LMFDB - Embedded newform 1368.2.g.b.685.1

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			685.1
Root			$-0.466170 - 1.33517i$ of defining polynomial
Character	$\chi$	$=$	1368.685
Dual form			1368.2.g.b.685.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33517 - 0.466170i) q^{2} +(1.56537 + 1.24484i) q^{4} -2.10882i q^{5} -2.73436 q^{7} +(-1.50973 - 2.39180i) q^{8} +O(q^{10})$	\(q+(-1.33517 - 0.466170i) q^{2} +(1.56537 + 1.24484i) q^{4} -2.10882i q^{5} -2.73436 q^{7} +(-1.50973 - 2.39180i) q^{8} +(-0.983067 + 2.81563i) q^{10} +4.66474i q^{11} -4.47791i q^{13} +(3.65084 + 1.27468i) q^{14} +(0.900771 + 3.89726i) q^{16} +6.85237 q^{17} +1.00000i q^{19} +(2.62513 - 3.30108i) q^{20} +(2.17456 - 6.22823i) q^{22} +1.20416 q^{23} +0.552894 q^{25} +(-2.08747 + 5.97878i) q^{26} +(-4.28028 - 3.40382i) q^{28} -9.57484i q^{29} -5.35842 q^{31} +(0.614101 - 5.62342i) q^{32} +(-9.14909 - 3.19437i) q^{34} +5.76625i q^{35} -1.09693i q^{37} +(0.466170 - 1.33517i) q^{38} +(-5.04386 + 3.18375i) q^{40} -7.33797 q^{41} -7.64408i q^{43} +(-5.80683 + 7.30205i) q^{44} +(-1.60777 - 0.561345i) q^{46} -7.56486 q^{47} +0.476702 q^{49} +(-0.738208 - 0.257743i) q^{50} +(5.57426 - 7.00959i) q^{52} +3.11949i q^{53} +9.83708 q^{55} +(4.12815 + 6.54003i) q^{56} +(-4.46351 + 12.7841i) q^{58} -10.2442i q^{59} -0.722061i q^{61} +(7.15441 + 2.49793i) q^{62} +(-3.44140 + 7.22196i) q^{64} -9.44309 q^{65} +6.13698i q^{67} +(10.7265 + 8.53007i) q^{68} +(2.68806 - 7.69894i) q^{70} -4.62247 q^{71} -6.19270 q^{73} +(-0.511358 + 1.46460i) q^{74} +(-1.24484 + 1.56537i) q^{76} -12.7551i q^{77} -3.26723 q^{79} +(8.21860 - 1.89956i) q^{80} +(9.79746 + 3.42075i) q^{82} -8.97934i q^{83} -14.4504i q^{85} +(-3.56344 + 10.2062i) q^{86} +(11.1571 - 7.04252i) q^{88} -0.620707 q^{89} +12.2442i q^{91} +(1.88496 + 1.49899i) q^{92} +(10.1004 + 3.52651i) q^{94} +2.10882 q^{95} -1.67284 q^{97} +(-0.636479 - 0.222224i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.33517	−	0.466170i	−0.944109	−	0.329632i
$2$	−1.33517	−	0.466170i	−0.944109	−	0.329632i
$3$		0			0
$3$		0			0
$4$	1.56537	+	1.24484i	0.782685	+	0.622418i
$5$		−	2.10882i		−	0.943091i	−0.881842	−	0.471546i	$-0.843696\pi$
$5$		−	2.10882i		−	0.943091i	0.881842	−	0.471546i	$-0.156304\pi$
$6$		0			0
$7$	−2.73436			−1.03349			−0.516745	−	0.856140i	$-0.672856\pi$
$7$	−2.73436			−1.03349			−0.516745	+	0.856140i	$0.672856\pi$
$8$	−1.50973	−	2.39180i	−0.533772	−	0.845629i
$9$		0			0
$10$	−0.983067	+	2.81563i	−0.310873	+	0.890381i
$11$			4.66474i			1.40647i	0.710957	+	0.703236i	$0.248262\pi$
$11$			4.66474i			1.40647i	−0.710957	+	0.703236i	$0.751738\pi$
$12$		0			0
$13$		−	4.47791i		−	1.24195i	−0.783831	−	0.620974i	$-0.786737\pi$
$13$		−	4.47791i		−	1.24195i	0.783831	−	0.620974i	$-0.213263\pi$
$14$	3.65084	+	1.27468i	0.975727	+	0.340671i
$15$		0			0
$16$	0.900771	+	3.89726i	0.225193	+	0.974314i
$17$	6.85237			1.66194			0.830972	−	0.556314i	$-0.187785\pi$
$17$	6.85237			1.66194			0.830972	+	0.556314i	$0.187785\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	2.62513	−	3.30108i	0.586997	−	0.738144i
$21$		0			0
$22$	2.17456	−	6.22823i	0.463618	−	1.32786i
$23$	1.20416			0.251085			0.125543	−	0.992088i	$-0.459933\pi$
$23$	1.20416			0.251085			0.125543	+	0.992088i	$0.459933\pi$
$24$		0			0
$25$	0.552894			0.110579
$26$	−2.08747	+	5.97878i	−0.409386	+	1.17254i
$27$		0			0
$28$	−4.28028	−	3.40382i	−0.808897	−	0.643262i
$29$		−	9.57484i		−	1.77800i	−0.457904	−	0.889002i	$-0.651400\pi$
$29$		−	9.57484i		−	1.77800i	0.457904	−	0.889002i	$-0.348600\pi$
$30$		0			0
$31$	−5.35842			−0.962400			−0.481200	−	0.876611i	$-0.659799\pi$
$31$	−5.35842			−0.962400			−0.481200	+	0.876611i	$0.659799\pi$
$32$	0.614101	−	5.62342i	0.108559	−	0.994090i
$33$		0			0
$34$	−9.14909	−	3.19437i	−1.56906	−	0.547830i
$35$			5.76625i			0.974675i
$36$		0			0
$37$		−	1.09693i		−	0.180335i	−0.995927	−	0.0901674i	$-0.971260\pi$
$37$		−	1.09693i		−	0.180335i	0.995927	−	0.0901674i	$-0.0287402\pi$
$38$	0.466170	−	1.33517i	0.0756228	−	0.216594i
$39$		0			0
$40$	−5.04386	+	3.18375i	−0.797505	+	0.503396i
$41$	−7.33797			−1.14600			−0.573000	−	0.819556i	$-0.694220\pi$
$41$	−7.33797			−1.14600			−0.573000	+	0.819556i	$0.694220\pi$
$42$		0			0
$43$		−	7.64408i		−	1.16571i	−0.812576	−	0.582856i	$-0.801935\pi$
$43$		−	7.64408i		−	1.16571i	0.812576	−	0.582856i	$-0.198065\pi$
$44$	−5.80683	+	7.30205i	−0.875413	+	1.10082i
$45$		0			0
$46$	−1.60777	−	0.561345i	−0.237052	−	0.0827658i
$47$	−7.56486			−1.10345			−0.551724	−	0.834027i	$-0.686030\pi$
$47$	−7.56486			−1.10345			−0.551724	+	0.834027i	$0.686030\pi$
$48$		0			0
$49$	0.476702			0.0681003
$50$	−0.738208	−	0.257743i	−0.104398	−	0.0364503i
$51$		0			0
$52$	5.57426	−	7.00959i	0.773011	−	0.972055i
$53$			3.11949i			0.428495i	0.976779	+	0.214248i	$0.0687300\pi$
$53$			3.11949i			0.428495i	−0.976779	+	0.214248i	$0.931270\pi$
$54$		0			0
$55$	9.83708			1.32643
$56$	4.12815	+	6.54003i	0.551648	+	0.873948i
$57$		0			0
$58$	−4.46351	+	12.7841i	−0.586087	+	1.67863i
$59$		−	10.2442i		−	1.33368i	−0.745201	−	0.666840i	$-0.767646\pi$
$59$		−	10.2442i		−	1.33368i	0.745201	−	0.666840i	$-0.232354\pi$
$60$		0			0
$61$		−	0.722061i		−	0.0924504i	−0.998931	−	0.0462252i	$-0.985281\pi$
$61$		−	0.722061i		−	0.0924504i	0.998931	−	0.0462252i	$-0.0147192\pi$
$62$	7.15441	+	2.49793i	0.908611	+	0.317238i
$63$		0			0
$64$	−3.44140	+	7.22196i	−0.430175	+	0.902745i
$65$	−9.44309			−1.17127
$66$		0			0
$67$			6.13698i			0.749752i	0.927075	+	0.374876i	$0.122315\pi$
$67$			6.13698i			0.749752i	−0.927075	+	0.374876i	$0.877685\pi$
$68$	10.7265	+	8.53007i	1.30078	+	1.03442i
$69$		0			0
$70$	2.68806	−	7.69894i	0.321284	−	0.920200i
$71$	−4.62247			−0.548587			−0.274293	−	0.961646i	$-0.588444\pi$
$71$	−4.62247			−0.548587			−0.274293	+	0.961646i	$0.588444\pi$
$72$		0			0
$73$	−6.19270			−0.724801			−0.362400	−	0.932022i	$-0.618043\pi$
$73$	−6.19270			−0.724801			−0.362400	+	0.932022i	$0.618043\pi$
$74$	−0.511358	+	1.46460i	−0.0594441	+	0.170256i
$75$		0			0
$76$	−1.24484	+	1.56537i	−0.142792	+	0.179560i
$77$		−	12.7551i		−	1.45357i
$78$		0			0
$79$	−3.26723			−0.367592			−0.183796	−	0.982964i	$-0.558839\pi$
$79$	−3.26723			−0.367592			−0.183796	+	0.982964i	$0.558839\pi$
$80$	8.21860	−	1.89956i	0.918867	−	0.212377i
$81$		0			0
$82$	9.79746	+	3.42075i	1.08195	+	0.377758i
$83$		−	8.97934i		−	0.985611i	−0.870140	−	0.492805i	$-0.835971\pi$
$83$		−	8.97934i		−	0.985611i	0.870140	−	0.492805i	$-0.164029\pi$
