LMFDB - Embedded newform 336.4.bj.e.95.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(95,336)] 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("336.95"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 3, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,0,0,0,-38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.11
Character	$\chi$	$=$	336.95
Dual form			336.4.bj.e.191.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.63380 - 4.47918i) q^{3} +(10.1094 - 5.83669i) q^{5} +(-17.9159 + 4.69245i) q^{7} +(-13.1262 - 23.5946i) q^{9} +(-26.0496 + 45.1192i) q^{11} -75.3352 q^{13} +(0.482652 - 60.6547i) q^{15} +(-81.3838 - 46.9870i) q^{17} +(17.7187 - 10.2299i) q^{19} +(-26.1687 + 92.6078i) q^{21} +(12.2188 + 21.1636i) q^{23} +(5.63383 - 9.75808i) q^{25} +(-140.256 - 3.34877i) q^{27} -145.322i q^{29} +(164.228 + 94.8169i) q^{31} +(133.488 + 235.516i) q^{33} +(-153.732 + 152.008i) q^{35} +(-65.9875 - 114.294i) q^{37} +(-198.418 + 337.440i) q^{39} -215.221i q^{41} -293.071i q^{43} +(-270.412 - 161.914i) q^{45} +(85.5222 + 148.129i) q^{47} +(298.962 - 168.139i) q^{49} +(-424.812 + 240.779i) q^{51} +(42.6773 + 24.6398i) q^{53} +608.173i q^{55} +(0.845940 - 106.309i) q^{57} +(-316.152 + 547.591i) q^{59} +(147.099 + 254.783i) q^{61} +(345.884 + 361.125i) q^{63} +(-761.597 + 439.708i) q^{65} +(-801.987 - 463.027i) q^{67} +(126.977 + 1.01041i) q^{69} -955.286 q^{71} +(408.236 - 707.085i) q^{73} +(-28.8699 - 50.9358i) q^{75} +(254.983 - 930.589i) q^{77} +(770.551 - 444.878i) q^{79} +(-384.407 + 619.413i) q^{81} +188.840 q^{83} -1096.99 q^{85} +(-650.922 - 382.748i) q^{87} +(-901.644 + 520.564i) q^{89} +(1349.70 - 353.507i) q^{91} +(857.245 - 485.877i) q^{93} +(119.418 - 206.837i) q^{95} -1630.72 q^{97} +(1406.50 + 22.3855i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 38 q^{7} - 70 q^{9} + 124 q^{13} + 462 q^{19} + 500 q^{21} + 566 q^{25} - 1266 q^{31} + 64 q^{33} + 338 q^{37} - 1254 q^{39} - 488 q^{45} - 206 q^{49} - 522 q^{51} + 2324 q^{57} - 340 q^{61} + 840 q^{63}+ \cdots - 3344 q^{97}+O(q^{100}) $ 28 * q - 38 * q^7 - 70 * q^9 + 124 * q^13 + 462 * q^19 + 500 * q^21 + 566 * q^25 - 1266 * q^31 + 64 * q^33 + 338 * q^37 - 1254 * q^39 - 488 * q^45 - 206 * q^49 - 522 * q^51 + 2324 * q^57 - 340 * q^61 + 840 * q^63 - 2934 * q^67 - 776 * q^69 + 2050 * q^73 + 1458 * q^75 - 2070 * q^79 + 910 * q^81 + 2400 * q^85 - 3132 * q^87 + 5170 * q^91 + 714 * q^93 - 3344 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	2.63380	−	4.47918i	0.506875	−	0.862019i
$3$	2.63380	−	4.47918i	0.506875	−	0.862019i
$4$		0			0
$5$	10.1094	−	5.83669i	0.904216	−	0.522049i	0.0256501	−	0.999671i	$-0.491834\pi$
$5$	10.1094	−	5.83669i	0.904216	−	0.522049i	0.878566	+	0.477622i	$0.158501\pi$
$6$		0			0
$7$	−17.9159	+	4.69245i	−0.967370	+	0.253368i
$7$	−17.9159	+	4.69245i	−0.967370	+	0.253368i
$8$		0			0
$9$	−13.1262	−	23.5946i	−0.486155	−	0.873873i
$10$		0			0
$11$	−26.0496	+	45.1192i	−0.714022	+	1.23672i	0.249314	+	0.968423i	$0.419795\pi$
$11$	−26.0496	+	45.1192i	−0.714022	+	1.23672i	−0.963336	+	0.268299i	$0.913538\pi$
$12$		0			0
$13$	−75.3352			−1.60725			−0.803624	−	0.595137i	$-0.797098\pi$
$13$	−75.3352			−1.60725			−0.803624	+	0.595137i	$0.797098\pi$
$14$		0			0
$15$	0.482652	−	60.6547i	0.00830801	−	1.04407i
$16$		0			0
$17$	−81.3838	−	46.9870i	−1.16109	−	0.670354i	−0.209522	−	0.977804i	$-0.567191\pi$
$17$	−81.3838	−	46.9870i	−1.16109	−	0.670354i	−0.951564	+	0.307450i	$0.900524\pi$
$18$		0			0
$19$	17.7187	−	10.2299i	0.213945	−	0.123521i	−0.389198	−	0.921154i	$-0.627248\pi$
$19$	17.7187	−	10.2299i	0.213945	−	0.123521i	0.603143	+	0.797633i	$0.293915\pi$
$20$		0			0
$21$	−26.1687	+	92.6078i	−0.271927	+	0.962318i
$22$		0			0
$23$	12.2188	+	21.1636i	0.110774	+	0.191866i	0.916082	−	0.400990i	$-0.131334\pi$
$23$	12.2188	+	21.1636i	0.110774	+	0.191866i	−0.805309	+	0.592856i	$0.798000\pi$
$24$		0			0
$25$	5.63383	−	9.75808i	0.0450707	−	0.0780647i
$26$		0			0
$27$	−140.256	−	3.34877i	−0.999715	−	0.0238693i
$28$		0			0
$29$		−	145.322i		−	0.930535i	−0.885170	−	0.465268i	$-0.845958\pi$
$29$		−	145.322i		−	0.930535i	0.885170	−	0.465268i	$-0.154042\pi$
$30$		0			0
$31$	164.228	+	94.8169i	0.951489	+	0.549343i	0.893543	−	0.448977i	$-0.148212\pi$
$31$	164.228	+	94.8169i	0.951489	+	0.549343i	0.0579460	+	0.998320i	$0.481545\pi$
$32$		0			0
$33$	133.488	+	235.516i	0.704158	+	1.24236i
$34$		0			0
$35$	−153.732	+	152.008i	−0.742440	+	0.734114i
$36$		0			0
$37$	−65.9875	−	114.294i	−0.293197	−	0.507831i	0.681367	−	0.731942i	$-0.261386\pi$
$37$	−65.9875	−	114.294i	−0.293197	−	0.507831i	−0.974564	+	0.224110i	$0.928052\pi$
$38$		0			0
$39$	−198.418	+	337.440i	−0.814674	+	1.38548i
$40$		0			0
$41$		−	215.221i		−	0.819803i	−0.912130	−	0.409902i	$-0.865563\pi$
$41$		−	215.221i		−	0.819803i	0.912130	−	0.409902i	$-0.134437\pi$
$42$		0			0
$43$		−	293.071i		−	1.03937i	−0.854358	−	0.519685i	$-0.826049\pi$
$43$		−	293.071i		−	1.03937i	0.854358	−	0.519685i	$-0.173951\pi$
$44$		0			0
$45$	−270.412	−	161.914i	−0.895793	−	0.536372i
$46$		0			0
$47$	85.5222	+	148.129i	0.265419	+	0.459719i	0.967673	−	0.252207i	$-0.0811564\pi$
$47$	85.5222	+	148.129i	0.265419	+	0.459719i	−0.702254	+	0.711926i	$0.747823\pi$
$48$		0			0
$49$	298.962	−	168.139i	0.871609	−	0.490202i
$50$		0			0
$51$	−424.812	+	240.779i	−1.16638	+	0.661093i
$52$		0			0
$53$	42.6773	+	24.6398i	0.110607	+	0.0638591i	0.554283	−	0.832328i	$-0.312993\pi$
$53$	42.6773	+	24.6398i	0.110607	+	0.0638591i	−0.443676	+	0.896187i	$0.646326\pi$
$54$		0			0
$55$			608.173i			1.49102i
$56$		0			0
$57$	0.845940	−	106.309i	0.00196574	−	0.247035i
$58$		0			0
$59$	−316.152	+	547.591i	−0.697618	+	1.20831i	0.271672	+	0.962390i	$0.412424\pi$
$59$	−316.152	+	547.591i	−0.697618	+	1.20831i	−0.969290	+	0.245920i	$0.920910\pi$
$60$		0			0
$61$	147.099	+	254.783i	0.308756	+	0.534781i	0.978091	−	0.208180i	$-0.0667540\pi$
$61$	147.099	+	254.783i	0.308756	+	0.534781i	−0.669334	+	0.742961i	$0.733421\pi$
$62$		0			0
$63$	345.884	+	361.125i	0.691703	+	0.722182i
$64$		0			0
$65$	−761.597	+	439.708i	−1.45330	+	0.839063i
$66$		0			0
$67$	−801.987	−	463.027i	−1.46236	−	0.844295i	−0.463242	−	0.886232i	$-0.653314\pi$
$67$	−801.987	−	463.027i	−1.46236	−	0.844295i	−0.999120	+	0.0419364i	$0.986647\pi$
$68$		0			0
$69$	126.977	+	1.01041i	0.221540	+	0.00176288i
$70$		0			0
$71$	−955.286			−1.59678			−0.798391	−	0.602139i	$-0.794315\pi$
$71$	−955.286			−1.59678			−0.798391	+	0.602139i	$0.794315\pi$
$72$		0			0
$73$	408.236	−	707.085i	0.654526	−	1.13367i	−0.327487	−	0.944856i	$-0.606202\pi$
$73$	408.236	−	707.085i	0.654526	−	1.13367i	0.982012	−	0.188816i	$-0.0604651\pi$
