LMFDB - Embedded newform 128.4.g.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	128.17
Dual form			128.4.g.a.113.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94138 + 4.68690i) q^{3} +(4.93338 - 2.04347i) q^{5} +(-14.0755 + 14.0755i) q^{7} +(0.893826 + 0.893826i) q^{9} +O(q^{10})$	\(q+(-1.94138 + 4.68690i) q^{3} +(4.93338 - 2.04347i) q^{5} +(-14.0755 + 14.0755i) q^{7} +(0.893826 + 0.893826i) q^{9} +(3.78733 + 9.14343i) q^{11} +(-64.7407 - 26.8165i) q^{13} +27.0894i q^{15} +79.3923i q^{17} +(-94.7756 - 39.2573i) q^{19} +(-38.6445 - 93.2961i) q^{21} +(-71.6801 - 71.6801i) q^{23} +(-68.2259 + 68.2259i) q^{25} +(-132.471 + 54.8712i) q^{27} +(-53.0409 + 128.052i) q^{29} +267.650 q^{31} -50.2070 q^{33} +(-40.6768 + 98.2026i) q^{35} +(205.678 - 85.1946i) q^{37} +(251.372 - 251.372i) q^{39} +(210.468 + 210.468i) q^{41} +(56.9749 + 137.550i) q^{43} +(6.23610 + 2.58308i) q^{45} +173.739i q^{47} -53.2384i q^{49} +(-372.103 - 154.130i) q^{51} +(-188.605 - 455.333i) q^{53} +(37.3687 + 37.3687i) q^{55} +(367.990 - 367.990i) q^{57} +(627.964 - 260.111i) q^{59} +(66.5782 - 160.734i) q^{61} -25.1621 q^{63} -374.189 q^{65} +(-211.710 + 511.113i) q^{67} +(475.115 - 196.799i) q^{69} +(226.201 - 226.201i) q^{71} +(802.290 + 802.290i) q^{73} +(-187.316 - 452.220i) q^{75} +(-182.007 - 75.3897i) q^{77} +552.368i q^{79} -693.272i q^{81} +(137.983 + 57.1544i) q^{83} +(162.236 + 391.672i) q^{85} +(-497.195 - 497.195i) q^{87} +(-579.803 + 579.803i) q^{89} +(1288.71 - 533.802i) q^{91} +(-519.610 + 1254.45i) q^{93} -547.785 q^{95} -912.077 q^{97} +(-4.78742 + 11.5579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.94138	+	4.68690i	−0.373618	+	0.901994i	0.619513	+	0.784986i	$0.287330\pi$
$3$	−1.94138	+	4.68690i	−0.373618	+	0.901994i	−0.993131	+	0.117007i	$0.962670\pi$
$4$		0			0
$5$	4.93338	−	2.04347i	0.441255	−	0.182774i	−0.150984	−	0.988536i	$-0.548244\pi$
$5$	4.93338	−	2.04347i	0.441255	−	0.182774i	0.592239	+	0.805762i	$0.298244\pi$
$6$		0			0
$7$	−14.0755	+	14.0755i	−0.760005	+	0.760005i	−0.976323	−	0.216318i	$-0.930595\pi$
$7$	−14.0755	+	14.0755i	−0.760005	+	0.760005i	0.216318	+	0.976323i	$0.430595\pi$
$8$		0			0
$9$	0.893826	+	0.893826i	0.0331047	+	0.0331047i
$10$		0			0
$11$	3.78733	+	9.14343i	0.103811	+	0.250623i	0.967247	−	0.253836i	$-0.0816922\pi$
$11$	3.78733	+	9.14343i	0.103811	+	0.250623i	−0.863436	+	0.504458i	$0.831692\pi$
$12$		0			0
$13$	−64.7407	−	26.8165i	−1.38122	−	0.572120i	−0.436412	−	0.899747i	$-0.643751\pi$
$13$	−64.7407	−	26.8165i	−1.38122	−	0.572120i	−0.944807	+	0.327627i	$0.893751\pi$
$14$		0			0
$15$			27.0894i			0.466297i
$16$		0			0
$17$			79.3923i			1.13267i	0.824174	+	0.566337i	$0.191640\pi$
$17$			79.3923i			1.13267i	−0.824174	+	0.566337i	$0.808360\pi$
$18$		0			0
$19$	−94.7756	−	39.2573i	−1.14437	−	0.474013i	−0.271727	−	0.962374i	$-0.587595\pi$
$19$	−94.7756	−	39.2573i	−1.14437	−	0.474013i	−0.872642	+	0.488361i	$0.837595\pi$
$20$		0			0
$21$	−38.6445	−	93.2961i	−0.401568	−	0.969471i
$22$		0			0
$23$	−71.6801	−	71.6801i	−0.649841	−	0.649841i	0.303114	−	0.952954i	$-0.401974\pi$
$23$	−71.6801	−	71.6801i	−0.649841	−	0.649841i	−0.952954	+	0.303114i	$0.901974\pi$
$24$		0			0
$25$	−68.2259	+	68.2259i	−0.545807	+	0.545807i
$26$		0			0
$27$	−132.471	+	54.8712i	−0.944222	+	0.391110i
$28$		0			0
$29$	−53.0409	+	128.052i	−0.339636	+	0.819955i	0.658114	+	0.752918i	$0.271354\pi$
$29$	−53.0409	+	128.052i	−0.339636	+	0.819955i	−0.997751	+	0.0670366i	$0.978646\pi$
$30$		0			0
$31$	267.650			1.55069			0.775346	−	0.631537i	$-0.217576\pi$
$31$	267.650			1.55069			0.775346	+	0.631537i	$0.217576\pi$
$32$		0			0
$33$	−50.2070			−0.264846
$34$		0			0
$35$	−40.6768	+	98.2026i	−0.196447	+	0.474265i
$36$		0			0
$37$	205.678	−	85.1946i	0.913872	−	0.378538i	0.124334	−	0.992240i	$-0.460321\pi$
$37$	205.678	−	85.1946i	0.913872	−	0.378538i	0.789537	+	0.613702i	$0.210321\pi$
$38$		0			0
$39$	251.372	−	251.372i	1.03210	−	1.03210i
$40$		0			0
$41$	210.468	+	210.468i	0.801697	+	0.801697i	0.983361	−	0.181664i	$-0.0581482\pi$
$41$	210.468	+	210.468i	0.801697	+	0.801697i	−0.181664	+	0.983361i	$0.558148\pi$
$42$		0			0
$43$	56.9749	+	137.550i	0.202060	+	0.487817i	0.992132	−	0.125198i	$-0.0399566\pi$
$43$	56.9749	+	137.550i	0.202060	+	0.487817i	−0.790072	+	0.613015i	$0.789957\pi$
$44$		0			0
$45$	6.23610	+	2.58308i	0.0206583	+	0.00855694i
$46$		0			0
$47$			173.739i			0.539201i	0.962972	+	0.269600i	$0.0868916\pi$
$47$			173.739i			0.539201i	−0.962972	+	0.269600i	$0.913108\pi$
$48$		0			0
$49$		−	53.2384i		−	0.155214i
$50$		0			0
$51$	−372.103	−	154.130i	−1.02166	−	0.423187i
$52$		0			0
$53$	−188.605	−	455.333i	−0.488810	−	1.18009i	−0.955319	−	0.295575i	$-0.904489\pi$
$53$	−188.605	−	455.333i	−0.488810	−	1.18009i	0.466510	−	0.884516i	$-0.345511\pi$
$54$		0			0
$55$	37.3687	+	37.3687i	0.0916145	+	0.0916145i
$56$		0			0
$57$	367.990	−	367.990i	0.855113	−	0.855113i
$58$		0			0
$59$	627.964	−	260.111i	1.38566	−	0.573959i	0.439671	−	0.898159i	$-0.355095\pi$
$59$	627.964	−	260.111i	1.38566	−	0.573959i	0.945989	+	0.324199i	$0.105095\pi$
$60$		0			0
$61$	66.5782	−	160.734i	0.139745	−	0.337375i	−0.838476	−	0.544938i	$-0.816553\pi$
$61$	66.5782	−	160.734i	0.139745	−	0.337375i	0.978222	+	0.207563i	$0.0665532\pi$
$62$		0			0
$63$	−25.1621			−0.0503194
$64$		0			0
$65$	−374.189			−0.714038
$66$		0			0
$67$	−211.710	+	511.113i	−0.386037	+	0.931975i	0.604734	+	0.796428i	$0.293279\pi$
$67$	−211.710	+	511.113i	−0.386037	+	0.931975i	−0.990771	+	0.135548i	$0.956721\pi$
$68$		0			0
$69$	475.115	−	196.799i	0.828945	−	0.343360i
$70$		0			0
$71$	226.201	−	226.201i	0.378100	−	0.378100i	−0.492316	−	0.870416i	$-0.663850\pi$
$71$	226.201	−	226.201i	0.378100	−	0.378100i	0.870416	+	0.492316i	$0.163850\pi$
$72$		0			0
$73$	802.290	+	802.290i	1.28631	+	1.28631i	0.937009	+	0.349305i	$0.113582\pi$
$73$	802.290	+	802.290i	1.28631	+	1.28631i	0.349305	+	0.937009i	$0.386418\pi$
$74$		0			0
$75$	−187.316	−	452.220i	−0.288391	−	0.696238i
$76$		0			0
$77$	−182.007	−	75.3897i	−0.269371	−	0.111577i
$78$		0			0
$79$			552.368i			0.786662i	0.919397	+	0.393331i	$0.128677\pi$
$79$			552.368i			0.786662i	−0.919397	+	0.393331i	$0.871323\pi$
$80$		0			0
$81$		−	693.272i		−	0.950991i
$82$		0			0
$83$	137.983	+	57.1544i	0.182477	+	0.0755845i	0.472051	−	0.881571i	$-0.343514\pi$
$83$	137.983	+	57.1544i	0.182477	+	0.0755845i	−0.289574	+	0.957156i	$0.593514\pi$
$84$		0			0
