LMFDB - Embedded newform 2627.1.x.b.1135.4

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			1135.4
Root			$0.270840 - 0.962624i$ of defining polynomial
Character	$\chi$	$=$	2627.1135
Dual form			2627.1.x.b.780.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.557790 + 0.664748i) q^{2} +(-0.698955 - 0.586493i) q^{3} +(0.0428876 - 0.243227i) q^{4} +(-0.512881 - 1.40913i) q^{5} -0.791770i q^{6} +(0.937116 - 0.541044i) q^{8} +(-0.0290839 - 0.164943i) q^{9} +O(q^{10})$	\(q+(0.557790 + 0.664748i) q^{2} +(-0.698955 - 0.586493i) q^{3} +(0.0428876 - 0.243227i) q^{4} +(-0.512881 - 1.40913i) q^{5} -0.791770i q^{6} +(0.937116 - 0.541044i) q^{8} +(-0.0290839 - 0.164943i) q^{9} +(0.650636 - 1.12693i) q^{10} +(-0.172628 + 0.144852i) q^{12} +(-0.467963 + 1.28572i) q^{15} +(0.650287 + 0.236685i) q^{16} +(0.0934228 - 0.111337i) q^{18} +(1.23753 - 1.47483i) q^{19} +(-0.364735 + 0.0643126i) q^{20} +(-0.972321 - 0.171446i) q^{24} +(-0.956550 + 0.802641i) q^{25} +(-0.532620 + 0.922525i) q^{27} +(-1.17809 + 0.680173i) q^{29} +(-1.11570 + 0.406083i) q^{30} +(-0.164708 - 0.452532i) q^{32} -0.0413660 q^{36} +(-0.270840 + 0.962624i) q^{37} +1.67067 q^{38} +(-1.24303 - 1.04303i) q^{40} +1.04287i q^{43} +(-0.217509 + 0.125579i) q^{45} +(-0.315708 - 0.546822i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-1.06711 - 0.188160i) q^{50} +(-0.910337 + 0.160517i) q^{54} +(-1.72995 + 0.305037i) q^{57} +(-1.10927 - 0.403742i) q^{58} +(0.292652 + 0.168963i) q^{60} +(0.554958 - 0.961216i) q^{64} +(-0.766044 - 0.642788i) q^{71} +(-0.116496 - 0.138835i) q^{72} -0.636973 q^{73} +(-0.790975 + 0.356902i) q^{74} +1.13933 q^{75} +(-0.305644 - 0.364252i) q^{76} +(-0.648420 - 1.78152i) q^{79} -1.03773i q^{80} +(0.755946 - 0.275142i) q^{81} +(0.0259535 + 0.147190i) q^{83} +(-0.693246 + 0.581703i) q^{86} +(1.22235 + 0.215534i) q^{87} +(0.0340966 - 0.0936796i) q^{89} +(-0.204803 - 0.0745421i) q^{90} +(-2.71292 - 0.987423i) q^{95} +(-0.150283 + 0.412900i) q^{96} +(0.854584 + 0.150686i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2627\mathbb{Z}\right)^\times$.

$n$	$149$	$853$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	0.557790	+	0.664748i	0.557790	+	0.664748i	0.969077	−	0.246757i	$-0.0793651\pi$
$2$	0.557790	+	0.664748i	0.557790	+	0.664748i	−0.411287	+	0.911506i	$0.634921\pi$
$3$	−0.698955	−	0.586493i	−0.698955	−	0.586493i	0.222521	−	0.974928i	$-0.428571\pi$
$3$	−0.698955	−	0.586493i	−0.698955	−	0.586493i	−0.921476	+	0.388435i	$0.873016\pi$
$4$	0.0428876	−	0.243227i	0.0428876	−	0.243227i
$5$	−0.512881	−	1.40913i	−0.512881	−	1.40913i	−0.878222	−	0.478254i	$-0.841270\pi$
$5$	−0.512881	−	1.40913i	−0.512881	−	1.40913i	0.365341	−	0.930874i	$-0.380952\pi$
$6$		−	0.791770i		−	0.791770i
$7$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$7$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$8$	0.937116	−	0.541044i	0.937116	−	0.541044i
$9$	−0.0290839	−	0.164943i	−0.0290839	−	0.164943i
$10$	0.650636	−	1.12693i	0.650636	−	1.12693i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	−0.172628	+	0.144852i	−0.172628	+	0.144852i
$13$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$13$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$14$		0			0
$15$	−0.467963	+	1.28572i	−0.467963	+	1.28572i
$16$	0.650287	+	0.236685i	0.650287	+	0.236685i
$17$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$17$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$18$	0.0934228	−	0.111337i	0.0934228	−	0.111337i
$19$	1.23753	−	1.47483i	1.23753	−	1.47483i	0.411287	−	0.911506i	$-0.365079\pi$
$19$	1.23753	−	1.47483i	1.23753	−	1.47483i	0.826239	−	0.563320i	$-0.190476\pi$
$20$	−0.364735	+	0.0643126i	−0.364735	+	0.0643126i
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−0.972321	−	0.171446i	−0.972321	−	0.171446i
$25$	−0.956550	+	0.802641i	−0.956550	+	0.802641i
$26$		0			0
$27$	−0.532620	+	0.922525i	−0.532620	+	0.922525i
$28$		0			0
$29$	−1.17809	+	0.680173i	−1.17809	+	0.680173i	−0.955573	−	0.294755i	$-0.904762\pi$
$29$	−1.17809	+	0.680173i	−1.17809	+	0.680173i	−0.222521	+	0.974928i	$0.571429\pi$
$30$	−1.11570	+	0.406083i	−1.11570	+	0.406083i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.164708	−	0.452532i	−0.164708	−	0.452532i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.0413660			−0.0413660
$37$	−0.270840	+	0.962624i	−0.270840	+	0.962624i
$37$	−0.270840	+	0.962624i	−0.270840	+	0.962624i
$38$	1.67067			1.67067
$39$		0			0
$40$	−1.24303	−	1.04303i	−1.24303	−	1.04303i
$41$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$41$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$42$		0			0
$43$			1.04287i			1.04287i	0.853291	+	0.521435i	$0.174603\pi$
$43$			1.04287i			1.04287i	−0.853291	+	0.521435i	$0.825397\pi$
$44$		0			0
$45$	−0.217509	+	0.125579i	−0.217509	+	0.125579i
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−0.315708	−	0.546822i	−0.315708	−	0.546822i
$49$	0.766044	−	0.642788i	0.766044	−	0.642788i
$50$	−1.06711	−	0.188160i	−1.06711	−	0.188160i
$51$		0			0
$52$		0			0
$53$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$53$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$54$	−0.910337	+	0.160517i	−0.910337	+	0.160517i
$55$		0			0
$56$		0			0
$57$	−1.72995	+	0.305037i	−1.72995	+	0.305037i
$58$	−1.10927	−	0.403742i	−1.10927	−	0.403742i
$59$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$59$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$60$	0.292652	+	0.168963i	0.292652	+	0.168963i
$61$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$61$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$62$		0			0
$63$		0			0
$64$	0.554958	−	0.961216i	0.554958	−	0.961216i
$65$		0			0
$66$		0			0
