LMFDB - Embedded newform 387.2.y.c.10.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			10.3
Character	$\chi$	$=$	387.10
Dual form			387.2.y.c.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483758 + 2.11948i) q^{2} +(-2.45624 + 1.18286i) q^{4} +(-0.0260188 + 0.00392170i) q^{5} +(1.56464 + 2.71003i) q^{7} +(-0.984367 - 1.23436i) q^{8} +O(q^{10})$	\(q+(0.483758 + 2.11948i) q^{2} +(-2.45624 + 1.18286i) q^{4} +(-0.0260188 + 0.00392170i) q^{5} +(1.56464 + 2.71003i) q^{7} +(-0.984367 - 1.23436i) q^{8} +(-0.0208988 - 0.0532492i) q^{10} +(-3.36665 - 1.62129i) q^{11} +(-1.78860 + 4.55728i) q^{13} +(-4.98695 + 4.62722i) q^{14} +(-1.25954 + 1.57942i) q^{16} +(5.84766 + 0.881392i) q^{17} +(0.296638 - 3.95836i) q^{19} +(0.0592696 - 0.0404093i) q^{20} +(1.80766 - 7.91985i) q^{22} +(-0.284113 + 0.193705i) q^{23} +(-4.77720 + 1.47357i) q^{25} +(-10.5243 - 1.58629i) q^{26} +(-7.04873 - 4.80574i) q^{28} +(-0.971806 + 0.901704i) q^{29} +(2.06955 + 0.638371i) q^{31} +(-6.80176 - 3.27556i) q^{32} +(0.960755 + 12.8204i) q^{34} +(-0.0513379 - 0.0643757i) q^{35} +(5.01814 - 8.69167i) q^{37} +(8.53318 - 1.28617i) q^{38} +(0.0304528 + 0.0282561i) q^{40} +(0.431814 + 1.89190i) q^{41} +(6.54856 + 0.341120i) q^{43} +10.1871 q^{44} +(-0.547996 - 0.508466i) q^{46} +(10.0138 - 4.82240i) q^{47} +(-1.39618 + 2.41825i) q^{49} +(-5.43422 - 9.41234i) q^{50} +(-0.997407 - 13.3095i) q^{52} +(2.12587 + 5.41662i) q^{53} +(0.0939542 + 0.0289810i) q^{55} +(1.80497 - 4.59898i) q^{56} +(-2.38126 - 1.62352i) q^{58} +(-0.107460 + 0.134751i) q^{59} +(5.31524 - 1.63953i) q^{61} +(-0.351855 + 4.69519i) q^{62} +(2.75302 - 12.0618i) q^{64} +(0.0286650 - 0.125589i) q^{65} +(-0.0822742 + 1.09787i) q^{67} +(-15.4058 + 4.75207i) q^{68} +(0.111608 - 0.139952i) q^{70} +(4.37443 + 2.98244i) q^{71} +(-2.70214 + 6.88494i) q^{73} +(20.8494 + 6.43119i) q^{74} +(3.95359 + 10.0736i) q^{76} +(-0.873829 - 11.6604i) q^{77} +(2.70765 + 4.68979i) q^{79} +(0.0265778 - 0.0460341i) q^{80} +(-3.80096 + 1.83044i) q^{82} +(1.49132 + 1.38374i) q^{83} -0.155605 q^{85} +(2.44492 + 14.0446i) q^{86} +(1.31276 + 5.75159i) q^{88} +(-2.93360 - 2.72198i) q^{89} +(-15.1489 + 2.28333i) q^{91} +(0.468724 - 0.811854i) q^{92} +(15.0652 + 18.8912i) q^{94} +(0.00780535 + 0.104155i) q^{95} +(-8.11049 - 3.90581i) q^{97} +(-5.80084 - 1.78932i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$1$

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 $

$2$	0.483758	+	2.11948i	0.342068	+	1.49870i	0.794700	+	0.607002i	$0.207628\pi$
$2$	0.483758	+	2.11948i	0.342068	+	1.49870i	−0.452632	+	0.891698i	$0.649515\pi$
$3$		0			0
$3$		0			0
$4$	−2.45624	+	1.18286i	−1.22812	+	0.591432i
$5$	−0.0260188	+	0.00392170i	−0.0116360	+	0.00175384i	−0.154858	−	0.987937i	$-0.549492\pi$
$5$	−0.0260188	+	0.00392170i	−0.0116360	+	0.00175384i	0.143222	+	0.989691i	$0.454254\pi$
$6$		0			0
$7$	1.56464	+	2.71003i	0.591377	+	1.02430i	0.994047	+	0.108950i	$0.0347489\pi$
$7$	1.56464	+	2.71003i	0.591377	+	1.02430i	−0.402670	+	0.915345i	$0.631918\pi$
$8$	−0.984367	−	1.23436i	−0.348026	−	0.436411i
$9$		0			0
$10$	−0.0208988	−	0.0532492i	−0.00660877	−	0.0168389i
$11$	−3.36665	−	1.62129i	−1.01508	−	0.488838i	−0.149052	−	0.988829i	$-0.547622\pi$
$11$	−3.36665	−	1.62129i	−1.01508	−	0.488838i	−0.866030	+	0.499992i	$0.833336\pi$
$12$		0			0
$13$	−1.78860	+	4.55728i	−0.496069	+	1.26396i	0.435431	+	0.900222i	$0.356596\pi$
$13$	−1.78860	+	4.55728i	−0.496069	+	1.26396i	−0.931500	+	0.363741i	$0.881499\pi$
$14$	−4.98695	+	4.62722i	−1.33282	+	1.23668i
$15$		0			0
$16$	−1.25954	+	1.57942i	−0.314886	+	0.394855i
$17$	5.84766	+	0.881392i	1.41827	+	0.213769i	0.813004	−	0.582258i	$-0.197831\pi$
$17$	5.84766	+	0.881392i	1.41827	+	0.213769i	0.605261	+	0.796027i	$0.293069\pi$
$18$		0			0
$19$	0.296638	−	3.95836i	0.0680535	−	0.908110i	−0.853807	−	0.520589i	$-0.825712\pi$
$19$	0.296638	−	3.95836i	0.0680535	−	0.908110i	0.921861	−	0.387521i	$-0.126669\pi$
$20$	0.0592696	−	0.0404093i	0.0132531	−	0.00903580i
$21$		0			0
$22$	1.80766	−	7.91985i	0.385393	−	1.68852i
$23$	−0.284113	+	0.193705i	−0.0592417	+	0.0403903i	−0.592579	−	0.805512i	$-0.701890\pi$
$23$	−0.284113	+	0.193705i	−0.0592417	+	0.0403903i	0.533337	+	0.845903i	$0.320938\pi$
$24$		0			0
$25$	−4.77720	+	1.47357i	−0.955440	+	0.294714i
$26$	−10.5243	−	1.58629i	−2.06399	−	0.311097i
$27$		0			0
$28$	−7.04873	−	4.80574i	−1.33208	−	0.908199i
$29$	−0.971806	+	0.901704i	−0.180460	+	0.167442i	−0.765230	−	0.643756i	$-0.777375\pi$
$29$	−0.971806	+	0.901704i	−0.180460	+	0.167442i	0.584771	+	0.811199i	$0.301185\pi$
$30$		0			0
$31$	2.06955	+	0.638371i	0.371702	+	0.114655i	0.474977	−	0.879998i	$-0.342456\pi$
$31$	2.06955	+	0.638371i	0.371702	+	0.114655i	−0.103276	+	0.994653i	$0.532932\pi$
$32$	−6.80176	−	3.27556i	−1.20239	−	0.579042i
$33$		0			0
$34$	0.960755	+	12.8204i	0.164768	+	2.19868i
$35$	−0.0513379	−	0.0643757i	−0.00867769	−	0.0108815i
$36$		0			0
$37$	5.01814	−	8.69167i	0.824977	−	1.42890i	−0.0769599	−	0.997034i	$-0.524521\pi$
$37$	5.01814	−	8.69167i	0.824977	−	1.42890i	0.901937	−	0.431868i	$-0.142145\pi$
$38$	8.53318	−	1.28617i	1.38426	−	0.208644i
$39$		0			0
$40$	0.0304528	+	0.0282561i	0.00481501	+	0.00446768i
$41$	0.431814	+	1.89190i	0.0674381	+	0.295465i	0.997389	−	0.0722186i	$-0.0230079\pi$
$41$	0.431814	+	1.89190i	0.0674381	+	0.295465i	−0.929951	+	0.367684i	$0.880151\pi$
$42$		0			0
$43$	6.54856	+	0.341120i	0.998646	+	0.0520203i
$43$	6.54856	+	0.341120i	0.998646	+	0.0520203i
$44$	10.1871			1.53576
$45$		0			0
$46$	−0.547996	−	0.508466i	−0.0807976	−	0.0749693i
$47$	10.0138	−	4.82240i	1.46066	−	0.703419i	0.476255	−	0.879307i	$-0.341994\pi$
$47$	10.0138	−	4.82240i	1.46066	−	0.703419i	0.984410	+	0.175888i	$0.0562798\pi$
$48$		0			0
$49$	−1.39618	+	2.41825i	−0.199454	+	0.345464i
$50$	−5.43422	−	9.41234i	−0.768514	−	1.33111i
$51$		0			0
$52$	−0.997407	−	13.3095i	−0.138315	−	1.84569i
$53$	2.12587	+	5.41662i	0.292010	+	0.744030i	0.999311	+	0.0371173i	$0.0118175\pi$
$53$	2.12587	+	5.41662i	0.292010	+	0.744030i	−0.707301	+	0.706913i	$0.750087\pi$
$54$		0			0
$55$	0.0939542	+	0.0289810i	0.0126688	+	0.00390780i
$56$	1.80497	−	4.59898i	0.241199	−	0.614565i
$57$		0			0
$58$	−2.38126	−	1.62352i	−0.312675	−	0.213178i
$59$	−0.107460	+	0.134751i	−0.0139901	+	0.0175431i	−0.788777	−	0.614679i	$-0.789286\pi$
$59$	−0.107460	+	0.134751i	−0.0139901	+	0.0175431i	0.774787	+	0.632222i	$0.217857\pi$
$60$		0			0
$61$	5.31524	−	1.63953i	0.680547	−	0.209921i	0.0648393	−	0.997896i	$-0.479347\pi$
$61$	5.31524	−	1.63953i	0.680547	−	0.209921i	0.615707	+	0.787975i	$0.288870\pi$
$62$	−0.351855	+	4.69519i	−0.0446857	+	0.596289i
$63$		0			0
$64$	2.75302	−	12.0618i	0.344128	−	1.50772i
$65$	0.0286650	−	0.125589i	0.00355545	−	0.0155774i
$66$		0			0
$67$	−0.0822742	+	1.09787i	−0.0100514	+	0.134126i	−0.999972	−	0.00749766i	$-0.997613\pi$
$67$	−0.0822742	+	1.09787i	−0.0100514	+	0.134126i	0.989921	+	0.141624i	$0.0452324\pi$
$68$	−15.4058	+	4.75207i	−1.86823	+	0.576273i
$69$		0			0
$70$	0.111608	−	0.139952i	0.0133397	−	0.0167275i
$71$	4.37443	+	2.98244i	0.519150	+	0.353950i	0.794373	−	0.607430i	$-0.207799\pi$
$71$	4.37443	+	2.98244i	0.519150	+	0.353950i	−0.275223	+	0.961380i	$0.588752\pi$
$72$		0			0
$73$	−2.70214	+	6.88494i	−0.316261	+	0.805821i	0.681029	+	0.732256i	$0.261533\pi$
$73$	−2.70214	+	6.88494i	−0.316261	+	0.805821i	−0.997290	+	0.0735646i	$0.976562\pi$
$74$	20.8494	+	6.43119i	2.42369	+	0.747611i
$75$		0			0
$76$	3.95359	+	10.0736i	0.453508	+	1.15552i
$77$	−0.873829	−	11.6604i	−0.0995821	−	1.32883i
$78$		0			0
$79$	2.70765	+	4.68979i	0.304635	+	0.527643i	0.977180	−	0.212413i	$-0.0681323\pi$
$79$	2.70765	+	4.68979i	0.304635	+	0.527643i	−0.672545	+	0.740056i	$0.734799\pi$
