LMFDB - Embedded newform 1470.2.b.d.881.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(881,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("1470.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.b (of order $2$, degree $1$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16x^{13} + 2x^{12} + 96x^{10} - 80x^{9} + 2x^{8} - 240x^{7} + 864x^{6} + 162x^{4} - 3888x^{3} + 6561 $ x^16 - 16x^13 + 2x^12 + 96x^10 - 80x^9 + 2x^8 - 240x^7 + 864x^6 + 162x^4 - 3888*x^3 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.13
Root			$-0.642116 + 1.60863i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.d.881.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.24045 + 1.20883i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-1.20883 + 1.24045i) q^{6} -1.00000i q^{8} +(0.0774422 + 2.99900i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.24045 + 1.20883i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-1.20883 + 1.24045i) q^{6} -1.00000i q^{8} +(0.0774422 + 2.99900i) q^{9} +1.00000i q^{10} +0.388831i q^{11} +(-1.24045 - 1.20883i) q^{12} +0.436189i q^{13} +(1.24045 + 1.20883i) q^{15} +1.00000 q^{16} +0.581546 q^{17} +(-2.99900 + 0.0774422i) q^{18} +0.597750i q^{19} -1.00000 q^{20} -0.388831 q^{22} +7.83308i q^{23} +(1.20883 - 1.24045i) q^{24} +1.00000 q^{25} -0.436189 q^{26} +(-3.52923 + 3.81373i) q^{27} -2.39564i q^{29} +(-1.20883 + 1.24045i) q^{30} +8.53890i q^{31} +1.00000i q^{32} +(-0.470031 + 0.482326i) q^{33} +0.581546i q^{34} +(-0.0774422 - 2.99900i) q^{36} +6.55608 q^{37} -0.597750 q^{38} +(-0.527280 + 0.541071i) q^{39} -1.00000i q^{40} -2.65306 q^{41} -11.1640 q^{43} -0.388831i q^{44} +(0.0774422 + 2.99900i) q^{45} -7.83308 q^{46} +5.35068 q^{47} +(1.24045 + 1.20883i) q^{48} +1.00000i q^{50} +(0.721380 + 0.702992i) q^{51} -0.436189i q^{52} -7.66134i q^{53} +(-3.81373 - 3.52923i) q^{54} +0.388831i q^{55} +(-0.722580 + 0.741480i) q^{57} +2.39564 q^{58} -5.33043 q^{59} +(-1.24045 - 1.20883i) q^{60} +14.8030i q^{61} -8.53890 q^{62} -1.00000 q^{64} +0.436189i q^{65} +(-0.482326 - 0.470031i) q^{66} +11.8218 q^{67} -0.581546 q^{68} +(-9.46889 + 9.71656i) q^{69} -14.5318i q^{71} +(2.99900 - 0.0774422i) q^{72} +7.51730i q^{73} +6.55608i q^{74} +(1.24045 + 1.20883i) q^{75} -0.597750i q^{76} +(-0.541071 - 0.527280i) q^{78} +4.78108 q^{79} +1.00000 q^{80} +(-8.98801 + 0.464498i) q^{81} -2.65306i q^{82} +0.157211 q^{83} +0.581546 q^{85} -11.1640i q^{86} +(2.89593 - 2.97167i) q^{87} +0.388831 q^{88} +11.1040 q^{89} +(-2.99900 + 0.0774422i) q^{90} -7.83308i q^{92} +(-10.3221 + 10.5921i) q^{93} +5.35068i q^{94} +0.597750i q^{95} +(-1.20883 + 1.24045i) q^{96} +1.08768i q^{97} +(-1.16610 + 0.0301119i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 16 q^{4} + 16 q^{5} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 16 * q^4 + 16 * q^5 + 8 * q^9	$ 16 q + 8 q^{3} - 16 q^{4} + 16 q^{5} + 8 q^{9} - 8 q^{12} + 8 q^{15} + 16 q^{16} - 48 q^{17} - 16 q^{20} + 16 q^{25} + 16 q^{26} + 8 q^{27} - 8 q^{36} - 16 q^{41} + 16 q^{43} + 8 q^{45} - 16 q^{46} - 32 q^{47} + 8 q^{48} + 16 q^{51} + 32 q^{57} + 16 q^{58} - 32 q^{59} - 8 q^{60} - 16 q^{62} - 16 q^{64} + 16 q^{67} + 48 q^{68} + 8 q^{75} - 32 q^{78} - 48 q^{79} + 16 q^{80} + 8 q^{81} - 48 q^{83} - 48 q^{85} - 16 q^{89} - 64 q^{93} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 - 16 * q^4 + 16 * q^5 + 8 * q^9 - 8 * q^12 + 8 * q^15 + 16 * q^16 - 48 * q^17 - 16 * q^20 + 16 * q^25 + 16 * q^26 + 8 * q^27 - 8 * q^36 - 16 * q^41 + 16 * q^43 + 8 * q^45 - 16 * q^46 - 32 * q^47 + 8 * q^48 + 16 * q^51 + 32 * q^57 + 16 * q^58 - 32 * q^59 - 8 * q^60 - 16 * q^62 - 16 * q^64 + 16 * q^67 + 48 * q^68 + 8 * q^75 - 32 * q^78 - 48 * q^79 + 16 * q^80 + 8 * q^81 - 48 * q^83 - 48 * q^85 - 16 * q^89 - 64 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.24045	+	1.20883i	0.716175	+	0.697920i
$3$	1.24045	+	1.20883i	0.716175	+	0.697920i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.20883	+	1.24045i	−0.493504	+	0.506412i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	0.0774422	+	2.99900i	0.0258141	+	0.999667i
$10$			1.00000i			0.316228i
$11$			0.388831i			0.117237i	0.998280	+	0.0586184i	$0.0186695\pi$
$11$			0.388831i			0.117237i	−0.998280	+	0.0586184i	$0.981330\pi$
$12$	−1.24045	−	1.20883i	−0.358088	−	0.348960i
$13$			0.436189i			0.120977i	0.998169	+	0.0604885i	$0.0192659\pi$
$13$			0.436189i			0.120977i	−0.998169	+	0.0604885i	$0.980734\pi$
$14$		0			0
$15$	1.24045	+	1.20883i	0.320283	+	0.312120i
$16$	1.00000			0.250000
$17$	0.581546			0.141046			0.0705228	−	0.997510i	$-0.477533\pi$
$17$	0.581546			0.141046			0.0705228	+	0.997510i	$0.477533\pi$
$18$	−2.99900	+	0.0774422i	−0.706871	+	0.0182533i
$19$			0.597750i			0.137133i	0.997647	+	0.0685666i	$0.0218426\pi$
$19$			0.597750i			0.137133i	−0.997647	+	0.0685666i	$0.978157\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−0.388831			−0.0828989
$23$			7.83308i			1.63331i	0.577126	+	0.816655i	$0.304174\pi$
$23$			7.83308i			1.63331i	−0.577126	+	0.816655i	$0.695826\pi$
$24$	1.20883	−	1.24045i	0.246752	−	0.253206i
$25$	1.00000			0.200000
$26$	−0.436189			−0.0855437
$27$	−3.52923	+	3.81373i	−0.679200	+	0.733953i
$28$		0			0
$29$		−	2.39564i		−	0.444859i	−0.974949	−	0.222429i	$-0.928601\pi$
$29$		−	2.39564i		−	0.444859i	0.974949	−	0.222429i	$-0.0713987\pi$
$30$	−1.20883	+	1.24045i	−0.220702	+	0.226475i
$31$			8.53890i			1.53363i	0.641868	+	0.766815i	$0.278160\pi$
$31$			8.53890i			1.53363i	−0.641868	+	0.766815i	$0.721840\pi$
$32$			1.00000i			0.176777i
$33$	−0.470031	+	0.482326i	−0.0818220	+	0.0839621i
$34$			0.581546i			0.0997343i
$35$		0			0
$36$	−0.0774422	−	2.99900i	−0.0129070	−	0.499833i
$37$	6.55608			1.07781			0.538907	−	0.842366i	$-0.318838\pi$
$37$	6.55608			1.07781			0.538907	+	0.842366i	$0.318838\pi$
$38$	−0.597750			−0.0969678
$39$	−0.527280	+	0.541071i	−0.0844324	+	0.0866408i
$40$		−	1.00000i		−	0.158114i
$41$	−2.65306			−0.414338			−0.207169	−	0.978305i	$-0.566425\pi$
$41$	−2.65306			−0.414338			−0.207169	+	0.978305i	$0.566425\pi$
$42$		0			0
$43$	−11.1640			−1.70250			−0.851250	−	0.524760i	$-0.824155\pi$
$43$	−11.1640			−1.70250			−0.851250	+	0.524760i	$0.824155\pi$
$44$		−	0.388831i		−	0.0586184i
$45$	0.0774422	+	2.99900i	0.0115444	+	0.447065i
$46$	−7.83308			−1.15492
$47$	5.35068			0.780477			0.390238	−	0.920714i	$-0.372393\pi$
$47$	5.35068			0.780477			0.390238	+	0.920714i	$0.372393\pi$
$48$	1.24045	+	1.20883i	0.179044	+	0.174480i
$49$		0			0
$50$			1.00000i			0.141421i
$51$	0.721380	+	0.702992i	0.101013	+	0.0984386i
$52$		−	0.436189i		−	0.0604885i
$53$		−	7.66134i		−	1.05237i	−0.850372	−	0.526183i	$-0.823623\pi$
$53$		−	7.66134i		−	1.05237i	0.850372	−	0.526183i	$-0.176377\pi$
$54$	−3.81373	−	3.52923i	−0.518983	−	0.480267i
$55$			0.388831i			0.0524299i
$56$		0			0
$57$	−0.722580	+	0.741480i	−0.0957081	+	0.0982114i
$58$	2.39564			0.314563
$59$	−5.33043			−0.693963			−0.346982	−	0.937872i	$-0.612793\pi$
$59$	−5.33043			−0.693963			−0.346982	+	0.937872i	$0.612793\pi$
$60$	−1.24045	−	1.20883i	−0.160142	−	0.156060i
