LMFDB - Embedded newform 168.2.ba.a.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			101.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.621320 + 0.358719i) q^{5} +2.44949i q^{6} +(-2.62132 - 0.358719i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.621320 + 0.358719i) q^{5} +2.44949i q^{6} +(-2.62132 - 0.358719i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.878680 + 0.507306i) q^{10} +(-2.91421 + 5.04757i) q^{11} +(3.00000 - 1.73205i) q^{12} +(1.41421 + 3.46410i) q^{14} +1.24264 q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.12132 - 3.67423i) q^{18} -1.43488i q^{20} +(3.62132 + 2.80821i) q^{21} +8.24264 q^{22} +(-4.24264 - 2.44949i) q^{24} +(-2.24264 + 3.88437i) q^{25} -5.19615i q^{27} +(3.24264 - 4.18154i) q^{28} -7.58579 q^{29} +(-0.878680 - 1.52192i) q^{30} +(-9.62132 - 5.55487i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.74264 - 5.04757i) q^{33} +(1.75736 - 0.717439i) q^{35} -6.00000 q^{36} +(-1.75736 + 1.01461i) q^{40} +(0.878680 - 6.42090i) q^{42} +(-5.82843 - 10.0951i) q^{44} +(-1.86396 - 1.07616i) q^{45} +6.92820i q^{48} +(6.74264 + 1.88064i) q^{49} +6.34315 q^{50} +(2.03553 - 3.52565i) q^{53} +(-6.36396 + 3.67423i) q^{54} -4.18154i q^{55} +(-7.41421 - 1.01461i) q^{56} +(5.36396 + 9.29065i) q^{58} +(12.9853 + 7.49706i) q^{59} +(-1.24264 + 2.15232i) q^{60} +15.7116i q^{62} +(-3.00000 - 7.34847i) q^{63} +8.00000 q^{64} +(-12.3640 - 7.13834i) q^{66} +(-2.12132 - 1.64501i) q^{70} +(4.24264 + 7.34847i) q^{72} +(-8.48528 - 4.89898i) q^{73} +(6.72792 - 3.88437i) q^{75} +(9.44975 - 12.1859i) q^{77} +(8.86396 + 15.3528i) q^{79} +(2.48528 + 1.43488i) q^{80} +(-4.50000 + 7.79423i) q^{81} -13.5592i q^{83} +(-8.48528 + 3.46410i) q^{84} +(11.3787 + 6.56948i) q^{87} +(-8.24264 + 14.2767i) q^{88} +3.04384i q^{90} +(9.62132 + 16.6646i) q^{93} +(8.48528 - 4.89898i) q^{96} +8.06591i q^{97} +(-2.46447 - 9.58783i) q^{98} -17.4853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 - 4 * q^4 + 6 * q^5 - 2 * q^7 + 6 * q^9	$ 4 q - 6 q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{7} + 6 q^{9} + 12 q^{10} - 6 q^{11} + 12 q^{12} - 12 q^{15} - 8 q^{16} + 6 q^{21} + 16 q^{22} + 8 q^{25} - 4 q^{28} - 36 q^{29} - 12 q^{30} - 30 q^{31} + 18 q^{33} + 24 q^{35} - 24 q^{36} - 24 q^{40} + 12 q^{42} - 12 q^{44} + 18 q^{45} + 10 q^{49} + 48 q^{50} - 6 q^{53} - 24 q^{56} - 4 q^{58} + 18 q^{59} + 12 q^{60} - 12 q^{63} + 32 q^{64} - 24 q^{66} - 24 q^{75} + 18 q^{77} + 10 q^{79} - 24 q^{80} - 18 q^{81} + 54 q^{87} - 16 q^{88} + 30 q^{93} - 24 q^{98} - 36 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 4 * q^4 + 6 * q^5 - 2 * q^7 + 6 * q^9 + 12 * q^10 - 6 * q^11 + 12 * q^12 - 12 * q^15 - 8 * q^16 + 6 * q^21 + 16 * q^22 + 8 * q^25 - 4 * q^28 - 36 * q^29 - 12 * q^30 - 30 * q^31 + 18 * q^33 + 24 * q^35 - 24 * q^36 - 24 * q^40 + 12 * q^42 - 12 * q^44 + 18 * q^45 + 10 * q^49 + 48 * q^50 - 6 * q^53 - 24 * q^56 - 4 * q^58 + 18 * q^59 + 12 * q^60 - 12 * q^63 + 32 * q^64 - 24 * q^66 - 24 * q^75 + 18 * q^77 + 10 * q^79 - 24 * q^80 - 18 * q^81 + 54 * q^87 - 16 * q^88 + 30 * q^93 - 24 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	−0.621320	+	0.358719i	−0.277863	+	0.160424i	−0.632456	−	0.774597i	$-0.717953\pi$
$5$	−0.621320	+	0.358719i	−0.277863	+	0.160424i	0.354593	+	0.935021i	$0.384620\pi$
$6$			2.44949i			1.00000i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$	2.82843			1.00000
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	0.878680	+	0.507306i	0.277863	+	0.160424i
$11$	−2.91421	+	5.04757i	−0.878668	+	1.52190i	−0.0258656	+	0.999665i	$0.508234\pi$
$11$	−2.91421	+	5.04757i	−0.878668	+	1.52190i	−0.852803	+	0.522233i	$0.825099\pi$
$12$	3.00000	−	1.73205i	0.866025	−	0.500000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	1.41421	+	3.46410i	0.377964	+	0.925820i
$15$	1.24264			0.320848
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	2.12132	−	3.67423i	0.500000	−	0.866025i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		−	1.43488i		−	0.320848i
$21$	3.62132	+	2.80821i	0.790237	+	0.612801i
$22$	8.24264			1.75734
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−4.24264	−	2.44949i	−0.866025	−	0.500000i
$25$	−2.24264	+	3.88437i	−0.448528	+	0.776874i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$	3.24264	−	4.18154i	0.612801	−	0.790237i
$29$	−7.58579			−1.40865			−0.704323	−	0.709880i	$-0.748749\pi$
$29$	−7.58579			−1.40865			−0.704323	+	0.709880i	$0.748749\pi$
$30$	−0.878680	−	1.52192i	−0.160424	−	0.277863i
$31$	−9.62132	−	5.55487i	−1.72804	−	0.997684i	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−9.62132	−	5.55487i	−1.72804	−	0.997684i	−0.830014	−	0.557743i	$-0.811667\pi$
$32$	−2.82843	+	4.89898i	−0.500000	+	0.866025i
$33$	8.74264	−	5.04757i	1.52190	−	0.878668i
$34$		0			0
$35$	1.75736	−	0.717439i	0.297048	−	0.121269i
$36$	−6.00000			−1.00000
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$		0			0
$40$	−1.75736	+	1.01461i	−0.277863	+	0.160424i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	0.878680	−	6.42090i	0.135583	−	0.990766i
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−5.82843	−	10.0951i	−0.878668	−	1.52190i
$45$	−1.86396	−	1.07616i	−0.277863	−	0.160424i
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$			6.92820i			1.00000i
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$	6.34315			0.897056
$51$		0			0
$52$		0			0
$53$	2.03553	−	3.52565i	0.279602	−	0.484285i	−0.691684	−	0.722200i	$-0.743131\pi$
$53$	2.03553	−	3.52565i	0.279602	−	0.484285i	0.971286	+	0.237915i	$0.0764641\pi$
$54$	−6.36396	+	3.67423i	−0.866025	+	0.500000i
$55$		−	4.18154i		−	0.563839i
$56$	−7.41421	−	1.01461i	−0.990766	−	0.135583i
$57$		0			0
$58$	5.36396	+	9.29065i	0.704323	+	1.21992i
$59$	12.9853	+	7.49706i	1.69054	+	0.976034i	0.954080	+	0.299552i	$0.0968372\pi$