$80$	0.0265778	−	0.0460341i	0.00297149	−	0.00514677i
$81$		0			0
$82$	−3.80096	+	1.83044i	−0.419746	+	0.202139i
$83$	1.49132	+	1.38374i	0.163694	+	0.151885i	0.757767	−	0.652526i	$-0.226291\pi$
$83$	1.49132	+	1.38374i	0.163694	+	0.151885i	−0.594073	+	0.804411i	$0.702481\pi$
$84$		0			0
$85$	−0.155605			−0.0168778
$86$	2.44492	+	14.0446i	0.263642	+	1.51447i
$87$		0			0
$88$	1.31276	+	5.75159i	0.139941	+	0.613121i
$89$	−2.93360	−	2.72198i	−0.310961	−	0.288530i	0.509217	−	0.860638i	$-0.329935\pi$
$89$	−2.93360	−	2.72198i	−0.310961	−	0.288530i	−0.820178	+	0.572109i	$0.806126\pi$
$90$		0			0
$91$	−15.1489	+	2.28333i	−1.58804	+	0.239358i
$92$	0.468724	−	0.811854i	0.0488679	−	0.0846416i
$93$		0			0
$94$	15.0652	+	18.8912i	1.55386	+	1.94848i
$95$	0.00780535	+	0.104155i	0.000800812	+	0.0106861i
$96$		0			0
$97$	−8.11049	−	3.90581i	−0.823495	−	0.396574i	−0.0258237	−	0.999667i	$-0.508221\pi$
$97$	−8.11049	−	3.90581i	−0.823495	−	0.396574i	−0.797672	+	0.603092i	$0.793935\pi$
$98$	−5.80084	−	1.78932i	−0.585974	−	0.180749i
$99$		0			0
$100$	9.99093	−	9.27023i	0.999093	−	0.927023i
$101$	−12.6400	−	8.61780i	−1.25773	−	0.857503i	−0.263484	−	0.964664i	$-0.584872\pi$
$101$	−12.6400	−	8.61780i	−1.25773	−	0.857503i	−0.994242	+	0.107161i	$0.965824\pi$
$102$		0			0
$103$	15.8309	+	2.38613i	1.55987	+	0.235112i	0.871554	−	0.490300i	$-0.163113\pi$
$103$	15.8309	+	2.38613i	1.55987	+	0.235112i	0.688315	+	0.725412i	$0.258351\pi$
$104$	7.38596	−	2.27827i	0.724253	−	0.223402i
$105$		0			0
$106$	−10.4520	+	7.12607i	−1.01519	+	0.692145i
$107$	3.68337	−	16.1379i	0.356085	−	1.56011i	−0.406765	−	0.913533i	$-0.633343\pi$
$107$	3.68337	−	16.1379i	0.356085	−	1.56011i	0.762850	−	0.646576i	$-0.223800\pi$
$108$		0			0
$109$	1.69999	−	1.15903i	0.162829	−	0.111015i	−0.479164	−	0.877725i	$-0.659060\pi$
$109$	1.69999	−	1.15903i	0.162829	−	0.111015i	0.641993	+	0.766710i	$0.278108\pi$
$110$	−0.0159737	+	0.213154i	−0.00152303	+	0.0203234i
$111$		0			0
$112$	−6.25100	−	0.942187i	−0.590664	−	0.0890283i
$113$	−7.27343	+	9.12059i	−0.684226	+	0.857993i	−0.995736	−	0.0922502i	$-0.970594\pi$
$113$	−7.27343	+	9.12059i	−0.684226	+	0.857993i	0.311509	+	0.950243i	$0.399165\pi$
$114$		0			0
$115$	0.00663263	−	0.00615418i	0.000618496	−	0.000573880i
$116$	1.32040	−	3.36432i	0.122596	−	0.312369i
$117$		0			0
$118$	−0.337586	−	0.162573i	−0.0310774	−	0.0149661i
$119$	6.76086	+	17.2264i	0.619767	+	1.57914i
$120$		0			0
$121$	1.84733	+	2.31648i	0.167939	+	0.210589i
$122$	6.04625	+	10.4724i	0.547402	+	0.948128i
$123$		0			0
$124$	−5.83842	+	0.880000i	−0.524305	+	0.0790263i
$125$	0.237053	−	0.114159i	0.0212026	−	0.0102106i
$126$		0			0
$127$	−1.67817	−	7.35255i	−0.148914	−	0.652433i	−0.993188	−	0.116522i	$-0.962825\pi$
$127$	−1.67817	−	7.35255i	−0.148914	−	0.652433i	0.844275	−	0.535911i	$-0.180032\pi$
$128$	11.7978			1.04278
$129$		0			0
$130$	0.280051			0.0245621
$131$	−1.97245	−	8.64186i	−0.172334	−	0.755043i	−0.985034	−	0.172361i	$-0.944861\pi$
$131$	−1.97245	−	8.64186i	−0.172334	−	0.755043i	0.812700	−	0.582682i	$-0.197997\pi$
$132$		0			0
$133$	11.1914	−	5.38950i	0.970418	−	0.467329i
$134$	−2.36672	+	0.356726i	−0.204454	+	0.0308164i
$135$		0			0
$136$	−4.66829	−	8.08571i	−0.400302	−	0.693344i
$137$	10.9540	+	13.7359i	0.935863	+	1.17354i	0.984617	+	0.174725i	$0.0559036\pi$
$137$	10.9540	+	13.7359i	0.935863	+	1.17354i	−0.0487538	+	0.998811i	$0.515525\pi$
$138$		0			0
$139$	−5.64316	−	14.3785i	−0.478646	−	1.21957i	−0.942663	−	0.333745i	$-0.891688\pi$
$139$	−5.64316	−	14.3785i	−0.478646	−	1.21957i	0.464017	−	0.885826i	$-0.346408\pi$
$140$	0.202246	+	0.0973965i	0.0170929	+	0.00823151i
$141$		0			0
$142$	−4.20506	+	10.7143i	−0.352880	+	0.899125i
$143$	13.4103	−	12.4429i	1.12142	−	1.04053i
$144$		0			0
$145$	0.0217490	−	0.0272724i	0.00180616	−	0.00226485i
$146$	−15.8997	−	2.39649i	−1.31587	−	0.198335i
$147$		0			0
$148$	−2.04470	+	27.2846i	−0.168073	+	2.24278i
$149$	5.99816	−	4.08947i	0.491388	−	0.335023i	−0.292144	−	0.956374i	$-0.594369\pi$
$149$	5.99816	−	4.08947i	0.491388	−	0.335023i	0.783532	+	0.621352i	$0.213416\pi$
$150$		0			0
$151$	2.23243	−	9.78091i	0.181673	−	0.795960i	−0.799162	−	0.601116i	$-0.794723\pi$
$151$	2.23243	−	9.78091i	0.181673	−	0.795960i	0.980834	−	0.194844i	$-0.0624199\pi$
$152$	−5.17803	+	3.53032i	−0.419994	+	0.286347i
$153$		0			0
$154$	24.2914	−	7.49290i	1.95745	−	0.603795i
$155$	−0.0563506	−	0.00849349i	−0.00452619	−	0.000682213i
$156$		0			0
$157$	7.98170	+	5.44183i	0.637009	+	0.434305i	0.838287	−	0.545229i	$-0.183557\pi$
$157$	7.98170	+	5.44183i	0.637009	+	0.434305i	−0.201279	+	0.979534i	$0.564510\pi$
$158$	−8.63008	+	8.00754i	−0.686572	+	0.637046i
$159$		0			0
$160$	0.189819	+	0.0585515i	0.0150065	+	0.00462890i
$161$	−0.969481	−	0.466877i	−0.0764058	−	0.0367951i
$162$		0			0
$163$	−0.507211	−	6.76827i	−0.0397279	−	0.530131i	−0.981194	−	0.193024i	$-0.938170\pi$
$163$	−0.507211	−	6.76827i	−0.0397279	−	0.530131i	0.941466	−	0.337107i	$-0.109449\pi$
$164$	−3.29850	−	4.13619i	−0.257570	−	0.322982i
$165$		0			0
$166$	−2.21138	+	3.83022i	−0.171636	+	0.297283i
$167$	−13.8043	+	2.08066i	−1.06821	+	0.161006i	−0.659534	−	0.751675i	$-0.729246\pi$
$167$	−13.8043	+	2.08066i	−1.06821	+	0.161006i	−0.408672	+	0.912681i	$0.634008\pi$
$168$		0			0
$169$	−8.04007	−	7.46009i	−0.618467	−	0.573853i
$170$	−0.0752754	−	0.329803i	−0.00577336	−	0.0252947i
$171$		0			0
$172$	−16.4884	+	6.90818i	−1.25722	+	0.526744i
$173$	−11.5110			−0.875168			−0.437584	−	0.899178i	$-0.644166\pi$
$173$	−11.5110			−0.875168			−0.437584	+	0.899178i	$0.644166\pi$
$174$		0			0
$175$	−11.4680	−	10.6408i	−0.866900	−	0.804366i
$176$	6.80113	−	3.27525i	0.512655	−	0.246882i
$177$		0			0
$178$	4.35004	−	7.53449i	0.326049	−	0.564734i
$179$	0.378359	+	0.655338i	0.0282799	+	0.0489823i	0.879819	−	0.475309i	$-0.157664\pi$
$179$	0.378359	+	0.655338i	0.0282799	+	0.0489823i	−0.851539	+	0.524291i	$0.824330\pi$
$180$		0			0
$181$	−0.0777475	−	1.03747i	−0.00577892	−	0.0771144i	0.993569	−	0.113231i	$-0.0361201\pi$
$181$	−0.0777475	−	1.03747i	−0.00577892	−	0.0771144i	−0.999348	+	0.0361170i	$0.988501\pi$
$182$	−12.1679	−	31.0032i	−0.901942	−	2.29811i
$183$		0			0
$184$	0.518773	+	0.160020i	0.0382444	+	0.0117968i
$185$	−0.0964797	+	0.245826i	−0.00709333	+	0.0180735i
$186$		0			0
$187$	−18.2580	−	12.4481i	−1.33516	−	0.910294i
$188$	−18.8921	+	23.6900i	−1.37785	+	1.72777i
$189$		0			0
$190$	−0.216979	+	0.0669291i	−0.0157413	+	0.00485555i
$191$	1.03588	−	13.8228i	0.0749534	−	1.00018i	−0.825265	−	0.564745i	$-0.808974\pi$
$191$	1.03588	−	13.8228i	0.0749534	−	1.00018i	0.900219	−	0.435438i	$-0.143407\pi$
$192$		0			0
$193$	−3.28671	+	14.4000i	−0.236583	+	1.03654i	0.707470	+	0.706743i	$0.249836\pi$
$193$	−3.28671	+	14.4000i	−0.236583	+	1.03654i	−0.944053	+	0.329794i	$0.893021\pi$
$194$	4.35477	−	19.0795i	0.312654	−	1.36983i
$195$		0			0
$196$	0.568889	−	7.59129i	0.0406349	−	0.542235i
$197$	7.25577	−	2.23811i	0.516952	−	0.159459i	−0.0252911	−	0.999680i	$-0.508051\pi$
$197$	7.25577	−	2.23811i	0.516952	−	0.159459i	0.542243	+	0.840221i	$0.317575\pi$
$198$		0			0
$199$	−15.6429	+	19.6156i	−1.10890	+	1.39051i	−0.196844	+	0.980435i	$0.563069\pi$
$199$	−15.6429	+	19.6156i	−1.10890	+	1.39051i	−0.912051	+	0.410076i	$0.865502\pi$
$200$	6.52143	+	4.44624i	0.461135	+	0.314396i
$201$		0			0
$202$	12.1506	−	30.9592i	0.854911	−	2.17828i
$203$	−3.96417	−	1.22278i	−0.278230	−	0.0858226i
$204$		0			0
$205$	−0.0186548	−	0.0475315i	−0.00130290	−	0.00331975i
$206$	2.60098	+	34.7077i	0.181219	+	2.41820i
$207$		0			0
$208$	−4.94504	−	8.56505i	−0.342876	−	0.593879i
$209$	−7.41633	+	12.8455i	−0.512998	+	0.888539i
$210$		0			0
$211$	14.4636	−	6.96528i	0.995712	−	0.479510i	0.136231	−	0.990677i	$-0.456501\pi$
