LMFDB - Embedded newform 252.2.bf.d.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(19,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("252.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	252.199
Dual form			252.2.bf.d.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39564 - 0.228425i) q^{2} +(1.89564 - 0.637600i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(2.29129 + 1.32288i) q^{7} +(2.50000 - 1.32288i) q^{8} +O(q^{10})$	\(q+(1.39564 - 0.228425i) q^{2} +(1.89564 - 0.637600i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(2.29129 + 1.32288i) q^{7} +(2.50000 - 1.32288i) q^{8} +(-1.89564 + 1.55130i) q^{10} +(2.29129 + 1.32288i) q^{11} -3.46410i q^{13} +(3.50000 + 1.32288i) q^{14} +(3.18693 - 2.41733i) q^{16} +(-6.00000 - 3.46410i) q^{17} +(-2.29129 + 2.59808i) q^{20} +(3.50000 + 1.32288i) q^{22} +(-4.58258 + 2.64575i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(-0.791288 - 4.83465i) q^{26} +(5.18693 + 1.04678i) q^{28} -5.00000 q^{29} +(-2.29129 + 3.96863i) q^{31} +(3.89564 - 4.10170i) q^{32} +(-9.16515 - 3.46410i) q^{34} -4.58258 q^{35} +(-2.60436 + 4.14938i) q^{40} +3.46410i q^{41} -10.5830i q^{43} +(5.18693 + 1.04678i) q^{44} +(-5.79129 + 4.73930i) q^{46} +(4.58258 + 7.93725i) q^{47} +(3.50000 + 6.06218i) q^{49} +(-1.00000 + 2.64575i) q^{50} +(-2.20871 - 6.56670i) q^{52} +(3.50000 - 6.06218i) q^{53} -4.58258 q^{55} +(7.47822 + 0.276100i) q^{56} +(-6.97822 + 1.14213i) q^{58} +(6.87386 - 11.9059i) q^{59} +(-9.00000 + 5.19615i) q^{61} +(-2.29129 + 6.06218i) q^{62} +(4.50000 - 6.61438i) q^{64} +(3.00000 + 5.19615i) q^{65} +(-13.5826 - 2.74110i) q^{68} +(-6.39564 + 1.04678i) q^{70} -5.29150i q^{71} +(-6.00000 - 3.46410i) q^{73} +(3.50000 + 6.06218i) q^{77} +(-6.87386 + 3.96863i) q^{79} +(-2.68693 + 6.38595i) q^{80} +(0.791288 + 4.83465i) q^{82} +4.58258 q^{83} +12.0000 q^{85} +(-2.41742 - 14.7701i) q^{86} +(7.47822 + 0.276100i) q^{88} +(9.00000 - 5.19615i) q^{89} +(4.58258 - 7.93725i) q^{91} +(-7.00000 + 7.93725i) q^{92} +(8.20871 + 10.0308i) q^{94} -8.66025i q^{97} +(6.26951 + 7.66115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 3 q^{4} - 6 q^{5} + 10 q^{8}+O(q^{10}) $ 4 * q + q^2 + 3 * q^4 - 6 * q^5 + 10 * q^8	$ 4 q + q^{2} + 3 q^{4} - 6 q^{5} + 10 q^{8} - 3 q^{10} + 14 q^{14} - q^{16} - 24 q^{17} + 14 q^{22} - 4 q^{25} + 6 q^{26} + 7 q^{28} - 20 q^{29} + 11 q^{32} - 15 q^{40} + 7 q^{44} - 14 q^{46} + 14 q^{49} - 4 q^{50} - 18 q^{52} + 14 q^{53} + 7 q^{56} - 5 q^{58} - 36 q^{61} + 18 q^{64} + 12 q^{65} - 36 q^{68} - 21 q^{70} - 24 q^{73} + 14 q^{77} + 3 q^{80} - 6 q^{82} + 48 q^{85} - 28 q^{86} + 7 q^{88} + 36 q^{89} - 28 q^{92} + 42 q^{94} - 7 q^{98}+O(q^{100}) $ 4 * q + q^2 + 3 * q^4 - 6 * q^5 + 10 * q^8 - 3 * q^10 + 14 * q^14 - q^16 - 24 * q^17 + 14 * q^22 - 4 * q^25 + 6 * q^26 + 7 * q^28 - 20 * q^29 + 11 * q^32 - 15 * q^40 + 7 * q^44 - 14 * q^46 + 14 * q^49 - 4 * q^50 - 18 * q^52 + 14 * q^53 + 7 * q^56 - 5 * q^58 - 36 * q^61 + 18 * q^64 + 12 * q^65 - 36 * q^68 - 21 * q^70 - 24 * q^73 + 14 * q^77 + 3 * q^80 - 6 * q^82 + 48 * q^85 - 28 * q^86 + 7 * q^88 + 36 * q^89 - 28 * q^92 + 42 * q^94 - 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.39564	−	0.228425i	0.986869	−	0.161521i
$2$	1.39564	−	0.228425i	0.986869	−	0.161521i
$3$		0			0
$3$		0			0
$4$	1.89564	−	0.637600i	0.947822	−	0.318800i
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$		0			0
$7$	2.29129	+	1.32288i	0.866025	+	0.500000i
$7$	2.29129	+	1.32288i	0.866025	+	0.500000i
$8$	2.50000	−	1.32288i	0.883883	−	0.467707i
$9$		0			0
$10$	−1.89564	+	1.55130i	−0.599455	+	0.490564i
$11$	2.29129	+	1.32288i	0.690849	+	0.398862i	0.803930	−	0.594724i	$-0.202739\pi$
$11$	2.29129	+	1.32288i	0.690849	+	0.398862i	−0.113081	+	0.993586i	$0.536072\pi$
$12$		0			0
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$	3.50000	+	1.32288i	0.935414	+	0.353553i
$15$		0			0
$16$	3.18693	−	2.41733i	0.796733	−	0.604332i
$17$	−6.00000	−	3.46410i	−1.45521	−	0.840168i	−0.456444	−	0.889752i	$-0.650877\pi$
$17$	−6.00000	−	3.46410i	−1.45521	−	0.840168i	−0.998770	+	0.0495842i	$0.984210\pi$
$18$		0			0
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−2.29129	+	2.59808i	−0.512348	+	0.580948i
$21$		0			0
$22$	3.50000	+	1.32288i	0.746203	+	0.282038i
$23$	−4.58258	+	2.64575i	−0.955533	+	0.551677i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.58258	+	2.64575i	−0.955533	+	0.551677i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	−0.791288	−	4.83465i	−0.155184	−	0.948153i
$27$		0			0
$28$	5.18693	+	1.04678i	0.980238	+	0.197822i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−2.29129	+	3.96863i	−0.411527	+	0.712786i	−0.995057	−	0.0993055i	$-0.968338\pi$
$31$	−2.29129	+	3.96863i	−0.411527	+	0.712786i	0.583530	+	0.812092i	$0.301671\pi$
$32$	3.89564	−	4.10170i	0.688659	−	0.725085i
$33$		0			0
$34$	−9.16515	−	3.46410i	−1.57181	−	0.594089i
$35$	−4.58258			−0.774597
$36$		0			0
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$		0			0
$39$		0			0
$40$	−2.60436	+	4.14938i	−0.411785	+	0.656074i
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$		0			0
$43$		−	10.5830i		−	1.61389i	−0.590624	−	0.806947i	$-0.701119\pi$
$43$		−	10.5830i		−	1.61389i	0.590624	−	0.806947i	$-0.298881\pi$
$44$	5.18693	+	1.04678i	0.781959	+	0.157807i
$45$		0			0
$46$	−5.79129	+	4.73930i	−0.853879	+	0.698772i
$47$	4.58258	+	7.93725i	0.668437	+	1.15777i	0.978341	+	0.207000i	$0.0663699\pi$
$47$	4.58258	+	7.93725i	0.668437	+	1.15777i	−0.309904	+	0.950768i	$0.600297\pi$
$48$		0			0
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$	−1.00000	+	2.64575i	−0.141421	+	0.374166i
$51$		0			0
$52$	−2.20871	−	6.56670i	−0.306293	−	0.910638i
$53$	3.50000	−	6.06218i	0.480762	−	0.832704i	−0.518994	−	0.854778i	$-0.673693\pi$
$53$	3.50000	−	6.06218i	0.480762	−	0.832704i	0.999756	+	0.0220735i	$0.00702678\pi$
$54$		0			0
$55$	−4.58258			−0.617914
$56$	7.47822	+	0.276100i	0.999319	+	0.0368954i
$57$		0			0
$58$	−6.97822	+	1.14213i	−0.916285	+	0.149968i
$59$	6.87386	−	11.9059i	0.894901	−	1.55001i	0.0609735	−	0.998139i	$-0.480579\pi$
$59$	6.87386	−	11.9059i	0.894901	−	1.55001i	0.833927	−	0.551874i	$-0.186087\pi$
$60$		0			0
$61$	−9.00000	+	5.19615i	−1.15233	+	0.665299i	−0.949454	−	0.313905i	$-0.898363\pi$
$61$	−9.00000	+	5.19615i	−1.15233	+	0.665299i	−0.202878	+	0.979204i	$0.565029\pi$
$62$	−2.29129	+	6.06218i	−0.290994	+	0.769897i
$63$		0			0
$64$	4.50000	−	6.61438i	0.562500	−	0.826797i
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−13.5826	−	2.74110i	−1.64713	−	0.332407i
$69$		0			0
$70$	−6.39564	+	1.04678i	−0.764426	+	0.125114i
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$		0			0
$73$	−6.00000	−	3.46410i	−0.702247	−	0.405442i	0.105937	−	0.994373i	$-0.466216\pi$
$73$	−6.00000	−	3.46410i	−0.702247	−	0.405442i	−0.808184	+	0.588930i	$0.799549\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.50000	+	6.06218i	0.398862	+	0.690849i
$78$		0			0
$79$	−6.87386	+	3.96863i	−0.773370	+	0.446505i	−0.834075	−	0.551650i	$-0.813998\pi$
$79$	−6.87386	+	3.96863i	−0.773370	+	0.446505i	0.0607054	+	0.998156i	$0.480665\pi$
