LMFDB - Embedded newform 171.2.u.c.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(28,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("171.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	171.100
Dual form			171.2.u.c.118.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826352 - 0.300767i) q^{2} +(-0.939693 + 0.788496i) q^{4} +(1.93969 + 1.62760i) q^{5} +(0.939693 + 1.62760i) q^{7} +(-1.41875 + 2.45734i) q^{8} +O(q^{10})$	\(q+(0.826352 - 0.300767i) q^{2} +(-0.939693 + 0.788496i) q^{4} +(1.93969 + 1.62760i) q^{5} +(0.939693 + 1.62760i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(2.09240 + 0.761570i) q^{10} +(1.70574 - 2.95442i) q^{11} +(-0.918748 - 5.21048i) q^{13} +(1.26604 + 1.06234i) q^{14} +(-0.00727396 + 0.0412527i) q^{16} +(1.55303 - 0.565258i) q^{17} +(-2.52094 + 3.55596i) q^{19} -3.10607 q^{20} +(0.520945 - 2.95442i) q^{22} +(-1.34730 + 1.13052i) q^{23} +(0.245100 + 1.39003i) q^{25} +(-2.32635 - 4.02936i) q^{26} +(-2.16637 - 0.788496i) q^{28} +(-3.25877 - 1.18610i) q^{29} +(-0.971782 - 1.68317i) q^{31} +(-0.979055 - 5.55250i) q^{32} +(1.11334 - 0.934204i) q^{34} +(-0.826352 + 4.68647i) q^{35} -0.837496 q^{37} +(-1.01367 + 3.69669i) q^{38} +(-6.75150 + 2.45734i) q^{40} +(0.779715 - 4.42198i) q^{41} +(3.67752 + 3.08580i) q^{43} +(0.726682 + 4.12122i) q^{44} +(-0.773318 + 1.33943i) q^{46} +(0.673648 + 0.245188i) q^{47} +(1.73396 - 3.00330i) q^{49} +(0.620615 + 1.07494i) q^{50} +(4.97178 + 4.17182i) q^{52} +(4.67752 - 3.92490i) q^{53} +(8.11721 - 2.95442i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(-10.1099 + 3.67972i) q^{59} +(3.36231 - 2.82131i) q^{61} +(-1.30928 - 1.09861i) q^{62} +(-2.52094 - 4.36640i) q^{64} +(6.69846 - 11.6021i) q^{65} +(-13.3550 - 4.86084i) q^{67} +(-1.01367 + 1.75573i) q^{68} +(0.726682 + 4.12122i) q^{70} +(10.5398 + 8.84397i) q^{71} +(-1.30541 + 7.40333i) q^{73} +(-0.692066 + 0.251892i) q^{74} +(-0.434945 - 5.32926i) q^{76} +6.41147 q^{77} +(-1.20914 + 6.85738i) q^{79} +(-0.0812519 + 0.0681784i) q^{80} +(-0.685670 - 3.88863i) q^{82} +(1.25624 + 2.17588i) q^{83} +(3.93242 + 1.43128i) q^{85} +(3.96703 + 1.44388i) q^{86} +(4.84002 + 8.38316i) q^{88} +(0.396459 + 2.24843i) q^{89} +(7.61721 - 6.39160i) q^{91} +(0.374638 - 2.12467i) q^{92} +0.630415 q^{94} +(-10.6775 + 2.79439i) q^{95} +(1.71301 - 0.623485i) q^{97} +(0.529563 - 3.00330i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8	$ 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8} + 9 q^{10} - 3 q^{13} + 3 q^{14} - 18 q^{16} - 3 q^{17} - 12 q^{19} + 6 q^{20} - 6 q^{23} - 15 q^{26} + 6 q^{28} + 3 q^{29} + 9 q^{31} - 9 q^{32} - 6 q^{35} + 15 q^{38} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 18 q^{46} + 3 q^{47} + 15 q^{49} + 15 q^{50} + 15 q^{52} + 3 q^{53} + 18 q^{55} + 6 q^{56} + 36 q^{58} - 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{64} + 12 q^{65} - 30 q^{67} + 15 q^{68} - 9 q^{70} + 6 q^{71} - 12 q^{73} - 15 q^{74} + 36 q^{76} + 18 q^{77} - 39 q^{79} - 3 q^{80} - 54 q^{82} - 24 q^{86} + 9 q^{88} + 12 q^{89} + 15 q^{91} - 42 q^{92} + 18 q^{94} - 39 q^{95} + 18 q^{97} + 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8 + 9 * q^10 - 3 * q^13 + 3 * q^14 - 18 * q^16 - 3 * q^17 - 12 * q^19 + 6 * q^20 - 6 * q^23 - 15 * q^26 + 6 * q^28 + 3 * q^29 + 9 * q^31 - 9 * q^32 - 6 * q^35 + 15 * q^38 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 18 * q^46 + 3 * q^47 + 15 * q^49 + 15 * q^50 + 15 * q^52 + 3 * q^53 + 18 * q^55 + 6 * q^56 + 36 * q^58 - 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^64 + 12 * q^65 - 30 * q^67 + 15 * q^68 - 9 * q^70 + 6 * q^71 - 12 * q^73 - 15 * q^74 + 36 * q^76 + 18 * q^77 - 39 * q^79 - 3 * q^80 - 54 * q^82 - 24 * q^86 + 9 * q^88 + 12 * q^89 + 15 * q^91 - 42 * q^92 + 18 * q^94 - 39 * q^95 + 18 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	0.826352	−	0.300767i	0.584319	−	0.212675i	−0.0329100	−	0.999458i	$-0.510477\pi$
$2$	0.826352	−	0.300767i	0.584319	−	0.212675i	0.617229	+	0.786784i	$0.288255\pi$
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.788496i	−0.469846	+	0.394248i
$5$	1.93969	+	1.62760i	0.867457	+	0.727883i	0.963561	−	0.267489i	$-0.0861937\pi$
$5$	1.93969	+	1.62760i	0.867457	+	0.727883i	−0.0961041	+	0.995371i	$0.530638\pi$
$6$		0			0
$7$	0.939693	+	1.62760i	0.355170	+	0.615173i	0.987147	−	0.159814i	$-0.0510895\pi$
$7$	0.939693	+	1.62760i	0.355170	+	0.615173i	−0.631977	+	0.774987i	$0.717756\pi$
$8$	−1.41875	+	2.45734i	−0.501603	+	0.868802i
$9$		0			0
$10$	2.09240	+	0.761570i	0.661674	+	0.240830i
$11$	1.70574	−	2.95442i	0.514299	−	0.890792i	−0.485563	−	0.874202i	$-0.661385\pi$
$11$	1.70574	−	2.95442i	0.514299	−	0.890792i	0.999862	−	0.0165906i	$-0.00528120\pi$
$12$		0			0
$13$	−0.918748	−	5.21048i	−0.254815	−	1.44513i	−0.796547	−	0.604576i	$-0.793343\pi$
$13$	−0.918748	−	5.21048i	−0.254815	−	1.44513i	0.541733	−	0.840551i	$-0.317769\pi$
$14$	1.26604	+	1.06234i	0.338365	+	0.283922i
$15$		0			0
$16$	−0.00727396	+	0.0412527i	−0.00181849	+	0.0103132i
$17$	1.55303	−	0.565258i	0.376666	−	0.137095i	−0.146748	−	0.989174i	$-0.546881\pi$
$17$	1.55303	−	0.565258i	0.376666	−	0.137095i	0.523414	+	0.852079i	$0.324658\pi$
$18$		0			0
$19$	−2.52094	+	3.55596i	−0.578344	+	0.815793i
$19$	−2.52094	+	3.55596i	−0.578344	+	0.815793i
$20$	−3.10607			−0.694538
$21$		0			0
$22$	0.520945	−	2.95442i	0.111066	−	0.629885i
$23$	−1.34730	+	1.13052i	−0.280931	+	0.235729i	−0.772354	−	0.635192i	$-0.780921\pi$
$23$	−1.34730	+	1.13052i	−0.280931	+	0.235729i	0.491424	+	0.870921i	$0.336477\pi$
$24$		0			0
$25$	0.245100	+	1.39003i	0.0490200	+	0.278006i
$26$	−2.32635	−	4.02936i	−0.456235	−	0.790222i
$27$		0			0
$28$	−2.16637	−	0.788496i	−0.409406	−	0.149012i
$29$	−3.25877	−	1.18610i	−0.605138	−	0.220252i	0.0212363	−	0.999774i	$-0.493240\pi$
$29$	−3.25877	−	1.18610i	−0.605138	−	0.220252i	−0.626375	+	0.779522i	$0.715462\pi$
$30$		0			0
$31$	−0.971782	−	1.68317i	−0.174537	−	0.302307i	0.765464	−	0.643479i	$-0.222510\pi$
$31$	−0.971782	−	1.68317i	−0.174537	−	0.302307i	−0.940001	+	0.341172i	$0.889176\pi$
$32$	−0.979055	−	5.55250i	−0.173074	−	0.981553i
$33$		0			0
$34$	1.11334	−	0.934204i	0.190936	−	0.160215i
$35$	−0.826352	+	4.68647i	−0.139679	+	0.792159i
$36$		0			0
$37$	−0.837496			−0.137684			−0.0688418	−	0.997628i	$-0.521930\pi$
$37$	−0.837496			−0.137684			−0.0688418	+	0.997628i	$0.521930\pi$
$38$	−1.01367	+	3.69669i	−0.164439	+	0.599682i
$39$		0			0
$40$	−6.75150	+	2.45734i	−1.06751	+	0.388540i
$41$	0.779715	−	4.42198i	0.121771	−	0.690598i	−0.861402	−	0.507923i	$-0.830413\pi$
$41$	0.779715	−	4.42198i	0.121771	−	0.690598i	0.983173	−	0.182675i	$-0.0584755\pi$
$42$		0			0
$43$	3.67752	+	3.08580i	0.560816	+	0.470581i	0.878584	−	0.477588i	$-0.158489\pi$
$43$	3.67752	+	3.08580i	0.560816	+	0.470581i	−0.317768	+	0.948169i	$0.602933\pi$
$44$	0.726682	+	4.12122i	0.109551	+	0.621297i
$45$		0			0
$46$	−0.773318	+	1.33943i	−0.114020	+	0.197488i
$47$	0.673648	+	0.245188i	0.0982617	+	0.0357643i	0.390683	−	0.920525i	$-0.372239\pi$
$47$	0.673648	+	0.245188i	0.0982617	+	0.0357643i	−0.292422	+	0.956290i	$0.594461\pi$
$48$		0			0
$49$	1.73396	−	3.00330i	0.247708	−	0.429043i
$50$	0.620615	+	1.07494i	0.0877682	+	0.152019i
$51$		0			0
$52$	4.97178	+	4.17182i	0.689462	+	0.578527i
$53$	4.67752	−	3.92490i	0.642507	−	0.539127i	−0.262280	−	0.964992i	$-0.584474\pi$
$53$	4.67752	−	3.92490i	0.642507	−	0.539127i	0.904787	+	0.425865i	$0.140030\pi$
$54$		0			0
$55$	8.11721	−	2.95442i	1.09452	−	0.398374i
$56$	−5.33275			−0.712618
$57$		0			0
$58$	−3.04963			−0.400436
$59$	−10.1099	+	3.67972i	−1.31620	+	0.479058i	−0.902239	−	0.431236i	$-0.858078\pi$
$59$	−10.1099	+	3.67972i	−1.31620	+	0.479058i	−0.413962	+	0.910294i	$0.635856\pi$
$60$		0			0
$61$	3.36231	−	2.82131i	0.430500	−	0.361232i	−0.401640	−	0.915797i	$-0.631560\pi$
$61$	3.36231	−	2.82131i	0.430500	−	0.361232i	0.832140	+	0.554565i	$0.187115\pi$
$62$	−1.30928	−	1.09861i	−0.166278	−	0.139524i
$63$		0			0
$64$	−2.52094	−	4.36640i	−0.315118	−	0.545801i
$65$	6.69846	−	11.6021i	0.830842	−	1.43906i
$66$		0			0
$67$	−13.3550	−	4.86084i	−1.63158	−	0.593846i	−0.646040	−	0.763304i	$-0.723576\pi$
