LMFDB - Embedded newform 882.2.l.b.509.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (of order $6$, degree $2$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.2
Root			$-1.68301 - 0.409224i$ of defining polynomial
Character	$\chi$	$=$	882.509
Dual form			882.2.l.b.227.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.38631 - 1.03834i) q^{3} -1.00000 q^{4} +(-0.714925 - 1.23829i) q^{5} +(-1.03834 + 1.38631i) q^{6} +1.00000i q^{8} +(0.843698 + 2.87892i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.38631 - 1.03834i) q^{3} -1.00000 q^{4} +(-0.714925 - 1.23829i) q^{5} +(-1.03834 + 1.38631i) q^{6} +1.00000i q^{8} +(0.843698 + 2.87892i) q^{9} +(-1.23829 + 0.714925i) q^{10} +(2.96133 + 1.70972i) q^{11} +(1.38631 + 1.03834i) q^{12} +(5.48813 + 3.16857i) q^{13} +(-0.294657 + 2.45898i) q^{15} +1.00000 q^{16} +(1.14201 + 1.97802i) q^{17} +(2.87892 - 0.843698i) q^{18} +(1.87673 + 1.08353i) q^{19} +(0.714925 + 1.23829i) q^{20} +(1.70972 - 2.96133i) q^{22} +(-6.97507 + 4.02706i) q^{23} +(1.03834 - 1.38631i) q^{24} +(1.47776 - 2.55956i) q^{25} +(3.16857 - 5.48813i) q^{26} +(1.81967 - 4.86711i) q^{27} +(-0.298879 + 0.172558i) q^{29} +(2.45898 + 0.294657i) q^{30} -4.34228i q^{31} -1.00000i q^{32} +(-2.33004 - 5.44507i) q^{33} +(1.97802 - 1.14201i) q^{34} +(-0.843698 - 2.87892i) q^{36} +(1.07786 - 1.86690i) q^{37} +(1.08353 - 1.87673i) q^{38} +(-4.31818 - 10.0912i) q^{39} +(1.23829 - 0.714925i) q^{40} +(-0.202180 + 0.350186i) q^{41} +(2.90883 + 5.03824i) q^{43} +(-2.96133 - 1.70972i) q^{44} +(2.96175 - 3.10295i) q^{45} +(4.02706 + 6.97507i) q^{46} +5.51829 q^{47} +(-1.38631 - 1.03834i) q^{48} +(-2.55956 - 1.47776i) q^{50} +(0.470680 - 3.92793i) q^{51} +(-5.48813 - 3.16857i) q^{52} +(8.56310 - 4.94391i) q^{53} +(-4.86711 - 1.81967i) q^{54} -4.88930i q^{55} +(-1.47666 - 3.45080i) q^{57} +(0.172558 + 0.298879i) q^{58} -11.0296 q^{59} +(0.294657 - 2.45898i) q^{60} +11.4797i q^{61} -4.34228 q^{62} -1.00000 q^{64} -9.06117i q^{65} +(-5.44507 + 2.33004i) q^{66} +4.25366 q^{67} +(-1.14201 - 1.97802i) q^{68} +(13.8510 + 1.65976i) q^{69} +3.55393i q^{71} +(-2.87892 + 0.843698i) q^{72} +(0.201057 - 0.116080i) q^{73} +(-1.86690 - 1.07786i) q^{74} +(-4.70633 + 2.01392i) q^{75} +(-1.87673 - 1.08353i) q^{76} +(-10.0912 + 4.31818i) q^{78} +14.5620 q^{79} +(-0.714925 - 1.23829i) q^{80} +(-7.57635 + 4.85787i) q^{81} +(0.350186 + 0.202180i) q^{82} +(-0.811624 - 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} +(5.03824 - 2.90883i) q^{86} +(0.593511 + 0.0711198i) q^{87} +(-1.70972 + 2.96133i) q^{88} +(2.02974 - 3.51562i) q^{89} +(-3.10295 - 2.96175i) q^{90} +(6.97507 - 4.02706i) q^{92} +(-4.50877 + 6.01974i) q^{93} -5.51829i q^{94} -3.09858i q^{95} +(-1.03834 + 1.38631i) q^{96} +(9.18719 - 5.30423i) q^{97} +(-2.42369 + 9.96791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} + 12 q^{11} - 6 q^{13} - 18 q^{15} + 16 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 36 q^{27} + 6 q^{29} - 2 q^{37} - 12 q^{39} + 6 q^{41} - 2 q^{43} - 12 q^{44} + 30 q^{45} + 6 q^{46} + 36 q^{47} - 12 q^{50} + 6 q^{51} + 6 q^{52} - 36 q^{53} - 18 q^{54} + 6 q^{57} + 6 q^{58} - 60 q^{59} + 18 q^{60} - 36 q^{62} - 16 q^{64} - 24 q^{66} - 28 q^{67} - 18 q^{68} + 42 q^{69} + 12 q^{72} + 18 q^{74} - 60 q^{75} + 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{86} + 24 q^{87} + 24 q^{89} - 18 q^{90} + 6 q^{92} - 42 q^{93} - 6 q^{97} + 18 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 12 * q^11 - 6 * q^13 - 18 * q^15 + 16 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 36 * q^27 + 6 * q^29 - 2 * q^37 - 12 * q^39 + 6 * q^41 - 2 * q^43 - 12 * q^44 + 30 * q^45 + 6 * q^46 + 36 * q^47 - 12 * q^50 + 6 * q^51 + 6 * q^52 - 36 * q^53 - 18 * q^54 + 6 * q^57 + 6 * q^58 - 60 * q^59 + 18 * q^60 - 36 * q^62 - 16 * q^64 - 24 * q^66 - 28 * q^67 - 18 * q^68 + 42 * q^69 + 12 * q^72 + 18 * q^74 - 60 * q^75 + 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^86 + 24 * q^87 + 24 * q^89 - 18 * q^90 + 6 * q^92 - 42 * q^93 - 6 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.38631	−	1.03834i	−0.800385	−	0.599486i
$3$	−1.38631	−	1.03834i	−0.800385	−	0.599486i
$4$	−1.00000			−0.500000
$5$	−0.714925	−	1.23829i	−0.319724	−	0.553779i	0.660706	−	0.750645i	$-0.270257\pi$
$5$	−0.714925	−	1.23829i	−0.319724	−	0.553779i	−0.980430	+	0.196866i	$0.936924\pi$
$6$	−1.03834	+	1.38631i	−0.423901	+	0.565958i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.843698	+	2.87892i	0.281233	+	0.959640i
$10$	−1.23829	+	0.714925i	−0.391581	+	0.226079i
$11$	2.96133	+	1.70972i	0.892874	+	0.515501i	0.874881	−	0.484337i	$-0.160939\pi$
$11$	2.96133	+	1.70972i	0.892874	+	0.515501i	0.0179923	+	0.999838i	$0.494273\pi$
$12$	1.38631	+	1.03834i	0.400193	+	0.299743i
$13$	5.48813	+	3.16857i	1.52213	+	0.878804i	0.999658	+	0.0261501i	$0.00832479\pi$
$13$	5.48813	+	3.16857i	1.52213	+	0.878804i	0.522476	+	0.852654i	$0.325009\pi$
$14$		0			0
$15$	−0.294657	+	2.45898i	−0.0760802	+	0.634907i
$16$	1.00000			0.250000
$17$	1.14201	+	1.97802i	0.276978	+	0.479739i	0.970632	−	0.240569i	$-0.0773339\pi$
$17$	1.14201	+	1.97802i	0.276978	+	0.479739i	−0.693655	+	0.720308i	$0.744001\pi$
$18$	2.87892	−	0.843698i	0.678568	−	0.198861i
$19$	1.87673	+	1.08353i	0.430553	+	0.248580i	0.699582	−	0.714552i	$-0.253370\pi$
$19$	1.87673	+	1.08353i	0.430553	+	0.248580i	−0.269029	+	0.963132i	$0.586703\pi$
$20$	0.714925	+	1.23829i	0.159862	+	0.276889i
$21$		0			0
$22$	1.70972	−	2.96133i	0.364514	−	0.631357i
$23$	−6.97507	+	4.02706i	−1.45440	+	0.839699i	−0.998727	−	0.0504469i	$-0.983935\pi$
$23$	−6.97507	+	4.02706i	−1.45440	+	0.839699i	−0.455675	+	0.890146i	$0.650602\pi$
$24$	1.03834	−	1.38631i	0.211950	−	0.282979i
$25$	1.47776	−	2.55956i	0.295553	−	0.511912i
$26$	3.16857	−	5.48813i	0.621408	−	1.07631i
$27$	1.81967	−	4.86711i	0.350196	−	0.936676i
$28$		0			0
$29$	−0.298879	+	0.172558i	−0.0555003	+	0.0320431i	−0.527493	−	0.849559i	$-0.676868\pi$
$29$	−0.298879	+	0.172558i	−0.0555003	+	0.0320431i	0.471993	+	0.881602i	$0.343535\pi$
$30$	2.45898	+	0.294657i	0.448947	+	0.0537968i
$31$		−	4.34228i		−	0.779896i	−0.920837	−	0.389948i	$-0.872493\pi$
$31$		−	4.34228i		−	0.779896i	0.920837	−	0.389948i	$-0.127507\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.33004	−	5.44507i	−0.405607	−	0.947865i
$34$	1.97802	−	1.14201i	0.339227	−	0.195853i
$35$		0			0
$36$	−0.843698	−	2.87892i	−0.140616	−	0.479820i
$37$	1.07786	−	1.86690i	0.177199	−	0.306917i	−0.763721	−	0.645546i	$-0.776630\pi$
$37$	1.07786	−	1.86690i	0.177199	−	0.306917i	0.940920	+	0.338629i	$0.109963\pi$
$38$	1.08353	−	1.87673i	0.175772	−	0.304447i
$39$	−4.31818	−	10.0912i	−0.691462	−	1.61588i
$40$	1.23829	−	0.714925i	0.195790	−	0.113040i
$41$	−0.202180	+	0.350186i	−0.0315752	+	0.0546898i	−0.881381	−	0.472406i	$-0.843386\pi$
$41$	−0.202180	+	0.350186i	−0.0315752	+	0.0546898i	0.849806	+	0.527096i	$0.176719\pi$
$42$		0			0
$43$	2.90883	+	5.03824i	0.443592	+	0.768325i	0.997953	−	0.0639521i	$-0.0203705\pi$
$43$	2.90883	+	5.03824i	0.443592	+	0.768325i	−0.554361	+	0.832277i	$0.687037\pi$
$44$	−2.96133	−	1.70972i	−0.446437	−	0.257750i
$45$	2.96175	−	3.10295i	0.441511	−	0.462561i
$46$	4.02706	+	6.97507i	0.593757	+	1.02842i
$47$	5.51829			0.804926			0.402463	−	0.915436i	$-0.368154\pi$
$47$	5.51829			0.804926			0.402463	+	0.915436i	$0.368154\pi$
$48$	−1.38631	−	1.03834i	−0.200096	−	0.149872i
$49$		0			0
$50$	−2.55956	−	1.47776i	−0.361977	−	0.208987i
$51$	0.470680	−	3.92793i	0.0659084	−	0.550020i
$52$	−5.48813	−	3.16857i	−0.761067	−	0.439402i
$53$	8.56310	−	4.94391i	1.17623	−	0.679098i	0.221093	−	0.975253i	$-0.429038\pi$
$53$	8.56310	−	4.94391i	1.17623	−	0.679098i	0.955140	+	0.296155i	$0.0957044\pi$
$54$	−4.86711	−	1.81967i	−0.662330	−	0.247626i
$55$		−	4.88930i		−	0.659273i
$56$		0			0
$57$	−1.47666	−	3.45080i	−0.195588	−	0.457070i
$58$	0.172558	+	0.298879i	0.0226579	+	0.0392447i
$59$	−11.0296			−1.43593			−0.717966	−	0.696079i	$-0.754926\pi$
$59$	−11.0296			−1.43593			−0.717966	+	0.696079i	$0.754926\pi$
$60$	0.294657	−	2.45898i	0.0380401	−	0.317453i
$61$			11.4797i			1.46983i	0.678159	+	0.734915i	$0.262778\pi$
$61$			11.4797i			1.46983i	−0.678159	+	0.734915i	$0.737222\pi$
$62$	−4.34228			−0.551470
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	9.06117i		−	1.12390i
$66$	−5.44507	+	2.33004i	−0.670242	+	0.286808i
$67$	4.25366			0.519667			0.259833	−	0.965653i	$-0.416332\pi$
$67$	4.25366			0.519667			0.259833	+	0.965653i	$0.416332\pi$
$68$	−1.14201	−	1.97802i	−0.138489	−	0.239870i
$69$	13.8510	+	1.65976i	1.66747	+	0.199811i
$70$		0			0
$71$			3.55393i			0.421773i	0.977511	+	0.210887i	$0.0676351\pi$
