LMFDB - Embedded newform 888.2.bo.c.673.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [888,2,Mod(49,888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(888, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 14]))

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

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

chi := DirichletCharacter("888.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.bo (of order $9$, degree $6$, 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:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			673.4
Character	$\chi$	$=$	888.673
Dual form			888.2.bo.c.793.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{3} +(0.299629 + 1.69928i) q^{5} +(-0.229436 - 1.30120i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{3} +(0.299629 + 1.69928i) q^{5} +(-0.229436 - 1.30120i) q^{7} +(0.766044 + 0.642788i) q^{9} +(2.05459 - 3.55865i) q^{11} +(-1.68246 + 1.41175i) q^{13} +(0.299629 - 1.69928i) q^{15} +(-0.0893478 - 0.0749717i) q^{17} +(2.12891 + 0.774859i) q^{19} +(-0.229436 + 1.30120i) q^{21} +(-0.660635 - 1.14425i) q^{23} +(1.90069 - 0.691796i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(1.31343 - 2.27492i) q^{29} +8.81670 q^{31} +(-3.14781 + 2.64133i) q^{33} +(2.14235 - 0.779752i) q^{35} +(-4.41526 + 4.18395i) q^{37} +(2.06385 - 0.751179i) q^{39} +(2.55621 - 2.14492i) q^{41} +11.1772 q^{43} +(-0.862746 + 1.49432i) q^{45} +(-0.225741 - 0.390994i) q^{47} +(4.93737 - 1.79706i) q^{49} +(0.0583177 + 0.101009i) q^{51} +(-0.545685 + 3.09474i) q^{53} +(6.66275 + 2.42504i) q^{55} +(-1.73550 - 1.45626i) q^{57} +(0.731091 - 4.14622i) q^{59} +(5.16100 - 4.33059i) q^{61} +(0.660635 - 1.14425i) q^{63} +(-2.90308 - 2.43597i) q^{65} +(0.0600486 + 0.340552i) q^{67} +(0.229436 + 1.30120i) q^{69} +(-4.43757 - 1.61514i) q^{71} +7.95444 q^{73} -2.02268 q^{75} +(-5.10190 - 1.85694i) q^{77} +(-2.14462 - 12.1627i) q^{79} +(0.173648 + 0.984808i) q^{81} +(4.11359 + 3.45171i) q^{83} +(0.100627 - 0.174291i) q^{85} +(-2.01229 + 1.68851i) q^{87} +(0.807523 - 4.57969i) q^{89} +(2.22299 + 1.86531i) q^{91} +(-8.28499 - 3.01549i) q^{93} +(-0.678820 + 3.84978i) q^{95} +(0.311196 + 0.539007i) q^{97} +(3.86136 - 1.40542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) $ 24 * q + 3 * q^5 + 15 * q^7	$ 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$		0			0
$5$	0.299629	+	1.69928i	0.133998	+	0.759940i	0.975552	+	0.219768i	$0.0705300\pi$
$5$	0.299629	+	1.69928i	0.133998	+	0.759940i	−0.841554	+	0.540173i	$0.818359\pi$
$6$		0			0
$7$	−0.229436	−	1.30120i	−0.0867187	−	0.491806i	−0.996972	−	0.0777555i	$-0.975225\pi$
$7$	−0.229436	−	1.30120i	−0.0867187	−	0.491806i	0.910254	−	0.414051i	$-0.135886\pi$
$8$		0			0
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$		0			0
$11$	2.05459	−	3.55865i	0.619481	−	1.07297i	−0.370099	−	0.928992i	$-0.620676\pi$
$11$	2.05459	−	3.55865i	0.619481	−	1.07297i	0.989580	−	0.143981i	$-0.0459904\pi$
$12$		0			0
$13$	−1.68246	+	1.41175i	−0.466631	+	0.391550i	−0.845564	−	0.533874i	$-0.820736\pi$
$13$	−1.68246	+	1.41175i	−0.466631	+	0.391550i	0.378933	+	0.925424i	$0.376291\pi$
$14$		0			0
$15$	0.299629	−	1.69928i	0.0773638	−	0.438752i
$16$		0			0
$17$	−0.0893478	−	0.0749717i	−0.0216700	−	0.0181833i	0.631888	−	0.775059i	$-0.282280\pi$
$17$	−0.0893478	−	0.0749717i	−0.0216700	−	0.0181833i	−0.653558	+	0.756876i	$0.726725\pi$
$18$		0			0
$19$	2.12891	+	0.774859i	0.488405	+	0.177765i	0.574472	−	0.818524i	$-0.305208\pi$
$19$	2.12891	+	0.774859i	0.488405	+	0.177765i	−0.0860666	+	0.996289i	$0.527430\pi$
$20$		0			0
$21$	−0.229436	+	1.30120i	−0.0500671	+	0.283945i
$22$		0			0
$23$	−0.660635	−	1.14425i	−0.137752	−	0.238593i	0.788893	−	0.614530i	$-0.210654\pi$
$23$	−0.660635	−	1.14425i	−0.137752	−	0.238593i	−0.926645	+	0.375937i	$0.877321\pi$
$24$		0			0
$25$	1.90069	−	0.691796i	0.380139	−	0.138359i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	1.31343	−	2.27492i	0.243897	−	0.422443i	−0.717924	−	0.696122i	$-0.754907\pi$
$29$	1.31343	−	2.27492i	0.243897	−	0.422443i	0.961821	+	0.273679i	$0.0882407\pi$
$30$		0			0
$31$	8.81670			1.58353			0.791763	−	0.610829i	$-0.209164\pi$
$31$	8.81670			1.58353			0.791763	+	0.610829i	$0.209164\pi$
$32$		0			0
$33$	−3.14781	+	2.64133i	−0.547964	+	0.459796i
$34$		0			0
$35$	2.14235	−	0.779752i	0.362123	−	0.131802i
$36$		0			0
$37$	−4.41526	+	4.18395i	−0.725865	+	0.687837i
$37$	−4.41526	+	4.18395i	−0.725865	+	0.687837i
$38$		0			0
$39$	2.06385	−	0.751179i	0.330480	−	0.120285i
$40$		0			0
$41$	2.55621	−	2.14492i	0.399214	−	0.334980i	−0.420976	−	0.907072i	$-0.638312\pi$
$41$	2.55621	−	2.14492i	0.399214	−	0.334980i	0.820190	+	0.572092i	$0.193868\pi$
$42$		0			0
$43$	11.1772			1.70451			0.852257	−	0.523123i	$-0.175233\pi$
$43$	11.1772			1.70451			0.852257	+	0.523123i	$0.175233\pi$
$44$		0			0
$45$	−0.862746	+	1.49432i	−0.128611	+	0.222760i
$46$		0			0
$47$	−0.225741	−	0.390994i	−0.0329276	−	0.0570324i	0.849092	−	0.528245i	$-0.177150\pi$
$47$	−0.225741	−	0.390994i	−0.0329276	−	0.0570324i	−0.882020	+	0.471213i	$0.843816\pi$
$48$		0			0
$49$	4.93737	−	1.79706i	0.705339	−	0.256722i
$50$		0			0
$51$	0.0583177	+	0.101009i	0.00816611	+	0.0141441i
$52$		0			0
$53$	−0.545685	+	3.09474i	−0.0749557	+	0.425095i	0.924120	+	0.382103i	$0.124800\pi$
$53$	−0.545685	+	3.09474i	−0.0749557	+	0.425095i	−0.999075	+	0.0429918i	$0.986311\pi$
$54$		0			0
$55$	6.66275	+	2.42504i	0.898405	+	0.326993i
$56$		0			0
$57$	−1.73550	−	1.45626i	−0.229873	−	0.192886i
$58$		0			0
$59$	0.731091	−	4.14622i	0.0951799	−	0.539792i	−0.899512	−	0.436896i	$-0.856078\pi$
$59$	0.731091	−	4.14622i	0.0951799	−	0.539792i	0.994692	−	0.102896i	$-0.0328110\pi$
$60$		0			0
$61$	5.16100	−	4.33059i	0.660798	−	0.554475i	−0.249528	−	0.968368i	$-0.580275\pi$
$61$	5.16100	−	4.33059i	0.660798	−	0.554475i	0.910326	+	0.413892i	$0.135831\pi$
$62$		0			0
$63$	0.660635	−	1.14425i	0.0832322	−	0.144162i
$64$		0			0
$65$	−2.90308	−	2.43597i	−0.360083	−	0.302145i
$66$		0			0
$67$	0.0600486	+	0.340552i	0.00733610	+	0.0416051i	0.988256	−	0.152807i	$-0.0488312\pi$
$67$	0.0600486	+	0.340552i	0.00733610	+	0.0416051i	−0.980920	+	0.194412i	$0.937720\pi$
$68$		0			0
$69$	0.229436	+	1.30120i	0.0276209	+	0.156646i
$70$		0			0
$71$	−4.43757	−	1.61514i	−0.526642	−	0.191682i	0.0649962	−	0.997886i	$-0.479296\pi$
$71$	−4.43757	−	1.61514i	−0.526642	−	0.191682i	−0.591638	+	0.806203i	$0.701519\pi$
$72$		0			0
$73$	7.95444			0.930997			0.465498	−	0.885049i	$-0.345875\pi$
$73$	7.95444			0.930997			0.465498	+	0.885049i	$0.345875\pi$
$74$		0			0
$75$	−2.02268			−0.233558
$76$		0			0
$77$	−5.10190	−	1.85694i	−0.581416	−	0.211618i
$78$		0			0
$79$	−2.14462	−	12.1627i	−0.241289	−	1.36842i	−0.828956	−	0.559313i	$-0.811065\pi$
