LMFDB - Embedded newform 570.2.n.a.179.9

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			179.9
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.488805 - 1.66165i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.56304 - 1.59903i) q^{5} +(-0.407506 + 1.68343i) q^{6} -1.83012i q^{7} -1.00000i q^{8} +(-2.52214 + 1.62444i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.488805 - 1.66165i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.56304 - 1.59903i) q^{5} +(-0.407506 + 1.68343i) q^{6} -1.83012i q^{7} -1.00000i q^{8} +(-2.52214 + 1.62444i) q^{9} +(0.554116 + 2.16632i) q^{10} -0.0175522i q^{11} +(1.19463 - 1.25414i) q^{12} +(-1.18833 - 2.05825i) q^{13} +(-0.915058 + 1.58493i) q^{14} +(-1.89301 + 3.37884i) 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} +(-3.04101 + 0.894570i) q^{21} +(-0.00877612 + 0.0152007i) q^{22} +(0.470036 + 0.814125i) q^{23} +(-1.66165 + 0.488805i) q^{24} +(-0.113813 + 4.99870i) 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} +(-0.0291656 + 0.00857962i) q^{33} +(-1.42394 + 0.822112i) q^{34} +(-2.92642 + 2.86055i) q^{35} +(-2.66788 - 1.37202i) q^{36} -3.63380 q^{37} +(3.52444 + 2.56482i) q^{38} +(-2.83923 + 2.98068i) q^{39} +(-1.59903 + 1.56304i) q^{40} +(3.33436 - 5.77528i) q^{41} +(3.08087 + 0.745783i) 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} +(1.68343 + 0.407506i) q^{48} +3.65067 q^{49} +(2.59792 - 4.27210i) q^{50} +(-2.76794 - 0.670031i) q^{51} +(1.18833 - 2.05825i) q^{52} +(-6.48959 + 3.74677i) q^{53} +(-1.70685 - 4.90782i) q^{54} +(-0.0280666 + 0.0274348i) q^{55} -1.83012 q^{56} +(1.35614 + 7.42704i) q^{57} -0.468414i q^{58} +(-5.69687 + 9.86726i) q^{59} +(-3.87266 + 0.0500261i) q^{60} +(4.23617 + 7.33727i) q^{61} +(3.17236 - 5.49469i) q^{62} +(2.97292 + 4.61581i) q^{63} -1.00000 q^{64} +(-1.43380 + 5.11732i) q^{65} +(0.0295480 + 0.00715264i) q^{66} +(-2.42123 - 4.19369i) q^{67} +1.64422 q^{68} +(1.12303 - 1.17898i) q^{69} +(3.96462 - 1.01410i) q^{70} +(4.63854 - 8.03419i) q^{71} +(1.62444 + 2.52214i) 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} +(3.94918 - 1.16173i) q^{78} +(-6.49918 - 3.75230i) q^{79} +(2.16632 - 0.554116i) q^{80} +(3.72237 - 8.19414i) q^{81} +(-5.77528 + 3.33436i) q^{82} -11.9877 q^{83} +(-2.29522 - 2.18630i) q^{84} +(-3.56192 + 0.911090i) q^{85} +(4.13139 + 7.15578i) q^{86} +(0.559579 - 0.587457i) q^{87} -0.0175522 q^{88} +(0.189295 + 0.327868i) q^{89} +(-4.91662 - 4.56364i) q^{90} +(-3.76685 + 2.17479i) q^{91} +(-0.470036 + 0.814125i) q^{92} +(10.5427 - 3.10133i) q^{93} -6.00243i q^{94} +(6.04133 + 7.64868i) q^{95} +(-1.25414 - 1.19463i) q^{96} +(1.26367 - 2.18875i) q^{97} +(-3.16158 - 1.82534i) q^{98} +(0.0285126 + 0.0442692i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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
$3$	−0.488805	−	1.66165i	−0.282212	−	0.959352i
$3$	−0.488805	−	1.66165i	−0.282212	−	0.959352i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.56304	−	1.59903i	−0.699013	−	0.715109i
$5$	−1.56304	−	1.59903i	−0.699013	−	0.715109i
$6$	−0.407506	+	1.68343i	−0.166364	+	0.687258i
$7$		−	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
$9$	−2.52214	+	1.62444i	−0.840713	+	0.541481i
$10$	0.554116	+	2.16632i	0.175227	+	0.685052i
$11$		−	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	$-0.273575\pi$
$13$	−1.18833	−	2.05825i	−0.329584	−	0.570857i	−0.982429	+	0.186635i	$0.940242\pi$
$14$	−0.915058	+	1.58493i	−0.244560	+	0.423590i
$15$	−1.89301	+	3.37884i	−0.488772	+	0.872411i
$16$	−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
$21$	−3.04101	+	0.894570i	−0.663602	+	0.195211i
$22$	−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	$0.802086\pi$
$24$	−1.66165	+	0.488805i	−0.339182	+	0.0997769i
$25$	−0.113813	+	4.99870i	−0.0227627	+	0.999741i
$26$			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	$-0.152819\pi$
$29$	0.234207	+	0.405658i	0.0434911	+	0.0753288i	−0.843460	+	0.537191i	$0.819485\pi$
$30$	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
$33$	−0.0291656	+	0.00857962i	−0.00507708	+	0.00149352i
$34$	−1.42394	+	0.822112i	−0.244204	+	0.140991i
$35$	−2.92642	+	2.86055i	−0.494655	+	0.483520i
$36$	−2.66788	−	1.37202i	−0.444646	−	0.228669i
$37$	−3.63380			−0.597393			−0.298697	−	0.954348i	$-0.596552\pi$
$37$	−3.63380			−0.597393			−0.298697	+	0.954348i	$0.596552\pi$
$38$	3.52444	+	2.56482i	0.571740	+	0.416070i
$39$	−2.83923	+	2.98068i	−0.454640	+	0.477290i
$40$	−1.59903	+	1.56304i	−0.252829	+	0.247138i
$41$	3.33436	−	5.77528i	0.520740	−	0.901948i	−0.478969	−	0.877832i	$-0.658989\pi$
$41$	3.33436	−	5.77528i	0.520740	−	0.901948i	0.999709	−	0.0241163i	$-0.00767719\pi$
$42$	3.08087	+	0.745783i	0.475389	+	0.115077i
$43$	−7.15578	−	4.13139i	−1.09125	−	0.630031i	−0.157338	−	0.987545i	$-0.550291\pi$
$43$	−7.15578	−	4.13139i	−1.09125	−	0.630031i	−0.933908	+	0.357513i	$0.883625\pi$
$44$	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	$0.689101\pi$
$48$	1.68343	+	0.407506i	0.242982	+	0.0588184i
$49$	3.65067			0.521525
$50$	2.59792	−	4.27210i	0.367401	−	0.604166i
$51$	−2.76794	−	0.670031i	−0.387589	−	0.0938231i
$52$	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	$0.505414\pi$
$54$	−1.70685	−	4.90782i	−0.232273	−	0.667869i
$55$	−0.0280666	+	0.0274348i	−0.00378450	+	0.00369931i
$56$	−1.83012			−0.244560
$57$	1.35614	+	7.42704i	0.179625	+	0.983735i
$58$		−	0.468414i		−	0.0615057i
$59$	−5.69687	+	9.86726i	−0.741669	+	1.28461i	0.210066	+	0.977687i	$0.432632\pi$
$59$	−5.69687	+	9.86726i	−0.741669	+	1.28461i	−0.951735	+	0.306921i	$0.900701\pi$
$60$	−3.87266	+	0.0500261i	−0.499958	+	0.00645834i
$61$	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
$63$	2.97292	+	4.61581i	0.374553	+	0.581537i
$64$	−1.00000			−0.125000
$65$	−1.43380	+	5.11732i	−0.177841	+	0.634725i
$66$	0.0295480	+	0.00715264i	0.00363710	+	0.000880429i
$67$	−2.42123	−	4.19369i	−0.295800	−	0.512341i	0.679370	−	0.733796i	$-0.262253\pi$
$67$	−2.42123	−	4.19369i	−0.295800	−	0.512341i	−0.975171	+	0.221454i	$0.928920\pi$
$68$	1.64422			0.199391
$69$	1.12303	−	1.17898i	0.135197	−	0.141933i
$70$	3.96462	−	1.01410i	0.473863	−	0.121208i
$71$	4.63854	−	8.03419i	0.550494	−	0.953483i	−0.447745	−	0.894161i	$-0.647773\pi$
$71$	4.63854	−	8.03419i	0.550494	−	0.953483i	0.998239	−	0.0593220i	$-0.0188939\pi$
$72$	1.62444	+	2.52214i	0.191442	+	0.297237i
$73$	−3.78470	−	2.18510i	−0.442966	−	0.255746i	0.261889	−	0.965098i	$-0.415654\pi$
