LMFDB - Embedded newform 912.2.ci.g.751.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			751.2
Character	$\chi$	$=$	912.751
Dual form			912.2.ci.g.895.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{3} +(-0.800469 - 0.291347i) q^{5} +(1.70402 + 0.983816i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{3} +(-0.800469 - 0.291347i) q^{5} +(1.70402 + 0.983816i) q^{7} +(0.173648 - 0.984808i) q^{9} +(0.742729 - 0.428815i) q^{11} +(2.79888 - 3.33557i) q^{13} +(-0.800469 + 0.291347i) q^{15} +(1.26058 + 7.14912i) q^{17} +(-0.199195 - 4.35435i) q^{19} +(1.93774 - 0.341676i) q^{21} +(-0.620043 - 1.70355i) q^{23} +(-3.27435 - 2.74751i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(9.99678 + 1.76270i) q^{29} +(1.88028 - 3.25675i) q^{31} +(0.293327 - 0.805909i) q^{33} +(-1.07738 - 1.28398i) q^{35} +8.42925i q^{37} -4.35428i q^{39} +(-0.985372 - 1.17432i) q^{41} +(3.98472 - 10.9479i) q^{43} +(-0.425921 + 0.737716i) q^{45} +(7.46077 + 1.31554i) q^{47} +(-1.56421 - 2.70930i) q^{49} +(5.56103 + 4.66626i) q^{51} +(1.86020 + 5.11085i) q^{53} +(-0.719466 + 0.126861i) q^{55} +(-2.95151 - 3.20758i) q^{57} +(-1.02896 - 5.83551i) q^{59} +(2.62536 - 0.955551i) q^{61} +(1.26477 - 1.50729i) q^{63} +(-3.21222 + 1.85458i) q^{65} +(-1.41820 + 8.04303i) q^{67} +(-1.57000 - 0.906442i) q^{69} +(-11.8385 - 4.30887i) q^{71} +(4.45656 - 3.73950i) q^{73} -4.27437 q^{75} +1.68750 q^{77} +(3.58938 - 3.01184i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-11.1639 - 6.44550i) q^{83} +(1.07382 - 6.08992i) q^{85} +(8.79102 - 5.07550i) q^{87} +(-6.05909 + 7.22094i) q^{89} +(8.05093 - 2.93030i) q^{91} +(-0.653015 - 3.70343i) q^{93} +(-1.10918 + 3.54355i) q^{95} +(-7.66765 + 1.35201i) q^{97} +(-0.293327 - 0.805909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{7}+O(q^{10}) $ 24 * q - 9 * q^7	$ 24 q - 9 q^{7} + 9 q^{11} - 9 q^{13} - 6 q^{17} - 3 q^{19} - 6 q^{21} + 15 q^{23} + 6 q^{25} - 12 q^{27} - 6 q^{29} + 12 q^{31} - 3 q^{33} + 30 q^{41} - 9 q^{43} + 3 q^{45} - 15 q^{47} + 27 q^{49} + 3 q^{51} + 6 q^{53} + 21 q^{55} - 9 q^{57} - 36 q^{59} - 21 q^{61} - 3 q^{63} - 9 q^{65} + 45 q^{67} - 36 q^{71} + 42 q^{75} + 108 q^{77} + 36 q^{79} - 27 q^{83} - 9 q^{85} - 9 q^{87} - 27 q^{89} - 36 q^{91} - 18 q^{93} + 30 q^{95} - 51 q^{97} + 3 q^{99}+O(q^{100}) $ 24 * q - 9 * q^7 + 9 * q^11 - 9 * q^13 - 6 * q^17 - 3 * q^19 - 6 * q^21 + 15 * q^23 + 6 * q^25 - 12 * q^27 - 6 * q^29 + 12 * q^31 - 3 * q^33 + 30 * q^41 - 9 * q^43 + 3 * q^45 - 15 * q^47 + 27 * q^49 + 3 * q^51 + 6 * q^53 + 21 * q^55 - 9 * q^57 - 36 * q^59 - 21 * q^61 - 3 * q^63 - 9 * q^65 + 45 * q^67 - 36 * q^71 + 42 * q^75 + 108 * q^77 + 36 * q^79 - 27 * q^83 - 9 * q^85 - 9 * q^87 - 27 * q^89 - 36 * q^91 - 18 * q^93 + 30 * q^95 - 51 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$		0			0
$5$	−0.800469	−	0.291347i	−0.357981	−	0.130294i	0.156768	−	0.987635i	$-0.449893\pi$
$5$	−0.800469	−	0.291347i	−0.357981	−	0.130294i	−0.514749	+	0.857341i	$0.672115\pi$
$6$		0			0
$7$	1.70402	+	0.983816i	0.644059	+	0.371847i	0.786176	−	0.618002i	$-0.212058\pi$
$7$	1.70402	+	0.983816i	0.644059	+	0.371847i	−0.142118	+	0.989850i	$0.545391\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	0.742729	−	0.428815i	0.223941	−	0.129293i	−0.383833	−	0.923403i	$-0.625396\pi$
$11$	0.742729	−	0.428815i	0.223941	−	0.129293i	0.607774	+	0.794110i	$0.292063\pi$
$12$		0			0
$13$	2.79888	−	3.33557i	0.776268	−	0.925121i	−0.222490	−	0.974935i	$-0.571418\pi$
$13$	2.79888	−	3.33557i	0.776268	−	0.925121i	0.998758	+	0.0498143i	$0.0158629\pi$
$14$		0			0
$15$	−0.800469	+	0.291347i	−0.206680	+	0.0752255i
$16$		0			0
$17$	1.26058	+	7.14912i	0.305736	+	1.73392i	0.620018	+	0.784587i	$0.287125\pi$
$17$	1.26058	+	7.14912i	0.305736	+	1.73392i	−0.314282	+	0.949330i	$0.601764\pi$
$18$		0			0
$19$	−0.199195	−	4.35435i	−0.0456984	−	0.998955i
$19$	−0.199195	−	4.35435i	−0.0456984	−	0.998955i
$20$		0			0
$21$	1.93774	−	0.341676i	0.422849	−	0.0745598i
$22$		0			0
$23$	−0.620043	−	1.70355i	−0.129288	−	0.355215i	0.858112	−	0.513463i	$-0.171638\pi$
$23$	−0.620043	−	1.70355i	−0.129288	−	0.355215i	−0.987399	+	0.158248i	$0.949415\pi$
$24$		0			0
$25$	−3.27435	−	2.74751i	−0.654871	−	0.549502i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	9.99678	+	1.76270i	1.85636	+	0.327326i	0.986214	−	0.165476i	$-0.0529161\pi$
$29$	9.99678	+	1.76270i	1.85636	+	0.327326i	0.870142	+	0.492802i	$0.164027\pi$
$30$		0			0
$31$	1.88028	−	3.25675i	0.337709	−	0.584929i	−0.646293	−	0.763090i	$-0.723681\pi$
$31$	1.88028	−	3.25675i	0.337709	−	0.584929i	0.984001	+	0.178161i	$0.0570148\pi$
$32$		0			0
$33$	0.293327	−	0.805909i	0.0510616	−	0.140291i
$34$		0			0
$35$	−1.07738	−	1.28398i	−0.182111	−	0.217031i
$36$		0			0
$37$			8.42925i			1.38576i	0.721053	+	0.692880i	$0.243659\pi$
$37$			8.42925i			1.38576i	−0.721053	+	0.692880i	$0.756341\pi$
$38$		0			0
$39$		−	4.35428i		−	0.697242i
$40$		0			0
$41$	−0.985372	−	1.17432i	−0.153889	−	0.183398i	0.683592	−	0.729865i	$-0.260417\pi$
$41$	−0.985372	−	1.17432i	−0.153889	−	0.183398i	−0.837481	+	0.546467i	$0.815973\pi$
$42$		0			0
$43$	3.98472	−	10.9479i	0.607665	−	1.66954i	−0.127650	−	0.991819i	$-0.540743\pi$
$43$	3.98472	−	10.9479i	0.607665	−	1.66954i	0.735315	−	0.677726i	$-0.237034\pi$
$44$		0			0
$45$	−0.425921	+	0.737716i	−0.0634925	+	0.109972i
$46$		0			0
$47$	7.46077	+	1.31554i	1.08827	+	0.191891i	0.688868	−	0.724887i	$-0.258108\pi$
$47$	7.46077	+	1.31554i	1.08827	+	0.191891i	0.399398	+	0.916778i	$0.369219\pi$
$48$		0			0
$49$	−1.56421	−	2.70930i	−0.223459	−	0.387042i
$50$		0			0
$51$	5.56103	+	4.66626i	0.778700	+	0.653407i
$52$		0			0
$53$	1.86020	+	5.11085i	0.255518	+	0.702029i	0.999430	+	0.0337518i	$0.0107456\pi$
$53$	1.86020	+	5.11085i	0.255518	+	0.702029i	−0.743913	+	0.668277i	$0.767032\pi$
$54$		0			0
$55$	−0.719466	+	0.126861i	−0.0970128	+	0.0171060i
$56$		0			0
$57$	−2.95151	−	3.20758i	−0.390937	−	0.424855i
$58$		0			0
$59$	−1.02896	−	5.83551i	−0.133959	−	0.759719i	−0.975579	−	0.219649i	$-0.929509\pi$
$59$	−1.02896	−	5.83551i	−0.133959	−	0.759719i	0.841620	−	0.540070i	$-0.181602\pi$
$60$		0			0
$61$	2.62536	−	0.955551i	0.336142	−	0.122346i	−0.168434	−	0.985713i	$-0.553871\pi$
$61$	2.62536	−	0.955551i	0.336142	−	0.122346i	0.504576	+	0.863367i	$0.331649\pi$
$62$		0			0
$63$	1.26477	−	1.50729i	0.159346	−	0.189901i
$64$		0			0
$65$	−3.21222	+	1.85458i	−0.398427	+	0.230032i
$66$		0			0
$67$	−1.41820	+	8.04303i	−0.173261	+	0.982613i	0.766871	+	0.641802i	$0.221813\pi$
$67$	−1.41820	+	8.04303i	−0.173261	+	0.982613i	−0.940132	+	0.340811i	$0.889298\pi$
$68$		0			0
$69$	−1.57000	−	0.906442i	−0.189006	−	0.109123i
$70$		0			0
$71$	−11.8385	−	4.30887i	−1.40497	−	0.511369i	−0.475323	−	0.879811i	$-0.657669\pi$
$71$	−11.8385	−	4.30887i	−1.40497	−	0.511369i	−0.929650	+	0.368443i	$0.879891\pi$
$72$		0			0
