LMFDB - Embedded newform 2001.1.bf.c.620.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,1,Mod(68,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 14, 23]))

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

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

chi := DirichletCharacter("2001.68");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2001.bf (of order $28$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.998629090279$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{28})$
Coefficient field:	$\Q(\zeta_{84})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 $ x^24 + x^22 - x^18 - x^16 + x^12 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{84}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{84} - \cdots)$

Embedding invariants

Embedding label			620.2
Root			$0.930874 - 0.365341i$ of defining polynomial
Character	$\chi$	$=$	2001.620
Dual form			2001.1.bf.c.965.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500684 + 1.43087i) q^{2} +(0.955573 - 0.294755i) q^{3} +(-1.01488 + 0.809342i) q^{4} +(0.900198 + 1.21972i) q^{6} +(-0.382617 - 0.240414i) q^{8} +(0.826239 - 0.563320i) q^{9} +O(q^{10})$	\(q+(0.500684 + 1.43087i) q^{2} +(0.955573 - 0.294755i) q^{3} +(-1.01488 + 0.809342i) q^{4} +(0.900198 + 1.21972i) q^{6} +(-0.382617 - 0.240414i) q^{8} +(0.826239 - 0.563320i) q^{9} +(-0.731237 + 1.07253i) q^{12} +(0.145713 + 0.0332580i) q^{13} +(-0.136419 + 0.597690i) q^{16} +(1.21972 + 0.900198i) q^{18} +(-0.433884 - 0.900969i) q^{23} +(-0.436482 - 0.116955i) q^{24} +(0.623490 + 0.781831i) q^{25} +(0.0253681 + 0.225149i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.930874 - 0.365341i) q^{29} +(0.488590 - 0.170965i) q^{31} +(-1.37256 + 0.154650i) q^{32} +(-0.382617 + 1.24041i) q^{36} +(0.149042 - 0.0111692i) q^{39} +(-1.41322 + 1.41322i) q^{41} +(1.07193 - 1.07193i) q^{46} +(0.425511 + 0.677197i) q^{47} +(0.0458141 + 0.611347i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(-0.806531 + 1.28359i) q^{50} +(-0.174799 + 0.0841786i) q^{52} +(1.43087 + 0.500684i) q^{54} +(0.0566829 - 1.51488i) q^{58} -1.24698i q^{59} +(0.489259 + 0.613511i) q^{62} +(-0.642507 - 1.33418i) q^{64} +(-0.680173 - 0.733052i) q^{69} +(-0.250701 + 1.09839i) q^{71} +(-0.451563 + 0.0168963i) q^{72} +(-1.12099 - 0.392253i) q^{73} +(0.826239 + 0.563320i) q^{75} +(0.0906048 + 0.207668i) q^{78} +(0.365341 - 0.930874i) q^{81} +(-2.72973 - 1.31457i) q^{82} +(-0.997204 - 0.0747301i) q^{87} +(1.16953 + 0.563218i) q^{92} +(0.416490 - 0.307384i) q^{93} +(-0.755936 + 0.947914i) q^{94} +(-1.26600 + 0.552349i) q^{96} +(1.28359 - 0.806531i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 2 * q^3 + 14 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9	$ 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 6 q^{12} - 6 q^{16} + 4 q^{18} - 6 q^{24} - 4 q^{25} + 2 q^{26} - 4 q^{27} - 2 q^{31} + 4 q^{32} + 6 q^{36} + 2 q^{41} + 2 q^{46} - 2 q^{47} - 4 q^{48} - 4 q^{49} - 2 q^{50} - 10 q^{52} + 12 q^{54} + 4 q^{58} + 4 q^{62} - 28 q^{64} + 14 q^{72} - 2 q^{73} + 2 q^{75} + 10 q^{78} + 2 q^{81} - 4 q^{82} + 4 q^{92} - 2 q^{93} - 8 q^{94} - 24 q^{96} - 2 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 + 2 * q^3 + 14 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 6 * q^12 - 6 * q^16 + 4 * q^18 - 6 * q^24 - 4 * q^25 + 2 * q^26 - 4 * q^27 - 2 * q^31 + 4 * q^32 + 6 * q^36 + 2 * q^41 + 2 * q^46 - 2 * q^47 - 4 * q^48 - 4 * q^49 - 2 * q^50 - 10 * q^52 + 12 * q^54 + 4 * q^58 + 4 * q^62 - 28 * q^64 + 14 * q^72 - 2 * q^73 + 2 * q^75 + 10 * q^78 + 2 * q^81 - 4 * q^82 + 4 * q^92 - 2 * q^93 - 8 * q^94 - 24 * q^96 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{25}{28}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.500684	+	1.43087i	0.500684	+	1.43087i	0.866025	+	0.500000i	$0.166667\pi$
$2$	0.500684	+	1.43087i	0.500684	+	1.43087i	−0.365341	+	0.930874i	$0.619048\pi$
$3$	0.955573	−	0.294755i	0.955573	−	0.294755i
$3$	0.955573	−	0.294755i	0.955573	−	0.294755i
$4$	−1.01488	+	0.809342i	−1.01488	+	0.809342i
$5$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$5$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$6$	0.900198	+	1.21972i	0.900198	+	1.21972i
$7$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$7$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$8$	−0.382617	−	0.240414i	−0.382617	−	0.240414i
$9$	0.826239	−	0.563320i	0.826239	−	0.563320i
$10$		0			0
$11$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$11$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$12$	−0.731237	+	1.07253i	−0.731237	+	1.07253i
$13$	0.145713	+	0.0332580i	0.145713	+	0.0332580i	0.294755	−	0.955573i	$-0.404762\pi$
$13$	0.145713	+	0.0332580i	0.145713	+	0.0332580i	−0.149042	+	0.988831i	$0.547619\pi$
$14$		0			0
$15$		0			0
$16$	−0.136419	+	0.597690i	−0.136419	+	0.597690i
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	1.21972	+	0.900198i	1.21972	+	0.900198i
$19$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$19$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$23$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$24$	−0.436482	−	0.116955i	−0.436482	−	0.116955i
$25$	0.623490	+	0.781831i	0.623490	+	0.781831i
$26$	0.0253681	+	0.225149i	0.0253681	+	0.225149i
$27$	0.623490	−	0.781831i	0.623490	−	0.781831i
$28$		0			0
$29$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$29$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$30$		0			0
$31$	0.488590	−	0.170965i	0.488590	−	0.170965i	−0.0747301	−	0.997204i	$-0.523810\pi$
$31$	0.488590	−	0.170965i	0.488590	−	0.170965i	0.563320	+	0.826239i	$0.309524\pi$
$32$	−1.37256	+	0.154650i	−1.37256	+	0.154650i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.382617	+	1.24041i	−0.382617	+	1.24041i
$37$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$37$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$38$		0			0
$39$	0.149042	−	0.0111692i	0.149042	−	0.0111692i
$40$		0			0
$41$	−1.41322	+	1.41322i	−1.41322	+	1.41322i	−0.680173	+	0.733052i	$0.738095\pi$
