LMFDB - Embedded newform 208.2.k.b.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(31,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("208.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 147x^{8} + 662x^{6} + 2233x^{4} + 588x^{2} + 144 $ x^12 + 14x^10 + 147x^8 + 662x^6 + 2233x^4 + 588*x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.6
Root			$-1.43257 + 2.48129i$ of defining polynomial
Character	$\chi$	$=$	208.47
Dual form			208.2.k.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.86514i q^{3} +(-0.376763 - 0.376763i) q^{5} +(2.21257 + 2.21257i) q^{7} -5.20905 q^{9} +(-1.73205 - 1.73205i) q^{11} +(0.376763 + 3.58581i) q^{13} +(1.07948 - 1.07948i) q^{15} -4.20905i q^{17} +(-4.59719 + 4.59719i) q^{19} +(-6.33934 + 6.33934i) q^{21} +4.76925 q^{23} -4.71610i q^{25} -6.32925i q^{27} +9.17162 q^{29} +(1.13309 - 1.13309i) q^{31} +(4.96257 - 4.96257i) q^{33} -1.66723i q^{35} +(3.62324 - 3.62324i) q^{37} +(-10.2739 + 1.07948i) q^{39} +(7.96257 + 7.96257i) q^{41} +6.32925 q^{43} +(1.96257 + 1.96257i) q^{45} +(-4.47876 - 4.47876i) q^{47} +2.79095i q^{49} +12.0595 q^{51} +0.753525 q^{53} +1.30514i q^{55} +(-13.1716 - 13.1716i) q^{57} +(-9.02234 - 9.02234i) q^{59} -7.50705 q^{61} +(-11.5254 - 11.5254i) q^{63} +(1.20905 - 1.49295i) q^{65} +(0.771008 - 0.771008i) q^{67} +13.6646i q^{69} +(4.47876 - 4.47876i) q^{71} +(-3.20905 + 3.20905i) q^{73} +13.5123 q^{75} -7.66457i q^{77} +3.22723i q^{79} +2.50705 q^{81} +(-5.19615 + 5.19615i) q^{83} +(-1.58581 + 1.58581i) q^{85} +26.2780i q^{87} +(-0.455525 + 0.455525i) q^{89} +(-7.10025 + 8.76748i) q^{91} +(3.24647 + 3.24647i) q^{93} +3.46410 q^{95} +(-1.75353 - 1.75353i) q^{97} +(9.02234 + 9.02234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5} - 20 q^{9} - 4 q^{13} - 8 q^{21} + 8 q^{29} + 52 q^{37} + 36 q^{41} - 36 q^{45} - 8 q^{53} - 56 q^{57} - 56 q^{61} - 28 q^{65} + 4 q^{73} - 4 q^{81} + 32 q^{85} + 20 q^{89} + 56 q^{93} - 4 q^{97}+O(q^{100}) $ 12 * q + 4 * q^5 - 20 * q^9 - 4 * q^13 - 8 * q^21 + 8 * q^29 + 52 * q^37 + 36 * q^41 - 36 * q^45 - 8 * q^53 - 56 * q^57 - 56 * q^61 - 28 * q^65 + 4 * q^73 - 4 * q^81 + 32 * q^85 + 20 * q^89 + 56 * q^93 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$			2.86514i			1.65419i	0.562061	+	0.827096i	$0.310009\pi$
$3$			2.86514i			1.65419i	−0.562061	+	0.827096i	$0.689991\pi$
$4$		0			0
$5$	−0.376763	−	0.376763i	−0.168493	−	0.168493i	0.617823	−	0.786317i	$-0.288015\pi$
$5$	−0.376763	−	0.376763i	−0.168493	−	0.168493i	−0.786317	+	0.617823i	$0.788015\pi$
$6$		0			0
$7$	2.21257	+	2.21257i	0.836274	+	0.836274i	0.988366	−	0.152093i	$-0.0486012\pi$
$7$	2.21257	+	2.21257i	0.836274	+	0.836274i	−0.152093	+	0.988366i	$0.548601\pi$
$8$		0			0
$9$	−5.20905			−1.73635
$10$		0			0
$11$	−1.73205	−	1.73205i	−0.522233	−	0.522233i	0.396012	−	0.918245i	$-0.370394\pi$
$11$	−1.73205	−	1.73205i	−0.522233	−	0.522233i	−0.918245	+	0.396012i	$0.870394\pi$
$12$		0			0
$13$	0.376763	+	3.58581i	0.104495	+	0.994525i
$13$	0.376763	+	3.58581i	0.104495	+	0.994525i
$14$		0			0
$15$	1.07948	−	1.07948i	0.278720	−	0.278720i
$16$		0			0
$17$		−	4.20905i		−	1.02084i	−0.859924	−	0.510422i	$-0.829489\pi$
$17$		−	4.20905i		−	1.02084i	0.859924	−	0.510422i	$-0.170511\pi$
$18$		0			0
$19$	−4.59719	+	4.59719i	−1.05467	+	1.05467i	−0.0562522	+	0.998417i	$0.517915\pi$
$19$	−4.59719	+	4.59719i	−1.05467	+	1.05467i	−0.998417	+	0.0562522i	$0.982085\pi$
$20$		0			0
$21$	−6.33934	+	6.33934i	−1.38336	+	1.38336i
$22$		0			0
$23$	4.76925			0.994456			0.497228	−	0.867620i	$-0.334351\pi$
$23$	4.76925			0.994456			0.497228	+	0.867620i	$0.334351\pi$
$24$		0			0
$25$		−	4.71610i		−	0.943220i
$26$		0			0
$27$		−	6.32925i		−	1.21806i
$28$		0			0
$29$	9.17162			1.70313			0.851564	−	0.524251i	$-0.175655\pi$
$29$	9.17162			1.70313			0.851564	+	0.524251i	$0.175655\pi$
$30$		0			0
$31$	1.13309	−	1.13309i	0.203510	−	0.203510i	−0.597992	−	0.801502i	$-0.704035\pi$
$31$	1.13309	−	1.13309i	0.203510	−	0.203510i	0.801502	+	0.597992i	$0.204035\pi$
$32$		0			0
$33$	4.96257	−	4.96257i	0.863873	−	0.863873i
$34$		0			0
$35$		−	1.66723i		−	0.281813i
$36$		0			0
$37$	3.62324	−	3.62324i	0.595657	−	0.595657i	−0.343497	−	0.939154i	$-0.611612\pi$
$37$	3.62324	−	3.62324i	0.595657	−	0.595657i	0.939154	+	0.343497i	$0.111612\pi$
$38$		0			0
$39$	−10.2739	+	1.07948i	−1.64514	+	0.172855i
$40$		0			0
$41$	7.96257	+	7.96257i	1.24355	+	1.24355i	0.958520	+	0.285025i	$0.0920020\pi$
$41$	7.96257	+	7.96257i	1.24355	+	1.24355i	0.285025	+	0.958520i	$0.407998\pi$
$42$		0			0
$43$	6.32925			0.965201			0.482600	−	0.875841i	$-0.339692\pi$
$43$	6.32925			0.965201			0.482600	+	0.875841i	$0.339692\pi$
$44$		0			0
$45$	1.96257	+	1.96257i	0.292563	+	0.292563i
$46$		0			0
$47$	−4.47876	−	4.47876i	−0.653294	−	0.653294i	0.300491	−	0.953785i	$-0.402850\pi$
$47$	−4.47876	−	4.47876i	−0.653294	−	0.653294i	−0.953785	+	0.300491i	$0.902850\pi$
$48$		0			0
$49$			2.79095i			0.398707i
$50$		0			0
$51$	12.0595			1.68867
$52$		0			0
$53$	0.753525			0.103505			0.0517523	−	0.998660i	$-0.483519\pi$
$53$	0.753525			0.103505			0.0517523	+	0.998660i	$0.483519\pi$
$54$		0			0
$55$			1.30514i			0.175986i
$56$		0			0
$57$	−13.1716	−	13.1716i	−1.74462	−	1.74462i
$58$		0			0
$59$	−9.02234	−	9.02234i	−1.17461	−	1.17461i	−0.981098	−	0.193510i	$-0.938013\pi$
$59$	−9.02234	−	9.02234i	−1.17461	−	1.17461i	−0.193510	−	0.981098i	$-0.561987\pi$
$60$		0			0
$61$	−7.50705			−0.961179			−0.480590	−	0.876946i	$-0.659577\pi$
$61$	−7.50705			−0.961179			−0.480590	+	0.876946i	$0.659577\pi$
$62$		0			0
$63$	−11.5254	−	11.5254i	−1.45206	−	1.45206i
$64$		0			0
$65$	1.20905	−	1.49295i	0.149964	−	0.185178i
$66$		0			0
$67$	0.771008	−	0.771008i	0.0941937	−	0.0941937i	−0.658440	−	0.752633i	$-0.728783\pi$
$67$	0.771008	−	0.771008i	0.0941937	−	0.0941937i	0.752633	+	0.658440i	$0.228783\pi$
$68$		0			0
$69$			13.6646i			1.64502i
$70$		0			0
$71$	4.47876	−	4.47876i	0.531531	−	0.531531i	−0.389497	−	0.921028i	$-0.627351\pi$
$71$	4.47876	−	4.47876i	0.531531	−	0.531531i	0.921028	+	0.389497i	$0.127351\pi$
$72$		0			0
$73$	−3.20905	+	3.20905i	−0.375591	+	0.375591i	−0.869509	−	0.493918i	$-0.835564\pi$
$73$	−3.20905	+	3.20905i	−0.375591	+	0.375591i	0.493918	+	0.869509i	$0.335564\pi$