$71$			3.55393i			0.421773i	−0.977511	+	0.210887i	$0.932365\pi$
$72$	−2.87892	+	0.843698i	−0.339284	+	0.0994307i
$73$	0.201057	−	0.116080i	0.0235320	−	0.0135862i	−0.488188	−	0.872739i	$-0.662342\pi$
$73$	0.201057	−	0.116080i	0.0235320	−	0.0135862i	0.511720	+	0.859152i	$0.329009\pi$
$74$	−1.86690	−	1.07786i	−0.217023	−	0.125298i
$75$	−4.70633	+	2.01392i	−0.543440	+	0.232547i
$76$	−1.87673	−	1.08353i	−0.215276	−	0.124290i
$77$		0			0
$78$	−10.0912	+	4.31818i	−1.14260	+	0.488937i
$79$	14.5620			1.63835			0.819177	−	0.573541i	$-0.194431\pi$
$79$	14.5620			1.63835			0.819177	+	0.573541i	$0.194431\pi$
$80$	−0.714925	−	1.23829i	−0.0799311	−	0.138445i
$81$	−7.57635	+	4.85787i	−0.841817	+	0.539764i
$82$	0.350186	+	0.202180i	0.0386716	+	0.0223270i
$83$	−0.811624	−	1.40577i	−0.0890873	−	0.154304i	0.818038	−	0.575164i	$-0.195062\pi$
$83$	−0.811624	−	1.40577i	−0.0890873	−	0.154304i	−0.907126	+	0.420860i	$0.861728\pi$
$84$		0			0
$85$	1.63290	−	2.82827i	0.177113	−	0.306769i
$86$	5.03824	−	2.90883i	0.543287	−	0.313667i
$87$	0.593511	+	0.0711198i	0.0636311	+	0.00762484i
$88$	−1.70972	+	2.96133i	−0.182257	+	0.315679i
$89$	2.02974	−	3.51562i	0.215152	−	0.372655i	−0.738167	−	0.674618i	$-0.764309\pi$
$89$	2.02974	−	3.51562i	0.215152	−	0.372655i	0.953320	+	0.301963i	$0.0976419\pi$
$90$	−3.10295	−	2.96175i	−0.327080	−	0.312196i
$91$		0			0
$92$	6.97507	−	4.02706i	0.727201	−	0.419850i
$93$	−4.50877	+	6.01974i	−0.467537	+	0.624218i
$94$		−	5.51829i		−	0.569169i
$95$		−	3.09858i		−	0.317908i
$96$	−1.03834	+	1.38631i	−0.105975	+	0.141489i
$97$	9.18719	−	5.30423i	0.932818	−	0.538563i	0.0451164	−	0.998982i	$-0.485634\pi$
$97$	9.18719	−	5.30423i	0.932818	−	0.538563i	0.887702	+	0.460419i	$0.152301\pi$
$98$		0			0
$99$	−2.42369	+	9.96791i	−0.243590	+	1.00181i
$100$	−1.47776	+	2.55956i	−0.147776	+	0.255956i
$101$	4.02443	−	6.97052i	0.400446	−	0.693593i	−0.593334	−	0.804957i	$-0.702189\pi$
$101$	4.02443	−	6.97052i	0.400446	−	0.693593i	0.993780	+	0.111364i	$0.0355219\pi$
$102$	−3.92793	−	0.470680i	−0.388923	−	0.0466043i
$103$	2.43692	−	1.40695i	0.240117	−	0.138631i	−0.375114	−	0.926979i	$-0.622396\pi$
$103$	2.43692	−	1.40695i	0.240117	−	0.138631i	0.615230	+	0.788347i	$0.289063\pi$
$104$	−3.16857	+	5.48813i	−0.310704	+	0.538156i
$105$		0			0
$106$	−4.94391	−	8.56310i	−0.480195	−	0.831722i
$107$	−13.7019	−	7.91078i	−1.32461	−	0.764764i	−0.340150	−	0.940371i	$-0.610478\pi$
$107$	−13.7019	−	7.91078i	−1.32461	−	0.764764i	−0.984460	+	0.175607i	$0.943811\pi$
$108$	−1.81967	+	4.86711i	−0.175098	+	0.468338i
$109$	5.10675	+	8.84514i	0.489138	+	0.847211i	0.999922	−	0.0124977i	$-0.00397826\pi$
$109$	5.10675	+	8.84514i	0.489138	+	0.847211i	−0.510784	+	0.859709i	$0.670645\pi$
$110$	−4.88930			−0.466176
$111$	−3.43272	+	1.46892i	−0.325819	+	0.139424i
$112$		0			0
$113$	7.28808	+	4.20778i	0.685605	+	0.395834i	0.801963	−	0.597373i	$-0.203789\pi$
$113$	7.28808	+	4.20778i	0.685605	+	0.395834i	−0.116359	+	0.993207i	$0.537122\pi$
$114$	−3.45080	+	1.47666i	−0.323197	+	0.138301i
$115$	9.97330	+	5.75809i	0.930015	+	0.536945i
$116$	0.298879	−	0.172558i	0.0277502	−	0.0160216i
$117$	−4.49174	+	18.4732i	−0.415262	+	1.70785i
$118$			11.0296i			1.01536i
$119$		0			0
$120$	−2.45898	−	0.294657i	−0.224473	−	0.0268984i
$121$	0.346305	+	0.599818i	0.0314823	+	0.0545289i
$122$	11.4797			1.03933
$123$	0.643896	−	0.275534i	0.0580581	−	0.0248440i
$124$			4.34228i			0.389948i
$125$	−11.3752			−1.01743
$126$		0			0
$127$	5.77773			0.512691			0.256345	−	0.966585i	$-0.417482\pi$
$127$	5.77773			0.512691			0.256345	+	0.966585i	$0.417482\pi$
$128$			1.00000i			0.0883883i
$129$	1.19888	−	10.0049i	0.105555	−	0.880883i
$130$	−9.06117			−0.794718
$131$	−2.22833	−	3.85959i	−0.194690	−	0.337214i	0.752109	−	0.659039i	$-0.229037\pi$
$131$	−2.22833	−	3.85959i	−0.194690	−	0.337214i	−0.946799	+	0.321825i	$0.895704\pi$
$132$	2.33004	+	5.44507i	0.202804	+	0.473932i
$133$		0			0
$134$		−	4.25366i		−	0.367460i
$135$	−7.32781	+	1.22634i	−0.630678	+	0.105547i
$136$	−1.97802	+	1.14201i	−0.169613	+	0.0979264i
$137$	8.36293	+	4.82834i	0.714493	+	0.412513i	0.812723	−	0.582651i	$-0.197984\pi$
$137$	8.36293	+	4.82834i	0.714493	+	0.412513i	−0.0982292	+	0.995164i	$0.531318\pi$
$138$	1.65976	−	13.8510i	0.141288	−	1.17908i
$139$	−16.0680	−	9.27686i	−1.36287	−	0.786853i	−0.372864	−	0.927886i	$-0.621624\pi$
$139$	−16.0680	−	9.27686i	−1.36287	−	0.786853i	−0.990005	+	0.141033i	$0.954958\pi$
$140$		0			0
$141$	−7.65005	−	5.72987i	−0.644251	−	0.482542i
$142$	3.55393			0.298239
$143$	10.8348	+	18.7664i	0.906049	+	1.56932i
$144$	0.843698	+	2.87892i	0.0703081	+	0.239910i
$145$	0.427352	+	0.246732i	0.0354896	+	0.0204899i
$146$	−0.116080	−	0.201057i	−0.00960689	−	0.0166396i
$147$		0			0
$148$	−1.07786	+	1.86690i	−0.0885993	+	0.153458i
$149$	−5.63517	+	3.25347i	−0.461651	+	0.266535i	−0.712738	−	0.701430i	$-0.752545\pi$
$149$	−5.63517	+	3.25347i	−0.461651	+	0.266535i	0.251087	+	0.967965i	$0.419212\pi$
$150$	2.01392	+	4.70633i	0.164436	+	0.384270i
$151$	−2.87950	+	4.98745i	−0.234331	+	0.405873i	−0.959078	−	0.283142i	$-0.908623\pi$
$151$	−2.87950	+	4.98745i	−0.234331	+	0.405873i	0.724747	+	0.689015i	$0.241956\pi$
$152$	−1.08353	+	1.87673i	−0.0878862	+	0.152223i
$153$	−4.73104	+	4.95660i	−0.382482	+	0.400717i
$154$		0			0
$155$	−5.37699	+	3.10441i	−0.431890	+	0.249352i
$156$	4.31818	+	10.0912i	0.345731	+	0.807940i
$157$			7.96361i			0.635565i	0.948164	+	0.317783i	$0.102938\pi$
$157$			7.96361i			0.635565i	−0.948164	+	0.317783i	$0.897062\pi$
$158$		−	14.5620i		−	1.15849i
$159$	−17.0046	−	2.03764i	−1.34855	−	0.161595i
$160$	−1.23829	+	0.714925i	−0.0978952	+	0.0565198i
$161$		0			0
$162$	4.85787	+	7.57635i	0.381671	+	0.595254i
$163$	5.69256	−	9.85980i	0.445876	−	0.772279i	−0.552237	−	0.833687i	$-0.686226\pi$
$163$	5.69256	−	9.85980i	0.445876	−	0.772279i	0.998113	+	0.0614080i	$0.0195591\pi$
$164$	0.202180	−	0.350186i	0.0157876	−	0.0273449i
$165$	−5.07676	+	6.77807i	−0.395225	+	0.527672i
$166$	−1.40577	+	0.811624i	−0.109109	+	0.0629942i
$167$	5.66418	−	9.81065i	0.438308	−	0.759171i	−0.559252	−	0.828998i	$-0.688911\pi$
$167$	5.66418	−	9.81065i	0.438308	−	0.759171i	0.997559	+	0.0698271i	$0.0222447\pi$
$168$		0			0
$169$	13.5797	+	23.5208i	1.04459	+	1.80929i
$170$	−2.82827	−	1.63290i	−0.216918	−	0.125238i
$171$	−1.53601	+	6.31714i	−0.117461	+	0.483084i
$172$	−2.90883	−	5.03824i	−0.221796	−	0.384162i
$173$	21.6914			1.64917			0.824584	−	0.565739i	$-0.191409\pi$
$173$	21.6914			1.64917			0.824584	+	0.565739i	$0.191409\pi$
$174$	0.0711198	−	0.593511i	0.00539158	−	0.0449940i
$175$		0			0
$176$	2.96133	+	1.70972i	0.223218	+	0.128875i
$177$	15.2904	+	11.4525i	1.14930	+	0.860821i
$178$	−3.51562	−	2.02974i	−0.263507	−	0.152136i
$179$	−18.0057	+	10.3956i	−1.34581	+	0.777002i	−0.987653	−	0.156660i	$-0.949927\pi$
$179$	−18.0057	+	10.3956i	−1.34581	+	0.777002i	−0.358155	+	0.933662i	$0.616594\pi$
$180$	−2.96175	+	3.10295i	−0.220756	+	0.231280i
$181$			21.5301i			1.60032i	0.599788	+	0.800159i	$0.295252\pi$
$181$			21.5301i			1.60032i	−0.599788	+	0.800159i	$0.704748\pi$
$182$		0			0
$183$	11.9199	−	15.9145i	0.881143	−	1.17643i
$184$	−4.02706	−	6.97507i	−0.296879	−	0.514209i
$185$	−3.08235			−0.226619
$186$	6.01974	+	4.50877i	0.441388	+	0.330599i
$187$			7.81007i			0.571129i
$188$	−5.51829			−0.402463
$189$		0			0
$190$	−3.09858			−0.224795
$191$			7.36938i			0.533230i	0.963803	+	0.266615i	$0.0859052\pi$
$191$			7.36938i			0.533230i	−0.963803	+	0.266615i	$0.914095\pi$
$192$	1.38631	+	1.03834i	0.100048	+	0.0749358i
$193$	−2.82559			−0.203390			−0.101695	−	0.994816i	$-0.532427\pi$
$193$	−2.82559			−0.203390			−0.101695	+	0.994816i	$0.532427\pi$
$194$	−5.30423	−	9.18719i	−0.380821	−	0.659602i
$195$	−9.40859	+	12.5616i	−0.673763	+	0.899553i
$196$		0			0
$197$		−	26.0883i		−	1.85871i	−0.369183	−	0.929357i	$-0.620363\pi$
$197$		−	26.0883i		−	1.85871i	0.369183	−	0.929357i	$-0.379637\pi$
$198$	9.96791	+	2.42369i	0.708388	+	0.172244i
$199$	−13.3511	+	7.70826i	−0.946434	+	0.546424i	−0.891971	−	0.452092i	$-0.850678\pi$
$199$	−13.3511	+	7.70826i	−0.946434	+	0.546424i	−0.0544625	+	0.998516i	$0.517345\pi$
$200$	2.55956	+	1.47776i	0.180988	+	0.104494i
$201$	−5.89688	−	4.41674i	−0.415934	−	0.311533i
$202$	−6.97052	−	4.02443i	−0.490444	−	0.283158i
$203$		0			0
$204$	−0.470680	+	3.92793i	−0.0329542	+	0.275010i
$205$	0.578174			0.0403814
$206$	−1.40695	−	2.43692i	−0.0980272	−	0.169788i
$207$	−17.4784	−	16.6830i	−1.21483	−	1.15955i
$208$	5.48813	+	3.16857i	0.380533	+	0.219701i
$209$	3.70508	+	6.41739i	0.256286	+	0.443900i
$210$		0			0
