LMFDB - Embedded newform 216.4.l.b.179.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,4,Mod(35,216)] 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("216.35"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$216 = 2^{3} \cdot 3^{3}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	216.l (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$12.7444125612$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.13
Character	$\chi$	$=$	216.179
Dual form			216.4.l.b.35.13

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.960011 + 2.66052i) q^{2} +(-6.15676 - 5.10826i) q^{4} +(-1.46312 + 2.53420i) q^{5} +(4.48829 - 2.59132i) q^{7} +(19.5012 - 11.4762i) q^{8} +(-5.33769 - 6.32553i) q^{10} +(13.6440 - 7.87738i) q^{11} +(37.3474 + 21.5625i) q^{13} +(2.58544 + 14.4289i) q^{14} +(11.8113 + 62.9007i) q^{16} +3.31600i q^{17} -15.0818 q^{19} +(21.9535 - 8.12845i) q^{20} +(7.85952 + 43.8626i) q^{22} +(-61.7219 + 106.905i) q^{23} +(58.2185 + 100.837i) q^{25} +(-93.2215 + 78.6633i) q^{26} +(-40.8704 - 6.97327i) q^{28} +(11.7175 + 20.2953i) q^{29} +(274.752 + 158.628i) q^{31} +(-178.688 - 28.9612i) q^{32} +(-8.82229 - 3.18340i) q^{34} +15.1657i q^{35} +286.660i q^{37} +(14.4787 - 40.1255i) q^{38} +(0.550346 + 66.2111i) q^{40} +(-284.954 - 164.518i) q^{41} +(-175.008 - 303.123i) q^{43} +(-124.243 - 21.1982i) q^{44} +(-225.170 - 266.843i) q^{46} +(165.936 + 287.410i) q^{47} +(-158.070 + 273.786i) q^{49} +(-324.171 + 58.0866i) q^{50} +(-119.792 - 323.536i) q^{52} +521.214 q^{53} +46.1023i q^{55} +(57.7886 - 102.042i) q^{56} +(-65.2451 + 11.6910i) q^{58} +(130.749 + 75.4878i) q^{59} +(-650.051 + 375.307i) q^{61} +(-685.799 + 578.699i) q^{62} +(248.594 - 447.599i) q^{64} +(-109.288 + 63.0972i) q^{65} +(126.364 - 218.868i) q^{67} +(16.9390 - 20.4158i) q^{68} +(-40.3485 - 14.5592i) q^{70} +1083.28 q^{71} +678.405 q^{73} +(-762.665 - 275.197i) q^{74} +(92.8551 + 77.0419i) q^{76} +(40.8256 - 70.7119i) q^{77} +(-97.5980 + 56.3482i) q^{79} +(-176.684 - 62.0992i) q^{80} +(711.263 - 600.187i) q^{82} +(857.418 - 495.030i) q^{83} +(-8.40342 - 4.85171i) q^{85} +(974.475 - 174.611i) q^{86} +(175.673 - 310.200i) q^{88} +566.656i q^{89} +223.501 q^{91} +(926.107 - 342.899i) q^{92} +(-923.960 + 165.560i) q^{94} +(22.0666 - 38.2204i) q^{95} +(73.8806 + 127.965i) q^{97} +(-576.663 - 683.386i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$64 q + 3 q^{2} - 17 q^{4} + 12 q^{10} - 48 q^{11} - 72 q^{14} + 127 q^{16} - 220 q^{19} + 234 q^{20} - 217 q^{22} - 902 q^{25} - 132 q^{28} + 693 q^{32} + 509 q^{34} + 1977 q^{38} - 36 q^{40} - 1620 q^{41}+ \cdots - 1912 q^{97}+O(q^{100})$ 64 * q + 3 * q^2 - 17 * q^4 + 12 * q^10 - 48 * q^11 - 72 * q^14 + 127 * q^16 - 220 * q^19 + 234 * q^20 - 217 * q^22 - 902 * q^25 - 132 * q^28 + 693 * q^32 + 509 * q^34 + 1977 * q^38 - 36 * q^40 - 1620 * q^41 - 292 * q^43 + 48 * q^46 + 1762 * q^49 + 1227 * q^50 + 330 * q^52 - 942 * q^56 - 282 * q^58 - 5592 * q^59 + 1090 * q^64 + 6 * q^65 + 68 * q^67 + 2025 * q^68 + 600 * q^70 - 868 * q^73 + 420 * q^74 - 1471 * q^76 + 362 * q^82 - 3654 * q^83 + 4119 * q^86 + 3155 * q^88 - 1380 * q^91 + 744 * q^92 - 138 * q^94 - 1912 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$ .

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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

)

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

$2$	−0.960011	+	2.66052i	−0.339415	+	0.940637i
$2$	−0.960011	+	2.66052i	−0.339415	+	0.940637i
$3$		0			0
$3$		0			0
$4$	−6.15676	−	5.10826i	−0.769594	−	0.638533i
$5$	−1.46312	+	2.53420i	−0.130866	+	0.226666i	−0.924011	−	0.382367i	$-0.875109\pi$
$5$	−1.46312	+	2.53420i	−0.130866	+	0.226666i	0.793145	+	0.609033i	$0.208442\pi$
$6$		0			0
$7$	4.48829	−	2.59132i	0.242345	−	0.139918i	−0.373909	−	0.927465i	$-0.621983\pi$
$7$	4.48829	−	2.59132i	0.242345	−	0.139918i	0.616254	+	0.787547i	$0.288649\pi$
$8$	19.5012	−	11.4762i	0.861840	−	0.507181i
$9$		0			0
$10$	−5.33769	−	6.32553i	−0.168793	−	0.200031i
$11$	13.6440	−	7.87738i	0.373984	−	0.215920i	−0.301213	−	0.953557i	$-0.597392\pi$
$11$	13.6440	−	7.87738i	0.373984	−	0.215920i	0.675198	+	0.737637i	$0.264058\pi$
$12$		0			0
$13$	37.3474	+	21.5625i	0.796793	+	0.460028i	0.842348	−	0.538933i	$-0.181173\pi$
$13$	37.3474	+	21.5625i	0.796793	+	0.460028i	−0.0455558	+	0.998962i	$0.514506\pi$
$14$	2.58544	+	14.4289i	0.0493563	+	0.275449i
$15$		0			0
$16$	11.8113	+	62.9007i	0.184551	+	0.982823i
$17$			3.31600i			0.0473087i	0.999720	+	0.0236544i	$0.00753012\pi$
$17$			3.31600i			0.0473087i	−0.999720	+	0.0236544i	$0.992470\pi$
$18$		0			0
$19$	−15.0818			−0.182106			−0.0910528	−	0.995846i	$-0.529023\pi$
$19$	−15.0818			−0.182106			−0.0910528	+	0.995846i	$0.529023\pi$
$20$	21.9535	−	8.12845i	0.245447	−	0.0908788i
$21$		0			0
$22$	7.85952	+	43.8626i	0.0761662	+	0.425070i
$23$	−61.7219	+	106.905i	−0.559561	+	0.969188i	0.437972	+	0.898988i	$0.355697\pi$
$23$	−61.7219	+	106.905i	−0.559561	+	0.969188i	−0.997533	+	0.0701991i	$0.977637\pi$
$24$		0			0
$25$	58.2185	+	100.837i	0.465748	+	0.806700i
$26$	−93.2215	+	78.6633i	−0.703163	+	0.593352i
$27$		0			0
$28$	−40.8704	−	6.97327i	−0.275849	−	0.0470652i
$29$	11.7175	+	20.2953i	0.0750306	+	0.129957i	0.901100	−	0.433612i	$-0.142761\pi$
$29$	11.7175	+	20.2953i	0.0750306	+	0.129957i	−0.826069	+	0.563569i	$0.809428\pi$
$30$		0			0
$31$	274.752	+	158.628i	1.59184	+	0.919048i	0.992992	+	0.118183i	$0.0377070\pi$
$31$	274.752	+	158.628i	1.59184	+	0.919048i	0.598846	+	0.800865i	$0.295626\pi$
$32$	−178.688	−	28.9612i	−0.987119	−	0.159989i
$33$		0			0
$34$	−8.82229	−	3.18340i	−0.0445003	−	0.0160573i
$35$			15.1657i			0.0732418i
$36$		0			0
$37$			286.660i			1.27369i	0.770991	+	0.636846i	$0.219761\pi$
$37$			286.660i			1.27369i	−0.770991	+	0.636846i	$0.780239\pi$
$38$	14.4787	−	40.1255i	0.0618094	−	0.171295i
$39$		0			0
$40$	0.550346	+	66.2111i	0.00217544	+	0.261722i
$41$	−284.954	−	164.518i	−1.08542	−	0.626669i	−0.153068	−	0.988216i	$-0.548915\pi$
$41$	−284.954	−	164.518i	−1.08542	−	0.626669i	−0.932354	+	0.361547i	$0.882249\pi$
$42$		0			0
$43$	−175.008	−	303.123i	−0.620663	−	1.07502i	−0.989363	−	0.145471i	$-0.953530\pi$
$43$	−175.008	−	303.123i	−0.620663	−	1.07502i	0.368700	−	0.929548i	$-0.379803\pi$
$44$	−124.243	−	21.1982i	−0.425688	−	0.0726305i
$45$		0			0
$46$	−225.170	−	266.843i	−0.721730	−	0.855300i
$47$	165.936	+	287.410i	0.514984	+	0.891979i	0.999849	+	0.0173897i	$0.00553559\pi$
$47$	165.936	+	287.410i	0.514984	+	0.891979i	−0.484864	+	0.874589i	$0.661131\pi$
$48$		0			0
$49$	−158.070	+	273.786i	−0.460846	+	0.798209i
$50$	−324.171	+	58.0866i	−0.916894	+	0.164294i
$51$		0			0
$52$	−119.792	−	323.536i	−0.319464	−	0.862814i
$53$	521.214			1.35083			0.675417	−	0.737436i	$-0.263964\pi$
$53$	521.214			1.35083			0.675417	+	0.737436i	$0.263964\pi$
$54$		0			0
$55$			46.1023i			0.113026i
$56$	57.7886	−	102.042i	0.137899	−	0.243500i
$57$		0			0
$58$	−65.2451	+	11.6910i	−0.147709	+	0.0264672i
$59$	130.749	+	75.4878i	0.288509	+	0.166571i	0.637269	−	0.770641i	$-0.280064\pi$
$59$	130.749	+	75.4878i	0.288509	+	0.166571i	−0.348760	+	0.937212i	$0.613397\pi$
$60$		0			0
$61$	−650.051	+	375.307i	−1.36443	+	0.787756i	−0.990210	−	0.139582i	$-0.955424\pi$