$85$	162.236	+	391.672i	0.207023	+	0.499798i
$86$		0			0
$87$	−497.195	−	497.195i	−0.612700	−	0.612700i
$88$		0			0
$89$	−579.803	+	579.803i	−0.690550	+	0.690550i	−0.962353	−	0.271803i	$-0.912380\pi$
$89$	−579.803	+	579.803i	−0.690550	+	0.690550i	0.271803	+	0.962353i	$0.412380\pi$
$90$		0			0
$91$	1288.71	−	533.802i	1.48455	−	0.614919i
$92$		0			0
$93$	−519.610	+	1254.45i	−0.579366	+	1.39871i
$94$		0			0
$95$	−547.785			−0.591595
$96$		0			0
$97$	−912.077			−0.954716			−0.477358	−	0.878709i	$-0.658405\pi$
$97$	−912.077			−0.954716			−0.477358	+	0.878709i	$0.658405\pi$
$98$		0			0
$99$	−4.78742	+	11.5579i	−0.00486014	+	0.0117334i
$100$		0			0
$101$	−968.800	+	401.290i	−0.954447	+	0.395345i	−0.804901	−	0.593410i	$-0.797781\pi$
$101$	−968.800	+	401.290i	−0.954447	+	0.395345i	−0.149547	+	0.988755i	$0.547781\pi$
$102$		0			0
$103$	−351.683	+	351.683i	−0.336430	+	0.336430i	−0.855022	−	0.518592i	$-0.826457\pi$
$103$	−351.683	+	351.683i	−0.336430	+	0.336430i	0.518592	+	0.855022i	$0.326457\pi$
$104$		0			0
$105$	−381.296	−	381.296i	−0.354388	−	0.354388i
$106$		0			0
$107$	95.4774	+	230.503i	0.0862631	+	0.208257i	0.961124	−	0.276116i	$-0.0890475\pi$
$107$	95.4774	+	230.503i	0.0862631	+	0.208257i	−0.874861	+	0.484374i	$0.839047\pi$
$108$		0			0
$109$	858.330	+	355.532i	0.754249	+	0.312420i	0.726474	−	0.687194i	$-0.241158\pi$
$109$	858.330	+	355.532i	0.754249	+	0.312420i	0.0277749	+	0.999614i	$0.491158\pi$
$110$		0			0
$111$			1129.39i			0.965735i
$112$		0			0
$113$		−	1154.63i		−	0.961222i	−0.876934	−	0.480611i	$-0.840415\pi$
$113$		−	1154.63i		−	0.961222i	0.876934	−	0.480611i	$-0.159585\pi$
$114$		0			0
$115$	−500.102	−	207.149i	−0.405519	−	0.167972i
$116$		0			0
$117$	−33.8977	−	81.8362i	−0.0267850	−	0.0646646i
$118$		0			0
$119$	−1117.48	−	1117.48i	−0.860838	−	0.860838i
$120$		0			0
$121$	871.901	−	871.901i	0.655072	−	0.655072i
$122$		0			0
$123$	−1395.04	+	577.844i	−1.02265	+	0.423597i
$124$		0			0
$125$	−452.601	+	1092.67i	−0.323855	+	0.781854i
$126$		0			0
$127$	−953.091			−0.665930			−0.332965	−	0.942939i	$-0.608049\pi$
$127$	−953.091			−0.665930			−0.332965	+	0.942939i	$0.608049\pi$
$128$		0			0
$129$	−755.290			−0.515501
$130$		0			0
$131$	−26.3943	+	63.7216i	−0.0176037	+	0.0424991i	−0.932437	−	0.361333i	$-0.882322\pi$
$131$	−26.3943	+	63.7216i	−0.0176037	+	0.0424991i	0.914833	+	0.403832i	$0.132322\pi$
$132$		0			0
$133$	1886.58	−	781.446i	1.22998	−	0.509473i
$134$		0			0
$135$	−541.401	+	541.401i	−0.345158	+	0.345158i
$136$		0			0
$137$	−1910.45	−	1910.45i	−1.19139	−	1.19139i	−0.976677	−	0.214713i	$-0.931118\pi$
$137$	−1910.45	−	1910.45i	−1.19139	−	1.19139i	−0.214713	−	0.976677i	$-0.568882\pi$
$138$		0			0
$139$	525.552	+	1268.79i	0.320696	+	0.774228i	0.999214	+	0.0396445i	$0.0126225\pi$
$139$	525.552	+	1268.79i	0.320696	+	0.774228i	−0.678518	+	0.734584i	$0.737377\pi$
$140$		0			0
$141$	−814.297	−	337.293i	−0.486356	−	0.201455i
$142$		0			0
$143$		−	693.516i		−	0.405557i
$144$		0			0
$145$			740.118i			0.423886i
$146$		0			0
$147$	249.523	+	103.356i	0.140002	+	0.0579908i
$148$		0			0
$149$	477.450	+	1152.67i	0.262512	+	0.633759i	0.999093	−	0.0425902i	$-0.0135610\pi$
$149$	477.450	+	1152.67i	0.262512	+	0.633759i	−0.736581	+	0.676349i	$0.763561\pi$
$150$		0			0
$151$	1185.23	+	1185.23i	0.638757	+	0.638757i	0.950249	−	0.311492i	$-0.100829\pi$
$151$	1185.23	+	1185.23i	0.638757	+	0.638757i	−0.311492	+	0.950249i	$0.600829\pi$
$152$		0			0
$153$	−70.9629	+	70.9629i	−0.0374968	+	0.0374968i
$154$		0			0
$155$	1320.42	−	546.937i	0.684250	−	0.283426i
$156$		0			0
$157$	187.368	−	452.347i	0.0952460	−	0.229944i	−0.869075	−	0.494681i	$-0.835285\pi$
$157$	187.368	−	452.347i	0.0952460	−	0.229944i	0.964321	+	0.264737i	$0.0852850\pi$
$158$		0			0
$159$	2500.25			1.24706
$160$		0			0
$161$	2017.87			0.987764
$162$		0			0
$163$	926.026	−	2235.62i	0.444981	−	1.07428i	−0.529197	−	0.848499i	$-0.677507\pi$
$163$	926.026	−	2235.62i	0.444981	−	1.07428i	0.974178	−	0.225781i	$-0.0724933\pi$
$164$		0			0
$165$	−247.690	+	102.597i	−0.116865	+	0.0484069i
$166$		0			0
$167$	−753.289	+	753.289i	−0.349049	+	0.349049i	−0.859755	−	0.510706i	$-0.829384\pi$
$167$	−753.289	+	753.289i	−0.349049	+	0.349049i	0.510706	+	0.859755i	$0.329384\pi$
$168$		0			0
$169$	1918.72	+	1918.72i	0.873338	+	0.873338i
$170$		0			0
$171$	−49.6237	−	119.802i	−0.0221919	−	0.0535760i
$172$		0			0
$173$	−186.646	−	77.3114i	−0.0820257	−	0.0339762i	0.341293	−	0.939957i	$-0.389135\pi$
$173$	−186.646	−	77.3114i	−0.0820257	−	0.0339762i	−0.423319	+	0.905981i	$0.639135\pi$
$174$		0			0
$175$		−	1920.62i		−	0.829632i
$176$		0			0
$177$			3448.18i			1.46430i
$178$		0			0
$179$	1509.31	+	625.176i	0.630229	+	0.261049i	0.674850	−	0.737955i	$-0.264208\pi$
$179$	1509.31	+	625.176i	0.630229	+	0.261049i	−0.0446216	+	0.999004i	$0.514208\pi$
$180$		0			0
$181$	−772.420	−	1864.79i	−0.317202	−	0.765793i	−0.999400	−	0.0346258i	$-0.988976\pi$
$181$	−772.420	−	1864.79i	−0.317202	−	0.765793i	0.682199	−	0.731167i	$-0.261024\pi$
$182$		0			0
$183$	624.090	+	624.090i	0.252099	+	0.252099i
$184$		0			0
$185$	840.595	−	840.595i	0.334064	−	0.334064i
$186$		0			0
$187$	−725.918	+	300.685i	−0.283874	+	0.117584i
$188$		0			0
$189$	1092.25	−	2636.93i	0.420368	−	1.01486i
$190$		0			0
$191$	−1509.32			−0.571784			−0.285892	−	0.958262i	$-0.592290\pi$
$191$	−1509.32			−0.571784			−0.285892	+	0.958262i	$0.592290\pi$
$192$		0			0
$193$	3625.68			1.35224			0.676120	−	0.736791i	$-0.263660\pi$
$193$	3625.68			1.35224			0.676120	+	0.736791i	$0.263660\pi$
$194$		0			0
$195$	726.442	−	1753.79i	0.266778	−	0.644058i
$196$		0			0
$197$	−1764.33	+	730.811i	−0.638090	+	0.264305i	−0.678186	−	0.734890i	$-0.737234\pi$
$197$	−1764.33	+	730.811i	−0.638090	+	0.264305i	0.0400962	+	0.999196i	$0.487234\pi$
$198$		0			0
$199$	2008.70	−	2008.70i	0.715544	−	0.715544i	−0.252146	−	0.967689i	$-0.581136\pi$
$199$	2008.70	−	2008.70i	0.715544	−	0.715544i	0.967689	+	0.252146i	$0.0811362\pi$
$200$		0			0
$201$	−1984.52	−	1984.52i	−0.696406	−	0.696406i
$202$		0			0
$203$	−1055.82	−	2548.97i	−0.365044	−	0.881295i
$204$		0			0
$205$	1468.40	+	608.233i	0.500282	+	0.207224i
$206$		0			0
$207$		−	128.139i		−	0.0430255i
$208$		0			0
$209$		−	1015.25i		−	0.336013i
$210$		0			0
$211$	1133.08	+	469.337i	0.369689	+	0.153130i	0.559790	−	0.828634i	$-0.310882\pi$
$211$	1133.08	+	469.337i	0.369689	+	0.153130i	−0.190101	+	0.981764i	$0.560882\pi$