$73$	4.45656	−	3.73950i	0.521601	−	0.437675i	−0.343589	−	0.939120i	$-0.611643\pi$
$73$	4.45656	−	3.73950i	0.521601	−	0.437675i	0.865189	+	0.501445i	$0.167198\pi$
$74$		0			0
$75$	−4.27437			−0.493561
$76$		0			0
$77$	1.68750			0.192309
$78$		0			0
$79$	3.58938	−	3.01184i	0.403836	−	0.338859i	−0.418138	−	0.908384i	$-0.637317\pi$
$79$	3.58938	−	3.01184i	0.403836	−	0.338859i	0.821974	+	0.569525i	$0.192873\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	−11.1639	−	6.44550i	−1.22540	−	0.707486i	−0.259337	−	0.965787i	$-0.583504\pi$
$83$	−11.1639	−	6.44550i	−1.22540	−	0.707486i	−0.966064	+	0.258301i	$0.916837\pi$
$84$		0			0
$85$	1.07382	−	6.08992i	0.116472	−	0.660544i
$86$		0			0
$87$	8.79102	−	5.07550i	0.942496	−	0.544151i
$88$		0			0
$89$	−6.05909	+	7.22094i	−0.642262	+	0.765418i	−0.984726	−	0.174113i	$-0.944294\pi$
$89$	−6.05909	+	7.22094i	−0.642262	+	0.765418i	0.342463	+	0.939531i	$0.388739\pi$
$90$		0			0
$91$	8.05093	−	2.93030i	0.843966	−	0.307179i
$92$		0			0
$93$	−0.653015	−	3.70343i	−0.0677145	−	0.384028i
$94$		0			0
$95$	−1.10918	+	3.54355i	−0.113799	+	0.363561i
$96$		0			0
$97$	−7.66765	+	1.35201i	−0.778531	+	0.137276i	−0.548773	−	0.835972i	$-0.684905\pi$
$97$	−7.66765	+	1.35201i	−0.778531	+	0.137276i	−0.229759	+	0.973248i	$0.573794\pi$
$98$		0			0
$99$	−0.293327	−	0.805909i	−0.0294804	−	0.0809969i
$100$		0			0
$101$	6.41580	+	5.38350i	0.638396	+	0.535678i	0.903525	−	0.428535i	$-0.140970\pi$
$101$	6.41580	+	5.38350i	0.638396	+	0.535678i	−0.265129	+	0.964213i	$0.585415\pi$
$102$		0			0
$103$	5.29565	+	9.17233i	0.521796	+	0.903777i	0.999679	+	0.0253533i	$0.00807107\pi$
$103$	5.29565	+	9.17233i	0.521796	+	0.903777i	−0.477883	+	0.878424i	$0.658596\pi$
$104$		0			0
$105$	−1.65065	−	0.291054i	−0.161087	−	0.0284039i
$106$		0			0
$107$	−3.02073	+	5.23205i	−0.292025	+	0.505802i	−0.974288	−	0.225305i	$-0.927662\pi$
$107$	−3.02073	+	5.23205i	−0.292025	+	0.505802i	0.682264	+	0.731106i	$0.260996\pi$
$108$		0			0
$109$	1.80109	−	4.94844i	0.172513	−	0.473975i	−0.823062	−	0.567952i	$-0.807736\pi$
$109$	1.80109	−	4.94844i	0.172513	−	0.473975i	0.995574	+	0.0939772i	$0.0299581\pi$
$110$		0			0
$111$	5.41822	+	6.45718i	0.514274	+	0.612888i
$112$		0			0
$113$			12.8993i			1.21346i	0.794906	+	0.606732i	$0.207520\pi$
$113$			12.8993i			1.21346i	−0.794906	+	0.606732i	$0.792480\pi$
$114$		0			0
$115$			1.54429i			0.144006i
$116$		0			0
$117$	−2.79888	−	3.33557i	−0.258756	−	0.308374i
$118$		0			0
$119$	−4.88536	+	13.4224i	−0.447840	+	1.23043i
$120$		0			0
$121$	−5.13224	+	8.88929i	−0.466567	+	0.808117i
$122$		0			0
$123$	−1.50968	−	0.266197i	−0.136123	−	0.0240022i
$124$		0			0
$125$	3.95015	+	6.84185i	0.353312	+	0.611954i
$126$		0			0
$127$	−6.65573	−	5.58482i	−0.590601	−	0.495573i	0.297808	−	0.954626i	$-0.403744\pi$
$127$	−6.65573	−	5.58482i	−0.590601	−	0.495573i	−0.888409	+	0.459053i	$0.848189\pi$
$128$		0			0
$129$	−3.98472	−	10.9479i	−0.350835	−	0.963912i
$130$		0			0
$131$	9.35147	−	1.64892i	0.817042	−	0.144067i	0.250518	−	0.968112i	$-0.419399\pi$
$131$	9.35147	−	1.64892i	0.817042	−	0.144067i	0.566524	+	0.824045i	$0.308288\pi$
$132$		0			0
$133$	3.94444	−	7.61586i	0.342027	−	0.660379i
$134$		0			0
$135$	0.147921	+	0.838900i	0.0127310	+	0.0722010i
$136$		0			0
$137$	−2.26166	+	0.823178i	−0.193227	+	0.0703288i	−0.436821	−	0.899548i	$-0.643896\pi$
$137$	−2.26166	+	0.823178i	−0.193227	+	0.0703288i	0.243594	+	0.969877i	$0.421673\pi$
$138$		0			0
$139$	−14.4845	+	17.2619i	−1.22856	+	1.46414i	−0.388666	+	0.921379i	$0.627064\pi$
$139$	−14.4845	+	17.2619i	−1.22856	+	1.46414i	−0.839890	+	0.542757i	$0.817381\pi$
$140$		0			0
$141$	6.56089	−	3.78793i	0.552527	−	0.319002i
$142$		0			0
$143$	0.648465	−	3.67763i	0.0542273	−	0.307539i
$144$		0			0
$145$	−7.48856	−	4.32352i	−0.621891	−	0.359049i
$146$		0			0
$147$	−2.93976	−	1.06998i	−0.242467	−	0.0882508i
$148$		0			0
$149$	7.14636	−	5.99651i	0.585453	−	0.491253i	−0.301280	−	0.953536i	$-0.597414\pi$
$149$	7.14636	−	5.99651i	0.585453	−	0.491253i	0.886733	+	0.462283i	$0.152969\pi$
$150$		0			0
$151$	4.22796			0.344066			0.172033	−	0.985091i	$-0.444966\pi$
$151$	4.22796			0.344066			0.172033	+	0.985091i	$0.444966\pi$
$152$		0			0
$153$	7.25941			0.586888
$154$		0			0
$155$	−2.45395	+	2.05911i	−0.197106	+	0.165392i
$156$		0			0
$157$	12.3948	+	4.51133i	0.989210	+	0.360043i	0.785414	−	0.618970i	$-0.212450\pi$
$157$	12.3948	+	4.51133i	0.989210	+	0.360043i	0.203796	+	0.979013i	$0.434672\pi$
$158$		0			0
$159$	4.71018	+	2.71942i	0.373542	+	0.215664i
$160$		0			0
$161$	0.619418	−	3.51289i	0.0488170	−	0.276855i
$162$		0			0
$163$	−4.55574	+	2.63026i	−0.356833	+	0.206018i	−0.667691	−	0.744439i	$-0.732717\pi$
$163$	−4.55574	+	2.63026i	−0.356833	+	0.206018i	0.310858	+	0.950456i	$0.399384\pi$
$164$		0			0
$165$	−0.469598	+	0.559645i	−0.0365582	+	0.0435683i
$166$		0			0
$167$	−20.5365	+	7.47468i	−1.58916	+	0.578408i	−0.977171	−	0.212456i	$-0.931854\pi$
$167$	−20.5365	+	7.47468i	−1.58916	+	0.578408i	−0.611992	+	0.790864i	$0.709632\pi$
$168$		0			0
$169$	−1.03490	−	5.86919i	−0.0796074	−	0.451476i
$170$		0			0
$171$	−4.32278	−	0.559956i	−0.330571	−	0.0428209i
$172$		0			0
$173$	−14.7330	+	2.59783i	−1.12013	+	0.197510i	−0.702899	−	0.711290i	$-0.748111\pi$
$173$	−14.7330	+	2.59783i	−1.12013	+	0.197510i	−0.417233	+	0.908799i	$0.637000\pi$
$174$		0			0
$175$	−2.87652	−	7.90317i	−0.217444	−	0.597424i
$176$		0			0
$177$	−4.53922	−	3.80886i	−0.341189	−	0.286291i
$178$		0			0
$179$	7.06049	+	12.2291i	0.527726	+	0.914048i	0.999478	+	0.0323163i	$0.0102884\pi$
$179$	7.06049	+	12.2291i	0.527726	+	0.914048i	−0.471752	+	0.881731i	$0.656378\pi$
$180$		0			0
$181$	−19.9761	−	3.52232i	−1.48481	−	0.261812i	−0.628311	−	0.777962i	$-0.716254\pi$
$181$	−19.9761	−	3.52232i	−1.48481	−	0.261812i	−0.856498	+	0.516150i	$0.827365\pi$
$182$		0			0
$183$	1.39692	−	2.41954i	0.103264	−	0.178858i
$184$		0			0
$185$	2.45584	−	6.74736i	0.180557	−	0.496075i
$186$		0			0
$187$	4.00192	+	4.76931i	0.292650	+	0.348766i
$188$		0			0
$189$		−	1.96763i		−	0.143124i
$190$		0			0
$191$			4.19654i			0.303651i	0.988407	+	0.151825i	$0.0485152\pi$
$191$			4.19654i			0.303651i	−0.988407	+	0.151825i	$0.951485\pi$
$192$		0			0
$193$	−10.8141	−	12.8878i	−0.778417	−	0.927682i	0.220444	−	0.975400i	$-0.429250\pi$
$193$	−10.8141	−	12.8878i	−0.778417	−	0.927682i	−0.998861	+	0.0477181i	$0.984805\pi$
$194$		0			0
$195$	−1.26861	+	3.48546i	−0.0908467	+	0.249599i
$196$		0			0
$197$	−2.74941	+	4.76212i	−0.195887	+	0.339287i	−0.947191	−	0.320670i	$-0.896092\pi$
$197$	−2.74941	+	4.76212i	−0.195887	+	0.339287i	0.751304	+	0.659957i	$0.229425\pi$
$198$		0			0
$199$	9.35141	+	1.64891i	0.662904	+	0.116888i	0.494970	−	0.868910i	$-0.335179\pi$
$199$	9.35141	+	1.64891i	0.662904	+	0.116888i	0.167934	+	0.985798i	$0.446290\pi$
$200$		0			0
$201$	4.08356	+	7.07293i	0.288032	+	0.498886i
$202$		0			0
$203$	15.3005	+	12.8387i	1.07389	+	0.901098i