$80$	−2.68693	+	6.38595i	−0.300408	+	0.713971i
$81$		0			0
$82$	0.791288	+	4.83465i	0.0873831	+	0.533898i
$83$	4.58258			0.503003			0.251502	−	0.967857i	$-0.419076\pi$
$83$	4.58258			0.503003			0.251502	+	0.967857i	$0.419076\pi$
$84$		0			0
$85$	12.0000			1.30158
$86$	−2.41742	−	14.7701i	−0.260678	−	1.59270i
$87$		0			0
$88$	7.47822	+	0.276100i	0.797181	+	0.0294324i
$89$	9.00000	−	5.19615i	0.953998	−	0.550791i	0.0596775	−	0.998218i	$-0.480993\pi$
$89$	9.00000	−	5.19615i	0.953998	−	0.550791i	0.894321	+	0.447427i	$0.147659\pi$
$90$		0			0
$91$	4.58258	−	7.93725i	0.480384	−	0.832050i
$92$	−7.00000	+	7.93725i	−0.729800	+	0.827516i
$93$		0			0
$94$	8.20871	+	10.0308i	0.846664	+	1.03460i
$95$		0			0
$96$		0			0
$97$		−	8.66025i		−	0.879316i	−0.898165	−	0.439658i	$-0.855100\pi$
$97$		−	8.66025i		−	0.879316i	0.898165	−	0.439658i	$-0.144900\pi$
$98$	6.26951	+	7.66115i	0.633316	+	0.773893i
$99$		0			0
$100$	−0.791288	+	3.92095i	−0.0791288	+	0.392095i
$101$	6.00000	+	3.46410i	0.597022	+	0.344691i	0.767869	−	0.640607i	$-0.221317\pi$
$101$	6.00000	+	3.46410i	0.597022	+	0.344691i	−0.170847	+	0.985298i	$0.554650\pi$
$102$		0			0
$103$	9.16515	+	15.8745i	0.903069	+	1.56416i	0.823488	+	0.567333i	$0.192025\pi$
$103$	9.16515	+	15.8745i	0.903069	+	1.56416i	0.0795810	+	0.996828i	$0.474642\pi$
$104$	−4.58258	−	8.66025i	−0.449359	−	0.849208i
$105$		0			0
$106$	3.50000	−	9.26013i	0.339950	−	0.899423i
$107$	−16.0390	+	9.26013i	−1.55055	+	0.895211i	−0.552453	+	0.833544i	$0.686308\pi$
$107$	−16.0390	+	9.26013i	−1.55055	+	0.895211i	−0.998097	+	0.0616667i	$0.980358\pi$
$108$		0			0
$109$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$109$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$110$	−6.39564	+	1.04678i	−0.609801	+	0.0998061i
$111$		0			0
$112$	10.5000	−	1.32288i	0.992157	−	0.125000i
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$		0			0
$115$	4.58258	−	7.93725i	0.427327	−	0.740153i
$116$	−9.47822	+	3.18800i	−0.880031	+	0.295998i
$117$		0			0
$118$	6.87386	−	18.1865i	0.632790	−	1.67421i
$119$	−9.16515	−	15.8745i	−0.840168	−	1.45521i
$120$		0			0
$121$	−2.00000	−	3.46410i	−0.181818	−	0.314918i
$122$	−11.3739	+	9.30780i	−1.02974	+	0.842689i
$123$		0			0
$124$	−1.81307	+	8.98403i	−0.162818	+	0.806790i
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$			7.93725i			0.704317i	0.935940	+	0.352159i	$0.114552\pi$
$127$			7.93725i			0.704317i	−0.935940	+	0.352159i	$0.885448\pi$
$128$	4.76951	−	10.2592i	0.421569	−	0.906796i
$129$		0			0
$130$	5.37386	+	6.56670i	0.471319	+	0.575938i
$131$	6.87386	+	11.9059i	0.600572	+	1.04022i	0.992734	+	0.120326i	$0.0383938\pi$
$131$	6.87386	+	11.9059i	0.600572	+	1.04022i	−0.392162	+	0.919896i	$0.628273\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−19.5826	−	0.723000i	−1.67919	−	0.0619967i
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$		0			0
$139$	−9.16515			−0.777378			−0.388689	−	0.921369i	$-0.627072\pi$
$139$	−9.16515			−0.777378			−0.388689	+	0.921369i	$0.627072\pi$
$140$	−8.68693	+	2.92185i	−0.734180	+	0.246942i
$141$		0			0
$142$	−1.20871	−	7.38505i	−0.101433	−	0.619740i
$143$	4.58258	−	7.93725i	0.383214	−	0.663747i
$144$		0			0
$145$	7.50000	−	4.33013i	0.622841	−	0.359597i
$146$	−9.16515	−	3.46410i	−0.758513	−	0.286691i
$147$		0			0
$148$		0			0
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	0.996207	+	0.0870170i	$0.0277334\pi$
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	−0.422744	+	0.906249i	$0.638933\pi$
$150$		0			0
$151$	11.4564	+	6.61438i	0.932312	+	0.538270i	0.887542	−	0.460727i	$-0.152411\pi$
$151$	11.4564	+	6.61438i	0.932312	+	0.538270i	0.0447698	+	0.998997i	$0.485745\pi$
$152$		0			0
$153$		0			0
$154$	6.26951	+	7.66115i	0.505211	+	0.617353i
$155$		−	7.93725i		−	0.637536i
$156$		0			0
$157$	6.00000	+	3.46410i	0.478852	+	0.276465i	0.719938	−	0.694038i	$-0.244170\pi$
$157$	6.00000	+	3.46410i	0.478852	+	0.276465i	−0.241086	+	0.970504i	$0.577504\pi$
$158$	−8.68693	+	7.10895i	−0.691095	+	0.565558i
$159$		0			0
$160$	−2.29129	+	9.52628i	−0.181142	+	0.753119i
$161$	−14.0000			−1.10335
$162$		0			0
$163$	13.7477	−	7.93725i	1.07681	−	0.621694i	0.146772	−	0.989170i	$-0.453112\pi$
$163$	13.7477	−	7.93725i	1.07681	−	0.621694i	0.930033	+	0.367477i	$0.119778\pi$
$164$	2.20871	+	6.56670i	0.172471	+	0.512773i
$165$		0			0
$166$	6.39564	−	1.04678i	0.496398	−	0.0812455i
$167$	18.3303			1.41844			0.709221	−	0.704987i	$-0.249047\pi$
$167$	18.3303			1.41844			0.709221	+	0.704987i	$0.249047\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	16.7477	−	2.74110i	1.28449	−	0.210233i
$171$		0			0
$172$	−6.74773	−	20.0616i	−0.514509	−	1.52968i
$173$	12.0000	−	6.92820i	0.912343	−	0.526742i	0.0311588	−	0.999514i	$-0.490080\pi$
$173$	12.0000	−	6.92820i	0.912343	−	0.526742i	0.881184	+	0.472773i	$0.156747\pi$
$174$		0			0
$175$	−4.58258	+	2.64575i	−0.346410	+	0.200000i
$176$	10.5000	−	1.32288i	0.791467	−	0.0997155i
$177$		0			0
$178$	11.3739	−	9.30780i	0.852507	−	0.697649i
$179$	4.58258	+	2.64575i	0.342518	+	0.197753i	0.661385	−	0.750047i	$-0.269969\pi$
$179$	4.58258	+	2.64575i	0.342518	+	0.197753i	−0.318867	+	0.947799i	$0.603302\pi$
$180$		0			0
$181$			3.46410i			0.257485i	0.991678	+	0.128742i	$0.0410940\pi$
$181$			3.46410i			0.257485i	−0.991678	+	0.128742i	$0.958906\pi$
$182$	4.58258	−	12.1244i	0.339683	−	0.898717i
$183$		0			0
$184$	−7.95644	+	12.6766i	−0.586556	+	0.934528i
$185$		0			0
$186$		0			0
$187$	−9.16515	−	15.8745i	−0.670222	−	1.16086i
$188$	13.7477	+	12.1244i	1.00266	+	0.884260i
$189$		0			0
$190$		0			0
$191$	−9.16515	+	5.29150i	−0.663167	+	0.382880i	−0.793483	−	0.608593i	$-0.791734\pi$
$191$	−9.16515	+	5.29150i	−0.663167	+	0.382880i	0.130316	+	0.991473i	$0.458401\pi$
$192$		0			0
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	−0.914949	−	0.403570i	$-0.867769\pi$
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	0.806976	+	0.590584i	$0.201102\pi$
$194$	−1.97822	−	12.0866i	−0.142028	−	0.867770i
$195$		0			0
$196$	10.5000	+	9.26013i	0.750000	+	0.661438i
$197$	−14.0000			−0.997459			−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000			−0.997459			−0.498729	+	0.866758i	$0.666200\pi$
$198$		0			0
$199$	−9.16515	+	15.8745i	−0.649700	+	1.12531i	0.333494	+	0.942752i	$0.391772\pi$
$199$	−9.16515	+	15.8745i	−0.649700	+	1.12531i	−0.983194	+	0.182562i	$0.941561\pi$
$200$	−0.208712	+	5.65300i	−0.0147582	+	0.399728i
$201$		0			0
$202$	9.16515	+	3.46410i	0.644858	+	0.243733i
$203$	−11.4564	−	6.61438i	−0.804084	−	0.464238i
$204$		0			0
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	16.4174	+	20.0616i	1.14386	+	1.39776i
$207$		0			0
$208$	−8.37386	−	11.0399i	−0.580623	−	0.765476i
$209$		0			0
$210$		0			0
$211$		−	5.29150i		−	0.364282i	−0.983272	−	0.182141i	$-0.941697\pi$
$211$		−	5.29150i		−	0.364282i	0.983272	−	0.182141i	$-0.0583027\pi$
$212$	2.76951	−	13.7233i	0.190211	−	0.942522i
$213$		0			0
$214$	−20.2695	+	16.5876i	−1.38560	+	1.13390i
$215$	9.16515	+	15.8745i	0.625058	+	1.08263i
$216$		0			0