$74$		0			0
$75$	13.5123			1.56027
$76$		0			0
$77$		−	7.66457i		−	0.873459i
$78$		0			0
$79$			3.22723i			0.363092i	0.983382	+	0.181546i	$0.0581101\pi$
$79$			3.22723i			0.363092i	−0.983382	+	0.181546i	$0.941890\pi$
$80$		0			0
$81$	2.50705			0.278561
$82$		0			0
$83$	−5.19615	+	5.19615i	−0.570352	+	0.570352i	−0.932227	−	0.361875i	$-0.882137\pi$
$83$	−5.19615	+	5.19615i	−0.570352	+	0.570352i	0.361875	+	0.932227i	$0.382137\pi$
$84$		0			0
$85$	−1.58581	+	1.58581i	−0.172005	+	0.172005i
$86$		0			0
$87$			26.2780i			2.81730i
$88$		0			0
$89$	−0.455525	+	0.455525i	−0.0482855	+	0.0482855i	−0.730837	−	0.682552i	$-0.760870\pi$
$89$	−0.455525	+	0.455525i	−0.0482855	+	0.0482855i	0.682552	+	0.730837i	$0.260870\pi$
$90$		0			0
$91$	−7.10025	+	8.76748i	−0.744309	+	0.919082i
$92$		0			0
$93$	3.24647	+	3.24647i	0.336644	+	0.336644i
$94$		0			0
$95$	3.46410			0.355409
$96$		0			0
$97$	−1.75353	−	1.75353i	−0.178043	−	0.178043i	0.612459	−	0.790502i	$-0.290180\pi$
$97$	−1.75353	−	1.75353i	−0.178043	−	0.178043i	−0.790502	+	0.612459i	$0.790180\pi$
$98$		0			0
$99$	9.02234	+	9.02234i	0.906779	+	0.906779i
$100$		0			0
$101$		−	1.50705i		−	0.149957i	−0.997185	−	0.0749785i	$-0.976111\pi$
$101$		−	1.50705i		−	0.149957i	0.997185	−	0.0749785i	$-0.0238888\pi$
$102$		0			0
$103$	−3.57133			−0.351894			−0.175947	−	0.984400i	$-0.556299\pi$
$103$	−3.57133			−0.351894			−0.175947	+	0.984400i	$0.556299\pi$
$104$		0			0
$105$	4.77685			0.466173
$106$		0			0
$107$		−	6.07439i		−	0.587233i	−0.955923	−	0.293617i	$-0.905141\pi$
$107$		−	6.07439i		−	0.587233i	0.955923	−	0.293617i	$-0.0948589\pi$
$108$		0			0
$109$	5.13029	+	5.13029i	0.491392	+	0.491392i	0.908745	−	0.417352i	$-0.137042\pi$
$109$	5.13029	+	5.13029i	0.491392	+	0.491392i	−0.417352	+	0.908745i	$0.637042\pi$
$110$		0			0
$111$	10.3811	+	10.3811i	0.985330	+	0.985330i
$112$		0			0
$113$	2.41810			0.227476			0.113738	−	0.993511i	$-0.463718\pi$
$113$	2.41810			0.227476			0.113738	+	0.993511i	$0.463718\pi$
$114$		0			0
$115$	−1.79687	−	1.79687i	−0.167559	−	0.167559i
$116$		0			0
$117$	−1.96257	−	18.6787i	−0.181440	−	1.72684i
$118$		0			0
$119$	9.31283	−	9.31283i	0.853705	−	0.853705i
$120$		0			0
$121$		−	5.00000i		−	0.454545i
$122$		0			0
$123$	−22.8139	+	22.8139i	−2.05706	+	2.05706i
$124$		0			0
$125$	−3.66066	+	3.66066i	−0.327420	+	0.327420i
$126$		0			0
$127$	9.08716			0.806355			0.403178	−	0.915122i	$-0.367906\pi$
$127$	9.08716			0.806355			0.403178	+	0.915122i	$0.367906\pi$
$128$		0			0
$129$			18.1342i			1.59663i
$130$		0			0
$131$		−	12.9133i		−	1.12824i	−0.825691	−	0.564122i	$-0.809215\pi$
$131$		−	12.9133i		−	1.12824i	0.825691	−	0.564122i	$-0.190785\pi$
$132$		0			0
$133$	−20.3432			−1.76398
$134$		0			0
$135$	−2.38462	+	2.38462i	−0.205236	+	0.205236i
$136$		0			0
$137$	−12.9251	+	12.9251i	−1.10427	+	1.10427i	−0.110381	+	0.993889i	$0.535207\pi$
$137$	−12.9251	+	12.9251i	−1.10427	+	1.10427i	−0.993889	+	0.110381i	$0.964793\pi$
$138$		0			0
$139$			0.943059i			0.0799892i	0.999200	+	0.0399946i	$0.0127341\pi$
$139$			0.943059i			0.0799892i	−0.999200	+	0.0399946i	$0.987266\pi$
$140$		0			0
$141$	12.8323	−	12.8323i	1.08067	−	1.08067i
$142$		0			0
$143$	5.55824	−	6.86338i	0.464803	−	0.573945i
$144$		0			0
$145$	−3.45552	−	3.45552i	−0.286966	−	0.286966i
$146$		0			0
$147$	−7.99647			−0.659538
$148$		0			0
$149$	−15.6271	−	15.6271i	−1.28023	−	1.28023i	−0.940538	−	0.339688i	$-0.889679\pi$
$149$	−15.6271	−	15.6271i	−1.28023	−	1.28023i	−0.339688	−	0.940538i	$-0.610321\pi$
$150$		0			0
$151$	2.21257	+	2.21257i	0.180057	+	0.180057i	0.791380	−	0.611324i	$-0.209363\pi$
$151$	2.21257	+	2.21257i	0.180057	+	0.180057i	−0.611324	+	0.791380i	$0.709363\pi$
$152$		0			0
$153$			21.9251i			1.77254i
$154$		0			0
$155$	−0.853814			−0.0685800
$156$		0			0
$157$	9.43220			0.752772			0.376386	−	0.926463i	$-0.377167\pi$
$157$	9.43220			0.752772			0.376386	+	0.926463i	$0.377167\pi$
$158$		0			0
$159$			2.15896i			0.171216i
$160$		0			0
$161$	10.5523	+	10.5523i	0.831638	+	0.831638i
$162$		0			0
$163$	−5.30338	−	5.30338i	−0.415393	−	0.415393i	0.468219	−	0.883612i	$-0.344896\pi$
$163$	−5.30338	−	5.30338i	−0.415393	−	0.415393i	−0.883612	+	0.468219i	$0.844896\pi$
$164$		0			0
$165$	−3.73942			−0.291114
$166$		0			0
$167$	−13.7916	−	13.7916i	−1.06722	−	1.06722i	−0.997571	−	0.0696536i	$-0.977811\pi$
$167$	−13.7916	−	13.7916i	−1.06722	−	1.06722i	−0.0696536	−	0.997571i	$-0.522189\pi$
$168$		0			0
$169$	−12.7161	+	2.70200i	−0.978162	+	0.207846i
$170$		0			0
$171$	23.9470	−	23.9470i	1.83127	−	1.83127i
$172$		0			0
$173$		−	10.0827i		−	0.766572i	−0.923630	−	0.383286i	$-0.874792\pi$
$173$		−	10.0827i		−	0.766572i	0.923630	−	0.383286i	$-0.125208\pi$
$174$		0			0
$175$	10.4347	−	10.4347i	0.788790	−	0.788790i
$176$		0			0
$177$	25.8503	−	25.8503i	1.94303	−	1.94303i
$178$		0			0
$179$	−19.7119			−1.47334			−0.736669	−	0.676254i	$-0.763602\pi$
$179$	−19.7119			−1.47334			−0.736669	+	0.676254i	$0.763602\pi$
$180$		0			0
$181$			23.5897i			1.75341i	0.481028	+	0.876705i	$0.340264\pi$
$181$			23.5897i			1.75341i	−0.481028	+	0.876705i	$0.659736\pi$
$182$		0			0
$183$		−	21.5088i		−	1.58997i
$184$		0			0
$185$	−2.73020			−0.200728
$186$		0			0
$187$	−7.29029	+	7.29029i	−0.533119	+	0.533119i
$188$		0			0
$189$	14.0039	−	14.0039i	1.01863	−	1.01863i
$190$		0			0
$191$			15.1616i			1.09705i	0.836134	+	0.548526i	$0.184811\pi$
$191$			15.1616i			1.09705i	−0.836134	+	0.548526i	$0.815189\pi$
$192$		0			0
$193$	6.66457	−	6.66457i	0.479727	−	0.479727i	−0.425318	−	0.905044i	$-0.639838\pi$
$193$	6.66457	−	6.66457i	0.479727	−	0.479727i	0.905044	+	0.425318i	$0.139838\pi$
$194$		0			0
$195$	4.27752	+	3.46410i	0.306319	+	0.248069i
$196$		0			0
$197$	−3.54839	−	3.54839i	−0.252812	−	0.252812i	0.569310	−	0.822123i	$-0.307210\pi$
$197$	−3.54839	−	3.54839i	−0.252812	−	0.252812i	−0.822123	+	0.569310i	$0.807210\pi$
$198$		0			0
$199$	4.76925			0.338083			0.169041	−	0.985609i	$-0.445933\pi$
$199$	4.76925			0.338083			0.169041	+	0.985609i	$0.445933\pi$
$200$		0			0
$201$	2.20905	+	2.20905i	0.155814	+	0.155814i
$202$		0			0
$203$	20.2929	+	20.2929i	1.42428	+	1.42428i
$204$		0			0
$205$		−	6.00000i		−	0.419058i
