LMFDB - Embedded newform 1368.2.g.b.685.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(685,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1368.685");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 4x^12 + 4x^11 - 10x^10 + 24x^9 - 40x^8 + 48x^7 - 40x^6 + 32x^5 + 64x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			685.4
Root			$-0.889165 + 1.09972i$ of defining polynomial
Character	$\chi$	$=$	1368.685
Dual form			1368.2.g.b.685.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09972 + 0.889165i) q^{2} +(0.418773 - 1.95567i) q^{4} -3.13887i q^{5} -0.535658 q^{7} +(1.27838 + 2.52304i) q^{8} +O(q^{10})$	\(q+(-1.09972 + 0.889165i) q^{2} +(0.418773 - 1.95567i) q^{4} -3.13887i q^{5} -0.535658 q^{7} +(1.27838 + 2.52304i) q^{8} +(2.79097 + 3.45188i) q^{10} +0.425227i q^{11} -6.65786i q^{13} +(0.589074 - 0.476288i) q^{14} +(-3.64926 - 1.63796i) q^{16} -7.33239 q^{17} -1.00000i q^{19} +(-6.13858 - 1.31447i) q^{20} +(-0.378097 - 0.467631i) q^{22} +5.90033 q^{23} -4.85252 q^{25} +(5.91994 + 7.32179i) q^{26} +(-0.224319 + 1.04757i) q^{28} +0.837037i q^{29} -3.16999 q^{31} +(5.46958 - 1.44349i) q^{32} +(8.06359 - 6.51970i) q^{34} +1.68136i q^{35} +3.49490i q^{37} +(0.889165 + 1.09972i) q^{38} +(7.91951 - 4.01266i) q^{40} +0.123059 q^{41} +5.39744i q^{43} +(0.831602 + 0.178073i) q^{44} +(-6.48872 + 5.24637i) q^{46} +2.02928 q^{47} -6.71307 q^{49} +(5.33641 - 4.31469i) q^{50} +(-13.0206 - 2.78813i) q^{52} +5.82785i q^{53} +1.33473 q^{55} +(-0.684772 - 1.35149i) q^{56} +(-0.744264 - 0.920508i) q^{58} -5.56633i q^{59} +6.99606i q^{61} +(3.48610 - 2.81864i) q^{62} +(-4.73151 + 6.45080i) q^{64} -20.8982 q^{65} -12.3777i q^{67} +(-3.07061 + 14.3397i) q^{68} +(-1.49501 - 1.84903i) q^{70} -12.1786 q^{71} -6.99382 q^{73} +(-3.10754 - 3.84341i) q^{74} +(-1.95567 - 0.418773i) q^{76} -0.227776i q^{77} +2.07996 q^{79} +(-5.14134 + 11.4546i) q^{80} +(-0.135331 + 0.109420i) q^{82} +11.8227i q^{83} +23.0154i q^{85} +(-4.79921 - 5.93567i) q^{86} +(-1.07287 + 0.543600i) q^{88} -13.7684 q^{89} +3.56633i q^{91} +(2.47090 - 11.5391i) q^{92} +(-2.23164 + 1.80436i) q^{94} -3.13887 q^{95} +0.801240 q^{97} +(7.38251 - 5.96902i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 2 * q^4 - 8 * q^7 + 12 * q^8	$ 16 q + 2 q^{4} - 8 q^{7} + 12 q^{8} - 8 q^{10} - 4 q^{14} + 2 q^{16} + 8 q^{17} - 8 q^{20} + 20 q^{22} - 24 q^{25} + 10 q^{26} - 14 q^{28} + 16 q^{31} + 20 q^{32} - 2 q^{38} + 28 q^{40} - 16 q^{41} + 28 q^{44} - 48 q^{46} - 24 q^{47} + 24 q^{49} - 12 q^{50} + 8 q^{52} + 16 q^{55} + 48 q^{56} + 38 q^{58} + 16 q^{62} + 14 q^{64} - 16 q^{65} + 26 q^{68} - 32 q^{70} - 48 q^{71} + 20 q^{74} - 4 q^{76} - 48 q^{79} - 4 q^{80} - 12 q^{82} - 48 q^{86} + 40 q^{88} + 16 q^{89} - 62 q^{92} - 36 q^{94} - 16 q^{95} + 32 q^{97} + 48 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 - 8 * q^7 + 12 * q^8 - 8 * q^10 - 4 * q^14 + 2 * q^16 + 8 * q^17 - 8 * q^20 + 20 * q^22 - 24 * q^25 + 10 * q^26 - 14 * q^28 + 16 * q^31 + 20 * q^32 - 2 * q^38 + 28 * q^40 - 16 * q^41 + 28 * q^44 - 48 * q^46 - 24 * q^47 + 24 * q^49 - 12 * q^50 + 8 * q^52 + 16 * q^55 + 48 * q^56 + 38 * q^58 + 16 * q^62 + 14 * q^64 - 16 * q^65 + 26 * q^68 - 32 * q^70 - 48 * q^71 + 20 * q^74 - 4 * q^76 - 48 * q^79 - 4 * q^80 - 12 * q^82 - 48 * q^86 + 40 * q^88 + 16 * q^89 - 62 * q^92 - 36 * q^94 - 16 * q^95 + 32 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−1.09972	+	0.889165i	−0.777620	+	0.628734i
$2$	−1.09972	+	0.889165i	−0.777620	+	0.628734i
$3$		0			0
$3$		0			0
$4$	0.418773	−	1.95567i	0.209386	−	0.977833i
$5$		−	3.13887i		−	1.40375i	−0.712302	−	0.701873i	$-0.752347\pi$
$5$		−	3.13887i		−	1.40375i	0.712302	−	0.701873i	$-0.247653\pi$
$6$		0			0
$7$	−0.535658			−0.202460			−0.101230	−	0.994863i	$-0.532278\pi$
$7$	−0.535658			−0.202460			−0.101230	+	0.994863i	$0.532278\pi$
$8$	1.27838	+	2.52304i	0.451974	+	0.892031i
$9$		0			0
$10$	2.79097	+	3.45188i	0.882583	+	1.09158i
$11$			0.425227i			0.128211i	0.997943	+	0.0641054i	$0.0204194\pi$
$11$			0.425227i			0.128211i	−0.997943	+	0.0641054i	$0.979581\pi$
$12$		0			0
$13$		−	6.65786i		−	1.84656i	−0.384129	−	0.923279i	$-0.625498\pi$
$13$		−	6.65786i		−	1.84656i	0.384129	−	0.923279i	$-0.374502\pi$
$14$	0.589074	−	0.476288i	0.157437	−	0.127293i
$15$		0			0
$16$	−3.64926	−	1.63796i	−0.912315	−	0.409490i
$17$	−7.33239			−1.77837			−0.889183	−	0.457552i	$-0.848727\pi$
$17$	−7.33239			−1.77837			−0.889183	+	0.457552i	$0.848727\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−6.13858	−	1.31447i	−1.37263	−	0.293925i
$21$		0			0
$22$	−0.378097	−	0.467631i	−0.0806105	−	0.0996993i
$23$	5.90033			1.23030			0.615152	−	0.788408i	$-0.289095\pi$
$23$	5.90033			1.23030			0.615152	+	0.788408i	$0.289095\pi$
$24$		0			0
$25$	−4.85252			−0.970503
$26$	5.91994	+	7.32179i	1.16099	+	1.43592i
$27$		0			0
$28$	−0.224319	+	1.04757i	−0.0423923	+	0.197972i
$29$			0.837037i			0.155434i	0.996975	+	0.0777170i	$0.0247631\pi$
$29$			0.837037i			0.155434i	−0.996975	+	0.0777170i	$0.975237\pi$
$30$		0			0
$31$	−3.16999			−0.569347			−0.284674	−	0.958625i	$-0.591885\pi$
$31$	−3.16999			−0.569347			−0.284674	+	0.958625i	$0.591885\pi$
$32$	5.46958	−	1.44349i	0.966895	−	0.255176i
$33$		0			0
$34$	8.06359	−	6.51970i	1.38289	−	1.11812i
$35$			1.68136i			0.284202i
$36$		0			0
$37$			3.49490i			0.574558i	0.957847	+	0.287279i	$0.0927507\pi$
$37$			3.49490i			0.574558i	−0.957847	+	0.287279i	$0.907249\pi$
$38$	0.889165	+	1.09972i	0.144242	+	0.178398i
$39$		0			0
$40$	7.91951	−	4.01266i	1.25219	−	0.634457i
$41$	0.123059			0.0192186			0.00960932	−	0.999954i	$-0.496941\pi$
$41$	0.123059			0.0192186			0.00960932	+	0.999954i	$0.496941\pi$
$42$		0			0
$43$			5.39744i			0.823101i	0.911387	+	0.411551i	$0.135013\pi$
$43$			5.39744i			0.823101i	−0.911387	+	0.411551i	$0.864987\pi$
$44$	0.831602	+	0.178073i	0.125369	+	0.0268456i
$45$		0			0
$46$	−6.48872	+	5.24637i	−0.956710	+	0.773535i
$47$	2.02928			0.296001			0.148000	−	0.988987i	$-0.452716\pi$
$47$	2.02928			0.296001			0.148000	+	0.988987i	$0.452716\pi$
$48$		0			0
$49$	−6.71307			−0.959010
$50$	5.33641	−	4.31469i	0.754683	−	0.610189i
$51$		0			0
$52$	−13.0206	−	2.78813i	−1.80563	−	0.386644i
$53$			5.82785i			0.800517i	0.916402	+	0.400259i	$0.131080\pi$
$53$			5.82785i			0.800517i	−0.916402	+	0.400259i	$0.868920\pi$
$54$		0			0
$55$	1.33473			0.179975
$56$	−0.684772	−	1.35149i	−0.0915065	−	0.180600i
$57$		0			0
$58$	−0.744264	−	0.920508i	−0.0977267	−	0.120869i
$59$		−	5.56633i		−	0.724675i	−0.932047	−	0.362337i	$-0.881979\pi$
$59$		−	5.56633i		−	0.724675i	0.932047	−	0.362337i	$-0.118021\pi$
$60$		0			0
$61$			6.99606i			0.895753i	0.894095	+	0.447877i	$0.147820\pi$
$61$			6.99606i			0.895753i	−0.894095	+	0.447877i	$0.852180\pi$
$62$	3.48610	−	2.81864i	0.442736	−	0.357968i
