LMFDB - Embedded newform 1917.1.s.b.709.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1917,1,Mod(70,1917)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1917, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 9]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("1917.70");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1917 = 3^{3} \cdot 71 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1917.s (of order $18$, degree $6$, 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:	$0.956707629217$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{63})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{36} - x^{33} + x^{27} - x^{24} + x^{18} - x^{12} + x^{9} - x^{3} + 1 $ x^36 - x^33 + x^27 - x^24 + x^18 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{63}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{63} - \cdots)$

Embedding invariants

Embedding label			709.6
Root			$0.270840 + 0.962624i$ of defining polynomial
Character	$\chi$	$=$	1917.709
Dual form			1917.1.s.b.922.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60366 - 0.583685i) q^{2} +(-0.583744 - 0.811938i) q^{3} +(1.46500 - 1.22928i) q^{4} +(-0.254586 - 1.44383i) q^{5} +(-1.41004 - 0.961352i) q^{6} +(0.778561 - 1.34851i) q^{8} +(-0.318487 + 0.947927i) q^{9} +O(q^{10})$	\(q+(1.60366 - 0.583685i) q^{2} +(-0.583744 - 0.811938i) q^{3} +(1.46500 - 1.22928i) q^{4} +(-0.254586 - 1.44383i) q^{5} +(-1.41004 - 0.961352i) q^{6} +(0.778561 - 1.34851i) q^{8} +(-0.318487 + 0.947927i) q^{9} +(-1.25101 - 2.16682i) q^{10} +(-1.85328 - 0.471904i) q^{12} +(-1.02369 + 1.04954i) q^{15} +(0.129356 - 0.733617i) q^{16} +(0.0425463 + 1.70605i) q^{18} +(0.0249307 - 0.0431812i) q^{19} +(-2.14784 - 1.80225i) q^{20} +(-1.54938 + 0.155039i) q^{24} +(-1.08014 + 0.393139i) q^{25} +(0.955573 - 0.294755i) q^{27} +(0.772967 - 0.281337i) q^{29} +(-1.02905 + 2.28061i) q^{30} +(0.0496340 + 0.281488i) q^{32} +(0.698686 + 1.78022i) q^{36} +(-0.365341 - 0.632789i) q^{37} +(0.0147762 - 0.0837998i) q^{38} +(-2.14523 - 0.780798i) q^{40} +(-0.276841 + 1.57004i) q^{43} +(1.44973 + 0.218511i) q^{45} +(-0.671162 + 0.323215i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-1.50271 + 1.26092i) q^{50} +(1.36037 - 1.03044i) q^{54} +(-0.0496136 + 0.00496459i) q^{57} +(1.07537 - 0.902339i) q^{58} +(-0.209529 + 2.79597i) q^{60} +(0.616364 + 1.06757i) q^{64} +(-0.500000 - 0.866025i) q^{71} +(1.03033 + 1.16750i) q^{72} +(0.222521 - 0.385418i) q^{73} +(-0.955233 - 0.801536i) q^{74} +(0.949729 + 0.647514i) q^{75} +(-0.0165584 - 0.0939073i) q^{76} +(-1.79589 + 0.653650i) q^{79} -1.09215 q^{80} +(-0.797133 - 0.603804i) q^{81} +(1.85839 - 0.676400i) q^{83} +(0.472452 + 2.67941i) q^{86} +(-0.679643 - 0.463373i) q^{87} +(0.969077 - 1.67849i) q^{89} +(2.45242 - 0.495767i) q^{90} +(-0.0686934 - 0.0250023i) q^{95} +(0.199578 - 0.204617i) q^{96} +(0.853291 + 1.47794i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} - 6 q^{4} - 3 q^{8}+O(q^{10}) $ 36 * q - 6 * q^2 - 6 * q^4 - 3 * q^8	$ 36 q - 6 q^{2} - 6 q^{4} - 3 q^{8} - 6 q^{12} - 3 q^{16} - 18 q^{18} - 15 q^{20} - 6 q^{24} + 3 q^{27} + 3 q^{29} - 3 q^{30} - 3 q^{32} + 3 q^{36} - 3 q^{37} + 3 q^{38} + 6 q^{40} + 3 q^{43} - 3 q^{45} - 6 q^{48} + 3 q^{54} + 3 q^{57} + 3 q^{58} - 3 q^{60} - 21 q^{64} - 18 q^{71} + 3 q^{72} + 6 q^{73} - 24 q^{74} - 21 q^{75} - 3 q^{76} + 6 q^{80} + 3 q^{86} + 39 q^{90} - 3 q^{95} - 3 q^{96}+O(q^{100}) $ 36 * q - 6 * q^2 - 6 * q^4 - 3 * q^8 - 6 * q^12 - 3 * q^16 - 18 * q^18 - 15 * q^20 - 6 * q^24 + 3 * q^27 + 3 * q^29 - 3 * q^30 - 3 * q^32 + 3 * q^36 - 3 * q^37 + 3 * q^38 + 6 * q^40 + 3 * q^43 - 3 * q^45 - 6 * q^48 + 3 * q^54 + 3 * q^57 + 3 * q^58 - 3 * q^60 - 21 * q^64 - 18 * q^71 + 3 * q^72 + 6 * q^73 - 24 * q^74 - 21 * q^75 - 3 * q^76 + 6 * q^80 + 3 * q^86 + 39 * q^90 - 3 * q^95 - 3 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1917\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.60366	−	0.583685i	1.60366	−	0.583685i	0.623490	−	0.781831i	$-0.285714\pi$
$2$	1.60366	−	0.583685i	1.60366	−	0.583685i	0.980172	+	0.198146i	$0.0634921\pi$
$3$	−0.583744	−	0.811938i	−0.583744	−	0.811938i
$3$	−0.583744	−	0.811938i	−0.583744	−	0.811938i
$4$	1.46500	−	1.22928i	1.46500	−	1.22928i
$5$	−0.254586	−	1.44383i	−0.254586	−	1.44383i	−0.797133	−	0.603804i	$-0.793651\pi$
$5$	−0.254586	−	1.44383i	−0.254586	−	1.44383i	0.542546	−	0.840026i	$-0.317460\pi$
$6$	−1.41004	−	0.961352i	−1.41004	−	0.961352i
$7$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$7$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$8$	0.778561	−	1.34851i	0.778561	−	1.34851i
$9$	−0.318487	+	0.947927i	−0.318487	+	0.947927i
$10$	−1.25101	−	2.16682i	−1.25101	−	2.16682i
$11$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$11$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$12$	−1.85328	−	0.471904i	−1.85328	−	0.471904i
$13$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$13$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$14$		0			0
$15$	−1.02369	+	1.04954i	−1.02369	+	1.04954i
$16$	0.129356	−	0.733617i	0.129356	−	0.733617i
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$	0.0425463	+	1.70605i	0.0425463	+	1.70605i
$19$	0.0249307	−	0.0431812i	0.0249307	−	0.0431812i	−0.853291	−	0.521435i	$-0.825397\pi$
$19$	0.0249307	−	0.0431812i	0.0249307	−	0.0431812i	0.878222	+	0.478254i	$0.158730\pi$
$20$	−2.14784	−	1.80225i	−2.14784	−	1.80225i
$21$		0			0
$22$		0			0
$23$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$23$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$24$	−1.54938	+	0.155039i	−1.54938	+	0.155039i
$25$	−1.08014	+	0.393139i	−1.08014	+	0.393139i
$26$		0			0
$27$	0.955573	−	0.294755i	0.955573	−	0.294755i
$28$		0			0
$29$	0.772967	−	0.281337i	0.772967	−	0.281337i	0.0747301	−	0.997204i	$-0.476190\pi$
$29$	0.772967	−	0.281337i	0.772967	−	0.281337i	0.698237	+	0.715867i	$0.253968\pi$
$30$	−1.02905	+	2.28061i	−1.02905	+	2.28061i
$31$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$31$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$32$	0.0496340	+	0.281488i	0.0496340	+	0.281488i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.698686	+	1.78022i	0.698686	+	1.78022i