$79$	−2.14462	−	12.1627i	−0.241289	−	1.36842i	0.587668	−	0.809102i	$-0.300046\pi$
$80$		0			0
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$		0			0
$83$	4.11359	+	3.45171i	0.451525	+	0.378874i	0.840001	−	0.542584i	$-0.182554\pi$
$83$	4.11359	+	3.45171i	0.451525	+	0.378874i	−0.388477	+	0.921459i	$0.626999\pi$
$84$		0			0
$85$	0.100627	−	0.174291i	0.0109145	−	0.0189045i
$86$		0			0
$87$	−2.01229	+	1.68851i	−0.215740	+	0.181027i
$88$		0			0
$89$	0.807523	−	4.57969i	0.0855972	−	0.485446i	−0.911629	−	0.411014i	$-0.865175\pi$
$89$	0.807523	−	4.57969i	0.0855972	−	0.485446i	0.997226	−	0.0744317i	$-0.0237143\pi$
$90$		0			0
$91$	2.22299	+	1.86531i	0.233033	+	0.195538i
$92$		0			0
$93$	−8.28499	−	3.01549i	−0.859113	−	0.312692i
$94$		0			0
$95$	−0.678820	+	3.84978i	−0.0696454	+	0.394979i
$96$		0			0
$97$	0.311196	+	0.539007i	0.0315971	+	0.0547278i	0.881392	−	0.472386i	$-0.156607\pi$
$97$	0.311196	+	0.539007i	0.0315971	+	0.0547278i	−0.849794	+	0.527114i	$0.823274\pi$
$98$		0			0
$99$	3.86136	−	1.40542i	0.388081	−	0.141250i
$100$		0			0
$101$	5.26954	+	9.12710i	0.524338	+	0.908181i	0.999598	+	0.0283355i	$0.00902066\pi$
$101$	5.26954	+	9.12710i	0.524338	+	0.908181i	−0.475260	+	0.879845i	$0.657646\pi$
$102$		0			0
$103$	6.77937	−	11.7422i	0.667991	−	1.15700i	−0.310474	−	0.950582i	$-0.600488\pi$
$103$	6.77937	−	11.7422i	0.667991	−	1.15700i	0.978465	−	0.206413i	$-0.0661790\pi$
$104$		0			0
$105$	−2.27984			−0.222490
$106$		0			0
$107$	−9.84230	+	8.25867i	−0.951491	+	0.798396i	−0.979548	−	0.201210i	$-0.935513\pi$
$107$	−9.84230	+	8.25867i	−0.951491	+	0.798396i	0.0280568	+	0.999606i	$0.491068\pi$
$108$		0			0
$109$	−12.4376	+	4.52690i	−1.19130	+	0.433598i	−0.860180	−	0.509990i	$-0.829649\pi$
$109$	−12.4376	+	4.52690i	−1.19130	+	0.433598i	−0.331121	+	0.943588i	$0.607427\pi$
$110$		0			0
$111$	5.57999	−	2.42152i	0.529629	−	0.229840i
$112$		0			0
$113$	−5.27266	+	1.91909i	−0.496010	+	0.180533i	−0.577898	−	0.816109i	$-0.696127\pi$
$113$	−5.27266	+	1.91909i	−0.496010	+	0.180533i	0.0818887	+	0.996641i	$0.473905\pi$
$114$		0			0
$115$	1.74646	−	1.46545i	0.162858	−	0.136654i
$116$		0			0
$117$	−2.19630			−0.203048
$118$		0			0
$119$	−0.0770534	+	0.133460i	−0.00706347	+	0.0122343i
$120$		0			0
$121$	−2.94266	−	5.09684i	−0.267515	−	0.463349i
$122$		0			0
$123$	−3.13566	+	1.14129i	−0.282733	+	0.102906i
$124$		0			0
$125$	6.05879	+	10.4941i	0.541914	+	0.938623i
$126$		0			0
$127$	−0.312856	+	1.77429i	−0.0277614	+	0.157443i	−0.995537	−	0.0943710i	$-0.969916\pi$
$127$	−0.312856	+	1.77429i	−0.0277614	+	0.157443i	0.967776	+	0.251814i	$0.0810271\pi$
$128$		0			0
$129$	−10.5032	−	3.82284i	−0.924753	−	0.336583i
$130$		0			0
$131$	−12.6930	−	10.6507i	−1.10899	−	0.930555i	−0.110996	−	0.993821i	$-0.535404\pi$
$131$	−12.6930	−	10.6507i	−1.10899	−	0.930555i	−0.997997	+	0.0632657i	$0.979848\pi$
$132$		0			0
$133$	0.519796	−	2.94791i	0.0450721	−	0.255616i
$134$		0			0
$135$	1.32180	−	1.10913i	0.113763	−	0.0954583i
$136$		0			0
$137$	−0.894286	+	1.54895i	−0.0764040	+	0.132336i	−0.901696	−	0.432371i	$-0.857677\pi$
$137$	−0.894286	+	1.54895i	−0.0764040	+	0.132336i	0.825292	+	0.564706i	$0.191011\pi$
$138$		0			0
$139$	8.30310	+	6.96713i	0.704260	+	0.590944i	0.922982	−	0.384843i	$-0.125744\pi$
$139$	8.30310	+	6.96713i	0.704260	+	0.590944i	−0.218722	+	0.975787i	$0.570189\pi$
$140$		0			0
$141$	0.0783989	+	0.444622i	0.00660238	+	0.0374439i
$142$		0			0
$143$	1.56717	+	8.88787i	0.131053	+	0.743241i
$144$		0			0
$145$	4.25927	+	1.55025i	0.353713	+	0.128741i
$146$		0			0
$147$	−5.25424			−0.433363
$148$		0			0
$149$	−2.25888			−0.185055			−0.0925274	−	0.995710i	$-0.529495\pi$
$149$	−2.25888			−0.185055			−0.0925274	+	0.995710i	$0.529495\pi$
$150$		0			0
$151$	−3.96121	−	1.44176i	−0.322359	−	0.117329i	0.175772	−	0.984431i	$-0.443758\pi$
$151$	−3.96121	−	1.44176i	−0.322359	−	0.117329i	−0.498131	+	0.867102i	$0.665980\pi$
$152$		0			0
$153$	−0.0202535	−	0.114863i	−0.00163740	−	0.00928615i
$154$		0			0
$155$	2.64174	+	14.9820i	0.212189	+	1.20339i
$156$		0			0
$157$	7.56251	+	6.34570i	0.603554	+	0.506442i	0.892586	−	0.450878i	$-0.148889\pi$
$157$	7.56251	+	6.34570i	0.603554	+	0.506442i	−0.289032	+	0.957319i	$0.593333\pi$
$158$		0			0
$159$	1.57124	−	2.72147i	0.124607	−	0.215826i
$160$		0			0
$161$	−1.33733	+	1.12215i	−0.105396	+	0.0884378i
$162$		0			0
$163$	−1.85399	+	10.5145i	−0.145215	+	0.823557i	0.821979	+	0.569518i	$0.192870\pi$
$163$	−1.85399	+	10.5145i	−0.145215	+	0.823557i	−0.967194	+	0.254039i	$0.918241\pi$
$164$		0			0
$165$	−5.43152	−	4.55759i	−0.422844	−	0.354808i
$166$		0			0
$167$	−18.2433	−	6.64001i	−1.41171	−	0.513819i	−0.480077	−	0.877227i	$-0.659391\pi$
$167$	−18.2433	−	6.64001i	−1.41171	−	0.513819i	−0.931630	+	0.363407i	$0.881613\pi$
$168$		0			0
$169$	−1.41979	+	8.05205i	−0.109215	+	0.619388i
$170$		0			0
$171$	1.13277	+	1.96201i	0.0866250	+	0.150039i
$172$		0			0
$173$	−2.93094	+	1.06677i	−0.222835	+	0.0811053i	−0.451025	−	0.892511i	$-0.648941\pi$
$173$	−2.93094	+	1.06677i	−0.222835	+	0.0811053i	0.228190	+	0.973617i	$0.426719\pi$
$174$		0			0
$175$	−1.33625	−	2.31445i	−0.101011	−	0.174956i
$176$		0			0
$177$	−2.10509	+	3.64613i	−0.158228	+	0.274060i
$178$		0			0
$179$	−17.4099			−1.30128			−0.650640	−	0.759386i	$-0.725499\pi$
$179$	−17.4099			−1.30128			−0.650640	+	0.759386i	$0.725499\pi$
$180$		0			0
$181$	−15.2950	+	12.8340i	−1.13687	+	0.953944i	−0.999332	−	0.0365535i	$-0.988362\pi$
$181$	−15.2950	+	12.8340i	−1.13687	+	0.953944i	−0.137534	+	0.990497i	$0.543918\pi$
$182$		0			0
$183$	−6.33090	+	2.30426i	−0.467994	+	0.170336i
$184$		0			0
$185$	−8.43264	−	6.24913i	−0.619980	−	0.459445i
$186$		0			0
$187$	−0.450371	+	0.163922i	−0.0329344	+	0.0119871i
$188$		0			0
$189$	−1.01215	+	0.849296i	−0.0736232	+	0.0617772i
$190$		0			0
$191$	0.947123			0.0685314			0.0342657	−	0.999413i	$-0.489091\pi$
$191$	0.947123			0.0685314			0.0342657	+	0.999413i	$0.489091\pi$
$192$		0			0
$193$	−2.09396	+	3.62685i	−0.150727	+	0.261066i	−0.931495	−	0.363755i	$-0.881495\pi$
$193$	−2.09396	+	3.62685i	−0.150727	+	0.261066i	0.780768	+	0.624821i	$0.214828\pi$
$194$		0			0
$195$	1.89485	+	3.28198i	0.135693	+	0.235027i
$196$		0			0
$197$	−7.84977	+	2.85708i	−0.559273	+	0.203559i	−0.606162	−	0.795341i	$-0.707292\pi$
$197$	−7.84977	+	2.85708i	−0.559273	+	0.203559i	0.0468887	+	0.998900i	$0.485069\pi$
$198$		0			0
$199$	1.89347	+	3.27958i	0.134224	+	0.232483i	0.925301	−	0.379234i	$-0.123812\pi$
$199$	1.89347	+	3.27958i	0.134224	+	0.232483i	−0.791077	+	0.611717i	$0.790479\pi$
$200$		0			0
$201$	0.0600486	−	0.340552i	0.00423550	−	0.0240207i
$202$		0			0
$203$	−3.26147	−	1.18708i	−0.228910	−	0.0833166i
$204$		0			0