$67$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$67$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$68$		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
$72$	−0.116496	−	0.138835i	−0.116496	−	0.138835i
$73$	−0.636973			−0.636973			−0.318487	−	0.947927i	$-0.603175\pi$
$73$	−0.636973			−0.636973			−0.318487	+	0.947927i	$0.603175\pi$
$74$	−0.790975	+	0.356902i	−0.790975	+	0.356902i
$75$	1.13933			1.13933
$76$	−0.305644	−	0.364252i	−0.305644	−	0.364252i
$77$		0			0
$78$		0			0
$79$	−0.648420	−	1.78152i	−0.648420	−	1.78152i	−0.623490	−	0.781831i	$-0.714286\pi$
$79$	−0.648420	−	1.78152i	−0.648420	−	1.78152i	−0.0249307	−	0.999689i	$-0.507937\pi$
$80$		−	1.03773i		−	1.03773i
$81$	0.755946	−	0.275142i	0.755946	−	0.275142i
$82$		0			0
$83$	0.0259535	+	0.147190i	0.0259535	+	0.147190i	0.995031	−	0.0995678i	$-0.0317460\pi$
$83$	0.0259535	+	0.147190i	0.0259535	+	0.147190i	−0.969077	+	0.246757i	$0.920635\pi$
$84$		0			0
$85$		0			0
$86$	−0.693246	+	0.581703i	−0.693246	+	0.581703i
$87$	1.22235	+	0.215534i	1.22235	+	0.215534i
$88$		0			0
$89$	0.0340966	−	0.0936796i	0.0340966	−	0.0936796i	−0.921476	−	0.388435i	$-0.873016\pi$
$89$	0.0340966	−	0.0936796i	0.0340966	−	0.0936796i	0.955573	+	0.294755i	$0.0952381\pi$
$90$	−0.204803	−	0.0745421i	−0.204803	−	0.0745421i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.71292	−	0.987423i	−2.71292	−	0.987423i
$96$	−0.150283	+	0.412900i	−0.150283	+	0.412900i
$97$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$97$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$98$	0.854584	+	0.150686i	0.854584	+	0.150686i
$99$		0			0
$100$	0.154200	+	0.267083i	0.154200	+	0.267083i
$101$	−0.411287	+	0.712370i	−0.411287	+	0.712370i	−0.995031	−	0.0995678i	$-0.968254\pi$
$101$	−0.411287	+	0.712370i	−0.411287	+	0.712370i	0.583744	+	0.811938i	$0.301587\pi$
$102$		0			0
$103$	1.54130	−	0.889872i	1.54130	−	0.889872i	0.542546	−	0.840026i	$-0.317460\pi$
$103$	1.54130	−	0.889872i	1.54130	−	0.889872i	0.998757	−	0.0498459i	$-0.0158730\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$107$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$108$	0.201541	+	0.169113i	0.201541	+	0.169113i
$109$	1.14400	+	1.36336i	1.14400	+	1.36336i	0.921476	+	0.388435i	$0.126984\pi$
$109$	1.14400	+	1.36336i	1.14400	+	1.36336i	0.222521	+	0.974928i	$0.428571\pi$
$110$		0			0
$111$	0.753878	−	0.513985i	0.753878	−	0.513985i
$112$		0			0
$113$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$113$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$114$	−1.16772	−	0.979835i	−1.16772	−	0.979835i
$115$		0			0
$116$	0.114911	+	0.315716i	0.114911	+	0.315716i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.257095	+	1.45806i	0.257095	+	1.45806i
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.322960	+	0.186461i	0.322960	+	0.186461i
$126$		0			0
$127$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$127$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$128$	0.474258	−	0.0836246i	0.474258	−	0.0836246i
$129$	0.611636	−	0.728920i	0.611636	−	0.728920i
$130$		0			0
$131$	1.96900	−	0.347188i	1.96900	−	0.347188i	0.980172	−	0.198146i	$-0.0634921\pi$
$131$	1.96900	−	0.347188i	1.96900	−	0.347188i	0.988831	−	0.149042i	$-0.0476190\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.57313	+	0.277385i	1.57313	+	0.277385i
$136$		0			0
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$		0			0
$139$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$139$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$140$		0			0
$141$		0			0
$142$		−	0.867767i		−	0.867767i
$143$		0			0
$144$	0.0201267	−	0.114144i	0.0201267	−	0.114144i
$145$	1.56267	+	1.31124i	1.56267	+	1.31124i
$146$	−0.355297	−	0.423427i	−0.355297	−	0.423427i
$147$	−0.912421			−0.912421
$148$	0.222521	+	0.107160i	0.222521	+	0.107160i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	0.635507	+	0.757367i	0.635507	+	0.757367i
$151$	−1.22128	−	1.02477i	−1.22128	−	1.02477i	−0.998757	−	0.0498459i	$-0.984127\pi$
$151$	−1.22128	−	1.02477i	−1.22128	−	1.02477i	−0.222521	−	0.974928i	$-0.571429\pi$
$152$	0.361759	−	2.05164i	0.361759	−	2.05164i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.0431841	−	0.244909i	−0.0431841	−	0.244909i	0.955573	−	0.294755i	$-0.0952381\pi$
$157$	−0.0431841	−	0.244909i	−0.0431841	−	0.244909i	−0.998757	+	0.0498459i	$0.984127\pi$
$158$	0.822581	−	1.42475i	0.822581	−	1.42475i
$159$		0			0
$160$	−0.553200	+	0.464190i	−0.553200	+	0.464190i
$161$		0			0
$162$	0.604559	+	0.349042i	0.604559	+	0.349042i
$163$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$163$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$164$		0			0
$165$		0			0
$166$	−0.0833674	+	0.0993534i	−0.0833674	+	0.0993534i
$167$	1.19671	−	1.42618i	1.19671	−	1.42618i	0.318487	−	0.947927i	$-0.396825\pi$
$167$	1.19671	−	1.42618i	1.19671	−	1.42618i	0.878222	−	0.478254i	$-0.158730\pi$
$168$		0			0
$169$	0.939693	+	0.342020i	0.939693	+	0.342020i
$170$		0			0
$171$	−0.279254	−	0.161227i	−0.279254	−	0.161227i
$172$	0.253655	+	0.0447262i	0.253655	+	0.0447262i
$173$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$173$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$174$	0.538540	+	0.932779i	0.538540	+	0.932779i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.0812921	−	0.0295879i	0.0812921	−	0.0295879i
$179$			0.298085i			0.298085i	0.988831	+	0.149042i	$0.0476190\pi$
$179$			0.298085i			0.298085i	−0.988831	+	0.149042i	$0.952381\pi$
$180$	0.0212158	+	0.0582899i	0.0212158	+	0.0582899i
$181$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$181$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.49537	−	0.112062i	1.49537	−	0.112062i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−0.856853	−	2.35418i	−0.856853	−	2.35418i
