LMFDB - Embedded newform 2303.1.q.b.2020.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,1,Mod(46,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([22, 21]))

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

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

chi := DirichletCharacter("2303.46");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2303.q (of order $42$, 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:	$1.14934672409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{42})$
Coefficient field:	$\Q(\zeta_{210})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{48} - x^{47} + x^{46} + x^{43} - x^{42} + 2 x^{41} - x^{40} + x^{39} + x^{36} - x^{35} + x^{34} + \cdots + 1 $ x^48 - x^47 + x^46 + x^43 - x^42 + 2x^41 - x^40 + x^39 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 - x^28 - x^26 - x^24 - x^22 - x^20 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 + x^9 - x^8 + 2x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{105}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{105} - \cdots)$

Embedding invariants

Embedding label			2020.3
Root			$-0.251587 + 0.967835i$ of defining polynomial
Character	$\chi$	$=$	2303.2020
Dual form			2303.1.q.b.2067.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.153250 - 0.142195i) q^{2} +(1.36669 - 0.205995i) q^{3} +(-0.0714640 + 0.953621i) q^{4} +(0.180153 - 0.225905i) q^{6} +(0.992847 + 0.119394i) q^{7} +(0.254993 + 0.319751i) q^{8} +(0.869830 - 0.268307i) q^{9} +O(q^{10})$	\(q+(0.153250 - 0.142195i) q^{2} +(1.36669 - 0.205995i) q^{3} +(-0.0714640 + 0.953621i) q^{4} +(0.180153 - 0.225905i) q^{6} +(0.992847 + 0.119394i) q^{7} +(0.254993 + 0.319751i) q^{8} +(0.869830 - 0.268307i) q^{9} +(0.0987722 + 1.31802i) q^{12} +(0.169131 - 0.122881i) q^{14} +(-0.861070 - 0.129785i) q^{16} +(-0.270705 + 0.184564i) q^{17} +(0.0951492 - 0.164803i) q^{18} +(1.38151 - 0.0413469i) q^{21} +(0.414363 + 0.384473i) q^{24} +(-0.733052 - 0.680173i) q^{25} +(-0.111736 + 0.0538092i) q^{27} +(-0.184810 + 0.938267i) q^{28} +(-0.488326 + 0.332935i) q^{32} +(-0.0152415 + 0.0667772i) q^{34} +(0.193702 + 0.848662i) q^{36} +(-0.130540 - 1.74193i) q^{37} +(0.205836 - 0.202779i) q^{42} +(-0.733052 + 0.680173i) q^{47} -1.20355 q^{48} +(0.971490 + 0.237080i) q^{49} -0.209057 q^{50} +(-0.331951 + 0.308005i) q^{51} +(-0.149393 + 1.99351i) q^{53} +(-0.00947210 + 0.0241345i) q^{54} +(0.214993 + 0.347909i) q^{56} +(-0.615761 - 1.56893i) q^{59} +(-0.141438 - 1.88736i) q^{61} +(0.895642 - 0.162535i) q^{63} +(0.166276 - 0.728503i) q^{64} +(-0.156658 - 0.271340i) q^{68} +(0.505313 - 0.243346i) q^{71} +(0.307592 + 0.209713i) q^{72} +(-0.267699 - 0.248388i) q^{74} +(-1.14197 - 0.778579i) q^{75} +(0.550897 + 0.954182i) q^{79} +(-0.893725 + 0.609331i) q^{81} +(-0.0332580 + 0.145713i) q^{83} +(-0.0592987 + 1.32039i) q^{84} +(-1.54615 + 0.476924i) q^{89} +(-0.0156228 + 0.208472i) q^{94} +(-0.598806 + 0.555611i) q^{96} +1.82709 q^{97} +(0.182592 - 0.101808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9	$ 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 40 q^{12} - 18 q^{14} + 6 q^{16} + q^{17} - 9 q^{18} + 5 q^{21} + 8 q^{24} + 4 q^{25} - 6 q^{27} - 5 q^{32} + 2 q^{34} - 10 q^{36} + q^{37} + 7 q^{42} + 4 q^{47} + 6 q^{48} - q^{49} + 12 q^{50} + 4 q^{51} + 8 q^{53} - q^{54} - 11 q^{56} - 13 q^{59} + q^{61} - 4 q^{63} - 8 q^{64} - 5 q^{68} + 5 q^{71} - 8 q^{72} + 13 q^{74} + 5 q^{75} - 2 q^{79} + 8 q^{83} + 5 q^{84} - 2 q^{89} + q^{94} + 10 q^{96} + 12 q^{97} + q^{98}+O(q^{100}) $ 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - 40 * q^12 - 18 * q^14 + 6 * q^16 + q^17 - 9 * q^18 + 5 * q^21 + 8 * q^24 + 4 * q^25 - 6 * q^27 - 5 * q^32 + 2 * q^34 - 10 * q^36 + q^37 + 7 * q^42 + 4 * q^47 + 6 * q^48 - q^49 + 12 * q^50 + 4 * q^51 + 8 * q^53 - q^54 - 11 * q^56 - 13 * q^59 + q^61 - 4 * q^63 - 8 * q^64 - 5 * q^68 + 5 * q^71 - 8 * q^72 + 13 * q^74 + 5 * q^75 - 2 * q^79 + 8 * q^83 + 5 * q^84 - 2 * q^89 + q^94 + 10 * q^96 + 12 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2303\mathbb{Z}\right)^\times$.

