LMFDB - Embedded newform 570.2.c.d.569.4

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			569.4
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	570.569
Dual form			570.2.c.d.569.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.73205 q^{3} -1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} -1.73205i q^{6} -2.44949i q^{7} +1.00000i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.73205 q^{3} -1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} -1.73205i q^{6} -2.44949i q^{7} +1.00000i q^{8} +3.00000 q^{9} +(1.73205 - 1.41421i) q^{10} +3.46410i q^{11} -1.73205 q^{12} -2.44949 q^{14} +(2.44949 + 3.00000i) q^{15} +1.00000 q^{16} +7.07107 q^{17} -3.00000i q^{18} +(-1.00000 - 4.24264i) q^{19} +(-1.41421 - 1.73205i) q^{20} -4.24264i q^{21} +3.46410 q^{22} -5.65685 q^{23} +1.73205i q^{24} +(-1.00000 + 4.89898i) q^{25} +5.19615 q^{27} +2.44949i q^{28} -4.89898 q^{29} +(3.00000 - 2.44949i) q^{30} -4.24264i q^{31} -1.00000i q^{32} +6.00000i q^{33} -7.07107i q^{34} +(4.24264 - 3.46410i) q^{35} -3.00000 q^{36} +6.92820 q^{37} +(-4.24264 + 1.00000i) q^{38} +(-1.73205 + 1.41421i) q^{40} +2.44949 q^{41} -4.24264 q^{42} +9.79796i q^{43} -3.46410i q^{44} +(4.24264 + 5.19615i) q^{45} +5.65685i q^{46} -2.82843 q^{47} +1.73205 q^{48} +1.00000 q^{49} +(4.89898 + 1.00000i) q^{50} +12.2474 q^{51} -12.0000i q^{53} -5.19615i q^{54} +(-6.00000 + 4.89898i) q^{55} +2.44949 q^{56} +(-1.73205 - 7.34847i) q^{57} +4.89898i q^{58} -7.34847 q^{59} +(-2.44949 - 3.00000i) q^{60} -10.0000 q^{61} -4.24264 q^{62} -7.34847i q^{63} -1.00000 q^{64} +6.00000 q^{66} -13.8564 q^{67} -7.07107 q^{68} -9.79796 q^{69} +(-3.46410 - 4.24264i) q^{70} -4.89898 q^{71} +3.00000i q^{72} -9.79796i q^{73} -6.92820i q^{74} +(-1.73205 + 8.48528i) q^{75} +(1.00000 + 4.24264i) q^{76} +8.48528 q^{77} +4.24264i q^{79} +(1.41421 + 1.73205i) q^{80} +9.00000 q^{81} -2.44949i q^{82} +1.41421 q^{83} +4.24264i q^{84} +(10.0000 + 12.2474i) q^{85} +9.79796 q^{86} -8.48528 q^{87} -3.46410 q^{88} -12.2474 q^{89} +(5.19615 - 4.24264i) q^{90} +5.65685 q^{92} -7.34847i q^{93} +2.82843i q^{94} +(5.93426 - 7.73205i) q^{95} -1.73205i q^{96} -3.46410 q^{97} -1.00000i q^{98} +10.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 24 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 24 * q^9	$ 8 q - 8 q^{4} + 24 q^{9} + 8 q^{16} - 8 q^{19} - 8 q^{25} + 24 q^{30} - 24 q^{36} + 8 q^{49} - 48 q^{55} - 80 q^{61} - 8 q^{64} + 48 q^{66} + 8 q^{76} + 72 q^{81} + 80 q^{85}+O(q^{100}) $ 8 * q - 8 * q^4 + 24 * q^9 + 8 * q^16 - 8 * q^19 - 8 * q^25 + 24 * q^30 - 24 * q^36 + 8 * q^49 - 48 * q^55 - 80 * q^61 - 8 * q^64 + 48 * q^66 + 8 * q^76 + 72 * q^81 + 80 * q^85

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
$3$	1.73205			1.00000
$3$	1.73205			1.00000
$4$	−1.00000			−0.500000
$5$	1.41421	+	1.73205i	0.632456	+	0.774597i
$5$	1.41421	+	1.73205i	0.632456	+	0.774597i
$6$		−	1.73205i		−	0.707107i
$7$		−	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
$9$	3.00000			1.00000
$10$	1.73205	−	1.41421i	0.547723	−	0.447214i
$11$			3.46410i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$	−1.73205			−0.500000
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−2.44949			−0.654654
$15$	2.44949	+	3.00000i	0.632456	+	0.774597i
$16$	1.00000			0.250000
$17$	7.07107			1.71499			0.857493	−	0.514496i	$-0.172021\pi$
$17$	7.07107			1.71499			0.857493	+	0.514496i	$0.172021\pi$
$18$		−	3.00000i		−	0.707107i
$19$	−1.00000	−	4.24264i	−0.229416	−	0.973329i
$19$	−1.00000	−	4.24264i	−0.229416	−	0.973329i
$20$	−1.41421	−	1.73205i	−0.316228	−	0.387298i
$21$		−	4.24264i		−	0.925820i
$22$	3.46410			0.738549
$23$	−5.65685			−1.17954			−0.589768	−	0.807573i	$-0.700781\pi$
$23$	−5.65685			−1.17954			−0.589768	+	0.807573i	$0.700781\pi$
$24$			1.73205i			0.353553i
$25$	−1.00000	+	4.89898i	−0.200000	+	0.979796i
$26$		0			0
$27$	5.19615			1.00000
$28$			2.44949i			0.462910i
$29$	−4.89898			−0.909718			−0.454859	−	0.890564i	$-0.650310\pi$
$29$	−4.89898			−0.909718			−0.454859	+	0.890564i	$0.650310\pi$
$30$	3.00000	−	2.44949i	0.547723	−	0.447214i
$31$		−	4.24264i		−	0.762001i	−0.924575	−	0.381000i	$-0.875580\pi$
$31$		−	4.24264i		−	0.762001i	0.924575	−	0.381000i	$-0.124420\pi$
$32$		−	1.00000i		−	0.176777i
$33$			6.00000i			1.04447i
$34$		−	7.07107i		−	1.21268i
$35$	4.24264	−	3.46410i	0.717137	−	0.585540i
$36$	−3.00000			−0.500000
$37$	6.92820			1.13899			0.569495	−	0.821995i	$-0.307139\pi$
$37$	6.92820			1.13899			0.569495	+	0.821995i	$0.307139\pi$
$38$	−4.24264	+	1.00000i	−0.688247	+	0.162221i
$39$		0			0
$40$	−1.73205	+	1.41421i	−0.273861	+	0.223607i
$41$	2.44949			0.382546			0.191273	−	0.981537i	$-0.438738\pi$
$41$	2.44949			0.382546			0.191273	+	0.981537i	$0.438738\pi$
$42$	−4.24264			−0.654654
$43$			9.79796i			1.49417i	0.664726	+	0.747087i	$0.268548\pi$
$43$			9.79796i			1.49417i	−0.664726	+	0.747087i	$0.731452\pi$
$44$		−	3.46410i		−	0.522233i
$45$	4.24264	+	5.19615i	0.632456	+	0.774597i
$46$			5.65685i			0.834058i
$47$	−2.82843			−0.412568			−0.206284	−	0.978492i	$-0.566137\pi$
$47$	−2.82843			−0.412568			−0.206284	+	0.978492i	$0.566137\pi$
$48$	1.73205			0.250000
$49$	1.00000			0.142857
$50$	4.89898	+	1.00000i	0.692820	+	0.141421i
$51$	12.2474			1.71499
$52$		0			0
$53$		−	12.0000i		−	1.64833i	−0.566352	−	0.824163i	$-0.691646\pi$
$53$		−	12.0000i		−	1.64833i	0.566352	−	0.824163i	$-0.308354\pi$
$54$		−	5.19615i		−	0.707107i
$55$	−6.00000	+	4.89898i	−0.809040	+	0.660578i
$56$	2.44949			0.327327
$57$	−1.73205	−	7.34847i	−0.229416	−	0.973329i
$58$			4.89898i			0.643268i
$59$	−7.34847			−0.956689			−0.478345	−	0.878172i	$-0.658763\pi$
$59$	−7.34847			−0.956689			−0.478345	+	0.878172i	$0.658763\pi$
$60$	−2.44949	−	3.00000i	−0.316228	−	0.387298i
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$	−4.24264			−0.538816
$63$		−	7.34847i		−	0.925820i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	6.00000			0.738549
$67$	−13.8564			−1.69283			−0.846415	−	0.532524i	$-0.821244\pi$
$67$	−13.8564			−1.69283			−0.846415	+	0.532524i	$0.821244\pi$
$68$	−7.07107			−0.857493
$69$	−9.79796			−1.17954
$70$	−3.46410	−	4.24264i	−0.414039	−	0.507093i
$71$	−4.89898			−0.581402			−0.290701	−	0.956814i	$-0.593888\pi$
$71$	−4.89898			−0.581402			−0.290701	+	0.956814i	$0.593888\pi$
$72$			3.00000i			0.353553i
$73$		−	9.79796i		−	1.14676i	−0.819288	−	0.573382i	$-0.805631\pi$
$73$		−	9.79796i		−	1.14676i	0.819288	−	0.573382i	$-0.194369\pi$
