LMFDB - Embedded newform 936.2.be.a.685.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(685,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("936.685");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			685.8
Character	$\chi$	$=$	936.685
Dual form			936.2.be.a.757.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.628723 - 1.26677i) q^{2} +(-1.20941 - 1.59290i) q^{4} +2.59989i q^{5} +(-0.300588 - 0.520633i) q^{7} +(-2.77822 + 0.530559i) q^{8} +(3.29346 + 1.63461i) q^{10} +(2.40956 + 1.39116i) q^{11} +(3.60516 + 0.0531995i) q^{13} +(-0.848509 + 0.0534414i) q^{14} +(-1.07463 + 3.85294i) q^{16} +(1.29402 + 2.24132i) q^{17} +(-4.38088 + 2.52930i) q^{19} +(4.14135 - 3.14434i) q^{20} +(3.27722 - 2.17770i) q^{22} +(-2.94353 + 5.09835i) q^{23} -1.75942 q^{25} +(2.33404 - 4.53346i) q^{26} +(-0.465779 + 1.10847i) q^{28} +(1.54071 + 0.889530i) q^{29} +5.09421 q^{31} +(4.20514 + 3.78375i) q^{32} +(3.65282 - 0.230064i) q^{34} +(1.35359 - 0.781495i) q^{35} +(8.82719 + 5.09638i) q^{37} +(0.449684 + 7.13981i) q^{38} +(-1.37940 - 7.22306i) q^{40} +(5.26242 - 9.11477i) q^{41} +(8.44267 - 4.87438i) q^{43} +(-0.698182 - 5.52066i) q^{44} +(4.60777 + 6.93423i) q^{46} -2.13951 q^{47} +(3.31929 - 5.74919i) q^{49} +(-1.10619 + 2.22879i) q^{50} +(-4.27539 - 5.80698i) q^{52} +6.01748i q^{53} +(-3.61686 + 6.26458i) q^{55} +(1.11133 + 1.28695i) q^{56} +(2.09551 - 1.39246i) q^{58} +(-9.44349 + 5.45220i) q^{59} +(-1.84865 + 1.06732i) q^{61} +(3.20285 - 6.45319i) q^{62} +(7.43701 - 2.94802i) q^{64} +(-0.138313 + 9.37301i) q^{65} +(-3.39076 - 1.95766i) q^{67} +(2.00517 - 4.77193i) q^{68} +(-0.138942 - 2.20603i) q^{70} +(-0.230832 - 0.399814i) q^{71} -14.8806 q^{73} +(12.0058 - 7.97781i) q^{74} +(9.32722 + 3.91932i) q^{76} -1.67266i q^{77} -7.83968 q^{79} +(-10.0172 - 2.79393i) q^{80} +(-8.23772 - 12.3969i) q^{82} +0.930501i q^{83} +(-5.82717 + 3.36432i) q^{85} +(-0.866614 - 13.7596i) q^{86} +(-7.43237 - 2.58653i) q^{88} +(-1.17791 + 2.04019i) q^{89} +(-1.05597 - 1.89296i) q^{91} +(11.6811 - 1.47727i) q^{92} +(-1.34516 + 2.71027i) q^{94} +(-6.57591 - 11.3898i) q^{95} +(5.91151 + 10.2390i) q^{97} +(-5.19598 - 7.81943i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) $ 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.628723	−	1.26677i	0.444574	−	0.895742i
$2$	0.628723	−	1.26677i	0.444574	−	0.895742i
$3$		0			0
$3$		0			0
$4$	−1.20941	−	1.59290i	−0.604707	−	0.796448i
$5$			2.59989i			1.16271i	0.813651	+	0.581353i	$0.197476\pi$
$5$			2.59989i			1.16271i	−0.813651	+	0.581353i	$0.802524\pi$
$6$		0			0
$7$	−0.300588	−	0.520633i	−0.113611	−	0.196781i	0.803612	−	0.595153i	$-0.202909\pi$
$7$	−0.300588	−	0.520633i	−0.113611	−	0.196781i	−0.917224	+	0.398372i	$0.869575\pi$
$8$	−2.77822	+	0.530559i	−0.982249	+	0.187581i
$9$		0			0
$10$	3.29346	+	1.63461i	1.04148	+	0.516909i
$11$	2.40956	+	1.39116i	0.726509	+	0.419450i	0.817144	−	0.576434i	$-0.195556\pi$
$11$	2.40956	+	1.39116i	0.726509	+	0.419450i	−0.0906348	+	0.995884i	$0.528890\pi$
$12$		0			0
$13$	3.60516	+	0.0531995i	0.999891	+	0.0147549i
$13$	3.60516	+	0.0531995i	0.999891	+	0.0147549i
$14$	−0.848509	+	0.0534414i	−0.226774	+	0.0142828i
$15$		0			0
$16$	−1.07463	+	3.85294i	−0.268659	+	0.963235i
$17$	1.29402	+	2.24132i	0.313847	+	0.543599i	0.979192	−	0.202937i	$-0.0650487\pi$
$17$	1.29402	+	2.24132i	0.313847	+	0.543599i	−0.665345	+	0.746536i	$0.731715\pi$
$18$		0			0
$19$	−4.38088	+	2.52930i	−1.00504	+	0.580262i	−0.909737	−	0.415186i	$-0.863717\pi$
$19$	−4.38088	+	2.52930i	−1.00504	+	0.580262i	−0.0953071	+	0.995448i	$0.530383\pi$
$20$	4.14135	−	3.14434i	0.926035	−	0.703096i
$21$		0			0
$22$	3.27722	−	2.17770i	0.698706	−	0.464288i
$23$	−2.94353	+	5.09835i	−0.613769	+	1.06308i	0.376830	+	0.926282i	$0.377014\pi$
$23$	−2.94353	+	5.09835i	−0.613769	+	1.06308i	−0.990599	+	0.136797i	$0.956319\pi$
$24$		0			0
$25$	−1.75942			−0.351885
$26$	2.33404	−	4.53346i	0.457743	−	0.889085i
$27$		0			0
$28$	−0.465779	+	1.10847i	−0.0880240	+	0.209480i
$29$	1.54071	+	0.889530i	0.286103	+	0.165182i	0.636183	−	0.771538i	$-0.280512\pi$
$29$	1.54071	+	0.889530i	0.286103	+	0.165182i	−0.350080	+	0.936720i	$0.613846\pi$
$30$		0			0
$31$	5.09421			0.914947			0.457473	−	0.889223i	$-0.348755\pi$
$31$	5.09421			0.914947			0.457473	+	0.889223i	$0.348755\pi$
$32$	4.20514	+	3.78375i	0.743372	+	0.668879i
$33$		0			0
$34$	3.65282	−	0.230064i	0.626453	−	0.0394557i
$35$	1.35359	−	0.781495i	0.228798	−	0.132097i
$36$		0			0
$37$	8.82719	+	5.09638i	1.45118	+	0.837840i	0.998549	−	0.0538570i	$-0.0171515\pi$
$37$	8.82719	+	5.09638i	1.45118	+	0.837840i	0.452633	+	0.891697i	$0.350485\pi$
$38$	0.449684	+	7.13981i	0.0729484	+	1.15823i
$39$		0			0
$40$	−1.37940	−	7.22306i	−0.218102	−	1.14207i
$41$	5.26242	−	9.11477i	0.821851	−	1.42349i	−0.0824509	−	0.996595i	$-0.526275\pi$
$41$	5.26242	−	9.11477i	0.821851	−	1.42349i	0.904302	−	0.426893i	$-0.140392\pi$
$42$		0			0
$43$	8.44267	−	4.87438i	1.28749	−	0.743335i	0.309288	−	0.950968i	$-0.399909\pi$
$43$	8.44267	−	4.87438i	1.28749	−	0.743335i	0.978207	+	0.207633i	$0.0665759\pi$
$44$	−0.698182	−	5.52066i	−0.105255	−	0.832271i
$45$		0			0
$46$	4.60777	+	6.93423i	0.679379	+	1.02240i
$47$	−2.13951			−0.312080			−0.156040	−	0.987751i	$-0.549873\pi$
$47$	−2.13951			−0.312080			−0.156040	+	0.987751i	$0.549873\pi$
$48$		0			0
$49$	3.31929	−	5.74919i	0.474185	−	0.821312i
$50$	−1.10619	+	2.22879i	−0.156439	+	0.315198i
$51$		0			0
$52$	−4.27539	−	5.80698i	−0.592890	−	0.805284i
$53$			6.01748i			0.826565i	0.910603	+	0.413282i	$0.135618\pi$
$53$			6.01748i			0.826565i	−0.910603	+	0.413282i	$0.864382\pi$
$54$		0			0
$55$	−3.61686	+	6.26458i	−0.487697	+	0.844716i
$56$	1.11133	+	1.28695i	0.148507	+	0.171976i
$57$		0			0
$58$	2.09551	−	1.39246i	0.275154	−	0.182839i
$59$	−9.44349	+	5.45220i	−1.22944	+	0.709816i	−0.966912	−	0.255109i	$-0.917889\pi$
$59$	−9.44349	+	5.45220i	−1.22944	+	0.709816i	−0.262526	+	0.964925i	$0.584555\pi$
$60$		0			0
$61$	−1.84865	+	1.06732i	−0.236696	+	0.136656i	−0.613657	−	0.789573i	$-0.710302\pi$
$61$	−1.84865	+	1.06732i	−0.236696	+	0.136656i	0.376961	+	0.926229i	$0.376969\pi$
$62$	3.20285	−	6.45319i	0.406762	−	0.819556i
$63$		0			0
$64$	7.43701	−	2.94802i	0.929627	−	0.368503i
$65$	−0.138313	+	9.37301i	−0.0171556	+	1.16258i
$66$		0			0
$67$	−3.39076	−	1.95766i	−0.414247	−	0.239166i	0.278366	−	0.960475i	$-0.410207\pi$
$67$	−3.39076	−	1.95766i	−0.414247	−	0.239166i	−0.692613	+	0.721309i	$0.743541\pi$
$68$	2.00517	−	4.77193i	0.243163	−	0.578681i
$69$		0			0
$70$	−0.138942	−	2.20603i	−0.0166067	−	0.263671i
$71$	−0.230832	−	0.399814i	−0.0273948	−	0.0474491i	0.852003	−	0.523537i	$-0.175388\pi$
$71$	−0.230832	−	0.399814i	−0.0273948	−	0.0474491i	−0.879398	+	0.476088i	$0.842054\pi$
$72$		0			0
$73$	−14.8806			−1.74165			−0.870824	−	0.491595i	$-0.836414\pi$
$73$	−14.8806			−1.74165			−0.870824	+	0.491595i	$0.836414\pi$
$74$	12.0058	−	7.97781i	1.39565	−	0.927402i
$75$		0			0
$76$	9.32722	+	3.91932i	1.06991	+	0.449576i
$77$		−	1.67266i		−	0.190617i
$78$		0			0
$79$	−7.83968			−0.882033			−0.441017	−	0.897499i	$-0.645382\pi$
$79$	−7.83968			−0.882033			−0.441017	+	0.897499i	$0.645382\pi$
$80$	−10.0172	−	2.79393i	−1.11996	−	0.312371i
$81$		0			0
$82$	−8.23772	−	12.3969i	−0.909704	−	1.36901i
$83$			0.930501i			0.102136i	0.998695	+	0.0510679i	$0.0162625\pi$