$211$	4.42465	−	7.66371i	0.304605	−	0.527592i	−0.672568	−	0.740035i	$-0.734809\pi$
$211$	4.42465	−	7.66371i	0.304605	−	0.527592i	0.977173	+	0.212443i	$0.0681421\pi$
$212$	−8.56310	+	4.94391i	−0.588116	+	0.339549i
$213$	3.69019	−	4.92684i	0.252847	−	0.337581i
$214$	−7.91078	+	13.7019i	−0.540770	+	0.936641i
$215$	4.15919	−	7.20393i	0.283655	−	0.491304i
$216$	4.86711	+	1.81967i	0.331165	+	0.123813i
$217$		0			0
$218$	8.84514	−	5.10675i	0.599069	−	0.345873i
$219$	−0.399258	−	0.0478427i	−0.0269794	−	0.00323291i
$220$			4.88930i			0.329636i
$221$			14.4741i			0.973637i
$222$	1.46892	+	3.43272i	0.0985874	+	0.230389i
$223$	6.88961	−	3.97772i	0.461363	−	0.266368i	−0.251254	−	0.967921i	$-0.580843\pi$
$223$	6.88961	−	3.97772i	0.461363	−	0.266368i	0.712617	+	0.701553i	$0.247510\pi$
$224$		0			0
$225$	8.61556	+	2.09487i	0.574370	+	0.139658i
$226$	4.20778	−	7.28808i	0.279897	−	0.484796i
$227$	−4.61984	+	8.00180i	−0.306630	+	0.531098i	−0.977623	−	0.210365i	$-0.932535\pi$
$227$	−4.61984	+	8.00180i	−0.306630	+	0.531098i	0.670993	+	0.741464i	$0.265868\pi$
$228$	1.47666	+	3.45080i	0.0977939	+	0.228535i
$229$	7.31319	−	4.22227i	0.483269	−	0.279016i	−0.238509	−	0.971140i	$-0.576659\pi$
$229$	7.31319	−	4.22227i	0.483269	−	0.279016i	0.721778	+	0.692125i	$0.243325\pi$
$230$	5.75809	−	9.97330i	0.379677	−	0.657620i
$231$		0			0
$232$	−0.172558	−	0.298879i	−0.0113290	−	0.0196223i
$233$	14.4176	+	8.32399i	0.944526	+	0.545323i	0.891376	−	0.453264i	$-0.149741\pi$
$233$	14.4176	+	8.32399i	0.944526	+	0.545323i	0.0531500	+	0.998587i	$0.483074\pi$
$234$	18.4732	+	4.49174i	1.20763	+	0.293635i
$235$	−3.94517	−	6.83323i	−0.257354	−	0.445751i
$236$	11.0296			0.717966
$237$	−20.1874	−	15.1203i	−1.31131	−	0.982170i
$238$		0			0
$239$	−23.6325	−	13.6442i	−1.52866	−	0.882572i	−0.999418	−	0.0341012i	$-0.989143\pi$
$239$	−23.6325	−	13.6442i	−1.52866	−	0.882572i	−0.529242	−	0.848471i	$-0.677524\pi$
$240$	−0.294657	+	2.45898i	−0.0190200	+	0.158727i
$241$	21.9018	+	12.6450i	1.41082	+	0.814537i	0.995466	−	0.0951223i	$-0.0303242\pi$
$241$	21.9018	+	12.6450i	1.41082	+	0.814537i	0.415354	+	0.909660i	$0.363658\pi$
$242$	0.599818	−	0.346305i	0.0385578	−	0.0222613i
$243$	15.5473	+	1.13232i	0.997358	+	0.0726386i
$244$		−	11.4797i		−	0.734915i
$245$		0			0
$246$	−0.275534	−	0.643896i	−0.0175674	−	0.0410533i
$247$	6.86651	+	11.8931i	0.436906	+	0.756743i
$248$	4.34228			0.275735
$249$	−0.334512	+	2.79158i	−0.0211988	+	0.176909i
$250$			11.3752i			0.719432i
$251$	8.19337			0.517161			0.258581	−	0.965990i	$-0.416745\pi$
$251$	8.19337			0.517161			0.258581	+	0.965990i	$0.416745\pi$
$252$		0			0
$253$	−27.5406			−1.73146
$254$		−	5.77773i		−	0.362527i
$255$	−5.20041	+	2.22534i	−0.325662	+	0.139356i
$256$	1.00000			0.0625000
$257$	3.31723	+	5.74560i	0.206923	+	0.358401i	0.950744	−	0.309978i	$-0.100322\pi$
$257$	3.31723	+	5.74560i	0.206923	+	0.358401i	−0.743821	+	0.668379i	$0.766988\pi$
$258$	−10.0049	−	1.19888i	−0.622878	−	0.0746388i
$259$		0			0
$260$			9.06117i			0.561950i
$261$	−0.748942	−	0.714861i	−0.0463584	−	0.0442488i
$262$	−3.85959	+	2.22833i	−0.238446	+	0.137667i
$263$	5.23590	+	3.02295i	0.322860	+	0.186403i	0.652666	−	0.757645i	$-0.273650\pi$
$263$	5.23590	+	3.02295i	0.322860	+	0.186403i	−0.329807	+	0.944048i	$0.606984\pi$
$264$	5.44507	−	2.33004i	0.335121	−	0.143404i
$265$	−12.2440	−	7.06905i	−0.752140	−	0.434248i
$266$		0			0
$267$	−6.46426	+	2.76616i	−0.395606	+	0.169286i
$268$	−4.25366			−0.259833
$269$	−3.41069	−	5.90750i	−0.207954	−	0.360186i	0.743116	−	0.669163i	$-0.233347\pi$
$269$	−3.41069	−	5.90750i	−0.207954	−	0.360186i	−0.951070	+	0.308976i	$0.900014\pi$
$270$	1.22634	+	7.32781i	0.0746329	+	0.445956i
$271$	4.39780	+	2.53907i	0.267148	+	0.154238i	0.627591	−	0.778543i	$-0.284041\pi$
$271$	4.39780	+	2.53907i	0.267148	+	0.154238i	−0.360443	+	0.932781i	$0.617375\pi$
$272$	1.14201	+	1.97802i	0.0692444	+	0.119935i
$273$		0			0
$274$	4.82834	−	8.36293i	0.291691	−	0.505223i
$275$	8.75228	−	5.05313i	0.527783	−	0.304715i
$276$	−13.8510	−	1.65976i	−0.833735	−	0.0999055i
$277$	0.989567	−	1.71398i	0.0594573	−	0.102983i	−0.834765	−	0.550607i	$-0.814396\pi$
$277$	0.989567	−	1.71398i	0.0594573	−	0.102983i	0.894222	+	0.447624i	$0.147730\pi$
$278$	−9.27686	+	16.0680i	−0.556389	+	0.963694i
$279$	12.5011	−	3.66357i	0.748420	−	0.219332i
$280$		0			0
$281$	−15.2703	+	8.81631i	−0.910950	+	0.525937i	−0.880737	−	0.473606i	$-0.842952\pi$
$281$	−15.2703	+	8.81631i	−0.910950	+	0.525937i	−0.0302131	+	0.999543i	$0.509619\pi$
$282$	−5.72987	+	7.65005i	−0.341209	+	0.455554i
$283$			5.15385i			0.306365i	0.988198	+	0.153182i	$0.0489522\pi$
$283$			5.15385i			0.306365i	−0.988198	+	0.153182i	$0.951048\pi$
$284$		−	3.55393i		−	0.210887i
$285$	−3.21738	+	4.29559i	−0.190581	+	0.254449i
$286$	18.7664	−	10.8348i	1.10968	−	0.640673i
$287$		0			0
$288$	2.87892	−	0.843698i	0.169642	−	0.0497154i
$289$	5.89164	−	10.2046i	0.346567	−	0.600271i
$290$	0.246732	−	0.427352i	0.0144886	−	0.0250949i
$291$	−18.2439	−	2.18614i	−1.06947	−	0.128154i
$292$	−0.201057	+	0.116080i	−0.0117660	+	0.00679310i
$293$	−1.03248	+	1.78831i	−0.0603183	+	0.104474i	−0.894608	−	0.446852i	$-0.852545\pi$
$293$	−1.03248	+	1.78831i	−0.0603183	+	0.104474i	0.834289	+	0.551327i	$0.185878\pi$
$294$		0			0
$295$	7.88534	+	13.6578i	0.459102	+	0.795188i
$296$	1.86690	+	1.07786i	0.108511	+	0.0626491i
$297$	13.7101	−	11.3020i	0.795539	−	0.655807i
$298$	3.25347	+	5.63517i	0.188468	+	0.326437i
$299$	−51.0401			−2.95173
$300$	4.70633	−	2.01392i	0.271720	−	0.116274i
$301$		0			0
$302$	4.98745	+	2.87950i	0.286995	+	0.165697i
$303$	−12.8169	+	5.48455i	−0.736310	+	0.315079i
$304$	1.87673	+	1.08353i	0.107638	+	0.0621449i
$305$	14.2152	−	8.20716i	0.813961	−	0.469941i
$306$	4.95660	+	4.73104i	0.283350	+	0.270455i
$307$		−	1.09119i		−	0.0622772i	−0.999515	−	0.0311386i	$-0.990087\pi$
$307$		−	1.09119i		−	0.0622772i	0.999515	−	0.0311386i	$-0.00991333\pi$
$308$		0			0
$309$	−4.83921	−	0.579878i	−0.275293	−	0.0329881i
$310$	3.10441	+	5.37699i	0.176318	+	0.305392i
$311$	−15.2220			−0.863161			−0.431580	−	0.902075i	$-0.642044\pi$
$311$	−15.2220			−0.863161			−0.431580	+	0.902075i	$0.642044\pi$
$312$	10.0912	−	4.31818i	0.571300	−	0.244469i
$313$		−	11.5704i		−	0.653996i	−0.945025	−	0.326998i	$-0.893963\pi$
$313$		−	11.5704i		−	0.653996i	0.945025	−	0.326998i	$-0.106037\pi$
$314$	7.96361			0.449412
$315$		0			0
$316$	−14.5620			−0.819177
$317$		−	17.1604i		−	0.963824i	−0.876220	−	0.481912i	$-0.839942\pi$
$317$		−	17.1604i		−	0.963824i	0.876220	−	0.481912i	$-0.160058\pi$
$318$	−2.03764	+	17.0046i	−0.114265	+	0.953568i
$319$	−1.18010			−0.0660731
$320$	0.714925	+	1.23829i	0.0399655	+	0.0692223i
$321$	10.7809	+	25.1940i	0.601733	+	1.40619i
$322$		0			0
$323$			4.94962i			0.275404i
$324$	7.57635	−	4.85787i	0.420908	−	0.269882i
$325$	16.2203	−	9.36481i	0.899742	−	0.519466i
$326$	−9.85980	−	5.69256i	−0.546084	−	0.315282i
$327$	2.10475	−	17.5646i	0.116393	−	0.971326i
$328$	−0.350186	−	0.202180i	−0.0193358	−	0.0111635i
$329$		0			0
$330$	6.77807	+	5.07676i	0.373120	+	0.279466i
$331$	−26.4931			−1.45619			−0.728096	−	0.685475i	$-0.759595\pi$
$331$	−26.4931			−1.45619			−0.728096	+	0.685475i	$0.759595\pi$
$332$	0.811624	+	1.40577i	0.0445436	+	0.0771519i
$333$	6.28404	+	1.52796i	0.344364	+	0.0837317i
$334$	−9.81065	−	5.66418i	−0.536815	−	0.309930i
$335$	−3.04105	−	5.26725i	−0.166150	−	0.287780i
$336$		0			0
$337$	4.06451	−	7.03993i	0.221408	−	0.383490i	−0.733828	−	0.679335i	$-0.762268\pi$
$337$	4.06451	−	7.03993i	0.221408	−	0.383490i	0.955236	+	0.295846i	$0.0956015\pi$
$338$	23.5208	−	13.5797i	1.27936	−	0.738640i
$339$	−5.73442	−	13.4008i	−0.311451	−	0.727830i
$340$	−1.63290	+	2.82827i	−0.0885565	+	0.153384i
$341$	7.42410	−	12.8589i	0.402037	−	0.696349i
$342$	6.31714	+	1.53601i	0.341592	+	0.0830578i
$343$		0			0
$344$	−5.03824	+	2.90883i	−0.271644	+	0.156834i
$345$	−7.84721	−	18.3382i	−0.422479	−	0.987294i
$346$		−	21.6914i		−	1.16614i
$347$		−	25.6171i		−	1.37520i	−0.726090	−	0.687599i	$-0.758665\pi$
$347$		−	25.6171i		−	1.37520i	0.726090	−	0.687599i	$-0.241335\pi$
$348$	−0.593511	−	0.0711198i	−0.0318155	−	0.00381242i
$349$	−9.11932	+	5.26504i	−0.488146	+	0.281831i	−0.723805	−	0.690005i	$-0.757609\pi$
$349$	−9.11932	+	5.26504i	−0.488146	+	0.281831i	0.235659	+	0.971836i	$0.424275\pi$
$350$		0			0
$351$	25.4084	−	20.9456i	1.35620	−	1.11799i
$352$	1.70972	−	2.96133i	0.0911285	−	0.157839i
$353$	−6.42186	+	11.1230i	−0.341801	+	0.592017i	−0.984767	−	0.173878i	$-0.944370\pi$
$353$	−6.42186	+	11.1230i	−0.341801	+	0.592017i	0.642966	+	0.765895i	$0.277704\pi$
$354$	11.4525	−	15.2904i	0.608692	−	0.812676i
$355$	4.40078	−	2.54079i	0.233569	−	0.134851i