$206$		0			0
$207$	−24.8432			−1.72672
$208$		0			0
$209$	15.9251			1.10157
$210$		0			0
$211$		−	10.5175i		−	0.724056i	−0.932167	−	0.362028i	$-0.882085\pi$
$211$		−	10.5175i		−	0.724056i	0.932167	−	0.362028i	$-0.117915\pi$
$212$		0			0
$213$	12.8323	+	12.8323i	0.879254	+	0.879254i
$214$		0			0
$215$	−2.38462	−	2.38462i	−0.162630	−	0.162630i
$216$		0			0
$217$	5.01410			0.340379
$218$		0			0
$219$	−9.19439	−	9.19439i	−0.621299	−	0.621299i
$220$		0			0
$221$	15.0929	−	1.58581i	1.01526	−	0.106673i
$222$		0			0
$223$	−6.98182	+	6.98182i	−0.467537	+	0.467537i	−0.901116	−	0.433579i	$-0.857251\pi$
$223$	−6.98182	+	6.98182i	−0.467537	+	0.467537i	0.433579	+	0.901116i	$0.357251\pi$
$224$		0			0
$225$			24.5664i			1.63776i
$226$		0			0
$227$	11.1813	−	11.1813i	0.742129	−	0.742129i	−0.230859	−	0.972987i	$-0.574153\pi$
$227$	11.1813	−	11.1813i	0.742129	−	0.742129i	0.972987	+	0.230859i	$0.0741535\pi$
$228$		0			0
$229$	15.2130	−	15.2130i	1.00530	−	1.00530i	0.00531493	−	0.999986i	$-0.498308\pi$
$229$	15.2130	−	15.2130i	1.00530	−	1.00530i	0.999986	−	0.00531493i	$-0.00169180\pi$
$230$		0			0
$231$	21.9601			1.44487
$232$		0			0
$233$		−	6.28390i		−	0.411672i	−0.978587	−	0.205836i	$-0.934009\pi$
$233$		−	6.28390i		−	0.411672i	0.978587	−	0.205836i	$-0.0659913\pi$
$234$		0			0
$235$			3.37486i			0.220151i
$236$		0			0
$237$	−9.24647			−0.600623
$238$		0			0
$239$	−14.8711	+	14.8711i	−0.961929	+	0.961929i	−0.999301	−	0.0373723i	$-0.988101\pi$
$239$	−14.8711	+	14.8711i	−0.961929	+	0.961929i	0.0373723	+	0.999301i	$0.488101\pi$
$240$		0			0
$241$	−5.96257	+	5.96257i	−0.384083	+	0.384083i	−0.872571	−	0.488488i	$-0.837549\pi$
$241$	−5.96257	+	5.96257i	−0.384083	+	0.384083i	0.488488	+	0.872571i	$0.337549\pi$
$242$		0			0
$243$		−	11.8047i		−	0.757270i
$244$		0			0
$245$	1.05153	−	1.05153i	0.0671795	−	0.0671795i
$246$		0			0
$247$	−18.2167	−	14.7526i	−1.15910	−	0.938687i
$248$		0			0
$249$	−14.8877	−	14.8877i	−0.943471	−	0.943471i
$250$		0			0
$251$	7.65237			0.483013			0.241507	−	0.970399i	$-0.422358\pi$
$251$	7.65237			0.483013			0.241507	+	0.970399i	$0.422358\pi$
$252$		0			0
$253$	−8.26058	−	8.26058i	−0.519338	−	0.519338i
$254$		0			0
$255$	−4.54358	−	4.54358i	−0.284530	−	0.284530i
$256$		0			0
$257$			26.1342i			1.63021i	0.579316	+	0.815103i	$0.303320\pi$
$257$			26.1342i			1.63021i	−0.579316	+	0.815103i	$0.696680\pi$
$258$		0			0
$259$	16.0333			0.996264
$260$		0			0
$261$	−47.7754			−2.95723
$262$		0			0
$263$		−	17.3205i		−	1.06803i	−0.845476	−	0.534014i	$-0.820683\pi$
$263$		−	17.3205i		−	1.06803i	0.845476	−	0.534014i	$-0.179317\pi$
$264$		0			0
$265$	−0.283900	−	0.283900i	−0.0174398	−	0.0174398i
$266$		0			0
$267$	−1.30514	−	1.30514i	−0.0798735	−	0.0798735i
$268$		0			0
$269$	−4.49295			−0.273940			−0.136970	−	0.990575i	$-0.543736\pi$
$269$	−4.49295			−0.273940			−0.136970	+	0.990575i	$0.543736\pi$
$270$		0			0
$271$	18.4424	+	18.4424i	1.12030	+	1.12030i	0.991697	+	0.128599i	$0.0410480\pi$
$271$	18.4424	+	18.4424i	1.12030	+	1.12030i	0.128599	+	0.991697i	$0.458952\pi$
$272$		0			0
$273$	−25.1201	−	20.3432i	−1.52034	−	1.23123i
$274$		0			0
$275$	−8.16852	+	8.16852i	−0.492581	+	0.492581i
$276$		0			0
$277$			0.567800i			0.0341158i	0.999855	+	0.0170579i	$0.00542996\pi$
$277$			0.567800i			0.0341158i	−0.999855	+	0.0170579i	$0.994570\pi$
$278$		0			0
$279$	−5.90234	+	5.90234i	−0.353364	+	0.353364i
$280$		0			0
$281$	−11.8877	+	11.8877i	−0.709162	+	0.709162i	−0.966359	−	0.257197i	$-0.917201\pi$
$281$	−11.8877	+	11.8877i	−0.709162	+	0.709162i	0.257197	+	0.966359i	$0.417201\pi$
$282$		0			0
$283$	2.61029			0.155165			0.0775827	−	0.996986i	$-0.475280\pi$
$283$	2.61029			0.155165			0.0775827	+	0.996986i	$0.475280\pi$
$284$		0			0
$285$			9.92515i			0.587915i
$286$		0			0
$287$			35.2355i			2.07989i
$288$		0			0
$289$	−0.716100			−0.0421235
$290$		0			0
$291$	5.02410	−	5.02410i	0.294518	−	0.294518i
$292$		0			0
$293$	3.20514	−	3.20514i	0.187246	−	0.187246i	−0.607258	−	0.794504i	$-0.707731\pi$
$293$	3.20514	−	3.20514i	0.187246	−	0.187246i	0.794504	+	0.607258i	$0.207731\pi$
$294$		0			0
$295$			6.79856i			0.395827i
$296$		0			0
$297$	−10.9626	+	10.9626i	−0.636113	+	0.636113i
$298$		0			0
$299$	1.79687	+	17.1016i	0.103916	+	0.989012i
$300$		0			0
$301$	14.0039	+	14.0039i	0.807172	+	0.807172i
$302$		0			0
$303$	4.31792			0.248058
$304$		0			0
$305$	2.82838	+	2.82838i	0.161952	+	0.161952i
$306$		0			0
$307$	−10.2203	−	10.2203i	−0.583301	−	0.583301i	0.352508	−	0.935809i	$-0.385329\pi$
$307$	−10.2203	−	10.2203i	−0.583301	−	0.583301i	−0.935809	+	0.352508i	$0.885329\pi$
$308$		0			0
$309$		−	10.2324i		−	0.582099i
$310$		0			0
$311$	0.724170			0.0410639			0.0205319	−	0.999789i	$-0.493464\pi$
$311$	0.724170			0.0410639			0.0205319	+	0.999789i	$0.493464\pi$
$312$		0			0
$313$	25.2232			1.42570			0.712848	−	0.701318i	$-0.247405\pi$
$313$	25.2232			1.42570			0.712848	+	0.701318i	$0.247405\pi$
$314$		0			0
$315$			8.68468i			0.489326i
$316$		0			0
$317$	−5.13420	−	5.13420i	−0.288365	−	0.288365i	0.548068	−	0.836434i	$-0.315363\pi$
$317$	−5.13420	−	5.13420i	−0.288365	−	0.288365i	−0.836434	+	0.548068i	$0.815363\pi$
$318$		0			0
$319$	−15.8857	−	15.8857i	−0.889430	−	0.889430i
$320$		0			0
$321$	17.4040			0.971397
$322$		0			0
$323$	19.3498	+	19.3498i	1.07665	+	1.07665i
$324$		0			0
$325$	16.9110	−	1.77685i	0.938056	−	0.0985619i
$326$		0			0
$327$	−14.6990	+	14.6990i	−0.812857	+	0.812857i
$328$		0			0
$329$		−	19.8192i		−	1.09267i
$330$		0			0
$331$	−3.99824	+	3.99824i	−0.219763	+	0.219763i	−0.808399	−	0.588636i	$-0.799665\pi$
$331$	−3.99824	+	3.99824i	−0.219763	+	0.219763i	0.588636	+	0.808399i	$0.299665\pi$
$332$		0			0
$333$	−18.8736	+	18.8736i	−1.03427	+	1.03427i
$334$		0			0
$335$	−0.580974			−0.0317420
$336$		0			0
$337$		−	16.0593i		−	0.874808i	−0.899265	−	0.437404i	$-0.855898\pi$
$337$		−	16.0593i		−	0.874808i	0.899265	−	0.437404i	$-0.144102\pi$
$338$		0			0
$339$			6.92820i			0.376288i
$340$		0			0
$341$	−3.92515			−0.212559
$342$		0			0
$343$	9.31283	−	9.31283i	0.502845	−	0.502845i
$344$		0			0
$345$	5.14830	−	5.14830i	0.277175	−	0.277175i
$346$		0			0
$347$			20.5657i			1.10403i	0.833836	+	0.552013i	$0.186140\pi$
