LMFDB - Embedded newform 416.2.z.a.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(81,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("416.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.z (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.32177672409$
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			113.3
Character	$\chi$	$=$	416.113
Dual form			416.2.z.a.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.47584 - 0.852079i) q^{3} +2.59989i q^{5} +(0.300588 + 0.520633i) q^{7} +(-0.0479214 - 0.0830022i) q^{9} +(-2.40956 - 1.39116i) q^{11} +(-3.60516 - 0.0531995i) q^{13} +(2.21531 - 3.83703i) q^{15} +(-1.29402 - 2.24132i) q^{17} +(-4.38088 + 2.52930i) q^{19} -1.02450i q^{21} +(-2.94353 + 5.09835i) q^{23} -1.75942 q^{25} +5.27581i q^{27} +(1.54071 + 0.889530i) q^{29} -5.09421 q^{31} +(2.37076 + 4.10627i) q^{33} +(-1.35359 + 0.781495i) q^{35} +(-8.82719 - 5.09638i) q^{37} +(5.27532 + 3.15040i) q^{39} +(-5.26242 + 9.11477i) q^{41} +(8.44267 - 4.87438i) q^{43} +(0.215797 - 0.124590i) q^{45} -2.13951 q^{47} +(3.31929 - 5.74919i) q^{49} +4.41045i q^{51} +6.01748i q^{53} +(3.61686 - 6.26458i) q^{55} +8.62067 q^{57} +(9.44349 - 5.45220i) q^{59} +(1.84865 - 1.06732i) q^{61} +(0.0288091 - 0.0498989i) q^{63} +(0.138313 - 9.37301i) q^{65} +(-3.39076 - 1.95766i) q^{67} +(8.68840 - 5.01625i) q^{69} +(-0.230832 - 0.399814i) q^{71} -14.8806 q^{73} +(2.59664 + 1.49917i) q^{75} -1.67266i q^{77} +7.83968 q^{79} +(4.35164 - 7.53727i) q^{81} -0.930501i q^{83} +(5.82717 - 3.36432i) q^{85} +(-1.51590 - 2.62562i) q^{87} +(1.17791 - 2.04019i) q^{89} +(-1.05597 - 1.89296i) q^{91} +(7.51826 + 4.34067i) q^{93} +(-6.57591 - 11.3898i) q^{95} +(5.91151 + 10.2390i) q^{97} +0.266665i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{7} + 6 q^{9} - 4 q^{15} + 14 q^{23} - 12 q^{25} + 8 q^{31} - 14 q^{33} + 34 q^{39} - 4 q^{41} + 8 q^{47} + 6 q^{49} - 8 q^{55} - 52 q^{57} - 32 q^{63} + 30 q^{65} - 30 q^{71} - 12 q^{73} + 48 q^{79}+ \cdots + 2 q^{97}+O(q^{100}) $ 24 * q + 2 * q^7 + 6 * q^9 - 4 * q^15 + 14 * q^23 - 12 * q^25 + 8 * q^31 - 14 * q^33 + 34 * q^39 - 4 * q^41 + 8 * q^47 + 6 * q^49 - 8 * q^55 - 52 * q^57 - 32 * q^63 + 30 * q^65 - 30 * q^71 - 12 * q^73 + 48 * q^79 + 8 * q^81 + 26 * q^87 - 22 * q^89 - 60 * q^95 + 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.47584	−	0.852079i	−0.852079	−	0.491948i	0.00927251	−	0.999957i	$-0.497048\pi$
$3$	−1.47584	−	0.852079i	−0.852079	−	0.491948i	−0.861352	+	0.508009i	$0.830382\pi$
$4$		0			0
$5$			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	0.917224	−	0.398372i	$-0.130425\pi$
$7$	0.300588	+	0.520633i	0.113611	+	0.196781i	−0.803612	+	0.595153i	$0.797091\pi$
$8$		0			0
$9$	−0.0479214	−	0.0830022i	−0.0159738	−	0.0276674i
$10$		0			0
$11$	−2.40956	−	1.39116i	−0.726509	−	0.419450i	0.0906348	−	0.995884i	$-0.471110\pi$
$11$	−2.40956	−	1.39116i	−0.726509	−	0.419450i	−0.817144	+	0.576434i	$0.804444\pi$
$12$		0			0
$13$	−3.60516	−	0.0531995i	−0.999891	−	0.0147549i
$13$	−3.60516	−	0.0531995i	−0.999891	−	0.0147549i
$14$		0			0
$15$	2.21531	−	3.83703i	0.571991	−	0.990718i
$16$		0			0
$17$	−1.29402	−	2.24132i	−0.313847	−	0.543599i	0.665345	−	0.746536i	$-0.268285\pi$
$17$	−1.29402	−	2.24132i	−0.313847	−	0.543599i	−0.979192	+	0.202937i	$0.934951\pi$
$18$		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	$0.530383\pi$
$20$		0			0
$21$		−	1.02450i		−	0.223564i
$22$		0			0
$23$	−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
$26$		0			0
$27$			5.27581i			1.01533i
$28$		0			0
$29$	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	$-0.651245\pi$
$31$	−5.09421			−0.914947			−0.457473	+	0.889223i	$0.651245\pi$
$32$		0			0
$33$	2.37076	+	4.10627i	0.412696	+	0.714810i
$34$		0			0
$35$	−1.35359	+	0.781495i	−0.228798	+	0.132097i
$36$		0			0
$37$	−8.82719	−	5.09638i	−1.45118	−	0.837840i	−0.452633	−	0.891697i	$-0.649515\pi$
$37$	−8.82719	−	5.09638i	−1.45118	−	0.837840i	−0.998549	+	0.0538570i	$0.982848\pi$
$38$		0			0
$39$	5.27532	+	3.15040i	0.844728	+	0.504467i
$40$		0			0
$41$	−5.26242	+	9.11477i	−0.821851	+	1.42349i	0.0824509	+	0.996595i	$0.473725\pi$
$41$	−5.26242	+	9.11477i	−0.821851	+	1.42349i	−0.904302	+	0.426893i	$0.859608\pi$
$42$		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			0
$45$	0.215797	−	0.124590i	0.0321691	−	0.0185728i
$46$		0			0
$47$	−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
$50$		0			0
$51$			4.41045i			0.617586i
$52$		0			0
$53$			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
$56$		0			0
$57$	8.62067			1.14184
$58$		0			0
$59$	9.44349	−	5.45220i	1.22944	−	0.709816i	0.262526	−	0.964925i	$-0.415445\pi$
$59$	9.44349	−	5.45220i	1.22944	−	0.709816i	0.966912	+	0.255109i	$0.0821112\pi$
$60$		0			0
$61$	1.84865	−	1.06732i	0.236696	−	0.136656i	−0.376961	−	0.926229i	$-0.623031\pi$
$61$	1.84865	−	1.06732i	0.236696	−	0.136656i	0.613657	+	0.789573i	$0.289698\pi$
$62$		0			0
$63$	0.0288091	−	0.0498989i	0.00362961	−	0.00628667i
$64$		0			0
$65$	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	$0.743541\pi$
$68$		0			0
$69$	8.68840	−	5.01625i	1.04596	−	0.603885i
$70$		0			0