$217$	−10.5000	+	6.06218i	−0.712786	+	0.411527i
$218$		0			0
$219$		0			0
$220$	−8.68693	+	2.92185i	−0.585673	+	0.196991i
$221$	−12.0000	+	20.7846i	−0.807207	+	1.39812i
$222$		0			0
$223$	−4.58258			−0.306872			−0.153436	−	0.988159i	$-0.549034\pi$
$223$	−4.58258			−0.306872			−0.153436	+	0.988159i	$0.549034\pi$
$224$	14.3521	−	4.24473i	0.958939	−	0.283613i
$225$		0			0
$226$	19.5390	−	3.19795i	1.29972	−	0.212725i
$227$	−2.29129	+	3.96863i	−0.152078	+	0.263407i	−0.931991	−	0.362481i	$-0.881930\pi$
$227$	−2.29129	+	3.96863i	−0.152078	+	0.263407i	0.779913	+	0.625888i	$0.215263\pi$
$228$		0			0
$229$	−9.00000	+	5.19615i	−0.594737	+	0.343371i	−0.766968	−	0.641685i	$-0.778236\pi$
$229$	−9.00000	+	5.19615i	−0.594737	+	0.343371i	0.172231	+	0.985057i	$0.444902\pi$
$230$	4.58258	−	12.1244i	0.302166	−	0.799456i
$231$		0			0
$232$	−12.5000	+	6.61438i	−0.820665	+	0.434255i
$233$	−10.0000	−	17.3205i	−0.655122	−	1.13470i	−0.981863	−	0.189590i	$-0.939284\pi$
$233$	−10.0000	−	17.3205i	−0.655122	−	1.13470i	0.326741	−	0.945114i	$-0.394049\pi$
$234$		0			0
$235$	−13.7477	−	7.93725i	−0.896803	−	0.517769i
$236$	5.43920	−	26.9521i	0.354062	−	1.75443i
$237$		0			0
$238$	−16.4174	−	20.0616i	−1.06418	−	1.30040i
$239$			5.29150i			0.342279i	0.985247	+	0.171139i	$0.0547449\pi$
$239$			5.29150i			0.342279i	−0.985247	+	0.171139i	$0.945255\pi$
$240$		0			0
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	0.348013	−	0.937490i	$-0.386857\pi$
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	−0.637883	+	0.770133i	$0.720190\pi$
$242$	−3.58258	−	4.37780i	−0.230297	−	0.281416i
$243$		0			0
$244$	−13.7477	+	15.5885i	−0.880108	+	0.997949i
$245$	−10.5000	−	6.06218i	−0.670820	−	0.387298i
$246$		0			0
$247$		0			0
$248$	−0.478220	+	12.9527i	−0.0303670	+	0.822494i
$249$		0			0
$250$	−2.76951	−	16.9213i	−0.175159	−	1.07020i
$251$	−4.58258			−0.289250			−0.144625	−	0.989487i	$-0.546198\pi$
$251$	−4.58258			−0.289250			−0.144625	+	0.989487i	$0.546198\pi$
$252$		0			0
$253$	−14.0000			−0.880172
$254$	1.81307	+	11.0776i	0.113762	+	0.695069i
$255$		0			0
$256$	4.31307	−	15.4077i	0.269567	−	0.962982i
$257$	−9.00000	+	5.19615i	−0.561405	+	0.324127i	−0.753709	−	0.657208i	$-0.771737\pi$
$257$	−9.00000	+	5.19615i	−0.561405	+	0.324127i	0.192304	+	0.981335i	$0.438404\pi$
$258$		0			0
$259$		0			0
$260$	9.00000	+	7.93725i	0.558156	+	0.492248i
$261$		0			0
$262$	12.3131	+	15.0462i	0.760704	+	0.929558i
$263$	−9.16515	−	5.29150i	−0.565147	−	0.326288i	0.190061	−	0.981772i	$-0.439131\pi$
$263$	−9.16515	−	5.29150i	−0.565147	−	0.326288i	−0.755209	+	0.655484i	$0.772465\pi$
$264$		0			0
$265$			12.1244i			0.744793i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−16.5000	−	9.52628i	−1.00602	−	0.580828i	−0.0959980	−	0.995382i	$-0.530604\pi$
$269$	−16.5000	−	9.52628i	−1.00602	−	0.580828i	−0.910025	+	0.414554i	$0.863938\pi$
$270$		0			0
$271$	−6.87386	−	11.9059i	−0.417557	−	0.723231i	0.578136	−	0.815941i	$-0.303780\pi$
$271$	−6.87386	−	11.9059i	−0.417557	−	0.723231i	−0.995693	+	0.0927099i	$0.970447\pi$
$272$	−27.4955	+	3.46410i	−1.66716	+	0.210042i
$273$		0			0
$274$	−2.00000	+	5.29150i	−0.120824	+	0.319671i
$275$	−4.58258	+	2.64575i	−0.276340	+	0.159545i
$276$		0			0
$277$	2.00000	−	3.46410i	0.120168	−	0.208138i	−0.799666	−	0.600446i	$-0.794990\pi$
$277$	2.00000	−	3.46410i	0.120168	−	0.208138i	0.919834	+	0.392308i	$0.128323\pi$
$278$	−12.7913	+	2.09355i	−0.767170	+	0.125563i
$279$		0			0
$280$	−11.4564	+	6.06218i	−0.684653	+	0.362284i
$281$	−16.0000			−0.954480			−0.477240	−	0.878773i	$-0.658363\pi$
$281$	−16.0000			−0.954480			−0.477240	+	0.878773i	$0.658363\pi$
$282$		0			0
$283$	9.16515	−	15.8745i	0.544812	−	0.943642i	−0.453807	−	0.891100i	$-0.649934\pi$
$283$	9.16515	−	15.8745i	0.544812	−	0.943642i	0.998619	−	0.0525416i	$-0.0167322\pi$
$284$	−3.37386	−	10.0308i	−0.200202	−	0.595219i
$285$		0			0
$286$	4.58258	−	12.1244i	0.270973	−	0.716928i
$287$	−4.58258	+	7.93725i	−0.270501	+	0.468521i
$288$		0			0
$289$	15.5000	+	26.8468i	0.911765	+	1.57922i
$290$	9.47822	−	7.75650i	0.556580	−	0.455478i
$291$		0			0
$292$	−13.5826	−	2.74110i	−0.794860	−	0.160411i
$293$		−	15.5885i		−	0.910687i	−0.890316	−	0.455344i	$-0.849516\pi$
$293$		−	15.5885i		−	0.910687i	0.890316	−	0.455344i	$-0.150484\pi$
$294$		0			0
$295$			23.8118i			1.38637i
$296$		0			0
$297$		0			0
$298$	12.5390	+	15.3223i	0.726366	+	0.887597i
$299$	9.16515	+	15.8745i	0.530034	+	0.918046i
$300$		0			0
$301$	14.0000	−	24.2487i	0.806947	−	1.39767i
$302$	17.5000	+	6.61438i	1.00701	+	0.380615i
$303$		0			0
$304$		0			0
$305$	9.00000	−	15.5885i	0.515339	−	0.892592i
$306$		0			0
$307$	27.4955			1.56925			0.784624	−	0.619972i	$-0.212856\pi$
$307$	27.4955			1.56925			0.784624	+	0.619972i	$0.212856\pi$
$308$	10.5000	+	9.26013i	0.598293	+	0.527645i
$309$		0			0
$310$	−1.81307	−	11.0776i	−0.102975	−	0.629164i
$311$	4.58258	−	7.93725i	0.259854	−	0.450080i	−0.706349	−	0.707864i	$-0.749659\pi$
$311$	4.58258	−	7.93725i	0.259854	−	0.450080i	0.966203	+	0.257784i	$0.0829922\pi$
$312$		0			0
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.165406	−	0.986226i	$-0.447107\pi$
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.936799	+	0.349867i	$0.113773\pi$
$314$	9.16515	+	3.46410i	0.517219	+	0.195491i
$315$		0			0
$316$	−10.5000	+	11.9059i	−0.590671	+	0.669758i
$317$	3.50000	+	6.06218i	0.196580	+	0.340486i	0.947417	−	0.320001i	$-0.103683\pi$
$317$	3.50000	+	6.06218i	0.196580	+	0.340486i	−0.750838	+	0.660487i	$0.770350\pi$
$318$		0			0
$319$	−11.4564	−	6.61438i	−0.641437	−	0.370334i
$320$	−1.02178	+	13.8187i	−0.0571193	+	0.772488i
$321$		0			0
$322$	−19.5390	+	3.19795i	−1.08887	+	0.178215i
$323$		0			0
$324$		0			0
$325$	6.00000	+	3.46410i	0.332820	+	0.192154i
$326$	17.3739	−	14.2179i	0.962249	−	0.787457i
$327$		0			0
$328$	4.58258	+	8.66025i	0.253030	+	0.478183i
$329$			24.2487i			1.33687i
$330$		0			0
$331$	−9.16515	+	5.29150i	−0.503762	+	0.290847i	−0.730266	−	0.683163i	$-0.760604\pi$
$331$	−9.16515	+	5.29150i	−0.503762	+	0.290847i	0.226504	+	0.974010i	$0.427270\pi$
$332$	8.68693	−	2.92185i	0.476757	−	0.160357i
$333$		0			0
$334$	25.5826	−	4.18710i	1.39982	−	0.229108i
$335$		0			0
$336$		0			0
$337$	−21.0000			−1.14394			−0.571971	−	0.820274i	$-0.693821\pi$
$337$	−21.0000			−1.14394			−0.571971	+	0.820274i	$0.693821\pi$
$338$	1.39564	−	0.228425i	0.0759130	−	0.0124247i
$339$		0			0
$340$	22.7477	−	7.65120i	1.23367	−	0.414945i
$341$	−10.5000	+	6.06218i	−0.568607	+	0.328285i
$342$		0			0
$343$			18.5203i			1.00000i
$344$	−14.0000	−	26.4575i	−0.754829	−	1.42649i
$345$		0			0
$346$	15.1652	−	12.4104i	0.815284	−	0.667188i
$347$	4.58258	+	2.64575i	0.246006	+	0.142031i	0.617934	−	0.786230i	$-0.287970\pi$
$347$	4.58258	+	2.64575i	0.246006	+	0.142031i	−0.371928	+	0.928261i	$0.621303\pi$
$348$		0			0
$349$			20.7846i			1.11257i	0.830990	+	0.556287i	$0.187775\pi$
$349$			20.7846i			1.11257i	−0.830990	+	0.556287i	$0.812225\pi$
$350$	−5.79129	+	4.73930i	−0.309557	+	0.253326i
$351$		0			0
$352$	14.3521	−	4.24473i	0.764969	−	0.226245i
$353$	6.00000	+	3.46410i	0.319348	+	0.184376i	0.651102	−	0.758990i	$-0.274307\pi$
