LMFDB - Embedded newform 1008.2.ca.c.257.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(257,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))

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

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

chi := DirichletCharacter("1008.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (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:	$8.04892052375$
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^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.3
Root			$-1.68301 - 0.409224i$ of defining polynomial
Character	$\chi$	$=$	1008.257
Dual form			1008.2.ca.c.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38631 - 1.03834i) q^{3} +(0.714925 + 1.23829i) q^{5} +(-0.327442 + 2.62541i) q^{7} +(0.843698 + 2.87892i) q^{9} +(-2.96133 - 1.70972i) q^{11} +(-5.48813 - 3.16857i) q^{13} +(0.294657 - 2.45898i) q^{15} +(-1.14201 - 1.97802i) q^{17} +(1.87673 + 1.08353i) q^{19} +(3.18001 - 3.29963i) q^{21} +(6.97507 - 4.02706i) q^{23} +(1.47776 - 2.55956i) q^{25} +(1.81967 - 4.86711i) q^{27} +(-0.298879 + 0.172558i) q^{29} -4.34228i q^{31} +(2.33004 + 5.44507i) q^{33} +(-3.48511 + 1.47150i) q^{35} +(1.07786 - 1.86690i) q^{37} +(4.31818 + 10.0912i) q^{39} +(0.202180 - 0.350186i) q^{41} +(-2.90883 - 5.03824i) q^{43} +(-2.96175 + 3.10295i) q^{45} +5.51829 q^{47} +(-6.78556 - 1.71934i) q^{49} +(-0.470680 + 3.92793i) q^{51} +(8.56310 - 4.94391i) q^{53} -4.88930i q^{55} +(-1.47666 - 3.45080i) q^{57} -11.0296 q^{59} -11.4797i q^{61} +(-7.83461 + 1.27237i) q^{63} -9.06117i q^{65} -4.25366 q^{67} +(-13.8510 - 1.65976i) q^{69} -3.55393i q^{71} +(-0.201057 + 0.116080i) q^{73} +(-4.70633 + 2.01392i) q^{75} +(5.45839 - 7.21486i) q^{77} -14.5620 q^{79} +(-7.57635 + 4.85787i) q^{81} +(-0.811624 - 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} +(0.593511 + 0.0711198i) q^{87} +(-2.02974 + 3.51562i) q^{89} +(10.1159 - 13.3711i) q^{91} +(-4.50877 + 6.01974i) q^{93} +3.09858i q^{95} +(-9.18719 + 5.30423i) q^{97} +(2.42369 - 9.96791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49}+ \cdots - 18 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.38631	−	1.03834i	−0.800385	−	0.599486i
$3$	−1.38631	−	1.03834i	−0.800385	−	0.599486i
$4$		0			0
$5$	0.714925	+	1.23829i	0.319724	+	0.553779i	0.980430	−	0.196866i	$-0.0630764\pi$
$5$	0.714925	+	1.23829i	0.319724	+	0.553779i	−0.660706	+	0.750645i	$0.729743\pi$
$6$		0			0
$7$	−0.327442	+	2.62541i	−0.123762	+	0.992312i
$7$	−0.327442	+	2.62541i	−0.123762	+	0.992312i
$8$		0			0
$9$	0.843698	+	2.87892i	0.281233	+	0.959640i
$10$		0			0
$11$	−2.96133	−	1.70972i	−0.892874	−	0.515501i	−0.0179923	−	0.999838i	$-0.505727\pi$
$11$	−2.96133	−	1.70972i	−0.892874	−	0.515501i	−0.874881	+	0.484337i	$0.839061\pi$
$12$		0			0
$13$	−5.48813	−	3.16857i	−1.52213	−	0.878804i	−0.999658	−	0.0261501i	$-0.991675\pi$
$13$	−5.48813	−	3.16857i	−1.52213	−	0.878804i	−0.522476	−	0.852654i	$-0.674991\pi$
$14$		0			0
$15$	0.294657	−	2.45898i	0.0760802	−	0.634907i
$16$		0			0
$17$	−1.14201	−	1.97802i	−0.276978	−	0.479739i	0.693655	−	0.720308i	$-0.255999\pi$
$17$	−1.14201	−	1.97802i	−0.276978	−	0.479739i	−0.970632	+	0.240569i	$0.922666\pi$
$18$		0			0
$19$	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			0
$21$	3.18001	−	3.29963i	0.693934	−	0.720038i
$22$		0			0
$23$	6.97507	−	4.02706i	1.45440	−	0.839699i	0.455675	−	0.890146i	$-0.349398\pi$
$23$	6.97507	−	4.02706i	1.45440	−	0.839699i	0.998727	+	0.0504469i	$0.0160646\pi$
$24$		0			0
$25$	1.47776	−	2.55956i	0.295553	−	0.511912i
$26$		0			0
$27$	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	$0.343535\pi$
$30$		0			0
$31$		−	4.34228i		−	0.779896i	−0.920837	−	0.389948i	$-0.872493\pi$
$31$		−	4.34228i		−	0.779896i	0.920837	−	0.389948i	$-0.127507\pi$
$32$		0			0
$33$	2.33004	+	5.44507i	0.405607	+	0.947865i
$34$		0			0
$35$	−3.48511	+	1.47150i	−0.589091	+	0.248730i
$36$		0			0
$37$	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	$0.109963\pi$
$38$		0			0
$39$	4.31818	+	10.0912i	0.691462	+	1.61588i
$40$		0			0
$41$	0.202180	−	0.350186i	0.0315752	−	0.0546898i	−0.849806	−	0.527096i	$-0.823281\pi$
$41$	0.202180	−	0.350186i	0.0315752	−	0.0546898i	0.881381	+	0.472406i	$0.156614\pi$
$42$		0			0
$43$	−2.90883	−	5.03824i	−0.443592	−	0.768325i	0.554361	−	0.832277i	$-0.312963\pi$
$43$	−2.90883	−	5.03824i	−0.443592	−	0.768325i	−0.997953	+	0.0639521i	$0.979630\pi$
$44$		0			0
$45$	−2.96175	+	3.10295i	−0.441511	+	0.462561i
$46$		0			0
$47$	5.51829			0.804926			0.402463	−	0.915436i	$-0.368154\pi$
$47$	5.51829			0.804926			0.402463	+	0.915436i	$0.368154\pi$
$48$		0			0
$49$	−6.78556	−	1.71934i	−0.969366	−	0.245620i
$50$		0			0
$51$	−0.470680	+	3.92793i	−0.0659084	+	0.550020i
$52$		0			0
$53$	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	$0.0957044\pi$
$54$		0			0
$55$		−	4.88930i		−	0.659273i
$56$		0			0
$57$	−1.47666	−	3.45080i	−0.195588	−	0.457070i
$58$		0			0
$59$	−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			0
$61$		−	11.4797i		−	1.46983i	−0.678159	−	0.734915i	$-0.737222\pi$
$61$		−	11.4797i		−	1.46983i	0.678159	−	0.734915i	$-0.262778\pi$
$62$		0			0
$63$	−7.83461	+	1.27237i	−0.987068	+	0.160304i
$64$		0			0
$65$		−	9.06117i		−	1.12390i
$66$		0			0
$67$	−4.25366			−0.519667			−0.259833	−	0.965653i	$-0.583668\pi$
$67$	−4.25366			−0.519667			−0.259833	+	0.965653i	$0.583668\pi$
$68$		0			0
$69$	−13.8510	−	1.65976i	−1.66747	−	0.199811i
$70$		0			0
$71$		−	3.55393i		−	0.421773i	−0.977511	−	0.210887i	$-0.932365\pi$
$71$		−	3.55393i		−	0.421773i	0.977511	−	0.210887i	$-0.0676351\pi$
$72$		0			0
$73$	−0.201057	+	0.116080i	−0.0235320	+	0.0135862i	−0.511720	−	0.859152i	$-0.670991\pi$
$73$	−0.201057	+	0.116080i	−0.0235320	+	0.0135862i	0.488188	+	0.872739i	$0.337658\pi$
$74$		0			0
$75$	−4.70633	+	2.01392i	−0.543440	+	0.232547i
$76$		0			0
