LMFDB - Embedded newform 1386.2.k.t.991.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1386,2,Mod(793,1386)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1386.793"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1386, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,2,0,-2,-4,0,-2,-4,0,4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1386.991
Dual form			1386.2.k.t.793.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.292893 - 0.507306i) q^{5} +(1.62132 - 2.09077i) q^{7} -1.00000 q^{8} +(0.292893 - 0.507306i) q^{10} +(0.500000 - 0.866025i) q^{11} -3.82843 q^{13} +(2.62132 + 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.82843 - 3.16693i) q^{17} +(0.292893 + 0.507306i) q^{19} +0.585786 q^{20} +1.00000 q^{22} +(-3.12132 - 5.40629i) q^{23} +(2.32843 - 4.03295i) q^{25} +(-1.91421 - 3.31552i) q^{26} +(1.00000 + 2.44949i) q^{28} -2.65685 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +3.65685 q^{34} +(-1.53553 - 0.210133i) q^{35} +(4.70711 + 8.15295i) q^{37} +(-0.292893 + 0.507306i) q^{38} +(0.292893 + 0.507306i) q^{40} +5.41421 q^{41} -5.65685 q^{43} +(0.500000 + 0.866025i) q^{44} +(3.12132 - 5.40629i) q^{46} +(-5.24264 - 9.08052i) q^{47} +(-1.74264 - 6.77962i) q^{49} +4.65685 q^{50} +(1.91421 - 3.31552i) q^{52} +(3.94975 - 6.84116i) q^{53} -0.585786 q^{55} +(-1.62132 + 2.09077i) q^{56} +(-1.32843 - 2.30090i) q^{58} +(-2.79289 + 4.83743i) q^{59} +(-5.91421 - 10.2437i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.12132 + 1.94218i) q^{65} +(-1.37868 + 2.38794i) q^{67} +(1.82843 + 3.16693i) q^{68} +(-0.585786 - 1.43488i) q^{70} +11.0711 q^{71} +(4.70711 - 8.15295i) q^{73} +(-4.70711 + 8.15295i) q^{74} -0.585786 q^{76} +(-1.00000 - 2.44949i) q^{77} +(6.62132 + 11.4685i) q^{79} +(-0.292893 + 0.507306i) q^{80} +(2.70711 + 4.68885i) q^{82} +12.1421 q^{83} -2.14214 q^{85} +(-2.82843 - 4.89898i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(6.24264 + 10.8126i) q^{89} +(-6.20711 + 8.00436i) q^{91} +6.24264 q^{92} +(5.24264 - 9.08052i) q^{94} +(0.171573 - 0.297173i) q^{95} -3.82843 q^{97} +(5.00000 - 4.89898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} + 2 q^{14} - 2 q^{16} - 4 q^{17} + 4 q^{19} + 8 q^{20} + 4 q^{22} - 4 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 12 q^{29}+ \cdots + 20 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8 + 4 * q^10 + 2 * q^11 - 4 * q^13 + 2 * q^14 - 2 * q^16 - 4 * q^17 + 4 * q^19 + 8 * q^20 + 4 * q^22 - 4 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 12 * q^29 + 8 * q^31 + 2 * q^32 - 8 * q^34 + 8 * q^35 + 16 * q^37 - 4 * q^38 + 4 * q^40 + 16 * q^41 + 2 * q^44 + 4 * q^46 - 4 * q^47 + 10 * q^49 - 4 * q^50 + 2 * q^52 - 4 * q^53 - 8 * q^55 + 2 * q^56 + 6 * q^58 - 14 * q^59 - 18 * q^61 + 16 * q^62 + 4 * q^64 - 4 * q^65 - 14 * q^67 - 4 * q^68 - 8 * q^70 + 16 * q^71 + 16 * q^73 - 16 * q^74 - 8 * q^76 - 4 * q^77 + 18 * q^79 - 4 * q^80 + 8 * q^82 - 8 * q^83 + 48 * q^85 - 2 * q^88 + 8 * q^89 - 22 * q^91 + 8 * q^92 + 4 * q^94 + 12 * q^95 - 4 * q^97 + 20 * q^98

Character values

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

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.292893	−	0.507306i	−0.130986	−	0.226874i	0.793071	−	0.609129i	$-0.208481\pi$
$5$	−0.292893	−	0.507306i	−0.130986	−	0.226874i	−0.924057	+	0.382255i	$0.875148\pi$
$6$		0			0
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.292893	−	0.507306i	0.0926210	−	0.160424i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	−3.82843			−1.06181			−0.530907	−	0.847430i	$-0.678149\pi$
$13$	−3.82843			−1.06181			−0.530907	+	0.847430i	$0.678149\pi$
$14$	2.62132	+	0.358719i	0.700577	+	0.0958718i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.82843	−	3.16693i	0.443459	−	0.768093i	−0.554485	−	0.832194i	$-0.687085\pi$
$17$	1.82843	−	3.16693i	0.443459	−	0.768093i	0.997943	+	0.0641009i	$0.0204179\pi$
$18$		0			0
$19$	0.292893	+	0.507306i	0.0671943	+	0.116384i	0.897665	−	0.440678i	$-0.145262\pi$
$19$	0.292893	+	0.507306i	0.0671943	+	0.116384i	−0.830471	+	0.557062i	$0.811929\pi$
$20$	0.585786			0.130986
$21$		0			0
$22$	1.00000			0.213201
$23$	−3.12132	−	5.40629i	−0.650840	−	1.12729i	−0.982919	−	0.184037i	$-0.941083\pi$
$23$	−3.12132	−	5.40629i	−0.650840	−	1.12729i	0.332079	−	0.943252i	$-0.392250\pi$
$24$		0			0
$25$	2.32843	−	4.03295i	0.465685	−	0.806591i
$26$	−1.91421	−	3.31552i	−0.375408	−	0.650226i
$27$		0			0
$28$	1.00000	+	2.44949i	0.188982	+	0.462910i
$29$	−2.65685			−0.493365			−0.246683	−	0.969096i	$-0.579341\pi$
$29$	−2.65685			−0.493365			−0.246683	+	0.969096i	$0.579341\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.65685			0.627145
$35$	−1.53553	−	0.210133i	−0.259553	−	0.0355190i
$36$		0			0
$37$	4.70711	+	8.15295i	0.773844	+	1.34034i	0.935442	+	0.353480i	$0.115002\pi$
$37$	4.70711	+	8.15295i	0.773844	+	1.34034i	−0.161599	+	0.986857i	$0.551665\pi$
$38$	−0.292893	+	0.507306i	−0.0475136	+	0.0822959i
$39$		0			0
$40$	0.292893	+	0.507306i	0.0463105	+	0.0802121i
$41$	5.41421			0.845558			0.422779	−	0.906233i	$-0.361055\pi$
$41$	5.41421			0.845558			0.422779	+	0.906233i	$0.361055\pi$
$42$		0			0
$43$	−5.65685			−0.862662			−0.431331	−	0.902194i	$-0.641956\pi$
$43$	−5.65685			−0.862662			−0.431331	+	0.902194i	$0.641956\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$		0			0
$46$	3.12132	−	5.40629i	0.460214	−	0.797113i
$47$	−5.24264	−	9.08052i	−0.764718	−	1.32453i	−0.940396	−	0.340082i	$-0.889545\pi$
$47$	−5.24264	−	9.08052i	−0.764718	−	1.32453i	0.175678	−	0.984448i	$-0.443788\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	4.65685			0.658579
$51$		0			0
$52$	1.91421	−	3.31552i	0.265454	−	0.459779i
$53$	3.94975	−	6.84116i	0.542540	−	0.939706i	−0.456218	−	0.889868i	$-0.650796\pi$
$53$	3.94975	−	6.84116i	0.542540	−	0.939706i	0.998757	−	0.0498379i	$-0.0158705\pi$
$54$		0			0
$55$	−0.585786			−0.0789874
$56$	−1.62132	+	2.09077i	−0.216658	+	0.279391i
$57$		0			0
$58$	−1.32843	−	2.30090i	−0.174431	−	0.302123i
$59$	−2.79289	+	4.83743i	−0.363604	+	0.629780i	−0.988551	−	0.150887i	$-0.951787\pi$
$59$	−2.79289	+	4.83743i	−0.363604	+	0.629780i	0.624947	+	0.780667i	$0.285120\pi$
$60$		0			0
$61$	−5.91421	−	10.2437i	−0.757237	−	1.31157i	−0.944254	−	0.329217i	$-0.893215\pi$
$61$	−5.91421	−	10.2437i	−0.757237	−	1.31157i	0.187017	−	0.982357i	$-0.440118\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	1.12132	+	1.94218i	0.139083	+	0.240898i
$66$		0			0
$67$	−1.37868	+	2.38794i	−0.168433	+	0.291734i	−0.937869	−	0.346990i	$-0.887204\pi$
$67$	−1.37868	+	2.38794i	−0.168433	+	0.291734i	0.769436	+	0.638723i	$0.220537\pi$
$68$	1.82843	+	3.16693i	0.221729	+	0.384047i
$69$		0			0
$70$	−0.585786	−	1.43488i	−0.0700149	−	0.171501i
$71$	11.0711			1.31389			0.656947	−	0.753937i	$-0.271848\pi$
$71$	11.0711			1.31389			0.656947	+	0.753937i	$0.271848\pi$
$72$		0			0
$73$	4.70711	−	8.15295i	0.550925	−	0.954230i	−0.447283	−	0.894393i	$-0.647608\pi$
$73$	4.70711	−	8.15295i	0.550925	−	0.954230i	0.998208	−	0.0598379i	$-0.0190584\pi$
$74$	−4.70711	+	8.15295i	−0.547190	+	0.947761i
$75$		0			0
$76$	−0.585786			−0.0671943