$83$			0.930501i			0.102136i	−0.998695	+	0.0510679i	$0.983738\pi$
$84$		0			0
$85$	−5.82717	+	3.36432i	−0.632046	+	0.364912i
$86$	−0.866614	−	13.7596i	−0.0934494	−	1.48373i
$87$		0			0
$88$	−7.43237	−	2.58653i	−0.792294	−	0.275725i
$89$	−1.17791	+	2.04019i	−0.124858	+	0.216260i	−0.921677	−	0.387957i	$-0.873181\pi$
$89$	−1.17791	+	2.04019i	−0.124858	+	0.216260i	0.796820	+	0.604217i	$0.206514\pi$
$90$		0			0
$91$	−1.05597	−	1.89296i	−0.110696	−	0.198436i
$92$	11.6811	−	1.47727i	1.21784	−	0.154016i
$93$		0			0
$94$	−1.34516	+	2.71027i	−0.138743	+	0.279543i
$95$	−6.57591	−	11.3898i	−0.674674	−	1.16857i
$96$		0			0
$97$	5.91151	+	10.2390i	0.600223	+	1.03962i	0.992787	+	0.119892i	$0.0382549\pi$
$97$	5.91151	+	10.2390i	0.600223	+	1.03962i	−0.392564	+	0.919725i	$0.628412\pi$
$98$	−5.19598	−	7.81943i	−0.524873	−	0.789882i
$99$		0			0
$100$	2.12787	+	2.80258i	0.212787	+	0.280258i
$101$	11.2176	+	6.47646i	1.11619	+	0.644432i	0.940425	−	0.340001i	$-0.110427\pi$
$101$	11.2176	+	6.47646i	1.11619	+	0.644432i	0.175763	+	0.984432i	$0.443761\pi$
$102$		0			0
$103$	6.61141			0.651441			0.325721	−	0.945466i	$-0.394393\pi$
$103$	6.61141			0.651441			0.325721	+	0.945466i	$0.394393\pi$
$104$	−10.0442	+	1.76495i	−0.984910	+	0.173068i
$105$		0			0
$106$	7.62277	+	3.78333i	0.740389	+	0.367470i
$107$	−8.87612	−	5.12463i	−0.858087	−	0.495417i	0.00528438	−	0.999986i	$-0.498318\pi$
$107$	−8.87612	−	5.12463i	−0.858087	−	0.495417i	−0.863371	+	0.504569i	$0.831651\pi$
$108$		0			0
$109$			10.8192i			1.03630i	0.855291	+	0.518148i	$0.173378\pi$
$109$			10.8192i			1.03630i	−0.855291	+	0.518148i	$0.826622\pi$
$110$	5.66178	+	8.52042i	0.539830	+	0.812390i
$111$		0			0
$112$	2.32899	−	0.598656i	0.220069	−	0.0565677i
$113$	−4.75708	−	8.23951i	−0.447509	−	0.775108i	0.550714	−	0.834694i	$-0.314355\pi$
$113$	−4.75708	−	8.23951i	−0.447509	−	0.775108i	−0.998223	+	0.0595859i	$0.981022\pi$
$114$		0			0
$115$	−13.2551	−	7.65286i	−1.23605	−	0.713633i
$116$	−0.446429	−	3.53000i	−0.0414499	−	0.327752i
$117$		0			0
$118$	0.969346	+	15.3907i	0.0892355	+	1.41683i
$119$	0.777936	−	1.34742i	0.0713133	−	0.123518i
$120$		0			0
$121$	−1.62936	−	2.82213i	−0.148123	−	0.256557i
$122$	0.189758	+	3.01287i	0.0171799	+	0.272772i
$123$		0			0
$124$	−6.16101	−	8.11454i	−0.553275	−	0.728707i
$125$			8.42514i			0.753567i
$126$		0			0
$127$	9.21128	−	15.9544i	0.817369	−	1.41572i	−0.0902451	−	0.995920i	$-0.528765\pi$
$127$	9.21128	−	15.9544i	0.817369	−	1.41572i	0.907614	−	0.419805i	$-0.137902\pi$
$128$	0.941358	−	11.2745i	0.0832051	−	0.996532i
$129$		0			0
$130$	11.7865	+	6.06824i	1.03374	+	0.532220i
$131$		−	0.795820i		−	0.0695311i	−0.999395	−	0.0347655i	$-0.988932\pi$
$131$		−	0.795820i		−	0.0695311i	0.999395	−	0.0347655i	$-0.0110684\pi$
$132$		0			0
$133$	2.63368	+	1.52056i	0.228369	+	0.131849i
$134$	−4.61175	+	3.06449i	−0.398394	+	0.264732i
$135$		0			0
$136$	−4.78424	−	5.54031i	−0.410245	−	0.475078i
$137$	−1.77845	−	3.08037i	−0.151943	−	0.263174i	0.779998	−	0.625781i	$-0.215220\pi$
$137$	−1.77845	−	3.08037i	−0.151943	−	0.263174i	−0.931942	+	0.362608i	$0.881886\pi$
$138$		0			0
$139$	−1.86181	+	1.07491i	−0.157916	+	0.0911731i	−0.576876	−	0.816832i	$-0.695728\pi$
$139$	−1.86181	+	1.07491i	−0.157916	+	0.0911731i	0.418959	+	0.908005i	$0.362395\pi$
$140$	−2.88189	−	1.21097i	−0.243564	−	0.102346i
$141$		0			0
$142$	−0.651602	+	0.0410396i	−0.0546812	+	0.00344397i
$143$	8.61283	+	5.14353i	0.720241	+	0.430124i
$144$		0			0
$145$	−2.31268	+	4.00568i	−0.192058	+	0.332653i
$146$	−9.35581	+	18.8504i	−0.774292	+	1.56007i
$147$		0			0
$148$	−2.55773	−	20.2244i	−0.210244	−	1.66244i
$149$	−2.87752	+	1.66134i	−0.235736	+	0.136102i	−0.613215	−	0.789916i	$-0.710124\pi$
$149$	−2.87752	+	1.66134i	−0.235736	+	0.136102i	0.377480	+	0.926018i	$0.376791\pi$
$150$		0			0
$151$	−6.66412			−0.542318			−0.271159	−	0.962535i	$-0.587407\pi$
$151$	−6.66412			−0.542318			−0.271159	+	0.962535i	$0.587407\pi$
$152$	10.8291	−	9.35128i	0.878357	−	0.758489i
$153$		0			0
$154$	−2.11888	−	1.05164i	−0.170744	−	0.0847436i
$155$			13.2444i			1.06381i
$156$		0			0
$157$		−	1.24154i		−	0.0990854i	−0.998772	−	0.0495427i	$-0.984224\pi$
$157$		−	1.24154i		−	0.0990854i	0.998772	−	0.0495427i	$-0.0157764\pi$
$158$	−4.92899	+	9.93108i	−0.392129	+	0.790074i
$159$		0			0
$160$	−9.83733	+	10.9329i	−0.777709	+	0.864322i
$161$	3.53916			0.278925
$162$		0			0
$163$	−9.43363	+	5.44651i	−0.738899	+	0.426604i	−0.821669	−	0.569965i	$-0.806957\pi$
$163$	−9.43363	+	5.44651i	−0.738899	+	0.426604i	0.0827698	+	0.996569i	$0.473623\pi$
$164$	−20.8833	+	2.64105i	−1.63071	+	0.206232i
$165$		0			0
$166$	1.17873	+	0.585028i	0.0914873	+	0.0454070i
$167$	6.68150	−	11.5727i	0.517030	−	0.895522i	−0.482775	−	0.875745i	$-0.660371\pi$
$167$	6.68150	−	11.5727i	0.517030	−	0.895522i	0.999804	−	0.0197773i	$-0.00629571\pi$
$168$		0			0
$169$	12.9943	+	0.383585i	0.999565	+	0.0295065i
$170$	0.598142	+	9.49692i	0.0458754	+	0.728380i
$171$		0			0
$172$	−17.9751	−	7.55315i	−1.37059	−	0.575922i
$173$	−5.66761	+	3.27220i	−0.430901	+	0.248781i	−0.699730	−	0.714407i	$-0.746696\pi$
$173$	−5.66761	+	3.27220i	−0.430901	+	0.248781i	0.268830	+	0.963188i	$0.413363\pi$
$174$		0			0
$175$	0.528861	+	0.916015i	0.0399782	+	0.0692442i
$176$	−7.94945	+	7.78890i	−0.599212	+	0.587110i
$177$		0			0
$178$	1.84388	+	2.77485i	0.138205	+	0.207984i
$179$	−13.5832	−	7.84225i	−1.01525	−	0.586157i	−0.102528	−	0.994730i	$-0.532693\pi$
$179$	−13.5832	−	7.84225i	−1.01525	−	0.586157i	−0.912726	+	0.408573i	$0.866027\pi$
$180$		0			0
$181$			4.65816i			0.346238i	0.984901	+	0.173119i	$0.0553846\pi$
$181$			4.65816i			0.346238i	−0.984901	+	0.173119i	$0.944615\pi$
$182$	−3.06185	+	0.147525i	−0.226960	+	0.0109352i
$183$		0			0
$184$	5.47281	−	15.7261i	0.403461	−	1.15934i
$185$	−13.2500	+	22.9497i	−0.974162	+	1.68730i
$186$		0			0
$187$			7.20077i			0.526573i
$188$	2.58755	+	3.40802i	0.188717	+	0.248555i
$189$		0			0
$190$	−18.5627	+	1.16913i	−1.34668	+	0.0848176i
$191$	−4.34236	−	7.52119i	−0.314202	−	0.544214i	0.665066	−	0.746785i	$-0.268404\pi$
$191$	−4.34236	−	7.52119i	−0.314202	−	0.544214i	−0.979268	+	0.202571i	$0.935070\pi$
$192$		0			0
$193$	0.788692	−	1.36605i	0.0567713	−	0.0983308i	−0.836243	−	0.548359i	$-0.815253\pi$
$193$	0.788692	−	1.36605i	0.0567713	−	0.0983308i	0.893014	+	0.450028i	$0.148586\pi$
$194$	16.6872	−	1.05101i	1.19807	−	0.0754578i
$195$		0			0
$196$	−13.1723	+	1.66586i	−0.940875	+	0.118990i
$197$	−22.1460	−	12.7860i	−1.57784	−	0.910964i	−0.995161	−	0.0982592i	$-0.968673\pi$
$197$	−22.1460	−	12.7860i	−1.57784	−	0.910964i	−0.582675	−	0.812705i	$-0.697994\pi$
$198$		0			0
$199$	10.3516	+	17.9295i	0.733807	+	1.27099i	0.955245	+	0.295816i	$0.0955915\pi$
$199$	10.3516	+	17.9295i	0.733807	+	1.27099i	−0.221438	+	0.975174i	$0.571075\pi$
$200$	4.88807	−	0.933479i	0.345639	−	0.0660069i
$201$		0			0
$202$	15.2569	−	10.1382i	1.07347	−	0.713319i
$203$		−	1.06953i		−	0.0750661i
$204$		0			0
$205$	23.6974	+	13.6817i	1.65510	+	0.955571i
$206$	4.15675	−	8.37513i	0.289614	−	0.583523i
$207$		0			0
$208$	−4.07920	+	13.8333i	−0.282842	+	0.959167i
$209$	−14.0747			−0.973564
$210$		0			0
$211$	−18.3083	−	10.5703i	−1.26040	−	0.727691i	−0.287246	−	0.957857i	$-0.592740\pi$
$211$	−18.3083	−	10.5703i	−1.26040	−	0.727691i	−0.973151	+	0.230166i	$0.926073\pi$
$212$	9.58522	−	7.27763i	0.658316	−	0.499830i