$63$		0			0
$64$	−4.73151	+	6.45080i	−0.591439	+	0.806350i
$65$	−20.8982			−2.59210
$66$		0			0
$67$		−	12.3777i		−	1.51217i	−0.654471	−	0.756087i	$-0.727109\pi$
$67$		−	12.3777i		−	1.51217i	0.654471	−	0.756087i	$-0.272891\pi$
$68$	−3.07061	+	14.3397i	−0.372366	+	1.73895i
$69$		0			0
$70$	−1.49501	−	1.84903i	−0.178687	−	0.221001i
$71$	−12.1786			−1.44534			−0.722669	−	0.691194i	$-0.757085\pi$
$71$	−12.1786			−1.44534			−0.722669	+	0.691194i	$0.757085\pi$
$72$		0			0
$73$	−6.99382			−0.818565			−0.409282	−	0.912408i	$-0.634221\pi$
$73$	−6.99382			−0.818565			−0.409282	+	0.912408i	$0.634221\pi$
$74$	−3.10754	−	3.84341i	−0.361244	−	0.446788i
$75$		0			0
$76$	−1.95567	−	0.418773i	−0.224330	−	0.0480365i
$77$		−	0.227776i		−	0.0259575i
$78$		0			0
$79$	2.07996			0.234014			0.117007	−	0.993131i	$-0.462670\pi$
$79$	2.07996			0.234014			0.117007	+	0.993131i	$0.462670\pi$
$80$	−5.14134	+	11.4546i	−0.574820	+	1.28066i
$81$		0			0
$82$	−0.135331	+	0.109420i	−0.0149448	+	0.0120834i
$83$			11.8227i			1.29771i	0.760914	+	0.648853i	$0.224751\pi$
$83$			11.8227i			1.29771i	−0.760914	+	0.648853i	$0.775249\pi$
$84$		0			0
$85$			23.0154i			2.49637i
$86$	−4.79921	−	5.93567i	−0.517512	−	0.640060i
$87$		0			0
$88$	−1.07287	+	0.543600i	−0.114368	+	0.0579480i
$89$	−13.7684			−1.45945			−0.729723	−	0.683743i	$-0.760351\pi$
$89$	−13.7684			−1.45945			−0.729723	+	0.683743i	$0.760351\pi$
$90$		0			0
$91$			3.56633i			0.373853i
$92$	2.47090	−	11.5391i	0.257609	−	1.20303i
$93$		0			0
$94$	−2.23164	+	1.80436i	−0.230176	+	0.186106i
$95$	−3.13887			−0.322041
$96$		0			0
$97$	0.801240			0.0813536			0.0406768	−	0.999172i	$-0.487049\pi$
$97$	0.801240			0.0813536			0.0406768	+	0.999172i	$0.487049\pi$
$98$	7.38251	−	5.96902i	0.745746	−	0.602963i
$99$		0			0
$100$	−2.03210	+	9.48990i	−0.203210	+	0.948990i
$101$		−	12.4171i		−	1.23555i	−0.786356	−	0.617773i	$-0.788035\pi$
$101$		−	12.4171i		−	1.23555i	0.786356	−	0.617773i	$-0.211965\pi$
$102$		0			0
$103$	−2.84869			−0.280690			−0.140345	−	0.990103i	$-0.544821\pi$
$103$	−2.84869			−0.280690			−0.140345	+	0.990103i	$0.544821\pi$
$104$	16.7981	−	8.51125i	1.64719	−	0.834597i
$105$		0			0
$106$	−5.18192	−	6.40901i	−0.503313	−	0.622498i
$107$			0.288142i			0.0278557i	0.999903	+	0.0139278i	$0.00443352\pi$
$107$			0.288142i			0.0278557i	−0.999903	+	0.0139278i	$0.995566\pi$
$108$		0			0
$109$			1.91873i			0.183781i	0.995769	+	0.0918905i	$0.0292910\pi$
$109$			1.91873i			0.183781i	−0.995769	+	0.0918905i	$0.970709\pi$
$110$	−1.46783	+	1.18680i	−0.139952	+	0.113157i
$111$		0			0
$112$	1.95475	+	0.877385i	0.184707	+	0.0829051i
$113$	13.4370			1.26405			0.632024	−	0.774949i	$-0.282224\pi$
$113$	13.4370			1.26405			0.632024	+	0.774949i	$0.282224\pi$
$114$		0			0
$115$		−	18.5204i		−	1.72704i
$116$	1.63697	+	0.350528i	0.151988	+	0.0325457i
$117$		0			0
$118$	4.94939	+	6.12141i	0.455628	+	0.563522i
$119$	3.92765			0.360047
$120$		0			0
$121$	10.8192			0.983562
$122$	−6.22064	−	7.69371i	−0.563191	−	0.696556i
$123$		0			0
$124$	−1.32751	+	6.19944i	−0.119213	+	0.556726i
$125$		−	0.462931i		−	0.0414058i
$126$		0			0
$127$	−18.9992			−1.68591			−0.842953	−	0.537987i	$-0.819185\pi$
$127$	−18.9992			−1.68591			−0.842953	+	0.537987i	$0.819185\pi$
$128$	−0.532480	−	11.3012i	−0.0470650	−	0.998892i
$129$		0			0
$130$	22.9822	−	18.5819i	2.01567	−	1.62974i
$131$		−	10.1330i		−	0.885322i	−0.896689	−	0.442661i	$-0.854035\pi$
$131$		−	10.1330i		−	0.885322i	0.896689	−	0.442661i	$-0.145965\pi$
$132$		0			0
$133$			0.535658i			0.0464474i
$134$	11.0058	+	13.6120i	0.950756	+	1.17590i
$135$		0			0
$136$	−9.37355	−	18.5000i	−0.803775	−	1.58636i
$137$	3.28221			0.280418			0.140209	−	0.990122i	$-0.455222\pi$
$137$	3.28221			0.280418			0.140209	+	0.990122i	$0.455222\pi$
$138$		0			0
$139$		−	10.5345i		−	0.893527i	−0.894652	−	0.446763i	$-0.852577\pi$
$139$		−	10.5345i		−	0.893527i	0.894652	−	0.446763i	$-0.147423\pi$
$140$	3.28818	+	0.704108i	0.277902	+	0.0595080i
$141$		0			0
$142$	13.3931	−	10.8288i	1.12392	−	0.908734i
$143$	2.83110			0.236749
$144$		0			0
$145$	2.62735			0.218190
$146$	7.69125	−	6.21866i	0.636532	−	0.514660i
$147$		0			0
$148$	6.83486	+	1.46357i	0.561822	+	0.120305i
$149$		−	5.93244i		−	0.486005i	−0.970026	−	0.243002i	$-0.921868\pi$
$149$		−	5.93244i		−	0.486005i	0.970026	−	0.243002i	$-0.0781323\pi$
$150$		0			0
$151$	4.57907			0.372639			0.186320	−	0.982489i	$-0.440344\pi$
$151$	4.57907			0.372639			0.186320	+	0.982489i	$0.440344\pi$
$152$	2.52304	−	1.27838i	0.204646	−	0.103690i
$153$		0			0
$154$	0.202530	+	0.250490i	0.0163204	+	0.0201851i
$155$			9.95019i			0.799219i
$156$		0			0
$157$		−	3.80861i		−	0.303960i	−0.988384	−	0.151980i	$-0.951435\pi$
$157$		−	3.80861i		−	0.303960i	0.988384	−	0.151980i	$-0.0485649\pi$
$158$	−2.28738	+	1.84943i	−0.181974	+	0.147133i
$159$		0			0
$160$	−4.53094	−	17.1683i	−0.358202	−	1.35727i
$161$	−3.16056			−0.249087
$162$		0			0
$163$			17.9293i			1.40433i	0.712016	+	0.702164i	$0.247783\pi$
$163$			17.9293i			1.40433i	−0.712016	+	0.702164i	$0.752217\pi$
$164$	0.0515339	−	0.240663i	0.00402412	−	0.0187926i
$165$		0			0
$166$	−10.5123	−	13.0016i	−0.815912	−	1.00912i
$167$	−18.8189			−1.45625			−0.728123	−	0.685446i	$-0.759607\pi$
$167$	−18.8189			−1.45625			−0.728123	+	0.685446i	$0.759607\pi$
$168$		0			0
$169$	−31.3271			−2.40978
$170$	−20.4645	−	25.3106i	−1.56956	−	1.94123i
$171$		0			0
$172$	10.5556	+	2.26030i	0.804856	+	0.172346i
$173$			5.87750i			0.446858i	0.974720	+	0.223429i	$0.0717251\pi$
$173$			5.87750i			0.446858i	−0.974720	+	0.223429i	$0.928275\pi$
$174$		0			0
$175$	2.59929			0.196488
$176$	0.696504	−	1.55176i	0.0525010	−	0.116969i
$177$		0			0
$178$	15.1414	−	12.2424i	1.13489	−	0.917604i
$179$		−	18.9245i		−	1.41448i	−0.706973	−	0.707241i	$-0.749940\pi$
$179$		−	18.9245i		−	1.41448i	0.706973	−	0.707241i	$-0.250060\pi$
$180$		0			0
$181$		−	10.5330i		−	0.782914i	−0.920196	−	0.391457i	$-0.871971\pi$
$181$		−	10.5330i		−	0.782914i	0.920196	−	0.391457i	$-0.128029\pi$
$182$	−3.17106	−	3.92197i	−0.235054	−	0.290716i
$183$		0			0
$184$	7.54284	+	14.8868i	0.556066	+	1.09747i
$185$	10.9700			0.806534
$186$		0			0
$187$		−	3.11793i		−	0.228006i
$188$	0.849807	−	3.96859i	0.0619785	−	0.289439i
$189$		0			0
$190$	3.45188	−	2.79097i	0.250426	−	0.202479i
$191$	−1.60481			−0.116120			−0.0580600	−	0.998313i	$-0.518491\pi$
$191$	−1.60481			−0.116120			−0.0580600	+	0.998313i	$0.518491\pi$
$192$		0			0
$193$	−13.2889			−0.956554			−0.478277	−	0.878209i	$-0.658739\pi$
$193$	−13.2889			−0.956554			−0.478277	+	0.878209i	$0.658739\pi$
$194$	−0.881140	+	0.712434i	−0.0632622	+	0.0511498i
$195$		0			0
$196$	−2.81125	+	13.1285i	−0.200804	+	0.937752i
$197$		−	4.06689i		−	0.289754i	−0.989450	−	0.144877i	$-0.953721\pi$
$197$		−	4.06689i		−	0.289754i	0.989450	−	0.144877i	$-0.0462787\pi$