$84$		0			0
$85$		−	14.4504i		−	1.56736i
$86$	−3.56344	+	10.2062i	−0.384256	+	1.10056i
$87$		0			0
$88$	11.1571	−	7.04252i	1.18935	−	0.750735i
$89$	−0.620707			−0.0657948			−0.0328974	−	0.999459i	$-0.510473\pi$
$89$	−0.620707			−0.0657948			−0.0328974	+	0.999459i	$0.510473\pi$
$90$		0			0
$91$			12.2442i			1.28354i
$92$	1.88496	+	1.49899i	0.196521	+	0.156280i
$93$		0			0
$94$	10.1004	+	3.52651i	1.04178	+	0.363732i
$95$	2.10882			0.216360
$96$		0			0
$97$	−1.67284			−0.169851			−0.0849257	−	0.996387i	$-0.527065\pi$
$97$	−1.67284			−0.169851			−0.0849257	+	0.996387i	$0.527065\pi$
$98$	−0.636479	−	0.222224i	−0.0642941	−	0.0224480i
$99$		0			0
$100$	0.865484	+	0.688261i	0.0865484	+	0.0688261i
$101$			7.30571i			0.726946i	0.931605	+	0.363473i	$0.118409\pi$
$101$			7.30571i			0.726946i	−0.931605	+	0.363473i	$0.881591\pi$
$102$		0			0
$103$	−8.77332			−0.864461			−0.432231	−	0.901763i	$-0.642273\pi$
$103$	−8.77332			−0.864461			−0.432231	+	0.901763i	$0.642273\pi$
$104$	−10.7103	+	6.76045i	−1.05023	+	0.662917i
$105$		0			0
$106$	1.45421	−	4.16506i	0.141246	−	0.404546i
$107$		−	9.91355i		−	0.958379i	−0.877711	−	0.479190i	$-0.840931\pi$
$107$		−	9.91355i		−	0.958379i	0.877711	−	0.479190i	$-0.159069\pi$
$108$		0			0
$109$		−	2.84589i		−	0.272587i	−0.990669	−	0.136293i	$-0.956481\pi$
$109$		−	2.84589i		−	0.272587i	0.990669	−	0.136293i	$-0.0435189\pi$
$110$	−13.1342	−	4.58575i	−1.25230	−	0.437234i
$111$		0			0
$112$	−2.46303	−	10.6565i	−0.232734	−	1.00694i
$113$	1.58487			0.149092			0.0745462	−	0.997218i	$-0.476249\pi$
$113$	1.58487			0.149092			0.0745462	+	0.997218i	$0.476249\pi$
$114$		0			0
$115$		−	2.53936i		−	0.236797i
$116$	11.9191	−	14.9882i	1.10666	−	1.39162i
$117$		0			0
$118$	−4.77554	+	13.6778i	−0.439624	+	1.25914i
$119$	−18.7368			−1.71760
$120$		0			0
$121$	−10.7598			−0.978163
$122$	−0.336603	+	0.964075i	−0.0304746	+	0.0872833i
$123$		0			0
$124$	−8.38791	−	6.67034i	−0.753256	−	0.599015i
$125$		−	11.7100i		−	1.04738i
$126$		0			0
$127$	14.2933			1.26833			0.634163	−	0.773199i	$-0.281345\pi$
$127$	14.2933			1.26833			0.634163	+	0.773199i	$0.281345\pi$
$128$	7.96153	−	8.03829i	0.703706	−	0.710491i
$129$		0			0
$130$	12.6081	+	4.40209i	1.10581	+	0.386088i
$131$		−	0.609006i		−	0.0532091i	−0.999646	−	0.0266046i	$-0.991531\pi$
$131$		−	0.609006i		−	0.0532091i	0.999646	−	0.0266046i	$-0.00846949\pi$
$132$		0			0
$133$		−	2.73436i		−	0.237099i
$134$	2.86088	−	8.19393i	0.247142	−	0.707848i
$135$		0			0
$136$	−10.3453	−	16.3895i	−0.887099	−	1.40539i
$137$	−18.1589			−1.55142			−0.775710	−	0.631089i	$-0.782608\pi$
$137$	−18.1589			−1.55142			−0.775710	+	0.631089i	$0.782608\pi$
$138$		0			0
$139$		−	1.93421i		−	0.164058i	−0.996630	−	0.0820289i	$-0.973860\pi$
$139$		−	1.93421i		−	0.164058i	0.996630	−	0.0820289i	$-0.0261400\pi$
$140$	−7.17804	+	9.02633i	−0.606655	+	0.762864i
$141$		0			0
$142$	6.17180	+	2.15486i	0.517926	+	0.180832i
$143$	20.8883			1.74677
$144$		0			0
$145$	−20.1916			−1.67682
$146$	8.26832	+	2.88685i	0.684291	+	0.238918i
$147$		0			0
$148$	1.36550	−	1.71711i	0.112244	−	0.141145i
$149$			15.5775i			1.27616i	0.769970	+	0.638080i	$0.220271\pi$
$149$			15.5775i			1.27616i	−0.769970	+	0.638080i	$0.779729\pi$
$150$		0			0
$151$	−19.9746			−1.62551			−0.812756	−	0.582605i	$-0.802034\pi$
$151$	−19.9746			−1.62551			−0.812756	+	0.582605i	$0.802034\pi$
$152$	2.39180	−	1.50973i	0.194000	−	0.122456i
$153$		0			0
$154$	−5.94603	+	17.0302i	−0.479145	+	1.37233i
$155$			11.2999i			0.907631i
$156$		0			0
$157$		−	20.8872i		−	1.66698i	−0.552536	−	0.833489i	$-0.686340\pi$
$157$		−	20.8872i		−	1.66698i	0.552536	−	0.833489i	$-0.313660\pi$
$158$	4.36232	+	1.52309i	0.347047	+	0.121170i
$159$		0			0
$160$	−11.8588	−	1.29503i	−0.937518	−	0.102381i
$161$	−3.29261			−0.259494
$162$		0			0
$163$		−	2.54835i		−	0.199602i	−0.995007	−	0.0998010i	$-0.968179\pi$
$163$		−	2.54835i		−	0.199602i	0.995007	−	0.0998010i	$-0.0318206\pi$
$164$	−11.4867	−	9.13457i	−0.896957	−	0.713290i
$165$		0			0
$166$	−4.18590	+	11.9890i	−0.324889	+	0.930524i
$167$	18.6644			1.44429			0.722146	−	0.691740i	$-0.243156\pi$
$167$	18.6644			1.44429			0.722146	+	0.691740i	$0.243156\pi$
$168$		0			0
$169$	−7.05167			−0.542436
$170$	−6.73634	+	19.2938i	−0.516654	+	1.47976i
$171$		0			0
$172$	9.51562	−	11.9658i	0.725559	−	0.912385i
$173$			8.42370i			0.640442i	0.947343	+	0.320221i	$0.103757\pi$
$173$			8.42370i			0.640442i	−0.947343	+	0.320221i	$0.896243\pi$
$174$		0			0
$175$	−1.51181			−0.114282
$176$	−18.1797	+	4.20186i	−1.37035	+	0.316727i
$177$		0			0
$178$	0.828751	+	0.289355i	0.0621175	+	0.0216881i
$179$		−	16.6809i		−	1.24679i	−0.781908	−	0.623394i	$-0.785753\pi$
$179$		−	16.6809i		−	1.24679i	0.781908	−	0.623394i	$-0.214247\pi$
$180$		0			0
$181$		−	4.65888i		−	0.346292i	−0.984896	−	0.173146i	$-0.944607\pi$
$181$		−	4.65888i		−	0.346292i	0.984896	−	0.173146i	$-0.0553932\pi$
$182$	5.70788	−	16.3481i	0.423096	−	1.21180i
$183$		0			0
$184$	−1.81797	−	2.88012i	−0.134022	−	0.212325i
$185$	−2.31323			−0.170072
$186$		0			0
$187$			31.9645i			2.33748i
$188$	−11.8418	−	9.41700i	−0.863653	−	0.686805i
$189$		0			0
$190$	−2.81563	−	0.983067i	−0.204268	−	0.0713192i
$191$	−20.0609			−1.45155			−0.725777	−	0.687930i	$-0.758520\pi$
$191$	−20.0609			−1.45155			−0.725777	+	0.687930i	$0.758520\pi$
$192$		0			0
$193$	1.85117			0.133250			0.0666251	−	0.997778i	$-0.478777\pi$
$193$	1.85117			0.133250			0.0666251	+	0.997778i	$0.478777\pi$
$194$	2.23353	+	0.779829i	0.160358	+	0.0559885i
$195$		0			0
$196$	0.746215	+	0.593416i	0.0533011	+	0.0423868i
$197$			0.224883i			0.0160222i	0.999968	+	0.00801112i	$0.00255005\pi$
$197$			0.224883i			0.0160222i	−0.999968	+	0.00801112i	$0.997450\pi$
$198$		0			0
$199$	−1.77685			−0.125957			−0.0629787	−	0.998015i	$-0.520060\pi$
$199$	−1.77685			−0.125957			−0.0629787	+	0.998015i	$0.520060\pi$
$200$	−0.834723	−	1.32241i	−0.0590238	−	0.0935085i
$201$		0			0
$202$	3.40571	−	9.75439i	0.239625	−	0.686316i
$203$			26.1810i			1.83755i
$204$		0			0
$205$			15.4744i			1.08078i
$206$	11.7139	+	4.08986i	0.816146	+	0.284954i
$207$		0			0
$208$	17.4516	−	4.03357i	1.21005	−	0.279678i
$209$	−4.66474			−0.322667
$210$		0			0
$211$		−	17.0194i		−	1.17166i	−0.810433	−	0.585831i	$-0.800768\pi$
$211$		−	17.0194i		−	1.17166i	0.810433	−	0.585831i	$-0.199232\pi$
$212$	−3.88325	+	4.88316i	−0.266703	+	0.335377i
$213$		0			0
$214$	−4.62140	+	13.2363i	−0.315913	+	0.904815i
