LMFDB - Embedded newform 768.2.n.b.481.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(97,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("768.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.n (of order $8$, degree $4$, not 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			481.1
Character	$\chi$	$=$	768.481
Dual form			768.2.n.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382683 - 0.923880i) q^{3} +(-2.14986 - 0.890503i) q^{5} +(1.10001 + 1.10001i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.382683 - 0.923880i) q^{3} +(-2.14986 - 0.890503i) q^{5} +(1.10001 + 1.10001i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(0.999449 - 2.41288i) q^{11} +(2.03123 - 0.841362i) q^{13} +2.32700i q^{15} -5.68481i q^{17} +(-6.02698 + 2.49646i) q^{19} +(0.595322 - 1.43723i) q^{21} +(-3.60241 + 3.60241i) q^{23} +(0.293385 + 0.293385i) q^{25} +(0.923880 + 0.382683i) q^{27} +(-3.82608 - 9.23698i) q^{29} -1.98933 q^{31} -2.61168 q^{33} +(-1.38531 - 3.34444i) q^{35} +(-5.97179 - 2.47360i) q^{37} +(-1.55463 - 1.55463i) q^{39} +(-4.33228 + 4.33228i) q^{41} +(-4.39793 + 10.6175i) q^{43} +(2.14986 - 0.890503i) q^{45} -5.32331i q^{47} -4.57995i q^{49} +(-5.25208 + 2.17548i) q^{51} +(-0.802971 + 1.93854i) q^{53} +(-4.29736 + 4.29736i) q^{55} +(4.61285 + 4.61285i) q^{57} +(5.97225 + 2.47379i) q^{59} +(3.53897 + 8.54384i) q^{61} -1.55565 q^{63} -5.11610 q^{65} +(-2.25745 - 5.44997i) q^{67} +(4.70677 + 1.94961i) q^{69} +(-2.57276 - 2.57276i) q^{71} +(8.01131 - 8.01131i) q^{73} +(0.158779 - 0.383327i) q^{75} +(3.75360 - 1.55479i) q^{77} -14.4931i q^{79} -1.00000i q^{81} +(2.50672 - 1.03832i) q^{83} +(-5.06234 + 12.2216i) q^{85} +(-7.06968 + 7.06968i) q^{87} +(-2.98746 - 2.98746i) q^{89} +(3.15988 + 1.30887i) q^{91} +(0.761282 + 1.83790i) q^{93} +15.1803 q^{95} -5.81093 q^{97} +(0.999449 + 2.41288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$		0			0
$5$	−2.14986	−	0.890503i	−0.961448	−	0.398245i	−0.153926	−	0.988082i	$-0.549192\pi$
$5$	−2.14986	−	0.890503i	−0.961448	−	0.398245i	−0.807522	+	0.589837i	$0.799192\pi$
$6$		0			0
$7$	1.10001	+	1.10001i	0.415765	+	0.415765i	0.883741	−	0.467976i	$-0.155017\pi$
$7$	1.10001	+	1.10001i	0.415765	+	0.415765i	−0.467976	+	0.883741i	$0.655017\pi$
$8$		0			0
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$		0			0
$11$	0.999449	−	2.41288i	0.301345	−	0.727511i	−0.698583	−	0.715529i	$-0.746186\pi$
$11$	0.999449	−	2.41288i	0.301345	−	0.727511i	0.999928	−	0.0119825i	$-0.00381423\pi$
$12$		0			0
$13$	2.03123	−	0.841362i	0.563361	−	0.233352i	−0.0827824	−	0.996568i	$-0.526381\pi$
$13$	2.03123	−	0.841362i	0.563361	−	0.233352i	0.646144	+	0.763216i	$0.276381\pi$
$14$		0			0
$15$			2.32700i			0.600828i
$16$		0			0
$17$		−	5.68481i		−	1.37877i	−0.724396	−	0.689384i	$-0.757881\pi$
$17$		−	5.68481i		−	1.37877i	0.724396	−	0.689384i	$-0.242119\pi$
$18$		0			0
$19$	−6.02698	+	2.49646i	−1.38268	+	0.572726i	−0.945197	−	0.326499i	$-0.894131\pi$
$19$	−6.02698	+	2.49646i	−1.38268	+	0.572726i	−0.437486	+	0.899225i	$0.644131\pi$
$20$		0			0
$21$	0.595322	−	1.43723i	0.129910	−	0.313630i
$22$		0			0
$23$	−3.60241	+	3.60241i	−0.751154	+	0.751154i	−0.974695	−	0.223541i	$-0.928238\pi$
$23$	−3.60241	+	3.60241i	−0.751154	+	0.751154i	0.223541	+	0.974695i	$0.428238\pi$
$24$		0			0
$25$	0.293385	+	0.293385i	0.0586771	+	0.0586771i
$26$		0			0
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$		0			0
$29$	−3.82608	−	9.23698i	−0.710485	−	1.71526i	−0.698785	−	0.715332i	$-0.746275\pi$
$29$	−3.82608	−	9.23698i	−0.710485	−	1.71526i	−0.0117007	−	0.999932i	$-0.503725\pi$
$30$		0			0
$31$	−1.98933			−0.357294			−0.178647	−	0.983913i	$-0.557172\pi$
$31$	−1.98933			−0.357294			−0.178647	+	0.983913i	$0.557172\pi$
$32$		0			0
$33$	−2.61168			−0.454636
$34$		0			0
$35$	−1.38531	−	3.34444i	−0.234160	−	0.565313i
$36$		0			0
$37$	−5.97179	−	2.47360i	−0.981756	−	0.406657i	−0.166681	−	0.986011i	$-0.553305\pi$
$37$	−5.97179	−	2.47360i	−0.981756	−	0.406657i	−0.815076	+	0.579354i	$0.803305\pi$
$38$		0			0
$39$	−1.55463	−	1.55463i	−0.248941	−	0.248941i
$40$		0			0
$41$	−4.33228	+	4.33228i	−0.676589	+	0.676589i	−0.959227	−	0.282638i	$-0.908791\pi$
$41$	−4.33228	+	4.33228i	−0.676589	+	0.676589i	0.282638	+	0.959227i	$0.408791\pi$
$42$		0			0
$43$	−4.39793	+	10.6175i	−0.670678	+	1.61916i	0.109784	+	0.993955i	$0.464984\pi$
$43$	−4.39793	+	10.6175i	−0.670678	+	1.61916i	−0.780462	+	0.625204i	$0.785016\pi$
$44$		0			0
$45$	2.14986	−	0.890503i	0.320483	−	0.132748i
$46$		0			0
$47$		−	5.32331i		−	0.776485i	−0.921557	−	0.388242i	$-0.873082\pi$
$47$		−	5.32331i		−	0.776485i	0.921557	−	0.388242i	$-0.126918\pi$
$48$		0			0
$49$		−	4.57995i		−	0.654278i
$50$		0			0
$51$	−5.25208	+	2.17548i	−0.735438	+	0.304628i
$52$		0			0
$53$	−0.802971	+	1.93854i	−0.110297	+	0.266279i	−0.969384	−	0.245549i	$-0.921032\pi$
$53$	−0.802971	+	1.93854i	−0.110297	+	0.266279i	0.859088	+	0.511829i	$0.171032\pi$
$54$		0			0
$55$	−4.29736	+	4.29736i	−0.579455	+	0.579455i
$56$		0			0
$57$	4.61285	+	4.61285i	0.610987	+	0.610987i
$58$		0			0
$59$	5.97225	+	2.47379i	0.777521	+	0.322060i	0.735915	−	0.677074i	$-0.236752\pi$
$59$	5.97225	+	2.47379i	0.777521	+	0.322060i	0.0416066	+	0.999134i	$0.486752\pi$
$60$		0			0
$61$	3.53897	+	8.54384i	0.453119	+	1.09393i	0.971130	+	0.238552i	$0.0766728\pi$
$61$	3.53897	+	8.54384i	0.453119	+	1.09393i	−0.518010	+	0.855374i	$0.673327\pi$
$62$		0			0
$63$	−1.55565			−0.195994
$64$		0			0
$65$	−5.11610			−0.634574
$66$		0			0
$67$	−2.25745	−	5.44997i	−0.275792	−	0.665820i	0.723919	−	0.689885i	$-0.242339\pi$
$67$	−2.25745	−	5.44997i	−0.275792	−	0.665820i	−0.999710	+	0.0240652i	$0.992339\pi$
$68$		0			0
$69$	4.70677	+	1.94961i	0.566629	+	0.234705i
$70$		0			0
$71$	−2.57276	−	2.57276i	−0.305330	−	0.305330i	0.537765	−	0.843095i	$-0.319269\pi$
$71$	−2.57276	−	2.57276i	−0.305330	−	0.305330i	−0.843095	+	0.537765i	$0.819269\pi$
$72$		0			0
$73$	8.01131	−	8.01131i	0.937653	−	0.937653i	−0.0605139	−	0.998167i	$-0.519274\pi$
$73$	8.01131	−	8.01131i	0.937653	−	0.937653i	0.998167	+	0.0605139i	$0.0192740\pi$
$74$		0			0
$75$	0.158779	−	0.383327i	0.0183342	−	0.0442627i
$76$		0			0
$77$	3.75360	−	1.55479i	0.427763	−	0.177185i
$78$		0			0
$79$		−	14.4931i		−	1.63060i	−0.579039	−	0.815300i	$-0.696572\pi$
$79$		−	14.4931i		−	1.63060i	0.579039	−	0.815300i	$-0.303428\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	2.50672	−	1.03832i	0.275148	−	0.113970i	−0.240843	−	0.970564i	$-0.577424\pi$
