LMFDB - Embedded newform 570.2.c.e.569.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(569,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("570.569");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.c (of order $2$, degree $1$, 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:	$8$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			569.7
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	570.569
Dual form			570.2.c.e.569.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000 q^{4} +(-1.73205 + 1.41421i) q^{5} +(1.00000 + 1.41421i) q^{6} -2.44949i q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000 q^{4} +(-1.73205 + 1.41421i) q^{5} +(1.00000 + 1.41421i) q^{6} -2.44949i q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +(-1.41421 - 1.73205i) q^{10} +1.41421i q^{11} +(-1.41421 + 1.00000i) q^{12} +4.24264 q^{13} +2.44949 q^{14} +(-1.03528 + 3.73205i) q^{15} +1.00000 q^{16} +6.92820 q^{17} +(2.82843 + 1.00000i) q^{18} +(4.00000 - 1.73205i) q^{19} +(1.73205 - 1.41421i) q^{20} +(-2.44949 - 3.46410i) q^{21} -1.41421 q^{22} +3.46410 q^{23} +(-1.00000 - 1.41421i) q^{24} +(1.00000 - 4.89898i) q^{25} +4.24264i q^{26} +(-1.41421 - 5.00000i) q^{27} +2.44949i q^{28} -2.44949 q^{29} +(-3.73205 - 1.03528i) q^{30} +6.92820i q^{31} +1.00000i q^{32} +(1.41421 + 2.00000i) q^{33} +6.92820i q^{34} +(3.46410 + 4.24264i) q^{35} +(-1.00000 + 2.82843i) q^{36} -4.24264 q^{37} +(1.73205 + 4.00000i) q^{38} +(6.00000 - 4.24264i) q^{39} +(1.41421 + 1.73205i) q^{40} -12.2474 q^{41} +(3.46410 - 2.44949i) q^{42} -7.34847i q^{43} -1.41421i q^{44} +(2.26795 + 6.31319i) q^{45} +3.46410i q^{46} -3.46410 q^{47} +(1.41421 - 1.00000i) q^{48} +1.00000 q^{49} +(4.89898 + 1.00000i) q^{50} +(9.79796 - 6.92820i) q^{51} -4.24264 q^{52} -6.00000i q^{53} +(5.00000 - 1.41421i) q^{54} +(-2.00000 - 2.44949i) q^{55} -2.44949 q^{56} +(3.92480 - 6.44949i) q^{57} -2.44949i q^{58} +4.89898 q^{59} +(1.03528 - 3.73205i) q^{60} -8.00000 q^{61} -6.92820 q^{62} +(-6.92820 - 2.44949i) q^{63} -1.00000 q^{64} +(-7.34847 + 6.00000i) q^{65} +(-2.00000 + 1.41421i) q^{66} -6.92820 q^{68} +(4.89898 - 3.46410i) q^{69} +(-4.24264 + 3.46410i) q^{70} +4.89898 q^{71} +(-2.82843 - 1.00000i) q^{72} +14.6969i q^{73} -4.24264i q^{74} +(-3.48477 - 7.92820i) q^{75} +(-4.00000 + 1.73205i) q^{76} +3.46410 q^{77} +(4.24264 + 6.00000i) q^{78} +10.3923i q^{79} +(-1.73205 + 1.41421i) q^{80} +(-7.00000 - 5.65685i) q^{81} -12.2474i q^{82} +10.3923 q^{83} +(2.44949 + 3.46410i) q^{84} +(-12.0000 + 9.79796i) q^{85} +7.34847 q^{86} +(-3.46410 + 2.44949i) q^{87} +1.41421 q^{88} +2.44949 q^{89} +(-6.31319 + 2.26795i) q^{90} -10.3923i q^{91} -3.46410 q^{92} +(6.92820 + 9.79796i) q^{93} -3.46410i q^{94} +(-4.47871 + 8.65685i) q^{95} +(1.00000 + 1.41421i) q^{96} -12.7279 q^{97} +1.00000i q^{98} +(4.00000 + 1.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 8 q^{6} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 8 * q^6 + 8 * q^9	$ 8 q - 8 q^{4} + 8 q^{6} + 8 q^{9} + 8 q^{16} + 32 q^{19} - 8 q^{24} + 8 q^{25} - 16 q^{30} - 8 q^{36} + 48 q^{39} + 32 q^{45} + 8 q^{49} + 40 q^{54} - 16 q^{55} - 64 q^{61} - 8 q^{64} - 16 q^{66} - 32 q^{76} - 56 q^{81} - 96 q^{85} + 8 q^{96} + 32 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 8 * q^6 + 8 * q^9 + 8 * q^16 + 32 * q^19 - 8 * q^24 + 8 * q^25 - 16 * q^30 - 8 * q^36 + 48 * q^39 + 32 * q^45 + 8 * q^49 + 40 * q^54 - 16 * q^55 - 64 * q^61 - 8 * q^64 - 16 * q^66 - 32 * q^76 - 56 * q^81 - 96 * q^85 + 8 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.41421	−	1.00000i	0.816497	−	0.577350i
$3$	1.41421	−	1.00000i	0.816497	−	0.577350i
$4$	−1.00000			−0.500000
$5$	−1.73205	+	1.41421i	−0.774597	+	0.632456i
$5$	−1.73205	+	1.41421i	−0.774597	+	0.632456i
$6$	1.00000	+	1.41421i	0.408248	+	0.577350i
$7$		−	2.44949i		−	0.925820i	−0.886405	−	0.462910i	$-0.846805\pi$
$7$		−	2.44949i		−	0.925820i	0.886405	−	0.462910i	$-0.153195\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000	−	2.82843i	0.333333	−	0.942809i
$10$	−1.41421	−	1.73205i	−0.447214	−	0.547723i
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$	−1.41421	+	1.00000i	−0.408248	+	0.288675i
$13$	4.24264			1.17670			0.588348	−	0.808608i	$-0.299778\pi$
$13$	4.24264			1.17670			0.588348	+	0.808608i	$0.299778\pi$
$14$	2.44949			0.654654
$15$	−1.03528	+	3.73205i	−0.267307	+	0.963611i
$16$	1.00000			0.250000
$17$	6.92820			1.68034			0.840168	−	0.542326i	$-0.182456\pi$
$17$	6.92820			1.68034			0.840168	+	0.542326i	$0.182456\pi$
$18$	2.82843	+	1.00000i	0.666667	+	0.235702i
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$20$	1.73205	−	1.41421i	0.387298	−	0.316228i
$21$	−2.44949	−	3.46410i	−0.534522	−	0.755929i
$22$	−1.41421			−0.301511
$23$	3.46410			0.722315			0.361158	−	0.932505i	$-0.382382\pi$
$23$	3.46410			0.722315			0.361158	+	0.932505i	$0.382382\pi$
$24$	−1.00000	−	1.41421i	−0.204124	−	0.288675i
$25$	1.00000	−	4.89898i	0.200000	−	0.979796i
$26$			4.24264i			0.832050i
$27$	−1.41421	−	5.00000i	−0.272166	−	0.962250i
$28$			2.44949i			0.462910i
$29$	−2.44949			−0.454859			−0.227429	−	0.973795i	$-0.573032\pi$
$29$	−2.44949			−0.454859			−0.227429	+	0.973795i	$0.573032\pi$
$30$	−3.73205	−	1.03528i	−0.681376	−	0.189015i
$31$			6.92820i			1.24434i	0.782881	+	0.622171i	$0.213749\pi$
$31$			6.92820i			1.24434i	−0.782881	+	0.622171i	$0.786251\pi$
$32$			1.00000i			0.176777i
$33$	1.41421	+	2.00000i	0.246183	+	0.348155i
$34$			6.92820i			1.18818i
$35$	3.46410	+	4.24264i	0.585540	+	0.717137i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$	−4.24264			−0.697486			−0.348743	−	0.937218i	$-0.613391\pi$
$37$	−4.24264			−0.697486			−0.348743	+	0.937218i	$0.613391\pi$
$38$	1.73205	+	4.00000i	0.280976	+	0.648886i
$39$	6.00000	−	4.24264i	0.960769	−	0.679366i
$40$	1.41421	+	1.73205i	0.223607	+	0.273861i
$41$	−12.2474			−1.91273			−0.956365	−	0.292174i	$-0.905621\pi$
$41$	−12.2474			−1.91273			−0.956365	+	0.292174i	$0.905621\pi$
$42$	3.46410	−	2.44949i	0.534522	−	0.377964i
$43$		−	7.34847i		−	1.12063i	−0.828279	−	0.560316i	$-0.810680\pi$
$43$		−	7.34847i		−	1.12063i	0.828279	−	0.560316i	$-0.189320\pi$
$44$		−	1.41421i		−	0.213201i
$45$	2.26795	+	6.31319i	0.338086	+	0.941115i
$46$			3.46410i			0.510754i
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$	1.41421	−	1.00000i	0.204124	−	0.144338i
$49$	1.00000			0.142857
$50$	4.89898	+	1.00000i	0.692820	+	0.141421i
$51$	9.79796	−	6.92820i	1.37199	−	0.970143i
$52$	−4.24264			−0.588348
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	5.00000	−	1.41421i	0.680414	−	0.192450i
$55$	−2.00000	−	2.44949i	−0.269680	−	0.330289i
$56$	−2.44949			−0.327327
$57$	3.92480	−	6.44949i	0.519853	−	0.854256i
$58$		−	2.44949i		−	0.321634i
$59$	4.89898			0.637793			0.318896	−	0.947790i	$-0.396688\pi$
$59$	4.89898			0.637793			0.318896	+	0.947790i	$0.396688\pi$
$60$	1.03528	−	3.73205i	0.133654	−	0.481806i
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$	−6.92820			−0.879883
$63$	−6.92820	−	2.44949i	−0.872872	−	0.308607i
$64$	−1.00000			−0.125000
$65$	−7.34847	+	6.00000i	−0.911465	+	0.744208i
$66$	−2.00000	+	1.41421i	−0.246183	+	0.174078i
$67$		0			0			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$	−6.92820			−0.840168
$69$	4.89898	−	3.46410i	0.589768	−	0.417029i
$70$	−4.24264	+	3.46410i	−0.507093	+	0.414039i
$71$	4.89898			0.581402			0.290701	−	0.956814i	$-0.406112\pi$
$71$	4.89898			0.581402			0.290701	+	0.956814i	$0.406112\pi$
