364i
$814$		0			0
$815$		−	6.16295i		−	0.215879i
$816$		0			0
$817$	−3.59210	+	3.59210i	−0.125672	+	0.125672i
$818$		0			0
$819$	38.5751	−	15.4024i	1.34792	−	0.538203i
$820$		0			0
$821$	−2.58269	−	2.58269i	−0.0901366	−	0.0901366i	0.660601	−	0.750737i	$-0.270302\pi$
$821$	−2.58269	−	2.58269i	−0.0901366	−	0.0901366i	−0.750737	+	0.660601i	$0.770302\pi$
$822$		0			0
$823$	−29.7700			−1.03772			−0.518859	−	0.854860i	$-0.673643\pi$
$823$	−29.7700			−1.03772			−0.518859	+	0.854860i	$0.673643\pi$
$824$		0			0
$825$	0.849722	+	0.849722i	0.0295835	+	0.0295835i
$826$		0			0
$827$	−30.8280	−	30.8280i	−1.07200	−	1.07200i	−0.997199	−	0.0747966i	$-0.976169\pi$
$827$	−30.8280	−	30.8280i	−1.07200	−	1.07200i	−0.0747966	−	0.997199i	$-0.523831\pi$
$828$		0			0
$829$			14.4418i			0.501585i	0.968041	+	0.250793i	$0.0806912\pi$
$829$			14.4418i			0.501585i	−0.968041	+	0.250793i	$0.919309\pi$
$830$		0			0
$831$	−4.16188			−0.144374
$832$		0			0
$833$	−40.1023			−1.38946
$834$		0			0
$835$		−	10.3923i		−	0.359641i
$836$		0			0
$837$	6.62629	+	6.62629i	0.229038	+	0.229038i
$838$		0			0
$839$	23.3618	+	23.3618i	0.806539	+	0.806539i	0.984108	−	0.177570i	$-0.0568235\pi$
$839$	23.3618	+	23.3618i	0.806539	+	0.806539i	−0.177570	+	0.984108i	$0.556823\pi$
$840$		0			0
$841$	−7.59741			−0.261980
$842$		0			0
$843$	2.91735	+	2.91735i	0.100479	+	0.100479i
$844$		0			0
$845$	−0.669894	+	26.1409i	−0.0230450	+	0.899273i
$846$		0			0
$847$	14.8894	−	14.8894i	0.511605	−	0.511605i
$848$		0			0
$849$		−	5.06811i		−	0.173937i
$850$		0			0
$851$	−21.6297	+	21.6297i	−0.741458	+	0.741458i
$852$		0			0
$853$	3.33011	−	3.33011i	0.114021	−	0.114021i	−0.647794	−	0.761815i	$-0.724308\pi$
$853$	3.33011	−	3.33011i	0.114021	−	0.114021i	0.761815	+	0.647794i	$0.224308\pi$
$854$		0			0
$855$	−9.47601			−0.324073
$856$		0			0
$857$		−	45.2526i		−	1.54580i	−0.634529	−	0.772899i	$-0.718806\pi$
$857$		−	45.2526i		−	1.54580i	0.634529	−	0.772899i	$-0.281194\pi$
$858$		0			0
$859$		−	34.3276i		−	1.17124i	−0.810584	−	0.585622i	$-0.800850\pi$
$859$		−	34.3276i		−	1.17124i	0.810584	−	0.585622i	$-0.199150\pi$
$860$		0			0
$861$	−6.46063			−0.220178
$862$		0			0
$863$	9.09339	−	9.09339i	0.309542	−	0.309542i	−0.535190	−	0.844732i	$-0.679760\pi$
$863$	9.09339	−	9.09339i	0.309542	−	0.309542i	0.844732	+	0.535190i	$0.179760\pi$
$864$		0			0
$865$	33.8328	−	33.8328i	1.15035	−	1.15035i
$866$		0			0
$867$			1.56664i			0.0532058i
$868$		0			0
$869$	−24.0973	+	24.0973i	−0.817444	+	0.817444i
$870$		0			0
$871$	21.0861	+	52.8097i	0.714474	+	1.78939i
$872$		0			0
$873$	−10.5171	−	10.5171i	−0.355950	−	0.355950i
$874$		0			0
$875$	−50.4361			−1.70505