$213$		0			0
$214$	−12.0724	+	8.02203i	−0.825249	+	0.548375i
$215$	12.6728	+	21.9500i	0.864281	+	1.49698i
$216$		0			0
$217$	−1.53126	−	2.65221i	−0.103948	−	0.180044i
$218$	13.7055	+	6.80231i	0.928254	+	0.460711i
$219$		0			0
$220$	14.3531	−	1.81520i	0.967686	−	0.122380i
$221$	4.54593	+	8.14914i	0.305792	+	0.548171i
$222$		0			0
$223$	4.03692	−	6.99214i	0.270332	−	0.468229i	−0.698615	−	0.715498i	$-0.746200\pi$
$223$	4.03692	−	6.99214i	0.270332	−	0.468229i	0.968947	+	0.247269i	$0.0795332\pi$
$224$	0.705931	−	3.32669i	0.0471670	−	0.222274i
$225$		0			0
$226$	−13.4285	+	0.845760i	−0.893248	+	0.0562591i
$227$	19.8519	−	11.4615i	1.31761	−	0.760725i	0.334270	−	0.942477i	$-0.391510\pi$
$227$	19.8519	−	11.4615i	1.31761	−	0.760725i	0.983344	+	0.181752i	$0.0581768\pi$
$228$		0			0
$229$			0.594709i			0.0392995i	0.999807	+	0.0196497i	$0.00625511\pi$
$229$			0.594709i			0.0392995i	−0.999807	+	0.0196497i	$0.993745\pi$
$230$	−18.0282	+	11.9797i	−1.18875	+	0.789918i
$231$		0			0
$232$	−4.75238	−	1.65387i	−0.312009	−	0.108582i
$233$	0.0945847			0.00619645			0.00309823	−	0.999995i	$-0.499014\pi$
$233$	0.0945847			0.00619645			0.00309823	+	0.999995i	$0.499014\pi$
$234$		0			0
$235$		−	5.56249i		−	0.362857i
$236$	20.1059	+	8.44853i	1.30878	+	0.549952i
$237$		0			0
$238$	−1.21777	−	1.83262i	−0.0789364	−	0.118791i
$239$	15.3694			0.994166			0.497083	−	0.867703i	$-0.334404\pi$
$239$	15.3694			0.994166			0.497083	+	0.867703i	$0.334404\pi$
$240$		0			0
$241$	5.02102	+	8.69665i	0.323432	+	0.560201i	0.981194	−	0.193025i	$-0.0618300\pi$
$241$	5.02102	+	8.69665i	0.323432	+	0.560201i	−0.657762	+	0.753226i	$0.728497\pi$
$242$	−4.59940	+	0.289683i	−0.295661	+	0.0186215i
$243$		0			0
$244$	3.93591	+	1.65388i	0.251971	+	0.105879i
$245$	14.9472	+	8.62980i	0.954945	+	0.551338i
$246$		0			0
$247$	−15.9283	+	8.88548i	−1.01350	+	0.565370i
$248$	−14.1528	+	2.70278i	−0.898705	+	0.171627i
$249$		0			0
$250$	10.6727	+	5.29708i	0.675002	+	0.335017i
$251$	14.8114	−	8.55135i	0.934886	−	0.539757i	0.0465324	−	0.998917i	$-0.485183\pi$
$251$	14.8114	−	8.55135i	0.934886	−	0.539757i	0.888353	+	0.459160i	$0.151850\pi$
$252$		0			0
$253$	−14.1852	+	8.18984i	−0.891818	+	0.514891i
$254$	−14.4192	−	21.6995i	−0.904743	−	1.36155i
$255$		0			0
$256$	−13.6903	−	8.28101i	−0.855645	−	0.517563i
$257$	10.3500	−	17.9267i	0.645616	−	1.11824i	−0.338543	−	0.940951i	$-0.609934\pi$
$257$	10.3500	−	17.9267i	0.645616	−	1.11824i	0.984159	−	0.177288i	$-0.0567325\pi$
$258$		0			0
$259$		−	6.12764i		−	0.380753i
$260$	15.0975	−	11.1155i	0.936308	−	0.689356i
$261$		0			0
$262$	−1.00812	−	0.500350i	−0.0622819	−	0.0309117i
$263$	0.515631	−	0.893099i	0.0317952	−	0.0550708i	−0.849690	−	0.527283i	$-0.823211\pi$
$263$	0.515631	−	0.893099i	0.0317952	−	0.0550708i	0.881485	+	0.472212i	$0.156544\pi$
$264$		0			0
$265$	−15.6448			−0.961052
$266$	3.58205	−	2.38026i	0.219630	−	0.145943i
$267$		0			0
$268$	0.982490	+	7.76874i	0.0600151	+	0.474551i
$269$	5.34569	−	3.08633i	0.325932	−	0.188177i	−0.328101	−	0.944642i	$-0.606409\pi$
$269$	5.34569	−	3.08633i	0.325932	−	0.188177i	0.654034	+	0.756465i	$0.273075\pi$
$270$		0			0
$271$	6.85287	−	11.8695i	0.416282	−	0.721022i	−0.579280	−	0.815129i	$-0.696666\pi$
$271$	6.85287	−	11.8695i	0.416282	−	0.721022i	0.995562	+	0.0941065i	$0.0299994\pi$
$272$	−10.0263	+	2.57720i	−0.607932	+	0.156266i
$273$		0			0
$274$	−5.02027	+	0.316191i	−0.303286	+	0.0191018i
$275$	−4.23944	−	2.44764i	−0.255648	−	0.147598i
$276$		0			0
$277$	24.4764	−	14.1314i	1.47064	−	0.849076i	0.471187	−	0.882033i	$-0.343826\pi$
$277$	24.4764	−	14.1314i	1.47064	−	0.849076i	0.999457	+	0.0329570i	$0.0104924\pi$
$278$	0.191109	+	3.03430i	0.0114619	+	0.181986i
$279$		0			0
$280$	−3.34594	+	2.88932i	−0.199958	+	0.172670i
$281$	12.3330			0.735724			0.367862	−	0.929880i	$-0.380090\pi$
$281$	12.3330			0.735724			0.367862	+	0.929880i	$0.380090\pi$
$282$		0			0
$283$	−17.0408	−	9.83851i	−1.01297	−	0.584838i	−0.100910	−	0.994896i	$-0.532175\pi$
$283$	−17.0408	−	9.83851i	−1.01297	−	0.584838i	−0.912060	+	0.410057i	$0.865509\pi$
$284$	−0.357689	+	0.851232i	−0.0212250	+	0.0505113i
$285$		0			0
$286$	11.9308	−	7.67662i	0.705481	−	0.453928i
$287$	−6.32727			−0.373487
$288$		0			0
$289$	5.15100	−	8.92179i	0.303000	−	0.524811i
$290$	3.62024	+	5.44810i	0.212588	+	0.319923i
$291$		0			0
$292$	17.9969	+	23.7033i	1.05319	+	1.38713i
$293$	10.1639	−	5.86812i	0.593780	−	0.342819i	−0.172811	−	0.984955i	$-0.555285\pi$
$293$	10.1639	−	5.86812i	0.593780	−	0.342819i	0.766591	+	0.642136i	$0.221952\pi$
$294$		0			0
$295$	−14.1751	−	24.5520i	−0.825308	−	1.42947i
$296$	−27.2278	−	9.47552i	−1.58258	−	0.550754i
$297$		0			0
$298$	0.295369	+	4.68968i	0.0171103	+	0.271666i
$299$	−10.8831	+	18.2238i	−0.629388	+	1.05391i
$300$		0			0
$301$	−5.07552	−	2.93036i	−0.292548	−	0.168903i
$302$	−4.18989	+	8.44191i	−0.241101	+	0.485777i
$303$		0			0
$304$	−5.03741	−	19.5974i	−0.288915	−	1.12399i
$305$	−2.77491	−	4.80629i	−0.158891	−	0.275207i
$306$		0			0
$307$			5.08990i			0.290496i	0.989395	+	0.145248i	$0.0463980\pi$
$307$			5.08990i			0.290496i	−0.989395	+	0.145248i	$0.953602\pi$
$308$	−2.66437	+	2.02294i	−0.151817	+	0.115268i
$309$		0			0
$310$	16.7776	+	8.32705i	0.952902	+	0.472944i
$311$	−25.1578			−1.42657			−0.713284	−	0.700875i	$-0.752793\pi$
$311$	−25.1578			−1.42657			−0.713284	+	0.700875i	$0.752793\pi$
$312$		0			0
$313$	12.4651			0.704569			0.352285	−	0.935893i	$-0.385405\pi$
$313$	12.4651			0.704569			0.352285	+	0.935893i	$0.385405\pi$
$314$	−1.57274	−	0.780583i	−0.0887549	−	0.0440508i
$315$		0			0
$316$	9.48142	+	12.4878i	0.533372	+	0.702493i
$317$			11.0238i			0.619160i	0.950873	+	0.309580i	$0.100189\pi$
$317$			11.0238i			0.619160i	−0.950873	+	0.309580i	$0.899811\pi$
$318$		0			0
$319$	2.47495	+	4.28675i	0.138571	+	0.240012i
$320$	7.66453	+	19.3354i	0.428460	+	1.08088i
$321$		0			0
$322$	2.22515	−	4.48330i	0.124003	−	0.249845i
$323$	−11.3379	−	6.54597i	−0.630860	−	0.364227i
$324$		0			0
$325$	−6.34301	−	0.0936005i	−0.351847	−	0.00519202i
$326$	0.968334	+	15.3746i	0.0536310	+	0.851520i
$327$		0			0
$328$	−9.78422	+	28.1149i	−0.540243	+	1.55238i
$329$	0.643110	+	1.11390i	0.0354558	+	0.0614113i
$330$		0			0
$331$	14.3890	−	8.30750i	0.790891	−	0.456621i	−0.0493848	−	0.998780i	$-0.515726\pi$
$331$	14.3890	−	8.30750i	0.790891	−	0.456621i	0.840276	+	0.542158i	$0.182393\pi$
$332$	1.48219	−	1.12536i	0.0813458	−	0.0617622i
$333$		0			0
$334$	−10.4591	−	15.7399i	−0.572298	−	0.861251i
$335$	5.08969	−	8.81560i	0.278079	−	0.481647i
$336$		0			0
$337$	−11.0591			−0.602427			−0.301214	−	0.953557i	$-0.597392\pi$
$337$	−11.0591			−0.602427			−0.301214	+	0.953557i	$0.597392\pi$
$338$	8.65576	−	16.2197i	0.470811	−	0.882234i
$339$		0			0
$340$	12.4065	+	5.21323i	0.672836	+	0.282727i
$341$	12.2748	+	7.08685i	0.664717	+	0.383774i
$342$		0			0
$343$	−8.19918			−0.442714
$344$	−20.8694	+	18.0214i	−1.12521	+	0.971650i
$345$		0			0
$346$	0.581763	+	9.23687i	0.0312758	+	0.496577i
$347$	−1.92350	+	1.11054i	−0.103259	+	0.0596167i	−0.550740	−	0.834677i	$-0.685655\pi$
$347$	−1.92350	+	1.11054i	−0.103259	+	0.0596167i	0.447481	+	0.894293i	$0.352321\pi$
$348$		0			0
$349$	−11.6899	−	6.74919i	−0.625748	−	0.361276i	0.153355	−	0.988171i	$-0.450992\pi$
$349$	−11.6899	−	6.74919i	−0.625748	−	0.361276i	−0.779104	+	0.626895i	$0.784325\pi$