$212$		0			0
$213$	621.039	+	1499.32i	0.199779	+	0.482309i
$214$		0			0
$215$	562.158	+	562.158i	0.178320	+	0.178320i
$216$		0			0
$217$	−3767.31	+	3767.31i	−1.17853	+	1.17853i
$218$		0			0
$219$	−5317.80	+	2202.70i	−1.64084	+	0.679657i
$220$		0			0
$221$	2129.02	−	5139.91i	0.648025	−	1.56447i
$222$		0			0
$223$	3100.74			0.931125			0.465562	−	0.885015i	$-0.345852\pi$
$223$	3100.74			0.931125			0.465562	+	0.885015i	$0.345852\pi$
$224$		0			0
$225$	−121.964			−0.0361375
$226$		0			0
$227$	−1661.15	+	4010.36i	−0.485701	+	1.17259i	0.471162	+	0.882047i	$0.343835\pi$
$227$	−1661.15	+	4010.36i	−0.485701	+	1.17259i	−0.956863	+	0.290539i	$0.906165\pi$
$228$		0			0
$229$	−2972.95	+	1231.44i	−0.857895	+	0.355352i	−0.767884	−	0.640589i	$-0.778690\pi$
$229$	−2972.95	+	1231.44i	−0.857895	+	0.355352i	−0.0900110	+	0.995941i	$0.528690\pi$
$230$		0			0
$231$	706.687	−	706.687i	0.201284	−	0.201284i
$232$		0			0
$233$	1590.35	+	1590.35i	0.447155	+	0.447155i	0.894408	−	0.447253i	$-0.147597\pi$
$233$	1590.35	+	1590.35i	0.447155	+	0.447155i	−0.447253	+	0.894408i	$0.647597\pi$
$234$		0			0
$235$	355.031	+	857.121i	0.0985518	+	0.237925i
$236$		0			0
$237$	−2588.89	−	1072.35i	−0.709564	−	0.293911i
$238$		0			0
$239$		−	6173.19i		−	1.67076i	−0.549676	−	0.835378i	$-0.685249\pi$
$239$		−	6173.19i		−	1.67076i	0.549676	−	0.835378i	$-0.314751\pi$
$240$		0			0
$241$		−	1436.00i		−	0.383822i	−0.981412	−	0.191911i	$-0.938531\pi$
$241$		−	1436.00i		−	0.383822i	0.981412	−	0.191911i	$-0.0614685\pi$
$242$		0			0
$243$	−327.413	−	135.619i	−0.0864344	−	0.0358023i
$244$		0			0
$245$	−108.791	−	262.646i	−0.0283691	−	0.0684890i
$246$		0			0
$247$	5083.09	+	5083.09i	1.30943	+	1.30943i
$248$		0			0
$249$	−535.754	+	535.754i	−0.136354	+	0.136354i
$250$		0			0
$251$	−4781.23	+	1980.45i	−1.20235	+	0.498028i	−0.891756	−	0.452516i	$-0.850526\pi$
$251$	−4781.23	+	1980.45i	−1.20235	+	0.498028i	−0.310589	+	0.950544i	$0.600526\pi$
$252$		0			0
$253$	383.926	−	926.879i	0.0954040	−	0.230326i
$254$		0			0
$255$	−2150.69			−0.528162
$256$		0			0
$257$	−246.466			−0.0598215			−0.0299107	−	0.999553i	$-0.509522\pi$
$257$	−246.466			−0.0598215			−0.0299107	+	0.999553i	$0.509522\pi$
$258$		0			0
$259$	−1695.86	+	4094.17i	−0.406856	+	0.982237i
$260$		0			0
$261$	−161.866	+	67.0470i	−0.0383879	+	0.0159008i
$262$		0			0
$263$	−3454.60	+	3454.60i	−0.809960	+	0.809960i	−0.984628	−	0.174667i	$-0.944115\pi$
$263$	−3454.60	+	3454.60i	−0.809960	+	0.809960i	0.174667	+	0.984628i	$0.444115\pi$
$264$		0			0
$265$	−1860.92	−	1860.92i	−0.431380	−	0.431380i
$266$		0			0
$267$	−1591.86	−	3843.09i	−0.364870	−	0.880874i
$268$		0			0
$269$	2611.67	+	1081.79i	0.591958	+	0.245197i	0.658493	−	0.752587i	$-0.271194\pi$
$269$	2611.67	+	1081.79i	0.591958	+	0.245197i	−0.0665350	+	0.997784i	$0.521194\pi$
$270$		0			0
$271$			3464.52i			0.776585i	0.921536	+	0.388292i	$0.126935\pi$
$271$			3464.52i			0.776585i	−0.921536	+	0.388292i	$0.873065\pi$
$272$		0			0
$273$			7076.37i			1.56880i
$274$		0			0
$275$	−882.213	−	365.425i	−0.193453	−	0.0801307i
$276$		0			0
$277$	1186.33	+	2864.06i	0.257328	+	0.621245i	0.998760	−	0.0497833i	$-0.0158531\pi$
$277$	1186.33	+	2864.06i	0.257328	+	0.621245i	−0.741432	+	0.671028i	$0.765853\pi$
$278$		0			0
$279$	239.233	+	239.233i	0.0513352	+	0.0513352i
$280$		0			0
$281$	3210.39	−	3210.39i	0.681552	−	0.681552i	−0.278798	−	0.960350i	$-0.589936\pi$
$281$	3210.39	−	3210.39i	0.681552	−	0.681552i	0.960350	+	0.278798i	$0.0899360\pi$
$282$		0			0
$283$	2512.41	−	1040.67i	0.527729	−	0.218593i	−0.102879	−	0.994694i	$-0.532806\pi$
$283$	2512.41	−	1040.67i	0.527729	−	0.218593i	0.630608	+	0.776101i	$0.282806\pi$
$284$		0			0
$285$	1063.46	−	2567.41i	0.221031	−	0.533615i
$286$		0			0
$287$	−5924.88			−1.21859
$288$		0			0
$289$	−1390.14			−0.282950
$290$		0			0
$291$	1770.68	−	4274.81i	0.356699	−	0.861147i
$292$		0			0
$293$	−7264.11	+	3008.89i	−1.44838	+	0.599937i	−0.961812	−	0.273709i	$-0.911749\pi$
$293$	−7264.11	+	3008.89i	−1.44838	+	0.599937i	−0.486563	+	0.873646i	$0.661749\pi$
$294$		0			0
$295$	2566.46	−	2566.46i	0.506525	−	0.506525i
$296$		0			0
$297$	−1003.42	−	1003.42i	−0.196042	−	0.196042i
$298$		0			0
$299$	2718.41	+	6562.83i	0.525786	+	1.26936i
$300$		0			0
$301$	−2738.03	−	1134.13i	−0.524310	−	0.217176i
$302$		0			0
$303$		−	5319.72i		−	1.00861i
$304$		0			0
$305$		−	929.012i		−	0.174410i
$306$		0			0
$307$	−1055.79	−	437.322i	−0.196277	−	0.0813006i	0.282380	−	0.959303i	$-0.408876\pi$
$307$	−1055.79	−	437.322i	−0.196277	−	0.0813006i	−0.478657	+	0.878002i	$0.658876\pi$
$308$		0			0
$309$	−965.552	−	2331.05i	−0.177762	−	0.429155i
$310$		0			0
$311$	−2154.35	−	2154.35i	−0.392804	−	0.392804i	0.482882	−	0.875686i	$-0.339590\pi$
$311$	−2154.35	−	2154.35i	−0.392804	−	0.392804i	−0.875686	+	0.482882i	$0.839590\pi$
$312$		0			0
$313$	−3659.65	+	3659.65i	−0.660881	+	0.660881i	−0.955588	−	0.294706i	$-0.904778\pi$
$313$	−3659.65	+	3659.65i	−0.660881	+	0.660881i	0.294706	+	0.955588i	$0.404778\pi$
$314$		0			0
$315$	−124.134	+	51.4180i	−0.0222037	+	0.00919707i
$316$		0			0
$317$	−3106.88	+	7500.68i	−0.550473	+	1.32896i	0.366652	+	0.930358i	$0.380504\pi$
$317$	−3106.88	+	7500.68i	−0.550473	+	1.32896i	−0.917125	+	0.398601i	$0.869496\pi$
$318$		0			0
$319$	−1371.72			−0.240757
$320$		0			0
$321$	−1265.70			−0.220076
$322$		0			0
$323$	3116.73	−	7524.45i	0.536902	−	1.29620i
$324$		0			0
$325$	6246.57	−	2587.41i	1.06615	−	0.441612i
$326$		0			0
$327$	−3332.68	+	3332.68i	−0.563602	+	0.563602i
$328$		0			0
$329$	−2445.46	−	2445.46i	−0.409795	−	0.409795i
$330$		0			0
$331$	−2372.98	−	5728.87i	−0.394050	−	0.951321i	−0.989048	−	0.147594i	$-0.952847\pi$
$331$	−2372.98	−	5728.87i	−0.394050	−	0.951321i	0.594998	−	0.803727i	$-0.297153\pi$
$332$		0			0
$333$	259.990	+	107.691i	0.0427848	+	0.0177220i
$334$		0			0
$335$			2954.14i			0.481796i
$336$		0			0
$337$		−	5514.75i		−	0.891418i	−0.895178	−	0.445709i	$-0.852952\pi$
$337$		−	5514.75i		−	0.891418i	0.895178	−	0.445709i	$-0.147048\pi$
$338$		0			0
$339$	5411.61	+	2241.56i	0.867016	+	0.359130i
$340$		0			0
$341$	1013.68	+	2447.24i	0.160979	+	0.388638i
$342$		0			0
$343$	−4078.53	−	4078.53i	−0.642041	−	0.642041i
$344$		0			0
$345$	1941.77	−	1941.77i	0.303019	−	0.303019i
$346$		0			0
$347$	9323.05	−	3861.74i	1.44233	−	0.597432i	0.481966	−	0.876190i	$-0.339923\pi$
$347$	9323.05	−	3861.74i	1.44233	−	0.597432i	0.960361	+	0.278758i	$0.0899227\pi$
