LMFDB - Embedded newform 2627.1.x.b.780.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2627,1,Mod(141,2627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2627, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 9]))

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

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

chi := DirichletCharacter("2627.141");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2627 = 37 \cdot 71 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2627.x (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:	$1.31104378819$
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:	$D_{126}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{126} - \cdots)$

Embedding invariants

Embedding label			780.2
Root			$-0.661686 - 0.749781i$ of defining polynomial
Character	$\chi$	$=$	2627.780
Dual form			2627.1.x.b.1135.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00510 + 1.19784i) q^{2} +(1.48471 - 1.24582i) q^{3} +(-0.250929 - 1.42309i) q^{4} +(0.0340966 - 0.0936796i) q^{5} +3.03062i q^{6} +(0.602663 + 0.347948i) q^{8} +(0.478651 - 2.71457i) q^{9} +O(q^{10})$	\(q+(-1.00510 + 1.19784i) q^{2} +(1.48471 - 1.24582i) q^{3} +(-0.250929 - 1.42309i) q^{4} +(0.0340966 - 0.0936796i) q^{5} +3.03062i q^{6} +(0.602663 + 0.347948i) q^{8} +(0.478651 - 2.71457i) q^{9} +(0.0779422 + 0.135000i) q^{10} +(-2.14547 - 1.80026i) q^{12} +(-0.0660845 - 0.181566i) q^{15} +(0.335372 - 0.122066i) q^{16} +(2.77051 + 3.30176i) q^{18} +(-0.963900 - 1.14873i) q^{19} +(-0.141870 - 0.0250155i) q^{20} +(1.32826 - 0.234209i) q^{24} +(0.758431 + 0.636399i) q^{25} +(-1.70213 - 2.94817i) q^{27} +(-0.975699 - 0.563320i) q^{29} +(0.283907 + 0.103334i) q^{30} +(-0.428880 + 1.17834i) q^{32} -3.98318 q^{36} +(0.661686 + 0.749781i) q^{37} +2.34481 q^{38} +(0.0531444 - 0.0445934i) q^{40} -1.98448i q^{43} +(-0.237979 - 0.137397i) q^{45} +(0.345860 - 0.599047i) q^{48} +(0.766044 + 0.642788i) q^{49} +(-1.52460 + 0.268829i) q^{50} +(5.24224 + 0.924349i) q^{54} +(-2.86223 - 0.504688i) q^{57} +(1.65544 - 0.602532i) q^{58} +(-0.241801 + 0.139604i) q^{60} +(-0.801938 - 1.38900i) q^{64} +(-0.766044 + 0.642788i) q^{71} +(1.23299 - 1.46942i) q^{72} +1.08509 q^{73} +(-1.56318 + 0.0389832i) q^{74} +1.91889 q^{75} +(-1.39288 + 1.65997i) q^{76} +(-0.574612 + 1.57873i) q^{79} -0.0355796i q^{80} +(-3.60986 - 1.31388i) q^{81} +(0.126882 - 0.719581i) q^{83} +(2.37708 + 1.99461i) q^{86} +(-2.15043 + 0.379179i) q^{87} +(0.658474 + 1.80914i) q^{89} +(0.403773 - 0.146961i) q^{90} +(-0.140478 + 0.0511300i) q^{95} +(0.831235 + 2.28380i) q^{96} +(-1.53991 + 0.271527i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9}+O(q^{10}) $ 36 * q + 6 * q^3 + 3 * q^5 - 6 * q^9	$ 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9} + 6 q^{12} - 3 q^{15} + 21 q^{18} + 3 q^{19} - 36 q^{20} - 21 q^{24} + 3 q^{25} + 3 q^{27} - 9 q^{29} - 21 q^{30} - 48 q^{36} - 3 q^{57} + 54 q^{60} + 24 q^{64} + 21 q^{72} - 6 q^{75} - 3 q^{76} + 6 q^{79} - 3 q^{81} - 12 q^{87} + 3 q^{89} + 42 q^{90} - 6 q^{95} - 21 q^{96}+O(q^{100}) $ 36 * q + 6 * q^3 + 3 * q^5 - 6 * q^9 + 6 * q^12 - 3 * q^15 + 21 * q^18 + 3 * q^19 - 36 * q^20 - 21 * q^24 + 3 * q^25 + 3 * q^27 - 9 * q^29 - 21 * q^30 - 48 * q^36 - 3 * q^57 + 54 * q^60 + 24 * q^64 + 21 * q^72 - 6 * q^75 - 3 * q^76 + 6 * q^79 - 3 * q^81 - 12 * q^87 + 3 * q^89 + 42 * q^90 - 6 * q^95 - 21 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2627\mathbb{Z}\right)^\times$.

$n$	$149$	$853$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.00510	+	1.19784i	−1.00510	+	1.19784i	−0.0249307	+	0.999689i	$0.507937\pi$
$2$	−1.00510	+	1.19784i	−1.00510	+	1.19784i	−0.980172	+	0.198146i	$0.936508\pi$
$3$	1.48471	−	1.24582i	1.48471	−	1.24582i	0.583744	−	0.811938i	$-0.301587\pi$
$3$	1.48471	−	1.24582i	1.48471	−	1.24582i	0.900969	−	0.433884i	$-0.142857\pi$
$4$	−0.250929	−	1.42309i	−0.250929	−	1.42309i
$5$	0.0340966	−	0.0936796i	0.0340966	−	0.0936796i	−0.921476	−	0.388435i	$-0.873016\pi$
$5$	0.0340966	−	0.0936796i	0.0340966	−	0.0936796i	0.955573	+	0.294755i	$0.0952381\pi$
$6$			3.03062i			3.03062i
$7$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$7$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$8$	0.602663	+	0.347948i	0.602663	+	0.347948i
$9$	0.478651	−	2.71457i	0.478651	−	2.71457i
$10$	0.0779422	+	0.135000i	0.0779422	+	0.135000i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−2.14547	−	1.80026i	−2.14547	−	1.80026i
$13$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$13$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$14$		0			0
$15$	−0.0660845	−	0.181566i	−0.0660845	−	0.181566i
$16$	0.335372	−	0.122066i	0.335372	−	0.122066i
$17$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$17$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$18$	2.77051	+	3.30176i	2.77051	+	3.30176i
$19$	−0.963900	−	1.14873i	−0.963900	−	1.14873i	−0.988831	−	0.149042i	$-0.952381\pi$
$19$	−0.963900	−	1.14873i	−0.963900	−	1.14873i	0.0249307	−	0.999689i	$-0.492063\pi$
$20$	−0.141870	−	0.0250155i	−0.141870	−	0.0250155i
$21$		0			0
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	1.32826	−	0.234209i	1.32826	−	0.234209i
$25$	0.758431	+	0.636399i	0.758431	+	0.636399i
$26$		0			0
$27$	−1.70213	−	2.94817i	−1.70213	−	2.94817i
$28$		0			0
$29$	−0.975699	−	0.563320i	−0.975699	−	0.563320i	−0.0747301	−	0.997204i	$-0.523810\pi$
$29$	−0.975699	−	0.563320i	−0.975699	−	0.563320i	−0.900969	+	0.433884i	$0.857143\pi$
$30$	0.283907	+	0.103334i	0.283907	+	0.103334i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.428880	+	1.17834i	−0.428880	+	1.17834i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−3.98318			−3.98318
$37$	0.661686	+	0.749781i	0.661686	+	0.749781i
$37$	0.661686	+	0.749781i	0.661686	+	0.749781i
$38$	2.34481			2.34481
$39$		0			0
$40$	0.0531444	−	0.0445934i	0.0531444	−	0.0445934i
$41$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$41$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$42$		0			0