$n$	$99$	$2257$
$\chi(n)$	$-1$	$e\left(\frac{20}{21}\right)$

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 $

$2$	0.153250	−	0.142195i	0.153250	−	0.142195i	−0.599822	−	0.800134i	$-0.704762\pi$
$2$	0.153250	−	0.142195i	0.153250	−	0.142195i	0.753071	+	0.657939i	$0.228571\pi$
$3$	1.36669	−	0.205995i	1.36669	−	0.205995i	0.575617	−	0.817719i	$-0.304762\pi$
$3$	1.36669	−	0.205995i	1.36669	−	0.205995i	0.791071	+	0.611724i	$0.209524\pi$
$4$	−0.0714640	+	0.953621i	−0.0714640	+	0.953621i
$5$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$5$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$6$	0.180153	−	0.225905i	0.180153	−	0.225905i
$7$	0.992847	+	0.119394i	0.992847	+	0.119394i
$7$	0.992847	+	0.119394i	0.992847	+	0.119394i
$8$	0.254993	+	0.319751i	0.254993	+	0.319751i
$9$	0.869830	−	0.268307i	0.869830	−	0.268307i
$10$		0			0
$11$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$11$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$12$	0.0987722	+	1.31802i	0.0987722	+	1.31802i
$13$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$13$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$14$	0.169131	−	0.122881i	0.169131	−	0.122881i
$15$		0			0
$16$	−0.861070	−	0.129785i	−0.861070	−	0.129785i
$17$	−0.270705	+	0.184564i	−0.270705	+	0.184564i	−0.691063	−	0.722795i	$-0.742857\pi$
$17$	−0.270705	+	0.184564i	−0.270705	+	0.184564i	0.420357	+	0.907359i	$0.361905\pi$
$18$	0.0951492	−	0.164803i	0.0951492	−	0.164803i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$	1.38151	−	0.0413469i	1.38151	−	0.0413469i
$22$		0			0
$23$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$23$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$24$	0.414363	+	0.384473i	0.414363	+	0.384473i
$25$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$26$		0			0
$27$	−0.111736	+	0.0538092i	−0.111736	+	0.0538092i
$28$	−0.184810	+	0.938267i	−0.184810	+	0.938267i
$29$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$29$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	−0.488326	+	0.332935i	−0.488326	+	0.332935i
$33$		0			0
$34$	−0.0152415	+	0.0667772i	−0.0152415	+	0.0667772i
$35$		0			0
$36$	0.193702	+	0.848662i	0.193702	+	0.848662i
$37$	−0.130540	−	1.74193i	−0.130540	−	1.74193i	−0.550897	−	0.834573i	$-0.685714\pi$
$37$	−0.130540	−	1.74193i	−0.130540	−	1.74193i	0.420357	−	0.907359i	$-0.361905\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$41$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$42$	0.205836	−	0.202779i	0.205836	−	0.202779i
$43$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$43$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$47$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$48$	−1.20355			−1.20355
$49$	0.971490	+	0.237080i	0.971490	+	0.237080i
$50$	−0.209057			−0.209057
$51$	−0.331951	+	0.308005i	−0.331951	+	0.308005i
$52$		0			0
$53$	−0.149393	+	1.99351i	−0.149393	+	1.99351i	−0.0448648	+	0.998993i	$0.514286\pi$
$53$	−0.149393	+	1.99351i	−0.149393	+	1.99351i	−0.104528	+	0.994522i	$0.533333\pi$
$54$	−0.00947210	+	0.0241345i	−0.00947210	+	0.0241345i
$55$		0			0
$56$	0.214993	+	0.347909i	0.214993	+	0.347909i
$57$		0			0
$58$		0			0
$59$	−0.615761	−	1.56893i	−0.615761	−	1.56893i	−0.809017	−	0.587785i	$-0.800000\pi$
$59$	−0.615761	−	1.56893i	−0.615761	−	1.56893i	0.193256	−	0.981148i	$-0.438095\pi$
$60$		0			0
$61$	−0.141438	−	1.88736i	−0.141438	−	1.88736i	−0.393025	−	0.919528i	$-0.628571\pi$
$61$	−0.141438	−	1.88736i	−0.141438	−	1.88736i	0.251587	−	0.967835i	$-0.419048\pi$
$62$		0			0
$63$	0.895642	−	0.162535i	0.895642	−	0.162535i
$64$	0.166276	−	0.728503i	0.166276	−	0.728503i
$65$		0			0
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−0.156658	−	0.271340i	−0.156658	−	0.271340i
$69$		0			0
$70$		0			0
$71$	0.505313	−	0.243346i	0.505313	−	0.243346i	−0.163818	−	0.986491i	$-0.552381\pi$
$71$	0.505313	−	0.243346i	0.505313	−	0.243346i	0.669131	+	0.743145i	$0.266667\pi$
$72$	0.307592	+	0.209713i	0.307592	+	0.209713i
$73$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$73$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$74$	−0.267699	−	0.248388i	−0.267699	−	0.248388i
$75$	−1.14197	−	0.778579i	−1.14197	−	0.778579i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.550897	+	0.954182i	0.550897	+	0.954182i	0.998210	+	0.0598042i	$0.0190476\pi$
$79$	0.550897	+	0.954182i	0.550897	+	0.954182i	−0.447313	+	0.894377i	$0.647619\pi$
$80$		0			0
$81$	−0.893725	+	0.609331i	−0.893725	+	0.609331i
$82$		0			0
$83$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	−0.988831	−	0.149042i	$-0.952381\pi$
$83$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	0.955573	+	0.294755i	$0.0952381\pi$
$84$	−0.0592987	+	1.32039i	−0.0592987	+	1.32039i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.54615	+	0.476924i	−1.54615	+	0.476924i	−0.946327	−	0.323210i	$-0.895238\pi$
$89$	−1.54615	+	0.476924i	−1.54615	+	0.476924i	−0.599822	+	0.800134i	$0.704762\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−0.0156228	+	0.208472i	−0.0156228	+	0.208472i
$95$		0			0
$96$	−0.598806	+	0.555611i	−0.598806	+	0.555611i
$97$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$97$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$98$	0.182592	−	0.101808i	0.182592	−	0.101808i
$99$		0			0
$100$	0.701014	−	0.650446i	0.701014	−	0.650446i
$101$	1.52758	−	0.230246i	1.52758	−	0.230246i	0.669131	−	0.743145i	$-0.266667\pi$
$101$	1.52758	−	0.230246i	1.52758	−	0.230246i	0.858449	+	0.512899i	$0.171429\pi$
$102$	−0.00707455	+	0.0944033i	−0.00707455	+	0.0944033i
$103$	0.0109306	−	0.0278506i	0.0109306	−	0.0278506i	−0.925304	−	0.379225i	$-0.876190\pi$
$103$	0.0109306	−	0.0278506i	0.0109306	−	0.0278506i	0.936235	+	0.351375i	$0.114286\pi$
$104$		0			0
$105$		0			0
$106$	0.260573	+	0.326748i	0.260573	+	0.326748i
$107$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$107$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$108$	−0.0433285	−	0.110399i	−0.0433285	−	0.110399i
$109$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$109$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$110$		0			0
$111$	−0.537237	−	2.35379i	−0.537237	−	2.35379i
$112$	−0.839415	−	0.231664i	−0.839415	−	0.231664i
$113$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$113$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.317459	−	0.152880i	−0.317459	−	0.152880i
$119$	−0.290805	+	0.150923i	−0.290805	+	0.150923i
$120$		0			0
$121$	0.826239	+	0.563320i	0.826239	+	0.563320i
$122$	−0.290049	−	0.269126i	−0.290049	−	0.269126i
