LMFDB - Embedded newform 1386.2.r.d.1277.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(89,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("1386.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1277.10
Character	$\chi$	$=$	1386.1277
Dual form			1386.2.r.d.89.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.645853 - 1.11865i) q^{5} +(2.63647 - 0.221466i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.645853 - 1.11865i) q^{5} +(2.63647 - 0.221466i) q^{7} -1.00000i q^{8} +(-1.11865 - 0.645853i) q^{10} +(-0.866025 - 0.500000i) q^{11} -3.78742i q^{13} +(2.17251 - 1.51003i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.552825 + 0.957521i) q^{17} +(2.02517 - 1.16923i) q^{19} -1.29171 q^{20} -1.00000 q^{22} +(-2.83782 + 1.63842i) q^{23} +(1.66575 - 2.88516i) q^{25} +(-1.89371 - 3.28000i) q^{26} +(1.12644 - 2.39398i) q^{28} -2.78548i q^{29} +(3.81931 + 2.20508i) q^{31} +(-0.866025 - 0.500000i) q^{32} +1.10565i q^{34} +(-1.95051 - 2.80625i) q^{35} +(-3.09743 - 5.36491i) q^{37} +(1.16923 - 2.02517i) q^{38} +(-1.11865 + 0.645853i) q^{40} +2.16639 q^{41} -8.44892 q^{43} +(-0.866025 + 0.500000i) q^{44} +(-1.63842 + 2.83782i) q^{46} +(1.74371 + 3.02020i) q^{47} +(6.90191 - 1.16778i) q^{49} -3.33150i q^{50} +(-3.28000 - 1.89371i) q^{52} +(-2.02952 - 1.17174i) q^{53} +1.29171i q^{55} +(-0.221466 - 2.63647i) q^{56} +(-1.39274 - 2.41230i) q^{58} +(2.30664 - 3.99523i) q^{59} +(1.60176 - 0.924776i) q^{61} +4.41016 q^{62} -1.00000 q^{64} +(-4.23679 + 2.44611i) q^{65} +(5.79630 - 10.0395i) q^{67} +(0.552825 + 0.957521i) q^{68} +(-3.09232 - 1.45503i) q^{70} -1.96495i q^{71} +(4.98535 + 2.87829i) q^{73} +(-5.36491 - 3.09743i) q^{74} -2.33847i q^{76} +(-2.39398 - 1.12644i) q^{77} +(2.49285 + 4.31774i) q^{79} +(-0.645853 + 1.11865i) q^{80} +(1.87615 - 1.08319i) q^{82} -8.95734 q^{83} +1.42817 q^{85} +(-7.31698 + 4.22446i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-1.79901 - 3.11598i) q^{89} +(-0.838784 - 9.98539i) q^{91} +3.27683i q^{92} +(3.02020 + 1.74371i) q^{94} +(-2.61593 - 1.51031i) q^{95} +15.8884i q^{97} +(5.39334 - 4.46228i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 8 * q^7	$ 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.645853	−	1.11865i	−0.288834	−	0.500275i	0.684698	−	0.728827i	$-0.259934\pi$
$5$	−0.645853	−	1.11865i	−0.288834	−	0.500275i	−0.973532	+	0.228552i	$0.926601\pi$
$6$		0			0
$7$	2.63647	−	0.221466i	0.996490	−	0.0837063i
$7$	2.63647	−	0.221466i	0.996490	−	0.0837063i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.11865	−	0.645853i	−0.353748	−	0.204237i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$12$		0			0
$13$		−	3.78742i		−	1.05044i	−0.850966	−	0.525220i	$-0.823983\pi$
$13$		−	3.78742i		−	1.05044i	0.850966	−	0.525220i	$-0.176017\pi$
$14$	2.17251	−	1.51003i	0.580629	−	0.403572i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.552825	+	0.957521i	−0.134080	+	0.232233i	−0.925246	−	0.379369i	$-0.876141\pi$
$17$	−0.552825	+	0.957521i	−0.134080	+	0.232233i	0.791166	+	0.611602i	$0.209475\pi$
$18$		0			0
$19$	2.02517	−	1.16923i	0.464607	−	0.268241i	−0.249373	−	0.968408i	$-0.580224\pi$
$19$	2.02517	−	1.16923i	0.464607	−	0.268241i	0.713979	+	0.700167i	$0.246891\pi$
$20$	−1.29171			−0.288834
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−2.83782	+	1.63842i	−0.591726	+	0.341633i	−0.765780	−	0.643103i	$-0.777647\pi$
$23$	−2.83782	+	1.63842i	−0.591726	+	0.341633i	0.174054	+	0.984736i	$0.444313\pi$
$24$		0			0
$25$	1.66575	−	2.88516i	0.333150	−	0.577032i
$26$	−1.89371	−	3.28000i	−0.371387	−	0.643261i
$27$		0			0
$28$	1.12644	−	2.39398i	0.212877	−	0.452420i
$29$		−	2.78548i		−	0.517251i	−0.965978	−	0.258626i	$-0.916730\pi$
$29$		−	2.78548i		−	0.517251i	0.965978	−	0.258626i	$-0.0832696\pi$
$30$		0			0
$31$	3.81931	+	2.20508i	0.685968	+	0.396044i	0.802100	−	0.597190i	$-0.203716\pi$
$31$	3.81931	+	2.20508i	0.685968	+	0.396044i	−0.116132	+	0.993234i	$0.537049\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			1.10565i			0.189617i
$35$	−1.95051	−	2.80625i	−0.329697	−	0.474342i
$36$		0			0
$37$	−3.09743	−	5.36491i	−0.509215	−	0.881986i	−0.999943	−	0.0106735i	$-0.996602\pi$
$37$	−3.09743	−	5.36491i	−0.509215	−	0.881986i	0.490728	−	0.871313i	$-0.336731\pi$
$38$	1.16923	−	2.02517i	0.189675	−	0.328527i
$39$		0			0
$40$	−1.11865	+	0.645853i	−0.176874	+	0.102118i
$41$	2.16639			0.338333			0.169166	−	0.985588i	$-0.445892\pi$
$41$	2.16639			0.338333			0.169166	+	0.985588i	$0.445892\pi$
$42$		0			0
$43$	−8.44892			−1.28845			−0.644224	−	0.764837i	$-0.722819\pi$
$43$	−8.44892			−1.28845			−0.644224	+	0.764837i	$0.722819\pi$
$44$	−0.866025	+	0.500000i	−0.130558	+	0.0753778i
$45$		0			0
$46$	−1.63842	+	2.83782i	−0.241571	+	0.418414i
$47$	1.74371	+	3.02020i	0.254346	+	0.440541i	0.964718	−	0.263286i	$-0.0848063\pi$
$47$	1.74371	+	3.02020i	0.254346	+	0.440541i	−0.710371	+	0.703827i	$0.751473\pi$
$48$		0			0
$49$	6.90191	−	1.16778i	0.985987	−	0.166825i
$50$		−	3.33150i		−	0.471145i
$51$		0			0
$52$	−3.28000	−	1.89371i	−0.454854	−	0.262610i
$53$	−2.02952	−	1.17174i	−0.278776	−	0.160951i	0.354093	−	0.935210i	$-0.384790\pi$
$53$	−2.02952	−	1.17174i	−0.278776	−	0.160951i	−0.632869	+	0.774259i	$0.718123\pi$
$54$		0			0
$55$			1.29171i			0.174174i
$56$	−0.221466	−	2.63647i	−0.0295946	−	0.352313i
$57$		0			0
$58$	−1.39274	−	2.41230i	−0.182876	−	0.316750i
$59$	2.30664	−	3.99523i	0.300300	−	0.520134i	−0.675904	−	0.736989i	$-0.736247\pi$
$59$	2.30664	−	3.99523i	0.300300	−	0.520134i	0.976204	+	0.216855i	$0.0695800\pi$
$60$		0			0
$61$	1.60176	−	0.924776i	0.205084	−	0.118405i	−0.393941	−	0.919136i	$-0.628888\pi$
$61$	1.60176	−	0.924776i	0.205084	−	0.118405i	0.599025	+	0.800731i	$0.295555\pi$
$62$	4.41016			0.560091
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.23679	+	2.44611i	−0.525509	+	0.303403i
$66$		0			0
$67$	5.79630	−	10.0395i	0.708131	−	1.22652i	−0.257419	−	0.966300i	$-0.582872\pi$
$67$	5.79630	−	10.0395i	0.708131	−	1.22652i	0.965550	−	0.260219i	$-0.0837946\pi$
$68$	0.552825	+	0.957521i	0.0670399	+	0.116117i
$69$		0			0
$70$	−3.09232	−	1.45503i	−0.369603	−	0.173909i
$71$		−	1.96495i		−	0.233197i	−0.993179	−	0.116598i	$-0.962801\pi$
$71$		−	1.96495i		−	0.233197i	0.993179	−	0.116598i	$-0.0371990\pi$
$72$		0			0
$73$	4.98535	+	2.87829i	0.583491	+	0.336879i	0.762519	−	0.646965i	$-0.223962\pi$
$73$	4.98535	+	2.87829i	0.583491	+	0.336879i	−0.179029	+	0.983844i	$0.557295\pi$
$74$	−5.36491	−	3.09743i	−0.623658	−	0.360069i
$75$		0			0
$76$		−	2.33847i		−	0.268241i
$77$	−2.39398	−	1.12644i	−0.272819	−	0.128370i
$78$		0			0
$79$	2.49285	+	4.31774i	0.280467	+	0.485783i	0.971500	−	0.237040i	$-0.0761773\pi$
$79$	2.49285	+	4.31774i	0.280467	+	0.485783i	−0.691033	+	0.722823i	$0.742844\pi$
$80$	−0.645853	+	1.11865i	−0.0722085	+	0.125069i
$81$		0			0
$82$	1.87615	−	1.08319i	0.207186	−	0.119619i
$83$	−8.95734			−0.983196			−0.491598	−	0.870822i	$-0.663587\pi$
$83$	−8.95734			−0.983196			−0.491598	+	0.870822i	$0.663587\pi$
$84$		0			0
$85$	1.42817			0.154907
