LMFDB - Embedded newform 320.4.n.f.63.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [320,4,Mod(63,320)] 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("320.63"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	320.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-6,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$18.8806112018$
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:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.2
Root			$-5.14642i$ of defining polynomial
Character	$\chi$	$=$	320.63
Dual form			320.4.n.f.127.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.38984 + 2.38984i) q^{3} +(6.76288 - 8.90300i) q^{5} +(-9.83542 - 9.83542i) q^{7} +15.5773i q^{9} -60.2313i q^{11} +(32.8373 + 32.8373i) q^{13} +(5.11455 + 37.4390i) q^{15} +(-74.8159 + 74.8159i) q^{17} -90.8743 q^{19} +47.0102 q^{21} +(-25.8438 + 25.8438i) q^{23} +(-33.5269 - 120.420i) q^{25} +(-101.753 - 101.753i) q^{27} -81.7198i q^{29} +125.331i q^{31} +(143.943 + 143.943i) q^{33} +(-154.080 + 21.0490i) q^{35} +(62.5837 - 62.5837i) q^{37} -156.952 q^{39} -328.200 q^{41} +(22.6577 - 22.6577i) q^{43} +(138.685 + 105.347i) q^{45} +(-300.531 - 300.531i) q^{47} -149.529i q^{49} -357.597i q^{51} +(-220.639 - 220.639i) q^{53} +(-536.239 - 407.337i) q^{55} +(217.176 - 217.176i) q^{57} -834.953 q^{59} -453.586 q^{61} +(153.209 - 153.209i) q^{63} +(514.425 - 70.2757i) q^{65} +(456.134 + 456.134i) q^{67} -123.525i q^{69} -303.513i q^{71} +(43.9342 + 43.9342i) q^{73} +(367.909 + 207.661i) q^{75} +(-592.400 + 592.400i) q^{77} -147.287 q^{79} +65.7612 q^{81} +(-718.981 + 718.981i) q^{83} +(160.115 + 1172.06i) q^{85} +(195.297 + 195.297i) q^{87} +336.094i q^{89} -645.936i q^{91} +(-299.522 - 299.522i) q^{93} +(-614.572 + 809.054i) q^{95} +(104.454 - 104.454i) q^{97} +938.241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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	$-0.855437\pi$
$3$	−2.38984	+	2.38984i	−0.459926	+	0.459926i	0.438705	+	0.898631i	$0.355437\pi$
$4$		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	0.389826	−	0.920889i	$-0.372535\pi$
$7$	−9.83542	−	9.83542i	−0.531063	−	0.531063i	−0.920889	+	0.389826i	$0.872535\pi$
$8$		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	$-0.0850295\pi$
$13$	32.8373	+	32.8373i	0.700571	+	0.700571i	−0.263962	+	0.964533i	$0.585029\pi$
$14$		0			0
$15$	5.11455	+	37.4390i	0.0880381	+	0.644448i
$16$		0			0
$17$	−74.8159	+	74.8159i	−1.06738	+	1.06738i	−0.0698243	+	0.997559i	$0.522244\pi$
$17$	−74.8159	+	74.8159i	−1.06738	+	1.06738i	−0.997559	+	0.0698243i	$0.977756\pi$
$18$		0			0
$19$	−90.8743			−1.09726			−0.548632	−	0.836064i	$-0.684851\pi$
$19$	−90.8743			−1.09726			−0.548632	+	0.836064i	$0.684851\pi$
$20$		0			0
$21$	47.0102			0.488499
$22$		0			0
$23$	−25.8438	+	25.8438i	−0.234296	+	0.234296i	−0.814483	−	0.580187i	$-0.802979\pi$
$23$	−25.8438	+	25.8438i	−0.234296	+	0.234296i	0.580187	+	0.814483i	$0.302979\pi$
$24$		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	$0.118270\pi$
$31$			125.331i			0.726133i	−0.931763	+	0.363066i	$0.881730\pi$
$32$		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	$-0.687001\pi$
$37$	62.5837	−	62.5837i	0.278073	−	0.278073i	0.832339	+	0.554266i	$0.187001\pi$
$38$		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	$-0.731904\pi$
$43$	22.6577	−	22.6577i	0.0803552	−	0.0803552i	0.746142	+	0.665787i	$0.231904\pi$
$44$		0			0
