LMFDB - Embedded newform 840.2.bt.a.433.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(97,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.97"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bt (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.4
Character	$\chi$	$=$	840.433
Dual form			840.2.bt.a.97.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.503511 - 2.17864i) q^{5} +(0.918874 + 2.48106i) q^{7} -1.00000i q^{9} -5.08039 q^{11} +(3.79668 - 3.79668i) q^{13} +(1.89657 + 1.18450i) q^{15} +(-2.83651 - 2.83651i) q^{17} +3.66311 q^{19} +(-2.40412 - 1.10463i) q^{21} +(-0.591502 - 0.591502i) q^{23} +(-4.49295 + 2.19394i) q^{25} +(0.707107 + 0.707107i) q^{27} -1.05509i q^{29} -8.77757i q^{31} +(3.59238 - 3.59238i) q^{33} +(4.94268 - 3.25114i) q^{35} +(4.95648 - 4.95648i) q^{37} +5.36932i q^{39} +2.91664i q^{41} +(-6.86314 - 6.86314i) q^{43} +(-2.17864 + 0.503511i) q^{45} +(-1.97475 - 1.97475i) q^{47} +(-5.31134 + 4.55957i) q^{49} +4.01144 q^{51} +(-5.54555 - 5.54555i) q^{53} +(2.55803 + 11.0684i) q^{55} +(-2.59021 + 2.59021i) q^{57} +1.49914 q^{59} -12.3856i q^{61} +(2.48106 - 0.918874i) q^{63} +(-10.1833 - 6.35993i) q^{65} +(4.30496 - 4.30496i) q^{67} +0.836510 q^{69} +9.87966 q^{71} +(7.02795 - 7.02795i) q^{73} +(1.62565 - 4.72835i) q^{75} +(-4.66824 - 12.6048i) q^{77} +11.9511i q^{79} -1.00000 q^{81} +(5.33465 - 5.33465i) q^{83} +(-4.75153 + 7.60796i) q^{85} +(0.746061 + 0.746061i) q^{87} +1.75715 q^{89} +(12.9085 + 5.93113i) q^{91} +(6.20668 + 6.20668i) q^{93} +(-1.84442 - 7.98061i) q^{95} +(-3.26203 - 3.26203i) q^{97} +5.08039i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 + 20 * q^17 + 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 - 4 * q^45 - 24 * q^47 + 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 + 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−0.503511	−	2.17864i	−0.225177	−	0.974318i
$5$	−0.503511	−	2.17864i	−0.225177	−	0.974318i
$6$		0			0
$7$	0.918874	+	2.48106i	0.347302	+	0.937753i
$7$	0.918874	+	2.48106i	0.347302	+	0.937753i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−5.08039			−1.53180			−0.765898	−	0.642962i	$-0.777705\pi$
$11$	−5.08039			−1.53180			−0.765898	+	0.642962i	$0.777705\pi$
$12$		0			0
$13$	3.79668	−	3.79668i	1.05301	−	1.05301i	0.0544954	−	0.998514i	$-0.482645\pi$
$13$	3.79668	−	3.79668i	1.05301	−	1.05301i	0.998514	−	0.0544954i	$-0.0173550\pi$
$14$		0			0
$15$	1.89657	+	1.18450i	0.489692	+	0.305835i
$16$		0			0
$17$	−2.83651	−	2.83651i	−0.687956	−	0.687956i	0.273824	−	0.961780i	$-0.411711\pi$
$17$	−2.83651	−	2.83651i	−0.687956	−	0.687956i	−0.961780	+	0.273824i	$0.911711\pi$
$18$		0			0
$19$	3.66311			0.840376			0.420188	−	0.907437i	$-0.361964\pi$
$19$	3.66311			0.840376			0.420188	+	0.907437i	$0.361964\pi$
$20$		0			0
$21$	−2.40412	−	1.10463i	−0.524622	−	0.241051i
$22$		0			0
$23$	−0.591502	−	0.591502i	−0.123337	−	0.123337i	0.642744	−	0.766081i	$-0.277796\pi$
$23$	−0.591502	−	0.591502i	−0.123337	−	0.123337i	−0.766081	+	0.642744i	$0.777796\pi$
$24$		0			0
$25$	−4.49295	+	2.19394i	−0.898591	+	0.438788i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	1.05509i		−	0.195925i	−0.995190	−	0.0979627i	$-0.968767\pi$
$29$		−	1.05509i		−	0.195925i	0.995190	−	0.0979627i	$-0.0312326\pi$
$30$		0			0
$31$		−	8.77757i		−	1.57650i	−0.615357	−	0.788249i	$-0.710988\pi$
$31$		−	8.77757i		−	1.57650i	0.615357	−	0.788249i	$-0.289012\pi$
$32$		0			0
$33$	3.59238	−	3.59238i	0.625353	−	0.625353i
$34$		0			0
$35$	4.94268	−	3.25114i	0.835465	−	0.549543i
$36$		0			0
$37$	4.95648	−	4.95648i	0.814840	−	0.814840i	−0.170515	−	0.985355i	$-0.554543\pi$
$37$	4.95648	−	4.95648i	0.814840	−	0.814840i	0.985355	+	0.170515i	$0.0545432\pi$
$38$		0			0
$39$			5.36932i			0.859779i
$40$		0			0
$41$			2.91664i			0.455502i	0.973719	+	0.227751i	$0.0731372\pi$
$41$			2.91664i			0.455502i	−0.973719	+	0.227751i	$0.926863\pi$
$42$		0			0
$43$	−6.86314	−	6.86314i	−1.04662	−	1.04662i	−0.998859	−	0.0477606i	$-0.984792\pi$
$43$	−6.86314	−	6.86314i	−1.04662	−	1.04662i	−0.0477606	−	0.998859i	$-0.515208\pi$
$44$		0			0
$45$	−2.17864	+	0.503511i	−0.324773	+	0.0750590i
$46$		0			0
$47$	−1.97475	−	1.97475i	−0.288047	−	0.288047i	0.548261	−	0.836307i	$-0.315290\pi$
$47$	−1.97475	−	1.97475i	−0.288047	−	0.288047i	−0.836307	+	0.548261i	$0.815290\pi$
$48$		0			0
$49$	−5.31134	+	4.55957i	−0.758763	+	0.651367i
$50$		0			0
$51$	4.01144			0.561713
$52$		0			0
$53$	−5.54555	−	5.54555i	−0.761740	−	0.761740i	0.214897	−	0.976637i	$-0.431058\pi$
$53$	−5.54555	−	5.54555i	−0.761740	−	0.761740i	−0.976637	+	0.214897i	$0.931058\pi$
$54$		0			0
$55$	2.55803	+	11.0684i	0.344925	+	1.49246i
$56$		0			0
$57$	−2.59021	+	2.59021i	−0.343082	+	0.343082i
$58$		0			0
$59$	1.49914			0.195172			0.0975859	−	0.995227i	$-0.468888\pi$
$59$	1.49914			0.195172			0.0975859	+	0.995227i	$0.468888\pi$
$60$		0			0
$61$		−	12.3856i		−	1.58581i	−0.609345	−	0.792905i	$-0.708568\pi$
$61$		−	12.3856i		−	1.58581i	0.609345	−	0.792905i	$-0.291432\pi$
$62$		0			0
$63$	2.48106	−	0.918874i	0.312584	−	0.115767i
$64$		0			0
$65$	−10.1833	−	6.35993i	−1.26308	−	0.788852i
$66$		0			0
$67$	4.30496	−	4.30496i	0.525935	−	0.525935i	−0.393423	−	0.919358i	$-0.628709\pi$
$67$	4.30496	−	4.30496i	0.525935	−	0.525935i	0.919358	+	0.393423i	$0.128709\pi$
$68$		0			0
$69$	0.836510			0.100704
$70$		0			0
$71$	9.87966			1.17250			0.586250	−	0.810130i	$-0.300604\pi$
$71$	9.87966			1.17250			0.586250	+	0.810130i	$0.300604\pi$
$72$		0			0
$73$	7.02795	−	7.02795i	0.822560	−	0.822560i	−0.163915	−	0.986474i	$-0.552412\pi$
$73$	7.02795	−	7.02795i	0.822560	−	0.822560i	0.986474	+	0.163915i	$0.0524123\pi$
$74$		0			0
$75$	1.62565	−	4.72835i	0.187714	−	0.545983i
$76$		0			0
$77$	−4.66824	−	12.6048i	−0.531996	−	1.43645i
$78$		0			0
$79$			11.9511i			1.34460i	0.740279	+	0.672300i	$0.234694\pi$
$79$			11.9511i			1.34460i	−0.740279	+	0.672300i	$0.765306\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	5.33465	−	5.33465i	0.585554	−	0.585554i	−0.350870	−	0.936424i	$-0.614114\pi$
$83$	5.33465	−	5.33465i	0.585554	−	0.585554i	0.936424	+	0.350870i	$0.114114\pi$
$84$		0			0
$85$	−4.75153	+	7.60796i	−0.515376	+	0.825199i
$86$		0			0