$77$	5.45839	−	7.21486i	0.622041	−	0.822210i
$78$		0			0
$79$	−14.5620			−1.63835			−0.819177	−	0.573541i	$-0.805569\pi$
$79$	−14.5620			−1.63835			−0.819177	+	0.573541i	$0.805569\pi$
$80$		0			0
$81$	−7.57635	+	4.85787i	−0.841817	+	0.539764i
$82$		0			0
$83$	−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
$86$		0			0
$87$	0.593511	+	0.0711198i	0.0636311	+	0.00762484i
$88$		0			0
$89$	−2.02974	+	3.51562i	−0.215152	+	0.372655i	−0.953320	−	0.301963i	$-0.902358\pi$
$89$	−2.02974	+	3.51562i	−0.215152	+	0.372655i	0.738167	+	0.674618i	$0.235691\pi$
$90$		0			0
$91$	10.1159	−	13.3711i	1.06043	−	1.40167i
$92$		0			0
$93$	−4.50877	+	6.01974i	−0.467537	+	0.624218i
$94$		0			0
$95$			3.09858i			0.317908i
$96$		0			0
$97$	−9.18719	+	5.30423i	−0.932818	+	0.538563i	−0.887702	−	0.460419i	$-0.847699\pi$
$97$	−9.18719	+	5.30423i	−0.932818	+	0.538563i	−0.0451164	+	0.998982i	$0.514366\pi$
$98$		0			0
$99$	2.42369	−	9.96791i	0.243590	−	1.00181i
$100$		0			0
$101$	−4.02443	+	6.97052i	−0.400446	+	0.693593i	−0.993780	−	0.111364i	$-0.964478\pi$
$101$	−4.02443	+	6.97052i	−0.400446	+	0.693593i	0.593334	+	0.804957i	$0.297811\pi$
$102$		0			0
$103$	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	$0.289063\pi$
$104$		0			0
$105$	6.35936	+	1.57877i	0.620610	+	0.154072i
$106$		0			0
$107$	13.7019	+	7.91078i	1.32461	+	0.764764i	0.984460	−	0.175607i	$-0.0561888\pi$
$107$	13.7019	+	7.91078i	1.32461	+	0.764764i	0.340150	+	0.940371i	$0.389522\pi$
$108$		0			0
$109$	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	$0.670645\pi$
$110$		0			0
$111$	−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	$0.537122\pi$
$114$		0			0
$115$	9.97330	+	5.75809i	0.930015	+	0.536945i
$116$		0			0
$117$	4.49174	−	18.4732i	0.415262	−	1.70785i
$118$		0			0
$119$	5.56705	−	2.35055i	0.510330	−	0.215475i
$120$		0			0
$121$	0.346305	+	0.599818i	0.0314823	+	0.0545289i
$122$		0			0
$123$	−0.643896	+	0.275534i	−0.0580581	+	0.0248440i
$124$		0			0
$125$	11.3752			1.01743
$126$		0			0
$127$	−5.77773			−0.512691			−0.256345	−	0.966585i	$-0.582518\pi$
$127$	−5.77773			−0.512691			−0.256345	+	0.966585i	$0.582518\pi$
$128$		0			0
$129$	−1.19888	+	10.0049i	−0.105555	+	0.880883i
$130$		0			0
$131$	−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	$0.895704\pi$
$132$		0			0
$133$	−3.45924	+	4.57241i	−0.299954	+	0.396478i
$134$		0			0
$135$	7.32781	−	1.22634i	0.630678	−	0.105547i
$136$		0			0
$137$	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	$0.531318\pi$
$138$		0			0
$139$	−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
$142$		0			0
$143$	10.8348	+	18.7664i	0.906049	+	1.56932i
$144$		0			0
$145$	−0.427352	−	0.246732i	−0.0354896	−	0.0204899i
$146$		0			0
$147$	7.62162	+	9.42926i	0.628620	+	0.777712i
$148$		0			0
$149$	−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	$0.419212\pi$
$150$		0			0
$151$	2.87950	−	4.98745i	0.234331	−	0.405873i	−0.724747	−	0.689015i	$-0.758044\pi$
$151$	2.87950	−	4.98745i	0.234331	−	0.405873i	0.959078	+	0.283142i	$0.0913768\pi$
$152$		0			0
$153$	4.73104	−	4.95660i	0.382482	−	0.400717i
$154$		0			0
$155$	5.37699	−	3.10441i	0.431890	−	0.249352i
$156$		0			0
$157$		−	7.96361i		−	0.635565i	−0.948164	−	0.317783i	$-0.897062\pi$
$157$		−	7.96361i		−	0.635565i	0.948164	−	0.317783i	$-0.102938\pi$
$158$		0			0
$159$	−17.0046	−	2.03764i	−1.34855	−	0.161595i
$160$		0			0
$161$	8.28874	+	19.6310i	0.653245	+	1.54714i
$162$		0			0
$163$	−5.69256	+	9.85980i	−0.445876	+	0.772279i	−0.998113	−	0.0614080i	$-0.980441\pi$
$163$	−5.69256	+	9.85980i	−0.445876	+	0.772279i	0.552237	+	0.833687i	$0.313774\pi$
$164$		0			0
$165$	−5.07676	+	6.77807i	−0.395225	+	0.527672i
$166$		0			0
$167$	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
$170$		0			0
$171$	−1.53601	+	6.31714i	−0.117461	+	0.483084i
$172$		0			0
$173$	−21.6914			−1.64917			−0.824584	−	0.565739i	$-0.808591\pi$
$173$	−21.6914			−1.64917			−0.824584	+	0.565739i	$0.808591\pi$
$174$		0			0
$175$	6.23602	+	4.71785i	0.471399	+	0.356636i
$176$		0			0
$177$	15.2904	+	11.4525i	1.14930	+	0.860821i
$178$		0			0
$179$	18.0057	−	10.3956i	1.34581	−	0.777002i	0.358155	−	0.933662i	$-0.383406\pi$
$179$	18.0057	−	10.3956i	1.34581	−	0.777002i	0.987653	+	0.156660i	$0.0500726\pi$
$180$		0			0
$181$		−	21.5301i		−	1.60032i	−0.599788	−	0.800159i	$-0.704748\pi$
$181$		−	21.5301i		−	1.60032i	0.599788	−	0.800159i	$-0.295252\pi$
$182$		0			0
$183$	−11.9199	+	15.9145i	−0.881143	+	1.17643i
$184$		0			0
$185$	3.08235			0.226619
$186$		0			0
$187$			7.81007i			0.571129i
$188$		0			0
$189$	12.1823	+	6.37109i	0.886134	+	0.463429i
$190$		0			0
$191$		−	7.36938i		−	0.533230i	−0.963803	−	0.266615i	$-0.914095\pi$
$191$		−	7.36938i		−	0.533230i	0.963803	−	0.266615i	$-0.0859052\pi$
$192$		0			0
$193$	−2.82559			−0.203390			−0.101695	−	0.994816i	$-0.532427\pi$
$193$	−2.82559			−0.203390			−0.101695	+	0.994816i	$0.532427\pi$
$194$		0			0
$195$	−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	$-0.379637\pi$
$198$		0			0
$199$	−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	$0.517345\pi$
$200$		0			0
$201$	5.89688	+	4.41674i	0.415934	+	0.311533i
$202$		0			0
$203$	−0.355169	−	0.841182i	−0.0249280	−	0.0590394i
$204$		0			0
$205$	0.578174			0.0403814
$206$		0			0
$207$	17.4784	+	16.6830i	1.21483	+	1.15955i
$208$		0			0
$209$	−3.70508	−	6.41739i	−0.256286	−	0.443900i
$210$		0			0
$211$	−4.42465	+	7.66371i	−0.304605	+	0.527592i	−0.977173	−	0.212443i	$-0.931858\pi$
$211$	−4.42465	+	7.66371i	−0.304605	+	0.527592i	0.672568	+	0.740035i	$0.265191\pi$
$212$		0			0
$213$	−3.69019	+	4.92684i	−0.252847	+	0.337581i
$214$		0			0
$215$	4.15919	−	7.20393i	0.283655	−	0.491304i
$216$		0			0
$217$	11.4003	+	1.42185i	0.773901	+	0.0965212i
$218$		0			0
$219$	0.399258	+	0.0478427i	0.0269794	+	0.00323291i
$220$		0			0
$221$			14.4741i			0.973637i
$222$		0			0
$223$	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