$204$		0			0
$205$	0.446625	+	1.22709i	0.0311937	+	0.0857039i
$206$		0			0
$207$	−1.78534	+	0.314804i	−0.124090	+	0.0218804i
$208$		0			0
$209$	−2.01516	−	3.14868i	−0.139391	−	0.217799i
$210$		0			0
$211$	0.462859	+	2.62500i	0.0318645	+	0.180713i	0.996586	−	0.0825594i	$-0.0263094\pi$
$211$	0.462859	+	2.62500i	0.0318645	+	0.180713i	−0.964722	+	0.263272i	$0.915198\pi$
$212$		0			0
$213$	−11.8385	+	4.30887i	−0.811162	+	0.295239i
$214$		0			0
$215$	−6.37930	+	7.60255i	−0.435064	+	0.518490i
$216$		0			0
$217$	6.40808	−	3.69970i	0.435009	−	0.251152i
$218$		0			0
$219$	1.01022	−	5.72924i	0.0682643	−	0.387146i
$220$		0			0
$221$	27.3746	+	15.8047i	1.84142	+	1.06314i
$222$		0			0
$223$	12.1593	+	4.42561i	0.814244	+	0.296361i	0.715376	−	0.698740i	$-0.246255\pi$
$223$	12.1593	+	4.42561i	0.814244	+	0.296361i	0.0988685	+	0.995101i	$0.468478\pi$
$224$		0			0
$225$	−3.27435	+	2.74751i	−0.218290	+	0.183167i
$226$		0			0
$227$	7.14194			0.474027			0.237013	−	0.971506i	$-0.423831\pi$
$227$	7.14194			0.474027			0.237013	+	0.971506i	$0.423831\pi$
$228$		0			0
$229$	4.86891			0.321747			0.160873	−	0.986975i	$-0.448569\pi$
$229$	4.86891			0.321747			0.160873	+	0.986975i	$0.448569\pi$
$230$		0			0
$231$	1.29270	−	1.08470i	0.0850534	−	0.0713683i
$232$		0			0
$233$	−11.4863	−	4.18068i	−0.752494	−	0.273886i	−0.0628394	−	0.998024i	$-0.520016\pi$
$233$	−11.4863	−	4.18068i	−0.752494	−	0.273886i	−0.689655	+	0.724138i	$0.742238\pi$
$234$		0			0
$235$	−5.58884	−	3.22672i	−0.364576	−	0.210488i
$236$		0			0
$237$	0.813645	−	4.61441i	0.0528519	−	0.299738i
$238$		0			0
$239$	−24.7586	+	14.2944i	−1.60150	+	0.924626i	−0.610311	+	0.792162i	$0.708956\pi$
$239$	−24.7586	+	14.2944i	−1.60150	+	0.924626i	−0.991188	+	0.132464i	$0.957711\pi$
$240$		0			0
$241$	4.50570	−	5.36969i	0.290238	−	0.345892i	−0.601148	−	0.799138i	$-0.705290\pi$
$241$	4.50570	−	5.36969i	0.290238	−	0.345892i	0.891385	+	0.453246i	$0.149734\pi$
$242$		0			0
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$		0			0
$245$	0.462759	+	2.62444i	0.0295646	+	0.167669i
$246$		0			0
$247$	−15.0817	−	11.5228i	−0.959628	−	0.733181i
$248$		0			0
$249$	−12.6952	+	2.23850i	−0.804523	+	0.141859i
$250$		0			0
$251$	−4.36817	−	12.0014i	−0.275716	−	0.757524i	−0.997836	−	0.0657559i	$-0.979054\pi$
$251$	−4.36817	−	12.0014i	−0.275716	−	0.757524i	0.722119	−	0.691768i	$-0.243168\pi$
$252$		0			0
$253$	−1.19103	−	0.999395i	−0.0748796	−	0.0628314i
$254$		0			0
$255$	−3.09193	−	5.35538i	−0.193624	−	0.335367i
$256$		0			0
$257$	−27.1921	−	4.79470i	−1.69620	−	0.299085i	−0.759833	−	0.650118i	$-0.774719\pi$
$257$	−27.1921	−	4.79470i	−1.69620	−	0.299085i	−0.936363	+	0.351033i	$0.885831\pi$
$258$		0			0
$259$	−8.29283	+	14.3636i	−0.515291	+	0.892511i
$260$		0			0
$261$	3.47185	−	9.53882i	0.214902	−	0.590438i
$262$		0			0
$263$	−0.384094	−	0.457745i	−0.0236842	−	0.0282258i	0.754072	−	0.656791i	$-0.228087\pi$
$263$	−0.384094	−	0.457745i	−0.0236842	−	0.0282258i	−0.777757	+	0.628566i	$0.783642\pi$
$264$		0			0
$265$		−	4.63304i		−	0.284605i
$266$		0			0
$267$			9.42627i			0.576878i
$268$		0			0
$269$	−8.10278	−	9.65652i	−0.494035	−	0.588768i	0.460204	−	0.887813i	$-0.347776\pi$
$269$	−8.10278	−	9.65652i	−0.494035	−	0.588768i	−0.954239	+	0.299045i	$0.903332\pi$
$270$		0			0
$271$	−8.31754	+	22.8523i	−0.505255	+	1.38818i	0.380827	+	0.924646i	$0.375639\pi$
$271$	−8.31754	+	22.8523i	−0.505255	+	1.38818i	−0.886082	+	0.463529i	$0.846583\pi$
$272$		0			0
$273$	4.28381	−	7.41977i	0.259268	−	0.449065i
$274$		0			0
$275$	−3.61013	−	0.636564i	−0.217699	−	0.0383862i
$276$		0			0
$277$	10.1987	+	17.6647i	0.612781	+	1.06137i	0.990770	+	0.135557i	$0.0432824\pi$
$277$	10.1987	+	17.6647i	0.612781	+	1.06137i	−0.377989	+	0.925810i	$0.623384\pi$
$278$		0			0
$279$	−2.88076	−	2.41724i	−0.172467	−	0.144717i
$280$		0			0
$281$	4.99122	+	13.7133i	0.297751	+	0.818065i	0.994875	+	0.101114i	$0.0322406\pi$
$281$	4.99122	+	13.7133i	0.297751	+	0.818065i	−0.697124	+	0.716951i	$0.745537\pi$
$282$		0			0
$283$	−1.44800	+	0.255322i	−0.0860748	+	0.0151773i	−0.216520	−	0.976278i	$-0.569471\pi$
$283$	−1.44800	+	0.255322i	−0.0860748	+	0.0151773i	0.130445	+	0.991456i	$0.458359\pi$
$284$		0			0
$285$	1.42807	+	3.42748i	0.0845918	+	0.203027i
$286$		0			0
$287$	−0.523778	−	2.97049i	−0.0309176	−	0.175343i
$288$		0			0
$289$	−33.5461	+	12.2098i	−1.97330	+	0.718223i
$290$		0			0
$291$	−5.00470	+	5.96437i	−0.293381	+	0.349638i
$292$		0			0
$293$	−20.0610	+	11.5823i	−1.17198	+	0.676642i	−0.954145	−	0.299344i	$-0.903232\pi$
$293$	−20.0610	+	11.5823i	−1.17198	+	0.676642i	−0.217833	+	0.975986i	$0.569899\pi$
$294$		0			0
$295$	−0.876509	+	4.97093i	−0.0510323	+	0.289419i
$296$		0			0
$297$	−0.742729	−	0.428815i	−0.0430975	−	0.0248824i
$298$		0			0
$299$	−7.41774	−	2.69984i	−0.428979	−	0.156136i
$300$		0			0
$301$	17.5608	−	14.7353i	1.01219	−	0.849326i
$302$		0			0
$303$	8.37523			0.481145
$304$		0			0
$305$	−2.37991			−0.136273
$306$		0			0
$307$	21.0623	−	17.6733i	1.20209	−	1.00867i	0.202519	−	0.979278i	$-0.435087\pi$
$307$	21.0623	−	17.6733i	1.20209	−	1.00867i	0.999568	−	0.0293928i	$-0.00935736\pi$
$308$		0			0
$309$	9.95257	+	3.62244i	0.566182	+	0.206073i
$310$		0			0
$311$	−8.12090	−	4.68860i	−0.460494	−	0.265866i	0.251758	−	0.967790i	$-0.418991\pi$
$311$	−8.12090	−	4.68860i	−0.460494	−	0.265866i	−0.712252	+	0.701924i	$0.752325\pi$
$312$		0			0
$313$	−2.20327	+	12.4954i	−0.124536	+	0.706281i	0.857046	+	0.515241i	$0.172297\pi$
$313$	−2.20327	+	12.4954i	−0.124536	+	0.706281i	−0.981582	+	0.191041i	$0.938814\pi$
$314$		0			0
$315$	−1.45155	+	0.838055i	−0.0817858	+	0.0472191i
$316$		0			0
$317$	7.52390	−	8.96664i	0.422584	−	0.503616i	−0.512183	−	0.858876i	$-0.671163\pi$
$317$	7.52390	−	8.96664i	0.422584	−	0.503616i	0.934768	+	0.355260i	$0.115608\pi$
$318$		0			0
$319$	8.18078	−	2.97756i	0.458035	−	0.166711i
$320$		0			0
$321$	1.04909	+	5.94967i	0.0585544	+	0.332078i
$322$		0			0
$323$	30.8786	−	6.91308i	1.71813	−	0.384654i
$324$		0			0
$325$	−18.3290	+	3.23190i	−1.01671	+	0.179274i
$326$		0			0
$327$	−1.80109	−	4.94844i	−0.0996003	−	0.273650i
$328$		0			0
$329$	11.4191	+	9.58172i	0.629553	+	0.528258i
$330$		0			0
$331$	−3.92921	−	6.80559i	−0.215969	−	0.374069i	0.737603	−	0.675235i	$-0.235958\pi$
$331$	−3.92921	−	6.80559i	−0.215969	−	0.374069i	−0.953572	+	0.301166i	$0.902624\pi$
$332$		0			0
$333$	8.30119	+	1.46372i	0.454902	+	0.0802116i
$334$		0			0
$335$	3.47854	−	6.02501i	0.190053	−	0.329182i
$336$		0			0
$337$	0.341119	−	0.937218i	0.0185820	−	0.0510535i	−0.930055	−	0.367421i	$-0.880241\pi$
$337$	0.341119	−	0.937218i	0.0185820	−	0.0510535i	0.948637	+	0.316367i	$0.102463\pi$
$338$		0			0
$339$	8.29151	+	9.88144i	0.450333	+	0.536686i
$340$		0			0
$341$		−	3.22517i		−	0.174653i
$342$		0			0
$343$		−	19.9290i		−	1.07607i
$344$		0			0
$345$	0.992650	+	1.18299i	0.0534425	+	0.0636903i