$353$	6.00000	+	3.46410i	0.319348	+	0.184376i	−0.331754	+	0.943366i	$0.607640\pi$
$354$		0			0
$355$	4.58258	+	7.93725i	0.243218	+	0.421266i
$356$	13.7477	−	15.5885i	0.728628	−	0.826187i
$357$		0			0
$358$	7.00000	+	2.64575i	0.369961	+	0.139832i
$359$	−9.16515	+	5.29150i	−0.483718	+	0.279275i	−0.721965	−	0.691930i	$-0.756761\pi$
$359$	−9.16515	+	5.29150i	−0.483718	+	0.279275i	0.238247	+	0.971205i	$0.423427\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	0.791288	+	4.83465i	0.0415892	+	0.254104i
$363$		0			0
$364$	3.62614	−	17.9681i	0.190061	−	0.941782i
$365$	12.0000			0.628109
$366$		0			0
$367$	2.29129	−	3.96863i	0.119604	−	0.207161i	−0.800007	−	0.599991i	$-0.795171\pi$
$367$	2.29129	−	3.96863i	0.119604	−	0.207161i	0.919611	+	0.392831i	$0.128504\pi$
$368$	−8.20871	+	19.5094i	−0.427909	+	1.01700i
$369$		0			0
$370$		0			0
$371$	16.0390	−	9.26013i	0.832704	−	0.480762i
$372$		0			0
$373$	−17.0000	−	29.4449i	−0.880227	−	1.52460i	−0.851089	−	0.525022i	$-0.824057\pi$
$373$	−17.0000	−	29.4449i	−0.880227	−	1.52460i	−0.0291379	−	0.999575i	$-0.509276\pi$
$374$	−16.4174	−	20.0616i	−0.848925	−	1.03736i
$375$		0			0
$376$	21.9564	+	13.7810i	1.13232	+	0.710699i
$377$			17.3205i			0.892052i
$378$		0			0
$379$		−	5.29150i		−	0.271806i	−0.990722	−	0.135903i	$-0.956606\pi$
$379$		−	5.29150i		−	0.271806i	0.990722	−	0.135903i	$-0.0433936\pi$
$380$		0			0
$381$		0			0
$382$	−11.5826	+	9.47860i	−0.592616	+	0.484968i
$383$	−13.7477	−	23.8118i	−0.702476	−	1.21672i	−0.967595	−	0.252508i	$-0.918744\pi$
$383$	−13.7477	−	23.8118i	−0.702476	−	1.21672i	0.265119	−	0.964216i	$-0.414589\pi$
$384$		0			0
$385$	−10.5000	−	6.06218i	−0.535130	−	0.308957i
$386$	−1.50000	+	3.96863i	−0.0763480	+	0.201998i
$387$		0			0
$388$	−5.52178	−	16.4168i	−0.280326	−	0.833435i
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	−0.710980	−	0.703213i	$-0.751748\pi$
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	0.964490	+	0.264120i	$0.0850816\pi$
$390$		0			0
$391$	36.6606			1.85401
$392$	16.7695	+	10.5254i	0.846988	+	0.531612i
$393$		0			0
$394$	−19.5390	+	3.19795i	−0.984361	+	0.161110i
$395$	6.87386	−	11.9059i	0.345862	−	0.599050i
$396$		0			0
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$	−9.16515	+	24.2487i	−0.459408	+	1.21548i
$399$		0			0
$400$	1.00000	+	7.93725i	0.0500000	+	0.396863i
$401$	4.00000	+	6.92820i	0.199750	+	0.345978i	0.948447	−	0.316934i	$-0.102654\pi$
$401$	4.00000	+	6.92820i	0.199750	+	0.345978i	−0.748697	+	0.662912i	$0.769320\pi$
$402$		0			0
$403$	13.7477	+	7.93725i	0.684823	+	0.395383i
$404$	13.5826	+	2.74110i	0.675758	+	0.136375i
$405$		0			0
$406$	−17.5000	−	6.61438i	−0.868510	−	0.328266i
$407$		0			0
$408$		0			0
$409$	4.50000	+	2.59808i	0.222511	+	0.128467i	0.607112	−	0.794616i	$-0.292328\pi$
$409$	4.50000	+	2.59808i	0.222511	+	0.128467i	−0.384602	+	0.923083i	$0.625661\pi$
$410$	−5.37386	−	6.56670i	−0.265396	−	0.324306i
$411$		0			0
$412$	27.4955	+	24.2487i	1.35460	+	1.19465i
$413$	31.5000	−	18.1865i	1.55001	−	0.894901i
$414$		0			0
$415$	−6.87386	+	3.96863i	−0.337425	+	0.194812i
$416$	−14.2087	−	13.4949i	−0.696639	−	0.661642i
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−1.20871	−	7.38505i	−0.0588392	−	0.359499i
$423$		0			0
$424$	0.730493	−	19.7855i	0.0354759	−	0.960869i
$425$	12.0000	−	6.92820i	0.582086	−	0.336067i
$426$		0			0
$427$	−27.4955			−1.33060
$428$	−24.5000	+	27.7804i	−1.18425	+	1.34282i
$429$		0			0
$430$	16.4174	+	20.0616i	0.791719	+	0.967457i
$431$	22.9129	+	13.2288i	1.10367	+	0.637207i	0.937184	−	0.348836i	$-0.113423\pi$
$431$	22.9129	+	13.2288i	1.10367	+	0.637207i	0.166491	+	0.986043i	$0.446756\pi$
$432$		0			0
$433$		−	20.7846i		−	0.998845i	−0.866359	−	0.499422i	$-0.833546\pi$
$433$		−	20.7846i		−	0.998845i	0.866359	−	0.499422i	$-0.166454\pi$
$434$	−13.2695	+	10.8591i	−0.636957	+	0.521254i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	2.29129	+	3.96863i	0.109357	+	0.189412i	0.915510	−	0.402295i	$-0.131787\pi$
$439$	2.29129	+	3.96863i	0.109357	+	0.189412i	−0.806153	+	0.591707i	$0.798454\pi$
$440$	−11.4564	+	6.06218i	−0.546164	+	0.289003i
$441$		0			0
$442$	−12.0000	+	31.7490i	−0.570782	+	1.51015i
$443$	16.0390	−	9.26013i	0.762037	−	0.439962i	−0.0679899	−	0.997686i	$-0.521659\pi$
$443$	16.0390	−	9.26013i	0.762037	−	0.439962i	0.830026	+	0.557724i	$0.188325\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	−6.39564	+	1.04678i	−0.302843	+	0.0495663i
$447$		0			0
$448$	19.0608	−	9.20250i	0.900538	−	0.434777i
$449$	14.0000			0.660701			0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000			0.660701			0.330350	+	0.943858i	$0.392833\pi$
$450$		0			0
$451$	−4.58258	+	7.93725i	−0.215785	+	0.373751i
$452$	26.5390	−	8.92640i	1.24829	−	0.419863i
$453$		0			0
$454$	−2.29129	+	6.06218i	−0.107535	+	0.284512i
$455$			15.8745i			0.744208i
$456$		0			0
$457$	13.5000	+	23.3827i	0.631503	+	1.09380i	0.987245	+	0.159211i	$0.0508951\pi$
$457$	13.5000	+	23.3827i	0.631503	+	1.09380i	−0.355741	+	0.934585i	$0.615772\pi$
$458$	−11.3739	+	9.30780i	−0.531466	+	0.434925i
$459$		0			0
$460$	3.62614	−	17.9681i	0.169069	−	0.837765i
$461$			27.7128i			1.29071i	0.763881	+	0.645357i	$0.223291\pi$
$461$			27.7128i			1.29071i	−0.763881	+	0.645357i	$0.776709\pi$
$462$		0			0
$463$		−	15.8745i		−	0.737751i	−0.929479	−	0.368875i	$-0.879743\pi$
$463$		−	15.8745i		−	0.737751i	0.929479	−	0.368875i	$-0.120257\pi$
$464$	−15.9347	+	12.0866i	−0.739748	+	0.561108i
$465$		0			0
$466$	−17.9129	−	21.8890i	−0.829798	−	1.01399i
$467$	−18.3303	−	31.7490i	−0.848225	−	1.46917i	−0.882791	−	0.469767i	$-0.844338\pi$
$467$	−18.3303	−	31.7490i	−0.848225	−	1.46917i	0.0345653	−	0.999402i	$-0.488995\pi$
$468$		0			0
$469$		0			0
$470$	−21.0000	−	7.93725i	−0.968658	−	0.366118i
$471$		0			0
$472$	1.43466	−	38.8580i	0.0660355	−	1.78858i
$473$	14.0000	−	24.2487i	0.643721	−	1.11496i
$474$		0			0
$475$		0			0
$476$	−27.4955	−	24.2487i	−1.26025	−	1.11144i
$477$		0			0
$478$	1.20871	+	7.38505i	0.0552852	+	0.337784i
$479$	−9.16515	+	15.8745i	−0.418766	+	0.725325i	−0.995816	−	0.0913846i	$-0.970871\pi$
$479$	−9.16515	+	15.8745i	−0.418766	+	0.725325i	0.577049	+	0.816709i	$0.304204\pi$
$480$		0			0
$481$		0			0
$482$	−6.87386	−	2.59808i	−0.313096	−	0.118339i
$483$		0			0
$484$	−6.00000	−	5.29150i	−0.272727	−	0.240523i
$485$	7.50000	+	12.9904i	0.340557	+	0.589863i
$486$		0			0
$487$	2.29129	+	1.32288i	0.103828	+	0.0599452i	0.551015	−	0.834495i	$-0.314241\pi$
$487$	2.29129	+	1.32288i	0.103828	+	0.0599452i	−0.447187	+	0.894441i	$0.647574\pi$
$488$	−15.6261	+	24.8963i	−0.707362	+	1.12700i
$489$		0			0
$490$	−16.0390	−	6.06218i	−0.724569	−	0.273861i
$491$		−	2.64575i		−	0.119401i	−0.998216	−	0.0597005i	$-0.980985\pi$
$491$		−	2.64575i		−	0.119401i	0.998216	−	0.0597005i	$-0.0190146\pi$
$492$		0			0
$493$	30.0000	+	17.3205i	1.35113	+	0.780076i
$494$		0			0
$495$		0			0
$496$	2.29129	+	18.1865i	0.102882	+	0.816599i
$497$	7.00000	−	12.1244i	0.313993	−	0.543852i
$498$		0			0
$499$	−4.58258	+	2.64575i	−0.205144	+	0.118440i	−0.599053	−	0.800710i	$-0.704456\pi$
