LMFDB - Embedded newform 1386.2.ba.a.989.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(989,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1386.989");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			989.14
Character	$\chi$	$=$	1386.989
Dual form			1386.2.ba.a.1187.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.34835 + 1.35582i) q^{5} +(-0.222226 - 2.63640i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.34835 + 1.35582i) q^{5} +(-0.222226 - 2.63640i) q^{7} +1.00000 q^{8} +(-2.34835 + 1.35582i) q^{10} +(-2.96348 + 1.48923i) q^{11} -2.18074i q^{13} +(2.39430 + 1.12575i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0281751 + 0.0488007i) q^{17} +(2.38555 + 1.37730i) q^{19} -2.71165i q^{20} +(0.192032 - 3.31106i) q^{22} +(6.02718 + 3.47980i) q^{23} +(1.17651 + 2.03778i) q^{25} +(1.88857 + 1.09037i) q^{26} +(-2.17208 + 1.51065i) q^{28} +6.43297 q^{29} +(3.65147 + 6.32453i) q^{31} +(-0.500000 - 0.866025i) q^{32} -0.0563502 q^{34} +(3.05263 - 6.49251i) q^{35} +(-1.62140 + 2.80836i) q^{37} +(-2.38555 + 1.37730i) q^{38} +(2.34835 + 1.35582i) q^{40} +2.71397 q^{41} -10.6345i q^{43} +(2.77145 + 1.82183i) q^{44} +(-6.02718 + 3.47980i) q^{46} +(-2.58268 - 1.49111i) q^{47} +(-6.90123 + 1.17175i) q^{49} -2.35302 q^{50} +(-1.88857 + 1.09037i) q^{52} +(10.1931 - 5.88497i) q^{53} +(-8.97843 - 0.520722i) q^{55} +(-0.222226 - 2.63640i) q^{56} +(-3.21649 + 5.57112i) q^{58} +(12.2489 - 7.07189i) q^{59} +(10.2720 + 5.93056i) q^{61} -7.30294 q^{62} +1.00000 q^{64} +(2.95669 - 5.12114i) q^{65} +(0.749028 + 1.29735i) q^{67} +(0.0281751 - 0.0488007i) q^{68} +(4.09636 + 5.88991i) q^{70} -1.82248i q^{71} +(6.82420 - 3.93995i) q^{73} +(-1.62140 - 2.80836i) q^{74} -2.75460i q^{76} +(4.58476 + 7.48198i) q^{77} +(-7.82062 - 4.51524i) q^{79} +(-2.34835 + 1.35582i) q^{80} +(-1.35699 + 2.35037i) q^{82} -17.2299 q^{83} +0.152802i q^{85} +(9.20975 + 5.31725i) q^{86} +(-2.96348 + 1.48923i) q^{88} +(7.43764 + 4.29412i) q^{89} +(-5.74929 + 0.484616i) q^{91} -6.95959i q^{92} +(2.58268 - 1.49111i) q^{94} +(3.73475 + 6.46878i) q^{95} +6.25716 q^{97} +(2.43585 - 6.56252i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.34835	+	1.35582i	1.05022	+	0.606343i	0.922710	−	0.385495i	$-0.125969\pi$
$5$	2.34835	+	1.35582i	1.05022	+	0.606343i	0.127506	+	0.991838i	$0.459303\pi$
$6$		0			0
$7$	−0.222226	−	2.63640i	−0.0839935	−	0.996466i
$7$	−0.222226	−	2.63640i	−0.0839935	−	0.996466i
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.34835	+	1.35582i	−0.742615	+	0.428749i
$11$	−2.96348	+	1.48923i	−0.893522	+	0.449019i
$11$	−2.96348	+	1.48923i	−0.893522	+	0.449019i
$12$		0			0
$13$		−	2.18074i		−	0.604827i	−0.953177	−	0.302414i	$-0.902208\pi$
$13$		−	2.18074i		−	0.604827i	0.953177	−	0.302414i	$-0.0977924\pi$
$14$	2.39430	+	1.12575i	0.639905	+	0.300869i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0281751	+	0.0488007i	0.00683347	+	0.0118359i	0.869422	−	0.494070i	$-0.164491\pi$
$17$	0.0281751	+	0.0488007i	0.00683347	+	0.0118359i	−0.862588	+	0.505906i	$0.831158\pi$
$18$		0			0
$19$	2.38555	+	1.37730i	0.547284	+	0.315974i	0.748026	−	0.663670i	$-0.231002\pi$
$19$	2.38555	+	1.37730i	0.547284	+	0.315974i	−0.200742	+	0.979644i	$0.564335\pi$
$20$		−	2.71165i		−	0.606343i
$21$		0			0
$22$	0.192032	−	3.31106i	0.0409413	−	0.705921i
$23$	6.02718	+	3.47980i	1.25675	+	0.725587i	0.972442	−	0.233144i	$-0.0749014\pi$
$23$	6.02718	+	3.47980i	1.25675	+	0.725587i	0.284312	+	0.958732i	$0.408235\pi$
$24$		0			0
$25$	1.17651	+	2.03778i	0.235302	+	0.407556i
$26$	1.88857	+	1.09037i	0.370379	+	0.213839i
$27$		0			0
$28$	−2.17208	+	1.51065i	−0.410484	+	0.285487i
$29$	6.43297			1.19457			0.597286	−	0.802028i	$-0.296246\pi$
$29$	6.43297			1.19457			0.597286	+	0.802028i	$0.296246\pi$
$30$		0			0
$31$	3.65147	+	6.32453i	0.655823	+	1.13592i	0.981687	+	0.190502i	$0.0610116\pi$
$31$	3.65147	+	6.32453i	0.655823	+	1.13592i	−0.325864	+	0.945417i	$0.605655\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−0.0563502			−0.00966399
$35$	3.05263	−	6.49251i	0.515989	−	1.09743i
$36$		0			0
$37$	−1.62140	+	2.80836i	−0.266557	+	0.461691i	−0.967970	−	0.251064i	$-0.919219\pi$
$37$	−1.62140	+	2.80836i	−0.266557	+	0.461691i	0.701413	+	0.712755i	$0.252553\pi$
$38$	−2.38555	+	1.37730i	−0.386988	+	0.223428i
$39$		0			0
$40$	2.34835	+	1.35582i	0.371307	+	0.214374i
$41$	2.71397			0.423852			0.211926	−	0.977286i	$-0.432026\pi$
$41$	2.71397			0.423852			0.211926	+	0.977286i	$0.432026\pi$
$42$		0			0
$43$		−	10.6345i		−	1.62175i	−0.585221	−	0.810874i	$-0.698992\pi$
$43$		−	10.6345i		−	1.62175i	0.585221	−	0.810874i	$-0.301008\pi$
$44$	2.77145	+	1.82183i	0.417811	+	0.274652i
$45$		0			0
$46$	−6.02718	+	3.47980i	−0.888660	+	0.513068i
$47$	−2.58268	−	1.49111i	−0.376723	−	0.217501i	0.299669	−	0.954043i	$-0.403124\pi$
$47$	−2.58268	−	1.49111i	−0.376723	−	0.217501i	−0.676391	+	0.736542i	$0.736457\pi$
$48$		0			0
$49$	−6.90123	+	1.17175i	−0.985890	+	0.167393i
$50$	−2.35302			−0.332768
$51$		0			0
$52$	−1.88857	+	1.09037i	−0.261898	+	0.151207i
$53$	10.1931	−	5.88497i	1.40012	−	0.808362i	0.405719	−	0.913998i	$-0.367021\pi$
$53$	10.1931	−	5.88497i	1.40012	−	0.808362i	0.994405	+	0.105636i	$0.0336877\pi$
$54$		0			0
$55$	−8.97843	−	0.520722i	−1.21065	−	0.0702142i
$56$	−0.222226	−	2.63640i	−0.0296962	−	0.352304i
$57$		0			0
$58$	−3.21649	+	5.57112i	−0.422345	+	0.731524i
$59$	12.2489	−	7.07189i	1.59467	−	0.920681i	0.602175	−	0.798364i	$-0.294301\pi$
$59$	12.2489	−	7.07189i	1.59467	−	0.920681i	0.992491	−	0.122317i	$-0.0390326\pi$
$60$		0			0
$61$	10.2720	+	5.93056i	1.31520	+	0.759331i	0.982952	−	0.183861i	$-0.0588597\pi$
$61$	10.2720	+	5.93056i	1.31520	+	0.759331i	0.332247	+	0.943192i	$0.392193\pi$
$62$	−7.30294			−0.927474
$63$		0			0
$64$	1.00000			0.125000
$65$	2.95669	−	5.12114i	0.366732	−	0.635199i
$66$		0			0
$67$	0.749028	+	1.29735i	0.0915083	+	0.158497i	0.908146	−	0.418654i	$-0.137498\pi$
$67$	0.749028	+	1.29735i	0.0915083	+	0.158497i	−0.816638	+	0.577151i	$0.804165\pi$
$68$	0.0281751	−	0.0488007i	0.00341674	−	0.00591796i
$69$		0			0
$70$	4.09636	+	5.88991i	0.489609	+	0.703979i
$71$		−	1.82248i		−	0.216288i	−0.994135	−	0.108144i	$-0.965509\pi$
$71$		−	1.82248i		−	0.216288i	0.994135	−	0.108144i	$-0.0344908\pi$
$72$		0			0
$73$	6.82420	−	3.93995i	0.798712	−	0.461137i	−0.0443085	−	0.999018i	$-0.514108\pi$
$73$	6.82420	−	3.93995i	0.798712	−	0.461137i	0.843021	+	0.537881i	$0.180775\pi$
$74$	−1.62140	−	2.80836i	−0.188484	−	0.326465i
$75$		0			0
$76$		−	2.75460i		−	0.315974i
$77$	4.58476	+	7.48198i	0.522482	+	0.852650i
$78$		0			0
$79$	−7.82062	−	4.51524i	−0.879889	−	0.508004i	−0.00926708	−	0.999957i	$-0.502950\pi$
$79$	−7.82062	−	4.51524i	−0.879889	−	0.508004i	−0.870622	+	0.491953i	$0.836283\pi$
$80$	−2.34835	+	1.35582i	−0.262554	+	0.151586i
$81$		0			0
$82$	−1.35699	+	2.35037i	−0.149854	+	0.259555i
$83$	−17.2299			−1.89123			−0.945615	−	0.325288i	$-0.894539\pi$
$83$	−17.2299			−1.89123			−0.945615	+	0.325288i	$0.894539\pi$
$84$		0			0
$85$			0.152802i			0.0165737i
$86$	9.20975	+	5.31725i	0.993113	+	0.573374i
$87$		0			0