$205$	4.41073	+	3.70104i	0.308059	+	0.258492i
$206$		0			0
$207$	0.229436	−	1.30120i	0.0159469	−	0.0904395i
$208$		0			0
$209$	7.13148	−	5.98402i	0.493295	−	0.413924i
$210$		0			0
$211$	2.52207	−	4.36836i	0.173627	−	0.300730i	−0.766058	−	0.642771i	$-0.777785\pi$
$211$	2.52207	−	4.36836i	0.173627	−	0.300730i	0.939685	+	0.342041i	$0.111118\pi$
$212$		0			0
$213$	3.61754	+	3.03547i	0.247870	+	0.207987i
$214$		0			0
$215$	3.34902	+	18.9933i	0.228401	+	1.29533i
$216$		0			0
$217$	−2.02287	−	11.4723i	−0.137321	−	0.778788i
$218$		0			0
$219$	−7.47473	−	2.72058i	−0.505095	−	0.183840i
$220$		0			0
$221$	0.256166			0.0172316
$222$		0			0
$223$	−7.90712			−0.529500			−0.264750	−	0.964317i	$-0.585289\pi$
$223$	−7.90712			−0.529500			−0.264750	+	0.964317i	$0.585289\pi$
$224$		0			0
$225$	1.90069	+	0.691796i	0.126713	+	0.0461197i
$226$		0			0
$227$	−3.31879	−	18.8218i	−0.220276	−	1.24924i	−0.871514	−	0.490371i	$-0.836861\pi$
$227$	−3.31879	−	18.8218i	−0.220276	−	1.24924i	0.651238	−	0.758874i	$-0.274250\pi$
$228$		0			0
$229$	2.17801	+	12.3521i	0.143927	+	0.816249i	0.968223	+	0.250090i	$0.0804601\pi$
$229$	2.17801	+	12.3521i	0.143927	+	0.816249i	−0.824296	+	0.566159i	$0.808429\pi$
$230$		0			0
$231$	4.15911	+	3.48991i	0.273649	+	0.229619i
$232$		0			0
$233$	11.7159	−	20.2925i	0.767533	−	1.32941i	−0.171363	−	0.985208i	$-0.554817\pi$
$233$	11.7159	−	20.2925i	0.767533	−	1.32941i	0.938897	−	0.344199i	$-0.111849\pi$
$234$		0			0
$235$	0.596770	−	0.500749i	0.0389290	−	0.0326653i
$236$		0			0
$237$	−2.14462	+	12.1627i	−0.139308	+	0.790055i
$238$		0			0
$239$	−11.1055	−	9.31864i	−0.718356	−	0.602772i	0.208574	−	0.978007i	$-0.433118\pi$
$239$	−11.1055	−	9.31864i	−0.718356	−	0.602772i	−0.926930	+	0.375234i	$0.877562\pi$
$240$		0			0
$241$	8.71467	+	3.17188i	0.561362	+	0.204319i	0.607087	−	0.794635i	$-0.292338\pi$
$241$	8.71467	+	3.17188i	0.561362	+	0.204319i	−0.0457258	+	0.998954i	$0.514560\pi$
$242$		0			0
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$		0			0
$245$	4.53308	+	7.85152i	0.289608	+	0.501615i
$246$		0			0
$247$	−4.67572	+	1.70182i	−0.297509	+	0.108284i
$248$		0			0
$249$	−2.68495	−	4.65047i	−0.170152	−	0.294712i
$250$		0			0
$251$	3.14309	−	5.44400i	0.198390	−	0.343622i	−0.749616	−	0.661873i	$-0.769762\pi$
$251$	3.14309	−	5.44400i	0.198390	−	0.343622i	0.948007	+	0.318250i	$0.103095\pi$
$252$		0			0
$253$	−5.42933			−0.341339
$254$		0			0
$255$	−0.154169	+	0.129363i	−0.00965444	+	0.00810104i
$256$		0			0
$257$	1.26148	−	0.459141i	0.0786890	−	0.0286405i	−0.302376	−	0.953189i	$-0.597780\pi$
$257$	1.26148	−	0.459141i	0.0786890	−	0.0286405i	0.381065	+	0.924548i	$0.375558\pi$
$258$		0			0
$259$	6.45717	+	4.78518i	0.401229	+	0.297337i
$260$		0			0
$261$	2.46844	−	0.898437i	0.152792	−	0.0556119i
$262$		0			0
$263$	−16.9228	+	14.2000i	−1.04351	+	0.875607i	−0.992396	−	0.123086i	$-0.960721\pi$
$263$	−16.9228	+	14.2000i	−1.04351	+	0.875607i	−0.0511116	+	0.998693i	$0.516276\pi$
$264$		0			0
$265$	−5.42232			−0.333091
$266$		0			0
$267$	−2.32517	+	4.02731i	−0.142298	+	0.246467i
$268$		0			0
$269$	−7.49412	−	12.9802i	−0.456924	−	0.791416i	0.541872	−	0.840461i	$-0.317716\pi$
$269$	−7.49412	−	12.9802i	−0.456924	−	0.791416i	−0.998797	+	0.0490446i	$0.984382\pi$
$270$		0			0
$271$	6.85771	−	2.49600i	0.416576	−	0.151621i	−0.125224	−	0.992128i	$-0.539965\pi$
$271$	6.85771	−	2.49600i	0.416576	−	0.151621i	0.541801	+	0.840507i	$0.317743\pi$
$272$		0			0
$273$	−1.45095	−	2.51312i	−0.0878157	−	0.152101i
$274$		0			0
$275$	1.44328	−	8.18526i	0.0870332	−	0.493590i
$276$		0			0
$277$	9.20885	+	3.35175i	0.553306	+	0.201387i	0.603515	−	0.797352i	$-0.293766\pi$
$277$	9.20885	+	3.35175i	0.553306	+	0.201387i	−0.0502086	+	0.998739i	$0.515989\pi$
$278$		0			0
$279$	6.75398	+	5.66726i	0.404350	+	0.339290i
$280$		0			0
$281$	4.98867	−	28.2922i	0.297599	−	1.68777i	−0.358847	−	0.933396i	$-0.616830\pi$
$281$	4.98867	−	28.2922i	0.297599	−	1.68777i	0.656446	−	0.754373i	$-0.272059\pi$
$282$		0			0
$283$	7.96280	−	6.68158i	0.473339	−	0.397179i	−0.374672	−	0.927158i	$-0.622245\pi$
$283$	7.96280	−	6.68158i	0.473339	−	0.397179i	0.848011	+	0.529979i	$0.177800\pi$
$284$		0			0
$285$	1.95458	−	3.38544i	0.115780	−	0.200536i
$286$		0			0
$287$	−3.37745	−	2.83402i	−0.199365	−	0.167287i
$288$		0			0
$289$	−2.94966	−	16.7283i	−0.173509	−	0.984020i
$290$		0			0
$291$	−0.108077	−	0.612936i	−0.00633559	−	0.0359309i
$292$		0			0
$293$	21.0586	+	7.66469i	1.23025	+	0.447776i	0.873684	−	0.486493i	$-0.161724\pi$
$293$	21.0586	+	7.66469i	1.23025	+	0.447776i	0.356569	+	0.934269i	$0.383946\pi$
$294$		0			0
$295$	7.26464			0.422964
$296$		0			0
$297$	−4.10918			−0.238439
$298$		0			0
$299$	2.72690	+	0.992510i	0.157701	+	0.0573984i
$300$		0			0
$301$	−2.56446	−	14.5438i	−0.147813	−	0.838291i
$302$		0			0
$303$	−1.83009	−	10.3790i	−0.105136	−	0.596256i
$304$		0			0
$305$	8.90526	+	7.47240i	0.509914	+	0.427869i
$306$		0			0
$307$	−8.54679	+	14.8035i	−0.487791	+	0.844879i	−0.999901	−	0.0140410i	$-0.995530\pi$
$307$	−8.54679	+	14.8035i	−0.487791	+	0.844879i	0.512111	+	0.858920i	$0.328864\pi$
$308$		0			0
$309$	−10.3866	+	8.71539i	−0.590873	+	0.495801i
$310$		0			0
$311$	−1.00877	+	5.72104i	−0.0572023	+	0.324411i	−0.999959	−	0.00907131i	$-0.997112\pi$
$311$	−1.00877	+	5.72104i	−0.0572023	+	0.324411i	0.942757	+	0.333482i	$0.108224\pi$
$312$		0			0
$313$	−19.7552	−	16.5765i	−1.11663	−	0.936962i	−0.118198	−	0.992990i	$-0.537712\pi$
$313$	−19.7552	−	16.5765i	−1.11663	−	0.936962i	−0.998429	+	0.0560284i	$0.982156\pi$
$314$		0			0
$315$	2.14235	+	0.779752i	0.120708	+	0.0439341i
$316$		0			0
$317$	−1.87560	+	10.6370i	−0.105344	+	0.597436i	0.885738	+	0.464185i	$0.153653\pi$
$317$	−1.87560	+	10.6370i	−0.105344	+	0.597436i	−0.991082	+	0.133251i	$0.957458\pi$
$318$		0			0
$319$	−5.39710	−	9.34806i	−0.302180	−	0.523391i
$320$		0			0
$321$	12.0734	−	4.39435i	0.673870	−	0.245269i
$322$		0			0
$323$	−0.132121	−	0.228840i	−0.00735140	−	0.0127330i
$324$		0			0
$325$	−2.22120	+	3.84723i	−0.123210	+	0.213406i
$326$		0			0
$327$	13.2358			0.731940
$328$		0			0
$329$	−0.456968	+	0.383441i	−0.0251934	+	0.0211398i
$330$		0			0
$331$	−1.51133	+	0.550078i	−0.0830700	+	0.0302350i	−0.383221	−	0.923657i	$-0.625185\pi$
$331$	−1.51133	+	0.550078i	−0.0830700	+	0.0302350i	0.300151	+	0.953892i	$0.402963\pi$
$332$		0			0
$333$	−6.07168	+	0.367014i	−0.332726	+	0.0201123i
$334$		0			0
$335$	−0.560701	+	0.204078i	−0.0306344	+	0.0111500i
$336$		0			0
$337$	−12.1072	+	10.1592i	−0.659523	+	0.553406i	−0.909944	−	0.414731i	$-0.863876\pi$
$337$	−12.1072	+	10.1592i	−0.659523	+	0.553406i	0.250421	+	0.968137i	$0.419431\pi$
$338$		0			0
$339$	5.61104			0.304750
$340$		0			0
$341$	18.1147	−	31.3755i	0.980965	−	1.69908i
