LMFDB - Embedded newform 768.2.n.b.673.2

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			673.2
Character	$\chi$	$=$	768.673
Dual form			768.2.n.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 - 0.382683i) q^{3} +(-0.705805 - 1.70396i) q^{5} +(-3.24150 + 3.24150i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.923880 - 0.382683i) q^{3} +(-0.705805 - 1.70396i) q^{5} +(-3.24150 + 3.24150i) q^{7} +(0.707107 + 0.707107i) q^{9} +(3.38931 - 1.40390i) q^{11} +(0.503962 - 1.21667i) q^{13} +1.84436i q^{15} +0.622706i q^{17} +(-2.14250 + 5.17245i) q^{19} +(4.23522 - 1.75429i) q^{21} +(2.47578 + 2.47578i) q^{23} +(1.13020 - 1.13020i) q^{25} +(-0.382683 - 0.923880i) q^{27} +(2.16691 + 0.897562i) q^{29} +10.4506 q^{31} -3.66856 q^{33} +(7.81126 + 3.23553i) q^{35} +(0.0714604 + 0.172521i) q^{37} +(-0.931200 + 0.931200i) q^{39} +(8.50664 + 8.50664i) q^{41} +(-3.62132 + 1.50000i) q^{43} +(0.705805 - 1.70396i) q^{45} +5.02899i q^{47} -14.0146i q^{49} +(0.238299 - 0.575305i) q^{51} +(7.15914 - 2.96541i) q^{53} +(-4.78438 - 4.78438i) q^{55} +(3.95882 - 3.95882i) q^{57} +(-1.52516 - 3.68206i) q^{59} +(3.07333 + 1.27302i) q^{61} -4.58417 q^{63} -2.42886 q^{65} +(-2.17574 - 0.901222i) q^{67} +(-1.33988 - 3.23477i) q^{69} +(1.11161 - 1.11161i) q^{71} +(3.71598 + 3.71598i) q^{73} +(-1.47668 + 0.611660i) q^{75} +(-6.43570 + 15.5372i) q^{77} -10.2251i q^{79} +1.00000i q^{81} +(-4.69181 + 11.3270i) q^{83} +(1.06107 - 0.439509i) q^{85} +(-1.65848 - 1.65848i) q^{87} +(-3.54033 + 3.54033i) q^{89} +(2.31025 + 5.57743i) q^{91} +(-9.65514 - 3.99929i) q^{93} +10.3259 q^{95} +0.139594 q^{97} +(3.38931 + 1.40390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$4$		0			0
$5$	−0.705805	−	1.70396i	−0.315646	−	0.762036i	−0.999475	−	0.0323942i	$-0.989687\pi$
$5$	−0.705805	−	1.70396i	−0.315646	−	0.762036i	0.683829	−	0.729642i	$-0.260313\pi$
$6$		0			0
$7$	−3.24150	+	3.24150i	−1.22517	+	1.22517i	−0.259402	+	0.965769i	$0.583525\pi$
$7$	−3.24150	+	3.24150i	−1.22517	+	1.22517i	−0.965769	+	0.259402i	$0.916475\pi$
$8$		0			0
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$		0			0
$11$	3.38931	−	1.40390i	1.02191	−	0.423291i	0.192127	−	0.981370i	$-0.438462\pi$
$11$	3.38931	−	1.40390i	1.02191	−	0.423291i	0.829788	+	0.558079i	$0.188462\pi$
$12$		0			0
$13$	0.503962	−	1.21667i	0.139774	−	0.337444i	−0.838456	−	0.544970i	$-0.816541\pi$
$13$	0.503962	−	1.21667i	0.139774	−	0.337444i	0.978230	+	0.207526i	$0.0665411\pi$
$14$		0			0
$15$			1.84436i			0.476211i
$16$		0			0
$17$			0.622706i			0.151028i	0.997145	+	0.0755142i	$0.0240598\pi$
$17$			0.622706i			0.151028i	−0.997145	+	0.0755142i	$0.975940\pi$
$18$		0			0
$19$	−2.14250	+	5.17245i	−0.491523	+	1.18664i	0.462422	+	0.886660i	$0.346980\pi$
$19$	−2.14250	+	5.17245i	−0.491523	+	1.18664i	−0.953945	+	0.299981i	$0.903020\pi$
$20$		0			0
$21$	4.23522	−	1.75429i	0.924201	−	0.382817i
$22$		0			0
$23$	2.47578	+	2.47578i	0.516236	+	0.516236i	0.916430	−	0.400194i	$-0.131057\pi$
$23$	2.47578	+	2.47578i	0.516236	+	0.516236i	−0.400194	+	0.916430i	$0.631057\pi$
$24$		0			0
$25$	1.13020	−	1.13020i	0.226040	−	0.226040i
$26$		0			0
$27$	−0.382683	−	0.923880i	−0.0736475	−	0.177801i
$28$		0			0
$29$	2.16691	+	0.897562i	0.402384	+	0.166673i	0.574691	−	0.818370i	$-0.305122\pi$
$29$	2.16691	+	0.897562i	0.402384	+	0.166673i	−0.172307	+	0.985043i	$0.555122\pi$
$30$		0			0
$31$	10.4506			1.87699			0.938496	−	0.345290i	$-0.112220\pi$
$31$	10.4506			1.87699			0.938496	+	0.345290i	$0.112220\pi$
$32$		0			0
$33$	−3.66856			−0.638614
$34$		0			0
$35$	7.81126	+	3.23553i	1.32034	+	0.546905i
$36$		0			0
$37$	0.0714604	+	0.172521i	0.0117480	+	0.0283622i	0.929645	−	0.368457i	$-0.120114\pi$
$37$	0.0714604	+	0.172521i	0.0117480	+	0.0283622i	−0.917897	+	0.396819i	$0.870114\pi$
$38$		0			0
$39$	−0.931200	+	0.931200i	−0.149111	+	0.149111i
$40$		0			0
$41$	8.50664	+	8.50664i	1.32851	+	1.32851i	0.906667	+	0.421847i	$0.138618\pi$
$41$	8.50664	+	8.50664i	1.32851	+	1.32851i	0.421847	+	0.906667i	$0.361382\pi$
$42$		0			0
$43$	−3.62132	+	1.50000i	−0.552247	+	0.228748i	−0.641315	−	0.767277i	$-0.721611\pi$
$43$	−3.62132	+	1.50000i	−0.552247	+	0.228748i	0.0890686	+	0.996025i	$0.471611\pi$
$44$		0			0
$45$	0.705805	−	1.70396i	0.105215	−	0.254012i
$46$		0			0
$47$			5.02899i			0.733554i	0.930309	+	0.366777i	$0.119539\pi$
$47$			5.02899i			0.733554i	−0.930309	+	0.366777i	$0.880461\pi$
$48$		0			0
$49$		−	14.0146i		−	2.00209i
$50$		0			0
$51$	0.238299	−	0.575305i	0.0333686	−	0.0805588i
$52$		0			0
$53$	7.15914	−	2.96541i	0.983383	−	0.407331i	0.167706	−	0.985837i	$-0.446364\pi$
$53$	7.15914	−	2.96541i	0.983383	−	0.407331i	0.815678	+	0.578506i	$0.196364\pi$
$54$		0			0
$55$	−4.78438	−	4.78438i	−0.645126	−	0.645126i
$56$		0			0
$57$	3.95882	−	3.95882i	0.524359	−	0.524359i
$58$		0			0
$59$	−1.52516	−	3.68206i	−0.198559	−	0.479363i	0.792968	−	0.609263i	$-0.208535\pi$
$59$	−1.52516	−	3.68206i	−0.198559	−	0.479363i	−0.991527	+	0.129900i	$0.958535\pi$
$60$		0			0
$61$	3.07333	+	1.27302i	0.393500	+	0.162993i	0.570655	−	0.821190i	$-0.306689\pi$
$61$	3.07333	+	1.27302i	0.393500	+	0.162993i	−0.177155	+	0.984183i	$0.556689\pi$
$62$		0			0
$63$	−4.58417			−0.577551
$64$		0			0
$65$	−2.42886			−0.301264
$66$		0			0
$67$	−2.17574	−	0.901222i	−0.265809	−	0.110102i	0.245798	−	0.969321i	$-0.420950\pi$
$67$	−2.17574	−	0.901222i	−0.265809	−	0.110102i	−0.511608	+	0.859219i	$0.670950\pi$
$68$		0			0
$69$	−1.33988	−	3.23477i	−0.161303	−	0.389420i
$70$		0			0
$71$	1.11161	−	1.11161i	0.131924	−	0.131924i	−0.638061	−	0.769986i	$-0.720263\pi$
$71$	1.11161	−	1.11161i	0.131924	−	0.131924i	0.769986	+	0.638061i	$0.220263\pi$
$72$		0			0
$73$	3.71598	+	3.71598i	0.434923	+	0.434923i	0.890299	−	0.455376i	$-0.150495\pi$
$73$	3.71598	+	3.71598i	0.434923	+	0.434923i	−0.455376	+	0.890299i	$0.650495\pi$
$74$		0			0
$75$	−1.47668	+	0.611660i	−0.170512	+	0.0706284i
$76$		0			0
$77$	−6.43570	+	15.5372i	−0.733416	+	1.77062i
$78$		0			0
$79$		−	10.2251i		−	1.15041i	−0.818008	−	0.575207i	$-0.804921\pi$
$79$		−	10.2251i		−	1.15041i	0.818008	−	0.575207i	$-0.195079\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	−4.69181	+	11.3270i	−0.514993	+	1.24330i	0.425953	+	0.904745i	$0.359939\pi$
$83$	−4.69181	+	11.3270i	−0.514993	+	1.24330i	−0.940946	+	0.338558i	$0.890061\pi$
$84$		0			0
$85$	1.06107	−	0.439509i	0.115089	−	0.0476714i
$86$		0			0
$87$	−1.65848	−	1.65848i	−0.177808	−	0.177808i
$88$		0			0