$876$		0			0
$877$	−1.95136	−	1.95136i	−0.0658929	−	0.0658929i	0.673392	−	0.739285i	$-0.264836\pi$
$877$	−1.95136	−	1.95136i	−0.0658929	−	0.0658929i	−0.739285	+	0.673392i	$0.764836\pi$
$878$		0			0
$879$	9.28252	+	9.28252i	0.313092	+	0.313092i
$880$		0			0
$881$			51.3088i			1.72864i	0.502945	+	0.864318i	$0.332250\pi$
$881$			51.3088i			1.72864i	−0.502945	+	0.864318i	$0.667750\pi$
$882$		0			0
$883$	−17.9471			−0.603969			−0.301985	−	0.953313i	$-0.597649\pi$
$883$	−17.9471			−0.603969			−0.301985	+	0.953313i	$0.597649\pi$
$884$		0			0
$885$	−6.93189			−0.233013
$886$		0			0
$887$		−	25.3422i		−	0.850908i	−0.904980	−	0.425454i	$-0.860114\pi$
$887$		−	25.3422i		−	0.850908i	0.904980	−	0.425454i	$-0.139886\pi$
$888$		0			0
$889$	−16.2746	−	16.2746i	−0.545832	−	0.545832i
$890$		0			0
$891$	11.5863	+	11.5863i	0.388157	+	0.388157i
$892$		0			0
$893$	−18.1945			−0.608857
$894$		0			0
$895$	25.5270	+	25.5270i	0.853273	+	0.853273i
$896$		0			0
$897$	−14.2984	−	6.13835i	−0.477411	−	0.204954i
$898$		0			0
$899$	−10.3923	+	10.3923i	−0.346603	+	0.346603i
$900$		0			0
$901$			10.6263i			0.354013i
$902$		0			0
$903$	4.51773	−	4.51773i	0.150341	−	0.150341i
$904$		0			0
$905$	−8.67241	+	8.67241i	−0.288281	+	0.288281i
$906$		0			0
$907$	5.00702			0.166255			0.0831277	−	0.996539i	$-0.473509\pi$
$907$	5.00702			0.166255			0.0831277	+	0.996539i	$0.473509\pi$
$908$		0			0
$909$		−	15.5632i		−	0.516199i
$910$		0			0
$911$			5.68367i			0.188308i	0.995558	+	0.0941542i	$0.0300147\pi$
$911$			5.68367i			0.188308i	−0.995558	+	0.0941542i	$0.969985\pi$
$912$		0			0
$913$	18.0000			0.595713
$914$		0			0
$915$	−8.55100	+	8.55100i	−0.282687	+	0.282687i
$916$		0			0
$917$	13.3081	−	13.3081i	0.439473	−	0.439473i
$918$		0			0
$919$			1.67896i			0.0553837i	0.999617	+	0.0276918i	$0.00881571\pi$
$919$			1.67896i			0.0553837i	−0.999617	+	0.0276918i	$0.991184\pi$
$920$		0			0
$921$	−1.65545	+	1.65545i	−0.0545490	+	0.0545490i
$922$		0			0
$923$	−14.1254	−	35.3769i	−0.464944	−	1.16444i
$924$		0			0
$925$	−2.45878	−	2.45878i	−0.0808442	−	0.0808442i
$926$		0			0
$927$	1.18837			0.0390312
$928$		0			0
$929$	11.5751	+	11.5751i	0.379768	+	0.379768i	0.871018	−	0.491250i	$-0.163460\pi$
$929$	11.5751	+	11.5751i	0.379768	+	0.379768i	−0.491250	+	0.871018i	$0.663460\pi$
$930$		0			0
$931$	13.0731	+	13.0731i	0.428453	+	0.428453i
$932$		0			0
$933$			13.7816i			0.451190i
$934$		0			0
$935$	18.4053			0.601917
$936$		0			0
$937$	−15.7917			−0.515892			−0.257946	−	0.966159i	$-0.583046\pi$
$937$	−15.7917			−0.515892			−0.257946	+	0.966159i	$0.583046\pi$
$938$		0			0
$939$			13.1885i			0.430390i
$940$		0			0