$37$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$37$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$38$	0.0147762	−	0.0837998i	0.0147762	−	0.0837998i
$39$		0			0
$40$	−2.14523	−	0.780798i	−2.14523	−	0.780798i
$41$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$41$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$42$		0			0
$43$	−0.276841	+	1.57004i	−0.276841	+	1.57004i	0.456211	+	0.889872i	$0.349206\pi$
$43$	−0.276841	+	1.57004i	−0.276841	+	1.57004i	−0.733052	+	0.680173i	$0.761905\pi$
$44$		0			0
$45$	1.44973	+	0.218511i	1.44973	+	0.218511i
$46$		0			0
$47$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$47$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$48$	−0.671162	+	0.323215i	−0.671162	+	0.323215i
$49$	0.173648	+	0.984808i	0.173648	+	0.984808i
$50$	−1.50271	+	1.26092i	−1.50271	+	1.26092i
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	1.36037	−	1.03044i	1.36037	−	1.03044i
$55$		0			0
$56$		0			0
$57$	−0.0496136	+	0.00496459i	−0.0496136	+	0.00496459i
$58$	1.07537	−	0.902339i	1.07537	−	0.902339i
$59$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$59$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$60$	−0.209529	+	2.79597i	−0.209529	+	2.79597i
$61$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$61$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$62$		0			0
$63$		0			0
$64$	0.616364	+	1.06757i	0.616364	+	1.06757i
$65$		0			0
$66$		0			0
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$71$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$72$	1.03033	+	1.16750i	1.03033	+	1.16750i
$73$	0.222521	−	0.385418i	0.222521	−	0.385418i	−0.733052	−	0.680173i	$-0.761905\pi$
$73$	0.222521	−	0.385418i	0.222521	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$74$	−0.955233	−	0.801536i	−0.955233	−	0.801536i
$75$	0.949729	+	0.647514i	0.949729	+	0.647514i
$76$	−0.0165584	−	0.0939073i	−0.0165584	−	0.0939073i
$77$		0			0
$78$		0			0
$79$	−1.79589	+	0.653650i	−1.79589	+	0.653650i	−0.797133	+	0.603804i	$0.793651\pi$
$79$	−1.79589	+	0.653650i	−1.79589	+	0.653650i	−0.998757	+	0.0498459i	$0.984127\pi$
$80$	−1.09215			−1.09215
$81$	−0.797133	−	0.603804i	−0.797133	−	0.603804i
$82$		0			0
$83$	1.85839	−	0.676400i	1.85839	−	0.676400i	0.878222	−	0.478254i	$-0.158730\pi$
$83$	1.85839	−	0.676400i	1.85839	−	0.676400i	0.980172	−	0.198146i	$-0.0634921\pi$
$84$		0			0
$85$		0			0
$86$	0.472452	+	2.67941i	0.472452	+	2.67941i
$87$	−0.679643	−	0.463373i	−0.679643	−	0.463373i
$88$		0			0
$89$	0.969077	−	1.67849i	0.969077	−	1.67849i	0.270840	−	0.962624i	$-0.412698\pi$
$89$	0.969077	−	1.67849i	0.969077	−	1.67849i	0.698237	−	0.715867i	$-0.253968\pi$
$90$	2.45242	−	0.495767i	2.45242	−	0.495767i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0686934	−	0.0250023i	−0.0686934	−	0.0250023i
$96$	0.199578	−	0.204617i	0.199578	−	0.204617i
$97$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$97$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$98$	0.853291	+	1.47794i	0.853291	+	1.47794i
$99$		0			0
$100$	−1.09913	+	1.90374i	−1.09913	+	1.90374i
$101$	−0.487950	−	0.409439i	−0.487950	−	0.409439i	0.365341	−	0.930874i	$-0.380952\pi$
$101$	−0.487950	−	0.409439i	−0.487950	−	0.409439i	−0.853291	+	0.521435i	$0.825397\pi$
$102$		0			0
$103$	−0.142839	−	0.810077i	−0.142839	−	0.810077i	−0.969077	−	0.246757i	$-0.920635\pi$
$103$	−0.142839	−	0.810077i	−0.142839	−	0.810077i	0.826239	−	0.563320i	$-0.190476\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$107$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$108$	1.03758	−	1.60648i	1.03758	−	1.60648i
$109$	1.99006			1.99006			0.995031	−	0.0995678i	$-0.0317460\pi$
$109$	1.99006			1.99006			0.995031	+	0.0995678i	$0.0317460\pi$
$110$		0			0
$111$	−0.300520	+	0.666021i	−0.300520	+	0.666021i
$112$		0			0
$113$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$113$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$114$	−0.0766657	+	0.0369203i	−0.0766657	+	0.0369203i
$115$		0			0
$116$	0.786554	−	1.36235i	0.786554	−	1.36235i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.618302	+	2.19758i	0.618302	+	2.19758i
$121$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.109562	+	0.189767i	0.109562	+	0.189767i
$126$		0			0
$127$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$127$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$128$	1.39261	+	1.16854i	1.39261	+	1.16854i
$129$	1.43638	−	0.691726i	1.43638	−	0.691726i
$130$		0			0
$131$	−1.53018	+	1.28398i	−1.53018	+	1.28398i	−0.733052	+	0.680173i	$0.761905\pi$
$131$	−1.53018	+	1.28398i	−1.53018	+	1.28398i	−0.797133	+	0.603804i	$0.793651\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.668852	−	1.30464i	−0.668852	−	1.30464i
$136$		0			0
$137$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$137$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$138$		0			0
$139$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$139$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$140$		0			0
$141$		0			0
$142$	−1.30732	−	1.09697i	−1.30732	−	1.09697i
$143$		0			0
$144$	0.654217	+	0.356268i	0.654217	+	0.356268i
$145$	−0.602990	−	1.04441i	−0.602990	−	1.04441i
$146$	0.131886	−	0.747962i	0.131886	−	0.747962i
$147$	0.698237	−	0.715867i	0.698237	−	0.715867i
$148$	−1.31310	−	0.477929i	−1.31310	−	0.477929i
$149$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$149$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$150$	1.90099	+	0.484051i	1.90099	+	0.484051i
$151$	−0.336557	+	1.90871i	−0.336557	+	1.90871i	0.0747301	+	0.997204i	$0.476190\pi$
$151$	−0.336557	+	1.90871i	−0.336557	+	1.90871i	−0.411287	+	0.911506i	$0.634921\pi$
$152$	−0.0388201	−	0.0672384i	−0.0388201	−	0.0672384i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.242495	+	1.37526i	0.242495	+	1.37526i	0.826239	+	0.563320i	$0.190476\pi$
$157$	0.242495	+	1.37526i	0.242495	+	1.37526i	−0.583744	+	0.811938i	$0.698413\pi$
$158$	−2.49847	+	2.09647i	−2.49847	+	2.09647i
$159$		0			0
$160$	0.393785	−	0.143326i	0.393785	−	0.143326i