$198$		0			0
$199$	12.8273			0.909307			0.454653	−	0.890668i	$-0.349763\pi$
$199$	12.8273			0.909307			0.454653	+	0.890668i	$0.349763\pi$
$200$	−6.20334	−	12.2431i	−0.438642	−	0.865719i
$201$		0			0
$202$	11.0408	+	13.6553i	0.776830	+	0.960786i
$203$		−	0.448365i		−	0.0314691i
$204$		0			0
$205$		−	0.386268i		−	0.0269781i
$206$	3.13277	−	2.53296i	0.218270	−	0.176479i
$207$		0			0
$208$	−10.9053	+	24.2963i	−0.756147	+	1.68464i
$209$	0.425227			0.0294136
$210$		0			0
$211$		−	15.9906i		−	1.10084i	−0.834888	−	0.550420i	$-0.814468\pi$
$211$		−	15.9906i		−	1.10084i	0.834888	−	0.550420i	$-0.185532\pi$
$212$	11.3973	+	2.44055i	0.782772	+	0.167617i
$213$		0			0
$214$	−0.256205	−	0.316875i	−0.0175138	−	0.0216612i
$215$	16.9419			1.15543
$216$		0			0
$217$	1.69803			0.115270
$218$	−1.70607	−	2.11007i	−0.115549	−	0.142912i
$219$		0			0
$220$	0.558950	−	2.61029i	0.0376844	−	0.175986i
$221$			48.8181i			3.28386i
$222$		0			0
$223$	21.1424			1.41580			0.707899	−	0.706314i	$-0.249643\pi$
$223$	21.1424			1.41580			0.707899	+	0.706314i	$0.249643\pi$
$224$	−2.92982	+	0.773218i	−0.195757	+	0.0516628i
$225$		0			0
$226$	−14.7770	+	11.9477i	−0.982949	+	0.794750i
$227$			22.2056i			1.47384i	0.675982	+	0.736918i	$0.263720\pi$
$227$			22.2056i			1.47384i	−0.675982	+	0.736918i	$0.736280\pi$
$228$		0			0
$229$			12.6331i			0.834816i	0.908719	+	0.417408i	$0.137061\pi$
$229$			12.6331i			0.834816i	−0.908719	+	0.417408i	$0.862939\pi$
$230$	16.4677	+	20.3673i	1.08585	+	1.34298i
$231$		0			0
$232$	−2.11188	+	1.07005i	−0.138652	+	0.0702521i
$233$	−3.01852			−0.197750			−0.0988749	−	0.995100i	$-0.531524\pi$
$233$	−3.01852			−0.197750			−0.0988749	+	0.995100i	$0.531524\pi$
$234$		0			0
$235$		−	6.36965i		−	0.415510i
$236$	−10.8859	−	2.33103i	−0.708611	−	0.151737i
$237$		0			0
$238$	−4.31932	+	3.49233i	−0.279980	+	0.226374i
$239$	−12.7156			−0.822504			−0.411252	−	0.911522i	$-0.634908\pi$
$239$	−12.7156			−0.822504			−0.411252	+	0.911522i	$0.634908\pi$
$240$		0			0
$241$	−1.05734			−0.0681091			−0.0340545	−	0.999420i	$-0.510842\pi$
$241$	−1.05734			−0.0681091			−0.0340545	+	0.999420i	$0.510842\pi$
$242$	−11.8981	+	9.62003i	−0.764838	+	0.618399i
$243$		0			0
$244$	13.6819	+	2.92976i	0.875897	+	0.187558i
$245$			21.0715i			1.34621i
$246$		0			0
$247$	−6.65786			−0.423630
$248$	−4.05244	−	7.99803i	−0.257330	−	0.507875i
$249$		0			0
$250$	0.411622	+	0.509095i	0.0260333	+	0.0321980i
$251$		−	13.4689i		−	0.850151i	−0.905158	−	0.425076i	$-0.860248\pi$
$251$		−	13.4689i		−	0.850151i	0.905158	−	0.425076i	$-0.139752\pi$
$252$		0			0
$253$			2.50898i			0.157738i
$254$	20.8938	−	16.8934i	1.31099	−	1.05999i
$255$		0			0
$256$	10.6342	+	11.9547i	0.664636	+	0.747167i
$257$	−19.1631			−1.19536			−0.597680	−	0.801734i	$-0.703911\pi$
$257$	−19.1631			−1.19536			−0.597680	+	0.801734i	$0.703911\pi$
$258$		0			0
$259$		−	1.87207i		−	0.116325i
$260$	−8.75159	+	40.8699i	−0.542750	+	2.53464i
$261$		0			0
$262$	9.00988	+	11.1434i	0.556632	+	0.688444i
$263$	2.55940			0.157819			0.0789097	−	0.996882i	$-0.474856\pi$
$263$	2.55940			0.157819			0.0789097	+	0.996882i	$0.474856\pi$
$264$		0			0
$265$	18.2929			1.12372
$266$	−0.476288	−	0.589074i	−0.0292031	−	0.0361184i
$267$		0			0
$268$	−24.2066	−	5.18343i	−1.47865	−	0.316629i
$269$		−	4.88596i		−	0.297902i	−0.988845	−	0.148951i	$-0.952410\pi$
$269$		−	4.88596i		−	0.297902i	0.988845	−	0.148951i	$-0.0475897\pi$
$270$		0			0
$271$	32.1299			1.95175			0.975875	−	0.218329i	$-0.0700604\pi$
$271$	32.1299			1.95175			0.975875	+	0.218329i	$0.0700604\pi$
$272$	26.7578	+	12.0102i	1.62243	+	0.728223i
$273$		0			0
$274$	−3.60952	+	2.91843i	−0.218059	+	0.176309i
$275$		−	2.06342i		−	0.124429i
$276$		0			0
$277$		−	7.46639i		−	0.448612i	−0.974519	−	0.224306i	$-0.927988\pi$
$277$		−	7.46639i		−	0.448612i	0.974519	−	0.224306i	$-0.0720115\pi$
$278$	9.36692	+	11.5850i	0.561791	+	0.694824i
$279$		0			0
$280$	−4.24215	+	2.14941i	−0.253517	+	0.128452i
$281$	−18.9770			−1.13208			−0.566038	−	0.824379i	$-0.691524\pi$
$281$	−18.9770			−1.13208			−0.566038	+	0.824379i	$0.691524\pi$
$282$		0			0
$283$			1.24321i			0.0739012i	0.999317	+	0.0369506i	$0.0117644\pi$
$283$			1.24321i			0.0739012i	−0.999317	+	0.0369506i	$0.988236\pi$
$284$	−5.10008	+	23.8173i	−0.302634	+	1.41330i
$285$		0			0
$286$	−3.11342	+	2.51732i	−0.184101	+	0.148852i
$287$	−0.0659177			−0.00389100
$288$		0			0
$289$	36.7640			2.16259
$290$	−2.88936	+	2.33615i	−0.169669	+	0.137183i
$291$		0			0
$292$	−2.92882	+	13.6776i	−0.171396	+	0.800420i
$293$		−	5.35018i		−	0.312561i	−0.987713	−	0.156280i	$-0.950050\pi$
$293$		−	5.35018i		−	0.312561i	0.987713	−	0.156280i	$-0.0499504\pi$
$294$		0			0
$295$	−17.4720			−1.01726
$296$	−8.81779	+	4.46779i	−0.512524	+	0.259685i
$297$		0			0
$298$	5.27492	+	6.52403i	0.305568	+	0.377927i
$299$		−	39.2836i		−	2.27183i
$300$		0			0
$301$		−	2.89118i		−	0.166645i
$302$	−5.03570	+	4.07155i	−0.289772	+	0.234291i
$303$		0			0
$304$	−1.63796	+	3.64926i	−0.0939434	+	0.209299i
$305$	21.9597			1.25741
$306$		0			0
$307$		−	10.4800i		−	0.598123i	−0.954234	−	0.299062i	$-0.903326\pi$
$307$		−	10.4800i		−	0.598123i	0.954234	−	0.299062i	$-0.0966737\pi$
$308$	−0.445454	−	0.0953864i	−0.0253821	−	0.00543514i
$309$		0			0
$310$	−8.84736	−	10.9424i	−0.502496	−	0.621489i
$311$	27.3720			1.55212			0.776061	−	0.630658i	$-0.217215\pi$
$311$	27.3720			1.55212			0.776061	+	0.630658i	$0.217215\pi$
$312$		0			0
$313$	−16.9214			−0.956451			−0.478226	−	0.878237i	$-0.658720\pi$
$313$	−16.9214			−0.956451			−0.478226	+	0.878237i	$0.658720\pi$
$314$	3.38648	+	4.18841i	0.191110	+	0.236365i
$315$		0			0
$316$	0.871032	−	4.06771i	0.0489994	−	0.228827i
$317$			3.82118i			0.214619i	0.994226	+	0.107309i	$0.0342235\pi$
$317$			3.82118i			0.214619i	−0.994226	+	0.107309i	$0.965776\pi$
$318$		0			0
$319$	−0.355931			−0.0199283
$320$	20.2482	+	14.8516i	1.13191	+	0.830230i
$321$		0			0
$322$	3.47573	−	2.81026i	0.193695	−	0.156609i
$323$			7.33239i			0.407985i
$324$		0			0
$325$			32.3074i			1.79209i
$326$	−15.9421	−	19.7172i	−0.882949	−	1.09203i
$327$		0			0
$328$	0.157316	+	0.310484i	0.00868633	+	0.0171436i
$329$	−1.08700			−0.0599282
$330$		0			0
$331$		−	26.6082i		−	1.46252i	−0.682101	−	0.731258i	$-0.738933\pi$
$331$		−	26.6082i		−	1.46252i	0.682101	−	0.731258i	$-0.261067\pi$
$332$	23.1212	+	4.95101i	1.26894	+	0.271722i
$333$		0			0
$334$	20.6955	−	16.7331i	1.13241	−	0.915592i
$335$	−38.8520			−2.12271
$336$		0			0
$337$	−11.6884			−0.636707			−0.318354	−	0.947972i	$-0.603130\pi$
$337$	−11.6884			−0.636707			−0.318354	+	0.947972i	$0.603130\pi$
$338$	34.4511	−	27.8550i	1.87389	−	1.51511i
$339$		0			0
$340$	45.0105	+	9.63824i	2.44104	+	0.522707i
$341$		−	1.34797i		−	0.0729964i
$342$		0			0
$343$	7.34551			0.396620