$71$	−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	$0.836414\pi$
$74$		0			0
$75$	2.59664	+	1.49917i	0.299834	+	0.173109i
$76$		0			0
$77$		−	1.67266i		−	0.190617i
$78$		0			0
$79$	7.83968			0.882033			0.441017	−	0.897499i	$-0.354618\pi$
$79$	7.83968			0.882033			0.441017	+	0.897499i	$0.354618\pi$
$80$		0			0
$81$	4.35164	−	7.53727i	0.483516	−	0.837474i
$82$		0			0
$83$		−	0.930501i		−	0.102136i	−0.998695	−	0.0510679i	$-0.983738\pi$
$83$		−	0.930501i		−	0.102136i	0.998695	−	0.0510679i	$-0.0162625\pi$
$84$		0			0
$85$	5.82717	−	3.36432i	0.632046	−	0.364912i
$86$		0			0
$87$	−1.51590	−	2.62562i	−0.162522	−	0.281496i
$88$		0			0
$89$	1.17791	−	2.04019i	0.124858	−	0.216260i	−0.796820	−	0.604217i	$-0.793486\pi$
$89$	1.17791	−	2.04019i	0.124858	−	0.216260i	0.921677	+	0.387957i	$0.126819\pi$
$90$		0			0
$91$	−1.05597	−	1.89296i	−0.110696	−	0.198436i
$92$		0			0
$93$	7.51826	+	4.34067i	0.779607	+	0.450106i
$94$		0			0
$95$	−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	$0.628412\pi$
$98$		0			0
$99$			0.266665i			0.0268008i
$100$		0			0
$101$	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	$-0.605607\pi$
$103$	−6.61141			−0.651441			−0.325721	+	0.945466i	$0.605607\pi$
$104$		0			0
$105$	2.66358			0.259939
$106$		0			0
$107$	8.87612	+	5.12463i	0.858087	+	0.495417i	0.863371	−	0.504569i	$-0.168349\pi$
$107$	8.87612	+	5.12463i	0.858087	+	0.495417i	−0.00528438	+	0.999986i	$0.501682\pi$
$108$		0			0
$109$		−	10.8192i		−	1.03630i	−0.855291	−	0.518148i	$-0.826622\pi$
$109$		−	10.8192i		−	1.03630i	0.855291	−	0.518148i	$-0.173378\pi$
$110$		0			0
$111$	8.68504	+	15.0429i	0.824348	+	1.42781i
$112$		0			0
$113$	4.75708	+	8.23951i	0.447509	+	0.775108i	0.998223	−	0.0595859i	$-0.0189780\pi$
$113$	4.75708	+	8.23951i	0.447509	+	0.775108i	−0.550714	+	0.834694i	$0.685645\pi$
$114$		0			0
$115$	−13.2551	−	7.65286i	−1.23605	−	0.713633i
$116$		0			0
$117$	0.168348	+	0.301786i	0.0155638	+	0.0279001i
$118$		0			0
$119$	0.777936	−	1.34742i	0.0713133	−	0.123518i
$120$		0			0
$121$	−1.62936	−	2.82213i	−0.148123	−	0.256557i
$122$		0			0
$123$	15.5330	−	8.96799i	1.40057	−	0.808617i
$124$		0			0
$125$			8.42514i			0.753567i
$126$		0			0
$127$	−9.21128	+	15.9544i	−0.817369	+	1.41572i	0.0902451	+	0.995920i	$0.471235\pi$
$127$	−9.21128	+	15.9544i	−0.817369	+	1.41572i	−0.907614	+	0.419805i	$0.862098\pi$
$128$		0			0
$129$	−16.6134			−1.46273
$130$		0			0
$131$			0.795820i			0.0695311i	0.999395	+	0.0347655i	$0.0110684\pi$
$131$			0.795820i			0.0695311i	−0.999395	+	0.0347655i	$0.988932\pi$
$132$		0			0
$133$	−2.63368	−	1.52056i	−0.228369	−	0.131849i
$134$		0			0
$135$	−13.7165			−1.18053
$136$		0			0
$137$	1.77845	+	3.08037i	0.151943	+	0.263174i	0.931942	−	0.362608i	$-0.118114\pi$
$137$	1.77845	+	3.08037i	0.151943	+	0.263174i	−0.779998	+	0.625781i	$0.784780\pi$
$138$		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	$0.362395\pi$
$140$		0			0
$141$	3.15759	+	1.82303i	0.265917	+	0.153527i
$142$		0			0
$143$	8.61283	+	5.14353i	0.720241	+	0.430124i
$144$		0			0
$145$	−2.31268	+	4.00568i	−0.192058	+	0.332653i
$146$		0			0
$147$	−9.79753	+	5.65660i	−0.808086	+	0.466549i
$148$		0			0
$149$	−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	$-0.412593\pi$
$151$	6.66412			0.542318			0.271159	+	0.962535i	$0.412593\pi$
$152$		0			0
$153$	−0.124023	+	0.214814i	−0.0100267	+	0.0173667i
$154$		0			0
$155$		−	13.2444i		−	1.06381i
$156$		0			0
$157$			1.24154i			0.0990854i	0.998772	+	0.0495427i	$0.0157764\pi$
$157$			1.24154i			0.0990854i	−0.998772	+	0.0495427i	$0.984224\pi$
$158$		0			0
$159$	5.12737	−	8.88087i	0.406627	−	0.704299i
$160$		0			0
$161$	−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	$0.473623\pi$
$164$		0			0
$165$	−10.6758	+	6.16370i	−0.831113	+	0.479843i
$166$		0			0
$167$	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			0
$171$	0.419876	+	0.242415i	0.0321087	+	0.0185380i
$172$		0			0
$173$	−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
$176$		0			0
$177$	−18.5828			−1.39677
$178$		0			0
$179$	13.5832	+	7.84225i	1.01525	+	0.586157i	0.912726	−	0.408573i	$-0.133973\pi$
$179$	13.5832	+	7.84225i	1.01525	+	0.586157i	0.102528	+	0.994730i	$0.467307\pi$
$180$		0			0
$181$		−	4.65816i		−	0.346238i	−0.984901	−	0.173119i	$-0.944615\pi$
$181$		−	4.65816i		−	0.346238i	0.984901	−	0.173119i	$-0.0553846\pi$
$182$		0			0
$183$	−3.63776			−0.268911
$184$		0			0
$185$	13.2500	−	22.9497i	0.974162	−	1.68730i
$186$		0			0
$187$			7.20077i			0.526573i
$188$		0			0
$189$	−2.74676	+	1.58584i	−0.199797	+	0.115353i
$190$		0			0
$191$	−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	$0.148586\pi$
$194$		0			0
$195$	−8.19068	+	13.7153i	−0.586547	+	0.982170i
$196$		0			0
$197$	−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	$-0.904408\pi$
$199$	−10.3516	−	17.9295i	−0.733807	−	1.27099i	0.221438	−	0.975174i	$-0.428925\pi$
$200$		0			0
$201$	3.33616	+	5.77839i	0.235314	+	0.407576i
$202$		0			0
$203$			1.06953i			0.0750661i
$204$		0			0
$205$	−23.6974	−	13.6817i	−1.65510	−	0.955571i
$206$		0			0
$207$	0.564233			0.0392169
$208$		0			0
$209$	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	$0.926073\pi$