$43$		−	1.98448i		−	1.98448i	−0.124344	−	0.992239i	$-0.539683\pi$
$43$		−	1.98448i		−	1.98448i	0.124344	−	0.992239i	$-0.460317\pi$
$44$		0			0
$45$	−0.237979	−	0.137397i	−0.237979	−	0.137397i
$46$		0			0
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$	0.345860	−	0.599047i	0.345860	−	0.599047i
$49$	0.766044	+	0.642788i	0.766044	+	0.642788i
$50$	−1.52460	+	0.268829i	−1.52460	+	0.268829i
$51$		0			0
$52$		0			0
$53$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$53$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$54$	5.24224	+	0.924349i	5.24224	+	0.924349i
$55$		0			0
$56$		0			0
$57$	−2.86223	−	0.504688i	−2.86223	−	0.504688i
$58$	1.65544	−	0.602532i	1.65544	−	0.602532i
$59$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$59$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$60$	−0.241801	+	0.139604i	−0.241801	+	0.139604i
$61$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$61$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$62$		0			0
$63$		0			0
$64$	−0.801938	−	1.38900i	−0.801938	−	1.38900i
$65$		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
$71$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$71$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$72$	1.23299	−	1.46942i	1.23299	−	1.46942i
$73$	1.08509			1.08509			0.542546	−	0.840026i	$-0.317460\pi$
$73$	1.08509			1.08509			0.542546	+	0.840026i	$0.317460\pi$
$74$	−1.56318	+	0.0389832i	−1.56318	+	0.0389832i
$75$	1.91889			1.91889
$76$	−1.39288	+	1.65997i	−1.39288	+	1.65997i
$77$		0			0
$78$		0			0
$79$	−0.574612	+	1.57873i	−0.574612	+	1.57873i	0.222521	+	0.974928i	$0.428571\pi$
$79$	−0.574612	+	1.57873i	−0.574612	+	1.57873i	−0.797133	+	0.603804i	$0.793651\pi$
$80$		−	0.0355796i		−	0.0355796i
$81$	−3.60986	−	1.31388i	−3.60986	−	1.31388i
$82$		0			0
$83$	0.126882	−	0.719581i	0.126882	−	0.719581i	−0.853291	−	0.521435i	$-0.825397\pi$
$83$	0.126882	−	0.719581i	0.126882	−	0.719581i	0.980172	−	0.198146i	$-0.0634921\pi$
$84$		0			0
$85$		0			0
$86$	2.37708	+	1.99461i	2.37708	+	1.99461i
$87$	−2.15043	+	0.379179i	−2.15043	+	0.379179i
$88$		0			0
$89$	0.658474	+	1.80914i	0.658474	+	1.80914i	0.583744	+	0.811938i	$0.301587\pi$
$89$	0.658474	+	1.80914i	0.658474	+	1.80914i	0.0747301	+	0.997204i	$0.476190\pi$
$90$	0.403773	−	0.146961i	0.403773	−	0.146961i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.140478	+	0.0511300i	−0.140478	+	0.0511300i
$96$	0.831235	+	2.28380i	0.831235	+	2.28380i
$97$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$97$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$98$	−1.53991	+	0.271527i	−1.53991	+	0.271527i
$99$		0			0
$100$	0.715340	−	1.23901i	0.715340	−	1.23901i
$101$	−0.0249307	−	0.0431812i	−0.0249307	−	0.0431812i	0.853291	−	0.521435i	$-0.174603\pi$
$101$	−0.0249307	−	0.0431812i	−0.0249307	−	0.0431812i	−0.878222	+	0.478254i	$0.841270\pi$
$102$		0			0
$103$	0.427396	+	0.246757i	0.427396	+	0.246757i	0.698237	−	0.715867i	$-0.253968\pi$
$103$	0.427396	+	0.246757i	0.427396	+	0.246757i	−0.270840	+	0.962624i	$0.587302\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$107$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$108$	−3.76840	+	3.16206i	−3.76840	+	3.16206i
$109$	0.317225	−	0.378054i	0.317225	−	0.378054i	−0.583744	−	0.811938i	$-0.698413\pi$
$109$	0.317225	−	0.378054i	0.317225	−	0.378054i	0.900969	+	0.433884i	$0.142857\pi$
$110$		0			0
$111$	1.91651	+	0.288867i	1.91651	+	0.288867i
$112$		0			0
$113$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$113$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$114$	3.48137	−	2.92122i	3.48137	−	2.92122i
$115$		0			0
$116$	−0.556823	+	1.52986i	−0.556823	+	1.52986i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.0233487	−	0.132417i	0.0233487	−	0.132417i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.171813	−	0.0991964i	0.171813	−	0.0991964i
$126$		0			0
$127$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$127$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$128$	1.23491	+	0.217748i	1.23491	+	0.217748i
$129$	−2.47231	−	2.94638i	−2.47231	−	2.94638i
$130$		0			0
$131$	1.18926	+	0.209699i	1.18926	+	0.209699i	0.733052	−	0.680173i	$-0.238095\pi$
$131$	1.18926	+	0.209699i	1.18926	+	0.209699i	0.456211	+	0.889872i	$0.349206\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.334221	+	0.0589321i	−0.334221	+	0.0589321i
$136$		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		0.173648	−	0.984808i	$-0.444444\pi$
$139$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$140$		0			0
$141$		0			0
$142$		−	1.56366i		−	1.56366i
$143$		0			0
$144$	−0.170829	−	0.968818i	−0.170829	−	0.968818i
$145$	−0.0860396	+	0.0721958i	−0.0860396	+	0.0721958i
$146$	−1.09063	+	1.29976i	−1.09063	+	1.29976i
$147$	1.93815			1.93815
$148$	0.900969	−	1.12978i	0.900969	−	1.12978i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	−1.92868	+	2.29852i	−1.92868	+	2.29852i
$151$	−0.630128	+	0.528741i	−0.630128	+	0.528741i	−0.900969	−	0.433884i	$-0.857143\pi$
$151$	−0.630128	+	0.528741i	−0.630128	+	0.528741i	0.270840	+	0.962624i	$0.412698\pi$
$152$	−0.181209	−	1.02769i	−0.181209	−	1.02769i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.345571	−	1.95983i	0.345571	−	1.95983i	0.0747301	−	0.997204i	$-0.476190\pi$
$157$	0.345571	−	1.95983i	0.345571	−	1.95983i	0.270840	−	0.962624i	$-0.412698\pi$
$158$	−1.31352	−	2.27508i	−1.31352	−	2.27508i
$159$		0			0
$160$	0.0957629	+	0.0803546i	0.0957629	+	0.0803546i
$161$		0			0
$162$	5.20210	−	3.00343i	5.20210	−	3.00343i
$163$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$163$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$164$		0			0
$165$		0			0
$166$	0.734411	+	0.875237i	0.734411	+	0.875237i
$167$	0.378930	+	0.451591i	0.378930	+	0.451591i	0.921476	−	0.388435i	$-0.126984\pi$
$167$	0.378930	+	0.451591i	0.378930	+	0.451591i	−0.542546	+	0.840026i	$0.682540\pi$
$168$		0			0
$169$	0.939693	−	0.342020i	0.939693	−	0.342020i