$67$	−13.3550	−	4.86084i	−1.63158	−	0.593846i	−0.985537	+	0.169458i	$0.945798\pi$
$68$	−1.01367	+	1.75573i	−0.122926	+	0.212913i
$69$		0			0
$70$	0.726682	+	4.12122i	0.0868551	+	0.492580i
$71$	10.5398	+	8.84397i	1.25085	+	1.04959i	0.996595	+	0.0824479i	$0.0262738\pi$
$71$	10.5398	+	8.84397i	1.25085	+	1.04959i	0.254252	+	0.967138i	$0.418171\pi$
$72$		0			0
$73$	−1.30541	+	7.40333i	−0.152786	+	0.866495i	0.807995	+	0.589189i	$0.200553\pi$
$73$	−1.30541	+	7.40333i	−0.152786	+	0.866495i	−0.960782	+	0.277306i	$0.910559\pi$
$74$	−0.692066	+	0.251892i	−0.0804511	+	0.0292818i
$75$		0			0
$76$	−0.434945	−	5.32926i	−0.0498916	−	0.611308i
$77$	6.41147			0.730655
$78$		0			0
$79$	−1.20914	+	6.85738i	−0.136039	+	0.771515i	0.838092	+	0.545529i	$0.183671\pi$
$79$	−1.20914	+	6.85738i	−0.136039	+	0.771515i	−0.974131	+	0.225986i	$0.927440\pi$
$80$	−0.0812519	+	0.0681784i	−0.00908424	+	0.00762258i
$81$		0			0
$82$	−0.685670	−	3.88863i	−0.0757196	−	0.429427i
$83$	1.25624	+	2.17588i	0.137891	+	0.238834i	0.926698	−	0.375807i	$-0.122634\pi$
$83$	1.25624	+	2.17588i	0.137891	+	0.238834i	−0.788807	+	0.614641i	$0.789301\pi$
$84$		0			0
$85$	3.93242	+	1.43128i	0.426531	+	0.155244i
$86$	3.96703	+	1.44388i	0.427776	+	0.155698i
$87$		0			0
$88$	4.84002	+	8.38316i	0.515948	+	0.893648i
$89$	0.396459	+	2.24843i	0.0420246	+	0.238333i	0.998584	−	0.0532055i	$-0.0169438\pi$
$89$	0.396459	+	2.24843i	0.0420246	+	0.238333i	−0.956559	+	0.291539i	$0.905833\pi$
$90$		0			0
$91$	7.61721	−	6.39160i	0.798501	−	0.670022i
$92$	0.374638	−	2.12467i	0.0390587	−	0.221513i
$93$		0			0
$94$	0.630415			0.0650223
$95$	−10.6775	+	2.79439i	−1.09549	+	0.286698i
$96$		0			0
$97$	1.71301	−	0.623485i	0.173930	−	0.0633053i	−0.253587	−	0.967312i	$-0.581611\pi$
$97$	1.71301	−	0.623485i	0.173930	−	0.0633053i	0.427517	+	0.904007i	$0.359388\pi$
$98$	0.529563	−	3.00330i	0.0534939	−	0.303379i
$99$		0			0
$100$	−1.32635	−	1.11294i	−0.132635	−	0.111294i
$101$	1.37551	+	7.80093i	0.136869	+	0.776222i	0.973540	+	0.228516i	$0.0733874\pi$
$101$	1.37551	+	7.80093i	0.136869	+	0.776222i	−0.836671	+	0.547705i	$0.815501\pi$
$102$		0			0
$103$	0.00727396	−	0.0125989i	0.000716725	−	0.00124140i	−0.865667	−	0.500621i	$-0.833105\pi$
$103$	0.00727396	−	0.0125989i	0.000716725	−	0.00124140i	0.866384	+	0.499379i	$0.166439\pi$
$104$	14.1074	+	5.13468i	1.38335	+	0.503497i
$105$		0			0
$106$	2.68479	−	4.65020i	0.260770	−	0.451667i
$107$	−1.77719	−	3.07818i	−0.171807	−	0.297579i	0.767244	−	0.641355i	$-0.221627\pi$
$107$	−1.77719	−	3.07818i	−0.171807	−	0.297579i	−0.939052	+	0.343776i	$0.888294\pi$
$108$		0			0
$109$	5.64543	+	4.73708i	0.540734	+	0.453730i	0.871789	−	0.489882i	$-0.162960\pi$
$109$	5.64543	+	4.73708i	0.540734	+	0.453730i	−0.331055	+	0.943612i	$0.607404\pi$
$110$	5.81908	−	4.88279i	0.554827	−	0.465555i
$111$		0			0
$112$	−0.0739780	+	0.0269258i	−0.00699026	+	0.00254425i
$113$	−7.37733			−0.694000			−0.347000	−	0.937865i	$-0.612800\pi$
$113$	−7.37733			−0.694000			−0.347000	+	0.937865i	$0.612800\pi$
$114$		0			0
$115$	−4.45336			−0.415278
$116$	3.99747	−	1.45496i	0.371156	−	0.135090i
$117$		0			0
$118$	−7.24763	+	6.08148i	−0.667198	+	0.559846i
$119$	2.37939	+	1.99654i	0.218118	+	0.183023i
$120$		0			0
$121$	−0.319078	−	0.552659i	−0.0290071	−	0.0502417i
$122$	1.92989	−	3.34267i	0.174724	−	0.302631i
$123$		0			0
$124$	2.24035	+	0.815422i	0.201190	+	0.0732270i
$125$	4.54323	−	7.86911i	0.406359	−	0.703835i
$126$		0			0
$127$	−0.0175410	−	0.0994798i	−0.00155651	−	0.00882740i	0.984020	−	0.178060i	$-0.0569822\pi$
$127$	−0.0175410	−	0.0994798i	−0.00155651	−	0.00882740i	−0.985576	+	0.169233i	$0.945871\pi$
$128$	5.24170	+	4.39831i	0.463305	+	0.388759i
$129$		0			0
$130$	2.04576	−	11.6021i	0.179425	−	1.01757i
$131$	−2.85369	+	1.03866i	−0.249328	+	0.0907481i	−0.463661	−	0.886013i	$-0.653464\pi$
$131$	−2.85369	+	1.03866i	−0.249328	+	0.0907481i	0.214333	+	0.976761i	$0.431242\pi$
$132$		0			0
$133$	−8.15657	−	0.761570i	−0.707265	−	0.0660365i
$134$	−12.4979			−1.07966
$135$		0			0
$136$	−0.814330	+	4.61830i	−0.0698282	+	0.396016i
$137$	−14.9684	+	12.5600i	−1.27883	+	1.07307i	−0.285431	+	0.958399i	$0.592137\pi$
$137$	−14.9684	+	12.5600i	−1.27883	+	1.07307i	−0.993404	+	0.114671i	$0.963419\pi$
$138$		0			0
$139$	2.67365	+	15.1630i	0.226776	+	1.28611i	0.859261	+	0.511537i	$0.170924\pi$
$139$	2.67365	+	15.1630i	0.226776	+	1.28611i	−0.632485	+	0.774573i	$0.717965\pi$
$140$	−2.91875	−	5.05542i	−0.246679	−	0.427261i
$141$		0			0
$142$	11.3696	+	4.13819i	0.954114	+	0.347269i
$143$	−16.9611	−	6.17334i	−1.41836	−	0.516240i
$144$		0			0
$145$	−4.39053	−	7.60462i	−0.364614	−	0.631529i
$146$	1.14796	+	6.51038i	0.0950055	+	0.538803i
$147$		0			0
$148$	0.786989	−	0.660362i	0.0646901	−	0.0542814i
$149$	0.654048	−	3.70929i	0.0535817	−	0.303877i	−0.946226	−	0.323507i	$-0.895138\pi$
$149$	0.654048	−	3.70929i	0.0535817	−	0.303877i	0.999807	+	0.0196306i	$0.00624903\pi$
$150$		0			0
$151$	−14.5963			−1.18783			−0.593914	−	0.804529i	$-0.702418\pi$
$151$	−14.5963			−1.18783			−0.593914	+	0.804529i	$0.702418\pi$
$152$	−5.16163	−	11.2398i	−0.418663	−	0.911671i
$153$		0			0
$154$	5.29813	−	1.92836i	0.426936	−	0.155392i
$155$	0.854570	−	4.84651i	0.0686407	−	0.389281i
$156$		0			0
$157$	−7.94743	−	6.66869i	−0.634274	−	0.532219i	0.267980	−	0.963425i	$-0.413644\pi$
$157$	−7.94743	−	6.66869i	−0.634274	−	0.532219i	−0.902254	+	0.431205i	$0.858088\pi$
$158$	1.06330	+	6.03028i	0.0845916	+	0.479743i
$159$		0			0
$160$	7.13816	−	12.3636i	0.564321	−	0.977432i
$161$	−3.10607	−	1.13052i	−0.244792	−	0.0890971i
$162$		0			0
$163$	1.01114	−	1.75135i	0.0791989	−	0.137177i	−0.823706	−	0.567018i	$-0.808097\pi$
$163$	1.01114	−	1.75135i	0.0791989	−	0.137177i	0.902905	+	0.429841i	$0.141430\pi$
$164$	2.75402	+	4.77011i	0.215053	+	0.372483i
$165$		0			0
$166$	1.69253	+	1.42020i	0.131366	+	0.110229i
$167$	17.8157	−	14.9491i	1.37862	−	1.15680i	0.408898	−	0.912580i	$-0.365913\pi$
$167$	17.8157	−	14.9491i	1.37862	−	1.15680i	0.969720	−	0.244218i	$-0.0785312\pi$
$168$		0			0
$169$	−14.0890	+	5.12797i	−1.08377	+	0.394460i
$170$	3.68004			0.282247
$171$		0			0
$172$	−5.88888			−0.449023
$173$	0.842549	−	0.306663i	0.0640578	−	0.0233151i	−0.309793	−	0.950804i	$-0.600260\pi$
$173$	0.842549	−	0.306663i	0.0640578	−	0.0233151i	0.373850	+	0.927489i	$0.378037\pi$
$174$		0			0
$175$	−2.03209	+	1.70513i	−0.153611	+	0.128895i
$176$	0.109470	+	0.0918566i	0.00825164	+	0.00692395i
$177$		0			0
$178$	1.00387	+	1.73875i	0.0752433	+	0.130325i
$179$	−10.6591	+	18.4621i	−0.796699	+	1.37992i	0.125056	+	0.992150i	$0.460089\pi$
$179$	−10.6591	+	18.4621i	−0.796699	+	1.37992i	−0.921755	+	0.387773i	$0.873245\pi$
$180$		0			0
$181$	15.1284	+	5.50627i	1.12448	+	0.409278i	0.836286	−	0.548294i	$-0.184722\pi$
$181$	15.1284	+	5.50627i	1.12448	+	0.409278i	0.288196	+	0.957571i	$0.406945\pi$
$182$	4.37211	−	7.57272i	0.324082	−	0.561327i
$183$		0			0
$184$	−0.866592	−	4.91469i	−0.0638860	−	0.362316i
$185$	−1.62449	−	1.36310i	−0.119435	−	0.100217i
$186$		0			0
$187$	0.979055	−	5.55250i	0.0715956	−	0.406039i
$188$	−0.826352	+	0.300767i	−0.0602679	+	0.0219357i
$189$		0			0
$190$	−7.98293	+	5.52060i	−0.579142	+	0.400506i
$191$	−18.9486			−1.37107			−0.685537	−	0.728038i	$-0.740432\pi$
$191$	−18.9486			−1.37107			−0.685537	+	0.728038i	$0.740432\pi$
$192$		0			0
$193$	2.24035	−	12.7057i	0.161264	−	0.914574i	−0.791569	−	0.611080i	$-0.790736\pi$
$193$	2.24035	−	12.7057i	0.161264	−	0.914574i	0.952833	−	0.303494i	$-0.0981534\pi$
$194$	1.22803	−	1.03044i	0.0881671	−	0.0739810i
$195$		0			0
$196$	0.738703	+	4.18939i	0.0527645	+	0.299242i
$197$	−11.6001	−	20.0920i	−0.826476	−	1.43150i	−0.900786	−	0.434263i	$-0.857009\pi$
$197$	−11.6001	−	20.0920i	−0.826476	−	1.43150i	0.0743108	−	0.997235i	$-0.476324\pi$
$198$		0			0
$199$	−8.66550	−	3.15398i	−0.614281	−	0.223580i	0.0160945	−	0.999870i	$-0.494877\pi$
$199$	−8.66550	−	3.15398i	−0.614281	−	0.223580i	−0.630375	+	0.776291i	$0.717099\pi$
$200$	−3.76352	−	1.36981i	−0.266121	−	0.0968601i
$201$		0			0
$202$	3.48293	+	6.03260i	0.245058	+	0.424453i
$203$	−1.13176	−	6.41852i	−0.0794339	−	0.450492i
$204$		0			0
$205$	8.70961	−	7.30823i	0.608305	−	0.510429i