$212$		0			0
$213$			0.786750i			0.0539072i
$214$		0			0
$215$	12.6728	+	21.9500i	0.864281	+	1.49698i
$216$		0			0
$217$	−1.53126	−	2.65221i	−0.103948	−	0.180044i
$218$		0			0
$219$	21.9615	+	12.6795i	1.48402	+	0.856800i
$220$		0			0
$221$	4.54593	+	8.14914i	0.305792	+	0.548171i
$222$		0			0
$223$	−4.03692	+	6.99214i	−0.270332	+	0.468229i	−0.968947	−	0.247269i	$-0.920467\pi$
$223$	−4.03692	+	6.99214i	−0.270332	+	0.468229i	0.698615	+	0.715498i	$0.253800\pi$
$224$		0			0
$225$	0.0843141	+	0.146036i	0.00562094	+	0.00973575i
$226$		0			0
$227$	−19.8519	+	11.4615i	−1.31761	+	0.760725i	−0.983344	−	0.181752i	$-0.941823\pi$
$227$	−19.8519	+	11.4615i	−1.31761	+	0.760725i	−0.334270	+	0.942477i	$0.608490\pi$
$228$		0			0
$229$		−	0.594709i		−	0.0392995i	−0.999807	−	0.0196497i	$-0.993745\pi$
$229$		−	0.594709i		−	0.0392995i	0.999807	−	0.0196497i	$-0.00625511\pi$
$230$		0			0
$231$	−1.42524	+	2.46859i	−0.0937739	+	0.162421i
$232$		0			0
$233$	−0.0945847			−0.00619645			−0.00309823	−	0.999995i	$-0.500986\pi$
$233$	−0.0945847			−0.00619645			−0.00309823	+	0.999995i	$0.500986\pi$
$234$		0			0
$235$		−	5.56249i		−	0.362857i
$236$		0			0
$237$	−11.5702	−	6.68003i	−0.751562	−	0.433915i
$238$		0			0
$239$	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	$0.728497\pi$
$242$		0			0
$243$	0.862251	−	0.497821i	0.0553134	−	0.0319352i
$244$		0			0
$245$	14.9472	+	8.62980i	0.954945	+	0.551338i
$246$		0			0
$247$	15.9283	−	8.88548i	1.01350	−	0.565370i
$248$		0			0
$249$	−0.792861	+	1.37328i	−0.0502455	+	0.0870278i
$250$		0			0
$251$	−14.8114	+	8.55135i	−0.934886	+	0.539757i	−0.888353	−	0.459160i	$-0.848150\pi$
$251$	−14.8114	+	8.55135i	−0.934886	+	0.539757i	−0.0465324	+	0.998917i	$0.514817\pi$
$252$		0			0
$253$	14.1852	−	8.18984i	0.891818	−	0.514891i
$254$		0			0
$255$	−11.4667			−0.718071
$256$		0			0
$257$	−10.3500	+	17.9267i	−0.645616	+	1.11824i	0.338543	+	0.940951i	$0.390066\pi$
$257$	−10.3500	+	17.9267i	−0.645616	+	1.11824i	−0.984159	+	0.177288i	$0.943267\pi$
$258$		0			0
$259$		−	6.12764i		−	0.380753i
$260$		0			0
$261$		−	0.170510i		−	0.0105543i
$262$		0			0
$263$	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
$266$		0			0
$267$	−3.47681	+	2.00734i	−0.212777	+	0.122847i
$268$		0			0
$269$	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	−0.995562	−	0.0941065i	$-0.970001\pi$
$271$	−6.85287	+	11.8695i	−0.416282	+	0.721022i	0.579280	+	0.815129i	$0.303334\pi$
$272$		0			0
$273$	−0.0545028	+	3.69348i	−0.00329866	+	0.223540i
$274$		0			0
$275$	4.23944	+	2.44764i	0.255648	+	0.147598i
$276$		0			0
$277$	−24.4764	+	14.1314i	−1.47064	+	0.849076i	−0.999457	−	0.0329570i	$-0.989508\pi$
$277$	−24.4764	+	14.1314i	−1.47064	+	0.849076i	−0.471187	+	0.882033i	$0.656174\pi$
$278$		0			0
$279$	0.244121	+	0.422831i	0.0146152	+	0.0253142i
$280$		0			0
$281$	−12.3330			−0.735724			−0.367862	−	0.929880i	$-0.619910\pi$
$281$	−12.3330			−0.735724			−0.367862	+	0.929880i	$0.619910\pi$
$282$		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			0
$285$			22.4128i			1.32762i
$286$		0			0
$287$	−6.32727			−0.373487
$288$		0			0
$289$	5.15100	−	8.92179i	0.303000	−	0.524811i
$290$		0			0
$291$		−	20.1483i		−	1.18111i
$292$		0			0
$293$	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
$296$		0			0
$297$	7.33949	−	12.7124i	0.425880	−	0.737646i
$298$		0			0
$299$	10.8831	−	18.2238i	0.629388	−	1.05391i
$300$		0			0
$301$	5.07552	+	2.93036i	0.292548	+	0.168903i
$302$		0			0
$303$	−11.0369	−	19.1165i	−0.634054	−	1.09821i
$304$		0			0
$305$	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	$0.953602\pi$
$308$		0			0
$309$	9.75741	+	5.63344i	0.555080	+	0.320475i
$310$		0			0
$311$	−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	$0.385405\pi$
$314$		0			0
$315$	0.129732	+	0.0749006i	0.00730955	+	0.00422017i
$316$		0			0
$317$			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
$320$		0			0
$321$	−8.73318	−	15.1263i	−0.487439	−	0.844269i
$322$		0			0
$323$	11.3379	+	6.54597i	0.630860	+	0.364227i
$324$		0			0
$325$	6.34301	+	0.0936005i	0.351847	+	0.00519202i
$326$		0			0
$327$	−9.21886	+	15.9675i	−0.509804	+	0.883006i
$328$		0			0
$329$	−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	$0.182393\pi$
$332$		0			0
$333$			0.976902i			0.0535339i
$334$		0			0
$335$	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	$0.597392\pi$
$338$		0			0
$339$		−	16.2136i		−	0.880605i
$340$		0			0
$341$	12.2748	+	7.08685i	0.664717	+	0.383774i
$342$		0			0
$343$	8.19918			0.442714
$344$		0			0
$345$	13.0417	+	22.5889i	0.702141	+	1.21614i
$346$		0			0
$347$	1.92350	−	1.11054i	0.103259	−	0.0596167i	−0.447481	−	0.894293i	$-0.647679\pi$
$347$	1.92350	−	1.11054i	0.103259	−	0.0596167i	0.550740	+	0.834677i	$0.314345\pi$
$348$		0			0
$349$	11.6899	+	6.74919i	0.625748	+	0.361276i	0.779104	−	0.626895i	$-0.215675\pi$
$349$	11.6899	+	6.74919i	0.625748	+	0.361276i	−0.153355	+	0.988171i	$0.549008\pi$
$350$		0			0
$351$	0.280670	−	19.0201i	0.0149811	−	1.01522i
$352$		0			0
$353$	−1.75509	+	3.03991i	−0.0934143	+	0.161798i	−0.908946	−	0.416915i	$-0.863111\pi$