$74$		0			0
$75$	−28.8699	−	50.9358i	−0.0444481	−	0.0784208i
$76$		0			0
$77$	254.983	−	930.589i	0.377377	−	1.37728i
$78$		0			0
$79$	770.551	−	444.878i	1.09739	−	0.633578i	0.161855	−	0.986815i	$-0.448252\pi$
$79$	770.551	−	444.878i	1.09739	−	0.633578i	0.935534	+	0.353237i	$0.114919\pi$
$80$		0			0
$81$	−384.407	+	619.413i	−0.527307	+	0.849675i
$82$		0			0
$83$	188.840			0.249733			0.124867	−	0.992174i	$-0.460150\pi$
$83$	188.840			0.249733			0.124867	+	0.992174i	$0.460150\pi$
$84$		0			0
$85$	−1096.99			−1.39983
$86$		0			0
$87$	−650.922	−	382.748i	−0.802140	−	0.471665i
$88$		0			0
$89$	−901.644	+	520.564i	−1.07387	+	0.619997i	−0.929235	−	0.369489i	$-0.879533\pi$
$89$	−901.644	+	520.564i	−1.07387	+	0.619997i	−0.144631	+	0.989486i	$0.546199\pi$
$90$		0			0
$91$	1349.70	−	353.507i	1.55480	−	0.407226i
$92$		0			0
$93$	857.245	−	485.877i	0.955830	−	0.541754i
$94$		0			0
$95$	119.418	−	206.837i	0.128968	−	0.223380i
$96$		0			0
$97$	−1630.72			−1.70695			−0.853476	−	0.521132i	$-0.825510\pi$
$97$	−1630.72			−1.70695			−0.853476	+	0.521132i	$0.825510\pi$
$98$		0			0
$99$	1406.50	+	22.3855i	1.42786	+	0.0227255i
$100$		0			0
$101$	1340.54	+	773.963i	1.32068	+	0.762497i	0.983838	−	0.179063i	$-0.0573066\pi$
$101$	1340.54	+	773.963i	1.32068	+	0.762497i	0.336846	+	0.941560i	$0.390640\pi$
$102$		0			0
$103$	247.491	−	142.889i	0.236758	−	0.136692i	−0.376928	−	0.926243i	$-0.623020\pi$
$103$	247.491	−	142.889i	0.236758	−	0.136692i	0.613686	+	0.789551i	$0.289686\pi$
$104$		0			0
$105$	275.972	+	1088.95i	0.256496	+	1.01210i
$106$		0			0
$107$	−46.1409	−	79.9183i	−0.0416879	−	0.0722056i	0.844429	−	0.535668i	$-0.179940\pi$
$107$	−46.1409	−	79.9183i	−0.0416879	−	0.0722056i	−0.886117	+	0.463463i	$0.846607\pi$
$108$		0			0
$109$	1054.05	−	1825.67i	0.926238	−	1.60429i	0.136680	−	0.990615i	$-0.456357\pi$
$109$	1054.05	−	1825.67i	0.926238	−	1.60429i	0.789558	−	0.613676i	$-0.210310\pi$
$110$		0			0
$111$	−685.740	−	5.45669i	−0.586375	−	0.00466600i
$112$		0			0
$113$		−	196.677i		−	0.163733i	−0.996643	−	0.0818665i	$-0.973912\pi$
$113$		−	196.677i		−	0.163733i	0.996643	−	0.0818665i	$-0.0260881\pi$
$114$		0			0
$115$	247.050	+	142.635i	0.200327	+	0.115659i
$116$		0			0
$117$	988.864	+	1777.50i	0.781372	+	1.40453i
$118$		0			0
$119$	1678.55	+	459.926i	1.29305	+	0.354297i
$120$		0			0
$121$	−691.660	−	1197.99i	−0.519654	−	0.900068i
$122$		0			0
$123$	−964.016	−	566.850i	−0.706686	−	0.415538i
$124$		0			0
$125$			1327.64i			0.949982i
$126$		0			0
$127$		−	347.624i		−	0.242887i	−0.992598	−	0.121443i	$-0.961248\pi$
$127$		−	347.624i		−	0.242887i	0.992598	−	0.121443i	$-0.0387523\pi$
$128$		0			0
$129$	−1312.72	−	771.891i	−0.895958	−	0.526831i
$130$		0			0
$131$	−1118.75	−	1937.73i	−0.746148	−	1.29237i	−0.949656	−	0.313294i	$-0.898568\pi$
$131$	−1118.75	−	1937.73i	−0.746148	−	1.29237i	0.203508	−	0.979073i	$-0.434766\pi$
$132$		0			0
$133$	−269.444	+	266.423i	−0.175668	+	0.173698i
$134$		0			0
$135$	−1437.46	+	784.777i	−0.916419	+	0.500317i
$136$		0			0
$137$	1325.50	+	765.277i	0.826605	+	0.477241i	0.852689	−	0.522419i	$-0.174970\pi$
$137$	1325.50	+	765.277i	0.826605	+	0.477241i	−0.0260835	+	0.999660i	$0.508304\pi$
$138$		0			0
$139$			1941.36i			1.18463i	0.805705	+	0.592317i	$0.201787\pi$
$139$			1941.36i			1.18463i	−0.805705	+	0.592317i	$0.798213\pi$
$140$		0			0
$141$	888.744	+	7.07206i	0.530821	+	0.00422394i
$142$		0			0
$143$	1962.45	−	3399.06i	1.14761	−	1.98772i
$144$		0			0
$145$	−848.196	−	1469.12i	−0.485785	−	0.841405i
$146$		0			0
$147$	34.2792	−	1781.95i	0.0192333	−	0.999815i
$148$		0			0
$149$	1120.99	−	647.206i	0.616344	−	0.355847i	−0.159100	−	0.987262i	$-0.550859\pi$
$149$	1120.99	−	647.206i	0.616344	−	0.355847i	0.775444	+	0.631416i	$0.217526\pi$
$150$		0			0
$151$	−80.5558	−	46.5089i	−0.0434142	−	0.0250652i	0.478136	−	0.878286i	$-0.341313\pi$
$151$	−80.5558	−	46.5089i	−0.0434142	−	0.0250652i	−0.521550	+	0.853221i	$0.674646\pi$
$152$		0			0
$153$	−40.3778	+	2536.97i	−0.0213356	+	1.34054i
$154$		0			0
$155$	2213.67			1.14714
$156$		0			0
$157$	−80.3111	+	139.103i	−0.0408250	+	0.0707110i	−0.885716	−	0.464228i	$-0.846332\pi$
$157$	−80.3111	+	139.103i	−0.0408250	+	0.0707110i	0.844891	+	0.534939i	$0.179665\pi$
$158$		0			0
$159$	222.770	−	126.263i	0.111112	−	0.0629770i
$160$		0			0
$161$	−318.220	−	321.829i	−0.155772	−	0.157539i
$162$		0			0
$163$	−836.490	+	482.948i	−0.401957	+	0.232070i	−0.687328	−	0.726347i	$-0.741216\pi$
$163$	−836.490	+	482.948i	−0.401957	+	0.232070i	0.285371	+	0.958417i	$0.407883\pi$
$164$		0			0
$165$	2724.12	+	1601.81i	1.28529	+	0.755760i
$166$		0			0
$167$	820.917			0.380386			0.190193	−	0.981747i	$-0.439089\pi$
$167$	820.917			0.380386			0.190193	+	0.981747i	$0.439089\pi$
$168$		0			0
$169$	3478.39			1.58325
$170$		0			0
$171$	−473.950	−	283.786i	−0.211952	−	0.126910i
$172$		0			0
$173$	402.310	−	232.274i	0.176804	−	0.102078i	−0.408986	−	0.912541i	$-0.634118\pi$
$173$	402.310	−	232.274i	0.176804	−	0.102078i	0.585790	+	0.810463i	$0.300784\pi$
$174$		0			0
$175$	−55.1461	+	201.262i	−0.0238209	+	0.0869369i
$176$		0			0
$177$	1620.08	+	2858.35i	0.687982	+	1.21382i
$178$		0			0
$179$	−587.268	+	1017.18i	−0.245220	+	0.424734i	−0.962194	−	0.272367i	$-0.912194\pi$
$179$	−587.268	+	1017.18i	−0.245220	+	0.424734i	0.716973	+	0.697101i	$0.245527\pi$
$180$		0			0
$181$	820.675			0.337018			0.168509	−	0.985700i	$-0.446105\pi$
$181$	820.675			0.337018			0.168509	+	0.985700i	$0.446105\pi$
$182$		0			0
$183$	1528.65	+	12.1640i	0.617492	+	0.00491361i
$184$		0			0
$185$	−1334.19	−	770.297i	−0.530226	−	0.306126i
$186$		0			0
$187$	4240.03	−	2447.98i	1.65808	−	0.957294i
$188$		0			0
$189$	2528.53	−	598.148i	0.973142	−	0.230206i
$190$		0			0
$191$	488.766	+	846.567i	0.185162	+	0.320709i	0.943631	−	0.330999i	$-0.107386\pi$
$191$	488.766	+	846.567i	0.185162	+	0.320709i	−0.758469	+	0.651709i	$0.774052\pi$
$192$		0			0
$193$	−70.2833	+	121.734i	−0.0262130	+	0.0454022i	−0.878834	−	0.477127i	$-0.841678\pi$
$193$	−70.2833	+	121.734i	−0.0262130	+	0.0454022i	0.852621	+	0.522529i	$0.175011\pi$
$194$		0			0
$195$	−36.3607	+	4569.44i	−0.0133530	+	1.67807i
$196$		0			0
$197$		−	4489.07i		−	1.62352i	−0.583994	−	0.811758i	$-0.698511\pi$
$197$		−	4489.07i		−	1.62352i	0.583994	−	0.811758i	$-0.301489\pi$
$198$		0			0
$199$	751.774	+	434.037i	0.267798	+	0.154613i	0.627887	−	0.778305i	$-0.283920\pi$
$199$	751.774	+	434.037i	0.267798	+	0.154613i	−0.360088	+	0.932918i	$0.617253\pi$
$200$		0			0
$201$	−4186.26	+	2372.73i	−1.46903	+	0.832632i
$202$		0			0
$203$	681.914	+	2603.57i	0.235768	+	0.900172i
