LMFDB - Embedded newform 765.2.k.b.676.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(361,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("765.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			676.4
Root			$-3.48265i$ of defining polynomial
Character	$\chi$	$=$	765.676
Dual form			765.2.k.b.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.12708i q^{2} +0.729699 q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.72715 + 1.72715i) q^{7} +3.07658i q^{8} +(-0.796963 + 0.796963i) q^{10} +(-2.57251 + 2.57251i) q^{11} +3.64168 q^{13} +(-1.94663 - 1.94663i) q^{14} -2.00814 q^{16} +(-3.03394 - 2.79199i) q^{17} +2.61358i q^{19} +(0.515975 + 0.515975i) q^{20} +(-2.89941 - 2.89941i) q^{22} +(-0.993850 + 0.993850i) q^{23} +1.00000i q^{25} +4.10445i q^{26} +(-1.26030 + 1.26030i) q^{28} +(-0.601589 - 0.601589i) q^{29} +(-6.67744 - 6.67744i) q^{31} +3.88983i q^{32} +(3.14678 - 3.41948i) q^{34} -2.44256 q^{35} +(7.78199 + 7.78199i) q^{37} -2.94570 q^{38} +(-2.17547 + 2.17547i) q^{40} +(6.74550 - 6.74550i) q^{41} +7.47280i q^{43} +(-1.87716 + 1.87716i) q^{44} +(-1.12014 - 1.12014i) q^{46} +5.42683 q^{47} +1.03389i q^{49} -1.12708 q^{50} +2.65733 q^{52} +12.9453i q^{53} -3.63808 q^{55} +(-5.31372 - 5.31372i) q^{56} +(0.678037 - 0.678037i) q^{58} -1.40270i q^{59} +(0.804485 - 0.804485i) q^{61} +(7.52598 - 7.52598i) q^{62} -8.40042 q^{64} +(2.57506 + 2.57506i) q^{65} -2.07908 q^{67} +(-2.21387 - 2.03731i) q^{68} -2.75295i q^{70} +(-8.69168 - 8.69168i) q^{71} +(1.04359 + 1.04359i) q^{73} +(-8.77090 + 8.77090i) q^{74} +1.90713i q^{76} -8.88623i q^{77} +(6.34470 - 6.34470i) q^{79} +(-1.41997 - 1.41997i) q^{80} +(7.60269 + 7.60269i) q^{82} -2.52680i q^{83} +(-0.171086 - 4.11955i) q^{85} -8.42242 q^{86} +(-7.91453 - 7.91453i) q^{88} +1.66373 q^{89} +(-6.28973 + 6.28973i) q^{91} +(-0.725212 + 0.725212i) q^{92} +6.11645i q^{94} +(-1.84808 + 1.84808i) q^{95} +(-8.67432 - 8.67432i) q^{97} -1.16527 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 4 q^{10} + 4 q^{11} + 4 q^{14} + 4 q^{16} - 12 q^{17} + 8 q^{20} + 20 q^{22} - 12 q^{23} + 4 q^{28} + 12 q^{29} - 12 q^{34} - 16 q^{35} + 12 q^{37} - 24 q^{38} - 8 q^{40} + 24 q^{41} - 8 q^{44}+ \cdots - 44 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 - 4 * q^10 + 4 * q^11 + 4 * q^14 + 4 * q^16 - 12 * q^17 + 8 * q^20 + 20 * q^22 - 12 * q^23 + 4 * q^28 + 12 * q^29 - 12 * q^34 - 16 * q^35 + 12 * q^37 - 24 * q^38 - 8 * q^40 + 24 * q^41 - 8 * q^44 - 24 * q^46 + 48 * q^47 - 4 * q^50 - 56 * q^52 - 40 * q^56 + 36 * q^58 + 40 * q^61 - 40 * q^62 + 28 * q^64 - 4 * q^65 - 8 * q^67 + 40 * q^68 - 28 * q^71 - 48 * q^73 - 28 * q^74 - 8 * q^79 - 16 * q^80 + 40 * q^82 - 4 * q^85 + 96 * q^86 - 72 * q^88 - 24 * q^89 - 36 * q^91 + 16 * q^92 + 8 * q^95 + 4 * q^97 - 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$			1.12708i			0.796963i	0.917176	+	0.398482i	$0.130463\pi$
$2$			1.12708i			0.796963i	−0.917176	+	0.398482i	$0.869537\pi$
$3$		0			0
$3$		0			0
$4$	0.729699			0.364850
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$	−1.72715	+	1.72715i	−0.652802	+	0.652802i	−0.953667	−	0.300865i	$-0.902725\pi$
$7$	−1.72715	+	1.72715i	−0.652802	+	0.652802i	0.300865	+	0.953667i	$0.402725\pi$
$8$			3.07658i			1.08773i
$9$		0			0
$10$	−0.796963	+	0.796963i	−0.252022	+	0.252022i
$11$	−2.57251	+	2.57251i	−0.775641	+	0.775641i	−0.979086	−	0.203446i	$-0.934786\pi$
$11$	−2.57251	+	2.57251i	−0.775641	+	0.775641i	0.203446	+	0.979086i	$0.434786\pi$
$12$		0			0
$13$	3.64168			1.01002			0.505010	−	0.863113i	$-0.331489\pi$
$13$	3.64168			1.01002			0.505010	+	0.863113i	$0.331489\pi$
$14$	−1.94663	−	1.94663i	−0.520259	−	0.520259i
$15$		0			0
$16$	−2.00814			−0.502035
$17$	−3.03394	−	2.79199i	−0.735839	−	0.677157i
$17$	−3.03394	−	2.79199i	−0.735839	−	0.677157i
$18$		0			0
$19$			2.61358i			0.599596i	0.954003	+	0.299798i	$0.0969193\pi$
$19$			2.61358i			0.599596i	−0.954003	+	0.299798i	$0.903081\pi$
$20$	0.515975	+	0.515975i	0.115376	+	0.115376i
$21$		0			0
$22$	−2.89941	−	2.89941i	−0.618157	−	0.618157i
$23$	−0.993850	+	0.993850i	−0.207232	+	0.207232i	−0.803090	−	0.595858i	$-0.796812\pi$
$23$	−0.993850	+	0.993850i	−0.207232	+	0.207232i	0.595858	+	0.803090i	$0.296812\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$			4.10445i			0.804949i
$27$		0			0
$28$	−1.26030	+	1.26030i	−0.238175	+	0.238175i
$29$	−0.601589	−	0.601589i	−0.111712	−	0.111712i	0.649041	−	0.760753i	$-0.275170\pi$
$29$	−0.601589	−	0.601589i	−0.111712	−	0.111712i	−0.760753	+	0.649041i	$0.775170\pi$
$30$		0			0
$31$	−6.67744	−	6.67744i	−1.19930	−	1.19930i	−0.974376	−	0.224928i	$-0.927785\pi$
$31$	−6.67744	−	6.67744i	−1.19930	−	1.19930i	−0.224928	−	0.974376i	$-0.572215\pi$
$32$			3.88983i			0.687632i
$33$		0			0
$34$	3.14678	−	3.41948i	0.539669	−	0.586436i
$35$	−2.44256			−0.412868
$36$		0			0
$37$	7.78199	+	7.78199i	1.27935	+	1.27935i	0.941031	+	0.338320i	$0.109859\pi$
$37$	7.78199	+	7.78199i	1.27935	+	1.27935i	0.338320	+	0.941031i	$0.390141\pi$
$38$	−2.94570			−0.477856
$39$		0			0
$40$	−2.17547	+	2.17547i	−0.343972	+	0.343972i
$41$	6.74550	−	6.74550i	1.05347	−	1.05347i	0.0549831	−	0.998487i	$-0.482489\pi$
$41$	6.74550	−	6.74550i	1.05347	−	1.05347i	0.998487	−	0.0549831i	$-0.0175105\pi$
$42$		0			0
$43$			7.47280i			1.13959i	0.821786	+	0.569796i	$0.192978\pi$
$43$			7.47280i			1.13959i	−0.821786	+	0.569796i	$0.807022\pi$
$44$	−1.87716	+	1.87716i	−0.282992	+	0.282992i
$45$		0			0
$46$	−1.12014	−	1.12014i	−0.165156	−	0.165156i
$47$	5.42683			0.791585			0.395792	−	0.918340i	$-0.370470\pi$
$47$	5.42683			0.791585			0.395792	+	0.918340i	$0.370470\pi$
$48$		0			0
$49$			1.03389i			0.147699i
$50$	−1.12708			−0.159393
$51$		0			0
$52$	2.65733			0.368506
$53$			12.9453i			1.77817i	0.457737	+	0.889087i	$0.348660\pi$
$53$			12.9453i			1.77817i	−0.457737	+	0.889087i	$0.651340\pi$
$54$		0			0
$55$	−3.63808			−0.490558
$56$	−5.31372	−	5.31372i	−0.710076	−	0.710076i
$57$		0			0
$58$	0.678037	−	0.678037i	0.0890306	−	0.0890306i
$59$		−	1.40270i		−	0.182616i	−0.995823	−	0.0913081i	$-0.970895\pi$
$59$		−	1.40270i		−	0.182616i	0.995823	−	0.0913081i	$-0.0291048\pi$
$60$		0			0
$61$	0.804485	−	0.804485i	0.103004	−	0.103004i	−0.653727	−	0.756731i	$-0.726795\pi$
$61$	0.804485	−	0.804485i	0.103004	−	0.103004i	0.756731	+	0.653727i	$0.226795\pi$
$62$	7.52598	−	7.52598i	0.955800	−	0.955800i
$63$		0			0
$64$	−8.40042			−1.05005
$65$	2.57506	+	2.57506i	0.319396	+	0.319396i
$66$		0			0
$67$	−2.07908			−0.254000			−0.127000	−	0.991903i	$-0.540535\pi$
$67$	−2.07908			−0.254000			−0.127000	+	0.991903i	$0.540535\pi$
$68$	−2.21387	−	2.03731i	−0.268471	−	0.247060i
$69$		0			0
$70$		−	2.75295i		−	0.329041i
$71$	−8.69168	−	8.69168i	−1.03151	−	1.03151i	−0.999487	−	0.0320251i	$-0.989804\pi$
$71$	−8.69168	−	8.69168i	−1.03151	−	1.03151i	−0.0320251	−	0.999487i	$-0.510196\pi$
$72$		0			0
$73$	1.04359	+	1.04359i	0.122143	+	0.122143i	0.765536	−	0.643393i	$-0.222474\pi$