$346$		0			0
$347$	6.21872	−	17.0858i	0.333839	−	0.917214i	−0.653265	−	0.757130i	$-0.726601\pi$
$347$	6.21872	−	17.0858i	0.333839	−	0.917214i	0.987103	−	0.160084i	$-0.0511766\pi$
$348$		0			0
$349$	9.39679	−	16.2757i	0.502998	−	0.871219i	−0.496996	−	0.867753i	$-0.665563\pi$
$349$	9.39679	−	16.2757i	0.502998	−	0.871219i	0.999994	−	0.00346578i	$-0.00110319\pi$
$350$		0			0
$351$	−4.28813	−	0.756112i	−0.228883	−	0.0403583i
$352$		0			0
$353$	10.5265	+	18.2324i	0.560268	+	0.970412i	0.997473	+	0.0710504i	$0.0226351\pi$
$353$	10.5265	+	18.2324i	0.560268	+	0.970412i	−0.437205	+	0.899362i	$0.644032\pi$
$354$		0			0
$355$	8.22099	+	6.89823i	0.436325	+	0.366120i
$356$		0			0
$357$	4.88536	+	13.4224i	0.258561	+	0.710390i
$358$		0			0
$359$	−4.60842	+	0.812589i	−0.243223	+	0.0428868i	−0.293931	−	0.955827i	$-0.594963\pi$
$359$	−4.60842	+	0.812589i	−0.243223	+	0.0428868i	0.0507076	+	0.998714i	$0.483852\pi$
$360$		0			0
$361$	−18.9206	+	1.73472i	−0.995823	+	0.0913013i
$362$		0			0
$363$	1.78241	+	10.1085i	0.0935521	+	0.530560i
$364$		0			0
$365$	−4.65683	+	1.69495i	−0.243750	+	0.0887176i
$366$		0			0
$367$	−1.19016	+	1.41838i	−0.0621257	+	0.0740386i	−0.796212	−	0.605017i	$-0.793166\pi$
$367$	−1.19016	+	1.41838i	−0.0621257	+	0.0740386i	0.734087	+	0.679056i	$0.237611\pi$
$368$		0			0
$369$	−1.32759	+	0.766484i	−0.0691115	+	0.0399015i
$370$		0			0
$371$	−1.85832	+	10.5391i	−0.0964793	+	0.547161i
$372$		0			0
$373$	3.83269	+	2.21280i	0.198449	+	0.114575i	0.595932	−	0.803035i	$-0.296783\pi$
$373$	3.83269	+	2.21280i	0.198449	+	0.114575i	−0.397483	+	0.917610i	$0.630116\pi$
$374$		0			0
$375$	7.42384	+	2.70206i	0.383366	+	0.139534i
$376$		0			0
$377$	33.8594	−	28.4114i	1.74385	−	1.46326i
$378$		0			0
$379$	−16.4546			−0.845215			−0.422607	−	0.906313i	$-0.638885\pi$
$379$	−16.4546			−0.845215			−0.422607	+	0.906313i	$0.638885\pi$
$380$		0			0
$381$	−8.68844			−0.445122
$382$		0			0
$383$	15.4689	−	12.9799i	0.790424	−	0.663244i	−0.155427	−	0.987847i	$-0.549675\pi$
$383$	15.4689	−	12.9799i	0.790424	−	0.663244i	0.945850	+	0.324603i	$0.105231\pi$
$384$		0			0
$385$	−1.35079	−	0.491648i	−0.0688427	−	0.0250567i
$386$		0			0
$387$	−10.0897	−	5.82528i	−0.512887	−	0.296115i
$388$		0			0
$389$	5.08711	−	28.8505i	0.257927	−	1.46278i	−0.530519	−	0.847673i	$-0.678003\pi$
$389$	5.08711	−	28.8505i	0.257927	−	1.46278i	0.788446	−	0.615104i	$-0.210886\pi$
$390$		0			0
$391$	11.3973	−	6.58023i	0.576386	−	0.332777i
$392$		0			0
$393$	6.10374	−	7.27415i	0.307893	−	0.366933i
$394$		0			0
$395$	−3.75068	+	1.36513i	−0.188717	+	0.0686874i
$396$		0			0
$397$	−0.813518	−	4.61369i	−0.0408293	−	0.231554i	0.957564	−	0.288221i	$-0.0930639\pi$
$397$	−0.813518	−	4.61369i	−0.0408293	−	0.231554i	−0.998393	+	0.0566668i	$0.981953\pi$
$398$		0			0
$399$	−1.87376	−	8.36953i	−0.0938054	−	0.419000i
$400$		0			0
$401$	−5.37590	+	0.947915i	−0.268459	+	0.0473366i	−0.306257	−	0.951949i	$-0.599077\pi$
$401$	−5.37590	+	0.947915i	−0.268459	+	0.0473366i	0.0377979	+	0.999285i	$0.487966\pi$
$402$		0			0
$403$	−5.60042	−	15.3870i	−0.278977	−	0.766483i
$404$		0			0
$405$	0.652548	+	0.547553i	0.0324254	+	0.0272081i
$406$		0			0
$407$	3.61459	+	6.26065i	0.179169	+	0.310329i
$408$		0			0
$409$	32.8575	+	5.79367i	1.62470	+	0.286478i	0.910514	−	0.413478i	$-0.135686\pi$
$409$	32.8575	+	5.79367i	1.62470	+	0.286478i	0.714186	+	0.699956i	$0.246797\pi$
$410$		0			0
$411$	−1.20341	+	2.08436i	−0.0593596	+	0.102814i
$412$		0			0
$413$	3.98770	−	10.9561i	0.196222	−	0.539116i
$414$		0			0
$415$	7.05851	+	8.41200i	0.346489	+	0.412929i
$416$		0			0
$417$			22.5338i			1.10349i
$418$		0			0
$419$		−	32.7170i		−	1.59833i	−0.601112	−	0.799165i	$-0.705276\pi$
$419$		−	32.7170i		−	1.59833i	0.601112	−	0.799165i	$-0.294724\pi$
$420$		0			0
$421$	2.41145	+	2.87385i	0.117527	+	0.140063i	0.821600	−	0.570064i	$-0.193082\pi$
$421$	2.41145	+	2.87385i	0.117527	+	0.140063i	−0.704073	+	0.710127i	$0.748637\pi$
$422$		0			0
$423$	2.59110	−	7.11899i	0.125984	−	0.346137i
$424$		0			0
$425$	15.5147	−	26.8722i	0.752573	−	1.30349i
$426$		0			0
$427$	5.41374	+	0.954589i	0.261989	+	0.0461958i
$428$		0			0
$429$	−1.86718	−	3.23405i	−0.0901483	−	0.156141i
$430$		0			0
$431$	−12.8225	−	10.7594i	−0.617640	−	0.518261i	0.279421	−	0.960169i	$-0.409857\pi$
$431$	−12.8225	−	10.7594i	−0.617640	−	0.518261i	−0.897061	+	0.441908i	$0.854302\pi$
$432$		0			0
$433$	6.08362	+	16.7146i	0.292360	+	0.803253i	0.995720	+	0.0924192i	$0.0294600\pi$
$433$	6.08362	+	16.7146i	0.292360	+	0.803253i	−0.703360	+	0.710834i	$0.748318\pi$
$434$		0			0
$435$	−8.51567	+	1.50154i	−0.408295	+	0.0719935i
$436$		0			0
$437$	−7.29435	+	3.03922i	−0.348936	+	0.145386i
$438$		0			0
$439$	−3.32943	−	18.8821i	−0.158905	−	0.901194i	−0.955129	−	0.296192i	$-0.904283\pi$
$439$	−3.32943	−	18.8821i	−0.158905	−	0.901194i	0.796224	−	0.605002i	$-0.206828\pi$
$440$		0			0
$441$	−2.93976	+	1.06998i	−0.139988	+	0.0509516i
$442$		0			0
$443$	9.83193	−	11.7172i	0.467129	−	0.556703i	−0.480119	−	0.877203i	$-0.659407\pi$
$443$	9.83193	−	11.7172i	0.467129	−	0.556703i	0.947248	+	0.320500i	$0.103851\pi$
$444$		0			0
$445$	6.95391	−	4.01484i	0.329647	−	0.190322i
$446$		0			0
$447$	1.61995	−	9.18718i	0.0766209	−	0.434539i
$448$		0			0
$449$	−19.5849	−	11.3073i	−0.924268	−	0.533627i	−0.0392742	−	0.999228i	$-0.512505\pi$
$449$	−19.5849	−	11.3073i	−0.924268	−	0.533627i	−0.884994	+	0.465602i	$0.845838\pi$
$450$		0			0
$451$	−1.23543	−	0.449660i	−0.0581742	−	0.0211737i
$452$		0			0
$453$	3.23880	−	2.71768i	0.152172	−	0.127688i
$454$		0			0
$455$	−7.29825			−0.342147
$456$		0			0
$457$	29.7517			1.39173			0.695863	−	0.718174i	$-0.255022\pi$
$457$	29.7517			1.39173			0.695863	+	0.718174i	$0.255022\pi$
$458$		0			0
$459$	5.56103	−	4.66626i	0.259567	−	0.217802i
$460$		0			0
$461$	6.41065	+	2.33329i	0.298574	+	0.108672i	0.486963	−	0.873422i	$-0.338105\pi$
$461$	6.41065	+	2.33329i	0.298574	+	0.108672i	−0.188389	+	0.982094i	$0.560327\pi$
$462$		0			0
$463$	11.4519	+	6.61175i	0.532214	+	0.307274i	0.741918	−	0.670491i	$-0.233916\pi$
$463$	11.4519	+	6.61175i	0.532214	+	0.307274i	−0.209703	+	0.977765i	$0.567250\pi$
$464$		0			0
$465$	−0.556266	+	3.15474i	−0.0257962	+	0.146298i
$466$		0			0
$467$	19.9450	−	11.5153i	0.922947	−	0.532864i	0.0383728	−	0.999263i	$-0.487783\pi$
$467$	19.9450	−	11.5153i	0.922947	−	0.532864i	0.884574	+	0.466400i	$0.154449\pi$
$468$		0			0
$469$	−10.3295	+	12.3102i	−0.476973	+	0.568434i
$470$		0			0
$471$	12.3948	−	4.51133i	0.571121	−	0.207871i
$472$		0			0
$473$	−1.73507	−	9.84006i	−0.0797786	−	0.452447i
$474$		0			0
$475$	−11.3114	+	14.8050i	−0.519001	+	0.679298i
$476$		0			0
$477$	5.35622	−	0.944446i	0.245244	−	0.0432432i
$478$		0			0
$479$	7.96557	+	21.8852i	0.363956	+	0.999961i	0.977617	+	0.210391i	$0.0674738\pi$
$479$	7.96557	+	21.8852i	0.363956	+	0.999961i	−0.613661	+	0.789569i	$0.710304\pi$