$61$	−650.051	+	375.307i	−1.36443	+	0.787756i	−0.374223	+	0.927339i	$0.622091\pi$
$62$	−685.799	+	578.699i	−1.40478	+	1.18540i
$63$		0			0
$64$	248.594	−	447.599i	0.485535	−	0.874217i
$65$	−109.288	+	63.0972i	−0.208546	+	0.120404i
$66$		0			0
$67$	126.364	−	218.868i	0.230415	−	0.399090i	−0.727515	−	0.686091i	$-0.759325\pi$
$67$	126.364	−	218.868i	0.230415	−	0.399090i	0.957930	+	0.287001i	$0.0926584\pi$
$68$	16.9390	−	20.4158i	0.0302082	−	0.0364085i
$69$		0			0
$70$	−40.3485	−	14.5592i	−0.0688939	−	0.0248594i
$71$	1083.28			1.81072			0.905362	−	0.424640i	$-0.139599\pi$
$71$	1083.28			1.81072			0.905362	+	0.424640i	$0.139599\pi$
$72$		0			0
$73$	678.405			1.08769			0.543845	−	0.839186i	$-0.316968\pi$
$73$	678.405			1.08769			0.543845	+	0.839186i	$0.316968\pi$
$74$	−762.665	−	275.197i	−1.19808	−	0.432311i
$75$		0			0
$76$	92.8551	+	77.0419i	0.140147	+	0.116280i
$77$	40.8256	−	70.7119i	0.0604221	−	0.104654i
$78$		0			0
$79$	−97.5980	+	56.3482i	−0.138995	+	0.0802490i	−0.567885	−	0.823108i	$-0.692238\pi$
$79$	−97.5980	+	56.3482i	−0.138995	+	0.0802490i	0.428890	+	0.903357i	$0.358905\pi$
$80$	−176.684	−	62.0992i	−0.246924	−	0.0867863i
$81$		0			0
$82$	711.263	−	600.187i	0.957877	−	0.808287i
$83$	857.418	−	495.030i	1.13390	−	0.654658i	0.188988	−	0.981979i	$-0.439479\pi$
$83$	857.418	−	495.030i	1.13390	−	0.654658i	0.944913	+	0.327321i	$0.106146\pi$
$84$		0			0
$85$	−8.40342	−	4.85171i	−0.0107233	−	0.00619109i
$86$	974.475	−	174.611i	1.22186	−	0.218940i
$87$		0			0
$88$	175.673	−	310.200i	0.212804	−	0.375766i
$89$			566.656i			0.674893i	0.941345	+	0.337446i	$0.109563\pi$
$89$			566.656i			0.674893i	−0.941345	+	0.337446i	$0.890437\pi$
$90$		0			0
$91$	223.501			0.257465
$92$	926.107	−	342.899i	1.04949	−	0.388583i
$93$		0			0
$94$	−923.960	+	165.560i	−1.01382	+	0.181662i
$95$	22.0666	−	38.2204i	0.0238314	−	0.0412771i
$96$		0			0
$97$	73.8806	+	127.965i	0.0773344	+	0.133947i	0.902099	−	0.431529i	$-0.142026\pi$
$97$	73.8806	+	127.965i	0.0773344	+	0.133947i	−0.824765	+	0.565476i	$0.808692\pi$
$98$	−576.663	−	683.386i	−0.594406	−	0.704413i
$99$		0			0
$100$	156.667	−	918.227i	0.156667	−	0.918227i
$101$	−733.536	−	1270.52i	−0.722669	−	1.25170i	−0.959926	−	0.280252i	$-0.909582\pi$
$101$	−733.536	−	1270.52i	−0.722669	−	1.25170i	0.237258	−	0.971447i	$-0.423751\pi$
$102$		0			0
$103$	1005.07	+	580.278i	0.961482	+	0.555112i	0.896629	−	0.442783i	$-0.146009\pi$
$103$	1005.07	+	580.278i	0.961482	+	0.555112i	0.0648531	+	0.997895i	$0.479342\pi$
$104$	975.775	−	8.11064i	0.920025	−	0.00764725i
$105$		0			0
$106$	−500.371	+	1386.70i	−0.458494	+	1.27064i
$107$		−	1244.09i		−	1.12402i	−0.827130	−	0.562011i	$-0.810028\pi$
$107$		−	1244.09i		−	1.12402i	0.827130	−	0.562011i	$-0.189972\pi$
$108$		0			0
$109$		−	569.937i		−	0.500826i	−0.968139	−	0.250413i	$-0.919434\pi$
$109$		−	569.937i		−	0.500826i	0.968139	−	0.250413i	$-0.0805664\pi$
$110$	−122.656	−	44.2587i	−0.106316	−	0.0383628i
$111$		0			0
$112$	216.008	+	251.710i	0.182240	+	0.212360i
$113$	824.716	+	476.150i	0.686573	+	0.396393i	0.802327	−	0.596885i	$-0.203595\pi$
$113$	824.716	+	476.150i	0.686573	+	0.396393i	−0.115754	+	0.993278i	$0.536928\pi$
$114$		0			0
$115$	−180.613	−	312.831i	−0.146455	−	0.253667i
$116$	31.5320	−	184.809i	0.0252386	−	0.147924i
$117$		0			0
$118$	−326.357	+	275.391i	−0.254607	+	0.214845i
$119$	8.59280	+	14.8832i	0.00661934	+	0.0114650i
$120$		0			0
$121$	−541.394	+	937.722i	−0.406757	+	0.704524i
$122$	−374.456	−	2089.77i	−0.277883	−	1.55081i
$123$		0			0
$124$	−881.267	−	2380.14i	−0.638227	−	1.72373i
$125$	−706.504			−0.505533
$126$		0			0
$127$		−	1274.79i		−	0.890701i	−0.895356	−	0.445350i	$-0.853079\pi$
$127$		−	1274.79i		−	0.890701i	0.895356	−	0.445350i	$-0.146921\pi$
$128$	952.194	+	1091.09i	0.657523	+	0.753435i
$129$		0			0
$130$	−62.9542	−	351.336i	−0.0424727	−	0.237033i
$131$	470.494	+	271.640i	0.313796	+	0.181170i	0.648624	−	0.761109i	$-0.275345\pi$
$131$	470.494	+	271.640i	0.313796	+	0.181170i	−0.334828	+	0.942279i	$0.608678\pi$
$132$		0			0
$133$	−67.6916	+	39.0818i	−0.0441324	+	0.0254798i
$134$	460.994	+	546.310i	0.297192	+	0.352194i
$135$		0			0
$136$	38.0551	+	64.6660i	0.0239941	+	0.0407725i
$137$	−2185.39	+	1261.73i	−1.36285	+	0.786840i	−0.990002	−	0.141053i	$-0.954951\pi$
$137$	−2185.39	+	1261.73i	−1.36285	+	0.786840i	−0.372846	+	0.927893i	$0.621618\pi$
$138$		0			0
$139$	937.946	−	1624.57i	0.572342	−	0.991326i	−0.423983	−	0.905670i	$-0.639368\pi$
$139$	937.946	−	1624.57i	0.572342	−	0.991326i	0.996325	−	0.0856555i	$-0.0272984\pi$
$140$	77.4701	−	93.3712i	0.0467673	−	0.0563665i
$141$		0			0
$142$	−1039.96	+	2882.08i	−0.614588	+	1.70323i
$143$	679.425			0.397317
$144$		0			0
$145$	−68.5766			−0.0392757
$146$	−651.277	+	1804.91i	−0.369179	+	1.02312i
$147$		0			0
$148$	1464.34	−	1764.90i	0.813295	−	0.980227i
$149$	−998.646	+	1729.71i	−0.549076	+	0.951027i	0.449263	+	0.893400i	$0.351687\pi$
$149$	−998.646	+	1729.71i	−0.549076	+	0.951027i	−0.998338	+	0.0576270i	$0.981647\pi$
$150$		0			0
$151$	35.3646	−	20.4177i	0.0190591	−	0.0110038i	−0.490440	−	0.871475i	$-0.663164\pi$
$151$	35.3646	−	20.4177i	0.0190591	−	0.0110038i	0.509499	+	0.860471i	$0.329831\pi$
$152$	−294.114	+	173.082i	−0.156946	+	0.0923605i
$153$		0			0
$154$	148.938	+	176.502i	0.0779334	+	0.0923565i
$155$	−803.992	+	464.185i	−0.416634	+	0.240544i
$156$		0			0
$157$	−1170.05	−	675.530i	−0.594779	−	0.343396i	0.172206	−	0.985061i	$-0.444911\pi$
$157$	−1170.05	−	675.530i	−0.594779	−	0.343396i	−0.766985	+	0.641665i	$0.778244\pi$
$158$	−56.2205	−	313.757i	−0.0283080	−	0.157982i
$159$		0			0
$160$	334.835	−	410.457i	0.165444	−	0.202809i
$161$			639.763i			0.313170i
$162$		0			0
$163$	−1922.43			−0.923779			−0.461890	−	0.886937i	$-0.652828\pi$
$163$	−1922.43			−0.923779			−0.461890	+	0.886937i	$0.652828\pi$
$164$	913.989	+	2468.52i	0.435186	+	1.17536i
$165$		0			0
$166$	493.908	+	2756.41i	0.230932	+	1.28879i
$167$	−1311.20	+	2271.06i	−0.607566	+	1.05234i	0.384074	+	0.923302i	$0.374521\pi$
$167$	−1311.20	+	2271.06i	−0.607566	+	1.05234i	−0.991640	+	0.129033i	$0.958813\pi$
$168$		0			0
$169$	−168.615	−	292.049i	−0.0767477	−	0.132931i
$170$	20.9755	−	17.6998i	0.00946321	−	0.00798536i
$171$		0			0
$172$	−470.950	+	2760.24i	−0.208777	+	1.22364i
$173$	−1385.77	−	2400.23i	−0.609008	−	1.05483i	−0.991404	−	0.130834i	$-0.958234\pi$
$173$	−1385.77	−	2400.23i	−0.609008	−	1.05483i	0.382396	−	0.923998i	$-0.375099\pi$
$174$		0			0
$175$	522.603	+	301.725i	0.225743	+	0.130333i
$176$	656.646	+	765.176i	0.281230	+	0.327712i
$177$		0			0
$178$	−1507.60	−	543.997i	−0.634829	−	0.229069i
$179$		−	2108.40i		−	0.880389i	−0.897903	−	0.440194i	$-0.854910\pi$
$179$		−	2108.40i		−	0.880389i	0.897903	−	0.440194i	$-0.145090\pi$
$180$		0			0
$181$			583.190i			0.239493i	0.992805	+	0.119746i	$0.0382081\pi$
$181$			583.190i			0.239493i	−0.992805	+	0.119746i	$0.961792\pi$
$182$	−214.564	+	594.630i	−0.0873875	+	0.242181i
$183$		0			0
$184$	23.2164	+	2793.12i	0.00930181	+	1.11908i
$185$	−726.455	−	419.419i	−0.288703	−	0.166683i
$186$		0			0
$187$	26.1214	+	45.2436i	0.0102149	+	0.0176927i
$188$	446.537	−	2617.16i	0.173229	−	1.01530i
$189$		0			0
$190$	80.5020	+	95.4006i	0.0307381	+	0.0364268i
$191$	−622.663	−	1078.48i	−0.235886	−	0.408567i	0.723644	−	0.690174i	$-0.242466\pi$