$87$	0.746061	+	0.746061i	0.0799862	+	0.0799862i
$88$		0			0
$89$	1.75715			0.186258			0.0931290	−	0.995654i	$-0.470313\pi$
$89$	1.75715			0.186258			0.0931290	+	0.995654i	$0.470313\pi$
$90$		0			0
$91$	12.9085	+	5.93113i	1.35318	+	0.621751i
$92$		0			0
$93$	6.20668	+	6.20668i	0.643603	+	0.643603i
$94$		0			0
$95$	−1.84442	−	7.98061i	−0.189233	−	0.818793i
$96$		0			0
$97$	−3.26203	−	3.26203i	−0.331209	−	0.331209i	0.521836	−	0.853046i	$-0.325247\pi$
$97$	−3.26203	−	3.26203i	−0.331209	−	0.331209i	−0.853046	+	0.521836i	$0.825247\pi$
$98$		0			0
$99$			5.08039i			0.510599i
$100$		0			0
$101$			5.83234i			0.580339i	0.956975	+	0.290170i	$0.0937117\pi$
$101$			5.83234i			0.580339i	−0.956975	+	0.290170i	$0.906288\pi$
$102$		0			0
$103$	−10.8302	+	10.8302i	−1.06713	+	1.06713i	−0.0695538	+	0.997578i	$0.522158\pi$
$103$	−10.8302	+	10.8302i	−1.06713	+	1.06713i	−0.997578	+	0.0695538i	$0.977842\pi$
$104$		0			0
$105$	−1.19610	+	5.79391i	−0.116727	+	0.565427i
$106$		0			0
$107$	7.42709	−	7.42709i	0.718003	−	0.718003i	−0.250193	−	0.968196i	$-0.580494\pi$
$107$	7.42709	−	7.42709i	0.718003	−	0.718003i	0.968196	+	0.250193i	$0.0804939\pi$
$108$		0			0
$109$			19.8285i			1.89922i	0.313428	+	0.949612i	$0.398523\pi$
$109$			19.8285i			1.89922i	−0.313428	+	0.949612i	$0.601477\pi$
$110$		0			0
$111$			7.00952i			0.665314i
$112$		0			0
$113$	−8.77932	−	8.77932i	−0.825889	−	0.825889i	0.161056	−	0.986945i	$-0.448510\pi$
$113$	−8.77932	−	8.77932i	−0.825889	−	0.825889i	−0.986945	+	0.161056i	$0.948510\pi$
$114$		0			0
$115$	−0.990842	+	1.58650i	−0.0923965	+	0.147942i
$116$		0			0
$117$	−3.79668	−	3.79668i	−0.351003	−	0.351003i
$118$		0			0
$119$	4.43117	−	9.64397i	0.406204	−	0.884061i
$120$		0			0
$121$	14.8104			1.34640
$122$		0			0
$123$	−2.06237	−	2.06237i	−0.185958	−	0.185958i
$124$		0			0
$125$	7.04206	+	8.68386i	0.629861	+	0.776708i
$126$		0			0
$127$	−10.2392	+	10.2392i	−0.908584	+	0.908584i	−0.996158	−	0.0875740i	$-0.972089\pi$
$127$	−10.2392	+	10.2392i	−0.908584	+	0.908584i	0.0875740	+	0.996158i	$0.472089\pi$
$128$		0			0
$129$	9.70595			0.854561
$130$		0			0
$131$			7.00093i			0.611674i	0.952084	+	0.305837i	$0.0989363\pi$
$131$			7.00093i			0.611674i	−0.952084	+	0.305837i	$0.901064\pi$
$132$		0			0
$133$	3.36594	+	9.08841i	0.291864	+	0.788065i
$134$		0			0
$135$	1.18450	−	1.89657i	0.101945	−	0.163231i
$136$		0			0
$137$	−7.58950	+	7.58950i	−0.648414	+	0.648414i	−0.952610	−	0.304195i	$-0.901612\pi$
$137$	−7.58950	+	7.58950i	−0.648414	+	0.648414i	0.304195	+	0.952610i	$0.401612\pi$
$138$		0			0
$139$	2.97723			0.252525			0.126262	−	0.991997i	$-0.459702\pi$
$139$	2.97723			0.252525			0.126262	+	0.991997i	$0.459702\pi$
$140$		0			0
$141$	2.79272			0.235189
$142$		0			0
$143$	−19.2886	+	19.2886i	−1.61300	+	1.61300i
$144$		0			0
$145$	−2.29866	+	0.531250i	−0.190894	+	0.0441179i
$146$		0			0
$147$	0.531583	−	6.97979i	0.0438442	−	0.575683i
$148$		0			0
$149$			0.823646i			0.0674757i	0.999431	+	0.0337379i	$0.0107411\pi$
$149$			0.823646i			0.0674757i	−0.999431	+	0.0337379i	$0.989259\pi$
$150$		0			0
$151$	−14.0056			−1.13976			−0.569878	−	0.821729i	$-0.693010\pi$
$151$	−14.0056			−1.13976			−0.569878	+	0.821729i	$0.693010\pi$
$152$		0			0
$153$	−2.83651	+	2.83651i	−0.229319	+	0.229319i
$154$		0			0
$155$	−19.1232	+	4.41960i	−1.53601	+	0.354991i
$156$		0			0
$157$	5.47815	+	5.47815i	0.437204	+	0.437204i	0.891070	−	0.453866i	$-0.149956\pi$
$157$	5.47815	+	5.47815i	0.437204	+	0.437204i	−0.453866	+	0.891070i	$0.649956\pi$
$158$		0			0
$159$	7.84259			0.621958
$160$		0			0
$161$	0.924037	−	2.01107i	0.0728243	−	0.158494i
$162$		0			0
$163$	−7.94626	−	7.94626i	−0.622399	−	0.622399i	0.323745	−	0.946144i	$-0.395058\pi$
$163$	−7.94626	−	7.94626i	−0.622399	−	0.622399i	−0.946144	+	0.323745i	$0.895058\pi$
$164$		0			0
$165$	−9.63531	−	6.01770i	−0.750108	−	0.468477i
$166$		0			0
$167$	−3.60896	−	3.60896i	−0.279270	−	0.279270i	0.553548	−	0.832817i	$-0.313274\pi$
$167$	−3.60896	−	3.60896i	−0.279270	−	0.279270i	−0.832817	+	0.553548i	$0.813274\pi$
$168$		0			0
$169$		−	15.8296i		−	1.21766i
$170$		0			0
$171$		−	3.66311i		−	0.280125i
$172$		0			0
$173$	−13.8617	+	13.8617i	−1.05389	+	1.05389i	−0.0554234	+	0.998463i	$0.517651\pi$
$173$	−13.8617	+	13.8617i	−1.05389	+	1.05389i	−0.998463	+	0.0554234i	$0.982349\pi$
$174$		0			0
$175$	−9.57176	−	9.13134i	−0.723557	−	0.690264i
$176$		0			0
$177$	−1.06005	+	1.06005i	−0.0796786	+	0.0796786i
$178$		0			0
$179$			5.59676i			0.418321i	0.977881	+	0.209161i	$0.0670732\pi$
$179$			5.59676i			0.418321i	−0.977881	+	0.209161i	$0.932927\pi$
$180$		0			0
$181$			5.12872i			0.381215i	0.981666	+	0.190607i	$0.0610458\pi$
$181$			5.12872i			0.381215i	−0.981666	+	0.190607i	$0.938954\pi$
$182$		0			0
$183$	8.75792	+	8.75792i	0.647404	+	0.647404i
$184$		0			0
$185$	−13.2940	−	8.30274i	−0.977396	−	0.610430i
$186$		0			0
$187$	14.4106	+	14.4106i	1.05381	+	1.05381i
$188$		0			0
$189$	−1.10463	+	2.40412i	−0.0803503	+	0.174874i
$190$		0			0
$191$	20.7696			1.50283			0.751417	−	0.659828i	$-0.229371\pi$
$191$	20.7696			1.50283			0.751417	+	0.659828i	$0.229371\pi$
$192$		0			0
$193$	8.70770	+	8.70770i	0.626794	+	0.626794i	0.947260	−	0.320466i	$-0.103840\pi$
$193$	8.70770	+	8.70770i	0.626794	+	0.626794i	−0.320466	+	0.947260i	$0.603840\pi$
$194$		0			0
$195$	11.6978	−	2.70351i	0.837698	−	0.193602i
$196$		0			0
$197$	16.5465	−	16.5465i	1.17889	−	1.17889i	0.198866	−	0.980027i	$-0.436274\pi$
$197$	16.5465	−	16.5465i	1.17889	−	1.17889i	0.980027	−	0.198866i	$-0.0637258\pi$
$198$		0			0
$199$	−18.7309			−1.32780			−0.663898	−	0.747823i	$-0.731099\pi$
$199$	−18.7309			−1.32780			−0.663898	+	0.747823i	$0.731099\pi$
$200$		0			0
$201$			6.08814i			0.429424i
$202$		0			0
$203$	2.61774	−	0.969495i	0.183730	−	0.0680452i
$204$		0			0
$205$	6.35430	−	1.46856i	0.443804	−	0.102569i
$206$		0			0
$207$	−0.591502	+	0.591502i	−0.0411122	+	0.0411122i
$208$		0			0
$209$	−18.6100			−1.28728
$210$		0			0
$211$	−3.46472			−0.238521			−0.119261	−	0.992863i	$-0.538052\pi$
$211$	−3.46472			−0.238521			−0.119261	+	0.992863i	$0.538052\pi$
$212$		0			0
$213$	−6.98598	+	6.98598i	−0.478671	+	0.478671i
$214$		0			0
$215$	−11.4967	+	18.4080i	−0.784065	+	1.25541i
