LMFDB - Embedded newform 784.2.x.h.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			373.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	784.373
Dual form			784.2.x.h.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-0.500000 - 0.133975i) q^{3} +2.00000i q^{4} +(0.866025 - 0.232051i) q^{5} +(-0.366025 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-0.500000 - 0.133975i) q^{3} +2.00000i q^{4} +(0.866025 - 0.232051i) q^{5} +(-0.366025 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 1.36603i) q^{9} +(1.09808 + 0.633975i) q^{10} +(-0.767949 + 2.86603i) q^{11} +(0.267949 - 1.00000i) q^{12} +(-3.73205 + 3.73205i) q^{13} -0.464102 q^{15} -4.00000 q^{16} +(3.23205 + 5.59808i) q^{17} +(-1.00000 - 3.73205i) q^{18} +(-0.767949 - 2.86603i) q^{19} +(0.464102 + 1.73205i) q^{20} +(-3.63397 + 2.09808i) q^{22} +(3.86603 + 2.23205i) q^{23} +(1.26795 - 0.732051i) q^{24} +(-3.63397 + 2.09808i) q^{25} -7.46410 q^{26} +(2.09808 + 2.09808i) q^{27} +(-0.267949 + 0.267949i) q^{29} +(-0.464102 - 0.464102i) q^{30} +(1.86603 + 3.23205i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(0.767949 - 1.33013i) q^{33} +(-2.36603 + 8.83013i) q^{34} +(2.73205 - 4.73205i) q^{36} +(-1.13397 + 0.303848i) q^{37} +(2.09808 - 3.63397i) q^{38} +(2.36603 - 1.36603i) q^{39} +(-1.26795 + 2.19615i) q^{40} -4.92820i q^{41} +(6.46410 + 6.46410i) q^{43} +(-5.73205 - 1.53590i) q^{44} +(-2.36603 - 0.633975i) q^{45} +(1.63397 + 6.09808i) q^{46} +(2.13397 - 3.69615i) q^{47} +(2.00000 + 0.535898i) q^{48} +(-5.73205 - 1.53590i) q^{50} +(-0.866025 - 3.23205i) q^{51} +(-7.46410 - 7.46410i) q^{52} +(-1.06218 + 3.96410i) q^{53} +4.19615i q^{54} +2.66025i q^{55} +1.53590i q^{57} -0.535898 q^{58} +(3.03590 - 11.3301i) q^{59} -0.928203i q^{60} +(-1.86603 - 6.96410i) q^{61} +(-1.36603 + 5.09808i) q^{62} -8.00000i q^{64} +(-2.36603 + 4.09808i) q^{65} +(2.09808 - 0.562178i) q^{66} +(-4.96410 - 1.33013i) q^{67} +(-11.1962 + 6.46410i) q^{68} +(-1.63397 - 1.63397i) q^{69} -0.535898i q^{71} +(7.46410 - 2.00000i) q^{72} +(-6.23205 + 3.59808i) q^{73} +(-1.43782 - 0.830127i) q^{74} +(2.09808 - 0.562178i) q^{75} +(5.73205 - 1.53590i) q^{76} +(3.73205 + 1.00000i) q^{78} +(8.33013 - 14.4282i) q^{79} +(-3.46410 + 0.928203i) q^{80} +(3.33013 + 5.76795i) q^{81} +(4.92820 - 4.92820i) q^{82} +(-1.53590 + 1.53590i) q^{83} +(4.09808 + 4.09808i) q^{85} +12.9282i q^{86} +(0.169873 - 0.0980762i) q^{87} +(-4.19615 - 7.26795i) q^{88} +(4.50000 + 2.59808i) q^{89} +(-1.73205 - 3.00000i) q^{90} +(-4.46410 + 7.73205i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(5.83013 - 1.56218i) q^{94} +(-1.33013 - 2.30385i) q^{95} +(1.46410 + 2.53590i) q^{96} +2.92820 q^{97} +(5.73205 - 5.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{3} + 2 q^{6} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 2 * q^3 + 2 * q^6 - 8 * q^8 - 6 * q^9	$ 4 q + 4 q^{2} - 2 q^{3} + 2 q^{6} - 8 q^{8} - 6 q^{9} - 6 q^{10} - 10 q^{11} + 8 q^{12} - 8 q^{13} + 12 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} - 10 q^{19} - 12 q^{20} - 18 q^{22} + 12 q^{23} + 12 q^{24} - 18 q^{25} - 16 q^{26} - 2 q^{27} - 8 q^{29} + 12 q^{30} + 4 q^{31} - 16 q^{32} + 10 q^{33} - 6 q^{34} + 4 q^{36} - 8 q^{37} - 2 q^{38} + 6 q^{39} - 12 q^{40} + 12 q^{43} - 16 q^{44} - 6 q^{45} + 10 q^{46} + 12 q^{47} + 8 q^{48} - 16 q^{50} - 16 q^{52} + 20 q^{53} - 16 q^{58} + 26 q^{59} - 4 q^{61} - 2 q^{62} - 6 q^{65} - 2 q^{66} - 6 q^{67} - 24 q^{68} - 10 q^{69} + 16 q^{72} - 18 q^{73} - 30 q^{74} - 2 q^{75} + 16 q^{76} + 8 q^{78} + 16 q^{79} - 4 q^{81} - 8 q^{82} - 20 q^{83} + 6 q^{85} + 18 q^{87} + 4 q^{88} + 18 q^{89} - 4 q^{92} - 2 q^{93} + 6 q^{94} + 12 q^{95} - 8 q^{96} - 16 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 2 * q^3 + 2 * q^6 - 8 * q^8 - 6 * q^9 - 6 * q^10 - 10 * q^11 + 8 * q^12 - 8 * q^13 + 12 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 - 10 * q^19 - 12 * q^20 - 18 * q^22 + 12 * q^23 + 12 * q^24 - 18 * q^25 - 16 * q^26 - 2 * q^27 - 8 * q^29 + 12 * q^30 + 4 * q^31 - 16 * q^32 + 10 * q^33 - 6 * q^34 + 4 * q^36 - 8 * q^37 - 2 * q^38 + 6 * q^39 - 12 * q^40 + 12 * q^43 - 16 * q^44 - 6 * q^45 + 10 * q^46 + 12 * q^47 + 8 * q^48 - 16 * q^50 - 16 * q^52 + 20 * q^53 - 16 * q^58 + 26 * q^59 - 4 * q^61 - 2 * q^62 - 6 * q^65 - 2 * q^66 - 6 * q^67 - 24 * q^68 - 10 * q^69 + 16 * q^72 - 18 * q^73 - 30 * q^74 - 2 * q^75 + 16 * q^76 + 8 * q^78 + 16 * q^79 - 4 * q^81 - 8 * q^82 - 20 * q^83 + 6 * q^85 + 18 * q^87 + 4 * q^88 + 18 * q^89 - 4 * q^92 - 2 * q^93 + 6 * q^94 + 12 * q^95 - 8 * q^96 - 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	−0.500000	−	0.133975i	−0.288675	−	0.0773503i	0.111576	−	0.993756i	$-0.464410\pi$
$3$	−0.500000	−	0.133975i	−0.288675	−	0.0773503i	−0.400251	+	0.916406i	$0.631077\pi$
$4$			2.00000i			1.00000i
$5$	0.866025	−	0.232051i	0.387298	−	0.103776i	−0.0599153	−	0.998203i	$-0.519083\pi$
$5$	0.866025	−	0.232051i	0.387298	−	0.103776i	0.447214	+	0.894427i	$0.352416\pi$
$6$	−0.366025	−	0.633975i	−0.149429	−	0.258819i
$7$		0			0
$7$		0			0
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−2.36603	−	1.36603i	−0.788675	−	0.455342i
$10$	1.09808	+	0.633975i	0.347242	+	0.200480i
$11$	−0.767949	+	2.86603i	−0.231545	+	0.864139i	0.748130	+	0.663552i	$0.230952\pi$
$11$	−0.767949	+	2.86603i	−0.231545	+	0.864139i	−0.979676	+	0.200587i	$0.935715\pi$
$12$	0.267949	−	1.00000i	0.0773503	−	0.288675i
$13$	−3.73205	+	3.73205i	−1.03508	+	1.03508i	−0.0357229	+	0.999362i	$0.511373\pi$
$13$	−3.73205	+	3.73205i	−1.03508	+	1.03508i	−0.999362	+	0.0357229i	$0.988627\pi$
$14$		0			0
$15$	−0.464102			−0.119831
$16$	−4.00000			−1.00000
$17$	3.23205	+	5.59808i	0.783887	+	1.35773i	0.929661	+	0.368415i	$0.120099\pi$
$17$	3.23205	+	5.59808i	0.783887	+	1.35773i	−0.145774	+	0.989318i	$0.546567\pi$
$18$	−1.00000	−	3.73205i	−0.235702	−	0.879653i
$19$	−0.767949	−	2.86603i	−0.176180	−	0.657511i	−0.996348	−	0.0853887i	$-0.972787\pi$
$19$	−0.767949	−	2.86603i	−0.176180	−	0.657511i	0.820168	−	0.572123i	$-0.193880\pi$
$20$	0.464102	+	1.73205i	0.103776	+	0.387298i
$21$		0			0
$22$	−3.63397	+	2.09808i	−0.774766	+	0.447311i
$23$	3.86603	+	2.23205i	0.806122	+	0.465415i	0.845607	−	0.533805i	$-0.179239\pi$
$23$	3.86603	+	2.23205i	0.806122	+	0.465415i	−0.0394853	+	0.999220i	$0.512572\pi$
$24$	1.26795	−	0.732051i	0.258819	−	0.149429i
$25$	−3.63397	+	2.09808i	−0.726795	+	0.419615i
$26$	−7.46410			−1.46383
$27$	2.09808	+	2.09808i	0.403775	+	0.403775i
$28$		0			0
$29$	−0.267949	+	0.267949i	−0.0497569	+	0.0497569i	−0.731547	−	0.681791i	$-0.761202\pi$
$29$	−0.267949	+	0.267949i	−0.0497569	+	0.0497569i	0.681791	+	0.731547i	$0.261202\pi$
$30$	−0.464102	−	0.464102i	−0.0847330	−	0.0847330i
$31$	1.86603	+	3.23205i	0.335148	+	0.580493i	0.983513	−	0.180836i	$-0.0578803\pi$
$31$	1.86603	+	3.23205i	0.335148	+	0.580493i	−0.648365	+	0.761329i	$0.724547\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	0.767949	−	1.33013i	0.133683	−	0.231545i
$34$	−2.36603	+	8.83013i	−0.405770	+	1.51435i
$35$		0			0
$36$	2.73205	−	4.73205i	0.455342	−	0.788675i
$37$	−1.13397	+	0.303848i	−0.186424	+	0.0499522i	−0.350823	−	0.936442i	$-0.614098\pi$
$37$	−1.13397	+	0.303848i	−0.186424	+	0.0499522i	0.164399	+	0.986394i	$0.447432\pi$
$38$	2.09808	−	3.63397i	0.340353	−	0.589509i
$39$	2.36603	−	1.36603i	0.378867	−	0.218739i
$40$	−1.26795	+	2.19615i	−0.200480	+	0.347242i
$41$		−	4.92820i		−	0.769656i	−0.922988	−	0.384828i	$-0.874261\pi$
$41$		−	4.92820i		−	0.769656i	0.922988	−	0.384828i	$-0.125739\pi$
$42$		0			0
$43$	6.46410	+	6.46410i	0.985766	+	0.985766i	0.999900	−	0.0141339i	$-0.00449910\pi$
$43$	6.46410	+	6.46410i	0.985766	+	0.985766i	−0.0141339	+	0.999900i	$0.504499\pi$
$44$	−5.73205	−	1.53590i	−0.864139	−	0.231545i
$45$	−2.36603	−	0.633975i	−0.352706	−	0.0945074i
$46$	1.63397	+	6.09808i	0.240916	+	0.899112i
$47$	2.13397	−	3.69615i	0.311272	−	0.539139i	−0.667366	−	0.744730i	$-0.732578\pi$
$47$	2.13397	−	3.69615i	0.311272	−	0.539139i	0.978638	+	0.205591i	$0.0659116\pi$
$48$	2.00000	+	0.535898i	0.288675	+	0.0773503i
$49$		0			0
$50$	−5.73205	−	1.53590i	−0.810634	−	0.217209i
$51$	−0.866025	−	3.23205i	−0.121268	−	0.452578i
$52$	−7.46410	−	7.46410i	−1.03508	−	1.03508i
$53$	−1.06218	+	3.96410i	−0.145901	+	0.544511i	0.853812	+	0.520581i	$0.174285\pi$
$53$	−1.06218	+	3.96410i	−0.145901	+	0.544511i	−0.999714	+	0.0239302i	$0.992382\pi$
$54$			4.19615i			0.571024i
$55$			2.66025i			0.358709i
$56$		0			0
$57$			1.53590i			0.203435i
$58$	−0.535898			−0.0703669
$59$	3.03590	−	11.3301i	0.395240	−	1.47506i	−0.426130	−	0.904662i	$-0.640123\pi$
$59$	3.03590	−	11.3301i	0.395240	−	1.47506i	0.821370	−	0.570395i	$-0.193210\pi$
$60$		−	0.928203i		−	0.119831i
$61$	−1.86603	−	6.96410i	−0.238920	−	0.891662i	−0.976342	−	0.216230i	$-0.930624\pi$