$348$		0			0
$349$	−1844.20	+	4452.29i	−0.282859	+	0.682882i	−0.999900	−	0.0141493i	$-0.995496\pi$
$349$	−1844.20	+	4452.29i	−0.282859	+	0.682882i	0.717041	+	0.697031i	$0.245496\pi$
$350$		0			0
$351$	10047.7			1.52794
$352$		0			0
$353$	7343.73			1.10727			0.553636	−	0.832759i	$-0.313240\pi$
$353$	7343.73			1.10727			0.553636	+	0.832759i	$0.313240\pi$
$354$		0			0
$355$	653.700	−	1578.17i	0.0977317	−	0.235945i
$356$		0			0
$357$	7406.99	−	3068.08i	1.09809	−	0.454846i
$358$		0			0
$359$	−4187.33	+	4187.33i	−0.615596	+	0.615596i	−0.944399	−	0.328802i	$-0.893355\pi$
$359$	−4187.33	+	4187.33i	−0.615596	+	0.615596i	0.328802	+	0.944399i	$0.393355\pi$
$360$		0			0
$361$	2591.22	+	2591.22i	0.377784	+	0.377784i
$362$		0			0
$363$	2393.82	+	5779.20i	0.346124	+	0.835617i
$364$		0			0
$365$	5597.46	+	2318.54i	0.802697	+	0.332488i
$366$		0			0
$367$			9231.47i			1.31302i	0.754317	+	0.656510i	$0.227968\pi$
$367$			9231.47i			1.31302i	−0.754317	+	0.656510i	$0.772032\pi$
$368$		0			0
$369$			376.244i			0.0530798i
$370$		0			0
$371$	9063.75	+	3754.33i	1.26837	+	0.525377i
$372$		0			0
$373$	−117.113	−	282.737i	−0.0162571	−	0.0392481i	0.915543	−	0.402221i	$-0.131762\pi$
$373$	−117.113	−	282.737i	−0.0162571	−	0.0392481i	−0.931800	+	0.362973i	$0.881762\pi$
$374$		0			0
$375$	−4242.58	−	4242.58i	−0.584230	−	0.584230i
$376$		0			0
$377$	6867.82	−	6867.82i	0.938224	−	0.938224i
$378$		0			0
$379$	−3068.05	+	1270.83i	−0.415819	+	0.172238i	−0.580777	−	0.814063i	$-0.697251\pi$
$379$	−3068.05	+	1270.83i	−0.415819	+	0.172238i	0.164958	+	0.986301i	$0.447251\pi$
$380$		0			0
$381$	1850.31	−	4467.04i	0.248804	−	0.600665i
$382$		0			0
$383$	−1379.97			−0.184107			−0.0920537	−	0.995754i	$-0.529343\pi$
$383$	−1379.97			−0.184107			−0.0920537	+	0.995754i	$0.529343\pi$
$384$		0			0
$385$	−1051.97			−0.139255
$386$		0			0
$387$	−72.0198	+	173.871i	−0.00945987	+	0.0228381i
$388$		0			0
$389$	1279.89	−	530.148i	0.166820	−	0.0690992i	−0.297711	−	0.954656i	$-0.596223\pi$
$389$	1279.89	−	530.148i	0.166820	−	0.0690992i	0.464531	+	0.885557i	$0.346223\pi$
$390$		0			0
$391$	5690.85	−	5690.85i	0.736058	−	0.736058i
$392$		0			0
$393$	−247.415	−	247.415i	−0.0317568	−	0.0317568i
$394$		0			0
$395$	1128.75	+	2725.04i	0.143781	+	0.347118i
$396$		0			0
$397$	−706.615	−	292.690i	−0.0893300	−	0.0370017i	0.337571	−	0.941300i	$-0.390395\pi$
$397$	−706.615	−	292.690i	−0.0893300	−	0.0370017i	−0.426901	+	0.904298i	$0.640395\pi$
$398$		0			0
$399$			10359.3i			1.29978i
$400$		0			0
$401$		−	9680.79i		−	1.20557i	−0.797902	−	0.602787i	$-0.794057\pi$
$401$		−	9680.79i		−	1.20557i	0.797902	−	0.602787i	$-0.205943\pi$
$402$		0			0
$403$	−17327.9	−	7177.45i	−2.14184	−	0.887181i
$404$		0			0
$405$	−1416.68	−	3420.18i	−0.173816	−	0.419630i
$406$		0			0
$407$	1557.94	+	1557.94i	0.189740	+	0.189740i
$408$		0			0
$409$	−1231.14	+	1231.14i	−0.148841	+	0.148841i	−0.777600	−	0.628759i	$-0.783563\pi$
$409$	−1231.14	+	1231.14i	−0.148841	+	0.148841i	0.628759	+	0.777600i	$0.283563\pi$
$410$		0			0
$411$	12663.0	−	5245.17i	1.51975	−	0.629502i
$412$		0			0
$413$	−5177.71	+	12500.1i	−0.616896	+	1.48932i
$414$		0			0
$415$	797.516			0.0943338
$416$		0			0
$417$	−6967.00			−0.818167
$418$		0			0
$419$	−3904.87	+	9427.19i	−0.455287	+	1.09916i	0.514997	+	0.857192i	$0.327793\pi$
$419$	−3904.87	+	9427.19i	−0.455287	+	1.09916i	−0.970284	+	0.241968i	$0.922207\pi$
$420$		0			0
$421$	10566.0	−	4376.59i	1.22318	−	0.506656i	0.324758	−	0.945797i	$-0.394717\pi$
$421$	10566.0	−	4376.59i	1.22318	−	0.506656i	0.898418	+	0.439141i	$0.144717\pi$
$422$		0			0
$423$	−155.292	+	155.292i	−0.0178501	+	0.0178501i
$424$		0			0
$425$	−5416.61	−	5416.61i	−0.618222	−	0.618222i
$426$		0			0
$427$	1325.29	+	3199.53i	0.150199	+	0.362614i
$428$		0			0
$429$	3250.44	+	1346.37i	0.365810	+	0.151523i
$430$		0			0
$431$		−	16965.2i		−	1.89602i	−0.318242	−	0.948010i	$-0.603092\pi$
$431$		−	16965.2i		−	1.89602i	0.318242	−	0.948010i	$-0.396908\pi$
$432$		0			0
$433$		−	5628.82i		−	0.624720i	−0.949964	−	0.312360i	$-0.898880\pi$
$433$		−	5628.82i		−	0.624720i	0.949964	−	0.312360i	$-0.101120\pi$
$434$		0			0
$435$	−3468.86	−	1436.85i	−0.382342	−	0.158371i
$436$		0			0
$437$	3979.55	+	9607.49i	0.435625	+	1.05169i
$438$		0			0
$439$	−6003.38	−	6003.38i	−0.652678	−	0.652678i	0.300959	−	0.953637i	$-0.402693\pi$
$439$	−6003.38	−	6003.38i	−0.652678	−	0.652678i	−0.953637	+	0.300959i	$0.902693\pi$
$440$		0			0
$441$	47.5859	−	47.5859i	0.00513831	−	0.00513831i
$442$		0			0
$443$	−1448.22	+	599.872i	−0.155321	+	0.0643359i	−0.458989	−	0.888442i	$-0.651788\pi$
$443$	−1448.22	+	599.872i	−0.155321	+	0.0643359i	0.303669	+	0.952778i	$0.401788\pi$
$444$		0			0
$445$	−1675.58	+	4045.20i	−0.178494	+	0.430923i
$446$		0			0
$447$	−6329.34			−0.669726
$448$		0			0
$449$	−12533.6			−1.31737			−0.658683	−	0.752421i	$-0.728886\pi$
$449$	−12533.6			−1.31737			−0.658683	+	0.752421i	$0.728886\pi$
$450$		0			0
$451$	−1127.29	+	2721.51i	−0.117698	+	0.284149i
$452$		0			0
$453$	−7856.00	+	3254.06i	−0.814806	+	0.337504i
$454$		0			0
$455$	5266.90	−	5266.90i	0.542672	−	0.542672i
$456$		0			0
$457$	11661.6	+	11661.6i	1.19367	+	1.19367i	0.976029	+	0.217641i	$0.0698361\pi$
$457$	11661.6	+	11661.6i	1.19367	+	1.19367i	0.217641	+	0.976029i	$0.430164\pi$
$458$		0			0
$459$	−4356.35	−	10517.2i	−0.443000	−	1.06950i
$460$		0			0
$461$	−8424.31	−	3489.46i	−0.851104	−	0.352539i	−0.0858823	−	0.996305i	$-0.527371\pi$
$461$	−8424.31	−	3489.46i	−0.851104	−	0.352539i	−0.765222	+	0.643766i	$0.777371\pi$
$462$		0			0
$463$			11549.8i			1.15932i	0.814860	+	0.579658i	$0.196814\pi$
$463$			11549.8i			1.15932i	−0.814860	+	0.579658i	$0.803186\pi$
$464$		0			0
$465$			7250.49i			0.723083i
$466$		0			0
$467$	6314.42	+	2615.52i	0.625689	+	0.259169i	0.672920	−	0.739715i	$-0.265040\pi$
$467$	6314.42	+	2615.52i	0.625689	+	0.259169i	−0.0472314	+	0.998884i	$0.515040\pi$
$468$		0			0
$469$	−4214.24	−	10174.1i	−0.414916	−	1.00170i
$470$		0			0
$471$	1756.35	+	1756.35i	0.171823	+	0.171823i
$472$		0			0
$473$	−1041.89	+	1041.89i	−0.101282	+	0.101282i
$474$		0			0
$475$	9144.51	−	3787.78i	0.883324	−	0.365885i
$476$		0			0
$477$	238.409	−	575.569i	0.0228847	−	0.0552484i
$478$		0			0
$479$	10874.6			1.03731			0.518655	−	0.854983i	$-0.326433\pi$
$479$	10874.6			1.03731			0.518655	+	0.854983i	$0.326433\pi$
$480$		0			0
$481$	−15600.4			−1.47883
$482$		0			0