$73$	1.04359	+	1.04359i	0.122143	+	0.122143i	−0.643393	+	0.765536i	$0.722474\pi$
$74$	−8.77090	+	8.77090i	−1.01960	+	1.01960i
$75$		0			0
$76$			1.90713i			0.218762i
$77$		−	8.88623i		−	1.01268i
$78$		0			0
$79$	6.34470	−	6.34470i	0.713834	−	0.713834i	−0.253501	−	0.967335i	$-0.581582\pi$
$79$	6.34470	−	6.34470i	0.713834	−	0.713834i	0.967335	+	0.253501i	$0.0815821\pi$
$80$	−1.41997	−	1.41997i	−0.158757	−	0.158757i
$81$		0			0
$82$	7.60269	+	7.60269i	0.839577	+	0.839577i
$83$		−	2.52680i		−	0.277353i	−0.990338	−	0.138676i	$-0.955715\pi$
$83$		−	2.52680i		−	0.277353i	0.990338	−	0.138676i	$-0.0442848\pi$
$84$		0			0
$85$	−0.171086	−	4.11955i	−0.0185569	−	0.446828i
$86$	−8.42242			−0.908213
$87$		0			0
$88$	−7.91453	−	7.91453i	−0.843691	−	0.843691i
$89$	1.66373			0.176355			0.0881775	−	0.996105i	$-0.471896\pi$
$89$	1.66373			0.176355			0.0881775	+	0.996105i	$0.471896\pi$
$90$		0			0
$91$	−6.28973	+	6.28973i	−0.659343	+	0.659343i
$92$	−0.725212	+	0.725212i	−0.0756086	+	0.0756086i
$93$		0			0
$94$			6.11645i			0.630864i
$95$	−1.84808	+	1.84808i	−0.189609	+	0.189609i
$96$		0			0
$97$	−8.67432	−	8.67432i	−0.880744	−	0.880744i	0.112867	−	0.993610i	$-0.463997\pi$
$97$	−8.67432	−	8.67432i	−0.880744	−	0.880744i	−0.993610	+	0.112867i	$0.963997\pi$
$98$	−1.16527			−0.117710
$99$		0			0
$100$			0.729699i			0.0729699i
$101$	4.18131			0.416056			0.208028	−	0.978123i	$-0.433296\pi$
$101$	4.18131			0.416056			0.208028	+	0.978123i	$0.433296\pi$
$102$		0			0
$103$	8.08417			0.796557			0.398279	−	0.917265i	$-0.369608\pi$
$103$	8.08417			0.796557			0.398279	+	0.917265i	$0.369608\pi$
$104$			11.2039i			1.09863i
$105$		0			0
$106$	−14.5903			−1.41714
$107$	6.22304	+	6.22304i	0.601604	+	0.601604i	0.940738	−	0.339134i	$-0.110134\pi$
$107$	6.22304	+	6.22304i	0.601604	+	0.601604i	−0.339134	+	0.940738i	$0.610134\pi$
$108$		0			0
$109$	10.1218	−	10.1218i	0.969496	−	0.969496i	−0.0300524	−	0.999548i	$-0.509567\pi$
$109$	10.1218	−	10.1218i	0.969496	−	0.969496i	0.999548	+	0.0300524i	$0.00956740\pi$
$110$		−	4.10039i		−	0.390957i
$111$		0			0
$112$	3.46836	−	3.46836i	0.327730	−	0.327730i
$113$	8.10334	−	8.10334i	0.762298	−	0.762298i	−0.214440	−	0.976737i	$-0.568792\pi$
$113$	8.10334	−	8.10334i	0.762298	−	0.762298i	0.976737	+	0.214440i	$0.0687925\pi$
$114$		0			0
$115$	−1.40552			−0.131065
$116$	−0.438979	−	0.438979i	−0.0407582	−	0.0407582i
$117$		0			0
$118$	1.58095			0.145538
$119$	10.0623	−	0.417888i	0.922407	−	0.0383077i
$120$		0			0
$121$		−	2.23561i		−	0.203237i
$122$	0.906716	+	0.906716i	0.0820902	+	0.0820902i
$123$		0			0
$124$	−4.87252	−	4.87252i	−0.437565	−	0.437565i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$		−	2.51562i		−	0.223225i	−0.993752	−	0.111613i	$-0.964398\pi$
$127$		−	2.51562i		−	0.223225i	0.993752	−	0.111613i	$-0.0356015\pi$
$128$		−	1.68825i		−	0.149221i
$129$		0			0
$130$	−2.90228	+	2.90228i	−0.254547	+	0.254547i
$131$	1.57140	+	1.57140i	0.137294	+	0.137294i	0.772414	−	0.635120i	$-0.219049\pi$
$131$	1.57140	+	1.57140i	0.137294	+	0.137294i	−0.635120	+	0.772414i	$0.719049\pi$
$132$		0			0
$133$	−4.51405	−	4.51405i	−0.391417	−	0.391417i
$134$		−	2.34328i		−	0.202428i
$135$		0			0
$136$	8.58977	−	9.33416i	0.736567	−	0.800398i
$137$	22.1633			1.89354			0.946771	−	0.321908i	$-0.104324\pi$
$137$	22.1633			1.89354			0.946771	+	0.321908i	$0.104324\pi$
$138$		0			0
$139$	9.81865	+	9.81865i	0.832807	+	0.832807i	0.987900	−	0.155093i	$-0.0495676\pi$
$139$	9.81865	+	9.81865i	0.832807	+	0.832807i	−0.155093	+	0.987900i	$0.549568\pi$
$140$	−1.78234			−0.150635
$141$		0			0
$142$	9.79618	−	9.79618i	0.822077	−	0.822077i
$143$	−9.36825	+	9.36825i	−0.783413	+	0.783413i
$144$		0			0
$145$		−	0.850775i		−	0.0706530i
$146$	−1.17621	+	1.17621i	−0.0973438	+	0.0973438i
$147$		0			0
$148$	5.67851	+	5.67851i	0.466771	+	0.466771i
$149$	11.6461			0.954087			0.477044	−	0.878880i	$-0.341708\pi$
$149$	11.6461			0.954087			0.477044	+	0.878880i	$0.341708\pi$
$150$		0			0
$151$		−	2.82731i		−	0.230083i	−0.993361	−	0.115042i	$-0.963300\pi$
$151$		−	2.82731i		−	0.230083i	0.993361	−	0.115042i	$-0.0367002\pi$
$152$	−8.04088			−0.652201
$153$		0			0
$154$	10.0155			0.807068
$155$		−	9.44332i		−	0.758506i
$156$		0			0
$157$	1.36913			0.109268			0.0546342	−	0.998506i	$-0.482601\pi$
$157$	1.36913			0.109268			0.0546342	+	0.998506i	$0.482601\pi$
$158$	7.15096	+	7.15096i	0.568900	+	0.568900i
$159$		0			0
$160$	−2.75053	+	2.75053i	−0.217448	+	0.217448i
$161$		−	3.43306i		−	0.270563i
$162$		0			0
$163$	−8.54984	+	8.54984i	−0.669675	+	0.669675i	−0.957641	−	0.287966i	$-0.907021\pi$
$163$	−8.54984	+	8.54984i	−0.669675	+	0.669675i	0.287966	+	0.957641i	$0.407021\pi$
$164$	4.92219	−	4.92219i	0.384358	−	0.384358i
$165$		0			0
$166$	2.84790			0.221040
$167$	−4.16611	−	4.16611i	−0.322383	−	0.322383i	0.527297	−	0.849681i	$-0.323205\pi$
$167$	−4.16611	−	4.16611i	−0.322383	−	0.322383i	−0.849681	+	0.527297i	$0.823205\pi$
$168$		0			0
$169$	0.261831			0.0201408
$170$	4.64305	−	0.192827i	0.356106	−	0.0147892i
$171$		0			0
$172$			5.45290i			0.415780i
$173$	−1.46761	−	1.46761i	−0.111580	−	0.111580i	0.649112	−	0.760693i	$-0.275141\pi$
$173$	−1.46761	−	1.46761i	−0.111580	−	0.111580i	−0.760693	+	0.649112i	$0.775141\pi$
$174$		0			0
$175$	−1.72715	−	1.72715i	−0.130560	−	0.130560i
$176$	5.16596	−	5.16596i	0.389399	−	0.389399i
$177$		0			0
$178$			1.87515i			0.140548i
$179$		−	10.5373i		−	0.787597i	−0.919197	−	0.393799i	$-0.871161\pi$
$179$		−	10.5373i		−	0.787597i	0.919197	−	0.393799i	$-0.128839\pi$
$180$		0			0
$181$	−2.39758	+	2.39758i	−0.178210	+	0.178210i	−0.790575	−	0.612365i	$-0.790218\pi$
$181$	−2.39758	+	2.39758i	−0.178210	+	0.178210i	0.612365	+	0.790575i	$0.290218\pi$
$182$	−7.08901	−	7.08901i	−0.525472	−	0.525472i
$183$		0			0
$184$	−3.05766	−	3.05766i	−0.225414	−	0.225414i
$185$			11.0054i			0.809133i
$186$		0			0
$187$	14.9873	−	0.622424i	1.09598	−	0.0455162i
$188$	3.95995			0.288809
$189$		0			0
$190$	−2.08293	−	2.08293i	−0.151111	−	0.151111i
$191$	12.3426			0.893077			0.446538	−	0.894764i	$-0.352657\pi$
$191$	12.3426			0.893077			0.446538	+	0.894764i	$0.352657\pi$
$192$		0			0
$193$	8.45396	−	8.45396i	0.608529	−	0.608529i	−0.334032	−	0.942562i	$-0.608409\pi$
$193$	8.45396	−	8.45396i	0.608529	−	0.608529i	0.942562	+	0.334032i	$0.108409\pi$
$194$	9.77662	−	9.77662i	0.701920	−	0.701920i
$195$		0			0
$196$			0.754430i			0.0538878i
$197$	−0.864156	+	0.864156i	−0.0615686	+	0.0615686i	−0.737221	−	0.675652i	$-0.763862\pi$
$197$	−0.864156	+	0.864156i	−0.0615686	+	0.0615686i	0.675652	+	0.737221i	$0.263862\pi$
$198$		0			0
$199$	15.3689	+	15.3689i	1.08947	+	1.08947i	0.995583	+	0.0938906i	$0.0299304\pi$
$199$	15.3689	+	15.3689i	1.08947	+	1.08947i	0.0938906	+	0.995583i	$0.470070\pi$
$200$	−3.07658			−0.217547
$201$		0			0
$202$			4.71265i			0.331581i
$203$	2.07807			0.145852
$204$		0			0
$205$	9.53958			0.666273
$206$			9.11148i			0.634827i
$207$		0			0
$208$	−7.31300			−0.507065