$161$		0			0
$162$	−1.63076	−	0.503024i	−1.63076	−	0.503024i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$	2.58543	−	2.16943i	2.58543	−	2.16943i
$167$	−0.0431841	−	0.244909i	−0.0431841	−	0.244909i	0.955573	−	0.294755i	$-0.0952381\pi$
$167$	−0.0431841	−	0.244909i	−0.0431841	−	0.244909i	−0.998757	+	0.0498459i	$0.984127\pi$
$168$		0			0
$169$	0.766044	+	0.642788i	0.766044	+	0.642788i
$170$		0			0
$171$	0.0329926	+	0.0373851i	0.0329926	+	0.0373851i
$172$	1.52445	+	2.64043i	1.52445	+	2.64043i
$173$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$173$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$174$	−1.36038	−	0.346396i	−1.36038	−	0.346396i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.574362	−	3.25737i	0.574362	−	3.25737i
$179$	0.797133	+	1.38067i	0.797133	+	1.38067i	0.921476	+	0.388435i	$0.126984\pi$
$179$	0.797133	+	1.38067i	0.797133	+	1.38067i	−0.124344	+	0.992239i	$0.539683\pi$
$180$	2.39246	−	1.46200i	2.39246	−	1.46200i
$181$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$181$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.820629	+	0.688590i	−0.820629	+	0.688590i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−0.124754			−0.124754
$191$	−1.55282	+	0.565181i	−1.55282	+	0.565181i	−0.969077	−	0.246757i	$-0.920635\pi$
$191$	−1.55282	+	0.565181i	−1.55282	+	0.565181i	−0.583744	+	0.811938i	$0.698413\pi$
$192$	0.507005	−	1.12364i	0.507005	−	1.12364i
$193$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$193$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$194$		0			0
$195$		0			0
$196$	1.46500	+	1.22928i	1.46500	+	1.22928i
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$		0			0
$199$	0.661686	+	1.14607i	0.661686	+	1.14607i	0.980172	+	0.198146i	$0.0634921\pi$
$199$	0.661686	+	1.14607i	0.661686	+	1.14607i	−0.318487	+	0.947927i	$0.603175\pi$
$200$	−0.310804	+	1.76266i	−0.310804	+	1.76266i
$201$		0			0
$202$	−1.02149	−	0.371792i	−1.02149	−	0.371792i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.701895	−	1.21572i	−0.701895	−	1.21572i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$211$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$212$		0			0
$213$	−0.411287	+	0.911506i	−0.411287	+	0.911506i
$214$	2.45695	−	0.894258i	2.45695	−	0.894258i
$215$	2.33736			2.33736
$216$	0.346492	−	1.51808i	0.346492	−	1.51808i
$217$		0			0
$218$	3.19139	−	1.16157i	3.19139	−	1.16157i
$219$	−0.442830	+	0.0443119i	−0.442830	+	0.0443119i
$220$		0			0
$221$		0			0
$222$	−0.0931861	+	1.24348i	−0.0931861	+	1.24348i
$223$	−1.51498	−	1.27122i	−1.51498	−	1.27122i	−0.853291	−	0.521435i	$-0.825397\pi$
$223$	−1.51498	−	1.27122i	−1.51498	−	1.27122i	−0.661686	−	0.749781i	$-0.730159\pi$
$224$		0			0
$225$	−0.0286568	−	1.14910i	−0.0286568	−	1.14910i
$226$		0			0
$227$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$227$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$228$	−0.0665811	+	0.0682622i	−0.0665811	+	0.0682622i
$229$	0.233690	+	0.0850561i	0.233690	+	0.0850561i	0.456211	−	0.889872i	$-0.349206\pi$
$229$	0.233690	+	0.0850561i	0.233690	+	0.0850561i	−0.222521	+	0.974928i	$0.571429\pi$
$230$		0			0
$231$		0			0
$232$	0.222417	−	1.26139i	0.222417	−	1.26139i
$233$	−0.980172	−	1.69771i	−0.980172	−	1.69771i	−0.661686	−	0.749781i	$-0.730159\pi$
$233$	−0.980172	−	1.69771i	−0.980172	−	1.69771i	−0.318487	−	0.947927i	$-0.603175\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.57906	+	1.07659i	1.57906	+	1.07659i
$238$		0			0
$239$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$239$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$240$	0.637536	+	0.886758i	0.637536	+	0.886758i
$241$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$241$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$242$	−1.70658			−1.70658
$243$	−0.0249307	+	0.999689i	−0.0249307	+	0.999689i
$244$		0			0
$245$	1.37769	−	0.501437i	1.37769	−	0.501437i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$250$	0.286465	+	0.240373i	0.286465	+	0.240373i
$251$	−0.980172	+	1.69771i	−0.980172	+	1.69771i	−0.318487	+	0.947927i	$0.603175\pi$
$251$	−0.980172	+	1.69771i	−0.980172	+	1.69771i	−0.661686	+	0.749781i	$0.730159\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	1.75694	+	0.639475i	1.75694	+	0.639475i
$257$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$257$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$258$	1.89972	−	1.94769i	1.89972	−	1.94769i
$259$		0			0
$260$		0			0
$261$	0.0205073	+	0.822319i	0.0205073	+	0.822319i
$262$	−1.70446	+	2.95221i	−1.70446	+	2.95221i
$263$	0.698955	+	0.586493i	0.698955	+	0.586493i	0.921476	−	0.388435i	$-0.126984\pi$
$263$	0.698955	+	0.586493i	0.698955	+	0.586493i	−0.222521	+	0.974928i	$0.571429\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.92852	+	0.192978i	−1.92852	+	0.192978i
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	−1.83411	−	1.70181i	−1.83411	−	1.70181i
$271$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$271$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.01376	−	0.850647i	−1.01376	−	0.850647i	−0.0249307	−	0.999689i	$-0.507937\pi$
$277$	−1.01376	−	0.850647i	−1.01376	−	0.850647i	−0.988831	+	0.149042i	$0.952381\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$281$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$282$		0			0
$283$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$283$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$284$	−1.79709	−	0.654087i	−1.79709	−	0.654087i
$285$	0.0197990	+	0.0703697i	0.0197990	+	0.0703697i
$286$		0			0
$287$		0			0
$288$	−0.282638	−	0.0426009i	−0.282638	−	0.0426009i
$289$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$290$	−1.57660	−	1.32292i	−1.57660	−	1.32292i
$291$		0			0
$292$	−0.147793	−	0.838177i	−0.147793	−	0.838177i
$293$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$293$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$294$	0.701895	−	1.55556i	0.701895	−	1.55556i
$295$		0			0
$296$	−1.13776			−1.13776
$297$		0			0
$298$		0			0
$299$		0			0
$300$	2.18733	−	0.218875i	2.18733	−	0.218875i
$301$		0			0
$302$	0.574362	+	3.25737i	0.574362	+	3.25737i