$226$		0			0
$227$	−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	$0.265868\pi$
$228$		0			0
$229$	−7.31319	+	4.22227i	−0.483269	+	0.279016i	−0.721778	−	0.692125i	$-0.756675\pi$
$229$	−7.31319	+	4.22227i	−0.483269	+	0.279016i	0.238509	+	0.971140i	$0.423341\pi$
$230$		0			0
$231$	−15.0585	+	4.33435i	−0.990776	+	0.285180i
$232$		0			0
$233$	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	$0.483074\pi$
$234$		0			0
$235$	3.94517	+	6.83323i	0.257354	+	0.445751i
$236$		0			0
$237$	20.1874	+	15.1203i	1.31131	+	0.982170i
$238$		0			0
$239$	23.6325	+	13.6442i	1.52866	+	0.882572i	0.999418	+	0.0341012i	$0.0108569\pi$
$239$	23.6325	+	13.6442i	1.52866	+	0.882572i	0.529242	+	0.848471i	$0.322476\pi$
$240$		0			0
$241$	−21.9018	−	12.6450i	−1.41082	−	0.814537i	−0.415354	−	0.909660i	$-0.636342\pi$
$241$	−21.9018	−	12.6450i	−1.41082	−	0.814537i	−0.995466	+	0.0951223i	$0.969676\pi$
$242$		0			0
$243$	15.5473	+	1.13232i	0.997358	+	0.0726386i
$244$		0			0
$245$	−2.72213	−	9.63167i	−0.173911	−	0.615345i
$246$		0			0
$247$	−6.86651	−	11.8931i	−0.436906	−	0.756743i
$248$		0			0
$249$	−0.334512	+	2.79158i	−0.0211988	+	0.176909i
$250$		0			0
$251$	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
$254$		0			0
$255$	−5.20041	+	2.22534i	−0.325662	+	0.139356i
$256$		0			0
$257$	−3.31723	−	5.74560i	−0.206923	−	0.358401i	0.743821	−	0.668379i	$-0.233012\pi$
$257$	−3.31723	−	5.74560i	−0.206923	−	0.358401i	−0.950744	+	0.309978i	$0.899678\pi$
$258$		0			0
$259$	4.54845	+	3.44112i	0.282627	+	0.213821i
$260$		0			0
$261$	−0.748942	−	0.714861i	−0.0463584	−	0.0442488i
$262$		0			0
$263$	−5.23590	−	3.02295i	−0.322860	−	0.186403i	0.329807	−	0.944048i	$-0.393016\pi$
$263$	−5.23590	−	3.02295i	−0.322860	−	0.186403i	−0.652666	+	0.757645i	$0.726350\pi$
$264$		0			0
$265$	12.2440	+	7.06905i	0.752140	+	0.434248i
$266$		0			0
$267$	6.46426	−	2.76616i	0.395606	−	0.169286i
$268$		0			0
$269$	3.41069	+	5.90750i	0.207954	+	0.360186i	0.951070	−	0.308976i	$-0.0999863\pi$
$269$	3.41069	+	5.90750i	0.207954	+	0.360186i	−0.743116	+	0.669163i	$0.766653\pi$
$270$		0			0
$271$	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	$0.617375\pi$
$272$		0			0
$273$	−27.9074	+	8.03272i	−1.68903	+	0.486162i
$274$		0			0
$275$	−8.75228	+	5.05313i	−0.527783	+	0.304715i
$276$		0			0
$277$	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	$0.147730\pi$
$278$		0			0
$279$	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	$0.509619\pi$
$282$		0			0
$283$			5.15385i			0.306365i	0.988198	+	0.153182i	$0.0489522\pi$
$283$			5.15385i			0.306365i	−0.988198	+	0.153182i	$0.951048\pi$
$284$		0			0
$285$	3.21738	−	4.29559i	0.190581	−	0.254449i
$286$		0			0
$287$	0.853179	+	0.645471i	0.0503616	+	0.0381009i
$288$		0			0
$289$	5.89164	−	10.2046i	0.346567	−	0.600271i
$290$		0			0
$291$	18.2439	+	2.18614i	1.06947	+	0.128154i
$292$		0			0
$293$	1.03248	−	1.78831i	0.0603183	−	0.104474i	−0.834289	−	0.551327i	$-0.814122\pi$
$293$	1.03248	−	1.78831i	0.0603183	−	0.104474i	0.894608	+	0.446852i	$0.147455\pi$
$294$		0			0
$295$	−7.88534	−	13.6578i	−0.459102	−	0.795188i
$296$		0			0
$297$	−13.7101	+	11.3020i	−0.795539	+	0.655807i
$298$		0			0
$299$	−51.0401			−2.95173
$300$		0			0
$301$	14.1799	−	5.98714i	0.817317	−	0.345093i
$302$		0			0
$303$	12.8169	−	5.48455i	0.736310	−	0.315079i
$304$		0			0
$305$	14.2152	−	8.20716i	0.813961	−	0.469941i
$306$		0			0
$307$		−	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
$310$		0			0
$311$	−15.2220			−0.863161			−0.431580	−	0.902075i	$-0.642044\pi$
$311$	−15.2220			−0.863161			−0.431580	+	0.902075i	$0.642044\pi$
$312$		0			0
$313$			11.5704i			0.653996i	0.945025	+	0.326998i	$0.106037\pi$
$313$			11.5704i			0.653996i	−0.945025	+	0.326998i	$0.893963\pi$
$314$		0			0
$315$	−7.17672	−	8.79184i	−0.404362	−	0.495364i
$316$		0			0
$317$		−	17.1604i		−	0.963824i	−0.876220	−	0.481912i	$-0.839942\pi$
$317$		−	17.1604i		−	0.963824i	0.876220	−	0.481912i	$-0.160058\pi$
$318$		0			0
$319$	1.18010			0.0660731
$320$		0			0
$321$	−10.7809	−	25.1940i	−0.601733	−	1.40619i
$322$		0			0
$323$		−	4.94962i		−	0.275404i
$324$		0			0
$325$	−16.2203	+	9.36481i	−0.899742	+	0.519466i
$326$		0			0
$327$	2.10475	−	17.5646i	0.116393	−	0.971326i
$328$		0			0
$329$	−1.80692	+	14.4878i	−0.0996189	+	0.798738i
$330$		0			0
$331$	26.4931			1.45619			0.728096	−	0.685475i	$-0.240405\pi$
$331$	26.4931			1.45619			0.728096	+	0.685475i	$0.240405\pi$
$332$		0			0
$333$	6.28404	+	1.52796i	0.344364	+	0.0837317i
$334$		0			0
$335$	−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	$0.0956015\pi$
$338$		0			0
$339$	−5.73442	−	13.4008i	−0.311451	−	0.727830i
$340$		0			0
$341$	−7.42410	+	12.8589i	−0.402037	+	0.696349i
$342$		0			0
$343$	6.73586	−	17.2519i	0.363702	−	0.931515i
$344$		0			0
$345$	−7.84721	−	18.3382i	−0.422479	−	0.987294i
$346$		0			0
$347$			25.6171i			1.37520i	0.726090	+	0.687599i	$0.241335\pi$
$347$			25.6171i			1.37520i	−0.726090	+	0.687599i	$0.758665\pi$
$348$		0			0
$349$	9.11932	−	5.26504i	0.488146	−	0.281831i	−0.235659	−	0.971836i	$-0.575725\pi$
$349$	9.11932	−	5.26504i	0.488146	−	0.281831i	0.723805	+	0.690005i	$0.242391\pi$
$350$		0			0
$351$	−25.4084	+	20.9456i	−1.35620	+	1.11799i
$352$		0			0
$353$	6.42186	−	11.1230i	0.341801	−	0.592017i	−0.642966	−	0.765895i	$-0.722296\pi$
$353$	6.42186	−	11.1230i	0.341801	−	0.592017i	0.984767	+	0.173878i	$0.0556297\pi$
$354$		0			0
$355$	4.40078	−	2.54079i	0.233569	−	0.134851i
$356$		0			0
$357$	−10.1583	−	2.52190i	−0.537635	−	0.133473i
$358$		0			0
$359$	−25.6881	−	14.8311i	−1.35577	−	0.782753i	−0.366718	−	0.930332i	$-0.619518\pi$
$359$	−25.6881	−	14.8311i	−1.35577	−	0.782753i	−0.989050	+	0.147579i	$0.952852\pi$
$360$		0			0
$361$	−7.15191	−	12.3875i	−0.376416	−	0.651972i
$362$		0			0
$363$	0.142730	−	1.19112i	0.00749139	−	0.0625173i
$364$		0			0