$83$	2.50672	−	1.03832i	0.275148	−	0.113970i	0.515991	+	0.856594i	$0.327424\pi$
$84$		0			0
$85$	−5.06234	+	12.2216i	−0.549088	+	1.32561i
$86$		0			0
$87$	−7.06968	+	7.06968i	−0.757949	+	0.757949i
$88$		0			0
$89$	−2.98746	−	2.98746i	−0.316670	−	0.316670i	0.530817	−	0.847487i	$-0.321885\pi$
$89$	−2.98746	−	2.98746i	−0.316670	−	0.316670i	−0.847487	+	0.530817i	$0.821885\pi$
$90$		0			0
$91$	3.15988	+	1.30887i	0.331246	+	0.137206i
$92$		0			0
$93$	0.761282	+	1.83790i	0.0789413	+	0.190581i
$94$		0			0
$95$	15.1803			1.55746
$96$		0			0
$97$	−5.81093			−0.590010			−0.295005	−	0.955496i	$-0.595321\pi$
$97$	−5.81093			−0.590010			−0.295005	+	0.955496i	$0.595321\pi$
$98$		0			0
$99$	0.999449	+	2.41288i	0.100448	+	0.242504i
$100$		0			0
$101$	−2.91259	−	1.20644i	−0.289814	−	0.120045i	0.233040	−	0.972467i	$-0.425133\pi$
$101$	−2.91259	−	1.20644i	−0.289814	−	0.120045i	−0.522854	+	0.852422i	$0.675133\pi$
$102$		0			0
$103$	5.84034	+	5.84034i	0.575466	+	0.575466i	0.933651	−	0.358185i	$-0.116604\pi$
$103$	5.84034	+	5.84034i	0.575466	+	0.575466i	−0.358185	+	0.933651i	$0.616604\pi$
$104$		0			0
$105$	−2.55972	+	2.55972i	−0.249803	+	0.249803i
$106$		0			0
$107$	3.26727	−	7.88789i	0.315859	−	0.762551i	−0.683606	−	0.729851i	$-0.739589\pi$
$107$	3.26727	−	7.88789i	0.315859	−	0.762551i	0.999465	−	0.0327002i	$-0.0104107\pi$
$108$		0			0
$109$	12.3255	−	5.10538i	1.18057	−	0.489006i	0.295894	−	0.955221i	$-0.404382\pi$
$109$	12.3255	−	5.10538i	1.18057	−	0.489006i	0.884672	+	0.466214i	$0.154382\pi$
$110$		0			0
$111$			6.46382i			0.613519i
$112$		0			0
$113$		−	13.6962i		−	1.28843i	−0.764844	−	0.644216i	$-0.777184\pi$
$113$		−	13.6962i		−	1.28843i	0.764844	−	0.644216i	$-0.222816\pi$
$114$		0			0
$115$	10.9526	−	4.53673i	1.02134	−	0.423052i
$116$		0			0
$117$	−0.841362	+	2.03123i	−0.0777840	+	0.187787i
$118$		0			0
$119$	6.25336	−	6.25336i	0.573244	−	0.573244i
$120$		0			0
$121$	2.95507	+	2.95507i	0.268643	+	0.268643i
$122$		0			0
$123$	5.66040	+	2.34461i	0.510381	+	0.211407i
$124$		0			0
$125$	4.08304	+	9.85732i	0.365198	+	0.881665i
$126$		0			0
$127$	−4.61080			−0.409142			−0.204571	−	0.978852i	$-0.565580\pi$
$127$	−4.61080			−0.409142			−0.204571	+	0.978852i	$0.565580\pi$
$128$		0			0
$129$	11.4923			1.01184
$130$		0			0
$131$	0.640651	+	1.54667i	0.0559740	+	0.135133i	0.949393	−	0.314092i	$-0.101700\pi$
$131$	0.640651	+	1.54667i	0.0559740	+	0.135133i	−0.893419	+	0.449225i	$0.851700\pi$
$132$		0			0
$133$	−9.37587	−	3.88361i	−0.812991	−	0.336752i
$134$		0			0
$135$	−1.64543	−	1.64543i	−0.141616	−	0.141616i
$136$		0			0
$137$	−2.84955	+	2.84955i	−0.243454	+	0.243454i	−0.818277	−	0.574824i	$-0.805071\pi$
$137$	−2.84955	+	2.84955i	−0.243454	+	0.243454i	0.574824	+	0.818277i	$0.305071\pi$
$138$		0			0
$139$	−0.112341	+	0.271215i	−0.00952863	+	0.0230041i	−0.928572	−	0.371152i	$-0.878963\pi$
$139$	−0.112341	+	0.271215i	−0.00952863	+	0.0230041i	0.919044	+	0.394156i	$0.128963\pi$
$140$		0			0
$141$	−4.91810	+	2.03714i	−0.414178	+	0.171558i
$142$		0			0
$143$		−	5.74201i		−	0.480171i
$144$		0			0
$145$			23.2654i			1.93208i
$146$		0			0
$147$	−4.23132	+	1.75267i	−0.348993	+	0.144558i
$148$		0			0
$149$	5.19437	−	12.5403i	0.425539	−	1.02734i	−0.555147	−	0.831752i	$-0.687338\pi$
$149$	5.19437	−	12.5403i	0.425539	−	1.02734i	0.980686	−	0.195590i	$-0.0626621\pi$
$150$		0			0
$151$	1.03696	−	1.03696i	0.0843863	−	0.0843863i	−0.663654	−	0.748040i	$-0.730995\pi$
$151$	1.03696	−	1.03696i	0.0843863	−	0.0843863i	0.748040	+	0.663654i	$0.230995\pi$
$152$		0			0
$153$	4.01977	+	4.01977i	0.324979	+	0.324979i
$154$		0			0
$155$	4.27678	+	1.77150i	0.343519	+	0.142290i
$156$		0			0
$157$	−0.319782	−	0.772022i	−0.0255214	−	0.0616140i	0.910605	−	0.413278i	$-0.135616\pi$
$157$	−0.319782	−	0.772022i	−0.0255214	−	0.0616140i	−0.936126	+	0.351664i	$0.885616\pi$
$158$		0			0
$159$	2.09826			0.166403
$160$		0			0
$161$	−7.92538			−0.624607
$162$		0			0
$163$	1.96818	+	4.75161i	0.154160	+	0.372175i	0.982025	−	0.188753i	$-0.0604446\pi$
$163$	1.96818	+	4.75161i	0.154160	+	0.372175i	−0.827865	+	0.560928i	$0.810445\pi$
$164$		0			0
$165$	5.61477	+	2.32571i	0.437109	+	0.181056i
$166$		0			0
$167$	4.63248	+	4.63248i	0.358472	+	0.358472i	0.863249	−	0.504778i	$-0.168426\pi$
$167$	4.63248	+	4.63248i	0.358472	+	0.358472i	−0.504778	+	0.863249i	$0.668426\pi$
$168$		0			0
$169$	−5.77439	+	5.77439i	−0.444184	+	0.444184i
$170$		0			0
$171$	2.49646	−	6.02698i	0.190909	−	0.460894i
$172$		0			0
$173$	−12.6684	+	5.24743i	−0.963163	+	0.398955i	−0.808163	−	0.588959i	$-0.799538\pi$
$173$	−12.6684	+	5.24743i	−0.963163	+	0.398955i	−0.155000	+	0.987914i	$0.549538\pi$
$174$		0			0
$175$			0.645455i			0.0487918i
$176$		0			0
$177$		−	6.46432i		−	0.485888i
$178$		0			0
$179$	−8.55352	+	3.54299i	−0.639320	+	0.264815i	−0.678707	−	0.734409i	$-0.737460\pi$
$179$	−8.55352	+	3.54299i	−0.639320	+	0.264815i	0.0393869	+	0.999224i	$0.487460\pi$
$180$		0			0
$181$	0.495989	−	1.19742i	0.0368666	−	0.0890039i	−0.904374	−	0.426741i	$-0.859662\pi$
$181$	0.495989	−	1.19742i	0.0368666	−	0.0890039i	0.941240	+	0.337737i	$0.109662\pi$
$182$		0			0
$183$	6.53917	−	6.53917i	0.483390	−	0.483390i
$184$		0			0
$185$	10.6358	+	10.6358i	0.781959	+	0.781959i
$186$		0			0
$187$	−13.7168	−	5.68167i	−1.00307	−	0.415485i
$188$		0			0
$189$	0.595322	+	1.43723i	0.0433033	+	0.104543i
$190$		0			0
$191$	0.646843			0.0468039			0.0234019	−	0.999726i	$-0.492550\pi$
$191$	0.646843			0.0468039			0.0234019	+	0.999726i	$0.492550\pi$
$192$		0			0
$193$	18.7195			1.34746			0.673730	−	0.738978i	$-0.264691\pi$
$193$	18.7195			1.34746			0.673730	+	0.738978i	$0.264691\pi$
$194$		0			0
$195$	1.95785	+	4.72666i	0.140204	+	0.338483i
$196$		0			0
$197$	0.597874	+	0.247647i	0.0425967	+	0.0176441i	0.403880	−	0.914812i	$-0.367661\pi$
$197$	0.597874	+	0.247647i	0.0425967	+	0.0176441i	−0.361283	+	0.932456i	$0.617661\pi$
$198$		0			0
$199$	13.5447	+	13.5447i	0.960158	+	0.960158i	0.999236	−	0.0390782i	$-0.0124421\pi$
$199$	13.5447	+	13.5447i	0.960158	+	0.960158i	−0.0390782	+	0.999236i	$0.512442\pi$
$200$		0			0
$201$	−4.17123	+	4.17123i	−0.294216	+	0.294216i
$202$		0			0
$203$	5.95205	−	14.3695i	0.417752	−	1.00854i
$204$		0			0
$205$	13.1717	−	5.45591i	0.919953	−	0.381057i
$206$		0			0
$207$		−	5.09457i		−	0.354097i
$208$		0			0
$209$			17.0375i			1.17851i
$210$		0			0
$211$	23.9743	−	9.93047i	1.65046	−	0.683642i	0.653168	−	0.757213i	$-0.273440\pi$
$211$	23.9743	−	9.93047i	1.65046	−	0.683642i	0.997290	+	0.0735712i	$0.0234396\pi$
