LMFDB - Embedded newform 160.4.n.f.127.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,4,Mod(63,160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("160.63"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 48x^{6} + 628x^{4} + 1556x^{2} + 400 $ x^8 + 48x^6 + 628x^4 + 1556*x^2 + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.3
Root			$-5.14642i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.4.n.f.63.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.38984 + 2.38984i) q^{3} +(-6.76288 - 8.90300i) q^{5} +(-9.83542 + 9.83542i) q^{7} -15.5773i q^{9} -60.2313i q^{11} +(-32.8373 + 32.8373i) q^{13} +(5.11455 - 37.4390i) q^{15} +(-74.8159 - 74.8159i) q^{17} +90.8743 q^{19} -47.0102 q^{21} +(-25.8438 - 25.8438i) q^{23} +(-33.5269 + 120.420i) q^{25} +(101.753 - 101.753i) q^{27} -81.7198i q^{29} -125.331i q^{31} +(143.943 - 143.943i) q^{33} +(154.080 + 21.0490i) q^{35} +(-62.5837 - 62.5837i) q^{37} -156.952 q^{39} -328.200 q^{41} +(-22.6577 - 22.6577i) q^{43} +(-138.685 + 105.347i) q^{45} +(-300.531 + 300.531i) q^{47} +149.529i q^{49} -357.597i q^{51} +(220.639 - 220.639i) q^{53} +(-536.239 + 407.337i) q^{55} +(217.176 + 217.176i) q^{57} +834.953 q^{59} +453.586 q^{61} +(153.209 + 153.209i) q^{63} +(514.425 + 70.2757i) q^{65} +(-456.134 + 456.134i) q^{67} -123.525i q^{69} +303.513i q^{71} +(43.9342 - 43.9342i) q^{73} +(-367.909 + 207.661i) q^{75} +(592.400 + 592.400i) q^{77} -147.287 q^{79} +65.7612 q^{81} +(718.981 + 718.981i) q^{83} +(-160.115 + 1172.06i) q^{85} +(195.297 - 195.297i) q^{87} -336.094i q^{89} -645.936i q^{91} +(299.522 - 299.522i) q^{93} +(-614.572 - 809.054i) q^{95} +(104.454 + 104.454i) q^{97} -938.241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - 6 q^{5} + 70 q^{7} + 144 q^{13} - 134 q^{15} - 100 q^{17} + 176 q^{19} - 516 q^{21} - 198 q^{23} - 172 q^{25} - 288 q^{27} + 172 q^{33} + 170 q^{35} + 492 q^{37} + 756 q^{39} - 28 q^{41}+ \cdots + 8412 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 - 6 * q^5 + 70 * q^7 + 144 * q^13 - 134 * q^15 - 100 * q^17 + 176 * q^19 - 516 * q^21 - 198 * q^23 - 172 * q^25 - 288 * q^27 + 172 * q^33 + 170 * q^35 + 492 * q^37 + 756 * q^39 - 28 * q^41 + 654 * q^43 + 10 * q^45 - 690 * q^47 + 580 * q^53 - 2392 * q^55 - 248 * q^57 + 1808 * q^59 - 1068 * q^61 + 3106 * q^63 + 2200 * q^65 - 1878 * q^67 + 1952 * q^73 - 2178 * q^75 + 340 * q^77 - 1808 * q^79 - 7844 * q^81 - 506 * q^83 + 184 * q^85 + 784 * q^87 + 3708 * q^93 - 5800 * q^95 + 5576 * q^97 + 8412 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.38984	+	2.38984i	0.459926	+	0.459926i	0.898631	−	0.438705i	$-0.144563\pi$
$3$	2.38984	+	2.38984i	0.459926	+	0.459926i	−0.438705	+	0.898631i	$0.644563\pi$
$4$		0			0
$5$	−6.76288	−	8.90300i	−0.604891	−	0.796309i
$5$	−6.76288	−	8.90300i	−0.604891	−	0.796309i
$6$		0			0
$7$	−9.83542	+	9.83542i	−0.531063	+	0.531063i	−0.920889	−	0.389826i	$-0.872535\pi$
$7$	−9.83542	+	9.83542i	−0.531063	+	0.531063i	0.389826	+	0.920889i	$0.372535\pi$
$8$		0			0
$9$		−	15.5773i		−	0.576937i
$10$		0			0
$11$		−	60.2313i		−	1.65095i	−0.564440	−	0.825474i	$-0.690908\pi$
$11$		−	60.2313i		−	1.65095i	0.564440	−	0.825474i	$-0.309092\pi$
$12$		0			0
$13$	−32.8373	+	32.8373i	−0.700571	+	0.700571i	−0.964533	−	0.263962i	$-0.914971\pi$
$13$	−32.8373	+	32.8373i	−0.700571	+	0.700571i	0.263962	+	0.964533i	$0.414971\pi$
$14$		0			0
$15$	5.11455	−	37.4390i	0.0880381	−	0.644448i
$16$		0			0
$17$	−74.8159	−	74.8159i	−1.06738	−	1.06738i	−0.997559	−	0.0698243i	$-0.977756\pi$
$17$	−74.8159	−	74.8159i	−1.06738	−	1.06738i	−0.0698243	−	0.997559i	$-0.522244\pi$
$18$		0			0
$19$	90.8743			1.09726			0.548632	−	0.836064i	$-0.315149\pi$
$19$	90.8743			1.09726			0.548632	+	0.836064i	$0.315149\pi$
$20$		0			0
$21$	−47.0102			−0.488499
$22$		0			0
$23$	−25.8438	−	25.8438i	−0.234296	−	0.234296i	0.580187	−	0.814483i	$-0.302979\pi$
$23$	−25.8438	−	25.8438i	−0.234296	−	0.234296i	−0.814483	+	0.580187i	$0.802979\pi$
$24$		0			0
$25$	−33.5269	+	120.420i	−0.268215	+	0.963359i
$26$		0			0
$27$	101.753	−	101.753i	0.725274	−	0.725274i
$28$		0			0
$29$		−	81.7198i		−	0.523275i	−0.965166	−	0.261638i	$-0.915737\pi$
$29$		−	81.7198i		−	0.523275i	0.965166	−	0.261638i	$-0.0842625\pi$
$30$		0			0
$31$		−	125.331i		−	0.726133i	−0.931763	−	0.363066i	$-0.881730\pi$
$31$		−	125.331i		−	0.726133i	0.931763	−	0.363066i	$-0.118270\pi$
$32$		0			0
$33$	143.943	−	143.943i	0.759313	−	0.759313i
$34$		0			0
$35$	154.080	+	21.0490i	0.744124	+	0.101655i
$36$		0			0
$37$	−62.5837	−	62.5837i	−0.278073	−	0.278073i	0.554266	−	0.832339i	$-0.312999\pi$
$37$	−62.5837	−	62.5837i	−0.278073	−	0.278073i	−0.832339	+	0.554266i	$0.812999\pi$
$38$		0			0
$39$	−156.952			−0.644421
$40$		0			0
$41$	−328.200			−1.25015			−0.625075	−	0.780564i	$-0.714932\pi$
$41$	−328.200			−1.25015			−0.625075	+	0.780564i	$0.714932\pi$
$42$		0			0
$43$	−22.6577	−	22.6577i	−0.0803552	−	0.0803552i	0.665787	−	0.746142i	$-0.268096\pi$
$43$	−22.6577	−	22.6577i	−0.0803552	−	0.0803552i	−0.746142	+	0.665787i	$0.768096\pi$
$44$		0			0
$45$	−138.685	+	105.347i	−0.459420	+	0.348984i
$46$		0			0
$47$	−300.531	+	300.531i	−0.932701	+	0.932701i	−0.997874	−	0.0651734i	$-0.979240\pi$
$47$	−300.531	+	300.531i	−0.932701	+	0.932701i	0.0651734	+	0.997874i	$0.479240\pi$
$48$		0			0
$49$			149.529i			0.435945i
$50$		0			0
$51$		−	357.597i		−	0.981834i
$52$		0			0
$53$	220.639	−	220.639i	0.571831	−	0.571831i	−0.360809	−	0.932640i	$-0.617499\pi$
$53$	220.639	−	220.639i	0.571831	−	0.571831i	0.932640	+	0.360809i	$0.117499\pi$
$54$		0			0
$55$	−536.239	+	407.337i	−1.31466	+	0.998643i
$56$		0			0
$57$	217.176	+	217.176i	0.504660	+	0.504660i
$58$		0			0
$59$	834.953			1.84240			0.921200	−	0.389089i	$-0.127210\pi$
$59$	834.953			1.84240			0.921200	+	0.389089i	$0.127210\pi$
$60$		0			0
$61$	453.586			0.952061			0.476031	−	0.879429i	$-0.342075\pi$
$61$	453.586			0.952061			0.476031	+	0.879429i	$0.342075\pi$
$62$		0			0
$63$	153.209	+	153.209i	0.306389	+	0.306389i
$64$		0			0
$65$	514.425	+	70.2757i	0.981639	+	0.134102i
$66$		0			0
$67$	−456.134	+	456.134i	−0.831726	+	0.831726i	−0.987753	−	0.156027i	$-0.950131\pi$
$67$	−456.134	+	456.134i	−0.831726	+	0.831726i	0.156027	+	0.987753i	$0.450131\pi$
$68$		0			0
$69$		−	123.525i		−	0.215518i
$70$		0			0
$71$			303.513i			0.507328i	0.967292	+	0.253664i	$0.0816358\pi$