$86$	−7.31698	+	4.22446i	−0.789010	+	0.455535i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−1.79901	−	3.11598i	−0.190695	−	0.330293i	0.754786	−	0.655971i	$-0.227741\pi$
$89$	−1.79901	−	3.11598i	−0.190695	−	0.330293i	−0.945481	+	0.325678i	$0.894407\pi$
$90$		0			0
$91$	−0.838784	−	9.98539i	−0.0879285	−	1.04675i
$92$			3.27683i			0.341633i
$93$		0			0
$94$	3.02020	+	1.74371i	0.311509	+	0.179850i
$95$	−2.61593	−	1.51031i	−0.268389	−	0.154954i
$96$		0			0
$97$			15.8884i			1.61322i	0.591085	+	0.806609i	$0.298700\pi$
$97$			15.8884i			1.61322i	−0.591085	+	0.806609i	$0.701300\pi$
$98$	5.39334	−	4.46228i	0.544809	−	0.450758i
$99$		0			0
$100$	−1.66575	−	2.88516i	−0.166575	−	0.288516i
$101$	−1.42778	+	2.47299i	−0.142070	+	0.246072i	−0.928276	−	0.371892i	$-0.878709\pi$
$101$	−1.42778	+	2.47299i	−0.142070	+	0.246072i	0.786206	+	0.617964i	$0.212042\pi$
$102$		0			0
$103$	−2.43622	+	1.40655i	−0.240048	+	0.138592i	−0.615199	−	0.788372i	$-0.710924\pi$
$103$	−2.43622	+	1.40655i	−0.240048	+	0.138592i	0.375151	+	0.926964i	$0.377591\pi$
$104$	−3.78742			−0.371387
$105$		0			0
$106$	−2.34349			−0.227620
$107$	−7.44855	+	4.30042i	−0.720078	+	0.415737i	−0.814782	−	0.579768i	$-0.803143\pi$
$107$	−7.44855	+	4.30042i	−0.720078	+	0.415737i	0.0947032	+	0.995506i	$0.469810\pi$
$108$		0			0
$109$	2.72966	−	4.72792i	0.261454	−	0.452852i	−0.705174	−	0.709034i	$-0.749131\pi$
$109$	2.72966	−	4.72792i	0.261454	−	0.452852i	0.966629	+	0.256182i	$0.0824646\pi$
$110$	0.645853	+	1.11865i	0.0615796	+	0.106659i
$111$		0			0
$112$	−1.51003	−	2.17251i	−0.142684	−	0.205283i
$113$		−	11.7670i		−	1.10695i	−0.832867	−	0.553473i	$-0.813302\pi$
$113$		−	11.7670i		−	1.10695i	0.832867	−	0.553473i	$-0.186698\pi$
$114$		0			0
$115$	3.66563	+	2.11635i	0.341821	+	0.197351i
$116$	−2.41230	−	1.39274i	−0.223976	−	0.129313i
$117$		0			0
$118$		−	4.61329i		−	0.424688i
$119$	−1.24545	+	2.64690i	−0.114170	+	0.242641i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	0.924776	−	1.60176i	0.0837252	−	0.145016i
$123$		0			0
$124$	3.81931	−	2.20508i	0.342984	−	0.198022i
$125$	−10.7618			−0.962568
$126$		0			0
$127$	13.2680			1.17734			0.588672	−	0.808372i	$-0.299651\pi$
$127$	13.2680			1.17734			0.588672	+	0.808372i	$0.299651\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.44611	+	4.23679i	−0.214538	+	0.371591i
$131$	8.88475	+	15.3888i	0.776264	+	1.34453i	0.934081	+	0.357061i	$0.116221\pi$
$131$	8.88475	+	15.3888i	0.776264	+	1.34453i	−0.157817	+	0.987468i	$0.550446\pi$
$132$		0			0
$133$	5.08036	−	3.53115i	0.440523	−	0.306190i
$134$		−	11.5926i		−	1.00145i
$135$		0			0
$136$	0.957521	+	0.552825i	0.0821068	+	0.0474044i
$137$	−6.74719	−	3.89549i	−0.576451	−	0.332814i	0.183270	−	0.983063i	$-0.441332\pi$
$137$	−6.74719	−	3.89549i	−0.576451	−	0.332814i	−0.759722	+	0.650248i	$0.774665\pi$
$138$		0			0
$139$		−	0.342557i		−	0.0290553i	−0.999894	−	0.0145277i	$-0.995376\pi$
$139$		−	0.342557i		−	0.0290553i	0.999894	−	0.0145277i	$-0.00462446\pi$
$140$	−3.40554	+	0.286069i	−0.287820	+	0.0241772i
$141$		0			0
$142$	−0.982475	−	1.70170i	−0.0824474	−	0.142803i
$143$	−1.89371	+	3.28000i	−0.158360	+	0.274287i
$144$		0			0
$145$	−3.11598	+	1.79901i	−0.258768	+	0.149400i
$146$	5.75658			0.476418
$147$		0			0
$148$	−6.19487			−0.509215
$149$	7.16340	−	4.13579i	0.586849	−	0.338817i	−0.177002	−	0.984211i	$-0.556640\pi$
$149$	7.16340	−	4.13579i	0.586849	−	0.338817i	0.763850	+	0.645393i	$0.223306\pi$
$150$		0			0
$151$	0.880131	−	1.52443i	0.0716241	−	0.124057i	−0.827989	−	0.560744i	$-0.810515\pi$
$151$	0.880131	−	1.52443i	0.0716241	−	0.124057i	0.899613	+	0.436688i	$0.143848\pi$
$152$	−1.16923	−	2.02517i	−0.0948375	−	0.164263i
$153$		0			0
$154$	−2.63647	+	0.221466i	−0.212452	+	0.0178462i
$155$		−	5.69663i		−	0.457564i
$156$		0			0
$157$	9.80424	+	5.66048i	0.782464	+	0.451756i	0.837303	−	0.546739i	$-0.184131\pi$
$157$	9.80424	+	5.66048i	0.782464	+	0.451756i	−0.0548389	+	0.998495i	$0.517465\pi$
$158$	4.31774	+	2.49285i	0.343501	+	0.198320i
$159$		0			0
$160$			1.29171i			0.102118i
$161$	−7.11896	+	4.94811i	−0.561053	+	0.389965i
$162$		0			0
$163$	11.1919	+	19.3850i	0.876618	+	1.51835i	0.855029	+	0.518581i	$0.173539\pi$
$163$	11.1919	+	19.3850i	0.876618	+	1.51835i	0.0215899	+	0.999767i	$0.493127\pi$
$164$	1.08319	−	1.87615i	0.0845832	−	0.146502i
$165$		0			0
$166$	−7.75729	+	4.47867i	−0.602082	+	0.347612i
$167$	24.2239			1.87450			0.937252	−	0.348652i	$-0.113360\pi$
$167$	24.2239			1.87450			0.937252	+	0.348652i	$0.113360\pi$
$168$		0			0
$169$	−1.34452			−0.103425
$170$	1.23684	−	0.714087i	0.0948610	−	0.0547680i
$171$		0			0
$172$	−4.22446	+	7.31698i	−0.322112	+	0.557914i
$173$	7.95025	+	13.7702i	0.604446	+	1.04693i	0.992139	+	0.125143i	$0.0399388\pi$
$173$	7.95025	+	13.7702i	0.604446	+	1.04693i	−0.387693	+	0.921789i	$0.626728\pi$
$174$		0			0
$175$	3.75272	−	7.97554i	0.283679	−	0.602894i
$176$			1.00000i			0.0753778i
$177$		0			0
$178$	−3.11598	−	1.79901i	−0.233553	−	0.134842i
$179$	7.64555	+	4.41416i	0.571455	+	0.329930i	0.757730	−	0.652568i	$-0.226308\pi$
$179$	7.64555	+	4.41416i	0.571455	+	0.329930i	−0.186275	+	0.982498i	$0.559642\pi$
$180$		0			0
$181$			20.7819i			1.54470i	0.635194	+	0.772352i	$0.280920\pi$
$181$			20.7819i			1.54470i	−0.635194	+	0.772352i	$0.719080\pi$
$182$	−5.71911	−	8.22821i	−0.423928	−	0.609916i
$183$		0			0
$184$	1.63842	+	2.83782i	0.120786	+	0.209207i
$185$	−4.00097	+	6.92989i	−0.294157	+	0.509495i
$186$		0			0
$187$	0.957521	−	0.552825i	0.0700209	−	0.0404266i
$188$	3.48742			0.254346
$189$		0			0
$190$	−3.02061			−0.219138
$191$	−11.8164	+	6.82219i	−0.855003	+	0.493636i	−0.862336	−	0.506337i	$-0.830999\pi$
$191$	−11.8164	+	6.82219i	−0.855003	+	0.493636i	0.00733261	+	0.999973i	$0.497666\pi$
$192$		0			0
$193$	−2.33050	+	4.03654i	−0.167753	+	0.290556i	−0.937629	−	0.347636i	$-0.886984\pi$
$193$	−2.33050	+	4.03654i	−0.167753	+	0.290556i	0.769877	+	0.638193i	$0.220318\pi$
$194$	7.94418	+	13.7597i	0.570359	+	0.987890i
$195$		0			0
$196$	2.43963	−	6.56111i	0.174259	−	0.468651i
$197$		−	1.92007i		−	0.136799i	−0.997658	−	0.0683997i	$-0.978211\pi$
$197$		−	1.92007i		−	0.136799i	0.997658	−	0.0683997i	$-0.0217893\pi$
$198$		0			0
$199$	5.47439	+	3.16064i	0.388069	+	0.224052i	0.681323	−	0.731983i	$-0.261405\pi$
$199$	5.47439	+	3.16064i	0.388069	+	0.224052i	−0.293254	+	0.956035i	$0.594738\pi$
$200$	−2.88516	−	1.66575i	−0.204012	−	0.117786i
$201$		0			0
$202$			2.85557i			0.200917i
$203$	−0.616890	−	7.34383i	−0.0432972	−	0.515436i
$204$		0			0
$205$	−1.39917	−	2.42343i	−0.0977220	−	0.169259i
$206$	−1.40655	+	2.43622i	−0.0979990	+	0.169739i
$207$		0			0
$208$	−3.28000	+	1.89371i	−0.227427	+	0.131305i
$209$	−2.33847			−0.161755
$210$		0			0
$211$	−12.9534			−0.891748			−0.445874	−	0.895096i	$-0.647107\pi$
$211$	−12.9534			−0.891748			−0.445874	+	0.895096i	$0.647107\pi$
$212$	−2.02952	+	1.17174i	−0.139388	+	0.0804757i
$213$		0			0
$214$	−4.30042	+	7.44855i	−0.293971	+	0.509172i
$215$	5.45676	+	9.45138i	0.372148	+	0.644579i
$216$		0			0
