LMFDB - Embedded newform 570.2.n.a.179.2

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.n (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.2
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.2

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.68343 + 0.407506i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.16632 + 0.554116i) q^{5} +(1.66165 + 0.488805i) q^{6} +1.83012i q^{7} -1.00000i q^{8} +(2.66788 - 1.37202i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.68343 + 0.407506i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.16632 + 0.554116i) q^{5} +(1.66165 + 0.488805i) q^{6} +1.83012i q^{7} -1.00000i q^{8} +(2.66788 - 1.37202i) q^{9} +(-1.59903 - 1.56304i) q^{10} +0.0175522i q^{11} +(-1.19463 - 1.25414i) q^{12} +(1.18833 + 2.05825i) q^{13} +(0.915058 - 1.58493i) q^{14} +(-3.87266 - 0.0500261i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.822112 - 1.42394i) q^{17} +(-2.99646 - 0.145739i) q^{18} +(-4.33467 - 0.458984i) q^{19} +(0.603283 + 2.15315i) q^{20} +(-0.745783 - 3.08087i) q^{21} +(0.00877612 - 0.0152007i) q^{22} +(0.470036 + 0.814125i) q^{23} +(0.407506 + 1.68343i) q^{24} +(4.38591 + 2.40079i) q^{25} -2.37667i q^{26} +(-3.93208 + 3.39687i) q^{27} +(-1.58493 + 0.915058i) q^{28} +(-0.234207 - 0.405658i) q^{29} +(3.32881 + 1.97965i) q^{30} +6.34473i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.00715264 - 0.0295480i) q^{33} +(-1.42394 + 0.822112i) q^{34} +(-1.01410 + 3.96462i) q^{35} +(2.52214 + 1.62444i) q^{36} +3.63380 q^{37} +(3.52444 + 2.56482i) q^{38} +(-2.83923 - 2.98068i) q^{39} +(0.554116 - 2.16632i) q^{40} +(-3.33436 + 5.77528i) q^{41} +(-0.894570 + 3.04101i) q^{42} +(7.15578 + 4.13139i) q^{43} +(-0.0152007 + 0.00877612i) q^{44} +(6.53974 - 1.49392i) q^{45} -0.940071i q^{46} +(3.00121 + 5.19826i) q^{47} +(0.488805 - 1.66165i) q^{48} +3.65067 q^{49} +(-2.59792 - 4.27210i) q^{50} +(-0.803705 + 2.73212i) q^{51} +(-1.18833 + 2.05825i) q^{52} +(-6.48959 + 3.74677i) q^{53} +(5.10372 - 0.975733i) q^{54} +(-0.00972597 + 0.0380238i) q^{55} +1.83012 q^{56} +(7.48415 - 0.993734i) q^{57} +0.468414i q^{58} +(5.69687 - 9.86726i) q^{59} +(-1.89301 - 3.37884i) q^{60} +(4.23617 + 7.33727i) q^{61} +(3.17236 - 5.49469i) q^{62} +(2.51095 + 4.88253i) q^{63} -1.00000 q^{64} +(1.43380 + 5.11732i) q^{65} +(-0.00857962 + 0.0291656i) q^{66} +(2.42123 + 4.19369i) q^{67} +1.64422 q^{68} +(-1.12303 - 1.17898i) q^{69} +(2.86055 - 2.92642i) q^{70} +(-4.63854 + 8.03419i) q^{71} +(-1.37202 - 2.66788i) q^{72} +(3.78470 + 2.18510i) q^{73} +(-3.14696 - 1.81690i) q^{74} +(-8.36171 - 2.25427i) q^{75} +(-1.76984 - 3.98342i) q^{76} -0.0321226 q^{77} +(0.968506 + 4.00095i) q^{78} +(-6.49918 - 3.75230i) q^{79} +(-1.56304 + 1.59903i) q^{80} +(5.23515 - 7.32074i) q^{81} +(5.77528 - 3.33436i) q^{82} -11.9877 q^{83} +(2.29522 - 2.18630i) q^{84} +(2.56999 - 2.62917i) q^{85} +(-4.13139 - 7.15578i) q^{86} +(0.559579 + 0.587457i) q^{87} +0.0175522 q^{88} +(-0.189295 - 0.327868i) q^{89} +(-6.41054 - 1.97610i) q^{90} +(-3.76685 + 2.17479i) q^{91} +(-0.470036 + 0.814125i) q^{92} +(-2.58551 - 10.6809i) q^{93} -6.00243i q^{94} +(-9.13596 - 3.39621i) q^{95} +(-1.25414 + 1.19463i) q^{96} +(-1.26367 + 2.18875i) q^{97} +(-3.16158 - 1.82534i) q^{98} +(0.0240819 + 0.0468272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80q + 40q^{4} + O(q^{10}) $	$ 80q + 40q^{4} + 30q^{15} - 40q^{16} + 8q^{19} + 8q^{25} - 4q^{30} + 48q^{39} + 12q^{45} - 128q^{49} - 36q^{54} + 12q^{55} + 30q^{60} - 24q^{61} - 80q^{64} + 4q^{66} + 36q^{70} + 16q^{76} + 24q^{79} + 32q^{81} - 8q^{85} - 54q^{90} + 24q^{91} - 60q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.68343	+	0.407506i	−0.971929	+	0.235274i
$3$	−1.68343	+	0.407506i	−0.971929	+	0.235274i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.16632	+	0.554116i	0.968809	+	0.247808i
$5$	2.16632	+	0.554116i	0.968809	+	0.247808i
$6$	1.66165	+	0.488805i	0.678364	+	0.199554i
$7$			1.83012i			0.691719i	0.938286	+	0.345860i	$0.112413\pi$
$7$			1.83012i			0.691719i	−0.938286	+	0.345860i	$0.887587\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.66788	−	1.37202i	0.889293	−	0.457339i
$10$	−1.59903	−	1.56304i	−0.505659	−	0.494277i
$11$			0.0175522i			0.00529220i	0.999996	+	0.00264610i	$0.000842280\pi$
$11$			0.0175522i			0.00529220i	−0.999996	+	0.00264610i	$0.999158\pi$
$12$	−1.19463	−	1.25414i	−0.344859	−	0.362039i
$13$	1.18833	+	2.05825i	0.329584	+	0.570857i	0.982429	−	0.186635i	$-0.0597580\pi$
$13$	1.18833	+	2.05825i	0.329584	+	0.570857i	−0.652845	+	0.757492i	$0.726425\pi$
$14$	0.915058	−	1.58493i	0.244560	−	0.423590i
$15$	−3.87266	−	0.0500261i	−0.999917	−	0.0129167i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.822112	−	1.42394i	0.199391	−	0.345356i	−0.748940	−	0.662638i	$-0.769437\pi$
$17$	0.822112	−	1.42394i	0.199391	−	0.345356i	0.948331	+	0.317282i	$0.102770\pi$
$18$	−2.99646	−	0.145739i	−0.706272	−	0.0343510i
$19$	−4.33467	−	0.458984i	−0.994441	−	0.105298i
$19$	−4.33467	−	0.458984i	−0.994441	−	0.105298i
$20$	0.603283	+	2.15315i	0.134898	+	0.481459i
$21$	−0.745783	−	3.08087i	−0.162743	−	0.672302i
$22$	0.00877612	−	0.0152007i	0.00187107	−	0.00324080i
$23$	0.470036	+	0.814125i	0.0980092	+	0.169757i	0.910861	−	0.412714i	$-0.135419\pi$
$23$	0.470036	+	0.814125i	0.0980092	+	0.169757i	−0.812851	+	0.582471i	$0.802086\pi$
$24$	0.407506	+	1.68343i	0.0831818	+	0.343629i
$25$	4.38591	+	2.40079i	0.877182	+	0.480157i
$26$		−	2.37667i		−	0.466103i
$27$	−3.93208	+	3.39687i	−0.756730	+	0.653728i
$28$	−1.58493	+	0.915058i	−0.299523	+	0.172930i
$29$	−0.234207	−	0.405658i	−0.0434911	−	0.0753288i	0.843460	−	0.537191i	$-0.180515\pi$
$29$	−0.234207	−	0.405658i	−0.0434911	−	0.0753288i	−0.886952	+	0.461863i	$0.847181\pi$
$30$	3.32881	+	1.97965i	0.607755	+	0.361434i
$31$			6.34473i			1.13955i	0.821802	+	0.569773i	$0.192969\pi$
$31$			6.34473i			1.13955i	−0.821802	+	0.569773i	$0.807031\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.00715264	−	0.0295480i	−0.00124511	−	0.00514364i
$34$	−1.42394	+	0.822112i	−0.244204	+	0.140991i
$35$	−1.01410	+	3.96462i	−0.171414	+	0.670144i
$36$	2.52214	+	1.62444i	0.420357	+	0.270740i
$37$	3.63380			0.597393			0.298697	−	0.954348i	$-0.403448\pi$
$37$	3.63380			0.597393			0.298697	+	0.954348i	$0.403448\pi$
$38$	3.52444	+	2.56482i	0.571740	+	0.416070i
$39$	−2.83923	−	2.98068i	−0.454640	−	0.477290i
$40$	0.554116	−	2.16632i	0.0876134	−	0.342526i
$41$	−3.33436	+	5.77528i	−0.520740	+	0.901948i	0.478969	+	0.877832i	$0.341011\pi$
$41$	−3.33436	+	5.77528i	−0.520740	+	0.901948i	−0.999709	+	0.0241163i	$0.992323\pi$
$42$	−0.894570	+	3.04101i	−0.138035	+	0.469238i
$43$	7.15578	+	4.13139i	1.09125	+	0.630031i	0.933908	−	0.357513i	$-0.116375\pi$
$43$	7.15578	+	4.13139i	1.09125	+	0.630031i	0.157338	+	0.987545i	$0.449709\pi$
$44$	−0.0152007	+	0.00877612i	−0.00229159	+	0.00132305i
$45$	6.53974	−	1.49392i	0.974887	−	0.222700i
$46$		−	0.940071i		−	0.138606i
$47$	3.00121	+	5.19826i	0.437772	+	0.758244i	0.997517	−	0.0704212i	$-0.0224343\pi$
$47$	3.00121	+	5.19826i	0.437772	+	0.758244i	−0.559745	+	0.828665i	$0.689101\pi$
$48$	0.488805	−	1.66165i	0.0705529	−	0.239838i
$49$	3.65067			0.521525
$50$	−2.59792	−	4.27210i	−0.367401	−	0.604166i