$480$		0			0
$481$	28.1164	+	23.5924i	1.28200	+	1.07572i
$482$		0			0
$483$	−1.78354	−	3.08919i	−0.0811540	−	0.140563i
$484$		0			0
$485$	6.53162	+	1.15170i	0.296586	+	0.0522960i
$486$		0			0
$487$	9.13609	−	15.8242i	0.413996	−	0.717062i	−0.581327	−	0.813670i	$-0.697466\pi$
$487$	9.13609	−	15.8242i	0.413996	−	0.717062i	0.995322	+	0.0966084i	$0.0307994\pi$
$488$		0			0
$489$	−1.79920	+	4.94326i	−0.0813627	+	0.223542i
$490$		0			0
$491$	12.6101	+	15.0282i	0.569087	+	0.678211i	0.971443	−	0.237272i	$-0.0762533\pi$
$491$	12.6101	+	15.0282i	0.569087	+	0.678211i	−0.402357	+	0.915483i	$0.631809\pi$
$492$		0			0
$493$			73.6902i			3.31884i
$494$		0			0
$495$			0.730565i			0.0328364i
$496$		0			0
$497$	−15.9339	−	18.9893i	−0.714734	−	0.851787i
$498$		0			0
$499$	−12.0370	+	33.0713i	−0.538848	+	1.48047i	0.309430	+	0.950922i	$0.399862\pi$
$499$	−12.0370	+	33.0713i	−0.538848	+	1.48047i	−0.848278	+	0.529551i	$0.822360\pi$
$500$		0			0
$501$	−10.9272	+	18.9265i	−0.488193	+	0.845576i
$502$		0			0
$503$	28.0629	+	4.94825i	1.25126	+	0.220631i	0.759736	−	0.650231i	$-0.225328\pi$
$503$	28.0629	+	4.94825i	1.25126	+	0.220631i	0.491527	+	0.870863i	$0.336439\pi$
$504$		0			0
$505$	−3.56719	−	6.17855i	−0.158738	−	0.274942i
$506$		0			0
$507$	−4.56542	−	3.83084i	−0.202757	−	0.170134i
$508$		0			0
$509$	0.620753	+	1.70550i	0.0275144	+	0.0755952i	0.952689	−	0.303946i	$-0.0983042\pi$
$509$	0.620753	+	1.70550i	0.0275144	+	0.0755952i	−0.925175	+	0.379541i	$0.876082\pi$
$510$		0			0
$511$	11.2730	−	1.98774i	0.498690	−	0.0879325i
$512$		0			0
$513$	−3.67138	+	2.34968i	−0.162095	+	0.103741i
$514$		0			0
$515$	−1.56667	−	8.88504i	−0.0690359	−	0.391522i
$516$		0			0
$517$	6.10546	−	2.22220i	0.268518	−	0.0977324i
$518$		0			0
$519$	−9.61631	+	11.4603i	−0.422109	+	0.503050i
$520$		0			0
$521$	5.43453	−	3.13762i	0.238091	−	0.137462i	−0.376208	−	0.926535i	$-0.622772\pi$
$521$	5.43453	−	3.13762i	0.238091	−	0.137462i	0.614299	+	0.789073i	$0.289439\pi$
$522$		0			0
$523$	5.25604	−	29.8085i	0.229830	−	1.30343i	−0.623402	−	0.781902i	$-0.714250\pi$
$523$	5.25604	−	29.8085i	0.229830	−	1.30343i	0.853232	−	0.521531i	$-0.174639\pi$
$524$		0			0
$525$	−7.28360	−	4.20519i	−0.317882	−	0.183530i
$526$		0			0
$527$	25.6531	+	9.33697i	1.11747	+	0.406725i
$528$		0			0
$529$	15.1014	−	12.6716i	0.656582	−	0.550938i
$530$		0			0
$531$	−5.92553			−0.257146
$532$		0			0
$533$	−6.67496			−0.289125
$534$		0			0
$535$	3.94234	−	3.30802i	0.170442	−	0.143018i
$536$		0			0
$537$	13.2694	+	4.82966i	0.572616	+	0.208415i
$538$		0			0
$539$	−2.32357	−	1.34152i	−0.100083	−	0.0577832i
$540$		0			0
$541$	6.02864	−	34.1901i	0.259192	−	1.46995i	−0.525888	−	0.850554i	$-0.676267\pi$
$541$	6.02864	−	34.1901i	0.259192	−	1.46995i	0.785079	−	0.619395i	$-0.212622\pi$
$542$		0			0
$543$	−17.5667	+	10.1421i	−0.753858	+	0.435240i
$544$		0			0
$545$	−2.88343	+	3.43634i	−0.123512	+	0.147196i
$546$		0			0
$547$	−36.3521	+	13.2311i	−1.55430	+	0.565720i	−0.969422	−	0.245400i	$-0.921081\pi$
$547$	−36.3521	+	13.2311i	−1.55430	+	0.565720i	−0.584880	+	0.811120i	$0.698858\pi$
$548$		0			0
$549$	−0.485146	−	2.75140i	−0.0207055	−	0.117427i
$550$		0			0
$551$	5.68411	−	43.8806i	0.242151	−	1.86937i
$552$		0			0
$553$	9.07946	−	1.60095i	0.386098	−	0.0680795i
$554$		0			0
$555$	−2.45584	−	6.74736i	−0.104244	−	0.286409i
$556$		0			0
$557$	19.2011	+	16.1116i	0.813576	+	0.682671i	0.951458	−	0.307777i	$-0.0995852\pi$
$557$	19.2011	+	16.1116i	0.813576	+	0.682671i	−0.137883	+	0.990449i	$0.544030\pi$
$558$		0			0
$559$	−25.3649	−	43.9332i	−1.07282	−	1.85818i
$560$		0			0
$561$	6.13130	+	1.08111i	0.258864	+	0.0456447i
$562$		0			0
$563$	22.4774	−	38.9321i	0.947311	−	1.64079i	0.196256	−	0.980553i	$-0.437122\pi$
$563$	22.4774	−	38.9321i	0.947311	−	1.64079i	0.751056	−	0.660239i	$-0.229545\pi$
$564$		0			0
$565$	3.75817	−	10.3255i	0.158108	−	0.434397i
$566$		0			0
$567$	−1.26477	−	1.50729i	−0.0531153	−	0.0633004i
$568$		0			0
$569$			13.6063i			0.570405i	0.958467	+	0.285203i	$0.0920609\pi$
$569$			13.6063i			0.570405i	−0.958467	+	0.285203i	$0.907939\pi$
$570$		0			0
$571$			4.95760i			0.207469i	0.994605	+	0.103735i	$0.0330793\pi$
$571$			4.95760i			0.207469i	−0.994605	+	0.103735i	$0.966921\pi$
$572$		0			0
$573$	2.69748	+	3.21474i	0.112689	+	0.134298i
$574$		0			0
$575$	−2.65029	+	7.28161i	−0.110525	+	0.303664i
$576$		0			0
$577$	−13.2788	+	22.9996i	−0.552806	+	0.957487i	0.445265	+	0.895399i	$0.353109\pi$
$577$	−13.2788	+	22.9996i	−0.552806	+	0.957487i	−0.998071	+	0.0620885i	$0.980224\pi$
$578$		0			0
$579$	−16.5682	−	2.92142i	−0.688551	−	0.121410i
$580$		0			0
$581$	−12.6824	−	21.9665i	−0.526153	−	0.911325i
$582$		0			0
$583$	3.57323	+	2.99830i	0.147988	+	0.124177i
$584$		0			0
$585$	1.26861	+	3.48546i	0.0524504	+	0.144106i
$586$		0			0
$587$	3.84329	−	0.677676i	0.158630	−	0.0279707i	−0.0937693	−	0.995594i	$-0.529892\pi$
$587$	3.84329	−	0.677676i	0.158630	−	0.0279707i	0.252399	+	0.967623i	$0.418781\pi$
$588$		0			0
$589$	−14.5555	−	7.53867i	−0.599750	−	0.310626i
$590$		0			0
$591$	0.954860	+	5.41528i	0.0392777	+	0.222755i
$592$		0			0
$593$	−8.03449	+	2.92431i	−0.329937	+	0.120087i	−0.501677	−	0.865055i	$-0.667283\pi$
$593$	−8.03449	+	2.92431i	−0.329937	+	0.120087i	0.171740	+	0.985142i	$0.445061\pi$
$594$		0			0
$595$	7.82116	−	9.32090i	0.320636	−	0.382120i
$596$		0			0
$597$	8.22349	−	4.74784i	0.336565	−	0.194316i
$598$		0			0
$599$	−7.77203	+	44.0774i	−0.317557	+	1.80095i	0.239955	+	0.970784i	$0.422867\pi$
$599$	−7.77203	+	44.0774i	−0.317557	+	1.80095i	−0.557512	+	0.830169i	$0.688244\pi$
$600$		0			0
$601$	−4.85704	−	2.80421i	−0.198123	−	0.114386i	0.397657	−	0.917534i	$-0.369823\pi$
$601$	−4.85704	−	2.80421i	−0.198123	−	0.114386i	−0.595780	+	0.803148i	$0.703157\pi$
$602$		0			0
$603$	7.67457	+	2.79332i	0.312533	+	0.113753i
$604$		0			0
$605$	6.69806	−	5.62034i	0.272315	−	0.228499i
$606$		0			0
$607$	1.64607			0.0668121			0.0334060	−	0.999442i	$-0.489365\pi$
$607$	1.64607			0.0668121			0.0334060	+	0.999442i	$0.489365\pi$
$608$		0			0
$609$	19.9734			0.809364
$610$		0			0
$611$	25.2698	−	21.2039i	1.02231	−	0.857818i
$612$		0			0
$613$	−39.5205	−	14.3843i	−1.59622	−	0.580975i	−0.617569	−	0.786517i	$-0.711882\pi$
$613$	−39.5205	−	14.3843i	−1.59622	−	0.580975i	−0.978648	+	0.205542i	$0.934104\pi$
$614$		0			0
$615$	1.13090	+	0.652923i	0.0456021	+	0.0263284i
$616$		0			0
$617$	5.82163	−	33.0161i	0.234370	−	1.32918i	−0.609567	−	0.792735i	$-0.708657\pi$
$617$	5.82163	−	33.0161i	0.234370	−	1.32918i	0.843937	−	0.536443i	$-0.180232\pi$
$618$		0			0
$619$	−8.58580	+	4.95701i	−0.345092	+	0.199239i	−0.662522	−	0.749043i	$-0.730514\pi$
$619$	−8.58580	+	4.95701i	−0.345092	+	0.199239i	0.317429	+	0.948282i	$0.397180\pi$
$620$		0			0
$621$	−1.16530	+	1.38875i	−0.0467618	+	0.0557286i
$622$		0			0
$623$	−17.4289	+	6.34360i	−0.698274	+	0.254151i
$624$		0			0