$483$	−3917.43	+	9457.52i	−0.369046	+	0.890957i
$484$		0			0
$485$	−4499.62	+	1863.81i	−0.421273	+	0.174497i
$486$		0			0
$487$	−538.006	+	538.006i	−0.0500603	+	0.0500603i	−0.731694	−	0.681633i	$-0.761270\pi$
$487$	−538.006	+	538.006i	−0.0500603	+	0.0500603i	0.681633	+	0.731694i	$0.261270\pi$
$488$		0			0
$489$	8680.37	+	8680.37i	0.802741	+	0.802741i
$490$		0			0
$491$	−1701.48	−	4107.75i	−0.156389	−	0.377556i	0.826193	−	0.563387i	$-0.190502\pi$
$491$	−1701.48	−	4107.75i	−0.156389	−	0.377556i	−0.982582	+	0.185831i	$0.940502\pi$
$492$		0			0
$493$	−10166.4	−	4211.04i	−0.928742	−	0.384697i
$494$		0			0
$495$			66.8023i			0.00606574i
$496$		0			0
$497$			6367.77i			0.574716i
$498$		0			0
$499$	−19571.5	−	8106.78i	−1.75579	−	0.727273i	−0.997123	−	0.0757967i	$-0.975850\pi$
$499$	−19571.5	−	8106.78i	−1.75579	−	0.727273i	−0.758669	−	0.651476i	$-0.774150\pi$
$500$		0			0
$501$	−2068.17	−	4993.00i	−0.184429	−	0.445251i
$502$		0			0
$503$	373.535	+	373.535i	0.0331115	+	0.0331115i	0.723469	−	0.690357i	$-0.242547\pi$
$503$	373.535	+	373.535i	0.0331115	+	0.0331115i	−0.690357	+	0.723469i	$0.742547\pi$
$504$		0			0
$505$	−3959.43	+	3959.43i	−0.348896	+	0.348896i
$506$		0			0
$507$	−12717.8	+	5267.90i	−1.11404	+	0.461451i
$508$		0			0
$509$	874.883	−	2112.15i	0.0761857	−	0.183928i	−0.881198	−	0.472747i	$-0.843262\pi$
$509$	874.883	−	2112.15i	0.0761857	−	0.183928i	0.957384	+	0.288819i	$0.0932624\pi$
$510$		0			0
$511$	−22585.2			−1.95521
$512$		0			0
$513$	14709.1			1.26593
$514$		0			0
$515$	−1016.33	+	2453.64i	−0.0869609	+	0.209942i
$516$		0			0
$517$	−1588.57	+	658.008i	−0.135136	+	0.0559751i
$518$		0			0
$519$	724.701	−	724.701i	0.0612926	−	0.0612926i
$520$		0			0
$521$	15352.0	+	15352.0i	1.29095	+	1.29095i	0.934203	+	0.356743i	$0.116113\pi$
$521$	15352.0	+	15352.0i	1.29095	+	1.29095i	0.356743	+	0.934203i	$0.383887\pi$
$522$		0			0
$523$	2376.45	+	5737.26i	0.198690	+	0.479680i	0.991550	−	0.129723i	$-0.0414089\pi$
$523$	2376.45	+	5737.26i	0.198690	+	0.479680i	−0.792860	+	0.609404i	$0.791409\pi$
$524$		0			0
$525$	9001.77	+	3728.65i	0.748323	+	0.309965i
$526$		0			0
$527$			21249.4i			1.75643i
$528$		0			0
$529$		−	1890.92i		−	0.155414i
$530$		0			0
$531$	793.785	+	328.796i	0.0648726	+	0.0268711i
$532$		0			0
$533$	−7981.84	−	19269.9i	−0.648653	−	1.56599i
$534$		0			0
$535$	942.053	+	942.053i	0.0761280	+	0.0761280i
$536$		0			0
$537$	−5860.27	+	5860.27i	−0.470930	+	0.470930i
$538$		0			0
$539$	486.782	−	201.632i	0.0389002	−	0.0161130i
$540$		0			0
$541$	2381.59	−	5749.66i	0.189265	−	0.456926i	−0.800553	−	0.599261i	$-0.795461\pi$
$541$	2381.59	−	5749.66i	0.189265	−	0.456926i	0.989819	+	0.142335i	$0.0454610\pi$
$542$		0			0
$543$	10239.6			0.809252
$544$		0			0
$545$	4960.99			0.389918
$546$		0			0
$547$	2560.31	−	6181.14i	0.200130	−	0.483156i	−0.791671	−	0.610947i	$-0.790789\pi$
$547$	2560.31	−	6181.14i	0.200130	−	0.483156i	0.991801	+	0.127791i	$0.0407887\pi$
$548$		0			0
$549$	203.178	−	84.1589i	0.0157949	−	0.00654247i
$550$		0			0
$551$	10054.0	−	10054.0i	0.777338	−	0.777338i
$552$		0			0
$553$	−7774.85	−	7774.85i	−0.597866	−	0.597866i
$554$		0			0
$555$	2307.87	+	5571.69i	0.176511	+	0.426135i
$556$		0			0
$557$	10306.9	+	4269.27i	0.784055	+	0.324766i	0.738551	−	0.674198i	$-0.235511\pi$
$557$	10306.9	+	4269.27i	0.784055	+	0.324766i	0.0455041	+	0.998964i	$0.485511\pi$
$558$		0			0
$559$		−	10432.9i		−	0.789384i
$560$		0			0
$561$		−	3986.05i		−	0.299984i
$562$		0			0
$563$	8478.56	+	3511.93i	0.634687	+	0.262896i	0.676743	−	0.736219i	$-0.263391\pi$
$563$	8478.56	+	3511.93i	0.634687	+	0.262896i	−0.0420563	+	0.999115i	$0.513391\pi$
$564$		0			0
$565$	−2359.45	−	5696.21i	−0.175686	−	0.424144i
$566$		0			0
$567$	9758.15	+	9758.15i	0.722758	+	0.722758i
$568$		0			0
$569$	304.321	−	304.321i	0.0224214	−	0.0224214i	−0.695807	−	0.718229i	$-0.744953\pi$
$569$	304.321	−	304.321i	0.0224214	−	0.0224214i	0.718229	+	0.695807i	$0.244953\pi$
$570$		0			0
$571$	−7459.96	+	3090.02i	−0.546742	+	0.226468i	−0.638918	−	0.769275i	$-0.720618\pi$
$571$	−7459.96	+	3090.02i	−0.546742	+	0.226468i	0.0921763	+	0.995743i	$0.470618\pi$
$572$		0			0
$573$	2930.16	−	7074.04i	0.213629	−	0.515746i
$574$		0			0
$575$	9780.88			0.709376
$576$		0			0
$577$	−11616.3			−0.838118			−0.419059	−	0.907959i	$-0.637640\pi$
$577$	−11616.3			−0.838118			−0.419059	+	0.907959i	$0.637640\pi$
$578$		0			0
$579$	−7038.82	+	16993.2i	−0.505221	+	1.21971i
$580$		0			0
$581$	−2746.65	+	1137.70i	−0.196128	+	0.0812389i
$582$		0			0
$583$	3449.00	−	3449.00i	0.245014	−	0.245014i
$584$		0			0
$585$	−334.460	−	334.460i	−0.0236380	−	0.0236380i
$586$		0			0
$587$	−6654.96	−	16066.5i	−0.467938	−	1.12970i	−0.965062	−	0.262023i	$-0.915610\pi$
$587$	−6654.96	−	16066.5i	−0.467938	−	1.12970i	0.497123	−	0.867680i	$-0.334390\pi$
$588$		0			0
$589$	−25366.7	−	10507.2i	−1.77456	−	0.735048i
$590$		0			0
$591$		−	9688.04i		−	0.674302i
$592$		0			0
$593$			9365.10i			0.648530i	0.945966	+	0.324265i	$0.105117\pi$
$593$			9365.10i			0.648530i	−0.945966	+	0.324265i	$0.894883\pi$
$594$		0			0
$595$	−7796.53	−	3229.43i	−0.537187	−	0.222510i
$596$		0			0
$597$	5514.93	+	13314.2i	0.378076	+	0.912756i
$598$		0			0
$599$	−12280.1	−	12280.1i	−0.837647	−	0.837647i	0.150902	−	0.988549i	$-0.451782\pi$
$599$	−12280.1	−	12280.1i	−0.837647	−	0.837647i	−0.988549	+	0.150902i	$0.951782\pi$
$600$		0			0
$601$	11681.6	−	11681.6i	0.792852	−	0.792852i	−0.189105	−	0.981957i	$-0.560559\pi$
$601$	11681.6	−	11681.6i	0.792852	−	0.792852i	0.981957	+	0.189105i	$0.0605587\pi$
$602$		0			0
$603$	−646.078	+	267.614i	−0.0436324	+	0.0180731i
$604$		0			0
$605$	2519.71	−	6083.12i	0.169324	−	0.408784i
$606$		0			0
$607$	20354.6			1.36107			0.680535	−	0.732716i	$-0.261747\pi$
$607$	20354.6			1.36107			0.680535	+	0.732716i	$0.261747\pi$
$608$		0			0
$609$	13996.5			0.931309
$610$		0			0
$611$	4659.07	−	11248.0i	0.308487	−	0.744754i
$612$		0			0
$613$	23946.8	−	9919.08i	1.57782	−	0.653553i	0.589751	−	0.807585i	$-0.299226\pi$
$613$	23946.8	−	9919.08i	1.57782	−	0.653553i	0.988066	+	0.154032i	$0.0492260\pi$
$614$		0			0
$615$	−5701.45	+	5701.45i	−0.373829	+	0.373829i
$616$		0			0
$617$	−17139.4	−	17139.4i	−1.11833	−	1.11833i	−0.991987	−	0.126340i	$-0.959677\pi$
$617$	−17139.4	−	17139.4i	−1.11833	−	1.11833i	−0.126340	−	0.991987i	$-0.540323\pi$
$618$		0			0
$619$	9612.31	+	23206.2i	0.624154	+	1.50684i	0.846783	+	0.531938i	$0.178536\pi$