$88$	−2.96348	+	1.48923i	−0.315908	+	0.158752i
$89$	7.43764	+	4.29412i	0.788388	+	0.455176i	0.839395	−	0.543522i	$-0.182910\pi$
$89$	7.43764	+	4.29412i	0.788388	+	0.455176i	−0.0510066	+	0.998698i	$0.516243\pi$
$90$		0			0
$91$	−5.74929	+	0.484616i	−0.602690	+	0.0508015i
$92$		−	6.95959i		−	0.725587i
$93$		0			0
$94$	2.58268	−	1.49111i	0.266383	−	0.153796i
$95$	3.73475	+	6.46878i	0.383177	+	0.663683i
$96$		0			0
$97$	6.25716			0.635319			0.317659	−	0.948205i	$-0.397103\pi$
$97$	6.25716			0.635319			0.317659	+	0.948205i	$0.397103\pi$
$98$	2.43585	−	6.56252i	0.246058	−	0.662914i
$99$		0			0
$100$	1.17651	−	2.03778i	0.117651	−	0.203778i
$101$	7.86795	+	13.6277i	0.782891	+	1.35601i	0.930251	+	0.366924i	$0.119589\pi$
$101$	7.86795	+	13.6277i	0.782891	+	1.35601i	−0.147360	+	0.989083i	$0.547078\pi$
$102$		0			0
$103$	−4.13406	+	7.16040i	−0.407341	+	0.705535i	−0.994591	−	0.103870i	$-0.966877\pi$
$103$	−4.13406	+	7.16040i	−0.407341	+	0.705535i	0.587250	+	0.809406i	$0.300211\pi$
$104$		−	2.18074i		−	0.213839i
$105$		0			0
$106$			11.7699i			1.14320i
$107$	−5.86711	+	10.1621i	−0.567195	+	0.982410i	0.429647	+	0.902997i	$0.358638\pi$
$107$	−5.86711	+	10.1621i	−0.567195	+	0.982410i	−0.996842	+	0.0794132i	$0.974695\pi$
$108$		0			0
$109$	−5.76234	+	3.32689i	−0.551932	+	0.318658i	−0.749901	−	0.661550i	$-0.769899\pi$
$109$	−5.76234	+	3.32689i	−0.551932	+	0.318658i	0.197969	+	0.980208i	$0.436566\pi$
$110$	4.94017	−	7.51518i	0.471027	−	0.716545i
$111$		0			0
$112$	2.39430	+	1.12575i	0.226240	+	0.106373i
$113$			12.8006i			1.20418i	0.798428	+	0.602090i	$0.205665\pi$
$113$			12.8006i			1.20418i	−0.798428	+	0.602090i	$0.794335\pi$
$114$		0			0
$115$	9.43597	+	16.3436i	0.879909	+	1.52405i
$116$	−3.21649	−	5.57112i	−0.298643	−	0.517265i
$117$		0			0
$118$			14.1438i			1.30204i
$119$	0.122397	−	0.0851257i	0.0112201	−	0.00780346i
$120$		0			0
$121$	6.56441	−	8.82658i	0.596765	−	0.802416i
$122$	−10.2720	+	5.93056i	−0.929987	+	0.536928i
$123$		0			0
$124$	3.65147	−	6.32453i	0.327911	−	0.567959i
$125$		−	7.17766i		−	0.641989i
$126$		0			0
$127$		−	5.80675i		−	0.515265i	−0.966243	−	0.257633i	$-0.917058\pi$
$127$		−	5.80675i		−	0.515265i	0.966243	−	0.257633i	$-0.0829424\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	2.95669	+	5.12114i	0.259319	+	0.449154i
$131$	0.981044	−	1.69922i	0.0857142	−	0.148461i	−0.819981	−	0.572391i	$-0.806016\pi$
$131$	0.981044	−	1.69922i	0.0857142	−	0.148461i	0.905695	+	0.423929i	$0.139349\pi$
$132$		0			0
$133$	3.10098	−	6.59535i	0.268889	−	0.571889i
$134$	−1.49806			−0.129412
$135$		0			0
$136$	0.0281751	+	0.0488007i	0.00241600	+	0.00418463i
$137$	5.51740	−	3.18547i	0.471383	−	0.272153i	−0.245435	−	0.969413i	$-0.578931\pi$
$137$	5.51740	−	3.18547i	0.471383	−	0.272153i	0.716819	+	0.697260i	$0.245598\pi$
$138$		0			0
$139$		−	11.2048i		−	0.950382i	−0.879883	−	0.475191i	$-0.842379\pi$
$139$		−	11.2048i		−	0.950382i	0.879883	−	0.475191i	$-0.157621\pi$
$140$	−7.14899	+	0.602598i	−0.604200	+	0.0509288i
$141$		0			0
$142$	1.57831	+	0.911240i	0.132449	+	0.0764695i
$143$	3.24761	+	6.46256i	0.271579	+	0.540427i
$144$		0			0
$145$	15.1069	+	8.72197i	1.25456	+	0.724320i
$146$			7.87991i			0.652146i
$147$		0			0
$148$	3.24281			0.266557
$149$	−8.08008	+	13.9951i	−0.661946	+	1.14652i	0.318157	+	0.948038i	$0.396936\pi$
$149$	−8.08008	+	13.9951i	−0.661946	+	1.14652i	−0.980104	+	0.198487i	$0.936397\pi$
$150$		0			0
$151$	−11.4616	+	6.61738i	−0.932734	+	0.538514i	−0.887675	−	0.460470i	$-0.847681\pi$
$151$	−11.4616	+	6.61738i	−0.932734	+	0.538514i	−0.0450590	+	0.998984i	$0.514348\pi$
$152$	2.38555	+	1.37730i	0.193494	+	0.111714i
$153$		0			0
$154$	−8.77196	+	0.229531i	−0.706865	+	0.0184961i
$155$			19.8030i			1.59061i
$156$		0			0
$157$	−0.671466	−	1.16301i	−0.0535888	−	0.0928185i	0.837987	−	0.545691i	$-0.183733\pi$
$157$	−0.671466	−	1.16301i	−0.0535888	−	0.0928185i	−0.891575	+	0.452872i	$0.850399\pi$
$158$	7.82062	−	4.51524i	0.622175	−	0.359213i
$159$		0			0
$160$		−	2.71165i		−	0.214374i
$161$	7.83474	−	16.6634i	0.617464	−	1.31326i
$162$		0			0
$163$	9.16486	−	15.8740i	0.717847	−	1.24335i	−0.244004	−	0.969774i	$-0.578461\pi$
$163$	9.16486	−	15.8740i	0.717847	−	1.24335i	0.961851	−	0.273574i	$-0.0882057\pi$
$164$	−1.35699	−	2.35037i	−0.105963	−	0.183533i
$165$		0			0
$166$	8.61496	−	14.9216i	0.668651	−	1.15814i
$167$	−5.04452			−0.390357			−0.195178	−	0.980768i	$-0.562529\pi$
$167$	−5.04452			−0.390357			−0.195178	+	0.980768i	$0.562529\pi$
$168$		0			0
$169$	8.24439			0.634184
$170$	−0.132330	−	0.0764010i	−0.0101493	−	0.00585969i
$171$		0			0
$172$	−9.20975	+	5.31725i	−0.702237	+	0.405437i
$173$	0.459832	−	0.796453i	0.0349604	−	0.0605532i	−0.848016	−	0.529971i	$-0.822203\pi$
$173$	0.459832	−	0.796453i	0.0349604	−	0.0605532i	0.882976	+	0.469418i	$0.155536\pi$
$174$		0			0
$175$	5.11095	−	3.55461i	0.386352	−	0.268703i
$176$	0.192032	−	3.31106i	0.0144749	−	0.249581i
$177$		0			0
$178$	−7.43764	+	4.29412i	−0.557475	+	0.321858i
$179$	−14.9660	+	8.64063i	−1.11861	+	0.645831i	−0.941046	−	0.338278i	$-0.890156\pi$
$179$	−14.9660	+	8.64063i	−1.11861	+	0.645831i	−0.177566	+	0.984109i	$0.556822\pi$
$180$		0			0
$181$	−9.68621			−0.719970			−0.359985	−	0.932958i	$-0.617218\pi$
$181$	−9.68621			−0.719970			−0.359985	+	0.932958i	$0.617218\pi$
$182$	2.45496	−	5.22134i	0.181974	−	0.387032i
$183$		0			0
$184$	6.02718	+	3.47980i	0.444330	+	0.256534i
$185$	−7.61527	+	4.39668i	−0.559885	+	0.323250i
$186$		0			0
$187$	−0.156172	−	0.102661i	−0.0114204	−	0.00750730i
$188$			2.98222i			0.217501i
$189$		0			0
$190$	−7.46950			−0.541895
$191$	−10.5752	−	6.10561i	−0.765197	−	0.441787i	0.0659616	−	0.997822i	$-0.478989\pi$
$191$	−10.5752	−	6.10561i	−0.765197	−	0.441787i	−0.831159	+	0.556035i	$0.812322\pi$
$192$		0			0
$193$	6.93577	−	4.00437i	0.499248	−	0.288241i	−0.229155	−	0.973390i	$-0.573596\pi$
$193$	6.93577	−	4.00437i	0.499248	−	0.288241i	0.728403	+	0.685149i	$0.240263\pi$
$194$	−3.12858	+	5.41886i	−0.224619	+	0.389052i
$195$		0			0
$196$	4.46538	+	5.39076i	0.318956	+	0.385055i
$197$	−6.14148			−0.437562			−0.218781	−	0.975774i	$-0.570208\pi$
$197$	−6.14148			−0.437562			−0.218781	+	0.975774i	$0.570208\pi$
$198$		0			0
$199$	−5.93851	−	10.2858i	−0.420970	−	0.729141i	0.575065	−	0.818108i	$-0.304977\pi$
$199$	−5.93851	−	10.2858i	−0.420970	−	0.729141i	−0.996035	+	0.0889669i	$0.971643\pi$
$200$	1.17651	+	2.03778i	0.0831920	+	0.144093i
$201$		0			0
$202$	−15.7359			−1.10717
$203$	−1.42957	−	16.9599i	−0.100336	−	1.19035i
$204$		0			0
$205$	6.37337	+	3.67967i	0.445136	+	0.256999i
$206$	−4.13406	−	7.16040i	−0.288034	−	0.498889i
$207$		0			0
$208$	1.88857	+	1.09037i	0.130949	+	0.0756034i
$209$	−9.12065	−	0.528971i	−0.630888	−	0.0365897i
$210$		0			0
$211$			19.9499i			1.37341i	0.726936	+	0.686706i	$0.240944\pi$
$211$			19.9499i			1.37341i	−0.726936	+	0.686706i	$0.759056\pi$
$212$	−10.1931	−	5.88497i	−0.700062	−	0.404181i
$213$		0			0
$214$	−5.86711	−	10.1621i	−0.401067	−	0.694669i
$215$	14.4185	−	24.9736i	0.983334	−	1.70318i
$216$		0			0
$217$	15.8625	−	11.0322i	1.07682	−	0.748915i