$45$	138.685	+	105.347i	0.459420	+	0.348984i
$46$		0			0
$47$	−300.531	−	300.531i	−0.932701	−	0.932701i	0.0651734	−	0.997874i	$-0.479240\pi$
$47$	−300.531	−	300.531i	−0.932701	−	0.932701i	−0.997874	+	0.0651734i	$0.979240\pi$
$48$		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	$-0.382501\pi$
$53$	−220.639	−	220.639i	−0.571831	−	0.571831i	−0.932640	+	0.360809i	$0.882501\pi$
$54$		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	$-0.872790\pi$
$59$	−834.953			−1.84240			−0.921200	+	0.389089i	$0.872790\pi$
$60$		0			0
$61$	−453.586			−0.952061			−0.476031	−	0.879429i	$-0.657925\pi$
$61$	−453.586			−0.952061			−0.476031	+	0.879429i	$0.657925\pi$
$62$		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	$-0.0498687\pi$
$67$	456.134	+	456.134i	0.831726	+	0.831726i	−0.156027	+	0.987753i	$0.549869\pi$
$68$		0			0
$69$		−	123.525i		−	0.215518i
$70$		0			0
$71$		−	303.513i		−	0.507328i	−0.967292	−	0.253664i	$-0.918364\pi$
$71$		−	303.513i		−	0.507328i	0.967292	−	0.253664i	$-0.0816358\pi$
$72$		0			0
$73$	43.9342	+	43.9342i	0.0704398	+	0.0704398i	0.741449	−	0.671009i	$-0.234139\pi$
$73$	43.9342	+	43.9342i	0.0704398	+	0.0704398i	−0.671009	+	0.741449i	$0.734139\pi$
$74$		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	$-0.984708\pi$
$83$	−718.981	+	718.981i	−0.950825	+	0.950825i	0.0480214	+	0.998846i	$0.484708\pi$
$84$		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	$0.0641415\pi$
$89$			336.094i			0.400291i	−0.979766	+	0.200146i	$0.935858\pi$
$90$		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	−0.650322	−	0.759659i	$-0.725366\pi$
$97$	104.454	−	104.454i	0.109337	−	0.109337i	0.759659	+	0.650322i	$0.225366\pi$
$98$		0			0
$99$	938.241			0.952492
$100$		0			0
$101$	1892.29			1.86426			0.932130	−	0.362124i	$-0.117948\pi$
$101$	1892.29			1.86426			0.932130	+	0.362124i	$0.117948\pi$
$102$		0			0
$103$	682.131	−	682.131i	0.652547	−	0.652547i	−0.301059	−	0.953606i	$-0.597340\pi$
$103$	682.131	−	682.131i	0.652547	−	0.652547i	0.953606	+	0.301059i	$0.0973400\pi$
$104$		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	$-0.107855\pi$
$107$	675.992	+	675.992i	0.610753	+	0.610753i	−0.332389	+	0.943142i	$0.607855\pi$
$108$		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	0.980609	−	0.195976i	$-0.0627874\pi$
$113$	942.506	+	942.506i	0.784633	+	0.784633i	−0.195976	+	0.980609i	$0.562787\pi$
$114$		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	0.999970	−	0.00770877i	$-0.00245380\pi$
$127$	1420.14	+	1420.14i	0.992262	+	0.992262i	−0.00770877	+	0.999970i	$0.502454\pi$
$128$		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	−0.942952	−	0.332929i	$-0.891963\pi$
$137$	−978.198	+	978.198i	−0.610023	+	0.610023i	0.332929	+	0.942952i	$0.391963\pi$
$138$		0			0
$139$	−1260.91			−0.769418			−0.384709	−	0.923038i	$-0.625698\pi$
$139$	−1260.91			−0.769418			−0.384709	+	0.923038i	$0.625698\pi$
$140$		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	$0.318360\pi$
$151$			3123.05i			1.68311i	−0.540169	+	0.841556i	$0.681640\pi$
$152$		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	$-0.765815\pi$
$157$	−138.171	+	138.171i	−0.0702375	+	0.0702375i	0.671115	+	0.741353i	$0.265815\pi$
$158$		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	$-0.599154\pi$
$163$	1343.08	−	1343.08i	0.645388	−	0.645388i	0.951875	+	0.306487i	$0.0991536\pi$
$164$		0			0
$165$	2255.00	−	308.056i	1.06395	−	0.145346i
$166$		0			0