$206$	0.00222152	−	0.0125989i	0.000154781	−	0.000877805i
$207$		0			0
$208$	0.221629			0.0153672
$209$	6.20574	+	13.5135i	0.429260	+	0.934746i
$210$		0			0
$211$	−13.7417	+	5.00157i	−0.946017	+	0.344322i	−0.768539	−	0.639803i	$-0.779016\pi$
$211$	−13.7417	+	5.00157i	−0.946017	+	0.344322i	−0.177478	+	0.984125i	$0.556794\pi$
$212$	−1.30066	+	7.37641i	−0.0893297	+	0.506614i
$213$		0			0
$214$	−2.39440	−	2.00914i	−0.163678	−	0.137342i
$215$	2.11081	+	11.9710i	0.143956	+	0.816417i
$216$		0			0
$217$	1.82635	−	3.16333i	0.123981	−	0.214741i
$218$	6.08987	+	2.21653i	0.412458	+	0.150122i
$219$		0			0
$220$	−5.29813	+	9.17664i	−0.357200	+	0.618689i
$221$	−4.37211	−	7.57272i	−0.294100	−	0.509396i
$222$		0			0
$223$	−2.30928	−	1.93771i	−0.154641	−	0.129759i	0.562185	−	0.827012i	$-0.309961\pi$
$223$	−2.30928	−	1.93771i	−0.154641	−	0.129759i	−0.716825	+	0.697253i	$0.754405\pi$
$224$	8.11721	−	6.81115i	0.542354	−	0.455089i
$225$		0			0
$226$	−6.09627	+	2.21886i	−0.405518	+	0.147596i
$227$	13.7219			0.910757			0.455378	−	0.890298i	$-0.349504\pi$
$227$	13.7219			0.910757			0.455378	+	0.890298i	$0.349504\pi$
$228$		0			0
$229$	9.41416			0.622105			0.311053	−	0.950393i	$-0.399318\pi$
$229$	9.41416			0.622105			0.311053	+	0.950393i	$0.399318\pi$
$230$	−3.68004	+	1.33943i	−0.242655	+	0.0883192i
$231$		0			0
$232$	7.53802	−	6.32515i	0.494895	−	0.415266i
$233$	18.5273	+	15.5463i	1.21377	+	1.01847i	0.999127	+	0.0417777i	$0.0133021\pi$
$233$	18.5273	+	15.5463i	1.21377	+	1.01847i	0.214640	+	0.976693i	$0.431142\pi$
$234$		0			0
$235$	0.907604	+	1.57202i	0.0592055	+	0.102547i
$236$	6.59879	−	11.4294i	0.429545	−	0.743993i
$237$		0			0
$238$	2.56670	+	0.934204i	0.166375	+	0.0605554i
$239$	−11.6630	+	20.2009i	−0.754415	+	1.30668i	0.191250	+	0.981541i	$0.438746\pi$
$239$	−11.6630	+	20.2009i	−0.754415	+	1.30668i	−0.945665	+	0.325143i	$0.894587\pi$
$240$		0			0
$241$	0.0516892	+	0.293144i	0.00332960	+	0.0188831i	0.986427	−	0.164199i	$-0.0525038\pi$
$241$	0.0516892	+	0.293144i	0.00332960	+	0.0188831i	−0.983098	+	0.183082i	$0.941393\pi$
$242$	−0.429892	−	0.360723i	−0.0276345	−	0.0231881i
$243$		0			0
$244$	−0.934945	+	5.30234i	−0.0598537	+	0.339447i
$245$	8.25150	−	3.00330i	0.527169	−	0.191874i
$246$		0			0
$247$	20.8444	+	9.86830i	1.32629	+	0.627905i
$248$	5.51485			0.350193
$249$		0			0
$250$	1.38754	−	7.86911i	0.0877555	−	0.497686i
$251$	12.4081	−	10.4116i	0.783190	−	0.657175i	−0.160859	−	0.986977i	$-0.551427\pi$
$251$	12.4081	−	10.4116i	0.783190	−	0.657175i	0.944050	+	0.329802i	$0.106982\pi$
$252$		0			0
$253$	1.04189	+	5.90885i	0.0655030	+	0.371486i
$254$	−0.0444153	−	0.0769295i	−0.00278686	−	0.00482699i
$255$		0			0
$256$	15.1300	+	5.50687i	0.945625	+	0.344179i
$257$	14.4290	+	5.25173i	0.900057	+	0.327594i	0.750276	−	0.661125i	$-0.229921\pi$
$257$	14.4290	+	5.25173i	0.900057	+	0.327594i	0.149782	+	0.988719i	$0.452143\pi$
$258$		0			0
$259$	−0.786989	−	1.36310i	−0.0489011	−	0.0846992i
$260$	2.85369	+	16.1841i	0.176979	+	1.00370i
$261$		0			0
$262$	−2.04576	+	1.71660i	−0.126387	+	0.106052i
$263$	−1.67453	+	9.49671i	−0.103256	+	0.585592i	0.888647	+	0.458592i	$0.151646\pi$
$263$	−1.67453	+	9.49671i	−0.103256	+	0.585592i	−0.991903	+	0.127000i	$0.959465\pi$
$264$		0			0
$265$	15.4611			0.949768
$266$	−6.96926	+	1.82391i	−0.427312	+	0.111831i
$267$		0			0
$268$	16.3824	−	5.96270i	1.00071	−	0.364230i
$269$	3.17412	−	18.0013i	0.193529	−	1.09756i	−0.720969	−	0.692968i	$-0.756303\pi$
$269$	3.17412	−	18.0013i	0.193529	−	1.09756i	0.914498	−	0.404591i	$-0.132586\pi$
$270$		0			0
$271$	14.5273	+	12.1899i	0.882473	+	0.740483i	0.966686	−	0.255965i	$-0.0823932\pi$
$271$	14.5273	+	12.1899i	0.882473	+	0.740483i	−0.0842129	+	0.996448i	$0.526838\pi$
$272$	0.0120217	+	0.0681784i	0.000728923	+	0.00413393i
$273$		0			0
$274$	−8.59152	+	14.8809i	−0.519033	+	0.898991i
$275$	4.52481	+	1.64690i	0.272857	+	0.0993117i
$276$		0			0
$277$	−6.88191	+	11.9198i	−0.413494	+	0.716193i	−0.995269	−	0.0971571i	$-0.969025\pi$
$277$	−6.88191	+	11.9198i	−0.413494	+	0.716193i	0.581775	+	0.813350i	$0.302358\pi$
$278$	6.76991	+	11.7258i	0.406033	+	0.703269i
$279$		0			0
$280$	−10.3439	−	8.67956i	−0.618166	−	0.518703i
$281$	−10.0437	+	8.42767i	−0.599157	+	0.502752i	−0.891175	−	0.453661i	$-0.850118\pi$
$281$	−10.0437	+	8.42767i	−0.599157	+	0.502752i	0.292018	+	0.956413i	$0.405673\pi$
$282$		0			0
$283$	16.3293	−	5.94340i	0.970679	−	0.353298i	0.192469	−	0.981303i	$-0.438350\pi$
$283$	16.3293	−	5.94340i	0.970679	−	0.353298i	0.778209	+	0.628005i	$0.216128\pi$
$284$	−16.8776			−1.00150
$285$		0			0
$286$	−15.8726			−0.938565
$287$	7.92989	−	2.88624i	0.468087	−	0.170370i
$288$		0			0
$289$	−10.9304	+	9.17166i	−0.642962	+	0.539509i
$290$	−5.91534	−	4.96356i	−0.347361	−	0.291470i
$291$		0			0
$292$	−4.61081	−	7.98617i	−0.269828	−	0.467355i
$293$	7.80200	−	13.5135i	0.455798	−	0.789465i	−0.542936	−	0.839774i	$-0.682687\pi$
$293$	7.80200	−	13.5135i	0.455798	−	0.789465i	0.998734	+	0.0503091i	$0.0160206\pi$
$294$		0			0
$295$	−25.5993	−	9.31737i	−1.49045	−	0.542478i
$296$	1.18820	−	2.05802i	0.0690625	−	0.119620i
$297$		0			0
$298$	−0.575160	−	3.26189i	−0.0333181	−	0.188956i
$299$	7.12836	+	5.98140i	0.412243	+	0.345913i
$300$		0			0
$301$	−1.56670	+	8.88522i	−0.0903033	+	0.512136i
$302$	−12.0617	+	4.39008i	−0.694070	+	0.252621i
$303$		0			0
$304$	−0.128356	−	0.129862i	−0.00736170	−	0.00744807i
$305$	11.1138			0.636375
$306$		0			0
$307$	3.73695	−	21.1933i	0.213279	−	1.20956i	−0.670589	−	0.741829i	$-0.733959\pi$
$307$	3.73695	−	21.1933i	0.213279	−	1.20956i	0.883868	−	0.467736i	$-0.154930\pi$
$308$	−6.02481	+	5.05542i	−0.343296	+	0.288059i
$309$		0			0
$310$	−0.751497	−	4.26195i	−0.0426821	−	0.242062i
$311$	7.24763	+	12.5533i	0.410975	+	0.711830i	0.994997	−	0.0999083i	$-0.0318550\pi$
$311$	7.24763	+	12.5533i	0.410975	+	0.711830i	−0.584021	+	0.811738i	$0.698522\pi$
$312$		0			0
$313$	−18.3414	−	6.67571i	−1.03672	−	0.377334i	−0.233081	−	0.972457i	$-0.574881\pi$
$313$	−18.3414	−	6.67571i	−1.03672	−	0.377334i	−0.803634	+	0.595124i	$0.797103\pi$
$314$	−8.57310	−	3.12035i	−0.483808	−	0.176092i
$315$		0			0
$316$	−4.27079	−	7.39723i	−0.240251	−	0.416127i
$317$	−4.92246	−	27.9166i	−0.276473	−	1.56795i	−0.734245	−	0.678885i	$-0.762464\pi$
$317$	−4.92246	−	27.9166i	−0.276473	−	1.56795i	0.457772	−	0.889070i	$-0.348648\pi$
$318$		0			0
$319$	−9.06283	+	7.60462i	−0.507421	+	0.425777i
$320$	2.21688	−	12.5726i	0.123927	−	0.702827i
$321$		0			0
$322$	−2.90673			−0.161986
$323$	−1.90508	+	6.94751i	−0.106001	+	0.386570i
$324$		0			0
$325$	7.01754	−	2.55418i	0.389263	−	0.141680i
$326$	0.308811	−	1.75135i	0.0171035	−	0.0969985i
$327$		0			0
$328$	9.76011	+	8.18971i	0.538912	+	0.452201i
$329$	0.233956	+	1.32683i	0.0128984	+	0.0731504i
$330$		0			0
$331$	0.855037	−	1.48097i	0.0469971	−	0.0814014i	−0.841570	−	0.540148i	$-0.818368\pi$
$331$	0.855037	−	1.48097i	0.0469971	−	0.0814014i	0.888567	+	0.458747i	$0.151702\pi$
$332$	−2.89615	−	1.05411i	−0.158947	−	0.0578520i
$333$		0			0
$334$	10.2258	−	17.7116i	0.559531	−	0.969136i
$335$	−17.9932	−	31.1651i	−0.983073	−	1.70273i
$336$		0			0
$337$	19.4873	+	16.3518i	1.06154	+	0.890737i	0.994259	−	0.106997i	$-0.0341236\pi$
$337$	19.4873	+	16.3518i	1.06154	+	0.890737i	0.0672796	+	0.997734i	$0.478568\pi$
$338$	−10.1001	+	8.47502i	−0.549375	+	0.460980i
$339$		0			0
$340$	−4.82383	+	1.75573i	−0.261609	+	0.0952178i
$341$	−6.63041			−0.359057
$342$		0			0
$343$	19.6732			1.06225
$344$	−12.8004	+	4.65895i	−0.690149	+	0.251194i
$345$		0			0
$346$	0.604007	−	0.506822i	0.0324716	−	0.0272469i
$347$	−5.90033	−	4.95096i	−0.316746	−	0.265782i	0.470527	−	0.882385i	$-0.344064\pi$
$347$	−5.90033	−	4.95096i	−0.316746	−	0.265782i	−0.787274	+	0.616604i	$0.788508\pi$
$348$		0			0
$349$	−11.3785	−	19.7082i	−0.609078	−	1.05495i	−0.991393	−	0.130921i	$-0.958206\pi$
$349$	−11.3785	−	19.7082i	−0.609078	−	1.05495i	0.382315	−	0.924032i	$-0.375127\pi$
$350$	−1.16637	+	2.02022i	−0.0623453	+	0.107985i
$351$		0			0
$352$	−18.0744	−	6.57856i	−0.963371	−	0.350638i
$353$	−5.72281	+	9.91220i	−0.304595	+	0.527573i	−0.977171	−	0.212454i	$-0.931854\pi$