$212$		0			0
$213$	−1.39237	+	3.36147i	−0.0954034	+	0.230324i
$214$		0			0
$215$	18.9099	−	18.9099i	1.28964	−	1.28964i
$216$		0			0
$217$	−2.18828	−	2.18828i	−0.148550	−	0.148550i
$218$		0			0
$219$	−10.4673	−	4.33569i	−0.707314	−	0.292979i
$220$		0			0
$221$	−4.78298	−	11.5471i	−0.321738	−	0.776745i
$222$		0			0
$223$	−1.90075			−0.127284			−0.0636420	−	0.997973i	$-0.520272\pi$
$223$	−1.90075			−0.127284			−0.0636420	+	0.997973i	$0.520272\pi$
$224$		0			0
$225$	−0.414910			−0.0276606
$226$		0			0
$227$	−6.11900	−	14.7726i	−0.406132	−	0.980490i	−0.986145	−	0.165883i	$-0.946953\pi$
$227$	−6.11900	−	14.7726i	−0.406132	−	0.980490i	0.580013	−	0.814607i	$-0.303047\pi$
$228$		0			0
$229$	11.9674	+	4.95706i	0.790828	+	0.327572i	0.741277	−	0.671200i	$-0.234221\pi$
$229$	11.9674	+	4.95706i	0.790828	+	0.327572i	0.0495519	+	0.998772i	$0.484221\pi$
$230$		0			0
$231$	−2.87288	−	2.87288i	−0.189022	−	0.189022i
$232$		0			0
$233$	5.40070	−	5.40070i	0.353811	−	0.353811i	−0.507714	−	0.861526i	$-0.669509\pi$
$233$	5.40070	−	5.40070i	0.353811	−	0.353811i	0.861526	+	0.507714i	$0.169509\pi$
$234$		0			0
$235$	−4.74042	+	11.4444i	−0.309231	+	0.746550i
$236$		0			0
$237$	−13.3899	+	5.54626i	−0.869765	+	0.360268i
$238$		0			0
$239$			22.6418i			1.46458i	0.680995	+	0.732288i	$0.261547\pi$
$239$			22.6418i			1.46458i	−0.680995	+	0.732288i	$0.738453\pi$
$240$		0			0
$241$			20.4844i			1.31951i	0.751479	+	0.659757i	$0.229341\pi$
$241$			20.4844i			1.31951i	−0.751479	+	0.659757i	$0.770659\pi$
$242$		0			0
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$		0			0
$245$	−4.07846	+	9.84627i	−0.260563	+	0.629055i
$246$		0			0
$247$	−10.1417	+	10.1417i	−0.645303	+	0.645303i
$248$		0			0
$249$	−1.91856	−	1.91856i	−0.121584	−	0.121584i
$250$		0			0
$251$	12.6079	+	5.22237i	0.795804	+	0.329633i	0.743275	−	0.668986i	$-0.233272\pi$
$251$	12.6079	+	5.22237i	0.795804	+	0.329633i	0.0525298	+	0.998619i	$0.483272\pi$
$252$		0			0
$253$	5.09176	+	12.2926i	0.320116	+	0.772829i
$254$		0			0
$255$	13.2285			0.828402
$256$		0			0
$257$	12.4131			0.774307			0.387153	−	0.922015i	$-0.373458\pi$
$257$	12.4131			0.774307			0.387153	+	0.922015i	$0.373458\pi$
$258$		0			0
$259$	−3.84805	−	9.29003i	−0.239106	−	0.577254i
$260$		0			0
$261$	9.23698	+	3.82608i	0.571755	+	0.236828i
$262$		0			0
$263$	−17.4830	−	17.4830i	−1.07805	−	1.07805i	−0.996684	−	0.0813652i	$-0.974072\pi$
$263$	−17.4830	−	17.4830i	−1.07805	−	1.07805i	−0.0813652	−	0.996684i	$-0.525928\pi$
$264$		0			0
$265$	3.45256	−	3.45256i	0.212089	−	0.212089i
$266$		0			0
$267$	−1.61680	+	3.90330i	−0.0989466	+	0.238878i
$268$		0			0
$269$	−11.1213	+	4.60660i	−0.678079	+	0.280869i	−0.695023	−	0.718987i	$-0.744606\pi$
$269$	−11.1213	+	4.60660i	−0.678079	+	0.280869i	0.0169449	+	0.999856i	$0.494606\pi$
$270$		0			0
$271$			18.4077i			1.11819i	0.829105	+	0.559093i	$0.188850\pi$
$271$			18.4077i			1.11819i	−0.829105	+	0.559093i	$0.811150\pi$
$272$		0			0
$273$		−	3.42023i		−	0.207002i
$274$		0			0
$275$	1.00113	−	0.414681i	0.0603703	−	0.0250062i
$276$		0			0
$277$	4.36873	−	10.5471i	0.262492	−	0.633711i	−0.736600	−	0.676329i	$-0.763570\pi$
$277$	4.36873	−	10.5471i	0.262492	−	0.633711i	0.999091	+	0.0426179i	$0.0135698\pi$
$278$		0			0
$279$	1.40667	−	1.40667i	0.0842149	−	0.0842149i
$280$		0			0
$281$	−5.71168	−	5.71168i	−0.340730	−	0.340730i	0.515912	−	0.856642i	$-0.327453\pi$
$281$	−5.71168	−	5.71168i	−0.340730	−	0.340730i	−0.856642	+	0.515912i	$0.827453\pi$
$282$		0			0
$283$	−8.28088	−	3.43005i	−0.492247	−	0.203896i	0.122730	−	0.992440i	$-0.460835\pi$
$283$	−8.28088	−	3.43005i	−0.492247	−	0.203896i	−0.614978	+	0.788545i	$0.710835\pi$
$284$		0			0
$285$	−5.80924	−	14.0247i	−0.344110	−	0.830754i
$286$		0			0
$287$	−9.53112			−0.562604
$288$		0			0
$289$	−15.3170			−0.901003
$290$		0			0
$291$	2.22374	+	5.36860i	0.130358	+	0.314713i
$292$		0			0
$293$	17.2497	+	7.14508i	1.00774	+	0.417420i	0.824630	−	0.565672i	$-0.191383\pi$
$293$	17.2497	+	7.14508i	1.00774	+	0.417420i	0.183111	+	0.983092i	$0.441383\pi$
$294$		0			0
$295$	−10.6366	−	10.6366i	−0.619288	−	0.619288i
$296$		0			0
$297$	1.84674	−	1.84674i	0.107159	−	0.107159i
$298$		0			0
$299$	−4.28638	+	10.3482i	−0.247888	+	0.598454i
$300$		0			0
$301$	−16.5172	+	6.84164i	−0.952035	+	0.394346i
$302$		0			0
$303$			3.15257i			0.181110i
$304$		0			0
$305$		−	21.5196i		−	1.23221i
$306$		0			0
$307$	−0.294424	+	0.121954i	−0.0168036	+	0.00696030i	−0.391069	−	0.920361i	$-0.627895\pi$
$307$	−0.294424	+	0.121954i	−0.0168036	+	0.00696030i	0.374266	+	0.927321i	$0.377895\pi$
$308$		0			0
$309$	3.16077	−	7.63077i	0.179810	−	0.434099i
$310$		0			0
$311$	−9.49039	+	9.49039i	−0.538151	+	0.538151i	−0.922986	−	0.384835i	$-0.874258\pi$
$311$	−9.49039	+	9.49039i	−0.538151	+	0.538151i	0.384835	+	0.922986i	$0.374258\pi$
$312$		0			0
$313$	−23.1330	−	23.1330i	−1.30756	−	1.30756i	−0.923174	−	0.384383i	$-0.874414\pi$
$313$	−23.1330	−	23.1330i	−1.30756	−	1.30756i	−0.384383	−	0.923174i	$-0.625586\pi$
$314$		0			0
$315$	3.34444	+	1.38531i	0.188438	+	0.0780535i
$316$		0			0
$317$	1.17141	+	2.82804i	0.0657931	+	0.158839i	0.953356	−	0.301848i	$-0.0976034\pi$
$317$	1.17141	+	2.82804i	0.0657931	+	0.158839i	−0.887563	+	0.460686i	$0.847603\pi$
$318$		0			0
$319$	−26.1117			−1.46198
$320$		0			0
$321$	−8.53779			−0.476533
$322$		0			0
$323$	14.1919	+	34.2622i	0.789657	+	1.90640i
$324$		0			0
$325$	0.842776	+	0.349089i	0.0467488	+	0.0193640i
$326$		0			0
$327$	−9.43351	−	9.43351i	−0.521674	−	0.521674i
$328$		0			0
$329$	5.85570	−	5.85570i	0.322835	−	0.322835i
$330$		0			0
$331$	5.82090	−	14.0529i	0.319946	−	0.772417i	−0.679310	−	0.733851i	$-0.737721\pi$
$331$	5.82090	−	14.0529i	0.319946	−	0.772417i	0.999256	−	0.0385662i	$-0.0122791\pi$
$332$		0			0
$333$	5.97179	−	2.47360i	0.327252	−	0.135552i
$334$		0			0
$335$			13.7270i			0.749984i
$336$		0			0
$337$			4.16517i			0.226891i	0.993544	+	0.113446i	$0.0361888\pi$
$337$			4.16517i			0.226891i	−0.993544	+	0.113446i	$0.963811\pi$
$338$		0			0
$339$	−12.6537	+	5.24132i	−0.687252	+	0.284669i
$340$		0			0
$341$	−1.98823	+	4.80001i	−0.107669	+	0.259935i
$342$		0			0
$343$	12.7381	−	12.7381i	0.687792	−	0.687792i
$344$		0			0
$345$	−8.38278	−	8.38278i	−0.451314	−	0.451314i
$346$		0			0
$347$	−29.5450	−	12.2380i	−1.58606	−	0.656968i	−0.596702	−	0.802463i	$-0.703522\pi$
$347$	−29.5450	−	12.2380i	−1.58606	−	0.656968i	−0.989359	+	0.145495i	$0.953522\pi$
$348$		0			0