$59$	12.9853	+	7.49706i	1.69054	+	0.976034i	0.736460	+	0.676481i	$0.236496\pi$
$60$	−1.24264	+	2.15232i	−0.160424	+	0.277863i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$			15.7116i			1.99537i
$63$	−3.00000	−	7.34847i	−0.377964	−	0.925820i
$64$	8.00000			1.00000
$65$		0			0
$66$	−12.3640	−	7.13834i	−1.52190	−	0.878668i
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$		0			0
$70$	−2.12132	−	1.64501i	−0.253546	−	0.196616i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	4.24264	+	7.34847i	0.500000	+	0.866025i
$73$	−8.48528	−	4.89898i	−0.993127	−	0.573382i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	−8.48528	−	4.89898i	−0.993127	−	0.573382i	−0.906208	+	0.422833i	$0.861036\pi$
$74$		0			0
$75$	6.72792	−	3.88437i	0.776874	−	0.448528i
$76$		0			0
$77$	9.44975	−	12.1859i	1.07690	−	1.38871i
$78$		0			0
$79$	8.86396	+	15.3528i	0.997274	+	1.72733i	0.562544	+	0.826767i	$0.309823\pi$
$79$	8.86396	+	15.3528i	0.997274	+	1.72733i	0.434730	+	0.900561i	$0.356844\pi$
$80$	2.48528	+	1.43488i	0.277863	+	0.160424i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$		−	13.5592i		−	1.48832i	−0.668002	−	0.744160i	$-0.732850\pi$
$83$		−	13.5592i		−	1.48832i	0.668002	−	0.744160i	$-0.267150\pi$
$84$	−8.48528	+	3.46410i	−0.925820	+	0.377964i
$85$		0			0
$86$		0			0
$87$	11.3787	+	6.56948i	1.21992	+	0.704323i
$88$	−8.24264	+	14.2767i	−0.878668	+	1.52190i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$			3.04384i			0.320848i
$91$		0			0
$92$		0			0
$93$	9.62132	+	16.6646i	0.997684	+	1.72804i
$94$		0			0
$95$		0			0
$96$	8.48528	−	4.89898i	0.866025	−	0.500000i
$97$			8.06591i			0.818969i	0.912317	+	0.409484i	$0.134291\pi$
$97$			8.06591i			0.818969i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−2.46447	−	9.58783i	−0.248949	−	0.968517i
$99$	−17.4853			−1.75734
$100$	−4.48528	−	7.76874i	−0.448528	−	0.776874i
$101$	−3.00000	−	1.73205i	−0.298511	−	0.172345i	0.343263	−	0.939239i	$-0.388468\pi$
$101$	−3.00000	−	1.73205i	−0.298511	−	0.172345i	−0.641774	+	0.766894i	$0.721801\pi$
$102$		0			0
$103$	−12.7279	+	7.34847i	−1.25412	+	0.724066i	−0.971925	−	0.235291i	$-0.924396\pi$
$103$	−12.7279	+	7.34847i	−1.25412	+	0.724066i	−0.282194	+	0.959357i	$0.591062\pi$
$104$		0			0
$105$	−3.25736	−	0.445759i	−0.317886	−	0.0435017i
$106$	−5.75736			−0.559204
$107$	4.67157	+	8.09140i	0.451618	+	0.782225i	0.998487	−	0.0549930i	$-0.0175137\pi$
$107$	4.67157	+	8.09140i	0.451618	+	0.782225i	−0.546869	+	0.837218i	$0.684180\pi$
$108$	9.00000	+	5.19615i	0.866025	+	0.500000i
$109$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$109$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$110$	−5.12132	+	2.95680i	−0.488299	+	0.281919i
$111$		0			0
$112$	4.00000	+	9.79796i	0.377964	+	0.925820i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$		0			0
$116$	7.58579	−	13.1390i	0.704323	−	1.21992i
$117$		0			0
$118$		−	21.2049i		−	1.95207i
$119$		0			0
$120$	3.51472			0.320848
$121$	−11.4853	−	19.8931i	−1.04412	−	1.80846i
$122$		0			0
$123$		0			0
$124$	19.2426	−	11.1097i	1.72804	−	0.997684i
$125$		−	6.80511i		−	0.608668i
$126$	−6.87868	+	8.87039i	−0.612801	+	0.790237i
$127$	15.2426			1.35257			0.676283	−	0.736642i	$-0.263590\pi$
$127$	15.2426			1.35257			0.676283	+	0.736642i	$0.263590\pi$
$128$	−5.65685	−	9.79796i	−0.500000	−	0.866025i
$129$		0			0
$130$		0			0
$131$	−15.4706	+	8.93193i	−1.35167	+	0.780387i	−0.988483	−	0.151330i	$-0.951644\pi$
$131$	−15.4706	+	8.93193i	−1.35167	+	0.780387i	−0.363186	+	0.931717i	$0.618311\pi$
$132$			20.1903i			1.75734i
$133$		0			0
$134$		0			0
$135$	1.86396	+	3.22848i	0.160424	+	0.277863i
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−0.514719	+	3.76127i	−0.0435017	+	0.317886i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	6.00000	−	10.3923i	0.500000	−	0.866025i
$145$	4.71320	−	2.72117i	0.391410	−	0.225981i
$146$			13.8564i			1.14676i
$147$	−8.48528	−	8.66025i	−0.699854	−	0.714286i
$148$		0			0
$149$	−1.41421	−	2.44949i	−0.115857	−	0.200670i	0.802265	−	0.596968i	$-0.203628\pi$
$149$	−1.41421	−	2.44949i	−0.115857	−	0.200670i	−0.918122	+	0.396298i	$0.870295\pi$
$150$	−9.51472	−	5.49333i	−0.776874	−	0.448528i
$151$	10.1066	−	17.5051i	0.822464	−	1.42455i	−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	10.1066	−	17.5051i	0.822464	−	1.42455i	0.903842	−	0.427865i	$-0.140734\pi$
$152$		0			0
$153$		0			0
$154$	−21.6066	−	2.95680i	−1.74111	−	0.238265i
$155$	7.97056			0.640211
$156$		0			0
$157$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$157$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$158$	12.5355	−	21.7122i	0.997274	−	1.72733i
$159$	−6.10660	+	3.52565i	−0.484285	+	0.279602i
$160$		−	4.05845i		−	0.320848i
$161$		0			0
$162$	12.7279			1.00000
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$		0			0
$165$	−3.62132	+	6.27231i	−0.281919	+	0.488299i
$166$	−16.6066	+	9.58783i	−1.28892	+	0.744160i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	10.2426	+	7.94282i	0.790237	+	0.612801i
$169$	−13.0000			−1.00000
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−15.0000	+	8.66025i	−1.14043	+	0.658427i	−0.946537	−	0.322596i	$-0.895445\pi$
$173$	−15.0000	+	8.66025i	−1.14043	+	0.658427i	−0.193892	+	0.981023i	$0.562111\pi$
$174$		−	18.5813i		−	1.40865i
$175$	7.27208	−	9.37769i	0.549717	−	0.708887i
$176$	23.3137			1.75734
$177$	−12.9853	−	22.4912i	−0.976034	−	1.69054i
$178$		0			0
$179$	−5.65685	+	9.79796i	−0.422813	+	0.732334i	−0.996213	−	0.0869415i	$-0.972291\pi$
$179$	−5.65685	+	9.79796i	−0.422813	+	0.732334i	0.573400	+	0.819275i	$0.305624\pi$
$180$	3.72792	−	2.15232i	0.277863	−	0.160424i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	13.6066	−	23.5673i	0.997684	−	1.72804i
$187$		0			0
$188$		0			0
$189$	−1.86396	+	13.6208i	−0.135583	+	0.990766i