$209$	−6.72345	−	6.72345i	−0.465071	−	0.465071i
$210$		0			0
$211$	−11.9397	+	11.9397i	−0.821965	+	0.821965i	−0.986390	−	0.164425i	$-0.947423\pi$
$211$	−11.9397	+	11.9397i	−0.821965	+	0.821965i	0.164425	+	0.986390i	$0.447423\pi$
$212$			9.44618i			0.648767i
$213$		0			0
$214$	−7.01384	+	7.01384i	−0.479456	+	0.479456i
$215$	−5.28407	+	5.28407i	−0.360371	+	0.360371i
$216$		0			0
$217$	23.0659			1.56582
$218$	11.4081	+	11.4081i	0.772653	+	0.772653i
$219$		0			0
$220$	−2.65470			−0.178980
$221$	−11.0486	−	10.1675i	−0.743212	−	0.683942i
$222$		0			0
$223$		−	9.61320i		−	0.643748i	−0.946783	−	0.321874i	$-0.895687\pi$
$223$		−	9.61320i		−	0.643748i	0.946783	−	0.321874i	$-0.104313\pi$
$224$	−6.71833	−	6.71833i	−0.448887	−	0.448887i
$225$		0			0
$226$	9.13308	+	9.13308i	0.607523	+	0.607523i
$227$	−1.25815	+	1.25815i	−0.0835064	+	0.0835064i	−0.747626	−	0.664120i	$-0.768806\pi$
$227$	−1.25815	+	1.25815i	−0.0835064	+	0.0835064i	0.664120	+	0.747626i	$0.268806\pi$
$228$		0			0
$229$		−	16.7429i		−	1.10640i	−0.833048	−	0.553201i	$-0.813406\pi$
$229$		−	16.7429i		−	1.10640i	0.833048	−	0.553201i	$-0.186594\pi$
$230$		−	1.58412i		−	0.104454i
$231$		0			0
$232$	1.85084	−	1.85084i	0.121513	−	0.121513i
$233$	−9.25323	−	9.25323i	−0.606199	−	0.606199i	0.335751	−	0.941951i	$-0.391010\pi$
$233$	−9.25323	−	9.25323i	−0.606199	−	0.606199i	−0.941951	+	0.335751i	$0.891010\pi$
$234$		0			0
$235$	3.83735	+	3.83735i	0.250321	+	0.250321i
$236$		−	1.02355i		−	0.0666275i
$237$		0			0
$238$	0.470992	+	11.3409i	0.0305299	+	0.735124i
$239$	23.9469			1.54900			0.774498	−	0.632577i	$-0.218003\pi$
$239$	23.9469			1.54900			0.774498	+	0.632577i	$0.218003\pi$
$240$		0			0
$241$	−12.2266	−	12.2266i	−0.787587	−	0.787587i	0.193511	−	0.981098i	$-0.438012\pi$
$241$	−12.2266	−	12.2266i	−0.787587	−	0.787587i	−0.981098	+	0.193511i	$0.938012\pi$
$242$	2.51970			0.161972
$243$		0			0
$244$	0.587032	−	0.587032i	0.0375809	−	0.0375809i
$245$	−0.731071	+	0.731071i	−0.0467064	+	0.0467064i
$246$		0			0
$247$			9.51781i			0.605604i
$248$	20.5437	−	20.5437i	1.30452	−	1.30452i
$249$		0			0
$250$	−0.796963	−	0.796963i	−0.0504044	−	0.0504044i
$251$	−18.2106			−1.14944			−0.574722	−	0.818349i	$-0.694890\pi$
$251$	−18.2106			−1.14944			−0.574722	+	0.818349i	$0.694890\pi$
$252$		0			0
$253$		−	5.11338i		−	0.321475i
$254$	2.83529			0.177902
$255$		0			0
$256$	−14.8981			−0.931128
$257$			2.58018i			0.160947i	0.996757	+	0.0804735i	$0.0256432\pi$
$257$			2.58018i			0.160947i	−0.996757	+	0.0804735i	$0.974357\pi$
$258$		0			0
$259$	−26.8814			−1.67033
$260$	1.87902	+	1.87902i	0.116532	+	0.116532i
$261$		0			0
$262$	−1.77109	+	1.77109i	−0.109418	+	0.109418i
$263$		−	9.58787i		−	0.591213i	−0.955310	−	0.295607i	$-0.904478\pi$
$263$		−	9.58787i		−	0.591213i	0.955310	−	0.295607i	$-0.0955218\pi$
$264$		0			0
$265$	−9.15372	+	9.15372i	−0.562308	+	0.562308i
$266$	5.08767	−	5.08767i	0.311945	−	0.311945i
$267$		0			0
$268$	−1.51710			−0.0926717
$269$	5.01049	+	5.01049i	0.305495	+	0.305495i	0.843159	−	0.537664i	$-0.180693\pi$
$269$	5.01049	+	5.01049i	0.305495	+	0.305495i	−0.537664	+	0.843159i	$0.680693\pi$
$270$		0			0
$271$	−13.7773			−0.836909			−0.418454	−	0.908238i	$-0.637428\pi$
$271$	−13.7773			−0.836909			−0.418454	+	0.908238i	$0.637428\pi$
$272$	6.09258	+	5.60670i	0.369417	+	0.339956i
$273$		0			0
$274$			24.9798i			1.50908i
$275$	−2.57251	−	2.57251i	−0.155128	−	0.155128i
$276$		0			0
$277$	3.19263	+	3.19263i	0.191827	+	0.191827i	0.796485	−	0.604658i	$-0.206690\pi$
$277$	3.19263	+	3.19263i	0.191827	+	0.191827i	−0.604658	+	0.796485i	$0.706690\pi$
$278$	−11.0664	+	11.0664i	−0.663717	+	0.663717i
$279$		0			0
$280$		−	7.51473i		−	0.449091i
$281$			3.44172i			0.205316i	0.994717	+	0.102658i	$0.0327347\pi$
$281$			3.44172i			0.205316i	−0.994717	+	0.102658i	$0.967265\pi$
$282$		0			0
$283$	16.6458	−	16.6458i	0.989493	−	0.989493i	−0.0104528	−	0.999945i	$-0.503327\pi$
$283$	16.6458	−	16.6458i	0.989493	−	0.989493i	0.999945	+	0.0104528i	$0.00332730\pi$
$284$	−6.34231	−	6.34231i	−0.376347	−	0.376347i
$285$		0			0
$286$	−10.5587	−	10.5587i	−0.624351	−	0.624351i
$287$			23.3010i			1.37542i
$288$		0			0
$289$	1.40960	+	16.9415i	0.0829174	+	0.996556i
$290$	0.958888			0.0563079
$291$		0			0
$292$	0.761510	+	0.761510i	0.0445640	+	0.0445640i
$293$	−15.5924			−0.910918			−0.455459	−	0.890257i	$-0.650525\pi$
$293$	−15.5924			−0.910918			−0.455459	+	0.890257i	$0.650525\pi$
$294$		0			0
$295$	0.991860	−	0.991860i	0.0577483	−	0.0577483i
$296$	−23.9419	+	23.9419i	−1.39160	+	1.39160i
$297$		0			0
$298$			13.1261i			0.760372i
$299$	−3.61928	+	3.61928i	−0.209309	+	0.209309i
$300$		0			0
$301$	−12.9067	−	12.9067i	−0.743928	−	0.743928i
$302$	3.18660			0.183368
$303$		0			0
$304$		−	5.24843i		−	0.301018i
$305$	1.13771			0.0651453
$306$		0			0
$307$	21.6549			1.23591			0.617955	−	0.786214i	$-0.287962\pi$
$307$	21.6549			1.23591			0.617955	+	0.786214i	$0.287962\pi$
$308$		−	6.48428i		−	0.369476i
$309$		0			0
$310$	10.6433			0.604501
$311$	6.26814	+	6.26814i	0.355434	+	0.355434i	0.862127	−	0.506693i	$-0.169132\pi$
$311$	6.26814	+	6.26814i	0.355434	+	0.355434i	−0.506693	+	0.862127i	$0.669132\pi$
$312$		0			0
$313$	−12.1015	+	12.1015i	−0.684016	+	0.684016i	−0.960903	−	0.276887i	$-0.910697\pi$
$313$	−12.1015	+	12.1015i	−0.684016	+	0.684016i	0.276887	+	0.960903i	$0.410697\pi$
$314$			1.54311i			0.0870828i
$315$		0			0
$316$	4.62972	−	4.62972i	0.260442	−	0.260442i
$317$	−7.30027	+	7.30027i	−0.410024	+	0.410024i	−0.881747	−	0.471723i	$-0.843632\pi$
$317$	−7.30027	+	7.30027i	−0.410024	+	0.410024i	0.471723	+	0.881747i	$0.343632\pi$
$318$		0			0
$319$	3.09519			0.173297
$320$	−5.93999	−	5.93999i	−0.332056	−	0.332056i
$321$		0			0
$322$	3.86932			0.215629
$323$	7.29708	−	7.92944i	0.406020	−	0.441206i
$324$		0			0
$325$			3.64168i			0.202004i
$326$	−9.63632	−	9.63632i	−0.533706	−	0.533706i
$327$		0			0
$328$	20.7531	+	20.7531i	1.14590	+	1.14590i
$329$	−9.37296	+	9.37296i	−0.516748	+	0.516748i
$330$		0			0
$331$		−	6.56727i		−	0.360970i	−0.983578	−	0.180485i	$-0.942233\pi$
$331$		−	6.56727i		−	0.360970i	0.983578	−	0.180485i	$-0.0577667\pi$
$332$		−	1.84381i		−	0.101192i
$333$		0			0
$334$	4.69553	−	4.69553i	0.256928	−	0.256928i
$335$	−1.47013	−	1.47013i	−0.0803217	−	0.0803217i
$336$		0			0
$337$	−21.3377	−	21.3377i	−1.16234	−	1.16234i	−0.983962	−	0.178379i	$-0.942915\pi$
$337$	−21.3377	−	21.3377i	−1.16234	−	1.16234i	−0.178379	−	0.983962i	$-0.557085\pi$
$338$			0.295103i			0.0160515i
$339$		0			0
$340$	−0.124841	−	3.00604i	−0.00677047	−	0.163025i
$341$	34.3555			1.86046
$342$		0			0
$343$	−13.8758	−	13.8758i	−0.749220	−	0.749220i
$344$	−22.9907			−1.23957
$345$		0			0
$346$	1.65411	−	1.65411i	0.0889254	−	0.0889254i
$347$	−4.97815	+	4.97815i	−0.267241	+	0.267241i	−0.827988	−	0.560746i	$-0.810514\pi$
$347$	−4.97815	+	4.97815i	−0.267241	+	0.267241i	0.560746	+	0.827988i	$0.310514\pi$
$348$		0			0
$349$		−	35.4396i		−	1.89704i	−0.316723	−	0.948518i	$-0.602583\pi$