$347$			20.5657i			1.10403i	−0.833836	+	0.552013i	$0.813860\pi$
$348$		0			0
$349$	−7.54839	+	7.54839i	−0.404056	+	0.404056i	−0.879660	−	0.475604i	$-0.842230\pi$
$349$	−7.54839	+	7.54839i	−0.404056	+	0.404056i	0.475604	+	0.879660i	$0.342230\pi$
$350$		0			0
$351$	22.6955	−	2.38462i	1.21140	−	0.127282i
$352$		0			0
$353$	−1.33543	−	1.33543i	−0.0710775	−	0.0710775i	0.670674	−	0.741752i	$-0.266005\pi$
$353$	−1.33543	−	1.33543i	−0.0710775	−	0.0710775i	−0.741752	+	0.670674i	$0.766005\pi$
$354$		0			0
$355$	−3.37486			−0.179119
$356$		0			0
$357$	26.6826	+	26.6826i	1.41219	+	1.41219i
$358$		0			0
$359$	14.6454	+	14.6454i	0.772955	+	0.772955i	0.978622	−	0.205667i	$-0.0659365\pi$
$359$	14.6454	+	14.6454i	0.772955	+	0.772955i	−0.205667	+	0.978622i	$0.565937\pi$
$360$		0			0
$361$		−	23.2684i		−	1.22465i
$362$		0			0
$363$	14.3257			0.751905
$364$		0			0
$365$	2.41810			0.126569
$366$		0			0
$367$			29.7421i			1.55253i	0.630409	+	0.776263i	$0.282887\pi$
$367$			29.7421i			1.55253i	−0.630409	+	0.776263i	$0.717113\pi$
$368$		0			0
$369$	−41.4774	−	41.4774i	−2.15923	−	2.15923i
$370$		0			0
$371$	1.66723	+	1.66723i	0.0865582	+	0.0865582i
$372$		0			0
$373$	11.4040			0.590477			0.295238	−	0.955424i	$-0.404601\pi$
$373$	11.4040			0.590477			0.295238	+	0.955424i	$0.404601\pi$
$374$		0			0
$375$	−10.4883	−	10.4883i	−0.541615	−	0.541615i
$376$		0			0
$377$	3.45552	+	32.8877i	0.177969	+	1.69380i
$378$		0			0
$379$	1.49518	−	1.49518i	0.0768021	−	0.0768021i	−0.667662	−	0.744464i	$-0.732705\pi$
$379$	1.49518	−	1.49518i	0.0768021	−	0.0768021i	0.744464	+	0.667662i	$0.232705\pi$
$380$		0			0
$381$			26.0360i			1.33387i
$382$		0			0
$383$	3.75459	−	3.75459i	0.191851	−	0.191851i	−0.604645	−	0.796495i	$-0.706685\pi$
$383$	3.75459	−	3.75459i	0.191851	−	0.191851i	0.796495	+	0.604645i	$0.206685\pi$
$384$		0			0
$385$	−2.88772	+	2.88772i	−0.147172	+	0.147172i
$386$		0			0
$387$	−32.9694			−1.67593
$388$		0			0
$389$		−	21.3573i		−	1.08286i	−0.840746	−	0.541430i	$-0.817883\pi$
$389$		−	21.3573i		−	1.08286i	0.840746	−	0.541430i	$-0.182117\pi$
$390$		0			0
$391$		−	20.0740i		−	1.01519i
$392$		0			0
$393$	36.9986			1.86633
$394$		0			0
$395$	1.21590	−	1.21590i	0.0611785	−	0.0611785i
$396$		0			0
$397$	−19.6271	+	19.6271i	−0.985058	+	0.985058i	−0.999890	−	0.0148316i	$-0.995279\pi$
$397$	−19.6271	+	19.6271i	−0.985058	+	0.985058i	0.0148316	+	0.999890i	$0.495279\pi$
$398$		0			0
$399$		−	58.2863i		−	2.91797i
$400$		0			0
$401$	−6.58190	+	6.58190i	−0.328684	+	0.328684i	−0.852086	−	0.523402i	$-0.824663\pi$
$401$	−6.58190	+	6.58190i	−0.328684	+	0.328684i	0.523402	+	0.852086i	$0.324663\pi$
$402$		0			0
$403$	4.48997	+	3.63615i	0.223661	+	0.181130i
$404$		0			0
$405$	−0.944563	−	0.944563i	−0.0469357	−	0.0469357i
$406$		0			0
$407$	−12.5513			−0.622143
$408$		0			0
$409$	−4.40400	−	4.40400i	−0.217764	−	0.217764i	0.589792	−	0.807555i	$-0.299210\pi$
$409$	−4.40400	−	4.40400i	−0.217764	−	0.217764i	−0.807555	+	0.589792i	$0.799210\pi$
$410$		0			0
$411$	−37.0324	−	37.0324i	−1.82667	−	1.82667i
$412$		0			0
$413$		−	39.9251i		−	1.96459i
$414$		0			0
$415$	3.91543			0.192201
$416$		0			0
$417$	−2.70200			−0.132317
$418$		0			0
$419$		−	7.87126i		−	0.384536i	−0.981342	−	0.192268i	$-0.938416\pi$
$419$		−	7.87126i		−	0.384536i	0.981342	−	0.192268i	$-0.0615843\pi$
$420$		0			0
$421$	21.8090	+	21.8090i	1.06290	+	1.06290i	0.997884	+	0.0650198i	$0.0207111\pi$
$421$	21.8090	+	21.8090i	1.06290	+	1.06290i	0.0650198	+	0.997884i	$0.479289\pi$
$422$		0			0
$423$	23.3301	+	23.3301i	1.13435	+	1.13435i
$424$		0			0
$425$	−19.8503			−0.962881
$426$		0			0
$427$	−16.6099	−	16.6099i	−0.803809	−	0.803809i
$428$		0			0
$429$	19.6646	+	15.9251i	0.949415	+	0.768873i
$430$		0			0
$431$	−1.01466	+	1.01466i	−0.0488743	+	0.0488743i	−0.731122	−	0.682247i	$-0.761003\pi$
$431$	−1.01466	+	1.01466i	−0.0488743	+	0.0488743i	0.682247	+	0.731122i	$0.261003\pi$
$432$		0			0
$433$		−	26.9704i		−	1.29611i	−0.761592	−	0.648057i	$-0.775582\pi$
$433$		−	26.9704i		−	1.29611i	0.761592	−	0.648057i	$-0.224418\pi$
$434$		0			0
$435$	9.90058	−	9.90058i	0.474696	−	0.474696i
$436$		0			0
$437$	−21.9251	+	21.9251i	−1.04882	+	1.04882i
$438$		0			0
$439$	1.92209			0.0917361			0.0458681	−	0.998948i	$-0.485395\pi$
$439$	1.92209			0.0917361			0.0458681	+	0.998948i	$0.485395\pi$
$440$		0			0
$441$		−	14.5382i		−	0.692295i
$442$		0			0
$443$			0.943059i			0.0448061i	0.999749	+	0.0224030i	$0.00713171\pi$
$443$			0.943059i			0.0448061i	−0.999749	+	0.0224030i	$0.992868\pi$
$444$		0			0
$445$	0.343249			0.0162716
$446$		0			0
$447$	44.7740	−	44.7740i	2.11774	−	2.11774i
$448$		0			0
$449$	−7.67867	+	7.67867i	−0.362379	+	0.362379i	−0.864688	−	0.502309i	$-0.832484\pi$
$449$	−7.67867	+	7.67867i	−0.362379	+	0.362379i	0.502309	+	0.864688i	$0.332484\pi$
$450$		0			0
$451$		−	27.5832i		−	1.29884i
$452$		0			0
$453$	−6.33934	+	6.33934i	−0.297848	+	0.297848i
$454$		0			0
$455$	5.97837	−	0.628149i	0.280270	−	0.0294481i
$456$		0			0
$457$	13.8877	+	13.8877i	0.649640	+	0.649640i	0.952906	−	0.303266i	$-0.0980770\pi$
$457$	13.8877	+	13.8877i	0.649640	+	0.649640i	−0.303266	+	0.952906i	$0.598077\pi$
$458$		0			0
$459$	−26.6401			−1.24345
$460$		0			0
$461$	−8.63734	−	8.63734i	−0.402281	−	0.402281i	0.476755	−	0.879036i	$-0.341813\pi$
$461$	−8.63734	−	8.63734i	−0.402281	−	0.402281i	−0.879036	+	0.476755i	$0.841813\pi$
$462$		0			0
$463$	−25.2522	−	25.2522i	−1.17357	−	1.17357i	−0.981353	−	0.192214i	$-0.938433\pi$
$463$	−25.2522	−	25.2522i	−1.17357	−	1.17357i	−0.192214	−	0.981353i	$-0.561567\pi$
$464$		0			0
$465$		−	2.44630i		−	0.113444i
$466$		0			0
$467$	−35.3652			−1.63651			−0.818253	−	0.574859i	$-0.805057\pi$
$467$	−35.3652			−1.63651			−0.818253	+	0.574859i	$0.805057\pi$
$468$		0			0
$469$	3.41182			0.157543
$470$		0			0
$471$			27.0246i			1.24523i
$472$		0			0
$473$	−10.9626	−	10.9626i	−0.504060	−	0.504060i
$474$		0			0
$475$	21.6808	+	21.6808i	0.994785	+	0.994785i
$476$		0			0
$477$	−3.92515			−0.179720
$478$		0			0
$479$	24.4096	+	24.4096i	1.11530	+	1.11530i	0.992422	+	0.122879i	$0.0392128\pi$
$479$	24.4096	+	24.4096i	1.11530	+	1.11530i	0.122879	+	0.992422i	$0.460787\pi$
$480$		0			0