$303$	−0.0476011	+	0.635192i	−0.0476011	+	0.635192i
$304$	−0.0284535	−	0.0238753i	−0.0284535	−	0.0238753i
$305$		0			0
$306$		0			0
$307$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$307$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$308$		0			0
$309$	−0.574352	+	0.588854i	−0.574352	+	0.588854i
$310$		0			0
$311$	−0.686617	−	0.249908i	−0.686617	−	0.249908i	−0.0249307	−	0.999689i	$-0.507937\pi$
$311$	−0.686617	−	0.249908i	−0.686617	−	0.249908i	−0.661686	+	0.749781i	$0.730159\pi$
$312$		0			0
$313$	−0.296345	+	1.68065i	−0.296345	+	1.68065i	0.365341	+	0.930874i	$0.380952\pi$
$313$	−0.296345	+	1.68065i	−0.296345	+	1.68065i	−0.661686	+	0.749781i	$0.730159\pi$
$314$	1.19160	+	2.06391i	1.19160	+	2.06391i
$315$		0			0
$316$	−1.82746	+	3.16525i	−1.82746	+	3.16525i
$317$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$317$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$318$		0			0
$319$		0			0
$320$	1.38448	−	1.16171i	1.38448	−	1.16171i
$321$	−0.894347	−	1.24396i	−0.894347	−	1.24396i
$322$		0			0
$323$		0			0
$324$	−1.91004	+	0.0953263i	−1.91004	+	0.0953263i
$325$		0			0
$326$		0			0
$327$	−1.16169	−	1.61581i	−1.16169	−	1.61581i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$331$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$332$	1.89106	−	3.27541i	1.89106	−	3.27541i
$333$	0.716194	−	0.144782i	0.716194	−	0.144782i
$334$	−0.212203	−	0.367546i	−0.212203	−	0.367546i
$335$		0			0
$336$		0			0
$337$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$337$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$338$	1.60366	+	0.583685i	1.60366	+	0.583685i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	0.0747301	+	0.0406958i	0.0747301	+	0.0406958i
$343$		0			0
$344$	1.90168	+	1.59570i	1.90168	+	1.59570i
$345$		0			0
$346$		0			0
$347$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$347$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$348$	−1.56529	+	0.156631i	−1.56529	+	0.156631i
$349$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$349$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$353$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$354$		0			0
$355$	−1.12310	+	0.942393i	−1.12310	+	0.942393i
$356$	−0.643639	−	3.65026i	−0.643639	−	3.65026i
$357$		0			0
$358$	2.08421	+	1.74886i	2.08421	+	1.74886i
$359$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	0.456211	+	0.889872i	$0.349206\pi$
$359$	−0.542546	+	0.939718i	−0.542546	+	0.939718i	−0.998757	+	0.0498459i	$0.984127\pi$
$360$	1.42337	−	1.78484i	1.42337	−	1.78484i
$361$	0.498757	+	0.863872i	0.498757	+	0.863872i
$362$		0			0
$363$	0.270840	+	0.962624i	0.270840	+	0.962624i
$364$		0			0
$365$	−0.613128	−	0.223160i	−0.613128	−	0.223160i
$366$		0			0
$367$	0.188424	−	1.06861i	0.188424	−	1.06861i	−0.733052	−	0.680173i	$-0.761905\pi$
$367$	0.188424	−	1.06861i	0.188424	−	1.06861i	0.921476	−	0.388435i	$-0.126984\pi$
$368$		0			0
$369$		0			0
$370$	−0.914093	+	1.58326i	−0.914093	+	1.58326i
$371$		0			0
$372$		0			0
$373$	−0.254586	−	1.44383i	−0.254586	−	1.44383i	−0.797133	−	0.603804i	$-0.793651\pi$
$373$	−0.254586	−	1.44383i	−0.254586	−	1.44383i	0.542546	−	0.840026i	$-0.317460\pi$
$374$		0			0
$375$	0.0901229	−	0.199733i	0.0901229	−	0.199733i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.39647			1.39647			0.698237	−	0.715867i	$-0.253968\pi$
$379$	1.39647			1.39647			0.698237	+	0.715867i	$0.253968\pi$
$380$	−0.131371	+	0.0478150i	−0.131371	+	0.0478150i
$381$		0			0
$382$	−2.16031	+	1.81272i	−2.16031	+	1.81272i
$383$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$383$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$384$	0.135853	−	1.81284i	0.135853	−	1.81284i
$385$		0			0
$386$		0			0
$387$	−1.40012	−	0.762464i	−1.40012	−	0.762464i
$388$		0			0
$389$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$389$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$390$		0			0
$391$		0			0
$392$	1.46322	+	0.532567i	1.46322	+	0.532567i
$393$	1.93575	+	0.492901i	1.93575	+	0.492901i
$394$		0			0
$395$	1.40097	+	2.42655i	1.40097	+	2.42655i
$396$		0			0
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$	1.73007	+	1.45170i	1.73007	+	1.45170i
$399$		0			0
$400$	0.148690	+	0.843263i	0.148690	+	0.843263i
$401$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$401$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$402$		0			0
$403$		0			0
$404$	−1.21816			−1.21816
$405$	−0.668852	+	1.30464i	−0.668852	+	1.30464i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.48471	+	1.24582i	−1.48471	+	1.24582i	−0.583744	+	0.811938i	$0.698413\pi$
$409$	−1.48471	+	1.24582i	−1.48471	+	1.24582i	−0.900969	+	0.433884i	$0.857143\pi$
$410$		0			0
$411$		0			0
$412$	−1.20507	−	1.01117i	−1.20507	−	1.01117i
$413$		0			0
$414$		0			0
$415$	−1.44973	−	2.51100i	−1.44973	−	2.51100i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.09708	+	0.399304i	1.09708	+	0.399304i	0.826239	−	0.563320i	$-0.190476\pi$
$419$	1.09708	+	0.399304i	1.09708	+	0.399304i	0.270840	+	0.962624i	$0.412698\pi$
$420$		0			0
$421$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$421$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.127533	+	1.70181i	−0.127533	+	1.70181i
$427$		0			0
$428$	2.24451	−	1.88337i	2.24451	−	1.88337i
$429$		0			0
$430$	3.74833	−	1.36428i	3.74833	−	1.36428i
$431$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$431$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$432$	−0.0926278	−	0.739153i	−0.0926278	−	0.739153i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$	−0.496004	+	1.09926i	−0.496004	+	1.09926i
$436$	2.91544	−	2.44634i	2.91544	−	2.44634i
$437$		0			0
$438$	−0.684286	+	0.329535i	−0.684286	+	0.329535i
$439$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$439$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$440$		0			0
$441$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$442$		0			0
$443$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$443$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$444$	0.378465	+	1.34514i	0.378465	+	1.34514i
$445$	−2.67017	−	0.971862i	−2.67017	−	0.971862i