$211$	14.4636	−	6.96528i	0.995712	−	0.479510i	0.859481	+	0.511167i	$0.170787\pi$
$212$	−11.6288	−	10.7899i	−0.798668	−	0.741055i
$213$		0			0
$214$	35.9858			2.45994
$215$	−0.171723	+	0.0168060i	−0.0117114	+	0.00114616i
$216$		0			0
$217$	1.50809	+	6.60736i	0.102376	+	0.448537i
$218$	3.27893	+	3.04241i	0.222077	+	0.206058i
$219$		0			0
$220$	−0.265055	+	0.0399506i	−0.0178700	+	0.00269347i
$221$	−14.4759	+	25.0730i	−0.973754	+	1.68659i
$222$		0			0
$223$	−9.41103	−	11.8011i	−0.630209	−	0.790257i	0.359532	−	0.933133i	$-0.382937\pi$
$223$	−9.41103	−	11.8011i	−0.630209	−	0.790257i	−0.989741	+	0.142876i	$0.954365\pi$
$224$	−1.76543	−	23.5580i	−0.117958	−	1.57404i
$225$		0			0
$226$	−22.8495	−	11.0037i	−1.51993	−	0.731958i
$227$	−19.2669	−	5.94305i	−1.27879	−	0.394454i	−0.420346	−	0.907364i	$-0.638091\pi$
$227$	−19.2669	−	5.94305i	−1.27879	−	0.394454i	−0.858442	+	0.512910i	$0.828567\pi$
$228$		0			0
$229$	−9.80918	+	9.10159i	−0.648209	+	0.601450i	−0.934186	−	0.356786i	$-0.883872\pi$
$229$	−9.80918	+	9.10159i	−0.648209	+	0.601450i	0.285977	+	0.958236i	$0.407682\pi$
$230$	0.0162523	+	0.0110806i	0.00107164	+	0.000730633i
$231$		0			0
$232$	2.06964	+	0.311948i	0.135878	+	0.0204804i
$233$	−8.84939	+	2.72968i	−0.579743	+	0.178827i	−0.570738	−	0.821132i	$-0.693343\pi$
$233$	−8.84939	+	2.72968i	−0.579743	+	0.178827i	−0.00900522	+	0.999959i	$0.502866\pi$
$234$		0			0
$235$	−0.241635	+	0.164744i	−0.0157625	+	0.0107467i
$236$	0.104556	−	0.458091i	0.00680604	−	0.0298192i
$237$		0			0
$238$	−33.2404	+	22.6629i	−2.15465	+	1.46902i
$239$	1.43677	−	19.1723i	0.0929366	−	1.24015i	−0.734506	−	0.678602i	$-0.762586\pi$
$239$	1.43677	−	19.1723i	0.0929366	−	1.24015i	0.827442	−	0.561550i	$-0.189795\pi$
$240$		0			0
$241$	−5.72297	−	0.862599i	−0.368649	−	0.0555649i	−0.0378946	−	0.999282i	$-0.512065\pi$
$241$	−5.72297	−	0.862599i	−0.368649	−	0.0555649i	−0.330755	+	0.943717i	$0.607303\pi$
$242$	−4.01607	+	5.03599i	−0.258163	+	0.323726i
$243$		0			0
$244$	−11.1162	+	10.3143i	−0.711640	+	0.660305i
$245$	0.0268432	−	0.0683953i	0.00171495	−	0.00436961i
$246$		0			0
$247$	17.5088	+	8.43180i	1.11406	+	0.536503i
$248$	−1.24922	−	3.18295i	−0.0793253	−	0.202118i
$249$		0			0
$250$	0.356633	+	0.447204i	0.0225554	+	0.0282836i
$251$	3.71016	+	6.42619i	0.234184	+	0.405618i	0.959035	−	0.283287i	$-0.0914250\pi$
$251$	3.71016	+	6.42619i	0.234184	+	0.405618i	−0.724852	+	0.688905i	$0.758092\pi$
$252$		0			0
$253$	1.27056	−	0.191506i	0.0798795	−	0.0120399i
$254$	14.7718	−	7.11370i	0.926863	−	0.446353i
$255$		0			0
$256$	0.201207	+	0.881545i	0.0125754	+	0.0550966i
$257$	22.5274			1.40522			0.702609	−	0.711576i	$-0.252018\pi$
$257$	22.5274			1.40522			0.702609	+	0.711576i	$0.252018\pi$
$258$		0			0
$259$	31.4063			1.95149
$260$	0.0781471	+	0.342385i	0.00484648	+	0.0212338i
$261$		0			0
$262$	17.3621	−	8.36113i	1.07263	−	0.516552i
$263$	−5.37090	+	0.809533i	−0.331184	+	0.0499180i	−0.312530	−	0.949908i	$-0.601176\pi$
$263$	−5.37090	+	0.809533i	−0.331184	+	0.0499180i	−0.0186545	+	0.999826i	$0.505938\pi$
$264$		0			0
$265$	−0.0765549	−	0.132597i	−0.00470273	−	0.00814536i
$266$	16.8369	+	21.1128i	1.03234	+	1.29451i
$267$		0			0
$268$	−1.09655	−	2.79396i	−0.0669824	−	0.170668i
$269$	−2.16753	−	1.04383i	−0.132156	−	0.0636432i	0.366637	−	0.930364i	$-0.380509\pi$
$269$	−2.16753	−	1.04383i	−0.132156	−	0.0636432i	−0.498793	+	0.866721i	$0.666223\pi$
$270$		0			0
$271$	−1.20518	+	3.07074i	−0.0732093	+	0.186534i	−0.962794	−	0.270236i	$-0.912898\pi$
$271$	−1.20518	+	3.07074i	−0.0732093	+	0.186534i	0.889585	+	0.456770i	$0.150994\pi$
$272$	−8.75747	+	8.12574i	−0.531000	+	0.492696i
$273$		0			0
$274$	−23.8139	+	29.8616i	−1.43865	+	1.80401i
$275$	18.4722	+	2.78424i	1.11392	+	0.167896i
$276$		0			0
$277$	−1.03223	+	13.7742i	−0.0620207	+	0.827609i	0.876283	+	0.481797i	$0.160016\pi$
$277$	−1.03223	+	13.7742i	−0.0620207	+	0.827609i	−0.938304	+	0.345812i	$0.887603\pi$
$278$	27.7451	−	18.9163i	1.66404	−	1.13452i
$279$		0			0
$280$	−0.0289272	+	0.126739i	−0.00172873	+	0.00757407i
$281$	−14.8789	+	10.1443i	−0.887603	+	0.605157i	−0.918960	−	0.394351i	$-0.870969\pi$
$281$	−14.8789	+	10.1443i	−0.887603	+	0.605157i	0.0313571	+	0.999508i	$0.490017\pi$
$282$		0			0
$283$	−12.7020	+	3.91805i	−0.755057	+	0.232904i	−0.648304	−	0.761382i	$-0.724521\pi$
$283$	−12.7020	+	3.91805i	−0.755057	+	0.232904i	−0.106752	+	0.994286i	$0.534045\pi$
$284$	−14.2725	−	2.15123i	−0.846916	−	0.127652i
$285$		0			0
$286$	32.8599	+	22.4035i	1.94304	+	1.32475i
$287$	−4.45148	+	4.13037i	−0.262763	+	0.243808i
$288$		0			0
$289$	17.1735	+	5.29732i	1.01021	+	0.311607i
$290$	0.0683246	+	0.0329034i	0.00401216	+	0.00193215i
$291$		0			0
$292$	−1.50684	−	20.1073i	−0.0881810	−	1.17669i
$293$	2.31732	+	2.90583i	0.135379	+	0.169760i	0.844900	−	0.534924i	$-0.179660\pi$
$293$	2.31732	+	2.90583i	0.135379	+	0.169760i	−0.709521	+	0.704685i	$0.751088\pi$
$294$		0			0
$295$	0.00226753	−	0.00392748i	0.000132021	−	0.000228667i
$296$	−15.6683	+	2.36162i	−0.910702	+	0.137266i
$297$		0			0
$298$	11.5692	+	10.7347i	0.670187	+	0.621842i
$299$	−0.374604	−	1.64125i	−0.0216639	−	0.0949157i
$300$		0			0
$301$	9.32167	+	18.2805i	0.537292	+	1.05367i
$302$	21.8104			1.25505
$303$		0			0
$304$	5.87828	+	5.45425i	0.337142	+	0.312823i
$305$	−0.131866	+	0.0635035i	−0.00755064	+	0.00363620i
$306$		0			0
$307$	−4.87728	+	8.44770i	−0.278361	+	0.482136i	−0.970978	−	0.239170i	$-0.923125\pi$
$307$	−4.87728	+	8.44770i	−0.278361	+	0.482136i	0.692617	+	0.721306i	$0.256458\pi$
$308$	15.9391	+	27.6073i	0.908212	+	1.57307i
$309$		0			0
$310$	−0.00925826	−	0.123543i	−0.000525834	−	0.00701676i
$311$	1.43950	+	3.66777i	0.0816263	+	0.207980i	0.965860	−	0.259064i	$-0.0834141\pi$
$311$	1.43950	+	3.66777i	0.0816263	+	0.207980i	−0.884234	+	0.467044i	$0.845319\pi$
$312$		0			0
$313$	−21.8743	−	6.74733i	−1.23641	−	0.381382i	−0.393444	−	0.919349i	$-0.628716\pi$
$313$	−21.8743	−	6.74733i	−1.23641	−	0.381382i	−0.842966	+	0.537967i	$0.819193\pi$
$314$	−7.67265	+	19.5496i	−0.432992	+	1.10325i
$315$		0			0
$316$	−12.1980	−	8.31648i	−0.686193	−	0.467839i
$317$	−6.42280	+	8.05394i	−0.360740	+	0.452354i	−0.928771	−	0.370653i	$-0.879134\pi$
$317$	−6.42280	+	8.05394i	−0.360740	+	0.452354i	0.568031	+	0.823007i	$0.307705\pi$
$318$		0			0
$319$	4.73365	−	1.46014i	0.265034	−	0.0817520i
$320$	−0.0243276	+	0.324630i	−0.00135996	+	0.0181473i
$321$		0			0
$322$	0.520544	−	2.28065i	0.0290088	−	0.127096i
$323$	5.22351	−	22.8857i	0.290644	−	1.27339i
$324$		0			0
$325$	1.82903	−	24.4067i	0.101456	−	1.35384i
$326$	14.0998	−	4.34923i	0.780918	−	0.240881i
$327$		0			0
$328$	1.91022	−	2.39534i	0.105474	−	0.132260i
$329$	28.7368	+	19.5924i	1.58431	+	1.08017i
$330$		0			0
$331$	−4.35233	+	11.0896i	−0.239226	+	0.609537i	−0.999182	−	0.0404371i	$-0.987125\pi$
$331$	−4.35233	+	11.0896i	−0.239226	+	0.609537i	0.759956	+	0.649974i	$0.225220\pi$
$332$	−5.29982	−	1.63478i	−0.290865	−	0.0897201i
$333$		0			0
$334$	−11.0878	−	28.2514i	−0.606700	−	1.54585i
$335$	−0.00216485	−	0.0288880i	−0.000118279	−	0.00157832i
$336$		0			0
$337$	1.63994	+	2.84045i	0.0893330	+	0.154729i	0.907229	−	0.420636i	$-0.138193\pi$
$337$	1.63994	+	2.84045i	0.0893330	+	0.154729i	−0.817896	+	0.575366i	$0.804860\pi$
$338$	11.9221	−	20.6497i	0.648476	−	1.12319i
$339$		0			0
$340$	0.382205	−	0.184060i	0.0207280	−	0.00998206i
$341$	−5.93245	−	5.50451i	−0.321260	−	0.298086i
$342$		0			0
$343$	13.1669			0.710945
$344$	−6.02512	−	8.41905i	−0.324853	−	0.453925i
$345$		0			0
$346$	−5.56856	−	24.3974i	−0.299367	−	1.31161i
$347$	−9.18271	−	8.52031i	−0.492954	−	0.457394i	0.394095	−	0.919070i	$-0.371058\pi$
$347$	−9.18271	−	8.52031i	−0.492954	−	0.457394i	−0.887049	+	0.461675i	$0.847248\pi$