$344$	−13.6180	+	6.89995i	−0.734232	+	0.372021i
$345$		0			0
$346$	−5.22606	−	6.46361i	−0.280955	−	0.347486i
$347$			16.2573i			0.872739i	0.899767	+	0.436370i	$0.143736\pi$
$347$			16.2573i			0.872739i	−0.899767	+	0.436370i	$0.856264\pi$
$348$		0			0
$349$		−	22.5885i		−	1.20913i	−0.796554	−	0.604567i	$-0.793346\pi$
$349$		−	22.5885i		−	1.20913i	0.796554	−	0.604567i	$-0.206654\pi$
$350$	−2.85849	+	2.31119i	−0.152793	+	0.123539i
$351$		0			0
$352$	0.613813	+	2.32581i	0.0327163	+	0.123966i
$353$	10.2804			0.547169			0.273584	−	0.961848i	$-0.411791\pi$
$353$	10.2804			0.547169			0.273584	+	0.961848i	$0.411791\pi$
$354$		0			0
$355$			38.2272i			2.02889i
$356$	−5.76582	+	26.9264i	−0.305588	+	1.42709i
$357$		0			0
$358$	16.8270	+	20.8116i	0.889333	+	1.09993i
$359$	16.1694			0.853386			0.426693	−	0.904397i	$-0.359679\pi$
$359$	16.1694			0.853386			0.426693	+	0.904397i	$0.359679\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	9.36559	+	11.5834i	0.492245	+	0.608810i
$363$		0			0
$364$	6.97456	+	1.49348i	0.365566	+	0.0782798i
$365$			21.9527i			1.14906i
$366$		0			0
$367$	19.5371			1.01983			0.509914	−	0.860225i	$-0.329677\pi$
$367$	19.5371			1.01983			0.509914	+	0.860225i	$0.329677\pi$
$368$	−21.5318	−	9.66450i	−1.12242	−	0.503797i
$369$		0			0
$370$	−12.0640	+	9.75417i	−0.627177	+	0.507095i
$371$		−	3.12173i		−	0.162072i
$372$		0			0
$373$			12.9672i			0.671418i	0.941966	+	0.335709i	$0.108976\pi$
$373$			12.9672i			0.671418i	−0.941966	+	0.335709i	$0.891024\pi$
$374$	2.77235	+	3.42885i	0.143355	+	0.177302i
$375$		0			0
$376$	2.59418	+	5.11996i	0.133785	+	0.264042i
$377$	5.57288			0.287018
$378$		0			0
$379$		−	0.229262i		−	0.0117764i	−0.999983	−	0.00588821i	$-0.998126\pi$
$379$		−	0.229262i		−	0.0117764i	0.999983	−	0.00588821i	$-0.00187428\pi$
$380$	−1.31447	+	6.13858i	−0.0674311	+	0.314903i
$381$		0			0
$382$	1.76484	−	1.42694i	0.0902972	−	0.0730086i
$383$	18.9168			0.966601			0.483301	−	0.875455i	$-0.339438\pi$
$383$	18.9168			0.966601			0.483301	+	0.875455i	$0.339438\pi$
$384$		0			0
$385$	−0.714960			−0.0364377
$386$	14.6141	−	11.8160i	0.743836	−	0.601418i
$387$		0			0
$388$	0.335537	−	1.56696i	0.0170343	−	0.0795502i
$389$		−	9.38404i		−	0.475790i	−0.971291	−	0.237895i	$-0.923543\pi$
$389$		−	9.38404i		−	0.475790i	0.971291	−	0.237895i	$-0.0764573\pi$
$390$		0			0
$391$	−43.2636			−2.18793
$392$	−8.58183	−	16.9374i	−0.433448	−	0.855467i
$393$		0			0
$394$	3.61614	+	4.47245i	0.182178	+	0.225319i
$395$		−	6.52874i		−	0.328496i
$396$		0			0
$397$			18.3307i			0.919990i	0.887921	+	0.459995i	$0.152149\pi$
$397$			18.3307i			0.919990i	−0.887921	+	0.459995i	$0.847851\pi$
$398$	−14.1065	+	11.4056i	−0.707095	+	0.571712i
$399$		0			0
$400$	17.7081	+	7.94822i	0.885404	+	0.397411i
$401$	22.7518			1.13617			0.568085	−	0.822970i	$-0.307684\pi$
$401$	22.7518			1.13617			0.568085	+	0.822970i	$0.307684\pi$
$402$		0			0
$403$			21.1054i			1.05133i
$404$	−24.2837	−	5.19994i	−1.20816	−	0.258707i
$405$		0			0
$406$	0.398671	+	0.493077i	0.0197857	+	0.0244710i
$407$	−1.48613			−0.0736645
$408$		0			0
$409$	−19.3401			−0.956305			−0.478152	−	0.878277i	$-0.658693\pi$
$409$	−19.3401			−0.956305			−0.478152	+	0.878277i	$0.658693\pi$
$410$	0.343456	+	0.424787i	0.0169621	+	0.0209787i
$411$		0			0
$412$	−1.19295	+	5.57109i	−0.0587726	+	0.274468i
$413$			2.98165i			0.146717i
$414$		0			0
$415$	37.1098			1.82165
$416$	−9.61058	−	36.4157i	−0.471198	−	1.78543i
$417$		0			0
$418$	−0.467631	+	0.378097i	−0.0228726	+	0.0184933i
$419$		−	28.0225i		−	1.36899i	−0.729017	−	0.684495i	$-0.760023\pi$
$419$		−	28.0225i		−	1.36899i	0.729017	−	0.684495i	$-0.239977\pi$
$420$		0			0
$421$		−	15.5487i		−	0.757798i	−0.925438	−	0.378899i	$-0.876303\pi$
$421$		−	15.5487i		−	0.757798i	0.925438	−	0.378899i	$-0.123697\pi$
$422$	14.2183	+	17.5852i	0.692136	+	0.856035i
$423$		0			0
$424$	−14.7039	+	7.45019i	−0.714086	+	0.361813i
$425$	35.5806			1.72591
$426$		0			0
$427$		−	3.74749i		−	0.181354i
$428$	0.563509	+	0.120666i	0.0272382	+	0.00583260i
$429$		0			0
$430$	−18.6313	+	15.0641i	−0.898482	+	0.726456i
$431$	−15.5573			−0.749368			−0.374684	−	0.927153i	$-0.622249\pi$
$431$	−15.5573			−0.749368			−0.374684	+	0.927153i	$0.622249\pi$
$432$		0			0
$433$	4.16219			0.200022			0.100011	−	0.994986i	$-0.468112\pi$
$433$	4.16219			0.200022			0.100011	+	0.994986i	$0.468112\pi$
$434$	−1.86736	+	1.50983i	−0.0896361	+	0.0724740i
$435$		0			0
$436$	3.75239	+	0.803511i	0.179707	+	0.0384812i
$437$		−	5.90033i		−	0.282251i
$438$		0			0
$439$	24.6600			1.17696			0.588478	−	0.808513i	$-0.299727\pi$
$439$	24.6600			1.17696			0.588478	+	0.808513i	$0.299727\pi$
$440$	1.70629	+	3.36759i	0.0813442	+	0.160544i
$441$		0			0
$442$	−43.4073	−	53.6862i	−2.06467	−	2.55359i
$443$			19.7595i			0.938801i	0.882985	+	0.469401i	$0.155530\pi$
$443$			19.7595i			0.938801i	−0.882985	+	0.469401i	$0.844470\pi$
$444$		0			0
$445$			43.2172i			2.04869i
$446$	−23.2507	+	18.7991i	−1.10095	+	0.890161i
$447$		0			0
$448$	2.53447	−	3.45542i	0.119742	−	0.163253i
$449$	16.4826			0.777862			0.388931	−	0.921267i	$-0.372844\pi$
$449$	16.4826			0.777862			0.388931	+	0.921267i	$0.372844\pi$
$450$		0			0
$451$			0.0523282i			0.00246404i
$452$	5.62705	−	26.2783i	0.264674	−	1.23603i
$453$		0			0
$454$	−19.7444	−	24.4199i	−0.926652	−	1.14609i
$455$	11.1943			0.524795
$456$		0			0
$457$	7.44504			0.348264			0.174132	−	0.984722i	$-0.444288\pi$
$457$	7.44504			0.348264			0.174132	+	0.984722i	$0.444288\pi$
$458$	−11.2329	−	13.8928i	−0.524877	−	0.649170i
$459$		0			0
$460$	−36.2197	−	7.75583i	−1.68875	−	0.361618i
$461$		−	14.9337i		−	0.695532i	−0.937581	−	0.347766i	$-0.886940\pi$
$461$		−	14.9337i		−	0.695532i	0.937581	−	0.347766i	$-0.113060\pi$
$462$		0			0
$463$	−23.6042			−1.09698			−0.548491	−	0.836156i	$-0.684798\pi$
$463$	−23.6042			−1.09698			−0.548491	+	0.836156i	$0.684798\pi$
$464$	1.37103	−	3.05457i	0.0636486	−	0.141805i
$465$		0			0
$466$	3.31953	−	2.68396i	0.153774	−	0.124332i
$467$		−	0.808996i		−	0.0374359i	−0.999825	−	0.0187179i	$-0.994042\pi$
$467$		−	0.808996i		−	0.0374359i	0.999825	−	0.0187179i	$-0.00595845\pi$
$468$		0			0
$469$			6.63020i			0.306154i
$470$	5.66366	+	7.00483i	0.261245	+	0.323109i
$471$		0			0
$472$	14.0441	−	7.11587i	0.646433	−	0.327534i
$473$	−2.29514			−0.105530
$474$		0			0
$475$			4.85252i			0.222649i
$476$	1.64479	−	7.68117i	0.0753890	−	0.352066i
$477$		0			0
$478$	13.9836	−	11.3063i	0.639596	−	0.517137i
$479$	12.2547			0.559933			0.279966	−	0.960010i	$-0.409677\pi$
$479$	12.2547			0.559933			0.279966	+	0.960010i	$0.409677\pi$
$480$		0			0
$481$	23.2686			1.06095
$482$	1.16278	−	0.940147i	0.0529630	−	0.0428225i
$483$		0			0
$484$	4.53078	−	21.1587i	0.205944	−	0.961759i
$485$		−	2.51499i		−	0.114200i
$486$		0			0
$487$	23.1692			1.04990			0.524948	−	0.851134i	$-0.324085\pi$