$204$		0			0
$205$	−1256.18	−	2175.77i	−0.427978	−	0.741279i
$206$		0			0
$207$	338.959	−	566.094i	0.113813	−	0.190079i
$208$		0			0
$209$			1065.94i			0.352787i
$210$		0			0
$211$		−	2999.07i		−	0.978506i	−0.872142	−	0.489253i	$-0.837270\pi$
$211$		−	2999.07i		−	0.978506i	0.872142	−	0.489253i	$-0.162730\pi$
$212$		0			0
$213$	−2516.03	+	4278.90i	−0.809370	+	1.37646i
$214$		0			0
$215$	−1710.57	−	2962.79i	−0.542603	−	0.939815i
$216$		0			0
$217$	−3387.22	−	928.104i	−1.05963	−	0.290340i
$218$		0			0
$219$	−2091.95	−	3690.89i	−0.645484	−	1.13884i
$220$		0			0
$221$	6131.07	+	3539.77i	1.86615	+	1.07742i
$222$		0			0
$223$		−	4094.88i		−	1.22966i	−0.788661	−	0.614828i	$-0.789225\pi$
$223$		−	4094.88i		−	1.22966i	0.788661	−	0.614828i	$-0.210775\pi$
$224$		0			0
$225$	−304.188	−	4.84138i	−0.0901299	−	0.00143448i
$226$		0			0
$227$	632.034	−	1094.71i	0.184800	−	0.320083i	−0.758709	−	0.651429i	$-0.774170\pi$
$227$	632.034	−	1094.71i	0.184800	−	0.320083i	0.943509	+	0.331347i	$0.107503\pi$
$228$		0			0
$229$	−2748.83	−	4761.11i	−0.793221	−	1.37390i	−0.923962	−	0.382483i	$-0.875069\pi$
$229$	−2748.83	−	4761.11i	−0.793221	−	1.37390i	0.130741	−	0.991417i	$-0.458264\pi$
$230$		0			0
$231$	−3496.70	−	3593.10i	−0.995958	−	1.02341i
$232$		0			0
$233$	−5790.08	+	3342.91i	−1.62799	+	0.939919i	−0.643294	+	0.765619i	$0.722433\pi$
$233$	−5790.08	+	3342.91i	−1.62799	+	0.939919i	−0.984693	+	0.174299i	$0.944234\pi$
$234$		0			0
$235$	1729.16	+	998.332i	0.479992	+	0.277123i
$236$		0			0
$237$	36.7882	−	4623.16i	0.0100829	−	1.26712i
$238$		0			0
$239$	−2110.79			−0.571278			−0.285639	−	0.958337i	$-0.592206\pi$
$239$	−2110.79			−0.571278			−0.285639	+	0.958337i	$0.592206\pi$
$240$		0			0
$241$	−198.046	+	343.026i	−0.0529348	+	0.0916858i	−0.891279	−	0.453456i	$-0.850191\pi$
$241$	−198.046	+	343.026i	−0.0529348	+	0.0916858i	0.838344	+	0.545142i	$0.183524\pi$
$242$		0			0
$243$	1762.02	+	3353.24i	0.465158	+	0.885228i
$244$		0			0
$245$	2040.96	−	3444.74i	0.532213	−	0.898271i
$246$		0			0
$247$	−1334.84	+	770.673i	−0.343863	+	0.198529i
$248$		0			0
$249$	497.366	−	845.848i	0.126584	−	0.215275i
$250$		0			0
$251$	−2121.66			−0.533538			−0.266769	−	0.963760i	$-0.585956\pi$
$251$	−2121.66			−0.533538			−0.266769	+	0.963760i	$0.585956\pi$
$252$		0			0
$253$	−1273.18			−0.316379
$254$		0			0
$255$	−2889.26	+	4913.63i	−0.709539	+	1.20668i
$256$		0			0
$257$	−5065.60	+	2924.62i	−1.22951	+	0.709856i	−0.966927	−	0.255054i	$-0.917907\pi$
$257$	−5065.60	+	2924.62i	−1.22951	+	0.709856i	−0.262580	+	0.964910i	$0.584573\pi$
$258$		0			0
$259$	1718.55	+	1738.04i	0.412298	+	0.416974i
$260$		0			0
$261$	−3428.80	+	1907.52i	−0.813169	+	0.452384i
$262$		0			0
$263$	−3645.55	+	6314.27i	−0.854730	+	1.48044i	0.0221652	+	0.999754i	$0.492944\pi$
$263$	−3645.55	+	6314.27i	−0.854730	+	1.48044i	−0.876895	+	0.480681i	$0.840389\pi$
$264$		0			0
$265$	575.259			0.133350
$266$		0			0
$267$	−43.0469	+	5409.69i	−0.00986677	+	1.23995i
$268$		0			0
$269$	−3404.04	−	1965.33i	−0.771555	−	0.445457i	0.0618741	−	0.998084i	$-0.480292\pi$
$269$	−3404.04	−	1965.33i	−0.771555	−	0.445457i	−0.833429	+	0.552627i	$0.813626\pi$
$270$		0			0
$271$	−5473.93	+	3160.37i	−1.22700	+	0.708410i	−0.966401	−	0.257037i	$-0.917254\pi$
$271$	−5473.93	+	3160.37i	−1.22700	+	0.708410i	−0.260600	+	0.965447i	$0.583920\pi$
$272$		0			0
$273$	1971.42	−	6976.63i	0.437055	−	1.54668i
$274$		0			0
$275$	293.518	+	508.388i	0.0643629	+	0.111480i
$276$		0			0
$277$	609.453	−	1055.60i	0.132197	−	0.228972i	−0.792326	−	0.610098i	$-0.791130\pi$
$277$	609.453	−	1055.60i	0.132197	−	0.228972i	0.924523	+	0.381126i	$0.124464\pi$
$278$		0			0
$279$	81.4801	−	5119.46i	0.0174842	−	1.09855i
$280$		0			0
$281$		−	6339.31i		−	1.34581i	−0.739730	−	0.672903i	$-0.765047\pi$
$281$		−	6339.31i		−	1.34581i	0.739730	−	0.672903i	$-0.234953\pi$
$282$		0			0
$283$	−3048.55	−	1760.08i	−0.640344	−	0.369703i	0.144403	−	0.989519i	$-0.453874\pi$
$283$	−3048.55	−	1760.08i	−0.640344	−	0.369703i	−0.784747	+	0.619816i	$0.787207\pi$
$284$		0			0
$285$	−611.940	−	1079.66i	−0.127187	−	0.224399i
$286$		0			0
$287$	1009.92	+	3855.89i	0.207712	+	0.793053i
$288$		0			0
$289$	1959.05	+	3393.17i	0.398748	+	0.690651i
$290$		0			0
$291$	−4294.99	+	7304.29i	−0.865212	+	1.47143i
$292$		0			0
$293$			4735.36i			0.944173i	0.881552	+	0.472087i	$0.156499\pi$
$293$			4735.36i			0.944173i	−0.881552	+	0.472087i	$0.843501\pi$
$294$		0			0
$295$			7381.12i			1.45676i
$296$		0			0
$297$	3804.71	−	6241.01i	0.743338	−	1.21933i
$298$		0			0
$299$	−920.506	−	1594.36i	−0.178041	−	0.308376i
$300$		0			0
$301$	1375.22	+	5250.65i	0.263344	+	1.00546i
$302$		0			0
$303$	6997.45	−	3966.07i	1.32671	−	0.751964i
$304$		0			0
$305$	2974.18	+	1717.14i	0.558364	+	0.322372i
$306$		0			0
$307$		−	5508.31i		−	1.02403i	−0.858978	−	0.512013i	$-0.828900\pi$
$307$		−	5508.31i		−	1.02403i	0.858978	−	0.512013i	$-0.171100\pi$
$308$		0			0
$309$	11.8159	−	1484.90i	0.00217535	−	0.273375i
$310$		0			0
$311$	−638.753	+	1106.35i	−0.116464	+	0.201722i	−0.918364	−	0.395737i	$-0.870489\pi$
$311$	−638.753	+	1106.35i	−0.116464	+	0.201722i	0.801900	+	0.597458i	$0.203823\pi$
$312$		0			0
$313$	2335.14	+	4044.58i	0.421693	+	0.730394i	0.996105	−	0.0881723i	$-0.0281026\pi$
$313$	2335.14	+	4044.58i	0.421693	+	0.730394i	−0.574412	+	0.818566i	$0.694769\pi$
$314$		0			0
$315$	5604.47	+	1631.95i	1.00246	+	0.291905i
$316$		0			0
$317$	3745.92	−	2162.71i	0.663697	−	0.383186i	−0.129987	−	0.991516i	$-0.541494\pi$
$317$	3745.92	−	2162.71i	0.663697	−	0.383186i	0.793684	+	0.608330i	$0.208160\pi$
$318$		0			0
$319$	6556.79	+	3785.56i	1.15081	+	0.664423i
$320$		0			0
$321$	−479.495	−	3.81551i	−0.0833732	−	0.000663431i
$322$		0			0
$323$	−1922.69			−0.331211
$324$		0			0
$325$	−424.426	+	735.127i	−0.0724397	+	0.125469i
$326$		0			0
$327$	−5401.36	−	9529.75i	−0.913443	−	1.61161i
$328$		0			0
$329$	−2227.30	−	2252.56i	−0.373237	−	0.377470i
$330$		0			0
$331$	4609.30	−	2661.18i	0.765407	−	0.441908i	−0.0658265	−	0.997831i	$-0.520968\pi$
$331$	4609.30	−	2661.18i	0.765407	−	0.441908i	0.831234	+	0.555923i	$0.187635\pi$
$332$		0			0
$333$	−1830.55	+	3057.19i	−0.301241	+	0.503101i
$334$		0			0
$335$	−10810.2			−1.76305
$336$		0			0
$337$	−498.469			−0.0805738			−0.0402869	−	0.999188i	$-0.512827\pi$
$337$	−498.469			−0.0805738			−0.0402869	+	0.999188i	$0.512827\pi$
$338$		0			0
$339$	−880.953	−	518.008i	−0.141141	−	0.0829922i
$340$		0			0
$341$	−8556.12	+	4939.88i	−1.35877	+	0.784485i
$342$		0			0
$343$	−4567.20	+	4415.24i	−0.718966	+	0.695045i
$344$		0			0
$345$	1289.57	−	730.913i	0.201241	−	0.114061i
$346$		0			0