$191$	−622.663	−	1078.48i	−0.235886	−	0.408567i	−0.959530	+	0.281607i	$0.909133\pi$
$192$		0			0
$193$	−1316.15	+	2279.63i	−0.490872	+	0.850215i	−0.999945	−	0.0105083i	$-0.996655\pi$
$193$	−1316.15	+	2279.63i	−0.490872	+	0.850215i	0.509073	+	0.860723i	$0.329988\pi$
$194$	−411.380	+	73.7131i	−0.152244	+	0.0272799i
$195$		0			0
$196$	2371.77	−	878.167i	0.864347	−	0.320032i
$197$	−1210.94			−0.437948			−0.218974	−	0.975731i	$-0.570271\pi$
$197$	−1210.94			−0.437948			−0.218974	+	0.975731i	$0.570271\pi$
$198$		0			0
$199$		−	2015.72i		−	0.718043i	−0.933329	−	0.359021i	$-0.883110\pi$
$199$		−	2015.72i		−	0.718043i	0.933329	−	0.359021i	$-0.116890\pi$
$200$	2292.56	+	1298.33i	0.810543	+	0.459027i
$201$		0			0
$202$	4084.45	−	731.873i	1.42268	−	0.254923i
$203$	105.183	+	60.7275i	0.0363666	+	0.0209962i
$204$		0			0
$205$	833.845	−	481.421i	0.284089	−	0.164019i
$206$	−2508.72	+	2116.94i	−0.848500	+	0.715992i
$207$		0			0
$208$	−915.177	+	2603.86i	−0.305077	+	0.868005i
$209$	−205.777	+	118.805i	−0.0681046	+	0.0393202i
$210$		0			0
$211$	−601.260	+	1041.41i	−0.196173	+	0.339781i	−0.947284	−	0.320394i	$-0.896185\pi$
$211$	−601.260	+	1041.41i	−0.196173	+	0.339781i	0.751112	+	0.660175i	$0.229518\pi$
$212$	−3208.99	−	2662.50i	−1.03959	−	0.862552i
$213$		0			0
$214$	3309.92	+	1194.34i	1.05730	+	0.381510i
$215$	1024.23			0.324894
$216$		0			0
$217$	1644.22			0.514365
$218$	1516.33	+	547.146i	0.471095	+	0.169988i
$219$		0			0
$220$	235.503	−	283.841i	0.0721708	−	0.0869842i
$221$	−71.5013	+	123.844i	−0.0217634	+	0.0376952i
$222$		0			0
$223$	1135.80	−	655.752i	0.341070	−	0.196917i	−0.319675	−	0.947527i	$-0.603574\pi$
$223$	1135.80	−	655.752i	0.341070	−	0.196917i	0.660745	+	0.750611i	$0.270241\pi$
$224$	−877.049	+	333.050i	−0.261609	+	0.0993430i
$225$		0			0
$226$	−2058.54	+	1737.07i	−0.605895	+	0.511274i
$227$	2494.70	−	1440.32i	0.729423	−	0.421133i	−0.0887881	−	0.996051i	$-0.528299\pi$
$227$	2494.70	−	1440.32i	0.729423	−	0.421133i	0.818211	+	0.574918i	$0.194966\pi$
$228$		0			0
$229$	−3858.07	−	2227.46i	−1.11331	−	0.642771i	−0.173627	−	0.984812i	$-0.555549\pi$
$229$	−3858.07	−	2227.46i	−1.11331	−	0.642771i	−0.939685	+	0.342040i	$0.888882\pi$
$230$	1005.69	−	180.204i	0.288317	−	0.0516621i
$231$		0			0
$232$	461.419	+	261.311i	0.130576	+	0.0739478i
$233$		−	1085.86i		−	0.305309i	−0.988280	−	0.152654i	$-0.951218\pi$
$233$		−	1085.86i		−	0.305309i	0.988280	−	0.152654i	$-0.0487821\pi$
$234$		0			0
$235$	−971.139			−0.269575
$236$	−419.376	−	1132.66i	−0.115674	−	0.312414i
$237$		0			0
$238$	−47.8462	+	8.57333i	−0.0130311	+	0.00233498i
$239$	−1617.59	+	2801.74i	−0.437795	+	0.758283i	−0.997519	−	0.0703960i	$-0.977574\pi$
$239$	−1617.59	+	2801.74i	−0.437795	+	0.758283i	0.559724	+	0.828679i	$0.310907\pi$
$240$		0			0
$241$	715.242	+	1238.84i	0.191173	+	0.331122i	0.945639	−	0.325217i	$-0.105437\pi$
$241$	715.242	+	1238.84i	0.191173	+	0.331122i	−0.754466	+	0.656339i	$0.772104\pi$
$242$	−1975.08	−	2340.61i	−0.524642	−	0.621737i
$243$		0			0
$244$	5919.37	+	1009.96i	1.55307	+	0.264983i
$245$	−462.552	−	801.164i	−0.120618	−	0.208916i
$246$		0			0
$247$	−563.267	−	325.202i	−0.145100	−	0.0837738i
$248$	7178.45	−	59.6673i	1.83803	−	0.0152777i
$249$		0			0
$250$	678.252	−	1879.67i	0.171586	−	0.475523i
$251$			5903.80i			1.48464i	0.670046	+	0.742320i	$0.266275\pi$
$251$			5903.80i			1.48464i	−0.670046	+	0.742320i	$0.733725\pi$
$252$		0			0
$253$			1944.83i			0.483281i
$254$	3391.60	+	1223.81i	0.837826	+	0.302317i
$255$		0			0
$256$	−3816.99	+	1485.88i	−0.931882	+	0.362763i
$257$	−1225.66	−	707.636i	−0.297489	−	0.171755i	0.343825	−	0.939034i	$-0.388277\pi$
$257$	−1225.66	−	707.636i	−0.297489	−	0.171755i	−0.641314	+	0.767278i	$0.721611\pi$
$258$		0			0
$259$	742.827	+	1286.61i	0.178212	+	0.308673i
$260$	995.175	+	169.796i	0.237377	+	0.0405011i
$261$		0			0
$262$	−1174.38	+	990.981i	−0.276922	+	0.233676i
$263$	−2793.50	−	4838.48i	−0.654959	−	1.13442i	−0.981904	−	0.189379i	$-0.939352\pi$
$263$	−2793.50	−	4838.48i	−0.654959	−	1.13442i	0.326945	−	0.945043i	$-0.393981\pi$
$264$		0			0
$265$	−762.599	+	1320.86i	−0.176778	+	0.306188i
$266$	−38.9932	−	217.614i	−0.00898806	−	0.0501608i
$267$		0			0
$268$	−1896.03	+	702.020i	−0.432158	+	0.160010i
$269$	5030.52			1.14021			0.570105	−	0.821572i	$-0.306903\pi$
$269$	5030.52			1.14021			0.570105	+	0.821572i	$0.306903\pi$
$270$		0			0
$271$		−	1317.52i		−	0.295328i	−0.989038	−	0.147664i	$-0.952825\pi$
$271$		−	1317.52i		−	0.295328i	0.989038	−	0.147664i	$-0.0471754\pi$
$272$	−208.579	+	39.1662i	−0.0464961	+	0.00873089i
$273$		0			0
$274$	−1258.87	−	7025.55i	−0.277560	−	1.54901i
$275$	1588.67	+	917.219i	0.348365	+	0.201129i
$276$		0			0
$277$	2626.49	−	1516.41i	0.569714	−	0.328924i	−0.187321	−	0.982299i	$-0.559981\pi$
$277$	2626.49	−	1516.41i	0.569714	−	0.328924i	0.757035	+	0.653374i	$0.226647\pi$
$278$	3421.77	+	4055.03i	0.738216	+	0.874837i
$279$		0			0
$280$	174.044	+	295.748i	0.0371468	+	0.0631227i
$281$	2118.05	−	1222.86i	0.449653	−	0.259607i	−0.258031	−	0.966137i	$-0.583074\pi$
$281$	2118.05	−	1222.86i	0.449653	−	0.259607i	0.707683	+	0.706530i	$0.249740\pi$
$282$		0			0
$283$	4229.51	−	7325.72i	0.888403	−	1.53876i	0.0466401	−	0.998912i	$-0.485149\pi$
$283$	4229.51	−	7325.72i	0.888403	−	1.53876i	0.841763	−	0.539847i	$-0.181518\pi$
$284$	−6669.48	−	5533.67i	−1.39352	−	1.15621i
$285$		0			0
$286$	−652.256	+	1807.62i	−0.134856	+	0.373731i
$287$	−1705.27			−0.350729
$288$		0			0
$289$	4902.00			0.997762
$290$	65.8343	−	182.450i	0.0133308	−	0.0369442i
$291$		0			0
$292$	−4176.78	−	3465.47i	−0.837080	−	0.694526i
$293$	−219.370	+	379.960i	−0.0437397	+	0.0757593i	−0.887066	−	0.461642i	$-0.847261\pi$
$293$	−219.370	+	379.960i	−0.0437397	+	0.0757593i	0.843327	+	0.537401i	$0.180594\pi$
$294$		0			0
$295$	−382.603	+	220.896i	−0.0755118	+	0.0435968i
$296$	3289.77	+	5590.22i	0.645992	+	1.09772i
$297$		0			0
$298$	−3643.21	−	4317.46i	−0.708206	−	0.839274i
$299$	−4610.30	+	2661.76i	−0.891708	+	0.514828i
$300$		0			0
$301$	−1570.97	−	907.003i	−0.300829	−	0.173684i
$302$	20.3715	+	113.689i	0.00388161	+	0.0216626i
$303$		0			0
$304$	−178.136	−	948.657i	−0.0336078	−	0.178978i
$305$		−	2196.48i		−	0.412361i
$306$		0			0
$307$	−7875.21			−1.46405			−0.732023	−	0.681280i	$-0.761423\pi$
$307$	−7875.21			−1.46405			−0.732023	+	0.681280i	$0.761423\pi$
$308$	−612.568	+	226.808i	−0.113326	+	0.0419598i
$309$		0			0
$310$	−463.133	−	2584.66i	−0.0848522	−	0.473545i
$311$	532.946	−	923.090i	0.0971724	−	0.168308i	−0.813341	−	0.581788i	$-0.802354\pi$
$311$	532.946	−	923.090i	0.0971724	−	0.168308i	0.910513	+	0.413480i	$0.135687\pi$
$312$		0			0
$313$	−4954.30	−	8581.10i	−0.894676	−	1.54962i	−0.834206	−	0.551454i	$-0.814073\pi$
$313$	−4954.30	−	8581.10i	−0.894676	−	1.54962i	−0.0604700	−	0.998170i	$-0.519260\pi$
$314$	2920.53	−	2464.43i	0.524888	−	0.442917i
$315$		0			0
$316$	888.729	+	151.634i	0.158212	+	0.0269939i
$317$	35.1444	+	60.8718i	0.00622683	+	0.0107852i	0.869122	−	0.494598i	$-0.164685\pi$
$317$	35.1444	+	60.8718i	0.00622683	+	0.0107852i	−0.862895	+	0.505383i	$0.831351\pi$
$318$		0			0
$319$	319.748	+	184.607i	0.0561205	+	0.0324012i
$320$	770.584	+	1284.88i	0.134615	+	0.224459i
$321$		0			0
$322$	−1702.10	−	614.180i	−0.294579	−	0.106295i
$323$		−	50.0113i		−	0.00861518i
