LMFDB - Embedded newform 1264.2.n.i.767.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1264,2,Mod(735,1264)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1264, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1264.735");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1264 = 2^{4} \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1264.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.0930908155$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			767.14
Character	$\chi$	$=$	1264.767
Dual form			1264.2.n.i.735.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60192 + 2.77460i) q^{3} +(-1.45498 + 2.52010i) q^{5} +(-0.195200 + 0.338096i) q^{7} +(-3.63228 + 6.29129i) q^{9} +O(q^{10})$	\(q+(1.60192 + 2.77460i) q^{3} +(-1.45498 + 2.52010i) q^{5} +(-0.195200 + 0.338096i) q^{7} +(-3.63228 + 6.29129i) q^{9} +(4.62575 + 2.67068i) q^{11} +(-2.74986 - 4.76289i) q^{13} -9.32304 q^{15} +4.03669i q^{17} +(-1.77958 - 1.02744i) q^{19} -1.25077 q^{21} +(3.40983 + 1.96867i) q^{23} +(-1.73395 - 3.00328i) q^{25} -13.6629 q^{27} +(4.52756 + 2.61399i) q^{29} +(-5.25404 - 3.03342i) q^{31} +17.1128i q^{33} +(-0.568024 - 0.983847i) q^{35} +(8.16671 - 4.71505i) q^{37} +(8.81008 - 15.2595i) q^{39} -1.64388i q^{41} +(-5.59109 - 9.68406i) q^{43} +(-10.5698 - 18.3074i) q^{45} +(0.568024 - 0.983847i) q^{47} +(3.42379 + 5.93019i) q^{49} +(-11.2002 + 6.46644i) q^{51} +(-6.76663 - 3.90672i) q^{53} +(-13.4608 + 7.77158i) q^{55} -6.58352i q^{57} +(3.41419 + 5.91355i) q^{59} +10.6214i q^{61} +(-1.41804 - 2.45612i) q^{63} +16.0040 q^{65} +7.02785i q^{67} +12.6146i q^{69} +2.42312 q^{71} +(4.34552 - 7.52666i) q^{73} +(5.55528 - 9.62202i) q^{75} +(-1.80589 + 1.04263i) q^{77} +(2.66466 - 8.47936i) q^{79} +(-10.9900 - 19.0353i) q^{81} +(-5.07404 - 2.92950i) q^{83} +(-10.1729 - 5.87331i) q^{85} +16.7496i q^{87} +5.86283 q^{89} +2.14708 q^{91} -19.4372i q^{93} +(5.17853 - 2.98982i) q^{95} +10.3343 q^{97} +(-33.6040 + 19.4013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 20 q^{9}+O(q^{10}) $ 28 * q - 20 * q^9	$ 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) $ 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1264\mathbb{Z}\right)^\times$.

$n$	$159$	$161$	$949$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.60192	+	2.77460i	0.924867	+	1.60192i	0.791774	+	0.610814i	$0.209158\pi$
$3$	1.60192	+	2.77460i	0.924867	+	1.60192i	0.133093	+	0.991104i	$0.457509\pi$
$4$		0			0
$5$	−1.45498	+	2.52010i	−0.650688	+	1.12702i	0.332268	+	0.943185i	$0.392186\pi$
$5$	−1.45498	+	2.52010i	−0.650688	+	1.12702i	−0.982956	+	0.183839i	$0.941147\pi$
$6$		0			0
$7$	−0.195200	+	0.338096i	−0.0737785	+	0.127788i	−0.900554	−	0.434743i	$-0.856839\pi$
$7$	−0.195200	+	0.338096i	−0.0737785	+	0.127788i	0.826776	+	0.562531i	$0.190172\pi$
$8$		0			0
$9$	−3.63228	+	6.29129i	−1.21076	+	2.09710i
$10$		0			0
$11$	4.62575	+	2.67068i	1.39472	+	0.805240i	0.993833	−	0.110890i	$-0.0353700\pi$
$11$	4.62575	+	2.67068i	1.39472	+	0.805240i	0.400883	+	0.916129i	$0.368703\pi$
$12$		0			0
$13$	−2.74986	−	4.76289i	−0.762673	−	1.32099i	−0.941468	−	0.337101i	$-0.890553\pi$
$13$	−2.74986	−	4.76289i	−0.762673	−	1.32099i	0.178796	−	0.983886i	$-0.442780\pi$
$14$		0			0
$15$	−9.32304			−2.40720
$16$		0			0
$17$			4.03669i			0.979040i	0.871992	+	0.489520i	$0.162828\pi$
$17$			4.03669i			0.979040i	−0.871992	+	0.489520i	$0.837172\pi$
$18$		0			0
$19$	−1.77958	−	1.02744i	−0.408265	−	0.235712i	0.281779	−	0.959479i	$-0.409075\pi$
$19$	−1.77958	−	1.02744i	−0.408265	−	0.235712i	−0.690044	+	0.723768i	$0.742409\pi$
$20$		0			0
$21$	−1.25077			−0.272941
$22$		0			0
$23$	3.40983	+	1.96867i	0.710999	+	0.410495i	0.811431	−	0.584449i	$-0.198689\pi$
$23$	3.40983	+	1.96867i	0.710999	+	0.410495i	−0.100432	+	0.994944i	$0.532023\pi$
$24$		0			0
$25$	−1.73395	−	3.00328i	−0.346789	−	0.600657i
$26$		0			0
$27$	−13.6629			−2.62943
$28$		0			0
$29$	4.52756	+	2.61399i	0.840746	+	0.485405i	0.857518	−	0.514454i	$-0.172006\pi$
$29$	4.52756	+	2.61399i	0.840746	+	0.485405i	−0.0167717	+	0.999859i	$0.505339\pi$
$30$		0			0
$31$	−5.25404	−	3.03342i	−0.943653	−	0.544819i	−0.0525498	−	0.998618i	$-0.516735\pi$
$31$	−5.25404	−	3.03342i	−0.943653	−	0.544819i	−0.891104	+	0.453800i	$0.850068\pi$
$32$		0			0
$33$			17.1128i			2.97896i
$34$		0			0
$35$	−0.568024	−	0.983847i	−0.0960136	−	0.166300i
$36$		0			0
$37$	8.16671	−	4.71505i	1.34260	−	0.775150i	0.355411	−	0.934710i	$-0.384341\pi$
$37$	8.16671	−	4.71505i	1.34260	−	0.775150i	0.987188	+	0.159561i	$0.0510077\pi$
$38$		0			0
$39$	8.81008	−	15.2595i	1.41074	−	2.44348i
$40$		0			0
$41$		−	1.64388i		−	0.256731i	−0.991727	−	0.128366i	$-0.959027\pi$
$41$		−	1.64388i		−	0.256731i	0.991727	−	0.128366i	$-0.0409731\pi$
$42$		0			0
$43$	−5.59109	−	9.68406i	−0.852634	−	1.47680i	−0.878823	−	0.477148i	$-0.841671\pi$
$43$	−5.59109	−	9.68406i	−0.852634	−	1.47680i	0.0261897	−	0.999657i	$-0.491663\pi$
$44$		0			0
$45$	−10.5698	−	18.3074i	−1.57565	−	2.72911i
$46$		0			0
$47$	0.568024	−	0.983847i	0.0828548	−	0.143509i	−0.821620	−	0.570035i	$-0.806930\pi$
$47$	0.568024	−	0.983847i	0.0828548	−	0.143509i	0.904475	+	0.426526i	$0.140263\pi$
$48$		0			0
$49$	3.42379	+	5.93019i	0.489113	+	0.847169i
$50$		0			0
$51$	−11.2002	+	6.46644i	−1.56834	+	0.905482i
$52$		0			0
$53$	−6.76663	−	3.90672i	−0.929469	−	0.536629i	−0.0428251	−	0.999083i	$-0.513636\pi$
$53$	−6.76663	−	3.90672i	−0.929469	−	0.536629i	−0.886643	+	0.462454i	$0.846969\pi$
$54$		0			0
$55$	−13.4608	+	7.77158i	−1.81505	+	1.04792i
$56$		0			0
$57$		−	6.58352i		−	0.872008i
$58$		0			0
$59$	3.41419	+	5.91355i	0.444489	+	0.769878i	0.998017	−	0.0629529i	$-0.0200518\pi$
$59$	3.41419	+	5.91355i	0.444489	+	0.769878i	−0.553527	+	0.832831i	$0.686718\pi$
$60$		0			0
$61$			10.6214i			1.35993i	0.733245	+	0.679965i	$0.238005\pi$
$61$			10.6214i			1.35993i	−0.733245	+	0.679965i	$0.761995\pi$
$62$		0			0
$63$	−1.41804	−	2.45612i	−0.178656	−	0.309441i
$64$		0			0
$65$	16.0040			1.98505
$66$		0			0
$67$			7.02785i			0.858589i	0.903165	+	0.429294i	$0.141238\pi$
$67$			7.02785i			0.858589i	−0.903165	+	0.429294i	$0.858762\pi$
$68$		0			0
$69$			12.6146i			1.51861i
$70$		0			0
$71$	2.42312			0.287572			0.143786	−	0.989609i	$-0.454072\pi$
$71$	2.42312			0.287572			0.143786	+	0.989609i	$0.454072\pi$
$72$		0			0
$73$	4.34552	−	7.52666i	0.508604	−	0.880928i	−0.491346	−	0.870964i	$-0.663495\pi$