$61$			14.8030i			1.89532i	0.319276	+	0.947662i	$0.396560\pi$
$61$			14.8030i			1.89532i	−0.319276	+	0.947662i	$0.603440\pi$
$62$	−8.53890			−1.08444
$63$		0			0
$64$	−1.00000			−0.125000
$65$			0.436189i			0.0541026i
$66$	−0.482326	−	0.470031i	−0.0593702	−	0.0578569i
$67$	11.8218			1.44426			0.722130	−	0.691757i	$-0.243163\pi$
$67$	11.8218			1.44426			0.722130	+	0.691757i	$0.243163\pi$
$68$	−0.581546			−0.0705228
$69$	−9.46889	+	9.71656i	−1.13992	+	1.16974i
$70$		0			0
$71$		−	14.5318i		−	1.72461i	−0.506387	−	0.862306i	$-0.669019\pi$
$71$		−	14.5318i		−	1.72461i	0.506387	−	0.862306i	$-0.330981\pi$
$72$	2.99900	−	0.0774422i	0.353436	−	0.00912665i
$73$			7.51730i			0.879834i	0.898038	+	0.439917i	$0.144992\pi$
$73$			7.51730i			0.879834i	−0.898038	+	0.439917i	$0.855008\pi$
$74$			6.55608i			0.762129i
$75$	1.24045	+	1.20883i	0.143235	+	0.139584i
$76$		−	0.597750i		−	0.0685666i
$77$		0			0
$78$	−0.541071	−	0.527280i	−0.0612643	−	0.0597027i
$79$	4.78108			0.537913			0.268957	−	0.963152i	$-0.413321\pi$
$79$	4.78108			0.537913			0.268957	+	0.963152i	$0.413321\pi$
$80$	1.00000			0.111803
$81$	−8.98801	+	0.464498i	−0.998667	+	0.0516109i
$82$		−	2.65306i		−	0.292981i
$83$	0.157211			0.0172562			0.00862808	−	0.999963i	$-0.497254\pi$
$83$	0.157211			0.0172562			0.00862808	+	0.999963i	$0.497254\pi$
$84$		0			0
$85$	0.581546			0.0630775
$86$		−	11.1640i		−	1.20385i
$87$	2.89593	−	2.97167i	0.310476	−	0.318597i
$88$	0.388831			0.0414495
$89$	11.1040			1.17703			0.588513	−	0.808487i	$-0.299713\pi$
$89$	11.1040			1.17703			0.588513	+	0.808487i	$0.299713\pi$
$90$	−2.99900	+	0.0774422i	−0.316122	+	0.00816312i
$91$		0			0
$92$		−	7.83308i		−	0.816655i
$93$	−10.3221	+	10.5921i	−1.07035	+	1.09835i
$94$			5.35068i			0.551880i
$95$			0.597750i			0.0613278i
$96$	−1.20883	+	1.24045i	−0.123376	+	0.126603i
$97$			1.08768i			0.110437i	0.998474	+	0.0552186i	$0.0175856\pi$
$97$			1.08768i			0.110437i	−0.998474	+	0.0552186i	$0.982414\pi$
$98$		0			0
$99$	−1.16610	+	0.0301119i	−0.117198	+	0.00302636i
$100$	−1.00000			−0.100000
$101$	−16.5092			−1.64272			−0.821362	−	0.570408i	$-0.806785\pi$
$101$	−16.5092			−1.64272			−0.821362	+	0.570408i	$0.806785\pi$
$102$	−0.702992	+	0.721380i	−0.0696066	+	0.0714273i
$103$		−	2.68965i		−	0.265019i	−0.991182	−	0.132510i	$-0.957696\pi$
$103$		−	2.68965i		−	0.265019i	0.991182	−	0.132510i	$-0.0423035\pi$
$104$	0.436189			0.0427718
$105$		0			0
$106$	7.66134			0.744135
$107$		−	10.1568i		−	0.981895i	−0.871189	−	0.490947i	$-0.836651\pi$
$107$		−	10.1568i		−	0.981895i	0.871189	−	0.490947i	$-0.163349\pi$
$108$	3.52923	−	3.81373i	0.339600	−	0.366976i
$109$	9.81570			0.940174			0.470087	−	0.882620i	$-0.344223\pi$
$109$	9.81570			0.940174			0.470087	+	0.882620i	$0.344223\pi$
$110$	−0.388831			−0.0370735
$111$	8.13250	+	7.92521i	0.771903	+	0.752228i
$112$		0			0
$113$		−	8.68271i		−	0.816801i	−0.912803	−	0.408400i	$-0.866087\pi$
$113$		−	8.68271i		−	0.816801i	0.912803	−	0.408400i	$-0.133913\pi$
$114$	−0.741480	−	0.722580i	−0.0694460	−	0.0676758i
$115$			7.83308i			0.730439i
$116$			2.39564i			0.222429i
$117$	−1.30813	+	0.0337794i	−0.120937	+	0.00312291i
$118$		−	5.33043i		−	0.490706i
$119$		0			0
$120$	1.20883	−	1.24045i	0.110351	−	0.113237i
$121$	10.8488			0.986256
$122$	−14.8030			−1.34020
$123$	−3.29099	−	3.20710i	−0.296739	−	0.289175i
$124$		−	8.53890i		−	0.766815i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−18.1119			−1.60717			−0.803585	−	0.595190i	$-0.797077\pi$
$127$	−18.1119			−1.60717			−0.803585	+	0.595190i	$0.797077\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−13.8485	−	13.4955i	−1.21929	−	1.18821i
$130$	−0.436189			−0.0382563
$131$	2.03892			0.178141			0.0890707	−	0.996025i	$-0.471610\pi$
$131$	2.03892			0.178141			0.0890707	+	0.996025i	$0.471610\pi$
$132$	0.470031	−	0.482326i	0.0409110	−	0.0419811i
$133$		0			0
$134$			11.8218i			1.02125i
$135$	−3.52923	+	3.81373i	−0.303748	+	0.328234i
$136$		−	0.581546i		−	0.0498672i
$137$		−	16.1364i		−	1.37863i	−0.724462	−	0.689315i	$-0.757912\pi$
$137$		−	16.1364i		−	1.37863i	0.724462	−	0.689315i	$-0.242088\pi$
$138$	−9.71656	−	9.46889i	−0.827129	−	0.806046i
$139$			12.3487i			1.04741i	0.851901	+	0.523703i	$0.175450\pi$
$139$			12.3487i			1.04741i	−0.851901	+	0.523703i	$0.824550\pi$
$140$		0			0
$141$	6.63726	+	6.46808i	0.558958	+	0.544711i
$142$	14.5318			1.21949
$143$	−0.169604			−0.0141830
$144$	0.0774422	+	2.99900i	0.00645352	+	0.249917i
$145$		−	2.39564i		−	0.198947i
$146$	−7.51730			−0.622137
$147$		0			0
$148$	−6.55608			−0.538907
$149$		−	2.95913i		−	0.242421i	−0.992627	−	0.121211i	$-0.961322\pi$
$149$		−	2.95913i		−	0.242421i	0.992627	−	0.121211i	$-0.0386776\pi$
$150$	−1.20883	+	1.24045i	−0.0987009	+	0.101282i
$151$	8.33959			0.678666			0.339333	−	0.940666i	$-0.389799\pi$
$151$	8.33959			0.678666			0.339333	+	0.940666i	$0.389799\pi$
$152$	0.597750			0.0484839
$153$	0.0450362	+	1.74406i	0.00364096	+	0.140999i
$154$		0			0
$155$			8.53890i			0.685861i
$156$	0.527280	−	0.541071i	0.0422162	−	0.0433204i
$157$		−	22.4692i		−	1.79324i	−0.442805	−	0.896618i	$-0.646017\pi$
$157$		−	22.4692i		−	1.79324i	0.442805	−	0.896618i	$-0.353983\pi$
$158$			4.78108i			0.380362i
$159$	9.26128	−	9.50352i	0.734467	−	0.753678i
$160$			1.00000i			0.0790569i
$161$		0			0
$162$	−0.464498	−	8.98801i	−0.0364944	−	0.706164i
$163$	−13.6027			−1.06545			−0.532724	−	0.846289i	$-0.678831\pi$
$163$	−13.6027			−1.06545			−0.532724	+	0.846289i	$0.678831\pi$
$164$	2.65306			0.207169
$165$	−0.470031	+	0.482326i	−0.0365919	+	0.0375490i
$166$			0.157211i			0.0122020i
$167$	20.4857			1.58523			0.792615	−	0.609723i	$-0.208719\pi$
$167$	20.4857			1.58523			0.792615	+	0.609723i	$0.208719\pi$
$168$		0			0
$169$	12.8097			0.985365
$170$			0.581546i			0.0446025i
$171$	−1.79265	+	0.0462911i	−0.137088	+	0.00353997i
$172$	11.1640			0.851250
$173$	−15.3753			−1.16896			−0.584480	−	0.811408i	$-0.698701\pi$
$173$	−15.3753			−1.16896			−0.584480	+	0.811408i	$0.698701\pi$
$174$	2.97167	+	2.89593i	0.225282	+	0.219540i
$175$		0			0
$176$			0.388831i			0.0293092i
$177$	−6.61215	−	6.44361i	−0.496999	−	0.484331i
$178$			11.1040i			0.832284i
$179$			1.13504i			0.0848367i	0.999100	+	0.0424183i	$0.0135062\pi$
$179$			1.13504i			0.0848367i	−0.999100	+	0.0424183i	$0.986494\pi$
$180$	−0.0774422	−	2.99900i	−0.00577220	−	0.223532i
$181$		−	11.1559i		−	0.829211i	−0.910001	−	0.414605i	$-0.863920\pi$
$181$		−	11.1559i		−	0.829211i	0.910001	−	0.414605i	$-0.136080\pi$
$182$		0			0
$183$	−17.8943	+	18.3623i	−1.32279	+	1.35738i
$184$	7.83308			0.577462
$185$	6.55608			0.482013
$186$	−10.5921	−	10.3221i	−0.776650	−	0.756853i
$187$			0.226123i			0.0165357i
$188$	−5.35068			−0.390238
$189$		0			0
$190$	−0.597750			−0.0433653
$191$		−	5.87467i		−	0.425076i	−0.977153	−	0.212538i	$-0.931827\pi$
$191$		−	5.87467i		−	0.425076i	0.977153	−	0.212538i	$-0.0681730\pi$
$192$	−1.24045	−	1.20883i	−0.0895219	−	0.0872401i
$193$	2.60022			0.187168			0.0935839	−	0.995611i	$-0.470168\pi$
$193$	2.60022			0.187168			0.0935839	+	0.995611i	$0.470168\pi$
$194$	−1.08768			−0.0780909