$499$	−4.58258	+	2.64575i	−0.205144	+	0.118440i	0.393908	+	0.919150i	$0.371123\pi$
$500$	−7.73049	−	22.9835i	−0.345718	−	1.02785i
$501$		0			0
$502$	−6.39564	+	1.04678i	−0.285452	+	0.0467199i
$503$	−36.6606			−1.63462			−0.817308	−	0.576201i	$-0.804534\pi$
$503$	−36.6606			−1.63462			−0.817308	+	0.576201i	$0.804534\pi$
$504$		0			0
$505$	−12.0000			−0.533993
$506$	−19.5390	+	3.19795i	−0.868615	+	0.142166i
$507$		0			0
$508$	5.06080	+	15.0462i	0.224536	+	0.667567i
$509$	1.50000	−	0.866025i	0.0664863	−	0.0383859i	−0.466388	−	0.884580i	$-0.654445\pi$
$509$	1.50000	−	0.866025i	0.0664863	−	0.0383859i	0.532875	+	0.846194i	$0.321112\pi$
$510$		0			0
$511$	−9.16515	−	15.8745i	−0.405442	−	0.702247i
$512$	2.50000	−	22.4889i	0.110485	−	0.993878i
$513$		0			0
$514$	−11.3739	+	9.30780i	−0.501680	+	0.410550i
$515$	−27.4955	−	15.8745i	−1.21159	−	0.699514i
$516$		0			0
$517$			24.2487i			1.06646i
$518$		0			0
$519$		0			0
$520$	14.3739	+	9.02175i	0.630336	+	0.395630i
$521$	6.00000	+	3.46410i	0.262865	+	0.151765i	0.625641	−	0.780111i	$-0.284838\pi$
$521$	6.00000	+	3.46410i	0.262865	+	0.151765i	−0.362776	+	0.931876i	$0.618171\pi$
$522$		0			0
$523$	−13.7477	−	23.8118i	−0.601146	−	1.04122i	−0.992648	−	0.121038i	$-0.961378\pi$
$523$	−13.7477	−	23.8118i	−0.601146	−	1.04122i	0.391502	−	0.920177i	$-0.371956\pi$
$524$	20.6216	+	18.1865i	0.900858	+	0.794482i
$525$		0			0
$526$	−14.0000	−	5.29150i	−0.610429	−	0.230720i
$527$	27.4955	−	15.8745i	1.19772	−	0.691504i
$528$		0			0
$529$	2.50000	−	4.33013i	0.108696	−	0.188266i
$530$	2.76951	+	16.9213i	0.120300	+	0.735014i
$531$		0			0
$532$		0			0
$533$	12.0000			0.519778
$534$		0			0
$535$	16.0390	−	27.7804i	0.693427	−	1.20105i
$536$		0			0
$537$		0			0
$538$	−25.2042	−	9.52628i	−1.08663	−	0.410707i
$539$			18.5203i			0.797724i
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	−12.3131	−	15.0462i	−0.528892	−	0.646290i
$543$		0			0
$544$	−37.5826	+	11.1153i	−1.61134	+	0.476565i
$545$		0			0
$546$		0			0
$547$			31.7490i			1.35749i	0.734374	+	0.678745i	$0.237476\pi$
$547$			31.7490i			1.35749i	−0.734374	+	0.678745i	$0.762524\pi$
$548$	−1.58258	+	7.84190i	−0.0676043	+	0.334990i
$549$		0			0
$550$	−5.79129	+	4.73930i	−0.246941	+	0.202085i
$551$		0			0
$552$		0			0
$553$	−21.0000			−0.893011
$554$	2.00000	−	5.29150i	0.0849719	−	0.224814i
$555$		0			0
$556$	−17.3739	+	5.84370i	−0.736816	+	0.247828i
$557$	−3.50000	+	6.06218i	−0.148300	+	0.256863i	−0.930599	−	0.366040i	$-0.880713\pi$
$557$	−3.50000	+	6.06218i	−0.148300	+	0.256863i	0.782299	+	0.622903i	$0.214047\pi$
$558$		0			0
$559$	−36.6606			−1.55058
$560$	−14.6044	+	11.0776i	−0.617147	+	0.468113i
$561$		0			0
$562$	−22.3303	+	3.65480i	−0.941947	+	0.154169i
$563$	−11.4564	+	19.8431i	−0.482831	+	0.836288i	−0.999806	−	0.0197125i	$-0.993725\pi$
$563$	−11.4564	+	19.8431i	−0.482831	+	0.836288i	0.516974	+	0.856001i	$0.327058\pi$
$564$		0			0
$565$	−21.0000	+	12.1244i	−0.883477	+	0.510075i
$566$	9.16515	−	24.2487i	0.385240	−	1.01925i
$567$		0			0
$568$	−7.00000	−	13.2288i	−0.293713	−	0.555066i
$569$	−4.00000	−	6.92820i	−0.167689	−	0.290445i	0.769918	−	0.638143i	$-0.220297\pi$
$569$	−4.00000	−	6.92820i	−0.167689	−	0.290445i	−0.937607	+	0.347697i	$0.886964\pi$
$570$		0			0
$571$	−13.7477	−	7.93725i	−0.575324	−	0.332164i	0.183949	−	0.982936i	$-0.441112\pi$
$571$	−13.7477	−	7.93725i	−0.575324	−	0.332164i	−0.759273	+	0.650772i	$0.774445\pi$
$572$	3.62614	−	17.9681i	0.151616	−	0.751282i
$573$		0			0
$574$	−4.58258	+	12.1244i	−0.191273	+	0.506061i
$575$		−	10.5830i		−	0.441342i
$576$		0			0
$577$	−37.5000	−	21.6506i	−1.56115	−	0.901328i	−0.997142	−	0.0755556i	$-0.975927\pi$
$577$	−37.5000	−	21.6506i	−1.56115	−	0.901328i	−0.564004	−	0.825772i	$-0.690740\pi$
$578$	27.7650	+	33.9280i	1.15487	+	1.41122i
$579$		0			0
$580$	11.4564	−	12.9904i	0.475703	−	0.539396i
$581$	10.5000	+	6.06218i	0.435613	+	0.251502i
$582$		0			0
$583$	16.0390	−	9.26013i	0.664268	−	0.383515i
$584$	−19.5826	−	0.723000i	−0.810333	−	0.0299180i
$585$		0			0
$586$	−3.56080	−	21.7559i	−0.147095	−	0.898729i
$587$	22.9129			0.945716			0.472858	−	0.881139i	$-0.343222\pi$
$587$	22.9129			0.945716			0.472858	+	0.881139i	$0.343222\pi$
$588$		0			0
$589$		0			0
$590$	5.43920	+	33.2327i	0.223929	+	1.36817i
$591$		0			0
$592$		0			0
$593$	−9.00000	+	5.19615i	−0.369586	+	0.213380i	−0.673277	−	0.739390i	$-0.735114\pi$
$593$	−9.00000	+	5.19615i	−0.369586	+	0.213380i	0.303692	+	0.952770i	$0.401781\pi$
$594$		0			0
$595$	27.4955	+	15.8745i	1.12720	+	0.650791i
$596$	21.0000	+	18.5203i	0.860194	+	0.758619i
$597$		0			0
$598$	16.4174	+	20.0616i	0.671358	+	0.820380i
$599$	9.16515	+	5.29150i	0.374478	+	0.216205i	0.675413	−	0.737440i	$-0.263965\pi$
$599$	9.16515	+	5.29150i	0.374478	+	0.216205i	−0.300935	+	0.953645i	$0.597299\pi$
$600$		0			0
$601$			8.66025i			0.353259i	0.984277	+	0.176630i	$0.0565195\pi$
$601$			8.66025i			0.353259i	−0.984277	+	0.176630i	$0.943481\pi$
$602$	14.0000	−	37.0405i	0.570597	−	1.50966i
$603$		0			0
$604$	25.9347	+	5.23388i	1.05527	+	0.212963i
$605$	6.00000	+	3.46410i	0.243935	+	0.140836i
$606$		0			0
$607$	−6.87386	−	11.9059i	−0.279002	−	0.483245i	0.692135	−	0.721768i	$-0.256670\pi$
$607$	−6.87386	−	11.9059i	−0.279002	−	0.483245i	−0.971137	+	0.238523i	$0.923337\pi$
$608$		0			0
$609$		0			0
$610$	9.00000	−	23.8118i	0.364399	−	0.964110i
$611$	27.4955	−	15.8745i	1.11235	−	0.642214i
$612$		0			0
$613$	−7.00000	+	12.1244i	−0.282727	+	0.489698i	−0.972056	−	0.234751i	$-0.924572\pi$
$613$	−7.00000	+	12.1244i	−0.282727	+	0.489698i	0.689328	+	0.724449i	$0.257906\pi$
$614$	38.3739	−	6.28065i	1.54864	−	0.253467i
$615$		0			0
$616$	16.7695	+	10.5254i	0.675663	+	0.424080i
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$		0			0
$619$	−13.7477	+	23.8118i	−0.552568	+	0.957076i	0.445521	+	0.895272i	$0.353019\pi$
$619$	−13.7477	+	23.8118i	−0.552568	+	0.957076i	−0.998088	+	0.0618038i	$0.980315\pi$
$620$	−5.06080	−	15.0462i	−0.203246	−	0.604270i
$621$		0			0
$622$	4.58258	−	12.1244i	0.183745	−	0.486142i
$623$	27.4955			1.10158
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	24.6434	−	20.1669i	0.984947	−	0.806032i
$627$		0			0
$628$	13.5826	+	2.74110i	0.542004	+	0.109382i
$629$		0			0
$630$		0			0
$631$			7.93725i			0.315977i	0.987441	+	0.157989i	$0.0505009\pi$
$631$			7.93725i			0.315977i	−0.987441	+	0.157989i	$0.949499\pi$
$632$	−11.9347	+	19.0148i	−0.474735	+	0.756369i
$633$		0			0
$634$	6.26951	+	7.66115i	0.248994	+	0.304263i
$635$	−6.87386	−	11.9059i	−0.272781	−	0.472470i
$636$		0			0
$637$	21.0000	−	12.1244i	0.832050	−	0.480384i
$638$	−17.5000	−	6.61438i	−0.692832	−	0.261866i
$639$		0			0
$640$	1.73049	+	19.5194i	0.0684037	+	0.771570i
$641$	−19.0000	+	32.9090i	−0.750455	+	1.29983i	0.197148	+	0.980374i	$0.436832\pi$
$641$	−19.0000	+	32.9090i	−0.750455	+	1.29983i	−0.947602	+	0.319452i	$0.896501\pi$
$642$		0			0
$643$	−18.3303			−0.722877			−0.361438	−	0.932396i	$-0.617714\pi$
$643$	−18.3303			−0.722877			−0.361438	+	0.932396i	$0.617714\pi$
$644$	−26.5390	+	8.92640i	−1.04578	+	0.351750i