$73$	4.34552	−	7.52666i	0.508604	−	0.880928i	0.999950	−	0.00996406i	$-0.00317171\pi$
$74$		0			0
$75$	5.55528	−	9.62202i	0.641468	−	1.11106i
$76$		0			0
$77$	−1.80589	+	1.04263i	−0.205800	+	0.118819i
$78$		0			0
$79$	2.66466	−	8.47936i	0.299798	−	0.954003i
$79$	2.66466	−	8.47936i	0.299798	−	0.954003i
$80$		0			0
$81$	−10.9900	−	19.0353i	−1.22112	−	2.11504i
$82$		0			0
$83$	−5.07404	−	2.92950i	−0.556948	−	0.321554i	0.194972	−	0.980809i	$-0.437539\pi$
$83$	−5.07404	−	2.92950i	−0.556948	−	0.321554i	−0.751920	+	0.659255i	$0.770872\pi$
$84$		0			0
$85$	−10.1729	−	5.87331i	−1.10340	−	0.637050i
$86$		0			0
$87$			16.7496i			1.79574i
$88$		0			0
$89$	5.86283			0.621458			0.310729	−	0.950499i	$-0.399427\pi$
$89$	5.86283			0.621458			0.310729	+	0.950499i	$0.399427\pi$
$90$		0			0
$91$	2.14708			0.225076
$92$		0			0
$93$		−	19.4372i		−	2.01554i
$94$		0			0
$95$	5.17853	−	2.98982i	0.531306	−	0.306750i
$96$		0			0
$97$	10.3343			1.04929			0.524644	−	0.851321i	$-0.324198\pi$
$97$	10.3343			1.04929			0.524644	+	0.851321i	$0.324198\pi$
$98$		0			0
$99$	−33.6040	+	19.4013i	−3.37733	+	1.94990i
$100$		0			0
$101$	−8.37021			−0.832867			−0.416433	−	0.909166i	$-0.636720\pi$
$101$	−8.37021			−0.832867			−0.416433	+	0.909166i	$0.636720\pi$
$102$		0			0
$103$	4.23535	+	7.33584i	0.417321	+	0.722822i	0.995669	−	0.0929686i	$-0.0296356\pi$
$103$	4.23535	+	7.33584i	0.417321	+	0.722822i	−0.578348	+	0.815790i	$0.696302\pi$
$104$		0			0
$105$	1.81986	−	3.15208i	0.177600	−	0.307612i
$106$		0			0
$107$	−9.29855	−	16.1056i	−0.898925	−	1.55698i	−0.828871	−	0.559440i	$-0.811016\pi$
$107$	−9.29855	−	16.1056i	−0.898925	−	1.55698i	−0.0700538	−	0.997543i	$-0.522317\pi$
$108$		0			0
$109$	4.38428	−	2.53126i	0.419937	−	0.242451i	−0.275113	−	0.961412i	$-0.588715\pi$
$109$	4.38428	−	2.53126i	0.419937	−	0.242451i	0.695051	+	0.718961i	$0.255382\pi$
$110$		0			0
$111$	26.1648	+	15.1062i	2.48345	+	1.43382i
$112$		0			0
$113$	1.88546	−	1.08857i	0.177369	−	0.102404i	−0.408687	−	0.912675i	$-0.634013\pi$
$113$	1.88546	−	1.08857i	0.177369	−	0.102404i	0.586056	+	0.810270i	$0.300680\pi$
$114$		0			0
$115$	−9.92248	+	5.72875i	−0.925276	+	0.534208i
$116$		0			0
$117$	39.9529			3.69365
$118$		0			0
$119$	−1.36479	−	0.787960i	−0.125110	−	0.0722322i
$120$		0			0
$121$	8.76504	+	15.1815i	0.796821	+	1.38014i
$122$		0			0
$123$	4.56112	−	2.63337i	0.411263	−	0.237443i
$124$		0			0
$125$	−4.45838			−0.398770
$126$		0			0
$127$	−7.76729	+	13.4533i	−0.689235	+	1.19379i	0.282850	+	0.959164i	$0.408720\pi$
$127$	−7.76729	+	13.4533i	−0.689235	+	1.19379i	−0.972086	+	0.234626i	$0.924613\pi$
$128$		0			0
$129$	17.9129	−	31.0261i	1.57715	−	2.73170i
$130$		0			0
$131$		−	2.47705i		−	0.216421i	−0.994128	−	0.108210i	$-0.965488\pi$
$131$		−	2.47705i		−	0.216421i	0.994128	−	0.108210i	$-0.0345120\pi$
$132$		0			0
$133$	0.694749	−	0.401113i	0.0602424	−	0.0347809i
$134$		0			0
$135$	19.8793	−	34.4320i	1.71094	−	2.96343i
$136$		0			0
$137$			21.7591i			1.85900i	0.368819	+	0.929501i	$0.379762\pi$
$137$			21.7591i			1.85900i	−0.368819	+	0.929501i	$0.620238\pi$
$138$		0			0
$139$	−1.56919	+	2.71791i	−0.133097	+	0.230530i	−0.924869	−	0.380286i	$-0.875825\pi$
$139$	−1.56919	+	2.71791i	−0.133097	+	0.230530i	0.791772	+	0.610817i	$0.209159\pi$
$140$		0			0
$141$	3.63971			0.306519
$142$		0			0
$143$		−	29.3759i		−	2.45654i
$144$		0			0
$145$	−13.1750	+	7.60660i	−1.09413	+	0.631694i
$146$		0			0
$147$	−10.9693	+	18.9993i	−0.904730	+	1.56704i
$148$		0			0
$149$	2.04383	+	1.18001i	0.167437	+	0.0966698i	0.581377	−	0.813634i	$-0.302514\pi$
$149$	2.04383	+	1.18001i	0.167437	+	0.0966698i	−0.413940	+	0.910304i	$0.635848\pi$
$150$		0			0
$151$	−10.4028	−	6.00605i	−0.846567	−	0.488766i	0.0129240	−	0.999916i	$-0.495886\pi$
$151$	−10.4028	−	6.00605i	−0.846567	−	0.488766i	−0.859491	+	0.511151i	$0.829219\pi$
$152$		0			0
$153$	−25.3960	−	14.6624i	−2.05314	−	1.18538i
$154$		0			0
$155$	15.2891	−	8.82715i	1.22805	−	0.709014i
$156$		0			0
$157$			19.7842i			1.57895i	0.613783	+	0.789475i	$0.289647\pi$
$157$			19.7842i			1.57895i	−0.613783	+	0.789475i	$0.710353\pi$
$158$		0			0
$159$		−	25.0330i		−	1.98524i
$160$		0			0
$161$	−1.33120	+	0.768566i	−0.104913	+	0.0605715i
$162$		0			0
$163$	20.1216	+	11.6172i	1.57605	+	0.909931i	0.995403	+	0.0957726i	$0.0305322\pi$
$163$	20.1216	+	11.6172i	1.57605	+	0.909931i	0.580643	+	0.814158i	$0.302801\pi$
$164$		0			0
$165$	−43.1261	−	24.8988i	−3.35736	−	1.93837i
$166$		0			0
$167$	11.4676	+	6.62083i	0.887391	+	0.512335i	0.873088	−	0.487562i	$-0.162114\pi$
$167$	11.4676	+	6.62083i	0.887391	+	0.512335i	0.0143026	+	0.999898i	$0.495447\pi$
$168$		0			0
$169$	−8.62341	+	14.9362i	−0.663339	+	1.14894i
$170$		0			0
$171$	12.9279	−	7.46392i	0.988620	−	0.570780i
$172$		0			0
$173$		−	1.53473i		−	0.116683i	−0.998297	−	0.0583417i	$-0.981419\pi$
$173$		−	1.53473i		−	0.116683i	0.998297	−	0.0583417i	$-0.0185813\pi$
$174$		0			0
$175$	1.35386			0.102342
$176$		0			0
$177$	−10.9385	+	18.9460i	−0.822188	+	1.42407i
$178$		0			0
$179$			7.49569i			0.560254i	0.959963	+	0.280127i	$0.0903766\pi$
$179$			7.49569i			0.560254i	−0.959963	+	0.280127i	$0.909623\pi$
$180$		0			0
$181$	−7.75853	+	13.4382i	−0.576687	+	0.998852i	0.419169	+	0.907908i	$0.362322\pi$
$181$	−7.75853	+	13.4382i	−0.576687	+	0.998852i	−0.995856	+	0.0909434i	$0.971012\pi$
$182$		0			0
$183$	−29.4701	+	17.0146i	−2.17849	+	1.25775i
$184$		0			0
$185$			27.4413i			2.01752i
$186$		0			0
$187$	−10.7807	+	18.6727i	−0.788362	+	1.36548i
$188$		0			0
$189$	2.66700	−	4.61938i	0.193996	−	0.336010i
$190$		0			0
$191$	13.6808			0.989909			0.494954	−	0.868919i	$-0.335185\pi$
$191$	13.6808			0.989909			0.494954	+	0.868919i	$0.335185\pi$
$192$		0			0
$193$	−2.40819	+	1.39037i	−0.173345	+	0.100081i	−0.584162	−	0.811637i	$-0.698577\pi$
$193$	−2.40819	+	1.39037i	−0.173345	+	0.100081i	0.410817	+	0.911718i	$0.365243\pi$
$194$		0			0
$195$	25.6370	+	44.4046i	1.83591	+	3.17988i
$196$		0			0
$197$	−3.75802	−	2.16969i	−0.267748	−	0.154584i	0.360116	−	0.932908i	$-0.382737\pi$
$197$	−3.75802	−	2.16969i	−0.267748	−	0.154584i	−0.627864	+	0.778323i	$0.716071\pi$
$198$		0			0
$199$	−0.261147			−0.0185122			−0.00925610	−	0.999957i	$-0.502946\pi$
$199$	−0.261147			−0.0185122			−0.00925610	+	0.999957i	$0.502946\pi$
$200$		0			0