$195$	−0.527280	+	0.541071i	−0.0377593	+	0.0387469i
$196$		0			0
$197$		−	4.23018i		−	0.301388i	−0.988580	−	0.150694i	$-0.951849\pi$
$197$		−	4.23018i		−	0.301388i	0.988580	−	0.150694i	$-0.0481508\pi$
$198$	−0.0301119	−	1.16610i	−0.00213996	−	0.0828713i
$199$			4.74835i			0.336602i	0.985736	+	0.168301i	$0.0538280\pi$
$199$			4.74835i			0.336602i	−0.985736	+	0.168301i	$0.946172\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	14.6644	+	14.2906i	1.03434	+	1.00798i
$202$		−	16.5092i		−	1.16158i
$203$		0			0
$204$	−0.721380	−	0.702992i	−0.0505067	−	0.0492193i
$205$	−2.65306			−0.185298
$206$	2.68965			0.187397
$207$	−23.4914	+	0.606611i	−1.63277	+	0.0421624i
$208$			0.436189i			0.0302443i
$209$	−0.232423			−0.0160771
$210$		0			0
$211$	14.3905			0.990682			0.495341	−	0.868699i	$-0.335043\pi$
$211$	14.3905			0.990682			0.495341	+	0.868699i	$0.335043\pi$
$212$			7.66134i			0.526183i
$213$	17.5666	−	18.0261i	1.20364	−	1.23513i
$214$	10.1568			0.694304
$215$	−11.1640			−0.761381
$216$	3.81373	+	3.52923i	0.259491	+	0.240134i
$217$		0			0
$218$			9.81570i			0.664803i
$219$	−9.08717	+	9.32486i	−0.614054	+	0.630115i
$220$		−	0.388831i		−	0.0262149i
$221$			0.253664i			0.0170633i
$222$	−7.92521	+	8.13250i	−0.531905	+	0.545818i
$223$		−	17.3485i		−	1.16174i	−0.813996	−	0.580870i	$-0.802712\pi$
$223$		−	17.3485i		−	1.16174i	0.813996	−	0.580870i	$-0.197288\pi$
$224$		0			0
$225$	0.0774422	+	2.99900i	0.00516281	+	0.199933i
$226$	8.68271			0.577565
$227$	12.2684			0.814280			0.407140	−	0.913366i	$-0.366526\pi$
$227$	12.2684			0.814280			0.407140	+	0.913366i	$0.366526\pi$
$228$	0.722580	−	0.741480i	0.0478540	−	0.0491057i
$229$		−	1.44031i		−	0.0951784i	−0.998867	−	0.0475892i	$-0.984846\pi$
$229$		−	1.44031i		−	0.0951784i	0.998867	−	0.0475892i	$-0.0151538\pi$
$230$	−7.83308			−0.516498
$231$		0			0
$232$	−2.39564			−0.157281
$233$			27.2147i			1.78289i	0.453128	+	0.891446i	$0.350308\pi$
$233$			27.2147i			1.78289i	−0.453128	+	0.891446i	$0.649692\pi$
$234$	−0.0337794	−	1.30813i	−0.00220823	−	0.0855152i
$235$	5.35068			0.349040
$236$	5.33043			0.346982
$237$	5.93070	+	5.77953i	0.385240	+	0.375421i
$238$		0			0
$239$			20.6627i			1.33656i	0.743911	+	0.668278i	$0.232968\pi$
$239$			20.6627i			1.33656i	−0.743911	+	0.668278i	$0.767032\pi$
$240$	1.24045	+	1.20883i	0.0800708	+	0.0780299i
$241$		−	11.8237i		−	0.761633i	−0.924651	−	0.380816i	$-0.875643\pi$
$241$		−	11.8237i		−	0.761633i	0.924651	−	0.380816i	$-0.124357\pi$
$242$			10.8488i			0.697388i
$243$	−11.7107	−	10.2888i	−0.751241	−	0.660028i
$244$		−	14.8030i		−	0.947662i
$245$		0			0
$246$	3.20710	−	3.29099i	0.204478	−	0.209826i
$247$	−0.260732			−0.0165900
$248$	8.53890			0.542220
$249$	0.195013	+	0.190042i	0.0123584	+	0.0120434i
$250$			1.00000i			0.0632456i
$251$	26.0569			1.64470			0.822349	−	0.568983i	$-0.192663\pi$
$251$	26.0569			1.64470			0.822349	+	0.568983i	$0.192663\pi$
$252$		0			0
$253$	−3.04574			−0.191484
$254$		−	18.1119i		−	1.13644i
$255$	0.721380	+	0.702992i	0.0451746	+	0.0440231i
$256$	1.00000			0.0625000
$257$	6.94372			0.433137			0.216569	−	0.976267i	$-0.430514\pi$
$257$	6.94372			0.433137			0.216569	+	0.976267i	$0.430514\pi$
$258$	13.4955	−	13.8485i	0.840191	−	0.862167i
$259$		0			0
$260$		−	0.436189i		−	0.0270513i
$261$	7.18452	−	0.185523i	0.444711	−	0.0114836i
$262$			2.03892i			0.125965i
$263$		−	11.4248i		−	0.704484i	−0.935909	−	0.352242i	$-0.885419\pi$
$263$		−	11.4248i		−	0.704484i	0.935909	−	0.352242i	$-0.114581\pi$
$264$	0.482326	+	0.470031i	0.0296851	+	0.0289284i
$265$		−	7.66134i		−	0.470632i
$266$		0			0
$267$	13.7740	+	13.4229i	0.842957	+	0.821471i
$268$	−11.8218			−0.722130
$269$	11.2718			0.687257			0.343628	−	0.939106i	$-0.388344\pi$
$269$	11.2718			0.687257			0.343628	+	0.939106i	$0.388344\pi$
$270$	−3.81373	−	3.52923i	−0.232096	−	0.214782i
$271$			20.4663i			1.24324i	0.783318	+	0.621621i	$0.213526\pi$
$271$			20.4663i			1.24324i	−0.783318	+	0.621621i	$0.786474\pi$
$272$	0.581546			0.0352614
$273$		0			0
$274$	16.1364			0.974838
$275$			0.388831i			0.0234474i
$276$	9.46889	−	9.71656i	0.569960	−	0.584868i
$277$	7.48525			0.449745			0.224873	−	0.974388i	$-0.427803\pi$
$277$	7.48525			0.449745			0.224873	+	0.974388i	$0.427803\pi$
$278$	−12.3487			−0.740628
$279$	−25.6082	+	0.661271i	−1.53312	+	0.0395892i
$280$		0			0
$281$		−	11.1139i		−	0.662998i	−0.943456	−	0.331499i	$-0.892446\pi$
$281$		−	11.1139i		−	0.662998i	0.943456	−	0.331499i	$-0.107554\pi$
$282$	−6.46808	+	6.63726i	−0.385169	+	0.395243i
$283$			27.8744i			1.65696i	0.560016	+	0.828481i	$0.310795\pi$
$283$			27.8744i			1.65696i	−0.560016	+	0.828481i	$0.689205\pi$
$284$			14.5318i			0.862306i
$285$	−0.722580	+	0.741480i	−0.0428020	+	0.0439215i
$286$		−	0.169604i		−	0.0100289i
$287$		0			0
$288$	−2.99900	+	0.0774422i	−0.176718	+	0.00456332i
$289$	−16.6618			−0.980106
$290$	2.39564			0.140677
$291$	−1.31482	+	1.34922i	−0.0770764	+	0.0790924i
$292$		−	7.51730i		−	0.439917i
$293$	−19.7545			−1.15407			−0.577034	−	0.816720i	$-0.695790\pi$
$293$	−19.7545			−1.15407			−0.577034	+	0.816720i	$0.695790\pi$
$294$		0			0
$295$	−5.33043			−0.310350
$296$		−	6.55608i		−	0.381065i
$297$	−1.48289	−	1.37227i	−0.0860463	−	0.0796273i
$298$	2.95913			0.171418
$299$	−3.41670			−0.197593
$300$	−1.24045	−	1.20883i	−0.0716175	−	0.0697920i
$301$		0			0
$302$			8.33959i			0.479889i
$303$	−20.4788	−	19.9568i	−1.17648	−	1.14649i
$304$			0.597750i			0.0342833i
$305$			14.8030i			0.847614i
$306$	−1.74406	+	0.0450362i	−0.0997011	+	0.00257455i
$307$			8.92019i			0.509102i	0.967059	+	0.254551i	$0.0819277\pi$
$307$			8.92019i			0.509102i	−0.967059	+	0.254551i	$0.918072\pi$
$308$		0			0
$309$	3.25134	−	3.33638i	0.184962	−	0.189800i
$310$	−8.53890			−0.484977
$311$	0.960152			0.0544452			0.0272226	−	0.999629i	$-0.491334\pi$
$311$	0.960152			0.0544452			0.0272226	+	0.999629i	$0.491334\pi$
$312$	0.541071	+	0.527280i	0.0306321	+	0.0298513i
$313$		−	4.56673i		−	0.258127i	−0.991636	−	0.129063i	$-0.958803\pi$
$313$		−	4.56673i		−	0.258127i	0.991636	−	0.129063i	$-0.0411971\pi$
$314$	22.4692			1.26801
$315$		0			0
$316$	−4.78108			−0.268957
$317$		−	12.2121i		−	0.685900i	−0.939354	−	0.342950i	$-0.888574\pi$
$317$		−	12.2121i		−	0.685900i	0.939354	−	0.342950i	$-0.111426\pi$
$318$	9.50352	+	9.26128i	0.532931	+	0.519347i
$319$	0.931497			0.0521538
$320$	−1.00000			−0.0559017
$321$	12.2779	−	12.5990i	0.685284	−	0.703209i
$322$		0			0
$323$			0.347619i			0.0193420i
$324$	8.98801	−	0.464498i	0.499334	−	0.0258055i
$325$			0.436189i			0.0241954i
$326$		−	13.6027i		−	0.753385i
$327$	12.1759	+	11.8655i	0.673329	+	0.656166i
$328$			2.65306i			0.146491i
$329$		0			0
$330$	−0.482326	−	0.470031i	−0.0265511	−	0.0258744i
$331$	19.3496			1.06355			0.531775	−	0.846886i	$-0.321525\pi$
$331$	19.3496			1.06355			0.531775	+	0.846886i	$0.321525\pi$
$332$	−0.157211			−0.00862808
$333$	0.507717	+	19.6617i	0.0278227	+	1.07745i
$334$			20.4857i			1.12093i
$335$	11.8218			0.645893
$336$		0			0
$337$	32.9183			1.79317			0.896587	−	0.442867i	$-0.146039\pi$
$337$	32.9183			1.79317			0.896587	+	0.442867i	$0.146039\pi$