$61$	−1.86603	−	6.96410i	−0.238920	−	0.891662i	0.737422	−	0.675432i	$-0.236043\pi$
$62$	−1.36603	+	5.09808i	−0.173485	+	0.647456i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	−2.36603	+	4.09808i	−0.293469	+	0.508304i
$66$	2.09808	−	0.562178i	0.258255	−	0.0691993i
$67$	−4.96410	−	1.33013i	−0.606462	−	0.162501i	−0.0574958	−	0.998346i	$-0.518312\pi$
$67$	−4.96410	−	1.33013i	−0.606462	−	0.162501i	−0.548966	+	0.835845i	$0.684978\pi$
$68$	−11.1962	+	6.46410i	−1.35773	+	0.783887i
$69$	−1.63397	−	1.63397i	−0.196707	−	0.196707i
$70$		0			0
$71$		−	0.535898i		−	0.0635994i	−0.999494	−	0.0317997i	$-0.989876\pi$
$71$		−	0.535898i		−	0.0635994i	0.999494	−	0.0317997i	$-0.0101239\pi$
$72$	7.46410	−	2.00000i	0.879653	−	0.235702i
$73$	−6.23205	+	3.59808i	−0.729406	+	0.421123i	−0.818205	−	0.574927i	$-0.805031\pi$
$73$	−6.23205	+	3.59808i	−0.729406	+	0.421123i	0.0887986	+	0.996050i	$0.471697\pi$
$74$	−1.43782	−	0.830127i	−0.167143	−	0.0965003i
$75$	2.09808	−	0.562178i	0.242265	−	0.0649147i
$76$	5.73205	−	1.53590i	0.657511	−	0.176180i
$77$		0			0
$78$	3.73205	+	1.00000i	0.422572	+	0.113228i
$79$	8.33013	−	14.4282i	0.937213	−	1.62330i	0.166572	−	0.986029i	$-0.446730\pi$
$79$	8.33013	−	14.4282i	0.937213	−	1.62330i	0.770640	−	0.637270i	$-0.219937\pi$
$80$	−3.46410	+	0.928203i	−0.387298	+	0.103776i
$81$	3.33013	+	5.76795i	0.370014	+	0.640883i
$82$	4.92820	−	4.92820i	0.544229	−	0.544229i
$83$	−1.53590	+	1.53590i	−0.168587	+	0.168587i	−0.786358	−	0.617771i	$-0.788036\pi$
$83$	−1.53590	+	1.53590i	−0.168587	+	0.168587i	0.617771	+	0.786358i	$0.288036\pi$
$84$		0			0
$85$	4.09808	+	4.09808i	0.444499	+	0.444499i
$86$			12.9282i			1.39408i
$87$	0.169873	−	0.0980762i	0.0182123	−	0.0105149i
$88$	−4.19615	−	7.26795i	−0.447311	−	0.774766i
$89$	4.50000	+	2.59808i	0.476999	+	0.275396i	0.719165	−	0.694839i	$-0.244525\pi$
$89$	4.50000	+	2.59808i	0.476999	+	0.275396i	−0.242166	+	0.970235i	$0.577858\pi$
$90$	−1.73205	−	3.00000i	−0.182574	−	0.316228i
$91$		0			0
$92$	−4.46410	+	7.73205i	−0.465415	+	0.806122i
$93$	−0.500000	−	1.86603i	−0.0518476	−	0.193498i
$94$	5.83013	−	1.56218i	0.601332	−	0.161126i
$95$	−1.33013	−	2.30385i	−0.136468	−	0.236370i
$96$	1.46410	+	2.53590i	0.149429	+	0.258819i
$97$	2.92820			0.297314			0.148657	−	0.988889i	$-0.452505\pi$
$97$	2.92820			0.297314			0.148657	+	0.988889i	$0.452505\pi$
$98$		0			0
$99$	5.73205	−	5.73205i	0.576093	−	0.576093i
$100$	−4.19615	−	7.26795i	−0.419615	−	0.726795i
$101$	−5.06218	+	18.8923i	−0.503706	+	1.87985i	−0.0292559	+	0.999572i	$0.509314\pi$
$101$	−5.06218	+	18.8923i	−0.503706	+	1.87985i	−0.474450	+	0.880283i	$0.657353\pi$
$102$	2.36603	−	4.09808i	0.234271	−	0.405770i
$103$	5.59808	+	3.23205i	0.551595	+	0.318463i	0.749765	−	0.661704i	$-0.230167\pi$
$103$	5.59808	+	3.23205i	0.551595	+	0.318463i	−0.198170	+	0.980168i	$0.563500\pi$
$104$		−	14.9282i		−	1.46383i
$105$		0			0
$106$	−5.02628	+	2.90192i	−0.488195	+	0.281860i
$107$	3.23205	−	0.866025i	0.312454	−	0.0837218i	−0.0991843	−	0.995069i	$-0.531623\pi$
$107$	3.23205	−	0.866025i	0.312454	−	0.0837218i	0.411638	+	0.911347i	$0.364957\pi$
$108$	−4.19615	+	4.19615i	−0.403775	+	0.403775i
$109$	−2.13397	−	0.571797i	−0.204398	−	0.0547682i	0.155167	−	0.987888i	$-0.450408\pi$
$109$	−2.13397	−	0.571797i	−0.204398	−	0.0547682i	−0.359565	+	0.933120i	$0.617075\pi$
$110$	−2.66025	+	2.66025i	−0.253645	+	0.253645i
$111$	0.607695			0.0576799
$112$		0			0
$113$	−1.46410			−0.137731			−0.0688655	−	0.997626i	$-0.521938\pi$
$113$	−1.46410			−0.137731			−0.0688655	+	0.997626i	$0.521938\pi$
$114$	−1.53590	+	1.53590i	−0.143850	+	0.143850i
$115$	3.86603	+	1.03590i	0.360509	+	0.0965980i
$116$	−0.535898	−	0.535898i	−0.0497569	−	0.0497569i
$117$	13.9282	−	3.73205i	1.28766	−	0.345028i
$118$	14.3660	−	8.29423i	1.32250	−	0.763546i
$119$		0			0
$120$	0.928203	−	0.928203i	0.0847330	−	0.0847330i
$121$	1.90192	+	1.09808i	0.172902	+	0.0998251i
$122$	5.09808	−	8.83013i	0.461558	−	0.799442i
$123$	−0.660254	+	2.46410i	−0.0595331	+	0.222181i
$124$	−6.46410	+	3.73205i	−0.580493	+	0.335148i
$125$	−5.83013	+	5.83013i	−0.521462	+	0.521462i
$126$		0			0
$127$	9.46410			0.839803			0.419902	−	0.907570i	$-0.362065\pi$
$127$	9.46410			0.839803			0.419902	+	0.907570i	$0.362065\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	−2.36603	−	4.09808i	−0.208317	−	0.360815i
$130$	−6.46410	+	1.73205i	−0.566939	+	0.151911i
$131$	2.03590	+	7.59808i	0.177877	+	0.663847i	0.996044	+	0.0888654i	$0.0283241\pi$
$131$	2.03590	+	7.59808i	0.177877	+	0.663847i	−0.818166	+	0.574982i	$0.805009\pi$
$132$	2.66025	+	1.53590i	0.231545	+	0.133683i
$133$		0			0
$134$	−3.63397	−	6.29423i	−0.313928	−	0.543739i
$135$	2.30385	+	1.33013i	0.198284	+	0.114479i
$136$	−17.6603	−	4.73205i	−1.51435	−	0.405770i
$137$	15.2321	−	8.79423i	1.30136	−	0.751342i	0.320724	−	0.947173i	$-0.396074\pi$
$137$	15.2321	−	8.79423i	1.30136	−	0.751342i	0.980638	+	0.195831i	$0.0627404\pi$
$138$		−	3.26795i		−	0.278186i
$139$	11.9282	+	11.9282i	1.01174	+	1.01174i	0.999930	+	0.0118067i	$0.00375827\pi$
$139$	11.9282	+	11.9282i	1.01174	+	1.01174i	0.0118067	+	0.999930i	$0.496242\pi$
$140$		0			0
$141$	−1.56218	+	1.56218i	−0.131559	+	0.131559i
$142$	0.535898	−	0.535898i	0.0449716	−	0.0449716i
$143$	−7.83013	−	13.5622i	−0.654788	−	1.13413i
$144$	9.46410	+	5.46410i	0.788675	+	0.455342i
$145$	−0.169873	+	0.294229i	−0.0141072	+	0.0244344i
$146$	−9.83013	−	2.63397i	−0.813547	−	0.217989i
$147$		0			0
$148$	−0.607695	−	2.26795i	−0.0499522	−	0.186424i
$149$	−7.59808	+	2.03590i	−0.622459	+	0.166787i	−0.556245	−	0.831018i	$-0.687758\pi$
$149$	−7.59808	+	2.03590i	−0.622459	+	0.166787i	−0.0662134	+	0.997805i	$0.521092\pi$
$150$	2.66025	+	1.53590i	0.217209	+	0.125406i
$151$	9.86603	−	5.69615i	0.802886	−	0.463546i	−0.0415935	−	0.999135i	$-0.513243\pi$
$151$	9.86603	−	5.69615i	0.802886	−	0.463546i	0.844479	+	0.535588i	$0.179910\pi$
$152$	7.26795	+	4.19615i	0.589509	+	0.340353i
$153$		−	17.6603i		−	1.42775i
$154$		0			0
$155$	2.36603	+	2.36603i	0.190044	+	0.190044i
$156$	2.73205	+	4.73205i	0.218739	+	0.378867i
$157$	18.2583	+	4.89230i	1.45717	+	0.390448i	0.898513	−	0.438948i	$-0.144649\pi$
$157$	18.2583	+	4.89230i	1.45717	+	0.390448i	0.558661	+	0.829396i	$0.311315\pi$
$158$	22.7583	−	6.09808i	1.81056	−	0.485137i
$159$	1.06218	−	1.83975i	0.0842362	−	0.145901i
$160$	−4.39230	−	2.53590i	−0.347242	−	0.200480i
$161$		0			0
$162$	−2.43782	+	9.09808i	−0.191533	+	0.714812i
$163$	3.23205	+	12.0622i	0.253154	+	0.944783i	0.969108	+	0.246636i	$0.0793251\pi$
$163$	3.23205	+	12.0622i	0.253154	+	0.944783i	−0.715954	+	0.698147i	$0.754008\pi$
$164$	9.85641			0.769656
$165$	0.356406	−	1.33013i	0.0277462	−	0.103550i
$166$	−3.07180			−0.238418
$167$		−	21.8564i		−	1.69130i	−0.533738	−	0.845650i	$-0.679213\pi$
$167$		−	21.8564i		−	1.69130i	0.533738	−	0.845650i	$-0.320787\pi$
$168$		0			0
$169$		−	14.8564i		−	1.14280i
$170$			8.19615i			0.628616i
$171$	−2.09808	+	7.83013i	−0.160444	+	0.598785i
$172$	−12.9282	+	12.9282i	−0.985766	+	0.985766i
$173$	−0.598076	−	2.23205i	−0.0454709	−	0.169700i	0.939456	−	0.342668i	$-0.111331\pi$
$173$	−0.598076	−	2.23205i	−0.0454709	−	0.169700i	−0.984927	+	0.172969i	$0.944664\pi$
$174$	0.267949	+	0.0717968i	0.0203132	+	0.00544290i
$175$		0			0
$176$	3.07180	−	11.4641i	0.231545	−	0.864139i
$177$	−3.03590	+	5.25833i	−0.228192	+	0.395240i
$178$	1.90192	+	7.09808i	0.142555	+	0.532023i
$179$	8.96410	+	2.40192i	0.670008	+	0.179528i	0.577759	−	0.816208i	$-0.303928\pi$
$179$	8.96410	+	2.40192i	0.670008	+	0.179528i	0.0922498	+	0.995736i	$0.470594\pi$
$180$	1.26795	−	4.73205i	0.0945074	−	0.352706i
$181$	−13.3923	−	13.3923i	−0.995442	−	0.995442i	0.00454748	−	0.999990i	$-0.498552\pi$
$181$	−13.3923	−	13.3923i	−0.995442	−	0.995442i	−0.999990	+	0.00454748i	$0.998552\pi$
$182$		0			0
$183$			3.73205i			0.275881i
$184$	−12.1962	+	3.26795i	−0.899112	+	0.240916i
$185$	−0.911543	+	0.526279i	−0.0670180	+	0.0386928i
$186$	1.36603	−	2.36603i	0.100162	−	0.173485i
$187$	−18.5263	+	4.96410i	−1.35478	+	0.363011i
$188$	7.39230	+	4.26795i	0.539139	+	0.311272i
$189$		0			0
$190$	0.973721	−	3.63397i	0.0706411	−	0.263636i
$191$	−4.33013	+	7.50000i	−0.313317	+	0.542681i	−0.979078	−	0.203484i	$-0.934774\pi$
$191$	−4.33013	+	7.50000i	−0.313317	+	0.542681i	0.665761	+	0.746165i	$0.268107\pi$
$192$	−1.07180	+	4.00000i	−0.0773503	+	0.288675i
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	0.899770	+	0.436365i	$0.143734\pi$
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	2.92820	+	2.92820i	0.210233	+	0.210233i
$195$	1.73205	−	1.73205i	0.124035	−	0.124035i
$196$		0			0
$197$	−16.6603	−	16.6603i	−1.18699	−	1.18699i	−0.977894	−	0.209100i	$-0.932947\pi$
$197$	−16.6603	−	16.6603i	−1.18699	−	1.18699i	−0.209100	−	0.977894i	$-0.567053\pi$
$198$	11.4641			0.814718
