LMFDB - Embedded newform 570.2.n.a.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(179,570)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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			449.2
Character	$\chi$	$=$	570.449
Dual form			570.2.n.a.179.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.68343 - 0.407506i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.16632 - 0.554116i) q^{5} +(1.66165 - 0.488805i) q^{6} -1.83012i q^{7} +1.00000i q^{8} +(2.66788 + 1.37202i) q^{9} +O(q^{10})$	\(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})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 40 q^{4}+O(q^{10}) $ 80 * q + 40 * q^4	$ 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) $ 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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	$-0.887587\pi$
$7$		−	1.83012i		−	0.691719i	0.938286	−	0.345860i	$-0.112413\pi$
$8$			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	$-0.999158\pi$
$11$		−	0.0175522i		−	0.00529220i	0.999996	−	0.00264610i	$-0.000842280\pi$
$12$	−1.19463	+	1.25414i	−0.344859	+	0.362039i
$13$	1.18833	−	2.05825i	0.329584	−	0.570857i	−0.652845	−	0.757492i	$-0.726425\pi$
$13$	1.18833	−	2.05825i	0.329584	−	0.570857i	0.982429	+	0.186635i	$0.0597580\pi$
$14$	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	0.948331	−	0.317282i	$-0.102770\pi$
$17$	0.822112	+	1.42394i	0.199391	+	0.345356i	−0.748940	+	0.662638i	$0.769437\pi$
$18$	−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	−0.812851	−	0.582471i	$-0.802086\pi$
$23$	0.470036	−	0.814125i	0.0980092	−	0.169757i	0.910861	+	0.412714i	$0.135419\pi$
$24$	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	−0.886952	−	0.461863i	$-0.847181\pi$
$29$	−0.234207	+	0.405658i	−0.0434911	+	0.0753288i	0.843460	+	0.537191i	$0.180515\pi$
$30$	3.32881	−	1.97965i	0.607755	−	0.361434i
$31$		−	6.34473i		−	1.13955i	−0.821802	−	0.569773i	$-0.807031\pi$
$31$		−	6.34473i		−	1.13955i	0.821802	−	0.569773i	$-0.192969\pi$
$32$	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	−0.999709	−	0.0241163i	$-0.992323\pi$
$41$	−3.33436	−	5.77528i	−0.520740	−	0.901948i	0.478969	−	0.877832i	$-0.341011\pi$
$42$	−0.894570	−	3.04101i	−0.138035	−	0.469238i
$43$	7.15578	−	4.13139i	1.09125	−	0.630031i	0.157338	−	0.987545i	$-0.449709\pi$
$43$	7.15578	−	4.13139i	1.09125	−	0.630031i	0.933908	+	0.357513i	$0.116375\pi$
$44$	−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	−0.559745	−	0.828665i	$-0.689101\pi$
$47$	3.00121	−	5.19826i	0.437772	−	0.758244i	0.997517	+	0.0704212i	$0.0224343\pi$
$48$	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	−0.0170090	−	0.999855i	$-0.505414\pi$
$53$	−6.48959	−	3.74677i	−0.891414	−	0.514658i	−0.874405	+	0.485197i	$0.838748\pi$
$54$	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	0.951735	+	0.306921i	$0.0992988\pi$
$59$	5.69687	+	9.86726i	0.741669	+	1.28461i	−0.210066	+	0.977687i	$0.567368\pi$
$60$	−1.89301	+	3.37884i	−0.244386	+	0.436206i
$61$	4.23617	−	7.33727i	0.542387	−	0.939441i	−0.456380	−	0.889785i	$-0.650854\pi$
$61$	4.23617	−	7.33727i	0.542387	−	0.939441i	0.998766	−	0.0496560i	$-0.0158125\pi$
$62$	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	−0.679370	−	0.733796i	$-0.737747\pi$
$67$	2.42123	−	4.19369i	0.295800	−	0.512341i	0.975171	+	0.221454i	$0.0710804\pi$
$68$	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	−0.998239	−	0.0593220i	$-0.981106\pi$
$71$	−4.63854	−	8.03419i	−0.550494	−	0.953483i	0.447745	−	0.894161i	$-0.352227\pi$
$72$	−1.37202	+	2.66788i	−0.161694	+	0.314412i
$73$	3.78470	−	2.18510i	0.442966	−	0.255746i	−0.261889	−	0.965098i	$-0.584346\pi$
$73$	3.78470	−	2.18510i	0.442966	−	0.255746i	0.704855	+	0.709352i	$0.251012\pi$
$74$	−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	−0.818866	−	0.573984i	$-0.805397\pi$
$79$	−6.49918	+	3.75230i	−0.731214	+	0.422167i	0.0876519	+	0.996151i	$0.472064\pi$
$80$	−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	−0.875884	−	0.482522i	$-0.839721\pi$
$89$	−0.189295	+	0.327868i	−0.0200652	+	0.0347539i	0.855818	+	0.517276i	$0.173054\pi$
$90$	−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	0.794714	−	0.606984i	$-0.207621\pi$
$97$	−1.26367	−	2.18875i	−0.128307	−	0.222234i	−0.923021	+	0.384750i	$0.874287\pi$
$98$	−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	0.264664	−	0.964341i	$-0.414739\pi$
$101$	−4.40332	−	2.54226i	−0.438147	−	0.252964i	−0.702811	+	0.711376i	$0.748072\pi$