$338$			12.8097i			0.696758i
$339$	10.4960	−	10.7705i	0.570062	−	0.584972i
$340$	−0.581546			−0.0315388
$341$	−3.32018			−0.179798
$342$	−0.0462911	−	1.79265i	−0.00250313	−	0.0969355i
$343$		0			0
$344$			11.1640i			0.601925i
$345$	−9.46889	+	9.71656i	−0.509788	+	0.523122i
$346$		−	15.3753i		−	0.826579i
$347$			6.94260i			0.372698i	0.982484	+	0.186349i	$0.0596655\pi$
$347$			6.94260i			0.372698i	−0.982484	+	0.186349i	$0.940334\pi$
$348$	−2.89593	+	2.97167i	−0.155238	+	0.159298i
$349$		−	22.3154i		−	1.19451i	−0.802050	−	0.597257i	$-0.796257\pi$
$349$		−	22.3154i		−	1.19451i	0.802050	−	0.597257i	$-0.203743\pi$
$350$		0			0
$351$	−1.66351	−	1.53941i	−0.0887914	−	0.0821677i
$352$	−0.388831			−0.0207247
$353$	27.3114			1.45364			0.726820	−	0.686828i	$-0.240997\pi$
$353$	27.3114			1.45364			0.726820	+	0.686828i	$0.240997\pi$
$354$	6.44361	−	6.61215i	0.342474	−	0.351432i
$355$		−	14.5318i		−	0.771270i
$356$	−11.1040			−0.588513
$357$		0			0
$358$	−1.13504			−0.0599886
$359$		−	10.2004i		−	0.538357i	−0.963090	−	0.269178i	$-0.913248\pi$
$359$		−	10.2004i		−	0.538357i	0.963090	−	0.269178i	$-0.0867521\pi$
$360$	2.99900	−	0.0774422i	0.158061	−	0.00408156i
$361$	18.6427			0.981194
$362$	11.1559			0.586341
$363$	13.4574	+	13.1144i	0.706332	+	0.688328i
$364$		0			0
$365$			7.51730i			0.393474i
$366$	−18.3623	−	17.8943i	−0.959815	−	0.935350i
$367$		−	9.33458i		−	0.487261i	−0.969868	−	0.243631i	$-0.921662\pi$
$367$		−	9.33458i		−	0.487261i	0.969868	−	0.243631i	$-0.0783385\pi$
$368$			7.83308i			0.408328i
$369$	−0.205459	−	7.95652i	−0.0106957	−	0.414200i
$370$			6.55608i			0.340834i
$371$		0			0
$372$	10.3221	−	10.5921i	0.535176	−	0.549174i
$373$	−7.34793			−0.380461			−0.190231	−	0.981739i	$-0.560924\pi$
$373$	−7.34793			−0.380461			−0.190231	+	0.981739i	$0.560924\pi$
$374$	−0.226123			−0.0116925
$375$	1.24045	+	1.20883i	0.0640567	+	0.0624239i
$376$		−	5.35068i		−	0.275940i
$377$	1.04495			0.0538177
$378$		0			0
$379$	11.2225			0.576462			0.288231	−	0.957561i	$-0.406933\pi$
$379$	11.2225			0.576462			0.288231	+	0.957561i	$0.406933\pi$
$380$		−	0.597750i		−	0.0306639i
$381$	−22.4669	−	21.8943i	−1.15102	−	1.12168i
$382$	5.87467			0.300574
$383$	−22.5133			−1.15038			−0.575188	−	0.818021i	$-0.695071\pi$
$383$	−22.5133			−1.15038			−0.575188	+	0.818021i	$0.695071\pi$
$384$	1.20883	−	1.24045i	0.0616880	−	0.0633015i
$385$		0			0
$386$			2.60022i			0.132348i
$387$	−0.864568	−	33.4810i	−0.0439484	−	1.70193i
$388$		−	1.08768i		−	0.0552186i
$389$		−	20.8569i		−	1.05749i	−0.848782	−	0.528743i	$-0.822664\pi$
$389$		−	20.8569i		−	1.05749i	0.848782	−	0.528743i	$-0.177336\pi$
$390$	−0.541071	−	0.527280i	−0.0273982	−	0.0266999i
$391$			4.55530i			0.230371i
$392$		0			0
$393$	2.52918	+	2.46472i	0.127580	+	0.124329i
$394$	4.23018			0.213113
$395$	4.78108			0.240562
$396$	1.16610	−	0.0301119i	0.0585989	−	0.00151318i
$397$			5.80599i			0.291394i	0.989329	+	0.145697i	$0.0465425\pi$
$397$			5.80599i			0.291394i	−0.989329	+	0.145697i	$0.953457\pi$
$398$	−4.74835			−0.238013
$399$		0			0
$400$	1.00000			0.0500000
$401$		−	7.60821i		−	0.379936i	−0.981790	−	0.189968i	$-0.939162\pi$
$401$		−	7.60821i		−	0.379936i	0.981790	−	0.189968i	$-0.0608384\pi$
$402$	−14.2906	+	14.6644i	−0.712749	+	0.731392i
$403$	−3.72457			−0.185534
$404$	16.5092			0.821362
$405$	−8.98801	+	0.464498i	−0.446618	+	0.0230811i
$406$		0			0
$407$			2.54920i			0.126359i
$408$	0.702992	−	0.721380i	0.0348033	−	0.0357136i
$409$			25.4555i			1.25869i	0.777124	+	0.629347i	$0.216678\pi$
$409$			25.4555i			1.25869i	−0.777124	+	0.629347i	$0.783322\pi$
$410$		−	2.65306i		−	0.131025i
$411$	19.5063	−	20.0165i	0.962174	−	0.987341i
$412$			2.68965i			0.132510i
$413$		0			0
$414$	−0.606611	−	23.4914i	−0.0298133	−	1.15454i
$415$	0.157211			0.00771719
$416$	−0.436189			−0.0213859
$417$	−14.9276	+	15.3180i	−0.731006	+	0.750126i
$418$		−	0.232423i		−	0.0113682i
$419$	32.2860			1.57727			0.788636	−	0.614860i	$-0.210787\pi$
$419$	32.2860			1.57727			0.788636	+	0.614860i	$0.210787\pi$
$420$		0			0
$421$	2.83642			0.138239			0.0691194	−	0.997608i	$-0.477981\pi$
$421$	2.83642			0.138239			0.0691194	+	0.997608i	$0.477981\pi$
$422$			14.3905i			0.700518i
$423$	0.414368	+	16.0467i	0.0201473	+	0.780217i
$424$	−7.66134			−0.372067
$425$	0.581546			0.0282091
$426$	18.0261	+	17.5666i	0.873365	+	0.851104i
$427$		0			0
$428$			10.1568i			0.490947i
$429$	−0.210385	−	0.205023i	−0.0101575	−	0.00989858i
$430$		−	11.1640i		−	0.538378i
$431$			33.8559i			1.63078i	0.578911	+	0.815391i	$0.303478\pi$
$431$			33.8559i			1.63078i	−0.578911	+	0.815391i	$0.696522\pi$
$432$	−3.52923	+	3.81373i	−0.169800	+	0.183488i
$433$		−	36.2694i		−	1.74300i	−0.490398	−	0.871499i	$-0.663149\pi$
$433$		−	36.2694i		−	1.74300i	0.490398	−	0.871499i	$-0.336851\pi$
$434$		0			0
$435$	2.89593	−	2.97167i	0.138849	−	0.142481i
$436$	−9.81570			−0.470087
$437$	−4.68222			−0.223981
$438$	−9.32486	−	9.08717i	−0.445559	−	0.434202i
$439$			27.1425i			1.29544i	0.761878	+	0.647721i	$0.224278\pi$
$439$			27.1425i			1.29544i	−0.761878	+	0.647721i	$0.775722\pi$
$440$	0.388831			0.0185368
$441$		0			0
$442$	−0.253664			−0.0120656
$443$			11.7451i			0.558025i	0.960287	+	0.279012i	$0.0900071\pi$
$443$			11.7451i			0.558025i	−0.960287	+	0.279012i	$0.909993\pi$
$444$	−8.13250	−	7.92521i	−0.385952	−	0.376114i
$445$	11.1040			0.526382
$446$	17.3485			0.821474
$447$	3.57709	−	3.67066i	0.169191	−	0.173616i
$448$		0			0
$449$		−	19.2663i		−	0.909235i	−0.890687	−	0.454618i	$-0.849776\pi$
$449$		−	19.2663i		−	0.909235i	0.890687	−	0.454618i	$-0.150224\pi$
$450$	−2.99900	+	0.0774422i	−0.141374	+	0.00365066i
$451$		−	1.03159i		−	0.0485756i
$452$			8.68271i			0.408400i
$453$	10.3449	+	10.0812i	0.486044	+	0.473655i
$454$			12.2684i			0.575783i
$455$		0			0
$456$	0.741480	+	0.722580i	0.0347230	+	0.0338379i
$457$	−9.32357			−0.436138			−0.218069	−	0.975933i	$-0.569976\pi$
$457$	−9.32357			−0.436138			−0.218069	+	0.975933i	$0.569976\pi$
$458$	1.44031			0.0673013
$459$	−2.05241	+	2.21786i	−0.0957983	+	0.103521i
$460$		−	7.83308i		−	0.365219i
$461$	−6.36590			−0.296490			−0.148245	−	0.988951i	$-0.547362\pi$
$461$	−6.36590			−0.296490			−0.148245	+	0.988951i	$0.547362\pi$
$462$		0			0
$463$	−1.83216			−0.0851475			−0.0425737	−	0.999093i	$-0.513556\pi$
$463$	−1.83216			−0.0851475			−0.0425737	+	0.999093i	$0.513556\pi$
$464$		−	2.39564i		−	0.111215i
$465$	−10.3221	+	10.5921i	−0.478676	+	0.491196i
$466$	−27.2147			−1.26069
$467$	2.25893			0.104531			0.0522653	−	0.998633i	$-0.483356\pi$
$467$	2.25893			0.104531			0.0522653	+	0.998633i	$0.483356\pi$
$468$	1.30813	−	0.0337794i	0.0604684	−	0.00156145i
$469$		0			0
$470$			5.35068i			0.246808i
$471$	27.1615	−	27.8719i	1.25154	−	1.28427i
$472$			5.33043i			0.245353i
$473$		−	4.34092i		−	0.199596i
$474$	−5.77953	+	5.93070i	−0.265463	+	0.272406i
$475$			0.597750i			0.0274266i
$476$		0			0
$477$	22.9763	−	0.593311i	1.05201	−	0.0271658i
$478$	−20.6627			−0.945088
$479$	37.0085			1.69096			0.845480	−	0.534007i	$-0.179315\pi$
$479$	37.0085			1.69096			0.845480	+	0.534007i	$0.179315\pi$