$356$	−2.02974	+	3.51562i	−0.107576	+	0.186327i
$357$		0			0
$358$	10.3956	+	18.0057i	0.549424	+	0.951630i
$359$	25.6881	+	14.8311i	1.35577	+	0.782753i	0.989050	−	0.147579i	$-0.0471482\pi$
$359$	25.6881	+	14.8311i	1.35577	+	0.782753i	0.366718	+	0.930332i	$0.380482\pi$
$360$	3.10295	+	2.96175i	0.163540	+	0.156098i
$361$	−7.15191	−	12.3875i	−0.376416	−	0.651972i
$362$	21.5301			1.13160
$363$	0.142730	−	1.19112i	0.00749139	−	0.0625173i
$364$		0			0
$365$	−0.287482	−	0.165978i	−0.0150475	−	0.00868767i
$366$	−15.9145	−	11.9199i	−0.831862	−	0.623062i
$367$	−20.7828	−	11.9989i	−1.08485	−	0.626340i	−0.152651	−	0.988280i	$-0.548781\pi$
$367$	−20.7828	−	11.9989i	−1.08485	−	0.626340i	−0.932201	+	0.361940i	$0.882115\pi$
$368$	−6.97507	+	4.02706i	−0.363600	+	0.209925i
$369$	−1.17874	−	0.286609i	−0.0613625	−	0.0149202i
$370$			3.08235i			0.160244i
$371$		0			0
$372$	4.50877	−	6.01974i	0.233769	−	0.312109i
$373$	5.91948	+	10.2528i	0.306499	+	0.530872i	0.977594	−	0.210500i	$-0.0675091\pi$
$373$	5.91948	+	10.2528i	0.306499	+	0.530872i	−0.671095	+	0.741371i	$0.734176\pi$
$374$	7.81007			0.403849
$375$	15.7695	+	11.8113i	0.814336	+	0.609935i
$376$			5.51829i			0.284584i
$377$	−2.18705			−0.112639
$378$		0			0
$379$	−13.1379			−0.674850			−0.337425	−	0.941352i	$-0.609556\pi$
$379$	−13.1379			−0.674850			−0.337425	+	0.941352i	$0.609556\pi$
$380$			3.09858i			0.158954i
$381$	−8.00971	−	5.99925i	−0.410350	−	0.307351i
$382$	7.36938			0.377050
$383$	8.77603	+	15.2005i	0.448434	+	0.776711i	0.998284	−	0.0585527i	$-0.0186486\pi$
$383$	8.77603	+	15.2005i	0.448434	+	0.776711i	−0.549850	+	0.835263i	$0.685315\pi$
$384$	1.03834	−	1.38631i	0.0529876	−	0.0707447i
$385$		0			0
$386$			2.82559i			0.143819i
$387$	−12.0505	+	12.6250i	−0.612562	+	0.641767i
$388$	−9.18719	+	5.30423i	−0.466409	+	0.269281i
$389$	18.9148	+	10.9205i	0.959020	+	0.553691i	0.895871	−	0.444313i	$-0.146552\pi$
$389$	18.9148	+	10.9205i	0.959020	+	0.553691i	0.0631489	+	0.998004i	$0.479886\pi$
$390$	12.5616	+	9.40859i	0.636080	+	0.476422i
$391$	−15.9312	−	9.19786i	−0.805674	−	0.465156i
$392$		0			0
$393$	−0.918411	+	7.66435i	−0.0463277	+	0.386615i
$394$	−26.0883			−1.31431
$395$	−10.4107	−	18.0319i	−0.523821	−	0.907285i
$396$	2.42369	−	9.96791i	0.121795	−	0.500906i
$397$	−33.7636	−	19.4935i	−1.69455	−	0.978348i	−0.950757	−	0.309937i	$-0.899692\pi$
$397$	−33.7636	−	19.4935i	−1.69455	−	0.978348i	−0.743792	−	0.668411i	$-0.766975\pi$
$398$	7.70826	+	13.3511i	0.386380	+	0.669230i
$399$		0			0
$400$	1.47776	−	2.55956i	0.0738882	−	0.127978i
$401$	−20.0899	+	11.5989i	−1.00324	+	0.579223i	−0.909206	−	0.416346i	$-0.863311\pi$
$401$	−20.0899	+	11.5989i	−1.00324	+	0.579223i	−0.0940373	+	0.995569i	$0.529977\pi$
$402$	−4.41674	+	5.89688i	−0.220287	+	0.294109i
$403$	13.7588	−	23.8310i	0.685376	−	1.18711i
$404$	−4.02443	+	6.97052i	−0.200223	+	0.346796i
$405$	11.4320	+	5.90868i	0.568059	+	0.293605i
$406$		0			0
$407$	6.38377	−	3.68567i	0.316432	−	0.182692i
$408$	3.92793	+	0.470680i	0.194462	+	0.0233021i
$409$		−	24.6187i		−	1.21732i	−0.793432	−	0.608659i	$-0.791708\pi$
$409$		−	24.6187i		−	1.21732i	0.793432	−	0.608659i	$-0.208292\pi$
$410$		−	0.578174i		−	0.0285540i
$411$	−6.58013	−	15.3771i	−0.324574	−	0.758498i
$412$	−2.43692	+	1.40695i	−0.120058	+	0.0693157i
$413$		0			0
$414$	−16.6830	+	17.4784i	−0.819926	+	0.859017i
$415$	−1.16050	+	2.01005i	−0.0569667	+	0.0986693i
$416$	3.16857	−	5.48813i	0.155352	−	0.269078i
$417$	12.6426	+	29.5446i	0.619113	+	1.44681i
$418$	6.41739	−	3.70508i	0.313885	−	0.181222i
$419$	−8.53996	+	14.7916i	−0.417204	+	0.722619i	−0.995657	−	0.0930969i	$-0.970323\pi$
$419$	−8.53996	+	14.7916i	−0.417204	+	0.722619i	0.578453	+	0.815716i	$0.303657\pi$
$420$		0			0
$421$	−7.35652	−	12.7419i	−0.358535	−	0.621000i	0.629182	−	0.777258i	$-0.283390\pi$
$421$	−7.35652	−	12.7419i	−0.358535	−	0.621000i	−0.987716	+	0.156258i	$0.950057\pi$
$422$	−7.66371	−	4.42465i	−0.373064	−	0.215388i
$423$	4.65577	+	15.8867i	0.226371	+	0.772439i
$424$	4.94391	+	8.56310i	0.240097	+	0.415861i
$425$	6.75047			0.327446
$426$	−4.92684	−	3.69019i	−0.238706	−	0.178790i
$427$		0			0
$428$	13.7019	+	7.91078i	0.662305	+	0.382382i
$429$	4.46556	−	37.2661i	0.215599	−	1.79923i
$430$	−7.20393	−	4.15919i	−0.347404	−	0.200574i
$431$	−8.32286	+	4.80521i	−0.400898	+	0.231459i	−0.686871	−	0.726779i	$-0.741016\pi$
$431$	−8.32286	+	4.80521i	−0.400898	+	0.231459i	0.285973	+	0.958238i	$0.407683\pi$
$432$	1.81967	−	4.86711i	0.0875491	−	0.234169i
$433$			9.04314i			0.434585i	0.976106	+	0.217293i	$0.0697226\pi$
$433$			9.04314i			0.434585i	−0.976106	+	0.217293i	$0.930277\pi$
$434$		0			0
$435$	−0.336249	−	0.785782i	−0.0161219	−	0.0376754i
$436$	−5.10675	−	8.84514i	−0.244569	−	0.423606i
$437$	−17.4538			−0.834929
$438$	−0.0478427	+	0.399258i	−0.00228601	+	0.0190773i
$439$		−	0.913795i		−	0.0436131i	−0.999762	−	0.0218065i	$-0.993058\pi$
$439$		−	0.913795i		−	0.0436131i	0.999762	−	0.0218065i	$-0.00694178\pi$
$440$	4.88930			0.233088
$441$		0			0
$442$	14.4741			0.688465
$443$			29.3616i			1.39501i	0.716578	+	0.697507i	$0.245707\pi$
$443$			29.3616i			1.39501i	−0.716578	+	0.697507i	$0.754293\pi$
$444$	3.43272	−	1.46892i	0.162910	−	0.0697118i
$445$	−5.80446			−0.275158
$446$	−3.97772	−	6.88961i	−0.188351	−	0.326233i
$447$	11.1903	+	1.34092i	0.529283	+	0.0634234i
$448$		0			0
$449$		−	3.36736i		−	0.158915i	−0.996838	−	0.0794577i	$-0.974681\pi$
$449$		−	3.36736i		−	0.158915i	0.996838	−	0.0794577i	$-0.0253189\pi$
$450$	2.09487	−	8.61556i	0.0987529	−	0.406141i
$451$	−1.19744	+	0.691343i	−0.0563853	+	0.0325541i
$452$	−7.28808	−	4.20778i	−0.342802	−	0.197917i
$453$	9.17054	−	3.92423i	0.430870	−	0.184376i
$454$	8.00180	+	4.61984i	0.375543	+	0.216820i
$455$		0			0
$456$	3.45080	−	1.47666i	0.161599	−	0.0691507i
$457$	−15.1139			−0.706996			−0.353498	−	0.935435i	$-0.615008\pi$
$457$	−15.1139			−0.706996			−0.353498	+	0.935435i	$0.615008\pi$
$458$	−4.22227	−	7.31319i	−0.197294	−	0.341723i
$459$	11.7053	−	1.95894i	0.546357	−	0.0914354i
$460$	−9.97330	−	5.75809i	−0.465008	−	0.268472i
$461$	−5.19445	−	8.99706i	−0.241930	−	0.419035i	0.719334	−	0.694664i	$-0.244447\pi$
$461$	−5.19445	−	8.99706i	−0.241930	−	0.419035i	−0.961264	+	0.275629i	$0.911114\pi$
$462$		0			0
$463$	−2.65722	+	4.60244i	−0.123492	+	0.213894i	−0.921142	−	0.389226i	$-0.872743\pi$
$463$	−2.65722	+	4.60244i	−0.123492	+	0.213894i	0.797651	+	0.603120i	$0.206076\pi$
$464$	−0.298879	+	0.172558i	−0.0138751	+	0.00801078i
$465$	10.6776	+	1.27948i	0.495161	+	0.0593347i
$466$	8.32399	−	14.4176i	0.385601	−	0.667881i
$467$	−9.74994	+	16.8874i	−0.451173	+	0.781455i	−0.998459	−	0.0554907i	$-0.982328\pi$
$467$	−9.74994	+	16.8874i	−0.451173	+	0.781455i	0.547286	+	0.836946i	$0.315661\pi$
$468$	4.49174	−	18.4732i	0.207631	−	0.853924i
$469$		0			0
$470$	−6.83323	+	3.94517i	−0.315193	+	0.181977i
$471$	8.26894	−	11.0400i	0.381012	−	0.508697i
$472$		−	11.0296i		−	0.507678i
$473$			19.8932i			0.914689i
$474$	−15.1203	+	20.1874i	−0.694499	+	0.927239i
$475$	5.54674	−	3.20241i	0.254502	−	0.146937i
$476$		0			0
$477$	21.4578	+	20.4813i	0.982484	+	0.937775i
$478$	−13.6442	+	23.6325i	−0.624073	+	1.08093i
$479$	13.9012	−	24.0776i	0.635163	−	1.10013i	−0.351318	−	0.936256i	$-0.614266\pi$
$479$	13.9012	−	24.0776i	0.635163	−	1.10013i	0.986481	−	0.163878i	$-0.0524003\pi$
$480$	2.45898	+	0.294657i	0.112237	+	0.0134492i
$481$	11.8308	−	6.83054i	0.539440	−	0.311446i
$482$	12.6450	−	21.9018i	0.575965	−	0.997600i
$483$		0			0
$484$	−0.346305	−	0.599818i	−0.0157411	−	0.0272645i
$485$	−13.1363	−	7.58425i	−0.596489	−	0.344383i
$486$	1.13232	−	15.5473i	0.0513632	−	0.705239i
$487$	3.73838	+	6.47506i	0.169402	+	0.293413i	0.938210	−	0.346067i	$-0.112483\pi$
$487$	3.73838	+	6.47506i	0.169402	+	0.293413i	−0.768808	+	0.639480i	$0.779150\pi$
$488$	−11.4797			−0.519664
$489$	−18.1295	+	7.75790i	−0.819843	+	0.350824i
$490$		0			0
$491$	19.1466	+	11.0543i	0.864073	+	0.498873i	0.865374	−	0.501126i	$-0.167081\pi$
$491$	19.1466	+	11.0543i	0.864073	+	0.498873i	−0.00130103	+	0.999999i	$0.500414\pi$
$492$	−0.643896	+	0.275534i	−0.0290291	+	0.0124220i
$493$	−0.682643	−	0.394124i	−0.0307447	−	0.0177505i
$494$	11.8931	−	6.86651i	0.535098	−	0.308939i
$495$	14.0759	−	4.12509i	0.632664	−	0.185409i
$496$		−	4.34228i		−	0.194974i
$497$		0			0
$498$	2.79158	+	0.334512i	0.125094	+	0.0149898i
$499$	−16.4521	−	28.4959i	−0.736498	−	1.27565i	−0.954063	−	0.299606i	$-0.903145\pi$
$499$	−16.4521	−	28.4959i	−0.736498	−	1.27565i	0.217565	−	0.976046i	$-0.430189\pi$
$500$	11.3752			0.508715
$501$	−18.0391	+	7.71923i	−0.805927	+	0.344870i
$502$		−	8.19337i		−	0.365688i