$199$	10.3301	−	5.96410i	0.732283	−	0.422784i	−0.0869736	−	0.996211i	$-0.527720\pi$
$199$	10.3301	−	5.96410i	0.732283	−	0.422784i	0.819257	+	0.573427i	$0.194386\pi$
$200$	3.07180	−	11.4641i	0.217209	−	0.810634i
$201$	2.30385	+	1.33013i	0.162501	+	0.0938199i
$202$	−23.9545	+	13.8301i	−1.68543	+	0.973084i
$203$		0			0
$204$	6.46410	−	1.73205i	0.452578	−	0.121268i
$205$	−1.14359	−	4.26795i	−0.0798720	−	0.298087i
$206$	2.36603	+	8.83013i	0.164849	+	0.615224i
$207$	−6.09808	−	10.5622i	−0.423846	−	0.734122i
$208$	14.9282	−	14.9282i	1.03508	−	1.03508i
$209$	8.80385			0.608975
$210$		0			0
$211$	−15.9282	+	15.9282i	−1.09654	+	1.09654i	−0.101731	+	0.994812i	$0.532438\pi$
$211$	−15.9282	+	15.9282i	−1.09654	+	1.09654i	−0.994812	+	0.101731i	$0.967562\pi$
$212$	−7.92820	−	2.12436i	−0.544511	−	0.145901i
$213$	−0.0717968	+	0.267949i	−0.00491943	+	0.0183596i
$214$	4.09808	+	2.36603i	0.280139	+	0.161738i
$215$	7.09808	+	4.09808i	0.484085	+	0.279486i
$216$	−8.39230			−0.571024
$217$		0			0
$218$	−1.56218	−	2.70577i	−0.105804	−	0.183258i
$219$	3.59808	−	0.964102i	0.243135	−	0.0651479i
$220$	−5.32051			−0.358709
$221$	−32.9545	−	8.83013i	−2.21676	−	0.593979i
$222$	0.607695	+	0.607695i	0.0407858	+	0.0407858i
$223$	−9.85641			−0.660034			−0.330017	−	0.943975i	$-0.607054\pi$
$223$	−9.85641			−0.660034			−0.330017	+	0.943975i	$0.607054\pi$
$224$		0			0
$225$	11.4641			0.764273
$226$	−1.46410	−	1.46410i	−0.0973906	−	0.0973906i
$227$	−11.1603	−	2.99038i	−0.740732	−	0.198479i	−0.131329	−	0.991339i	$-0.541924\pi$
$227$	−11.1603	−	2.99038i	−0.740732	−	0.198479i	−0.609403	+	0.792860i	$0.708591\pi$
$228$	−3.07180			−0.203435
$229$	−13.3301	+	3.57180i	−0.880880	+	0.236031i	−0.670787	−	0.741650i	$-0.734043\pi$
$229$	−13.3301	+	3.57180i	−0.880880	+	0.236031i	−0.210093	+	0.977681i	$0.567377\pi$
$230$	2.83013	+	4.90192i	0.186613	+	0.323223i
$231$		0			0
$232$		−	1.07180i		−	0.0703669i
$233$	0.696152	+	0.401924i	0.0456065	+	0.0263309i	0.522630	−	0.852560i	$-0.324951\pi$
$233$	0.696152	+	0.401924i	0.0456065	+	0.0263309i	−0.477023	+	0.878891i	$0.658284\pi$
$234$	17.6603	+	10.1962i	1.15449	+	0.666543i
$235$	0.990381	−	3.69615i	0.0646053	−	0.241110i
$236$	22.6603	+	6.07180i	1.47506	+	0.395240i
$237$	−6.09808	+	6.09808i	−0.396113	+	0.396113i
$238$		0			0
$239$	−8.53590			−0.552141			−0.276071	−	0.961137i	$-0.589032\pi$
$239$	−8.53590			−0.552141			−0.276071	+	0.961137i	$0.589032\pi$
$240$	1.85641			0.119831
$241$	6.96410	+	12.0622i	0.448597	+	0.776993i	0.998295	−	0.0583704i	$-0.0185905\pi$
$241$	6.96410	+	12.0622i	0.448597	+	0.776993i	−0.549698	+	0.835364i	$0.685257\pi$
$242$	0.803848	+	3.00000i	0.0516733	+	0.192847i
$243$	−3.19615	−	11.9282i	−0.205033	−	0.765195i
$244$	13.9282	−	3.73205i	0.891662	−	0.238920i
$245$		0			0
$246$	−3.12436	+	1.80385i	−0.199202	+	0.115009i
$247$	13.5622	+	7.83013i	0.862941	+	0.498219i
$248$	−10.1962	−	2.73205i	−0.647456	−	0.173485i
$249$	0.973721	−	0.562178i	0.0617070	−	0.0356266i
$250$	−11.6603			−0.737459
$251$	17.5885	+	17.5885i	1.11017	+	1.11017i	0.993126	+	0.117047i	$0.0373429\pi$
$251$	17.5885	+	17.5885i	1.11017	+	1.11017i	0.117047	+	0.993126i	$0.462657\pi$
$252$		0			0
$253$	−9.36603	+	9.36603i	−0.588837	+	0.588837i
$254$	9.46410	+	9.46410i	0.593831	+	0.593831i
$255$	−1.50000	−	2.59808i	−0.0939336	−	0.162698i
$256$	16.0000			1.00000
$257$	−9.69615	+	16.7942i	−0.604829	+	1.04760i	0.387249	+	0.921975i	$0.373425\pi$
$257$	−9.69615	+	16.7942i	−0.604829	+	1.04760i	−0.992078	+	0.125620i	$0.959908\pi$
$258$	1.73205	−	6.46410i	0.107833	−	0.402437i
$259$		0			0
$260$	−8.19615	−	4.73205i	−0.508304	−	0.293469i
$261$	1.00000	−	0.267949i	0.0618984	−	0.0165856i
$262$	−5.56218	+	9.63397i	−0.343632	+	0.595189i
$263$	3.99038	−	2.30385i	0.246057	−	0.142061i	−0.371900	−	0.928273i	$-0.621294\pi$
$263$	3.99038	−	2.30385i	0.246057	−	0.142061i	0.617958	+	0.786211i	$0.287960\pi$
$264$	1.12436	+	4.19615i	0.0691993	+	0.258255i
$265$			3.67949i			0.226029i
$266$		0			0
$267$	−1.90192	−	1.90192i	−0.116396	−	0.116396i
$268$	2.66025	−	9.92820i	0.162501	−	0.606462i
$269$	−9.79423	−	2.62436i	−0.597165	−	0.160010i	−0.0524390	−	0.998624i	$-0.516700\pi$
$269$	−9.79423	−	2.62436i	−0.597165	−	0.160010i	−0.544726	+	0.838614i	$0.683366\pi$
$270$	0.973721	+	3.63397i	0.0592587	+	0.221157i
$271$	6.06218	−	10.5000i	0.368251	−	0.637830i	−0.621041	−	0.783778i	$-0.713290\pi$
$271$	6.06218	−	10.5000i	0.368251	−	0.637830i	0.989292	+	0.145948i	$0.0466233\pi$
$272$	−12.9282	−	22.3923i	−0.783887	−	1.35773i
$273$		0			0
$274$	24.0263	+	6.43782i	1.45148	+	0.388923i
$275$	−3.22243	−	12.0263i	−0.194320	−	0.725212i
$276$	3.26795	−	3.26795i	0.196707	−	0.196707i
$277$	−1.20577	+	4.50000i	−0.0724478	+	0.270379i	−0.992642	−	0.121082i	$-0.961364\pi$
$277$	−1.20577	+	4.50000i	−0.0724478	+	0.270379i	0.920195	+	0.391461i	$0.128030\pi$
$278$			23.8564i			1.43081i
$279$		−	10.1962i		−	0.610428i
$280$		0			0
$281$			0.928203i			0.0553720i	0.999617	+	0.0276860i	$0.00881385\pi$
$281$			0.928203i			0.0553720i	−0.999617	+	0.0276860i	$0.991186\pi$
$282$	−3.12436			−0.186053
$283$	3.89230	−	14.5263i	0.231374	−	0.863498i	−0.748377	−	0.663274i	$-0.769166\pi$
$283$	3.89230	−	14.5263i	0.231374	−	0.863498i	0.979750	−	0.200224i	$-0.0641669\pi$
$284$	1.07180			0.0635994
$285$	0.356406	+	1.33013i	0.0211117	+	0.0787899i
$286$	5.73205	−	21.3923i	0.338943	−	1.26495i
$287$		0			0
$288$	4.00000	+	14.9282i	0.235702	+	0.879653i
$289$	−12.3923	+	21.4641i	−0.728959	+	1.26259i
$290$	−0.464102	+	0.124356i	−0.0272530	+	0.00730242i
$291$	−1.46410	−	0.392305i	−0.0858272	−	0.0229973i
$292$	−7.19615	−	12.4641i	−0.421123	−	0.729406i
$293$	7.92820	+	7.92820i	0.463171	+	0.463171i	0.899693	−	0.436523i	$-0.143790\pi$
$293$	7.92820	+	7.92820i	0.463171	+	0.463171i	−0.436523	+	0.899693i	$0.643790\pi$
$294$		0			0
$295$		−	10.5167i		−	0.612304i
$296$	1.66025	−	2.87564i	0.0965003	−	0.167143i
$297$	−7.62436	+	4.40192i	−0.442410	+	0.255426i
$298$	−9.63397	−	5.56218i	−0.558081	−	0.322208i
$299$	−22.7583	+	6.09808i	−1.31615	+	0.352661i
$300$	1.12436	+	4.19615i	0.0649147	+	0.242265i
$301$		0			0
$302$	15.5622	+	4.16987i	0.895503	+	0.239949i
$303$	5.06218	−	8.76795i	0.290815	−	0.503706i
$304$	3.07180	+	11.4641i	0.176180	+	0.657511i
$305$	−3.23205	−	5.59808i	−0.185067	−	0.320545i
$306$	17.6603	−	17.6603i	1.00957	−	1.00957i
$307$	−9.00000	+	9.00000i	−0.513657	+	0.513657i	−0.915645	−	0.401988i	$-0.868319\pi$
$307$	−9.00000	+	9.00000i	−0.513657	+	0.513657i	0.401988	+	0.915645i	$0.368319\pi$
$308$		0			0
$309$	−2.36603	−	2.36603i	−0.134598	−	0.134598i
$310$			4.73205i			0.268762i
$311$	−5.59808	+	3.23205i	−0.317438	+	0.183273i	−0.650250	−	0.759720i	$-0.725336\pi$
$311$	−5.59808	+	3.23205i	−0.317438	+	0.183273i	0.332812	+	0.942993i	$0.392002\pi$
$312$	−2.00000	+	7.46410i	−0.113228	+	0.422572i
$313$	18.6962	+	10.7942i	1.05677	+	0.610126i	0.924537	−	0.381093i	$-0.124452\pi$
$313$	18.6962	+	10.7942i	1.05677	+	0.610126i	0.132232	+	0.991219i	$0.457786\pi$
$314$	13.3660	+	23.1506i	0.754288	+	1.30647i
$315$		0			0
$316$	28.8564	+	16.6603i	1.62330	+	0.937213i
$317$	−3.79423	−	14.1603i	−0.213105	−	0.795319i	−0.986825	−	0.161791i	$-0.948273\pi$
$317$	−3.79423	−	14.1603i	−0.213105	−	0.795319i	0.773720	−	0.633528i	$-0.218394\pi$
$318$	2.90192	−	0.777568i	0.162732	−	0.0436039i
$319$	−0.562178	−	0.973721i	−0.0314759	−	0.0545179i
$320$	−1.85641	−	6.92820i	−0.103776	−	0.387298i
$321$	−1.73205			−0.0966736
$322$		0			0
$323$	13.5622	−	13.5622i	0.754620	−	0.754620i
$324$	−11.5359	+	6.66025i	−0.640883	+	0.370014i
$325$	5.73205	−	21.3923i	0.317957	−	1.18663i
$326$	−8.83013	+	15.2942i	−0.489056	+	0.847069i
$327$	0.990381	+	0.571797i	0.0547682	+	0.0316204i
$328$	9.85641	+	9.85641i	0.544229	+	0.544229i
$329$		0			0
$330$	1.68653	−	0.973721i	0.0928406	−	0.0536016i
$331$	−19.6244	+	5.25833i	−1.07865	+	0.289024i	−0.754044	−	0.656824i	$-0.771899\pi$
$331$	−19.6244	+	5.25833i	−1.07865	+	0.289024i	−0.324609	+	0.945848i	$0.605233\pi$
$332$	−3.07180	−	3.07180i	−0.168587	−	0.168587i
$333$	3.09808	+	0.830127i	0.169774	+	0.0454907i
$334$	21.8564	−	21.8564i	1.19593	−	1.19593i
$335$	−4.60770			−0.251745
$336$		0			0
$337$	−6.14359			−0.334663			−0.167331	−	0.985901i	$-0.553515\pi$
$337$	−6.14359			−0.334663			−0.167331	+	0.985901i	$0.553515\pi$
$338$	14.8564	−	14.8564i	0.808082	−	0.808082i
$339$	0.732051	+	0.196152i	0.0397595	+	0.0106535i
$340$	−8.19615	+	8.19615i	−0.444499	+	0.444499i
$341$	−10.6962	+	2.86603i	−0.579229	+	0.155204i
$342$	−9.92820	+	5.73205i	−0.536856	+	0.309954i
$343$		0			0
$344$	−25.8564			−1.39408
$345$	−1.79423	−	1.03590i	−0.0965980	−	0.0557709i
$346$	1.63397	−	2.83013i	0.0878430	−	0.152149i
$347$	−6.30385	+	23.5263i	−0.338408	+	1.26296i	0.561718	+	0.827329i	$0.310140\pi$
$347$	−6.30385	+	23.5263i	−0.338408	+	1.26296i	−0.900127	+	0.435628i	$0.856526\pi$