$480$	−1.20883	+	1.24045i	−0.0551755	+	0.0566186i
$481$			2.85969i			0.130391i
$482$	11.8237			0.538556
$483$		0			0
$484$	−10.8488			−0.493128
$485$			1.08768i			0.0493890i
$486$	10.2888	−	11.7107i	0.466710	−	0.531208i
$487$	−40.3476			−1.82832			−0.914162	−	0.405349i	$-0.867150\pi$
$487$	−40.3476			−1.82832			−0.914162	+	0.405349i	$0.867150\pi$
$488$	14.8030			0.670098
$489$	−16.8735	−	16.4434i	−0.763047	−	0.743598i
$490$		0			0
$491$		−	27.8602i		−	1.25731i	−0.777684	−	0.628656i	$-0.783605\pi$
$491$		−	27.8602i		−	1.25731i	0.777684	−	0.628656i	$-0.216395\pi$
$492$	3.29099	+	3.20710i	0.148369	+	0.144587i
$493$		−	1.39317i		−	0.0627454i
$494$		−	0.260732i		−	0.0117309i
$495$	−1.16610	+	0.0301119i	−0.0524124	+	0.00135343i
$496$			8.53890i			0.383408i
$497$		0			0
$498$	−0.190042	+	0.195013i	−0.00851599	+	0.00873874i
$499$	14.0739			0.630034			0.315017	−	0.949086i	$-0.397990\pi$
$499$	14.0739			0.630034			0.315017	+	0.949086i	$0.397990\pi$
$500$	−1.00000			−0.0447214
$501$	25.4115	+	24.7638i	1.13530	+	1.10636i
$502$			26.0569i			1.16298i
$503$	−5.77708			−0.257587			−0.128794	−	0.991671i	$-0.541110\pi$
$503$	−5.77708			−0.257587			−0.128794	+	0.991671i	$0.541110\pi$
$504$		0			0
$505$	−16.5092			−0.734648
$506$		−	3.04574i		−	0.135400i
$507$	15.8899	+	15.4848i	0.705694	+	0.687706i
$508$	18.1119			0.803585
$509$	−13.8369			−0.613308			−0.306654	−	0.951821i	$-0.599209\pi$
$509$	−13.8369			−0.613308			−0.306654	+	0.951821i	$0.599209\pi$
$510$	−0.702992	+	0.721380i	−0.0311290	+	0.0319432i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−2.27966	−	2.10960i	−0.100649	−	0.0931410i
$514$			6.94372i			0.306274i
$515$		−	2.68965i		−	0.118520i
$516$	13.8485	+	13.4955i	0.609644	+	0.594105i
$517$			2.08051i			0.0915006i
$518$		0			0
$519$	−19.0723	−	18.5861i	−0.837180	−	0.815841i
$520$	0.436189			0.0191282
$521$	−31.9328			−1.39900			−0.699501	−	0.714632i	$-0.746594\pi$
$521$	−31.9328			−1.39900			−0.699501	+	0.714632i	$0.746594\pi$
$522$	0.185523	+	7.18452i	0.00812014	+	0.314458i
$523$		−	28.6600i		−	1.25322i	−0.779335	−	0.626608i	$-0.784443\pi$
$523$		−	28.6600i		−	1.25322i	0.779335	−	0.626608i	$-0.215557\pi$
$524$	−2.03892			−0.0890707
$525$		0			0
$526$	11.4248			0.498146
$527$			4.96576i			0.216312i
$528$	−0.470031	+	0.482326i	−0.0204555	+	0.0209905i
$529$	−38.3572			−1.66770
$530$	7.66134			0.332787
$531$	−0.412800	−	15.9860i	−0.0179140	−	0.693732i
$532$		0			0
$533$		−	1.15723i		−	0.0501254i
$534$	−13.4229	+	13.7740i	−0.580868	+	0.596061i
$535$		−	10.1568i		−	0.439117i
$536$		−	11.8218i		−	0.510623i
$537$	−1.37207	+	1.40796i	−0.0592092	+	0.0607579i
$538$			11.2718i			0.485964i
$539$		0			0
$540$	3.52923	−	3.81373i	0.151874	−	0.164117i
$541$	23.0782			0.992211			0.496106	−	0.868262i	$-0.334763\pi$
$541$	23.0782			0.992211			0.496106	+	0.868262i	$0.334763\pi$
$542$	−20.4663			−0.879105
$543$	13.4856	−	13.8383i	0.578723	−	0.593860i
$544$			0.581546i			0.0249336i
$545$	9.81570			0.420458
$546$		0			0
$547$	−7.41240			−0.316931			−0.158466	−	0.987365i	$-0.550655\pi$
$547$	−7.41240			−0.316931			−0.158466	+	0.987365i	$0.550655\pi$
$548$			16.1364i			0.689315i
$549$	−44.3941	+	1.14637i	−1.89469	+	0.0489260i
$550$	−0.388831			−0.0165798
$551$	1.43199			0.0610049
$552$	9.71656	+	9.46889i	0.413564	+	0.403023i
$553$		0			0
$554$			7.48525i			0.318018i
$555$	8.13250	+	7.92521i	0.345206	+	0.336407i
$556$		−	12.3487i		−	0.523703i
$557$		−	26.7659i		−	1.13411i	−0.823681	−	0.567054i	$-0.808083\pi$
$557$		−	26.7659i		−	1.13411i	0.823681	−	0.567054i	$-0.191917\pi$
$558$	−0.661271	−	25.6082i	−0.0279938	−	1.08408i
$559$		−	4.86963i		−	0.205963i
$560$		0			0
$561$	−0.273345	+	0.280495i	−0.0115406	+	0.0118425i
$562$	11.1139			0.468810
$563$	−23.0597			−0.971851			−0.485926	−	0.874000i	$-0.661517\pi$
$563$	−23.0597			−0.971851			−0.485926	+	0.874000i	$0.661517\pi$
$564$	−6.63726	−	6.46808i	−0.279479	−	0.272355i
$565$		−	8.68271i		−	0.365284i
$566$	−27.8744			−1.17165
$567$		0			0
$568$	−14.5318			−0.609743
$569$		−	25.8069i		−	1.08188i	−0.841061	−	0.540940i	$-0.818069\pi$
$569$		−	25.8069i		−	1.08188i	0.841061	−	0.540940i	$-0.181931\pi$
$570$	−0.741480	−	0.722580i	−0.0310572	−	0.0302656i
$571$	31.4767			1.31726			0.658629	−	0.752468i	$-0.271137\pi$
$571$	31.4767			1.31726			0.658629	+	0.752468i	$0.271137\pi$
$572$	0.169604			0.00709148
$573$	7.10150	−	7.28725i	0.296670	−	0.304429i
$574$		0			0
$575$			7.83308i			0.326662i
$576$	−0.0774422	−	2.99900i	−0.00322676	−	0.124958i
$577$		−	2.04044i		−	0.0849445i	−0.999098	−	0.0424722i	$-0.986477\pi$
$577$		−	2.04044i		−	0.0849445i	0.999098	−	0.0424722i	$-0.0135234\pi$
$578$		−	16.6618i		−	0.693040i
$579$	3.22545	+	3.14323i	0.134045	+	0.130628i
$580$			2.39564i			0.0994735i
$581$		0			0
$582$	−1.34922	−	1.31482i	−0.0559268	−	0.0545012i
$583$	2.97896			0.123376
$584$	7.51730			0.311068
$585$	−1.30813	+	0.0337794i	−0.0540846	+	0.00139661i
$586$		−	19.7545i		−	0.816049i
$587$	−31.1133			−1.28418			−0.642092	−	0.766627i	$-0.721933\pi$
$587$	−31.1133			−1.28418			−0.642092	+	0.766627i	$0.721933\pi$
$588$		0			0
$589$	−5.10412			−0.210312
$590$		−	5.33043i		−	0.219450i
$591$	5.11358	−	5.24733i	0.210345	−	0.215846i
$592$	6.55608			0.269453
$593$	14.5622			0.597997			0.298999	−	0.954254i	$-0.403347\pi$
$593$	14.5622			0.597997			0.298999	+	0.954254i	$0.403347\pi$
$594$	1.37227	−	1.48289i	0.0563050	−	0.0608439i
$595$		0			0
$596$			2.95913i			0.121211i
$597$	−5.73997	+	5.89010i	−0.234921	+	0.241066i
$598$		−	3.41670i		−	0.139719i
$599$			1.64056i			0.0670316i	0.999438	+	0.0335158i	$0.0106704\pi$
$599$			1.64056i			0.0670316i	−0.999438	+	0.0335158i	$0.989330\pi$
$600$	1.20883	−	1.24045i	0.0493504	−	0.0506412i
$601$		−	9.87727i		−	0.402902i	−0.979499	−	0.201451i	$-0.935434\pi$
$601$		−	9.87727i		−	0.402902i	0.979499	−	0.201451i	$-0.0645658\pi$
$602$		0			0
$603$	0.915505	+	35.4535i	0.0372822	+	1.44378i
$604$	−8.33959			−0.339333
$605$	10.8488			0.441067
$606$	19.9568	−	20.4788i	0.810691	−	0.831895i
$607$		−	13.7514i		−	0.558153i	−0.960269	−	0.279076i	$-0.909972\pi$
$607$		−	13.7514i		−	0.558153i	0.960269	−	0.279076i	$-0.0900283\pi$
$608$	−0.597750			−0.0242420
$609$		0			0
$610$	−14.8030			−0.599354
$611$			2.33391i			0.0944198i
$612$	−0.0450362	−	1.74406i	−0.00182048	−	0.0704993i
$613$	−19.7544			−0.797872			−0.398936	−	0.916979i	$-0.630620\pi$
$613$	−19.7544			−0.797872			−0.398936	+	0.916979i	$0.630620\pi$
$614$	−8.92019			−0.359990
$615$	−3.29099	−	3.20710i	−0.132706	−	0.129323i
$616$		0			0
$617$		−	14.3699i		−	0.578509i	−0.957252	−	0.289255i	$-0.906593\pi$
$617$		−	14.3699i		−	0.578509i	0.957252	−	0.289255i	$-0.0934074\pi$
$618$	3.33638	+	3.25134i	0.134209	+	0.130788i
$619$		−	5.11190i		−	0.205465i	−0.994709	−	0.102732i	$-0.967242\pi$
$619$		−	5.11190i		−	0.205465i	0.994709	−	0.102732i	$-0.0327585\pi$
$620$		−	8.53890i		−	0.342930i
$621$	−29.8733	−	27.6447i	−1.19877	−	1.10935i
$622$			0.960152i			0.0384986i
$623$		0			0
$624$	−0.527280	+	0.541071i	−0.0211081	+	0.0216602i
$625$	1.00000			0.0400000
$626$	4.56673			0.182523
$627$	−0.288310	−	0.280961i	−0.0115140	−	0.0112205i