$167$	2579.83	+	2579.83i	1.19541	+	1.19541i	0.975527	+	0.219880i	$0.0705664\pi$
$167$	2579.83	+	2579.83i	1.19541	+	1.19541i	0.219880	+	0.975527i	$0.429434\pi$
$168$		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	−0.983273	−	0.182138i	$-0.941698\pi$
$173$	−2651.85	−	2651.85i	−1.16541	−	1.16541i	−0.182138	−	0.983273i	$-0.558302\pi$
$174$		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	$-0.596814\pi$
$179$	−1434.43			−0.598962			−0.299481	+	0.954102i	$0.596814\pi$
$180$		0			0
$181$	167.754			0.0688898			0.0344449	−	0.999407i	$-0.489034\pi$
$181$	167.754			0.0688898			0.0344449	+	0.999407i	$0.489034\pi$
$182$		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	$-0.654725\pi$
$191$		−	4667.83i		−	1.76834i	0.467167	−	0.884169i	$-0.345275\pi$
$192$		0			0
$193$	2283.88	+	2283.88i	0.851800	+	0.851800i	0.990355	−	0.138555i	$-0.0442457\pi$
$193$	2283.88	+	2283.88i	0.851800	+	0.851800i	−0.138555	+	0.990355i	$0.544246\pi$
$194$		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	$-0.605152\pi$
$197$	1718.64	−	1718.64i	0.621563	−	0.621563i	0.945931	+	0.324368i	$0.105152\pi$
$198$		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	−0.974272	−	0.225377i	$-0.927639\pi$
$223$	−2493.89	+	2493.89i	−0.748895	+	0.748895i	0.225377	+	0.974272i	$0.427639\pi$
$224$		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	$-0.211911\pi$
$227$	577.387	+	577.387i	0.168822	+	0.168822i	−0.617640	+	0.786461i	$0.711911\pi$
$228$		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	0.390957	−	0.920409i	$-0.372144\pi$
$233$	−1883.04	−	1883.04i	−0.529452	−	0.529452i	−0.920409	+	0.390957i	$0.872144\pi$
$234$		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	−0.632485	−	0.774572i	$-0.717965\pi$
$257$	585.402	−	585.402i	0.142087	−	0.142087i	0.774572	+	0.632485i	$0.217965\pi$
$258$		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	0.139280	−	0.990253i	$-0.455521\pi$
$263$	4817.62	−	4817.62i	1.12953	−	1.12953i	0.990253	−	0.139280i	$-0.0444788\pi$
$264$		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	$-0.908412\pi$
$271$		−	2531.99i		−	0.567555i	0.958890	−	0.283778i	$-0.0915878\pi$
$272$		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	$-0.738539\pi$
$277$	234.701	−	234.701i	0.0509090	−	0.0509090i	0.732103	+	0.681194i	$0.238539\pi$
$278$		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	$-0.886492\pi$
$283$	−2799.36	+	2799.36i	−0.588003	+	0.588003i	0.349087	+	0.937090i	$0.386492\pi$
$284$		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	$-0.307440\pi$
$293$	−1272.98	−	1272.98i	−0.253817	−	0.253817i	−0.822534	+	0.568716i	$0.807440\pi$
$294$		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	$-0.267943\pi$
$307$	−428.574	−	428.574i	−0.0796743	−	0.0796743i	−0.745821	+	0.666147i	$0.767943\pi$
$308$		0			0
$309$			3260.37i			0.600246i
$310$		0			0
$311$		−	2997.74i		−	0.546580i	−0.961932	−	0.273290i	$-0.911888\pi$
$311$		−	2997.74i		−	0.546580i	0.961932	−	0.273290i	$-0.0881118\pi$
$312$		0			0
$313$	−5654.33	−	5654.33i	−1.02109	−	1.02109i	−0.999773	−	0.0213178i	$-0.993214\pi$
$313$	−5654.33	−	5654.33i	−1.02109	−	1.02109i	−0.0213178	−	0.999773i	$-0.506786\pi$
$314$		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	$-0.673720\pi$
$317$	1894.53	−	1894.53i	0.335670	−	0.335670i	0.854735	+	0.519065i	$0.173720\pi$
$318$		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	−0.805807	−	0.592178i	$-0.798268\pi$