$72$	−2.82843	−	1.00000i	−0.333333	−	0.117851i
$73$			14.6969i			1.72015i	0.510171	+	0.860073i	$0.329582\pi$
$73$			14.6969i			1.72015i	−0.510171	+	0.860073i	$0.670418\pi$
$74$		−	4.24264i		−	0.493197i
$75$	−3.48477	−	7.92820i	−0.402386	−	0.915470i
$76$	−4.00000	+	1.73205i	−0.458831	+	0.198680i
$77$	3.46410			0.394771
$78$	4.24264	+	6.00000i	0.480384	+	0.679366i
$79$			10.3923i			1.16923i	0.811312	+	0.584613i	$0.198754\pi$
$79$			10.3923i			1.16923i	−0.811312	+	0.584613i	$0.801246\pi$
$80$	−1.73205	+	1.41421i	−0.193649	+	0.158114i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$		−	12.2474i		−	1.35250i
$83$	10.3923			1.14070			0.570352	−	0.821401i	$-0.306807\pi$
$83$	10.3923			1.14070			0.570352	+	0.821401i	$0.306807\pi$
$84$	2.44949	+	3.46410i	0.267261	+	0.377964i
$85$	−12.0000	+	9.79796i	−1.30158	+	1.06274i
$86$	7.34847			0.792406
$87$	−3.46410	+	2.44949i	−0.371391	+	0.262613i
$88$	1.41421			0.150756
$89$	2.44949			0.259645			0.129823	−	0.991537i	$-0.458559\pi$
$89$	2.44949			0.259645			0.129823	+	0.991537i	$0.458559\pi$
$90$	−6.31319	+	2.26795i	−0.665469	+	0.239063i
$91$		−	10.3923i		−	1.08941i
$92$	−3.46410			−0.361158
$93$	6.92820	+	9.79796i	0.718421	+	1.01600i
$94$		−	3.46410i		−	0.357295i
$95$	−4.47871	+	8.65685i	−0.459506	+	0.888175i
$96$	1.00000	+	1.41421i	0.102062	+	0.144338i
$97$	−12.7279			−1.29232			−0.646162	−	0.763200i	$-0.723627\pi$
$97$	−12.7279			−1.29232			−0.646162	+	0.763200i	$0.723627\pi$
$98$			1.00000i			0.101015i
$99$	4.00000	+	1.41421i	0.402015	+	0.142134i
$100$	−1.00000	+	4.89898i	−0.100000	+	0.489898i
$101$		−	2.82843i		−	0.281439i	−0.990050	−	0.140720i	$-0.955058\pi$
$101$		−	2.82843i		−	0.281439i	0.990050	−	0.140720i	$-0.0449416\pi$
$102$	6.92820	+	9.79796i	0.685994	+	0.970143i
$103$	−8.48528			−0.836080			−0.418040	−	0.908429i	$-0.637283\pi$
$103$	−8.48528			−0.836080			−0.418040	+	0.908429i	$0.637283\pi$
$104$		−	4.24264i		−	0.416025i
$105$	9.14162	+	2.53590i	0.892131	+	0.247478i
$106$	6.00000			0.582772
$107$			18.0000i			1.74013i	0.492941	+	0.870063i	$0.335922\pi$
$107$			18.0000i			1.74013i	−0.492941	+	0.870063i	$0.664078\pi$
$108$	1.41421	+	5.00000i	0.136083	+	0.481125i
$109$			6.92820i			0.663602i	0.943349	+	0.331801i	$0.107656\pi$
$109$			6.92820i			0.663602i	−0.943349	+	0.331801i	$0.892344\pi$
$110$	2.44949	−	2.00000i	0.233550	−	0.190693i
$111$	−6.00000	+	4.24264i	−0.569495	+	0.402694i
$112$		−	2.44949i		−	0.231455i
$113$		−	18.0000i		−	1.69330i	−0.532152	−	0.846649i	$-0.678617\pi$
$113$		−	18.0000i		−	1.69330i	0.532152	−	0.846649i	$-0.321383\pi$
$114$	6.44949	+	3.92480i	0.604050	+	0.367592i
$115$	−6.00000	+	4.89898i	−0.559503	+	0.456832i
$116$	2.44949			0.227429
$117$	4.24264	−	12.0000i	0.392232	−	1.10940i
$118$			4.89898i			0.450988i
$119$		−	16.9706i		−	1.55569i
$120$	3.73205	+	1.03528i	0.340688	+	0.0945074i
$121$	9.00000			0.818182
$122$		−	8.00000i		−	0.724286i
$123$	−17.3205	+	12.2474i	−1.56174	+	1.10432i
$124$		−	6.92820i		−	0.622171i
$125$	5.19615	+	9.89949i	0.464758	+	0.885438i
$126$	2.44949	−	6.92820i	0.218218	−	0.617213i
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−7.34847	−	10.3923i	−0.646997	−	0.914991i
$130$	−6.00000	−	7.34847i	−0.526235	−	0.644503i
$131$		−	1.41421i		−	0.123560i	−0.998090	−	0.0617802i	$-0.980322\pi$
$131$		−	1.41421i		−	0.123560i	0.998090	−	0.0617802i	$-0.0196778\pi$
$132$	−1.41421	−	2.00000i	−0.123091	−	0.174078i
$133$	−4.24264	−	9.79796i	−0.367884	−	0.849591i
$134$		0			0
$135$	9.52056	+	6.66025i	0.819399	+	0.573223i
$136$		−	6.92820i		−	0.594089i
$137$	−17.3205			−1.47979			−0.739895	−	0.672722i	$-0.765125\pi$
$137$	−17.3205			−1.47979			−0.739895	+	0.672722i	$0.765125\pi$
$138$	3.46410	+	4.89898i	0.294884	+	0.417029i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$	−3.46410	−	4.24264i	−0.292770	−	0.358569i
$141$	−4.89898	+	3.46410i	−0.412568	+	0.291730i
$142$			4.89898i			0.411113i
$143$			6.00000i			0.501745i
$144$	1.00000	−	2.82843i	0.0833333	−	0.235702i
$145$	4.24264	−	3.46410i	0.352332	−	0.287678i
$146$	−14.6969			−1.21633
$147$	1.41421	−	1.00000i	0.116642	−	0.0824786i
$148$	4.24264			0.348743
$149$		−	11.3137i		−	0.926855i	−0.886135	−	0.463428i	$-0.846619\pi$
$149$		−	11.3137i		−	0.926855i	0.886135	−	0.463428i	$-0.153381\pi$
$150$	7.92820	−	3.48477i	0.647335	−	0.284530i
$151$			13.8564i			1.12762i	0.825905	+	0.563809i	$0.190665\pi$
$151$			13.8564i			1.12762i	−0.825905	+	0.563809i	$0.809335\pi$
$152$	−1.73205	−	4.00000i	−0.140488	−	0.324443i
$153$	6.92820	−	19.5959i	0.560112	−	1.58424i
$154$			3.46410i			0.279145i
$155$	−9.79796	−	12.0000i	−0.786991	−	0.963863i
$156$	−6.00000	+	4.24264i	−0.480384	+	0.339683i
$157$			14.6969i			1.17294i	0.809970	+	0.586472i	$0.199483\pi$
$157$			14.6969i			1.17294i	−0.809970	+	0.586472i	$0.800517\pi$
$158$	−10.3923			−0.826767
$159$	−6.00000	−	8.48528i	−0.475831	−	0.672927i
$160$	−1.41421	−	1.73205i	−0.111803	−	0.136931i
$161$		−	8.48528i		−	0.668734i
$162$	5.65685	−	7.00000i	0.444444	−	0.549972i
$163$		−	12.2474i		−	0.959294i	−0.877461	−	0.479647i	$-0.840765\pi$
$163$		−	12.2474i		−	0.959294i	0.877461	−	0.479647i	$-0.159235\pi$
$164$	12.2474			0.956365
$165$	−5.27792	−	1.46410i	−0.410885	−	0.113980i
$166$			10.3923i			0.806599i
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$	−3.46410	+	2.44949i	−0.267261	+	0.188982i
$169$	5.00000			0.384615
$170$	−9.79796	−	12.0000i	−0.751469	−	0.920358i
$171$	−0.898979	−	13.0458i	−0.0687467	−	0.997634i
$172$			7.34847i			0.560316i
$173$		−	6.00000i		−	0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$173$		−	6.00000i		−	0.456172i	0.973641	−	0.228086i	$-0.0732467\pi$
$174$	−2.44949	−	3.46410i	−0.185695	−	0.262613i
$175$	−12.0000	−	2.44949i	−0.907115	−	0.185164i
$176$			1.41421i			0.106600i
$177$	6.92820	−	4.89898i	0.520756	−	0.368230i
$178$			2.44949i			0.183597i
$179$	4.89898			0.366167			0.183083	−	0.983097i	$-0.441392\pi$
$179$	4.89898			0.366167			0.183083	+	0.983097i	$0.441392\pi$
$180$	−2.26795	−	6.31319i	−0.169043	−	0.470558i
$181$		−	13.8564i		−	1.02994i	−0.857209	−	0.514969i	$-0.827803\pi$
$181$		−	13.8564i		−	1.02994i	0.857209	−	0.514969i	$-0.172197\pi$
$182$	10.3923			0.770329
$183$	−11.3137	+	8.00000i	−0.836333	+	0.591377i
$184$		−	3.46410i		−	0.255377i
$185$	7.34847	−	6.00000i	0.540270	−	0.441129i
$186$	−9.79796	+	6.92820i	−0.718421	+	0.508001i
$187$			9.79796i			0.716498i
$188$	3.46410			0.252646
$189$	−12.2474	+	3.46410i	−0.890871	+	0.251976i
$190$	−8.65685	−	4.47871i	−0.628034	−	0.324920i
$191$			24.0416i			1.73959i	0.493412	+	0.869796i	$0.335749\pi$
$191$			24.0416i			1.73959i	−0.493412	+	0.869796i	$0.664251\pi$
$192$	−1.41421	+	1.00000i	−0.102062	+	0.0721688i
$193$	−12.7279			−0.916176			−0.458088	−	0.888907i	$-0.651466\pi$
$193$	−12.7279			−0.916176			−0.458088	+	0.888907i	$0.651466\pi$
$194$		−	12.7279i		−	0.913812i
$195$	−4.39230	+	15.8338i	−0.314539	+	1.13388i
$196$	−1.00000			−0.0714286
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−1.41421	+	4.00000i	−0.100504	+	0.284268i
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−4.89898	−	1.00000i	−0.346410	−	0.0707107i
$201$		0			0
$202$	2.82843			0.199007
$203$			6.00000i			0.421117i
$204$	−9.79796	+	6.92820i	−0.685994	+	0.485071i
$205$	21.2132	−	17.3205i	1.48159	−	1.20972i
$206$		−	8.48528i		−	0.591198i
$207$	3.46410	−	9.79796i	0.240772	−	0.681005i
$208$	4.24264			0.294174
$209$	2.44949	+	5.65685i	0.169435	+	0.391293i
$210$	−2.53590	+	9.14162i	−0.174994	+	0.630832i