$941$	−1.07779	−	1.07779i	−0.0351351	−	0.0351351i	0.689321	−	0.724456i	$-0.257909\pi$
$941$	−1.07779	−	1.07779i	−0.0351351	−	0.0351351i	−0.724456	+	0.689321i	$0.757909\pi$
$942$		0			0
$943$	−17.6988	−	17.6988i	−0.576351	−	0.576351i
$944$		0			0
$945$	24.9881			0.812862
$946$		0			0
$947$	1.73205	+	1.73205i	0.0562841	+	0.0562841i	0.734689	−	0.678405i	$-0.237328\pi$
$947$	1.73205	+	1.73205i	0.0562841	+	0.0562841i	−0.678405	+	0.734689i	$0.737328\pi$
$948$		0			0
$949$	−8.95388	−	22.4249i	−0.290655	−	0.727942i
$950$		0			0
$951$	−7.46623	+	7.46623i	−0.242109	+	0.242109i
$952$		0			0
$953$		−	3.39094i		−	0.109843i	−0.998491	−	0.0549217i	$-0.982509\pi$
$953$		−	3.39094i		−	0.109843i	0.998491	−	0.0549217i	$-0.0174909\pi$
$954$		0			0
$955$	−26.7166	+	26.7166i	−0.864530	+	0.864530i
$956$		0			0
$957$	4.12112	−	4.12112i	0.133217	−	0.133217i
$958$		0			0
$959$	−7.25644			−0.234323
$960$		0			0
$961$			20.9078i			0.674444i
$962$		0			0
$963$			36.4323i			1.17401i
$964$		0			0
$965$	32.1895			1.03622
$966$		0			0
$967$	13.8046	−	13.8046i	0.443926	−	0.443926i	−0.449403	−	0.893329i	$-0.648363\pi$
$967$	13.8046	−	13.8046i	0.443926	−	0.443926i	0.893329	+	0.449403i	$0.148363\pi$
$968$		0			0
$969$	−2.33951	+	2.33951i	−0.0751560	+	0.0751560i
$970$		0			0
$971$		−	33.0981i		−	1.06217i	−0.847319	−	0.531084i	$-0.821785\pi$
$971$		−	33.0981i		−	1.06217i	0.847319	−	0.531084i	$-0.178215\pi$
$972$		0			0
$973$	54.5708	−	54.5708i	1.74946	−	1.74946i
$974$		0			0
$975$	0.697783	−	1.62539i	0.0223469	−	0.0520540i
$976$		0			0
$977$	23.9420	+	23.9420i	0.765971	+	0.765971i	0.977395	−	0.211423i	$-0.0678099\pi$
$977$	23.9420	+	23.9420i	0.765971	+	0.765971i	−0.211423	+	0.977395i	$0.567810\pi$
$978$		0			0
$979$	33.1867			1.06065
$980$		0			0
$981$	22.6144	+	22.6144i	0.722021	+	0.722021i
$982$		0			0
$983$	−25.1694	−	25.1694i	−0.802778	−	0.802778i	0.180751	−	0.983529i	$-0.442147\pi$
$983$	−25.1694	−	25.1694i	−0.802778	−	0.802778i	−0.983529	+	0.180751i	$0.942147\pi$
$984$		0			0
$985$		−	26.1823i		−	0.834239i
$986$		0			0
$987$	22.8830			0.728374
$988$		0			0
$989$	24.7524			0.787082
$990$		0			0
$991$			18.4140i			0.584940i	0.956275	+	0.292470i	$0.0944772\pi$
$991$			18.4140i			0.584940i	−0.956275	+	0.292470i	$0.905523\pi$
$992$		0			0
$993$	−1.41982	−	1.41982i	−0.0450568	−	0.0450568i
$994$		0			0
$995$	11.9352	+	11.9352i	0.378372	+	0.378372i
$996$		0			0
$997$	−15.3737			−0.486890			−0.243445	−	0.969915i	$-0.578278\pi$
$997$	−15.3737			−0.486890			−0.243445	+	0.969915i	$0.578278\pi$
$998$		0			0
$999$	7.60356	+	7.60356i	0.240566	+	0.240566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.k.b.47.4	yes	12