$74$		−	6.92820i		−	0.805387i
$75$	−1.73205	+	8.48528i	−0.200000	+	0.979796i
$76$	1.00000	+	4.24264i	0.114708	+	0.486664i
$77$	8.48528			0.966988
$78$		0			0
$79$			4.24264i			0.477334i	0.971101	+	0.238667i	$0.0767105\pi$
$79$			4.24264i			0.477334i	−0.971101	+	0.238667i	$0.923290\pi$
$80$	1.41421	+	1.73205i	0.158114	+	0.193649i
$81$	9.00000			1.00000
$82$		−	2.44949i		−	0.270501i
$83$	1.41421			0.155230			0.0776151	−	0.996983i	$-0.475269\pi$
$83$	1.41421			0.155230			0.0776151	+	0.996983i	$0.475269\pi$
$84$			4.24264i			0.462910i
$85$	10.0000	+	12.2474i	1.08465	+	1.32842i
$86$	9.79796			1.05654
$87$	−8.48528			−0.909718
$88$	−3.46410			−0.369274
$89$	−12.2474			−1.29823			−0.649113	−	0.760692i	$-0.724860\pi$
$89$	−12.2474			−1.29823			−0.649113	+	0.760692i	$0.724860\pi$
$90$	5.19615	−	4.24264i	0.547723	−	0.447214i
$91$		0			0
$92$	5.65685			0.589768
$93$		−	7.34847i		−	0.762001i
$94$			2.82843i			0.291730i
$95$	5.93426	−	7.73205i	0.608842	−	0.793292i
$96$		−	1.73205i		−	0.176777i
$97$	−3.46410			−0.351726			−0.175863	−	0.984415i	$-0.556272\pi$
$97$	−3.46410			−0.351726			−0.175863	+	0.984415i	$0.556272\pi$
$98$		−	1.00000i		−	0.101015i
$99$			10.3923i			1.04447i
$100$	1.00000	−	4.89898i	0.100000	−	0.489898i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		−	12.2474i		−	1.21268i
$103$	3.46410			0.341328			0.170664	−	0.985329i	$-0.445409\pi$
$103$	3.46410			0.341328			0.170664	+	0.985329i	$0.445409\pi$
$104$		0			0
$105$	7.34847	−	6.00000i	0.717137	−	0.585540i
$106$	−12.0000			−1.16554
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$	−5.19615			−0.500000
$109$			12.7279i			1.21911i	0.792742	+	0.609557i	$0.208653\pi$
$109$			12.7279i			1.21911i	−0.792742	+	0.609557i	$0.791347\pi$
$110$	4.89898	+	6.00000i	0.467099	+	0.572078i
$111$	12.0000			1.13899
$112$		−	2.44949i		−	0.231455i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	−7.34847	+	1.73205i	−0.688247	+	0.162221i
$115$	−8.00000	−	9.79796i	−0.746004	−	0.913664i
$116$	4.89898			0.454859
$117$		0			0
$118$			7.34847i			0.676481i
$119$		−	17.3205i		−	1.58777i
$120$	−3.00000	+	2.44949i	−0.273861	+	0.223607i
$121$	−1.00000			−0.0909091
$122$			10.0000i			0.905357i
$123$	4.24264			0.382546
$124$			4.24264i			0.381000i
$125$	−9.89949	+	5.19615i	−0.885438	+	0.464758i
$126$	−7.34847			−0.654654
$127$	3.46410			0.307389			0.153695	−	0.988118i	$-0.450883\pi$
$127$	3.46410			0.307389			0.153695	+	0.988118i	$0.450883\pi$
$128$			1.00000i			0.0883883i
$129$			16.9706i			1.49417i
$130$		0			0
$131$			3.46410i			0.302660i	0.988483	+	0.151330i	$0.0483556\pi$
$131$			3.46410i			0.302660i	−0.988483	+	0.151330i	$0.951644\pi$
$132$		−	6.00000i		−	0.522233i
$133$	−10.3923	+	2.44949i	−0.901127	+	0.212398i
$134$			13.8564i			1.19701i
$135$	7.34847	+	9.00000i	0.632456	+	0.774597i
$136$			7.07107i			0.606339i
$137$	7.07107			0.604122			0.302061	−	0.953289i	$-0.402325\pi$
$137$	7.07107			0.604122			0.302061	+	0.953289i	$0.402325\pi$
$138$			9.79796i			0.834058i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$	−4.24264	+	3.46410i	−0.358569	+	0.292770i
$141$	−4.89898			−0.412568
$142$			4.89898i			0.411113i
$143$		0			0
$144$	3.00000			0.250000
$145$	−6.92820	−	8.48528i	−0.575356	−	0.704664i
$146$	−9.79796			−0.810885
$147$	1.73205			0.142857
$148$	−6.92820			−0.569495
$149$			13.8564i			1.13516i	0.823318	+	0.567581i	$0.192120\pi$
$149$			13.8564i			1.13516i	−0.823318	+	0.567581i	$0.807880\pi$
$150$	8.48528	+	1.73205i	0.692820	+	0.141421i
$151$			12.7279i			1.03578i	0.855446	+	0.517892i	$0.173283\pi$
$151$			12.7279i			1.03578i	−0.855446	+	0.517892i	$0.826717\pi$
$152$	4.24264	−	1.00000i	0.344124	−	0.0811107i
$153$	21.2132			1.71499
$154$		−	8.48528i		−	0.683763i
$155$	7.34847	−	6.00000i	0.590243	−	0.481932i
$156$		0			0
$157$			7.34847i			0.586472i	0.956040	+	0.293236i	$0.0947321\pi$
$157$			7.34847i			0.586472i	−0.956040	+	0.293236i	$0.905268\pi$
$158$	4.24264			0.337526
$159$		−	20.7846i		−	1.64833i
$160$	1.73205	−	1.41421i	0.136931	−	0.111803i
$161$			13.8564i			1.09204i
$162$		−	9.00000i		−	0.707107i
$163$		−	14.6969i		−	1.15115i	−0.817748	−	0.575577i	$-0.804778\pi$
$163$		−	14.6969i		−	1.15115i	0.817748	−	0.575577i	$-0.195222\pi$
$164$	−2.44949			−0.191273
$165$	−10.3923	+	8.48528i	−0.809040	+	0.660578i
$166$		−	1.41421i		−	0.109764i
$167$		−	18.0000i		−	1.39288i	−0.717614	−	0.696441i	$-0.754766\pi$
$167$		−	18.0000i		−	1.39288i	0.717614	−	0.696441i	$-0.245234\pi$
$168$	4.24264			0.327327
$169$	−13.0000			−1.00000
$170$	12.2474	−	10.0000i	0.939336	−	0.766965i
$171$	−3.00000	−	12.7279i	−0.229416	−	0.973329i
$172$		−	9.79796i		−	0.747087i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$			8.48528i			0.643268i
$175$	12.0000	+	2.44949i	0.907115	+	0.185164i
$176$			3.46410i			0.261116i
$177$	−12.7279			−0.956689
$178$			12.2474i			0.917985i
$179$	−17.1464			−1.28158			−0.640792	−	0.767714i	$-0.721394\pi$
$179$	−17.1464			−1.28158			−0.640792	+	0.767714i	$0.721394\pi$
$180$	−4.24264	−	5.19615i	−0.316228	−	0.387298i
$181$		−	12.7279i		−	0.946059i	−0.881047	−	0.473029i	$-0.843160\pi$
$181$		−	12.7279i		−	0.946059i	0.881047	−	0.473029i	$-0.156840\pi$
$182$		0			0
$183$	−17.3205			−1.28037
$184$		−	5.65685i		−	0.417029i
$185$	9.79796	+	12.0000i	0.720360	+	0.882258i
$186$	−7.34847			−0.538816
$187$			24.4949i			1.79124i
$188$	2.82843			0.206284
$189$		−	12.7279i		−	0.925820i
$190$	−7.73205	−	5.93426i	−0.560942	−	0.430516i
$191$		−	17.3205i		−	1.25327i	−0.779314	−	0.626634i	$-0.784432\pi$
$191$		−	17.3205i		−	1.25327i	0.779314	−	0.626634i	$-0.215568\pi$
$192$	−1.73205			−0.125000
$193$	20.7846			1.49611			0.748054	−	0.663637i	$-0.230988\pi$
$193$	20.7846			1.49611			0.748054	+	0.663637i	$0.230988\pi$
$194$			3.46410i			0.248708i
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	5.65685			0.403034			0.201517	−	0.979485i	$-0.435413\pi$
$197$	5.65685			0.403034			0.201517	+	0.979485i	$0.435413\pi$
$198$	10.3923			0.738549
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	−4.89898	−	1.00000i	−0.346410	−	0.0707107i
$201$	−24.0000			−1.69283
$202$		0			0
$203$			12.0000i			0.842235i
$204$	−12.2474			−0.857493
$205$	3.46410	+	4.24264i	0.241943	+	0.296319i
$206$		−	3.46410i		−	0.241355i
$207$	−16.9706			−1.17954
$208$		0			0
$209$	14.6969	−	3.46410i	1.01661	−	0.239617i
$210$	−6.00000	−	7.34847i	−0.414039	−	0.507093i
$211$			25.4558i			1.75245i	0.481900	+	0.876226i	$0.339947\pi$