$628$			22.4692i			0.896618i
$629$	3.81266			0.152021
$630$		0			0
$631$	−38.6945			−1.54040			−0.770202	−	0.637800i	$-0.779845\pi$
$631$	−38.6945			−1.54040			−0.770202	+	0.637800i	$0.779845\pi$
$632$		−	4.78108i		−	0.190181i
$633$	17.8507	+	17.3957i	0.709502	+	0.691417i
$634$	12.2121			0.485004
$635$	−18.1119			−0.718749
$636$	−9.26128	+	9.50352i	−0.367234	+	0.376839i
$637$		0			0
$638$			0.931497i			0.0368783i
$639$	43.5810	−	1.12538i	1.72404	−	0.0445193i
$640$		−	1.00000i		−	0.0395285i
$641$		−	20.7823i		−	0.820851i	−0.911894	−	0.410426i	$-0.865380\pi$
$641$		−	20.7823i		−	0.820851i	0.911894	−	0.410426i	$-0.134620\pi$
$642$	12.5990	+	12.2779i	0.497244	+	0.484569i
$643$			36.2631i			1.43008i	0.699084	+	0.715039i	$0.253591\pi$
$643$			36.2631i			1.43008i	−0.699084	+	0.715039i	$0.746409\pi$
$644$		0			0
$645$	−13.8485	−	13.4955i	−0.545282	−	0.531383i
$646$	−0.347619			−0.0136769
$647$	−2.34138			−0.0920492			−0.0460246	−	0.998940i	$-0.514655\pi$
$647$	−2.34138			−0.0920492			−0.0460246	+	0.998940i	$0.514655\pi$
$648$	0.464498	+	8.98801i	0.0182472	+	0.353082i
$649$		−	2.07263i		−	0.0813580i
$650$	−0.436189			−0.0171087
$651$		0			0
$652$	13.6027			0.532724
$653$			44.9330i			1.75836i	0.476487	+	0.879182i	$0.341910\pi$
$653$			44.9330i			1.75836i	−0.476487	+	0.879182i	$0.658090\pi$
$654$	−11.8655	+	12.1759i	−0.463980	+	0.476116i
$655$	2.03892			0.0796672
$656$	−2.65306			−0.103584
$657$	−22.5444	+	0.582157i	−0.879541	+	0.0227121i
$658$		0			0
$659$			21.9425i			0.854759i	0.904072	+	0.427380i	$0.140563\pi$
$659$			21.9425i			0.854759i	−0.904072	+	0.427380i	$0.859437\pi$
$660$	0.470031	−	0.482326i	0.0182959	−	0.0187745i
$661$		−	10.3004i		−	0.400639i	−0.979731	−	0.200319i	$-0.935802\pi$
$661$		−	10.3004i		−	0.400639i	0.979731	−	0.200319i	$-0.0641980\pi$
$662$			19.3496i			0.752044i
$663$	−0.306638	+	0.314658i	−0.0119088	+	0.0122203i
$664$		−	0.157211i		−	0.00610098i
$665$		0			0
$666$	−19.6617	+	0.507717i	−0.761875	+	0.0196736i
$667$	18.7652			0.726592
$668$	−20.4857			−0.792615
$669$	20.9714	−	21.5200i	0.810802	−	0.832010i
$670$			11.8218i			0.456715i
$671$	−5.75584			−0.222202
$672$		0			0
$673$	16.4103			0.632569			0.316284	−	0.948664i	$-0.397565\pi$
$673$	16.4103			0.632569			0.316284	+	0.948664i	$0.397565\pi$
$674$			32.9183i			1.26797i
$675$	−3.52923	+	3.81373i	−0.135840	+	0.146791i
$676$	−12.8097			−0.492682
$677$	−34.8088			−1.33781			−0.668906	−	0.743347i	$-0.733237\pi$
$677$	−34.8088			−1.33781			−0.668906	+	0.743347i	$0.733237\pi$
$678$	10.7705	+	10.4960i	0.413638	+	0.403095i
$679$		0			0
$680$		−	0.581546i		−	0.0223013i
$681$	15.2183	+	14.8304i	0.583167	+	0.568302i
$682$		−	3.32018i		−	0.127136i
$683$		−	8.67671i		−	0.332005i	−0.986125	−	0.166002i	$-0.946914\pi$
$683$		−	8.67671i		−	0.332005i	0.986125	−	0.166002i	$-0.0530860\pi$
$684$	1.79265	−	0.0462911i	0.0685438	−	0.00176998i
$685$		−	16.1364i		−	0.616542i
$686$		0			0
$687$	1.74110	−	1.78664i	0.0664270	−	0.0681644i
$688$	−11.1640			−0.425625
$689$	3.34179			0.127312
$690$	−9.71656	−	9.46889i	−0.369903	−	0.360475i
$691$		−	8.45771i		−	0.321746i	−0.986975	−	0.160873i	$-0.948569\pi$
$691$		−	8.45771i		−	0.321746i	0.986975	−	0.160873i	$-0.0514310\pi$
$692$	15.3753			0.584480
$693$		0			0
$694$	−6.94260			−0.263537
$695$			12.3487i			0.468414i
$696$	−2.97167	−	2.89593i	−0.112641	−	0.109770i
$697$	−1.54287			−0.0584405
$698$	22.3154			0.844649
$699$	−32.8980	+	33.7585i	−1.24432	+	1.27686i
$700$		0			0
$701$			8.82591i			0.333350i	0.986012	+	0.166675i	$0.0533031\pi$
$701$			8.82591i			0.333350i	−0.986012	+	0.166675i	$0.946697\pi$
$702$	1.53941	−	1.66351i	0.0581013	−	0.0627850i
$703$			3.91890i			0.147804i
$704$		−	0.388831i		−	0.0146546i
$705$	6.63726	+	6.46808i	0.249974	+	0.243602i
$706$			27.3114i			1.02788i
$707$		0			0
$708$	6.61215	+	6.44361i	0.248500	+	0.242166i
$709$	−12.1827			−0.457533			−0.228766	−	0.973481i	$-0.573469\pi$
$709$	−12.1827			−0.457533			−0.228766	+	0.973481i	$0.573469\pi$
$710$	14.5318			0.545370
$711$	0.370257	+	14.3385i	0.0138857	+	0.537734i
$712$		−	11.1040i		−	0.416142i
$713$	−66.8859			−2.50490
$714$		0			0
$715$	−0.169604			−0.00634281
$716$		−	1.13504i		−	0.0424183i
$717$	−24.9777	+	25.6310i	−0.932810	+	0.957209i
$718$	10.2004			0.380676
$719$	−40.6750			−1.51692			−0.758460	−	0.651719i	$-0.774048\pi$
$719$	−40.6750			−1.51692			−0.758460	+	0.651719i	$0.774048\pi$
$720$	0.0774422	+	2.99900i	0.00288610	+	0.111766i
$721$		0			0
$722$			18.6427i			0.693809i
$723$	14.2929	−	14.6668i	0.531559	−	0.545462i
$724$			11.1559i			0.414605i
$725$		−	2.39564i		−	0.0889718i
$726$	−13.1144	+	13.4574i	−0.486721	+	0.499452i
$727$			36.8741i			1.36758i	0.729677	+	0.683792i	$0.239671\pi$
$727$			36.8741i			1.36758i	−0.729677	+	0.683792i	$0.760329\pi$
$728$		0			0
$729$	−2.08908	−	26.9191i	−0.0773734	−	0.997002i
$730$	−7.51730			−0.278228
$731$	−6.49240			−0.240130
$732$	17.8943	−	18.3623i	0.661393	−	0.678692i
$733$		−	39.5252i		−	1.45990i	−0.683503	−	0.729948i	$-0.739544\pi$
$733$		−	39.5252i		−	1.45990i	0.683503	−	0.729948i	$-0.260456\pi$
$734$	9.33458			0.344546
$735$		0			0
$736$	−7.83308			−0.288731
$737$			4.59667i			0.169321i
$738$	7.95652	−	0.205459i	0.292883	−	0.00756303i
$739$	−41.5566			−1.52868			−0.764341	−	0.644812i	$-0.776936\pi$
$739$	−41.5566			−1.52868			−0.764341	+	0.644812i	$0.776936\pi$
$740$	−6.55608			−0.241006
$741$	−0.323425	−	0.315181i	−0.0118813	−	0.0115785i
$742$		0			0
$743$		−	0.833494i		−	0.0305779i	−0.999883	−	0.0152890i	$-0.995133\pi$
$743$		−	0.833494i		−	0.0305779i	0.999883	−	0.0152890i	$-0.00486682\pi$
$744$	10.5921	+	10.3221i	0.388325	+	0.378427i
$745$		−	2.95913i		−	0.108414i
$746$		−	7.34793i		−	0.269027i
$747$	0.0121748	+	0.471476i	0.000445452	+	0.0172504i
$748$		−	0.226123i		−	0.00826787i
$749$		0			0
$750$	−1.20883	+	1.24045i	−0.0441404	+	0.0452949i
$751$	12.7670			0.465874			0.232937	−	0.972492i	$-0.425166\pi$
$751$	12.7670			0.465874			0.232937	+	0.972492i	$0.425166\pi$
$752$	5.35068			0.195119
$753$	32.3224	+	31.4985i	1.17789	+	1.14787i
$754$			1.04495i			0.0380549i
$755$	8.33959			0.303509
$756$		0			0
$757$	−35.3506			−1.28484			−0.642420	−	0.766353i	$-0.722070\pi$
$757$	−35.3506			−1.28484			−0.642420	+	0.766353i	$0.722070\pi$
$758$			11.2225i			0.407620i
$759$	−3.77810	−	3.68179i	−0.137136	−	0.133641i
$760$	0.597750			0.0216827
$761$	−38.2309			−1.38587			−0.692935	−	0.721000i	$-0.743683\pi$
$761$	−38.2309			−1.38587			−0.692935	+	0.721000i	$0.743683\pi$
$762$	21.8943	−	22.4669i	0.793146	−	0.813891i
$763$		0			0
$764$			5.87467i			0.212538i
$765$	0.0450362	+	1.74406i	0.00162829	+	0.0630565i
$766$		−	22.5133i		−	0.813438i
$767$		−	2.32508i		−	0.0839536i
$768$	1.24045	+	1.20883i	0.0447610	+	0.0436200i
$769$			35.5109i			1.28056i	0.768143	+	0.640279i	$0.221181\pi$
$769$			35.5109i			1.28056i	−0.768143	+	0.640279i	$0.778819\pi$
$770$		0			0
$771$	8.61335	+	8.39380i	0.310202	+	0.302295i
$772$	−2.60022			−0.0935839
$773$	−13.4235			−0.482811			−0.241406	−	0.970424i	$-0.577608\pi$
$773$	−13.4235			−0.482811			−0.241406	+	0.970424i	$0.577608\pi$