$51$	−0.803705	+	2.73212i	−0.112541	+	0.382573i
$52$	−1.18833	+	2.05825i	−0.164792	+	0.285428i
$53$	−6.48959	+	3.74677i	−0.891414	+	0.514658i	−0.874405	−	0.485197i	$-0.838748\pi$
$53$	−6.48959	+	3.74677i	−0.891414	+	0.514658i	−0.0170090	+	0.999855i	$0.505414\pi$
$54$	5.10372	−	0.975733i	0.694528	−	0.132780i
$55$	−0.00972597	+	0.0380238i	−0.00131145	+	0.00512713i
$56$	1.83012			0.244560
$57$	7.48415	−	0.993734i	0.991300	−	0.131623i
$58$			0.468414i			0.0615057i
$59$	5.69687	−	9.86726i	0.741669	−	1.28461i	−0.210066	−	0.977687i	$-0.567368\pi$
$59$	5.69687	−	9.86726i	0.741669	−	1.28461i	0.951735	−	0.306921i	$-0.0992988\pi$
$60$	−1.89301	−	3.37884i	−0.244386	−	0.436206i
$61$	4.23617	+	7.33727i	0.542387	+	0.939441i	0.998766	+	0.0496560i	$0.0158125\pi$
$61$	4.23617	+	7.33727i	0.542387	+	0.939441i	−0.456380	+	0.889785i	$0.650854\pi$
$62$	3.17236	−	5.49469i	0.402890	−	0.697827i
$63$	2.51095	+	4.88253i	0.316350	+	0.615141i
$64$	−1.00000			−0.125000
$65$	1.43380	+	5.11732i	0.177841	+	0.634725i
$66$	−0.00857962	+	0.0291656i	−0.00105608	+	0.00359004i
$67$	2.42123	+	4.19369i	0.295800	+	0.512341i	0.975171	−	0.221454i	$-0.0710804\pi$
$67$	2.42123	+	4.19369i	0.295800	+	0.512341i	−0.679370	+	0.733796i	$0.737747\pi$
$68$	1.64422			0.199391
$69$	−1.12303	−	1.17898i	−0.135197	−	0.141933i
$70$	2.86055	−	2.92642i	0.341901	−	0.349774i
$71$	−4.63854	+	8.03419i	−0.550494	+	0.953483i	0.447745	+	0.894161i	$0.352227\pi$
$71$	−4.63854	+	8.03419i	−0.550494	+	0.953483i	−0.998239	+	0.0593220i	$0.981106\pi$
$72$	−1.37202	−	2.66788i	−0.161694	−	0.314412i
$73$	3.78470	+	2.18510i	0.442966	+	0.255746i	0.704855	−	0.709352i	$-0.251012\pi$
$73$	3.78470	+	2.18510i	0.442966	+	0.255746i	−0.261889	+	0.965098i	$0.584346\pi$
$74$	−3.14696	−	1.81690i	−0.365827	−	0.211210i
$75$	−8.36171	−	2.25427i	−0.965527	−	0.260301i
$76$	−1.76984	−	3.98342i	−0.203015	−	0.456930i
$77$	−0.0321226			−0.00366071
$78$	0.968506	+	4.00095i	0.109662	+	0.453019i
$79$	−6.49918	−	3.75230i	−0.731214	−	0.422167i	0.0876519	−	0.996151i	$-0.472064\pi$
$79$	−6.49918	−	3.75230i	−0.731214	−	0.422167i	−0.818866	+	0.573984i	$0.805397\pi$
$80$	−1.56304	+	1.59903i	−0.174753	+	0.178777i
$81$	5.23515	−	7.32074i	0.581683	−	0.813416i
$82$	5.77528	−	3.33436i	0.637773	−	0.368219i
$83$	−11.9877			−1.31583			−0.657913	−	0.753094i	$-0.728560\pi$
$83$	−11.9877			−1.31583			−0.657913	+	0.753094i	$0.728560\pi$
$84$	2.29522	−	2.18630i	0.250429	−	0.238545i
$85$	2.56999	−	2.62917i	0.278754	−	0.285173i
$86$	−4.13139	−	7.15578i	−0.445499	−	0.771628i
$87$	0.559579	+	0.587457i	0.0599931	+	0.0629820i
$88$	0.0175522			0.00187107
$89$	−0.189295	−	0.327868i	−0.0200652	−	0.0347539i	0.855818	−	0.517276i	$-0.173054\pi$
$89$	−0.189295	−	0.327868i	−0.0200652	−	0.0347539i	−0.875884	+	0.482522i	$0.839721\pi$
$90$	−6.41054	−	1.97610i	−0.675730	−	0.208299i
$91$	−3.76685	+	2.17479i	−0.394873	+	0.227980i
$92$	−0.470036	+	0.814125i	−0.0490046	+	0.0848784i
$93$	−2.58551	−	10.6809i	−0.268105	−	1.10756i
$94$		−	6.00243i		−	0.619103i
$95$	−9.13596	−	3.39621i	−0.937330	−	0.348444i
$96$	−1.25414	+	1.19463i	−0.128000	+	0.121926i
$97$	−1.26367	+	2.18875i	−0.128307	+	0.222234i	−0.923021	−	0.384750i	$-0.874287\pi$
$97$	−1.26367	+	2.18875i	−0.128307	+	0.222234i	0.794714	+	0.606984i	$0.207621\pi$
$98$	−3.16158	−	1.82534i	−0.319367	−	0.184387i
$99$	0.0240819	+	0.0468272i	0.00242033	+	0.00470631i
$100$	0.113813	+	4.99870i	0.0113813	+	0.499870i
$101$	−4.40332	+	2.54226i	−0.438147	+	0.252964i	−0.702811	−	0.711376i	$-0.748072\pi$
$101$	−4.40332	+	2.54226i	−0.438147	+	0.252964i	0.264664	+	0.964341i	$0.414739\pi$
$102$	2.06209	−	1.96423i	0.204177	−	0.194488i
$103$	2.58734			0.254938			0.127469	−	0.991843i	$-0.459315\pi$
$103$	2.58734			0.254938			0.127469	+	0.991843i	$0.459315\pi$
$104$	2.05825	−	1.18833i	0.201828	−	0.116526i
$105$	0.0915536	−	7.08742i	0.00893472	−	0.691661i
$106$	7.49353			0.727836
$107$		−	14.2675i		−	1.37929i	−0.724146	−	0.689646i	$-0.757766\pi$
$107$		−	14.2675i		−	1.37929i	0.724146	−	0.689646i	$-0.242234\pi$
$108$	−4.90782	−	1.70685i	−0.472255	−	0.164242i
$109$	−14.7909	−	8.53953i	−1.41671	−	0.817938i	−0.420703	−	0.907199i	$-0.638216\pi$
$109$	−14.7909	−	8.53953i	−1.41671	−	0.817938i	−0.996008	+	0.0892602i	$0.971550\pi$
$110$	0.0274348	−	0.0280666i	0.00261581	−	0.00267605i
$111$	−6.11725	+	1.48079i	−0.580624	+	0.140551i
$112$	−1.58493	−	0.915058i	−0.149762	−	0.0864649i
$113$		−	13.8676i		−	1.30456i	−0.757980	−	0.652278i	$-0.773813\pi$
$113$		−	13.8676i		−	1.30456i	0.757980	−	0.652278i	$-0.226187\pi$
$114$	−6.97833	−	2.88148i	−0.653581	−	0.269875i
$115$	0.567129	+	2.02411i	0.0528851	+	0.188749i
$116$	0.234207	−	0.405658i	0.0217456	−	0.0376644i
$117$	5.99429	+	3.86076i	0.554172	+	0.356927i
$118$	−9.86726	+	5.69687i	−0.908355	+	0.524439i
$119$	2.60598	+	1.50456i	0.238889	+	0.137923i
$120$	−0.0500261	+	3.87266i	−0.00456674	+	0.353524i
$121$	10.9997			0.999972
$122$		−	8.47235i		−	0.767050i
$123$	3.25971	−	11.0811i	0.293918	−	0.999146i
$124$	−5.49469	+	3.17236i	−0.493438	+	0.284887i
$125$	8.17099	+	7.63118i	0.730835	+	0.682554i
$126$	0.266719	−	5.48387i	0.0237612	−	0.488542i
$127$	8.97167	+	15.5394i	0.796107	+	1.37890i	0.922134	+	0.386872i	$0.126444\pi$
$127$	8.97167	+	15.5394i	0.796107	+	1.37890i	−0.126026	+	0.992027i	$0.540222\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−13.7298	−	4.03889i	−1.20884	−	0.355604i
$130$	1.31695	−	5.14863i	0.115504	−	0.451565i
$131$	3.22196	+	1.86020i	0.281504	+	0.162526i	0.634104	−	0.773248i	$-0.281369\pi$
$131$	3.22196	+	1.86020i	0.281504	+	0.162526i	−0.352600	+	0.935774i	$0.614702\pi$
$132$	0.0220130	−	0.0209684i	0.00191598	−	0.00182506i
$133$	0.839994	−	7.93295i	0.0728367	−	0.687874i
$134$		−	4.84246i		−	0.418325i
$135$	−10.4004	+	5.17989i	−0.895126	+	0.445814i
$136$	−1.42394	−	0.822112i	−0.122102	−	0.0704955i
$137$	0.467172	+	0.809165i	0.0399132	+	0.0691316i	0.885292	−	0.465036i	$-0.153959\pi$
$137$	0.467172	+	0.809165i	0.0399132	+	0.0691316i	−0.845379	+	0.534167i	$0.820625\pi$
$138$	0.383084	+	1.58254i	0.0326103	+	0.134715i
$139$	−5.01682	−	8.68939i	−0.425521	−	0.737024i	0.570948	−	0.820986i	$-0.306576\pi$
$139$	−5.01682	−	8.68939i	−0.425521	−	0.737024i	−0.996469	+	0.0839623i	$0.973242\pi$
$140$	−3.94051	+	1.10408i	−0.333034	+	0.0933117i
$141$	−7.17066	−	7.52789i	−0.603878	−	0.633963i
$142$	8.03419	−	4.63854i	0.674214	−	0.389258i
$143$	−0.0361270	+	0.0208579i	−0.00302109	+	0.00174423i
$144$	−0.145739	+	2.99646i	−0.0121449	+	0.249705i
$145$	−0.282586	−	1.00856i	−0.0234675	−	0.0837567i
$146$	−2.18510	−	3.78470i	−0.180840	−	0.313224i
$147$	−6.14566	+	1.48767i	−0.506885	+	0.122701i
$148$	1.81690	+	3.14696i	0.149348	+	0.258679i
$149$	2.25005	+	1.29906i	0.184331	+	0.106424i	0.589326	−	0.807895i	$-0.299393\pi$
$149$	2.25005	+	1.29906i	0.184331	+	0.106424i	−0.404995	+	0.914319i	$0.632727\pi$
$150$	6.11432	+	6.13312i	0.499232	+	0.500767i
$151$		−	15.5474i		−	1.26523i	−0.774468	−	0.632613i	$-0.781982\pi$
$151$		−	15.5474i		−	1.26523i	0.774468	−	0.632613i	$-0.218018\pi$
$152$	−0.458984	+	4.33467i	−0.0372285	+	0.351588i
$153$	0.239627	−	4.92685i	0.0193727	−	0.398312i
$154$	0.0278190	+	0.0160613i	0.00224172	+	0.00129426i
$155$	−3.51571	+	13.7447i	−0.282389	+	1.10400i
