LMFDB - Embedded newform 384.2.o.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(47,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("384.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.o (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	384.47
Dual form			384.2.o.a.335.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47792 - 0.903198i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(0.543879 + 0.543879i) q^{7} +(1.36847 + 2.66970i) q^{9} +O(q^{10})$	\(q+(-1.47792 - 0.903198i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(0.543879 + 0.543879i) q^{7} +(1.36847 + 2.66970i) q^{9} +(3.96678 - 1.64309i) q^{11} +(1.13904 - 2.74988i) q^{13} +(5.21329 + 0.819208i) q^{15} +5.73443 q^{17} +(-0.0793211 - 0.0328559i) q^{19} +(-0.312577 - 1.29504i) q^{21} +(1.46457 + 1.46457i) q^{23} +(3.02867 - 3.02867i) q^{25} +(0.388788 - 5.18159i) q^{27} +(0.520422 - 1.25641i) q^{29} -5.64072i q^{31} +(-7.34659 - 1.15443i) q^{33} +(-2.16511 - 0.896820i) q^{35} +(4.19628 + 10.1307i) q^{37} +(-4.16709 + 3.03532i) q^{39} +(4.93573 - 4.93573i) q^{41} +(3.50661 + 8.46571i) q^{43} +(-6.96490 - 5.91936i) q^{45} +8.98904i q^{47} -6.40839i q^{49} +(-8.47500 - 5.17932i) q^{51} +(1.04873 + 2.53186i) q^{53} +(-9.25030 + 9.25030i) q^{55} +(0.0875545 + 0.120201i) q^{57} +(0.498592 + 1.20371i) q^{59} +(-3.69353 - 1.52991i) q^{61} +(-0.707713 + 2.19627i) q^{63} +9.06875i q^{65} +(3.35550 - 8.10090i) q^{67} +(-0.841717 - 3.48732i) q^{69} +(4.08070 - 4.08070i) q^{71} +(1.59075 + 1.59075i) q^{73} +(-7.21160 + 1.74063i) q^{75} +(3.05109 + 1.26380i) q^{77} -0.637492 q^{79} +(-5.25459 + 7.30679i) q^{81} +(1.94530 - 4.69638i) q^{83} +(-16.1419 + 6.68618i) q^{85} +(-1.90393 + 1.38682i) q^{87} +(0.902588 + 0.902588i) q^{89} +(2.11510 - 0.876104i) q^{91} +(-5.09469 + 8.33651i) q^{93} +0.261590 q^{95} -13.3054 q^{97} +(9.81497 + 8.34158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9	$ 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 8 q^{19} - 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} - 8 q^{37} + 28 q^{39} + 8 q^{43} - 4 q^{45} + 16 q^{51} - 24 q^{55} - 4 q^{57} - 40 q^{61} - 56 q^{67} - 4 q^{69} - 8 q^{73} - 16 q^{75} - 16 q^{79} - 48 q^{85} - 52 q^{87} - 40 q^{91} + 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9 - 8 * q^13 + 8 * q^15 + 8 * q^19 - 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 - 8 * q^37 + 28 * q^39 + 8 * q^43 - 4 * q^45 + 16 * q^51 - 24 * q^55 - 4 * q^57 - 40 * q^61 - 56 * q^67 - 4 * q^69 - 8 * q^73 - 16 * q^75 - 16 * q^79 - 48 * q^85 - 52 * q^87 - 40 * q^91 + 8 * q^93 - 16 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$	$-1$

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			0
$2$		0			0
$3$	−1.47792	−	0.903198i	−0.853275	−	0.521461i
$3$	−1.47792	−	0.903198i	−0.853275	−	0.521461i
$4$		0			0
$5$	−2.81491	+	1.16597i	−1.25886	+	0.521438i	−0.909561	−	0.415571i	$-0.863582\pi$
$5$	−2.81491	+	1.16597i	−1.25886	+	0.521438i	−0.349303	+	0.937010i	$0.613582\pi$
$6$		0			0
$7$	0.543879	+	0.543879i	0.205567	+	0.205567i	0.802380	−	0.596813i	$-0.203567\pi$
$7$	0.543879	+	0.543879i	0.205567	+	0.205567i	−0.596813	+	0.802380i	$0.703567\pi$
$8$		0			0
$9$	1.36847	+	2.66970i	0.456156	+	0.889900i
$10$		0			0
$11$	3.96678	−	1.64309i	1.19603	−	0.495411i	0.306314	−	0.951930i	$-0.400904\pi$
$11$	3.96678	−	1.64309i	1.19603	−	0.495411i	0.889713	+	0.456520i	$0.150904\pi$
$12$		0			0
$13$	1.13904	−	2.74988i	0.315912	−	0.762680i	−0.683550	−	0.729903i	$-0.739565\pi$
$13$	1.13904	−	2.74988i	0.315912	−	0.762680i	0.999463	−	0.0327767i	$-0.0104350\pi$
$14$		0			0
$15$	5.21329	+	0.819208i	1.34607	+	0.211519i
$16$		0			0
$17$	5.73443			1.39080			0.695402	−	0.718621i	$-0.255226\pi$
$17$	5.73443			1.39080			0.695402	+	0.718621i	$0.255226\pi$
$18$		0			0
$19$	−0.0793211	−	0.0328559i	−0.0181975	−	0.00753765i	0.373566	−	0.927604i	$-0.378135\pi$
$19$	−0.0793211	−	0.0328559i	−0.0181975	−	0.00753765i	−0.391764	+	0.920066i	$0.628135\pi$
$20$		0			0
$21$	−0.312577	−	1.29504i	−0.0682098	−	0.282600i
$22$		0			0
$23$	1.46457	+	1.46457i	0.305385	+	0.305385i	0.843116	−	0.537731i	$-0.180719\pi$
$23$	1.46457	+	1.46457i	0.305385	+	0.305385i	−0.537731	+	0.843116i	$0.680719\pi$
$24$		0			0
$25$	3.02867	−	3.02867i	0.605733	−	0.605733i
$26$		0			0
$27$	0.388788	−	5.18159i	0.0748222	−	0.997197i
$28$		0			0
$29$	0.520422	−	1.25641i	0.0966400	−	0.233310i	−0.868165	−	0.496275i	$-0.834701\pi$
$29$	0.520422	−	1.25641i	0.0966400	−	0.233310i	0.964805	+	0.262966i	$0.0847006\pi$
$30$		0			0
$31$		−	5.64072i		−	1.01310i	−0.862210	−	0.506552i	$-0.830920\pi$
$31$		−	5.64072i		−	1.01310i	0.862210	−	0.506552i	$-0.169080\pi$
$32$		0			0
$33$	−7.34659	−	1.15443i	−1.27888	−	0.200961i
$34$		0			0
$35$	−2.16511	−	0.896820i	−0.365971	−	0.151590i
$36$		0			0
$37$	4.19628	+	10.1307i	0.689864	+	1.66548i	0.745055	+	0.667003i	$0.232423\pi$
$37$	4.19628	+	10.1307i	0.689864	+	1.66548i	−0.0551907	+	0.998476i	$0.517577\pi$
$38$		0			0
$39$	−4.16709	+	3.03532i	−0.667269	+	0.486040i
$40$		0			0
$41$	4.93573	−	4.93573i	0.770831	−	0.770831i	−0.207421	−	0.978252i	$-0.566507\pi$
$41$	4.93573	−	4.93573i	0.770831	−	0.770831i	0.978252	+	0.207421i	$0.0665069\pi$
$42$		0			0
$43$	3.50661	+	8.46571i	0.534753	+	1.29101i	0.928344	+	0.371722i	$0.121233\pi$
$43$	3.50661	+	8.46571i	0.534753	+	1.29101i	−0.393591	+	0.919286i	$0.628767\pi$
$44$		0			0
$45$	−6.96490	−	5.91936i	−1.03827	−	0.882406i
$46$		0			0
$47$			8.98904i			1.31119i	0.755115	+	0.655593i	$0.227581\pi$
$47$			8.98904i			1.31119i	−0.755115	+	0.655593i	$0.772419\pi$
$48$		0			0
$49$		−	6.40839i		−	0.915485i
$50$		0			0
$51$	−8.47500	−	5.17932i	−1.18674	−	0.725250i
$52$		0			0
$53$	1.04873	+	2.53186i	0.144054	+	0.347777i	0.979395	−	0.201955i	$-0.0647296\pi$
$53$	1.04873	+	2.53186i	0.144054	+	0.347777i	−0.835341	+	0.549733i	$0.814730\pi$
$54$		0			0
$55$	−9.25030	+	9.25030i	−1.24731	+	1.24731i
$56$		0			0
$57$	0.0875545	+	0.120201i	0.0115969	+	0.0159210i
$58$		0			0
$59$	0.498592	+	1.20371i	0.0649111	+	0.156709i	0.953006	−	0.302950i	$-0.0979715\pi$
$59$	0.498592	+	1.20371i	0.0649111	+	0.156709i	−0.888095	+	0.459659i	$0.847972\pi$
$60$		0			0
$61$	−3.69353	−	1.52991i	−0.472908	−	0.195885i	0.133484	−	0.991051i	$-0.457384\pi$
$61$	−3.69353	−	1.52991i	−0.472908	−	0.195885i	−0.606392	+	0.795166i	$0.707384\pi$
$62$		0			0
$63$	−0.707713	+	2.19627i	−0.0891634	+	0.276704i
$64$		0			0
$65$			9.06875i			1.12484i
$66$		0			0
$67$	3.35550	−	8.10090i	0.409940	−	0.989682i	−0.575213	−	0.818004i	$-0.695081\pi$
$67$	3.35550	−	8.10090i	0.409940	−	0.989682i	0.985153	−	0.171679i	$-0.0549191\pi$
$68$		0			0
$69$	−0.841717	−	3.48732i	−0.101331	−	0.419824i
$70$		0			0
$71$	4.08070	−	4.08070i	0.484290	−	0.484290i	−0.422209	−	0.906499i	$-0.638745\pi$
$71$	4.08070	−	4.08070i	0.484290	−	0.484290i	0.906499	+	0.422209i	$0.138745\pi$