$211$			3.46410i			0.238479i	0.992866	+	0.119239i	$0.0380456\pi$
$211$			3.46410i			0.238479i	−0.992866	+	0.119239i	$0.961954\pi$
$212$			6.00000i			0.412082i
$213$	6.92820	−	4.89898i	0.474713	−	0.335673i
$214$	−18.0000			−1.23045
$215$	10.3923	+	12.7279i	0.708749	+	0.868037i
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$	16.9706			1.15204
$218$	−6.92820			−0.469237
$219$	14.6969	+	20.7846i	0.993127	+	1.40449i
$220$	2.00000	+	2.44949i	0.134840	+	0.165145i
$221$	29.3939			1.97725
$222$	−4.24264	−	6.00000i	−0.284747	−	0.402694i
$223$	−25.4558			−1.70465			−0.852325	−	0.523013i	$-0.824808\pi$
$223$	−25.4558			−1.70465			−0.852325	+	0.523013i	$0.824808\pi$
$224$	2.44949			0.163663
$225$	−12.8564	−	7.72741i	−0.857094	−	0.515160i
$226$	18.0000			1.19734
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$	−3.92480	+	6.44949i	−0.259926	+	0.427128i
$229$	28.0000			1.85029			0.925146	−	0.379611i	$-0.123942\pi$
$229$	28.0000			1.85029			0.925146	+	0.379611i	$0.123942\pi$
$230$	−4.89898	−	6.00000i	−0.323029	−	0.395628i
$231$	4.89898	−	3.46410i	0.322329	−	0.227921i
$232$			2.44949i			0.160817i
$233$	−10.3923			−0.680823			−0.340411	−	0.940277i	$-0.610566\pi$
$233$	−10.3923			−0.680823			−0.340411	+	0.940277i	$0.610566\pi$
$234$	12.0000	+	4.24264i	0.784465	+	0.277350i
$235$	6.00000	−	4.89898i	0.391397	−	0.319574i
$236$	−4.89898			−0.318896
$237$	10.3923	+	14.6969i	0.675053	+	0.954669i
$238$	16.9706			1.10004
$239$		−	1.41421i		−	0.0914779i	−0.998953	−	0.0457389i	$-0.985436\pi$
$239$		−	1.41421i		−	0.0914779i	0.998953	−	0.0457389i	$-0.0145642\pi$
$240$	−1.03528	+	3.73205i	−0.0668268	+	0.240903i
$241$			13.8564i			0.892570i	0.894891	+	0.446285i	$0.147253\pi$
$241$			13.8564i			0.892570i	−0.894891	+	0.446285i	$0.852747\pi$
$242$			9.00000i			0.578542i
$243$	−15.5563	−	1.00000i	−0.997940	−	0.0641500i
$244$	8.00000			0.512148
$245$	−1.73205	+	1.41421i	−0.110657	+	0.0903508i
$246$	−12.2474	−	17.3205i	−0.780869	−	1.10432i
$247$	16.9706	−	7.34847i	1.07981	−	0.467572i
$248$	6.92820			0.439941
$249$	14.6969	−	10.3923i	0.931381	−	0.658586i
$250$	−9.89949	+	5.19615i	−0.626099	+	0.328634i
$251$		−	1.41421i		−	0.0892644i	−0.999003	−	0.0446322i	$-0.985788\pi$
$251$		−	1.41421i		−	0.0892644i	0.999003	−	0.0446322i	$-0.0142116\pi$
$252$	6.92820	+	2.44949i	0.436436	+	0.154303i
$253$			4.89898i			0.307996i
$254$		0			0
$255$	−7.17260	+	25.8564i	−0.449166	+	1.61919i
$256$	1.00000			0.0625000
$257$			6.00000i			0.374270i	0.982334	+	0.187135i	$0.0599201\pi$
$257$			6.00000i			0.374270i	−0.982334	+	0.187135i	$0.940080\pi$
$258$	10.3923	−	7.34847i	0.646997	−	0.457496i
$259$			10.3923i			0.645746i
$260$	7.34847	−	6.00000i	0.455733	−	0.372104i
$261$	−2.44949	+	6.92820i	−0.151620	+	0.428845i
$262$	1.41421			0.0873704
$263$	−3.46410			−0.213606			−0.106803	−	0.994280i	$-0.534061\pi$
$263$	−3.46410			−0.213606			−0.106803	+	0.994280i	$0.534061\pi$
$264$	2.00000	−	1.41421i	0.123091	−	0.0870388i
$265$	8.48528	+	10.3923i	0.521247	+	0.638394i
$266$	9.79796	−	4.24264i	0.600751	−	0.260133i
$267$	3.46410	−	2.44949i	0.212000	−	0.149906i
$268$		0			0
$269$	−17.1464			−1.04544			−0.522718	−	0.852506i	$-0.675082\pi$
$269$	−17.1464			−1.04544			−0.522718	+	0.852506i	$0.675082\pi$
$270$	−6.66025	+	9.52056i	−0.405330	+	0.579403i
$271$	4.00000			0.242983			0.121491	−	0.992592i	$-0.461232\pi$
$271$	4.00000			0.242983			0.121491	+	0.992592i	$0.461232\pi$
$272$	6.92820			0.420084
$273$	−10.3923	−	14.6969i	−0.628971	−	0.889499i
$274$		−	17.3205i		−	1.04637i
$275$	6.92820	+	1.41421i	0.417786	+	0.0852803i
$276$	−4.89898	+	3.46410i	−0.294884	+	0.208514i
$277$		−	19.5959i		−	1.17740i	−0.808350	−	0.588702i	$-0.799639\pi$
$277$		−	19.5959i		−	1.17740i	0.808350	−	0.588702i	$-0.200361\pi$
$278$			4.00000i			0.239904i
$279$	19.5959	+	6.92820i	1.17318	+	0.414781i
$280$	4.24264	−	3.46410i	0.253546	−	0.207020i
$281$	−7.34847			−0.438373			−0.219186	−	0.975683i	$-0.570340\pi$
$281$	−7.34847			−0.438373			−0.219186	+	0.975683i	$0.570340\pi$
$282$	−3.46410	−	4.89898i	−0.206284	−	0.291730i
$283$		−	12.2474i		−	0.728035i	−0.931392	−	0.364018i	$-0.881405\pi$
$283$		−	12.2474i		−	0.728035i	0.931392	−	0.364018i	$-0.118595\pi$
$284$	−4.89898			−0.290701
$285$	2.32300	+	16.7214i	0.137602	+	0.990488i
$286$	−6.00000			−0.354787
$287$			30.0000i			1.77084i
$288$	2.82843	+	1.00000i	0.166667	+	0.0589256i
$289$	31.0000			1.82353
$290$	3.46410	+	4.24264i	0.203419	+	0.249136i
$291$	−18.0000	+	12.7279i	−1.05518	+	0.746124i
$292$		−	14.6969i		−	0.860073i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	1.00000	+	1.41421i	0.0583212	+	0.0824786i
$295$	−8.48528	+	6.92820i	−0.494032	+	0.403376i
$296$			4.24264i			0.246598i
$297$	7.07107	−	2.00000i	0.410305	−	0.116052i
$298$	11.3137			0.655386
$299$	14.6969			0.849946
$300$	3.48477	+	7.92820i	0.201193	+	0.457735i
$301$	−18.0000			−1.03750
$302$	−13.8564			−0.797347
$303$	−2.82843	−	4.00000i	−0.162489	−	0.229794i
$304$	4.00000	−	1.73205i	0.229416	−	0.0993399i
$305$	13.8564	−	11.3137i	0.793416	−	0.647821i
$306$	19.5959	+	6.92820i	1.12022	+	0.396059i
$307$	25.4558			1.45284			0.726421	−	0.687250i	$-0.241182\pi$
$307$	25.4558			1.45284			0.726421	+	0.687250i	$0.241182\pi$
$308$	−3.46410			−0.197386
$309$	−12.0000	+	8.48528i	−0.682656	+	0.482711i
$310$	12.0000	−	9.79796i	0.681554	−	0.556487i
$311$			26.8701i			1.52366i	0.647776	+	0.761831i	$0.275699\pi$
$311$			26.8701i			1.52366i	−0.647776	+	0.761831i	$0.724301\pi$
$312$	−4.24264	−	6.00000i	−0.240192	−	0.339683i
$313$		−	4.89898i		−	0.276907i	−0.990369	−	0.138453i	$-0.955787\pi$
$313$		−	4.89898i		−	0.276907i	0.990369	−	0.138453i	$-0.0442131\pi$
$314$	−14.6969			−0.829396
$315$	15.4641	−	5.55532i	0.871303	−	0.313007i
$316$		−	10.3923i		−	0.584613i
$317$			18.0000i			1.01098i	0.862832	+	0.505490i	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$	8.48528	−	6.00000i	0.475831	−	0.336463i
$319$		−	3.46410i		−	0.193952i
$320$	1.73205	−	1.41421i	0.0968246	−	0.0790569i
$321$	18.0000	+	25.4558i	1.00466	+	1.42081i
$322$	8.48528			0.472866
$323$	27.7128	−	12.0000i	1.54198	−	0.667698i
$324$	7.00000	+	5.65685i	0.388889	+	0.314270i
$325$	4.24264	−	20.7846i	0.235339	−	1.15292i
$326$	12.2474			0.678323
$327$	6.92820	+	9.79796i	0.383131	+	0.541828i
$328$			12.2474i			0.676252i
$329$			8.48528i			0.467809i
$330$	1.46410	−	5.27792i	0.0805961	−	0.290540i
$331$		−	6.92820i		−	0.380808i	−0.981706	−	0.190404i	$-0.939020\pi$
$331$		−	6.92820i		−	0.380808i	0.981706	−	0.190404i	$-0.0609799\pi$
$332$	−10.3923			−0.570352
$333$	−4.24264	+	12.0000i	−0.232495	+	0.657596i
$334$		0			0
$335$		0			0
$336$	−2.44949	−	3.46410i	−0.133631	−	0.188982i
$337$	−4.24264			−0.231111			−0.115556	−	0.993301i	$-0.536865\pi$
$337$	−4.24264			−0.231111			−0.115556	+	0.993301i	$0.536865\pi$
$338$			5.00000i			0.271964i
$339$	−18.0000	−	25.4558i	−0.977626	−	1.38257i
$340$	12.0000	−	9.79796i	0.650791	−	0.531369i
$341$	−9.79796			−0.530589
$342$	13.0458	−	0.898979i	0.705434	−	0.0486112i
$343$		−	19.5959i		−	1.05808i
$344$	−7.34847			−0.396203
$345$	−3.58630	+	12.9282i	−0.193080	+	0.696031i
$346$	6.00000			0.322562
$347$	−24.2487			−1.30174			−0.650870	−	0.759190i	$-0.725596\pi$
$347$	−24.2487			−1.30174			−0.650870	+	0.759190i	$0.725596\pi$
$348$	3.46410	−	2.44949i	0.185695	−	0.131306i
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$	2.44949	−	12.0000i	0.130931	−	0.641427i
$351$	−6.00000	−	21.2132i	−0.320256	−	1.13228i
$352$	−1.41421			−0.0753778