$337$	−1321.62	+	1321.62i	−0.213630	+	0.213630i	0.592178	+	0.805807i	$0.298268\pi$
$338$		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	$-0.382130\pi$
$347$	−3686.52	−	3686.52i	−0.570325	−	0.570325i	−0.932219	+	0.361894i	$0.882130\pi$
$348$		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	0.456171	−	0.889892i	$-0.349220\pi$
$353$	−2876.55	−	2876.55i	−0.433720	−	0.433720i	−0.889892	+	0.456171i	$0.849220\pi$
$354$		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	0.986276	+	0.165104i	$0.0527960\pi$
$367$	8095.02	+	8095.02i	1.15138	+	1.15138i	0.165104	+	0.986276i	$0.447204\pi$
$368$		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	$-0.147163\pi$
$373$	3234.41	+	3234.41i	0.448985	+	0.448985i	−0.446032	+	0.895017i	$0.647163\pi$
$374$		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	$-0.516366\pi$
$379$	−758.390			−0.102786			−0.0513930	+	0.998679i	$0.516366\pi$
$380$		0			0
$381$	−6787.84			−0.912733
$382$		0			0
$383$	5789.34	−	5789.34i	0.772379	−	0.772379i	−0.206143	−	0.978522i	$-0.566091\pi$
$383$	5789.34	−	5789.34i	0.772379	−	0.772379i	0.978522	+	0.206143i	$0.0660911\pi$
$384$		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	$-0.686911\pi$
$397$	2202.72	−	2202.72i	0.278467	−	0.278467i	0.832497	+	0.554030i	$0.186911\pi$
$398$		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	$0.0400417\pi$
$409$			2075.54i			0.250926i	−0.992098	+	0.125463i	$0.959958\pi$
$410$		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	$-0.183888\pi$
$419$	14369.8			1.67544			0.837720	+	0.546100i	$0.183888\pi$
$420$		0			0
$421$	−12114.5			−1.40244			−0.701219	−	0.712946i	$-0.747360\pi$
$421$	−12114.5			−1.40244			−0.701219	+	0.712946i	$0.747360\pi$
$422$		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	$0.0736818\pi$
$431$			4105.54i			0.458833i	−0.973328	+	0.229417i	$0.926318\pi$
$432$		0			0
$433$	−4397.74	−	4397.74i	−0.488088	−	0.488088i	0.419614	−	0.907702i	$-0.362165\pi$
$433$	−4397.74	−	4397.74i	−0.488088	−	0.488088i	−0.907702	+	0.419614i	$0.862165\pi$
$434$		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	$-0.708693\pi$
$443$	1706.39	−	1706.39i	0.183009	−	0.183009i	0.792666	+	0.609656i	$0.208693\pi$
$444$		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	$-0.723710\pi$
$449$		−	14519.2i		−	1.52606i	0.646362	−	0.763031i	$-0.276290\pi$
$450$		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	−0.820272	−	0.571974i	$-0.806178\pi$
$457$	−2425.76	+	2425.76i	−0.248298	+	0.248298i	0.571974	+	0.820272i	$0.306178\pi$
$458$		0			0
$459$	15225.5			1.54829
$460$		0			0
$461$	−8549.98			−0.863801			−0.431901	−	0.901921i	$-0.642157\pi$
$461$	−8549.98			−0.863801			−0.431901	+	0.901921i	$0.642157\pi$
$462$		0			0
$463$	−334.169	+	334.169i	−0.0335424	+	0.0335424i	−0.723679	−	0.690137i	$-0.757550\pi$
$463$	−334.169	+	334.169i	−0.0335424	+	0.0335424i	0.690137	+	0.723679i	$0.257550\pi$
$464$		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	$-0.0999698\pi$
$467$	6480.64	+	6480.64i	0.642159	+	0.642159i	−0.308927	+	0.951086i	$0.599970\pi$
$468$		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	0.817704	−	0.575639i	$-0.195246\pi$
$487$	2601.52	+	2601.52i	0.242066	+	0.242066i	−0.575639	+	0.817704i	$0.695246\pi$
$488$		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	$-0.442947\pi$
$499$	3974.46			0.356555			0.178278	+	0.983980i	$0.442947\pi$
$500$		0			0
$501$	−12330.8			−1.09960
$502$		0			0