$645$		0			0
$646$		0			0
$647$	4.58258	−	7.93725i	0.180160	−	0.312046i	−0.761775	−	0.647842i	$-0.775672\pi$
$647$	4.58258	−	7.93725i	0.180160	−	0.312046i	0.941935	+	0.335796i	$0.109005\pi$
$648$		0			0
$649$	31.5000	−	18.1865i	1.23648	−	0.713884i
$650$	9.16515	+	3.46410i	0.359487	+	0.135873i
$651$		0			0
$652$	21.0000	−	23.8118i	0.822423	−	0.932541i
$653$	−21.5000	−	37.2391i	−0.841360	−	1.45728i	−0.888745	−	0.458402i	$-0.848422\pi$
$653$	−21.5000	−	37.2391i	−0.841360	−	1.45728i	0.0473852	−	0.998877i	$-0.484911\pi$
$654$		0			0
$655$	−20.6216	−	11.9059i	−0.805752	−	0.465201i
$656$	8.37386	+	11.0399i	0.326944	+	0.431034i
$657$		0			0
$658$	5.53901	+	33.8426i	0.215933	+	1.31932i
$659$			26.4575i			1.03064i	0.856998	+	0.515319i	$0.172327\pi$
$659$			26.4575i			1.03064i	−0.856998	+	0.515319i	$0.827673\pi$
$660$		0			0
$661$	6.00000	+	3.46410i	0.233373	+	0.134738i	0.612127	−	0.790759i	$-0.290314\pi$
$661$	6.00000	+	3.46410i	0.233373	+	0.134738i	−0.378754	+	0.925497i	$0.623647\pi$
$662$	−11.5826	+	9.47860i	−0.450170	+	0.368396i
$663$		0			0
$664$	11.4564	−	6.06218i	0.444596	−	0.235258i
$665$		0			0
$666$		0			0
$667$	22.9129	−	13.2288i	0.887190	−	0.512219i
$668$	34.7477	−	11.6874i	1.34443	−	0.452199i
$669$		0			0
$670$		0			0
$671$	−27.4955			−1.06145
$672$		0			0
$673$	21.0000			0.809491			0.404745	−	0.914429i	$-0.367360\pi$
$673$	21.0000			0.809491			0.404745	+	0.914429i	$0.367360\pi$
$674$	−29.3085	+	4.79693i	−1.12892	+	0.184771i
$675$		0			0
$676$	1.89564	−	0.637600i	0.0729094	−	0.0245231i
$677$	−19.5000	+	11.2583i	−0.749446	+	0.432693i	−0.825494	−	0.564411i	$-0.809103\pi$
$677$	−19.5000	+	11.2583i	−0.749446	+	0.432693i	0.0760478	+	0.997104i	$0.475770\pi$
$678$		0			0
$679$	11.4564	−	19.8431i	0.439658	−	0.761510i
$680$	30.0000	−	15.8745i	1.15045	−	0.608760i
$681$		0			0
$682$	−13.2695	+	10.8591i	−0.508116	+	0.415817i
$683$	2.29129	+	1.32288i	0.0876737	+	0.0506184i	0.543196	−	0.839606i	$-0.317214\pi$
$683$	2.29129	+	1.32288i	0.0876737	+	0.0506184i	−0.455522	+	0.890224i	$0.650547\pi$
$684$		0			0
$685$		−	6.92820i		−	0.264713i
$686$	4.23049	+	25.8477i	0.161521	+	0.986869i
$687$		0			0
$688$	−25.5826	−	33.7273i	−0.975327	−	1.28584i
$689$	−21.0000	−	12.1244i	−0.800036	−	0.461901i
$690$		0			0
$691$	22.9129	+	39.6863i	0.871647	+	1.50974i	0.860292	+	0.509801i	$0.170281\pi$
$691$	22.9129	+	39.6863i	0.871647	+	1.50974i	0.0113548	+	0.999936i	$0.496386\pi$
$692$	18.3303	−	20.7846i	0.696814	−	0.790112i
$693$		0			0
$694$	7.00000	+	2.64575i	0.265716	+	0.100431i
$695$	13.7477	−	7.93725i	0.521481	−	0.301077i
$696$		0			0
$697$	12.0000	−	20.7846i	0.454532	−	0.787273i
$698$	4.74773	+	29.0079i	0.179704	+	1.09797i
$699$		0			0
$700$	−7.00000	+	7.93725i	−0.264575	+	0.300000i
$701$	−23.0000			−0.868698			−0.434349	−	0.900745i	$-0.643022\pi$
$701$	−23.0000			−0.868698			−0.434349	+	0.900745i	$0.643022\pi$
$702$		0			0
$703$		0			0
$704$	19.0608	−	9.20250i	0.718381	−	0.346832i
$705$		0			0
$706$	9.16515	+	3.46410i	0.344935	+	0.130373i
$707$	9.16515	+	15.8745i	0.344691	+	0.597022i
$708$		0			0
$709$	−21.0000	−	36.3731i	−0.788672	−	1.36602i	−0.926781	−	0.375602i	$-0.877436\pi$
$709$	−21.0000	−	36.3731i	−0.788672	−	1.36602i	0.138109	−	0.990417i	$-0.455897\pi$
$710$	8.20871	+	10.0308i	0.308067	+	0.376449i
$711$		0			0
$712$	15.6261	−	24.8963i	0.585614	−	0.933027i
$713$		−	24.2487i		−	0.908121i
$714$		0			0
$715$			15.8745i			0.593673i
$716$	10.3739	+	2.09355i	0.387689	+	0.0782397i
$717$		0			0
$718$	−11.5826	+	9.47860i	−0.432258	+	0.353738i
$719$	−13.7477	−	23.8118i	−0.512704	−	0.888029i	−0.999891	−	0.0147316i	$-0.995311\pi$
$719$	−13.7477	−	23.8118i	−0.512704	−	0.888029i	0.487188	−	0.873297i	$-0.338023\pi$
$720$		0			0
$721$			48.4974i			1.80614i
$722$	9.50000	−	25.1346i	0.353553	−	0.935414i
$723$		0			0
$724$	2.20871	+	6.56670i	0.0820861	+	0.244050i
$725$	5.00000	−	8.66025i	0.185695	−	0.321634i
$726$		0			0
$727$	13.7477			0.509875			0.254937	−	0.966958i	$-0.417945\pi$
$727$	13.7477			0.509875			0.254937	+	0.966958i	$0.417945\pi$
$728$	0.956439	−	25.9053i	0.0354480	−	0.960115i
$729$		0			0
$730$	16.7477	−	2.74110i	0.619861	−	0.101453i
$731$	−36.6606	+	63.4980i	−1.35594	+	2.34856i
$732$		0			0
$733$	−30.0000	+	17.3205i	−1.10808	+	0.639748i	−0.938330	−	0.345740i	$-0.887628\pi$
$733$	−30.0000	+	17.3205i	−1.10808	+	0.639748i	−0.169745	+	0.985488i	$0.554294\pi$
$734$	2.29129	−	6.06218i	0.0845730	−	0.223759i
$735$		0			0
$736$	−7.00000	+	29.1033i	−0.258023	+	1.07276i
$737$		0			0
$738$		0			0
$739$	41.2432	+	23.8118i	1.51715	+	0.875930i	0.999797	+	0.0201609i	$0.00641784\pi$
$739$	41.2432	+	23.8118i	1.51715	+	0.875930i	0.517358	+	0.855769i	$0.326915\pi$
$740$		0			0
$741$		0			0
$742$	20.2695	−	16.5876i	0.744117	−	0.608948i
$743$			21.1660i			0.776506i	0.921553	+	0.388253i	$0.126921\pi$
$743$			21.1660i			0.776506i	−0.921553	+	0.388253i	$0.873079\pi$
$744$		0			0
$745$	−21.0000	−	12.1244i	−0.769380	−	0.444202i
$746$	−30.4519	−	37.2113i	−1.11492	−	1.36240i
$747$		0			0
$748$	−27.4955	−	24.2487i	−1.00533	−	0.886621i
$749$	−49.0000			−1.79042
$750$		0			0
$751$	11.4564	−	6.61438i	0.418051	−	0.241362i	−0.276192	−	0.961103i	$-0.589073\pi$
$751$	11.4564	−	6.61438i	0.418051	−	0.241362i	0.694243	+	0.719740i	$0.255739\pi$
$752$	33.7913	+	14.2179i	1.23224	+	0.518474i
$753$		0			0
$754$	3.95644	+	24.1733i	0.144085	+	0.880338i
$755$	−22.9129			−0.833885
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$	−1.20871	−	7.38505i	−0.0439024	−	0.268237i
$759$		0			0
$760$		0			0
$761$	−33.0000	+	19.0526i	−1.19625	+	0.690655i	−0.959717	−	0.280969i	$-0.909344\pi$
$761$	−33.0000	+	19.0526i	−1.19625	+	0.690655i	−0.236532	+	0.971624i	$0.576011\pi$
$762$		0			0
$763$		0			0
$764$	−14.0000	+	15.8745i	−0.506502	+	0.574320i
$765$		0			0
$766$	−24.6261	−	30.0924i	−0.889778	−	1.08728i
$767$	−41.2432	−	23.8118i	−1.48920	−	0.859793i
$768$		0			0
$769$		−	32.9090i		−	1.18673i	−0.804934	−	0.593364i	$-0.797800\pi$
$769$		−	32.9090i		−	1.18673i	0.804934	−	0.593364i	$-0.202200\pi$
$770$	−16.0390	−	6.06218i	−0.578006	−	0.218466i
$771$		0			0
$772$	−1.18693	+	5.88143i	−0.0427186	+	0.211677i
$773$	36.0000	+	20.7846i	1.29483	+	0.747570i	0.979506	−	0.201414i	$-0.0645536\pi$
$773$	36.0000	+	20.7846i	1.29483	+	0.747570i	0.315324	+	0.948984i	$0.397887\pi$
$774$		0			0
$775$	−4.58258	−	7.93725i	−0.164611	−	0.285115i
$776$	−11.4564	−	21.6506i	−0.411262	−	0.777213i
$777$		0			0
$778$	5.00000	−	13.2288i	0.179259	−	0.474274i
$779$		0			0
$780$		0			0
$781$	7.00000	−	12.1244i	0.250480	−	0.433844i
$782$	51.1652	−	8.37420i	1.82966	−	0.299461i
$783$		0			0
$784$	25.8085	+	10.8591i	0.921733	+	0.387825i
$785$	−12.0000			−0.428298
$786$		0			0
$787$	−13.7477	+	23.8118i	−0.490054	+	0.848798i	−0.999934	−	0.0114473i	$-0.996356\pi$
$787$	−13.7477	+	23.8118i	−0.490054	+	0.848798i	0.509881	+	0.860245i	$0.329689\pi$
$788$	−26.5390	+	8.92640i	−0.945413	+	0.317990i
$789$		0			0
$790$	6.87386	−	18.1865i	0.244561	−	0.647048i
$791$	32.0780	+	18.5203i	1.14056	+	0.658505i
$792$		0			0
$793$	18.0000	+	31.1769i	0.639199	+	1.10712i