$216$		0			0
$217$	21.7777	−	8.06548i	1.47837	−	0.547521i
$218$		0			0
$219$			9.93903i			0.671617i
$220$		0			0
$221$	−21.5387			−1.44885
$222$		0			0
$223$	4.32013	−	4.32013i	0.289298	−	0.289298i	−0.547505	−	0.836802i	$-0.684422\pi$
$223$	4.32013	−	4.32013i	0.289298	−	0.289298i	0.836802	+	0.547505i	$0.184422\pi$
$224$		0			0
$225$	2.19394	+	4.49295i	0.146263	+	0.299530i
$226$		0			0
$227$	5.66818	+	5.66818i	0.376211	+	0.376211i	0.869733	−	0.493522i	$-0.164291\pi$
$227$	5.66818	+	5.66818i	0.376211	+	0.376211i	−0.493522	+	0.869733i	$0.664291\pi$
$228$		0			0
$229$	12.7174			0.840391			0.420196	−	0.907434i	$-0.361961\pi$
$229$	12.7174			0.840391			0.420196	+	0.907434i	$0.361961\pi$
$230$		0			0
$231$	12.2139	+	5.61197i	0.803613	+	0.369241i
$232$		0			0
$233$	6.79433	+	6.79433i	0.445111	+	0.445111i	0.893726	−	0.448614i	$-0.148082\pi$
$233$	6.79433	+	6.79433i	0.445111	+	0.445111i	−0.448614	+	0.893726i	$0.648082\pi$
$234$		0			0
$235$	−3.30796	+	5.29658i	−0.215788	+	0.345511i
$236$		0			0
$237$	−8.45068	−	8.45068i	−0.548931	−	0.548931i
$238$		0			0
$239$			28.2489i			1.82727i	0.406538	+	0.913634i	$0.366736\pi$
$239$			28.2489i			1.82727i	−0.406538	+	0.913634i	$0.633264\pi$
$240$		0			0
$241$			6.78799i			0.437253i	0.975809	+	0.218626i	$0.0701576\pi$
$241$			6.78799i			0.437253i	−0.975809	+	0.218626i	$0.929842\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	12.6080	+	9.27571i	0.805494	+	0.592603i
$246$		0			0
$247$	13.9077	−	13.9077i	0.884923	−	0.884923i
$248$		0			0
$249$			7.54433i			0.478103i
$250$		0			0
$251$		−	18.7505i		−	1.18352i	−0.806113	−	0.591762i	$-0.798432\pi$
$251$		−	18.7505i		−	1.18352i	0.806113	−	0.591762i	$-0.201568\pi$
$252$		0			0
$253$	3.00506	+	3.00506i	0.188927	+	0.188927i
$254$		0			0
$255$	−2.01980	−	8.73948i	−0.126485	−	0.547287i
$256$		0			0
$257$	5.38224	+	5.38224i	0.335735	+	0.335735i	0.854759	−	0.519024i	$-0.173705\pi$
$257$	5.38224	+	5.38224i	0.335735	+	0.335735i	−0.519024	+	0.854759i	$0.673705\pi$
$258$		0			0
$259$	16.8517	+	7.74295i	1.04711	+	0.481124i
$260$		0			0
$261$	−1.05509			−0.0653084
$262$		0			0
$263$	−8.81499	−	8.81499i	−0.543555	−	0.543555i	0.381014	−	0.924569i	$-0.375575\pi$
$263$	−8.81499	−	8.81499i	−0.543555	−	0.543555i	−0.924569	+	0.381014i	$0.875575\pi$
$264$		0			0
$265$	−9.28951	+	14.8740i	−0.570650	+	0.913703i
$266$		0			0
$267$	−1.24250	+	1.24250i	−0.0760395	+	0.0760395i
$268$		0			0
$269$	21.3194			1.29987			0.649934	−	0.759991i	$-0.274797\pi$
$269$	21.3194			1.29987			0.649934	+	0.759991i	$0.274797\pi$
$270$		0			0
$271$		−	12.9351i		−	0.785753i	−0.919591	−	0.392877i	$-0.871480\pi$
$271$		−	12.9351i		−	0.785753i	0.919591	−	0.392877i	$-0.128520\pi$
$272$		0			0
$273$	−13.3216	+	4.93373i	−0.806260	+	0.298603i
$274$		0			0
$275$	22.8260	−	11.1461i	1.37646	−	0.672134i
$276$		0			0
$277$	−15.1831	+	15.1831i	−0.912266	+	0.912266i	−0.996450	−	0.0841838i	$-0.973172\pi$
$277$	−15.1831	+	15.1831i	−0.912266	+	0.912266i	0.0841838	+	0.996450i	$0.473172\pi$
$278$		0			0
$279$	−8.77757			−0.525499
$280$		0			0
$281$	20.8186			1.24193			0.620967	−	0.783836i	$-0.286740\pi$
$281$	20.8186			1.24193			0.620967	+	0.783836i	$0.286740\pi$
$282$		0			0
$283$	5.35026	−	5.35026i	0.318040	−	0.318040i	−0.529974	−	0.848014i	$-0.677798\pi$
$283$	5.35026	−	5.35026i	0.318040	−	0.318040i	0.848014	+	0.529974i	$0.177798\pi$
$284$		0			0
$285$	6.94734	+	4.33894i	0.411525	+	0.257017i
$286$		0			0
$287$	−7.23636	+	2.68002i	−0.427149	+	0.158197i
$288$		0			0
$289$		−	0.908384i		−	0.0534343i
$290$		0			0
$291$	4.61321			0.270431
$292$		0			0
$293$	18.0617	−	18.0617i	1.05517	−	1.05517i	0.0567868	−	0.998386i	$-0.481914\pi$
$293$	18.0617	−	18.0617i	1.05517	−	1.05517i	0.998386	−	0.0567868i	$-0.0180855\pi$
$294$		0			0
$295$	−0.754836	−	3.26610i	−0.0439482	−	0.190159i
$296$		0			0
$297$	−3.59238	−	3.59238i	−0.208451	−	0.208451i
$298$		0			0
$299$	−4.49149			−0.259749
$300$		0			0
$301$	10.7215	−	23.3342i	0.617978	−	1.34496i
$302$		0			0
$303$	−4.12409	−	4.12409i	−0.236923	−	0.236923i
$304$		0			0
$305$	−26.9837	+	6.23627i	−1.54508	+	0.357088i
$306$		0			0
$307$	−9.25219	−	9.25219i	−0.528051	−	0.528051i	0.391940	−	0.919991i	$-0.371804\pi$
$307$	−9.25219	−	9.25219i	−0.528051	−	0.528051i	−0.919991	+	0.391940i	$0.871804\pi$
$308$		0			0
$309$		−	15.3162i		−	0.871310i
$310$		0			0
$311$		−	20.0604i		−	1.13752i	−0.822503	−	0.568761i	$-0.807423\pi$
$311$		−	20.0604i		−	1.13752i	0.822503	−	0.568761i	$-0.192577\pi$
$312$		0			0
$313$	14.6085	−	14.6085i	0.825719	−	0.825719i	−0.161202	−	0.986921i	$-0.551537\pi$
$313$	14.6085	−	14.6085i	0.825719	−	0.825719i	0.986921	+	0.161202i	$0.0515371\pi$
$314$		0			0
$315$	−3.25114	−	4.94268i	−0.183181	−	0.278488i
$316$		0			0
$317$	22.5736	−	22.5736i	1.26786	−	1.26786i	0.320666	−	0.947192i	$-0.396093\pi$
$317$	22.5736	−	22.5736i	1.26786	−	1.26786i	0.947192	−	0.320666i	$-0.103907\pi$
$318$		0			0
$319$			5.36027i			0.300118i
$320$		0			0
$321$			10.5035i			0.586247i
$322$		0			0
$323$	−10.3905	−	10.3905i	−0.578141	−	0.578141i
$324$		0			0
$325$	−8.72861	+	25.3880i	−0.484176	+	1.40827i
$326$		0			0
$327$	−14.0209	−	14.0209i	−0.775355	−	0.775355i
$328$		0			0
$329$	3.08493	−	6.71402i	0.170078	−	0.370156i
$330$		0			0
$331$	−25.6086			−1.40758			−0.703788	−	0.710410i	$-0.748510\pi$
$331$	−25.6086			−1.40758			−0.703788	+	0.710410i	$0.748510\pi$
$332$		0			0
$333$	−4.95648	−	4.95648i	−0.271613	−	0.271613i
$334$		0			0
$335$	−11.5466	−	7.21137i	−0.630856	−	0.393999i
$336$		0			0
$337$	20.4201	−	20.4201i	1.11236	−	1.11236i	0.119524	−	0.992831i	$-0.461863\pi$
$337$	20.4201	−	20.4201i	1.11236	−	1.11236i	0.992831	−	0.119524i	$-0.0381369\pi$
$338$		0			0
$339$	12.4158			0.674335
$340$		0			0
$341$			44.5935i			2.41487i
$342$		0			0
$343$	−16.1930	−	8.98810i	−0.874341	−	0.485312i
$344$		0			0
$345$	−0.421192	−	1.82245i	−0.0226762	−	0.0981177i
$346$		0			0
$347$	−4.09932	+	4.09932i	−0.220063	+	0.220063i	−0.808525	−	0.588462i	$-0.799734\pi$
$347$	−4.09932	+	4.09932i	−0.220063	+	0.220063i	0.588462	+	0.808525i	$0.299734\pi$
$348$		0			0
$349$	−12.1807			−0.652020			−0.326010	−	0.945366i	$-0.605704\pi$
$349$	−12.1807			−0.652020			−0.326010	+	0.945366i	$0.605704\pi$