$347$	−3278.79	+	5679.03i	−0.507247	+	0.878578i	0.492718	+	0.870189i	$0.336003\pi$
$347$	−3278.79	+	5679.03i	−0.507247	+	0.878578i	−0.999965	+	0.00838846i	$0.997330\pi$
$348$		0			0
$349$	10542.3			1.61695			0.808475	−	0.588530i	$-0.200293\pi$
$349$	10542.3			1.61695			0.808475	+	0.588530i	$0.200293\pi$
$350$		0			0
$351$	10566.2	+	252.281i	1.60679	+	0.0383639i
$352$		0			0
$353$	−7715.99	−	4454.83i	−1.16340	−	0.671690i	−0.211284	−	0.977425i	$-0.567765\pi$
$353$	−7715.99	−	4454.83i	−1.16340	−	0.671690i	−0.952117	+	0.305735i	$0.901098\pi$
$354$		0			0
$355$	−9657.40	+	5575.71i	−1.44384	+	0.833599i
$356$		0			0
$357$	6481.06	−	6307.19i	0.960824	−	0.935047i
$358$		0			0
$359$	2919.13	+	5056.08i	0.429153	+	0.743314i	0.996798	−	0.0799588i	$-0.0254789\pi$
$359$	2919.13	+	5056.08i	0.429153	+	0.743314i	−0.567645	+	0.823273i	$0.692146\pi$
$360$		0			0
$361$	−3220.20	+	5577.55i	−0.469485	+	0.813172i
$362$		0			0
$363$	−7187.71	−	57.1953i	−1.03928	−	0.00826990i
$364$		0			0
$365$		−	9530.98i		−	1.36678i
$366$		0			0
$367$	6368.54	+	3676.88i	0.905818	+	0.522974i	0.879083	−	0.476668i	$-0.158156\pi$
$367$	6368.54	+	3676.88i	0.905818	+	0.522974i	0.0267348	+	0.999643i	$0.491489\pi$
$368$		0			0
$369$	−5078.05	+	2825.04i	−0.716404	+	0.398551i
$370$		0			0
$371$	−880.226	−	241.183i	−0.123178	−	0.0337510i
$372$		0			0
$373$	2446.46	+	4237.39i	0.339605	+	0.588214i	0.984358	−	0.176177i	$-0.0563732\pi$
$373$	2446.46	+	4237.39i	0.339605	+	0.588214i	−0.644753	+	0.764391i	$0.723040\pi$
$374$		0			0
$375$	5946.74	+	3496.74i	0.818903	+	0.481522i
$376$		0			0
$377$			10947.8i			1.49560i
$378$		0			0
$379$		−	9460.50i		−	1.28220i	−0.767458	−	0.641099i	$-0.778479\pi$
$379$		−	9460.50i		−	1.28220i	0.767458	−	0.641099i	$-0.221521\pi$
$380$		0			0
$381$	−1557.07	−	915.572i	−0.209373	−	0.123113i
$382$		0			0
$383$	1020.83	+	1768.13i	0.136193	+	0.235893i	0.926053	−	0.377395i	$-0.123180\pi$
$383$	1020.83	+	1768.13i	0.136193	+	0.235893i	−0.789860	+	0.613288i	$0.789847\pi$
$384$		0			0
$385$	−2853.82	−	10896.0i	−0.377777	−	1.44237i
$386$		0			0
$387$	−6914.89	+	3846.91i	−0.908278	+	0.505295i
$388$		0			0
$389$	10891.2	+	6288.02i	1.41955	+	0.819576i	0.996259	−	0.0864182i	$-0.0275421\pi$
$389$	10891.2	+	6288.02i	1.41955	+	0.819576i	0.423289	+	0.905995i	$0.360875\pi$
$390$		0			0
$391$		−	2296.50i		−	0.297030i
$392$		0			0
$393$	−11626.0	−	92.5123i	−1.49225	−	0.0118744i
$394$		0			0
$395$	5193.22	−	8994.93i	0.661518	−	1.14578i
$396$		0			0
$397$	118.194	+	204.717i	0.0149420	+	0.0258803i	0.873400	−	0.487004i	$-0.161910\pi$
$397$	118.194	+	204.717i	0.0149420	+	0.0258803i	−0.858458	+	0.512884i	$0.828577\pi$
$398$		0			0
$399$	483.694	+	1908.60i	0.0606892	+	0.239472i
$400$		0			0
$401$	7501.26	−	4330.85i	0.934152	−	0.539333i	0.0460297	−	0.998940i	$-0.485343\pi$
$401$	7501.26	−	4330.85i	0.934152	−	0.539333i	0.888122	+	0.459607i	$0.152010\pi$
$402$		0			0
$403$	−12372.1	−	7143.05i	−1.52928	−	0.882930i
$404$		0			0
$405$	−270.814	+	8505.58i	−0.0332268	+	1.04357i
$406$		0			0
$407$	6875.78			0.837395
$408$		0			0
$409$	−1584.33	+	2744.14i	−0.191540	+	0.331757i	−0.945761	−	0.324864i	$-0.894682\pi$
$409$	−1584.33	+	2744.14i	−0.191540	+	0.331757i	0.754221	+	0.656621i	$0.228015\pi$
$410$		0			0
$411$	6918.91	−	3921.56i	0.830377	−	0.470648i
$412$		0			0
$413$	3094.62	−	11294.1i	0.368707	−	1.34564i
$414$		0			0
$415$	1909.06	−	1102.20i	0.225813	−	0.130373i
$416$		0			0
$417$	8695.72	+	5113.16i	1.02118	+	0.600462i
$418$		0			0
$419$	11943.0			1.39249			0.696246	−	0.717803i	$-0.254852\pi$
$419$	11943.0			1.39249			0.696246	+	0.717803i	$0.254852\pi$
$420$		0			0
$421$	−5960.13			−0.689974			−0.344987	−	0.938607i	$-0.612117\pi$
$421$	−5960.13			−0.689974			−0.344987	+	0.938607i	$0.612117\pi$
$422$		0			0
$423$	2372.45	−	3962.22i	0.272701	−	0.455437i
$424$		0			0
$425$	−917.005	+	529.433i	−0.104662	+	0.0604266i
$426$		0			0
$427$	−3830.98	−	3874.43i	−0.434178	−	0.439102i
$428$		0			0
$429$	−10056.3	−	17742.6i	−1.13176	−	1.99679i
$430$		0			0
$431$	4126.21	−	7146.80i	0.461143	−	0.798722i	−0.537876	−	0.843024i	$-0.680773\pi$
$431$	4126.21	−	7146.80i	0.461143	−	0.798722i	0.999018	+	0.0443019i	$0.0141063\pi$
$432$		0			0
$433$	−4148.78			−0.460457			−0.230228	−	0.973137i	$-0.573947\pi$
$433$	−4148.78			−0.460457			−0.230228	+	0.973137i	$0.573947\pi$
$434$		0			0
$435$	−8814.43	−	70.1397i	−0.971540	−	0.00773090i
$436$		0			0
$437$	433.003	+	249.994i	0.0473990	+	0.0273658i
$438$		0			0
$439$	−12371.3	+	7142.59i	−1.34499	+	0.776531i	−0.987535	−	0.157399i	$-0.949689\pi$
$439$	−12371.3	+	7142.59i	−1.34499	+	0.776531i	−0.357456	+	0.933930i	$0.616356\pi$
$440$		0			0
$441$	−7891.40	−	4846.85i	−0.852111	−	0.523361i
$442$		0			0
$443$	−3084.40	−	5342.34i	−0.330800	−	0.572963i	0.651869	−	0.758332i	$-0.273985\pi$
$443$	−3084.40	−	5342.34i	−0.330800	−	0.572963i	−0.982669	+	0.185369i	$0.940652\pi$
$444$		0			0
$445$	−6076.74	+	10525.2i	−0.647338	+	1.12122i
$446$		0			0
$447$	53.5192	−	6725.74i	0.00566302	−	0.711671i
$448$		0			0
$449$		−	4035.96i		−	0.424207i	−0.977247	−	0.212103i	$-0.931969\pi$
$449$		−	4035.96i		−	0.424207i	0.977247	−	0.212103i	$-0.0680314\pi$
$450$		0			0
$451$	9710.61	+	5606.42i	1.01387	+	0.585357i
$452$		0			0
$453$	−420.490	+	238.329i	−0.0436122	+	0.0247189i
$454$		0			0
$455$	11581.4	−	11451.5i	1.19329	−	1.17990i
$456$		0			0
$457$	4942.07	+	8559.92i	0.505865	+	0.876184i	0.999977	+	0.00678547i	$0.00215990\pi$
$457$	4942.07	+	8559.92i	0.505865	+	0.876184i	−0.494112	+	0.869398i	$0.664507\pi$
$458$		0			0
$459$	11257.2	+	6862.74i	1.14475	+	0.697877i
$460$		0			0
$461$			1480.53i			0.149577i	0.997199	+	0.0747885i	$0.0238282\pi$
$461$			1480.53i			0.149577i	−0.997199	+	0.0747885i	$0.976172\pi$
$462$		0			0
$463$		−	8933.95i		−	0.896751i	−0.893845	−	0.448375i	$-0.852003\pi$
$463$		−	8933.95i		−	0.896751i	0.893845	−	0.448375i	$-0.147997\pi$
$464$		0			0
$465$	5830.36	−	9915.42i	0.581454	−	0.988853i
$466$		0			0
$467$	−5745.73	−	9951.90i	−0.569338	−	0.986122i	−0.996632	−	0.0820095i	$-0.973866\pi$
$467$	−5745.73	−	9951.90i	−0.569338	−	0.986122i	0.427293	−	0.904113i	$-0.359467\pi$
$468$		0			0
$469$	16541.1	+	4532.29i	1.62856	+	0.446229i
$470$		0			0
$471$	411.544	+	726.098i	0.0402610	+	0.0710336i
$472$		0			0
$473$	13223.1	+	7634.38i	1.28541	+	0.742133i
$474$		0			0
$475$		−	230.534i		−	0.0222687i
$476$		0			0
$477$	21.1740	−	1330.38i	0.00203247	−	0.127702i
$478$		0			0
$479$	−2746.28	+	4756.69i	−0.261964	+	0.453734i	−0.966764	−	0.255672i	$-0.917703\pi$
$479$	−2746.28	+	4756.69i	−0.261964	+	0.453734i	0.704800	+	0.709406i	$0.251037\pi$
$480$		0			0