$73$	−3.78470	−	2.18510i	−0.442966	−	0.255746i	−0.704855	+	0.709352i	$0.748988\pi$
$74$	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
$78$	3.94918	−	1.16173i	0.447157	−	0.131540i
$79$	−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	$0.805397\pi$
$80$	2.16632	−	0.554116i	0.242202	−	0.0619520i
$81$	3.72237	−	8.19414i	0.413597	−	0.910460i
$82$	−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
$85$	−3.56192	+	0.911090i	−0.386345	+	0.0988216i
$86$	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	$-0.160279\pi$
$89$	0.189295	+	0.327868i	0.0200652	+	0.0347539i	−0.855818	+	0.517276i	$0.826946\pi$
$90$	−4.91662	−	4.56364i	−0.518258	−	0.481050i
$91$	−3.76685	+	2.17479i	−0.394873	+	0.227980i
$92$	−0.470036	+	0.814125i	−0.0490046	+	0.0848784i
$93$	10.5427	−	3.10133i	1.09323	−	0.321593i
$94$		−	6.00243i		−	0.619103i
$95$	6.04133	+	7.64868i	0.619827	+	0.784739i
$96$	−1.25414	−	1.19463i	−0.128000	−	0.121926i
$97$	1.26367	−	2.18875i	0.128307	−	0.222234i	−0.794714	−	0.606984i	$-0.792379\pi$
$97$	1.26367	−	2.18875i	0.128307	−	0.222234i	0.923021	+	0.384750i	$0.125713\pi$
$98$	−3.16158	−	1.82534i	−0.319367	−	0.184387i
$99$	0.0285126	+	0.0442692i	0.00286562	+	0.00444922i
$100$	−4.38591	+	2.40079i	−0.438591	+	0.240079i
$101$	4.40332	−	2.54226i	0.438147	−	0.252964i	−0.264664	−	0.964341i	$-0.585261\pi$
$101$	4.40332	−	2.54226i	0.438147	−	0.252964i	0.702811	+	0.711376i	$0.251928\pi$
$102$	2.06209	+	1.96423i	0.204177	+	0.194488i
$103$	−2.58734			−0.254938			−0.127469	−	0.991843i	$-0.540685\pi$
$103$	−2.58734			−0.254938			−0.127469	+	0.991843i	$0.540685\pi$
$104$	−2.05825	+	1.18833i	−0.201828	+	0.116526i
$105$	6.18366	+	3.46442i	0.603464	+	0.338093i
$106$	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	$-0.242234\pi$
$108$	−0.975733	+	5.10372i	−0.0938899	+	0.491106i
$109$	−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	$0.971550\pi$
$110$	0.0380238	−	0.00972597i	0.00362543	−	0.000927335i
$111$	1.77622	+	6.03809i	0.168591	+	0.573110i
$112$	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	$-0.226187\pi$
$114$	2.53907	−	7.11007i	0.237806	−	0.665919i
$115$	0.567129	−	2.02411i	0.0528851	−	0.188749i
$116$	−0.234207	+	0.405658i	−0.0217456	+	0.0376644i
$117$	6.34066	+	3.26082i	0.586194	+	0.301463i
$118$	9.86726	−	5.69687i	0.908355	−	0.524439i
$119$	−2.60598	−	1.50456i	−0.238889	−	0.137923i
$120$	3.37884	+	1.89301i	0.308444	+	0.172807i
$121$	10.9997			0.999972
$122$		−	8.47235i		−	0.767050i
$123$	−11.2263	−	2.71754i	−1.01224	−	0.245033i
$124$	−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	$-0.873556\pi$
$127$	−8.97167	−	15.5394i	−0.796107	−	1.37890i	0.126026	−	0.992027i	$-0.459778\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.36713	+	13.9098i	−0.296459	+	1.22469i
$130$	3.80037	−	3.71483i	0.333314	−	0.325812i
$131$	−3.22196	−	1.86020i	−0.281504	−	0.162526i	0.352600	−	0.935774i	$-0.385298\pi$
$131$	−3.22196	−	1.86020i	−0.281504	−	0.162526i	−0.634104	+	0.773248i	$0.718631\pi$
$132$	−0.0220130	−	0.0209684i	−0.00191598	−	0.00182506i
$133$	−0.839994	+	7.93295i	−0.0728367	+	0.687874i
$134$			4.84246i			0.418325i
$135$	−0.714298	−	11.5970i	−0.0614770	−	0.998109i
$136$	−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	$0.820625\pi$
$138$	−1.56207	+	0.459511i	−0.132972	+	0.0391162i
$139$	−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
$147$	−1.78447	−	6.06613i	−0.147180	−	0.500326i
$148$	−1.81690	−	3.14696i	−0.149348	−	0.258679i
$149$	−2.25005	−	1.29906i	−0.184331	−	0.106424i	0.404995	−	0.914319i	$-0.367273\pi$
$149$	−2.25005	−	1.29906i	−0.184331	−	0.106424i	−0.589326	+	0.807895i	$0.700607\pi$
$150$	−8.36859	−	2.22860i	−0.683293	−	0.181964i
$151$		−	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
$155$	10.1454	−	9.91706i	0.814900	−	0.796557i
$156$	−4.00095	−	0.968506i	−0.320333	−	0.0775425i
$157$	13.0792	+	7.55130i	1.04384	+	0.602659i	0.920918	−	0.389757i	$-0.127441\pi$
$157$	13.0792	+	7.55130i	1.04384	+	0.602659i	0.122919	+	0.992417i	$0.460774\pi$
$158$	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
$162$	−7.32074	+	5.23515i	−0.575172	+	0.411312i
$163$			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
$165$	0.0593061	+	0.0332265i	0.00461697	+	0.00258668i
$166$	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	$0.554654\pi$
$168$	0.894570	+	3.04101i	0.0690176	+	0.234619i
$169$	3.67573	−	6.36655i	0.282748	−	0.489734i
$170$	3.54026	+	0.991933i	0.271526	+	0.0760778i
$171$	11.6782	−	5.88380i	0.893056	−	0.449945i
$172$		−	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	$0.442004\pi$
$174$	−0.778338	+	0.228963i	−0.0590056	+	0.0173576i
$175$	9.14821	+	0.208292i	0.691540	+	0.0157454i
$176$	0.0152007	+	0.00877612i	0.00114579	+	0.000661525i
$177$	19.1806	+	4.64301i	1.44170	+	0.348990i
$178$		−	0.378589i		−	0.0283765i
$179$	−21.4936			−1.60651			−0.803255	−	0.595636i	$-0.796900\pi$
$179$	−21.4936			−1.60651			−0.803255	+	0.595636i	$0.796900\pi$
$180$	1.97610	+	6.41054i	0.147290	+	0.477813i
$181$	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
$185$	5.67978	+	5.81057i	0.417585	+	0.427201i
$186$	−10.6809	−	2.58551i	−0.783162	−	0.189579i
$187$	−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
$190$	−1.40760	−	9.64462i	−0.102118	−	0.699694i
$191$		−	13.3659i		−	0.967125i	−0.875310	−	0.483562i	$-0.839343\pi$
$191$		−	13.3659i		−	0.967125i	0.875310	−	0.483562i	$-0.160657\pi$
$192$	0.488805	+	1.66165i	0.0352765	+	0.119919i
$193$	−6.79547	+	11.7701i	−0.489149	+	0.847231i	−0.999922	−	0.0124848i	$-0.996026\pi$
$193$	−6.79547	+	11.7701i	−0.489149	+	0.847231i	0.510773	+	0.859716i	$0.329359\pi$
$194$	−2.18875	+	1.26367i	−0.157143	+	0.0907265i
$195$	9.20402	−	0.118895i	0.659114	−	0.00851428i
$196$	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	$0.883589\pi$
$200$	4.99870	+	0.113813i	0.353462	+	0.00804781i
$201$	−5.78493	+	6.07313i	−0.408037	+	0.428365i
$202$	−5.08452			−0.357746
$203$	0.742401	−	0.428626i	0.0521064	−	0.0300836i
$204$	−0.803705	−	2.73212i	−0.0562706	−	0.191287i
$205$	−14.4466	+	3.69524i	−1.00900	+	0.258087i
$206$	2.24070	+	1.29367i	0.156117	+	0.0901342i
$207$	−2.50799	−	1.28979i	−0.174318	−	0.0896467i
$208$	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
$213$	−15.6173	−	3.78047i	−1.07008	−	0.259033i
$214$	−7.13376	+	12.3560i	−0.487654	+	0.844641i
$215$	4.57854	+	17.8999i	0.312254	+	1.22076i
$216$	3.39687	−	3.93208i	0.231128	−	0.267544i
$217$	11.6116			0.788246
$218$	8.53953	+	14.7909i	0.578370	+	1.00177i