$349$		−	35.4396i		−	1.89704i	0.316723	−	0.948518i	$-0.397417\pi$
$350$	1.94663	−	1.94663i	0.104052	−	0.104052i
$351$		0			0
$352$	−10.0066	−	10.0066i	−0.533355	−	0.533355i
$353$	8.54669			0.454895			0.227447	−	0.973790i	$-0.426962\pi$
$353$	8.54669			0.454895			0.227447	+	0.973790i	$0.426962\pi$
$354$		0			0
$355$		−	12.2919i		−	0.652386i
$356$	1.21402			0.0643430
$357$		0			0
$358$	11.8764			0.627686
$359$		−	20.2839i		−	1.07054i	−0.844681	−	0.535271i	$-0.820210\pi$
$359$		−	20.2839i		−	1.07054i	0.844681	−	0.535271i	$-0.179790\pi$
$360$		0			0
$361$	12.1692			0.640485
$362$	−2.70225	−	2.70225i	−0.142027	−	0.142027i
$363$		0			0
$364$	−4.58962	+	4.58962i	−0.240561	+	0.240561i
$365$			1.47586i			0.0772503i
$366$		0			0
$367$	−8.99600	+	8.99600i	−0.469587	+	0.469587i	−0.901781	−	0.432193i	$-0.857740\pi$
$367$	−8.99600	+	8.99600i	−0.469587	+	0.469587i	0.432193	+	0.901781i	$0.357740\pi$
$368$	1.99579	−	1.99579i	0.104038	−	0.104038i
$369$		0			0
$370$	−12.4039			−0.644849
$371$	−22.3585	−	22.3585i	−1.16080	−	1.16080i
$372$		0			0
$373$	−11.1454			−0.577086			−0.288543	−	0.957467i	$-0.593171\pi$
$373$	−11.1454			−0.577086			−0.288543	+	0.957467i	$0.593171\pi$
$374$	0.701519	+	16.8918i	0.0362747	+	0.873453i
$375$		0			0
$376$			16.6961i			0.861034i
$377$	−2.19079	−	2.19079i	−0.112832	−	0.112832i
$378$		0			0
$379$	8.96691	+	8.96691i	0.460599	+	0.460599i	0.898852	−	0.438253i	$-0.144402\pi$
$379$	8.96691	+	8.96691i	0.460599	+	0.460599i	−0.438253	+	0.898852i	$0.644402\pi$
$380$	−1.34854	+	1.34854i	−0.0691787	+	0.0691787i
$381$		0			0
$382$			13.9110i			0.711749i
$383$		−	17.3523i		−	0.886661i	−0.896358	−	0.443331i	$-0.853797\pi$
$383$		−	17.3523i		−	0.886661i	0.896358	−	0.443331i	$-0.146203\pi$
$384$		0			0
$385$	6.28351	−	6.28351i	0.320237	−	0.320237i
$386$	9.52825	+	9.52825i	0.484975	+	0.484975i
$387$		0			0
$388$	−6.32965	−	6.32965i	−0.321339	−	0.321339i
$389$			19.4510i			0.986205i	0.869971	+	0.493103i	$0.164137\pi$
$389$			19.4510i			0.986205i	−0.869971	+	0.493103i	$0.835863\pi$
$390$		0			0
$391$	5.79010	−	0.240464i	0.292818	−	0.0121608i
$392$	−3.18085			−0.160657
$393$		0			0
$394$	−0.973970	−	0.973970i	−0.0490679	−	0.0490679i
$395$	8.97276			0.451468
$396$		0			0
$397$	−3.36574	+	3.36574i	−0.168922	+	0.168922i	−0.786505	−	0.617584i	$-0.788112\pi$
$397$	−3.36574	+	3.36574i	−0.168922	+	0.168922i	0.617584	+	0.786505i	$0.288112\pi$
$398$	−17.3219	+	17.3219i	−0.868270	+	0.868270i
$399$		0			0
$400$		−	2.00814i		−	0.100407i
$401$	−17.1148	+	17.1148i	−0.854672	+	0.854672i	−0.990704	−	0.136032i	$-0.956565\pi$
$401$	−17.1148	+	17.1148i	−0.854672	+	0.854672i	0.136032	+	0.990704i	$0.456565\pi$
$402$		0			0
$403$	−24.3171	−	24.3171i	−1.21132	−	1.21132i
$404$	3.05110			0.151798
$405$		0			0
$406$			2.34214i			0.116239i
$407$	−40.0385			−1.98463
$408$		0			0
$409$	18.2463			0.902221			0.451111	−	0.892468i	$-0.351028\pi$
$409$	18.2463			0.902221			0.451111	+	0.892468i	$0.351028\pi$
$410$			10.7518i			0.530995i
$411$		0			0
$412$	5.89901			0.290624
$413$	2.42268	+	2.42268i	0.119212	+	0.119212i
$414$		0			0
$415$	1.78672	−	1.78672i	0.0877066	−	0.0877066i
$416$			14.1655i			0.694522i
$417$		0			0
$418$	7.57784	−	7.57784i	0.370644	−	0.370644i
$419$	−1.23229	+	1.23229i	−0.0602015	+	0.0602015i	−0.736567	−	0.676365i	$-0.763554\pi$
$419$	−1.23229	+	1.23229i	−0.0602015	+	0.0602015i	0.676365	+	0.736567i	$0.263554\pi$
$420$		0			0
$421$	−37.0251			−1.80449			−0.902247	−	0.431220i	$-0.858083\pi$
$421$	−37.0251			−1.80449			−0.902247	+	0.431220i	$0.858083\pi$
$422$	−13.4570	−	13.4570i	−0.655076	−	0.655076i
$423$		0			0
$424$	−39.8273			−1.93418
$425$	2.79199	−	3.03394i	0.135431	−	0.147168i
$426$		0			0
$427$			2.77894i			0.134482i
$428$	4.54095	+	4.54095i	0.219495	+	0.219495i
$429$		0			0
$430$	−5.95555	−	5.95555i	−0.287202	−	0.287202i
$431$	−21.4877	+	21.4877i	−1.03503	+	1.03503i	−0.0356645	+	0.999364i	$0.511355\pi$
$431$	−21.4877	+	21.4877i	−1.03503	+	1.03503i	−0.999364	+	0.0356645i	$0.988645\pi$
$432$		0			0
$433$			15.8246i			0.760483i	0.924887	+	0.380242i	$0.124159\pi$
$433$			15.8246i			0.760483i	−0.924887	+	0.380242i	$0.875841\pi$
$434$			25.9970i			1.24790i
$435$		0			0
$436$	7.38590	−	7.38590i	0.353720	−	0.353720i
$437$	−2.59751	−	2.59751i	−0.124256	−	0.124256i
$438$		0			0
$439$	−2.94661	−	2.94661i	−0.140634	−	0.140634i	0.633285	−	0.773919i	$-0.281706\pi$
$439$	−2.94661	−	2.94661i	−0.140634	−	0.140634i	−0.773919	+	0.633285i	$0.781706\pi$
$440$		−	11.1928i		−	0.533597i
$441$		0			0
$442$	11.4596	−	12.4527i	0.545077	−	0.592313i
$443$	−15.7201			−0.746884			−0.373442	−	0.927654i	$-0.621823\pi$
$443$	−15.7201			−0.746884			−0.373442	+	0.927654i	$0.621823\pi$
$444$		0			0
$445$	1.17643	+	1.17643i	0.0557683	+	0.0557683i
$446$	10.8348			0.513043
$447$		0			0
$448$	14.5088	−	14.5088i	0.685476	−	0.685476i
$449$	11.7004	−	11.7004i	0.552176	−	0.552176i	−0.374892	−	0.927068i	$-0.622320\pi$
$449$	11.7004	−	11.7004i	0.552176	−	0.552176i	0.927068	+	0.374892i	$0.122320\pi$
$450$		0			0
$451$			34.7057i			1.63423i
$452$	5.91300	−	5.91300i	0.278124	−	0.278124i
$453$		0			0
$454$	−1.41803	−	1.41803i	−0.0665515	−	0.0665515i
$455$	−8.89503			−0.417005
$456$		0			0
$457$			1.42830i			0.0668131i	0.999442	+	0.0334066i	$0.0106356\pi$
$457$			1.42830i			0.0668131i	−0.999442	+	0.0334066i	$0.989364\pi$
$458$	18.8705			0.881761
$459$		0			0
$460$	−1.02560			−0.0478191
$461$			11.1662i			0.520062i	0.965600	+	0.260031i	$0.0837327\pi$
$461$			11.1662i			0.520062i	−0.965600	+	0.260031i	$0.916267\pi$
$462$		0			0
$463$	−29.2204			−1.35799			−0.678994	−	0.734144i	$-0.737584\pi$
$463$	−29.2204			−1.35799			−0.678994	+	0.734144i	$0.737584\pi$
$464$	1.20807	+	1.20807i	0.0560835	+	0.0560835i
$465$		0			0
$466$	10.4291	−	10.4291i	0.483119	−	0.483119i
$467$			10.9388i			0.506187i	0.967442	+	0.253093i	$0.0814480\pi$
$467$			10.9388i			0.506187i	−0.967442	+	0.253093i	$0.918552\pi$
$468$		0			0
$469$	3.59088	−	3.59088i	0.165811	−	0.165811i
$470$	−4.32498	+	4.32498i	−0.199497	+	0.199497i
$471$		0			0
$472$	4.31552			0.198638
$473$	−19.2239	−	19.2239i	−0.883914	−	0.883914i
$474$		0			0
$475$	−2.61358			−0.119919
$476$	7.34243	−	0.304933i	0.336540	−	0.0139766i
$477$		0			0
$478$			26.9900i			1.23449i
$479$	12.1620	+	12.1620i	0.555695	+	0.555695i	0.928079	−	0.372384i	$-0.121460\pi$
$479$	12.1620	+	12.1620i	0.555695	+	0.555695i	−0.372384	+	0.928079i	$0.621460\pi$
$480$		0			0
$481$	28.3395	+	28.3395i	1.29217	+	1.29217i
$482$	13.7803	−	13.7803i	0.627678	−	0.627678i
$483$		0			0
$484$		−	1.63132i		−	0.0741509i
$485$		−	12.2673i		−	0.557031i
$486$		0			0
$487$	−18.2749	+	18.2749i	−0.828113	+	0.828113i	−0.987256	−	0.159143i	$-0.949127\pi$
$487$	−18.2749	+	18.2749i	−0.828113	+	0.828113i	0.159143	+	0.987256i	$0.449127\pi$
$488$	2.47506	+	2.47506i	0.112041	+	0.112041i
$489$		0			0
$490$	−0.823973	−	0.823973i	−0.0372233	−	0.0372233i
$491$			12.2373i			0.552261i	0.961120	+	0.276131i	$0.0890523\pi$