$774$	33.4810	−	0.864568i	1.20345	−	0.0310762i
$775$			8.53890i			0.306726i
$776$	1.08768			0.0390455
$777$		0			0
$778$	20.8569			0.747755
$779$		−	1.58586i		−	0.0568195i
$780$	0.527280	−	0.541071i	0.0188796	−	0.0193735i
$781$	5.65042			0.202188
$782$	−4.55530			−0.162897
$783$	9.13632	+	8.45476i	0.326505	+	0.302148i
$784$		0			0
$785$		−	22.4692i		−	0.801959i
$786$	−2.46472	+	2.52918i	−0.0879135	+	0.0902130i
$787$		−	4.82661i		−	0.172050i	−0.996293	−	0.0860251i	$-0.972583\pi$
$787$		−	4.82661i		−	0.172050i	0.996293	−	0.0860251i	$-0.0274165\pi$
$788$			4.23018i			0.150694i
$789$	13.8107	−	14.1719i	0.491674	−	0.504534i
$790$			4.78108i			0.170103i
$791$		0			0
$792$	0.0301119	+	1.16610i	0.00106998	+	0.0414357i
$793$	−6.45688			−0.229291
$794$	−5.80599			−0.206047
$795$	9.26128	−	9.50352i	0.328464	−	0.337055i
$796$		−	4.74835i		−	0.168301i
$797$	−43.5755			−1.54352			−0.771762	−	0.635912i	$-0.780624\pi$
$797$	−43.5755			−1.54352			−0.771762	+	0.635912i	$0.780624\pi$
$798$		0			0
$799$	3.11167			0.110083
$800$			1.00000i			0.0353553i
$801$	0.859922	+	33.3010i	0.0303838	+	1.17663i
$802$	7.60821			0.268655
$803$	−2.92296			−0.103149
$804$	−14.6644	−	14.2906i	−0.517172	−	0.503990i
$805$		0			0
$806$		−	3.72457i		−	0.131192i
$807$	13.9822	+	13.6258i	0.492196	+	0.479650i
$808$			16.5092i			0.580790i
$809$			27.0518i			0.951091i	0.879691	+	0.475546i	$0.157749\pi$
$809$			27.0518i			0.951091i	−0.879691	+	0.475546i	$0.842251\pi$
$810$	−0.464498	−	8.98801i	−0.0163208	−	0.315806i
$811$			36.2283i			1.27215i	0.771628	+	0.636074i	$0.219443\pi$
$811$			36.2283i			1.27215i	−0.771628	+	0.636074i	$0.780557\pi$
$812$		0			0
$813$	−24.7404	+	25.3875i	−0.867684	+	0.890379i
$814$	−2.54920			−0.0893496
$815$	−13.6027			−0.476483
$816$	0.721380	+	0.702992i	0.0252533	+	0.0246097i
$817$		−	6.67330i		−	0.233469i
$818$	−25.4555			−0.890032
$819$		0			0
$820$	2.65306			0.0926488
$821$			35.5633i			1.24117i	0.784140	+	0.620583i	$0.213104\pi$
$821$			35.5633i			1.24117i	−0.784140	+	0.620583i	$0.786896\pi$
$822$	20.0165	+	19.5063i	0.698155	+	0.680360i
$823$	−31.5533			−1.09988			−0.549940	−	0.835204i	$-0.685349\pi$
$823$	−31.5533			−1.09988			−0.549940	+	0.835204i	$0.685349\pi$
$824$	−2.68965			−0.0936984
$825$	−0.470031	+	0.482326i	−0.0163644	+	0.0167924i
$826$		0			0
$827$		−	34.3366i		−	1.19400i	−0.802241	−	0.597000i	$-0.796359\pi$
$827$		−	34.3366i		−	1.19400i	0.802241	−	0.597000i	$-0.203641\pi$
$828$	23.4914	−	0.606611i	0.816383	−	0.0210812i
$829$		−	14.9753i		−	0.520115i	−0.965593	−	0.260057i	$-0.916258\pi$
$829$		−	14.9753i		−	0.520115i	0.965593	−	0.260057i	$-0.0837415\pi$
$830$			0.157211i			0.00545688i
$831$	9.28509	+	9.04842i	0.322096	+	0.313886i
$832$		−	0.436189i		−	0.0151221i
$833$		0			0
$834$	−15.3180	−	14.9276i	−0.530419	−	0.516899i
$835$	20.4857			0.708936
$836$	0.232423			0.00803853
$837$	−32.5650	−	30.1357i	−1.12561	−	1.04164i
$838$			32.2860i			1.11530i
$839$	36.5386			1.26145			0.630727	−	0.776005i	$-0.282757\pi$
$839$	36.5386			1.26145			0.630727	+	0.776005i	$0.282757\pi$
$840$		0			0
$841$	23.2609			0.802101
$842$			2.83642i			0.0977496i
$843$	13.4348	−	13.7862i	0.462720	−	0.474822i
$844$	−14.3905			−0.495341
$845$	12.8097			0.440668
$846$	−16.0467	+	0.414368i	−0.551697	+	0.0142463i
$847$		0			0
$848$		−	7.66134i		−	0.263091i
$849$	−33.6956	+	34.5769i	−1.15643	+	1.18668i
$850$			0.581546i			0.0199469i
$851$			51.3543i			1.76040i
$852$	−17.5666	+	18.0261i	−0.601821	+	0.617563i
$853$			28.9097i			0.989848i	0.868936	+	0.494924i	$0.164804\pi$
$853$			28.9097i			0.989848i	−0.868936	+	0.494924i	$0.835196\pi$
$854$		0			0
$855$	−1.79265	+	0.0462911i	−0.0613074	+	0.00158312i
$856$	−10.1568			−0.347152
$857$	8.54473			0.291882			0.145941	−	0.989293i	$-0.453379\pi$
$857$	8.54473			0.291882			0.145941	+	0.989293i	$0.453379\pi$
$858$	0.205023	−	0.210385i	0.00699935	−	0.00718243i
$859$			2.49789i			0.0852268i	0.999092	+	0.0426134i	$0.0135684\pi$
$859$			2.49789i			0.0852268i	−0.999092	+	0.0426134i	$0.986432\pi$
$860$	11.1640			0.380691
$861$		0			0
$862$	−33.8559			−1.15314
$863$		−	20.9966i		−	0.714734i	−0.933964	−	0.357367i	$-0.883675\pi$
$863$		−	20.9966i		−	0.714734i	0.933964	−	0.357367i	$-0.116325\pi$
$864$	−3.81373	−	3.52923i	−0.129746	−	0.120067i
$865$	−15.3753			−0.522774
$866$	36.2694			1.23249
$867$	−20.6682	−	20.1414i	−0.701928	−	0.684036i
$868$		0			0
$869$			1.85903i			0.0630633i
$870$	2.97167	+	2.89593i	0.100749	+	0.0981812i
$871$			5.15653i			0.174722i
$872$		−	9.81570i		−	0.332402i
$873$	−3.26195	+	0.0842324i	−0.110400	+	0.00285083i
$874$		−	4.68222i		−	0.158379i
$875$		0			0
$876$	9.08717	−	9.32486i	0.307027	−	0.315058i
$877$	−29.8881			−1.00925			−0.504625	−	0.863339i	$-0.668369\pi$
$877$	−29.8881			−1.00925			−0.504625	+	0.863339i	$0.668369\pi$
$878$	−27.1425			−0.916015
$879$	−24.5045	−	23.8799i	−0.826515	−	0.805447i
$880$			0.388831i			0.0131075i
$881$	−34.6874			−1.16865			−0.584324	−	0.811521i	$-0.698640\pi$
$881$	−34.6874			−1.16865			−0.584324	+	0.811521i	$0.698640\pi$
$882$		0			0
$883$	10.8034			0.363564			0.181782	−	0.983339i	$-0.441813\pi$
$883$	10.8034			0.363564			0.181782	+	0.983339i	$0.441813\pi$
$884$		−	0.253664i		−	0.00853164i
$885$	−6.61215	−	6.44361i	−0.222265	−	0.216599i
$886$	−11.7451			−0.394583
$887$	16.6529			0.559150			0.279575	−	0.960124i	$-0.409806\pi$
$887$	16.6529			0.559150			0.279575	+	0.960124i	$0.409806\pi$
$888$	7.92521	−	8.13250i	0.265953	−	0.272909i
$889$		0			0
$890$			11.1040i			0.372209i
$891$	−0.180611	−	3.49481i	−0.00605070	−	0.117081i
$892$			17.3485i			0.580870i
$893$			3.19837i			0.107029i
$894$	3.67066	+	3.57709i	0.122765	+	0.119636i
$895$			1.13504i			0.0379401i
$896$		0			0
$897$	−4.23826	−	4.13023i	−0.141511	−	0.137904i
$898$	19.2663			0.642926
$899$	20.4561			0.682249
$900$	−0.0774422	−	2.99900i	−0.00258141	−	0.0999667i
$901$		−	4.45542i		−	0.148432i
$902$	1.03159			0.0343482
$903$		0			0
$904$	−8.68271			−0.288783
$905$		−	11.1559i		−	0.370834i
$906$	−10.0812	+	10.3449i	−0.334925	+	0.343685i
$907$	0.100841			0.00334836			0.00167418	−	0.999999i	$-0.499467\pi$
$907$	0.100841			0.00334836			0.00167418	+	0.999999i	$0.499467\pi$
$908$	−12.2684			−0.407140
$909$	−1.27851	−	49.5110i	−0.0424054	−	1.64218i
$910$		0			0
$911$		−	0.686016i		−	0.0227287i	−0.999935	−	0.0113644i	$-0.996383\pi$
$911$		−	0.686016i		−	0.0227287i	0.999935	−	0.0113644i	$-0.00361747\pi$
$912$	−0.722580	+	0.741480i	−0.0239270	+	0.0245529i
$913$			0.0611285i			0.00202306i
$914$		−	9.32357i		−	0.308396i
$915$	−17.8943	+	18.3623i	−0.591567	+	0.607041i
$916$			1.44031i			0.0475892i
$917$		0			0
$918$	−2.21786	−	2.05241i	−0.0732003	−	0.0677396i
$919$	2.42356			0.0799459			0.0399729	−	0.999201i	$-0.487273\pi$
$919$	2.42356			0.0799459			0.0399729	+	0.999201i	$0.487273\pi$
$920$	7.83308			0.258249
$921$	−10.7830	+	11.0651i	−0.355313	+	0.364606i
$922$		−	6.36590i		−	0.209650i
$923$	6.33863			0.208639
$924$		0			0
$925$	6.55608			0.215563
$926$		−	1.83216i		−	0.0602083i
$927$	8.06627	−	0.208292i	0.264931	−	0.00684122i