$219$	−1.78088	+	7.35692i	−0.120341	+	0.497135i
$220$	−0.0377926	−	0.0105890i	−0.00254797	−	0.000713908i
$221$	−3.90777			−0.262865
$222$	1.48079	−	6.11725i	0.0993844	−	0.410563i
$223$	−12.0170	+	20.8140i	−0.804718	+	1.39381i	0.111764	+	0.993735i	$0.464350\pi$
$223$	−12.0170	+	20.8140i	−0.804718	+	1.39381i	−0.916482	+	0.400077i	$0.868983\pi$
$224$	−0.915058	−	1.58493i	−0.0611399	−	0.105897i
$225$	−7.83305	−	12.7923i	−0.522204	−	0.852821i
$226$	−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	$-0.416651\pi$
$228$	−5.75393	+	4.88797i	−0.381064	+	0.323714i
$229$	−10.8460			−0.716724			−0.358362	−	0.933583i	$-0.616665\pi$
$229$	−10.8460			−0.716724			−0.358362	+	0.933583i	$0.616665\pi$
$230$	−1.50320	+	1.46937i	−0.0991184	+	0.0968873i
$231$	0.0157017	+	0.0533765i	0.00103310	+	0.00351191i
$232$	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	$0.120692\pi$
$234$	−3.86076	−	5.99429i	−0.252386	−	0.391859i
$235$	3.62117	−	12.9241i	0.236219	−	0.843077i
$236$	−11.3937			−0.741669
$237$	−3.05817	+	12.6335i	−0.198649	+	0.820632i
$238$	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	−0.550815	−	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
$243$	−15.4353	−	2.17993i	−0.990174	−	0.139843i
$244$	−4.23617	+	7.33727i	−0.271193	+	0.469721i
$245$	−5.70615	−	5.83755i	−0.364552	−	0.372947i
$246$	8.36352	+	7.96663i	0.533239	+	0.507934i
$247$	4.20632	+	9.46727i	0.267642	+	0.602388i
$248$	6.34473			0.402890
$249$	5.85967	+	19.9194i	0.371341	+	1.26234i
$250$	−10.8919	+	2.52330i	−0.688863	+	0.159588i
$251$	−22.8209	+	13.1757i	−1.44044	+	0.831641i	−0.997879	−	0.0650960i	$-0.979265\pi$
$251$	−22.8209	+	13.1757i	−1.44044	+	0.831641i	−0.442565	+	0.896737i	$0.645931\pi$
$252$	−2.51095	+	4.88253i	−0.158175	+	0.307570i
$253$	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
$260$	−5.14863	+	1.31695i	−0.319304	+	0.0816737i
$261$	−1.24967	−	0.642671i	−0.0773526	−	0.0397803i
$262$	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	$0.267499\pi$
$264$	0.00857962	+	0.0291656i	0.000528039	+	0.00179502i
$265$	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	$-0.711484\pi$
$269$	6.12619	−	10.6109i	0.373520	−	0.646956i	0.990104	+	0.140333i	$0.0448172\pi$
$270$	−5.17989	+	10.4004i	−0.315238	+	0.632950i
$271$	−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
$275$	0.0877384	+	0.00199768i	0.00529083	+	0.000120464i
$276$	1.58254	+	0.383084i	0.0952580	+	0.0230590i
$277$			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
$279$	−10.3066	−	16.0023i	−0.617042	−	0.958032i
$280$	2.86055	+	2.92642i	0.170950	+	0.174887i
$281$	−14.5706	−	25.2370i	−0.869209	−	1.50551i	−0.862806	−	0.505535i	$-0.831295\pi$
$281$	−14.5706	−	25.2370i	−0.869209	−	1.50551i	−0.00640302	−	0.999980i	$-0.502038\pi$
$282$	−9.97392	+	2.93402i	−0.593938	+	0.174718i
$283$	22.6635	+	13.0848i	1.34720	+	0.777808i	0.987852	−	0.155395i	$-0.0496650\pi$
$283$	22.6635	+	13.0848i	1.34720	+	0.777808i	0.359350	+	0.933203i	$0.382998\pi$
$284$	9.27709			0.550494
$285$	9.75638	−	13.7773i	0.577918	−	0.816095i
$286$	0.0417158			0.00246671
$287$	−10.5694	−	6.10227i	−0.623895	−	0.360206i
$288$	−1.37202	+	2.66788i	−0.0808468	+	0.157206i
$289$	7.14826	+	12.3812i	0.420486	+	0.728303i
$290$	−0.749009	+	0.732149i	−0.0439833	+	0.0429933i
$291$	−4.25461	−	1.02991i	−0.249410	−	0.0603743i
$292$		−	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	$-0.261101\pi$
$294$	−1.48767	+	6.14566i	−0.0867627	+	0.358422i
$295$	24.6825	−	6.31345i	1.43707	−	0.367583i
$296$			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
$300$	6.13312	+	6.11432i	0.354096	+	0.353010i
$301$	−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
$306$	2.25590	−	4.38659i	0.128961	−	0.250765i
$307$	11.4277	−	19.7934i	0.652213	−	1.12967i	−0.330371	−	0.943851i	$-0.607174\pi$
$307$	11.4277	−	19.7934i	0.652213	−	1.12967i	0.982585	−	0.185816i	$-0.0594927\pi$
$308$	−0.0160613	−	0.0278190i	−0.000915179	−	0.00158514i
$309$	1.26470	+	4.29924i	0.0719465	+	0.244575i
$310$	−13.7447	+	3.51571i	−0.780648	+	0.199679i
$311$			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	$-0.595634\pi$
$313$	6.78155	−	3.91533i	0.383316	−	0.221308i	0.679260	+	0.733898i	$0.262301\pi$
$314$	−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	$0.499287\pi$
$318$	−3.66288	−	12.4516i	−0.205404	−	0.698251i
$319$	0.00712020	−	0.00411085i	0.000398655	−	0.000230164i
$320$	1.56304	+	1.59903i	0.0873766	+	0.0893887i
$321$	−23.7076	+	6.97403i	−1.32323	+	0.389253i
$322$	−1.72044			−0.0958764
$323$	−4.21715	+	5.79497i	−0.234648	+	0.322441i
$324$	8.95752	−	0.873400i	0.497640	−	0.0485222i
$325$	10.4239	−	5.70587i	0.578211	−	0.316505i
$326$	0.310527	−	0.537848i	0.0171985	−	0.0297887i
$327$	−6.95981	+	28.7514i	−0.384879	+	1.58996i
$328$	−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
$333$	9.16495	−	5.90290i	0.502236	−	0.323477i
$334$	16.5571			0.905966
$335$	−2.92138	+	10.4265i	−0.159612	+	0.569663i
$336$	0.745783	−	3.08087i	0.0406858	−	0.168075i
$337$	−3.30626	+	5.72662i	−0.180104	+	0.311949i	−0.941916	−	0.335849i	$-0.890977\pi$
$337$	−3.30626	+	5.72662i	−0.180104	+	0.311949i	0.761812	+	0.647798i	$0.224310\pi$
$338$	−6.36655	+	3.67573i	−0.346294	+	0.199933i
$339$	−23.0431	+	6.77856i	−1.25153	+	0.368161i
$340$	−2.56999	−	2.62917i	−0.139377	−	0.142587i
$341$	0.111364			0.00603070
$342$	−13.0555	−	0.743597i	−0.705963	−	0.0402091i
$343$		−	19.4920i		−	1.05247i
$344$	−4.13139	+	7.15578i	−0.222750	+	0.385814i
$345$	−3.64058	+	0.0470281i	−0.196002	+	0.00253191i
$346$	−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	$0.0968513\pi$
$348$	0.788542	+	0.190881i	0.0422703	+	0.0102323i
$349$	−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
$351$	2.31899	−	12.1298i	0.123779	−	0.647443i
$352$	−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
$355$	−20.0972	+	5.14058i	−1.06665	+	0.272834i
$356$	−0.189295	+	0.327868i	−0.0100326	+	0.0173770i
$357$	−1.22623	+	5.06565i	−0.0648992	+	0.268103i
$358$	18.6140	+	10.7468i	0.983782	+	0.567987i
$359$	−15.9731	−	9.22208i	−0.843029	−	0.486723i	0.0152639	−	0.999884i	$-0.495141\pi$
$359$	−15.9731	−	9.22208i	−0.843029	−	0.486723i	−0.858293	+	0.513161i	$0.828475\pi$
$360$	1.49392	−	6.53974i	0.0787363	−	0.344675i
$361$	18.5787	+	3.97908i	0.977825	+	0.209425i
$362$	−9.34312			−0.491063
$363$	−5.37670	−	18.2776i	−0.282204	−	0.959325i
$364$	−3.76685	−	2.17479i	−0.197436	−	0.113990i
$365$	2.42159	+	9.46725i	0.126752	+	0.495539i
$366$	−14.0780	+	4.14133i	−0.735871	+	0.216471i