$215$	−16.1200			−1.09937
$216$		0			0
$217$	14.6518			0.994630
$218$	−1.32667	+	3.79975i	−0.0898533	+	0.257352i
$219$		0			0
$220$	15.3987	+	12.2455i	1.03818	+	0.825594i
$221$		−	30.6843i		−	2.06405i
$222$		0			0
$223$	13.6634			0.914971			0.457486	−	0.889217i	$-0.348750\pi$
$223$	13.6634			0.914971			0.457486	+	0.889217i	$0.348750\pi$
$224$	−1.67917	+	15.3764i	−0.112194	+	1.02738i
$225$		0			0
$226$	−2.11608	−	0.738821i	−0.140760	−	0.0491457i
$227$		−	5.46152i		−	0.362494i	−0.983438	−	0.181247i	$-0.941987\pi$
$227$		−	5.46152i		−	0.362494i	0.983438	−	0.181247i	$-0.0580133\pi$
$228$		0			0
$229$		−	3.22791i		−	0.213306i	−0.994296	−	0.106653i	$-0.965987\pi$
$229$		−	3.22791i		−	0.213306i	0.994296	−	0.106653i	$-0.0340135\pi$
$230$	−1.18377	+	3.39048i	−0.0780557	+	0.223562i
$231$		0			0
$232$	−22.9011	+	14.4555i	−1.50353	+	0.949048i
$233$	17.8344			1.16837			0.584185	−	0.811621i	$-0.301414\pi$
$233$	17.8344			1.16837			0.584185	+	0.811621i	$0.301414\pi$
$234$		0			0
$235$			15.9529i			1.04065i
$236$	12.7523	−	16.0360i	0.830106	−	1.04385i
$237$		0			0
$238$	25.0169	+	8.73455i	1.62160	+	0.566176i
$239$	−1.82556			−0.118086			−0.0590428	−	0.998255i	$-0.518805\pi$
$239$	−1.82556			−0.118086			−0.0590428	+	0.998255i	$0.518805\pi$
$240$		0			0
$241$	6.47608			0.417161			0.208581	−	0.978005i	$-0.433116\pi$
$241$	6.47608			0.417161			0.208581	+	0.978005i	$0.433116\pi$
$242$	14.3662	+	5.01589i	0.923493	+	0.322434i
$243$		0			0
$244$	0.898846	−	1.13029i	0.0575427	−	0.0723596i
$245$		−	1.00528i		−	0.0642248i
$246$		0			0
$247$	4.47791			0.284923
$248$	8.08979	+	12.8163i	0.513702	+	0.813833i
$249$		0			0
$250$	−5.45887	+	15.6349i	−0.345249	+	0.988839i
$251$			3.10899i			0.196238i	0.995175	+	0.0981189i	$0.0312825\pi$
$251$			3.10899i			0.196238i	−0.995175	+	0.0981189i	$0.968717\pi$
$252$		0			0
$253$			5.61711i			0.353145i
$254$	−19.0840	−	6.66312i	−1.19744	−	0.418081i
$255$		0			0
$256$	−14.3772	+	7.02107i	−0.898576	+	0.438817i
$257$	−5.75606			−0.359053			−0.179526	−	0.983753i	$-0.557457\pi$
$257$	−5.75606			−0.359053			−0.179526	+	0.983753i	$0.557457\pi$
$258$		0			0
$259$			2.99941i			0.186374i
$260$	−14.7819	−	11.7551i	−0.916737	−	0.729020i
$261$		0			0
$262$	−0.283900	+	0.813128i	−0.0175394	+	0.0502352i
$263$	4.58595			0.282782			0.141391	−	0.989954i	$-0.454843\pi$
$263$	4.58595			0.282782			0.141391	+	0.989954i	$0.454843\pi$
$264$		0			0
$265$	6.57844			0.404110
$266$	−1.27468	+	3.65084i	−0.0781554	+	0.223847i
$267$		0			0
$268$	−7.63953	+	9.60665i	−0.466659	+	0.586820i
$269$		−	11.3913i		−	0.694542i	−0.937765	−	0.347271i	$-0.887108\pi$
$269$		−	11.3913i		−	0.694542i	0.937765	−	0.347271i	$-0.112892\pi$
$270$		0			0
$271$	25.1252			1.52625			0.763124	−	0.646252i	$-0.223664\pi$
$271$	25.1252			1.52625			0.763124	+	0.646252i	$0.223664\pi$
$272$	6.17241	+	26.7054i	0.374258	+	1.61926i
$273$		0			0
$274$	24.2453	+	8.46514i	1.46471	+	0.511398i
$275$			2.57910i			0.155526i
$276$		0			0
$277$		−	18.2998i		−	1.09953i	−0.835321	−	0.549763i	$-0.814718\pi$
$277$		−	18.2998i		−	1.09953i	0.835321	−	0.549763i	$-0.185282\pi$
$278$	−0.901672	+	2.58251i	−0.0540787	+	0.154888i
$279$		0			0
$280$	13.7917	−	8.70551i	0.824213	−	0.520254i
$281$	18.0708			1.07802			0.539008	−	0.842301i	$-0.318799\pi$
$281$	18.0708			1.07802			0.539008	+	0.842301i	$0.318799\pi$
$282$		0			0
$283$		−	15.3972i		−	0.915269i	−0.889140	−	0.457634i	$-0.848697\pi$
$283$		−	15.3972i		−	0.915269i	0.889140	−	0.457634i	$-0.151303\pi$
$284$	−7.23589	−	5.75422i	−0.429371	−	0.341450i
$285$		0			0
$286$	−27.8894	−	9.73749i	−1.64914	−	0.575790i
$287$	20.0646			1.18438
$288$		0			0
$289$	29.9550			1.76206
$290$	26.9592	+	9.41271i	1.58310	+	0.552734i
$291$		0			0
$292$	−9.69387	−	7.70889i	−0.567291	−	0.451129i
$293$			11.4407i			0.668374i	0.942507	+	0.334187i	$0.108462\pi$
$293$			11.4407i			0.668374i	−0.942507	+	0.334187i	$0.891538\pi$
$294$		0			0
$295$	−21.6031			−1.25778
$296$	−2.62364	+	1.65608i	−0.152496	+	0.0962576i
$297$		0			0
$298$	7.26178	−	20.7987i	0.420664	−	1.20484i
$299$		−	5.39214i		−	0.311835i
$300$		0			0
$301$			20.9016i			1.20475i
$302$	26.6696	+	9.31157i	1.53466	+	0.535821i
$303$		0			0
$304$	−3.89726	+	0.900771i	−0.223523	+	0.0516628i
$305$	−1.52269			−0.0871892
$306$		0			0
$307$			21.3453i			1.21824i	0.793077	+	0.609122i	$0.208478\pi$
$307$			21.3453i			1.21824i	−0.793077	+	0.609122i	$0.791522\pi$
$308$	15.8779	−	19.9664i	0.904730	−	1.13769i
$309$		0			0
$310$	5.26768	−	15.0873i	0.299184	−	0.856903i
$311$	21.7295			1.23216			0.616082	−	0.787682i	$-0.288719\pi$
$311$	21.7295			1.23216			0.616082	+	0.787682i	$0.288719\pi$
$312$		0			0
$313$	34.1009			1.92750			0.963748	−	0.266814i	$-0.0859710\pi$
$313$	34.1009			1.92750			0.963748	+	0.266814i	$0.0859710\pi$
$314$	−9.73698	+	27.8880i	−0.549490	+	1.57381i
$315$		0			0
$316$	−5.11443	−	4.06716i	−0.287709	−	0.228796i
$317$		−	22.2281i		−	1.24845i	−0.781244	−	0.624226i	$-0.785414\pi$
$317$		−	22.2281i		−	1.24845i	0.781244	−	0.624226i	$-0.214586\pi$
$318$		0			0
$319$	44.6641			2.50071
$320$	15.2298	+	7.25729i	0.851371	+	0.405695i
$321$		0			0
$322$	4.39620	+	1.53492i	0.244991	+	0.0855376i
$323$			6.85237i			0.381276i
$324$		0			0
$325$		−	2.47581i		−	0.137333i
$326$	−1.18796	+	3.40248i	−0.0657952	+	0.188446i
$327$		0			0
$328$	11.0784	+	17.5510i	0.611702	+	0.969090i
$329$	20.6850			1.14040
$330$		0			0
$331$		−	24.1969i		−	1.32998i	−0.746852	−	0.664991i	$-0.768436\pi$
$331$		−	24.1969i		−	1.32998i	0.746852	−	0.664991i	$-0.231564\pi$
$332$	11.1778	−	14.0560i	0.613461	−	0.771423i
$333$		0			0
$334$	−24.9202	−	8.70077i	−1.36357	−	0.476085i
$335$	12.9418			0.707084
$336$		0			0
$337$	−34.2735			−1.86700			−0.933498	−	0.358583i	$-0.883260\pi$
$337$	−34.2735			−1.86700			−0.933498	+	0.358583i	$0.883260\pi$
$338$	9.41519	+	3.28728i	0.512119	+	0.178804i
$339$		0			0
$340$	17.9884	−	22.6202i	0.975555	−	1.22675i
$341$		−	24.9956i		−	1.35359i
$342$		0			0
$343$	17.8370			0.963108
$344$	−18.2831	+	11.5405i	−0.985759	+	0.622224i
$345$		0			0
$346$	3.92688	−	11.2471i	0.211110	−	0.604647i
$347$			26.9233i			1.44532i	0.691206	+	0.722658i	$0.257080\pi$
$347$			26.9233i			1.44532i	−0.691206	+	0.722658i	$0.742920\pi$
$348$		0			0
$349$		−	8.65769i		−	0.463436i	−0.972783	−	0.231718i	$-0.925565\pi$
$349$		−	8.65769i		−	0.463436i	0.972783	−	0.231718i	$-0.0744346\pi$
$350$	2.01852	+	0.704760i	0.107895	+	0.0376710i
$351$		0			0
$352$	26.2318	+	2.86462i	1.39816	+	0.152685i