$481$	4971.18	+	8610.34i	0.471240	+	0.816211i
$482$		0			0
$483$	−2279.66	+	577.733i	−0.214758	+	0.0544260i
$484$		0			0
$485$	−16485.6	+	9517.99i	−1.54345	+	0.891113i
$486$		0			0
$487$	−841.476	−	485.826i	−0.0782976	−	0.0452051i	0.460340	−	0.887743i	$-0.347727\pi$
$487$	−841.476	−	485.826i	−0.0782976	−	0.0452051i	−0.538638	+	0.842538i	$0.681061\pi$
$488$		0			0
$489$	−39.9363	+	5018.78i	−0.00369321	+	0.464125i
$490$		0			0
$491$	17356.7			1.59531			0.797655	−	0.603114i	$-0.206074\pi$
$491$	17356.7			1.59531			0.797655	+	0.603114i	$0.206074\pi$
$492$		0			0
$493$	−6828.21	+	11826.8i	−0.623788	+	1.08043i
$494$		0			0
$495$	14349.6	−	7982.99i	1.30296	−	0.724866i
$496$		0			0
$497$	17114.8	−	4482.63i	1.54468	−	0.404574i
$498$		0			0
$499$	4002.76	−	2311.00i	0.359095	−	0.207324i	−0.309589	−	0.950871i	$-0.600191\pi$
$499$	4002.76	−	2311.00i	0.359095	−	0.207324i	0.668684	+	0.743547i	$0.266858\pi$
$500$		0			0
$501$	2162.13	−	3677.04i	0.192808	−	0.327900i
$502$		0			0
$503$	−436.260			−0.0386718			−0.0193359	−	0.999813i	$-0.506155\pi$
$503$	−436.260			−0.0386718			−0.0193359	+	0.999813i	$0.506155\pi$
$504$		0			0
$505$	18069.5			1.59224
$506$		0			0
$507$	9161.40	−	15580.4i	0.802509	−	1.36479i
$508$		0			0
$509$	−15929.7	+	9197.00i	−1.38717	+	0.800884i	−0.992996	−	0.118151i	$-0.962303\pi$
$509$	−15929.7	+	9197.00i	−1.38717	+	0.800884i	−0.394176	+	0.919035i	$0.628970\pi$
$510$		0			0
$511$	−3995.97	+	14583.7i	−0.345932	+	1.26252i
$512$		0			0
$513$	−2519.42	+	1375.47i	−0.216832	+	0.118379i
$514$		0			0
$515$	1668.00	−	2889.06i	0.142720	−	0.247198i
$516$		0			0
$517$	−8911.26			−0.758060
$518$		0			0
$519$	19.2074	−	2413.78i	0.00162449	−	0.204149i
$520$		0			0
$521$	16719.7	+	9653.11i	1.40595	+	0.811728i	0.994995	−	0.0999257i	$-0.0318605\pi$
$521$	16719.7	+	9653.11i	1.40595	+	0.811728i	0.410959	+	0.911654i	$0.365194\pi$
$522$		0			0
$523$	−3908.72	+	2256.70i	−0.326800	+	0.188678i	−0.654419	−	0.756132i	$-0.727087\pi$
$523$	−3908.72	+	2256.70i	−0.326800	+	0.188678i	0.327620	+	0.944810i	$0.393754\pi$
$524$		0			0
$525$	756.245	+	777.093i	0.0628671	+	0.0646002i
$526$		0			0
$527$	−8910.32	−	15433.1i	−0.736507	−	1.27567i
$528$		0			0
$529$	5784.90	−	10019.7i	0.475458	−	0.823518i
$530$		0			0
$531$	17070.0	+	271.682i	1.39506	+	0.0222034i
$532$		0			0
$533$			16213.7i			1.31763i
$534$		0			0
$535$	−932.916	−	538.620i	−0.0753897	−	0.0435263i
$536$		0			0
$537$	3009.38	+	5309.52i	0.241833	+	0.426672i
$538$		0			0
$539$	−201.521	+	17868.9i	−0.0161042	+	1.42795i
$540$		0			0
$541$	−355.701	−	616.093i	−0.0282676	−	0.0489610i	0.851546	−	0.524281i	$-0.175666\pi$
$541$	−355.701	−	616.093i	−0.0282676	−	0.0489610i	−0.879813	+	0.475320i	$0.842332\pi$
$542$		0			0
$543$	2161.49	−	3675.95i	0.170826	−	0.290516i
$544$		0			0
$545$		−	24608.7i		−	1.93417i
$546$		0			0
$547$			3530.92i			0.275999i	0.990432	+	0.137999i	$0.0440672\pi$
$547$			3530.92i			0.275999i	−0.990432	+	0.137999i	$0.955933\pi$
$548$		0			0
$549$	4080.65	−	6815.07i	0.317227	−	0.529800i
$550$		0			0
$551$	−1486.63	−	2574.91i	−0.114941	−	0.199083i
$552$		0			0
$553$	−11717.6	+	11586.2i	−0.901052	+	0.890948i
$554$		0			0
$555$	−6964.30	+	3947.29i	−0.532645	+	0.301897i
$556$		0			0
$557$	−3130.25	−	1807.25i	−0.238120	−	0.137479i	0.376192	−	0.926542i	$-0.377233\pi$
$557$	−3130.25	−	1807.25i	−0.238120	−	0.137479i	−0.614313	+	0.789063i	$0.710567\pi$
$558$		0			0
$559$			22078.6i			1.67053i
$560$		0			0
$561$	202.430	−	25439.3i	0.0152346	−	1.91453i
$562$		0			0
$563$	−4095.04	+	7092.82i	−0.306546	+	0.530954i	−0.977604	−	0.210451i	$-0.932507\pi$
$563$	−4095.04	+	7092.82i	−0.306546	+	0.530954i	0.671058	+	0.741405i	$0.265840\pi$
$564$		0			0
$565$	−1147.94	−	1988.29i	−0.0854766	−	0.148050i
$566$		0			0
$567$	3980.44	−	12901.2i	0.294820	−	0.955553i
$568$		0			0
$569$	−8058.29	+	4652.46i	−0.593711	+	0.342779i	−0.766563	−	0.642169i	$-0.778035\pi$
$569$	−8058.29	+	4652.46i	−0.593711	+	0.342779i	0.172853	+	0.984948i	$0.444702\pi$
$570$		0			0
$571$	−9931.69	−	5734.06i	−0.727895	−	0.420250i	0.0897565	−	0.995964i	$-0.471391\pi$
$571$	−9931.69	−	5734.06i	−0.727895	−	0.420250i	−0.817652	+	0.575713i	$0.804724\pi$
$572$		0			0
$573$	5079.24	+	40.4174i	0.370311	+	0.00294670i
$574$		0			0
$575$	275.355			0.0199706
$576$		0			0
$577$	3705.95	−	6418.89i	0.267384	−	0.463123i	−0.700801	−	0.713356i	$-0.747174\pi$
$577$	3705.95	−	6418.89i	0.267384	−	0.463123i	0.968185	+	0.250234i	$0.0805074\pi$
$578$		0			0
$579$	360.158	+	635.436i	0.0258509	+	0.0456094i
$580$		0			0
$581$	−3383.24	+	886.121i	−0.241584	+	0.0632745i
$582$		0			0
$583$	−2223.45	+	1283.71i	−0.157952	+	0.0911936i
$584$		0			0
$585$	20371.6	+	12197.8i	1.43976	+	0.862084i
$586$		0			0
$587$	−5262.08			−0.369999			−0.184999	−	0.982739i	$-0.559228\pi$
$587$	−5262.08			−0.369999			−0.184999	+	0.982739i	$0.559228\pi$
$588$		0			0
$589$	3879.87			0.271422
$590$		0			0
$591$	−20107.4	−	11823.3i	−1.39950	−	0.822920i
$592$		0			0
$593$	19317.8	−	11153.1i	1.33775	−	0.772351i	0.351277	−	0.936272i	$-0.385748\pi$
$593$	19317.8	−	11153.1i	1.33775	−	0.772351i	0.986473	+	0.163921i	$0.0524142\pi$
$594$		0			0
$595$	19653.7	−	5147.58i	1.35415	−	0.354673i
$596$		0			0
$597$	3924.16	−	2224.17i	0.269020	−	0.152478i
$598$		0			0
$599$	−12850.2	+	22257.2i	−0.876537	+	1.51821i	−0.0214205	+	0.999771i	$0.506819\pi$
$599$	−12850.2	+	22257.2i	−0.876537	+	1.51821i	−0.855116	+	0.518436i	$0.826514\pi$
$600$		0			0
$601$	3267.67			0.221782			0.110891	−	0.993833i	$-0.464630\pi$
$601$	3267.67			0.221782			0.110891	+	0.993833i	$0.464630\pi$
$602$		0			0
$603$	−397.898	+	25000.3i	−0.0268718	+	1.68838i
$604$		0			0
$605$	−13984.6	−	8074.01i	−0.939759	−	0.542570i
$606$		0			0
$607$	−10939.9	+	6316.14i	−0.731526	+	0.422347i	−0.818980	−	0.573822i	$-0.805460\pi$
$607$	−10939.9	+	6316.14i	−0.731526	+	0.422347i	0.0874544	+	0.996169i	$0.472127\pi$
$608$		0			0
$609$	13457.9	+	3802.87i	0.895471	+	0.253038i
$610$		0			0
$611$	−6442.83	−	11159.3i	−0.426594	−	0.738883i
$612$		0			0
$613$	12415.0	−	21503.3i	0.818002	−	1.41682i	−0.0891504	−	0.996018i	$-0.528415\pi$
$613$	12415.0	−	21503.3i	0.818002	−	1.41682i	0.907152	−	0.420803i	$-0.138251\pi$
$614$		0			0
$615$	−13054.2	−	103.877i	−0.855928	−	0.00681093i
$616$		0			0
$617$			19575.4i			1.27727i	0.769509	+	0.638636i	$0.220501\pi$
$617$			19575.4i			1.27727i	−0.769509	+	0.638636i	$0.779499\pi$
$618$		0			0
$619$	−6109.81	−	3527.50i	−0.396727	−	0.229050i	0.288344	−	0.957527i	$-0.406895\pi$
$619$	−6109.81	−	3527.50i	−0.396727	−	0.229050i	−0.685071	+	0.728477i	$0.740229\pi$
$620$		0			0
$621$	−1642.89	−	3009.24i	−0.106162	−	0.194455i
$622$		0			0