$324$		0			0
$325$			5021.36i			0.857030i
$326$	1845.55	−	5114.66i	0.313545	−	0.868940i
$327$		0			0
$328$	−7444.99	+	61.8827i	−1.25329	+	0.0104174i
$329$	1489.54	+	859.986i	0.249608	+	0.144111i
$330$		0			0
$331$	4684.34	+	8113.51i	0.777868	+	1.34731i	0.933168	+	0.359440i	$0.117032\pi$
$331$	4684.34	+	8113.51i	0.777868	+	1.34731i	−0.155300	+	0.987867i	$0.549634\pi$
$332$	−7807.66	−	1332.13i	−1.29067	−	0.220212i
$333$		0			0
$334$	−4783.44	−	5668.71i	−0.783648	−	0.928677i
$335$	369.771	+	640.463i	0.0603067	+	0.104454i
$336$		0			0
$337$	3086.72	−	5346.35i	0.498944	−	0.864197i	−0.501055	−	0.865416i	$-0.667055\pi$
$337$	3086.72	−	5346.35i	0.498944	−	0.864197i	0.999999	+	0.00121842i	$0.000387836\pi$
$338$	938.875	−	168.232i	0.151089	−	0.0270729i
$339$		0			0
$340$	26.9539	+	72.7977i	0.00429936	+	0.0116118i
$341$	4998.30			0.793763
$342$		0			0
$343$			3416.08i			0.537758i
$344$	−6891.57	−	3902.84i	−1.08014	−	0.611706i
$345$		0			0
$346$	7716.22	−	1382.63i	1.19892	−	0.214829i
$347$	−5102.09	−	2945.69i	−0.789321	−	0.455715i	0.0504023	−	0.998729i	$-0.483950\pi$
$347$	−5102.09	−	2945.69i	−0.789321	−	0.455715i	−0.839724	+	0.543014i	$0.817283\pi$
$348$		0			0
$349$	8150.29	−	4705.57i	1.25007	−	0.721729i	0.278948	−	0.960306i	$-0.410014\pi$
$349$	8150.29	−	4705.57i	1.25007	−	0.721729i	0.971123	+	0.238577i	$0.0766811\pi$
$350$	−1304.45	+	1100.74i	−0.199217	+	0.168106i
$351$		0			0
$352$	−2666.16	+	1012.44i	−0.403712	+	0.153305i
$353$	6050.47	−	3493.24i	0.912278	−	0.526704i	0.0311148	−	0.999516i	$-0.490094\pi$
$353$	6050.47	−	3493.24i	0.912278	−	0.526704i	0.881163	+	0.472812i	$0.156761\pi$
$354$		0			0
$355$	−1584.97	+	2745.25i	−0.236962	+	0.410430i
$356$	2894.63	−	3488.76i	0.430941	−	0.519394i
$357$		0			0
$358$	5609.46	+	2024.09i	0.828126	+	0.298817i
$359$	3844.64			0.565215			0.282607	−	0.959236i	$-0.408801\pi$
$359$	3844.64			0.565215			0.282607	+	0.959236i	$0.408801\pi$
$360$		0			0
$361$	−6631.54			−0.966838
$362$	−1551.59	−	559.869i	−0.225275	−	0.0812874i
$363$		0			0
$364$	−1376.04	−	1141.70i	−0.198144	−	0.164400i
$365$	−992.590	+	1719.22i	−0.142341	+	0.246542i
$366$		0			0
$367$	−11663.0	+	6733.63i	−1.65886	+	0.957746i	−0.685624	+	0.727956i	$0.740470\pi$
$367$	−11663.0	+	6733.63i	−1.65886	+	0.957746i	−0.973240	+	0.229789i	$0.926196\pi$
$368$	−7453.43	−	2619.66i	−1.05581	−	0.371084i
$369$		0			0
$370$	1813.28	−	1530.10i	0.254778	−	0.214990i
$371$	2339.36	−	1350.63i	0.327368	−	0.189006i
$372$		0			0
$373$	5361.43	+	3095.42i	0.744248	+	0.429692i	0.823612	−	0.567154i	$-0.191956\pi$
$373$	5361.43	+	3095.42i	0.744248	+	0.429692i	−0.0793639	+	0.996846i	$0.525289\pi$
$374$	−145.448	+	26.0622i	−0.0201095	+	0.00360332i
$375$		0			0
$376$	6534.32	+	3700.52i	0.896229	+	0.507553i
$377$			1010.64i			0.138065i
$378$		0			0
$379$	7854.31			1.06451			0.532255	−	0.846584i	$-0.321345\pi$
$379$	7854.31			1.06451			0.532255	+	0.846584i	$0.321345\pi$
$380$	−331.098	+	122.592i	−0.0446973	+	0.0165495i
$381$		0			0
$382$	3467.09	−	621.251i	0.464377	−	0.0832094i
$383$	5216.45	−	9035.15i	0.695948	−	1.20542i	−0.273912	−	0.961755i	$-0.588318\pi$
$383$	5216.45	−	9035.15i	0.695948	−	1.20542i	0.969860	−	0.243662i	$-0.0783489\pi$
$384$		0			0
$385$	119.466	+	206.920i	0.0158144	+	0.0273913i
$386$	−4801.50	−	5690.11i	−0.633134	−	0.750308i
$387$		0			0
$388$	198.814	−	1165.25i	0.0260135	−	0.152466i
$389$	5731.82	+	9927.81i	0.747082	+	1.29398i	0.949216	+	0.314626i	$0.101879\pi$
$389$	5731.82	+	9927.81i	0.747082	+	1.29398i	−0.202133	+	0.979358i	$0.564787\pi$
$390$		0			0
$391$	−354.498	−	204.670i	−0.0458510	−	0.0264721i
$392$	59.4573	+	7153.19i	0.00766084	+	0.921660i
$393$		0			0
$394$	1162.51	−	3221.72i	0.148646	−	0.411950i
$395$		−	329.777i		−	0.0420074i
$396$		0			0
$397$			8809.54i			1.11370i	0.830614	+	0.556849i	$0.187990\pi$
$397$			8809.54i			1.11370i	−0.830614	+	0.556849i	$0.812010\pi$
$398$	5362.87	+	1935.11i	0.675418	+	0.243715i
$399$		0			0
$400$	−5655.11	+	4853.01i	−0.706889	+	0.606626i
$401$	6817.45	+	3936.06i	0.848996	+	0.490168i	0.860312	−	0.509768i	$-0.170269\pi$
$401$	6817.45	+	3936.06i	0.848996	+	0.490168i	−0.0113159	+	0.999936i	$0.503602\pi$
$402$		0			0
$403$	6840.85	+	11848.7i	0.845576	+	1.46458i
$404$	−1973.96	+	11569.4i	−0.243089	+	1.42475i
$405$		0			0
$406$	−262.544	+	221.543i	−0.0320932	+	0.0270813i
$407$	2258.13	+	3911.20i	0.275016	+	0.476341i
$408$		0			0
$409$	170.965	−	296.120i	0.0206691	−	0.0358000i	−0.855506	−	0.517793i	$-0.826754\pi$
$409$	170.965	−	296.120i	0.0206691	−	0.0358000i	0.876175	+	0.481993i	$0.160087\pi$
$410$	480.329	+	2680.63i	0.0578580	+	0.322895i
$411$		0			0
$412$	−3223.77	−	8706.80i	−0.385494	−	1.04115i
$413$	782.451			0.0932249
$414$		0			0
$415$			2897.16i			0.342689i
$416$	−6049.04	−	4934.58i	−0.712929	−	0.581581i
$417$		0			0
$418$	−118.536	−	661.528i	−0.0138703	−	0.0774076i
$419$	−1154.35	−	666.463i	−0.134591	−	0.0777060i	0.431193	−	0.902260i	$-0.358093\pi$
$419$	−1154.35	−	666.463i	−0.134591	−	0.0777060i	−0.565784	+	0.824554i	$0.691426\pi$
$420$		0			0
$421$	5457.42	−	3150.84i	0.631777	−	0.364757i	−0.149663	−	0.988737i	$-0.547819\pi$
$421$	5457.42	−	3150.84i	0.631777	−	0.364757i	0.781440	+	0.623980i	$0.214485\pi$
$422$	−2193.49	−	2599.44i	−0.253027	−	0.299854i
$423$		0			0
$424$	10164.3	−	5981.55i	1.16420	−	0.685117i
$425$	−334.377	+	193.053i	−0.0381639	+	0.0220340i
$426$		0			0
$427$	−1945.08	+	3368.97i	−0.220442	+	0.381817i
$428$	−6355.12	+	7659.53i	−0.717725	+	0.865041i
$429$		0			0
$430$	−983.276	+	2725.00i	−0.110274	+	0.305607i
$431$	1791.33			0.200198			0.100099	−	0.994977i	$-0.468084\pi$
$431$	1791.33			0.200198			0.100099	+	0.994977i	$0.468084\pi$
$432$		0			0
$433$	7947.77			0.882092			0.441046	−	0.897485i	$-0.354608\pi$
$433$	7947.77			0.882092			0.441046	+	0.897485i	$0.354608\pi$
$434$	−1578.47	+	4374.49i	−0.174583	+	0.483830i
$435$		0			0
$436$	−2911.39	+	3508.96i	−0.319794	+	0.385433i
$437$	930.878	−	1612.33i	0.101899	−	0.176495i
$438$		0			0
$439$	−10066.8	+	5812.07i	−1.09445	+	0.631879i	−0.934757	−	0.355288i	$-0.884383\pi$
$439$	−10066.8	+	5812.07i	−1.09445	+	0.631879i	−0.159690	+	0.987167i	$0.551049\pi$
$440$	529.079	+	899.050i	0.0573246	+	0.0974103i
$441$		0			0
$442$	−260.848	−	309.123i	−0.0280707	−	0.0332657i
$443$	−12771.4	+	7373.55i	−1.36972	+	0.790808i	−0.990892	−	0.134660i	$-0.957006\pi$
$443$	−12771.4	+	7373.55i	−1.36972	+	0.790808i	−0.378827	+	0.925467i	$0.623672\pi$
$444$		0			0
$445$	−1436.02	−	829.088i	−0.152975	−	0.0883203i
$446$	654.266	+	3651.34i	0.0694627	+	0.387659i
$447$		0			0
$448$	−44.1089	−	2653.14i	−0.00465167	−	0.279797i
$449$		−	8413.52i		−	0.884317i	−0.896937	−	0.442159i	$-0.854213\pi$
$449$		−	8413.52i		−	0.884317i	0.896937	−	0.442159i	$-0.145787\pi$
$450$		0			0
$451$	−5183.89			−0.541241
$452$	−2645.27	−	7144.40i	−0.275273	−	0.743461i
$453$		0			0
$454$	1437.05	+	8019.92i	0.148555	+	0.829061i
$455$	−327.010	+	566.398i	−0.0336933	+	0.0583585i
$456$		0			0
$457$	−9060.70	−	15693.6i	−0.927443	−	1.60638i	−0.787584	−	0.616208i	$-0.788668\pi$
$457$	−9060.70	−	15693.6i	−0.927443	−	1.60638i	−0.139860	−	0.990171i	$-0.544665\pi$
$458$	9629.99	−	8126.10i	0.982489	−	0.829056i
$459$		0			0
$460$	−486.033	+	2848.65i	−0.0492639	+	0.288737i