$348$	0.196152	+	0.339746i	0.0105149	+	0.0182123i
$349$	−6.12436	+	6.12436i	−0.327829	+	0.327829i	−0.851761	−	0.523931i	$-0.824465\pi$
$349$	−6.12436	+	6.12436i	−0.327829	+	0.327829i	0.523931	+	0.851761i	$0.324465\pi$
$350$		0			0
$351$	−15.6603			−0.835883
$352$	14.5359	−	8.39230i	0.774766	−	0.447311i
$353$	−13.8923	−	24.0622i	−0.739413	−	1.28070i	−0.952760	−	0.303724i	$-0.901770\pi$
$353$	−13.8923	−	24.0622i	−0.739413	−	1.28070i	0.213347	−	0.976976i	$-0.431563\pi$
$354$	−8.29423	+	2.22243i	−0.440833	+	0.118121i
$355$	−0.124356	−	0.464102i	−0.00660011	−	0.0246320i
$356$	−5.19615	+	9.00000i	−0.275396	+	0.476999i
$357$		0			0
$358$	6.56218	+	11.3660i	0.346822	+	0.600713i
$359$	−3.86603	−	2.23205i	−0.204041	−	0.117803i	0.394498	−	0.918897i	$-0.370919\pi$
$359$	−3.86603	−	2.23205i	−0.204041	−	0.117803i	−0.598539	+	0.801094i	$0.704252\pi$
$360$	6.00000	−	3.46410i	0.316228	−	0.182574i
$361$	8.83013	−	5.09808i	0.464744	−	0.268320i
$362$		−	26.7846i		−	1.40777i
$363$	−0.803848	−	0.803848i	−0.0421911	−	0.0421911i
$364$		0			0
$365$	−4.56218	+	4.56218i	−0.238795	+	0.238795i
$366$	−3.73205	+	3.73205i	−0.195077	+	0.195077i
$367$	3.06218	+	5.30385i	0.159844	+	0.276859i	0.934812	−	0.355142i	$-0.115567\pi$
$367$	3.06218	+	5.30385i	0.159844	+	0.276859i	−0.774968	+	0.632000i	$0.782234\pi$
$368$	−15.4641	−	8.92820i	−0.806122	−	0.465415i
$369$	−6.73205	+	11.6603i	−0.350457	+	0.607009i
$370$	−1.43782	−	0.385263i	−0.0747488	−	0.0200289i
$371$		0			0
$372$	3.73205	−	1.00000i	0.193498	−	0.0518476i
$373$	0.866025	−	0.232051i	0.0448411	−	0.0120151i	−0.236329	−	0.971673i	$-0.575944\pi$
$373$	0.866025	−	0.232051i	0.0448411	−	0.0120151i	0.281170	+	0.959658i	$0.409278\pi$
$374$	−23.4904	−	13.5622i	−1.21466	−	0.701284i
$375$	3.69615	−	2.13397i	0.190868	−	0.110198i
$376$	3.12436	+	11.6603i	0.161126	+	0.601332i
$377$		−	2.00000i		−	0.103005i
$378$		0			0
$379$	0.124356	+	0.124356i	0.00638772	+	0.00638772i	0.710293	−	0.703906i	$-0.248562\pi$
$379$	0.124356	+	0.124356i	0.00638772	+	0.00638772i	−0.703906	+	0.710293i	$0.748562\pi$
$380$	4.60770	−	2.66025i	0.236370	−	0.136468i
$381$	−4.73205	−	1.26795i	−0.242430	−	0.0649590i
$382$	−11.8301	+	3.16987i	−0.605282	+	0.162185i
$383$	−12.5981	+	21.8205i	−0.643732	+	1.11498i	0.340861	+	0.940114i	$0.389281\pi$
$383$	−12.5981	+	21.8205i	−0.643732	+	1.11498i	−0.984593	+	0.174862i	$0.944052\pi$
$384$	−5.07180	+	2.92820i	−0.258819	+	0.149429i
$385$		0			0
$386$	−8.41858	+	31.4186i	−0.428495	+	1.59916i
$387$	−6.46410	−	24.1244i	−0.328589	−	1.22631i
$388$			5.85641i			0.297314i
$389$	5.99038	−	22.3564i	0.303724	−	1.13351i	−0.630313	−	0.776341i	$-0.717074\pi$
$389$	5.99038	−	22.3564i	0.303724	−	1.13351i	0.934038	−	0.357174i	$-0.116260\pi$
$390$	3.46410			0.175412
$391$			28.8564i			1.45933i
$392$		0			0
$393$		−	4.07180i		−	0.205395i
$394$		−	33.3205i		−	1.67866i
$395$	3.86603	−	14.4282i	0.194521	−	0.725962i
$396$	11.4641	+	11.4641i	0.576093	+	0.576093i
$397$	−6.86603	−	25.6244i	−0.344596	−	1.28605i	−0.893084	−	0.449891i	$-0.851463\pi$
$397$	−6.86603	−	25.6244i	−0.344596	−	1.28605i	0.548488	−	0.836159i	$-0.315204\pi$
$398$	16.2942	+	4.36603i	0.816756	+	0.218849i
$399$		0			0
$400$	14.5359	−	8.39230i	0.726795	−	0.419615i
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$	0.973721	+	3.63397i	0.0485648	+	0.181246i
$403$	−19.0263	−	5.09808i	−0.947766	−	0.253953i
$404$	−37.7846	−	10.1244i	−1.87985	−	0.503706i
$405$	4.22243	+	4.22243i	0.209814	+	0.209814i
$406$		0			0
$407$		−	3.48334i		−	0.172663i
$408$	8.19615	+	4.73205i	0.405770	+	0.234271i
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	0.673830	+	0.738886i	$0.264648\pi$
$410$	3.12436	−	5.41154i	0.154301	−	0.267257i
$411$	−8.79423	+	2.35641i	−0.433787	+	0.116233i
$412$	−6.46410	+	11.1962i	−0.318463	+	0.551595i
$413$		0			0
$414$	4.46410	−	16.6603i	0.219399	−	0.818807i
$415$	−0.973721	+	1.68653i	−0.0477981	+	0.0827887i
$416$	29.8564			1.46383
$417$	−4.36603	−	7.56218i	−0.213805	−	0.370321i
$418$	8.80385	+	8.80385i	0.430610	+	0.430610i
$419$	19.0000	−	19.0000i	0.928211	−	0.928211i	−0.0693796	−	0.997590i	$-0.522102\pi$
$419$	19.0000	−	19.0000i	0.928211	−	0.928211i	0.997590	+	0.0693796i	$0.0221020\pi$
$420$		0			0
$421$	8.66025	+	8.66025i	0.422075	+	0.422075i	0.885918	−	0.463843i	$-0.153530\pi$
$421$	8.66025	+	8.66025i	0.422075	+	0.422075i	−0.463843	+	0.885918i	$0.653530\pi$
$422$	−31.8564			−1.55075
$423$	−10.0981	+	5.83013i	−0.490985	+	0.283470i
$424$	−5.80385	−	10.0526i	−0.281860	−	0.488195i
$425$	−23.4904	−	13.5622i	−1.13945	−	0.657862i
$426$	−0.339746	+	0.196152i	−0.0164607	+	0.00950362i
$427$		0			0
$428$	1.73205	+	6.46410i	0.0837218	+	0.312454i
$429$	2.09808	+	7.83013i	0.101296	+	0.378042i
$430$	3.00000	+	11.1962i	0.144673	+	0.539926i
$431$	−15.3301	−	26.5526i	−0.738426	−	1.27899i	−0.953204	−	0.302329i	$-0.902236\pi$
$431$	−15.3301	−	26.5526i	−0.738426	−	1.27899i	0.214777	−	0.976663i	$-0.431097\pi$
$432$	−8.39230	−	8.39230i	−0.403775	−	0.403775i
$433$	33.1769			1.59438			0.797190	−	0.603728i	$-0.206319\pi$
$433$	33.1769			1.59438			0.797190	+	0.603728i	$0.206319\pi$
$434$		0			0
$435$	0.124356	−	0.124356i	0.00596240	−	0.00596240i
$436$	1.14359	−	4.26795i	0.0547682	−	0.204398i
$437$	3.42820	−	12.7942i	0.163993	−	0.612031i
$438$	4.56218	+	2.63397i	0.217989	+	0.125856i
$439$	−6.52628	−	3.76795i	−0.311482	−	0.179834i	0.336107	−	0.941824i	$-0.390890\pi$
$439$	−6.52628	−	3.76795i	−0.311482	−	0.179834i	−0.647590	+	0.761989i	$0.724223\pi$
$440$	−5.32051	−	5.32051i	−0.253645	−	0.253645i
$441$		0			0
$442$	−24.1244	−	41.7846i	−1.14748	−	1.98749i
$443$	−10.4282	+	2.79423i	−0.495459	+	0.132758i	−0.497892	−	0.867239i	$-0.665892\pi$
$443$	−10.4282	+	2.79423i	−0.495459	+	0.132758i	0.00243278	+	0.999997i	$0.499226\pi$
$444$			1.21539i			0.0576799i
$445$	4.50000	+	1.20577i	0.213320	+	0.0571590i
$446$	−9.85641	−	9.85641i	−0.466714	−	0.466714i
$447$	4.07180			0.192589
$448$		0			0
$449$	−23.3205			−1.10056			−0.550281	−	0.834979i	$-0.685480\pi$
$449$	−23.3205			−1.10056			−0.550281	+	0.834979i	$0.685480\pi$
$450$	11.4641	+	11.4641i	0.540423	+	0.540423i
$451$	14.1244	+	3.78461i	0.665090	+	0.178210i
$452$		−	2.92820i		−	0.137731i
$453$	−5.69615	+	1.52628i	−0.267629	+	0.0717109i
$454$	−8.16987	−	14.1506i	−0.383431	−	0.664122i
$455$		0			0
$456$	−3.07180	−	3.07180i	−0.143850	−	0.143850i
$457$	16.2846	+	9.40192i	0.761762	+	0.439803i	0.829928	−	0.557871i	$-0.188381\pi$
$457$	16.2846	+	9.40192i	0.761762	+	0.439803i	−0.0681661	+	0.997674i	$0.521715\pi$
$458$	−16.9019	−	9.75833i	−0.789775	−	0.455977i
$459$	−4.96410	+	18.5263i	−0.231704	+	0.864733i
$460$	−2.07180	+	7.73205i	−0.0965980	+	0.360509i
$461$	−18.6603	+	18.6603i	−0.869095	+	0.869095i	−0.992372	−	0.123278i	$-0.960659\pi$
$461$	−18.6603	+	18.6603i	−0.869095	+	0.869095i	0.123278	+	0.992372i	$0.460659\pi$
$462$		0			0
$463$	2.14359			0.0996212			0.0498106	−	0.998759i	$-0.484138\pi$
$463$	2.14359			0.0996212			0.0498106	+	0.998759i	$0.484138\pi$
$464$	1.07180	−	1.07180i	0.0497569	−	0.0497569i
$465$	−0.866025	−	1.50000i	−0.0401610	−	0.0695608i
$466$	0.294229	+	1.09808i	0.0136299	+	0.0508674i
$467$	6.96410	+	25.9904i	0.322260	+	1.20269i	0.917038	+	0.398801i	$0.130574\pi$
$467$	6.96410	+	25.9904i	0.322260	+	1.20269i	−0.594777	+	0.803890i	$0.702760\pi$
$468$	7.46410	+	27.8564i	0.345028	+	1.28766i
$469$		0			0
$470$	4.68653	−	2.70577i	0.216174	−	0.124808i
$471$	−8.47372	−	4.89230i	−0.390448	−	0.225426i
$472$	16.5885	+	28.7321i	0.763546	+	1.32250i
$473$	−23.4904	+	13.5622i	−1.08009	+	0.623590i
$474$	−12.1962			−0.560188
$475$	8.80385	+	8.80385i	0.403948	+	0.403948i
$476$		0			0
$477$	7.92820	−	7.92820i	0.363007	−	0.363007i
$478$	−8.53590	−	8.53590i	−0.390423	−	0.390423i
$479$	7.79423	+	13.5000i	0.356127	+	0.616831i	0.987310	−	0.158803i	$-0.0507636\pi$
$479$	7.79423	+	13.5000i	0.356127	+	0.616831i	−0.631183	+	0.775634i	$0.717430\pi$
$480$	1.85641	+	1.85641i	0.0847330	+	0.0847330i
$481$	3.09808	−	5.36603i	0.141260	−	0.244670i
$482$	−5.09808	+	19.0263i	−0.232211	+	0.866623i
$483$		0			0
$484$	−2.19615	+	3.80385i	−0.0998251	+	0.172902i
$485$	2.53590	−	0.679492i	0.115149	−	0.0308541i
$486$	8.73205	−	15.1244i	0.396094	−	0.686055i
$487$	10.6699	−	6.16025i	0.483498	−	0.279148i	−0.238375	−	0.971173i	$-0.576615\pi$
$487$	10.6699	−	6.16025i	0.483498	−	0.279148i	0.721873	+	0.692025i	$0.243281\pi$
$488$	17.6603	+	10.1962i	0.799442	+	0.461558i
$489$		−	6.46410i		−	0.292317i
$490$		0			0
$491$	−3.58846	−	3.58846i	−0.161945	−	0.161945i	0.621483	−	0.783428i	$-0.286531\pi$
$491$	−3.58846	−	3.58846i	−0.161945	−	0.161945i	−0.783428	+	0.621483i	$0.786531\pi$
$492$	−4.92820	−	1.32051i	−0.222181	−	0.0595331i
$493$	−2.36603	−	0.633975i	−0.106560	−	0.0285528i
$494$	5.73205	+	21.3923i	0.257897	+	0.962485i
$495$	3.63397	−	6.29423i	0.163335	−	0.282905i