$72$		0			0
$73$	1.59075	+	1.59075i	0.186183	+	0.186183i	0.794044	−	0.607861i	$-0.207972\pi$
$73$	1.59075	+	1.59075i	0.186183	+	0.186183i	−0.607861	+	0.794044i	$0.707972\pi$
$74$		0			0
$75$	−7.21160	+	1.74063i	−0.832724	+	0.200990i
$76$		0			0
$77$	3.05109	+	1.26380i	0.347704	+	0.144024i
$78$		0			0
$79$	−0.637492			−0.0717235			−0.0358618	−	0.999357i	$-0.511418\pi$
$79$	−0.637492			−0.0717235			−0.0358618	+	0.999357i	$0.511418\pi$
$80$		0			0
$81$	−5.25459	+	7.30679i	−0.583844	+	0.811866i
$82$		0			0
$83$	1.94530	−	4.69638i	0.213525	−	0.515495i	−0.780435	−	0.625237i	$-0.785002\pi$
$83$	1.94530	−	4.69638i	0.213525	−	0.515495i	0.993960	+	0.109742i	$0.0350025\pi$
$84$		0			0
$85$	−16.1419	+	6.68618i	−1.75083	+	0.725218i
$86$		0			0
$87$	−1.90393	+	1.38682i	−0.204122	+	0.148683i
$88$		0			0
$89$	0.902588	+	0.902588i	0.0956742	+	0.0956742i	0.753324	−	0.657650i	$-0.228449\pi$
$89$	0.902588	+	0.902588i	0.0956742	+	0.0956742i	−0.657650	+	0.753324i	$0.728449\pi$
$90$		0			0
$91$	2.11510	−	0.876104i	0.221723	−	0.0918406i
$92$		0			0
$93$	−5.09469	+	8.33651i	−0.528295	+	0.864456i
$94$		0			0
$95$	0.261590			0.0268386
$96$		0			0
$97$	−13.3054			−1.35095			−0.675477	−	0.737381i	$-0.736062\pi$
$97$	−13.3054			−1.35095			−0.675477	+	0.737381i	$0.736062\pi$
$98$		0			0
$99$	9.81497	+	8.34158i	0.986441	+	0.838360i
$100$		0			0
$101$	5.49437	−	2.27584i	0.546710	−	0.226455i	−0.0921939	−	0.995741i	$-0.529388\pi$
$101$	5.49437	−	2.27584i	0.546710	−	0.226455i	0.638904	+	0.769286i	$0.279388\pi$
$102$		0			0
$103$	−7.86860	−	7.86860i	−0.775316	−	0.775316i	0.203714	−	0.979030i	$-0.434699\pi$
$103$	−7.86860	−	7.86860i	−0.775316	−	0.775316i	−0.979030	+	0.203714i	$0.934699\pi$
$104$		0			0
$105$	2.38985	+	3.28095i	0.233226	+	0.320188i
$106$		0			0
$107$	0.901495	−	0.373412i	0.0871508	−	0.0360991i	−0.338682	−	0.940901i	$-0.609981\pi$
$107$	0.901495	−	0.373412i	0.0871508	−	0.0360991i	0.425833	+	0.904802i	$0.359981\pi$
$108$		0			0
$109$	0.457650	−	1.10486i	0.0438349	−	0.105827i	−0.900446	−	0.434969i	$-0.856759\pi$
$109$	0.457650	−	1.10486i	0.0438349	−	0.105827i	0.944280	+	0.329142i	$0.106759\pi$
$110$		0			0
$111$	2.94829	−	18.7624i	0.279840	−	1.78085i
$112$		0			0
$113$	−8.48446			−0.798151			−0.399076	−	0.916918i	$-0.630669\pi$
$113$	−8.48446			−0.798151			−0.399076	+	0.916918i	$0.630669\pi$
$114$		0			0
$115$	−5.83029	−	2.41499i	−0.543678	−	0.225199i
$116$		0			0
$117$	8.90010	−	0.722234i	0.822814	−	0.0667706i
$118$		0			0
$119$	3.11883	+	3.11883i	0.285903	+	0.285903i
$120$		0			0
$121$	5.25738	−	5.25738i	0.477944	−	0.477944i
$122$		0			0
$123$	−11.7525	+	2.83665i	−1.05969	+	0.255772i
$124$		0			0
$125$	0.835790	−	2.01777i	0.0747553	−	0.180475i
$126$		0			0
$127$		−	7.01144i		−	0.622165i	−0.950383	−	0.311083i	$-0.899308\pi$
$127$		−	7.01144i		−	0.622165i	0.950383	−	0.311083i	$-0.100692\pi$
$128$		0			0
$129$	2.46373	−	15.6788i	0.216920	−	1.38044i
$130$		0			0
$131$	−4.09398	−	1.69578i	−0.357693	−	0.148161i	0.196598	−	0.980484i	$-0.437011\pi$
$131$	−4.09398	−	1.69578i	−0.357693	−	0.148161i	−0.554291	+	0.832323i	$0.687011\pi$
$132$		0			0
$133$	−0.0252714	−	0.0610107i	−0.00219131	−	0.00529029i
$134$		0			0
$135$	4.94718	+	15.0390i	0.425786	+	1.29435i
$136$		0			0
$137$	−6.04464	+	6.04464i	−0.516428	+	0.516428i	−0.916489	−	0.400061i	$-0.868989\pi$
$137$	−6.04464	+	6.04464i	−0.516428	+	0.516428i	0.400061	+	0.916489i	$0.368989\pi$
$138$		0			0
$139$	3.82265	+	9.22869i	0.324233	+	0.782767i	0.998999	+	0.0447354i	$0.0142445\pi$
$139$	3.82265	+	9.22869i	0.324233	+	0.782767i	−0.674766	+	0.738032i	$0.735756\pi$
$140$		0			0
$141$	8.11888	−	13.2850i	0.683733	−	1.11880i
$142$		0			0
$143$		−	12.7797i		−	1.06869i
$144$		0			0
$145$			4.14347i			0.344097i
$146$		0			0
$147$	−5.78805	+	9.47106i	−0.477390	+	0.781160i
$148$		0			0
$149$	−4.03660	−	9.74522i	−0.330691	−	0.798359i	−0.998538	−	0.0540601i	$-0.982784\pi$
$149$	−4.03660	−	9.74522i	−0.330691	−	0.798359i	0.667846	−	0.744299i	$-0.267216\pi$
$150$		0			0
$151$	7.98901	−	7.98901i	0.650136	−	0.650136i	−0.302889	−	0.953026i	$-0.597951\pi$
$151$	7.98901	−	7.98901i	0.650136	−	0.650136i	0.953026	+	0.302889i	$0.0979512\pi$
$152$		0			0
$153$	7.84738	+	15.3092i	0.634423	+	1.23768i
$154$		0			0
$155$	6.57692	+	15.8781i	0.528271	+	1.27536i
$156$		0			0
$157$	2.65449	+	1.09953i	0.211852	+	0.0877518i	0.486086	−	0.873911i	$-0.338424\pi$
$157$	2.65449	+	1.09953i	0.211852	+	0.0877518i	−0.274234	+	0.961663i	$0.588424\pi$
$158$		0			0
$159$	0.736834	−	4.68908i	0.0584347	−	0.371868i
$160$		0			0
$161$			1.59310i			0.125554i
$162$		0			0
$163$	−3.51824	+	8.49377i	−0.275570	+	0.665284i	−0.999703	−	0.0243763i	$-0.992240\pi$
$163$	−3.51824	+	8.49377i	−0.275570	+	0.665284i	0.724133	+	0.689660i	$0.242240\pi$
$164$		0			0
$165$	22.0260	−	5.31631i	1.71472	−	0.413874i
$166$		0			0
$167$	6.70414	−	6.70414i	0.518782	−	0.518782i	−0.398421	−	0.917203i	$-0.630442\pi$
$167$	6.70414	−	6.70414i	0.518782	−	0.518782i	0.917203	+	0.398421i	$0.130442\pi$
$168$		0			0
$169$	2.92794	+	2.92794i	0.225226	+	0.225226i
$170$		0			0
$171$	−0.0208330	−	0.256726i	−0.00159314	−	0.0196323i
$172$		0			0
$173$	18.7129	+	7.75114i	1.42272	+	0.589308i	0.955541	−	0.294857i	$-0.0952720\pi$
$173$	18.7129	+	7.75114i	1.42272	+	0.589308i	0.467174	+	0.884165i	$0.345272\pi$
$174$		0			0
$175$	3.29446			0.249037
$176$		0			0
$177$	0.350309	−	2.22930i	0.0263308	−	0.167565i
$178$		0			0
$179$	−7.00110	+	16.9021i	−0.523286	+	1.26333i	0.412564	+	0.910928i	$0.364633\pi$
$179$	−7.00110	+	16.9021i	−0.523286	+	1.26333i	−0.935851	+	0.352397i	$0.885367\pi$
$180$		0			0
$181$	14.4907	−	6.00226i	1.07709	−	0.446144i	0.227601	−	0.973754i	$-0.426912\pi$
$181$	14.4907	−	6.00226i	1.07709	−	0.446144i	0.849487	+	0.527610i	$0.176912\pi$
$182$		0			0
$183$	4.07691	+	5.59706i	0.301374	+	0.413747i
$184$		0			0
$185$	−23.6243	−	23.6243i	−1.73689	−	1.73689i
$186$		0			0
$187$	22.7472	−	9.42220i	1.66344	−	0.689019i
$188$		0			0
$189$	3.02961	−	2.60670i	0.220372	−	0.189610i
$190$		0			0
$191$	−15.7313			−1.13828			−0.569139	−	0.822241i	$-0.692723\pi$
$191$	−15.7313			−1.13828			−0.569139	+	0.822241i	$0.692723\pi$
$192$		0			0
$193$	12.2248			0.879962			0.439981	−	0.898007i	$-0.354985\pi$
$193$	12.2248			0.879962			0.439981	+	0.898007i	$0.354985\pi$
$194$		0			0
$195$	8.19087	−	13.4028i	0.586560	−	0.959797i
$196$		0			0
$197$	−21.5949	+	8.94488i	−1.53857	+	0.637297i	−0.981205	−	0.192971i	$-0.938188\pi$
$197$	−21.5949	+	8.94488i	−1.53857	+	0.637297i	−0.557365	+	0.830267i	$0.688188\pi$
$198$		0			0
$199$	1.57778	+	1.57778i	0.111846	+	0.111846i	0.760815	−	0.648969i	$-0.224799\pi$
$199$	1.57778	+	1.57778i	0.111846	+	0.111846i	−0.648969	+	0.760815i	$0.724799\pi$
$200$		0			0
$201$	−12.2759	+	8.94176i	−0.865873	+	0.630703i
$202$		0			0
$203$	0.966382	−	0.400288i	0.0678267	−	0.0280947i
$204$		0			0