$211$			25.4558i			1.75245i	−0.481900	+	0.876226i	$0.660053\pi$
$212$			12.0000i			0.824163i
$213$	−8.48528			−0.581402
$214$	12.0000			0.820303
$215$	−16.9706	+	13.8564i	−1.15738	+	0.944999i
$216$			5.19615i			0.353553i
$217$	−10.3923			−0.705476
$218$	12.7279			0.862044
$219$		−	16.9706i		−	1.14676i
$220$	6.00000	−	4.89898i	0.404520	−	0.330289i
$221$		0			0
$222$		−	12.0000i		−	0.805387i
$223$	3.46410			0.231973			0.115987	−	0.993251i	$-0.462997\pi$
$223$	3.46410			0.231973			0.115987	+	0.993251i	$0.462997\pi$
$224$	−2.44949			−0.163663
$225$	−3.00000	+	14.6969i	−0.200000	+	0.979796i
$226$	6.00000			0.399114
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$	1.73205	+	7.34847i	0.114708	+	0.486664i
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$	−9.79796	+	8.00000i	−0.646058	+	0.527504i
$231$	14.6969			0.966988
$232$		−	4.89898i		−	0.321634i
$233$	7.07107			0.463241			0.231621	−	0.972806i	$-0.425597\pi$
$233$	7.07107			0.463241			0.231621	+	0.972806i	$0.425597\pi$
$234$		0			0
$235$	−4.00000	−	4.89898i	−0.260931	−	0.319574i
$236$	7.34847			0.478345
$237$			7.34847i			0.477334i
$238$	−17.3205			−1.12272
$239$		−	6.92820i		−	0.448148i	−0.974572	−	0.224074i	$-0.928064\pi$
$239$		−	6.92820i		−	0.448148i	0.974572	−	0.224074i	$-0.0719358\pi$
$240$	2.44949	+	3.00000i	0.158114	+	0.193649i
$241$		−	8.48528i		−	0.546585i	−0.961931	−	0.273293i	$-0.911887\pi$
$241$		−	8.48528i		−	0.546585i	0.961931	−	0.273293i	$-0.0881127\pi$
$242$			1.00000i			0.0642824i
$243$	15.5885			1.00000
$244$	10.0000			0.640184
$245$	1.41421	+	1.73205i	0.0903508	+	0.110657i
$246$		−	4.24264i		−	0.270501i
$247$		0			0
$248$	4.24264			0.269408
$249$	2.44949			0.155230
$250$	5.19615	+	9.89949i	0.328634	+	0.626099i
$251$		−	24.2487i		−	1.53057i	−0.643695	−	0.765283i	$-0.722599\pi$
$251$		−	24.2487i		−	1.53057i	0.643695	−	0.765283i	$-0.277401\pi$
$252$			7.34847i			0.462910i
$253$		−	19.5959i		−	1.23198i
$254$		−	3.46410i		−	0.217357i
$255$	17.3205	+	21.2132i	1.08465	+	1.32842i
$256$	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	$0.940080\pi$
$258$	16.9706			1.05654
$259$		−	16.9706i		−	1.05450i
$260$		0			0
$261$	−14.6969			−0.909718
$262$	3.46410			0.214013
$263$	−28.2843			−1.74408			−0.872041	−	0.489432i	$-0.837204\pi$
$263$	−28.2843			−1.74408			−0.872041	+	0.489432i	$0.837204\pi$
$264$	−6.00000			−0.369274
$265$	20.7846	−	16.9706i	1.27679	−	1.04249i
$266$	2.44949	+	10.3923i	0.150188	+	0.637193i
$267$	−21.2132			−1.29823
$268$	13.8564			0.846415
$269$	−19.5959			−1.19478			−0.597392	−	0.801949i	$-0.703796\pi$
$269$	−19.5959			−1.19478			−0.597392	+	0.801949i	$0.703796\pi$
$270$	9.00000	−	7.34847i	0.547723	−	0.447214i
$271$	28.0000			1.70088			0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000			1.70088			0.850439	+	0.526073i	$0.176336\pi$
$272$	7.07107			0.428746
$273$		0			0
$274$		−	7.07107i		−	0.427179i
$275$	−16.9706	−	3.46410i	−1.02336	−	0.208893i
$276$	9.79796			0.589768
$277$		−	12.2474i		−	0.735878i	−0.929850	−	0.367939i	$-0.880064\pi$
$277$		−	12.2474i		−	0.735878i	0.929850	−	0.367939i	$-0.119936\pi$
$278$			10.0000i			0.599760i
$279$		−	12.7279i		−	0.762001i
$280$	3.46410	+	4.24264i	0.207020	+	0.253546i
$281$	31.8434			1.89962			0.949808	−	0.312833i	$-0.101278\pi$
$281$	31.8434			1.89962			0.949808	+	0.312833i	$0.101278\pi$
$282$			4.89898i			0.291730i
$283$		−	24.4949i		−	1.45607i	−0.685540	−	0.728035i	$-0.740434\pi$
$283$		−	24.4949i		−	1.45607i	0.685540	−	0.728035i	$-0.259566\pi$
$284$	4.89898			0.290701
$285$	10.2784	−	13.3923i	0.608842	−	0.793292i
$286$		0			0
$287$		−	6.00000i		−	0.354169i
$288$		−	3.00000i		−	0.176777i
$289$	33.0000			1.94118
$290$	−8.48528	+	6.92820i	−0.498273	+	0.406838i
$291$	−6.00000			−0.351726
$292$			9.79796i			0.573382i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$		−	1.73205i		−	0.101015i
$295$	−10.3923	−	12.7279i	−0.605063	−	0.741048i
$296$			6.92820i			0.402694i
$297$			18.0000i			1.04447i
$298$	13.8564			0.802680
$299$		0			0
$300$	1.73205	−	8.48528i	0.100000	−	0.489898i
$301$	24.0000			1.38334
$302$	12.7279			0.732410
$303$		0			0
$304$	−1.00000	−	4.24264i	−0.0573539	−	0.243332i
$305$	−14.1421	−	17.3205i	−0.809776	−	0.991769i
$306$		−	21.2132i		−	1.21268i
$307$	6.92820			0.395413			0.197707	−	0.980261i	$-0.436651\pi$
$307$	6.92820			0.395413			0.197707	+	0.980261i	$0.436651\pi$
$308$	−8.48528			−0.483494
$309$	6.00000			0.341328
$310$	−6.00000	−	7.34847i	−0.340777	−	0.417365i
$311$		−	3.46410i		−	0.196431i	−0.995165	−	0.0982156i	$-0.968687\pi$
$311$		−	3.46410i		−	0.196431i	0.995165	−	0.0982156i	$-0.0313135\pi$
$312$		0			0
$313$			14.6969i			0.830720i	0.909657	+	0.415360i	$0.136344\pi$
$313$			14.6969i			0.830720i	−0.909657	+	0.415360i	$0.863656\pi$
$314$	7.34847			0.414698
$315$	12.7279	−	10.3923i	0.717137	−	0.585540i
$316$		−	4.24264i		−	0.238667i
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$	−20.7846			−1.16554
$319$		−	16.9706i		−	0.950169i
$320$	−1.41421	−	1.73205i	−0.0790569	−	0.0968246i
$321$			20.7846i			1.16008i
$322$	13.8564			0.772187
$323$	−7.07107	−	30.0000i	−0.393445	−	1.66924i
$324$	−9.00000			−0.500000
$325$		0			0
$326$	−14.6969			−0.813988
$327$			22.0454i			1.21911i
$328$			2.44949i			0.135250i
$329$			6.92820i			0.381964i
$330$	8.48528	+	10.3923i	0.467099	+	0.572078i
$331$		−	8.48528i		−	0.466393i	−0.972430	−	0.233197i	$-0.925081\pi$
$331$		−	8.48528i		−	0.466393i	0.972430	−	0.233197i	$-0.0749186\pi$
$332$	−1.41421			−0.0776151
$333$	20.7846			1.13899
$334$	−18.0000			−0.984916
$335$	−19.5959	−	24.0000i	−1.07064	−	1.31126i
$336$		−	4.24264i		−	0.231455i
$337$	20.7846			1.13221			0.566105	−	0.824333i	$-0.308450\pi$
$337$	20.7846			1.13221			0.566105	+	0.824333i	$0.308450\pi$
$338$			13.0000i			0.707107i
$339$			10.3923i			0.564433i
$340$	−10.0000	−	12.2474i	−0.542326	−	0.664211i
$341$	14.6969			0.795884
$342$	−12.7279	+	3.00000i	−0.688247	+	0.162221i
$343$		−	19.5959i		−	1.05808i
$344$	−9.79796			−0.528271
$345$	−13.8564	−	16.9706i	−0.746004	−	0.913664i
$346$		0			0
$347$	24.0416			1.29062			0.645311	−	0.763920i	$-0.276728\pi$
$347$	24.0416			1.29062			0.645311	+	0.763920i	$0.276728\pi$
$348$	8.48528			0.454859
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	2.44949	−	12.0000i	0.130931	−	0.641427i
$351$		0			0
$352$	3.46410			0.184637
$353$	15.5563			0.827981			0.413990	−	0.910281i	$-0.364135\pi$
$353$	15.5563			0.827981			0.413990	+	0.910281i	$0.364135\pi$