$218$		−	6.65378i		−	0.450651i
$219$		0			0
$220$	4.03825	+	8.03591i	0.272259	+	0.541781i
$221$	0.106421	−	0.0614425i	0.00715868	−	0.00413307i
$222$		0			0
$223$	−13.6887			−0.916665			−0.458333	−	0.888781i	$-0.651553\pi$
$223$	−13.6887			−0.916665			−0.458333	+	0.888781i	$0.651553\pi$
$224$	−2.17208	+	1.51065i	−0.145128	+	0.100935i
$225$		0			0
$226$	−11.0856	−	6.40030i	−0.737406	−	0.425742i
$227$	−3.18180	−	5.51104i	−0.211184	−	0.365781i	0.740902	−	0.671614i	$-0.234398\pi$
$227$	−3.18180	−	5.51104i	−0.211184	−	0.365781i	−0.952085	+	0.305833i	$0.901065\pi$
$228$		0			0
$229$	−5.17077	+	8.95604i	−0.341694	+	0.591832i	−0.984747	−	0.173990i	$-0.944334\pi$
$229$	−5.17077	+	8.95604i	−0.341694	+	0.591832i	0.643053	+	0.765822i	$0.277667\pi$
$230$	−18.8719			−1.24438
$231$		0			0
$232$	6.43297			0.422345
$233$	−4.45228	+	7.71157i	−0.291678	+	0.505202i	−0.974207	−	0.225657i	$-0.927547\pi$
$233$	−4.45228	+	7.71157i	−0.291678	+	0.505202i	0.682528	+	0.730859i	$0.260880\pi$
$234$		0			0
$235$	−4.04336	−	7.00331i	−0.263760	−	0.456846i
$236$	−12.2489	−	7.07189i	−0.797333	−	0.460341i
$237$		0			0
$238$	0.0125225	+	0.148562i	0.000811712	+	0.00962984i
$239$	22.6090			1.46246			0.731228	−	0.682133i	$-0.238947\pi$
$239$	22.6090			1.46246			0.731228	+	0.682133i	$0.238947\pi$
$240$		0			0
$241$	8.06528	−	4.65649i	0.519530	−	0.299951i	−0.217212	−	0.976124i	$-0.569696\pi$
$241$	8.06528	−	4.65649i	0.519530	−	0.299951i	0.736742	+	0.676173i	$0.236363\pi$
$242$	4.36184	+	10.0982i	0.280389	+	0.649139i
$243$		0			0
$244$		−	11.8611i		−	0.759331i
$245$	−17.7952	−	6.60516i	−1.13690	−	0.421988i
$246$		0			0
$247$	3.00353	−	5.20226i	0.191110	−	0.331012i
$248$	3.65147	+	6.32453i	0.231868	+	0.401608i
$249$		0			0
$250$	6.21604	+	3.58883i	0.393137	+	0.226978i
$251$		−	4.12748i		−	0.260524i	−0.991480	−	0.130262i	$-0.958418\pi$
$251$		−	4.12748i		−	0.260524i	0.991480	−	0.130262i	$-0.0415819\pi$
$252$		0			0
$253$	−23.0436	−	1.33646i	−1.44874	−	0.0840227i
$254$	5.02879	+	2.90337i	0.315534	+	0.182174i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.1583	−	7.59695i	−0.820792	−	0.473885i	0.0298973	−	0.999553i	$-0.490482\pi$
$257$	−13.1583	−	7.59695i	−0.820792	−	0.473885i	−0.850690	+	0.525668i	$0.823815\pi$
$258$		0			0
$259$	7.76427	+	3.65058i	0.482448	+	0.226836i
$260$	−5.91338			−0.366732
$261$		0			0
$262$	0.981044	+	1.69922i	0.0606091	+	0.104978i
$263$	8.24623	+	14.2829i	0.508484	+	0.880720i	0.999952	+	0.00982443i	$0.00312726\pi$
$263$	8.24623	+	14.2829i	0.508484	+	0.880720i	−0.491468	+	0.870896i	$0.663539\pi$
$264$		0			0
$265$	31.9159			1.96058
$266$	4.16125	+	5.98321i	0.255143	+	0.366854i
$267$		0			0
$268$	0.749028	−	1.29735i	0.0457541	−	0.0792485i
$269$	−12.6371	+	7.29606i	−0.770500	+	0.444848i	−0.833053	−	0.553193i	$-0.813409\pi$
$269$	−12.6371	+	7.29606i	−0.770500	+	0.444848i	0.0625529	+	0.998042i	$0.480076\pi$
$270$		0			0
$271$	−21.0688	−	12.1641i	−1.27984	−	0.738914i	−0.303018	−	0.952985i	$-0.597994\pi$
$271$	−21.0688	−	12.1641i	−1.27984	−	0.738914i	−0.976818	+	0.214071i	$0.931328\pi$
$272$	−0.0563502			−0.00341674
$273$		0			0
$274$			6.37094i			0.384883i
$275$	−6.52128	−	4.28682i	−0.393248	−	0.258505i
$276$		0			0
$277$	2.92994	−	1.69160i	0.176043	−	0.101638i	−0.409389	−	0.912360i	$-0.634258\pi$
$277$	2.92994	−	1.69160i	0.176043	−	0.101638i	0.585432	+	0.810721i	$0.300925\pi$
$278$	9.70368	+	5.60242i	0.581988	+	0.336011i
$279$		0			0
$280$	3.05263	−	6.49251i	0.182430	−	0.388001i
$281$	−7.92539			−0.472789			−0.236395	−	0.971657i	$-0.575966\pi$
$281$	−7.92539			−0.472789			−0.236395	+	0.971657i	$0.575966\pi$
$282$		0			0
$283$	−20.8485	+	12.0369i	−1.23931	+	0.715518i	−0.968954	−	0.247241i	$-0.920476\pi$
$283$	−20.8485	+	12.0369i	−1.23931	+	0.715518i	−0.270360	+	0.962759i	$0.587143\pi$
$284$	−1.57831	+	0.911240i	−0.0936557	+	0.0540721i
$285$		0			0
$286$	−7.22055	−	0.418770i	−0.426960	−	0.0247624i
$287$	−0.603115	−	7.15513i	−0.0356008	−	0.422354i
$288$		0			0
$289$	8.49841	−	14.7197i	0.499907	−	0.865864i
$290$	−15.1069	+	8.72197i	−0.887108	+	0.512172i
$291$		0			0
$292$	−6.82420	−	3.93995i	−0.399356	−	0.230568i
$293$	−16.6528			−0.972864			−0.486432	−	0.873718i	$-0.661702\pi$
$293$	−16.6528			−0.972864			−0.486432	+	0.873718i	$0.661702\pi$
$294$		0			0
$295$	38.3529			2.23299
$296$	−1.62140	+	2.80836i	−0.0942422	+	0.163232i
$297$		0			0
$298$	−8.08008	−	13.9951i	−0.468067	−	0.810715i
$299$	7.58851	−	13.1437i	0.438855	−	0.760119i
$300$		0			0
$301$	−28.0368	+	2.36326i	−1.61602	+	0.136216i
$302$		−	13.2348i		−	0.761574i
$303$		0			0
$304$	−2.38555	+	1.37730i	−0.136821	+	0.0789936i
$305$	16.0816	+	27.8541i	0.920829	+	1.59492i
$306$		0			0
$307$		−	29.4599i		−	1.68137i	−0.541528	−	0.840683i	$-0.682154\pi$
$307$		−	29.4599i		−	1.68137i	0.541528	−	0.840683i	$-0.317846\pi$
$308$	4.18720	−	7.71151i	0.238588	−	0.439404i
$309$		0			0
$310$	−17.1499	−	9.90149i	−0.974048	−	0.562367i
$311$	0.466034	−	0.269065i	0.0264263	−	0.0152573i	−0.486729	−	0.873553i	$-0.661810\pi$
$311$	0.466034	−	0.269065i	0.0264263	−	0.0152573i	0.513155	+	0.858296i	$0.328477\pi$
$312$		0			0
$313$	−6.81418	+	11.8025i	−0.385160	+	0.667117i	−0.991791	−	0.127866i	$-0.959187\pi$
$313$	−6.81418	+	11.8025i	−0.385160	+	0.667117i	0.606631	+	0.794984i	$0.292521\pi$
$314$	1.34293			0.0757860
$315$		0			0
$316$			9.03048i			0.508004i
$317$	0.730381	+	0.421686i	0.0410223	+	0.0236842i	0.520371	−	0.853940i	$-0.325794\pi$
$317$	0.730381	+	0.421686i	0.0410223	+	0.0236842i	−0.479349	+	0.877625i	$0.659127\pi$
$318$		0			0
$319$	−19.0640	+	9.58015i	−1.06738	+	0.536385i
$320$	2.34835	+	1.35582i	0.131277	+	0.0757928i
$321$		0			0
$322$	10.5135	+	15.1168i	0.585896	+	0.842425i
$323$			0.155222i			0.00863681i
$324$		0			0
$325$	4.44386	−	2.56566i	0.246501	−	0.142317i
$326$	9.16486	+	15.8740i	0.507595	+	0.879180i
$327$		0			0
$328$	2.71397			0.149854
$329$	−3.35723	+	7.14034i	−0.185090	+	0.393660i
$330$		0			0
$331$	5.79849	−	10.0433i	0.318714	−	0.552028i	−0.661506	−	0.749940i	$-0.730082\pi$
$331$	5.79849	−	10.0433i	0.318714	−	0.552028i	0.980220	+	0.197911i	$0.0634158\pi$
$332$	8.61496	+	14.9216i	0.472808	+	0.818927i
$333$		0			0
$334$	2.52226	−	4.36868i	0.138012	−	0.239044i
$335$			4.06220i			0.221941i
$336$		0			0
$337$			0.863660i			0.0470466i	0.999723	+	0.0235233i	$0.00748838\pi$
$337$			0.863660i			0.0470466i	−0.999723	+	0.0235233i	$0.992512\pi$
$338$	−4.12220	+	7.13986i	−0.224218	+	0.388357i
$339$		0			0
$340$	0.132330	−	0.0764010i	0.00717662	−	0.00414342i
$341$	−20.2397	−	13.3047i	−1.09604	−	0.720492i
$342$		0			0
$343$	4.62285	+	17.9340i	0.249610	+	0.968346i
$344$		−	10.6345i		−	0.573374i
$345$		0			0
$346$	0.459832	+	0.796453i	0.0247207	+	0.0428176i
$347$	−3.69571	−	6.40116i	−0.198396	−	0.343632i	0.749612	−	0.661877i	$-0.230240\pi$
$347$	−3.69571	−	6.40116i	−0.198396	−	0.343632i	−0.948009	+	0.318245i	$0.896907\pi$
$348$		0			0
$349$		−	31.5777i		−	1.69032i	−0.534515	−	0.845159i	$-0.679506\pi$
$349$		−	31.5777i		−	1.69032i	0.534515	−	0.845159i	$-0.320494\pi$
$350$	0.522903	+	6.20352i	0.0279503	+	0.331592i
$351$		0			0