$41$	−1.41322	+	1.41322i	−1.41322	+	1.41322i	−0.733052	+	0.680173i	$0.761905\pi$
$42$		0			0
$43$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$43$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$44$		0			0
$45$		0			0
$46$	1.07193	−	1.07193i	1.07193	−	1.07193i
$47$	0.425511	+	0.677197i	0.425511	+	0.677197i	0.988831	−	0.149042i	$-0.0476190\pi$
$47$	0.425511	+	0.677197i	0.425511	+	0.677197i	−0.563320	+	0.826239i	$0.690476\pi$
$48$	0.0458141	+	0.611347i	0.0458141	+	0.611347i
$49$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$50$	−0.806531	+	1.28359i	−0.806531	+	1.28359i
$51$		0			0
$52$	−0.174799	+	0.0841786i	−0.174799	+	0.0841786i
$53$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$53$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$54$	1.43087	+	0.500684i	1.43087	+	0.500684i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.0566829	−	1.51488i	0.0566829	−	1.51488i
$59$		−	1.24698i		−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$59$		−	1.24698i		−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$60$		0			0
$61$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$61$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$62$	0.489259	+	0.613511i	0.489259	+	0.613511i
$63$		0			0
$64$	−0.642507	−	1.33418i	−0.642507	−	1.33418i
$65$		0			0
$66$		0			0
$67$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$67$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$68$		0			0
$69$	−0.680173	−	0.733052i	−0.680173	−	0.733052i
$70$		0			0
$71$	−0.250701	+	1.09839i	−0.250701	+	1.09839i	0.680173	+	0.733052i	$0.261905\pi$
$71$	−0.250701	+	1.09839i	−0.250701	+	1.09839i	−0.930874	+	0.365341i	$0.880952\pi$
$72$	−0.451563	+	0.0168963i	−0.451563	+	0.0168963i
$73$	−1.12099	−	0.392253i	−1.12099	−	0.392253i	−0.294755	−	0.955573i	$-0.595238\pi$
$73$	−1.12099	−	0.392253i	−1.12099	−	0.392253i	−0.826239	+	0.563320i	$0.809524\pi$
$74$		0			0
$75$	0.826239	+	0.563320i	0.826239	+	0.563320i
$76$		0			0
$77$		0			0
$78$	0.0906048	+	0.207668i	0.0906048	+	0.207668i
$79$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$79$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$80$		0			0
$81$	0.365341	−	0.930874i	0.365341	−	0.930874i
$82$	−2.72973	−	1.31457i	−2.72973	−	1.31457i
$83$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$83$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.997204	−	0.0747301i	−0.997204	−	0.0747301i
$88$		0			0
$89$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$89$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$90$		0			0
$91$		0			0
$92$	1.16953	+	0.563218i	1.16953	+	0.563218i
$93$	0.416490	−	0.307384i	0.416490	−	0.307384i
$94$	−0.755936	+	0.947914i	−0.755936	+	0.947914i
$95$		0			0
$96$	−1.26600	+	0.552349i	−1.26600	+	0.552349i
$97$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$97$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$98$	1.28359	−	0.806531i	1.28359	−	0.806531i
$99$		0			0
$100$	−1.26554	−	0.288851i	−1.26554	−	0.288851i
$101$	−1.87590	−	0.656405i	−1.87590	−	0.656405i	−0.974928	−	0.222521i	$-0.928571\pi$
$101$	−1.87590	−	0.656405i	−1.87590	−	0.656405i	−0.900969	−	0.433884i	$-0.857143\pi$
$102$		0			0
$103$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$103$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$104$	−0.0477566	−	0.0477566i	−0.0477566	−	0.0477566i
$105$		0			0
$106$		0			0
$107$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$107$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$108$			1.29808i			1.29808i
$109$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$109$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$113$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$114$		0			0
$115$		0			0
$116$	1.24041	−	0.382617i	1.24041	−	0.382617i
$117$	0.139129	−	0.0546039i	0.139129	−	0.0546039i
$118$	1.78427	−	0.624343i	1.78427	−	0.624343i
$119$		0			0
$120$		0			0
$121$	0.433884	−	0.900969i	0.433884	−	0.900969i
$122$		0			0
$123$	−0.933884	+	1.76699i	−0.933884	+	1.76699i
$124$	−0.357493	+	0.568946i	−0.357493	+	0.568946i
$125$		0			0
$126$		0			0
$127$	−0.497204	−	0.791295i	−0.497204	−	0.791295i	0.500000	−	0.866025i	$-0.333333\pi$
$127$	−0.497204	−	0.791295i	−0.497204	−	0.791295i	−0.997204	+	0.0747301i	$0.976190\pi$
$128$	0.610662	−	0.610662i	0.610662	−	0.610662i
$129$		0			0
$130$		0			0
$131$	0.430874	−	1.23137i	0.430874	−	1.23137i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	0.430874	−	1.23137i	0.430874	−	1.23137i	0.930874	−	0.365341i	$-0.119048\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$137$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$138$	0.708353	−	1.34027i	0.708353	−	1.34027i
$139$	1.01507	−	0.488831i	1.01507	−	0.488831i	0.149042	−	0.988831i	$-0.452381\pi$
$139$	1.01507	−	0.488831i	1.01507	−	0.488831i	0.866025	+	0.500000i	$0.166667\pi$
$140$		0			0
$141$	0.606214	+	0.521689i	0.606214	+	0.521689i
$142$	−1.69718	+	0.191227i	−1.69718	+	0.191227i
$143$		0			0
$144$	0.223976	+	0.570682i	0.223976	+	0.570682i
$145$		0			0
$146$		−	1.80040i		−	1.80040i
$147$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$148$		0			0
$149$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$149$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$150$	−0.392355	+	1.46429i	−0.392355	+	1.46429i
$151$	0.433884	+	0.900969i	0.433884	+	0.900969i	0.997204	+	0.0747301i	$0.0238095\pi$
$151$	0.433884	+	0.900969i	0.433884	+	0.900969i	−0.563320	+	0.826239i	$0.690476\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.142221	+	0.131962i	−0.142221	+	0.131962i
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	1.51488	+	0.0566829i	1.51488	+	0.0566829i
$163$	0.677197	−	0.425511i	0.677197	−	0.425511i	−0.149042	−	0.988831i	$-0.547619\pi$
$163$	0.677197	−	0.425511i	0.677197	−	0.425511i	0.826239	+	0.563320i	$0.190476\pi$
$164$	0.290475	−	2.57804i	0.290475	−	2.57804i
$165$		0			0
$166$		0			0
$167$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$167$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$168$		0			0