$353$	−1.75509	+	3.03991i	−0.0934143	+	0.161798i	0.815531	+	0.578713i	$0.196445\pi$
$354$		0			0
$355$	1.03947	−	0.600139i	0.0551694	−	0.0318521i
$356$		0			0
$357$	−2.29622	+	1.32573i	−0.121529	+	0.0701649i
$358$		0			0
$359$	−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
$362$		0			0
$363$			5.55336i			0.291476i
$364$		0			0
$365$		−	38.6880i		−	2.02502i
$366$		0			0
$367$	10.2910	−	17.8245i	0.537186	−	0.930434i	−0.461868	−	0.886949i	$-0.652821\pi$
$367$	10.2910	−	17.8245i	0.537186	−	0.930434i	0.999054	−	0.0434851i	$-0.0138461\pi$
$368$		0			0
$369$	1.00873			0.0525123
$370$		0			0
$371$	−3.13290	+	1.80878i	−0.162652	+	0.0939072i
$372$		0			0
$373$	12.3015	−	7.10225i	0.636946	−	0.367741i	−0.146491	−	0.989212i	$-0.546798\pi$
$373$	12.3015	−	7.10225i	0.636946	−	0.367741i	0.783437	+	0.621471i	$0.213465\pi$
$374$		0			0
$375$	7.17889	−	12.4342i	0.370716	−	0.642099i
$376$		0			0
$377$	−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	$0.607452\pi$
$380$		0			0
$381$	27.1888	−	15.6975i	1.39293	−	0.804207i
$382$		0			0
$383$	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
$386$		0			0
$387$	−0.809168	−	0.467174i	−0.0411323	−	0.0237478i
$388$		0			0
$389$		−	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
$392$		0			0
$393$	0.678101	−	1.17451i	0.0342057	−	0.0592460i
$394$		0			0
$395$			20.3823i			1.02554i
$396$		0			0
$397$	−25.6669	+	14.8188i	−1.28819	+	0.743734i	−0.978330	−	0.207050i	$-0.933614\pi$
$397$	−25.6669	+	14.8188i	−1.28819	+	0.743734i	−0.309855	+	0.950784i	$0.600280\pi$
$398$		0			0
$399$	2.59127	+	4.48821i	0.129726	+	0.224691i
$400$		0			0
$401$	5.32482	−	9.22286i	0.265909	−	0.460568i	−0.701892	−	0.712283i	$-0.747661\pi$
$401$	5.32482	−	9.22286i	0.265909	−	0.460568i	0.967801	+	0.251715i	$0.0809946\pi$
$402$		0			0
$403$	18.3654	+	0.271009i	0.914847	+	0.0134999i
$404$		0			0
$405$	19.5961	+	11.3138i	0.973736	+	0.562187i
$406$		0			0
$407$	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	$0.837605\pi$
$410$		0			0
$411$		−	6.06153i		−	0.298993i
$412$		0			0
$413$	5.67720	+	3.27773i	0.279357	+	0.161287i
$414$		0			0
$415$	2.41920			0.118754
$416$		0			0
$417$	3.66365			0.179410
$418$		0			0
$419$	17.8473	+	10.3042i	0.871900	+	0.503392i	0.867979	−	0.496601i	$-0.165419\pi$
$419$	17.8473	+	10.3042i	0.871900	+	0.503392i	0.00392074	+	0.999992i	$0.498752\pi$
$420$		0			0
$421$			2.14198i			0.104394i	0.998637	+	0.0521968i	$0.0166223\pi$
$421$			2.14198i			0.104394i	−0.998637	+	0.0521968i	$0.983378\pi$
$422$		0			0
$423$	0.102528	+	0.177584i	0.00498510	+	0.00863444i
$424$		0			0
$425$	2.27674	+	3.94343i	0.110438	+	0.191284i
$426$		0			0
$427$	1.11136	+	0.641646i	0.0537827	+	0.0310514i
$428$		0			0
$429$	−8.32850	−	14.9299i	−0.402104	−	0.720821i
$430$		0			0
$431$	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	$0.961411\pi$
$434$		0			0
$435$	6.82631	−	3.94117i	0.327297	−	0.188965i
$436$		0			0
$437$		−	29.7804i		−	1.42459i
$438$		0			0
$439$	1.34252	−	2.32532i	0.0640751	−	0.110981i	−0.832208	−	0.554463i	$-0.812924\pi$
$439$	1.34252	−	2.32532i	0.0640751	−	0.110981i	0.896283	+	0.443482i	$0.146257\pi$
$440$		0			0
$441$	−0.636260			−0.0302981
$442$		0			0
$443$			14.6679i			0.696891i	0.937329	+	0.348446i	$0.113290\pi$
$443$			14.6679i			0.696891i	−0.937329	+	0.348446i	$0.886710\pi$
$444$		0			0
$445$	5.30428	+	3.06242i	0.251447	+	0.145173i
$446$		0			0
$447$	5.66237			0.267821
$448$		0			0
$449$	0.656457	+	1.13702i	0.0309801	+	0.0536591i	0.881100	−	0.472930i	$-0.156804\pi$
$449$	0.656457	+	1.13702i	0.0309801	+	0.0536591i	−0.850120	+	0.526590i	$0.823470\pi$
$450$		0			0
$451$	25.3602	−	14.6417i	1.19416	−	0.689451i
$452$		0			0
$453$	−9.83521	−	5.67836i	−0.462098	−	0.266793i
$454$		0			0
$455$	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			0
$459$	11.8248	−	6.82703i	0.551932	−	0.318658i
$460$		0			0
$461$	−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	$-0.654617\pi$
$463$	−20.0915			−0.933731			−0.466866	+	0.884328i	$0.654617\pi$
$464$		0			0
$465$	−11.2853	+	19.5466i	−0.523341	+	0.906454i
$466$		0			0
$467$			38.0472i			1.76061i	0.474405	+	0.880307i	$0.342663\pi$
$467$			38.0472i			1.76061i	−0.474405	+	0.880307i	$0.657337\pi$
$468$		0			0
$469$		−	2.35379i		−	0.108688i
$470$		0			0
$471$	1.05789	−	1.83231i	0.0487449	−	0.0844286i
$472$		0			0
$473$	−27.1241			−1.24717
$474$		0			0
$475$	7.70784	−	4.45012i	0.353660	−	0.204186i
$476$		0			0
$477$	0.499465	−	0.288366i	0.0228689	−	0.0132034i
$478$		0			0
$479$	−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
$482$		0			0
$483$	5.22325	+	3.01565i	0.237666	+	0.137217i
$484$		0			0
$485$	−26.6204	+	15.3693i	−1.20877	+	0.697883i
$486$		0			0
$487$	−11.7461	−	20.3448i	−0.532265	−	0.921910i	−0.999290	−	0.0376664i	$-0.988008\pi$
$487$	−11.7461	−	20.3448i	−0.532265	−	0.921910i	0.467025	−	0.884244i	$-0.345326\pi$
$488$		0			0
$489$	18.5634			0.839468
$490$		0			0
$491$	−26.6538	−	15.3886i	−1.20287	−	0.694478i	−0.241679	−	0.970356i	$-0.577698\pi$
$491$	−26.6538	−	15.3886i	−1.20287	−	0.694478i	−0.961193	+	0.275878i	$0.911031\pi$
$492$		0			0
$493$		−	4.60429i		−	0.207367i
$494$		0			0