$156$	1.16173	−	3.94918i	0.0930126	−	0.316188i
$157$	−13.0792	−	7.55130i	−1.04384	−	0.602659i	−0.122919	−	0.992417i	$-0.539226\pi$
$157$	−13.0792	−	7.55130i	−1.04384	−	0.602659i	−0.920918	+	0.389757i	$0.872559\pi$
$158$	3.75230	+	6.49918i	0.298517	+	0.517047i
$159$	9.39794	−	8.95197i	0.745305	−	0.709937i
$160$	2.15315	−	0.603283i	0.170221	−	0.0476937i
$161$	−1.48994	+	0.860220i	−0.117424	+	0.0677948i
$162$	−8.19414	+	3.72237i	−0.643792	+	0.292457i
$163$		−	0.621054i		−	0.0486447i	−0.999704	−	0.0243223i	$-0.992257\pi$
$163$		−	0.621054i		−	0.0486447i	0.999704	−	0.0243223i	$-0.00774280\pi$
$164$	−6.66872			−0.520740
$165$	0.000878070	−	0.0679738i	6.83577e−5	−	0.00529176i
$166$	10.3817	+	5.99387i	0.805775	+	0.465214i
$167$	−14.3389	+	8.27857i	−1.10958	+	0.640615i	−0.938720	−	0.344681i	$-0.887987\pi$
$167$	−14.3389	+	8.27857i	−1.10958	+	0.640615i	−0.170857	+	0.985296i	$0.554654\pi$
$168$	−3.08087	+	0.745783i	−0.237695	+	0.0575384i
$169$	3.67573	−	6.36655i	0.282748	−	0.489734i
$170$	−3.54026	+	0.991933i	−0.271526	+	0.0760778i
$171$	−12.1941	+	4.72272i	−0.932506	+	0.361155i
$172$			8.26278i			0.630031i
$173$	14.7771	+	8.53156i	1.12348	+	0.648643i	0.942288	−	0.334805i	$-0.108670\pi$
$173$	14.7771	+	8.53156i	1.12348	+	0.648643i	0.181194	+	0.983447i	$0.442004\pi$
$174$	−0.190881	−	0.788542i	−0.0144707	−	0.0597792i
$175$	−4.39372	+	8.02673i	−0.332134	+	0.606764i
$176$	−0.0152007	−	0.00877612i	−0.00114579	−	0.000661525i
$177$	−5.56931	+	18.9324i	−0.418615	+	1.42304i
$178$			0.378589i			0.0283765i
$179$	21.4936			1.60651			0.803255	−	0.595636i	$-0.203100\pi$
$179$	21.4936			1.60651			0.803255	+	0.595636i	$0.203100\pi$
$180$	4.56364	+	4.91662i	0.340154	+	0.366464i
$181$	8.09138	−	4.67156i	0.601427	−	0.347234i	−0.168176	−	0.985757i	$-0.553788\pi$
$181$	8.09138	−	4.67156i	0.601427	−	0.347234i	0.769603	+	0.638523i	$0.220454\pi$
$182$	4.34958			0.322412
$183$	−10.1213	−	10.6255i	−0.748187	−	0.785461i
$184$	0.814125	−	0.470036i	0.0600181	−	0.0346515i
$185$	7.87199	+	2.01355i	0.578760	+	0.148039i
$186$	−3.10133	+	10.5427i	−0.227401	+	0.773028i
$187$	0.0249933	+	0.0144299i	0.00182769	+	0.00105522i
$188$	−3.00121	+	5.19826i	−0.218886	+	0.379122i
$189$	−6.21667	−	7.19617i	−0.452196	−	0.523444i
$190$	6.21386	+	7.50919i	0.450801	+	0.544774i
$191$			13.3659i			0.967125i	0.875310	+	0.483562i	$0.160657\pi$
$191$			13.3659i			0.967125i	−0.875310	+	0.483562i	$0.839343\pi$
$192$	1.68343	−	0.407506i	0.121491	−	0.0294092i
$193$	6.79547	−	11.7701i	0.489149	−	0.847231i	−0.510773	−	0.859716i	$-0.670641\pi$
$193$	6.79547	−	11.7701i	0.489149	−	0.847231i	0.999922	+	0.0124848i	$0.00397414\pi$
$194$	2.18875	−	1.26367i	0.157143	−	0.0907265i
$195$	−4.49905	−	8.03037i	−0.322183	−	0.575066i
$196$	1.82534	+	3.16158i	0.130381	+	0.225827i
$197$	−3.55021			−0.252942			−0.126471	−	0.991970i	$-0.540365\pi$
$197$	−3.55021			−0.252942			−0.126471	+	0.991970i	$0.540365\pi$
$198$	0.00255804	−	0.0525945i	0.000181792	−	0.00373773i
$199$	−2.21798	−	3.84166i	−0.157229	−	0.272328i	0.776640	−	0.629945i	$-0.216923\pi$
$199$	−2.21798	−	3.84166i	−0.157229	−	0.272328i	−0.933868	+	0.357617i	$0.883589\pi$
$200$	2.40079	−	4.38591i	0.169761	−	0.310131i
$201$	−5.78493	−	6.07313i	−0.408037	−	0.428365i
$202$	5.08452			0.357746
$203$	0.742401	−	0.428626i	0.0521064	−	0.0300836i
$204$	−2.76794	+	0.670031i	−0.193794	+	0.0469115i
$205$	−10.4235	+	10.6635i	−0.728008	+	0.744772i
$206$	−2.24070	−	1.29367i	−0.156117	−	0.0901342i
$207$	2.37099	+	1.52709i	0.164795	+	0.106140i
$208$	−2.37667			−0.164792
$209$	0.00805619	−	0.0760831i	0.000557258	−	0.00526278i
$210$	−3.62300	+	6.09211i	−0.250011	+	0.420395i
$211$	14.2113	+	8.20491i	0.978348	+	0.564849i	0.901771	−	0.432214i	$-0.142268\pi$
$211$	14.2113	+	8.20491i	0.978348	+	0.564849i	0.0765769	+	0.997064i	$0.475601\pi$
$212$	−6.48959	−	3.74677i	−0.445707	−	0.257329i
$213$	4.53469	−	15.4152i	0.310712	−	1.05623i
$214$	−7.13376	+	12.3560i	−0.487654	+	0.844641i
$215$	13.2125	+	12.9151i	0.901083	+	0.880800i
$216$	3.39687	+	3.93208i	0.231128	+	0.267544i
$217$	−11.6116			−0.788246
$218$	8.53953	+	14.7909i	0.578370	+	1.00177i
$219$	−7.26172	−	2.13617i	−0.490701	−	0.144349i
$220$	−0.0377926	+	0.0105890i	−0.00254797	+	0.000713908i
$221$	3.90777			0.262865
$222$	6.03809	+	1.77622i	0.405250	+	0.119212i
$223$	12.0170	−	20.8140i	0.804718	−	1.39381i	−0.111764	−	0.993735i	$-0.535650\pi$
$223$	12.0170	−	20.8140i	0.804718	−	1.39381i	0.916482	−	0.400077i	$-0.131017\pi$
$224$	0.915058	+	1.58493i	0.0611399	+	0.105897i
$225$	14.9950	+	0.387468i	0.999666	+	0.0258312i
$226$	−6.93381	+	12.0097i	−0.461230	+	0.798874i
$227$		−	29.1059i		−	1.93183i	−0.258868	−	0.965913i	$-0.583349\pi$
$227$		−	29.1059i		−	1.93183i	0.258868	−	0.965913i	$-0.416651\pi$
$228$	4.60267	+	5.98460i	0.304820	+	0.396340i
$229$	−10.8460			−0.716724			−0.358362	−	0.933583i	$-0.616665\pi$
$229$	−10.8460			−0.716724			−0.358362	+	0.933583i	$0.616665\pi$
$230$	0.520908	−	2.03650i	0.0343477	−	0.134283i
$231$	0.0540762	−	0.0130902i	0.00355796	−	0.000861269i
$232$	−0.405658	+	0.234207i	−0.0266328	+	0.0153764i
$233$	2.19705	−	3.80540i	0.143934	−	0.249300i	−0.785041	−	0.619444i	$-0.787358\pi$
$233$	2.19705	−	3.80540i	0.143934	−	0.249300i	0.928975	+	0.370144i	$0.120692\pi$
$234$	−3.26082	−	6.34066i	−0.213167	−	0.414502i
$235$	3.62117	+	12.9241i	0.236219	+	0.843077i
$236$	11.3937			0.741669
$237$	12.4700	+	3.66829i	0.810013	+	0.238281i
$238$	−1.50456	−	2.60598i	−0.0975262	−	0.168920i
$239$		−	22.9719i		−	1.48593i	−0.669332	−	0.742963i	$-0.733420\pi$
$239$		−	22.9719i		−	1.48593i	0.669332	−	0.742963i	$-0.266580\pi$
$240$	1.97965	−	3.32881i	0.127786	−	0.214874i
$241$	−1.60542	+	0.926892i	−0.103414	+	0.0597064i	−0.550815	−	0.834627i	$-0.685683\pi$
$241$	−1.60542	+	0.926892i	−0.103414	+	0.0597064i	0.447401	+	0.894334i	$0.352350\pi$
$242$	−9.52601	−	5.49985i	−0.612355	−	0.353543i
$243$	−5.82976	+	14.4573i	−0.373979	+	0.927437i
$244$	−4.23617	+	7.33727i	−0.271193	+	0.469721i
$245$	7.90854	+	2.02289i	0.505258	+	0.129238i
$246$	−8.36352	+	7.96663i	−0.533239	+	0.507934i
$247$	−4.20632	−	9.46727i	−0.267642	−	0.602388i
$248$	6.34473			0.402890
$249$	20.1805	−	4.88507i	1.27889	−	0.309579i
$250$	−3.26069	−	10.6943i	−0.206224	−	0.676366i
$251$	22.8209	−	13.1757i	1.44044	−	0.831641i	0.442565	−	0.896737i	$-0.354069\pi$
$251$	22.8209	−	13.1757i	1.44044	−	0.831641i	0.997879	+	0.0650960i	$0.0207354\pi$
$252$	−2.97292	+	4.61581i	−0.187276	+	0.290769i
$253$	−0.0142897	+	0.00825017i	−0.000898387	+	0.000518684i
$254$		−	17.9433i		−	1.12587i
$255$	−3.25500	+	5.47331i	−0.203836	+	0.342752i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.74183	−	1.58300i	0.171031	−	0.0987446i	−0.412041	−	0.911165i	$-0.635184\pi$
$257$	2.74183	−	1.58300i	0.171031	−	0.0987446i	0.583072	+	0.812421i	$0.301851\pi$
$258$	9.87093	+	10.3627i	0.614538	+	0.645153i
$259$			6.65028i			0.413228i
$260$	−3.71483	+	3.80037i	−0.230384	+	0.235689i
$261$	−1.18140	−	0.760911i	−0.0731271	−	0.0470992i
$262$	−1.86020	−	3.22196i	−0.114924	−	0.199053i
$263$	−5.05171	+	8.74981i	−0.311502	+	0.539537i	−0.978688	−	0.205355i	$-0.934165\pi$
$263$	−5.05171	+	8.74981i	−0.311502	+	0.539537i	0.667186	+	0.744891i	$0.267499\pi$