$354$			12.7279i			0.676481i
$355$	−6.92820	−	8.48528i	−0.367711	−	0.450352i
$356$	12.2474			0.649113
$357$		−	30.0000i		−	1.58777i
$358$			17.1464i			0.906217i
$359$		−	13.8564i		−	0.731313i	−0.930750	−	0.365657i	$-0.880844\pi$
$359$		−	13.8564i		−	0.731313i	0.930750	−	0.365657i	$-0.119156\pi$
$360$	−5.19615	+	4.24264i	−0.273861	+	0.223607i
$361$	−17.0000	+	8.48528i	−0.894737	+	0.446594i
$362$	−12.7279			−0.668965
$363$	−1.73205			−0.0909091
$364$		0			0
$365$	16.9706	−	13.8564i	0.888280	−	0.725277i
$366$			17.3205i			0.905357i
$367$			7.34847i			0.383587i	0.981435	+	0.191793i	$0.0614304\pi$
$367$			7.34847i			0.383587i	−0.981435	+	0.191793i	$0.938570\pi$
$368$	−5.65685			−0.294884
$369$	7.34847			0.382546
$370$	12.0000	−	9.79796i	0.623850	−	0.509372i
$371$	−29.3939			−1.52605
$372$			7.34847i			0.381000i
$373$	6.92820			0.358729			0.179364	−	0.983783i	$-0.442596\pi$
$373$	6.92820			0.358729			0.179364	+	0.983783i	$0.442596\pi$
$374$	24.4949			1.26660
$375$	−17.1464	+	9.00000i	−0.885438	+	0.464758i
$376$		−	2.82843i		−	0.145865i
$377$		0			0
$378$	−12.7279			−0.654654
$379$			25.4558i			1.30758i	0.756677	+	0.653789i	$0.226822\pi$
$379$			25.4558i			1.30758i	−0.756677	+	0.653789i	$0.773178\pi$
$380$	−5.93426	+	7.73205i	−0.304421	+	0.396646i
$381$	6.00000			0.307389
$382$	−17.3205			−0.886194
$383$		−	24.0000i		−	1.22634i	−0.789950	−	0.613171i	$-0.789894\pi$
$383$		−	24.0000i		−	1.22634i	0.789950	−	0.613171i	$-0.210106\pi$
$384$			1.73205i			0.0883883i
$385$	12.0000	+	14.6969i	0.611577	+	0.749025i
$386$		−	20.7846i		−	1.05791i
$387$			29.3939i			1.49417i
$388$	3.46410			0.175863
$389$		−	13.8564i		−	0.702548i	−0.936273	−	0.351274i	$-0.885749\pi$
$389$		−	13.8564i		−	0.702548i	0.936273	−	0.351274i	$-0.114251\pi$
$390$		0			0
$391$	−40.0000			−2.02289
$392$			1.00000i			0.0505076i
$393$			6.00000i			0.302660i
$394$		−	5.65685i		−	0.284988i
$395$	−7.34847	+	6.00000i	−0.369742	+	0.301893i
$396$		−	10.3923i		−	0.522233i
$397$		−	26.9444i		−	1.35230i	−0.736764	−	0.676150i	$-0.763647\pi$
$397$		−	26.9444i		−	1.35230i	0.736764	−	0.676150i	$-0.236353\pi$
$398$		−	20.0000i		−	1.00251i
$399$	−18.0000	+	4.24264i	−0.901127	+	0.212398i
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$	−17.1464			−0.856252			−0.428126	−	0.903719i	$-0.640826\pi$
$401$	−17.1464			−0.856252			−0.428126	+	0.903719i	$0.640826\pi$
$402$			24.0000i			1.19701i
$403$		0			0
$404$		0			0
$405$	12.7279	+	15.5885i	0.632456	+	0.774597i
$406$	12.0000			0.595550
$407$			24.0000i			1.18964i
$408$			12.2474i			0.606339i
$409$			33.9411i			1.67828i	0.543915	+	0.839140i	$0.316941\pi$
$409$			33.9411i			1.67828i	−0.543915	+	0.839140i	$0.683059\pi$
$410$	4.24264	−	3.46410i	0.209529	−	0.171080i
$411$	12.2474			0.604122
$412$	−3.46410			−0.170664
$413$			18.0000i			0.885722i
$414$			16.9706i			0.834058i
$415$	2.00000	+	2.44949i	0.0981761	+	0.120241i
$416$		0			0
$417$	−17.3205			−0.848189
$418$	−3.46410	−	14.6969i	−0.169435	−	0.718851i
$419$			31.1769i			1.52309i	0.648111	+	0.761546i	$0.275559\pi$
$419$			31.1769i			1.52309i	−0.648111	+	0.761546i	$0.724441\pi$
$420$	−7.34847	+	6.00000i	−0.358569	+	0.292770i
$421$			4.24264i			0.206774i	0.994641	+	0.103387i	$0.0329680\pi$
$421$			4.24264i			0.206774i	−0.994641	+	0.103387i	$0.967032\pi$
$422$	25.4558			1.23917
$423$	−8.48528			−0.412568
$424$	12.0000			0.582772
$425$	−7.07107	+	34.6410i	−0.342997	+	1.68034i
$426$			8.48528i			0.411113i
$427$			24.4949i			1.18539i
$428$		−	12.0000i		−	0.580042i
$429$		0			0
$430$	13.8564	+	16.9706i	0.668215	+	0.818393i
$431$	−9.79796			−0.471951			−0.235976	−	0.971759i	$-0.575829\pi$
$431$	−9.79796			−0.471951			−0.235976	+	0.971759i	$0.575829\pi$
$432$	5.19615			0.250000
$433$	−20.7846			−0.998845			−0.499422	−	0.866359i	$-0.666454\pi$
$433$	−20.7846			−0.998845			−0.499422	+	0.866359i	$0.666454\pi$
$434$			10.3923i			0.498847i
$435$	−12.0000	−	14.6969i	−0.575356	−	0.704664i
$436$		−	12.7279i		−	0.609557i
$437$	5.65685	+	24.0000i	0.270604	+	1.14808i
$438$	−16.9706			−0.810885
$439$		−	12.7279i		−	0.607471i	−0.952756	−	0.303735i	$-0.901766\pi$
$439$		−	12.7279i		−	0.607471i	0.952756	−	0.303735i	$-0.0982338\pi$
$440$	−4.89898	−	6.00000i	−0.233550	−	0.286039i
$441$	3.00000			0.142857
$442$		0			0
$443$	15.5563			0.739104			0.369552	−	0.929210i	$-0.379511\pi$
$443$	15.5563			0.739104			0.369552	+	0.929210i	$0.379511\pi$
$444$	−12.0000			−0.569495
$445$	−17.3205	−	21.2132i	−0.821071	−	1.00560i
$446$		−	3.46410i		−	0.164030i
$447$			24.0000i			1.13516i
$448$			2.44949i			0.115728i
$449$	22.0454			1.04039			0.520194	−	0.854048i	$-0.325860\pi$
$449$	22.0454			1.04039			0.520194	+	0.854048i	$0.325860\pi$
$450$	14.6969	+	3.00000i	0.692820	+	0.141421i
$451$			8.48528i			0.399556i
$452$		−	6.00000i		−	0.282216i
$453$			22.0454i			1.03578i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	7.34847	−	1.73205i	0.344124	−	0.0811107i
$457$		−	9.79796i		−	0.458329i	−0.973388	−	0.229165i	$-0.926401\pi$
$457$		−	9.79796i		−	0.458329i	0.973388	−	0.229165i	$-0.0735994\pi$
$458$			22.0000i			1.02799i
$459$	36.7423			1.71499
$460$	8.00000	+	9.79796i	0.373002	+	0.456832i
$461$			17.3205i			0.806696i	0.915047	+	0.403348i	$0.132154\pi$
$461$			17.3205i			0.806696i	−0.915047	+	0.403348i	$0.867846\pi$
$462$		−	14.6969i		−	0.683763i
$463$		−	12.2474i		−	0.569187i	−0.958648	−	0.284594i	$-0.908141\pi$
$463$		−	12.2474i		−	0.569187i	0.958648	−	0.284594i	$-0.0918587\pi$
$464$	−4.89898			−0.227429
$465$	12.7279	−	10.3923i	0.590243	−	0.481932i
$466$		−	7.07107i		−	0.327561i
$467$	26.8701			1.24340			0.621699	−	0.783256i	$-0.286443\pi$
$467$	26.8701			1.24340			0.621699	+	0.783256i	$0.286443\pi$
$468$		0			0
$469$			33.9411i			1.56726i
$470$	−4.89898	+	4.00000i	−0.225973	+	0.184506i
$471$			12.7279i			0.586472i
$472$		−	7.34847i		−	0.338241i
$473$	−33.9411			−1.56061
$474$	7.34847			0.337526
$475$	21.7846	−	0.656339i	0.999546	−	0.0301149i
$476$			17.3205i			0.793884i
$477$		−	36.0000i		−	1.64833i
$478$	−6.92820			−0.316889
$479$			10.3923i			0.474837i	0.971408	+	0.237418i	$0.0763012\pi$
$479$			10.3923i			0.474837i	−0.971408	+	0.237418i	$0.923699\pi$
$480$	3.00000	−	2.44949i	0.136931	−	0.111803i
$481$		0			0
$482$	−8.48528			−0.386494
$483$			24.0000i			1.09204i
$484$	1.00000			0.0454545
$485$	−4.89898	−	6.00000i	−0.222451	−	0.272446i
$486$		−	15.5885i		−	0.707107i
$487$	−3.46410			−0.156973			−0.0784867	−	0.996915i	$-0.525009\pi$