$350$		0			0
$351$	5.36932			0.286593
$352$		0			0
$353$	−2.45858	+	2.45858i	−0.130857	+	0.130857i	−0.769502	−	0.638645i	$-0.779495\pi$
$353$	−2.45858	+	2.45858i	−0.130857	+	0.130857i	0.638645	+	0.769502i	$0.279495\pi$
$354$		0			0
$355$	−4.97452	−	21.5242i	−0.264020	−	1.14239i
$356$		0			0
$357$	3.68600	+	9.95262i	0.195084	+	0.526749i
$358$		0			0
$359$			14.6393i			0.772634i	0.922366	+	0.386317i	$0.126253\pi$
$359$			14.6393i			0.772634i	−0.922366	+	0.386317i	$0.873747\pi$
$360$		0			0
$361$	−5.58161			−0.293769
$362$		0			0
$363$	−10.4725	+	10.4725i	−0.549665	+	0.549665i
$364$		0			0
$365$	−18.8500	−	11.7727i	−0.986656	−	0.616213i
$366$		0			0
$367$	12.2264	+	12.2264i	0.638215	+	0.638215i	0.950115	−	0.311900i	$-0.100965\pi$
$367$	12.2264	+	12.2264i	0.638215	+	0.638215i	−0.311900	+	0.950115i	$0.600965\pi$
$368$		0			0
$369$	2.91664			0.151834
$370$		0			0
$371$	8.66319	−	18.8545i	0.449770	−	0.978878i
$372$		0			0
$373$	14.8689	+	14.8689i	0.769880	+	0.769880i	0.978085	−	0.208205i	$-0.0667621\pi$
$373$	14.8689	+	14.8689i	0.769880	+	0.769880i	−0.208205	+	0.978085i	$0.566762\pi$
$374$		0			0
$375$	−11.1199	−	1.16093i	−0.574229	−	0.0599499i
$376$		0			0
$377$	−4.00584	−	4.00584i	−0.206311	−	0.206311i
$378$		0			0
$379$			26.4447i			1.35837i	0.733967	+	0.679185i	$0.237667\pi$
$379$			26.4447i			1.35837i	−0.733967	+	0.679185i	$0.762333\pi$
$380$		0			0
$381$		−	14.4804i		−	0.741856i
$382$		0			0
$383$	−6.67462	+	6.67462i	−0.341057	+	0.341057i	−0.856765	−	0.515707i	$-0.827529\pi$
$383$	−6.67462	+	6.67462i	−0.341057	+	0.341057i	0.515707	+	0.856765i	$0.327529\pi$
$384$		0			0
$385$	−25.1108	+	16.5171i	−1.27976	+	0.841788i
$386$		0			0
$387$	−6.86314	+	6.86314i	−0.348873	+	0.348873i
$388$		0			0
$389$		−	11.5269i		−	0.584436i	−0.956352	−	0.292218i	$-0.905607\pi$
$389$		−	11.5269i		−	0.584436i	0.956352	−	0.292218i	$-0.0943933\pi$
$390$		0			0
$391$			3.35561i			0.169700i
$392$		0			0
$393$	−4.95041	−	4.95041i	−0.249715	−	0.249715i
$394$		0			0
$395$	26.0371	−	6.01750i	1.31007	−	0.302773i
$396$		0			0
$397$	−5.96065	−	5.96065i	−0.299156	−	0.299156i	0.541527	−	0.840683i	$-0.317846\pi$
$397$	−5.96065	−	5.96065i	−0.299156	−	0.299156i	−0.840683	+	0.541527i	$0.817846\pi$
$398$		0			0
$399$	−8.80655	−	4.04640i	−0.440879	−	0.202573i
$400$		0			0
$401$	−13.9884			−0.698549			−0.349275	−	0.937020i	$-0.613572\pi$
$401$	−13.9884			−0.698549			−0.349275	+	0.937020i	$0.613572\pi$
$402$		0			0
$403$	−33.3256	−	33.3256i	−1.66007	−	1.66007i
$404$		0			0
$405$	0.503511	+	2.17864i	0.0250197	+	0.108258i
$406$		0			0
$407$	−25.1809	+	25.1809i	−1.24817	+	1.24817i
$408$		0			0
$409$	12.3032			0.608355			0.304177	−	0.952615i	$-0.401618\pi$
$409$	12.3032			0.608355			0.304177	+	0.952615i	$0.401618\pi$
$410$		0			0
$411$		−	10.7332i		−	0.529428i
$412$		0			0
$413$	1.37752	+	3.71947i	0.0677835	+	0.183023i
$414$		0			0
$415$	−14.3083	−	8.93623i	−0.702369	−	0.438662i
$416$		0			0
$417$	−2.10522	+	2.10522i	−0.103093	+	0.103093i
$418$		0			0
$419$	37.8137			1.84732			0.923660	−	0.383213i	$-0.125182\pi$
$419$	37.8137			1.84732			0.923660	+	0.383213i	$0.125182\pi$
$420$		0			0
$421$	−25.0323			−1.22000			−0.610001	−	0.792401i	$-0.708831\pi$
$421$	−25.0323			−1.22000			−0.610001	+	0.792401i	$0.708831\pi$
$422$		0			0
$423$	−1.97475	+	1.97475i	−0.0960156	+	0.0960156i
$424$		0			0
$425$	18.9675	+	6.52118i	0.920057	+	0.316324i
$426$		0			0
$427$	30.7294	−	11.3808i	1.48710	−	0.550755i
$428$		0			0
$429$		−	27.2782i		−	1.31701i
$430$		0			0
$431$	8.96315			0.431740			0.215870	−	0.976422i	$-0.430741\pi$
$431$	8.96315			0.431740			0.215870	+	0.976422i	$0.430741\pi$
$432$		0			0
$433$	10.3418	−	10.3418i	0.496994	−	0.496994i	−0.413507	−	0.910501i	$-0.635696\pi$
$433$	10.3418	−	10.3418i	0.496994	−	0.496994i	0.910501	+	0.413507i	$0.135696\pi$
$434$		0			0
$435$	1.24975	−	2.00105i	0.0599209	−	0.0959430i
$436$		0			0
$437$	−2.16674	−	2.16674i	−0.103649	−	0.103649i
$438$		0			0
$439$	−18.1867			−0.868004			−0.434002	−	0.900912i	$-0.642899\pi$
$439$	−18.1867			−0.868004			−0.434002	+	0.900912i	$0.642899\pi$
$440$		0			0
$441$	4.55957	+	5.31134i	0.217122	+	0.252921i
$442$		0			0
$443$	11.5143	+	11.5143i	0.547059	+	0.547059i	0.925589	−	0.378530i	$-0.123570\pi$
$443$	11.5143	+	11.5143i	0.547059	+	0.547059i	−0.378530	+	0.925589i	$0.623570\pi$
$444$		0			0
$445$	−0.884747	−	3.82821i	−0.0419410	−	0.181474i
$446$		0			0
$447$	−0.582406	−	0.582406i	−0.0275468	−	0.0275468i
$448$		0			0
$449$			27.6618i			1.30544i	0.757598	+	0.652721i	$0.226373\pi$
$449$			27.6618i			1.30544i	−0.757598	+	0.652721i	$0.773627\pi$
$450$		0			0
$451$		−	14.8177i		−	0.697736i
$452$		0			0
$453$	9.90343	−	9.90343i	0.465304	−	0.465304i
$454$		0			0
$455$	6.42224	−	31.1093i	0.301079	−	1.45843i
$456$		0			0
$457$	15.6299	−	15.6299i	0.731135	−	0.731135i	−0.239710	−	0.970845i	$-0.577052\pi$
$457$	15.6299	−	15.6299i	0.731135	−	0.731135i	0.970845	+	0.239710i	$0.0770523\pi$
$458$		0			0
$459$		−	4.01144i		−	0.187238i
$460$		0			0
$461$		−	31.1692i		−	1.45170i	−0.687855	−	0.725848i	$-0.741448\pi$
$461$		−	31.1692i		−	1.45170i	0.687855	−	0.725848i	$-0.258552\pi$
$462$		0			0
$463$	−11.6018	−	11.6018i	−0.539181	−	0.539181i	0.384108	−	0.923288i	$-0.374509\pi$
$463$	−11.6018	−	11.6018i	−0.539181	−	0.539181i	−0.923288	+	0.384108i	$0.874509\pi$
$464$		0			0
$465$	10.3970	−	16.6473i	0.482149	−	0.771998i
$466$		0			0
$467$	−21.0876	−	21.0876i	−0.975817	−	0.975817i	0.0238976	−	0.999714i	$-0.492392\pi$
$467$	−21.0876	−	21.0876i	−0.975817	−	0.975817i	−0.999714	+	0.0238976i	$0.992392\pi$
$468$		0			0
$469$	14.6366	+	6.72516i	0.675855	+	0.310539i
$470$		0			0
$471$	−7.74727			−0.356975
$472$		0			0
$473$	34.8675	+	34.8675i	1.60321	+	1.60321i
$474$		0			0
$475$	−16.4582	+	8.03665i	−0.755154	+	0.368747i
$476$		0			0
$477$	−5.54555	+	5.54555i	−0.253913	+	0.253913i
$478$		0			0
$479$	33.9667			1.55198			0.775989	−	0.630746i	$-0.217251\pi$
$479$	33.9667			1.55198			0.775989	+	0.630746i	$0.217251\pi$
$480$		0			0
$481$		−	37.6363i		−	1.71607i
$482$		0			0
$483$	0.768647	+	2.07543i	0.0349747	+	0.0944355i
$484$		0			0
$485$	−5.46433	+	8.74927i	−0.248122	+	0.397284i
$486$		0			0