$342$		0			0
$343$	−8.09559	−	14.0220i	−0.437121	−	0.757115i
$344$		0			0
$345$	−2.14235	+	0.779752i	−0.115340	+	0.0419804i
$346$		0			0
$347$	11.8430	+	20.5127i	0.635765	+	1.10118i	0.986352	+	0.164648i	$0.0526488\pi$
$347$	11.8430	+	20.5127i	0.635765	+	1.10118i	−0.350587	+	0.936530i	$0.614018\pi$
$348$		0			0
$349$	−2.11356	+	11.9866i	−0.113136	+	0.641628i	0.874520	+	0.484990i	$0.161177\pi$
$349$	−2.11356	+	11.9866i	−0.113136	+	0.641628i	−0.987656	+	0.156638i	$0.949934\pi$
$350$		0			0
$351$	2.06385	+	0.751179i	0.110160	+	0.0400950i
$352$		0			0
$353$	0.0144717	+	0.0121432i	0.000770253	+	0.000646319i	0.643173	−	0.765721i	$-0.277618\pi$
$353$	0.0144717	+	0.0121432i	0.000770253	+	0.000646319i	−0.642402	+	0.766368i	$0.722062\pi$
$354$		0			0
$355$	1.41495	−	8.02460i	0.0750980	−	0.425902i
$356$		0			0
$357$	0.118053	−	0.0990580i	0.00624801	−	0.00524270i
$358$		0			0
$359$	−7.20966	+	12.4875i	−0.380511	+	0.659065i	−0.991135	−	0.132856i	$-0.957585\pi$
$359$	−7.20966	+	12.4875i	−0.380511	+	0.659065i	0.610624	+	0.791921i	$0.290919\pi$
$360$		0			0
$361$	−10.6230	−	8.91376i	−0.559105	−	0.469145i
$362$		0			0
$363$	1.02198	+	5.79591i	0.0536398	+	0.304206i
$364$		0			0
$365$	2.38338	+	13.5168i	0.124752	+	0.707502i
$366$		0			0
$367$	−2.78436	−	1.01342i	−0.145342	−	0.0529002i	0.268325	−	0.963329i	$-0.413530\pi$
$367$	−2.78436	−	1.01342i	−0.145342	−	0.0529002i	−0.413667	+	0.910428i	$0.635752\pi$
$368$		0			0
$369$	3.33690			0.173712
$370$		0			0
$371$	4.15206			0.215564
$372$		0			0
$373$	19.6576	+	7.15478i	1.01783	+	0.370460i	0.796435	−	0.604724i	$-0.206716\pi$
$373$	19.6576	+	7.15478i	1.01783	+	0.370460i	0.221396	+	0.975184i	$0.428939\pi$
$374$		0			0
$375$	−2.10419	−	11.9335i	−0.108660	−	0.616242i
$376$		0			0
$377$	1.00184	+	5.68171i	0.0515973	+	0.292623i
$378$		0			0
$379$	8.29166	+	6.95753i	0.425914	+	0.357384i	0.830407	−	0.557157i	$-0.188108\pi$
$379$	8.29166	+	6.95753i	0.425914	+	0.357384i	−0.404493	+	0.914541i	$0.632552\pi$
$380$		0			0
$381$	0.900832	−	1.56029i	0.0461510	−	0.0799359i
$382$		0			0
$383$	−2.20712	+	1.85199i	−0.112778	+	0.0946323i	−0.697433	−	0.716650i	$-0.745675\pi$
$383$	−2.20712	+	1.85199i	−0.112778	+	0.0946323i	0.584655	+	0.811282i	$0.301230\pi$
$384$		0			0
$385$	1.62678	−	9.22595i	0.0829086	−	0.470198i
$386$		0			0
$387$	8.56227	+	7.18459i	0.435244	+	0.365213i
$388$		0			0
$389$	28.6362	+	10.4227i	1.45191	+	0.528453i	0.943125	−	0.332438i	$-0.107871\pi$
$389$	28.6362	+	10.4227i	1.45191	+	0.528453i	0.508788	+	0.860892i	$0.330094\pi$
$390$		0			0
$391$	−0.0267604	+	0.151766i	−0.00135333	+	0.00767512i
$392$		0			0
$393$	8.28477	+	14.3496i	0.417911	+	0.723843i
$394$		0			0
$395$	20.0253	−	7.28861i	1.00758	−	0.366730i
$396$		0			0
$397$	9.72198	+	16.8390i	0.487932	+	0.845124i	0.999904	−	0.0138790i	$-0.00441795\pi$
$397$	9.72198	+	16.8390i	0.487932	+	0.845124i	−0.511971	+	0.859003i	$0.671085\pi$
$398$		0			0
$399$	−1.49669	+	2.59235i	−0.0749284	+	0.129780i
$400$		0			0
$401$	15.4608			0.772075			0.386037	−	0.922483i	$-0.373844\pi$
$401$	15.4608			0.772075			0.386037	+	0.922483i	$0.373844\pi$
$402$		0			0
$403$	−14.8338	+	12.4470i	−0.738923	+	0.620030i
$404$		0			0
$405$	−1.62143	+	0.590153i	−0.0805696	+	0.0293249i
$406$		0			0
$407$	5.81767	+	24.3087i	0.288371	+	1.20494i
$408$		0			0
$409$	26.2675	−	9.56060i	1.29885	−	0.472741i	0.402225	−	0.915541i	$-0.368237\pi$
$409$	26.2675	−	9.56060i	1.29885	−	0.472741i	0.896621	+	0.442799i	$0.146015\pi$
$410$		0			0
$411$	1.37013	−	1.14967i	0.0675833	−	0.0567091i
$412$		0			0
$413$	−5.56279			−0.273727
$414$		0			0
$415$	−4.63287	+	8.02436i	−0.227418	+	0.393900i
$416$		0			0
$417$	−5.41946	−	9.38679i	−0.265392	−	0.459673i
$418$		0			0
$419$	−22.4116	+	8.15716i	−1.09488	+	0.398503i	−0.825426	−	0.564510i	$-0.809065\pi$
$419$	−22.4116	+	8.15716i	−1.09488	+	0.398503i	−0.269453	+	0.963014i	$0.586843\pi$
$420$		0			0
$421$	−1.32136	−	2.28867i	−0.0643993	−	0.111543i	0.832028	−	0.554734i	$-0.187180\pi$
$421$	−1.32136	−	2.28867i	−0.0643993	−	0.111543i	−0.896427	+	0.443191i	$0.853846\pi$
$422$		0			0
$423$	0.0783989	−	0.444622i	0.00381188	−	0.0216183i
$424$		0			0
$425$	−0.221688	−	0.0806878i	−0.0107534	−	0.00391393i
$426$		0			0
$427$	−6.81907	−	5.72188i	−0.329998	−	0.276901i
$428$		0			0
$429$	1.56717	−	8.88787i	0.0756638	−	0.429111i
$430$		0			0
$431$	−10.0272	+	8.41384i	−0.482994	+	0.405280i	−0.851508	−	0.524342i	$-0.824311\pi$
$431$	−10.0272	+	8.41384i	−0.482994	+	0.405280i	0.368513	+	0.929622i	$0.379867\pi$
$432$		0			0
$433$	14.3122	−	24.7895i	0.687802	−	1.19131i	−0.284746	−	0.958603i	$-0.591909\pi$
$433$	14.3122	−	24.7895i	0.687802	−	1.19131i	0.972548	−	0.232704i	$-0.0747574\pi$
$434$		0			0
$435$	−3.47219	−	2.91351i	−0.166479	−	0.139692i
$436$		0			0
$437$	−0.519796	−	2.94791i	−0.0248652	−	0.141018i
$438$		0			0
$439$	5.03670	+	28.5646i	0.240389	+	1.36331i	0.830962	+	0.556328i	$0.187790\pi$
$439$	5.03670	+	28.5646i	0.240389	+	1.36331i	−0.590574	+	0.806984i	$0.701099\pi$
$440$		0			0
$441$	4.93737	+	1.79706i	0.235113	+	0.0855742i
$442$		0			0
$443$	6.67144			0.316970			0.158485	−	0.987361i	$-0.449339\pi$
$443$	6.67144			0.316970			0.158485	+	0.987361i	$0.449339\pi$
$444$		0			0
$445$	8.02412			0.380380
$446$		0			0
$447$	2.12266	+	0.772583i	0.100398	+	0.0365419i
$448$		0			0
$449$	−0.194744	−	1.10445i	−0.00919055	−	0.0521222i	0.979868	−	0.199648i	$-0.0639800\pi$
$449$	−0.194744	−	1.10445i	−0.00919055	−	0.0521222i	−0.989058	+	0.147526i	$0.952869\pi$
$450$		0			0
$451$	−2.38105	−	13.5036i	−0.112119	−	0.635860i
$452$		0			0
$453$	3.22921	+	2.70963i	0.151721	+	0.127309i
$454$		0			0
$455$	−2.50361	+	4.33638i	−0.117371	+	0.203293i
$456$		0			0
$457$	−15.0171	+	12.6008i	−0.702470	+	0.589442i	−0.922475	−	0.386056i	$-0.873837\pi$
$457$	−15.0171	+	12.6008i	−0.702470	+	0.589442i	0.220005	+	0.975499i	$0.429393\pi$
$458$		0			0
$459$	−0.0202535	+	0.114863i	−0.000945353	+	0.00536136i
$460$		0			0
$461$	8.94819	+	7.50842i	0.416759	+	0.349702i	0.826929	−	0.562307i	$-0.190086\pi$
$461$	8.94819	+	7.50842i	0.416759	+	0.349702i	−0.410170	+	0.912009i	$0.634531\pi$
$462$		0			0
$463$	−5.73037	−	2.08568i	−0.266313	−	0.0969300i	0.205412	−	0.978675i	$-0.434146\pi$
$463$	−5.73037	−	2.08568i	−0.266313	−	0.0969300i	−0.471725	+	0.881746i	$0.656369\pi$
$464$		0			0
$465$	2.64174	−	14.9820i	0.122508	−	0.694775i
$466$		0			0
$467$	−14.0011	−	24.2506i	−0.647894	−	1.12219i	−0.983625	−	0.180228i	$-0.942317\pi$
$467$	−14.0011	−	24.2506i	−0.647894	−	1.12219i	0.335731	−	0.941958i	$-0.391017\pi$
$468$		0			0
$469$	0.429349	−	0.156270i	0.0198255	−	0.00721588i
$470$		0			0
$471$	−4.93608	−	8.54954i	−0.227442	−	0.393942i
$472$		0			0
$473$	22.9646	−	39.7759i	1.05591	−	1.82890i