$353$	−5.72281	+	9.91220i	−0.304595	+	0.527573i	0.672576	+	0.740028i	$0.265188\pi$
$354$		0			0
$355$	6.04963	+	34.3092i	0.321081	+	1.82094i
$356$	−2.14543	−	1.80023i	−0.113708	−	0.0954120i
$357$		0			0
$358$	−3.25537	+	18.4621i	−0.172051	+	0.975752i
$359$	9.75789	−	3.55158i	0.515002	−	0.187445i	−0.0714274	−	0.997446i	$-0.522755\pi$
$359$	9.75789	−	3.55158i	0.515002	−	0.187445i	0.586429	+	0.810000i	$0.300533\pi$
$360$		0			0
$361$	−6.28968	−	17.9287i	−0.331036	−	0.943618i
$362$	14.1575			0.744099
$363$		0			0
$364$	−2.11809	+	12.0123i	−0.111018	+	0.629614i
$365$	−14.5817	+	12.2355i	−0.763242	+	0.640436i
$366$		0			0
$367$	−5.64930	−	32.0388i	−0.294891	−	1.67241i	−0.667645	−	0.744480i	$-0.732697\pi$
$367$	−5.64930	−	32.0388i	−0.294891	−	1.67241i	0.372754	−	0.927930i	$-0.378414\pi$
$368$	−0.0368366	−	0.0638029i	−0.00192024	−	0.00332596i
$369$		0			0
$370$	−1.75237	−	0.637812i	−0.0911016	−	0.0331583i
$371$	10.7836	+	3.92490i	0.559856	+	0.203771i
$372$		0			0
$373$	−15.2429	−	26.4014i	−0.789246	−	1.36701i	−0.926429	−	0.376469i	$-0.877138\pi$
$373$	−15.2429	−	26.4014i	−0.789246	−	1.36701i	0.137183	−	0.990546i	$-0.456195\pi$
$374$	−0.860967	−	4.88279i	−0.0445195	−	0.252483i
$375$		0			0
$376$	−1.55825	+	1.30753i	−0.0803605	+	0.0674305i
$377$	−3.18614	+	18.0695i	−0.164094	+	0.930626i
$378$		0			0
$379$	17.8598			0.917396			0.458698	−	0.888592i	$-0.348316\pi$
$379$	17.8598			0.917396			0.458698	+	0.888592i	$0.348316\pi$
$380$	7.83022	−	11.0450i	0.401682	−	0.566599i
$381$		0			0
$382$	−15.6582	+	5.69913i	−0.801144	+	0.291593i
$383$	4.07310	−	23.0997i	0.208126	−	1.18034i	−0.684319	−	0.729183i	$-0.739900\pi$
$383$	4.07310	−	23.0997i	0.208126	−	1.18034i	0.892445	−	0.451157i	$-0.148988\pi$
$384$		0			0
$385$	12.4363	+	10.4353i	0.633812	+	0.531831i
$386$	−1.97013	−	11.1732i	−0.100277	−	0.568700i
$387$		0			0
$388$	−1.11809	+	1.93659i	−0.0567623	+	0.0983153i
$389$	3.67365	+	1.33710i	0.186261	+	0.0677936i	0.433467	−	0.901169i	$-0.357290\pi$
$389$	3.67365	+	1.33710i	0.186261	+	0.0677936i	−0.247206	+	0.968963i	$0.579512\pi$
$390$		0			0
$391$	−1.45336	+	2.51730i	−0.0734997	+	0.127305i
$392$	4.92009	+	8.52185i	0.248502	+	0.430418i
$393$		0			0
$394$	−15.6288	−	13.1141i	−0.787369	−	0.660681i
$395$	−13.5064	+	11.3332i	−0.679581	+	0.570236i
$396$		0			0
$397$	−8.41875	+	3.06417i	−0.422525	+	0.153786i	−0.544527	−	0.838743i	$-0.683291\pi$
$397$	−8.41875	+	3.06417i	−0.422525	+	0.153786i	0.122002	+	0.992530i	$0.461069\pi$
$398$	−8.10936			−0.406486
$399$		0			0
$400$	−0.0591253			−0.00295627
$401$	−1.90508	+	0.693392i	−0.0951350	+	0.0346263i	−0.389149	−	0.921175i	$-0.627231\pi$
$401$	−1.90508	+	0.693392i	−0.0951350	+	0.0346263i	0.294014	+	0.955801i	$0.405009\pi$
$402$		0			0
$403$	−7.87733	+	6.60986i	−0.392398	+	0.329261i
$404$	−7.44356	−	6.24589i	−0.370331	−	0.310745i
$405$		0			0
$406$	−2.86571	−	4.96356i	−0.142223	−	0.246338i
$407$	−1.42855	+	2.47432i	−0.0708105	+	0.122647i
$408$		0			0
$409$	30.2656	+	11.0158i	1.49654	+	0.544696i	0.955162	−	0.296084i	$-0.0956808\pi$
$409$	30.2656	+	11.0158i	1.49654	+	0.544696i	0.541377	+	0.840780i	$0.317903\pi$
$410$	4.99912	−	8.65873i	0.246889	−	0.427624i
$411$		0			0
$412$	0.00309887	+	0.0175745i	0.000152670	+	0.000865836i
$413$	−15.4893	−	12.9971i	−0.762180	−	0.639545i
$414$		0			0
$415$	−1.10472	+	6.26519i	−0.0542287	+	0.307546i
$416$	−28.0317	+	10.2027i	−1.37437	+	0.500228i
$417$		0			0
$418$	9.19253	+	9.30039i	0.449622	+	0.454897i
$419$	23.2499			1.13583			0.567916	−	0.823086i	$-0.307750\pi$
$419$	23.2499			1.13583			0.567916	+	0.823086i	$0.307750\pi$
$420$		0			0
$421$	1.12061	−	6.35532i	0.0546154	−	0.309739i	−0.945246	−	0.326357i	$-0.894179\pi$
$421$	1.12061	−	6.35532i	0.0546154	−	0.309739i	0.999862	+	0.0166178i	$0.00528986\pi$
$422$	−9.85117	+	8.26611i	−0.479547	+	0.402388i
$423$		0			0
$424$	3.00862	+	17.0627i	0.146111	+	0.828639i
$425$	1.16637	+	2.02022i	0.0565775	+	0.0979950i
$426$		0			0
$427$	7.75150	+	2.82131i	0.375121	+	0.136533i
$428$	4.09714	+	1.49124i	0.198043	+	0.0720817i
$429$		0			0
$430$	5.34477	+	9.25741i	0.257748	+	0.446432i
$431$	2.43061	+	13.7847i	0.117078	+	0.663984i	0.985700	+	0.168508i	$0.0538950\pi$
$431$	2.43061	+	13.7847i	0.117078	+	0.663984i	−0.868622	+	0.495475i	$0.834994\pi$
$432$		0			0
$433$	−21.9800	+	18.4434i	−1.05629	+	0.886333i	−0.993741	−	0.111709i	$-0.964368\pi$
$433$	−21.9800	+	18.4434i	−1.05629	+	0.886333i	−0.0625499	+	0.998042i	$0.519923\pi$
$434$	0.557781	−	3.16333i	0.0267744	−	0.151845i
$435$		0			0
$436$	−9.04013			−0.432944
$437$	−0.623608	−	7.64090i	−0.0298312	−	0.365514i
$438$		0			0
$439$	12.5376	−	4.56332i	0.598387	−	0.217795i	−0.0250271	−	0.999687i	$-0.507967\pi$
$439$	12.5376	−	4.56332i	0.598387	−	0.217795i	0.623414	+	0.781892i	$0.285745\pi$
$440$	−4.25624	+	24.1384i	−0.202908	+	1.15075i
$441$		0			0
$442$	−5.89053	−	4.94274i	−0.280184	−	0.235102i
$443$	−5.88372	−	33.3682i	−0.279544	−	1.58537i	−0.724147	−	0.689646i	$-0.757766\pi$
$443$	−5.88372	−	33.3682i	−0.279544	−	1.58537i	0.444603	−	0.895728i	$-0.353345\pi$
$444$		0			0
$445$	−2.89053	+	5.00654i	−0.137024	+	0.237333i
$446$	−2.49108	−	0.906678i	−0.117956	−	0.0429324i
$447$		0			0
$448$	4.73783	−	8.20616i	0.223841	−	0.387704i
$449$	9.42009	+	16.3161i	0.444562	+	0.770003i	0.998022	−	0.0628725i	$-0.0200261\pi$
$449$	9.42009	+	16.3161i	0.444562	+	0.770003i	−0.553460	+	0.832876i	$0.686693\pi$
$450$		0			0
$451$	−11.7344	−	9.84635i	−0.552552	−	0.463646i
$452$	6.93242	−	5.81699i	0.326074	−	0.273608i
$453$		0			0
$454$	11.3391	−	4.12711i	0.532172	−	0.193695i
$455$	25.1780			1.18036
$456$		0			0
$457$	14.2790			0.667943			0.333972	−	0.942583i	$-0.391611\pi$
$457$	14.2790			0.667943			0.333972	+	0.942583i	$0.391611\pi$
$458$	7.77941	−	2.83147i	0.363508	−	0.132306i
$459$		0			0
$460$	4.18479	−	3.51146i	0.195117	−	0.163723i
$461$	10.6695	+	8.95280i	0.496930	+	0.416973i	0.856502	−	0.516144i	$-0.172633\pi$
$461$	10.6695	+	8.95280i	0.496930	+	0.416973i	−0.359572	+	0.933117i	$0.617077\pi$
$462$		0			0
$463$	0.881445	+	1.52671i	0.0409642	+	0.0709521i	0.885781	−	0.464104i	$-0.153624\pi$
$463$	0.881445	+	1.52671i	0.0409642	+	0.0709521i	−0.844816	+	0.535056i	$0.820290\pi$
$464$	0.0726338	−	0.125805i	0.00337194	−	0.00584037i
$465$		0			0
$466$	19.9859	+	7.27428i	0.925830	+	0.336974i
$467$	11.0209	−	19.0888i	0.509988	−	0.883326i	−0.489945	−	0.871754i	$-0.662983\pi$
$467$	11.0209	−	19.0888i	0.509988	−	0.883326i	0.999933	−	0.0115724i	$-0.00368368\pi$
$468$		0			0
$469$	−4.63816	−	26.3043i	−0.214170	−	1.21462i
$470$	1.22281	+	1.02606i	0.0564041	+	0.0473286i
$471$		0			0
$472$	5.30113	−	30.0642i	0.244004	−	1.38382i
$473$	15.3897	−	5.60138i	0.707617	−	0.257552i
$474$		0			0
$475$	−5.56077	−	2.63263i	−0.255146	−	0.120793i
$476$	−3.81016			−0.174638
$477$		0			0
$478$	−3.56196	+	20.2009i	−0.162920	+	0.923966i
$479$	19.5012	−	16.3634i	0.891032	−	0.747664i	−0.0773851	−	0.997001i	$-0.524657\pi$
$479$	19.5012	−	16.3634i	0.891032	−	0.747664i	0.968417	+	0.249337i	$0.0802126\pi$
$480$		0			0
$481$	0.769448	+	4.36376i	0.0350838	+	0.198970i
$482$	0.130882	+	0.226694i	0.00596150	+	0.0103256i
$483$		0			0
$484$	0.735604	+	0.267738i	0.0334366	+	0.0121699i
$485$	4.33750	+	1.57872i	0.196956	+	0.0716860i
$486$		0			0
$487$	11.2554	+	19.4949i	0.510029	+	0.883397i	0.999932	+	0.0116199i	$0.00369881\pi$
$487$	11.2554	+	19.4949i	0.510029	+	0.883397i	−0.489903	+	0.871777i	$0.662968\pi$
$488$	2.16267	+	12.2651i	0.0978993	+	0.555214i
$489$		0			0
$490$	5.91534	−	4.96356i	0.267228	−	0.224231i
$491$	−2.71482	+	15.3965i	−0.122518	+	0.694835i	0.860233	+	0.509902i	$0.170318\pi$
$491$	−2.71482	+	15.3965i	−0.122518	+	0.694835i	−0.982751	+	0.184934i	$0.940793\pi$
$492$		0			0
$493$	−5.73143			−0.258131
$494$	20.1928	+	1.88538i	0.908519	+	0.0848274i
$495$		0			0
$496$	0.0765042	−	0.0278452i	0.00343514	−	0.00125029i
$497$	−4.49020	+	25.4652i	−0.201413	+	1.14227i
$498$		0			0
$499$	−21.9217	−	18.3945i	−0.981352	−	0.823452i	0.00294090	−	0.999996i	$-0.499064\pi$
$499$	−21.9217	−	18.3945i	−0.981352	−	0.823452i	−0.984293	+	0.176544i	$0.943508\pi$
$500$	1.93552	+	10.9769i	0.0865590	+	0.490900i
$501$		0			0
$502$	7.12196	−	12.3356i	0.317869	−	0.550565i