$205$	−8.13869	+	19.6485i	−0.568431	+	1.37231i
$206$		0			0
$207$	−1.90575	+	5.91420i	−0.132459	+	0.411065i
$208$		0			0
$209$	−0.368634			−0.0254990
$210$		0			0
$211$	25.3543	+	10.5021i	1.74546	+	0.722994i	0.998296	+	0.0583569i	$0.0185861\pi$
$211$	25.3543	+	10.5021i	1.74546	+	0.722994i	0.747166	+	0.664637i	$0.231414\pi$
$212$		0			0
$213$	−9.71660	+	2.34525i	−0.665771	+	0.160694i
$214$		0			0
$215$	−19.7415	−	19.7415i	−1.34636	−	1.34636i
$216$		0			0
$217$	3.06787	−	3.06787i	0.208261	−	0.208261i
$218$		0			0
$219$	−0.914229	−	3.78774i	−0.0617779	−	0.255952i
$220$		0			0
$221$	6.53174	−	15.7690i	0.439372	−	1.06074i
$222$		0			0
$223$			23.6266i			1.58216i	0.611716	+	0.791078i	$0.290480\pi$
$223$			23.6266i			1.58216i	−0.611716	+	0.791078i	$0.709520\pi$
$224$		0			0
$225$	12.2303	+	3.94100i	0.815351	+	0.262733i
$226$		0			0
$227$	−16.7455	−	6.93620i	−1.11144	−	0.460372i	−0.250004	−	0.968245i	$-0.580432\pi$
$227$	−16.7455	−	6.93620i	−1.11144	−	0.460372i	−0.861432	+	0.507873i	$0.830432\pi$
$228$		0			0
$229$	−5.05650	−	12.2075i	−0.334143	−	0.806693i	−0.998254	−	0.0590592i	$-0.981190\pi$
$229$	−5.05650	−	12.2075i	−0.334143	−	0.806693i	0.664111	−	0.747634i	$-0.268810\pi$
$230$		0			0
$231$	−3.36779	−	4.62353i	−0.221584	−	0.304206i
$232$		0			0
$233$	7.93372	−	7.93372i	0.519756	−	0.519756i	−0.397742	−	0.917497i	$-0.630206\pi$
$233$	7.93372	−	7.93372i	0.519756	−	0.519756i	0.917497	+	0.397742i	$0.130206\pi$
$234$		0			0
$235$	−10.4810	−	25.3033i	−0.683703	−	1.65060i
$236$		0			0
$237$	0.942160	+	0.575782i	0.0611999	+	0.0374010i
$238$		0			0
$239$			16.7260i			1.08191i	0.841051	+	0.540956i	$0.181937\pi$
$239$			16.7260i			1.08191i	−0.841051	+	0.540956i	$0.818063\pi$
$240$		0			0
$241$		−	9.00218i		−	0.579881i	−0.957045	−	0.289941i	$-0.906364\pi$
$241$		−	9.00218i		−	0.579881i	0.957045	−	0.289941i	$-0.0936356\pi$
$242$		0			0
$243$	14.3653	−	6.05289i	0.921536	−	0.388293i
$244$		0			0
$245$	7.47200	+	18.0390i	0.477369	+	1.15247i
$246$		0			0
$247$	−0.180700	+	0.180700i	−0.0114976	+	0.0114976i
$248$		0			0
$249$	−7.11675	+	5.18386i	−0.451006	+	0.328514i
$250$		0			0
$251$	0.601450	+	1.45203i	0.0379632	+	0.0916513i	0.941724	−	0.336387i	$-0.109205\pi$
$251$	0.601450	+	1.45203i	0.0379632	+	0.0916513i	−0.903761	+	0.428038i	$0.859205\pi$
$252$		0			0
$253$	8.21607	+	3.40321i	0.516540	+	0.213958i
$254$		0			0
$255$	29.8953	+	4.69769i	1.87211	+	0.294181i
$256$		0			0
$257$			8.28941i			0.517079i	0.966001	+	0.258539i	$0.0832412\pi$
$257$			8.28941i			0.517079i	−0.966001	+	0.258539i	$0.916759\pi$
$258$		0			0
$259$	−3.22761	+	7.79215i	−0.200554	+	0.484181i
$260$		0			0
$261$	4.06642	−	0.329986i	0.251705	−	0.0204256i
$262$		0			0
$263$	8.76126	−	8.76126i	0.540243	−	0.540243i	−0.383357	−	0.923600i	$-0.625232\pi$
$263$	8.76126	−	8.76126i	0.540243	−	0.540243i	0.923600	+	0.383357i	$0.125232\pi$
$264$		0			0
$265$	−5.90415	−	5.90415i	−0.362689	−	0.362689i
$266$		0			0
$267$	−0.518733	−	2.14916i	−0.0317460	−	0.131527i
$268$		0			0
$269$	−15.1023	−	6.25558i	−0.920804	−	0.381409i	−0.128621	−	0.991694i	$-0.541055\pi$
$269$	−15.1023	−	6.25558i	−0.920804	−	0.381409i	−0.792182	+	0.610284i	$0.791055\pi$
$270$		0			0
$271$	−17.5035			−1.06326			−0.531631	−	0.846976i	$-0.678421\pi$
$271$	−17.5035			−1.06326			−0.531631	+	0.846976i	$0.678421\pi$
$272$		0			0
$273$	−3.91724	−	0.615548i	−0.237082	−	0.0372547i
$274$		0			0
$275$	7.03766	−	16.9904i	0.424387	−	1.02456i
$276$		0			0
$277$	21.3684	−	8.85109i	1.28390	−	0.531811i	0.366742	−	0.930323i	$-0.380473\pi$
$277$	21.3684	−	8.85109i	1.28390	−	0.531811i	0.917163	+	0.398512i	$0.130473\pi$
$278$		0			0
$279$	15.0590	−	7.71915i	0.901561	−	0.462133i
$280$		0			0
$281$	5.93438	+	5.93438i	0.354015	+	0.354015i	0.861601	−	0.507586i	$-0.169462\pi$
$281$	5.93438	+	5.93438i	0.354015	+	0.354015i	−0.507586	+	0.861601i	$0.669462\pi$
$282$		0			0
$283$	−23.7525	+	9.83861i	−1.41194	+	0.584845i	−0.952822	−	0.303530i	$-0.901835\pi$
$283$	−23.7525	+	9.83861i	−1.41194	+	0.584845i	−0.459119	+	0.888375i	$0.651835\pi$
$284$		0			0
$285$	−0.386608	−	0.236268i	−0.0229007	−	0.0139953i
$286$		0			0
$287$	5.36888			0.316915
$288$		0			0
$289$	15.8837			0.934334
$290$		0			0
$291$	19.6642	+	12.0174i	1.15274	+	0.704471i
$292$		0			0
$293$	−4.20032	+	1.73983i	−0.245386	+	0.101642i	−0.501987	−	0.864875i	$-0.667397\pi$
$293$	−4.20032	+	1.73983i	−0.245386	+	0.101642i	0.256601	+	0.966517i	$0.417397\pi$
$294$		0			0
$295$	−2.80698	−	2.80698i	−0.163429	−	0.163429i
$296$		0			0
$297$	−6.97159	−	21.1930i	−0.404533	−	1.22974i
$298$		0			0
$299$	5.69562	−	2.35920i	0.329386	−	0.136436i
$300$		0			0
$301$	−2.69715	+	6.51149i	−0.155461	+	0.375316i
$302$		0			0
$303$	−10.1758	−	1.59900i	−0.584582	−	0.0918602i
$304$		0			0
$305$	12.1808			0.697469
$306$		0			0
$307$	−12.3645	−	5.12154i	−0.705678	−	0.292302i	0.000836540	−	1.00000i	$-0.499734\pi$
$307$	−12.3645	−	5.12154i	−0.705678	−	0.292302i	−0.706515	+	0.707698i	$0.749734\pi$
$308$		0			0
$309$	4.52222	+	18.7360i	0.257260	+	1.06586i
$310$		0			0
$311$	−10.7303	−	10.7303i	−0.608462	−	0.608462i	0.334082	−	0.942544i	$-0.391574\pi$
$311$	−10.7303	−	10.7303i	−0.608462	−	0.608462i	−0.942544	+	0.334082i	$0.891574\pi$
$312$		0			0
$313$	−17.8971	+	17.8971i	−1.01160	+	1.01160i	−0.0116708	+	0.999932i	$0.503715\pi$
$313$	−17.8971	+	17.8971i	−1.01160	+	1.01160i	−0.999932	+	0.0116708i	$0.996285\pi$
$314$		0			0
$315$	−0.568650	−	7.00747i	−0.0320398	−	0.394826i
$316$		0			0
$317$	−2.59675	+	6.26910i	−0.145848	+	0.352108i	−0.979874	−	0.199617i	$-0.936030\pi$
$317$	−2.59675	+	6.26910i	−0.145848	+	0.352108i	0.834026	+	0.551725i	$0.186030\pi$
$318$		0			0
$319$		−	5.83900i		−	0.326921i
$320$		0			0
$321$	−1.66960	−	0.262358i	−0.0931879	−	0.0146434i
$322$		0			0
$323$	−0.454861	−	0.188410i	−0.0253091	−	0.0104834i
$324$		0			0
$325$	−4.87871	−	11.7782i	−0.270622	−	0.653340i
$326$		0			0
$327$	−1.67428	+	1.21955i	−0.0925878	+	0.0674411i
$328$		0			0
$329$	−4.88895	+	4.88895i	−0.269536	+	0.269536i
$330$		0			0
$331$	−4.00950	−	9.67979i	−0.220382	−	0.532050i	0.774560	−	0.632501i	$-0.217971\pi$
$331$	−4.00950	−	9.67979i	−0.220382	−	0.532050i	−0.994942	+	0.100451i	$0.967971\pi$
$332$		0			0
$333$	−21.3035	+	25.0664i	−1.16742	+	1.37363i
$334$		0			0
$335$			26.7157i			1.45963i
$336$		0			0
$337$			4.80498i			0.261744i	0.991399	+	0.130872i	$0.0417777\pi$
$337$			4.80498i			0.261744i	−0.991399	+	0.130872i	$0.958222\pi$
$338$		0			0
$339$	12.5393	+	7.66315i	0.681042	+	0.416205i
$340$		0			0
$341$	−9.26823	−	22.3755i	−0.501903	−	1.21170i
$342$		0			0
$343$	7.29254	−	7.29254i	0.393760	−	0.393760i
$344$		0			0
$345$	6.43547	+	8.83505i	0.346474	+	0.475663i
$346$		0			0
$347$	−5.87587	−	14.1856i	−0.315433	−	0.761523i	−0.999485	−	0.0320898i	$-0.989784\pi$
$347$	−5.87587	−	14.1856i	−0.315433	−	0.761523i	0.684052	−	0.729434i	$-0.260216\pi$