$481$	14.3573	+	11.6271i	0.654639	+	0.530152i
$482$		0			0
$483$	−30.2339	+	30.2339i	−1.37569	+	1.37569i
$484$		0			0
$485$			1.32133i			0.0599983i
$486$		0			0
$487$	−9.12957	+	9.12957i	−0.413700	+	0.413700i	−0.883025	−	0.469325i	$-0.844497\pi$
$487$	−9.12957	+	9.12957i	−0.413700	+	0.413700i	0.469325	+	0.883025i	$0.344497\pi$
$488$		0			0
$489$	15.1949	−	15.1949i	0.687139	−	0.687139i
$490$		0			0
$491$	16.1182			0.727402			0.363701	−	0.931516i	$-0.381513\pi$
$491$	16.1182			0.727402			0.363701	+	0.931516i	$0.381513\pi$
$492$		0			0
$493$		−	38.6038i		−	1.73863i
$494$		0			0
$495$		−	6.79856i		−	0.305572i
$496$		0			0
$497$	19.8192			0.889010
$498$		0			0
$499$	29.0604	−	29.0604i	1.30092	−	1.30092i	0.373149	−	0.927771i	$-0.378278\pi$
$499$	29.0604	−	29.0604i	1.30092	−	1.30092i	0.927771	−	0.373149i	$-0.121722\pi$
$500$		0			0
$501$	39.5149	−	39.5149i	1.76539	−	1.76539i
$502$		0			0
$503$		−	7.78202i		−	0.346983i	−0.984835	−	0.173492i	$-0.944495\pi$
$503$		−	7.78202i		−	0.346983i	0.984835	−	0.173492i	$-0.0555049\pi$
$504$		0			0
$505$	−0.567800	+	0.567800i	−0.0252668	+	0.0252668i
$506$		0			0
$507$	−7.74162	−	36.4335i	−0.343817	−	1.61807i
$508$		0			0
$509$	17.7302	+	17.7302i	0.785877	+	0.785877i	0.980816	−	0.194938i	$-0.0624506\pi$
$509$	17.7302	+	17.7302i	0.785877	+	0.785877i	−0.194938	+	0.980816i	$0.562451\pi$
$510$		0			0
$511$	−14.2005			−0.628193
$512$		0			0
$513$	29.0968	+	29.0968i	1.28465	+	1.28465i
$514$		0			0
$515$	1.34554	+	1.34554i	0.0592917	+	0.0592917i
$516$		0			0
$517$			15.5149i			0.682343i
$518$		0			0
$519$	28.8883			1.26806
$520$		0			0
$521$	−8.13420			−0.356366			−0.178183	−	0.983997i	$-0.557022\pi$
$521$	−8.13420			−0.356366			−0.178183	+	0.983997i	$0.557022\pi$
$522$		0			0
$523$		−	6.07439i		−	0.265614i	−0.991142	−	0.132807i	$-0.957601\pi$
$523$		−	6.07439i		−	0.265614i	0.991142	−	0.132807i	$-0.0423991\pi$
$524$		0			0
$525$	29.8969	+	29.8969i	1.30481	+	1.30481i
$526$		0			0
$527$	−4.76925	−	4.76925i	−0.207752	−	0.207752i
$528$		0			0
$529$	−0.254299			−0.0110565
$530$		0			0
$531$	46.9978	+	46.9978i	2.03953	+	2.03953i
$532$		0			0
$533$	−25.5523	+	31.5523i	−1.10679	+	1.36668i
$534$		0			0
$535$	−2.28860	+	2.28860i	−0.0989449	+	0.0989449i
$536$		0			0
$537$		−	56.4774i		−	2.43718i
$538$		0			0
$539$	4.83407	−	4.83407i	0.208218	−	0.208218i
$540$		0			0
$541$	−21.6311	+	21.6311i	−0.929992	+	0.929992i	−0.997705	−	0.0677129i	$-0.978430\pi$
$541$	−21.6311	+	21.6311i	−0.929992	+	0.929992i	0.0677129	+	0.997705i	$0.478430\pi$
$542$		0			0
$543$	−67.5880			−2.90048
$544$		0			0
$545$		−	3.86580i		−	0.165593i
$546$		0			0
$547$			35.3248i			1.51038i	0.655507	+	0.755189i	$0.272455\pi$
$547$			35.3248i			1.51038i	−0.655507	+	0.755189i	$0.727545\pi$
$548$		0			0
$549$	39.1046			1.66894
$550$		0			0
$551$	−42.1637	+	42.1637i	−1.79624	+	1.79624i
$552$		0			0
$553$	−7.14048	+	7.14048i	−0.303644	+	0.303644i
$554$		0			0
$555$		−	7.82242i		−	0.332043i
$556$		0			0
$557$	6.53429	−	6.53429i	0.276867	−	0.276867i	−0.554990	−	0.831857i	$-0.687278\pi$
$557$	6.53429	−	6.53429i	0.276867	−	0.276867i	0.831857	+	0.554990i	$0.187278\pi$
$558$		0			0
$559$	2.38462	+	22.6955i	0.100859	+	0.959917i
$560$		0			0
$561$	−20.8877	−	20.8877i	−0.881880	−	0.881880i
$562$		0			0
$563$	24.0298			1.01274			0.506368	−	0.862317i	$-0.330988\pi$
$563$	24.0298			1.01274			0.506368	+	0.862317i	$0.330988\pi$
$564$		0			0
$565$	−0.911049	−	0.911049i	−0.0383281	−	0.0383281i
$566$		0			0
$567$	5.54703	+	5.54703i	0.232953	+	0.232953i
$568$		0			0
$569$		−	4.20905i		−	0.176453i	−0.996100	−	0.0882263i	$-0.971880\pi$
$569$		−	4.20905i		−	0.176453i	0.996100	−	0.0882263i	$-0.0281199\pi$
$570$		0			0
$571$	8.72508			0.365133			0.182567	−	0.983194i	$-0.441560\pi$
$571$	8.72508			0.365133			0.182567	+	0.983194i	$0.441560\pi$
$572$		0			0
$573$	−43.4400			−1.81473
$574$		0			0
$575$		−	22.4922i		−	0.937991i
$576$		0			0
$577$	−19.7302	−	19.7302i	−0.821379	−	0.821379i	0.164927	−	0.986306i	$-0.447261\pi$
$577$	−19.7302	−	19.7302i	−0.821379	−	0.821379i	−0.986306	+	0.164927i	$0.947261\pi$
$578$		0			0
$579$	19.0950	+	19.0950i	0.793560	+	0.793560i
$580$		0			0
$581$	−22.9937			−0.953940
$582$		0			0
$583$	−1.30514	−	1.30514i	−0.0540535	−	0.0540535i
$584$		0			0
$585$	−6.29800	+	7.77685i	−0.260390	+	0.321533i
$586$		0			0
$587$	3.89101	−	3.89101i	0.160599	−	0.160599i	−0.622233	−	0.782832i	$-0.713774\pi$
$587$	3.89101	−	3.89101i	0.160599	−	0.160599i	0.782832	+	0.622233i	$0.213774\pi$
$588$		0			0
$589$			10.4181i			0.429270i
$590$		0			0
$591$	10.1666	−	10.1666i	0.418200	−	0.418200i
$592$		0			0
$593$	3.75353	−	3.75353i	0.154139	−	0.154139i	−0.625825	−	0.779964i	$-0.715238\pi$
$593$	3.75353	−	3.75353i	0.154139	−	0.154139i	0.779964	+	0.625825i	$0.215238\pi$
$594$		0			0
$595$	−7.01745			−0.287687
$596$		0			0
$597$			13.6646i			0.559254i
$598$		0			0
$599$			24.9729i			1.02036i	0.860066	+	0.510182i	$0.170422\pi$
$599$			24.9729i			1.02036i	−0.860066	+	0.510182i	$0.829578\pi$
$600$		0			0
$601$	−35.1483			−1.43373			−0.716865	−	0.697212i	$-0.754423\pi$
$601$	−35.1483			−1.43373			−0.716865	+	0.697212i	$0.754423\pi$
$602$		0			0
$603$	−4.01622	+	4.01622i	−0.163553	+	0.163553i
$604$		0			0
$605$	−1.88381	+	1.88381i	−0.0765879	+	0.0765879i
$606$		0			0
$607$		−	37.1217i		−	1.50672i	−0.657607	−	0.753361i	$-0.728431\pi$
$607$		−	37.1217i		−	1.50672i	0.657607	−	0.753361i	$-0.271569\pi$
$608$		0			0
$609$	−58.1420	+	58.1420i	−2.35603	+	2.35603i
$610$		0			0
$611$	14.3726	−	17.7474i	0.581451	−	0.717984i
$612$		0			0
$613$	−28.8736	−	28.8736i	−1.16619	−	1.16619i	−0.983094	−	0.183100i	$-0.941387\pi$
$613$	−28.8736	−	28.8736i	−1.16619	−	1.16619i	−0.183100	−	0.983094i	$-0.558613\pi$
$614$		0			0
$615$	17.1909			0.693203
$616$		0			0
$617$	21.6271	+	21.6271i	0.870676	+	0.870676i	0.992546	−	0.121870i	$-0.0388890\pi$
$617$	21.6271	+	21.6271i	0.870676	+	0.870676i	−0.121870	+	0.992546i	$0.538889\pi$
$618$		0			0
$619$	−1.60684	−	1.60684i	−0.0645843	−	0.0645843i	0.674077	−	0.738661i	$-0.264542\pi$
$619$	−1.60684	−	1.60684i	−0.0645843	−	0.0645843i	−0.738661	+	0.674077i	$0.764542\pi$
$620$		0			0
$621$		−	30.1857i		−	1.21131i
$622$		0			0
$623$	−2.01576			−0.0807598