$367$	1.09348	−	0.631323i	0.0570794	−	0.0329548i	−0.471189	−	0.882032i	$-0.656175\pi$
$367$	1.09348	−	0.631323i	0.0570794	−	0.0329548i	0.528268	+	0.849078i	$0.322842\pi$
$368$	−0.940071			−0.0490046
$369$	0.971892	+	19.9826i	0.0505947	+	1.04025i
$370$	−2.01355	−	7.87199i	−0.104679	−	0.409245i
$371$	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	$-0.510068\pi$
$373$	−1.22155			−0.0632497			−0.0316248	+	0.999500i	$0.510068\pi$
$374$	0.0144299	+	0.0249933i	0.000746153	+	0.00129237i
$375$	−16.6743	−	9.84714i	−0.861060	−	0.508504i
$376$	5.19826	−	3.00121i	0.268080	−	0.154776i
$377$	0.556631	−	0.964114i	0.0286680	−	0.0496544i
$378$	−8.98188	+	3.12373i	−0.461978	+	0.160668i
$379$		−	36.6243i		−	1.88126i	−0.339428	−	0.940632i	$-0.610233\pi$
$379$		−	36.6243i		−	1.88126i	0.339428	−	0.940632i	$-0.389767\pi$
$380$	−3.60329	+	9.05628i	−0.184845	+	0.464578i
$381$	−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	$0.502739\pi$
$384$	0.407506	−	1.68343i	0.0207954	−	0.0859072i
$385$	0.0502090	+	0.0513652i	0.00255889	+	0.00261781i
$386$	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	$-0.467095\pi$
$389$	20.0424	−	11.5715i	1.01619	−	0.586697i	0.912998	+	0.407964i	$0.133761\pi$
$390$	−8.03037	−	4.49905i	−0.406633	−	0.227818i
$391$	1.54569			0.0781688
$392$		−	3.65067i		−	0.184387i
$393$	−1.51608	+	6.26304i	−0.0764763	+	0.315928i
$394$	3.07457	+	1.77510i	0.154895	+	0.0894284i
$395$	4.15842	+	16.2574i	0.209233	+	0.817998i
$396$	−0.0240819	+	0.0468272i	−0.00121016	+	0.00235316i
$397$	23.9763	+	13.8427i	1.20334	+	0.694746i	0.961295	−	0.275520i	$-0.0888502\pi$
$397$	23.9763	+	13.8427i	1.20334	+	0.694746i	0.242040	+	0.970266i	$0.422184\pi$
$398$			4.43597i			0.222355i
$399$	13.5923	−	2.48189i	0.680468	−	0.124250i
$400$	−4.27210	−	2.59792i	−0.213605	−	0.129896i
$401$	−7.69191	+	13.3228i	−0.384115	+	0.665307i	−0.991646	−	0.128989i	$-0.958827\pi$
$401$	−7.69191	+	13.3228i	−0.384115	+	0.665307i	0.607531	+	0.794296i	$0.292160\pi$
$402$	8.04646	−	2.36702i	0.401321	−	0.118056i
$403$	13.0591	−	7.53965i	0.650518	−	0.375577i
$404$	4.40332	+	2.54226i	0.219074	+	0.126482i
$405$	−18.9209	+	6.85557i	−0.940188	+	0.340656i
$406$	−0.857251			−0.0425447
$407$			0.0637813i			0.00316152i
$408$	−0.670031	+	2.76794i	−0.0331715	+	0.137033i
$409$	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
$414$	1.52709	+	2.37099i	0.0750524	+	0.116528i
$415$	18.7373	+	19.1688i	0.919778	+	0.940959i
$416$	−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	$-0.103441\pi$
$420$	0.0915536	+	7.08742i	0.00446736	+	0.345831i
$421$	−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
$423$	−16.0137	−	8.23543i	−0.778615	−	0.400420i
$424$	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	$-0.0570853\pi$
$431$	7.00669	+	12.1359i	0.337500	+	0.584567i	−0.646462	+	0.762946i	$0.723752\pi$
$432$	−4.90782	+	1.70685i	−0.236127	+	0.0821209i
$433$	−10.0290	−	17.3707i	−0.481962	−	0.834783i	0.517823	−	0.855488i	$-0.326742\pi$
$433$	−10.0290	−	17.3707i	−0.481962	−	0.834783i	−0.999786	+	0.0207044i	$0.993409\pi$
$434$	−10.0559	−	5.80579i	−0.482700	−	0.278687i
$435$	−1.81401	+	0.0234329i	−0.0869750	+	0.00112352i
$436$		−	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	$0.416877\pi$
$440$	0.0274348	+	0.0280666i	0.00130790	+	0.00133802i
$441$	−9.20751	+	5.93031i	−0.438453	+	0.282396i
$442$	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
$447$	−1.05875	+	4.37377i	−0.0500773	+	0.206872i
$448$			1.83012i			0.0864649i
$449$	24.2472			1.14430			0.572148	−	0.820150i	$-0.306110\pi$
$449$	24.2472			1.14430			0.572148	+	0.820150i	$0.306110\pi$
$450$	0.387468	+	14.9950i	0.0182654	+	0.706871i
$451$	−0.101369	−	0.0585255i	−0.00477329	−	0.00275586i
$452$	12.0097	−	6.93381i	0.564889	−	0.326139i
$453$	−25.8342	+	7.59963i	−1.21380	+	0.357062i
$454$	−14.5529	+	25.2064i	−0.683004	+	1.18300i
$455$	9.36529	+	2.62403i	0.439051	+	0.123016i
$456$	7.42704	−	1.35614i	0.347803	−	0.0635070i
$457$			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
$459$	8.06955	−	2.80644i	0.376654	−	0.130994i
$460$	2.03650	−	0.520908i	0.0949522	−	0.0242875i
$461$	0.564904	+	0.326148i	0.0263102	+	0.0151902i	0.513097	−	0.858330i	$-0.328498\pi$
$461$	0.564904	+	0.326148i	0.0263102	+	0.0151902i	−0.486787	+	0.873521i	$0.661831\pi$
$462$	0.0130902	−	0.0540762i	0.000609009	−	0.00251585i
$463$			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
$465$	−21.4378	−	12.0106i	−0.994153	−	0.556978i
$466$	−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
$470$	−9.59808	+	9.38204i	−0.442727	+	0.432761i
$471$	6.15440	−	25.4242i	0.283580	−	1.17148i
$472$	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
$475$	2.78767	−	21.6155i	0.127907	−	0.991786i
$476$		−	3.00912i		−	0.137923i
$477$	10.2812	−	19.9918i	0.470746	−	0.915363i
$478$	11.4859	−	19.8942i	0.525354	−	0.909941i
$479$	6.63996	−	3.83358i	0.303388	−	0.175161i	−0.340576	−	0.940217i	$-0.610622\pi$
$479$	6.63996	−	3.83358i	0.303388	−	0.175161i	0.643964	+	0.765056i	$0.277289\pi$
$480$	0.0500261	+	3.87266i	0.00228337	+	0.176762i
$481$	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
$485$	−5.47505	+	1.40044i	−0.248609	+	0.0635908i
$486$	12.2774	+	9.60552i	0.556913	+	0.435715i
$487$	−38.4027			−1.74019			−0.870095	−	0.492884i	$-0.835943\pi$
$487$	−38.4027			−1.74019			−0.870095	+	0.492884i	$0.835943\pi$
$488$	7.33727	−	4.23617i	0.332143	−	0.191763i
$489$	1.03197	−	0.303574i	0.0466674	−	0.0137281i
$490$	2.02289	+	7.90854i	0.0913851	+	0.357271i
$491$	24.2445	+	13.9976i	1.09414	+	0.631701i	0.934675	−	0.355503i	$-0.115690\pi$
$491$	24.2445	+	13.9976i	1.09414	+	0.631701i	0.159463	+	0.987204i	$0.449024\pi$
$492$	−3.25971	−	11.0811i	−0.146959	−	0.499573i
$493$	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
$498$	4.88507	−	20.1805i	0.218905	−	0.904311i
$499$	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	$0.0576523\pi$
$500$	10.6943	+	3.26069i	0.478263	+	0.145823i
$501$	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	$0.745747\pi$
$504$	4.61581	−	2.97292i	0.205604	−	0.132424i
$505$	−10.9477	−	3.06741i	−0.487168	−	0.136498i
$506$	−0.0165003			−0.000733530
$507$	−12.3757	−	2.99576i	−0.549622	−	0.133046i
$508$	8.97167	−	15.5394i	0.398054	−	0.689449i
$509$	−10.5618	−	18.2935i	−0.468142	−	0.810846i	0.531195	−	0.847250i	$-0.321743\pi$
$509$	−10.5618	−	18.2935i	−0.468142	−	0.810846i	−0.999337	+	0.0364036i	$0.988410\pi$
$510$	−0.0822541	−	6.36752i	−0.00364227	−	0.281959i