$474$		0			0
$475$	4.58245			0.210257
$476$		0			0
$477$	−2.40728	+	2.01995i	−0.110222	+	0.0924870i
$478$		0			0
$479$	30.5019	−	11.1018i	1.39367	−	0.507253i	0.467375	−	0.884059i	$-0.345200\pi$
$479$	30.5019	−	11.1018i	1.39367	−	0.507253i	0.926292	+	0.376806i	$0.122978\pi$
$480$		0			0
$481$	1.52181	−	13.2726i	0.0693886	−	0.605179i
$482$		0			0
$483$	1.64047	−	0.597084i	0.0746441	−	0.0271682i
$484$		0			0
$485$	−0.822679	+	0.690310i	−0.0373559	+	0.0313454i
$486$		0			0
$487$	19.9414			0.903629			0.451814	−	0.892112i	$-0.350777\pi$
$487$	19.9414			0.903629			0.451814	+	0.892112i	$0.350777\pi$
$488$		0			0
$489$	5.33834	−	9.24627i	0.241408	−	0.418131i
$490$		0			0
$491$	−13.8545	−	23.9968i	−0.625247	−	1.08296i	−0.988493	−	0.151266i	$-0.951665\pi$
$491$	−13.8545	−	23.9968i	−0.625247	−	1.08296i	0.363246	−	0.931693i	$-0.381668\pi$
$492$		0			0
$493$	−0.287907	+	0.104790i	−0.0129667	+	0.00471948i
$494$		0			0
$495$	3.54518	+	6.14042i	0.159344	+	0.275992i
$496$		0			0
$497$	−1.08348	+	6.14472i	−0.0486007	+	0.275628i
$498$		0			0
$499$	−38.2841	−	13.9343i	−1.71383	−	0.623783i	−0.716554	−	0.697532i	$-0.754282\pi$
$499$	−38.2841	−	13.9343i	−1.71383	−	0.623783i	−0.997277	+	0.0737485i	$0.976504\pi$
$500$		0			0
$501$	14.8721	+	12.4791i	0.664434	+	0.557527i
$502$		0			0
$503$	−5.76646	+	32.7032i	−0.257114	+	1.45816i	0.533474	+	0.845816i	$0.320886\pi$
$503$	−5.76646	+	32.7032i	−0.257114	+	1.45816i	−0.790588	+	0.612348i	$0.790225\pi$
$504$		0			0
$505$	−13.9306	+	11.6892i	−0.619903	+	0.520160i
$506$		0			0
$507$	4.08813	−	7.08085i	0.181560	−	0.314472i
$508$		0			0
$509$	−25.5121	−	21.4072i	−1.13081	−	0.948858i	−0.131706	−	0.991289i	$-0.542045\pi$
$509$	−25.5121	−	21.4072i	−1.13081	−	0.948858i	−0.999099	+	0.0424304i	$0.986490\pi$
$510$		0			0
$511$	−1.82504	−	10.3503i	−0.0807349	−	0.457870i
$512$		0			0
$513$	−0.393406	−	2.23112i	−0.0173693	−	0.0985063i
$514$		0			0
$515$	21.9846	+	8.00174i	0.968757	+	0.352599i
$516$		0			0
$517$	−1.85522			−0.0815923
$518$		0			0
$519$	3.11904			0.136911
$520$		0			0
$521$	17.5979	+	6.40512i	0.770979	+	0.280614i	0.697406	−	0.716676i	$-0.254337\pi$
$521$	17.5979	+	6.40512i	0.770979	+	0.280614i	0.0735734	+	0.997290i	$0.476560\pi$
$522$		0			0
$523$	−4.06207	−	23.0372i	−0.177622	−	1.00734i	−0.935074	−	0.354454i	$-0.884667\pi$
$523$	−4.06207	−	23.0372i	−0.177622	−	1.00734i	0.757452	−	0.652891i	$-0.226444\pi$
$524$		0			0
$525$	0.464075	+	2.63190i	0.0202539	+	0.114866i
$526$		0			0
$527$	−0.787753	−	0.661003i	−0.0343151	−	0.0287938i
$528$		0			0
$529$	10.6271	−	18.4067i	0.462049	−	0.800292i
$530$		0			0
$531$	3.22519	−	2.70625i	0.139961	−	0.117441i
$532$		0			0
$533$	−1.27264	+	7.21750i	−0.0551241	+	0.312624i
$534$		0			0
$535$	−16.9828	−	14.2503i	−0.734231	−	0.616093i
$536$		0			0
$537$	16.3600	+	5.95455i	0.705986	+	0.256958i
$538$		0			0
$539$	3.74917	−	21.2626i	0.161488	−	0.915845i
$540$		0			0
$541$	−10.2131	−	17.6896i	−0.439096	−	0.760536i	0.558524	−	0.829488i	$-0.311368\pi$
$541$	−10.2131	−	17.6896i	−0.439096	−	0.760536i	−0.997620	+	0.0689520i	$0.978034\pi$
$542$		0			0
$543$	18.7621	−	6.82883i	0.805157	−	0.293053i
$544$		0			0
$545$	−11.4191	−	19.7785i	−0.489141	−	0.847217i
$546$		0			0
$547$	−9.18593	+	15.9105i	−0.392762	+	0.680284i	−0.992813	−	0.119678i	$-0.961814\pi$
$547$	−9.18593	+	15.9105i	−0.392762	+	0.680284i	0.600051	+	0.799962i	$0.295147\pi$
$548$		0			0
$549$	6.73720			0.287537
$550$		0			0
$551$	4.55891	−	3.82538i	0.194216	−	0.162967i
$552$		0			0
$553$	−15.3341	+	5.58115i	−0.652071	+	0.237335i
$554$		0			0
$555$	5.78676	+	8.75640i	0.245634	+	0.371688i
$556$		0			0
$557$	6.75382	−	2.45819i	0.286168	−	0.104157i	−0.194948	−	0.980814i	$-0.562454\pi$
$557$	6.75382	−	2.45819i	0.286168	−	0.104157i	0.481116	+	0.876657i	$0.340232\pi$
$558$		0			0
$559$	−18.8053	+	15.7795i	−0.795380	+	0.667403i
$560$		0			0
$561$	0.479275			0.0202350
$562$		0			0
$563$	11.0507	−	19.1403i	0.465730	−	0.806668i	−0.533504	−	0.845797i	$-0.679125\pi$
$563$	11.0507	−	19.1403i	0.465730	−	0.806668i	0.999234	+	0.0391294i	$0.0124585\pi$
$564$		0			0
$565$	−4.84091	−	8.38470i	−0.203658	−	0.352747i
$566$		0			0
$567$	1.24159	−	0.451901i	0.0521418	−	0.0189781i
$568$		0			0
$569$	20.0403	+	34.7108i	0.840133	+	1.45515i	0.889782	+	0.456386i	$0.150856\pi$
$569$	20.0403	+	34.7108i	0.840133	+	1.45515i	−0.0496492	+	0.998767i	$0.515810\pi$
$570$		0			0
$571$	−7.27473	+	41.2571i	−0.304438	+	1.72655i	0.321700	+	0.946842i	$0.395746\pi$
$571$	−7.27473	+	41.2571i	−0.304438	+	1.72655i	−0.626138	+	0.779712i	$0.715365\pi$
$572$		0			0
$573$	−0.890004	−	0.323935i	−0.0371805	−	0.0135326i
$574$		0			0
$575$	−2.04725	−	1.71785i	−0.0853764	−	0.0716393i
$576$		0			0
$577$	−1.96448	+	11.1411i	−0.0817825	+	0.463812i	0.916222	+	0.400671i	$0.131223\pi$
$577$	−1.96448	+	11.1411i	−0.0817825	+	0.463812i	−0.998005	+	0.0631410i	$0.979888\pi$
$578$		0			0
$579$	3.20813	−	2.69194i	0.133325	−	0.111873i
$580$		0			0
$581$	3.54755	−	6.14453i	0.147177	−	0.254918i
$582$		0			0
$583$	9.89192	+	8.30031i	0.409682	+	0.343764i
$584$		0			0
$585$	−0.658074	−	3.73213i	−0.0272080	−	0.154304i
$586$		0			0
$587$	1.07120	+	6.07508i	0.0442132	+	0.250745i	0.998901	−	0.0468626i	$-0.0149223\pi$
$587$	1.07120	+	6.07508i	0.0442132	+	0.250745i	−0.954688	+	0.297608i	$0.903811\pi$
$588$		0			0
$589$	18.7699	+	6.83170i	0.773402	+	0.281495i
$590$		0			0
$591$	8.35355			0.343619
$592$		0			0
$593$	29.0674			1.19366			0.596828	−	0.802369i	$-0.296428\pi$
$593$	29.0674			1.19366			0.596828	+	0.802369i	$0.296428\pi$
$594$		0			0
$595$	−0.249874	−	0.0909466i	−0.0102438	−	0.00372845i
$596$		0			0
$597$	−0.657594	−	3.72940i	−0.0269135	−	0.152634i
$598$		0			0
$599$	2.26594	+	12.8508i	0.0925836	+	0.525068i	0.995461	+	0.0951697i	$0.0303394\pi$
$599$	2.26594	+	12.8508i	0.0925836	+	0.525068i	−0.902877	+	0.429898i	$0.858550\pi$
$600$		0			0
$601$	−0.616815	−	0.517569i	−0.0251604	−	0.0211121i	0.630121	−	0.776497i	$-0.283005\pi$
$601$	−0.616815	−	0.517569i	−0.0251604	−	0.0211121i	−0.655281	+	0.755385i	$0.727450\pi$
$602$		0			0
$603$	−0.172903	+	0.299477i	−0.00704115	+	0.0121956i
$604$		0			0
$605$	7.77924	−	6.52756i	0.316271	−	0.265383i
$606$		0			0
$607$	−1.84267	+	10.4503i	−0.0747916	+	0.424164i	0.924304	+	0.381656i	$0.124646\pi$
$607$	−1.84267	+	10.4503i	−0.0747916	+	0.424164i	−0.999096	+	0.0425085i	$0.986465\pi$
$608$		0			0
$609$	2.65878	+	2.23098i	0.107739	+	0.0904038i
$610$		0			0
$611$	0.931788	+	0.339143i	0.0376961	+	0.0137203i
$612$		0			0
$613$	1.34859	−	7.64824i	0.0544691	−	0.308909i	−0.945386	−	0.325954i	$-0.894315\pi$
$613$	1.34859	−	7.64824i	0.0544691	−	0.308909i	0.999855	+	0.0170445i	$0.00542569\pi$
$614$		0			0
$615$	−2.87890	−	4.98640i	−0.116088	−	0.201071i