$487$	−3.46410			−0.156973			−0.0784867	+	0.996915i	$0.525009\pi$
$488$		−	10.0000i		−	0.452679i
$489$		−	25.4558i		−	1.15115i
$490$	1.73205	−	1.41421i	0.0782461	−	0.0638877i
$491$			10.3923i			0.468998i	0.972116	+	0.234499i	$0.0753450\pi$
$491$			10.3923i			0.468998i	−0.972116	+	0.234499i	$0.924655\pi$
$492$	−4.24264			−0.191273
$493$	−34.6410			−1.56015
$494$		0			0
$495$	−18.0000	+	14.6969i	−0.809040	+	0.660578i
$496$		−	4.24264i		−	0.190500i
$497$			12.0000i			0.538274i
$498$		−	2.44949i		−	0.109764i
$499$	14.0000			0.626726			0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000			0.626726			0.313363	+	0.949633i	$0.398544\pi$
$500$	9.89949	−	5.19615i	0.442719	−	0.232379i
$501$		−	31.1769i		−	1.39288i
$502$	−24.2487			−1.08227
$503$	5.65685			0.252227			0.126113	−	0.992016i	$-0.459750\pi$
$503$	5.65685			0.252227			0.126113	+	0.992016i	$0.459750\pi$
$504$	7.34847			0.327327
$505$		0			0
$506$	−19.5959			−0.871145
$507$	−22.5167			−1.00000
$508$	−3.46410			−0.153695
$509$	24.4949			1.08572			0.542859	−	0.839824i	$-0.317342\pi$
$509$	24.4949			1.08572			0.542859	+	0.839824i	$0.317342\pi$
$510$	21.2132	−	17.3205i	0.939336	−	0.766965i
$511$	−24.0000			−1.06170
$512$		−	1.00000i		−	0.0441942i
$513$	−5.19615	−	22.0454i	−0.229416	−	0.973329i
$514$	6.00000			0.264649
$515$	4.89898	+	6.00000i	0.215875	+	0.264392i
$516$		−	16.9706i		−	0.747087i
$517$		−	9.79796i		−	0.430914i
$518$	−16.9706			−0.745644
$519$		0			0
$520$		0			0
$521$	−22.0454			−0.965827			−0.482913	−	0.875668i	$-0.660421\pi$
$521$	−22.0454			−0.965827			−0.482913	+	0.875668i	$0.660421\pi$
$522$			14.6969i			0.643268i
$523$	13.8564			0.605898			0.302949	−	0.953007i	$-0.402029\pi$
$523$	13.8564			0.605898			0.302949	+	0.953007i	$0.402029\pi$
$524$		−	3.46410i		−	0.151330i
$525$	20.7846	+	4.24264i	0.907115	+	0.185164i
$526$			28.2843i			1.23325i
$527$		−	30.0000i		−	1.30682i
$528$			6.00000i			0.261116i
$529$	9.00000			0.391304
$530$	−16.9706	−	20.7846i	−0.737154	−	0.902826i
$531$	−22.0454			−0.956689
$532$	10.3923	−	2.44949i	0.450564	−	0.106199i
$533$		0			0
$534$			21.2132i			0.917985i
$535$	−20.7846	+	16.9706i	−0.898597	+	0.733701i
$536$		−	13.8564i		−	0.598506i
$537$	−29.6985			−1.28158
$538$			19.5959i			0.844840i
$539$			3.46410i			0.149209i
$540$	−7.34847	−	9.00000i	−0.316228	−	0.387298i
$541$	34.0000			1.46177			0.730887	−	0.682498i	$-0.239107\pi$
$541$	34.0000			1.46177			0.730887	+	0.682498i	$0.239107\pi$
$542$		−	28.0000i		−	1.20270i
$543$		−	22.0454i		−	0.946059i
$544$		−	7.07107i		−	0.303170i
$545$	−22.0454	+	18.0000i	−0.944322	+	0.771035i
$546$		0			0
$547$	−34.6410			−1.48114			−0.740571	−	0.671978i	$-0.765445\pi$
$547$	−34.6410			−1.48114			−0.740571	+	0.671978i	$0.765445\pi$
$548$	−7.07107			−0.302061
$549$	−30.0000			−1.28037
$550$	−3.46410	+	16.9706i	−0.147710	+	0.723627i
$551$	4.89898	+	20.7846i	0.208704	+	0.885454i
$552$		−	9.79796i		−	0.417029i
$553$	10.3923			0.441926
$554$	−12.2474			−0.520344
$555$	16.9706	+	20.7846i	0.720360	+	0.882258i
$556$	10.0000			0.424094
$557$	5.65685			0.239689			0.119844	−	0.992793i	$-0.461760\pi$
$557$	5.65685			0.239689			0.119844	+	0.992793i	$0.461760\pi$
$558$	−12.7279			−0.538816
$559$		0			0
$560$	4.24264	−	3.46410i	0.179284	−	0.146385i
$561$			42.4264i			1.79124i
$562$		−	31.8434i		−	1.34323i
$563$		−	12.0000i		−	0.505740i	−0.967500	−	0.252870i	$-0.918626\pi$
$563$		−	12.0000i		−	0.505740i	0.967500	−	0.252870i	$-0.0813744\pi$
$564$	4.89898			0.206284
$565$	−10.3923	+	8.48528i	−0.437208	+	0.356978i
$566$	−24.4949			−1.02960
$567$		−	22.0454i		−	0.925820i
$568$		−	4.89898i		−	0.205557i
$569$	−2.44949			−0.102688			−0.0513440	−	0.998681i	$-0.516350\pi$
$569$	−2.44949			−0.102688			−0.0513440	+	0.998681i	$0.516350\pi$
$570$	−13.3923	−	10.2784i	−0.560942	−	0.430516i
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$		0			0
$573$		−	30.0000i		−	1.25327i
$574$	−6.00000			−0.250435
$575$	5.65685	−	27.7128i	0.235907	−	1.15570i
$576$	−3.00000			−0.125000
$577$		−	4.89898i		−	0.203947i	−0.994787	−	0.101974i	$-0.967484\pi$
$577$		−	4.89898i		−	0.203947i	0.994787	−	0.101974i	$-0.0325157\pi$
$578$		−	33.0000i		−	1.37262i
$579$	36.0000			1.49611
$580$	6.92820	+	8.48528i	0.287678	+	0.352332i
$581$		−	3.46410i		−	0.143715i
$582$			6.00000i			0.248708i
$583$	41.5692			1.72162
$584$	9.79796			0.405442
$585$		0			0
$586$	6.00000			0.247858
$587$	9.89949			0.408596			0.204298	−	0.978909i	$-0.434509\pi$
$587$	9.89949			0.408596			0.204298	+	0.978909i	$0.434509\pi$
$588$	−1.73205			−0.0714286
$589$	−18.0000	+	4.24264i	−0.741677	+	0.174815i
$590$	−12.7279	+	10.3923i	−0.524000	+	0.427844i
$591$	9.79796			0.403034
$592$	6.92820			0.284747
$593$	18.3848			0.754972			0.377486	−	0.926015i	$-0.376789\pi$
$593$	18.3848			0.754972			0.377486	+	0.926015i	$0.376789\pi$
$594$	18.0000			0.738549
$595$	30.0000	−	24.4949i	1.22988	−	1.00419i
$596$		−	13.8564i		−	0.567581i
$597$	34.6410			1.41776
$598$		0			0
$599$	39.1918			1.60134			0.800668	−	0.599109i	$-0.204478\pi$
$599$	39.1918			1.60134			0.800668	+	0.599109i	$0.204478\pi$
$600$	−8.48528	−	1.73205i	−0.346410	−	0.0707107i
$601$			25.4558i			1.03837i	0.854663	+	0.519183i	$0.173764\pi$
$601$			25.4558i			1.03837i	−0.854663	+	0.519183i	$0.826236\pi$
$602$		−	24.0000i		−	0.978167i
$603$	−41.5692			−1.69283
$604$		−	12.7279i		−	0.517892i
$605$	−1.41421	−	1.73205i	−0.0574960	−	0.0704179i
$606$		0			0
$607$	10.3923			0.421811			0.210905	−	0.977506i	$-0.432359\pi$
$607$	10.3923			0.421811			0.210905	+	0.977506i	$0.432359\pi$
$608$	−4.24264	+	1.00000i	−0.172062	+	0.0405554i
$609$			20.7846i			0.842235i
$610$	−17.3205	+	14.1421i	−0.701287	+	0.572598i
$611$		0			0
$612$	−21.2132			−0.857493
$613$			2.44949i			0.0989340i	0.998776	+	0.0494670i	$0.0157523\pi$
$613$			2.44949i			0.0989340i	−0.998776	+	0.0494670i	$0.984248\pi$
$614$		−	6.92820i		−	0.279600i
$615$	6.00000	+	7.34847i	0.241943	+	0.296319i
$616$			8.48528i			0.341882i
$617$	−1.41421			−0.0569341			−0.0284670	−	0.999595i	$-0.509063\pi$
$617$	−1.41421			−0.0569341			−0.0284670	+	0.999595i	$0.509063\pi$
$618$		−	6.00000i		−	0.241355i
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$	−7.34847	+	6.00000i	−0.295122	+	0.240966i
$621$	−29.3939			−1.17954
$622$	−3.46410			−0.138898
$623$			30.0000i			1.20192i
$624$		0			0
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	14.6969			0.587408
$627$	25.4558	−	6.00000i	1.01661	−	0.239617i
$628$		−	7.34847i		−	0.293236i