$624$		0			0
$625$	−20.8221			−0.832884
$626$		0			0
$627$			45.6278i			1.82220i
$628$		0			0
$629$	−15.2504	−	15.2504i	−0.608073	−	0.608073i
$630$		0			0
$631$	−29.7957	−	29.7957i	−1.18615	−	1.18615i	−0.978123	−	0.208027i	$-0.933296\pi$
$631$	−29.7957	−	29.7957i	−1.18615	−	1.18615i	−0.208027	−	0.978123i	$-0.566704\pi$
$632$		0			0
$633$	30.1342			1.19773
$634$		0			0
$635$	−3.42370	−	3.42370i	−0.135865	−	0.135865i
$636$		0			0
$637$	−10.0078	+	1.05153i	−0.396524	+	0.0416630i
$638$		0			0
$639$	−23.3301	+	23.3301i	−0.922924	+	0.922924i
$640$		0			0
$641$			9.35735i			0.369593i	0.982777	+	0.184797i	$0.0591626\pi$
$641$			9.35735i			0.369593i	−0.982777	+	0.184797i	$0.940837\pi$
$642$		0			0
$643$	25.6142	−	25.6142i	1.01013	−	1.01013i	0.0101790	−	0.999948i	$-0.496760\pi$
$643$	25.6142	−	25.6142i	1.01013	−	1.01013i	0.999948	−	0.0101790i	$-0.00324014\pi$
$644$		0			0
$645$	6.83229	−	6.83229i	0.269021	−	0.269021i
$646$		0			0
$647$	−13.8564			−0.544752			−0.272376	−	0.962191i	$-0.587809\pi$
$647$	−13.8564			−0.544752			−0.272376	+	0.962191i	$0.587809\pi$
$648$		0			0
$649$			31.2543i			1.22684i
$650$		0			0
$651$			14.3661i			0.563053i
$652$		0			0
$653$	−8.76135			−0.342858			−0.171429	−	0.985196i	$-0.554838\pi$
$653$	−8.76135			−0.342858			−0.171429	+	0.985196i	$0.554838\pi$
$654$		0			0
$655$	−4.86527	+	4.86527i	−0.190102	+	0.190102i
$656$		0			0
$657$	16.7161	−	16.7161i	0.652157	−	0.652157i
$658$		0			0
$659$		−	0.853814i		−	0.0332599i	−0.999862	−	0.0166299i	$-0.994706\pi$
$659$		−	0.853814i		−	0.0332599i	0.999862	−	0.0166299i	$-0.00529372\pi$
$660$		0			0
$661$	19.8129	−	19.8129i	0.770631	−	0.770631i	−0.207585	−	0.978217i	$-0.566560\pi$
$661$	19.8129	−	19.8129i	0.770631	−	0.770631i	0.978217	+	0.207585i	$0.0665605\pi$
$662$		0			0
$663$	4.54358	+	43.2432i	0.176458	+	1.67943i
$664$		0			0
$665$	7.66457	+	7.66457i	0.297219	+	0.297219i
$666$		0			0
$667$	43.7417			1.69369
$668$		0			0
$669$	−20.0039	−	20.0039i	−0.773396	−	0.773396i
$670$		0			0
$671$	13.0026	+	13.0026i	0.501960	+	0.501960i
$672$		0			0
$673$			21.0452i			0.811235i	0.914043	+	0.405617i	$0.132943\pi$
$673$			21.0452i			0.811235i	−0.914043	+	0.405617i	$0.867057\pi$
$674$		0			0
$675$	−29.8494			−1.14890
$676$		0			0
$677$	5.02192			0.193008			0.0965041	−	0.995333i	$-0.469234\pi$
$677$	5.02192			0.193008			0.0965041	+	0.995333i	$0.469234\pi$
$678$		0			0
$679$		−	7.75960i		−	0.297786i
$680$		0			0
$681$	32.0360	+	32.0360i	1.22762	+	1.22762i
$682$		0			0
$683$	−16.3126	−	16.3126i	−0.624185	−	0.624185i	0.322414	−	0.946599i	$-0.395506\pi$
$683$	−16.3126	−	16.3126i	−0.624185	−	0.624185i	−0.946599	+	0.322414i	$0.895506\pi$
$684$		0			0
$685$	9.73942			0.372124
$686$		0			0
$687$	43.5873	+	43.5873i	1.66296	+	1.66296i
$688$		0			0
$689$	0.283900	+	2.70200i	0.0108157	+	0.102938i
$690$		0			0
$691$	−34.2097	+	34.2097i	−1.30140	+	1.30140i	−0.373948	+	0.927450i	$0.621996\pi$
$691$	−34.2097	+	34.2097i	−1.30140	+	1.30140i	−0.927450	+	0.373948i	$0.878004\pi$
$692$		0			0
$693$			39.9251i			1.51663i
$694$		0			0
$695$	0.355309	−	0.355309i	0.0134776	−	0.0134776i
$696$		0			0
$697$	33.5149	−	33.5149i	1.26947	−	1.26947i
$698$		0			0
$699$	18.0043			0.680984
$700$		0			0
$701$			12.1575i			0.459183i	0.973287	+	0.229592i	$0.0737391\pi$
$701$			12.1575i			0.459183i	−0.973287	+	0.229592i	$0.926261\pi$
$702$		0			0
$703$			33.3135i			1.25644i
$704$		0			0
$705$	−9.66945			−0.364173
$706$		0			0
$707$	3.33446	−	3.33446i	0.125405	−	0.125405i
$708$		0			0
$709$	−6.12010	+	6.12010i	−0.229845	+	0.229845i	−0.812628	−	0.582783i	$-0.801964\pi$
$709$	−6.12010	+	6.12010i	−0.229845	+	0.229845i	0.582783	+	0.812628i	$0.301964\pi$
$710$		0			0
$711$		−	16.8108i		−	0.630454i
$712$		0			0
$713$	5.40400	−	5.40400i	0.202381	−	0.202381i
$714$		0			0
$715$	−4.68000	+	0.491729i	−0.175022	+	0.0183896i
$716$		0			0
$717$	−42.6077	−	42.6077i	−1.59122	−	1.59122i
$718$		0			0
$719$	−38.2483			−1.42642			−0.713211	−	0.700950i	$-0.752760\pi$
$719$	−38.2483			−1.42642			−0.713211	+	0.700950i	$0.752760\pi$
$720$		0			0
$721$	−7.90182	−	7.90182i	−0.294279	−	0.294279i
$722$		0			0
$723$	−17.0836	−	17.0836i	−0.635347	−	0.635347i
$724$		0			0
$725$		−	43.2543i		−	1.60642i
$726$		0			0
$727$	28.8883			1.07141			0.535704	−	0.844406i	$-0.320046\pi$
$727$	28.8883			1.07141			0.535704	+	0.844406i	$0.320046\pi$
$728$		0			0
$729$	41.3432			1.53123
$730$		0			0
$731$		−	26.6401i		−	0.985320i
$732$		0			0
$733$	21.1303	+	21.1303i	0.780465	+	0.780465i	0.979909	−	0.199444i	$-0.0639137\pi$
$733$	21.1303	+	21.1303i	0.780465	+	0.780465i	−0.199444	+	0.979909i	$0.563914\pi$
$734$		0			0
$735$	3.01277	+	3.01277i	0.111128	+	0.111128i
$736$		0			0
$737$	−2.67085			−0.0983821
$738$		0			0
$739$	−3.05518	−	3.05518i	−0.112387	−	0.112387i	0.648677	−	0.761064i	$-0.275323\pi$
$739$	−3.05518	−	3.05518i	−0.112387	−	0.112387i	−0.761064	+	0.648677i	$0.775323\pi$
$740$		0			0
$741$	42.2684	−	52.1935i	1.55277	−	1.91738i
$742$		0			0
$743$	34.0912	−	34.0912i	1.25069	−	1.25069i	0.295274	−	0.955413i	$-0.404589\pi$
$743$	34.0912	−	34.0912i	1.25069	−	1.25069i	0.955413	−	0.295274i	$-0.0954108\pi$
$744$		0			0
$745$			11.7754i			0.431419i
$746$		0			0
$747$	27.0670	−	27.0670i	0.990330	−	0.990330i
$748$		0			0
$749$	13.4400	−	13.4400i	0.491088	−	0.491088i
$750$		0			0
$751$	−11.2821			−0.411689			−0.205845	−	0.978585i	$-0.565994\pi$
$751$	−11.2821			−0.411689			−0.205845	+	0.978585i	$0.565994\pi$
$752$		0			0
$753$			21.9251i			0.798997i
$754$		0			0
$755$		−	1.66723i		−	0.0606767i
$756$		0			0
$757$	17.5897			0.639309			0.319655	−	0.947534i	$-0.396433\pi$
$757$	17.5897			0.639309			0.319655	+	0.947534i	$0.396433\pi$
$758$		0			0
$759$	23.6677	−	23.6677i	0.859084	−	0.859084i
$760$		0			0
$761$	−7.77685	+	7.77685i	−0.281911	+	0.281911i	−0.833871	−	0.551960i	$-0.813880\pi$
$761$	−7.77685	+	7.77685i	−0.281911	+	0.281911i	0.551960	+	0.833871i	$0.313880\pi$
$762$		0			0
$763$			22.7023i			0.821877i
$764$		0			0
$765$	8.26058	−	8.26058i	0.298662	−	0.298662i
$766$		0			0
$767$	28.9531	−	35.7517i	1.04544	−	1.29092i
$768$		0			0
$769$	0.120099	+	0.120099i	0.00433088	+	0.00433088i	0.709269	−	0.704938i	$-0.249025\pi$