$495$	−0.693299			−0.0311615
$496$		0			0
$497$	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	$-0.0329590\pi$
$500$		0			0
$501$	−19.7217	+	11.3863i	−0.881101	+	0.508704i
$502$		0			0
$503$	−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
$506$		0			0
$507$	−18.8508	−	11.6383i	−0.837193	−	0.516876i
$508$		0			0
$509$	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
$512$		0			0
$513$	−13.3441	−	23.1127i	−0.589158	−	1.02045i
$514$		0			0
$515$		−	17.1889i		−	0.757435i
$516$		0			0
$517$	5.15527	+	2.97640i	0.226729	+	0.130902i
$518$		0			0
$519$	11.1527			0.489549
$520$		0			0
$521$	−11.7037			−0.512747			−0.256374	−	0.966578i	$-0.582528\pi$
$521$	−11.7037			−0.512747			−0.256374	+	0.966578i	$0.582528\pi$
$522$		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	$0.577733\pi$
$524$		0			0
$525$			1.80253i			0.0786688i
$526$		0			0
$527$	6.59203	+	11.4177i	0.287153	+	0.497364i
$528$		0			0
$529$	−5.82878	−	10.0957i	−0.253425	−	0.438945i
$530$		0			0
$531$	−0.905090	−	0.522554i	−0.0392776	−	0.0226769i
$532$		0			0
$533$	19.4567	−	32.5802i	0.842765	−	1.41121i
$534$		0			0
$535$	−13.3235	+	23.0769i	−0.576024	+	0.997703i
$536$		0			0
$537$	−13.3644	−	23.1479i	−0.576718	−	0.998905i
$538$		0			0
$539$	−15.9961	+	9.23533i	−0.688999	+	0.397794i
$540$		0			0
$541$			40.4799i			1.74037i	0.492728	+	0.870183i	$0.336000\pi$
$541$			40.4799i			1.74037i	−0.492728	+	0.870183i	$0.664000\pi$
$542$		0			0
$543$	−3.96912	+	6.87472i	−0.170331	+	0.295023i
$544$		0			0
$545$	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	$-0.197169\pi$
$548$		0			0
$549$	−0.177180	−	0.102295i	−0.00756185	−	0.00436584i
$550$		0			0
$551$	−8.99957			−0.383394
$552$		0			0
$553$	2.35651	+	4.08160i	0.100209	+	0.173567i
$554$		0			0
$555$	−39.1100	+	22.5802i	−1.66013	+	0.958474i
$556$		0			0
$557$	−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
$560$		0			0
$561$	6.13563	−	10.6272i	0.259047	−	0.448682i
$562$		0			0
$563$	7.83182	−	4.52170i	0.330072	−	0.190567i	−0.325801	−	0.945438i	$-0.605634\pi$
$563$	7.83182	−	4.52170i	0.330072	−	0.190567i	0.655873	+	0.754871i	$0.272301\pi$
$564$		0			0
$565$	−21.4218	+	12.3679i	−0.901222	+	0.520321i
$566$		0			0
$567$	5.23220			0.219732
$568$		0			0
$569$	−18.1496	+	31.4361i	−0.760872	+	1.31787i	0.181529	+	0.983386i	$0.441895\pi$
$569$	−18.1496	+	31.4361i	−0.760872	+	1.31787i	−0.942401	+	0.334484i	$0.891438\pi$
$570$		0			0
$571$			24.9740i			1.04513i	0.852599	+	0.522566i	$0.175025\pi$
$571$			24.9740i			1.04513i	−0.852599	+	0.522566i	$0.824975\pi$
$572$		0			0
$573$			14.8001i			0.618285i
$574$		0			0
$575$	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	$0.400559\pi$
$578$		0			0
$579$	−2.32797	+	1.34406i	−0.0967473	+	0.0558571i
$580$		0			0
$581$	0.484450	−	0.279697i	0.0200984	−	0.0116038i
$582$		0			0
$583$	8.37127	−	14.4995i	0.346703	−	0.600507i
$584$		0			0
$585$	−0.784609	+	0.437687i	−0.0324396	+	0.0180961i
$586$		0			0
$587$	−33.7254	−	19.4714i	−1.39200	−	0.803669i	−0.398460	−	0.917186i	$-0.630455\pi$
$587$	−33.7254	−	19.4714i	−1.39200	−	0.803669i	−0.993536	+	0.113517i	$0.963788\pi$
$588$		0			0
$589$	22.3171	−	12.8848i	0.919561	−	0.530909i
$590$		0			0
$591$	21.7894	+	37.7403i	0.896295	+	1.55243i
$592$		0			0
$593$	19.6722			0.807842			0.403921	−	0.914794i	$-0.367647\pi$
$593$	19.6722			0.807842			0.403921	+	0.914794i	$0.367647\pi$
$594$		0			0
$595$	3.50315	+	2.02255i	0.143615	+	0.0829163i
$596$		0			0
$597$			35.2816i			1.44398i
$598$		0			0
$599$	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	$0.984028\pi$
$602$		0			0
$603$			0.375254i			0.0152815i
$604$		0			0
$605$	7.33722	−	4.23614i	0.298300	−	0.172224i
$606$		0			0
$607$	4.23231	+	7.33058i	0.171784	+	0.297539i	0.939044	−	0.343798i	$-0.111713\pi$
$607$	4.23231	+	7.33058i	0.171784	+	0.297539i	−0.767259	+	0.641337i	$0.778380\pi$
$608$		0			0
$609$	0.911322	−	1.57846i	0.0369286	−	0.0639622i
$610$		0			0
$611$	7.71327	+	0.113821i	0.312046	+	0.00460470i
$612$		0			0
$613$	−11.1194	−	6.41977i	−0.449107	−	0.259292i	0.258346	−	0.966053i	$-0.416823\pi$
$613$	−11.1194	−	6.41977i	−0.449107	−	0.259292i	−0.707453	+	0.706760i	$0.750156\pi$
$614$		0			0
$615$	23.3158	+	40.3841i	0.940183	+	1.62845i
$616$		0			0
$617$	−2.51106	−	4.34928i	−0.101091	−	0.175095i	0.811043	−	0.584986i	$-0.198900\pi$
$617$	−2.51106	−	4.34928i	−0.101091	−	0.175095i	−0.912135	+	0.409891i	$0.865567\pi$
$618$		0			0
$619$			25.2782i			1.01602i	0.861353	+	0.508008i	$0.169618\pi$
$619$			25.2782i			1.01602i	−0.861353	+	0.508008i	$0.830382\pi$
$620$		0			0
$621$	−26.8979	−	15.5295i	−1.07938	−	0.623178i
$622$		0			0
$623$	1.41626			0.0567411
$624$		0			0
$625$	−30.7015			−1.22806
$626$		0			0
$627$	−20.7720	−	11.9927i	−0.829554	−	0.478943i
$628$		0			0
$629$			26.3794i			1.05181i
$630$		0			0
$631$	−16.7070	−	28.9374i	−0.665097	−	1.15198i	−0.979259	−	0.202612i	$-0.935057\pi$
$631$	−16.7070	−	28.9374i	−0.665097	−	1.15198i	0.314163	−	0.949369i	$-0.398276\pi$
$632$		0			0
$633$	18.0135	+	31.2003i	0.715972	+	1.24010i
$634$		0			0
$635$	−41.4797	−	23.9483i	−1.64607	−	0.950360i
$636$		0			0
$637$	−12.2724	+	20.5501i	−0.486252	+	0.814226i