$349$	−11.3566	−	27.4173i	−0.607907	−	1.46762i	−0.865272	−	0.501302i	$-0.832854\pi$
$349$	−11.3566	−	27.4173i	−0.607907	−	1.46762i	0.257365	−	0.966314i	$-0.417146\pi$
$350$		0			0
$351$	2.19859			0.117352
$352$		0			0
$353$	4.26063			0.226771			0.113385	−	0.993551i	$-0.463831\pi$
$353$	4.26063			0.226771			0.113385	+	0.993551i	$0.463831\pi$
$354$		0			0
$355$	3.24003	+	7.82213i	0.171963	+	0.415156i
$356$		0			0
$357$	−8.17040	−	3.38429i	−0.432424	−	0.179116i
$358$		0			0
$359$	−4.97012	−	4.97012i	−0.262313	−	0.262313i	0.563680	−	0.825993i	$-0.309385\pi$
$359$	−4.97012	−	4.97012i	−0.262313	−	0.262313i	−0.825993	+	0.563680i	$0.809385\pi$
$360$		0			0
$361$	16.6571	−	16.6571i	0.876691	−	0.876691i
$362$		0			0
$363$	1.59927	−	3.86099i	0.0839401	−	0.202649i
$364$		0			0
$365$	−24.3573	+	10.0891i	−1.27492	+	0.528090i
$366$		0			0
$367$		−	15.0671i		−	0.786495i	−0.919433	−	0.393247i	$-0.871352\pi$
$367$		−	15.0671i		−	0.786495i	0.919433	−	0.393247i	$-0.128648\pi$
$368$		0			0
$369$		−	6.12677i		−	0.318947i
$370$		0			0
$371$	−3.01570	+	1.24914i	−0.156567	+	0.0648523i
$372$		0			0
$373$	6.17375	−	14.9048i	0.319665	−	0.771739i	−0.679607	−	0.733577i	$-0.737850\pi$
$373$	6.17375	−	14.9048i	0.319665	−	0.771739i	0.999272	−	0.0381624i	$-0.0121504\pi$
$374$		0			0
$375$	7.54447	−	7.54447i	0.389595	−	0.389595i
$376$		0			0
$377$	−15.5433	−	15.5433i	−0.800520	−	0.800520i
$378$		0			0
$379$	0.511585	+	0.211905i	0.0262783	+	0.0108848i	0.395784	−	0.918344i	$-0.370473\pi$
$379$	0.511585	+	0.211905i	0.0262783	+	0.0108848i	−0.369506	+	0.929229i	$0.620473\pi$
$380$		0			0
$381$	1.76448	+	4.25983i	0.0903969	+	0.218237i
$382$		0			0
$383$	−6.05003			−0.309142			−0.154571	−	0.987982i	$-0.549400\pi$
$383$	−6.05003			−0.309142			−0.154571	+	0.987982i	$0.549400\pi$
$384$		0			0
$385$	−9.45429			−0.481835
$386$		0			0
$387$	−4.39793	−	10.6175i	−0.223559	−	0.539720i
$388$		0			0
$389$	10.1717	+	4.21324i	0.515724	+	0.213620i	0.625338	−	0.780354i	$-0.284961\pi$
$389$	10.1717	+	4.21324i	0.515724	+	0.213620i	−0.109613	+	0.993974i	$0.534961\pi$
$390$		0			0
$391$	20.4790	+	20.4790i	1.03567	+	1.03567i
$392$		0			0
$393$	1.18377	−	1.18377i	0.0597133	−	0.0597133i
$394$		0			0
$395$	−12.9061	+	31.1582i	−0.649378	+	1.56774i
$396$		0			0
$397$	22.5585	−	9.34403i	1.13218	−	0.468963i	0.263657	−	0.964616i	$-0.415071\pi$
$397$	22.5585	−	9.34403i	1.13218	−	0.468963i	0.868521	+	0.495653i	$0.165071\pi$
$398$		0			0
$399$			10.1484i			0.508054i
$400$		0			0
$401$			26.6309i			1.32988i	0.746895	+	0.664942i	$0.231544\pi$
$401$			26.6309i			1.32988i	−0.746895	+	0.664942i	$0.768456\pi$
$402$		0			0
$403$	−4.04077	+	1.67374i	−0.201285	+	0.0833751i
$404$		0			0
$405$	−0.890503	+	2.14986i	−0.0442494	+	0.106828i
$406$		0			0
$407$	−11.9370	+	11.9370i	−0.591695	+	0.591695i
$408$		0			0
$409$	−15.3022	−	15.3022i	−0.756647	−	0.756647i	0.219064	−	0.975710i	$-0.429700\pi$
$409$	−15.3022	−	15.3022i	−0.756647	−	0.756647i	−0.975710	+	0.219064i	$0.929700\pi$
$410$		0			0
$411$	3.72312	+	1.54217i	0.183648	+	0.0760695i
$412$		0			0
$413$	3.84835	+	9.29075i	0.189365	+	0.457168i
$414$		0			0
$415$	−6.31374			−0.309929
$416$		0			0
$417$	0.293561			0.0143757
$418$		0			0
$419$	7.92030	+	19.1213i	0.386932	+	0.934136i	0.990586	+	0.136890i	$0.0437107\pi$
$419$	7.92030	+	19.1213i	0.386932	+	0.934136i	−0.603654	+	0.797246i	$0.706289\pi$
$420$		0			0
$421$	−29.2323	−	12.1084i	−1.42469	−	0.590128i	−0.468659	−	0.883379i	$-0.655263\pi$
$421$	−29.2323	−	12.1084i	−1.42469	−	0.590128i	−0.956035	+	0.293251i	$0.905263\pi$
$422$		0			0
$423$	3.76415	+	3.76415i	0.183019	+	0.183019i
$424$		0			0
$425$	1.66784	−	1.66784i	0.0809021	−	0.0809021i
$426$		0			0
$427$	−5.50541	+	13.2912i	−0.266425	+	0.643208i
$428$		0			0
$429$	−5.30493	+	2.19737i	−0.256124	+	0.106090i
$430$		0			0
$431$		−	1.99673i		−	0.0961789i	−0.998843	−	0.0480895i	$-0.984687\pi$
$431$		−	1.99673i		−	0.0961789i	0.998843	−	0.0480895i	$-0.0153133\pi$
$432$		0			0
$433$		−	16.8123i		−	0.807948i	−0.914770	−	0.403974i	$-0.867629\pi$
$433$		−	16.8123i		−	0.807948i	0.914770	−	0.403974i	$-0.132371\pi$
$434$		0			0
$435$	21.4944	−	8.90328i	1.03058	−	0.426879i
$436$		0			0
$437$	12.7184	−	30.7049i	0.608402	−	1.46881i
$438$		0			0
$439$	23.5940	−	23.5940i	1.12608	−	1.12608i	0.135274	−	0.990808i	$-0.456809\pi$
$439$	23.5940	−	23.5940i	1.12608	−	1.12608i	0.990808	−	0.135274i	$-0.0431914\pi$
$440$		0			0
$441$	3.23851	+	3.23851i	0.154215	+	0.154215i
$442$		0			0
$443$	−21.0559	−	8.72163i	−1.00039	−	0.414377i	−0.178453	−	0.983948i	$-0.557109\pi$
$443$	−21.0559	−	8.72163i	−1.00039	−	0.414377i	−0.821942	+	0.569571i	$0.807109\pi$
$444$		0			0
$445$	3.76229	+	9.08297i	0.178350	+	0.430574i
$446$		0			0
$447$	−13.5735			−0.642006
$448$		0			0
$449$	29.2703			1.38135			0.690675	−	0.723165i	$-0.257314\pi$
$449$	29.2703			1.38135			0.690675	+	0.723165i	$0.257314\pi$
$450$		0			0
$451$	6.12339	+	14.7832i	0.288339	+	0.696113i
$452$		0			0
$453$	−1.35485	−	0.561197i	−0.0636564	−	0.0263673i
$454$		0			0
$455$	−5.62777	−	5.62777i	−0.263834	−	0.263834i
$456$		0			0
$457$	−13.2549	+	13.2549i	−0.620040	+	0.620040i	−0.945541	−	0.325502i	$-0.894467\pi$
$457$	−13.2549	+	13.2549i	−0.620040	+	0.620040i	0.325502	+	0.945541i	$0.394467\pi$
$458$		0			0
$459$	2.17548	−	5.25208i	0.101543	−	0.245146i
$460$		0			0
$461$	36.5469	−	15.1382i	1.70216	−	0.705057i	0.702182	−	0.711997i	$-0.252209\pi$
$461$	36.5469	−	15.1382i	1.70216	−	0.705057i	0.999976	+	0.00694059i	$0.00220928\pi$
$462$		0			0
$463$		−	18.4673i		−	0.858250i	−0.903245	−	0.429125i	$-0.858822\pi$
$463$		−	18.4673i		−	0.858250i	0.903245	−	0.429125i	$-0.141178\pi$
$464$		0			0
$465$		−	4.62915i		−	0.214672i
$466$		0			0
$467$	0.983296	−	0.407295i	0.0455015	−	0.0188474i	−0.359817	−	0.933023i	$-0.617161\pi$
$467$	0.983296	−	0.407295i	0.0455015	−	0.0188474i	0.405318	+	0.914176i	$0.367161\pi$
$468$		0			0
$469$	3.51181	−	8.47826i	0.162160	−	0.391490i
$470$		0			0
$471$	−0.590880	+	0.590880i	−0.0272263	+	0.0272263i
$472$		0			0
$473$	21.2234	+	21.2234i	0.975851	+	0.975851i
$474$		0			0
$475$	−2.50065	−	1.03580i	−0.114738	−	0.0475259i
$476$		0			0
$477$	−0.802971	−	1.93854i	−0.0367655	−	0.0887598i
$478$		0			0
$479$	−19.1585			−0.875375			−0.437687	−	0.899127i	$-0.644202\pi$
$479$	−19.1585			−0.875375			−0.437687	+	0.899127i	$0.644202\pi$
$480$		0			0
$481$	−14.2113			−0.647978
$482$		0			0
$483$	3.03291	+	7.32209i	0.138002	+	0.333167i
$484$		0			0
$485$	12.4927	+	5.17465i	0.567264	+	0.234969i
$486$		0			0