$487$	−5.25831	+	5.25831i	−0.238277	+	0.238277i	−0.816136	−	0.577860i	$-0.803888\pi$
$487$	−5.25831	+	5.25831i	−0.238277	+	0.238277i	0.577860	+	0.816136i	$0.303888\pi$
$488$		0			0
$489$	11.2377			0.508187
$490$		0			0
$491$	−13.1492			−0.593416			−0.296708	−	0.954968i	$-0.595889\pi$
$491$	−13.1492			−0.593416			−0.296708	+	0.954968i	$0.595889\pi$
$492$		0			0
$493$	−2.99278	+	2.99278i	−0.134788	+	0.134788i
$494$		0			0
$495$	11.0684	−	2.55803i	0.497485	−	0.114975i
$496$		0			0
$497$	9.07817	+	24.5121i	0.407211	+	1.09952i
$498$		0			0
$499$		−	7.15984i		−	0.320519i	−0.987075	−	0.160259i	$-0.948767\pi$
$499$		−	7.15984i		−	0.320519i	0.987075	−	0.160259i	$-0.0512330\pi$
$500$		0			0
$501$	5.10384			0.228023
$502$		0			0
$503$	14.6373	−	14.6373i	0.652646	−	0.652646i	−0.300983	−	0.953629i	$-0.597315\pi$
$503$	14.6373	−	14.6373i	0.652646	−	0.652646i	0.953629	+	0.300983i	$0.0973148\pi$
$504$		0			0
$505$	12.7066	−	2.93665i	0.565435	−	0.130679i
$506$		0			0
$507$	11.1932	+	11.1932i	0.497107	+	0.497107i
$508$		0			0
$509$	−37.3089			−1.65369			−0.826844	−	0.562432i	$-0.809866\pi$
$509$	−37.3089			−1.65369			−0.826844	+	0.562432i	$0.809866\pi$
$510$		0			0
$511$	23.8946	+	10.9790i	1.05703	+	0.485682i
$512$		0			0
$513$	2.59021	+	2.59021i	0.114361	+	0.114361i
$514$		0			0
$515$	29.0483	+	18.1420i	1.28002	+	0.799432i
$516$		0			0
$517$	10.0325	+	10.0325i	0.441229	+	0.441229i
$518$		0			0
$519$		−	19.6034i		−	0.860495i
$520$		0			0
$521$			21.3380i			0.934835i	0.884037	+	0.467418i	$0.154816\pi$
$521$			21.3380i			0.934835i	−0.884037	+	0.467418i	$0.845184\pi$
$522$		0			0
$523$	29.0131	−	29.0131i	1.26865	−	1.26865i	0.321869	−	0.946784i	$-0.395689\pi$
$523$	29.0131	−	29.0131i	1.26865	−	1.26865i	0.946784	−	0.321869i	$-0.104311\pi$
$524$		0			0
$525$	13.2251	−	0.311425i	0.577190	−	0.0135917i
$526$		0			0
$527$	−24.8977	+	24.8977i	−1.08456	+	1.08456i
$528$		0			0
$529$		−	22.3003i		−	0.969576i
$530$		0			0
$531$		−	1.49914i		−	0.0650573i
$532$		0			0
$533$	11.0735	+	11.0735i	0.479648	+	0.479648i
$534$		0			0
$535$	−19.9206	−	12.4413i	−0.861242	−	0.537886i
$536$		0			0
$537$	−3.95751	−	3.95751i	−0.170779	−	0.170779i
$538$		0			0
$539$	26.9837	−	23.1644i	1.16227	−	0.997761i
$540$		0			0
$541$	−8.65845			−0.372256			−0.186128	−	0.982526i	$-0.559594\pi$
$541$	−8.65845			−0.372256			−0.186128	+	0.982526i	$0.559594\pi$
$542$		0			0
$543$	−3.62655	−	3.62655i	−0.155630	−	0.155630i
$544$		0			0
$545$	43.1991	−	9.98386i	1.85045	−	0.427662i
$546$		0			0
$547$	−14.4212	+	14.4212i	−0.616607	+	0.616607i	−0.944659	−	0.328053i	$-0.893608\pi$
$547$	−14.4212	+	14.4212i	−0.616607	+	0.616607i	0.328053	+	0.944659i	$0.393608\pi$
$548$		0			0
$549$	−12.3856			−0.528603
$550$		0			0
$551$		−	3.86491i		−	0.164651i
$552$		0			0
$553$	−29.6513	+	10.9815i	−1.26090	+	0.466982i
$554$		0			0
$555$	15.2712	−	3.52937i	0.648227	−	0.149813i
$556$		0			0
$557$	−27.5065	+	27.5065i	−1.16549	+	1.16549i	−0.182234	+	0.983255i	$0.558333\pi$
$557$	−27.5065	+	27.5065i	−1.16549	+	1.16549i	−0.983255	+	0.182234i	$0.941667\pi$
$558$		0			0
$559$	−52.1143			−2.20420
$560$		0			0
$561$	−20.3797			−0.860430
$562$		0			0
$563$	−21.2610	+	21.2610i	−0.896045	+	0.896045i	−0.995084	−	0.0990389i	$-0.968423\pi$
$563$	−21.2610	+	21.2610i	−0.896045	+	0.896045i	0.0990389	+	0.995084i	$0.468423\pi$
$564$		0			0
$565$	−14.7065	+	23.5475i	−0.618707	+	0.990649i
$566$		0			0
$567$	−0.918874	−	2.48106i	−0.0385891	−	0.104195i
$568$		0			0
$569$		−	10.3990i		−	0.435951i	−0.975954	−	0.217975i	$-0.930055\pi$
$569$		−	10.3990i		−	0.435951i	0.975954	−	0.217975i	$-0.0699452\pi$
$570$		0			0
$571$	−3.29077			−0.137714			−0.0688572	−	0.997627i	$-0.521935\pi$
$571$	−3.29077			−0.137714			−0.0688572	+	0.997627i	$0.521935\pi$
$572$		0			0
$573$	−14.6863	+	14.6863i	−0.613529	+	0.613529i
$574$		0			0
$575$	3.95531	+	1.35987i	0.164948	+	0.0567105i
$576$		0			0
$577$	−2.14044	−	2.14044i	−0.0891077	−	0.0891077i	0.661148	−	0.750256i	$-0.270070\pi$
$577$	−2.14044	−	2.14044i	−0.0891077	−	0.0891077i	−0.750256	+	0.661148i	$0.770070\pi$
$578$		0			0
$579$	−12.3145			−0.511775
$580$		0			0
$581$	18.1375	+	8.33373i	0.752469	+	0.345741i
$582$		0			0
$583$	28.1736	+	28.1736i	1.16683	+	1.16683i
$584$		0			0
$585$	−6.35993	+	10.1833i	−0.262951	+	0.421026i
$586$		0			0
$587$	−30.3080	−	30.3080i	−1.25095	−	1.25095i	−0.955296	−	0.295650i	$-0.904464\pi$
$587$	−30.3080	−	30.3080i	−1.25095	−	1.25095i	−0.295650	−	0.955296i	$-0.595536\pi$
$588$		0			0
$589$		−	32.1532i		−	1.32485i
$590$		0			0
$591$			23.4003i			0.962562i
$592$		0			0
$593$	17.1981	−	17.1981i	0.706240	−	0.706240i	−0.259503	−	0.965742i	$-0.583559\pi$
$593$	17.1981	−	17.1981i	0.706240	−	0.706240i	0.965742	+	0.259503i	$0.0835587\pi$
$594$		0			0
$595$	−23.2419	−	4.79808i	−0.952824	−	0.196702i
$596$		0			0
$597$	13.2447	−	13.2447i	0.542071	−	0.542071i
$598$		0			0
$599$		−	11.8799i		−	0.485398i	−0.970102	−	0.242699i	$-0.921967\pi$
$599$		−	11.8799i		−	0.485398i	0.970102	−	0.242699i	$-0.0780327\pi$
$600$		0			0
$601$			22.3993i			0.913688i	0.889547	+	0.456844i	$0.151020\pi$
$601$			22.3993i			0.913688i	−0.889547	+	0.456844i	$0.848980\pi$
$602$		0			0
$603$	−4.30496	−	4.30496i	−0.175312	−	0.175312i
$604$		0			0
$605$	−7.45720	−	32.2665i	−0.303178	−	1.31182i
$606$		0			0
$607$	8.64290	+	8.64290i	0.350805	+	0.350805i	0.860409	−	0.509604i	$-0.170208\pi$
$607$	8.64290	+	8.64290i	0.350805	+	0.350805i	−0.509604	+	0.860409i	$0.670208\pi$
$608$		0			0
$609$	−1.16549	+	2.53656i	−0.0472280	+	0.102787i
$610$		0			0
$611$	−14.9950			−0.606632
$612$		0			0
$613$	−9.65057	−	9.65057i	−0.389783	−	0.389783i	0.484827	−	0.874610i	$-0.338882\pi$
$613$	−9.65057	−	9.65057i	−0.389783	−	0.389783i	−0.874610	+	0.484827i	$0.838882\pi$
$614$		0			0
$615$	−3.45474	+	5.53160i	−0.139309	+	0.223056i
$616$		0			0
$617$	7.44264	−	7.44264i	0.299629	−	0.299629i	−0.541239	−	0.840869i	$-0.682045\pi$
$617$	7.44264	−	7.44264i	0.299629	−	0.299629i	0.840869	+	0.541239i	$0.182045\pi$
$618$		0			0
$619$	8.47487			0.340634			0.170317	−	0.985389i	$-0.445521\pi$
$619$	8.47487			0.340634			0.170317	+	0.985389i	$0.445521\pi$
$620$		0			0
$621$		−	0.836510i		−	0.0335680i
$622$		0			0