$350$	1.49289	−	0.0940261i	0.0797982	−	0.00502591i
$351$		0			0
$352$	4.86874	+	14.9672i	0.259505	+	0.797754i
$353$	1.75509	−	3.03991i	0.0934143	−	0.161798i	−0.815531	−	0.578713i	$-0.803555\pi$
$353$	1.75509	−	3.03991i	0.0934143	−	0.161798i	0.908946	+	0.416915i	$0.136889\pi$
$354$		0			0
$355$	1.03947	−	0.600139i	0.0551694	−	0.0318521i
$356$	4.67439	−	0.591157i	0.247742	−	0.0313312i
$357$		0			0
$358$	−18.4744	+	12.2762i	−0.976401	+	0.648815i
$359$	−25.0138			−1.32018			−0.660090	−	0.751187i	$-0.729482\pi$
$359$	−25.0138			−1.32018			−0.660090	+	0.751187i	$0.729482\pi$
$360$		0			0
$361$	3.29476	−	5.70670i	0.173409	−	0.300353i
$362$	5.90082	+	2.92869i	0.310140	+	0.153929i
$363$		0			0
$364$	−1.73818	+	3.97142i	−0.0911053	+	0.208159i
$365$		−	38.6880i		−	2.02502i
$366$		0			0
$367$	−10.2910	+	17.8245i	−0.537186	+	0.930434i	0.461868	+	0.886949i	$0.347179\pi$
$367$	−10.2910	+	17.8245i	−0.537186	+	0.930434i	−0.999054	+	0.0434851i	$0.986154\pi$
$368$	−16.4804	−	16.8201i	−0.859101	−	0.876810i
$369$		0			0
$370$	20.7414	+	31.2138i	1.07830	+	1.62273i
$371$	3.13290	−	1.80878i	0.162652	−	0.0939072i
$372$		0			0
$373$	−12.3015	+	7.10225i	−0.636946	+	0.367741i	−0.783437	−	0.621471i	$-0.786535\pi$
$373$	−12.3015	+	7.10225i	−0.636946	+	0.367741i	0.146491	+	0.989212i	$0.453202\pi$
$374$	9.12173	+	4.52729i	0.471673	+	0.234101i
$375$		0			0
$376$	5.94403	−	1.13514i	0.306540	−	0.0585402i
$377$	5.50718	+	3.28886i	0.283634	+	0.169385i
$378$		0			0
$379$	6.23669	+	3.60075i	0.320357	+	0.184958i	0.651552	−	0.758604i	$-0.274118\pi$
$379$	6.23669	+	3.60075i	0.320357	+	0.184958i	−0.331195	+	0.943562i	$0.607452\pi$
$380$	−10.1898	+	24.2497i	−0.522725	+	1.24399i
$381$		0			0
$382$	−12.2578	+	0.772027i	−0.627161	+	0.0395003i
$383$	11.8763	+	20.5704i	0.606852	+	1.05110i	0.991756	+	0.128142i	$0.0409014\pi$
$383$	11.8763	+	20.5704i	0.606852	+	1.05110i	−0.384903	+	0.922957i	$0.625765\pi$
$384$		0			0
$385$	4.34873			0.221632
$386$	−1.23461	−	1.85796i	−0.0628399	−	0.0945678i
$387$		0			0
$388$	9.16026	−	21.7997i	0.465042	−	1.10671i
$389$		−	20.6264i		−	1.04580i	−0.852394	−	0.522900i	$-0.824850\pi$
$389$		−	20.6264i		−	1.04580i	0.852394	−	0.522900i	$-0.175150\pi$
$390$		0			0
$391$	−15.2360			−0.770519
$392$	−6.17145	+	17.7336i	−0.311705	+	0.895681i
$393$		0			0
$394$	−30.1206	+	20.0150i	−1.51745	+	1.00834i
$395$		−	20.3823i		−	1.02554i
$396$		0			0
$397$	25.6669	−	14.8188i	1.28819	−	0.743734i	0.309855	−	0.950784i	$-0.399720\pi$
$397$	25.6669	−	14.8188i	1.28819	−	0.743734i	0.978330	+	0.207050i	$0.0663862\pi$
$398$	29.2209	−	1.84041i	1.46471	−	0.0922515i
$399$		0			0
$400$	1.89074	−	6.77896i	0.0945370	−	0.338948i
$401$	−5.32482	+	9.22286i	−0.265909	+	0.460568i	−0.967801	−	0.251715i	$-0.919005\pi$
$401$	−5.32482	+	9.22286i	−0.265909	+	0.460568i	0.701892	+	0.712283i	$0.252339\pi$
$402$		0			0
$403$	18.3654	+	0.271009i	0.914847	+	0.0134999i
$404$	−3.25035	−	25.7011i	−0.161711	−	1.27868i
$405$		0			0
$406$	−1.35484	−	0.672436i	−0.0672398	−	0.0333725i
$407$	14.1798	+	24.5600i	0.702864	+	1.21740i
$408$		0			0
$409$	−0.271387	−	0.470056i	−0.0134192	−	0.0232428i	0.859238	−	0.511576i	$-0.170938\pi$
$409$	−0.271387	−	0.470056i	−0.0134192	−	0.0232428i	−0.872657	+	0.488334i	$0.837605\pi$
$410$	32.2307	−	21.4172i	1.59176	−	1.05772i
$411$		0			0
$412$	−7.99593	−	10.5313i	−0.393931	−	0.518839i
$413$	5.67720	+	3.27773i	0.279357	+	0.161287i
$414$		0			0
$415$	−2.41920			−0.118754
$416$	14.9589	+	13.8647i	0.733421	+	0.679774i
$417$		0			0
$418$	−8.84906	+	17.8294i	−0.432822	+	0.872062i
$419$	−17.8473	−	10.3042i	−0.871900	−	0.503392i	−0.00392074	−	0.999992i	$-0.501248\pi$
$419$	−17.8473	−	10.3042i	−0.871900	−	0.503392i	−0.867979	+	0.496601i	$0.834581\pi$
$420$		0			0
$421$		−	2.14198i		−	0.104394i	−0.998637	−	0.0521968i	$-0.983378\pi$
$421$		−	2.14198i		−	0.104394i	0.998637	−	0.0521968i	$-0.0166223\pi$
$422$	−24.9010	+	16.5466i	−1.21216	+	0.805478i
$423$		0			0
$424$	−3.19263	−	16.7179i	−0.155048	−	0.811893i
$425$	−2.27674	−	3.94343i	−0.110438	−	0.191284i
$426$		0			0
$427$	1.11136	+	0.641646i	0.0537827	+	0.0310514i
$428$	2.57190	+	20.3365i	0.124318	+	0.983003i
$429$		0			0
$430$	35.7733	−	2.25310i	1.72514	−	0.108654i
$431$	5.72822	−	9.92157i	0.275919	−	0.477905i	−0.694448	−	0.719543i	$-0.744351\pi$
$431$	5.72822	−	9.92157i	0.275919	−	0.477905i	0.970366	+	0.241638i	$0.0776846\pi$
$432$		0			0
$433$	−8.14866	−	14.1139i	−0.391600	−	0.678270i	0.601061	−	0.799203i	$-0.294745\pi$
$433$	−8.14866	−	14.1139i	−0.391600	−	0.678270i	−0.992661	+	0.120933i	$0.961411\pi$
$434$	−4.32248	+	0.272242i	−0.207486	+	0.0130680i
$435$		0			0
$436$	17.2339	−	13.0850i	0.825356	−	0.626656i
$437$		−	29.7804i		−	1.42459i
$438$		0			0
$439$	−1.34252	+	2.32532i	−0.0640751	+	0.110981i	−0.896283	−	0.443482i	$-0.853743\pi$
$439$	−1.34252	+	2.32532i	−0.0640751	+	0.110981i	0.832208	+	0.554463i	$0.187076\pi$
$440$	6.72470	−	19.3233i	0.320587	−	0.921204i
$441$		0			0
$442$	13.1812	−	0.635090i	0.626967	−	0.0302082i
$443$		−	14.6679i		−	0.696891i	−0.937329	−	0.348446i	$-0.886710\pi$
$443$		−	14.6679i		−	0.696891i	0.937329	−	0.348446i	$-0.113290\pi$
$444$		0			0
$445$	−5.30428	−	3.06242i	−0.251447	−	0.145173i
$446$	−6.31934	−	9.50997i	−0.299229	−	0.450310i
$447$		0			0
$448$	−3.77031	−	2.98582i	−0.178130	−	0.141067i
$449$	−0.656457	−	1.13702i	−0.0309801	−	0.0536591i	0.850120	−	0.526590i	$-0.176530\pi$
$449$	−0.656457	−	1.13702i	−0.0309801	−	0.0536591i	−0.881100	+	0.472930i	$0.843196\pi$
$450$		0			0
$451$	25.3602	−	14.6417i	1.19416	−	0.689451i
$452$	−7.37140	+	17.5425i	−0.346721	+	0.825131i
$453$		0			0
$454$	−2.03773	−	32.3539i	−0.0956356	−	1.51844i
$455$	4.92148	−	2.74540i	0.230722	−	0.128706i
$456$		0			0
$457$	9.83743	−	17.0389i	0.460176	−	0.797048i	−0.538794	−	0.842438i	$-0.681120\pi$
$457$	9.83743	−	17.0389i	0.460176	−	0.797048i	0.998969	+	0.0453901i	$0.0144531\pi$
$458$	0.753360	+	0.373907i	0.0352022	+	0.0174715i
$459$		0			0
$460$	3.84075	+	30.3695i	0.179076	+	1.41599i
$461$	−10.1402	+	5.85445i	−0.472277	+	0.272669i	−0.717192	−	0.696875i	$-0.754573\pi$
$461$	−10.1402	+	5.85445i	−0.472277	+	0.272669i	0.244916	+	0.969544i	$0.421240\pi$
$462$		0			0
$463$	20.0915			0.933731			0.466866	−	0.884328i	$-0.345383\pi$
$463$	20.0915			0.933731			0.466866	+	0.884328i	$0.345383\pi$
$464$	−5.08301	+	4.98035i	−0.235973	+	0.231207i
$465$		0			0
$466$	0.0594676	−	0.119817i	0.00275478	−	0.00555042i
$467$		−	38.0472i		−	1.76061i	−0.474405	−	0.880307i	$-0.657337\pi$
$467$		−	38.0472i		−	1.76061i	0.474405	−	0.880307i	$-0.342663\pi$
$468$		0			0
$469$			2.35379i			0.108688i
$470$	−7.04640	−	3.49727i	−0.325026	−	0.161317i
$471$		0			0
$472$	23.3434	−	20.1578i	1.07447	−	0.927836i
$473$	27.1241			1.24717
$474$		0			0
$475$	7.70784	−	4.45012i	0.353660	−	0.204186i
$476$	−3.08715	+	0.390423i	−0.141499	+	0.0178950i
$477$		0			0
$478$	9.66312	−	19.4695i	0.441981	−	0.890516i
$479$	−4.96607	+	8.60149i	−0.226906	+	0.393012i	−0.956889	−	0.290452i	$-0.906194\pi$
$479$	−4.96607	+	8.60149i	−0.226906	+	0.393012i	0.729984	+	0.683465i	$0.239528\pi$
$480$		0			0
$481$	31.5523	+	18.8429i	1.43866	+	0.859161i
$482$	14.1735	−	0.892685i	0.645585	−	0.0406607i
$483$		0			0
$484$	−2.52479	+	6.00851i	−0.114763	+	0.273114i
$485$	−26.6204	+	15.3693i	−1.20877	+	0.697883i
$486$		0			0
$487$	11.7461	+	20.3448i	0.532265	+	0.921910i	0.999290	+	0.0376664i	$0.0119924\pi$