$264$	−0.0295480	+	0.00715264i	−0.00181855	+	0.000440214i
$265$	−16.1347	+	4.52072i	−0.991146	+	0.277706i
$266$	−4.69393	+	6.45014i	−0.287803	+	0.395483i
$267$	0.452273	+	0.474805i	0.0276786	+	0.0290576i
$268$	−2.42123	+	4.19369i	−0.147900	+	0.256171i
$269$	−6.12619	+	10.6109i	−0.373520	+	0.646956i	−0.990104	−	0.140333i	$-0.955183\pi$
$269$	−6.12619	+	10.6109i	−0.373520	+	0.646956i	0.616584	+	0.787289i	$0.288516\pi$
$270$	11.5970	+	0.714298i	0.705769	+	0.0434708i
$271$	−4.49464	+	7.78495i	−0.273030	+	0.472902i	−0.969636	−	0.244552i	$-0.921359\pi$
$271$	−4.49464	+	7.78495i	−0.273030	+	0.472902i	0.696606	+	0.717454i	$0.254693\pi$
$272$	0.822112	+	1.42394i	0.0498479	+	0.0863390i
$273$	5.45498	−	5.19612i	0.330151	−	0.314483i
$274$		−	0.934343i		−	0.0564458i
$275$	−0.0421392	+	0.0769826i	−0.00254109	+	0.00464222i
$276$	0.459511	−	1.56207i	0.0276593	−	0.0940253i
$277$		−	30.5006i		−	1.83260i	−0.400489	−	0.916302i	$-0.631160\pi$
$277$		−	30.5006i		−	1.83260i	0.400489	−	0.916302i	$-0.368840\pi$
$278$			10.0336i			0.601778i
$279$	8.70506	+	16.9270i	0.521158	+	1.01339i
$280$	3.96462	+	1.01410i	0.236932	+	0.0606038i
$281$	14.5706	+	25.2370i	0.869209	+	1.50551i	0.862806	+	0.505535i	$0.168705\pi$
$281$	14.5706	+	25.2370i	0.869209	+	1.50551i	0.00640302	+	0.999980i	$0.497962\pi$
$282$	2.44602	+	10.1047i	0.145659	+	0.601725i
$283$	−22.6635	−	13.0848i	−1.34720	−	0.777808i	−0.359350	−	0.933203i	$-0.617002\pi$
$283$	−22.6635	−	13.0848i	−1.34720	−	0.777808i	−0.987852	+	0.155395i	$0.950335\pi$
$284$	−9.27709			−0.550494
$285$	16.7637	+	1.99433i	0.992998	+	0.118134i
$286$	0.0417158			0.00246671
$287$	−10.5694	−	6.10227i	−0.623895	−	0.360206i
$288$	1.62444	−	2.52214i	0.0957212	−	0.148618i
$289$	7.14826	+	12.3812i	0.420486	+	0.728303i
$290$	−0.259555	+	1.01474i	−0.0152416	+	0.0595873i
$291$	1.23538	−	4.19956i	0.0724193	−	0.246182i
$292$			4.37019i			0.255746i
$293$		−	25.0368i		−	1.46266i	−0.682021	−	0.731332i	$-0.738899\pi$
$293$		−	25.0368i		−	1.46266i	0.682021	−	0.731332i	$-0.261101\pi$
$294$	6.06613	+	1.78447i	0.353784	+	0.104072i
$295$	17.8089	−	18.2190i	1.03687	−	1.06075i
$296$		−	3.63380i		−	0.211210i
$297$	−0.0596226	−	0.0690169i	−0.00345966	−	0.00400476i
$298$	−1.29906	−	2.25005i	−0.0752528	−	0.130342i
$299$	−1.11712	+	1.93491i	−0.0646046	+	0.111898i
$300$	−2.22860	−	8.36859i	−0.128668	−	0.483161i
$301$	−7.56093	+	13.0959i	−0.435805	+	0.754836i
$302$	−7.77368	+	13.4644i	−0.447325	+	0.774790i
$303$	6.37671	−	6.07410i	0.366332	−	0.348948i
$304$	2.56482	−	3.52444i	0.147103	−	0.202140i
$305$	5.11123	+	18.2422i	0.292668	+	1.04455i
$306$	−2.67095	+	4.14696i	−0.152688	+	0.237066i
$307$	−11.4277	+	19.7934i	−0.652213	+	1.12967i	0.330371	+	0.943851i	$0.392826\pi$
$307$	−11.4277	+	19.7934i	−0.652213	+	1.12967i	−0.982585	+	0.185816i	$0.940507\pi$
$308$	−0.0160613	−	0.0278190i	−0.000915179	−	0.00158514i
$309$	−4.35560	+	1.05436i	−0.247782	+	0.0599802i
$310$	9.91706	−	10.1454i	0.563251	−	0.576221i
$311$		−	28.2446i		−	1.60160i	−0.598930	−	0.800802i	$-0.704407\pi$
$311$		−	28.2446i		−	1.60160i	0.598930	−	0.800802i	$-0.295593\pi$
$312$	−2.98068	+	2.83923i	−0.168748	+	0.160740i
$313$	−6.78155	+	3.91533i	−0.383316	+	0.221308i	−0.679260	−	0.733898i	$-0.737699\pi$
$313$	−6.78155	+	3.91533i	−0.383316	+	0.221308i	0.295944	+	0.955205i	$0.404366\pi$
$314$	7.55130	+	13.0792i	0.426145	+	0.738104i
$315$	2.73404	+	11.9685i	0.154046	+	0.674348i
$316$		−	7.50460i		−	0.422167i
$317$	−15.3593	+	8.86769i	−0.862663	+	0.498059i	−0.864903	−	0.501939i	$-0.832620\pi$
$317$	−15.3593	+	8.86769i	−0.862663	+	0.498059i	0.00223995	+	0.999997i	$0.499287\pi$
$318$	−12.6148	+	3.05366i	−0.707405	+	0.171241i
$319$	0.00712020	−	0.00411085i	0.000398655	−	0.000230164i
$320$	−2.16632	−	0.554116i	−0.121101	−	0.0309760i
$321$	5.81410	+	24.0184i	0.324511	+	1.34058i
$322$	1.72044			0.0958764
$323$	−4.21715	+	5.79497i	−0.234648	+	0.322441i
$324$	8.95752	+	0.873400i	0.497640	+	0.0485222i
$325$	0.270496	+	11.8803i	0.0150044	+	0.658998i
$326$	−0.310527	+	0.537848i	−0.0171985	+	0.0297887i
$327$	28.3794	+	8.34833i	1.56938	+	0.461664i
$328$	5.77528	+	3.33436i	0.318887	+	0.184109i
$329$	−9.51342	+	5.49257i	−0.524492	+	0.302815i
$330$	−0.0347474	+	0.0584280i	−0.00191278	+	0.00321636i
$331$			11.1421i			0.612427i	0.951963	+	0.306213i	$0.0990621\pi$
$331$			11.1421i			0.612427i	−0.951963	+	0.306213i	$0.900938\pi$
$332$	−5.99387	−	10.3817i	−0.328956	−	0.569769i
$333$	9.69454	−	4.98563i	0.531257	−	0.273211i
$334$	16.5571			0.905966
$335$	2.92138	+	10.4265i	0.159612	+	0.569663i
$336$	3.04101	+	0.894570i	0.165901	+	0.0488028i
$337$	3.30626	−	5.72662i	0.180104	−	0.311949i	−0.761812	−	0.647798i	$-0.775690\pi$
$337$	3.30626	−	5.72662i	0.180104	−	0.311949i	0.941916	+	0.335849i	$0.109023\pi$
$338$	−6.36655	+	3.67573i	−0.346294	+	0.199933i
$339$	5.65114	+	23.3452i	0.306928	+	1.26794i
$340$	3.56192	+	0.911090i	0.193172	+	0.0494108i
$341$	−0.111364			−0.00603070
$342$	12.9218	+	2.00705i	0.698728	+	0.108529i
$343$			19.4920i			1.05247i
$344$	4.13139	−	7.15578i	0.222750	−	0.385814i
$345$	−1.77956	−	3.17635i	−0.0958083	−	0.171009i
$346$	−8.53156	−	14.7771i	−0.458660	−	0.794422i
$347$	4.05301	−	7.02002i	0.217577	−	0.376855i	−0.736490	−	0.676449i	$-0.763518\pi$
$347$	4.05301	−	7.02002i	0.217577	−	0.376855i	0.954067	+	0.299594i	$0.0968513\pi$
$348$	−0.228963	+	0.778338i	−0.0122737	+	0.0417233i
$349$	−4.32430			−0.231474			−0.115737	−	0.993280i	$-0.536923\pi$
$349$	−4.32430			−0.231474			−0.115737	+	0.993280i	$0.536923\pi$
$350$	7.81844	−	4.75449i	0.417913	−	0.254138i
$351$	−11.6642	−	4.05661i	−0.622591	−	0.216526i
$352$	0.00877612	+	0.0152007i	0.000467769	+	0.000810199i
$353$	−3.82099			−0.203371			−0.101685	−	0.994817i	$-0.532424\pi$
$353$	−3.82099			−0.203371			−0.101685	+	0.994817i	$0.532424\pi$
$354$	14.2893	−	13.6112i	0.759470	−	0.723430i
$355$	−14.5005	+	14.8344i	−0.769604	+	0.787326i
$356$	0.189295	−	0.327868i	0.0100326	−	0.0173770i
$357$	−5.00010	−	1.47087i	−0.264633	−	0.0778469i
$358$	−18.6140	−	10.7468i	−0.983782	−	0.567987i
$359$	15.9731	+	9.22208i	0.843029	+	0.486723i	0.858293	−	0.513161i	$-0.171525\pi$
$359$	15.9731	+	9.22208i	0.843029	+	0.486723i	−0.0152639	+	0.999884i	$0.504859\pi$
$360$	−1.49392	−	6.53974i	−0.0787363	−	0.344675i
$361$	18.5787	+	3.97908i	0.977825	+	0.209425i
$362$	−9.34312			−0.491063
$363$	−18.5172	+	4.48244i	−0.971902	+	0.235267i
$364$	−3.76685	−	2.17479i	−0.197436	−	0.113990i
$365$	6.98808	+	6.83079i	0.365773	+	0.357540i
$366$	3.45253	+	14.2626i	0.180467	+	0.745519i
$367$	−1.09348	+	0.631323i	−0.0570794	+	0.0329548i	−0.528268	−	0.849078i	$-0.677158\pi$
$367$	−1.09348	+	0.631323i	−0.0570794	+	0.0329548i	0.471189	+	0.882032i	$0.343825\pi$
$368$	−0.940071			−0.0490046
$369$	−0.971892	+	19.9826i	−0.0505947	+	1.04025i
$370$	−5.81057	−	5.67978i	−0.302077	−	0.295277i
$371$	−6.85702	−	11.8767i	−0.355999	−	0.616608i
$372$	7.95718	−	7.57957i	0.412561	−	0.392983i
$373$	1.22155			0.0632497			0.0316248	−	0.999500i	$-0.489932\pi$
$373$	1.22155			0.0632497			0.0316248	+	0.999500i	$0.489932\pi$
$374$	−0.0144299	−	0.0249933i	−0.000746153	−	0.00129237i
$375$	−16.8650	−	9.51684i	−0.870907	−	0.491448i
$376$	5.19826	−	3.00121i	0.268080	−	0.154776i
$377$	0.556631	−	0.964114i	0.0286680	−	0.0496544i