$353$	9.11265			0.485018			0.242509	−	0.970149i	$-0.422030\pi$
$353$	9.11265			0.485018			0.242509	+	0.970149i	$0.422030\pi$
$354$		0			0
$355$			9.74795i			0.517367i
$356$	−0.971636	−	0.772678i	−0.0514966	−	0.0409518i
$357$		0			0
$358$	−7.77613	+	22.2719i	−0.410981	+	1.17710i
$359$	−4.29978			−0.226934			−0.113467	−	0.993542i	$-0.536196\pi$
$359$	−4.29978			−0.226934			−0.113467	+	0.993542i	$0.536196\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−2.17183	+	6.22041i	−0.114149	+	0.326938i
$363$		0			0
$364$	−15.2420	+	19.1667i	−0.798898	+	1.00461i
$365$			13.0593i			0.683553i
$366$		0			0
$367$	−21.2873			−1.11119			−0.555594	−	0.831454i	$-0.687509\pi$
$367$	−21.2873			−1.11119			−0.555594	+	0.831454i	$0.687509\pi$
$368$	1.08468	+	4.69294i	0.0565426	+	0.244636i
$369$		0			0
$370$	3.08856	+	1.07836i	0.160567	+	0.0560612i
$371$		−	8.52980i		−	0.442845i
$372$		0			0
$373$			11.1076i			0.575129i	0.957761	+	0.287565i	$0.0928456\pi$
$373$			11.1076i			0.575129i	−0.957761	+	0.287565i	$0.907154\pi$
$374$	14.9009	−	42.6781i	0.770507	−	2.20683i
$375$		0			0
$376$	11.4209	+	18.0936i	0.588990	+	0.933107i
$377$	−42.8753			−2.20819
$378$		0			0
$379$			20.6908i			1.06281i	0.847117	+	0.531407i	$0.178336\pi$
$379$			20.6908i			1.06281i	−0.847117	+	0.531407i	$0.821664\pi$
$380$	3.30108	+	2.62513i	0.169342	+	0.134666i
$381$		0			0
$382$	26.7847	+	9.35178i	1.37043	+	0.478479i
$383$	12.1869			0.622720			0.311360	−	0.950292i	$-0.399215\pi$
$383$	12.1869			0.622720			0.311360	+	0.950292i	$0.399215\pi$
$384$		0			0
$385$	−26.8981			−1.37085
$386$	−2.47163	−	0.862960i	−0.125803	−	0.0439235i
$387$		0			0
$388$	−2.61862	−	2.08241i	−0.132940	−	0.105719i
$389$			26.1769i			1.32722i	0.748078	+	0.663611i	$0.230977\pi$
$389$			26.1769i			1.32722i	−0.748078	+	0.663611i	$0.769023\pi$
$390$		0			0
$391$	8.25137			0.417290
$392$	−0.719694	−	1.14018i	−0.0363500	−	0.0575876i
$393$		0			0
$394$	0.104834	−	0.300257i	0.00528145	−	0.0151268i
$395$			6.88999i			0.346673i
$396$		0			0
$397$			14.8451i			0.745055i	0.928021	+	0.372528i	$0.121509\pi$
$397$			14.8451i			0.745055i	−0.928021	+	0.372528i	$0.878491\pi$
$398$	2.37240	+	0.828314i	0.118918	+	0.0415196i
$399$		0			0
$400$	0.498030	+	2.15477i	0.0249015	+	0.107738i
$401$	−34.4111			−1.71841			−0.859205	−	0.511632i	$-0.829041\pi$
$401$	−34.4111			−1.71841			−0.859205	+	0.511632i	$0.829041\pi$
$402$		0			0
$403$			23.9945i			1.19525i
$404$	−9.09441	+	11.4361i	−0.452464	+	0.568970i
$405$		0			0
$406$	12.2048	−	34.9562i	0.605715	−	1.73485i
$407$	5.11691			0.253636
$408$		0			0
$409$	1.43283			0.0708487			0.0354243	−	0.999372i	$-0.488722\pi$
$409$	1.43283			0.0708487			0.0354243	+	0.999372i	$0.488722\pi$
$410$	7.21372	−	20.6610i	0.356260	−	1.02038i
$411$		0			0
$412$	−13.7335	−	10.9213i	−0.676601	−	0.538056i
$413$			28.0113i			1.37834i
$414$		0			0
$415$	−18.9358			−0.929521
$416$	−25.1812	−	2.74989i	−1.23461	−	0.134824i
$417$		0			0
$418$	6.22823	+	2.17456i	0.304633	+	0.106361i
$419$			33.6886i			1.64579i	0.568190	+	0.822897i	$0.307644\pi$
$419$			33.6886i			1.64579i	−0.568190	+	0.822897i	$0.692356\pi$
$420$		0			0
$421$		−	0.237430i		−	0.0115716i	−0.999983	−	0.00578582i	$-0.998158\pi$
$421$		−	0.237430i		−	0.0115716i	0.999983	−	0.00578582i	$-0.00184169\pi$
$422$	−7.93393	+	22.7238i	−0.386218	+	1.10618i
$423$		0			0
$424$	7.46120	−	4.70961i	0.362348	−	0.228719i
$425$	3.78863			0.183776
$426$		0			0
$427$			1.97437i			0.0955465i
$428$	12.3407	−	15.5184i	0.596512	−	0.750109i
$429$		0			0
$430$	21.5229	+	7.51464i	1.03793	+	0.362388i
$431$	−13.0743			−0.629766			−0.314883	−	0.949130i	$-0.601965\pi$
$431$	−13.0743			−0.629766			−0.314883	+	0.949130i	$0.601965\pi$
$432$		0			0
$433$	−9.67718			−0.465056			−0.232528	−	0.972590i	$-0.574700\pi$
$433$	−9.67718			−0.465056			−0.232528	+	0.972590i	$0.574700\pi$
$434$	−19.5627	−	6.83024i	−0.939040	−	0.327862i
$435$		0			0
$436$	3.54266	−	4.45487i	0.169663	−	0.213350i
$437$			1.20416i			0.0576030i
$438$		0			0
$439$	17.7983			0.849468			0.424734	−	0.905318i	$-0.360368\pi$
$439$	17.7983			0.849468			0.424734	+	0.905318i	$0.360368\pi$
$440$	−14.8514	−	23.5283i	−0.708012	−	1.12167i
$441$		0			0
$442$	−14.3041	+	40.9688i	−0.680377	+	1.94869i
$443$		−	3.30468i		−	0.157010i	−0.996914	−	0.0785050i	$-0.974985\pi$
$443$		−	3.30468i		−	0.157010i	0.996914	−	0.0785050i	$-0.0250147\pi$
$444$		0			0
$445$			1.30896i			0.0620505i
$446$	−18.2430	−	6.36949i	−0.863833	−	0.301604i
$447$		0			0
$448$	9.41002	−	19.7474i	0.444582	−	0.932978i
$449$	29.6543			1.39947			0.699735	−	0.714402i	$-0.253301\pi$
$449$	29.6543			1.39947			0.699735	+	0.714402i	$0.253301\pi$
$450$		0			0
$451$		−	34.2297i		−	1.61182i
$452$	2.48092	+	1.97291i	0.116692	+	0.0927978i
$453$		0			0
$454$	−2.54600	+	7.29207i	−0.119490	+	0.342234i
$455$	25.8208			1.21050
$456$		0			0
$457$	−20.2310			−0.946368			−0.473184	−	0.880964i	$-0.656895\pi$
$457$	−20.2310			−0.946368			−0.473184	+	0.880964i	$0.656895\pi$
$458$	−1.50476	+	4.30982i	−0.0703126	+	0.201385i
$459$		0			0
$460$	3.16108	−	3.97504i	0.147386	−	0.185337i
$461$		−	41.2429i		−	1.92087i	−0.278502	−	0.960436i	$-0.589838\pi$
$461$		−	41.2429i		−	1.92087i	0.278502	−	0.960436i	$-0.410162\pi$
$462$		0			0
$463$	−16.5232			−0.767896			−0.383948	−	0.923355i	$-0.625436\pi$
$463$	−16.5232			−0.767896			−0.383948	+	0.923355i	$0.625436\pi$
$464$	37.3156	−	8.62474i	1.73233	−	0.400393i
$465$		0			0
$466$	−23.8120	−	8.31386i	−1.10307	−	0.385132i
$467$		−	24.9967i		−	1.15671i	−0.815786	−	0.578355i	$-0.803695\pi$
$467$		−	24.9967i		−	1.15671i	0.815786	−	0.578355i	$-0.196305\pi$
$468$		0			0
$469$		−	16.7807i		−	0.774860i
$470$	7.43677	−	21.2999i	0.343032	−	0.982490i
$471$		0			0
$472$	−24.5021	+	15.4660i	−1.12780	+	0.711881i
$473$	35.6576			1.63954
$474$		0			0
$475$			0.552894i			0.0253685i
$476$	−29.3301	−	23.3242i	−1.34434	−	1.06907i
$477$		0			0
$478$	2.43744	+	0.851022i	0.111486	+	0.0389248i
$479$	−10.0298			−0.458273			−0.229137	−	0.973394i	$-0.573590\pi$
$479$	−10.0298			−0.458273			−0.229137	+	0.973394i	$0.573590\pi$
$480$		0			0
$481$	−4.91197			−0.223966
$482$	−8.64669	−	3.01896i	−0.393846	−	0.137510i
$483$		0			0
$484$	−16.8431	−	13.3942i	−0.765594	−	0.608826i
$485$			3.52772i			0.160185i
$486$		0			0
$487$	41.6248			1.88620			0.943101	−	0.332508i	$-0.107895\pi$
$487$	41.6248			1.88620			0.943101	+	0.332508i	$0.107895\pi$
$488$	−1.72702	+	1.09012i	−0.0781787	+	0.0493474i
$489$		0			0