$503$	−23.5351	−	8.56607i	−1.04938	−	0.381942i	−0.240950	−	0.970538i	$-0.577459\pi$
$503$	−23.5351	−	8.56607i	−1.04938	−	0.381942i	−0.808428	+	0.588595i	$0.799681\pi$
$504$		0			0
$505$	−10.0287	+	17.3702i	−0.446271	+	0.772963i
$506$	2.63816	+	4.56942i	0.117280	+	0.203135i
$507$		0			0
$508$	0.0949225	+	0.0796494i	0.00421150	+	0.00353387i
$509$	−25.6787	+	21.5470i	−1.13819	+	0.955053i	−0.999378	−	0.0352655i	$-0.988772\pi$
$509$	−25.6787	+	21.5470i	−1.13819	+	0.955053i	−0.138810	+	0.990319i	$0.544328\pi$
$510$		0			0
$511$	−13.2763	+	4.83218i	−0.587309	+	0.213763i
$512$	0.473897			0.0209435
$513$		0			0
$514$	13.5030			0.595591
$515$	0.0346151	−	0.0125989i	0.00152532	−	0.000555172i
$516$		0			0
$517$	1.87346	−	1.57202i	0.0823945	−	0.0691372i
$518$	−1.06031	−	0.889704i	−0.0465872	−	0.0390913i
$519$		0			0
$520$	19.0069	+	32.9209i	0.833506	+	1.44367i
$521$	−13.7392	+	23.7969i	−0.601924	+	1.04256i	0.390606	+	0.920558i	$0.372266\pi$
$521$	−13.7392	+	23.7969i	−0.601924	+	1.04256i	−0.992530	+	0.122005i	$0.961068\pi$
$522$		0			0
$523$	9.73277	+	3.54244i	0.425584	+	0.154900i	0.545928	−	0.837832i	$-0.316177\pi$
$523$	9.73277	+	3.54244i	0.425584	+	0.154900i	−0.120343	+	0.992732i	$0.538400\pi$
$524$	1.86262	−	3.22615i	0.0813687	−	0.140935i
$525$		0			0
$526$	1.47255	+	8.35126i	0.0642064	+	0.364132i
$527$	−2.46064	−	2.06472i	−0.107187	−	0.0899406i
$528$		0			0
$529$	−3.45677	+	19.6043i	−0.150294	+	0.852361i
$530$	12.7763	−	4.65020i	0.554968	−	0.201992i
$531$		0			0
$532$	8.26517	−	5.71578i	0.358340	−	0.247811i
$533$	−23.7570			−1.02903
$534$		0			0
$535$	1.56283	−	8.86327i	0.0675672	−	0.383193i
$536$	30.8922	−	25.9216i	1.33434	−	1.11964i
$537$		0			0
$538$	−2.79127	−	15.8301i	−0.120340	−	0.682483i
$539$	−5.91534	−	10.2457i	−0.254792	−	0.441313i
$540$		0			0
$541$	−2.37211	−	0.863378i	−0.101985	−	0.0371195i	0.290524	−	0.956868i	$-0.406170\pi$
$541$	−2.37211	−	0.863378i	−0.101985	−	0.0371195i	−0.392509	+	0.919748i	$0.628393\pi$
$542$	15.6710	+	5.70378i	0.673128	+	0.244998i
$543$		0			0
$544$	−4.65910	−	8.06980i	−0.199757	−	0.345990i
$545$	3.24035	+	18.3770i	0.138801	+	0.787182i
$546$		0			0
$547$	5.87939	−	4.93339i	0.251384	−	0.210937i	−0.508384	−	0.861131i	$-0.669757\pi$
$547$	5.87939	−	4.93339i	0.251384	−	0.210937i	0.759768	+	0.650194i	$0.225312\pi$
$548$	4.16220	−	23.6050i	0.177800	−	1.00836i
$549$		0			0
$550$	4.23442			0.180556
$551$	12.4329	−	8.59797i	0.529659	−	0.366286i
$552$		0			0
$553$	−12.2973	+	4.47584i	−0.522933	+	0.190332i
$554$	−2.10179	+	11.9198i	−0.0892963	+	0.506425i
$555$		0			0
$556$	−14.4684	−	12.1404i	−0.613596	−	0.514868i
$557$	−0.565360	−	3.20631i	−0.0239551	−	0.135856i	0.970485	−	0.241163i	$-0.0775287\pi$
$557$	−0.565360	−	3.20631i	−0.0239551	−	0.135856i	−0.994440	+	0.105307i	$0.966418\pi$
$558$		0			0
$559$	12.6998	−	21.9967i	0.537145	−	0.930362i
$560$	−0.187319	−	0.0681784i	−0.00791566	−	0.00288107i
$561$		0			0
$562$	−5.76486	+	9.98503i	−0.243176	+	0.421193i
$563$	2.62954	+	4.55449i	0.110822	+	0.191949i	0.916102	−	0.400946i	$-0.131318\pi$
$563$	2.62954	+	4.55449i	0.110822	+	0.191949i	−0.805280	+	0.592895i	$0.797985\pi$
$564$		0			0
$565$	−14.3097	−	12.0073i	−0.602015	−	0.505151i
$566$	11.7062	−	9.82267i	0.492048	−	0.412878i
$567$		0			0
$568$	−36.6860	+	13.3526i	−1.53931	+	0.560264i
$569$	29.9564			1.25584			0.627918	−	0.778280i	$-0.283907\pi$
$569$	29.9564			1.25584			0.627918	+	0.778280i	$0.283907\pi$
$570$		0			0
$571$	−16.7101			−0.699295			−0.349647	−	0.936881i	$-0.613699\pi$
$571$	−16.7101			−0.699295			−0.349647	+	0.936881i	$0.613699\pi$
$572$	20.8059	−	7.57272i	0.869937	−	0.316631i
$573$		0			0
$574$	5.68479	−	4.77011i	0.237279	−	0.199100i
$575$	−1.90167	−	1.59569i	−0.0793053	−	0.0665450i
$576$		0			0
$577$	6.84002	+	11.8473i	0.284754	+	0.493208i	0.972549	−	0.232696i	$-0.0747548\pi$
$577$	6.84002	+	11.8473i	0.284754	+	0.493208i	−0.687796	+	0.725904i	$0.741421\pi$
$578$	−6.27379	+	10.8665i	−0.260955	+	0.451987i
$579$		0			0
$580$	10.1220	+	3.68409i	0.420291	+	0.152974i
$581$	−2.36097	+	4.08931i	−0.0979494	+	0.169653i
$582$		0			0
$583$	−3.61721	−	20.5142i	−0.149810	−	0.849612i
$584$	−16.3405	−	13.7113i	−0.676174	−	0.567378i
$585$		0			0
$586$	2.38279	−	13.5135i	0.0984321	−	0.558236i
$587$	−22.5872	+	8.22108i	−0.932275	+	0.339320i	−0.763111	−	0.646268i	$-0.776329\pi$
$587$	−22.5872	+	8.22108i	−0.932275	+	0.339320i	−0.169164	+	0.985588i	$0.554107\pi$
$588$		0			0
$589$	8.43511	+	0.787576i	0.347563	+	0.0324515i
$590$	−23.9564			−0.986268
$591$		0			0
$592$	0.00609191	−	0.0345490i	0.000250376	−	0.00141995i
$593$	3.24897	−	2.72621i	0.133419	−	0.111952i	−0.573636	−	0.819110i	$-0.694468\pi$
$593$	3.24897	−	2.72621i	0.133419	−	0.111952i	0.707055	+	0.707158i	$0.250023\pi$
$594$		0			0
$595$	1.36571	+	7.74535i	0.0559888	+	0.317529i
$596$	2.31016	+	4.00131i	0.0946276	+	0.163900i
$597$		0			0
$598$	7.68954	+	2.79876i	0.314449	+	0.114450i
$599$	−24.6894	−	8.98622i	−1.00878	−	0.367167i	−0.215818	−	0.976434i	$-0.569242\pi$
$599$	−24.6894	−	8.98622i	−1.00878	−	0.367167i	−0.792965	+	0.609267i	$0.791464\pi$
$600$		0			0
$601$	21.1197	+	36.5805i	0.861492	+	1.49215i	0.870489	+	0.492188i	$0.163803\pi$
$601$	21.1197	+	36.5805i	0.861492	+	1.49215i	−0.00899659	+	0.999960i	$0.502864\pi$
$602$	1.37774	+	7.81353i	0.0561523	+	0.318456i
$603$		0			0
$604$	13.7160	−	11.5091i	0.558096	−	0.468298i
$605$	0.280592	−	1.59132i	0.0114077	−	0.0646963i
$606$		0			0
$607$	−22.0969			−0.896885			−0.448443	−	0.893812i	$-0.648021\pi$
$607$	−22.0969			−0.896885			−0.448443	+	0.893812i	$0.648021\pi$
$608$	22.2126	+	10.5161i	0.900840	+	0.426483i
$609$		0			0
$610$	9.18392	−	3.34267i	0.371846	−	0.135341i
$611$	0.658633	−	3.73530i	0.0266455	−	0.151114i
$612$		0			0
$613$	5.49794	+	4.61332i	0.222060	+	0.186330i	0.747030	−	0.664790i	$-0.231479\pi$
$613$	5.49794	+	4.61332i	0.222060	+	0.186330i	−0.524970	+	0.851121i	$0.675924\pi$
$614$	−3.28622	−	18.6371i	−0.132621	−	0.752131i
$615$		0			0
$616$	−9.09627	+	15.7552i	−0.366499	+	0.634795i
$617$	−46.3953	−	16.8865i	−1.86781	−	0.679826i	−0.971811	−	0.235761i	$-0.924242\pi$
$617$	−46.3953	−	16.8865i	−1.86781	−	0.679826i	−0.895995	−	0.444065i	$-0.853536\pi$
$618$		0			0
$619$	−13.2490	+	22.9479i	−0.532521	+	0.922354i	0.466758	+	0.884385i	$0.345422\pi$
$619$	−13.2490	+	22.9479i	−0.532521	+	0.922354i	−0.999279	+	0.0379684i	$0.987911\pi$
$620$	3.01842	+	5.22805i	0.121223	+	0.209964i
$621$		0			0
$622$	9.76470	+	8.19356i	0.391529	+	0.328532i
$623$	−3.28699	+	2.75811i	−0.131690	+	0.110501i
$624$		0			0
$625$	28.2520	−	10.2829i	1.13008	−	0.411315i
$626$	−17.1643			−0.686022
$627$		0			0
$628$	12.7264			0.507838
$629$	−1.30066	+	0.473401i	−0.0518607	+	0.0188757i
$630$		0			0
$631$	25.5253	−	21.4183i	1.01615	−	0.852647i	0.0270071	−	0.999635i	$-0.491402\pi$
$631$	25.5253	−	21.4183i	1.01615	−	0.852647i	0.989138	+	0.146988i	$0.0469579\pi$
$632$	−15.1355	−	12.7002i	−0.602057	−	0.505185i
$633$		0			0
$634$	−12.4641	−	21.5884i	−0.495013	−	0.857387i
$635$	0.127889	−	0.221510i	0.00507511	−	0.00879035i
$636$		0			0
$637$	−17.2417	−	6.27546i	−0.683141	−	0.248643i
$638$	−5.20187	+	9.00990i	−0.205944	+	0.356705i
$639$		0			0
$640$	3.00862	+	17.0627i	0.118926	+	0.674463i
$641$	0.104256	+	0.0874810i	0.00411786	+	0.00345529i	0.644844	−	0.764314i	$-0.276922\pi$
$641$	0.104256	+	0.0874810i	0.00411786	+	0.00345529i	−0.640726	+	0.767769i	$0.721367\pi$
$642$		0			0
$643$	8.36602	−	47.4461i	0.329924	−	1.87109i	−0.142613	−	0.989779i	$-0.545550\pi$
$643$	8.36602	−	47.4461i	0.329924	−	1.87109i	0.472536	−	0.881311i	$-0.343339\pi$
$644$	3.81016	−	1.38678i	0.150141	−	0.0546469i
$645$		0			0
$646$	0.515319	+	6.31407i	0.0202750	+	0.248424i
$647$	36.9718			1.45351			0.726756	−	0.686895i	$-0.241027\pi$
$647$	36.9718			1.45351			0.726756	+	0.686895i	$0.241027\pi$
$648$		0			0
$649$	−6.37346	+	36.1457i	−0.250180	+	1.41884i
$650$	5.03074	−	4.22130i	0.197322	−	0.165573i
$651$		0			0
$652$	0.430770	+	2.44302i	0.0168702	+	0.0956759i
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$		0			0
$655$	−7.22580	−	2.62998i	−0.282336	−	0.102762i
$656$	0.176747	+	0.0643307i	0.00690081	+	0.00251169i
$657$		0			0