$378$	1.78570	+	9.34040i	0.0918468	+	0.480418i
$379$		−	36.6243i		−	1.88126i	−0.339428	−	0.940632i	$-0.610233\pi$
$379$		−	36.6243i		−	1.88126i	0.339428	−	0.940632i	$-0.389767\pi$
$380$	−1.62677	−	9.61008i	−0.0834516	−	0.492987i
$381$	−21.4356	−	22.5035i	−1.09818	−	1.15289i
$382$	6.68296	−	11.5752i	0.341930	−	0.592240i
$383$	16.6952	+	9.63898i	0.853085	+	0.492529i	0.861691	−	0.507434i	$-0.169406\pi$
$383$	16.6952	+	9.63898i	0.853085	+	0.492529i	−0.00860539	+	0.999963i	$0.502739\pi$
$384$	−1.66165	−	0.488805i	−0.0847956	−	0.0249442i
$385$	−0.0695880	−	0.0177997i	−0.00354653	−	0.000907154i
$386$	−11.7701	+	6.79547i	−0.599083	+	0.345880i
$387$	24.7591	+	1.20421i	1.25857	+	0.0612133i
$388$	−2.52735			−0.128307
$389$	−20.0424	+	11.5715i	−1.01619	+	0.586697i	−0.912998	−	0.407964i	$-0.866239\pi$
$389$	−20.0424	+	11.5715i	−1.01619	+	0.586697i	−0.103192	+	0.994661i	$0.532905\pi$
$390$	−0.118895	+	9.20402i	−0.00602050	+	0.466064i
$391$	1.54569			0.0781688
$392$		−	3.65067i		−	0.184387i
$393$	−6.18199	−	1.81855i	−0.311840	−	0.0917337i
$394$	3.07457	+	1.77510i	0.154895	+	0.0894284i
$395$	−12.0001	−	11.7300i	−0.603791	−	0.590200i
$396$	−0.0285126	+	0.0442692i	−0.00143281	+	0.00222461i
$397$	−23.9763	−	13.8427i	−1.20334	−	0.694746i	−0.242040	−	0.970266i	$-0.577816\pi$
$397$	−23.9763	−	13.8427i	−1.20334	−	0.694746i	−0.961295	+	0.275520i	$0.911150\pi$
$398$			4.43597i			0.222355i
$399$	1.81865	+	13.6969i	0.0910464	+	0.685701i
$400$	−4.27210	+	2.59792i	−0.213605	+	0.129896i
$401$	7.69191	−	13.3228i	0.384115	−	0.665307i	−0.607531	−	0.794296i	$-0.707840\pi$
$401$	7.69191	−	13.3228i	0.384115	−	0.665307i	0.991646	+	0.128989i	$0.0411731\pi$
$402$	1.97333	+	8.15195i	0.0984208	+	0.406582i
$403$	−13.0591	+	7.53965i	−0.650518	+	0.375577i
$404$	−4.40332	−	2.54226i	−0.219074	−	0.126482i
$405$	15.3976	−	12.9582i	0.765111	−	0.643899i
$406$	−0.857251			−0.0425447
$407$			0.0637813i			0.00316152i
$408$	2.73212	+	0.803705i	0.135260	+	0.0397893i
$409$	18.9652	−	10.9496i	0.937770	−	0.541422i	0.0485092	−	0.998823i	$-0.484553\pi$
$409$	18.9652	−	10.9496i	0.937770	−	0.541422i	0.889260	+	0.457401i	$0.151220\pi$
$410$	14.3588	−	4.02313i	0.709128	−	0.198688i
$411$	−1.11619	−	1.17180i	−0.0550576	−	0.0578005i
$412$	1.29367	+	2.24070i	0.0637345	+	0.110391i
$413$	18.0582	+	10.4259i	0.888588	+	0.513027i
$414$	−1.28979	−	2.50799i	−0.0633898	−	0.123261i
$415$	−25.9693	−	6.64259i	−1.27478	−	0.326072i
$416$	2.05825	+	1.18833i	0.100914	+	0.0582628i
$417$	11.9864	+	12.5836i	0.586979	+	0.616221i
$418$	−0.0450184	+	0.0618618i	−0.00220192	+	0.00302576i
$419$			13.0710i			0.638559i	0.947661	+	0.319279i	$0.103441\pi$
$419$			13.0710i			0.638559i	−0.947661	+	0.319279i	$0.896559\pi$
$420$	6.18366	−	3.46442i	0.301732	−	0.169046i
$421$	−16.8330	−	9.71851i	−0.820388	−	0.473651i	0.0301623	−	0.999545i	$-0.490398\pi$
$421$	−16.8330	−	9.71851i	−0.820388	−	0.473651i	−0.850550	+	0.525894i	$0.823731\pi$
$422$	−8.20491	−	14.2113i	−0.399409	−	0.691796i
$423$	15.1390	+	9.75060i	0.736082	+	0.474090i
$424$	3.74677	+	6.48959i	0.181959	+	0.315162i
$425$	7.02429	−	4.27156i	0.340728	−	0.207201i
$426$	−11.6348	+	11.0826i	−0.563707	+	0.536956i
$427$	−13.4281	+	7.75269i	−0.649829	+	0.375179i
$428$	12.3560	−	7.13376i	0.597251	−	0.344823i
$429$	0.0523175	−	0.0498348i	0.00252591	−	0.00240605i
$430$	−4.98480	−	17.7910i	−0.240388	−	0.857958i
$431$	−7.00669	−	12.1359i	−0.337500	−	0.584567i	0.646462	−	0.762946i	$-0.276248\pi$
$431$	−7.00669	−	12.1359i	−0.337500	−	0.584567i	−0.983962	+	0.178379i	$0.942915\pi$
$432$	−0.975733	−	5.10372i	−0.0469450	−	0.245553i
$433$	10.0290	+	17.3707i	0.481962	+	0.834783i	0.999786	−	0.0207044i	$-0.00659087\pi$
$433$	10.0290	+	17.3707i	0.481962	+	0.834783i	−0.517823	+	0.855488i	$0.673258\pi$
$434$	10.0559	+	5.80579i	0.482700	+	0.278687i
$435$	0.886710	+	1.58269i	0.0425145	+	0.0758843i
$436$		−	17.0791i		−	0.817938i
$437$	−1.66378	−	3.74470i	−0.0795892	−	0.179133i
$438$	5.22075	+	5.48084i	0.249457	+	0.261885i
$439$	25.6443	+	14.8057i	1.22394	+	0.706640i	0.965755	−	0.259457i	$-0.0835435\pi$
$439$	25.6443	+	14.8057i	1.22394	+	0.706640i	0.258181	+	0.966097i	$0.416877\pi$
$440$	0.0380238	+	0.00972597i	0.00181271	+	0.000463667i
$441$	9.73955	−	5.00878i	0.463788	−	0.238513i
$442$	−3.38423	−	1.95389i	−0.160971	−	0.0929369i
$443$	−17.1231	−	29.6581i	−0.813542	−	1.40910i	−0.910370	−	0.413796i	$-0.864203\pi$
$443$	−17.1231	−	29.6581i	−0.813542	−	1.40910i	0.0968274	−	0.995301i	$-0.469131\pi$
$444$	−4.34103	−	4.55730i	−0.206016	−	0.216280i
$445$	−0.228397	−	0.815159i	−0.0108270	−	0.0386423i
$446$	−20.8140	+	12.0170i	−0.985574	+	0.569021i
$447$	−4.31717	−	1.26998i	−0.204195	−	0.0600679i
$448$		−	1.83012i		−	0.0864649i
$449$	−24.2472			−1.14430			−0.572148	−	0.820150i	$-0.693890\pi$
$449$	−24.2472			−1.14430			−0.572148	+	0.820150i	$0.693890\pi$
$450$	−12.7923	−	7.83305i	−0.603035	−	0.369254i
$451$	−0.101369	−	0.0585255i	−0.00477329	−	0.00275586i
$452$	12.0097	−	6.93381i	0.564889	−	0.326139i
$453$	6.33564	+	26.1729i	0.297674	+	1.22971i
$454$	−14.5529	+	25.2064i	−0.683004	+	1.18300i
$455$	−9.36529	+	2.62403i	−0.439051	+	0.123016i
$456$	−0.993734	−	7.48415i	−0.0465359	−	0.350477i
$457$		−	26.4451i		−	1.23705i	−0.785765	−	0.618525i	$-0.787731\pi$
$457$		−	26.4451i		−	1.23705i	0.785765	−	0.618525i	$-0.212269\pi$
$458$	9.39292	+	5.42300i	0.438902	+	0.253400i
$459$	1.60432	+	8.39166i	0.0748834	+	0.391689i
$460$	−1.46937	+	1.50320i	−0.0685097	+	0.0700873i
$461$	−0.564904	−	0.326148i	−0.0263102	−	0.0151902i	0.486787	−	0.873521i	$-0.338169\pi$
$461$	−0.564904	−	0.326148i	−0.0263102	−	0.0151902i	−0.513097	+	0.858330i	$0.671502\pi$
$462$	−0.0533765	−	0.0157017i	−0.00248330	−	0.000730509i
$463$		−	6.47173i		−	0.300767i	−0.988628	−	0.150383i	$-0.951949\pi$
$463$		−	6.47173i		−	0.300767i	0.988628	−	0.150383i	$-0.0480508\pi$
$464$	0.468414			0.0217456
$465$	0.317402	−	24.5710i	0.0147192	−	1.13945i
$466$	−3.80540	+	2.19705i	−0.176282	+	0.101776i
$467$	−6.40986			−0.296613			−0.148307	−	0.988941i	$-0.547382\pi$
$467$	−6.40986			−0.296613			−0.148307	+	0.988941i	$0.547382\pi$
$468$	−0.346372	+	7.12158i	−0.0160111	+	0.329195i
$469$	−7.67495	+	4.43113i	−0.354396	+	0.204611i
$470$	3.32604	−	13.0032i	0.153419	−	0.599793i
$471$	25.0952	+	7.38223i	1.15633	+	0.340155i
$472$	−9.86726	−	5.69687i	−0.454178	−	0.262220i
$473$	−0.0725152	+	0.125600i	−0.00333425	+	0.00577509i
$474$	−8.96519	−	9.41183i	−0.411785	−	0.432300i
$475$	−17.9095	−	12.4197i	−0.821746	−	0.569854i
$476$			3.00912i			0.137923i
$477$	−12.1728	+	18.8997i	−0.557355	+	0.865359i
$478$	−11.4859	+	19.8942i	−0.525354	+	0.909941i
$479$	−6.63996	+	3.83358i	−0.303388	+	0.175161i	−0.643964	−	0.765056i	$-0.722711\pi$
$479$	−6.63996	+	3.83358i	−0.303388	+	0.175161i	0.340576	+	0.940217i	$0.389378\pi$
$480$	−3.37884	+	1.89301i	−0.154222	+	0.0864035i
$481$	4.31817	+	7.47929i	0.196891	+	0.341026i
$482$	1.85378			0.0844376
$483$	2.15767	−	2.05528i	0.0981776	−	0.0935185i
$484$	5.49985	+	9.52601i	0.249993	+	0.433001i
$485$	−3.95034	+	4.04131i	−0.179376	+	0.183507i
$486$	12.2774	−	9.60552i	0.556913	−	0.435715i
$487$	38.4027			1.74019			0.870095	−	0.492884i	$-0.164057\pi$
$487$	38.4027			1.74019			0.870095	+	0.492884i	$0.164057\pi$