$77$	−1.00000	−	2.44949i	−0.113961	−	0.279145i
$78$		0			0
$79$	6.62132	+	11.4685i	0.744957	+	1.29030i	0.950215	+	0.311595i	$0.100863\pi$
$79$	6.62132	+	11.4685i	0.744957	+	1.29030i	−0.205258	+	0.978708i	$0.565803\pi$
$80$	−0.292893	+	0.507306i	−0.0327465	+	0.0567185i
$81$		0			0
$82$	2.70711	+	4.68885i	0.298950	+	0.517796i
$83$	12.1421			1.33277			0.666386	−	0.745607i	$-0.267840\pi$
$83$	12.1421			1.33277			0.666386	+	0.745607i	$0.267840\pi$
$84$		0			0
$85$	−2.14214			−0.232347
$86$	−2.82843	−	4.89898i	−0.304997	−	0.528271i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	6.24264	+	10.8126i	0.661719	+	1.14613i	0.980164	+	0.198189i	$0.0635060\pi$
$89$	6.24264	+	10.8126i	0.661719	+	1.14613i	−0.318445	+	0.947941i	$0.603161\pi$
$90$		0			0
$91$	−6.20711	+	8.00436i	−0.650682	+	0.839085i
$92$	6.24264			0.650840
$93$		0			0
$94$	5.24264	−	9.08052i	0.540737	−	0.936584i
$95$	0.171573	−	0.297173i	0.0176030	−	0.0304893i
$96$		0			0
$97$	−3.82843			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$97$	−3.82843			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$98$	5.00000	−	4.89898i	0.505076	−	0.494872i
$99$		0			0
$100$	2.32843	+	4.03295i	0.232843	+	0.403295i
$101$	3.08579	−	5.34474i	0.307047	−	0.531821i	−0.670668	−	0.741758i	$-0.733992\pi$
$101$	3.08579	−	5.34474i	0.307047	−	0.531821i	0.977715	+	0.209936i	$0.0673257\pi$
$102$		0			0
$103$	−6.70711	−	11.6170i	−0.660871	−	1.14466i	−0.980387	−	0.197081i	$-0.936854\pi$
$103$	−6.70711	−	11.6170i	−0.660871	−	1.14466i	0.319516	−	0.947581i	$-0.396480\pi$
$104$	3.82843			0.375408
$105$		0			0
$106$	7.89949			0.767267
$107$	−1.53553	−	2.65962i	−0.148446	−	0.257115i	0.782207	−	0.623018i	$-0.214094\pi$
$107$	−1.53553	−	2.65962i	−0.148446	−	0.257115i	−0.930653	+	0.365903i	$0.880760\pi$
$108$		0			0
$109$	−8.24264	+	14.2767i	−0.789502	+	1.36746i	0.136771	+	0.990603i	$0.456328\pi$
$109$	−8.24264	+	14.2767i	−0.789502	+	1.36746i	−0.926272	+	0.376854i	$0.877006\pi$
$110$	−0.292893	−	0.507306i	−0.0279263	−	0.0483697i
$111$		0			0
$112$	−2.62132	−	0.358719i	−0.247691	−	0.0338958i
$113$	8.17157			0.768717			0.384358	−	0.923184i	$-0.374423\pi$
$113$	8.17157			0.768717			0.384358	+	0.923184i	$0.374423\pi$
$114$		0			0
$115$	−1.82843	+	3.16693i	−0.170502	+	0.295318i
$116$	1.32843	−	2.30090i	0.123341	−	0.213634i
$117$		0			0
$118$	−5.58579			−0.514213
$119$	−3.65685	−	8.95743i	−0.335223	−	0.821126i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	5.91421	−	10.2437i	0.535448	−	0.927423i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−5.65685			−0.505964
$126$		0			0
$127$	15.7279			1.39563			0.697814	−	0.716279i	$-0.254156\pi$
$127$	15.7279			1.39563			0.697814	+	0.716279i	$0.254156\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.12132	+	1.94218i	−0.0983463	+	0.170341i
$131$	−0.292893	−	0.507306i	−0.0255902	−	0.0443235i	0.852947	−	0.521998i	$-0.174813\pi$
$131$	−0.292893	−	0.507306i	−0.0255902	−	0.0443235i	−0.878537	+	0.477674i	$0.841480\pi$
$132$		0			0
$133$	1.53553	+	0.210133i	0.133148	+	0.0182208i
$134$	−2.75736			−0.238200
$135$		0			0
$136$	−1.82843	+	3.16693i	−0.156786	+	0.271562i
$137$	−8.32843	+	14.4253i	−0.711546	+	1.23243i	0.252731	+	0.967537i	$0.418671\pi$
$137$	−8.32843	+	14.4253i	−0.711546	+	1.23243i	−0.964277	+	0.264897i	$0.914662\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	0.949747	−	1.22474i	0.0802683	−	0.103510i
$141$		0			0
$142$	5.53553	+	9.58783i	0.464532	+	0.804592i
$143$	−1.91421	+	3.31552i	−0.160075	+	0.277257i
$144$		0			0
$145$	0.778175	+	1.34784i	0.0646239	+	0.111932i
$146$	9.41421			0.779126
$147$		0			0
$148$	−9.41421			−0.773844
$149$	8.82843	+	15.2913i	0.723253	+	1.25271i	0.959689	+	0.281064i	$0.0906873\pi$
$149$	8.82843	+	15.2913i	0.723253	+	1.25271i	−0.236436	+	0.971647i	$0.575979\pi$
$150$		0			0
$151$	7.86396	−	13.6208i	0.639960	−	1.10844i	−0.345481	−	0.938426i	$-0.612284\pi$
$151$	7.86396	−	13.6208i	0.639960	−	1.10844i	0.985441	−	0.170018i	$-0.0543825\pi$
$152$	−0.292893	−	0.507306i	−0.0237568	−	0.0411479i
$153$		0			0
$154$	1.62132	−	2.09077i	0.130650	−	0.168479i
$155$	−2.34315			−0.188206
$156$		0			0
$157$	−8.82843	+	15.2913i	−0.704585	+	1.22038i	0.262256	+	0.964998i	$0.415534\pi$
$157$	−8.82843	+	15.2913i	−0.704585	+	1.22038i	−0.966841	+	0.255379i	$0.917800\pi$
$158$	−6.62132	+	11.4685i	−0.526764	+	0.912382i
$159$		0			0
$160$	−0.585786			−0.0463105
$161$	−16.3640	−	2.23936i	−1.28966	−	0.176486i
$162$		0			0
$163$	−4.86396	−	8.42463i	−0.380975	−	0.659868i	0.610227	−	0.792227i	$-0.291078\pi$
$163$	−4.86396	−	8.42463i	−0.380975	−	0.659868i	−0.991202	+	0.132359i	$0.957745\pi$
$164$	−2.70711	+	4.68885i	−0.211390	+	0.366137i
$165$		0			0
$166$	6.07107	+	10.5154i	0.471206	+	0.816153i
$167$	−13.7279			−1.06230			−0.531149	−	0.847278i	$-0.678240\pi$
$167$	−13.7279			−1.06230			−0.531149	+	0.847278i	$0.678240\pi$
$168$		0			0
$169$	1.65685			0.127450
$170$	−1.07107	−	1.85514i	−0.0821472	−	0.142283i
$171$		0			0
$172$	2.82843	−	4.89898i	0.215666	−	0.373544i
$173$	−4.91421	−	8.51167i	−0.373621	−	0.647130i	0.616499	−	0.787356i	$-0.288551\pi$
$173$	−4.91421	−	8.51167i	−0.373621	−	0.647130i	−0.990120	+	0.140226i	$0.955217\pi$
$174$		0			0
$175$	−4.65685	−	11.4069i	−0.352025	−	0.862282i
$176$	−1.00000			−0.0753778
$177$		0			0
$178$	−6.24264	+	10.8126i	−0.467906	+	0.810436i
$179$	0.449747	−	0.778985i	0.0336157	−	0.0582241i	−0.848728	−	0.528829i	$-0.822631\pi$
$179$	0.449747	−	0.778985i	0.0336157	−	0.0582241i	0.882344	+	0.470605i	$0.155964\pi$
$180$		0			0
$181$	−7.65685			−0.569129			−0.284565	−	0.958657i	$-0.591849\pi$
$181$	−7.65685			−0.569129			−0.284565	+	0.958657i	$0.591849\pi$
$182$	−10.0355	−	1.37333i	−0.743883	−	0.101798i
$183$		0			0
$184$	3.12132	+	5.40629i	0.230107	+	0.398557i
$185$	2.75736	−	4.77589i	0.202725	−	0.351130i
$186$		0			0
$187$	−1.82843	−	3.16693i	−0.133708	−	0.231589i
$188$	10.4853			0.764718
$189$		0			0
$190$	0.343146			0.0248944
$191$	−3.58579	−	6.21076i	−0.259458	−	0.449395i	0.706639	−	0.707575i	$-0.250211\pi$
$191$	−3.58579	−	6.21076i	−0.259458	−	0.449395i	−0.966097	+	0.258180i	$0.916877\pi$
$192$		0			0
$193$	−10.9497	+	18.9655i	−0.788180	+	1.36517i	0.138901	+	0.990306i	$0.455643\pi$
$193$	−10.9497	+	18.9655i	−0.788180	+	1.36517i	−0.927081	+	0.374862i	$0.877690\pi$
$194$	−1.91421	−	3.31552i	−0.137433	−	0.238040i
$195$		0			0
$196$	6.74264	+	1.88064i	0.481617	+	0.134331i
$197$	0.514719			0.0366722			0.0183361	−	0.999832i	$-0.494163\pi$
$197$	0.514719			0.0366722			0.0183361	+	0.999832i	$0.494163\pi$
$198$		0			0
$199$	−0.0502525	+	0.0870399i	−0.00356231	+	0.00617010i	−0.867801	−	0.496912i	$-0.834467\pi$
$199$	−0.0502525	+	0.0870399i	−0.00356231	+	0.00617010i	0.864239	+	0.503082i	$0.167801\pi$
$200$	−2.32843	+	4.03295i	−0.164645	+	0.285173i
$201$		0			0
$202$	6.17157			0.434230
$203$	−4.30761	+	5.55487i	−0.302335	+	0.389876i
$204$		0			0
$205$	−1.58579	−	2.74666i	−0.110756	−	0.191835i
$206$	6.70711	−	11.6170i	0.467306	−	0.809398i
$207$		0			0
$208$	1.91421	+	3.31552i	0.132727	+	0.229890i
$209$	0.585786			0.0405197
$210$		0			0
$211$	7.41421			0.510416			0.255208	−	0.966886i	$-0.417856\pi$