$511$	−3.99898	+	6.92644i	−0.176905	+	0.306408i
$512$			1.00000i			0.0441942i
$513$	−15.4852	−	16.5291i	−0.683687	−	0.729776i
$514$	−3.16599			−0.139646
$515$	4.04411	+	4.13724i	0.178205	+	0.182309i
$516$	−13.7298	+	4.03889i	−0.604422	+	0.177802i
$517$	0.0912410	−	0.0526780i	0.00401278	−	0.00231678i
$518$	3.32514	−	5.75931i	0.146098	−	0.253050i
$519$	6.95332	−	28.7246i	0.305217	−	1.26087i
$520$	5.11732	+	1.43380i	0.224409	+	0.0628764i
$521$	13.3244			0.583755			0.291877	−	0.956456i	$-0.405720\pi$
$521$	13.3244			0.583755			0.291877	+	0.956456i	$0.405720\pi$
$522$	0.760911	+	1.18140i	0.0333042	+	0.0517087i
$523$	−8.64305	−	14.9702i	−0.377934	−	0.654601i	0.612827	−	0.790217i	$-0.290032\pi$
$523$	−8.64305	−	14.9702i	−0.377934	−	0.654601i	−0.990762	+	0.135616i	$0.956699\pi$
$524$		−	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
$528$	0.00715264	−	0.0295480i	0.000311279	−	0.00128591i
$529$	11.0581	−	19.1532i	0.480788	−	0.832750i
$530$	−11.7127	−	11.9824i	−0.508767	−	0.520482i
$531$	−1.66051	−	34.1408i	−0.0720599	−	1.48159i
$532$	−7.29013	+	3.23902i	−0.316067	+	0.140429i
$533$	−15.8493			−0.686511
$534$	−0.629082	+	0.185056i	−0.0272230	+	0.00800817i
$535$	−22.8142	+	22.3007i	−0.986345	+	0.964143i
$536$	−4.19369	+	2.42123i	−0.181140	+	0.104581i
$537$	10.5062	+	35.7148i	0.453376	+	1.54121i
$538$	−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
$545$	9.46377	+	36.9988i	0.405383	+	1.58485i
$546$	−2.12610	−	7.22746i	−0.0909885	−	0.309307i
$547$	0.0296601	+	0.0513728i	0.00126817	+	0.00219654i	0.866659	−	0.498901i	$-0.166263\pi$
$547$	0.0296601	+	0.0513728i	0.00126817	+	0.00219654i	−0.865391	+	0.501098i	$0.832930\pi$
$548$	−0.467172	+	0.809165i	−0.0199566	+	0.0345658i
$549$	−22.6032	−	11.6242i	−0.964681	−	0.496109i
$550$	−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
$555$	6.87881	−	12.2780i	0.291989	−	0.521173i
$556$	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
$560$	−1.01410	−	3.96462i	−0.0428534	−	0.167536i
$561$	−0.0117605	+	0.0485835i	−0.000496530	+	0.00205120i
$562$			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	$-0.0510446\pi$
$564$	10.1047	+	2.44602i	0.425484	+	0.102996i
$565$	−22.1748	+	21.6756i	−0.932900	+	0.911901i
$566$	−13.0848	−	22.6635i	−0.549993	−	0.952616i
$567$	−14.9962	−	6.81238i	−0.629783	−	0.286093i
$568$	−8.03419	−	4.63854i	−0.337107	−	0.194629i
$569$	45.8204			1.92089			0.960446	−	0.278468i	$-0.0898266\pi$
$569$	45.8204			1.92089			0.960446	+	0.278468i	$0.0898266\pi$
$570$	−15.3379	+	7.05327i	−0.642434	+	0.295429i
$571$	−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
$573$	−22.2095	+	6.53333i	−0.927813	+	0.272934i
$574$	6.10227	+	10.5694i	0.254704	+	0.441160i
$575$	−4.12307	+	2.25691i	−0.171944	+	0.0941197i
$576$	2.52214	−	1.62444i	0.105089	−	0.0676851i
$577$		−	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
$579$	22.8794	+	5.53839i	0.950836	+	0.230168i
$580$	1.01474	−	0.259555i	0.0421346	−	0.0107774i
$581$			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
$585$	−4.69654	−	15.2357i	−0.194178	−	0.629919i
$586$	−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
$591$	1.73536	+	5.89919i	0.0713831	+	0.242660i
$592$	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	$0.558776\pi$
$594$	−0.0861431	+	0.0299590i	−0.00353450	+	0.00122923i
$595$	1.66740	+	6.51873i	0.0683568	+	0.267242i
$596$		−	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	$-0.169262\pi$
$599$	−0.199563	−	0.345652i	−0.00815390	−	0.0141230i	−0.870074	+	0.492922i	$0.835929\pi$
$600$	−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
$603$	12.9191	+	6.64393i	0.526106	+	0.270562i
$604$	13.4644	−	7.77368i	0.547859	−	0.316307i
$605$	−17.1930	−	17.5889i	−0.698993	−	0.715089i
$606$	2.48534	+	8.44868i	0.100960	+	0.343204i
$607$	−33.2087			−1.34790			−0.673950	−	0.738777i	$-0.735404\pi$
$607$	−33.2087			−1.34790			−0.673950	+	0.738777i	$0.735404\pi$
$608$	−3.98342	+	1.76984i	−0.161549	+	0.0717766i
$609$	−1.07511	−	1.02409i	−0.0435658	−	0.0414984i
$610$	−13.5476	+	13.2426i	−0.548525	+	0.536178i
$611$	7.13289	−	12.3545i	0.288566	−	0.499811i
$612$	−4.14696	+	2.67095i	−0.167631	+	0.107967i
$613$	−25.8070	−	14.8997i	−1.04233	−	0.601792i	−0.121841	−	0.992550i	$-0.538880\pi$
$613$	−25.8070	−	14.8997i	−1.04233	−	0.601792i	−0.920494	+	0.390758i	$0.872213\pi$
$614$	−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	$0.894872\pi$
$618$	1.05436	−	4.35560i	0.0424124	−	0.175208i
$619$	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
$621$	−0.917258	+	4.79786i	−0.0368083	+	0.192531i
$622$	14.1223	−	24.4605i	0.566252	−	0.980778i
$623$	0.600037	−	0.346431i	0.0240400	−	0.0138795i
$624$	−1.16173	−	3.94918i	−0.0465063	−	0.158094i
$625$	−24.9741	−	1.13784i	−0.998964	−	0.0455135i
$626$	−7.83066			−0.312976
$627$	0.130361	−	0.0238032i	0.00520612	−	0.000950610i
$628$			15.1026i			0.602659i
$629$	−2.98739	+	5.17431i	−0.119115	+	0.206313i
$630$	−8.35199	+	8.99800i	−0.332751	+	0.358489i
$631$	−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
$633$	6.68710	−	27.6248i	0.265788	−	1.09799i
$634$	17.7354			0.704362
$635$	−10.8249	+	38.6347i	−0.429574	+	1.53317i
$636$	−3.05366	+	12.6148i	−0.121085	+	0.500211i
$637$	−4.33822	−	7.51401i	−0.171886	−	0.297716i
$638$	−0.00822170			−0.000325500
$639$	1.35203	+	27.7984i	0.0534855	+	1.09969i
$640$	−0.554116	−	2.16632i	−0.0219033	−	0.0856314i
$641$	12.3068	−	21.3160i	0.486089	−	0.841931i	−0.513783	−	0.857920i	$-0.671756\pi$
$641$	12.3068	−	21.3160i	0.486089	−	0.841931i	0.999872	+	0.0159890i	$0.00508968\pi$
$642$	24.0184	+	5.81410i	0.947930	+	0.229464i
$643$	31.4932	+	18.1826i	1.24197	+	0.717053i	0.969495	−	0.245109i	$-0.0788238\pi$
$643$	31.4932	+	18.1826i	1.24197	+	0.717053i	0.272477	+	0.962162i	$0.412157\pi$
$644$	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	$0.490539\pi$
$648$	−8.19414	−	3.72237i	−0.321896	−	0.146229i
$649$	0.173193	+	0.0999927i	0.00679840	+	0.00392506i
$650$	−11.8803	−	0.270496i	−0.465982	−	0.0106097i
$651$	−5.67580	−	19.2944i	−0.222452	−	0.756205i
$652$	−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
$655$	2.06153	+	8.05959i	0.0805507	+	0.314914i
$656$	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	$-0.0754015\pi$
$659$	7.25991	+	12.5745i	0.282806	+	0.489834i	−0.689269	+	0.724506i	$0.742068\pi$
$660$	0.000878070		0.0679738i	3.41788e−5		0.00264588i
$661$	−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
$663$	1.91014	+	6.49334i	0.0741837	+	0.252180i