$503$	−7191.87	+	7191.87i	−0.637514	+	0.637514i	−0.949942	−	0.312427i	$-0.898858\pi$
$503$	−7191.87	+	7191.87i	−0.637514	+	0.637514i	0.312427	+	0.949942i	$0.398858\pi$
$504$		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	$-0.782783\pi$
$523$	−1739.01	+	1739.01i	−0.145395	+	0.145395i	0.630662	+	0.776057i	$0.282783\pi$
$524$		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	$-0.150192\pi$
$541$	22416.8			1.78146			0.890732	+	0.454529i	$0.150192\pi$
$542$		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	$-0.271037\pi$
$547$	−1194.86	−	1194.86i	−0.0933978	−	0.0933978i	−0.752262	+	0.658864i	$0.771037\pi$
$548$		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	$-0.682892\pi$
$557$	3890.45	−	3890.45i	0.295949	−	0.295949i	0.839425	+	0.543476i	$0.182892\pi$
$558$		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	$-0.712322\pi$
$563$	2231.00	−	2231.00i	0.167008	−	0.167008i	0.785663	+	0.618655i	$0.212322\pi$
$564$		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	$-0.624492\pi$
$569$		−	25095.8i		−	1.84898i	0.381208	−	0.924489i	$-0.375508\pi$
$570$		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	−0.745920	−	0.666036i	$-0.767990\pi$
$577$	−1107.19	+	1107.19i	−0.0798836	+	0.0798836i	0.666036	+	0.745920i	$0.267990\pi$
$578$		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	$-0.466638\pi$
$587$	−12656.0	−	12656.0i	−0.889896	−	0.889896i	−0.994513	+	0.104617i	$0.966638\pi$
$588$		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	0.930735	−	0.365695i	$-0.119169\pi$
$593$	8159.45	+	8159.45i	0.565040	+	0.565040i	−0.365695	+	0.930735i	$0.619169\pi$
$594$		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	0.206119	−	0.978527i	$-0.433916\pi$
$607$	−11551.3	−	11551.3i	−0.772407	−	0.772407i	−0.978527	+	0.206119i	$0.933916\pi$
$608$		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	−0.987239	−	0.159246i	$-0.949094\pi$
$613$	−17400.4	−	17400.4i	−1.14649	−	1.14649i	−0.159246	−	0.987239i	$-0.550906\pi$
$614$		0			0
$615$	−1678.59	−	12287.5i	−0.110061	−	0.805657i
$616$		0			0
$617$	−19751.3	+	19751.3i	−1.28875	+	1.28875i	−0.353203	+	0.935547i	$0.614907\pi$
$617$	−19751.3	+	19751.3i	−1.28875	+	1.28875i	−0.935547	+	0.353203i	$0.885093\pi$
$618$		0			0
$619$	−22265.2			−1.44574			−0.722870	−	0.690984i	$-0.757177\pi$
$619$	−22265.2			−1.44574			−0.722870	+	0.690984i	$0.757177\pi$
$620$		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	$0.323592\pi$
$631$			26956.1i			1.70064i	−0.526264	+	0.850321i	$0.676408\pi$
$632$		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	−0.118274	+	0.992981i	$0.537736\pi$
$643$	−18118.8	+	18118.8i	−1.11125	+	1.11125i	−0.992981	+	0.118274i	$0.962264\pi$
$644$		0			0
$645$	964.168	+	732.400i	0.0588590	+	0.0447104i
$646$		0			0
$647$	−7164.48	−	7164.48i	−0.435339	−	0.435339i	0.455101	−	0.890440i	$-0.349603\pi$
$647$	−7164.48	−	7164.48i	−0.435339	−	0.435339i	−0.890440	+	0.455101i	$0.849603\pi$
$648$		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	$-0.0404643\pi$
$653$	14436.5	+	14436.5i	0.865151	+	0.865151i	−0.126780	+	0.991931i	$0.540464\pi$
$654$		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	$-0.439934\pi$
$659$	6346.82			0.375170			0.187585	+	0.982248i	$0.439934\pi$
$660$		0			0
$661$	−7456.31			−0.438755			−0.219377	−	0.975640i	$-0.570403\pi$
$661$	−7456.31			−0.438755			−0.219377	+	0.975640i	$0.570403\pi$
$662$		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	0.368013	−	0.929821i	$-0.380038\pi$