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.114145	−	0.152264i	0.114145	−	0.152264i
$127$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$127$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$128$	−0.373619	−	0.647127i	−0.373619	−	0.647127i
$129$		0			0
$130$		0			0
$131$	−0.382195	−	0.0576066i	−0.382195	−	0.0576066i	−0.0448648	−	0.998993i	$-0.514286\pi$
$131$	−0.382195	−	0.0576066i	−0.382195	−	0.0576066i	−0.337330	+	0.941386i	$0.609524\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.128042	−	0.0394959i	−0.128042	−	0.0394959i
$137$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$137$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$138$		0			0
$139$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$139$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$140$		0			0
$141$	−0.861741	+	1.08059i	−0.861741	+	1.08059i
$142$	0.0428364	−	0.109145i	0.0428364	−	0.109145i
$143$		0			0
$144$	−0.783806	+	0.118140i	−0.783806	+	0.118140i
$145$		0			0
$146$		0			0
$147$	1.37656	+	0.123893i	1.37656	+	0.123893i
$148$	1.67047			1.67047
$149$	−1.15979	+	1.07613i	−1.15979	+	1.07613i	−0.163818	+	0.986491i	$0.552381\pi$
$149$	−1.15979	+	1.07613i	−1.15979	+	1.07613i	−0.995974	+	0.0896393i	$0.971429\pi$
$150$	−0.285716	+	0.0430647i	−0.285716	+	0.0430647i
$151$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$151$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$152$		0			0
$153$	−0.185948	+	0.233171i	−0.185948	+	0.233171i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.287176	−	0.731713i	−0.287176	−	0.731713i	−0.999552	−	0.0299155i	$-0.990476\pi$
$157$	−0.287176	−	0.731713i	−0.287176	−	0.731713i	0.712376	−	0.701798i	$-0.247619\pi$
$158$	0.220104	+	0.0678932i	0.220104	+	0.0678932i
$159$	0.206480	+	2.75529i	0.206480	+	2.75529i
$160$		0			0
$161$		0			0
$162$	−0.0503192	+	0.220463i	−0.0503192	+	0.220463i
$163$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$163$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$164$		0			0
$165$		0			0
$166$	0.0156228	+	0.0270596i	0.0156228	+	0.0270596i
$167$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$167$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$168$	0.365495	+	0.431195i	0.365495	+	0.431195i
$169$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.65174	−	1.12614i	−1.65174	−	1.12614i	−0.842721	−	0.538351i	$-0.819048\pi$
$173$	−1.65174	−	1.12614i	−1.65174	−	1.12614i	−0.809017	−	0.587785i	$-0.800000\pi$
$174$		0			0
$175$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$176$		0			0
$177$	−1.16475	−	2.01740i	−1.16475	−	2.01740i
$178$	−0.169131	+	0.292943i	−0.169131	+	0.292943i
$179$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$179$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$180$		0			0
$181$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$181$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$182$		0			0
$183$	−0.582089	−	2.55030i	−0.582089	−	2.55030i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.596240	−	0.747662i	−0.596240	−	0.747662i
$189$	−0.117361	+	0.0400837i	−0.117361	+	0.0400837i
$190$		0			0
$191$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.0747301	−	0.997204i	$-0.476190\pi$
$191$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.623490	−	0.781831i	$-0.285714\pi$
$192$	0.0771795	−	1.02989i	0.0771795	−	1.02989i
$193$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$193$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$194$	0.280001	−	0.259803i	0.280001	−	0.259803i
$195$		0			0
$196$	−0.295511	+	0.909491i	−0.295511	+	0.909491i
$197$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$197$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$198$		0			0
$199$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$199$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$200$	0.0305629	−	0.407833i	0.0305629	−	0.407833i
$201$		0			0
$202$	0.201361	−	0.252499i	0.201361	−	0.252499i
$203$		0			0
$204$	−0.269998	−	0.338566i	−0.269998	−	0.338566i
$205$		0			0
$206$	−0.00228511	−	0.00582237i	−0.00228511	−	0.00582237i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$211$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$212$	−1.89038	−	0.284929i	−1.89038	−	0.284929i
$213$	0.640477	−	0.436670i	0.640477	−	0.436670i
$214$		0			0
$215$		0			0
$216$	−0.0456975	−	0.0220067i	−0.0456975	−	0.0220067i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−0.417028	−	0.284325i	−0.417028	−	0.284325i
$223$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$223$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$224$	−0.524584	+	0.272250i	−0.524584	+	0.272250i
$225$	−0.820125	−	0.394951i	−0.820125	−	0.394951i
$226$		0			0
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$		0			0
$229$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$229$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$233$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$234$		0			0
$235$		0			0
$236$	1.54017	−	0.475081i	1.54017	−	0.475081i
$237$	0.949461	+	1.19059i	0.949461	+	1.19059i
$238$	−0.0231053	+	0.0644798i	−0.0231053	+	0.0644798i
$239$	0.0186541	−	0.0233915i	0.0186541	−	0.0233915i	−0.772417	−	0.635116i	$-0.780952\pi$
$239$	0.0186541	−	0.0233915i	0.0186541	−	0.0233915i	0.791071	+	0.611724i	$0.209524\pi$
$240$		0			0
$241$	0.0628267	−	0.838364i	0.0628267	−	0.838364i	−0.873408	−	0.486989i	$-0.838095\pi$
$241$	0.0628267	−	0.838364i	0.0628267	−	0.838364i	0.936235	−	0.351375i	$-0.114286\pi$
$242$	0.206722	−	0.0311583i	0.206722	−	0.0311583i
$243$	−1.00501	+	0.932515i	−1.00501	+	0.932515i
$244$	1.80994			1.80994
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.0154372	+	0.205995i	−0.0154372	+	0.205995i
$250$		0			0
$251$	−0.557790	+	0.699447i	−0.557790	+	0.699447i	−0.978148	−	0.207912i	$-0.933333\pi$
$251$	−0.557790	+	0.699447i	−0.557790	+	0.699447i	0.420357	+	0.907359i	$0.361905\pi$
$252$	0.0909907	+	0.865719i	0.0909907	+	0.865719i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.564765	+	0.174207i	0.564765	+	0.174207i
$257$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$257$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$258$		0			0
$259$	0.0783706	−	1.74506i	0.0783706	−	1.74506i
$260$		0			0
$261$		0			0
$262$	−0.0667626	+	0.0455179i	−0.0667626	+	0.0455179i
$263$	−0.753071	+	1.30436i	−0.753071	+	1.30436i	0.193256	+	0.981148i	$0.438095\pi$
$263$	−0.753071	+	1.30436i	−0.753071	+	1.30436i	−0.946327	+	0.323210i	$0.895238\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.01486	+	0.970305i	−2.01486	+	0.970305i