$487$	23.1692			1.04990			0.524948	+	0.851134i	$0.324085\pi$
$488$	−17.6514	+	8.94359i	−0.799040	+	0.404857i
$489$		0			0
$490$	−18.7360	−	23.1727i	−0.846406	−	1.04684i
$491$		−	20.6669i		−	0.932684i	−0.884605	−	0.466342i	$-0.845572\pi$
$491$		−	20.6669i		−	0.932684i	0.884605	−	0.466342i	$-0.154428\pi$
$492$		0			0
$493$		−	6.13749i		−	0.276418i
$494$	7.32179	−	5.91994i	0.329423	−	0.266350i
$495$		0			0
$496$	11.5681	+	5.19231i	0.519424	+	0.233142i
$497$	6.52358			0.292623
$498$		0			0
$499$		−	5.36134i		−	0.240007i	−0.992773	−	0.120003i	$-0.961709\pi$
$499$		−	5.36134i		−	0.240007i	0.992773	−	0.120003i	$-0.0382905\pi$
$500$	−0.905339	−	0.193863i	−0.0404880	−	0.00866981i
$501$		0			0
$502$	11.9761	+	14.8121i	0.534519	+	0.661095i
$503$	25.6878			1.14536			0.572681	−	0.819778i	$-0.305903\pi$
$503$	25.6878			1.14536			0.572681	+	0.819778i	$0.305903\pi$
$504$		0			0
$505$	−38.9757			−1.73439
$506$	−2.23090	−	2.75918i	−0.0991755	−	0.122660i
$507$		0			0
$508$	−7.95635	+	37.1561i	−0.353006	+	1.64853i
$509$		−	16.2273i		−	0.719261i	−0.933095	−	0.359631i	$-0.882903\pi$
$509$		−	16.2273i		−	0.719261i	0.933095	−	0.359631i	$-0.117097\pi$
$510$		0			0
$511$	3.74629			0.165726
$512$	−22.3243	−	3.69127i	−0.986604	−	0.163133i
$513$		0			0
$514$	21.0741	−	17.0391i	0.929537	−	0.751564i
$515$			8.94168i			0.394017i
$516$		0			0
$517$			0.862904i			0.0379505i
$518$	1.66458	+	2.05875i	0.0731373	+	0.0904565i
$519$		0			0
$520$	−26.7157	−	52.7270i	−1.17156	−	2.31223i
$521$	−32.4863			−1.42325			−0.711626	−	0.702559i	$-0.752041\pi$
$521$	−32.4863			−1.42325			−0.711626	+	0.702559i	$0.752041\pi$
$522$		0			0
$523$		−	11.1406i		−	0.487143i	−0.969883	−	0.243571i	$-0.921681\pi$
$523$		−	11.1406i		−	0.487143i	0.969883	−	0.243571i	$-0.0783190\pi$
$524$	−19.8167	−	4.24341i	−0.865697	−	0.185374i
$525$		0			0
$526$	−2.81463	+	2.27573i	−0.122724	+	0.0992265i
$527$	23.2436			1.01251
$528$		0			0
$529$	11.8139			0.513649
$530$	−20.1171	+	16.2654i	−0.873830	+	0.706523i
$531$		0			0
$532$	1.04757	+	0.224319i	0.0454178	+	0.00972545i
$533$		−	0.819312i		−	0.0354884i
$534$		0			0
$535$	0.904439			0.0391023
$536$	31.2294	−	15.8233i	1.34891	−	0.683464i
$537$		0			0
$538$	4.34442	+	5.37319i	0.187301	+	0.231655i
$539$		−	2.85458i		−	0.122955i
$540$		0			0
$541$			1.33136i			0.0572394i	0.999590	+	0.0286197i	$0.00911118\pi$
$541$			1.33136i			0.0572394i	−0.999590	+	0.0286197i	$0.990889\pi$
$542$	−35.3339	+	28.5687i	−1.51772	+	1.22713i
$543$		0			0
$544$	−40.1051	+	10.5843i	−1.71949	+	0.453796i
$545$	6.02264			0.257982
$546$		0			0
$547$			21.1345i			0.903644i	0.892108	+	0.451822i	$0.149226\pi$
$547$			21.1345i			0.903644i	−0.892108	+	0.451822i	$0.850774\pi$
$548$	1.37450	−	6.41891i	0.0587158	−	0.274202i
$549$		0			0
$550$	1.83472	+	2.26919i	0.0782328	+	0.0967585i
$551$	0.837037			0.0356590
$552$		0			0
$553$	−1.11415			−0.0473784
$554$	6.63885	+	8.21095i	0.282058	+	0.348850i
$555$		0			0
$556$	−20.6020	−	4.41157i	−0.873720	−	0.187092i
$557$			6.60875i			0.280022i	0.990150	+	0.140011i	$0.0447138\pi$
$557$			6.60875i			0.280022i	−0.990150	+	0.140011i	$0.955286\pi$
$558$		0			0
$559$	35.9354			1.51991
$560$	2.75400	−	6.13572i	0.116378	−	0.259281i
$561$		0			0
$562$	20.8695	−	16.8737i	0.880325	−	0.711775i
$563$			4.42073i			0.186312i	0.995652	+	0.0931559i	$0.0296955\pi$
$563$			4.42073i			0.186312i	−0.995652	+	0.0931559i	$0.970305\pi$
$564$		0			0
$565$		−	42.1771i		−	1.77440i
$566$	−1.10542	−	1.36719i	−0.0464642	−	0.0574671i
$567$		0			0
$568$	−15.5689	−	30.7273i	−0.653256	−	1.28929i
$569$	−8.59442			−0.360297			−0.180149	−	0.983639i	$-0.557658\pi$
$569$	−8.59442			−0.360297			−0.180149	+	0.983639i	$0.557658\pi$
$570$		0			0
$571$			34.6802i			1.45132i	0.688052	+	0.725661i	$0.258466\pi$
$571$			34.6802i			1.45132i	−0.688052	+	0.725661i	$0.741534\pi$
$572$	1.18559	−	5.53669i	0.0495720	−	0.231501i
$573$		0			0
$574$	0.0724911	−	0.0586117i	0.00302572	−	0.00244640i
$575$	−28.6315			−1.19401
$576$		0			0
$577$	26.2877			1.09437			0.547185	−	0.837012i	$-0.315699\pi$
$577$	26.2877			1.09437			0.547185	+	0.837012i	$0.315699\pi$
$578$	−40.4301	+	32.6892i	−1.68167	+	1.35969i
$579$		0			0
$580$	1.10026	−	5.13823i	0.0456860	−	0.213353i
$581$		−	6.33290i		−	0.262733i
$582$		0			0
$583$	−2.47816			−0.102635
$584$	−8.94073	−	17.6457i	−0.369970	−	0.730185i
$585$		0			0
$586$	4.75719	+	5.88371i	0.196518	+	0.243054i
$587$			7.01067i			0.289361i	0.989478	+	0.144681i	$0.0462155\pi$
$587$			7.01067i			0.289361i	−0.989478	+	0.144681i	$0.953785\pi$
$588$		0			0
$589$			3.16999i			0.130617i
$590$	19.2143	−	15.5355i	0.791042	−	0.639586i
$591$		0			0
$592$	5.72450	−	12.7538i	0.235276	−	0.524178i
$593$	−34.7115			−1.42543			−0.712716	−	0.701453i	$-0.752535\pi$
$593$	−34.7115			−1.42543			−0.712716	+	0.701453i	$0.752535\pi$
$594$		0			0
$595$		−	12.3284i		−	0.505415i
$596$	−11.6019	−	2.48435i	−0.475231	−	0.101763i
$597$		0			0
$598$	34.9296	+	43.2010i	1.42838	+	1.76662i
$599$	32.4456			1.32569			0.662845	−	0.748757i	$-0.269349\pi$
$599$	32.4456			1.32569			0.662845	+	0.748757i	$0.269349\pi$
$600$		0			0
$601$	−36.2901			−1.48030			−0.740152	−	0.672440i	$-0.765246\pi$
$601$	−36.2901			−1.48030			−0.740152	+	0.672440i	$0.765246\pi$
$602$	2.57073	+	3.17949i	0.104775	+	0.129586i
$603$		0			0
$604$	1.91759	−	8.95513i	0.0780256	−	0.364379i
$605$		−	33.9600i		−	1.38067i
$606$		0			0
$607$	5.54708			0.225149			0.112575	−	0.993643i	$-0.464090\pi$
$607$	5.54708			0.225149			0.112575	+	0.993643i	$0.464090\pi$
$608$	−1.44349	−	5.46958i	−0.0585414	−	0.221821i
$609$		0			0
$610$	−24.1496	+	19.5258i	−0.977787	+	0.790577i
$611$		−	13.5107i		−	0.546583i
$612$		0			0
$613$		−	41.7239i		−	1.68521i	−0.538530	−	0.842606i	$-0.681020\pi$
$613$		−	41.7239i		−	1.68521i	0.538530	−	0.842606i	$-0.318980\pi$
$614$	9.31842	+	11.5250i	0.376061	+	0.465113i
$615$		0			0
$616$	0.574689	−	0.291183i	0.0231549	−	0.0117321i
$617$	−16.0859			−0.647593			−0.323797	−	0.946127i	$-0.604959\pi$
$617$	−16.0859			−0.647593			−0.323797	+	0.946127i	$0.604959\pi$
$618$		0			0
$619$			2.93257i			0.117870i	0.998262	+	0.0589349i	$0.0187704\pi$
$619$			2.93257i			0.117870i	−0.998262	+	0.0589349i	$0.981230\pi$
$620$	19.4593	+	4.16687i	0.781502	+	0.167345i
$621$		0			0
$622$	−30.1015	+	24.3382i	−1.20696	+	0.975872i
$623$	7.37514			0.295479
$624$		0			0
$625$	−25.7157			−1.02863
$626$	18.6088	−	15.0459i	0.743756	−	0.601354i
$627$		0			0
$628$	−7.44837	−	1.59494i	−0.297222	−	0.0636451i
$629$		−	25.6260i		−	1.02177i
$630$		0			0
$631$	−23.0095			−0.915994			−0.457997	−	0.888954i	$-0.651433\pi$
$631$	−23.0095			−0.915994			−0.457997	+	0.888954i	$0.651433\pi$
$632$	2.65897	+	5.24784i	0.105768	+	0.208748i
$633$		0			0
$634$	−3.39765	−	4.20223i	−0.134938	−	0.166892i