$623$	1.61460	+	4.35961i	0.0646877	+	0.174664i
$624$		0			0
$625$	15.3733	−	19.7145i	0.614930	−	0.788582i
$626$		0			0
$627$	13.1593	−	13.1593i	0.525531	−	0.525531i
$628$		0			0
$629$	−28.1182			−1.12115
$630$		0			0
$631$	−9.06900			−0.361031			−0.180516	−	0.983572i	$-0.557777\pi$
$631$	−9.06900			−0.361031			−0.180516	+	0.983572i	$0.557777\pi$
$632$		0			0
$633$	2.44993	−	2.44993i	0.0973758	−	0.0973758i
$634$		0			0
$635$	27.4632	+	17.1520i	1.08984	+	0.680657i
$636$		0			0
$637$	−2.85424	+	37.4767i	−0.113089	+	1.48488i
$638$		0			0
$639$		−	9.87966i		−	0.390833i
$640$		0			0
$641$	9.82777			0.388174			0.194087	−	0.980984i	$-0.437826\pi$
$641$	9.82777			0.388174			0.194087	+	0.980984i	$0.437826\pi$
$642$		0			0
$643$	15.5098	−	15.5098i	0.611648	−	0.611648i	−0.331727	−	0.943375i	$-0.607631\pi$
$643$	15.5098	−	15.5098i	0.611648	−	0.611648i	0.943375	+	0.331727i	$0.107631\pi$
$644$		0			0
$645$	−4.88705	−	21.1458i	−0.192428	−	0.832614i
$646$		0			0
$647$	−9.72240	−	9.72240i	−0.382227	−	0.382227i	0.489677	−	0.871904i	$-0.337115\pi$
$647$	−9.72240	−	9.72240i	−0.382227	−	0.382227i	−0.871904	+	0.489677i	$0.837115\pi$
$648$		0			0
$649$	−7.61624			−0.298963
$650$		0			0
$651$	−9.69600	+	21.1023i	−0.380016	+	0.827065i
$652$		0			0
$653$	4.17455	+	4.17455i	0.163363	+	0.163363i	0.784055	−	0.620692i	$-0.213148\pi$
$653$	4.17455	+	4.17455i	0.163363	+	0.163363i	−0.620692	+	0.784055i	$0.713148\pi$
$654$		0			0
$655$	15.2525	−	3.52505i	0.595965	−	0.137735i
$656$		0			0
$657$	−7.02795	−	7.02795i	−0.274187	−	0.274187i
$658$		0			0
$659$		−	8.93891i		−	0.348210i	−0.984727	−	0.174105i	$-0.944297\pi$
$659$		−	8.93891i		−	0.348210i	0.984727	−	0.174105i	$-0.0557033\pi$
$660$		0			0
$661$		−	18.8737i		−	0.734103i	−0.930201	−	0.367052i	$-0.880367\pi$
$661$		−	18.8737i		−	0.734103i	0.930201	−	0.367052i	$-0.119633\pi$
$662$		0			0
$663$	15.2301	−	15.2301i	0.591489	−	0.591489i
$664$		0			0
$665$	18.1056	−	11.9093i	0.702105	−	0.461822i
$666$		0			0
$667$	−0.624088	+	0.624088i	−0.0241648	+	0.0241648i
$668$		0			0
$669$			6.10959i			0.236210i
$670$		0			0
$671$			62.9236i			2.42914i
$672$		0			0
$673$	7.82024	+	7.82024i	0.301448	+	0.301448i	0.841580	−	0.540132i	$-0.181626\pi$
$673$	7.82024	+	7.82024i	0.301448	+	0.301448i	−0.540132	+	0.841580i	$0.681626\pi$
$674$		0			0
$675$	−4.72835	−	1.62565i	−0.181994	−	0.0625712i
$676$		0			0
$677$	−0.751759	−	0.751759i	−0.0288925	−	0.0288925i	0.692513	−	0.721405i	$-0.256504\pi$
$677$	−0.751759	−	0.751759i	−0.0288925	−	0.0288925i	−0.721405	+	0.692513i	$0.756504\pi$
$678$		0			0
$679$	5.09591	−	11.0907i	0.195563	−	0.425622i
$680$		0			0
$681$	−8.01602			−0.307175
$682$		0			0
$683$	−8.20512	−	8.20512i	−0.313960	−	0.313960i	0.532482	−	0.846442i	$-0.321260\pi$
$683$	−8.20512	−	8.20512i	−0.313960	−	0.313960i	−0.846442	+	0.532482i	$0.821260\pi$
$684$		0			0
$685$	20.3562	+	12.7134i	0.777770	+	0.485754i
$686$		0			0
$687$	−8.99258	+	8.99258i	−0.343088	+	0.343088i
$688$		0			0
$689$	−42.1093			−1.60424
$690$		0			0
$691$			10.5920i			0.402939i	0.979495	+	0.201469i	$0.0645717\pi$
$691$			10.5920i			0.402939i	−0.979495	+	0.201469i	$0.935428\pi$
$692$		0			0
$693$	−12.6048	+	4.66824i	−0.478816	+	0.177332i
$694$		0			0
$695$	−1.49907	−	6.48631i	−0.0568628	−	0.246040i
$696$		0			0
$697$	8.27308	−	8.27308i	0.313365	−	0.313365i
$698$		0			0
$699$	−9.60864			−0.363432
$700$		0			0
$701$	31.8176			1.20173			0.600867	−	0.799349i	$-0.294822\pi$
$701$	31.8176			1.20173			0.600867	+	0.799349i	$0.294822\pi$
$702$		0			0
$703$	18.1561	−	18.1561i	0.684772	−	0.684772i
$704$		0			0
$705$	−1.40616	−	6.08433i	−0.0529592	−	0.229149i
$706$		0			0
$707$	−14.4704	+	5.35919i	−0.544215	+	0.201553i
$708$		0			0
$709$			42.1965i			1.58472i	0.610053	+	0.792361i	$0.291148\pi$
$709$			42.1965i			1.58472i	−0.610053	+	0.792361i	$0.708852\pi$
$710$		0			0
$711$	11.9511			0.448200
$712$		0			0
$713$	−5.19195	+	5.19195i	−0.194440	+	0.194440i
$714$		0			0
$715$	51.7350	+	32.3109i	1.93478	+	1.20836i
$716$		0			0
$717$	−19.9750	−	19.9750i	−0.745979	−	0.745979i
$718$		0			0
$719$	1.40331			0.0523347			0.0261673	−	0.999658i	$-0.491670\pi$
$719$	1.40331			0.0523347			0.0261673	+	0.999658i	$0.491670\pi$
$720$		0			0
$721$	−36.8220	−	16.9188i	−1.37132	−	0.630090i
$722$		0			0
$723$	−4.79983	−	4.79983i	−0.178508	−	0.178508i
$724$		0			0
$725$	2.31480	+	4.74047i	0.0859697	+	0.176057i
$726$		0			0
$727$	35.1101	+	35.1101i	1.30216	+	1.30216i	0.926933	+	0.375227i	$0.122435\pi$
$727$	35.1101	+	35.1101i	1.30216	+	1.30216i	0.375227	+	0.926933i	$0.377565\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			38.9348i			1.44006i
$732$		0			0
$733$	27.0142	−	27.0142i	0.997794	−	0.997794i	−0.00220403	−	0.999998i	$-0.500702\pi$
$733$	27.0142	−	27.0142i	0.997794	−	0.997794i	0.999998	+	0.00220403i	$0.000701565\pi$
$734$		0			0
$735$	−15.4741	+	2.35627i	−0.570771	+	0.0869124i
$736$		0			0
$737$	−21.8709	+	21.8709i	−0.805625	+	0.805625i
$738$		0			0
$739$		−	23.2327i		−	0.854629i	−0.904103	−	0.427315i	$-0.859460\pi$
$739$		−	23.2327i		−	0.854629i	0.904103	−	0.427315i	$-0.140540\pi$
$740$		0			0
$741$			19.6684i			0.722537i
$742$		0			0
$743$	29.5948	+	29.5948i	1.08573	+	1.08573i	0.995963	+	0.0897655i	$0.0286118\pi$
$743$	29.5948	+	29.5948i	1.08573	+	1.08573i	0.0897655	+	0.995963i	$0.471388\pi$
$744$		0			0
$745$	1.79443	−	0.414715i	0.0657428	−	0.0151940i
$746$		0			0
$747$	−5.33465	−	5.33465i	−0.195185	−	0.195185i
$748$		0			0
$749$	25.2516	+	11.6025i	0.922674	+	0.423946i
$750$		0			0
$751$	38.7569			1.41426			0.707129	−	0.707084i	$-0.249990\pi$
$751$	38.7569			1.41426			0.707129	+	0.707084i	$0.249990\pi$
$752$		0			0
$753$	13.2586	+	13.2586i	0.483172	+	0.483172i
$754$		0			0
$755$	7.05196	+	30.5131i	0.256647	+	1.11049i
$756$		0			0
$757$	6.96551	−	6.96551i	0.253166	−	0.253166i	−0.569101	−	0.822267i	$-0.692709\pi$
$757$	6.96551	−	6.96551i	0.253166	−	0.253166i	0.822267	+	0.569101i	$0.192709\pi$
$758$		0			0
$759$	−4.24980			−0.154258
$760$		0			0
$761$			50.6708i			1.83681i	0.395637	+	0.918407i	$0.370524\pi$
$761$			50.6708i			1.83681i	−0.395637	+	0.918407i	$0.629476\pi$
$762$		0			0
$763$	−49.1957	+	18.2199i	−1.78100	+	0.659604i
$764$		0			0