$488$	7.33727	−	4.23617i	0.332143	−	0.191763i
$489$	0.253083	+	1.04550i	0.0114448	+	0.0472792i
$490$	−5.83755	−	5.70615i	−0.263713	−	0.257777i
$491$	−24.2445	−	13.9976i	−1.09414	−	0.631701i	−0.159463	−	0.987204i	$-0.550976\pi$
$491$	−24.2445	−	13.9976i	−1.09414	−	0.631701i	−0.934675	+	0.355503i	$0.884310\pi$
$492$	11.2263	−	2.71754i	0.506122	−	0.122516i
$493$	−0.770177			−0.0346870
$494$	−1.09085	+	10.3021i	−0.0490797	+	0.463512i
$495$	0.0262216	+	0.114787i	0.00117857	+	0.00515930i
$496$	−5.49469	−	3.17236i	−0.246719	−	0.142443i
$497$	−14.7035	−	8.48908i	−0.659543	−	0.380787i
$498$	−19.9194	−	5.85967i	−0.892609	−	0.262578i
$499$	7.50172	−	12.9934i	0.335823	−	0.581662i	−0.647820	−	0.761794i	$-0.724319\pi$
$499$	7.50172	−	12.9934i	0.335823	−	0.581662i	0.983643	+	0.180131i	$0.0576523\pi$
$500$	−2.52330	+	10.8919i	−0.112846	+	0.487099i
$501$	20.7650	−	19.7796i	0.927711	−	0.883686i
$502$	−26.3513			−1.17612
$503$	6.09363	+	10.5545i	0.271701	+	0.470601i	0.969298	−	0.245890i	$-0.0790803\pi$
$503$	6.09363	+	10.5545i	0.271701	+	0.470601i	−0.697596	+	0.716491i	$0.745747\pi$
$504$	4.88253	−	2.51095i	0.217485	−	0.111847i
$505$	−10.9477	+	3.06741i	−0.487168	+	0.136498i
$506$	0.0165003			0.000733530
$507$	−3.59343	+	12.2155i	−0.159590	+	0.542510i
$508$	−8.97167	+	15.5394i	−0.398054	+	0.689449i
$509$	10.5618	+	18.2935i	0.468142	+	0.810846i	0.999337	−	0.0364036i	$-0.0115902\pi$
$509$	10.5618	+	18.2935i	0.468142	+	0.810846i	−0.531195	+	0.847250i	$0.678257\pi$
$510$	5.55556	−	3.11253i	0.246004	−	0.137825i
$511$	−3.99898	+	6.92644i	−0.176905	+	0.306408i
$512$			1.00000i			0.0441942i
$513$	18.6034	−	12.9195i	0.821359	−	0.570411i
$514$	−3.16599			−0.139646
$515$	5.60501	+	1.43368i	0.246986	+	0.0631757i
$516$	−3.36713	−	13.9098i	−0.148230	−	0.612346i
$517$	−0.0912410	+	0.0526780i	−0.00401278	+	0.00231678i
$518$	3.32514	−	5.75931i	0.146098	−	0.253050i
$519$	−28.3529	−	8.34054i	−1.24455	−	0.366109i
$520$	5.11732	−	1.43380i	0.224409	−	0.0628764i
$521$	−13.3244			−0.583755			−0.291877	−	0.956456i	$-0.594280\pi$
$521$	−13.3244			−0.583755			−0.291877	+	0.956456i	$0.594280\pi$
$522$	0.642671	+	1.24967i	0.0281289	+	0.0546966i
$523$	8.64305	+	14.9702i	0.377934	+	0.654601i	0.990762	−	0.135616i	$-0.0433013\pi$
$523$	8.64305	+	14.9702i	0.377934	+	0.654601i	−0.612827	+	0.790217i	$0.709968\pi$
$524$			3.72040i			0.162526i
$525$	4.12559	−	15.3029i	0.180055	−	0.667874i
$526$	8.74981	−	5.05171i	0.381510	−	0.220265i
$527$	9.03451	+	5.21608i	0.393549	+	0.227216i
$528$	0.0291656	+	0.00857962i	0.00126927	+	0.000373380i
$529$	11.0581	−	19.1532i	0.480788	−	0.832750i
$530$	16.2334	+	4.15228i	0.705134	+	0.180364i
$531$	1.66051	−	34.1408i	0.0720599	−	1.48159i
$532$	7.29013	−	3.23902i	0.316067	−	0.140429i
$533$	−15.8493			−0.686511
$534$	−0.154277	−	0.637329i	−0.00667624	−	0.0275799i
$535$	7.90585	−	30.9081i	0.341800	−	1.33627i
$536$	4.19369	−	2.42123i	0.181140	−	0.104581i
$537$	−36.1830	+	8.75878i	−1.56141	+	0.377969i
$538$	10.6109	−	6.12619i	0.457467	−	0.264119i
$539$			0.0640775i			0.00276001i
$540$	−9.68612	−	6.41709i	−0.416824	−	0.276147i
$541$	−19.4840	−	33.7472i	−0.837682	−	1.45091i	−0.891828	−	0.452374i	$-0.850577\pi$
$541$	−19.4840	−	33.7472i	−0.837682	−	1.45091i	0.0541465	−	0.998533i	$-0.482756\pi$
$542$	7.78495	−	4.49464i	0.334392	−	0.193061i
$543$	−11.7176	+	11.1615i	−0.502850	+	0.478987i
$544$		−	1.64422i		−	0.0704955i
$545$	−27.3100	−	26.6952i	−1.16983	−	1.14350i
$546$	−7.32221	+	1.77248i	−0.313362	+	0.0758551i
$547$	−0.0296601	−	0.0513728i	−0.00126817	−	0.00219654i	0.865391	−	0.501098i	$-0.167070\pi$
$547$	−0.0296601	−	0.0513728i	−0.00126817	−	0.00219654i	−0.866659	+	0.498901i	$0.833737\pi$
$548$	−0.467172	+	0.809165i	−0.0199566	+	0.0345658i
$549$	21.3684	+	13.7628i	0.911983	+	0.587384i
$550$	0.0749849	−	0.0455993i	0.00319737	−	0.00194436i
$551$	0.829018	+	1.86589i	0.0353173	+	0.0794896i
$552$	−1.17898	+	1.12303i	−0.0501808	+	0.0477995i
$553$	6.86715	−	11.8942i	0.292021	−	0.505795i
$554$	−15.2503	+	26.4143i	−0.647923	+	1.12224i
$555$	−14.0725	−	0.181785i	−0.597343	−	0.00771634i
$556$	5.01682	−	8.68939i	0.212761	−	0.368512i
$557$	−16.1900	−	28.0419i	−0.685993	−	1.18818i	−0.973124	−	0.230284i	$-0.926035\pi$
$557$	−16.1900	−	28.0419i	−0.685993	−	1.18818i	0.287130	−	0.957892i	$-0.407299\pi$
$558$	0.924672	−	19.0117i	0.0391445	−	0.804830i
$559$			19.6379i			0.830594i
$560$	−2.92642	−	2.86055i	−0.123664	−	0.120880i
$561$	−0.0479548	−	0.0141068i	−0.00202465	−	0.000595590i
$562$		−	29.1412i		−	1.22925i
$563$		−	7.57742i		−	0.319350i	−0.987170	−	0.159675i	$-0.948955\pi$
$563$		−	7.57742i		−	0.319350i	0.987170	−	0.159675i	$-0.0510446\pi$
$564$	2.93402	−	9.97392i	0.123544	−	0.419978i
$565$	7.68427	−	30.0418i	0.323280	−	1.26387i
$566$	13.0848	+	22.6635i	0.549993	+	0.952616i
$567$	13.3978	+	9.58093i	0.562655	+	0.402361i
$568$	8.03419	+	4.63854i	0.337107	+	0.194629i
$569$	−45.8204			−1.92089			−0.960446	−	0.278468i	$-0.910173\pi$
$569$	−45.8204			−1.92089			−0.960446	+	0.278468i	$0.910173\pi$
$570$	−13.5206	−	10.1090i	−0.566318	−	0.423420i
$571$	−19.8944			−0.832554			−0.416277	−	0.909238i	$-0.636665\pi$
$571$	−19.8944			−0.832554			−0.416277	+	0.909238i	$0.636665\pi$
$572$	−0.0361270	−	0.0208579i	−0.00151054	−	0.000872113i
$573$	−5.44669	−	22.5006i	−0.227539	−	0.939977i
$574$	6.10227	+	10.5694i	0.254704	+	0.441160i
$575$	0.106993	+	4.69914i	0.00446190	+	0.195968i
$576$	−2.66788	+	1.37202i	−0.111162	+	0.0571673i
$577$			45.0449i			1.87524i	0.347656	+	0.937622i	$0.386978\pi$
$577$			45.0449i			1.87524i	−0.347656	+	0.937622i	$0.613022\pi$
$578$		−	14.2965i		−	0.594657i
$579$	−6.64332	+	22.5834i	−0.276087	+	0.938532i
$580$	0.732149	−	0.749009i	0.0304008	−	0.0311009i
$581$		−	21.9390i		−	0.910181i
$582$	−3.16965	+	3.01923i	−0.131386	+	0.125151i
$583$	−0.0657641	−	0.113907i	−0.00272367	−	0.00471754i
$584$	2.18510	−	3.78470i	0.0904200	−	0.156612i
$585$	10.8463	+	11.6852i	0.448437	+	0.483123i
$586$	−12.5184	+	21.6825i	−0.517130	+	0.895696i
$587$	11.5995	−	20.0908i	0.478761	−	0.829238i	−0.520943	−	0.853592i	$-0.674419\pi$
$587$	11.5995	−	20.0908i	0.478761	−	0.829238i	0.999703	+	0.0243538i	$0.00775282\pi$
$588$	−4.36119	−	4.57846i	−0.179852	−	0.188812i
$589$	2.91213	−	27.5023i	0.119992	−	1.13321i
$590$	−24.5324	+	6.87365i	−1.00998	+	0.282984i
$591$	5.97653	−	1.44673i	0.245842	−	0.0595105i
$592$	−1.81690	+	3.14696i	−0.0746742	+	0.129339i
$593$	18.4951	+	32.0344i	0.759501	+	1.31549i	0.943105	+	0.332494i	$0.107890\pi$
$593$	18.4951	+	32.0344i	0.759501	+	1.31549i	−0.183604	+	0.983000i	$0.558776\pi$
$594$	0.0171263	+	0.0895817i	0.000702700	+	0.00367558i
$595$	4.81169	+	4.70338i	0.197260	+	0.192820i
$596$			2.59813i			0.106424i
$597$	5.29932	+	5.56333i	0.216887	+	0.227692i
$598$	1.93491	−	1.11712i	0.0791241	−	0.0456823i
$599$	0.199563	+	0.345652i	0.00815390	+	0.0141230i	0.870074	−	0.492922i	$-0.164071\pi$
$599$	0.199563	+	0.345652i	0.00815390	+	0.0141230i	−0.861920	+	0.507045i	$0.830738\pi$
$600$	−2.25427	+	8.36171i	−0.0920304	+	0.341366i
$601$		−	11.9930i		−	0.489204i	−0.969624	−	0.244602i	$-0.921343\pi$
$601$		−	11.9930i		−	0.489204i	0.969624	−	0.244602i	$-0.0786573\pi$
$602$	13.0959	−	7.56093i	0.533750	−	0.308160i