$169$	−0.880843	−	0.424191i	−0.880843	−	0.424191i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$173$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$174$	−0.392355	−	1.46429i	−0.392355	−	1.46429i
$175$		0			0
$176$		0			0
$177$	−0.367554	−	1.19158i	−0.367554	−	1.19158i
$178$		0			0
$179$	1.72188	+	0.829215i	1.72188	+	0.829215i	0.988831	+	0.149042i	$0.0476190\pi$
$179$	1.72188	+	0.829215i	1.72188	+	0.829215i	0.733052	+	0.680173i	$0.238095\pi$
$180$		0			0
$181$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$181$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$182$		0			0
$183$		0			0
$184$	−0.0505944	+	0.449038i	−0.0505944	+	0.449038i
$185$		0			0
$186$	0.648358	+	0.442043i	0.648358	+	0.442043i
$187$		0			0
$188$	−0.979928	−	0.342892i	−0.979928	−	0.342892i
$189$		0			0
$190$		0			0
$191$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$191$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$192$	−1.00722	−	1.08552i	−1.00722	−	1.08552i
$193$	1.59908	+	0.180173i	1.59908	+	0.180173i	0.866025	−	0.500000i	$-0.166667\pi$
$193$	1.59908	+	0.180173i	1.59908	+	0.180173i	0.733052	+	0.680173i	$0.238095\pi$
$194$		0			0
$195$		0			0
$196$	1.01488	+	0.809342i	1.01488	+	0.809342i
$197$	−0.751509	−	1.56052i	−0.751509	−	1.56052i	−0.826239	−	0.563320i	$-0.809524\pi$
$197$	−0.751509	−	1.56052i	−0.751509	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$198$		0			0
$199$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$199$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$200$	−0.0505944	−	0.449038i	−0.0505944	−	0.449038i
$201$		0			0
$202$		−	3.01282i		−	3.01282i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$208$	−0.0397560	+	0.0825542i	−0.0397560	+	0.0825542i
$209$		0			0
$210$		0			0
$211$	−0.752407	+	1.19745i	−0.752407	+	1.19745i	0.222521	+	0.974928i	$0.428571\pi$
$211$	−0.752407	+	1.19745i	−0.752407	+	1.19745i	−0.974928	+	0.222521i	$0.928571\pi$
$212$		0			0
$213$	0.0841939	+	1.12349i	0.0841939	+	1.12349i
$214$		0			0
$215$		0			0
$216$	−0.426521	+	0.149246i	−0.426521	+	0.149246i
$217$		0			0
$218$		0			0
$219$	−1.18681	−	0.0444073i	−1.18681	−	0.0444073i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$223$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	−1.00000			$\pi$
$224$		0			0
$225$	0.955573	+	0.294755i	0.955573	+	0.294755i
$226$		0			0
$227$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$227$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$228$		0			0
$229$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$229$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$230$		0			0
$231$		0			0
$232$	0.268335	+	0.363581i	0.268335	+	0.363581i
$233$		−	1.46610i		−	1.46610i	−0.680173	−	0.733052i	$-0.738095\pi$
$233$		−	1.46610i		−	1.46610i	0.680173	−	0.733052i	$-0.261905\pi$
$234$	0.147791	+	0.171736i	0.147791	+	0.171736i
$235$		0			0
$236$	1.00923	+	1.26554i	1.00923	+	1.26554i
$237$		0			0
$238$		0			0
$239$	−1.06356	−	0.848162i	−1.06356	−	0.848162i	−0.0747301	−	0.997204i	$-0.523810\pi$
$239$	−1.06356	−	0.848162i	−1.06356	−	0.848162i	−0.988831	+	0.149042i	$0.952381\pi$
$240$		0			0
$241$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$241$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$242$	1.50641	+	0.169732i	1.50641	+	0.169732i
$243$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$244$		0			0
$245$		0			0
$246$	−2.99593	−	0.451563i	−2.99593	−	0.451563i
$247$		0			0
$248$	−0.228045	−	0.0520499i	−0.228045	−	0.0520499i
$249$		0			0
$250$		0			0
$251$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$251$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$252$		0			0
$253$		0			0
$254$	0.883302	−	1.10763i	0.883302	−	1.10763i
$255$		0			0
$256$	−0.154650	−	0.0744757i	−0.154650	−	0.0744757i
$257$	−1.45557	+	1.16078i	−1.45557	+	1.16078i	−0.500000	+	0.866025i	$0.666667\pi$
$257$	−1.45557	+	1.16078i	−1.45557	+	1.16078i	−0.955573	+	0.294755i	$0.904762\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$262$	1.97766			1.97766
$263$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$263$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.791295	+	0.497204i	0.791295	+	0.497204i	0.866025	−	0.500000i	$-0.166667\pi$
$269$	0.791295	+	0.497204i	0.791295	+	0.497204i	−0.0747301	+	0.997204i	$0.523810\pi$
$270$		0			0
$271$	0.0739590	−	0.656405i	0.0739590	−	0.656405i	−0.900969	−	0.433884i	$-0.857143\pi$
$271$	0.0739590	−	0.656405i	0.0739590	−	0.656405i	0.974928	−	0.222521i	$-0.0714286\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	1.28359	+	0.193469i	1.28359	+	0.193469i
$277$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	0.365341	+	0.930874i	$0.380952\pi$
$277$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	−0.733052	+	0.680173i	$0.761905\pi$
$278$	1.20768	+	1.20768i	1.20768	+	1.20768i
$279$	0.307384	−	0.416490i	0.307384	−	0.416490i
$280$		0			0
$281$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$281$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$282$	−0.442949	+	1.12862i	−0.442949	+	1.12862i
$283$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$283$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$284$	−0.634544	−	1.31764i	−0.634544	−	1.31764i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.04694	+	0.900969i	−1.04694	+	0.900969i
$289$			1.00000i			1.00000i
$290$		0			0
$291$		0			0
$292$	1.45514	−	0.509177i	1.45514	−	0.509177i
$293$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$293$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$294$	0.988831	−	1.14904i	0.988831	−	1.14904i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0332580	−	0.145713i	−0.0332580	−	0.145713i
$300$	−1.29445	+	0.0970060i	−1.29445	+	0.0970060i
$301$		0			0
$302$	−1.07193	+	1.07193i	−1.07193	+	1.07193i
$303$	−1.98603	−	0.0743122i	−1.98603	−	0.0743122i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.158342	−	0.158342i	0.158342	−	0.158342i	−0.623490	−	0.781831i	$-0.714286\pi$
$307$	0.158342	−	0.158342i	0.158342	−	0.158342i	0.781831	+	0.623490i	$0.214286\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.197822	−	0.314832i	0.197822	−	0.314832i	−0.733052	−	0.680173i	$-0.761905\pi$