$89$	−3.54033	+	3.54033i	−0.375274	+	0.375274i	−0.869394	−	0.494120i	$-0.835490\pi$
$89$	−3.54033	+	3.54033i	−0.375274	+	0.375274i	0.494120	+	0.869394i	$0.335490\pi$
$90$		0			0
$91$	2.31025	+	5.57743i	0.242180	+	0.584674i
$92$		0			0
$93$	−9.65514	−	3.99929i	−1.00119	−	0.414707i
$94$		0			0
$95$	10.3259			1.05941
$96$		0			0
$97$	0.139594			0.0141737			0.00708683	−	0.999975i	$-0.497744\pi$
$97$	0.139594			0.0141737			0.00708683	+	0.999975i	$0.497744\pi$
$98$		0			0
$99$	3.38931	+	1.40390i	0.340638	+	0.141097i
$100$		0			0
$101$	4.89005	+	11.8056i	0.486578	+	1.17470i	0.956431	+	0.291958i	$0.0943068\pi$
$101$	4.89005	+	11.8056i	0.486578	+	1.17470i	−0.469853	+	0.882744i	$0.655693\pi$
$102$		0			0
$103$	−3.64510	+	3.64510i	−0.359162	+	0.359162i	−0.863504	−	0.504342i	$-0.831735\pi$
$103$	−3.64510	+	3.64510i	−0.359162	+	0.359162i	0.504342	+	0.863504i	$0.331735\pi$
$104$		0			0
$105$	−5.97848	−	5.97848i	−0.583440	−	0.583440i
$106$		0			0
$107$	6.93872	−	2.87411i	0.670792	−	0.277851i	−0.0211799	−	0.999776i	$-0.506742\pi$
$107$	6.93872	−	2.87411i	0.670792	−	0.277851i	0.691972	+	0.721925i	$0.256742\pi$
$108$		0			0
$109$	−5.91722	+	14.2854i	−0.566767	+	1.36830i	0.337498	+	0.941326i	$0.390419\pi$
$109$	−5.91722	+	14.2854i	−0.566767	+	1.36830i	−0.904266	+	0.426971i	$0.859581\pi$
$110$		0			0
$111$		−	0.186735i		−	0.0177241i
$112$		0			0
$113$			9.04489i			0.850872i	0.904989	+	0.425436i	$0.139879\pi$
$113$			9.04489i			0.850872i	−0.904989	+	0.425436i	$0.860121\pi$
$114$		0			0
$115$	2.47122	−	5.96606i	0.230443	−	0.556338i
$116$		0			0
$117$	1.21667	−	0.503962i	0.112481	−	0.0465913i
$118$		0			0
$119$	−2.01850	−	2.01850i	−0.185036	−	0.185036i
$120$		0			0
$121$	1.73830	−	1.73830i	0.158027	−	0.158027i
$122$		0			0
$123$	−4.60376	−	11.1145i	−0.415107	−	1.00216i
$124$		0			0
$125$	−11.2433	−	4.65715i	−1.00564	−	0.416548i
$126$		0			0
$127$	−5.82989			−0.517319			−0.258659	−	0.965969i	$-0.583281\pi$
$127$	−5.82989			−0.517319			−0.258659	+	0.965969i	$0.583281\pi$
$128$		0			0
$129$	3.91969			0.345110
$130$		0			0
$131$	6.80141	+	2.81723i	0.594242	+	0.246143i	0.659474	−	0.751727i	$-0.270779\pi$
$131$	6.80141	+	2.81723i	0.594242	+	0.246143i	−0.0652326	+	0.997870i	$0.520779\pi$
$132$		0			0
$133$	−9.82158	−	23.7114i	−0.851639	−	2.05604i
$134$		0			0
$135$	−1.30416	+	1.30416i	−0.112244	+	0.112244i
$136$		0			0
$137$	−13.7370	−	13.7370i	−1.17363	−	1.17363i	−0.981337	−	0.192295i	$-0.938407\pi$
$137$	−13.7370	−	13.7370i	−1.17363	−	1.17363i	−0.192295	−	0.981337i	$-0.561593\pi$
$138$		0			0
$139$	2.14254	−	0.887468i	0.181728	−	0.0752740i	−0.289964	−	0.957037i	$-0.593643\pi$
$139$	2.14254	−	0.887468i	0.181728	−	0.0752740i	0.471692	+	0.881763i	$0.343643\pi$
$140$		0			0
$141$	1.92451	−	4.64619i	0.162073	−	0.391279i
$142$		0			0
$143$		−	4.83118i		−	0.404004i
$144$		0			0
$145$		−	4.32584i		−	0.359241i
$146$		0			0
$147$	−5.36316	+	12.9478i	−0.442346	+	1.06792i
$148$		0			0
$149$	−0.926481	+	0.383761i	−0.0759003	+	0.0314389i	−0.420311	−	0.907380i	$-0.638079\pi$
$149$	−0.926481	+	0.383761i	−0.0759003	+	0.0314389i	0.344410	+	0.938819i	$0.388079\pi$
$150$		0			0
$151$	−7.02526	−	7.02526i	−0.571707	−	0.571707i	0.360898	−	0.932605i	$-0.382470\pi$
$151$	−7.02526	−	7.02526i	−0.571707	−	0.571707i	−0.932605	+	0.360898i	$0.882470\pi$
$152$		0			0
$153$	−0.440320	+	0.440320i	−0.0355977	+	0.0355977i
$154$		0			0
$155$	−7.37612	−	17.8075i	−0.592464	−	1.43034i
$156$		0			0
$157$	5.63224	+	2.33295i	0.449502	+	0.186190i	0.595938	−	0.803030i	$-0.296780\pi$
$157$	5.63224	+	2.33295i	0.449502	+	0.186190i	−0.146436	+	0.989220i	$0.546780\pi$
$158$		0			0
$159$	−7.74900			−0.614535
$160$		0			0
$161$	−16.0505			−1.26496
$162$		0			0
$163$	−20.2647	−	8.39392i	−1.58726	−	0.657463i	−0.597714	−	0.801709i	$-0.703924\pi$
$163$	−20.2647	−	8.39392i	−1.58726	−	0.657463i	−0.989542	+	0.144246i	$0.953924\pi$
$164$		0			0
$165$	2.58929	+	6.25109i	0.201576	+	0.486647i
$166$		0			0
$167$	9.26966	−	9.26966i	0.717308	−	0.717308i	−0.250745	−	0.968053i	$-0.580676\pi$
$167$	9.26966	−	9.26966i	0.717308	−	0.717308i	0.968053	+	0.250745i	$0.0806756\pi$
$168$		0			0
$169$	7.96608	+	7.96608i	0.612775	+	0.612775i
$170$		0			0
$171$	−5.17245	+	2.14250i	−0.395547	+	0.163841i
$172$		0			0
$173$	5.07428	−	12.2504i	0.385790	−	0.931380i	−0.605031	−	0.796202i	$-0.706839\pi$
$173$	5.07428	−	12.2504i	0.385790	−	0.931380i	0.990821	−	0.135178i	$-0.0431607\pi$
$174$		0			0
$175$			7.32708i			0.553875i
$176$		0			0
$177$			3.98543i			0.299563i
$178$		0			0
$179$	7.17721	−	17.3273i	0.536449	−	1.29510i	−0.390737	−	0.920503i	$-0.627780\pi$
$179$	7.17721	−	17.3273i	0.536449	−	1.29510i	0.927186	−	0.374601i	$-0.122220\pi$
$180$		0			0
$181$	−13.7526	+	5.69651i	−1.02222	+	0.423418i	−0.829899	−	0.557914i	$-0.811602\pi$
$181$	−13.7526	+	5.69651i	−1.02222	+	0.423418i	−0.192322	+	0.981332i	$0.561602\pi$
$182$		0			0
$183$	−2.35223	−	2.35223i	−0.173882	−	0.173882i
$184$		0			0
$185$	0.243532	−	0.243532i	0.0179048	−	0.0179048i
$186$		0			0
$187$	0.874215	+	2.11054i	0.0639289	+	0.154338i
$188$		0			0
$189$	4.23522	+	1.75429i	0.308067	+	0.127606i
$190$		0			0
$191$	10.2073			0.738576			0.369288	−	0.929315i	$-0.379602\pi$
$191$	10.2073			0.738576			0.369288	+	0.929315i	$0.379602\pi$
$192$		0			0
$193$	−10.7026			−0.770391			−0.385196	−	0.922835i	$-0.625866\pi$
$193$	−10.7026			−0.770391			−0.385196	+	0.922835i	$0.625866\pi$
$194$		0			0
$195$	2.24398	+	0.929486i	0.160695	+	0.0665619i
$196$		0			0
$197$	1.95833	+	4.72783i	0.139525	+	0.336844i	0.978161	−	0.207849i	$-0.0666462\pi$
$197$	1.95833	+	4.72783i	0.139525	+	0.336844i	−0.838636	+	0.544693i	$0.816646\pi$
$198$		0			0
$199$	−9.72068	+	9.72068i	−0.689081	+	0.689081i	−0.962029	−	0.272948i	$-0.912001\pi$
$199$	−9.72068	+	9.72068i	−0.689081	+	0.689081i	0.272948	+	0.962029i	$0.412001\pi$
$200$		0			0
$201$	1.66524	+	1.66524i	0.117457	+	0.117457i
$202$		0			0
$203$	−9.93347	+	4.11458i	−0.697193	+	0.288787i
$204$		0			0
$205$	8.49098	−	20.4990i	0.593036	−	1.43172i
$206$		0			0
$207$			3.50128i			0.243356i
$208$		0			0
$209$			20.5389i			1.42070i
$210$		0			0
$211$	9.52388	−	22.9927i	0.655651	−	1.58288i	−0.148804	−	0.988867i	$-0.547542\pi$
$211$	9.52388	−	22.9927i	0.655651	−	1.58288i	0.804455	−	0.594014i	$-0.202458\pi$
$212$		0			0
$213$	−1.45239	+	0.601601i	−0.0995163	+	0.0412210i
$214$		0			0
$215$	5.11190	+	5.11190i	0.348629	+	0.348629i
$216$		0			0
$217$	−33.8758	+	33.8758i	−2.29964	+	2.29964i
$218$		0			0