$348$		0			0
$349$	−31.6460	+	4.76987i	−1.69397	+	0.255325i	−0.923900	−	0.382633i	$-0.875017\pi$
$349$	−31.6460	+	4.76987i	−1.69397	+	0.255325i	−0.770071	+	0.637958i	$0.779779\pi$
$350$	17.0052	−	29.4538i	0.908964	−	1.57437i
$351$		0			0
$352$	17.5885	+	22.0553i	0.937470	+	1.17555i
$353$	0.179426	+	2.39427i	0.00954988	+	0.127434i	0.999941	−	0.0108603i	$-0.00345700\pi$
$353$	0.179426	+	2.39427i	0.00954988	+	0.127434i	−0.990391	+	0.138295i	$0.955838\pi$
$354$		0			0
$355$	−0.125514	−	0.0604442i	−0.00666157	−	0.00320805i
$356$	10.4254	+	3.21580i	0.552543	+	0.170437i
$357$		0			0
$358$	−1.20594	+	1.11895i	−0.0637360	+	0.0591384i
$359$	−6.81331	−	4.64523i	−0.359593	−	0.245166i	0.370024	−	0.929022i	$-0.379349\pi$
$359$	−6.81331	−	4.64523i	−0.359593	−	0.245166i	−0.729617	+	0.683856i	$0.760302\pi$
$360$		0			0
$361$	3.20715	+	0.483400i	0.168797	+	0.0254421i
$362$	2.16128	−	0.666667i	0.113595	−	0.0350393i
$363$		0			0
$364$	34.5085	−	23.5275i	1.80874	−	1.23318i
$365$	0.0433057	−	0.189735i	0.00226672	−	0.00993117i
$366$		0			0
$367$	8.55721	−	5.83421i	0.446683	−	0.304543i	−0.319008	−	0.947752i	$-0.603350\pi$
$367$	8.55721	−	5.83421i	0.446683	−	0.304543i	0.765691	+	0.643209i	$0.222397\pi$
$368$	0.0519117	−	0.692714i	0.00270608	−	0.0361102i
$369$		0			0
$370$	−0.567697	−	0.0855666i	−0.0295132	−	0.00444840i
$371$	−11.3530	+	14.2362i	−0.589418	+	0.739107i
$372$		0			0
$373$	−8.47754	+	7.86601i	−0.438950	+	0.407286i	−0.868447	−	0.495782i	$-0.834882\pi$
$373$	−8.47754	+	7.86601i	−0.438950	+	0.407286i	0.429497	+	0.903068i	$0.358691\pi$
$374$	17.5510	−	44.7193i	0.907543	−	2.31238i
$375$		0			0
$376$	−15.8098	−	7.61361i	−0.815329	−	0.392642i
$377$	−2.37115	−	6.04159i	−0.122120	−	0.311158i
$378$		0			0
$379$	7.24547	+	9.08554i	0.372175	+	0.466693i	0.932284	−	0.361726i	$-0.117812\pi$
$379$	7.24547	+	9.08554i	0.372175	+	0.466693i	−0.560110	+	0.828419i	$0.689241\pi$
$380$	−0.142373	−	0.246598i	−0.00730359	−	0.0126502i
$381$		0			0
$382$	29.7983	−	4.49137i	1.52461	−	0.229799i
$383$	−15.8309	+	7.62376i	−0.808921	+	0.389556i	−0.792167	−	0.610304i	$-0.791047\pi$
$383$	−15.8309	+	7.62376i	−0.808921	+	0.389556i	−0.0167535	+	0.999860i	$0.505333\pi$
$384$		0			0
$385$	0.0684647	+	0.299964i	0.00348929	+	0.0152876i
$386$	−32.1106			−1.63439
$387$		0			0
$388$	24.5414			1.24590
$389$	1.45910	+	6.39272i	0.0739792	+	0.324124i	0.998353	−	0.0573631i	$-0.0182693\pi$
$389$	1.45910	+	6.39272i	0.0739792	+	0.324124i	−0.924374	+	0.381487i	$0.875412\pi$
$390$		0			0
$391$	−1.83213	+	0.882306i	−0.0926546	+	0.0446201i
$392$	4.35933	−	0.657063i	0.220179	−	0.0331867i
$393$		0			0
$394$	8.25367	+	14.2958i	0.415814	+	0.720210i
$395$	−0.0888418	−	0.111404i	−0.00447012	−	0.00560535i
$396$		0			0
$397$	−10.7843	−	27.4779i	−0.541248	−	1.37908i	−0.895973	−	0.444108i	$-0.853521\pi$
$397$	−10.7843	−	27.4779i	−0.541248	−	1.37908i	0.354725	−	0.934971i	$-0.384575\pi$
$398$	−49.1422	−	23.6656i	−2.46328	−	1.18625i
$399$		0			0
$400$	3.68971	−	9.40123i	0.184486	−	0.470061i
$401$	18.2470	−	16.9307i	0.911210	−	0.845479i	−0.0772425	−	0.997012i	$-0.524612\pi$
$401$	18.2470	−	16.9307i	0.911210	−	0.845479i	0.988452	+	0.151533i	$0.0484211\pi$
$402$		0			0
$403$	−6.61084	+	8.28973i	−0.329309	+	0.412941i
$404$	41.2406	+	6.21602i	2.05180	+	0.309258i
$405$		0			0
$406$	0.673971	−	8.99352i	0.0334486	−	0.446341i
$407$	−30.9860	+	21.1259i	−1.53592	+	1.04717i
$408$		0			0
$409$	2.84836	−	12.4795i	0.140843	−	0.617072i	−0.854398	−	0.519620i	$-0.826074\pi$
$409$	2.84836	−	12.4795i	0.140843	−	0.617072i	0.995240	−	0.0974519i	$-0.0310692\pi$
$410$	0.0917178	−	0.0625322i	0.00452962	−	0.00308824i
$411$		0			0
$412$	−41.7071	+	12.8649i	−2.05476	+	0.633810i
$413$	−0.533315	−	0.0803843i	−0.0262427	−	0.00395545i
$414$		0			0
$415$	−0.0442289	−	0.0301548i	−0.00217111	−	0.00148024i
$416$	27.0933	−	25.1389i	1.32836	−	1.23254i
$417$		0			0
$418$	−30.8134	−	9.50468i	−1.50713	−	0.464889i
$419$	25.2233	+	12.1469i	1.23224	+	0.593415i	0.932695	−	0.360667i	$-0.117451\pi$
$419$	25.2233	+	12.1469i	1.23224	+	0.593415i	0.299545	+	0.954082i	$0.403165\pi$
$420$		0			0
$421$	1.03389	+	13.7963i	0.0503885	+	0.672388i	0.964017	+	0.265839i	$0.0856490\pi$
$421$	1.03389	+	13.7963i	0.0503885	+	0.672388i	−0.913629	+	0.406549i	$0.866732\pi$
$422$	21.7596	+	27.2857i	1.05924	+	1.32825i
$423$		0			0
$424$	4.59341	−	7.95602i	0.223076	−	0.386379i
$425$	−29.2342	+	4.40635i	−1.41807	+	0.213739i
$426$		0			0
$427$	12.7596	+	11.8392i	0.617481	+	0.572938i
$428$	10.0417	+	43.9955i	0.485383	+	2.12660i
$429$		0			0
$430$	−0.118692	−	0.355834i	−0.00572386	−	0.0171599i
$431$	32.0319			1.54292			0.771462	−	0.636276i	$-0.219526\pi$
$431$	32.0319			1.54292			0.771462	+	0.636276i	$0.219526\pi$
$432$		0			0
$433$	−0.278233	−	0.258163i	−0.0133710	−	0.0124065i	0.673459	−	0.739225i	$-0.264808\pi$
$433$	−0.278233	−	0.258163i	−0.0133710	−	0.0124065i	−0.686830	+	0.726818i	$0.740998\pi$
$434$	−13.2746	+	6.39272i	−0.637202	+	0.306860i
$435$		0			0
$436$	−2.80461	+	4.85772i	−0.134316	+	0.232643i
$437$	0.682476	+	1.18208i	0.0326473	+	0.0565467i
$438$		0			0
$439$	0.364516	+	4.86413i	0.0173974	+	0.232152i	0.999124	+	0.0418540i	$0.0133264\pi$
$439$	0.364516	+	4.86413i	0.0173974	+	0.232152i	−0.981726	+	0.190298i	$0.939055\pi$
$440$	−0.0567125	−	0.144501i	−0.00270366	−	0.00688882i
$441$		0			0
$442$	−60.1445	−	18.5521i	−2.86078	−	0.882435i
$443$	−2.16832	+	5.52479i	−0.103020	+	0.262491i	−0.973085	−	0.230446i	$-0.925981\pi$
$443$	−2.16832	+	5.52479i	−0.103020	+	0.262491i	0.870065	+	0.492937i	$0.164077\pi$
$444$		0			0
$445$	0.0870035	+	0.0593180i	0.00412436	+	0.00281194i
$446$	20.4595	−	25.6554i	0.968784	−	1.21482i
$447$		0			0
$448$	36.9953	−	11.4115i	1.74786	−	0.539144i
$449$	−2.44448	+	32.6193i	−0.115362	+	1.53940i	0.576336	+	0.817213i	$0.304482\pi$
$449$	−2.44448	+	32.6193i	−0.115362	+	1.53940i	−0.691698	+	0.722187i	$0.743137\pi$
$450$		0			0
$451$	1.61356	−	7.06946i	0.0759795	−	0.332888i
$452$	7.07688	−	31.0059i	0.332869	−	1.45839i
$453$		0			0
$454$	3.27567	−	43.7108i	0.153735	−	2.05145i
$455$	0.385201	−	0.118819i	0.0180585	−	0.00557031i
$456$		0			0
$457$	18.1197	−	22.7213i	0.847602	−	1.06286i	−0.149647	−	0.988739i	$-0.547814\pi$
$457$	18.1197	−	22.7213i	0.847602	−	1.06286i	0.997249	−	0.0741197i	$-0.0236147\pi$
$458$	−24.0359	−	16.3874i	−1.12312	−	0.765734i
$459$		0			0
$460$	−0.00901178	+	0.0229616i	−0.000420177	+	0.00107059i
$461$	13.8948	+	4.28598i	0.647146	+	0.199618i	0.600915	−	0.799313i	$-0.294803\pi$
$461$	13.8948	+	4.28598i	0.647146	+	0.199618i	0.0462305	+	0.998931i	$0.485279\pi$
$462$		0			0
$463$	−2.25869	−	5.75504i	−0.104970	−	0.267459i	0.868733	−	0.495281i	$-0.164935\pi$
$463$	−2.25869	−	5.75504i	−0.104970	−	0.267459i	−0.973703	+	0.227822i	$0.926840\pi$
$464$	−0.200136	−	2.67062i	−0.00929106	−	0.123981i
$465$		0			0
$466$	−10.0665	−	17.4356i	−0.466320	−	0.807689i
$467$	−7.90363	+	13.6895i	−0.365736	+	0.633474i	−0.988894	−	0.148622i	$-0.952516\pi$
$467$	−7.90363	+	13.6895i	−0.365736	+	0.633474i	0.623158	+	0.782096i	$0.285850\pi$
$468$		0			0
$469$	−3.10400	+	1.49481i	−0.143329	+	0.0690237i
$470$	−0.466065	−	0.432445i	−0.0214980	−	0.0199472i
$471$		0			0
$472$	0.272111			0.0125249
$473$	−21.4936	−	11.7656i	−0.988278	−	0.540981i
$474$		0			0
$475$	4.41583	+	19.3470i	0.202612	+	0.887702i
$476$	−36.9828	−	34.3150i	−1.69510	−	1.57283i
$477$		0			0
$478$	41.3304	−	6.22955i	1.89041	−	0.284933i
$479$	19.2621	−	33.3629i	0.880107	−	1.52439i	0.0288864	−	0.999583i	$-0.490804\pi$
$479$	19.2621	−	33.3629i	0.880107	−	1.52439i	0.851221	−	0.524808i	$-0.175863\pi$
$480$		0			0
$481$	30.6350	+	38.4150i	1.39683	+	1.75157i
$482$	−0.940270	−	12.5470i	−0.0428281	−	0.571501i