$616$		0			0
$617$	−27.9451	+	10.1712i	−1.12503	+	0.409476i	−0.836484	−	0.547991i	$-0.815393\pi$
$617$	−27.9451	+	10.1712i	−1.12503	+	0.409476i	−0.288542	+	0.957467i	$0.593171\pi$
$618$		0			0
$619$	−2.51963	−	4.36414i	−0.101273	−	0.175409i	0.810937	−	0.585134i	$-0.198958\pi$
$619$	−2.51963	−	4.36414i	−0.101273	−	0.175409i	−0.912209	+	0.409725i	$0.865625\pi$
$620$		0			0
$621$	−0.660635	+	1.14425i	−0.0265104	+	0.0459173i
$622$		0			0
$623$	−6.14435			−0.246168
$624$		0			0
$625$	−8.26976	+	6.93915i	−0.330791	+	0.277566i
$626$		0			0
$627$	−8.74806	+	3.18403i	−0.349364	+	0.127158i
$628$		0			0
$629$	0.708172	−	0.0428068i	0.0282367	−	0.00170682i
$630$		0			0
$631$	40.4556	−	14.7246i	1.61051	−	0.586178i	0.628970	−	0.777430i	$-0.283477\pi$
$631$	40.4556	−	14.7246i	1.61051	−	0.586178i	0.981541	+	0.191252i	$0.0612547\pi$
$632$		0			0
$633$	−3.86404	+	3.24232i	−0.153582	+	0.128870i
$634$		0			0
$635$	−3.10876			−0.123367
$636$		0			0
$637$	−5.76995	+	9.99384i	−0.228614	+	0.395970i
$638$		0			0
$639$	−2.36118	−	4.08968i	−0.0934068	−	0.161785i
$640$		0			0
$641$	13.0344	−	4.74413i	0.514827	−	0.187382i	−0.0715239	−	0.997439i	$-0.522786\pi$
$641$	13.0344	−	4.74413i	0.514827	−	0.187382i	0.586351	+	0.810057i	$0.300564\pi$
$642$		0			0
$643$	5.47589	+	9.48452i	0.215948	+	0.374033i	0.953565	−	0.301186i	$-0.0973825\pi$
$643$	5.47589	+	9.48452i	0.215948	+	0.374033i	−0.737617	+	0.675219i	$0.764049\pi$
$644$		0			0
$645$	3.34902	−	18.9933i	0.131868	−	0.747859i
$646$		0			0
$647$	43.1495	+	15.7051i	1.69638	+	0.617433i	0.995405	−	0.0957499i	$-0.0305249\pi$
$647$	43.1495	+	15.7051i	1.69638	+	0.617433i	0.700978	+	0.713183i	$0.252747\pi$
$648$		0			0
$649$	−13.2529	−	11.1205i	−0.520220	−	0.436517i
$650$		0			0
$651$	−2.02287	+	11.4723i	−0.0792825	+	0.449633i
$652$		0			0
$653$	−29.9648	+	25.1435i	−1.17261	+	0.983941i	−0.999999	−	0.00104881i	$-0.999666\pi$
$653$	−29.9648	+	25.1435i	−1.17261	+	0.983941i	−0.172615	+	0.984989i	$0.555222\pi$
$654$		0			0
$655$	14.2953	−	24.7602i	0.558564	−	0.967461i
$656$		0			0
$657$	6.09345	+	5.11302i	0.237728	+	0.199478i
$658$		0			0
$659$	0.849174	+	4.81591i	0.0330791	+	0.187601i	0.996870	−	0.0790582i	$-0.0251913\pi$
$659$	0.849174	+	4.81591i	0.0330791	+	0.187601i	−0.963791	+	0.266659i	$0.914080\pi$
$660$		0			0
$661$	−1.46228	−	8.29299i	−0.0568760	−	0.322560i	0.943074	−	0.332584i	$-0.107920\pi$
$661$	−1.46228	−	8.29299i	−0.0568760	−	0.322560i	−0.999950	+	0.0100238i	$0.996809\pi$
$662$		0			0
$663$	−0.240717	−	0.0876140i	−0.00934869	−	0.00340265i
$664$		0			0
$665$	5.16507			0.200293
$666$		0			0
$667$	−3.47079			−0.134389
$668$		0			0
$669$	7.43026	+	2.70439i	0.287270	+	0.104558i
$670$		0			0
$671$	−4.80734	−	27.2638i	−0.185585	−	1.05251i
$672$		0			0
$673$	0.203007	+	1.15131i	0.00782533	+	0.0443796i	0.988470	−	0.151414i	$-0.0483827\pi$
$673$	0.203007	+	1.15131i	0.00782533	+	0.0443796i	−0.980645	+	0.195794i	$0.937272\pi$
$674$		0			0
$675$	−1.54946	−	1.30015i	−0.0596387	−	0.0500428i
$676$		0			0
$677$	−15.3875	+	26.6519i	−0.591389	+	1.02432i	0.402657	+	0.915351i	$0.368087\pi$
$677$	−15.3875	+	26.6519i	−0.591389	+	1.02432i	−0.994046	+	0.108964i	$0.965247\pi$
$678$		0			0
$679$	0.629955	−	0.528595i	0.0241754	−	0.0202856i
$680$		0			0
$681$	−3.31879	+	18.8218i	−0.127176	+	0.721252i
$682$		0			0
$683$	10.0292	+	8.41549i	0.383756	+	0.322010i	0.814175	−	0.580620i	$-0.197190\pi$
$683$	10.0292	+	8.41549i	0.383756	+	0.322010i	−0.430419	+	0.902629i	$0.641634\pi$
$684$		0			0
$685$	−2.90005	−	1.05553i	−0.110805	−	0.0403298i
$686$		0			0
$687$	2.17801	−	12.3521i	0.0830961	−	0.471261i
$688$		0			0
$689$	−3.45091	−	5.97715i	−0.131469	−	0.227711i
$690$		0			0
$691$	−27.5289	+	10.0197i	−1.04725	+	0.381167i	−0.807623	−	0.589699i	$-0.799246\pi$
$691$	−27.5289	+	10.0197i	−1.04725	+	0.381167i	−0.239624	+	0.970866i	$0.577024\pi$
$692$		0			0
$693$	−2.71467	−	4.70194i	−0.103122	−	0.178612i
$694$		0			0
$695$	−9.35124	+	16.1968i	−0.354713	+	0.614381i
$696$		0			0
$697$	−0.389201			−0.0147420
$698$		0			0
$699$	−17.9498	+	15.0617i	−0.678923	+	0.569684i
$700$		0			0
$701$	7.52915	−	2.74039i	0.284372	−	0.103503i	−0.195896	−	0.980625i	$-0.562762\pi$
$701$	7.52915	−	2.74039i	0.284372	−	0.103503i	0.480268	+	0.877122i	$0.340539\pi$
$702$		0			0
$703$	−12.6417	+	5.48604i	−0.476789	+	0.206910i
$704$		0			0
$705$	−0.732046	+	0.266443i	−0.0275705	+	0.0100348i
$706$		0			0
$707$	10.6671	−	8.95080i	0.401179	−	0.336629i
$708$		0			0
$709$	−39.7253			−1.49191			−0.745957	−	0.665995i	$-0.768007\pi$
$709$	−39.7253			−1.49191			−0.745957	+	0.665995i	$0.768007\pi$
$710$		0			0
$711$	6.17519	−	10.6957i	0.231588	−	0.401122i
$712$		0			0
$713$	−5.82462	−	10.0885i	−0.218134	−	0.377819i
$714$		0			0
$715$	−14.6334	+	5.32612i	−0.547258	+	0.199186i
$716$		0			0
$717$	7.24861	+	12.5550i	0.270704	+	0.468874i
$718$		0			0
$719$	2.61693	−	14.8414i	0.0975951	−	0.553489i	−0.896326	−	0.443395i	$-0.853774\pi$
$719$	2.61693	−	14.8414i	0.0975951	−	0.553489i	0.993921	−	0.110094i	$-0.0351151\pi$
$720$		0			0
$721$	−16.8344	−	6.12721i	−0.626945	−	0.228189i
$722$		0			0
$723$	−7.10427	−	5.96119i	−0.264211	−	0.221699i
$724$		0			0
$725$	0.922640	−	5.23255i	0.0342660	−	0.194332i
$726$		0			0
$727$	−32.8940	+	27.6014i	−1.21997	+	1.02368i	−0.221146	+	0.975241i	$0.570980\pi$
$727$	−32.8940	+	27.6014i	−1.21997	+	1.02368i	−0.998826	+	0.0484376i	$0.984576\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−0.998663	−	0.837978i	−0.0369369	−	0.0309937i
$732$		0			0
$733$	−3.62583	−	20.5631i	−0.133923	−	0.759516i	−0.975604	−	0.219540i	$-0.929544\pi$
$733$	−3.62583	−	20.5631i	−0.133923	−	0.759516i	0.841680	−	0.539976i	$-0.181567\pi$
$734$		0			0
$735$	−1.57432	−	8.92842i	−0.0580697	−	0.329330i
$736$		0			0
$737$	1.33528	+	0.486003i	0.0491857	+	0.0179021i
$738$		0			0
$739$	−2.26691			−0.0833898			−0.0416949	−	0.999130i	$-0.513276\pi$
$739$	−2.26691			−0.0833898			−0.0416949	+	0.999130i	$0.513276\pi$
$740$		0			0
$741$	4.97580			0.182791
$742$		0			0
$743$	−28.8861	−	10.5137i	−1.05973	−	0.385709i	−0.247401	−	0.968913i	$-0.579576\pi$
$743$	−28.8861	−	10.5137i	−1.05973	−	0.385709i	−0.812326	+	0.583204i	$0.801799\pi$
$744$		0			0
$745$	−0.676826	−	3.83847i	−0.0247970	−	0.140631i
$746$		0			0
$747$	0.932474	+	5.28832i	0.0341174	+	0.193490i
$748$		0			0
$749$	13.0043	+	10.9119i	0.475168	+	0.398714i
$750$		0			0
$751$	−0.872984	+	1.51205i	−0.0318557	+	0.0551756i	−0.881514	−	0.472158i	$-0.843475\pi$
$751$	−0.872984	+	1.51205i	−0.0318557	+	0.0551756i	0.849658	+	0.527334i	$0.176808\pi$
$752$		0			0
$753$	−4.81550	+	4.04068i	−0.175487	+	0.147251i
$754$		0			0
$755$	1.26306	−	7.16319i	0.0459676	−	0.260695i
$756$		0			0