$658$	0.592396	+	1.02606i	0.0230940	+	0.0400000i
$659$	−3.27760	−	18.5882i	−0.127677	−	0.724093i	−0.979682	−	0.200559i	$-0.935724\pi$
$659$	−3.27760	−	18.5882i	−0.127677	−	0.724093i	0.852005	−	0.523534i	$-0.175387\pi$
$660$		0			0
$661$	−23.4500	+	19.6769i	−0.912098	+	0.765341i	−0.972517	−	0.232832i	$-0.925201\pi$
$661$	−23.4500	+	19.6769i	−0.912098	+	0.765341i	0.0604192	+	0.998173i	$0.480756\pi$
$662$	0.261135	−	1.48097i	0.0101493	−	0.0575594i
$663$		0			0
$664$	−7.12918			−0.276666
$665$	−14.5817	−	14.7528i	−0.565455	−	0.572090i
$666$		0			0
$667$	5.73143	−	2.08607i	0.221922	−	0.0807729i
$668$	−4.95394	+	28.0952i	−0.191674	+	1.08703i
$669$		0			0
$670$	−24.2422	−	20.3416i	−0.936556	−	0.785864i
$671$	−2.60014	−	14.7461i	−0.100377	−	0.569267i
$672$		0			0
$673$	−5.95471	+	10.3139i	−0.229537	+	0.397570i	−0.957671	−	0.287865i	$-0.907055\pi$
$673$	−5.95471	+	10.3139i	−0.229537	+	0.397570i	0.728134	+	0.685435i	$0.240388\pi$
$674$	21.0214	+	7.65117i	0.809715	+	0.294712i
$675$		0			0
$676$	9.19594	−	15.9278i	0.353690	−	0.612609i
$677$	2.89053	+	5.00654i	0.111092	+	0.192417i	0.916211	−	0.400696i	$-0.131232\pi$
$677$	2.89053	+	5.00654i	0.111092	+	0.192417i	−0.805119	+	0.593114i	$0.797898\pi$
$678$		0			0
$679$	2.62449	+	2.20220i	0.100718	+	0.0845129i
$680$	−9.09627	+	7.63267i	−0.348826	+	0.292700i
$681$		0			0
$682$	−5.47906	+	1.99421i	−0.209804	+	0.0763624i
$683$	−21.0496			−0.805442			−0.402721	−	0.915323i	$-0.631935\pi$
$683$	−21.0496			−0.805442			−0.402721	+	0.915323i	$0.631935\pi$
$684$		0			0
$685$	−49.4766			−1.89040
$686$	16.2570	−	5.91707i	0.620696	−	0.225915i
$687$		0			0
$688$	−0.154048	+	0.129261i	−0.00587302	+	0.00492805i
$689$	−24.7481	−	20.7661i	−0.942827	−	0.791126i
$690$		0			0
$691$	16.4688	+	28.5249i	0.626504	+	1.08514i	0.988248	+	0.152860i	$0.0488483\pi$
$691$	16.4688	+	28.5249i	0.626504	+	1.08514i	−0.361744	+	0.932278i	$0.617818\pi$
$692$	−0.549935	+	0.952515i	−0.0209054	+	0.0362092i
$693$		0			0
$694$	−6.36484	−	2.31661i	−0.241606	−	0.0879374i
$695$	−19.4932	+	33.7632i	−0.739419	+	1.28071i
$696$		0			0
$697$	−1.28864	−	7.30823i	−0.0488106	−	0.276819i
$698$	−15.3302	−	12.8636i	−0.580257	−	0.486894i
$699$		0			0
$700$	0.565055	−	3.20459i	0.0213571	−	0.121122i
$701$	20.0694	−	7.30466i	0.758010	−	0.275893i	0.0660380	−	0.997817i	$-0.478964\pi$
$701$	20.0694	−	7.30466i	0.758010	−	0.275893i	0.691973	+	0.721924i	$0.256742\pi$
$702$		0			0
$703$	2.11128	−	2.97810i	0.0796285	−	0.112321i
$704$	−17.2003			−0.648260
$705$		0			0
$706$	−1.74779	+	9.91220i	−0.0657789	+	0.373051i
$707$	−11.4042	+	9.56926i	−0.428899	+	0.359889i
$708$		0			0
$709$	−2.73854	−	15.5310i	−0.102848	−	0.583280i	−0.992058	−	0.125781i	$-0.959856\pi$
$709$	−2.73854	−	15.5310i	−0.102848	−	0.583280i	0.889210	−	0.457499i	$-0.151255\pi$
$710$	15.3182	+	26.5319i	0.574882	+	0.995725i
$711$		0			0
$712$	−6.08765	−	2.21572i	−0.228144	−	0.0830377i
$713$	3.21213	+	1.16912i	0.120295	+	0.0437839i
$714$		0			0
$715$	−22.8516	−	39.5802i	−0.854603	−	1.48022i
$716$	−4.54101	−	25.7534i	−0.169706	−	0.962448i
$717$		0			0
$718$	6.99525	−	5.86971i	0.261060	−	0.219056i
$719$	6.13470	−	34.7916i	0.228786	−	1.29751i	−0.626529	−	0.779398i	$-0.715525\pi$
$719$	6.13470	−	34.7916i	0.228786	−	1.29751i	0.855314	−	0.518109i	$-0.173364\pi$
$720$		0			0
$721$	0.0273411			0.00101824
$722$	−10.5899	−	12.9237i	−0.394114	−	0.480971i
$723$		0			0
$724$	−18.5577	+	6.75444i	−0.689691	+	0.251027i
$725$	0.849985	−	4.82050i	0.0315676	−	0.179029i
$726$		0			0
$727$	30.9647	+	25.9825i	1.14842	+	0.963637i	0.999681	−	0.0252396i	$-0.00803487\pi$
$727$	30.9647	+	25.9825i	1.14842	+	0.963637i	0.148737	+	0.988877i	$0.452479\pi$
$728$	4.89945	+	27.7862i	0.181586	+	1.02982i
$729$		0			0
$730$	−8.36959	+	14.4965i	−0.309772	+	0.536541i
$731$	7.45558	+	2.71361i	0.275755	+	0.100367i
$732$		0			0
$733$	18.1382	−	31.4162i	0.669948	−	1.16038i	−0.307970	−	0.951396i	$-0.599650\pi$
$733$	18.1382	−	31.4162i	0.669948	−	1.16038i	0.977918	−	0.208988i	$-0.0670170\pi$
$734$	−14.3045	−	24.7762i	−0.527990	−	0.914505i
$735$		0			0
$736$	7.59627	+	6.37402i	0.280002	+	0.234950i
$737$	−37.1411	+	31.1651i	−1.36811	+	1.14798i
$738$		0			0
$739$	19.4290	−	7.07158i	0.714708	−	0.260132i	0.0410304	−	0.999158i	$-0.486936\pi$
$739$	19.4290	−	7.07158i	0.714708	−	0.260132i	0.673677	+	0.739026i	$0.264714\pi$
$740$	2.60132			0.0956264
$741$		0			0
$742$	10.0915			0.370471
$743$	6.29978	−	2.29293i	0.231117	−	0.0841196i	−0.223866	−	0.974620i	$-0.571868\pi$
$743$	6.29978	−	2.29293i	0.231117	−	0.0841196i	0.454982	+	0.890500i	$0.349646\pi$
$744$		0			0
$745$	7.30587	−	6.13036i	0.267667	−	0.224599i
$746$	−20.5367	−	17.2323i	−0.751901	−	0.630920i
$747$		0			0
$748$	3.45811	+	5.98962i	0.126441	+	0.219002i
$749$	3.34002	−	5.78509i	0.122042	−	0.211383i
$750$		0			0
$751$	−10.0617	−	3.66214i	−0.367155	−	0.133633i	0.151853	−	0.988403i	$-0.451476\pi$
$751$	−10.0617	−	3.66214i	−0.367155	−	0.133633i	−0.519007	+	0.854770i	$0.673698\pi$
$752$	−0.0150147	+	0.0260063i	−0.000547531	+	0.000948352i
$753$		0			0
$754$	2.80184	+	15.8900i	0.102037	+	0.578681i
$755$	−28.3123	−	23.7568i	−1.03039	−	0.864599i
$756$		0			0
$757$	−0.705432	+	4.00071i	−0.0256394	+	0.145408i	−0.994940	−	0.100470i	$-0.967965\pi$
$757$	−0.705432	+	4.00071i	−0.0256394	+	0.145408i	0.969301	+	0.245878i	$0.0790764\pi$
$758$	14.7585	−	5.37164i	0.536052	−	0.195107i
$759$		0			0
$760$	8.28194	−	30.2029i	0.300417	−	1.09557i
$761$	11.0077			0.399030			0.199515	−	0.979895i	$-0.436063\pi$
$761$	11.0077			0.399030			0.199515	+	0.979895i	$0.436063\pi$
$762$		0			0
$763$	−2.40508	+	13.6399i	−0.0870697	+	0.493797i
$764$	17.8059	−	14.9409i	0.644194	−	0.540543i
$765$		0			0
$766$	−3.58182	−	20.3135i	−0.129417	−	0.733958i
$767$	28.4616	+	49.2969i	1.02769	+	1.78001i
$768$		0			0
$769$	−20.0599	−	7.30121i	−0.723378	−	0.263288i	−0.0460191	−	0.998941i	$-0.514654\pi$
$769$	−20.0599	−	7.30121i	−0.723378	−	0.263288i	−0.677359	+	0.735652i	$0.736876\pi$
$770$	13.4153	+	4.88279i	0.483455	+	0.175963i
$771$		0			0
$772$	7.91312	+	13.7059i	0.284800	+	0.493287i
$773$	−3.11128	−	17.6450i	−0.111905	−	0.634645i	−0.988236	−	0.152936i	$-0.951127\pi$
$773$	−3.11128	−	17.6450i	−0.111905	−	0.634645i	0.876331	−	0.481709i	$-0.159984\pi$
$774$		0			0
$775$	2.10148	−	1.76335i	0.0754874	−	0.0633415i
$776$	−0.898214	+	5.09403i	−0.0322440	+	0.182865i
$777$		0			0
$778$	3.43788			0.123254
$779$	13.7588	+	13.9202i	0.492959	+	0.498743i
$780$		0			0
$781$	44.1070	−	16.0536i	1.57827	−	0.574444i
$782$	−0.443868	+	2.51730i	−0.0158727	+	0.0900184i
$783$		0			0
$784$	0.111281	+	0.0933762i	0.00397434	+	0.00333486i
$785$	−4.56165	−	25.8704i	−0.162812	−	0.923355i
$786$		0			0
$787$	−24.4158	+	42.2894i	−0.870330	+	1.50746i	−0.00867371	+	0.999962i	$0.502761\pi$
$787$	−24.4158	+	42.2894i	−0.870330	+	1.50746i	−0.861656	+	0.507493i	$0.830572\pi$
$788$	26.7430	+	9.73367i	0.952681	+	0.346748i
$789$		0			0
$790$	−7.75237	+	13.4275i	−0.275817	+	0.477729i
$791$	−6.93242	−	12.0073i	−0.246488	−	0.426930i
$792$		0			0
$793$	−17.7895	−	14.9272i	−0.631724	−	0.530080i
$794$	−6.03524	+	5.06417i	−0.214183	+	0.179721i
$795$		0			0
$796$	10.6298	−	3.86893i	0.376763	−	0.137131i
$797$	28.5262			1.01045			0.505225	−	0.862988i	$-0.331409\pi$
$797$	28.5262			1.01045			0.505225	+	0.862988i	$0.331409\pi$
$798$		0			0
$799$	1.18479			0.0419149
$800$	7.47818	−	2.72183i	0.264394	−	0.0962314i
$801$		0			0
$802$	−1.36571	+	1.14597i	−0.0482251	+	0.0404656i
$803$	19.6459	+	16.4849i	0.693289	+	0.581738i
$804$		0			0
$805$	−4.18479	−	7.24827i	−0.147495	−	0.255468i
$806$	−4.52141	+	7.83131i	−0.159260	+	0.275846i
$807$		0			0
$808$	−21.1211	−	7.68745i	−0.743037	−	0.270443i
$809$	−7.41834	+	12.8489i	−0.260815	+	0.451745i	−0.966459	−	0.256822i	$-0.917325\pi$
$809$	−7.41834	+	12.8489i	−0.260815	+	0.451745i	0.705644	+	0.708567i	$0.250658\pi$
$810$		0			0
$811$	−1.45471	−	8.25006i	−0.0510817	−	0.289699i	0.948556	−	0.316609i	$-0.102544\pi$
$811$	−1.45471	−	8.25006i	−0.0510817	−	0.289699i	−0.999638	+	0.0269103i	$0.991433\pi$
$812$	6.12449	+	5.13905i	0.214927	+	0.180345i
$813$		0			0
$814$	−0.436289	+	2.47432i	−0.0152919	+	0.0867248i