$311$	0.197822	−	0.314832i	0.197822	−	0.314832i	0.930874	+	0.365341i	$0.119048\pi$
$312$	−0.0597114	−	0.0315584i	−0.0597114	−	0.0315584i
$313$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$313$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.78183	+	0.623490i	−1.78183	+	0.623490i	−0.781831	+	0.623490i	$0.785714\pi$
$317$	−1.78183	+	0.623490i	−1.78183	+	0.623490i	−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.382617	+	1.24041i	0.382617	+	1.24041i
$325$	0.0648483	+	0.134659i	0.0648483	+	0.134659i
$326$	0.947914	+	0.755936i	0.947914	+	0.755936i
$327$		0			0
$328$	0.880483	−	0.200965i	0.880483	−	0.200965i
$329$		0			0
$330$		0			0
$331$	1.25033	+	1.25033i	1.25033	+	1.25033i	0.955573	+	0.294755i	$0.0952381\pi$
$331$	1.25033	+	1.25033i	1.25033	+	1.25033i	0.294755	+	0.955573i	$0.404762\pi$
$332$		0			0
$333$		0			0
$334$	−2.57835	−	0.902202i	−2.57835	−	0.902202i
$335$		0			0
$336$		0			0
$337$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$337$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$338$	0.165940	−	1.47276i	0.165940	−	1.47276i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.222826	+	0.636799i	0.222826	+	0.636799i
$347$	1.94986			1.94986			0.974928	−	0.222521i	$-0.0714286\pi$
$347$	1.94986			1.94986			0.974928	+	0.222521i	$0.0714286\pi$
$348$	1.07253	−	0.731237i	1.07253	−	0.731237i
$349$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$349$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$350$		0			0
$351$	0.116853	−	0.0931869i	0.116853	−	0.0931869i
$352$		0			0
$353$	0.531130	+	0.255779i	0.531130	+	0.255779i	0.680173	−	0.733052i	$-0.261905\pi$
$353$	0.531130	+	0.255779i	0.531130	+	0.255779i	−0.149042	+	0.988831i	$0.547619\pi$
$354$	1.52097	−	1.12253i	1.52097	−	1.12253i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.324382	+	2.87897i	−0.324382	+	2.87897i
$359$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$359$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$360$		0			0
$361$	0.974928	+	0.222521i	0.974928	+	0.222521i
$362$		0			0
$363$	0.149042	−	0.988831i	0.149042	−	0.988831i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$367$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$368$	0.597690	−	0.136419i	0.597690	−	0.136419i
$369$	−0.371563	+	1.96376i	−0.371563	+	1.96376i
$370$		0			0
$371$		0			0
$372$	−0.173910	+	0.649042i	−0.173910	+	0.649042i
$373$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$373$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$374$		0			0
$375$		0			0
$376$		−	0.361406i		−	0.361406i
$377$	−0.123490	−	0.0841939i	−0.123490	−	0.0841939i
$378$		0			0
$379$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$379$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$380$		0			0
$381$	−0.708353	−	0.609587i	−0.708353	−	0.609587i
$382$		0			0
$383$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$383$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$384$	0.403537	−	0.763528i	0.403537	−	0.763528i
$385$		0			0
$386$	0.542829	+	2.37829i	0.542829	+	2.37829i
$387$		0			0
$388$		0			0
$389$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$389$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$390$		0			0
$391$		0			0
$392$	−0.149246	+	0.426521i	−0.149246	+	0.426521i
$393$	0.0487796	−	1.30366i	0.0487796	−	1.30366i
$394$	1.85664	−	1.85664i	1.85664	−	1.85664i
$395$		0			0
$396$		0			0
$397$	−0.302705	−	1.32624i	−0.302705	−	1.32624i	−0.866025	−	0.500000i	$-0.833333\pi$
$397$	−0.302705	−	1.32624i	−0.302705	−	1.32624i	0.563320	−	0.826239i	$-0.309524\pi$
$398$		0			0
$399$		0			0
$400$	−0.552349	+	0.265997i	−0.552349	+	0.265997i
$401$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$401$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$402$		0			0
$403$	0.0768798	−	0.00866228i	0.0768798	−	0.00866228i
$404$	2.43507	−	0.852069i	2.43507	−	0.852069i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.223772	+	1.98603i	0.223772	+	1.98603i	0.149042	+	0.988831i	$0.452381\pi$
$409$	0.223772	+	1.98603i	0.223772	+	1.98603i	0.0747301	+	0.997204i	$0.476190\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.281831	−	1.48952i	0.281831	−	1.48952i
$415$		0			0
$416$	−0.205143	−	0.0231141i	−0.205143	−	0.0231141i
$417$	0.825886	−	0.766310i	0.825886	−	0.766310i
$418$		0			0
$419$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$419$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$420$		0			0
$421$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$421$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$422$	−2.09012	−	0.477055i	−2.09012	−	0.477055i
$423$	0.733052	+	0.319827i	0.733052	+	0.319827i
$424$		0			0
$425$		0			0
$426$	−1.56542	+	0.682985i	−1.56542	+	0.682985i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$431$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$432$	0.382237	+	0.479310i	0.382237	+	0.479310i
$433$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$433$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.530676	−	1.72041i	−0.530676	−	1.72041i
$439$	−1.06356	+	0.848162i	−1.06356	+	0.848162i	−0.988831	−	0.149042i	$-0.952381\pi$
$439$	−1.06356	+	0.848162i	−1.06356	+	0.848162i	−0.0747301	+	0.997204i	$0.523810\pi$
$440$		0			0
$441$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$442$		0			0
$443$	1.36254	+	0.856144i	1.36254	+	0.856144i	0.997204	−	0.0747301i	$-0.0238095\pi$
$443$	1.36254	+	0.856144i	1.36254	+	0.856144i	0.365341	+	0.930874i	$0.380952\pi$
$444$		0			0
$445$		0			0
$446$	0.571250	−	0.358940i	0.571250	−	0.358940i
$447$		0			0
$448$		0			0
$449$	0.623490	+	0.218169i	0.623490	+	0.218169i	0.623490	−	0.781831i	$-0.285714\pi$
$449$	0.623490	+	0.218169i	0.623490	+	0.218169i			1.00000i	$0.5\pi$
$450$	0.0566829	+	1.51488i	0.0566829	+	1.51488i
$451$		0			0
$452$		0			0
$453$	0.680173	+	0.733052i	0.680173	+	0.733052i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$457$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.197979	+	1.75711i	0.197979	+	1.75711i	0.563320	+	0.826239i	$0.309524\pi$