$201$	−19.4995	+	11.2580i	−1.37539	+	0.794081i
$202$		0			0
$203$	−1.76755	+	1.02050i	−0.124058	+	0.0716249i
$204$		0			0
$205$	4.14276	+	2.39182i	0.289343	+	0.167052i
$206$		0			0
$207$	−24.7709	+	14.3015i	−1.72170	+	0.994022i
$208$		0			0
$209$	−5.48794	−	9.50539i	−0.379609	−	0.657502i
$210$		0			0
$211$	11.4634	−	19.8552i	0.789175	−	1.36689i	−0.137299	−	0.990530i	$-0.543842\pi$
$211$	11.4634	−	19.8552i	0.789175	−	1.36689i	0.926473	−	0.376361i	$-0.122825\pi$
$212$		0			0
$213$	3.88164	+	6.72320i	0.265966	+	0.460666i
$214$		0			0
$215$	32.5398			2.21919
$216$		0			0
$217$	2.05117	−	1.18425i	0.139243	−	0.0803918i
$218$		0			0
$219$	27.8446			1.88157
$220$		0			0
$221$	19.2263	−	11.1003i	1.29330	−	0.746687i
$222$		0			0
$223$		−	14.6107i		−	0.978407i	−0.872170	−	0.489204i	$-0.837287\pi$
$223$		−	14.6107i		−	0.978407i	0.872170	−	0.489204i	$-0.162713\pi$
$224$		0			0
$225$	25.1927			1.67951
$226$		0			0
$227$	−17.5626			−1.16567			−0.582834	−	0.812591i	$-0.698056\pi$
$227$	−17.5626			−1.16567			−0.582834	+	0.812591i	$0.698056\pi$
$228$		0			0
$229$		−	2.01062i		−	0.132866i	−0.997791	−	0.0664328i	$-0.978838\pi$
$229$		−	2.01062i		−	0.132866i	0.997791	−	0.0664328i	$-0.0211618\pi$
$230$		0			0
$231$	−5.78577	−	3.34042i	−0.380676	−	0.219783i
$232$		0			0
$233$	14.3326	+	8.27492i	0.938958	+	0.542108i	0.889634	−	0.456675i	$-0.150960\pi$
$233$	14.3326	+	8.27492i	0.938958	+	0.542108i	0.0493246	+	0.998783i	$0.484293\pi$
$234$		0			0
$235$	1.65293	+	2.86296i	0.107825	+	0.186759i
$236$		0			0
$237$	27.7954	−	6.18985i	1.80551	−	0.402074i
$238$		0			0
$239$	−15.2392	+	8.79836i	−0.985742	+	0.569119i	−0.903999	−	0.427535i	$-0.859382\pi$
$239$	−15.2392	+	8.79836i	−0.985742	+	0.569119i	−0.0817434	+	0.996653i	$0.526049\pi$
$240$		0			0
$241$	−13.2977	+	23.0323i	−0.856581	+	1.48364i	0.0185899	+	0.999827i	$0.494082\pi$
$241$	−13.2977	+	23.0323i	−0.856581	+	1.48364i	−0.875171	+	0.483814i	$0.839251\pi$
$242$		0			0
$243$	14.7159	−	25.4887i	0.944025	−	1.63510i
$244$		0			0
$245$	−19.9262			−1.27304
$246$		0			0
$247$			11.3013i			0.719084i
$248$		0			0
$249$		−	18.7712i		−	1.18958i
$250$		0			0
$251$	2.75669			0.174001			0.0870005	−	0.996208i	$-0.472272\pi$
$251$	2.75669			0.174001			0.0870005	+	0.996208i	$0.472272\pi$
$252$		0			0
$253$	10.5153	+	18.2131i	0.661094	+	1.14505i
$254$		0			0
$255$		−	37.6342i		−	2.35675i
$256$		0			0
$257$	2.27509	+	3.94057i	0.141916	+	0.245806i	0.928218	−	0.372036i	$-0.121340\pi$
$257$	2.27509	+	3.94057i	0.141916	+	0.245806i	−0.786302	+	0.617842i	$0.788007\pi$
$258$		0			0
$259$			3.68151i			0.228758i
$260$		0			0
$261$	−32.8907	+	18.9894i	−2.03588	+	1.17542i
$262$		0			0
$263$	−7.22556	−	4.17168i	−0.445547	−	0.257237i	0.260401	−	0.965501i	$-0.416145\pi$
$263$	−7.22556	−	4.17168i	−0.445547	−	0.257237i	−0.705948	+	0.708264i	$0.749479\pi$
$264$		0			0
$265$	19.6907	−	11.3684i	1.20959	−	0.698356i
$266$		0			0
$267$	9.39176	+	16.2670i	0.574766	+	0.995525i
$268$		0			0
$269$	−6.34783	+	10.9948i	−0.387034	+	0.670362i	−0.992049	−	0.125852i	$-0.959834\pi$
$269$	−6.34783	+	10.9948i	−0.387034	+	0.670362i	0.605015	+	0.796214i	$0.293167\pi$
$270$		0			0
$271$	2.83603	+	4.91216i	0.172277	+	0.298392i	0.939216	−	0.343328i	$-0.111554\pi$
$271$	2.83603	+	4.91216i	0.172277	+	0.298392i	−0.766939	+	0.641720i	$0.778221\pi$
$272$		0			0
$273$	3.43945	+	5.95730i	0.208165	+	0.360552i
$274$		0			0
$275$		−	18.5232i		−	1.11699i
$276$		0			0
$277$	8.09536	−	14.0216i	0.486403	−	0.842475i	−0.513475	−	0.858105i	$-0.671642\pi$
$277$	8.09536	−	14.0216i	0.486403	−	0.842475i	0.999878	+	0.0156300i	$0.00497537\pi$
$278$		0			0
$279$	38.1683	−	22.0365i	2.28507	−	1.31929i
$280$		0			0
$281$	7.58390	+	13.1357i	0.452418	+	0.783611i	0.998536	−	0.0540978i	$-0.0172283\pi$
$281$	7.58390	+	13.1357i	0.452418	+	0.783611i	−0.546118	+	0.837708i	$0.683895\pi$
$282$		0			0
$283$		−	17.3501i		−	1.03136i	−0.856782	−	0.515679i	$-0.827540\pi$
$283$		−	17.3501i		−	1.03136i	0.856782	−	0.515679i	$-0.172460\pi$
$284$		0			0
$285$	16.5911	+	9.57890i	0.982775	+	0.567405i
$286$		0			0
$287$	0.555790	+	0.320886i	0.0328073	+	0.0189413i
$288$		0			0
$289$	0.705159			0.0414800
$290$		0			0
$291$	16.5547	+	28.6736i	0.970453	+	1.68087i
$292$		0			0
$293$	−2.47971	−	1.43166i	−0.144866	−	0.0836387i	0.425815	−	0.904810i	$-0.359987\pi$
$293$	−2.47971	−	1.43166i	−0.144866	−	0.0836387i	−0.570681	+	0.821172i	$0.693321\pi$
$294$		0			0
$295$	−19.8703			−1.15690
$296$		0			0
$297$	−63.2013	−	36.4893i	−3.66731	−	2.11732i
$298$		0			0
$299$		−	21.6542i		−	1.25229i
$300$		0			0
$301$	4.36552			0.251624
$302$		0			0
$303$	−13.4084	−	23.2240i	−0.770291	−	1.33418i
$304$		0			0
$305$	−26.7670	−	15.4539i	−1.53267	−	0.884889i
$306$		0			0
$307$	5.29065	−	9.16368i	0.301953	−	0.522999i	−0.674625	−	0.738161i	$-0.735695\pi$
$307$	5.29065	−	9.16368i	0.301953	−	0.522999i	0.976578	+	0.215162i	$0.0690280\pi$
$308$		0			0
$309$	−13.5694	+	23.5028i	−0.771934	+	1.33703i
$310$		0			0
$311$	11.8213	−	20.4751i	0.670325	−	1.16104i	−0.307486	−	0.951552i	$-0.599488\pi$
$311$	11.8213	−	20.4751i	0.670325	−	1.16104i	0.977812	−	0.209485i	$-0.0671788\pi$
$312$		0			0
$313$	−5.87629	−	10.1780i	−0.332148	−	0.575296i	0.650785	−	0.759262i	$-0.274440\pi$
$313$	−5.87629	−	10.1780i	−0.332148	−	0.575296i	−0.982933	+	0.183966i	$0.941107\pi$
$314$		0			0
$315$	8.25288			0.464997
$316$		0			0
$317$	34.1531			1.91823			0.959114	−	0.283021i	$-0.0913367\pi$
$317$	34.1531			1.91823			0.959114	+	0.283021i	$0.0913367\pi$
$318$		0			0
$319$	13.9622	+	24.1833i	0.781734	+	1.35400i
$320$		0			0
$321$	29.7910	−	51.5995i	1.66277	−	2.88001i
$322$		0			0
$323$	4.14747	−	7.18363i	0.230771	−	0.399708i
$324$		0			0
$325$	−9.53620	+	16.5172i	−0.528973	+	0.916209i
$326$		0			0
$327$	14.0465	+	8.10975i	0.776773	+	0.448470i
$328$		0			0
$329$	0.221756	+	0.384093i	0.0122258	+	0.0211757i
$330$		0			0
$331$	−14.3014			−0.786074			−0.393037	−	0.919523i	$-0.628576\pi$
$331$	−14.3014			−0.786074			−0.393037	+	0.919523i	$0.628576\pi$
$332$		0			0
$333$			68.5055i			3.75408i
$334$		0			0
$335$	−17.7109	−	10.2254i	−0.967650	−	0.558673i
$336$		0			0
$337$	29.6553			1.61543			0.807713	−	0.589576i	$-0.200705\pi$
$337$	29.6553			1.61543			0.807713	+	0.589576i	$0.200705\pi$
$338$		0			0
$339$	6.04071	+	3.48760i	0.328086	+	0.189421i
$340$		0			0
$341$	−16.2026	−	28.0637i	−0.877419	−	1.51973i