$191$			1.98448i			1.98448i	0.124344	+	0.992239i	$0.460317\pi$
$191$			1.98448i			1.98448i	−0.124344	+	0.992239i	$0.539683\pi$
$192$	−0.951637	+	0.346368i	−0.951637	+	0.346368i
$193$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$193$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$194$		0			0
$195$		0			0
$196$	−0.123490	−	0.213891i	−0.123490	−	0.213891i
$197$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$197$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$198$		0			0
$199$	−0.172457	−	0.0995678i	−0.172457	−	0.0995678i	0.411287	−	0.911506i	$-0.365079\pi$
$199$	−0.172457	−	0.0995678i	−0.172457	−	0.0995678i	−0.583744	+	0.811938i	$0.698413\pi$
$200$	−0.462134	+	1.26970i	−0.462134	+	1.26970i
$201$		0			0
$202$	−0.702959	+	0.123951i	−0.702959	+	0.123951i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	1.45126	+	0.528217i	1.45126	+	0.528217i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$	0.158440	+	0.898560i	0.158440	+	0.898560i
$214$	−0.751509	+	0.433884i	−0.751509	+	0.433884i
$215$	1.46954	−	0.534868i	1.46954	−	0.534868i
$216$			1.15268i			1.15268i
$217$		0			0
$218$	−0.268183	+	1.52094i	−0.268183	+	1.52094i
$219$	0.445216	+	0.373580i	0.445216	+	0.373580i
$220$		0			0
$221$		0			0
$222$	0.762177	+	0.214443i	0.762177	+	0.214443i
$223$	1.93815			1.93815			0.969077	−	0.246757i	$-0.0793651\pi$
$223$	1.93815			1.93815			0.969077	+	0.246757i	$0.0793651\pi$
$224$		0			0
$225$	0.160210	+	0.134432i	0.160210	+	0.134432i
$226$		0			0
$227$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$227$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$228$			0.433854i			0.433854i
$229$	0.686617	−	0.249908i	0.686617	−	0.249908i	0.0249307	−	0.999689i	$-0.492063\pi$
$229$	0.686617	−	0.249908i	0.686617	−	0.249908i	0.661686	+	0.749781i	$0.269841\pi$
$230$		0			0
$231$		0			0
$232$	−0.736007	+	1.27480i	−0.736007	+	1.27480i
$233$	0.826239	+	1.43109i	0.826239	+	1.43109i	0.900969	+	0.433884i	$0.142857\pi$
$233$	0.826239	+	1.43109i	0.826239	+	1.43109i	−0.0747301	+	0.997204i	$0.523810\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.591633	+	1.62550i	−0.591633	+	1.62550i
$238$		0			0
$239$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$239$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$240$	−0.608621	+	0.725326i	−0.608621	+	0.725326i
$241$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$241$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$242$	−0.854584	+	0.150686i	−0.854584	+	0.150686i
$243$	0.311257	+	0.113288i	0.311257	+	0.113288i
$244$		0			0
$245$	−1.29866	−	0.749781i	−1.29866	−	0.749781i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	0.0681853	−	0.118100i	0.0681853	−	0.118100i
$250$	0.0561943	+	0.318693i	0.0561943	+	0.318693i
$251$	−0.751509	+	0.433884i	−0.751509	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$251$	−0.751509	+	0.433884i	−0.751509	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.530119	−	0.444823i	−0.530119	−	0.444823i
$257$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$257$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$258$	0.825713			0.825713
$259$		0			0
$260$		0			0
$261$	0.146453	+	0.174536i	0.146453	+	0.174536i
$262$	1.32908	+	1.11523i	1.32908	+	1.11523i
$263$	0.229801	−	1.30327i	0.229801	−	1.30327i	−0.623490	−	0.781831i	$-0.714286\pi$
$263$	0.229801	−	1.30327i	0.229801	−	1.30327i	0.853291	−	0.521435i	$-0.174603\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.0787744	+	0.0454804i	−0.0787744	+	0.0454804i
$268$		0			0
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$	0.693083	+	1.20046i	0.693083	+	1.20046i
$271$	0.340922	−	0.286067i	0.340922	−	0.286067i	−0.456211	−	0.889872i	$-0.650794\pi$
$271$	0.340922	−	0.286067i	0.340922	−	0.286067i	0.797133	+	0.603804i	$0.206349\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.28198	+	1.52780i	−1.28198	+	1.52780i	−0.583744	+	0.811938i	$0.698413\pi$
$277$	−1.28198	+	1.52780i	−1.28198	+	1.52780i	−0.698237	+	0.715867i	$0.746032\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$281$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$282$		0			0
$283$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$283$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$284$	−0.189197	+	0.158755i	−0.189197	+	0.158755i
$285$	1.31709	+	2.28127i	1.31709	+	2.28127i
$286$		0			0
$287$		0			0
$288$	−0.0698516	+	0.0403288i	−0.0698516	+	0.0403288i
$289$	0.939693	−	0.342020i	0.939693	−	0.342020i
$290$			1.77018i			1.77018i
$291$		0			0
$292$	−0.0273182	+	0.154929i	−0.0273182	+	0.154929i
$293$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$293$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$294$	−0.508940	−	0.606531i	−0.508940	−	0.606531i
$295$		0			0
$296$	0.267013	+	1.04863i	0.267013	+	1.04863i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.0488630	−	0.277116i	0.0488630	−	0.277116i
$301$		0			0
$302$		−	1.38345i		−	1.38345i
$303$	0.705271	−	0.256698i	0.705271	−	0.256698i
$304$	1.15382	−	0.666157i	1.15382	−	0.666157i
$305$		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
$309$	−1.59921	−	0.281983i	−1.59921	−	0.281983i
$310$		0			0
$311$	0.489682	−	1.34539i	0.489682	−	1.34539i	−0.411287	−	0.911506i	$-0.634921\pi$
$311$	0.489682	−	1.34539i	0.489682	−	1.34539i	0.900969	−	0.433884i	$-0.142857\pi$
$312$		0			0
$313$	1.40998	−	0.248618i	1.40998	−	0.248618i	0.583744	−	0.811938i	$-0.301587\pi$
$313$	1.40998	−	0.248618i	1.40998	−	0.248618i	0.826239	+	0.563320i	$0.190476\pi$
$314$	0.138715	−	0.165315i	0.138715	−	0.165315i
$315$		0			0
$316$	−0.461124	+	0.0813086i	−0.461124	+	0.0813086i