$348$		0			0
$349$	−6.41003	−	2.65512i	−0.343121	−	0.142125i	0.204467	−	0.978873i	$-0.434454\pi$
$349$	−6.41003	−	2.65512i	−0.343121	−	0.142125i	−0.547588	+	0.836748i	$0.684454\pi$
$350$		0			0
$351$	−13.8059	−	6.97115i	−0.736905	−	0.372092i
$352$		0			0
$353$			10.7742i			0.573453i	0.958012	+	0.286726i	$0.0925671\pi$
$353$			10.7742i			0.573453i	−0.958012	+	0.286726i	$0.907433\pi$
$354$		0			0
$355$	−6.72880	+	16.2448i	−0.357128	+	0.862182i
$356$		0			0
$357$	−1.79245	−	7.42630i	−0.0948665	−	0.393041i
$358$		0			0
$359$	−7.99933	+	7.99933i	−0.422189	+	0.422189i	−0.885957	−	0.463768i	$-0.846497\pi$
$359$	−7.99933	+	7.99933i	−0.422189	+	0.422189i	0.463768	+	0.885957i	$0.346497\pi$
$360$		0			0
$361$	−13.4298	−	13.4298i	−0.706832	−	0.706832i
$362$		0			0
$363$	−12.5184	+	3.02151i	−0.657046	+	0.158588i
$364$		0			0
$365$	−6.33256	−	2.62303i	−0.331461	−	0.137296i
$366$		0			0
$367$	4.78544			0.249798			0.124899	−	0.992169i	$-0.460139\pi$
$367$	4.78544			0.249798			0.124899	+	0.992169i	$0.460139\pi$
$368$		0			0
$369$	19.9313	+	6.42253i	1.03758	+	0.334343i
$370$		0			0
$371$	−0.806641	+	1.94740i	−0.0418787	+	0.101104i
$372$		0			0
$373$	−24.5505	+	10.1691i	−1.27118	+	0.526538i	−0.913322	−	0.407239i	$-0.866492\pi$
$373$	−24.5505	+	10.1691i	−1.27118	+	0.526538i	−0.357855	+	0.933777i	$0.616492\pi$
$374$		0			0
$375$	−3.05768	+	2.22722i	−0.157898	+	0.115013i
$376$		0			0
$377$	−2.86220	−	2.86220i	−0.147411	−	0.147411i
$378$		0			0
$379$	−26.9921	+	11.1805i	−1.38649	+	0.574304i	−0.946209	−	0.323556i	$-0.895122\pi$
$379$	−26.9921	+	11.1805i	−1.38649	+	0.574304i	−0.440282	+	0.897859i	$0.645122\pi$
$380$		0			0
$381$	−6.33272	+	10.3623i	−0.324435	+	0.530878i
$382$		0			0
$383$	−16.7272			−0.854721			−0.427360	−	0.904081i	$-0.640556\pi$
$383$	−16.7272			−0.854721			−0.427360	+	0.904081i	$0.640556\pi$
$384$		0			0
$385$	−10.0621			−0.512811
$386$		0			0
$387$	−17.8022	+	20.9466i	−0.904937	+	1.06478i
$388$		0			0
$389$	−30.3193	+	12.5587i	−1.53725	+	0.636749i	−0.980955	−	0.194236i	$-0.937777\pi$
$389$	−30.3193	+	12.5587i	−1.53725	+	0.636749i	−0.556294	+	0.830985i	$0.687777\pi$
$390$		0			0
$391$	8.39850	+	8.39850i	0.424730	+	0.424730i
$392$		0			0
$393$	4.51893	+	6.20390i	0.227950	+	0.312945i
$394$		0			0
$395$	1.79448	−	0.743298i	0.0902901	−	0.0373994i
$396$		0			0
$397$	8.13703	−	19.6445i	0.408386	−	0.985931i	−0.577177	−	0.816619i	$-0.695846\pi$
$397$	8.13703	−	19.6445i	0.408386	−	0.985931i	0.985563	−	0.169312i	$-0.0541545\pi$
$398$		0			0
$399$	−0.0177556	+	0.112994i	−0.000888894	+	0.00565676i
$400$		0			0
$401$	−0.509396			−0.0254380			−0.0127190	−	0.999919i	$-0.504049\pi$
$401$	−0.509396			−0.0254380			−0.0127190	+	0.999919i	$0.504049\pi$
$402$		0			0
$403$	−15.5113	−	6.42500i	−0.772674	−	0.320052i
$404$		0			0
$405$	6.27166	−	26.6946i	0.311641	−	1.32647i
$406$		0			0
$407$	33.2914	+	33.2914i	1.65019	+	1.65019i
$408$		0			0
$409$	−6.54063	+	6.54063i	−0.323413	+	0.323413i	−0.850075	−	0.526662i	$-0.823443\pi$
$409$	−6.54063	+	6.54063i	−0.323413	+	0.323413i	0.526662	+	0.850075i	$0.323443\pi$
$410$		0			0
$411$	14.3930	−	3.47396i	0.709952	−	0.171358i
$412$		0			0
$413$	−0.383497	+	0.925844i	−0.0188707	+	0.0455578i
$414$		0			0
$415$			15.4880i			0.760278i
$416$		0			0
$417$	2.68578	−	17.0918i	0.131523	−	0.836990i
$418$		0			0
$419$	−20.7965	−	8.61418i	−1.01597	−	0.420830i	−0.188343	−	0.982103i	$-0.560312\pi$
$419$	−20.7965	−	8.61418i	−1.01597	−	0.420830i	−0.827631	+	0.561273i	$0.810312\pi$
$420$		0			0
$421$	−8.30131	−	20.0411i	−0.404581	−	0.976745i	−0.986539	−	0.163526i	$-0.947713\pi$
$421$	−8.30131	−	20.0411i	−0.404581	−	0.976745i	0.581958	−	0.813219i	$-0.302287\pi$
$422$		0			0
$423$	−23.9980	+	12.3012i	−1.16682	+	0.598105i
$424$		0			0
$425$	17.3677	−	17.3677i	0.842456	−	0.842456i
$426$		0			0
$427$	−1.17675	−	2.84092i	−0.0569468	−	0.137482i
$428$		0			0
$429$	−11.5426	+	18.8873i	−0.557282	+	0.911889i
$430$		0			0
$431$		−	1.97237i		−	0.0950057i	−0.998871	−	0.0475028i	$-0.984874\pi$
$431$		−	1.97237i		−	0.0950057i	0.998871	−	0.0475028i	$-0.0151263\pi$
$432$		0			0
$433$			29.4876i			1.41709i	0.705668	+	0.708543i	$0.250647\pi$
$433$			29.4876i			1.41709i	−0.705668	+	0.708543i	$0.749353\pi$
$434$		0			0
$435$	3.74238	−	6.12370i	0.179433	−	0.293609i
$436$		0			0
$437$	−0.0680518	−	0.164292i	−0.00325536	−	0.00785913i
$438$		0			0
$439$	17.1823	−	17.1823i	0.820067	−	0.820067i	−0.166050	−	0.986117i	$-0.553101\pi$
$439$	17.1823	−	17.1823i	0.820067	−	0.820067i	0.986117	+	0.166050i	$0.0531014\pi$
$440$		0			0
$441$	17.1085	−	8.76968i	0.814690	−	0.417604i
$442$		0			0
$443$	4.22858	+	10.2087i	0.200906	+	0.485029i	0.991935	−	0.126749i	$-0.0404543\pi$
$443$	4.22858	+	10.2087i	0.200906	+	0.485029i	−0.791029	+	0.611779i	$0.790454\pi$
$444$		0			0
$445$	−3.59309	−	1.48831i	−0.170329	−	0.0705526i
$446$		0			0
$447$	−2.83610	+	18.0485i	−0.134143	+	0.853663i
$448$		0			0
$449$		−	27.4116i		−	1.29363i	−0.762645	−	0.646817i	$-0.776100\pi$
$449$		−	27.4116i		−	1.29363i	0.762645	−	0.646817i	$-0.223900\pi$
$450$		0			0
$451$	11.4691	−	27.6888i	0.540057	−	1.30381i
$452$		0			0
$453$	−19.0227	+	4.59143i	−0.893766	+	0.215724i
$454$		0			0
$455$	−4.93230	+	4.93230i	−0.231230	+	0.231230i
$456$		0			0
$457$	5.05963	+	5.05963i	0.236680	+	0.236680i	0.815474	−	0.578794i	$-0.196477\pi$
$457$	5.05963	+	5.05963i	0.236680	+	0.236680i	−0.578794	+	0.815474i	$0.696477\pi$
$458$		0			0
$459$	2.22947	−	29.7134i	0.104063	−	1.38690i
$460$		0			0
$461$	28.5768	+	11.8369i	1.33095	+	0.551298i	0.930927	−	0.365206i	$-0.119001\pi$
$461$	28.5768	+	11.8369i	1.33095	+	0.551298i	0.400025	+	0.916504i	$0.369001\pi$
$462$		0			0
$463$	−8.48410			−0.394290			−0.197145	−	0.980374i	$-0.563167\pi$
$463$	−8.48410			−0.394290			−0.197145	+	0.980374i	$0.563167\pi$
$464$		0			0
$465$	4.62093	−	29.4067i	0.214290	−	1.36371i
$466$		0			0
$467$	6.00576	−	14.4992i	0.277913	−	0.670942i	−0.721864	−	0.692035i	$-0.756714\pi$
$467$	6.00576	−	14.4992i	0.277913	−	0.670942i	0.999778	+	0.0210925i	$0.00671443\pi$
$468$		0			0
$469$	6.23089	−	2.58092i	0.287716	−	0.119176i
$470$		0			0
$471$	−2.93003	−	4.02254i	−0.135008	−	0.185349i
$472$		0			0
$473$	27.8199	+	27.8199i	1.27916	+	1.27916i
$474$		0			0
$475$	−0.339747	+	0.140728i	−0.0155886	+	0.00645703i
$476$		0			0
$477$	−5.32414	+	6.26455i	−0.243776	+	0.286834i
$478$		0			0
$479$	28.2696			1.29167			0.645835	−	0.763477i	$-0.276509\pi$
$479$	28.2696			1.29167			0.645835	+	0.763477i	$0.276509\pi$
$480$		0			0
$481$	32.6380			1.48816
$482$		0			0
$483$	1.43889	−	2.35447i	0.0654716	−	0.107132i
$484$		0			0
$485$	37.4533	−	15.5137i	1.70067	−	0.704440i
$486$		0			0
$487$	22.4971	+	22.4971i	1.01944	+	1.01944i	0.999807	+	0.0196335i	$0.00624994\pi$
$487$	22.4971	+	22.4971i	1.01944	+	1.01944i	0.0196335	+	0.999807i	$0.493750\pi$
$488$		0			0