$219$	−2.01107	−	4.85516i	−0.135896	−	0.328081i
$220$		0			0
$221$	0.757629	+	0.313820i	0.0509636	+	0.0211098i
$222$		0			0
$223$	0.519173			0.0347664			0.0173832	−	0.999849i	$-0.494466\pi$
$223$	0.519173			0.0347664			0.0173832	+	0.999849i	$0.494466\pi$
$224$		0			0
$225$	1.59834			0.106556
$226$		0			0
$227$	−4.61839	−	1.91300i	−0.306533	−	0.126970i	0.224114	−	0.974563i	$-0.428051\pi$
$227$	−4.61839	−	1.91300i	−0.306533	−	0.126970i	−0.530647	+	0.847593i	$0.678051\pi$
$228$		0			0
$229$	2.20642	+	5.32677i	0.145804	+	0.352003i	0.979862	−	0.199674i	$-0.0639882\pi$
$229$	2.20642	+	5.32677i	0.145804	+	0.352003i	−0.834058	+	0.551677i	$0.813988\pi$
$230$		0			0
$231$	11.8916	−	11.8916i	0.782412	−	0.782412i
$232$		0			0
$233$	11.4133	+	11.4133i	0.747713	+	0.747713i	0.974049	−	0.226336i	$-0.0726749\pi$
$233$	11.4133	+	11.4133i	0.747713	+	0.747713i	−0.226336	+	0.974049i	$0.572675\pi$
$234$		0			0
$235$	8.56923	−	3.54949i	0.558995	−	0.231543i
$236$		0			0
$237$	−3.91298	+	9.44677i	−0.254175	+	0.613634i
$238$		0			0
$239$		−	4.75090i		−	0.307310i	−0.988125	−	0.153655i	$-0.950896\pi$
$239$		−	4.75090i		−	0.307310i	0.988125	−	0.153655i	$-0.0491044\pi$
$240$		0			0
$241$		−	5.92434i		−	0.381620i	−0.981627	−	0.190810i	$-0.938888\pi$
$241$		−	5.92434i		−	0.381620i	0.981627	−	0.190810i	$-0.0611115\pi$
$242$		0			0
$243$	0.382683	−	0.923880i	0.0245492	−	0.0592669i
$244$		0			0
$245$	−23.8804	+	9.89159i	−1.52566	+	0.631951i
$246$		0			0
$247$	5.21343	+	5.21343i	0.331723	+	0.331723i
$248$		0			0
$249$	8.66933	−	8.66933i	0.549397	−	0.549397i
$250$		0			0
$251$	10.2886	+	24.8389i	0.649411	+	1.56782i	0.813624	+	0.581392i	$0.197492\pi$
$251$	10.2886	+	24.8389i	0.649411	+	1.56782i	−0.164212	+	0.986425i	$0.552508\pi$
$252$		0			0
$253$	11.8669	+	4.91544i	0.746067	+	0.309031i
$254$		0			0
$255$	−1.14849			−0.0719214
$256$		0			0
$257$	21.7192			1.35480			0.677402	−	0.735613i	$-0.263106\pi$
$257$	21.7192			1.35480			0.677402	+	0.735613i	$0.263106\pi$
$258$		0			0
$259$	−0.790865	−	0.327587i	−0.0491419	−	0.0203553i
$260$		0			0
$261$	0.897562	+	2.16691i	0.0555577	+	0.134128i
$262$		0			0
$263$	1.86567	−	1.86567i	0.115042	−	0.115042i	−0.647242	−	0.762284i	$-0.724078\pi$
$263$	1.86567	−	1.86567i	0.115042	−	0.115042i	0.762284	+	0.647242i	$0.224078\pi$
$264$		0			0
$265$	−10.1059	−	10.1059i	−0.620801	−	0.620801i
$266$		0			0
$267$	4.62566	−	1.91601i	0.283086	−	0.117258i
$268$		0			0
$269$	−2.52305	+	6.09118i	−0.153833	+	0.371386i	−0.981942	−	0.189181i	$-0.939417\pi$
$269$	−2.52305	+	6.09118i	−0.153833	+	0.371386i	0.828109	+	0.560567i	$0.189417\pi$
$270$		0			0
$271$		−	0.286319i		−	0.0173926i	−0.999962	−	0.00869632i	$-0.997232\pi$
$271$		−	0.286319i		−	0.0173926i	0.999962	−	0.00869632i	$-0.00276816\pi$
$272$		0			0
$273$		−	6.03697i		−	0.365374i
$274$		0			0
$275$	2.24391	−	5.41728i	0.135313	−	0.326674i
$276$		0			0
$277$	0.181363	−	0.0751232i	0.0108971	−	0.00451371i	−0.377228	−	0.926120i	$-0.623123\pi$
$277$	0.181363	−	0.0751232i	0.0108971	−	0.00451371i	0.388125	+	0.921607i	$0.373123\pi$
$278$		0			0
$279$	7.38972	+	7.38972i	0.442411	+	0.442411i
$280$		0			0
$281$	20.3637	−	20.3637i	1.21480	−	1.21480i	0.245365	−	0.969431i	$-0.421092\pi$
$281$	20.3637	−	20.3637i	1.21480	−	1.21480i	0.969431	−	0.245365i	$-0.0789078\pi$
$282$		0			0
$283$	5.49343	+	13.2623i	0.326550	+	0.788362i	0.998844	+	0.0480775i	$0.0153094\pi$
$283$	5.49343	+	13.2623i	0.326550	+	0.788362i	−0.672293	+	0.740285i	$0.734691\pi$
$284$		0			0
$285$	−9.53984	−	3.95153i	−0.565092	−	0.234069i
$286$		0			0
$287$	−55.1485			−3.25531
$288$		0			0
$289$	16.6122			0.977190
$290$		0			0
$291$	−0.128968	−	0.0534204i	−0.00756026	−	0.00313156i
$292$		0			0
$293$	3.82263	+	9.22865i	0.223321	+	0.539143i	0.995337	−	0.0964591i	$-0.0307517\pi$
$293$	3.82263	+	9.22865i	0.223321	+	0.539143i	−0.772016	+	0.635603i	$0.780752\pi$
$294$		0			0
$295$	−5.19763	+	5.19763i	−0.302618	+	0.302618i
$296$		0			0
$297$	−2.59406	−	2.59406i	−0.150523	−	0.150523i
$298$		0			0
$299$	4.25991	−	1.76451i	0.246357	−	0.102044i
$300$		0			0
$301$	6.87626	−	16.6008i	0.396341	−	0.956853i
$302$		0			0
$303$		−	12.7783i		−	0.734094i
$304$		0			0
$305$		−	6.13535i		−	0.351309i
$306$		0			0
$307$	−2.37991	+	5.74561i	−0.135829	+	0.327919i	−0.977129	−	0.212649i	$-0.931791\pi$
$307$	−2.37991	+	5.74561i	−0.135829	+	0.327919i	0.841300	+	0.540568i	$0.181791\pi$
$308$		0			0
$309$	4.76255	−	1.97271i	0.270932	−	0.112224i
$310$		0			0
$311$	−0.675375	−	0.675375i	−0.0382970	−	0.0382970i	0.687699	−	0.725996i	$-0.258621\pi$
$311$	−0.675375	−	0.675375i	−0.0382970	−	0.0382970i	−0.725996	+	0.687699i	$0.758621\pi$
$312$		0			0
$313$	11.3106	−	11.3106i	0.639315	−	0.639315i	−0.311072	−	0.950386i	$-0.600688\pi$
$313$	11.3106	−	11.3106i	0.639315	−	0.639315i	0.950386	+	0.311072i	$0.100688\pi$
$314$		0			0
$315$	3.23553	+	7.81126i	0.182302	+	0.440115i
$316$		0			0
$317$	−10.5105	−	4.35358i	−0.590327	−	0.244522i	0.0674641	−	0.997722i	$-0.478509\pi$
$317$	−10.5105	−	4.35358i	−0.590327	−	0.244522i	−0.657791	+	0.753200i	$0.728509\pi$
$318$		0			0
$319$	8.60439			0.481754
$320$		0			0
$321$	−7.51042			−0.419191
$322$		0			0
$323$	−3.22091	−	1.33415i	−0.179216	−	0.0742339i
$324$		0			0
$325$	−0.805505	−	1.94466i	−0.0446814	−	0.107870i
$326$		0			0
$327$	10.9336	−	10.9336i	0.604629	−	0.604629i
$328$		0			0
$329$	−16.3015	−	16.3015i	−0.898730	−	0.898730i
$330$		0			0
$331$	−4.12595	+	1.70902i	−0.226783	+	0.0939365i	−0.493182	−	0.869926i	$-0.664166\pi$
$331$	−4.12595	+	1.70902i	−0.226783	+	0.0939365i	0.266399	+	0.963863i	$0.414166\pi$
$332$		0			0
$333$	−0.0714604	+	0.172521i	−0.00391601	+	0.00945408i
$334$		0			0
$335$			4.34348i			0.237309i
$336$		0			0
$337$			4.39557i			0.239442i	0.992808	+	0.119721i	$0.0382000\pi$
$337$			4.39557i			0.239442i	−0.992808	+	0.119721i	$0.961800\pi$
$338$		0			0
$339$	3.46133	−	8.35639i	0.187994	−	0.453857i
$340$		0			0
$341$	35.4204	−	14.6716i	1.91812	−	0.794513i
$342$		0			0
$343$	22.7379	+	22.7379i	1.22773	+	1.22773i
$344$		0			0
$345$	−4.56623	+	4.56623i	−0.245837	+	0.245837i
$346$		0			0
$347$	8.23821	+	19.8888i	0.442250	+	1.06769i	0.975158	+	0.221513i	$0.0710994\pi$
$347$	8.23821	+	19.8888i	0.442250	+	1.06769i	−0.532907	+	0.846174i	$0.678901\pi$
$348$		0			0
$349$	17.5916	+	7.28668i	0.941657	+	0.390047i	0.800089	−	0.599881i	$-0.204785\pi$
$349$	17.5916	+	7.28668i	0.941657	+	0.390047i	0.141568	+	0.989928i	$0.454785\pi$
$350$		0			0
$351$	−1.31692			−0.0702918