$317$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$317$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$318$		0			0
$319$		0			0
$320$	−1.63910	−	0.289018i	−1.63910	−	0.289018i
$321$	0.698955	−	0.586493i	0.698955	−	0.586493i
$322$		0			0
$323$		0			0
$324$	−0.0345014	−	0.195667i	−0.0345014	−	0.195667i
$325$		0			0
$326$		0			0
$327$		−	1.62388i		−	1.62388i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$331$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$332$	0.0369136			0.0369136
$333$	0.166655	+	0.0166764i	0.166655	+	0.0166764i
$334$	1.61556			1.61556
$335$		0			0
$336$		0			0
$337$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$337$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$338$	0.296794	+	0.815435i	0.296794	+	0.815435i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−0.0485895	−	0.275565i	−0.0485895	−	0.275565i
$343$		0			0
$344$	0.564239	+	0.977291i	0.564239	+	0.977291i
$345$		0			0
$346$		0			0
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$	0.104847	−	0.288066i	0.104847	−	0.288066i
$349$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$349$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$353$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$354$		0			0
$355$	−0.512881	+	1.40913i	−0.512881	+	1.40913i
$356$	−0.0213231	−	0.0123109i	−0.0213231	−	0.0123109i
$357$		0			0
$358$	−0.198151	+	0.166269i	−0.198151	+	0.166269i
$359$	−0.853291	−	1.47794i	−0.853291	−	1.47794i	−0.878222	−	0.478254i	$-0.841270\pi$
$359$	−0.853291	−	1.47794i	−0.853291	−	1.47794i	0.0249307	−	0.999689i	$-0.492063\pi$
$360$	−0.135887	+	0.235364i	−0.135887	+	0.235364i
$361$	−0.469993	−	2.66546i	−0.469993	−	2.66546i
$362$		0			0
$363$	0.857396	−	0.312066i	0.857396	−	0.312066i
$364$		0			0
$365$	0.326691	+	0.897577i	0.326691	+	0.897577i
$366$		0			0
$367$	−0.0381960	−	0.0320503i	−0.0381960	−	0.0320503i	0.623490	−	0.781831i	$-0.285714\pi$
$367$	−0.0381960	−	0.0320503i	−0.0381960	−	0.0320503i	−0.661686	+	0.749781i	$0.730159\pi$
$368$		0			0
$369$		0			0
$370$	0.908596	+	0.931537i	0.908596	+	0.931537i
$371$		0			0
$372$		0			0
$373$	1.01376	+	0.850647i	1.01376	+	0.850647i	0.988831	−	0.149042i	$-0.0476190\pi$
$373$	1.01376	+	0.850647i	1.01376	+	0.850647i	0.0249307	+	0.999689i	$0.492063\pi$
$374$		0			0
$375$	−0.116377	−	0.319742i	−0.116377	−	0.319742i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.276841	−	1.57004i	−0.276841	−	1.57004i	−0.733052	−	0.680173i	$-0.761905\pi$
$379$	−0.276841	−	1.57004i	−0.276841	−	1.57004i	0.456211	−	0.889872i	$-0.349206\pi$
$380$	−0.356519	+	0.617509i	−0.356519	+	0.617509i
$381$		0			0
$382$	−1.31918	+	1.10692i	−1.31918	+	1.10692i
$383$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$383$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$384$	−0.380531	−	0.219699i	−0.380531	−	0.219699i
$385$		0			0
$386$		0			0
$387$	0.172014	−	0.0303307i	0.172014	−	0.0303307i
$388$		0			0
$389$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$389$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$390$		0			0
$391$		0			0
$392$	0.370096	−	1.01683i	0.370096	−	1.01683i
$393$	−1.57987	−	0.912138i	−1.57987	−	0.912138i
$394$		0			0
$395$	−2.17783	+	1.82741i	−2.17783	+	1.82741i
$396$		0			0
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$	−0.0300070	−	0.170178i	−0.0300070	−	0.170178i
$399$		0			0
$400$	−0.812006	+	0.295546i	−0.812006	+	0.295546i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		0			0
$404$	0.155629	+	0.130588i	0.155629	+	0.130588i
$405$	−0.775420	−	0.924109i	−0.775420	−	0.924109i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.378930	+	0.451591i	0.378930	+	0.451591i	0.921476	−	0.388435i	$-0.126984\pi$
$409$	0.378930	+	0.451591i	0.378930	+	0.451591i	−0.542546	+	0.840026i	$0.682540\pi$
$410$		0			0
$411$		0			0
$412$	−0.150339	−	0.413052i	−0.150339	−	0.413052i
$413$		0			0
$414$		0			0
$415$	0.194098	−	0.112062i	0.194098	−	0.112062i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.46402	+	1.22846i	−1.46402	+	1.22846i	−0.542546	+	0.840026i	$0.682540\pi$
$419$	−1.46402	+	1.22846i	−1.46402	+	1.22846i	−0.921476	+	0.388435i	$0.873016\pi$
$420$		0			0
$421$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$421$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.508940	+	0.606531i	−0.508940	+	0.606531i
$427$		0			0
$428$	0.232085	+	0.0844720i	0.232085	+	0.0844720i
$429$		0			0
$430$	1.17525	+	0.678529i	1.17525	+	0.678529i
$431$	−1.79532	−	0.316563i	−1.79532	−	0.316563i	−0.826239	−	0.563320i	$-0.809524\pi$
$431$	−1.79532	−	0.316563i	−1.79532	−	0.316563i	−0.969077	+	0.246757i	$0.920635\pi$
$432$	−0.564704	+	0.473843i	−0.564704	+	0.473843i
$433$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$433$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$434$		0			0
$435$	−0.323206	−	1.83299i	−0.323206	−	1.83299i
$436$	0.380670	−	0.219780i	0.380670	−	0.219780i
$437$		0			0
$438$			0.504336i			0.504336i
$439$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$439$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$440$		0			0
$441$	−0.128303	−	0.107659i	−0.128303	−	0.107659i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	−0.0926833	−	0.205407i	−0.0926833	−	0.205407i
$445$	−0.149494			−0.149494
$446$	1.08108	+	1.28839i	1.08108	+	1.28839i
$447$		0			0
$448$		0			0
$449$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$449$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$450$			0.181484i			0.181484i
$451$		0			0
$452$		0			0
$453$	0.252596	+	1.43254i	0.252596	+	1.43254i
$454$		0			0
$455$		0			0
$456$	−1.45613	+	1.22183i	−1.45613	+	1.22183i