$487$	−26.4107	−	26.4107i	−1.19678	−	1.19678i	−0.975124	−	0.221660i	$-0.928852\pi$
$487$	−26.4107	−	26.4107i	−1.19678	−	1.19678i	−0.221660	−	0.975124i	$-0.571148\pi$
$488$		0			0
$489$	3.63672	−	3.63672i	0.164458	−	0.164458i
$490$		0			0
$491$	9.74865	−	23.5353i	0.439951	−	1.06213i	−0.536015	−	0.844209i	$-0.680071\pi$
$491$	9.74865	−	23.5353i	0.439951	−	1.06213i	0.975965	−	0.217926i	$-0.0699292\pi$
$492$		0			0
$493$	−52.5104	+	21.7505i	−2.36495	+	0.979595i
$494$		0			0
$495$		−	6.07738i		−	0.273158i
$496$		0			0
$497$		−	5.66013i		−	0.253892i
$498$		0			0
$499$	12.2231	−	5.06299i	0.547183	−	0.226651i	−0.0919272	−	0.995766i	$-0.529303\pi$
$499$	12.2231	−	5.06299i	0.547183	−	0.226651i	0.639110	+	0.769115i	$0.279303\pi$
$500$		0			0
$501$	2.50708	−	6.05262i	0.112008	−	0.270411i
$502$		0			0
$503$	−21.6420	+	21.6420i	−0.964970	+	0.964970i	−0.999407	−	0.0344366i	$-0.989036\pi$
$503$	−21.6420	+	21.6420i	−0.964970	+	0.964970i	0.0344366	+	0.999407i	$0.489036\pi$
$504$		0			0
$505$	5.18734	+	5.18734i	0.230834	+	0.230834i
$506$		0			0
$507$	7.54461	+	3.12508i	0.335068	+	0.138790i
$508$		0			0
$509$	−1.14400	−	2.76185i	−0.0507067	−	0.122417i	0.896496	−	0.443051i	$-0.146104\pi$
$509$	−1.14400	−	2.76185i	−0.0507067	−	0.122417i	−0.947203	+	0.320634i	$0.896104\pi$
$510$		0			0
$511$	17.6251			0.779688
$512$		0			0
$513$	−6.52355			−0.288022
$514$		0			0
$515$	−7.35510	−	17.7568i	−0.324104	−	0.782457i
$516$		0			0
$517$	−12.8445	−	5.32037i	−0.564901	−	0.233990i
$518$		0			0
$519$	9.69599	+	9.69599i	0.425607	+	0.425607i
$520$		0			0
$521$	−16.6745	+	16.6745i	−0.730525	+	0.730525i	−0.970724	−	0.240199i	$-0.922787\pi$
$521$	−16.6745	+	16.6745i	−0.730525	+	0.730525i	0.240199	+	0.970724i	$0.422787\pi$
$522$		0			0
$523$	0.461277	−	1.11362i	0.0201703	−	0.0486953i	−0.913474	−	0.406898i	$-0.866610\pi$
$523$	0.461277	−	1.11362i	0.0201703	−	0.0486953i	0.933644	+	0.358203i	$0.116610\pi$
$524$		0			0
$525$	0.596323	−	0.247005i	0.0260256	−	0.0107802i
$526$		0			0
$527$			11.3089i			0.492625i
$528$		0			0
$529$		−	2.95466i		−	0.128463i
$530$		0			0
$531$	−5.97225	+	2.47379i	−0.259174	+	0.107353i
$532$		0			0
$533$	−5.15484	+	12.4449i	−0.223281	+	0.539047i
$534$		0			0
$535$	−14.0484	+	14.0484i	−0.607364	+	0.607364i
$536$		0			0
$537$	6.54658	+	6.54658i	0.282506	+	0.282506i
$538$		0			0
$539$	−11.0509	−	4.57742i	−0.475995	−	0.197164i
$540$		0			0
$541$	4.79193	+	11.5687i	0.206021	+	0.497379i	0.992790	−	0.119869i	$-0.0382474\pi$
$541$	4.79193	+	11.5687i	0.206021	+	0.497379i	−0.786768	+	0.617248i	$0.788247\pi$
$542$		0			0
$543$	−1.29608			−0.0556202
$544$		0			0
$545$	−31.0444			−1.32980
$546$		0			0
$547$	−10.4863	−	25.3162i	−0.448363	−	1.08244i	−0.972935	−	0.231078i	$-0.925775\pi$
$547$	−10.4863	−	25.3162i	−0.448363	−	1.08244i	0.524573	−	0.851366i	$-0.324225\pi$
$548$		0			0
$549$	−8.54384	−	3.53897i	−0.364642	−	0.151040i
$550$		0			0
$551$	46.1194	+	46.1194i	1.96475	+	1.96475i
$552$		0			0
$553$	15.9426	−	15.9426i	0.677947	−	0.677947i
$554$		0			0
$555$	5.75605	−	13.8963i	0.244331	−	0.589867i
$556$		0			0
$557$	10.9293	−	4.52708i	0.463091	−	0.191818i	−0.138925	−	0.990303i	$-0.544365\pi$
$557$	10.9293	−	4.52708i	0.463091	−	0.191818i	0.602015	+	0.798485i	$0.294365\pi$
$558$		0			0
$559$			25.2669i			1.06868i
$560$		0			0
$561$			14.8469i			0.626838i
$562$		0			0
$563$	−33.9735	+	14.0723i	−1.43181	+	0.593076i	−0.957798	−	0.287442i	$-0.907195\pi$
$563$	−33.9735	+	14.0723i	−1.43181	+	0.593076i	−0.474014	+	0.880518i	$0.657195\pi$
$564$		0			0
$565$	−12.1965	+	29.4450i	−0.513112	+	1.23876i
$566$		0			0
$567$	1.10001	−	1.10001i	0.0461961	−	0.0461961i
$568$		0			0
$569$	−3.61769	−	3.61769i	−0.151661	−	0.151661i	0.627198	−	0.778860i	$-0.284202\pi$
$569$	−3.61769	−	3.61769i	−0.151661	−	0.151661i	−0.778860	+	0.627198i	$0.784202\pi$
$570$		0			0
$571$	−14.7686	−	6.11734i	−0.618045	−	0.256003i	0.0516188	−	0.998667i	$-0.483562\pi$
$571$	−14.7686	−	6.11734i	−0.618045	−	0.256003i	−0.669664	+	0.742664i	$0.733562\pi$
$572$		0			0
$573$	−0.247536	−	0.597605i	−0.0103410	−	0.0249653i
$574$		0			0
$575$	−2.11379			−0.0881510
$576$		0			0
$577$	42.0367			1.75001			0.875005	−	0.484114i	$-0.160858\pi$
$577$	42.0367			1.75001			0.875005	+	0.484114i	$0.160858\pi$
$578$		0			0
$579$	−7.16365	−	17.2946i	−0.297711	−	0.718738i
$580$		0			0
$581$	3.89959	+	1.61526i	0.161782	+	0.0670123i
$582$		0			0
$583$	3.87495	+	3.87495i	0.160484	+	0.160484i
$584$		0			0
$585$	3.61763	−	3.61763i	0.149571	−	0.149571i
$586$		0			0
$587$	−8.05275	+	19.4411i	−0.332372	+	0.802418i	0.666031	+	0.745925i	$0.267992\pi$
$587$	−8.05275	+	19.4411i	−0.332372	+	0.802418i	−0.998403	+	0.0564936i	$0.982008\pi$
$588$		0			0
$589$	11.9896	−	4.96626i	0.494024	−	0.204631i
$590$		0			0
$591$		−	0.647134i		−	0.0266195i
$592$		0			0
$593$			24.6856i			1.01372i	0.862029	+	0.506858i	$0.169193\pi$
$593$			24.6856i			1.01372i	−0.862029	+	0.506858i	$0.830807\pi$
$594$		0			0
$595$	−19.0125	+	7.87523i	−0.779436	+	0.322853i
$596$		0			0
$597$	7.33034	−	17.6970i	0.300011	−	0.724290i
$598$		0			0
$599$	0.292862	−	0.292862i	0.0119660	−	0.0119660i	−0.701098	−	0.713064i	$-0.747307\pi$
$599$	0.292862	−	0.292862i	0.0119660	−	0.0119660i	0.713064	+	0.701098i	$0.247307\pi$
$600$		0			0
$601$	17.9233	+	17.9233i	0.731107	+	0.731107i	0.970839	−	0.239732i	$-0.0770595\pi$
$601$	17.9233	+	17.9233i	0.731107	+	0.731107i	−0.239732	+	0.970839i	$0.577059\pi$
$602$		0			0
$603$	5.44997	+	2.25745i	0.221940	+	0.0919306i
$604$		0			0
$605$	−3.72150	−	8.98450i	−0.151301	−	0.365272i
$606$		0			0
$607$	30.0813			1.22096			0.610481	−	0.792031i	$-0.290976\pi$
$607$	30.0813			1.22096			0.610481	+	0.792031i	$0.290976\pi$
$608$		0			0
$609$	−15.5535			−0.630258
$610$		0			0
$611$	−4.47883	−	10.8129i	−0.181194	−	0.437441i
$612$		0			0
$613$	8.13147	+	3.36816i	0.328427	+	0.136039i	0.540803	−	0.841149i	$-0.318120\pi$
$613$	8.13147	+	3.36816i	0.328427	+	0.136039i	−0.212377	+	0.977188i	$0.568120\pi$
$614$		0			0
$615$	−10.0812	−	10.0812i	−0.406513	−	0.406513i
$616$		0			0
$617$	−13.3355	+	13.3355i	−0.536869	+	0.536869i	−0.922608	−	0.385739i	$-0.873946\pi$
$617$	−13.3355	+	13.3355i	−0.536869	+	0.536869i	0.385739	+	0.922608i	$0.373946\pi$
$618$		0			0
$619$	9.84872	−	23.7769i	0.395853	−	0.955674i	−0.592785	−	0.805361i	$-0.701972\pi$
$619$	9.84872	−	23.7769i	0.395853	−	0.955674i	0.988638	−	0.150314i	$-0.0480284\pi$
$620$		0			0
$621$	−4.70677	+	1.94961i	−0.188876	+	0.0782351i
$622$		0			0