$461$	8300.14	+	14376.3i	0.838560	+	1.45243i	0.891099	+	0.453809i	$0.149935\pi$
$461$	8300.14	+	14376.3i	0.838560	+	1.45243i	−0.0525393	+	0.998619i	$0.516731\pi$
$462$		0			0
$463$	9006.61	+	5199.97i	0.904045	+	0.521950i	0.878510	−	0.477724i	$-0.158538\pi$
$463$	9006.61	+	5199.97i	0.904045	+	0.521950i	0.0255344	+	0.999674i	$0.491871\pi$
$464$	−1138.19	+	976.753i	−0.113878	+	0.0977255i
$465$		0			0
$466$	2888.95	+	1042.44i	0.287185	+	0.103626i
$467$		−	4926.33i		−	0.488144i	−0.969757	−	0.244072i	$-0.921517\pi$
$467$		−	4926.33i		−	0.488144i	0.969757	−	0.244072i	$-0.0784833\pi$
$468$		0			0
$469$		−	1309.79i		−	0.128957i
$470$	932.305	−	2583.74i	0.0914979	−	0.253572i
$471$		0			0
$472$	3416.07	−	28.3944i	0.333130	−	0.00276898i
$473$	−4775.63	−	2757.21i	−0.464236	−	0.268027i
$474$		0			0
$475$	−878.042	−	1520.81i	−0.0848154	−	0.146905i
$476$	23.1234	−	135.526i	0.00222659	−	0.0130501i
$477$		0			0
$478$	−5901.20	−	6993.33i	−0.564674	−	0.669179i
$479$	934.274	+	1618.21i	0.0891191	+	0.154359i	0.907139	−	0.420831i	$-0.138261\pi$
$479$	934.274	+	1618.21i	0.0891191	+	0.154359i	−0.818020	+	0.575190i	$0.804928\pi$
$480$		0			0
$481$	−6181.12	+	10706.0i	−0.585935	+	1.01487i
$482$	−3982.59	+	713.621i	−0.376353	+	0.0674368i
$483$		0			0
$484$	8123.36	−	3007.74i	0.762900	−	0.282470i
$485$	−432.385			−0.0404817
$486$		0			0
$487$		−	3289.20i		−	0.306053i	−0.988222	−	0.153026i	$-0.951098\pi$
$487$		−	3289.20i		−	0.306053i	0.988222	−	0.153026i	$-0.0489020\pi$
$488$	−8369.68	+	14779.0i	−0.776388	+	1.37093i
$489$		0			0
$490$	2575.57	−	461.504i	0.237454	−	0.0425482i
$491$	1189.49	+	686.750i	0.109329	+	0.0631214i	0.553668	−	0.832738i	$-0.313228\pi$
$491$	1189.49	+	686.750i	0.109329	+	0.0631214i	−0.444338	+	0.895859i	$0.646561\pi$
$492$		0			0
$493$	−67.2993	+	38.8553i	−0.00614809	+	0.00354960i
$494$	1405.95	−	1186.39i	0.128050	−	0.108053i
$495$		0			0
$496$	−6732.65	+	19155.7i	−0.609485	+	1.73411i
$497$	4862.07	−	2807.11i	0.438820	−	0.253353i
$498$		0			0
$499$	−925.039	+	1602.21i	−0.0829868	+	0.143737i	−0.904532	−	0.426407i	$-0.859779\pi$
$499$	−925.039	+	1602.21i	−0.0829868	+	0.143737i	0.821545	+	0.570144i	$0.193113\pi$
$500$	4349.77	+	3609.01i	0.389056	+	0.322800i
$501$		0			0
$502$	−15707.2	−	5667.72i	−1.39651	−	0.503910i
$503$	−17948.3			−1.59100			−0.795502	−	0.605951i	$-0.792793\pi$
$503$	−17948.3			−1.59100			−0.795502	+	0.605951i	$0.792793\pi$
$504$		0			0
$505$	4293.01			0.378290
$506$	−5174.25	−	1867.06i	−0.454592	−	0.164033i
$507$		0			0
$508$	−6511.94	+	7848.55i	−0.568742	+	0.685478i
$509$	131.163	−	227.180i	0.0114218	−	0.0197831i	−0.860258	−	0.509859i	$-0.829698\pi$
$509$	131.163	−	227.180i	0.0114218	−	0.0197831i	0.871680	+	0.490076i	$0.163031\pi$
$510$		0			0
$511$	3044.88	−	1757.96i	0.263596	−	0.152187i
$512$	−288.853	−	11581.6i	−0.0249328	−	0.999689i
$513$		0			0
$514$	3059.33	−	2581.56i	0.262532	−	0.221533i
$515$	−2941.09	+	1698.04i	−0.251650	+	0.145290i
$516$		0			0
$517$	4528.07	+	2614.28i	0.385192	+	0.222391i
$518$	−4136.19	+	741.143i	−0.350837	+	0.0628648i
$519$		0			0
$520$	−1407.12	+	2484.68i	−0.118666	+	0.209539i
$521$			938.595i			0.0789263i	0.999221	+	0.0394631i	$0.0125648\pi$
$521$			938.595i			0.0789263i	−0.999221	+	0.0394631i	$0.987435\pi$
$522$		0			0
$523$	−7118.07			−0.595127			−0.297563	−	0.954702i	$-0.596174\pi$
$523$	−7118.07			−0.595127			−0.297563	+	0.954702i	$0.596174\pi$
$524$	−1509.11	−	4075.82i	−0.125812	−	0.339796i
$525$		0			0
$526$	15554.7	−	2787.16i	1.28938	−	0.231038i
$527$	−526.011	+	911.078i	−0.0434790	+	0.0753078i
$528$		0			0
$529$	−1535.67	−	2659.87i	−0.126216	−	0.218613i
$530$	−2782.08	−	3296.95i	−0.228011	−	0.270209i
$531$		0			0
$532$	616.401	+	105.170i	0.0502337	+	0.00857083i
$533$	−7094.86	−	12288.7i	−0.576571	−	0.998650i
$534$		0			0
$535$	3152.77	+	1820.25i	0.254777	+	0.147096i
$536$	−47.5311	−	5718.37i	−0.00383028	−	0.460814i
$537$		0			0
$538$	−4829.36	+	13383.8i	−0.387004	+	1.07252i
$539$			4980.71i			0.398023i
$540$		0			0
$541$		−	6529.45i		−	0.518896i	−0.965757	−	0.259448i	$-0.916459\pi$
$541$		−	6529.45i		−	0.518896i	0.965757	−	0.259448i	$-0.0835407\pi$
$542$	3505.30	+	1264.84i	0.277796	+	0.100239i
$543$		0			0
$544$	96.0353	−	592.528i	0.00756889	−	0.0466993i
$545$	1444.33	+	833.887i	0.113520	+	0.0655409i
$546$		0			0
$547$	−902.529	−	1563.23i	−0.0705473	−	0.122192i	0.828594	−	0.559850i	$-0.189141\pi$
$547$	−902.529	−	1563.23i	−0.0705473	−	0.122192i	−0.899141	+	0.437658i	$0.855808\pi$
$548$	19900.2	+	3395.34i	1.55126	+	0.264675i
$549$		0			0
$550$	−3965.42	+	3346.15i	−0.307429	+	0.259419i
$551$	−176.721	−	306.090i	−0.0136635	−	0.0236659i
$552$		0			0
$553$	−292.032	+	505.814i	−0.0224565	+	0.0388959i
$554$	1512.97	+	8443.61i	0.116029	+	0.647536i
$555$		0			0
$556$	−14073.4	+	5210.81i	−1.07347	+	0.397460i
$557$	−25569.6			−1.94510			−0.972550	−	0.232694i	$-0.925246\pi$
$557$	−25569.6			−1.94510			−0.972550	+	0.232694i	$0.925246\pi$
$558$		0			0
$559$		−	15094.5i		−	1.14209i
$560$	−953.929	+	179.126i	−0.0719837	+	0.0135169i
$561$		0			0
$562$	1220.09	+	6809.08i	0.0915769	+	0.511074i
$563$	4254.07	+	2456.09i	0.318451	+	0.183858i	0.650702	−	0.759333i	$-0.274475\pi$
$563$	4254.07	+	2456.09i	0.318451	+	0.183858i	−0.332251	+	0.943191i	$0.607808\pi$
$564$		0			0
$565$	−2413.32	+	1393.33i	−0.179698	+	0.103748i
$566$	15429.9	+	18285.5i	1.14588	+	1.35794i
$567$		0			0
$568$	21125.2	−	12431.9i	1.56055	−	0.918365i
$569$	−13142.2	+	7587.64i	−0.968275	+	0.559034i	−0.898710	−	0.438544i	$-0.855494\pi$
$569$	−13142.2	+	7587.64i	−0.968275	+	0.559034i	−0.0695650	+	0.997577i	$0.522161\pi$
$570$		0			0
$571$	6558.52	−	11359.7i	0.480675	−	0.832554i	−0.519079	−	0.854726i	$-0.673725\pi$
$571$	6558.52	−	11359.7i	0.480675	−	0.832554i	0.999754	+	0.0221726i	$0.00705833\pi$
$572$	−4183.05	−	3470.68i	−0.305773	−	0.253700i
$573$		0			0
$574$	1637.08	−	4536.92i	0.119043	−	0.329908i
$575$	−14373.4			−1.04246
$576$		0			0
$577$	9122.28			0.658173			0.329086	−	0.944300i	$-0.393259\pi$
$577$	9122.28			0.658173			0.329086	+	0.944300i	$0.393259\pi$
$578$	−4705.98	+	13041.9i	−0.338656	+	0.938531i
$579$		0			0
$580$	422.209	+	350.307i	0.0302264	+	0.0250788i
$581$	2565.56	−	4443.68i	0.183197	−	0.317306i
$582$		0			0
$583$	7111.45	−	4105.80i	0.505191	−	0.291672i
$584$	13229.7	−	7785.51i	0.937414	−	0.551655i
$585$		0			0
$586$	−800.294	−	948.404i	−0.0564161	−	0.0668570i
$587$	13405.1	−	7739.45i	0.942570	−	0.544193i	0.0518051	−	0.998657i	$-0.483503\pi$
$587$	13405.1	−	7739.45i	0.942570	−	0.544193i	0.890765	+	0.454464i	$0.150169\pi$
$588$		0			0
$589$	−4143.76	−	2392.40i	−0.289883	−	0.167364i
$590$	−220.395	−	1229.99i	−0.0153789	−	0.0858266i
$591$		0			0
$592$	−18031.1	+	3385.82i	−1.25181	+	0.235062i
$593$			13499.3i			0.934824i	0.884040	+	0.467412i	$0.154813\pi$
$593$			13499.3i			0.934824i	−0.884040	+	0.467412i	$0.845187\pi$
$594$		0			0
$595$	−50.2893			−0.00346498
$596$	14984.2	−	5548.03i	1.02983	−	0.381302i
$597$		0			0
$598$	−2655.73	−	14821.1i	−0.181607	−	1.01351i
$599$	7097.54	−	12293.3i	0.484136	−	0.838548i	−0.515698	−	0.856771i	$-0.672467\pi$
$599$	7097.54	−	12293.3i	0.484136	−	0.838548i	0.999834	+	0.0182222i	$0.00580063\pi$
$600$		0			0
$601$	505.327	+	875.253i	0.0342974	+	0.0594048i	0.882665	−	0.470003i	$-0.155747\pi$