$353$	17.3205			0.921878			0.460939	−	0.887432i	$-0.347513\pi$
$353$	17.3205			0.921878			0.460939	+	0.887432i	$0.347513\pi$
$354$	4.89898	+	6.92820i	0.260378	+	0.368230i
$355$	−8.48528	+	6.92820i	−0.450352	+	0.367711i
$356$	−2.44949			−0.129823
$357$	−16.9706	−	24.0000i	−0.898177	−	1.27021i
$358$			4.89898i			0.258919i
$359$			18.3848i			0.970311i	0.874428	+	0.485156i	$0.161237\pi$
$359$			18.3848i			0.970311i	−0.874428	+	0.485156i	$0.838763\pi$
$360$	6.31319	−	2.26795i	0.332734	−	0.119531i
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	13.8564			0.728277
$363$	12.7279	−	9.00000i	0.668043	−	0.472377i
$364$			10.3923i			0.544705i
$365$	−20.7846	−	25.4558i	−1.08792	−	1.33242i
$366$	−8.00000	−	11.3137i	−0.418167	−	0.591377i
$367$			31.8434i			1.66221i	0.556115	+	0.831105i	$0.312291\pi$
$367$			31.8434i			1.66221i	−0.556115	+	0.831105i	$0.687709\pi$
$368$	3.46410			0.180579
$369$	−12.2474	+	34.6410i	−0.637577	+	1.80334i
$370$	6.00000	+	7.34847i	0.311925	+	0.382029i
$371$	−14.6969			−0.763027
$372$	−6.92820	−	9.79796i	−0.359211	−	0.508001i
$373$	−12.7279			−0.659027			−0.329513	−	0.944151i	$-0.606885\pi$
$373$	−12.7279			−0.659027			−0.329513	+	0.944151i	$0.606885\pi$
$374$	−9.79796			−0.506640
$375$	17.2480	+	8.80385i	0.890681	+	0.454629i
$376$			3.46410i			0.178647i
$377$	−10.3923			−0.535231
$378$	−3.46410	−	12.2474i	−0.178174	−	0.629941i
$379$		−	20.7846i		−	1.06763i	−0.845600	−	0.533817i	$-0.820757\pi$
$379$		−	20.7846i		−	1.06763i	0.845600	−	0.533817i	$-0.179243\pi$
$380$	4.47871	−	8.65685i	0.229753	−	0.444087i
$381$		0			0
$382$	−24.0416			−1.23008
$383$		−	6.00000i		−	0.306586i	−0.988181	−	0.153293i	$-0.951012\pi$
$383$		−	6.00000i		−	0.306586i	0.988181	−	0.153293i	$-0.0489878\pi$
$384$	−1.00000	−	1.41421i	−0.0510310	−	0.0721688i
$385$	−6.00000	+	4.89898i	−0.305788	+	0.249675i
$386$		−	12.7279i		−	0.647834i
$387$	−20.7846	−	7.34847i	−1.05654	−	0.373544i
$388$	12.7279			0.646162
$389$			19.7990i			1.00385i	0.864912	+	0.501924i	$0.167374\pi$
$389$			19.7990i			1.00385i	−0.864912	+	0.501924i	$0.832626\pi$
$390$	−15.8338	−	4.39230i	−0.801773	−	0.222413i
$391$	24.0000			1.21373
$392$		−	1.00000i		−	0.0505076i
$393$	−1.41421	−	2.00000i	−0.0713376	−	0.100887i
$394$		0			0
$395$	−14.6969	−	18.0000i	−0.739483	−	0.905678i
$396$	−4.00000	−	1.41421i	−0.201008	−	0.0710669i
$397$		−	19.5959i		−	0.983491i	−0.870739	−	0.491745i	$-0.836359\pi$
$397$		−	19.5959i		−	0.983491i	0.870739	−	0.491745i	$-0.163641\pi$
$398$		−	16.0000i		−	0.802008i
$399$	−15.7980	−	9.61377i	−0.790887	−	0.481290i
$400$	1.00000	−	4.89898i	0.0500000	−	0.244949i
$401$	−22.0454			−1.10090			−0.550448	−	0.834870i	$-0.685543\pi$
$401$	−22.0454			−1.10090			−0.550448	+	0.834870i	$0.685543\pi$
$402$		0			0
$403$			29.3939i			1.46421i
$404$			2.82843i			0.140720i
$405$	20.1244	−	0.101536i	0.999987	−	0.00504536i
$406$	−6.00000			−0.297775
$407$		−	6.00000i		−	0.297409i
$408$	−6.92820	−	9.79796i	−0.342997	−	0.485071i
$409$		−	20.7846i		−	1.02773i	−0.857870	−	0.513866i	$-0.828213\pi$
$409$		−	20.7846i		−	1.02773i	0.857870	−	0.513866i	$-0.171787\pi$
$410$	17.3205	+	21.2132i	0.855399	+	1.04765i
$411$	−24.4949	+	17.3205i	−1.20824	+	0.854358i
$412$	8.48528			0.418040
$413$		−	12.0000i		−	0.590481i
$414$	9.79796	+	3.46410i	0.481543	+	0.170251i
$415$	−18.0000	+	14.6969i	−0.883585	+	0.721444i
$416$			4.24264i			0.208013i
$417$	5.65685	−	4.00000i	0.277017	−	0.195881i
$418$	−5.65685	+	2.44949i	−0.276686	+	0.119808i
$419$		−	9.89949i		−	0.483622i	−0.970323	−	0.241811i	$-0.922259\pi$
$419$		−	9.89949i		−	0.483622i	0.970323	−	0.241811i	$-0.0777414\pi$
$420$	−9.14162	−	2.53590i	−0.446065	−	0.123739i
$421$			13.8564i			0.675320i	0.941268	+	0.337660i	$0.109635\pi$
$421$			13.8564i			0.675320i	−0.941268	+	0.337660i	$0.890365\pi$
$422$	−3.46410			−0.168630
$423$	−3.46410	+	9.79796i	−0.168430	+	0.476393i
$424$	−6.00000			−0.291386
$425$	6.92820	−	33.9411i	0.336067	−	1.64639i
$426$	4.89898	+	6.92820i	0.237356	+	0.335673i
$427$			19.5959i			0.948313i
$428$		−	18.0000i		−	0.870063i
$429$	6.00000	+	8.48528i	0.289683	+	0.409673i
$430$	−12.7279	+	10.3923i	−0.613795	+	0.501161i
$431$	19.5959			0.943902			0.471951	−	0.881625i	$-0.343550\pi$
$431$	19.5959			0.943902			0.471951	+	0.881625i	$0.343550\pi$
$432$	−1.41421	−	5.00000i	−0.0680414	−	0.240563i
$433$	38.1838			1.83499			0.917497	−	0.397742i	$-0.130206\pi$
$433$	38.1838			1.83499			0.917497	+	0.397742i	$0.130206\pi$
$434$			16.9706i			0.814613i
$435$	2.53590	−	9.14162i	0.121587	−	0.438307i
$436$		−	6.92820i		−	0.331801i
$437$	13.8564	−	6.00000i	0.662842	−	0.287019i
$438$	−20.7846	+	14.6969i	−0.993127	+	0.702247i
$439$			3.46410i			0.165333i	0.996577	+	0.0826663i	$0.0263436\pi$
$439$			3.46410i			0.165333i	−0.996577	+	0.0826663i	$0.973656\pi$
$440$	−2.44949	+	2.00000i	−0.116775	+	0.0953463i
$441$	1.00000	−	2.82843i	0.0476190	−	0.134687i
$442$			29.3939i			1.39812i
$443$	17.3205			0.822922			0.411461	−	0.911427i	$-0.365019\pi$
$443$	17.3205			0.822922			0.411461	+	0.911427i	$0.365019\pi$
$444$	6.00000	−	4.24264i	0.284747	−	0.201347i
$445$	−4.24264	+	3.46410i	−0.201120	+	0.164214i
$446$		−	25.4558i		−	1.20537i
$447$	−11.3137	−	16.0000i	−0.535120	−	0.756774i
$448$			2.44949i			0.115728i
$449$	−12.2474			−0.577993			−0.288996	−	0.957330i	$-0.593322\pi$
$449$	−12.2474			−0.577993			−0.288996	+	0.957330i	$0.593322\pi$
$450$	7.72741	−	12.8564i	0.364273	−	0.606057i
$451$		−	17.3205i		−	0.815591i
$452$			18.0000i			0.846649i
$453$	13.8564	+	19.5959i	0.651031	+	0.920697i
$454$	−12.0000			−0.563188
$455$	14.6969	+	18.0000i	0.689003	+	0.843853i
$456$	−6.44949	−	3.92480i	−0.302025	−	0.183796i
$457$		−	24.4949i		−	1.14582i	−0.819617	−	0.572911i	$-0.805814\pi$
$457$		−	24.4949i		−	1.14582i	0.819617	−	0.572911i	$-0.194186\pi$
$458$			28.0000i			1.30835i
$459$	−9.79796	−	34.6410i	−0.457330	−	1.61690i
$460$	6.00000	−	4.89898i	0.279751	−	0.228416i
$461$		−	22.6274i		−	1.05386i	−0.849907	−	0.526932i	$-0.823342\pi$
$461$		−	22.6274i		−	1.05386i	0.849907	−	0.526932i	$-0.176658\pi$
$462$	3.46410	+	4.89898i	0.161165	+	0.227921i
$463$			12.2474i			0.569187i	0.958648	+	0.284594i	$0.0918587\pi$
$463$			12.2474i			0.569187i	−0.958648	+	0.284594i	$0.908141\pi$
$464$	−2.44949			−0.113715
$465$	−25.8564	−	7.17260i	−1.19906	−	0.332622i
$466$		−	10.3923i		−	0.481414i
$467$	24.2487			1.12210			0.561048	−	0.827783i	$-0.310398\pi$
$467$	24.2487			1.12210			0.561048	+	0.827783i	$0.310398\pi$
$468$	−4.24264	+	12.0000i	−0.196116	+	0.554700i
$469$		0			0
$470$	4.89898	+	6.00000i	0.225973	+	0.276759i
$471$	14.6969	+	20.7846i	0.677199	+	0.957704i
$472$		−	4.89898i		−	0.225494i
$473$	10.3923			0.477839
$474$	−14.6969	+	10.3923i	−0.675053	+	0.477334i
$475$	−4.48528	−	21.3280i	−0.205799	−	0.978594i
$476$			16.9706i			0.777844i
$477$	−16.9706	−	6.00000i	−0.777029	−	0.274721i
$478$	1.41421			0.0646846
$479$			9.89949i			0.452319i	0.974090	+	0.226160i	$0.0726171\pi$
$479$			9.89949i			0.452319i	−0.974090	+	0.226160i	$0.927383\pi$
$480$	−3.73205	−	1.03528i	−0.170344	−	0.0472537i
$481$	−18.0000			−0.820729
$482$	−13.8564			−0.631142
$483$	−8.48528	−	12.0000i	−0.386094	−	0.546019i
$484$	−9.00000			−0.409091
$485$	22.0454	−	18.0000i	1.00103	−	0.817338i
$486$	1.00000	−	15.5563i	0.0453609	−	0.705650i
$487$	33.9411			1.53802			0.769010	−	0.639237i	$-0.220750\pi$
$487$	33.9411			1.53802			0.769010	+	0.639237i	$0.220750\pi$
$488$			8.00000i			0.362143i
$489$	−12.2474	−	17.3205i	−0.553849	−	0.783260i