$794$	15.1652	−	12.4104i	0.538191	−	0.440429i
$795$		0			0
$796$	−7.25227	+	35.9361i	−0.257050	+	1.27372i
$797$		−	15.5885i		−	0.552171i	−0.961133	−	0.276086i	$-0.910963\pi$
$797$		−	15.5885i		−	0.552171i	0.961133	−	0.276086i	$-0.0890374\pi$
$798$		0			0
$799$		−	63.4980i		−	2.24640i
$800$	3.20871	+	10.8492i	0.113445	+	0.383576i
$801$		0			0
$802$	7.16515	+	8.75560i	0.253010	+	0.309171i
$803$	−9.16515	−	15.8745i	−0.323431	−	0.560199i
$804$		0			0
$805$	21.0000	−	12.1244i	0.740153	−	0.427327i
$806$	21.0000	+	7.93725i	0.739693	+	0.279578i
$807$		0			0
$808$	19.5826	+	0.723000i	0.688913	+	0.0254351i
$809$	−14.0000	+	24.2487i	−0.492214	+	0.852539i	−0.999960	−	0.00896753i	$-0.997146\pi$
$809$	−14.0000	+	24.2487i	−0.492214	+	0.852539i	0.507746	+	0.861507i	$0.330479\pi$
$810$		0			0
$811$	−36.6606			−1.28733			−0.643664	−	0.765308i	$-0.722587\pi$
$811$	−36.6606			−1.28733			−0.643664	+	0.765308i	$0.722587\pi$
$812$	−25.9347	−	5.23388i	−0.910128	−	0.183673i
$813$		0			0
$814$		0			0
$815$	−13.7477	+	23.8118i	−0.481562	+	0.834090i
$816$		0			0
$817$		0			0
$818$	6.87386	+	2.59808i	0.240339	+	0.0908396i
$819$		0			0
$820$	−9.00000	−	7.93725i	−0.314294	−	0.277181i
$821$	−24.5000	−	42.4352i	−0.855056	−	1.48100i	−0.876593	−	0.481232i	$-0.840189\pi$
$821$	−24.5000	−	42.4352i	−0.855056	−	1.48100i	0.0215373	−	0.999768i	$-0.493144\pi$
$822$		0			0
$823$	41.2432	+	23.8118i	1.43765	+	0.830026i	0.997686	−	0.0679910i	$-0.0216589\pi$
$823$	41.2432	+	23.8118i	1.43765	+	0.830026i	0.439961	+	0.898017i	$0.354992\pi$
$824$	43.9129	+	27.5619i	1.52978	+	0.960165i
$825$		0			0
$826$	39.8085	−	32.5773i	1.38512	−	1.13351i
$827$			34.3948i			1.19602i	0.801487	+	0.598012i	$0.204042\pi$
$827$			34.3948i			1.19602i	−0.801487	+	0.598012i	$0.795958\pi$
$828$		0			0
$829$	6.00000	+	3.46410i	0.208389	+	0.120313i	0.600562	−	0.799578i	$-0.294943\pi$
$829$	6.00000	+	3.46410i	0.208389	+	0.120313i	−0.392174	+	0.919891i	$0.628277\pi$
$830$	−8.68693	+	7.10895i	−0.301528	+	0.246755i
$831$		0			0
$832$	−22.9129	−	15.5885i	−0.794361	−	0.540433i
$833$		−	48.4974i		−	1.68034i
$834$		0			0
$835$	−27.4955	+	15.8745i	−0.951519	+	0.549360i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	36.6606			1.26566			0.632832	−	0.774289i	$-0.281892\pi$
$839$	36.6606			1.26566			0.632832	+	0.774289i	$0.281892\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	−2.79129	+	0.456850i	−0.0961941	+	0.0157441i
$843$		0			0
$844$	−3.37386	−	10.0308i	−0.116133	−	0.345275i
$845$	−1.50000	+	0.866025i	−0.0516016	+	0.0297922i
$846$		0			0
$847$		−	10.5830i		−	0.363636i
$848$	−3.50000	−	27.7804i	−0.120190	−	0.953982i
$849$		0			0
$850$	15.1652	−	12.4104i	0.520160	−	0.425673i
$851$		0			0
$852$		0			0
$853$		−	27.7128i		−	0.948869i	−0.880291	−	0.474434i	$-0.842653\pi$
$853$		−	27.7128i		−	0.948869i	0.880291	−	0.474434i	$-0.157347\pi$
$854$	−38.3739	+	6.28065i	−1.31313	+	0.214920i
$855$		0			0
$856$	−27.8475	+	44.3679i	−0.951809	+	1.51647i
$857$	27.0000	+	15.5885i	0.922302	+	0.532492i	0.884369	−	0.466789i	$-0.154589\pi$
$857$	27.0000	+	15.5885i	0.922302	+	0.532492i	0.0379336	+	0.999280i	$0.487922\pi$
$858$		0			0
$859$	18.3303	+	31.7490i	0.625422	+	1.08326i	0.988459	+	0.151488i	$0.0484064\pi$
$859$	18.3303	+	31.7490i	0.625422	+	1.08326i	−0.363037	+	0.931775i	$0.618260\pi$
$860$	27.4955	+	24.2487i	0.937587	+	0.826874i
$861$		0			0
$862$	35.0000	+	13.2288i	1.19210	+	0.450573i
$863$	22.9129	−	13.2288i	0.779963	−	0.450312i	−0.0564539	−	0.998405i	$-0.517979\pi$
$863$	22.9129	−	13.2288i	0.779963	−	0.450312i	0.836417	+	0.548093i	$0.184646\pi$
$864$		0			0
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$	−4.74773	−	29.0079i	−0.161334	−	0.985729i
$867$		0			0
$868$	−16.0390	+	18.1865i	−0.544400	+	0.617291i
$869$	−21.0000			−0.712376
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	16.0390	−	27.7804i	0.542218	−	0.939149i
$876$		0			0
$877$	−14.0000	−	24.2487i	−0.472746	−	0.818821i	0.526767	−	0.850010i	$-0.323404\pi$
$877$	−14.0000	−	24.2487i	−0.472746	−	0.818821i	−0.999514	+	0.0311889i	$0.990071\pi$
$878$	4.10436	+	5.01540i	0.138515	+	0.169262i
$879$		0			0
$880$	−14.6044	+	11.0776i	−0.492313	+	0.373425i
$881$			27.7128i			0.933668i	0.884345	+	0.466834i	$0.154606\pi$
$881$			27.7128i			0.933668i	−0.884345	+	0.466834i	$0.845394\pi$
$882$		0			0
$883$			5.29150i			0.178073i	0.996028	+	0.0890366i	$0.0283788\pi$
$883$			5.29150i			0.178073i	−0.996028	+	0.0890366i	$0.971621\pi$
$884$	−9.49545	+	47.0514i	−0.319367	+	1.58251i
$885$		0			0
$886$	20.2695	−	16.5876i	0.680967	−	0.557270i
$887$	−13.7477	−	23.8118i	−0.461603	−	0.799521i	0.537438	−	0.843304i	$-0.319392\pi$
$887$	−13.7477	−	23.8118i	−0.461603	−	0.799521i	−0.999041	+	0.0437828i	$0.986059\pi$
$888$		0			0
$889$	−10.5000	+	18.1865i	−0.352159	+	0.609957i
$890$	−9.00000	+	23.8118i	−0.301681	+	0.798172i
$891$		0			0
$892$	−8.68693	+	2.92185i	−0.290860	+	0.0978308i
$893$		0			0
$894$		0			0
$895$	−9.16515			−0.306357
$896$	24.5000	−	17.1974i	0.818488	−	0.574524i
$897$		0			0
$898$	19.5390	−	3.19795i	0.652025	−	0.106717i
$899$	11.4564	−	19.8431i	0.382094	−	0.661806i
$900$		0			0
$901$	−42.0000	+	24.2487i	−1.39922	+	0.807842i
$902$	−4.58258	+	12.1244i	−0.152583	+	0.403697i
$903$		0			0
$904$	35.0000	−	18.5203i	1.16408	−	0.615975i
$905$	−3.00000	−	5.19615i	−0.0997234	−	0.172726i
$906$		0			0
$907$	−32.0780	−	18.5203i	−1.06513	−	0.614955i	−0.138286	−	0.990392i	$-0.544159\pi$
$907$	−32.0780	−	18.5203i	−1.06513	−	0.614955i	−0.926848	+	0.375437i	$0.877493\pi$
$908$	−1.81307	+	8.98403i	−0.0601688	+	0.298145i
$909$		0			0
$910$	3.62614	+	22.1552i	0.120205	+	0.734436i
$911$		−	5.29150i		−	0.175315i	−0.996151	−	0.0876577i	$-0.972062\pi$
$911$		−	5.29150i		−	0.175315i	0.996151	−	0.0876577i	$-0.0279382\pi$
$912$		0			0
$913$	10.5000	+	6.06218i	0.347499	+	0.200629i
$914$	24.1824	+	29.5502i	0.799882	+	0.977433i
$915$		0			0
$916$	−13.7477	+	15.5885i	−0.454238	+	0.515057i
$917$			36.3731i			1.20114i
$918$		0			0
$919$	4.58258	−	2.64575i	0.151165	−	0.0872753i	−0.422510	−	0.906358i	$-0.638851\pi$
$919$	4.58258	−	2.64575i	0.151165	−	0.0872753i	0.573675	+	0.819083i	$0.305517\pi$
$920$	0.956439	−	25.9053i	0.0315329	−	0.854073i
$921$		0			0
$922$	6.33030	+	38.6772i	0.208477	+	1.27377i
$923$	−18.3303			−0.603349
$924$		0			0
$925$		0			0
$926$	−3.62614	−	22.1552i	−0.119162	−	0.728064i
$927$		0			0
$928$	−19.4782	+	20.5085i	−0.639404	+	0.673225i
$929$	30.0000	−	17.3205i	0.984268	−	0.568267i	0.0807121	−	0.996737i	$-0.474281\pi$
$929$	30.0000	−	17.3205i	0.984268	−	0.568267i	0.903556	+	0.428470i	$0.140947\pi$
$930$		0			0
$931$		0			0
$932$	−30.0000	−	26.4575i	−0.982683	−	0.866645i
$933$		0			0
$934$	−32.8348	−	40.1232i	−1.07439	−	1.31287i
$935$	27.4955	+	15.8745i	0.899198	+	0.519152i
$936$		0			0
$937$		−	15.5885i		−	0.509253i	−0.967040	−	0.254626i	$-0.918048\pi$
$937$		−	15.5885i		−	0.509253i	0.967040	−	0.254626i	$-0.0819525\pi$
$938$		0			0
$939$		0			0
$940$	−31.1216	−	6.28065i	−1.01507	−	0.204852i
$941$	4.50000	+	2.59808i	0.146696	+	0.0846949i	0.571551	−	0.820566i	$-0.306342\pi$