$170$		0			0
$171$	−3.57968	+	2.06673i	−3.57968	+	2.06673i
$172$	−2.82409	+	0.497963i	−2.82409	+	0.497963i
$173$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$173$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$174$	1.70721	−	2.95697i	1.70721	−	2.95697i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−2.82889	−	1.02963i	−2.82889	−	1.02963i
$179$			1.36035i			1.36035i	0.733052	+	0.680173i	$0.238095\pi$
$179$			1.36035i			1.36035i	−0.733052	+	0.680173i	$0.761905\pi$
$180$	−0.135813	+	0.373142i	−0.135813	+	0.373142i
$181$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$181$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.0928005	−	0.0364215i	0.0928005	−	0.0364215i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	0.0799500	−	0.219661i	0.0799500	−	0.219661i
$191$			0.199136i			0.199136i	0.995031	+	0.0995678i	$0.0317460\pi$
$191$			0.199136i			0.199136i	−0.995031	+	0.0995678i	$0.968254\pi$
$192$	−2.92109	−	1.06319i	−2.92109	−	1.06319i
$193$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$193$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$194$		0			0
$195$		0			0
$196$	0.722521	−	1.25144i	0.722521	−	1.25144i
$197$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$197$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$198$		0			0
$199$	0.903152	−	0.521435i	0.903152	−	0.521435i	0.0249307	−	0.999689i	$-0.492063\pi$
$199$	0.903152	−	0.521435i	0.903152	−	0.521435i	0.878222	+	0.478254i	$0.158730\pi$
$200$	0.235645	+	0.647429i	0.235645	+	0.647429i
$201$		0			0
$202$	0.0767819	+	0.0135387i	0.0767819	+	0.0135387i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.725152	+	0.263934i	−0.725152	+	0.263934i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	−0.336557	+	1.90871i	−0.336557	+	1.90871i
$214$	1.35417	+	0.781831i	1.35417	+	0.781831i
$215$	−0.185905	−	0.0676640i	−0.185905	−	0.0676640i
$216$		−	2.36901i		−	2.36901i
$217$		0			0
$218$	0.134003	+	0.759967i	0.134003	+	0.759967i
$219$	1.61105	−	1.35183i	1.61105	−	1.35183i
$220$		0			0
$221$		0			0
$222$	−2.27230	+	2.00532i	−2.27230	+	2.00532i
$223$	−1.96034			−1.96034			−0.980172	−	0.198146i	$-0.936508\pi$
$223$	−1.96034			−1.96034			−0.980172	+	0.198146i	$0.936508\pi$
$224$		0			0
$225$	2.09057	−	1.75420i	2.09057	−	1.75420i
$226$		0			0
$227$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$227$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$228$			4.19985i			4.19985i
$229$	1.79589	+	0.653650i	1.79589	+	0.653650i	0.998757	+	0.0498459i	$0.0158730\pi$
$229$	1.79589	+	0.653650i	1.79589	+	0.653650i	0.797133	+	0.603804i	$0.206349\pi$
$230$		0			0
$231$		0			0
$232$	−0.392012	−	0.678985i	−0.392012	−	0.678985i
$233$	−0.988831	+	1.71271i	−0.988831	+	1.71271i	−0.365341	+	0.930874i	$0.619048\pi$
$233$	−0.988831	+	1.71271i	−0.988831	+	1.71271i	−0.623490	+	0.781831i	$0.714286\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.11369	+	3.05983i	1.11369	+	3.05983i
$238$		0			0
$239$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$239$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$240$	−0.0443258	−	0.0528255i	−0.0443258	−	0.0528255i
$241$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$241$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$242$	1.53991	+	0.271527i	1.53991	+	0.271527i
$243$	−3.79752	+	1.38218i	−3.79752	+	1.38218i
$244$		0			0
$245$	0.0863356	−	0.0498459i	0.0863356	−	0.0498459i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.708087	−	1.22644i	−0.708087	−	1.22644i
$250$	−0.0538690	+	0.305506i	−0.0538690	+	0.305506i
$251$	1.35417	+	0.781831i	1.35417	+	0.781831i	0.988831	−	0.149042i	$-0.0476190\pi$
$251$	1.35417	+	0.781831i	1.35417	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.273398	+	0.229408i	−0.273398	+	0.229408i
$257$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$257$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$258$	6.01420			6.01420
$259$		0			0
$260$		0			0
$261$	−1.99619	+	2.37897i	−1.99619	+	2.37897i
$262$	−1.44652	+	1.21377i	−1.44652	+	1.21377i
$263$	0.346865	+	1.96717i	0.346865	+	1.96717i	0.222521	+	0.974928i	$0.428571\pi$
$263$	0.346865	+	1.96717i	0.346865	+	1.96717i	0.124344	+	0.992239i	$0.460317\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	3.23151	+	1.86571i	3.23151	+	1.86571i
$268$		0			0
$269$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$269$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$270$	0.265335	−	0.459574i	0.265335	−	0.459574i
$271$	1.38036	+	1.15826i	1.38036	+	1.15826i	0.969077	+	0.246757i	$0.0793651\pi$
$271$	1.38036	+	1.15826i	1.38036	+	1.15826i	0.411287	+	0.911506i	$0.365079\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.19671	+	1.42618i	1.19671	+	1.42618i	0.878222	+	0.478254i	$0.158730\pi$
$277$	1.19671	+	1.42618i	1.19671	+	1.42618i	0.318487	+	0.947927i	$0.396825\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$281$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$282$		0			0
$283$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$283$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$284$	1.10697	+	0.928855i	1.10697	+	0.928855i
$285$	−0.144871	+	0.250924i	−0.144871	+	0.250924i
$286$		0			0
$287$		0			0
$288$	2.99339	+	1.72824i	2.99339	+	1.72824i
$289$	0.939693	+	0.342020i	0.939693	+	0.342020i
$290$		−	0.175626i		−	0.175626i
$291$		0			0
$292$	−0.272281	−	1.54418i	−0.272281	−	1.54418i
$293$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$293$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$294$	−1.94805	+	2.32159i	−1.94805	+	2.32159i
$295$		0			0
$296$	0.137889	+	0.682098i	0.137889	+	0.682098i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.481506	−	2.73075i	−0.481506	−	2.73075i
$301$		0			0
$302$		−	1.28623i		−	1.28623i
$303$	−0.0908110	−	0.0330525i	−0.0908110	−	0.0330525i
$304$	−0.463486	−	0.267594i	−0.463486	−	0.267594i
$305$		0			0
$306$		0			0
$307$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$307$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$308$		0			0