$446$	−3.17150	−	1.15433i	−3.17150	−	1.15433i
$447$		0			0
$448$		0			0
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	−0.716670	−	1.82605i	−0.716670	−	1.82605i
$451$		0			0
$452$		0			0
$453$	1.74622	−	0.840934i	1.74622	−	0.840934i
$454$		0			0
$455$		0			0
$456$	−0.0319324	+	0.0707695i	−0.0319324	+	0.0707695i
$457$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$457$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$458$	0.424405			0.424405
$459$		0			0
$460$		0			0
$461$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$461$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$462$		0			0
$463$	−0.487950	+	0.409439i	−0.487950	+	0.409439i	−0.853291	−	0.521435i	$-0.825397\pi$
$463$	−0.487950	+	0.409439i	−0.487950	+	0.409439i	0.365341	+	0.930874i	$0.380952\pi$
$464$	−0.106405	−	0.603454i	−0.106405	−	0.603454i
$465$		0			0
$466$	−2.56279	−	2.15044i	−2.56279	−	2.15044i
$467$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$467$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.975069	−	0.999689i	0.975069	−	0.999689i
$472$		0			0
$473$		0			0
$474$	3.16067	+	0.804806i	3.16067	+	0.804806i
$475$	−0.00995242	+	0.0564430i	−0.00995242	+	0.0564430i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$479$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$480$	−0.346242	−	0.236064i	−0.346242	−	0.236064i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.79709	+	0.654087i	−1.79709	+	0.654087i
$485$		0			0
$486$	0.543524	+	1.61772i	0.543524	+	1.61772i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$	1.91666	−	1.60827i	1.91666	−	1.60827i
$491$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$491$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−3.27068	−	0.832816i	−3.27068	−	0.832816i
$499$	−1.55282	−	0.565181i	−1.55282	−	0.565181i	−0.583744	−	0.811938i	$-0.698413\pi$
$499$	−1.55282	−	0.565181i	−1.55282	−	0.565181i	−0.969077	+	0.246757i	$0.920635\pi$
$500$	0.393785	+	0.143326i	0.393785	+	0.143326i
$501$	−0.173643	+	0.178027i	−0.173643	+	0.178027i
$502$	−0.580938	+	3.29466i	−0.580938	+	3.29466i
$503$	0.583744	+	1.01107i	0.583744	+	1.01107i	0.995031	+	0.0995678i	$0.0317460\pi$
$503$	0.583744	+	1.01107i	0.583744	+	1.01107i	−0.411287	+	0.911506i	$0.634921\pi$
$504$		0			0
$505$	−0.466934	+	0.808754i	−0.466934	+	0.808754i
$506$		0			0
$507$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$508$		0			0
$509$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$509$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$510$		0			0
$511$		0			0
$512$	1.37288			1.37288
$513$	0.0110952	−	0.0486113i	0.0110952	−	0.0486113i
$514$		0			0
$515$	−1.13325	+	0.412469i	−1.13325	+	0.412469i
$516$	1.25398	−	2.77910i	1.25398	−	2.77910i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	−0.998757	−	0.0498459i	$-0.984127\pi$
$521$	−0.456211	+	0.790180i	−0.456211	+	0.790180i	0.542546	+	0.840026i	$0.317460\pi$
$522$	0.512862	+	1.30675i	0.512862	+	1.30675i
$523$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$523$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$524$	−0.663351	+	3.76205i	−0.663351	+	3.76205i
$525$		0			0
$526$	1.46322	+	0.532567i	1.46322	+	0.532567i
$527$		0			0
$528$		0			0
$529$	0.173648	−	0.984808i	0.173648	−	0.984808i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−2.98006	+	1.43512i	−2.98006	+	1.43512i
$535$	−0.390049	−	2.21208i	−0.390049	−	2.21208i
$536$		0			0
$537$	0.655701	−	1.45318i	0.655701	−	1.45318i
$538$		0			0
$539$		0			0
$540$	−2.58364	−	1.08910i	−2.58364	−	1.08910i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$	−2.88970	+	1.05176i	−2.88970	+	1.05176i
$543$		0			0
$544$		0			0
$545$	−0.506642	−	2.87331i	−0.506642	−	2.87331i
$546$		0			0
$547$	−0.487950	−	0.409439i	−0.487950	−	0.409439i	0.365341	−	0.930874i	$-0.380952\pi$
$547$	−0.487950	−	0.409439i	−0.487950	−	0.409439i	−0.853291	+	0.521435i	$0.825397\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.00712213	−	0.0403916i	0.00712213	−	0.0403916i
$552$		0			0
$553$		0			0
$554$	−2.12224	−	0.772433i	−2.12224	−	0.772433i
$555$	1.03813	+	0.264340i	1.03813	+	0.264340i
$556$		0			0
$557$	−0.698237	−	1.20938i	−0.698237	−	1.20938i	−0.969077	−	0.246757i	$-0.920635\pi$
$557$	−0.698237	−	1.20938i	−0.698237	−	1.20938i	0.270840	−	0.962624i	$-0.412698\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$563$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−1.55712			−1.55712
$569$	0.233690	−	0.0850561i	0.233690	−	0.0850561i	−0.222521	−	0.974928i	$-0.571429\pi$
$569$	0.233690	−	0.0850561i	0.233690	−	0.0850561i	0.456211	+	0.889872i	$0.349206\pi$
$570$	0.0728246	+	0.101293i	0.0728246	+	0.101293i
$571$	0.955242	−	0.801543i	0.955242	−	0.801543i	−0.0249307	−	0.999689i	$-0.507937\pi$
$571$	0.955242	−	0.801543i	0.955242	−	0.801543i	0.980172	+	0.198146i	$0.0634921\pi$
$572$		0			0
$573$	1.36534	+	0.930874i	1.36534	+	0.930874i
$574$		0			0
$575$		0			0
$576$	−1.20829	+	0.244260i	−1.20829	+	0.244260i
$577$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	−0.998757	−	0.0498459i	$-0.984127\pi$
$577$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	0.456211	−	0.889872i	$-0.349206\pi$
$578$	−0.296345	+	1.68065i	−0.296345	+	1.68065i
$579$		0			0
$580$	−2.16725	−	0.788815i	−2.16725	−	0.788815i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.346492	−	0.600142i	−0.346492	−	0.600142i
$585$		0			0
$586$	0.296345	−	0.513284i	0.296345	−	0.513284i
$587$	−1.48471	−	1.24582i	−1.48471	−	1.24582i	−0.900969	−	0.433884i	$-0.857143\pi$
$587$	−1.48471	−	1.24582i	−1.48471	−	1.24582i	−0.583744	−	0.811938i	$-0.698413\pi$
$588$	0.142915	−	1.90707i	0.142915	−	1.90707i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.511484	+	0.186165i	−0.511484	+	0.186165i
$593$	1.65248			1.65248			0.826239	−	0.563320i	$-0.190476\pi$
$593$	1.65248			1.65248			0.826239	+	0.563320i	$0.190476\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.544286	−	1.20626i	0.544286	−	1.20626i
$598$		0			0
$599$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$599$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$600$	1.61260	−	0.776586i	1.61260	−	0.776586i