$490$	−0.468630	+	1.34222i	−0.0211706	+	0.0606352i
$491$			34.6939i			1.56572i	0.622200	+	0.782858i	$0.286239\pi$
$491$			34.6939i			1.56572i	−0.622200	+	0.782858i	$0.713761\pi$
$492$		0			0
$493$		−	65.6104i		−	2.95494i
$494$	−5.97878	−	2.08747i	−0.268998	−	0.0939196i
$495$		0			0
$496$	−4.82671	−	20.8831i	−0.216725	−	0.937680i
$497$	12.6395			0.566959
$498$		0			0
$499$			14.1270i			0.632413i	0.948690	+	0.316207i	$0.102409\pi$
$499$			14.1270i			0.632413i	−0.948690	+	0.316207i	$0.897591\pi$
$500$	14.5771	−	18.3305i	0.651906	−	0.819767i
$501$		0			0
$502$	1.44932	−	4.15104i	0.0646863	−	0.185270i
$503$	−3.01157			−0.134279			−0.0671395	−	0.997744i	$-0.521387\pi$
$503$	−3.01157			−0.134279			−0.0671395	+	0.997744i	$0.521387\pi$
$504$		0			0
$505$	15.4064			0.685576
$506$	2.61853	−	7.49981i	0.116408	−	0.333407i
$507$		0			0
$508$	22.3743	+	17.7928i	0.992701	+	0.789429i
$509$		−	2.38122i		−	0.105546i	−0.998607	−	0.0527730i	$-0.983194\pi$
$509$		−	2.38122i		−	0.105546i	0.998607	−	0.0527730i	$-0.0168060\pi$
$510$		0			0
$511$	16.9330			0.749074
$512$	22.4691	−	2.67211i	0.993003	−	0.118092i
$513$		0			0
$514$	7.68533	+	2.68330i	0.338985	+	0.118355i
$515$			18.5013i			0.815266i
$516$		0			0
$517$		−	35.2881i		−	1.55197i
$518$	1.39823	−	4.00472i	0.0614349	−	0.175957i
$519$		0			0
$520$	14.2566	+	22.5860i	0.625191	+	0.990460i
$521$	−17.9133			−0.784798			−0.392399	−	0.919795i	$-0.628355\pi$
$521$	−17.9133			−0.784798			−0.392399	+	0.919795i	$0.628355\pi$
$522$		0			0
$523$			18.9602i			0.829071i	0.910033	+	0.414536i	$0.136056\pi$
$523$			18.9602i			0.829071i	−0.910033	+	0.414536i	$0.863944\pi$
$524$	0.758112	−	0.953320i	0.0331183	−	0.0416460i
$525$		0			0
$526$	−6.12304	−	2.13783i	−0.266977	−	0.0932140i
$527$	−36.7178			−1.59945
$528$		0			0
$529$	−21.5500			−0.936956
$530$	−8.78335	−	3.06667i	−0.381524	−	0.133208i
$531$		0			0
$532$	3.40382	−	4.28028i	0.147574	−	0.185574i
$533$			32.8588i			1.42327i
$534$		0			0
$535$	−20.9059			−0.903839
$536$	14.6784	−	9.26521i	0.634011	−	0.400196i
$537$		0			0
$538$	−5.31030	+	15.2094i	−0.228943	+	0.655724i
$539$			2.22369i			0.0957811i
$540$		0			0
$541$			34.2027i			1.47049i	0.677802	+	0.735245i	$0.262933\pi$
$541$			34.2027i			1.47049i	−0.677802	+	0.735245i	$0.737067\pi$
$542$	−33.5465	−	11.7126i	−1.44095	−	0.503100i
$543$		0			0
$544$	4.20804	−	38.5338i	0.180418	−	1.65212i
$545$	−6.00145			−0.257074
$546$		0			0
$547$			0.645113i			0.0275830i	0.999905	+	0.0137915i	$0.00439011\pi$
$547$			0.645113i			0.0275830i	−0.999905	+	0.0137915i	$0.995610\pi$
$548$	−28.4254	−	22.6049i	−1.21427	−	0.965632i
$549$		0			0
$550$	1.20230	−	3.44355i	0.0512663	−	0.146833i
$551$	9.57484			0.407902
$552$		0			0
$553$	8.93377			0.379903
$554$	−8.53080	+	24.4333i	−0.362439	+	1.03807i
$555$		0			0
$556$	2.40778	−	3.02776i	0.102112	−	0.128406i
$557$			10.2596i			0.434714i	0.976092	+	0.217357i	$0.0697436\pi$
$557$			10.2596i			0.434714i	−0.976092	+	0.217357i	$0.930256\pi$
$558$		0			0
$559$	−34.2295			−1.44775
$560$	−22.4726	+	5.19407i	−0.949640	+	0.219490i
$561$		0			0
$562$	−24.1277	−	8.42408i	−1.01776	−	0.355349i
$563$		−	12.9293i		−	0.544906i	−0.962169	−	0.272453i	$-0.912165\pi$
$563$		−	12.9293i		−	0.544906i	0.962169	−	0.272453i	$-0.0878350\pi$
$564$		0			0
$565$		−	3.34221i		−	0.140608i
$566$	−7.17772	+	20.5579i	−0.301702	+	0.864114i
$567$		0			0
$568$	6.97871	+	11.0560i	0.292820	+	0.463901i
$569$	−6.32637			−0.265215			−0.132608	−	0.991169i	$-0.542335\pi$
$569$	−6.32637			−0.265215			−0.132608	+	0.991169i	$0.542335\pi$
$570$		0			0
$571$			31.1997i			1.30566i	0.757502	+	0.652832i	$0.226419\pi$
$571$			31.1997i			1.30566i	−0.757502	+	0.652832i	$0.773581\pi$
$572$	32.6979	+	26.0025i	1.36717	+	1.08722i
$573$		0			0
$574$	−26.7897	−	9.35353i	−1.11818	−	0.390409i
$575$	0.665774			0.0277647
$576$		0			0
$577$	5.48996			0.228550			0.114275	−	0.993449i	$-0.463545\pi$
$577$	5.48996			0.228550			0.114275	+	0.993449i	$0.463545\pi$
$578$	−39.9950	−	13.9641i	−1.66357	−	0.580830i
$579$		0			0
$580$	−31.6073	−	25.1352i	−1.31242	−	1.04368i
$581$			24.5527i			1.01862i
$582$		0			0
$583$	−14.5516			−0.602666
$584$	9.34934	+	14.8117i	0.386878	+	0.612912i
$585$		0			0
$586$	5.33332	−	15.2753i	0.220318	−	0.631018i
$587$		−	17.4576i		−	0.720552i	−0.932846	−	0.360276i	$-0.882683\pi$
$587$		−	17.4576i		−	0.720552i	0.932846	−	0.360276i	$-0.117317\pi$
$588$		0			0
$589$		−	5.35842i		−	0.220790i
$590$	28.8439	+	10.0707i	1.18748	+	0.414606i
$591$		0			0
$592$	4.27503	−	0.988086i	0.175703	−	0.0406101i
$593$	16.7657			0.688486			0.344243	−	0.938881i	$-0.388136\pi$
$593$	16.7657			0.688486			0.344243	+	0.938881i	$0.388136\pi$
$594$		0			0
$595$			39.5125i			1.61985i
$596$	−19.3915	+	24.3846i	−0.794305	+	0.998832i
$597$		0			0
$598$	−2.51365	+	7.19943i	−0.102791	+	0.294407i
$599$	0.357982			0.0146267			0.00731337	−	0.999973i	$-0.497672\pi$
$599$	0.357982			0.0146267			0.00731337	+	0.999973i	$0.497672\pi$
$600$		0			0
$601$	22.8949			0.933903			0.466952	−	0.884283i	$-0.345352\pi$
$601$	22.8949			0.933903			0.466952	+	0.884283i	$0.345352\pi$
$602$	9.74372	−	27.9073i	0.397124	−	1.13742i
$603$		0			0
$604$	−31.2677	−	24.8651i	−1.27226	−	1.01175i
$605$			22.6904i			0.922497i
$606$		0			0
$607$	1.33917			0.0543551			0.0271775	−	0.999631i	$-0.491348\pi$
$607$	1.33917			0.0543551			0.0271775	+	0.999631i	$0.491348\pi$
$608$	5.62342	+	0.614101i	0.228060	+	0.0249051i
$609$		0			0
$610$	2.03306	+	0.709834i	0.0823161	+	0.0287403i
$611$			33.8747i			1.37043i
$612$		0			0
$613$			29.8667i			1.20631i	0.797625	+	0.603153i	$0.206089\pi$
$613$			29.8667i			1.20631i	−0.797625	+	0.603153i	$0.793911\pi$
$614$	9.95056	−	28.4997i	0.401572	−	1.15015i
$615$		0			0
$616$	−30.5075	+	19.2568i	−1.22918	+	0.775877i
$617$	36.4935			1.46917			0.734587	−	0.678514i	$-0.237376\pi$
$617$	36.4935			1.46917			0.734587	+	0.678514i	$0.237376\pi$
$618$		0			0
$619$			8.88669i			0.357186i	0.983923	+	0.178593i	$0.0571546\pi$
$619$			8.88669i			0.357186i	−0.983923	+	0.178593i	$0.942845\pi$
$620$	−14.0665	+	17.6886i	−0.564926	+	0.710390i
$621$		0			0
$622$	−29.0126	−	10.1296i	−1.16330	−	0.406161i
$623$	1.69723			0.0679982
$624$		0			0
$625$	−21.9298			−0.877194
$626$	−45.5306	−	15.8968i	−1.81977	−	0.635365i
$627$		0			0
$628$	26.0011	−	32.6962i	1.03756	−	1.30472i
$629$		−	7.51659i		−	0.299706i
$630$		0			0
$631$	−28.1724			−1.12153			−0.560763	−	0.827977i	$-0.689492\pi$
$631$	−28.1724			−1.12153			−0.560763	+	0.827977i	$0.689492\pi$