$342$		0			0
$343$	−5.40609			−0.291901
$344$		0			0
$345$	−31.7900	−	18.3540i	−1.71152	−	0.988144i
$346$		0			0
$347$	−24.4051	−	14.0903i	−1.31013	−	0.756407i	−0.328016	−	0.944672i	$-0.606380\pi$
$347$	−24.4051	−	14.0903i	−1.31013	−	0.756407i	−0.982118	+	0.188265i	$0.939713\pi$
$348$		0			0
$349$		−	21.7093i		−	1.16207i	−0.813877	−	0.581037i	$-0.802647\pi$
$349$		−	21.7093i		−	1.16207i	0.813877	−	0.581037i	$-0.197353\pi$
$350$		0			0
$351$	37.5711	+	65.0750i	2.00540	+	3.47345i
$352$		0			0
$353$	24.2928	−	14.0254i	1.29297	−	0.746498i	0.313793	−	0.949492i	$-0.398400\pi$
$353$	24.2928	−	14.0254i	1.29297	−	0.746498i	0.979180	+	0.202993i	$0.0650670\pi$
$354$		0			0
$355$	−3.52560	+	6.10651i	−0.187119	+	0.324100i
$356$		0			0
$357$		−	5.04899i		−	0.267221i
$358$		0			0
$359$	−4.64332	−	8.04247i	−0.245065	−	0.424465i	0.717085	−	0.696986i	$-0.245476\pi$
$359$	−4.64332	−	8.04247i	−0.245065	−	0.424465i	−0.962150	+	0.272521i	$0.912143\pi$
$360$		0			0
$361$	−7.38872	−	12.7976i	−0.388880	−	0.673560i
$362$		0			0
$363$	−28.0817	+	48.6390i	−1.47391	+	2.55288i
$364$		0			0
$365$	12.6453	+	21.9023i	0.661885	+	1.14642i
$366$		0			0
$367$	11.3331	−	6.54315i	0.591582	−	0.341550i	−0.174141	−	0.984721i	$-0.555715\pi$
$367$	11.3331	−	6.54315i	0.591582	−	0.341550i	0.765723	+	0.643171i	$0.222382\pi$
$368$		0			0
$369$	10.3421	+	5.97104i	0.538391	+	0.310840i
$370$		0			0
$371$	2.64169	−	1.52518i	0.137150	−	0.0791834i
$372$		0			0
$373$		−	9.20691i		−	0.476716i	−0.971177	−	0.238358i	$-0.923391\pi$
$373$		−	9.20691i		−	0.476716i	0.971177	−	0.238358i	$-0.0766091\pi$
$374$		0			0
$375$	−7.14195	−	12.3702i	−0.368809	−	0.638796i
$376$		0			0
$377$		−	28.7523i		−	1.48082i
$378$		0			0
$379$	−2.24066	−	3.88093i	−0.115095	−	0.199350i	0.802723	−	0.596352i	$-0.203384\pi$
$379$	−2.24066	−	3.88093i	−0.115095	−	0.199350i	−0.917818	+	0.397002i	$0.870050\pi$
$380$		0			0
$381$	−49.7702			−2.54980
$382$		0			0
$383$			21.0667i			1.07646i	0.842798	+	0.538229i	$0.180907\pi$
$383$			21.0667i			1.07646i	−0.842798	+	0.538229i	$0.819093\pi$
$384$		0			0
$385$		−	6.06804i		−	0.309256i
$386$		0			0
$387$	81.2336			4.12934
$388$		0			0
$389$	−3.46359	+	5.99912i	−0.175611	+	0.304168i	−0.940373	−	0.340146i	$-0.889523\pi$
$389$	−3.46359	+	5.99912i	−0.175611	+	0.304168i	0.764761	+	0.644314i	$0.222857\pi$
$390$		0			0
$391$	−7.94689	+	13.7644i	−0.401891	+	0.696096i
$392$		0			0
$393$	6.87283	−	3.96803i	0.346688	−	0.200161i
$394$		0			0
$395$	17.4918	+	19.0525i	0.880109	+	0.958638i
$396$		0			0
$397$	6.13492	+	10.6260i	0.307903	+	0.533303i	0.977903	−	0.209057i	$-0.0670395\pi$
$397$	6.13492	+	10.6260i	0.307903	+	0.533303i	−0.670001	+	0.742360i	$0.733706\pi$
$398$		0			0
$399$	2.22586	+	1.28510i	0.111432	+	0.0643355i
$400$		0			0
$401$	33.1585	+	19.1441i	1.65586	+	0.956009i	0.974597	+	0.223966i	$0.0719004\pi$
$401$	33.1585	+	19.1441i	1.65586	+	0.956009i	0.681259	+	0.732043i	$0.261433\pi$
$402$		0			0
$403$			33.3659i			1.66207i
$404$		0			0
$405$	63.9613			3.17826
$406$		0			0
$407$	50.3695			2.49672
$408$		0			0
$409$		−	13.6418i		−	0.674543i	−0.941407	−	0.337272i	$-0.890496\pi$
$409$		−	13.6418i		−	0.674543i	0.941407	−	0.337272i	$-0.109504\pi$
$410$		0			0
$411$	−60.3728	+	34.8562i	−2.97797	+	1.71933i
$412$		0			0
$413$	−2.66579			−0.131175
$414$		0			0
$415$	14.7653	−	8.52473i	0.724799	−	0.418463i
$416$		0			0
$417$	−10.0548			−0.492387
$418$		0			0
$419$	15.6863	+	27.1695i	0.766326	+	1.32732i	0.939543	+	0.342432i	$0.111251\pi$
$419$	15.6863	+	27.1695i	0.766326	+	1.32732i	−0.173216	+	0.984884i	$0.555416\pi$
$420$		0			0
$421$	14.6308	−	25.3413i	0.713061	−	1.23506i	−0.250641	−	0.968080i	$-0.580642\pi$
$421$	14.6308	−	25.3413i	0.713061	−	1.23506i	0.963703	−	0.266978i	$-0.0860252\pi$
$422$		0			0
$423$	4.12644	+	7.14721i	0.200634	+	0.347509i
$424$		0			0
$425$	12.1233	−	6.99940i	0.588067	−	0.339521i
$426$		0			0
$427$	−3.59105	−	2.07329i	−0.173783	−	0.100334i
$428$		0			0
$429$	81.5064	−	47.0578i	3.93517	−	2.27197i
$430$		0			0
$431$	0.940875	−	0.543214i	0.0453204	−	0.0261657i	−0.477169	−	0.878812i	$-0.658337\pi$
$431$	0.940875	−	0.543214i	0.0453204	−	0.0261657i	0.522489	+	0.852646i	$0.325004\pi$
$432$		0			0
$433$	−26.8383			−1.28977			−0.644884	−	0.764280i	$-0.723094\pi$
$433$	−26.8383			−1.28977			−0.644884	+	0.764280i	$0.723094\pi$
$434$		0			0
$435$	−42.2106	−	24.3703i	−2.02384	−	1.16847i
$436$		0			0
$437$	−4.04539	−	7.00682i	−0.193517	−	0.335181i
$438$		0			0
$439$	−8.15394	+	4.70768i	−0.389167	+	0.224685i	−0.681799	−	0.731540i	$-0.738802\pi$
$439$	−8.15394	+	4.70768i	−0.389167	+	0.224685i	0.292632	+	0.956225i	$0.405469\pi$
$440$		0			0
$441$	−49.7447			−2.36879
$442$		0			0
$443$	15.3494	−	26.5859i	0.729272	−	1.26314i	−0.227920	−	0.973680i	$-0.573192\pi$
$443$	15.3494	−	26.5859i	0.729272	−	1.26314i	0.957191	−	0.289456i	$-0.0934742\pi$
$444$		0			0
$445$	−8.53031	+	14.7749i	−0.404375	+	0.700399i
$446$		0			0
$447$			7.56109i			0.357627i
$448$		0			0
$449$	−5.41358	+	3.12553i	−0.255483	+	0.147503i	−0.622272	−	0.782801i	$-0.713790\pi$
$449$	−5.41358	+	3.12553i	−0.255483	+	0.147503i	0.366790	+	0.930304i	$0.380457\pi$
$450$		0			0
$451$	4.39028	−	7.60419i	0.206730	−	0.358067i
$452$		0			0
$453$		−	38.4848i		−	1.80817i
$454$		0			0
$455$	−3.12397	+	5.41087i	−0.146454	+	0.253666i
$456$		0			0
$457$	18.6901			0.874288			0.437144	−	0.899391i	$-0.355990\pi$
$457$	18.6901			0.874288			0.437144	+	0.899391i	$0.355990\pi$
$458$		0			0
$459$		−	55.1530i		−	2.57432i
$460$		0			0
$461$	−15.1386	+	8.74026i	−0.705074	+	0.407075i	−0.809234	−	0.587486i	$-0.800118\pi$
$461$	−15.1386	+	8.74026i	−0.705074	+	0.407075i	0.104161	+	0.994561i	$0.466784\pi$
$462$		0			0
$463$	−6.11709	+	10.5951i	−0.284285	+	0.492397i	−0.972436	−	0.233171i	$-0.925090\pi$
$463$	−6.11709	+	10.5951i	−0.284285	+	0.492397i	0.688150	+	0.725568i	$0.258423\pi$
$464$		0			0
$465$	48.9836	+	28.2807i	2.27156	+	1.31149i
$466$		0			0
$467$	0.833852	+	0.481425i	0.0385861	+	0.0222777i	0.519169	−	0.854672i	$-0.326242\pi$
$467$	0.833852	+	0.481425i	0.0385861	+	0.0222777i	−0.480583	+	0.876949i	$0.659575\pi$
$468$		0			0
$469$	−2.37609	−	1.37183i	−0.109717	−	0.0633454i
$470$		0			0
$471$	−54.8933	+	31.6926i	−2.52935	+	1.46032i
$472$		0			0
$473$		−	59.7280i		−	2.74630i
$474$		0			0
$475$			7.12613i			0.326969i
$476$		0			0