$352$		0			0
$353$	15.0586			0.801490			0.400745	−	0.916190i	$-0.368751\pi$
$353$	15.0586			0.801490			0.400745	+	0.916190i	$0.368751\pi$
$354$		0			0
$355$	−2.67873	−	1.10957i	−0.142172	−	0.0588897i
$356$		0			0
$357$	1.09240	+	2.63730i	0.0578162	+	0.139581i
$358$		0			0
$359$	1.78051	−	1.78051i	0.0939719	−	0.0939719i	−0.658558	−	0.752530i	$-0.728833\pi$
$359$	1.78051	−	1.78051i	0.0939719	−	0.0939719i	0.752530	+	0.658558i	$0.228833\pi$
$360$		0			0
$361$	−8.72889	−	8.72889i	−0.459415	−	0.459415i
$362$		0			0
$363$	−2.27120	+	0.940760i	−0.119207	+	0.0493771i
$364$		0			0
$365$	3.70914	−	8.95466i	0.194145	−	0.468708i
$366$		0			0
$367$		−	19.5858i		−	1.02237i	−0.859470	−	0.511186i	$-0.829206\pi$
$367$		−	19.5858i		−	1.02237i	0.859470	−	0.511186i	$-0.170794\pi$
$368$		0			0
$369$			12.0302i			0.626268i
$370$		0			0
$371$	−13.5940	+	32.8187i	−0.705763	+	1.70386i
$372$		0			0
$373$	−27.0247	+	11.1940i	−1.39928	+	0.579603i	−0.949566	−	0.313568i	$-0.898476\pi$
$373$	−27.0247	+	11.1940i	−1.39928	+	0.579603i	−0.449719	+	0.893170i	$0.648476\pi$
$374$		0			0
$375$	8.60528	+	8.60528i	0.444375	+	0.444375i
$376$		0			0
$377$	2.18408	−	2.18408i	0.112486	−	0.112486i
$378$		0			0
$379$	5.77531	+	13.9428i	0.296658	+	0.716195i	0.999986	+	0.00532948i	$0.00169643\pi$
$379$	5.77531	+	13.9428i	0.296658	+	0.716195i	−0.703328	+	0.710865i	$0.748304\pi$
$380$		0			0
$381$	5.38611	+	2.23100i	0.275939	+	0.114298i
$382$		0			0
$383$	10.9987			0.562008			0.281004	−	0.959707i	$-0.409333\pi$
$383$	10.9987			0.562008			0.281004	+	0.959707i	$0.409333\pi$
$384$		0			0
$385$	31.0171			1.58078
$386$		0			0
$387$	−3.62132	−	1.50000i	−0.184082	−	0.0762494i
$388$		0			0
$389$	−7.85456	−	18.9626i	−0.398242	−	0.961441i	−0.988083	−	0.153922i	$-0.950810\pi$
$389$	−7.85456	−	18.9626i	−0.398242	−	0.961441i	0.589841	−	0.807519i	$-0.299190\pi$
$390$		0			0
$391$	−1.54168	+	1.54168i	−0.0779663	+	0.0779663i
$392$		0			0
$393$	−5.20557	−	5.20557i	−0.262586	−	0.262586i
$394$		0			0
$395$	−17.4232	+	7.21694i	−0.876658	+	0.363123i
$396$		0			0
$397$	1.90361	−	4.59572i	0.0955395	−	0.230653i	−0.868884	−	0.495017i	$-0.835162\pi$
$397$	1.90361	−	4.59572i	0.0955395	−	0.230653i	0.964423	+	0.264364i	$0.0851620\pi$
$398$		0			0
$399$			25.6650i			1.28486i
$400$		0			0
$401$		−	33.4589i		−	1.67086i	−0.549599	−	0.835429i	$-0.685220\pi$
$401$		−	33.4589i		−	1.67086i	0.549599	−	0.835429i	$-0.314780\pi$
$402$		0			0
$403$	5.26673	−	12.7150i	0.262354	−	0.633380i
$404$		0			0
$405$	1.70396	−	0.705805i	0.0846707	−	0.0350717i
$406$		0			0
$407$	0.484403	+	0.484403i	0.0240109	+	0.0240109i
$408$		0			0
$409$	−2.46531	+	2.46531i	−0.121902	+	0.121902i	−0.765426	−	0.643524i	$-0.777472\pi$
$409$	−2.46531	+	2.46531i	−0.121902	+	0.121902i	0.643524	+	0.765426i	$0.277472\pi$
$410$		0			0
$411$	7.43442	+	17.9483i	0.366713	+	0.885323i
$412$		0			0
$413$	16.8792	+	6.99159i	0.830570	+	0.344034i
$414$		0			0
$415$	22.6124			1.11000
$416$		0			0
$417$	−2.31907			−0.113565
$418$		0			0
$419$	−14.6327	−	6.06106i	−0.714854	−	0.296102i	−0.00454254	−	0.999990i	$-0.501446\pi$
$419$	−14.6327	−	6.06106i	−0.714854	−	0.296102i	−0.710312	+	0.703887i	$0.751446\pi$
$420$		0			0
$421$	10.0070	+	24.1590i	0.487711	+	1.17744i	0.955869	+	0.293793i	$0.0949178\pi$
$421$	10.0070	+	24.1590i	0.487711	+	1.17744i	−0.468158	+	0.883645i	$0.655082\pi$
$422$		0			0
$423$	−3.55604	+	3.55604i	−0.172900	+	0.172900i
$424$		0			0
$425$	0.703782	+	0.703782i	0.0341384	+	0.0341384i
$426$		0			0
$427$	−14.0887	+	5.83573i	−0.681799	+	0.282411i
$428$		0			0
$429$	−1.84881	+	4.46343i	−0.0892616	+	0.215497i
$430$		0			0
$431$			23.7227i			1.14268i	0.820713	+	0.571341i	$0.193577\pi$
$431$			23.7227i			1.14268i	−0.820713	+	0.571341i	$0.806423\pi$
$432$		0			0
$433$			23.6074i			1.13450i	0.823546	+	0.567249i	$0.191992\pi$
$433$			23.6074i			1.13450i	−0.823546	+	0.567249i	$0.808008\pi$
$434$		0			0
$435$	−1.65543	+	3.99655i	−0.0793716	+	0.191620i
$436$		0			0
$437$	−18.1102	+	7.50150i	−0.866329	+	0.358845i
$438$		0			0
$439$	−17.9050	−	17.9050i	−0.854557	−	0.854557i	0.136134	−	0.990690i	$-0.456532\pi$
$439$	−17.9050	−	17.9050i	−0.854557	−	0.854557i	−0.990690	+	0.136134i	$0.956532\pi$
$440$		0			0
$441$	9.90984	−	9.90984i	0.471897	−	0.471897i
$442$		0			0
$443$	−6.84608	−	16.5279i	−0.325267	−	0.785265i	−0.998931	−	0.0462266i	$-0.985280\pi$
$443$	−6.84608	−	16.5279i	−0.325267	−	0.785265i	0.673664	−	0.739038i	$-0.264720\pi$
$444$		0			0
$445$	8.53138	+	3.53381i	0.404426	+	0.167519i
$446$		0			0
$447$	1.00282			0.0474316
$448$		0			0
$449$	−20.0312			−0.945332			−0.472666	−	0.881242i	$-0.656708\pi$
$449$	−20.0312			−0.945332			−0.472666	+	0.881242i	$0.656708\pi$
$450$		0			0
$451$	40.7741	+	16.8892i	1.91998	+	0.795280i
$452$		0			0
$453$	3.80204	+	9.17894i	0.178635	+	0.431264i
$454$		0			0
$455$	7.87316	−	7.87316i	0.369099	−	0.369099i
$456$		0			0
$457$	−1.43011	−	1.43011i	−0.0668975	−	0.0668975i	0.672866	−	0.739764i	$-0.265063\pi$
$457$	−1.43011	−	1.43011i	−0.0668975	−	0.0668975i	−0.739764	+	0.672866i	$0.765063\pi$
$458$		0			0
$459$	0.575305	−	0.238299i	0.0268529	−	0.0111229i
$460$		0			0
$461$	11.8633	−	28.6405i	0.552528	−	1.33392i	−0.363046	−	0.931771i	$-0.618263\pi$
$461$	11.8633	−	28.6405i	0.552528	−	1.33392i	0.915574	−	0.402150i	$-0.131737\pi$
$462$		0			0
$463$			23.3331i			1.08438i	0.840255	+	0.542191i	$0.182405\pi$
$463$			23.3331i			1.08438i	−0.840255	+	0.542191i	$0.817595\pi$
$464$		0			0
$465$			19.2747i			0.893844i
$466$		0			0
$467$	1.25228	−	3.02327i	0.0579485	−	0.139900i	−0.892253	−	0.451535i	$-0.850877\pi$
$467$	1.25228	−	3.02327i	0.0579485	−	0.139900i	0.950202	+	0.311635i	$0.100877\pi$
$468$		0			0
$469$	9.97398	−	4.13136i	0.460556	−	0.190768i
$470$		0			0
$471$	−4.31073	−	4.31073i	−0.198628	−	0.198628i
$472$		0			0
$473$	−10.1679	+	10.1679i	−0.467522	+	0.467522i
$474$		0			0
$475$	3.42445	+	8.26735i	0.157124	+	0.379332i
$476$		0			0
$477$	7.15914	+	2.96541i	0.327794	+	0.135777i
$478$		0			0
$479$	−20.4084			−0.932486			−0.466243	−	0.884657i	$-0.654393\pi$
$479$	−20.4084			−0.932486			−0.466243	+	0.884657i	$0.654393\pi$
$480$		0			0
$481$	0.245914			0.0112127
$482$		0			0
$483$	14.8287	+	6.14226i	0.674730	+	0.279482i
$484$		0			0
$485$	−0.0985264	−	0.237864i	−0.00447385	−	0.0108008i
$486$		0			0
$487$	14.1551	−	14.1551i	0.641430	−	0.641430i	−0.309477	−	0.950907i	$-0.600154\pi$
$487$	14.1551	−	14.1551i	0.641430	−	0.641430i	0.950907	+	0.309477i	$0.100154\pi$