$309$	0.941976	−	0.166096i	0.941976	−	0.166096i
$310$		0			0
$311$	−0.648420	−	1.78152i	−0.648420	−	1.78152i	−0.623490	−	0.781831i	$-0.714286\pi$
$311$	−0.648420	−	1.78152i	−0.648420	−	1.78152i	−0.0249307	−	0.999689i	$-0.507937\pi$
$312$		0			0
$313$	−1.86705	−	0.329212i	−1.86705	−	0.329212i	−0.878222	−	0.478254i	$-0.841270\pi$
$313$	−1.86705	−	0.329212i	−1.86705	−	0.329212i	−0.988831	+	0.149042i	$0.952381\pi$
$314$	2.00022	+	2.38377i	2.00022	+	2.38377i
$315$		0			0
$316$	2.39086	+	0.421574i	2.39086	+	0.421574i
$317$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$317$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$318$		0			0
$319$		0			0
$320$	−0.157464	+	0.0277652i	−0.157464	+	0.0277652i
$321$	−1.48471	−	1.24582i	−1.48471	−	1.24582i
$322$		0			0
$323$		0			0
$324$	−0.963952	+	5.46684i	−0.963952	+	5.46684i
$325$		0			0
$326$		0			0
$327$		−	0.956508i		−	0.956508i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$331$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$332$	−1.05587			−1.05587
$333$	2.35205	−	1.43731i	2.35205	−	1.43731i
$334$	−0.921795			−0.921795
$335$		0			0
$336$		0			0
$337$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$337$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$338$	−0.534804	+	1.46936i	−0.534804	+	1.46936i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	1.12235	−	6.36514i	1.12235	−	6.36514i
$343$		0			0
$344$	0.690495	−	1.19597i	0.690495	−	1.19597i
$345$		0			0
$346$		0			0
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	1.07921	+	2.96510i	1.07921	+	2.96510i
$349$		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		−0.984808	−	0.173648i	$-0.944444\pi$
$353$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$354$		0			0
$355$	0.0340966	+	0.0936796i	0.0340966	+	0.0936796i
$356$	2.40934	−	1.39103i	2.40934	−	1.39103i
$357$		0			0
$358$	−1.62947	−	1.36729i	−1.62947	−	1.36729i
$359$	−0.124344	+	0.215370i	−0.124344	+	0.215370i	−0.921476	−	0.388435i	$-0.873016\pi$
$359$	−0.124344	+	0.215370i	−0.124344	+	0.215370i	0.797133	+	0.603804i	$0.206349\pi$
$360$	−0.0956142	−	0.165609i	−0.0956142	−	0.165609i
$361$	−0.216832	+	1.22972i	−0.216832	+	1.22972i
$362$		0			0
$363$	−1.82127	−	0.662888i	−1.82127	−	0.662888i
$364$		0			0
$365$	0.0369980	−	0.101651i	0.0369980	−	0.101651i
$366$		0			0
$367$	−1.22128	+	1.02477i	−1.22128	+	1.02477i	−0.222521	+	0.974928i	$0.571429\pi$
$367$	−1.22128	+	1.02477i	−1.22128	+	1.02477i	−0.998757	+	0.0498459i	$0.984127\pi$
$368$		0			0
$369$		0			0
$370$	−0.0496471	+	0.147767i	−0.0496471	+	0.147767i
$371$		0			0
$372$		0			0
$373$	1.53018	−	1.28398i	1.53018	−	1.28398i	0.733052	−	0.680173i	$-0.238095\pi$
$373$	1.53018	−	1.28398i	1.53018	−	1.28398i	0.797133	−	0.603804i	$-0.206349\pi$
$374$		0			0
$375$	0.131512	−	0.361327i	0.131512	−	0.361327i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.142839	+	0.810077i	−0.142839	+	0.810077i	0.826239	+	0.563320i	$0.190476\pi$
$379$	−0.142839	+	0.810077i	−0.142839	+	0.810077i	−0.969077	+	0.246757i	$0.920635\pi$
$380$	0.108013	+	0.187083i	0.108013	+	0.187083i
$381$		0			0
$382$	−0.238532	−	0.200152i	−0.238532	−	0.200152i
$383$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$383$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$384$	2.10476	−	1.21518i	2.10476	−	1.21518i
$385$		0			0
$386$		0			0
$387$	−5.38700	−	0.949873i	−5.38700	−	0.949873i
$388$		0			0
$389$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$389$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$390$		0			0
$391$		0			0
$392$	0.238010	+	0.653928i	0.238010	+	0.653928i
$393$	2.02696	−	1.17027i	2.02696	−	1.17027i
$394$		0			0
$395$	0.128303	+	0.107659i	0.128303	+	0.107659i
$396$		0			0
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$	−0.283168	+	1.60592i	−0.283168	+	1.60592i
$399$		0			0
$400$	0.332039	+	0.120852i	0.332039	+	0.120852i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		0			0
$404$	−0.0551949	+	0.0463140i	−0.0551949	+	0.0463140i
$405$	−0.246168	+	0.293372i	−0.246168	+	0.293372i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.28198	+	1.52780i	−1.28198	+	1.52780i	−0.583744	+	0.811938i	$0.698413\pi$
$409$	−1.28198	+	1.52780i	−1.28198	+	1.52780i	−0.698237	+	0.715867i	$0.746032\pi$
$410$		0			0
$411$		0			0
$412$	0.243912	−	0.670141i	0.243912	−	0.670141i
$413$		0			0
$414$		0			0
$415$	−0.0630839	−	0.0364215i	−0.0630839	−	0.0364215i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.114493	−	0.0960712i	−0.114493	−	0.0960712i	0.583744	−	0.811938i	$-0.301587\pi$
$419$	−0.114493	−	0.0960712i	−0.114493	−	0.0960712i	−0.698237	+	0.715867i	$0.746032\pi$
$420$		0			0
$421$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$421$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−1.94805	−	2.32159i	−1.94805	−	2.32159i
$427$		0			0
$428$	−1.35790	+	0.494233i	−1.35790	+	0.494233i
$429$		0			0
$430$	0.267904	−	0.154675i	0.267904	−	0.154675i
$431$	1.96900	−	0.347188i	1.96900	−	0.347188i	0.980172	−	0.198146i	$-0.0634921\pi$
$431$	1.96900	−	0.347188i	1.96900	−	0.347188i	0.988831	−	0.149042i	$-0.0476190\pi$
$432$	−0.930718	−	0.780965i	−0.930718	−	0.780965i
$433$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$433$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$434$		0			0
$435$	−0.0378010	+	0.214380i	−0.0378010	+	0.214380i
$436$	−0.617606	−	0.356575i	−0.617606	−	0.356575i
$437$		0			0
$438$			3.28850i			3.28850i
$439$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$439$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$440$		0			0
$441$	2.11156	−	1.77181i	2.11156	−	1.77181i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	−0.0698237	−	2.79984i	−0.0698237	−	2.79984i
$445$	0.191931			0.191931
$446$	1.97035	−	2.34817i	1.97035	−	2.34817i
$447$		0			0
$448$		0			0
$449$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$449$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$450$			4.26731i			4.26731i