$629$	48.9898			1.95335
$630$	−10.3923	−	12.7279i	−0.414039	−	0.507093i
$631$	−4.00000			−0.159237			−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000			−0.159237			−0.0796187	+	0.996825i	$0.525370\pi$
$632$	−4.24264			−0.168763
$633$			44.0908i			1.75245i
$634$	6.00000			0.238290
$635$	4.89898	+	6.00000i	0.194410	+	0.238103i
$636$			20.7846i			0.824163i
$637$		0			0
$638$	−16.9706			−0.671871
$639$	−14.6969			−0.581402
$640$	−1.73205	+	1.41421i	−0.0684653	+	0.0559017i
$641$	17.1464			0.677243			0.338622	−	0.940923i	$-0.390039\pi$
$641$	17.1464			0.677243			0.338622	+	0.940923i	$0.390039\pi$
$642$	20.7846			0.820303
$643$			34.2929i			1.35238i	0.736728	+	0.676189i	$0.236370\pi$
$643$			34.2929i			1.35238i	−0.736728	+	0.676189i	$0.763630\pi$
$644$		−	13.8564i		−	0.546019i
$645$	−29.3939	+	24.0000i	−1.15738	+	0.944999i
$646$	−30.0000	+	7.07107i	−1.18033	+	0.278207i
$647$	11.3137			0.444788			0.222394	−	0.974957i	$-0.428613\pi$
$647$	11.3137			0.444788			0.222394	+	0.974957i	$0.428613\pi$
$648$			9.00000i			0.353553i
$649$		−	25.4558i		−	0.999229i
$650$		0			0
$651$	−18.0000			−0.705476
$652$			14.6969i			0.575577i
$653$	−36.7696			−1.43890			−0.719452	−	0.694542i	$-0.755607\pi$
$653$	−36.7696			−1.43890			−0.719452	+	0.694542i	$0.755607\pi$
$654$	22.0454			0.862044
$655$	−6.00000	+	4.89898i	−0.234439	+	0.191419i
$656$	2.44949			0.0956365
$657$		−	29.3939i		−	1.14676i
$658$	6.92820			0.270089
$659$	−2.44949			−0.0954186			−0.0477093	−	0.998861i	$-0.515192\pi$
$659$	−2.44949			−0.0954186			−0.0477093	+	0.998861i	$0.515192\pi$
$660$	10.3923	−	8.48528i	0.404520	−	0.330289i
$661$		−	38.1838i		−	1.48518i	−0.669748	−	0.742588i	$-0.733598\pi$
$661$		−	38.1838i		−	1.48518i	0.669748	−	0.742588i	$-0.266402\pi$
$662$	−8.48528			−0.329790
$663$		0			0
$664$			1.41421i			0.0548821i
$665$	−18.9396	−	14.5359i	−0.734445	−	0.563678i
$666$		−	20.7846i		−	0.805387i
$667$	27.7128			1.07304
$668$			18.0000i			0.696441i
$669$	6.00000			0.231973
$670$	−24.0000	+	19.5959i	−0.927201	+	0.757056i
$671$		−	34.6410i		−	1.33730i
$672$	−4.24264			−0.163663
$673$	−38.1051			−1.46884			−0.734422	−	0.678693i	$-0.762547\pi$
$673$	−38.1051			−1.46884			−0.734422	+	0.678693i	$0.762547\pi$
$674$		−	20.7846i		−	0.800593i
$675$	−5.19615	+	25.4558i	−0.200000	+	0.979796i
$676$	13.0000			0.500000
$677$			42.0000i			1.61419i	0.590421	+	0.807096i	$0.298962\pi$
$677$			42.0000i			1.61419i	−0.590421	+	0.807096i	$0.701038\pi$
$678$	10.3923			0.399114
$679$			8.48528i			0.325635i
$680$	−12.2474	+	10.0000i	−0.469668	+	0.383482i
$681$		−	20.7846i		−	0.796468i
$682$		−	14.6969i		−	0.562775i
$683$			24.0000i			0.918334i	0.888350	+	0.459167i	$0.151852\pi$
$683$			24.0000i			0.918334i	−0.888350	+	0.459167i	$0.848148\pi$
$684$	3.00000	+	12.7279i	0.114708	+	0.486664i
$685$	10.0000	+	12.2474i	0.382080	+	0.467951i
$686$	−19.5959			−0.748176
$687$	−38.1051			−1.45380
$688$			9.79796i			0.373544i
$689$		0			0
$690$	−16.9706	+	13.8564i	−0.646058	+	0.527504i
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$		0			0
$693$	25.4558			0.966988
$694$		−	24.0416i		−	0.912608i
$695$	−14.1421	−	17.3205i	−0.536442	−	0.657004i
$696$		−	8.48528i		−	0.321634i
$697$	17.3205			0.656061
$698$		−	2.00000i		−	0.0757011i
$699$	12.2474			0.463241
$700$	−12.0000	−	2.44949i	−0.453557	−	0.0925820i
$701$			31.1769i			1.17754i	0.808302	+	0.588768i	$0.200387\pi$
$701$			31.1769i			1.17754i	−0.808302	+	0.588768i	$0.799613\pi$
$702$		0			0
$703$	−6.92820	−	29.3939i	−0.261302	−	1.10861i
$704$		−	3.46410i		−	0.130558i
$705$	−6.92820	−	8.48528i	−0.260931	−	0.319574i
$706$		−	15.5563i		−	0.585471i
$707$		0			0
$708$	12.7279			0.478345
$709$	−22.0000			−0.826227			−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000			−0.826227			−0.413114	+	0.910679i	$0.635559\pi$
$710$	−8.48528	+	6.92820i	−0.318447	+	0.260011i
$711$			12.7279i			0.477334i
$712$		−	12.2474i		−	0.458993i
$713$			24.0000i			0.898807i
$714$	−30.0000			−1.12272
$715$		0			0
$716$	17.1464			0.640792
$717$		−	12.0000i		−	0.448148i
$718$	−13.8564			−0.517116
$719$			13.8564i			0.516757i	0.966044	+	0.258378i	$0.0831881\pi$
$719$			13.8564i			0.516757i	−0.966044	+	0.258378i	$0.916812\pi$
$720$	4.24264	+	5.19615i	0.158114	+	0.193649i
$721$		−	8.48528i		−	0.316008i
$722$	8.48528	+	17.0000i	0.315789	+	0.632674i
$723$		−	14.6969i		−	0.546585i
$724$			12.7279i			0.473029i
$725$	4.89898	−	24.0000i	0.181944	−	0.891338i
$726$			1.73205i			0.0642824i
$727$			41.6413i			1.54439i	0.635385	+	0.772196i	$0.280841\pi$
$727$			41.6413i			1.54439i	−0.635385	+	0.772196i	$0.719159\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−13.8564	−	16.9706i	−0.512849	−	0.628109i
$731$			69.2820i			2.56249i
$732$	17.3205			0.640184
$733$			22.0454i			0.814266i	0.913369	+	0.407133i	$0.133471\pi$
$733$			22.0454i			0.814266i	−0.913369	+	0.407133i	$0.866529\pi$
$734$	7.34847			0.271237
$735$	2.44949	+	3.00000i	0.0903508	+	0.110657i
$736$			5.65685i			0.208514i
$737$		−	48.0000i		−	1.76810i
$738$		−	7.34847i		−	0.270501i
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$	−9.79796	−	12.0000i	−0.360180	−	0.441129i
$741$		0			0
$742$			29.3939i			1.07908i
$743$			18.0000i			0.660356i	0.943919	+	0.330178i	$0.107109\pi$
$743$			18.0000i			0.660356i	−0.943919	+	0.330178i	$0.892891\pi$
$744$	7.34847			0.269408
$745$	−24.0000	+	19.5959i	−0.879292	+	0.717939i
$746$		−	6.92820i		−	0.253660i
$747$	4.24264			0.155230
$748$		−	24.4949i		−	0.895622i
$749$	29.3939			1.07403
$750$	9.00000	+	17.1464i	0.328634	+	0.626099i
$751$		−	21.2132i		−	0.774081i	−0.922063	−	0.387040i	$-0.873497\pi$
$751$		−	21.2132i		−	0.774081i	0.922063	−	0.387040i	$-0.126503\pi$
$752$	−2.82843			−0.103142
$753$		−	42.0000i		−	1.53057i
$754$		0			0
$755$	−22.0454	+	18.0000i	−0.802315	+	0.655087i
$756$			12.7279i			0.462910i
$757$		−	17.1464i		−	0.623198i	−0.950214	−	0.311599i	$-0.899136\pi$
$757$		−	17.1464i		−	0.623198i	0.950214	−	0.311599i	$-0.100864\pi$
$758$	25.4558			0.924598
$759$		−	33.9411i		−	1.23198i
$760$	7.73205	+	5.93426i	0.280471	+	0.215258i
$761$		−	48.4974i		−	1.75803i	−0.476794	−	0.879015i	$-0.658201\pi$
$761$		−	48.4974i		−	1.75803i	0.476794	−	0.879015i	$-0.341799\pi$
$762$		−	6.00000i		−	0.217357i
$763$	31.1769			1.12868
$764$			17.3205i			0.626634i
$765$	30.0000	+	36.7423i	1.08465	+	1.32842i
$766$	−24.0000			−0.867155
$767$		0			0
$768$	1.73205			0.0625000
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$	14.6969	−	12.0000i	0.529641	−	0.432450i