$71$			303.513i			0.507328i	−0.967292	+	0.253664i	$0.918364\pi$
$72$		0			0
$73$	43.9342	−	43.9342i	0.0704398	−	0.0704398i	−0.671009	−	0.741449i	$-0.734139\pi$
$73$	43.9342	−	43.9342i	0.0704398	−	0.0704398i	0.741449	+	0.671009i	$0.234139\pi$
$74$		0			0
$75$	−367.909	+	207.661i	−0.566433	+	0.319715i
$76$		0			0
$77$	592.400	+	592.400i	0.876756	+	0.876756i
$78$		0			0
$79$	−147.287			−0.209760			−0.104880	−	0.994485i	$-0.533446\pi$
$79$	−147.287			−0.209760			−0.104880	+	0.994485i	$0.533446\pi$
$80$		0			0
$81$	65.7612			0.0902075
$82$		0			0
$83$	718.981	+	718.981i	0.950825	+	0.950825i	0.998846	−	0.0480214i	$-0.0152916\pi$
$83$	718.981	+	718.981i	0.950825	+	0.950825i	−0.0480214	+	0.998846i	$0.515292\pi$
$84$		0			0
$85$	−160.115	+	1172.06i	−0.204317	+	1.49562i
$86$		0			0
$87$	195.297	−	195.297i	0.240668	−	0.240668i
$88$		0			0
$89$		−	336.094i		−	0.400291i	−0.979766	−	0.200146i	$-0.935858\pi$
$89$		−	336.094i		−	0.400291i	0.979766	−	0.200146i	$-0.0641415\pi$
$90$		0			0
$91$		−	645.936i		−	0.744094i
$92$		0			0
$93$	299.522	−	299.522i	0.333967	−	0.333967i
$94$		0			0
$95$	−614.572	−	809.054i	−0.663724	−	0.873760i
$96$		0			0
$97$	104.454	+	104.454i	0.109337	+	0.109337i	0.759659	−	0.650322i	$-0.225366\pi$
$97$	104.454	+	104.454i	0.109337	+	0.109337i	−0.650322	+	0.759659i	$0.725366\pi$
$98$		0			0
$99$	−938.241			−0.952492
$100$		0			0
$101$	−1892.29			−1.86426			−0.932130	−	0.362124i	$-0.882052\pi$
$101$	−1892.29			−1.86426			−0.932130	+	0.362124i	$0.882052\pi$
$102$		0			0
$103$	682.131	+	682.131i	0.652547	+	0.652547i	0.953606	−	0.301059i	$-0.0973400\pi$
$103$	682.131	+	682.131i	0.652547	+	0.652547i	−0.301059	+	0.953606i	$0.597340\pi$
$104$		0			0
$105$	317.925	+	418.532i	0.295488	+	0.388996i
$106$		0			0
$107$	−675.992	+	675.992i	−0.610753	+	0.610753i	−0.943142	−	0.332389i	$-0.892145\pi$
$107$	−675.992	+	675.992i	−0.610753	+	0.610753i	0.332389	+	0.943142i	$0.392145\pi$
$108$		0			0
$109$		−	1884.44i		−	1.65594i	−0.560775	−	0.827968i	$-0.689497\pi$
$109$		−	1884.44i		−	1.65594i	0.560775	−	0.827968i	$-0.310503\pi$
$110$		0			0
$111$		−	299.131i		−	0.255786i
$112$		0			0
$113$	942.506	−	942.506i	0.784633	−	0.784633i	−0.195976	−	0.980609i	$-0.562787\pi$
$113$	942.506	−	942.506i	0.784633	−	0.784633i	0.980609	+	0.195976i	$0.0627874\pi$
$114$		0			0
$115$	−55.3089	+	404.866i	−0.0448485	+	0.328295i
$116$		0			0
$117$	511.516	+	511.516i	0.404185	+	0.404185i
$118$		0			0
$119$	1471.69			1.13369
$120$		0			0
$121$	−2296.81			−1.72563
$122$		0			0
$123$	−784.346	−	784.346i	−0.574976	−	0.574976i
$124$		0			0
$125$	1298.84	−	515.896i	0.929372	−	0.369145i
$126$		0			0
$127$	1420.14	−	1420.14i	0.992262	−	0.992262i	−0.00770877	−	0.999970i	$-0.502454\pi$
$127$	1420.14	−	1420.14i	0.992262	−	0.992262i	0.999970	+	0.00770877i	$0.00245380\pi$
$128$		0			0
$129$		−	108.297i		−	0.0739149i
$130$		0			0
$131$		−	1733.01i		−	1.15583i	−0.816097	−	0.577915i	$-0.803867\pi$
$131$		−	1733.01i		−	1.15583i	0.816097	−	0.577915i	$-0.196133\pi$
$132$		0			0
$133$	−893.787	+	893.787i	−0.582715	+	0.582715i
$134$		0			0
$135$	−1594.05	−	217.764i	−1.01625	−	0.138831i
$136$		0			0
$137$	−978.198	−	978.198i	−0.610023	−	0.610023i	0.332929	−	0.942952i	$-0.391963\pi$
$137$	−978.198	−	978.198i	−0.610023	−	0.610023i	−0.942952	+	0.332929i	$0.891963\pi$
$138$		0			0
$139$	1260.91			0.769418			0.384709	−	0.923038i	$-0.374302\pi$
$139$	1260.91			0.769418			0.384709	+	0.923038i	$0.374302\pi$
$140$		0			0
$141$	−1436.44			−0.857946
$142$		0			0
$143$	1977.83	+	1977.83i	1.15661	+	1.15661i
$144$		0			0
$145$	−727.551	+	552.661i	−0.416689	+	0.316524i
$146$		0			0
$147$	−357.352	+	357.352i	−0.200502	+	0.200502i
$148$		0			0
$149$		−	482.658i		−	0.265375i	−0.991158	−	0.132687i	$-0.957639\pi$
$149$		−	482.658i		−	0.265375i	0.991158	−	0.132687i	$-0.0423607\pi$
$150$		0			0
$151$		−	3123.05i		−	1.68311i	−0.540169	−	0.841556i	$-0.681640\pi$
$151$		−	3123.05i		−	1.68311i	0.540169	−	0.841556i	$-0.318360\pi$
$152$		0			0
$153$	−1165.43	+	1165.43i	−0.615813	+	0.615813i
$154$		0			0
$155$	−1115.82	+	847.599i	−0.578226	+	0.439231i
$156$		0			0
$157$	138.171	+	138.171i	0.0702375	+	0.0702375i	0.741353	−	0.671115i	$-0.234185\pi$
$157$	138.171	+	138.171i	0.0702375	+	0.0702375i	−0.671115	+	0.741353i	$0.734185\pi$
$158$		0			0
$159$	1054.58			0.525999
$160$		0			0
$161$	508.369			0.248852
$162$		0			0
$163$	−1343.08	−	1343.08i	−0.645388	−	0.645388i	0.306487	−	0.951875i	$-0.400846\pi$
$163$	−1343.08	−	1343.08i	−0.645388	−	0.645388i	−0.951875	+	0.306487i	$0.900846\pi$
$164$		0			0
$165$	−2255.00	−	308.056i	−1.06395	−	0.145346i
$166$		0			0
$167$	2579.83	−	2579.83i	1.19541	−	1.19541i	0.219880	−	0.975527i	$-0.429434\pi$
$167$	2579.83	−	2579.83i	1.19541	−	1.19541i	0.975527	−	0.219880i	$-0.0705664\pi$
$168$		0			0
$169$			40.4281i			0.0184015i
$170$		0			0
$171$		−	1415.58i		−	0.633051i
$172$		0			0
$173$	2651.85	−	2651.85i	1.16541	−	1.16541i	0.182138	−	0.983273i	$-0.441698\pi$
$173$	2651.85	−	2651.85i	1.16541	−	1.16541i	0.983273	−	0.182138i	$-0.0583018\pi$
$174$		0			0
$175$	−854.629	−	1514.13i	−0.369165	−	0.654043i
$176$		0			0
$177$	1995.41	+	1995.41i	0.847367	+	0.847367i
$178$		0			0
$179$	1434.43			0.598962			0.299481	−	0.954102i	$-0.403186\pi$
$179$	1434.43			0.598962			0.299481	+	0.954102i	$0.403186\pi$
$180$		0			0
$181$	−167.754			−0.0688898			−0.0344449	−	0.999407i	$-0.510966\pi$
$181$	−167.754			−0.0688898			−0.0344449	+	0.999407i	$0.510966\pi$
$182$		0			0
$183$	1084.00	+	1084.00i	0.437878	+	0.437878i
$184$		0			0
$185$	−133.937	+	980.429i	−0.0532282	+	0.389636i
$186$		0			0
$187$	−4506.26	+	4506.26i	−1.76219	+	1.76219i
$188$		0			0
$189$			2001.57i			0.770331i
$190$		0			0
$191$			4667.83i			1.76834i	0.467167	+	0.884169i	$0.345275\pi$
$191$			4667.83i			1.76834i	−0.467167	+	0.884169i	$0.654725\pi$
$192$		0			0
$193$	2283.88	−	2283.88i	0.851800	−	0.851800i	−0.138555	−	0.990355i	$-0.544246\pi$
$193$	2283.88	−	2283.88i	0.851800	−	0.851800i	0.990355	+	0.138555i	$0.0442457\pi$
$194$		0			0
$195$	1061.45	+	1397.34i	0.389804	+	0.513158i
$196$		0			0
$197$	−1718.64	−	1718.64i	−0.621563	−	0.621563i	0.324368	−	0.945931i	$-0.394848\pi$
$197$	−1718.64	−	1718.64i	−0.621563	−	0.621563i	−0.945931	+	0.324368i	$0.894848\pi$
$198$		0			0
$199$	−2761.98			−0.983877			−0.491938	−	0.870630i	$-0.663711\pi$