$503$	25.6142			1.14208			0.571039	−	0.820923i	$-0.306540\pi$
$503$	25.6142			1.14208			0.571039	+	0.820923i	$0.306540\pi$
$504$		0			0
$505$	−11.5087			−0.512129
$506$			27.5406i			1.22433i
$507$	5.59690	−	46.7074i	0.248567	−	2.07435i
$508$	−5.77773			−0.256345
$509$	10.7358	+	18.5950i	0.475857	+	0.824209i	0.999617	−	0.0276567i	$-0.00880451\pi$
$509$	10.7358	+	18.5950i	0.475857	+	0.824209i	−0.523760	+	0.851866i	$0.675471\pi$
$510$	2.22534	+	5.20041i	0.0985398	+	0.230278i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	8.68873	−	7.16260i	0.383617	−	0.316237i
$514$	5.74560	−	3.31723i	0.253428	−	0.146317i
$515$	−3.48443	−	2.01173i	−0.153542	−	0.0886476i
$516$	−1.19888	+	10.0049i	−0.0527776	+	0.440441i
$517$	16.3415	+	9.43475i	0.718697	+	0.414940i
$518$		0			0
$519$	−30.0710	−	22.5231i	−1.31997	−	0.988654i
$520$	9.06117			0.397359
$521$	3.23087	+	5.59604i	0.141547	+	0.245167i	0.928079	−	0.372382i	$-0.121459\pi$
$521$	3.23087	+	5.59604i	0.141547	+	0.245167i	−0.786532	+	0.617549i	$0.788126\pi$
$522$	−0.714861	+	0.748942i	−0.0312886	+	0.0327803i
$523$	−11.7830	−	6.80291i	−0.515234	−	0.297470i	0.219749	−	0.975557i	$-0.429476\pi$
$523$	−11.7830	−	6.80291i	−0.515234	−	0.297470i	−0.734982	+	0.678086i	$0.762810\pi$
$524$	2.22833	+	3.85959i	0.0973452	+	0.168607i
$525$		0			0
$526$	3.02295	−	5.23590i	0.131807	−	0.228296i
$527$	8.58910	−	4.95892i	0.374147	−	0.216014i
$528$	−2.33004	−	5.44507i	−0.101402	−	0.236966i
$529$	20.9344	−	36.2594i	0.910190	−	1.57649i
$530$	−7.06905	+	12.2440i	−0.307060	+	0.531843i
$531$	−9.30564	−	31.7533i	−0.403830	−	1.37798i
$532$		0			0
$533$	−2.21918	+	1.28124i	−0.0961233	+	0.0554968i
$534$	2.76616	+	6.46426i	0.119704	+	0.279736i
$535$			22.6225i			0.978055i
$536$			4.25366i			0.183730i
$537$	35.7556	+	4.28455i	1.54297	+	0.184892i
$538$	−5.90750	+	3.41069i	−0.254690	+	0.147045i
$539$		0			0
$540$	7.32781	−	1.22634i	0.315339	−	0.0527734i
$541$	−14.9288	+	25.8574i	−0.641838	+	1.11170i	0.343184	+	0.939268i	$0.388494\pi$
$541$	−14.9288	+	25.8574i	−0.641838	+	1.11170i	−0.985022	+	0.172428i	$0.944839\pi$
$542$	2.53907	−	4.39780i	0.109063	−	0.188902i
$543$	22.3556	−	29.8473i	0.959369	−	1.28087i
$544$	1.97802	−	1.14201i	0.0848067	−	0.0489632i
$545$	7.30188	−	12.6472i	0.312778	−	0.541748i
$546$		0			0
$547$	−9.07207	−	15.7133i	−0.387894	−	0.671852i	0.604272	−	0.796778i	$-0.293464\pi$
$547$	−9.07207	−	15.7133i	−0.387894	−	0.671852i	−0.992166	+	0.124926i	$0.960131\pi$
$548$	−8.36293	−	4.82834i	−0.357247	−	0.206256i
$549$	−33.0493	+	9.68543i	−1.41051	+	0.413364i
$550$	−5.05313	−	8.75228i	−0.215466	−	0.373199i
$551$	−0.747888			−0.0318611
$552$	−1.65976	+	13.8510i	−0.0706439	+	0.589540i
$553$		0			0
$554$	−1.71398	−	0.989567i	−0.0728201	−	0.0420427i
$555$	4.27308	+	3.20053i	0.181382	+	0.135855i
$556$	16.0680	+	9.27686i	0.681435	+	0.393426i
$557$	−32.5079	+	18.7684i	−1.37740	+	0.795245i	−0.991846	−	0.127439i	$-0.959324\pi$
$557$	−32.5079	+	18.7684i	−1.37740	+	0.795245i	−0.385558	+	0.922684i	$0.625991\pi$
$558$	−3.66357	−	12.5011i	−0.155091	−	0.529213i
$559$			36.8674i			1.55932i
$560$		0			0
$561$	8.10951	−	10.8272i	0.342384	−	0.457123i
$562$	8.81631	+	15.2703i	0.371894	+	0.644139i
$563$	−7.10681			−0.299516			−0.149758	−	0.988723i	$-0.547850\pi$
$563$	−7.10681			−0.299516			−0.149758	+	0.988723i	$0.547850\pi$
$564$	7.65005	+	5.72987i	0.322125	+	0.241271i
$565$		−	12.0330i		−	0.506231i
$566$	5.15385			0.216633
$567$		0			0
$568$	−3.55393			−0.149119
$569$		−	41.1650i		−	1.72572i	−0.505439	−	0.862862i	$-0.668669\pi$
$569$		−	41.1650i		−	1.72572i	0.505439	−	0.862862i	$-0.331331\pi$
$570$	4.29559	+	3.21738i	0.179922	+	0.134761i
$571$	4.42585			0.185216			0.0926080	−	0.995703i	$-0.470480\pi$
$571$	4.42585			0.185216			0.0926080	+	0.995703i	$0.470480\pi$
$572$	−10.8348	−	18.7664i	−0.453024	−	0.784661i
$573$	7.65193	−	10.2162i	0.319664	−	0.426789i
$574$		0			0
$575$			23.8042i			0.992702i
$576$	−0.843698	−	2.87892i	−0.0351541	−	0.119955i
$577$	−2.37542	+	1.37145i	−0.0988900	+	0.0570941i	−0.548629	−	0.836066i	$-0.684850\pi$
$577$	−2.37542	+	1.37145i	−0.0988900	+	0.0570941i	0.449739	+	0.893160i	$0.351517\pi$
$578$	−10.2046	−	5.89164i	−0.424456	−	0.245060i
$579$	3.91713	+	2.93392i	0.162791	+	0.121930i
$580$	−0.427352	−	0.246732i	−0.0177448	−	0.0102450i
$581$		0			0
$582$	−2.18614	+	18.2439i	−0.0906186	+	0.756233i
$583$	33.8109			1.40030
$584$	0.116080	+	0.201057i	0.00480344	+	0.00831981i
$585$	26.0864	−	7.64489i	1.07854	−	0.316077i
$586$	1.78831	+	1.03248i	0.0738745	+	0.0426515i
$587$	−9.90248	−	17.1516i	−0.408719	−	0.707922i	0.586027	−	0.810291i	$-0.300691\pi$
$587$	−9.90248	−	17.1516i	−0.408719	−	0.707922i	−0.994747	+	0.102369i	$0.967358\pi$
$588$		0			0
$589$	4.70501	−	8.14931i	0.193866	−	0.335786i
$590$	13.6578	−	7.88534i	0.562283	−	0.324634i
$591$	−27.0885	+	36.1664i	−1.11427	+	1.48769i
$592$	1.07786	−	1.86690i	0.0442996	−	0.0767292i
$593$	−0.434850	+	0.753183i	−0.0178572	+	0.0309295i	−0.874816	−	0.484456i	$-0.839018\pi$
$593$	−0.434850	+	0.753183i	−0.0178572	+	0.0309295i	0.856959	+	0.515385i	$0.172351\pi$
$594$	−11.3020	−	13.7101i	−0.463726	−	0.562531i
$595$		0			0
$596$	5.63517	−	3.25347i	0.230826	−	0.133267i
$597$	26.5125	+	3.17697i	1.08509	+	0.130025i
$598$			51.0401i			2.08719i
$599$			2.69365i			0.110059i	0.998485	+	0.0550297i	$0.0175254\pi$
$599$			2.69365i			0.110059i	−0.998485	+	0.0550297i	$0.982475\pi$
$600$	−2.01392	−	4.70633i	−0.0822179	−	0.192135i
$601$	−0.115325	+	0.0665827i	−0.00470419	+	0.00271596i	−0.502350	−	0.864664i	$-0.667531\pi$
$601$	−0.115325	+	0.0665827i	−0.00470419	+	0.00271596i	0.497646	+	0.867380i	$0.334198\pi$
$602$		0			0
$603$	3.58880	+	12.2459i	0.146147	+	0.498693i
$604$	2.87950	−	4.98745i	0.117165	−	0.202936i
$605$	0.495165	−	0.857650i	0.0201313	−	0.0348684i
$606$	5.48455	+	12.8169i	0.222795	+	0.520650i
$607$	38.3860	−	22.1622i	1.55804	−	0.899534i	0.560594	−	0.828091i	$-0.310573\pi$
$607$	38.3860	−	22.1622i	1.55804	−	0.899534i	0.997445	−	0.0714432i	$-0.0227605\pi$
$608$	1.08353	−	1.87673i	0.0439431	−	0.0761117i
$609$		0			0
$610$	−8.20716	−	14.2152i	−0.332298	−	0.575557i
$611$	30.2851	+	17.4851i	1.22520	+	0.707372i
$612$	4.73104	−	4.95660i	0.191241	−	0.200359i
$613$	3.29901	+	5.71406i	0.133246	+	0.230789i	0.924926	−	0.380147i	$-0.124127\pi$
$613$	3.29901	+	5.71406i	0.133246	+	0.230789i	−0.791680	+	0.610936i	$0.790793\pi$
$614$	−1.09119			−0.0440367
$615$	−0.801527	−	0.600342i	−0.0323207	−	0.0242081i
$616$		0			0
$617$	−7.99450	−	4.61563i	−0.321846	−	0.185818i	0.330369	−	0.943852i	$-0.392827\pi$
$617$	−7.99450	−	4.61563i	−0.321846	−	0.185818i	−0.652215	+	0.758034i	$0.726160\pi$
$618$	−0.579878	+	4.83921i	−0.0233261	+	0.194662i
$619$	5.66289	+	3.26947i	0.227611	+	0.131411i	0.609469	−	0.792810i	$-0.291383\pi$
$619$	5.66289	+	3.26947i	0.227611	+	0.131411i	−0.381859	+	0.924221i	$0.624716\pi$
$620$	5.37699	−	3.10441i	0.215945	−	0.124676i
$621$	6.90779	+	41.2764i	0.277200	+	1.65636i
$622$			15.2220i			0.610347i
$623$		0			0
$624$	−4.31818	−	10.0912i	−0.172866	−	0.403970i
$625$	0.743610	+	1.28797i	0.0297444	+	0.0515188i
$626$	−11.5704			−0.462445
$627$	1.52705	−	12.7436i	0.0609847	−	0.508931i
$628$		−	7.96361i		−	0.317783i
$629$	4.92368			0.196320
$630$		0			0
$631$	13.8837			0.552699			0.276350	−	0.961057i	$-0.410875\pi$
$631$	13.8837			0.552699			0.276350	+	0.961057i	$0.410875\pi$
$632$			14.5620i			0.579245i
$633$	−14.0915	+	6.02997i	−0.560086	+	0.239670i
$634$	−17.1604			−0.681526
$635$	−4.13064	−	7.15449i	−0.163920	−	0.283917i
$636$	17.0046	+	2.03764i	0.674274	+	0.0807976i
$637$		0			0
$638$			1.18010i			0.0467207i
$639$	−10.2315	+	2.99844i	−0.404751	+	0.118616i
$640$	1.23829	−	0.714925i	0.0489476	−	0.0282599i
$641$	−13.1940	−	7.61757i	−0.521133	−	0.300876i	0.216265	−	0.976335i	$-0.430612\pi$
$641$	−13.1940	−	7.61757i	−0.521133	−	0.300876i	−0.737398	+	0.675459i	$0.763946\pi$
$642$	25.1940	−	10.7809i	0.994328	−	0.425489i
$643$	16.5813	+	9.57324i	0.653904	+	0.377532i	0.789950	−	0.613171i	$-0.210106\pi$
$643$	16.5813	+	9.57324i	0.653904	+	0.377532i	−0.136046	+	0.990702i	$0.543440\pi$
$644$		0			0
$645$	−13.2461	+	5.66821i	−0.521563	+	0.223185i
$646$	4.94962			0.194740
$647$	−0.793991	−	1.37523i	−0.0312150	−	0.0540660i	0.849996	−	0.526789i	$-0.176604\pi$
$647$	−0.793991	−	1.37523i	−0.0312150	−	0.0540660i	−0.881211	+	0.472723i	$0.843271\pi$
$648$	−4.85787	−	7.57635i	−0.190835	−	0.297627i
$649$	−32.6622	−	18.8576i	−1.28211	−	0.740224i
$650$	−9.36481	−	16.2203i	−0.367318	−	0.636213i
$651$		0			0
$652$	−5.69256	+	9.85980i	−0.222938	+	0.386140i
$653$	−15.5572	+	8.98197i	−0.608802	+	0.351492i	−0.772496	−	0.635019i	$-0.780992\pi$