$487$	11.7461	+	20.3448i	0.532265	+	0.921910i	−0.467025	+	0.884244i	$0.654674\pi$
$488$	4.56968	−	3.94607i	0.206860	−	0.178630i
$489$		0			0
$490$	20.3297	−	13.5090i	0.918400	−	0.610273i
$491$	26.6538	+	15.3886i	1.20287	+	0.694478i	0.961193	−	0.275878i	$-0.0889687\pi$
$491$	26.6538	+	15.3886i	1.20287	+	0.694478i	0.241679	+	0.970356i	$0.422302\pi$
$492$		0			0
$493$			4.60429i			0.207367i
$494$	1.24135	+	25.7641i	0.0558510	+	1.15918i
$495$		0			0
$496$	−5.47441	+	19.6277i	−0.245808	+	0.881309i
$497$	−0.138771	+	0.240358i	−0.00622472	+	0.0107815i
$498$		0			0
$499$		−	4.61772i		−	0.206718i	−0.994644	−	0.103359i	$-0.967041\pi$
$499$		−	4.61772i		−	0.206718i	0.994644	−	0.103359i	$-0.0329590\pi$
$500$	13.4204	−	10.1895i	0.600177	−	0.455687i
$501$		0			0
$502$	−1.52034	−	24.1390i	−0.0678562	−	1.07738i
$503$	−14.8441	−	25.7107i	−0.661865	−	1.14638i	−0.980125	−	0.198381i	$-0.936432\pi$
$503$	−14.8441	−	25.7107i	−0.661865	−	1.14638i	0.318260	−	0.948004i	$-0.396902\pi$
$504$		0			0
$505$	−16.8381	+	29.1644i	−0.749285	+	1.29780i
$506$	1.45607	+	23.1186i	0.0647302	+	1.02775i
$507$		0			0
$508$	−36.5540	+	4.62287i	−1.62182	+	0.205107i
$509$	20.3599	+	11.7548i	0.902438	+	0.521023i	0.877990	−	0.478678i	$-0.158884\pi$
$509$	20.3599	+	11.7548i	0.902438	+	0.521023i	0.0244475	+	0.999701i	$0.492217\pi$
$510$		0			0
$511$	4.47294	+	7.74736i	0.197871	+	0.342723i
$512$	−19.0976	+	12.1360i	−0.844001	+	0.536342i
$513$		0			0
$514$	−16.2018	−	24.3820i	−0.714629	−	1.07545i
$515$			17.1889i			0.757435i
$516$		0			0
$517$	−5.15527	−	2.97640i	−0.226729	−	0.130902i
$518$	−7.76231	−	3.85259i	−0.341056	−	0.169273i
$519$		0			0
$520$	−4.58868	−	26.1137i	−0.201227	−	1.14516i
$521$	11.7037			0.512747			0.256374	−	0.966578i	$-0.417472\pi$
$521$	11.7037			0.512747			0.256374	+	0.966578i	$0.417472\pi$
$522$		0			0
$523$	10.9235	+	6.30668i	0.477651	+	0.275772i	0.719437	−	0.694558i	$-0.244400\pi$
$523$	10.9235	+	6.30668i	0.477651	+	0.275772i	−0.241786	+	0.970330i	$0.577733\pi$
$524$	−1.26766	+	0.962475i	−0.0553779	+	0.0420459i
$525$		0			0
$526$	−0.807162	−	1.21470i	−0.0351939	−	0.0529633i
$527$	6.59203	+	11.4177i	0.287153	+	0.497364i
$528$		0			0
$529$	−5.82878	−	10.0957i	−0.253425	−	0.438945i
$530$	−9.83624	+	19.8184i	−0.427259	+	0.860854i
$531$		0			0
$532$	−0.763123	−	6.03416i	−0.0330856	−	0.261614i
$533$	19.4567	−	32.5802i	0.842765	−	1.41121i
$534$		0			0
$535$	13.3235	−	23.0769i	0.576024	−	0.997703i
$536$	10.4589	+	3.63980i	0.451757	+	0.157215i
$537$		0			0
$538$	−0.548718	−	8.71221i	−0.0236569	−	0.375610i
$539$	15.9961	−	9.23533i	0.688999	−	0.397794i
$540$		0			0
$541$		−	40.4799i		−	1.74037i	−0.492728	−	0.870183i	$-0.664000\pi$
$541$		−	40.4799i		−	1.74037i	0.492728	−	0.870183i	$-0.336000\pi$
$542$	−10.7274	−	16.1437i	−0.460781	−	0.693430i
$543$		0			0
$544$	−3.03902	+	14.3213i	−0.130297	+	0.614022i
$545$	−28.1288			−1.20491
$546$		0			0
$547$		−	27.1567i		−	1.16114i	−0.814212	−	0.580568i	$-0.802831\pi$
$547$		−	27.1567i		−	1.16114i	0.814212	−	0.580568i	$-0.197169\pi$
$548$	−2.75582	+	6.55833i	−0.117723	+	0.280158i
$549$		0			0
$550$	−5.76603	+	3.83150i	−0.245864	+	0.163376i
$551$	−8.99957			−0.383394
$552$		0			0
$553$	2.35651	+	4.08160i	0.100209	+	0.173567i
$554$	−2.51243	−	39.8907i	−0.106743	−	1.69479i
$555$		0			0
$556$	3.96392	+	1.66565i	0.168108	+	0.0706392i
$557$	−26.2789	−	15.1721i	−1.11347	−	0.642863i	−0.173746	−	0.984791i	$-0.555587\pi$
$557$	−26.2789	−	15.1721i	−1.11347	−	0.642863i	−0.939726	+	0.341927i	$0.888920\pi$
$558$		0			0
$559$	30.6965	−	17.1238i	1.29832	−	0.724258i
$560$	1.55644	+	6.05512i	0.0657716	+	0.255875i
$561$		0			0
$562$	7.75403	−	15.6230i	0.327084	−	0.659018i
$563$	−7.83182	+	4.52170i	−0.330072	+	0.190567i	−0.655873	−	0.754871i	$-0.727699\pi$
$563$	−7.83182	+	4.52170i	−0.330072	+	0.190567i	0.325801	+	0.945438i	$0.394366\pi$
$564$		0			0
$565$	21.4218	−	12.3679i	0.901222	−	0.520321i
$566$	−23.1771	+	15.4011i	−0.974205	+	0.647355i
$567$		0			0
$568$	0.853428	+	0.988300i	0.0358090	+	0.0414681i
$569$	18.1496	−	31.4361i	0.760872	−	1.31787i	−0.181529	−	0.983386i	$-0.558105\pi$
$569$	18.1496	−	31.4361i	0.760872	−	1.31787i	0.942401	−	0.334484i	$-0.108562\pi$
$570$		0			0
$571$			24.9740i			1.04513i	0.852599	+	0.522566i	$0.175025\pi$
$571$			24.9740i			1.04513i	−0.852599	+	0.522566i	$0.824975\pi$
$572$	−2.22336	−	19.9400i	−0.0929634	−	0.833733i
$573$		0			0
$574$	−3.97810	+	8.01520i	−0.166043	+	0.334548i
$575$	5.17893	−	8.97016i	0.215976	−	0.374082i
$576$		0			0
$577$	14.7654			0.614692			0.307346	−	0.951598i	$-0.400559\pi$
$577$	14.7654			0.614692			0.307346	+	0.951598i	$0.400559\pi$
$578$	−8.06331	−	12.1345i	−0.335390	−	0.504728i
$579$		0			0
$580$	9.17761	−	1.16067i	0.381080	−	0.0481940i
$581$	0.484450	−	0.279697i	0.0200984	−	0.0116038i
$582$		0			0
$583$	−8.37127	+	14.4995i	−0.346703	+	0.600507i
$584$	41.3417	−	7.89506i	1.71073	−	0.326700i
$585$		0			0
$586$	−1.04329	−	16.5647i	−0.0430979	−	0.684282i
$587$	33.7254	+	19.4714i	1.39200	+	0.803669i	0.993536	−	0.113517i	$-0.0362115\pi$
$587$	33.7254	+	19.4714i	1.39200	+	0.803669i	0.398460	+	0.917186i	$0.369545\pi$
$588$		0			0
$589$	−22.3171	+	12.8848i	−0.919561	+	0.530909i
$590$	−40.0140	+	2.52019i	−1.64735	+	0.103755i
$591$		0			0
$592$	−29.1221	+	28.5339i	−1.19691	+	1.17274i
$593$	−19.6722			−0.807842			−0.403921	−	0.914794i	$-0.632353\pi$
$593$	−19.6722			−0.807842			−0.403921	+	0.914794i	$0.632353\pi$
$594$		0			0
$595$	3.50315	+	2.02255i	0.143615	+	0.0829163i
$596$	6.12645	+	2.57435i	0.250949	+	0.105449i
$597$		0			0
$598$	16.2428	+	25.2441i	0.664219	+	1.03231i
$599$	0.289136			0.0118138			0.00590689	−	0.999983i	$-0.498120\pi$
$599$	0.289136			0.0118138			0.00590689	+	0.999983i	$0.498120\pi$
$600$		0			0
$601$	−13.3071	+	23.0486i	−0.542808	+	0.940171i	0.455933	+	0.890014i	$0.349305\pi$
$601$	−13.3071	+	23.0486i	−0.542808	+	0.940171i	−0.998741	+	0.0501569i	$0.984028\pi$
$602$	−6.90319	+	4.58714i	−0.281353	+	0.186958i
$603$		0			0
$604$	8.05968	+	10.6152i	0.327944	+	0.431928i
$605$	7.33722	−	4.23614i	0.298300	−	0.172224i
$606$		0			0
$607$	−4.23231	−	7.33058i	−0.171784	−	0.297539i	0.767259	−	0.641337i	$-0.221620\pi$
$607$	−4.23231	−	7.33058i	−0.171784	−	0.297539i	−0.939044	+	0.343798i	$0.888287\pi$
$608$	−27.9925	−	5.94008i	−1.13525	−	0.240902i
$609$		0			0
$610$	−7.83312	+	0.493351i	−0.317154	+	0.0199752i
$611$	−7.71327	−	0.113821i	−0.312046	−	0.00460470i
$612$		0			0
$613$	11.1194	+	6.41977i	0.449107	+	0.259292i	0.707453	−	0.706760i	$-0.249844\pi$
$613$	11.1194	+	6.41977i	0.449107	+	0.259292i	−0.258346	+	0.966053i	$0.583177\pi$
$614$	6.44774	+	3.20014i	0.260209	+	0.129147i
$615$		0			0
$616$	0.887446	+	4.64702i	0.0357562	+	0.187234i
$617$	2.51106	+	4.34928i	0.101091	+	0.175095i	0.912135	−	0.409891i	$-0.134433\pi$
$617$	2.51106	+	4.34928i	0.101091	+	0.175095i	−0.811043	+	0.584986i	$0.801100\pi$
$618$		0			0
$619$			25.2782i			1.01602i	0.861353	+	0.508008i	$0.169618\pi$
$619$			25.2782i			1.01602i	−0.861353	+	0.508008i	$0.830382\pi$
$620$	21.0969	−	16.0179i	0.847272	−	0.643296i
$621$		0			0
$622$	−15.8173	+	31.8692i	−0.634216	+	1.27784i
$623$	1.41626			0.0567411
$624$		0			0
$625$	−30.7015			−1.22806
$626$	7.83710	−	15.7904i	0.313234	−	0.631112i
$627$		0			0
$628$	−1.97764	+	1.50153i	−0.0789163	+	0.0599176i