$488$		0			0
$489$	15.5100	+	15.5100i	0.701384	+	0.701384i
$490$		0			0
$491$	−9.93954	+	4.11709i	−0.448565	+	0.185802i	−0.595518	−	0.803342i	$-0.703053\pi$
$491$	−9.93954	+	4.11709i	−0.448565	+	0.185802i	0.146953	+	0.989143i	$0.453053\pi$
$492$		0			0
$493$	−0.558917	+	1.34935i	−0.0251724	+	0.0607715i
$494$		0			0
$495$		−	6.76614i		−	0.304115i
$496$		0			0
$497$			7.20658i			0.323259i
$498$		0			0
$499$	−2.81268	+	6.79042i	−0.125913	+	0.303981i	−0.974248	−	0.225479i	$-0.927605\pi$
$499$	−2.81268	+	6.79042i	−0.125913	+	0.303981i	0.848335	+	0.529460i	$0.177605\pi$
$500$		0			0
$501$	−12.1114	+	5.01671i	−0.541097	+	0.224130i
$502$		0			0
$503$	8.42826	+	8.42826i	0.375798	+	0.375798i	0.869584	−	0.493786i	$-0.164387\pi$
$503$	8.42826	+	8.42826i	0.375798	+	0.375798i	−0.493786	+	0.869584i	$0.664387\pi$
$504$		0			0
$505$	16.6649	−	16.6649i	0.741580	−	0.741580i
$506$		0			0
$507$	−4.31121	−	10.4082i	−0.191468	−	0.462243i
$508$		0			0
$509$	−2.80732	−	1.16283i	−0.124432	−	0.0515415i	0.319599	−	0.947553i	$-0.396452\pi$
$509$	−2.80732	−	1.16283i	−0.124432	−	0.0515415i	−0.444031	+	0.896011i	$0.646452\pi$
$510$		0			0
$511$	−24.0907			−1.06571
$512$		0			0
$513$	5.59862			0.247185
$514$		0			0
$515$	8.78384	+	3.63839i	0.387062	+	0.160326i
$516$		0			0
$517$	7.06019	+	17.0448i	0.310507	+	0.749630i
$518$		0			0
$519$	−9.37604	+	9.37604i	−0.411563	+	0.411563i
$520$		0			0
$521$	−23.5959	−	23.5959i	−1.03376	−	1.03376i	−0.999410	−	0.0343468i	$-0.989065\pi$
$521$	−23.5959	−	23.5959i	−1.03376	−	1.03376i	−0.0343468	−	0.999410i	$-0.510935\pi$
$522$		0			0
$523$	30.1407	−	12.4847i	1.31796	−	0.545916i	0.390762	−	0.920492i	$-0.372211\pi$
$523$	30.1407	−	12.4847i	1.31796	−	0.545916i	0.927196	+	0.374575i	$0.122211\pi$
$524$		0			0
$525$	2.80395	−	6.76934i	0.122375	−	0.295438i
$526$		0			0
$527$			6.50768i			0.283479i
$528$		0			0
$529$		−	10.7410i		−	0.467000i
$530$		0			0
$531$	1.52516	−	3.68206i	0.0661862	−	0.159788i
$532$		0			0
$533$	14.6368	−	6.06277i	0.633991	−	0.262608i
$534$		0			0
$535$	−9.79478	−	9.79478i	−0.423465	−	0.423465i
$536$		0			0
$537$	−13.2617	+	13.2617i	−0.572287	+	0.572287i
$538$		0			0
$539$	−19.6751	−	47.4999i	−0.847466	−	2.04596i
$540$		0			0
$541$	−27.9752	−	11.5877i	−1.20275	−	0.498194i	−0.310861	−	0.950455i	$-0.600617\pi$
$541$	−27.9752	−	11.5877i	−1.20275	−	0.498194i	−0.891885	+	0.452261i	$0.850617\pi$
$542$		0			0
$543$	14.8857			0.638806
$544$		0			0
$545$	28.5183			1.22159
$546$		0			0
$547$	−29.3726	−	12.1665i	−1.25588	−	0.520204i	−0.347240	−	0.937776i	$-0.612881\pi$
$547$	−29.3726	−	12.1665i	−1.25588	−	0.520204i	−0.908644	+	0.417573i	$0.862881\pi$
$548$		0			0
$549$	1.27302	+	3.07333i	0.0543310	+	0.131167i
$550$		0			0
$551$	−9.28519	+	9.28519i	−0.395562	+	0.395562i
$552$		0			0
$553$	33.1447	+	33.1447i	1.40946	+	1.40946i
$554$		0			0
$555$	−0.318190	+	0.131799i	−0.0135064	+	0.00559454i
$556$		0			0
$557$	7.20303	−	17.3897i	0.305202	−	0.736824i	−0.694645	−	0.719353i	$-0.744439\pi$
$557$	7.20303	−	17.3897i	0.305202	−	0.736824i	0.999847	−	0.0174710i	$-0.00556147\pi$
$558$		0			0
$559$			5.16191i			0.218325i
$560$		0			0
$561$		−	2.28443i		−	0.0964488i
$562$		0			0
$563$	10.5977	−	25.5852i	0.446641	−	1.07829i	−0.526931	−	0.849908i	$-0.676657\pi$
$563$	10.5977	−	25.5852i	0.446641	−	1.07829i	0.973572	−	0.228379i	$-0.0733427\pi$
$564$		0			0
$565$	15.4122	−	6.38393i	0.648395	−	0.268574i
$566$		0			0
$567$	−3.24150	−	3.24150i	−0.136130	−	0.136130i
$568$		0			0
$569$	10.6978	−	10.6978i	0.448475	−	0.448475i	−0.446372	−	0.894847i	$-0.647284\pi$
$569$	10.6978	−	10.6978i	0.448475	−	0.448475i	0.894847	+	0.446372i	$0.147284\pi$
$570$		0			0
$571$	−1.08014	−	2.60770i	−0.0452026	−	0.109129i	0.899666	−	0.436580i	$-0.143810\pi$
$571$	−1.08014	−	2.60770i	−0.0452026	−	0.109129i	−0.944868	+	0.327451i	$0.893810\pi$
$572$		0			0
$573$	−9.43034	−	3.90617i	−0.393958	−	0.163183i
$574$		0			0
$575$	5.59626			0.233380
$576$		0			0
$577$	−21.4373			−0.892445			−0.446223	−	0.894922i	$-0.647231\pi$
$577$	−21.4373			−0.892445			−0.446223	+	0.894922i	$0.647231\pi$
$578$		0			0
$579$	9.88793	+	4.09571i	0.410928	+	0.170212i
$580$		0			0
$581$	−21.5081	−	51.9250i	−0.892305	−	2.15421i
$582$		0			0
$583$	20.1014	−	20.1014i	0.832514	−	0.832514i
$584$		0			0
$585$	−1.71747	−	1.71747i	−0.0710085	−	0.0710085i
$586$		0			0
$587$	1.40199	−	0.580725i	0.0578665	−	0.0239691i	−0.353562	−	0.935411i	$-0.615030\pi$
$587$	1.40199	−	0.580725i	0.0578665	−	0.0239691i	0.411429	+	0.911442i	$0.365030\pi$
$588$		0			0
$589$	−22.3905	+	54.0554i	−0.922584	+	2.22732i
$590$		0			0
$591$		−	5.11737i		−	0.210500i
$592$		0			0
$593$			2.08256i			0.0855207i	0.999085	+	0.0427603i	$0.0136152\pi$
$593$			2.08256i			0.0855207i	−0.999085	+	0.0427603i	$0.986385\pi$
$594$		0			0
$595$	−2.01478	+	4.86412i	−0.0825981	+	0.199409i
$596$		0			0
$597$	12.7007	−	5.26079i	0.519804	−	0.215310i
$598$		0			0
$599$	−13.5781	−	13.5781i	−0.554786	−	0.554786i	0.373033	−	0.927818i	$-0.378318\pi$
$599$	−13.5781	−	13.5781i	−0.554786	−	0.554786i	−0.927818	+	0.373033i	$0.878318\pi$
$600$		0			0
$601$	5.03476	−	5.03476i	0.205372	−	0.205372i	−0.596925	−	0.802297i	$-0.703611\pi$
$601$	5.03476	−	5.03476i	0.205372	−	0.205372i	0.802297	+	0.596925i	$0.203611\pi$
$602$		0			0
$603$	−0.901222	−	2.17574i	−0.0367006	−	0.0886031i
$604$		0			0
$605$	−4.18890	−	1.73510i	−0.170303	−	0.0705418i
$606$		0			0
$607$	8.30054			0.336909			0.168454	−	0.985709i	$-0.446122\pi$
$607$	8.30054			0.336909			0.168454	+	0.985709i	$0.446122\pi$
$608$		0			0
$609$	10.7519			0.435689
$610$		0			0
$611$	6.11864	+	2.53442i	0.247533	+	0.102532i
$612$		0			0
$613$	−10.3825	−	25.0655i	−0.419344	−	1.01239i	−0.982538	−	0.186062i	$-0.940428\pi$
$613$	−10.3825	−	25.0655i	−0.419344	−	1.01239i	0.563194	−	0.826325i	$-0.309572\pi$
$614$		0			0
$615$	−15.6893	+	15.6893i	−0.632653	+	0.632653i
$616$		0			0
$617$	4.65911	+	4.65911i	0.187569	+	0.187569i	0.794644	−	0.607076i	$-0.207657\pi$
$617$	4.65911	+	4.65911i	0.187569	+	0.187569i	−0.607076	+	0.794644i	$0.707657\pi$
$618$		0			0
$619$	−14.6048	+	6.04953i	−0.587018	+	0.243151i	−0.656367	−	0.754441i	$-0.727908\pi$
$619$	−14.6048	+	6.04953i	−0.587018	+	0.243151i	0.0693489	+	0.997592i	$0.477908\pi$
$620$		0			0
$621$	1.33988	−	3.23477i	0.0537677	−	0.129807i
$622$		0			0
$623$		−	22.9519i		−	0.919550i
$624$		0			0
$625$			14.4536i			0.578143i
$626$		0			0
$627$	7.85988	−	18.9754i	0.313893	−	0.757806i