$477$	49.1566	−	28.3806i	2.25073	−	1.29946i
$478$		0			0
$479$	2.96154	+	1.70985i	0.135316	+	0.0781249i	0.566130	−	0.824316i	$-0.308440\pi$
$479$	2.96154	+	1.70985i	0.135316	+	0.0781249i	−0.430814	+	0.902441i	$0.641773\pi$
$480$		0			0
$481$	−44.9145	−	25.9314i	−2.04793	−	1.18237i
$482$		0			0
$483$	−4.26493	−	2.46236i	−0.194061	−	0.112041i
$484$		0			0
$485$	−15.0362	+	26.0435i	−0.682759	+	1.18257i
$486$		0			0
$487$	18.5321	−	10.6995i	0.839768	−	0.484840i	−0.0174174	−	0.999848i	$-0.505544\pi$
$487$	18.5321	−	10.6995i	0.839768	−	0.484840i	0.857185	+	0.515008i	$0.172211\pi$
$488$		0			0
$489$			74.4393i			3.36626i
$490$		0			0
$491$	−6.56262			−0.296167			−0.148084	−	0.988975i	$-0.547310\pi$
$491$	−6.56262			−0.296167			−0.148084	+	0.988975i	$0.547310\pi$
$492$		0			0
$493$	−10.5518	+	18.2763i	−0.475231	+	0.823124i
$494$		0			0
$495$		−	112.914i		−	5.07511i
$496$		0			0
$497$	−0.472992	+	0.819247i	−0.0212166	+	0.0367483i
$498$		0			0
$499$	21.5059	−	12.4165i	0.962738	−	0.555837i	0.0657235	−	0.997838i	$-0.479064\pi$
$499$	21.5059	−	12.4165i	0.962738	−	0.555837i	0.897015	+	0.442001i	$0.145731\pi$
$500$		0			0
$501$			42.4241i			1.89537i
$502$		0			0
$503$	18.4878	−	32.0217i	0.824328	−	1.42778i	−0.0781037	−	0.996945i	$-0.524887\pi$
$503$	18.4878	−	32.0217i	0.824328	−	1.42778i	0.902432	−	0.430833i	$-0.141780\pi$
$504$		0			0
$505$	12.1785	−	21.0938i	0.541936	−	0.938661i
$506$		0			0
$507$	−55.2559			−2.45400
$508$		0			0
$509$	−5.64391	+	3.25851i	−0.250162	+	0.144431i	−0.619838	−	0.784730i	$-0.712802\pi$
$509$	−5.64391	+	3.25851i	−0.250162	+	0.144431i	0.369677	+	0.929161i	$0.379469\pi$
$510$		0			0
$511$	1.69649	+	2.93840i	0.0750482	+	0.129987i
$512$		0			0
$513$	24.3143	+	14.0379i	1.07350	+	0.619788i
$514$		0			0
$515$	−24.6494			−1.08618
$516$		0			0
$517$	5.25507	−	3.03402i	0.231118	−	0.133436i
$518$		0			0
$519$	4.25827	−	2.45851i	0.186917	−	0.107917i
$520$		0			0
$521$	−23.9156	−	13.8077i	−1.04776	−	0.604926i	−0.125740	−	0.992063i	$-0.540130\pi$
$521$	−23.9156	−	13.8077i	−1.04776	−	0.604926i	−0.922022	+	0.387138i	$0.873464\pi$
$522$		0			0
$523$	23.5394	−	13.5905i	1.02930	−	0.594269i	0.112519	−	0.993650i	$-0.464108\pi$
$523$	23.5394	−	13.5905i	1.02930	−	0.594269i	0.916785	+	0.399381i	$0.130775\pi$
$524$		0			0
$525$	2.16878	+	3.75643i	0.0946532	+	0.163944i
$526$		0			0
$527$	12.2450	−	21.2089i	0.533399	−	0.923875i
$528$		0			0
$529$	−3.74871	−	6.49296i	−0.162987	−	0.282302i
$530$		0			0
$531$	−49.6051			−2.15268
$532$		0			0
$533$	−7.82963	+	4.52044i	−0.339139	+	0.195802i
$534$		0			0
$535$	54.1169			2.33968
$536$		0			0
$537$	−20.7976	+	12.0075i	−0.897481	+	0.518161i
$538$		0			0
$539$			36.5754i			1.57541i
$540$		0			0
$541$	−21.5630			−0.927067			−0.463533	−	0.886079i	$-0.653419\pi$
$541$	−21.5630			−0.927067			−0.463533	+	0.886079i	$0.653419\pi$
$542$		0			0
$543$	−49.7141			−2.13344
$544$		0			0
$545$			14.7318i			0.631040i
$546$		0			0
$547$	−14.8376	−	8.56648i	−0.634409	−	0.366276i	0.148048	−	0.988980i	$-0.452701\pi$
$547$	−14.8376	−	8.56648i	−0.634409	−	0.366276i	−0.782458	+	0.622704i	$0.786034\pi$
$548$		0			0
$549$	−66.8222	−	38.5798i	−2.85190	−	1.64655i
$550$		0			0
$551$	−5.37145	−	9.30362i	−0.228831	−	0.396347i
$552$		0			0
$553$	2.34669	+	2.55608i	0.0997916	+	0.108696i
$554$		0			0
$555$	−76.1386	+	43.9586i	−3.23190	+	1.86594i
$556$		0			0
$557$	−9.63282	+	16.6845i	−0.408156	+	0.706946i	−0.994683	−	0.102983i	$-0.967161\pi$
$557$	−9.63282	+	16.6845i	−0.408156	+	0.706946i	0.586528	+	0.809929i	$0.300495\pi$
$558$		0			0
$559$	−30.7494	+	53.2595i	−1.30056	+	2.25264i
$560$		0			0
$561$	−69.0791			−2.91652
$562$		0			0
$563$			3.74425i			0.157801i	0.996882	+	0.0789006i	$0.0251410\pi$
$563$			3.74425i			0.157801i	−0.996882	+	0.0789006i	$0.974859\pi$
$564$		0			0
$565$			6.33541i			0.266533i
$566$		0			0
$567$	8.58101			0.360369
$568$		0			0
$569$	7.19461	+	12.4614i	0.301614	+	0.522410i	0.976502	−	0.215510i	$-0.0691414\pi$
$569$	7.19461	+	12.4614i	0.301614	+	0.522410i	−0.674888	+	0.737920i	$0.735808\pi$
$570$		0			0
$571$		−	13.9037i		−	0.581851i	−0.956746	−	0.290926i	$-0.906037\pi$
$571$		−	13.9037i		−	0.581851i	0.956746	−	0.290926i	$-0.0939632\pi$
$572$		0			0
$573$	21.9155	+	37.9588i	0.915534	+	1.58575i
$574$		0			0
$575$		−	13.6542i		−	0.569421i
$576$		0			0
$577$	28.7705	−	16.6107i	1.19773	−	0.691510i	0.237682	−	0.971343i	$-0.423612\pi$
$577$	28.7705	−	16.6107i	1.19773	−	0.691510i	0.960049	+	0.279832i	$0.0902789\pi$
$578$		0			0
$579$	−7.71544	−	4.45451i	−0.320643	−	0.185123i
$580$		0			0
$581$	1.98090	−	1.14367i	0.0821816	−	0.0474476i
$582$		0			0
$583$	−20.8672	−	36.1430i	−0.864230	−	1.49689i
$584$		0			0
$585$	−58.1308	+	100.686i	−2.40341	+	4.16283i
$586$		0			0
$587$	−17.2798	−	29.9295i	−0.713214	−	1.23532i	−0.963644	−	0.267188i	$-0.913905\pi$
$587$	−17.2798	−	29.9295i	−0.713214	−	1.23532i	0.250430	−	0.968135i	$-0.419428\pi$
$588$		0			0
$589$	6.23334	+	10.7965i	0.256840	+	0.444860i
$590$		0			0
$591$		−	13.9027i		−	0.571880i
$592$		0			0
$593$	10.6761	−	18.4915i	0.438413	−	0.759354i	−0.559154	−	0.829064i	$-0.688874\pi$
$593$	10.6761	−	18.4915i	0.438413	−	0.759354i	0.997567	+	0.0697097i	$0.0222073\pi$
$594$		0			0
$595$	3.97148	−	2.29294i	0.162815	−	0.0940012i
$596$		0			0
$597$	−0.418335	−	0.724578i	−0.0171213	−	0.0296550i
$598$		0			0
$599$			18.1660i			0.742242i	0.928585	+	0.371121i	$0.121026\pi$
$599$			18.1660i			0.742242i	−0.928585	+	0.371121i	$0.878974\pi$
$600$		0			0
$601$	11.7458	+	6.78143i	0.479120	+	0.276620i	0.720050	−	0.693922i	$-0.244119\pi$
$601$	11.7458	+	6.78143i	0.479120	+	0.276620i	−0.240930	+	0.970543i	$0.577452\pi$
$602$		0			0
$603$	−44.2142	−	25.5271i	−1.80054	−	1.03954i
$604$		0			0
$605$	−51.0119			−2.07393
$606$		0			0
$607$	12.6617	+	21.9307i	0.513924	+	0.890142i	0.999870	+	0.0161528i	$0.00514182\pi$
$607$	12.6617	+	21.9307i	0.513924	+	0.890142i	−0.485946	+	0.873989i	$0.661525\pi$
$608$		0			0
$609$	−5.66295	−	3.26951i	−0.229474	−	0.132487i
$610$		0			0
$611$	−6.24794			−0.252764
$612$		0			0
$613$	−2.01933	−	1.16586i	−0.0815598	−	0.0470886i	0.458665	−	0.888609i	$-0.348328\pi$
$613$	−2.01933	−	1.16586i	−0.0815598	−	0.0470886i	−0.540225	+	0.841520i	$0.681661\pi$
$614$		0			0
$615$			15.3260i			0.618004i
$616$		0			0
$617$	2.27330			0.0915196			0.0457598	−	0.998952i	$-0.485429\pi$