$629$			26.3794i			1.05181i
$630$		0			0
$631$	16.7070	+	28.9374i	0.665097	+	1.15198i	0.979259	+	0.202612i	$0.0649430\pi$
$631$	16.7070	+	28.9374i	0.665097	+	1.15198i	−0.314163	+	0.949369i	$0.601724\pi$
$632$	21.7804	−	4.15942i	0.866376	−	0.165453i
$633$		0			0
$634$	13.9647	+	6.93094i	0.554608	+	0.275263i
$635$	41.4797	+	23.9483i	1.64607	+	0.950360i
$636$		0			0
$637$	12.2724	−	20.5501i	0.486252	−	0.814226i
$638$	6.98638	−	0.440021i	0.276594	−	0.0174206i
$639$		0			0
$640$	29.3124	+	2.44743i	1.15867	+	0.0967430i
$641$	5.95235	+	10.3098i	0.235104	+	0.407212i	0.959303	−	0.282379i	$-0.0911236\pi$
$641$	5.95235	+	10.3098i	0.235104	+	0.407212i	−0.724199	+	0.689591i	$0.757790\pi$
$642$		0			0
$643$	−29.4994	+	17.0315i	−1.16334	+	0.671656i	−0.952103	−	0.305778i	$-0.901083\pi$
$643$	−29.4994	+	17.0315i	−1.16334	+	0.671656i	−0.211239	+	0.977434i	$0.567750\pi$
$644$	−4.28031	−	5.63751i	−0.168668	−	0.222149i
$645$		0			0
$646$	−15.4207	+	10.2470i	−0.606718	+	0.403162i
$647$	19.9224	−	34.5065i	0.783229	−	1.35659i	−0.146823	−	0.989163i	$-0.546905\pi$
$647$	19.9224	−	34.5065i	0.783229	−	1.35659i	0.930052	−	0.367429i	$-0.119762\pi$
$648$		0			0
$649$	−30.3395			−1.19093
$650$	−4.10657	+	7.97628i	−0.161073	+	0.312856i
$651$		0			0
$652$	20.0849	+	8.43971i	0.786585	+	0.330524i
$653$	−17.1513	−	9.90232i	−0.671183	−	0.387508i	0.125342	−	0.992114i	$-0.459997\pi$
$653$	−17.1513	−	9.90232i	−0.671183	−	0.387508i	−0.796525	+	0.604606i	$0.793331\pi$
$654$		0			0
$655$	2.06904			0.0808442
$656$	29.4635	+	30.0708i	1.15036	+	1.17407i
$657$		0			0
$658$	1.81539	−	0.114338i	0.0707714	−	0.00445738i
$659$	−24.1533	+	13.9449i	−0.940880	+	0.543218i	−0.890236	−	0.455499i	$-0.849461\pi$
$659$	−24.1533	+	13.9449i	−0.940880	+	0.543218i	−0.0506442	+	0.998717i	$0.516127\pi$
$660$		0			0
$661$	−17.0661	−	9.85313i	−0.663795	−	0.383242i	0.129926	−	0.991524i	$-0.458526\pi$
$661$	−17.0661	−	9.85313i	−0.663795	−	0.383242i	−0.793722	+	0.608281i	$0.791859\pi$
$662$	−1.47699	−	23.4507i	−0.0574048	−	0.911437i
$663$		0			0
$664$	−0.493686	−	2.58514i	−0.0191587	−	0.100323i
$665$	−3.95328	+	6.84728i	−0.153301	+	0.265526i
$666$		0			0
$667$	−9.07027	+	5.23672i	−0.351202	+	0.202767i
$668$	−26.5148	+	3.35325i	−1.02589	+	0.129741i
$669$		0			0
$670$	−7.96733	−	11.9900i	−0.307805	−	0.463215i
$671$	−5.93924			−0.229282
$672$		0			0
$673$	18.0814	−	31.3179i	0.696986	−	1.20722i	−0.272521	−	0.962150i	$-0.587857\pi$
$673$	18.0814	−	31.3179i	0.696986	−	1.20722i	0.969507	−	0.245065i	$-0.0788094\pi$
$674$	−6.95311	+	14.0093i	−0.267824	+	0.539619i
$675$		0			0
$676$	−15.1045	−	21.1625i	−0.580943	−	0.813944i
$677$			43.5560i			1.67399i	0.547209	+	0.836996i	$0.315690\pi$
$677$			43.5560i			1.67399i	−0.547209	+	0.836996i	$0.684310\pi$
$678$		0			0
$679$	3.55386	−	6.15546i	0.136384	−	0.236225i
$680$	14.4042	−	12.4385i	0.552376	−	0.476994i
$681$		0			0
$682$	16.6949	−	11.0937i	0.639279	−	0.424798i
$683$	6.89615	−	3.98149i	0.263874	−	0.152348i	−0.362227	−	0.932090i	$-0.617983\pi$
$683$	6.89615	−	3.98149i	0.263874	−	0.152348i	0.626100	+	0.779742i	$0.284650\pi$
$684$		0			0
$685$	8.00862	−	4.62378i	0.305994	−	0.176666i
$686$	−5.15502	+	10.3865i	−0.196819	+	0.396558i
$687$		0			0
$688$	9.70790	+	37.7673i	0.370110	+	1.43986i
$689$	−0.320127	+	21.6940i	−0.0121959	+	0.826475i
$690$		0			0
$691$	30.2709	+	17.4769i	1.15156	+	0.664854i	0.949267	−	0.314471i	$-0.101827\pi$
$691$	30.2709	+	17.4769i	1.15156	+	0.664854i	0.202294	+	0.979325i	$0.435160\pi$
$692$	12.0668	+	5.07047i	0.458709	+	0.192751i
$693$		0			0
$694$	0.197442	+	3.13486i	0.00749479	+	0.118998i
$695$	−2.79466	−	4.84049i	−0.106007	−	0.183610i
$696$		0			0
$697$	27.2388			1.03174
$698$	−15.8994	+	10.5651i	−0.601802	+	0.399895i
$699$		0			0
$700$	0.819504	−	1.95026i	0.0309743	−	0.0737130i
$701$		−	10.8831i		−	0.411050i	−0.978652	−	0.205525i	$-0.934110\pi$
$701$		−	10.8831i		−	0.411050i	0.978652	−	0.205525i	$-0.0658901\pi$
$702$		0			0
$703$	−51.5612			−1.94467
$704$	22.0211	+	3.24264i	0.829951	+	0.122212i
$705$		0			0
$706$	−2.74740	−	4.13457i	−0.103400	−	0.155606i
$707$		−	7.78698i		−	0.292859i
$708$		0			0
$709$	−31.1767	+	17.9999i	−1.17087	+	0.676000i	−0.953884	−	0.300176i	$-0.902955\pi$
$709$	−31.1767	+	17.9999i	−1.17087	+	0.676000i	−0.216982	+	0.976176i	$0.569621\pi$
$710$	−0.106699	−	1.69409i	−0.00400432	−	0.0635781i
$711$		0			0
$712$	2.19004	−	6.29305i	0.0820752	−	0.235842i
$713$	−14.9950	+	25.9720i	−0.561566	+	0.972661i
$714$		0			0
$715$	−13.3726	+	22.3924i	−0.500108	+	0.837428i
$716$	3.93580	+	31.1211i	0.147088	+	1.16305i
$717$		0			0
$718$	−15.7268	+	31.6868i	−0.586918	+	1.18254i
$719$	2.97642	+	5.15531i	0.111002	+	0.192261i	0.916174	−	0.400780i	$-0.131261\pi$
$719$	2.97642	+	5.15531i	0.111002	+	0.192261i	−0.805173	+	0.593040i	$0.797927\pi$
$720$		0			0
$721$	−1.98731	−	3.44212i	−0.0740112	−	0.128191i
$722$	−5.15758	−	7.76164i	−0.191945	−	0.288858i
$723$		0			0
$724$	7.41997	−	5.63365i	0.275761	−	0.209373i
$725$	−2.71076	−	1.56506i	−0.100675	−	0.0581249i
$726$		0			0
$727$	34.3229			1.27297			0.636484	−	0.771290i	$-0.280388\pi$
$727$	34.3229			1.27297			0.636484	+	0.771290i	$0.280388\pi$
$728$	3.93804	+	4.69879i	0.145953	+	0.174149i
$729$		0			0
$730$	−49.0088	−	24.3241i	−1.81390	−	0.900274i
$731$	21.8500	+	12.6151i	0.808153	+	0.466587i
$732$		0			0
$733$			6.24499i			0.230664i	0.993327	+	0.115332i	$0.0367932\pi$
$733$			6.24499i			0.230664i	−0.993327	+	0.115332i	$0.963207\pi$
$734$	16.1094	+	24.2431i	0.594609	+	0.894827i
$735$		0			0
$736$	−31.6689	+	10.3017i	−1.16733	+	0.379726i
$737$	−5.44682	−	9.43417i	−0.200636	−	0.347512i
$738$		0			0
$739$	5.26210	+	3.03807i	0.193569	+	0.111757i	0.593652	−	0.804722i	$-0.297685\pi$
$739$	5.26210	+	3.03807i	0.193569	+	0.111757i	−0.400083	+	0.916479i	$0.631019\pi$
$740$	52.5813	−	6.64980i	1.93293	−	0.244452i
$741$		0			0
$742$	−0.321583	−	5.10589i	−0.0118057	−	0.187443i
$743$	4.10832	−	7.11582i	0.150720	−	0.261054i	−0.780773	−	0.624815i	$-0.785174\pi$
$743$	4.10832	−	7.11582i	0.150720	−	0.261054i	0.931492	+	0.363761i	$0.118508\pi$
$744$		0			0
$745$	−4.31929	−	7.48124i	−0.158247	−	0.274091i
$746$	1.26271	+	20.0485i	0.0462310	+	0.734027i
$747$		0			0
$748$	11.4701	−	8.70872i	0.419388	−	0.318422i
$749$			6.16160i			0.225140i
$750$		0			0
$751$	−10.9266	+	18.9254i	−0.398717	+	0.690599i	−0.993568	−	0.113238i	$-0.963878\pi$
$751$	−10.9266	+	18.9254i	−0.398717	+	0.690599i	0.594851	+	0.803836i	$0.297211\pi$
$752$	2.29919	−	8.24341i	0.0838429	−	0.300606i
$753$		0			0
$754$	7.62873	−	4.90855i	0.277822	−	0.178759i
$755$		−	17.3260i		−	0.630557i
$756$		0			0
$757$	−18.5854	−	10.7303i	−0.675498	−	0.389999i	0.122659	−	0.992449i	$-0.460858\pi$
$757$	−18.5854	−	10.7303i	−0.675498	−	0.389999i	−0.798157	+	0.602450i	$0.794191\pi$
$758$	8.48248	−	5.63658i	0.308098	−	0.204730i
$759$		0			0
$760$	24.3123	+	28.1545i	0.881900	+	1.02127i
$761$	11.7372	+	20.3294i	0.425472	+	0.736939i	0.996464	−	0.0840166i	$-0.0267749\pi$
$761$	11.7372	+	20.3294i	0.425472	+	0.736939i	−0.570993	+	0.820955i	$0.693442\pi$
$762$		0			0
$763$	5.63286	−	3.25213i	0.203923	−	0.117735i
$764$	−6.72876	+	16.0132i	−0.243438	+	0.579336i
$765$		0			0
$766$	33.5249	−	2.11149i	1.21130	−	0.0762912i
$767$	−34.3353	+	19.1537i	−1.23978	+	0.691599i
$768$		0			0
$769$	−5.94997	+	10.3056i	−0.214561	+	0.371631i	−0.953137	−	0.302540i	$-0.902165\pi$