$451$		0			0
$452$		0			0
$453$	−0.276843	+	1.57006i	−0.276843	+	1.57006i
$454$		0			0
$455$		0			0
$456$	−1.54936	−	1.30006i	−1.54936	−	1.30006i
$457$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$457$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$458$	−2.58802	+	1.49419i	−2.58802	+	1.49419i
$459$		0			0
$460$		0			0
$461$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$461$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$462$		0			0
$463$	0.191605	+	0.228346i	0.191605	+	0.228346i	0.853291	−	0.521435i	$-0.174603\pi$
$463$	0.191605	+	0.228346i	0.191605	+	0.228346i	−0.661686	+	0.749781i	$0.730159\pi$
$464$	−0.395985	−	0.0698228i	−0.395985	−	0.0698228i
$465$		0			0
$466$	−1.05766	−	2.90590i	−1.05766	−	2.90590i
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.92852	−	3.34030i	−1.92852	−	3.34030i
$472$		0			0
$473$		0			0
$474$	−4.78454	−	1.74143i	−4.78454	−	1.74143i
$475$		−	1.48466i		−	1.48466i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$479$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$480$	0.242288			0.242288
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.10697	+	0.928855i	−1.10697	+	0.928855i
$485$		0			0
$486$	2.16127	−	5.93803i	2.16127	−	5.93803i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$	−0.0270690	+	0.153516i	−0.0270690	+	0.153516i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.18078	+	0.384530i	2.18078	+	0.384530i
$499$	−0.920301	−	1.09677i	−0.920301	−	1.09677i	−0.995031	−	0.0995678i	$-0.968254\pi$
$499$	−0.920301	−	1.09677i	−0.920301	−	1.09677i	0.0747301	−	0.997204i	$-0.476190\pi$
$500$	−0.184278	−	0.219614i	−0.184278	−	0.219614i
$501$	1.12520	+	0.198404i	1.12520	+	0.198404i
$502$	−2.29759	+	0.836254i	−2.29759	+	0.836254i
$503$	−0.682128	−	1.87413i	−0.682128	−	1.87413i	−0.411287	−	0.911506i	$-0.634921\pi$
$503$	−0.682128	−	1.87413i	−0.682128	−	1.87413i	−0.270840	−	0.962624i	$-0.587302\pi$
$504$		0			0
$505$	−0.00489525		0.000863165i	−0.00489525		0.000863165i
$506$		0			0
$507$	0.969077	−	1.67849i	0.969077	−	1.67849i
$508$		0			0
$509$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$509$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$510$		0			0
$511$		0			0
$512$			0.695895i			0.695895i
$513$	−1.74598	+	4.79703i	−1.74598	+	4.79703i
$514$		0			0
$515$	0.0376889	−	0.0316247i	0.0376889	−	0.0316247i
$516$	−3.57259	+	4.25764i	−3.57259	+	4.25764i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.12310	+	0.942393i	−1.12310	+	0.942393i	−0.998757	−	0.0498459i	$-0.984127\pi$
$521$	−1.12310	+	0.942393i	−1.12310	+	0.942393i	−0.124344	+	0.992239i	$0.539683\pi$
$522$	−0.843233	−	4.78221i	−0.843233	−	4.78221i
$523$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$523$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$524$		−	1.74505i		−	1.74505i
$525$		0			0
$526$	−2.70498	−	1.56172i	−2.70498	−	1.56172i
$527$		0			0
$528$		0			0
$529$	0.500000	−	0.866025i	0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−5.48282	+	1.99558i	−5.48282	+	1.99558i
$535$	−0.0981772	−	0.0173113i	−0.0981772	−	0.0173113i
$536$		0			0
$537$	1.69475	+	2.01972i	1.69475	+	2.01972i
$538$		0			0
$539$		0			0
$540$	0.167731	+	0.460838i	0.167731	+	0.460838i
$541$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$541$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$542$	−2.77482	+	0.489275i	−2.77482	+	0.489275i
$543$		0			0
$544$		0			0
$545$	−0.0245997	−	0.0426079i	−0.0245997	−	0.0426079i
$546$		0			0
$547$	−0.828360	−	0.478254i	−0.828360	−	0.478254i	0.0249307	−	0.999689i	$-0.492063\pi$
$547$	−0.828360	−	0.478254i	−0.828360	−	0.478254i	−0.853291	+	0.521435i	$0.825397\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.293373	+	1.66380i	0.293373	+	1.66380i
$552$		0			0
$553$		0			0
$554$	−2.91115			−2.91115
$555$	0.0924073	−	0.169688i	0.0924073	−	0.169688i
$556$		0			0
$557$	−1.17181	+	1.39651i	−1.17181	+	1.39651i	−0.270840	+	0.962624i	$0.587302\pi$
$557$	−1.17181	+	1.39651i	−1.17181	+	1.39651i	−0.900969	+	0.433884i	$0.857143\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−0.685323	+	0.120841i	−0.685323	+	0.120841i
$569$	1.68862	−	0.974928i	1.68862	−	0.974928i	0.733052	−	0.680173i	$-0.238095\pi$
$569$	1.68862	−	0.974928i	1.68862	−	0.974928i	0.955573	−	0.294755i	$-0.0952381\pi$
$570$	−0.154956	−	0.425737i	−0.154956	−	0.425737i
$571$	−1.60366	+	0.583685i	−1.60366	+	0.583685i	−0.980172	−	0.198146i	$-0.936508\pi$
$571$	−1.60366	+	0.583685i	−1.60366	+	0.583685i	−0.623490	+	0.781831i	$0.714286\pi$
$572$		0			0
$573$	0.248088	+	0.295659i	0.248088	+	0.295659i
$574$		0			0
$575$		0			0
$576$	−4.15437	+	1.51207i	−4.15437	+	1.51207i
$577$	0.465266	+	1.27831i	0.465266	+	1.27831i	0.921476	+	0.388435i	$0.126984\pi$
$577$	0.465266	+	1.27831i	0.465266	+	1.27831i	−0.456211	+	0.889872i	$0.650794\pi$
$578$	−1.35417	+	0.781831i	−1.35417	+	0.781831i
$579$		0			0
$580$	0.124331	+	0.104326i	0.124331	+	0.104326i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.653945	+	0.377555i	0.653945	+	0.377555i
$585$		0			0
$586$		−	2.93873i		−	2.93873i
$587$	0.682128	−	1.87413i	0.682128	−	1.87413i	0.270840	−	0.962624i	$-0.412698\pi$
$587$	0.682128	−	1.87413i	0.682128	−	1.87413i	0.411287	−	0.911506i	$-0.365079\pi$
$588$	−0.486339	−	2.75817i	−0.486339	−	2.75817i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.313434	+	0.170687i	0.313434	+	0.170687i
$593$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$593$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.691306	−	1.89935i	0.691306	−	1.89935i
$598$		0			0
$599$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$599$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$600$	1.15645	+	0.667674i	1.15645	+	0.667674i
$601$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$601$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$602$		0			0
$603$		0			0
$604$	0.910562	+	0.764052i	0.910562	+	0.764052i
$605$	−0.0981772	+	0.0173113i	−0.0981772	+	0.0173113i