$102$	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	$0.242234\pi$
$107$			14.2675i			1.37929i	−0.724146	+	0.689646i	$0.757766\pi$
$108$	−4.90782	+	1.70685i	−0.472255	+	0.164242i
$109$	−14.7909	+	8.53953i	−1.41671	+	0.817938i	−0.996008	−	0.0892602i	$-0.971550\pi$
$109$	−14.7909	+	8.53953i	−1.41671	+	0.817938i	−0.420703	+	0.907199i	$0.638216\pi$
$110$	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	$0.226187\pi$
$113$			13.8676i			1.30456i	−0.757980	+	0.652278i	$0.773813\pi$
$114$	−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	−0.126026	−	0.992027i	$-0.540222\pi$
$127$	8.97167	−	15.5394i	0.796107	−	1.37890i	0.922134	−	0.386872i	$-0.126444\pi$
$128$	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	−0.352600	−	0.935774i	$-0.614702\pi$
$131$	3.22196	−	1.86020i	0.281504	−	0.162526i	0.634104	+	0.773248i	$0.281369\pi$
$132$	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	−0.845379	−	0.534167i	$-0.820625\pi$
$137$	0.467172	−	0.809165i	0.0399132	−	0.0691316i	0.885292	+	0.465036i	$0.153959\pi$
$138$	0.383084	−	1.58254i	0.0326103	−	0.134715i
$139$	−5.01682	+	8.68939i	−0.425521	+	0.737024i	−0.996469	−	0.0839623i	$-0.973242\pi$
$139$	−5.01682	+	8.68939i	−0.425521	+	0.737024i	0.570948	+	0.820986i	$0.306576\pi$
$140$	−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	−0.404995	−	0.914319i	$-0.632727\pi$
$149$	2.25005	−	1.29906i	0.184331	−	0.106424i	0.589326	+	0.807895i	$0.299393\pi$
$150$	6.11432	−	6.13312i	0.499232	−	0.500767i
$151$			15.5474i			1.26523i	0.774468	+	0.632613i	$0.218018\pi$
$151$			15.5474i			1.26523i	−0.774468	+	0.632613i	$0.781982\pi$
$152$	−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	−0.920918	−	0.389757i	$-0.872559\pi$
$157$	−13.0792	+	7.55130i	−1.04384	+	0.602659i	−0.122919	+	0.992417i	$0.539226\pi$
$158$	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	$0.00774280\pi$
$163$			0.621054i			0.0486447i	−0.999704	+	0.0243223i	$0.992257\pi$
$164$	−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	−0.170857	−	0.985296i	$-0.554654\pi$
$167$	−14.3389	−	8.27857i	−1.10958	−	0.640615i	−0.938720	+	0.344681i	$0.887987\pi$
$168$	−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	0.181194	−	0.983447i	$-0.442004\pi$
$173$	14.7771	−	8.53156i	1.12348	−	0.648643i	0.942288	+	0.334805i	$0.108670\pi$
$174$	−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	0.769603	−	0.638523i	$-0.220454\pi$
$181$	8.09138	+	4.67156i	0.601427	+	0.347234i	−0.168176	+	0.985757i	$0.553788\pi$
$182$	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	$-0.839343\pi$
$191$		−	13.3659i		−	0.967125i	0.875310	−	0.483562i	$-0.160657\pi$
$192$	1.68343	+	0.407506i	0.121491	+	0.0294092i
$193$	6.79547	+	11.7701i	0.489149	+	0.847231i	0.999922	−	0.0124848i	$-0.00397414\pi$
$193$	6.79547	+	11.7701i	0.489149	+	0.847231i	−0.510773	+	0.859716i	$0.670641\pi$
$194$	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	−0.933868	−	0.357617i	$-0.883589\pi$
$199$	−2.21798	+	3.84166i	−0.157229	+	0.272328i	0.776640	+	0.629945i	$0.216923\pi$
$200$	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	0.0765769	−	0.997064i	$-0.475601\pi$
$211$	14.2113	−	8.20491i	0.978348	−	0.564849i	0.901771	+	0.432214i	$0.142268\pi$
$212$	−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	0.916482	+	0.400077i	$0.131017\pi$
$223$	12.0170	+	20.8140i	0.804718	+	1.39381i	−0.111764	+	0.993735i	$0.535650\pi$
$224$	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	$0.416651\pi$
$227$			29.1059i			1.93183i	−0.258868	+	0.965913i	$0.583349\pi$
$228$	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	0.928975	−	0.370144i	$-0.120692\pi$
$233$	2.19705	+	3.80540i	0.143934	+	0.249300i	−0.785041	+	0.619444i	$0.787358\pi$
$234$	−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	$0.266580\pi$
$239$			22.9719i			1.48593i	−0.669332	+	0.742963i	$0.733420\pi$
$240$	1.97965	+	3.32881i	0.127786	+	0.214874i
$241$	−1.60542	−	0.926892i	−0.103414	−	0.0597064i	0.447401	−	0.894334i	$-0.352350\pi$
$241$	−1.60542	−	0.926892i	−0.103414	−	0.0597064i	−0.550815	+	0.834627i	$0.685683\pi$
$242$	−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	0.997879	−	0.0650960i	$-0.0207354\pi$
$251$	22.8209	+	13.1757i	1.44044	+	0.831641i	0.442565	+	0.896737i	$0.354069\pi$
$252$	−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	0.583072	−	0.812421i	$-0.301851\pi$
$257$	2.74183	+	1.58300i	0.171031	+	0.0987446i	−0.412041	+	0.911165i	$0.635184\pi$
$258$	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	0.667186	−	0.744891i	$-0.267499\pi$