$632$	4.93265	+	7.81456i	0.196210	+	0.310846i
$633$		0			0
$634$	−10.3621	+	29.6783i	−0.411530	+	1.17868i
$635$		−	30.1420i		−	1.19615i
$636$		0			0
$637$		−	2.13463i		−	0.0845771i
$638$	−59.6343	−	20.8211i	−2.36095	−	0.824315i
$639$		0			0
$640$	−16.9513	−	16.7894i	−0.670058	−	0.663659i
$641$	−3.58435			−0.141573			−0.0707867	−	0.997491i	$-0.522551\pi$
$641$	−3.58435			−0.141573			−0.0707867	+	0.997491i	$0.522551\pi$
$642$		0			0
$643$		−	19.8837i		−	0.784137i	−0.919936	−	0.392069i	$-0.871760\pi$
$643$		−	19.8837i		−	0.784137i	0.919936	−	0.392069i	$-0.128240\pi$
$644$	−5.15416	−	4.09876i	−0.203102	−	0.161514i
$645$		0			0
$646$	3.19437	−	9.14909i	0.125681	−	0.359966i
$647$	−35.7712			−1.40631			−0.703156	−	0.711036i	$-0.748226\pi$
$647$	−35.7712			−1.40631			−0.703156	+	0.711036i	$0.748226\pi$
$648$		0			0
$649$	47.7865			1.87578
$650$	−1.15415	+	3.30563i	−0.0452694	+	0.129657i
$651$		0			0
$652$	3.17227	−	3.98911i	0.124236	−	0.156226i
$653$		−	8.57378i		−	0.335518i	−0.985828	−	0.167759i	$-0.946347\pi$
$653$		−	8.57378i		−	0.335518i	0.985828	−	0.167759i	$-0.0536531\pi$
$654$		0			0
$655$	−1.28428			−0.0501810
$656$	−6.60983	−	28.5980i	−0.258071	−	1.11656i
$657$		0			0
$658$	−27.6181	−	9.64274i	−1.07666	−	0.375913i
$659$		−	22.9993i		−	0.895927i	−0.894052	−	0.447964i	$-0.852149\pi$
$659$		−	22.9993i		−	0.895927i	0.894052	−	0.447964i	$-0.147851\pi$
$660$		0			0
$661$			28.4720i			1.10743i	0.832706	+	0.553716i	$0.186791\pi$
$661$			28.4720i			1.10743i	−0.832706	+	0.553716i	$0.813209\pi$
$662$	−11.2799	+	32.3070i	−0.438405	+	1.25565i
$663$		0			0
$664$	−21.4768	+	13.5564i	−0.833461	+	0.526091i
$665$	−5.76625			−0.223606
$666$		0			0
$667$		−	11.5297i		−	0.446431i
$668$	29.2167	+	23.2341i	1.13043	+	0.898953i
$669$		0			0
$670$	−17.2795	−	6.03307i	−0.667565	−	0.233078i
$671$	3.36822			0.130029
$672$		0			0
$673$	6.63685			0.255832			0.127916	−	0.991785i	$-0.459171\pi$
$673$	6.63685			0.255832			0.127916	+	0.991785i	$0.459171\pi$
$674$	45.7610	+	15.9773i	1.76265	+	0.615422i
$675$		0			0
$676$	−11.0385	−	8.77816i	−0.424557	−	0.337622i
$677$			29.0823i			1.11772i	0.829261	+	0.558862i	$0.188762\pi$
$677$			29.0823i			1.11772i	−0.829261	+	0.558862i	$0.811238\pi$
$678$		0			0
$679$	4.57415			0.175540
$680$	−34.5624	+	21.8163i	−1.32541	+	0.836615i
$681$		0			0
$682$	−11.6522	+	33.3735i	−0.446186	+	1.27794i
$683$			4.63939i			0.177521i	0.996053	+	0.0887607i	$0.0282906\pi$
$683$			4.63939i			0.177521i	−0.996053	+	0.0887607i	$0.971709\pi$
$684$		0			0
$685$			38.2938i			1.46313i
$686$	−23.8155	−	8.31509i	−0.909280	−	0.317471i
$687$		0			0
$688$	29.7909	−	6.88556i	1.13577	−	0.262510i
$689$	13.9688			0.532169
$690$		0			0
$691$		−	5.11245i		−	0.194487i	−0.995261	−	0.0972434i	$-0.968997\pi$
$691$		−	5.11245i		−	0.194487i	0.995261	−	0.0972434i	$-0.0310025\pi$
$692$	−10.4861	+	13.1862i	−0.398622	+	0.501264i
$693$		0			0
$694$	12.5508	−	35.9472i	0.476423	−	1.36454i
$695$	−4.07890			−0.154721
$696$		0			0
$697$	−50.2825			−1.90459
$698$	−4.03596	+	11.5595i	−0.152763	+	0.437534i
$699$		0			0
$700$	−2.36654	−	1.88195i	−0.0894468	−	0.0711311i
$701$			5.27938i			0.199399i	0.995018	+	0.0996997i	$0.0317882\pi$
$701$			5.27938i			0.199399i	−0.995018	+	0.0996997i	$0.968212\pi$
$702$		0			0
$703$	1.09693			0.0413716
$704$	−33.6886	−	16.0532i	−1.26969	−	0.605029i
$705$		0			0
$706$	−12.1670	−	4.24805i	−0.457910	−	0.159877i
$707$		−	19.9764i		−	0.751290i
$708$		0			0
$709$			28.1441i			1.05697i	0.848942	+	0.528486i	$0.177240\pi$
$709$			28.1441i			1.05697i	−0.848942	+	0.528486i	$0.822760\pi$
$710$	4.54420	−	13.0152i	0.170541	−	0.488451i
$711$		0			0
$712$	0.937103	+	1.48461i	0.0351194	+	0.0556379i
$713$	−6.45241			−0.241645
$714$		0			0
$715$		−	44.0495i		−	1.64736i
$716$	20.7650	−	26.1118i	0.776023	−	0.975843i
$717$		0			0
$718$	5.74094	+	2.00443i	0.214250	+	0.0748046i
$719$	−9.51160			−0.354723			−0.177361	−	0.984146i	$-0.556756\pi$
$719$	−9.51160			−0.354723			−0.177361	+	0.984146i	$0.556756\pi$
$720$		0			0
$721$	23.9894			0.893412
$722$	1.33517	+	0.466170i	0.0496900	+	0.0173491i
$723$		0			0
$724$	5.79954	−	7.29288i	0.215538	−	0.271038i
$725$		−	5.29387i		−	0.196609i
$726$		0			0
$727$	7.06196			0.261914			0.130957	−	0.991388i	$-0.458195\pi$
$727$	7.06196			0.261914			0.130957	+	0.991388i	$0.458195\pi$
$728$	29.2857	−	18.4855i	1.08540	−	0.685118i
$729$		0			0
$730$	6.08784	−	17.4364i	0.225321	−	0.645349i
$731$		−	52.3801i		−	1.93735i
$732$		0			0
$733$		−	7.62443i		−	0.281615i	−0.990037	−	0.140807i	$-0.955030\pi$
$733$		−	7.62443i		−	0.281615i	0.990037	−	0.140807i	$-0.0449698\pi$
$734$	28.4222	+	9.92350i	1.04908	+	0.366283i
$735$		0			0
$736$	0.739478	−	6.77152i	0.0272575	−	0.249602i
$737$	−28.6274			−1.05450
$738$		0			0
$739$		−	45.0131i		−	1.65583i	−0.560851	−	0.827917i	$-0.689526\pi$
$739$		−	45.0131i		−	1.65583i	0.560851	−	0.827917i	$-0.310474\pi$
$740$	−3.62106	−	2.87959i	−0.133113	−	0.105856i
$741$		0			0
$742$	−3.97634	+	11.3888i	−0.145976	+	0.418094i
$743$	−15.3137			−0.561805			−0.280903	−	0.959736i	$-0.590634\pi$
$743$	−15.3137			−0.561805			−0.280903	+	0.959736i	$0.590634\pi$
$744$		0			0
$745$	32.8501			1.20354
$746$	5.17803	−	14.8306i	0.189581	−	0.542985i
$747$		0			0
$748$	−39.7906	+	50.0363i	−1.45489	+	1.82951i
$749$			27.1072i			0.990475i
$750$		0			0
$751$	4.09580			0.149458			0.0747290	−	0.997204i	$-0.476191\pi$
$751$	4.09580			0.149458			0.0747290	+	0.997204i	$0.476191\pi$
$752$	−6.81420	−	29.4822i	−0.248488	−	1.07511i
$753$		0			0
$754$	57.2459	+	19.9872i	2.08477	+	0.727890i
$755$			42.1228i			1.53301i
$756$		0			0
$757$			9.51720i			0.345909i	0.984930	+	0.172954i	$0.0553313\pi$
$757$			9.51720i			0.345909i	−0.984930	+	0.172954i	$0.944669\pi$
$758$	9.64542	−	27.6258i	0.350338	−	1.00341i
$759$		0			0
$760$	−3.18375	−	5.04386i	−0.115487	−	0.182960i
$761$	38.4841			1.39505			0.697523	−	0.716562i	$-0.254285\pi$
$761$	38.4841			1.39505			0.697523	+	0.716562i	$0.254285\pi$
$762$		0			0
$763$			7.78167i			0.281715i
$764$	−31.4027	−	24.9725i	−1.13611	−	0.903473i
$765$		0			0
$766$	−16.2716	−	5.68116i	−0.587916	−	0.205269i
$767$	−45.8726			−1.65636
$768$		0			0
$769$	15.0210			0.541670			0.270835	−	0.962626i	$-0.412700\pi$
$769$	15.0210			0.541670			0.270835	+	0.962626i	$0.412700\pi$
$770$	35.9136	+	12.5391i	1.29423	+	0.451877i
$771$		0			0
$772$	2.89777	+	2.30440i	0.104293	+	0.0829372i
$773$		−	38.4471i		−	1.38285i	−0.722451	−	0.691423i	$-0.756984\pi$