$617$	2.27330			0.0915196			0.0457598	+	0.998952i	$0.485429\pi$
$618$		0			0
$619$	−3.59454	−	6.22593i	−0.144477	−	0.250241i	0.784701	−	0.619875i	$-0.212817\pi$
$619$	−3.59454	−	6.22593i	−0.144477	−	0.250241i	−0.929178	+	0.369634i	$0.879483\pi$
$620$		0			0
$621$	−46.5882	−	26.8977i	−1.86952	−	1.07937i
$622$		0			0
$623$	−1.14442	+	1.98220i	−0.0458503	+	0.0794150i
$624$		0			0
$625$	15.1566	−	26.2520i	0.606264	−	1.05008i
$626$		0			0
$627$	17.5825	−	30.4537i	0.702176	−	1.21620i
$628$		0			0
$629$	19.0332	+	32.9664i	0.758903	+	1.31446i
$630$		0			0
$631$	−38.3375			−1.52619			−0.763095	−	0.646286i	$-0.776321\pi$
$631$	−38.3375			−1.52619			−0.763095	+	0.646286i	$0.776321\pi$
$632$		0			0
$633$	73.4538			2.91953
$634$		0			0
$635$	−22.6025	−	39.1487i	−0.896954	−	1.55357i
$636$		0			0
$637$	18.8299	−	32.6143i	0.746067	−	1.29223i
$638$		0			0
$639$	−8.80145	+	15.2446i	−0.348180	+	0.603065i
$640$		0			0
$641$	10.0812	−	17.4611i	0.398182	−	0.689672i	−0.595320	−	0.803489i	$-0.702975\pi$
$641$	10.0812	−	17.4611i	0.398182	−	0.689672i	0.993502	+	0.113817i	$0.0363078\pi$
$642$		0			0
$643$	15.7713	+	9.10555i	0.621959	+	0.359088i	0.777631	−	0.628721i	$-0.216421\pi$
$643$	15.7713	+	9.10555i	0.621959	+	0.359088i	−0.155672	+	0.987809i	$0.549754\pi$
$644$		0			0
$645$	52.1260	+	90.2849i	2.05246	+	3.55496i
$646$		0			0
$647$	16.1531			0.635044			0.317522	−	0.948251i	$-0.397149\pi$
$647$	16.1531			0.635044			0.317522	+	0.948251i	$0.397149\pi$
$648$		0			0
$649$			36.4728i			1.43168i
$650$		0			0
$651$	6.57162	+	3.79413i	0.257562	+	0.148704i
$652$		0			0
$653$	13.1793			0.515745			0.257873	−	0.966179i	$-0.416979\pi$
$653$	13.1793			0.515745			0.257873	+	0.966179i	$0.416979\pi$
$654$		0			0
$655$	6.24242	+	3.60406i	0.243912	+	0.140822i
$656$		0			0
$657$	31.5682	+	54.6778i	1.23159	+	2.13318i
$658$		0			0
$659$	−37.0528			−1.44337			−0.721686	−	0.692221i	$-0.756632\pi$
$659$	−37.0528			−1.44337			−0.721686	+	0.692221i	$0.756632\pi$
$660$		0			0
$661$	−3.26003	−	1.88218i	−0.126800	−	0.0732082i	0.435258	−	0.900306i	$-0.356657\pi$
$661$	−3.26003	−	1.88218i	−0.126800	−	0.0732082i	−0.562059	+	0.827097i	$0.689990\pi$
$662$		0			0
$663$	61.5979	+	35.5635i	2.39226	+	1.38117i
$664$		0			0
$665$			2.33445i			0.0905261i
$666$		0			0
$667$	10.2921	+	17.8265i	0.398513	+	0.690244i
$668$		0			0
$669$	40.5390	−	23.4052i	1.56733	−	0.904897i
$670$		0			0
$671$	−28.3663	+	49.1319i	−1.09507	+	1.89671i
$672$		0			0
$673$			2.16670i			0.0835201i	0.999128	+	0.0417600i	$0.0132965\pi$
$673$			2.16670i			0.0835201i	−0.999128	+	0.0417600i	$0.986703\pi$
$674$		0			0
$675$	23.6908	+	41.0336i	0.911858	+	1.57939i
$676$		0			0
$677$	3.53173	+	6.11714i	0.135736	+	0.235101i	0.925878	−	0.377822i	$-0.123327\pi$
$677$	3.53173	+	6.11714i	0.135736	+	0.235101i	−0.790143	+	0.612923i	$0.789994\pi$
$678$		0			0
$679$	−2.01725	+	3.49398i	−0.0774150	+	0.134087i
$680$		0			0
$681$	−28.1338	−	48.7291i	−1.07809	−	1.86730i
$682$		0			0
$683$	20.8918	−	12.0619i	0.799403	−	0.461535i	−0.0438596	−	0.999038i	$-0.513965\pi$
$683$	20.8918	−	12.0619i	0.799403	−	0.461535i	0.843262	+	0.537502i	$0.180632\pi$
$684$		0			0
$685$	−54.8351	−	31.6591i	−2.09514	−	1.20963i
$686$		0			0
$687$	5.57868	−	3.22085i	0.212840	−	0.122883i
$688$		0			0
$689$			42.9716i			1.63709i
$690$		0			0
$691$	−1.24544	−	2.15717i	−0.0473789	−	0.0820627i	0.841363	−	0.540470i	$-0.181753\pi$
$691$	−1.24544	−	2.15717i	−0.0473789	−	0.0820627i	−0.888742	+	0.458407i	$0.848420\pi$
$692$		0			0
$693$		−	15.1485i		−	0.575444i
$694$		0			0
$695$	−4.56628	−	7.90903i	−0.173209	−	0.300007i
$696$		0			0
$697$	6.63584			0.251350
$698$		0			0
$699$			53.0229i			2.00551i
$700$		0			0
$701$		−	34.6011i		−	1.30686i	−0.756985	−	0.653432i	$-0.773328\pi$
$701$		−	34.6011i		−	1.30686i	0.756985	−	0.653432i	$-0.226672\pi$
$702$		0			0
$703$	−19.3778			−0.730848
$704$		0			0
$705$	−5.29571	+	9.17245i	−0.199448	+	0.345454i
$706$		0			0
$707$	1.63386	−	2.82993i	0.0614477	−	0.106431i
$708$		0			0
$709$	−8.81822	+	5.09120i	−0.331175	+	0.191204i	−0.656363	−	0.754445i	$-0.727906\pi$
$709$	−8.81822	+	5.09120i	−0.331175	+	0.191204i	0.325188	+	0.945650i	$0.394573\pi$
$710$		0			0
$711$	43.6673	+	47.5636i	1.63765	+	1.78377i
$712$		0			0
$713$	−11.9436	−	20.6869i	−0.447291	−	0.774730i
$714$		0			0
$715$	74.0303	+	42.7414i	2.76858	+	1.59844i
$716$		0			0
$717$	−48.8239	−	28.1885i	−1.82336	−	1.05272i
$718$		0			0
$719$		−	5.85764i		−	0.218453i	−0.994017	−	0.109226i	$-0.965163\pi$
$719$		−	5.85764i		−	0.218453i	0.994017	−	0.109226i	$-0.0348374\pi$
$720$		0			0
$721$	−3.30696			−0.123157
$722$		0			0
$723$	−85.2073			−3.16889
$724$		0			0
$725$		−	18.1300i		−	0.673333i
$726$		0			0
$727$	−25.1381	+	14.5135i	−0.932319	+	0.538275i	−0.887544	−	0.460722i	$-0.847590\pi$
$727$	−25.1381	+	14.5135i	−0.932319	+	0.538275i	−0.0447750	+	0.998997i	$0.514257\pi$
$728$		0			0
$729$	28.3543			1.05016
$730$		0			0
$731$	39.0915	−	22.5695i	1.44585	−	0.834763i
$732$		0			0
$733$	−49.2849			−1.82038			−0.910189	−	0.414193i	$-0.864064\pi$
$733$	−49.2849			−1.82038			−0.910189	+	0.414193i	$0.864064\pi$
$734$		0			0
$735$	−31.9202	−	55.2874i	−1.17739	−	2.03931i
$736$		0			0
$737$	−18.7691	+	32.5091i	−0.691370	+	1.19749i
$738$		0			0
$739$	−6.87958	−	11.9158i	−0.253069	−	0.438329i	0.711300	−	0.702889i	$-0.248107\pi$
$739$	−6.87958	−	11.9158i	−0.253069	−	0.438329i	−0.964369	+	0.264560i	$0.914773\pi$
$740$		0			0
$741$	−31.3566	+	18.1037i	−1.15191	+	0.665057i
$742$		0			0
$743$	−35.1603	−	20.2998i	−1.28991	−	0.744727i	−0.311268	−	0.950322i	$-0.600754\pi$
$743$	−35.1603	−	20.2998i	−1.28991	−	0.744727i	−0.978637	+	0.205595i	$0.934087\pi$
$744$		0			0
$745$	−5.94747	+	3.43377i	−0.217899	+	0.125804i
$746$		0			0
$747$	36.8606	−	21.2815i	1.34866	−	0.778649i
$748$		0			0
$749$	7.26030			0.265285
$750$		0			0
$751$	−18.7859	−	10.8460i	−0.685506	−	0.395777i	0.116420	−	0.993200i	$-0.462858\pi$
$751$	−18.7859	−	10.8460i	−0.685506	−	0.395777i	−0.801926	+	0.597423i	$0.796191\pi$
$752$		0			0
$753$	4.41600	+	7.64873i	0.160928	+	0.278735i
$754$		0			0
$755$	30.2718	−	17.4774i	1.10170	−	0.636068i
$756$		0			0
$757$	−41.2915			−1.50077			−0.750383	−	0.661004i	$-0.770131\pi$
$757$	−41.2915			−1.50077			−0.750383	+	0.661004i	$0.770131\pi$
$758$		0			0
$759$	−33.6894	+	58.3518i	−1.22285	+	2.11804i
$760$		0			0