$483$		0			0
$484$	−7.27757	−	3.50469i	−0.330798	−	0.159304i
$485$	0.226342	+	0.0698174i	0.0102777	+	0.00317024i
$486$		0			0
$487$	9.12024	−	8.46235i	0.413277	−	0.383465i	−0.445951	−	0.895057i	$-0.647134\pi$
$487$	9.12024	−	8.46235i	0.413277	−	0.383465i	0.859229	+	0.511592i	$0.170944\pi$
$488$	−7.25591	−	4.94700i	−0.328460	−	0.223940i
$489$		0			0
$490$	0.157948	+	0.0238068i	0.00713537	+	0.00107548i
$491$	36.8246	−	11.3589i	1.66187	−	0.512619i	0.685381	−	0.728185i	$-0.259636\pi$
$491$	36.8246	−	11.3589i	1.66187	−	0.512619i	0.976489	+	0.215566i	$0.0691597\pi$
$492$		0			0
$493$	−6.47754	+	4.41631i	−0.291734	+	0.198901i
$494$	−9.40102	+	41.1886i	−0.422972	+	1.85316i
$495$		0			0
$496$	−3.61494	+	2.46463i	−0.162316	+	0.110665i
$497$	−1.23810	+	16.5213i	−0.0555363	+	0.741081i
$498$		0			0
$499$	41.3979	+	6.23973i	1.85322	+	0.279329i	0.978645	−	0.205556i	$-0.0659002\pi$
$499$	41.3979	+	6.23973i	1.85322	+	0.279329i	0.874578	+	0.484884i	$0.161138\pi$
$500$	−0.447225	+	0.560802i	−0.0200005	+	0.0250798i
$501$		0			0
$502$	−11.8254	+	10.9723i	−0.527792	+	0.489720i
$503$	5.36535	−	13.6707i	0.239229	−	0.609546i	−0.759953	−	0.649978i	$-0.774778\pi$
$503$	5.36535	−	13.6707i	0.239229	−	0.609546i	0.999182	+	0.0404321i	$0.0128734\pi$
$504$		0			0
$505$	0.362674	+	0.174654i	0.0161388	+	0.00777202i
$506$	1.02054	+	2.60029i	0.0453684	+	0.115597i
$507$		0			0
$508$	12.8191	+	16.0746i	0.568754	+	0.713195i
$509$	−11.0632	−	19.1620i	−0.490368	−	0.849342i	0.509571	−	0.860429i	$-0.329804\pi$
$509$	−11.0632	−	19.1620i	−0.490368	−	0.849342i	−0.999939	+	0.0110868i	$0.996471\pi$
$510$		0			0
$511$	−22.8863	+	3.44955i	−1.01243	+	0.152599i
$512$	19.4877	−	9.38480i	0.861244	−	0.414753i
$513$		0			0
$514$	10.8978	+	47.7463i	0.480681	+	2.10600i
$515$	−0.421259			−0.0185629
$516$		0			0
$517$	−41.5315			−1.82655
$518$	15.1930	+	66.5650i	0.667543	+	2.92470i
$519$		0			0
$520$	−0.183239	+	0.0882432i	−0.00803556	+	0.00386972i
$521$	−25.2437	+	3.80487i	−1.10594	+	0.166694i	−0.676531	−	0.736414i	$-0.736518\pi$
$521$	−25.2437	+	3.80487i	−1.10594	+	0.166694i	−0.429413	+	0.903108i	$0.641280\pi$
$522$		0			0
$523$	−14.2828	−	24.7386i	−0.624544	−	1.08174i	−0.988629	−	0.150376i	$-0.951952\pi$
$523$	−14.2828	−	24.7386i	−0.624544	−	1.08174i	0.364085	−	0.931366i	$-0.381382\pi$
$524$	15.0670	+	18.8934i	0.658203	+	0.825360i
$525$		0			0
$526$	−4.31401	−	10.9919i	−0.188100	−	0.479270i
$527$	11.5393	+	5.55706i	0.502662	+	0.242069i
$528$		0			0
$529$	−8.35964	+	21.3000i	−0.363463	+	0.926088i
$530$	0.244003	−	0.226401i	0.0105988	−	0.00983425i
$531$		0			0
$532$	−21.1138	+	26.4758i	−0.915398	+	1.14787i
$533$	−9.39428	−	1.41596i	−0.406911	−	0.0613320i
$534$		0			0
$535$	−0.0325488	+	0.434333i	−0.00140721	+	0.0187779i
$536$	1.43615	−	0.979154i	0.0620324	−	0.0422930i
$537$		0			0
$538$	1.16381	−	5.09899i	0.0501755	−	0.219833i
$539$	8.62112	−	5.87778i	0.371338	−	0.253174i
$540$		0			0
$541$	−1.66509	+	0.513613i	−0.0715879	+	0.0220819i	−0.330342	−	0.943861i	$-0.607164\pi$
$541$	−1.66509	+	0.513613i	−0.0715879	+	0.0220819i	0.258754	+	0.965943i	$0.416688\pi$
$542$	−7.09139	−	1.06886i	−0.304601	−	0.0459113i
$543$		0			0
$544$	−36.8873	−	25.1494i	−1.58153	−	1.07827i
$545$	−0.0396863	+	0.0368235i	−0.00169997	+	0.00157735i
$546$		0			0
$547$	10.3354	+	3.18805i	0.441909	+	0.136311i	0.507722	−	0.861521i	$-0.330488\pi$
$547$	10.3354	+	3.18805i	0.441909	+	0.136311i	−0.0658126	+	0.997832i	$0.520964\pi$
$548$	−43.1534	−	20.7816i	−1.84342	−	0.887745i
$549$		0			0
$550$	3.03494	+	40.4985i	0.129410	+	1.72686i
$551$	3.28100	+	4.11424i	0.139775	+	0.175273i
$552$		0			0
$553$	−8.47299	+	14.6756i	−0.360308	+	0.624072i
$554$	−29.6934	+	4.47556i	−1.26155	+	0.190148i
$555$		0			0
$556$	30.8688	+	28.6421i	1.30913	+	1.21469i
$557$	0.0339125	+	0.148580i	0.00143692	+	0.00629554i	0.975641	−	0.219372i	$-0.0704008\pi$
$557$	0.0339125	+	0.148580i	0.00143692	+	0.00629554i	−0.974204	+	0.225668i	$0.927544\pi$
$558$		0			0
$559$	−13.2674	+	29.2335i	−0.561149	+	1.23645i
$560$	0.166338			0.00702908
$561$		0			0
$562$	−28.6984	−	26.6283i	−1.21057	−	1.12324i
$563$	−21.4601	+	10.3347i	−0.904437	+	0.435554i	−0.827489	−	0.561481i	$-0.810232\pi$
$563$	−21.4601	+	10.3347i	−0.904437	+	0.435554i	−0.0769474	+	0.997035i	$0.524517\pi$
$564$		0			0
$565$	0.153478	−	0.265831i	0.00645685	−	0.0111836i
$566$	−14.4489	−	25.0263i	−0.607334	−	1.05193i
$567$		0			0
$568$	−0.624654	−	8.33542i	−0.0262099	−	0.349747i
$569$	−11.4363	−	29.1391i	−0.479433	−	1.22158i	−0.942187	−	0.335088i	$-0.891234\pi$
$569$	−11.4363	−	29.1391i	−0.479433	−	1.22158i	0.462754	−	0.886487i	$-0.346861\pi$
$570$		0			0
$571$	−4.21255	−	1.29940i	−0.176290	−	0.0543782i	0.205354	−	0.978688i	$-0.434166\pi$
$571$	−4.21255	−	1.29940i	−0.176290	−	0.0543782i	−0.381643	+	0.924310i	$0.624642\pi$
$572$	−18.2206	+	46.4254i	−0.761842	+	1.94114i
$573$		0			0
$574$	−10.9077	−	7.43673i	−0.455278	−	0.310403i
$575$	1.07183	−	1.34403i	0.0446983	−	0.0560499i
$576$		0			0
$577$	24.4740	−	7.54924i	1.01887	−	0.314279i	0.260059	−	0.965593i	$-0.416258\pi$
$577$	24.4740	−	7.54924i	1.01887	−	0.314279i	0.758809	+	0.651314i	$0.225782\pi$
$578$	−2.91976	+	38.9615i	−0.121446	+	1.62059i
$579$		0			0
$580$	−0.0211613	+	0.0927137i	−0.000878675	+	0.00384973i
$581$	−1.41661	+	6.20657i	−0.0587709	+	0.257492i
$582$		0			0
$583$	1.62488	−	21.6825i	0.0672956	−	0.897997i
$584$	11.1584	−	3.44190i	0.461736	−	0.142427i
$585$		0			0
$586$	−5.03783	+	6.31724i	−0.208111	+	0.260963i
$587$	−21.8609	−	14.9045i	−0.902298	−	0.615176i	0.0207824	−	0.999784i	$-0.493384\pi$
$587$	−21.8609	−	14.9045i	−0.902298	−	0.615176i	−0.923080	+	0.384608i	$0.874337\pi$
$588$		0			0
$589$	3.14081	−	8.00265i	0.129415	−	0.329744i
$590$	0.00942115	+	0.00290604i	0.000387863	+	0.000119640i
$591$		0			0
$592$	7.40722	+	18.8733i	0.304435	+	0.775687i
$593$	2.82909	+	37.7516i	0.116177	+	1.55027i	0.685448	+	0.728121i	$0.259606\pi$
$593$	2.82909	+	37.7516i	0.116177	+	1.55027i	−0.569272	+	0.822149i	$0.692775\pi$
$594$		0			0
$595$	−0.243466	−	0.421696i	−0.00998114	−	0.0172878i
$596$	−9.89563	+	17.1397i	−0.405341	+	0.702071i
$597$		0			0
$598$	3.29737	−	1.58793i	0.134840	−	0.0649353i
$599$	−5.30017	−	4.91784i	−0.216559	−	0.200938i	0.564432	−	0.825480i	$-0.309095\pi$
$599$	−5.30017	−	4.91784i	−0.216559	−	0.200938i	−0.780991	+	0.624542i	$0.785286\pi$
$600$		0			0
$601$	1.42190			0.0580006			0.0290003	−	0.999579i	$-0.490768\pi$
$601$	1.42190			0.0580006			0.0290003	+	0.999579i	$0.490768\pi$
$602$	−34.2358	+	28.6005i	−1.39535	+	1.16567i
$603$		0			0
$604$	6.08610	+	26.6650i	0.247640	+	1.08498i
$605$	−0.0571498	−	0.0530272i	−0.00232347	−	0.00215586i
$606$		0			0
$607$	−11.6641	+	1.75808i	−0.473432	+	0.0713583i	−0.381424	−	0.924400i	$-0.624566\pi$
$607$	−11.6641	+	1.75808i	−0.473432	+	0.0713583i	−0.0920071	+	0.995758i	$0.529328\pi$
$608$	−14.9835	+	25.9522i	−0.607661	+	1.05250i
$609$		0			0
$610$	−0.198386	−	0.248768i	−0.00803241	−	0.0100723i
$611$	4.06631	+	54.2611i	0.164505	+	2.19517i
$612$		0			0
$613$	21.6428	+	10.4226i	0.874145	+	0.420966i	0.816483	−	0.577370i	$-0.195921\pi$
$613$	21.6428	+	10.4226i	0.874145	+	0.420966i	0.0576626	+	0.998336i	$0.481635\pi$
$614$	−20.2642	−	6.25067i	−0.817795	−	0.252256i
$615$		0			0
$616$	−13.5330	+	12.5568i	−0.545259	+	0.505927i
$617$	−1.32647	−	0.904369i	−0.0534015	−	0.0364085i	0.536325	−	0.844011i	$-0.319812\pi$
$617$	−1.32647	−	0.904369i	−0.0534015	−	0.0364085i	−0.589727	+	0.807603i	$0.700764\pi$
$618$		0			0
$619$	−48.0499	−	7.24235i	−1.93129	−	0.291095i	−0.933557	−	0.358428i	$-0.883313\pi$
$619$	−48.0499	−	7.24235i	−1.93129	−	0.291095i	−0.997731	+	0.0673331i	$0.978551\pi$
$620$	0.148457	−	0.0457931i	0.00596219	−	0.00183909i