$211$	7.41421			0.510416			0.255208	+	0.966886i	$0.417856\pi$
$212$	3.94975	+	6.84116i	0.271270	+	0.469853i
$213$		0			0
$214$	1.53553	−	2.65962i	0.104967	−	0.181808i
$215$	1.65685	+	2.86976i	0.112997	+	0.195716i
$216$		0			0
$217$	−4.00000	−	9.79796i	−0.271538	−	0.665129i
$218$	−16.4853			−1.11652
$219$		0			0
$220$	0.292893	−	0.507306i	0.0197469	−	0.0342026i
$221$	−7.00000	+	12.1244i	−0.470871	+	0.815572i
$222$		0			0
$223$	8.58579			0.574947			0.287473	−	0.957789i	$-0.407185\pi$
$223$	8.58579			0.574947			0.287473	+	0.957789i	$0.407185\pi$
$224$	−1.00000	−	2.44949i	−0.0668153	−	0.163663i
$225$		0			0
$226$	4.08579	+	7.07679i	0.271782	+	0.470741i
$227$	−14.4142	+	24.9662i	−0.956705	+	1.65706i	−0.226288	+	0.974061i	$0.572659\pi$
$227$	−14.4142	+	24.9662i	−0.956705	+	1.65706i	−0.730417	+	0.683001i	$0.760674\pi$
$228$		0			0
$229$	−11.6569	−	20.1903i	−0.770307	−	1.33421i	−0.937395	−	0.348268i	$-0.886770\pi$
$229$	−11.6569	−	20.1903i	−0.770307	−	1.33421i	0.167088	−	0.985942i	$-0.446564\pi$
$230$	−3.65685			−0.241126
$231$		0			0
$232$	2.65685			0.174431
$233$	0.707107	+	1.22474i	0.0463241	+	0.0802357i	0.888258	−	0.459345i	$-0.151916\pi$
$233$	0.707107	+	1.22474i	0.0463241	+	0.0802357i	−0.841934	+	0.539581i	$0.818583\pi$
$234$		0			0
$235$	−3.07107	+	5.31925i	−0.200334	+	0.346989i
$236$	−2.79289	−	4.83743i	−0.181802	−	0.314890i
$237$		0			0
$238$	5.92893	−	7.64564i	0.384316	−	0.495593i
$239$	−20.2132			−1.30748			−0.653742	−	0.756718i	$-0.726802\pi$
$239$	−20.2132			−1.30748			−0.653742	+	0.756718i	$0.726802\pi$
$240$		0			0
$241$	−6.12132	+	10.6024i	−0.394309	+	0.682963i	−0.993013	−	0.118007i	$-0.962349\pi$
$241$	−6.12132	+	10.6024i	−0.394309	+	0.682963i	0.598704	+	0.800971i	$0.295683\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$		0			0
$244$	11.8284			0.757237
$245$	−2.92893	+	2.86976i	−0.187123	+	0.183342i
$246$		0			0
$247$	−1.12132	−	1.94218i	−0.0713479	−	0.123578i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$		0			0
$250$	−2.82843	−	4.89898i	−0.178885	−	0.309839i
$251$	26.1421			1.65008			0.825038	−	0.565077i	$-0.191153\pi$
$251$	26.1421			1.65008			0.825038	+	0.565077i	$0.191153\pi$
$252$		0			0
$253$	−6.24264			−0.392471
$254$	7.86396	+	13.6208i	0.493429	+	0.854644i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.5711	−	21.7737i	−0.784162	−	1.35821i	−0.929499	−	0.368826i	$-0.879760\pi$
$257$	−12.5711	−	21.7737i	−0.784162	−	1.35821i	0.145337	−	0.989382i	$-0.453573\pi$
$258$		0			0
$259$	24.6777	+	3.37706i	1.53340	+	0.209840i
$260$	−2.24264			−0.139083
$261$		0			0
$262$	0.292893	−	0.507306i	0.0180950	−	0.0313415i
$263$	−8.52082	+	14.7585i	−0.525416	+	0.910047i	0.474146	+	0.880446i	$0.342757\pi$
$263$	−8.52082	+	14.7585i	−0.525416	+	0.910047i	−0.999562	+	0.0296008i	$0.990576\pi$
$264$		0			0
$265$	−4.62742			−0.284260
$266$	0.585786	+	1.43488i	0.0359169	+	0.0879780i
$267$		0			0
$268$	−1.37868	−	2.38794i	−0.0842163	−	0.145867i
$269$	1.17157	−	2.02922i	0.0714321	−	0.123724i	−0.828097	−	0.560585i	$-0.810576\pi$
$269$	1.17157	−	2.02922i	0.0714321	−	0.123724i	0.899529	+	0.436861i	$0.143910\pi$
$270$		0			0
$271$	−2.27817	−	3.94591i	−0.138389	−	0.239697i	0.788498	−	0.615038i	$-0.210859\pi$
$271$	−2.27817	−	3.94591i	−0.138389	−	0.239697i	−0.926887	+	0.375340i	$0.877526\pi$
$272$	−3.65685			−0.221729
$273$		0			0
$274$	−16.6569			−1.00628
$275$	−2.32843	−	4.03295i	−0.140409	−	0.243196i
$276$		0			0
$277$	−0.914214	+	1.58346i	−0.0549298	+	0.0951412i	−0.892183	−	0.451675i	$-0.850827\pi$
$277$	−0.914214	+	1.58346i	−0.0549298	+	0.0951412i	0.837253	+	0.546816i	$0.184160\pi$
$278$		0			0
$279$		0			0
$280$	1.53553	+	0.210133i	0.0917657	+	0.0125578i
$281$	−8.72792			−0.520664			−0.260332	−	0.965519i	$-0.583832\pi$
$281$	−8.72792			−0.520664			−0.260332	+	0.965519i	$0.583832\pi$
$282$		0			0
$283$	11.7071	−	20.2773i	0.695915	−	1.20536i	−0.273956	−	0.961742i	$-0.588332\pi$
$283$	11.7071	−	20.2773i	0.695915	−	1.20536i	0.969871	−	0.243618i	$-0.0783344\pi$
$284$	−5.53553	+	9.58783i	−0.328474	+	0.568933i
$285$		0			0
$286$	−3.82843			−0.226380
$287$	8.77817	−	11.3199i	0.518159	−	0.668191i
$288$		0			0
$289$	1.81371	+	3.14144i	0.106689	+	0.184790i
$290$	−0.778175	+	1.34784i	−0.0456960	+	0.0791478i
$291$		0			0
$292$	4.70711	+	8.15295i	0.275463	+	0.477115i
$293$	10.8284			0.632603			0.316302	−	0.948659i	$-0.397559\pi$
$293$	10.8284			0.632603			0.316302	+	0.948659i	$0.397559\pi$
$294$		0			0
$295$	3.27208			0.190508
$296$	−4.70711	−	8.15295i	−0.273595	−	0.473880i
$297$		0			0
$298$	−8.82843	+	15.2913i	−0.511417	+	0.885800i
$299$	11.9497	+	20.6976i	0.691072	+	1.19697i
$300$		0			0
$301$	−9.17157	+	11.8272i	−0.528641	+	0.681707i
$302$	15.7279			0.905040
$303$		0			0
$304$	0.292893	−	0.507306i	0.0167986	−	0.0290960i
$305$	−3.46447	+	6.00063i	−0.198375	+	0.343595i
$306$		0			0
$307$	9.89949			0.564994			0.282497	−	0.959268i	$-0.408837\pi$
$307$	9.89949			0.564994			0.282497	+	0.959268i	$0.408837\pi$
$308$	2.62132	+	0.358719i	0.149364	+	0.0204399i
$309$		0			0
$310$	−1.17157	−	2.02922i	−0.0665409	−	0.115252i
$311$	8.36396	−	14.4868i	0.474277	−	0.821471i	−0.525289	−	0.850924i	$-0.676043\pi$
$311$	8.36396	−	14.4868i	0.474277	−	0.821471i	0.999566	+	0.0294522i	$0.00937629\pi$
$312$		0			0
$313$	10.3284	+	17.8894i	0.583797	+	1.01117i	0.995024	+	0.0996335i	$0.0317670\pi$
$313$	10.3284	+	17.8894i	0.583797	+	1.01117i	−0.411227	+	0.911533i	$0.634900\pi$
$314$	−17.6569			−0.996434
$315$		0			0
$316$	−13.2426			−0.744957
$317$	4.34315	+	7.52255i	0.243935	+	0.422508i	0.961832	−	0.273642i	$-0.0882282\pi$
$317$	4.34315	+	7.52255i	0.243935	+	0.422508i	−0.717896	+	0.696150i	$0.754895\pi$
$318$		0			0
$319$	−1.32843	+	2.30090i	−0.0743776	+	0.128826i
$320$	−0.292893	−	0.507306i	−0.0163732	−	0.0283593i
$321$		0			0
$322$	−6.24264	−	15.2913i	−0.347889	−	0.852150i
$323$	2.14214			0.119192
$324$		0			0
$325$	−8.91421	+	15.4399i	−0.494472	+	0.856450i
$326$	4.86396	−	8.42463i	0.269390	−	0.466597i
$327$		0			0
$328$	−5.41421			−0.298950
$329$	−27.4853	−	3.76127i	−1.51531	−	0.207366i
$330$		0			0
$331$	12.0355	+	20.8462i	0.661533	+	1.14581i	0.980213	+	0.197946i	$0.0634271\pi$
$331$	12.0355	+	20.8462i	0.661533	+	1.14581i	−0.318680	+	0.947862i	$0.603240\pi$
$332$	−6.07107	+	10.5154i	−0.333193	+	0.577107i
$333$		0			0
$334$	−6.86396	−	11.8887i	−0.375579	−	0.650522i
$335$	1.61522			0.0882491
$336$		0			0
$337$	−28.2426			−1.53847			−0.769237	−	0.638963i	$-0.779364\pi$
$337$	−28.2426			−1.53847			−0.769237	+	0.638963i	$0.779364\pi$
$338$	0.828427	+	1.43488i	0.0450605	+	0.0780471i
$339$		0			0
$340$	1.07107	−	1.85514i	0.0580868	−	0.100609i
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	5.65685			0.304997
$345$		0			0
$346$	4.91421	−	8.51167i	0.264190	−	0.457590i
$347$	8.70711	−	15.0812i	0.467422	−	0.809599i	−0.531885	−	0.846816i	$-0.678516\pi$
$347$	8.70711	−	15.0812i	0.467422	−	0.809599i	0.999307	+	0.0372179i	$0.0118495\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	7.55025	−	9.73641i	0.403578	−	0.520433i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−1.34315	+	2.32640i	−0.0714884	+	0.123822i	−0.899554	−	0.436810i	$-0.856108\pi$