$263$	−5.05171	−	8.74981i	−0.311502	−	0.539537i	−0.978688	+	0.205355i	$0.934165\pi$
$264$	−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	0.616584	−	0.787289i	$-0.288516\pi$
$269$	−6.12619	−	10.6109i	−0.373520	−	0.646956i	−0.990104	+	0.140333i	$0.955183\pi$
$270$	11.5970	−	0.714298i	0.705769	−	0.0434708i
$271$	−4.49464	−	7.78495i	−0.273030	−	0.472902i	0.696606	−	0.717454i	$-0.254693\pi$
$271$	−4.49464	−	7.78495i	−0.273030	−	0.472902i	−0.969636	+	0.244552i	$0.921359\pi$
$272$	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	$0.368840\pi$
$277$			30.5006i			1.83260i	−0.400489	+	0.916302i	$0.631160\pi$
$278$		−	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	0.00640302	−	0.999980i	$-0.497962\pi$
$281$	14.5706	−	25.2370i	0.869209	−	1.50551i	0.862806	−	0.505535i	$-0.168705\pi$
$282$	2.44602	−	10.1047i	0.145659	−	0.601725i
$283$	−22.6635	+	13.0848i	−1.34720	+	0.777808i	−0.987852	−	0.155395i	$-0.950335\pi$
$283$	−22.6635	+	13.0848i	−1.34720	+	0.777808i	−0.359350	+	0.933203i	$0.617002\pi$
$284$	−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	$0.261101\pi$
$293$			25.0368i			1.46266i	−0.682021	+	0.731332i	$0.738899\pi$
$294$	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	−0.982585	−	0.185816i	$-0.940507\pi$
$307$	−11.4277	−	19.7934i	−0.652213	−	1.12967i	0.330371	−	0.943851i	$-0.392826\pi$
$308$	−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	$0.295593\pi$
$311$			28.2446i			1.60160i	−0.598930	+	0.800802i	$0.704407\pi$
$312$	−2.98068	−	2.83923i	−0.168748	−	0.160740i
$313$	−6.78155	−	3.91533i	−0.383316	−	0.221308i	0.295944	−	0.955205i	$-0.404366\pi$
$313$	−6.78155	−	3.91533i	−0.383316	−	0.221308i	−0.679260	+	0.733898i	$0.737699\pi$
$314$	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	0.00223995	−	0.999997i	$-0.499287\pi$
$317$	−15.3593	−	8.86769i	−0.862663	−	0.498059i	−0.864903	+	0.501939i	$0.832620\pi$
$318$	−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	$-0.900938\pi$
$331$		−	11.1421i		−	0.612427i	0.951963	−	0.306213i	$-0.0990621\pi$
$332$	−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	0.941916	−	0.335849i	$-0.109023\pi$
$337$	3.30626	+	5.72662i	0.180104	+	0.311949i	−0.761812	+	0.647798i	$0.775690\pi$
$338$	−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	0.954067	−	0.299594i	$-0.0968513\pi$
$347$	4.05301	+	7.02002i	0.217577	+	0.376855i	−0.736490	+	0.676449i	$0.763518\pi$
$348$	−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	−0.0152639	−	0.999884i	$-0.504859\pi$
$359$	15.9731	−	9.22208i	0.843029	−	0.486723i	0.858293	+	0.513161i	$0.171525\pi$
$360$	−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	0.471189	−	0.882032i	$-0.343825\pi$
$367$	−1.09348	−	0.631323i	−0.0570794	−	0.0329548i	−0.528268	+	0.849078i	$0.677158\pi$
$368$	−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	$0.389767\pi$
$379$			36.6243i			1.88126i	−0.339428	+	0.940632i	$0.610233\pi$
$380$	−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	−0.00860539	−	0.999963i	$-0.502739\pi$
$383$	16.6952	−	9.63898i	0.853085	−	0.492529i	0.861691	+	0.507434i	$0.169406\pi$
$384$	−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	−0.103192	−	0.994661i	$-0.532905\pi$
$389$	−20.0424	−	11.5715i	−1.01619	−	0.586697i	−0.912998	+	0.407964i	$0.866239\pi$
$390$	−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	−0.961295	−	0.275520i	$-0.911150\pi$
$397$	−23.9763	+	13.8427i	−1.20334	+	0.694746i	−0.242040	+	0.970266i	$0.577816\pi$
$398$		−	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	0.991646	−	0.128989i	$-0.0411731\pi$
$401$	7.69191	+	13.3228i	0.384115	+	0.665307i	−0.607531	+	0.794296i	$0.707840\pi$
$402$	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	0.889260	−	0.457401i	$-0.151220\pi$
$409$	18.9652	+	10.9496i	0.937770	+	0.541422i	0.0485092	+	0.998823i	$0.484553\pi$
$410$	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	$-0.896559\pi$
$419$		−	13.0710i		−	0.638559i	0.947661	−	0.319279i	$-0.103441\pi$
$420$	6.18366	+	3.46442i	0.301732	+	0.169046i
$421$	−16.8330	+	9.71851i	−0.820388	+	0.473651i	−0.850550	−	0.525894i	$-0.823731\pi$
$421$	−16.8330	+	9.71851i	−0.820388	+	0.473651i	0.0301623	+	0.999545i	$0.490398\pi$
$422$	−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	−0.983962	−	0.178379i	$-0.942915\pi$
$431$	−7.00669	+	12.1359i	−0.337500	+	0.584567i	0.646462	+	0.762946i	$0.276248\pi$
$432$	−0.975733	+	5.10372i	−0.0469450	+	0.245553i