$757$	−32.4685	−	27.2443i	−1.18009	−	0.990211i	−0.999978	−	0.00656434i	$-0.997910\pi$
$757$	−32.4685	−	27.2443i	−1.18009	−	0.990211i	−0.180109	−	0.983647i	$-0.557645\pi$
$758$		0			0
$759$	5.10190	+	1.85694i	0.185187	+	0.0674027i
$760$		0			0
$761$	2.37063	−	13.4445i	0.0859352	−	0.487363i	−0.911216	−	0.411930i	$-0.864855\pi$
$761$	2.37063	−	13.4445i	0.0859352	−	0.487363i	0.997151	−	0.0754331i	$-0.0240339\pi$
$762$		0			0
$763$	8.74402	+	15.1451i	0.316555	+	0.548289i
$764$		0			0
$765$	0.189116	−	0.0688327i	0.00683752	−	0.00248865i
$766$		0			0
$767$	4.62341	+	8.00799i	0.166942	+	0.289152i
$768$		0			0
$769$	−14.5476	+	25.1971i	−0.524599	+	0.908632i	0.474991	+	0.879991i	$0.342451\pi$
$769$	−14.5476	+	25.1971i	−0.524599	+	0.908632i	−0.999590	+	0.0286411i	$0.990882\pi$
$770$		0			0
$771$	−1.34244			−0.0483468
$772$		0			0
$773$	−26.6215	+	22.3381i	−0.957508	+	0.803445i	−0.980546	−	0.196290i	$-0.937111\pi$
$773$	−26.6215	+	22.3381i	−0.957508	+	0.803445i	0.0230375	+	0.999735i	$0.492666\pi$
$774$		0			0
$775$	16.7578	−	6.09935i	0.601959	−	0.219095i
$776$		0			0
$777$	−4.43112	−	6.70508i	−0.158966	−	0.240543i
$778$		0			0
$779$	7.10396	−	2.58563i	0.254526	−	0.0926398i
$780$		0			0
$781$	−14.8651	+	12.4733i	−0.531915	+	0.446330i
$782$		0			0
$783$	−2.62686			−0.0938761
$784$		0			0
$785$	−8.51716	+	14.7522i	−0.303991	+	0.526527i
$786$		0			0
$787$	−27.1762	−	47.0706i	−0.968727	−	1.67788i	−0.699249	−	0.714878i	$-0.746482\pi$
$787$	−27.1762	−	47.0706i	−0.968727	−	1.67788i	−0.269478	−	0.963006i	$-0.586851\pi$
$788$		0			0
$789$	20.7589	−	7.55564i	0.739038	−	0.268988i
$790$		0			0
$791$	3.70685	+	6.42046i	0.131801	+	0.228285i
$792$		0			0
$793$	−2.56946	+	14.5721i	−0.0912442	+	0.517471i
$794$		0			0
$795$	5.09532	+	1.85454i	0.180712	+	0.0657739i
$796$		0			0
$797$	−27.6107	−	23.1681i	−0.978020	−	0.820656i	0.00576940	−	0.999983i	$-0.498164\pi$
$797$	−27.6107	−	23.1681i	−0.978020	−	0.820656i	−0.983790	+	0.179327i	$0.942608\pi$
$798$		0			0
$799$	−0.00914408	+	0.0518587i	−0.000323494	+	0.00183463i
$800$		0			0
$801$	3.56237	−	2.98918i	0.125870	−	0.105617i
$802$		0			0
$803$	16.3431	−	28.3071i	0.576735	−	0.998935i
$804$		0			0
$805$	−2.30755	−	1.93626i	−0.0813303	−	0.0682443i
$806$		0			0
$807$	2.60268	+	14.7605i	0.0916187	+	0.519595i
$808$		0			0
$809$	4.36074	+	24.7310i	0.153316	+	0.869495i	0.960310	+	0.278936i	$0.0899818\pi$
$809$	4.36074	+	24.7310i	0.153316	+	0.869495i	−0.806994	+	0.590559i	$0.798907\pi$
$810$		0			0
$811$	41.1701	+	14.9847i	1.44568	+	0.526184i	0.941381	−	0.337346i	$-0.109529\pi$
$811$	41.1701	+	14.9847i	1.44568	+	0.526184i	0.504298	+	0.863530i	$0.331751\pi$
$812$		0			0
$813$	−7.29782			−0.255946
$814$		0			0
$815$	−18.4225			−0.645313
$816$		0			0
$817$	23.7953	+	8.66079i	0.832493	+	0.303003i
$818$		0			0
$819$	0.503911	+	2.85782i	0.0176081	+	0.0998603i
$820$		0			0
$821$	6.71030	+	38.0560i	0.234191	+	1.32816i	0.844311	+	0.535854i	$0.180010\pi$
$821$	6.71030	+	38.0560i	0.234191	+	1.32816i	−0.610120	+	0.792309i	$0.708879\pi$
$822$		0			0
$823$	9.00590	+	7.55685i	0.313926	+	0.263415i	0.786112	−	0.618083i	$-0.212091\pi$
$823$	9.00590	+	7.55685i	0.313926	+	0.263415i	−0.472186	+	0.881499i	$0.656535\pi$
$824$		0			0
$825$	−4.15576	+	7.19799i	−0.144685	+	0.250602i
$826$		0			0
$827$	32.7708	−	27.4980i	1.13955	−	0.956199i	0.140129	−	0.990133i	$-0.455248\pi$
$827$	32.7708	−	27.4980i	1.13955	−	0.956199i	0.999424	+	0.0339346i	$0.0108038\pi$
$828$		0			0
$829$	−3.84201	+	21.7891i	−0.133439	+	0.756767i	0.842496	+	0.538703i	$0.181085\pi$
$829$	−3.84201	+	21.7891i	−0.133439	+	0.756767i	−0.975934	+	0.218065i	$0.930026\pi$
$830$		0			0
$831$	−7.50712	−	6.29923i	−0.260419	−	0.218518i
$832$		0			0
$833$	−0.575872	−	0.209600i	−0.0199528	−	0.00726222i
$834$		0			0
$835$	5.81702	−	32.9899i	0.201306	−	1.14166i
$836$		0			0
$837$	−4.40835	−	7.63548i	−0.152375	−	0.263921i
$838$		0			0
$839$	15.8165	−	5.75673i	0.546046	−	0.198744i	−0.0542429	−	0.998528i	$-0.517275\pi$
$839$	15.8165	−	5.75673i	0.546046	−	0.198744i	0.600289	+	0.799783i	$0.295052\pi$
$840$		0			0
$841$	11.0498	+	19.1388i	0.381028	+	0.659960i
$842$		0			0
$843$	−14.3643	+	24.8797i	−0.494733	+	0.856903i
$844$		0			0
$845$	−14.1081			−0.485333
$846$		0			0
$847$	−5.95684	+	4.99838i	−0.204679	+	0.171746i
$848$		0			0
$849$	−9.76782	+	3.55519i	−0.335231	+	0.122014i
$850$		0			0
$851$	7.70438	+	2.28812i	0.264103	+	0.0784357i
$852$		0			0
$853$	15.1086	−	5.49907i	0.517308	−	0.188285i	−0.0701547	−	0.997536i	$-0.522349\pi$
$853$	15.1086	−	5.49907i	0.517308	−	0.188285i	0.587462	+	0.809252i	$0.300127\pi$
$854$		0			0
$855$	−2.99460	+	2.51276i	−0.102413	+	0.0859347i
$856$		0			0
$857$	−30.3418			−1.03646			−0.518228	−	0.855242i	$-0.673408\pi$
$857$	−30.3418			−1.03646			−0.518228	+	0.855242i	$0.673408\pi$
$858$		0			0
$859$	−25.3147	+	43.8463i	−0.863725	+	1.49602i	0.00458253	+	0.999990i	$0.498541\pi$
$859$	−25.3147	+	43.8463i	−0.863725	+	1.49602i	−0.868308	+	0.496026i	$0.834792\pi$
$860$		0			0
$861$	2.20447	+	3.81826i	0.0751283	+	0.130126i
$862$		0			0
$863$	−50.3101	+	18.3114i	−1.71258	+	0.623327i	−0.997156	−	0.0753673i	$-0.975987\pi$
$863$	−50.3101	+	18.3114i	−1.71258	+	0.623327i	−0.715421	+	0.698694i	$0.753765\pi$
$864$		0			0
$865$	−2.69094	−	4.66084i	−0.0914946	−	0.158473i
$866$		0			0
$867$	−2.94966	+	16.7283i	−0.100176	+	0.568124i
$868$		0			0
$869$	−47.6893	−	17.3575i	−1.61775	−	0.588812i
$870$		0			0
$871$	−0.581806	−	0.488193i	−0.0197137	−	0.0165418i
$872$		0			0
$873$	−0.108077	+	0.612936i	−0.00365786	+	0.0207447i
$874$		0			0
$875$	12.2648	−	10.2914i	0.414627	−	0.347913i
$876$		0			0
$877$	−20.8310	+	36.0804i	−0.703415	+	1.21835i	0.263846	+	0.964565i	$0.415009\pi$
$877$	−20.8310	+	36.0804i	−0.703415	+	1.21835i	−0.967261	+	0.253785i	$0.918324\pi$
$878$		0			0
$879$	−17.1671	−	14.4049i	−0.579032	−	0.485865i
$880$		0			0
$881$	4.58483	+	26.0018i	0.154467	+	0.876024i	0.959272	+	0.282485i	$0.0911588\pi$
$881$	4.58483	+	26.0018i	0.154467	+	0.876024i	−0.804805	+	0.593539i	$0.797730\pi$
$882$		0			0
$883$	−1.19102	−	6.75459i	−0.0400809	−	0.227310i	0.958187	−	0.286143i	$-0.0923732\pi$
$883$	−1.19102	−	6.75459i	−0.0400809	−	0.227310i	−0.998268	+	0.0588328i	$0.981262\pi$
$884$		0			0
$885$	−6.82653	−	2.48465i	−0.229471	−	0.0835207i
$886$		0			0
$887$	−5.93737			−0.199357			−0.0996786	−	0.995020i	$-0.531781\pi$
$887$	−5.93737			−0.199357			−0.0996786	+	0.995020i	$0.531781\pi$
$888$		0			0
$889$	2.38048			0.0798389
$890$		0			0
$891$	3.86136	+	1.40542i	0.129360	+	0.0470834i
$892$		0			0
$893$	−0.177616	−	1.00731i	−0.00594368	−	0.0337083i
$894$		0			0
$895$	−5.21652	−	29.5844i	−0.174369	−	0.988896i
$896$		0			0
$897$	−2.22299	−	1.86531i	−0.0742235	−	0.0622809i
$898$		0			0