$628$		0			0
$629$	−0.107430	+	0.0444988i	−0.00428350	+	0.00177428i
$630$		0			0
$631$	34.7967	+	34.7967i	1.38524	+	1.38524i	0.835028	+	0.550208i	$0.185451\pi$
$631$	34.7967	+	34.7967i	1.38524	+	1.38524i	0.550208	+	0.835028i	$0.314549\pi$
$632$		0			0
$633$	−17.5978	+	17.5978i	−0.699451	+	0.699451i
$634$		0			0
$635$	4.11477	+	9.93392i	0.163289	+	0.394216i
$636$		0			0
$637$	−17.0512	−	7.06284i	−0.675593	−	0.279840i
$638$		0			0
$639$	1.57206			0.0621897
$640$		0			0
$641$	−34.7091			−1.37093			−0.685464	−	0.728107i	$-0.740401\pi$
$641$	−34.7091			−1.37093			−0.685464	+	0.728107i	$0.740401\pi$
$642$		0			0
$643$	−18.3692	−	7.60876i	−0.724409	−	0.300060i	−0.0101569	−	0.999948i	$-0.503233\pi$
$643$	−18.3692	−	7.60876i	−0.724409	−	0.300060i	−0.714252	+	0.699888i	$0.753233\pi$
$644$		0			0
$645$	−2.76654	−	6.67902i	−0.108932	−	0.262986i
$646$		0			0
$647$	−31.4202	+	31.4202i	−1.23526	+	1.23526i	−0.273339	+	0.961918i	$0.588128\pi$
$647$	−31.4202	+	31.4202i	−1.23526	+	1.23526i	−0.961918	+	0.273339i	$0.911872\pi$
$648$		0			0
$649$	−10.3385	−	10.3385i	−0.405820	−	0.405820i
$650$		0			0
$651$	44.2608	−	18.3334i	1.73472	−	0.718544i
$652$		0			0
$653$	−7.10749	+	17.1590i	−0.278138	+	0.671484i	−0.999784	−	0.0207782i	$-0.993386\pi$
$653$	−7.10749	+	17.1590i	−0.278138	+	0.671484i	0.721647	+	0.692262i	$0.243386\pi$
$654$		0			0
$655$		−	13.5778i		−	0.530528i
$656$		0			0
$657$			5.25519i			0.205024i
$658$		0			0
$659$	−2.78866	+	6.73242i	−0.108631	+	0.262258i	−0.968842	−	0.247680i	$-0.920332\pi$
$659$	−2.78866	+	6.73242i	−0.108631	+	0.262258i	0.860211	+	0.509938i	$0.170332\pi$
$660$		0			0
$661$	24.8628	−	10.2985i	0.967049	−	0.400565i	0.157436	−	0.987529i	$-0.449677\pi$
$661$	24.8628	−	10.2985i	0.967049	−	0.400565i	0.809613	+	0.586964i	$0.199677\pi$
$662$		0			0
$663$	−0.579864	−	0.579864i	−0.0225200	−	0.0225200i
$664$		0			0
$665$	−33.4712	+	33.4712i	−1.29796	+	1.29796i
$666$		0			0
$667$	3.14262	+	7.58696i	0.121683	+	0.293768i
$668$		0			0
$669$	−0.479653	−	0.198679i	−0.0185445	−	0.00768137i
$670$		0			0
$671$	12.2037			0.471117
$672$		0			0
$673$	−30.7959			−1.18710			−0.593548	−	0.804799i	$-0.702273\pi$
$673$	−30.7959			−1.18710			−0.593548	+	0.804799i	$0.702273\pi$
$674$		0			0
$675$	−1.47668	−	0.611660i	−0.0568373	−	0.0235428i
$676$		0			0
$677$	13.2209	+	31.9181i	0.508121	+	1.22671i	0.944964	+	0.327175i	$0.106097\pi$
$677$	13.2209	+	31.9181i	0.508121	+	1.22671i	−0.436842	+	0.899538i	$0.643903\pi$
$678$		0			0
$679$	−0.452495	+	0.452495i	−0.0173652	+	0.0173652i
$680$		0			0
$681$	3.53476	+	3.53476i	0.135452	+	0.135452i
$682$		0			0
$683$	30.6208	−	12.6835i	1.17167	−	0.485322i	0.289927	−	0.957049i	$-0.406369\pi$
$683$	30.6208	−	12.6835i	1.17167	−	0.485322i	0.881745	+	0.471726i	$0.156369\pi$
$684$		0			0
$685$	−13.7117	+	33.1030i	−0.523898	+	1.26480i
$686$		0			0
$687$		−	5.76566i		−	0.219974i
$688$		0			0
$689$		−	10.2048i		−	0.388771i
$690$		0			0
$691$	−5.49715	+	13.2713i	−0.209121	+	0.504864i	−0.993285	−	0.115690i	$-0.963092\pi$
$691$	−5.49715	+	13.2713i	−0.209121	+	0.504864i	0.784164	+	0.620554i	$0.213092\pi$
$692$		0			0
$693$	−15.5372	+	6.43570i	−0.590208	+	0.244472i
$694$		0			0
$695$	−3.02443	−	3.02443i	−0.114723	−	0.114723i
$696$		0			0
$697$	−5.29714	+	5.29714i	−0.200643	+	0.200643i
$698$		0			0
$699$	−6.17685	−	14.9122i	−0.233630	−	0.564033i
$700$		0			0
$701$	20.5608	+	8.51658i	0.776572	+	0.321667i	0.735531	−	0.677491i	$-0.236933\pi$
$701$	20.5608	+	8.51658i	0.776572	+	0.321667i	0.0410410	+	0.999157i	$0.486933\pi$
$702$		0			0
$703$	−1.04546			−0.0394302
$704$		0			0
$705$	−9.27527			−0.349327
$706$		0			0
$707$	−54.1190	−	22.4168i	−2.03535	−	0.843071i
$708$		0			0
$709$	−6.40422	−	15.4612i	−0.240516	−	0.580656i	0.756819	−	0.653625i	$-0.226753\pi$
$709$	−6.40422	−	15.4612i	−0.240516	−	0.580656i	−0.997334	+	0.0729689i	$0.976753\pi$
$710$		0			0
$711$	7.23025	−	7.23025i	0.271155	−	0.271155i
$712$		0			0
$713$	25.8735	+	25.8735i	0.968971	+	0.968971i
$714$		0			0
$715$	−8.23216	+	3.40987i	−0.307866	+	0.127522i
$716$		0			0
$717$	−1.81809	+	4.38926i	−0.0678978	+	0.163920i
$718$		0			0
$719$		−	43.9490i		−	1.63902i	−0.573063	−	0.819511i	$-0.694245\pi$
$719$		−	43.9490i		−	1.63902i	0.573063	−	0.819511i	$-0.305755\pi$
$720$		0			0
$721$		−	23.6311i		−	0.880070i
$722$		0			0
$723$	−2.26715	+	5.47338i	−0.0843161	+	0.203557i
$724$		0			0
$725$	3.46346	−	1.43461i	0.128630	−	0.0532802i
$726$		0			0
$727$	−21.5021	−	21.5021i	−0.797468	−	0.797468i	0.185228	−	0.982696i	$-0.440698\pi$
$727$	−21.5021	−	21.5021i	−0.797468	−	0.797468i	−0.982696	+	0.185228i	$0.940698\pi$
$728$		0			0
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$		0			0
$731$	−0.934060	−	2.25502i	−0.0345475	−	0.0834049i
$732$		0			0
$733$	−26.7967	−	11.0995i	−0.989758	−	0.409971i	−0.171726	−	0.985145i	$-0.554934\pi$
$733$	−26.7967	−	11.0995i	−0.989758	−	0.409971i	−0.818031	+	0.575174i	$0.804934\pi$
$734$		0			0
$735$	25.8480			0.953417
$736$		0			0
$737$	−8.63948			−0.318239
$738$		0			0
$739$	49.0126	+	20.3017i	1.80296	+	0.746810i	0.985237	+	0.171195i	$0.0547628\pi$
$739$	49.0126	+	20.3017i	1.80296	+	0.746810i	0.817721	+	0.575615i	$0.195237\pi$
$740$		0			0
$741$	−2.82149	−	6.81168i	−0.103650	−	0.250233i
$742$		0			0
$743$	−23.7552	+	23.7552i	−0.871494	+	0.871494i	−0.992635	−	0.121141i	$-0.961345\pi$
$743$	−23.7552	+	23.7552i	−0.871494	+	0.871494i	0.121141	+	0.992635i	$0.461345\pi$
$744$		0			0
$745$	1.30783	+	1.30783i	0.0479152	+	0.0479152i
$746$		0			0
$747$	−11.3270	+	4.69181i	−0.414434	+	0.171664i
$748$		0			0
$749$	−13.1754	+	31.8083i	−0.481420	+	1.16225i
$750$		0			0
$751$		−	25.2687i		−	0.922066i	−0.887383	−	0.461033i	$-0.847479\pi$
$751$		−	25.2687i		−	0.922066i	0.887383	−	0.461033i	$-0.152521\pi$
$752$		0			0
$753$		−	26.8854i		−	0.979759i
$754$		0			0
$755$	−7.01233	+	16.9293i	−0.255205	+	0.616119i
$756$		0			0
$757$	−39.9969	+	16.5672i	−1.45371	+	0.602147i	−0.963079	−	0.269220i	$-0.913234\pi$
$757$	−39.9969	+	16.5672i	−1.45371	+	0.602147i	−0.490632	+	0.871367i	$0.663234\pi$
$758$		0			0
$759$	−9.08255	−	9.08255i	−0.329676	−	0.329676i
$760$		0			0
$761$	14.0902	−	14.0902i	0.510769	−	0.510769i	−0.403993	−	0.914762i	$-0.632378\pi$
$761$	14.0902	−	14.0902i	0.510769	−	0.510769i	0.914762	+	0.403993i	$0.132378\pi$
$762$		0			0
$763$	−27.1256	−	65.4869i	−0.982011	−	2.37078i
$764$		0			0
$765$	1.06107	+	0.439509i	0.0383630	+	0.0158905i
$766$		0			0
$767$	−5.24848			−0.189512