$365$	−0.287482	−	0.165978i	−0.0150475	−	0.00868767i
$366$		0			0
$367$	−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	$0.882115\pi$
$368$		0			0
$369$	1.17874	+	0.286609i	0.0613625	+	0.0149202i
$370$		0			0
$371$	10.1759	+	24.1005i	0.528305	+	1.25124i
$372$		0			0
$373$	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	$0.734176\pi$
$374$		0			0
$375$	−15.7695	−	11.8113i	−0.814336	−	0.609935i
$376$		0			0
$377$	2.18705			0.112639
$378$		0			0
$379$	13.1379			0.674850			0.337425	−	0.941352i	$-0.390444\pi$
$379$	13.1379			0.674850			0.337425	+	0.941352i	$0.390444\pi$
$380$		0			0
$381$	8.00971	+	5.99925i	0.410350	+	0.307351i
$382$		0			0
$383$	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	$0.685315\pi$
$384$		0			0
$385$	12.8364	+	1.60096i	0.654204	+	0.0815926i
$386$		0			0
$387$	12.0505	−	12.6250i	0.612562	−	0.641767i
$388$		0			0
$389$	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	$0.479886\pi$
$390$		0			0
$391$	−15.9312	−	9.19786i	−0.805674	−	0.465156i
$392$		0			0
$393$	−0.918411	+	7.66435i	−0.0463277	+	0.386615i
$394$		0			0
$395$	−10.4107	−	18.0319i	−0.523821	−	0.907285i
$396$		0			0
$397$	33.7636	+	19.4935i	1.69455	+	0.978348i	0.950757	+	0.309937i	$0.100308\pi$
$397$	33.7636	+	19.4935i	1.69455	+	0.978348i	0.743792	+	0.668411i	$0.233025\pi$
$398$		0			0
$399$	9.54329	−	2.74689i	0.477762	−	0.137516i
$400$		0			0
$401$	−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	$0.529977\pi$
$402$		0			0
$403$	−13.7588	+	23.8310i	−0.685376	+	1.18711i
$404$		0			0
$405$	−11.4320	−	5.90868i	−0.568059	−	0.293605i
$406$		0			0
$407$	−6.38377	+	3.68567i	−0.316432	+	0.182692i
$408$		0			0
$409$			24.6187i			1.21732i	0.793432	+	0.608659i	$0.208292\pi$
$409$			24.6187i			1.21732i	−0.793432	+	0.608659i	$0.791708\pi$
$410$		0			0
$411$	−6.58013	−	15.3771i	−0.324574	−	0.758498i
$412$		0			0
$413$	3.61156	−	28.9572i	0.177713	−	1.42489i
$414$		0			0
$415$	1.16050	−	2.01005i	0.0569667	−	0.0986693i
$416$		0			0
$417$	12.6426	+	29.5446i	0.619113	+	1.44681i
$418$		0			0
$419$	−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	$0.950057\pi$
$422$		0			0
$423$	4.65577	+	15.8867i	0.226371	+	0.772439i
$424$		0			0
$425$	−6.75047			−0.327446
$426$		0			0
$427$	30.1391	+	3.75896i	1.45853	+	0.181909i
$428$		0			0
$429$	4.46556	−	37.2661i	0.215599	−	1.79923i
$430$		0			0
$431$	8.32286	−	4.80521i	0.400898	−	0.231459i	−0.285973	−	0.958238i	$-0.592317\pi$
$431$	8.32286	−	4.80521i	0.400898	−	0.231459i	0.686871	+	0.726779i	$0.258984\pi$
$432$		0			0
$433$		−	9.04314i		−	0.434585i	−0.976106	−	0.217293i	$-0.930277\pi$
$433$		−	9.04314i		−	0.434585i	0.976106	−	0.217293i	$-0.0697226\pi$
$434$		0			0
$435$	0.336249	+	0.785782i	0.0161219	+	0.0376754i
$436$		0			0
$437$	17.4538			0.834929
$438$		0			0
$439$		−	0.913795i		−	0.0436131i	−0.999762	−	0.0218065i	$-0.993058\pi$
$439$		−	0.913795i		−	0.0436131i	0.999762	−	0.0218065i	$-0.00694178\pi$
$440$		0			0
$441$	−0.775118	−	20.9857i	−0.0369104	−	0.999319i
$442$		0			0
$443$		−	29.3616i		−	1.39501i	−0.716578	−	0.697507i	$-0.754293\pi$
$443$		−	29.3616i		−	1.39501i	0.716578	−	0.697507i	$-0.245707\pi$
$444$		0			0
$445$	−5.80446			−0.275158
$446$		0			0
$447$	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	$-0.0253189\pi$
$450$		0			0
$451$	−1.19744	+	0.691343i	−0.0563853	+	0.0325541i
$452$		0			0
$453$	−9.17054	+	3.92423i	−0.430870	+	0.184376i
$454$		0			0
$455$	23.7893	+	2.96701i	1.11526	+	0.139096i
$456$		0			0
$457$	−15.1139			−0.706996			−0.353498	−	0.935435i	$-0.615008\pi$
$457$	−15.1139			−0.706996			−0.353498	+	0.935435i	$0.615008\pi$
$458$		0			0
$459$	−11.7053	+	1.95894i	−0.546357	+	0.0914354i
$460$		0			0
$461$	5.19445	+	8.99706i	0.241930	+	0.419035i	0.961264	−	0.275629i	$-0.0888863\pi$
$461$	5.19445	+	8.99706i	0.241930	+	0.419035i	−0.719334	+	0.694664i	$0.755553\pi$
$462$		0			0
$463$	2.65722	−	4.60244i	0.123492	−	0.213894i	−0.797651	−	0.603120i	$-0.793924\pi$
$463$	2.65722	−	4.60244i	0.123492	−	0.213894i	0.921142	+	0.389226i	$0.127257\pi$
$464$		0			0
$465$	−10.6776	−	1.27948i	−0.495161	−	0.0593347i
$466$		0			0
$467$	−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	$0.315661\pi$
$468$		0			0
$469$	1.39283	−	11.1676i	0.0643148	−	0.515672i
$470$		0			0
$471$	−8.26894	+	11.0400i	−0.381012	+	0.508697i
$472$		0			0
$473$			19.8932i			0.914689i
$474$		0			0
$475$	5.54674	−	3.20241i	0.254502	−	0.146937i
$476$		0			0
$477$	21.4578	+	20.4813i	0.982484	+	0.937775i
$478$		0			0
$479$	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	$-0.0524003\pi$
$480$		0			0
$481$	−11.8308	+	6.83054i	−0.539440	+	0.311446i
$482$		0			0
$483$	8.89296	−	35.8212i	0.404644	−	1.62992i
$484$		0			0
$485$	−13.1363	−	7.58425i	−0.596489	−	0.344383i
$486$		0			0
$487$	−3.73838	−	6.47506i	−0.169402	−	0.293413i	0.768808	−	0.639480i	$-0.220850\pi$
$487$	−3.73838	−	6.47506i	−0.169402	−	0.293413i	−0.938210	+	0.346067i	$0.887517\pi$
$488$		0			0
$489$	18.1295	−	7.75790i	0.819843	−	0.350824i
$490$		0			0
$491$	−19.1466	−	11.0543i	−0.864073	−	0.498873i	0.00130103	−	0.999999i	$-0.499586\pi$
$491$	−19.1466	−	11.0543i	−0.864073	−	0.498873i	−0.865374	+	0.501126i	$0.832919\pi$
$492$		0			0
$493$	0.682643	+	0.394124i	0.0307447	+	0.0177505i
$494$		0			0
$495$	14.0759	−	4.12509i	0.632664	−	0.185409i
$496$		0			0
$497$	9.33052	+	1.16371i	0.418531	+	0.0521994i
$498$		0			0
$499$	16.4521	+	28.4959i	0.736498	+	1.27565i	0.954063	+	0.299606i	$0.0968554\pi$
$499$	16.4521	+	28.4959i	0.736498	+	1.27565i	−0.217565	+	0.976046i	$0.569811\pi$
$500$		0			0
$501$	−18.0391	+	7.71923i	−0.805927	+	0.344870i
$502$		0			0
$503$	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
$506$		0			0
$507$	5.59690	−	46.7074i	0.248567	−	2.07435i
$508$		0			0
$509$	−10.7358	−	18.5950i	−0.475857	−	0.824209i	0.523760	−	0.851866i	$-0.324529\pi$
$509$	−10.7358	−	18.5950i	−0.475857	−	0.824209i	−0.999617	+	0.0276567i	$0.991195\pi$