$773$		−	38.4471i		−	1.38285i	0.722451	−	0.691423i	$-0.243016\pi$
$774$		0			0
$775$	−2.96263			−0.106421
$776$	2.52555	+	4.00110i	0.0906619	+	0.143631i
$777$		0			0
$778$	12.2029	−	34.9507i	0.437495	−	1.25304i
$779$		−	7.33797i		−	0.262910i
$780$		0			0
$781$		−	21.5626i		−	0.771572i
$782$	−11.0170	−	3.84654i	−0.393967	−	0.137552i
$783$		0			0
$784$	0.429399	+	1.85783i	0.0153357	+	0.0663511i
$785$	−44.0472			−1.57211
$786$		0			0
$787$			30.8457i			1.09953i	0.835319	+	0.549765i	$0.185283\pi$
$787$			30.8457i			1.09953i	−0.835319	+	0.549765i	$0.814717\pi$
$788$	−0.279942	+	0.352025i	−0.00997253	+	0.0125404i
$789$		0			0
$790$	3.21191	−	9.19932i	0.114275	−	0.327297i
$791$	−4.33361			−0.154085
$792$		0			0
$793$	−3.23332			−0.114819
$794$	6.92035	−	19.8208i	0.245594	−	0.703414i
$795$		0			0
$796$	−2.78143	−	2.21188i	−0.0985850	−	0.0783981i
$797$		−	34.1285i		−	1.20889i	−0.796646	−	0.604446i	$-0.793394\pi$
$797$		−	34.1285i		−	1.20889i	0.796646	−	0.604446i	$-0.206606\pi$
$798$		0			0
$799$	−51.8372			−1.83387
$800$	0.339532	−	3.10915i	0.0120043	−	0.109925i
$801$		0			0
$802$	45.9448	+	16.0414i	1.62237	+	0.566443i
$803$		−	28.8873i		−	1.01941i
$804$		0			0
$805$			6.94351i			0.244727i
$806$	11.1855	−	32.0368i	0.393993	−	1.12845i
$807$		0			0
$808$	17.4738	−	11.0297i	0.614726	−	0.388023i
$809$	25.9170			0.911192			0.455596	−	0.890187i	$-0.349426\pi$
$809$	25.9170			0.911192			0.455596	+	0.890187i	$0.349426\pi$
$810$		0			0
$811$		−	33.7874i		−	1.18644i	−0.805041	−	0.593219i	$-0.797857\pi$
$811$		−	33.7874i		−	1.18644i	0.805041	−	0.593219i	$-0.202143\pi$
$812$	−32.5911	+	40.9830i	−1.14372	+	1.43822i
$813$		0			0
$814$	−6.83195	−	2.38535i	−0.239460	−	0.0836065i
$815$	−5.37400			−0.188243
$816$		0			0
$817$	7.64408			0.267432
$818$	−1.91307	−	0.667941i	−0.0668889	−	0.0233540i
$819$		0			0
$820$	−19.2631	+	24.2232i	−0.672698	+	0.845912i
$821$		−	27.6475i		−	0.964903i	−0.875923	−	0.482451i	$-0.839746\pi$
$821$		−	27.6475i		−	0.964903i	0.875923	−	0.482451i	$-0.160254\pi$
$822$		0			0
$823$	−12.4983			−0.435665			−0.217832	−	0.975986i	$-0.569899\pi$
$823$	−12.4983			−0.435665			−0.217832	+	0.975986i	$0.569899\pi$
$824$	13.2454	+	20.9840i	0.461425	+	0.731013i
$825$		0			0
$826$	13.0580	−	37.3999i	0.454347	−	1.30131i
$827$			9.03084i			0.314033i	0.987596	+	0.157017i	$0.0501876\pi$
$827$			9.03084i			0.314033i	−0.987596	+	0.157017i	$0.949812\pi$
$828$		0			0
$829$		−	55.7684i		−	1.93692i	−0.249175	−	0.968458i	$-0.580159\pi$
$829$		−	55.7684i		−	1.93692i	0.249175	−	0.968458i	$-0.419841\pi$
$830$	25.2825	+	8.82730i	0.877569	+	0.306400i
$831$		0			0
$832$	32.3393	+	15.4103i	1.12116	+	0.534256i
$833$	3.26654			0.113179
$834$		0			0
$835$		−	39.3597i		−	1.36210i
$836$	−7.30205	−	5.80683i	−0.252547	−	0.200833i
$837$		0			0
$838$	15.7046	−	44.9800i	0.542507	−	1.55381i
$839$	14.3128			0.494134			0.247067	−	0.968998i	$-0.420533\pi$
$839$	14.3128			0.494134			0.247067	+	0.968998i	$0.420533\pi$
$840$		0			0
$841$	−62.6776			−2.16130
$842$	−0.110683	+	0.317010i	−0.00381438	+	0.0109249i
$843$		0			0
$844$	21.1863	−	26.6416i	0.729264	−	0.917043i
$845$			14.8707i			0.511567i
$846$		0			0
$847$	29.4211			1.01092
$848$	−12.1575	+	2.80995i	−0.417489	+	0.0964940i
$849$		0			0
$850$	−5.05848	−	1.76615i	−0.173504	−	0.0605783i
$851$		−	1.32089i		−	0.0452794i
$852$		0			0
$853$			38.0325i			1.30221i	0.758988	+	0.651105i	$0.225694\pi$
$853$			38.0325i			1.30221i	−0.758988	+	0.651105i	$0.774306\pi$
$854$	0.920393	−	2.63612i	0.0314952	−	0.0902063i
$855$		0			0
$856$	−23.7112	+	14.9668i	−0.810433	+	0.511556i
$857$	23.1869			0.792048			0.396024	−	0.918240i	$-0.370390\pi$
$857$	23.1869			0.792048			0.396024	+	0.918240i	$0.370390\pi$
$858$		0			0
$859$		−	46.5870i		−	1.58953i	−0.606919	−	0.794764i	$-0.707595\pi$
$859$		−	46.5870i		−	1.58953i	0.606919	−	0.794764i	$-0.292405\pi$
$860$	−25.2337	−	20.0667i	−0.860462	−	0.684269i
$861$		0			0
$862$	17.4564	+	6.09484i	0.594568	+	0.207591i
$863$	54.3149			1.84890			0.924451	−	0.381301i	$-0.124524\pi$
$863$	54.3149			1.84890			0.924451	+	0.381301i	$0.124524\pi$
$864$		0			0
$865$	17.7640			0.603995
$866$	12.9207	+	4.51121i	0.439063	+	0.153297i
$867$		0			0
$868$	22.9355	+	18.2391i	0.778482	+	0.619075i
$869$		−	15.2408i		−	0.517008i
$870$		0			0
$871$	27.4808			0.931153
$872$	−6.80679	+	4.29653i	−0.230507	+	0.145499i
$873$		0			0
$874$	0.561345	−	1.60777i	0.0189878	−	0.0543835i
$875$			32.0194i			1.08245i
$876$		0			0
$877$		−	1.80324i		−	0.0608910i	−0.999536	−	0.0304455i	$-0.990307\pi$
$877$		−	1.80324i		−	0.0608910i	0.999536	−	0.0304455i	$-0.00969260\pi$
$878$	−23.7639	−	8.29705i	−0.801991	−	0.280012i
$879$		0			0
$880$	8.86095	+	38.3376i	0.298703	+	1.29236i
$881$	−12.6372			−0.425759			−0.212880	−	0.977078i	$-0.568284\pi$
$881$	−12.6372			−0.425759			−0.212880	+	0.977078i	$0.568284\pi$
$882$		0			0
$883$		−	39.9276i		−	1.34367i	−0.740700	−	0.671835i	$-0.765506\pi$
$883$		−	39.9276i		−	1.34367i	0.740700	−	0.671835i	$-0.234494\pi$
$884$	38.1969	−	48.0323i	1.28470	−	1.61550i
$885$		0			0
$886$	−1.54054	+	4.41232i	−0.0517555	+	0.148235i
$887$	14.3642			0.482304			0.241152	−	0.970487i	$-0.422475\pi$
$887$	14.3642			0.482304			0.241152	+	0.970487i	$0.422475\pi$
$888$		0			0
$889$	−39.0830			−1.31080
$890$	0.610197	−	1.74768i	0.0204538	−	0.0585825i
$891$		0			0
$892$	21.3883	+	17.0087i	0.716135	+	0.569494i
$893$		−	7.56486i		−	0.253148i
$894$		0			0
$895$	−35.1769			−1.17584
$896$	−21.7697	+	21.9795i	−0.727273	+	0.734285i
$897$		0			0
$898$	−39.5935	−	13.8239i	−1.32125	−	0.461311i
$899$			51.3060i			1.71115i
$900$		0			0
$901$			21.3759i			0.712135i
$902$	−15.9569	+	45.7026i	−0.531306	+	1.52173i
$903$		0			0
$904$	−2.39274	−	3.79070i	−0.0795814	−	0.126077i
$905$	−9.82473			−0.326585
$906$		0			0
$907$			3.32787i			0.110500i	0.998473	+	0.0552501i	$0.0175956\pi$
$907$			3.32787i			0.110500i	−0.998473	+	0.0552501i	$0.982404\pi$
$908$	6.79869	−	8.54930i	0.225623	−	0.283719i
$909$		0			0
$910$	−34.4752	−	12.0369i	−1.14284	−	0.399018i
$911$	35.8252			1.18694			0.593471	−	0.804855i	$-0.297757\pi$
$911$	35.8252			1.18694			0.593471	+	0.804855i	$0.297757\pi$
$912$		0			0
$913$	41.8863			1.38623
$914$	27.0119	+	9.43111i	0.893475	+	0.311953i
$915$		0			0
$916$	4.01822	−	5.05288i	0.132766	−	0.166952i
$917$			1.66524i			0.0549910i
$918$		0			0
$919$	−48.3186			−1.59388			−0.796942	−	0.604055i	$-0.793551\pi$
$919$	−48.3186			−1.59388			−0.796942	+	0.604055i	$0.793551\pi$