$623$		−	6.57248i		−	0.263321i
$624$		0			0
$625$		−	26.9024i		−	1.07610i
$626$		0			0
$627$	15.7406	−	6.51995i	0.628618	−	0.260382i
$628$		0			0
$629$	−14.0619	+	33.9485i	−0.560686	+	1.35361i
$630$		0			0
$631$	−3.24320	+	3.24320i	−0.129110	+	0.129110i	−0.768709	−	0.639599i	$-0.779100\pi$
$631$	−3.24320	+	3.24320i	−0.129110	+	0.129110i	0.639599	+	0.768709i	$0.279100\pi$
$632$		0			0
$633$	−18.3491	−	18.3491i	−0.729312	−	0.729312i
$634$		0			0
$635$	9.91260	+	4.10593i	0.393369	+	0.162939i
$636$		0			0
$637$	−3.85340	−	9.30292i	−0.152677	−	0.368595i
$638$		0			0
$639$	3.63843			0.143934
$640$		0			0
$641$	27.4171			1.08291			0.541455	−	0.840729i	$-0.317874\pi$
$641$	27.4171			1.08291			0.541455	+	0.840729i	$0.317874\pi$
$642$		0			0
$643$	−0.821316	−	1.98283i	−0.0323896	−	0.0781953i	0.906857	−	0.421438i	$-0.138475\pi$
$643$	−0.821316	−	1.98283i	−0.0323896	−	0.0781953i	−0.939247	+	0.343243i	$0.888475\pi$
$644$		0			0
$645$	−24.7070	−	10.2340i	−0.972836	−	0.402962i
$646$		0			0
$647$	−13.6349	−	13.6349i	−0.536044	−	0.536044i	0.386321	−	0.922365i	$-0.373746\pi$
$647$	−13.6349	−	13.6349i	−0.536044	−	0.536044i	−0.922365	+	0.386321i	$0.873746\pi$
$648$		0			0
$649$	11.9379	−	11.9379i	0.468604	−	0.468604i
$650$		0			0
$651$	−1.18429	+	2.85913i	−0.0464160	+	0.112058i
$652$		0			0
$653$	12.3455	−	5.11368i	0.483118	−	0.200114i	−0.127813	−	0.991798i	$-0.540796\pi$
$653$	12.3455	−	5.11368i	0.483118	−	0.200114i	0.610930	+	0.791684i	$0.290796\pi$
$654$		0			0
$655$		−	3.89563i		−	0.152215i
$656$		0			0
$657$			11.3297i			0.442014i
$658$		0			0
$659$	26.7406	−	11.0763i	1.04166	−	0.431472i	0.204755	−	0.978813i	$-0.434360\pi$
$659$	26.7406	−	11.0763i	1.04166	−	0.431472i	0.836909	+	0.547342i	$0.184360\pi$
$660$		0			0
$661$	−5.00939	+	12.0937i	−0.194843	+	0.470392i	−0.990862	−	0.134879i	$-0.956935\pi$
$661$	−5.00939	+	12.0937i	−0.194843	+	0.470392i	0.796019	+	0.605271i	$0.206935\pi$
$662$		0			0
$663$	−8.83780	+	8.83780i	−0.343232	+	0.343232i
$664$		0			0
$665$	16.6985	+	16.6985i	0.647539	+	0.647539i
$666$		0			0
$667$	47.0584	+	19.4922i	1.82211	+	0.754743i
$668$		0			0
$669$	0.727387	+	1.75607i	0.0281224	+	0.0678935i
$670$		0			0
$671$	24.1523			0.932389
$672$		0			0
$673$	−25.2282			−0.972477			−0.486239	−	0.873826i	$-0.661631\pi$
$673$	−25.2282			−0.972477			−0.486239	+	0.873826i	$0.661631\pi$
$674$		0			0
$675$	0.158779	+	0.383327i	0.00611141	+	0.0147542i
$676$		0			0
$677$	−10.3092	−	4.27021i	−0.396214	−	0.164117i	0.175675	−	0.984448i	$-0.443789\pi$
$677$	−10.3092	−	4.27021i	−0.396214	−	0.164117i	−0.571889	+	0.820331i	$0.693789\pi$
$678$		0			0
$679$	−6.39209	−	6.39209i	−0.245306	−	0.245306i
$680$		0			0
$681$	−11.3064	+	11.3064i	−0.433264	+	0.433264i
$682$		0			0
$683$	−4.79116	+	11.5669i	−0.183329	+	0.442595i	−0.988649	−	0.150246i	$-0.951994\pi$
$683$	−4.79116	+	11.5669i	−0.183329	+	0.442595i	0.805320	+	0.592840i	$0.201994\pi$
$684$		0			0
$685$	8.66369	−	3.58862i	0.331023	−	0.137114i
$686$		0			0
$687$		−	12.9534i		−	0.494204i
$688$		0			0
$689$			4.61321i			0.175749i
$690$		0			0
$691$	5.63700	−	2.33492i	0.214441	−	0.0888245i	−0.272877	−	0.962049i	$-0.587975\pi$
$691$	5.63700	−	2.33492i	0.214441	−	0.0888245i	0.487318	+	0.873224i	$0.337975\pi$
$692$		0			0
$693$	−1.55479	+	3.75360i	−0.0590617	+	0.142588i
$694$		0			0
$695$	0.483035	−	0.483035i	0.0183226	−	0.0183226i
$696$		0			0
$697$	24.6282	+	24.6282i	0.932860	+	0.932860i
$698$		0			0
$699$	−7.05635	−	2.92284i	−0.266896	−	0.110552i
$700$		0			0
$701$	9.95368	+	24.0303i	0.375945	+	0.907612i	0.992717	+	0.120470i	$0.0384402\pi$
$701$	9.95368	+	24.0303i	0.375945	+	0.907612i	−0.616772	+	0.787142i	$0.711560\pi$
$702$		0			0
$703$	42.1671			1.59036
$704$		0			0
$705$	12.3873			0.466533
$706$		0			0
$707$	−1.87679	−	4.53098i	−0.0705840	−	0.170405i
$708$		0			0
$709$	36.9193	+	15.2925i	1.38653	+	0.574322i	0.946221	−	0.323522i	$-0.104867\pi$
$709$	36.9193	+	15.2925i	1.38653	+	0.574322i	0.440314	+	0.897844i	$0.354867\pi$
$710$		0			0
$711$	10.2482	+	10.2482i	0.384336	+	0.384336i
$712$		0			0
$713$	7.16636	−	7.16636i	0.268382	−	0.268382i
$714$		0			0
$715$	−5.11328	+	12.3445i	−0.191226	+	0.461660i
$716$		0			0
$717$	20.9183	−	8.66464i	0.781208	−	0.323587i
$718$		0			0
$719$		−	38.7035i		−	1.44340i	−0.692208	−	0.721698i	$-0.743362\pi$
$719$		−	38.7035i		−	1.44340i	0.692208	−	0.721698i	$-0.256638\pi$
$720$		0			0
$721$			12.8489i			0.478518i
$722$		0			0
$723$	18.9251	−	7.83903i	0.703832	−	0.291537i
$724$		0			0
$725$	1.58748	−	3.83251i	0.0589575	−	0.142336i
$726$		0			0
$727$	8.44191	−	8.44191i	0.313093	−	0.313093i	−0.533014	−	0.846107i	$-0.678941\pi$
$727$	8.44191	−	8.44191i	0.313093	−	0.313093i	0.846107	+	0.533014i	$0.178941\pi$
$728$		0			0
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$		0			0
$731$	60.3587	+	25.0014i	2.23245	+	0.924709i
$732$		0			0
$733$	−8.42070	−	20.3294i	−0.311026	−	0.750883i	−0.999668	−	0.0257810i	$-0.991793\pi$
$733$	−8.42070	−	20.3294i	−0.311026	−	0.750883i	0.688642	−	0.725102i	$-0.258207\pi$
$734$		0			0
$735$	10.6575			0.393109
$736$		0			0
$737$	−15.4064			−0.567500
$738$		0			0
$739$	6.97881	+	16.8483i	0.256720	+	0.619776i	0.998718	−	0.0506261i	$-0.0161217\pi$
$739$	6.97881	+	16.8483i	0.256720	+	0.619776i	−0.741998	+	0.670402i	$0.766122\pi$
$740$		0			0
$741$	13.2508	+	5.48867i	0.486781	+	0.201631i
$742$		0			0
$743$	−12.3355	−	12.3355i	−0.452546	−	0.452546i	0.443653	−	0.896199i	$-0.353682\pi$
$743$	−12.3355	−	12.3355i	−0.452546	−	0.452546i	−0.896199	+	0.443653i	$0.853682\pi$
$744$		0			0
$745$	−22.3344	+	22.3344i	−0.818267	+	0.818267i
$746$		0			0
$747$	−1.03832	+	2.50672i	−0.0379901	+	0.0917162i
$748$		0			0
$749$	12.2708	−	5.08274i	0.448366	−	0.185719i
$750$		0			0
$751$		−	17.5511i		−	0.640449i	−0.947342	−	0.320224i	$-0.896242\pi$
$751$		−	17.5511i		−	0.640449i	0.947342	−	0.320224i	$-0.103758\pi$
$752$		0			0
$753$		−	13.6467i		−	0.497314i
$754$		0			0
$755$	−3.15273	+	1.30590i	−0.114740	+	0.0475267i
$756$		0			0
$757$	−2.89105	+	6.97962i	−0.105077	+	0.253679i	−0.967670	−	0.252220i	$-0.918839\pi$
$757$	−2.89105	+	6.97962i	−0.105077	+	0.253679i	0.862593	+	0.505899i	$0.168839\pi$
$758$		0			0
$759$	9.40835	−	9.40835i	0.341501	−	0.341501i
$760$		0			0
$761$	22.3535	+	22.3535i	0.810314	+	0.810314i	0.984681	−	0.174367i	$-0.0557879\pi$
$761$	22.3535	+	22.3535i	0.810314	+	0.810314i	−0.174367	+	0.984681i	$0.555788\pi$
$762$		0			0
$763$	19.1741	+	7.94219i	0.694150	+	0.287527i
$764$		0			0