$510$		0			0
$511$	−0.238924	−	0.565868i	−0.0105694	−	0.0250325i
$512$		0			0
$513$	8.68873	−	7.16260i	0.383617	−	0.316237i
$514$		0			0
$515$	3.48443	+	2.01173i	0.153542	+	0.0886476i
$516$		0			0
$517$	−16.3415	−	9.43475i	−0.718697	−	0.414940i
$518$		0			0
$519$	30.0710	+	22.5231i	1.31997	+	0.988654i
$520$		0			0
$521$	−3.23087	−	5.59604i	−0.141547	−	0.245167i	0.786532	−	0.617549i	$-0.211874\pi$
$521$	−3.23087	−	5.59604i	−0.141547	−	0.245167i	−0.928079	+	0.372382i	$0.878541\pi$
$522$		0			0
$523$	−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	$0.762810\pi$
$524$		0			0
$525$	−3.74631	−	13.0155i	−0.163502	−	0.568043i
$526$		0			0
$527$	−8.58910	+	4.95892i	−0.374147	+	0.216014i
$528$		0			0
$529$	20.9344	−	36.2594i	0.910190	−	1.57649i
$530$		0			0
$531$	−9.30564	−	31.7533i	−0.403830	−	1.37798i
$532$		0			0
$533$	−2.21918	+	1.28124i	−0.0961233	+	0.0554968i
$534$		0			0
$535$			22.6225i			0.978055i
$536$		0			0
$537$	−35.7556	−	4.28455i	−1.54297	−	0.184892i
$538$		0			0
$539$	17.1547	+	16.6930i	0.738904	+	0.719017i
$540$		0			0
$541$	−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	$0.944839\pi$
$542$		0			0
$543$	−22.3556	+	29.8473i	−0.959369	+	1.28087i
$544$		0			0
$545$	−7.30188	+	12.6472i	−0.312778	+	0.541748i
$546$		0			0
$547$	9.07207	+	15.7133i	0.387894	+	0.671852i	0.992166	−	0.124926i	$-0.0398694\pi$
$547$	9.07207	+	15.7133i	0.387894	+	0.671852i	−0.604272	+	0.796778i	$0.706536\pi$
$548$		0			0
$549$	33.0493	−	9.68543i	1.41051	−	0.413364i
$550$		0			0
$551$	−0.747888			−0.0318611
$552$		0			0
$553$	4.76822	−	38.2312i	0.202765	−	1.62576i
$554$		0			0
$555$	−4.27308	−	3.20053i	−0.181382	−	0.135855i
$556$		0			0
$557$	−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	$0.625991\pi$
$558$		0			0
$559$			36.8674i			1.55932i
$560$		0			0
$561$	8.10951	−	10.8272i	0.342384	−	0.457123i
$562$		0			0
$563$	−7.10681			−0.299516			−0.149758	−	0.988723i	$-0.547850\pi$
$563$	−7.10681			−0.299516			−0.149758	+	0.988723i	$0.547850\pi$
$564$		0			0
$565$			12.0330i			0.506231i
$566$		0			0
$567$	−10.2731	−	21.4817i	−0.431429	−	0.902147i
$568$		0			0
$569$		−	41.1650i		−	1.72572i	−0.505439	−	0.862862i	$-0.668669\pi$
$569$		−	41.1650i		−	1.72572i	0.505439	−	0.862862i	$-0.331331\pi$
$570$		0			0
$571$	−4.42585			−0.185216			−0.0926080	−	0.995703i	$-0.529520\pi$
$571$	−4.42585			−0.185216			−0.0926080	+	0.995703i	$0.529520\pi$
$572$		0			0
$573$	−7.65193	+	10.2162i	−0.319664	+	0.426789i
$574$		0			0
$575$		−	23.8042i		−	0.992702i
$576$		0			0
$577$	2.37542	−	1.37145i	0.0988900	−	0.0570941i	−0.449739	−	0.893160i	$-0.648483\pi$
$577$	2.37542	−	1.37145i	0.0988900	−	0.0570941i	0.548629	+	0.836066i	$0.315150\pi$
$578$		0			0
$579$	3.91713	+	2.93392i	0.162791	+	0.121930i
$580$		0			0
$581$	3.95649	−	1.67054i	0.164143	−	0.0693055i
$582$		0			0
$583$	−33.8109			−1.40030
$584$		0			0
$585$	26.0864	−	7.64489i	1.07854	−	0.316077i
$586$		0			0
$587$	−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
$590$		0			0
$591$	−27.0885	+	36.1664i	−1.11427	+	1.48769i
$592$		0			0
$593$	0.434850	−	0.753183i	0.0178572	−	0.0309295i	−0.856959	−	0.515385i	$-0.827649\pi$
$593$	0.434850	−	0.753183i	0.0178572	−	0.0309295i	0.874816	+	0.484456i	$0.160982\pi$
$594$		0			0
$595$	6.89068	+	5.21313i	0.282490	+	0.213717i
$596$		0			0
$597$	26.5125	+	3.17697i	1.08509	+	0.130025i
$598$		0			0
$599$		−	2.69365i		−	0.110059i	−0.998485	−	0.0550297i	$-0.982475\pi$
$599$		−	2.69365i		−	0.110059i	0.998485	−	0.0550297i	$-0.0175254\pi$
$600$		0			0
$601$	0.115325	−	0.0665827i	0.00470419	−	0.00271596i	−0.497646	−	0.867380i	$-0.665802\pi$
$601$	0.115325	−	0.0665827i	0.00470419	−	0.00271596i	0.502350	+	0.864664i	$0.332469\pi$
$602$		0			0
$603$	−3.58880	−	12.2459i	−0.146147	−	0.498693i
$604$		0			0
$605$	−0.495165	+	0.857650i	−0.0201313	+	0.0348684i
$606$		0			0
$607$	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	$-0.0227605\pi$
$608$		0			0
$609$	−0.381059	+	1.53492i	−0.0154413	+	0.0621982i
$610$		0			0
$611$	−30.2851	−	17.4851i	−1.22520	−	0.707372i
$612$		0			0
$613$	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	$0.790793\pi$
$614$		0			0
$615$	−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			0
$619$	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	$0.624716\pi$
$620$		0			0
$621$	−6.90779	−	41.2764i	−0.277200	−	1.65636i
$622$		0			0
$623$	−8.56532	−	6.48007i	−0.343162	−	0.259619i
$624$		0			0
$625$	0.743610	+	1.28797i	0.0297444	+	0.0515188i
$626$		0			0
$627$	−1.52705	+	12.7436i	−0.0609847	+	0.508931i
$628$		0			0
$629$	−4.92368			−0.196320
$630$		0			0
$631$	−13.8837			−0.552699			−0.276350	−	0.961057i	$-0.589125\pi$
$631$	−13.8837			−0.552699			−0.276350	+	0.961057i	$0.589125\pi$
$632$		0			0
$633$	14.0915	−	6.02997i	0.560086	−	0.239670i
$634$		0			0
$635$	−4.13064	−	7.15449i	−0.163920	−	0.283917i
$636$		0			0
$637$	31.7922	+	30.9365i	1.25965	+	1.22575i
$638$		0			0
$639$	10.2315	−	2.99844i	0.404751	−	0.118616i
$640$		0			0
$641$	−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	$0.763946\pi$
$642$		0			0
$643$	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
$646$		0			0
$647$	−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	$0.843271\pi$
$648$		0			0
$649$	32.6622	+	18.8576i	1.28211	+	0.740224i
$650$		0			0
$651$	−14.3279	−	13.8085i	−0.561555	−	0.541197i
$652$		0			0
$653$	−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	$0.447659\pi$
$654$		0			0
$655$	3.18619	−	5.51863i	0.124495	−	0.215631i
$656$		0			0
$657$	−0.503818	−	0.480891i	−0.0196558	−	0.0187613i
$658$		0			0
$659$	−10.0955	+	5.82866i	−0.393266	+	0.227052i	−0.683574	−	0.729881i	$-0.739576\pi$
$659$	−10.0955	+	5.82866i	−0.393266	+	0.227052i	0.290308	+	0.956933i	$0.406242\pi$
$660$		0			0
$661$			18.2195i			0.708657i	0.935121	+	0.354328i	$0.115290\pi$