$433$	10.0290	−	17.3707i	0.481962	−	0.834783i	−0.517823	−	0.855488i	$-0.673258\pi$
$433$	10.0290	−	17.3707i	0.481962	−	0.834783i	0.999786	+	0.0207044i	$0.00659087\pi$
$434$	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	0.258181	−	0.966097i	$-0.416877\pi$
$439$	25.6443	−	14.8057i	1.22394	−	0.706640i	0.965755	+	0.259457i	$0.0835435\pi$
$440$	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	0.0968274	+	0.995301i	$0.469131\pi$
$443$	−17.1231	+	29.6581i	−0.813542	+	1.40910i	−0.910370	+	0.413796i	$0.864203\pi$
$444$	−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	$0.212269\pi$
$457$			26.4451i			1.23705i	−0.785765	+	0.618525i	$0.787731\pi$
$458$	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	−0.513097	−	0.858330i	$-0.671502\pi$
$461$	−0.564904	+	0.326148i	−0.0263102	+	0.0151902i	0.486787	+	0.873521i	$0.338169\pi$
$462$	−0.0533765	+	0.0157017i	−0.00248330	+	0.000730509i
$463$			6.47173i			0.300767i	0.988628	+	0.150383i	$0.0480508\pi$
$463$			6.47173i			0.300767i	−0.988628	+	0.150383i	$0.951949\pi$
$464$	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	0.340576	−	0.940217i	$-0.389378\pi$
$479$	−6.63996	−	3.83358i	−0.303388	−	0.175161i	−0.643964	+	0.765056i	$0.722711\pi$
$480$	−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	−0.934675	−	0.355503i	$-0.884310\pi$
$491$	−24.2445	+	13.9976i	−1.09414	+	0.631701i	−0.159463	+	0.987204i	$0.550976\pi$
$492$	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	0.983643	−	0.180131i	$-0.0576523\pi$
$499$	7.50172	+	12.9934i	0.335823	+	0.581662i	−0.647820	+	0.761794i	$0.724319\pi$
$500$	−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	−0.697596	−	0.716491i	$-0.745747\pi$
$503$	6.09363	−	10.5545i	0.271701	−	0.470601i	0.969298	+	0.245890i	$0.0790803\pi$
$504$	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	−0.531195	−	0.847250i	$-0.678257\pi$
$509$	10.5618	−	18.2935i	0.468142	−	0.810846i	0.999337	+	0.0364036i	$0.0115902\pi$
$510$	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	−0.612827	−	0.790217i	$-0.709968\pi$
$523$	8.64305	−	14.9702i	0.377934	−	0.654601i	0.990762	+	0.135616i	$0.0433013\pi$
$524$		−	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	0.0541465	+	0.998533i	$0.482756\pi$
$541$	−19.4840	+	33.7472i	−0.837682	+	1.45091i	−0.891828	+	0.452374i	$0.850577\pi$
$542$	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	−0.866659	−	0.498901i	$-0.833737\pi$
$547$	−0.0296601	+	0.0513728i	−0.00126817	+	0.00219654i	0.865391	+	0.501098i	$0.167070\pi$
$548$	−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	0.287130	+	0.957892i	$0.407299\pi$
$557$	−16.1900	+	28.0419i	−0.685993	+	1.18818i	−0.973124	+	0.230284i	$0.926035\pi$
$558$	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	$0.0510446\pi$
$563$			7.57742i			0.319350i	−0.987170	+	0.159675i	$0.948955\pi$
$564$	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	$-0.613022\pi$
$577$		−	45.0449i		−	1.87524i	0.347656	−	0.937622i	$-0.386978\pi$
$578$			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	0.999703	−	0.0243538i	$-0.00775282\pi$
$587$	11.5995	+	20.0908i	0.478761	+	0.829238i	−0.520943	+	0.853592i	$0.674419\pi$
$588$	−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	−0.183604	−	0.983000i	$-0.558776\pi$
$593$	18.4951	−	32.0344i	0.759501	−	1.31549i	0.943105	−	0.332494i	$-0.107890\pi$
$594$	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	−0.861920	−	0.507045i	$-0.830738\pi$
$599$	0.199563	−	0.345652i	0.00815390	−	0.0141230i	0.870074	+	0.492922i	$0.164071\pi$
$600$	−2.25427	−	8.36171i	−0.0920304	−	0.341366i
$601$			11.9930i			0.489204i	0.969624	+	0.244602i	$0.0786573\pi$
$601$			11.9930i			0.489204i	−0.969624	+	0.244602i	$0.921343\pi$
$602$	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	0.121841	−	0.992550i	$-0.461120\pi$
$613$	25.8070	−	14.8997i	1.04233	−	0.601792i	0.920494	+	0.390758i	$0.127787\pi$
$614$	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	−0.945955	−	0.324299i	$-0.894872\pi$
$617$	−4.77232	+	8.26590i	−0.192126	+	0.332773i	0.753828	+	0.657071i	$0.228205\pi$
$618$	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	−0.973911	−	0.226930i	$-0.927131\pi$
$631$	−7.29547	+	12.6361i	−0.290428	+	0.503036i	0.683483	+	0.729967i	$0.260464\pi$
$632$	−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	0.513783	−	0.857920i	$-0.328244\pi$
$641$	−12.3068	−	21.3160i	−0.486089	−	0.841931i	−0.999872	+	0.0159890i	$0.994910\pi$
$642$	6.97403	+	23.7076i	0.275243	+	0.935663i