$461$	0.197979	+	1.75711i	0.197979	+	1.75711i	−0.365341	+	0.930874i	$0.619048\pi$
$462$		0			0
$463$			1.80194i			1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$463$			1.80194i			1.80194i	−0.433884	+	0.900969i	$0.642857\pi$
$464$	0.345350	−	0.506535i	0.345350	−	0.506535i
$465$		0			0
$466$	2.09781	−	0.734055i	2.09781	−	0.734055i
$467$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$467$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$468$	−0.0970060	+	0.168019i	−0.0970060	+	0.168019i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.299792	+	0.477116i	−0.299792	+	0.477116i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.681104	−	1.94648i	0.681104	−	1.94648i
$479$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$479$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.288851	+	1.26554i	0.288851	+	1.26554i
$485$		0			0
$486$	1.46429	−	0.392355i	1.46429	−	0.392355i
$487$	0.531130	−	0.255779i	0.531130	−	0.255779i	−0.149042	−	0.988831i	$-0.547619\pi$
$487$	0.531130	−	0.255779i	0.531130	−	0.255779i	0.680173	+	0.733052i	$0.261905\pi$
$488$		0			0
$489$	0.521689	−	0.606214i	0.521689	−	0.606214i
$490$		0			0
$491$	−0.0705858	+	0.0246991i	−0.0705858	+	0.0246991i	−0.365341	−	0.930874i	$-0.619048\pi$
$491$	−0.0705858	+	0.0246991i	−0.0705858	+	0.0246991i	0.294755	+	0.955573i	$0.404762\pi$
$492$	−0.482320	−	2.54912i	−0.482320	−	2.54912i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.0355312	+	0.315348i	0.0355312	+	0.315348i
$497$		0			0
$498$		0			0
$499$	0.317031	+	0.658322i	0.317031	+	0.658322i	0.997204	−	0.0747301i	$-0.0238095\pi$
$499$	0.317031	+	0.658322i	0.317031	+	0.658322i	−0.680173	+	0.733052i	$0.738095\pi$
$500$		0			0
$501$	−0.658322	+	1.67738i	−0.658322	+	1.67738i
$502$		0			0
$503$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$503$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.966742	−	0.145713i	−0.966742	−	0.145713i
$508$	1.14503	+	0.400664i	1.14503	+	0.400664i
$509$	0.290611	+	0.0663300i	0.290611	+	0.0663300i	0.365341	−	0.930874i	$-0.380952\pi$
$509$	0.290611	+	0.0663300i	0.290611	+	0.0663300i	−0.0747301	+	0.997204i	$0.523810\pi$
$510$		0			0
$511$		0			0
$512$	0.125828	−	1.11675i	0.125828	−	1.11675i
$513$		0			0
$514$	−2.38971	−	1.50156i	−2.38971	−	1.50156i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.425270	−	0.131178i	0.425270	−	0.131178i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.806531	−	1.28359i	−0.806531	−	1.28359i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	0.559311	+	1.59842i	0.559311	+	1.59842i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$530$		0			0
$531$	−0.702449	−	1.03030i	−0.702449	−	1.03030i
$532$		0			0
$533$	−0.252926	+	0.158924i	−0.252926	+	0.158924i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	1.88980	+	0.284841i	1.88980	+	0.284841i
$538$	−0.315247	+	1.38119i	−0.315247	+	1.38119i
$539$		0			0
$540$		0			0
$541$	−1.82160	−	0.205245i	−1.82160	−	0.205245i	−0.866025	−	0.500000i	$-0.833333\pi$
$541$	−1.82160	−	0.205245i	−1.82160	−	0.205245i	−0.955573	+	0.294755i	$0.904762\pi$
$542$	0.976262	−	0.222826i	0.976262	−	0.222826i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.914101	+	1.14625i	0.914101	+	1.14625i	0.988831	+	0.149042i	$0.0476190\pi$
$547$	0.914101	+	1.14625i	0.914101	+	1.14625i	−0.0747301	+	0.997204i	$0.523810\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	0.0840096	+	0.444001i	0.0840096	+	0.444001i
$553$		0			0
$554$	−2.48931	+	0.280478i	−2.48931	+	0.280478i
$555$		0			0
$556$	−0.634544	+	1.31764i	−0.634544	+	1.31764i
$557$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$557$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$558$	0.749848	+	0.231297i	0.749848	+	0.231297i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$563$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$564$	−1.03746	−	0.0388191i	−1.03746	−	0.0388191i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	0.359992	−	0.359992i	0.359992	−	0.359992i
$569$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$569$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$570$		0			0
$571$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$571$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.433884	−	0.900969i	0.433884	−	0.900969i
$576$	−1.28244	−	0.740414i	−1.28244	−	0.740414i
$577$	−1.75711	+	0.197979i	−1.75711	+	0.197979i	−0.930874	−	0.365341i	$-0.880952\pi$
$577$	−1.75711	+	0.197979i	−1.75711	+	0.197979i	−0.826239	+	0.563320i	$0.809524\pi$
$578$	−1.43087	+	0.500684i	−1.43087	+	0.500684i
$579$	1.58114	−	0.299168i	1.58114	−	0.299168i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.334608	+	0.419586i	0.334608	+	0.419586i
$585$		0			0
$586$		0			0
$587$	0.460898	+	0.367554i	0.460898	+	0.367554i	0.826239	−	0.563320i	$-0.190476\pi$
$587$	0.460898	+	0.367554i	0.460898	+	0.367554i	−0.365341	+	0.930874i	$0.619048\pi$
$588$	1.20835	+	0.474244i	1.20835	+	0.474244i
$589$		0			0
$590$		0			0
$591$	−1.17809	−	1.26968i	−1.17809	−	1.26968i
$592$		0			0
$593$	0.433884	−	1.90097i	0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$593$	0.433884	−	1.90097i	0.433884	−	1.90097i	0.433884	−	0.900969i	$-0.357143\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.191845	−	0.120544i	0.191845	−	0.120544i
$599$	−0.0739590	+	0.656405i	−0.0739590	+	0.656405i	0.900969	+	0.433884i	$0.142857\pi$
$599$	−0.0739590	+	0.656405i	−0.0739590	+	0.656405i	−0.974928	+	0.222521i	$0.928571\pi$
$600$	−0.180703	−	0.414176i	−0.180703	−	0.414176i
$601$	−1.63575	−	1.02781i	−1.63575	−	1.02781i	−0.955573	−	0.294755i	$-0.904762\pi$
$601$	−1.63575	−	1.02781i	−1.63575	−	1.02781i	−0.680173	−	0.733052i	$-0.738095\pi$
$602$		0			0
$603$		0			0
$604$	−1.16953	−	0.563218i	−1.16953	−	0.563218i
$605$		0			0
$606$	−0.888045	−	2.87897i	−0.888045	−	2.87897i
$607$	−0.559311	−	1.59842i	−0.559311	−	1.59842i	−0.781831	−	0.623490i	$-0.785714\pi$