$490$	−1.41421	−	1.73205i	−0.0638877	−	0.0782461i
$491$			7.07107i			0.319113i	0.987189	+	0.159556i	$0.0510064\pi$
$491$			7.07107i			0.319113i	−0.987189	+	0.159556i	$0.948994\pi$
$492$	17.3205	−	12.2474i	0.780869	−	0.552158i
$493$	−16.9706			−0.764316
$494$	7.34847	+	16.9706i	0.330623	+	0.763542i
$495$	−8.92820	+	3.20736i	−0.401293	+	0.144160i
$496$			6.92820i			0.311086i
$497$		−	12.0000i		−	0.538274i
$498$	10.3923	+	14.6969i	0.465690	+	0.658586i
$499$	−20.0000			−0.895323			−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000			−0.895323			−0.447661	+	0.894203i	$0.647743\pi$
$500$	−5.19615	−	9.89949i	−0.232379	−	0.442719i
$501$		0			0
$502$	1.41421			0.0631194
$503$	−17.3205			−0.772283			−0.386142	−	0.922440i	$-0.626192\pi$
$503$	−17.3205			−0.772283			−0.386142	+	0.922440i	$0.626192\pi$
$504$	−2.44949	+	6.92820i	−0.109109	+	0.308607i
$505$	4.00000	+	4.89898i	0.177998	+	0.218002i
$506$	−4.89898			−0.217786
$507$	7.07107	−	5.00000i	0.314037	−	0.222058i
$508$		0			0
$509$	−22.0454			−0.977146			−0.488573	−	0.872523i	$-0.662482\pi$
$509$	−22.0454			−0.977146			−0.488573	+	0.872523i	$0.662482\pi$
$510$	−25.8564	−	7.17260i	−1.14494	−	0.317608i
$511$	36.0000			1.59255
$512$			1.00000i			0.0441942i
$513$	−14.3171	−	17.5505i	−0.632116	−	0.774874i
$514$	−6.00000			−0.264649
$515$	14.6969	−	12.0000i	0.647624	−	0.528783i
$516$	7.34847	+	10.3923i	0.323498	+	0.457496i
$517$		−	4.89898i		−	0.215457i
$518$	−10.3923			−0.456612
$519$	−6.00000	−	8.48528i	−0.263371	−	0.372463i
$520$	6.00000	+	7.34847i	0.263117	+	0.322252i
$521$	22.0454			0.965827			0.482913	−	0.875668i	$-0.339579\pi$
$521$	22.0454			0.965827			0.482913	+	0.875668i	$0.339579\pi$
$522$	−6.92820	−	2.44949i	−0.303239	−	0.107211i
$523$	16.9706			0.742071			0.371035	−	0.928619i	$-0.379003\pi$
$523$	16.9706			0.742071			0.371035	+	0.928619i	$0.379003\pi$
$524$			1.41421i			0.0617802i
$525$	−19.4201	+	8.53590i	−0.847561	+	0.372537i
$526$		−	3.46410i		−	0.151042i
$527$			48.0000i			2.09091i
$528$	1.41421	+	2.00000i	0.0615457	+	0.0870388i
$529$	−11.0000			−0.478261
$530$	−10.3923	+	8.48528i	−0.451413	+	0.368577i
$531$	4.89898	−	13.8564i	0.212598	−	0.601317i
$532$	4.24264	+	9.79796i	0.183942	+	0.424795i
$533$	−51.9615			−2.25070
$534$	2.44949	+	3.46410i	0.106000	+	0.149906i
$535$	−25.4558	−	31.1769i	−1.10055	−	1.34790i
$536$		0			0
$537$	6.92820	−	4.89898i	0.298974	−	0.211407i
$538$		−	17.1464i		−	0.739235i
$539$			1.41421i			0.0609145i
$540$	−9.52056	−	6.66025i	−0.409700	−	0.286612i
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$			4.00000i			0.171815i
$543$	−13.8564	−	19.5959i	−0.594635	−	0.840941i
$544$			6.92820i			0.297044i
$545$	−9.79796	−	12.0000i	−0.419698	−	0.514024i
$546$	14.6969	−	10.3923i	0.628971	−	0.444750i
$547$	−25.4558			−1.08841			−0.544207	−	0.838951i	$-0.683169\pi$
$547$	−25.4558			−1.08841			−0.544207	+	0.838951i	$0.683169\pi$
$548$	17.3205			0.739895
$549$	−8.00000	+	22.6274i	−0.341432	+	0.965715i
$550$	−1.41421	+	6.92820i	−0.0603023	+	0.295420i
$551$	−9.79796	+	4.24264i	−0.417407	+	0.180743i
$552$	−3.46410	−	4.89898i	−0.147442	−	0.208514i
$553$	25.4558			1.08249
$554$	19.5959			0.832551
$555$	4.39230	−	15.8338i	0.186443	−	0.672105i
$556$	−4.00000			−0.169638
$557$	−10.3923			−0.440336			−0.220168	−	0.975462i	$-0.570661\pi$
$557$	−10.3923			−0.440336			−0.220168	+	0.975462i	$0.570661\pi$
$558$	−6.92820	+	19.5959i	−0.293294	+	0.829561i
$559$		−	31.1769i		−	1.31864i
$560$	3.46410	+	4.24264i	0.146385	+	0.179284i
$561$	9.79796	+	13.8564i	0.413670	+	0.585018i
$562$		−	7.34847i		−	0.309976i
$563$		−	36.0000i		−	1.51722i	−0.651546	−	0.758610i	$-0.725879\pi$
$563$		−	36.0000i		−	1.51722i	0.651546	−	0.758610i	$-0.274121\pi$
$564$	4.89898	−	3.46410i	0.206284	−	0.145865i
$565$	25.4558	+	31.1769i	1.07094	+	1.31162i
$566$	12.2474			0.514799
$567$	−13.8564	+	17.1464i	−0.581914	+	0.720082i
$568$		−	4.89898i		−	0.205557i
$569$	46.5403			1.95107			0.975536	−	0.219842i	$-0.0705541\pi$
$569$	46.5403			1.95107			0.975536	+	0.219842i	$0.0705541\pi$
$570$	−16.7214	+	2.32300i	−0.700380	+	0.0972996i
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$		−	6.00000i		−	0.250873i
$573$	24.0416	+	34.0000i	1.00435	+	1.42037i
$574$	−30.0000			−1.25218
$575$	3.46410	−	16.9706i	0.144463	−	0.707721i
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$			24.4949i			1.01974i	0.860253	+	0.509868i	$0.170306\pi$
$577$			24.4949i			1.01974i	−0.860253	+	0.509868i	$0.829694\pi$
$578$			31.0000i			1.28943i
$579$	−18.0000	+	12.7279i	−0.748054	+	0.528954i
$580$	−4.24264	+	3.46410i	−0.176166	+	0.143839i
$581$		−	25.4558i		−	1.05609i
$582$	−12.7279	−	18.0000i	−0.527589	−	0.746124i
$583$	8.48528			0.351424
$584$	14.6969			0.608164
$585$	9.62209	+	26.7846i	0.397825	+	1.10741i
$586$	−6.00000			−0.247858
$587$	−3.46410			−0.142979			−0.0714894	−	0.997441i	$-0.522775\pi$
$587$	−3.46410			−0.142979			−0.0714894	+	0.997441i	$0.522775\pi$
$588$	−1.41421	+	1.00000i	−0.0583212	+	0.0412393i
$589$	12.0000	+	27.7128i	0.494451	+	1.14189i
$590$	−6.92820	−	8.48528i	−0.285230	−	0.349334i
$591$		0			0
$592$	−4.24264			−0.174371
$593$	−3.46410			−0.142254			−0.0711268	−	0.997467i	$-0.522659\pi$
$593$	−3.46410			−0.142254			−0.0711268	+	0.997467i	$0.522659\pi$
$594$	2.00000	+	7.07107i	0.0820610	+	0.290129i
$595$	24.0000	+	29.3939i	0.983904	+	1.20503i
$596$			11.3137i			0.463428i
$597$	−22.6274	+	16.0000i	−0.926079	+	0.654836i
$598$			14.6969i			0.601003i
$599$	4.89898			0.200167			0.100083	−	0.994979i	$-0.468089\pi$
$599$	4.89898			0.200167			0.100083	+	0.994979i	$0.468089\pi$
$600$	−7.92820	+	3.48477i	−0.323668	+	0.142265i
$601$		−	6.92820i		−	0.282607i	−0.989966	−	0.141304i	$-0.954871\pi$
$601$		−	6.92820i		−	0.282607i	0.989966	−	0.141304i	$-0.0451294\pi$
$602$		−	18.0000i		−	0.733625i
$603$		0			0
$604$		−	13.8564i		−	0.563809i
$605$	−15.5885	+	12.7279i	−0.633761	+	0.517464i
$606$	4.00000	−	2.82843i	0.162489	−	0.114897i
$607$	−16.9706			−0.688814			−0.344407	−	0.938820i	$-0.611920\pi$
$607$	−16.9706			−0.688814			−0.344407	+	0.938820i	$0.611920\pi$
$608$	1.73205	+	4.00000i	0.0702439	+	0.162221i
$609$	6.00000	+	8.48528i	0.243132	+	0.343841i
$610$	11.3137	+	13.8564i	0.458079	+	0.561029i
$611$	−14.6969			−0.594574
$612$	−6.92820	+	19.5959i	−0.280056	+	0.792118i
$613$			44.0908i			1.78081i	0.455168	+	0.890406i	$0.349579\pi$
$613$			44.0908i			1.78081i	−0.455168	+	0.890406i	$0.650421\pi$
$614$			25.4558i			1.02731i
$615$	12.6795	−	45.7081i	0.511286	−	1.84313i
$616$		−	3.46410i		−	0.139573i
$617$	−20.7846			−0.836757			−0.418378	−	0.908273i	$-0.637401\pi$
$617$	−20.7846			−0.836757			−0.418378	+	0.908273i	$0.637401\pi$
$618$	−8.48528	−	12.0000i	−0.341328	−	0.482711i
$619$	16.0000			0.643094			0.321547	−	0.946894i	$-0.395797\pi$
$619$	16.0000			0.643094			0.321547	+	0.946894i	$0.395797\pi$
$620$	9.79796	+	12.0000i	0.393496	+	0.481932i
$621$	−4.89898	−	17.3205i	−0.196589	−	0.695048i
$622$	−26.8701			−1.07739
$623$		−	6.00000i		−	0.240385i
$624$	6.00000	−	4.24264i	0.240192	−	0.169842i
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	4.89898			0.195803
$627$	9.12096	+	5.55051i	0.364256	+	0.221666i
$628$		−	14.6969i		−	0.586472i
$629$	−29.3939			−1.17201
$630$	5.55532	+	15.4641i	0.221329	+	0.616105i
$631$	−44.0000			−1.75161			−0.875806	−	0.482663i	$-0.839670\pi$
$631$	−44.0000			−1.75161			−0.875806	+	0.482663i	$0.839670\pi$
$632$	10.3923			0.413384
$633$	3.46410	+	4.89898i	0.137686	+	0.194717i
$634$	−18.0000			−0.714871