$761$	−14.4471	+	25.0231i	−0.523706	+	0.907085i	0.475913	+	0.879492i	$0.342118\pi$
$761$	−14.4471	+	25.0231i	−0.523706	+	0.907085i	−0.999619	+	0.0275932i	$0.991216\pi$
$762$		0			0
$763$			1.97641i			0.0715507i
$764$		0			0
$765$	73.9013	−	42.6670i	2.67191	−	1.54263i
$766$		0			0
$767$	18.7770	−	32.5228i	0.678000	−	1.17433i
$768$		0			0
$769$			27.1430i			0.978803i	0.872059	+	0.489401i	$0.162785\pi$
$769$			27.1430i			0.978803i	−0.872059	+	0.489401i	$0.837215\pi$
$770$		0			0
$771$	−7.28901	+	12.6249i	−0.262507	+	0.454676i
$772$		0			0
$773$	6.22967			0.224066			0.112033	−	0.993705i	$-0.464264\pi$
$773$	6.22967			0.224066			0.112033	+	0.993705i	$0.464264\pi$
$774$		0			0
$775$			21.0392i			0.755749i
$776$		0			0
$777$	−10.2147	+	5.89747i	−0.366451	+	0.211571i
$778$		0			0
$779$	−1.68900	+	2.92543i	−0.0605146	+	0.104814i
$780$		0			0
$781$	11.2088	+	6.47137i	0.401081	+	0.231564i
$782$		0			0
$783$	−61.8597	−	35.7147i	−2.21068	−	1.27634i
$784$		0			0
$785$	−49.8582	−	28.7856i	−1.77952	−	1.02740i
$786$		0			0
$787$	39.5087	−	22.8104i	1.40833	−	0.813102i	0.413106	−	0.910683i	$-0.364444\pi$
$787$	39.5087	−	22.8104i	1.40833	−	0.813102i	0.995228	+	0.0975810i	$0.0311105\pi$
$788$		0			0
$789$		−	26.7307i		−	0.951640i
$790$		0			0
$791$			0.849955i			0.0302209i
$792$		0			0
$793$	50.5885	−	29.2073i	1.79645	−	1.03718i
$794$		0			0
$795$	63.0856	+	36.4225i	2.23742	+	1.29177i
$796$		0			0
$797$	−0.125834	−	0.0726502i	−0.00445726	−	0.00257340i	0.497770	−	0.867309i	$-0.334152\pi$
$797$	−0.125834	−	0.0726502i	−0.00445726	−	0.00257340i	−0.502227	+	0.864736i	$0.667486\pi$
$798$		0			0
$799$	3.97148	+	2.29294i	0.140501	+	0.0811182i
$800$		0			0
$801$	−21.2954	+	36.8847i	−0.752436	+	1.30326i
$802$		0			0
$803$	40.2025	−	23.2109i	1.41872	−	0.819097i
$804$		0			0
$805$		−	4.47300i		−	0.157652i
$806$		0			0
$807$	−40.6748			−1.43182
$808$		0			0
$809$	25.5837	−	44.3123i	0.899475	−	1.55794i	0.0713096	−	0.997454i	$-0.477282\pi$
$809$	25.5837	−	44.3123i	0.899475	−	1.55794i	0.828166	−	0.560483i	$-0.189384\pi$
$810$		0			0
$811$			15.6875i			0.550862i	0.961321	+	0.275431i	$0.0888205\pi$
$811$			15.6875i			0.550862i	−0.961321	+	0.275431i	$0.911179\pi$
$812$		0			0
$813$	−9.08619	+	15.7377i	−0.318666	+	0.551946i
$814$		0			0
$815$	−58.5532	+	33.8057i	−2.05103	+	1.18416i
$816$		0			0
$817$			22.9781i			0.803903i
$818$		0			0
$819$	−7.79880	+	13.5079i	−0.272512	+	0.472005i
$820$		0			0
$821$	−6.86207	+	11.8855i	−0.239488	+	0.414805i	−0.960567	−	0.278047i	$-0.910313\pi$
$821$	−6.86207	+	11.8855i	−0.239488	+	0.414805i	0.721079	+	0.692852i	$0.243646\pi$
$822$		0			0
$823$	−55.4730			−1.93367			−0.966834	−	0.255406i	$-0.917791\pi$
$823$	−55.4730			−1.93367			−0.966834	+	0.255406i	$0.917791\pi$
$824$		0			0
$825$	51.3946	−	29.6727i	1.78933	−	1.03307i
$826$		0			0
$827$	−13.1047	−	22.6980i	−0.455694	−	0.789286i	0.543034	−	0.839711i	$-0.317276\pi$
$827$	−13.1047	−	22.6980i	−0.455694	−	0.789286i	−0.998728	+	0.0504254i	$0.983942\pi$
$828$		0			0
$829$	0.497941	+	0.287486i	0.0172942	+	0.00998481i	0.508622	−	0.860990i	$-0.330155\pi$
$829$	0.497941	+	0.287486i	0.0172942	+	0.00998481i	−0.491328	+	0.870975i	$0.663488\pi$
$830$		0			0
$831$	51.8724			1.79943
$832$		0			0
$833$	−23.9383	+	13.8208i	−0.829413	+	0.478862i
$834$		0			0
$835$	−33.3704	+	19.2664i	−1.15483	+	0.666741i
$836$		0			0
$837$	71.7856	+	41.4454i	2.48127	+	1.43256i
$838$		0			0
$839$	14.1393	−	8.16330i	0.488141	−	0.281829i	−0.235662	−	0.971835i	$-0.575726\pi$
$839$	14.1393	−	8.16330i	0.488141	−	0.281829i	0.723803	+	0.690007i	$0.242392\pi$
$840$		0			0
$841$	−0.834160	−	1.44481i	−0.0287641	−	0.0498210i
$842$		0			0
$843$	−24.2976	+	42.0846i	−0.836853	+	1.44947i
$844$		0			0
$845$	−25.0938	−	43.4637i	−0.863253	−	1.49520i
$846$		0			0
$847$	−6.84373			−0.235153
$848$		0			0
$849$	48.1397	−	27.7934i	1.65215	−	0.953869i
$850$		0			0
$851$	37.1294			1.27278
$852$		0			0
$853$	−20.1652	+	11.6424i	−0.690445	+	0.398628i	−0.803779	−	0.594928i	$-0.797180\pi$
$853$	−20.1652	+	11.6424i	−0.690445	+	0.398628i	0.113334	+	0.993557i	$0.463847\pi$
$854$		0			0
$855$			43.4395i			1.48560i
$856$		0			0
$857$	41.9756			1.43386			0.716930	−	0.697145i	$-0.245547\pi$
$857$	41.9756			1.43386			0.716930	+	0.697145i	$0.245547\pi$
$858$		0			0
$859$	−35.3667			−1.20670			−0.603348	−	0.797478i	$-0.706167\pi$
$859$	−35.3667			−1.20670			−0.603348	+	0.797478i	$0.706167\pi$
$860$		0			0
$861$			2.05613i			0.0700727i
$862$		0			0
$863$	−22.2525	−	12.8475i	−0.757483	−	0.437333i	0.0709083	−	0.997483i	$-0.477410\pi$
$863$	−22.2525	−	12.8475i	−0.757483	−	0.437333i	−0.828391	+	0.560150i	$0.810744\pi$
$864$		0			0
$865$	3.86768	+	2.23301i	0.131505	+	0.0759245i
$866$		0			0
$867$	1.12961	+	1.95654i	0.0383635	+	0.0664475i
$868$		0			0
$869$	34.9717	−	32.1069i	1.18633	−	1.08915i
$870$		0			0
$871$	33.4729	−	19.3256i	1.13419	−	0.654822i
$872$		0			0
$873$	−37.5370	+	65.0160i	−1.27044	+	2.20046i
$874$		0			0
$875$	0.870274	−	1.50736i	0.0294206	−	0.0509580i
$876$		0			0
$877$	4.51548			0.152477			0.0762385	−	0.997090i	$-0.475709\pi$
$877$	4.51548			0.152477			0.0762385	+	0.997090i	$0.475709\pi$
$878$		0			0
$879$		−	9.17363i		−	0.309419i
$880$		0			0
$881$			11.7794i			0.396858i	0.980115	+	0.198429i	$0.0635840\pi$
$881$			11.7794i			0.396858i	−0.980115	+	0.198429i	$0.936416\pi$
$882$		0			0
$883$	−3.26911			−0.110014			−0.0550072	−	0.998486i	$-0.517518\pi$
$883$	−3.26911			−0.110014			−0.0550072	+	0.998486i	$0.517518\pi$
$884$		0			0
$885$	−31.8306	−	55.1323i	−1.06997	−	1.85325i
$886$		0			0
$887$			56.3309i			1.89141i	0.325031	+	0.945703i	$0.394625\pi$
$887$			56.3309i			1.89141i	−0.325031	+	0.945703i	$0.605375\pi$
$888$		0			0
$889$	−3.03234	−	5.25217i	−0.101702	−	0.176152i
$890$		0			0
$891$		−	117.403i		−	3.93316i
$892$		0			0
$893$	−2.02169	+	1.16723i	−0.0676534	+	0.0390597i
$894$		0			0
$895$	−18.8899	−	10.9061i	−0.631420	−	0.364551i
$896$		0			0
$897$	60.0817	−	34.6882i	2.00607	−	1.15821i
$898$		0			0
$899$	−15.8586	−	27.4680i	−0.528915	−	0.916108i
$900$		0			0
$901$	15.7702	−	27.3148i	0.525381	−	0.909987i
$902$		0			0
$903$	6.99320	+	12.1126i	0.232719	+	0.403081i
$904$		0			0
$905$	−22.5771	−	39.1046i	−0.750487	−	1.29988i
$906$		0			0
$907$		−	41.0711i		−	1.36374i	−0.731471	−	0.681872i	$-0.761166\pi$
$907$		−	41.0711i		−	1.36374i	0.731471	−	0.681872i	$-0.238834\pi$