$606$	0.130866	−	0.0755555i	0.130866	−	0.0755555i
$607$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$607$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$608$	1.76699	−	0.643132i	1.76699	−	0.643132i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.140447	−	0.0511184i	0.140447	−	0.0511184i	−0.270840	−	0.962624i	$-0.587302\pi$
$613$	0.140447	−	0.0511184i	0.140447	−	0.0511184i	0.411287	+	0.911506i	$0.365079\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.41178	−	1.18463i	−1.41178	−	1.18463i	−0.955573	−	0.294755i	$-0.904762\pi$
$617$	−1.41178	−	1.18463i	−1.41178	−	1.18463i	−0.456211	−	0.889872i	$-0.650794\pi$
$618$	−0.747828	+	1.29528i	−0.747828	+	1.29528i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$		0			0
$622$	2.78570	+	1.01391i	2.78570	+	1.01391i
$623$		0			0
$624$		0			0
$625$	0.168488	+	0.955543i	0.168488	+	0.955543i
$626$	2.27092	−	1.90553i	2.27092	−	1.90553i
$627$		0			0
$628$	−2.87572			−2.87572
$629$		0			0
$630$		0			0
$631$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$631$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$632$	−0.895614	+	0.751509i	−0.895614	+	0.751509i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.37822	+	2.38715i	1.37822	+	2.38715i
$640$	0.0625048	−	0.108261i	0.0625048	−	0.108261i
$641$	−0.487950	−	0.409439i	−0.487950	−	0.409439i	0.365341	−	0.930874i	$-0.380952\pi$
$641$	−0.487950	−	0.409439i	−0.487950	−	0.409439i	−0.853291	+	0.521435i	$0.825397\pi$
$642$	2.98458	−	0.526262i	2.98458	−	0.526262i
$643$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$643$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−1.00000			$\pi$
$644$		0			0
$645$	−0.360313	+	0.131143i	−0.360313	+	0.131143i
$646$		0			0
$647$	−1.11334	−	1.32683i	−1.11334	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$647$	−1.11334	−	1.32683i	−1.11334	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$648$	−1.71837	−	2.04787i	−1.71837	−	2.04787i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$653$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$654$	1.14574	+	0.961389i	1.14574	+	0.961389i
$655$	0.0601943	−	0.104260i	0.0601943	−	0.104260i
$656$		0			0
$657$	0.519381	−	2.94556i	0.519381	−	2.94556i
$658$		0			0
$659$	−1.55282	−	0.565181i	−1.55282	−	0.565181i	−0.583744	−	0.811938i	$-0.698413\pi$
$659$	−1.55282	−	0.565181i	−1.55282	−	0.565181i	−0.969077	+	0.246757i	$0.920635\pi$
$660$		0			0
$661$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$661$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$662$		0			0
$663$		0			0
$664$	0.326844	−	0.389517i	0.326844	−	0.389517i
$665$		0			0
$666$	−0.642394	+	4.26201i	−0.642394	+	4.26201i
$667$		0			0
$668$	0.547570	−	0.652568i	0.547570	−	0.652568i
$669$	−2.91055	+	2.44224i	−2.91055	+	2.44224i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$673$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$674$		0			0
$675$	0.585268	−	3.31922i	0.585268	−	3.31922i
$676$	−0.722521	−	1.25144i	−0.722521	−	1.25144i
$677$	−0.270840	+	0.469109i	−0.270840	+	0.469109i	−0.969077	−	0.246757i	$-0.920635\pi$
$677$	−0.270840	+	0.469109i	−0.270840	+	0.469109i	0.698237	+	0.715867i	$0.253968\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$683$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$684$	3.83938	+	4.57560i	3.83938	+	4.57560i
$685$		0			0
$686$		0			0
$687$	3.48071	−	1.26688i	3.48071	−	1.26688i
$688$	−0.242237	−	0.665539i	−0.242237	−	0.665539i
$689$		0			0
$690$		0			0
$691$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$691$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	−1.42792	−	0.519720i	−1.42792	−	0.519720i
$697$		0			0
$698$		0			0
$699$	0.665596	+	3.77478i	0.665596	+	3.77478i
$700$		0			0
$701$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$701$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$702$		0			0
$703$	0.223498	−	1.48281i	0.223498	−	1.48281i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$	−0.146483	−	0.0533156i	−0.146483	−	0.0533156i
$711$	4.01054	+	2.31548i	4.01054	+	2.31548i
$712$	−0.232649	+	1.31942i	−0.232649	+	1.31942i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.93589	−	0.341350i	1.93589	−	0.341350i
$717$		0			0
$718$	−0.132999	−	0.365412i	−0.132999	−	0.365412i
$719$	1.60366	−	0.583685i	1.60366	−	0.583685i	0.623490	−	0.781831i	$-0.285714\pi$
$719$	1.60366	−	0.583685i	1.60366	−	0.583685i	0.980172	+	0.198146i	$0.0634921\pi$
$720$	−0.0965831	−	0.0170302i	−0.0965831	−	0.0170302i
$721$		0			0
$722$	−1.25506	−	1.49572i	−1.25506	−	1.49572i
$723$		0			0
$724$		0			0
$725$	−0.381504	−	1.04817i	−0.381504	−	1.04817i
$726$	2.62459	−	1.51531i	2.62459	−	1.51531i
$727$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$727$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$728$		0			0
$729$	−1.99550	+	3.45630i	−1.99550	+	3.45630i
$730$	0.0845745	+	0.146487i	0.0845745	+	0.146487i
$731$		0			0
$732$		0			0
$733$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$733$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$734$		−	2.49289i		−	2.49289i
$735$	0.0660845	−	0.181566i	0.0660845	−	0.181566i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$739$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$740$	−0.0751173	−	0.122924i	−0.0751173	−	0.122924i
$741$		0			0
$742$		0			0
$743$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$743$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$744$		0			0
$745$		0			0
$746$			3.12344i			3.12344i
$747$	−1.89262	−	0.688857i	−1.89262	−	0.688857i
$748$		0			0
$749$		0			0
$750$	0.300627	+	0.520701i	0.300627	+	0.520701i
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$	2.98458	−	0.526262i	2.98458	−	0.526262i
$754$		0			0
$755$	0.0280470	+	0.0770584i	0.0280470	+	0.0770584i
$756$		0			0
$757$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$757$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$758$	−0.826772	−	0.985308i	−0.826772	−	0.985308i