$769$	0.120099	+	0.120099i	0.00433088	+	0.00433088i	−0.704938	+	0.709269i	$0.749025\pi$
$770$		0			0
$771$	−74.8782			−2.69667
$772$		0			0
$773$	18.5343	+	18.5343i	0.666632	+	0.666632i	0.956935	−	0.290303i	$-0.0937560\pi$
$773$	18.5343	+	18.5343i	0.666632	+	0.666632i	−0.290303	+	0.956935i	$0.593756\pi$
$774$		0			0
$775$	−5.34378	−	5.34378i	−0.191954	−	0.191954i
$776$		0			0
$777$			45.9378i			1.64801i
$778$		0			0
$779$	−73.2110			−2.62306
$780$		0			0
$781$	−15.5149			−0.555166
$782$		0			0
$783$		−	58.0495i		−	2.07452i
$784$		0			0
$785$	−3.55370	−	3.55370i	−0.126837	−	0.126837i
$786$		0			0
$787$	8.40540	+	8.40540i	0.299620	+	0.299620i	0.840865	−	0.541245i	$-0.182047\pi$
$787$	8.40540	+	8.40540i	0.299620	+	0.299620i	−0.541245	+	0.840865i	$0.682047\pi$
$788$		0			0
$789$	49.6257			1.76672
$790$		0			0
$791$	5.35022	+	5.35022i	0.190232	+	0.190232i
$792$		0			0
$793$	−2.82838	−	26.9189i	−0.100439	−	0.955917i
$794$		0			0
$795$	0.813414	−	0.813414i	0.0288488	−	0.0288488i
$796$		0			0
$797$		−	36.9393i		−	1.30846i	−0.756298	−	0.654228i	$-0.772994\pi$
$797$		−	36.9393i		−	1.30846i	0.756298	−	0.654228i	$-0.227006\pi$
$798$		0			0
$799$	−18.8513	+	18.8513i	−0.666912	+	0.666912i
$800$		0			0
$801$	2.37285	−	2.37285i	0.0838406	−	0.0838406i
$802$		0			0
$803$	11.1165			0.392292
$804$		0			0
$805$		−	7.95142i		−	0.280251i
$806$		0			0
$807$		−	12.8729i		−	0.453149i
$808$		0			0
$809$	−35.4633			−1.24682			−0.623412	−	0.781893i	$-0.714254\pi$
$809$	−35.4633			−1.24682			−0.623412	+	0.781893i	$0.714254\pi$
$810$		0			0
$811$	−19.6291	+	19.6291i	−0.689271	+	0.689271i	−0.962071	−	0.272800i	$-0.912050\pi$
$811$	−19.6291	+	19.6291i	−0.689271	+	0.689271i	0.272800	+	0.962071i	$0.412050\pi$
$812$		0			0
$813$	−52.8401	+	52.8401i	−1.85318	+	1.85318i
$814$		0			0
$815$			3.99623i			0.139982i
$816$		0			0
$817$	−29.0968	+	29.0968i	−1.01797	+	1.01797i
$818$		0			0
$819$	36.9856	−	45.6703i	1.29238	−	1.59585i
$820$		0			0
$821$	18.5343	+	18.5343i	0.646851	+	0.646851i	0.952231	−	0.305380i	$-0.0987834\pi$
$821$	18.5343	+	18.5343i	0.646851	+	0.646851i	−0.305380	+	0.952231i	$0.598783\pi$
$822$		0			0
$823$	16.2522			0.566517			0.283259	−	0.959044i	$-0.408584\pi$
$823$	16.2522			0.566517			0.283259	+	0.959044i	$0.408584\pi$
$824$		0			0
$825$	−23.4040	−	23.4040i	−0.814823	−	0.814823i
$826$		0			0
$827$	33.7224	+	33.7224i	1.17264	+	1.17264i	0.981577	+	0.191065i	$0.0611940\pi$
$827$	33.7224	+	33.7224i	1.17264	+	1.17264i	0.191065	+	0.981577i	$0.438806\pi$
$828$		0			0
$829$			15.6928i			0.545033i	0.962151	+	0.272516i	$0.0878559\pi$
$829$			15.6928i			0.545033i	−0.962151	+	0.272516i	$0.912144\pi$
$830$		0			0
$831$	−1.62683			−0.0564341
$832$		0			0
$833$	11.7472			0.407018
$834$		0			0
$835$			10.3923i			0.359641i
$836$		0			0
$837$	−7.17162	−	7.17162i	−0.247888	−	0.247888i
$838$		0			0
$839$	−19.0122	−	19.0122i	−0.656373	−	0.656373i	0.298147	−	0.954520i	$-0.403631\pi$
$839$	−19.0122	−	19.0122i	−0.656373	−	0.656373i	−0.954520	+	0.298147i	$0.903631\pi$
$840$		0			0
$841$	55.1187			1.90064
$842$		0			0
$843$	−34.0600	−	34.0600i	−1.17309	−	1.17309i
$844$		0			0
$845$	5.80896	+	3.77294i	0.199834	+	0.129793i
$846$		0			0
$847$	11.0629	−	11.0629i	0.380124	−	0.380124i
$848$		0			0
$849$			7.47885i			0.256673i
$850$		0			0
$851$	17.2801	−	17.2801i	0.592354	−	0.592354i
$852$		0			0
$853$	9.80896	−	9.80896i	0.335852	−	0.335852i	−0.518951	−	0.854804i	$-0.673677\pi$
$853$	9.80896	−	9.80896i	0.335852	−	0.335852i	0.854804	+	0.518951i	$0.173677\pi$
$854$		0			0
$855$	−18.0447			−0.617115
$856$		0			0
$857$		−	17.6568i		−	0.603143i	−0.953444	−	0.301572i	$-0.902489\pi$
$857$		−	17.6568i		−	0.603143i	0.953444	−	0.301572i	$-0.0975112\pi$
$858$		0			0
$859$		−	41.4755i		−	1.41513i	−0.706650	−	0.707564i	$-0.749794\pi$
$859$		−	41.4755i		−	1.41513i	0.706650	−	0.707564i	$-0.250206\pi$
$860$		0			0
$861$	−100.955			−3.44053
$862$		0			0
$863$	19.5107	−	19.5107i	0.664151	−	0.664151i	−0.292205	−	0.956356i	$-0.594389\pi$
$863$	19.5107	−	19.5107i	0.664151	−	0.664151i	0.956356	+	0.292205i	$0.0943890\pi$
$864$		0			0
$865$	−3.79877	+	3.79877i	−0.129162	+	0.129162i
$866$		0			0
$867$		−	2.05173i		−	0.0696804i
$868$		0			0
$869$	5.58972	−	5.58972i	0.189618	−	0.189618i
$870$		0			0
$871$	3.05518	+	2.47420i	0.103521	+	0.0838352i
$872$		0			0
$873$	9.13420	+	9.13420i	0.309146	+	0.309146i
$874$		0			0
$875$	−16.1990			−0.547625
$876$		0			0
$877$	−16.7949	−	16.7949i	−0.567122	−	0.567122i	0.364199	−	0.931321i	$-0.381343\pi$
$877$	−16.7949	−	16.7949i	−0.567122	−	0.567122i	−0.931321	+	0.364199i	$0.881343\pi$
$878$		0			0
$879$	9.18318	+	9.18318i	0.309741	+	0.309741i
$880$		0			0
$881$		−	24.3744i		−	0.821194i	−0.911817	−	0.410597i	$-0.865320\pi$
$881$		−	24.3744i		−	0.821194i	0.911817	−	0.410597i	$-0.134680\pi$
$882$		0			0
$883$	−19.7119			−0.663358			−0.331679	−	0.943392i	$-0.607615\pi$
$883$	−19.7119			−0.663358			−0.331679	+	0.943392i	$0.607615\pi$
$884$		0			0
$885$	−19.4788			−0.654774
$886$		0			0
$887$		−	36.9432i		−	1.24043i	−0.784432	−	0.620215i	$-0.787045\pi$
$887$		−	36.9432i		−	1.24043i	0.784432	−	0.620215i	$-0.212955\pi$
$888$		0			0
$889$	20.1060	+	20.1060i	0.674334	+	0.674334i
$890$		0			0
$891$	−4.34234	−	4.34234i	−0.145474	−	0.145474i
$892$		0			0
$893$	41.1794			1.37802
$894$		0			0
$895$	7.42671	+	7.42671i	0.248247	+	0.248247i
$896$		0			0
$897$	−48.9986	+	5.14830i	−1.63602	+	0.171897i
$898$		0			0
$899$	10.3923	−	10.3923i	0.346603	−	0.346603i
$900$		0			0
$901$		−	3.17162i		−	0.105662i
$902$		0			0
$903$	−40.1232	+	40.1232i	−1.33522	+	1.33522i
$904$		0			0
$905$	8.88772	−	8.88772i	0.295438	−	0.295438i
$906$		0			0
$907$	5.13133			0.170383			0.0851915	−	0.996365i	$-0.472850\pi$
$907$	5.13133			0.170383			0.0851915	+	0.996365i	$0.472850\pi$
$908$		0			0
$909$			7.85030i			0.260378i
$910$		0			0
$911$		−	42.6151i		−	1.41190i	−0.708261	−	0.705950i	$-0.750520\pi$
$911$		−	42.6151i		−	1.41190i	0.708261	−	0.705950i	$-0.249480\pi$
$912$		0			0
$913$	18.0000			0.595713
$914$		0			0
$915$	−8.10370	+	8.10370i	−0.267900	+	0.267900i
$916$		0			0
$917$	28.5717	−	28.5717i	0.943521	−	0.943521i
$918$		0			0
$919$			32.1155i			1.05939i	0.848187	+	0.529697i	$0.177694\pi$