$199$	−2761.98			−0.983877			−0.491938	+	0.870630i	$0.663711\pi$
$200$		0			0
$201$	−2180.18			−0.765064
$202$		0			0
$203$	803.748	+	803.748i	0.277892	+	0.277892i
$204$		0			0
$205$	2219.58	+	2921.96i	0.756204	+	0.995506i
$206$		0			0
$207$	−402.577	+	402.577i	−0.135174	+	0.135174i
$208$		0			0
$209$		−	5473.48i		−	1.81152i
$210$		0			0
$211$			476.824i			0.155573i	0.996970	+	0.0777865i	$0.0247853\pi$
$211$			476.824i			0.155573i	−0.996970	+	0.0777865i	$0.975215\pi$
$212$		0			0
$213$	−725.348	+	725.348i	−0.233333	+	0.233333i
$214$		0			0
$215$	−48.4903	+	354.954i	−0.0153814	+	0.112594i
$216$		0			0
$217$	1232.68	+	1232.68i	0.385622	+	0.385622i
$218$		0			0
$219$	209.992			0.0647941
$220$		0			0
$221$	4913.50			1.49556
$222$		0			0
$223$	−2493.89	−	2493.89i	−0.748895	−	0.748895i	0.225377	−	0.974272i	$-0.427639\pi$
$223$	−2493.89	−	2493.89i	−0.748895	−	0.748895i	−0.974272	+	0.225377i	$0.927639\pi$
$224$		0			0
$225$	1875.82	+	522.258i	0.555797	+	0.154743i
$226$		0			0
$227$	−577.387	+	577.387i	−0.168822	+	0.168822i	−0.786461	−	0.617640i	$-0.788089\pi$
$227$	−577.387	+	577.387i	−0.168822	+	0.168822i	0.617640	+	0.786461i	$0.288089\pi$
$228$		0			0
$229$			3726.88i			1.07546i	0.843119	+	0.537728i	$0.180717\pi$
$229$			3726.88i			1.07546i	−0.843119	+	0.537728i	$0.819283\pi$
$230$		0			0
$231$			2831.49i			0.806486i
$232$		0			0
$233$	−1883.04	+	1883.04i	−0.529452	+	0.529452i	−0.920409	−	0.390957i	$-0.872144\pi$
$233$	−1883.04	+	1883.04i	−0.529452	+	0.529452i	0.390957	+	0.920409i	$0.372144\pi$
$234$		0			0
$235$	4708.08	+	643.172i	1.30690	+	0.178536i
$236$		0			0
$237$	−351.993	−	351.993i	−0.0964741	−	0.0964741i
$238$		0			0
$239$	−2519.46			−0.681884			−0.340942	−	0.940084i	$-0.610746\pi$
$239$	−2519.46			−0.681884			−0.340942	+	0.940084i	$0.610746\pi$
$240$		0			0
$241$	4105.09			1.09723			0.548614	−	0.836076i	$-0.315156\pi$
$241$	4105.09			1.09723			0.548614	+	0.836076i	$0.315156\pi$
$242$		0			0
$243$	−2590.17	−	2590.17i	−0.683785	−	0.683785i
$244$		0			0
$245$	1331.26	−	1011.25i	0.347147	−	0.263699i
$246$		0			0
$247$	−2984.06	+	2984.06i	−0.768711	+	0.768711i
$248$		0			0
$249$			3436.51i			0.874618i
$250$		0			0
$251$		−	5434.77i		−	1.36669i	−0.730095	−	0.683346i	$-0.760524\pi$
$251$		−	5434.77i		−	1.36669i	0.730095	−	0.683346i	$-0.239476\pi$
$252$		0			0
$253$	−1556.61	+	1556.61i	−0.386810	+	0.386810i
$254$		0			0
$255$	−3183.68	+	2418.38i	−0.781843	+	0.593902i
$256$		0			0
$257$	585.402	+	585.402i	0.142087	+	0.142087i	0.774572	−	0.632485i	$-0.217965\pi$
$257$	585.402	+	585.402i	0.142087	+	0.142087i	−0.632485	+	0.774572i	$0.717965\pi$
$258$		0			0
$259$	1231.07			0.295348
$260$		0			0
$261$	−1272.97			−0.301897
$262$		0			0
$263$	4817.62	+	4817.62i	1.12953	+	1.12953i	0.990253	+	0.139280i	$0.0444788\pi$
$263$	4817.62	+	4817.62i	1.12953	+	1.12953i	0.139280	+	0.990253i	$0.455521\pi$
$264$		0			0
$265$	−3456.50	−	472.193i	−0.801249	−	0.109459i
$266$		0			0
$267$	803.213	−	803.213i	0.184104	−	0.184104i
$268$		0			0
$269$		−	1051.12i		−	0.238244i	−0.992880	−	0.119122i	$-0.961992\pi$
$269$		−	1051.12i		−	0.238244i	0.992880	−	0.119122i	$-0.0380080\pi$
$270$		0			0
$271$			2531.99i			0.567555i	0.958890	+	0.283778i	$0.0915878\pi$
$271$			2531.99i			0.567555i	−0.958890	+	0.283778i	$0.908412\pi$
$272$		0			0
$273$	1543.69	−	1543.69i	0.342228	−	0.342228i
$274$		0			0
$275$	7253.05	+	2019.37i	1.59046	+	0.442809i
$276$		0			0
$277$	−234.701	−	234.701i	−0.0509090	−	0.0509090i	0.681194	−	0.732103i	$-0.261461\pi$
$277$	−234.701	−	234.701i	−0.0509090	−	0.0509090i	−0.732103	+	0.681194i	$0.761461\pi$
$278$		0			0
$279$	−1952.32			−0.418933
$280$		0			0
$281$	7723.69			1.63970			0.819852	−	0.572575i	$-0.194056\pi$
$281$	7723.69			1.63970			0.819852	+	0.572575i	$0.194056\pi$
$282$		0			0
$283$	2799.36	+	2799.36i	0.588003	+	0.588003i	0.937090	−	0.349087i	$-0.113508\pi$
$283$	2799.36	+	2799.36i	0.588003	+	0.588003i	−0.349087	+	0.937090i	$0.613508\pi$
$284$		0			0
$285$	464.782	−	3402.25i	0.0966010	−	0.707129i
$286$		0			0
$287$	3227.98	−	3227.98i	0.663908	−	0.663908i
$288$		0			0
$289$			6281.84i			1.27862i
$290$		0			0
$291$			499.257i			0.100574i
$292$		0			0
$293$	1272.98	−	1272.98i	0.253817	−	0.253817i	−0.568716	−	0.822534i	$-0.692560\pi$
$293$	1272.98	−	1272.98i	0.253817	−	0.253817i	0.822534	+	0.568716i	$0.192560\pi$
$294$		0			0
$295$	−5646.69	−	7433.59i	−1.11445	−	1.46712i
$296$		0			0
$297$	−6128.72	−	6128.72i	−1.19739	−	1.19739i
$298$		0			0
$299$	1697.28			0.328282
$300$		0			0
$301$	445.697			0.0853473
$302$		0			0
$303$	−4522.29	−	4522.29i	−0.857421	−	0.857421i
$304$		0			0
$305$	−3067.55	−	4038.28i	−0.575893	−	0.758135i
$306$		0			0
$307$	428.574	−	428.574i	0.0796743	−	0.0796743i	−0.666147	−	0.745821i	$-0.732057\pi$
$307$	428.574	−	428.574i	0.0796743	−	0.0796743i	0.745821	+	0.666147i	$0.232057\pi$
$308$		0			0
$309$			3260.37i			0.600246i
$310$		0			0
$311$			2997.74i			0.546580i	0.961932	+	0.273290i	$0.0881118\pi$
$311$			2997.74i			0.546580i	−0.961932	+	0.273290i	$0.911888\pi$
$312$		0			0
$313$	−5654.33	+	5654.33i	−1.02109	+	1.02109i	−0.0213178	+	0.999773i	$0.506786\pi$
$313$	−5654.33	+	5654.33i	−1.02109	+	1.02109i	−0.999773	+	0.0213178i	$0.993214\pi$
$314$		0			0
$315$	327.886	−	2400.16i	0.0586485	−	0.429313i
$316$		0			0
$317$	−1894.53	−	1894.53i	−0.335670	−	0.335670i	0.519065	−	0.854735i	$-0.326280\pi$
$317$	−1894.53	−	1894.53i	−0.335670	−	0.335670i	−0.854735	+	0.519065i	$0.826280\pi$
$318$		0			0
$319$	−4922.09			−0.863900
$320$		0			0
$321$	−3231.03			−0.561802
$322$		0			0
$323$	−6798.85	−	6798.85i	−1.17120	−	1.17120i
$324$		0			0
$325$	−2853.33	−	5055.19i	−0.486998	−	0.862805i
$326$		0			0
$327$	4503.53	−	4503.53i	0.761608	−	0.761608i
$328$		0			0
$329$		−	5911.69i		−	0.990645i
$330$		0			0
$331$			2414.52i			0.400948i	0.979699	+	0.200474i	$0.0642483\pi$
$331$			2414.52i			0.400948i	−0.979699	+	0.200474i	$0.935752\pi$
$332$		0			0
$333$	−974.885	+	974.885i	−0.160431	+	0.160431i
$334$		0			0
$335$	7145.74	+	976.181i	1.16541	+	0.159207i
$336$		0			0
$337$	−1321.62	−	1321.62i	−0.213630	−	0.213630i	0.592178	−	0.805807i	$-0.298268\pi$
$337$	−1321.62	−	1321.62i	−0.213630	−	0.213630i	−0.805807	+	0.592178i	$0.798268\pi$
$338$		0			0
$339$	4504.89			0.721746
$340$		0			0
$341$	−7548.85			−1.19881