$653$	−15.5572	+	8.98197i	−0.608802	+	0.351492i	0.163695	+	0.986511i	$0.447659\pi$
$654$	−17.5646	−	2.10475i	−0.686831	−	0.0823023i
$655$	−3.18619	+	5.51863i	−0.124495	+	0.215631i
$656$	−0.202180	+	0.350186i	−0.00789380	+	0.0136725i
$657$	0.503818	+	0.480891i	0.0196558	+	0.0187613i
$658$		0			0
$659$	10.0955	−	5.82866i	0.393266	−	0.227052i	−0.290308	−	0.956933i	$-0.593758\pi$
$659$	10.0955	−	5.82866i	0.393266	−	0.227052i	0.683574	+	0.729881i	$0.260424\pi$
$660$	5.07676	−	6.77807i	0.197612	−	0.263836i
$661$		−	18.2195i		−	0.708657i	−0.935121	−	0.354328i	$-0.884710\pi$
$661$		−	18.2195i		−	0.708657i	0.935121	−	0.354328i	$-0.115290\pi$
$662$			26.4931i			1.02968i
$663$	15.0291	−	20.0656i	0.583682	−	0.779284i
$664$	1.40577	−	0.811624i	0.0545546	−	0.0314971i
$665$		0			0
$666$	1.52796	−	6.28404i	0.0592073	−	0.243502i
$667$	1.38980	−	2.40720i	0.0538132	−	0.0932072i
$668$	−5.66418	+	9.81065i	−0.219154	+	0.379585i
$669$	−13.6814	−	1.63942i	−0.528952	−	0.0633837i
$670$	−5.26725	+	3.04105i	−0.203491	+	0.117486i
$671$	−19.6272	+	33.9953i	−0.757699	+	1.31237i
$672$		0			0
$673$	2.41106	+	4.17608i	0.0929395	+	0.160976i	0.908747	−	0.417348i	$-0.137040\pi$
$673$	2.41106	+	4.17608i	0.0929395	+	0.160976i	−0.815807	+	0.578324i	$0.803707\pi$
$674$	−7.03993	−	4.06451i	−0.271168	−	0.156559i
$675$	−9.76863	−	11.8500i	−0.375995	−	0.456107i
$676$	−13.5797	−	23.5208i	−0.522297	−	0.904645i
$677$	−23.1290			−0.888920			−0.444460	−	0.895799i	$-0.646604\pi$
$677$	−23.1290			−0.888920			−0.444460	+	0.895799i	$0.646604\pi$
$678$	−13.4008	+	5.73442i	−0.514654	+	0.220229i
$679$		0			0
$680$	2.82827	+	1.63290i	0.108459	+	0.0626189i
$681$	14.7131	−	6.29599i	0.563808	−	0.241263i
$682$	−12.8589	−	7.42410i	−0.492393	−	0.284283i
$683$	−6.80041	+	3.92622i	−0.260210	+	0.150233i	−0.624431	−	0.781080i	$-0.714669\pi$
$683$	−6.80041	+	3.92622i	−0.260210	+	0.150233i	0.364220	+	0.931313i	$0.381336\pi$
$684$	1.53601	−	6.31714i	0.0587307	−	0.241542i
$685$		−	13.8076i		−	0.527562i
$686$		0			0
$687$	−14.5225	−	1.74021i	−0.554067	−	0.0663933i
$688$	2.90883	+	5.03824i	0.110898	+	0.192081i
$689$	62.6606			2.38718
$690$	−18.3382	+	7.84721i	−0.698122	+	0.298738i
$691$			17.1676i			0.653085i	0.945182	+	0.326543i	$0.105884\pi$
$691$			17.1676i			0.653085i	−0.945182	+	0.326543i	$0.894116\pi$
$692$	−21.6914			−0.824584
$693$		0			0
$694$	−25.6171			−0.972412
$695$			26.5290i			1.00630i
$696$	−0.0711198	+	0.593511i	−0.00269579	+	0.0224970i
$697$	−0.923564			−0.0349825
$698$	5.26504	+	9.11932i	0.199285	+	0.345171i
$699$	−11.3441	−	26.5100i	−0.429071	−	1.00270i
$700$		0			0
$701$			34.9404i			1.31968i	0.751406	+	0.659840i	$0.229376\pi$
$701$			34.9404i			1.31968i	−0.751406	+	0.659840i	$0.770624\pi$
$702$	−20.9456	−	25.4084i	−0.790540	−	0.958979i
$703$	4.04570	−	2.33579i	0.152587	−	0.0880959i
$704$	−2.96133	−	1.70972i	−0.111609	−	0.0644376i
$705$	−1.62601	+	13.5694i	−0.0612389	+	0.511053i
$706$	11.1230	+	6.42186i	0.418619	+	0.241690i
$707$		0			0
$708$	−15.2904	−	11.4525i	−0.574649	−	0.430410i
$709$	−24.3336			−0.913867			−0.456933	−	0.889501i	$-0.651052\pi$
$709$	−24.3336			−0.913867			−0.456933	+	0.889501i	$0.651052\pi$
$710$	−2.54079	−	4.40078i	−0.0953542	−	0.165158i
$711$	12.2859	+	41.9228i	0.460758	+	1.57223i
$712$	3.51562	+	2.02974i	0.131753	+	0.0760678i
$713$	17.4866	+	30.2877i	0.654879	+	1.13428i
$714$		0			0
$715$	15.4921	−	26.8331i	0.579372	−	1.00350i
$716$	18.0057	−	10.3956i	0.672904	−	0.388501i
$717$	18.5946	+	43.4537i	0.694427	+	1.62281i
$718$	14.8311	−	25.6881i	0.553490	−	0.958673i
$719$	−8.76887	+	15.1881i	−0.327024	+	0.566422i	−0.981920	−	0.189297i	$-0.939379\pi$
$719$	−8.76887	+	15.1881i	−0.327024	+	0.566422i	0.654896	+	0.755719i	$0.272712\pi$
$720$	2.96175	−	3.10295i	0.110378	−	0.115640i
$721$		0			0
$722$	−12.3875	+	7.15191i	−0.461014	+	0.266167i
$723$	−17.2328	−	40.2714i	−0.640895	−	1.49771i
$724$		−	21.5301i		−	0.800159i
$725$			1.02000i			0.0378818i
$726$	−1.19112	−	0.142730i	−0.0442064	−	0.00529721i
$727$	33.8627	−	19.5507i	1.25590	−	0.725094i	0.283625	−	0.958935i	$-0.408463\pi$
$727$	33.8627	−	19.5507i	1.25590	−	0.725094i	0.972275	+	0.233841i	$0.0751296\pi$
$728$		0			0
$729$	−20.3776	−	17.7131i	−0.754725	−	0.656041i
$730$	−0.165978	+	0.287482i	−0.00614311	+	0.0106402i
$731$	−6.64381	+	11.5074i	−0.245730	+	0.425617i
$732$	−11.9199	+	15.9145i	−0.440572	+	0.588215i
$733$	−20.3073	+	11.7245i	−0.750069	+	0.433053i	−0.825719	−	0.564082i	$-0.809230\pi$
$733$	−20.3073	+	11.7245i	−0.750069	+	0.433053i	0.0756499	+	0.997134i	$0.475897\pi$
$734$	−11.9989	+	20.7828i	−0.442889	+	0.767107i
$735$		0			0
$736$	4.02706	+	6.97507i	0.148439	+	0.257104i
$737$	12.5965	+	7.27257i	0.463997	+	0.267889i
$738$	−0.286609	+	1.17874i	−0.0105502	+	0.0433898i
$739$	13.3662	+	23.1509i	0.491682	+	0.851618i	0.999954	−	0.00957820i	$-0.00304888\pi$
$739$	13.3662	+	23.1509i	0.491682	+	0.851618i	−0.508272	+	0.861197i	$0.669716\pi$
$740$	3.08235			0.113309
$741$	2.83004	−	23.6173i	0.103964	−	0.867605i
$742$		0			0
$743$	−11.0914	−	6.40360i	−0.406903	−	0.234925i	0.282555	−	0.959251i	$-0.408818\pi$
$743$	−11.0914	−	6.40360i	−0.406903	−	0.234925i	−0.689458	+	0.724326i	$0.742151\pi$
$744$	−6.01974	−	4.50877i	−0.220694	−	0.165299i
$745$	8.05745	+	4.65197i	0.295202	+	0.170435i
$746$	10.2528	−	5.91948i	0.375383	−	0.216727i
$747$	3.36234	−	3.52265i	0.123022	−	0.128887i
$748$		−	7.81007i		−	0.285564i
$749$		0			0
$750$	11.8113	−	15.7695i	0.431289	−	0.575822i
$751$	5.12417	+	8.87532i	0.186984	+	0.323865i	0.944243	−	0.329249i	$-0.106796\pi$
$751$	5.12417	+	8.87532i	0.186984	+	0.323865i	−0.757260	+	0.653114i	$0.773462\pi$
$752$	5.51829			0.201231
$753$	−11.3585	−	8.50751i	−0.413928	−	0.310031i
$754$			2.18705i			0.0796475i
$755$	8.23452			0.299685
$756$		0			0
$757$	11.0844			0.402868			0.201434	−	0.979502i	$-0.435440\pi$
$757$	11.0844			0.402868			0.201434	+	0.979502i	$0.435440\pi$
$758$			13.1379i			0.477191i
$759$	38.1797	+	28.5965i	1.38584	+	1.03799i
$760$	3.09858			0.112397
$761$	8.14993	+	14.1161i	0.295435	+	0.511708i	0.975086	−	0.221827i	$-0.0712022\pi$
$761$	8.14993	+	14.1161i	0.295435	+	0.511708i	−0.679651	+	0.733536i	$0.737869\pi$
$762$	−5.99925	+	8.00971i	−0.217330	+	0.290161i
$763$		0			0
$764$		−	7.36938i		−	0.266615i
$765$	9.52003	+	2.31479i	0.344197	+	0.0836913i
$766$	15.2005	−	8.77603i	0.549217	−	0.317091i
$767$	−60.5319	−	34.9481i	−2.18568	−	1.26190i
$768$	−1.38631	−	1.03834i	−0.0500241	−	0.0374679i
$769$	−41.4043	−	23.9048i	−1.49308	−	0.862029i	−0.493110	−	0.869967i	$-0.664140\pi$
$769$	−41.4043	−	23.9048i	−1.49308	−	0.862029i	−0.999968	+	0.00793771i	$0.997473\pi$
$770$		0			0
$771$	1.36720	−	11.4096i	0.0492384	−	0.410906i
$772$	2.82559			0.101695
$773$	6.25441	+	10.8330i	0.224956	+	0.389635i	0.956306	−	0.292367i	$-0.0944429\pi$
$773$	6.25441	+	10.8330i	0.224956	+	0.389635i	−0.731350	+	0.682002i	$0.761110\pi$
$774$	12.6250	+	12.0505i	0.453798	+	0.433147i
$775$	−11.1143	−	6.41686i	−0.399239	−	0.230501i
$776$	5.30423	+	9.18719i	0.190411	+	0.329801i
$777$		0			0
$778$	10.9205	−	18.9148i	0.391518	−	0.678130i
$779$	−0.758876	+	0.438137i	−0.0271896	+	0.0156979i
$780$	9.40859	−	12.5616i	0.336881	−	0.449777i
$781$	−6.07623	+	10.5243i	−0.217425	+	0.376590i
$782$	−9.19786	+	15.9312i	−0.328915	+	0.569697i
$783$	0.295996	+	1.76867i	0.0105780	+	0.0632073i
$784$		0			0
$785$	9.86123	−	5.69338i	0.351962	−	0.203206i
$786$	7.66435	+	0.918411i	0.273378	+	0.0327586i
$787$			0.261017i			0.00930426i	0.999989	+	0.00465213i	$0.00148082\pi$
$787$			0.261017i			0.00930426i	−0.999989	+	0.00465213i	$0.998519\pi$
$788$			26.0883i			0.929357i
$789$	−4.11972	−	9.62739i	−0.146666	−	0.342744i
$790$	−18.0319	+	10.4107i	−0.641548	+	0.370398i
$791$		0			0
$792$	−9.96791	−	2.42369i	−0.354194	−	0.0861221i
$793$	−36.3744	+	63.0024i	−1.29169	+	2.23728i
$794$	−19.4935	+	33.7636i	−0.691797	+	1.19823i
$795$	9.63381	+	22.5133i	0.341676	+	0.798464i
$796$	13.3511	−	7.70826i	0.473217	−	0.273212i
$797$	−1.85220	+	3.20810i	−0.0656083	+	0.113637i	−0.896964	−	0.442104i	$-0.854232\pi$
$797$	−1.85220	+	3.20810i	−0.0656083	+	0.113637i	0.831355	+	0.555741i	$0.187565\pi$
$798$		0			0
$799$	6.30194	+	10.9153i	0.222946	+	0.386155i
$800$	−2.55956	−	1.47776i	−0.0904942	−	0.0522468i
$801$	11.8337	+	2.87735i	0.418122	+	0.101666i
$802$	11.5989	+	20.0899i	0.409573	+	0.709400i
$803$	0.793862			0.0280148
$804$	5.89688	+	4.41674i	0.207967	+	0.155767i
$805$		0			0
$806$	−23.8310	−	13.7588i	−0.839411	−	0.484634i
$807$	−1.40572	+	11.7311i	−0.0494837	+	0.412953i
$808$	6.97052	+	4.02443i	0.245222	+	0.141579i