$621$		0			0
$622$	−7.07741	+	4.82530i	−0.283778	+	0.193477i
$623$	2.78664	−	12.2091i	0.111644	−	0.489146i
$624$		0			0
$625$	20.6474	−	14.0772i	0.825896	−	0.563086i
$626$	3.71898	−	49.6263i	0.148640	−	1.98347i
$627$		0			0
$628$	−26.0419	−	3.92519i	−1.03919	−	0.156632i
$629$	37.0051	−	46.4030i	1.47549	−	1.85021i
$630$		0			0
$631$	14.5938	−	13.5411i	0.580971	−	0.539062i	−0.334005	−	0.942571i	$-0.608400\pi$
$631$	14.5938	−	13.5411i	0.580971	−	0.539062i	0.914975	+	0.403509i	$0.132210\pi$
$632$	3.12355	−	7.95868i	0.124248	−	0.316579i
$633$		0			0
$634$	−20.1773	−	9.71685i	−0.801341	−	0.385905i
$635$	0.0724985	+	0.184723i	0.00287701	+	0.00733051i
$636$		0			0
$637$	−8.52344	−	10.6881i	−0.337711	−	0.423476i
$638$	5.38468	+	9.32653i	0.213181	+	0.369241i
$639$		0			0
$640$	−0.306963	+	0.0462673i	−0.0121338	+	0.00182887i
$641$	19.5056	−	9.39338i	0.770423	−	0.371016i	−0.00701500	−	0.999975i	$-0.502233\pi$
$641$	19.5056	−	9.39338i	0.770423	−	0.371016i	0.777438	+	0.628959i	$0.216519\pi$
$642$		0			0
$643$	−0.473254	−	2.07346i	−0.0186633	−	0.0817694i	0.964739	−	0.263210i	$-0.0847812\pi$
$643$	−0.473254	−	2.07346i	−0.0186633	−	0.0817694i	−0.983402	+	0.181440i	$0.941924\pi$
$644$	2.93353			0.115597
$645$		0			0
$646$	51.0327			2.00785
$647$	−0.593026	−	2.59822i	−0.0233143	−	0.102146i	0.961932	−	0.273289i	$-0.0881114\pi$
$647$	−0.593026	−	2.59822i	−0.0233143	−	0.102146i	−0.985246	+	0.171142i	$0.945254\pi$
$648$		0			0
$649$	0.580250	−	0.279434i	0.0227768	−	0.0109687i
$650$	52.6144	−	7.93034i	2.06371	−	0.311054i
$651$		0			0
$652$	9.25177	+	16.0245i	0.362327	+	0.627569i
$653$	−8.03489	−	10.0754i	−0.314429	−	0.394282i	0.599354	−	0.800484i	$-0.295424\pi$
$653$	−8.03489	−	10.0754i	−0.314429	−	0.394282i	−0.913783	+	0.406202i	$0.866853\pi$
$654$		0			0
$655$	0.0852115	+	0.217115i	0.00332949	+	0.00848340i
$656$	−3.53199	−	1.70092i	−0.137901	−	0.0664097i
$657$		0			0
$658$	−27.6241	+	70.3852i	−1.07690	+	2.74390i
$659$	−28.5593	+	26.4992i	−1.11251	+	1.03226i	−0.113261	+	0.993565i	$0.536130\pi$
$659$	−28.5593	+	26.4992i	−1.11251	+	1.03226i	−0.999251	+	0.0386951i	$0.987680\pi$
$660$		0			0
$661$	24.8200	−	31.1233i	0.965387	−	1.21056i	−0.0121787	−	0.999926i	$-0.503877\pi$
$661$	24.8200	−	31.1233i	0.965387	−	1.21056i	0.977566	−	0.210631i	$-0.0675519\pi$
$662$	−25.6096	−	3.86002i	−0.995344	−	0.150024i
$663$		0			0
$664$	0.240026	−	3.20293i	0.00931483	−	0.124298i
$665$	−0.270051	+	0.184118i	−0.0104721	+	0.00713977i
$666$		0			0
$667$	0.101438	−	0.444430i	0.00392770	−	0.0172084i
$668$	31.4455	−	21.4392i	1.21666	−	0.829507i
$669$		0			0
$670$	0.0601803	−	0.0185631i	0.00232497	−	0.000717157i
$671$	−20.5527	−	3.09782i	−0.793428	−	0.119590i
$672$		0			0
$673$	−30.9218	−	21.0822i	−1.19195	−	0.812657i	−0.205813	−	0.978591i	$-0.565984\pi$
$673$	−30.9218	−	21.0822i	−1.19195	−	0.812657i	−0.986137	+	0.165934i	$0.946936\pi$
$674$	−5.22696	+	4.84991i	−0.201335	+	0.186811i
$675$		0			0
$676$	28.5726	+	8.81349i	1.09895	+	0.338980i
$677$	−4.02286	−	1.93731i	−0.154611	−	0.0744567i	0.354978	−	0.934875i	$-0.384488\pi$
$677$	−4.02286	−	1.93731i	−0.154611	−	0.0744567i	−0.509589	+	0.860418i	$0.670203\pi$
$678$		0			0
$679$	−2.10512	−	28.0908i	−0.0807870	−	1.07803i
$680$	0.153173	+	0.192073i	0.00587391	+	0.00736565i
$681$		0			0
$682$	8.79683	−	15.2366i	0.336848	−	0.583438i
$683$	37.5870	−	5.66533i	1.43823	−	0.216778i	0.616812	−	0.787110i	$-0.288424\pi$
$683$	37.5870	−	5.66533i	1.43823	−	0.216778i	0.821414	+	0.570333i	$0.193186\pi$
$684$		0			0
$685$	−0.338878	−	0.314433i	−0.0129479	−	0.0120139i
$686$	6.36958	+	27.9070i	0.243192	+	1.06549i
$687$		0			0
$688$	−8.78697	+	9.91326i	−0.335000	+	0.377939i
$689$	−28.4874			−1.08528
$690$		0			0
$691$	4.15300	+	3.85342i	0.157988	+	0.146591i	0.755206	−	0.655488i	$-0.227537\pi$
$691$	4.15300	+	3.85342i	0.157988	+	0.146591i	−0.597218	+	0.802079i	$0.703727\pi$
$692$	28.2739	−	13.6160i	1.07481	−	0.517602i
$693$		0			0
$694$	13.6164	−	23.5844i	0.516873	−	0.895250i
$695$	0.203216	+	0.351981i	0.00770844	+	0.0133514i
$696$		0			0
$697$	0.857594	+	11.4438i	0.0324837	+	0.433464i
$698$	−25.4186	−	64.7656i	−0.962110	−	2.45142i
$699$		0			0
$700$	40.7548	+	12.5712i	1.54039	+	0.475146i
$701$	9.33779	−	23.7923i	0.352683	−	0.898623i	−0.638916	−	0.769276i	$-0.720617\pi$
$701$	9.33779	−	23.7923i	0.352683	−	0.898623i	0.991600	−	0.129346i	$-0.0412878\pi$
$702$		0			0
$703$	−32.9162	−	22.4419i	−1.24146	−	0.846412i
$704$	−28.8241	+	36.1443i	−1.08635	+	1.36224i
$705$		0			0
$706$	−4.98782	+	1.53854i	−0.187719	+	0.0579036i
$707$	3.57750	−	47.7385i	0.134546	−	1.79539i
$708$		0			0
$709$	7.82205	−	34.2706i	0.293763	−	1.28706i	−0.585480	−	0.810687i	$-0.699094\pi$
$709$	7.82205	−	34.2706i	0.293763	−	1.28706i	0.879243	−	0.476373i	$-0.158049\pi$
$710$	0.0673921	−	0.295264i	0.00252918	−	0.0110811i
$711$		0			0
$712$	−0.472160	+	6.30054i	−0.0176949	+	0.236123i
$713$	−0.711641	+	0.219512i	−0.0266512	+	0.00822080i
$714$		0			0
$715$	−0.300122	+	0.376341i	−0.0112239	+	0.0140743i
$716$	−1.70452	−	1.16212i	−0.0637008	−	0.0434305i
$717$		0			0
$718$	6.54950	−	16.6878i	0.244425	−	0.622785i
$719$	−4.82456	−	1.48818i	−0.179926	−	0.0554998i	0.203483	−	0.979078i	$-0.434774\pi$
$719$	−4.82456	−	1.48818i	−0.179926	−	0.0554998i	−0.383409	+	0.923579i	$0.625250\pi$
$720$		0			0
$721$	18.3032	+	46.6357i	0.681646	+	1.73681i
$722$	0.526927	+	7.03135i	0.0196102	+	0.261680i
$723$		0			0
$724$	1.41815	+	2.45631i	0.0527051	+	0.0912880i
$725$	3.31379	−	5.73965i	0.123071	−	0.213165i
$726$		0			0
$727$	14.8389	−	7.14602i	0.550343	−	0.265031i	−0.137981	−	0.990435i	$-0.544061\pi$
$727$	14.8389	−	7.14602i	0.550343	−	0.265031i	0.688324	+	0.725404i	$0.258347\pi$
$728$	17.7305	+	16.4515i	0.657136	+	0.609733i
$729$		0			0
$730$	0.423089			0.0156592
$731$	37.9931	+	7.76660i	1.40522	+	0.287258i
$732$		0			0
$733$	−2.52808	−	11.0763i	−0.0933769	−	0.409111i	0.906538	−	0.422123i	$-0.138715\pi$
$733$	−2.52808	−	11.0763i	−0.0933769	−	0.409111i	−0.999915	+	0.0130123i	$0.995858\pi$
$734$	16.5051	+	15.3145i	0.609215	+	0.565269i
$735$		0			0
$736$	2.56696	−	0.386907i	0.0946195	−	0.0142616i
$737$	2.05696	−	3.56276i	0.0757691	−	0.131236i
$738$		0			0
$739$	−18.4052	−	23.0794i	−0.677047	−	0.848990i	0.318032	−	0.948080i	$-0.396978\pi$
$739$	−18.4052	−	23.0794i	−0.677047	−	0.848990i	−0.995078	+	0.0990901i	$0.968407\pi$
$740$	−0.0538015	−	0.717932i	−0.00197778	−	0.0263917i
$741$		0			0
$742$	−35.6655	−	17.1756i	−1.30932	−	0.630536i
$743$	16.0390	+	4.94738i	0.588414	+	0.181502i	0.574644	−	0.818403i	$-0.305140\pi$
$743$	16.0390	+	4.94738i	0.588414	+	0.181502i	0.0137702	+	0.999905i	$0.495617\pi$
$744$		0			0
$745$	−0.140027	+	0.129926i	−0.00513019	+	0.00476012i
$746$	−20.7729	−	14.1627i	−0.760551	−	0.518535i
$747$		0			0
$748$	59.5705	+	8.97880i	2.17811	+	0.328298i
$749$	49.4973	−	15.2679i	1.80859	−	0.557877i
$750$		0			0
$751$	−44.5875	+	30.3993i	−1.62702	+	1.10928i	−0.715015	+	0.699110i	$0.753580\pi$
$751$	−44.5875	+	30.3993i	−1.62702	+	1.10928i	−0.912007	+	0.410175i	$0.865468\pi$
$752$	−4.99625	+	21.8900i	−0.182195	+	0.798247i
$753$		0			0
$754$	11.6580	−	7.94827i	0.424558	−	0.289459i
$755$	−0.0197273	+	0.263242i	−0.000717950	+	0.00958037i
$756$		0			0
$757$	−19.4613	−	2.93332i	−0.707332	−	0.106613i	−0.214483	−	0.976728i	$-0.568807\pi$
$757$	−19.4613	−	2.93332i	−0.707332	−	0.106613i	−0.492850	+	0.870115i	$0.664045\pi$
$758$	−15.7516	+	19.7518i	−0.572123	+	0.717419i
$759$		0			0
$760$	0.120881	−	0.112161i	0.00438482	−	0.00406852i
$761$	−13.7137	+	34.9420i	−0.497122	+	1.26665i	0.433662	+	0.901076i	$0.357221\pi$
$761$	−13.7137	+	34.9420i	−0.497122	+	1.26665i	−0.930784	+	0.365571i	$0.880874\pi$
$762$		0			0