$607$	−0.559311	−	1.59842i	−0.559311	−	1.59842i	0.222521	−	0.974928i	$-0.428571\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0394802	+	0.112828i	0.0394802	+	0.112828i
$612$		0			0
$613$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$613$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$614$	0.305846	+	0.147288i	0.305846	+	0.147288i
$615$		0			0
$616$		0			0
$617$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$617$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$618$		0			0
$619$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$619$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$620$		0			0
$621$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$622$	0.549531	+	0.125427i	0.549531	+	0.125427i
$623$		0			0
$624$	−0.0136565	+	0.0906048i	−0.0136565	+	0.0906048i
$625$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$631$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$632$		0			0
$633$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$634$	−1.78427	−	2.23740i	−1.78427	−	2.23740i
$635$		0			0
$636$		0			0
$637$		−	0.149460i		−	0.149460i
$638$		0			0
$639$	0.411608	+	1.04876i	0.411608	+	1.04876i
$640$		0			0
$641$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$641$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$642$		0			0
$643$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$643$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.0663300	−	0.290611i	−0.0663300	−	0.290611i	0.930874	−	0.365341i	$-0.119048\pi$
$647$	−0.0663300	−	0.290611i	−0.0663300	−	0.290611i	−0.997204	+	0.0747301i	$0.976190\pi$
$648$	−0.363581	+	0.268335i	−0.363581	+	0.268335i
$649$		0			0
$650$	−0.160211	+	0.160211i	−0.160211	+	0.160211i
$651$		0			0
$652$	−0.342892	+	0.979928i	−0.342892	+	0.979928i
$653$	0.638050	−	1.82344i	0.638050	−	1.82344i	0.0747301	−	0.997204i	$-0.476190\pi$
$653$	0.638050	−	1.82344i	0.638050	−	1.82344i	0.563320	−	0.826239i	$-0.309524\pi$
$654$		0			0
$655$		0			0
$656$	−0.651880	−	1.03746i	−0.651880	−	1.03746i
$657$	−1.14717	+	0.307384i	−1.14717	+	0.307384i
$658$		0			0
$659$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$659$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$660$		0			0
$661$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$661$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$662$	−1.16304	+	2.41508i	−1.16304	+	2.41508i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$668$		−	2.33907i		−	2.33907i
$669$	−0.222521	−	0.385418i	−0.222521	−	0.385418i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.255779	−	0.531130i	−0.255779	−	0.531130i	0.733052	−	0.680173i	$-0.238095\pi$
$673$	−0.255779	−	0.531130i	−0.255779	−	0.531130i	−0.988831	+	0.149042i	$0.952381\pi$
$674$		0			0
$675$	1.00000			1.00000
$676$	1.23727	−	0.282399i	1.23727	−	0.282399i
$677$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$677$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.81507	+	0.414278i	1.81507	+	0.414278i	0.988831	−	0.149042i	$-0.0476190\pi$
$683$	1.81507	+	0.414278i	1.81507	+	0.414278i	0.826239	+	0.563320i	$0.190476\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.781831	−	0.376510i	−0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$691$	−0.781831	−	0.376510i	−0.781831	−	0.376510i	−0.781831	+	0.623490i	$0.785714\pi$
$692$	−0.451666	+	0.360191i	−0.451666	+	0.360191i
$693$		0			0
$694$	0.976262	+	2.79000i	0.976262	+	2.79000i
$695$		0			0
$696$	0.363581	+	0.268335i	0.363581	+	0.268335i
$697$		0			0
$698$	0.365841	+	1.04551i	0.365841	+	1.04551i
$699$	−0.432142	−	1.40097i	−0.432142	−	1.40097i
$700$		0			0
$701$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$701$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$702$	0.191845	+	0.120544i	0.191845	+	0.120544i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.100059	+	0.888045i	−0.100059	+	0.888045i
$707$		0			0
$708$	1.33742	+	0.911838i	1.33742	+	0.911838i
$709$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$709$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$714$		0			0
$715$		0			0
$716$	−2.41863	+	0.552036i	−2.41863	+	0.552036i
$717$	−1.26631	−	0.496990i	−1.26631	−	0.496990i
$718$		0			0
$719$	0.376510	+	0.781831i	0.376510	+	0.781831i	1.00000			$0$
$719$	0.376510	+	0.781831i	0.376510	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$720$		0			0
$721$		0			0
$722$	0.169732	+	1.50641i	0.169732	+	1.50641i
$723$		0			0
$724$		0			0
$725$	−0.294755	−	0.955573i	−0.294755	−	0.955573i
$726$	1.48952	−	0.281831i	1.48952	−	0.281831i
$727$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$727$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$728$		0			0
$729$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$733$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$734$		0			0
$735$		0			0
$736$	0.734867	+	1.16953i	0.734867	+	1.16953i
$737$		0			0
$738$	−2.99593	+	0.451563i	−2.99593	+	0.451563i
$739$	−0.660096	+	1.88645i	−0.660096	+	1.88645i	−0.294755	+	0.955573i	$0.595238\pi$
$739$	−0.660096	+	1.88645i	−0.660096	+	1.88645i	−0.365341	+	0.930874i	$0.619048\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$743$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$744$	−0.233256	+	0.0174801i	−0.233256	+	0.0174801i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$751$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$752$	−0.462802	+	0.161941i	−0.462802	+	0.161941i
$753$		0			0
$754$	0.0586415	−	0.218853i	0.0586415	−	0.218853i
$755$		0			0
$756$		0			0
$757$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$757$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.29196	+	1.03030i	1.29196	+	1.03030i	0.997204	+	0.0747301i	$0.0238095\pi$
$761$	1.29196	+	1.03030i	1.29196	+	1.03030i	0.294755	+	0.955573i	$0.404762\pi$
$762$	0.517581	−	1.31877i	0.517581	−	1.31877i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.0414721	−	0.181701i	0.0414721	−	0.181701i
$768$	−0.169732	−	0.0255830i	−0.169732	−	0.0255830i
$769$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$769$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$770$		0			0
$771$	−1.04876	+	1.53825i	−1.04876	+	1.53825i