$601$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$601$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$602$		0			0
$603$		0			0
$604$	1.85328	+	3.20998i	1.85328	+	3.20998i
$605$	−0.254586	+	1.44383i	−0.254586	+	1.44383i
$606$	0.294416	+	1.04642i	0.294416	+	1.04642i
$607$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$607$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$608$	0.0133924	+	0.00487444i	0.0133924	+	0.00487444i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.969077	−	1.67849i	0.969077	−	1.67849i	0.270840	−	0.962624i	$-0.412698\pi$
$613$	0.969077	−	1.67849i	0.969077	−	1.67849i	0.698237	−	0.715867i	$-0.253968\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.831229	−	0.697484i	0.831229	−	0.697484i	−0.124344	−	0.992239i	$-0.539683\pi$
$617$	0.831229	−	0.697484i	0.831229	−	0.697484i	0.955573	+	0.294755i	$0.0952381\pi$
$618$	−0.577361	+	1.27956i	−0.577361	+	1.27956i
$619$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$619$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$620$		0			0
$621$		0			0
$622$	−1.24697			−1.24697
$623$		0			0
$624$		0			0
$625$	−0.634439	+	0.532358i	−0.634439	+	0.532358i
$626$	0.505737	+	2.86818i	0.505737	+	2.86818i
$627$		0			0
$628$	2.04583	+	1.71666i	2.04583	+	1.71666i
$629$		0			0
$630$		0			0
$631$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$631$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$632$	−0.516757	+	2.93068i	−0.516757	+	2.93068i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.980172	−	0.198146i	0.980172	−	0.198146i
$640$	1.33263	−	2.30818i	1.33263	−	2.30818i
$641$	−1.51498	−	1.27122i	−1.51498	−	1.27122i	−0.853291	−	0.521435i	$-0.825397\pi$
$641$	−1.51498	−	1.27122i	−1.51498	−	1.27122i	−0.661686	−	0.749781i	$-0.730159\pi$
$642$	−2.16031	−	1.47288i	−2.16031	−	1.47288i
$643$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$643$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$644$		0			0
$645$	−1.36442	−	1.89779i	−1.36442	−	1.89779i
$646$		0			0
$647$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$647$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$648$	−1.43485	+	0.604840i	−1.43485	+	0.604840i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$653$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$654$	−2.80607	−	1.91315i	−2.80607	−	1.91315i
$655$	2.24341	+	1.88244i	2.24341	+	1.88244i
$656$		0			0
$657$	0.294478	+	0.333684i	0.294478	+	0.333684i
$658$		0			0
$659$	0.0940619	−	0.533452i	0.0940619	−	0.533452i	−0.900969	−	0.433884i	$-0.857143\pi$
$659$	0.0940619	−	0.533452i	0.0940619	−	0.533452i	0.995031	−	0.0995678i	$-0.0317460\pi$
$660$		0			0
$661$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$661$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$662$		0			0
$663$		0			0
$664$	0.534743	−	3.03268i	0.534743	−	3.03268i
$665$		0			0
$666$	1.06403	−	0.650213i	1.06403	−	0.650213i
$667$		0			0
$668$	−0.364327	−	0.305707i	−0.364327	−	0.305707i
$669$	−0.147791	+	1.97213i	−0.147791	+	1.97213i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$673$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$674$		0			0
$675$	−0.916272	+	0.694049i	−0.916272	+	0.694049i
$676$	1.91242			1.91242
$677$	−0.509014	+	0.185266i	−0.509014	+	0.185266i	−0.583744	−	0.811938i	$-0.698413\pi$
$677$	−0.509014	+	0.185266i	−0.509014	+	0.185266i	0.0747301	+	0.997204i	$0.476190\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$	0.0942909	+	0.0142121i	0.0942909	+	0.0142121i
$685$		0			0
$686$		0			0
$687$	−0.0673546	−	0.239393i	−0.0673546	−	0.239393i
$688$	1.11600	+	0.406191i	1.11600	+	0.406191i
$689$		0			0
$690$		0			0
$691$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$691$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	−1.15400	+	0.555739i	−1.15400	+	0.555739i
$697$		0			0
$698$		0			0
$699$	−0.806265	+	1.78687i	−0.806265	+	1.78687i
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	−0.0364328			−0.0364328
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$709$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$710$	−1.25101	+	2.16682i	−1.25101	+	2.16682i
$711$	−0.0476462	−	1.91055i	−0.0476462	−	1.91055i
$712$	−1.50897	−	2.61361i	−1.50897	−	2.61361i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	2.86503	+	1.04279i	2.86503	+	1.04279i
$717$		0			0
$718$	−0.321562	+	1.82367i	−0.321562	+	1.82367i
$719$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	0.878222	−	0.478254i	$-0.158730\pi$
$719$	0.0249307	+	0.0431812i	0.0249307	+	0.0431812i	−0.853291	+	0.521435i	$0.825397\pi$
$720$	0.347835	−	1.03528i	0.347835	−	1.03528i
$721$		0			0
$722$	1.30407	+	1.09424i	1.30407	+	1.09424i
$723$		0			0
$724$		0			0
$725$	−0.724308	+	0.607766i	−0.724308	+	0.607766i
$726$	0.996206	+	1.38564i	0.996206	+	1.38564i
$727$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$727$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$728$		0			0
$729$	0.826239	−	0.563320i	0.826239	−	0.563320i
$730$	−1.11351			−1.11351
$731$		0			0
$732$		0			0
$733$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$733$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$734$	−0.321562	−	1.82367i	−0.321562	−	1.82367i
$735$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$739$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$740$	−0.355752	+	2.01757i	−0.355752	+	2.01757i
$741$		0			0
$742$		0			0
$743$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$743$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$744$		0			0
$745$		0			0
$746$	−1.25101	−	2.16682i	−1.25101	−	2.16682i
$747$	0.0493045	+	1.97705i	0.0493045	+	1.97705i
$748$		0			0
$749$		0			0
$750$	0.0279456	−	0.372908i	0.0279456	−	0.372908i
$751$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$751$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$752$		0			0
$753$	1.95060	−	0.195187i	1.95060	−	0.195187i
$754$		0			0
$755$	2.84154			2.84154
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	2.23947	−	0.815101i	2.23947	−	0.815101i
$759$		0			0
$760$	−0.0871978	+	0.0731676i	−0.0871978	+	0.0731676i