$769$	−5.94997	+	10.3056i	−0.214561	+	0.371631i	0.738575	+	0.674171i	$0.235499\pi$
$770$	2.73415	−	5.50885i	0.0985319	−	0.198525i
$771$		0			0
$772$	−3.12984	+	0.395822i	−0.112645	+	0.0142459i
$773$	−12.2803	+	7.09004i	−0.441692	+	0.255011i	−0.704315	−	0.709888i	$-0.748746\pi$
$773$	−12.2803	+	7.09004i	−0.441692	+	0.255011i	0.262623	+	0.964898i	$0.415412\pi$
$774$		0			0
$775$	−8.96287			−0.321956
$776$	−21.8559	−	25.3099i	−0.784581	−	0.908572i
$777$		0			0
$778$	−26.1289	−	12.9683i	−0.936767	−	0.464936i
$779$			53.2410i			1.90756i
$780$		0			0
$781$		−	1.28450i		−	0.0459630i
$782$	−9.57924	+	19.3005i	−0.342553	+	0.690186i
$783$		0			0
$784$	18.5842	+	18.9673i	0.663723	+	0.677404i
$785$	3.22786			0.115207
$786$		0			0
$787$	7.12142	−	4.11155i	0.253851	−	0.146561i	−0.367675	−	0.929954i	$-0.619846\pi$
$787$	7.12142	−	4.11155i	0.253851	−	0.146561i	0.621526	+	0.783393i	$0.286513\pi$
$788$	6.41692	+	50.7398i	0.228593	+	1.80753i
$789$		0			0
$790$	−25.8197	−	12.8148i	−0.918624	−	0.455931i
$791$	−2.85984	+	4.95339i	−0.101684	+	0.176122i
$792$		0			0
$793$	−6.72146	+	3.74951i	−0.238686	+	0.133149i
$794$	−2.63463	−	41.8310i	−0.0934995	−	1.48453i
$795$		0			0
$796$	16.0405	−	38.1733i	0.568540	−	1.35302i
$797$	1.61224	−	0.930825i	0.0571083	−	0.0329715i	−0.471174	−	0.882040i	$-0.656170\pi$
$797$	1.61224	−	0.930825i	0.0571083	−	0.0329715i	0.528282	+	0.849069i	$0.322836\pi$
$798$		0			0
$799$	−2.76858	−	4.79532i	−0.0979453	−	0.169646i
$800$	−7.39864	−	6.65722i	−0.261581	−	0.235368i
$801$		0			0
$802$	8.33541	+	12.5440i	0.294334	+	0.442942i
$803$	−35.8558	−	20.7013i	−1.26532	−	0.730534i
$804$		0			0
$805$			9.20142i			0.324308i
$806$	11.8901	−	23.0944i	0.418810	−	0.813465i
$807$		0			0
$808$	−34.6010	−	12.0415i	−1.21726	−	0.423617i
$809$	18.9274	−	32.7832i	0.665452	−	1.15260i	−0.313711	−	0.949519i	$-0.601572\pi$
$809$	18.9274	−	32.7832i	0.665452	−	1.15260i	0.979163	−	0.203078i	$-0.0650943\pi$
$810$		0			0
$811$			16.1872i			0.568409i	0.958764	+	0.284205i	$0.0917295\pi$
$811$			16.1872i			0.568409i	−0.958764	+	0.284205i	$0.908270\pi$
$812$	−1.70364	+	1.29350i	−0.0597862	+	0.0453930i
$813$		0			0
$814$	40.0271	−	2.52101i	1.40295	−	0.0883615i
$815$	−14.1603	−	24.5264i	−0.496015	−	0.859122i
$816$		0			0
$817$	−24.6576	+	42.7082i	−0.862659	+	1.49417i
$818$	−0.766080	+	0.0482498i	−0.0267854	+	0.00168702i
$819$		0			0
$820$	−6.86645	−	54.2943i	−0.239787	−	1.89604i
$821$	−23.9391	−	13.8212i	−0.835479	−	0.482364i	0.0202456	−	0.999795i	$-0.493555\pi$
$821$	−23.9391	−	13.8212i	−0.835479	−	0.482364i	−0.855725	+	0.517431i	$0.826889\pi$
$822$		0			0
$823$	−16.9386	−	29.3385i	−0.590442	−	1.02268i	−0.994173	−	0.107797i	$-0.965620\pi$
$823$	−16.9386	−	29.3385i	−0.590442	−	1.02268i	0.403731	−	0.914878i	$-0.367713\pi$
$824$	−18.3679	+	3.50774i	−0.639878	+	0.122198i
$825$		0			0
$826$	7.72152	−	5.13092i	0.268666	−	0.178527i
$827$			1.10220i			0.0383272i	0.999816	+	0.0191636i	$0.00610034\pi$
$827$			1.10220i			0.0383272i	−0.999816	+	0.0191636i	$0.993900\pi$
$828$		0			0
$829$	−17.1870	−	9.92292i	−0.596929	−	0.344637i	0.170903	−	0.985288i	$-0.445331\pi$
$829$	−17.1870	−	9.92292i	−0.596929	−	0.344637i	−0.767833	+	0.640650i	$0.778665\pi$
$830$	−1.52101	+	3.06457i	−0.0527949	+	0.106373i
$831$		0			0
$832$	26.9684	−	10.2324i	0.934963	−	0.354746i
$833$	17.1810			0.595286
$834$		0			0
$835$	30.0877	+	17.3712i	1.04123	+	0.601154i
$836$	17.0221	+	22.4195i	0.588721	+	0.775393i
$837$		0			0
$838$	−24.2741	+	16.1300i	−0.838533	+	0.557202i
$839$	8.38043	+	14.5153i	0.289325	+	0.501125i	0.973649	−	0.228053i	$-0.0732359\pi$
$839$	8.38043	+	14.5153i	0.289325	+	0.501125i	−0.684324	+	0.729178i	$0.739903\pi$
$840$		0			0
$841$	−12.9175	−	22.3737i	−0.445430	−	0.771508i
$842$	−2.71339	−	1.34671i	−0.0935097	−	0.0464107i
$843$		0			0
$844$	5.30493	+	41.9471i	0.182603	+	1.44388i
$845$	−0.997279	+	33.7838i	−0.0343074	+	1.16220i
$846$		0			0
$847$	−0.979528	+	1.69659i	−0.0336570	+	0.0582956i
$848$	−23.1850	−	6.46660i	−0.796177	−	0.222064i
$849$		0			0
$850$	−6.42686	+	0.404781i	−0.220439	+	0.0138839i
$851$	−51.9663	+	30.0027i	−1.78138	+	1.02848i
$852$		0			0
$853$		−	12.5392i		−	0.429333i	−0.976687	−	0.214666i	$-0.931134\pi$
$853$		−	12.5392i		−	0.429333i	0.976687	−	0.214666i	$-0.0688664\pi$
$854$	1.51156	−	1.00442i	0.0517245	−	0.0343707i
$855$		0			0
$856$	27.3787	+	9.52804i	0.935786	+	0.325662i
$857$	−34.8182			−1.18937			−0.594684	−	0.803960i	$-0.702723\pi$
$857$	−34.8182			−1.18937			−0.594684	+	0.803960i	$0.702723\pi$
$858$		0			0
$859$			33.1090i			1.12966i	0.825206	+	0.564832i	$0.191059\pi$
$859$			33.1090i			1.12966i	−0.825206	+	0.564832i	$0.808941\pi$
$860$	19.6374	−	46.7332i	0.669628	−	1.59359i
$861$		0			0
$862$	−8.96689	−	13.4943i	−0.305413	−	0.459616i
$863$	48.3902			1.64722			0.823611	−	0.567155i	$-0.191956\pi$
$863$	48.3902			1.64722			0.823611	+	0.567155i	$0.191956\pi$
$864$		0			0
$865$	−8.50735	−	14.7352i	−0.289259	−	0.501011i
$866$	−23.0023	+	1.44875i	−0.781650	+	0.0492305i
$867$		0			0
$868$	−2.37278	+	5.64675i	−0.0805373	+	0.191663i
$869$	−18.8902	−	10.9062i	−0.640805	−	0.369969i
$870$		0			0
$871$	−12.1201	−	7.23804i	−0.410673	−	0.245252i
$872$	−5.74025	−	30.0583i	−0.194389	−	1.01790i
$873$		0			0
$874$	−37.7249	−	18.7236i	−1.27606	−	0.633336i
$875$	4.38641	−	2.53249i	0.148288	−	0.0856139i
$876$		0			0
$877$	−36.8042	+	21.2489i	−1.24279	+	0.717524i	−0.969661	−	0.244454i	$-0.921391\pi$
$877$	−36.8042	+	21.2489i	−1.24279	+	0.717524i	−0.273127	+	0.961978i	$0.588058\pi$
$878$	2.10157	+	3.16265i	0.0709245	+	0.106734i
$879$		0			0
$880$	−20.2503	−	20.6677i	−0.682636	−	0.696707i
$881$	−0.254151	+	0.440202i	−0.00856257	+	0.0148308i	−0.870275	−	0.492566i	$-0.836059\pi$
$881$	−0.254151	+	0.440202i	−0.00856257	+	0.0148308i	0.861712	+	0.507397i	$0.169392\pi$
$882$		0			0
$883$		−	47.2885i		−	1.59139i	−0.605700	−	0.795693i	$-0.707107\pi$
$883$		−	47.2885i		−	1.59139i	0.605700	−	0.795693i	$-0.292893\pi$
$884$	7.48283	−	17.0969i	0.251675	−	0.575030i
$885$		0			0
$886$	−18.5808	−	9.22203i	−0.624235	−	0.309820i
$887$	−5.21481	+	9.03232i	−0.175096	+	0.303276i	−0.940195	−	0.340638i	$-0.889357\pi$
$887$	−5.21481	+	9.03232i	−0.175096	+	0.303276i	0.765098	+	0.643914i	$0.222690\pi$
$888$		0			0
$889$	−11.0752			−0.371450
$890$	−7.21431	+	4.79388i	−0.241824	+	0.160691i
$891$		0			0
$892$	−16.0201	+	2.02601i	−0.536391	+	0.0678358i
$893$	9.37295	−	5.41147i	0.313654	−	0.181088i
$894$		0			0
$895$	20.3890	−	35.3147i	0.681528	−	1.18044i
$896$	−6.15283	+	2.89887i	−0.205552	+	0.0968443i
$897$		0			0
$898$	−1.85307	+	0.116711i	−0.0618377	+	0.00389470i
$899$	7.84870	+	4.53145i	0.261769	+	0.151132i
$900$		0			0
$901$	−13.4871	+	7.78677i	−0.449320	+	0.259415i
$902$	−2.60315	−	41.3311i	−0.0866753	−	1.37618i
$903$		0			0
$904$	17.5878	+	20.3673i	0.584961	+	0.677405i
$905$	−12.1107			−0.402573
$906$		0			0
$907$	20.2878	+	11.7132i	0.673646	+	0.388930i	0.797457	−	0.603376i	$-0.206178\pi$
$907$	20.2878	+	11.7132i	0.673646	+	0.388930i	−0.123811	+	0.992306i	$0.539512\pi$
$908$	−42.2661	−	17.7603i	−1.40265	−	0.589396i
$909$		0			0
$910$	−0.383547	−	7.96048i	−0.0127145	−	0.263887i
$911$	−53.8994			−1.78577			−0.892883	−	0.450289i	$-0.851321\pi$
$911$	−53.8994			−1.78577			−0.892883	+	0.450289i	$0.851321\pi$
$912$		0			0