$765$	7.60796	+	4.75153i	0.275066	+	0.171792i
$766$		0			0
$767$	5.69177	−	5.69177i	0.205518	−	0.205518i
$768$		0			0
$769$	−46.6219			−1.68123			−0.840615	−	0.541633i	$-0.817806\pi$
$769$	−46.6219			−1.68123			−0.840615	+	0.541633i	$0.817806\pi$
$770$		0			0
$771$	−7.61164			−0.274126
$772$		0			0
$773$	1.27891	−	1.27891i	0.0459993	−	0.0459993i	−0.683733	−	0.729732i	$-0.739645\pi$
$773$	1.27891	−	1.27891i	0.0459993	−	0.0459993i	0.729732	+	0.683733i	$0.239645\pi$
$774$		0			0
$775$	19.2575	+	39.4372i	0.691748	+	1.41663i
$776$		0			0
$777$	−17.3911	+	6.44087i	−0.623900	+	0.231065i
$778$		0			0
$779$			10.6840i			0.382793i
$780$		0			0
$781$	−50.1926			−1.79603
$782$		0			0
$783$	0.746061	−	0.746061i	0.0266621	−	0.0266621i
$784$		0			0
$785$	9.17661	−	14.6932i	0.327527	−	0.524424i
$786$		0			0
$787$	2.35551	+	2.35551i	0.0839648	+	0.0839648i	0.747842	−	0.663877i	$-0.231090\pi$
$787$	2.35551	+	2.35551i	0.0839648	+	0.0839648i	−0.663877	+	0.747842i	$0.731090\pi$
$788$		0			0
$789$	12.4663			0.443811
$790$		0			0
$791$	13.7149	−	29.8491i	0.487647	−	1.06131i
$792$		0			0
$793$	−47.0240	−	47.0240i	−1.66987	−	1.66987i
$794$		0			0
$795$	−3.94883	−	17.0862i	−0.140051	−	0.605985i
$796$		0			0
$797$	−9.61236	−	9.61236i	−0.340487	−	0.340487i	0.516063	−	0.856551i	$-0.327397\pi$
$797$	−9.61236	−	9.61236i	−0.340487	−	0.340487i	−0.856551	+	0.516063i	$0.827397\pi$
$798$		0			0
$799$			11.2028i			0.396327i
$800$		0			0
$801$		−	1.75715i		−	0.0620860i
$802$		0			0
$803$	−35.7048	+	35.7048i	−1.25999	+	1.25999i
$804$		0			0
$805$	−4.84666	−	1.00055i	−0.170822	−	0.0352647i
$806$		0			0
$807$	−15.0751	+	15.0751i	−0.530669	+	0.530669i
$808$		0			0
$809$			44.2735i			1.55657i	0.627909	+	0.778287i	$0.283911\pi$
$809$			44.2735i			1.55657i	−0.627909	+	0.778287i	$0.716089\pi$
$810$		0			0
$811$			11.3215i			0.397552i	0.980045	+	0.198776i	$0.0636966\pi$
$811$			11.3215i			0.397552i	−0.980045	+	0.198776i	$0.936303\pi$
$812$		0			0
$813$	9.14652	+	9.14652i	0.320782	+	0.320782i
$814$		0			0
$815$	−13.3110	+	21.3131i	−0.466265	+	0.746565i
$816$		0			0
$817$	−25.1405	−	25.1405i	−0.879553	−	0.879553i
$818$		0			0
$819$	5.93113	−	12.9085i	0.207250	−	0.451058i
$820$		0			0
$821$	1.84371			0.0643458			0.0321729	−	0.999482i	$-0.489757\pi$
$821$	1.84371			0.0643458			0.0321729	+	0.999482i	$0.489757\pi$
$822$		0			0
$823$	30.7730	+	30.7730i	1.07268	+	1.07268i	0.997143	+	0.0755344i	$0.0240663\pi$
$823$	30.7730	+	30.7730i	1.07268	+	1.07268i	0.0755344	+	0.997143i	$0.475934\pi$
$824$		0			0
$825$	−8.25893	+	24.0219i	−0.287539	+	0.836334i
$826$		0			0
$827$	27.0430	−	27.0430i	0.940376	−	0.940376i	−0.0579435	−	0.998320i	$-0.518454\pi$
$827$	27.0430	−	27.0430i	0.940376	−	0.940376i	0.998320	+	0.0579435i	$0.0184543\pi$
$828$		0			0
$829$	5.40143			0.187599			0.0937997	−	0.995591i	$-0.470099\pi$
$829$	5.40143			0.187599			0.0937997	+	0.995591i	$0.470099\pi$
$830$		0			0
$831$		−	21.4722i		−	0.744862i
$832$		0			0
$833$	27.9990	+	2.13241i	0.970107	+	0.0738837i
$834$		0			0
$835$	−6.04548	+	9.67978i	−0.209212	+	0.334983i
$836$		0			0
$837$	6.20668	−	6.20668i	0.214534	−	0.214534i
$838$		0			0
$839$	26.0436			0.899125			0.449562	−	0.893249i	$-0.351580\pi$
$839$	26.0436			0.899125			0.449562	+	0.893249i	$0.351580\pi$
$840$		0			0
$841$	27.8868			0.961613
$842$		0			0
$843$	−14.7210	+	14.7210i	−0.507018	+	0.507018i
$844$		0			0
$845$	−34.4869	+	7.97036i	−1.18639	+	0.274189i
$846$		0			0
$847$	13.6089	+	36.7455i	0.467607	+	1.26259i
$848$		0			0
$849$			7.56642i			0.259679i
$850$		0			0
$851$	−5.86353			−0.200999
$852$		0			0
$853$	3.78906	−	3.78906i	0.129735	−	0.129735i	−0.639258	−	0.768993i	$-0.720758\pi$
$853$	3.78906	−	3.78906i	0.129735	−	0.129735i	0.768993	+	0.639258i	$0.220758\pi$
$854$		0			0
$855$	−7.98061	+	1.84442i	−0.272931	+	0.0630778i
$856$		0			0
$857$	36.7692	+	36.7692i	1.25601	+	1.25601i	0.952980	+	0.303032i	$0.0979990\pi$
$857$	36.7692	+	36.7692i	1.25601	+	1.25601i	0.303032	+	0.952980i	$0.402001\pi$
$858$		0			0
$859$	−33.1556			−1.13125			−0.565626	−	0.824662i	$-0.691366\pi$
$859$	−33.1556			−1.13125			−0.565626	+	0.824662i	$0.691366\pi$
$860$		0			0
$861$	3.22182	−	7.01194i	0.109799	−	0.238966i
$862$		0			0
$863$	−1.68139	−	1.68139i	−0.0572350	−	0.0572350i	0.677910	−	0.735145i	$-0.262886\pi$
$863$	−1.68139	−	1.68139i	−0.0572350	−	0.0572350i	−0.735145	+	0.677910i	$0.762886\pi$
$864$		0			0
$865$	37.1792	+	23.2202i	1.26413	+	0.789509i
$866$		0			0
$867$	0.642324	+	0.642324i	0.0218145	+	0.0218145i
$868$		0			0
$869$		−	60.7161i		−	2.05965i
$870$		0			0
$871$		−	32.6891i		−	1.10763i
$872$		0			0
$873$	−3.26203	+	3.26203i	−0.110403	+	0.110403i
$874$		0			0
$875$	−15.0744	+	25.4512i	−0.509609	+	0.860406i
$876$		0			0
$877$	−2.69980	+	2.69980i	−0.0911658	+	0.0911658i	−0.751219	−	0.660053i	$-0.770534\pi$
$877$	−2.69980	+	2.69980i	−0.0911658	+	0.0911658i	0.660053	+	0.751219i	$0.270534\pi$
$878$		0			0
$879$			25.5430i			0.861545i
$880$		0			0
$881$		−	44.2080i		−	1.48940i	−0.667397	−	0.744702i	$-0.732592\pi$
$881$		−	44.2080i		−	1.48940i	0.667397	−	0.744702i	$-0.267408\pi$
$882$		0			0
$883$	13.9894	+	13.9894i	0.470781	+	0.470781i	0.902167	−	0.431386i	$-0.141975\pi$
$883$	13.9894	+	13.9894i	0.470781	+	0.470781i	−0.431386	+	0.902167i	$0.641975\pi$
$884$		0			0
$885$	2.84323	+	1.77573i	0.0955740	+	0.0596905i
$886$		0			0
$887$	25.3656	+	25.3656i	0.851693	+	0.851693i	0.990342	−	0.138649i	$-0.0442760\pi$
$887$	25.3656	+	25.3656i	0.851693	+	0.851693i	−0.138649	+	0.990342i	$0.544276\pi$
$888$		0			0
$889$	−34.8127	−	15.9956i	−1.16758	−	0.536475i
$890$		0			0
$891$	5.08039			0.170200
$892$		0			0
$893$	−7.23373	−	7.23373i	−0.242067	−	0.242067i
$894$		0			0
$895$	12.1933	−	2.81803i	0.407578	−	0.0941964i
$896$		0			0
$897$	3.17596	−	3.17596i	0.106042	−	0.106042i
$898$		0			0
$899$	−9.26113			−0.308876
$900$		0			0
$901$			31.4600i			1.04809i
$902$		0			0
$903$	8.91855	+	24.0811i	0.296791	+	0.801368i
$904$		0			0
$905$	11.1736	−	2.58237i	0.371425	−	0.0858409i
$906$		0			0
$907$	19.2797	−	19.2797i	0.640170	−	0.640170i	−0.310427	−	0.950597i	$-0.600472\pi$
$907$	19.2797	−	19.2797i	0.640170	−	0.640170i	0.950597	+	0.310427i	$0.100472\pi$
$908$		0			0