$625$	2.54256	+	14.4196i	0.101703	+	0.576784i
$626$		0			0
$627$	−3.56763	−	1.11671i	−0.142478	−	0.0445972i
$628$		0			0
$629$	−60.2617	+	10.6258i	−2.40279	+	0.423677i
$630$		0			0
$631$	1.65511	+	4.54739i	0.0658890	+	0.181029i	0.968268	−	0.249915i	$-0.0804028\pi$
$631$	1.65511	+	4.54739i	0.0658890	+	0.181029i	−0.902379	+	0.430944i	$0.858181\pi$
$632$		0			0
$633$	2.04189	+	1.71335i	0.0811578	+	0.0680995i
$634$		0			0
$635$	3.70059	+	6.40960i	0.146853	+	0.254357i
$636$		0			0
$637$	−13.4151	−	2.36544i	−0.531525	−	0.0937222i
$638$		0			0
$639$	−6.29914	+	10.9104i	−0.249190	+	0.431610i
$640$		0			0
$641$	2.55310	−	7.01459i	0.100841	−	0.277060i	−0.879005	−	0.476813i	$-0.841792\pi$
$641$	2.55310	−	7.01459i	0.100841	−	0.277060i	0.979846	+	0.199753i	$0.0640141\pi$
$642$		0			0
$643$	18.4893	+	22.0347i	0.729148	+	0.868965i	0.995485	−	0.0949147i	$-0.0302578\pi$
$643$	18.4893	+	22.0347i	0.729148	+	0.868965i	−0.266337	+	0.963880i	$0.585813\pi$
$644$		0			0
$645$			9.92442i			0.390774i
$646$		0			0
$647$			43.5929i			1.71381i	0.515472	+	0.856907i	$0.327617\pi$
$647$			43.5929i			1.71381i	−0.515472	+	0.856907i	$0.672383\pi$
$648$		0			0
$649$	−3.26659	−	3.89297i	−0.128225	−	0.152813i
$650$		0			0
$651$	2.53075	−	6.95317i	0.0991878	−	0.272516i
$652$		0			0
$653$	5.04936	−	8.74574i	0.197597	−	0.342247i	−0.750152	−	0.661265i	$-0.770020\pi$
$653$	5.04936	−	8.74574i	0.197597	−	0.342247i	0.947749	+	0.319018i	$0.103353\pi$
$654$		0			0
$655$	−7.96597	−	1.40462i	−0.311256	−	0.0548829i
$656$		0			0
$657$	−2.90881	−	5.03821i	−0.113484	−	0.196559i
$658$		0			0
$659$	−17.1365	−	14.3793i	−0.667544	−	0.560136i	0.244793	−	0.969575i	$-0.421280\pi$
$659$	−17.1365	−	14.3793i	−0.667544	−	0.560136i	−0.912337	+	0.409439i	$0.865724\pi$
$660$		0			0
$661$	12.7301	+	34.9757i	0.495144	+	1.36040i	0.895917	+	0.444221i	$0.146519\pi$
$661$	12.7301	+	34.9757i	0.495144	+	1.36040i	−0.400773	+	0.916177i	$0.631258\pi$
$662$		0			0
$663$	31.1293	−	5.48893i	1.20896	−	0.213172i
$664$		0			0
$665$	−5.37626	+	4.94706i	−0.208483	+	0.191839i
$666$		0			0
$667$	−3.19557	−	18.1230i	−0.123733	−	0.701725i
$668$		0			0
$669$	12.1593	−	4.42561i	0.470104	−	0.171104i
$670$		0			0
$671$	1.54017	−	1.83551i	0.0594578	−	0.0708590i
$672$		0			0
$673$	12.0703	−	6.96876i	0.465274	−	0.268626i	−0.248985	−	0.968507i	$-0.580097\pi$
$673$	12.0703	−	6.96876i	0.465274	−	0.268626i	0.714259	+	0.699881i	$0.246764\pi$
$674$		0			0
$675$	−0.742236	+	4.20943i	−0.0285687	+	0.162021i
$676$		0			0
$677$	−10.4820	−	6.05180i	−0.402857	−	0.232590i	0.284859	−	0.958569i	$-0.408053\pi$
$677$	−10.4820	−	6.05180i	−0.402857	−	0.232590i	−0.687716	+	0.725980i	$0.741387\pi$
$678$		0			0
$679$	−14.3959	−	5.23970i	−0.552466	−	0.201081i
$680$		0			0
$681$	5.47104	−	4.59075i	0.209651	−	0.175918i
$682$		0			0
$683$	−48.5477			−1.85763			−0.928813	−	0.370548i	$-0.879170\pi$
$683$	−48.5477			−1.85763			−0.928813	+	0.370548i	$0.879170\pi$
$684$		0			0
$685$	2.05022			0.0783349
$686$		0			0
$687$	3.72980	−	3.12967i	0.142301	−	0.119405i
$688$		0			0
$689$	22.2540	+	8.09981i	0.847811	+	0.308578i
$690$		0			0
$691$	−4.82718	−	2.78697i	−0.183635	−	0.106021i	0.405365	−	0.914155i	$-0.367145\pi$
$691$	−4.82718	−	2.78697i	−0.183635	−	0.106021i	−0.588999	+	0.808134i	$0.700478\pi$
$692$		0			0
$693$	0.293031	−	1.66186i	0.0111313	−	0.0631290i
$694$		0			0
$695$	16.6236	−	9.59762i	0.630568	−	0.364058i
$696$		0			0
$697$	7.15322	−	8.52488i	0.270948	−	0.322903i
$698$		0			0
$699$	−11.4863	+	4.18068i	−0.434453	+	0.158128i
$700$		0			0
$701$	−2.58781	−	14.6762i	−0.0977404	−	0.554313i	−0.993873	−	0.110527i	$-0.964746\pi$
$701$	−2.58781	−	14.6762i	−0.0977404	−	0.554313i	0.896133	−	0.443786i	$-0.146365\pi$
$702$		0			0
$703$	36.7039	−	1.67906i	1.38431	−	0.0633270i
$704$		0			0
$705$	−6.35540	+	1.12063i	−0.239358	+	0.0422053i
$706$		0			0
$707$	5.63628	+	15.4855i	0.211974	+	0.582394i
$708$		0			0
$709$	−6.01903	−	5.05057i	−0.226049	−	0.189678i	0.522728	−	0.852500i	$-0.324914\pi$
$709$	−6.01903	−	5.05057i	−0.226049	−	0.189678i	−0.748777	+	0.662822i	$0.769359\pi$
$710$		0			0
$711$	−2.34280	−	4.05785i	−0.0878618	−	0.152181i
$712$		0			0
$713$	−6.71389	−	1.18384i	−0.251437	−	0.0443352i
$714$		0			0
$715$	−1.59054	+	2.75490i	−0.0594829	+	0.103027i
$716$		0			0
$717$	−9.77793	+	26.8646i	−0.365163	+	1.00328i
$718$		0			0
$719$	−23.7050	−	28.2505i	−0.884047	−	1.05357i	−0.998192	−	0.0601017i	$-0.980857\pi$
$719$	−23.7050	−	28.2505i	−0.884047	−	1.05357i	0.114146	−	0.993464i	$-0.463587\pi$
$720$		0			0
$721$			20.8398i			0.776114i
$722$		0			0
$723$		−	7.00963i		−	0.260691i
$724$		0			0
$725$	−27.8900	−	33.2380i	−1.03581	−	1.23443i
$726$		0			0
$727$	−4.87963	+	13.4067i	−0.180976	+	0.497226i	−0.996696	−	0.0812197i	$-0.974118\pi$
$727$	−4.87963	+	13.4067i	−0.180976	+	0.497226i	0.815721	+	0.578446i	$0.196341\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	83.2912	+	14.6865i	3.08064	+	0.543199i
$732$		0			0
$733$	18.2926	+	31.6838i	0.675654	+	1.17027i	0.976277	+	0.216524i	$0.0694721\pi$
$733$	18.2926	+	31.6838i	0.675654	+	1.17027i	−0.300623	+	0.953743i	$0.597195\pi$
$734$		0			0
$735$	2.04145	+	1.71298i	0.0753000	+	0.0631842i
$736$		0			0
$737$	2.39563	+	6.58195i	0.0882442	+	0.242449i
$738$		0			0
$739$	−45.2919	+	7.98618i	−1.66609	+	0.293776i	−0.925659	−	0.378358i	$-0.876489\pi$
$739$	−45.2919	+	7.98618i	−1.66609	+	0.293776i	−0.740429	+	0.672134i	$0.765378\pi$
$740$		0			0
$741$	−18.9600	+	0.867349i	−0.696514	+	0.0318629i
$742$		0			0
$743$	−3.43607	−	19.4869i	−0.126057	−	0.714905i	−0.980674	−	0.195647i	$-0.937319\pi$
$743$	−3.43607	−	19.4869i	−0.126057	−	0.714905i	0.854617	−	0.519258i	$-0.173792\pi$
$744$		0			0
$745$	−7.46750	+	2.71795i	−0.273588	+	0.0995780i
$746$		0			0
$747$	−8.28618	+	9.87508i	−0.303175	+	0.361310i
$748$		0			0
$749$	−10.2948	+	5.94368i	−0.376162	+	0.217177i
$750$		0			0
$751$	1.30443	−	7.39777i	0.0475992	−	0.269948i	−0.951715	−	0.306984i	$-0.900680\pi$
$751$	1.30443	−	7.39777i	0.0475992	−	0.269948i	0.999314	+	0.0370353i	$0.0117914\pi$
$752$		0			0
$753$	−11.0606	−	6.38583i	−0.403070	−	0.232713i
$754$		0			0
$755$	−3.38435	−	1.23180i	−0.123169	−	0.0448299i
$756$		0			0
$757$	−27.5534	+	23.1200i	−1.00144	+	0.840311i	−0.987184	−	0.159587i	$-0.948984\pi$
$757$	−27.5534	+	23.1200i	−1.00144	+	0.840311i	−0.0142599	+	0.999898i	$0.504539\pi$
$758$		0			0
$759$	−1.55478			−0.0564351
$760$		0			0
$761$	26.0381			0.943880			0.471940	−	0.881631i	$-0.343554\pi$
$761$	26.0381			0.943880			0.471940	+	0.881631i	$0.343554\pi$
$762$		0			0
$763$	7.93744	−	6.66031i	0.287355	−	0.241119i
$764$		0			0
$765$	−5.81093	−	2.11501i	−0.210095	−	0.0764682i
$766$		0			0
$767$	−22.3447	−	12.9007i	−0.806820	−	0.465817i
$768$		0			0
$769$	7.11549	−	40.3540i	0.256591	−	1.45520i	−0.535364	−	0.844622i	$-0.679826\pi$
$769$	7.11549	−	40.3540i	0.256591	−	1.45520i	0.791955	−	0.610579i	$-0.209063\pi$