$763$	5.80088	+	2.79356i	0.210006	+	0.101134i
$764$	13.8061	+	35.1775i	0.499489	+	1.27268i
$765$		0			0
$766$	−23.8167	−	29.8652i	−0.860533	−	1.07907i
$767$	−0.421894	−	0.730742i	−0.0152337	−	0.0263856i
$768$		0			0
$769$	30.4201	−	4.58509i	1.09698	−	0.165342i	0.424475	−	0.905439i	$-0.360459\pi$
$769$	30.4201	−	4.58509i	1.09698	−	0.165342i	0.672500	+	0.740097i	$0.265220\pi$
$770$	−0.602647	+	0.290220i	−0.0217179	+	0.0104588i
$771$		0			0
$772$	−8.96032	−	39.2577i	−0.322489	−	1.41292i
$773$	41.3365			1.48677			0.743386	−	0.668863i	$-0.233219\pi$
$773$	41.3365			1.48677			0.743386	+	0.668863i	$0.233219\pi$
$774$		0			0
$775$	−10.8273			−0.388929
$776$	3.16254	+	13.8560i	0.113528	+	0.497401i
$777$		0			0
$778$	−12.8434	+	6.18506i	−0.460459	+	0.221745i
$779$	7.61692	−	1.14807i	0.272905	−	0.0411338i
$780$		0			0
$781$	−9.89177	−	17.1330i	−0.353955	−	0.613068i
$782$	−2.75634	−	3.45634i	−0.0985664	−	0.123598i
$783$		0			0
$784$	−2.06088	−	5.25104i	−0.0736029	−	0.187537i
$785$	−0.229015	−	0.110288i	−0.00817391	−	0.00393635i
$786$		0			0
$787$	3.59809	−	9.16779i	0.128258	−	0.326796i	−0.852292	−	0.523067i	$-0.824788\pi$
$787$	3.59809	−	9.16779i	0.128258	−	0.326796i	0.980550	+	0.196270i	$0.0628831\pi$
$788$	−15.1746	+	14.0799i	−0.540571	+	0.501577i
$789$		0			0
$790$	0.193141	−	0.242191i	0.00687165	−	0.00861677i
$791$	−36.0973	−	5.44080i	−1.28347	−	0.193453i
$792$		0			0
$793$	−2.03503	+	27.1555i	−0.0722659	+	0.964321i
$794$	53.0220	−	36.1498i	1.88168	−	1.28291i
$795$		0			0
$796$	15.2202	−	66.6840i	0.539465	−	2.36355i
$797$	12.9391	−	8.82176i	0.458328	−	0.312483i	−0.312055	−	0.950064i	$-0.601017\pi$
$797$	12.9391	−	8.82176i	0.458328	−	0.312483i	0.770383	+	0.637581i	$0.220065\pi$
$798$		0			0
$799$	62.8078	−	19.3736i	2.22198	−	0.685390i
$800$	37.3202	+	5.62511i	1.31947	+	0.198878i
$801$		0			0
$802$	44.7114	+	30.4837i	1.57882	+	1.07642i
$803$	20.2596	−	18.7982i	0.714947	−	0.663374i
$804$		0			0
$805$	0.0270557	+	0.00834557i	0.000953587	+	0.000294143i
$806$	−20.7680	−	10.0013i	−0.731520	−	0.352282i
$807$		0			0
$808$	1.80495	+	24.0853i	0.0634978	+	0.847319i
$809$	−32.3483	−	40.5635i	−1.13731	−	1.42614i	−0.889268	−	0.457387i	$-0.848785\pi$
$809$	−32.3483	−	40.5635i	−1.13731	−	1.42614i	−0.248039	−	0.968750i	$-0.579786\pi$
$810$		0			0
$811$	−5.67356	+	9.82690i	−0.199226	+	0.345069i	−0.948278	−	0.317442i	$-0.897176\pi$
$811$	−5.67356	+	9.82690i	−0.199226	+	0.345069i	0.749052	+	0.662511i	$0.230509\pi$
$812$	11.1833	−	1.68562i	0.392459	−	0.0591536i
$813$		0			0
$814$	−59.7657	−	55.4545i	−2.09479	−	1.94368i
$815$	0.0397401	+	0.174113i	0.00139204	+	0.00609891i
$816$		0			0
$817$	3.29283	−	25.8204i	0.115202	−	0.903341i
$818$	27.8280			0.972983
$819$		0			0
$820$	0.102044	+	0.0946830i	0.00356353	+	0.00330647i
$821$	−12.6582	+	6.09588i	−0.441775	+	0.212748i	−0.641529	−	0.767098i	$-0.721700\pi$
$821$	−12.6582	+	6.09588i	−0.441775	+	0.212748i	0.199755	+	0.979846i	$0.435986\pi$
$822$		0			0
$823$	4.75616	−	8.23791i	0.165789	−	0.287156i	−0.771146	−	0.636658i	$-0.780316\pi$
$823$	4.75616	−	8.23791i	0.165789	−	0.287156i	0.936935	+	0.349503i	$0.113649\pi$
$824$	−12.6381	−	21.8898i	−0.440269	−	0.762569i
$825$		0			0
$826$	−0.0876222	−	1.16924i	−0.00304877	−	0.0406830i
$827$	−12.3551	−	31.4803i	−0.429629	−	1.09468i	−0.967773	−	0.251823i	$-0.918970\pi$
$827$	−12.3551	−	31.4803i	−0.429629	−	1.09468i	0.538145	−	0.842852i	$-0.319125\pi$
$828$		0			0
$829$	29.4594	+	9.08703i	1.02317	+	0.315606i	0.760540	−	0.649291i	$-0.224934\pi$
$829$	29.4594	+	9.08703i	1.02317	+	0.315606i	0.262628	+	0.964897i	$0.415411\pi$
$830$	0.0425164	−	0.108330i	0.00147577	−	0.00376019i
$831$		0			0
$832$	50.0449	+	34.1201i	1.73500	+	1.18290i
$833$	−10.2958	+	12.9105i	−0.356728	+	0.447323i
$834$		0			0
$835$	0.351011	−	0.108272i	0.0121472	−	0.00374692i
$836$	3.02187	−	40.3241i	0.104514	−	1.39464i
$837$		0			0
$838$	−13.5432	+	59.3365i	−0.467841	+	2.04975i
$839$	−4.39393	+	19.2511i	−0.151695	+	0.664621i	0.840697	+	0.541506i	$0.182146\pi$
$839$	−4.39393	+	19.2511i	−0.151695	+	0.664621i	−0.992392	+	0.123115i	$0.960712\pi$
$840$		0			0
$841$	−2.03584	+	27.1663i	−0.0702013	+	0.936771i
$842$	−28.7407	+	8.86535i	−0.990472	+	0.305520i
$843$		0			0
$844$	−27.2870	+	34.2168i	−0.939258	+	1.17779i
$845$	0.238449	+	0.162572i	0.00820290	+	0.00559264i
$846$		0			0
$847$	−3.38732	+	8.63076i	−0.116390	+	0.296557i
$848$	−11.2327	−	3.46484i	−0.385734	−	0.118983i
$849$		0			0
$850$	−23.4815	−	59.8298i	−0.805408	−	2.05215i
$851$	0.257902	+	3.44146i	0.00884075	+	0.117972i
$852$		0			0
$853$	−26.3040	−	45.5599i	−0.900632	−	1.55994i	−0.826676	−	0.562678i	$-0.809771\pi$
$853$	−26.3040	−	45.5599i	−0.900632	−	1.55994i	−0.0739557	−	0.997262i	$-0.523562\pi$
$854$	−18.9204	+	32.7710i	−0.647442	+	1.12140i
$855$		0			0
$856$	−23.5457	+	11.3390i	−0.804776	+	0.387559i
$857$	29.8684	+	27.7139i	1.02029	+	0.946687i	0.998590	−	0.0530773i	$-0.0169030\pi$
$857$	29.8684	+	27.7139i	1.02029	+	0.946687i	0.0216959	+	0.999765i	$0.493093\pi$
$858$		0			0
$859$	36.3447			1.24006			0.620032	−	0.784577i	$-0.287120\pi$
$859$	36.3447			1.24006			0.620032	+	0.784577i	$0.287120\pi$
$860$	0.401915	−	0.244405i	0.0137052	−	0.00833414i
$861$		0			0
$862$	15.4957	+	67.8911i	0.527786	+	2.31238i
$863$	−21.1458	−	19.6204i	−0.719811	−	0.667887i	0.232646	−	0.972562i	$-0.425262\pi$
$863$	−21.1458	−	19.6204i	−0.719811	−	0.667887i	−0.952456	+	0.304675i	$0.901452\pi$
$864$		0			0
$865$	0.299503	−	0.0451429i	0.0101834	−	0.00153490i
$866$	0.412573	−	0.714598i	0.0140198	−	0.0242830i
$867$		0			0
$868$	−11.5198	−	14.4454i	−0.391008	−	0.490309i
$869$	−1.51219	−	20.1788i	−0.0512975	−	0.684518i
$870$		0			0
$871$	−4.85616	−	2.33860i	−0.164545	−	0.0792406i
$872$	−3.10407	−	0.957480i	−0.105117	−	0.0324244i
$873$		0			0
$874$	−2.17525	+	2.01834i	−0.0735789	+	0.0682713i
$875$	0.680274	+	0.463803i	0.0229975	+	0.0156794i
$876$		0			0
$877$	4.72066	+	0.711525i	0.159405	+	0.0240265i	0.228260	−	0.973600i	$-0.426696\pi$
$877$	4.72066	+	0.711525i	0.159405	+	0.0240265i	−0.0688546	+	0.997627i	$0.521934\pi$
$878$	−10.1331	+	3.12564i	−0.341975	+	0.105485i
$879$		0			0
$880$	−0.164113	+	0.111890i	−0.00553224	+	0.00377182i
$881$	−6.83266	+	29.9359i	−0.230198	+	1.00856i	0.719277	+	0.694723i	$0.244473\pi$
$881$	−6.83266	+	29.9359i	−0.230198	+	1.00856i	−0.949475	+	0.313841i	$0.898384\pi$
$882$		0			0
$883$	−17.0934	+	11.6541i	−0.575238	+	0.392191i	−0.815706	−	0.578466i	$-0.803651\pi$
$883$	−17.0934	+	11.6541i	−0.575238	+	0.392191i	0.240468	+	0.970657i	$0.422699\pi$
$884$	5.89837	−	78.7083i	0.198384	−	2.64725i
$885$		0			0
$886$	−12.7586	−	1.92305i	−0.428635	−	0.0646063i
$887$	1.55633	−	1.95158i	0.0522565	−	0.0655276i	−0.755016	−	0.655706i	$-0.772371\pi$
$887$	1.55633	−	1.95158i	0.0522565	−	0.0655276i	0.807273	+	0.590178i	$0.200943\pi$
$888$		0			0
$889$	17.2999	−	16.0520i	0.580220	−	0.538365i
$890$	−0.0836348	+	0.213098i	−0.00280344	+	0.00714306i
$891$		0			0
$892$	37.0748	+	17.8543i	1.24136	+	0.597806i
$893$	−16.1183	−	41.0688i	−0.539379	−	1.37432i
$894$		0			0
$895$	−0.0124145	−	0.0155673i	−0.000414971	−	0.000520357i
$896$	18.4592	+	31.9723i	0.616678	+	1.06812i
$897$		0			0
$898$	−70.3185	+	10.5988i	−2.34656	+	0.353687i
$899$	−2.58682	+	1.24575i	−0.0862753	+	0.0415480i
$900$		0			0
$901$	7.65717	+	33.5483i	0.255097	+	1.11765i
$902$	15.7642			0.524889
$903$		0			0
$904$	18.4178			0.612566
$905$	0.00609153	+	0.0266887i	0.000202489	+	0.000887164i
$906$		0			0
$907$	20.8618	−	10.0465i	0.692703	−	0.333588i	−0.0541915	−	0.998531i	$-0.517258\pi$
$907$	20.8618	−	10.0465i	0.692703	−	0.333588i	0.746895	+	0.664942i	$0.231544\pi$
$908$	54.3539	−	8.19254i	1.80380	−	0.271879i
$909$		0			0
$910$	0.438179	+	0.758947i	0.0145255	+	0.0251589i