$491$			12.2373i			0.552261i	−0.961120	+	0.276131i	$0.910948\pi$
$492$		0			0
$493$	0.145556	+	3.50481i	0.00655550	+	0.157849i
$494$	−10.7273			−0.482644
$495$		0			0
$496$	13.4092	+	13.4092i	0.602092	+	0.602092i
$497$	30.0237			1.34675
$498$		0			0
$499$	4.53684	−	4.53684i	0.203097	−	0.203097i	−0.598229	−	0.801325i	$-0.704129\pi$
$499$	4.53684	−	4.53684i	0.203097	−	0.203097i	0.801325	+	0.598229i	$0.204129\pi$
$500$	−0.515975	+	0.515975i	−0.0230751	+	0.0230751i
$501$		0			0
$502$		−	20.5248i		−	0.916065i
$503$	−15.0825	+	15.0825i	−0.672497	+	0.672497i	−0.958291	−	0.285794i	$-0.907743\pi$
$503$	−15.0825	+	15.0825i	−0.672497	+	0.672497i	0.285794	+	0.958291i	$0.407743\pi$
$504$		0			0
$505$	2.95663	+	2.95663i	0.131568	+	0.131568i
$506$	5.76317			0.256204
$507$		0			0
$508$		−	1.83565i		−	0.0814436i
$509$	−14.2265			−0.630577			−0.315289	−	0.948996i	$-0.602101\pi$
$509$	−14.2265			−0.630577			−0.315289	+	0.948996i	$0.602101\pi$
$510$		0			0
$511$	−3.60489			−0.159471
$512$		−	20.1677i		−	0.891296i
$513$		0			0
$514$	−2.90805			−0.128269
$515$	5.71637	+	5.71637i	0.251893	+	0.251893i
$516$		0			0
$517$	−13.9606	+	13.9606i	−0.613985	+	0.613985i
$518$		−	30.2973i		−	1.33119i
$519$		0			0
$520$	−7.92236	+	7.92236i	−0.347419	+	0.347419i
$521$	17.3636	−	17.3636i	0.760714	−	0.760714i	−0.215738	−	0.976451i	$-0.569216\pi$
$521$	17.3636	−	17.3636i	0.760714	−	0.760714i	0.976451	+	0.215738i	$0.0692156\pi$
$522$		0			0
$523$	39.8642			1.74314			0.871570	−	0.490271i	$-0.163102\pi$
$523$	39.8642			1.74314			0.871570	+	0.490271i	$0.163102\pi$
$524$	1.14665	+	1.14665i	0.0500917	+	0.0500917i
$525$		0			0
$526$	10.8063			0.471175
$527$	1.61562	+	38.9023i	0.0703775	+	1.69461i
$528$		0			0
$529$			21.0245i			0.914110i
$530$	−10.3169	−	10.3169i	−0.448139	−	0.448139i
$531$		0			0
$532$	−3.29390	−	3.29390i	−0.142809	−	0.142809i
$533$	24.5650	−	24.5650i	1.06403	−	1.06403i
$534$		0			0
$535$			8.80071i			0.380488i
$536$		−	6.39644i		−	0.276284i
$537$		0			0
$538$	−5.64720	+	5.64720i	−0.243468	+	0.243468i
$539$	−2.65969	−	2.65969i	−0.114561	−	0.114561i
$540$		0			0
$541$	16.1805	+	16.1805i	0.695654	+	0.695654i	0.963470	−	0.267816i	$-0.0863020\pi$
$541$	16.1805	+	16.1805i	0.695654	+	0.695654i	−0.267816	+	0.963470i	$0.586302\pi$
$542$		−	15.5280i		−	0.666985i
$543$		0			0
$544$	10.8604	−	11.8015i	0.465634	−	0.505986i
$545$	14.3144			0.613163
$546$		0			0
$547$	10.9849	+	10.9849i	0.469682	+	0.469682i	0.901812	−	0.432130i	$-0.142238\pi$
$547$	10.9849	+	10.9849i	0.469682	+	0.469682i	−0.432130	+	0.901812i	$0.642238\pi$
$548$	16.1726			0.690858
$549$		0			0
$550$	2.89941	−	2.89941i	0.123631	−	0.123631i
$551$	1.57230	−	1.57230i	0.0669822	−	0.0669822i
$552$		0			0
$553$			21.9165i			0.931985i
$554$	−3.59834	+	3.59834i	−0.152879	+	0.152879i
$555$		0			0
$556$	7.16467	+	7.16467i	0.303849	+	0.303849i
$557$	0.980081			0.0415274			0.0207637	−	0.999784i	$-0.493390\pi$
$557$	0.980081			0.0415274			0.0207637	+	0.999784i	$0.493390\pi$
$558$		0			0
$559$			27.2136i			1.15101i
$560$	4.90501			0.207274
$561$		0			0
$562$	−3.87908			−0.163629
$563$			28.8837i			1.21730i	0.793437	+	0.608652i	$0.208289\pi$
$563$			28.8837i			1.21730i	−0.793437	+	0.608652i	$0.791711\pi$
$564$		0			0
$565$	11.4598			0.482119
$566$	18.7611	+	18.7611i	0.788589	+	0.788589i
$567$		0			0
$568$	26.7406	−	26.7406i	1.12201	−	1.12201i
$569$		−	18.2893i		−	0.766729i	−0.923597	−	0.383365i	$-0.874765\pi$
$569$		−	18.2893i		−	0.766729i	0.923597	−	0.383365i	$-0.125235\pi$
$570$		0			0
$571$	−7.35702	+	7.35702i	−0.307882	+	0.307882i	−0.844087	−	0.536206i	$-0.819857\pi$
$571$	−7.35702	+	7.35702i	−0.307882	+	0.307882i	0.536206	+	0.844087i	$0.319857\pi$
$572$	−6.83601	+	6.83601i	−0.285828	+	0.285828i
$573$		0			0
$574$	−26.2620			−1.09616
$575$	−0.993850	−	0.993850i	−0.0414464	−	0.0414464i
$576$		0			0
$577$	−28.3066			−1.17842			−0.589209	−	0.807980i	$-0.700561\pi$
$577$	−28.3066			−1.17842			−0.589209	+	0.807980i	$0.700561\pi$
$578$	−19.0943	+	1.58872i	−0.794219	+	0.0660821i
$579$		0			0
$580$		−	0.620810i		−	0.0257777i
$581$	4.36417	+	4.36417i	0.181056	+	0.181056i
$582$		0			0
$583$	−33.3019	−	33.3019i	−1.37922	−	1.37922i
$584$	−3.21070	+	3.21070i	−0.132860	+	0.132860i
$585$		0			0
$586$		−	17.5738i		−	0.725968i
$587$		−	2.68137i		−	0.110672i	−0.998468	−	0.0553360i	$-0.982377\pi$
$587$		−	2.68137i		−	0.110672i	0.998468	−	0.0553360i	$-0.0176230\pi$
$588$		0			0
$589$	17.4520	−	17.4520i	0.719097	−	0.719097i
$590$	1.11790	+	1.11790i	0.0460233	+	0.0460233i
$591$		0			0
$592$	−15.6273	−	15.6273i	−0.642279	−	0.642279i
$593$		−	15.3155i		−	0.628934i	−0.949268	−	0.314467i	$-0.898174\pi$
$593$		−	15.3155i		−	0.628934i	0.949268	−	0.314467i	$-0.101826\pi$
$594$		0			0
$595$	7.41059	+	6.81961i	0.303805	+	0.279577i
$596$	8.49817			0.348098
$597$		0			0
$598$	−4.07921	−	4.07921i	−0.166811	−	0.166811i
$599$	−43.5243			−1.77836			−0.889178	−	0.457561i	$-0.848723\pi$
$599$	−43.5243			−1.77836			−0.889178	+	0.457561i	$0.848723\pi$
$600$		0			0
$601$	21.7299	−	21.7299i	0.886381	−	0.886381i	−0.107792	−	0.994173i	$-0.534378\pi$
$601$	21.7299	−	21.7299i	0.886381	−	0.886381i	0.994173	+	0.107792i	$0.0343782\pi$
$602$	14.5468	−	14.5468i	0.592883	−	0.592883i
$603$		0			0
$604$		−	2.06309i		−	0.0839459i
$605$	1.58081	−	1.58081i	0.0642692	−	0.0642692i
$606$		0			0
$607$	−10.3997	−	10.3997i	−0.422112	−	0.422112i	0.463818	−	0.885930i	$-0.346479\pi$
$607$	−10.3997	−	10.3997i	−0.422112	−	0.422112i	−0.885930	+	0.463818i	$0.846479\pi$
$608$	−10.1664			−0.412301
$609$		0			0
$610$			1.28229i			0.0519184i
$611$	19.7628			0.799516
$612$		0			0
$613$	23.6535			0.955354			0.477677	−	0.878535i	$-0.341479\pi$
$613$	23.6535			0.955354			0.477677	+	0.878535i	$0.341479\pi$
$614$			24.4067i			0.984974i
$615$		0			0
$616$	27.3392			1.10153
$617$	−7.10492	−	7.10492i	−0.286033	−	0.286033i	0.549476	−	0.835509i	$-0.314827\pi$
$617$	−7.10492	−	7.10492i	−0.286033	−	0.286033i	−0.835509	+	0.549476i	$0.814827\pi$
$618$		0			0
$619$	−24.3145	+	24.3145i	−0.977281	+	0.977281i	−0.999748	−	0.0224668i	$-0.992848\pi$
$619$	−24.3145	+	24.3145i	−0.977281	+	0.977281i	0.0224668	+	0.999748i	$0.492848\pi$
$620$		−	6.89079i		−	0.276741i
$621$		0			0
$622$	−7.06467	+	7.06467i	−0.283268	+	0.283268i
$623$	−2.87351	+	2.87351i	−0.115125	+	0.115125i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−13.6393	−	13.6393i	−0.545136	−	0.545136i
$627$		0			0
$628$	0.999052			0.0398665
$629$	−1.88287	−	45.3373i	−0.0750749	−	1.80772i
$630$		0			0
$631$		−	8.25061i		−	0.328451i	−0.986423	−	0.164226i	$-0.947487\pi$
$631$		−	8.25061i		−	0.328451i	0.986423	−	0.164226i	$-0.0525125\pi$
$632$	19.5200	+	19.5200i	0.776462	+	0.776462i
$633$		0			0
$634$	−8.22796	−	8.22796i	−0.326774	−	0.326774i
$635$	1.77881	−	1.77881i	0.0705900	−	0.0705900i
$636$		0			0
$637$			3.76510i			0.149179i
$638$			3.48851i			0.138111i
$639$		0			0
$640$	1.19377	−	1.19377i	0.0471879	−	0.0471879i