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	−12.0000	−	6.92820i	−0.866025	−	0.500000i
$193$	2.25736	−	3.90986i	0.162488	−	0.281438i	−0.773272	−	0.634074i	$-0.781381\pi$
$193$	2.25736	−	3.90986i	0.162488	−	0.281438i	0.935760	+	0.352636i	$0.114715\pi$
$194$	9.87868	−	5.70346i	0.709248	−	0.409484i
$195$		0			0
$196$	−10.0000	+	9.79796i	−0.714286	+	0.699854i
$197$	−14.1421			−1.00759			−0.503793	−	0.863825i	$-0.668062\pi$
$197$	−14.1421			−1.00759			−0.503793	+	0.863825i	$0.668062\pi$
$198$	12.3640	+	21.4150i	0.878668	+	1.52190i
$199$	21.2132	+	12.2474i	1.50376	+	0.868199i	0.999990	+	0.00436292i	$0.00138876\pi$
$199$	21.2132	+	12.2474i	1.50376	+	0.868199i	0.503774	+	0.863836i	$0.331945\pi$
$200$	−6.34315	+	10.9867i	−0.448528	+	0.776874i
$201$		0			0
$202$			4.89898i			0.344691i
$203$	19.8848	+	2.72117i	1.39564	+	0.190989i
$204$		0			0
$205$		0			0
$206$	18.0000	+	10.3923i	1.25412	+	0.724066i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	1.75736	+	4.30463i	0.121269	+	0.297048i
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$	4.07107	+	7.05130i	0.279602	+	0.484285i
$213$		0			0
$214$	6.60660	−	11.4430i	0.451618	−	0.782225i
$215$		0			0
$216$		−	14.6969i		−	1.00000i
$217$	23.2279	+	18.0125i	1.57681	+	1.22277i
$218$		0			0
$219$	8.48528	+	14.6969i	0.573382	+	0.993127i
$220$	7.24264	+	4.18154i	0.488299	+	0.281919i
$221$		0			0
$222$		0			0
$223$			15.1682i			1.01574i	0.861435	+	0.507869i	$0.169566\pi$
$223$			15.1682i			1.01574i	−0.861435	+	0.507869i	$0.830434\pi$
$224$	9.17157	−	11.8272i	0.612801	−	0.790237i
$225$	−13.4558			−0.897056
$226$		0			0
$227$	−16.7132	−	9.64937i	−1.10929	−	0.640451i	−0.170648	−	0.985332i	$-0.554586\pi$
$227$	−16.7132	−	9.64937i	−1.10929	−	0.640451i	−0.938647	+	0.344881i	$0.887919\pi$
$228$		0			0
$229$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$229$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$230$		0			0
$231$	−24.7279	+	10.0951i	−1.62698	+	0.664211i
$232$	−21.4558			−1.40865
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$		0			0
$235$		0			0
$236$	−25.9706	+	14.9941i	−1.69054	+	0.976034i
$237$		−	30.7057i		−	1.99455i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−2.48528	−	4.30463i	−0.160424	−	0.277863i
$241$	5.22792	+	3.01834i	0.336760	+	0.194429i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	5.22792	+	3.01834i	0.336760	+	0.194429i	−0.322078	+	0.946713i	$0.604381\pi$
$242$	−16.2426	+	28.1331i	−1.04412	+	1.80846i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$		0			0
$245$	−4.86396	+	1.25024i	−0.310747	+	0.0798748i
$246$		0			0
$247$		0			0
$248$	−27.2132	−	15.7116i	−1.72804	−	0.997684i
$249$	−11.7426	+	20.3389i	−0.744160	+	1.28892i
$250$	−8.33452	+	4.81194i	−0.527122	+	0.304334i
$251$			10.6895i			0.674714i	0.941377	+	0.337357i	$0.109533\pi$
$251$			10.6895i			0.674714i	−0.941377	+	0.337357i	$0.890467\pi$
$252$	15.7279	+	2.15232i	0.990766	+	0.135583i
$253$		0			0
$254$	−10.7782	−	18.6683i	−0.676283	−	1.17136i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−11.3787	−	19.7085i	−0.704323	−	1.21992i
$262$	21.8787	+	12.6317i	1.35167	+	0.780387i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	24.7279	−	14.2767i	1.52190	−	0.878668i
$265$			2.92074i			0.179420i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	27.8345	+	16.0703i	1.69710	+	0.979822i	0.948487	+	0.316815i	$0.102613\pi$
$269$	27.8345	+	16.0703i	1.69710	+	0.979822i	0.748614	+	0.663007i	$0.230720\pi$
$270$	2.63604	−	4.56575i	0.160424	−	0.277863i
$271$	−27.1066	+	15.6500i	−1.64661	+	0.950670i	−0.668202	+	0.743980i	$0.732936\pi$
$271$	−27.1066	+	15.6500i	−1.64661	+	0.950670i	−0.978406	+	0.206691i	$0.933731\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−13.0711	−	22.6398i	−0.788215	−	1.36523i
$276$		0			0
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		−	33.3292i		−	1.99537i
$280$	4.97056	−	2.02922i	0.297048	−	0.121269i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		0			0
$283$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$283$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−16.9706			−1.00000
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−6.66548	−	3.84831i	−0.391410	−	0.225981i
$291$	6.98528	−	12.0989i	0.409484	−	0.709248i
$292$	16.9706	−	9.79796i	0.993127	−	0.573382i
$293$			27.8359i			1.62619i	0.582130	+	0.813095i	$0.302219\pi$
$293$			27.8359i			1.62619i	−0.582130	+	0.813095i	$0.697781\pi$
$294$	−4.60660	+	16.5160i	−0.268662	+	0.963234i
$295$	−10.7574			−0.626318
$296$		0			0
$297$	26.2279	+	15.1427i	1.52190	+	0.878668i
$298$	−2.00000	+	3.46410i	−0.115857	+	0.200670i
$299$		0			0
$300$			15.5375i			0.897056i
$301$		0			0
$302$	−28.5858			−1.64493
$303$	3.00000	+	5.19615i	0.172345	+	0.298511i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	11.6569	+	28.5533i	0.664211	+	1.62698i
$309$	25.4558			1.44813
$310$	−5.63604	−	9.76191i	−0.320106	−	0.554439i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	29.7426	−	17.1719i	1.68115	−	0.970614i	0.720257	−	0.693708i	$-0.244024\pi$
$313$	29.7426	−	17.1719i	1.68115	−	0.970614i	0.960897	−	0.276907i	$-0.0893093\pi$
$314$		0			0
$315$	4.50000	+	3.48960i	0.253546	+	0.196616i
$316$	−35.4558			−1.99455
$317$	−0.278175	−	0.481813i	−0.0156238	−	0.0270613i	0.858108	−	0.513470i	$-0.171640\pi$
$317$	−0.278175	−	0.481813i	−0.0156238	−	0.0270613i	−0.873732	+	0.486408i	$0.838307\pi$
$318$	8.63604	+	4.98602i	0.484285	+	0.279602i
$319$	22.1066	−	38.2898i	1.23773	−	2.14381i
$320$	−4.97056	+	2.86976i	−0.277863	+	0.160424i
$321$		−	16.1828i		−	0.903236i
$322$		0			0
$323$		0			0
$324$	−9.00000	−	15.5885i	−0.500000	−	0.866025i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	10.2426			0.563839
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	23.4853	+	13.5592i	1.28892	+	0.744160i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	2.48528	−	18.1610i	0.135583	−	0.990766i