$638$		0			0
$639$	−0.0221236	+	0.0383192i	−0.000875197	+	0.00151589i
$640$		0			0
$641$	−5.95235	−	10.3098i	−0.235104	−	0.407212i	0.724199	−	0.689591i	$-0.242210\pi$
$641$	−5.95235	−	10.3098i	−0.235104	−	0.407212i	−0.959303	+	0.282379i	$0.908876\pi$
$642$		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	$0.567750\pi$
$644$		0			0
$645$		−	43.1931i		−	1.70073i
$646$		0			0
$647$	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
$650$		0			0
$651$			5.21901i			0.204549i
$652$		0			0
$653$	−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
$656$		0			0
$657$	0.713101	+	1.23513i	0.0278207	+	0.0481869i
$658$		0			0
$659$	24.1533	−	13.9449i	0.940880	−	0.543218i	0.0506442	−	0.998717i	$-0.483873\pi$
$659$	24.1533	−	13.9449i	0.940880	−	0.543218i	0.890236	+	0.455499i	$0.150539\pi$
$660$		0			0
$661$	17.0661	+	9.85313i	0.663795	+	0.383242i	0.793722	−	0.608281i	$-0.208141\pi$
$661$	17.0661	+	9.85313i	0.663795	+	0.383242i	−0.129926	+	0.991524i	$0.541474\pi$
$662$		0			0
$663$	0.234633	−	15.9004i	0.00911241	−	0.617519i
$664$		0			0
$665$	3.95328	−	6.84728i	0.153301	−	0.265526i
$666$		0			0
$667$	−9.07027	+	5.23672i	−0.351202	+	0.202767i
$668$		0			0
$669$	11.9157	−	6.87955i	0.460688	−	0.265979i
$670$		0			0
$671$	−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	$-0.0788094\pi$
$674$		0			0
$675$		−	9.28239i		−	0.357279i
$676$		0			0
$677$			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
$680$		0			0
$681$	39.0644			1.49695
$682$		0			0
$683$	−6.89615	+	3.98149i	−0.263874	+	0.152348i	−0.626100	−	0.779742i	$-0.715350\pi$
$683$	−6.89615	+	3.98149i	−0.263874	+	0.152348i	0.362227	+	0.932090i	$0.382017\pi$
$684$		0			0
$685$	−8.00862	+	4.62378i	−0.305994	+	0.176666i
$686$		0			0
$687$	−0.506739	+	0.877698i	−0.0193333	+	0.0334863i
$688$		0			0
$689$	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	$0.435160\pi$
$692$		0			0
$693$	−0.138835	+	0.0801562i	−0.00527389	+	0.00304488i
$694$		0			0
$695$	−2.79466	−	4.84049i	−0.106007	−	0.183610i
$696$		0			0
$697$	27.2388			1.03174
$698$		0			0
$699$	0.139592	+	0.0805937i	0.00527987	+	0.00304833i
$700$		0			0
$701$		−	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
$704$		0			0
$705$	−4.73968	+	8.20937i	−0.178507	+	0.309183i
$706$		0			0
$707$			7.78698i			0.292859i
$708$		0			0
$709$	31.1767	−	17.9999i	1.17087	−	0.676000i	0.216982	−	0.976176i	$-0.430379\pi$
$709$	31.1767	−	17.9999i	1.17087	−	0.676000i	0.953884	+	0.300176i	$0.0970454\pi$
$710$		0			0
$711$	−0.375688	−	0.650711i	−0.0140894	−	0.0244036i
$712$		0			0
$713$	14.9950	−	25.9720i	0.561566	−	0.972661i
$714$		0			0
$715$	−13.3726	+	22.3924i	−0.500108	+	0.837428i
$716$		0			0
$717$	−22.6829	−	13.0960i	−0.847108	−	0.489078i
$718$		0			0
$719$	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
$722$		0			0
$723$		−	17.1132i		−	0.636447i
$724$		0			0
$725$	−2.71076	−	1.56506i	−0.100675	−	0.0581249i
$726$		0			0
$727$	−34.3229			−1.27297			−0.636484	−	0.771290i	$-0.719612\pi$
$727$	−34.3229			−1.27297			−0.636484	+	0.771290i	$0.719612\pi$
$728$		0			0
$729$	−27.8066			−1.02987
$730$		0			0
$731$	−21.8500	−	12.6151i	−0.808153	−	0.466587i
$732$		0			0
$733$		−	6.24499i		−	0.230664i	−0.993327	−	0.115332i	$-0.963207\pi$
$733$		−	6.24499i		−	0.230664i	0.993327	−	0.115332i	$-0.0367932\pi$
$734$		0			0
$735$	−14.7065	−	25.4725i	−0.542459	−	0.939567i
$736$		0			0
$737$	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	$0.631019\pi$
$740$		0			0
$741$	−31.0789	−	0.458615i	−1.14171	−	0.0168476i
$742$		0			0
$743$	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
$746$		0			0
$747$	−0.0772337	+	0.0445909i	−0.00282583	+	0.00163150i
$748$		0			0
$749$			6.16160i			0.225140i
$750$		0			0
$751$	10.9266	−	18.9254i	0.398717	−	0.690599i	−0.594851	−	0.803836i	$-0.702789\pi$
$751$	10.9266	−	18.9254i	0.398717	−	0.690599i	0.993568	+	0.113238i	$0.0361221\pi$
$752$		0			0
$753$	29.1457			1.06213
$754$		0			0
$755$			17.3260i			0.630557i
$756$		0			0
$757$	18.5854	+	10.7303i	0.675498	+	0.389999i	0.798157	−	0.602450i	$-0.205809\pi$
$757$	18.5854	+	10.7303i	0.675498	+	0.389999i	−0.122659	+	0.992449i	$0.539142\pi$
$758$		0			0
$759$	−27.9136			−1.01320
$760$		0			0
$761$	−11.7372	−	20.3294i	−0.425472	−	0.736939i	0.570993	−	0.820955i	$-0.306558\pi$
$761$	−11.7372	−	20.3294i	−0.425472	−	0.736939i	−0.996464	+	0.0840166i	$0.973225\pi$
$762$		0			0
$763$	5.63286	−	3.25213i	0.203923	−	0.117735i
$764$		0			0
$765$	−0.558492	−	0.322446i	−0.0201923	−	0.0116581i
$766$		0			0
$767$	−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	$0.235499\pi$
$770$		0			0
$771$	30.5500	−	17.6381i	1.10023	−	0.635219i
$772$		0			0
$773$	−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
$776$		0			0
$777$	−5.22123	+	9.04344i	−0.187311	+	0.324432i
$778$		0			0
$779$		−	53.2410i		−	1.90756i
$780$		0			0
$781$			1.28450i			0.0459630i
$782$		0			0
$783$	−4.69299	+	8.12849i	−0.167714	+	0.290489i
$784$		0			0
$785$	−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	$0.286513\pi$
$788$		0			0
$789$	−1.52198	+	0.878717i	−0.0541840	+	0.0312832i
$790$		0			0