$635$		0			0
$636$	6.00000	+	8.48528i	0.237915	+	0.336463i
$637$	4.24264			0.168100
$638$	3.46410			0.137145
$639$	4.89898	−	13.8564i	0.193801	−	0.548151i
$640$	1.41421	+	1.73205i	0.0559017	+	0.0684653i
$641$	12.2474			0.483745			0.241873	−	0.970308i	$-0.422238\pi$
$641$	12.2474			0.483745			0.241873	+	0.970308i	$0.422238\pi$
$642$	−25.4558	+	18.0000i	−1.00466	+	0.710403i
$643$		−	7.34847i		−	0.289795i	−0.989447	−	0.144898i	$-0.953715\pi$
$643$		−	7.34847i		−	0.289795i	0.989447	−	0.144898i	$-0.0462853\pi$
$644$			8.48528i			0.334367i
$645$	27.4249	+	7.60770i	1.07985	+	0.299553i
$646$	12.0000	+	27.7128i	0.472134	+	1.09035i
$647$	−10.3923			−0.408564			−0.204282	−	0.978912i	$-0.565486\pi$
$647$	−10.3923			−0.408564			−0.204282	+	0.978912i	$0.565486\pi$
$648$	−5.65685	+	7.00000i	−0.222222	+	0.274986i
$649$			6.92820i			0.271956i
$650$	20.7846	+	4.24264i	0.815239	+	0.166410i
$651$	24.0000	−	16.9706i	0.940634	−	0.665129i
$652$			12.2474i			0.479647i
$653$		0			0			−	1.00000i	$-0.5\pi$
$653$		0			0				1.00000i	$0.5\pi$
$654$	−9.79796	+	6.92820i	−0.383131	+	0.270914i
$655$	2.00000	+	2.44949i	0.0781465	+	0.0957095i
$656$	−12.2474			−0.478183
$657$	41.5692	+	14.6969i	1.62177	+	0.573382i
$658$	−8.48528			−0.330791
$659$	−44.0908			−1.71753			−0.858767	−	0.512366i	$-0.828769\pi$
$659$	−44.0908			−1.71753			−0.858767	+	0.512366i	$0.828769\pi$
$660$	5.27792	+	1.46410i	0.205443	+	0.0569901i
$661$		−	48.4974i		−	1.88633i	−0.332323	−	0.943166i	$-0.607832\pi$
$661$		−	48.4974i		−	1.88633i	0.332323	−	0.943166i	$-0.392168\pi$
$662$	6.92820			0.269272
$663$	41.5692	−	29.3939i	1.61441	−	1.14156i
$664$		−	10.3923i		−	0.403300i
$665$	21.2049	+	10.9706i	0.822290	+	0.425420i
$666$	−12.0000	−	4.24264i	−0.464991	−	0.164399i
$667$	−8.48528			−0.328551
$668$		0			0
$669$	−36.0000	+	25.4558i	−1.39184	+	0.984180i
$670$		0			0
$671$		−	11.3137i		−	0.436761i
$672$	3.46410	−	2.44949i	0.133631	−	0.0944911i
$673$	12.7279			0.490625			0.245313	−	0.969444i	$-0.421109\pi$
$673$	12.7279			0.490625			0.245313	+	0.969444i	$0.421109\pi$
$674$		−	4.24264i		−	0.163420i
$675$	−25.9091	+	1.92820i	−0.997242	+	0.0742166i
$676$	−5.00000			−0.192308
$677$		−	30.0000i		−	1.15299i	−0.817099	−	0.576497i	$-0.804419\pi$
$677$		−	30.0000i		−	1.15299i	0.817099	−	0.576497i	$-0.195581\pi$
$678$	25.4558	−	18.0000i	0.977626	−	0.691286i
$679$			31.1769i			1.19646i
$680$	9.79796	+	12.0000i	0.375735	+	0.460179i
$681$	12.0000	+	16.9706i	0.459841	+	0.650313i
$682$		−	9.79796i		−	0.375183i
$683$			18.0000i			0.688751i	0.938832	+	0.344375i	$0.111909\pi$
$683$			18.0000i			0.688751i	−0.938832	+	0.344375i	$0.888091\pi$
$684$	0.898979	+	13.0458i	0.0343733	+	0.498817i
$685$	30.0000	−	24.4949i	1.14624	−	0.935902i
$686$	19.5959			0.748176
$687$	39.5980	−	28.0000i	1.51076	−	1.06827i
$688$		−	7.34847i		−	0.280158i
$689$		−	25.4558i		−	0.969790i
$690$	−12.9282	−	3.58630i	−0.492168	−	0.136528i
$691$	−20.0000			−0.760836			−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000			−0.760836			−0.380418	+	0.924815i	$0.624220\pi$
$692$			6.00000i			0.228086i
$693$	3.46410	−	9.79796i	0.131590	−	0.372194i
$694$		−	24.2487i		−	0.920468i
$695$	−6.92820	+	5.65685i	−0.262802	+	0.214577i
$696$	2.44949	+	3.46410i	0.0928477	+	0.131306i
$697$	−84.8528			−3.21403
$698$		−	22.0000i		−	0.832712i
$699$	−14.6969	+	10.3923i	−0.555889	+	0.393073i
$700$	12.0000	+	2.44949i	0.453557	+	0.0925820i
$701$		−	28.2843i		−	1.06828i	−0.845395	−	0.534141i	$-0.820635\pi$
$701$		−	28.2843i		−	1.06828i	0.845395	−	0.534141i	$-0.179365\pi$
$702$	21.2132	−	6.00000i	0.800641	−	0.226455i
$703$	−16.9706	+	7.34847i	−0.640057	+	0.277153i
$704$		−	1.41421i		−	0.0533002i
$705$	3.58630	−	12.9282i	0.135068	−	0.486904i
$706$			17.3205i			0.651866i
$707$	−6.92820			−0.260562
$708$	−6.92820	+	4.89898i	−0.260378	+	0.184115i
$709$	−16.0000			−0.600893			−0.300446	−	0.953799i	$-0.597136\pi$
$709$	−16.0000			−0.600893			−0.300446	+	0.953799i	$0.597136\pi$
$710$	−6.92820	−	8.48528i	−0.260011	−	0.318447i
$711$	29.3939	+	10.3923i	1.10236	+	0.389742i
$712$		−	2.44949i		−	0.0917985i
$713$			24.0000i			0.898807i
$714$	24.0000	−	16.9706i	0.898177	−	0.635107i
$715$	−8.48528	−	10.3923i	−0.317332	−	0.388650i
$716$	−4.89898			−0.183083
$717$	−1.41421	−	2.00000i	−0.0528148	−	0.0746914i
$718$	−18.3848			−0.686114
$719$		−	7.07107i		−	0.263706i	−0.991269	−	0.131853i	$-0.957907\pi$
$719$		−	7.07107i		−	0.263706i	0.991269	−	0.131853i	$-0.0420927\pi$
$720$	2.26795	+	6.31319i	0.0845215	+	0.235279i
$721$			20.7846i			0.774059i
$722$	13.8564	+	13.0000i	0.515682	+	0.483810i
$723$	13.8564	+	19.5959i	0.515325	+	0.728780i
$724$			13.8564i			0.514969i
$725$	−2.44949	+	12.0000i	−0.0909718	+	0.445669i
$726$	9.00000	+	12.7279i	0.334021	+	0.472377i
$727$		−	31.8434i		−	1.18101i	−0.807036	−	0.590503i	$-0.798930\pi$
$727$		−	31.8434i		−	1.18101i	0.807036	−	0.590503i	$-0.201070\pi$
$728$	−10.3923			−0.385164
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$	25.4558	−	20.7846i	0.942163	−	0.769273i
$731$		−	50.9117i		−	1.88304i
$732$	11.3137	−	8.00000i	0.418167	−	0.295689i
$733$		−	4.89898i		−	0.180948i	−0.995899	−	0.0904740i	$-0.971162\pi$
$733$		−	4.89898i		−	0.180948i	0.995899	−	0.0904740i	$-0.0288382\pi$
$734$	−31.8434			−1.17536
$735$	−1.03528	+	3.73205i	−0.0381867	+	0.137659i
$736$			3.46410i			0.127688i
$737$		0			0
$738$	−34.6410	−	12.2474i	−1.27515	−	0.450835i
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	−7.34847	+	6.00000i	−0.270135	+	0.220564i
$741$	16.6515	−	27.3629i	0.611709	−	1.00520i
$742$		−	14.6969i		−	0.539542i
$743$		−	30.0000i		−	1.10059i	−0.834969	−	0.550297i	$-0.814515\pi$
$743$		−	30.0000i		−	1.10059i	0.834969	−	0.550297i	$-0.185485\pi$
$744$	9.79796	−	6.92820i	0.359211	−	0.254000i
$745$	16.0000	+	19.5959i	0.586195	+	0.717939i
$746$		−	12.7279i		−	0.466002i
$747$	10.3923	−	29.3939i	0.380235	−	1.07547i
$748$		−	9.79796i		−	0.358249i
$749$	44.0908			1.61104
$750$	−8.80385	+	17.2480i	−0.321471	+	0.629807i
$751$			41.5692i			1.51688i	0.651741	+	0.758441i	$0.274039\pi$
$751$			41.5692i			1.51688i	−0.651741	+	0.758441i	$0.725961\pi$
$752$	−3.46410			−0.126323
$753$	−1.41421	−	2.00000i	−0.0515368	−	0.0728841i
$754$		−	10.3923i		−	0.378465i
$755$	−19.5959	−	24.0000i	−0.713168	−	0.873449i
$756$	12.2474	−	3.46410i	0.445435	−	0.125988i
$757$			9.79796i			0.356113i	0.984020	+	0.178056i	$0.0569810\pi$
$757$			9.79796i			0.356113i	−0.984020	+	0.178056i	$0.943019\pi$
$758$	20.7846			0.754931
$759$	4.89898	+	6.92820i	0.177822	+	0.251478i
$760$	8.65685	+	4.47871i	0.314017	+	0.162460i
$761$			14.1421i			0.512652i	0.966590	+	0.256326i	$0.0825121\pi$
$761$			14.1421i			0.512652i	−0.966590	+	0.256326i	$0.917488\pi$
$762$		0			0
$763$	16.9706			0.614376
$764$		−	24.0416i		−	0.869796i
$765$	15.7128	+	43.7391i	0.568098	+	1.58139i
$766$	6.00000			0.216789
$767$	20.7846			0.750489
$768$	1.41421	−	1.00000i	0.0510310	−	0.0360844i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$	−4.89898	−	6.00000i	−0.176547	−	0.216225i
$771$	6.00000	+	8.48528i	0.216085	+	0.305590i
$772$	12.7279			0.458088
$773$			18.0000i			0.647415i	0.946157	+	0.323708i	$0.104929\pi$
$773$			18.0000i			0.647415i	−0.946157	+	0.323708i	$0.895071\pi$
$774$	7.34847	−	20.7846i	0.264135	−	0.747087i
$775$	33.9411	+	6.92820i	1.21920	+	0.248868i
$776$			12.7279i			0.456906i
$777$	10.3923	+	14.6969i	0.372822	+	0.527250i
$778$	−19.7990			−0.709828
$779$	−48.9898	+	21.2132i	−1.75524	+	0.760042i