$635$			59.6361i			2.36658i
$636$		0			0
$637$			44.6947i			1.77087i
$638$	0.391425	−	0.316481i	0.0154967	−	0.0125296i
$639$		0			0
$640$	−35.4729	+	1.67139i	−1.40219	+	0.0660674i
$641$	0.00476234			0.000188101			9.40506e−5	−	1.00000i	$-0.499970\pi$
$641$	0.00476234			0.000188101			9.40506e−5		1.00000i	$0.499970\pi$
$642$		0			0
$643$		−	37.6587i		−	1.48511i	−0.669783	−	0.742557i	$-0.733613\pi$
$643$		−	37.6587i		−	1.48511i	0.669783	−	0.742557i	$-0.266387\pi$
$644$	−1.32356	+	6.18100i	−0.0521554	+	0.243565i
$645$		0			0
$646$	−6.51970	−	8.06359i	−0.256514	−	0.317258i
$647$	−25.3744			−0.997570			−0.498785	−	0.866726i	$-0.666220\pi$
$647$	−25.3744			−0.997570			−0.498785	+	0.866726i	$0.666220\pi$
$648$		0			0
$649$	2.36696			0.0929111
$650$	−28.7266	−	35.5291i	−1.12675	−	1.39357i
$651$		0			0
$652$	35.0636	+	7.50828i	1.37320	+	0.294047i
$653$			22.5548i			0.882637i	0.897350	+	0.441319i	$0.145489\pi$
$653$			22.5548i			0.882637i	−0.897350	+	0.441319i	$0.854511\pi$
$654$		0			0
$655$	−31.8061			−1.24277
$656$	−0.449076	−	0.201566i	−0.0175335	−	0.00786984i
$657$		0			0
$658$	1.19540	−	0.966521i	0.0466014	−	0.0376789i
$659$			18.3990i			0.716724i	0.933583	+	0.358362i	$0.116665\pi$
$659$			18.3990i			0.716724i	−0.933583	+	0.358362i	$0.883335\pi$
$660$		0			0
$661$		−	39.9383i		−	1.55342i	−0.629859	−	0.776710i	$-0.716887\pi$
$661$		−	39.9383i		−	1.55342i	0.629859	−	0.776710i	$-0.283113\pi$
$662$	23.6590	+	29.2615i	0.919534	+	1.13728i
$663$		0			0
$664$	−29.8291	+	15.1138i	−1.15759	+	0.586529i
$665$	1.68136			0.0652004
$666$		0			0
$667$			4.93880i			0.191231i
$668$	−7.88082	+	36.8034i	−0.304918	+	1.42397i
$669$		0			0
$670$	42.7263	−	34.5458i	1.65066	−	1.33462i
$671$	−2.97491			−0.114845
$672$		0			0
$673$	−4.04663			−0.155986			−0.0779931	−	0.996954i	$-0.524851\pi$
$673$	−4.04663			−0.155986			−0.0779931	+	0.996954i	$0.524851\pi$
$674$	12.8540	−	10.3929i	0.495116	−	0.400320i
$675$		0			0
$676$	−13.1189	+	61.2654i	−0.504575	+	2.35636i
$677$		−	42.8041i		−	1.64509i	−0.568697	−	0.822547i	$-0.692552\pi$
$677$		−	42.8041i		−	1.64509i	0.568697	−	0.822547i	$-0.307448\pi$
$678$		0			0
$679$	−0.429190			−0.0164708
$680$	−58.0690	+	29.4224i	−2.22684	+	1.12830i
$681$		0			0
$682$	1.19856	+	1.48239i	0.0458954	+	0.0567635i
$683$		−	6.33556i		−	0.242423i	−0.992627	−	0.121212i	$-0.961322\pi$
$683$		−	6.33556i		−	0.242423i	0.992627	−	0.121212i	$-0.0386780\pi$
$684$		0			0
$685$		−	10.3024i		−	0.393636i
$686$	−8.07801	+	6.53137i	−0.308420	+	0.249369i
$687$		0			0
$688$	8.84078	−	19.6966i	0.337052	−	0.750928i
$689$	38.8010			1.47820
$690$		0			0
$691$		−	15.3700i		−	0.584702i	−0.956311	−	0.292351i	$-0.905562\pi$
$691$		−	15.3700i		−	0.584702i	0.956311	−	0.292351i	$-0.0944375\pi$
$692$	11.4944	+	2.46134i	0.436952	+	0.0935659i
$693$		0			0
$694$	−14.4554	−	17.8785i	−0.548721	−	0.678660i
$695$	−33.0665			−1.25428
$696$		0			0
$697$	−0.902320			−0.0341778
$698$	20.0849	+	24.8410i	0.760224	+	0.940248i
$699$		0			0
$700$	1.08851	−	5.08334i	0.0411418	−	0.192132i
$701$			36.0602i			1.36197i	0.732296	+	0.680987i	$0.238449\pi$
$701$			36.0602i			1.36197i	−0.732296	+	0.680987i	$0.761551\pi$
$702$		0			0
$703$	3.49490			0.131813
$704$	−2.74305	−	2.01197i	−0.103383	−	0.0758288i
$705$		0			0
$706$	−11.3055	+	9.14094i	−0.425489	+	0.344024i
$707$			6.65131i			0.250148i
$708$		0			0
$709$		−	18.1426i		−	0.681360i	−0.940179	−	0.340680i	$-0.889343\pi$
$709$		−	18.1426i		−	0.681360i	0.940179	−	0.340680i	$-0.110657\pi$
$710$	−33.9903	−	42.0392i	−1.27563	−	1.57770i
$711$		0			0
$712$	−17.6012	−	34.7383i	−0.659632	−	1.30187i
$713$	−18.7040			−0.700470
$714$		0			0
$715$		−	8.88647i		−	0.332335i
$716$	−37.0100	−	7.92505i	−1.38313	−	0.296173i
$717$		0			0
$718$	−17.7818	+	14.3772i	−0.663610	+	0.536553i
$719$	38.2801			1.42761			0.713804	−	0.700345i	$-0.246971\pi$
$719$	38.2801			1.42761			0.713804	+	0.700345i	$0.246971\pi$
$720$		0			0
$721$	1.52592			0.0568284
$722$	1.09972	−	0.889165i	0.0409274	−	0.0330913i
$723$		0			0
$724$	−20.5991	−	4.41094i	−0.765559	−	0.163931i
$725$		−	4.06174i		−	0.150849i
$726$		0			0
$727$	23.4550			0.869897			0.434949	−	0.900455i	$-0.356767\pi$
$727$	23.4550			0.869897			0.434949	+	0.900455i	$0.356767\pi$
$728$	−8.99802	+	4.55911i	−0.333489	+	0.168972i
$729$		0			0
$730$	−19.5196	−	24.1419i	−0.722452	−	0.893530i
$731$		−	39.5761i		−	1.46378i
$732$		0			0
$733$			19.3814i			0.715870i	0.933747	+	0.357935i	$0.116519\pi$
$733$			19.3814i			0.715870i	−0.933747	+	0.357935i	$0.883481\pi$
$734$	−21.4854	+	17.3717i	−0.793040	+	0.641201i
$735$		0			0
$736$	32.2724	−	8.51709i	1.18957	−	0.313944i
$737$	5.26332			0.193877
$738$		0			0
$739$			12.1161i			0.445697i	0.974853	+	0.222848i	$0.0715355\pi$
$739$			12.1161i			0.445697i	−0.974853	+	0.222848i	$0.928464\pi$
$740$	4.59395	−	21.4537i	0.168877	−	0.788655i
$741$		0			0
$742$	2.77573	+	3.43304i	0.101900	+	0.126031i
$743$	29.1148			1.06812			0.534060	−	0.845447i	$-0.320666\pi$
$743$	29.1148			1.06812			0.534060	+	0.845447i	$0.320666\pi$
$744$		0			0
$745$	−18.6212			−0.682227
$746$	−11.5300	−	14.2603i	−0.422143	−	0.522108i
$747$		0			0
$748$	−6.09763	−	1.30570i	−0.222952	−	0.0477413i
$749$		−	0.154345i		−	0.00563965i
$750$		0			0
$751$	−2.09618			−0.0764906			−0.0382453	−	0.999268i	$-0.512177\pi$
$751$	−2.09618			−0.0764906			−0.0382453	+	0.999268i	$0.512177\pi$
$752$	−7.40536	−	3.32388i	−0.270046	−	0.121209i
$753$		0			0
$754$	−6.12861	+	4.95521i	−0.223191	+	0.180458i
$755$		−	14.3731i		−	0.523091i
$756$		0			0
$757$		−	36.7044i		−	1.33404i	−0.745038	−	0.667022i	$-0.767569\pi$
$757$		−	36.7044i		−	1.33404i	0.745038	−	0.667022i	$-0.232431\pi$
$758$	0.203852	+	0.252125i	0.00740423	+	0.00915758i
$759$		0			0
$760$	−4.01266	−	7.91951i	−0.145554	−	0.287271i
$761$	−26.8362			−0.972812			−0.486406	−	0.873733i	$-0.661692\pi$
$761$	−26.8362			−0.972812			−0.486406	+	0.873733i	$0.661692\pi$
$762$		0			0
$763$		−	1.02778i		−	0.0372082i
$764$	−0.672051	+	3.13847i	−0.0243139	+	0.113546i
$765$		0			0
$766$	−20.8032	+	16.8201i	−0.751649	+	0.607735i
$767$	−37.0599			−1.33815
$768$		0			0
$769$	15.3434			0.553299			0.276649	−	0.960971i	$-0.410776\pi$
$769$	15.3434			0.553299			0.276649	+	0.960971i	$0.410776\pi$
$770$	0.786256	−	0.635717i	0.0283347	−	0.0229097i
$771$		0			0
$772$	−5.56502	+	25.9886i	−0.200289	+	0.935350i
$773$		−	54.9160i		−	1.97519i	−0.157017	−	0.987596i	$-0.550188\pi$
$773$		−	54.9160i		−	1.97519i	0.157017	−	0.987596i	$-0.449812\pi$
$774$		0			0
$775$	15.3824			0.552553
$776$	1.02429	+	2.02156i	0.0367697	+	0.0725699i
$777$		0			0
$778$	8.34395	+	10.3198i	0.299145	+	0.369984i
$779$		−	0.123059i		−	0.00440906i
$780$		0			0
$781$		−	5.17869i		−	0.185308i
$782$	47.5778	−	38.4684i	1.70138	−	1.37563i
$783$		0			0
$784$	24.4977	+	10.9957i	0.874919	+	0.392705i