$268$		0			0
$269$	1.44973	+	1.34515i	1.44973	+	1.34515i	0.826239	+	0.563320i	$0.190476\pi$
$269$	1.44973	+	1.34515i	1.44973	+	1.34515i	0.623490	+	0.781831i	$0.285714\pi$
$270$		0			0
$271$	−1.44329	−	0.984017i	−1.44329	−	0.984017i	−0.995974	−	0.0896393i	$-0.971429\pi$
$271$	−1.44329	−	0.984017i	−1.44329	−	0.984017i	−0.447313	−	0.894377i	$-0.647619\pi$
$272$	0.257050	−	0.123789i	0.257050	−	0.123789i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.41857	−	0.967163i	1.41857	−	0.967163i	0.420357	−	0.907359i	$-0.361905\pi$
$277$	1.41857	−	0.967163i	1.41857	−	0.967163i	0.998210	−	0.0598042i	$-0.0190476\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$281$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$282$	0.0215927	+	0.288135i	0.0215927	+	0.288135i
$283$	−1.14635	−	0.353601i	−1.14635	−	0.353601i	−0.337330	−	0.941386i	$-0.609524\pi$
$283$	−1.14635	−	0.353601i	−1.14635	−	0.353601i	−0.809017	+	0.587785i	$0.800000\pi$
$284$	0.195948	+	0.499267i	0.195948	+	0.499267i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.335432	+	0.420618i	−0.335432	+	0.420618i
$289$	−0.326123	+	0.830949i	−0.326123	+	0.830949i
$290$		0			0
$291$	2.49706	−	0.376372i	2.49706	−	0.376372i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	0.228574	−	0.176753i	0.228574	−	0.176753i
$295$		0			0
$296$	0.523698	−	0.485921i	0.523698	−	0.485921i
$297$		0			0
$298$	−0.0247176	+	0.329833i	−0.0247176	+	0.329833i
$299$		0			0
$300$	0.824079	−	1.03336i	0.824079	−	1.03336i
$301$		0			0
$302$		0			0
$303$	2.04030	−	0.629348i	2.04030	−	0.629348i
$304$		0			0
$305$		0			0
$306$	0.00465931	+	0.0621742i	0.00465931	+	0.0621742i
$307$	0.124802	+	0.546793i	0.124802	+	0.546793i	0.998210	+	0.0598042i	$0.0190476\pi$
$307$	0.124802	+	0.546793i	0.124802	+	0.546793i	−0.873408	+	0.486989i	$0.838095\pi$
$308$		0			0
$309$	0.00920159	−	0.0403148i	0.00920159	−	0.0403148i
$310$		0			0
$311$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$311$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$312$		0			0
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$	−0.148056	−	0.0712998i	−0.148056	−	0.0712998i
$315$		0			0
$316$	−0.949297	+	0.457157i	−0.949297	+	0.457157i
$317$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$317$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$318$	0.423431	+	0.392886i	0.423431	+	0.392886i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.517202	−	0.895820i	−0.517202	−	0.895820i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$330$		0			0
$331$	0.0708245	+	0.945087i	0.0708245	+	0.945087i	0.913545	+	0.406737i	$0.133333\pi$
$331$	0.0708245	+	0.945087i	0.0708245	+	0.945087i	−0.842721	+	0.538351i	$0.819048\pi$
$332$	−0.136578	−	0.0421288i	−0.136578	−	0.0421288i
$333$	−0.580920	−	1.48016i	−0.580920	−	1.48016i
$334$		0			0
$335$		0			0
$336$	−1.19494	−	0.143697i	−1.19494	−	0.143697i
$337$	−0.806297	+	1.01106i	−0.806297	+	1.01106i	0.193256	+	0.981148i	$0.438095\pi$
$337$	−0.806297	+	1.01106i	−0.806297	+	1.01106i	−0.999552	+	0.0299155i	$0.990476\pi$
$338$	−0.0763771	+	0.194606i	−0.0763771	+	0.194606i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.936235	+	0.351375i	0.936235	+	0.351375i
$344$		0			0
$345$		0			0
$346$	−0.413259	+	0.0622887i	−0.413259	+	0.0622887i
$347$	−0.0668555	+	0.892125i	−0.0668555	+	0.892125i	0.858449	+	0.512899i	$0.171429\pi$
$347$	−0.0668555	+	0.892125i	−0.0668555	+	0.892125i	−0.925304	+	0.379225i	$0.876190\pi$
$348$		0			0
$349$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$349$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$350$	−0.207562	−	0.0249602i	−0.207562	−	0.0249602i
$351$		0			0
$352$		0			0
$353$	−0.0763771	−	0.194606i	−0.0763771	−	0.194606i	0.887586	−	0.460642i	$-0.152381\pi$
$353$	−0.0763771	−	0.194606i	−0.0763771	−	0.194606i	−0.963963	+	0.266037i	$0.914286\pi$
$354$	−0.465361	−	0.143545i	−0.465361	−	0.143545i
$355$		0			0
$356$	−0.344311	−	1.50852i	−0.344311	−	1.50852i
$357$	−0.366350	+	0.266169i	−0.366350	+	0.266169i
$358$		0			0
$359$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$359$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	1.24525	+	0.599682i	1.24525	+	0.599682i
$364$		0			0
$365$		0			0
$366$	−0.451844	−	0.308062i	−0.451844	−	0.308062i
$367$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$367$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.386339	+	1.96142i	−0.386339	+	1.96142i
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$	−0.404409	−	0.0609549i	−0.404409	−	0.0609549i
$377$		0			0
$378$	−0.0122859	+	0.0228310i	−0.0122859	+	0.0228310i
$379$	0.375046	+	1.64318i	0.375046	+	1.64318i	0.712376	+	0.701798i	$0.247619\pi$
$379$	0.375046	+	1.64318i	0.375046	+	1.64318i	−0.337330	+	0.941386i	$0.609524\pi$
$380$		0			0
$381$		0			0
$382$	−0.145968	−	0.371920i	−0.145968	−	0.371920i
$383$	1.85666	−	0.572703i	1.85666	−	0.572703i	0.858449	−	0.512899i	$-0.171429\pi$
$383$	1.85666	−	0.572703i	1.85666	−	0.572703i	0.998210	−	0.0598042i	$-0.0190476\pi$
$384$	−0.643926	−	0.807458i	−0.643926	−	0.807458i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−0.130571	+	1.74235i	−0.130571	+	1.74235i
$389$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$389$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$390$		0			0
$391$		0			0
$392$	0.171916	+	0.371089i	0.171916	+	0.371089i
$393$	−0.534208			−0.534208
$394$	0.111977	−	0.103899i	0.111977	−	0.103899i
$395$		0			0
$396$		0			0
$397$	0.709850	−	1.80867i	0.709850	−	1.80867i	0.134233	−	0.990950i	$-0.457143\pi$
$397$	0.709850	−	1.80867i	0.709850	−	1.80867i	0.575617	−	0.817719i	$-0.304762\pi$
$398$		0			0
$399$		0			0
$400$	0.542932	+	0.680816i	0.542932	+	0.680816i
$401$	−1.76839	+	0.545476i	−1.76839	+	0.545476i	−0.995974	−	0.0896393i	$-0.971429\pi$
$401$	−1.76839	+	0.545476i	−1.76839	+	0.545476i	−0.772417	+	0.635116i	$0.780952\pi$
$402$		0			0
$403$		0			0
$404$	0.110400	+	1.47319i	0.110400	+	1.47319i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.183130	−	0.0276024i	−0.183130	−	0.0276024i
$409$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$409$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$410$		0			0
$411$		0			0
$412$	0.0257778	+	0.0124139i	0.0257778	+	0.0124139i
$413$	−0.424035	−	1.63123i	−0.424035	−	1.63123i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$419$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$420$		0			0
$421$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$421$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$422$		0			0
$423$	−0.455135	+	0.788317i	−0.455135	+	0.788317i