$772$	−1.76870	+	1.11135i	−1.76870	+	1.11135i
$773$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$773$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$774$		0			0
$775$	0.438297	+	0.275400i	0.438297	+	0.275400i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$784$	0.613061			0.613061
$785$		0			0
$786$	1.88980	−	0.582926i	1.88980	−	0.582926i
$787$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$787$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$788$	2.02569	+	0.975522i	2.02569	+	0.975522i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	1.74612	−	1.09716i	1.74612	−	1.09716i
$795$		0			0
$796$		0			0
$797$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$797$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$798$		0			0
$799$		0			0
$800$	−0.976688	−	0.976688i	−0.976688	−	0.976688i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	0.0508871	+	0.105668i	0.0508871	+	0.105668i
$807$	0.902694	+	0.241876i	0.902694	+	0.241876i
$808$	0.559941	+	0.702144i	0.559941	+	0.702144i
$809$	0.189606	+	1.68280i	0.189606	+	1.68280i	0.623490	+	0.781831i	$0.285714\pi$
$809$	0.189606	+	1.68280i	0.189606	+	1.68280i	−0.433884	+	0.900969i	$0.642857\pi$
$810$		0			0
$811$		−	1.73205i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$811$		−	1.73205i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$812$		0			0
$813$	−0.122805	−	0.649042i	−0.122805	−	0.649042i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−2.72973	+	1.31457i	−2.72973	+	1.31457i
$819$		0			0
$820$		0			0
$821$	0.347948	+	1.52446i	0.347948	+	1.52446i	0.781831	+	0.623490i	$0.214286\pi$
$821$	0.347948	+	1.52446i	0.347948	+	1.52446i	−0.433884	+	0.900969i	$0.642857\pi$
$822$		0			0
$823$	−0.0397866	−	0.0633201i	−0.0397866	−	0.0633201i	0.826239	−	0.563320i	$-0.190476\pi$
$823$	−0.0397866	−	0.0633201i	−0.0397866	−	0.0633201i	−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$827$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$828$	1.28359	−	0.193469i	1.28359	−	0.193469i
$829$	−1.33485	+	1.33485i	−1.33485	+	1.33485i	−0.433884	+	0.900969i	$0.642857\pi$
$829$	−1.33485	+	1.33485i	−1.33485	+	1.33485i	−0.900969	+	0.433884i	$0.857143\pi$
$830$		0			0
$831$	0.123490	+	1.64786i	0.123490	+	1.64786i
$832$	−0.0492494	−	0.215776i	−0.0492494	−	0.215776i
$833$		0			0
$834$	1.51000	+	0.798059i	1.51000	+	0.798059i
$835$		0			0
$836$		0			0
$837$	0.170965	−	0.488590i	0.170965	−	0.488590i
$838$		0			0
$839$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$839$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$840$		0			0
$841$	0.733052	+	0.680173i	0.733052	+	0.680173i
$842$		0			0
$843$		0			0
$844$	−0.205541	−	1.82423i	−0.205541	−	1.82423i
$845$		0			0
$846$	−0.0906048	+	1.20904i	−0.0906048	+	1.20904i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−0.994735	−	1.07207i	−0.994735	−	1.07207i
$853$	−1.40532	−	1.40532i	−1.40532	−	1.40532i	−0.781831	−	0.623490i	$-0.785714\pi$
$853$	−1.40532	−	1.40532i	−1.40532	−	1.40532i	−0.623490	−	0.781831i	$-0.714286\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.294755	−	0.955573i	$-0.595238\pi$
$857$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.680173	+	0.733052i	$0.738095\pi$
$858$		0			0
$859$	0.0633201	−	0.0397866i	0.0633201	−	0.0397866i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.0633201	−	0.0397866i	0.0633201	−	0.0397866i	0.563320	+	0.826239i	$0.309524\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	−0.988831	−	0.149042i	$-0.952381\pi$
$863$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$864$	−0.734867	+	1.16953i	−0.734867	+	1.16953i
$865$		0			0
$866$		0			0
$867$	0.294755	+	0.955573i	0.294755	+	0.955573i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	1.24041	−	0.915467i	1.24041	−	0.915467i
$877$	0.974928	−	1.22252i	0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$877$	0.974928	−	1.22252i	0.974928	−	1.22252i	0.974928	−	0.222521i	$-0.0714286\pi$
$878$	−1.74612	−	1.09716i	−1.74612	−	1.09716i
$879$		0			0
$880$		0			0
$881$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$881$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$882$	0.606214	−	1.38946i	0.606214	−	1.38946i
$883$	−1.21572	−	0.277479i	−1.21572	−	0.277479i	−0.433884	−	0.900969i	$-0.642857\pi$
$883$	−1.21572	−	0.277479i	−1.21572	−	0.277479i	−0.781831	+	0.623490i	$0.785714\pi$
$884$		0			0
$885$		0			0
$886$	−0.542829	+	2.37829i	−0.542829	+	2.37829i
$887$	−0.660818	−	0.660818i	−0.660818	−	0.660818i	0.294755	−	0.955573i	$-0.404762\pi$
$887$	−0.660818	−	0.660818i	−0.660818	−	0.660818i	−0.955573	+	0.294755i	$0.904762\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	0.451666	+	0.360191i	0.451666	+	0.360191i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i
$898$			1.00137i			1.00137i
$899$	−0.517276	−	0.0193551i	−0.517276	−	0.0193551i
$900$	−1.20835	+	0.474244i	−1.20835	+	0.474244i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.708353	+	1.34027i	−0.708353	+	1.34027i
$907$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$907$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$908$		0			0
$909$	−1.91970	+	0.514383i	−1.91970	+	0.514383i
$910$		0			0
$911$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$911$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$919$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$920$		0			0
$921$	0.104635	−	0.197979i	0.104635	−	0.197979i
$922$	−2.41508	+	1.16304i	−2.41508	+	1.16304i
$923$	−0.0730607	+	0.151712i	−0.0730607	+	0.151712i
$924$		0			0
$925$		0			0
$926$	−2.57835	+	0.902202i	−2.57835	+	0.902202i
$927$		0			0
$928$	1.33418	+	0.357493i	1.33418	+	0.357493i
$929$		−	0.149460i		−	0.149460i	−0.997204	−	0.0747301i	$-0.976190\pi$
$929$		−	0.149460i		−	0.149460i	0.997204	−	0.0747301i	$-0.0238095\pi$
$930$		0			0
$931$		0			0
$932$	1.18658	+	1.48792i	1.18658	+	1.48792i
$933$	0.0962349	−	0.359154i	0.0962349	−	0.359154i
$934$		0			0
$935$		0			0
$936$	−0.0663605	−	0.0125561i	−0.0663605	−	0.0125561i