$489$	12.8712	−	9.37542i	0.582056	−	0.423971i
$490$		0			0
$491$	0.871501	−	0.360988i	0.0393303	−	0.0162911i	−0.362932	−	0.931816i	$-0.618224\pi$
$491$	0.871501	−	0.360988i	0.0393303	−	0.0162911i	0.402262	+	0.915525i	$0.368224\pi$
$492$		0			0
$493$	2.98432	−	7.20480i	0.134407	−	0.324488i
$494$		0			0
$495$	−37.3542	−	12.0368i	−1.67895	−	0.541013i
$496$		0			0
$497$	4.43881			0.199108
$498$		0			0
$499$	29.0833	+	12.0467i	1.30195	+	0.539284i	0.922524	−	0.385939i	$-0.126122\pi$
$499$	29.0833	+	12.0467i	1.30195	+	0.539284i	0.379423	+	0.925223i	$0.376122\pi$
$500$		0			0
$501$	−15.9633	+	3.85299i	−0.713188	+	0.172139i
$502$		0			0
$503$	15.9266	+	15.9266i	0.710132	+	0.710132i	0.966563	−	0.256431i	$-0.0825465\pi$
$503$	15.9266	+	15.9266i	0.710132	+	0.710132i	−0.256431	+	0.966563i	$0.582546\pi$
$504$		0			0
$505$	−12.8126	+	12.8126i	−0.570152	+	0.570152i
$506$		0			0
$507$	−1.68274	−	6.97176i	−0.0747331	−	0.309627i
$508$		0			0
$509$	−0.374204	+	0.903408i	−0.0165863	+	0.0400428i	−0.931956	−	0.362572i	$-0.881899\pi$
$509$	−0.374204	+	0.903408i	−0.0165863	+	0.0400428i	0.915369	+	0.402615i	$0.131899\pi$
$510$		0			0
$511$			1.73035i			0.0765460i
$512$		0			0
$513$	−0.201085	+	0.398235i	−0.00887810	+	0.0175825i
$514$		0			0
$515$	31.3239	+	12.9748i	1.38030	+	0.571738i
$516$		0			0
$517$	14.7698	+	35.6575i	0.649576	+	1.56821i
$518$		0			0
$519$	−20.6553	−	28.3570i	−0.906666	−	1.24473i
$520$		0			0
$521$	−31.7757	+	31.7757i	−1.39212	+	1.39212i	−0.571558	+	0.820562i	$0.693661\pi$
$521$	−31.7757	+	31.7757i	−1.39212	+	1.39212i	−0.820562	+	0.571558i	$0.806339\pi$
$522$		0			0
$523$	2.56429	+	6.19074i	0.112128	+	0.270702i	0.969975	−	0.243203i	$-0.0781982\pi$
$523$	2.56429	+	6.19074i	0.112128	+	0.270702i	−0.857847	+	0.513905i	$0.828198\pi$
$524$		0			0
$525$	−4.86893	−	2.97554i	−0.212497	−	0.129863i
$526$		0			0
$527$		−	32.3463i		−	1.40903i
$528$		0			0
$529$		−	18.7100i		−	0.813480i
$530$		0			0
$531$	−2.53123	+	2.97832i	−0.109846	+	0.129248i
$532$		0			0
$533$	−7.95069	−	19.1947i	−0.344382	−	0.831413i
$534$		0			0
$535$	−2.10224	+	2.10224i	−0.0908876	+	0.0908876i
$536$		0			0
$537$	25.6130	−	18.6566i	1.10528	−	0.805090i
$538$		0			0
$539$	−10.5296	−	25.4206i	−0.453541	−	1.09494i
$540$		0			0
$541$	25.9983	+	10.7689i	1.11776	+	0.462989i	0.863602	−	0.504174i	$-0.168203\pi$
$541$	25.9983	+	10.7689i	1.11776	+	0.462989i	0.254154	+	0.967164i	$0.418203\pi$
$542$		0			0
$543$	−26.8373	−	4.21717i	−1.15170	−	0.180976i
$544$		0			0
$545$			3.64369i			0.156079i
$546$		0			0
$547$	8.74735	−	21.1180i	0.374010	−	0.902939i	−0.619053	−	0.785349i	$-0.712483\pi$
$547$	8.74735	−	21.1180i	0.374010	−	0.902939i	0.993062	−	0.117590i	$-0.0375167\pi$
$548$		0			0
$549$	−0.970075	−	11.9542i	−0.0414018	−	0.510195i
$550$		0			0
$551$	−0.0825609	+	0.0825609i	−0.00351721	+	0.00351721i
$552$		0			0
$553$	−0.346719	−	0.346719i	−0.0147440	−	0.0147440i
$554$		0			0
$555$	13.5773	+	56.2520i	0.576323	+	2.38777i
$556$		0			0
$557$	−21.4222	−	8.87338i	−0.907689	−	0.375977i	−0.120517	−	0.992711i	$-0.538455\pi$
$557$	−21.4222	−	8.87338i	−0.907689	−	0.375977i	−0.787171	+	0.616734i	$0.788455\pi$
$558$		0			0
$559$	27.2739			1.15356
$560$		0			0
$561$	−42.1285	−	6.62001i	−1.77867	−	0.279497i
$562$		0			0
$563$	3.72042	−	8.98190i	0.156797	−	0.378542i	−0.825886	−	0.563838i	$-0.809324\pi$
$563$	3.72042	−	8.98190i	0.156797	−	0.378542i	0.982683	+	0.185296i	$0.0593243\pi$
$564$		0			0
$565$	23.8830	−	9.89265i	1.00476	−	0.416187i
$566$		0			0
$567$	−6.83187	+	1.11615i	−0.286912	+	0.0468739i
$568$		0			0
$569$	−8.43864	−	8.43864i	−0.353766	−	0.353766i	0.507743	−	0.861509i	$-0.330480\pi$
$569$	−8.43864	−	8.43864i	−0.353766	−	0.353766i	−0.861509	+	0.507743i	$0.830480\pi$
$570$		0			0
$571$	17.9095	−	7.41834i	0.749488	−	0.310448i	0.0249551	−	0.999689i	$-0.492056\pi$
$571$	17.9095	−	7.41834i	0.749488	−	0.310448i	0.724532	+	0.689241i	$0.242056\pi$
$572$		0			0
$573$	23.2495	+	14.2085i	0.971264	+	0.593568i
$574$		0			0
$575$	8.87142			0.369964
$576$		0			0
$577$	−31.3503			−1.30513			−0.652565	−	0.757733i	$-0.726307\pi$
$577$	−31.3503			−1.30513			−0.652565	+	0.757733i	$0.726307\pi$
$578$		0			0
$579$	−18.0672	−	11.0414i	−0.750849	−	0.458866i
$580$		0			0
$581$	3.61227	−	1.49625i	0.149862	−	0.0620750i
$582$		0			0
$583$	8.32014	+	8.32014i	0.344585	+	0.344585i
$584$		0			0
$585$	−24.2108	+	12.4103i	−1.00099	+	0.513102i
$586$		0			0
$587$	−14.6871	+	6.08361i	−0.606202	+	0.251097i	−0.664604	−	0.747196i	$-0.731400\pi$
$587$	−14.6871	+	6.08361i	−0.606202	+	0.251097i	0.0584014	+	0.998293i	$0.481400\pi$
$588$		0			0
$589$	−0.185331	+	0.447428i	−0.00763642	+	0.0184360i
$590$		0			0
$591$	39.9944	+	6.28465i	1.64515	+	0.258516i
$592$		0			0
$593$	−6.53460			−0.268344			−0.134172	−	0.990958i	$-0.542837\pi$
$593$	−6.53460			−0.268344			−0.134172	+	0.990958i	$0.542837\pi$
$594$		0			0
$595$	−12.4157	−	5.14275i	−0.508994	−	0.210832i
$596$		0			0
$597$	−0.906779	−	3.75688i	−0.0371120	−	0.153759i
$598$		0			0
$599$	−20.5360	−	20.5360i	−0.839078	−	0.839078i	0.149659	−	0.988738i	$-0.452182\pi$
$599$	−20.5360	−	20.5360i	−0.839078	−	0.839078i	−0.988738	+	0.149659i	$0.952182\pi$
$600$		0			0
$601$	−1.20249	+	1.20249i	−0.0490506	+	0.0490506i	−0.731207	−	0.682156i	$-0.761042\pi$
$601$	−1.20249	+	1.20249i	−0.0490506	+	0.0490506i	0.682156	+	0.731207i	$0.261042\pi$
$602$		0			0
$603$	26.2189	−	2.12763i	1.06771	−	0.0866440i
$604$		0			0
$605$	−8.66907	+	20.9290i	−0.352448	+	0.850884i
$606$		0			0
$607$		−	42.2470i		−	1.71475i	−0.514692	−	0.857375i	$-0.672094\pi$
$607$		−	42.2470i		−	1.71475i	0.514692	−	0.857375i	$-0.327906\pi$
$608$		0			0
$609$	−1.78977	−	0.281241i	−0.0725251	−	0.0113965i
$610$		0			0
$611$	24.7188	+	10.2389i	1.00002	+	0.414220i
$612$		0			0
$613$	−3.20549	−	7.73873i	−0.129468	−	0.312564i	0.845831	−	0.533451i	$-0.179105\pi$
$613$	−3.20549	−	7.73873i	−0.129468	−	0.312564i	−0.975300	+	0.220886i	$0.929105\pi$
$614$		0			0
$615$	29.7748	−	21.6880i	1.20064	−	0.874545i
$616$		0			0
$617$	30.2757	−	30.2757i	1.21885	−	1.21885i	0.250821	−	0.968034i	$-0.419299\pi$
$617$	30.2757	−	30.2757i	1.21885	−	1.21885i	0.968034	−	0.250821i	$-0.0807005\pi$
$618$		0			0
$619$	−7.03045	−	16.9730i	−0.282578	−	0.682203i	0.717317	−	0.696747i	$-0.245370\pi$
$619$	−7.03045	−	16.9730i	−0.282578	−	0.682203i	−0.999894	+	0.0145446i	$0.995370\pi$
$620$		0			0
$621$	8.15823	−	7.01941i	0.327379	−	0.281679i
$622$		0			0
$623$			0.981797i			0.0393349i
$624$		0			0
$625$			28.0703i			1.12281i
$626$		0			0
$627$	0.544810	+	0.332949i	0.0217576	+	0.0132967i
$628$		0			0
$629$	24.0633	+	58.0939i	0.959465	+	2.31635i
$630$		0			0
$631$	−0.699961	+	0.699961i	−0.0278650	+	0.0278650i	−0.720902	−	0.693037i	$-0.756272\pi$
$631$	−0.699961	+	0.699961i	−0.0278650	+	0.0278650i	0.693037	+	0.720902i	$0.256272\pi$
$632$		0			0
$633$	−27.9860	−	38.4212i	−1.11235	−	1.52710i