$913$	−1.29447	+	2.24210i	−0.0428409	+	0.0742025i
$914$	−15.3994	−	23.1745i	−0.509367	−	0.766546i
$915$		0			0
$916$	0.947310	−	0.719249i	0.0313000	−	0.0237647i
$917$	−0.414330	+	0.239214i	−0.0136824	+	0.00789953i
$918$		0			0
$919$	−21.8643	−	37.8701i	−0.721237	−	1.24922i	−0.960504	−	0.278265i	$-0.910241\pi$
$919$	−21.8643	−	37.8701i	−0.721237	−	1.24922i	0.239268	−	0.970954i	$-0.423093\pi$
$920$	40.8860	+	14.2287i	1.34797	+	0.469106i
$921$		0			0
$922$	1.04086	+	16.5261i	0.0342789	+	0.544260i
$923$	−0.810918	−	1.45367i	−0.0266917	−	0.0478482i
$924$		0			0
$925$	−15.5308	−	8.96670i	−0.510649	−	0.294823i
$926$	12.6320	−	25.4513i	0.415113	−	0.836382i
$927$		0			0
$928$	3.11315	+	9.57026i	0.102194	+	0.314159i
$929$	2.52459	+	4.37272i	0.0828291	+	0.143464i	0.904464	−	0.426550i	$-0.140271\pi$
$929$	2.52459	+	4.37272i	0.0828291	+	0.143464i	−0.821635	+	0.570014i	$0.806938\pi$
$930$		0			0
$931$			33.5820i			1.10061i
$932$	−0.114392	−	0.150664i	−0.00374704	−	0.00493515i
$933$		0			0
$934$	−48.1970	−	23.9211i	−1.57706	−	0.782724i
$935$	−18.7212			−0.612249
$936$		0			0
$937$	44.5775			1.45628			0.728141	−	0.685427i	$-0.240385\pi$
$937$	44.5775			1.45628			0.728141	+	0.685427i	$0.240385\pi$
$938$	2.98171	+	1.47988i	0.0973562	+	0.0483198i
$939$		0			0
$940$	−8.86047	+	6.72735i	−0.288997	+	0.219422i
$941$		−	58.1679i		−	1.89622i	−0.317943	−	0.948110i	$-0.602992\pi$
$941$		−	58.1679i		−	1.89622i	0.317943	−	0.948110i	$-0.397008\pi$
$942$		0			0
$943$	30.9802	+	53.6593i	1.00885	+	1.74739i
$944$	−10.8587	−	42.2444i	−0.353421	−	1.37494i
$945$		0			0
$946$	17.0536	−	34.3600i	0.554459	−	1.11714i
$947$	8.18618	+	4.72629i	0.266015	+	0.153584i	0.627075	−	0.778959i	$-0.284252\pi$
$947$	8.18618	+	4.72629i	0.266015	+	0.153584i	−0.361060	+	0.932542i	$0.617585\pi$
$948$		0			0
$949$	−53.6471	−	0.791642i	−1.74146	−	0.0256978i
$950$	−0.791186	−	12.5620i	−0.0256695	−	0.407564i
$951$		0			0
$952$	−1.44639	+	4.15618i	−0.0468777	+	0.134703i
$953$	−9.38165	−	16.2495i	−0.303901	−	0.526373i	0.673115	−	0.739538i	$-0.264956\pi$
$953$	−9.38165	−	16.2495i	−0.303901	−	0.526373i	−0.977016	+	0.213165i	$0.931623\pi$
$954$		0			0
$955$	19.5542	−	11.2897i	0.632761	−	0.365325i
$956$	−18.5880	−	24.4819i	−0.601179	−	0.791801i
$957$		0			0
$958$	7.77383	+	11.6988i	0.251161	+	0.377972i
$959$	−1.06916	+	1.85184i	−0.0345250	+	0.0597991i
$960$		0			0
$961$	−5.04906			−0.162873
$962$	43.7073	−	28.1226i	1.40918	−	0.906708i
$963$		0			0
$964$	7.78038	−	18.5158i	0.250589	−	0.596354i
$965$	3.55159	+	2.05051i	0.114330	+	0.0660083i
$966$		0			0
$967$	13.9692			0.449218			0.224609	−	0.974449i	$-0.427889\pi$
$967$	13.9692			0.449218			0.224609	+	0.974449i	$0.427889\pi$
$968$	6.02401	+	6.97602i	0.193619	+	0.224218i
$969$		0			0
$970$	2.73250	+	43.3849i	0.0877353	+	1.39301i
$971$	10.8263	−	6.25059i	0.347434	−	0.200591i	−0.316121	−	0.948719i	$-0.602380\pi$
$971$	10.8263	−	6.25059i	0.347434	−	0.200591i	0.663555	+	0.748128i	$0.269047\pi$
$972$		0			0
$973$	1.11927	+	0.646212i	0.0358822	+	0.0207166i
$974$	33.1572	−	2.08833i	1.06243	−	0.0669144i
$975$		0			0
$976$	−2.12569	−	8.26973i	−0.0680418	−	0.264707i
$977$	7.03484	−	12.1847i	0.225065	−	0.389823i	−0.731274	−	0.682084i	$-0.761074\pi$
$977$	7.03484	−	12.1847i	0.225065	−	0.389823i	0.956339	+	0.292260i	$0.0944074\pi$
$978$		0			0
$979$	−5.67646	+	3.27731i	−0.181421	+	0.104743i
$980$	−4.33104	−	34.2464i	−0.138350	−	1.09396i
$981$		0			0
$982$	36.2517	−	24.0891i	1.15684	−	0.768715i
$983$	42.4961			1.35541			0.677707	−	0.735332i	$-0.262974\pi$
$983$	42.4961			1.35541			0.677707	+	0.735332i	$0.262974\pi$
$984$		0			0
$985$	33.2422	−	57.5771i	1.05918	−	1.83456i
$986$	5.83258	+	2.89483i	0.185747	+	0.0921901i
$987$		0			0
$988$	33.4176	+	14.6260i	1.06316	+	0.465314i
$989$			57.3916i			1.82495i
$990$		0			0
$991$	4.71260	−	8.16245i	0.149701	−	0.259289i	−0.781416	−	0.624010i	$-0.785502\pi$
$991$	4.71260	−	8.16245i	0.149701	−	0.259289i	0.931117	+	0.364721i	$0.118836\pi$
$992$	21.4219	+	19.2752i	0.680145	+	0.611988i
$993$		0			0
$994$	0.217230	+	0.326909i	0.00689012	+	0.0103689i
$995$	−46.6148	+	26.9131i	−1.47779	+	0.853201i
$996$		0			0
$997$	6.28844	−	3.63063i	0.199157	−	0.114983i	−0.397105	−	0.917773i	$-0.629985\pi$
$997$	6.28844	−	3.63063i	0.199157	−	0.114983i	0.596262	+	0.802790i	$0.296652\pi$
$998$	−5.84960	−	2.90327i	−0.185166	−	0.0919014i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.be.a.685.8		24
3.2	odd	2		104.2.r.a.61.5	yes	24
8.5	even	2	inner	936.2.be.a.685.9		24
12.11	even	2		416.2.z.a.113.10		24
13.3	even	3	inner	936.2.be.a.757.9		24
24.5	odd	2		104.2.r.a.61.4	yes	24
24.11	even	2		416.2.z.a.113.3		24
39.29	odd	6		104.2.r.a.29.4	✓	24
104.29	even	6	inner	936.2.be.a.757.8		24
156.107	even	6		416.2.z.a.81.3		24
312.29	odd	6		104.2.r.a.29.5	yes	24
312.107	even	6		416.2.z.a.81.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.4	✓	24	39.29	odd	6
104.2.r.a.29.5	yes	24	312.29	odd	6
104.2.r.a.61.4	yes	24	24.5	odd	2
104.2.r.a.61.5	yes	24	3.2	odd	2
416.2.z.a.81.3		24	156.107	even	6
416.2.z.a.81.10		24	312.107	even	6
416.2.z.a.113.3		24	24.11	even	2
416.2.z.a.113.10		24	12.11	even	2
936.2.be.a.685.8		24	1.1	even	1	trivial
936.2.be.a.685.9		24	8.5	even	2	inner
936.2.be.a.757.8		24	104.29	even	6	inner
936.2.be.a.757.9		24	13.3	even	3	inner

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.628723 - 1.26677i) q^{2} +(-1.20941 - 1.59290i) q^{4} +2.59989i q^{5} +(-0.300588 - 0.520633i) q^{7} +(-2.77822 + 0.530559i) q^{8} +(3.29346 + 1.63461i) q^{10} +(2.40956 + 1.39116i) q^{11} +(3.60516 + 0.0531995i) q^{13} +(-0.848509 + 0.0534414i) q^{14} +(-1.07463 + 3.85294i) q^{16} +(1.29402 + 2.24132i) q^{17} +(-4.38088 + 2.52930i) q^{19} +(4.14135 - 3.14434i) q^{20} +(3.27722 - 2.17770i) q^{22} +(-2.94353 + 5.09835i) q^{23} -1.75942 q^{25} +(2.33404 - 4.53346i) q^{26} +(-0.465779 + 1.10847i) q^{28} +(1.54071 + 0.889530i) q^{29} +5.09421 q^{31} +(4.20514 + 3.78375i) q^{32} +(3.65282 - 0.230064i) q^{34} +(1.35359 - 0.781495i) q^{35} +(8.82719 + 5.09638i) q^{37} +(0.449684 + 7.13981i) q^{38} +(-1.37940 - 7.22306i) q^{40} +(5.26242 - 9.11477i) q^{41} +(8.44267 - 4.87438i) q^{43} +(-0.698182 - 5.52066i) q^{44} +(4.60777 + 6.93423i) q^{46} -2.13951 q^{47} +(3.31929 - 5.74919i) q^{49} +(-1.10619 + 2.22879i) q^{50} +(-4.27539 - 5.80698i) q^{52} +6.01748i q^{53} +(-3.61686 + 6.26458i) q^{55} +(1.11133 + 1.28695i) q^{56} +(2.09551 - 1.39246i) q^{58} +(-9.44349 + 5.45220i) q^{59} +(-1.84865 + 1.06732i) q^{61} +(3.20285 - 6.45319i) q^{62} +(7.43701 - 2.94802i) q^{64} +(-0.138313 + 9.37301i) q^{65} +(-3.39076 - 1.95766i) q^{67} +(2.00517 - 4.77193i) q^{68} +(-0.138942 - 2.20603i) q^{70} +(-0.230832 - 0.399814i) q^{71} -14.8806 q^{73} +(12.0058 - 7.97781i) q^{74} +(9.32722 + 3.91932i) q^{76} -1.67266i q^{77} -7.83968 q^{79} +(-10.0172 - 2.79393i) q^{80} +(-8.23772 - 12.3969i) q^{82} +0.930501i q^{83} +(-5.82717 + 3.36432i) q^{85} +(-0.866614 - 13.7596i) q^{86} +(-7.43237 - 2.58653i) q^{88} +(-1.17791 + 2.04019i) q^{89} +(-1.05597 - 1.89296i) q^{91} +(11.6811 - 1.47727i) q^{92} +(-1.34516 + 2.71027i) q^{94} +(-6.57591 - 11.3898i) q^{95} +(5.91151 + 10.2390i) q^{97} +(-5.19598 - 7.81943i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) \) 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

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