$768$		0			0
$769$	−36.5306			−1.31733			−0.658663	−	0.752438i	$-0.728878\pi$
$769$	−36.5306			−1.31733			−0.658663	+	0.752438i	$0.728878\pi$
$770$		0			0
$771$	−20.0659	−	8.31157i	−0.722656	−	0.299334i
$772$		0			0
$773$	7.29955	+	17.6227i	0.262546	+	0.633843i	0.999095	−	0.0425418i	$-0.0135456\pi$
$773$	7.29955	+	17.6227i	0.262546	+	0.633843i	−0.736548	+	0.676385i	$0.763546\pi$
$774$		0			0
$775$	11.8113	−	11.8113i	0.424275	−	0.424275i
$776$		0			0
$777$	0.605302	+	0.605302i	0.0217151	+	0.0217151i
$778$		0			0
$779$	−62.2256	+	25.7747i	−2.22946	+	0.923474i
$780$		0			0
$781$	2.20701	−	5.32819i	0.0789729	−	0.190658i
$782$		0			0
$783$		−	2.34544i		−	0.0838193i
$784$		0			0
$785$		−	11.2437i		−	0.401306i
$786$		0			0
$787$	−11.4660	+	27.6814i	−0.408719	+	0.986735i	0.576756	+	0.816916i	$0.304318\pi$
$787$	−11.4660	+	27.6814i	−0.408719	+	0.986735i	−0.985475	+	0.169819i	$0.945682\pi$
$788$		0			0
$789$	−2.43761	+	1.00969i	−0.0867812	+	0.0359460i
$790$		0			0
$791$	−29.3190	−	29.3190i	−1.04246	−	1.04246i
$792$		0			0
$793$	3.09769	−	3.09769i	0.110002	−	0.110002i
$794$		0			0
$795$	5.46928	+	13.2040i	0.193975	+	0.468298i
$796$		0			0
$797$	−19.1294	−	7.92366i	−0.677599	−	0.280671i	0.0172239	−	0.999852i	$-0.494517\pi$
$797$	−19.1294	−	7.92366i	−0.677599	−	0.280671i	−0.694823	+	0.719181i	$0.744517\pi$
$798$		0			0
$799$	−3.13158			−0.110787
$800$		0			0
$801$	−5.00678			−0.176906
$802$		0			0
$803$	17.8114	+	7.37774i	0.628552	+	0.260355i
$804$		0			0
$805$	11.3285	+	27.3495i	0.399278	+	0.963942i
$806$		0			0
$807$	4.66198	−	4.66198i	0.164110	−	0.164110i
$808$		0			0
$809$	9.08298	+	9.08298i	0.319341	+	0.319341i	0.848514	−	0.529173i	$-0.177498\pi$
$809$	9.08298	+	9.08298i	0.319341	+	0.319341i	−0.529173	+	0.848514i	$0.677498\pi$
$810$		0			0
$811$	−2.93057	+	1.21388i	−0.102906	+	0.0426251i	−0.433543	−	0.901133i	$-0.642737\pi$
$811$	−2.93057	+	1.21388i	−0.102906	+	0.0426251i	0.330636	+	0.943758i	$0.392737\pi$
$812$		0			0
$813$	−0.109569	+	0.264524i	−0.00384277	+	0.00927727i
$814$		0			0
$815$			40.4549i			1.41707i
$816$		0			0
$817$		−	21.9449i		−	0.767754i
$818$		0			0
$819$	−2.31025	+	5.57743i	−0.0807266	+	0.194891i
$820$		0			0
$821$	−5.06148	+	2.09653i	−0.176647	+	0.0731696i	−0.469254	−	0.883063i	$-0.655477\pi$
$821$	−5.06148	+	2.09653i	−0.176647	+	0.0731696i	0.292607	+	0.956233i	$0.405477\pi$
$822$		0			0
$823$	−18.7772	−	18.7772i	−0.654534	−	0.654534i	0.299548	−	0.954081i	$-0.403164\pi$
$823$	−18.7772	−	18.7772i	−0.654534	−	0.654534i	−0.954081	+	0.299548i	$0.903164\pi$
$824$		0			0
$825$	−4.14620	+	4.14620i	−0.144352	+	0.144352i
$826$		0			0
$827$	7.97891	+	19.2628i	0.277454	+	0.669833i	0.999764	−	0.0217368i	$-0.00691960\pi$
$827$	7.97891	+	19.2628i	0.277454	+	0.669833i	−0.722310	+	0.691569i	$0.756920\pi$
$828$		0			0
$829$	6.18715	+	2.56280i	0.214889	+	0.0890098i	0.487531	−	0.873106i	$-0.337898\pi$
$829$	6.18715	+	2.56280i	0.214889	+	0.0890098i	−0.272642	+	0.962115i	$0.587898\pi$
$830$		0			0
$831$	−0.196306			−0.00680979
$832$		0			0
$833$	8.72699			0.302372
$834$		0			0
$835$	−22.3378	−	9.25260i	−0.773030	−	0.320199i
$836$		0			0
$837$	−3.99929	−	9.65514i	−0.138236	−	0.333730i
$838$		0			0
$839$	17.9608	−	17.9608i	0.620075	−	0.620075i	−0.325476	−	0.945550i	$-0.605524\pi$
$839$	17.9608	−	17.9608i	0.620075	−	0.620075i	0.945550	+	0.325476i	$0.105524\pi$
$840$		0			0
$841$	−16.6162	−	16.6162i	−0.572973	−	0.572973i
$842$		0			0
$843$	−26.6064	+	11.0207i	−0.916374	+	0.379575i
$844$		0			0
$845$	7.95141	−	19.1964i	0.273537	−	0.660377i
$846$		0			0
$847$			11.2694i			0.387220i
$848$		0			0
$849$		−	14.3550i		−	0.492663i
$850$		0			0
$851$	−0.250203	+	0.604044i	−0.00857686	+	0.0207064i
$852$		0			0
$853$	31.8461	−	13.1911i	1.09039	−	0.451655i	0.236248	−	0.971693i	$-0.424082\pi$
$853$	31.8461	−	13.1911i	1.09039	−	0.451655i	0.854143	+	0.520038i	$0.174082\pi$
$854$		0			0
$855$	7.30148	+	7.30148i	0.249705	+	0.249705i
$856$		0			0
$857$	−6.69068	+	6.69068i	−0.228549	+	0.228549i	−0.812086	−	0.583537i	$-0.801668\pi$
$857$	−6.69068	+	6.69068i	−0.228549	+	0.228549i	0.583537	+	0.812086i	$0.301668\pi$
$858$		0			0
$859$	−12.1865	−	29.4209i	−0.415799	−	1.00383i	−0.983551	−	0.180628i	$-0.942187\pi$
$859$	−12.1865	−	29.4209i	−0.415799	−	1.00383i	0.567752	−	0.823199i	$-0.307813\pi$
$860$		0			0
$861$	50.9506	+	21.1044i	1.73639	+	0.719237i
$862$		0			0
$863$	41.6835			1.41892			0.709461	−	0.704744i	$-0.248938\pi$
$863$	41.6835			1.41892			0.709461	+	0.704744i	$0.248938\pi$
$864$		0			0
$865$	−24.4557			−0.831518
$866$		0			0
$867$	−15.3477	−	6.35723i	−0.521235	−	0.215903i
$868$		0			0
$869$	−14.3550	−	34.6560i	−0.486960	−	1.17563i
$870$		0			0
$871$	−2.19298	+	2.19298i	−0.0743064	+	0.0743064i
$872$		0			0
$873$	0.0987081	+	0.0987081i	0.00334076	+	0.00334076i
$874$		0			0
$875$	51.5414	−	21.3492i	1.74242	−	0.721733i
$876$		0			0
$877$	13.1498	−	31.7463i	0.444036	−	1.07200i	−0.530484	−	0.847695i	$-0.677990\pi$
$877$	13.1498	−	31.7463i	0.444036	−	1.07200i	0.974520	−	0.224303i	$-0.0720104\pi$
$878$		0			0
$879$		−	9.98902i		−	0.336921i
$880$		0			0
$881$		−	23.2168i		−	0.782193i	−0.920350	−	0.391097i	$-0.872096\pi$
$881$		−	23.2168i		−	0.782193i	0.920350	−	0.391097i	$-0.127904\pi$
$882$		0			0
$883$	−7.49214	+	18.0876i	−0.252131	+	0.608697i	−0.998376	−	0.0569741i	$-0.981855\pi$
$883$	−7.49214	+	18.0876i	−0.252131	+	0.608697i	0.746245	+	0.665671i	$0.231855\pi$
$884$		0			0
$885$	6.79103	−	2.81294i	0.228278	−	0.0945559i
$886$		0			0
$887$	−27.3487	−	27.3487i	−0.918281	−	0.918281i	0.0786233	−	0.996904i	$-0.474948\pi$
$887$	−27.3487	−	27.3487i	−0.918281	−	0.918281i	−0.996904	+	0.0786233i	$0.974948\pi$
$888$		0			0
$889$	18.8976	−	18.8976i	0.633804	−	0.633804i
$890$		0			0
$891$	1.40390	+	3.38931i	0.0470323	+	0.113546i
$892$		0			0
$893$	−26.0122	−	10.7746i	−0.870465	−	0.360559i
$894$		0			0
$895$	−34.5908			−1.15624
$896$		0			0
$897$	−4.61090			−0.153953
$898$		0			0
$899$	22.6456	+	9.38010i	0.755272	+	0.312844i
$900$		0			0
$901$	1.84658	+	4.45804i	0.0615185	+	0.148519i
$902$		0			0
$903$	−12.7057	+	12.7057i	−0.422819	+	0.422819i
$904$		0			0
$905$	19.4133	+	19.4133i	0.645319	+	0.645319i
$906$		0			0
$907$	25.0936	−	10.3941i	0.833219	−	0.345131i	0.0750427	−	0.997180i	$-0.476091\pi$
$907$	25.0936	−	10.3941i	0.833219	−	0.345131i	0.758176	+	0.652050i	$0.226091\pi$
$908$		0			0
$909$	−4.89005	+	11.8056i	−0.162193	+	0.391568i
$910$		0			0
$911$		−	42.9196i		−	1.42199i	−0.703197	−	0.710995i	$-0.748245\pi$