$785$	−11.9547			−0.426683
$786$		0			0
$787$		−	16.2826i		−	0.580413i	−0.956964	−	0.290206i	$-0.906276\pi$
$787$		−	16.2826i		−	0.580413i	0.956964	−	0.290206i	$-0.0937240\pi$
$788$	−7.95348	−	1.70310i	−0.283331	−	0.0606706i
$789$		0			0
$790$	5.80512	+	7.17979i	0.206537	+	0.255446i
$791$	−7.19764			−0.255918
$792$		0			0
$793$	46.5788			1.65406
$794$	−16.2990	−	20.1586i	−0.578429	−	0.715403i
$795$		0			0
$796$	5.37174	−	25.0860i	0.190396	−	0.889150i
$797$		−	20.2945i		−	0.718867i	−0.933171	−	0.359434i	$-0.882970\pi$
$797$		−	20.2945i		−	0.718867i	0.933171	−	0.359434i	$-0.117030\pi$
$798$		0			0
$799$	−14.8795			−0.526398
$800$	−26.5412	+	7.00458i	−0.938374	+	0.247649i
$801$		0			0
$802$	−25.0206	+	20.2301i	−0.883509	+	0.714349i
$803$		−	2.97396i		−	0.104949i
$804$		0			0
$805$			9.92059i			0.349655i
$806$	−18.7661	−	23.2100i	−0.661009	−	0.817538i
$807$		0			0
$808$	31.3289	−	15.8737i	1.10215	−	0.558435i
$809$	5.57944			0.196163			0.0980813	−	0.995178i	$-0.468729\pi$
$809$	5.57944			0.196163			0.0980813	+	0.995178i	$0.468729\pi$
$810$		0			0
$811$		−	28.4695i		−	0.999699i	−0.866112	−	0.499849i	$-0.833389\pi$
$811$		−	28.4695i		−	0.999699i	0.866112	−	0.499849i	$-0.166611\pi$
$812$	−0.876853	−	0.187763i	−0.0307715	−	0.00658920i
$813$		0			0
$814$	1.63432	−	1.32141i	0.0572830	−	0.0463154i
$815$	56.2776			1.97132
$816$		0			0
$817$	5.39744			0.188832
$818$	21.2687	−	17.1965i	0.743642	−	0.601262i
$819$		0			0
$820$	−0.755411	−	0.161758i	−0.0263801	−	0.00564885i
$821$			3.41291i			0.119111i	0.998225	+	0.0595556i	$0.0189684\pi$
$821$			3.41291i			0.119111i	−0.998225	+	0.0595556i	$0.981032\pi$
$822$		0			0
$823$	−12.8444			−0.447729			−0.223865	−	0.974620i	$-0.571867\pi$
$823$	−12.8444			−0.447729			−0.223865	+	0.974620i	$0.571867\pi$
$824$	−3.64170	−	7.18738i	−0.126865	−	0.250384i
$825$		0			0
$826$	−2.65118	−	3.27898i	−0.0922462	−	0.114090i
$827$		−	11.4599i		−	0.398501i	−0.979949	−	0.199251i	$-0.936149\pi$
$827$		−	11.4599i		−	0.398501i	0.979949	−	0.199251i	$-0.0638508\pi$
$828$		0			0
$829$			15.6953i			0.545119i	0.962139	+	0.272559i	$0.0878701\pi$
$829$			15.6953i			0.545119i	−0.962139	+	0.272559i	$0.912130\pi$
$830$	−40.8105	+	32.9967i	−1.41655	+	1.14533i
$831$		0			0
$832$	42.9485	+	31.5017i	1.48897	+	1.09213i
$833$	49.2229			1.70547
$834$		0			0
$835$			59.0700i			2.04420i
$836$	0.178073	−	0.831602i	0.00615880	−	0.0287616i
$837$		0			0
$838$	24.9166	+	30.8170i	0.860731	+	1.06455i
$839$	−40.4629			−1.39693			−0.698467	−	0.715642i	$-0.746134\pi$
$839$	−40.4629			−1.39693			−0.698467	+	0.715642i	$0.746134\pi$
$840$		0			0
$841$	28.2994			0.975840
$842$	13.8254	+	17.0992i	0.476454	+	0.589279i
$843$		0			0
$844$	−31.2723	−	6.69643i	−1.07644	−	0.230501i
$845$			98.3318i			3.38272i
$846$		0			0
$847$	−5.79538			−0.199131
$848$	9.54578	−	21.2673i	0.327804	−	0.730324i
$849$		0			0
$850$	−39.1287	+	31.6370i	−1.34210	+	1.08514i
$851$			20.6211i			0.706881i
$852$		0			0
$853$			1.22071i			0.0417962i	0.999782	+	0.0208981i	$0.00665255\pi$
$853$			1.22071i			0.0417962i	−0.999782	+	0.0208981i	$0.993347\pi$
$854$	3.33214	+	4.12119i	0.114023	+	0.141024i
$855$		0			0
$856$	−0.726994	+	0.368353i	−0.0248481	+	0.0125901i
$857$	49.3646			1.68626			0.843131	−	0.537709i	$-0.180710\pi$
$857$	49.3646			1.68626			0.843131	+	0.537709i	$0.180710\pi$
$858$		0			0
$859$		−	41.6828i		−	1.42220i	−0.703092	−	0.711099i	$-0.748198\pi$
$859$		−	41.6828i		−	1.42220i	0.703092	−	0.711099i	$-0.251802\pi$
$860$	7.09479	−	33.1326i	0.241930	−	1.12981i
$861$		0			0
$862$	17.1087	−	13.8330i	0.582723	−	0.471153i
$863$	22.0429			0.750348			0.375174	−	0.926954i	$-0.377583\pi$
$863$	22.0429			0.750348			0.375174	+	0.926954i	$0.377583\pi$
$864$		0			0
$865$	18.4487			0.627275
$866$	−4.57725	+	3.70087i	−0.155541	+	0.125761i
$867$		0			0
$868$	0.711088	−	3.32078i	0.0241359	−	0.112715i
$869$			0.884457i			0.0300031i
$870$		0			0
$871$	−82.4089			−2.79232
$872$	−4.84104	+	2.45286i	−0.163938	+	0.0830642i
$873$		0			0
$874$	5.24637	+	6.48872i	0.177461	+	0.219484i
$875$			0.247973i			0.00838300i
$876$		0			0
$877$		−	33.7237i		−	1.13877i	−0.822071	−	0.569385i	$-0.807181\pi$
$877$		−	33.7237i		−	1.13877i	0.822071	−	0.569385i	$-0.192819\pi$
$878$	−27.1191	+	21.9268i	−0.915225	+	0.739993i
$879$		0			0
$880$	−4.87079	−	2.18624i	−0.164194	−	0.0736981i
$881$	−7.24781			−0.244185			−0.122092	−	0.992519i	$-0.538960\pi$
$881$	−7.24781			−0.244185			−0.122092	+	0.992519i	$0.538960\pi$
$882$		0			0
$883$		−	24.1525i		−	0.812797i	−0.913696	−	0.406398i	$-0.866785\pi$
$883$		−	24.1525i		−	0.812797i	0.913696	−	0.406398i	$-0.133215\pi$
$884$	95.4718	+	20.4437i	3.21106	+	0.687595i
$885$		0			0
$886$	−17.5694	−	21.7299i	−0.590256	−	0.730031i
$887$	−20.3957			−0.684821			−0.342411	−	0.939550i	$-0.611243\pi$
$887$	−20.3957			−0.684821			−0.342411	+	0.939550i	$0.611243\pi$
$888$		0			0
$889$	10.1771			0.341328
$890$	−38.4272	−	47.5269i	−1.28808	−	1.59310i
$891$		0			0
$892$	8.85385	−	41.3474i	0.296449	−	1.38441i
$893$		−	2.02928i		−	0.0679072i
$894$		0			0
$895$	−59.4015			−1.98557
$896$	0.285227	+	6.05356i	0.00952877	+	0.202235i
$897$		0			0
$898$	−18.1263	+	14.6558i	−0.604882	+	0.489069i
$899$		−	2.65340i		−	0.0884959i
$900$		0			0
$901$		−	42.7321i		−	1.42361i
$902$	−0.0465284	−	0.0575464i	−0.00154923	−	0.00191609i
$903$		0			0
$904$	17.1776	+	33.9022i	0.571317	+	1.12757i
$905$	−33.0618			−1.09901
$906$		0			0
$907$			6.56562i			0.218008i	0.994041	+	0.109004i	$0.0347661\pi$
$907$			6.56562i			0.218008i	−0.994041	+	0.109004i	$0.965234\pi$
$908$	43.4267	+	9.29909i	1.44117	+	0.308601i
$909$		0			0
$910$	−12.3106	+	9.95354i	−0.408091	+	0.329957i
$911$	−6.98339			−0.231370			−0.115685	−	0.993286i	$-0.536906\pi$
$911$	−6.98339			−0.231370			−0.115685	+	0.993286i	$0.536906\pi$
$912$		0			0
$913$	−5.02732			−0.166380
$914$	−8.18747	+	6.61987i	−0.270818	+	0.218966i
$915$		0			0
$916$	24.7060	+	5.29038i	0.816310	+	0.174799i
$917$			5.42780i			0.179242i
$918$		0			0
$919$	12.4237			0.409819			0.204910	−	0.978781i	$-0.434310\pi$
$919$	12.4237			0.409819			0.204910	+	0.978781i	$0.434310\pi$
$920$	46.7278	−	23.6760i	1.54057	−	0.780575i
$921$		0			0
$922$	13.2785	+	16.4229i	0.437305	+	0.540860i
$923$			81.0837i			2.66890i
$924$		0			0
$925$		−	16.9591i		−	0.557610i
$926$	25.9581	−	20.9881i	0.853035	−	0.689710i
$927$		0			0
$928$	1.20826	+	4.57824i	0.0396630	+	0.150288i
$929$	23.0649			0.756735			0.378367	−	0.925655i	$-0.376486\pi$
$929$	23.0649			0.756735			0.378367	+	0.925655i	$0.376486\pi$
$930$		0			0
$931$			6.71307i			0.220012i
$932$	−1.26407	+	5.90322i	−0.0414061	+	0.193366i
$933$		0			0
$934$	0.719331	+	0.889670i	0.0235372	+	0.0291109i
$935$	−9.78679			−0.320062
$936$		0			0
$937$	−20.2747			−0.662347			−0.331173	−	0.943570i	$-0.607445\pi$