$928$	2.39564			0.0786407
$929$	22.4384			0.736179			0.368090	−	0.929790i	$-0.380012\pi$
$929$	22.4384			0.736179			0.368090	+	0.929790i	$0.380012\pi$
$930$	−10.5921	−	10.3221i	−0.347328	−	0.338475i
$931$		0			0
$932$		−	27.2147i		−	0.891446i
$933$	1.19102	+	1.16066i	0.0389923	+	0.0379984i
$934$			2.25893i			0.0739143i
$935$			0.226123i			0.00739501i
$936$	0.0337794	+	1.30813i	0.00110412	+	0.0427576i
$937$		−	8.08505i		−	0.264127i	−0.991241	−	0.132063i	$-0.957840\pi$
$937$		−	8.08505i		−	0.264127i	0.991241	−	0.132063i	$-0.0421603\pi$
$938$		0			0
$939$	5.52042	−	5.66481i	0.180152	−	0.184864i
$940$	−5.35068			−0.174520
$941$	−29.7880			−0.971062			−0.485531	−	0.874219i	$-0.661374\pi$
$941$	−29.7880			−0.971062			−0.485531	+	0.874219i	$0.661374\pi$
$942$	27.8719	+	27.1615i	0.908117	+	0.884970i
$943$		−	20.7816i		−	0.676742i
$944$	−5.33043			−0.173491
$945$		0			0
$946$	4.34092			0.141135
$947$		−	28.2621i		−	0.918395i	−0.888334	−	0.459198i	$-0.848137\pi$
$947$		−	28.2621i		−	0.918395i	0.888334	−	0.459198i	$-0.151863\pi$
$948$	−5.93070	−	5.77953i	−0.192620	−	0.187710i
$949$	−3.27897			−0.106440
$950$	−0.597750			−0.0193936
$951$	14.7624	−	15.1485i	0.478703	−	0.491224i
$952$		0			0
$953$		−	27.9316i		−	0.904794i	−0.891817	−	0.452397i	$-0.850569\pi$
$953$		−	27.9316i		−	0.904794i	0.891817	−	0.452397i	$-0.149431\pi$
$954$	0.593311	+	22.9763i	0.0192091	+	0.743887i
$955$		−	5.87467i		−	0.190100i
$956$		−	20.6627i		−	0.668278i
$957$	1.15548	+	1.12603i	0.0373513	+	0.0363992i
$958$			37.0085i			1.19569i
$959$		0			0
$960$	−1.24045	−	1.20883i	−0.0400354	−	0.0390149i
$961$	−41.9127			−1.35202
$962$	−2.85969			−0.0922001
$963$	30.4602	−	0.786565i	0.981568	−	0.0253467i
$964$			11.8237i			0.380816i
$965$	2.60022			0.0837040
$966$		0			0
$967$	4.70893			0.151429			0.0757144	−	0.997130i	$-0.475876\pi$
$967$	4.70893			0.151429			0.0757144	+	0.997130i	$0.475876\pi$
$968$		−	10.8488i		−	0.348694i
$969$	−0.420214	+	0.431205i	−0.0134992	+	0.0138523i
$970$	−1.08768			−0.0349233
$971$	29.4048			0.943646			0.471823	−	0.881693i	$-0.343596\pi$
$971$	29.4048			0.943646			0.471823	+	0.881693i	$0.343596\pi$
$972$	11.7107	+	10.2888i	0.375621	+	0.330014i
$973$		0			0
$974$		−	40.3476i		−	1.29282i
$975$	−0.527280	+	0.541071i	−0.0168865	+	0.0173282i
$976$			14.8030i			0.473831i
$977$		−	22.8318i		−	0.730455i	−0.930918	−	0.365228i	$-0.880991\pi$
$977$		−	22.8318i		−	0.730455i	0.930918	−	0.365228i	$-0.119009\pi$
$978$	16.4434	−	16.8735i	0.525803	−	0.539556i
$979$			4.31759i			0.137991i
$980$		0			0
$981$	0.760149	+	29.4373i	0.0242697	+	0.939860i
$982$	27.8602			0.889054
$983$	−51.8878			−1.65496			−0.827482	−	0.561493i	$-0.810227\pi$
$983$	−51.8878			−1.65496			−0.827482	+	0.561493i	$0.810227\pi$
$984$	−3.20710	+	3.29099i	−0.102239	+	0.104913i
$985$		−	4.23018i		−	0.134785i
$986$	1.39317			0.0443677
$987$		0			0
$988$	0.260732			0.00829499
$989$		−	87.4488i		−	2.78071i
$990$	−0.0301119	−	1.16610i	−0.000957019	−	0.0370612i
$991$	−25.7580			−0.818231			−0.409115	−	0.912483i	$-0.634163\pi$
$991$	−25.7580			−0.818231			−0.409115	+	0.912483i	$0.634163\pi$
$992$	−8.53890			−0.271110
$993$	24.0023	+	23.3904i	0.761688	+	0.742273i
$994$		0			0
$995$			4.74835i			0.150533i
$996$	−0.195013	−	0.190042i	−0.00617922	−	0.00602171i
$997$		−	49.2249i		−	1.55897i	−0.626423	−	0.779484i	$-0.715482\pi$
$997$		−	49.2249i		−	1.55897i	0.626423	−	0.779484i	$-0.284518\pi$
$998$			14.0739i			0.445501i
$999$	−23.1379	+	25.0031i	−0.732051	+	0.791064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.d.881.13	yes	16
3.2	odd	2		1470.2.b.c.881.4	✓	16
7.6	odd	2		1470.2.b.c.881.12	yes	16
21.20	even	2	inner	1470.2.b.d.881.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.b.c.881.4	✓	16	3.2	odd	2
1470.2.b.c.881.12	yes	16	7.6	odd	2
1470.2.b.d.881.5	yes	16	21.20	even	2	inner
1470.2.b.d.881.13	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.24045 + 1.20883i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-1.20883 + 1.24045i) q^{6} -1.00000i q^{8} +(0.0774422 + 2.99900i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.24045 + 1.20883i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-1.20883 + 1.24045i) q^{6} -1.00000i q^{8} +(0.0774422 + 2.99900i) q^{9} +1.00000i q^{10} +0.388831i q^{11} +(-1.24045 - 1.20883i) q^{12} +0.436189i q^{13} +(1.24045 + 1.20883i) q^{15} +1.00000 q^{16} +0.581546 q^{17} +(-2.99900 + 0.0774422i) q^{18} +0.597750i q^{19} -1.00000 q^{20} -0.388831 q^{22} +7.83308i q^{23} +(1.20883 - 1.24045i) q^{24} +1.00000 q^{25} -0.436189 q^{26} +(-3.52923 + 3.81373i) q^{27} -2.39564i q^{29} +(-1.20883 + 1.24045i) q^{30} +8.53890i q^{31} +1.00000i q^{32} +(-0.470031 + 0.482326i) q^{33} +0.581546i q^{34} +(-0.0774422 - 2.99900i) q^{36} +6.55608 q^{37} -0.597750 q^{38} +(-0.527280 + 0.541071i) q^{39} -1.00000i q^{40} -2.65306 q^{41} -11.1640 q^{43} -0.388831i q^{44} +(0.0774422 + 2.99900i) q^{45} -7.83308 q^{46} +5.35068 q^{47} +(1.24045 + 1.20883i) q^{48} +1.00000i q^{50} +(0.721380 + 0.702992i) q^{51} -0.436189i q^{52} -7.66134i q^{53} +(-3.81373 - 3.52923i) q^{54} +0.388831i q^{55} +(-0.722580 + 0.741480i) q^{57} +2.39564 q^{58} -5.33043 q^{59} +(-1.24045 - 1.20883i) q^{60} +14.8030i q^{61} -8.53890 q^{62} -1.00000 q^{64} +0.436189i q^{65} +(-0.482326 - 0.470031i) q^{66} +11.8218 q^{67} -0.581546 q^{68} +(-9.46889 + 9.71656i) q^{69} -14.5318i q^{71} +(2.99900 - 0.0774422i) q^{72} +7.51730i q^{73} +6.55608i q^{74} +(1.24045 + 1.20883i) q^{75} -0.597750i q^{76} +(-0.541071 - 0.527280i) q^{78} +4.78108 q^{79} +1.00000 q^{80} +(-8.98801 + 0.464498i) q^{81} -2.65306i q^{82} +0.157211 q^{83} +0.581546 q^{85} -11.1640i q^{86} +(2.89593 - 2.97167i) q^{87} +0.388831 q^{88} +11.1040 q^{89} +(-2.99900 + 0.0774422i) q^{90} -7.83308i q^{92} +(-10.3221 + 10.5921i) q^{93} +5.35068i q^{94} +0.597750i q^{95} +(-1.20883 + 1.24045i) q^{96} +1.08768i q^{97} +(-1.16610 + 0.0301119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} + 16 q^{5} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 16 * q^4 + 16 * q^5 + 8 * q^9	\( 16 q + 8 q^{3} - 16 q^{4} + 16 q^{5} + 8 q^{9} - 8 q^{12} + 8 q^{15} + 16 q^{16} - 48 q^{17} - 16 q^{20} + 16 q^{25} + 16 q^{26} + 8 q^{27} - 8 q^{36} - 16 q^{41} + 16 q^{43} + 8 q^{45} - 16 q^{46} - 32 q^{47} + 8 q^{48} + 16 q^{51} + 32 q^{57} + 16 q^{58} - 32 q^{59} - 8 q^{60} - 16 q^{62} - 16 q^{64} + 16 q^{67} + 48 q^{68} + 8 q^{75} - 32 q^{78} - 48 q^{79} + 16 q^{80} + 8 q^{81} - 48 q^{83} - 48 q^{85} - 16 q^{89} - 64 q^{93} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 16 * q^4 + 16 * q^5 + 8 * q^9 - 8 * q^12 + 8 * q^15 + 16 * q^16 - 48 * q^17 - 16 * q^20 + 16 * q^25 + 16 * q^26 + 8 * q^27 - 8 * q^36 - 16 * q^41 + 16 * q^43 + 8 * q^45 - 16 * q^46 - 32 * q^47 + 8 * q^48 + 16 * q^51 + 32 * q^57 + 16 * q^58 - 32 * q^59 - 8 * q^60 - 16 * q^62 - 16 * q^64 + 16 * q^67 + 48 * q^68 + 8 * q^75 - 32 * q^78 - 48 * q^79 + 16 * q^80 + 8 * q^81 - 48 * q^83 - 48 * q^85 - 16 * q^89 - 64 * q^93 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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