$770$		0			0
$771$	−23.9123	+	13.8058i	−0.861181	+	0.497203i
$772$		0			0
$773$	19.0480	−	22.7005i	0.685109	−	0.816481i	−0.305646	−	0.952145i	$-0.598873\pi$
$773$	19.0480	−	22.7005i	0.685109	−	0.816481i	0.990755	+	0.135665i	$0.0433169\pi$
$774$		0			0
$775$	−15.1046	+	5.49764i	−0.542575	+	0.197481i
$776$		0			0
$777$	2.88007	+	16.3337i	0.103322	+	0.585968i
$778$		0			0
$779$	−4.91712	+	4.52457i	−0.176174	+	0.162110i
$780$		0			0
$781$	−10.6405	+	1.87621i	−0.380748	+	0.0671361i
$782$		0			0
$783$	−3.47185	−	9.53882i	−0.124074	−	0.340889i
$784$		0			0
$785$	−8.60727	−	7.22236i	−0.307207	−	0.257777i
$786$		0			0
$787$	23.6348	+	40.9367i	0.842490	+	1.45924i	0.887783	+	0.460262i	$0.152244\pi$
$787$	23.6348	+	40.9367i	0.842490	+	1.45924i	−0.0452932	+	0.998974i	$0.514422\pi$
$788$		0			0
$789$	−0.588466	−	0.103762i	−0.0209499	−	0.00369404i
$790$		0			0
$791$	−12.6905	+	21.9807i	−0.451224	+	0.781542i
$792$		0			0
$793$	4.16074	−	11.4315i	0.147752	−	0.405945i
$794$		0			0
$795$	−2.97806	−	3.54911i	−0.105621	−	0.125874i
$796$		0			0
$797$		−	42.1044i		−	1.49141i	−0.666274	−	0.745707i	$-0.732112\pi$
$797$		−	42.1044i		−	1.49141i	0.666274	−	0.745707i	$-0.267888\pi$
$798$		0			0
$799$			54.9963i			1.94563i
$800$		0			0
$801$	6.05909	+	7.22094i	0.214087	+	0.255139i
$802$		0			0
$803$	1.70646	−	4.68847i	0.0602198	−	0.165453i
$804$		0			0
$805$	−1.51930	+	2.63150i	−0.0535482	+	0.0927481i
$806$		0			0
$807$	−12.4142	−	2.18895i	−0.437000	−	0.0770549i
$808$		0			0
$809$	16.9993	+	29.4437i	0.597664	+	1.03518i	0.993165	+	0.116719i	$0.0372376\pi$
$809$	16.9993	+	29.4437i	0.597664	+	1.03518i	−0.395501	+	0.918465i	$0.629429\pi$
$810$		0			0
$811$	1.71268	+	1.43711i	0.0601404	+	0.0504638i	0.672362	−	0.740222i	$-0.265280\pi$
$811$	1.71268	+	1.43711i	0.0601404	+	0.0504638i	−0.612222	+	0.790686i	$0.709724\pi$
$812$		0			0
$813$	8.31754	+	22.8523i	0.291709	+	0.801464i
$814$		0			0
$815$	4.41304	−	0.778139i	0.154582	−	0.0272570i
$816$		0			0
$817$	−48.4648	−	15.1701i	−1.69557	−	0.530734i
$818$		0			0
$819$	−1.48775	−	8.43745i	−0.0519862	−	0.294829i
$820$		0			0
$821$	−52.4764	+	19.0999i	−1.83144	+	0.666590i	−0.838958	+	0.544196i	$0.816835\pi$
$821$	−52.4764	+	19.0999i	−1.83144	+	0.666590i	−0.992482	+	0.122394i	$0.960943\pi$
$822$		0			0
$823$	−19.7996	+	23.5963i	−0.690172	+	0.822515i	−0.991376	−	0.131045i	$-0.958167\pi$
$823$	−19.7996	+	23.5963i	−0.690172	+	0.822515i	0.301204	+	0.953560i	$0.402611\pi$
$824$		0			0
$825$	−3.17470	+	1.83291i	−0.110529	+	0.0638138i
$826$		0			0
$827$	−6.14752	+	34.8643i	−0.213770	+	1.21235i	0.669257	+	0.743031i	$0.266612\pi$
$827$	−6.14752	+	34.8643i	−0.213770	+	1.21235i	−0.883028	+	0.469321i	$0.844499\pi$
$828$		0			0
$829$	−10.8046	−	6.23806i	−0.375261	−	0.216657i	0.300494	−	0.953784i	$-0.402849\pi$
$829$	−10.8046	−	6.23806i	−0.375261	−	0.216657i	−0.675754	+	0.737127i	$0.736182\pi$
$830$		0			0
$831$	19.1673	+	6.97632i	0.664906	+	0.242006i
$832$		0			0
$833$	17.3973	−	14.5980i	0.602779	−	0.505792i
$834$		0			0
$835$	18.6166			0.644253
$836$		0			0
$837$	−3.76057			−0.129984
$838$		0			0
$839$	−37.5980	+	31.5484i	−1.29803	+	1.08917i	−0.307543	+	0.951534i	$0.599507\pi$
$839$	−37.5980	+	31.5484i	−1.29803	+	1.08917i	−0.990482	+	0.137639i	$0.956049\pi$
$840$		0			0
$841$	69.5774	+	25.3241i	2.39922	+	0.873245i
$842$		0			0
$843$	12.6382	+	7.29668i	0.435283	+	0.251311i
$844$		0			0
$845$	−0.881568	+	4.99962i	−0.0303269	+	0.171992i
$846$		0			0
$847$	−17.4909	+	10.0984i	−0.600993	+	0.346983i
$848$		0			0
$849$	−0.945116	+	1.12635i	−0.0324363	+	0.0386561i
$850$		0			0
$851$	14.3597	−	5.22649i	0.492243	−	0.179162i
$852$		0			0
$853$	−4.91769	−	27.8896i	−0.168379	−	0.954922i	−0.945512	−	0.325587i	$-0.894438\pi$
$853$	−4.91769	−	27.8896i	−0.168379	−	0.954922i	0.777134	−	0.629336i	$-0.216673\pi$
$854$		0			0
$855$	3.29711	+	1.70766i	0.112759	+	0.0584006i
$856$		0			0
$857$	−4.51845	+	0.796724i	−0.154347	+	0.0272156i	−0.250288	−	0.968171i	$-0.580525\pi$
$857$	−4.51845	+	0.796724i	−0.154347	+	0.0272156i	0.0959406	+	0.995387i	$0.469414\pi$
$858$		0			0
$859$	−10.3429	−	28.4169i	−0.352895	−	0.969571i	−0.981435	−	0.191794i	$-0.938569\pi$
$859$	−10.3429	−	28.4169i	−0.352895	−	0.969571i	0.628540	−	0.777777i	$-0.283653\pi$
$860$		0			0
$861$	−2.31063	−	1.93885i	−0.0787461	−	0.0660758i
$862$		0			0
$863$	−3.54644	−	6.14261i	−0.120722	−	0.209097i	0.799330	−	0.600892i	$-0.205188\pi$
$863$	−3.54644	−	6.14261i	−0.120722	−	0.209097i	−0.920053	+	0.391795i	$0.871854\pi$
$864$		0			0
$865$	12.5502	+	2.21294i	0.426720	+	0.0752423i
$866$		0			0
$867$	−17.8495	+	30.9163i	−0.606201	+	1.04997i
$868$		0			0
$869$	1.37441	−	3.77616i	0.0466237	−	0.128098i
$870$		0			0
$871$	22.8587	+	27.2420i	0.774538	+	0.923059i
$872$		0			0
$873$			7.78593i			0.263514i
$874$		0			0
$875$			15.5449i			0.525512i
$876$		0			0
$877$	−14.4916	−	17.2704i	−0.489347	−	0.583181i	0.463704	−	0.885990i	$-0.346520\pi$
$877$	−14.4916	−	17.2704i	−0.489347	−	0.583181i	−0.953051	+	0.302809i	$0.902076\pi$
$878$		0			0
$879$	−7.92273	+	21.7675i	−0.267227	+	0.734200i
$880$		0			0
$881$	−6.93793	+	12.0168i	−0.233745	+	0.404858i	−0.958907	−	0.283720i	$-0.908431\pi$
$881$	−6.93793	+	12.0168i	−0.233745	+	0.404858i	0.725162	+	0.688578i	$0.241765\pi$
$882$		0			0
$883$	−42.4697	−	7.48855i	−1.42922	−	0.252010i	−0.595125	−	0.803633i	$-0.702898\pi$
$883$	−42.4697	−	7.48855i	−1.42922	−	0.252010i	−0.834094	+	0.551623i	$0.814009\pi$
$884$		0			0
$885$	2.52381	+	4.37136i	0.0848369	+	0.146942i
$886$		0			0
$887$	38.2408	+	32.0878i	1.28400	+	1.07740i	0.992680	+	0.120778i	$0.0385390\pi$
$887$	38.2408	+	32.0878i	1.28400	+	1.07740i	0.291320	+	0.956626i	$0.405905\pi$
$888$		0			0
$889$	−5.84706	−	16.0647i	−0.196104	−	0.538791i
$890$		0			0
$891$	−0.844601	+	0.148926i	−0.0282952	+	0.00498921i
$892$		0			0
$893$	4.24215	−	32.7488i	0.141958	−	1.09590i
$894$		0			0
$895$	−2.08878	−	11.8461i	−0.0698204	−	0.395971i
$896$		0			0
$897$	−7.41774	+	2.69984i	−0.247671	+	0.0901449i
$898$		0			0
$899$	24.5374	−	29.2426i	0.818370	−	0.975295i
$900$		0			0
$901$	−34.1931	+	19.7414i	−1.13914	+	0.657682i
$902$		0			0
$903$	3.98071	−	22.5757i	0.132470	−	0.751273i
$904$		0			0
$905$	14.9640	+	8.63948i	0.497421	+	0.287186i
$906$		0			0
$907$	10.1423	+	3.69149i	0.336769	+	0.122574i	0.504869	−	0.863196i	$-0.331541\pi$
$907$	10.1423	+	3.69149i	0.336769	+	0.122574i	−0.168100	+	0.985770i	$0.553763\pi$
$908$		0			0
$909$	6.41580	−	5.38350i	0.212799	−	0.178559i
$910$		0			0
$911$	−43.2346			−1.43243			−0.716214	−	0.697881i	$-0.754127\pi$
$911$	−43.2346			−1.43243			−0.716214	+	0.697881i	$0.754127\pi$
$912$		0			0
$913$	−11.0557			−0.365891
$914$		0			0
$915$	−1.82312	+	1.52978i	−0.0602705	+	0.0505729i
$916$		0			0
$917$	17.5573	+	6.39034i	0.579794	+	0.211028i
$918$		0			0
$919$	18.5061	+	10.6845i	0.610459	+	0.352449i	0.773145	−	0.634229i	$-0.218682\pi$