$809$	5.94276	−	3.43105i	0.208936	−	0.120629i	−0.391881	−	0.920016i	$-0.628175\pi$
$809$	5.94276	−	3.43105i	0.208936	−	0.120629i	0.600817	+	0.799387i	$0.294842\pi$
$810$	5.90868	−	11.4320i	0.207610	−	0.401678i
$811$		−	23.1945i		−	0.814470i	−0.913323	−	0.407235i	$-0.866493\pi$
$811$		−	23.1945i		−	0.814470i	0.913323	−	0.407235i	$-0.133507\pi$
$812$		0			0
$813$	−3.46029	−	8.08635i	−0.121358	−	0.283601i
$814$	−3.68567	−	6.38377i	−0.129183	−	0.223751i
$815$	−16.2790			−0.570229
$816$	0.470680	−	3.92793i	0.0164771	−	0.137505i
$817$			12.6073i			0.441072i
$818$	−24.6187			−0.860774
$819$		0			0
$820$	−0.578174			−0.0201907
$821$			3.79377i			0.132403i	0.997806	+	0.0662017i	$0.0210881\pi$
$821$			3.79377i			0.132403i	−0.997806	+	0.0662017i	$0.978912\pi$
$822$	−15.3771	+	6.58013i	−0.536339	+	0.229508i
$823$	−14.9079			−0.519656			−0.259828	−	0.965655i	$-0.583666\pi$
$823$	−14.9079			−0.519656			−0.259828	+	0.965655i	$0.583666\pi$
$824$	1.40695	+	2.43692i	0.0490136	+	0.0848940i
$825$	−17.3802	−	2.08265i	−0.605102	−	0.0725087i
$826$		0			0
$827$			21.9819i			0.764384i	0.924083	+	0.382192i	$0.124831\pi$
$827$			21.9819i			0.764384i	−0.924083	+	0.382192i	$0.875169\pi$
$828$	17.4784	+	16.6830i	0.607417	+	0.579775i
$829$	−12.2406	+	7.06713i	−0.425135	+	0.245452i	−0.697272	−	0.716807i	$-0.745603\pi$
$829$	−12.2406	+	7.06713i	−0.425135	+	0.245452i	0.272137	+	0.962259i	$0.412270\pi$
$830$	2.01005	+	1.16050i	0.0697697	+	0.0402816i
$831$	−3.15154	+	1.34860i	−0.109326	+	0.0467823i
$832$	−5.48813	−	3.16857i	−0.190267	−	0.109851i
$833$		0			0
$834$	29.5446	−	12.6426i	1.02305	−	0.437779i
$835$	−16.1979			−0.560550
$836$	−3.70508	−	6.41739i	−0.128143	−	0.221950i
$837$	−21.1344	−	7.90153i	−0.730511	−	0.273117i
$838$	14.7916	+	8.53996i	0.510969	+	0.295008i
$839$	−8.92488	−	15.4583i	−0.308121	−	0.533681i	0.669830	−	0.742514i	$-0.266367\pi$
$839$	−8.92488	−	15.4583i	−0.308121	−	0.533681i	−0.977951	+	0.208833i	$0.933034\pi$
$840$		0			0
$841$	−14.4404	+	25.0116i	−0.497946	+	0.862469i
$842$	−12.7419	+	7.35652i	−0.439114	+	0.253522i
$843$	30.3237	+	3.63365i	1.04440	+	0.125150i
$844$	−4.42465	+	7.66371i	−0.152303	+	0.263796i
$845$	19.4170	−	33.6312i	0.667964	−	1.15695i
$846$	15.8867	−	4.65577i	0.546197	−	0.160069i
$847$		0			0
$848$	8.56310	−	4.94391i	0.294058	−	0.169775i
$849$	5.35145	−	7.14482i	0.183661	−	0.245210i
$850$		−	6.75047i		−	0.231539i
$851$			17.3624i			0.595174i
$852$	−3.69019	+	4.92684i	−0.126424	+	0.168791i
$853$	−35.2392	+	20.3454i	−1.20657	+	0.696612i	−0.962008	−	0.273022i	$-0.911977\pi$
$853$	−35.2392	+	20.3454i	−1.20657	+	0.696612i	−0.244559	+	0.969634i	$0.578643\pi$
$854$		0			0
$855$	8.92057	−	2.61427i	0.305077	−	0.0894060i
$856$	7.91078	−	13.7019i	0.270385	−	0.468320i
$857$	−2.72896	+	4.72669i	−0.0932194	+	0.161461i	−0.908864	−	0.417092i	$-0.863049\pi$
$857$	−2.72896	+	4.72669i	−0.0932194	+	0.161461i	0.815645	+	0.578553i	$0.196382\pi$
$858$	−37.2661	−	4.46556i	−1.27224	−	0.152452i
$859$	−38.8822	+	22.4487i	−1.32664	+	0.765938i	−0.984779	−	0.173810i	$-0.944392\pi$
$859$	−38.8822	+	22.4487i	−1.32664	+	0.765938i	−0.341865	+	0.939749i	$0.611059\pi$
$860$	−4.15919	+	7.20393i	−0.141827	+	0.245652i
$861$		0			0
$862$	4.80521	+	8.32286i	0.163666	+	0.283478i
$863$	19.6689	+	11.3559i	0.669539	+	0.386558i	0.795902	−	0.605426i	$-0.206997\pi$
$863$	19.6689	+	11.3559i	0.669539	+	0.386558i	−0.126363	+	0.991984i	$0.540330\pi$
$864$	−4.86711	−	1.81967i	−0.165583	−	0.0619066i
$865$	−15.5077	−	26.8602i	−0.527279	−	0.913274i
$866$	9.04314			0.307298
$867$	−18.7635	+	8.02921i	−0.637241	+	0.272686i
$868$		0			0
$869$	43.1229	+	24.8970i	1.46284	+	0.844573i
$870$	−0.785782	+	0.336249i	−0.0266405	+	0.0113999i
$871$	23.3446	+	13.4780i	0.791002	+	0.456685i
$872$	−8.84514	+	5.10675i	−0.299534	+	0.172936i
$873$	23.0217	+	21.9740i	0.779165	+	0.743708i
$874$			17.4538i			0.590384i
$875$		0			0
$876$	0.399258	+	0.0478427i	0.0134897	+	0.00161645i
$877$	15.2445	+	26.4043i	0.514771	+	0.891610i	0.999853	+	0.0171413i	$0.00545653\pi$
$877$	15.2445	+	26.4043i	0.514771	+	0.891610i	−0.485082	+	0.874469i	$0.661210\pi$
$878$	−0.913795			−0.0308391
$879$	3.28822	−	1.40708i	0.110909	−	0.0474597i
$880$		−	4.88930i		−	0.164818i
$881$	−29.3810			−0.989871			−0.494935	−	0.868930i	$-0.664808\pi$
$881$	−29.3810			−0.989871			−0.494935	+	0.868930i	$0.664808\pi$
$882$		0			0
$883$	14.1682			0.476798			0.238399	−	0.971167i	$-0.423377\pi$
$883$	14.1682			0.476798			0.238399	+	0.971167i	$0.423377\pi$
$884$		−	14.4741i		−	0.486818i
$885$	3.24995	−	27.1216i	0.109246	−	0.911682i
$886$	29.3616			0.986424
$887$	16.3537	+	28.3254i	0.549103	+	0.951074i	0.998336	+	0.0576593i	$0.0183637\pi$
$887$	16.3537	+	28.3254i	0.549103	+	0.951074i	−0.449234	+	0.893414i	$0.648303\pi$
$888$	−1.46892	−	3.43272i	−0.0492937	−	0.115195i
$889$		0			0
$890$			5.80446i			0.194566i
$891$	−30.7417	+	1.43230i	−1.02988	+	0.0479837i
$892$	−6.88961	+	3.97772i	−0.230681	+	0.133184i
$893$	10.3564	+	5.97926i	0.346563	+	0.200088i
$894$	1.34092	−	11.1903i	0.0448471	−	0.374259i
$895$	25.7454	+	14.8641i	0.860575	+	0.496853i
$896$		0			0
$897$	70.7573	+	52.9970i	2.36252	+	1.76952i
$898$	−3.36736			−0.112370
$899$	0.749293	+	1.29781i	0.0249903	+	0.0432845i
$900$	−8.61556	−	2.09487i	−0.287185	−	0.0698289i
$901$	19.5583	+	11.2920i	0.651580	+	0.376190i
$902$	0.691343	+	1.19744i	0.0230192	+	0.0398704i
$903$		0			0
$904$	−4.20778	+	7.28808i	−0.139949	+	0.242398i
$905$	26.6604	−	15.3924i	0.886222	−	0.511661i
$906$	−3.92423	−	9.17054i	−0.130374	−	0.304671i
$907$	−28.3467	+	49.0980i	−0.941238	+	1.63027i	−0.178123	+	0.984008i	$0.557002\pi$
$907$	−28.3467	+	49.0980i	−0.941238	+	1.63027i	−0.763115	+	0.646263i	$0.776331\pi$
$908$	4.61984	−	8.00180i	0.153315	−	0.265549i
$909$	23.4630	+	5.70500i	0.778218	+	0.189223i
$910$		0			0
$911$	0.621795	−	0.358994i	0.0206010	−	0.0118940i	−0.489664	−	0.871911i	$-0.662881\pi$
$911$	0.621795	−	0.358994i	0.0206010	−	0.0118940i	0.510265	+	0.860017i	$0.329547\pi$
$912$	−1.47666	−	3.45080i	−0.0488969	−	0.114267i
$913$		−	5.55061i		−	0.183698i
$914$			15.1139i			0.499922i
$915$	−28.2285	−	3.38259i	−0.933205	−	0.111825i
$916$	−7.31319	+	4.22227i	−0.241635	+	0.139508i
$917$		0			0
$918$	−1.95894	−	11.7053i	−0.0646546	−	0.386333i
$919$	18.9720	−	32.8605i	0.625829	−	1.08397i	−0.362550	−	0.931964i	$-0.618094\pi$
$919$	18.9720	−	32.8605i	0.625829	−	1.08397i	0.988380	−	0.152004i	$-0.0485727\pi$
$920$	−5.75809	+	9.97330i	−0.189839	+	0.328810i
$921$	−1.13302	+	1.51272i	−0.0373343	+	0.0498458i
$922$	−8.99706	+	5.19445i	−0.296302	+	0.171070i
$923$	−11.2609	+	19.5044i	−0.370656	+	0.641996i
$924$		0			0
$925$	−3.18563	−	5.51768i	−0.104743	−	0.181420i
$926$	4.60244	+	2.65722i	0.151246	+	0.0873217i
$927$	6.10653	+	5.82864i	0.200565	+	0.191438i
$928$	0.172558	+	0.298879i	0.00566448	+	0.00981117i
$929$	−42.8700			−1.40652			−0.703259	−	0.710934i	$-0.748273\pi$
$929$	−42.8700			−1.40652			−0.703259	+	0.710934i	$0.748273\pi$
$930$	1.27948	−	10.6776i	0.0419559	−	0.350132i
$931$		0			0
$932$	−14.4176	−	8.32399i	−0.472263	−	0.272661i
$933$	21.1024	+	15.8056i	0.690861	+	0.517453i
$934$	16.8874	+	9.74994i	0.552572	+	0.319028i
$935$	9.67111	−	5.58362i	0.316279	−	0.182604i
$936$	−18.4732	−	4.49174i	−0.603816	−	0.146817i
$937$			8.64637i			0.282464i	0.989976	+	0.141232i	$0.0451064\pi$
$937$			8.64637i			0.282464i	−0.989976	+	0.141232i	$0.954894\pi$
$938$		0			0
$939$	−12.0140	+	16.0401i	−0.392061	+	0.523448i
$940$	3.94517	+	6.83323i	0.128677	+	0.222875i
$941$	−10.0921			−0.328991			−0.164496	−	0.986378i	$-0.552600\pi$
$941$	−10.0921			−0.328991			−0.164496	+	0.986378i	$0.552600\pi$
$942$	−11.0400	−	8.26894i	−0.359703	−	0.269417i
$943$		−	3.25676i		−	0.106055i
$944$	−11.0296			−0.358983
$945$		0			0
$946$	19.8932			0.646783
$947$		−	58.2693i		−	1.89350i	−0.321973	−	0.946749i	$-0.604346\pi$
$947$		−	58.2693i		−	1.89350i	0.321973	−	0.946749i	$-0.395654\pi$
$948$	20.1874	+	15.1203i	0.655657	+	0.491085i
$949$	1.47124			0.0477584
$950$	−3.20241	−	5.54674i	−0.103900	−	0.179960i
$951$	−17.8183	+	23.7896i	−0.577799	+	0.771430i
$952$		0			0
$953$		−	46.9356i		−	1.52039i	−0.649694	−	0.760196i	$-0.725103\pi$
$953$		−	46.9356i		−	1.52039i	0.649694	−	0.760196i	$-0.274897\pi$
$954$	20.4813	−	21.4578i	0.663107	−	0.694721i
$955$	9.12541	−	5.26856i	0.295291	−	0.170487i
$956$	23.6325	+	13.6442i	0.764330	+	0.441286i
$957$	1.63599	+	1.22535i	0.0528839	+	0.0396099i
$958$	−24.0776	−	13.9012i	−0.777912	−	0.449128i
$959$		0			0
$960$	0.294657	−	2.45898i	0.00951002	−	0.0793633i
$961$	12.1446			0.391761
$962$	−6.83054	−	11.8308i	−0.220225	−	0.381441i
$963$	11.2143	−	46.1209i	0.361374	−	1.48623i