$337$	−14.4558			−0.787460			−0.393730	−	0.919226i	$-0.628816\pi$
$337$	−14.4558			−0.787460			−0.393730	+	0.919226i	$0.628816\pi$
$338$	9.19239	+	15.9217i	0.500000	+	0.866025i
$339$		0			0
$340$		0			0
$341$	56.0772	−	32.3762i	3.03675	−	1.75327i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$		0			0
$345$		0			0
$346$	21.2132	+	12.2474i	1.14043	+	0.658427i
$347$	14.1421	−	24.4949i	0.759190	−	1.31495i	−0.184075	−	0.982912i	$-0.558929\pi$
$347$	14.1421	−	24.4949i	0.759190	−	1.31495i	0.943264	−	0.332043i	$-0.107738\pi$
$348$	−22.7574	+	13.1390i	−1.21992	+	0.704323i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	−16.6274	−	2.27541i	−0.888773	−	0.121626i
$351$		0			0
$352$	−16.4853	−	28.5533i	−0.878668	−	1.52190i
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$	−18.3640	+	31.8073i	−0.976034	+	1.69054i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	16.0000			0.845626
$359$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$359$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$360$	−5.27208	−	3.04384i	−0.277863	−	0.160424i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$		0			0
$363$			39.7862i			2.08823i
$364$		0			0
$365$	7.02944			0.367938
$366$		0			0
$367$	−30.6213	−	17.6792i	−1.59842	−	0.922848i	−0.991792	−	0.127862i	$-0.959188\pi$
$367$	−30.6213	−	17.6792i	−1.59842	−	0.922848i	−0.606628	−	0.794986i	$-0.707478\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.60051	+	8.51167i	−0.342681	+	0.441904i
$372$	−38.4853			−1.99537
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	−5.89340	+	10.2077i	−0.304334	+	0.527122i
$376$		0			0
$377$		0			0
$378$	18.0000	−	7.34847i	0.925820	−	0.377964i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	−22.8640	−	13.2005i	−1.17136	−	0.676283i
$382$		0			0
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$			19.5959i			1.00000i
$385$	−1.50000	+	10.9612i	−0.0764471	+	0.558632i
$386$	−6.38478			−0.324977
$387$		0			0
$388$	−13.9706	−	8.06591i	−0.709248	−	0.409484i
$389$	−15.5563	+	26.9444i	−0.788738	+	1.36613i	0.138002	+	0.990432i	$0.455932\pi$
$389$	−15.5563	+	26.9444i	−0.788738	+	1.36613i	−0.926740	+	0.375703i	$0.877401\pi$
$390$		0			0
$391$		0			0
$392$	19.0711	+	5.31925i	0.963234	+	0.268662i
$393$	30.9411			1.56077
$394$	10.0000	+	17.3205i	0.503793	+	0.872595i
$395$	−11.0147	−	6.35935i	−0.554211	−	0.319974i
$396$	17.4853	−	30.2854i	0.878668	−	1.52190i
$397$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$397$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$398$		−	34.6410i		−	1.73640i
$399$		0			0
$400$	17.9411			0.897056
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$		0			0
$404$	6.00000	−	3.46410i	0.298511	−	0.172345i
$405$		−	6.45695i		−	0.320848i
$406$	−10.7279	−	26.2779i	−0.532418	−	1.30415i
$407$		0			0
$408$		0			0
$409$	−24.4706	−	14.1281i	−1.20999	−	0.698589i	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−24.4706	−	14.1281i	−1.20999	−	0.698589i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		0			0
$411$		0			0
$412$		−	29.3939i		−	1.44813i
$413$	−31.3492	−	24.3103i	−1.54260	−	1.19623i
$414$		0			0
$415$	4.86396	+	8.42463i	0.238762	+	0.413549i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	10.3923i		−	0.507697i	−0.967244	−	0.253849i	$-0.918303\pi$
$419$		−	10.3923i		−	0.507697i	0.967244	−	0.253849i	$-0.0816965\pi$
$420$	4.02944	−	5.19615i	0.196616	−	0.253546i
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		0			0
$423$		0			0
$424$	5.75736	−	9.97204i	0.279602	−	0.484285i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−18.6863			−0.903236
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	−18.0000	+	10.3923i	−0.866025	+	0.500000i
$433$			39.1918i			1.88344i	0.336399	+	0.941720i	$0.390791\pi$
$433$			39.1918i			1.88344i	−0.336399	+	0.941720i	$0.609209\pi$
$434$	5.63604	−	41.1850i	0.270539	−	1.97694i
$435$	−9.42641			−0.451962
$436$		0			0
$437$		0			0
$438$	12.0000	−	20.7846i	0.573382	−	0.993127i
$439$	14.8934	−	8.59871i	0.710823	−	0.410394i	−0.100543	−	0.994933i	$-0.532058\pi$
$439$	14.8934	−	8.59871i	0.710823	−	0.410394i	0.811366	+	0.584539i	$0.198725\pi$
$440$		−	11.8272i		−	0.563839i
$441$	5.22792	+	20.3389i	0.248949	+	0.968517i
$442$		0			0
$443$	−6.42893	−	11.1352i	−0.305448	−	0.529051i	0.671913	−	0.740630i	$-0.265473\pi$
$443$	−6.42893	−	11.1352i	−0.305448	−	0.529051i	−0.977361	+	0.211579i	$0.932139\pi$
$444$		0			0
$445$		0			0
$446$	18.5772	−	10.7255i	0.879654	−	0.507869i
$447$			4.89898i			0.231714i
$448$	−20.9706	−	2.86976i	−0.990766	−	0.135583i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	9.51472	+	16.4800i	0.448528	+	0.776874i
$451$		0			0
$452$		0			0
$453$	−30.3198	+	17.5051i	−1.42455	+	0.822464i
$454$			27.2925i			1.28090i
$455$		0			0
$456$		0			0
$457$	1.01472	+	1.75754i	0.0474665	+	0.0822145i	0.888783	−	0.458329i	$-0.151552\pi$
$457$	1.01472	+	1.75754i	0.0474665	+	0.0822145i	−0.841316	+	0.540544i	$0.818219\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			38.1051i			1.77473i	0.461065	+	0.887366i	$0.347467\pi$
$461$			38.1051i			1.77473i	−0.461065	+	0.887366i	$0.652533\pi$
$462$	29.8492	+	23.1471i	1.38871	+	1.07690i
$463$	−26.0000			−1.20832			−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000			−1.20832			−0.604161	+	0.796862i	$0.706492\pi$
$464$	15.1716	+	26.2779i	0.704323	+	1.21992i
$465$	−11.9558	−	6.90271i	−0.554439	−	0.320106i
$466$		0			0
$467$	−15.0000	+	8.66025i	−0.694117	+	0.400749i	−0.805153	−	0.593068i	$-0.797917\pi$
$467$	−15.0000	+	8.66025i	−0.694117	+	0.400749i	0.111035	+	0.993816i	$0.464583\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	36.7279	+	21.2049i	1.69054	+	0.976034i
$473$		0			0
$474$	−37.6066	+	21.7122i	−1.72733	+	0.997274i