$342$		0			0
$343$	−4844.23	−	4844.23i	−0.762577	−	0.762577i
$344$		0			0
$345$	−1099.75	+	835.388i	−0.171618	+	0.130365i
$346$		0			0
$347$	3686.52	−	3686.52i	0.570325	−	0.570325i	−0.361894	−	0.932219i	$-0.617870\pi$
$347$	3686.52	−	3686.52i	0.570325	−	0.570325i	0.932219	+	0.361894i	$0.117870\pi$
$348$		0			0
$349$		−	8288.46i		−	1.27126i	−0.771992	−	0.635632i	$-0.780740\pi$
$349$		−	8288.46i		−	1.27126i	0.771992	−	0.635632i	$-0.219260\pi$
$350$		0			0
$351$			6682.59i			1.01621i
$352$		0			0
$353$	−2876.55	+	2876.55i	−0.433720	+	0.433720i	−0.889892	−	0.456171i	$-0.849220\pi$
$353$	−2876.55	+	2876.55i	−0.433720	+	0.433720i	0.456171	+	0.889892i	$0.349220\pi$
$354$		0			0
$355$	2702.17	−	2052.62i	0.403990	−	0.306878i
$356$		0			0
$357$	3517.11	+	3517.11i	0.521415	+	0.521415i
$358$		0			0
$359$	−4569.19			−0.671735			−0.335867	−	0.941909i	$-0.609029\pi$
$359$	−4569.19			−0.671735			−0.335867	+	0.941909i	$0.609029\pi$
$360$		0			0
$361$	1399.15			0.203987
$362$		0			0
$363$	−5489.02	−	5489.02i	−0.793661	−	0.793661i
$364$		0			0
$365$	−688.267	−	94.0244i	−0.0987002	−	0.0134835i
$366$		0			0
$367$	8095.02	−	8095.02i	1.15138	−	1.15138i	0.165104	−	0.986276i	$-0.447204\pi$
$367$	8095.02	−	8095.02i	1.15138	−	1.15138i	0.986276	−	0.165104i	$-0.0527960\pi$
$368$		0			0
$369$			5112.46i			0.721258i
$370$		0			0
$371$			4340.14i			0.607356i
$372$		0			0
$373$	−3234.41	+	3234.41i	−0.448985	+	0.448985i	−0.895017	−	0.446032i	$-0.852837\pi$
$373$	−3234.41	+	3234.41i	−0.448985	+	0.448985i	0.446032	+	0.895017i	$0.352837\pi$
$374$		0			0
$375$	4336.93	+	1871.11i	0.597221	+	0.257663i
$376$		0			0
$377$	2683.45	+	2683.45i	0.366591	+	0.366591i
$378$		0			0
$379$	758.390			0.102786			0.0513930	−	0.998679i	$-0.483634\pi$
$379$	758.390			0.102786			0.0513930	+	0.998679i	$0.483634\pi$
$380$		0			0
$381$	6787.84			0.912733
$382$		0			0
$383$	5789.34	+	5789.34i	0.772379	+	0.772379i	0.978522	−	0.206143i	$-0.0660911\pi$
$383$	5789.34	+	5789.34i	0.772379	+	0.772379i	−0.206143	+	0.978522i	$0.566091\pi$
$384$		0			0
$385$	1267.81	−	9280.47i	0.167827	−	1.22851i
$386$		0			0
$387$	−352.946	+	352.946i	−0.0463599	+	0.0463599i
$388$		0			0
$389$			5305.99i			0.691580i	0.938312	+	0.345790i	$0.112389\pi$
$389$			5305.99i			0.691580i	−0.938312	+	0.345790i	$0.887611\pi$
$390$		0			0
$391$			3867.06i			0.500167i
$392$		0			0
$393$	4141.62	−	4141.62i	0.531596	−	0.531596i
$394$		0			0
$395$	996.083	+	1311.29i	0.126882	+	0.167034i
$396$		0			0
$397$	−2202.72	−	2202.72i	−0.278467	−	0.278467i	0.554030	−	0.832497i	$-0.313089\pi$
$397$	−2202.72	−	2202.72i	−0.278467	−	0.278467i	−0.832497	+	0.554030i	$0.813089\pi$
$398$		0			0
$399$	−4272.02			−0.536012
$400$		0			0
$401$	−1182.36			−0.147243			−0.0736213	−	0.997286i	$-0.523456\pi$
$401$	−1182.36			−0.147243			−0.0736213	+	0.997286i	$0.523456\pi$
$402$		0			0
$403$	4115.53	+	4115.53i	0.508707	+	0.508707i
$404$		0			0
$405$	−444.735	−	585.472i	−0.0545656	−	0.0718330i
$406$		0			0
$407$	−3769.50	+	3769.50i	−0.459084	+	0.459084i
$408$		0			0
$409$		−	2075.54i		−	0.250926i	−0.992098	−	0.125463i	$-0.959958\pi$
$409$		−	2075.54i		−	0.250926i	0.992098	−	0.125463i	$-0.0400417\pi$
$410$		0			0
$411$		−	4675.48i		−	0.561130i
$412$		0			0
$413$	−8212.11	+	8212.11i	−0.978430	+	0.978430i
$414$		0			0
$415$	1538.71	−	11263.5i	0.182005	−	1.33230i
$416$		0			0
$417$	3013.38	+	3013.38i	0.353875	+	0.353875i
$418$		0			0
$419$	−14369.8			−1.67544			−0.837720	−	0.546100i	$-0.816112\pi$
$419$	−14369.8			−1.67544			−0.837720	+	0.546100i	$0.816112\pi$
$420$		0			0
$421$	12114.5			1.40244			0.701219	−	0.712946i	$-0.252640\pi$
$421$	12114.5			1.40244			0.701219	+	0.712946i	$0.252640\pi$
$422$		0			0
$423$	4681.46	+	4681.46i	0.538109	+	0.538109i
$424$		0			0
$425$	11517.7	−	6500.98i	1.31456	−	0.741985i
$426$		0			0
$427$	−4461.21	+	4461.21i	−0.505604	+	0.505604i
$428$		0			0
$429$			9453.42i			1.06391i
$430$		0			0
$431$		−	4105.54i		−	0.458833i	−0.973328	−	0.229417i	$-0.926318\pi$
$431$		−	4105.54i		−	0.458833i	0.973328	−	0.229417i	$-0.0736818\pi$
$432$		0			0
$433$	−4397.74	+	4397.74i	−0.488088	+	0.488088i	−0.907702	−	0.419614i	$-0.862165\pi$
$433$	−4397.74	+	4397.74i	−0.488088	+	0.488088i	0.419614	+	0.907702i	$0.362165\pi$
$434$		0			0
$435$	−3059.51	−	417.960i	−0.337223	−	0.0460682i
$436$		0			0
$437$	−2348.54	−	2348.54i	−0.257084	−	0.257084i
$438$		0			0
$439$	13707.5			1.49026			0.745132	−	0.666917i	$-0.232387\pi$
$439$	13707.5			1.49026			0.745132	+	0.666917i	$0.232387\pi$
$440$		0			0
$441$	2329.26			0.251513
$442$		0			0
$443$	−1706.39	−	1706.39i	−0.183009	−	0.183009i	0.609656	−	0.792666i	$-0.291307\pi$
$443$	−1706.39	−	1706.39i	−0.183009	−	0.183009i	−0.792666	+	0.609656i	$0.791307\pi$
$444$		0			0
$445$	−2992.25	+	2272.97i	−0.318755	+	0.242132i
$446$		0			0
$447$	1153.48	−	1153.48i	0.122053	−	0.122053i
$448$		0			0
$449$			14519.2i			1.52606i	0.646362	+	0.763031i	$0.276290\pi$
$449$			14519.2i			1.52606i	−0.646362	+	0.763031i	$0.723710\pi$
$450$		0			0
$451$			19767.9i			2.06393i
$452$		0			0
$453$	7463.60	−	7463.60i	0.774107	−	0.774107i
$454$		0			0
$455$	−5750.77	+	4368.39i	−0.592528	+	0.450095i
$456$		0			0
$457$	−2425.76	−	2425.76i	−0.248298	−	0.248298i	0.571974	−	0.820272i	$-0.306178\pi$
$457$	−2425.76	−	2425.76i	−0.248298	−	0.248298i	−0.820272	+	0.571974i	$0.806178\pi$
$458$		0			0
$459$	−15225.5			−1.54829
$460$		0			0
$461$	8549.98			0.863801			0.431901	−	0.901921i	$-0.357843\pi$
$461$	8549.98			0.863801			0.431901	+	0.901921i	$0.357843\pi$
$462$		0			0
$463$	−334.169	−	334.169i	−0.0335424	−	0.0335424i	0.690137	−	0.723679i	$-0.257550\pi$
$463$	−334.169	−	334.169i	−0.0335424	−	0.0335424i	−0.723679	+	0.690137i	$0.757550\pi$
$464$		0			0
$465$	−4692.27	−	641.012i	−0.467955	−	0.0639274i
$466$		0			0
$467$	−6480.64	+	6480.64i	−0.642159	+	0.642159i	−0.951086	−	0.308927i	$-0.900030\pi$
$467$	−6480.64	+	6480.64i	−0.642159	+	0.642159i	0.308927	+	0.951086i	$0.400030\pi$
$468$		0			0
$469$		−	8972.53i		−	0.883397i
$470$		0			0
$471$			660.416i			0.0646080i
$472$		0			0
$473$	−1364.71	+	1364.71i	−0.132662	+	0.132662i
$474$		0			0
$475$	−3046.73	+	10943.1i	−0.294302	+	1.05706i
$476$		0			0
$477$	−3436.95	−	3436.95i	−0.329910	−	0.329910i
$478$		0			0
$479$	−496.867			−0.0473954			−0.0236977	−	0.999719i	$-0.507544\pi$