$496$	−7.46410	−	12.9282i	−0.335148	−	0.580493i
$497$		0			0
$498$	1.53590	+	0.411543i	0.0688253	+	0.0184417i
$499$	6.69615	+	24.9904i	0.299761	+	1.11872i	0.937362	+	0.348356i	$0.113260\pi$
$499$	6.69615	+	24.9904i	0.299761	+	1.11872i	−0.637601	+	0.770367i	$0.720073\pi$
$500$	−11.6603	−	11.6603i	−0.521462	−	0.521462i
$501$	−2.92820	+	10.9282i	−0.130822	+	0.488236i
$502$			35.1769i			1.57002i
$503$		−	31.8564i		−	1.42041i	−0.703996	−	0.710203i	$-0.748603\pi$
$503$		−	31.8564i		−	1.42041i	0.703996	−	0.710203i	$-0.251397\pi$
$504$		0			0
$505$			17.5359i			0.780337i
$506$	−18.7321			−0.832741
$507$	−1.99038	+	7.42820i	−0.0883959	+	0.329898i
$508$			18.9282i			0.839803i
$509$	−2.52628	−	9.42820i	−0.111975	−	0.417898i	0.887067	−	0.461640i	$-0.152739\pi$
$509$	−2.52628	−	9.42820i	−0.111975	−	0.417898i	−0.999043	+	0.0437420i	$0.986072\pi$
$510$	1.09808	−	4.09808i	0.0486236	−	0.181466i
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	4.40192	−	7.62436i	0.194350	−	0.336624i
$514$	−26.4904	+	7.09808i	−1.16844	+	0.313083i
$515$	5.59808	+	1.50000i	0.246681	+	0.0660979i
$516$	8.19615	−	4.73205i	0.360815	−	0.208317i
$517$	8.95448	+	8.95448i	0.393818	+	0.393818i
$518$		0			0
$519$			1.19615i			0.0525053i
$520$	−3.46410	−	12.9282i	−0.151911	−	0.566939i
$521$	13.3756	−	7.72243i	0.585998	−	0.338326i	−0.177516	−	0.984118i	$-0.556806\pi$
$521$	13.3756	−	7.72243i	0.585998	−	0.338326i	0.763513	+	0.645792i	$0.223473\pi$
$522$	1.26795	+	0.732051i	0.0554966	+	0.0320410i
$523$	32.2846	−	8.65064i	1.41171	−	0.378266i	0.529173	−	0.848514i	$-0.322502\pi$
$523$	32.2846	−	8.65064i	1.41171	−	0.378266i	0.882534	+	0.470248i	$0.155836\pi$
$524$	−15.1962	+	4.07180i	−0.663847	+	0.177877i
$525$		0			0
$526$	6.29423	+	1.68653i	0.274441	+	0.0735364i
$527$	−12.0622	+	20.8923i	−0.525437	+	0.910083i
$528$	−3.07180	+	5.32051i	−0.133683	+	0.231545i
$529$	−1.53590	−	2.66025i	−0.0667782	−	0.115663i
$530$	−3.67949	+	3.67949i	−0.159827	+	0.159827i
$531$	−22.6603	+	22.6603i	−0.983371	+	0.983371i
$532$		0			0
$533$	18.3923	+	18.3923i	0.796659	+	0.796659i
$534$		−	3.80385i		−	0.164609i
$535$	2.59808	−	1.50000i	0.112325	−	0.0648507i
$536$	12.5885	−	7.26795i	0.543739	−	0.313928i
$537$	−4.16025	−	2.40192i	−0.179528	−	0.103651i
$538$	−7.16987	−	12.4186i	−0.309115	−	0.535403i
$539$		0			0
$540$	−2.66025	+	4.60770i	−0.114479	+	0.198284i
$541$	2.47372	+	9.23205i	0.106354	+	0.396917i	0.998495	−	0.0548389i	$-0.0174645\pi$
$541$	2.47372	+	9.23205i	0.106354	+	0.396917i	−0.892142	+	0.451756i	$0.850798\pi$
$542$	16.5622	−	4.43782i	0.711406	−	0.190621i
$543$	4.90192	+	8.49038i	0.210362	+	0.364357i
$544$	9.46410	−	35.3205i	0.405770	−	1.51435i
$545$	−1.98076			−0.0848465
$546$		0			0
$547$	−23.0526	+	23.0526i	−0.985656	+	0.985656i	−0.999899	−	0.0142423i	$-0.995466\pi$
$547$	−23.0526	+	23.0526i	−0.985656	+	0.985656i	0.0142423	+	0.999899i	$0.495466\pi$
$548$	17.5885	+	30.4641i	0.751342	+	1.30136i
$549$	−5.09808	+	19.0263i	−0.217581	+	0.812022i
$550$	8.80385	−	15.2487i	0.375397	−	0.650207i
$551$	0.973721	+	0.562178i	0.0414819	+	0.0239496i
$552$	6.53590			0.278186
$553$		0			0
$554$	−5.70577	+	3.29423i	−0.242415	+	0.139958i
$555$	0.526279	−	0.141016i	0.0223393	−	0.00598580i
$556$	−23.8564	+	23.8564i	−1.01174	+	1.01174i
$557$	6.59808	+	1.76795i	0.279569	+	0.0749104i	0.395879	−	0.918303i	$-0.370440\pi$
$557$	6.59808	+	1.76795i	0.279569	+	0.0749104i	−0.116310	+	0.993213i	$0.537107\pi$
$558$	10.1962	−	10.1962i	0.431638	−	0.431638i
$559$	−48.2487			−2.04070
$560$		0			0
$561$	9.92820			0.419169
$562$	−0.928203	+	0.928203i	−0.0391539	+	0.0391539i
$563$	2.42820	+	0.650635i	0.102337	+	0.0274210i	0.309624	−	0.950859i	$-0.399797\pi$
$563$	2.42820	+	0.650635i	0.102337	+	0.0274210i	−0.207287	+	0.978280i	$0.566464\pi$
$564$	−3.12436	−	3.12436i	−0.131559	−	0.131559i
$565$	−1.26795	+	0.339746i	−0.0533430	+	0.0142932i
$566$	18.4186	−	10.6340i	0.774191	−	0.446979i
$567$		0			0
$568$	1.07180	+	1.07180i	0.0449716	+	0.0449716i
$569$	−5.08846	−	2.93782i	−0.213319	−	0.123160i	0.389534	−	0.921012i	$-0.372636\pi$
$569$	−5.08846	−	2.93782i	−0.213319	−	0.123160i	−0.602853	+	0.797852i	$0.705969\pi$
$570$	−0.973721	+	1.68653i	−0.0407847	+	0.0706411i
$571$	−7.16025	+	26.7224i	−0.299647	+	1.11830i	0.637809	+	0.770195i	$0.279841\pi$
$571$	−7.16025	+	26.7224i	−0.299647	+	1.11830i	−0.937456	+	0.348104i	$0.886826\pi$
$572$	27.1244	−	15.6603i	1.13413	−	0.654788i
$573$	3.16987	−	3.16987i	0.132423	−	0.132423i
$574$		0			0
$575$	−18.7321			−0.781181
$576$	−10.9282	+	18.9282i	−0.455342	+	0.788675i
$577$	6.62436	+	11.4737i	0.275776	+	0.477657i	0.970330	−	0.241782i	$-0.0777320\pi$
$577$	6.62436	+	11.4737i	0.275776	+	0.477657i	−0.694555	+	0.719440i	$0.744399\pi$
$578$	−33.8564	+	9.07180i	−1.40824	+	0.377337i
$579$	−3.08142	−	11.5000i	−0.128059	−	0.477924i
$580$	−0.588457	−	0.339746i	−0.0244344	−	0.0141072i
$581$		0			0
$582$	−1.07180	−	1.85641i	−0.0444274	−	0.0769505i
$583$	−10.5455	−	6.08846i	−0.436751	−	0.252158i
$584$	5.26795	−	19.6603i	0.217989	−	0.813547i
$585$	11.1962	−	6.46410i	0.462904	−	0.267258i
$586$			15.8564i			0.655022i
$587$	−21.9282	−	21.9282i	−0.905074	−	0.905074i	0.0907957	−	0.995870i	$-0.471059\pi$
$587$	−21.9282	−	21.9282i	−0.905074	−	0.905074i	−0.995870	+	0.0907957i	$0.971059\pi$
$588$		0			0
$589$	7.83013	−	7.83013i	0.322635	−	0.322635i
$590$	10.5167	−	10.5167i	0.432964	−	0.432964i
$591$	6.09808	+	10.5622i	0.250841	+	0.434470i
$592$	4.53590	−	1.21539i	0.186424	−	0.0499522i
$593$	−5.69615	+	9.86603i	−0.233913	+	0.405149i	−0.958956	−	0.283554i	$-0.908486\pi$
$593$	−5.69615	+	9.86603i	−0.233913	+	0.405149i	0.725043	+	0.688703i	$0.241820\pi$
$594$	−12.0263	−	3.22243i	−0.493444	−	0.132218i
$595$		0			0
$596$	−4.07180	−	15.1962i	−0.166787	−	0.622459i
$597$	−5.96410	+	1.59808i	−0.244094	+	0.0654049i
$598$	−28.8564	−	16.6603i	−1.18003	−	0.681288i
$599$	16.6699	−	9.62436i	0.681113	−	0.393241i	−0.119162	−	0.992875i	$-0.538021\pi$
$599$	16.6699	−	9.62436i	0.681113	−	0.393241i	0.800274	+	0.599634i	$0.204687\pi$
$600$	−3.07180	+	5.32051i	−0.125406	+	0.217209i
$601$			10.0000i			0.407909i	0.978980	+	0.203954i	$0.0653794\pi$
$601$			10.0000i			0.407909i	−0.978980	+	0.203954i	$0.934621\pi$
$602$		0			0
$603$	9.92820	+	9.92820i	0.404308	+	0.404308i
$604$	11.3923	+	19.7321i	0.463546	+	0.802886i
$605$	1.90192	+	0.509619i	0.0773242	+	0.0207190i
$606$	13.8301	−	3.70577i	0.561811	−	0.150537i
$607$	8.52628	−	14.7679i	0.346071	−	0.599413i	−0.639477	−	0.768810i	$-0.720849\pi$
$607$	8.52628	−	14.7679i	0.346071	−	0.599413i	0.985548	+	0.169398i	$0.0541823\pi$
$608$	−8.39230	+	14.5359i	−0.340353	+	0.589509i
$609$		0			0
$610$	2.36603	−	8.83013i	0.0957976	−	0.357521i
$611$	5.83013	+	21.7583i	0.235862	+	0.880248i
$612$	35.3205			1.42775
$613$	2.47372	−	9.23205i	0.0999126	−	0.372879i	−0.897806	−	0.440392i	$-0.854840\pi$
$613$	2.47372	−	9.23205i	0.0999126	−	0.372879i	0.997718	+	0.0675126i	$0.0215063\pi$
$614$	−18.0000			−0.726421
$615$			2.28719i			0.0922283i
$616$		0			0
$617$		−	0.535898i		−	0.0215745i	−0.999942	−	0.0107872i	$-0.996566\pi$
$617$		−	0.535898i		−	0.0215745i	0.999942	−	0.0107872i	$-0.00343375\pi$
$618$		−	4.73205i		−	0.190351i
$619$	−5.10770	+	19.0622i	−0.205296	+	0.766174i	0.784064	+	0.620680i	$0.213144\pi$
$619$	−5.10770	+	19.0622i	−0.205296	+	0.766174i	−0.989359	+	0.145493i	$0.953523\pi$
$620$	−4.73205	+	4.73205i	−0.190044	+	0.190044i
$621$	3.42820	+	12.7942i	0.137569	+	0.513415i
$622$	−8.83013	−	2.36603i	−0.354056	−	0.0948690i
$623$		0			0
$624$	−9.46410	+	5.46410i	−0.378867	+	0.218739i
$625$	6.79423	−	11.7679i	0.271769	−	0.470718i
$626$	7.90192	+	29.4904i	0.315824	+	1.17867i
$627$	−4.40192	−	1.17949i	−0.175796	−	0.0471044i
$628$	−9.78461	+	36.5167i	−0.390448	+	1.45717i
$629$	−5.36603	−	5.36603i	−0.213957	−	0.213957i
$630$		0			0
$631$		−	32.2487i		−	1.28380i	−0.766788	−	0.641900i	$-0.778146\pi$
$631$		−	32.2487i		−	1.28380i	0.766788	−	0.641900i	$-0.221854\pi$
$632$	12.1962	+	45.5167i	0.485137	+	1.81056i
$633$	10.0981	−	5.83013i	0.401362	−	0.231727i
$634$	10.3660	−	17.9545i	0.411687	−	0.713064i
$635$	8.19615	−	2.19615i	0.325254	−	0.0871517i
$636$	3.67949	+	2.12436i	0.145901	+	0.0842362i
$637$		0			0
$638$	0.411543	−	1.53590i	0.0162931	−	0.0608068i
$639$	−0.732051	+	1.26795i	−0.0289595	+	0.0501593i
$640$	5.07180	−	8.78461i	0.200480	−	0.347242i
$641$	5.57180	+	9.65064i	0.220073	+	0.381177i	0.954830	−	0.297153i	$-0.0960372\pi$
$641$	5.57180	+	9.65064i	0.220073	+	0.381177i	−0.734757	+	0.678330i	$0.762704\pi$
$642$	−1.73205	−	1.73205i	−0.0683586	−	0.0683586i
$643$	5.39230	−	5.39230i	0.212652	−	0.212652i	−0.592741	−	0.805393i	$-0.701954\pi$
$643$	5.39230	−	5.39230i	0.212652	−	0.212652i	0.805393	+	0.592741i	$0.201954\pi$
$644$		0			0
$645$	−3.00000	−	3.00000i	−0.118125	−	0.118125i