$641$	−12.1786	−	12.1786i	−0.481024	−	0.481024i	0.424434	−	0.905459i	$-0.360473\pi$
$641$	−12.1786	−	12.1786i	−0.481024	−	0.481024i	−0.905459	+	0.424434i	$0.860473\pi$
$642$		0			0
$643$	−8.88071	−	8.88071i	−0.350221	−	0.350221i	0.509971	−	0.860192i	$-0.329656\pi$
$643$	−8.88071	−	8.88071i	−0.350221	−	0.350221i	−0.860192	+	0.509971i	$0.829656\pi$
$644$		−	2.50510i		−	0.0987149i
$645$		0			0
$646$	8.93708	+	8.22436i	0.351625	+	0.323583i
$647$	3.62337			0.142449			0.0712247	−	0.997460i	$-0.477309\pi$
$647$	3.62337			0.142449			0.0712247	+	0.997460i	$0.477309\pi$
$648$		0			0
$649$	3.60846	+	3.60846i	0.141645	+	0.141645i
$650$	−4.10445			−0.160990
$651$		0			0
$652$	−6.23881	+	6.23881i	−0.244331	+	0.244331i
$653$	−6.89142	+	6.89142i	−0.269682	+	0.269682i	−0.828972	−	0.559290i	$-0.811074\pi$
$653$	−6.89142	+	6.89142i	−0.269682	+	0.269682i	0.559290	+	0.828972i	$0.311074\pi$
$654$		0			0
$655$			2.22230i			0.0868325i
$656$	−13.5459	+	13.5459i	−0.528879	+	0.528879i
$657$		0			0
$658$	−10.5640	−	10.5640i	−0.411829	−	0.411829i
$659$	7.19930			0.280445			0.140222	−	0.990120i	$-0.455218\pi$
$659$	7.19930			0.280445			0.140222	+	0.990120i	$0.455218\pi$
$660$		0			0
$661$			11.0362i			0.429258i	0.976696	+	0.214629i	$0.0688542\pi$
$661$			11.0362i			0.429258i	−0.976696	+	0.214629i	$0.931146\pi$
$662$	7.40181			0.287680
$663$		0			0
$664$	7.77391			0.301686
$665$		−	6.38383i		−	0.247554i
$666$		0			0
$667$	1.19578			0.0463007
$668$	−3.04001	−	3.04001i	−0.117621	−	0.117621i
$669$		0			0
$670$	1.65695	−	1.65695i	0.0640135	−	0.0640135i
$671$			4.13909i			0.159788i
$672$		0			0
$673$	20.8675	−	20.8675i	0.804382	−	0.804382i	−0.179395	−	0.983777i	$-0.557414\pi$
$673$	20.8675	−	20.8675i	0.804382	−	0.804382i	0.983777	+	0.179395i	$0.0574141\pi$
$674$	24.0493	−	24.0493i	0.926343	−	0.926343i
$675$		0			0
$676$	0.191058			0.00734837
$677$	−0.394531	−	0.394531i	−0.0151631	−	0.0151631i	0.699485	−	0.714648i	$-0.253413\pi$
$677$	−0.394531	−	0.394531i	−0.0151631	−	0.0151631i	−0.714648	+	0.699485i	$0.753413\pi$
$678$		0			0
$679$	29.9637			1.14990
$680$	12.6741	−	0.526360i	0.486031	−	0.0201850i
$681$		0			0
$682$			38.7213i			1.48272i
$683$	25.5664	+	25.5664i	0.978272	+	0.978272i	0.999769	−	0.0214974i	$-0.00684335\pi$
$683$	25.5664	+	25.5664i	0.978272	+	0.978272i	−0.0214974	+	0.999769i	$0.506843\pi$
$684$		0			0
$685$	15.6718	+	15.6718i	0.598790	+	0.598790i
$686$	15.6390	−	15.6390i	0.597101	−	0.597101i
$687$		0			0
$688$		−	15.0064i		−	0.572115i
$689$			47.1427i			1.79599i
$690$		0			0
$691$	28.1588	−	28.1588i	1.07121	−	1.07121i	0.0739501	−	0.997262i	$-0.476439\pi$
$691$	28.1588	−	28.1588i	1.07121	−	1.07121i	0.997262	−	0.0739501i	$-0.0235606\pi$
$692$	−1.07091	−	1.07091i	−0.0407100	−	0.0407100i
$693$		0			0
$694$	−5.61075	−	5.61075i	−0.212981	−	0.212981i
$695$			13.8857i			0.526714i
$696$		0			0
$697$	−39.2988	+	1.63209i	−1.48855	+	0.0618198i
$698$	39.9431			1.51187
$699$		0			0
$700$	−1.26030	−	1.26030i	−0.0476349	−	0.0476349i
$701$	−20.0299			−0.756520			−0.378260	−	0.925699i	$-0.623478\pi$
$701$	−20.0299			−0.756520			−0.378260	+	0.925699i	$0.623478\pi$
$702$		0			0
$703$	−20.3388	+	20.3388i	−0.767094	+	0.767094i
$704$	21.6101	−	21.6101i	0.814463	−	0.814463i
$705$		0			0
$706$			9.63277i			0.362534i
$707$	−7.22175	+	7.22175i	−0.271602	+	0.271602i
$708$		0			0
$709$	−6.86493	−	6.86493i	−0.257818	−	0.257818i	0.566348	−	0.824166i	$-0.308356\pi$
$709$	−6.86493	−	6.86493i	−0.257818	−	0.257818i	−0.824166	+	0.566348i	$0.808356\pi$
$710$	13.8539			0.519927
$711$		0			0
$712$			5.11859i			0.191827i
$713$	13.2727			0.497068
$714$		0			0
$715$	−13.2487			−0.495474
$716$		−	7.68909i		−	0.287355i
$717$		0			0
$718$	22.8615			0.853182
$719$	−14.7143	−	14.7143i	−0.548750	−	0.548750i	0.377329	−	0.926079i	$-0.376843\pi$
$719$	−14.7143	−	14.7143i	−0.548750	−	0.548750i	−0.926079	+	0.377329i	$0.876843\pi$
$720$		0			0
$721$	−13.9626	+	13.9626i	−0.519994	+	0.519994i
$722$			13.7156i			0.510443i
$723$		0			0
$724$	−1.74951	+	1.74951i	−0.0650200	+	0.0650200i
$725$	0.601589	−	0.601589i	0.0223425	−	0.0223425i
$726$		0			0
$727$	39.1557			1.45220			0.726102	−	0.687587i	$-0.241330\pi$
$727$	39.1557			1.45220			0.726102	+	0.687587i	$0.241330\pi$
$728$	−19.3509	−	19.3509i	−0.717191	−	0.717191i
$729$		0			0
$730$	−1.66341			−0.0615656
$731$	20.8640	−	22.6720i	0.771682	−	0.838556i
$732$		0			0
$733$		−	12.9215i		−	0.477265i	−0.971110	−	0.238633i	$-0.923301\pi$
$733$		−	12.9215i		−	0.477265i	0.971110	−	0.238633i	$-0.0766992\pi$
$734$	−10.1392	−	10.1392i	−0.374244	−	0.374244i
$735$		0			0
$736$	−3.86591	−	3.86591i	−0.142499	−	0.142499i
$737$	5.34844	−	5.34844i	0.197012	−	0.197012i
$738$		0			0
$739$		−	37.9866i		−	1.39736i	−0.715434	−	0.698680i	$-0.753771\pi$
$739$		−	37.9866i		−	1.39736i	0.715434	−	0.698680i	$-0.246229\pi$
$740$			8.03063i			0.295212i
$741$		0			0
$742$	25.1998	−	25.1998i	0.925112	−	0.925112i
$743$	−8.65513	−	8.65513i	−0.317526	−	0.317526i	0.530290	−	0.847816i	$-0.322083\pi$
$743$	−8.65513	−	8.65513i	−0.317526	−	0.317526i	−0.847816	+	0.530290i	$0.822083\pi$
$744$		0			0
$745$	8.23505	+	8.23505i	0.301709	+	0.301709i
$746$		−	12.5617i		−	0.459916i
$747$		0			0
$748$	10.9362	−	0.454183i	0.399867	−	0.0166066i
$749$	−21.4963			−0.785457
$750$		0			0
$751$	−9.97504	−	9.97504i	−0.363995	−	0.363995i	0.501287	−	0.865281i	$-0.332860\pi$
$751$	−9.97504	−	9.97504i	−0.363995	−	0.363995i	−0.865281	+	0.501287i	$0.832860\pi$
$752$	−10.8978			−0.397403
$753$		0			0
$754$	2.46919	−	2.46919i	0.0899227	−	0.0899227i
$755$	1.99921	−	1.99921i	0.0727588	−	0.0727588i
$756$		0			0
$757$		−	0.782070i		−	0.0284248i	−0.999899	−	0.0142124i	$-0.995476\pi$
$757$		−	0.782070i		−	0.0284248i	0.999899	−	0.0142124i	$-0.00452410\pi$
$758$	−10.1064	+	10.1064i	−0.367081	+	0.367081i
$759$		0			0
$760$	−5.68576	−	5.68576i	−0.206244	−	0.206244i
$761$	−2.86350			−0.103802			−0.0519009	−	0.998652i	$-0.516528\pi$
$761$	−2.86350			−0.103802			−0.0519009	+	0.998652i	$0.516528\pi$
$762$		0			0
$763$			34.9639i			1.26578i
$764$	9.00636			0.325839
$765$		0			0
$766$	19.5574			0.706636
$767$		−	5.10819i		−	0.184446i
$768$		0			0
$769$	38.6633			1.39423			0.697117	−	0.716957i	$-0.254466\pi$
$769$	38.6633			1.39423			0.697117	+	0.716957i	$0.254466\pi$
$770$	7.08200	+	7.08200i	0.255217	+	0.255217i
$771$		0			0
$772$	6.16885	−	6.16885i	0.222022	−	0.222022i
$773$			37.9989i			1.36672i	0.730080	+	0.683362i	$0.239483\pi$
$773$			37.9989i			1.36672i	−0.730080	+	0.683362i	$0.760517\pi$
$774$		0			0
$775$	6.67744	−	6.67744i	0.239861	−	0.239861i
$776$	26.6872	−	26.6872i	0.958016	−	0.958016i
$777$		0			0
$778$	−21.9228			−0.785969
$779$	17.6299	+	17.6299i	0.631656	+	0.631656i
$780$		0			0
$781$	44.7188			1.60017
$782$	0.271021	+	6.52589i	0.00969171	+	0.233365i
$783$		0			0
$784$		−	2.07620i		−	0.0741499i
$785$	0.968120	+	0.968120i	0.0345537	+	0.0345537i
$786$		0			0
$787$	−25.0127	−	25.0127i	−0.891606	−	0.891606i	0.103068	−	0.994674i	$-0.467134\pi$