$479$	−496.867			−0.0473954			−0.0236977	+	0.999719i	$0.507544\pi$
$480$		0			0
$481$	4110.16			0.389620
$482$		0			0
$483$	1214.92	+	1214.92i	0.114453	+	0.114453i
$484$		0			0
$485$	223.544	−	1636.36i	0.0209291	−	0.153203i
$486$		0			0
$487$	2601.52	−	2601.52i	0.242066	−	0.242066i	−0.575639	−	0.817704i	$-0.695246\pi$
$487$	2601.52	−	2601.52i	0.242066	−	0.242066i	0.817704	+	0.575639i	$0.195246\pi$
$488$		0			0
$489$		−	6419.51i		−	0.593661i
$490$		0			0
$491$			6142.42i			0.564569i	0.959331	+	0.282285i	$0.0910923\pi$
$491$			6142.42i			0.564569i	−0.959331	+	0.282285i	$0.908908\pi$
$492$		0			0
$493$	−6113.94	+	6113.94i	−0.558535	+	0.558535i
$494$		0			0
$495$	6345.21	+	8353.16i	0.576153	+	0.758478i
$496$		0			0
$497$	−2985.17	−	2985.17i	−0.269423	−	0.269423i
$498$		0			0
$499$	−3974.46			−0.356555			−0.178278	−	0.983980i	$-0.557053\pi$
$499$	−3974.46			−0.356555			−0.178278	+	0.983980i	$0.557053\pi$
$500$		0			0
$501$	12330.8			1.09960
$502$		0			0
$503$	−7191.87	−	7191.87i	−0.637514	−	0.637514i	0.312427	−	0.949942i	$-0.398858\pi$
$503$	−7191.87	−	7191.87i	−0.637514	−	0.637514i	−0.949942	+	0.312427i	$0.898858\pi$
$504$		0			0
$505$	12797.4	+	16847.1i	1.12767	+	1.48453i
$506$		0			0
$507$	−96.6168	+	96.6168i	−0.00846331	+	0.00846331i
$508$		0			0
$509$			2397.25i			0.208755i	0.994538	+	0.104377i	$0.0332850\pi$
$509$			2397.25i			0.208755i	−0.994538	+	0.104377i	$0.966715\pi$
$510$		0			0
$511$			864.221i			0.0748159i
$512$		0			0
$513$	9246.74	−	9246.74i	0.795816	−	0.795816i
$514$		0			0
$515$	1459.84	−	10686.2i	0.124909	−	0.914348i
$516$		0			0
$517$	18101.4	+	18101.4i	1.53984	+	1.53984i
$518$		0			0
$519$	12675.0			1.07201
$520$		0			0
$521$	−1573.20			−0.132290			−0.0661452	−	0.997810i	$-0.521070\pi$
$521$	−1573.20			−0.132290			−0.0661452	+	0.997810i	$0.521070\pi$
$522$		0			0
$523$	1739.01	+	1739.01i	0.145395	+	0.145395i	0.776057	−	0.630662i	$-0.217217\pi$
$523$	1739.01	+	1739.01i	0.145395	+	0.145395i	−0.630662	+	0.776057i	$0.717217\pi$
$524$		0			0
$525$	1576.11	−	5660.97i	0.131023	−	0.470600i
$526$		0			0
$527$	−9376.76	+	9376.76i	−0.775062	+	0.775062i
$528$		0			0
$529$		−	10831.2i		−	0.890211i
$530$		0			0
$531$		−	13006.3i		−	1.06295i
$532$		0			0
$533$	10777.2	−	10777.2i	0.875819	−	0.875819i
$534$		0			0
$535$	10590.0	+	1446.70i	0.855787	+	0.116909i
$536$		0			0
$537$	3428.06	+	3428.06i	0.275478	+	0.275478i
$538$		0			0
$539$	9006.34			0.719723
$540$		0			0
$541$	−22416.8			−1.78146			−0.890732	−	0.454529i	$-0.849808\pi$
$541$	−22416.8			−1.78146			−0.890732	+	0.454529i	$0.849808\pi$
$542$		0			0
$543$	−400.906	−	400.906i	−0.0316842	−	0.0316842i
$544$		0			0
$545$	−16777.2	+	12744.3i	−1.31864	+	1.00166i
$546$		0			0
$547$	1194.86	−	1194.86i	0.0933978	−	0.0933978i	−0.658864	−	0.752262i	$-0.728963\pi$
$547$	1194.86	−	1194.86i	0.0933978	−	0.0933978i	0.752262	+	0.658864i	$0.228963\pi$
$548$		0			0
$549$		−	7065.64i		−	0.549279i
$550$		0			0
$551$		−	7426.23i		−	0.574171i
$552$		0			0
$553$	1448.63	−	1448.63i	0.111396	−	0.111396i
$554$		0			0
$555$	−2663.16	+	2022.99i	−0.203685	+	0.154722i
$556$		0			0
$557$	−3890.45	−	3890.45i	−0.295949	−	0.295949i	0.543476	−	0.839425i	$-0.317108\pi$
$557$	−3890.45	−	3890.45i	−0.295949	−	0.295949i	−0.839425	+	0.543476i	$0.817108\pi$
$558$		0			0
$559$	1488.04			0.112589
$560$		0			0
$561$	−21538.5			−1.62096
$562$		0			0
$563$	−2231.00	−	2231.00i	−0.167008	−	0.167008i	0.618655	−	0.785663i	$-0.287678\pi$
$563$	−2231.00	−	2231.00i	−0.167008	−	0.167008i	−0.785663	+	0.618655i	$0.787678\pi$
$564$		0			0
$565$	−14765.2	−	2017.08i	−1.09943	−	0.150193i
$566$		0			0
$567$	−646.789	+	646.789i	−0.0479058	+	0.0479058i
$568$		0			0
$569$			25095.8i			1.84898i	0.381208	+	0.924489i	$0.375508\pi$
$569$			25095.8i			1.84898i	−0.381208	+	0.924489i	$0.624492\pi$
$570$		0			0
$571$		−	802.779i		−	0.0588359i	−0.999567	−	0.0294179i	$-0.990635\pi$
$571$		−	802.779i		−	0.0588359i	0.999567	−	0.0294179i	$-0.00936537\pi$
$572$		0			0
$573$	−11155.4	+	11155.4i	−0.813304	+	0.813304i
$574$		0			0
$575$	3978.57	−	2245.65i	0.288553	−	0.162870i
$576$		0			0
$577$	−1107.19	−	1107.19i	−0.0798836	−	0.0798836i	0.666036	−	0.745920i	$-0.267990\pi$
$577$	−1107.19	−	1107.19i	−0.0798836	−	0.0798836i	−0.745920	+	0.666036i	$0.767990\pi$
$578$		0			0
$579$	10916.2			0.783529
$580$		0			0
$581$	−14143.0			−1.00989
$582$		0			0
$583$	−13289.3	−	13289.3i	−0.944063	−	0.944063i
$584$		0			0
$585$	1094.70	−	8013.34i	0.0773683	−	0.566344i
$586$		0			0
$587$	12656.0	−	12656.0i	0.889896	−	0.889896i	−0.104617	−	0.994513i	$-0.533362\pi$
$587$	12656.0	−	12656.0i	0.889896	−	0.889896i	0.994513	+	0.104617i	$0.0333616\pi$
$588$		0			0
$589$		−	11389.4i		−	0.796759i
$590$		0			0
$591$		−	8214.55i		−	0.571745i
$592$		0			0
$593$	8159.45	−	8159.45i	0.565040	−	0.565040i	−0.365695	−	0.930735i	$-0.619169\pi$
$593$	8159.45	−	8159.45i	0.565040	−	0.565040i	0.930735	+	0.365695i	$0.119169\pi$
$594$		0			0
$595$	−9952.87	−	13102.5i	−0.685761	−	0.902771i
$596$		0			0
$597$	−6600.70	−	6600.70i	−0.452510	−	0.452510i
$598$		0			0
$599$	−5817.45			−0.396819			−0.198409	−	0.980119i	$-0.563578\pi$
$599$	−5817.45			−0.396819			−0.198409	+	0.980119i	$0.563578\pi$
$600$		0			0
$601$	20432.8			1.38681			0.693404	−	0.720549i	$-0.256110\pi$
$601$	20432.8			1.38681			0.693404	+	0.720549i	$0.256110\pi$
$602$		0			0
$603$	7105.33	+	7105.33i	0.479853	+	0.479853i
$604$		0			0
$605$	15533.1	+	20448.5i	1.04382	+	1.37413i
$606$		0			0
$607$	−11551.3	+	11551.3i	−0.772407	+	0.772407i	−0.978527	−	0.206119i	$-0.933916\pi$
$607$	−11551.3	+	11551.3i	−0.772407	+	0.772407i	0.206119	+	0.978527i	$0.433916\pi$
$608$		0			0
$609$			3841.66i			0.255619i
$610$		0			0
$611$		−	19737.2i		−	1.30685i
$612$		0			0
$613$	17400.4	−	17400.4i	1.14649	−	1.14649i	0.159246	−	0.987239i	$-0.449094\pi$
$613$	17400.4	−	17400.4i	1.14649	−	1.14649i	0.987239	−	0.159246i	$-0.0509064\pi$
$614$		0			0
$615$	−1678.59	+	12287.5i	−0.110061	+	0.805657i
$616$		0			0
$617$	−19751.3	−	19751.3i	−1.28875	−	1.28875i	−0.935547	−	0.353203i	$-0.885093\pi$
$617$	−19751.3	−	19751.3i	−1.28875	−	1.28875i	−0.353203	−	0.935547i	$-0.614907\pi$
$618$		0			0
$619$	22265.2			1.44574			0.722870	−	0.690984i	$-0.242823\pi$
$619$	22265.2			1.44574			0.722870	+	0.690984i	$0.242823\pi$
$620$		0			0
$621$	−5259.38			−0.339857
$622$		0			0