$353$	−1.34315	+	2.32640i	−0.0714884	+	0.123822i	0.828065	+	0.560632i	$0.189442\pi$
$354$		0			0
$355$	−3.24264	−	5.61642i	−0.172101	−	0.298089i
$356$	−12.4853			−0.661719
$357$		0			0
$358$	0.899495			0.0475398
$359$	9.62132	+	16.6646i	0.507794	+	0.879525i	0.999959	+	0.00902308i	$0.00287218\pi$
$359$	9.62132	+	16.6646i	0.507794	+	0.879525i	−0.492165	+	0.870502i	$0.663794\pi$
$360$		0			0
$361$	9.32843	−	16.1573i	0.490970	−	0.850385i
$362$	−3.82843	−	6.63103i	−0.201218	−	0.348519i
$363$		0			0
$364$	−3.82843	−	9.37769i	−0.200664	−	0.491525i
$365$	−5.51472			−0.288654
$366$		0			0
$367$	5.36396	−	9.29065i	0.279996	−	0.484968i	−0.691387	−	0.722485i	$-0.743000\pi$
$367$	5.36396	−	9.29065i	0.279996	−	0.484968i	0.971384	+	0.237516i	$0.0763334\pi$
$368$	−3.12132	+	5.40629i	−0.162710	+	0.281822i
$369$		0			0
$370$	5.51472			0.286697
$371$	−7.89949	−	19.3497i	−0.410121	−	1.00459i
$372$		0			0
$373$	9.98528	+	17.2950i	0.517018	+	0.895502i	0.999805	+	0.0197638i	$0.00629142\pi$
$373$	9.98528	+	17.2950i	0.517018	+	0.895502i	−0.482786	+	0.875738i	$0.660375\pi$
$374$	1.82843	−	3.16693i	0.0945457	−	0.163758i
$375$		0			0
$376$	5.24264	+	9.08052i	0.270369	+	0.468292i
$377$	10.1716			0.523863
$378$		0			0
$379$	27.8701			1.43159			0.715794	−	0.698311i	$-0.246065\pi$
$379$	27.8701			1.43159			0.715794	+	0.698311i	$0.246065\pi$
$380$	0.171573	+	0.297173i	0.00880150	+	0.0152447i
$381$		0			0
$382$	3.58579	−	6.21076i	0.183465	−	0.317770i
$383$	−3.19239	−	5.52938i	−0.163123	−	0.282538i	0.772864	−	0.634572i	$-0.218824\pi$
$383$	−3.19239	−	5.52938i	−0.163123	−	0.282538i	−0.935987	+	0.352034i	$0.885490\pi$
$384$		0			0
$385$	−0.949747	+	1.22474i	−0.0484036	+	0.0624188i
$386$	−21.8995			−1.11465
$387$		0			0
$388$	1.91421	−	3.31552i	0.0971795	−	0.168320i
$389$	−11.3640	+	19.6830i	−0.576176	+	0.997966i	0.419737	+	0.907646i	$0.362122\pi$
$389$	−11.3640	+	19.6830i	−0.576176	+	0.997966i	−0.995913	+	0.0903199i	$0.971211\pi$
$390$		0			0
$391$	−22.8284			−1.15448
$392$	1.74264	+	6.77962i	0.0880166	+	0.342422i
$393$		0			0
$394$	0.257359	+	0.445759i	0.0129656	+	0.0224570i
$395$	3.87868	−	6.71807i	0.195158	−	0.338023i
$396$		0			0
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	−0.998125	−	0.0612128i	$-0.980503\pi$
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	0.446051	−	0.895008i	$-0.352830\pi$
$398$	−0.100505			−0.00503786
$399$		0			0
$400$	−4.65685			−0.232843
$401$	9.15685	+	15.8601i	0.457271	+	0.792017i	0.998816	−	0.0486549i	$-0.0154934\pi$
$401$	9.15685	+	15.8601i	0.457271	+	0.792017i	−0.541544	+	0.840672i	$0.682160\pi$
$402$		0			0
$403$	−7.65685	+	13.2621i	−0.381415	+	0.660630i
$404$	3.08579	+	5.34474i	0.153524	+	0.265911i
$405$		0			0
$406$	−6.96447	−	0.953065i	−0.345641	−	0.0472998i
$407$	9.41421			0.466645
$408$		0			0
$409$	−1.36396	+	2.36245i	−0.0674435	+	0.116816i	−0.897775	−	0.440454i	$-0.854818\pi$
$409$	−1.36396	+	2.36245i	−0.0674435	+	0.116816i	0.830332	+	0.557269i	$0.188151\pi$
$410$	1.58579	−	2.74666i	0.0783164	−	0.135648i
$411$		0			0
$412$	13.4142			0.660871
$413$	5.58579	+	13.6823i	0.274859	+	0.673263i
$414$		0			0
$415$	−3.55635	−	6.15978i	−0.174574	−	0.302372i
$416$	−1.91421	+	3.31552i	−0.0938520	+	0.162557i
$417$		0			0
$418$	0.292893	+	0.507306i	0.0143259	+	0.0248131i
$419$	26.1421			1.27713			0.638563	−	0.769569i	$-0.279529\pi$
$419$	26.1421			1.27713			0.638563	+	0.769569i	$0.279529\pi$
$420$		0			0
$421$	0.686292			0.0334478			0.0167239	−	0.999860i	$-0.494676\pi$
$421$	0.686292			0.0334478			0.0167239	+	0.999860i	$0.494676\pi$
$422$	3.70711	+	6.42090i	0.180459	+	0.312564i
$423$		0			0
$424$	−3.94975	+	6.84116i	−0.191817	+	0.332236i
$425$	−8.51472	−	14.7479i	−0.413025	−	0.715379i
$426$		0			0
$427$	−31.0061	−	4.24309i	−1.50049	−	0.205337i
$428$	3.07107			0.148446
$429$		0			0
$430$	−1.65685	+	2.86976i	−0.0799006	+	0.138392i
$431$	−8.79289	+	15.2297i	−0.423539	+	0.733591i	−0.996283	−	0.0861437i	$-0.972546\pi$
$431$	−8.79289	+	15.2297i	−0.423539	+	0.733591i	0.572744	+	0.819734i	$0.305879\pi$
$432$		0			0
$433$	26.1421			1.25631			0.628155	−	0.778088i	$-0.283810\pi$
$433$	26.1421			1.25631			0.628155	+	0.778088i	$0.283810\pi$
$434$	6.48528	−	8.36308i	0.311303	−	0.401441i
$435$		0			0
$436$	−8.24264	−	14.2767i	−0.394751	−	0.683729i
$437$	1.82843	−	3.16693i	0.0874655	−	0.151495i
$438$		0			0
$439$	13.6924	+	23.7159i	0.653502	+	1.13190i	0.982267	+	0.187487i	$0.0600342\pi$
$439$	13.6924	+	23.7159i	0.653502	+	1.13190i	−0.328765	+	0.944412i	$0.606632\pi$
$440$	0.585786			0.0279263
$441$		0			0
$442$	−14.0000			−0.665912
$443$	6.31371	+	10.9357i	0.299973	+	0.519569i	0.976130	−	0.217189i	$-0.0696889\pi$
$443$	6.31371	+	10.9357i	0.299973	+	0.519569i	−0.676156	+	0.736758i	$0.736356\pi$
$444$		0			0
$445$	3.65685	−	6.33386i	0.173352	−	0.300254i
$446$	4.29289	+	7.43551i	0.203274	+	0.352082i
$447$		0			0
$448$	1.62132	−	2.09077i	0.0766002	−	0.0987796i
$449$	−22.3431			−1.05444			−0.527219	−	0.849729i	$-0.676765\pi$
$449$	−22.3431			−1.05444			−0.527219	+	0.849729i	$0.676765\pi$
$450$		0			0
$451$	2.70711	−	4.68885i	0.127473	−	0.220789i
$452$	−4.08579	+	7.07679i	−0.192179	+	0.332864i
$453$		0			0
$454$	−28.8284			−1.35299
$455$	5.87868	+	0.804479i	0.275597	+	0.0377146i
$456$		0			0
$457$	5.82843	+	10.0951i	0.272642	+	0.472230i	0.969538	−	0.244943i	$-0.0787691\pi$
$457$	5.82843	+	10.0951i	0.272642	+	0.472230i	−0.696895	+	0.717173i	$0.745436\pi$
$458$	11.6569	−	20.1903i	0.544689	−	0.943429i
$459$		0			0
$460$	−1.82843	−	3.16693i	−0.0852509	−	0.147659i
$461$	8.31371			0.387208			0.193604	−	0.981080i	$-0.437982\pi$
$461$	8.31371			0.387208			0.193604	+	0.981080i	$0.437982\pi$
$462$		0			0
$463$	12.8284			0.596188			0.298094	−	0.954537i	$-0.403649\pi$
$463$	12.8284			0.596188			0.298094	+	0.954537i	$0.403649\pi$
$464$	1.32843	+	2.30090i	0.0616707	+	0.106817i
$465$		0			0
$466$	−0.707107	+	1.22474i	−0.0327561	+	0.0567352i
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	−0.927999	−	0.372584i	$-0.878472\pi$
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	0.141332	−	0.989962i	$-0.454861\pi$
$468$		0			0
$469$	2.75736	+	6.75412i	0.127323	+	0.311876i
$470$	−6.14214			−0.283316
$471$		0			0
$472$	2.79289	−	4.83743i	0.128553	−	0.222661i
$473$	−2.82843	+	4.89898i	−0.130051	+	0.225255i
$474$		0			0
$475$	2.72792			0.125166
$476$	9.58579	+	1.31178i	0.439364	+	0.0601256i
$477$		0			0
$478$	−10.1066	−	17.5051i	−0.462265	−	0.800667i
$479$	−5.96447	+	10.3308i	−0.272523	+	0.472024i	−0.969507	−	0.245062i	$-0.921192\pi$
$479$	−5.96447	+	10.3308i	−0.272523	+	0.472024i	0.696984	+	0.717087i	$0.254525\pi$
$480$		0			0
$481$	−18.0208	−	31.2130i	−0.821678	−	1.42319i
$482$	−12.2426			−0.557637
$483$		0			0
$484$	1.00000			0.0454545
$485$	1.12132	+	1.94218i	0.0509165	+	0.0881900i
$486$		0			0
$487$	4.82843	−	8.36308i	0.218797	−	0.378967i	−0.735644	−	0.677369i	$-0.763120\pi$
$487$	4.82843	−	8.36308i	0.218797	−	0.378967i	0.954440	+	0.298402i	$0.0964534\pi$
$488$	5.91421	+	10.2437i	0.267724	+	0.463711i
$489$		0			0