$771$			10.3923i			0.374270i
$772$	−20.7846			−0.748054
$773$		−	24.0000i		−	0.863220i	−0.902060	−	0.431610i	$-0.857946\pi$
$773$		−	24.0000i		−	0.863220i	0.902060	−	0.431610i	$-0.142054\pi$
$774$	29.3939			1.05654
$775$	20.7846	+	4.24264i	0.746605	+	0.152400i
$776$		−	3.46410i		−	0.124354i
$777$		−	29.3939i		−	1.05450i
$778$	−13.8564			−0.496776
$779$	−2.44949	−	10.3923i	−0.0877621	−	0.372343i
$780$		0			0
$781$		−	16.9706i		−	0.607254i
$782$			40.0000i			1.43040i
$783$	−25.4558			−0.909718
$784$	1.00000			0.0357143
$785$	−12.7279	+	10.3923i	−0.454279	+	0.370917i
$786$	6.00000			0.214013
$787$	−24.2487			−0.864373			−0.432187	−	0.901784i	$-0.642258\pi$
$787$	−24.2487			−0.864373			−0.432187	+	0.901784i	$0.642258\pi$
$788$	−5.65685			−0.201517
$789$	−48.9898			−1.74408
$790$	6.00000	+	7.34847i	0.213470	+	0.261447i
$791$	14.6969			0.522563
$792$	−10.3923			−0.369274
$793$		0			0
$794$	−26.9444			−0.956221
$795$	36.0000	−	29.3939i	1.27679	−	1.04249i
$796$	−20.0000			−0.708881
$797$			30.0000i			1.06265i	0.847167	+	0.531327i	$0.178307\pi$
$797$			30.0000i			1.06265i	−0.847167	+	0.531327i	$0.821693\pi$
$798$	4.24264	+	18.0000i	0.150188	+	0.637193i
$799$	−20.0000			−0.707549
$800$	4.89898	+	1.00000i	0.173205	+	0.0353553i
$801$	−36.7423			−1.29823
$802$			17.1464i			0.605461i
$803$	33.9411			1.19776
$804$	24.0000			0.846415
$805$	−24.0000	+	19.5959i	−0.845889	+	0.690665i
$806$		0			0
$807$	−33.9411			−1.19478
$808$		0			0
$809$			48.4974i			1.70508i	0.522663	+	0.852539i	$0.324939\pi$
$809$			48.4974i			1.70508i	−0.522663	+	0.852539i	$0.675061\pi$
$810$	15.5885	−	12.7279i	0.547723	−	0.447214i
$811$		−	8.48528i		−	0.297959i	−0.988840	−	0.148979i	$-0.952401\pi$
$811$		−	8.48528i		−	0.297959i	0.988840	−	0.148979i	$-0.0475988\pi$
$812$		−	12.0000i		−	0.421117i
$813$	48.4974			1.70088
$814$	24.0000			0.841200
$815$	25.4558	−	20.7846i	0.891679	−	0.728053i
$816$	12.2474			0.428746
$817$	41.5692	−	9.79796i	1.45432	−	0.342787i
$818$	33.9411			1.18672
$819$		0			0
$820$	−3.46410	−	4.24264i	−0.120972	−	0.148159i
$821$		−	27.7128i		−	0.967184i	−0.875294	−	0.483592i	$-0.839332\pi$
$821$		−	27.7128i		−	0.967184i	0.875294	−	0.483592i	$-0.160668\pi$
$822$		−	12.2474i		−	0.427179i
$823$			12.2474i			0.426919i	0.976952	+	0.213460i	$0.0684732\pi$
$823$			12.2474i			0.426919i	−0.976952	+	0.213460i	$0.931527\pi$
$824$			3.46410i			0.120678i
$825$	−29.3939	−	6.00000i	−1.02336	−	0.208893i
$826$	18.0000			0.626300
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$	16.9706			0.589768
$829$			46.6690i			1.62088i	0.585820	+	0.810442i	$0.300773\pi$
$829$			46.6690i			1.62088i	−0.585820	+	0.810442i	$0.699227\pi$
$830$	2.44949	−	2.00000i	0.0850230	−	0.0694210i
$831$		−	21.2132i		−	0.735878i
$832$		0			0
$833$	7.07107			0.244998
$834$			17.3205i			0.599760i
$835$	31.1769	−	25.4558i	1.07892	−	0.880936i
$836$	−14.6969	+	3.46410i	−0.508304	+	0.119808i
$837$		−	22.0454i		−	0.762001i
$838$	31.1769			1.07699
$839$	39.1918			1.35305			0.676526	−	0.736419i	$-0.263485\pi$
$839$	39.1918			1.35305			0.676526	+	0.736419i	$0.263485\pi$
$840$	6.00000	+	7.34847i	0.207020	+	0.253546i
$841$	−5.00000			−0.172414
$842$	4.24264			0.146211
$843$	55.1543			1.89962
$844$		−	25.4558i		−	0.876226i
$845$	−18.3848	−	22.5167i	−0.632456	−	0.774597i
$846$			8.48528i			0.291730i
$847$			2.44949i			0.0841655i
$848$		−	12.0000i		−	0.412082i
$849$		−	42.4264i		−	1.45607i
$850$	34.6410	+	7.07107i	1.18818	+	0.242536i
$851$	−39.1918			−1.34348
$852$	8.48528			0.290701
$853$			36.7423i			1.25803i	0.777392	+	0.629017i	$0.216542\pi$
$853$			36.7423i			1.25803i	−0.777392	+	0.629017i	$0.783458\pi$
$854$	24.4949			0.838198
$855$	17.8028	−	23.1962i	0.608842	−	0.793292i
$856$	−12.0000			−0.410152
$857$		−	54.0000i		−	1.84460i	−0.386469	−	0.922302i	$-0.626305\pi$
$857$		−	54.0000i		−	1.84460i	0.386469	−	0.922302i	$-0.373695\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	16.9706	−	13.8564i	0.578691	−	0.472500i
$861$		−	10.3923i		−	0.354169i
$862$			9.79796i			0.333720i
$863$		−	48.0000i		−	1.63394i	−0.576681	−	0.816970i	$-0.695652\pi$
$863$		−	48.0000i		−	1.63394i	0.576681	−	0.816970i	$-0.304348\pi$
$864$		−	5.19615i		−	0.176777i
$865$		0			0
$866$			20.7846i			0.706290i
$867$	57.1577			1.94118
$868$	10.3923			0.352738
$869$	−14.6969			−0.498559
$870$	−14.6969	+	12.0000i	−0.498273	+	0.406838i
$871$		0			0
$872$	−12.7279			−0.431022
$873$	−10.3923			−0.351726
$874$	24.0000	−	5.65685i	0.811812	−	0.191346i
$875$	12.7279	+	24.2487i	0.430282	+	0.819756i
$876$			16.9706i			0.573382i
$877$	−41.5692			−1.40369			−0.701846	−	0.712328i	$-0.747641\pi$
$877$	−41.5692			−1.40369			−0.701846	+	0.712328i	$0.747641\pi$
$878$	−12.7279			−0.429547
$879$			10.3923i			0.350524i
$880$	−6.00000	+	4.89898i	−0.202260	+	0.165145i
$881$		−	13.8564i		−	0.466834i	−0.972377	−	0.233417i	$-0.925009\pi$
$881$		−	13.8564i		−	0.466834i	0.972377	−	0.233417i	$-0.0749907\pi$
$882$		−	3.00000i		−	0.101015i
$883$			34.2929i			1.15405i	0.816728	+	0.577023i	$0.195786\pi$
$883$			34.2929i			1.15405i	−0.816728	+	0.577023i	$0.804214\pi$
$884$		0			0
$885$	−18.0000	−	22.0454i	−0.605063	−	0.741048i
$886$		−	15.5563i		−	0.522626i
$887$			6.00000i			0.201460i	0.994914	+	0.100730i	$0.0321179\pi$
$887$			6.00000i			0.201460i	−0.994914	+	0.100730i	$0.967882\pi$
$888$			12.0000i			0.402694i
$889$		−	8.48528i		−	0.284587i
$890$	−21.2132	+	17.3205i	−0.711068	+	0.580585i
$891$			31.1769i			1.04447i
$892$	−3.46410			−0.115987
$893$	2.82843	+	12.0000i	0.0946497	+	0.401565i
$894$	24.0000			0.802680
$895$	−24.2487	−	29.6985i	−0.810545	−	0.992711i
$896$	2.44949			0.0818317
$897$		0			0
$898$		−	22.0454i		−	0.735665i
$899$			20.7846i			0.693206i
$900$	3.00000	−	14.6969i	0.100000	−	0.489898i
$901$		−	84.8528i		−	2.82686i
$902$	8.48528			0.282529
$903$	41.5692			1.38334
$904$	−6.00000			−0.199557
$905$	22.0454	−	18.0000i	0.732814	−	0.598340i
$906$	22.0454			0.732410
$907$	17.3205			0.575118			0.287559	−	0.957763i	$-0.407156\pi$
$907$	17.3205			0.575118			0.287559	+	0.957763i	$0.407156\pi$
$908$			12.0000i			0.398234i
$909$		0			0
$910$		0			0
$911$	−29.3939			−0.973863			−0.486931	−	0.873440i	$-0.661884\pi$
$911$	−29.3939			−0.973863			−0.486931	+	0.873440i	$0.661884\pi$
$912$	−1.73205	−	7.34847i	−0.0573539	−	0.243332i
$913$			4.89898i			0.162133i
$914$	−9.79796			−0.324088
$915$	−24.4949	−	30.0000i	−0.809776	−	0.991769i
$916$	22.0000			0.726900