$634$		0			0
$635$	8.17515	+	19.7366i	0.324421	+	0.783221i
$636$		0			0
$637$	−17.6223	−	7.29941i	−0.698222	−	0.289213i
$638$		0			0
$639$	16.4785	+	5.30993i	0.651881	+	0.210058i
$640$		0			0
$641$			36.4715i			1.44054i	0.693695	+	0.720269i	$0.255981\pi$
$641$			36.4715i			1.44054i	−0.693695	+	0.720269i	$0.744019\pi$
$642$		0			0
$643$	−13.4470	+	32.4640i	−0.530298	+	1.28025i	0.401027	+	0.916066i	$0.368653\pi$
$643$	−13.4470	+	32.4640i	−0.530298	+	1.28025i	−0.931326	+	0.364187i	$0.881347\pi$
$644$		0			0
$645$	11.3458	+	47.0069i	0.446741	+	1.85089i
$646$		0			0
$647$	−7.01510	+	7.01510i	−0.275792	+	0.275792i	−0.831427	−	0.555635i	$-0.812475\pi$
$647$	−7.01510	+	7.01510i	−0.275792	+	0.275792i	0.555635	+	0.831427i	$0.312475\pi$
$648$		0			0
$649$	3.95560	+	3.95560i	0.155271	+	0.155271i
$650$		0			0
$651$	−7.30494	+	1.76316i	−0.286303	+	0.0691036i
$652$		0			0
$653$	7.33264	+	3.03728i	0.286948	+	0.118858i	0.521515	−	0.853242i	$-0.325367\pi$
$653$	7.33264	+	3.03728i	0.286948	+	0.118858i	−0.234567	+	0.972100i	$0.575367\pi$
$654$		0			0
$655$	13.5014			0.527544
$656$		0			0
$657$	−2.06993	+	6.42370i	−0.0807556	+	0.250612i
$658$		0			0
$659$	−9.46381	+	22.8477i	−0.368658	+	0.890018i	0.625313	+	0.780374i	$0.284971\pi$
$659$	−9.46381	+	22.8477i	−0.368658	+	0.890018i	−0.993971	+	0.109644i	$0.965029\pi$
$660$		0			0
$661$	−4.59417	+	1.90297i	−0.178693	+	0.0740169i	−0.470236	−	0.882541i	$-0.655831\pi$
$661$	−4.59417	+	1.90297i	−0.178693	+	0.0740169i	0.291543	+	0.956558i	$0.405831\pi$
$662$		0			0
$663$	−23.8959	+	17.4058i	−0.928039	+	0.675986i
$664$		0			0
$665$	0.142273	+	0.142273i	0.00551713	+	0.00551713i
$666$		0			0
$667$	2.60230	−	1.07791i	0.100762	−	0.0417368i
$668$		0			0
$669$	21.3395	−	34.9181i	0.825033	−	1.35001i
$670$		0			0
$671$	−17.1652			−0.662654
$672$		0			0
$673$	−14.0193			−0.540404			−0.270202	−	0.962804i	$-0.587090\pi$
$673$	−14.0193			−0.540404			−0.270202	+	0.962804i	$0.587090\pi$
$674$		0			0
$675$	−14.5158	−	16.8708i	−0.558713	−	0.649358i
$676$		0			0
$677$	25.4610	−	10.5463i	0.978545	−	0.405327i	0.164659	−	0.986351i	$-0.447348\pi$
$677$	25.4610	−	10.5463i	0.978545	−	0.405327i	0.813886	+	0.581024i	$0.197348\pi$
$678$		0			0
$679$	−7.23650	−	7.23650i	−0.277712	−	0.277712i
$680$		0			0
$681$	18.4836	+	25.3756i	0.708294	+	0.972395i
$682$		0			0
$683$	7.18630	−	2.97666i	0.274976	−	0.113899i	−0.240934	−	0.970541i	$-0.577454\pi$
$683$	7.18630	−	2.97666i	0.274976	−	0.113899i	0.515910	+	0.856643i	$0.327454\pi$
$684$		0			0
$685$	9.96720	−	24.0630i	0.380827	−	0.919398i
$686$		0			0
$687$	−3.55268	+	22.6086i	−0.135543	+	0.862573i
$688$		0			0
$689$	8.15685			0.310751
$690$		0			0
$691$	−21.5412	−	8.92265i	−0.819466	−	0.339434i	−0.0667419	−	0.997770i	$-0.521260\pi$
$691$	−21.5412	−	8.92265i	−0.819466	−	0.339434i	−0.752724	+	0.658336i	$0.771260\pi$
$692$		0			0
$693$	0.801343	+	9.87496i	0.0304405	+	0.375119i
$694$		0			0
$695$	−21.5208	−	21.5208i	−0.816330	−	0.816330i
$696$		0			0
$697$	28.3036	−	28.3036i	1.07207	−	1.07207i
$698$		0			0
$699$	−18.8911	+	4.55965i	−0.714527	+	0.172462i
$700$		0			0
$701$	12.8390	−	30.9961i	0.484922	−	1.17071i	−0.472322	−	0.881426i	$-0.656584\pi$
$701$	12.8390	−	30.9961i	0.484922	−	1.17071i	0.957244	−	0.289280i	$-0.0934160\pi$
$702$		0			0
$703$		−	0.941452i		−	0.0355075i
$704$		0			0
$705$	−7.36389	+	46.8625i	−0.277340	+	1.76494i
$706$		0			0
$707$	4.22606	+	1.75049i	0.158937	+	0.0658339i
$708$		0			0
$709$	−0.0401422	−	0.0969118i	−0.00150757	−	0.00363960i	0.923124	−	0.384502i	$-0.125627\pi$
$709$	−0.0401422	−	0.0969118i	−0.00150757	−	0.00363960i	−0.924632	+	0.380863i	$0.875627\pi$
$710$		0			0
$711$	−0.872388	−	1.70191i	−0.0327171	−	0.0638267i
$712$		0			0
$713$	8.26126	−	8.26126i	0.309387	−	0.309387i
$714$		0			0
$715$	14.9008	+	35.9737i	0.557258	+	1.34534i
$716$		0			0
$717$	15.1068	−	24.7195i	0.564175	−	0.923168i
$718$		0			0
$719$			7.25362i			0.270515i	0.990811	+	0.135257i	$0.0431861\pi$
$719$			7.25362i			0.270515i	−0.990811	+	0.135257i	$0.956814\pi$
$720$		0			0
$721$		−	8.55913i		−	0.318759i
$722$		0			0
$723$	−8.13075	+	13.3045i	−0.302386	+	0.494798i
$724$		0			0
$725$	−2.22906	−	5.38143i	−0.0827853	−	0.199861i
$726$		0			0
$727$	−33.8662	+	33.8662i	−1.25603	+	1.25603i	−0.303055	+	0.952973i	$0.598007\pi$
$727$	−33.8662	+	33.8662i	−1.25603	+	1.25603i	−0.952973	+	0.303055i	$0.901993\pi$
$728$		0			0
$729$	−26.6977	−	4.02907i	−0.988803	−	0.149225i
$730$		0			0
$731$	20.1084	+	48.5460i	0.743736	+	1.79554i
$732$		0			0
$733$	−46.5930	−	19.2995i	−1.72095	−	0.712842i	−0.999799	−	0.0200663i	$-0.993612\pi$
$733$	−46.5930	−	19.2995i	−1.72095	−	0.712842i	−0.721153	−	0.692775i	$-0.756388\pi$
$734$		0			0
$735$	5.24981	−	33.4088i	0.193642	−	1.23230i
$736$		0			0
$737$		−	37.6478i		−	1.38678i
$738$		0			0
$739$	11.4353	−	27.6072i	0.420653	−	1.01555i	−0.561502	−	0.827475i	$-0.689776\pi$
$739$	11.4353	−	27.6072i	0.420653	−	1.01555i	0.982155	−	0.188072i	$-0.0602237\pi$
$740$		0			0
$741$	0.430266	−	0.103851i	0.0158062	−	0.00381507i
$742$		0			0
$743$	31.4330	−	31.4330i	1.15317	−	1.15317i	0.167252	−	0.985914i	$-0.446511\pi$
$743$	31.4330	−	31.4330i	1.15317	−	1.15317i	0.985914	−	0.167252i	$-0.0534894\pi$
$744$		0			0
$745$	22.7253	+	22.7253i	0.832590	+	0.832590i
$746$		0			0
$747$	15.2000	−	1.23347i	0.556139	−	0.0451301i
$748$		0			0
$749$	0.693395	+	0.287214i	0.0253361	+	0.0104946i
$750$		0			0
$751$	9.38556			0.342484			0.171242	−	0.985229i	$-0.445222\pi$
$751$	9.38556			0.342484			0.171242	+	0.985229i	$0.445222\pi$
$752$		0			0
$753$	0.422577	−	2.68920i	0.0153996	−	0.0980001i
$754$		0			0
$755$	−13.1733	+	31.8033i	−0.479427	+	1.15744i
$756$		0			0
$757$	−21.2091	+	8.78508i	−0.770857	+	0.319299i	−0.733219	−	0.679992i	$-0.761983\pi$
$757$	−21.2091	+	8.78508i	−0.770857	+	0.319299i	−0.0376373	+	0.999291i	$0.511983\pi$
$758$		0			0
$759$	−9.06889	−	12.4504i	−0.329180	−	0.451921i
$760$		0			0
$761$	−17.8648	−	17.8648i	−0.647599	−	0.647599i	0.304813	−	0.952412i	$-0.401406\pi$
$761$	−17.8648	−	17.8648i	−0.647599	−	0.647599i	−0.952412	+	0.304813i	$0.901406\pi$
$762$		0			0
$763$	0.849818	−	0.352006i	0.0307655	−	0.0127435i
$764$		0			0
$765$	−39.9397	−	33.9441i	−1.44402	−	1.22725i
$766$		0			0
$767$	3.87797			0.140025
$768$		0			0
$769$	−1.71307			−0.0617750			−0.0308875	−	0.999523i	$-0.509833\pi$
$769$	−1.71307			−0.0617750			−0.0308875	+	0.999523i	$0.509833\pi$
$770$		0			0
$771$	7.48697	−	12.2510i	0.269637	−	0.441210i
$772$		0			0
$773$	25.0667	−	10.3830i	0.901587	−	0.373450i	0.116757	−	0.993161i	$-0.462750\pi$
$773$	25.0667	−	10.3830i	0.901587	−	0.373450i	0.784830	+	0.619711i	$0.212750\pi$
$774$		0			0
$775$	−17.0839	−	17.0839i	−0.613671	−	0.613671i
$776$		0			0
$777$	11.8080	−	8.60096i	0.423609	−	0.308558i
$778$		0			0
$779$	−0.553675	+	0.229340i	−0.0198375	+	0.00821694i
$780$		0			0