$964$	−21.9018	−	12.6450i	−0.705410	−	0.407269i
$965$	2.02008	+	3.49889i	0.0650288	+	0.112633i
$966$		0			0
$967$	6.43145	−	11.1396i	0.206822	−	0.358226i	−0.743890	−	0.668302i	$-0.767021\pi$
$967$	6.43145	−	11.1396i	0.206822	−	0.358226i	0.950712	+	0.310077i	$0.100355\pi$
$968$	−0.599818	+	0.346305i	−0.0192789	+	0.0111307i
$969$	5.13939	−	6.86169i	0.165101	−	0.220429i
$970$	−7.58425	+	13.1363i	−0.243516	+	0.421782i
$971$	−17.3742	+	30.0930i	−0.557565	+	0.965731i	0.440134	+	0.897932i	$0.354931\pi$
$971$	−17.3742	+	30.0930i	−0.557565	+	0.965731i	−0.997699	+	0.0677990i	$0.978402\pi$
$972$	−15.5473	−	1.13232i	−0.498679	−	0.0363193i
$973$		0			0
$974$	6.47506	−	3.73838i	0.207474	−	0.119785i
$975$	−32.2102	−	3.85972i	−1.03155	−	0.123610i
$976$			11.4797i			0.367458i
$977$		−	20.3667i		−	0.651590i	−0.945441	−	0.325795i	$-0.894368\pi$
$977$		−	20.3667i		−	0.651590i	0.945441	−	0.325795i	$-0.105632\pi$
$978$	7.75790	+	18.1295i	0.248070	+	0.579716i
$979$	12.0215	−	6.94060i	0.384208	−	0.221822i
$980$		0			0
$981$	−21.1559	+	22.1645i	−0.675456	+	0.707659i
$982$	11.0543	−	19.1466i	0.352756	−	0.610992i
$983$	14.6682	−	25.4061i	0.467843	−	0.810328i	−0.531482	−	0.847070i	$-0.678365\pi$
$983$	14.6682	−	25.4061i	0.467843	−	0.810328i	0.999325	+	0.0367416i	$0.0116978\pi$
$984$	0.275534	+	0.643896i	0.00878369	+	0.0205266i
$985$	−32.3048	+	18.6512i	−1.02932	+	0.594276i
$986$	−0.394124	+	0.682643i	−0.0125515	+	0.0217398i
$987$		0			0
$988$	−6.86651	−	11.8931i	−0.218453	−	0.378371i
$989$	−40.5786	−	23.4280i	−1.29032	−	0.744968i
$990$	−4.12509	−	14.0759i	−0.131104	−	0.447361i
$991$	−14.8114	−	25.6540i	−0.470498	−	0.814927i	0.528933	−	0.848664i	$-0.322592\pi$
$991$	−14.8114	−	25.6540i	−0.470498	−	0.814927i	−0.999431	+	0.0337371i	$0.989259\pi$
$992$	−4.34228			−0.137868
$993$	36.7276	+	27.5089i	1.16551	+	0.872967i
$994$		0			0
$995$	19.0901	+	11.0217i	0.605196	+	0.349410i
$996$	0.334512	−	2.79158i	0.0105994	−	0.0884545i
$997$	−23.4011	−	13.5106i	−0.741120	−	0.427886i	0.0813562	−	0.996685i	$-0.474075\pi$
$997$	−23.4011	−	13.5106i	−0.741120	−	0.427886i	−0.822477	+	0.568799i	$0.807408\pi$
$998$	−28.4959	+	16.4521i	−0.902022	+	0.520783i
$999$	−7.12508	−	8.64320i	−0.225427	−	0.273459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.b.509.2		16
3.2	odd	2		2646.2.l.a.1097.7		16
7.2	even	3		882.2.m.a.293.4		16
7.3	odd	6		882.2.t.a.815.7		16
7.4	even	3		126.2.t.a.59.6	yes	16
7.5	odd	6		882.2.m.b.293.1		16
7.6	odd	2		126.2.l.a.5.3	✓	16
9.2	odd	6		882.2.t.a.803.7		16
9.7	even	3		2646.2.t.b.1979.3		16
21.2	odd	6		2646.2.m.a.881.7		16
21.5	even	6		2646.2.m.b.881.6		16
21.11	odd	6		378.2.t.a.17.2		16
21.17	even	6		2646.2.t.b.2285.3		16
21.20	even	2		378.2.l.a.341.6		16
28.11	odd	6		1008.2.df.c.689.6		16
28.27	even	2		1008.2.ca.c.257.3		16
63.2	odd	6		882.2.m.b.587.1		16
63.4	even	3		1134.2.k.b.647.2		16
63.11	odd	6		126.2.l.a.101.7	yes	16
63.13	odd	6		1134.2.k.a.971.7		16
63.16	even	3		2646.2.m.b.1763.6		16
63.20	even	6		126.2.t.a.47.6	yes	16
63.25	even	3		378.2.l.a.143.2		16
63.32	odd	6		1134.2.k.a.647.7		16
63.34	odd	6		378.2.t.a.89.2		16
63.38	even	6	inner	882.2.l.b.227.6		16
63.41	even	6		1134.2.k.b.971.2		16
63.47	even	6		882.2.m.a.587.4		16
63.52	odd	6		2646.2.l.a.521.3		16
63.61	odd	6		2646.2.m.a.1763.7		16
84.11	even	6		3024.2.df.c.17.3		16
84.83	odd	2		3024.2.ca.c.2609.3		16
252.11	even	6		1008.2.ca.c.353.3		16
252.83	odd	6		1008.2.df.c.929.6		16
252.151	odd	6		3024.2.ca.c.2033.3		16
252.223	even	6		3024.2.df.c.1601.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.3	✓	16	7.6	odd	2
126.2.l.a.101.7	yes	16	63.11	odd	6
126.2.t.a.47.6	yes	16	63.20	even	6
126.2.t.a.59.6	yes	16	7.4	even	3
378.2.l.a.143.2		16	63.25	even	3
378.2.l.a.341.6		16	21.20	even	2
378.2.t.a.17.2		16	21.11	odd	6
378.2.t.a.89.2		16	63.34	odd	6
882.2.l.b.227.6		16	63.38	even	6	inner
882.2.l.b.509.2		16	1.1	even	1	trivial
882.2.m.a.293.4		16	7.2	even	3
882.2.m.a.587.4		16	63.47	even	6
882.2.m.b.293.1		16	7.5	odd	6
882.2.m.b.587.1		16	63.2	odd	6
882.2.t.a.803.7		16	9.2	odd	6
882.2.t.a.815.7		16	7.3	odd	6
1008.2.ca.c.257.3		16	28.27	even	2
1008.2.ca.c.353.3		16	252.11	even	6
1008.2.df.c.689.6		16	28.11	odd	6
1008.2.df.c.929.6		16	252.83	odd	6
1134.2.k.a.647.7		16	63.32	odd	6
1134.2.k.a.971.7		16	63.13	odd	6
1134.2.k.b.647.2		16	63.4	even	3
1134.2.k.b.971.2		16	63.41	even	6
2646.2.l.a.521.3		16	63.52	odd	6
2646.2.l.a.1097.7		16	3.2	odd	2
2646.2.m.a.881.7		16	21.2	odd	6
2646.2.m.a.1763.7		16	63.61	odd	6
2646.2.m.b.881.6		16	21.5	even	6
2646.2.m.b.1763.6		16	63.16	even	3
2646.2.t.b.1979.3		16	9.7	even	3
2646.2.t.b.2285.3		16	21.17	even	6
3024.2.ca.c.2033.3		16	252.151	odd	6
3024.2.ca.c.2609.3		16	84.83	odd	2
3024.2.df.c.17.3		16	84.11	even	6
3024.2.df.c.1601.3		16	252.223	even	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.38631 - 1.03834i) q^{3} -1.00000 q^{4} +(-0.714925 - 1.23829i) q^{5} +(-1.03834 + 1.38631i) q^{6} +1.00000i q^{8} +(0.843698 + 2.87892i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.38631 - 1.03834i) q^{3} -1.00000 q^{4} +(-0.714925 - 1.23829i) q^{5} +(-1.03834 + 1.38631i) q^{6} +1.00000i q^{8} +(0.843698 + 2.87892i) q^{9} +(-1.23829 + 0.714925i) q^{10} +(2.96133 + 1.70972i) q^{11} +(1.38631 + 1.03834i) q^{12} +(5.48813 + 3.16857i) q^{13} +(-0.294657 + 2.45898i) q^{15} +1.00000 q^{16} +(1.14201 + 1.97802i) q^{17} +(2.87892 - 0.843698i) q^{18} +(1.87673 + 1.08353i) q^{19} +(0.714925 + 1.23829i) q^{20} +(1.70972 - 2.96133i) q^{22} +(-6.97507 + 4.02706i) q^{23} +(1.03834 - 1.38631i) q^{24} +(1.47776 - 2.55956i) q^{25} +(3.16857 - 5.48813i) q^{26} +(1.81967 - 4.86711i) q^{27} +(-0.298879 + 0.172558i) q^{29} +(2.45898 + 0.294657i) q^{30} -4.34228i q^{31} -1.00000i q^{32} +(-2.33004 - 5.44507i) q^{33} +(1.97802 - 1.14201i) q^{34} +(-0.843698 - 2.87892i) q^{36} +(1.07786 - 1.86690i) q^{37} +(1.08353 - 1.87673i) q^{38} +(-4.31818 - 10.0912i) q^{39} +(1.23829 - 0.714925i) q^{40} +(-0.202180 + 0.350186i) q^{41} +(2.90883 + 5.03824i) q^{43} +(-2.96133 - 1.70972i) q^{44} +(2.96175 - 3.10295i) q^{45} +(4.02706 + 6.97507i) q^{46} +5.51829 q^{47} +(-1.38631 - 1.03834i) q^{48} +(-2.55956 - 1.47776i) q^{50} +(0.470680 - 3.92793i) q^{51} +(-5.48813 - 3.16857i) q^{52} +(8.56310 - 4.94391i) q^{53} +(-4.86711 - 1.81967i) q^{54} -4.88930i q^{55} +(-1.47666 - 3.45080i) q^{57} +(0.172558 + 0.298879i) q^{58} -11.0296 q^{59} +(0.294657 - 2.45898i) q^{60} +11.4797i q^{61} -4.34228 q^{62} -1.00000 q^{64} -9.06117i q^{65} +(-5.44507 + 2.33004i) q^{66} +4.25366 q^{67} +(-1.14201 - 1.97802i) q^{68} +(13.8510 + 1.65976i) q^{69} +3.55393i q^{71} +(-2.87892 + 0.843698i) q^{72} +(0.201057 - 0.116080i) q^{73} +(-1.86690 - 1.07786i) q^{74} +(-4.70633 + 2.01392i) q^{75} +(-1.87673 - 1.08353i) q^{76} +(-10.0912 + 4.31818i) q^{78} +14.5620 q^{79} +(-0.714925 - 1.23829i) q^{80} +(-7.57635 + 4.85787i) q^{81} +(0.350186 + 0.202180i) q^{82} +(-0.811624 - 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} +(5.03824 - 2.90883i) q^{86} +(0.593511 + 0.0711198i) q^{87} +(-1.70972 + 2.96133i) q^{88} +(2.02974 - 3.51562i) q^{89} +(-3.10295 - 2.96175i) q^{90} +(6.97507 - 4.02706i) q^{92} +(-4.50877 + 6.01974i) q^{93} -5.51829i q^{94} -3.09858i q^{95} +(-1.03834 + 1.38631i) q^{96} +(9.18719 - 5.30423i) q^{97} +(-2.42369 + 9.96791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} + 12 q^{11} - 6 q^{13} - 18 q^{15} + 16 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 36 q^{27} + 6 q^{29} - 2 q^{37} - 12 q^{39} + 6 q^{41} - 2 q^{43} - 12 q^{44} + 30 q^{45} + 6 q^{46} + 36 q^{47} - 12 q^{50} + 6 q^{51} + 6 q^{52} - 36 q^{53} - 18 q^{54} + 6 q^{57} + 6 q^{58} - 60 q^{59} + 18 q^{60} - 36 q^{62} - 16 q^{64} - 24 q^{66} - 28 q^{67} - 18 q^{68} + 42 q^{69} + 12 q^{72} + 18 q^{74} - 60 q^{75} + 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{86} + 24 q^{87} + 24 q^{89} - 18 q^{90} + 6 q^{92} - 42 q^{93} - 6 q^{97} + 18 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 12 * q^11 - 6 * q^13 - 18 * q^15 + 16 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 36 * q^27 + 6 * q^29 - 2 * q^37 - 12 * q^39 + 6 * q^41 - 2 * q^43 - 12 * q^44 + 30 * q^45 + 6 * q^46 + 36 * q^47 - 12 * q^50 + 6 * q^51 + 6 * q^52 - 36 * q^53 - 18 * q^54 + 6 * q^57 + 6 * q^58 - 60 * q^59 + 18 * q^60 - 36 * q^62 - 16 * q^64 - 24 * q^66 - 28 * q^67 - 18 * q^68 + 42 * q^69 + 12 * q^72 + 18 * q^74 - 60 * q^75 + 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^86 + 24 * q^87 + 24 * q^89 - 18 * q^90 + 6 * q^92 - 42 * q^93 - 6 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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