$601$	505.327	+	875.253i	0.0342974	+	0.0594048i	−0.848367	+	0.529408i	$0.822414\pi$
$602$	3921.25	−	3308.88i	0.265479	−	0.224020i
$603$		0			0
$604$	−322.030	−	54.9445i	−0.0216941	−	0.00370142i
$605$	−1584.25	−	2744.00i	−0.106461	−	0.184396i
$606$		0			0
$607$	−7769.04	−	4485.46i	−0.519498	−	0.299933i	0.217231	−	0.976120i	$-0.430298\pi$
$607$	−7769.04	−	4485.46i	−0.519498	−	0.299933i	−0.736729	+	0.676188i	$0.763631\pi$
$608$	2694.93	+	436.787i	0.179760	+	0.0291350i
$609$		0			0
$610$	5843.78	+	2108.65i	0.387882	+	0.139962i
$611$			14312.0i			0.947630i
$612$		0			0
$613$		−	14462.3i		−	0.952897i	−0.879202	−	0.476449i	$-0.841924\pi$
$613$		−	14462.3i		−	0.952897i	0.879202	−	0.476449i	$-0.158076\pi$
$614$	7560.29	−	20952.2i	0.496919	−	1.37713i
$615$		0			0
$616$	−15.3563	−	1847.49i	−0.00100442	−	0.120840i
$617$	−18159.9	−	10484.6i	−1.18491	−	0.684108i	−0.227764	−	0.973716i	$-0.573142\pi$
$617$	−18159.9	−	10484.6i	−1.18491	−	0.684108i	−0.957145	+	0.289608i	$0.906475\pi$
$618$		0			0
$619$	−3168.60	−	5488.18i	−0.205746	−	0.356363i	0.744624	−	0.667484i	$-0.232629\pi$
$619$	−3168.60	−	5488.18i	−0.205746	−	0.356363i	−0.950370	+	0.311121i	$0.899295\pi$
$620$	7321.17	+	1249.13i	0.474234	+	0.0809133i
$621$		0			0
$622$	1944.27	+	2304.09i	0.125334	+	0.148530i
$623$	1468.39	+	2543.32i	0.0944296	+	0.163557i
$624$		0			0
$625$	−6243.62	+	10814.3i	−0.399591	+	0.692113i
$626$	27586.4	−	4943.07i	1.76130	−	0.315599i
$627$		0			0
$628$	3752.94	+	10136.0i	0.238469	+	0.644062i
$629$	−950.565			−0.0602568
$630$		0			0
$631$		−	26190.2i		−	1.65232i	−0.563436	−	0.826160i	$-0.690521\pi$
$631$		−	26190.2i		−	1.65232i	0.563436	−	0.826160i	$-0.309479\pi$
$632$	−1256.62	+	2218.91i	−0.0790909	+	0.139658i
$633$		0			0
$634$	−195.690	+	35.0647i	−0.0122584	+	0.00219653i
$635$	3230.57	+	1865.17i	0.201892	+	0.116562i
$636$		0			0
$637$	−11807.0	+	6816.79i	−0.734397	+	0.424004i
$638$	−798.111	+	673.472i	−0.0495259	+	0.0417916i
$639$		0			0
$640$	−4158.22	+	816.655i	−0.256825	+	0.0504393i
$641$	21831.2	−	12604.3i	1.34521	−	0.776660i	0.357647	−	0.933857i	$-0.383579\pi$
$641$	21831.2	−	12604.3i	1.34521	−	0.776660i	0.987567	+	0.157197i	$0.0502458\pi$
$642$		0			0
$643$	3931.26	−	6809.13i	0.241110	−	0.417614i	−0.719921	−	0.694056i	$-0.755822\pi$
$643$	3931.26	−	6809.13i	0.241110	−	0.417614i	0.961031	+	0.276442i	$0.0891553\pi$
$644$	3268.08	−	3938.87i	0.199970	−	0.241014i
$645$		0			0
$646$	133.056	+	48.0114i	0.00810376	+	0.00292413i
$647$	188.733			0.0114681			0.00573404	−	0.999984i	$-0.498175\pi$
$647$	188.733			0.0114681			0.00573404	+	0.999984i	$0.498175\pi$
$648$		0			0
$649$	2378.58			0.143864
$650$	−13359.4	−	4820.56i	−0.806154	−	0.290889i
$651$		0			0
$652$	11835.9	+	9820.26i	0.710935	+	0.589863i
$653$	15259.4	−	26430.1i	0.914468	−	1.58390i	0.106790	−	0.994282i	$-0.465943\pi$
$653$	15259.4	−	26430.1i	0.914468	−	1.58390i	0.807678	−	0.589623i	$-0.200724\pi$
$654$		0			0
$655$	−1376.78	+	794.884i	−0.0821301	+	0.0474178i
$656$	6982.63	−	19867.0i	0.415588	−	1.18243i
$657$		0			0
$658$	−3717.98	+	3137.35i	−0.220277	+	0.185877i
$659$	16805.7	−	9702.80i	0.993412	−	0.573547i	0.0871197	−	0.996198i	$-0.472234\pi$
$659$	16805.7	−	9702.80i	0.993412	−	0.573547i	0.906292	+	0.422651i	$0.138900\pi$
$660$		0			0
$661$	−26953.4	−	15561.6i	−1.58603	−	0.915696i	−0.993952	−	0.109816i	$-0.964974\pi$
$661$	−26953.4	−	15561.6i	−1.58603	−	0.915696i	−0.592079	−	0.805880i	$-0.701693\pi$
$662$	−26083.2	+	4673.72i	−1.53135	+	0.274395i
$663$		0			0
$664$	11039.6	−	19493.6i	0.645211	−	1.13930i
$665$		−	228.726i		−	0.0133377i
$666$		0			0
$667$	−2892.91			−0.167937
$668$	19673.9	−	7284.42i	1.13953	−	0.421920i
$669$		0			0
$670$	−2058.95	+	368.933i	−0.118723	+	0.0212733i
$671$	−5912.87	+	10241.4i	−0.340185	+	0.589217i
$672$		0			0
$673$	16571.1	+	28701.9i	0.949134	+	1.64395i	0.747254	+	0.664539i	$0.231372\pi$
$673$	16571.1	+	28701.9i	0.949134	+	1.64395i	0.201880	+	0.979410i	$0.435295\pi$
$674$	11260.8	+	13344.8i	0.643546	+	0.762647i
$675$		0			0
$676$	−453.745	+	2659.40i	−0.0258162	+	0.151309i
$677$	−3831.16	−	6635.77i	−0.217494	−	0.376711i	0.736547	−	0.676386i	$-0.236455\pi$
$677$	−3831.16	−	6635.77i	−0.217494	−	0.376711i	−0.954041	+	0.299675i	$0.903122\pi$
$678$		0			0
$679$	663.195	+	382.896i	0.0374832	+	0.0216409i
$680$	−219.556	+	1.82495i	−0.0123817	+	0.000102917i
$681$		0			0
$682$	−4798.43	+	13298.1i	−0.269415	+	0.746642i
$683$		−	8233.45i		−	0.461265i	−0.973041	−	0.230633i	$-0.925920\pi$
$683$		−	8233.45i		−	0.461265i	0.973041	−	0.230633i	$-0.0740795\pi$
$684$		0			0
$685$		−	7384.28i		−	0.411882i
$686$	−9088.56	−	3279.48i	−0.505835	−	0.182523i
$687$		0			0
$688$	16999.6	−	14588.4i	0.942009	−	0.808398i
$689$	19466.0	+	11238.7i	1.07633	+	0.621422i
$690$		0			0
$691$	−9201.53	−	15937.5i	−0.506574	−	0.877412i	−0.999971	−	0.00760808i	$-0.997578\pi$
$691$	−9201.53	−	15937.5i	−0.506574	−	0.877412i	0.493397	−	0.869804i	$-0.335755\pi$
$692$	−3729.14	+	21856.5i	−0.204856	+	1.20067i
$693$		0			0
$694$	12735.1	−	10746.3i	0.696570	−	0.587788i
$695$	2744.66	+	4753.89i	0.149800	+	0.259461i
$696$		0			0
$697$	545.542	−	944.907i	0.0296469	−	0.0513499i
$698$	4694.90	+	26201.4i	0.254591	+	1.42083i
$699$		0			0
$700$	−1676.25	−	4527.25i	−0.0905090	−	0.244448i
$701$	2617.11			0.141008			0.0705041	−	0.997511i	$-0.477539\pi$
$701$	2617.11			0.141008			0.0705041	+	0.997511i	$0.477539\pi$
$702$		0			0
$703$		−	4323.36i		−	0.231947i
$704$	−134.087	−	8065.32i	−0.00717841	−	0.431780i
$705$		0			0
$706$	3485.32	+	19451.0i	0.185796	+	1.03689i
$707$	−6584.64	−	3801.65i	−0.350270	−	0.202229i
$708$		0			0
$709$	−15311.9	+	8840.30i	−0.811070	+	0.468271i	−0.847327	−	0.531071i	$-0.821790\pi$
$709$	−15311.9	+	8840.30i	−0.811070	+	0.468271i	0.0362573	+	0.999342i	$0.488456\pi$
$710$	−5782.20	−	6852.31i	−0.305637	−	0.362201i
$711$		0			0
$712$	6503.06	+	11050.5i	0.342293	+	0.581649i
$713$	−33916.4	+	19581.7i	−1.78146	+	1.02853i
$714$		0			0
$715$	−994.082	+	1721.80i	−0.0519952	+	0.0900583i
$716$	−10770.3	+	12980.9i	−0.562157	+	0.677542i
$717$		0			0
$718$	−3690.89	+	10228.7i	−0.191843	+	0.531662i
$719$	7767.21			0.402876			0.201438	−	0.979501i	$-0.435438\pi$
$719$	7767.21			0.402876			0.201438	+	0.979501i	$0.435438\pi$
$720$		0			0
$721$	6014.74			0.310680
$722$	6366.35	−	17643.4i	0.328159	−	0.909443i
$723$		0			0
$724$	2979.09	−	3590.56i	0.152924	−	0.184312i
$725$	−1364.35	+	2363.13i	−0.0698907	+	0.121054i
$726$		0			0
$727$	9187.03	−	5304.13i	0.468677	−	0.270591i	−0.247009	−	0.969013i	$-0.579448\pi$
$727$	9187.03	−	5304.13i	0.468677	−	0.270591i	0.715686	+	0.698423i	$0.246114\pi$
$728$	4358.54	−	2564.94i	0.221893	−	0.130581i
$729$		0			0
$730$	−3621.12	−	4291.28i	−0.183594	−	0.217572i
$731$	1005.16	−	580.327i	0.0508578	−	0.0293628i
$732$		0			0
$733$	7738.67	+	4467.92i	0.389951	+	0.225138i	0.682139	−	0.731223i	$-0.261050\pi$
$733$	7738.67	+	4467.92i	0.389951	+	0.225138i	−0.292188	+	0.956361i	$0.594383\pi$
$734$	−6718.37	−	37494.0i	−0.337847	−	1.88546i
$735$		0			0
$736$	14125.0	−	17315.1i	0.707413	−	0.867179i
$737$		−	3981.66i		−	0.199005i
$738$		0			0
$739$	5767.08			0.287071			0.143535	−	0.989645i	$-0.454153\pi$
$739$	5767.08			0.287071			0.143535	+	0.989645i	$0.454153\pi$
$740$	2330.10	+	6293.18i	0.115752	+	0.312624i
$741$		0			0