$217$	10.5578	+	4.96777i	0.716712	+	0.337234i
$218$		−	5.45933i		−	0.369752i
$219$		0			0
$220$	1.11865	+	0.645853i	0.0754194	+	0.0435434i
$221$	3.62653	+	2.09378i	0.243947	+	0.140843i
$222$		0			0
$223$			9.38102i			0.628200i	0.949390	+	0.314100i	$0.101703\pi$
$223$			9.38102i			0.628200i	−0.949390	+	0.314100i	$0.898297\pi$
$224$	−2.39398	−	1.12644i	−0.159954	−	0.0752633i
$225$		0			0
$226$	−5.88350	−	10.1905i	−0.391365	−	0.677864i
$227$	1.26300	−	2.18759i	0.0838285	−	0.145195i	−0.821063	−	0.570838i	$-0.806619\pi$
$227$	1.26300	−	2.18759i	0.0838285	−	0.145195i	0.904891	+	0.425643i	$0.139952\pi$
$228$		0			0
$229$	−12.7173	+	7.34235i	−0.840384	+	0.485196i	−0.857395	−	0.514659i	$-0.827918\pi$
$229$	−12.7173	+	7.34235i	−0.840384	+	0.485196i	0.0170109	+	0.999855i	$0.494585\pi$
$230$	4.23270			0.279096
$231$		0			0
$232$	−2.78548			−0.182876
$233$	−6.69706	+	3.86655i	−0.438739	+	0.253306i	−0.703062	−	0.711128i	$-0.748185\pi$
$233$	−6.69706	+	3.86655i	−0.438739	+	0.253306i	0.264324	+	0.964434i	$0.414851\pi$
$234$		0			0
$235$	2.25236	−	3.90120i	0.146928	−	0.254486i
$236$	−2.30664	−	3.99523i	−0.150150	−	0.260067i
$237$		0			0
$238$	0.244864	+	2.91501i	0.0158722	+	0.188952i
$239$			20.7911i			1.34486i	0.740159	+	0.672432i	$0.234750\pi$
$239$			20.7911i			1.34486i	−0.740159	+	0.672432i	$0.765250\pi$
$240$		0			0
$241$	−13.3669	−	7.71741i	−0.861041	−	0.497122i	0.00331988	−	0.999994i	$-0.498943\pi$
$241$	−13.3669	−	7.71741i	−0.861041	−	0.497122i	−0.864361	+	0.502872i	$0.832277\pi$
$242$	0.866025	+	0.500000i	0.0556702	+	0.0321412i
$243$		0			0
$244$		−	1.84955i		−	0.118405i
$245$	−5.76395	−	6.96660i	−0.368245	−	0.445080i
$246$		0			0
$247$	−4.42838	−	7.67018i	−0.281771	−	0.488042i
$248$	2.20508	−	3.81931i	0.140023	−	0.242526i
$249$		0			0
$250$	−9.32003	+	5.38092i	−0.589450	+	0.340319i
$251$	5.10396			0.322159			0.161079	−	0.986941i	$-0.448502\pi$
$251$	5.10396			0.322159			0.161079	+	0.986941i	$0.448502\pi$
$252$		0			0
$253$	3.27683			0.206013
$254$	11.4904	−	6.63400i	0.720973	−	0.416254i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.9547	+	24.1702i	0.870469	+	1.50770i	0.861512	+	0.507737i	$0.169518\pi$
$257$	13.9547	+	24.1702i	0.870469	+	1.50770i	0.00895701	+	0.999960i	$0.497149\pi$
$258$		0			0
$259$	−9.35443	−	13.4584i	−0.581256	−	0.836266i
$260$			4.89223i			0.303403i
$261$		0			0
$262$	15.3888	+	8.88475i	0.950726	+	0.548902i
$263$	15.4662	+	8.92939i	0.953685	+	0.550610i	0.894224	−	0.447621i	$-0.147728\pi$
$263$	15.4662	+	8.92939i	0.953685	+	0.550610i	0.0594610	+	0.998231i	$0.481062\pi$
$264$		0			0
$265$			3.02709i			0.185953i
$266$	2.63414	−	5.59825i	0.161509	−	0.343251i
$267$		0			0
$268$	−5.79630	−	10.0395i	−0.354065	−	0.613259i
$269$	10.8042	−	18.7133i	0.658741	−	1.14097i	−0.322201	−	0.946671i	$-0.604423\pi$
$269$	10.8042	−	18.7133i	0.658741	−	1.14097i	0.980942	−	0.194302i	$-0.0622441\pi$
$270$		0			0
$271$	9.38753	−	5.41989i	0.570252	−	0.329235i	−0.186998	−	0.982360i	$-0.559876\pi$
$271$	9.38753	−	5.41989i	0.570252	−	0.329235i	0.757250	+	0.653125i	$0.226543\pi$
$272$	1.10565			0.0670399
$273$		0			0
$274$	−7.79099			−0.470671
$275$	−2.88516	+	1.66575i	−0.173982	+	0.100448i
$276$		0			0
$277$	−1.92620	+	3.33628i	−0.115734	+	0.200458i	−0.918073	−	0.396411i	$-0.870255\pi$
$277$	−1.92620	+	3.33628i	−0.115734	+	0.200458i	0.802339	+	0.596869i	$0.203589\pi$
$278$	−0.171279	−	0.296663i	−0.0102726	−	0.0177927i
$279$		0			0
$280$	−2.80625	+	1.95051i	−0.167705	+	0.116565i
$281$		−	15.5841i		−	0.929669i	−0.885398	−	0.464834i	$-0.846114\pi$
$281$		−	15.5841i		−	0.929669i	0.885398	−	0.464834i	$-0.153886\pi$
$282$		0			0
$283$	6.00438	+	3.46663i	0.356923	+	0.206070i	0.667730	−	0.744403i	$-0.267266\pi$
$283$	6.00438	+	3.46663i	0.356923	+	0.206070i	−0.310807	+	0.950473i	$0.600599\pi$
$284$	−1.70170	−	0.982475i	−0.100977	−	0.0582991i
$285$		0			0
$286$			3.78742i			0.223955i
$287$	5.71160	−	0.479781i	0.337145	−	0.0283206i
$288$		0			0
$289$	7.88877	+	13.6637i	0.464045	+	0.803750i
$290$	−1.79901	+	3.11598i	−0.105642	+	0.182977i
$291$		0			0
$292$	4.98535	−	2.87829i	0.291745	−	0.168439i
$293$	−6.52214			−0.381028			−0.190514	−	0.981685i	$-0.561015\pi$
$293$	−6.52214			−0.381028			−0.190514	+	0.981685i	$0.561015\pi$
$294$		0			0
$295$	−5.95901			−0.346947
$296$	−5.36491	+	3.09743i	−0.311829	+	0.180035i
$297$		0			0
$298$	4.13579	−	7.16340i	0.239580	−	0.414965i
$299$	6.20536	+	10.7480i	0.358865	+	0.621573i
$300$		0			0
$301$	−22.2753	+	1.87115i	−1.28393	+	0.107851i
$302$		−	1.76026i		−	0.101292i
$303$		0			0
$304$	−2.02517	−	1.16923i	−0.116152	−	0.0670602i
$305$	−2.06900	−	1.19454i	−0.118471	−	0.0683990i
$306$		0			0
$307$		−	14.5303i		−	0.829286i	−0.909984	−	0.414643i	$-0.863906\pi$
$307$		−	14.5303i		−	0.829286i	0.909984	−	0.414643i	$-0.136094\pi$
$308$	−2.17251	+	1.51003i	−0.123790	+	0.0860418i
$309$		0			0
$310$	−2.84831	−	4.93342i	−0.161773	−	0.280200i
$311$	9.48405	−	16.4269i	0.537791	−	0.931482i	−0.461232	−	0.887280i	$-0.652592\pi$
$311$	9.48405	−	16.4269i	0.537791	−	0.931482i	0.999023	−	0.0442017i	$-0.0140744\pi$
$312$		0			0
$313$	−14.5397	+	8.39451i	−0.821834	+	0.474486i	−0.851048	−	0.525087i	$-0.824033\pi$
$313$	−14.5397	+	8.39451i	−0.821834	+	0.474486i	0.0292146	+	0.999573i	$0.490699\pi$
$314$	11.3210			0.638879
$315$		0			0
$316$	4.98569			0.280467
$317$	−17.9319	+	10.3530i	−1.00715	+	0.581481i	−0.910357	−	0.413823i	$-0.864193\pi$
$317$	−17.9319	+	10.3530i	−1.00715	+	0.581481i	−0.0967974	+	0.995304i	$0.530860\pi$
$318$		0			0
$319$	−1.39274	+	2.41230i	−0.0779785	+	0.135063i
$320$	0.645853	+	1.11865i	0.0361043	+	0.0625344i
$321$		0			0
$322$	−3.69115	+	7.84467i	−0.205700	+	0.437166i
$323$			2.58553i			0.143863i
$324$		0			0
$325$	−10.9273	−	6.30888i	−0.606138	−	0.349954i
$326$	19.3850	+	11.1919i	1.07363	+	0.619863i
$327$		0			0
$328$		−	2.16639i		−	0.119619i
$329$	5.26611	+	7.57647i	0.290330	+	0.417704i
$330$		0			0
$331$	−15.9538	−	27.6327i	−0.876898	−	1.51883i	−0.854727	−	0.519077i	$-0.826276\pi$
$331$	−15.9538	−	27.6327i	−0.876898	−	1.51883i	−0.0221703	−	0.999754i	$-0.507058\pi$
$332$	−4.47867	+	7.75729i	−0.245799	+	0.425736i
$333$		0			0
$334$	20.9785	−	12.1120i	1.14790	−	0.662738i
$335$	−14.9742			−0.818129
$336$		0			0
$337$	−27.1316			−1.47795			−0.738977	−	0.673730i	$-0.764691\pi$
$337$	−27.1316			−1.47795			−0.738977	+	0.673730i	$0.764691\pi$
$338$	−1.16439	+	0.672261i	−0.0633345	+	0.0365662i
$339$		0			0
$340$	0.714087	−	1.23684i	0.0387268	−	0.0670768i
$341$	−2.20508	−	3.81931i	−0.119412	−	0.206827i
$342$		0			0
$343$	17.9380	−	4.60734i	0.968562	−	0.248773i
$344$			8.44892i			0.455535i
$345$		0			0
$346$	13.7702	+	7.95025i	0.740292	+	0.427408i
$347$	28.6515	+	16.5420i	1.53809	+	0.888019i	0.998950	+	0.0458058i	$0.0145855\pi$
$347$	28.6515	+	16.5420i	1.53809	+	0.888019i	0.539144	+	0.842213i	$0.318748\pi$
$348$		0			0
$349$			33.7423i			1.80618i	0.429450	+	0.903091i	$0.358708\pi$
$349$			33.7423i			1.80618i	−0.429450	+	0.903091i	$0.641292\pi$