$475$		0			0
$476$		0			0
$477$	12.2132			0.559204
$478$		0			0
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	−3.51472	+	6.08767i	−0.160424	+	0.277863i
$481$		0			0
$482$		−	8.53716i		−	0.388857i
$483$		0			0
$484$	45.9411			2.08823
$485$	−2.89340	−	5.01151i	−0.131382	−	0.227561i
$486$	−19.0919	−	11.0227i	−0.866025	−	0.500000i
$487$	−19.5919	+	33.9341i	−0.887793	+	1.53770i	−0.0453143	+	0.998973i	$0.514429\pi$
$487$	−19.5919	+	33.9341i	−0.887793	+	1.53770i	−0.842479	+	0.538730i	$0.818904\pi$
$488$		0			0
$489$		0			0
$490$	4.97056	+	5.07306i	0.224547	+	0.229177i
$491$	44.3137			1.99985			0.999925	−	0.0122607i	$-0.00390281\pi$
$491$	44.3137			1.99985			0.999925	+	0.0122607i	$0.00390281\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	10.8640	−	6.27231i	0.488299	−	0.281919i
$496$			44.4390i			1.99537i
$497$		0			0
$498$	33.2132			1.48832
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	11.7868	+	6.80511i	0.527122	+	0.304334i
$501$		0			0
$502$	13.0919	−	7.55860i	0.584319	−	0.337357i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−8.48528	−	20.7846i	−0.377964	−	0.925820i
$505$	2.48528			0.110594
$506$		0			0
$507$	19.5000	+	11.2583i	0.866025	+	0.500000i
$508$	−15.2426	+	26.4010i	−0.676283	+	1.17136i
$509$	−21.6213	+	12.4831i	−0.958348	+	0.553303i	−0.895664	−	0.444731i	$-0.853299\pi$
$509$	−21.6213	+	12.4831i	−0.958348	+	0.553303i	−0.0626839	+	0.998033i	$0.519966\pi$
$510$		0			0
$511$	20.4853	+	15.8856i	0.906215	+	0.702739i
$512$	22.6274			1.00000
$513$		0			0
$514$		0			0
$515$	5.27208	−	9.13151i	0.232316	−	0.402382i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	30.0000			1.31685
$520$		0			0
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$	−16.0919	+	27.8720i	−0.704323	+	1.21992i
$523$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$523$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$524$		−	35.7277i		−	1.56077i
$525$	−19.0294	+	7.76874i	−0.830513	+	0.339055i
$526$		0			0
$527$		0			0
$528$	−34.9706	−	20.1903i	−1.52190	−	0.878668i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$	3.57716	−	2.06528i	0.155382	−	0.0897099i
$531$			44.9823i			1.95207i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−5.80509	−	3.35157i	−0.250976	−	0.144901i
$536$		0			0
$537$	16.9706	−	9.79796i	0.732334	−	0.422813i
$538$		−	45.4536i		−	1.95964i
$539$	−29.1421	+	28.5533i	−1.25524	+	1.22988i
$540$	−7.45584			−0.320848
$541$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$541$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$542$	38.3345	+	22.1324i	1.64661	+	0.950670i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		0			0
$549$		0			0
$550$	−18.4853	+	32.0174i	−0.788215	+	1.36523i
$551$		0			0
$552$		0			0
$553$	−17.7279	−	43.4244i	−0.753868	−	1.84659i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	23.0355	−	39.8987i	0.976047	−	1.69056i	0.299611	−	0.954062i	$-0.403143\pi$
$557$	23.0355	−	39.8987i	0.976047	−	1.69056i	0.676436	−	0.736501i	$-0.263523\pi$
$558$	−40.8198	+	23.5673i	−1.72804	+	0.997684i
$559$		0			0
$560$	−6.00000	−	4.65279i	−0.253546	−	0.196616i
$561$		0			0
$562$		0			0
$563$	−37.7132	−	21.7737i	−1.58942	−	0.917653i	−0.993402	−	0.114684i	$-0.963415\pi$
$563$	−37.7132	−	21.7737i	−1.58942	−	0.917653i	−0.596020	−	0.802970i	$-0.703252\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	14.5919	−	18.8169i	0.612801	−	0.790237i
$568$		0			0
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$		0			0
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	12.0000	+	20.7846i	0.500000	+	0.866025i
$577$	−15.7721	−	9.10601i	−0.656600	−	0.379088i	0.134380	−	0.990930i	$-0.457096\pi$
$577$	−15.7721	−	9.10601i	−0.656600	−	0.379088i	−0.790980	+	0.611842i	$0.790429\pi$
$578$	12.0208	−	20.8207i	0.500000	−	0.866025i
$579$	−6.77208	+	3.90986i	−0.281438	+	0.162488i
$580$			10.8847i			0.451962i
$581$	−4.86396	+	35.5431i	−0.201791	+	1.47458i
$582$	−19.7574			−0.818969
$583$	11.8640	+	20.5490i	0.491355	+	0.851052i
$584$	−24.0000	−	13.8564i	−0.993127	−	0.573382i
$585$		0			0
$586$	34.0919	−	19.6830i	1.40832	−	0.813095i
$587$		−	47.8521i		−	1.97507i	−0.157409	−	0.987534i	$-0.550314\pi$
$587$		−	47.8521i		−	1.97507i	0.157409	−	0.987534i	$-0.449686\pi$
$588$	23.4853	−	6.03668i	0.968517	−	0.248949i
$589$		0			0
$590$	7.60660	+	13.1750i	0.313159	+	0.542407i
$591$	21.2132	+	12.2474i	0.872595	+	0.503793i
$592$		0			0
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		−	42.8300i		−	1.75734i
$595$		0			0
$596$	5.65685			0.231714
$597$	−21.2132	−	36.7423i	−0.868199	−	1.50376i
$598$		0			0
$599$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$599$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$600$	19.0294	−	10.9867i	0.776874	−	0.448528i
$601$		−	26.2269i		−	1.06982i	−0.844909	−	0.534910i	$-0.820346\pi$
$601$		−	26.2269i		−	1.06982i	0.844909	−	0.534910i	$-0.179654\pi$
$602$		0			0
$603$		0			0
$604$	20.2132	+	35.0103i	0.822464	+	1.42455i
$605$	14.2721	+	8.23999i	0.580242	+	0.335003i
$606$	4.24264	−	7.34847i	0.172345	−	0.298511i
$607$	2.59188	−	1.49642i	0.105201	−	0.0607380i	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	2.59188	−	1.49642i	0.105201	−	0.0607380i	0.551678	+	0.834058i	$0.313988\pi$
$608$		0			0
$609$	−27.4706	−	21.3025i	−1.11316	−	0.863220i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$613$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$614$		0			0
$615$		0			0
$616$	26.7279	−	34.4669i	1.07690	−	1.38871i
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$	−18.0000	−	31.1769i	−0.724066	−	1.25412i
$619$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$619$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$620$	−7.97056	+	13.8054i	−0.320106	+	0.554439i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−8.77208	−	15.1937i	−0.350883	−	0.607747i