$424$	−0.675523	+	0.460564i	−0.675523	+	0.460564i
$425$	0.323976	+	0.0488316i	0.323976	+	0.0488316i
$426$	0.0360606	−	0.157992i	0.0360606	−	0.157992i
$427$	0.0849136	−	1.89075i	0.0849136	−	1.89075i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.472459	−	1.20381i	−0.472459	−	1.20381i	−0.946327	−	0.323210i	$-0.895238\pi$
$431$	−0.472459	−	1.20381i	−0.472459	−	1.20381i	0.473869	−	0.880596i	$-0.342857\pi$
$432$	0.103196	−	0.0318318i	0.103196	−	0.0318318i
$433$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$433$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.535628	+	0.496990i	−0.535628	+	0.496990i	−0.900969	−	0.433884i	$-0.857143\pi$
$439$	−0.535628	+	0.496990i	−0.535628	+	0.496990i	0.365341	+	0.930874i	$0.380952\pi$
$440$		0			0
$441$	0.908641	−	0.0544379i	0.908641	−	0.0544379i
$442$		0			0
$443$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$443$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$444$	2.28301	−	0.344109i	2.28301	−	0.344109i
$445$		0			0
$446$		0			0
$447$	−1.36340	+	1.70965i	−1.36340	+	1.70965i
$448$	0.252066	−	0.703440i	0.252066	−	0.703440i
$449$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$449$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$450$	−0.181844	+	0.0560914i	−0.181844	+	0.0560914i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.85156	−	0.279077i	−1.85156	−	0.279077i	−0.873408	−	0.486989i	$-0.838095\pi$
$457$	−1.85156	−	0.279077i	−1.85156	−	0.279077i	−0.978148	+	0.207912i	$0.933333\pi$
$458$		0			0
$459$	0.0203163	−	0.0351889i	0.0203163	−	0.0351889i
$460$		0			0
$461$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$461$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$462$		0			0
$463$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$463$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$467$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.543210	−	0.940867i	−0.543210	−	0.940867i
$472$	0.344654	−	0.596957i	0.344654	−	0.596957i
$473$		0			0
$474$	0.314800	+	0.0474484i	0.314800	+	0.0474484i
$475$		0			0
$476$	−0.123141	−	0.288103i	−0.123141	−	0.288103i
$477$	0.404927	+	1.77410i	0.404927	+	1.77410i
$478$	−0.000467417	−	0.00623725i	−0.000467417	−	0.00623725i
$479$	1.88043	+	0.580037i	1.88043	+	0.580037i	0.992847	+	0.119394i	$0.0380952\pi$
$479$	1.88043	+	0.580037i	1.88043	+	0.580037i	0.887586	+	0.460642i	$0.152381\pi$
$480$		0			0
$481$		0			0
$482$	−0.109583	−	0.137412i	−0.109583	−	0.137412i
$483$		0			0
$484$	−0.596240	+	0.747662i	−0.596240	+	0.747662i
$485$		0			0
$486$	−0.0214189	+	0.285815i	−0.0214189	+	0.285815i
$487$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.623490	−	0.781831i	$-0.285714\pi$
$487$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.826239	+	0.563320i	$0.190476\pi$
$488$	0.567421	−	0.526489i	0.567421	−	0.526489i
$489$		0			0
$490$		0			0
$491$	−1.92793			−1.92793			−0.963963	−	0.266037i	$-0.914286\pi$
$491$	−1.92793			−1.92793			−0.963963	+	0.266037i	$0.914286\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.530752	−	0.181274i	0.530752	−	0.181274i
$498$	0.0269257	+	0.0337637i	0.0269257	+	0.0337637i
$499$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$499$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$500$		0			0
$501$		0			0
$502$	0.0139766	+	0.186505i	0.0139766	+	0.186505i
$503$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$503$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$504$	0.280353	+	0.244937i	0.280353	+	0.244937i
$505$		0			0
$506$		0			0
$507$	−1.14197	+	0.778579i	−1.14197	+	0.778579i
$508$		0			0
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$		0			0
$512$	0.784560	−	0.377824i	0.784560	−	0.377824i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.236128	−	0.278573i	−0.236128	−	0.278573i
$519$	−2.48939	−	1.19883i	−2.48939	−	1.19883i
$520$		0			0
$521$	0.599822	−	1.03892i	0.599822	−	1.03892i	−0.393025	−	0.919528i	$-0.628571\pi$
$521$	0.599822	−	1.03892i	0.599822	−	1.03892i	0.992847	−	0.119394i	$-0.0380952\pi$
$522$		0			0
$523$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.826239	−	0.563320i	$-0.190476\pi$
$523$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.623490	+	0.781831i	$0.285714\pi$
$524$	0.0822481	−	0.360352i	0.0822481	−	0.360352i
$525$	−1.04084	−	0.909354i	−1.04084	−	0.909354i
$526$	0.0700651	+	0.306975i	0.0700651	+	0.306975i
$527$		0			0
$528$		0			0
$529$	0.365341	+	0.930874i	0.365341	+	0.930874i
$530$		0			0
$531$	−0.956563	−	1.19949i	−0.956563	−	1.19949i
$532$		0			0
$533$		0			0
$534$	−0.170804	+	0.435202i	−0.170804	+	0.435202i
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.413444			0.413444
$539$		0			0
$540$		0			0
$541$	−1.45562	+	1.35061i	−1.45562	+	1.35061i	−0.646600	+	0.762830i	$0.723810\pi$
$541$	−1.45562	+	1.35061i	−1.45562	+	1.35061i	−0.809017	+	0.587785i	$0.800000\pi$
$542$	−0.361105	+	0.0544279i	−0.361105	+	0.0544279i
$543$		0			0
$544$	0.0707447	−	0.180255i	0.0707447	−	0.180255i
$545$		0			0
$546$		0			0
$547$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$547$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$548$		0			0
$549$	−0.629420	−	1.60373i	−0.629420	−	1.60373i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.433033	+	1.01313i	0.433033	+	1.01313i
$554$	0.0798693	−	0.349930i	0.0798693	−	0.349930i
$555$		0			0
$556$		0			0
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$563$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$564$	−0.968889	−	0.898998i	−0.968889	−	0.898998i
$565$		0			0
$566$	−0.225957	+	0.108815i	−0.225957	+	0.108815i
$567$	−0.960082	+	0.498267i	−0.960082	+	0.498267i
$568$	0.206661	+	0.0995228i	0.206661	+	0.0995228i
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$		0			0
$571$	0.951194	−	0.648513i	0.951194	−	0.648513i	0.0149594	−	0.999888i	$-0.495238\pi$
$571$	0.951194	−	0.648513i	0.951194	−	0.648513i	0.936235	+	0.351375i	$0.114286\pi$
$572$		0			0
$573$	0.587776	−	2.57522i	0.587776	−	2.57522i
$574$		0			0
$575$		0			0
$576$	−0.0508306	−	0.678287i	−0.0508306	−	0.678287i
$577$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$577$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$578$	0.0681784	+	0.173716i	0.0681784	+	0.173716i
$579$		0			0
$580$		0			0
$581$	−0.0504174	+	0.140700i	−0.0504174	+	0.140700i
$582$	0.329156	−	0.412748i	0.329156	−	0.412748i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−0.216521	+	1.30386i	−0.216521	+	1.30386i
$589$		0			0
$590$		0			0
$591$	0.998614	−	0.150517i	0.998614	−	0.150517i
$592$	−0.113673	+	1.51687i	−0.113673	+	1.51687i