$646$	27.1244			1.06719
$647$	−30.8660	+	17.8205i	−1.21347	+	0.700596i	−0.963513	−	0.267661i	$-0.913749\pi$
$647$	−30.8660	+	17.8205i	−1.21347	+	0.700596i	−0.249955	+	0.968257i	$0.580416\pi$
$648$	−18.1962	−	4.87564i	−0.714812	−	0.191533i
$649$	30.1410	+	17.4019i	1.18314	+	0.683085i
$650$	27.1244	−	15.6603i	1.06390	−	0.614246i
$651$		0			0
$652$	−24.1244	+	6.46410i	−0.944783	+	0.253154i
$653$	−8.72243	−	32.5526i	−0.341335	−	1.27388i	−0.896836	−	0.442364i	$-0.854140\pi$
$653$	−8.72243	−	32.5526i	−0.341335	−	1.27388i	0.555501	−	0.831516i	$-0.312527\pi$
$654$	0.418584	+	1.56218i	0.0163679	+	0.0610860i
$655$	3.52628	+	6.10770i	0.137783	+	0.238647i
$656$			19.7128i			0.769656i
$657$	19.6603			0.767020
$658$		0			0
$659$	18.8564	−	18.8564i	0.734541	−	0.734541i	−0.236975	−	0.971516i	$-0.576156\pi$
$659$	18.8564	−	18.8564i	0.734541	−	0.734541i	0.971516	+	0.236975i	$0.0761558\pi$
$660$	2.66025	+	0.712813i	0.103550	+	0.0277462i
$661$	5.93782	−	22.1603i	0.230955	−	0.861934i	−0.748976	−	0.662597i	$-0.769454\pi$
$661$	5.93782	−	22.1603i	0.230955	−	0.861934i	0.979931	−	0.199337i	$-0.0638789\pi$
$662$	−24.8827	−	14.3660i	−0.967093	−	0.558351i
$663$	15.2942	+	8.83013i	0.593979	+	0.342934i
$664$		−	6.14359i		−	0.238418i
$665$		0			0
$666$	2.26795	+	3.92820i	0.0878812	+	0.152215i
$667$	−1.63397	+	0.437822i	−0.0632677	+	0.0169525i
$668$	43.7128			1.69130
$669$	4.92820	+	1.32051i	0.190535	+	0.0510538i
$670$	−4.60770	−	4.60770i	−0.178011	−	0.178011i
$671$	21.3923			0.825841
$672$		0			0
$673$	40.7846			1.57213			0.786066	−	0.618143i	$-0.212115\pi$
$673$	40.7846			1.57213			0.786066	+	0.618143i	$0.212115\pi$
$674$	−6.14359	−	6.14359i	−0.236642	−	0.236642i
$675$	−12.0263	−	3.22243i	−0.462892	−	0.124031i
$676$	29.7128			1.14280
$677$	42.7224	−	11.4474i	1.64196	−	0.439961i	0.684611	−	0.728908i	$-0.259972\pi$
$677$	42.7224	−	11.4474i	1.64196	−	0.439961i	0.957345	+	0.288947i	$0.0933052\pi$
$678$	0.535898	+	0.928203i	0.0205811	+	0.0356474i
$679$		0			0
$680$	−16.3923			−0.628616
$681$	5.17949	+	2.99038i	0.198479	+	0.114592i
$682$	−13.5622	−	7.83013i	−0.519323	−	0.299831i
$683$	12.2128	−	45.5788i	0.467310	−	1.74403i	−0.181804	−	0.983335i	$-0.558194\pi$
$683$	12.2128	−	45.5788i	0.467310	−	1.74403i	0.649114	−	0.760691i	$-0.275140\pi$
$684$	−15.6603	−	4.19615i	−0.598785	−	0.160444i
$685$	11.1506	−	11.1506i	0.426044	−	0.426044i
$686$		0			0
$687$	7.14359			0.272545
$688$	−25.8564	−	25.8564i	−0.985766	−	0.985766i
$689$	−10.8301	−	18.7583i	−0.412595	−	0.714635i
$690$	−0.758330	−	2.83013i	−0.0288691	−	0.107741i
$691$	−6.16025	−	22.9904i	−0.234347	−	0.874595i	−0.978442	−	0.206521i	$-0.933786\pi$
$691$	−6.16025	−	22.9904i	−0.234347	−	0.874595i	0.744095	−	0.668074i	$-0.232881\pi$
$692$	4.46410	−	1.19615i	0.169700	−	0.0454709i
$693$		0			0
$694$	−29.8301	+	17.2224i	−1.13234	+	0.653755i
$695$	13.0981	+	7.56218i	0.496838	+	0.286850i
$696$	−0.143594	+	0.535898i	−0.00544290	+	0.0203132i
$697$	27.5885	−	15.9282i	1.04499	−	0.603324i
$698$	−12.2487			−0.463621
$699$	−0.294229	−	0.294229i	−0.0111287	−	0.0111287i
$700$		0			0
$701$	−13.3923	+	13.3923i	−0.505820	+	0.505820i	−0.913241	−	0.407420i	$-0.866428\pi$
$701$	−13.3923	+	13.3923i	−0.505820	+	0.505820i	0.407420	+	0.913241i	$0.366428\pi$
$702$	−15.6603	−	15.6603i	−0.591058	−	0.591058i
$703$	1.74167	+	3.01666i	0.0656883	+	0.113776i
$704$	22.9282	+	6.14359i	0.864139	+	0.231545i
$705$	−0.990381	+	1.71539i	−0.0372999	+	0.0646053i
$706$	10.1699	−	37.9545i	0.382748	−	1.42844i
$707$		0			0
$708$	−10.5167	−	6.07180i	−0.395240	−	0.228192i
$709$	45.6506	−	12.2321i	1.71445	−	0.459384i	0.737938	−	0.674868i	$-0.235800\pi$
$709$	45.6506	−	12.2321i	1.71445	−	0.459384i	0.976507	+	0.215484i	$0.0691329\pi$
$710$	0.339746	−	0.588457i	0.0127504	−	0.0220844i
$711$	−39.4186	+	22.7583i	−1.47831	+	0.853504i
$712$	−14.1962	+	3.80385i	−0.532023	+	0.142555i
$713$			16.6603i			0.623931i
$714$		0			0
$715$	−9.92820	−	9.92820i	−0.371294	−	0.371294i
$716$	−4.80385	+	17.9282i	−0.179528	+	0.670008i
$717$	4.26795	+	1.14359i	0.159389	+	0.0427083i
$718$	−1.63397	−	6.09808i	−0.0609794	−	0.227578i
$719$	0.205771	−	0.356406i	0.00767398	−	0.0132917i	−0.862163	−	0.506631i	$-0.830891\pi$
$719$	0.205771	−	0.356406i	0.00767398	−	0.0132917i	0.869837	+	0.493339i	$0.164224\pi$
$720$	9.46410	+	2.53590i	0.352706	+	0.0945074i
$721$		0			0
$722$	13.9282	+	3.73205i	0.518354	+	0.138893i
$723$	−1.86603	−	6.96410i	−0.0693982	−	0.258998i
$724$	26.7846	−	26.7846i	0.995442	−	0.995442i
$725$	0.411543	−	1.53590i	0.0152843	−	0.0570418i
$726$		−	1.60770i		−	0.0596672i
$727$		−	41.3205i		−	1.53249i	−0.642547	−	0.766246i	$-0.722122\pi$
$727$		−	41.3205i		−	1.53249i	0.642547	−	0.766246i	$-0.277878\pi$
$728$		0			0
$729$		−	13.5885i		−	0.503276i
$730$	−9.12436			−0.337708
$731$	−15.2942	+	57.0788i	−0.565677	+	2.11114i
$732$	−7.46410			−0.275881
$733$	8.81347	+	32.8923i	0.325533	+	1.21490i	0.913775	+	0.406220i	$0.133153\pi$
$733$	8.81347	+	32.8923i	0.325533	+	1.21490i	−0.588242	+	0.808685i	$0.700180\pi$
$734$	−2.24167	+	8.36603i	−0.0827415	+	0.308796i
$735$		0			0
$736$	−6.53590	−	24.3923i	−0.240916	−	0.899112i
$737$	7.62436	−	13.2058i	0.280847	−	0.486441i
$738$	−18.3923	+	4.92820i	−0.677030	+	0.181410i
$739$	38.4808	+	10.3109i	1.41554	+	0.379292i	0.883899	−	0.467679i	$-0.154910\pi$
$739$	38.4808	+	10.3109i	1.41554	+	0.379292i	0.531639	+	0.846971i	$0.321576\pi$
$740$	−1.05256	−	1.82309i	−0.0386928	−	0.0670180i
$741$	−5.73205	−	5.73205i	−0.210572	−	0.210572i
$742$		0			0
$743$			11.0718i			0.406185i	0.979160	+	0.203092i	$0.0650992\pi$
$743$			11.0718i			0.406185i	−0.979160	+	0.203092i	$0.934901\pi$
$744$	4.73205	+	2.73205i	0.173485	+	0.100162i
$745$	−6.10770	+	3.52628i	−0.223769	+	0.129193i
$746$	1.09808	+	0.633975i	0.0402034	+	0.0232115i
$747$	5.73205	−	1.53590i	0.209725	−	0.0561956i
$748$	−9.92820	−	37.0526i	−0.363011	−	1.35478i
$749$		0			0
$750$	5.83013	+	1.56218i	0.212886	+	0.0570427i
$751$	−6.52628	+	11.3038i	−0.238147	+	0.412483i	−0.960183	−	0.279373i	$-0.909873\pi$
$751$	−6.52628	+	11.3038i	−0.238147	+	0.412483i	0.722035	+	0.691856i	$0.243207\pi$
$752$	−8.53590	+	14.7846i	−0.311272	+	0.539139i
$753$	−6.43782	−	11.1506i	−0.234607	−	0.406352i
$754$	2.00000	−	2.00000i	0.0728357	−	0.0728357i
$755$	7.22243	−	7.22243i	0.262851	−	0.262851i
$756$		0			0
$757$	−18.6603	−	18.6603i	−0.678218	−	0.678218i	0.281378	−	0.959597i	$-0.409208\pi$
$757$	−18.6603	−	18.6603i	−0.678218	−	0.678218i	−0.959597	+	0.281378i	$0.909208\pi$
$758$			0.248711i			0.00903360i
$759$	5.93782	−	3.42820i	0.215529	−	0.124436i
$760$	7.26795	+	1.94744i	0.263636	+	0.0706411i
$761$	−11.7679	−	6.79423i	−0.426588	−	0.246291i	0.271304	−	0.962494i	$-0.412545\pi$
$761$	−11.7679	−	6.79423i	−0.426588	−	0.246291i	−0.697892	+	0.716203i	$0.745878\pi$
$762$	−3.46410	−	6.00000i	−0.125491	−	0.217357i
$763$		0			0
$764$	−15.0000	−	8.66025i	−0.542681	−	0.313317i
$765$	−4.09808	−	15.2942i	−0.148166	−	0.552964i
$766$	−34.4186	+	9.22243i	−1.24359	+	0.333220i
$767$	30.9545	+	53.6147i	1.11770	+	1.93592i
$768$	−8.00000	−	2.14359i	−0.288675	−	0.0773503i
$769$	−9.85641			−0.355431			−0.177716	−	0.984082i	$-0.556871\pi$
$769$	−9.85641			−0.355431			−0.177716	+	0.984082i	$0.556871\pi$
$770$		0			0
$771$	7.09808	−	7.09808i	0.255631	−	0.255631i
$772$	−39.8372	+	23.0000i	−1.43377	+	0.827788i
$773$	2.93782	−	10.9641i	0.105666	−	0.394351i	−0.892754	−	0.450545i	$-0.851230\pi$
$773$	2.93782	−	10.9641i	0.105666	−	0.394351i	0.998420	+	0.0561936i	$0.0178964\pi$
$774$	17.6603	−	30.5885i	0.634785	−	1.09948i
$775$	−13.5622	−	7.83013i	−0.487168	−	0.281266i
$776$	−5.85641	+	5.85641i	−0.210233	+	0.210233i
$777$		0			0
$778$	28.3468	−	16.3660i	1.01628	−	0.586750i
$779$	−14.1244	+	3.78461i	−0.506058	+	0.135598i
$780$	3.46410	+	3.46410i	0.124035	+	0.124035i
$781$	1.53590	+	0.411543i	0.0549588	+	0.0147262i
$782$	−28.8564	+	28.8564i	−1.03190	+	1.03190i
$783$	−1.12436			−0.0401812
$784$		0			0
$785$	16.9474			0.604880
$786$	4.07180	−	4.07180i	0.145236	−	0.145236i
$787$	13.1603	+	3.52628i	0.469112	+	0.125698i	0.485628	−	0.874165i	$-0.338591\pi$
$787$	13.1603	+	3.52628i	0.469112	+	0.125698i	−0.0165161	+	0.999864i	$0.505257\pi$
$788$	33.3205	−	33.3205i	1.18699	−	1.18699i
$789$	−2.30385	+	0.617314i	−0.0820191	+	0.0219770i
$790$	18.2942	−	10.5622i	0.650879	−	0.375785i
$791$		0			0
$792$			22.9282i			0.814718i
$793$	32.9545	+	19.0263i	1.17025	+	0.675643i
$794$	18.7583	−	32.4904i	0.665708	−	1.15304i
$795$	0.492958	−	1.83975i	0.0174834	−	0.0652491i
$796$	11.9282	+	20.6603i	0.422784	+	0.732283i
$797$	13.3397	−	13.3397i	0.472518	−	0.472518i	−0.430211	−	0.902729i	$-0.641561\pi$
$797$	13.3397	−	13.3397i	0.472518	−	0.472518i	0.902729	+	0.430211i	$0.141561\pi$
$798$		0			0
$799$	27.5885			0.976009
$800$	22.9282	+	6.14359i	0.810634	+	0.217209i