$661$			18.2195i			0.708657i	−0.935121	+	0.354328i	$0.884710\pi$
$662$		0			0
$663$	15.0291	−	20.0656i	0.583682	−	0.779284i
$664$		0			0
$665$	−8.13505	−	1.01461i	−0.315464	−	0.0393448i
$666$		0			0
$667$	−1.38980	+	2.40720i	−0.0538132	+	0.0932072i
$668$		0			0
$669$	−13.6814	−	1.63942i	−0.528952	−	0.0633837i
$670$		0			0
$671$	−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	$0.803707\pi$
$674$		0			0
$675$	−9.76863	−	11.8500i	−0.375995	−	0.456107i
$676$		0			0
$677$	23.1290			0.888920			0.444460	−	0.895799i	$-0.353396\pi$
$677$	23.1290			0.888920			0.444460	+	0.895799i	$0.353396\pi$
$678$		0			0
$679$	−10.9175	−	25.8570i	−0.418975	−	0.992300i
$680$		0			0
$681$	14.7131	−	6.29599i	0.563808	−	0.241263i
$682$		0			0
$683$	6.80041	−	3.92622i	0.260210	−	0.150233i	−0.364220	−	0.931313i	$-0.618664\pi$
$683$	6.80041	−	3.92622i	0.260210	−	0.150233i	0.624431	+	0.781080i	$0.285331\pi$
$684$		0			0
$685$			13.8076i			0.527562i
$686$		0			0
$687$	14.5225	+	1.74021i	0.554067	+	0.0663933i
$688$		0			0
$689$	−62.6606			−2.38718
$690$		0			0
$691$			17.1676i			0.653085i	0.945182	+	0.326543i	$0.105884\pi$
$691$			17.1676i			0.653085i	−0.945182	+	0.326543i	$0.894116\pi$
$692$		0			0
$693$	25.3762	+	9.62710i	0.963964	+	0.365703i
$694$		0			0
$695$		−	26.5290i		−	1.00630i
$696$		0			0
$697$	−0.923564			−0.0349825
$698$		0			0
$699$	−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	$0.770624\pi$
$702$		0			0
$703$	4.04570	−	2.33579i	0.152587	−	0.0880959i
$704$		0			0
$705$	1.62601	−	13.5694i	0.0612389	−	0.511053i
$706$		0			0
$707$	−16.9827	−	12.8482i	−0.638701	−	0.483207i
$708$		0			0
$709$	−24.3336			−0.913867			−0.456933	−	0.889501i	$-0.651052\pi$
$709$	−24.3336			−0.913867			−0.456933	+	0.889501i	$0.651052\pi$
$710$		0			0
$711$	−12.2859	−	41.9228i	−0.460758	−	1.57223i
$712$		0			0
$713$	−17.4866	−	30.2877i	−0.654879	−	1.13428i
$714$		0			0
$715$	−15.4921	+	26.8331i	−0.579372	+	1.00350i
$716$		0			0
$717$	−18.5946	−	43.4537i	−0.694427	−	1.62281i
$718$		0			0
$719$	−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	$0.272712\pi$
$720$		0			0
$721$	2.89588	+	6.85860i	0.107848	+	0.255428i
$722$		0			0
$723$	17.2328	+	40.2714i	0.640895	+	1.49771i
$724$		0			0
$725$			1.02000i			0.0378818i
$726$		0			0
$727$	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			0
$731$	−6.64381	+	11.5074i	−0.245730	+	0.425617i
$732$		0			0
$733$	20.3073	−	11.7245i	0.750069	−	0.433053i	−0.0756499	−	0.997134i	$-0.524103\pi$
$733$	20.3073	−	11.7245i	0.750069	−	0.433053i	0.825719	+	0.564082i	$0.190770\pi$
$734$		0			0
$735$	−6.22725	+	16.1790i	−0.229695	+	0.596770i
$736$		0			0
$737$	12.5965	+	7.27257i	0.463997	+	0.267889i
$738$		0			0
$739$	−13.3662	−	23.1509i	−0.491682	−	0.851618i	0.508272	−	0.861197i	$-0.330284\pi$
$739$	−13.3662	−	23.1509i	−0.491682	−	0.851618i	−0.999954	+	0.00957820i	$0.996951\pi$
$740$		0			0
$741$	−2.83004	+	23.6173i	−0.103964	+	0.867605i
$742$		0			0
$743$	11.0914	+	6.40360i	0.406903	+	0.234925i	0.689458	−	0.724326i	$-0.257849\pi$
$743$	11.0914	+	6.40360i	0.406903	+	0.234925i	−0.282555	+	0.959251i	$0.591182\pi$
$744$		0			0
$745$	−8.05745	−	4.65197i	−0.295202	−	0.170435i
$746$		0			0
$747$	3.36234	−	3.52265i	0.123022	−	0.128887i
$748$		0			0
$749$	−25.2556	+	33.3827i	−0.922821	+	1.21978i
$750$		0			0
$751$	−5.12417	−	8.87532i	−0.186984	−	0.323865i	0.757260	−	0.653114i	$-0.226538\pi$
$751$	−5.12417	−	8.87532i	−0.186984	−	0.323865i	−0.944243	+	0.329249i	$0.893204\pi$
$752$		0			0
$753$	−11.3585	−	8.50751i	−0.413928	−	0.310031i
$754$		0			0
$755$	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	$0.435440\pi$
$758$		0			0
$759$	38.1797	+	28.5965i	1.38584	+	1.03799i
$760$		0			0
$761$	−8.14993	−	14.1161i	−0.295435	−	0.511708i	0.679651	−	0.733536i	$-0.262131\pi$
$761$	−8.14993	−	14.1161i	−0.295435	−	0.511708i	−0.975086	+	0.221827i	$0.928798\pi$
$762$		0			0
$763$	−24.8943	+	10.5110i	−0.901234	+	0.380525i
$764$		0			0
$765$	9.52003	+	2.31479i	0.344197	+	0.0836913i
$766$		0			0
$767$	60.5319	+	34.9481i	2.18568	+	1.26190i
$768$		0			0
$769$	41.4043	+	23.9048i	1.49308	+	0.862029i	0.999968	−	0.00793771i	$-0.00252668\pi$
$769$	41.4043	+	23.9048i	1.49308	+	0.862029i	0.493110	+	0.869967i	$0.335860\pi$
$770$		0			0
$771$	−1.36720	+	11.4096i	−0.0492384	+	0.410906i
$772$		0			0
$773$	−6.25441	−	10.8330i	−0.224956	−	0.389635i	0.731350	−	0.682002i	$-0.238890\pi$
$773$	−6.25441	−	10.8330i	−0.224956	−	0.389635i	−0.956306	+	0.292367i	$0.905557\pi$
$774$		0			0
$775$	−11.1143	−	6.41686i	−0.399239	−	0.230501i
$776$		0			0
$777$	−2.73250	−	9.49329i	−0.0980277	−	0.340570i
$778$		0			0
$779$	0.758876	−	0.438137i	0.0271896	−	0.0156979i
$780$		0			0
$781$	−6.07623	+	10.5243i	−0.217425	+	0.376590i
$782$		0			0
$783$	0.295996	+	1.76867i	0.0105780	+	0.0632073i
$784$		0			0
$785$	9.86123	−	5.69338i	0.351962	−	0.203206i
$786$		0			0
$787$			0.261017i			0.00930426i	0.999989	+	0.00465213i	$0.00148082\pi$
$787$			0.261017i			0.00930426i	−0.999989	+	0.00465213i	$0.998519\pi$
$788$		0			0
$789$	4.11972	+	9.62739i	0.146666	+	0.342744i
$790$		0			0
$791$	−13.4336	+	17.7564i	−0.477643	+	0.631345i
$792$		0			0
$793$	−36.3744	+	63.0024i	−1.29169	+	2.23728i
$794$		0			0
$795$	−9.63381	−	22.5133i	−0.341676	−	0.798464i
$796$		0			0
$797$	1.85220	−	3.20810i	0.0656083	−	0.113637i	−0.831355	−	0.555741i	$-0.812435\pi$
$797$	1.85220	−	3.20810i	0.0656083	−	0.113637i	0.896964	+	0.442104i	$0.145768\pi$
$798$		0			0
$799$	−6.30194	−	10.9153i	−0.222946	−	0.386155i
$800$		0			0
$801$	−11.8337	−	2.87735i	−0.418122	−	0.101666i
$802$		0			0
$803$	0.793862			0.0280148
$804$		0			0
$805$	−18.3830	+	24.2986i	−0.647917	+	0.856412i
$806$		0			0
$807$	1.40572	−	11.7311i	0.0494837	−	0.412953i
$808$		0			0
$809$	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	$0.294842\pi$
$810$		0			0
$811$		−	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
$814$		0			0