$350$	−0.737813	−	8.78338i	−0.0394378	−	0.469491i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	10.8107	−	18.7248i	0.575398	−	0.996618i	−0.420601	−	0.907246i	$-0.638181\pi$
$353$	10.8107	−	18.7248i	0.575398	−	0.996618i	0.995998	−	0.0893722i	$-0.0284861\pi$
$354$		0			0
$355$	−2.19809	+	1.26907i	−0.116663	+	0.0673551i
$356$	−3.59802			−0.190695
$357$		0			0
$358$	8.82832			0.466591
$359$	5.27247	−	3.04406i	0.278270	−	0.160659i	−0.354370	−	0.935105i	$-0.615305\pi$
$359$	5.27247	−	3.04406i	0.278270	−	0.160659i	0.632640	+	0.774446i	$0.281971\pi$
$360$		0			0
$361$	−6.76578	+	11.7187i	−0.356094	+	0.616772i
$362$	10.3909	+	17.9976i	0.546136	+	0.945934i
$363$		0			0
$364$	−9.06700	−	4.26629i	−0.475240	−	0.223614i
$365$		−	7.43581i		−	0.389208i
$366$		0			0
$367$	−6.38821	−	3.68823i	−0.333462	−	0.192524i	0.323915	−	0.946086i	$-0.395001\pi$
$367$	−6.38821	−	3.68823i	−0.333462	−	0.192524i	−0.657377	+	0.753562i	$0.728334\pi$
$368$	2.83782	+	1.63842i	0.147932	+	0.0854083i
$369$		0			0
$370$			8.00195i			0.416001i
$371$	−5.61026	−	2.63979i	−0.291270	−	0.137051i
$372$		0			0
$373$	−15.0027	−	25.9855i	−0.776812	−	1.34548i	−0.933770	−	0.357873i	$-0.883502\pi$
$373$	−15.0027	−	25.9855i	−0.776812	−	1.34548i	0.156958	−	0.987605i	$-0.449831\pi$
$374$	0.552825	−	0.957521i	0.0285859	−	0.0495122i
$375$		0			0
$376$	3.02020	−	1.74371i	0.155755	−	0.0899250i
$377$	−10.5498			−0.543341
$378$		0			0
$379$	26.8038			1.37682			0.688408	−	0.725323i	$-0.258310\pi$
$379$	26.8038			1.37682			0.688408	+	0.725323i	$0.258310\pi$
$380$	−2.61593	+	1.51031i	−0.134194	+	0.0774771i
$381$		0			0
$382$	−6.82219	+	11.8164i	−0.349054	+	0.604579i
$383$	7.88721	+	13.6610i	0.403017	+	0.698047i	0.994089	−	0.108573i	$-0.0346280\pi$
$383$	7.88721	+	13.6610i	0.403017	+	0.698047i	−0.591071	+	0.806620i	$0.701295\pi$
$384$		0			0
$385$	0.286069	+	3.40554i	0.0145794	+	0.173562i
$386$			4.66099i			0.237238i
$387$		0			0
$388$	13.7597	+	7.94418i	0.698544	+	0.403304i
$389$	22.8865	+	13.2135i	1.16039	+	0.669951i	0.951397	−	0.307966i	$-0.0996484\pi$
$389$	22.8865	+	13.2135i	1.16039	+	0.669951i	0.208992	+	0.977917i	$0.432982\pi$
$390$		0			0
$391$		−	3.62303i		−	0.183224i
$392$	−1.16778	−	6.90191i	−0.0589816	−	0.348599i
$393$		0			0
$394$	−0.960036	−	1.66283i	−0.0483659	−	0.0837722i
$395$	3.22002	−	5.57724i	0.162017	−	0.280622i
$396$		0			0
$397$	−4.79107	+	2.76613i	−0.240457	+	0.138828i	−0.615387	−	0.788225i	$-0.711000\pi$
$397$	−4.79107	+	2.76613i	−0.240457	+	0.138828i	0.374930	+	0.927053i	$0.377667\pi$
$398$	6.32128			0.316857
$399$		0			0
$400$	−3.33150			−0.166575
$401$	−16.3967	+	9.46667i	−0.818814	+	0.472743i	−0.850007	−	0.526771i	$-0.823403\pi$
$401$	−16.3967	+	9.46667i	−0.818814	+	0.472743i	0.0311930	+	0.999513i	$0.490069\pi$
$402$		0			0
$403$	8.35155	−	14.4653i	0.416020	−	0.720569i
$404$	1.42778	+	2.47299i	0.0710349	+	0.123036i
$405$		0			0
$406$	−4.20616	−	6.05150i	−0.208748	−	0.300331i
$407$			6.19487i			0.307068i
$408$		0			0
$409$	−16.4329	−	9.48751i	−0.812552	−	0.469127i	0.0352892	−	0.999377i	$-0.488765\pi$
$409$	−16.4329	−	9.48751i	−0.812552	−	0.469127i	−0.847841	+	0.530250i	$0.822098\pi$
$410$	−2.42343	−	1.39917i	−0.119685	−	0.0690999i
$411$		0			0
$412$			2.81310i			0.138592i
$413$	5.19658	−	11.0441i	0.255707	−	0.543446i
$414$		0			0
$415$	5.78512	+	10.0201i	0.283981	+	0.491869i
$416$	−1.89371	+	3.28000i	−0.0928467	+	0.160815i
$417$		0			0
$418$	−2.02517	+	1.16923i	−0.0990545	+	0.0571891i
$419$	25.7600			1.25846			0.629229	−	0.777220i	$-0.283371\pi$
$419$	25.7600			1.25846			0.629229	+	0.777220i	$0.283371\pi$
$420$		0			0
$421$	−10.9714			−0.534715			−0.267357	−	0.963597i	$-0.586150\pi$
$421$	−10.9714			−0.534715			−0.267357	+	0.963597i	$0.586150\pi$
$422$	−11.2180	+	6.47670i	−0.546082	+	0.315281i
$423$		0			0
$424$	−1.17174	+	2.02952i	−0.0569049	+	0.0985621i
$425$	1.84174	+	3.18998i	0.0893373	+	0.154737i
$426$		0			0
$427$	4.01817	−	2.79287i	0.194453	−	0.135157i
$428$			8.60084i			0.415737i
$429$		0			0
$430$	9.45138	+	5.45676i	0.455786	+	0.263148i
$431$	14.0938	+	8.13704i	0.678872	+	0.391947i	0.799430	−	0.600759i	$-0.205135\pi$
$431$	14.0938	+	8.13704i	0.678872	+	0.391947i	−0.120558	+	0.992706i	$0.538468\pi$
$432$		0			0
$433$			29.7766i			1.43097i	0.698626	+	0.715487i	$0.253795\pi$
$433$			29.7766i			1.43097i	−0.698626	+	0.715487i	$0.746205\pi$
$434$	11.6272	−	0.976700i	0.558125	−	0.0468831i
$435$		0			0
$436$	−2.72966	−	4.72792i	−0.130727	−	0.226426i
$437$	−3.83138	+	6.63615i	−0.183280	+	0.317450i
$438$		0			0
$439$	−23.1092	+	13.3421i	−1.10294	+	0.636785i	−0.936993	−	0.349349i	$-0.886403\pi$
$439$	−23.1092	+	13.3421i	−1.10294	+	0.636785i	−0.165951	+	0.986134i	$0.553070\pi$
$440$	1.29171			0.0615796
$441$		0			0
$442$	4.18756			0.199182
$443$	−22.9075	+	13.2256i	−1.08837	+	0.628369i	−0.933141	−	0.359510i	$-0.882944\pi$
$443$	−22.9075	+	13.2256i	−1.08837	+	0.628369i	−0.155225	+	0.987879i	$0.549610\pi$
$444$		0			0
$445$	−2.32379	+	4.02493i	−0.110158	+	0.190800i
$446$	4.69051	+	8.12420i	0.222102	+	0.384692i
$447$		0			0
$448$	−2.63647	+	0.221466i	−0.124561	+	0.0104633i
$449$		−	5.34120i		−	0.252067i	−0.992026	−	0.126033i	$-0.959775\pi$
$449$		−	5.34120i		−	0.252067i	0.992026	−	0.126033i	$-0.0402247\pi$
$450$		0			0
$451$	−1.87615	−	1.08319i	−0.0883442	−	0.0510056i
$452$	−10.1905	−	5.88350i	−0.479322	−	0.276737i
$453$		0			0
$454$		−	2.52601i		−	0.118551i
$455$	−10.6284	+	7.38740i	−0.498268	+	0.346327i
$456$		0			0
$457$	−10.9652	−	18.9923i	−0.512931	−	0.888423i	−0.999888	−	0.0149966i	$-0.995226\pi$
$457$	−10.9652	−	18.9923i	−0.512931	−	0.888423i	0.486956	−	0.873426i	$-0.338107\pi$
$458$	−7.34235	+	12.7173i	−0.343085	+	0.594241i
$459$		0			0
$460$	3.66563	−	2.11635i	0.170911	−	0.0986753i
$461$	24.3961			1.13624			0.568119	−	0.822946i	$-0.307671\pi$
$461$	24.3961			1.13624			0.568119	+	0.822946i	$0.307671\pi$
$462$		0			0
$463$	13.1999			0.613451			0.306726	−	0.951798i	$-0.400767\pi$
$463$	13.1999			0.613451			0.306726	+	0.951798i	$0.400767\pi$
$464$	−2.41230	+	1.39274i	−0.111988	+	0.0646564i
$465$		0			0
$466$	−3.86655	+	6.69706i	−0.179114	+	0.310235i
$467$	0.185827	+	0.321862i	0.00859906	+	0.0148940i	0.870293	−	0.492535i	$-0.163929\pi$
$467$	0.185827	+	0.321862i	0.00859906	+	0.0148940i	−0.861694	+	0.507429i	$0.830596\pi$
$468$		0			0
$469$	13.0583	−	27.7524i	0.602978	−	1.28149i
$470$		−	4.50472i		−	0.207787i
$471$		0			0
$472$	−3.99523	−	2.30664i	−0.183895	−	0.106172i
$473$	7.31698	+	4.22446i	0.336435	+	0.194241i
$474$		0			0
$475$		−	7.79060i		−	0.357457i
$476$	1.66956	+	2.40204i	0.0765243	+	0.110097i
$477$		0			0
$478$	10.3955	+	18.0056i	0.475481	+	0.823557i
$479$	19.2663	−	33.3702i	0.880298	−	1.52472i	0.0292891	−	0.999571i	$-0.490676\pi$
$479$	19.2663	−	33.3702i	0.880298	−	1.52472i	0.851009	−	0.525151i	$-0.175991\pi$
$480$		0			0
$481$	−20.3192	+	11.7313i	−0.926474	+	0.534900i
$482$	−15.4348			−0.703037
$483$		0			0
$484$	1.00000			0.0454545
$485$	17.7735	−	10.2615i	0.807053	−	0.465952i
$486$		0			0