$619$	9612.31	+	23206.2i	0.624154	+	1.50684i	−0.222629	+	0.974903i	$0.571464\pi$
$620$		0			0
$621$	13428.7	+	5562.35i	0.867753	+	0.359435i
$622$		0			0
$623$		−	16322.0i		−	1.04964i
$624$		0			0
$625$		−	5745.29i		−	0.367699i
$626$		0			0
$627$	4758.39	+	1970.99i	0.303081	+	0.125540i
$628$		0			0
$629$	6763.80	+	16329.2i	0.428760	+	1.03512i
$630$		0			0
$631$	−2243.98	−	2243.98i	−0.141571	−	0.141571i	0.632769	−	0.774340i	$-0.281918\pi$
$631$	−2243.98	−	2243.98i	−0.141571	−	0.141571i	−0.774340	+	0.632769i	$0.781918\pi$
$632$		0			0
$633$	−4399.46	+	4399.46i	−0.276245	+	0.276245i
$634$		0			0
$635$	−4701.96	+	1947.62i	−0.293845	+	0.121715i
$636$		0			0
$637$	−1427.67	+	3446.70i	−0.0888010	+	0.214385i
$638$		0			0
$639$	404.369			0.0250338
$640$		0			0
$641$	19815.9			1.22103			0.610515	−	0.792005i	$-0.290963\pi$
$641$	19815.9			1.22103			0.610515	+	0.792005i	$0.290963\pi$
$642$		0			0
$643$	5189.74	−	12529.1i	0.318295	−	0.768431i	−0.681050	−	0.732237i	$-0.738476\pi$
$643$	5189.74	−	12529.1i	0.318295	−	0.768431i	0.999345	−	0.0361945i	$-0.0115236\pi$
$644$		0			0
$645$	−3726.13	+	1543.42i	−0.227467	+	0.0942200i
$646$		0			0
$647$	−18031.1	+	18031.1i	−1.09563	+	1.09563i	−0.100717	+	0.994915i	$0.532114\pi$
$647$	−18031.1	+	18031.1i	−1.09563	+	1.09563i	−0.994915	+	0.100717i	$0.967886\pi$
$648$		0			0
$649$	4756.62	+	4756.62i	0.287694	+	0.287694i
$650$		0			0
$651$	−10343.2	−	24970.8i	−0.622708	−	1.50335i
$652$		0			0
$653$	4031.36	+	1669.85i	0.241592	+	0.100071i	0.500194	−	0.865913i	$-0.333262\pi$
$653$	4031.36	+	1669.85i	0.241592	+	0.100071i	−0.258602	+	0.965984i	$0.583262\pi$
$654$		0			0
$655$			368.299i			0.0219704i
$656$		0			0
$657$			1434.22i			0.0851660i
$658$		0			0
$659$	16047.0	+	6646.88i	0.948561	+	0.392907i	0.802690	−	0.596397i	$-0.203401\pi$
$659$	16047.0	+	6646.88i	0.948561	+	0.392907i	0.145871	+	0.989304i	$0.453401\pi$
$660$		0			0
$661$	6313.25	+	15241.5i	0.371493	+	0.896864i	0.993498	+	0.113850i	$0.0363185\pi$
$661$	6313.25	+	15241.5i	0.371493	+	0.896864i	−0.622005	+	0.783014i	$0.713682\pi$
$662$		0			0
$663$	19957.0	+	19957.0i	1.16903	+	1.16903i
$664$		0			0
$665$	7710.34	−	7710.34i	0.449615	−	0.449615i
$666$		0			0
$667$	12980.8	−	5376.81i	0.753550	−	0.312131i
$668$		0			0
$669$	−6019.70	+	14532.8i	−0.347885	+	0.839869i
$670$		0			0
$671$	1721.81			0.0990609
$672$		0			0
$673$	9059.04			0.518871			0.259436	−	0.965760i	$-0.416463\pi$
$673$	9059.04			0.518871			0.259436	+	0.965760i	$0.416463\pi$
$674$		0			0
$675$	5294.30	−	12781.6i	0.301893	−	0.728834i
$676$		0			0
$677$	1398.12	−	579.121i	0.0793710	−	0.0328765i	−0.342645	−	0.939465i	$-0.611323\pi$
$677$	1398.12	−	579.121i	0.0793710	−	0.0328765i	0.422016	+	0.906589i	$0.361323\pi$
$678$		0			0
$679$	12837.9	−	12837.9i	0.725588	−	0.725588i
$680$		0			0
$681$	−15571.2	−	15571.2i	−0.876199	−	0.876199i
$682$		0			0
$683$	11645.5	+	28114.8i	0.652422	+	1.57509i	0.809252	+	0.587462i	$0.199873\pi$
$683$	11645.5	+	28114.8i	0.652422	+	1.57509i	−0.156830	+	0.987626i	$0.550127\pi$
$684$		0			0
$685$	−13328.9	−	5521.01i	−0.743462	−	0.307952i
$686$		0			0
$687$		−	16324.6i		−	0.906582i
$688$		0			0
$689$			34536.3i			1.90962i
$690$		0			0
$691$	4362.78	+	1807.12i	0.240185	+	0.0994879i	0.499529	−	0.866297i	$-0.333506\pi$
$691$	4362.78	+	1807.12i	0.240185	+	0.0994879i	−0.259344	+	0.965785i	$0.583506\pi$
$692$		0			0
$693$	−95.2972	−	230.068i	−0.00522372	−	0.0126112i
$694$		0			0
$695$	5185.49	+	5185.49i	0.283017	+	0.283017i
$696$		0			0
$697$	−16709.5	+	16709.5i	−0.908061	+	0.908061i
$698$		0			0
$699$	−10541.3	+	4366.33i	−0.570396	+	0.236266i
$700$		0			0
$701$	6417.56	−	15493.3i	0.345774	−	0.834773i	−0.651335	−	0.758790i	$-0.725791\pi$
$701$	6417.56	−	15493.3i	0.345774	−	0.834773i	0.997109	−	0.0759825i	$-0.0242093\pi$
$702$		0			0
$703$	−22837.8			−1.22524
$704$		0			0
$705$	−4706.48			−0.251428
$706$		0			0
$707$	7987.97	−	19284.7i	0.424920	−	1.02585i
$708$		0			0
$709$	−17513.4	+	7254.29i	−0.927686	+	0.384260i	−0.794800	−	0.606871i	$-0.792424\pi$
$709$	−17513.4	+	7254.29i	−0.927686	+	0.384260i	−0.132886	+	0.991131i	$0.542424\pi$
$710$		0			0
$711$	−493.721	+	493.721i	−0.0260422	+	0.0260422i
$712$		0			0
$713$	−19185.2	−	19185.2i	−1.00770	−	1.00770i
$714$		0			0
$715$	−1417.18	−	3421.38i	−0.0741252	−	0.178954i
$716$		0			0
$717$	28933.1	+	11984.5i	1.50701	+	0.624224i
$718$		0			0
$719$			4682.98i			0.242901i	0.992598	+	0.121450i	$0.0387545\pi$
$719$			4682.98i			0.242901i	−0.992598	+	0.121450i	$0.961245\pi$
$720$		0			0
$721$		−	9900.21i		−	0.511377i
$722$		0			0
$723$	6730.40	+	2787.82i	0.346205	+	0.143403i
$724$		0			0
$725$	−5117.71	−	12355.2i	−0.262161	−	0.632913i
$726$		0			0
$727$	−20269.6	−	20269.6i	−1.03405	−	1.03405i	−0.999399	−	0.0346553i	$-0.988967\pi$
$727$	−20269.6	−	20269.6i	−1.03405	−	1.03405i	−0.0346553	−	0.999399i	$-0.511033\pi$
$728$		0			0
$729$	14507.1	−	14507.1i	0.737039	−	0.737039i
$730$		0			0
$731$	−10920.4	+	4523.37i	−0.552537	+	0.228868i
$732$		0			0
$733$	1705.29	−	4116.94i	0.0859297	−	0.207453i	−0.875073	−	0.483990i	$-0.839187\pi$
$733$	1705.29	−	4116.94i	0.0859297	−	0.207453i	0.961003	+	0.276538i	$0.0891870\pi$
$734$		0			0
$735$	1442.20			0.0723758
$736$		0			0
$737$	−5475.14			−0.273649
$738$		0			0
$739$	467.052	−	1127.56i	0.0232487	−	0.0561273i	−0.911829	−	0.410570i	$-0.865330\pi$
$739$	467.052	−	1127.56i	0.0232487	−	0.0561273i	0.935078	+	0.354443i	$0.115330\pi$
$740$		0			0
$741$	−33692.1	+	13955.7i	−1.67033	+	0.691872i
$742$		0			0
$743$	−27671.7	+	27671.7i	−1.36632	+	1.36632i	−0.500701	+	0.865620i	$0.666924\pi$
$743$	−27671.7	+	27671.7i	−1.36632	+	1.36632i	−0.865620	+	0.500701i	$0.833076\pi$
$744$		0			0
$745$	4710.89	+	4710.89i	0.231669	+	0.231669i
$746$		0			0
$747$	72.2467	+	174.419i	0.00353865	+	0.00854305i
$748$		0			0
$749$	−4588.33	−	1900.55i	−0.223837	−	0.0927163i
$750$		0			0
$751$			22288.5i			1.08298i	0.840707	+	0.541490i	$0.182140\pi$
$751$			22288.5i			1.08298i	−0.840707	+	0.541490i	$0.817860\pi$
$752$		0			0
$753$		−	26253.9i		−	1.27058i
$754$		0			0
$755$	8269.15	+	3425.19i	0.398603	+	0.165107i
$756$		0			0
$757$	10902.9	+	26321.9i	0.523478	+	1.26379i	0.935730	+	0.352718i	$0.114742\pi$
$757$	10902.9	+	26321.9i	0.523478	+	1.26379i	−0.412252	+	0.911070i	$0.635258\pi$
$758$		0			0
$759$	3598.84	+	3598.84i	0.172108	+	0.172108i
$760$		0			0
$761$	−6249.83	+	6249.83i	−0.297709	+	0.297709i	−0.840116	−	0.542407i	$-0.817513\pi$