$742$	1347.57	+	7520.53i	0.0666722	+	0.372086i
$743$	711.865	−	1232.99i	0.0351491	−	0.0608801i	−0.847916	−	0.530131i	$-0.822143\pi$
$743$	711.865	−	1232.99i	0.0351491	−	0.0608801i	0.883065	+	0.469251i	$0.155476\pi$
$744$		0			0
$745$	−2922.28	−	5061.54i	−0.143710	−	0.248913i
$746$	−13382.5	+	11292.6i	−0.656793	+	0.554223i
$747$		0			0
$748$	70.2931	−	411.989i	0.00343606	−	0.0201388i
$749$	−3223.82	−	5583.82i	−0.157271	−	0.272401i
$750$		0			0
$751$	16310.8	+	9417.02i	0.792527	+	0.457566i	0.840851	−	0.541266i	$-0.182055\pi$
$751$	16310.8	+	9417.02i	0.792527	+	0.457566i	−0.0483243	+	0.998832i	$0.515388\pi$
$752$	−16118.3	+	13832.2i	−0.781616	+	0.670754i
$753$		0			0
$754$	−2688.82	−	970.223i	−0.129869	−	0.0468613i
$755$			119.495i			0.00576007i
$756$		0			0
$757$			21381.1i			1.02657i	0.858219	+	0.513283i	$0.171571\pi$
$757$			21381.1i			1.02657i	−0.858219	+	0.513283i	$0.828429\pi$
$758$	−7540.23	+	20896.6i	−0.361311	+	1.00132i
$759$		0			0
$760$	−8.30023	−	998.584i	−0.000396159	−	0.0476611i
$761$	−15809.6	−	9127.66i	−0.753083	−	0.434793i	0.0737237	−	0.997279i	$-0.476512\pi$
$761$	−15809.6	−	9127.66i	−0.753083	−	0.434793i	−0.826807	+	0.562486i	$0.809845\pi$
$762$		0			0
$763$	−1476.89	−	2558.04i	−0.0700745	−	0.121373i
$764$	−1675.60	+	9820.68i	−0.0793467	+	0.465052i
$765$		0			0
$766$	19030.4	+	22552.3i	0.897644	+	1.06377i
$767$	3255.42	+	5638.55i	0.153255	+	0.265445i
$768$		0			0
$769$	−7996.45	+	13850.3i	−0.374980	+	0.649484i	−0.990324	−	0.138774i	$-0.955684\pi$
$769$	−7996.45	+	13850.3i	−0.374980	+	0.649484i	0.615344	+	0.788259i	$0.289017\pi$
$770$	−665.205	+	119.195i	−0.0311329	+	0.00557855i
$771$		0			0
$772$	19748.2	−	7311.92i	0.920663	−	0.340883i
$773$	−23733.1			−1.10429			−0.552147	−	0.833747i	$-0.686191\pi$
$773$	−23733.1			−1.10429			−0.552147	+	0.833747i	$0.686191\pi$
$774$		0			0
$775$			36940.4i			1.71218i
$776$	2909.31	+	1647.60i	0.134585	+	0.0762184i
$777$		0			0
$778$	−31915.8	+	5718.83i	−1.47074	+	0.263535i
$779$	4297.62	+	2481.23i	0.197662	+	0.114120i
$780$		0			0
$781$	14780.3	−	8533.39i	0.677182	−	0.390971i
$782$	884.851	−	746.665i	0.0404632	−	0.0341441i
$783$		0			0
$784$	−19088.3	−	6708.96i	−0.869547	−	0.305619i
$785$	3423.86	−	1976.77i	0.155672	−	0.0898775i
$786$		0			0
$787$	3774.80	−	6538.15i	0.170975	−	0.296137i	−0.767786	−	0.640706i	$-0.778642\pi$
$787$	3774.80	−	6538.15i	0.170975	−	0.296137i	0.938761	+	0.344569i	$0.111975\pi$
$788$	7455.44	+	6185.78i	0.337042	+	0.279644i
$789$		0			0
$790$	877.380	+	316.590i	0.0395137	+	0.0142579i
$791$	4935.42			0.221850
$792$		0			0
$793$	−32370.3			−1.44956
$794$	−23438.0	−	8457.26i	−1.04759	−	0.378006i
$795$		0			0
$796$	−10296.8	+	12410.3i	−0.458494	+	0.552602i
$797$	−13480.4	+	23348.7i	−0.599120	+	1.03771i	0.393831	+	0.919183i	$0.371149\pi$
$797$	−13480.4	+	23348.7i	−0.599120	+	1.03771i	−0.992951	+	0.118524i	$0.962184\pi$
$798$		0			0
$799$	−953.051	+	550.244i	−0.0421984	+	0.0243632i
$800$	−7482.56	−	19704.5i	−0.330686	−	0.870823i
$801$		0			0
$802$	−17016.8	+	14359.3i	−0.749232	+	0.632226i
$803$	9256.18	−	5344.06i	0.406779	−	0.234854i
$804$		0			0
$805$	−1621.29	−	936.052i	−0.0709850	−	0.0409832i
$806$	−38091.0	+	6825.35i	−1.66464	+	0.298279i
$807$		0			0
$808$	−28885.6	−	16358.5i	−1.25766	−	0.712240i
$809$			33739.1i			1.46626i	0.680090	+	0.733129i	$0.261941\pi$
$809$			33739.1i			1.46626i	−0.680090	+	0.733129i	$0.738059\pi$
$810$		0			0
$811$	−9809.12			−0.424716			−0.212358	−	0.977192i	$-0.568114\pi$
$811$	−9809.12			−0.424716			−0.212358	+	0.977192i	$0.568114\pi$
$812$	−337.375	−	911.188i	−0.0145807	−	0.0393798i
$813$		0			0
$814$	−12573.7	+	2253.01i	−0.541408	+	0.0970123i
$815$	2812.74	−	4871.82i	0.120891	−	0.209389i
$816$		0			0
$817$	2639.44	+	4571.65i	0.113026	+	0.195767i
$818$	623.705	+	739.135i	0.0266593	+	0.0315932i
$819$		0			0
$820$	−7593.00	−	1295.51i	−0.323365	−	0.0551722i
$821$	9274.38	+	16063.7i	0.394248	+	0.682858i	0.993005	−	0.118073i	$-0.0376716\pi$
$821$	9274.38	+	16063.7i	0.394248	+	0.682858i	−0.598756	+	0.800931i	$0.704338\pi$
$822$		0			0
$823$	1262.62	+	728.972i	0.0534775	+	0.0308753i	0.526500	−	0.850175i	$-0.323504\pi$
$823$	1262.62	+	728.972i	0.0534775	+	0.0308753i	−0.473023	+	0.881050i	$0.656837\pi$
$824$	26259.5	−	218.269i	1.11019	−	0.00922786i
$825$		0			0
$826$	−751.162	+	2081.73i	−0.0316420	+	0.0876908i
$827$		−	42187.5i		−	1.77388i	−0.461881	−	0.886942i	$-0.652825\pi$
$827$		−	42187.5i		−	1.77388i	0.461881	−	0.886942i	$-0.347175\pi$
$828$		0			0
$829$			22370.3i			0.937218i	0.883406	+	0.468609i	$0.155245\pi$
$829$			22370.3i			0.937218i	−0.883406	+	0.468609i	$0.844755\pi$
$830$	−7707.96	−	2781.31i	−0.322346	−	0.116314i
$831$		0			0
$832$	18935.7	−	11356.3i	0.789036	−	0.473210i
$833$	−907.873	−	524.161i	−0.0377622	−	0.0218020i
$834$		0			0
$835$	−3836.89	−	6645.68i	−0.159019	−	0.275429i
$836$	1873.81	+	319.707i	0.0775202	+	0.0132264i
$837$		0			0
$838$	2881.32	−	2431.35i	0.118775	−	0.100226i
$839$	24035.3	+	41630.3i	0.989023	+	1.71304i	0.622476	+	0.782639i	$0.286127\pi$
$839$	24035.3	+	41630.3i	0.989023	+	1.71304i	0.366548	+	0.930399i	$0.380540\pi$
$840$		0			0
$841$	11919.9	−	20645.9i	0.488741	−	0.846524i
$842$	3143.70	+	17544.4i	0.128669	+	0.718077i
$843$		0			0
$844$	9021.63	−	3340.33i	0.367935	−	0.136231i
$845$	986.816			0.0401745
$846$		0			0
$847$			5611.69i			0.227650i
$848$	6156.20	+	32784.7i	0.249298	+	1.32763i
$849$		0			0
$850$	−192.615	−	1074.95i	−0.00777252	−	0.0433771i
$851$	−30645.5	−	17693.2i	−1.23445	−	0.712708i
$852$		0			0
$853$	14708.0	−	8491.65i	0.590377	−	0.340854i	−0.174870	−	0.984592i	$-0.555950\pi$
$853$	14708.0	−	8491.65i	0.590377	−	0.340854i	0.765246	+	0.643737i	$0.222617\pi$
$854$	−7095.93	−	8409.17i	−0.284330	−	0.336951i
$855$		0			0
$856$	−14277.4	−	24261.2i	−0.570082	−	0.968727i
$857$	−22340.4	+	12898.3i	−0.890473	+	0.514115i	−0.874097	−	0.485751i	$-0.838546\pi$
$857$	−22340.4	+	12898.3i	−0.890473	+	0.514115i	−0.0163755	+	0.999866i	$0.505213\pi$
$858$		0			0
$859$	−9914.38	+	17172.2i	−0.393800	+	0.682082i	−0.992947	−	0.118557i	$-0.962173\pi$
$859$	−9914.38	+	17172.2i	−0.393800	+	0.682082i	0.599147	+	0.800639i	$0.295506\pi$
$860$	−6305.96	−	5232.05i	−0.250036	−	0.207455i
$861$		0			0
$862$	−1719.70	+	4765.88i	−0.0679503	+	0.188314i
$863$	42561.4			1.67880			0.839401	−	0.543513i	$-0.182906\pi$
$863$	42561.4			1.67880			0.839401	+	0.543513i	$0.182906\pi$
$864$		0			0
$865$	8110.22			0.318793
$866$	−7629.95	+	21145.2i	−0.299395	+	0.829728i
$867$		0			0
$868$	−10123.1	−	8399.13i	−0.395852	−	0.328439i
$869$	−887.753	+	1537.63i	−0.0346547	+	0.0600237i
$870$		0			0
$871$	9438.71	−	5449.44i	0.367185	−	0.211995i
$872$	−6540.70	−	11114.5i	−0.254009	−	0.431632i
$873$		0			0
$874$	3395.98	+	4024.47i	0.131431	+	0.155755i
$875$	−3171.00	+	1830.78i	−0.122513	+	0.0707331i
$876$		0			0
$877$	13338.6	+	7701.03i	0.513582	+	0.296517i	0.734305	−	0.678820i	$-0.237508\pi$
$877$	13338.6	+	7701.03i	0.513582	+	0.296517i	−0.220723	+	0.975337i	$0.570842\pi$
$878$	−5798.90	−	32362.6i	−0.222897	−	1.24395i
$879$		0			0
$880$	−2899.86	+	544.527i	−0.111085	+	0.0208591i
$881$			408.896i			0.0156368i	0.999969	+	0.00781842i	$0.00248871\pi$
$881$			408.896i			0.0156368i	−0.999969	+	0.00781842i	$0.997511\pi$
$882$		0			0
$883$	24945.2			0.950704			0.475352	−	0.879796i	$-0.342321\pi$