$487$	9.39671	−	16.2756i	0.425806	−	0.737517i	−0.570690	−	0.821166i	$-0.693324\pi$
$487$	9.39671	−	16.2756i	0.425806	−	0.737517i	0.996495	+	0.0836488i	$0.0266574\pi$
$488$	−0.924776	−	1.60176i	−0.0418626	−	0.0725082i
$489$		0			0
$490$	−8.47503	−	3.15128i	−0.382863	−	0.142360i
$491$		−	31.4249i		−	1.41819i	−0.705115	−	0.709093i	$-0.749105\pi$
$491$		−	31.4249i		−	1.41819i	0.705115	−	0.709093i	$-0.250895\pi$
$492$		0			0
$493$	2.66716	+	1.53988i	0.120123	+	0.0693529i
$494$	−7.67018	−	4.42838i	−0.345098	−	0.199242i
$495$		0			0
$496$		−	4.41016i		−	0.198022i
$497$	−0.435170	−	5.18052i	−0.0195200	−	0.232378i
$498$		0			0
$499$	−7.87992	−	13.6484i	−0.352754	−	0.610987i	0.633977	−	0.773352i	$-0.281421\pi$
$499$	−7.87992	−	13.6484i	−0.352754	−	0.610987i	−0.986731	+	0.162365i	$0.948088\pi$
$500$	−5.38092	+	9.32003i	−0.240642	+	0.416804i
$501$		0			0
$502$	4.42016	−	2.55198i	0.197281	−	0.113900i
$503$	−23.5500			−1.05004			−0.525021	−	0.851089i	$-0.675942\pi$
$503$	−23.5500			−1.05004			−0.525021	+	0.851089i	$0.675942\pi$
$504$		0			0
$505$	3.68855			0.164138
$506$	2.83782	−	1.63842i	0.126156	−	0.0728364i
$507$		0			0
$508$	6.63400	−	11.4904i	0.294336	−	0.509805i
$509$	1.81262	+	3.13955i	0.0803429	+	0.139158i	0.903397	−	0.428805i	$-0.141065\pi$
$509$	1.81262	+	3.13955i	0.0803429	+	0.139158i	−0.823054	+	0.567963i	$0.807732\pi$
$510$		0			0
$511$	13.7811	+	6.48443i	0.609642	+	0.286854i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	24.1702	+	13.9547i	1.06610	+	0.615515i
$515$	3.14687	+	1.81685i	0.138668	+	0.0800599i
$516$		0			0
$517$		−	3.48742i		−	0.153377i
$518$	−14.8304	−	6.97813i	−0.651610	−	0.306602i
$519$		0			0
$520$	2.44611	+	4.23679i	0.107269	+	0.185796i
$521$	17.9563	−	31.1012i	0.786680	−	1.36257i	−0.141310	−	0.989965i	$-0.545131\pi$
$521$	17.9563	−	31.1012i	0.786680	−	1.36257i	0.927990	−	0.372605i	$-0.121535\pi$
$522$		0			0
$523$	15.2893	−	8.82730i	0.668556	−	0.385991i	−0.126973	−	0.991906i	$-0.540526\pi$
$523$	15.2893	−	8.82730i	0.668556	−	0.385991i	0.795529	+	0.605915i	$0.207193\pi$
$524$	17.7695			0.776264
$525$		0			0
$526$	17.8588			0.778680
$527$	−4.22282	+	2.43805i	−0.183949	+	0.106203i
$528$		0			0
$529$	−6.13119	+	10.6195i	−0.266574	+	0.461719i
$530$	1.51355	+	2.62154i	0.0657443	+	0.113872i
$531$		0			0
$532$	−0.517891	−	6.16529i	−0.0224534	−	0.267299i
$533$		−	8.20501i		−	0.355398i
$534$		0			0
$535$	9.62133	+	5.55488i	0.415966	+	0.240158i
$536$	−10.0395	−	5.79630i	−0.433640	−	0.250362i
$537$		0			0
$538$		−	21.6083i		−	0.931601i
$539$	−6.56111	−	2.43963i	−0.282607	−	0.105082i
$540$		0			0
$541$	−10.2783	−	17.8026i	−0.441900	−	0.765393i	0.555931	−	0.831229i	$-0.312362\pi$
$541$	−10.2783	−	17.8026i	−0.441900	−	0.765393i	−0.997830	+	0.0658357i	$0.979029\pi$
$542$	5.41989	−	9.38753i	0.232804	−	0.403229i
$543$		0			0
$544$	0.957521	−	0.552825i	0.0410534	−	0.0237022i
$545$	−7.05184			−0.302068
$546$		0			0
$547$	7.83053			0.334809			0.167405	−	0.985888i	$-0.446461\pi$
$547$	7.83053			0.334809			0.167405	+	0.985888i	$0.446461\pi$
$548$	−6.74719	+	3.89549i	−0.288226	+	0.166407i
$549$		0			0
$550$	−1.66575	+	2.88516i	−0.0710278	+	0.123024i
$551$	−3.25688	−	5.64109i	−0.138748	−	0.240318i
$552$		0			0
$553$	7.52853	+	10.8315i	0.320146	+	0.460601i
$554$			3.85240i			0.163673i
$555$		0			0
$556$	−0.296663	−	0.171279i	−0.0125813	−	0.00726383i
$557$	−35.4548	−	20.4698i	−1.50227	−	0.867334i	−0.999997	−	0.00262279i	$-0.999165\pi$
$557$	−35.4548	−	20.4698i	−1.50227	−	0.867334i	−0.502270	−	0.864711i	$-0.667502\pi$
$558$		0			0
$559$			31.9996i			1.35344i
$560$	−1.45503	+	3.09232i	−0.0614861	+	0.130674i
$561$		0			0
$562$	−7.79204	−	13.4962i	−0.328688	−	0.569303i
$563$	21.7611	−	37.6913i	0.917120	−	1.58850i	0.113352	−	0.993555i	$-0.463841\pi$
$563$	21.7611	−	37.6913i	0.917120	−	1.58850i	0.803768	−	0.594943i	$-0.202825\pi$
$564$		0			0
$565$	−13.1632	+	7.59975i	−0.553778	+	0.319724i
$566$	6.93326			0.291426
$567$		0			0
$568$	−1.96495			−0.0824474
$569$	−33.1929	+	19.1639i	−1.39152	+	0.803393i	−0.993483	−	0.113977i	$-0.963641\pi$
$569$	−33.1929	+	19.1639i	−1.39152	+	0.803393i	−0.398035	+	0.917370i	$0.630308\pi$
$570$		0			0
$571$	8.89437	−	15.4055i	0.372218	−	0.644700i	−0.617689	−	0.786423i	$-0.711931\pi$
$571$	8.89437	−	15.4055i	0.372218	−	0.644700i	0.989906	+	0.141723i	$0.0452641\pi$
$572$	1.89371	+	3.28000i	0.0791799	+	0.137144i
$573$		0			0
$574$	4.70650	−	3.27130i	0.196446	−	0.136542i
$575$			10.9168i			0.455260i
$576$		0			0
$577$	30.1606	+	17.4132i	1.25560	+	0.724921i	0.972216	−	0.234085i	$-0.0752094\pi$
$577$	30.1606	+	17.4132i	1.25560	+	0.724921i	0.283385	+	0.959006i	$0.408543\pi$
$578$	13.6637	+	7.88877i	0.568337	+	0.328130i
$579$		0			0
$580$			3.59802i			0.149400i
$581$	−23.6157	+	1.98375i	−0.979745	+	0.0822997i
$582$		0			0
$583$	1.17174	+	2.02952i	0.0485286	+	0.0840541i
$584$	2.87829	−	4.98535i	0.119105	−	0.206295i
$585$		0			0
$586$	−5.64834	+	3.26107i	−0.233331	+	0.134714i
$587$	−31.2081			−1.28809			−0.644047	−	0.764986i	$-0.722746\pi$
$587$	−31.2081			−1.28809			−0.644047	+	0.764986i	$0.722746\pi$
$588$		0			0
$589$	10.3130			0.424941
$590$	−5.16065	+	2.97951i	−0.212461	+	0.122664i
$591$		0			0
$592$	−3.09743	+	5.36491i	−0.127304	+	0.220497i
$593$	−20.7651	−	35.9663i	−0.852722	−	1.47696i	−0.878743	−	0.477296i	$-0.841617\pi$
$593$	−20.7651	−	35.9663i	−0.852722	−	1.47696i	0.0260210	−	0.999661i	$-0.491716\pi$
$594$		0			0
$595$	3.76533	−	0.316292i	0.154364	−	0.0129667i
$596$		−	8.27158i		−	0.338817i
$597$		0			0
$598$	10.7480	+	6.20536i	0.439518	+	0.253756i
$599$	−18.8698	−	10.8945i	−0.770999	−	0.445136i	0.0622321	−	0.998062i	$-0.480178\pi$
$599$	−18.8698	−	10.8945i	−0.770999	−	0.445136i	−0.833231	+	0.552925i	$0.813511\pi$
$600$		0			0
$601$			10.3578i			0.422502i	0.977432	+	0.211251i	$0.0677538\pi$
$601$			10.3578i			0.422502i	−0.977432	+	0.211251i	$0.932246\pi$
$602$	−18.3554	+	12.7581i	−0.748110	+	0.519981i
$603$		0			0
$604$	−0.880131	−	1.52443i	−0.0358120	−	0.0620283i
$605$	0.645853	−	1.11865i	0.0262576	−	0.0454796i
$606$		0			0
$607$	5.22532	−	3.01684i	0.212089	−	0.122450i	−0.390193	−	0.920733i	$-0.627592\pi$
$607$	5.22532	−	3.01684i	0.212089	−	0.122450i	0.602282	+	0.798283i	$0.294258\pi$
$608$	−2.33847			−0.0948375
$609$		0			0
$610$	−2.38908			−0.0967308
$611$	11.4387	−	6.60416i	0.462762	−	0.267176i
$612$		0			0
$613$	−8.89665	+	15.4094i	−0.359332	+	0.622382i	−0.987849	−	0.155414i	$-0.950329\pi$
$613$	−8.89665	+	15.4094i	−0.359332	+	0.622382i	0.628517	+	0.777796i	$0.283662\pi$
$614$	−7.26513	−	12.5836i	−0.293197	−	0.507832i
$615$		0			0
$616$	−1.12644	+	2.39398i	−0.0453855	+	0.0964562i
$617$			13.5580i			0.545825i	0.962039	+	0.272913i	$0.0879870\pi$
$617$			13.5580i			0.545825i	−0.962039	+	0.272913i	$0.912013\pi$
$618$		0			0
$619$	−8.51244	−	4.91466i	−0.342144	−	0.197537i	0.319076	−	0.947729i	$-0.396628\pi$
$619$	−8.51244	−	4.91466i	−0.342144	−	0.197537i	−0.661220	+	0.750192i	$0.729961\pi$
$620$	−4.93342	−	2.84831i	−0.198131	−	0.114391i
$621$		0			0
$622$		−	18.9681i		−	0.760551i