$791$	−2.85984	+	4.95339i	−0.101684	+	0.176122i
$792$		0			0
$793$	−6.72146	+	3.74951i	−0.238686	+	0.133149i
$794$		0			0
$795$	23.0893	+	13.3306i	0.818892	+	0.472788i
$796$		0			0
$797$	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
$800$		0			0
$801$	−0.225787			−0.00797781
$802$		0			0
$803$	35.8558	+	20.7013i	1.26532	+	0.730534i
$804$		0			0
$805$		−	9.20142i		−	0.324308i
$806$		0			0
$807$	−10.5192			−0.370294
$808$		0			0
$809$	−18.9274	+	32.7832i	−0.665452	+	1.15260i	0.313711	+	0.949519i	$0.398428\pi$
$809$	−18.9274	+	32.7832i	−0.665452	+	1.15260i	−0.979163	+	0.203078i	$0.934906\pi$
$810$		0			0
$811$			16.1872i			0.568409i	0.958764	+	0.284205i	$0.0917295\pi$
$811$			16.1872i			0.568409i	−0.958764	+	0.284205i	$0.908270\pi$
$812$		0			0
$813$	20.2276	−	11.6784i	0.709411	−	0.409579i
$814$		0			0
$815$	−14.1603	−	24.5264i	−0.496015	−	0.859122i
$816$		0			0
$817$	−24.6576	+	42.7082i	−0.862659	+	1.49417i
$818$		0			0
$819$	−0.106516	+	0.178361i	−0.00372198	+	0.00623243i
$820$		0			0
$821$	−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	$0.0343798\pi$
$823$	16.9386	+	29.3385i	0.590442	+	1.02268i	−0.403731	+	0.914878i	$0.632287\pi$
$824$		0			0
$825$	−4.17117	−	7.22467i	−0.145221	−	0.251531i
$826$		0			0
$827$		−	1.10220i		−	0.0383272i	−0.999816	−	0.0191636i	$-0.993900\pi$
$827$		−	1.10220i		−	0.0383272i	0.999816	−	0.0191636i	$-0.00610034\pi$
$828$		0			0
$829$	17.1870	+	9.92292i	0.596929	+	0.344637i	0.767833	−	0.640650i	$-0.221335\pi$
$829$	17.1870	+	9.92292i	0.596929	+	0.344637i	−0.170903	+	0.985288i	$0.554669\pi$
$830$		0			0
$831$	48.1645			1.67081
$832$		0			0
$833$	−17.1810			−0.595286
$834$		0			0
$835$	30.0877	+	17.3712i	1.04123	+	0.601154i
$836$		0			0
$837$		−	26.8761i		−	0.928972i
$838$		0			0
$839$	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
$842$		0			0
$843$	18.2016	+	10.5087i	0.626895	+	0.361938i
$844$		0			0
$845$	−0.997279	+	33.7838i	−0.0343074	+	1.16220i
$846$		0			0
$847$	0.979528	−	1.69659i	0.0336570	−	0.0582956i
$848$		0			0
$849$	16.7664	+	29.0402i	0.575421	+	0.996658i
$850$		0			0
$851$	51.9663	−	30.0027i	1.78138	−	1.02848i
$852$		0			0
$853$			12.5392i			0.429333i	0.976687	+	0.214666i	$0.0688664\pi$
$853$			12.5392i			0.429333i	−0.976687	+	0.214666i	$0.931134\pi$
$854$		0			0
$855$	−0.630253	+	1.09163i	−0.0215542	+	0.0373330i
$856$		0			0
$857$	34.8182			1.18937			0.594684	−	0.803960i	$-0.297277\pi$
$857$	34.8182			1.18937			0.594684	+	0.803960i	$0.297277\pi$
$858$		0			0
$859$			33.1090i			1.12966i	0.825206	+	0.564832i	$0.191059\pi$
$859$			33.1090i			1.12966i	−0.825206	+	0.564832i	$0.808941\pi$
$860$		0			0
$861$	9.33807	+	5.39134i	0.318240	+	0.183736i
$862$		0			0
$863$	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
$866$		0			0
$867$	−15.2042	+	8.77812i	−0.516360	+	0.298121i
$868$		0			0
$869$	−18.8902	−	10.9062i	−0.640805	−	0.369969i
$870$		0			0
$871$	12.1201	+	7.23804i	0.410673	+	0.245252i
$872$		0			0
$873$	0.566576	−	0.981338i	0.0191757	−	0.0332132i
$874$		0			0
$875$	−4.38641	+	2.53249i	−0.148288	+	0.0856139i
$876$		0			0
$877$	36.8042	−	21.2489i	1.24279	−	0.717524i	0.273127	−	0.961978i	$-0.411942\pi$
$877$	36.8042	−	21.2489i	1.24279	−	0.717524i	0.969661	+	0.244454i	$0.0786087\pi$
$878$		0			0
$879$	−20.0004			−0.674597
$880$		0			0
$881$	0.254151	−	0.440202i	0.00856257	−	0.0148308i	−0.861712	−	0.507397i	$-0.830608\pi$
$881$	0.254151	−	0.440202i	0.00856257	−	0.0148308i	0.870275	+	0.492566i	$0.163941\pi$
$882$		0			0
$883$		−	47.2885i		−	1.59139i	−0.605700	−	0.795693i	$-0.707107\pi$
$883$		−	47.2885i		−	1.59139i	0.605700	−	0.795693i	$-0.292893\pi$
$884$		0			0
$885$		−	48.3133i		−	1.62403i
$886$		0			0
$887$	−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
$890$		0			0
$891$	−20.9711	+	12.1077i	−0.702557	+	0.405622i
$892$		0			0
$893$	9.37295	−	5.41147i	0.313654	−	0.181088i
$894$		0			0
$895$	−20.3890	+	35.3147i	−0.681528	+	1.18044i
$896$		0			0
$897$	−31.5899	+	17.6222i	−1.05476	+	0.588387i
$898$		0			0
$899$	−7.84870	−	4.53145i	−0.261769	−	0.151132i
$900$		0			0
$901$	13.4871	−	7.78677i	0.449320	−	0.259415i
$902$		0			0
$903$	−4.99379	−	8.64950i	−0.166183	−	0.287837i
$904$		0			0
$905$	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	$0.539512\pi$
$908$		0			0
$909$		−	1.24144i		−	0.0411761i
$910$		0			0
$911$	−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
$914$		0			0
$915$		−	9.45778i		−	0.312665i
$916$		0			0
$917$	−0.414330	+	0.239214i	−0.0136824	+	0.00789953i
$918$		0			0
$919$	21.8643	+	37.8701i	0.721237	+	1.24922i	0.960504	+	0.278265i	$0.0897593\pi$
$919$	21.8643	+	37.8701i	0.721237	+	1.24922i	−0.239268	+	0.970954i	$0.576907\pi$
$920$		0			0
$921$	4.33700	−	7.51190i	0.142909	−	0.247526i
$922$		0			0
$923$	0.810918	+	1.45367i	0.0266917	+	0.0478482i
$924$		0			0
$925$	15.5308	+	8.96670i	0.510649	+	0.294823i
$926$		0			0
$927$	0.316828	+	0.548762i	0.0104060	+	0.0180237i
$928$		0			0
$929$	−2.52459	−	4.37272i	−0.0828291	−	0.143464i	0.821635	−	0.570014i	$-0.193062\pi$
$929$	−2.52459	−	4.37272i	−0.0828291	−	0.143464i	−0.904464	+	0.426550i	$0.859729\pi$
$930$		0			0
$931$			33.5820i			1.10061i
$932$		0			0