$761$	−6249.83	+	6249.83i	−0.297709	+	0.297709i	0.542407	+	0.840116i	$0.317513\pi$
$762$		0			0
$763$	−17085.7	+	7077.13i	−0.810673	+	0.335792i
$764$		0			0
$765$	−205.076	+	495.098i	−0.00969222	+	0.0233991i
$766$		0			0
$767$	−47630.1			−2.24227
$768$		0			0
$769$	5109.01			0.239578			0.119789	−	0.992799i	$-0.461778\pi$
$769$	5109.01			0.239578			0.119789	+	0.992799i	$0.461778\pi$
$770$		0			0
$771$	478.483	−	1155.16i	0.0223504	−	0.0539586i
$772$		0			0
$773$	119.699	−	49.5811i	0.00556958	−	0.00230699i	−0.379897	−	0.925029i	$-0.624041\pi$
$773$	119.699	−	49.5811i	0.00556958	−	0.00230699i	0.385466	+	0.922722i	$0.374041\pi$
$774$		0			0
$775$	−18260.7	+	18260.7i	−0.846379	+	0.846379i
$776$		0			0
$777$	−15896.7	−	15896.7i	−0.733963	−	0.733963i
$778$		0			0
$779$	−11684.8	−	28209.6i	−0.537422	−	1.29745i
$780$		0			0
$781$	2924.95	+	1211.55i	0.134011	+	0.0555094i
$782$		0			0
$783$		−	19873.6i		−	0.907055i
$784$		0			0
$785$		−	2614.48i		−	0.118872i
$786$		0			0
$787$	24341.3	+	10082.5i	1.10251	+	0.456674i	0.858352	−	0.513062i	$-0.171489\pi$
$787$	24341.3	+	10082.5i	1.10251	+	0.456674i	0.244157	+	0.969736i	$0.421489\pi$
$788$		0			0
$789$	−9484.67	−	22898.0i	−0.427963	−	1.03319i
$790$		0			0
$791$	16251.9	+	16251.9i	0.730533	+	0.730533i
$792$		0			0
$793$	−8620.64	+	8620.64i	−0.386038	+	0.386038i
$794$		0			0
$795$	12334.7	−	5109.20i	0.550273	−	0.227930i
$796$		0			0
$797$	9871.79	−	23832.6i	0.438741	−	1.05921i	−0.537643	−	0.843173i	$-0.680685\pi$
$797$	9871.79	−	23832.6i	0.438741	−	1.05921i	0.976384	−	0.216042i	$-0.0693149\pi$
$798$		0			0
$799$	−13793.5			−0.610739
$800$		0			0
$801$	−1036.49			−0.0457209
$802$		0			0
$803$	−4297.14	+	10374.2i	−0.188845	+	0.455913i
$804$		0			0
$805$	9954.90	−	4123.45i	0.435856	−	0.180537i
$806$		0			0
$807$	−10140.5	+	10140.5i	−0.442332	+	0.442332i
$808$		0			0
$809$	12475.0	+	12475.0i	0.542147	+	0.542147i	0.924158	−	0.382011i	$-0.124768\pi$
$809$	12475.0	+	12475.0i	0.542147	+	0.542147i	−0.382011	+	0.924158i	$0.624768\pi$
$810$		0			0
$811$	711.024	+	1716.56i	0.0307860	+	0.0743239i	0.938525	−	0.345212i	$-0.112193\pi$
$811$	711.024	+	1716.56i	0.0307860	+	0.0743239i	−0.907739	+	0.419536i	$0.862193\pi$
$812$		0			0
$813$	−16237.8	−	6725.93i	−0.700475	−	0.290146i
$814$		0			0
$815$		−	12921.5i		−	0.555362i
$816$		0			0
$817$		−	15273.0i		−	0.654021i
$818$		0			0
$819$	1629.01	+	674.758i	0.0695021	+	0.0287887i
$820$		0			0
$821$	7001.23	+	16902.5i	0.297618	+	0.718514i	0.999978	+	0.00669143i	$0.00212996\pi$
$821$	7001.23	+	16902.5i	0.297618	+	0.718514i	−0.702359	+	0.711823i	$0.747870\pi$
$822$		0			0
$823$	6527.87	+	6527.87i	0.276485	+	0.276485i	0.831704	−	0.555219i	$-0.187366\pi$
$823$	6527.87	+	6527.87i	0.276485	+	0.276485i	−0.555219	+	0.831704i	$0.687366\pi$
$824$		0			0
$825$	3425.41	−	3425.41i	0.144555	−	0.144555i
$826$		0			0
$827$	−22099.6	+	9153.94i	−0.929235	+	0.384902i	−0.795388	−	0.606100i	$-0.792733\pi$
$827$	−22099.6	+	9153.94i	−0.929235	+	0.384902i	−0.133847	+	0.991002i	$0.542733\pi$
$828$		0			0
$829$	−13794.8	+	33303.5i	−0.577939	+	1.39527i	0.316720	+	0.948519i	$0.397418\pi$
$829$	−13794.8	+	33303.5i	−0.577939	+	1.39527i	−0.894659	+	0.446749i	$0.852582\pi$
$830$		0			0
$831$	−15726.7			−0.656501
$832$		0			0
$833$	4226.72			0.175807
$834$		0			0
$835$	−2176.93	+	5255.59i	−0.0902227	+	0.217817i
$836$		0			0
$837$	−35455.9	+	14686.3i	−1.46420	+	0.606491i
$838$		0			0
$839$	22145.1	−	22145.1i	0.911243	−	0.911243i	−0.0851272	−	0.996370i	$-0.527130\pi$
$839$	22145.1	−	22145.1i	0.911243	−	0.911243i	0.996370	+	0.0851272i	$0.0271297\pi$
$840$		0			0
$841$	3661.61	+	3661.61i	0.150134	+	0.150134i
$842$		0			0
$843$	8814.20	+	21279.4i	0.360115	+	0.869395i
$844$		0			0
$845$	13386.7	+	5544.93i	0.544988	+	0.225741i
$846$		0			0
$847$			24544.8i			0.995715i
$848$		0			0
$849$			13795.7i			0.557678i
$850$		0			0
$851$	−20849.8	−	8636.26i	−0.839861	−	0.347882i
$852$		0			0
$853$	9655.46	+	23310.3i	0.387569	+	0.935675i	0.990454	+	0.137847i	$0.0440181\pi$
$853$	9655.46	+	23310.3i	0.387569	+	0.935675i	−0.602884	+	0.797829i	$0.705982\pi$
$854$		0			0
$855$	−489.625	−	489.625i	−0.0195846	−	0.0195846i
$856$		0			0
$857$	−7592.18	+	7592.18i	−0.302619	+	0.302619i	−0.842038	−	0.539419i	$-0.818644\pi$
$857$	−7592.18	+	7592.18i	−0.302619	+	0.302619i	0.539419	+	0.842038i	$0.318644\pi$
$858$		0			0
$859$	39825.7	−	16496.4i	1.58188	−	0.655237i	0.593171	−	0.805076i	$-0.297876\pi$
$859$	39825.7	−	16496.4i	1.58188	−	0.655237i	0.988710	+	0.149839i	$0.0478756\pi$
$860$		0			0
$861$	11502.4	−	27769.3i	0.455286	−	1.09916i
$862$		0			0
$863$	48726.7			1.92199			0.960995	−	0.276565i	$-0.0891962\pi$
$863$	48726.7			1.92199			0.960995	+	0.276565i	$0.0891962\pi$
$864$		0			0
$865$	−1078.78			−0.0424042
$866$		0			0
$867$	2698.78	−	6515.42i	0.105715	−	0.255219i
$868$		0			0
$869$	−5050.54	+	2092.00i	−0.197155	+	0.0816644i
$870$		0			0
$871$	27412.5	−	27412.5i	1.06640	−	1.06640i
$872$		0			0
$873$	−815.239	−	815.239i	−0.0316055	−	0.0316055i
$874$		0			0
$875$	−9009.35	−	21750.5i	−0.348082	−	0.840344i
$876$		0			0
$877$	17160.7	+	7108.21i	0.660749	+	0.273691i	0.687754	−	0.725944i	$-0.258597\pi$
$877$	17160.7	+	7108.21i	0.660749	+	0.273691i	−0.0270046	+	0.999635i	$0.508597\pi$
$878$		0			0
$879$		−	39887.5i		−	1.53057i
$880$		0			0
$881$			25601.4i			0.979039i	0.871992	+	0.489520i	$0.162828\pi$
$881$			25601.4i			0.979039i	−0.871992	+	0.489520i	$0.837172\pi$
$882$		0			0
$883$	−2470.51	−	1023.32i	−0.0941555	−	0.0390005i	0.335109	−	0.942180i	$-0.391227\pi$
$883$	−2470.51	−	1023.32i	−0.0941555	−	0.0390005i	−0.429264	+	0.903179i	$0.641227\pi$
$884$		0			0
$885$	7046.25	+	17011.2i	0.267635	+	0.646129i
$886$		0			0
$887$	3316.04	+	3316.04i	0.125526	+	0.125526i	0.767079	−	0.641553i	$-0.221709\pi$
$887$	3316.04	+	3316.04i	0.125526	+	0.125526i	−0.641553	+	0.767079i	$0.721709\pi$
$888$		0			0
$889$	13415.2	−	13415.2i	0.506110	−	0.506110i
$890$		0			0
$891$	6338.89	−	2625.65i	0.238340	−	0.0987236i
$892$		0			0
$893$	6820.53	−	16466.2i	0.255588	−	0.617044i
$894$		0			0
$895$	8723.52			0.325805
$896$		0			0
$897$	−36036.8			−1.34140
$898$		0			0
$899$	−14196.4	+	34273.2i	−0.526671	+	1.27150i
$900$		0			0
$901$	36150.0	−	14973.8i	1.33666	−	0.553662i
$902$		0			0
$903$	10631.1	−	10631.1i	0.391783	−	0.391783i
$904$		0			0
$905$	−7621.28	−	7621.28i	−0.279934	−	0.279934i
$906$		0			0