$780$	4.39230	−	15.8338i	0.157270	−	0.566939i
$781$			6.92820i			0.247911i
$782$			24.0000i			0.858238i
$783$	3.46410	+	12.2474i	0.123797	+	0.437688i
$784$	1.00000			0.0357143
$785$	−20.7846	−	25.4558i	−0.741835	−	0.908558i
$786$	2.00000	−	1.41421i	0.0713376	−	0.0504433i
$787$	50.9117			1.81481			0.907403	−	0.420262i	$-0.138062\pi$
$787$	50.9117			1.81481			0.907403	+	0.420262i	$0.138062\pi$
$788$		0			0
$789$	−4.89898	+	3.46410i	−0.174408	+	0.123325i
$790$	18.0000	−	14.6969i	0.640411	−	0.522894i
$791$	−44.0908			−1.56769
$792$	1.41421	−	4.00000i	0.0502519	−	0.142134i
$793$	−33.9411			−1.20528
$794$	19.5959			0.695433
$795$	22.3923	+	6.21166i	0.794173	+	0.220305i
$796$	16.0000			0.567105
$797$		−	6.00000i		−	0.212531i	−0.994338	−	0.106265i	$-0.966111\pi$
$797$		−	6.00000i		−	0.212531i	0.994338	−	0.106265i	$-0.0338893\pi$
$798$	9.61377	−	15.7980i	0.340324	−	0.559242i
$799$	−24.0000			−0.849059
$800$	4.89898	+	1.00000i	0.173205	+	0.0353553i
$801$	2.44949	−	6.92820i	0.0865485	−	0.244796i
$802$		−	22.0454i		−	0.778450i
$803$	−20.7846			−0.733473
$804$		0			0
$805$	12.0000	+	14.6969i	0.422944	+	0.517999i
$806$	−29.3939			−1.03536
$807$	−24.2487	+	17.1464i	−0.853595	+	0.603583i
$808$	−2.82843			−0.0995037
$809$			45.2548i			1.59108i	0.605904	+	0.795538i	$0.292811\pi$
$809$			45.2548i			1.59108i	−0.605904	+	0.795538i	$0.707189\pi$
$810$	0.101536	+	20.1244i	0.00356761	+	0.707098i
$811$			38.1051i			1.33805i	0.743239	+	0.669026i	$0.233288\pi$
$811$			38.1051i			1.33805i	−0.743239	+	0.669026i	$0.766712\pi$
$812$		−	6.00000i		−	0.210559i
$813$	5.65685	−	4.00000i	0.198395	−	0.140286i
$814$	6.00000			0.210300
$815$	17.3205	+	21.2132i	0.606711	+	0.743066i
$816$	9.79796	−	6.92820i	0.342997	−	0.242536i
$817$	−12.7279	−	29.3939i	−0.445294	−	1.02836i
$818$	20.7846			0.726717
$819$	−29.3939	−	10.3923i	−1.02711	−	0.363137i
$820$	−21.2132	+	17.3205i	−0.740797	+	0.604858i
$821$		−	14.1421i		−	0.493564i	−0.969071	−	0.246782i	$-0.920627\pi$
$821$		−	14.1421i		−	0.493564i	0.969071	−	0.246782i	$-0.0793731\pi$
$822$	−17.3205	−	24.4949i	−0.604122	−	0.854358i
$823$		−	56.3383i		−	1.96383i	−0.189326	−	0.981914i	$-0.560630\pi$
$823$		−	56.3383i		−	1.96383i	0.189326	−	0.981914i	$-0.439370\pi$
$824$			8.48528i			0.295599i
$825$	11.2122	−	4.92820i	0.390358	−	0.171578i
$826$	12.0000			0.417533
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$	−3.46410	+	9.79796i	−0.120386	+	0.340503i
$829$		−	27.7128i		−	0.962506i	−0.876582	−	0.481253i	$-0.840182\pi$
$829$		−	27.7128i		−	0.962506i	0.876582	−	0.481253i	$-0.159818\pi$
$830$	−14.6969	−	18.0000i	−0.510138	−	0.624789i
$831$	−19.5959	−	27.7128i	−0.679775	−	0.961347i
$832$	−4.24264			−0.147087
$833$	6.92820			0.240048
$834$	4.00000	+	5.65685i	0.138509	+	0.195881i
$835$		0			0
$836$	−2.44949	−	5.65685i	−0.0847174	−	0.195646i
$837$	34.6410	−	9.79796i	1.19737	−	0.338667i
$838$	9.89949			0.341972
$839$	53.8888			1.86045			0.930224	−	0.366993i	$-0.119613\pi$
$839$	53.8888			1.86045			0.930224	+	0.366993i	$0.119613\pi$
$840$	2.53590	−	9.14162i	0.0874968	−	0.315416i
$841$	−23.0000			−0.793103
$842$	−13.8564			−0.477523
$843$	−10.3923	+	7.34847i	−0.357930	+	0.253095i
$844$		−	3.46410i		−	0.119239i
$845$	−8.66025	+	7.07107i	−0.297922	+	0.243252i
$846$	−9.79796	−	3.46410i	−0.336861	−	0.119098i
$847$		−	22.0454i		−	0.757489i
$848$		−	6.00000i		−	0.206041i
$849$	−12.2474	−	17.3205i	−0.420331	−	0.594438i
$850$	33.9411	+	6.92820i	1.16417	+	0.237635i
$851$	−14.6969			−0.503805
$852$	−6.92820	+	4.89898i	−0.237356	+	0.167836i
$853$		−	39.1918i		−	1.34190i	−0.741501	−	0.670951i	$-0.765886\pi$
$853$		−	39.1918i		−	1.34190i	0.741501	−	0.670951i	$-0.234114\pi$
$854$	−19.5959			−0.670559
$855$	20.0066	+	21.3246i	0.684210	+	0.729285i
$856$	18.0000			0.615227
$857$		−	54.0000i		−	1.84460i	−0.386469	−	0.922302i	$-0.626305\pi$
$857$		−	54.0000i		−	1.84460i	0.386469	−	0.922302i	$-0.373695\pi$
$858$	−8.48528	+	6.00000i	−0.289683	+	0.204837i
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$	−10.3923	−	12.7279i	−0.354375	−	0.434019i
$861$	30.0000	+	42.4264i	1.02240	+	1.44589i
$862$			19.5959i			0.667440i
$863$			6.00000i			0.204242i	0.994772	+	0.102121i	$0.0325630\pi$
$863$			6.00000i			0.204242i	−0.994772	+	0.102121i	$0.967437\pi$
$864$	5.00000	−	1.41421i	0.170103	−	0.0481125i
$865$	8.48528	+	10.3923i	0.288508	+	0.353349i
$866$			38.1838i			1.29754i
$867$	43.8406	−	31.0000i	1.48891	−	1.05282i
$868$	−16.9706			−0.576018
$869$	−14.6969			−0.498559
$870$	9.14162	+	2.53590i	0.309930	+	0.0859750i
$871$		0			0
$872$	6.92820			0.234619
$873$	−12.7279	+	36.0000i	−0.430775	+	1.21842i
$874$	6.00000	+	13.8564i	0.202953	+	0.468700i
$875$	24.2487	−	12.7279i	0.819756	−	0.430282i
$876$	−14.6969	−	20.7846i	−0.496564	−	0.702247i
$877$	−4.24264			−0.143264			−0.0716319	−	0.997431i	$-0.522821\pi$
$877$	−4.24264			−0.143264			−0.0716319	+	0.997431i	$0.522821\pi$
$878$	−3.46410			−0.116908
$879$	6.00000	+	8.48528i	0.202375	+	0.286201i
$880$	−2.00000	−	2.44949i	−0.0674200	−	0.0825723i
$881$			56.5685i			1.90584i	0.303218	+	0.952921i	$0.401939\pi$
$881$			56.5685i			1.90584i	−0.303218	+	0.952921i	$0.598061\pi$
$882$	2.82843	+	1.00000i	0.0952381	+	0.0336718i
$883$			26.9444i			0.906751i	0.891320	+	0.453375i	$0.149780\pi$
$883$			26.9444i			0.906751i	−0.891320	+	0.453375i	$0.850220\pi$
$884$	−29.3939			−0.988623
$885$	−5.07180	+	18.2832i	−0.170487	+	0.614584i
$886$			17.3205i			0.581894i
$887$		−	6.00000i		−	0.201460i	−0.994914	−	0.100730i	$-0.967882\pi$
$887$		−	6.00000i		−	0.201460i	0.994914	−	0.100730i	$-0.0321179\pi$
$888$	4.24264	+	6.00000i	0.142374	+	0.201347i
$889$		0			0
$890$	−3.46410	−	4.24264i	−0.116117	−	0.142214i
$891$	8.00000	−	9.89949i	0.268010	−	0.331646i
$892$	25.4558			0.852325
$893$	−13.8564	+	6.00000i	−0.463687	+	0.200782i
$894$	16.0000	−	11.3137i	0.535120	−	0.378387i
$895$	−8.48528	+	6.92820i	−0.283632	+	0.231584i
$896$	−2.44949			−0.0818317
$897$	20.7846	−	14.6969i	0.693978	−	0.490716i
$898$		−	12.2474i		−	0.408703i
$899$		−	16.9706i		−	0.566000i
$900$	12.8564	+	7.72741i	0.428547	+	0.257580i
$901$		−	41.5692i		−	1.38487i
$902$	17.3205			0.576710
$903$	−25.4558	+	18.0000i	−0.847117	+	0.599002i
$904$	−18.0000			−0.598671
$905$	19.5959	+	24.0000i	0.651390	+	0.797787i
$906$	−19.5959	+	13.8564i	−0.651031	+	0.460348i
$907$		0			0			−	1.00000i	$-0.5\pi$
$907$		0			0				1.00000i	$0.5\pi$
$908$		−	12.0000i		−	0.398234i
$909$	−8.00000	−	2.82843i	−0.265343	−	0.0938130i
$910$	−18.0000	+	14.6969i	−0.596694	+	0.487199i
$911$	48.9898			1.62310			0.811552	−	0.584280i	$-0.198623\pi$
$911$	48.9898			1.62310			0.811552	+	0.584280i	$0.198623\pi$
$912$	3.92480	−	6.44949i	0.129963	−	0.213564i
$913$			14.6969i			0.486398i
$914$	24.4949			0.810219
$915$	8.28221	−	29.8564i	0.273801	−	0.987022i
$916$	−28.0000			−0.925146
$917$	−3.46410			−0.114395
$918$	34.6410	−	9.79796i	1.14332	−	0.323381i
$919$	56.0000			1.84727			0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000			1.84727			0.923635	+	0.383274i	$0.125203\pi$
$920$	4.89898	+	6.00000i	0.161515	+	0.197814i
$921$	36.0000	−	25.4558i	1.18624	−	0.838799i
$922$	22.6274			0.745194
$923$	20.7846			0.684134
$924$	−4.89898	+	3.46410i	−0.161165	+	0.113961i
$925$	−4.24264	+	20.7846i	−0.139497	+	0.683394i
$926$	−12.2474			−0.402476
$927$	−8.48528	+	24.0000i	−0.278693	+	0.788263i
$928$		−	2.44949i		−	0.0804084i
$929$			2.82843i			0.0927977i	0.998923	+	0.0463988i	$0.0147745\pi$
$929$			2.82843i			0.0927977i	−0.998923	+	0.0463988i	$0.985225\pi$