$623$	13711.1	−	13557.3i	0.881738	−	0.871850i
$624$		0			0
$625$	8453.25	+	14641.5i	0.541008	+	0.937053i
$626$		0			0
$627$	4774.54	+	2807.47i	0.304110	+	0.178819i
$628$		0			0
$629$			12402.2i			0.786182i
$630$		0			0
$631$			6505.94i			0.410456i	0.978714	+	0.205228i	$0.0657935\pi$
$631$			6505.94i			0.410456i	−0.978714	+	0.205228i	$0.934206\pi$
$632$		0			0
$633$	−13433.4	−	7898.96i	−0.843491	−	0.495980i
$634$		0			0
$635$	−2028.97	−	3514.28i	−0.126799	−	0.219622i
$636$		0			0
$637$	−22522.4	+	12666.8i	−1.40089	+	0.787876i
$638$		0			0
$639$	12539.3	+	22539.6i	0.776284	+	1.39538i
$640$		0			0
$641$	−20288.8	−	11713.7i	−1.25017	−	0.721785i	−0.279025	−	0.960284i	$-0.590011\pi$
$641$	−20288.8	−	11713.7i	−1.25017	−	0.721785i	−0.971143	+	0.238499i	$0.923345\pi$
$642$		0			0
$643$		−	9474.99i		−	0.581115i	−0.956857	−	0.290558i	$-0.906159\pi$
$643$		−	9474.99i		−	0.581115i	0.956857	−	0.290558i	$-0.0938408\pi$
$644$		0			0
$645$	−17776.2	−	141.451i	−1.08517	−	0.00863510i
$646$		0			0
$647$	−1446.08	+	2504.69i	−0.0878692	+	0.152194i	−0.906610	−	0.421969i	$-0.861339\pi$
$647$	−1446.08	+	2504.69i	−0.0878692	+	0.152194i	0.818741	+	0.574163i	$0.194672\pi$
$648$		0			0
$649$	−16471.2	−	28529.0i	−0.996229	−	1.72552i
$650$		0			0
$651$	−13078.4	+	12727.5i	−0.787378	+	0.766254i
$652$		0			0
$653$	2929.46	−	1691.32i	0.175557	−	0.101358i	−0.409647	−	0.912244i	$-0.634348\pi$
$653$	2929.46	−	1691.32i	0.175557	−	0.101358i	0.585203	+	0.810887i	$0.301015\pi$
$654$		0			0
$655$	−22619.8	−	13059.6i	−1.34936	−	0.779052i
$656$		0			0
$657$	−22041.9	−	350.814i	−1.30889	−	0.0208319i
$658$		0			0
$659$	8717.99			0.515333			0.257667	−	0.966234i	$-0.417046\pi$
$659$	8717.99			0.515333			0.257667	+	0.966234i	$0.417046\pi$
$660$		0			0
$661$	−12639.7	+	21892.6i	−0.743763	+	1.28823i	0.207008	+	0.978339i	$0.433627\pi$
$661$	−12639.7	+	21892.6i	−0.743763	+	1.28823i	−0.950771	+	0.309896i	$0.899706\pi$
$662$		0			0
$663$	32003.3	−	18139.1i	1.87467	−	1.06254i
$664$		0			0
$665$	−1168.90	+	4266.05i	−0.0681627	+	0.248767i
$666$		0			0
$667$	3075.52	−	1775.65i	0.178538	−	0.103079i
$668$		0			0
$669$	−18341.7	−	10785.1i	−1.05999	−	0.623282i
$670$		0			0
$671$	−15327.5			−0.881834
$672$		0			0
$673$	5616.01			0.321666			0.160833	−	0.986982i	$-0.448582\pi$
$673$	5616.01			0.321666			0.160833	+	0.986982i	$0.448582\pi$
$674$		0			0
$675$	−822.857	+	1349.76i	−0.0469212	+	0.0769666i
$676$		0			0
$677$	−14189.4	+	8192.27i	−0.805530	+	0.465073i	−0.845401	−	0.534132i	$-0.820639\pi$
$677$	−14189.4	+	8192.27i	−0.805530	+	0.465073i	0.0398713	+	0.999205i	$0.487305\pi$
$678$		0			0
$679$	29215.9	−	7652.06i	1.65125	−	0.432488i
$680$		0			0
$681$	−3238.78	−	5714.26i	−0.182247	−	0.321543i
$682$		0			0
$683$	−12238.1	+	21197.0i	−0.685619	+	1.18753i	0.287623	+	0.957744i	$0.407135\pi$
$683$	−12238.1	+	21197.0i	−0.685619	+	1.18753i	−0.973242	+	0.229783i	$0.926198\pi$
$684$		0			0
$685$	17866.7			0.996573
$686$		0			0
$687$	−28565.8	−	227.308i	−1.58639	−	0.0126235i
$688$		0			0
$689$	−3215.11	−	1856.24i	−0.177773	−	0.102637i
$690$		0			0
$691$	22386.9	−	12925.1i	1.23247	−	0.711567i	0.264925	−	0.964269i	$-0.414653\pi$
$691$	22386.9	−	12925.1i	1.23247	−	0.711567i	0.967544	+	0.252702i	$0.0813193\pi$
$692$		0			0
$693$	−25303.8	+	6198.87i	−1.38703	+	0.339791i
$694$		0			0
$695$	11331.1	+	19626.1i	0.618437	+	1.07116i
$696$		0			0
$697$	−10112.6	+	17515.5i	−0.549558	+	0.951862i
$698$		0			0
$699$	−276.434	+	34739.4i	−0.0149581	+	1.87978i
$700$		0			0
$701$		−	31618.3i		−	1.70357i	−0.523888	−	0.851787i	$-0.675519\pi$
$701$		−	31618.3i		−	1.70357i	0.523888	−	0.851787i	$-0.324481\pi$
$702$		0			0
$703$	−2338.43	−	1350.09i	−0.125456	−	0.0724320i
$704$		0			0
$705$	9025.98	−	5115.83i	0.482182	−	0.273295i
$706$		0			0
$707$	−27648.9	−	7575.84i	−1.47078	−	0.402997i
$708$		0			0
$709$	−8615.15	−	14921.9i	−0.456345	−	0.790413i	0.542419	−	0.840108i	$-0.317508\pi$
$709$	−8615.15	−	14921.9i	−0.456345	−	0.790413i	−0.998764	+	0.0496950i	$0.984175\pi$
$710$		0			0
$711$	−20611.1	−	12341.3i	−1.08717	−	0.650961i
$712$		0			0
$713$			4634.19i			0.243411i
$714$		0			0
$715$		−	45816.8i		−	2.39644i
$716$		0			0
$717$	−5559.39	+	9454.60i	−0.289567	+	0.492453i
$718$		0			0
$719$	12974.4	+	22472.2i	0.672965	+	1.16561i	0.977059	+	0.212967i	$0.0683128\pi$
$719$	12974.4	+	22472.2i	0.672965	+	1.16561i	−0.304094	+	0.952642i	$0.598354\pi$
$720$		0			0
$721$	−3763.54	+	3721.33i	−0.194399	+	0.192219i
$722$		0			0
$723$	1014.86	+	1790.55i	0.0522036	+	0.0921041i
$724$		0			0
$725$	−1418.06	−	818.717i	−0.0726419	−	0.0419398i
$726$		0			0
$727$			10478.2i			0.534548i	0.963621	+	0.267274i	$0.0861228\pi$
$727$			10478.2i			0.534548i	−0.963621	+	0.267274i	$0.913877\pi$
$728$		0			0
$729$	19660.6	+	939.372i	0.998861	+	0.0477250i
$730$		0			0
$731$	−13770.5	+	23851.2i	−0.696746	+	1.20680i
$732$		0			0
$733$	−3645.85	−	6314.79i	−0.183714	−	0.318202i	0.759428	−	0.650591i	$-0.225479\pi$
$733$	−3645.85	−	6314.79i	−0.183714	−	0.318202i	−0.943142	+	0.332389i	$0.892145\pi$
$734$		0			0
$735$	−10054.1	−	18214.6i	−0.504562	−	0.914089i
$736$		0			0
$737$	41782.8	−	24123.3i	2.08832	−	1.20569i
$738$		0			0
$739$	22208.1	+	12821.9i	1.10547	+	0.638241i	0.937651	−	0.347577i	$-0.112996\pi$
$739$	22208.1	+	12821.9i	1.10547	+	0.638241i	0.167815	+	0.985818i	$0.446329\pi$
$740$		0			0
$741$	−63.7290	+	8008.81i	−0.00315944	+	0.397046i
$742$		0			0
$743$	−14281.2			−0.705149			−0.352574	−	0.935784i	$-0.614694\pi$
$743$	−14281.2			−0.705149			−0.352574	+	0.935784i	$0.614694\pi$
$744$		0			0
$745$	7555.07	−	13085.8i	0.371539	−	0.643524i
$746$		0			0
$747$	−2478.74	−	4455.59i	−0.121409	−	0.218235i
$748$		0			0
$749$	1201.67	+	1215.30i	0.0586222	+	0.0592871i
$750$		0			0
$751$	−21658.6	+	12504.6i	−1.05237	+	0.607588i	−0.923313	−	0.384049i	$-0.874529\pi$
$751$	−21658.6	+	12504.6i	−1.05237	+	0.607588i	−0.129060	+	0.991637i	$0.541196\pi$
$752$		0			0
$753$	−5588.03	+	9503.31i	−0.270437	+	0.459920i
$754$		0			0
$755$	−1085.83			−0.0523410
$756$		0			0
$757$	24727.7			1.18724			0.593621	−	0.804745i	$-0.297698\pi$
$757$	24727.7			1.18724			0.593621	+	0.804745i	$0.297698\pi$
$758$		0			0
$759$	−3353.30	+	5702.80i	−0.160365	+	0.272725i
$760$		0			0
$761$	−6629.71	+	3827.67i	−0.315804	+	0.182330i	−0.649521	−	0.760344i	$-0.725030\pi$
$761$	−6629.71	+	3827.67i	−0.315804	+	0.182330i	0.333717	+	0.942673i	$0.391697\pi$
$762$		0			0
$763$	−10317.5	+	37654.7i	−0.489538	+	1.78662i
$764$		0			0
$765$	14399.3	+	25883.1i	0.680534	+	1.22327i
$766$		0			0
$767$	23817.4	−	41252.9i	1.12125	−	1.94205i
$768$		0			0
$769$	−25799.4			−1.20982			−0.604909	−	0.796295i	$-0.706791\pi$