$457$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$457$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$458$	0.549114	+	0.317031i	0.549114	+	0.317031i
$459$		0			0
$460$		0			0
$461$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$461$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$462$		0			0
$463$	−0.724190	+	0.863056i	−0.724190	+	0.863056i	−0.995031	−	0.0995678i	$-0.968254\pi$
$463$	−0.724190	+	0.863056i	−0.724190	+	0.863056i	0.270840	+	0.962624i	$0.412698\pi$
$464$	−0.927086	+	0.163470i	−0.927086	+	0.163470i
$465$		0			0
$466$	−0.490445	+	1.34749i	−0.490445	+	1.34749i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.113454	+	0.196508i	−0.113454	+	0.196508i
$472$		0			0
$473$		0			0
$474$	−1.41055	+	0.513400i	−1.41055	+	0.513400i
$475$			2.40403i			2.40403i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$479$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$480$	0.658906			0.658906
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.189197	+	0.158755i	0.189197	+	0.158755i
$485$		0			0
$486$	0.0983080	+	0.270099i	0.0983080	+	0.270099i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$	−0.225963	−	1.28150i	−0.225963	−	1.28150i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.116540	−	0.0205492i	0.116540	−	0.0205492i
$499$	1.07992	−	1.28699i	1.07992	−	1.28699i	0.124344	−	0.992239i	$-0.460317\pi$
$499$	1.07992	−	1.28699i	1.07992	−	1.28699i	0.955573	−	0.294755i	$-0.0952381\pi$
$500$	0.0592034	−	0.0705559i	0.0592034	−	0.0705559i
$501$	−1.67289	+	0.294976i	−1.67289	+	0.294976i
$502$	−0.707608	−	0.257548i	−0.707608	−	0.257548i
$503$	0.201624	−	0.553959i	0.201624	−	0.553959i	−0.797133	−	0.603804i	$-0.793651\pi$
$503$	0.201624	−	0.553959i	0.201624	−	0.553959i	0.998757	+	0.0498459i	$0.0158730\pi$
$504$		0			0
$505$	1.21476	+	0.214195i	1.21476	+	0.214195i
$506$		0			0
$507$	−0.456211	−	0.790180i	−0.456211	−	0.790180i
$508$		0			0
$509$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$509$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$510$		0			0
$511$		0			0
$512$		−	1.08209i		−	1.08209i
$513$	0.701433	+	1.92717i	0.701433	+	1.92717i
$514$		0			0
$515$	−2.04445	−	1.71550i	−2.04445	−	1.71550i
$516$	−0.151062	−	0.180028i	−0.151062	−	0.180028i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.51498	−	1.27122i	−1.51498	−	1.27122i	−0.853291	−	0.521435i	$-0.825397\pi$
$521$	−1.51498	−	1.27122i	−1.51498	−	1.27122i	−0.661686	−	0.749781i	$-0.730159\pi$
$522$	−0.0343325	+	0.194709i	−0.0343325	+	0.194709i
$523$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$523$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$524$		−	0.493806i		−	0.493806i
$525$		0			0
$526$	0.994525	−	0.574189i	0.994525	−	0.574189i
$527$		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
$534$	−0.0741727	−	0.0269966i	−0.0741727	−	0.0269966i
$535$	1.47678	−	0.260396i	1.47678	−	0.260396i
$536$		0			0
$537$	0.174825	−	0.208348i	0.174825	−	0.208348i
$538$		0			0
$539$		0			0
$540$	0.134935	−	0.370731i	0.134935	−	0.370731i
$541$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$541$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$542$	0.380326	+	0.0670617i	0.380326	+	0.0670617i
$543$		0			0
$544$		0			0
$545$	1.33442	−	2.31128i	1.33442	−	2.31128i
$546$		0			0
$547$	1.40632	−	0.811938i	1.40632	−	0.811938i	0.411287	−	0.911506i	$-0.365079\pi$
$547$	1.40632	−	0.811938i	1.40632	−	0.811938i	0.995031	+	0.0995678i	$0.0317460\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.454785	+	2.57921i	−0.454785	+	2.57921i
$552$		0			0
$553$		0			0
$554$	−1.73068			−1.73068
$555$	−1.11092	−	0.798697i	−1.11092	−	0.798697i
$556$		0			0
$557$	0.776236	+	0.925082i	0.776236	+	0.925082i	0.998757	−	0.0498459i	$-0.0158730\pi$
$557$	0.776236	+	0.925082i	0.776236	+	0.925082i	−0.222521	+	0.974928i	$0.571429\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−1.06565	−	0.187903i	−1.06565	−	0.187903i
$569$	1.35417	+	0.781831i	1.35417	+	0.781831i	0.988831	−	0.149042i	$-0.0476190\pi$
$569$	1.35417	+	0.781831i	1.35417	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$570$	−0.781811	+	2.14801i	−0.781811	+	2.14801i
$571$	1.87005	+	0.680641i	1.87005	+	0.680641i	0.969077	+	0.246757i	$0.0793651\pi$
$571$	1.87005	+	0.680641i	1.87005	+	0.680641i	0.900969	+	0.433884i	$0.142857\pi$
$572$		0			0
$573$	1.16388	−	1.38706i	1.16388	−	1.38706i
$574$		0			0
$575$		0			0
$576$	−0.174686	−	0.0635805i	−0.174686	−	0.0635805i
$577$	−0.101951	+	0.280108i	−0.101951	+	0.280108i	−0.980172	−	0.198146i	$-0.936508\pi$
$577$	−0.101951	+	0.280108i	−0.101951	+	0.280108i	0.878222	+	0.478254i	$0.158730\pi$
$578$	0.751509	+	0.433884i	0.751509	+	0.433884i
$579$		0			0
$580$	0.385948	−	0.323849i	0.385948	−	0.323849i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.596918	+	0.344631i	−0.596918	+	0.344631i
$585$		0			0
$586$		−	1.63087i		−	1.63087i
$587$	−0.201624	−	0.553959i	−0.201624	−	0.553959i	0.797133	−	0.603804i	$-0.206349\pi$
$587$	−0.201624	−	0.553959i	−0.201624	−	0.553959i	−0.998757	+	0.0498459i	$0.984127\pi$
$588$	−0.0391315	+	0.221926i	−0.0391315	+	0.221926i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.403963	+	0.561879i	−0.403963	+	0.561879i
$593$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$593$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.0621436	+	0.170738i	0.0621436	+	0.170738i
$598$		0			0
$599$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$599$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$600$	1.06768	−	0.616427i	1.06768	−	0.616427i
$601$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$601$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$602$		0			0
$603$		0			0
$604$	−0.301631	+	0.253098i	−0.301631	+	0.253098i
$605$	1.47678	+	0.260396i	1.47678	+	0.260396i