$759$		0			0
$760$	−0.102452	−	0.0180650i	−0.102452	−	0.0180650i
$761$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$761$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$762$		0			0
$763$		0			0
$764$	0.283388	−	0.0499689i	0.283388	−	0.0499689i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.120116	+	0.681211i	−0.120116	+	0.681211i
$769$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$769$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$773$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$774$	6.55228	−	5.49802i	6.55228	−	5.49802i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$			3.83537i			3.83537i
$784$	0.335372	+	0.122066i	0.335372	+	0.122066i
$785$	−0.171813	−	0.0991964i	−0.171813	−	0.0991964i
$786$	−0.635518	+	3.60420i	−0.635518	+	3.60420i
$787$	0.270840	+	0.469109i	0.270840	+	0.469109i	0.969077	−	0.246757i	$-0.0793651\pi$
$787$	0.270840	+	0.469109i	0.270840	+	0.469109i	−0.698237	+	0.715867i	$0.746032\pi$
$788$		0			0
$789$	2.96573	+	2.48855i	2.96573	+	2.48855i
$790$	−0.257915	+	0.0454774i	−0.257915	+	0.0454774i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.968675	−	1.15442i	−0.968675	−	1.15442i
$797$	1.96900	+	0.347188i	1.96900	+	0.347188i	0.988831	+	0.149042i	$0.0476190\pi$
$797$	1.96900	+	0.347188i	1.96900	+	0.347188i	0.980172	+	0.198146i	$0.0634921\pi$
$798$		0			0
$799$		0			0
$800$	−1.07517	+	0.620749i	−1.07517	+	0.620749i
$801$	5.22622	−	0.921523i	5.22622	−	0.921523i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		−	0.0346983i		−	0.0346983i
$809$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$809$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$810$	−0.103987	−	0.589738i	−0.103987	−	0.589738i
$811$	0.698955	−	0.586493i	0.698955	−	0.586493i	−0.222521	−	0.974928i	$-0.571429\pi$
$811$	0.698955	−	0.586493i	0.698955	−	0.586493i	0.921476	+	0.388435i	$0.126984\pi$
$812$		0			0
$813$	3.49243			3.49243
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.27963	+	1.91284i	−2.27963	+	1.91284i
$818$	−0.541536	−	3.07120i	−0.541536	−	3.07120i
$819$		0			0
$820$		0			0
$821$	−1.24356	−	0.452620i	−1.24356	−	0.452620i	−0.365341	−	0.930874i	$-0.619048\pi$
$821$	−1.24356	−	0.452620i	−1.24356	−	0.452620i	−0.878222	+	0.478254i	$0.841270\pi$
$822$		0			0
$823$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$823$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$824$	0.171717	+	0.297423i	0.171717	+	0.297423i
$825$		0			0
$826$		0			0
$827$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$827$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$828$		0			0
$829$	0.683828	+	1.87880i	0.683828	+	1.87880i	0.365341	+	0.930874i	$0.380952\pi$
$829$	0.683828	+	1.87880i	0.683828	+	1.87880i	0.318487	+	0.947927i	$0.396825\pi$
$830$	0.107033	−	0.0389567i	0.107033	−	0.0389567i
$831$	3.55354	+	0.626584i	3.55354	+	0.626584i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.0552251	−	0.0201003i	0.0552251	−	0.0201003i
$836$		0			0
$837$		0			0
$838$	0.230155	−	0.0405825i	0.230155	−	0.0405825i
$839$	0.559735	+	0.469673i	0.559735	+	0.469673i	0.878222	−	0.478254i	$-0.158730\pi$
$839$	0.559735	+	0.469673i	0.559735	+	0.469673i	−0.318487	+	0.947927i	$0.603175\pi$
$840$		0			0
$841$	0.134659	+	0.233236i	0.134659	+	0.233236i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	0.0996918i		−	0.0996918i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	2.80071			2.80071
$853$	−0.920301	+	1.09677i	−0.920301	+	1.09677i	0.0747301	+	0.997204i	$0.476190\pi$
$853$	−0.920301	+	1.09677i	−0.920301	+	1.09677i	−0.995031	+	0.0995678i	$0.968254\pi$
$854$		0			0
$855$	0.0715555	+	0.405812i	0.0715555	+	0.405812i
$856$	0.238010	−	0.653928i	0.238010	−	0.653928i
$857$		−	1.43173i		−	1.43173i	−0.698237	−	0.715867i	$-0.746032\pi$
$857$		−	1.43173i		−	1.43173i	0.698237	−	0.715867i	$-0.253968\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$	−0.0496428	+	0.281538i	−0.0496428	+	0.281538i
$861$		0			0
$862$	−1.56318	+	2.70750i	−1.56318	+	2.70750i
$863$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$863$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$864$	4.20395	−	0.741270i	4.20395	−	0.741270i
$865$		0			0
$866$		0			0
$867$	1.82127	−	0.662888i	1.82127	−	0.662888i
$868$		0			0
$869$		0			0
$870$	−0.218798	−	0.260753i	−0.218798	−	0.260753i
$871$		0			0
$872$	0.322723	−	0.117462i	0.322723	−	0.117462i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−2.32804	−	1.95345i	−2.32804	−	1.95345i
$877$	−0.733052	+	1.26968i	−0.733052	+	1.26968i	0.222521	+	0.974928i	$0.428571\pi$
$877$	−0.733052	+	1.26968i	−0.733052	+	1.26968i	−0.955573	+	0.294755i	$0.904762\pi$
$878$		0			0
$879$	−0.632520	+	3.58720i	−0.632520	+	3.58720i
$880$		0			0
$881$	−0.418203	−	0.152213i	−0.418203	−	0.152213i	0.124344	−	0.992239i	$-0.460317\pi$
$881$	−0.418203	−	0.152213i	−0.418203	−	0.152213i	−0.542546	+	0.840026i	$0.682540\pi$
$882$			4.31015i			4.31015i
$883$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$883$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$	1.05450	+	0.840934i	1.05450	+	0.840934i
$889$		0			0
$890$	−0.192911	+	0.229902i	−0.192911	+	0.229902i
$891$		0			0
$892$	0.491907	+	2.78974i	0.491907	+	2.78974i
$893$		0			0
$894$		0			0
$895$	0.127437	+	0.0463831i	0.127437	+	0.0463831i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−3.02096	−	2.53489i	−3.02096	−	2.53489i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−1.60241	−	1.90968i	−1.60241	−	1.90968i
$907$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$907$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$908$		0			0
$909$	−0.129151	+	0.0470073i	−0.129151	+	0.0470073i
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$	−1.02152	+	0.180121i	−1.02152	+	0.180121i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.479562	−	2.71973i	0.479562	−	2.71973i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.0246829	+	0.989754i	0.0246829	+	0.989754i
$926$	−0.466104			−0.466104