$919$	18.5061	+	10.6845i	0.610459	+	0.352449i	−0.162686	+	0.986678i	$0.552016\pi$
$920$		0			0
$921$	4.77443	−	27.0771i	0.157323	−	0.892222i
$922$		0			0
$923$	−47.5071	+	27.4282i	−1.56371	+	0.902811i
$924$		0			0
$925$	23.1594	−	27.6004i	0.761478	−	0.907494i
$926$		0			0
$927$	9.95257	−	3.62244i	0.326885	−	0.118976i
$928$		0			0
$929$	−5.88305	−	33.3644i	−0.193017	−	1.09465i	−0.915215	−	0.402966i	$-0.867979\pi$
$929$	−5.88305	−	33.3644i	−0.193017	−	1.09465i	0.722198	−	0.691686i	$-0.243132\pi$
$930$		0			0
$931$	−11.4856	+	7.35080i	−0.376426	+	0.240913i
$932$		0			0
$933$	−9.23475	+	1.62833i	−0.302332	+	0.0533093i
$934$		0			0
$935$	−1.81389	−	4.98363i	−0.0593207	−	0.162982i
$936$		0			0
$937$	10.4545	+	8.77233i	0.341532	+	0.286580i	0.797379	−	0.603479i	$-0.206219\pi$
$937$	10.4545	+	8.77233i	0.341532	+	0.286580i	−0.455847	+	0.890058i	$0.650664\pi$
$938$		0			0
$939$	6.34408	+	10.9883i	0.207031	+	0.358588i
$940$		0			0
$941$	−35.2822	−	6.22121i	−1.15017	−	0.202806i	−0.434119	−	0.900855i	$-0.642940\pi$
$941$	−35.2822	−	6.22121i	−1.15017	−	0.202806i	−0.716049	+	0.698050i	$0.754051\pi$
$942$		0			0
$943$	−1.38955	+	2.40676i	−0.0452498	+	0.0783750i
$944$		0			0
$945$	−0.573264	+	1.57503i	−0.0186483	+	0.0512357i
$946$		0			0
$947$	10.8663	+	12.9500i	0.353107	+	0.420817i	0.913135	−	0.407657i	$-0.133654\pi$
$947$	10.8663	+	12.9500i	0.353107	+	0.420817i	−0.560028	+	0.828474i	$0.689210\pi$
$948$		0			0
$949$		−	25.3315i		−	0.822297i
$950$		0			0
$951$		−	11.7051i		−	0.379564i
$952$		0			0
$953$	4.41479	+	5.26134i	0.143009	+	0.170432i	0.832794	−	0.553582i	$-0.186740\pi$
$953$	4.41479	+	5.26134i	0.143009	+	0.170432i	−0.689785	+	0.724014i	$0.742295\pi$
$954$		0			0
$955$	1.22265	−	3.35920i	0.0395640	−	0.108701i
$956$		0			0
$957$	4.35290	−	7.53944i	0.140709	−	0.243716i
$958$		0			0
$959$	−4.66377	−	0.822349i	−0.150601	−	0.0265550i
$960$		0			0
$961$	8.42907	+	14.5996i	0.271906	+	0.470954i
$962$		0			0
$963$	4.62802	+	3.88337i	0.149136	+	0.125140i
$964$		0			0
$965$	4.90156	+	13.4669i	0.157787	+	0.433515i
$966$		0			0
$967$	8.93779	−	1.57597i	0.287420	−	0.0506799i	−0.0280793	−	0.999606i	$-0.508939\pi$
$967$	8.93779	−	1.57597i	0.287420	−	0.0506799i	0.315499	+	0.948926i	$0.397828\pi$
$968$		0			0
$969$	19.2108	−	25.1441i	0.617139	−	0.807746i
$970$		0			0
$971$	3.12505	+	17.7230i	0.100288	+	0.568759i	0.992998	+	0.118129i	$0.0376896\pi$
$971$	3.12505	+	17.7230i	0.100288	+	0.568759i	−0.892711	+	0.450630i	$0.851199\pi$
$972$		0			0
$973$	−41.6643	+	15.1646i	−1.33570	+	0.486154i
$974$		0			0
$975$	−11.9634	+	14.2574i	−0.383136	+	0.456604i
$976$		0			0
$977$	19.5035	−	11.2604i	0.623974	−	0.360251i	−0.154441	−	0.988002i	$-0.549358\pi$
$977$	19.5035	−	11.2604i	0.623974	−	0.360251i	0.778414	+	0.627751i	$0.216024\pi$
$978$		0			0
$979$	−1.40382	+	7.96144i	−0.0448661	+	0.254449i
$980$		0			0
$981$	−4.56051	−	2.63301i	−0.145606	−	0.0840656i
$982$		0			0
$983$	−2.02337	−	0.736448i	−0.0645356	−	0.0234890i	0.309551	−	0.950883i	$-0.399821\pi$
$983$	−2.02337	−	0.736448i	−0.0645356	−	0.0234890i	−0.374086	+	0.927394i	$0.622044\pi$
$984$		0			0
$985$	3.58825	−	3.01090i	0.114331	−	0.0959352i
$986$		0			0
$987$	14.9065			0.474480
$988$		0			0
$989$	−21.1211			−0.671612
$990$		0			0
$991$	−4.76151	+	3.99538i	−0.151254	+	0.126917i	−0.715275	−	0.698843i	$-0.753698\pi$
$991$	−4.76151	+	3.99538i	−0.151254	+	0.126917i	0.564020	+	0.825761i	$0.309254\pi$
$992$		0			0
$993$	−7.38450	−	2.68774i	−0.234340	−	0.0852927i
$994$		0			0
$995$	−7.00511	−	4.04440i	−0.222077	−	0.128216i
$996$		0			0
$997$	2.60747	−	14.7877i	0.0825794	−	0.468331i	−0.915273	−	0.402833i	$-0.868025\pi$
$997$	2.60747	−	14.7877i	0.0825794	−	0.468331i	0.997853	−	0.0654975i	$-0.0208635\pi$
$998$		0			0
$999$	7.29995	−	4.21463i	0.230960	−	0.133345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.g.751.2	✓	24
4.3	odd	2		912.2.ci.h.751.2	yes	24
19.2	odd	18		912.2.ci.h.895.2	yes	24
76.59	even	18	inner	912.2.ci.g.895.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.751.2	✓	24	1.1	even	1	trivial
912.2.ci.g.895.2	yes	24	76.59	even	18	inner
912.2.ci.h.751.2	yes	24	4.3	odd	2
912.2.ci.h.895.2	yes	24	19.2	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{3} +(-0.800469 - 0.291347i) q^{5} +(1.70402 + 0.983816i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{3} +(-0.800469 - 0.291347i) q^{5} +(1.70402 + 0.983816i) q^{7} +(0.173648 - 0.984808i) q^{9} +(0.742729 - 0.428815i) q^{11} +(2.79888 - 3.33557i) q^{13} +(-0.800469 + 0.291347i) q^{15} +(1.26058 + 7.14912i) q^{17} +(-0.199195 - 4.35435i) q^{19} +(1.93774 - 0.341676i) q^{21} +(-0.620043 - 1.70355i) q^{23} +(-3.27435 - 2.74751i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(9.99678 + 1.76270i) q^{29} +(1.88028 - 3.25675i) q^{31} +(0.293327 - 0.805909i) q^{33} +(-1.07738 - 1.28398i) q^{35} +8.42925i q^{37} -4.35428i q^{39} +(-0.985372 - 1.17432i) q^{41} +(3.98472 - 10.9479i) q^{43} +(-0.425921 + 0.737716i) q^{45} +(7.46077 + 1.31554i) q^{47} +(-1.56421 - 2.70930i) q^{49} +(5.56103 + 4.66626i) q^{51} +(1.86020 + 5.11085i) q^{53} +(-0.719466 + 0.126861i) q^{55} +(-2.95151 - 3.20758i) q^{57} +(-1.02896 - 5.83551i) q^{59} +(2.62536 - 0.955551i) q^{61} +(1.26477 - 1.50729i) q^{63} +(-3.21222 + 1.85458i) q^{65} +(-1.41820 + 8.04303i) q^{67} +(-1.57000 - 0.906442i) q^{69} +(-11.8385 - 4.30887i) q^{71} +(4.45656 - 3.73950i) q^{73} -4.27437 q^{75} +1.68750 q^{77} +(3.58938 - 3.01184i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-11.1639 - 6.44550i) q^{83} +(1.07382 - 6.08992i) q^{85} +(8.79102 - 5.07550i) q^{87} +(-6.05909 + 7.22094i) q^{89} +(8.05093 - 2.93030i) q^{91} +(-0.653015 - 3.70343i) q^{93} +(-1.10918 + 3.54355i) q^{95} +(-7.66765 + 1.35201i) q^{97} +(-0.293327 - 0.805909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{7}+O(q^{10}) \) 24 * q - 9 * q^7	\( 24 q - 9 q^{7} + 9 q^{11} - 9 q^{13} - 6 q^{17} - 3 q^{19} - 6 q^{21} + 15 q^{23} + 6 q^{25} - 12 q^{27} - 6 q^{29} + 12 q^{31} - 3 q^{33} + 30 q^{41} - 9 q^{43} + 3 q^{45} - 15 q^{47} + 27 q^{49} + 3 q^{51} + 6 q^{53} + 21 q^{55} - 9 q^{57} - 36 q^{59} - 21 q^{61} - 3 q^{63} - 9 q^{65} + 45 q^{67} - 36 q^{71} + 42 q^{75} + 108 q^{77} + 36 q^{79} - 27 q^{83} - 9 q^{85} - 9 q^{87} - 27 q^{89} - 36 q^{91} - 18 q^{93} + 30 q^{95} - 51 q^{97} + 3 q^{99}+O(q^{100}) \) 24 * q - 9 * q^7 + 9 * q^11 - 9 * q^13 - 6 * q^17 - 3 * q^19 - 6 * q^21 + 15 * q^23 + 6 * q^25 - 12 * q^27 - 6 * q^29 + 12 * q^31 - 3 * q^33 + 30 * q^41 - 9 * q^43 + 3 * q^45 - 15 * q^47 + 27 * q^49 + 3 * q^51 + 6 * q^53 + 21 * q^55 - 9 * q^57 - 36 * q^59 - 21 * q^61 - 3 * q^63 - 9 * q^65 + 45 * q^67 - 36 * q^71 + 42 * q^75 + 108 * q^77 + 36 * q^79 - 27 * q^83 - 9 * q^85 - 9 * q^87 - 27 * q^89 - 36 * q^91 - 18 * q^93 + 30 * q^95 - 51 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more