$606$	0.564033	+	0.325645i	0.564033	+	0.325645i
$607$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$607$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$608$	−0.871237	−	0.317104i	−0.871237	−	0.317104i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.79589	+	0.653650i	1.79589	+	0.653650i	0.998757	+	0.0498459i	$0.0158730\pi$
$613$	1.79589	+	0.653650i	1.79589	+	0.653650i	0.797133	+	0.603804i	$0.206349\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.34551	+	1.12902i	−1.34551	+	1.12902i	−0.365341	+	0.930874i	$0.619048\pi$
$617$	−1.34551	+	1.12902i	−1.34551	+	1.12902i	−0.980172	+	0.198146i	$0.936508\pi$
$618$	−0.704573	−	1.22036i	−0.704573	−	1.22036i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$		0			0
$622$	1.16749	−	0.424930i	1.16749	−	0.424930i
$623$		0			0
$624$		0			0
$625$	−0.119725	+	0.678993i	−0.119725	+	0.678993i
$626$	0.951743	+	0.798607i	0.951743	+	0.798607i
$627$		0			0
$628$	−0.0614207			−0.0614207
$629$		0			0
$630$		0			0
$631$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$631$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$632$	−1.57153	−	1.31867i	−1.57153	−	1.31867i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.0837437	+	0.145048i	−0.0837437	+	0.145048i
$640$	−0.361076	−	0.625401i	−0.361076	−	0.625401i
$641$	1.06976	−	0.897636i	1.06976	−	0.897636i	0.0747301	−	0.997204i	$-0.476190\pi$
$641$	1.06976	−	0.897636i	1.06976	−	0.897636i	0.995031	+	0.0995678i	$0.0317460\pi$
$642$	0.779741	+	0.137489i	0.779741	+	0.137489i
$643$	−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
$645$	−1.34084	−	0.488025i	−1.34084	−	0.488025i
$646$		0			0
$647$	−1.11334	+	1.32683i	−1.11334	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$647$	−1.11334	+	1.32683i	−1.11334	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$648$	0.559545	−	0.666840i	0.559545	−	0.666840i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$653$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$654$	1.07947	−	0.905782i	1.07947	−	0.905782i
$655$	−1.49910	−	2.59651i	−1.49910	−	2.59651i
$656$		0			0
$657$	0.0185257	+	0.105064i	0.0185257	+	0.105064i
$658$		0			0
$659$	1.37769	−	0.501437i	1.37769	−	0.501437i	0.456211	−	0.889872i	$-0.349206\pi$
$659$	1.37769	−	0.501437i	1.37769	−	0.501437i	0.921476	+	0.388435i	$0.126984\pi$
$660$		0			0
$661$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$661$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$662$		0			0
$663$		0			0
$664$	0.103957	+	0.123892i	0.103957	+	0.123892i
$665$		0			0
$666$	0.0818730	+	0.120086i	0.0818730	+	0.120086i
$667$		0			0
$668$	−0.295563	−	0.352238i	−0.295563	−	0.352238i
$669$	−1.35468	−	1.13671i	−1.35468	−	1.13671i
$670$		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
$675$	−0.230979	−	1.30994i	−0.230979	−	1.30994i
$676$	0.123490	−	0.213891i	0.123490	−	0.213891i
$677$	0.998757	+	1.72990i	0.998757	+	1.72990i	0.542546	+	0.840026i	$0.317460\pi$
$677$	0.998757	+	1.72990i	0.998757	+	1.72990i	0.456211	+	0.889872i	$0.349206\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$683$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$684$	−0.0511914	+	0.0610076i	−0.0511914	+	0.0610076i
$685$		0			0
$686$		0			0
$687$	−0.626484	−	0.228021i	−0.626484	−	0.228021i
$688$	−0.246832	+	0.678166i	−0.246832	+	0.678166i
$689$		0			0
$690$		0			0
$691$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$691$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	1.26210	−	0.459366i	1.26210	−	0.459366i
$697$		0			0
$698$		0			0
$699$	0.261819	−	1.48485i	0.261819	−	1.48485i
$700$		0			0
$701$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$701$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$702$		0			0
$703$	1.08453	+	1.59071i	1.08453	+	1.59071i
$704$		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	$0.5\pi$
$710$	−1.22280	+	0.445061i	−1.22280	+	0.445061i
$711$	−0.274990	+	0.158766i	−0.274990	+	0.158766i
$712$	−0.0187323	−	0.106236i	−0.0187323	−	0.106236i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0725023	+	0.0127841i	0.0725023	+	0.0127841i
$717$		0			0
$718$	0.506503	−	1.39161i	0.506503	−	1.39161i
$719$	−1.87005	−	0.680641i	−1.87005	−	0.680641i	−0.969077	−	0.246757i	$-0.920635\pi$
$719$	−1.87005	−	0.680641i	−1.87005	−	0.680641i	−0.900969	−	0.433884i	$-0.857143\pi$
$720$	−0.171166	+	0.0301812i	−0.171166	+	0.0301812i
$721$		0			0
$722$	1.50970	−	1.79920i	1.50970	−	1.79920i
$723$		0			0
$724$		0			0
$725$	0.580971	−	1.59621i	0.580971	−	1.59621i
$726$	0.685693	+	0.395885i	0.685693	+	0.395885i
$727$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$727$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$728$		0			0
$729$	−0.553342	−	0.958417i	−0.553342	−	0.958417i
$730$	−0.414438	+	0.717827i	−0.414438	+	0.717827i
$731$		0			0
$732$		0			0
$733$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$733$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$734$		−	0.0432681i		−	0.0432681i
$735$	0.467963	+	1.28572i	0.467963	+	1.28572i
$736$		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	$0.555556\pi$
$740$	0.0368761	−	0.368521i	0.0368761	−	0.368521i
$741$		0			0
$742$		0			0
$743$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$743$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$744$		0			0
$745$		0			0
$746$			1.14838i			1.14838i
$747$	0.0235230	−	0.00856168i	0.0235230	−	0.00856168i
$748$		0			0
$749$		0			0
$750$	0.147634	−	0.255710i	0.147634	−	0.255710i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$	0.779741	+	0.137489i	0.779741	+	0.137489i
$754$		0			0
$755$	−0.817668	+	2.24652i	−0.817668	+	2.24652i
$756$		0			0