$593$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$593$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$594$		0			0
$595$		0			0
$596$	−0.943337	−	1.18291i	−0.943337	−	1.18291i
$597$		0			0
$598$		0			0
$599$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$599$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$600$	−0.0422417	−	0.563677i	−0.0422417	−	0.563677i
$601$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	0.983930	−	0.178557i	$-0.0571429\pi$
$601$	0.0199667	+	0.0874800i	0.0199667	+	0.0874800i	−0.963963	+	0.266037i	$0.914286\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	0.223184	−	0.386567i	0.223184	−	0.386567i
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.209068	−	0.193987i	−0.209068	−	0.193987i
$613$	0.494561	+	0.458885i	0.494561	+	0.458885i	0.887586	−	0.460642i	$-0.152381\pi$
$613$	0.494561	+	0.458885i	0.494561	+	0.458885i	−0.393025	+	0.919528i	$0.628571\pi$
$614$	0.0968770	+	0.0660496i	0.0968770	+	0.0660496i
$615$		0			0
$616$		0			0
$617$	−0.757458	−	0.364772i	−0.757458	−	0.364772i	0.0149594	−	0.999888i	$-0.495238\pi$
$617$	−0.757458	−	0.364772i	−0.757458	−	0.364772i	−0.772417	+	0.635116i	$0.780952\pi$
$618$	−0.00432241	−	0.00748664i	−0.00432241	−	0.00748664i
$619$	0.222521	−	0.385418i	0.222521	−	0.385418i	−0.733052	−	0.680173i	$-0.761905\pi$
$619$	0.222521	−	0.385418i	0.222521	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.59203	+	0.288911i	−1.59203	+	0.288911i
$624$		0			0
$625$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$626$		0			0
$627$		0			0
$628$	0.718300	−	0.221566i	0.718300	−	0.221566i
$629$	0.356835	+	0.447458i	0.356835	+	0.447458i
$630$		0			0
$631$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$631$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$632$	−0.164626	+	0.419460i	−0.164626	+	0.419460i
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−2.64226			−2.64226
$637$		0			0
$638$		0			0
$639$	0.374245	−	0.347248i	0.374245	−	0.347248i
$640$		0			0
$641$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$641$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$642$		0			0
$643$	−0.420644	+	0.527470i	−0.420644	+	0.527470i	−0.946327	−	0.323210i	$-0.895238\pi$
$643$	−0.420644	+	0.527470i	−0.420644	+	0.527470i	0.525684	+	0.850680i	$0.323810\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.648543	+	1.65246i	0.648543	+	1.65246i	0.753071	+	0.657939i	$0.228571\pi$
$647$	0.648543	+	1.65246i	0.648543	+	1.65246i	−0.104528	+	0.994522i	$0.533333\pi$
$648$	−0.422728	−	0.130394i	−0.422728	−	0.130394i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.265468	−	0.0400129i	−0.265468	−	0.0400129i	0.0149594	−	0.999888i	$-0.495238\pi$
$653$	−0.265468	−	0.0400129i	−0.265468	−	0.0400129i	−0.280427	+	0.959875i	$0.590476\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−0.0404015	+	0.205116i	−0.0404015	+	0.205116i
$659$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.995974	−	0.0896393i	$-0.971429\pi$
$659$	−1.54687	+	0.744934i	−1.54687	+	0.744934i	−0.550897	+	0.834573i	$0.685714\pi$
$660$		0			0
$661$	−0.843914	−	0.783038i	−0.843914	−	0.783038i	0.134233	−	0.990950i	$-0.457143\pi$
$661$	−0.843914	−	0.783038i	−0.843914	−	0.783038i	−0.978148	+	0.207912i	$0.933333\pi$
$662$	0.145240	+	0.134763i	0.145240	+	0.134763i
$663$		0			0
$664$	−0.0550724	+	0.0265215i	−0.0550724	+	0.0265215i
$665$		0			0
$666$	−0.299497	−	0.144230i	−0.299497	−	0.144230i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.660860	+	0.480143i	−0.660860	+	0.480143i
$673$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$673$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$674$	0.0202034	+	0.269596i	0.0202034	+	0.269596i
$675$	0.118508	+	0.0365548i	0.118508	+	0.0365548i
$676$	−0.349374	−	0.890190i	−0.349374	−	0.890190i
$677$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$677$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$678$		0			0
$679$	1.81402	+	0.218144i	1.81402	+	0.218144i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.59996	−	0.241155i	1.59996	−	0.241155i	0.712376	−	0.701798i	$-0.247619\pi$
$683$	1.59996	−	0.241155i	1.59996	−	0.241155i	0.887586	+	0.460642i	$0.152381\pi$
$684$		0			0
$685$		0			0
$686$	0.193441	−	0.0792797i	0.193441	−	0.0792797i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$691$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$692$	1.19195	−	1.49465i	1.19195	−	1.49465i
$693$		0			0
$694$	0.116610	+	0.146224i	0.116610	+	0.146224i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.773659	−	0.562096i	0.773659	−	0.562096i
$701$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$701$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.0393767	−	0.0189628i	−0.0393767	−	0.0189628i
$707$	1.54414	−	0.0462144i	1.54414	−	0.0462144i
$708$	2.00707	−	0.966555i	2.00707	−	0.966555i
$709$	1.46672	+	0.999990i	1.46672	+	0.999990i	0.992847	+	0.119394i	$0.0380952\pi$
$709$	1.46672	+	0.999990i	1.46672	+	0.999990i	0.473869	+	0.880596i	$0.342857\pi$
$710$		0			0
$711$	0.735200	+	0.682166i	0.735200	+	0.682166i
$712$	−0.546754	−	0.372771i	−0.546754	−	0.372771i
$713$		0			0
$714$	−0.0182952	+	0.0928834i	−0.0182952	+	0.0928834i
$715$		0			0
$716$		0			0
$717$	0.0206758	−	0.0358115i	0.0206758	−	0.0358115i
$718$		0			0
$719$	0.777271	+	0.117155i	0.777271	+	0.117155i	0.525684	−	0.850680i	$-0.323810\pi$
$719$	0.777271	+	0.117155i	0.777271	+	0.117155i	0.251587	+	0.967835i	$0.419048\pi$
$720$		0			0
$721$	0.0141776	−	0.0263464i	0.0141776	−	0.0263464i
$722$	0.0465195	+	0.203815i	0.0465195	+	0.203815i
$723$	−0.0868343	−	1.15872i	−0.0868343	−	1.15872i
$724$		0			0
$725$		0			0
$726$	0.276106	−	0.0851674i	0.276106	−	0.0851674i
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$		0			0
$729$	−0.507029	+	0.635795i	−0.507029	+	0.635795i
$730$		0			0
$731$		0			0
$732$	2.47362	−	0.372838i	2.47362	−	0.372838i
$733$	1.35659	−	1.25873i	1.35659	−	1.25873i	0.420357	−	0.907359i	$-0.361905\pi$
$733$	1.35659	−	1.25873i	1.35659	−	1.25873i	0.936235	−	0.351375i	$-0.114286\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.0288841	−	0.385431i	0.0288841	−	0.385431i	−0.963963	−	0.266037i	$-0.914286\pi$
$739$	0.0288841	−	0.385431i	0.0288841	−	0.385431i	0.992847	−	0.119394i	$-0.0380952\pi$
$740$		0			0
$741$		0			0
$742$	0.219697	+	0.355522i	0.219697	+	0.355522i
$743$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$743$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0101670	+	0.135669i	0.0101670	+	0.135669i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$751$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$752$	0.719485	−	0.490537i	0.719485	−	0.490537i