3.2	odd	2		1872.2.bf.o.1711.6		12
4.3	odd	2	inner	208.2.k.b.47.3	yes	12
8.3	odd	2		832.2.k.j.255.4		12
8.5	even	2		832.2.k.j.255.3		12
12.11	even	2		1872.2.bf.o.1711.5		12
13.5	odd	4	inner	208.2.k.b.31.4	yes	12
39.5	even	4		1872.2.bf.o.1279.5		12
52.31	even	4	inner	208.2.k.b.31.3	✓	12
104.5	odd	4		832.2.k.j.447.3		12
104.83	even	4		832.2.k.j.447.4		12
156.83	odd	4		1872.2.bf.o.1279.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.k.b.31.3	✓	12	52.31	even	4	inner
208.2.k.b.31.4	yes	12	13.5	odd	4	inner
208.2.k.b.47.3	yes	12	4.3	odd	2	inner
208.2.k.b.47.4	yes	12	1.1	even	1	trivial
832.2.k.j.255.3		12	8.5	even	2
832.2.k.j.255.4		12	8.3	odd	2
832.2.k.j.447.3		12	104.5	odd	4
832.2.k.j.447.4		12	104.83	even	4
1872.2.bf.o.1279.5		12	39.5	even	4
1872.2.bf.o.1279.6		12	156.83	odd	4
1872.2.bf.o.1711.5		12	12.11	even	2
1872.2.bf.o.1711.6		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.514306i q^{3} +(-1.42234 - 1.42234i) q^{5} +(2.97788 + 2.97788i) q^{7} +2.73549 q^{9} +(1.73205 + 1.73205i) q^{11} +(1.42234 - 3.31315i) q^{13} +(0.731519 - 0.731519i) q^{15} +3.73549i q^{17} +(1.21774 - 1.21774i) q^{19} +(-1.53154 + 1.53154i) q^{21} -8.39124 q^{23} -0.953882i q^{25} +2.94980i q^{27} -4.62629 q^{29} +(2.24636 - 2.24636i) q^{31} +(-0.890804 + 0.890804i) q^{33} -8.47112i q^{35} +(2.57766 - 2.57766i) q^{37} +(1.70397 + 0.731519i) q^{39} +(2.10920 + 2.10920i) q^{41} -2.94980 q^{43} +(-3.89080 - 3.89080i) q^{45} +(-7.47059 - 7.47059i) q^{47} +10.7355i q^{49} -1.92118 q^{51} +2.84469 q^{53} -4.92714i q^{55} +(0.626293 + 0.626293i) q^{57} +(-4.73801 - 4.73801i) q^{59} -11.6894 q^{61} +(8.14595 + 8.14595i) q^{63} +(-6.73549 + 2.68937i) q^{65} +(-11.1519 + 11.1519i) q^{67} -4.31566i q^{69} +(7.47059 - 7.47059i) q^{71} +(4.73549 - 4.73549i) q^{73} +0.490587 q^{75} +10.3157i q^{77} +13.9126i q^{79} +6.68937 q^{81} +(5.19615 - 5.19615i) q^{83} +(5.31315 - 5.31315i) q^{85} -2.37933i q^{87} +(9.58018 - 9.58018i) q^{89} +(14.1017 - 5.63058i) q^{91} +(1.15531 + 1.15531i) q^{93} -3.46410 q^{95} +(-3.84469 - 3.84469i) q^{97} +(4.73801 + 4.73801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 20 q^{9} - 4 q^{13} - 8 q^{21} + 8 q^{29} + 52 q^{37} + 36 q^{41} - 36 q^{45} - 8 q^{53} - 56 q^{57} - 56 q^{61} - 28 q^{65} + 4 q^{73} - 4 q^{81} + 32 q^{85} + 20 q^{89} + 56 q^{93} - 4 q^{97}+O(q^{100}) \) 12 * q + 4 * q^5 - 20 * q^9 - 4 * q^13 - 8 * q^21 + 8 * q^29 + 52 * q^37 + 36 * q^41 - 36 * q^45 - 8 * q^53 - 56 * q^57 - 56 * q^61 - 28 * q^65 + 4 * q^73 - 4 * q^81 + 32 * q^85 + 20 * q^89 + 56 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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