$909$	5.83234			0.193446
$910$		0			0
$911$	−40.8927			−1.35484			−0.677418	−	0.735598i	$-0.736901\pi$
$911$	−40.8927			−1.35484			−0.677418	+	0.735598i	$0.736901\pi$
$912$		0			0
$913$	−27.1021	+	27.1021i	−0.896949	+	0.896949i
$914$		0			0
$915$	14.6707	−	23.4901i	0.484997	−	0.776558i
$916$		0			0
$917$	−17.3698	+	6.43298i	−0.573600	+	0.212436i
$918$		0			0
$919$		−	21.9749i		−	0.724886i	−0.932006	−	0.362443i	$-0.881943\pi$
$919$		−	21.9749i		−	0.724886i	0.932006	−	0.362443i	$-0.118057\pi$
$920$		0			0
$921$	13.0846			0.431152
$922$		0			0
$923$	37.5099	−	37.5099i	1.23465	−	1.23465i
$924$		0			0
$925$	−11.3950	+	33.1434i	−0.374665	+	1.08975i
$926$		0			0
$927$	10.8302	+	10.8302i	0.355711	+	0.355711i
$928$		0			0
$929$	−22.1143			−0.725546			−0.362773	−	0.931878i	$-0.618170\pi$
$929$	−22.1143			−0.725546			−0.362773	+	0.931878i	$0.618170\pi$
$930$		0			0
$931$	−19.4560	+	16.7022i	−0.637646	+	0.547393i
$932$		0			0
$933$	14.1849	+	14.1849i	0.464391	+	0.464391i
$934$		0			0
$935$	24.1396	−	38.6514i	0.789450	−	1.26404i
$936$		0			0
$937$	10.7013	+	10.7013i	0.349595	+	0.349595i	0.859959	−	0.510364i	$-0.170489\pi$
$937$	10.7013	+	10.7013i	0.349595	+	0.349595i	−0.510364	+	0.859959i	$0.670489\pi$
$938$		0			0
$939$			20.6595i			0.674197i
$940$		0			0
$941$		−	12.6198i		−	0.411394i	−0.978616	−	0.205697i	$-0.934054\pi$
$941$		−	12.6198i		−	0.411394i	0.978616	−	0.205697i	$-0.0659461\pi$
$942$		0			0
$943$	1.72520	−	1.72520i	0.0561801	−	0.0561801i
$944$		0			0
$945$	5.79391	+	1.19610i	0.188476	+	0.0389091i
$946$		0			0
$947$	−8.86560	+	8.86560i	−0.288093	+	0.288093i	−0.836326	−	0.548233i	$-0.815301\pi$
$947$	−8.86560	+	8.86560i	−0.288093	+	0.288093i	0.548233	+	0.836326i	$0.315301\pi$
$948$		0			0
$949$		−	53.3658i		−	1.73233i
$950$		0			0
$951$			31.9239i			1.03520i
$952$		0			0
$953$	−33.3776	−	33.3776i	−1.08121	−	1.08121i	−0.996397	−	0.0848083i	$-0.972972\pi$
$953$	−33.3776	−	33.3776i	−1.08121	−	1.08121i	−0.0848083	−	0.996397i	$-0.527028\pi$
$954$		0			0
$955$	−10.4577	−	45.2494i	−0.338404	−	1.46424i
$956$		0			0
$957$	−3.79028	−	3.79028i	−0.122522	−	0.122522i
$958$		0			0
$959$	−25.8038	−	11.8562i	−0.833248	−	0.382857i
$960$		0			0
$961$	−46.0457			−1.48535
$962$		0			0
$963$	−7.42709	−	7.42709i	−0.239334	−	0.239334i
$964$		0			0
$965$	14.5865	−	23.3554i	0.469557	−	0.751836i
$966$		0			0
$967$	−9.46838	+	9.46838i	−0.304483	+	0.304483i	−0.842765	−	0.538282i	$-0.819074\pi$
$967$	−9.46838	+	9.46838i	−0.304483	+	0.304483i	0.538282	+	0.842765i	$0.319074\pi$
$968$		0			0
$969$	14.6943			0.472050
$970$		0			0
$971$			10.3533i			0.332254i	0.986104	+	0.166127i	$0.0531261\pi$
$971$			10.3533i			0.332254i	−0.986104	+	0.166127i	$0.946874\pi$
$972$		0			0
$973$	2.73570	+	7.38668i	0.0877024	+	0.236806i
$974$		0			0
$975$	−11.7800	−	24.1241i	−0.377261	−	0.772589i
$976$		0			0
$977$	41.5769	−	41.5769i	1.33016	−	1.33016i	0.424945	−	0.905219i	$-0.360293\pi$
$977$	41.5769	−	41.5769i	1.33016	−	1.33016i	0.905219	−	0.424945i	$-0.139707\pi$
$978$		0			0
$979$	−8.92703			−0.285309
$980$		0			0
$981$	19.8285			0.633075
$982$		0			0
$983$	−23.4334	+	23.4334i	−0.747409	+	0.747409i	−0.973992	−	0.226583i	$-0.927245\pi$
$983$	−23.4334	+	23.4334i	−0.747409	+	0.747409i	0.226583	+	0.973992i	$0.427245\pi$
$984$		0			0
$985$	−44.3804	−	27.7176i	−1.41408	−	0.883157i
$986$		0			0
$987$	2.56616	+	6.92890i	0.0816816	+	0.220549i
$988$		0			0
$989$			8.11912i			0.258173i
$990$		0			0
$991$	1.89662			0.0602482			0.0301241	−	0.999546i	$-0.490410\pi$
$991$	1.89662			0.0602482			0.0301241	+	0.999546i	$0.490410\pi$
$992$		0			0
$993$	18.1080	−	18.1080i	0.574641	−	0.574641i
$994$		0			0
$995$	9.43121	+	40.8079i	0.298989	+	1.29370i
$996$		0			0
$997$	33.5228	+	33.5228i	1.06168	+	1.06168i	0.997968	+	0.0637106i	$0.0202935\pi$
$997$	33.5228	+	33.5228i	1.06168	+	1.06168i	0.0637106	+	0.997968i	$0.479707\pi$
$998$		0			0
$999$	7.00952			0.221771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bt.a.433.4	yes	24
4.3	odd	2		1680.2.cz.f.433.7		24
5.2	odd	4		840.2.bt.b.97.9	yes	24
7.6	odd	2		840.2.bt.b.433.9	yes	24
20.7	even	4		1680.2.cz.e.97.6		24
28.27	even	2		1680.2.cz.e.433.6		24
35.27	even	4	inner	840.2.bt.a.97.4	✓	24
140.27	odd	4		1680.2.cz.f.97.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.4	✓	24	35.27	even	4	inner
840.2.bt.a.433.4	yes	24	1.1	even	1	trivial
840.2.bt.b.97.9	yes	24	5.2	odd	4
840.2.bt.b.433.9	yes	24	7.6	odd	2
1680.2.cz.e.97.6		24	20.7	even	4
1680.2.cz.e.433.6		24	28.27	even	2
1680.2.cz.f.97.7		24	140.27	odd	4
1680.2.cz.f.433.7		24	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bt (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.503511 - 2.17864i) q^{5} +(0.918874 + 2.48106i) q^{7} -1.00000i q^{9} -5.08039 q^{11} +(3.79668 - 3.79668i) q^{13} +(1.89657 + 1.18450i) q^{15} +(-2.83651 - 2.83651i) q^{17} +3.66311 q^{19} +(-2.40412 - 1.10463i) q^{21} +(-0.591502 - 0.591502i) q^{23} +(-4.49295 + 2.19394i) q^{25} +(0.707107 + 0.707107i) q^{27} -1.05509i q^{29} -8.77757i q^{31} +(3.59238 - 3.59238i) q^{33} +(4.94268 - 3.25114i) q^{35} +(4.95648 - 4.95648i) q^{37} +5.36932i q^{39} +2.91664i q^{41} +(-6.86314 - 6.86314i) q^{43} +(-2.17864 + 0.503511i) q^{45} +(-1.97475 - 1.97475i) q^{47} +(-5.31134 + 4.55957i) q^{49} +4.01144 q^{51} +(-5.54555 - 5.54555i) q^{53} +(2.55803 + 11.0684i) q^{55} +(-2.59021 + 2.59021i) q^{57} +1.49914 q^{59} -12.3856i q^{61} +(2.48106 - 0.918874i) q^{63} +(-10.1833 - 6.35993i) q^{65} +(4.30496 - 4.30496i) q^{67} +0.836510 q^{69} +9.87966 q^{71} +(7.02795 - 7.02795i) q^{73} +(1.62565 - 4.72835i) q^{75} +(-4.66824 - 12.6048i) q^{77} +11.9511i q^{79} -1.00000 q^{81} +(5.33465 - 5.33465i) q^{83} +(-4.75153 + 7.60796i) q^{85} +(0.746061 + 0.746061i) q^{87} +1.75715 q^{89} +(12.9085 + 5.93113i) q^{91} +(6.20668 + 6.20668i) q^{93} +(-1.84442 - 7.98061i) q^{95} +(-3.26203 - 3.26203i) q^{97} +5.08039i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 + 20 * q^17 + 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 - 4 * q^45 - 24 * q^47 + 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 + 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

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