$623$	3305.63	+	3305.63i	0.212580	+	0.212580i
$624$		0			0
$625$	−13376.9	−	8074.60i	−0.856122	−	0.516775i
$626$		0			0
$627$	13080.8	−	13080.8i	0.833167	−	0.833167i
$628$		0			0
$629$			9364.52i			0.593621i
$630$		0			0
$631$		−	26956.1i		−	1.70064i	−0.526264	−	0.850321i	$-0.676408\pi$
$631$		−	26956.1i		−	1.70064i	0.526264	−	0.850321i	$-0.323592\pi$
$632$		0			0
$633$	−1139.54	+	1139.54i	−0.0715521	+	0.0715521i
$634$		0			0
$635$	−22247.8	−	3039.27i	−1.39036	−	0.189937i
$636$		0			0
$637$	−4910.13	−	4910.13i	−0.305410	−	0.305410i
$638$		0			0
$639$	4727.90			0.292696
$640$		0			0
$641$	−15117.1			−0.931497			−0.465749	−	0.884917i	$-0.654215\pi$
$641$	−15117.1			−0.931497			−0.465749	+	0.884917i	$0.654215\pi$
$642$		0			0
$643$	18118.8	+	18118.8i	1.11125	+	1.11125i	0.992981	+	0.118274i	$0.0377360\pi$
$643$	18118.8	+	18118.8i	1.11125	+	1.11125i	0.118274	+	0.992981i	$0.462264\pi$
$644$		0			0
$645$	−964.168	+	732.400i	−0.0588590	+	0.0447104i
$646$		0			0
$647$	−7164.48	+	7164.48i	−0.435339	+	0.435339i	−0.890440	−	0.455101i	$-0.849603\pi$
$647$	−7164.48	+	7164.48i	−0.435339	+	0.435339i	0.455101	+	0.890440i	$0.349603\pi$
$648$		0			0
$649$		−	50290.3i		−	3.04171i
$650$		0			0
$651$			5891.84i			0.354715i
$652$		0			0
$653$	−14436.5	+	14436.5i	−0.865151	+	0.865151i	−0.991931	−	0.126780i	$-0.959536\pi$
$653$	−14436.5	+	14436.5i	−0.865151	+	0.865151i	0.126780	+	0.991931i	$0.459536\pi$
$654$		0			0
$655$	−15429.0	+	11720.1i	−0.920397	+	0.699150i
$656$		0			0
$657$	−684.375	−	684.375i	−0.0406393	−	0.0406393i
$658$		0			0
$659$	−6346.82			−0.375170			−0.187585	−	0.982248i	$-0.560066\pi$
$659$	−6346.82			−0.375170			−0.187585	+	0.982248i	$0.560066\pi$
$660$		0			0
$661$	7456.31			0.438755			0.219377	−	0.975640i	$-0.429597\pi$
$661$	7456.31			0.438755			0.219377	+	0.975640i	$0.429597\pi$
$662$		0			0
$663$	11742.5	+	11742.5i	0.687844	+	0.687844i
$664$		0			0
$665$	14002.0	+	1912.81i	0.816500	+	0.111542i
$666$		0			0
$667$	−2111.95	+	2111.95i	−0.122601	+	0.122601i
$668$		0			0
$669$		−	11920.0i		−	0.688872i
$670$		0			0
$671$		−	27320.1i		−	1.57180i
$672$		0			0
$673$	−9808.67	+	9808.67i	−0.561808	+	0.561808i	−0.929821	−	0.368013i	$-0.880038\pi$
$673$	−9808.67	+	9808.67i	−0.561808	+	0.561808i	0.368013	+	0.929821i	$0.380038\pi$
$674$		0			0
$675$	8841.63	+	15664.6i	0.504170	+	0.893228i
$676$		0			0
$677$	−208.219	−	208.219i	−0.0118206	−	0.0118206i	0.701172	−	0.712992i	$-0.252661\pi$
$677$	−208.219	−	208.219i	−0.0118206	−	0.0118206i	−0.712992	+	0.701172i	$0.752661\pi$
$678$		0			0
$679$	−2054.69			−0.116129
$680$		0			0
$681$	−2759.73			−0.155291
$682$		0			0
$683$	−1581.65	−	1581.65i	−0.0886095	−	0.0886095i	0.661413	−	0.750022i	$-0.269957\pi$
$683$	−1581.65	−	1581.65i	−0.0886095	−	0.0886095i	−0.750022	+	0.661413i	$0.769957\pi$
$684$		0			0
$685$	−2093.46	+	15324.3i	−0.116769	+	0.854763i
$686$		0			0
$687$	−8906.66	+	8906.66i	−0.494629	+	0.494629i
$688$		0			0
$689$			14490.3i			0.801216i
$690$		0			0
$691$			4783.76i			0.263362i	0.991292	+	0.131681i	$0.0420374\pi$
$691$			4783.76i			0.263362i	−0.991292	+	0.131681i	$0.957963\pi$
$692$		0			0
$693$	9227.99	−	9227.99i	0.505833	−	0.505833i
$694$		0			0
$695$	−8527.39	−	11225.9i	−0.465414	−	0.612694i
$696$		0			0
$697$	24554.6	+	24554.6i	1.33439	+	1.33439i
$698$		0			0
$699$	−9000.36			−0.487017
$700$		0			0
$701$	−27968.2			−1.50691			−0.753455	−	0.657499i	$-0.771614\pi$
$701$	−27968.2			−1.50691			−0.753455	+	0.657499i	$0.771614\pi$
$702$		0			0
$703$	−5687.26	−	5687.26i	−0.305119	−	0.305119i
$704$		0			0
$705$	9714.50	+	12788.7i	0.518963	+	0.683190i
$706$		0			0
$707$	18611.5	−	18611.5i	0.990039	−	0.990039i
$708$		0			0
$709$			15134.5i			0.801673i	0.916150	+	0.400837i	$0.131281\pi$
$709$			15134.5i			0.801673i	−0.916150	+	0.400837i	$0.868719\pi$
$710$		0			0
$711$			2294.33i			0.121018i
$712$		0			0
$713$	−3239.03	+	3239.03i	−0.170130	+	0.170130i
$714$		0			0
$715$	4232.80	−	30984.5i	0.221395	−	1.62063i
$716$		0			0
$717$	−6021.11	−	6021.11i	−0.313616	−	0.313616i
$718$		0			0
$719$	1567.13			0.0812853			0.0406426	−	0.999174i	$-0.487059\pi$
$719$	1567.13			0.0812853			0.0406426	+	0.999174i	$0.487059\pi$
$720$		0			0
$721$	−13418.1			−0.693086
$722$		0			0
$723$	9810.52	+	9810.52i	0.504643	+	0.504643i
$724$		0			0
$725$	9840.68	+	2739.81i	0.504102	+	0.140350i
$726$		0			0
$727$	−23414.4	+	23414.4i	−1.19449	+	1.19449i	−0.218694	+	0.975794i	$0.570180\pi$
$727$	−23414.4	+	23414.4i	−1.19449	+	1.19449i	−0.975794	+	0.218694i	$0.929820\pi$
$728$		0			0
$729$		−	14155.8i		−	0.719188i
$730$		0			0
$731$			3390.32i			0.171540i
$732$		0			0
$733$	20321.5	−	20321.5i	1.02400	−	1.02400i	0.0242936	−	0.999705i	$-0.492266\pi$
$733$	20321.5	−	20321.5i	1.02400	−	1.02400i	0.999705	−	0.0242936i	$-0.00773367\pi$
$734$		0			0
$735$	5598.23	+	764.775i	0.280944	+	0.0383798i
$736$		0			0
$737$	27473.5	+	27473.5i	1.37314	+	1.37314i
$738$		0			0
$739$	21986.1			1.09442			0.547208	−	0.836997i	$-0.315691\pi$
$739$	21986.1			1.09442			0.547208	+	0.836997i	$0.315691\pi$
$740$		0			0
$741$	−14262.9			−0.707099
$742$		0			0
$743$	3661.72	+	3661.72i	0.180801	+	0.180801i	0.791705	−	0.610904i	$-0.209194\pi$
$743$	3661.72	+	3661.72i	0.180801	+	0.180801i	−0.610904	+	0.791705i	$0.709194\pi$
$744$		0			0
$745$	−4297.10	+	3264.16i	−0.211320	+	0.160523i
$746$		0			0
$747$	11199.8	−	11199.8i	0.548566	−	0.548566i
$748$		0			0
$749$		−	13297.3i		−	0.648696i
$750$		0			0
$751$			11267.6i			0.547485i	0.961803	+	0.273742i	$0.0882616\pi$
$751$			11267.6i			0.547485i	−0.961803	+	0.273742i	$0.911738\pi$
$752$		0			0
$753$	12988.2	−	12988.2i	0.628576	−	0.628576i
$754$		0			0
$755$	−27804.5	+	21120.8i	−1.34028	+	1.01810i
$756$		0			0
$757$	19790.8	+	19790.8i	0.950210	+	0.950210i	0.998818	−	0.0486080i	$-0.0154785\pi$
$757$	19790.8	+	19790.8i	0.950210	+	0.950210i	−0.0486080	+	0.998818i	$0.515479\pi$
$758$		0			0
$759$	−7440.10			−0.355808
$760$		0			0
$761$	1784.14			0.0849867			0.0424933	−	0.999097i	$-0.486470\pi$
$761$	1784.14			0.0849867			0.0424933	+	0.999097i	$0.486470\pi$
$762$		0			0
$763$	18534.3	+	18534.3i	0.879405	+	0.879405i
$764$		0			0
$765$	18257.5	+	2494.16i	0.862876	+	0.117878i
$766$		0			0
$767$	−27417.6	+	27417.6i	−1.29073	+	1.29073i
$768$		0			0
$769$			639.893i			0.0300067i	0.999887	+	0.0150033i	$0.00477589\pi$