$761$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$761$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$762$		0			0
$763$		0			0
$764$	−1.58012	+	2.73684i	−1.58012	+	2.73684i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.506391	−	1.79982i	−0.506391	−	1.79982i
$769$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$769$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$	−2.69036	−	0.405506i	−2.69036	−	0.405506i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.655701	−	0.496674i	0.655701	−	0.496674i
$784$	0.744934			0.744934
$785$	1.92390	−	0.700244i	1.92390	−	0.700244i
$786$	3.39198	−	0.339419i	3.39198	−	0.339419i
$787$	−1.38036	+	1.15826i	−1.38036	+	1.15826i	−0.411287	+	0.911506i	$0.634921\pi$
$787$	−1.38036	+	1.15826i	−1.38036	+	1.15826i	−0.969077	+	0.246757i	$0.920635\pi$
$788$		0			0
$789$	0.0681853	−	0.909870i	0.0681853	−	0.909870i
$790$	3.66302	+	3.07364i	3.66302	+	3.07364i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	2.37822	+	0.865600i	2.37822	+	0.865600i
$797$	0.0468544	+	0.0170536i	0.0468544	+	0.0170536i	0.365341	−	0.930874i	$-0.380952\pi$
$797$	0.0468544	+	0.0170536i	0.0468544	+	0.0170536i	−0.318487	+	0.947927i	$0.603175\pi$
$798$		0			0
$799$		0			0
$800$	−0.164276	−	0.284534i	−0.164276	−	0.284534i
$801$	1.28245	+	1.45319i	1.28245	+	1.45319i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.932029	+	0.339231i	−0.932029	+	0.339231i
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$	−0.311111	+	2.48261i	−0.311111	+	2.48261i
$811$	1.08509			1.08509			0.542546	−	0.840026i	$-0.317460\pi$
$811$	1.08509			1.08509			0.542546	+	0.840026i	$0.317460\pi$
$812$		0			0
$813$	1.05187	+	1.46306i	1.05187	+	1.46306i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.0608946	+	0.0510966i	0.0608946	+	0.0510966i
$818$	−1.65381	+	2.86448i	−1.65381	+	2.86448i
$819$		0			0
$820$		0			0
$821$	−0.343417	+	1.94762i	−0.343417	+	1.94762i	−0.0249307	+	0.999689i	$0.507937\pi$
$821$	−0.343417	+	1.94762i	−0.343417	+	1.94762i	−0.318487	+	0.947927i	$0.603175\pi$
$822$		0			0
$823$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$823$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$824$	−1.20360	−	0.438076i	−1.20360	−	0.438076i
$825$		0			0
$826$		0			0
$827$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$827$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$828$		0			0
$829$	0.853291	−	1.47794i	0.853291	−	1.47794i	−0.0249307	−	0.999689i	$-0.507937\pi$
$829$	0.853291	−	1.47794i	0.853291	−	1.47794i	0.878222	−	0.478254i	$-0.158730\pi$
$830$	−3.79051	−	3.18062i	−3.79051	−	3.18062i
$831$	−0.0988957	+	1.31967i	−0.0988957	+	1.31967i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.342613	+	0.124701i	−0.342613	+	0.124701i
$836$		0			0
$837$		0			0
$838$	1.99241			1.99241
$839$	−1.65052	+	0.600739i	−1.65052	+	0.600739i	−0.988831	−	0.149042i	$-0.952381\pi$
$839$	−1.65052	+	0.600739i	−1.65052	+	0.600739i	−0.661686	+	0.749781i	$0.730159\pi$
$840$		0			0
$841$	−0.247717	+	0.207859i	−0.247717	+	0.207859i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.733052	−	1.26968i	0.733052	−	1.26968i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	0.517961	+	1.84094i	0.517961	+	1.84094i
$853$	−0.142839	+	0.810077i	−0.142839	+	0.810077i	0.826239	+	0.563320i	$0.190476\pi$
$853$	−0.142839	+	0.810077i	−0.142839	+	0.810077i	−0.969077	+	0.246757i	$0.920635\pi$
$854$		0			0
$855$	0.0455783	−	0.0571534i	0.0455783	−	0.0571534i
$856$	1.19282	−	2.06603i	1.19282	−	2.06603i
$857$	1.52448	+	1.27919i	1.52448	+	1.27919i	0.826239	+	0.563320i	$0.190476\pi$
$857$	1.52448	+	1.27919i	1.52448	+	1.27919i	0.698237	+	0.715867i	$0.253968\pi$
$858$		0			0
$859$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$859$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$860$	3.42423	−	2.87327i	3.42423	−	2.87327i
$861$		0			0
$862$	1.99973	−	0.727844i	1.99973	−	0.727844i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	0.130399	+	0.254353i	0.130399	+	0.254353i
$865$		0			0
$866$		0			0
$867$	0.995031	−	0.0995678i	0.995031	−	0.0995678i
$868$		0			0
$869$		0			0
$870$	−0.153802	+	2.05235i	−0.153802	+	2.05235i
$871$		0			0
$872$	1.54938	−	2.68361i	1.54938	−	2.68361i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−0.594275	+	0.609280i	−0.594275	+	0.609280i
$877$	1.87705	+	0.683190i	1.87705	+	0.683190i	0.955573	+	0.294755i	$0.0952381\pi$
$877$	1.87705	+	0.683190i	1.87705	+	0.683190i	0.921476	+	0.388435i	$0.126984\pi$
$878$		0			0
$879$	−0.336557	−	0.0856979i	−0.336557	−	0.0856979i
$880$		0			0
$881$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.797133	−	0.603804i	$-0.793651\pi$
$881$	−0.921476	−	1.59604i	−0.921476	−	1.59604i	−0.124344	−	0.992239i	$-0.539683\pi$
$882$	−1.67274	+	0.338153i	−1.67274	+	0.338153i
$883$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$883$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$887$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$888$	0.664161	+	0.923791i	0.664161	+	0.923791i
$889$		0			0
$890$	−4.84931			−4.84931
$891$		0			0
$892$	−3.78212			−3.78212
$893$		0			0
$894$		0			0
$895$	1.79052	−	1.50242i	1.79052	−	1.50242i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−1.45455	−	1.64821i	−1.45455	−	1.64821i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	2.30950	−	2.36781i	2.30950	−	2.36781i
$907$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$907$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$908$		0			0
$909$	0.543524	−	0.332140i	0.543524	−	0.332140i
$910$		0			0
$911$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$911$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$912$	−0.00277573	+	0.0370396i	−0.00277573	+	0.0370396i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.446913	−	0.162663i	0.446913	−	0.162663i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.643393	+	0.539871i	0.643393	+	0.539871i
$926$	−0.543524	+	0.941410i	−0.543524	+	0.941410i
$927$	0.813387	+	0.122598i	0.813387	+	0.122598i
$928$	0.117559	+	0.203617i	0.117559	+	0.203617i
$929$	0.305003	−	1.72976i	0.305003	−	1.72976i	−0.318487	−	0.947927i	$-0.603175\pi$