$643$	−31.4932	+	18.1826i	−1.24197	+	0.717053i	−0.969495	−	0.245109i	$-0.921176\pi$
$643$	−31.4932	+	18.1826i	−1.24197	+	0.717053i	−0.272477	+	0.962162i	$0.587843\pi$
$644$	−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	−0.972075	−	0.234672i	$-0.924599\pi$
$659$	−7.25991	+	12.5745i	−0.282806	+	0.489834i	0.689269	+	0.724506i	$0.257932\pi$
$660$	0.0593061	+	0.0332265i	0.00230849	+	0.00129334i
$661$	−0.0542368	−	0.0313136i	−0.00210957	−	0.00121796i	0.498945	−	0.866634i	$-0.333721\pi$
$661$	−0.0542368	−	0.0313136i	−0.00210957	−	0.00121796i	−0.501054	+	0.865416i	$0.667054\pi$
$662$	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	$-0.641228\pi$
$677$		−	47.0000i		−	1.80636i	0.429266	−	0.903178i	$-0.358772\pi$
$678$	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	$-0.953606\pi$
$683$		−	7.59129i		−	0.290472i	0.989397	−	0.145236i	$-0.0463942\pi$
$684$	−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	−0.501062	−	0.865412i	$-0.667057\pi$
$701$	−0.0562324	+	0.0324658i	−0.00212387	+	0.00122622i	0.498938	+	0.866638i	$0.333724\pi$
$702$	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	−0.156104	−	0.987741i	$-0.549894\pi$
$709$	20.6987	−	35.8512i	0.777356	−	1.34642i	0.933461	−	0.358680i	$-0.116773\pi$
$710$	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	−0.172888	−	0.984941i	$-0.555310\pi$
$719$	15.9183	−	9.19043i	0.593652	−	0.342745i	0.766540	+	0.642196i	$0.221977\pi$
$720$	−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	−0.507388	−	0.861718i	$-0.669389\pi$
$727$	−0.399410	+	0.230599i	−0.0148133	+	0.00855245i	0.492575	+	0.870270i	$0.336056\pi$
$728$	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	$-0.912252\pi$
$733$		−	14.7386i		−	0.544381i	0.962243	−	0.272191i	$-0.0877481\pi$
$734$	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	0.735119	−	0.677938i	$-0.237126\pi$
$739$	−5.96842	−	10.3376i	−0.219552	−	0.380275i	−0.954671	+	0.297663i	$0.903793\pi$
$740$	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	0.0736906	−	0.997281i	$-0.476522\pi$
$743$	26.5550	−	15.3315i	0.974207	−	0.562459i	0.900516	+	0.434823i	$0.143189\pi$
$744$	−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	−0.976353	−	0.216182i	$-0.930639\pi$
$751$	−45.2652	−	26.1338i	−1.65175	−	0.953638i	−0.675396	−	0.737455i	$-0.736027\pi$
$752$	−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	0.362546	−	0.931966i	$-0.381907\pi$
$757$	37.1689	−	21.4595i	1.35093	−	0.779957i	0.988379	+	0.152009i	$0.0485741\pi$
$758$	−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	$-0.911805\pi$
$761$		−	15.0920i		−	0.547084i	0.961860	−	0.273542i	$-0.0881953\pi$
$762$	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	−0.742935	−	0.669363i	$-0.766567\pi$
$769$	5.77407	−	10.0010i	0.208218	−	0.360644i	0.951153	+	0.308719i	$0.0999003\pi$
$770$	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	0.0168468	−	0.999858i	$-0.494637\pi$
$773$	−23.3720	−	13.4938i	−0.840632	−	0.485339i	−0.857479	+	0.514519i	$0.827971\pi$
$774$	−20.8399	+	13.4224i	−0.749074	+	0.482459i
$775$	−15.2323	−	27.8274i	−0.547162	−	0.999590i
$776$	2.18875	−	1.26367i	0.0785714	−	0.0453632i
$777$	−2.71003	+	11.1953i	−0.0972217	+	0.401629i
$778$	23.1430			0.829715
$779$	17.1041	+	23.5035i	0.612818	+	0.842101i
$780$	4.70498	+	7.91147i	0.168465	+	0.283276i
$781$	−0.141018	+	0.0814168i	−0.00504602	+	0.00291332i
$782$	−1.33860	+	0.772844i	−0.0478684	+	0.0276368i
$783$	2.29889	−	0.799512i	0.0821555	−	0.0285722i
$784$	−1.82534	−	3.16158i	−0.0651906	−	0.112913i
$785$	−24.1496	+	23.6060i	−0.861935	+	0.842533i
$786$	4.44449	−	4.66591i	0.158530	−	0.166427i
$787$	4.63678			0.165283			0.0826416	−	0.996579i	$-0.473664\pi$
$787$	4.63678			0.165283			0.0826416	+	0.996579i	$0.473664\pi$
$788$	−1.77510	+	3.07457i	−0.0632355	+	0.109527i
$789$	4.93860	+	16.7883i	0.175819	+	0.597679i
$790$	4.52740	−	16.1585i	0.161078	−	0.574894i
$791$	25.3794			0.902386
$792$	0.0468272	+	0.0240819i	0.00166393	+	0.000855714i
$793$	−10.0680	−	17.4382i	−0.357524	−	0.619250i
$794$	13.8427	−	23.9763i	0.491260	−	0.850886i
$795$	25.3194	+	14.1853i	0.897987	+	0.503101i
$796$	2.21798	+	3.84166i	0.0786143	+	0.136164i
$797$		−	13.6298i		−	0.482791i	−0.970427	−	0.241395i	$-0.922395\pi$
$797$		−	13.6298i		−	0.482791i	0.970427	−	0.241395i	$-0.0776050\pi$
$798$	5.27344	+	12.7712i	0.186678	+	0.452094i
$799$	9.86934			0.349152
$800$	4.99870	+	0.113813i	0.176731	+	0.00402391i
$801$	−0.954855	+	0.614997i	−0.0337382	+	0.0217298i
$802$	−13.3228	−	7.69191i	−0.470443	−	0.271611i