$933$	37.1290	+	21.4364i	1.21555	+	0.701798i
$934$		0			0
$935$	−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	$0.240385\pi$
$938$		0			0
$939$	−18.3966	−	10.6213i	−0.600349	−	0.346612i
$940$		0			0
$941$		−	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
$944$		0			0
$945$	−4.12302	−	7.14127i	−0.134122	−	0.232306i
$946$		0			0
$947$	−8.18618	−	4.72629i	−0.266015	−	0.153584i	0.361060	−	0.932542i	$-0.382415\pi$
$947$	−8.18618	−	4.72629i	−0.266015	−	0.153584i	−0.627075	+	0.778959i	$0.715748\pi$
$948$		0			0
$949$	53.6471	+	0.791642i	1.74146	+	0.0256978i
$950$		0			0
$951$	9.39319	−	16.2695i	0.304595	−	0.527574i
$952$		0			0
$953$	9.38165	+	16.2495i	0.303901	+	0.526373i	0.977016	−	0.213165i	$-0.0683773\pi$
$953$	9.38165	+	16.2495i	0.303901	+	0.526373i	−0.673115	+	0.739538i	$0.735044\pi$
$954$		0			0
$955$	19.5542	−	11.2897i	0.632761	−	0.365325i
$956$		0			0
$957$			8.43543i			0.272679i
$958$		0			0
$959$	−1.06916	+	1.85184i	−0.0345250	+	0.0597991i
$960$		0			0
$961$	−5.04906			−0.162873
$962$		0			0
$963$		−	0.982317i		−	0.0316547i
$964$		0			0
$965$	3.55159	+	2.05051i	0.114330	+	0.0660083i
$966$		0			0
$967$	−13.9692			−0.449218			−0.224609	−	0.974449i	$-0.572111\pi$
$967$	−13.9692			−0.449218			−0.224609	+	0.974449i	$0.572111\pi$
$968$		0			0
$969$	−11.1554	−	19.3217i	−0.358362	−	0.620701i
$970$		0			0
$971$	−10.8263	+	6.25059i	−0.347434	+	0.200591i	−0.663555	−	0.748128i	$-0.730953\pi$
$971$	−10.8263	+	6.25059i	−0.347434	+	0.200591i	0.316121	+	0.948719i	$0.397620\pi$
$972$		0			0
$973$	−1.11927	−	0.646212i	−0.0358822	−	0.0207166i
$974$		0			0
$975$	−9.28154	−	5.54288i	−0.297247	−	0.177514i
$976$		0			0
$977$	−7.03484	+	12.1847i	−0.225065	+	0.389823i	−0.956339	−	0.292260i	$-0.905593\pi$
$977$	−7.03484	+	12.1847i	−0.225065	+	0.389823i	0.731274	+	0.682084i	$0.238926\pi$
$978$		0			0
$979$	−5.67646	+	3.27731i	−0.181421	+	0.104743i
$980$		0			0
$981$	−0.898022	+	0.518473i	−0.0286716	+	0.0165536i
$982$		0			0
$983$	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
$986$		0			0
$987$			2.19192i			0.0697697i
$988$		0			0
$989$			57.3916i			1.82495i
$990$		0			0
$991$	−4.71260	+	8.16245i	−0.149701	+	0.259289i	−0.931117	−	0.364721i	$-0.881164\pi$
$991$	−4.71260	+	8.16245i	−0.149701	+	0.259289i	0.781416	+	0.624010i	$0.214498\pi$
$992$		0			0
$993$	−28.3146			−0.898536
$994$		0			0
$995$	46.6148	−	26.9131i	1.47779	−	0.853201i
$996$		0			0
$997$	−6.28844	+	3.63063i	−0.199157	+	0.114983i	−0.596262	−	0.802790i	$-0.703348\pi$
$997$	−6.28844	+	3.63063i	−0.199157	+	0.114983i	0.397105	+	0.917773i	$0.370015\pi$
$998$		0			0
$999$	26.8875	−	46.5706i	0.850684	−	1.47343i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.4	✓	24	104.3	odd	6
104.2.r.a.29.5	yes	24	52.3	odd	6
104.2.r.a.61.4	yes	24	4.3	odd	2
104.2.r.a.61.5	yes	24	8.3	odd	2
416.2.z.a.81.3		24	104.29	even	6	inner
416.2.z.a.81.10		24	13.3	even	3	inner
416.2.z.a.113.3		24	1.1	even	1	trivial
416.2.z.a.113.10		24	8.5	even	2	inner
936.2.be.a.685.8		24	24.11	even	2
936.2.be.a.685.9		24	12.11	even	2
936.2.be.a.757.8		24	156.107	even	6
936.2.be.a.757.9		24	312.107	even	6

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.47584 - 0.852079i) q^{3} +2.59989i q^{5} +(0.300588 + 0.520633i) q^{7} +(-0.0479214 - 0.0830022i) q^{9} +(-2.40956 - 1.39116i) q^{11} +(-3.60516 - 0.0531995i) q^{13} +(2.21531 - 3.83703i) q^{15} +(-1.29402 - 2.24132i) q^{17} +(-4.38088 + 2.52930i) q^{19} -1.02450i q^{21} +(-2.94353 + 5.09835i) q^{23} -1.75942 q^{25} +5.27581i q^{27} +(1.54071 + 0.889530i) q^{29} -5.09421 q^{31} +(2.37076 + 4.10627i) q^{33} +(-1.35359 + 0.781495i) q^{35} +(-8.82719 - 5.09638i) q^{37} +(5.27532 + 3.15040i) q^{39} +(-5.26242 + 9.11477i) q^{41} +(8.44267 - 4.87438i) q^{43} +(0.215797 - 0.124590i) q^{45} -2.13951 q^{47} +(3.31929 - 5.74919i) q^{49} +4.41045i q^{51} +6.01748i q^{53} +(3.61686 - 6.26458i) q^{55} +8.62067 q^{57} +(9.44349 - 5.45220i) q^{59} +(1.84865 - 1.06732i) q^{61} +(0.0288091 - 0.0498989i) q^{63} +(0.138313 - 9.37301i) q^{65} +(-3.39076 - 1.95766i) q^{67} +(8.68840 - 5.01625i) q^{69} +(-0.230832 - 0.399814i) q^{71} -14.8806 q^{73} +(2.59664 + 1.49917i) q^{75} -1.67266i q^{77} +7.83968 q^{79} +(4.35164 - 7.53727i) q^{81} -0.930501i q^{83} +(5.82717 - 3.36432i) q^{85} +(-1.51590 - 2.62562i) q^{87} +(1.17791 - 2.04019i) q^{89} +(-1.05597 - 1.89296i) q^{91} +(7.51826 + 4.34067i) q^{93} +(-6.57591 - 11.3898i) q^{95} +(5.91151 + 10.2390i) q^{97} +0.266665i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{7} + 6 q^{9} - 4 q^{15} + 14 q^{23} - 12 q^{25} + 8 q^{31} - 14 q^{33} + 34 q^{39} - 4 q^{41} + 8 q^{47} + 6 q^{49} - 8 q^{55} - 52 q^{57} - 32 q^{63} + 30 q^{65} - 30 q^{71} - 12 q^{73} + 48 q^{79}+ \cdots + 2 q^{97}+O(q^{100}) \) 24 * q + 2 * q^7 + 6 * q^9 - 4 * q^15 + 14 * q^23 - 12 * q^25 + 8 * q^31 - 14 * q^33 + 34 * q^39 - 4 * q^41 + 8 * q^47 + 6 * q^49 - 8 * q^55 - 52 * q^57 - 32 * q^63 + 30 * q^65 - 30 * q^71 - 12 * q^73 + 48 * q^79 + 8 * q^81 + 26 * q^87 - 22 * q^89 - 60 * q^95 + 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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