$929$	0.305003	−	1.72976i	0.305003	−	1.72976i	0.623490	−	0.781831i	$-0.285714\pi$
$930$		0			0
$931$	0.0468544	+	0.0170536i	0.0468544	+	0.0170536i
$932$	−3.52291	−	1.28224i	−3.52291	−	1.28224i
$933$	0.197898	+	0.703372i	0.197898	+	0.703372i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$937$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$	1.53758	−	0.740458i	1.53758	−	0.740458i
$940$		0			0
$941$	−1.01376	+	0.850647i	−1.01376	+	0.850647i	−0.988831	−	0.149042i	$-0.952381\pi$
$941$	−1.01376	+	0.850647i	−1.01376	+	0.850647i	−0.0249307	+	0.999689i	$0.507937\pi$
$942$	0.980178	−	2.17230i	0.980178	−	2.17230i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.857396	+	0.312066i	−0.857396	+	0.312066i	−0.733052	−	0.680173i	$-0.761905\pi$
$947$	−0.857396	+	0.312066i	−0.857396	+	0.312066i	−0.124344	+	0.992239i	$0.539683\pi$
$948$	3.63675	−	0.363912i	3.63675	−	0.363912i
$949$		0			0
$950$	0.0169846	+	0.0963245i	0.0169846	+	0.0963245i
$951$		0			0
$952$		0			0
$953$	−0.921476	+	1.59604i	−0.921476	+	1.59604i	−0.124344	+	0.992239i	$0.539683\pi$
$953$	−0.921476	+	1.59604i	−0.921476	+	1.59604i	−0.797133	+	0.603804i	$0.793651\pi$
$954$		0			0
$955$	1.21135	+	2.09812i	1.21135	+	2.09812i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−1.75142	−	0.445966i	−1.75142	−	0.445966i
$961$	0.173648	−	0.984808i	0.173648	−	0.984808i
$962$		0			0
$963$	−0.487950	+	1.45231i	−0.487950	+	1.45231i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$967$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$968$	−1.19282	+	1.00090i	−1.19282	+	1.00090i
$969$		0			0
$970$		0			0
$971$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$971$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$972$	1.19238	+	1.49519i	1.19238	+	1.49519i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.202732	−	1.14975i	−0.202732	−	1.14975i	−0.900969	−	0.433884i	$-0.857143\pi$
$977$	−0.202732	−	1.14975i	−0.202732	−	1.14975i	0.698237	−	0.715867i	$-0.253968\pi$
$978$		0			0
$979$		0			0
$980$	1.40190	−	2.42817i	1.40190	−	2.42817i
$981$	−0.633808	+	1.88643i	−0.633808	+	1.88643i
$982$		0			0
$983$	−0.110609	+	0.627296i	−0.110609	+	0.627296i	0.878222	+	0.478254i	$0.158730\pi$
$983$	−0.110609	+	0.627296i	−0.110609	+	0.627296i	−0.988831	+	0.149042i	$0.952381\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.48628	−	1.24714i	1.48628	−	1.24714i
$996$	−3.76333	+	0.376578i	−3.76333	+	0.376578i
$997$	1.87705	−	0.683190i	1.87705	−	0.683190i	0.921476	−	0.388435i	$-0.126984\pi$
$997$	1.87705	−	0.683190i	1.87705	−	0.683190i	0.955573	−	0.294755i	$-0.0952381\pi$
$998$	−2.82009			−2.82009
$999$	−0.535628	−	0.496990i	−0.535628	−	0.496990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1917.1.s.b.709.6	✓	36
27.4	even	9	inner	1917.1.s.b.922.6	yes	36
71.70	odd	2	CM	1917.1.s.b.709.6	✓	36
1917.922	odd	18	inner	1917.1.s.b.922.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1917.1.s.b.709.6	✓	36	1.1	even	1	trivial
1917.1.s.b.709.6	✓	36	71.70	odd	2	CM
1917.1.s.b.922.6	yes	36	27.4	even	9	inner
1917.1.s.b.922.6	yes	36	1917.922	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1917 = 3^{3} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1917.s (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60366 - 0.583685i) q^{2} +(-0.583744 - 0.811938i) q^{3} +(1.46500 - 1.22928i) q^{4} +(-0.254586 - 1.44383i) q^{5} +(-1.41004 - 0.961352i) q^{6} +(0.778561 - 1.34851i) q^{8} +(-0.318487 + 0.947927i) q^{9} +O(q^{10})\)	\(q+(1.60366 - 0.583685i) q^{2} +(-0.583744 - 0.811938i) q^{3} +(1.46500 - 1.22928i) q^{4} +(-0.254586 - 1.44383i) q^{5} +(-1.41004 - 0.961352i) q^{6} +(0.778561 - 1.34851i) q^{8} +(-0.318487 + 0.947927i) q^{9} +(-1.25101 - 2.16682i) q^{10} +(-1.85328 - 0.471904i) q^{12} +(-1.02369 + 1.04954i) q^{15} +(0.129356 - 0.733617i) q^{16} +(0.0425463 + 1.70605i) q^{18} +(0.0249307 - 0.0431812i) q^{19} +(-2.14784 - 1.80225i) q^{20} +(-1.54938 + 0.155039i) q^{24} +(-1.08014 + 0.393139i) q^{25} +(0.955573 - 0.294755i) q^{27} +(0.772967 - 0.281337i) q^{29} +(-1.02905 + 2.28061i) q^{30} +(0.0496340 + 0.281488i) q^{32} +(0.698686 + 1.78022i) q^{36} +(-0.365341 - 0.632789i) q^{37} +(0.0147762 - 0.0837998i) q^{38} +(-2.14523 - 0.780798i) q^{40} +(-0.276841 + 1.57004i) q^{43} +(1.44973 + 0.218511i) q^{45} +(-0.671162 + 0.323215i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-1.50271 + 1.26092i) q^{50} +(1.36037 - 1.03044i) q^{54} +(-0.0496136 + 0.00496459i) q^{57} +(1.07537 - 0.902339i) q^{58} +(-0.209529 + 2.79597i) q^{60} +(0.616364 + 1.06757i) q^{64} +(-0.500000 - 0.866025i) q^{71} +(1.03033 + 1.16750i) q^{72} +(0.222521 - 0.385418i) q^{73} +(-0.955233 - 0.801536i) q^{74} +(0.949729 + 0.647514i) q^{75} +(-0.0165584 - 0.0939073i) q^{76} +(-1.79589 + 0.653650i) q^{79} -1.09215 q^{80} +(-0.797133 - 0.603804i) q^{81} +(1.85839 - 0.676400i) q^{83} +(0.472452 + 2.67941i) q^{86} +(-0.679643 - 0.463373i) q^{87} +(0.969077 - 1.67849i) q^{89} +(2.45242 - 0.495767i) q^{90} +(-0.0686934 - 0.0250023i) q^{95} +(0.199578 - 0.204617i) q^{96} +(0.853291 + 1.47794i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} - 6 q^{4} - 3 q^{8}+O(q^{10}) \) 36 * q - 6 * q^2 - 6 * q^4 - 3 * q^8	\( 36 q - 6 q^{2} - 6 q^{4} - 3 q^{8} - 6 q^{12} - 3 q^{16} - 18 q^{18} - 15 q^{20} - 6 q^{24} + 3 q^{27} + 3 q^{29} - 3 q^{30} - 3 q^{32} + 3 q^{36} - 3 q^{37} + 3 q^{38} + 6 q^{40} + 3 q^{43} - 3 q^{45} - 6 q^{48} + 3 q^{54} + 3 q^{57} + 3 q^{58} - 3 q^{60} - 21 q^{64} - 18 q^{71} + 3 q^{72} + 6 q^{73} - 24 q^{74} - 21 q^{75} - 3 q^{76} + 6 q^{80} + 3 q^{86} + 39 q^{90} - 3 q^{95} - 3 q^{96}+O(q^{100}) \) 36 * q - 6 * q^2 - 6 * q^4 - 3 * q^8 - 6 * q^12 - 3 * q^16 - 18 * q^18 - 15 * q^20 - 6 * q^24 + 3 * q^27 + 3 * q^29 - 3 * q^30 - 3 * q^32 + 3 * q^36 - 3 * q^37 + 3 * q^38 + 6 * q^40 + 3 * q^43 - 3 * q^45 - 6 * q^48 + 3 * q^54 + 3 * q^57 + 3 * q^58 - 3 * q^60 - 21 * q^64 - 18 * q^71 + 3 * q^72 + 6 * q^73 - 24 * q^74 - 21 * q^75 - 3 * q^76 + 6 * q^80 + 3 * q^86 + 39 * q^90 - 3 * q^95 - 3 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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