$930$	7.17260	−	25.8564i	0.235199	−	0.847865i
$931$	4.00000	−	1.73205i	0.131095	−	0.0567657i
$932$	10.3923			0.340411
$933$	26.8701	+	38.0000i	0.879686	+	1.24406i
$934$			24.2487i			0.793442i
$935$	−13.8564	−	16.9706i	−0.453153	−	0.554997i
$936$	−12.0000	−	4.24264i	−0.392232	−	0.138675i
$937$		−	19.5959i		−	0.640171i	−0.947389	−	0.320085i	$-0.896288\pi$
$937$		−	19.5959i		−	0.640171i	0.947389	−	0.320085i	$-0.103712\pi$
$938$		0			0
$939$	−4.89898	−	6.92820i	−0.159872	−	0.226093i
$940$	−6.00000	+	4.89898i	−0.195698	+	0.159787i
$941$	51.4393			1.67687			0.838436	−	0.544999i	$-0.183470\pi$
$941$	51.4393			1.67687			0.838436	+	0.544999i	$0.183470\pi$
$942$	−20.7846	+	14.6969i	−0.677199	+	0.478852i
$943$	−42.4264			−1.38159
$944$	4.89898			0.159448
$945$	16.3142	−	23.3205i	0.530702	−	0.758616i
$946$			10.3923i			0.337883i
$947$	3.46410			0.112568			0.0562841	−	0.998415i	$-0.482075\pi$
$947$	3.46410			0.112568			0.0562841	+	0.998415i	$0.482075\pi$
$948$	−10.3923	−	14.6969i	−0.337526	−	0.477334i
$949$			62.3538i			2.02409i
$950$	21.3280	−	4.48528i	0.691971	−	0.145522i
$951$	18.0000	+	25.4558i	0.583690	+	0.825462i
$952$	−16.9706			−0.550019
$953$			54.0000i			1.74923i	0.484817	+	0.874616i	$0.338886\pi$
$953$			54.0000i			1.74923i	−0.484817	+	0.874616i	$0.661114\pi$
$954$	6.00000	−	16.9706i	0.194257	−	0.549442i
$955$	−34.0000	−	41.6413i	−1.10021	−	1.34748i
$956$			1.41421i			0.0457389i
$957$	−3.46410	−	4.89898i	−0.111979	−	0.158362i
$958$	−9.89949			−0.319838
$959$			42.4264i			1.37002i
$960$	1.03528	−	3.73205i	0.0334134	−	0.120451i
$961$	−17.0000			−0.548387
$962$		−	18.0000i		−	0.580343i
$963$	50.9117	+	18.0000i	1.64061	+	0.580042i
$964$		−	13.8564i		−	0.446285i
$965$	22.0454	−	18.0000i	0.709667	−	0.579441i
$966$	12.0000	−	8.48528i	0.386094	−	0.273009i
$967$		−	2.44949i		−	0.0787703i	−0.999224	−	0.0393851i	$-0.987460\pi$
$967$		−	2.44949i		−	0.0787703i	0.999224	−	0.0393851i	$-0.0125399\pi$
$968$		−	9.00000i		−	0.289271i
$969$	27.1918	−	44.6834i	0.873528	−	1.43544i
$970$	18.0000	+	22.0454i	0.577945	+	0.707835i
$971$	4.89898			0.157216			0.0786079	−	0.996906i	$-0.474952\pi$
$971$	4.89898			0.157216			0.0786079	+	0.996906i	$0.474952\pi$
$972$	15.5563	+	1.00000i	0.498970	+	0.0320750i
$973$		−	9.79796i		−	0.314108i
$974$			33.9411i			1.08754i
$975$	−14.7846	−	33.6365i	−0.473486	−	1.07723i
$976$	−8.00000			−0.256074
$977$			30.0000i			0.959785i	0.877327	+	0.479893i	$0.159324\pi$
$977$			30.0000i			0.959785i	−0.877327	+	0.479893i	$0.840676\pi$
$978$	17.3205	−	12.2474i	0.553849	−	0.391630i
$979$			3.46410i			0.110713i
$980$	1.73205	−	1.41421i	0.0553283	−	0.0451754i
$981$	19.5959	+	6.92820i	0.625650	+	0.221201i
$982$	−7.07107			−0.225647
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	12.2474	+	17.3205i	0.390434	+	0.552158i
$985$		0			0
$986$		−	16.9706i		−	0.540453i
$987$	8.48528	+	12.0000i	0.270089	+	0.381964i
$988$	−16.9706	+	7.34847i	−0.539906	+	0.233786i
$989$		−	25.4558i		−	0.809449i
$990$	−3.20736	−	8.92820i	−0.101937	−	0.283757i
$991$		−	38.1051i		−	1.21045i	−0.796055	−	0.605224i	$-0.793083\pi$
$991$		−	38.1051i		−	1.21045i	0.796055	−	0.605224i	$-0.206917\pi$
$992$	−6.92820			−0.219971
$993$	−6.92820	−	9.79796i	−0.219860	−	0.310929i
$994$	12.0000			0.380617
$995$	27.7128	−	22.6274i	0.878555	−	0.717337i
$996$	−14.6969	+	10.3923i	−0.465690	+	0.329293i
$997$		−	4.89898i		−	0.155152i	−0.996986	−	0.0775761i	$-0.975282\pi$
$997$		−	4.89898i		−	0.155152i	0.996986	−	0.0775761i	$-0.0247181\pi$
$998$		−	20.0000i		−	0.633089i
$999$	6.00000	+	21.2132i	0.189832	+	0.671156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.c.e.569.7	yes	8
3.2	odd	2	inner	570.2.c.e.569.4	yes	8
5.4	even	2	inner	570.2.c.e.569.2	yes	8
15.14	odd	2	inner	570.2.c.e.569.5	yes	8
19.18	odd	2	inner	570.2.c.e.569.1	✓	8
57.56	even	2	inner	570.2.c.e.569.6	yes	8
95.94	odd	2	inner	570.2.c.e.569.8	yes	8
285.284	even	2	inner	570.2.c.e.569.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.c.e.569.1	✓	8	19.18	odd	2	inner
570.2.c.e.569.2	yes	8	5.4	even	2	inner
570.2.c.e.569.3	yes	8	285.284	even	2	inner
570.2.c.e.569.4	yes	8	3.2	odd	2	inner
570.2.c.e.569.5	yes	8	15.14	odd	2	inner
570.2.c.e.569.6	yes	8	57.56	even	2	inner
570.2.c.e.569.7	yes	8	1.1	even	1	trivial
570.2.c.e.569.8	yes	8	95.94	odd	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000 q^{4} +(-1.73205 + 1.41421i) q^{5} +(1.00000 + 1.41421i) q^{6} -2.44949i q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.41421 - 1.00000i) q^{3} -1.00000 q^{4} +(-1.73205 + 1.41421i) q^{5} +(1.00000 + 1.41421i) q^{6} -2.44949i q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +(-1.41421 - 1.73205i) q^{10} +1.41421i q^{11} +(-1.41421 + 1.00000i) q^{12} +4.24264 q^{13} +2.44949 q^{14} +(-1.03528 + 3.73205i) q^{15} +1.00000 q^{16} +6.92820 q^{17} +(2.82843 + 1.00000i) q^{18} +(4.00000 - 1.73205i) q^{19} +(1.73205 - 1.41421i) q^{20} +(-2.44949 - 3.46410i) q^{21} -1.41421 q^{22} +3.46410 q^{23} +(-1.00000 - 1.41421i) q^{24} +(1.00000 - 4.89898i) q^{25} +4.24264i q^{26} +(-1.41421 - 5.00000i) q^{27} +2.44949i q^{28} -2.44949 q^{29} +(-3.73205 - 1.03528i) q^{30} +6.92820i q^{31} +1.00000i q^{32} +(1.41421 + 2.00000i) q^{33} +6.92820i q^{34} +(3.46410 + 4.24264i) q^{35} +(-1.00000 + 2.82843i) q^{36} -4.24264 q^{37} +(1.73205 + 4.00000i) q^{38} +(6.00000 - 4.24264i) q^{39} +(1.41421 + 1.73205i) q^{40} -12.2474 q^{41} +(3.46410 - 2.44949i) q^{42} -7.34847i q^{43} -1.41421i q^{44} +(2.26795 + 6.31319i) q^{45} +3.46410i q^{46} -3.46410 q^{47} +(1.41421 - 1.00000i) q^{48} +1.00000 q^{49} +(4.89898 + 1.00000i) q^{50} +(9.79796 - 6.92820i) q^{51} -4.24264 q^{52} -6.00000i q^{53} +(5.00000 - 1.41421i) q^{54} +(-2.00000 - 2.44949i) q^{55} -2.44949 q^{56} +(3.92480 - 6.44949i) q^{57} -2.44949i q^{58} +4.89898 q^{59} +(1.03528 - 3.73205i) q^{60} -8.00000 q^{61} -6.92820 q^{62} +(-6.92820 - 2.44949i) q^{63} -1.00000 q^{64} +(-7.34847 + 6.00000i) q^{65} +(-2.00000 + 1.41421i) q^{66} -6.92820 q^{68} +(4.89898 - 3.46410i) q^{69} +(-4.24264 + 3.46410i) q^{70} +4.89898 q^{71} +(-2.82843 - 1.00000i) q^{72} +14.6969i q^{73} -4.24264i q^{74} +(-3.48477 - 7.92820i) q^{75} +(-4.00000 + 1.73205i) q^{76} +3.46410 q^{77} +(4.24264 + 6.00000i) q^{78} +10.3923i q^{79} +(-1.73205 + 1.41421i) q^{80} +(-7.00000 - 5.65685i) q^{81} -12.2474i q^{82} +10.3923 q^{83} +(2.44949 + 3.46410i) q^{84} +(-12.0000 + 9.79796i) q^{85} +7.34847 q^{86} +(-3.46410 + 2.44949i) q^{87} +1.41421 q^{88} +2.44949 q^{89} +(-6.31319 + 2.26795i) q^{90} -10.3923i q^{91} -3.46410 q^{92} +(6.92820 + 9.79796i) q^{93} -3.46410i q^{94} +(-4.47871 + 8.65685i) q^{95} +(1.00000 + 1.41421i) q^{96} -12.7279 q^{97} +1.00000i q^{98} +(4.00000 + 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 8 q^{6} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 8 * q^6 + 8 * q^9	\( 8 q - 8 q^{4} + 8 q^{6} + 8 q^{9} + 8 q^{16} + 32 q^{19} - 8 q^{24} + 8 q^{25} - 16 q^{30} - 8 q^{36} + 48 q^{39} + 32 q^{45} + 8 q^{49} + 40 q^{54} - 16 q^{55} - 64 q^{61} - 8 q^{64} - 16 q^{66} - 32 q^{76} - 56 q^{81} - 96 q^{85} + 8 q^{96} + 32 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 8 * q^6 + 8 * q^9 + 8 * q^16 + 32 * q^19 - 8 * q^24 + 8 * q^25 - 16 * q^30 - 8 * q^36 + 48 * q^39 + 32 * q^45 + 8 * q^49 + 40 * q^54 - 16 * q^55 - 64 * q^61 - 8 * q^64 - 16 * q^66 - 32 * q^76 - 56 * q^81 - 96 * q^85 + 8 * q^96 + 32 * q^99

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