$781$	9.48225	−	22.8922i	0.339302	−	0.819146i
$782$		0			0
$783$	−6.30787	−	3.18509i	−0.225425	−	0.113826i
$784$		0			0
$785$	−8.75417			−0.312450
$786$		0			0
$787$	−47.6483	−	19.7366i	−1.69848	−	0.703533i	−0.698552	−	0.715560i	$-0.746172\pi$
$787$	−47.6483	−	19.7366i	−1.69848	−	0.703533i	−0.999928	+	0.0120263i	$0.996172\pi$
$788$		0			0
$789$	−20.8616	+	5.03525i	−0.742691	+	0.179260i
$790$		0			0
$791$	−4.61452	−	4.61452i	−0.164073	−	0.164073i
$792$		0			0
$793$	−8.41414	+	8.41414i	−0.298795	+	0.298795i
$794$		0			0
$795$	3.39322	+	14.0584i	0.120345	+	0.498601i
$796$		0			0
$797$	−9.69549	+	23.4070i	−0.343432	+	0.829118i	0.653932	+	0.756553i	$0.273118\pi$
$797$	−9.69549	+	23.4070i	−0.343432	+	0.829118i	−0.997364	+	0.0725644i	$0.976882\pi$
$798$		0			0
$799$			51.5470i			1.82360i
$800$		0			0
$801$	−1.17448	+	3.64480i	−0.0414981	+	0.128783i
$802$		0			0
$803$	8.92387	+	3.69639i	0.314917	+	0.130443i
$804$		0			0
$805$	−1.85751	−	4.48443i	−0.0654687	−	0.158055i
$806$		0			0
$807$	16.6699	+	22.8856i	0.586808	+	0.805611i
$808$		0			0
$809$	−31.1610	+	31.1610i	−1.09556	+	1.09556i	−0.100640	+	0.994923i	$0.532089\pi$
$809$	−31.1610	+	31.1610i	−1.09556	+	1.09556i	−0.994923	+	0.100640i	$0.967911\pi$
$810$		0			0
$811$	−3.17453	−	7.66400i	−0.111473	−	0.269120i	0.858291	−	0.513163i	$-0.171526\pi$
$811$	−3.17453	−	7.66400i	−0.111473	−	0.269120i	−0.969764	+	0.244043i	$0.921526\pi$
$812$		0			0
$813$	25.8687	+	15.8091i	0.907254	+	0.554450i
$814$		0			0
$815$		−	28.0113i		−	0.981194i
$816$		0			0
$817$		−	0.786722i		−	0.0275239i
$818$		0			0
$819$	5.23338	+	4.44777i	0.182869	+	0.155418i
$820$		0			0
$821$	1.18631	+	2.86400i	0.0414025	+	0.0999544i	0.943228	−	0.332146i	$-0.107773\pi$
$821$	1.18631	+	2.86400i	0.0414025	+	0.0999544i	−0.901826	+	0.432100i	$0.857773\pi$
$822$		0			0
$823$	−1.98030	+	1.98030i	−0.0690288	+	0.0690288i	−0.740778	−	0.671750i	$-0.765543\pi$
$823$	−1.98030	+	1.98030i	−0.0690288	+	0.0690288i	0.671750	+	0.740778i	$0.265543\pi$
$824$		0			0
$825$	−25.7468	+	18.7540i	−0.896388	+	0.652931i
$826$		0			0
$827$	−19.1750	−	46.2924i	−0.666779	−	1.60975i	−0.786967	−	0.616995i	$-0.788350\pi$
$827$	−19.1750	−	46.2924i	−0.666779	−	1.60975i	0.120189	−	0.992751i	$-0.461650\pi$
$828$		0			0
$829$	20.6566	+	8.55623i	0.717432	+	0.297170i	0.711376	−	0.702812i	$-0.248072\pi$
$829$	20.6566	+	8.55623i	0.717432	+	0.297170i	0.00605590	+	0.999982i	$0.498072\pi$
$830$		0			0
$831$	−39.5750	−	6.21875i	−1.37284	−	0.215726i
$832$		0			0
$833$		−	36.7485i		−	1.27326i
$834$		0			0
$835$	−11.0547	+	26.6884i	−0.382563	+	0.923589i
$836$		0			0
$837$	−29.2279	−	2.19304i	−1.01026	−	0.0758026i
$838$		0			0
$839$	−10.0632	+	10.0632i	−0.347420	+	0.347420i	−0.859148	−	0.511728i	$-0.829006\pi$
$839$	−10.0632	+	10.0632i	−0.347420	+	0.347420i	0.511728	+	0.859148i	$0.329006\pi$
$840$		0			0
$841$	19.1984	+	19.1984i	0.662013	+	0.662013i
$842$		0			0
$843$	−3.41059	−	14.1304i	−0.117467	−	0.486678i
$844$		0			0
$845$	−11.6558	−	4.82798i	−0.400971	−	0.166088i
$846$		0			0
$847$	5.71875			0.196499
$848$		0			0
$849$	43.9904	+	6.91258i	1.50975	+	0.237239i
$850$		0			0
$851$	−8.69142	+	20.9830i	−0.297938	+	0.719286i
$852$		0			0
$853$	−11.2850	+	4.67440i	−0.386391	+	0.160048i	−0.567418	−	0.823430i	$-0.692058\pi$
$853$	−11.2850	+	4.67440i	−0.386391	+	0.160048i	0.181027	+	0.983478i	$0.442058\pi$
$854$		0			0
$855$	0.357978	+	0.698368i	0.0122426	+	0.0238837i
$856$		0			0
$857$	22.7269	+	22.7269i	0.776335	+	0.776335i	0.979206	−	0.202871i	$-0.0650271\pi$
$857$	22.7269	+	22.7269i	0.776335	+	0.776335i	−0.202871	+	0.979206i	$0.565027\pi$
$858$		0			0
$859$	−11.7509	+	4.86736i	−0.400934	+	0.166072i	−0.574033	−	0.818832i	$-0.694622\pi$
$859$	−11.7509	+	4.86736i	−0.400934	+	0.166072i	0.173099	+	0.984904i	$0.444622\pi$
$860$		0			0
$861$	−7.93474	−	4.84916i	−0.270415	−	0.165259i
$862$		0			0
$863$	45.0560			1.53372			0.766862	−	0.641812i	$-0.221817\pi$
$863$	45.0560			1.53372			0.766862	+	0.641812i	$0.221817\pi$
$864$		0			0
$865$	−61.7127			−2.09829
$866$		0			0
$867$	−23.4747	−	14.3461i	−0.797244	−	0.487219i
$868$		0			0
$869$	−2.52879	+	1.04746i	−0.0857833	+	0.0355326i
$870$		0			0
$871$	−18.4545	−	18.4545i	−0.625306	−	0.625306i
$872$		0			0
$873$	−18.2080	−	35.5213i	−0.616246	−	1.20221i
$874$		0			0
$875$	1.55199	−	0.642857i	0.0524669	−	0.0217325i
$876$		0			0
$877$	−6.55184	+	15.8175i	−0.221240	+	0.534121i	−0.995059	−	0.0992863i	$-0.968344\pi$
$877$	−6.55184	+	15.8175i	−0.221240	+	0.534121i	0.773819	+	0.633407i	$0.218344\pi$
$878$		0			0
$879$	7.77914	+	1.22240i	0.262384	+	0.0412305i
$880$		0			0
$881$	−20.4889			−0.690289			−0.345144	−	0.938550i	$-0.612170\pi$
$881$	−20.4889			−0.690289			−0.345144	+	0.938550i	$0.612170\pi$
$882$		0			0
$883$	3.85593	+	1.59718i	0.129762	+	0.0537493i	0.446620	−	0.894724i	$-0.352628\pi$
$883$	3.85593	+	1.59718i	0.129762	+	0.0537493i	−0.316857	+	0.948473i	$0.602628\pi$
$884$		0			0
$885$	1.61322	+	6.68373i	0.0542278	+	0.224671i
$886$		0			0
$887$	29.9883	+	29.9883i	1.00691	+	1.00691i	0.999976	+	0.00693107i	$0.00220625\pi$
$887$	29.9883	+	29.9883i	1.00691	+	1.00691i	0.00693107	+	0.999976i	$0.497794\pi$
$888$		0			0
$889$	3.81338	−	3.81338i	0.127897	−	0.127897i
$890$		0			0
$891$	−8.83805	+	37.6182i	−0.296086	+	1.26026i
$892$		0			0
$893$	0.295343	−	0.713020i	0.00988326	−	0.0238603i
$894$		0			0
$895$		−	55.7410i		−	1.86322i
$896$		0			0
$897$	−10.5485	−	1.65757i	−0.352203	−	0.0553446i
$898$		0			0
$899$	−7.08706	−	2.93556i	−0.236367	−	0.0979063i
$900$		0			0
$901$	6.01386	+	14.5187i	0.200351	+	0.483690i
$902$		0			0
$903$	9.86732	−	7.18737i	0.328364	−	0.239181i
$904$		0			0
$905$	−33.7916	+	33.7916i	−1.12327	+	1.12327i
$906$		0			0
$907$	16.6011	+	40.0785i	0.551229	+	1.33078i	0.916557	+	0.399905i	$0.130957\pi$
$907$	16.6011	+	40.0785i	0.551229	+	1.33078i	−0.365328	+	0.930879i	$0.619043\pi$
$908$		0			0
$909$	13.5947	+	11.5539i	0.450907	+	0.383219i
$910$		0			0
$911$		−	42.9300i		−	1.42233i	−0.703023	−	0.711167i	$-0.748167\pi$
$911$		−	42.9300i		−	1.42233i	0.703023	−	0.711167i	$-0.251833\pi$
$912$		0			0
$913$		−	21.8258i		−	0.722328i
$914$		0			0
$915$	−18.0021	−	11.0016i	−0.595132	−	0.363703i
$916$		0			0
$917$	−1.30433	−	3.14893i	−0.0430728	−	0.103987i
$918$		0			0
$919$	−27.6253	+	27.6253i	−0.911275	+	0.911275i	−0.996373	−	0.0850978i	$-0.972880\pi$
$919$	−27.6253	+	27.6253i	−0.911275	+	0.911275i	0.0850978	+	0.996373i	$0.472880\pi$
$920$		0			0
$921$	13.6479	+	18.7368i	0.449714	+	0.617398i
$922$		0			0
$923$	−6.57337	−	15.8695i	−0.216365	−	0.522351i
$924$		0			0
$925$	43.3917	+	17.9734i	1.42671	+	0.590963i
$926$		0			0
$927$	10.2389	−	31.7747i	0.336289	−	1.04362i
$928$		0			0
$929$			26.5634i			0.871518i	0.900063	+	0.435759i	$0.143520\pi$
$929$			26.5634i			0.871518i	−0.900063	+	0.435759i	$0.856480\pi$
$930$		0			0