$664$			11.9877i			0.465214i
$665$	13.9980	−	11.0563i	0.542819	−	0.428746i
$666$	−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
$669$	40.4596	+	9.79399i	1.56426	+	0.378658i
$670$	7.74325	−	7.56896i	0.299148	−	0.292414i
$671$	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	$-0.643471\pi$
$673$	−22.6019			−0.871239			−0.435619	+	0.900131i	$0.643471\pi$
$674$	5.72662	−	3.30626i	0.220581	−	0.127353i
$675$	−17.4275	+	19.2687i	−0.670784	+	0.741653i
$676$	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	$0.641228\pi$
$678$	23.3452	+	5.65114i	0.896566	+	0.217031i
$679$	−4.00566	−	2.31267i	−0.153723	−	0.0887521i
$680$	0.911090	+	3.56192i	0.0349387	+	0.136593i
$681$	−48.3637	+	14.2271i	−1.85330	+	0.545184i
$682$	−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	$0.953606\pi$
$684$	10.9346	+	7.17174i	0.418096	+	0.274218i
$685$	0.563674	−	2.01178i	0.0215369	−	0.0768662i
$686$	−9.74599	+	16.8805i	−0.372104	+	0.644502i
$687$	5.30158	+	18.0222i	0.202268	+	0.687591i
$688$	7.15578	−	4.13139i	0.272812	−	0.157508i
$689$	15.4236	+	8.90482i	0.587592	+	0.339246i
$690$	3.17635	+	1.77956i	0.120921	+	0.0677467i
$691$	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
$693$	0.0810178	−	0.0521814i	0.00307761	−	0.00198221i
$694$	−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
$699$	−7.39716	−	1.79062i	−0.279786	−	0.0677275i
$700$	4.39372	+	8.02673i	0.166067	+	0.303382i
$701$	0.0562324	+	0.0324658i	0.00212387	+	0.00122622i	0.501062	−	0.865412i	$-0.332943\pi$
$701$	0.0562324	+	0.0324658i	0.00212387	+	0.00122622i	−0.498938	+	0.866638i	$0.666276\pi$
$702$	−8.07323	+	9.34525i	−0.304704	+	0.352714i
$703$	15.7513	+	1.66786i	0.594072	+	0.0629044i
$704$			0.0175522i			0.000661525i
$705$	−23.2454	+	0.300278i	−0.875471	+	0.0113091i
$706$	3.30907	+	1.91049i	0.124539	+	0.0719024i
$707$	−4.65263	−	8.05860i	−0.174980	−	0.303075i
$708$	5.56931	+	18.9324i	0.209308	+	0.711522i
$709$	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
$717$	38.1711	−	11.2288i	1.42553	−	0.419346i
$718$	9.22208	+	15.9731i	0.344165	+	0.596111i
$719$	−15.9183	−	9.19043i	−0.593652	−	0.342745i	0.172888	−	0.984941i	$-0.444690\pi$
$719$	−15.9183	−	9.19043i	−0.593652	−	0.342745i	−0.766540	+	0.642196i	$0.778023\pi$
$720$	−4.56364	+	4.91662i	−0.170077	+	0.183232i
$721$			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
$725$	−2.05442	+	1.12456i	−0.0762993	+	0.0417652i
$726$	−4.48244	+	18.5172i	−0.166359	+	0.687238i
$727$	0.399410	+	0.230599i	0.0148133	+	0.00855245i	0.507388	−	0.861718i	$-0.330611\pi$
$727$	0.399410	+	0.230599i	0.0148133	+	0.00855245i	−0.492575	+	0.870270i	$0.663944\pi$
$728$	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
$732$	14.2626	+	3.45253i	0.527161	+	0.127609i
$733$		−	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
$735$	−6.91075	+	12.3350i	−0.254907	+	0.454984i
$736$	0.814125	+	0.470036i	0.0300091	+	0.0173257i
$737$	−0.0736087	+	0.0424980i	−0.00271141	+	0.00156543i
$738$	9.14959	−	17.7913i	0.336801	−	0.654908i
$739$	−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
$741$	13.6752	−	11.6171i	0.502371	−	0.426764i
$742$		−	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	$0.476522\pi$
$744$	−3.10133	−	10.5427i	−0.113700	−	0.386514i
$745$	1.43966	+	5.62839i	0.0527452	+	0.206208i
$746$	1.05790	+	0.610777i	0.0387323	+	0.0223621i
$747$	30.2347	−	19.4734i	1.10623	−	0.712494i
$748$		−	0.0288598i		−	0.00105522i
$749$	−26.1112			−0.954083
$750$	9.51684	+	16.8650i	0.347506	+	0.615824i
$751$	−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
$755$	−24.8607	+	24.3011i	−0.904775	+	0.884409i
$756$	9.34040	+	1.78570i	0.339707	+	0.0649455i
$757$	−37.1689	−	21.4595i	−1.35093	−	0.779957i	−0.362546	−	0.931966i	$-0.618093\pi$
$757$	−37.1689	−	21.4595i	−1.35093	−	0.779957i	−0.988379	+	0.152009i	$0.951426\pi$
$758$	−18.3122	+	31.7176i	−0.665127	+	1.15203i
$759$	−0.0206938	−	0.0197117i	−0.000751136	−	0.000715491i
$760$	7.64868	−	6.04133i	0.277447	−	0.219142i
$761$		−	15.0920i		−	0.547084i	−0.961860	−	0.273542i	$-0.911805\pi$
$761$		−	15.0920i		−	0.547084i	0.961860	−	0.273542i	$-0.0881953\pi$
$762$	29.8155	−	8.77080i	1.08010	−	0.317733i
$763$	−15.6283	+	27.0691i	−0.565784	+	0.979966i
$764$	11.5752	−	6.68296i	0.418777	−	0.241781i
$765$	7.50365	−	8.08403i	0.271295	−	0.292279i
$766$	−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	$0.766567\pi$
$770$	−0.0177997	−	0.0695880i	−0.000641455	−	0.00250778i
$771$	−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	$0.494637\pi$
$774$	−22.0441	−	11.3367i	−0.792359	−	0.407488i
$775$	−31.7154	−	0.722114i	−1.13925	−	0.0259391i
$776$	−2.18875	−	1.26367i	−0.0785714	−	0.0453632i
$777$	11.0504	−	3.25069i	0.396431	−	0.116618i
$778$	−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
$783$	−0.457046	+	2.39065i	−0.0163335	+	0.0854349i
$784$	−1.82534	+	3.16158i	−0.0651906	+	0.112913i
$785$	−8.36859	−	32.7171i	−0.298688	−	1.16772i
$786$	4.44449	−	4.66591i	0.158530	−	0.166427i
$787$	−4.63678			−0.165283			−0.0826416	−	0.996579i	$-0.526336\pi$
$787$	−4.63678			−0.165283			−0.0826416	+	0.996579i	$0.526336\pi$
$788$	−1.77510	−	3.07457i	−0.0632355	−	0.109527i
$789$	17.0084	+	4.11720i	0.605515	+	0.146576i
$790$	4.52740	−	16.1585i	0.161078	−	0.574894i
$791$	−25.3794			−0.902386
$792$	0.0442692	−	0.0285126i	0.00157304	−	0.00101315i
$793$	10.0680	−	17.4382i	0.357524	−	0.619250i
$794$	−13.8427	−	23.9763i	−0.491260	−	0.850886i
$795$	−0.374872	−	29.0199i	−0.0132953	−	1.02923i
$796$	2.21798	−	3.84166i	0.0786143	−	0.136164i
$797$			13.6298i			0.482791i	0.970427	+	0.241395i	$0.0776050\pi$
$797$			13.6298i			0.482791i	−0.970427	+	0.241395i	$0.922395\pi$
$798$	−13.0123	−	4.64679i	−0.460629	−	0.164495i
$799$	9.86934			0.349152
$800$	2.40079	+	4.38591i	0.0848806	+	0.155065i
$801$	−1.01003	−	0.519431i	−0.0356877	−	0.0183532i
$802$	13.3228	−	7.69191i	0.470443	−	0.271611i
$803$	−0.0383533	+	0.0664299i	−0.00135346	+	0.00234426i
$804$	−8.15195	−	1.97333i	−0.287497	−	0.0695940i
$805$	−3.70436	−	1.03791i	−0.130562	−	0.0365816i
$806$	−15.0793			−0.531146
$807$	−20.6260	−	4.99292i	−0.726071	−	0.175759i
$808$	−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	−0.824275	−	0.566189i	$-0.808417\pi$
$811$	−21.2469	+	12.2669i	−0.746079	+	0.430749i	0.0781964	+	0.996938i	$0.475084\pi$
$812$	0.742401	+	0.428626i	0.0260532	+	0.0150418i
$813$	15.1328	+	3.66319i	0.530732	+	0.128474i
$814$	0.0318907	−	0.0552363i	0.00111777	−	0.00193603i