$626$	−42.0624	−	24.2848i	−1.68115	−	0.970614i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	1.09188	−	7.97887i	0.0435017	−	0.317886i
$631$	29.2426			1.16413			0.582066	−	0.813142i	$-0.302245\pi$
$631$	29.2426			1.16413			0.582066	+	0.813142i	$0.302245\pi$
$632$	25.0711	+	43.4244i	0.997274	+	1.72733i
$633$		0			0
$634$	−0.393398	+	0.681386i	−0.0156238	+	0.0270613i
$635$	−9.47056	+	5.46783i	−0.375828	+	0.216984i
$636$		−	14.1026i		−	0.559204i
$637$		0			0
$638$	−62.5269			−2.47546
$639$		0			0
$640$	7.02944	+	4.05845i	0.277863	+	0.160424i
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	−19.8198	+	11.4430i	−0.782225	+	0.451618i
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−12.7279	+	22.0454i	−0.500000	+	0.866025i
$649$	−75.6838	+	43.6960i	−2.97085	+	1.71522i
$650$		0			0
$651$	−19.2426	−	47.1347i	−0.754179	−	1.84735i
$652$		0			0
$653$	19.5208	+	33.8110i	0.763909	+	1.32313i	0.940822	+	0.338902i	$0.110055\pi$
$653$	19.5208	+	33.8110i	0.763909	+	1.32313i	−0.176913	+	0.984226i	$0.556611\pi$
$654$		0			0
$655$	6.40812	−	11.0992i	0.250386	−	0.433681i
$656$		0			0
$657$		−	29.3939i		−	1.14676i
$658$		0			0
$659$	45.2548			1.76288			0.881439	−	0.472298i	$-0.156575\pi$
$659$	45.2548			1.76288			0.881439	+	0.472298i	$0.156575\pi$
$660$	−7.24264	−	12.5446i	−0.281919	−	0.488299i
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$		0			0
$663$		0			0
$664$		−	38.3513i		−	1.48832i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	13.1360	−	22.7523i	0.507869	−	0.879654i
$670$		0			0
$671$		0			0
$672$	−24.0000	+	9.79796i	−0.925820	+	0.377964i
$673$	16.9411			0.653032			0.326516	−	0.945192i	$-0.394125\pi$
$673$	16.9411			0.653032			0.326516	+	0.945192i	$0.394125\pi$
$674$	10.2218	+	17.7047i	0.393730	+	0.681960i
$675$	20.1838	+	11.6531i	0.776874	+	0.448528i
$676$	13.0000	−	22.5167i	0.500000	−	0.866025i
$677$	20.3787	−	11.7656i	0.783216	−	0.452190i	−0.0543526	−	0.998522i	$-0.517310\pi$
$677$	20.3787	−	11.7656i	0.783216	−	0.452190i	0.837569	+	0.546332i	$0.183976\pi$
$678$		0			0
$679$	2.89340	−	21.1433i	0.111038	−	0.811407i
$680$		0			0
$681$	16.7132	+	28.9481i	0.640451	+	1.10929i
$682$	−79.3051	−	45.7868i	−3.03675	−	1.75327i
$683$	−23.9142	+	41.4206i	−0.915052	+	1.58492i	−0.108227	+	0.994126i	$0.534517\pi$
$683$	−23.9142	+	41.4206i	−0.915052	+	1.58492i	−0.806825	+	0.590790i	$0.798816\pi$
$684$		0			0
$685$		0			0
$686$	3.02082	+	26.0168i	0.115335	+	0.993327i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$		−	34.6410i		−	1.31685i
$693$	45.8345	+	6.27231i	1.74111	+	0.238265i
$694$	−40.0000			−1.51838
$695$		0			0
$696$	32.1838	+	18.5813i	1.21992	+	0.704323i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	8.97056	+	21.9733i	0.339055	+	0.830513i
$701$	14.6152			0.552009			0.276005	−	0.961156i	$-0.410989\pi$
$701$	14.6152			0.552009			0.276005	+	0.961156i	$0.410989\pi$
$702$		0			0
$703$		0			0
$704$	−23.3137	+	40.3805i	−0.878668	+	1.52190i
$705$		0			0
$706$		0			0
$707$	7.24264	+	5.61642i	0.272388	+	0.211227i
$708$	51.9411			1.95207
$709$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$709$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$710$		0			0
$711$	−26.5919	+	46.0585i	−0.997274	+	1.72733i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−11.3137	−	19.5959i	−0.422813	−	0.732334i
$717$		0			0
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$			8.60927i			0.320848i
$721$	36.0000	−	14.6969i	1.34071	−	0.547343i
$722$	−26.8701			−1.00000
$723$	−5.22792	−	9.05503i	−0.194429	−	0.336760i
$724$		0			0
$725$	17.0122	−	29.4660i	0.631817	−	1.09434i
$726$	48.7279	−	28.1331i	1.80846	−	1.04412i
$727$			25.2123i			0.935074i	0.883974	+	0.467537i	$0.154858\pi$
$727$			25.2123i			0.935074i	−0.883974	+	0.467537i	$0.845142\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−4.97056	−	8.60927i	−0.183969	−	0.318643i
$731$		0			0
$732$		0			0
$733$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$733$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$734$			50.0044i			1.84570i
$735$	8.37868	+	2.33696i	0.309052	+	0.0861999i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$		0			0
$741$		0			0
$742$	15.0919	+	2.06528i	0.554040	+	0.0758187i
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$	27.2132	+	47.1347i	0.997684	+	1.72804i
$745$	1.75736	+	1.01461i	0.0643847	+	0.0371725i
$746$		0			0
$747$	35.2279	−	20.3389i	1.28892	−	0.744160i
$748$		0			0
$749$	−9.34315	−	22.8859i	−0.341391	−	0.836234i
$750$	16.6690			0.608668
$751$	−20.8345	−	36.0865i	−0.760263	−	1.31681i	−0.942715	−	0.333599i	$-0.891737\pi$
$751$	−20.8345	−	36.0865i	−0.760263	−	1.31681i	0.182453	−	0.983215i	$-0.441596\pi$
$752$		0			0
$753$	9.25736	−	16.0342i	0.337357	−	0.584319i
$754$		0			0
$755$			14.5017i			0.527772i
$756$	−21.7279	−	16.8493i	−0.790237	−	0.612801i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$			37.3367i			1.35257i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	24.0000	−	13.8564i	0.866025	−	0.500000i
$769$		−	1.97824i		−	0.0713370i	−0.999364	−	0.0356685i	$-0.988644\pi$
$769$		−	1.97824i		−	0.0713370i	0.999364	−	0.0356685i	$-0.0113561\pi$
$770$	14.4853	−	5.91359i	0.522013	−	0.213111i
$771$		0			0
$772$	4.51472	+	7.81972i	0.162488	+	0.281438i
$773$	−45.0000	−	25.9808i	−1.61854	−	0.934463i	−0.987299	−	0.158874i	$-0.949213\pi$
$773$	−45.0000	−	25.9808i	−1.61854	−	0.934463i	−0.631239	−	0.775589i	$-0.717453\pi$
$774$		0			0
$775$	43.1543	−	24.9152i	1.55015	−	0.894979i
$776$			22.8138i			0.818969i
$777$		0			0
$778$	44.0000			1.57748
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$			39.4169i			1.40865i
$784$	−6.97056	−	27.1185i	−0.248949	−	0.968517i
$785$		0			0
$786$	−21.8787	−	37.8950i	−0.780387	−	1.35167i
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	14.1421	−	24.4949i	0.503793	−	0.872595i