$769$			639.893i			0.0300067i	−0.999887	+	0.0150033i	$0.995224\pi$
$770$		0			0
$771$			2798.04i			0.130699i
$772$		0			0
$773$	11139.1	−	11139.1i	0.518299	−	0.518299i	−0.398757	−	0.917056i	$-0.630558\pi$
$773$	11139.1	−	11139.1i	0.518299	−	0.518299i	0.917056	+	0.398757i	$0.130558\pi$
$774$		0			0
$775$	15092.4	+	4201.96i	0.699527	+	0.194760i
$776$		0			0
$777$	2942.08	+	2942.08i	0.135838	+	0.135838i
$778$		0			0
$779$	−29824.9			−1.37174
$780$		0			0
$781$	18281.0			0.837573
$782$		0			0
$783$	−8315.24	−	8315.24i	−0.379518	−	0.379518i
$784$		0			0
$785$	295.703	−	2164.58i	0.0134447	−	0.0984167i
$786$		0			0
$787$	−3243.01	+	3243.01i	−0.146888	+	0.146888i	−0.776726	−	0.629838i	$-0.783121\pi$
$787$	−3243.01	+	3243.01i	−0.146888	+	0.146888i	0.629838	+	0.776726i	$0.283121\pi$
$788$		0			0
$789$			23026.7i			1.03900i
$790$		0			0
$791$			18539.9i			0.833378i
$792$		0			0
$793$	−14894.5	+	14894.5i	−0.666986	+	0.666986i
$794$		0			0
$795$	−7132.02	−	9388.96i	−0.318172	−	0.418858i
$796$		0			0
$797$	20592.8	+	20592.8i	0.915223	+	0.915223i	0.996677	−	0.0814541i	$-0.0259564\pi$
$797$	20592.8	+	20592.8i	0.915223	+	0.915223i	−0.0814541	+	0.996677i	$0.525956\pi$
$798$		0			0
$799$	44969.0			1.99110
$800$		0			0
$801$	−5235.44			−0.230943
$802$		0			0
$803$	−2646.21	−	2646.21i	−0.116292	−	0.116292i
$804$		0			0
$805$	−3438.04	−	4526.01i	−0.150528	−	0.198163i
$806$		0			0
$807$	2512.01	−	2512.01i	0.109575	−	0.109575i
$808$		0			0
$809$		−	25350.0i		−	1.10168i	−0.834611	−	0.550840i	$-0.814307\pi$
$809$		−	25350.0i		−	1.10168i	0.834611	−	0.550840i	$-0.185693\pi$
$810$		0			0
$811$			16833.1i			0.728842i	0.931234	+	0.364421i	$0.118733\pi$
$811$			16833.1i			0.728842i	−0.931234	+	0.364421i	$0.881267\pi$
$812$		0			0
$813$	−6051.07	+	6051.07i	−0.261033	+	0.261033i
$814$		0			0
$815$	−2874.35	+	21040.6i	−0.123539	+	0.904317i
$816$		0			0
$817$	−2059.01	−	2059.01i	−0.0881708	−	0.0881708i
$818$		0			0
$819$	−10061.9			−0.429295
$820$		0			0
$821$	−3557.99			−0.151248			−0.0756241	−	0.997136i	$-0.524095\pi$
$821$	−3557.99			−0.151248			−0.0756241	+	0.997136i	$0.524095\pi$
$822$		0			0
$823$	846.527	+	846.527i	0.0358543	+	0.0358543i	0.724807	−	0.688952i	$-0.241929\pi$
$823$	846.527	+	846.527i	0.0358543	+	0.0358543i	−0.688952	+	0.724807i	$0.741929\pi$
$824$		0			0
$825$	12507.7	+	22159.6i	0.527832	+	0.935150i
$826$		0			0
$827$	−234.539	+	234.539i	−0.00986180	+	0.00986180i	−0.712020	−	0.702159i	$-0.752220\pi$
$827$	−234.539	+	234.539i	−0.00986180	+	0.00986180i	0.702159	+	0.712020i	$0.252220\pi$
$828$		0			0
$829$		−	33859.6i		−	1.41857i	−0.704923	−	0.709284i	$-0.749018\pi$
$829$		−	33859.6i		−	1.41857i	0.704923	−	0.709284i	$-0.250982\pi$
$830$		0			0
$831$		−	1121.80i		−	0.0468287i
$832$		0			0
$833$	11187.2	−	11187.2i	0.465321	−	0.465321i
$834$		0			0
$835$	−40415.2	−	5521.14i	−1.67500	−	0.228822i
$836$		0			0
$837$	−12752.8	−	12752.8i	−0.526645	−	0.526645i
$838$		0			0
$839$	−22690.4			−0.933684			−0.466842	−	0.884341i	$-0.654608\pi$
$839$	−22690.4			−0.933684			−0.466842	+	0.884341i	$0.654608\pi$
$840$		0			0
$841$	17710.9			0.726183
$842$		0			0
$843$	18458.4	+	18458.4i	0.754142	+	0.754142i
$844$		0			0
$845$	359.931	−	273.410i	0.0146533	−	0.0111309i
$846$		0			0
$847$	22590.1	−	22590.1i	0.916416	−	0.916416i
$848$		0			0
$849$			13380.1i			0.540875i
$850$		0			0
$851$			3234.81i			0.130303i
$852$		0			0
$853$	−2509.72	+	2509.72i	−0.100740	+	0.100740i	−0.755681	−	0.654940i	$-0.772694\pi$
$853$	−2509.72	+	2509.72i	−0.100740	+	0.100740i	0.654940	+	0.755681i	$0.272694\pi$
$854$		0			0
$855$	−12602.9	+	9573.37i	−0.504104	+	0.382927i
$856$		0			0
$857$	−6154.50	−	6154.50i	−0.245313	−	0.245313i	0.573731	−	0.819044i	$-0.305496\pi$
$857$	−6154.50	−	6154.50i	−0.245313	−	0.245313i	−0.819044	+	0.573731i	$0.805496\pi$
$858$		0			0
$859$	14723.8			0.584830			0.292415	−	0.956292i	$-0.405541\pi$
$859$	14723.8			0.584830			0.292415	+	0.956292i	$0.405541\pi$
$860$		0			0
$861$	15428.7			0.610697
$862$		0			0
$863$	−7951.15	−	7951.15i	−0.313627	−	0.313627i	0.532686	−	0.846313i	$-0.321183\pi$
$863$	−7951.15	−	7951.15i	−0.313627	−	0.313627i	−0.846313	+	0.532686i	$0.821183\pi$
$864$		0			0
$865$	−41543.5	−	5675.27i	−1.63297	−	0.223081i
$866$		0			0
$867$	−15012.6	+	15012.6i	−0.588068	+	0.588068i
$868$		0			0
$869$			8871.28i			0.346303i
$870$		0			0
$871$		−	29956.4i		−	1.16537i
$872$		0			0
$873$	1627.11	−	1627.11i	0.0630804	−	0.0630804i
$874$		0			0
$875$	−7700.55	+	17848.6i	−0.297516	+	0.689594i
$876$		0			0
$877$	−19834.9	−	19834.9i	−0.763713	−	0.763713i	0.213278	−	0.976991i	$-0.431586\pi$
$877$	−19834.9	−	19834.9i	−0.763713	−	0.763713i	−0.976991	+	0.213278i	$0.931586\pi$
$878$		0			0
$879$	6084.46			0.233474
$880$		0			0
$881$	−11030.4			−0.421821			−0.210910	−	0.977505i	$-0.567643\pi$
$881$	−11030.4			−0.421821			−0.210910	+	0.977505i	$0.567643\pi$
$882$		0			0
$883$	−12089.6	−	12089.6i	−0.460756	−	0.460756i	0.438147	−	0.898903i	$-0.355635\pi$
$883$	−12089.6	−	12089.6i	−0.460756	−	0.460756i	−0.898903	+	0.438147i	$0.855635\pi$
$884$		0			0
$885$	4270.41	−	31259.8i	0.162201	−	1.18733i
$886$		0			0
$887$	28797.8	−	28797.8i	1.09012	−	1.09012i	0.0946032	−	0.995515i	$-0.469842\pi$
$887$	28797.8	−	28797.8i	1.09012	−	1.09012i	0.995515	−	0.0946032i	$-0.0301582\pi$
$888$		0			0
$889$			27935.4i			1.05391i
$890$		0			0
$891$		−	3960.89i		−	0.148928i
$892$		0			0
$893$	−27310.5	+	27310.5i	−1.02342	+	1.02342i
$894$		0			0
$895$	−9700.87	−	12770.7i	−0.362307	−	0.476959i
$896$		0			0
$897$	4056.24	+	4056.24i	0.150985	+	0.150985i
$898$		0			0
$899$	−10242.0			−0.379967
$900$		0			0
$901$	−33014.5			−1.22073
$902$		0			0
$903$	1065.15	+	1065.15i	0.0392534	+	0.0392534i
$904$		0			0
$905$	1134.50	+	1493.51i	0.0416708	+	0.0548575i
$906$		0			0
$907$	−17602.0	+	17602.0i	−0.644393	+	0.644393i	−0.951632	−	0.307239i	$-0.900595\pi$
$907$	−17602.0	+	17602.0i	−0.644393	+	0.644393i	0.307239	+	0.951632i	$0.400595\pi$
$908$		0			0
$909$			29476.8i			1.07556i
$910$		0			0
$911$		−	45374.9i		−	1.65021i	−0.564982	−	0.825103i	$-0.691117\pi$
$911$		−	45374.9i		−	1.65021i	0.564982	−	0.825103i	$-0.308883\pi$
$912$		0			0
$913$	43305.2	−	43305.2i	1.56976	−	1.56976i
$914$		0			0
$915$	2319.89	−	16981.8i	0.0838177	−	0.613554i
$916$		0			0
$917$	17044.9	+	17044.9i	0.613818	+	0.613818i
$918$		0			0