$490$	−3.94975	−	1.10165i	−0.178431	−	0.0497676i
$491$	−19.1716			−0.865201			−0.432600	−	0.901586i	$-0.642404\pi$
$491$	−19.1716			−0.865201			−0.432600	+	0.901586i	$0.642404\pi$
$492$		0			0
$493$	−4.85786	+	8.41407i	−0.218787	+	0.378951i
$494$	1.12132	−	1.94218i	0.0504506	−	0.0873830i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	17.9497	−	23.1471i	0.805156	−	1.03829i
$498$		0			0
$499$	−11.0711	−	19.1757i	−0.495609	−	0.858420i	0.504378	−	0.863483i	$-0.331722\pi$
$499$	−11.0711	−	19.1757i	−0.495609	−	0.858420i	−0.999987	+	0.00506282i	$0.998388\pi$
$500$	2.82843	−	4.89898i	0.126491	−	0.219089i
$501$		0			0
$502$	13.0711	+	22.6398i	0.583390	+	1.01046i
$503$	−4.21320			−0.187857			−0.0939287	−	0.995579i	$-0.529943\pi$
$503$	−4.21320			−0.187857			−0.0939287	+	0.995579i	$0.529943\pi$
$504$		0			0
$505$	−3.61522			−0.160875
$506$	−3.12132	−	5.40629i	−0.138760	−	0.240339i
$507$		0			0
$508$	−7.86396	+	13.6208i	−0.348907	+	0.604324i
$509$	4.65685	+	8.06591i	0.206411	+	0.357515i	0.950582	−	0.310475i	$-0.100488\pi$
$509$	4.65685	+	8.06591i	0.206411	+	0.357515i	−0.744170	+	0.667990i	$0.767155\pi$
$510$		0			0
$511$	−9.41421	−	23.0600i	−0.416460	−	1.02012i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	12.5711	−	21.7737i	0.554486	−	0.960398i
$515$	−3.92893	+	6.80511i	−0.173129	+	0.299869i
$516$		0			0
$517$	−10.4853			−0.461142
$518$	9.41421	+	23.0600i	0.413637	+	1.01320i
$519$		0			0
$520$	−1.12132	−	1.94218i	−0.0491731	−	0.0851704i
$521$	−14.1421	+	24.4949i	−0.619578	+	1.07314i	0.369984	+	0.929038i	$0.379363\pi$
$521$	−14.1421	+	24.4949i	−0.619578	+	1.07314i	−0.989563	+	0.144103i	$0.953970\pi$
$522$		0			0
$523$	6.36396	+	11.0227i	0.278277	+	0.481989i	0.970957	−	0.239256i	$-0.0769035\pi$
$523$	6.36396	+	11.0227i	0.278277	+	0.481989i	−0.692680	+	0.721245i	$0.743570\pi$
$524$	0.585786			0.0255902
$525$		0			0
$526$	−17.0416			−0.743050
$527$	−7.31371	−	12.6677i	−0.318590	−	0.551814i
$528$		0			0
$529$	−7.98528	+	13.8309i	−0.347186	+	0.601344i
$530$	−2.31371	−	4.00746i	−0.100501	−	0.174073i
$531$		0			0
$532$	−0.949747	+	1.22474i	−0.0411768	+	0.0530994i
$533$	−20.7279			−0.897826
$534$		0			0
$535$	−0.899495	+	1.55797i	−0.0388886	+	0.0673570i
$536$	1.37868	−	2.38794i	0.0595499	−	0.103143i
$537$		0			0
$538$	2.34315			0.101020
$539$	−6.74264	−	1.88064i	−0.290426	−	0.0810048i
$540$		0			0
$541$	6.42893	+	11.1352i	0.276401	+	0.478741i	0.970488	−	0.241151i	$-0.0775248\pi$
$541$	6.42893	+	11.1352i	0.276401	+	0.478741i	−0.694086	+	0.719892i	$0.744191\pi$
$542$	2.27817	−	3.94591i	0.0978560	−	0.169492i
$543$		0			0
$544$	−1.82843	−	3.16693i	−0.0783932	−	0.135781i
$545$	9.65685			0.413654
$546$		0			0
$547$	34.8701			1.49094			0.745468	−	0.666541i	$-0.232226\pi$
$547$	34.8701			1.49094			0.745468	+	0.666541i	$0.232226\pi$
$548$	−8.32843	−	14.4253i	−0.355773	−	0.616217i
$549$		0			0
$550$	2.32843	−	4.03295i	0.0992845	−	0.171966i
$551$	−0.778175	−	1.34784i	−0.0331514	−	0.0574198i
$552$		0			0
$553$	34.7132	+	4.75039i	1.47616	+	0.202007i
$554$	−1.82843			−0.0776824
$555$		0			0
$556$		0			0
$557$	3.75736	−	6.50794i	0.159204	−	0.275750i	−0.775378	−	0.631498i	$-0.782440\pi$
$557$	3.75736	−	6.50794i	0.159204	−	0.275750i	0.934582	+	0.355748i	$0.115774\pi$
$558$		0			0
$559$	21.6569			0.915987
$560$	0.585786	+	1.43488i	0.0247540	+	0.0606347i
$561$		0			0
$562$	−4.36396	−	7.55860i	−0.184083	−	0.318840i
$563$	4.53553	−	7.85578i	0.191150	−	0.331081i	−0.754482	−	0.656321i	$-0.772112\pi$
$563$	4.53553	−	7.85578i	0.191150	−	0.331081i	0.945632	+	0.325240i	$0.105445\pi$
$564$		0			0
$565$	−2.39340	−	4.14549i	−0.100691	−	0.174402i
$566$	23.4142			0.984173
$567$		0			0
$568$	−11.0711			−0.464532
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	0.821054	−	0.570851i	$-0.193387\pi$
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	−0.904898	+	0.425628i	$0.860053\pi$
$570$		0			0
$571$	−13.1924	+	22.8499i	−0.552084	+	0.956238i	0.446040	+	0.895013i	$0.352834\pi$
$571$	−13.1924	+	22.8499i	−0.552084	+	0.956238i	−0.998124	+	0.0612248i	$0.980499\pi$
$572$	−1.91421	−	3.31552i	−0.0800373	−	0.138629i
$573$		0			0
$574$	14.1924	+	1.94218i	0.592379	+	0.0810652i
$575$	−29.0711			−1.21235
$576$		0			0
$577$	4.84315	−	8.38857i	0.201623	−	0.349221i	−0.747429	−	0.664342i	$-0.768712\pi$
$577$	4.84315	−	8.38857i	0.201623	−	0.349221i	0.949051	+	0.315121i	$0.102045\pi$
$578$	−1.81371	+	3.14144i	−0.0754403	+	0.130666i
$579$		0			0
$580$	−1.55635			−0.0646239
$581$	19.6863	−	25.3864i	0.816725	−	1.05321i
$582$		0			0
$583$	−3.94975	−	6.84116i	−0.163582	−	0.283332i
$584$	−4.70711	+	8.15295i	−0.194781	+	0.337371i
$585$		0			0
$586$	5.41421	+	9.37769i	0.223659	+	0.387389i
$587$	25.1005			1.03601			0.518004	−	0.855378i	$-0.326675\pi$
$587$	25.1005			1.03601			0.518004	+	0.855378i	$0.326675\pi$
$588$		0			0
$589$	2.34315			0.0965476
$590$	1.63604	+	2.83370i	0.0673547	+	0.116662i
$591$		0			0
$592$	4.70711	−	8.15295i	0.193461	−	0.335084i
$593$	11.8492	+	20.5235i	0.486590	+	0.842799i	0.999881	−	0.0154159i	$-0.00490721\pi$
$593$	11.8492	+	20.5235i	0.486590	+	0.842799i	−0.513291	+	0.858215i	$0.671574\pi$
$594$		0			0
$595$	−3.47309	+	4.47871i	−0.142383	+	0.183609i
$596$	−17.6569			−0.723253
$597$		0			0
$598$	−11.9497	+	20.6976i	−0.488662	+	0.846387i
$599$	21.3137	−	36.9164i	0.870855	−	1.50836i	0.00974040	−	0.999953i	$-0.496899\pi$
$599$	21.3137	−	36.9164i	0.870855	−	1.50836i	0.861114	−	0.508412i	$-0.169767\pi$
$600$		0			0
$601$	31.9411			1.30291			0.651453	−	0.758689i	$-0.274160\pi$
$601$	31.9411			1.30291			0.651453	+	0.758689i	$0.274160\pi$
$602$	−14.8284	−	2.02922i	−0.604362	−	0.0827050i
$603$		0			0
$604$	7.86396	+	13.6208i	0.319980	+	0.554222i
$605$	−0.292893	+	0.507306i	−0.0119078	+	0.0206249i
$606$		0			0
$607$	21.4853	+	37.2136i	0.872061	+	1.51045i	0.859861	+	0.510528i	$0.170550\pi$
$607$	21.4853	+	37.2136i	0.872061	+	1.51045i	0.0121994	+	0.999926i	$0.496117\pi$
$608$	0.585786			0.0237568
$609$		0			0
$610$	−6.92893			−0.280544
$611$	20.0711	+	34.7641i	0.811988	+	1.40641i
$612$		0			0
$613$	−14.3137	+	24.7921i	−0.578125	+	1.00134i	0.417569	+	0.908645i	$0.362882\pi$
$613$	−14.3137	+	24.7921i	−0.578125	+	1.00134i	−0.995694	+	0.0926971i	$0.970451\pi$
$614$	4.94975	+	8.57321i	0.199756	+	0.345987i
$615$		0			0
$616$	1.00000	+	2.44949i	0.0402911	+	0.0986928i
$617$	41.9706			1.68967			0.844836	−	0.535026i	$-0.179698\pi$
$617$	41.9706			1.68967			0.844836	+	0.535026i	$0.179698\pi$
$618$		0			0
$619$	10.9706	−	19.0016i	0.440944	−	0.763738i	−0.556816	−	0.830636i	$-0.687977\pi$
$619$	10.9706	−	19.0016i	0.440944	−	0.763738i	0.997760	+	0.0668984i	$0.0213104\pi$
$620$	1.17157	−	2.02922i	0.0470515	−	0.0814956i
$621$		0			0
$622$	16.7279			0.670729
$623$	32.7279	+	4.47871i	1.31122	+	0.179436i
$624$		0			0
$625$	−9.98528	−	17.2950i	−0.399411	−	0.691801i
$626$	−10.3284	+	17.8894i	−0.412807	+	0.715003i
$627$		0			0
$628$	−8.82843	−	15.2913i	−0.352293	−	0.610189i
$629$	34.4264			1.37267
$630$		0			0
$631$	23.2721			0.926447			0.463223	−	0.886242i	$-0.346693\pi$
$631$	23.2721			0.926447			0.463223	+	0.886242i	$0.346693\pi$
$632$	−6.62132	−	11.4685i	−0.263382	−	0.456191i