$815$	−16.2790			−0.570229
$816$		0			0
$817$		−	12.6073i		−	0.441072i
$818$		0			0
$819$	47.0290	+	17.8416i	1.64332	+	0.623435i
$820$		0			0
$821$			3.79377i			0.132403i	0.997806	+	0.0662017i	$0.0210881\pi$
$821$			3.79377i			0.132403i	−0.997806	+	0.0662017i	$0.978912\pi$
$822$		0			0
$823$	14.9079			0.519656			0.259828	−	0.965655i	$-0.416334\pi$
$823$	14.9079			0.519656			0.259828	+	0.965655i	$0.416334\pi$
$824$		0			0
$825$	17.3802	+	2.08265i	0.605102	+	0.0725087i
$826$		0			0
$827$		−	21.9819i		−	0.764384i	−0.924083	−	0.382192i	$-0.875169\pi$
$827$		−	21.9819i		−	0.764384i	0.924083	−	0.382192i	$-0.124831\pi$
$828$		0			0
$829$	12.2406	−	7.06713i	0.425135	−	0.245452i	−0.272137	−	0.962259i	$-0.587730\pi$
$829$	12.2406	−	7.06713i	0.425135	−	0.245452i	0.697272	+	0.716807i	$0.254397\pi$
$830$		0			0
$831$	−3.15154	+	1.34860i	−0.109326	+	0.0467823i
$832$		0			0
$833$	4.34828	+	15.3855i	0.150659	+	0.533074i
$834$		0			0
$835$	16.1979			0.560550
$836$		0			0
$837$	−21.1344	−	7.90153i	−0.730511	−	0.273117i
$838$		0			0
$839$	−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
$842$		0			0
$843$	30.3237	+	3.63365i	1.04440	+	0.125150i
$844$		0			0
$845$	−19.4170	+	33.6312i	−0.667964	+	1.15695i
$846$		0			0
$847$	−1.68816	+	0.712787i	−0.0580060	+	0.0244917i
$848$		0			0
$849$	5.35145	−	7.14482i	0.183661	−	0.245210i
$850$		0			0
$851$		−	17.3624i		−	0.595174i
$852$		0			0
$853$	35.2392	−	20.3454i	1.20657	−	0.696612i	0.244559	−	0.969634i	$-0.421357\pi$
$853$	35.2392	−	20.3454i	1.20657	−	0.696612i	0.962008	+	0.273022i	$0.0880233\pi$
$854$		0			0
$855$	−8.92057	+	2.61427i	−0.305077	+	0.0894060i
$856$		0			0
$857$	2.72896	−	4.72669i	0.0932194	−	0.161461i	−0.815645	−	0.578553i	$-0.803618\pi$
$857$	2.72896	−	4.72669i	0.0932194	−	0.161461i	0.908864	+	0.417092i	$0.136951\pi$
$858$		0			0
$859$	−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	$0.611059\pi$
$860$		0			0
$861$	−0.512550	−	1.78071i	−0.0174677	−	0.0606865i
$862$		0			0
$863$	−19.6689	−	11.3559i	−0.669539	−	0.386558i	0.126363	−	0.991984i	$-0.459670\pi$
$863$	−19.6689	−	11.3559i	−0.669539	−	0.386558i	−0.795902	+	0.605426i	$0.793003\pi$
$864$		0			0
$865$	−15.5077	−	26.8602i	−0.527279	−	0.913274i
$866$		0			0
$867$	−18.7635	+	8.02921i	−0.637241	+	0.272686i
$868$		0			0
$869$	43.1229	+	24.8970i	1.46284	+	0.844573i
$870$		0			0
$871$	23.3446	+	13.4780i	0.791002	+	0.456685i
$872$		0			0
$873$	−23.0217	−	21.9740i	−0.779165	−	0.743708i
$874$		0			0
$875$	−3.72473	+	29.8646i	−0.125919	+	1.00961i
$876$		0			0
$877$	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			0
$879$	−3.28822	+	1.40708i	−0.110909	+	0.0474597i
$880$		0			0
$881$	29.3810			0.989871			0.494935	−	0.868930i	$-0.335192\pi$
$881$	29.3810			0.989871			0.494935	+	0.868930i	$0.335192\pi$
$882$		0			0
$883$	−14.1682			−0.476798			−0.238399	−	0.971167i	$-0.576623\pi$
$883$	−14.1682			−0.476798			−0.238399	+	0.971167i	$0.576623\pi$
$884$		0			0
$885$	−3.24995	+	27.1216i	−0.109246	+	0.911682i
$886$		0			0
$887$	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	$0.648303\pi$
$888$		0			0
$889$	1.89187	−	15.1689i	0.0634514	−	0.508749i
$890$		0			0
$891$	30.7417	−	1.43230i	1.02988	−	0.0479837i
$892$		0			0
$893$	10.3564	+	5.97926i	0.346563	+	0.200088i
$894$		0			0
$895$	25.7454	+	14.8641i	0.860575	+	0.496853i
$896$		0			0
$897$	70.7573	+	52.9970i	2.36252	+	1.76952i
$898$		0			0
$899$	0.749293	+	1.29781i	0.0249903	+	0.0432845i
$900$		0			0
$901$	−19.5583	−	11.2920i	−0.651580	−	0.376190i
$902$		0			0
$903$	−25.8744	−	6.42358i	−0.861047	−	0.213763i
$904$		0			0
$905$	26.6604	−	15.3924i	0.886222	−	0.511661i
$906$		0			0
$907$	28.3467	−	49.0980i	0.941238	−	1.63027i	0.178123	−	0.984008i	$-0.442998\pi$
$907$	28.3467	−	49.0980i	0.941238	−	1.63027i	0.763115	−	0.646263i	$-0.223669\pi$
$908$		0			0
$909$	−23.4630	−	5.70500i	−0.778218	−	0.189223i
$910$		0			0
$911$	−0.621795	+	0.358994i	−0.0206010	+	0.0118940i	−0.510265	−	0.860017i	$-0.670453\pi$
$911$	−0.621795	+	0.358994i	−0.0206010	+	0.0118940i	0.489664	+	0.871911i	$0.337119\pi$
$912$		0			0
$913$			5.55061i			0.183698i
$914$		0			0
$915$	−28.2285	−	3.38259i	−0.933205	−	0.111825i
$916$		0			0
$917$	10.8627	−	4.58650i	0.358717	−	0.151460i
$918$		0			0
$919$	−18.9720	+	32.8605i	−0.625829	+	1.08397i	0.362550	+	0.931964i	$0.381906\pi$
$919$	−18.9720	+	32.8605i	−0.625829	+	1.08397i	−0.988380	+	0.152004i	$0.951427\pi$
$920$		0			0
$921$	−1.13302	+	1.51272i	−0.0373343	+	0.0498458i
$922$		0			0
$923$	−11.2609	+	19.5044i	−0.370656	+	0.641996i
$924$		0			0
$925$	−3.18563	−	5.51768i	−0.104743	−	0.181420i
$926$		0			0
$927$	6.10653	+	5.82864i	0.200565	+	0.191438i
$928$		0			0
$929$	42.8700			1.40652			0.703259	−	0.710934i	$-0.251727\pi$
$929$	42.8700			1.40652			0.703259	+	0.710934i	$0.251727\pi$
$930$		0			0
$931$	−10.8717	−	10.5791i	−0.356307	−	0.346717i
$932$		0			0
$933$	21.1024	+	15.8056i	0.690861	+	0.517453i
$934$		0			0
$935$	−9.67111	+	5.58362i	−0.316279	+	0.182604i
$936$		0			0
$937$		−	8.64637i		−	0.282464i	−0.989976	−	0.141232i	$-0.954894\pi$
$937$		−	8.64637i		−	0.282464i	0.989976	−	0.141232i	$-0.0451064\pi$
$938$		0			0
$939$	12.0140	−	16.0401i	0.392061	−	0.523448i
$940$		0			0
$941$	10.0921			0.328991			0.164496	−	0.986378i	$-0.447400\pi$
$941$	10.0921			0.328991			0.164496	+	0.986378i	$0.447400\pi$
$942$		0			0
$943$		−	3.25676i		−	0.106055i
$944$		0			0
$945$	0.820218	+	19.6401i	0.0266817	+	0.638892i
$946$		0			0
$947$			58.2693i			1.89350i	0.321973	+	0.946749i	$0.395654\pi$
$947$			58.2693i			1.89350i	−0.321973	+	0.946749i	$0.604346\pi$
$948$		0			0
$949$	1.47124			0.0477584
$950$		0			0
$951$	−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	$-0.274897\pi$
$954$		0			0
$955$	9.12541	−	5.26856i	0.295291	−	0.170487i
$956$		0			0
$957$	−1.63599	−	1.22535i	−0.0528839	−	0.0396099i
$958$		0			0