$765$	−5.06234	−	12.2216i	−0.183029	−	0.441872i
$766$		0			0
$767$	14.2124			0.513179
$768$		0			0
$769$	−3.22764			−0.116392			−0.0581958	−	0.998305i	$-0.518535\pi$
$769$	−3.22764			−0.116392			−0.0581958	+	0.998305i	$0.518535\pi$
$770$		0			0
$771$	−4.75028	−	11.4682i	−0.171077	−	0.413017i
$772$		0			0
$773$	−6.48169	−	2.68480i	−0.233130	−	0.0965656i	0.263060	−	0.964779i	$-0.415268\pi$
$773$	−6.48169	−	2.68480i	−0.233130	−	0.0965656i	−0.496190	+	0.868214i	$0.665268\pi$
$774$		0			0
$775$	−0.583639	−	0.583639i	−0.0209649	−	0.0209649i
$776$		0			0
$777$	−7.11028	+	7.11028i	−0.255080	+	0.255080i
$778$		0			0
$779$	15.2952	−	36.9259i	0.548008	−	1.32301i
$780$		0			0
$781$	−8.77910	+	3.63642i	−0.314141	+	0.130121i
$782$		0			0
$783$		−	9.99803i		−	0.357301i
$784$		0			0
$785$			1.94451i			0.0694025i
$786$		0			0
$787$	−44.8838	+	18.5915i	−1.59994	+	0.662715i	−0.991407	−	0.130816i	$-0.958240\pi$
$787$	−44.8838	+	18.5915i	−1.59994	+	0.662715i	−0.608530	+	0.793531i	$0.708240\pi$
$788$		0			0
$789$	−9.46175	+	22.8427i	−0.336847	+	0.813221i
$790$		0			0
$791$	15.0660	−	15.0660i	0.535685	−	0.535685i
$792$		0			0
$793$	14.3769	+	14.3769i	0.510540	+	0.510540i
$794$		0			0
$795$	−4.51098	−	1.86851i	−0.159988	−	0.0662692i
$796$		0			0
$797$	9.68913	+	23.3916i	0.343207	+	0.828574i	0.997388	+	0.0722361i	$0.0230135\pi$
$797$	9.68913	+	23.3916i	0.343207	+	0.828574i	−0.654181	+	0.756338i	$0.726986\pi$
$798$		0			0
$799$	−30.2620			−1.07059
$800$		0			0
$801$	4.22491			0.149280
$802$		0			0
$803$	−11.3235	−	27.3373i	−0.399596	−	0.964711i
$804$		0			0
$805$	17.0385	+	7.05757i	0.600528	+	0.248747i
$806$		0			0
$807$	8.51189	+	8.51189i	0.299633	+	0.299633i
$808$		0			0
$809$	21.6097	−	21.6097i	0.759757	−	0.759757i	−0.216521	−	0.976278i	$-0.569471\pi$
$809$	21.6097	−	21.6097i	0.759757	−	0.759757i	0.976278	+	0.216521i	$0.0694708\pi$
$810$		0			0
$811$	0.140101	−	0.338233i	0.00491960	−	0.0118770i	−0.921401	−	0.388614i	$-0.872954\pi$
$811$	0.140101	−	0.338233i	0.00491960	−	0.0118770i	0.926320	+	0.376737i	$0.122954\pi$
$812$		0			0
$813$	17.0065	−	7.04430i	0.596442	−	0.247054i
$814$		0			0
$815$		−	11.9680i		−	0.419220i
$816$		0			0
$817$		−	74.9709i		−	2.62290i
$818$		0			0
$819$	−3.15988	+	1.30887i	−0.110415	+	0.0457355i
$820$		0			0
$821$	−1.08174	+	2.61154i	−0.0377528	+	0.0911434i	−0.941631	−	0.336646i	$-0.890707\pi$
$821$	−1.08174	+	2.61154i	−0.0377528	+	0.0911434i	0.903878	+	0.427789i	$0.140707\pi$
$822$		0			0
$823$	21.0047	−	21.0047i	0.732179	−	0.732179i	−0.238872	−	0.971051i	$-0.576778\pi$
$823$	21.0047	−	21.0047i	0.732179	−	0.732179i	0.971051	+	0.238872i	$0.0767777\pi$
$824$		0			0
$825$	−0.766230	−	0.766230i	−0.0266767	−	0.0266767i
$826$		0			0
$827$	19.4976	+	8.07616i	0.677997	+	0.280835i	0.694989	−	0.719020i	$-0.255409\pi$
$827$	19.4976	+	8.07616i	0.677997	+	0.280835i	−0.0169924	+	0.999856i	$0.505409\pi$
$828$		0			0
$829$	8.42223	+	20.3331i	0.292516	+	0.706196i	1.00000		0.000533349i	$-0.000169770\pi$
$829$	8.42223	+	20.3331i	0.292516	+	0.706196i	−0.707484	+	0.706730i	$0.750170\pi$
$830$		0			0
$831$	−11.4160			−0.396018
$832$		0			0
$833$	−26.0361			−0.902098
$834$		0			0
$835$	−5.83396	−	14.0844i	−0.201893	−	0.487412i
$836$		0			0
$837$	−1.83790	−	0.761282i	−0.0635270	−	0.0263138i
$838$		0			0
$839$	8.19553	+	8.19553i	0.282941	+	0.282941i	0.834281	−	0.551340i	$-0.185883\pi$
$839$	8.19553	+	8.19553i	0.282941	+	0.282941i	−0.551340	+	0.834281i	$0.685883\pi$
$840$		0			0
$841$	−50.1768	+	50.1768i	−1.73023	+	1.73023i
$842$		0			0
$843$	−3.09114	+	7.46267i	−0.106465	+	0.257028i
$844$		0			0
$845$	17.5563	−	7.27204i	0.603954	−	0.250166i
$846$		0			0
$847$			6.50123i			0.223385i
$848$		0			0
$849$			8.96316i			0.307615i
$850$		0			0
$851$	30.4237	−	12.6019i	1.04291	−	0.431988i
$852$		0			0
$853$	−3.85955	+	9.31778i	−0.132148	+	0.319035i	−0.976078	−	0.217419i	$-0.930236\pi$
$853$	−3.85955	+	9.31778i	−0.132148	+	0.319035i	0.843930	+	0.536453i	$0.180236\pi$
$854$		0			0
$855$	−10.7341	+	10.7341i	−0.367098	+	0.367098i
$856$		0			0
$857$	−16.3295	−	16.3295i	−0.557806	−	0.557806i	0.370876	−	0.928682i	$-0.379057\pi$
$857$	−16.3295	−	16.3295i	−0.557806	−	0.557806i	−0.928682	+	0.370876i	$0.879057\pi$
$858$		0			0
$859$	18.7583	+	7.76993i	0.640024	+	0.265107i	0.679005	−	0.734133i	$-0.262411\pi$
$859$	18.7583	+	7.76993i	0.640024	+	0.265107i	−0.0389814	+	0.999240i	$0.512411\pi$
$860$		0			0
$861$	3.64740	+	8.80561i	0.124303	+	0.300094i
$862$		0			0
$863$	−25.9774			−0.884280			−0.442140	−	0.896946i	$-0.645780\pi$
$863$	−25.9774			−0.884280			−0.442140	+	0.896946i	$0.645780\pi$
$864$		0			0
$865$	31.9082			1.08491
$866$		0			0
$867$	5.86158	+	14.1511i	0.199070	+	0.480597i
$868$		0			0
$869$	−34.9701	−	14.4851i	−1.18628	−	0.491373i
$870$		0			0
$871$	−9.17080	−	9.17080i	−0.310741	−	0.310741i
$872$		0			0
$873$	4.10894	−	4.10894i	0.139067	−	0.139067i
$874$		0			0
$875$	−6.35178	+	15.3346i	−0.214729	+	0.518403i
$876$		0			0
$877$	10.3735	−	4.29686i	0.350289	−	0.145095i	−0.200599	−	0.979673i	$-0.564289\pi$
$877$	10.3735	−	4.29686i	0.350289	−	0.145095i	0.550889	+	0.834579i	$0.314289\pi$
$878$		0			0
$879$		−	18.6710i		−	0.629757i
$880$		0			0
$881$		−	23.3514i		−	0.786727i	−0.919383	−	0.393364i	$-0.871311\pi$
$881$		−	23.3514i		−	0.786727i	0.919383	−	0.393364i	$-0.128689\pi$
$882$		0			0
$883$	−16.9363	+	7.01525i	−0.569953	+	0.236082i	−0.649000	−	0.760789i	$-0.724812\pi$
$883$	−16.9363	+	7.01525i	−0.569953	+	0.236082i	0.0790470	+	0.996871i	$0.474812\pi$
$884$		0			0
$885$	−5.75650	+	13.8974i	−0.193503	+	0.467156i
$886$		0			0
$887$	−31.0507	+	31.0507i	−1.04258	+	1.04258i	−0.0435268	+	0.999052i	$0.513859\pi$
$887$	−31.0507	+	31.0507i	−1.04258	+	1.04258i	−0.999052	+	0.0435268i	$0.986141\pi$
$888$		0			0
$889$	−5.07194	−	5.07194i	−0.170107	−	0.170107i
$890$		0			0
$891$	−2.41288	−	0.999449i	−0.0808346	−	0.0334828i
$892$		0			0
$893$	13.2894	+	32.0835i	0.444713	+	1.07363i
$894$		0			0
$895$	21.5440			0.720135
$896$		0			0
$897$	11.2009			0.373985
$898$		0			0
$899$	7.61132	+	18.3754i	0.253852	+	0.612853i
$900$		0			0
$901$	11.0202	+	4.56474i	0.367138	+	0.152073i
$902$		0			0
$903$	12.6417	+	12.6417i	0.420690	+	0.420690i
$904$		0			0
$905$	−2.13262	+	2.13262i	−0.0708907	+	0.0708907i
$906$		0			0
$907$	13.3144	−	32.1439i	0.442098	−	1.06732i	−0.533113	−	0.846044i	$-0.678978\pi$
$907$	13.3144	−	32.1439i	0.442098	−	1.06732i	0.975211	−	0.221276i	$-0.0710220\pi$
$908$		0			0
$909$	2.91259	−	1.20644i	0.0966046	−	0.0400149i