$787$	−25.0127	−	25.0127i	−0.891606	−	0.891606i	−0.994674	+	0.103068i	$0.967134\pi$
$788$	−0.630574	+	0.630574i	−0.0224633	+	0.0224633i
$789$		0			0
$790$			10.1130i			0.359804i
$791$			27.9914i			0.995259i
$792$		0			0
$793$	2.92968	−	2.92968i	0.104036	−	0.104036i
$794$	−3.79344	−	3.79344i	−0.134624	−	0.134624i
$795$		0			0
$796$	11.2147	+	11.2147i	0.397494	+	0.397494i
$797$		−	26.7826i		−	0.948688i	−0.880340	−	0.474344i	$-0.842685\pi$
$797$		−	26.7826i		−	0.948688i	0.880340	−	0.474344i	$-0.157315\pi$
$798$		0			0
$799$	−16.4647	−	15.1516i	−0.582479	−	0.536027i
$800$	−3.88983			−0.137526
$801$		0			0
$802$	−19.2897	−	19.2897i	−0.681142	−	0.681142i
$803$	−5.36931			−0.189479
$804$		0			0
$805$	2.42754	−	2.42754i	0.0855596	−	0.0855596i
$806$	27.4072	−	27.4072i	0.965378	−	0.965378i
$807$		0			0
$808$			12.8641i			0.452558i
$809$	38.1898	−	38.1898i	1.34268	−	1.34268i	0.449303	−	0.893379i	$-0.351672\pi$
$809$	38.1898	−	38.1898i	1.34268	−	1.34268i	0.893379	−	0.449303i	$-0.148328\pi$
$810$		0			0
$811$	−37.3327	−	37.3327i	−1.31093	−	1.31093i	−0.920730	−	0.390200i	$-0.872406\pi$
$811$	−37.3327	−	37.3327i	−1.31093	−	1.31093i	−0.390200	−	0.920730i	$-0.627594\pi$
$812$	1.51637			0.0532141
$813$		0			0
$814$		−	45.1264i		−	1.58168i
$815$	−12.0913			−0.423540
$816$		0			0
$817$	−19.5308			−0.683295
$818$			20.5650i			0.719037i
$819$		0			0
$820$	6.96103			0.243090
$821$	8.42042	+	8.42042i	0.293875	+	0.293875i	0.838609	−	0.544734i	$-0.183369\pi$
$821$	8.42042	+	8.42042i	0.293875	+	0.293875i	−0.544734	+	0.838609i	$0.683369\pi$
$822$		0			0
$823$	−27.9601	+	27.9601i	−0.974627	+	0.974627i	−0.999686	−	0.0250590i	$-0.992023\pi$
$823$	−27.9601	+	27.9601i	−0.974627	+	0.974627i	0.0250590	+	0.999686i	$0.492023\pi$
$824$			24.8716i			0.866443i
$825$		0			0
$826$	−2.73054	+	2.73054i	−0.0950078	+	0.0950078i
$827$	12.9612	−	12.9612i	0.450704	−	0.450704i	−0.444884	−	0.895588i	$-0.646755\pi$
$827$	12.9612	−	12.9612i	0.450704	−	0.450704i	0.895588	+	0.444884i	$0.146755\pi$
$828$		0			0
$829$	−39.4065			−1.36864			−0.684322	−	0.729180i	$-0.739902\pi$
$829$	−39.4065			−1.36864			−0.684322	+	0.729180i	$0.739902\pi$
$830$	2.01377	+	2.01377i	0.0698990	+	0.0698990i
$831$		0			0
$832$	−30.5916			−1.06057
$833$	2.88661	−	3.13676i	0.100015	−	0.108682i
$834$		0			0
$835$		−	5.89177i		−	0.203893i
$836$	−4.90610	−	4.90610i	−0.169681	−	0.169681i
$837$		0			0
$838$	−1.38889	−	1.38889i	−0.0479783	−	0.0479783i
$839$	14.5709	−	14.5709i	0.503043	−	0.503043i	−0.409339	−	0.912382i	$-0.634241\pi$
$839$	14.5709	−	14.5709i	0.503043	−	0.503043i	0.912382	+	0.409339i	$0.134241\pi$
$840$		0			0
$841$		−	28.2762i		−	0.975041i
$842$		−	41.7301i		−	1.43812i
$843$		0			0
$844$	−8.71241	+	8.71241i	−0.299894	+	0.299894i
$845$	0.185142	+	0.185142i	0.00636909	+	0.00636909i
$846$		0			0
$847$	3.86123	+	3.86123i	0.132673	+	0.132673i
$848$		−	25.9960i		−	0.892706i
$849$		0			0
$850$	3.41948	+	3.14678i	0.117287	+	0.107934i
$851$	−15.4683			−0.530245
$852$		0			0
$853$	5.82880	+	5.82880i	0.199574	+	0.199574i	0.799817	−	0.600243i	$-0.204930\pi$
$853$	5.82880	+	5.82880i	0.199574	+	0.199574i	−0.600243	+	0.799817i	$0.704930\pi$
$854$	−3.13207			−0.107177
$855$		0			0
$856$	−19.1457	+	19.1457i	−0.654386	+	0.654386i
$857$	−19.6053	+	19.6053i	−0.669703	+	0.669703i	−0.957647	−	0.287944i	$-0.907028\pi$
$857$	−19.6053	+	19.6053i	−0.669703	+	0.669703i	0.287944	+	0.957647i	$0.407028\pi$
$858$		0			0
$859$		−	7.00671i		−	0.239066i	−0.992830	−	0.119533i	$-0.961860\pi$
$859$		−	7.00671i		−	0.239066i	0.992830	−	0.119533i	$-0.0381397\pi$
$860$	−3.85578	+	3.85578i	−0.131481	+	0.131481i
$861$		0			0
$862$	−24.2183	−	24.2183i	−0.824879	−	0.824879i
$863$	−29.4176			−1.00139			−0.500693	−	0.865625i	$-0.666921\pi$
$863$	−29.4176			−1.00139			−0.500693	+	0.865625i	$0.666921\pi$
$864$		0			0
$865$		−	2.07551i		−	0.0705696i
$866$	−17.8356			−0.606077
$867$		0			0
$868$	16.8312			0.571287
$869$			32.6436i			1.10736i
$870$		0			0
$871$	−7.57133			−0.256545
$872$	31.1406	+	31.1406i	1.05455	+	1.05455i
$873$		0			0
$874$	2.92759	−	2.92759i	0.0990271	−	0.0990271i
$875$		−	2.44256i		−	0.0825737i
$876$		0			0
$877$	−36.4433	+	36.4433i	−1.23060	+	1.23060i	−0.266872	+	0.963732i	$0.585990\pi$
$877$	−36.4433	+	36.4433i	−1.23060	+	1.23060i	−0.963732	+	0.266872i	$0.914010\pi$
$878$	3.32106	−	3.32106i	0.112080	−	0.112080i
$879$		0			0
$880$	7.30577			0.246277
$881$	33.0055	+	33.0055i	1.11198	+	1.11198i	0.992882	+	0.119102i	$0.0380016\pi$
$881$	33.0055	+	33.0055i	1.11198	+	1.11198i	0.119102	+	0.992882i	$0.461998\pi$
$882$		0			0
$883$	9.95880			0.335140			0.167570	−	0.985860i	$-0.446408\pi$
$883$	9.95880			0.335140			0.167570	+	0.985860i	$0.446408\pi$
$884$	−8.06219	−	7.41924i	−0.271161	−	0.249536i
$885$		0			0
$886$		−	17.7177i		−	0.595239i
$887$	−13.3201	−	13.3201i	−0.447246	−	0.447246i	0.447192	−	0.894438i	$-0.352424\pi$
$887$	−13.3201	−	13.3201i	−0.447246	−	0.447246i	−0.894438	+	0.447192i	$0.852424\pi$
$888$		0			0
$889$	4.34486	+	4.34486i	0.145722	+	0.145722i
$890$	−1.32593	+	1.32593i	−0.0444453	+	0.0444453i
$891$		0			0
$892$		−	7.01475i		−	0.234871i
$893$			14.1834i			0.474631i
$894$		0			0
$895$	7.45102	−	7.45102i	0.249060	−	0.249060i
$896$	2.91586	+	2.91586i	0.0974119	+	0.0974119i
$897$		0			0
$898$	13.1872	+	13.1872i	0.440064	+	0.440064i
$899$			8.03414i			0.267954i
$900$		0			0
$901$	36.1432	−	39.2753i	1.20410	−	1.30845i
$902$	−39.1160			−1.30242
$903$		0			0
$904$	24.9306	+	24.9306i	0.829178	+	0.829178i
$905$	−3.39068			−0.112710
$906$		0			0
$907$	18.9094	−	18.9094i	0.627876	−	0.627876i	−0.319658	−	0.947533i	$-0.603568\pi$
$907$	18.9094	−	18.9094i	0.627876	−	0.627876i	0.947533	+	0.319658i	$0.103568\pi$
$908$	−0.918072	+	0.918072i	−0.0304673	+	0.0304673i
$909$		0			0
$910$		−	10.0254i		−	0.332338i
$911$	−7.34196	+	7.34196i	−0.243250	+	0.243250i	−0.818193	−	0.574943i	$-0.805024\pi$
$911$	−7.34196	+	7.34196i	−0.243250	+	0.243250i	0.574943	+	0.818193i	$0.305024\pi$
$912$		0			0
$913$	6.50023	+	6.50023i	0.215126	+	0.215126i
$914$	−1.60980			−0.0532476
$915$		0			0
$916$		−	12.2173i		−	0.403670i
$917$	−5.42811			−0.179252
$918$		0			0
$919$	20.4602			0.674919			0.337460	−	0.941340i	$-0.390432\pi$
$919$	20.4602			0.674919			0.337460	+	0.941340i	$0.390432\pi$
$920$		−	4.32418i		−	0.142564i
$921$		0			0
$922$	−12.5852			−0.414470
$923$	−31.6523	−	31.6523i	−1.04185	−	1.04185i
$924$		0			0
$925$	−7.78199	+	7.78199i	−0.255870	+	0.255870i
$926$		−	32.9337i		−	1.08227i
$927$		0			0
$928$	2.34008	−	2.34008i	0.0768169	−	0.0768169i
$929$	−3.22981	+	3.22981i	−0.105966	+	0.105966i	−0.758102	−	0.652136i	$-0.773873\pi$
$929$	−3.22981	+	3.22981i	−0.105966	+	0.105966i	0.652136	+	0.758102i	$0.273873\pi$
$930$		0			0
$931$	−2.70215			−0.0885595
$932$	−6.75208	−	6.75208i	−0.221172	−	0.221172i
$933$		0			0
$934$	−12.3288			−0.403412
$935$	11.0377	+	10.1575i	0.360972	+	0.332185i
$936$		0			0