$911$	−10.8608	−	13.6190i	−0.359834	−	0.451218i	0.568655	−	0.822576i	$-0.307464\pi$
$911$	−10.8608	−	13.6190i	−0.359834	−	0.451218i	−0.928490	+	0.371358i	$0.878892\pi$
$912$		0			0
$913$	−2.77729	−	7.07643i	−0.0919150	−	0.234196i
$914$	56.9230	+	27.4127i	1.88284	+	0.906730i
$915$		0			0
$916$	13.3278	−	33.9586i	0.440362	−	1.12203i
$917$	20.3335	−	18.8668i	0.671472	−	0.623035i
$918$		0			0
$919$	8.79901	−	11.0336i	0.290252	−	0.363965i	−0.615231	−	0.788347i	$-0.710937\pi$
$919$	8.79901	−	11.0336i	0.290252	−	0.363965i	0.905483	+	0.424382i	$0.139509\pi$
$920$	−0.0141254	−	0.00212906i	−0.000465700	−	7.01930e-5i
$921$		0			0
$922$	−2.36233	+	31.5232i	−0.0777993	+	1.03816i
$923$	−21.4159	+	14.6011i	−0.704914	+	0.480602i
$924$		0			0
$925$	−11.1649	+	48.9165i	−0.367098	+	1.60836i
$926$	11.1050	−	7.57129i	0.364934	−	0.248808i
$927$		0			0
$928$	9.56358	−	2.94997i	0.313940	−	0.0968376i
$929$	22.8960	+	3.45101i	0.751192	+	0.113224i	0.513468	−	0.858109i	$-0.328360\pi$
$929$	22.8960	+	3.45101i	0.751192	+	0.113224i	0.237724	+	0.971333i	$0.423599\pi$
$930$		0			0
$931$	9.15814	+	6.24392i	0.300146	+	0.204636i
$932$	18.5074	−	17.1724i	0.606231	−	0.562500i
$933$		0			0
$934$	−32.8381	−	10.1292i	−1.07449	−	0.331438i
$935$	0.523868	+	0.252282i	0.0171323	+	0.00825050i
$936$		0			0
$937$	2.99630	+	39.9829i	0.0978850	+	1.30618i	0.802525	+	0.596619i	$0.203490\pi$
$937$	2.99630	+	39.9829i	0.0978850	+	1.30618i	−0.704640	+	0.709565i	$0.748891\pi$
$938$	−4.66980	−	5.85574i	−0.152474	−	0.191197i
$939$		0			0
$940$	0.398645	−	0.690473i	0.0130024	−	0.0225208i
$941$	−33.4023	+	5.03458i	−1.08888	+	0.164123i	−0.668858	−	0.743390i	$-0.733217\pi$
$941$	−33.4023	+	5.03458i	−1.08888	+	0.164123i	−0.420025	+	0.907513i	$0.637979\pi$
$942$		0			0
$943$	−0.489155	−	0.453870i	−0.0159291	−	0.0147800i
$944$	−0.0774770	−	0.339449i	−0.00252166	−	0.0110481i
$945$		0			0
$946$	14.5392	−	51.2470i	0.472709	−	1.66618i
$947$	6.10756			0.198469			0.0992345	−	0.995064i	$-0.468361\pi$
$947$	6.10756			0.198469			0.0992345	+	0.995064i	$0.468361\pi$
$948$		0			0
$949$	−26.5436	−	24.6288i	−0.861641	−	0.799486i
$950$	−38.8694	+	18.7185i	−1.26109	+	0.607310i
$951$		0			0
$952$	14.6083	−	25.3024i	0.473459	−	0.820055i
$953$	22.1509	+	38.3665i	0.717538	+	1.24281i	0.961973	+	0.273146i	$0.0880642\pi$
$953$	22.1509	+	38.3665i	0.717538	+	1.24281i	−0.244435	+	0.969666i	$0.578603\pi$
$954$		0			0
$955$	0.0272567	+	0.363715i	0.000882006	+	0.0117695i
$956$	19.1492	+	48.7913i	0.619329	+	1.57802i
$957$		0			0
$958$	80.0303	+	24.6861i	2.58566	+	0.797571i
$959$	−20.0856	+	51.1773i	−0.648599	+	1.65260i
$960$		0			0
$961$	−21.7379	−	14.8206i	−0.701222	−	0.478085i
$962$	−66.6000	+	83.5138i	−2.14727	+	2.69259i
$963$		0			0
$964$	15.0773	−	4.65075i	0.485609	−	0.149790i
$965$	0.0290437	−	0.387561i	0.000934949	−	0.0124760i
$966$		0			0
$967$	−11.5379	+	50.5507i	−0.371033	+	1.62560i	0.352851	+	0.935680i	$0.385212\pi$
$967$	−11.5379	+	50.5507i	−0.371033	+	1.62560i	−0.723884	+	0.689922i	$0.757645\pi$
$968$	1.04091	−	4.56053i	0.0334561	−	0.146581i
$969$		0			0
$970$	−0.0384818	+	0.513503i	−0.00123557	+	0.0164876i
$971$	−39.1975	+	12.0908i	−1.25791	+	0.388013i	−0.850859	−	0.525394i	$-0.823918\pi$
$971$	−39.1975	+	12.0908i	−1.25791	+	0.388013i	−0.407048	+	0.913407i	$0.633442\pi$
$972$		0			0
$973$	30.1368	−	37.7903i	0.966140	−	1.21150i
$974$	22.3478	+	15.2365i	0.716069	+	0.488207i
$975$		0			0
$976$	−4.10527	+	10.4601i	−0.131406	+	0.334818i
$977$	38.3948	+	11.8432i	1.22836	+	0.378899i	0.839988	−	0.542605i	$-0.182562\pi$
$977$	38.3948	+	11.8432i	1.22836	+	0.378899i	0.388371	+	0.921503i	$0.373038\pi$
$978$		0			0
$979$	5.46326	+	13.9202i	0.174607	+	0.444891i
$980$	0.0149690	+	0.199747i	0.000478167	+	0.00638069i
$981$		0			0
$982$	41.8891	+	72.5541i	1.33674	+	2.31529i
$983$	21.7405	−	37.6556i	0.693414	−	1.20103i	−0.277298	−	0.960784i	$-0.589439\pi$
$983$	21.7405	−	37.6556i	0.693414	−	1.20103i	0.970712	−	0.240245i	$-0.0772276\pi$
$984$		0			0
$985$	−0.180009	+	0.0866878i	−0.00573557	+	0.00276210i
$986$	−12.4939	−	11.5926i	−0.397886	−	0.369184i
$987$		0			0
$988$	−52.9796			−1.68550
$989$	−1.92661	+	1.17157i	−0.0612626	+	0.0372538i
$990$		0			0
$991$	−5.52848	−	24.2218i	−0.175618	−	0.769432i	−0.983620	−	0.180253i	$-0.942308\pi$
$991$	−5.52848	−	24.2218i	−0.175618	−	0.769432i	0.808002	−	0.589179i	$-0.200549\pi$
$992$	−11.9856	−	11.1210i	−0.380542	−	0.353091i
$993$		0			0
$994$	−35.6155	+	5.36817i	−1.12965	+	0.170268i
$995$	0.330083	−	0.571720i	0.0104643	−	0.0181247i
$996$		0			0
$997$	17.7893	+	22.3071i	0.563394	+	0.706474i	0.979181	−	0.202988i	$-0.0650652\pi$
$997$	17.7893	+	22.3071i	0.563394	+	0.706474i	−0.415787	+	0.909462i	$0.636494\pi$
$998$	6.80156	+	90.7606i	0.215300	+	2.87298i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.10.3		36
3.2	odd	2		43.2.g.a.10.1	✓	36
12.11	even	2		688.2.bg.c.225.2		36
43.13	even	21	inner	387.2.y.c.271.3		36
129.20	even	42		1849.2.a.o.1.3		18
129.23	odd	42		1849.2.a.n.1.16		18
129.56	odd	42		43.2.g.a.13.1	yes	36
516.443	even	42		688.2.bg.c.529.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.10.1	✓	36	3.2	odd	2
43.2.g.a.13.1	yes	36	129.56	odd	42
387.2.y.c.10.3		36	1.1	even	1	trivial
387.2.y.c.271.3		36	43.13	even	21	inner
688.2.bg.c.225.2		36	12.11	even	2
688.2.bg.c.529.2		36	516.443	even	42
1849.2.a.n.1.16		18	129.23	odd	42
1849.2.a.o.1.3		18	129.20	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.483758 + 2.11948i) q^{2} +(-2.45624 + 1.18286i) q^{4} +(-0.0260188 + 0.00392170i) q^{5} +(1.56464 + 2.71003i) q^{7} +(-0.984367 - 1.23436i) q^{8} +O(q^{10})\)	\(q+(0.483758 + 2.11948i) q^{2} +(-2.45624 + 1.18286i) q^{4} +(-0.0260188 + 0.00392170i) q^{5} +(1.56464 + 2.71003i) q^{7} +(-0.984367 - 1.23436i) q^{8} +(-0.0208988 - 0.0532492i) q^{10} +(-3.36665 - 1.62129i) q^{11} +(-1.78860 + 4.55728i) q^{13} +(-4.98695 + 4.62722i) q^{14} +(-1.25954 + 1.57942i) q^{16} +(5.84766 + 0.881392i) q^{17} +(0.296638 - 3.95836i) q^{19} +(0.0592696 - 0.0404093i) q^{20} +(1.80766 - 7.91985i) q^{22} +(-0.284113 + 0.193705i) q^{23} +(-4.77720 + 1.47357i) q^{25} +(-10.5243 - 1.58629i) q^{26} +(-7.04873 - 4.80574i) q^{28} +(-0.971806 + 0.901704i) q^{29} +(2.06955 + 0.638371i) q^{31} +(-6.80176 - 3.27556i) q^{32} +(0.960755 + 12.8204i) q^{34} +(-0.0513379 - 0.0643757i) q^{35} +(5.01814 - 8.69167i) q^{37} +(8.53318 - 1.28617i) q^{38} +(0.0304528 + 0.0282561i) q^{40} +(0.431814 + 1.89190i) q^{41} +(6.54856 + 0.341120i) q^{43} +10.1871 q^{44} +(-0.547996 - 0.508466i) q^{46} +(10.0138 - 4.82240i) q^{47} +(-1.39618 + 2.41825i) q^{49} +(-5.43422 - 9.41234i) q^{50} +(-0.997407 - 13.3095i) q^{52} +(2.12587 + 5.41662i) q^{53} +(0.0939542 + 0.0289810i) q^{55} +(1.80497 - 4.59898i) q^{56} +(-2.38126 - 1.62352i) q^{58} +(-0.107460 + 0.134751i) q^{59} +(5.31524 - 1.63953i) q^{61} +(-0.351855 + 4.69519i) q^{62} +(2.75302 - 12.0618i) q^{64} +(0.0286650 - 0.125589i) q^{65} +(-0.0822742 + 1.09787i) q^{67} +(-15.4058 + 4.75207i) q^{68} +(0.111608 - 0.139952i) q^{70} +(4.37443 + 2.98244i) q^{71} +(-2.70214 + 6.88494i) q^{73} +(20.8494 + 6.43119i) q^{74} +(3.95359 + 10.0736i) q^{76} +(-0.873829 - 11.6604i) q^{77} +(2.70765 + 4.68979i) q^{79} +(0.0265778 - 0.0460341i) q^{80} +(-3.80096 + 1.83044i) q^{82} +(1.49132 + 1.38374i) q^{83} -0.155605 q^{85} +(2.44492 + 14.0446i) q^{86} +(1.31276 + 5.75159i) q^{88} +(-2.93360 - 2.72198i) q^{89} +(-15.1489 + 2.28333i) q^{91} +(0.468724 - 0.811854i) q^{92} +(15.0652 + 18.8912i) q^{94} +(0.00780535 + 0.104155i) q^{95} +(-8.11049 - 3.90581i) q^{97} +(-5.80084 - 1.78932i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

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