$803$	−0.0383533	−	0.0664299i	−0.00135346	−	0.00234426i
$804$	2.36702	+	8.04646i	0.0834783	+	0.283777i
$805$	−3.70436	−	1.03791i	−0.130562	−	0.0365816i
$806$	15.0793			0.531146
$807$	5.98903	+	20.3591i	0.210824	+	0.716675i
$808$	2.54226	−	4.40332i	0.0894364	−	0.154908i
$809$			0.639159i			0.0224716i	0.999937	+	0.0112358i	$0.00357655\pi$
$809$			0.639159i			0.0224716i	−0.999937	+	0.0112358i	$0.996423\pi$
$810$	−19.8138	−	3.52336i	−0.696185	−	0.123798i
$811$	−21.2469	−	12.2669i	−0.746079	−	0.430749i	0.0781964	−	0.996938i	$-0.475084\pi$
$811$	−21.2469	−	12.2669i	−0.746079	−	0.430749i	−0.824275	+	0.566189i	$0.808417\pi$
$812$	0.742401	−	0.428626i	0.0260532	−	0.0150418i
$813$	4.39401	+	14.9370i	0.154105	+	0.523864i
$814$	0.0318907	+	0.0552363i	0.00111777	+	0.00193603i
$815$	0.344135	+	1.34540i	0.0120545	+	0.0471274i
$816$	−1.96423	+	2.06209i	−0.0687619	+	0.0721876i
$817$	−29.1217	+	21.1926i	−1.01884	+	0.741435i
$818$	−21.8991			−0.765686
$819$	−7.06564	−	10.9702i	−0.246893	−	0.383331i
$820$	−14.4466	+	3.69524i	−0.504498	+	0.129044i
$821$	27.9511	+	16.1376i	0.975501	+	0.563206i	0.900909	−	0.434008i	$-0.142901\pi$
$821$	27.9511	+	16.1376i	0.975501	+	0.563206i	0.0745923	+	0.997214i	$0.476234\pi$
$822$	0.380750	−	1.57290i	0.0132802	−	0.0548613i
$823$	39.3652	+	22.7275i	1.37219	+	0.792232i	0.991203	−	0.132350i	$-0.0422523\pi$
$823$	39.3652	+	22.7275i	1.37219	+	0.792232i	0.380983	+	0.924582i	$0.375586\pi$
$824$			2.58734i			0.0901342i
$825$	0.0395676	+	0.146767i	0.00137757	+	0.00510976i
$826$	−10.4259	+	18.0582i	−0.362765	+	0.628327i
$827$	15.6189	+	9.01758i	0.543123	+	0.313572i	0.746344	−	0.665561i	$-0.231808\pi$
$827$	15.6189	+	9.01758i	0.543123	+	0.313572i	−0.203221	+	0.979133i	$0.565141\pi$
$828$	−0.137005	−	2.81688i	−0.00476124	−	0.0978935i
$829$			5.46280i			0.189731i	0.995490	+	0.0948655i	$0.0302421\pi$
$829$			5.46280i			0.189731i	−0.995490	+	0.0948655i	$0.969758\pi$
$830$	19.1688	−	18.7373i	0.665358	−	0.650382i
$831$	12.4292	−	51.3456i	0.431163	−	1.78116i
$832$	−1.18833	+	2.05825i	−0.0411981	+	0.0713571i
$833$	3.00126	+	5.19834i	0.103988	+	0.180112i
$834$	−4.08877	+	16.8909i	−0.141582	+	0.584885i
$835$	−35.6500	−	9.98864i	−1.23372	−	0.345671i
$836$	0.0699180	+	0.0310647i	0.00241816	+	0.00107439i
$837$	−21.5522	+	24.9480i	−0.744953	+	0.862329i
$838$	6.53548	+	11.3198i	0.225765	+	0.391036i
$839$	1.66762	+	2.88840i	0.0575725	+	0.0997185i	0.893375	−	0.449311i	$-0.148331\pi$
$839$	1.66762	+	2.88840i	0.0575725	+	0.0997185i	−0.835803	+	0.549030i	$0.814997\pi$
$840$	−7.08742	+	0.0915536i	−0.244539	+	0.00315890i
$841$	14.3903	+	24.9247i	0.496217	+	0.859473i
$842$	9.71851	−	16.8330i	0.334922	−	0.580102i
$843$	−34.8128	+	36.5472i	−1.19902	+	1.25875i
$844$		−	16.4098i		−	0.564849i
$845$	11.4906	+	11.7552i	0.395289	+	0.404392i
$846$	−8.23543	+	16.0137i	−0.283140	+	0.550564i
$847$		−	20.1307i		−	0.691700i
$848$			7.49353i			0.257329i
$849$	43.4845	−	12.7918i	1.49238	−	0.439013i
$850$	−8.21899	−	0.187135i	−0.281909	−	0.00641866i
$851$	1.70802	−	2.95837i	0.0585500	−	0.101412i
$852$	15.6173	+	3.78047i	0.535041	+	0.129517i
$853$	−28.2641	+	16.3183i	−0.967744	+	0.558727i	−0.898548	−	0.438876i	$-0.855377\pi$
$853$	−28.2641	+	16.3183i	−0.967744	+	0.558727i	−0.0691961	+	0.997603i	$0.522043\pi$
$854$	15.5054			0.530583
$855$	−29.0333	−	3.47399i	−0.992917	−	0.118808i
$856$	−14.2675			−0.487654
$857$	−28.2912	+	16.3339i	−0.966408	+	0.557956i	−0.898139	−	0.439711i	$-0.855081\pi$
$857$	−28.2912	+	16.3339i	−0.966408	+	0.557956i	−0.0682684	+	0.997667i	$0.521747\pi$
$858$	−0.0702257	−	0.0169994i	−0.00239747	−	0.000580351i
$859$	6.71516	−	11.6310i	0.229118	−	0.396844i	−0.728429	−	0.685121i	$-0.759749\pi$
$859$	6.71516	−	11.6310i	0.229118	−	0.396844i	0.957547	+	0.288277i	$0.0930824\pi$
$860$	−4.57854	−	17.8999i	−0.156127	−	0.610380i
$861$	20.2796	−	5.96564i	0.691128	−	0.203309i
$862$		−	14.0134i		−	0.477297i
$863$		−	8.87998i		−	0.302278i	−0.988513	−	0.151139i	$-0.951706\pi$
$863$		−	8.87998i		−	0.302278i	0.988513	−	0.151139i	$-0.0482941\pi$
$864$	−1.70685	−	4.90782i	−0.0580682	−	0.166967i
$865$	27.2845	−	26.6703i	0.927701	−	0.906819i
$866$			20.0580i			0.681598i
$867$	−17.0790	+	17.9299i	−0.580033	+	0.608930i
$868$	−5.80579	+	10.0559i	−0.197061	+	0.341321i
$869$	0.0658613	+	0.114075i	0.00223419	+	0.00386973i
$870$	0.0234329	+	1.81401i	0.000794450	+	0.0615006i
$871$	−5.75446	−	9.96701i	−0.194982	−	0.337719i
$872$	−8.53953	−	14.7909i	−0.289185	−	0.500883i