$899$	11.5801	−	20.0573i	0.386218	−	0.668949i
$900$		0			0
$901$	0.280774	−	0.235597i	0.00935392	−	0.00784887i
$902$		0			0
$903$	−2.56446	+	14.5438i	−0.0853400	+	0.483987i
$904$		0			0
$905$	−26.3913	−	22.1450i	−0.877278	−	0.736124i
$906$		0			0
$907$	−36.5607	−	13.3070i	−1.21398	−	0.441852i	−0.345896	−	0.938273i	$-0.612425\pi$
$907$	−36.5607	−	13.3070i	−1.21398	−	0.441852i	−0.868082	+	0.496421i	$0.834647\pi$
$908$		0			0
$909$	−1.83009	+	10.3790i	−0.0607003	+	0.344248i
$910$		0			0
$911$	−3.30211	−	5.71943i	−0.109404	−	0.189493i	0.806125	−	0.591745i	$-0.201561\pi$
$911$	−3.30211	−	5.71943i	−0.109404	−	0.189493i	−0.915529	+	0.402252i	$0.868228\pi$
$912$		0			0
$913$	20.7351	−	7.54697i	0.686233	−	0.249768i
$914$		0			0
$915$	−5.81250	−	10.0675i	−0.192155	−	0.332823i
$916$		0			0
$917$	−10.9464	+	18.9598i	−0.361483	+	0.626106i
$918$		0			0
$919$	7.95527			0.262420			0.131210	−	0.991355i	$-0.458114\pi$
$919$	7.95527			0.262420			0.131210	+	0.991355i	$0.458114\pi$
$920$		0			0
$921$	13.0944	−	10.9875i	0.431476	−	0.362052i
$922$		0			0
$923$	9.74623	−	3.54734i	0.320801	−	0.116762i
$924$		0			0
$925$	−5.49762	+	11.0069i	−0.180761	+	0.361904i
$926$		0			0
$927$	12.7411	−	4.63736i	0.418471	−	0.152311i
$928$		0			0
$929$	−45.3279	+	38.0346i	−1.48716	+	1.24788i	−0.589056	+	0.808092i	$0.700500\pi$
$929$	−45.3279	+	38.0346i	−1.48716	+	1.24788i	−0.898104	+	0.439783i	$0.855055\pi$
$930$		0			0
$931$	11.9037			0.390128
$932$		0			0
$933$	2.90465	−	5.03100i	0.0950939	−	0.164708i
$934$		0			0
$935$	−0.413493	−	0.716190i	−0.0135227	−	0.0234219i
$936$		0			0
$937$	−47.3410	+	17.2307i	−1.54656	+	0.562902i	−0.967608	−	0.252458i	$-0.918761\pi$
$937$	−47.3410	+	17.2307i	−1.54656	+	0.562902i	−0.578954	+	0.815360i	$0.696539\pi$
$938$		0			0
$939$	12.8943	+	22.3335i	0.420788	+	0.728827i
$940$		0			0
$941$	9.38110	−	53.2028i	0.305815	−	1.73436i	−0.313829	−	0.949480i	$-0.601612\pi$
$941$	9.38110	−	53.2028i	0.305815	−	1.73436i	0.619644	−	0.784883i	$-0.287277\pi$
$942$		0			0
$943$	−4.14306	−	1.50795i	−0.134917	−	0.0491056i
$944$		0			0
$945$	−1.74646	−	1.46545i	−0.0568124	−	0.0476712i
$946$		0			0
$947$	5.71193	−	32.3940i	0.185613	−	1.05266i	−0.739553	−	0.673099i	$-0.764963\pi$
$947$	5.71193	−	32.3940i	0.185613	−	1.05266i	0.925166	−	0.379564i	$-0.123926\pi$
$948$		0			0
$949$	−13.3831	+	11.2297i	−0.434432	+	0.364532i
$950$		0			0
$951$	5.40057	−	9.35406i	0.175125	−	0.303326i
$952$		0			0
$953$	−23.9107	−	20.0634i	−0.774542	−	0.649918i	0.167325	−	0.985902i	$-0.446487\pi$
$953$	−23.9107	−	20.0634i	−0.774542	−	0.649918i	−0.941868	+	0.335983i	$0.890931\pi$
$954$		0			0
$955$	0.283785	+	1.60943i	0.00918307	+	0.0520798i
$956$		0			0
$957$	1.87439	+	10.6302i	0.0605906	+	0.343626i
$958$		0			0
$959$	2.22067	+	0.808258i	0.0717092	+	0.0261000i
$960$		0			0
$961$	46.7342			1.50755
$962$		0			0
$963$	−12.8482			−0.414028
$964$		0			0
$965$	−6.79043	−	2.47151i	−0.218592	−	0.0795609i
$966$		0			0
$967$	−2.18897	−	12.4143i	−0.0703925	−	0.399216i	−0.999563	−	0.0295641i	$-0.990588\pi$
$967$	−2.18897	−	12.4143i	−0.0703925	−	0.399216i	0.929170	−	0.369652i	$-0.120523\pi$
$968$		0			0
$969$	0.0458851	+	0.260227i	0.00147404	+	0.00835970i
$970$		0			0
$971$	44.1545	+	37.0500i	1.41699	+	1.18899i	0.952932	+	0.303185i	$0.0980499\pi$
$971$	44.1545	+	37.0500i	1.41699	+	1.18899i	0.464053	+	0.885807i	$0.346395\pi$
$972$		0			0
$973$	7.16058	−	12.4025i	0.229558	−	0.397605i
$974$		0			0
$975$	3.40308	−	2.85552i	0.108986	−	0.0914499i
$976$		0			0
$977$	−9.60387	+	54.4662i	−0.307255	+	1.74253i	0.305442	+	0.952211i	$0.401196\pi$
$977$	−9.60387	+	54.4662i	−0.307255	+	1.74253i	−0.612696	+	0.790318i	$0.709915\pi$
$978$		0			0
$979$	−14.6384	−	12.2831i	−0.467845	−	0.392568i
$980$		0			0
$981$	−12.4376	−	4.52690i	−0.397101	−	0.144533i
$982$		0			0
$983$	−0.184012	+	1.04358i	−0.00586907	+	0.0332851i	−0.987602	−	0.156981i	$-0.949824\pi$
$983$	−0.184012	+	1.04358i	−0.00586907	+	0.0332851i	0.981733	+	0.190266i	$0.0609350\pi$
$984$		0			0
$985$	−7.20700	−	12.4829i	−0.229634	−	0.397738i
$986$		0			0
$987$	0.560554	−	0.204025i	0.0178426	−	0.00649418i
$988$		0			0
$989$	−7.38408	−	12.7896i	−0.234800	−	0.406686i
$990$		0			0
$991$	14.6060	−	25.2983i	0.463975	−	0.803629i	−0.535179	−	0.844738i	$-0.679756\pi$
$991$	14.6060	−	25.2983i	0.463975	−	0.803629i	0.999155	+	0.0411098i	$0.0130894\pi$
$992$		0			0
$993$	1.60832			0.0510385
$994$		0			0
$995$	−5.00558	+	4.20018i	−0.158688	+	0.133155i
$996$		0			0
$997$	−48.1974	+	17.5424i	−1.52643	+	0.555574i	−0.962744	−	0.270416i	$-0.912839\pi$
$997$	−48.1974	+	17.5424i	−1.52643	+	0.555574i	−0.563684	+	0.825990i	$0.690617\pi$
$998$		0			0
$999$	5.83104	+	1.73176i	0.184486	+	0.0547903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.bo.c.673.4	✓	24
37.16	even	9	inner	888.2.bo.c.793.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bo.c.673.4	✓	24	1.1	even	1	trivial
888.2.bo.c.793.4	yes	24	37.16	even	9	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:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.299629 + 1.69928i) q^{5} +(-0.229436 - 1.30120i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.299629 + 1.69928i) q^{5} +(-0.229436 - 1.30120i) q^{7} +(0.766044 + 0.642788i) q^{9} +(2.05459 - 3.55865i) q^{11} +(-1.68246 + 1.41175i) q^{13} +(0.299629 - 1.69928i) q^{15} +(-0.0893478 - 0.0749717i) q^{17} +(2.12891 + 0.774859i) q^{19} +(-0.229436 + 1.30120i) q^{21} +(-0.660635 - 1.14425i) q^{23} +(1.90069 - 0.691796i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(1.31343 - 2.27492i) q^{29} +8.81670 q^{31} +(-3.14781 + 2.64133i) q^{33} +(2.14235 - 0.779752i) q^{35} +(-4.41526 + 4.18395i) q^{37} +(2.06385 - 0.751179i) q^{39} +(2.55621 - 2.14492i) q^{41} +11.1772 q^{43} +(-0.862746 + 1.49432i) q^{45} +(-0.225741 - 0.390994i) q^{47} +(4.93737 - 1.79706i) q^{49} +(0.0583177 + 0.101009i) q^{51} +(-0.545685 + 3.09474i) q^{53} +(6.66275 + 2.42504i) q^{55} +(-1.73550 - 1.45626i) q^{57} +(0.731091 - 4.14622i) q^{59} +(5.16100 - 4.33059i) q^{61} +(0.660635 - 1.14425i) q^{63} +(-2.90308 - 2.43597i) q^{65} +(0.0600486 + 0.340552i) q^{67} +(0.229436 + 1.30120i) q^{69} +(-4.43757 - 1.61514i) q^{71} +7.95444 q^{73} -2.02268 q^{75} +(-5.10190 - 1.85694i) q^{77} +(-2.14462 - 12.1627i) q^{79} +(0.173648 + 0.984808i) q^{81} +(4.11359 + 3.45171i) q^{83} +(0.100627 - 0.174291i) q^{85} +(-2.01229 + 1.68851i) q^{87} +(0.807523 - 4.57969i) q^{89} +(2.22299 + 1.86531i) q^{91} +(-8.28499 - 3.01549i) q^{93} +(-0.678820 + 3.84978i) q^{95} +(0.311196 + 0.539007i) q^{97} +(3.86136 - 1.40542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) \) 24 * q + 3 * q^5 + 15 * q^7	\( 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more