$919$	36164.6			1.29811			0.649054	−	0.760743i	$-0.275165\pi$
$919$	36164.6			1.29811			0.649054	+	0.760743i	$0.275165\pi$
$920$		0			0
$921$	2048.45			0.0732885
$922$		0			0
$923$	−9966.52	−	9966.52i	−0.355419	−	0.355419i
$924$		0			0
$925$	9634.56	−	5438.09i	0.342468	−	0.193301i
$926$		0			0
$927$	10625.7	−	10625.7i	0.376478	−	0.376478i
$928$		0			0
$929$			2392.84i			0.0845064i	0.999107	+	0.0422532i	$0.0134536\pi$
$929$			2392.84i			0.0845064i	−0.999107	+	0.0422532i	$0.986546\pi$
$930$		0			0
$931$			13588.4i			0.478347i
$932$		0			0
$933$	−7164.13	+	7164.13i	−0.251386	+	0.251386i
$934$		0			0
$935$	70594.5	+	9643.94i	2.46919	+	0.337316i
$936$		0			0
$937$	−32944.5	−	32944.5i	−1.14861	−	1.14861i	−0.986826	−	0.161788i	$-0.948274\pi$
$937$	−32944.5	−	32944.5i	−1.14861	−	1.14861i	−0.161788	−	0.986826i	$-0.551726\pi$
$938$		0			0
$939$	−27025.9			−0.939252
$940$		0			0
$941$	19141.4			0.663114			0.331557	−	0.943435i	$-0.392426\pi$
$941$	19141.4			0.663114			0.331557	+	0.943435i	$0.392426\pi$
$942$		0			0
$943$	8481.93	+	8481.93i	0.292905	+	0.292905i
$944$		0			0
$945$	17820.0	−	13536.4i	0.613422	−	0.465966i
$946$		0			0
$947$	12173.1	−	12173.1i	0.417710	−	0.417710i	−0.466704	−	0.884414i	$-0.654558\pi$
$947$	12173.1	−	12173.1i	0.417710	−	0.417710i	0.884414	+	0.466704i	$0.154558\pi$
$948$		0			0
$949$			2885.35i			0.0986961i
$950$		0			0
$951$		−	9055.27i		−	0.308767i
$952$		0			0
$953$	−31150.3	+	31150.3i	−1.05882	+	1.05882i	−0.0606618	+	0.998158i	$0.519321\pi$
$953$	−31150.3	+	31150.3i	−1.05882	+	1.05882i	−0.998158	+	0.0606618i	$0.980679\pi$
$954$		0			0
$955$	41557.7	−	31568.0i	1.40814	−	1.06965i
$956$		0			0
$957$	−11763.0	−	11763.0i	−0.397330	−	0.397330i
$958$		0			0
$959$	19242.0			0.647921
$960$		0			0
$961$	14083.1			0.472731
$962$		0			0
$963$	10530.1	+	10530.1i	0.352366	+	0.352366i
$964$		0			0
$965$	−35779.0	−	4887.78i	−1.19354	−	0.163050i
$966$		0			0
$967$	−35609.3	+	35609.3i	−1.18420	+	1.18420i	−0.205549	+	0.978647i	$0.565898\pi$
$967$	−35609.3	+	35609.3i	−1.18420	+	1.18420i	−0.978647	+	0.205549i	$0.934102\pi$
$968$		0			0
$969$		−	32496.4i		−	1.07733i
$970$		0			0
$971$		−	1252.24i		−	0.0413864i	−0.999786	−	0.0206932i	$-0.993413\pi$
$971$		−	1252.24i		−	0.0413864i	0.999786	−	0.0206932i	$-0.00658733\pi$
$972$		0			0
$973$	−12401.6	+	12401.6i	−0.408609	+	0.408609i
$974$		0			0
$975$	5262.11	−	18900.1i	0.172843	−	0.620809i
$976$		0			0
$977$	−6417.48	−	6417.48i	−0.210147	−	0.210147i	0.594183	−	0.804330i	$-0.297475\pi$
$977$	−6417.48	−	6417.48i	−0.210147	−	0.210147i	−0.804330	+	0.594183i	$0.797475\pi$
$978$		0			0
$979$	−20243.4			−0.660860
$980$		0			0
$981$	−29354.5			−0.955370
$982$		0			0
$983$	9008.33	+	9008.33i	0.292290	+	0.292290i	0.837984	−	0.545694i	$-0.183734\pi$
$983$	9008.33	+	9008.33i	0.292290	+	0.292290i	−0.545694	+	0.837984i	$0.683734\pi$
$984$		0			0
$985$	−3678.09	+	26924.0i	−0.118978	+	0.870933i
$986$		0			0
$987$	14128.0	−	14128.0i	0.455623	−	0.455623i
$988$		0			0
$989$			1171.13i			0.0376538i
$990$		0			0
$991$			36054.2i			1.15570i	0.816143	+	0.577850i	$0.196108\pi$
$991$			36054.2i			1.15570i	−0.816143	+	0.577850i	$0.803892\pi$
$992$		0			0
$993$	−5770.32	+	5770.32i	−0.184406	+	0.184406i
$994$		0			0
$995$	18678.9	+	24589.9i	0.595138	+	0.783469i
$996$		0			0
$997$	1855.25	+	1855.25i	0.0589331	+	0.0589331i	0.735959	−	0.677026i	$-0.236732\pi$
$997$	1855.25	+	1855.25i	0.0589331	+	0.0589331i	−0.677026	+	0.735959i	$0.736732\pi$
$998$		0			0
$999$	−12736.2			−0.403358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.n.f.127.3	yes	8
4.3	odd	2		160.4.n.c.127.2	yes	8
5.3	odd	4		160.4.n.c.63.2	✓	8
8.3	odd	2		320.4.n.i.127.3		8
8.5	even	2		320.4.n.f.127.2		8
20.3	even	4	inner	160.4.n.f.63.3	yes	8
40.3	even	4		320.4.n.f.63.2		8
40.13	odd	4		320.4.n.i.63.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.n.c.63.2	✓	8	5.3	odd	4
160.4.n.c.127.2	yes	8	4.3	odd	2
160.4.n.f.63.3	yes	8	20.3	even	4	inner
160.4.n.f.127.3	yes	8	1.1	even	1	trivial
320.4.n.f.63.2		8	40.3	even	4
320.4.n.f.127.2		8	8.5	even	2
320.4.n.i.63.3		8	40.13	odd	4
320.4.n.i.127.3		8	8.3	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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.38984 + 2.38984i) q^{3} +(-6.76288 - 8.90300i) q^{5} +(-9.83542 + 9.83542i) q^{7} -15.5773i q^{9} -60.2313i q^{11} +(-32.8373 + 32.8373i) q^{13} +(5.11455 - 37.4390i) q^{15} +(-74.8159 - 74.8159i) q^{17} +90.8743 q^{19} -47.0102 q^{21} +(-25.8438 - 25.8438i) q^{23} +(-33.5269 + 120.420i) q^{25} +(101.753 - 101.753i) q^{27} -81.7198i q^{29} -125.331i q^{31} +(143.943 - 143.943i) q^{33} +(154.080 + 21.0490i) q^{35} +(-62.5837 - 62.5837i) q^{37} -156.952 q^{39} -328.200 q^{41} +(-22.6577 - 22.6577i) q^{43} +(-138.685 + 105.347i) q^{45} +(-300.531 + 300.531i) q^{47} +149.529i q^{49} -357.597i q^{51} +(220.639 - 220.639i) q^{53} +(-536.239 + 407.337i) q^{55} +(217.176 + 217.176i) q^{57} +834.953 q^{59} +453.586 q^{61} +(153.209 + 153.209i) q^{63} +(514.425 + 70.2757i) q^{65} +(-456.134 + 456.134i) q^{67} -123.525i q^{69} +303.513i q^{71} +(43.9342 - 43.9342i) q^{73} +(-367.909 + 207.661i) q^{75} +(592.400 + 592.400i) q^{77} -147.287 q^{79} +65.7612 q^{81} +(718.981 + 718.981i) q^{83} +(-160.115 + 1172.06i) q^{85} +(195.297 - 195.297i) q^{87} -336.094i q^{89} -645.936i q^{91} +(299.522 - 299.522i) q^{93} +(-614.572 - 809.054i) q^{95} +(104.454 + 104.454i) q^{97} -938.241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - 6 q^{5} + 70 q^{7} + 144 q^{13} - 134 q^{15} - 100 q^{17} + 176 q^{19} - 516 q^{21} - 198 q^{23} - 172 q^{25} - 288 q^{27} + 172 q^{33} + 170 q^{35} + 492 q^{37} + 756 q^{39} - 28 q^{41}+ \cdots + 8412 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 - 6 * q^5 + 70 * q^7 + 144 * q^13 - 134 * q^15 - 100 * q^17 + 176 * q^19 - 516 * q^21 - 198 * q^23 - 172 * q^25 - 288 * q^27 + 172 * q^33 + 170 * q^35 + 492 * q^37 + 756 * q^39 - 28 * q^41 + 654 * q^43 + 10 * q^45 - 690 * q^47 + 580 * q^53 - 2392 * q^55 - 248 * q^57 + 1808 * q^59 - 1068 * q^61 + 3106 * q^63 + 2200 * q^65 - 1878 * q^67 + 1952 * q^73 - 2178 * q^75 + 340 * q^77 - 1808 * q^79 - 7844 * q^81 - 506 * q^83 + 184 * q^85 + 784 * q^87 + 3708 * q^93 - 5800 * q^95 + 5576 * q^97 + 8412 * q^99

Introduction

L-functions

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