$352$	2.77145	+	1.82183i	0.147719	+	0.0971041i
$353$	−3.85186	+	2.22387i	−0.205014	+	0.118365i	−0.598992	−	0.800755i	$-0.704432\pi$
$353$	−3.85186	+	2.22387i	−0.205014	+	0.118365i	0.393978	+	0.919120i	$0.371099\pi$
$354$		0			0
$355$	2.47096	−	4.27983i	0.131145	−	0.227150i
$356$		−	8.58825i		−	0.455176i
$357$		0			0
$358$		−	17.2813i		−	0.913343i
$359$	10.0548	−	17.4154i	0.530673	−	0.919152i	−0.468687	−	0.883364i	$-0.655273\pi$
$359$	10.0548	−	17.4154i	0.530673	−	0.919152i	0.999359	−	0.0357874i	$-0.0113939\pi$
$360$		0			0
$361$	−5.70609	−	9.88324i	−0.300320	−	0.520170i
$362$	4.84310	−	8.38850i	0.254548	−	0.440890i
$363$		0			0
$364$	3.29434	+	4.73673i	0.172670	+	0.248272i
$365$	21.3675			1.11843
$366$		0			0
$367$	−6.39813	−	11.0819i	−0.333980	−	0.578470i	0.649309	−	0.760525i	$-0.275058\pi$
$367$	−6.39813	−	11.0819i	−0.333980	−	0.578470i	−0.983288	+	0.182055i	$0.941725\pi$
$368$	−6.02718	+	3.47980i	−0.314189	+	0.181397i
$369$		0			0
$370$		−	8.79335i		−	0.457145i
$371$	−17.7803	−	25.5652i	−0.923107	−	1.32728i
$372$		0			0
$373$	6.97826	+	4.02890i	0.361321	+	0.208609i	0.669660	−	0.742668i	$-0.266440\pi$
$373$	6.97826	+	4.02890i	0.361321	+	0.208609i	−0.308339	+	0.951276i	$0.599773\pi$
$374$	0.166993	−	0.0839183i	0.00863499	−	0.00433931i
$375$		0			0
$376$	−2.58268	−	1.49111i	−0.133192	−	0.0768982i
$377$		−	14.0286i		−	0.722510i
$378$		0			0
$379$	−30.6120			−1.57244			−0.786218	−	0.617950i	$-0.787964\pi$
$379$	−30.6120			−1.57244			−0.786218	+	0.617950i	$0.787964\pi$
$380$	3.73475	−	6.46878i	0.191589	−	0.331841i
$381$		0			0
$382$	10.5752	−	6.10561i	0.541076	−	0.312390i
$383$	0.763632	+	0.440883i	0.0390198	+	0.0225281i	0.519383	−	0.854542i	$-0.326162\pi$
$383$	0.763632	+	0.440883i	0.0390198	+	0.0225281i	−0.480363	+	0.877070i	$0.659495\pi$
$384$		0			0
$385$	0.622406	+	23.7865i	0.0317207	+	1.21227i
$386$			8.00874i			0.407634i
$387$		0			0
$388$	−3.12858	−	5.41886i	−0.158830	−	0.275101i
$389$	5.35275	−	3.09041i	0.271395	−	0.156690i	−0.358126	−	0.933673i	$-0.616584\pi$
$389$	5.35275	−	3.09041i	0.271395	−	0.156690i	0.629522	+	0.776983i	$0.283251\pi$
$390$		0			0
$391$			0.392175i			0.0198331i
$392$	−6.90123	+	1.17175i	−0.348565	+	0.0591825i
$393$		0			0
$394$	3.07074	−	5.31868i	0.154702	−	0.267951i
$395$	−12.2437	−	21.2068i	−0.616049	−	1.06703i
$396$		0			0
$397$	13.4710	−	23.3325i	0.676091	−	1.17102i	−0.300058	−	0.953921i	$-0.597006\pi$
$397$	13.4710	−	23.3325i	0.676091	−	1.17102i	0.976149	−	0.217103i	$-0.0696608\pi$
$398$	11.8770			0.595341
$399$		0			0
$400$	−2.35302			−0.117651
$401$	3.85186	+	2.22387i	0.192353	+	0.111055i	0.593083	−	0.805141i	$-0.297910\pi$
$401$	3.85186	+	2.22387i	0.192353	+	0.111055i	−0.400731	+	0.916196i	$0.631244\pi$
$402$		0			0
$403$	13.7921	−	7.96288i	0.687034	−	0.396659i
$404$	7.86795	−	13.6277i	0.391445	−	0.678003i
$405$		0			0
$406$	15.4025	+	7.24190i	0.764413	+	0.359410i
$407$	0.622722	−	10.7371i	0.0308672	−	0.532220i
$408$		0			0
$409$	1.50956	−	0.871544i	0.0746428	−	0.0430951i	−0.462214	−	0.886768i	$-0.652945\pi$
$409$	1.50956	−	0.871544i	0.0746428	−	0.0430951i	0.536857	+	0.843673i	$0.319612\pi$
$410$	−6.37337	+	3.67967i	−0.314758	+	0.181726i
$411$		0			0
$412$	8.26812			0.407341
$413$	−21.3663	−	30.7214i	−1.05137	−	1.51170i
$414$		0			0
$415$	−40.4620	−	23.3607i	−1.98620	−	1.14673i
$416$	−1.88857	+	1.09037i	−0.0925949	+	0.0534597i
$417$		0			0
$418$	5.01843	−	7.63423i	0.245459	−	0.373402i
$419$			22.8877i			1.11814i	0.829121	+	0.559069i	$0.188841\pi$
$419$			22.8877i			1.11814i	−0.829121	+	0.559069i	$0.811159\pi$
$420$		0			0
$421$	29.7817			1.45147			0.725735	−	0.687975i	$-0.241500\pi$
$421$	29.7817			1.45147			0.725735	+	0.687975i	$0.241500\pi$
$422$	−17.2772	−	9.97497i	−0.841039	−	0.485574i
$423$		0			0
$424$	10.1931	−	5.88497i	0.495019	−	0.285799i
$425$	−0.0662968	+	0.114829i	−0.00321587	+	0.00557004i
$426$		0			0
$427$	13.3526	−	28.3991i	0.646179	−	1.37433i
$428$	11.7342			0.567195
$429$		0			0
$430$	14.4185	+	24.9736i	0.695322	+	1.20433i
$431$	5.29786	+	9.17616i	0.255189	+	0.442000i	0.964947	−	0.262446i	$-0.0845290\pi$
$431$	5.29786	+	9.17616i	0.255189	+	0.442000i	−0.709758	+	0.704446i	$0.751196\pi$
$432$		0			0
$433$	−23.5494			−1.13171			−0.565856	−	0.824504i	$-0.691454\pi$
$433$	−23.5494			−1.13171			−0.565856	+	0.824504i	$0.691454\pi$
$434$	1.62290	+	19.2535i	0.0779018	+	0.924196i
$435$		0			0
$436$	5.76234	+	3.32689i	0.275966	+	0.159329i
$437$	9.58544	+	16.6025i	0.458534	+	0.794204i
$438$		0			0
$439$	10.0258	+	5.78842i	0.478507	+	0.276266i	0.719794	−	0.694188i	$-0.244236\pi$
$439$	10.0258	+	5.78842i	0.478507	+	0.276266i	−0.241287	+	0.970454i	$0.577570\pi$
$440$	−8.97843	−	0.520722i	−0.428030	−	0.0248245i
$441$		0			0
$442$			0.122885i			0.00584504i
$443$	32.4006	+	18.7065i	1.53940	+	0.888771i	0.998874	+	0.0474425i	$0.0151071\pi$
$443$	32.4006	+	18.7065i	1.53940	+	0.888771i	0.540523	+	0.841329i	$0.318226\pi$
$444$		0			0
$445$	11.6441	+	20.1682i	0.551985	+	0.956067i
$446$	6.84437	−	11.8548i	0.324090	−	0.561340i
$447$		0			0
$448$	−0.222226	−	2.63640i	−0.0104992	−	0.124558i
$449$			19.4749i			0.919075i	0.888158	+	0.459538i	$0.151985\pi$
$449$			19.4749i			0.919075i	−0.888158	+	0.459538i	$0.848015\pi$
$450$		0			0
$451$	−8.04280	+	4.04172i	−0.378721	+	0.190317i
$452$	11.0856	−	6.40030i	0.521425	−	0.301045i
$453$		0			0
$454$	6.36360			0.298659
$455$	−14.1584	−	6.65698i	−0.663758	−	0.312084i
$456$		0			0
$457$	−23.7421	−	13.7075i	−1.11061	−	0.641212i	−0.171623	−	0.985163i	$-0.554901\pi$
$457$	−23.7421	−	13.7075i	−1.11061	−	0.641212i	−0.938988	+	0.343951i	$0.888235\pi$
$458$	−5.17077	−	8.95604i	−0.241614	−	0.418488i
$459$		0			0
$460$	9.43597	−	16.3436i	0.439955	−	0.762024i
$461$	−38.6594			−1.80055			−0.900273	−	0.435325i	$-0.856634\pi$
$461$	−38.6594			−1.80055			−0.900273	+	0.435325i	$0.856634\pi$
$462$		0			0
$463$	35.4956			1.64962			0.824810	−	0.565409i	$-0.191282\pi$
$463$	35.4956			1.64962			0.824810	+	0.565409i	$0.191282\pi$
$464$	−3.21649	+	5.57112i	−0.149322	+	0.258633i
$465$		0			0
$466$	−4.45228	−	7.71157i	−0.206248	−	0.357232i
$467$	−9.49408	−	5.48141i	−0.439334	−	0.253649i	0.263981	−	0.964528i	$-0.414964\pi$
$467$	−9.49408	−	5.48141i	−0.439334	−	0.253649i	−0.703315	+	0.710878i	$0.748298\pi$
$468$		0			0
$469$	3.25389	−	2.26304i	0.150251	−	0.104498i
$470$	8.08673			0.373013
$471$		0			0
$472$	12.2489	−	7.07189i	0.563800	−	0.325510i
$473$	15.8372	+	31.5151i	0.728194	+	1.44907i
$474$		0			0
$475$			6.48164i			0.297398i
$476$	−0.134920	−	0.0634362i	−0.00618403	−	0.00290759i
$477$		0			0
$478$	−11.3045	+	19.5800i	−0.517057	+	0.895568i
$479$	6.08034	+	10.5315i	0.277818	+	0.481195i	0.970842	−	0.239719i	$-0.0770554\pi$
$479$	6.08034	+	10.5315i	0.277818	+	0.481195i	−0.693024	+	0.720914i	$0.743722\pi$
$480$		0			0
$481$	6.12428	+	3.53585i	0.279243	+	0.161221i
$482$			9.31298i			0.424195i
$483$		0			0
$484$	−10.9262	−	1.27166i	−0.496648	−	0.0578026i
$485$	14.6940	+	8.48360i	0.667222	+	0.385221i
$486$		0			0
$487$	−1.22436	−	2.12066i	−0.0554813	−	0.0960964i	0.836951	−	0.547278i	$-0.184336\pi$