$623$	−5.43312	−	7.81675i	−0.217673	−	0.313172i
$624$		0			0
$625$	−1.37818	−	2.38707i	−0.0551271	−	0.0954829i
$626$	−8.39451	+	14.5397i	−0.335512	+	0.581124i
$627$		0			0
$628$	9.80424	−	5.66048i	0.391232	−	0.225878i
$629$	6.84936			0.273102
$630$		0			0
$631$	−25.4402			−1.01276			−0.506380	−	0.862310i	$-0.669017\pi$
$631$	−25.4402			−1.01276			−0.506380	+	0.862310i	$0.669017\pi$
$632$	4.31774	−	2.49285i	0.171750	−	0.0991601i
$633$		0			0
$634$	−10.3530	+	17.9319i	−0.411169	+	0.712166i
$635$	−8.56917	−	14.8422i	−0.340057	−	0.588996i
$636$		0			0
$637$	−4.42285	−	26.1404i	−0.175240	−	1.03572i
$638$			2.78548i			0.110278i
$639$		0			0
$640$	1.11865	+	0.645853i	0.0442185	+	0.0255296i
$641$	−26.1275	−	15.0847i	−1.03198	−	0.595811i	−0.114425	−	0.993432i	$-0.536503\pi$
$641$	−26.1275	−	15.0847i	−1.03198	−	0.595811i	−0.917550	+	0.397621i	$0.869836\pi$
$642$		0			0
$643$		−	13.4197i		−	0.529223i	−0.964355	−	0.264611i	$-0.914756\pi$
$643$		−	13.4197i		−	0.529223i	0.964355	−	0.264611i	$-0.0852436\pi$
$644$	0.725707	+	8.63925i	0.0285968	+	0.340434i
$645$		0			0
$646$	1.29276	+	2.23913i	0.0508631	+	0.0880976i
$647$	−22.5290	+	39.0213i	−0.885706	+	1.53409i	−0.0408034	+	0.999167i	$0.512992\pi$
$647$	−22.5290	+	39.0213i	−0.885706	+	1.53409i	−0.844902	+	0.534920i	$0.820342\pi$
$648$		0			0
$649$	−3.99523	+	2.30664i	−0.156826	+	0.0905437i
$650$	−12.6178			−0.494909
$651$		0			0
$652$	22.3838			0.876618
$653$	13.0148	−	7.51411i	0.509309	−	0.294050i	−0.223240	−	0.974763i	$-0.571663\pi$
$653$	13.0148	−	7.51411i	0.509309	−	0.294050i	0.732550	+	0.680714i	$0.238330\pi$
$654$		0			0
$655$	11.4765	−	19.8779i	0.448423	−	0.776692i
$656$	−1.08319	−	1.87615i	−0.0422916	−	0.0732512i
$657$		0			0
$658$	8.34882	+	3.92836i	0.325471	+	0.153144i
$659$		−	1.57672i		−	0.0614203i	−0.999528	−	0.0307101i	$-0.990223\pi$
$659$		−	1.57672i		−	0.0614203i	0.999528	−	0.0307101i	$-0.00977687\pi$
$660$		0			0
$661$	−6.12555	−	3.53659i	−0.238256	−	0.137557i	0.376119	−	0.926571i	$-0.377258\pi$
$661$	−6.12555	−	3.53659i	−0.238256	−	0.137557i	−0.614375	+	0.789014i	$0.710592\pi$
$662$	−27.6327	−	15.9538i	−1.07398	−	0.620060i
$663$		0			0
$664$			8.95734i			0.347612i
$665$	−7.23129	−	3.40253i	−0.280417	−	0.131945i
$666$		0			0
$667$	4.56378	+	7.90469i	0.176710	+	0.306071i
$668$	12.1120	−	20.9785i	0.468626	−	0.811684i
$669$		0			0
$670$	−12.9681	+	7.48711i	−0.501000	+	0.289252i
$671$	−1.84955			−0.0714011
$672$		0			0
$673$	−6.98516			−0.269258			−0.134629	−	0.990896i	$-0.542984\pi$
$673$	−6.98516			−0.269258			−0.134629	+	0.990896i	$0.542984\pi$
$674$	−23.4967	+	13.5658i	−0.905059	+	0.522536i
$675$		0			0
$676$	−0.672261	+	1.16439i	−0.0258562	+	0.0447842i
$677$	−9.55841	−	16.5557i	−0.367360	−	0.636286i	0.621792	−	0.783182i	$-0.286405\pi$
$677$	−9.55841	−	16.5557i	−0.367360	−	0.636286i	−0.989152	+	0.146897i	$0.953072\pi$
$678$		0			0
$679$	3.51873	+	41.8891i	0.135036	+	1.60756i
$680$		−	1.42817i		−	0.0547680i
$681$		0			0
$682$	−3.81931	−	2.20508i	−0.146249	−	0.0844368i
$683$	38.9560	+	22.4912i	1.49061	+	0.860604i	0.999942	−	0.0107436i	$-0.00341986\pi$
$683$	38.9560	+	22.4912i	1.49061	+	0.860604i	0.490667	+	0.871347i	$0.336753\pi$
$684$		0			0
$685$			10.0637i			0.384513i
$686$	13.2311	−	12.9591i	0.505166	−	0.494780i
$687$		0			0
$688$	4.22446	+	7.31698i	0.161056	+	0.278957i
$689$	−4.43788	+	7.68663i	−0.169070	+	0.292837i
$690$		0			0
$691$	−14.0640	+	8.11985i	−0.535020	+	0.308894i	−0.743058	−	0.669227i	$-0.766625\pi$
$691$	−14.0640	+	8.11985i	−0.535020	+	0.308894i	0.208038	+	0.978121i	$0.433292\pi$
$692$	15.9005			0.604446
$693$		0			0
$694$	33.0839			1.25585
$695$	−0.383202	+	0.221242i	−0.0145357	+	0.00839217i
$696$		0			0
$697$	−1.19763	+	2.07436i	−0.0453636	+	0.0785720i
$698$	16.8711	+	29.2217i	0.638582	+	1.10606i
$699$		0			0
$700$	−5.03065	−	7.23772i	−0.190141	−	0.273560i
$701$		−	7.83700i		−	0.295999i	−0.988987	−	0.148000i	$-0.952717\pi$
$701$		−	7.83700i		−	0.295999i	0.988987	−	0.148000i	$-0.0472834\pi$
$702$		0			0
$703$	−12.5457	−	7.24325i	−0.473169	−	0.273185i
$704$	0.866025	+	0.500000i	0.0326396	+	0.0188445i
$705$		0			0
$706$		−	21.6215i		−	0.813735i
$707$	−3.21662	+	6.83617i	−0.120973	+	0.257101i
$708$		0			0
$709$	−0.595851	−	1.03204i	−0.0223776	−	0.0387592i	0.854620	−	0.519254i	$-0.173790\pi$
$709$	−0.595851	−	1.03204i	−0.0223776	−	0.0387592i	−0.876997	+	0.480495i	$0.840457\pi$
$710$	−1.26907	+	2.19809i	−0.0476273	+	0.0824929i
$711$		0			0
$712$	−3.11598	+	1.79901i	−0.116776	+	0.0674208i
$713$	−14.4513			−0.541207
$714$		0			0
$715$	4.89223			0.182959
$716$	7.64555	−	4.41416i	0.285728	−	0.164965i
$717$		0			0
$718$	3.04406	−	5.27247i	0.113603	−	0.196767i
$719$	12.6115	+	21.8438i	0.470330	+	0.814635i	0.999424	−	0.0339277i	$-0.0108016\pi$
$719$	12.6115	+	21.8438i	0.470330	+	0.814635i	−0.529094	+	0.848563i	$0.677468\pi$
$720$		0			0
$721$	−6.11150	+	4.24786i	−0.227604	+	0.158199i
$722$			13.5316i			0.503593i
$723$		0			0
$724$	17.9976	+	10.3909i	0.668877	+	0.386176i
$725$	−8.03656	−	4.63991i	−0.298471	−	0.172322i
$726$		0			0
$727$		−	28.1858i		−	1.04535i	−0.852531	−	0.522677i	$-0.824933\pi$
$727$		−	28.1858i		−	1.04535i	0.852531	−	0.522677i	$-0.175067\pi$
$728$	−9.98539	+	0.838784i	−0.370083	+	0.0310874i
$729$		0			0
$730$	−3.71791	−	6.43960i	−0.137606	−	0.238340i
$731$	4.67077	−	8.09002i	0.172755	−	0.299220i
$732$		0			0
$733$	−13.4432	+	7.76146i	−0.496538	+	0.286676i	−0.727283	−	0.686338i	$-0.759217\pi$
$733$	−13.4432	+	7.76146i	−0.496538	+	0.286676i	0.230745	+	0.973014i	$0.425884\pi$
$734$	−7.37647			−0.272270
$735$		0			0
$736$	3.27683			0.120786
$737$	−10.0395	+	5.79630i	−0.369809	+	0.213509i
$738$		0			0
$739$	17.6628	−	30.5929i	0.649738	−	1.12538i	−0.333447	−	0.942769i	$-0.608212\pi$
$739$	17.6628	−	30.5929i	0.649738	−	1.12538i	0.983185	−	0.182611i	$-0.0584548\pi$
$740$	4.00097	+	6.92989i	0.147079	+	0.254748i
$741$		0			0
$742$	−6.17852	+	0.519003i	−0.226821	+	0.0190532i
$743$		−	24.9417i		−	0.915023i	−0.889204	−	0.457511i	$-0.848741\pi$
$743$		−	24.9417i		−	0.915023i	0.889204	−	0.457511i	$-0.151259\pi$
$744$		0			0
$745$	−9.25301	−	5.34223i	−0.339004	−	0.195724i
$746$	−25.9855	−	15.0027i	−0.951397	−	0.549289i
$747$		0			0
$748$		−	1.10565i		−	0.0404266i
$749$	−18.6854	+	12.9875i	−0.682751	+	0.474553i
$750$		0			0
$751$	11.6303	+	20.1443i	0.424397	+	0.735078i	0.996364	−	0.0851993i	$-0.0271527\pi$
$751$	11.6303	+	20.1443i	0.424397	+	0.735078i	−0.571967	+	0.820277i	$0.693819\pi$
$752$	1.74371	−	3.02020i	0.0635866	−	0.110135i
$753$		0			0
$754$	−9.13638	+	5.27489i	−0.332727	+	0.192100i
$755$	−2.27374			−0.0827499
$756$		0			0
$757$	12.5404			0.455788			0.227894	−	0.973686i	$-0.426816\pi$
$757$	12.5404			0.455788			0.227894	+	0.973686i	$0.426816\pi$
$758$	23.2127	−	13.4019i	0.843124	−	0.486778i
$759$		0			0
$760$	−1.51031	+	2.61593i	−0.0547846	+	0.0948897i
$761$	8.53183	+	14.7776i	0.309279	+	0.535686i	0.978205	−	0.207643i	$-0.0665791\pi$
$761$	8.53183	+	14.7776i	0.309279	+	0.535686i	−0.668926	+	0.743329i	$0.733246\pi$
$762$		0			0