$769$	−25799.4			−1.20982			−0.604909	+	0.796295i	$0.706791\pi$
$770$		0			0
$771$	−241.845	+	30392.6i	−0.0112968	+	1.41967i
$772$		0			0
$773$	−12862.7	−	7426.30i	−0.598500	−	0.345544i	0.169951	−	0.985452i	$-0.445639\pi$
$773$	−12862.7	−	7426.30i	−0.598500	−	0.345544i	−0.768451	+	0.639908i	$0.778972\pi$
$774$		0			0
$775$	1850.46	−	1068.37i	0.0857685	−	0.0495185i
$776$		0			0
$777$	12311.3	−	3120.04i	0.568423	−	0.144055i
$778$		0			0
$779$	−2201.70	−	3813.45i	−0.101263	−	0.175393i
$780$		0			0
$781$	24884.8	−	43101.7i	1.14014	−	1.97478i
$782$		0			0
$783$	−486.649	+	20382.2i	−0.0222113	+	0.930270i
$784$		0			0
$785$			1875.00i			0.0852506i
$786$		0			0
$787$	8537.77	+	4929.29i	0.386707	+	0.223266i	0.680733	−	0.732532i	$-0.261662\pi$
$787$	8537.77	+	4929.29i	0.386707	+	0.223266i	−0.294025	+	0.955798i	$0.594995\pi$
$788$		0			0
$789$	18681.1	+	32959.6i	0.842923	+	1.48719i
$790$		0			0
$791$	922.897	+	3523.65i	0.0414848	+	0.158390i
$792$		0			0
$793$	−11081.7	−	19194.1i	−0.496248	−	0.859526i
$794$		0			0
$795$	1515.12	−	2576.69i	0.0675920	−	0.114951i
$796$		0			0
$797$		−	28441.8i		−	1.26407i	−0.774941	−	0.632034i	$-0.782220\pi$
$797$		−	28441.8i		−	1.26407i	0.774941	−	0.632034i	$-0.217780\pi$
$798$		0			0
$799$		−	16073.7i		−	0.711698i
$800$		0			0
$801$	24117.6	+	14440.9i	1.06386	+	0.637007i
$802$		0			0
$803$	21268.7	+	36838.5i	0.934692	+	1.61893i
$804$		0			0
$805$	−5095.45	−	1396.16i	−0.223094	−	0.0611282i
$806$		0			0
$807$	−17768.6	+	10071.1i	−0.775075	+	0.439304i
$808$		0			0
$809$	−27174.8	−	15689.4i	−1.18098	−	0.681842i	−0.224742	−	0.974418i	$-0.572154\pi$
$809$	−27174.8	−	15689.4i	−1.18098	−	0.681842i	−0.956242	+	0.292577i	$0.905487\pi$
$810$		0			0
$811$		−	21590.6i		−	0.934832i	−0.884037	−	0.467416i	$-0.845185\pi$
$811$		−	21590.6i		−	0.934832i	0.884037	−	0.467416i	$-0.154815\pi$
$812$		0			0
$813$	−261.340	+	32842.5i	−0.0112738	+	1.41677i
$814$		0			0
$815$	−5637.63	+	9764.66i	−0.242304	+	0.419682i
$816$		0			0
$817$	−2998.09	−	5192.85i	−0.128384	−	0.222368i
$818$		0			0
$819$	−26057.3	−	27205.4i	−1.11174	−	1.16073i
$820$		0			0
$821$	−19883.2	+	11479.6i	−0.845224	+	0.487990i	−0.859037	−	0.511914i	$-0.828937\pi$
$821$	−19883.2	+	11479.6i	−0.845224	+	0.487990i	0.0138124	+	0.999905i	$0.495603\pi$
$822$		0			0
$823$	−6481.85	−	3742.30i	−0.274536	−	0.158503i	0.356411	−	0.934329i	$-0.384000\pi$
$823$	−6481.85	−	3742.30i	−0.274536	−	0.158503i	−0.630947	+	0.775826i	$0.717334\pi$
$824$		0			0
$825$	3050.23	+	24.2718i	0.128722	+	0.00102429i
$826$		0			0
$827$	−16108.8			−0.677337			−0.338669	−	0.940906i	$-0.609977\pi$
$827$	−16108.8			−0.677337			−0.338669	+	0.940906i	$0.609977\pi$
$828$		0			0
$829$	4154.69	−	7196.14i	0.174063	−	0.301486i	−0.765773	−	0.643110i	$-0.777644\pi$
$829$	4154.69	−	7196.14i	0.174063	−	0.301486i	0.939837	+	0.341624i	$0.110977\pi$
$830$		0			0
$831$	−3123.07	−	5510.11i	−0.130371	−	0.230016i
$832$		0			0
$833$	−32231.0	−	363.495i	−1.34062	−	0.0151193i
$834$		0			0
$835$	8299.01	−	4791.44i	0.343951	−	0.198580i
$836$		0			0
$837$	−22716.4	−	13848.6i	−0.938106	−	0.571897i
$838$		0			0
$839$	−11408.7			−0.469452			−0.234726	−	0.972062i	$-0.575419\pi$
$839$	−11408.7			−0.469452			−0.234726	+	0.972062i	$0.575419\pi$
$840$		0			0
$841$	3270.66			0.134104
$842$		0			0
$843$	−28395.0	−	16696.5i	−1.16011	−	0.682156i
$844$		0			0
$845$	35164.6	−	20302.3i	1.43160	−	0.826533i
$846$		0			0
$847$	18013.2	+	18217.5i	0.730747	+	0.739034i
$848$		0			0
$849$	−15913.0	+	9019.30i	−0.643265	+	0.364596i
$850$		0			0
$851$	1612.58	−	2793.06i	0.0649570	−	0.112509i
$852$		0			0
$853$	−8924.84			−0.358242			−0.179121	−	0.983827i	$-0.557325\pi$
$853$	−8924.84			−0.358242			−0.179121	+	0.983827i	$0.557325\pi$
$854$		0			0
$855$	−6447.73	−	102.620i	−0.257904	−	0.00410473i
$856$		0			0
$857$	12075.9	+	6972.01i	0.481335	+	0.277899i	0.720973	−	0.692964i	$-0.243695\pi$
$857$	12075.9	+	6972.01i	0.481335	+	0.277899i	−0.239638	+	0.970862i	$0.577029\pi$
$858$		0			0
$859$	−34970.4	+	20190.1i	−1.38903	+	0.801954i	−0.993205	−	0.116374i	$-0.962873\pi$
$859$	−34970.4	+	20190.1i	−1.38903	+	0.801954i	−0.395820	+	0.918328i	$0.629540\pi$
$860$		0			0
$861$	19931.2	+	5632.06i	0.788911	+	0.222927i
$862$		0			0
$863$	15705.9	+	27203.4i	0.619507	+	1.07302i	0.989576	+	0.144013i	$0.0460008\pi$
$863$	15705.9	+	27203.4i	0.619507	+	1.07302i	−0.370069	+	0.929004i	$0.620666\pi$
$864$		0			0
$865$	2711.42	−	4696.32i	0.106579	−	0.184601i
$866$		0			0
$867$	20358.4	+	161.999i	0.797470	+	0.00634576i
$868$		0			0
$869$			46355.5i			1.80955i
$870$		0			0
$871$	60417.8	+	34882.3i	2.35038	+	1.35699i
$872$		0			0
$873$	21405.1	+	38476.1i	0.829843	+	1.49166i
$874$		0			0
$875$	−6229.88	−	23785.9i	−0.240695	−	0.918984i
$876$		0			0
$877$	−11933.0	−	20668.6i	−0.459463	−	0.795813i	0.539469	−	0.842005i	$-0.318625\pi$
$877$	−11933.0	−	20668.6i	−0.459463	−	0.795813i	−0.998933	+	0.0461917i	$0.985291\pi$
$878$		0			0
$879$	21210.6	+	12472.0i	0.813896	+	0.478578i
$880$		0			0
$881$			10693.7i			0.408944i	0.978872	+	0.204472i	$0.0655477\pi$
$881$			10693.7i			0.408944i	−0.978872	+	0.204472i	$0.934452\pi$
$882$		0			0
$883$		−	17145.5i		−	0.653443i	−0.945121	−	0.326722i	$-0.894056\pi$
$883$		−	17145.5i		−	0.653443i	0.945121	−	0.326722i	$-0.105944\pi$
$884$		0			0
$885$	33061.4	+	19440.4i	1.25576	+	0.738398i
$886$		0			0
$887$	−21163.0	−	36655.4i	−0.801109	−	1.38756i	−0.918887	−	0.394521i	$-0.870911\pi$
$887$	−21163.0	−	36655.4i	−0.801109	−	1.38756i	0.117779	−	0.993040i	$-0.462423\pi$
$888$		0			0
$889$	1631.21	+	6228.01i	0.0615398	+	0.234961i
$890$		0			0
$891$	−17933.8	−	33479.5i	−0.674303	−	1.25882i
$892$		0			0
$893$	3030.69	+	1749.77i	0.113570	+	0.0655697i
$894$		0			0
$895$			13710.8i			0.512068i
$896$		0			0
$897$	−9565.87	−	76.1191i	−0.356070	−	0.00283338i
$898$		0			0
$899$	13778.9	−	23865.8i	0.511183	−	0.885394i
$900$		0			0
$901$	−2315.50	−	4010.56i	−0.0856164	−	0.148292i
$902$		0			0
$903$	27140.7	+	7669.29i	1.00021	+	0.282633i
$904$		0			0
$905$	8296.56	−	4790.02i	0.304737	−	0.175940i
$906$		0			0
$907$	−13945.2	−	8051.25i	−0.510521	−	0.294749i	0.222527	−	0.974927i	$-0.428569\pi$
$907$	−13945.2	−	8051.25i	−0.510521	−	0.294749i	−0.733048	+	0.680177i	$0.761903\pi$
$908$		0			0
$909$	665.098	−	41788.7i	0.0242683	−	1.52480i
$910$		0			0
$911$	5902.78			0.214674			0.107337	−	0.994223i	$-0.465768\pi$
$911$	5902.78			0.214674			0.107337	+	0.994223i	$0.465768\pi$
$912$		0			0
$913$	−4919.19	+	8520.29i	−0.178315	+	0.308850i
$914$		0			0
$915$	15524.8	−	8799.29i	0.560912	−	0.317918i
$916$		0			0