$801$	−7.09808	−	12.2942i	−0.250798	−	0.434395i
$802$	20.4904	−	5.49038i	0.723541	−	0.193872i
$803$	−5.52628	−	20.6244i	−0.195018	−	0.727818i
$804$	−2.66025	+	4.60770i	−0.0938199	+	0.162501i
$805$		0			0
$806$	−13.9282	−	24.1244i	−0.490600	−	0.849744i
$807$	4.54552	+	2.62436i	0.160010	+	0.0923817i
$808$	−27.6603	−	47.9090i	−0.973084	−	1.68543i
$809$	−29.4282	+	16.9904i	−1.03464	+	0.597350i	−0.918311	−	0.395861i	$-0.870446\pi$
$809$	−29.4282	+	16.9904i	−1.03464	+	0.597350i	−0.116330	+	0.993211i	$0.537113\pi$
$810$			8.44486i			0.296722i
$811$	−24.3205	−	24.3205i	−0.854009	−	0.854009i	0.136616	−	0.990624i	$-0.456377\pi$
$811$	−24.3205	−	24.3205i	−0.854009	−	0.854009i	−0.990624	+	0.136616i	$0.956377\pi$
$812$		0			0
$813$	−4.43782	+	4.43782i	−0.155641	+	0.155641i
$814$	3.48334	−	3.48334i	0.122091	−	0.122091i
$815$	5.59808	+	9.69615i	0.196092	+	0.339641i
$816$	3.46410	+	12.9282i	0.121268	+	0.452578i
$817$	13.5622	−	23.4904i	0.474481	−	0.821824i
$818$	11.8301	+	3.16987i	0.413631	+	0.110832i
$819$		0			0
$820$	8.53590	−	2.28719i	0.298087	−	0.0798720i
$821$	0.598076	−	0.160254i	0.0208730	−	0.00559290i	−0.248367	−	0.968666i	$-0.579894\pi$
$821$	0.598076	−	0.160254i	0.0208730	−	0.00559290i	0.269240	+	0.963073i	$0.413227\pi$
$822$	−11.1506	−	6.43782i	−0.388923	−	0.224545i
$823$	−14.9378	+	8.62436i	−0.520700	+	0.300626i	−0.737221	−	0.675652i	$-0.763862\pi$
$823$	−14.9378	+	8.62436i	−0.520700	+	0.300626i	0.216521	+	0.976278i	$0.430529\pi$
$824$	−17.6603	+	4.73205i	−0.615224	+	0.164849i
$825$			6.44486i			0.224381i
$826$		0			0
$827$	−3.78461	−	3.78461i	−0.131604	−	0.131604i	0.638237	−	0.769840i	$-0.279664\pi$
$827$	−3.78461	−	3.78461i	−0.131604	−	0.131604i	−0.769840	+	0.638237i	$0.779664\pi$
$828$	21.1244	−	12.1962i	0.734122	−	0.423846i
$829$	3.06218	+	0.820508i	0.106354	+	0.0284974i	0.311603	−	0.950212i	$-0.399134\pi$
$829$	3.06218	+	0.820508i	0.106354	+	0.0284974i	−0.205250	+	0.978710i	$0.565801\pi$
$830$	−2.66025	+	0.712813i	−0.0923388	+	0.0247421i
$831$	1.20577	−	2.08846i	0.0418277	−	0.0724478i
$832$	29.8564	+	29.8564i	1.03508	+	1.03508i
$833$		0			0
$834$	3.19615	−	11.9282i	0.110674	−	0.413040i
$835$	−5.07180	−	18.9282i	−0.175517	−	0.655037i
$836$			17.6077i			0.608975i
$837$	−2.86603	+	10.6962i	−0.0990643	+	0.369713i
$838$	38.0000			1.31269
$839$			17.7128i			0.611514i	0.952110	+	0.305757i	$0.0989096\pi$
$839$			17.7128i			0.611514i	−0.952110	+	0.305757i	$0.901090\pi$
$840$		0			0
$841$			28.8564i			0.995048i
$842$			17.3205i			0.596904i
$843$	0.124356	−	0.464102i	0.00428304	−	0.0159845i
$844$	−31.8564	−	31.8564i	−1.09654	−	1.09654i
$845$	−3.44744	−	12.8660i	−0.118596	−	0.442605i
$846$	−15.9282	−	4.26795i	−0.547623	−	0.146735i
$847$		0			0
$848$	4.24871	−	15.8564i	0.145901	−	0.544511i
$849$	−3.89230	+	6.74167i	−0.133584	+	0.231374i
$850$	−9.92820	−	37.0526i	−0.340535	−	1.27089i
$851$	−5.06218	−	1.35641i	−0.173529	−	0.0464970i
$852$	−0.535898	−	0.143594i	−0.0183596	−	0.00491943i
$853$	11.8756	+	11.8756i	0.406614	+	0.406614i	0.880556	−	0.473942i	$-0.157169\pi$
$853$	11.8756	+	11.8756i	0.406614	+	0.406614i	−0.473942	+	0.880556i	$0.657169\pi$
$854$		0			0
$855$			7.26795i			0.248559i
$856$	−4.73205	+	8.19615i	−0.161738	+	0.280139i
$857$	−11.8923	+	6.86603i	−0.406233	+	0.234539i	−0.689170	−	0.724600i	$-0.742025\pi$
$857$	−11.8923	+	6.86603i	−0.406233	+	0.234539i	0.282937	+	0.959139i	$0.408691\pi$
$858$	−5.73205	+	9.92820i	−0.195689	+	0.338943i
$859$	−13.6244	+	3.65064i	−0.464857	+	0.124558i	−0.483643	−	0.875265i	$-0.660687\pi$
$859$	−13.6244	+	3.65064i	−0.464857	+	0.124558i	0.0187858	+	0.999824i	$0.494020\pi$
$860$	−8.19615	+	14.1962i	−0.279486	+	0.484085i
$861$		0			0
$862$	11.2224	−	41.8827i	0.382238	−	1.42653i
$863$	16.3301	−	28.2846i	0.555884	−	0.962819i	−0.441950	−	0.897040i	$-0.645713\pi$
$863$	16.3301	−	28.2846i	0.555884	−	0.962819i	0.997834	−	0.0657797i	$-0.0209535\pi$
$864$		−	16.7846i		−	0.571024i
$865$	−1.03590	−	1.79423i	−0.0352216	−	0.0610056i
$866$	33.1769	+	33.1769i	1.12740	+	1.12740i
$867$	9.07180	−	9.07180i	0.308094	−	0.308094i
$868$		0			0
$869$	34.9545	+	34.9545i	1.18575	+	1.18575i
$870$	0.248711			0.00843210
$871$	23.4904	−	13.5622i	0.795941	−	0.459537i
$872$	5.41154	−	3.12436i	0.183258	−	0.105804i
$873$	−6.92820	−	4.00000i	−0.234484	−	0.135379i
$874$	16.2224	−	9.36603i	0.548732	−	0.316811i
$875$		0			0
$876$	1.92820	+	7.19615i	0.0651479	+	0.243135i
$877$	8.18653	+	30.5526i	0.276440	+	1.03169i	0.954871	+	0.297022i	$0.0959936\pi$
$877$	8.18653	+	30.5526i	0.276440	+	1.03169i	−0.678431	+	0.734664i	$0.737340\pi$
$878$	−2.75833	−	10.2942i	−0.0930891	−	0.347413i
$879$	−2.90192	−	5.02628i	−0.0978795	−	0.169532i
$880$		−	10.6410i		−	0.358709i
$881$	−50.0000			−1.68454			−0.842271	−	0.539054i	$-0.818782\pi$
$881$	−50.0000			−1.68454			−0.842271	+	0.539054i	$0.818782\pi$
$882$		0			0
$883$	−5.00000	+	5.00000i	−0.168263	+	0.168263i	−0.786216	−	0.617952i	$-0.787963\pi$
$883$	−5.00000	+	5.00000i	−0.168263	+	0.168263i	0.617952	+	0.786216i	$0.287963\pi$
$884$	17.6603	−	65.9090i	0.593979	−	2.21676i
$885$	−1.40897	+	5.25833i	−0.0473619	+	0.176757i
$886$	−13.2224	−	7.63397i	−0.444216	−	0.256468i
$887$	39.7750	+	22.9641i	1.33551	+	0.771059i	0.986139	−	0.165924i	$-0.0530606\pi$
$887$	39.7750	+	22.9641i	1.33551	+	0.771059i	0.349375	+	0.936983i	$0.386394\pi$
$888$	−1.21539	+	1.21539i	−0.0407858	+	0.0407858i
$889$		0			0
$890$	3.29423	+	5.70577i	0.110423	+	0.191258i
$891$	−19.0885	+	5.11474i	−0.639487	+	0.171350i
$892$		−	19.7128i		−	0.660034i
$893$	−12.2321	−	3.27757i	−0.409330	−	0.109680i
$894$	4.07180	+	4.07180i	0.136181	+	0.136181i
$895$	8.32051			0.278124
$896$		0			0
$897$	12.1962			0.407218
$898$	−23.3205	−	23.3205i	−0.778215	−	0.778215i
$899$	−1.36603	−	0.366025i	−0.0455595	−	0.0122076i
$900$			22.9282i			0.764273i
$901$	−25.6244	+	6.86603i	−0.853671	+	0.228740i
$902$	10.3397	+	17.9090i	0.344276	+	0.596303i
$903$		0			0
$904$	2.92820	−	2.92820i	0.0973906	−	0.0973906i
$905$	−14.7058	−	8.49038i	−0.488836	−	0.282230i
$906$	−7.22243	−	4.16987i	−0.239949	−	0.138535i
$907$	7.16025	−	26.7224i	0.237752	−	0.887304i	−0.739136	−	0.673556i	$-0.764766\pi$
$907$	7.16025	−	26.7224i	0.237752	−	0.887304i	0.976889	−	0.213748i	$-0.0685672\pi$
$908$	5.98076	−	22.3205i	0.198479	−	0.740732i
$909$	37.7846	−	37.7846i	1.25324	−	1.25324i
$910$		0			0
$911$	7.32051			0.242539			0.121270	−	0.992620i	$-0.461303\pi$
$911$	7.32051			0.242539			0.121270	+	0.992620i	$0.461303\pi$
$912$		−	6.14359i		−	0.203435i
$913$	−3.22243	−	5.58142i	−0.106647	−	0.184718i
$914$	6.88269	+	25.6865i	0.227659	+	0.849635i
$915$	0.866025	+	3.23205i	0.0286299	+	0.106848i
$916$	−7.14359	−	26.6603i	−0.236031	−	0.880880i
$917$		0			0
$918$	−23.4904	+	13.5622i	−0.775298	+	0.447619i
$919$	−15.8660	−	9.16025i	−0.523372	−	0.302169i	0.214941	−	0.976627i	$-0.431044\pi$
$919$	−15.8660	−	9.16025i	−0.523372	−	0.302169i	−0.738313	+	0.674458i	$0.764377\pi$
$920$	−9.80385	+	5.66025i	−0.323223	+	0.186613i
$921$	5.70577	−	3.29423i	0.188012	−	0.108549i
$922$	−37.3205			−1.22909
$923$	2.00000	+	2.00000i	0.0658308	+	0.0658308i
$924$		0			0
$925$	3.48334	−	3.48334i	0.114531	−	0.114531i
$926$	2.14359	+	2.14359i	0.0704429	+	0.0704429i
$927$	−8.83013	−	15.2942i	−0.290019	−	0.502328i
$928$	2.14359			0.0703669
$929$	25.0167	−	43.3301i	0.820770	−	1.42162i	−0.0843396	−	0.996437i	$-0.526878\pi$
$929$	25.0167	−	43.3301i	0.820770	−	1.42162i	0.905110	−	0.425178i	$-0.139789\pi$
$930$	0.633975	−	2.36603i	0.0207888	−	0.0775850i
$931$		0			0
$932$	−0.803848	+	1.39230i	−0.0263309	+	0.0456065i
$933$	3.23205	−	0.866025i	0.105813	−	0.0283524i
$934$	−19.0263	+	32.9545i	−0.622559	+	1.07830i
$935$	−14.8923	+	8.59808i	−0.487030	+	0.281187i
$936$	−20.3923	+	35.3205i	−0.666543	+	1.15449i
$937$		−	29.0718i		−	0.949734i	−0.880058	−	0.474867i	$-0.842496\pi$
$937$		−	29.0718i		−	0.949734i	0.880058	−	0.474867i	$-0.157504\pi$
$938$		0			0
$939$	−7.90192	−	7.90192i	−0.257870	−	0.257870i
$940$	7.39230	+	1.98076i	0.241110	+	0.0646053i
$941$	23.5263	+	6.30385i	0.766935	+	0.205500i	0.621017	−	0.783797i	$-0.286720\pi$
$941$	23.5263	+	6.30385i	0.766935	+	0.205500i	0.145918	+	0.989297i	$0.453386\pi$
$942$	−3.58142	−	13.3660i	−0.116689	−	0.435489i
$943$	11.0000	−	19.0526i	0.358209	−	0.620437i
$944$	−12.1436	+	45.3205i	−0.395240	+	1.47506i
$945$		0			0
$946$	−37.0526	−	9.92820i	−1.20468	−	0.322794i
$947$	−1.44744	−	5.40192i	−0.0470355	−	0.175539i	0.938412	−	0.345518i	$-0.112297\pi$
$947$	−1.44744	−	5.40192i	−0.0470355	−	0.175539i	−0.985448	+	0.169979i	$0.945630\pi$
$948$	−12.1962	−	12.1962i	−0.396113	−	0.396113i
$949$	9.83013	−	36.6865i	0.319099	−	1.19090i
$950$			17.6077i			0.571269i
$951$			7.58846i			0.246073i
$952$		0			0
$953$		−	16.5359i		−	0.535650i	−0.963468	−	0.267825i	$-0.913695\pi$