$487$	−1.22436	−	2.12066i	−0.0554813	−	0.0960964i	−0.892432	+	0.451182i	$0.851003\pi$
$488$	10.2720	+	5.93056i	0.464993	+	0.268464i
$489$		0			0
$490$	14.6178	−	12.1085i	0.660367	−	0.547008i
$491$	0.134894			0.00608767			0.00304383	−	0.999995i	$-0.499031\pi$
$491$	0.134894			0.00608767			0.00304383	+	0.999995i	$0.499031\pi$
$492$		0			0
$493$	0.181250	+	0.313934i	0.00816308	+	0.0141389i
$494$	3.00353	+	5.20226i	0.135135	+	0.234061i
$495$		0			0
$496$	−7.30294			−0.327911
$497$	−4.80479	+	0.405002i	−0.215524	+	0.0181668i
$498$		0			0
$499$	−18.6333	+	32.2738i	−0.834140	+	1.44477i	0.0605888	+	0.998163i	$0.480702\pi$
$499$	−18.6333	+	32.2738i	−0.834140	+	1.44477i	−0.894729	+	0.446610i	$0.852631\pi$
$500$	−6.21604	+	3.58883i	−0.277990	+	0.160497i
$501$		0			0
$502$	3.57450	+	2.06374i	0.159538	+	0.0921092i
$503$	22.4935			1.00294			0.501469	−	0.865176i	$-0.332793\pi$
$503$	22.4935			1.00294			0.501469	+	0.865176i	$0.332793\pi$
$504$		0			0
$505$			42.6702i			1.89880i
$506$	12.6792	−	19.2881i	0.563660	−	0.857462i
$507$		0			0
$508$	−5.02879	+	2.90337i	−0.223116	+	0.128816i
$509$	−20.3512	−	11.7498i	−0.902053	−	0.520801i	−0.0241874	−	0.999707i	$-0.507700\pi$
$509$	−20.3512	−	11.7498i	−0.902053	−	0.520801i	−0.877866	+	0.478907i	$0.841033\pi$
$510$		0			0
$511$	−11.9038	−	17.1158i	−0.526594	−	0.757157i
$512$	1.00000			0.0441942
$513$		0			0
$514$	13.1583	−	7.59695i	0.580388	−	0.335087i
$515$	−19.4165	+	11.2101i	−0.855592	+	0.493976i
$516$		0			0
$517$	9.87432	+	0.572681i	0.434272	+	0.0251865i
$518$	−7.04363	+	4.89876i	−0.309480	+	0.215239i
$519$		0			0
$520$	2.95669	−	5.12114i	0.129659	−	0.224577i
$521$	−4.95557	+	2.86110i	−0.217107	+	0.125347i	−0.604610	−	0.796522i	$-0.706671\pi$
$521$	−4.95557	+	2.86110i	−0.217107	+	0.125347i	0.387503	+	0.921869i	$0.373338\pi$
$522$		0			0
$523$	1.75580	+	1.01371i	0.0767758	+	0.0443265i	0.537896	−	0.843011i	$-0.319219\pi$
$523$	1.75580	+	1.01371i	0.0767758	+	0.0443265i	−0.461121	+	0.887337i	$0.652552\pi$
$524$	−1.96209			−0.0857142
$525$		0			0
$526$	−16.4925			−0.719105
$527$	−0.205761	+	0.356389i	−0.00896309	+	0.0155245i
$528$		0			0
$529$	12.7179	+	22.0281i	0.552954	+	0.957745i
$530$	−15.9579	+	27.6400i	−0.693169	+	1.20060i
$531$		0			0
$532$	−7.26223	+	0.612144i	−0.314858	+	0.0265398i
$533$		−	5.91846i		−	0.256357i
$534$		0			0
$535$	−27.5561	+	15.9095i	−1.19135	+	0.687829i
$536$	0.749028	+	1.29735i	0.0323531	+	0.0560371i
$537$		0			0
$538$		−	14.5921i		−	0.629111i
$539$	18.7066	−	13.7500i	0.805752	−	0.592253i
$540$		0			0
$541$	12.1688	+	7.02567i	0.523179	+	0.302057i	0.738234	−	0.674544i	$-0.235660\pi$
$541$	12.1688	+	7.02567i	0.523179	+	0.302057i	−0.215056	+	0.976602i	$0.568993\pi$
$542$	21.0688	−	12.1641i	0.904981	−	0.522491i
$543$		0			0
$544$	0.0281751	−	0.0488007i	0.00120800	−	0.00209231i
$545$	−18.0427			−0.772864
$546$		0			0
$547$			14.9517i			0.639290i	0.947537	+	0.319645i	$0.103564\pi$
$547$			14.9517i			0.639290i	−0.947537	+	0.319645i	$0.896436\pi$
$548$	−5.51740	−	3.18547i	−0.235692	−	0.136077i
$549$		0			0
$550$	6.97314	−	3.50419i	0.297336	−	0.149419i
$551$	15.3462	+	8.86013i	0.653770	+	0.377454i
$552$		0			0
$553$	−10.1660	+	21.6217i	−0.432304	+	0.919449i
$554$			3.38320i			0.143738i
$555$		0			0
$556$	−9.70368	+	5.60242i	−0.411528	+	0.237596i
$557$	8.41830	+	14.5809i	0.356695	+	0.617813i	0.987406	−	0.158204i	$-0.0505703\pi$
$557$	8.41830	+	14.5809i	0.356695	+	0.617813i	−0.630712	+	0.776017i	$0.717237\pi$
$558$		0			0
$559$	−23.1910			−0.980876
$560$	4.09636	+	5.88991i	0.173103	+	0.248894i
$561$		0			0
$562$	3.96270	−	6.86359i	0.167156	−	0.289523i
$563$	−17.2551	−	29.8868i	−0.727218	−	1.25958i	−0.958055	−	0.286585i	$-0.907480\pi$
$563$	−17.2551	−	29.8868i	−0.727218	−	1.25958i	0.230837	−	0.972992i	$-0.425854\pi$
$564$		0			0
$565$	−17.3554	+	30.0604i	−0.730145	+	1.26465i
$566$		−	24.0738i		−	1.01190i
$567$		0			0
$568$		−	1.82248i		−	0.0764695i
$569$	−21.8150	+	37.7846i	−0.914531	+	1.58401i	−0.106944	+	0.994265i	$0.534106\pi$
$569$	−21.8150	+	37.7846i	−0.914531	+	1.58401i	−0.807587	+	0.589748i	$0.799227\pi$
$570$		0			0
$571$	−33.1381	+	19.1323i	−1.38678	+	0.800660i	−0.992951	−	0.118522i	$-0.962184\pi$
$571$	−33.1381	+	19.1323i	−1.38678	+	0.800660i	−0.393833	+	0.919182i	$0.628851\pi$
$572$	3.97294	−	6.04379i	0.166117	−	0.252704i
$573$		0			0
$574$	6.49808	+	3.05525i	0.271225	+	0.127524i
$575$			16.3761i			0.682930i
$576$		0			0
$577$	−18.5319	−	32.0982i	−0.771492	−	1.33626i	−0.936745	−	0.350013i	$-0.886177\pi$
$577$	−18.5319	−	32.0982i	−0.771492	−	1.33626i	0.165253	−	0.986251i	$-0.447156\pi$
$578$	8.49841	+	14.7197i	0.353487	+	0.612258i
$579$		0			0
$580$		−	17.4439i		−	0.724320i
$581$	3.82894	+	45.4250i	0.158851	+	1.88455i
$582$		0			0
$583$	−21.4429	+	32.6197i	−0.888073	+	1.35097i
$584$	6.82420	−	3.93995i	0.282387	−	0.163036i
$585$		0			0
$586$	8.32638	−	14.4217i	0.343960	−	0.595755i
$587$		−	40.7527i		−	1.68204i	−0.541002	−	0.841021i	$-0.681955\pi$
$587$		−	40.7527i		−	1.68204i	0.541002	−	0.841021i	$-0.318045\pi$
$588$		0			0
$589$			20.1167i			0.828893i
$590$	−19.1765	+	33.2146i	−0.789482	+	1.36742i
$591$		0			0
$592$	−1.62140	−	2.80836i	−0.0666393	−	0.115423i
$593$	−2.07883	+	3.60063i	−0.0853672	+	0.147860i	−0.905548	−	0.424245i	$-0.860540\pi$
$593$	−2.07883	+	3.60063i	−0.0853672	+	0.147860i	0.820180	+	0.572105i	$0.193873\pi$
$594$		0			0
$595$	0.402847	−	0.0339565i	0.0165151	−	0.00139208i
$596$	16.1602			0.661946
$597$		0			0
$598$	7.58851	+	13.1437i	0.310317	+	0.537485i
$599$	1.70659	−	0.985302i	0.0697295	−	0.0402584i	−0.464730	−	0.885452i	$-0.653849\pi$
$599$	1.70659	−	0.985302i	0.0697295	−	0.0402584i	0.534459	+	0.845194i	$0.320515\pi$
$600$		0			0
$601$			1.40392i			0.0572672i	0.999590	+	0.0286336i	$0.00911560\pi$
$601$			1.40392i			0.0572672i	−0.999590	+	0.0286336i	$0.990884\pi$
$602$	11.9718	−	25.4622i	0.487933	−	1.03776i
$603$		0			0
$604$	11.4616	+	6.61738i	0.466367	+	0.269257i
$605$	27.3828	−	11.8278i	1.11327	−	0.480867i
$606$		0			0
$607$	−11.4032	−	6.58367i	−0.462843	−	0.267223i	0.250396	−	0.968144i	$-0.419439\pi$
$607$	−11.4032	−	6.58367i	−0.462843	−	0.267223i	−0.713239	+	0.700921i	$0.752773\pi$
$608$		−	2.75460i		−	0.111714i
$609$		0			0
$610$	−32.1632			−1.30225
$611$	−3.25172	+	5.63214i	−0.131550	+	0.227852i
$612$		0			0
$613$	0.364197	−	0.210269i	0.0147098	−	0.00849270i	−0.492627	−	0.870241i	$-0.663963\pi$
$613$	0.364197	−	0.210269i	0.0147098	−	0.00849270i	0.507337	+	0.861748i	$0.330630\pi$
$614$	25.5130	+	14.7300i	1.02962	+	0.594453i
$615$		0			0
$616$	4.58476	+	7.48198i	0.184725	+	0.301457i
$617$		−	2.85323i		−	0.114867i	−0.998349	−	0.0574333i	$-0.981708\pi$
$617$		−	2.85323i		−	0.114867i	0.998349	−	0.0574333i	$-0.0182917\pi$
$618$		0			0
$619$	12.6081	+	21.8380i	0.506764	+	0.877741i	0.999969	+	0.00782835i	$0.00249187\pi$
$619$	12.6081	+	21.8380i	0.506764	+	0.877741i	−0.493205	+	0.869913i	$0.664175\pi$
$620$	17.1499	−	9.90149i	0.688756	−	0.397653i
$621$		0			0
$622$			0.538129i			0.0215770i
$623$	9.66820	−	20.5629i	0.387348	−	0.823834i
$624$		0			0
$625$	15.6142	−	27.0446i	0.624568	−	1.08178i