$763$	6.14959	−	13.0695i	0.222630	−	0.473148i
$764$			13.6444i			0.493636i
$765$		0			0
$766$	13.6610	+	7.88721i	0.493594	+	0.284976i
$767$	−15.1316	−	8.73622i	−0.546370	−	0.315447i
$768$		0			0
$769$		−	28.4374i		−	1.02548i	−0.858544	−	0.512740i	$-0.828630\pi$
$769$		−	28.4374i		−	1.02548i	0.858544	−	0.512740i	$-0.171370\pi$
$770$	1.95051	+	2.80625i	0.0702916	+	0.101130i
$771$		0			0
$772$	2.33050	+	4.03654i	0.0838764	+	0.145278i
$773$	8.37747	−	14.5102i	0.301317	−	0.521896i	−0.675118	−	0.737710i	$-0.735907\pi$
$773$	8.37747	−	14.5102i	0.301317	−	0.521896i	0.976434	+	0.215814i	$0.0692405\pi$
$774$		0			0
$775$	12.7240	−	7.34621i	0.457060	−	0.263884i
$776$	15.8884			0.570359
$777$		0			0
$778$	26.4270			0.947454
$779$	4.38731	−	2.53301i	0.157192	−	0.0907546i
$780$		0			0
$781$	−0.982475	+	1.70170i	−0.0351557	+	0.0608915i
$782$	−1.81151	−	3.13764i	−0.0647796	−	0.112202i
$783$		0			0
$784$	−4.46228	−	5.39334i	−0.159367	−	0.192619i
$785$		−	14.6234i		−	0.521930i
$786$		0			0
$787$	−20.7410	−	11.9748i	−0.739337	−	0.426856i	0.0824914	−	0.996592i	$-0.473712\pi$
$787$	−20.7410	−	11.9748i	−0.739337	−	0.426856i	−0.821828	+	0.569736i	$0.807046\pi$
$788$	−1.66283	−	0.960036i	−0.0592359	−	0.0341999i
$789$		0			0
$790$		−	6.44005i		−	0.229127i
$791$	−2.60599	−	31.0233i	−0.0926584	−	1.10306i
$792$		0			0
$793$	−3.50251	−	6.06653i	−0.124378	−	0.215429i
$794$	−2.76613	+	4.79107i	−0.0981662	+	0.170029i
$795$		0			0
$796$	5.47439	−	3.16064i	0.194034	−	0.112026i
$797$	−25.1833			−0.892037			−0.446018	−	0.895024i	$-0.647158\pi$
$797$	−25.1833			−0.892037			−0.446018	+	0.895024i	$0.647158\pi$
$798$		0			0
$799$	−3.85587			−0.136411
$800$	−2.88516	+	1.66575i	−0.102006	+	0.0588931i
$801$		0			0
$802$	−9.46667	+	16.3967i	−0.334280	+	0.578989i
$803$	−2.87829	−	4.98535i	−0.101573	−	0.175929i
$804$		0			0
$805$	10.1330	+	4.76787i	0.357141	+	0.168045i
$806$		−	16.7031i		−	0.588342i
$807$		0			0
$808$	2.47299	+	1.42778i	0.0869996	+	0.0502292i
$809$	20.9986	+	12.1236i	0.738273	+	0.426242i	0.821441	−	0.570294i	$-0.193171\pi$
$809$	20.9986	+	12.1236i	0.738273	+	0.426242i	−0.0831682	+	0.996536i	$0.526504\pi$
$810$		0			0
$811$		−	21.3904i		−	0.751119i	−0.926798	−	0.375560i	$-0.877451\pi$
$811$		−	21.3904i		−	0.751119i	0.926798	−	0.375560i	$-0.122549\pi$
$812$	−6.66839	−	3.13767i	−0.234015	−	0.110111i
$813$		0			0
$814$	3.09743	+	5.36491i	0.108565	+	0.188040i
$815$	14.4567	−	25.0397i	0.506395	−	0.877101i
$816$		0			0
$817$	−17.1105	+	9.87877i	−0.598621	+	0.345614i
$818$	−18.9750			−0.663446
$819$		0			0
$820$	−2.79833			−0.0977220
$821$	−28.3309	+	16.3568i	−0.988754	+	0.570858i	−0.904902	−	0.425621i	$-0.860056\pi$
$821$	−28.3309	+	16.3568i	−0.988754	+	0.570858i	−0.0838526	+	0.996478i	$0.526722\pi$
$822$		0			0
$823$	−20.1039	+	34.8210i	−0.700778	+	1.21378i	0.267416	+	0.963581i	$0.413830\pi$
$823$	−20.1039	+	34.8210i	−0.700778	+	1.21378i	−0.968194	+	0.250202i	$0.919503\pi$
$824$	1.40655	+	2.43622i	0.0489995	+	0.0848696i
$825$		0			0
$826$	−1.02169	−	12.1628i	−0.0355490	−	0.423197i
$827$			15.5399i			0.540374i	0.962808	+	0.270187i	$0.0870855\pi$
$827$			15.5399i			0.540374i	−0.962808	+	0.270187i	$0.912914\pi$
$828$		0			0
$829$	39.9830	+	23.0842i	1.38867	+	0.801747i	0.993165	−	0.116718i	$-0.0372374\pi$
$829$	39.9830	+	23.0842i	1.38867	+	0.801747i	0.395502	+	0.918465i	$0.370571\pi$
$830$	10.0201	+	5.78512i	0.347804	+	0.200805i
$831$		0			0
$832$			3.78742i			0.131305i
$833$	−2.69738	+	7.25430i	−0.0934586	+	0.251346i
$834$		0			0
$835$	−15.6451	−	27.0981i	−0.541421	−	0.937769i
$836$	−1.16923	+	2.02517i	−0.0404388	+	0.0700421i
$837$		0			0
$838$	22.3088	−	12.8800i	0.770645	−	0.444932i
$839$	10.6849			0.368882			0.184441	−	0.982844i	$-0.440953\pi$
$839$	10.6849			0.368882			0.184441	+	0.982844i	$0.440953\pi$
$840$		0			0
$841$	21.2411			0.732451
$842$	−9.50154	+	5.48571i	−0.327445	+	0.189050i
$843$		0			0
$844$	−6.47670	+	11.2180i	−0.222937	+	0.386138i
$845$	0.868363	+	1.50405i	0.0298726	+	0.0517409i
$846$		0			0
$847$	1.51003	+	2.17251i	0.0518852	+	0.0746484i
$848$			2.34349i			0.0804757i
$849$		0			0
$850$	3.18998	+	1.84174i	0.109415	+	0.0631710i
$851$	17.5799	+	10.1498i	0.602632	+	0.347930i
$852$		0			0
$853$			8.36124i			0.286283i	0.989702	+	0.143142i	$0.0457205\pi$
$853$			8.36124i			0.286283i	−0.989702	+	0.143142i	$0.954280\pi$
$854$	2.08340	−	4.42779i	0.0712926	−	0.151516i
$855$		0			0
$856$	4.30042	+	7.44855i	0.146985	+	0.254586i
$857$	−3.89205	+	6.74123i	−0.132950	+	0.230276i	−0.924812	−	0.380423i	$-0.875778\pi$
$857$	−3.89205	+	6.74123i	−0.132950	+	0.230276i	0.791863	+	0.610699i	$0.209112\pi$
$858$		0			0
$859$	−7.94215	+	4.58540i	−0.270983	+	0.156452i	−0.629334	−	0.777135i	$-0.716672\pi$
$859$	−7.94215	+	4.58540i	−0.270983	+	0.156452i	0.358351	+	0.933587i	$0.383339\pi$
$860$	10.9135			0.372148
$861$		0			0
$862$	16.2741			0.554297
$863$	−18.6773	+	10.7833i	−0.635781	+	0.367069i	−0.782988	−	0.622037i	$-0.786305\pi$
$863$	−18.6773	+	10.7833i	−0.635781	+	0.367069i	0.147206	+	0.989106i	$0.452972\pi$
$864$		0			0
$865$	10.2694	−	17.7871i	0.349169	−	0.604779i
$866$	14.8883	+	25.7873i	0.505926	+	0.876289i
$867$		0			0
$868$	9.58113	−	6.65946i	0.325205	−	0.226037i
$869$		−	4.98569i		−	0.169128i
$870$		0			0
$871$	−38.0237	−	21.9530i	−1.28838	−	0.743849i
$872$	−4.72792	−	2.72966i	−0.160107	−	0.0924381i
$873$		0			0
$874$			7.66277i			0.259197i
$875$	−28.3732	+	2.38338i	−0.959190	+	0.0805730i
$876$		0			0
$877$	−6.07291	−	10.5186i	−0.205068	−	0.355188i	0.745087	−	0.666968i	$-0.232408\pi$
$877$	−6.07291	−	10.5186i	−0.205068	−	0.355188i	−0.950154	+	0.311780i	$0.899075\pi$
$878$	−13.3421	+	23.1092i	−0.450275	+	0.779899i
$879$		0			0
$880$	1.11865	−	0.645853i	0.0377097	−	0.0217717i
$881$	38.4236			1.29452			0.647261	−	0.762268i	$-0.275914\pi$
$881$	38.4236			1.29452			0.647261	+	0.762268i	$0.275914\pi$
$882$		0			0
$883$	−31.9311			−1.07457			−0.537284	−	0.843401i	$-0.680550\pi$
$883$	−31.9311			−1.07457			−0.537284	+	0.843401i	$0.680550\pi$
$884$	3.62653	−	2.09378i	0.121973	−	0.0704214i
$885$		0			0
$886$	−13.2256	+	22.9075i	−0.444324	+	0.769591i
$887$	−10.5840	−	18.3320i	−0.355376	−	0.615529i	0.631807	−	0.775126i	$-0.282314\pi$
$887$	−10.5840	−	18.3320i	−0.355376	−	0.615529i	−0.987182	+	0.159598i	$0.948980\pi$
$888$		0			0
$889$	34.9806	−	2.93841i	1.17321	−	0.0985511i
$890$			4.64759i			0.155787i
$891$		0			0
$892$	8.12420	+	4.69051i	0.272018	+	0.157050i
$893$	7.06264	+	4.07761i	0.236342	+	0.136452i
$894$		0			0
$895$		−	11.4036i		−	0.381180i
$896$	−2.17251	+	1.51003i	−0.0725786	+	0.0504465i
$897$		0			0
$898$	−2.67060	−	4.62562i	−0.0891191	−	0.154359i
$899$	6.14221	−	10.6386i	0.204854	−	0.354818i
$900$		0			0
$901$	2.24394	−	1.29554i	0.0747564	−	0.0431606i
$902$	−2.16639			−0.0721328
$903$		0			0
$904$	−11.7670			−0.391365
$905$	23.2476	−	13.4220i	0.772778	−	0.446163i
$906$		0			0
$907$	18.6378	−	32.2816i	0.618857	−	1.07189i	−0.370837	−	0.928698i	$-0.620929\pi$
$907$	18.6378	−	32.2816i	0.618857	−	1.07189i	0.989695	−	0.143195i	$-0.0457375\pi$