$873$	−0.368332	−	7.57309i	−0.0124662	−	0.256310i
$874$	−0.431477	−	4.07489i	−0.0145949	−	0.137835i
$875$	−13.9660	−	14.9539i	−0.472135	−	0.505533i
$876$	−1.78088	+	7.35692i	−0.0601703	+	0.248567i
$877$	−19.4899	−	33.7575i	−0.658127	−	1.13991i	−0.981100	−	0.193501i	$-0.938016\pi$
$877$	−19.4899	−	33.7575i	−0.658127	−	1.13991i	0.322973	−	0.946408i	$-0.395318\pi$
$878$	−14.8057	+	25.6443i	−0.499670	+	0.865453i
$879$	10.2026	−	42.1477i	0.344126	−	1.42161i
$880$	−0.0280666	+	0.0274348i	−0.000946125	+	0.000924828i
$881$		−	14.1415i		−	0.476438i	−0.971211	−	0.238219i	$-0.923436\pi$
$881$		−	14.1415i		−	0.476438i	0.971211	−	0.238219i	$-0.0765636\pi$
$882$	−10.9391	+	0.532044i	−0.368338	+	0.0179149i
$883$	−39.2478	−	22.6597i	−1.32079	−	0.762560i	−0.336937	−	0.941527i	$-0.609391\pi$
$883$	−39.2478	−	22.6597i	−1.32079	−	0.762560i	−0.983855	+	0.178967i	$0.942724\pi$
$884$	1.95389	−	3.38423i	0.0657163	−	0.113824i
$885$	−22.5557	−	37.9276i	−0.758200	−	1.27492i
$886$		−	34.2462i		−	1.15052i
$887$	26.5783	+	15.3450i	0.892413	+	0.515235i	0.874731	−	0.484609i	$-0.161038\pi$
$887$	26.5783	+	15.3450i	0.892413	+	0.515235i	0.0176819	+	0.999844i	$0.494371\pi$
$888$	1.48079	−	6.11725i	0.0496922	−	0.205282i
$889$	−28.4389	−	16.4192i	−0.953810	−	0.550683i
$890$	−0.209782	−	0.820147i	−0.00703192	−	0.0274914i
$891$	0.128495	−	0.0918885i	0.00430476	−	0.00307838i
$892$	24.0340			0.804718
$893$	−10.6233	+	23.9102i	−0.355497	+	0.800125i
$894$	3.10379	−	3.25842i	0.103806	−	0.108978i
$895$	46.5622	−	11.9100i	1.55640	−	0.398106i
$896$	−0.915058	−	1.58493i	−0.0305700	−	0.0529487i
$897$	1.09211	+	3.71251i	0.0364643	+	0.123957i
$898$	20.9987	−	12.1236i	0.700735	−	0.404570i
$899$	2.57379	+	1.48598i	0.0858407	+	0.0495601i
$900$	7.16194	−	13.1798i	0.238731	−	0.439326i
$901$		−	12.3210i		−	0.410474i
$902$	0.0585255	−	0.101369i	0.00194869	−	0.00337522i
$903$	7.39164	+	25.1272i	0.245978	+	0.836180i
$904$	−13.8676			−0.461230
$905$	20.1171	+	5.63655i	0.668716	+	0.187365i
$906$	7.59963	+	25.8342i	0.252481	+	0.858285i
$907$	21.3528	+	36.9842i	0.709009	+	1.22804i	0.965225	+	0.261420i	$0.0841907\pi$
$907$	21.3528	+	36.9842i	0.709009	+	1.22804i	−0.256216	+	0.966619i	$0.582476\pi$
$908$	25.2064	+	14.5529i	0.836505	+	0.482956i
$909$	−8.25951	−	12.8239i	−0.273951	−	0.425341i
$910$	9.42259	−	2.41017i	0.312356	−	0.0798963i
$911$	−17.7467			−0.587974			−0.293987	−	0.955809i	$-0.594982\pi$
$911$	−17.7467			−0.587974			−0.293987	+	0.955809i	$0.594982\pi$
$912$	−2.88148	−	6.97833i	−0.0954152	−	0.231076i
$913$			0.210412i			0.00696361i
$914$	−13.2226	−	22.9021i	−0.437363	−	0.757535i
$915$	−16.0382	+	28.6267i	−0.530207	+	0.946369i
$916$	−5.42300	+	9.39292i	−0.179181	+	0.310351i
$917$	−3.40438	−	5.89656i	−0.112423	−	0.194722i
$918$	2.80644	+	8.06955i	0.0926265	+	0.266335i
$919$	19.0426			0.628156			0.314078	−	0.949397i	$-0.398305\pi$
$919$	19.0426			0.628156			0.314078	+	0.949397i	$0.398305\pi$
$920$	2.02411	+	0.567129i	0.0667330	+	0.0186977i
$921$	11.1718	+	37.9776i	0.368124	+	1.25140i
$922$	0.326148	−	0.564904i	0.0107411	−	0.0186041i
$923$	−22.0485			−0.725737
$924$	0.0383745	−	0.0402863i	0.00126243	−	0.00132532i
$925$	15.9375	−	8.72398i	0.524023	−	0.286843i
$926$	−3.23586	−	5.60468i	−0.106337	−	0.184181i
$927$	6.90270	+	3.54987i	0.226714	+	0.116593i
$928$	−0.405658	+	0.234207i	−0.0133164	+	0.00768821i
$929$	31.2455	−	18.0396i	1.02513	−	0.591860i	0.109546	−	0.993982i	$-0.465060\pi$
$929$	31.2455	−	18.0396i	1.02513	−	0.591860i	0.915586	+	0.402121i	$0.131727\pi$
$930$	−12.5604	−	21.1204i	−0.411870	−	0.692565i
$931$	−15.8244	+	1.67560i	−0.518625	+	0.0549156i
$932$	4.39410			0.143934
$933$	11.5098	−	47.5478i	0.376815	−	1.55664i
$934$	5.55111	−	3.20493i	0.181638	−	0.104869i
$935$	0.0461478	−	0.0451090i	0.00150919	−	0.00147522i
$936$	3.86076	+	5.99429i	0.126193	+	0.195929i
$937$	−14.1261	−	8.15573i	−0.461481	−	0.266436i	0.251186	−	0.967939i	$-0.419179\pi$
$937$	−14.1261	−	8.15573i	−0.461481	−	0.266436i	−0.712667	+	0.701503i	$0.752513\pi$
$938$	8.86227			0.289363
$939$	9.82076	+	9.35471i	0.320488	+	0.305280i
$940$	−9.38204	−	9.59808i	−0.306008	−	0.313055i
$941$	−6.27180	+	10.8631i	−0.204455	+	0.354126i	−0.949959	−	0.312375i	$-0.898875\pi$
$941$	−6.27180	+	10.8631i	−0.204455	+	0.354126i	0.745504	+	0.666501i	$0.232209\pi$
$942$	−18.0420	+	18.9408i	−0.587839	+	0.617124i
$943$	−6.26907			−0.204149
$944$	5.69687	−	9.86726i	0.185417	−	0.321152i
$945$	−9.47980	+	19.0340i	−0.308378	+	0.619176i