$757$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$757$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$758$	0.889265	−	1.05979i	0.889265	−	1.05979i
$759$		0			0
$760$	−3.07656	+	0.542481i	−3.07656	+	0.542481i
$761$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$761$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$762$		0			0
$763$		0			0
$764$	0.482680	+	0.0851094i	0.482680	+	0.0851094i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.109644	+	0.621823i	0.109644	+	0.621823i
$769$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$769$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$773$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$774$	0.116110	+	0.0974279i	0.116110	+	0.0974279i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	1.44909i		−	1.44909i
$784$	0.650287	−	0.236685i	0.650287	−	0.236685i
$785$	−0.322960	+	0.186461i	−0.322960	+	0.186461i
$786$	−0.274893	−	1.55900i	−0.274893	−	1.55900i
$787$	−0.998757	+	1.72990i	−0.998757	+	1.72990i	−0.456211	+	0.889872i	$0.650794\pi$
$787$	−0.998757	+	1.72990i	−0.998757	+	1.72990i	−0.542546	+	0.840026i	$0.682540\pi$
$788$		0			0
$789$	−0.924978	+	0.776148i	−0.924978	+	0.776148i
$790$	−2.42954	−	0.428394i	−2.42954	−	0.428394i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.0316139	+	0.0376759i	−0.0316139	+	0.0376759i
$797$	−1.79532	+	0.316563i	−1.79532	+	0.316563i	−0.969077	−	0.246757i	$-0.920635\pi$
$797$	−1.79532	+	0.316563i	−1.79532	+	0.316563i	−0.826239	+	0.563320i	$0.809524\pi$
$798$		0			0
$799$		0			0
$800$	0.520772	+	0.300668i	0.520772	+	0.300668i
$801$	−0.0164434	−	0.00289942i	−0.0164434	−	0.00289942i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$			0.890098i			0.890098i
$809$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$809$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$810$	0.181779	−	1.03092i	0.181779	−	1.03092i
$811$	1.50171	+	1.26009i	1.50171	+	1.26009i	0.878222	+	0.478254i	$0.158730\pi$
$811$	1.50171	+	1.26009i	1.50171	+	1.26009i	0.623490	+	0.781831i	$0.285714\pi$
$812$		0			0
$813$	−0.406066			−0.406066
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.53805	+	1.29058i	1.53805	+	1.29058i
$818$	−0.0888311	+	0.503786i	−0.0888311	+	0.503786i
$819$		0			0
$820$		0			0
$821$	0.509014	−	0.185266i	0.509014	−	0.185266i	−0.0747301	−	0.997204i	$-0.523810\pi$
$821$	0.509014	−	0.185266i	0.509014	−	0.185266i	0.583744	+	0.811938i	$0.301587\pi$
$822$		0			0
$823$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$823$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$824$	0.962920	−	1.66783i	0.962920	−	1.66783i
$825$		0			0
$826$		0			0
$827$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$827$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$828$		0			0
$829$	−0.623507	+	1.71307i	−0.623507	+	1.71307i	0.0747301	+	0.997204i	$0.476190\pi$
$829$	−0.623507	+	1.71307i	−0.623507	+	1.71307i	−0.698237	+	0.715867i	$0.746032\pi$
$830$	0.182759	+	0.0665189i	0.182759	+	0.0665189i
$831$	1.79209	−	0.315995i	1.79209	−	0.315995i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.62344	−	0.954854i	−2.62344	−	0.954854i
$836$		0			0
$837$		0			0
$838$	−1.63323	−	0.287983i	−1.63323	−	0.287983i
$839$	0.114493	−	0.0960712i	0.114493	−	0.0960712i	−0.583744	−	0.811938i	$-0.698413\pi$
$839$	0.114493	−	0.0960712i	0.114493	−	0.0960712i	0.698237	+	0.715867i	$0.253968\pi$
$840$		0			0
$841$	0.425270	−	0.736589i	0.425270	−	0.736589i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	1.49956i		−	1.49956i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	0.225349			0.225349
$853$	1.07992	+	1.28699i	1.07992	+	1.28699i	0.955573	+	0.294755i	$0.0952381\pi$
$853$	1.07992	+	1.28699i	1.07992	+	1.28699i	0.124344	+	0.992239i	$0.460317\pi$
$854$		0			0
$855$	−0.0839660	+	0.476195i	−0.0839660	+	0.476195i
$856$	0.370096	+	1.01683i	0.370096	+	1.01683i
$857$		−	1.68005i		−	1.68005i	−0.542546	−	0.840026i	$-0.682540\pi$
$857$		−	1.68005i		−	1.68005i	0.542546	−	0.840026i	$-0.317460\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$	−0.0670697	−	0.380371i	−0.0670697	−	0.380371i
$861$		0			0
$862$	−0.790975	−	1.37001i	−0.790975	−	1.37001i
$863$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$863$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$864$	0.505199	+	0.0890802i	0.505199	+	0.0890802i
$865$		0			0
$866$		0			0
$867$	−0.857396	−	0.312066i	−0.857396	−	0.312066i
$868$		0			0
$869$		0			0
$870$	1.03820	−	1.23728i	1.03820	−	1.23728i
$871$		0			0
$872$	1.80970	+	0.658676i	1.80970	+	0.658676i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.109959	−	0.0922668i	0.109959	−	0.0922668i
$877$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.623490	−	0.781831i	$-0.714286\pi$
$877$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.365341	−	0.930874i	$-0.619048\pi$
$878$		0			0
$879$	0.297770	+	1.68874i	0.297770	+	1.68874i
$880$		0			0
$881$	1.17178	−	0.426492i	1.17178	−	0.426492i	0.318487	−	0.947927i	$-0.396825\pi$
$881$	1.17178	−	0.426492i	1.17178	−	0.426492i	0.853291	+	0.521435i	$0.174603\pi$
$882$		−	0.145340i		−	0.145340i
$883$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$883$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$	0.428382	−	0.889545i	0.428382	−	0.889545i
$889$		0			0
$890$	−0.0833863	−	0.0993759i	−0.0833863	−	0.0993759i
$891$		0			0
$892$	0.0831227	−	0.471412i	0.0831227	−	0.471412i
$893$		0			0
$894$		0			0
$895$	0.420039	−	0.152882i	0.420039	−	0.152882i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.0395686	−	0.0332020i	0.0395686	−	0.0332020i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.811385	+	0.966971i	−0.811385	+	0.966971i
$907$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$907$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$908$		0			0