$917$	29136.1	+	29466.5i	1.04925	+	1.06115i
$918$		0			0
$919$	11472.8	−	6623.84i	0.411810	−	0.237759i	−0.279757	−	0.960071i	$-0.590254\pi$
$919$	11472.8	−	6623.84i	0.411810	−	0.237759i	0.691567	+	0.722312i	$0.256921\pi$
$920$		0			0
$921$	−24672.7	−	14507.8i	−0.882730	−	0.519053i
$922$		0			0
$923$	71966.7			2.56643
$924$		0			0
$925$	−1487.05			−0.0528583
$926$		0			0
$927$	−6620.02	−	3963.86i	−0.234552	−	0.140442i
$928$		0			0
$929$	30085.2	−	17369.7i	1.06250	−	0.613436i	0.136378	−	0.990657i	$-0.456454\pi$
$929$	30085.2	−	17369.7i	1.06250	−	0.613436i	0.926123	+	0.377221i	$0.123120\pi$
$930$		0			0
$931$	3577.17	−	6037.57i	0.125926	−	0.212538i
$932$		0			0
$933$	3273.21	+	5775.01i	0.114855	+	0.202642i
$934$		0			0
$935$	28576.2	−	49495.4i	0.999509	−	1.73120i
$936$		0			0
$937$	23961.5			0.835420			0.417710	−	0.908581i	$-0.362833\pi$
$937$	23961.5			0.835420			0.417710	+	0.908581i	$0.362833\pi$
$938$		0			0
$939$	24266.7	+	193.099i	0.843360	+	0.00671092i
$940$		0			0
$941$	22649.9	+	13076.9i	0.784660	+	0.453024i	0.838079	−	0.545548i	$-0.183679\pi$
$941$	22649.9	+	13076.9i	0.784660	+	0.453024i	−0.0534189	+	0.998572i	$0.517012\pi$
$942$		0			0
$943$	4554.85	−	2629.75i	0.157292	−	0.0908126i
$944$		0			0
$945$	22070.9	−	20805.2i	0.759751	−	0.716184i
$946$		0			0
$947$	−24556.6	−	42533.3i	−0.842642	−	1.45950i	−0.887653	−	0.460512i	$-0.847666\pi$
$947$	−24556.6	−	42533.3i	−0.842642	−	1.45950i	0.0450116	−	0.998986i	$-0.485668\pi$
$948$		0			0
$949$	−30754.5	+	53268.4i	−1.05199	+	1.82209i
$950$		0			0
$951$	178.840	−	22474.8i	0.00609810	−	0.766347i
$952$		0			0
$953$			34434.7i			1.17046i	0.810867	+	0.585230i	$0.198996\pi$
$953$			34434.7i			1.17046i	−0.810867	+	0.585230i	$0.801004\pi$
$954$		0			0
$955$	9882.30	+	5705.55i	0.334852	+	0.193327i
$956$		0			0
$957$	34225.5	−	19398.6i	1.15606	−	0.655244i
$958$		0			0
$959$	−27338.6	−	7490.82i	−0.920551	−	0.252233i
$960$		0			0
$961$	3084.99	+	5343.36i	0.103554	+	0.179362i
$962$		0			0
$963$	−1279.98	+	2137.70i	−0.0428317	+	0.0715330i
$964$		0			0
$965$			1640.89i			0.0547379i
$966$		0			0
$967$		−	23563.4i		−	0.783608i	−0.920049	−	0.391804i	$-0.871851\pi$
$967$		−	23563.4i		−	0.783608i	0.920049	−	0.391804i	$-0.128149\pi$
$968$		0			0
$969$	−5063.98	+	8612.08i	−0.167883	+	0.285511i
$970$		0			0
$971$	16309.1	+	28248.1i	0.539014	+	0.933600i	0.998957	+	0.0456516i	$0.0145364\pi$
$971$	16309.1	+	28248.1i	0.539014	+	0.933600i	−0.459943	+	0.887948i	$0.652130\pi$
$972$		0			0
$973$	−9109.74	−	34781.3i	−0.300149	−	1.14598i
$974$		0			0
$975$	2174.92	+	3837.26i	0.0714391	+	0.126042i
$976$		0			0
$977$	−7707.00	−	4449.64i	−0.252373	−	0.145708i	0.368477	−	0.929637i	$-0.379879\pi$
$977$	−7707.00	−	4449.64i	−0.252373	−	0.145708i	−0.620851	+	0.783929i	$0.713213\pi$
$978$		0			0
$979$		−	54241.9i		−	1.77076i
$980$		0			0
$981$	−56911.6	−	905.791i	−1.85224	−	0.0294798i
$982$		0			0
$983$	612.048	−	1060.10i	0.0198589	−	0.0343966i	−0.855925	−	0.517100i	$-0.827012\pi$
$983$	612.048	−	1060.10i	0.0198589	−	0.0343966i	0.875784	+	0.482703i	$0.160345\pi$
$984$		0			0
$985$	−26201.3	−	45381.9i	−0.847555	−	1.46801i
$986$		0			0
$987$	−15955.9	+	4043.68i	−0.514570	+	0.130407i
$988$		0			0
$989$	6202.44	−	3580.98i	0.199420	−	0.115135i
$990$		0			0
$991$	−284.983	−	164.535i	−0.00913501	−	0.00527410i	0.495426	−	0.868650i	$-0.335012\pi$
$991$	−284.983	−	164.535i	−0.00913501	−	0.00527410i	−0.504561	+	0.863376i	$0.668345\pi$
$992$		0			0
$993$	220.060	−	27654.9i	0.00703263	−	0.883788i
$994$		0			0
$995$	10133.4			0.322863
$996$		0			0
$997$	18061.8	−	31283.9i	0.573744	−	0.993753i	−0.422433	−	0.906394i	$-0.638824\pi$
$997$	18061.8	−	31283.9i	0.573744	−	0.993753i	0.996177	−	0.0873593i	$-0.0278428\pi$
$998$		0			0
$999$	8872.41	+	16251.4i	0.280992	+	0.514685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bj.e.95.11	yes	28
3.2	odd	2	inner	336.4.bj.e.95.5	✓	28
4.3	odd	2		336.4.bj.f.95.4	yes	28
7.2	even	3		336.4.bj.f.191.10	yes	28
12.11	even	2		336.4.bj.f.95.10	yes	28
21.2	odd	6		336.4.bj.f.191.4	yes	28
28.23	odd	6	inner	336.4.bj.e.191.5	yes	28
84.23	even	6	inner	336.4.bj.e.191.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bj.e.95.5	✓	28	3.2	odd	2	inner
336.4.bj.e.95.11	yes	28	1.1	even	1	trivial
336.4.bj.e.191.5	yes	28	28.23	odd	6	inner
336.4.bj.e.191.11	yes	28	84.23	even	6	inner
336.4.bj.f.95.4	yes	28	4.3	odd	2
336.4.bj.f.95.10	yes	28	12.11	even	2
336.4.bj.f.191.4	yes	28	21.2	odd	6
336.4.bj.f.191.10	yes	28	7.2	even	3

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.63380 - 4.47918i) q^{3} +(10.1094 - 5.83669i) q^{5} +(-17.9159 + 4.69245i) q^{7} +(-13.1262 - 23.5946i) q^{9} +(-26.0496 + 45.1192i) q^{11} -75.3352 q^{13} +(0.482652 - 60.6547i) q^{15} +(-81.3838 - 46.9870i) q^{17} +(17.7187 - 10.2299i) q^{19} +(-26.1687 + 92.6078i) q^{21} +(12.2188 + 21.1636i) q^{23} +(5.63383 - 9.75808i) q^{25} +(-140.256 - 3.34877i) q^{27} -145.322i q^{29} +(164.228 + 94.8169i) q^{31} +(133.488 + 235.516i) q^{33} +(-153.732 + 152.008i) q^{35} +(-65.9875 - 114.294i) q^{37} +(-198.418 + 337.440i) q^{39} -215.221i q^{41} -293.071i q^{43} +(-270.412 - 161.914i) q^{45} +(85.5222 + 148.129i) q^{47} +(298.962 - 168.139i) q^{49} +(-424.812 + 240.779i) q^{51} +(42.6773 + 24.6398i) q^{53} +608.173i q^{55} +(0.845940 - 106.309i) q^{57} +(-316.152 + 547.591i) q^{59} +(147.099 + 254.783i) q^{61} +(345.884 + 361.125i) q^{63} +(-761.597 + 439.708i) q^{65} +(-801.987 - 463.027i) q^{67} +(126.977 + 1.01041i) q^{69} -955.286 q^{71} +(408.236 - 707.085i) q^{73} +(-28.8699 - 50.9358i) q^{75} +(254.983 - 930.589i) q^{77} +(770.551 - 444.878i) q^{79} +(-384.407 + 619.413i) q^{81} +188.840 q^{83} -1096.99 q^{85} +(-650.922 - 382.748i) q^{87} +(-901.644 + 520.564i) q^{89} +(1349.70 - 353.507i) q^{91} +(857.245 - 485.877i) q^{93} +(119.418 - 206.837i) q^{95} -1630.72 q^{97} +(1406.50 + 22.3855i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 38 q^{7} - 70 q^{9} + 124 q^{13} + 462 q^{19} + 500 q^{21} + 566 q^{25} - 1266 q^{31} + 64 q^{33} + 338 q^{37} - 1254 q^{39} - 488 q^{45} - 206 q^{49} - 522 q^{51} + 2324 q^{57} - 340 q^{61} + 840 q^{63}+ \cdots - 3344 q^{97}+O(q^{100}) \) 28 * q - 38 * q^7 - 70 * q^9 + 124 * q^13 + 462 * q^19 + 500 * q^21 + 566 * q^25 - 1266 * q^31 + 64 * q^33 + 338 * q^37 - 1254 * q^39 - 488 * q^45 - 206 * q^49 - 522 * q^51 + 2324 * q^57 - 340 * q^61 + 840 * q^63 - 2934 * q^67 - 776 * q^69 + 2050 * q^73 + 1458 * q^75 - 2070 * q^79 + 910 * q^81 + 2400 * q^85 - 3132 * q^87 + 5170 * q^91 + 714 * q^93 - 3344 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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