$626$	−6.81418	−	11.8025i	−0.272350	−	0.471723i
$627$		0			0
$628$	−0.671466	+	1.16301i	−0.0267944	+	0.0464092i
$629$	−0.182733			−0.00728605
$630$		0			0
$631$	−1.15543			−0.0459968			−0.0229984	−	0.999736i	$-0.507321\pi$
$631$	−1.15543			−0.0459968			−0.0229984	+	0.999736i	$0.507321\pi$
$632$	−7.82062	−	4.51524i	−0.311088	−	0.179607i
$633$		0			0
$634$	−0.730381	+	0.421686i	−0.0290071	+	0.0167473i
$635$	7.87292	−	13.6363i	0.312427	−	0.541140i
$636$		0			0
$637$	2.55528	+	15.0498i	0.101244	+	0.596293i
$638$	1.23534	−	21.3000i	0.0489074	−	0.843274i
$639$		0			0
$640$	−2.34835	+	1.35582i	−0.0928269	+	0.0535936i
$641$	43.5123	−	25.1218i	1.71863	−	0.992252i	0.797197	−	0.603720i	$-0.206315\pi$
$641$	43.5123	−	25.1218i	1.71863	−	0.992252i	0.921435	−	0.388533i	$-0.127018\pi$
$642$		0			0
$643$	14.5727			0.574690			0.287345	−	0.957827i	$-0.407227\pi$
$643$	14.5727			0.574690			0.287345	+	0.957827i	$0.407227\pi$
$644$	−18.3483	+	1.54660i	−0.723023	+	0.0609446i
$645$		0			0
$646$	−0.134427	−	0.0776112i	−0.00528894	−	0.00305357i
$647$	−3.51582	+	2.02986i	−0.138221	+	0.0798020i	−0.567516	−	0.823362i	$-0.692095\pi$
$647$	−3.51582	+	2.02986i	−0.138221	+	0.0798020i	0.429295	+	0.903164i	$0.358762\pi$
$648$		0			0
$649$	−25.7676	+	39.1987i	−1.01147	+	1.53868i
$650$			5.13132i			0.201267i
$651$		0			0
$652$	−18.3297			−0.717847
$653$	1.95036	+	1.12604i	0.0763236	+	0.0440654i	0.537676	−	0.843151i	$-0.319302\pi$
$653$	1.95036	+	1.12604i	0.0763236	+	0.0440654i	−0.461353	+	0.887217i	$0.652636\pi$
$654$		0			0
$655$	4.60768	−	2.66024i	0.180037	−	0.103944i
$656$	−1.35699	+	2.35037i	−0.0529814	+	0.0917666i
$657$		0			0
$658$	−4.50511	−	6.47762i	−0.175627	−	0.252524i
$659$	−33.8978			−1.32047			−0.660236	−	0.751058i	$-0.729544\pi$
$659$	−33.8978			−1.32047			−0.660236	+	0.751058i	$0.729544\pi$
$660$		0			0
$661$	−0.411025	−	0.711916i	−0.0159870	−	0.0276903i	0.857921	−	0.513781i	$-0.171756\pi$
$661$	−0.411025	−	0.711916i	−0.0159870	−	0.0276903i	−0.873908	+	0.486091i	$0.838422\pi$
$662$	5.79849	+	10.0433i	0.225365	+	0.390343i
$663$		0			0
$664$	−17.2299			−0.668651
$665$	16.2243	−	11.2838i	0.629153	−	0.437568i
$666$		0			0
$667$	38.7727	+	22.3854i	1.50128	+	0.866767i
$668$	2.52226	+	4.36868i	0.0975892	+	0.169029i
$669$		0			0
$670$	−3.51796	−	2.03110i	−0.135911	−	0.0784682i
$671$	−39.2729	−	2.27771i	−1.51611	−	0.0879302i
$672$		0			0
$673$		−	22.8706i		−	0.881596i	−0.897606	−	0.440798i	$-0.854696\pi$
$673$		−	22.8706i		−	0.881596i	0.897606	−	0.440798i	$-0.145304\pi$
$674$	−0.747952	−	0.431830i	−0.0288100	−	0.0166335i
$675$		0			0
$676$	−4.12220	−	7.13986i	−0.158546	−	0.274610i
$677$	−7.34072	+	12.7145i	−0.282127	+	0.488658i	−0.971908	−	0.235360i	$-0.924373\pi$
$677$	−7.34072	+	12.7145i	−0.282127	+	0.488658i	0.689782	+	0.724018i	$0.257707\pi$
$678$		0			0
$679$	−1.39050	−	16.4964i	−0.0533626	−	0.633074i
$680$			0.152802i			0.00585969i
$681$		0			0
$682$	21.6421	−	10.8757i	0.828719	−	0.416453i
$683$	−34.3893	+	19.8546i	−1.31587	+	0.759717i	−0.983061	−	0.183278i	$-0.941329\pi$
$683$	−34.3893	+	19.8546i	−1.31587	+	0.759717i	−0.332807	+	0.942995i	$0.607996\pi$
$684$		0			0
$685$	17.2757			0.660072
$686$	−17.8427	−	4.96351i	−0.681239	−	0.189508i
$687$		0			0
$688$	9.20975	+	5.31725i	0.351119	+	0.202718i
$689$	−12.8335	−	22.2284i	−0.488919	−	0.846833i
$690$		0			0
$691$	−12.6830	+	21.9677i	−0.482486	+	0.835690i	−0.999798	−	0.0201070i	$-0.993599\pi$
$691$	−12.6830	+	21.9677i	−0.482486	+	0.835690i	0.517312	+	0.855797i	$0.326933\pi$
$692$	−0.919665			−0.0349604
$693$		0			0
$694$	7.39142			0.280574
$695$	15.1918	−	26.3129i	0.576257	−	0.998107i
$696$		0			0
$697$	0.0764666	+	0.132444i	0.00289638	+	0.00501667i
$698$	27.3471	+	15.7889i	1.03510	+	0.597617i
$699$		0			0
$700$	−5.63386	−	2.64891i	−0.212940	−	0.100119i
$701$	−36.3036			−1.37117			−0.685584	−	0.727994i	$-0.740453\pi$
$701$	−36.3036			−1.37117			−0.685584	+	0.727994i	$0.740453\pi$
$702$		0			0
$703$	−7.73590	+	4.46632i	−0.291765	+	0.168451i
$704$	−2.96348	+	1.48923i	−0.111690	+	0.0561273i
$705$		0			0
$706$		−	4.44774i		−	0.167393i
$707$	34.1796	−	23.7715i	1.28546	−	0.894020i
$708$		0			0
$709$	−2.73371	+	4.73492i	−0.102667	+	0.177824i	−0.912782	−	0.408446i	$-0.866071\pi$
$709$	−2.73371	+	4.73492i	−0.102667	+	0.177824i	0.810116	+	0.586270i	$0.199404\pi$
$710$	2.47096	+	4.27983i	0.0927335	+	0.160619i
$711$		0			0
$712$	7.43764	+	4.29412i	0.278737	+	0.160929i
$713$			50.8254i			1.90343i
$714$		0			0
$715$	−1.13556	+	19.5796i	−0.0424674	+	0.732234i
$716$	14.9660	+	8.64063i	0.559306	+	0.322915i
$717$		0			0
$718$	10.0548	+	17.4154i	0.375242	+	0.649938i
$719$	13.3827	+	7.72650i	0.499090	+	0.288150i	0.728338	−	0.685218i	$-0.240293\pi$
$719$	13.3827	+	7.72650i	0.499090	+	0.288150i	−0.229248	+	0.973368i	$0.573627\pi$
$720$		0			0
$721$	19.7964	+	9.30782i	0.737256	+	0.346641i
$722$	11.4122			0.424717
$723$		0			0
$724$	4.84310	+	8.38850i	0.179993	+	0.311756i
$725$	7.56847	+	13.1090i	0.281086	+	0.486855i
$726$		0			0
$727$	39.4347			1.46255			0.731276	−	0.682082i	$-0.238925\pi$
$727$	39.4347			1.46255			0.731276	+	0.682082i	$0.238925\pi$
$728$	−5.74929	+	0.484616i	−0.213083	+	0.0179611i
$729$		0			0
$730$	−10.6838	+	18.5048i	−0.395424	+	0.684894i
$731$	0.518972	−	0.299629i	0.0191949	−	0.0110822i
$732$		0			0
$733$	29.2219	+	16.8713i	1.07934	+	0.623156i	0.930717	−	0.365739i	$-0.119184\pi$
$733$	29.2219	+	16.8713i	1.07934	+	0.623156i	0.148620	+	0.988894i	$0.452517\pi$
$734$	12.7963			0.472319
$735$		0			0
$736$		−	6.95959i		−	0.256534i
$737$	−4.15178	−	2.72921i	−0.152933	−	0.100532i
$738$		0			0
$739$	−43.6352	+	25.1928i	−1.60515	+	0.926732i	−0.614713	+	0.788751i	$0.710728\pi$
$739$	−43.6352	+	25.1928i	−1.60515	+	0.926732i	−0.990435	+	0.137981i	$0.955939\pi$
$740$	7.61527	+	4.39668i	0.279943	+	0.161625i
$741$		0			0
$742$	31.0303	−	2.61558i	1.13916	−	0.0960211i
$743$	52.0125			1.90815			0.954077	−	0.299560i	$-0.0968400\pi$
$743$	52.0125			1.90815			0.954077	+	0.299560i	$0.0968400\pi$
$744$		0			0
$745$	−37.9498	+	21.9103i	−1.39037	+	0.802732i
$746$	−6.97826	+	4.02890i	−0.255492	+	0.147509i
$747$		0			0
$748$	−0.0108210	+	0.186579i	−0.000395656	+	0.00682201i
$749$	28.0953	+	13.2098i	1.02658	+	0.482674i
$750$		0			0
$751$	−12.9264	+	22.3892i	−0.471691	+	0.816993i	−0.999475	−	0.0323857i	$-0.989689\pi$
$751$	−12.9264	+	22.3892i	−0.471691	+	0.816993i	0.527785	+	0.849378i	$0.323023\pi$
$752$	2.58268	−	1.49111i	0.0941806	−	0.0543752i
$753$		0			0
$754$	12.1491	+	7.01430i	0.442445	+	0.255446i
$755$	−35.8880			−1.30610
$756$		0			0
$757$	17.3219			0.629576			0.314788	−	0.949162i	$-0.398067\pi$
$757$	17.3219			0.629576			0.314788	+	0.949162i	$0.398067\pi$
$758$	15.3060	−	26.5108i	0.555940	−	0.962916i
$759$		0			0
$760$	3.73475	+	6.46878i	0.135474	+	0.234647i
$761$	20.4262	−	35.3793i	0.740450	−	1.28250i	−0.211840	−	0.977304i	$-0.567946\pi$
$761$	20.4262	−	35.3793i	0.740450	−	1.28250i	0.952290	−	0.305193i	$-0.0987210\pi$
$762$		0			0
$763$	10.0516	+	14.4525i	0.363891	+	0.523217i
$764$			12.2112i			0.441787i
$765$		0			0