$907$	2525.01	+	6095.91i	0.0924382	+	0.223166i	0.963336	−	0.268299i	$-0.0864616\pi$
$907$	2525.01	+	6095.91i	0.0924382	+	0.223166i	−0.870897	+	0.491465i	$0.836462\pi$
$908$		0			0
$909$	−1224.62	−	507.255i	−0.0446844	−	0.0185089i
$910$		0			0
$911$			4913.39i			0.178692i	0.996001	+	0.0893458i	$0.0284776\pi$
$911$			4913.39i			0.178692i	−0.996001	+	0.0893458i	$0.971522\pi$
$912$		0			0
$913$			1478.10i			0.0535794i
$914$		0			0
$915$	4354.18	+	1803.56i	0.157317	+	0.0651628i
$916$		0			0
$917$	−525.399	−	1268.42i	−0.0189206	−	0.0456784i
$918$		0			0
$919$	17562.4	+	17562.4i	0.630392	+	0.630392i	0.948166	−	0.317774i	$-0.102935\pi$
$919$	17562.4	+	17562.4i	0.630392	+	0.630392i	−0.317774	+	0.948166i	$0.602935\pi$
$920$		0			0
$921$	4099.37	−	4099.37i	0.146665	−	0.146665i
$922$		0			0
$923$	−20710.3	+	8578.50i	−0.738557	+	0.305920i
$924$		0			0
$925$	−8220.09	+	19845.0i	−0.292189	+	0.705406i
$926$		0			0
$927$	−628.687			−0.0222748
$928$		0			0
$929$	4262.05			0.150520			0.0752602	−	0.997164i	$-0.476021\pi$
$929$	4262.05			0.150520			0.0752602	+	0.997164i	$0.476021\pi$
$930$		0			0
$931$	−2090.00	+	5045.70i	−0.0735735	+	0.177622i
$932$		0			0
$933$	14279.6	−	5914.81i	0.501065	−	0.207548i
$934$		0			0
$935$	−2966.79	+	2966.79i	−0.103769	+	0.103769i
$936$		0			0
$937$	20895.1	+	20895.1i	0.728511	+	0.728511i	0.970323	−	0.241812i	$-0.0777419\pi$
$937$	20895.1	+	20895.1i	0.728511	+	0.728511i	−0.241812	+	0.970323i	$0.577742\pi$
$938$		0			0
$939$	−10047.7	−	24257.2i	−0.349194	−	0.843028i
$940$		0			0
$941$	−16995.0	−	7039.57i	−0.588759	−	0.243872i	0.0683579	−	0.997661i	$-0.478224\pi$
$941$	−16995.0	−	7039.57i	−0.588759	−	0.243872i	−0.657116	+	0.753789i	$0.728224\pi$
$942$		0			0
$943$		−	30172.8i		−	1.04195i
$944$		0			0
$945$		−	15241.0i		−	0.524644i
$946$		0			0
$947$	−36843.7	−	15261.2i	−1.26427	−	0.523676i	−0.353050	−	0.935604i	$-0.614856\pi$
$947$	−36843.7	−	15261.2i	−1.26427	−	0.523676i	−0.911216	+	0.411928i	$0.864856\pi$
$948$		0			0
$949$	−30426.2	−	73455.4i	−1.04076	−	2.51261i
$950$		0			0
$951$	−29123.3	−	29123.3i	−0.993046	−	0.993046i
$952$		0			0
$953$	−9331.21	+	9331.21i	−0.317175	+	0.317175i	−0.847681	−	0.530506i	$-0.822002\pi$
$953$	−9331.21	+	9331.21i	−0.317175	+	0.317175i	0.530506	+	0.847681i	$0.322002\pi$
$954$		0			0
$955$	−7446.06	+	3084.26i	−0.252303	+	0.104507i
$956$		0			0
$957$	2663.02	−	6429.11i	0.0899513	−	0.217162i
$958$		0			0
$959$	53780.9			1.81092
$960$		0			0
$961$	41845.8			1.40465
$962$		0			0
$963$	−120.689	+	291.370i	−0.00403859	+	0.00975001i
$964$		0			0
$965$	17886.9	−	7408.99i	0.596683	−	0.247154i
$966$		0			0
$967$	16402.9	−	16402.9i	0.545483	−	0.545483i	−0.379648	−	0.925131i	$-0.623955\pi$
$967$	16402.9	−	16402.9i	0.545483	−	0.545483i	0.925131	+	0.379648i	$0.123955\pi$
$968$		0			0
$969$	29215.6	+	29215.6i	0.968565	+	0.968565i
$970$		0			0
$971$	2483.25	+	5995.10i	0.0820714	+	0.198138i	0.959588	−	0.281408i	$-0.0908014\pi$
$971$	2483.25	+	5995.10i	0.0820714	+	0.198138i	−0.877517	+	0.479546i	$0.840801\pi$
$972$		0			0
$973$	−25256.3	−	10461.5i	−0.832147	−	0.344687i
$974$		0			0
$975$			34300.2i			1.12665i
$976$		0			0
$977$		−	26525.8i		−	0.868613i	−0.900765	−	0.434307i	$-0.856993\pi$
$977$		−	26525.8i		−	0.868613i	0.900765	−	0.434307i	$-0.143007\pi$
$978$		0			0
$979$	−7497.30	−	3105.48i	−0.244754	−	0.101381i
$980$		0			0
$981$	449.414	+	1084.98i	0.0146266	+	0.0353117i
$982$		0			0
$983$	−3562.07	−	3562.07i	−0.115577	−	0.115577i	0.646953	−	0.762530i	$-0.276043\pi$
$983$	−3562.07	−	3562.07i	−0.115577	−	0.115577i	−0.762530	+	0.646953i	$0.776043\pi$
$984$		0			0
$985$	−7210.74	+	7210.74i	−0.233252	+	0.233252i
$986$		0			0
$987$	16209.2	−	6714.06i	0.522739	−	0.216526i
$988$		0			0
$989$	5775.60	−	13943.5i	0.185696	−	0.448310i
$990$		0			0
$991$	10011.3			0.320907			0.160453	−	0.987043i	$-0.448704\pi$
$991$	10011.3			0.320907			0.160453	+	0.987043i	$0.448704\pi$
$992$		0			0
$993$	31457.5			1.00531
$994$		0			0
$995$	5804.97	−	14014.4i	0.184955	−	0.446520i
$996$		0			0
$997$	19700.4	−	8160.16i	0.625795	−	0.259213i	−0.0471705	−	0.998887i	$-0.515020\pi$
$997$	19700.4	−	8160.16i	0.625795	−	0.259213i	0.672965	+	0.739674i	$0.265020\pi$
$998$		0			0
$999$	−22571.6	+	22571.6i	−0.714848	+	0.714848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.17.3		44
4.3	odd	2		32.4.g.a.13.3	yes	44
8.3	odd	2		256.4.g.b.33.3		44
8.5	even	2		256.4.g.a.33.9		44
32.5	even	8	inner	128.4.g.a.113.3		44
32.11	odd	8		256.4.g.b.225.3		44
32.21	even	8		256.4.g.a.225.9		44
32.27	odd	8		32.4.g.a.5.3	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.3	✓	44	32.27	odd	8
32.4.g.a.13.3	yes	44	4.3	odd	2
128.4.g.a.17.3		44	1.1	even	1	trivial
128.4.g.a.113.3		44	32.5	even	8	inner
256.4.g.a.33.9		44	8.5	even	2
256.4.g.a.225.9		44	32.21	even	8
256.4.g.b.33.3		44	8.3	odd	2
256.4.g.b.225.3		44	32.11	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.94138 + 4.68690i) q^{3} +(4.93338 - 2.04347i) q^{5} +(-14.0755 + 14.0755i) q^{7} +(0.893826 + 0.893826i) q^{9} +O(q^{10})\)	\(q+(-1.94138 + 4.68690i) q^{3} +(4.93338 - 2.04347i) q^{5} +(-14.0755 + 14.0755i) q^{7} +(0.893826 + 0.893826i) q^{9} +(3.78733 + 9.14343i) q^{11} +(-64.7407 - 26.8165i) q^{13} +27.0894i q^{15} +79.3923i q^{17} +(-94.7756 - 39.2573i) q^{19} +(-38.6445 - 93.2961i) q^{21} +(-71.6801 - 71.6801i) q^{23} +(-68.2259 + 68.2259i) q^{25} +(-132.471 + 54.8712i) q^{27} +(-53.0409 + 128.052i) q^{29} +267.650 q^{31} -50.2070 q^{33} +(-40.6768 + 98.2026i) q^{35} +(205.678 - 85.1946i) q^{37} +(251.372 - 251.372i) q^{39} +(210.468 + 210.468i) q^{41} +(56.9749 + 137.550i) q^{43} +(6.23610 + 2.58308i) q^{45} +173.739i q^{47} -53.2384i q^{49} +(-372.103 - 154.130i) q^{51} +(-188.605 - 455.333i) q^{53} +(37.3687 + 37.3687i) q^{55} +(367.990 - 367.990i) q^{57} +(627.964 - 260.111i) q^{59} +(66.5782 - 160.734i) q^{61} -25.1621 q^{63} -374.189 q^{65} +(-211.710 + 511.113i) q^{67} +(475.115 - 196.799i) q^{69} +(226.201 - 226.201i) q^{71} +(802.290 + 802.290i) q^{73} +(-187.316 - 452.220i) q^{75} +(-182.007 - 75.3897i) q^{77} +552.368i q^{79} -693.272i q^{81} +(137.983 + 57.1544i) q^{83} +(162.236 + 391.672i) q^{85} +(-497.195 - 497.195i) q^{87} +(-579.803 + 579.803i) q^{89} +(1288.71 - 533.802i) q^{91} +(-519.610 + 1254.45i) q^{93} -547.785 q^{95} -912.077 q^{97} +(-4.78742 + 11.5579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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