$753$	−0.618243	+	1.07083i	−0.618243	+	1.07083i
$754$		0			0
$755$		0			0
$756$	−0.0298376	−	0.114783i	−0.0298376	−	0.114783i
$757$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$757$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$758$	0.291128	+	0.198488i	0.291128	+	0.198488i
$759$		0			0
$760$		0			0
$761$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.222521	−	0.974928i	$-0.571429\pi$
$761$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.988831	+	0.149042i	$0.952381\pi$
$762$		0			0
$763$		0			0
$764$	1.64663	+	0.792974i	1.64663	+	0.792974i
$765$		0			0
$766$	0.203097	−	0.351774i	0.203097	−	0.351774i
$767$		0			0
$768$	0.807744	+	0.121748i	0.807744	+	0.121748i
$769$	−0.416664	+	1.82552i	−0.416664	+	1.82552i	0.134233	+	0.990950i	$0.457143\pi$
$769$	−0.416664	+	1.82552i	−0.416664	+	1.82552i	−0.550897	+	0.834573i	$0.685714\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.64062	+	0.506064i	1.64062	+	0.506064i	0.971490	−	0.237080i	$-0.0761905\pi$
$773$	1.64062	+	0.506064i	1.64062	+	0.506064i	0.669131	+	0.743145i	$0.266667\pi$
$774$		0			0
$775$		0			0
$776$	0.465895	+	0.584214i	0.465895	+	0.584214i
$777$	−0.252365	−	2.40109i	−0.252365	−	2.40109i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.805751	−	0.330228i	−0.805751	−	0.330228i
$785$		0			0
$786$	−0.0818671	+	0.0759616i	−0.0818671	+	0.0759616i
$787$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$787$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$788$	−0.0522175	+	0.696794i	−0.0522175	+	0.696794i
$789$	−0.760522	+	1.93778i	−0.760522	+	1.93778i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.148399	−	0.378115i	−0.148399	−	0.378115i
$795$		0			0
$796$		0			0
$797$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$797$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$798$		0			0
$799$	0.0729058	−	0.319421i	0.0729058	−	0.319421i
$800$	0.584422	+	0.0880874i	0.584422	+	0.0880874i
$801$	−1.21692	+	0.829685i	−1.21692	+	0.829685i
$802$	−0.193441	+	0.335050i	−0.193441	+	0.335050i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.25842	+	1.53977i	2.25842	+	1.53977i
$808$	0.463143	+	0.429734i	0.463143	+	0.429734i
$809$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$809$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$810$		0			0
$811$	1.76256	−	0.848805i	1.76256	−	0.848805i	0.791071	−	0.611724i	$-0.209524\pi$
$811$	1.76256	−	0.848805i	1.76256	−	0.848805i	0.971490	−	0.237080i	$-0.0761905\pi$
$812$		0			0
$813$	−2.17523	−	1.04753i	−2.17523	−	1.04753i
$814$		0			0
$815$		0			0
$816$	0.325807	−	0.222132i	0.325807	−	0.222132i
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$821$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$822$		0			0
$823$	0.266948	+	0.680173i	0.266948	+	0.680173i	1.00000			$0$
$823$	0.266948	+	0.680173i	0.266948	+	0.680173i	−0.733052	+	0.680173i	$0.761905\pi$
$824$	0.0116925	−	0.00360666i	0.0116925	−	0.00360666i
$825$		0			0
$826$	−0.296936	−	0.189690i	−0.296936	−	0.189690i
$827$	0.313724	−	0.393397i	0.313724	−	0.393397i	−0.599822	−	0.800134i	$-0.704762\pi$
$827$	0.313724	−	0.393397i	0.313724	−	0.393397i	0.913545	+	0.406737i	$0.133333\pi$
$828$		0			0
$829$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$829$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$830$		0			0
$831$	1.73951	−	1.61403i	1.73951	−	1.61403i
$832$		0			0
$833$	−0.306744	+	0.115123i	−0.306744	+	0.115123i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$839$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$840$		0			0
$841$	0.623490	+	0.781831i	0.623490	+	0.781831i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	0.0423454	+	0.185527i	0.0423454	+	0.185527i
$847$	0.753071	+	0.657939i	0.753071	+	0.657939i
$848$	0.387367	−	1.69717i	0.387367	−	1.69717i
$849$	−1.63954	−	0.247121i	−1.63954	−	0.247121i
$850$	0.0565928	−	0.0385843i	0.0565928	−	0.0385843i
$851$		0			0
$852$	0.370646	+	0.641978i	0.370646	+	0.641978i
$853$	−0.556829	−	0.268155i	−0.556829	−	0.268155i	0.134233	−	0.990950i	$-0.457143\pi$
$853$	−0.556829	−	0.268155i	−0.556829	−	0.268155i	−0.691063	+	0.722795i	$0.742857\pi$
$854$	−0.255842	−	0.301831i	−0.255842	−	0.301831i
$855$		0			0
$856$		0			0
$857$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$857$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$858$		0			0
$859$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$859$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$860$		0			0
$861$		0			0
$862$	−0.243579	−	0.117301i	−0.243579	−	0.117301i
$863$	0.691063	+	1.19696i	0.691063	+	1.19696i	0.971490	+	0.237080i	$0.0761905\pi$
$863$	0.691063	+	1.19696i	0.691063	+	1.19696i	−0.280427	+	0.959875i	$0.590476\pi$
$864$	0.0366486	−	0.0634773i	0.0366486	−	0.0634773i
$865$		0			0
$866$		0			0
$867$	−0.274538	+	1.20283i	−0.274538	+	1.20283i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.58926	−	0.490221i	1.58926	−	0.490221i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$877$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$878$	−0.0114153	+	0.152327i	−0.0114153	+	0.152327i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	0.131508	−	0.137547i	0.131508	−	0.137547i
$883$	1.42475			1.42475			0.712376	−	0.701798i	$-0.247619\pi$
$883$	1.42475			1.42475			0.712376	+	0.701798i	$0.247619\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$887$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$888$	0.615635	−	0.771981i	0.615635	−	0.771981i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	0.0341628	+	0.455870i	0.0341628	+	0.455870i
$895$		0			0
$896$	−0.293683	−	0.687106i	−0.293683	−	0.687106i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.435244	−	0.753864i	0.435244	−	0.753864i
$901$	−0.327489	−	0.567228i	−0.327489	−	0.567228i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.733052	+	0.680173i	0.733052	+	0.680173i	0.955573	−	0.294755i	$-0.0952381\pi$
$907$	0.733052	+	0.680173i	0.733052	+	0.680173i	−0.222521	+	0.974928i	$0.571429\pi$
$908$		0			0
$909$	1.26696	−	0.610134i	1.26696	−	0.610134i
$910$		0			0
$911$	−0.348235	−	0.167701i	−0.348235	−	0.167701i	0.251587	−	0.967835i	$-0.419048\pi$
$911$	−0.348235	−	0.167701i	−0.348235	−	0.167701i	−0.599822	+	0.800134i	$0.704762\pi$
$912$		0			0
$913$		0			0
$914$	−0.323433	+	0.220513i	−0.323433	+	0.220513i
$915$		0			0
$916$		0			0
$917$	−0.372583	−	0.102826i	−0.372583	−	0.102826i