$815$	0.993085	−	0.970731i	0.0347863	−	0.0340032i
$816$	1.96423	−	2.06209i	0.0687619	−	0.0721876i
$817$	29.1217	+	21.1926i	1.01884	+	0.741435i
$818$	−21.8991			−0.765686
$819$	5.96769	−	11.6041i	0.208528	−	0.405482i
$820$	−10.4235	−	10.6635i	−0.364004	−	0.372386i
$821$	−27.9511	+	16.1376i	−0.975501	+	0.563206i	−0.900909	−	0.434008i	$-0.857099\pi$
$821$	−27.9511	+	16.1376i	−0.975501	+	0.563206i	−0.0745923	+	0.997214i	$0.523766\pi$
$822$	−1.55255	+	0.456712i	−0.0541514	+	0.0159297i
$823$	−39.3652	+	22.7275i	−1.37219	+	0.792232i	−0.991203	−	0.132350i	$-0.957748\pi$
$823$	−39.3652	+	22.7275i	−1.37219	+	0.792232i	−0.380983	+	0.924582i	$0.624414\pi$
$824$			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	−0.203221	−	0.979133i	$-0.565141\pi$
$827$	15.6189	−	9.01758i	0.543123	−	0.313572i	0.746344	+	0.665561i	$0.231808\pi$
$828$	−0.137005	−	2.81688i	−0.00476124	−	0.0978935i
$829$		−	5.46280i		−	0.189731i	−0.995490	−	0.0948655i	$-0.969758\pi$
$829$		−	5.46280i		−	0.189731i	0.995490	−	0.0948655i	$-0.0302421\pi$
$830$	−6.64259	−	25.9693i	−0.230568	−	0.901408i
$831$	50.6812	−	14.9088i	1.75811	−	0.517182i
$832$	1.18833	+	2.05825i	0.0411981	+	0.0713571i
$833$	3.00126	−	5.19834i	0.103988	−	0.180112i
$834$	16.6724	−	4.90449i	0.577317	−	0.169829i
$835$	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	$-0.851669\pi$
$839$	−1.66762	+	2.88840i	−0.0575725	+	0.0997185i	0.835803	+	0.549030i	$0.185003\pi$
$840$	3.46442	−	6.18366i	0.119534	−	0.213357i
$841$	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
$845$	−15.9256	+	4.07356i	−0.547858	+	0.140135i
$846$	9.75060	+	15.1390i	0.335233	+	0.520488i
$847$		−	20.1307i		−	0.691700i
$848$		−	7.49353i		−	0.257329i
$849$	10.6642	−	44.0546i	0.365995	−	1.51195i
$850$	−3.94743	−	7.21142i	−0.135396	−	0.247350i
$851$	−1.70802	−	2.95837i	−0.0585500	−	0.101412i
$852$	−4.53469	−	15.4152i	−0.155356	−	0.528117i
$853$	28.2641	+	16.3183i	0.967744	+	0.558727i	0.898548	−	0.438876i	$-0.144623\pi$
$853$	28.2641	+	16.3183i	0.967744	+	0.558727i	0.0691961	+	0.997603i	$0.477957\pi$
$854$	−15.5054			−0.530583
$855$	−27.6619	−	9.47726i	−0.946018	−	0.324116i
$856$	−14.2675			−0.487654
$857$	−28.2912	−	16.3339i	−0.966408	−	0.557956i	−0.0682684	−	0.997667i	$-0.521747\pi$
$857$	−28.2912	−	16.3339i	−0.966408	−	0.557956i	−0.898139	+	0.439711i	$0.855081\pi$
$858$	−0.0203909	−	0.0693170i	−0.000696134	−	0.00236644i
$859$	6.71516	+	11.6310i	0.229118	+	0.396844i	0.957547	−	0.288277i	$-0.0930824\pi$
$859$	6.71516	+	11.6310i	0.229118	+	0.396844i	−0.728429	+	0.685121i	$0.759749\pi$
$860$	−13.2125	+	12.9151i	−0.450541	+	0.440400i
$861$	−4.97342	+	20.5455i	−0.169494	+	0.700189i
$862$		−	14.0134i		−	0.477297i
$863$			8.87998i			0.302278i	0.988513	+	0.151139i	$0.0482941\pi$
$863$			8.87998i			0.302278i	−0.988513	+	0.151139i	$0.951706\pi$
$864$	5.10372	+	0.975733i	0.173632	+	0.0331951i
$865$	−9.45494	−	36.9642i	−0.321478	−	1.25682i
$866$			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
$870$	1.58269	+	0.886710i	0.0536583	+	0.0300623i
$871$	−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
$876$	−7.26172	+	2.13617i	−0.245351	+	0.0721746i
$877$	19.4899	−	33.7575i	0.658127	−	1.13991i	−0.322973	−	0.946408i	$-0.604682\pi$
$877$	19.4899	−	33.7575i	0.658127	−	1.13991i	0.981100	−	0.193501i	$-0.0619843\pi$
$878$	−14.8057	−	25.6443i	−0.499670	−	0.865453i
$879$	−41.6023	+	12.2381i	−1.40321	+	0.412781i
$880$	−0.00972597	−	0.0380238i	−0.000327862	−	0.00128178i
$881$		−	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	$-0.390609\pi$
$883$	39.2478	−	22.6597i	1.32079	−	0.762560i	0.983855	+	0.178967i	$0.0572756\pi$
$884$	−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	0.0176819	−	0.999844i	$-0.494371\pi$
$887$	26.5783	−	15.3450i	0.892413	−	0.515235i	0.874731	+	0.484609i	$0.161038\pi$
$888$	6.03809	−	1.77622i	0.202625	−	0.0596060i
$889$	−28.4389	+	16.4192i	−0.953810	+	0.550683i
$890$	−0.605377	+	0.591750i	−0.0202923	+	0.0198355i
$891$	−0.143825	−	0.0653360i	−0.00481833	−	0.00218884i
$892$	−24.0340			−0.804718
$893$	−10.6233	−	23.9102i	−0.355497	−	0.800125i
$894$	3.10379	−	3.25842i	0.103806	−	0.108978i
$895$	33.5954	+	34.3690i	1.12297	+	1.14883i
$896$	0.915058	−	1.58493i	0.0305700	−	0.0529487i
$897$	−3.76118	−	0.910464i	−0.125582	−	0.0303995i
$898$	−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
$903$	25.4566	+	6.16224i	0.847143	+	0.205067i
$904$	−13.8676			−0.461230
$905$	−20.1171	−	5.63655i	−0.668716	−	0.187365i
$906$	26.1729	+	6.33564i	0.869537	+	0.210488i
$907$	−21.3528	+	36.9842i	−0.709009	+	1.22804i	0.256216	+	0.966619i	$0.417524\pi$
$907$	−21.3528	+	36.9842i	−0.709009	+	1.22804i	−0.965225	+	0.261420i	$0.915809\pi$
$908$	25.2064	−	14.5529i	0.836505	−	0.482956i
$909$	−6.97604	+	13.5649i	−0.231381	+	0.449919i
$910$	−6.79856	−	6.95512i	−0.225370	−	0.230560i
$911$	17.7467			0.587974			0.293987	−	0.955809i	$-0.405018\pi$
$911$	17.7467			0.587974			0.293987	+	0.955809i	$0.405018\pi$
$912$	−7.11007	−	2.53907i	−0.235438	−	0.0840770i
$913$			0.210412i			0.00696361i
$914$	13.2226	−	22.9021i	0.437363	−	0.757535i
$915$	−32.8105	+	0.423839i	−1.08468	+	0.0140117i
$916$	−5.42300	−	9.39292i	−0.179181	−	0.310351i
$917$	−3.40438	+	5.89656i	−0.112423	+	0.194722i
$918$	−8.39166	−	1.60432i	−0.276966	−	0.0529506i
$919$	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
$921$	−38.4755	−	9.31371i	−1.26781	−	0.306897i
$922$	−0.326148	−	0.564904i	−0.0107411	−	0.0186041i
$923$	−22.0485			−0.725737
$924$	−0.0383745	+	0.0402863i	−0.00126243	+	0.00132532i
$925$	0.413575	−	18.1643i	0.0135983	−	0.597238i
$926$	3.23586	−	5.60468i	0.106337	−	0.184181i
$927$	6.52563	−	4.20298i	0.214330	−	0.138044i
$928$	0.405658	+	0.234207i	0.0133164	+	0.00768821i
$929$	−31.2455	−	18.0396i	−1.02513	−	0.591860i	−0.109546	−	0.993982i	$-0.534940\pi$
$929$	−31.2455	−	18.0396i	−1.02513	−	0.591860i	−0.915586	+	0.402121i	$0.868273\pi$
$930$	12.5604	+	21.1204i	0.411870	+	0.692565i
$931$	−15.8244	−	1.67560i	−0.518625	−	0.0549156i
$932$	4.39410			0.143934
$933$	46.9325	−	13.8061i	1.53650	−	0.451991i
$934$	5.55111	+	3.20493i	0.181638	+	0.104869i
$935$	0.0159917	+	0.0625197i	0.000522984	+	0.00204461i
$936$	3.26082	−	6.34066i	0.106583	−	0.207251i
$937$	14.1261	−	8.15573i	0.461481	−	0.266436i	−0.251186	−	0.967939i	$-0.580821\pi$
$937$	14.1261	−	8.15573i	0.461481	−	0.266436i	0.712667	+	0.701503i	$0.247487\pi$
$938$	8.86227			0.289363
$939$	−9.82076	−	9.35471i	−0.320488	−	0.305280i
$940$	13.0032	−	3.32604i	0.424118	−	0.108483i