$883$	24945.2			0.950704			0.475352	+	0.879796i	$0.342321\pi$
$884$	1072.84	−	397.229i	0.0408186	−	0.0151134i
$885$		0			0
$886$	−7356.83	−	41057.2i	−0.278959	−	1.55682i
$887$	−5014.93	+	8686.11i	−0.189836	+	0.328806i	−0.945196	−	0.326505i	$-0.894129\pi$
$887$	−5014.93	+	8686.11i	−0.189836	+	0.328806i	0.755359	+	0.655311i	$0.227462\pi$
$888$		0			0
$889$	−3303.37	−	5721.61i	−0.124625	−	0.215857i
$890$	3584.40	−	3024.63i	0.134999	−	0.113917i
$891$		0			0
$892$	−10342.6	−	1764.64i	−0.388223	−	0.0662382i
$893$	−2502.62	−	4334.66i	−0.0937815	−	0.162434i
$894$		0			0
$895$	5343.12	+	3084.85i	0.199554	+	0.115213i
$896$	7101.08	+	2429.69i	0.264766	+	0.0905919i
$897$		0			0
$898$	22384.3	+	8077.07i	0.831821	+	0.300151i
$899$			7434.91i			0.275827i
$900$		0			0
$901$			1728.34i			0.0639062i
$902$	4976.59	−	13791.9i	0.183706	−	0.509111i
$903$		0			0
$904$	21547.3	−	179.101i	0.792759	−	0.00658941i
$905$	−1477.92	−	853.278i	−0.0542848	−	0.0313413i
$906$		0			0
$907$	3767.44	+	6525.40i	0.137923	+	0.238889i	0.926710	−	0.375777i	$-0.122624\pi$
$907$	3767.44	+	6525.40i	0.137923	+	0.238889i	−0.788788	+	0.614666i	$0.789291\pi$
$908$	−22716.8	−	3875.91i	−0.830267	−	0.141659i
$909$		0			0
$910$	−1192.98	−	1413.76i	−0.0434581	−	0.0515009i
$911$	−11159.9	−	19329.6i	−0.405867	−	0.702983i	0.588555	−	0.808457i	$-0.299697\pi$
$911$	−11159.9	−	19329.6i	−0.405867	−	0.702983i	−0.994422	+	0.105475i	$0.966364\pi$
$912$		0			0
$913$	7799.08	−	13508.4i	0.282708	−	0.489664i
$914$	50451.5	−	9040.16i	1.82581	−	0.327158i
$915$		0			0
$916$	12374.8	+	33422.0i	0.446368	+	1.20556i
$917$	2815.62			0.101396
$918$		0			0
$919$			40992.7i			1.47141i	0.677303	+	0.735704i	$0.263149\pi$
$919$			40992.7i			1.47141i	−0.677303	+	0.735704i	$0.736851\pi$
$920$	−7112.29	−	4027.84i	−0.254875	−	0.144341i
$921$		0			0
$922$	−46216.6	+	8281.33i	−1.65083	+	0.295804i
$923$	40457.6	+	23358.2i	1.44277	+	0.832985i
$924$		0			0
$925$	−28906.1	+	16688.9i	−1.02749	+	0.593220i
$926$	−22481.1	+	18970.3i	−0.797812	+	0.673220i
$927$		0			0
$928$	−1506.00	−	3965.88i	−0.0532724	−	0.140287i
$929$	20199.6	−	11662.2i	0.713376	−	0.411868i	−0.0989336	−	0.995094i	$-0.531543\pi$
$929$	20199.6	−	11662.2i	0.713376	−	0.411868i	0.812310	+	0.583226i	$0.198210\pi$
$930$		0			0
$931$	2383.99	−	4129.18i	0.0839226	−	0.145358i
$932$	−5546.85	+	6685.36i	−0.194950	+	0.234964i
$933$		0			0
$934$	13106.6	+	4729.33i	0.459166	+	0.165684i
$935$	−152.875			−0.00534712
$936$		0			0
$937$	−29355.3			−1.02348			−0.511738	−	0.859142i	$-0.670998\pi$
$937$	−29355.3			−1.02348			−0.511738	+	0.859142i	$0.670998\pi$
$938$	3484.73	+	1257.42i	0.121301	+	0.0437698i
$939$		0			0
$940$	5979.07	+	4960.84i	0.207463	+	0.172133i
$941$	−1391.16	+	2409.56i	−0.0481939	+	0.0834743i	−0.889116	−	0.457682i	$-0.848680\pi$
$941$	−1391.16	+	2409.56i	−0.0481939	+	0.0834743i	0.840922	+	0.541156i	$0.182013\pi$
$942$		0			0
$943$	35175.8	−	20308.7i	1.21472	−	0.701319i
$944$	−3203.92	+	9115.79i	−0.110465	+	0.314294i
$945$		0			0
$946$	11920.3	−	10058.7i	0.409685	−	0.345705i
$947$	−15438.1	+	8913.16i	−0.529746	+	0.305849i	−0.740913	−	0.671601i	$-0.765607\pi$
$947$	−15438.1	+	8913.16i	−0.529746	+	0.305849i	0.211167	+	0.977450i	$0.432274\pi$
$948$		0			0
$949$	25336.7	+	14628.1i	0.866663	+	0.500368i
$950$	4889.09	−	876.052i	0.166971	−	0.0299188i
$951$		0			0
$952$	338.372	+	191.627i	0.0115196	+	0.00652381i
$953$		−	21508.9i		−	0.731104i	−0.930791	−	0.365552i	$-0.880880\pi$
$953$		−	21508.9i		−	0.731104i	0.930791	−	0.365552i	$-0.119120\pi$
$954$		0			0
$955$	3644.13			0.123478
$956$	24271.1	−	8986.58i	0.821113	−	0.304024i
$957$		0			0
$958$	−5202.20	+	932.156i	−0.175444	+	0.0314370i
$959$	−6539.10	+	11326.1i	−0.220186	+	0.381374i
$960$		0			0
$961$	35430.4	+	61367.2i	1.18930	+	2.05992i
$962$	−22549.6	−	26722.9i	−0.755747	−	0.895614i
$963$		0			0
$964$	1924.73	−	11280.9i	0.0643064	−	0.376900i
$965$	−3851.37	−	6670.76i	−0.128477	−	0.222528i
$966$		0			0
$967$	−8410.42	−	4855.76i	−0.279691	−	0.161479i	0.353593	−	0.935399i	$-0.384960\pi$
$967$	−8410.42	−	4855.76i	−0.279691	−	0.161479i	−0.633283	+	0.773920i	$0.718293\pi$
$968$	203.643	+	24499.8i	0.00676170	+	0.813486i
$969$		0			0
$970$	415.095	−	1150.37i	0.0137401	−	0.0380785i
$971$		−	1908.56i		−	0.0630777i	−0.999503	−	0.0315389i	$-0.989959\pi$
$971$		−	1908.56i		−	0.0630777i	0.999503	−	0.0315389i	$-0.0100408\pi$
$972$		0			0
$973$		−	9722.06i		−	0.320324i
$974$	8750.98	+	3157.67i	0.287885	+	0.103879i
$975$		0			0
$976$	−31285.0	−	36455.8i	−1.02603	−	1.19562i
$977$	40899.7	+	23613.4i	1.33930	+	0.773245i	0.986704	−	0.162531i	$-0.0519656\pi$
$977$	40899.7	+	23613.4i	1.33930	+	0.773245i	0.352596	+	0.935776i	$0.385299\pi$
$978$		0			0
$979$	4463.77	+	7731.47i	0.145723	+	0.252399i
$980$	−1244.74	+	7295.41i	−0.0405731	+	0.237799i
$981$		0			0
$982$	−2969.03	+	2505.37i	−0.0964824	+	0.0814149i
$983$	−11777.7	−	20399.5i	−0.382146	−	0.661895i	0.609223	−	0.792999i	$-0.291481\pi$
$983$	−11777.7	−	20399.5i	−0.382146	−	0.661895i	−0.991369	+	0.131103i	$0.958148\pi$
$984$		0			0
$985$	1771.75	−	3068.76i	0.0573123	−	0.0992678i
$986$	−38.7672	−	216.353i	−0.00125213	−	0.00698791i
$987$		0			0
$988$	1806.68	+	4879.51i	0.0581762	+	0.157123i
$989$	43207.3			1.38919
$990$		0			0
$991$			31768.2i			1.01831i	0.860673	+	0.509157i	$0.170043\pi$
$991$			31768.2i			1.01831i	−0.860673	+	0.509157i	$0.829957\pi$
$992$	−44500.7	−	36302.0i	−1.42429	−	1.16189i
$993$		0			0
$994$	2800.75	+	15630.5i	0.0893707	+	0.498762i
$995$	5108.24	+	2949.24i	0.162756	+	0.0939672i
$996$		0			0
$997$	−3600.15	+	2078.55i	−0.114361	+	0.0660263i	−0.556089	−	0.831122i	$-0.687699\pi$
$997$	−3600.15	+	2078.55i	−0.114361	+	0.0660263i	0.441729	+	0.897149i	$0.354365\pi$
$998$	−3374.68	−	3999.23i	−0.107038	−	0.126847i
$999$		0			0

Display

a_p

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p

up to: 50 250 1000 (See

a_n

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.4.l.b.179.13		64
3.2	odd	2		72.4.l.b.59.20	yes	64
4.3	odd	2		864.4.p.b.719.15		64
8.3	odd	2	inner	216.4.l.b.179.3		64
8.5	even	2		864.4.p.b.719.18		64
9.2	odd	6	inner	216.4.l.b.35.3		64
9.7	even	3		72.4.l.b.11.30	yes	64
12.11	even	2		288.4.p.b.239.8		64
24.5	odd	2		288.4.p.b.239.7		64
24.11	even	2		72.4.l.b.59.30	yes	64
36.7	odd	6		288.4.p.b.47.7		64
36.11	even	6		864.4.p.b.143.18		64
72.11	even	6	inner	216.4.l.b.35.13		64
72.29	odd	6		864.4.p.b.143.15		64
72.43	odd	6		72.4.l.b.11.20	✓	64
72.61	even	6		288.4.p.b.47.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.20	✓	64	72.43	odd	6
72.4.l.b.11.30	yes	64	9.7	even	3
72.4.l.b.59.20	yes	64	3.2	odd	2
72.4.l.b.59.30	yes	64	24.11	even	2
216.4.l.b.35.3		64	9.2	odd	6	inner
216.4.l.b.35.13		64	72.11	even	6	inner
216.4.l.b.179.3		64	8.3	odd	2	inner
216.4.l.b.179.13		64	1.1	even	1	trivial
288.4.p.b.47.7		64	36.7	odd	6
288.4.p.b.47.8		64	72.61	even	6
288.4.p.b.239.7		64	24.5	odd	2
288.4.p.b.239.8		64	12.11	even	2
864.4.p.b.143.15		64	72.29	odd	6
864.4.p.b.143.18		64	36.11	even	6
864.4.p.b.719.15		64	4.3	odd	2
864.4.p.b.719.18		64	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	216.4.l.b.179.13

Level	$216$
Weight	$4$
Character	216.179
Analytic conductor	$12.744$
Analytic rank	$0$
Dimension	$64$
Inner twists	$4$