$920$	−6.07364	+	3.83376i	−0.200242	+	0.126395i
$921$		0			0
$922$	−19.2262	+	55.0663i	−0.633181	+	1.81351i
$923$			20.6990i			0.681316i
$924$		0			0
$925$		−	0.606487i		−	0.0199412i
$926$	22.0613	+	7.70261i	0.724978	+	0.253123i
$927$		0			0
$928$	−53.8434	−	5.87992i	−1.76750	−	0.193018i
$929$	23.2127			0.761585			0.380792	−	0.924661i	$-0.375651\pi$
$929$	23.2127			0.761585			0.380792	+	0.924661i	$0.375651\pi$
$930$		0			0
$931$			0.476702i			0.0156233i
$932$	27.9174	+	22.2009i	0.914466	+	0.727214i
$933$		0			0
$934$	−11.6527	+	33.3749i	−0.381288	+	1.09206i
$935$	67.4073			2.20445
$936$		0			0
$937$	7.10467			0.232099			0.116050	−	0.993243i	$-0.462977\pi$
$937$	7.10467			0.232099			0.116050	+	0.993243i	$0.462977\pi$
$938$	−7.82266	+	22.4051i	−0.255419	+	0.731553i
$939$		0			0
$940$	−19.8587	+	24.9722i	−0.647720	+	0.814503i
$941$			55.5352i			1.81040i	0.424989	+	0.905199i	$0.360278\pi$
$941$			55.5352i			1.81040i	−0.424989	+	0.905199i	$0.639722\pi$
$942$		0			0
$943$	−8.83612			−0.287744
$944$	39.9243	−	9.22767i	1.29942	−	0.300335i
$945$		0			0
$946$	−47.6091	−	16.6225i	−1.54791	−	0.540445i
$947$		−	15.5988i		−	0.506894i	−0.967349	−	0.253447i	$-0.918436\pi$
$947$		−	15.5988i		−	0.506894i	0.967349	−	0.253447i	$-0.0815643\pi$
$948$		0			0
$949$			27.7304i			0.900165i
$950$	0.257743	−	0.738208i	0.00836227	−	0.0239506i
$951$		0			0
$952$	28.2876	+	44.8147i	0.916807	+	1.45245i
$953$	−21.1243			−0.684282			−0.342141	−	0.939649i	$-0.611152\pi$
$953$	−21.1243			−0.684282			−0.342141	+	0.939649i	$0.611152\pi$
$954$		0			0
$955$			42.3047i			1.36895i
$956$	−2.85768	−	2.27252i	−0.0924239	−	0.0734986i
$957$		0			0
$958$	13.3915	+	4.67560i	0.432660	+	0.151062i
$959$	49.6529			1.60338
$960$		0			0
$961$	−2.28738			−0.0737863
$962$	6.55832	+	2.28981i	0.211449	+	0.0738265i
$963$		0			0
$964$	10.1375	+	8.06165i	0.326506	+	0.259648i
$965$		−	3.90378i		−	0.125667i
$966$		0			0
$967$	46.1207			1.48314			0.741570	−	0.670875i	$-0.234081\pi$
$967$	46.1207			1.48314			0.741570	+	0.670875i	$0.234081\pi$
$968$	16.2444	+	25.7353i	0.522116	+	0.827162i
$969$		0			0
$970$	1.64452	−	4.71011i	0.0528022	−	0.151233i
$971$			22.3253i			0.716454i	0.933635	+	0.358227i	$0.116619\pi$
$971$			22.3253i			0.716454i	−0.933635	+	0.358227i	$0.883381\pi$
$972$		0			0
$973$			5.28882i			0.169552i
$974$	−55.5763	−	19.4043i	−1.78078	−	0.621752i
$975$		0			0
$976$	2.81406	−	0.650411i	0.0900757	−	0.0208192i
$977$	−14.2650			−0.456379			−0.228190	−	0.973617i	$-0.573281\pi$
$977$	−14.2650			−0.456379			−0.228190	+	0.973617i	$0.573281\pi$
$978$		0			0
$979$		−	2.89544i		−	0.0925385i
$980$	1.25140	−	1.57363i	0.0399746	−	0.0502678i
$981$		0			0
$982$	16.1733	−	46.3224i	0.516110	−	1.47821i
$983$	−12.7242			−0.405838			−0.202919	−	0.979196i	$-0.565043\pi$
$983$	−12.7242			−0.405838			−0.202919	+	0.979196i	$0.565043\pi$
$984$		0			0
$985$	0.474237			0.0151104
$986$	−30.5856	+	87.6011i	−0.974044	+	2.78979i
$987$		0			0
$988$	7.00959	+	5.57426i	0.223005	+	0.177341i
$989$		−	9.20472i		−	0.292693i
$990$		0			0
$991$	−10.8169			−0.343611			−0.171806	−	0.985131i	$-0.554960\pi$
$991$	−10.8169			−0.343611			−0.171806	+	0.985131i	$0.554960\pi$
$992$	−3.29061	+	30.1326i	−0.104477	+	0.956712i
$993$		0			0
$994$	−16.8759	−	5.89215i	−0.535271	−	0.186888i
$995$			3.74705i			0.118789i
$996$		0			0
$997$		−	5.39134i		−	0.170746i	−0.996349	−	0.0853728i	$-0.972792\pi$
$997$		−	5.39134i		−	0.170746i	0.996349	−	0.0853728i	$-0.0272081\pi$
$998$	6.58561	−	18.8620i	0.208464	−	0.597067i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.g.b.685.1		16
3.2	odd	2		152.2.c.b.77.16	yes	16
4.3	odd	2		5472.2.g.b.2737.5		16
8.3	odd	2		5472.2.g.b.2737.12		16
8.5	even	2	inner	1368.2.g.b.685.2		16
12.11	even	2		608.2.c.b.305.9		16
24.5	odd	2		152.2.c.b.77.15	✓	16
24.11	even	2		608.2.c.b.305.8		16
48.5	odd	4		4864.2.a.bq.1.4		8
48.11	even	4		4864.2.a.bp.1.5		8
48.29	odd	4		4864.2.a.bo.1.5		8
48.35	even	4		4864.2.a.bn.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.c.b.77.15	✓	16	24.5	odd	2
152.2.c.b.77.16	yes	16	3.2	odd	2
608.2.c.b.305.8		16	24.11	even	2
608.2.c.b.305.9		16	12.11	even	2
1368.2.g.b.685.1		16	1.1	even	1	trivial
1368.2.g.b.685.2		16	8.5	even	2	inner
4864.2.a.bn.1.4		8	48.35	even	4
4864.2.a.bo.1.5		8	48.29	odd	4
4864.2.a.bp.1.5		8	48.11	even	4
4864.2.a.bq.1.4		8	48.5	odd	4
5472.2.g.b.2737.5		16	4.3	odd	2
5472.2.g.b.2737.12		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)

\(f(q)\)	\(=\)	\(q+(-1.33517 - 0.466170i) q^{2} +(1.56537 + 1.24484i) q^{4} -2.10882i q^{5} -2.73436 q^{7} +(-1.50973 - 2.39180i) q^{8} +O(q^{10})\)	\(q+(-1.33517 - 0.466170i) q^{2} +(1.56537 + 1.24484i) q^{4} -2.10882i q^{5} -2.73436 q^{7} +(-1.50973 - 2.39180i) q^{8} +(-0.983067 + 2.81563i) q^{10} +4.66474i q^{11} -4.47791i q^{13} +(3.65084 + 1.27468i) q^{14} +(0.900771 + 3.89726i) q^{16} +6.85237 q^{17} +1.00000i q^{19} +(2.62513 - 3.30108i) q^{20} +(2.17456 - 6.22823i) q^{22} +1.20416 q^{23} +0.552894 q^{25} +(-2.08747 + 5.97878i) q^{26} +(-4.28028 - 3.40382i) q^{28} -9.57484i q^{29} -5.35842 q^{31} +(0.614101 - 5.62342i) q^{32} +(-9.14909 - 3.19437i) q^{34} +5.76625i q^{35} -1.09693i q^{37} +(0.466170 - 1.33517i) q^{38} +(-5.04386 + 3.18375i) q^{40} -7.33797 q^{41} -7.64408i q^{43} +(-5.80683 + 7.30205i) q^{44} +(-1.60777 - 0.561345i) q^{46} -7.56486 q^{47} +0.476702 q^{49} +(-0.738208 - 0.257743i) q^{50} +(5.57426 - 7.00959i) q^{52} +3.11949i q^{53} +9.83708 q^{55} +(4.12815 + 6.54003i) q^{56} +(-4.46351 + 12.7841i) q^{58} -10.2442i q^{59} -0.722061i q^{61} +(7.15441 + 2.49793i) q^{62} +(-3.44140 + 7.22196i) q^{64} -9.44309 q^{65} +6.13698i q^{67} +(10.7265 + 8.53007i) q^{68} +(2.68806 - 7.69894i) q^{70} -4.62247 q^{71} -6.19270 q^{73} +(-0.511358 + 1.46460i) q^{74} +(-1.24484 + 1.56537i) q^{76} -12.7551i q^{77} -3.26723 q^{79} +(8.21860 - 1.89956i) q^{80} +(9.79746 + 3.42075i) q^{82} -8.97934i q^{83} -14.4504i q^{85} +(-3.56344 + 10.2062i) q^{86} +(11.1571 - 7.04252i) q^{88} -0.620707 q^{89} +12.2442i q^{91} +(1.88496 + 1.49899i) q^{92} +(10.1004 + 3.52651i) q^{94} +2.10882 q^{95} -1.67284 q^{97} +(-0.636479 - 0.222224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) 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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Representations

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Database

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