$941$	6.27180	+	10.8631i	0.204455	+	0.354126i	0.949959	−	0.312375i	$-0.101125\pi$
$941$	6.27180	+	10.8631i	0.204455	+	0.354126i	−0.745504	+	0.666501i	$0.767791\pi$
$942$	−18.0420	+	18.9408i	−0.587839	+	0.617124i
$943$	6.26907			0.204149
$944$	−5.69687	−	9.86726i	−0.185417	−	0.321152i
$945$	−21.2238	+	1.30725i	−0.690411	+	0.0425248i
$946$	0.125600	−	0.0725152i	0.00408361	−	0.00235767i
$947$	10.0502	−	17.4074i	0.326587	−	0.565665i	−0.655245	−	0.755416i	$-0.727435\pi$
$947$	10.0502	−	17.4074i	0.326587	−	0.565665i	0.981832	+	0.189751i	$0.0607681\pi$
$948$	−12.4700	+	3.66829i	−0.405007	+	0.119140i
$949$			10.3865i			0.337160i
$950$	−13.2219	+	17.3257i	−0.428976	+	0.562121i
$951$	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	−0.137723	−	0.990471i	$-0.543978\pi$
$953$	−32.8574	−	18.9703i	−1.06436	−	0.614507i	−0.926634	+	0.375964i	$0.877312\pi$
$954$	−18.8997	+	12.1728i	−0.611901	+	0.394109i
$955$	−21.3726	+	20.8915i	−0.691600	+	0.676032i
$956$	−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
$960$	1.89301	−	3.37884i	0.0610965	−	0.109051i
$961$	−9.25554			−0.298566
$962$		−	8.63634i		−	0.278447i
$963$	23.1768	+	35.9847i	0.746861	+	1.15959i
$964$	−1.60542	−	0.926892i	−0.0517072	−	0.0298532i
$965$	29.4424	−	7.53096i	0.947784	−	0.242430i
$966$	0.840960	+	2.85876i	0.0270574	+	0.0919792i
$967$	−1.89435	−	1.09370i	−0.0609181	−	0.0351711i	0.469232	−	0.883075i	$-0.344531\pi$
$967$	−1.89435	−	1.09370i	−0.0609181	−	0.0351711i	−0.530150	+	0.847904i	$0.677864\pi$
$968$		−	10.9997i		−	0.353543i
$969$	11.6906	+	4.17480i	0.375555	+	0.134114i
$970$	5.44175	+	1.52471i	0.174724	+	0.0489554i
$971$	−17.6378	+	30.5495i	−0.566023	+	0.980381i	0.430930	+	0.902385i	$0.358185\pi$
$971$	−17.6378	+	30.5495i	−0.566023	+	0.980381i	−0.996954	+	0.0779958i	$0.975148\pi$
$972$	−5.82976	−	14.4573i	−0.186990	−	0.463718i
$973$	−15.9026	+	9.18136i	−0.509814	+	0.294341i
$974$	33.2577	+	19.2013i	1.06564	+	0.615250i
$975$	−14.5764	−	14.5317i	−0.466818	−	0.465387i
$976$	−8.47235			−0.271193
$977$			50.7753i			1.62445i	0.583347	+	0.812223i	$0.301743\pi$
$977$			50.7753i			1.62445i	−0.583347	+	0.812223i	$0.698257\pi$
$978$	−1.04550	−	0.253083i	−0.0334314	−	0.00809270i
$979$	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	0.956480	−	0.291799i	$-0.0942540\pi$
$983$	37.0595	+	21.3963i	1.18201	+	0.682436i	0.225534	+	0.974235i	$0.427587\pi$
$984$	−2.71754	+	11.2263i	−0.0866321	+	0.357883i
$985$	5.54912	+	5.67690i	0.176810	+	0.180881i
$986$	−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
$990$	−0.0801021	+	0.0862977i	−0.00254581	+	0.00274272i
$991$	−2.97552	−	1.71792i	−0.0945205	−	0.0545715i	0.451995	−	0.892021i	$-0.350713\pi$
$991$	−2.97552	−	1.71792i	−0.0945205	−	0.0545715i	−0.546515	+	0.837449i	$0.684046\pi$
$992$	3.17236	+	5.49469i	0.100723	+	0.174457i
$993$	18.5143	−	5.44633i	0.587533	−	0.172834i
$994$	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	$-0.403944\pi$
$997$	40.1860	−	23.2014i	1.27270	−	0.734796i	0.975496	+	0.220016i	$0.0706111\pi$
$998$	−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.179.9	yes	80
3.2	odd	2	inner	570.2.n.a.179.39	yes	80
5.4	even	2	inner	570.2.n.a.179.32	yes	80
15.14	odd	2	inner	570.2.n.a.179.2	✓	80
19.12	odd	6	inner	570.2.n.a.449.2	yes	80
57.50	even	6	inner	570.2.n.a.449.32	yes	80
95.69	odd	6	inner	570.2.n.a.449.39	yes	80
285.164	even	6	inner	570.2.n.a.449.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.2	✓	80	15.14	odd	2	inner
570.2.n.a.179.9	yes	80	1.1	even	1	trivial
570.2.n.a.179.32	yes	80	5.4	even	2	inner
570.2.n.a.179.39	yes	80	3.2	odd	2	inner
570.2.n.a.449.2	yes	80	19.12	odd	6	inner
570.2.n.a.449.9	yes	80	285.164	even	6	inner
570.2.n.a.449.32	yes	80	57.50	even	6	inner
570.2.n.a.449.39	yes	80	95.69	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.488805 - 1.66165i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.56304 - 1.59903i) q^{5} +(-0.407506 + 1.68343i) q^{6} -1.83012i q^{7} -1.00000i q^{8} +(-2.52214 + 1.62444i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.488805 - 1.66165i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.56304 - 1.59903i) q^{5} +(-0.407506 + 1.68343i) q^{6} -1.83012i q^{7} -1.00000i q^{8} +(-2.52214 + 1.62444i) q^{9} +(0.554116 + 2.16632i) q^{10} -0.0175522i q^{11} +(1.19463 - 1.25414i) q^{12} +(-1.18833 - 2.05825i) q^{13} +(-0.915058 + 1.58493i) q^{14} +(-1.89301 + 3.37884i) 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} +(-3.04101 + 0.894570i) q^{21} +(-0.00877612 + 0.0152007i) q^{22} +(0.470036 + 0.814125i) q^{23} +(-1.66165 + 0.488805i) q^{24} +(-0.113813 + 4.99870i) 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} +(-0.0291656 + 0.00857962i) q^{33} +(-1.42394 + 0.822112i) q^{34} +(-2.92642 + 2.86055i) q^{35} +(-2.66788 - 1.37202i) q^{36} -3.63380 q^{37} +(3.52444 + 2.56482i) q^{38} +(-2.83923 + 2.98068i) q^{39} +(-1.59903 + 1.56304i) q^{40} +(3.33436 - 5.77528i) q^{41} +(3.08087 + 0.745783i) 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} +(1.68343 + 0.407506i) q^{48} +3.65067 q^{49} +(2.59792 - 4.27210i) q^{50} +(-2.76794 - 0.670031i) q^{51} +(1.18833 - 2.05825i) q^{52} +(-6.48959 + 3.74677i) q^{53} +(-1.70685 - 4.90782i) q^{54} +(-0.0280666 + 0.0274348i) q^{55} -1.83012 q^{56} +(1.35614 + 7.42704i) q^{57} -0.468414i q^{58} +(-5.69687 + 9.86726i) q^{59} +(-3.87266 + 0.0500261i) q^{60} +(4.23617 + 7.33727i) q^{61} +(3.17236 - 5.49469i) q^{62} +(2.97292 + 4.61581i) q^{63} -1.00000 q^{64} +(-1.43380 + 5.11732i) q^{65} +(0.0295480 + 0.00715264i) q^{66} +(-2.42123 - 4.19369i) q^{67} +1.64422 q^{68} +(1.12303 - 1.17898i) q^{69} +(3.96462 - 1.01410i) q^{70} +(4.63854 - 8.03419i) q^{71} +(1.62444 + 2.52214i) 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} +(3.94918 - 1.16173i) q^{78} +(-6.49918 - 3.75230i) q^{79} +(2.16632 - 0.554116i) q^{80} +(3.72237 - 8.19414i) q^{81} +(-5.77528 + 3.33436i) q^{82} -11.9877 q^{83} +(-2.29522 - 2.18630i) q^{84} +(-3.56192 + 0.911090i) q^{85} +(4.13139 + 7.15578i) q^{86} +(0.559579 - 0.587457i) q^{87} -0.0175522 q^{88} +(0.189295 + 0.327868i) q^{89} +(-4.91662 - 4.56364i) q^{90} +(-3.76685 + 2.17479i) q^{91} +(-0.470036 + 0.814125i) q^{92} +(10.5427 - 3.10133i) q^{93} -6.00243i q^{94} +(6.04133 + 7.64868i) q^{95} +(-1.25414 - 1.19463i) q^{96} +(1.26367 - 2.18875i) q^{97} +(-3.16158 - 1.82534i) q^{98} +(0.0285126 + 0.0442692i) 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

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