$766$	−0.763632	+	0.440883i	−0.0275912	+	0.0159298i
$767$	−15.4219	−	26.7115i	−0.556853	−	0.964497i
$768$		0			0
$769$		−	41.5890i		−	1.49974i	−0.661586	−	0.749869i	$-0.730116\pi$
$769$		−	41.5890i		−	1.49974i	0.661586	−	0.749869i	$-0.269884\pi$
$770$	−20.9109	−	11.3542i	−0.753576	−	0.409177i
$771$		0			0
$772$	−6.93577	−	4.00437i	−0.249624	−	0.144120i
$773$	42.1450	−	24.3325i	1.51585	−	0.875178i	0.516025	−	0.856574i	$-0.327411\pi$
$773$	42.1450	−	24.3325i	1.51585	−	0.875178i	0.999827	−	0.0186040i	$-0.00592219\pi$
$774$		0			0
$775$	−8.59199	+	14.8818i	−0.308634	+	0.534569i
$776$	6.25716			0.224619
$777$		0			0
$778$			6.18083i			0.221593i
$779$	6.47433	+	3.73796i	0.231967	+	0.133926i
$780$		0			0
$781$	2.71408	+	5.40088i	0.0971175	+	0.193259i
$782$	−0.339633	−	0.196087i	−0.0121453	−	0.00701207i
$783$		0			0
$784$	2.43585	−	6.56252i	0.0869945	−	0.234376i
$785$		−	3.64155i		−	0.129973i
$786$		0			0
$787$	37.6497	−	21.7371i	1.34207	−	0.774842i	0.354956	−	0.934883i	$-0.384496\pi$
$787$	37.6497	−	21.7371i	1.34207	−	0.774842i	0.987110	+	0.160041i	$0.0511625\pi$
$788$	3.07074	+	5.31868i	0.109391	+	0.189470i
$789$		0			0
$790$	24.4875			0.871225
$791$	33.7475	−	2.84463i	1.19992	−	0.101143i
$792$		0			0
$793$	12.9330	−	22.4006i	0.459264	−	0.795468i
$794$	13.4710	+	23.3325i	0.478069	+	0.828039i
$795$		0			0
$796$	−5.93851	+	10.2858i	−0.210485	+	0.364570i
$797$		−	0.736909i		−	0.0261026i	−0.999915	−	0.0130513i	$-0.995846\pi$
$797$		−	0.736909i		−	0.0261026i	0.999915	−	0.0130513i	$-0.00415448\pi$
$798$		0			0
$799$		−	0.168049i		−	0.00594514i
$800$	1.17651	−	2.03778i	0.0415960	−	0.0720464i
$801$		0			0
$802$	−3.85186	+	2.22387i	−0.136014	+	0.0785277i
$803$	−14.3559	+	21.8387i	−0.506608	+	0.770672i
$804$		0			0
$805$	40.9913	−	28.5090i	1.44475	−	1.00481i
$806$			15.9258i			0.560961i
$807$		0			0
$808$	7.86795	+	13.6277i	0.276794	+	0.479421i
$809$	−18.6491	−	32.3012i	−0.655668	−	1.13565i	−0.981726	−	0.190301i	$-0.939054\pi$
$809$	−18.6491	−	32.3012i	−0.655668	−	1.13565i	0.326057	−	0.945350i	$-0.394280\pi$
$810$		0			0
$811$			53.0883i			1.86418i	0.362223	+	0.932091i	$0.382018\pi$
$811$			53.0883i			1.86418i	−0.362223	+	0.932091i	$0.617982\pi$
$812$	−13.9729	+	9.71800i	−0.490353	+	0.341035i
$813$		0			0
$814$	8.98727	+	5.90786i	0.315004	+	0.207070i
$815$	43.0447	−	24.8519i	1.50779	−	0.870523i
$816$		0			0
$817$	14.6469	−	25.3692i	0.512430	−	0.887556i
$818$			1.74309i			0.0609456i
$819$		0			0
$820$		−	7.35934i		−	0.256999i
$821$	−11.8592	+	20.5407i	−0.413888	+	0.716875i	−0.995311	−	0.0967264i	$-0.969163\pi$
$821$	−11.8592	+	20.5407i	−0.413888	+	0.716875i	0.581423	+	0.813601i	$0.302496\pi$
$822$		0			0
$823$	12.9977	+	22.5127i	0.453072	+	0.784744i	0.998575	−	0.0533647i	$-0.0169946\pi$
$823$	12.9977	+	22.5127i	0.453072	+	0.784744i	−0.545503	+	0.838109i	$0.683661\pi$
$824$	−4.13406	+	7.16040i	−0.144017	+	0.249444i
$825$		0			0
$826$	37.2887	−	3.14311i	1.29744	−	0.109363i
$827$	4.74683			0.165064			0.0825318	−	0.996588i	$-0.473699\pi$
$827$	4.74683			0.165064			0.0825318	+	0.996588i	$0.473699\pi$
$828$		0			0
$829$	−25.4414	−	44.0659i	−0.883618	−	1.53047i	−0.847289	−	0.531131i	$-0.821767\pi$
$829$	−25.4414	−	44.0659i	−0.883618	−	1.53047i	−0.0363286	−	0.999340i	$-0.511566\pi$
$830$	40.4620	−	23.3607i	1.40446	−	0.810863i
$831$		0			0
$832$		−	2.18074i		−	0.0756034i
$833$	−0.251625	−	0.303771i	−0.00871831	−	0.0105250i
$834$		0			0
$835$	−11.8463	−	6.83948i	−0.409959	−	0.236690i
$836$	4.10222	+	8.16320i	0.141878	+	0.282330i
$837$		0			0
$838$	−19.8214	−	11.4439i	−0.684717	−	0.395322i
$839$			44.2410i			1.52737i	0.645589	+	0.763685i	$0.276612\pi$
$839$			44.2410i			1.52737i	−0.645589	+	0.763685i	$0.723388\pi$
$840$		0			0
$841$	12.3831			0.427005
$842$	−14.8908	+	25.7917i	−0.513172	+	0.888840i
$843$		0			0
$844$	17.2772	−	9.97497i	0.594704	−	0.343353i
$845$	19.3608	+	11.1779i	0.666030	+	0.384533i
$846$		0			0
$847$	−24.7292	−	15.3449i	−0.849705	−	0.527258i
$848$			11.7699i			0.404181i
$849$		0			0
$850$	−0.0662968	−	0.114829i	−0.00227396	−	0.00393861i
$851$	−19.5450	+	11.2843i	−0.669994	+	0.386821i
$852$		0			0
$853$			33.7537i			1.15570i	0.816142	+	0.577852i	$0.196109\pi$
$853$			33.7537i			1.15570i	−0.816142	+	0.577852i	$0.803891\pi$
$854$	17.9181	+	25.7633i	0.613144	+	0.881602i
$855$		0			0
$856$	−5.86711	+	10.1621i	−0.200534	+	0.347334i
$857$	8.96910	+	15.5349i	0.306379	+	0.530664i	0.977567	−	0.210623i	$-0.0675493\pi$
$857$	8.96910	+	15.5349i	0.306379	+	0.530664i	−0.671189	+	0.741287i	$0.734216\pi$
$858$		0			0
$859$	−2.69866	+	4.67422i	−0.0920771	+	0.159482i	−0.908385	−	0.418135i	$-0.862684\pi$
$859$	−2.69866	+	4.67422i	−0.0920771	+	0.159482i	0.816308	+	0.577617i	$0.196017\pi$
$860$	−28.8370			−0.983334
$861$		0			0
$862$	−10.5957			−0.360892
$863$	14.4176	+	8.32401i	0.490781	+	0.283353i	0.724899	−	0.688856i	$-0.241887\pi$
$863$	14.4176	+	8.32401i	0.490781	+	0.283353i	−0.234117	+	0.972208i	$0.575220\pi$
$864$		0			0
$865$	2.15970	−	1.24690i	0.0734320	−	0.0423960i
$866$	11.7747	−	20.3944i	0.400121	−	0.693029i
$867$		0			0
$868$	−17.4854	−	8.22126i	−0.593495	−	0.279048i
$869$	29.9005	+	1.73414i	1.01430	+	0.0588266i
$870$		0			0
$871$	2.82918	−	1.63343i	0.0958633	−	0.0553467i
$872$	−5.76234	+	3.32689i	−0.195138	+	0.112663i
$873$		0			0
$874$	−19.1709			−0.648465
$875$	−18.9232	+	1.59506i	−0.639721	+	0.0539229i
$876$		0			0
$877$	8.41495	+	4.85837i	0.284153	+	0.164056i	0.635302	−	0.772264i	$-0.280876\pi$
$877$	8.41495	+	4.85837i	0.284153	+	0.164056i	−0.351149	+	0.936320i	$0.614209\pi$
$878$	−10.0258	+	5.78842i	−0.338356	+	0.195350i
$879$		0			0
$880$	4.94017	−	7.51518i	0.166533	−	0.253337i
$881$			18.1403i			0.611162i	0.952166	+	0.305581i	$0.0988507\pi$
$881$			18.1403i			0.611162i	−0.952166	+	0.305581i	$0.901149\pi$
$882$		0			0
$883$	20.9584			0.705308			0.352654	−	0.935754i	$-0.385279\pi$
$883$	20.9584			0.705308			0.352654	+	0.935754i	$0.385279\pi$
$884$	−0.106421	−	0.0614425i	−0.00357934	−	0.00206653i
$885$		0			0
$886$	−32.4006	+	18.7065i	−1.08852	+	0.628456i
$887$	25.0314	−	43.3557i	0.840473	−	1.45574i	−0.0490221	−	0.998798i	$-0.515610\pi$
$887$	25.0314	−	43.3557i	0.840473	−	1.45574i	0.889495	−	0.456945i	$-0.151056\pi$
$888$		0			0
$889$	−15.3089	+	1.29041i	−0.513445	+	0.0432789i
$890$	−23.2883			−0.780625
$891$		0			0
$892$	6.84437	+	11.8548i	0.229166	+	0.396928i
$893$	−4.10741	−	7.11425i	−0.137449	−	0.238069i
$894$		0			0
$895$	−46.8606			−1.56638
$896$	2.39430	+	1.12575i	0.0799881	+	0.0376086i
$897$		0			0
$898$	−16.8657	−	9.73743i	−0.562816	−	0.324942i
$899$	23.4898	+	40.6855i	0.783428	+	1.35694i
$900$		0			0
$901$	0.574381	+	0.331619i	0.0191354	+	0.0110478i
$902$	0.521169	−	8.98613i	0.0173530	−	0.299206i
$903$		0			0
$904$			12.8006i			0.425742i
$905$	−22.7466	−	13.1328i	−0.756124	−	0.436548i
$906$		0			0
$907$	8.12111	+	14.0662i	0.269657	+	0.467060i	0.968773	−	0.247948i	$-0.0797563\pi$
$907$	8.12111	+	14.0662i	0.269657	+	0.467060i	−0.699116	+	0.715008i	$0.746423\pi$
$908$	−3.18180	+	5.51104i	−0.105592	+	0.182890i
$909$		0			0
$910$	12.8443	−	8.93308i	0.425785	−	0.296129i