$910$		0			0
$911$			30.1527i			0.999003i	0.866313	+	0.499501i	$0.166483\pi$
$911$			30.1527i			0.999003i	−0.866313	+	0.499501i	$0.833517\pi$
$912$		0			0
$913$		−	7.08617i		−	0.234518i
$914$		0			0
$915$	−19.8815	+	8.23518i	−0.657261	+	0.272247i
$916$		0			0
$917$	−0.996630	+	2.40608i	−0.0329116	+	0.0794557i
$918$		0			0
$919$	−40.8534	+	40.8534i	−1.34763	+	1.34763i	−0.459399	+	0.888230i	$0.651935\pi$
$919$	−40.8534	+	40.8534i	−1.34763	+	1.34763i	−0.888230	+	0.459399i	$0.848065\pi$
$920$		0			0
$921$	0.225342	+	0.225342i	0.00742527	+	0.00742527i
$922$		0			0
$923$	−7.39048	−	3.06124i	−0.243261	−	0.100762i
$924$		0			0
$925$	−1.02632	−	2.47775i	−0.0337452	−	0.0814681i
$926$		0			0
$927$	−8.25949			−0.271277
$928$		0			0
$929$	17.8445			0.585459			0.292730	−	0.956195i	$-0.405436\pi$
$929$	17.8445			0.585459			0.292730	+	0.956195i	$0.405436\pi$
$930$		0			0
$931$	11.4336	+	27.6032i	0.374722	+	0.904660i
$932$		0			0
$933$	12.3998	+	5.13616i	0.405951	+	0.168150i
$934$		0			0
$935$	24.4296	+	24.4296i	0.798935	+	0.798935i
$936$		0			0
$937$	−23.4570	+	23.4570i	−0.766305	+	0.766305i	−0.977454	−	0.211149i	$-0.932280\pi$
$937$	−23.4570	+	23.4570i	−0.766305	+	0.766305i	0.211149	+	0.977454i	$0.432280\pi$
$938$		0			0
$939$	−12.5195	+	30.2248i	−0.408559	+	0.986348i
$940$		0			0
$941$	−52.6462	+	21.8068i	−1.71622	+	0.710880i	−0.716303	+	0.697790i	$0.754167\pi$
$941$	−52.6462	+	21.8068i	−1.71622	+	0.710880i	−0.999914	+	0.0130904i	$0.995833\pi$
$942$		0			0
$943$		−	31.2133i		−	1.01644i
$944$		0			0
$945$		−	3.61999i		−	0.117758i
$946$		0			0
$947$	−16.8510	+	6.97991i	−0.547583	+	0.226817i	−0.639285	−	0.768970i	$-0.720769\pi$
$947$	−16.8510	+	6.97991i	−0.547583	+	0.226817i	0.0917013	+	0.995787i	$0.470769\pi$
$948$		0			0
$949$	9.53239	−	23.0132i	0.309434	−	0.747041i
$950$		0			0
$951$	2.16449	−	2.16449i	0.0701883	−	0.0701883i
$952$		0			0
$953$	−12.6109	−	12.6109i	−0.408508	−	0.408508i	0.472710	−	0.881218i	$-0.343276\pi$
$953$	−12.6109	−	12.6109i	−0.408508	−	0.408508i	−0.881218	+	0.472710i	$0.843276\pi$
$954$		0			0
$955$	−1.39062	−	0.576015i	−0.0449995	−	0.0186394i
$956$		0			0
$957$	9.99252	+	24.1241i	0.323012	+	0.779821i
$958$		0			0
$959$	−6.26909			−0.202439
$960$		0			0
$961$	−27.0426			−0.872341
$962$		0			0
$963$	3.26727	+	7.88789i	0.105286	+	0.254184i
$964$		0			0
$965$	−40.2444	−	16.6698i	−1.29551	−	0.536619i
$966$		0			0
$967$	−25.3370	−	25.3370i	−0.814782	−	0.814782i	0.170564	−	0.985347i	$-0.445441\pi$
$967$	−25.3370	−	25.3370i	−0.814782	−	0.814782i	−0.985347	+	0.170564i	$0.945441\pi$
$968$		0			0
$969$	26.2232	−	26.2232i	0.842409	−	0.842409i
$970$		0			0
$971$	−5.11357	+	12.3453i	−0.164102	+	0.396178i	−0.984445	−	0.175695i	$-0.943783\pi$
$971$	−5.11357	+	12.3453i	−0.164102	+	0.396178i	0.820342	+	0.571873i	$0.193783\pi$
$972$		0			0
$973$	−0.421916	+	0.174763i	−0.0135260	+	0.00560265i
$974$		0			0
$975$		−	0.912214i		−	0.0292142i
$976$		0			0
$977$		−	56.2505i		−	1.79961i	−0.436291	−	0.899806i	$-0.643708\pi$
$977$		−	56.2505i		−	1.79961i	0.436291	−	0.899806i	$-0.356292\pi$
$978$		0			0
$979$	−10.1942	+	4.22258i	−0.325808	+	0.134954i
$980$		0			0
$981$	−5.10538	+	12.3255i	−0.163002	+	0.393522i
$982$		0			0
$983$	36.5021	−	36.5021i	1.16424	−	1.16424i	0.180699	−	0.983538i	$-0.442164\pi$
$983$	36.5021	−	36.5021i	1.16424	−	1.16424i	0.983538	−	0.180699i	$-0.0578360\pi$
$984$		0			0
$985$	−1.06482	−	1.06482i	−0.0339279	−	0.0339279i
$986$		0			0
$987$	−7.65084	−	3.16908i	−0.243529	−	0.100873i
$988$		0			0
$989$	−22.4056	−	54.0918i	−0.712455	−	1.72002i
$990$		0			0
$991$	18.2602			0.580054			0.290027	−	0.957018i	$-0.406336\pi$
$991$	18.2602			0.580054			0.290027	+	0.957018i	$0.406336\pi$
$992$		0			0
$993$	−15.2108			−0.482699
$994$		0			0
$995$	−17.0577	−	41.1808i	−0.540764	−	1.30552i
$996$		0			0
$997$	−26.7726	−	11.0896i	−0.847898	−	0.351211i	−0.0839354	−	0.996471i	$-0.526749\pi$
$997$	−26.7726	−	11.0896i	−0.847898	−	0.351211i	−0.763963	+	0.645260i	$0.776749\pi$
$998$		0			0
$999$	−4.57061	−	4.57061i	−0.144608	−	0.144608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.481.1		32
4.3	odd	2		768.2.n.a.481.5		32
8.3	odd	2		96.2.n.a.37.6	yes	32
8.5	even	2		384.2.n.a.241.8		32
24.5	odd	2		1152.2.v.c.1009.2		32
24.11	even	2		288.2.v.d.37.3		32
32.3	odd	8		96.2.n.a.13.6	✓	32
32.13	even	8	inner	768.2.n.b.289.1		32
32.19	odd	8		768.2.n.a.289.5		32
32.29	even	8		384.2.n.a.145.8		32
96.29	odd	8		1152.2.v.c.145.2		32
96.35	even	8		288.2.v.d.109.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.6	✓	32	32.3	odd	8
96.2.n.a.37.6	yes	32	8.3	odd	2
288.2.v.d.37.3		32	24.11	even	2
288.2.v.d.109.3		32	96.35	even	8
384.2.n.a.145.8		32	32.29	even	8
384.2.n.a.241.8		32	8.5	even	2
768.2.n.a.289.5		32	32.19	odd	8
768.2.n.a.481.5		32	4.3	odd	2
768.2.n.b.289.1		32	32.13	even	8	inner
768.2.n.b.481.1		32	1.1	even	1	trivial
1152.2.v.c.145.2		32	96.29	odd	8
1152.2.v.c.1009.2		32	24.5	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 - 0.923880i) q^{3} +(-2.14986 - 0.890503i) q^{5} +(1.10001 + 1.10001i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.382683 - 0.923880i) q^{3} +(-2.14986 - 0.890503i) q^{5} +(1.10001 + 1.10001i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(0.999449 - 2.41288i) q^{11} +(2.03123 - 0.841362i) q^{13} +2.32700i q^{15} -5.68481i q^{17} +(-6.02698 + 2.49646i) q^{19} +(0.595322 - 1.43723i) q^{21} +(-3.60241 + 3.60241i) q^{23} +(0.293385 + 0.293385i) q^{25} +(0.923880 + 0.382683i) q^{27} +(-3.82608 - 9.23698i) q^{29} -1.98933 q^{31} -2.61168 q^{33} +(-1.38531 - 3.34444i) q^{35} +(-5.97179 - 2.47360i) q^{37} +(-1.55463 - 1.55463i) q^{39} +(-4.33228 + 4.33228i) q^{41} +(-4.39793 + 10.6175i) q^{43} +(2.14986 - 0.890503i) q^{45} -5.32331i q^{47} -4.57995i q^{49} +(-5.25208 + 2.17548i) q^{51} +(-0.802971 + 1.93854i) q^{53} +(-4.29736 + 4.29736i) q^{55} +(4.61285 + 4.61285i) q^{57} +(5.97225 + 2.47379i) q^{59} +(3.53897 + 8.54384i) q^{61} -1.55565 q^{63} -5.11610 q^{65} +(-2.25745 - 5.44997i) q^{67} +(4.70677 + 1.94961i) q^{69} +(-2.57276 - 2.57276i) q^{71} +(8.01131 - 8.01131i) q^{73} +(0.158779 - 0.383327i) q^{75} +(3.75360 - 1.55479i) q^{77} -14.4931i q^{79} -1.00000i q^{81} +(2.50672 - 1.03832i) q^{83} +(-5.06234 + 12.2216i) q^{85} +(-7.06968 + 7.06968i) q^{87} +(-2.98746 - 2.98746i) q^{89} +(3.15988 + 1.30887i) q^{91} +(0.761282 + 1.83790i) q^{93} +15.1803 q^{95} -5.81093 q^{97} +(0.999449 + 2.41288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more