$927$	0.874413	−	1.04209i	0.874413	−	1.04209i
$928$	1.08224	−	0.908106i	1.08224	−	0.908106i
$929$	0.216536	+	1.22804i	0.216536	+	1.22804i	0.878222	+	0.478254i	$0.158730\pi$
$929$	0.216536	+	1.22804i	0.216536	+	1.22804i	−0.661686	+	0.749781i	$0.730159\pi$
$930$		0			0
$931$		−	1.49956i		−	1.49956i
$932$	2.68546	+	0.977426i	2.68546	+	0.977426i
$933$	−3.18218	−	1.83723i	−3.18218	−	1.83723i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$937$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$938$		0			0
$939$	−3.18218	+	1.83723i	−3.18218	+	1.83723i
$940$		0			0
$941$	1.65052	−	0.600739i	1.65052	−	0.600739i	0.661686	−	0.749781i	$-0.269841\pi$
$941$	1.65052	−	0.600739i	1.65052	−	0.600739i	0.988831	+	0.149042i	$0.0476190\pi$
$942$	5.93950	+	1.04729i	5.93950	+	1.04729i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.678732	−	1.86480i	−0.678732	−	1.86480i	−0.456211	−	0.889872i	$-0.650794\pi$
$947$	−0.678732	−	1.86480i	−0.678732	−	1.86480i	−0.222521	−	0.974928i	$-0.571429\pi$
$948$	4.07495	−	2.35267i	4.07495	−	2.35267i
$949$		0			0
$950$	1.77838	+	1.49224i	1.77838	+	1.49224i
$951$		0			0
$952$		0			0
$953$	−0.158440	+	0.898560i	−0.158440	+	0.898560i	0.797133	+	0.603804i	$0.206349\pi$
$953$	−0.158440	+	0.898560i	−0.158440	+	0.898560i	−0.955573	+	0.294755i	$0.904762\pi$
$954$		0			0
$955$	0.0186550	+	0.00678985i	0.0186550	+	0.00678985i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.199198	+	0.237395i	−0.199198	+	0.237395i
$961$	−1.00000			−1.00000
$962$		0			0
$963$	−2.75644			−2.75644
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$967$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$968$		−	0.695895i		−	0.695895i
$969$		0			0
$970$		0			0
$971$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$971$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$972$	2.91987	+	5.05737i	2.91987	+	5.05737i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.555398	−	1.52594i	−0.555398	−	1.52594i	−0.826239	−	0.563320i	$-0.809524\pi$
$977$	−0.555398	−	1.52594i	−0.555398	−	1.52594i	0.270840	−	0.962624i	$-0.412698\pi$
$978$		0			0
$979$		0			0
$980$	−0.0925992	−	0.110355i	−0.0925992	−	0.110355i
$981$	−0.874413	−	1.04209i	−0.874413	−	1.04209i
$982$		0			0
$983$	−1.17178	+	0.426492i	−1.17178	+	0.426492i	−0.853291	−	0.521435i	$-0.825397\pi$
$983$	−1.17178	+	0.426492i	−1.17178	+	0.426492i	−0.318487	+	0.947927i	$0.603175\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.0180534	−	0.102386i	−0.0180534	−	0.102386i
$996$	−1.56766	+	1.31542i	−1.56766	+	1.31542i
$997$	−0.499362	+	0.595117i	−0.499362	+	0.595117i	−0.955573	−	0.294755i	$-0.904762\pi$
$997$	−0.499362	+	0.595117i	−0.499362	+	0.595117i	0.456211	+	0.889872i	$0.349206\pi$
$998$	2.23875			2.23875
$999$	1.08421	−	3.22699i	1.08421	−	3.22699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2627.1.x.b.780.2	✓	36
37.25	even	18	inner	2627.1.x.b.1135.2	yes	36
71.70	odd	2	CM	2627.1.x.b.780.2	✓	36
2627.1135	odd	18	inner	2627.1.x.b.1135.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2627.1.x.b.780.2	✓	36	1.1	even	1	trivial
2627.1.x.b.780.2	✓	36	71.70	odd	2	CM
2627.1.x.b.1135.2	yes	36	37.25	even	18	inner
2627.1.x.b.1135.2	yes	36	2627.1135	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:	\( N \)	\(=\)	\( 2627 = 37 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2627.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00510 + 1.19784i) q^{2} +(1.48471 - 1.24582i) q^{3} +(-0.250929 - 1.42309i) q^{4} +(0.0340966 - 0.0936796i) q^{5} +3.03062i q^{6} +(0.602663 + 0.347948i) q^{8} +(0.478651 - 2.71457i) q^{9} +O(q^{10})\)	\(q+(-1.00510 + 1.19784i) q^{2} +(1.48471 - 1.24582i) q^{3} +(-0.250929 - 1.42309i) q^{4} +(0.0340966 - 0.0936796i) q^{5} +3.03062i q^{6} +(0.602663 + 0.347948i) q^{8} +(0.478651 - 2.71457i) q^{9} +(0.0779422 + 0.135000i) q^{10} +(-2.14547 - 1.80026i) q^{12} +(-0.0660845 - 0.181566i) q^{15} +(0.335372 - 0.122066i) q^{16} +(2.77051 + 3.30176i) q^{18} +(-0.963900 - 1.14873i) q^{19} +(-0.141870 - 0.0250155i) q^{20} +(1.32826 - 0.234209i) q^{24} +(0.758431 + 0.636399i) q^{25} +(-1.70213 - 2.94817i) q^{27} +(-0.975699 - 0.563320i) q^{29} +(0.283907 + 0.103334i) q^{30} +(-0.428880 + 1.17834i) q^{32} -3.98318 q^{36} +(0.661686 + 0.749781i) q^{37} +2.34481 q^{38} +(0.0531444 - 0.0445934i) q^{40} -1.98448i q^{43} +(-0.237979 - 0.137397i) q^{45} +(0.345860 - 0.599047i) q^{48} +(0.766044 + 0.642788i) q^{49} +(-1.52460 + 0.268829i) q^{50} +(5.24224 + 0.924349i) q^{54} +(-2.86223 - 0.504688i) q^{57} +(1.65544 - 0.602532i) q^{58} +(-0.241801 + 0.139604i) q^{60} +(-0.801938 - 1.38900i) q^{64} +(-0.766044 + 0.642788i) q^{71} +(1.23299 - 1.46942i) q^{72} +1.08509 q^{73} +(-1.56318 + 0.0389832i) q^{74} +1.91889 q^{75} +(-1.39288 + 1.65997i) q^{76} +(-0.574612 + 1.57873i) q^{79} -0.0355796i q^{80} +(-3.60986 - 1.31388i) q^{81} +(0.126882 - 0.719581i) q^{83} +(2.37708 + 1.99461i) q^{86} +(-2.15043 + 0.379179i) q^{87} +(0.658474 + 1.80914i) q^{89} +(0.403773 - 0.146961i) q^{90} +(-0.140478 + 0.0511300i) q^{95} +(0.831235 + 2.28380i) q^{96} +(-1.53991 + 0.271527i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9}+O(q^{10}) \) 36 * q + 6 * q^3 + 3 * q^5 - 6 * q^9	\( 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9} + 6 q^{12} - 3 q^{15} + 21 q^{18} + 3 q^{19} - 36 q^{20} - 21 q^{24} + 3 q^{25} + 3 q^{27} - 9 q^{29} - 21 q^{30} - 48 q^{36} - 3 q^{57} + 54 q^{60} + 24 q^{64} + 21 q^{72} - 6 q^{75} - 3 q^{76} + 6 q^{79} - 3 q^{81} - 12 q^{87} + 3 q^{89} + 42 q^{90} - 6 q^{95} - 21 q^{96}+O(q^{100}) \) 36 * q + 6 * q^3 + 3 * q^5 - 6 * q^9 + 6 * q^12 - 3 * q^15 + 21 * q^18 + 3 * q^19 - 36 * q^20 - 21 * q^24 + 3 * q^25 + 3 * q^27 - 9 * q^29 - 21 * q^30 - 48 * q^36 - 3 * q^57 + 54 * q^60 + 24 * q^64 + 21 * q^72 - 6 * q^75 - 3 * q^76 + 6 * q^79 - 3 * q^81 - 12 * q^87 + 3 * q^89 + 42 * q^90 - 6 * q^95 - 21 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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