$946$	0.125600	+	0.0725152i	0.00408361	+	0.00235767i
$947$	10.0502	+	17.4074i	0.326587	+	0.565665i	0.981832	−	0.189751i	$-0.0607681\pi$
$947$	10.0502	+	17.4074i	0.326587	+	0.565665i	−0.655245	+	0.755416i	$0.727435\pi$
$948$	3.05817	−	12.6335i	0.0993247	−	0.410316i
$949$		−	10.3865i		−	0.337160i
$950$	9.30028	−	19.7105i	0.301741	−	0.639494i
$951$	22.2427	+	21.1871i	0.721268	+	0.687040i
$952$	1.50456	+	2.60598i	0.0487631	+	0.0844602i
$953$	−32.8574	+	18.9703i	−1.06436	+	0.614507i	−0.926634	−	0.375964i	$-0.877312\pi$
$953$	−32.8574	+	18.9703i	−1.06436	+	0.614507i	−0.137723	+	0.990471i	$0.543978\pi$
$954$	19.9918	+	10.2812i	0.647259	+	0.332867i
$955$	−7.40627	−	28.9549i	−0.239661	−	0.936959i
$956$	19.8942	+	11.4859i	0.643425	+	0.371482i
$957$	−0.0103112	−	0.00982186i	−0.000333313	−	0.000317496i
$958$	7.66717			0.247715
$959$	−1.48087	−	0.854979i	−0.0478197	−	0.0276087i
$960$	3.87266	−	0.0500261i	0.124990	−	0.00161459i
$961$	−9.25554			−0.298566
$962$			8.63634i			0.278447i
$963$	−19.5753	+	38.0640i	−0.630804	+	1.22660i
$964$	−1.60542	+	0.926892i	−0.0517072	+	0.0298532i
$965$	21.2432	+	21.7324i	0.683843	+	0.699590i
$966$	−2.89624	−	0.701089i	−0.0931850	−	0.0225572i
$967$	1.89435	−	1.09370i	0.0609181	−	0.0351711i	−0.469232	−	0.883075i	$-0.655469\pi$
$967$	1.89435	−	1.09370i	0.0609181	−	0.0351711i	0.530150	+	0.847904i	$0.322136\pi$
$968$			10.9997i			0.353543i
$969$	4.73779	+	11.4739i	0.152200	+	0.368596i
$970$	5.44175	+	1.52471i	0.174724	+	0.0489554i
$971$	17.6378	+	30.5495i	0.566023	+	0.980381i	0.996954	+	0.0779958i	$0.0248521\pi$
$971$	17.6378	+	30.5495i	0.566023	+	0.980381i	−0.430930	+	0.902385i	$0.641815\pi$
$972$	−15.4353	−	2.17993i	−0.495087	−	0.0699214i
$973$	15.9026	+	9.18136i	0.509814	+	0.294341i
$974$	−33.2577	+	19.2013i	−1.06564	+	0.615250i
$975$	−5.29663	+	19.8894i	−0.169628	+	0.636969i
$976$	−8.47235			−0.271193
$977$		−	50.7753i		−	1.62445i	−0.583347	−	0.812223i	$-0.698257\pi$
$977$		−	50.7753i		−	1.62445i	0.583347	−	0.812223i	$-0.301743\pi$
$978$	0.303574	+	1.03197i	0.00970723	+	0.0329988i
$979$	0.00575482	+	0.00332255i	0.000183925	+	0.000106189i
$980$	2.20239	−	7.86044i	0.0703528	−	0.251093i
$981$	−51.1767	+	2.48908i	−1.63395	+	0.0794702i
$982$	13.9976	−	24.2445i	0.446680	−	0.773672i
$983$	37.0595	−	21.3963i	1.18201	−	0.682436i	0.225534	−	0.974235i	$-0.427587\pi$
$983$	37.0595	−	21.3963i	1.18201	−	0.682436i	0.956480	+	0.291799i	$0.0942540\pi$
$984$	−11.0811	+	3.25971i	−0.353251	+	0.103916i
$985$	−7.69090	+	1.96723i	−0.245052	+	0.0626810i
$986$	0.666993	−	0.385088i	0.0212414	−	0.0122637i
$987$	13.7769	+	13.1231i	0.438524	+	0.417714i
$988$	6.09573	+	8.37642i	0.193931	+	0.266489i
$989$		−	7.76760i		−	0.246995i
$990$	0.0346850	+	0.112519i	0.00110236	+	0.00357610i
$991$	−2.97552	+	1.71792i	−0.0945205	+	0.0545715i	−0.546515	−	0.837449i	$-0.684046\pi$
$991$	−2.97552	+	1.71792i	−0.0945205	+	0.0545715i	0.451995	+	0.892021i	$0.350713\pi$
$992$	3.17236	−	5.49469i	0.100723	−	0.174457i
$993$	−4.54048	+	18.7570i	−0.144088	+	0.595236i
$994$	8.48908	−	14.7035i	0.269257	−	0.466367i
$995$	−2.67614	+	9.55129i	−0.0848395	+	0.302796i
$996$	14.3209	−	15.0343i	0.453774	−	0.476380i
$997$	−40.1860	−	23.2014i	−1.27270	−	0.734796i	−0.297208	−	0.954813i	$-0.596056\pi$
$997$	−40.1860	−	23.2014i	−1.27270	−	0.734796i	−0.975496	+	0.220016i	$0.929389\pi$
$998$	−12.9934	−	7.50172i	−0.411297	−	0.237463i
$999$	−14.2884	−	12.3435i	−0.452065	−	0.390532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.n.a.449.2	yes	80
3.2	odd	2	inner	570.2.n.a.449.32	yes	80
5.4	even	2	inner	570.2.n.a.449.39	yes	80
15.14	odd	2	inner	570.2.n.a.449.9	yes	80
19.8	odd	6	inner	570.2.n.a.179.9	yes	80
57.8	even	6	inner	570.2.n.a.179.39	yes	80
95.84	odd	6	inner	570.2.n.a.179.32	yes	80
285.179	even	6	inner	570.2.n.a.179.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.2	✓	80	285.179	even	6	inner
570.2.n.a.179.9	yes	80	19.8	odd	6	inner
570.2.n.a.179.32	yes	80	95.84	odd	6	inner
570.2.n.a.179.39	yes	80	57.8	even	6	inner
570.2.n.a.449.2	yes	80	1.1	even	1	trivial
570.2.n.a.449.9	yes	80	15.14	odd	2	inner
570.2.n.a.449.32	yes	80	3.2	odd	2	inner
570.2.n.a.449.39	yes	80	5.4	even	2	inner

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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 40 q^{4}+O(q^{10}) \) 80 * q + 40 * q^4	\( 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) \) 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Introduction

L-functions

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