$953$		−	16.5359i		−	0.535650i	0.963468	−	0.267825i	$-0.0863050\pi$
$954$	15.8564			0.513370
$955$	−2.00962	+	7.50000i	−0.0650297	+	0.242694i
$956$		−	17.0718i		−	0.552141i
$957$	0.150635	+	0.562178i	0.00486934	+	0.0181726i
$958$	−5.70577	+	21.2942i	−0.184345	+	0.687985i
$959$		0			0
$960$			3.71281i			0.119831i
$961$	8.53590	−	14.7846i	0.275352	−	0.476923i
$962$	8.46410	−	2.26795i	0.272894	−	0.0731216i
$963$	−8.83013	−	2.36603i	−0.284547	−	0.0762441i
$964$	−24.1244	+	13.9282i	−0.776993	+	0.448597i
$965$	14.5814	+	14.5814i	0.469392	+	0.469392i
$966$		0			0
$967$			60.2487i			1.93747i	0.248102	+	0.968734i	$0.420193\pi$
$967$			60.2487i			1.93747i	−0.248102	+	0.968734i	$0.579807\pi$
$968$	−6.00000	+	1.60770i	−0.192847	+	0.0516733i
$969$	−8.59808	+	4.96410i	−0.276210	+	0.159470i
$970$	3.21539	+	1.85641i	0.103240	+	0.0596056i
$971$	52.4090	−	14.0429i	1.68188	−	0.450659i	0.713608	−	0.700545i	$-0.247060\pi$
$971$	52.4090	−	14.0429i	1.68188	−	0.450659i	0.968275	+	0.249885i	$0.0803930\pi$
$972$	23.8564	−	6.39230i	0.765195	−	0.205033i
$973$		0			0
$974$	16.8301	+	4.50962i	0.539272	+	0.144498i
$975$	−5.73205	+	9.92820i	−0.183573	+	0.317957i
$976$	7.46410	+	27.8564i	0.238920	+	0.891662i
$977$	8.57180	+	14.8468i	0.274236	+	0.474991i	0.969942	−	0.243336i	$-0.0782417\pi$
$977$	8.57180	+	14.8468i	0.274236	+	0.474991i	−0.695706	+	0.718327i	$0.744908\pi$
$978$	6.46410	−	6.46410i	0.206699	−	0.206699i
$979$	−10.9019	+	10.9019i	−0.348427	+	0.348427i
$980$		0			0
$981$	4.26795	+	4.26795i	0.136265	+	0.136265i
$982$		−	7.17691i		−	0.229025i
$983$	−17.1340	+	9.89230i	−0.546489	+	0.315516i	−0.747705	−	0.664031i	$-0.768844\pi$
$983$	−17.1340	+	9.89230i	−0.546489	+	0.315516i	0.201216	+	0.979547i	$0.435511\pi$
$984$	−3.60770	−	6.24871i	−0.115009	−	0.199202i
$985$	−18.2942	−	10.5622i	−0.582903	−	0.336539i
$986$	−1.73205	−	3.00000i	−0.0551597	−	0.0955395i
$987$		0			0
$988$	−15.6603	+	27.1244i	−0.498219	+	0.862941i
$989$	10.5622	+	39.4186i	0.335858	+	1.25344i
$990$	9.92820	−	2.66025i	0.315539	−	0.0845484i
$991$	4.20577	+	7.28461i	0.133601	+	0.231403i	0.925062	−	0.379816i	$-0.124013\pi$
$991$	4.20577	+	7.28461i	0.133601	+	0.231403i	−0.791461	+	0.611219i	$0.790679\pi$
$992$	5.46410	−	20.3923i	0.173485	−	0.647456i
$993$	10.5167			0.333736
$994$		0			0
$995$	7.56218	−	7.56218i	0.239737	−	0.239737i
$996$	1.12436	+	1.94744i	0.0356266	+	0.0617070i
$997$	−0.401924	+	1.50000i	−0.0127291	+	0.0475055i	−0.971998	−	0.234988i	$-0.924495\pi$
$997$	−0.401924	+	1.50000i	−0.0127291	+	0.0475055i	0.959269	+	0.282494i	$0.0911616\pi$
$998$	−18.2942	+	31.6865i	−0.579094	+	1.00302i
$999$	−3.01666	−	1.74167i	−0.0954429	−	0.0551040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.h.373.1		4
7.2	even	3		784.2.m.d.197.2		4
7.3	odd	6		112.2.w.a.53.1	✓	4
7.4	even	3		784.2.x.a.165.1		4
7.5	odd	6		784.2.m.e.197.2		4
7.6	odd	2		112.2.w.b.37.1	yes	4
16.13	even	4		784.2.x.a.765.1		4
28.3	even	6		448.2.ba.b.305.1		4
28.27	even	2		448.2.ba.a.177.1		4
56.3	even	6		896.2.ba.a.865.1		4
56.13	odd	2		896.2.ba.b.737.1		4
56.27	even	2		896.2.ba.c.737.1		4
56.45	odd	6		896.2.ba.d.865.1		4
112.3	even	12		448.2.ba.a.81.1		4
112.13	odd	4		112.2.w.a.93.1	yes	4
112.27	even	4		896.2.ba.a.289.1		4
112.45	odd	12		112.2.w.b.109.1	yes	4
112.59	even	12		896.2.ba.c.417.1		4
112.61	odd	12		784.2.m.e.589.2		4
112.69	odd	4		896.2.ba.d.289.1		4
112.83	even	4		448.2.ba.b.401.1		4
112.93	even	12		784.2.m.d.589.2		4
112.101	odd	12		896.2.ba.b.417.1		4
112.109	even	12	inner	784.2.x.h.557.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.a.53.1	✓	4	7.3	odd	6
112.2.w.a.93.1	yes	4	112.13	odd	4
112.2.w.b.37.1	yes	4	7.6	odd	2
112.2.w.b.109.1	yes	4	112.45	odd	12
448.2.ba.a.81.1		4	112.3	even	12
448.2.ba.a.177.1		4	28.27	even	2
448.2.ba.b.305.1		4	28.3	even	6
448.2.ba.b.401.1		4	112.83	even	4
784.2.m.d.197.2		4	7.2	even	3
784.2.m.d.589.2		4	112.93	even	12
784.2.m.e.197.2		4	7.5	odd	6
784.2.m.e.589.2		4	112.61	odd	12
784.2.x.a.165.1		4	7.4	even	3
784.2.x.a.765.1		4	16.13	even	4
784.2.x.h.373.1		4	1.1	even	1	trivial
784.2.x.h.557.1		4	112.109	even	12	inner
896.2.ba.a.289.1		4	112.27	even	4
896.2.ba.a.865.1		4	56.3	even	6
896.2.ba.b.417.1		4	112.101	odd	12
896.2.ba.b.737.1		4	56.13	odd	2
896.2.ba.c.417.1		4	112.59	even	12
896.2.ba.c.737.1		4	56.27	even	2
896.2.ba.d.289.1		4	112.69	odd	4
896.2.ba.d.865.1		4	56.45	odd	6

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-0.500000 - 0.133975i) q^{3} +2.00000i q^{4} +(0.866025 - 0.232051i) q^{5} +(-0.366025 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-0.500000 - 0.133975i) q^{3} +2.00000i q^{4} +(0.866025 - 0.232051i) q^{5} +(-0.366025 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 1.36603i) q^{9} +(1.09808 + 0.633975i) q^{10} +(-0.767949 + 2.86603i) q^{11} +(0.267949 - 1.00000i) q^{12} +(-3.73205 + 3.73205i) q^{13} -0.464102 q^{15} -4.00000 q^{16} +(3.23205 + 5.59808i) q^{17} +(-1.00000 - 3.73205i) q^{18} +(-0.767949 - 2.86603i) q^{19} +(0.464102 + 1.73205i) q^{20} +(-3.63397 + 2.09808i) q^{22} +(3.86603 + 2.23205i) q^{23} +(1.26795 - 0.732051i) q^{24} +(-3.63397 + 2.09808i) q^{25} -7.46410 q^{26} +(2.09808 + 2.09808i) q^{27} +(-0.267949 + 0.267949i) q^{29} +(-0.464102 - 0.464102i) q^{30} +(1.86603 + 3.23205i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(0.767949 - 1.33013i) q^{33} +(-2.36603 + 8.83013i) q^{34} +(2.73205 - 4.73205i) q^{36} +(-1.13397 + 0.303848i) q^{37} +(2.09808 - 3.63397i) q^{38} +(2.36603 - 1.36603i) q^{39} +(-1.26795 + 2.19615i) q^{40} -4.92820i q^{41} +(6.46410 + 6.46410i) q^{43} +(-5.73205 - 1.53590i) q^{44} +(-2.36603 - 0.633975i) q^{45} +(1.63397 + 6.09808i) q^{46} +(2.13397 - 3.69615i) q^{47} +(2.00000 + 0.535898i) q^{48} +(-5.73205 - 1.53590i) q^{50} +(-0.866025 - 3.23205i) q^{51} +(-7.46410 - 7.46410i) q^{52} +(-1.06218 + 3.96410i) q^{53} +4.19615i q^{54} +2.66025i q^{55} +1.53590i q^{57} -0.535898 q^{58} +(3.03590 - 11.3301i) q^{59} -0.928203i q^{60} +(-1.86603 - 6.96410i) q^{61} +(-1.36603 + 5.09808i) q^{62} -8.00000i q^{64} +(-2.36603 + 4.09808i) q^{65} +(2.09808 - 0.562178i) q^{66} +(-4.96410 - 1.33013i) q^{67} +(-11.1962 + 6.46410i) q^{68} +(-1.63397 - 1.63397i) q^{69} -0.535898i q^{71} +(7.46410 - 2.00000i) q^{72} +(-6.23205 + 3.59808i) q^{73} +(-1.43782 - 0.830127i) q^{74} +(2.09808 - 0.562178i) q^{75} +(5.73205 - 1.53590i) q^{76} +(3.73205 + 1.00000i) q^{78} +(8.33013 - 14.4282i) q^{79} +(-3.46410 + 0.928203i) q^{80} +(3.33013 + 5.76795i) q^{81} +(4.92820 - 4.92820i) q^{82} +(-1.53590 + 1.53590i) q^{83} +(4.09808 + 4.09808i) q^{85} +12.9282i q^{86} +(0.169873 - 0.0980762i) q^{87} +(-4.19615 - 7.26795i) q^{88} +(4.50000 + 2.59808i) q^{89} +(-1.73205 - 3.00000i) q^{90} +(-4.46410 + 7.73205i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(5.83013 - 1.56218i) q^{94} +(-1.33013 - 2.30385i) q^{95} +(1.46410 + 2.53590i) q^{96} +2.92820 q^{97} +(5.73205 - 5.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{3} + 2 q^{6} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 2 * q^3 + 2 * q^6 - 8 * q^8 - 6 * q^9	\( 4 q + 4 q^{2} - 2 q^{3} + 2 q^{6} - 8 q^{8} - 6 q^{9} - 6 q^{10} - 10 q^{11} + 8 q^{12} - 8 q^{13} + 12 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} - 10 q^{19} - 12 q^{20} - 18 q^{22} + 12 q^{23} + 12 q^{24} - 18 q^{25} - 16 q^{26} - 2 q^{27} - 8 q^{29} + 12 q^{30} + 4 q^{31} - 16 q^{32} + 10 q^{33} - 6 q^{34} + 4 q^{36} - 8 q^{37} - 2 q^{38} + 6 q^{39} - 12 q^{40} + 12 q^{43} - 16 q^{44} - 6 q^{45} + 10 q^{46} + 12 q^{47} + 8 q^{48} - 16 q^{50} - 16 q^{52} + 20 q^{53} - 16 q^{58} + 26 q^{59} - 4 q^{61} - 2 q^{62} - 6 q^{65} - 2 q^{66} - 6 q^{67} - 24 q^{68} - 10 q^{69} + 16 q^{72} - 18 q^{73} - 30 q^{74} - 2 q^{75} + 16 q^{76} + 8 q^{78} + 16 q^{79} - 4 q^{81} - 8 q^{82} - 20 q^{83} + 6 q^{85} + 18 q^{87} + 4 q^{88} + 18 q^{89} - 4 q^{92} - 2 q^{93} + 6 q^{94} + 12 q^{95} - 8 q^{96} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 2 * q^6 - 8 * q^8 - 6 * q^9 - 6 * q^10 - 10 * q^11 + 8 * q^12 - 8 * q^13 + 12 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 - 10 * q^19 - 12 * q^20 - 18 * q^22 + 12 * q^23 + 12 * q^24 - 18 * q^25 - 16 * q^26 - 2 * q^27 - 8 * q^29 + 12 * q^30 + 4 * q^31 - 16 * q^32 + 10 * q^33 - 6 * q^34 + 4 * q^36 - 8 * q^37 - 2 * q^38 + 6 * q^39 - 12 * q^40 + 12 * q^43 - 16 * q^44 - 6 * q^45 + 10 * q^46 + 12 * q^47 + 8 * q^48 - 16 * q^50 - 16 * q^52 + 20 * q^53 - 16 * q^58 + 26 * q^59 - 4 * q^61 - 2 * q^62 - 6 * q^65 - 2 * q^66 - 6 * q^67 - 24 * q^68 - 10 * q^69 + 16 * q^72 - 18 * q^73 - 30 * q^74 - 2 * q^75 + 16 * q^76 + 8 * q^78 + 16 * q^79 - 4 * q^81 - 8 * q^82 - 20 * q^83 + 6 * q^85 + 18 * q^87 + 4 * q^88 + 18 * q^89 - 4 * q^92 - 2 * q^93 + 6 * q^94 + 12 * q^95 - 8 * q^96 - 16 * q^97 + 16 * q^99

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