$911$		−	42.9196i		−	1.42199i	0.703197	−	0.710995i	$-0.251755\pi$
$912$		0			0
$913$			44.9776i			1.48854i
$914$		0			0
$915$	−2.34790	+	5.66833i	−0.0776191	+	0.187389i
$916$		0			0
$917$	−31.1788	+	12.9147i	−1.02962	+	0.426481i
$918$		0			0
$919$	−4.48091	−	4.48091i	−0.147812	−	0.147812i	0.629328	−	0.777140i	$-0.283330\pi$
$919$	−4.48091	−	4.48091i	−0.147812	−	0.147812i	−0.777140	+	0.629328i	$0.783330\pi$
$920$		0			0
$921$	4.39750	−	4.39750i	0.144902	−	0.144902i
$922$		0			0
$923$	−0.792257	−	1.91268i	−0.0260775	−	0.0629566i
$924$		0			0
$925$	0.275748	+	0.114218i	0.00906652	+	0.00375548i
$926$		0			0
$927$	−5.15494			−0.169311
$928$		0			0
$929$	−41.1385			−1.34971			−0.674855	−	0.737950i	$-0.735794\pi$
$929$	−41.1385			−1.34971			−0.674855	+	0.737950i	$0.735794\pi$
$930$		0			0
$931$	72.4899	+	30.0263i	2.37576	+	0.984072i
$932$		0			0
$933$	0.365510	+	0.882420i	0.0119663	+	0.0288891i
$934$		0			0
$935$	2.97926	−	2.97926i	0.0974323	−	0.0974323i
$936$		0			0
$937$	9.98625	+	9.98625i	0.326237	+	0.326237i	0.851153	−	0.524917i	$-0.175904\pi$
$937$	9.98625	+	9.98625i	0.326237	+	0.326237i	−0.524917	+	0.851153i	$0.675904\pi$
$938$		0			0
$939$	−14.7781	+	6.12127i	−0.482263	+	0.199760i
$940$		0			0
$941$	−20.7835	+	50.1758i	−0.677522	+	1.63568i	0.0909934	+	0.995851i	$0.470996\pi$
$941$	−20.7835	+	50.1758i	−0.677522	+	1.63568i	−0.768515	+	0.639831i	$0.779004\pi$
$942$		0			0
$943$			42.1212i			1.37165i
$944$		0			0
$945$		−	8.45485i		−	0.275036i
$946$		0			0
$947$	8.98007	−	21.6798i	0.291813	−	0.704499i	−0.708186	−	0.706026i	$-0.750486\pi$
$947$	8.98007	−	21.6798i	0.291813	−	0.704499i	0.999999	+	0.00152707i	$0.000486083\pi$
$948$		0			0
$949$	6.39384	−	2.64842i	0.207553	−	0.0859712i
$950$		0			0
$951$	8.04437	+	8.04437i	0.260857	+	0.260857i
$952$		0			0
$953$	33.7694	−	33.7694i	1.09390	−	1.09390i	0.0987882	−	0.995108i	$-0.468503\pi$
$953$	33.7694	−	33.7694i	1.09390	−	1.09390i	0.995108	−	0.0987882i	$-0.0314966\pi$
$954$		0			0
$955$	−7.20438	−	17.3929i	−0.233128	−	0.562822i
$956$		0			0
$957$	−7.94942	−	3.29276i	−0.256968	−	0.106440i
$958$		0			0
$959$	89.0570			2.87580
$960$		0			0
$961$	78.2161			2.52310
$962$		0			0
$963$	6.93872	+	2.87411i	0.223597	+	0.0926170i
$964$		0			0
$965$	7.55396	+	18.2369i	0.243171	+	0.587066i
$966$		0			0
$967$	0.543237	−	0.543237i	0.0174693	−	0.0174693i	−0.698318	−	0.715787i	$-0.746068\pi$
$967$	0.543237	−	0.543237i	0.0174693	−	0.0174693i	0.715787	+	0.698318i	$0.246068\pi$
$968$		0			0
$969$	2.46518	+	2.46518i	0.0791930	+	0.0791930i
$970$		0			0
$971$	47.8546	−	19.8220i	1.53573	−	0.636119i	0.555062	−	0.831809i	$-0.312695\pi$
$971$	47.8546	−	19.8220i	1.53573	−	0.636119i	0.980666	+	0.195690i	$0.0626947\pi$
$972$		0			0
$973$	−4.06830	+	9.82176i	−0.130424	+	0.314871i
$974$		0			0
$975$			2.10488i			0.0674103i
$976$		0			0
$977$			0.231742i			0.00741408i	0.999993	+	0.00370704i	$0.00117999\pi$
$977$			0.231742i			0.00741408i	−0.999993	+	0.00370704i	$0.998820\pi$
$978$		0			0
$979$	−7.02901	+	16.9695i	−0.224648	+	0.542348i
$980$		0			0
$981$	−14.2854	+	5.91722i	−0.456099	+	0.188922i
$982$		0			0
$983$	31.7418	+	31.7418i	1.01241	+	1.01241i	0.999922	+	0.0124854i	$0.00397434\pi$
$983$	31.7418	+	31.7418i	1.01241	+	1.01241i	0.0124854	+	0.999922i	$0.496026\pi$
$984$		0			0
$985$	6.67386	−	6.67386i	0.212647	−	0.212647i
$986$		0			0
$987$	8.82230	+	21.2989i	0.280817	+	0.677952i
$988$		0			0
$989$	−12.6793	−	5.25193i	−0.403178	−	0.167002i
$990$		0			0
$991$	33.3427			1.05917			0.529583	−	0.848258i	$-0.322348\pi$
$991$	33.3427			1.05917			0.529583	+	0.848258i	$0.322348\pi$
$992$		0			0
$993$	4.46590			0.141721
$994$		0			0
$995$	23.4246	+	9.70279i	0.742610	+	0.307599i
$996$		0			0
$997$	18.9709	+	45.7997i	0.600813	+	1.45049i	0.872746	+	0.488175i	$0.162337\pi$
$997$	18.9709	+	45.7997i	0.600813	+	1.45049i	−0.271933	+	0.962316i	$0.587663\pi$
$998$		0			0
$999$	0.132042	−	0.132042i	0.00417761	−	0.00417761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.673.2		32
4.3	odd	2		768.2.n.a.673.6		32
8.3	odd	2		96.2.n.a.61.1	✓	32
8.5	even	2		384.2.n.a.337.7		32
24.5	odd	2		1152.2.v.c.721.3		32
24.11	even	2		288.2.v.d.253.8		32
32.5	even	8		384.2.n.a.49.7		32
32.11	odd	8		768.2.n.a.97.6		32
32.21	even	8	inner	768.2.n.b.97.2		32
32.27	odd	8		96.2.n.a.85.1	yes	32
96.5	odd	8		1152.2.v.c.433.3		32
96.59	even	8		288.2.v.d.181.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.1	✓	32	8.3	odd	2
96.2.n.a.85.1	yes	32	32.27	odd	8
288.2.v.d.181.8		32	96.59	even	8
288.2.v.d.253.8		32	24.11	even	2
384.2.n.a.49.7		32	32.5	even	8
384.2.n.a.337.7		32	8.5	even	2
768.2.n.a.97.6		32	32.11	odd	8
768.2.n.a.673.6		32	4.3	odd	2
768.2.n.b.97.2		32	32.21	even	8	inner
768.2.n.b.673.2		32	1.1	even	1	trivial
1152.2.v.c.433.3		32	96.5	odd	8
1152.2.v.c.721.3		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)

\(f(q)\)	\(=\)	\(q+(-0.923880 - 0.382683i) q^{3} +(-0.705805 - 1.70396i) q^{5} +(-3.24150 + 3.24150i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.923880 - 0.382683i) q^{3} +(-0.705805 - 1.70396i) q^{5} +(-3.24150 + 3.24150i) q^{7} +(0.707107 + 0.707107i) q^{9} +(3.38931 - 1.40390i) q^{11} +(0.503962 - 1.21667i) q^{13} +1.84436i q^{15} +0.622706i q^{17} +(-2.14250 + 5.17245i) q^{19} +(4.23522 - 1.75429i) q^{21} +(2.47578 + 2.47578i) q^{23} +(1.13020 - 1.13020i) q^{25} +(-0.382683 - 0.923880i) q^{27} +(2.16691 + 0.897562i) q^{29} +10.4506 q^{31} -3.66856 q^{33} +(7.81126 + 3.23553i) q^{35} +(0.0714604 + 0.172521i) q^{37} +(-0.931200 + 0.931200i) q^{39} +(8.50664 + 8.50664i) q^{41} +(-3.62132 + 1.50000i) q^{43} +(0.705805 - 1.70396i) q^{45} +5.02899i q^{47} -14.0146i q^{49} +(0.238299 - 0.575305i) q^{51} +(7.15914 - 2.96541i) q^{53} +(-4.78438 - 4.78438i) q^{55} +(3.95882 - 3.95882i) q^{57} +(-1.52516 - 3.68206i) q^{59} +(3.07333 + 1.27302i) q^{61} -4.58417 q^{63} -2.42886 q^{65} +(-2.17574 - 0.901222i) q^{67} +(-1.33988 - 3.23477i) q^{69} +(1.11161 - 1.11161i) q^{71} +(3.71598 + 3.71598i) q^{73} +(-1.47668 + 0.611660i) q^{75} +(-6.43570 + 15.5372i) q^{77} -10.2251i q^{79} +1.00000i q^{81} +(-4.69181 + 11.3270i) q^{83} +(1.06107 - 0.439509i) q^{85} +(-1.65848 - 1.65848i) q^{87} +(-3.54033 + 3.54033i) q^{89} +(2.31025 + 5.57743i) q^{91} +(-9.65514 - 3.99929i) q^{93} +10.3259 q^{95} +0.139594 q^{97} +(3.38931 + 1.40390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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