$603$	12.2134	+	7.86630i	0.497366	+	0.320340i
$604$	13.4644	−	7.77368i	0.547859	−	0.316307i
$605$	23.8289	+	6.09510i	0.968782	+	0.247801i
$606$	−8.55944	+	2.07197i	−0.347703	+	0.0841681i
$607$	33.2087			1.34790			0.673950	−	0.738777i	$-0.264596\pi$
$607$	33.2087			1.34790			0.673950	+	0.738777i	$0.264596\pi$
$608$	−3.98342	+	1.76984i	−0.161549	+	0.0717766i
$609$	−1.07511	+	1.02409i	−0.0435658	+	0.0414984i
$610$	4.69466	−	18.3538i	0.190081	−	0.743125i
$611$	−7.13289	+	12.3545i	−0.288566	+	0.499811i
$612$	4.38659	−	2.25590i	0.177317	−	0.0911894i
$613$	25.8070	+	14.8997i	1.04233	+	0.601792i	0.920494	−	0.390758i	$-0.127787\pi$
$613$	25.8070	+	14.8997i	1.04233	+	0.601792i	0.121841	+	0.992550i	$0.461120\pi$
$614$	19.7934	−	11.4277i	0.798795	−	0.461184i
$615$	13.2018	−	22.1989i	0.532347	−	0.895146i
$616$			0.0321226i			0.00129426i
$617$	−4.77232	−	8.26590i	−0.192126	−	0.332773i	0.753828	−	0.657071i	$-0.228205\pi$
$617$	−4.77232	−	8.26590i	−0.192126	−	0.332773i	−0.945955	+	0.324299i	$0.894872\pi$
$618$	4.29924	+	1.26470i	0.172941	+	0.0508738i
$619$	12.2127			0.490869			0.245434	−	0.969413i	$-0.421069\pi$
$619$	12.2127			0.490869			0.245434	+	0.969413i	$0.421069\pi$
$620$	−13.6611	+	3.82767i	−0.548644	+	0.153723i
$621$	−4.61370	−	1.60456i	−0.185141	−	0.0643888i
$622$	−14.1223	+	24.4605i	−0.566252	+	0.980778i
$623$	0.600037	−	0.346431i	0.0240400	−	0.0138795i
$624$	4.00095	−	0.968506i	0.160166	−	0.0387713i
$625$	13.4724	+	21.0593i	0.538898	+	0.842371i
$626$	7.83066			0.312976
$627$	0.0174423	+	0.131364i	0.000696577	+	0.00524615i
$628$		−	15.1026i		−	0.602659i
$629$	2.98739	−	5.17431i	0.119115	−	0.206313i
$630$	3.61650	−	11.7320i	0.144085	−	0.467416i
$631$	−7.29547	−	12.6361i	−0.290428	−	0.503036i	0.683483	−	0.729967i	$-0.260464\pi$
$631$	−7.29547	−	12.6361i	−0.290428	−	0.503036i	−0.973911	+	0.226930i	$0.927131\pi$
$632$	−3.75230	+	6.49918i	−0.149259	+	0.258523i
$633$	−27.2673	−	8.02120i	−1.08378	−	0.318814i
$634$	17.7354			0.704362
$635$	10.8249	+	38.6347i	0.429574	+	1.53317i
$636$	12.4516	+	3.66288i	0.493738	+	0.145242i
$637$	4.33822	+	7.51401i	0.171886	+	0.297716i
$638$	−0.00822170			−0.000325500
$639$	−1.35203	+	27.7984i	−0.0534855	+	1.09969i
$640$	1.59903	+	1.56304i	0.0632073	+	0.0617846i
$641$	−12.3068	+	21.3160i	−0.486089	+	0.841931i	−0.999872	−	0.0159890i	$-0.994910\pi$
$641$	−12.3068	+	21.3160i	−0.486089	+	0.841931i	0.513783	+	0.857920i	$0.328244\pi$
$642$	6.97403	−	23.7076i	0.275243	−	0.935663i
$643$	−31.4932	−	18.1826i	−1.24197	−	0.717053i	−0.272477	−	0.962162i	$-0.587843\pi$
$643$	−31.4932	−	18.1826i	−1.24197	−	0.717053i	−0.969495	+	0.245109i	$0.921176\pi$
$644$	−1.48994	−	0.860220i	−0.0587120	−	0.0338974i
$645$	−27.5052	−	16.3575i	−1.08302	−	0.644074i
$646$	6.54964	−	2.91002i	0.257692	−	0.114493i
$647$	1.51184			0.0594364			0.0297182	−	0.999558i	$-0.490539\pi$
$647$	1.51184			0.0594364			0.0297182	+	0.999558i	$0.490539\pi$
$648$	−7.32074	−	5.23515i	−0.287586	−	0.205656i
$649$	0.173193	+	0.0999927i	0.00679840	+	0.00392506i
$650$	5.70587	−	10.4239i	0.223803	−	0.408857i
$651$	19.5473	−	4.73179i	0.766119	−	0.185453i
$652$	0.537848	−	0.310527i	0.0210638	−	0.0121612i
$653$	11.7507			0.459839			0.229919	−	0.973210i	$-0.426154\pi$
$653$	11.7507			0.459839			0.229919	+	0.973210i	$0.426154\pi$
$654$	−20.4031	−	21.4195i	−0.797824	−	0.837570i
$655$	5.94904	+	5.81513i	0.232448	+	0.227216i
$656$	−3.33436	−	5.77528i	−0.130185	−	0.225487i
$657$	13.0951	+	0.636907i	0.510889	+	0.0248481i
$658$	10.9851			0.428246
$659$	−7.25991	−	12.5745i	−0.282806	−	0.489834i	0.689269	−	0.724506i	$-0.257932\pi$
$659$	−7.25991	−	12.5745i	−0.282806	−	0.489834i	−0.972075	+	0.234672i	$0.924599\pi$
$660$	0.0593061	−	0.0332265i	0.00230849	−	0.00129334i
$661$	−0.0542368	+	0.0313136i	−0.00210957	+	0.00121796i	−0.501054	−	0.865416i	$-0.667054\pi$
$661$	−0.0542368	+	0.0313136i	−0.00210957	+	0.00121796i	0.498945	+	0.866634i	$0.333721\pi$
$662$	5.57107	−	9.64937i	0.216526	−	0.375033i
$663$	−6.57847	+	1.59244i	−0.255486	+	0.0618453i
$664$			11.9877i			0.465214i
$665$	6.21547	−	16.7199i	0.241025	−	0.648369i
$666$	−10.8885	−	0.529586i	−0.421922	−	0.0205210i
$667$	0.220171	−	0.381347i	0.00852505	−	0.0147658i
$668$	−14.3389	−	8.27857i	−0.554789	−	0.320307i
$669$	−11.7479	+	39.9360i	−0.454201	+	1.54402i
$670$	2.68328	−	10.4903i	0.103664	−	0.405277i
$671$	−0.128785	+	0.0743543i	−0.00497171	+	0.00287042i
$672$	−2.18630	−	2.29522i	−0.0843385	−	0.0885402i
$673$	22.6019			0.871239			0.435619	−	0.900131i	$-0.356529\pi$
$673$	22.6019			0.871239			0.435619	+	0.900131i	$0.356529\pi$
$674$	−5.72662	+	3.30626i	−0.220581	+	0.127353i
$675$	−25.4009	+	5.45827i	−0.977682	+	0.210089i
$676$	7.35145			0.282748
$677$			47.0000i			1.80636i	0.429266	+	0.903178i	$0.358772\pi$
$677$			47.0000i			1.80636i	−0.429266	+	0.903178i	$0.641228\pi$
$678$	6.77856	−	23.0431i	0.260329	−	0.884964i
$679$	−4.00566	−	2.31267i	−0.153723	−	0.0887521i
$680$	−2.62917	−	2.56999i	−0.100824	−	0.0985545i
$681$	11.8608	+	48.9977i	0.454508	+	1.87760i
$682$	0.0964442	+	0.0556821i	0.00369304	+	0.00213218i
$683$			7.59129i			0.290472i	0.989397	+	0.145236i	$0.0463942\pi$
$683$			7.59129i			0.290472i	−0.989397	+	0.145236i	$0.953606\pi$
$684$	−10.1870	−	8.19904i	−0.389511	−	0.313498i
$685$	0.563674	+	2.01178i	0.0215369	+	0.0768662i
$686$	9.74599	−	16.8805i	0.372104	−	0.644502i
$687$	18.2585	−	4.41981i	0.696605	−	0.168626i
$688$	−7.15578	+	4.13139i	−0.272812	+	0.157508i
$689$	−15.4236	−	8.90482i	−0.587592	−	0.339246i
$690$	−0.0470281	+	3.64058i	−0.00179033	+	0.138594i
$691$	31.3634			1.19312			0.596560	−	0.802569i	$-0.296534\pi$
$691$	31.3634			1.19312			0.596560	+	0.802569i	$0.296534\pi$
$692$			17.0631i			0.648643i
$693$	−0.0856993	+	0.0440728i	−0.00325545	+	0.00167419i
$694$	−7.02002	+	4.05301i	−0.266476	+	0.153850i
$695$	−6.05313	−	21.6039i	−0.229608	−	0.819483i
$696$	0.587457	−	0.559579i	0.0222675	−	0.0212108i
$697$	5.48244	+	9.49586i	0.207662	+	0.359681i
$698$	3.74495	+	2.16215i	0.141748	+	0.0818385i
$699$	−2.14786	+	7.30144i	−0.0812394	+	0.276166i
$700$	−9.14821	+	0.208292i	−0.345770	+	0.00787268i
$701$	−0.0562324	−	0.0324658i	−0.00212387	−	0.00122622i	0.498938	−	0.866638i	$-0.333724\pi$
$701$	−0.0562324	−	0.0324658i	−0.00212387	−	0.00122622i	−0.501062	+	0.865412i	$0.667057\pi$
$702$	8.07323	+	9.34525i	0.304704	+	0.352714i
$703$	−15.7513	−	1.66786i	−0.594072	−	0.0629044i
$704$		−	0.0175522i		−	0.000661525i
$705$	−11.3626	−	20.2812i	−0.427942	−	0.763835i
$706$	3.30907	+	1.91049i	0.124539	+	0.0719024i
$707$	−4.65263	−	8.05860i	−0.174980	−	0.303075i
$708$	−19.1806	+	4.64301i	−0.720850	+	0.174495i
$709$	20.6987	+	35.8512i	0.777356	+	1.34642i	0.933461	+	0.358680i	$0.116773\pi$
$709$	20.6987	+	35.8512i	0.777356	+	1.34642i	−0.156104	+	0.987741i	$0.549894\pi$
$710$	19.9749	−	5.59671i	0.749646	−	0.210041i
$711$	−22.4872	−	1.09371i	−0.843337	−	0.0410174i
$712$	−0.327868	+	0.189295i	−0.0122874	+	0.00709412i
$713$	−5.16540	+	2.98225i	−0.193446	+	0.111686i
$714$	3.59477	+	3.77386i	0.134531	+	0.141233i
$715$	−0.0898204	+	0.0251665i	−0.00335909	+	0.000941172i
$716$	10.7468	+	18.6140i	0.401627	+	0.695639i
$717$	9.36117	+	38.6716i	0.349599	+	1.44422i
$718$	−9.22208	−	15.9731i	−0.344165	−	0.596111i