$919$			32.1155i			1.05939i	−0.848187	+	0.529697i	$0.822306\pi$
$920$		0			0
$921$	29.2825	−	29.2825i	0.964891	−	0.964891i
$922$		0			0
$923$	17.7474	+	14.3726i	0.584163	+	0.473079i
$924$		0			0
$925$	−17.0876	−	17.0876i	−0.561835	−	0.561835i
$926$		0			0
$927$	18.6032			0.611010
$928$		0			0
$929$	23.7020	+	23.7020i	0.777637	+	0.777637i	0.979429	−	0.201791i	$-0.0646762\pi$
$929$	23.7020	+	23.7020i	0.777637	+	0.777637i	−0.201791	+	0.979429i	$0.564676\pi$
$930$		0			0
$931$	−12.8305	−	12.8305i	−0.420504	−	0.420504i
$932$		0			0
$933$			2.07485i			0.0679275i
$934$		0			0
$935$	5.49342			0.179654
$936$		0			0
$937$	40.2402			1.31459			0.657295	−	0.753633i	$-0.271701\pi$
$937$	40.2402			1.31459			0.657295	+	0.753633i	$0.271701\pi$
$938$		0			0
$939$			72.2680i			2.35838i
$940$		0			0
$941$	30.9057	+	30.9057i	1.00750	+	1.00750i	0.999972	+	0.00752655i	$0.00239580\pi$
$941$	30.9057	+	30.9057i	1.00750	+	1.00750i	0.00752655	+	0.999972i	$0.497604\pi$
$942$		0			0
$943$	37.9755	+	37.9755i	1.23665	+	1.23665i
$944$		0			0
$945$	−10.5523			−0.343266
$946$		0			0
$947$	−1.73205	−	1.73205i	−0.0562841	−	0.0562841i	0.678405	−	0.734689i	$-0.262672\pi$
$947$	−1.73205	−	1.73205i	−0.0562841	−	0.0562841i	−0.734689	+	0.678405i	$0.762672\pi$
$948$		0			0
$949$	−12.7161	−	10.2980i	−0.412782	−	0.334287i
$950$		0			0
$951$	14.7102	−	14.7102i	0.477012	−	0.477012i
$952$		0			0
$953$			35.4915i			1.14968i	0.818264	+	0.574842i	$0.194936\pi$
$953$			35.4915i			1.14968i	−0.818264	+	0.574842i	$0.805064\pi$
$954$		0			0
$955$	5.71230	−	5.71230i	0.184846	−	0.184846i
$956$		0			0
$957$	45.5149	−	45.5149i	1.47129	−	1.47129i
$958$		0			0
$959$	−57.1957			−1.84694
$960$		0			0
$961$			28.4322i			0.917168i
$962$		0			0
$963$			31.6418i			1.01964i
$964$		0			0
$965$	−5.02192			−0.161661
$966$		0			0
$967$	−11.7511	+	11.7511i	−0.377889	+	0.377889i	−0.870340	−	0.492451i	$-0.836101\pi$
$967$	−11.7511	+	11.7511i	−0.377889	+	0.377889i	0.492451	+	0.870340i	$0.336101\pi$
$968$		0			0
$969$	−55.4400	+	55.4400i	−1.78099	+	1.78099i
$970$		0			0
$971$			43.2364i			1.38752i	0.720205	+	0.693762i	$0.244048\pi$
$971$			43.2364i			1.38752i	−0.720205	+	0.693762i	$0.755952\pi$
$972$		0			0
$973$	−2.08659	+	2.08659i	−0.0668929	+	0.0668929i
$974$		0			0
$975$	5.09093	+	48.4526i	0.163040	+	1.55172i
$976$		0			0
$977$	−7.83620	−	7.83620i	−0.250702	−	0.250702i	0.570556	−	0.821259i	$-0.306728\pi$
$977$	−7.83620	−	7.83620i	−0.250702	−	0.250702i	−0.821259	+	0.570556i	$0.806728\pi$
$978$		0			0
$979$	1.57798			0.0504326
$980$		0			0
$981$	−26.7239	−	26.7239i	−0.853229	−	0.853229i
$982$		0			0
$983$	33.4967	+	33.4967i	1.06838	+	1.06838i	0.997484	+	0.0708955i	$0.0225857\pi$
$983$	33.4967	+	33.4967i	1.06838	+	1.06838i	0.0708955	+	0.997484i	$0.477414\pi$
$984$		0			0
$985$			2.67380i			0.0851943i
$986$		0			0
$987$	56.7847			1.80748
$988$		0			0
$989$	30.1857			0.959850
$990$		0			0
$991$			43.8714i			1.39362i	0.717256	+	0.696810i	$0.245398\pi$
$991$			43.8714i			1.39362i	−0.717256	+	0.696810i	$0.754602\pi$
$992$		0			0
$993$	−11.4555	−	11.4555i	−0.363530	−	0.363530i
$994$		0			0
$995$	−1.79687	−	1.79687i	−0.0569647	−	0.0569647i
$996$		0			0
$997$	−29.1716			−0.923875			−0.461937	−	0.886913i	$-0.652845\pi$
$997$	−29.1716			−0.923875			−0.461937	+	0.886913i	$0.652845\pi$
$998$		0			0
$999$	−22.9324	−	22.9324i	−0.725548	−	0.725548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.k.b.47.6	yes	12
3.2	odd	2		1872.2.bf.o.1711.4		12
4.3	odd	2	inner	208.2.k.b.47.1	yes	12
8.3	odd	2		832.2.k.j.255.6		12
8.5	even	2		832.2.k.j.255.1		12
12.11	even	2		1872.2.bf.o.1711.3		12
13.5	odd	4	inner	208.2.k.b.31.6	yes	12
39.5	even	4		1872.2.bf.o.1279.3		12
52.31	even	4	inner	208.2.k.b.31.1	✓	12
104.5	odd	4		832.2.k.j.447.1		12
104.83	even	4		832.2.k.j.447.6		12
156.83	odd	4		1872.2.bf.o.1279.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.k.b.31.1	✓	12	52.31	even	4	inner
208.2.k.b.31.6	yes	12	13.5	odd	4	inner
208.2.k.b.47.1	yes	12	4.3	odd	2	inner
208.2.k.b.47.6	yes	12	1.1	even	1	trivial
832.2.k.j.255.1		12	8.5	even	2
832.2.k.j.255.6		12	8.3	odd	2
832.2.k.j.447.1		12	104.5	odd	4
832.2.k.j.447.6		12	104.83	even	4
1872.2.bf.o.1279.3		12	39.5	even	4
1872.2.bf.o.1279.4		12	156.83	odd	4
1872.2.bf.o.1711.3		12	12.11	even	2
1872.2.bf.o.1711.4		12	3.2	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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.86514i q^{3} +(-0.376763 - 0.376763i) q^{5} +(2.21257 + 2.21257i) q^{7} -5.20905 q^{9} +(-1.73205 - 1.73205i) q^{11} +(0.376763 + 3.58581i) q^{13} +(1.07948 - 1.07948i) q^{15} -4.20905i q^{17} +(-4.59719 + 4.59719i) q^{19} +(-6.33934 + 6.33934i) q^{21} +4.76925 q^{23} -4.71610i q^{25} -6.32925i q^{27} +9.17162 q^{29} +(1.13309 - 1.13309i) q^{31} +(4.96257 - 4.96257i) q^{33} -1.66723i q^{35} +(3.62324 - 3.62324i) q^{37} +(-10.2739 + 1.07948i) q^{39} +(7.96257 + 7.96257i) q^{41} +6.32925 q^{43} +(1.96257 + 1.96257i) q^{45} +(-4.47876 - 4.47876i) q^{47} +2.79095i q^{49} +12.0595 q^{51} +0.753525 q^{53} +1.30514i q^{55} +(-13.1716 - 13.1716i) q^{57} +(-9.02234 - 9.02234i) q^{59} -7.50705 q^{61} +(-11.5254 - 11.5254i) q^{63} +(1.20905 - 1.49295i) q^{65} +(0.771008 - 0.771008i) q^{67} +13.6646i q^{69} +(4.47876 - 4.47876i) q^{71} +(-3.20905 + 3.20905i) q^{73} +13.5123 q^{75} -7.66457i q^{77} +3.22723i q^{79} +2.50705 q^{81} +(-5.19615 + 5.19615i) q^{83} +(-1.58581 + 1.58581i) q^{85} +26.2780i q^{87} +(-0.455525 + 0.455525i) q^{89} +(-7.10025 + 8.76748i) q^{91} +(3.24647 + 3.24647i) q^{93} +3.46410 q^{95} +(-1.75353 - 1.75353i) q^{97} +(9.02234 + 9.02234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 20 q^{9} - 4 q^{13} - 8 q^{21} + 8 q^{29} + 52 q^{37} + 36 q^{41} - 36 q^{45} - 8 q^{53} - 56 q^{57} - 56 q^{61} - 28 q^{65} + 4 q^{73} - 4 q^{81} + 32 q^{85} + 20 q^{89} + 56 q^{93} - 4 q^{97}+O(q^{100}) \) 12 * q + 4 * q^5 - 20 * q^9 - 4 * q^13 - 8 * q^21 + 8 * q^29 + 52 * q^37 + 36 * q^41 - 36 * q^45 - 8 * q^53 - 56 * q^57 - 56 * q^61 - 28 * q^65 + 4 * q^73 - 4 * q^81 + 32 * q^85 + 20 * q^89 + 56 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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