$789$		0			0
$790$			17.9870i			0.639947i
$791$		0			0
$792$	−49.4558			−1.75734
$793$		0			0
$794$		0			0
$795$	2.52944	−	4.38111i	0.0897099	−	0.155382i
$796$	−42.4264	+	24.4949i	−1.50376	+	0.868199i
$797$			37.8801i			1.34178i	0.741557	+	0.670890i	$0.234088\pi$
$797$			37.8801i			1.34178i	−0.741557	+	0.670890i	$0.765912\pi$
$798$		0			0
$799$		0			0
$800$	−12.6863	−	21.9733i	−0.448528	−	0.776874i
$801$		0			0
$802$		0			0
$803$	49.4558	−	28.5533i	1.74526	−	1.00763i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−27.8345	−	48.2108i	−0.979822	−	1.69710i
$808$	−8.48528	−	4.89898i	−0.298511	−	0.172345i
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$	−7.90812	+	4.56575i	−0.277863	+	0.160424i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	−24.5980	+	31.7203i	−0.863220	+	1.11316i
$813$	54.2132			1.90134
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$			39.9603i			1.39718i
$819$		0			0
$820$		0			0
$821$	−1.47918	−	2.56202i	−0.0516239	−	0.0894152i	0.839059	−	0.544041i	$-0.183106\pi$
$821$	−1.47918	−	2.56202i	−0.0516239	−	0.0894152i	−0.890683	+	0.454626i	$0.849773\pi$
$822$		0			0
$823$	−23.0000	+	39.8372i	−0.801730	+	1.38864i	0.116747	+	0.993162i	$0.462753\pi$
$823$	−23.0000	+	39.8372i	−0.801730	+	1.38864i	−0.918477	+	0.395475i	$0.870580\pi$
$824$	−36.0000	+	20.7846i	−1.25412	+	0.724066i
$825$			45.2795i			1.57643i
$826$	−7.60660	+	55.5848i	−0.264668	+	1.93404i
$827$	−37.2843			−1.29650			−0.648251	−	0.761427i	$-0.724499\pi$
$827$	−37.2843			−1.29650			−0.648251	+	0.761427i	$0.724499\pi$
$828$		0			0
$829$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$829$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$830$	6.87868	−	11.9142i	0.238762	−	0.413549i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−28.8640	+	49.9938i	−0.997684	+	1.72804i
$838$	−12.7279	+	7.34847i	−0.439679	+	0.253849i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	−9.21320	−	1.26080i	−0.317886	−	0.0435017i
$841$	28.5442			0.984281
$842$		0			0
$843$		0			0
$844$		0			0
$845$	8.07716	−	4.66335i	0.277863	−	0.160424i
$846$		0			0
$847$	22.9706	+	56.2662i	0.789278	+	1.93333i
$848$	−16.2843			−0.559204
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$		0			0
$855$		0			0
$856$	13.2132	+	22.8859i	0.451618	+	0.782225i
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	25.4558	+	14.6969i	0.866025	+	0.500000i
$865$	6.21320	−	10.7616i	0.211255	−	0.365905i
$866$	48.0000	−	27.7128i	1.63111	−	0.941720i
$867$		−	29.4449i		−	1.00000i
$868$	−54.4264	+	22.2195i	−1.84735	+	0.754179i
$869$	−103.326			−3.50509
$870$	6.66548	+	11.5449i	0.225981	+	0.391410i
$871$		0			0
$872$		0			0
$873$	−20.9558	+	12.0989i	−0.709248	+	0.409484i
$874$		0			0
$875$	−2.44113	+	17.8384i	−0.0825251	+	0.603047i
$876$	−33.9411			−1.14676
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$	−21.0624	−	12.1604i	−0.710823	−	0.410394i
$879$	24.1066	−	41.7539i	0.813095	−	1.40832i
$880$	−14.4853	+	8.36308i	−0.488299	+	0.281919i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	21.2132	−	20.7846i	0.714286	−	0.699854i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$	16.1360	+	9.31615i	0.542407	+	0.313159i
$886$	−9.09188	+	15.7476i	−0.305448	+	0.529051i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$		0			0
$889$	−39.9558	−	5.46783i	−1.34008	−	0.183385i
$890$		0			0
$891$	−26.2279	−	45.4281i	−0.878668	−	1.52190i
$892$	−26.2721	−	15.1682i	−0.879654	−	0.507869i
$893$		0			0
$894$	6.00000	−	3.46410i	0.200670	−	0.115857i
$895$		−	8.11689i		−	0.271318i
$896$	11.3137	+	27.7128i	0.377964	+	0.925820i
$897$		0			0
$898$		0			0
$899$	72.9853	+	42.1381i	2.43420	+	1.40538i
$900$	13.4558	−	23.3062i	0.448528	−	0.776874i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	42.8787	+	24.7560i	1.42455	+	0.822464i
$907$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$907$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$908$	33.4264	−	19.2987i	1.10929	−	0.640451i
$909$		−	10.3923i		−	0.344691i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$	68.4411	+	39.5145i	2.26507	+	1.30774i
$914$	1.43503	−	2.48554i	0.0474665	−	0.0822145i
$915$		0			0
$916$		0			0
$917$	43.7574	−	17.8639i	1.44500	−	0.589917i
$918$		0			0
$919$	−25.0000	−	43.3013i	−0.824674	−	1.42838i	−0.902168	−	0.431384i	$-0.858025\pi$
$919$	−25.0000	−	43.3013i	−0.824674	−	1.42838i	0.0774944	−	0.996993i	$-0.475308\pi$
$920$		0			0
$921$		0			0
$922$	46.6690	−	26.9444i	1.53696	−	0.887366i
$923$		0			0
$924$	7.24264	−	52.9251i	0.238265	−	1.74111i
$925$		0			0
$926$	18.3848	+	31.8434i	0.604161	+	1.04644i
$927$	−38.1838	−	22.0454i	−1.25412	−	0.724066i
$928$	21.4558	−	37.1626i	0.704323	−	1.21992i
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$			19.5238i			0.640211i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	21.2132	+	12.2474i	0.694117	+	0.400749i
$935$		0			0
$936$		0			0
$937$		−	40.4315i		−	1.32084i	−0.750896	−	0.660420i	$-0.770378\pi$
$937$		−	40.4315i		−	1.32084i	0.750896	−	0.660420i	$-0.229622\pi$
$938$		0			0
$939$	−59.4853			−1.94123
$940$		0			0
$941$	−52.5624	−	30.3469i	−1.71349	−	0.989282i	−0.929752	−	0.368186i	$-0.879979\pi$
$941$	−52.5624	−	30.3469i	−1.71349	−	0.989282i	−0.783735	−	0.621096i	$-0.786688\pi$
$942$		0			0
$943$		0			0
$944$		−	59.9764i		−	1.95207i
$945$	−3.72792	−	9.13151i	−0.121269	−	0.297048i
$946$		0			0
$947$	28.2843	+	48.9898i	0.919115	+	1.59195i	0.800762	+	0.598983i	$0.204428\pi$
$947$	28.2843	+	48.9898i	0.919115	+	1.59195i	0.118354	+	0.992972i	$0.462238\pi$
$948$	53.1838	+	30.7057i	1.72733	+	0.997274i
$949$		0			0
$950$		0			0
$951$			0.963625i			0.0312477i
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$	−8.63604	−	14.9581i	−0.279602	−	0.484285i
$955$		0			0
$956$		0			0
$957$	−66.3198	+	38.2898i	−2.14381	+	1.23773i