$673$	−9808.67	−	9808.67i	−0.561808	−	0.561808i	−0.929821	+	0.368013i	$0.880038\pi$
$674$		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	$-0.747339\pi$
$677$	208.219	−	208.219i	0.0118206	−	0.0118206i	0.712992	+	0.701172i	$0.247339\pi$
$678$		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	$-0.730043\pi$
$683$	1581.65	−	1581.65i	0.0886095	−	0.0886095i	0.750022	+	0.661413i	$0.230043\pi$
$684$		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	$-0.228386\pi$
$701$	27968.2			1.50691			0.753455	+	0.657499i	$0.228386\pi$
$702$		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	−0.975794	−	0.218694i	$-0.929820\pi$
$727$	−23414.4	−	23414.4i	−1.19449	−	1.19449i	−0.218694	−	0.975794i	$-0.570180\pi$
$728$		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	−0.999705	−	0.0242936i	$-0.992266\pi$
$733$	−20321.5	−	20321.5i	−1.02400	−	1.02400i	−0.0242936	−	0.999705i	$-0.507734\pi$
$734$		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	$-0.684309\pi$
$739$	−21986.1			−1.09442			−0.547208	+	0.836997i	$0.684309\pi$
$740$		0			0
$741$	14262.9			0.707099
$742$		0			0
$743$	3661.72	−	3661.72i	0.180801	−	0.180801i	−0.610904	−	0.791705i	$-0.709194\pi$
$743$	3661.72	−	3661.72i	0.180801	−	0.180801i	0.791705	+	0.610904i	$0.209194\pi$
$744$		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	$-0.911738\pi$
$751$		−	11267.6i		−	0.547485i	0.961803	−	0.273742i	$-0.0882616\pi$
$752$		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	$-0.984521\pi$
$757$	−19790.8	+	19790.8i	−0.950210	+	0.950210i	0.0486080	+	0.998818i	$0.484521\pi$
$758$		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	$-0.995224\pi$
$769$		−	639.893i		−	0.0300067i	0.999887	−	0.0150033i	$-0.00477589\pi$
$770$		0			0
$771$			2798.04i			0.130699i
$772$		0			0
$773$	−11139.1	−	11139.1i	−0.518299	−	0.518299i	0.398757	−	0.917056i	$-0.369442\pi$
$773$	−11139.1	−	11139.1i	−0.518299	−	0.518299i	−0.917056	+	0.398757i	$0.869442\pi$
$774$		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	$-0.216879\pi$
$787$	3243.01	+	3243.01i	0.146888	+	0.146888i	−0.629838	+	0.776726i	$0.716879\pi$
$788$		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	$-0.974044\pi$
$797$	−20592.8	+	20592.8i	−0.915223	+	0.915223i	0.0814541	+	0.996677i	$0.474044\pi$
$798$		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	$0.185693\pi$
$809$			25350.0i			1.10168i	−0.834611	+	0.550840i	$0.814307\pi$
$810$		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	$-0.475905\pi$
$821$	3557.99			0.151248			0.0756241	+	0.997136i	$0.475905\pi$
$822$		0			0
$823$	846.527	−	846.527i	0.0358543	−	0.0358543i	−0.688952	−	0.724807i	$-0.741929\pi$
$823$	846.527	−	846.527i	0.0358543	−	0.0358543i	0.724807	+	0.688952i	$0.241929\pi$
$824$		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	$-0.247780\pi$
$827$	234.539	+	234.539i	0.00986180	+	0.00986180i	−0.702159	+	0.712020i	$0.747780\pi$
$828$		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	$-0.227306\pi$
$853$	2509.72	+	2509.72i	0.100740	+	0.100740i	−0.654940	+	0.755681i	$0.727306\pi$
$854$		0			0
$855$	−12602.9	−	9573.37i	−0.504104	−	0.382927i
$856$		0			0
$857$	−6154.50	+	6154.50i	−0.245313	+	0.245313i	−0.819044	−	0.573731i	$-0.805496\pi$
$857$	−6154.50	+	6154.50i	−0.245313	+	0.245313i	0.573731	+	0.819044i	$0.305496\pi$
$858$		0			0
$859$	−14723.8			−0.584830			−0.292415	−	0.956292i	$-0.594459\pi$
$859$	−14723.8			−0.584830			−0.292415	+	0.956292i	$0.594459\pi$