$633$		0			0
$634$	−4.34315	+	7.52255i	−0.172488	+	0.298759i
$635$	−4.60660	−	7.97887i	−0.182807	−	0.316632i
$636$		0			0
$637$	6.67157	+	25.9553i	0.264337	+	1.02839i
$638$	−2.65685			−0.105186
$639$		0			0
$640$	0.292893	−	0.507306i	0.0115776	−	0.0200530i
$641$	7.64214	−	13.2366i	0.301846	−	0.522813i	−0.674708	−	0.738085i	$-0.735730\pi$
$641$	7.64214	−	13.2366i	0.301846	−	0.522813i	0.976554	+	0.215272i	$0.0690638\pi$
$642$		0			0
$643$	1.58579			0.0625373			0.0312687	−	0.999511i	$-0.490045\pi$
$643$	1.58579			0.0625373			0.0312687	+	0.999511i	$0.490045\pi$
$644$	10.1213	−	13.0519i	0.398836	−	0.514318i
$645$		0			0
$646$	1.07107	+	1.85514i	0.0421406	+	0.0729897i
$647$	15.0919	−	26.1399i	0.593323	−	1.02767i	−0.400458	−	0.916315i	$-0.631149\pi$
$647$	15.0919	−	26.1399i	0.593323	−	1.02767i	0.993781	−	0.111351i	$-0.0355177\pi$
$648$		0			0
$649$	2.79289	+	4.83743i	0.109631	+	0.189886i
$650$	−17.8284			−0.699288
$651$		0			0
$652$	9.72792			0.380975
$653$	−9.19239	−	15.9217i	−0.359726	−	0.623064i	0.628189	−	0.778061i	$-0.283796\pi$
$653$	−9.19239	−	15.9217i	−0.359726	−	0.623064i	−0.987915	+	0.154997i	$0.950463\pi$
$654$		0			0
$655$	−0.171573	+	0.297173i	−0.00670391	+	0.0116115i
$656$	−2.70711	−	4.68885i	−0.105695	−	0.183069i
$657$		0			0
$658$	−10.4853	−	25.6836i	−0.408759	−	1.00125i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−9.48528	+	16.4290i	−0.368935	+	0.639014i	−0.989399	−	0.145221i	$-0.953611\pi$
$661$	−9.48528	+	16.4290i	−0.368935	+	0.639014i	0.620465	+	0.784234i	$0.286944\pi$
$662$	−12.0355	+	20.8462i	−0.467774	+	0.810209i
$663$		0			0
$664$	−12.1421			−0.471206
$665$	−0.343146	−	0.840532i	−0.0133066	−	0.0325944i
$666$		0			0
$667$	8.29289	+	14.3637i	0.321102	+	0.556165i
$668$	6.86396	−	11.8887i	0.265575	−	0.459989i
$669$		0			0
$670$	0.807612	+	1.39882i	0.0312008	+	0.0540413i
$671$	−11.8284			−0.456631
$672$		0			0
$673$	5.55635			0.214182			0.107091	−	0.994249i	$-0.465846\pi$
$673$	5.55635			0.214182			0.107091	+	0.994249i	$0.465846\pi$
$674$	−14.1213	−	24.4588i	−0.543933	−	0.942119i
$675$		0			0
$676$	−0.828427	+	1.43488i	−0.0318626	+	0.0551876i
$677$	−17.6569	−	30.5826i	−0.678608	−	1.17538i	−0.975400	−	0.220441i	$-0.929250\pi$
$677$	−17.6569	−	30.5826i	−0.678608	−	1.17538i	0.296792	−	0.954942i	$-0.404083\pi$
$678$		0			0
$679$	−6.20711	+	8.00436i	−0.238207	+	0.307179i
$680$	2.14214			0.0821472
$681$		0			0
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	6.79289	−	11.7656i	0.259923	−	0.450200i	−0.706298	−	0.707914i	$-0.749636\pi$
$683$	6.79289	−	11.7656i	0.259923	−	0.450200i	0.966221	+	0.257715i	$0.0829695\pi$
$684$		0			0
$685$	9.75736			0.372810
$686$	−2.13604	−	18.3967i	−0.0815543	−	0.702388i
$687$		0			0
$688$	2.82843	+	4.89898i	0.107833	+	0.186772i
$689$	−15.1213	+	26.1909i	−0.576076	+	0.997794i
$690$		0			0
$691$	−14.0355	−	24.3103i	−0.533937	−	0.924806i	−0.999214	−	0.0396407i	$-0.987379\pi$
$691$	−14.0355	−	24.3103i	−0.533937	−	0.924806i	0.465277	−	0.885165i	$-0.345955\pi$
$692$	9.82843			0.373621
$693$		0			0
$694$	17.4142			0.661035
$695$		0			0
$696$		0			0
$697$	9.89949	−	17.1464i	0.374970	−	0.649467i
$698$		0			0
$699$		0			0
$700$	12.2071	+	1.67050i	0.461385	+	0.0631391i
$701$	26.1127			0.986263			0.493132	−	0.869955i	$-0.335852\pi$
$701$	26.1127			0.986263			0.493132	+	0.869955i	$0.335852\pi$
$702$		0			0
$703$	−2.75736	+	4.77589i	−0.103996	+	0.180126i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	−2.68629			−0.101100
$707$	−6.17157	−	15.1172i	−0.232106	−	0.568541i
$708$		0			0
$709$	6.02082	+	10.4284i	0.226116	+	0.391645i	0.956654	−	0.291228i	$-0.0940637\pi$
$709$	6.02082	+	10.4284i	0.226116	+	0.391645i	−0.730537	+	0.682873i	$0.760730\pi$
$710$	3.24264	−	5.61642i	0.121694	−	0.210780i
$711$		0			0
$712$	−6.24264	−	10.8126i	−0.233953	−	0.405218i
$713$	−24.9706			−0.935155
$714$		0			0
$715$	2.24264			0.0838700
$716$	0.449747	+	0.778985i	0.0168079	+	0.0291121i
$717$		0			0
$718$	−9.62132	+	16.6646i	−0.359064	+	0.621918i
$719$	−0.757359	−	1.31178i	−0.0282447	−	0.0489213i	0.851558	−	0.524261i	$-0.175658\pi$
$719$	−0.757359	−	1.31178i	−0.0282447	−	0.0489213i	−0.879802	+	0.475340i	$0.842325\pi$
$720$		0			0
$721$	−35.1630	−	4.81194i	−1.30954	−	0.179206i
$722$	18.6569			0.694336
$723$		0			0
$724$	3.82843	−	6.63103i	0.142282	−	0.246440i
$725$	−6.18629	+	10.7150i	−0.229753	+	0.397944i
$726$		0			0
$727$	36.4264			1.35098			0.675490	−	0.737369i	$-0.263932\pi$
$727$	36.4264			1.35098			0.675490	+	0.737369i	$0.263932\pi$
$728$	6.20711	−	8.00436i	0.230051	−	0.296661i
$729$		0			0
$730$	−2.75736	−	4.77589i	−0.102054	−	0.176763i
$731$	−10.3431	+	17.9149i	−0.382555	+	0.662605i
$732$		0			0
$733$	6.50000	+	11.2583i	0.240083	+	0.415836i	0.960738	−	0.277458i	$-0.0894920\pi$
$733$	6.50000	+	11.2583i	0.240083	+	0.415836i	−0.720655	+	0.693294i	$0.756159\pi$
$734$	10.7279			0.395975
$735$		0			0
$736$	−6.24264			−0.230107
$737$	1.37868	+	2.38794i	0.0507843	+	0.0879610i
$738$		0			0
$739$	26.2132	−	45.4026i	0.964268	−	1.67016i	0.252700	−	0.967545i	$-0.418681\pi$
$739$	26.2132	−	45.4026i	0.964268	−	1.67016i	0.711568	−	0.702617i	$-0.247985\pi$
$740$	2.75736	+	4.77589i	0.101363	+	0.175565i
$741$		0			0
$742$	12.8076	−	16.5160i	0.470182	−	0.606323i
$743$	13.3137			0.488433			0.244216	−	0.969721i	$-0.421469\pi$
$743$	13.3137			0.488433			0.244216	+	0.969721i	$0.421469\pi$
$744$		0			0
$745$	5.17157	−	8.95743i	0.189472	−	0.328175i
$746$	−9.98528	+	17.2950i	−0.365587	+	0.633215i
$747$		0			0
$748$	3.65685			0.133708
$749$	−8.05025	−	1.10165i	−0.294150	−	0.0402535i
$750$		0			0
$751$	−22.8284	−	39.5400i	−0.833021	−	1.44283i	−0.895631	−	0.444797i	$-0.853276\pi$
$751$	−22.8284	−	39.5400i	−0.833021	−	1.44283i	0.0626103	−	0.998038i	$-0.480057\pi$
$752$	−5.24264	+	9.08052i	−0.191179	+	0.331132i
$753$		0			0
$754$	5.08579	+	8.80884i	0.185213	+	0.320799i
$755$	−9.21320			−0.335303
$756$		0			0
$757$	8.34315			0.303237			0.151618	−	0.988439i	$-0.451552\pi$
$757$	8.34315			0.303237			0.151618	+	0.988439i	$0.451552\pi$
$758$	13.9350	+	24.1362i	0.506143	+	0.876665i
$759$		0			0
$760$	−0.171573	+	0.297173i	−0.00622360	+	0.0107796i
$761$	15.4853	+	26.8213i	0.561341	+	0.972271i	0.997380	+	0.0723433i	$0.0230477\pi$
$761$	15.4853	+	26.8213i	0.561341	+	0.972271i	−0.436039	+	0.899928i	$0.643619\pi$
$762$		0			0
$763$	16.4853	+	40.3805i	0.596807	+	1.46187i
$764$	7.17157			0.259458
$765$		0			0
$766$	3.19239	−	5.52938i	0.115346	−	0.199785i
$767$	10.6924	−	18.5198i	0.386080	−	0.668710i
$768$		0			0
$769$	22.9706			0.828340			0.414170	−	0.910200i	$-0.364072\pi$
$769$	22.9706			0.828340			0.414170	+	0.910200i	$0.364072\pi$
$770$	−1.53553	−	0.210133i	−0.0553368	−	0.00757267i
$771$		0			0
$772$	−10.9497	−	18.9655i	−0.394090	−	0.682584i
$773$	−10.9706	+	19.0016i	−0.394584	+	0.683439i	−0.993048	−	0.117710i	$-0.962445\pi$
$773$	−10.9706	+	19.0016i	−0.394584	+	0.683439i	0.598464	+	0.801150i	$0.295778\pi$
$774$		0			0
$775$	−9.31371	−	16.1318i	−0.334558	−	0.579472i
$776$	3.82843			0.137433
$777$		0			0
$778$	−22.7279			−0.814835
$779$	1.58579	+	2.74666i	0.0568167	+	0.0984094i