$958$		0			0
$959$		0			0
$960$	9.94113			0.320848
$961$	46.2132	+	80.0436i	1.49075	+	2.58205i
$962$		0			0
$963$	−14.0147	+	24.2742i	−0.451618	+	0.782225i
$964$	−10.4558	+	6.03668i	−0.336760	+	0.194429i
$965$			3.23903i			0.104268i
$966$		0			0
$967$	−26.7574			−0.860459			−0.430229	−	0.902720i	$-0.641567\pi$
$967$	−26.7574			−0.860459			−0.430229	+	0.902720i	$0.641567\pi$
$968$	−32.4853	−	56.2662i	−1.04412	−	1.80846i
$969$		0			0
$970$	−4.09188	+	7.08735i	−0.131382	+	0.227561i
$971$	−45.1690	+	26.0784i	−1.44954	+	0.836894i	−0.998454	−	0.0555842i	$-0.982298\pi$
$971$	−45.1690	+	26.0784i	−1.44954	+	0.836894i	−0.451090	+	0.892479i	$0.648965\pi$
$972$			31.1769i			1.00000i
$973$		0			0
$974$	55.4142			1.77559
$975$		0			0
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$	2.69848	−	9.67487i	0.0861999	−	0.309052i
$981$		0			0
$982$	−31.3345	−	54.2730i	−0.999925	−	1.73192i
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$		0			0
$985$	8.78680	−	5.07306i	0.279971	−	0.161641i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−15.3640	−	8.87039i	−0.488299	−	0.281919i
$991$	−3.89340	+	6.74356i	−0.123678	+	0.214216i	−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−3.89340	+	6.74356i	−0.123678	+	0.214216i	0.797537	+	0.603269i	$0.206136\pi$
$992$	54.4264	−	31.4231i	1.72804	−	0.997684i
$993$		0			0
$994$		0			0
$995$	−17.5736			−0.557120
$996$	−23.4853	−	40.6777i	−0.744160	−	1.28892i
$997$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$997$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.a.101.1	yes	4
3.2	odd	2		168.2.ba.b.101.2	yes	4
4.3	odd	2		672.2.bi.b.17.1		4
7.5	odd	6	inner	168.2.ba.a.5.1	✓	4
8.3	odd	2		672.2.bi.a.17.2		4
8.5	even	2		168.2.ba.b.101.2	yes	4
12.11	even	2		672.2.bi.a.17.2		4
21.5	even	6		168.2.ba.b.5.2	yes	4
24.5	odd	2	CM	168.2.ba.a.101.1	yes	4
24.11	even	2		672.2.bi.b.17.1		4
28.19	even	6		672.2.bi.b.593.1		4
56.5	odd	6		168.2.ba.b.5.2	yes	4
56.19	even	6		672.2.bi.a.593.2		4
84.47	odd	6		672.2.bi.a.593.2		4
168.5	even	6	inner	168.2.ba.a.5.1	✓	4
168.131	odd	6		672.2.bi.b.593.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.a.5.1	✓	4	7.5	odd	6	inner
168.2.ba.a.5.1	✓	4	168.5	even	6	inner
168.2.ba.a.101.1	yes	4	1.1	even	1	trivial
168.2.ba.a.101.1	yes	4	24.5	odd	2	CM
168.2.ba.b.5.2	yes	4	21.5	even	6
168.2.ba.b.5.2	yes	4	56.5	odd	6
168.2.ba.b.101.2	yes	4	3.2	odd	2
168.2.ba.b.101.2	yes	4	8.5	even	2
672.2.bi.a.17.2		4	8.3	odd	2
672.2.bi.a.17.2		4	12.11	even	2
672.2.bi.a.593.2		4	56.19	even	6
672.2.bi.a.593.2		4	84.47	odd	6
672.2.bi.b.17.1		4	4.3	odd	2
672.2.bi.b.17.1		4	24.11	even	2
672.2.bi.b.593.1		4	28.19	even	6
672.2.bi.b.593.1		4	168.131	odd	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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.621320 + 0.358719i) q^{5} +2.44949i q^{6} +(-2.62132 - 0.358719i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-0.621320 + 0.358719i) q^{5} +2.44949i q^{6} +(-2.62132 - 0.358719i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.878680 + 0.507306i) q^{10} +(-2.91421 + 5.04757i) q^{11} +(3.00000 - 1.73205i) q^{12} +(1.41421 + 3.46410i) q^{14} +1.24264 q^{15} +(-2.00000 - 3.46410i) q^{16} +(2.12132 - 3.67423i) q^{18} -1.43488i q^{20} +(3.62132 + 2.80821i) q^{21} +8.24264 q^{22} +(-4.24264 - 2.44949i) q^{24} +(-2.24264 + 3.88437i) q^{25} -5.19615i q^{27} +(3.24264 - 4.18154i) q^{28} -7.58579 q^{29} +(-0.878680 - 1.52192i) q^{30} +(-9.62132 - 5.55487i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.74264 - 5.04757i) q^{33} +(1.75736 - 0.717439i) q^{35} -6.00000 q^{36} +(-1.75736 + 1.01461i) q^{40} +(0.878680 - 6.42090i) q^{42} +(-5.82843 - 10.0951i) q^{44} +(-1.86396 - 1.07616i) q^{45} +6.92820i q^{48} +(6.74264 + 1.88064i) q^{49} +6.34315 q^{50} +(2.03553 - 3.52565i) q^{53} +(-6.36396 + 3.67423i) q^{54} -4.18154i q^{55} +(-7.41421 - 1.01461i) q^{56} +(5.36396 + 9.29065i) q^{58} +(12.9853 + 7.49706i) q^{59} +(-1.24264 + 2.15232i) q^{60} +15.7116i q^{62} +(-3.00000 - 7.34847i) q^{63} +8.00000 q^{64} +(-12.3640 - 7.13834i) q^{66} +(-2.12132 - 1.64501i) q^{70} +(4.24264 + 7.34847i) q^{72} +(-8.48528 - 4.89898i) q^{73} +(6.72792 - 3.88437i) q^{75} +(9.44975 - 12.1859i) q^{77} +(8.86396 + 15.3528i) q^{79} +(2.48528 + 1.43488i) q^{80} +(-4.50000 + 7.79423i) q^{81} -13.5592i q^{83} +(-8.48528 + 3.46410i) q^{84} +(11.3787 + 6.56948i) q^{87} +(-8.24264 + 14.2767i) q^{88} +3.04384i q^{90} +(9.62132 + 16.6646i) q^{93} +(8.48528 - 4.89898i) q^{96} +8.06591i q^{97} +(-2.46447 - 9.58783i) q^{98} -17.4853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 - 4 * q^4 + 6 * q^5 - 2 * q^7 + 6 * q^9	\( 4 q - 6 q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{7} + 6 q^{9} + 12 q^{10} - 6 q^{11} + 12 q^{12} - 12 q^{15} - 8 q^{16} + 6 q^{21} + 16 q^{22} + 8 q^{25} - 4 q^{28} - 36 q^{29} - 12 q^{30} - 30 q^{31} + 18 q^{33} + 24 q^{35} - 24 q^{36} - 24 q^{40} + 12 q^{42} - 12 q^{44} + 18 q^{45} + 10 q^{49} + 48 q^{50} - 6 q^{53} - 24 q^{56} - 4 q^{58} + 18 q^{59} + 12 q^{60} - 12 q^{63} + 32 q^{64} - 24 q^{66} - 24 q^{75} + 18 q^{77} + 10 q^{79} - 24 q^{80} - 18 q^{81} + 54 q^{87} - 16 q^{88} + 30 q^{93} - 24 q^{98} - 36 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 4 * q^4 + 6 * q^5 - 2 * q^7 + 6 * q^9 + 12 * q^10 - 6 * q^11 + 12 * q^12 - 12 * q^15 - 8 * q^16 + 6 * q^21 + 16 * q^22 + 8 * q^25 - 4 * q^28 - 36 * q^29 - 12 * q^30 - 30 * q^31 + 18 * q^33 + 24 * q^35 - 24 * q^36 - 24 * q^40 + 12 * q^42 - 12 * q^44 + 18 * q^45 + 10 * q^49 + 48 * q^50 - 6 * q^53 - 24 * q^56 - 4 * q^58 + 18 * q^59 + 12 * q^60 - 12 * q^63 + 32 * q^64 - 24 * q^66 - 24 * q^75 + 18 * q^77 + 10 * q^79 - 24 * q^80 - 18 * q^81 + 54 * q^87 - 16 * q^88 + 30 * q^93 - 24 * q^98 - 36 * q^99

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