$918$	−0.00189021	−	0.00828155i	−0.00189021	−	0.00828155i
$919$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$919$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$920$		0			0
$921$	0.283202	+	0.721587i	0.283202	+	0.721587i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.08912	+	1.36572i	−1.08912	+	1.36572i
$926$		0			0
$927$	0.00203521	−	0.0271581i	0.00203521	−	0.0271581i
$928$		0			0
$929$	−0.196800	+	0.182604i	−0.196800	+	0.182604i	−0.772417	−	0.635116i	$-0.780952\pi$
$929$	−0.196800	+	0.182604i	−0.196800	+	0.182604i	0.575617	+	0.817719i	$0.304762\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$937$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.704350	−	1.79466i	−0.704350	−	1.79466i	−0.599822	−	0.800134i	$-0.704762\pi$
$941$	−0.704350	−	1.79466i	−0.704350	−	1.79466i	−0.104528	−	0.994522i	$-0.533333\pi$
$942$	−0.217033	−	0.0669458i	−0.217033	−	0.0669458i
$943$		0			0
$944$	0.326589	+	1.43088i	0.326589	+	1.43088i
$945$		0			0
$946$		0			0
$947$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.826239	−	0.563320i	$-0.190476\pi$
$947$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.623490	+	0.781831i	$0.285714\pi$
$948$	−1.20322	+	0.820342i	−1.20322	+	0.820342i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−0.122411	−	0.0545009i	−0.122411	−	0.0545009i
$953$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$953$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$954$	0.314323	+	0.214302i	0.314323	+	0.214302i
$955$		0			0
$956$	0.0209735	+	0.0194606i	0.0209735	+	0.0194606i
$957$		0			0
$958$	0.370654	−	0.178497i	0.370654	−	0.178497i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	0.794992	+	0.119826i	0.794992	+	0.119826i
$965$		0			0
$966$		0			0
$967$	0.429004	+	1.87959i	0.429004	+	1.87959i	0.473869	+	0.880596i	$0.342857\pi$
$967$	0.429004	+	1.87959i	0.429004	+	1.87959i	−0.0448648	+	0.998993i	$0.514286\pi$
$968$	0.0305629	+	0.407833i	0.0305629	+	0.407833i
$969$		0			0
$970$		0			0
$971$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$971$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$972$	−0.817444	−	1.02504i	−0.817444	−	1.02504i
$973$		0			0
$974$	0.191099	−	0.239631i	0.191099	−	0.239631i
$975$		0			0
$976$	−0.123164	+	1.64351i	−0.123164	+	1.64351i
$977$	−0.147791	+	0.0222759i	−0.147791	+	0.0222759i	−0.222521	−	0.974928i	$-0.571429\pi$
$977$	−0.147791	+	0.0222759i	−0.147791	+	0.0222759i	0.0747301	+	0.997204i	$0.476190\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.295454	+	0.274141i	−0.295454	+	0.274141i
$983$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$983$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.984593	+	0.969973i	−0.984593	+	0.969973i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.00466	+	0.309896i	1.00466	+	0.309896i	0.753071	−	0.657939i	$-0.228571\pi$
$991$	1.00466	+	0.309896i	1.00466	+	0.309896i	0.251587	+	0.967835i	$0.419048\pi$
$992$		0			0
$993$	0.291478	+	1.27705i	0.291478	+	1.27705i
$994$	0.0555614	−	0.103250i	0.0555614	−	0.103250i
$995$		0			0
$996$	−0.195338	−	0.0294425i	−0.195338	−	0.0294425i
$997$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$997$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$998$		0			0
$999$	0.108318	+	0.187612i	0.108318	+	0.187612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.1.q.b.2020.3	✓	48
47.46	odd	2	CM	2303.1.q.b.2020.3	✓	48
49.9	even	21	inner	2303.1.q.b.2067.3	yes	48
2303.2067	odd	42	inner	2303.1.q.b.2067.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.1.q.b.2020.3	✓	48	1.1	even	1	trivial
2303.1.q.b.2020.3	✓	48	47.46	odd	2	CM
2303.1.q.b.2067.3	yes	48	49.9	even	21	inner
2303.1.q.b.2067.3	yes	48	2303.2067	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2303.q (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.153250 - 0.142195i) q^{2} +(1.36669 - 0.205995i) q^{3} +(-0.0714640 + 0.953621i) q^{4} +(0.180153 - 0.225905i) q^{6} +(0.992847 + 0.119394i) q^{7} +(0.254993 + 0.319751i) q^{8} +(0.869830 - 0.268307i) q^{9} +O(q^{10})\)	\(q+(0.153250 - 0.142195i) q^{2} +(1.36669 - 0.205995i) q^{3} +(-0.0714640 + 0.953621i) q^{4} +(0.180153 - 0.225905i) q^{6} +(0.992847 + 0.119394i) q^{7} +(0.254993 + 0.319751i) q^{8} +(0.869830 - 0.268307i) q^{9} +(0.0987722 + 1.31802i) q^{12} +(0.169131 - 0.122881i) q^{14} +(-0.861070 - 0.129785i) q^{16} +(-0.270705 + 0.184564i) q^{17} +(0.0951492 - 0.164803i) q^{18} +(1.38151 - 0.0413469i) q^{21} +(0.414363 + 0.384473i) q^{24} +(-0.733052 - 0.680173i) q^{25} +(-0.111736 + 0.0538092i) q^{27} +(-0.184810 + 0.938267i) q^{28} +(-0.488326 + 0.332935i) q^{32} +(-0.0152415 + 0.0667772i) q^{34} +(0.193702 + 0.848662i) q^{36} +(-0.130540 - 1.74193i) q^{37} +(0.205836 - 0.202779i) q^{42} +(-0.733052 + 0.680173i) q^{47} -1.20355 q^{48} +(0.971490 + 0.237080i) q^{49} -0.209057 q^{50} +(-0.331951 + 0.308005i) q^{51} +(-0.149393 + 1.99351i) q^{53} +(-0.00947210 + 0.0241345i) q^{54} +(0.214993 + 0.347909i) q^{56} +(-0.615761 - 1.56893i) q^{59} +(-0.141438 - 1.88736i) q^{61} +(0.895642 - 0.162535i) q^{63} +(0.166276 - 0.728503i) q^{64} +(-0.156658 - 0.271340i) q^{68} +(0.505313 - 0.243346i) q^{71} +(0.307592 + 0.209713i) q^{72} +(-0.267699 - 0.248388i) q^{74} +(-1.14197 - 0.778579i) q^{75} +(0.550897 + 0.954182i) q^{79} +(-0.893725 + 0.609331i) q^{81} +(-0.0332580 + 0.145713i) q^{83} +(-0.0592987 + 1.32039i) q^{84} +(-1.54615 + 0.476924i) q^{89} +(-0.0156228 + 0.208472i) q^{94} +(-0.598806 + 0.555611i) q^{96} +1.82709 q^{97} +(0.182592 - 0.101808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 40 q^{12} - 18 q^{14} + 6 q^{16} + q^{17} - 9 q^{18} + 5 q^{21} + 8 q^{24} + 4 q^{25} - 6 q^{27} - 5 q^{32} + 2 q^{34} - 10 q^{36} + q^{37} + 7 q^{42} + 4 q^{47} + 6 q^{48} - q^{49} + 12 q^{50} + 4 q^{51} + 8 q^{53} - q^{54} - 11 q^{56} - 13 q^{59} + q^{61} - 4 q^{63} - 8 q^{64} - 5 q^{68} + 5 q^{71} - 8 q^{72} + 13 q^{74} + 5 q^{75} - 2 q^{79} + 8 q^{83} + 5 q^{84} - 2 q^{89} + q^{94} + 10 q^{96} + 12 q^{97} + q^{98}+O(q^{100}) \) 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - 40 * q^12 - 18 * q^14 + 6 * q^16 + q^17 - 9 * q^18 + 5 * q^21 + 8 * q^24 + 4 * q^25 - 6 * q^27 - 5 * q^32 + 2 * q^34 - 10 * q^36 + q^37 + 7 * q^42 + 4 * q^47 + 6 * q^48 - q^49 + 12 * q^50 + 4 * q^51 + 8 * q^53 - q^54 - 11 * q^56 - 13 * q^59 + q^61 - 4 * q^63 - 8 * q^64 - 5 * q^68 + 5 * q^71 - 8 * q^72 + 13 * q^74 + 5 * q^75 - 2 * q^79 + 8 * q^83 + 5 * q^84 - 2 * q^89 + q^94 + 10 * q^96 + 12 * q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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