$780$		0			0
$781$	5.53553	−	9.58783i	0.198077	−	0.343079i
$782$	−11.4142	−	19.7700i	−0.408171	−	0.706974i
$783$		0			0
$784$	−5.00000	+	4.89898i	−0.178571	+	0.174964i
$785$	10.3431			0.369163
$786$		0			0
$787$	−6.77817	+	11.7401i	−0.241616	+	0.418491i	−0.961175	−	0.275941i	$-0.911011\pi$
$787$	−6.77817	+	11.7401i	−0.241616	+	0.418491i	0.719559	+	0.694431i	$0.244344\pi$
$788$	−0.257359	+	0.445759i	−0.00916805	+	0.0158795i
$789$		0			0
$790$	7.75736			0.275994
$791$	13.2487	−	17.0849i	0.471071	−	0.607468i
$792$		0			0
$793$	22.6421	+	39.2173i	0.804046	+	1.39265i
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$		0			0
$796$	−0.0502525	−	0.0870399i	−0.00178115	−	0.00308505i
$797$	7.65685			0.271220			0.135610	−	0.990762i	$-0.456701\pi$
$797$	7.65685			0.271220			0.135610	+	0.990762i	$0.456701\pi$
$798$		0			0
$799$	−38.3431			−1.35648
$800$	−2.32843	−	4.03295i	−0.0823223	−	0.142586i
$801$		0			0
$802$	−9.15685	+	15.8601i	−0.323340	+	0.560041i
$803$	−4.70711	−	8.15295i	−0.166110	−	0.287711i
$804$		0			0
$805$	3.65685	+	8.95743i	0.128887	+	0.315708i
$806$	−15.3137			−0.539402
$807$		0			0
$808$	−3.08579	+	5.34474i	−0.108558	+	0.188027i
$809$	−23.3137	+	40.3805i	−0.819666	+	1.41970i	0.0862619	+	0.996272i	$0.472508\pi$
$809$	−23.3137	+	40.3805i	−0.819666	+	1.41970i	−0.905928	+	0.423431i	$0.860826\pi$
$810$		0			0
$811$	−24.2843			−0.852736			−0.426368	−	0.904550i	$-0.640207\pi$
$811$	−24.2843			−0.852736			−0.426368	+	0.904550i	$0.640207\pi$
$812$	−2.65685	−	6.50794i	−0.0932373	−	0.228384i
$813$		0			0
$814$	4.70711	+	8.15295i	0.164984	+	0.285761i
$815$	−2.84924	+	4.93503i	−0.0998046	+	0.172867i
$816$		0			0
$817$	−1.65685	−	2.86976i	−0.0579660	−	0.100400i
$818$	−2.72792			−0.0953796
$819$		0			0
$820$	3.17157			0.110756
$821$	−14.7426	−	25.5350i	−0.514522	−	0.891178i	−0.999858	−	0.0168502i	$-0.994636\pi$
$821$	−14.7426	−	25.5350i	−0.514522	−	0.891178i	0.485336	−	0.874328i	$-0.338697\pi$
$822$		0			0
$823$	21.7279	−	37.6339i	0.757388	−	1.31183i	−0.186791	−	0.982400i	$-0.559809\pi$
$823$	21.7279	−	37.6339i	0.757388	−	1.31183i	0.944178	−	0.329434i	$-0.106858\pi$
$824$	6.70711	+	11.6170i	0.233653	+	0.404699i
$825$		0			0
$826$	−9.05635	+	11.6786i	−0.315111	+	0.406350i
$827$	21.3553			0.742598			0.371299	−	0.928513i	$-0.378913\pi$
$827$	21.3553			0.742598			0.371299	+	0.928513i	$0.378913\pi$
$828$		0			0
$829$	−10.8787	+	18.8424i	−0.377832	+	0.654425i	−0.990747	−	0.135725i	$-0.956664\pi$
$829$	−10.8787	+	18.8424i	−0.377832	+	0.654425i	0.612914	+	0.790149i	$0.289997\pi$
$830$	3.55635	−	6.15978i	0.123443	−	0.213809i
$831$		0			0
$832$	−3.82843			−0.132727
$833$	−24.6569	−	6.87722i	−0.854309	−	0.238281i
$834$		0			0
$835$	4.02082	+	6.96426i	0.139146	+	0.241008i
$836$	−0.292893	+	0.507306i	−0.0101299	+	0.0175455i
$837$		0			0
$838$	13.0711	+	22.6398i	0.451533	+	0.782077i
$839$	18.4853			0.638183			0.319091	−	0.947724i	$-0.396622\pi$
$839$	18.4853			0.638183			0.319091	+	0.947724i	$0.396622\pi$
$840$		0			0
$841$	−21.9411			−0.756591
$842$	0.343146	+	0.594346i	0.0118256	+	0.0204825i
$843$		0			0
$844$	−3.70711	+	6.42090i	−0.127604	+	0.221016i
$845$	−0.485281	−	0.840532i	−0.0166942	−	0.0289152i
$846$		0			0
$847$	−2.62132	−	0.358719i	−0.0900696	−	0.0123257i
$848$	−7.89949			−0.271270
$849$		0			0
$850$	8.51472	−	14.7479i	0.292052	−	0.505850i
$851$	29.3848	−	50.8959i	1.00730	−	1.74469i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	−11.8284	−	28.9736i	−0.404760	−	0.991457i
$855$		0			0
$856$	1.53553	+	2.65962i	0.0524835	+	0.0909040i
$857$	−17.3137	+	29.9882i	−0.591425	+	1.02438i	0.402616	+	0.915369i	$0.368101\pi$
$857$	−17.3137	+	29.9882i	−0.591425	+	1.02438i	−0.994041	+	0.109009i	$0.965232\pi$
$858$		0			0
$859$	2.86396	+	4.96053i	0.0977171	+	0.169251i	0.910739	−	0.412982i	$-0.135513\pi$
$859$	2.86396	+	4.96053i	0.0977171	+	0.169251i	−0.813022	+	0.582233i	$0.802179\pi$
$860$	−3.31371			−0.112997
$861$		0			0
$862$	−17.5858			−0.598974
$863$	17.6066	+	30.4955i	0.599336	+	1.03808i	0.992919	+	0.118791i	$0.0379019\pi$
$863$	17.6066	+	30.4955i	0.599336	+	1.03808i	−0.393584	+	0.919289i	$0.628765\pi$
$864$		0			0
$865$	−2.87868	+	4.98602i	−0.0978780	+	0.169530i
$866$	13.0711	+	22.6398i	0.444173	+	0.769330i
$867$		0			0
$868$	10.4853	+	1.43488i	0.355894	+	0.0487029i
$869$	13.2426			0.449226
$870$		0			0
$871$	5.27817	−	9.14207i	0.178844	−	0.309767i
$872$	8.24264	−	14.2767i	0.279131	−	0.483469i
$873$		0			0
$874$	3.65685			0.123695
$875$	−9.17157	+	11.8272i	−0.310056	+	0.399832i
$876$		0			0
$877$	−9.81371	−	16.9978i	−0.331385	−	0.573976i	0.651398	−	0.758736i	$-0.274183\pi$
$877$	−9.81371	−	16.9978i	−0.331385	−	0.573976i	−0.982784	+	0.184760i	$0.940849\pi$
$878$	−13.6924	+	23.7159i	−0.462096	+	0.800373i
$879$		0			0
$880$	0.292893	+	0.507306i	0.00987343	+	0.0171013i
$881$	−6.45584			−0.217503			−0.108751	−	0.994069i	$-0.534685\pi$
$881$	−6.45584			−0.217503			−0.108751	+	0.994069i	$0.534685\pi$
$882$		0			0
$883$	15.7279			0.529287			0.264643	−	0.964346i	$-0.414746\pi$
$883$	15.7279			0.529287			0.264643	+	0.964346i	$0.414746\pi$
$884$	−7.00000	−	12.1244i	−0.235435	−	0.407786i
$885$		0			0
$886$	−6.31371	+	10.9357i	−0.212113	+	0.367391i
$887$	−1.55025	−	2.68512i	−0.0520524	−	0.0901574i	0.838825	−	0.544401i	$-0.183243\pi$
$887$	−1.55025	−	2.68512i	−0.0520524	−	0.0901574i	−0.890878	+	0.454243i	$0.849910\pi$
$888$		0			0
$889$	25.5000	−	32.8835i	0.855243	−	1.10288i
$890$	7.31371			0.245156
$891$		0			0
$892$	−4.29289	+	7.43551i	−0.143737	+	0.248959i
$893$	3.07107	−	5.31925i	0.102769	−	0.178002i
$894$		0			0
$895$	−0.526912			−0.0176127
$896$	2.62132	+	0.358719i	0.0875722	+	0.0119840i
$897$		0			0
$898$	−11.1716	−	19.3497i	−0.372800	−	0.645709i
$899$	−5.31371	+	9.20361i	−0.177222	+	0.306958i
$900$		0			0
$901$	−14.4437	−	25.0171i	−0.481188	−	0.833442i
$902$	5.41421			0.180274
$903$		0			0
$904$	−8.17157			−0.271782
$905$	2.24264	+	3.88437i	0.0745479	+	0.129121i
$906$		0			0
$907$	−5.34315	+	9.25460i	−0.177416	+	0.307294i	−0.940995	−	0.338421i	$-0.890107\pi$
$907$	−5.34315	+	9.25460i	−0.177416	+	0.307294i	0.763579	+	0.645715i	$0.223441\pi$
$908$	−14.4142	−	24.9662i	−0.478352	−	0.828531i
$909$		0			0
$910$	2.24264	+	5.49333i	0.0743428	+	0.182102i
$911$	30.4853			1.01002			0.505011	−	0.863113i	$-0.331488\pi$
$911$	30.4853			1.01002			0.505011	+	0.863113i	$0.331488\pi$
$912$		0			0
$913$	6.07107	−	10.5154i	0.200923	−	0.348009i
$914$	−5.82843	+	10.0951i	−0.192787	+	0.333917i
$915$		0			0
$916$	23.3137			0.770307
$917$	−1.53553	−	0.210133i	−0.0507078	−	0.00693920i
$918$		0			0
$919$	−11.0711	−	19.1757i	−0.365201	−	0.632546i	0.623608	−	0.781738i	$-0.285666\pi$
$919$	−11.0711	−	19.1757i	−0.365201	−	0.632546i	−0.988808	+	0.149191i	$0.952333\pi$
$920$	1.82843	−	3.16693i	0.0602815	−	0.104411i
$921$		0			0
$922$	4.15685	+	7.19988i	0.136899	+	0.237116i
$923$	−42.3848			−1.39511
$924$		0			0
$925$	43.8406			1.44147
$926$	6.41421	+	11.1097i	0.210784	+	0.365089i
$927$		0			0
$928$	−1.32843	+	2.30090i	−0.0436078	+	0.0755309i
$929$	−20.2279	−	35.0358i	−0.663657	−	1.14949i	−0.979648	−	0.200725i	$-0.935670\pi$