$959$	−15.4148	+	20.3751i	−0.497768	+	0.657947i
$960$		0			0
$961$	12.1446			0.391761
$962$		0			0
$963$	−11.2143	+	46.1209i	−0.361374	+	1.48623i
$964$		0			0
$965$	−2.02008	−	3.49889i	−0.0650288	−	0.112633i
$966$		0			0
$967$	−6.43145	+	11.1396i	−0.206822	+	0.358226i	−0.950712	−	0.310077i	$-0.899645\pi$
$967$	−6.43145	+	11.1396i	−0.206822	+	0.358226i	0.743890	+	0.668302i	$0.232979\pi$
$968$		0			0
$969$	−5.13939	+	6.86169i	−0.165101	+	0.220429i
$970$		0			0
$971$	−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	$0.978402\pi$
$972$		0			0
$973$	29.6169	−	39.1474i	0.949474	−	1.25501i
$974$		0			0
$975$	32.2102	+	3.85972i	1.03155	+	0.123610i
$976$		0			0
$977$		−	20.3667i		−	0.651590i	−0.945441	−	0.325795i	$-0.894368\pi$
$977$		−	20.3667i		−	0.651590i	0.945441	−	0.325795i	$-0.105632\pi$
$978$		0			0
$979$	12.0215	−	6.94060i	0.384208	−	0.221822i
$980$		0			0
$981$	−21.1559	+	22.1645i	−0.675456	+	0.707659i
$982$		0			0
$983$	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			0
$985$	32.3048	−	18.6512i	1.02932	−	0.594276i
$986$		0			0
$987$	17.5482	−	18.2083i	0.558566	−	0.579578i
$988$		0			0
$989$	−40.5786	−	23.4280i	−1.29032	−	0.744968i
$990$		0			0
$991$	14.8114	+	25.6540i	0.470498	+	0.814927i	0.999431	−	0.0337371i	$-0.0107409\pi$
$991$	14.8114	+	25.6540i	0.470498	+	0.814927i	−0.528933	+	0.848664i	$0.677408\pi$
$992$		0			0
$993$	−36.7276	−	27.5089i	−1.16551	−	0.872967i
$994$		0			0
$995$	−19.0901	−	11.0217i	−0.605196	−	0.349410i
$996$		0			0
$997$	23.4011	+	13.5106i	0.741120	+	0.427886i	0.822477	−	0.568799i	$-0.192592\pi$
$997$	23.4011	+	13.5106i	0.741120	+	0.427886i	−0.0813562	+	0.996685i	$0.525925\pi$
$998$		0			0
$999$	−7.12508	−	8.64320i	−0.225427	−	0.273459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.c.257.3		16
3.2	odd	2		3024.2.ca.c.2609.3		16
4.3	odd	2		126.2.l.a.5.3	✓	16
7.3	odd	6		1008.2.df.c.689.6		16
9.2	odd	6		1008.2.df.c.929.6		16
9.7	even	3		3024.2.df.c.1601.3		16
12.11	even	2		378.2.l.a.341.6		16
21.17	even	6		3024.2.df.c.17.3		16
28.3	even	6		126.2.t.a.59.6	yes	16
28.11	odd	6		882.2.t.a.815.7		16
28.19	even	6		882.2.m.a.293.4		16
28.23	odd	6		882.2.m.b.293.1		16
28.27	even	2		882.2.l.b.509.2		16
36.7	odd	6		378.2.t.a.89.2		16
36.11	even	6		126.2.t.a.47.6	yes	16
36.23	even	6		1134.2.k.b.971.2		16
36.31	odd	6		1134.2.k.a.971.7		16
63.38	even	6	inner	1008.2.ca.c.353.3		16
63.52	odd	6		3024.2.ca.c.2033.3		16
84.11	even	6		2646.2.t.b.2285.3		16
84.23	even	6		2646.2.m.b.881.6		16
84.47	odd	6		2646.2.m.a.881.7		16
84.59	odd	6		378.2.t.a.17.2		16
84.83	odd	2		2646.2.l.a.1097.7		16
252.11	even	6		882.2.l.b.227.6		16
252.31	even	6		1134.2.k.b.647.2		16
252.47	odd	6		882.2.m.b.587.1		16
252.59	odd	6		1134.2.k.a.647.7		16
252.79	odd	6		2646.2.m.a.1763.7		16
252.83	odd	6		882.2.t.a.803.7		16
252.115	even	6		378.2.l.a.143.2		16
252.151	odd	6		2646.2.l.a.521.3		16
252.187	even	6		2646.2.m.b.1763.6		16
252.191	even	6		882.2.m.a.587.4		16
252.223	even	6		2646.2.t.b.1979.3		16
252.227	odd	6		126.2.l.a.101.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.3	✓	16	4.3	odd	2
126.2.l.a.101.7	yes	16	252.227	odd	6
126.2.t.a.47.6	yes	16	36.11	even	6
126.2.t.a.59.6	yes	16	28.3	even	6
378.2.l.a.143.2		16	252.115	even	6
378.2.l.a.341.6		16	12.11	even	2
378.2.t.a.17.2		16	84.59	odd	6
378.2.t.a.89.2		16	36.7	odd	6
882.2.l.b.227.6		16	252.11	even	6
882.2.l.b.509.2		16	28.27	even	2
882.2.m.a.293.4		16	28.19	even	6
882.2.m.a.587.4		16	252.191	even	6
882.2.m.b.293.1		16	28.23	odd	6
882.2.m.b.587.1		16	252.47	odd	6
882.2.t.a.803.7		16	252.83	odd	6
882.2.t.a.815.7		16	28.11	odd	6
1008.2.ca.c.257.3		16	1.1	even	1	trivial
1008.2.ca.c.353.3		16	63.38	even	6	inner
1008.2.df.c.689.6		16	7.3	odd	6
1008.2.df.c.929.6		16	9.2	odd	6
1134.2.k.a.647.7		16	252.59	odd	6
1134.2.k.a.971.7		16	36.31	odd	6
1134.2.k.b.647.2		16	252.31	even	6
1134.2.k.b.971.2		16	36.23	even	6
2646.2.l.a.521.3		16	252.151	odd	6
2646.2.l.a.1097.7		16	84.83	odd	2
2646.2.m.a.881.7		16	84.47	odd	6
2646.2.m.a.1763.7		16	252.79	odd	6
2646.2.m.b.881.6		16	84.23	even	6
2646.2.m.b.1763.6		16	252.187	even	6
2646.2.t.b.1979.3		16	252.223	even	6
2646.2.t.b.2285.3		16	84.11	even	6
3024.2.ca.c.2033.3		16	63.52	odd	6
3024.2.ca.c.2609.3		16	3.2	odd	2
3024.2.df.c.17.3		16	21.17	even	6
3024.2.df.c.1601.3		16	9.7	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38631 - 1.03834i) q^{3} +(0.714925 + 1.23829i) q^{5} +(-0.327442 + 2.62541i) q^{7} +(0.843698 + 2.87892i) q^{9} +(-2.96133 - 1.70972i) q^{11} +(-5.48813 - 3.16857i) q^{13} +(0.294657 - 2.45898i) q^{15} +(-1.14201 - 1.97802i) q^{17} +(1.87673 + 1.08353i) q^{19} +(3.18001 - 3.29963i) q^{21} +(6.97507 - 4.02706i) q^{23} +(1.47776 - 2.55956i) q^{25} +(1.81967 - 4.86711i) q^{27} +(-0.298879 + 0.172558i) q^{29} -4.34228i q^{31} +(2.33004 + 5.44507i) q^{33} +(-3.48511 + 1.47150i) q^{35} +(1.07786 - 1.86690i) q^{37} +(4.31818 + 10.0912i) q^{39} +(0.202180 - 0.350186i) q^{41} +(-2.90883 - 5.03824i) q^{43} +(-2.96175 + 3.10295i) q^{45} +5.51829 q^{47} +(-6.78556 - 1.71934i) q^{49} +(-0.470680 + 3.92793i) q^{51} +(8.56310 - 4.94391i) q^{53} -4.88930i q^{55} +(-1.47666 - 3.45080i) q^{57} -11.0296 q^{59} -11.4797i q^{61} +(-7.83461 + 1.27237i) q^{63} -9.06117i q^{65} -4.25366 q^{67} +(-13.8510 - 1.65976i) q^{69} -3.55393i q^{71} +(-0.201057 + 0.116080i) q^{73} +(-4.70633 + 2.01392i) q^{75} +(5.45839 - 7.21486i) q^{77} -14.5620 q^{79} +(-7.57635 + 4.85787i) q^{81} +(-0.811624 - 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} +(0.593511 + 0.0711198i) q^{87} +(-2.02974 + 3.51562i) q^{89} +(10.1159 - 13.3711i) q^{91} +(-4.50877 + 6.01974i) q^{93} +3.09858i q^{95} +(-9.18719 + 5.30423i) q^{97} +(2.42369 - 9.96791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49}+ \cdots - 18 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Introduction

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