$917$	8.48528			0.280209
$918$		−	36.7423i		−	1.21268i
$919$	−8.00000			−0.263896			−0.131948	−	0.991257i	$-0.542123\pi$
$919$	−8.00000			−0.263896			−0.131948	+	0.991257i	$0.542123\pi$
$920$	9.79796	−	8.00000i	0.323029	−	0.263752i
$921$	12.0000			0.395413
$922$	17.3205			0.570421
$923$		0			0
$924$	−14.6969			−0.483494
$925$	−6.92820	+	33.9411i	−0.227798	+	1.11598i
$926$	−12.2474			−0.402476
$927$	10.3923			0.341328
$928$			4.89898i			0.160817i
$929$		−	20.7846i		−	0.681921i	−0.940078	−	0.340960i	$-0.889248\pi$
$929$		−	20.7846i		−	0.681921i	0.940078	−	0.340960i	$-0.110752\pi$
$930$	−10.3923	−	12.7279i	−0.340777	−	0.417365i
$931$	−1.00000	−	4.24264i	−0.0327737	−	0.139047i
$932$	−7.07107			−0.231621
$933$		−	6.00000i		−	0.196431i
$934$		−	26.8701i		−	0.879215i
$935$	−42.4264	+	34.6410i	−1.38749	+	1.13288i
$936$		0			0
$937$		−	34.2929i		−	1.12030i	−0.828392	−	0.560149i	$-0.810744\pi$
$937$		−	34.2929i		−	1.12030i	0.828392	−	0.560149i	$-0.189256\pi$
$938$	33.9411			1.10822
$939$			25.4558i			0.830720i
$940$	4.00000	+	4.89898i	0.130466	+	0.159787i
$941$	9.79796			0.319404			0.159702	−	0.987165i	$-0.448947\pi$
$941$	9.79796			0.319404			0.159702	+	0.987165i	$0.448947\pi$
$942$	12.7279			0.414698
$943$	−13.8564			−0.451227
$944$	−7.34847			−0.239172
$945$	22.0454	−	18.0000i	0.717137	−	0.585540i
$946$			33.9411i			1.10352i
$947$	−1.41421			−0.0459558			−0.0229779	−	0.999736i	$-0.507315\pi$
$947$	−1.41421			−0.0459558			−0.0229779	+	0.999736i	$0.507315\pi$
$948$		−	7.34847i		−	0.238667i
$949$		0			0
$950$	−0.656339	−	21.7846i	−0.0212944	−	0.706786i
$951$			10.3923i			0.336994i
$952$	17.3205			0.561361
$953$			30.0000i			0.971795i	0.874016	+	0.485898i	$0.161507\pi$
$953$			30.0000i			0.971795i	−0.874016	+	0.485898i	$0.838493\pi$
$954$	−36.0000			−1.16554
$955$	30.0000	−	24.4949i	0.970777	−	0.792636i
$956$			6.92820i			0.224074i
$957$		−	29.3939i		−	0.950169i
$958$	10.3923			0.335760
$959$		−	17.3205i		−	0.559308i
$960$	−2.44949	−	3.00000i	−0.0790569	−	0.0968246i
$961$	13.0000			0.419355
$962$		0			0
$963$			36.0000i			1.16008i
$964$			8.48528i			0.273293i
$965$	29.3939	+	36.0000i	0.946222	+	1.15888i
$966$	24.0000			0.772187
$967$			22.0454i			0.708933i	0.935069	+	0.354466i	$0.115337\pi$
$967$			22.0454i			0.708933i	−0.935069	+	0.354466i	$0.884663\pi$
$968$		−	1.00000i		−	0.0321412i
$969$	−12.2474	−	51.9615i	−0.393445	−	1.66924i
$970$	−6.00000	+	4.89898i	−0.192648	+	0.157297i
$971$	26.9444			0.864687			0.432343	−	0.901709i	$-0.357687\pi$
$971$	26.9444			0.864687			0.432343	+	0.901709i	$0.357687\pi$
$972$	−15.5885			−0.500000
$973$			24.4949i			0.785270i
$974$			3.46410i			0.110997i
$975$		0			0
$976$	−10.0000			−0.320092
$977$			42.0000i			1.34370i	0.740688	+	0.671850i	$0.234500\pi$
$977$			42.0000i			1.34370i	−0.740688	+	0.671850i	$0.765500\pi$
$978$	−25.4558			−0.813988
$979$		−	42.4264i		−	1.35595i
$980$	−1.41421	−	1.73205i	−0.0451754	−	0.0553283i
$981$			38.1838i			1.21911i
$982$	10.3923			0.331632
$983$		−	6.00000i		−	0.191370i	−0.995412	−	0.0956851i	$-0.969496\pi$
$983$		−	6.00000i		−	0.191370i	0.995412	−	0.0956851i	$-0.0305042\pi$
$984$			4.24264i			0.135250i
$985$	8.00000	+	9.79796i	0.254901	+	0.312189i
$986$			34.6410i			1.10319i
$987$			12.0000i			0.381964i
$988$		0			0
$989$		−	55.4256i		−	1.76243i
$990$	14.6969	+	18.0000i	0.467099	+	0.572078i
$991$			21.2132i			0.673860i	0.941530	+	0.336930i	$0.109389\pi$
$991$			21.2132i			0.673860i	−0.941530	+	0.336930i	$0.890611\pi$
$992$	−4.24264			−0.134704
$993$		−	14.6969i		−	0.466393i
$994$	12.0000			0.380617
$995$	28.2843	+	34.6410i	0.896672	+	1.09819i
$996$	−2.44949			−0.0776151
$997$		−	17.1464i		−	0.543033i	−0.962434	−	0.271516i	$-0.912475\pi$
$997$		−	17.1464i		−	0.543033i	0.962434	−	0.271516i	$-0.0875251\pi$
$998$		−	14.0000i		−	0.443162i
$999$	36.0000			1.13899

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.73205 q^{3} -1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} -1.73205i q^{6} -2.44949i q^{7} +1.00000i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.73205 q^{3} -1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} -1.73205i q^{6} -2.44949i q^{7} +1.00000i q^{8} +3.00000 q^{9} +(1.73205 - 1.41421i) q^{10} +3.46410i q^{11} -1.73205 q^{12} -2.44949 q^{14} +(2.44949 + 3.00000i) q^{15} +1.00000 q^{16} +7.07107 q^{17} -3.00000i q^{18} +(-1.00000 - 4.24264i) q^{19} +(-1.41421 - 1.73205i) q^{20} -4.24264i q^{21} +3.46410 q^{22} -5.65685 q^{23} +1.73205i q^{24} +(-1.00000 + 4.89898i) q^{25} +5.19615 q^{27} +2.44949i q^{28} -4.89898 q^{29} +(3.00000 - 2.44949i) q^{30} -4.24264i q^{31} -1.00000i q^{32} +6.00000i q^{33} -7.07107i q^{34} +(4.24264 - 3.46410i) q^{35} -3.00000 q^{36} +6.92820 q^{37} +(-4.24264 + 1.00000i) q^{38} +(-1.73205 + 1.41421i) q^{40} +2.44949 q^{41} -4.24264 q^{42} +9.79796i q^{43} -3.46410i q^{44} +(4.24264 + 5.19615i) q^{45} +5.65685i q^{46} -2.82843 q^{47} +1.73205 q^{48} +1.00000 q^{49} +(4.89898 + 1.00000i) q^{50} +12.2474 q^{51} -12.0000i q^{53} -5.19615i q^{54} +(-6.00000 + 4.89898i) q^{55} +2.44949 q^{56} +(-1.73205 - 7.34847i) q^{57} +4.89898i q^{58} -7.34847 q^{59} +(-2.44949 - 3.00000i) q^{60} -10.0000 q^{61} -4.24264 q^{62} -7.34847i q^{63} -1.00000 q^{64} +6.00000 q^{66} -13.8564 q^{67} -7.07107 q^{68} -9.79796 q^{69} +(-3.46410 - 4.24264i) q^{70} -4.89898 q^{71} +3.00000i q^{72} -9.79796i q^{73} -6.92820i q^{74} +(-1.73205 + 8.48528i) q^{75} +(1.00000 + 4.24264i) q^{76} +8.48528 q^{77} +4.24264i q^{79} +(1.41421 + 1.73205i) q^{80} +9.00000 q^{81} -2.44949i q^{82} +1.41421 q^{83} +4.24264i q^{84} +(10.0000 + 12.2474i) q^{85} +9.79796 q^{86} -8.48528 q^{87} -3.46410 q^{88} -12.2474 q^{89} +(5.19615 - 4.24264i) q^{90} +5.65685 q^{92} -7.34847i q^{93} +2.82843i q^{94} +(5.93426 - 7.73205i) q^{95} -1.73205i q^{96} -3.46410 q^{97} -1.00000i q^{98} +10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 24 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 24 * q^9	\( 8 q - 8 q^{4} + 24 q^{9} + 8 q^{16} - 8 q^{19} - 8 q^{25} + 24 q^{30} - 24 q^{36} + 8 q^{49} - 48 q^{55} - 80 q^{61} - 8 q^{64} + 48 q^{66} + 8 q^{76} + 72 q^{81} + 80 q^{85}+O(q^{100}) \) 8 * q - 8 * q^4 + 24 * q^9 + 8 * q^16 - 8 * q^19 - 8 * q^25 + 24 * q^30 - 24 * q^36 + 8 * q^49 - 48 * q^55 - 80 * q^61 - 8 * q^64 + 48 * q^66 + 8 * q^76 + 72 * q^81 + 80 * q^85

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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