$860$		0			0
$861$	−15428.7			−0.610697
$862$		0			0
$863$	−7951.15	+	7951.15i	−0.313627	+	0.313627i	−0.846313	−	0.532686i	$-0.821183\pi$
$863$	−7951.15	+	7951.15i	−0.313627	+	0.313627i	0.532686	+	0.846313i	$0.321183\pi$
$864$		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	$-0.568414\pi$
$877$	19834.9	−	19834.9i	0.763713	−	0.763713i	0.976991	+	0.213278i	$0.0684141\pi$
$878$		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	$-0.644365\pi$
$883$	12089.6	−	12089.6i	0.460756	−	0.460756i	0.898903	+	0.438147i	$0.144365\pi$
$884$		0			0
$885$	−4270.41	−	31259.8i	−0.162201	−	1.18733i
$886$		0			0
$887$	28797.8	+	28797.8i	1.09012	+	1.09012i	0.995515	+	0.0946032i	$0.0301582\pi$
$887$	28797.8	+	28797.8i	1.09012	+	1.09012i	0.0946032	+	0.995515i	$0.469842\pi$
$888$		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	$-0.0994051\pi$
$907$	17602.0	+	17602.0i	0.644393	+	0.644393i	−0.307239	+	0.951632i	$0.599405\pi$
$908$		0			0
$909$			29476.8i			1.07556i
$910$		0			0
$911$			45374.9i			1.65021i	0.564982	+	0.825103i	$0.308883\pi$
$911$			45374.9i			1.65021i	−0.564982	+	0.825103i	$0.691117\pi$
$912$		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	$-0.986546\pi$
$929$		−	2392.84i		−	0.0845064i	0.999107	−	0.0422532i	$-0.0134536\pi$
$930$		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	−0.161788	+	0.986826i	$0.551726\pi$
$937$	−32944.5	+	32944.5i	−1.14861	+	1.14861i	−0.986826	+	0.161788i	$0.948274\pi$
$938$		0			0
$939$	27025.9			0.939252
$940$		0			0
$941$	−19141.4			−0.663114			−0.331557	−	0.943435i	$-0.607574\pi$
$941$	−19141.4			−0.663114			−0.331557	+	0.943435i	$0.607574\pi$
$942$		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	$-0.345442\pi$
$947$	−12173.1	−	12173.1i	−0.417710	−	0.417710i	−0.884414	+	0.466704i	$0.845442\pi$
$948$		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	−0.998158	−	0.0606618i	$-0.980679\pi$
$953$	−31150.3	−	31150.3i	−1.05882	−	1.05882i	−0.0606618	−	0.998158i	$-0.519321\pi$
$954$		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	−0.978647	−	0.205549i	$-0.934102\pi$
$967$	−35609.3	−	35609.3i	−1.18420	−	1.18420i	−0.205549	−	0.978647i	$-0.565898\pi$
$968$		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	−0.804330	−	0.594183i	$-0.797475\pi$
$977$	−6417.48	+	6417.48i	−0.210147	+	0.210147i	0.594183	+	0.804330i	$0.297475\pi$
$978$		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	−0.545694	−	0.837984i	$-0.683734\pi$
$983$	9008.33	−	9008.33i	0.292290	−	0.292290i	0.837984	+	0.545694i	$0.183734\pi$
$984$		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	$-0.803892\pi$
$991$		−	36054.2i		−	1.15570i	0.816143	−	0.577850i	$-0.196108\pi$
$992$		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	$-0.763268\pi$
$997$	−1855.25	+	1855.25i	−0.0589331	+	0.0589331i	0.677026	+	0.735959i	$0.263268\pi$
$998$		0			0
$999$	−12736.2			−0.403358

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.n.c.63.2	✓	8	8.3	odd	2
160.4.n.c.127.2	yes	8	40.37	odd	4
160.4.n.f.63.3	yes	8	8.5	even	2
160.4.n.f.127.3	yes	8	40.27	even	4
320.4.n.f.63.2		8	1.1	even	1	trivial
320.4.n.f.127.2		8	20.7	even	4	inner
320.4.n.i.63.3		8	4.3	odd	2
320.4.n.i.127.3		8	5.2	odd	4

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	320.n (of order \(4\), degree \(2\), not 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

Modular forms

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