$909$	0.129462	+	0.0471204i	0.129462	+	0.0471204i
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$	−1.19716	−	0.211092i	−1.19716	−	0.211092i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.0313372	−	0.177722i	−0.0313372	−	0.177722i
$917$		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
$925$	−0.513569	−	1.13819i	−0.513569	−	1.13819i
$926$	−0.977662			−0.977662
$927$	−0.191605	−	0.228346i	−0.191605	−	0.228346i
$928$	0.501842	+	0.421095i	0.501842	+	0.421095i
$929$	−0.312903	+	1.77456i	−0.312903	+	1.77456i	0.270840	+	0.962624i	$0.412698\pi$
$929$	−0.312903	+	1.77456i	−0.312903	+	1.77456i	−0.583744	+	0.811938i	$0.698413\pi$
$930$		0			0
$931$		−	1.92525i		−	1.92525i
$932$	0.383515	−	0.139588i	0.383515	−	0.139588i
$933$	−1.13133	+	0.653172i	−1.13133	+	0.653172i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$937$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$938$		0			0
$939$	−1.13133	−	0.653172i	−1.13133	−	0.653172i
$940$		0			0
$941$	−1.09708	−	0.399304i	−1.09708	−	0.399304i	−0.270840	−	0.962624i	$-0.587302\pi$
$941$	−1.09708	−	0.399304i	−1.09708	−	0.399304i	−0.826239	+	0.563320i	$0.809524\pi$
$942$	−0.193912	+	0.0341919i	−0.193912	+	0.0341919i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.356683	+	0.979978i	−0.356683	+	0.979978i	0.623490	+	0.781831i	$0.285714\pi$
$947$	−0.356683	+	0.979978i	−0.356683	+	0.979978i	−0.980172	+	0.198146i	$0.936508\pi$
$948$	0.369992	+	0.213615i	0.369992	+	0.213615i
$949$		0			0
$950$	−1.59808	+	1.34095i	−1.59808	+	1.34095i
$951$		0			0
$952$		0			0
$953$	−0.340410	−	1.93056i	−0.340410	−	1.93056i	−0.365341	−	0.930874i	$-0.619048\pi$
$953$	−0.340410	−	1.93056i	−0.340410	−	1.93056i	0.0249307	−	0.999689i	$-0.492063\pi$
$954$		0			0
$955$	2.79638	−	1.01780i	2.79638	−	1.01780i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.976153	+	1.16333i	0.976153	+	1.16333i
$961$	−1.00000			−1.00000
$962$		0			0
$963$	0.167487			0.167487
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$967$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$968$			1.08209i			1.08209i
$969$		0			0
$970$		0			0
$971$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$971$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$972$	0.0409039	−	0.0708477i	0.0409039	−	0.0708477i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.265705	+	0.730019i	−0.265705	+	0.730019i	0.733052	+	0.680173i	$0.238095\pi$
$977$	−0.265705	+	0.730019i	−0.265705	+	0.730019i	−0.998757	+	0.0498459i	$0.984127\pi$
$978$		0			0
$979$		0			0
$980$	−0.238064	+	0.283713i	−0.238064	+	0.283713i
$981$	0.191605	−	0.228346i	0.191605	−	0.228346i
$982$		0			0
$983$	1.69327	+	0.616299i	1.69327	+	0.616299i	0.995031	−	0.0995678i	$-0.0317460\pi$
$983$	1.69327	+	0.616299i	1.69327	+	0.616299i	0.698237	+	0.715867i	$0.253968\pi$
$984$		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	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.0518542	+	0.294080i	−0.0518542	+	0.294080i
$996$	−0.0258010	−	0.0216496i	−0.0258010	−	0.0216496i
$997$	0.614831	+	0.732728i	0.614831	+	0.732728i	0.980172	−	0.198146i	$-0.0634921\pi$
$997$	0.614831	+	0.732728i	0.614831	+	0.732728i	−0.365341	+	0.930874i	$0.619048\pi$
$998$	1.45789			1.45789
$999$	−0.743790	−	0.762570i	−0.743790	−	0.762570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2627.1.x.b.1135.4	yes	36
37.3	even	18	inner	2627.1.x.b.780.4	✓	36
71.70	odd	2	CM	2627.1.x.b.1135.4	yes	36
2627.780	odd	18	inner	2627.1.x.b.780.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2627.1.x.b.780.4	✓	36	37.3	even	18	inner
2627.1.x.b.780.4	✓	36	2627.780	odd	18	inner
2627.1.x.b.1135.4	yes	36	1.1	even	1	trivial
2627.1.x.b.1135.4	yes	36	71.70	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(0.557790 + 0.664748i) q^{2} +(-0.698955 - 0.586493i) q^{3} +(0.0428876 - 0.243227i) q^{4} +(-0.512881 - 1.40913i) q^{5} -0.791770i q^{6} +(0.937116 - 0.541044i) q^{8} +(-0.0290839 - 0.164943i) q^{9} +O(q^{10})\)	\(q+(0.557790 + 0.664748i) q^{2} +(-0.698955 - 0.586493i) q^{3} +(0.0428876 - 0.243227i) q^{4} +(-0.512881 - 1.40913i) q^{5} -0.791770i q^{6} +(0.937116 - 0.541044i) q^{8} +(-0.0290839 - 0.164943i) q^{9} +(0.650636 - 1.12693i) q^{10} +(-0.172628 + 0.144852i) q^{12} +(-0.467963 + 1.28572i) q^{15} +(0.650287 + 0.236685i) q^{16} +(0.0934228 - 0.111337i) q^{18} +(1.23753 - 1.47483i) q^{19} +(-0.364735 + 0.0643126i) q^{20} +(-0.972321 - 0.171446i) q^{24} +(-0.956550 + 0.802641i) q^{25} +(-0.532620 + 0.922525i) q^{27} +(-1.17809 + 0.680173i) q^{29} +(-1.11570 + 0.406083i) q^{30} +(-0.164708 - 0.452532i) q^{32} -0.0413660 q^{36} +(-0.270840 + 0.962624i) q^{37} +1.67067 q^{38} +(-1.24303 - 1.04303i) q^{40} +1.04287i q^{43} +(-0.217509 + 0.125579i) q^{45} +(-0.315708 - 0.546822i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-1.06711 - 0.188160i) q^{50} +(-0.910337 + 0.160517i) q^{54} +(-1.72995 + 0.305037i) q^{57} +(-1.10927 - 0.403742i) q^{58} +(0.292652 + 0.168963i) q^{60} +(0.554958 - 0.961216i) q^{64} +(-0.766044 - 0.642788i) q^{71} +(-0.116496 - 0.138835i) q^{72} -0.636973 q^{73} +(-0.790975 + 0.356902i) q^{74} +1.13933 q^{75} +(-0.305644 - 0.364252i) q^{76} +(-0.648420 - 1.78152i) q^{79} -1.03773i q^{80} +(0.755946 - 0.275142i) q^{81} +(0.0259535 + 0.147190i) q^{83} +(-0.693246 + 0.581703i) q^{86} +(1.22235 + 0.215534i) q^{87} +(0.0340966 - 0.0936796i) q^{89} +(-0.204803 - 0.0745421i) q^{90} +(-2.71292 - 0.987423i) q^{95} +(-0.150283 + 0.412900i) q^{96} +(0.854584 + 0.150686i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9}+O(q^{10}) \) 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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