$937$		−	2.90874i		−	0.0950243i	−0.998871	−	0.0475122i	$-0.984871\pi$
$937$		−	2.90874i		−	0.0950243i	0.998871	−	0.0475122i	$-0.0151293\pi$
$938$	4.04720	+	4.04720i	0.132146	+	0.132146i
$939$		0			0
$940$	2.80011	+	2.80011i	0.0913296	+	0.0913296i
$941$	10.8860	−	10.8860i	0.354872	−	0.354872i	−0.507046	−	0.861919i	$-0.669263\pi$
$941$	10.8860	−	10.8860i	0.354872	−	0.354872i	0.861919	+	0.507046i	$0.169263\pi$
$942$		0			0
$943$			13.4080i			0.436626i
$944$			2.81682i			0.0916797i
$945$		0			0
$946$	21.6667	−	21.6667i	0.704447	−	0.704447i
$947$	−16.9623	−	16.9623i	−0.551200	−	0.551200i	0.375587	−	0.926787i	$-0.377441\pi$
$947$	−16.9623	−	16.9623i	−0.551200	−	0.551200i	−0.926787	+	0.375587i	$0.877441\pi$
$948$		0			0
$949$	3.80043	+	3.80043i	0.123367	+	0.123367i
$950$		−	2.94570i		−	0.0955712i
$951$		0			0
$952$	1.28567	+	30.9574i	0.0416687	+	1.00333i
$953$	9.31030			0.301590			0.150795	−	0.988565i	$-0.451817\pi$
$953$	9.31030			0.301590			0.150795	+	0.988565i	$0.451817\pi$
$954$		0			0
$955$	8.72751	+	8.72751i	0.282416	+	0.282416i
$956$	17.4740			0.565151
$957$		0			0
$958$	−13.7075	+	13.7075i	−0.442868	+	0.442868i
$959$	−38.2795	+	38.2795i	−1.23611	+	1.23611i
$960$		0			0
$961$			58.1763i			1.87666i
$962$	−31.9408	+	31.9408i	−1.02981	+	1.02981i
$963$		0			0
$964$	−8.92177	−	8.92177i	−0.287351	−	0.287351i
$965$	11.9557			0.384868
$966$		0			0
$967$			1.29315i			0.0415848i	0.999784	+	0.0207924i	$0.00661890\pi$
$967$			1.29315i			0.0415848i	−0.999784	+	0.0207924i	$0.993381\pi$
$968$	6.87802			0.221068
$969$		0			0
$970$	13.8262			0.443933
$971$		−	39.3251i		−	1.26200i	−0.775781	−	0.631002i	$-0.782644\pi$
$971$		−	39.3251i		−	1.26200i	0.775781	−	0.631002i	$-0.217356\pi$
$972$		0			0
$973$	−33.9166			−1.08732
$974$	−20.5972	−	20.5972i	−0.659976	−	0.659976i
$975$		0			0
$976$	−1.61552	+	1.61552i	−0.0517115	+	0.0517115i
$977$		−	53.3750i		−	1.70762i	−0.520586	−	0.853809i	$-0.674286\pi$
$977$		−	53.3750i		−	1.70762i	0.520586	−	0.853809i	$-0.325714\pi$
$978$		0			0
$979$	−4.27996	+	4.27996i	−0.136788	+	0.136788i
$980$	−0.533462	+	0.533462i	−0.0170408	+	0.0170408i
$981$		0			0
$982$	−13.7924			−0.440132
$983$	36.1157	+	36.1157i	1.15191	+	1.15191i	0.986169	+	0.165742i	$0.0530020\pi$
$983$	36.1157	+	36.1157i	1.15191	+	1.15191i	0.165742	+	0.986169i	$0.446998\pi$
$984$		0			0
$985$	−1.22210			−0.0389394
$986$	−3.95019	+	0.164052i	−0.125800	+	0.00522449i
$987$		0			0
$988$			6.94514i			0.220954i
$989$	−7.42685	−	7.42685i	−0.236160	−	0.236160i
$990$		0			0
$991$	7.48752	+	7.48752i	0.237849	+	0.237849i	0.815959	−	0.578110i	$-0.196210\pi$
$991$	7.48752	+	7.48752i	0.237849	+	0.237849i	−0.578110	+	0.815959i	$0.696210\pi$
$992$	25.9741	−	25.9741i	0.824679	−	0.824679i
$993$		0			0
$994$			33.8390i			1.07331i
$995$			21.7349i			0.689043i
$996$		0			0
$997$	−2.43619	+	2.43619i	−0.0771550	+	0.0771550i	−0.744631	−	0.667476i	$-0.767375\pi$
$997$	−2.43619	+	2.43619i	−0.0771550	+	0.0771550i	0.667476	+	0.744631i	$0.267375\pi$
$998$	5.11336	+	5.11336i	0.161861	+	0.161861i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.k.b.676.4		12
3.2	odd	2		85.2.e.a.81.3	yes	12
12.11	even	2		1360.2.bt.d.81.6		12
15.2	even	4		425.2.j.c.149.4		12
15.8	even	4		425.2.j.b.149.3		12
15.14	odd	2		425.2.e.f.251.4		12
17.4	even	4	inner	765.2.k.b.361.3		12
51.2	odd	8		1445.2.a.o.1.4		6
51.8	odd	8		1445.2.d.g.866.6		12
51.26	odd	8		1445.2.d.g.866.5		12
51.32	odd	8		1445.2.a.n.1.4		6
51.38	odd	4		85.2.e.a.21.4	✓	12
204.191	even	4		1360.2.bt.d.1041.6		12
255.38	even	4		425.2.j.c.174.4		12
255.89	odd	4		425.2.e.f.276.3		12
255.104	odd	8		7225.2.a.z.1.3		6
255.134	odd	8		7225.2.a.bb.1.3		6
255.242	even	4		425.2.j.b.174.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.4	✓	12	51.38	odd	4
85.2.e.a.81.3	yes	12	3.2	odd	2
425.2.e.f.251.4		12	15.14	odd	2
425.2.e.f.276.3		12	255.89	odd	4
425.2.j.b.149.3		12	15.8	even	4
425.2.j.b.174.3		12	255.242	even	4
425.2.j.c.149.4		12	15.2	even	4
425.2.j.c.174.4		12	255.38	even	4
765.2.k.b.361.3		12	17.4	even	4	inner
765.2.k.b.676.4		12	1.1	even	1	trivial
1360.2.bt.d.81.6		12	12.11	even	2
1360.2.bt.d.1041.6		12	204.191	even	4
1445.2.a.n.1.4		6	51.32	odd	8
1445.2.a.o.1.4		6	51.2	odd	8
1445.2.d.g.866.5		12	51.26	odd	8
1445.2.d.g.866.6		12	51.8	odd	8
7225.2.a.z.1.3		6	255.104	odd	8
7225.2.a.bb.1.3		6	255.134	odd	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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.12708i q^{2} +0.729699 q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.72715 + 1.72715i) q^{7} +3.07658i q^{8} +(-0.796963 + 0.796963i) q^{10} +(-2.57251 + 2.57251i) q^{11} +3.64168 q^{13} +(-1.94663 - 1.94663i) q^{14} -2.00814 q^{16} +(-3.03394 - 2.79199i) q^{17} +2.61358i q^{19} +(0.515975 + 0.515975i) q^{20} +(-2.89941 - 2.89941i) q^{22} +(-0.993850 + 0.993850i) q^{23} +1.00000i q^{25} +4.10445i q^{26} +(-1.26030 + 1.26030i) q^{28} +(-0.601589 - 0.601589i) q^{29} +(-6.67744 - 6.67744i) q^{31} +3.88983i q^{32} +(3.14678 - 3.41948i) q^{34} -2.44256 q^{35} +(7.78199 + 7.78199i) q^{37} -2.94570 q^{38} +(-2.17547 + 2.17547i) q^{40} +(6.74550 - 6.74550i) q^{41} +7.47280i q^{43} +(-1.87716 + 1.87716i) q^{44} +(-1.12014 - 1.12014i) q^{46} +5.42683 q^{47} +1.03389i q^{49} -1.12708 q^{50} +2.65733 q^{52} +12.9453i q^{53} -3.63808 q^{55} +(-5.31372 - 5.31372i) q^{56} +(0.678037 - 0.678037i) q^{58} -1.40270i q^{59} +(0.804485 - 0.804485i) q^{61} +(7.52598 - 7.52598i) q^{62} -8.40042 q^{64} +(2.57506 + 2.57506i) q^{65} -2.07908 q^{67} +(-2.21387 - 2.03731i) q^{68} -2.75295i q^{70} +(-8.69168 - 8.69168i) q^{71} +(1.04359 + 1.04359i) q^{73} +(-8.77090 + 8.77090i) q^{74} +1.90713i q^{76} -8.88623i q^{77} +(6.34470 - 6.34470i) q^{79} +(-1.41997 - 1.41997i) q^{80} +(7.60269 + 7.60269i) q^{82} -2.52680i q^{83} +(-0.171086 - 4.11955i) q^{85} -8.42242 q^{86} +(-7.91453 - 7.91453i) q^{88} +1.66373 q^{89} +(-6.28973 + 6.28973i) q^{91} +(-0.725212 + 0.725212i) q^{92} +6.11645i q^{94} +(-1.84808 + 1.84808i) q^{95} +(-8.67432 - 8.67432i) q^{97} -1.16527 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 4 q^{10} + 4 q^{11} + 4 q^{14} + 4 q^{16} - 12 q^{17} + 8 q^{20} + 20 q^{22} - 12 q^{23} + 4 q^{28} + 12 q^{29} - 12 q^{34} - 16 q^{35} + 12 q^{37} - 24 q^{38} - 8 q^{40} + 24 q^{41} - 8 q^{44}+ \cdots - 44 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 - 4 * q^10 + 4 * q^11 + 4 * q^14 + 4 * q^16 - 12 * q^17 + 8 * q^20 + 20 * q^22 - 12 * q^23 + 4 * q^28 + 12 * q^29 - 12 * q^34 - 16 * q^35 + 12 * q^37 - 24 * q^38 - 8 * q^40 + 24 * q^41 - 8 * q^44 - 24 * q^46 + 48 * q^47 - 4 * q^50 - 56 * q^52 - 40 * q^56 + 36 * q^58 + 40 * q^61 - 40 * q^62 + 28 * q^64 - 4 * q^65 - 8 * q^67 + 40 * q^68 - 28 * q^71 - 48 * q^73 - 28 * q^74 - 8 * q^79 - 16 * q^80 + 40 * q^82 - 4 * q^85 + 96 * q^86 - 72 * q^88 - 24 * q^89 - 36 * q^91 + 16 * q^92 + 8 * q^95 + 4 * q^97 - 44 * q^98

Introduction

L-functions

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