$815$	4.81180	−	1.75135i	0.168550	−	0.0613472i
$816$		0			0
$817$	−20.2438	+	5.29796i	−0.708241	+	0.185352i
$818$	28.3233			0.990299
$819$		0			0
$820$	−2.42185	+	13.7350i	−0.0845746	+	0.479646i
$821$	−4.80999	+	4.03606i	−0.167870	+	0.140860i	−0.722852	−	0.691002i	$-0.757169\pi$
$821$	−4.80999	+	4.03606i	−0.167870	+	0.140860i	0.554983	+	0.831862i	$0.312725\pi$
$822$		0			0
$823$	1.91472	+	10.8589i	0.0667428	+	0.378517i	0.999822	+	0.0188472i	$0.00599961\pi$
$823$	1.91472	+	10.8589i	0.0667428	+	0.378517i	−0.933080	+	0.359670i	$0.882889\pi$
$824$	0.0206398	+	0.0357492i	0.000719023	+	0.00124538i
$825$		0			0
$826$	−16.7087	−	6.08148i	−0.581371	−	0.211602i
$827$	31.8892	+	11.6067i	1.10890	+	0.403606i	0.830589	−	0.556886i	$-0.188004\pi$
$827$	31.8892	+	11.6067i	1.10890	+	0.403606i	0.278309	+	0.960492i	$0.410226\pi$
$828$		0			0
$829$	10.1834	+	17.6382i	0.353686	+	0.612602i	0.986892	−	0.161381i	$-0.0515949\pi$
$829$	10.1834	+	17.6382i	0.353686	+	0.612602i	−0.633206	+	0.773983i	$0.718262\pi$
$830$	0.971477	+	5.50952i	0.0337205	+	0.191238i
$831$		0			0
$832$	−20.4349	+	17.1470i	−0.708454	+	0.594464i
$833$	0.995252	−	5.64436i	0.0344834	−	0.195565i
$834$		0			0
$835$	58.8881			2.03791
$836$	−16.4868	−	7.80531i	−0.570208	−	0.269952i
$837$		0			0
$838$	19.2126	−	6.99281i	0.663688	−	0.241563i
$839$	−2.74526	+	15.5692i	−0.0947770	+	0.537507i	0.900038	+	0.435810i	$0.143538\pi$
$839$	−2.74526	+	15.5692i	−0.0947770	+	0.537507i	−0.994815	+	0.101697i	$0.967573\pi$
$840$		0			0
$841$	−13.0025	−	10.9104i	−0.448363	−	0.376221i
$842$	−0.985452	−	5.58878i	−0.0339609	−	0.192602i
$843$		0			0
$844$	8.96926	−	15.5352i	0.308734	−	0.534744i
$845$	−35.6746	−	12.9845i	−1.22724	−	0.446680i
$846$		0			0
$847$	0.599670	−	1.03866i	0.0206049	−	0.0356888i
$848$	0.127889	+	0.221510i	0.00439172	+	0.00760668i
$849$		0			0
$850$	1.57145	+	1.31860i	0.0539003	+	0.0452278i
$851$	1.12836	−	0.946803i	0.0386795	−	0.0324560i
$852$		0			0
$853$	49.4741	−	18.0071i	1.69396	−	0.616551i	0.698845	−	0.715274i	$-0.253698\pi$
$853$	49.4741	−	18.0071i	1.69396	−	0.616551i	0.995115	+	0.0987227i	$0.0314757\pi$
$854$	7.25402			0.248228
$855$		0			0
$856$	10.0855			0.344716
$857$	−21.6386	+	7.87581i	−0.739161	+	0.269033i	−0.684038	−	0.729447i	$-0.739778\pi$
$857$	−21.6386	+	7.87581i	−0.739161	+	0.269033i	−0.0551238	+	0.998480i	$0.517555\pi$
$858$		0			0
$859$	6.82501	−	5.72686i	0.232866	−	0.195398i	−0.518886	−	0.854843i	$-0.673653\pi$
$859$	6.82501	−	5.72686i	0.232866	−	0.195398i	0.751753	+	0.659445i	$0.229209\pi$
$860$	−11.4226	−	9.58471i	−0.389508	−	0.326836i
$861$		0			0
$862$	6.15451	+	10.6599i	0.209624	+	0.363079i
$863$	14.8849	−	25.7814i	0.506688	−	0.877609i	−0.493282	−	0.869869i	$-0.664203\pi$
$863$	14.8849	−	25.7814i	0.506688	−	0.877609i	0.999970	−	0.00773998i	$-0.00246374\pi$
$864$		0			0
$865$	2.13341	+	0.776497i	0.0725380	+	0.0264017i
$866$	−12.6160	+	21.8516i	−0.428710	+	0.742548i
$867$		0			0
$868$	0.778066	+	4.41263i	0.0264093	+	0.149775i
$869$	18.1971	+	15.2692i	0.617295	+	0.517972i
$870$		0			0
$871$	−13.0574	+	74.0520i	−0.442432	+	2.50916i
$872$	−19.6501	+	7.15204i	−0.665435	+	0.242199i
$873$		0			0
$874$	−2.81345	−	6.12651i	−0.0951665	−	0.207232i
$875$	17.0770			0.577307
$876$		0			0
$877$	−4.34642	+	24.6498i	−0.146768	+	0.832363i	0.819162	+	0.573562i	$0.194439\pi$
$877$	−4.34642	+	24.6498i	−0.146768	+	0.832363i	−0.965930	+	0.258802i	$0.916672\pi$
$878$	8.98798	−	7.54181i	0.303330	−	0.254524i
$879$		0			0
$880$	0.0628336	+	0.356347i	0.00211812	+	0.0120125i
$881$	10.1980	+	17.6634i	0.343579	+	0.595097i	0.985095	−	0.172014i	$-0.0550273\pi$
$881$	10.1980	+	17.6634i	0.343579	+	0.595097i	−0.641515	+	0.767110i	$0.721694\pi$
$882$		0			0
$883$	9.98710	+	3.63501i	0.336093	+	0.122328i	0.504553	−	0.863381i	$-0.331657\pi$
$883$	9.98710	+	3.63501i	0.336093	+	0.122328i	−0.168460	+	0.985708i	$0.553880\pi$
$884$	10.0795	+	3.66864i	0.339010	+	0.123390i
$885$		0			0
$886$	−14.8981	−	25.8043i	−0.500512	−	0.866912i
$887$	9.78312	+	55.4828i	0.328485	+	1.86293i	0.483959	+	0.875091i	$0.339198\pi$
$887$	9.78312	+	55.4828i	0.328485	+	1.86293i	−0.155474	+	0.987840i	$0.549690\pi$
$888$		0			0
$889$	0.145430	−	0.122030i	0.00487756	−	0.00409275i
$890$	−0.882789	+	5.00654i	−0.0295911	+	0.167820i
$891$		0			0
$892$	3.69789			0.123815
$893$	−2.57011	+	1.77736i	−0.0860054	+	0.0594771i
$894$		0			0
$895$	−50.7242	+	18.4621i	−1.69552	+	0.617120i
$896$	−2.23308	+	12.6644i	−0.0746019	+	0.423088i
$897$		0			0
$898$	12.6917	+	10.6496i	0.423526	+	0.355381i
$899$	1.17041	+	6.63771i	0.0390353	+	0.221380i
$900$		0			0
$901$	5.04576	−	8.73951i	0.168099	−	0.291155i
$902$	−12.6582	−	4.60722i	−0.421473	−	0.153404i
$903$		0			0
$904$	10.4666	−	18.1286i	0.348113	−	0.602949i
$905$	20.3824	+	35.3033i	0.677533	+	1.17352i
$906$		0			0
$907$	−4.53777	−	3.80764i	−0.150674	−	0.126431i	0.564334	−	0.825546i	$-0.309133\pi$
$907$	−4.53777	−	3.80764i	−0.150674	−	0.126431i	−0.715009	+	0.699116i	$0.753577\pi$
$908$	−12.8944	+	10.8197i	−0.427916	+	0.359064i
$909$		0			0
$910$	20.8059	−	7.57272i	0.689708	−	0.251033i
$911$	34.0591			1.12843			0.564215	−	0.825628i	$-0.309179\pi$
$911$	34.0591			1.12843			0.564215	+	0.825628i	$0.309179\pi$
$912$		0			0
$913$	8.57129			0.283668
$914$	11.7995	−	4.29466i	0.390292	−	0.142055i
$915$		0			0
$916$	−8.84642	+	7.42303i	−0.292294	+	0.245264i
$917$	−4.37211	−	3.66864i	−0.144380	−	0.121149i
$918$		0			0
$919$	3.13697	+	5.43340i	0.103479	+	0.179231i	0.913116	−	0.407700i	$-0.133669\pi$
$919$	3.13697	+	5.43340i	0.103479	+	0.179231i	−0.809637	+	0.586931i	$0.800336\pi$
$920$	6.31820	−	10.9434i	0.208305	−	0.360795i
$921$		0			0
$922$	11.5095	+	4.18911i	0.379045	+	0.137961i
$923$	36.3979	−	63.0429i	1.19805	−	2.07508i
$924$		0			0
$925$	−0.205270	−	1.16415i	−0.00674924	−	0.0382769i
$926$	1.18757	+	0.996487i	0.0390259	+	0.0327466i
$927$		0			0
$928$	−3.39528	+	19.2556i	−0.111455	+	0.632095i
$929$	26.6152	−	9.68712i	0.873215	−	0.317824i	0.133747	−	0.991016i	$-0.457299\pi$
$929$	26.6152	−	9.68712i	0.873215	−	0.317824i	0.739468	+	0.673191i	$0.235077\pi$
$930$		0			0
$931$	6.30840	+	13.7370i	0.206749	+	0.450213i
$932$	−29.6682			−0.971814
$933$		0			0
$934$	3.36588	−	19.0888i	0.110135	−	0.624606i
$935$	10.9363	−	9.17664i	0.357655	−	0.300108i
$936$		0			0
$937$	−3.48545	−	19.7670i	−0.113865	−	0.645759i	−0.987306	−	0.158830i	$-0.949228\pi$
$937$	−3.48545	−	19.7670i	−0.113865	−	0.645759i	0.873441	−	0.486930i	$-0.161883\pi$
$938$	−11.7442	−	20.3416i	−0.383462	−	0.664176i
$939$		0			0
$940$	−2.09240	−	0.761570i	−0.0682464	−	0.0248397i
$941$	5.06980	+	1.84526i	0.165271	+	0.0601537i	0.423331	−	0.905975i	$-0.360861\pi$
$941$	5.06980	+	1.84526i	0.165271	+	0.0601537i	−0.258060	+	0.966129i	$0.583083\pi$
$942$		0			0
$943$	3.94862	+	6.83920i	0.128585	+	0.222715i
$944$	−0.0782589	−	0.443828i	−0.00254711	−	0.0144454i
$945$		0			0
$946$	11.0326	−	9.25741i	0.358699	−	0.300984i
$947$	−1.15358	+	6.54228i	−0.0374863	+	0.212596i	−0.997797	−	0.0663359i	$-0.978869\pi$
$947$	−1.15358	+	6.54228i	−0.0374863	+	0.212596i	0.960311	+	0.278931i	$0.0899802\pi$
$948$		0			0
$949$	39.7743			1.29113
$950$	−5.38696	−	0.502975i	−0.174776	−	0.0163187i
$951$		0			0
$952$	−8.28194	+	3.01438i	−0.268419	+	0.0976966i
$953$	2.57414	−	14.5987i	0.0833846	−	0.472897i	−0.914309	−	0.405018i	$-0.867265\pi$
$953$	2.57414	−	14.5987i	0.0833846	−	0.472897i	0.997693	−	0.0678799i	$-0.0216235\pi$
$954$		0			0
$955$	−36.7545	−	30.8407i	−1.18935	−	0.997981i
$956$	−4.96868	−	28.1788i	−0.160699	−	0.911368i
$957$		0			0
$958$	11.1932	−	19.3873i	0.361637	−	0.626374i
$959$	−34.5082	−	12.5600i	−1.11433	−	0.405582i
$960$		0			0
$961$	13.6113	−	23.5754i	0.439074	−	0.760498i
$962$	1.94831	+	3.37457i	0.0628161	+	0.108801i
$963$		0			0
$964$	−0.279715	−	0.234709i	−0.00900901	−	0.00755946i
$965$	25.0253	−	20.9987i	0.805592	−	0.675972i
$966$		0			0
$967$	−19.9418	+	7.25822i	−0.641285	+	0.233409i	−0.642136	−	0.766591i	$-0.721951\pi$
$967$	−19.9418	+	7.25822i	−0.641285	+	0.233409i	0.000850519		1.00000i	$0.499729\pi$
$968$	1.81076			0.0582002
$969$		0			0
$970$	4.05913			0.130331
$971$	−35.3387	+	12.8622i	−1.13407	+	0.412769i	−0.839770	−	0.542943i	$-0.817310\pi$