$908$		0			0
$909$	30.4029	−	52.6594i	1.00840	−	1.74660i
$910$		0			0
$911$	43.4655	−	25.0948i	1.44008	−	0.831428i	0.442222	−	0.896906i	$-0.354190\pi$
$911$	43.4655	−	25.0948i	1.44008	−	0.831428i	0.997854	+	0.0654773i	$0.0208570\pi$
$912$		0			0
$913$	−15.6475	−	27.1022i	−0.517856	−	0.896953i
$914$		0			0
$915$		−	99.0237i		−	3.27362i
$916$		0			0
$917$	0.837480	+	0.483520i	0.0276560	+	0.0159672i
$918$		0			0
$919$	2.25238	+	1.30041i	0.0742991	+	0.0428966i	0.536689	−	0.843780i	$-0.319675\pi$
$919$	2.25238	+	1.30041i	0.0742991	+	0.0428966i	−0.462390	+	0.886677i	$0.653008\pi$
$920$		0			0
$921$	33.9007			1.11707
$922$		0			0
$923$	−6.66323	−	11.5411i	−0.219323	−	0.379879i
$924$		0			0
$925$	−28.3213	−	16.3513i	−0.931198	−	0.537627i
$926$		0			0
$927$	−61.5359			−2.02110
$928$		0			0
$929$	−35.3124	−	20.3876i	−1.15856	−	0.668896i	−0.207603	−	0.978213i	$-0.566566\pi$
$929$	−35.3124	−	20.3876i	−1.15856	−	0.668896i	−0.950959	+	0.309317i	$0.899900\pi$
$930$		0			0
$931$		−	14.0710i		−	0.461159i
$932$		0			0
$933$	75.7471			2.47985
$934$		0			0
$935$	−31.3714	−	54.3369i	−1.02596	−	1.77701i
$936$		0			0
$937$	24.4564	+	14.1199i	0.798955	+	0.461277i	0.843106	−	0.537748i	$-0.180725\pi$
$937$	24.4564	+	14.1199i	0.798955	+	0.461277i	−0.0441504	+	0.999025i	$0.514058\pi$
$938$		0			0
$939$	18.8267	−	32.6087i	0.614385	−	1.06415i
$940$		0			0
$941$	−1.76069	+	3.04961i	−0.0573969	+	0.0994144i	−0.893296	−	0.449469i	$-0.851613\pi$
$941$	−1.76069	+	3.04961i	−0.0573969	+	0.0994144i	0.835899	+	0.548883i	$0.184947\pi$
$942$		0			0
$943$	3.23626	−	5.60536i	0.105387	−	0.182536i
$944$		0			0
$945$	7.76087	+	13.4422i	0.252461	+	0.437276i
$946$		0			0
$947$	56.4798			1.83535			0.917673	−	0.397337i	$-0.130066\pi$
$947$	56.4798			1.83535			0.917673	+	0.397337i	$0.130066\pi$
$948$		0			0
$949$	−47.7982			−1.55159
$950$		0			0
$951$	54.7104	+	94.7612i	1.77411	+	3.07284i
$952$		0			0
$953$	−7.05293	+	12.2160i	−0.228467	+	0.395716i	−0.957354	−	0.288918i	$-0.906705\pi$
$953$	−7.05293	+	12.2160i	−0.228467	+	0.395716i	0.728887	+	0.684634i	$0.240038\pi$
$954$		0			0
$955$	−19.9053	+	34.4771i	−0.644122	+	1.11565i
$956$		0			0
$957$	−44.7327	+	77.4792i	−1.44600	+	2.50455i
$958$		0			0
$959$	−7.35665	−	4.24736i	−0.237559	−	0.137155i
$960$		0			0
$961$	2.90329	+	5.02865i	0.0936546	+	0.162215i
$962$		0			0
$963$	135.100			4.35352
$964$		0			0
$965$		−	8.09184i		−	0.260486i
$966$		0			0
$967$	−9.44552	−	5.45337i	−0.303747	−	0.175369i	0.340378	−	0.940289i	$-0.389445\pi$
$967$	−9.44552	−	5.45337i	−0.303747	−	0.175369i	−0.644125	+	0.764920i	$0.722778\pi$
$968$		0			0
$969$	26.5756			0.853731
$970$		0			0
$971$	−34.0135	−	19.6377i	−1.09154	−	0.630203i	−0.157557	−	0.987510i	$-0.550362\pi$
$971$	−34.0135	−	19.6377i	−1.09154	−	0.630203i	−0.933987	+	0.357306i	$0.883695\pi$
$972$		0			0
$973$	−0.612610	−	1.06107i	−0.0196394	−	0.0340164i
$974$		0			0
$975$	−61.1048			−1.95692
$976$		0			0
$977$	7.75177	+	4.47548i	0.248001	+	0.143183i	0.618849	−	0.785510i	$-0.287599\pi$
$977$	7.75177	+	4.47548i	0.248001	+	0.143183i	−0.370848	+	0.928694i	$0.620933\pi$
$978$		0			0
$979$	27.1200	+	15.6577i	0.866758	+	0.500423i
$980$		0			0
$981$			36.7770i			1.17420i
$982$		0			0
$983$	−6.73899	−	11.6723i	−0.214940	−	0.372288i	0.738314	−	0.674457i	$-0.235622\pi$
$983$	−6.73899	−	11.6723i	−0.214940	−	0.372288i	−0.953254	+	0.302170i	$0.902289\pi$
$984$		0			0
$985$	10.9357	−	6.31373i	0.348441	−	0.201172i
$986$		0			0
$987$	−0.710470	+	1.23057i	−0.0226145	+	0.0391695i
$988$		0			0
$989$		−	44.0280i		−	1.40001i
$990$		0			0
$991$	20.6633	+	35.7900i	0.656393	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$991$	20.6633	+	35.7900i	0.656393	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$992$		0			0
$993$	−22.9096	−	39.6806i	−0.727014	−	1.25923i
$994$		0			0
$995$	0.379964	−	0.658117i	0.0120457	−	0.0208637i
$996$		0			0
$997$	−11.5717	−	20.0428i	−0.366480	−	0.634761i	0.622533	−	0.782594i	$-0.286104\pi$
$997$	−11.5717	−	20.0428i	−0.366480	−	0.634761i	−0.989012	+	0.147832i	$0.952770\pi$
$998$		0			0
$999$	−111.581	+	64.4214i	−3.53027	+	2.03820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1264.2.n.i.767.14	yes	28
4.3	odd	2	inner	1264.2.n.i.767.1	yes	28
79.24	odd	6	inner	1264.2.n.i.735.1	✓	28
316.103	even	6	inner	1264.2.n.i.735.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1264.2.n.i.735.1	✓	28	79.24	odd	6	inner
1264.2.n.i.735.14	yes	28	316.103	even	6	inner
1264.2.n.i.767.1	yes	28	4.3	odd	2	inner
1264.2.n.i.767.14	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1264 = 2^{4} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1264.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60192 + 2.77460i) q^{3} +(-1.45498 + 2.52010i) q^{5} +(-0.195200 + 0.338096i) q^{7} +(-3.63228 + 6.29129i) q^{9} +O(q^{10})\)	\(q+(1.60192 + 2.77460i) q^{3} +(-1.45498 + 2.52010i) q^{5} +(-0.195200 + 0.338096i) q^{7} +(-3.63228 + 6.29129i) q^{9} +(4.62575 + 2.67068i) q^{11} +(-2.74986 - 4.76289i) q^{13} -9.32304 q^{15} +4.03669i q^{17} +(-1.77958 - 1.02744i) q^{19} -1.25077 q^{21} +(3.40983 + 1.96867i) q^{23} +(-1.73395 - 3.00328i) q^{25} -13.6629 q^{27} +(4.52756 + 2.61399i) q^{29} +(-5.25404 - 3.03342i) q^{31} +17.1128i q^{33} +(-0.568024 - 0.983847i) q^{35} +(8.16671 - 4.71505i) q^{37} +(8.81008 - 15.2595i) q^{39} -1.64388i q^{41} +(-5.59109 - 9.68406i) q^{43} +(-10.5698 - 18.3074i) q^{45} +(0.568024 - 0.983847i) q^{47} +(3.42379 + 5.93019i) q^{49} +(-11.2002 + 6.46644i) q^{51} +(-6.76663 - 3.90672i) q^{53} +(-13.4608 + 7.77158i) q^{55} -6.58352i q^{57} +(3.41419 + 5.91355i) q^{59} +10.6214i q^{61} +(-1.41804 - 2.45612i) q^{63} +16.0040 q^{65} +7.02785i q^{67} +12.6146i q^{69} +2.42312 q^{71} +(4.34552 - 7.52666i) q^{73} +(5.55528 - 9.62202i) q^{75} +(-1.80589 + 1.04263i) q^{77} +(2.66466 - 8.47936i) q^{79} +(-10.9900 - 19.0353i) q^{81} +(-5.07404 - 2.92950i) q^{83} +(-10.1729 - 5.87331i) q^{85} +16.7496i q^{87} +5.86283 q^{89} +2.14708 q^{91} -19.4372i q^{93} +(5.17853 - 2.98982i) q^{95} +10.3343 q^{97} +(-33.6040 + 19.4013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 20 q^{9}+O(q^{10}) \) 28 * q - 20 * q^9	\( 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) \) 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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