$937$	−20.2747			−0.662347			−0.331173	+	0.943570i	$0.607445\pi$
$938$	−5.89534	−	7.29137i	−0.192490	−	0.238072i
$939$		0			0
$940$	−12.4569	−	2.66743i	−0.406299	−	0.0870021i
$941$		−	33.8390i		−	1.10312i	−0.834136	−	0.551559i	$-0.814033\pi$
$941$		−	33.8390i		−	1.10312i	0.834136	−	0.551559i	$-0.185967\pi$
$942$		0			0
$943$	0.726091			0.0236448
$944$	−9.11743	+	20.3130i	−0.296747	+	0.661132i
$945$		0			0
$946$	2.52401	−	2.04075i	0.0820626	−	0.0663506i
$947$		−	55.4208i		−	1.80093i	−0.434926	−	0.900466i	$-0.643225\pi$
$947$		−	55.4208i		−	1.80093i	0.434926	−	0.900466i	$-0.356775\pi$
$948$		0			0
$949$			46.5639i			1.51153i
$950$	−4.31469	−	5.33641i	−0.139987	−	0.173136i
$951$		0			0
$952$	5.02101	+	9.90964i	0.162732	+	0.321173i
$953$	19.8530			0.643102			0.321551	−	0.946892i	$-0.395796\pi$
$953$	19.8530			0.643102			0.321551	+	0.946892i	$0.395796\pi$
$954$		0			0
$955$			5.03729i			0.163003i
$956$	−5.32495	+	24.8675i	−0.172221	+	0.804272i
$957$		0			0
$958$	−13.4768	+	10.8965i	−0.435415	+	0.352049i
$959$	−1.75814			−0.0567734
$960$		0			0
$961$	−20.9512			−0.675844
$962$	−25.5889	+	20.6896i	−0.825020	+	0.667059i
$963$		0			0
$964$	−0.442784	+	2.06780i	−0.0142611	+	0.0665993i
$965$			41.7121i			1.34276i
$966$		0			0
$967$	−5.95336			−0.191447			−0.0957236	−	0.995408i	$-0.530516\pi$
$967$	−5.95336			−0.191447			−0.0957236	+	0.995408i	$0.530516\pi$
$968$	13.8310	+	27.2973i	0.444545	+	0.877368i
$969$		0			0
$970$	2.23624	+	2.76579i	0.0718013	+	0.0888041i
$971$			5.33267i			0.171134i	0.996332	+	0.0855668i	$0.0272701\pi$
$971$			5.33267i			0.171134i	−0.996332	+	0.0855668i	$0.972730\pi$
$972$		0			0
$973$			5.64290i			0.180903i
$974$	−25.4796	+	20.6012i	−0.816420	+	0.660106i
$975$		0			0
$976$	11.4593	−	25.5304i	0.366802	−	0.817209i
$977$	12.6063			0.403312			0.201656	−	0.979456i	$-0.435368\pi$
$977$	12.6063			0.403312			0.201656	+	0.979456i	$0.435368\pi$
$978$		0			0
$979$		−	5.85469i		−	0.187117i
$980$	41.2088	+	8.82416i	1.31637	+	0.281877i
$981$		0			0
$982$	18.3763	+	22.7278i	0.586410	+	0.725274i
$983$	19.8397			0.632788			0.316394	−	0.948628i	$-0.397528\pi$
$983$	19.8397			0.632788			0.316394	+	0.948628i	$0.397528\pi$
$984$		0			0
$985$	−12.7655			−0.406741
$986$	5.45724	+	6.74952i	0.173794	+	0.214949i
$987$		0			0
$988$	−2.78813	+	13.0206i	−0.0887023	+	0.414239i
$989$			31.8467i			1.01267i
$990$		0			0
$991$	−53.9425			−1.71354			−0.856770	−	0.515699i	$-0.827532\pi$
$991$	−53.9425			−1.71354			−0.856770	+	0.515699i	$0.827532\pi$
$992$	−17.3385	+	4.57586i	−0.550499	+	0.145284i
$993$		0			0
$994$	−7.17412	+	5.80054i	−0.227549	+	0.183982i
$995$		−	40.2634i		−	1.27644i
$996$		0			0
$997$			20.6213i			0.653084i	0.945183	+	0.326542i	$0.105884\pi$
$997$			20.6213i			0.653084i	−0.945183	+	0.326542i	$0.894116\pi$
$998$	4.76712	+	5.89598i	0.150900	+	0.186634i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.g.b.685.4		16
3.2	odd	2		152.2.c.b.77.13	✓	16
4.3	odd	2		5472.2.g.b.2737.3		16
8.3	odd	2		5472.2.g.b.2737.14		16
8.5	even	2	inner	1368.2.g.b.685.3		16
12.11	even	2		608.2.c.b.305.3		16
24.5	odd	2		152.2.c.b.77.14	yes	16
24.11	even	2		608.2.c.b.305.14		16
48.5	odd	4		4864.2.a.bo.1.7		8
48.11	even	4		4864.2.a.bn.1.2		8
48.29	odd	4		4864.2.a.bq.1.2		8
48.35	even	4		4864.2.a.bp.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.c.b.77.13	✓	16	3.2	odd	2
152.2.c.b.77.14	yes	16	24.5	odd	2
608.2.c.b.305.3		16	12.11	even	2
608.2.c.b.305.14		16	24.11	even	2
1368.2.g.b.685.3		16	8.5	even	2	inner
1368.2.g.b.685.4		16	1.1	even	1	trivial
4864.2.a.bn.1.2		8	48.11	even	4
4864.2.a.bo.1.7		8	48.5	odd	4
4864.2.a.bp.1.7		8	48.35	even	4
4864.2.a.bq.1.2		8	48.29	odd	4
5472.2.g.b.2737.3		16	4.3	odd	2
5472.2.g.b.2737.14		16	8.3	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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09972 + 0.889165i) q^{2} +(0.418773 - 1.95567i) q^{4} -3.13887i q^{5} -0.535658 q^{7} +(1.27838 + 2.52304i) q^{8} +O(q^{10})\)	\(q+(-1.09972 + 0.889165i) q^{2} +(0.418773 - 1.95567i) q^{4} -3.13887i q^{5} -0.535658 q^{7} +(1.27838 + 2.52304i) q^{8} +(2.79097 + 3.45188i) q^{10} +0.425227i q^{11} -6.65786i q^{13} +(0.589074 - 0.476288i) q^{14} +(-3.64926 - 1.63796i) q^{16} -7.33239 q^{17} -1.00000i q^{19} +(-6.13858 - 1.31447i) q^{20} +(-0.378097 - 0.467631i) q^{22} +5.90033 q^{23} -4.85252 q^{25} +(5.91994 + 7.32179i) q^{26} +(-0.224319 + 1.04757i) q^{28} +0.837037i q^{29} -3.16999 q^{31} +(5.46958 - 1.44349i) q^{32} +(8.06359 - 6.51970i) q^{34} +1.68136i q^{35} +3.49490i q^{37} +(0.889165 + 1.09972i) q^{38} +(7.91951 - 4.01266i) q^{40} +0.123059 q^{41} +5.39744i q^{43} +(0.831602 + 0.178073i) q^{44} +(-6.48872 + 5.24637i) q^{46} +2.02928 q^{47} -6.71307 q^{49} +(5.33641 - 4.31469i) q^{50} +(-13.0206 - 2.78813i) q^{52} +5.82785i q^{53} +1.33473 q^{55} +(-0.684772 - 1.35149i) q^{56} +(-0.744264 - 0.920508i) q^{58} -5.56633i q^{59} +6.99606i q^{61} +(3.48610 - 2.81864i) q^{62} +(-4.73151 + 6.45080i) q^{64} -20.8982 q^{65} -12.3777i q^{67} +(-3.07061 + 14.3397i) q^{68} +(-1.49501 - 1.84903i) q^{70} -12.1786 q^{71} -6.99382 q^{73} +(-3.10754 - 3.84341i) q^{74} +(-1.95567 - 0.418773i) q^{76} -0.227776i q^{77} +2.07996 q^{79} +(-5.14134 + 11.4546i) q^{80} +(-0.135331 + 0.109420i) q^{82} +11.8227i q^{83} +23.0154i q^{85} +(-4.79921 - 5.93567i) q^{86} +(-1.07287 + 0.543600i) q^{88} -13.7684 q^{89} +3.56633i q^{91} +(2.47090 - 11.5391i) q^{92} +(-2.23164 + 1.80436i) q^{94} -3.13887 q^{95} +0.801240 q^{97} +(7.38251 - 5.96902i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 2 * q^4 - 8 * q^7 + 12 * q^8	\( 16 q + 2 q^{4} - 8 q^{7} + 12 q^{8} - 8 q^{10} - 4 q^{14} + 2 q^{16} + 8 q^{17} - 8 q^{20} + 20 q^{22} - 24 q^{25} + 10 q^{26} - 14 q^{28} + 16 q^{31} + 20 q^{32} - 2 q^{38} + 28 q^{40} - 16 q^{41} + 28 q^{44} - 48 q^{46} - 24 q^{47} + 24 q^{49} - 12 q^{50} + 8 q^{52} + 16 q^{55} + 48 q^{56} + 38 q^{58} + 16 q^{62} + 14 q^{64} - 16 q^{65} + 26 q^{68} - 32 q^{70} - 48 q^{71} + 20 q^{74} - 4 q^{76} - 48 q^{79} - 4 q^{80} - 12 q^{82} - 48 q^{86} + 40 q^{88} + 16 q^{89} - 62 q^{92} - 36 q^{94} - 16 q^{95} + 32 q^{97} + 48 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 - 8 * q^7 + 12 * q^8 - 8 * q^10 - 4 * q^14 + 2 * q^16 + 8 * q^17 - 8 * q^20 + 20 * q^22 - 24 * q^25 + 10 * q^26 - 14 * q^28 + 16 * q^31 + 20 * q^32 - 2 * q^38 + 28 * q^40 - 16 * q^41 + 28 * q^44 - 48 * q^46 - 24 * q^47 + 24 * q^49 - 12 * q^50 + 8 * q^52 + 16 * q^55 + 48 * q^56 + 38 * q^58 + 16 * q^62 + 14 * q^64 - 16 * q^65 + 26 * q^68 - 32 * q^70 - 48 * q^71 + 20 * q^74 - 4 * q^76 - 48 * q^79 - 4 * q^80 - 12 * q^82 - 48 * q^86 + 40 * q^88 + 16 * q^89 - 62 * q^92 - 36 * q^94 - 16 * q^95 + 32 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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