$941$	4.50000	+	2.59808i	0.146696	+	0.0846949i	−0.424856	+	0.905261i	$0.639675\pi$
$942$		0			0
$943$	−9.16515	−	15.8745i	−0.298458	−	0.516945i
$944$	−6.87386	−	54.5596i	−0.223725	−	1.77576i
$945$		0			0
$946$	14.0000	−	37.0405i	0.455179	−	1.20429i
$947$	32.0780	−	18.5203i	1.04240	−	0.601828i	0.121885	−	0.992544i	$-0.461106\pi$
$947$	32.0780	−	18.5203i	1.04240	−	0.601828i	0.920511	+	0.390717i	$0.127773\pi$
$948$		0			0
$949$	−12.0000	+	20.7846i	−0.389536	+	0.674697i
$950$		0			0
$951$		0			0
$952$	−43.9129	−	27.5619i	−1.42322	−	0.893287i
$953$	28.0000			0.907009			0.453504	−	0.891254i	$-0.350174\pi$
$953$	28.0000			0.907009			0.453504	+	0.891254i	$0.350174\pi$
$954$		0			0
$955$	9.16515	−	15.8745i	0.296577	−	0.513687i
$956$	3.37386	+	10.0308i	0.109119	+	0.324419i
$957$		0			0
$958$	−9.16515	+	24.2487i	−0.296113	+	0.783440i
$959$	−9.16515	+	5.29150i	−0.295958	+	0.170872i
$960$		0			0
$961$	5.00000	+	8.66025i	0.161290	+	0.279363i
$962$		0			0
$963$		0			0
$964$	−10.1869	−	2.05583i	−0.328099	−	0.0662137i
$965$		−	5.19615i		−	0.167270i
$966$		0			0
$967$		−	39.6863i		−	1.27622i	−0.769943	−	0.638112i	$-0.779716\pi$
$967$		−	39.6863i		−	1.27622i	0.769943	−	0.638112i	$-0.220284\pi$
$968$	−9.58258	−	6.01450i	−0.307996	−	0.193313i
$969$		0			0
$970$	13.4347	+	16.4168i	0.431361	+	0.527110i
$971$	−2.29129	−	3.96863i	−0.0735309	−	0.127359i	0.826916	−	0.562326i	$-0.190093\pi$
$971$	−2.29129	−	3.96863i	−0.0735309	−	0.127359i	−0.900446	+	0.434967i	$0.856760\pi$
$972$		0			0
$973$	−21.0000	−	12.1244i	−0.673229	−	0.388689i
$974$	3.50000	+	1.32288i	0.112147	+	0.0423877i
$975$		0			0
$976$	−16.1216	+	38.3157i	−0.516040	+	1.22646i
$977$	−16.0000	+	27.7128i	−0.511885	+	0.886611i	0.488020	+	0.872833i	$0.337719\pi$
$977$	−16.0000	+	27.7128i	−0.511885	+	0.886611i	−0.999905	+	0.0137788i	$0.995614\pi$
$978$		0			0
$979$	27.4955			0.878759
$980$	−23.7695	−	4.79693i	−0.759289	−	0.153232i
$981$		0			0
$982$	−0.604356	−	3.69253i	−0.0192858	−	0.117833i
$983$	−22.9129	+	39.6863i	−0.730807	+	1.26580i	0.225731	+	0.974190i	$0.427523\pi$
$983$	−22.9129	+	39.6863i	−0.730807	+	1.26580i	−0.956539	+	0.291606i	$0.905810\pi$
$984$		0			0
$985$	21.0000	−	12.1244i	0.669116	−	0.386314i
$986$	45.8258	+	17.3205i	1.45939	+	0.551597i
$987$		0			0
$988$		0			0
$989$	28.0000	+	48.4974i	0.890348	+	1.54213i
$990$		0			0
$991$	−43.5345	−	25.1346i	−1.38292	−	0.798428i	−0.390414	−	0.920639i	$-0.627668\pi$
$991$	−43.5345	−	25.1346i	−1.38292	−	0.798428i	−0.992504	+	0.122211i	$0.961001\pi$
$992$	7.35208	+	24.8585i	0.233429	+	0.789259i
$993$		0			0
$994$	7.00000	−	18.5203i	0.222027	−	0.587427i
$995$		−	31.7490i		−	1.00651i
$996$		0			0
$997$	6.00000	+	3.46410i	0.190022	+	0.109709i	0.591993	−	0.805943i	$-0.298341\pi$
$997$	6.00000	+	3.46410i	0.190022	+	0.109709i	−0.401971	+	0.915652i	$0.631675\pi$
$998$	−5.79129	+	4.73930i	−0.183320	+	0.150020i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bf.d.199.2	yes	4
3.2	odd	2		252.2.bf.a.199.1	yes	4
4.3	odd	2	inner	252.2.bf.d.199.1	yes	4
7.3	odd	6		1764.2.b.b.1567.4		4
7.4	even	3		1764.2.b.b.1567.3		4
7.5	odd	6	inner	252.2.bf.d.19.1	yes	4
12.11	even	2		252.2.bf.a.199.2	yes	4
21.5	even	6		252.2.bf.a.19.2	yes	4
21.11	odd	6		1764.2.b.h.1567.2		4
21.17	even	6		1764.2.b.h.1567.1		4
28.3	even	6		1764.2.b.b.1567.2		4
28.11	odd	6		1764.2.b.b.1567.1		4
28.19	even	6	inner	252.2.bf.d.19.2	yes	4
84.11	even	6		1764.2.b.h.1567.4		4
84.47	odd	6		252.2.bf.a.19.1	✓	4
84.59	odd	6		1764.2.b.h.1567.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bf.a.19.1	✓	4	84.47	odd	6
252.2.bf.a.19.2	yes	4	21.5	even	6
252.2.bf.a.199.1	yes	4	3.2	odd	2
252.2.bf.a.199.2	yes	4	12.11	even	2
252.2.bf.d.19.1	yes	4	7.5	odd	6	inner
252.2.bf.d.19.2	yes	4	28.19	even	6	inner
252.2.bf.d.199.1	yes	4	4.3	odd	2	inner
252.2.bf.d.199.2	yes	4	1.1	even	1	trivial
1764.2.b.b.1567.1		4	28.11	odd	6
1764.2.b.b.1567.2		4	28.3	even	6
1764.2.b.b.1567.3		4	7.4	even	3
1764.2.b.b.1567.4		4	7.3	odd	6
1764.2.b.h.1567.1		4	21.17	even	6
1764.2.b.h.1567.2		4	21.11	odd	6
1764.2.b.h.1567.3		4	84.59	odd	6
1764.2.b.h.1567.4		4	84.11	even	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39564 - 0.228425i) q^{2} +(1.89564 - 0.637600i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(2.29129 + 1.32288i) q^{7} +(2.50000 - 1.32288i) q^{8} +O(q^{10})\)	\(q+(1.39564 - 0.228425i) q^{2} +(1.89564 - 0.637600i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(2.29129 + 1.32288i) q^{7} +(2.50000 - 1.32288i) q^{8} +(-1.89564 + 1.55130i) q^{10} +(2.29129 + 1.32288i) q^{11} -3.46410i q^{13} +(3.50000 + 1.32288i) q^{14} +(3.18693 - 2.41733i) q^{16} +(-6.00000 - 3.46410i) q^{17} +(-2.29129 + 2.59808i) q^{20} +(3.50000 + 1.32288i) q^{22} +(-4.58258 + 2.64575i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(-0.791288 - 4.83465i) q^{26} +(5.18693 + 1.04678i) q^{28} -5.00000 q^{29} +(-2.29129 + 3.96863i) q^{31} +(3.89564 - 4.10170i) q^{32} +(-9.16515 - 3.46410i) q^{34} -4.58258 q^{35} +(-2.60436 + 4.14938i) q^{40} +3.46410i q^{41} -10.5830i q^{43} +(5.18693 + 1.04678i) q^{44} +(-5.79129 + 4.73930i) q^{46} +(4.58258 + 7.93725i) q^{47} +(3.50000 + 6.06218i) q^{49} +(-1.00000 + 2.64575i) q^{50} +(-2.20871 - 6.56670i) q^{52} +(3.50000 - 6.06218i) q^{53} -4.58258 q^{55} +(7.47822 + 0.276100i) q^{56} +(-6.97822 + 1.14213i) q^{58} +(6.87386 - 11.9059i) q^{59} +(-9.00000 + 5.19615i) q^{61} +(-2.29129 + 6.06218i) q^{62} +(4.50000 - 6.61438i) q^{64} +(3.00000 + 5.19615i) q^{65} +(-13.5826 - 2.74110i) q^{68} +(-6.39564 + 1.04678i) q^{70} -5.29150i q^{71} +(-6.00000 - 3.46410i) q^{73} +(3.50000 + 6.06218i) q^{77} +(-6.87386 + 3.96863i) q^{79} +(-2.68693 + 6.38595i) q^{80} +(0.791288 + 4.83465i) q^{82} +4.58258 q^{83} +12.0000 q^{85} +(-2.41742 - 14.7701i) q^{86} +(7.47822 + 0.276100i) q^{88} +(9.00000 - 5.19615i) q^{89} +(4.58258 - 7.93725i) q^{91} +(-7.00000 + 7.93725i) q^{92} +(8.20871 + 10.0308i) q^{94} -8.66025i q^{97} +(6.26951 + 7.66115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 3 q^{4} - 6 q^{5} + 10 q^{8}+O(q^{10}) \) 4 * q + q^2 + 3 * q^4 - 6 * q^5 + 10 * q^8	\( 4 q + q^{2} + 3 q^{4} - 6 q^{5} + 10 q^{8} - 3 q^{10} + 14 q^{14} - q^{16} - 24 q^{17} + 14 q^{22} - 4 q^{25} + 6 q^{26} + 7 q^{28} - 20 q^{29} + 11 q^{32} - 15 q^{40} + 7 q^{44} - 14 q^{46} + 14 q^{49} - 4 q^{50} - 18 q^{52} + 14 q^{53} + 7 q^{56} - 5 q^{58} - 36 q^{61} + 18 q^{64} + 12 q^{65} - 36 q^{68} - 21 q^{70} - 24 q^{73} + 14 q^{77} + 3 q^{80} - 6 q^{82} + 48 q^{85} - 28 q^{86} + 7 q^{88} + 36 q^{89} - 28 q^{92} + 42 q^{94} - 7 q^{98}+O(q^{100}) \) 4 * q + q^2 + 3 * q^4 - 6 * q^5 + 10 * q^8 - 3 * q^10 + 14 * q^14 - q^16 - 24 * q^17 + 14 * q^22 - 4 * q^25 + 6 * q^26 + 7 * q^28 - 20 * q^29 + 11 * q^32 - 15 * q^40 + 7 * q^44 - 14 * q^46 + 14 * q^49 - 4 * q^50 - 18 * q^52 + 14 * q^53 + 7 * q^56 - 5 * q^58 - 36 * q^61 + 18 * q^64 + 12 * q^65 - 36 * q^68 - 21 * q^70 - 24 * q^73 + 14 * q^77 + 3 * q^80 - 6 * q^82 + 48 * q^85 - 28 * q^86 + 7 * q^88 + 36 * q^89 - 28 * q^92 + 42 * q^94 - 7 * q^98

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