$937$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$937$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$941$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$942$		0			0
$943$	1.88645	+	0.660096i	1.88645	+	0.660096i
$944$	0.745308	+	0.170112i	0.745308	+	0.170112i
$945$		0			0
$946$		0			0
$947$	−0.104635	+	0.928661i	−0.104635	+	0.928661i	0.826239	+	0.563320i	$0.190476\pi$
$947$	−0.104635	+	0.928661i	−0.104635	+	0.928661i	−0.930874	+	0.365341i	$0.880952\pi$
$948$		0			0
$949$	−0.150298	−	0.0944383i	−0.150298	−	0.0944383i
$950$		0			0
$951$	−1.51889	+	1.12099i	−1.51889	+	1.12099i
$952$		0			0
$953$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$953$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$954$		0			0
$955$		0			0
$956$	1.76584			1.76584
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.572340	+	0.456426i	−0.572340	+	0.456426i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.180173	+	1.59908i	−0.180173	+	1.59908i	0.500000	+	0.866025i	$0.333333\pi$
$967$	−0.180173	+	1.59908i	−0.180173	+	1.59908i	−0.680173	+	0.733052i	$0.738095\pi$
$968$	−0.382617	+	0.240414i	−0.382617	+	0.240414i
$969$		0			0
$970$		0			0
$971$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$971$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$972$	0.731237	+	1.07253i	0.731237	+	1.07253i
$973$		0			0
$974$	0.631916	+	0.631916i	0.631916	+	0.631916i
$975$	0.101659	+	0.109562i	0.101659	+	0.109562i
$976$		0			0
$977$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$977$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$978$	1.12862	+	0.442949i	1.12862	+	0.442949i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.0706825	−	0.0886330i	−0.0706825	−	0.0886330i
$983$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$983$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$984$	0.782131	−	0.451563i	0.782131	−	0.451563i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.846011	−	1.75676i	0.846011	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$991$	0.846011	−	1.75676i	0.846011	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$992$	−0.644179	+	0.310220i	−0.644179	+	0.310220i
$993$	1.56332	+	0.826239i	1.56332	+	0.826239i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.351438	−	0.559311i	−0.351438	−	0.559311i	0.623490	−	0.781831i	$-0.285714\pi$
$997$	−0.351438	−	0.559311i	−0.351438	−	0.559311i	−0.974928	+	0.222521i	$0.928571\pi$
$998$	−0.783243	+	0.783243i	−0.783243	+	0.783243i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.c.620.2	✓	24
3.2	odd	2		2001.1.bf.d.620.1	yes	24
23.22	odd	2	CM	2001.1.bf.c.620.2	✓	24
29.8	odd	28		2001.1.bf.d.965.1	yes	24
69.68	even	2		2001.1.bf.d.620.1	yes	24
87.8	even	28	inner	2001.1.bf.c.965.2	yes	24
667.298	even	28		2001.1.bf.d.965.1	yes	24
2001.965	odd	28	inner	2001.1.bf.c.965.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.620.2	✓	24	1.1	even	1	trivial
2001.1.bf.c.620.2	✓	24	23.22	odd	2	CM
2001.1.bf.c.965.2	yes	24	87.8	even	28	inner
2001.1.bf.c.965.2	yes	24	2001.965	odd	28	inner
2001.1.bf.d.620.1	yes	24	3.2	odd	2
2001.1.bf.d.620.1	yes	24	69.68	even	2
2001.1.bf.d.965.1	yes	24	29.8	odd	28
2001.1.bf.d.965.1	yes	24	667.298	even	28

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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2001.bf (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500684 + 1.43087i) q^{2} +(0.955573 - 0.294755i) q^{3} +(-1.01488 + 0.809342i) q^{4} +(0.900198 + 1.21972i) q^{6} +(-0.382617 - 0.240414i) q^{8} +(0.826239 - 0.563320i) q^{9} +O(q^{10})\)	\(q+(0.500684 + 1.43087i) q^{2} +(0.955573 - 0.294755i) q^{3} +(-1.01488 + 0.809342i) q^{4} +(0.900198 + 1.21972i) q^{6} +(-0.382617 - 0.240414i) q^{8} +(0.826239 - 0.563320i) q^{9} +(-0.731237 + 1.07253i) q^{12} +(0.145713 + 0.0332580i) q^{13} +(-0.136419 + 0.597690i) q^{16} +(1.21972 + 0.900198i) q^{18} +(-0.433884 - 0.900969i) q^{23} +(-0.436482 - 0.116955i) q^{24} +(0.623490 + 0.781831i) q^{25} +(0.0253681 + 0.225149i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.930874 - 0.365341i) q^{29} +(0.488590 - 0.170965i) q^{31} +(-1.37256 + 0.154650i) q^{32} +(-0.382617 + 1.24041i) q^{36} +(0.149042 - 0.0111692i) q^{39} +(-1.41322 + 1.41322i) q^{41} +(1.07193 - 1.07193i) q^{46} +(0.425511 + 0.677197i) q^{47} +(0.0458141 + 0.611347i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(-0.806531 + 1.28359i) q^{50} +(-0.174799 + 0.0841786i) q^{52} +(1.43087 + 0.500684i) q^{54} +(0.0566829 - 1.51488i) q^{58} -1.24698i q^{59} +(0.489259 + 0.613511i) q^{62} +(-0.642507 - 1.33418i) q^{64} +(-0.680173 - 0.733052i) q^{69} +(-0.250701 + 1.09839i) q^{71} +(-0.451563 + 0.0168963i) q^{72} +(-1.12099 - 0.392253i) q^{73} +(0.826239 + 0.563320i) q^{75} +(0.0906048 + 0.207668i) q^{78} +(0.365341 - 0.930874i) q^{81} +(-2.72973 - 1.31457i) q^{82} +(-0.997204 - 0.0747301i) q^{87} +(1.16953 + 0.563218i) q^{92} +(0.416490 - 0.307384i) q^{93} +(-0.755936 + 0.947914i) q^{94} +(-1.26600 + 0.552349i) q^{96} +(1.28359 - 0.806531i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 2 * q^3 + 14 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9	\( 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 6 q^{12} - 6 q^{16} + 4 q^{18} - 6 q^{24} - 4 q^{25} + 2 q^{26} - 4 q^{27} - 2 q^{31} + 4 q^{32} + 6 q^{36} + 2 q^{41} + 2 q^{46} - 2 q^{47} - 4 q^{48} - 4 q^{49} - 2 q^{50} - 10 q^{52} + 12 q^{54} + 4 q^{58} + 4 q^{62} - 28 q^{64} + 14 q^{72} - 2 q^{73} + 2 q^{75} + 10 q^{78} + 2 q^{81} - 4 q^{82} + 4 q^{92} - 2 q^{93} - 8 q^{94} - 24 q^{96} - 2 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 + 2 * q^3 + 14 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 6 * q^12 - 6 * q^16 + 4 * q^18 - 6 * q^24 - 4 * q^25 + 2 * q^26 - 4 * q^27 - 2 * q^31 + 4 * q^32 + 6 * q^36 + 2 * q^41 + 2 * q^46 - 2 * q^47 - 4 * q^48 - 4 * q^49 - 2 * q^50 - 10 * q^52 + 12 * q^54 + 4 * q^58 + 4 * q^62 - 28 * q^64 + 14 * q^72 - 2 * q^73 + 2 * q^75 + 10 * q^78 + 2 * q^81 - 4 * q^82 + 4 * q^92 - 2 * q^93 - 8 * q^94 - 24 * q^96 - 2 * q^98

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