$719$	15.9183	+	9.19043i	0.593652	+	0.342745i	0.766540	−	0.642196i	$-0.221977\pi$
$719$	15.9183	+	9.19043i	0.593652	+	0.342745i	−0.172888	+	0.984941i	$0.555310\pi$
$720$	−1.97610	+	6.41054i	−0.0736450	+	0.238907i
$721$			4.73513i			0.176345i
$722$	−14.1001	−	12.7353i	−0.524750	−	0.473960i
$723$	2.32491	−	2.21458i	0.0864642	−	0.0823611i
$724$	8.09138	+	4.67156i	0.300714	+	0.173617i
$725$	−0.0533117	−	2.34146i	−0.00197995	−	0.0869597i
$726$	18.2776	+	5.37670i	0.678345	+	0.199548i
$727$	−0.399410	−	0.230599i	−0.0148133	−	0.00855245i	0.492575	−	0.870270i	$-0.336056\pi$
$727$	−0.399410	−	0.230599i	−0.0148133	−	0.00855245i	−0.507388	+	0.861718i	$0.669389\pi$
$728$	2.17479	+	3.76685i	0.0806030	+	0.139609i
$729$	3.92256	−	26.7135i	0.145280	−	0.989391i
$730$	−2.63647	−	9.40968i	−0.0975800	−	0.348268i
$731$	11.7657	−	6.79293i	0.435170	−	0.251246i
$732$	4.14133	−	14.0780i	0.153068	−	0.520340i
$733$			14.7386i			0.544381i	0.962243	+	0.272191i	$0.0877481\pi$
$733$			14.7386i			0.544381i	−0.962243	+	0.272191i	$0.912252\pi$
$734$	1.26265			0.0466051
$735$	−14.1378	−	0.182629i	−0.521481	−	0.00673637i
$736$	0.814125	+	0.470036i	0.0300091	+	0.0173257i
$737$	−0.0736087	+	0.0424980i	−0.00271141	+	0.00156543i
$738$	10.8330	−	16.8195i	0.398767	−	0.619133i
$739$	−5.96842	+	10.3376i	−0.219552	+	0.380275i	−0.954671	−	0.297663i	$-0.903793\pi$
$739$	−5.96842	+	10.3376i	−0.219552	+	0.380275i	0.735119	+	0.677938i	$0.237126\pi$
$740$	2.19221	+	7.82411i	0.0805873	+	0.287620i
$741$	10.9390	+	14.2234i	0.401855	+	0.522509i
$742$			13.7140i			0.503458i
$743$	26.5550	+	15.3315i	0.974207	+	0.562459i	0.900516	−	0.434823i	$-0.143189\pi$
$743$	26.5550	+	15.3315i	0.974207	+	0.562459i	0.0736906	+	0.997281i	$0.476522\pi$
$744$	−10.6809	+	2.58551i	−0.391581	+	0.0947895i
$745$	4.15449	+	4.06098i	0.152209	+	0.148783i
$746$	−1.05790	−	0.610777i	−0.0387323	−	0.0223621i
$747$	−31.9818	+	16.4474i	−1.17015	+	0.601778i
$748$			0.0288598i			0.00105522i
$749$	26.1112			0.954083
$750$	9.84714	+	16.6743i	0.359567	+	0.608861i
$751$	−45.2652	+	26.1338i	−1.65175	+	0.953638i	−0.675396	+	0.737455i	$0.736027\pi$
$751$	−45.2652	+	26.1338i	−1.65175	+	0.953638i	−0.976353	+	0.216182i	$0.930639\pi$
$752$	−6.00243			−0.218886
$753$	−33.0483	+	31.4800i	−1.20435	+	1.14719i
$754$	−0.964114	+	0.556631i	−0.0351110	+	0.0202713i
$755$	8.61504	−	33.6806i	0.313533	−	1.22576i
$756$	3.12373	−	8.98188i	0.113609	−	0.326668i
$757$	37.1689	+	21.4595i	1.35093	+	0.779957i	0.988379	−	0.152009i	$-0.0485741\pi$
$757$	37.1689	+	21.4595i	1.35093	+	0.779957i	0.362546	+	0.931966i	$0.381907\pi$
$758$	−18.3122	+	31.7176i	−0.665127	+	1.15203i
$759$	0.0206938	−	0.0197117i	0.000751136	−	0.000715491i
$760$	−3.39621	+	9.13596i	−0.123194	+	0.331396i
$761$			15.0920i			0.547084i	0.961860	+	0.273542i	$0.0881953\pi$
$761$			15.0920i			0.547084i	−0.961860	+	0.273542i	$0.911805\pi$
$762$	7.31202	+	30.2064i	0.264886	+	1.09426i
$763$	15.6283	−	27.0691i	0.565784	−	0.979966i
$764$	−11.5752	+	6.68296i	−0.418777	+	0.241781i
$765$	3.24915	−	10.5404i	0.117473	−	0.381088i
$766$	−9.63898	−	16.6952i	−0.348271	−	0.603222i
$767$	27.0791			0.977770
$768$	1.19463	+	1.25414i	0.0431073	+	0.0452549i
$769$	5.77407	+	10.0010i	0.208218	+	0.360644i	0.951153	−	0.308719i	$-0.0999003\pi$
$769$	5.77407	+	10.0010i	0.208218	+	0.360644i	−0.742935	+	0.669363i	$0.766567\pi$
$770$	0.0513652	+	0.0502090i	0.00185107	+	0.00180941i
$771$	−3.97060	+	3.78218i	−0.142998	+	0.136212i
$772$	13.5909			0.489149
$773$	−23.3720	+	13.4938i	−0.840632	+	0.485339i	−0.857479	−	0.514519i	$-0.827971\pi$
$773$	−23.3720	+	13.4938i	−0.840632	+	0.485339i	0.0168468	+	0.999858i	$0.494637\pi$
$774$	−20.8399	−	13.4224i	−0.749074	−	0.482459i
$775$	−15.2323	+	27.8274i	−0.547162	+	0.999590i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.68343 + 0.407506i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.16632 + 0.554116i) q^{5} +(1.66165 + 0.488805i) q^{6} +1.83012i q^{7} -1.00000i q^{8} +(2.66788 - 1.37202i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.68343 + 0.407506i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.16632 + 0.554116i) q^{5} +(1.66165 + 0.488805i) q^{6} +1.83012i q^{7} -1.00000i q^{8} +(2.66788 - 1.37202i) q^{9} +(-1.59903 - 1.56304i) q^{10} +0.0175522i q^{11} +(-1.19463 - 1.25414i) q^{12} +(1.18833 + 2.05825i) q^{13} +(0.915058 - 1.58493i) q^{14} +(-3.87266 - 0.0500261i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.822112 - 1.42394i) q^{17} +(-2.99646 - 0.145739i) q^{18} +(-4.33467 - 0.458984i) q^{19} +(0.603283 + 2.15315i) q^{20} +(-0.745783 - 3.08087i) q^{21} +(0.00877612 - 0.0152007i) q^{22} +(0.470036 + 0.814125i) q^{23} +(0.407506 + 1.68343i) q^{24} +(4.38591 + 2.40079i) q^{25} -2.37667i q^{26} +(-3.93208 + 3.39687i) q^{27} +(-1.58493 + 0.915058i) q^{28} +(-0.234207 - 0.405658i) q^{29} +(3.32881 + 1.97965i) q^{30} +6.34473i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.00715264 - 0.0295480i) q^{33} +(-1.42394 + 0.822112i) q^{34} +(-1.01410 + 3.96462i) q^{35} +(2.52214 + 1.62444i) q^{36} +3.63380 q^{37} +(3.52444 + 2.56482i) q^{38} +(-2.83923 - 2.98068i) q^{39} +(0.554116 - 2.16632i) q^{40} +(-3.33436 + 5.77528i) q^{41} +(-0.894570 + 3.04101i) q^{42} +(7.15578 + 4.13139i) q^{43} +(-0.0152007 + 0.00877612i) q^{44} +(6.53974 - 1.49392i) q^{45} -0.940071i q^{46} +(3.00121 + 5.19826i) q^{47} +(0.488805 - 1.66165i) q^{48} +3.65067 q^{49} +(-2.59792 - 4.27210i) q^{50} +(-0.803705 + 2.73212i) q^{51} +(-1.18833 + 2.05825i) q^{52} +(-6.48959 + 3.74677i) q^{53} +(5.10372 - 0.975733i) q^{54} +(-0.00972597 + 0.0380238i) q^{55} +1.83012 q^{56} +(7.48415 - 0.993734i) q^{57} +0.468414i q^{58} +(5.69687 - 9.86726i) q^{59} +(-1.89301 - 3.37884i) q^{60} +(4.23617 + 7.33727i) q^{61} +(3.17236 - 5.49469i) q^{62} +(2.51095 + 4.88253i) q^{63} -1.00000 q^{64} +(1.43380 + 5.11732i) q^{65} +(-0.00857962 + 0.0291656i) q^{66} +(2.42123 + 4.19369i) q^{67} +1.64422 q^{68} +(-1.12303 - 1.17898i) q^{69} +(2.86055 - 2.92642i) q^{70} +(-4.63854 + 8.03419i) q^{71} +(-1.37202 - 2.66788i) q^{72} +(3.78470 + 2.18510i) q^{73} +(-3.14696 - 1.81690i) q^{74} +(-8.36171 - 2.25427i) q^{75} +(-1.76984 - 3.98342i) q^{76} -0.0321226 q^{77} +(0.968506 + 4.00095i) q^{78} +(-6.49918 - 3.75230i) q^{79} +(-1.56304 + 1.59903i) q^{80} +(5.23515 - 7.32074i) q^{81} +(5.77528 - 3.33436i) q^{82} -11.9877 q^{83} +(2.29522 - 2.18630i) q^{84} +(2.56999 - 2.62917i) q^{85} +(-4.13139 - 7.15578i) q^{86} +(0.559579 + 0.587457i) q^{87} +0.0175522 q^{88} +(-0.189295 - 0.327868i) q^{89} +(-6.41054 - 1.97610i) q^{90} +(-3.76685 + 2.17479i) q^{91} +(-0.470036 + 0.814125i) q^{92} +(-2.58551 - 10.6809i) q^{93} -6.00243i q^{94} +(-9.13596 - 3.39621i) q^{95} +(-1.25414 + 1.19463i) q^{96} +(-1.26367 + 2.18875i) q^{97} +(-3.16158 - 1.82534i) q^{98} +(0.0240819 + 0.0468272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80q + 40q^{4} + O(q^{10}) \)	\( 80q + 40q^{4} + 30q^{15} - 40q^{16} + 8q^{19} + 8q^{25} - 4q^{30} + 48q^{39} + 12q^{45} - 128q^{49} - 36q^{54} + 12q^{55} + 30q^{60} - 24q^{61} - 80q^{64} + 4q^{66} + 36q^{70} + 16q^{76} + 24q^{79} + 32q^{81} - 8q^{85} - 54q^{90} + 24q^{91} - 60q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about