$971$	−35.3387	+	12.8622i	−1.13407	+	0.412769i	−0.294304	+	0.955712i	$0.595088\pi$
$972$		0			0
$973$	−22.1668	+	18.6002i	−0.710636	+	0.596295i
$974$	15.1643	+	12.7244i	0.485896	+	0.407715i
$975$		0			0
$976$	0.0919294	+	0.159226i	0.00294259	+	0.00509671i
$977$	−23.0107	+	39.8558i	−0.736179	+	1.27510i	0.218026	+	0.975943i	$0.430038\pi$
$977$	−23.0107	+	39.8558i	−0.736179	+	1.27510i	−0.954204	+	0.299156i	$0.903295\pi$
$978$		0			0
$979$	7.31908	+	2.66393i	0.233919	+	0.0851395i
$980$	−5.38578	+	9.32845i	−0.172042	+	0.297986i
$981$		0			0
$982$	2.38737	+	13.5395i	0.0761842	+	0.432062i
$983$	−46.4195	−	38.9506i	−1.48055	−	1.24233i	−0.905592	−	0.424150i	$-0.860573\pi$
$983$	−46.4195	−	38.9506i	−1.48055	−	1.24233i	−0.574961	−	0.818181i	$-0.694983\pi$
$984$		0			0
$985$	10.2010	−	57.8527i	0.325031	−	1.84334i
$986$	−4.73618	+	1.72383i	−0.150831	+	0.0548979i
$987$		0			0
$988$	−27.3684	+	7.16252i	−0.870705	+	0.227870i
$989$	−8.44326			−0.268480
$990$		0			0
$991$	7.27554	−	41.2616i	0.231115	−	1.31072i	−0.619528	−	0.784975i	$-0.712676\pi$
$991$	7.27554	−	41.2616i	0.231115	−	1.31072i	0.850643	−	0.525744i	$-0.176213\pi$
$992$	−8.39440	+	7.04374i	−0.266522	+	0.223639i
$993$		0			0
$994$	3.94862	+	22.3937i	0.125242	+	0.710285i
$995$	−11.6750	−	20.2217i	−0.370122	−	0.641070i
$996$		0			0
$997$	−31.6819	−	11.5313i	−1.00337	−	0.365198i	−0.212490	−	0.977163i	$-0.568157\pi$
$997$	−31.6819	−	11.5313i	−1.00337	−	0.365198i	−0.790885	+	0.611965i	$0.790379\pi$
$998$	−23.6475	−	8.60700i	−0.748550	−	0.272450i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.u.c.100.1		6
3.2	odd	2		19.2.e.a.5.1	yes	6
12.11	even	2		304.2.u.b.81.1		6
15.2	even	4		475.2.u.a.24.1		12
15.8	even	4		475.2.u.a.24.2		12
15.14	odd	2		475.2.l.a.176.1		6
19.2	odd	18		3249.2.a.s.1.3		3
19.4	even	9	inner	171.2.u.c.118.1		6
19.17	even	9		3249.2.a.z.1.1		3
21.2	odd	6		931.2.v.b.214.1		6
21.5	even	6		931.2.v.a.214.1		6
21.11	odd	6		931.2.x.a.765.1		6
21.17	even	6		931.2.x.b.765.1		6
21.20	even	2		931.2.w.a.442.1		6
57.2	even	18		361.2.a.h.1.1		3
57.5	odd	18		361.2.c.i.68.1		6
57.8	even	6		361.2.e.b.54.1		6
57.11	odd	6		361.2.e.f.54.1		6
57.14	even	18		361.2.c.h.68.3		6
57.17	odd	18		361.2.a.g.1.3		3
57.23	odd	18		19.2.e.a.4.1	✓	6
57.26	odd	6		361.2.e.g.245.1		6
57.29	even	18		361.2.e.b.234.1		6
57.32	even	18		361.2.e.a.28.1		6
57.35	odd	18		361.2.c.i.292.1		6
57.41	even	18		361.2.c.h.292.3		6
57.44	odd	18		361.2.e.g.28.1		6
57.47	odd	18		361.2.e.f.234.1		6
57.50	even	6		361.2.e.a.245.1		6
57.53	even	18		361.2.e.h.99.1		6
57.56	even	2		361.2.e.h.62.1		6
228.23	even	18		304.2.u.b.289.1		6
228.59	odd	18		5776.2.a.bi.1.3		3
228.131	even	18		5776.2.a.br.1.1		3
285.23	even	36		475.2.u.a.99.1		12
285.59	even	18		9025.2.a.x.1.3		3
285.74	odd	18		9025.2.a.bd.1.1		3
285.137	even	36		475.2.u.a.99.2		12
285.194	odd	18		475.2.l.a.251.1		6
399.23	odd	18		931.2.x.a.802.1		6
399.80	even	18		931.2.v.a.422.1		6
399.137	odd	18		931.2.v.b.422.1		6
399.194	even	18		931.2.x.b.802.1		6
399.251	even	18		931.2.w.a.99.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	57.23	odd	18
19.2.e.a.5.1	yes	6	3.2	odd	2
171.2.u.c.100.1		6	1.1	even	1	trivial
171.2.u.c.118.1		6	19.4	even	9	inner
304.2.u.b.81.1		6	12.11	even	2
304.2.u.b.289.1		6	228.23	even	18
361.2.a.g.1.3		3	57.17	odd	18
361.2.a.h.1.1		3	57.2	even	18
361.2.c.h.68.3		6	57.14	even	18
361.2.c.h.292.3		6	57.41	even	18
361.2.c.i.68.1		6	57.5	odd	18
361.2.c.i.292.1		6	57.35	odd	18
361.2.e.a.28.1		6	57.32	even	18
361.2.e.a.245.1		6	57.50	even	6
361.2.e.b.54.1		6	57.8	even	6
361.2.e.b.234.1		6	57.29	even	18
361.2.e.f.54.1		6	57.11	odd	6
361.2.e.f.234.1		6	57.47	odd	18
361.2.e.g.28.1		6	57.44	odd	18
361.2.e.g.245.1		6	57.26	odd	6
361.2.e.h.62.1		6	57.56	even	2
361.2.e.h.99.1		6	57.53	even	18
475.2.l.a.176.1		6	15.14	odd	2
475.2.l.a.251.1		6	285.194	odd	18
475.2.u.a.24.1		12	15.2	even	4
475.2.u.a.24.2		12	15.8	even	4
475.2.u.a.99.1		12	285.23	even	36
475.2.u.a.99.2		12	285.137	even	36
931.2.v.a.214.1		6	21.5	even	6
931.2.v.a.422.1		6	399.80	even	18
931.2.v.b.214.1		6	21.2	odd	6
931.2.v.b.422.1		6	399.137	odd	18
931.2.w.a.99.1		6	399.251	even	18
931.2.w.a.442.1		6	21.20	even	2
931.2.x.a.765.1		6	21.11	odd	6
931.2.x.a.802.1		6	399.23	odd	18
931.2.x.b.765.1		6	21.17	even	6
931.2.x.b.802.1		6	399.194	even	18
3249.2.a.s.1.3		3	19.2	odd	18
3249.2.a.z.1.1		3	19.17	even	9
5776.2.a.bi.1.3		3	228.59	odd	18
5776.2.a.br.1.1		3	228.131	even	18
9025.2.a.x.1.3		3	285.59	even	18
9025.2.a.bd.1.1		3	285.74	odd	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.826352 - 0.300767i) q^{2} +(-0.939693 + 0.788496i) q^{4} +(1.93969 + 1.62760i) q^{5} +(0.939693 + 1.62760i) q^{7} +(-1.41875 + 2.45734i) q^{8} +O(q^{10})\)	\(q+(0.826352 - 0.300767i) q^{2} +(-0.939693 + 0.788496i) q^{4} +(1.93969 + 1.62760i) q^{5} +(0.939693 + 1.62760i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(2.09240 + 0.761570i) q^{10} +(1.70574 - 2.95442i) q^{11} +(-0.918748 - 5.21048i) q^{13} +(1.26604 + 1.06234i) q^{14} +(-0.00727396 + 0.0412527i) q^{16} +(1.55303 - 0.565258i) q^{17} +(-2.52094 + 3.55596i) q^{19} -3.10607 q^{20} +(0.520945 - 2.95442i) q^{22} +(-1.34730 + 1.13052i) q^{23} +(0.245100 + 1.39003i) q^{25} +(-2.32635 - 4.02936i) q^{26} +(-2.16637 - 0.788496i) q^{28} +(-3.25877 - 1.18610i) q^{29} +(-0.971782 - 1.68317i) q^{31} +(-0.979055 - 5.55250i) q^{32} +(1.11334 - 0.934204i) q^{34} +(-0.826352 + 4.68647i) q^{35} -0.837496 q^{37} +(-1.01367 + 3.69669i) q^{38} +(-6.75150 + 2.45734i) q^{40} +(0.779715 - 4.42198i) q^{41} +(3.67752 + 3.08580i) q^{43} +(0.726682 + 4.12122i) q^{44} +(-0.773318 + 1.33943i) q^{46} +(0.673648 + 0.245188i) q^{47} +(1.73396 - 3.00330i) q^{49} +(0.620615 + 1.07494i) q^{50} +(4.97178 + 4.17182i) q^{52} +(4.67752 - 3.92490i) q^{53} +(8.11721 - 2.95442i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(-10.1099 + 3.67972i) q^{59} +(3.36231 - 2.82131i) q^{61} +(-1.30928 - 1.09861i) q^{62} +(-2.52094 - 4.36640i) q^{64} +(6.69846 - 11.6021i) q^{65} +(-13.3550 - 4.86084i) q^{67} +(-1.01367 + 1.75573i) q^{68} +(0.726682 + 4.12122i) q^{70} +(10.5398 + 8.84397i) q^{71} +(-1.30541 + 7.40333i) q^{73} +(-0.692066 + 0.251892i) q^{74} +(-0.434945 - 5.32926i) q^{76} +6.41147 q^{77} +(-1.20914 + 6.85738i) q^{79} +(-0.0812519 + 0.0681784i) q^{80} +(-0.685670 - 3.88863i) q^{82} +(1.25624 + 2.17588i) q^{83} +(3.93242 + 1.43128i) q^{85} +(3.96703 + 1.44388i) q^{86} +(4.84002 + 8.38316i) q^{88} +(0.396459 + 2.24843i) q^{89} +(7.61721 - 6.39160i) q^{91} +(0.374638 - 2.12467i) q^{92} +0.630415 q^{94} +(-10.6775 + 2.79439i) q^{95} +(1.71301 - 0.623485i) q^{97} +(0.529563 - 3.00330i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8	\( 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8} + 9 q^{10} - 3 q^{13} + 3 q^{14} - 18 q^{16} - 3 q^{17} - 12 q^{19} + 6 q^{20} - 6 q^{23} - 15 q^{26} + 6 q^{28} + 3 q^{29} + 9 q^{31} - 9 q^{32} - 6 q^{35} + 15 q^{38} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 18 q^{46} + 3 q^{47} + 15 q^{49} + 15 q^{50} + 15 q^{52} + 3 q^{53} + 18 q^{55} + 6 q^{56} + 36 q^{58} - 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{64} + 12 q^{65} - 30 q^{67} + 15 q^{68} - 9 q^{70} + 6 q^{71} - 12 q^{73} - 15 q^{74} + 36 q^{76} + 18 q^{77} - 39 q^{79} - 3 q^{80} - 54 q^{82} - 24 q^{86} + 9 q^{88} + 12 q^{89} + 15 q^{91} - 42 q^{92} + 18 q^{94} - 39 q^{95} + 18 q^{97} + 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8 + 9 * q^10 - 3 * q^13 + 3 * q^14 - 18 * q^16 - 3 * q^17 - 12 * q^19 + 6 * q^20 - 6 * q^23 - 15 * q^26 + 6 * q^28 + 3 * q^29 + 9 * q^31 - 9 * q^32 - 6 * q^35 + 15 * q^38 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 18 * q^46 + 3 * q^47 + 15 * q^49 + 15 * q^50 + 15 * q^52 + 3 * q^53 + 18 * q^55 + 6 * q^56 + 36 * q^58 - 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^64 + 12 * q^65 - 30 * q^67 + 15 * q^68 - 9 * q^70 + 6 * q^71 - 12 * q^73 - 15 * q^74 + 36 * q^76 + 18 * q^77 - 39 * q^79 - 3 * q^80 - 54 * q^82 - 24 * q^86 + 9 * q^88 + 12 * q^89 + 15 * q^91 - 42 * q^92 + 18 * q^94 - 39 * q^95 + 18 * q^97 + 9 * q^98

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