$911$		−	30.3752i		−	1.00637i	−0.864177	−	0.503187i	$-0.832161\pi$
$911$		−	30.3752i		−	1.00637i	0.864177	−	0.503187i	$-0.167839\pi$
$912$		0			0
$913$	51.0605	−	25.6593i	1.68986	−	0.849197i
$914$	23.7421	−	13.7075i	0.785321	−	0.453405i
$915$		0			0
$916$	10.3415			0.341694
$917$	−4.69784	−	2.20882i	−0.155136	−	0.0729416i
$918$		0			0
$919$	−36.4118	−	21.0224i	−1.20111	−	0.693463i	−0.240311	−	0.970696i	$-0.577249\pi$
$919$	−36.4118	−	21.0224i	−1.20111	−	0.693463i	−0.960803	+	0.277232i	$0.910583\pi$
$920$	9.43597	+	16.3436i	0.311095	+	0.538832i
$921$		0			0
$922$	19.3297	−	33.4800i	0.636589	−	1.10261i
$923$	−3.97434			−0.130817
$924$		0			0
$925$	−7.63041			−0.250886
$926$	−17.7478	+	30.7401i	−0.583229	+	1.01018i
$927$		0			0
$928$	−3.21649	−	5.57112i	−0.105586	−	0.182881i
$929$	−27.9603	−	16.1429i	−0.917347	−	0.529631i	−0.0345593	−	0.999403i	$-0.511003\pi$
$929$	−27.9603	−	16.1429i	−0.917347	−	0.529631i	−0.882788	+	0.469772i	$0.844336\pi$
$930$		0			0
$931$	−18.0771	−	6.70979i	−0.592454	−	0.219904i
$932$	8.90456			0.291678
$933$		0			0
$934$	9.49408	−	5.48141i	0.310656	−	0.179357i
$935$	−0.227557	−	0.452825i	−0.00744190	−	0.0148090i
$936$		0			0
$937$			8.45199i			0.276114i	0.990424	+	0.138057i	$0.0440858\pi$
$937$			8.45199i			0.276114i	−0.990424	+	0.138057i	$0.955914\pi$
$938$	0.332907	+	3.94948i	0.0108698	+	0.128955i
$939$		0			0
$940$	−4.04336	+	7.00331i	−0.131880	+	0.228423i
$941$	−4.52993	−	7.84606i	−0.147671	−	0.255774i	0.782695	−	0.622405i	$-0.213844\pi$
$941$	−4.52993	−	7.84606i	−0.147671	−	0.255774i	−0.930366	+	0.366631i	$0.880511\pi$
$942$		0			0
$943$	16.3576	+	9.44407i	0.532677	+	0.307541i
$944$			14.1438i			0.460341i
$945$		0			0
$946$	−35.2115	−	2.04216i	−1.14482	−	0.0663965i
$947$	−7.82779	−	4.51938i	−0.254369	−	0.146860i	0.367394	−	0.930065i	$-0.380250\pi$
$947$	−7.82779	−	4.51938i	−0.254369	−	0.146860i	−0.621763	+	0.783205i	$0.713583\pi$
$948$		0			0
$949$	−8.59199	−	14.8818i	−0.278908	−	0.483083i
$950$	−5.61327	−	3.24082i	−0.182118	−	0.105146i
$951$		0			0
$952$	0.122397	−	0.0851257i	0.00396691	−	0.00275894i
$953$	−9.69684			−0.314111			−0.157056	−	0.987590i	$-0.550200\pi$
$953$	−9.69684			−0.314111			−0.157056	+	0.987590i	$0.550200\pi$
$954$		0			0
$955$	−16.5563	−	28.6763i	−0.535748	−	0.927943i
$956$	−11.3045	−	19.5800i	−0.365614	−	0.633262i
$957$		0			0
$958$	−12.1607			−0.392894
$959$	−9.62429	−	13.8382i	−0.310785	−	0.446858i
$960$		0			0
$961$	−11.1664	+	19.3408i	−0.360207	+	0.623898i
$962$	−6.12428	+	3.53585i	−0.197455	+	0.114000i
$963$		0			0
$964$	−8.06528	−	4.65649i	−0.259765	−	0.149975i
$965$	21.7169			0.699091
$966$		0			0
$967$		−	43.0464i		−	1.38428i	−0.721764	−	0.692139i	$-0.756668\pi$
$967$		−	43.0464i		−	1.38428i	0.721764	−	0.692139i	$-0.243332\pi$
$968$	6.56441	−	8.82658i	0.210988	−	0.283697i
$969$		0			0
$970$	−14.6940	+	8.48360i	−0.471797	+	0.272392i
$971$	−3.16229	−	1.82575i	−0.101483	−	0.0585910i	0.448400	−	0.893833i	$-0.351994\pi$
$971$	−3.16229	−	1.82575i	−0.101483	−	0.0585910i	−0.549882	+	0.835242i	$0.685327\pi$
$972$		0			0
$973$	−29.5405	+	2.49001i	−0.947024	+	0.0798259i
$974$	2.44873			0.0784624
$975$		0			0
$976$	−10.2720	+	5.93056i	−0.328800	+	0.189833i
$977$	40.6302	−	23.4579i	1.29988	−	0.750483i	0.319493	−	0.947589i	$-0.396487\pi$
$977$	40.6302	−	23.4579i	1.29988	−	0.750483i	0.980382	+	0.197105i	$0.0631541\pi$
$978$		0			0
$979$	−28.4362	−	1.64922i	−0.908825	−	0.0527092i
$980$	3.17738	+	18.7137i	0.101498	+	0.597787i
$981$		0			0
$982$	−0.0674469	+	0.116821i	−0.00215232	+	0.00372792i
$983$	−27.9845	+	16.1568i	−0.892566	+	0.515323i	−0.874781	−	0.484518i	$-0.838995\pi$
$983$	−27.9845	+	16.1568i	−0.892566	+	0.515323i	−0.0177852	+	0.999842i	$0.505661\pi$
$984$		0			0
$985$	−14.4224	−	8.32676i	−0.459535	−	0.265313i
$986$	−0.362500			−0.0115443
$987$		0			0
$988$	−6.00705			−0.191110
$989$	37.0059	−	64.0961i	1.17672	−	2.03814i
$990$		0			0
$991$	14.8118	+	25.6549i	0.470514	+	0.814954i	0.999431	−	0.0337194i	$-0.0107352\pi$
$991$	14.8118	+	25.6549i	0.470514	+	0.814954i	−0.528918	+	0.848673i	$0.677402\pi$
$992$	3.65147	−	6.32453i	0.115934	−	0.200804i
$993$		0			0
$994$	2.05165	−	4.36357i	0.0650744	−	0.138404i
$995$		−	32.2063i		−	1.02101i
$996$		0			0
$997$	−11.8813	+	6.85966i	−0.376284	+	0.217248i	−0.676200	−	0.736718i	$-0.736375\pi$
$997$	−11.8813	+	6.85966i	−0.376284	+	0.217248i	0.299916	+	0.953965i	$0.403041\pi$
$998$	−18.6333	−	32.2738i	−0.589826	−	1.02161i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.ba.a.989.14	yes	32
3.2	odd	2		1386.2.ba.b.989.3	yes	32
7.4	even	3	inner	1386.2.ba.a.1187.3	yes	32
11.10	odd	2		1386.2.ba.b.989.14	yes	32
21.11	odd	6		1386.2.ba.b.1187.14	yes	32
33.32	even	2	inner	1386.2.ba.a.989.3	✓	32
77.32	odd	6		1386.2.ba.b.1187.3	yes	32
231.32	even	6	inner	1386.2.ba.a.1187.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.ba.a.989.3	✓	32	33.32	even	2	inner
1386.2.ba.a.989.14	yes	32	1.1	even	1	trivial
1386.2.ba.a.1187.3	yes	32	7.4	even	3	inner
1386.2.ba.a.1187.14	yes	32	231.32	even	6	inner
1386.2.ba.b.989.3	yes	32	3.2	odd	2
1386.2.ba.b.989.14	yes	32	11.10	odd	2
1386.2.ba.b.1187.3	yes	32	77.32	odd	6
1386.2.ba.b.1187.14	yes	32	21.11	odd	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.34835 + 1.35582i) q^{5} +(-0.222226 - 2.63640i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.34835 + 1.35582i) q^{5} +(-0.222226 - 2.63640i) q^{7} +1.00000 q^{8} +(-2.34835 + 1.35582i) q^{10} +(-2.96348 + 1.48923i) q^{11} -2.18074i q^{13} +(2.39430 + 1.12575i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0281751 + 0.0488007i) q^{17} +(2.38555 + 1.37730i) q^{19} -2.71165i q^{20} +(0.192032 - 3.31106i) q^{22} +(6.02718 + 3.47980i) q^{23} +(1.17651 + 2.03778i) q^{25} +(1.88857 + 1.09037i) q^{26} +(-2.17208 + 1.51065i) q^{28} +6.43297 q^{29} +(3.65147 + 6.32453i) q^{31} +(-0.500000 - 0.866025i) q^{32} -0.0563502 q^{34} +(3.05263 - 6.49251i) q^{35} +(-1.62140 + 2.80836i) q^{37} +(-2.38555 + 1.37730i) q^{38} +(2.34835 + 1.35582i) q^{40} +2.71397 q^{41} -10.6345i q^{43} +(2.77145 + 1.82183i) q^{44} +(-6.02718 + 3.47980i) q^{46} +(-2.58268 - 1.49111i) q^{47} +(-6.90123 + 1.17175i) q^{49} -2.35302 q^{50} +(-1.88857 + 1.09037i) q^{52} +(10.1931 - 5.88497i) q^{53} +(-8.97843 - 0.520722i) q^{55} +(-0.222226 - 2.63640i) q^{56} +(-3.21649 + 5.57112i) q^{58} +(12.2489 - 7.07189i) q^{59} +(10.2720 + 5.93056i) q^{61} -7.30294 q^{62} +1.00000 q^{64} +(2.95669 - 5.12114i) q^{65} +(0.749028 + 1.29735i) q^{67} +(0.0281751 - 0.0488007i) q^{68} +(4.09636 + 5.88991i) q^{70} -1.82248i q^{71} +(6.82420 - 3.93995i) q^{73} +(-1.62140 - 2.80836i) q^{74} -2.75460i q^{76} +(4.58476 + 7.48198i) q^{77} +(-7.82062 - 4.51524i) q^{79} +(-2.34835 + 1.35582i) q^{80} +(-1.35699 + 2.35037i) q^{82} -17.2299 q^{83} +0.152802i q^{85} +(9.20975 + 5.31725i) q^{86} +(-2.96348 + 1.48923i) q^{88} +(7.43764 + 4.29412i) q^{89} +(-5.74929 + 0.484616i) q^{91} -6.95959i q^{92} +(2.58268 - 1.49111i) q^{94} +(3.73475 + 6.46878i) q^{95} +6.25716 q^{97} +(2.43585 - 6.56252i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more