$908$	−1.26300	−	2.18759i	−0.0419142	−	0.0725976i
$909$		0			0
$910$	−5.51079	+	11.7119i	−0.182681	+	0.388245i
$911$		−	19.8401i		−	0.657333i	−0.944446	−	0.328667i	$-0.893401\pi$
$911$		−	19.8401i		−	0.657333i	0.944446	−	0.328667i	$-0.106599\pi$
$912$		0			0
$913$	7.75729	+	4.47867i	0.256729	+	0.148222i
$914$	−18.9923	−	10.9652i	−0.628210	−	0.362697i
$915$		0			0
$916$			14.6847i			0.485196i
$917$	26.8324	+	38.6045i	0.886086	+	1.27483i
$918$		0			0
$919$	2.27797	+	3.94556i	0.0751434	+	0.130152i	0.901149	−	0.433510i	$-0.142725\pi$
$919$	2.27797	+	3.94556i	0.0751434	+	0.130152i	−0.826005	+	0.563662i	$0.809392\pi$
$920$	2.11635	−	3.66563i	0.0697740	−	0.120852i
$921$		0			0
$922$	21.1276	−	12.1980i	0.695801	−	0.401721i
$923$	−7.44208			−0.244959
$924$		0			0
$925$	−20.6382			−0.678579
$926$	11.4314	−	6.59995i	0.375661	−	0.216888i
$927$		0			0
$928$	−1.39274	+	2.41230i	−0.0457190	+	0.0791876i
$929$	−19.4761	−	33.7336i	−0.638991	−	1.10676i	−0.985655	−	0.168775i	$-0.946019\pi$
$929$	−19.4761	−	33.7336i	−0.638991	−	1.10676i	0.346664	−	0.937989i	$-0.387314\pi$
$930$		0			0
$931$	12.6122	−	10.4349i	0.413347	−	0.341990i
$932$			7.73309i			0.253306i
$933$		0			0
$934$	0.321862	+	0.185827i	0.0105317	+	0.00608046i
$935$	−1.23684	−	0.714087i	−0.0404488	−	0.0233532i
$936$		0			0
$937$		−	43.3356i		−	1.41571i	−0.706356	−	0.707856i	$-0.749662\pi$
$937$		−	43.3356i		−	1.41571i	0.706356	−	0.707856i	$-0.250338\pi$
$938$	−2.56737	−	30.5635i	−0.0838275	−	0.997934i
$939$		0			0
$940$	−2.25236	−	3.90120i	−0.0734639	−	0.127243i
$941$	−2.69512	+	4.66808i	−0.0878583	+	0.152175i	−0.906606	−	0.421979i	$-0.861336\pi$
$941$	−2.69512	+	4.66808i	−0.0878583	+	0.152175i	0.818747	+	0.574154i	$0.194669\pi$
$942$		0			0
$943$	−6.14781	+	3.54944i	−0.200200	+	0.115586i
$944$	−4.61329			−0.150150
$945$		0			0
$946$	8.44892			0.274698
$947$	−26.4568	+	15.2748i	−0.859731	+	0.496366i	−0.863922	−	0.503625i	$-0.831999\pi$
$947$	−26.4568	+	15.2748i	−0.859731	+	0.496366i	0.00419136	+	0.999991i	$0.498666\pi$
$948$		0			0
$949$	10.9013	−	18.8816i	0.353871	−	0.612922i
$950$	−3.89530	−	6.74686i	−0.126380	−	0.218897i
$951$		0			0
$952$	2.64690	+	1.24545i	0.0857867	+	0.0403651i
$953$		−	4.77744i		−	0.154756i	−0.997002	−	0.0773782i	$-0.975345\pi$
$953$		−	4.77744i		−	0.154756i	0.997002	−	0.0773782i	$-0.0246549\pi$
$954$		0			0
$955$	15.2633	+	8.81226i	0.493908	+	0.285158i
$956$	18.0056	+	10.3955i	0.582343	+	0.336216i
$957$		0			0
$958$		−	38.5325i		−	1.24493i
$959$	−18.6515	−	8.77606i	−0.602287	−	0.283394i
$960$		0			0
$961$	−5.77525	−	10.0030i	−0.186298	−	0.322678i
$962$	−11.7313	+	20.3192i	−0.378231	+	0.655116i
$963$		0			0
$964$	−13.3669	+	7.71741i	−0.430520	+	0.248561i
$965$	6.02063			0.193811
$966$		0			0
$967$	24.8175			0.798078			0.399039	−	0.916934i	$-0.369344\pi$
$967$	24.8175			0.798078			0.399039	+	0.916934i	$0.369344\pi$
$968$	0.866025	−	0.500000i	0.0278351	−	0.0160706i
$969$		0			0
$970$	10.2615	−	17.7735i	0.329478	−	0.570673i
$971$	5.15562	+	8.92980i	0.165452	+	0.286571i	0.936816	−	0.349824i	$-0.113758\pi$
$971$	5.15562	+	8.92980i	0.165452	+	0.286571i	−0.771364	+	0.636394i	$0.780425\pi$
$972$		0			0
$973$	−0.0758648	−	0.903141i	−0.00243211	−	0.0289534i
$974$		−	18.7934i		−	0.602180i
$975$		0			0
$976$	−1.60176	−	0.924776i	−0.0512710	−	0.0296013i
$977$	−6.68793	−	3.86128i	−0.213966	−	0.123533i	0.389187	−	0.921159i	$-0.372756\pi$
$977$	−6.68793	−	3.86128i	−0.213966	−	0.123533i	−0.603153	+	0.797625i	$0.706089\pi$
$978$		0			0
$979$			3.59802i			0.114993i
$980$	−8.91523	+	1.50842i	−0.284787	+	0.0481848i
$981$		0			0
$982$	−15.7125	−	27.2148i	−0.501405	−	0.868458i
$983$	−0.880590	+	1.52523i	−0.0280865	+	0.0486472i	−0.879727	−	0.475479i	$-0.842275\pi$
$983$	−0.880590	+	1.52523i	−0.0280865	+	0.0486472i	0.851641	+	0.524126i	$0.175608\pi$
$984$		0			0
$985$	−2.14789	+	1.24008i	−0.0684374	+	0.0395123i
$986$	3.07977			0.0980798
$987$		0			0
$988$	−8.85676			−0.281771
$989$	23.9765	−	13.8428i	0.762408	−	0.440177i
$990$		0			0
$991$	−22.1534	+	38.3708i	−0.703726	+	1.21889i	0.263423	+	0.964680i	$0.415148\pi$
$991$	−22.1534	+	38.3708i	−0.703726	+	1.21889i	−0.967149	+	0.254209i	$0.918185\pi$
$992$	−2.20508	−	3.81931i	−0.0700113	−	0.121263i
$993$		0			0
$994$	−2.96713	−	4.26888i	−0.0941116	−	0.135401i
$995$		−	8.16523i		−	0.258855i
$996$		0			0
$997$	−33.6252	−	19.4135i	−1.06492	−	0.614832i	−0.138131	−	0.990414i	$-0.544109\pi$
$997$	−33.6252	−	19.4135i	−1.06492	−	0.614832i	−0.926789	+	0.375582i	$0.877443\pi$
$998$	−13.6484	−	7.87992i	−0.432033	−	0.249434i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.r.d.1277.10	yes	24
3.2	odd	2	inner	1386.2.r.d.1277.3	yes	24
7.5	odd	6	inner	1386.2.r.d.89.3	✓	24
21.5	even	6	inner	1386.2.r.d.89.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.r.d.89.3	✓	24	7.5	odd	6	inner
1386.2.r.d.89.10	yes	24	21.5	even	6	inner
1386.2.r.d.1277.3	yes	24	3.2	odd	2	inner
1386.2.r.d.1277.10	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.645853 - 1.11865i) q^{5} +(2.63647 - 0.221466i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.645853 - 1.11865i) q^{5} +(2.63647 - 0.221466i) q^{7} -1.00000i q^{8} +(-1.11865 - 0.645853i) q^{10} +(-0.866025 - 0.500000i) q^{11} -3.78742i q^{13} +(2.17251 - 1.51003i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.552825 + 0.957521i) q^{17} +(2.02517 - 1.16923i) q^{19} -1.29171 q^{20} -1.00000 q^{22} +(-2.83782 + 1.63842i) q^{23} +(1.66575 - 2.88516i) q^{25} +(-1.89371 - 3.28000i) q^{26} +(1.12644 - 2.39398i) q^{28} -2.78548i q^{29} +(3.81931 + 2.20508i) q^{31} +(-0.866025 - 0.500000i) q^{32} +1.10565i q^{34} +(-1.95051 - 2.80625i) q^{35} +(-3.09743 - 5.36491i) q^{37} +(1.16923 - 2.02517i) q^{38} +(-1.11865 + 0.645853i) q^{40} +2.16639 q^{41} -8.44892 q^{43} +(-0.866025 + 0.500000i) q^{44} +(-1.63842 + 2.83782i) q^{46} +(1.74371 + 3.02020i) q^{47} +(6.90191 - 1.16778i) q^{49} -3.33150i q^{50} +(-3.28000 - 1.89371i) q^{52} +(-2.02952 - 1.17174i) q^{53} +1.29171i q^{55} +(-0.221466 - 2.63647i) q^{56} +(-1.39274 - 2.41230i) q^{58} +(2.30664 - 3.99523i) q^{59} +(1.60176 - 0.924776i) q^{61} +4.41016 q^{62} -1.00000 q^{64} +(-4.23679 + 2.44611i) q^{65} +(5.79630 - 10.0395i) q^{67} +(0.552825 + 0.957521i) q^{68} +(-3.09232 - 1.45503i) q^{70} -1.96495i q^{71} +(4.98535 + 2.87829i) q^{73} +(-5.36491 - 3.09743i) q^{74} -2.33847i q^{76} +(-2.39398 - 1.12644i) q^{77} +(2.49285 + 4.31774i) q^{79} +(-0.645853 + 1.11865i) q^{80} +(1.87615 - 1.08319i) q^{82} -8.95734 q^{83} +1.42817 q^{85} +(-7.31698 + 4.22446i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-1.79901 - 3.11598i) q^{89} +(-0.838784 - 9.98539i) q^{91} +3.27683i q^{92} +(3.02020 + 1.74371i) q^{94} +(-2.61593 - 1.51031i) q^{95} +15.8884i q^{97} +(5.39334 - 4.46228i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 + 8 * q^7	\( 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) \) 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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