$929$	−20.2279	−	35.0358i	−0.663657	−	1.14949i	0.315991	−	0.948762i	$-0.397663\pi$
$930$		0			0
$931$	2.92893	−	2.86976i	0.0959919	−	0.0940524i
$932$	−1.41421			−0.0463241
$933$		0			0
$934$	17.0000	−	29.4449i	0.556257	−	0.963465i
$935$	−1.07107	+	1.85514i	−0.0350277	+	0.0606697i
$936$		0			0
$937$	−19.4142			−0.634235			−0.317117	−	0.948386i	$-0.602715\pi$
$937$	−19.4142			−0.634235			−0.317117	+	0.948386i	$0.602715\pi$
$938$	−4.47056	+	5.76500i	−0.145969	+	0.188234i
$939$		0			0
$940$	−3.07107	−	5.31925i	−0.100167	−	0.173495i
$941$	12.3284	−	21.3535i	0.401895	−	0.696103i	−0.592059	−	0.805894i	$-0.701685\pi$
$941$	12.3284	−	21.3535i	0.401895	−	0.696103i	0.993955	+	0.109791i	$0.0350183\pi$
$942$		0			0
$943$	−16.8995	−	29.2708i	−0.550323	−	0.953188i
$944$	5.58579			0.181802
$945$		0			0
$946$	−5.65685			−0.183920
$947$	17.4142	+	30.1623i	0.565886	+	0.980143i	0.996967	+	0.0778298i	$0.0247991\pi$
$947$	17.4142	+	30.1623i	0.565886	+	0.980143i	−0.431081	+	0.902313i	$0.641868\pi$
$948$		0			0
$949$	−18.0208	+	31.2130i	−0.584980	+	1.01322i
$950$	1.36396	+	2.36245i	0.0442527	+	0.0766480i
$951$		0			0
$952$	3.65685	+	8.95743i	0.118519	+	0.290312i
$953$	−5.55635			−0.179988			−0.0899939	−	0.995942i	$-0.528685\pi$
$953$	−5.55635			−0.179988			−0.0899939	+	0.995942i	$0.528685\pi$
$954$		0			0
$955$	−2.10051	+	3.63818i	−0.0679707	+	0.117729i
$956$	10.1066	−	17.5051i	0.326871	−	0.566157i
$957$		0			0
$958$	−11.9289			−0.385406
$959$	16.6569	+	40.8008i	0.537878	+	1.31753i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	18.0208	−	31.2130i	0.581014	−	1.00635i
$963$		0			0
$964$	−6.12132	−	10.6024i	−0.197154	−	0.341482i
$965$	12.8284			0.412962
$966$		0			0
$967$	−36.2843			−1.16682			−0.583412	−	0.812177i	$-0.698283\pi$
$967$	−36.2843			−1.16682			−0.583412	+	0.812177i	$0.698283\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$		0			0
$970$	−1.12132	+	1.94218i	−0.0360034	+	0.0623598i
$971$	11.1360	+	19.2882i	0.357372	+	0.618987i	0.987521	−	0.157487i	$-0.0503393\pi$
$971$	11.1360	+	19.2882i	0.357372	+	0.618987i	−0.630149	+	0.776475i	$0.717006\pi$
$972$		0			0
$973$		0			0
$974$	9.65685			0.309426
$975$		0			0
$976$	−5.91421	+	10.2437i	−0.189309	+	0.327893i
$977$	20.0000	−	34.6410i	0.639857	−	1.10826i	−0.345607	−	0.938379i	$-0.612327\pi$
$977$	20.0000	−	34.6410i	0.639857	−	1.10826i	0.985464	−	0.169885i	$-0.0543396\pi$
$978$		0			0
$979$	12.4853			0.399031
$980$	−1.02082	−	3.97141i	−0.0326087	−	0.126862i
$981$		0			0
$982$	−9.58579	−	16.6031i	−0.305895	−	0.529825i
$983$	16.2132	−	28.0821i	0.517121	−	0.895680i	−0.482681	−	0.875796i	$-0.660337\pi$
$983$	16.2132	−	28.0821i	0.517121	−	0.895680i	0.999802	−	0.0198836i	$-0.00632957\pi$
$984$		0			0
$985$	−0.150758	−	0.261120i	−0.00480354	−	0.00831997i
$986$	−9.71573			−0.309412
$987$		0			0
$988$	2.24264			0.0713479
$989$	17.6569	+	30.5826i	0.561455	+	0.972469i
$990$		0			0
$991$	0.807612	−	1.39882i	0.0256546	−	0.0444351i	−0.852913	−	0.522053i	$-0.825166\pi$
$991$	0.807612	−	1.39882i	0.0256546	−	0.0444351i	0.878568	+	0.477618i	$0.158500\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$	29.0208	+	3.97141i	0.920484	+	0.125965i
$995$	0.0588745			0.00186645
$996$		0			0
$997$	−6.58579	+	11.4069i	−0.208574	+	0.361261i	−0.951266	−	0.308373i	$-0.900216\pi$
$997$	−6.58579	+	11.4069i	−0.208574	+	0.361261i	0.742692	+	0.669634i	$0.233549\pi$
$998$	11.0711	−	19.1757i	0.350449	−	0.606995i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.t.991.2		4
3.2	odd	2		154.2.e.e.67.2	yes	4
7.2	even	3	inner	1386.2.k.t.793.2		4
7.3	odd	6		9702.2.a.ch.1.2		2
7.4	even	3		9702.2.a.cx.1.1		2
12.11	even	2		1232.2.q.f.529.1		4
21.2	odd	6		154.2.e.e.23.2	✓	4
21.5	even	6		1078.2.e.m.177.1		4
21.11	odd	6		1078.2.a.t.1.1		2
21.17	even	6		1078.2.a.x.1.2		2
21.20	even	2		1078.2.e.m.67.1		4
84.11	even	6		8624.2.a.cc.1.2		2
84.23	even	6		1232.2.q.f.177.1		4
84.59	odd	6		8624.2.a.bh.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.e.23.2	✓	4	21.2	odd	6
154.2.e.e.67.2	yes	4	3.2	odd	2
1078.2.a.t.1.1		2	21.11	odd	6
1078.2.a.x.1.2		2	21.17	even	6
1078.2.e.m.67.1		4	21.20	even	2
1078.2.e.m.177.1		4	21.5	even	6
1232.2.q.f.177.1		4	84.23	even	6
1232.2.q.f.529.1		4	12.11	even	2
1386.2.k.t.793.2		4	7.2	even	3	inner
1386.2.k.t.991.2		4	1.1	even	1	trivial
8624.2.a.bh.1.1		2	84.59	odd	6
8624.2.a.cc.1.2		2	84.11	even	6
9702.2.a.ch.1.2		2	7.3	odd	6
9702.2.a.cx.1.1		2	7.4	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.292893 - 0.507306i) q^{5} +(1.62132 - 2.09077i) q^{7} -1.00000 q^{8} +(0.292893 - 0.507306i) q^{10} +(0.500000 - 0.866025i) q^{11} -3.82843 q^{13} +(2.62132 + 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.82843 - 3.16693i) q^{17} +(0.292893 + 0.507306i) q^{19} +0.585786 q^{20} +1.00000 q^{22} +(-3.12132 - 5.40629i) q^{23} +(2.32843 - 4.03295i) q^{25} +(-1.91421 - 3.31552i) q^{26} +(1.00000 + 2.44949i) q^{28} -2.65685 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +3.65685 q^{34} +(-1.53553 - 0.210133i) q^{35} +(4.70711 + 8.15295i) q^{37} +(-0.292893 + 0.507306i) q^{38} +(0.292893 + 0.507306i) q^{40} +5.41421 q^{41} -5.65685 q^{43} +(0.500000 + 0.866025i) q^{44} +(3.12132 - 5.40629i) q^{46} +(-5.24264 - 9.08052i) q^{47} +(-1.74264 - 6.77962i) q^{49} +4.65685 q^{50} +(1.91421 - 3.31552i) q^{52} +(3.94975 - 6.84116i) q^{53} -0.585786 q^{55} +(-1.62132 + 2.09077i) q^{56} +(-1.32843 - 2.30090i) q^{58} +(-2.79289 + 4.83743i) q^{59} +(-5.91421 - 10.2437i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.12132 + 1.94218i) q^{65} +(-1.37868 + 2.38794i) q^{67} +(1.82843 + 3.16693i) q^{68} +(-0.585786 - 1.43488i) q^{70} +11.0711 q^{71} +(4.70711 - 8.15295i) q^{73} +(-4.70711 + 8.15295i) q^{74} -0.585786 q^{76} +(-1.00000 - 2.44949i) q^{77} +(6.62132 + 11.4685i) q^{79} +(-0.292893 + 0.507306i) q^{80} +(2.70711 + 4.68885i) q^{82} +12.1421 q^{83} -2.14214 q^{85} +(-2.82843 - 4.89898i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(6.24264 + 10.8126i) q^{89} +(-6.20711 + 8.00436i) q^{91} +6.24264 q^{92} +(5.24264 - 9.08052i) q^{94} +(0.171573 - 0.297173i) q^{95} -3.82843 q^{97} +(5.00000 - 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} + 2 q^{14} - 2 q^{16} - 4 q^{17} + 4 q^{19} + 8 q^{20} + 4 q^{22} - 4 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 12 q^{29}+ \cdots + 20 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8 + 4 * q^10 + 2 * q^11 - 4 * q^13 + 2 * q^14 - 2 * q^16 - 4 * q^17 + 4 * q^19 + 8 * q^20 + 4 * q^22 - 4 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 12 * q^29 + 8 * q^31 + 2 * q^32 - 8 * q^34 + 8 * q^35 + 16 * q^37 - 4 * q^38 + 4 * q^40 + 16 * q^41 + 2 * q^44 + 4 * q^46 - 4 * q^47 + 10 * q^49 - 4 * q^50 + 2 * q^52 - 4 * q^53 - 8 * q^55 + 2 * q^56 + 6 * q^58 - 14 * q^59 - 18 * q^61 + 16 * q^62 + 4 * q^64 - 4 * q^65 - 14 * q^67 - 4 * q^68 - 8 * q^70 + 16 * q^71 + 16 * q^73 - 16 * q^74 - 8 * q^76 - 4 * q^77 + 18 * q^79 - 4 * q^80 + 8 * q^82 - 8 * q^83 + 48 * q^85 - 2 * q^88 + 8 * q^89 - 22 * q^91 + 8 * q^92 + 4 * q^94 + 12 * q^95 - 4 * q^97 + 20 * q^98

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