$931$	−0.210553	+	0.508321i	−0.00690060	+	0.0166595i
$932$		0			0
$933$	6.16692	+	25.5502i	0.201896	+	0.836475i
$934$		0			0
$935$	−53.0452	+	53.0452i	−1.73476	+	1.73476i
$936$		0			0
$937$	−1.34624	−	1.34624i	−0.0439798	−	0.0439798i	0.684775	−	0.728755i	$-0.259901\pi$
$937$	−1.34624	−	1.34624i	−0.0439798	−	0.0439798i	−0.728755	+	0.684775i	$0.759901\pi$
$938$		0			0
$939$	42.6150	−	10.2858i	1.39069	−	0.335663i
$940$		0			0
$941$	−6.86683	−	2.84433i	−0.223852	−	0.0927226i	0.267939	−	0.963436i	$-0.413658\pi$
$941$	−6.86683	−	2.84433i	−0.223852	−	0.0927226i	−0.491791	+	0.870713i	$0.663658\pi$
$942$		0			0
$943$	14.4575			0.470801
$944$		0			0
$945$	−5.48872	+	10.8701i	−0.178548	+	0.353603i
$946$		0			0
$947$	13.0476	−	31.4996i	0.423989	−	1.02360i	−0.557170	−	0.830398i	$-0.688113\pi$
$947$	13.0476	−	31.4996i	0.423989	−	1.02360i	0.981159	−	0.193201i	$-0.0618871\pi$
$948$		0			0
$949$	6.18628	−	2.56244i	0.200815	−	0.0831804i
$950$		0			0
$951$	9.50001	−	6.91983i	0.308059	−	0.224391i
$952$		0			0
$953$	1.94423	+	1.94423i	0.0629798	+	0.0629798i	0.737895	−	0.674915i	$-0.235820\pi$
$953$	1.94423	+	1.94423i	0.0629798	+	0.0629798i	−0.674915	+	0.737895i	$0.735820\pi$
$954$		0			0
$955$	44.2822	−	18.3423i	1.43294	−	0.593542i
$956$		0			0
$957$	−5.27377	+	8.62955i	−0.170477	+	0.278954i
$958$		0			0
$959$	−6.57510			−0.212321
$960$		0			0
$961$	−0.817748			−0.0263790
$962$		0			0
$963$	2.23056	+	1.89572i	0.0718789	+	0.0610887i
$964$		0			0
$965$	−34.4117	+	14.2538i	−1.10775	+	0.458846i
$966$		0			0
$967$	−30.8641	−	30.8641i	−0.992522	−	0.992522i	0.00745003	−	0.999972i	$-0.497629\pi$
$967$	−30.8641	−	30.8641i	−0.992522	−	0.992522i	−0.999972	+	0.00745003i	$0.997629\pi$
$968$		0			0
$969$	0.502075	+	0.689283i	0.0161290	+	0.0221430i
$970$		0			0
$971$	10.5485	−	4.36935i	0.338519	−	0.140219i	−0.206947	−	0.978352i	$-0.566353\pi$
$971$	10.5485	−	4.36935i	0.338519	−	0.140219i	0.545466	+	0.838133i	$0.316353\pi$
$972$		0			0
$973$	−2.94023	+	7.09834i	−0.0942594	+	0.227562i
$974$		0			0
$975$	−3.42777	+	21.8137i	−0.109776	+	0.698597i
$976$		0			0
$977$	−19.0100			−0.608184			−0.304092	−	0.952643i	$-0.598353\pi$
$977$	−19.0100			−0.608184			−0.304092	+	0.952643i	$0.598353\pi$
$978$		0			0
$979$	5.06340	+	2.09733i	0.161827	+	0.0670309i
$980$		0			0
$981$	3.57593	−	0.290183i	0.114171	−	0.00926485i
$982$		0			0
$983$	20.9677	+	20.9677i	0.668767	+	0.668767i	0.957431	−	0.288664i	$-0.0932110\pi$
$983$	20.9677	+	20.9677i	0.668767	+	0.668767i	−0.288664	+	0.957431i	$0.593211\pi$
$984$		0			0
$985$	50.3580	−	50.3580i	1.60454	−	1.60454i
$986$		0			0
$987$	11.6411	−	2.80976i	0.370541	−	0.0894357i
$988$		0			0
$989$	−7.26297	+	17.5344i	−0.230949	+	0.557560i
$990$		0			0
$991$			45.2241i			1.43659i	0.695737	+	0.718296i	$0.255078\pi$
$991$			45.2241i			1.43659i	−0.695737	+	0.718296i	$0.744922\pi$
$992$		0			0
$993$	−2.81706	+	17.9273i	−0.0893968	+	0.568905i
$994$		0			0
$995$	−6.28096	−	2.60166i	−0.199120	−	0.0824781i
$996$		0			0
$997$	20.9163	+	50.4964i	0.662425	+	1.59924i	0.793991	+	0.607929i	$0.208000\pi$
$997$	20.9163	+	50.4964i	0.662425	+	1.59924i	−0.131566	+	0.991307i	$0.542000\pi$
$998$		0			0
$999$	54.1246	−	17.8047i	1.71243	−	0.563315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.o.a.47.2		56
3.2	odd	2	inner	384.2.o.a.47.13		56
4.3	odd	2		96.2.o.a.35.12	yes	56
8.3	odd	2		768.2.o.b.95.2		56
8.5	even	2		768.2.o.a.95.13		56
12.11	even	2		96.2.o.a.35.3	yes	56
24.5	odd	2		768.2.o.a.95.2		56
24.11	even	2		768.2.o.b.95.13		56
32.5	even	8		768.2.o.b.671.13		56
32.11	odd	8	inner	384.2.o.a.335.13		56
32.21	even	8		96.2.o.a.11.3	✓	56
32.27	odd	8		768.2.o.a.671.2		56
96.5	odd	8		768.2.o.b.671.2		56
96.11	even	8	inner	384.2.o.a.335.2		56
96.53	odd	8		96.2.o.a.11.12	yes	56
96.59	even	8		768.2.o.a.671.13		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.3	✓	56	32.21	even	8
96.2.o.a.11.12	yes	56	96.53	odd	8
96.2.o.a.35.3	yes	56	12.11	even	2
96.2.o.a.35.12	yes	56	4.3	odd	2
384.2.o.a.47.2		56	1.1	even	1	trivial
384.2.o.a.47.13		56	3.2	odd	2	inner
384.2.o.a.335.2		56	96.11	even	8	inner
384.2.o.a.335.13		56	32.11	odd	8	inner
768.2.o.a.95.2		56	24.5	odd	2
768.2.o.a.95.13		56	8.5	even	2
768.2.o.a.671.2		56	32.27	odd	8
768.2.o.a.671.13		56	96.59	even	8
768.2.o.b.95.2		56	8.3	odd	2
768.2.o.b.95.13		56	24.11	even	2
768.2.o.b.671.2		56	96.5	odd	8
768.2.o.b.671.13		56	32.5	even	8

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.47792 - 0.903198i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(0.543879 + 0.543879i) q^{7} +(1.36847 + 2.66970i) q^{9} +O(q^{10})\)	\(q+(-1.47792 - 0.903198i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(0.543879 + 0.543879i) q^{7} +(1.36847 + 2.66970i) q^{9} +(3.96678 - 1.64309i) q^{11} +(1.13904 - 2.74988i) q^{13} +(5.21329 + 0.819208i) q^{15} +5.73443 q^{17} +(-0.0793211 - 0.0328559i) q^{19} +(-0.312577 - 1.29504i) q^{21} +(1.46457 + 1.46457i) q^{23} +(3.02867 - 3.02867i) q^{25} +(0.388788 - 5.18159i) q^{27} +(0.520422 - 1.25641i) q^{29} -5.64072i q^{31} +(-7.34659 - 1.15443i) q^{33} +(-2.16511 - 0.896820i) q^{35} +(4.19628 + 10.1307i) q^{37} +(-4.16709 + 3.03532i) q^{39} +(4.93573 - 4.93573i) q^{41} +(3.50661 + 8.46571i) q^{43} +(-6.96490 - 5.91936i) q^{45} +8.98904i q^{47} -6.40839i q^{49} +(-8.47500 - 5.17932i) q^{51} +(1.04873 + 2.53186i) q^{53} +(-9.25030 + 9.25030i) q^{55} +(0.0875545 + 0.120201i) q^{57} +(0.498592 + 1.20371i) q^{59} +(-3.69353 - 1.52991i) q^{61} +(-0.707713 + 2.19627i) q^{63} +9.06875i q^{65} +(3.35550 - 8.10090i) q^{67} +(-0.841717 - 3.48732i) q^{69} +(4.08070 - 4.08070i) q^{71} +(1.59075 + 1.59075i) q^{73} +(-7.21160 + 1.74063i) q^{75} +(3.05109 + 1.26380i) q^{77} -0.637492 q^{79} +(-5.25459 + 7.30679i) q^{81} +(1.94530 - 4.69638i) q^{83} +(-16.1419 + 6.68618i) q^{85} +(-1.90393 + 1.38682i) q^{87} +(0.902588 + 0.902588i) q^{89} +(2.11510 - 0.876104i) q^{91} +(-5.09469 + 8.33651i) q^{93} +0.261590 q^{95} -13.3054 q^{97} +(9.81497 + 8.34158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9	\( 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 8 q^{19} - 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} - 8 q^{37} + 28 q^{39} + 8 q^{43} - 4 q^{45} + 16 q^{51} - 24 q^{55} - 4 q^{57} - 40 q^{61} - 56 q^{67} - 4 q^{69} - 8 q^{73} - 16 q^{75} - 16 q^{79} - 48 q^{85} - 52 q^{87} - 40 q^{91} + 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9 - 8 * q^13 + 8 * q^15 + 8 * q^19 - 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 - 8 * q^37 + 28 * q^39 + 8 * q^43 - 4 * q^45 + 16 * q^51 - 24 * q^55 - 4 * q^57 - 40 * q^61 - 56 * q^67 - 4 * q^69 - 8 * q^73 - 16 * q^75 - 16 * q^79 - 48 * q^85 - 52 * q^87 - 40 * q^91 + 8 * q^93 - 16 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

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Database

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