LMFDB - Embedded newform 414.2.i.d.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

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("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			325.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	414.325
Dual form			414.2.i.d.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(-1.69894 + 1.96068i) q^{5} +(-1.04019 + 0.668491i) q^{7} +(-0.415415 - 0.909632i) q^{8} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(-1.69894 + 1.96068i) q^{5} +(-1.04019 + 0.668491i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.18251 - 1.40261i) q^{10} +(-0.0886578 + 0.616629i) q^{11} +(-1.11435 - 0.716152i) q^{13} +(-0.809721 - 0.934468i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-4.51691 - 1.32628i) q^{17} +(-3.63667 + 1.06782i) q^{19} +(1.07773 - 2.35990i) q^{20} -0.622970 q^{22} +(-3.35197 - 3.42992i) q^{23} +(-0.246298 - 1.71304i) q^{25} +(0.550273 - 1.20493i) q^{26} +(0.809721 - 0.934468i) q^{28} +(-1.06699 - 0.313298i) q^{29} +(3.92849 + 8.60219i) q^{31} +(0.654861 + 0.755750i) q^{32} +(0.669961 - 4.65968i) q^{34} +(0.456526 - 3.17521i) q^{35} +(1.06560 + 1.22977i) q^{37} +(-1.57450 - 3.44768i) q^{38} +(2.48926 + 0.730913i) q^{40} +(-7.75992 + 8.95543i) q^{41} +(-0.697393 + 1.52708i) q^{43} +(-0.0886578 - 0.616629i) q^{44} +(2.91797 - 3.80598i) q^{46} +6.94494 q^{47} +(-2.27279 + 4.97671i) q^{49} +(1.66055 - 0.487583i) q^{50} +(1.27098 + 0.373193i) q^{52} +(9.46721 - 6.08421i) q^{53} +(-1.05839 - 1.22144i) q^{55} +(1.04019 + 0.668491i) q^{56} +(0.158260 - 1.10072i) q^{58} +(8.19910 + 5.26924i) q^{59} +(-5.97099 - 13.0746i) q^{61} +(-7.95555 + 5.11272i) q^{62} +(-0.654861 + 0.755750i) q^{64} +(3.29736 - 0.968193i) q^{65} +(0.871145 + 6.05895i) q^{67} +4.70760 q^{68} +3.20786 q^{70} +(0.923986 + 6.42646i) q^{71} +(12.5598 - 3.68788i) q^{73} +(-1.06560 + 1.22977i) q^{74} +(3.18852 - 2.04913i) q^{76} +(-0.319990 - 0.700679i) q^{77} +(-10.1643 - 6.53221i) q^{79} +(-0.369215 + 2.56794i) q^{80} +(-9.96863 - 6.40645i) q^{82} +(4.83987 + 5.58551i) q^{83} +(10.2744 - 6.60294i) q^{85} +(-1.61078 - 0.472968i) q^{86} +(0.597735 - 0.175511i) q^{88} +(-1.40618 + 3.07910i) q^{89} +1.63788 q^{91} +(4.18251 + 2.34662i) q^{92} +(0.988368 + 6.87425i) q^{94} +(4.08482 - 8.94450i) q^{95} +(-7.49539 + 8.65015i) q^{97} +(-5.24950 - 1.54139i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8}+O(q^{10}) $ 10 * q + q^2 - q^4 - 8 * q^5 + 8 * q^7 + q^8	$ 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8} - 3 q^{10} - 7 q^{11} + 3 q^{13} + 3 q^{14} - q^{16} - 4 q^{17} + 3 q^{20} - 26 q^{22} + 12 q^{23} - 15 q^{25} - 3 q^{26} - 3 q^{28} + 25 q^{29} + 6 q^{31} + q^{32} - 7 q^{34} - 2 q^{35} + 9 q^{37} - 11 q^{38} - 3 q^{40} - 24 q^{41} - 30 q^{43} - 7 q^{44} + 21 q^{46} + 48 q^{47} + 9 q^{49} - 7 q^{50} + 14 q^{52} - 15 q^{53} - 23 q^{55} - 8 q^{56} - 3 q^{58} - 5 q^{59} + 12 q^{61} - 28 q^{62} - q^{64} + 13 q^{65} + 18 q^{67} + 18 q^{68} + 2 q^{70} - 28 q^{71} + 19 q^{73} - 9 q^{74} + 22 q^{76} + 12 q^{77} - 52 q^{79} - 8 q^{80} - 20 q^{82} - 7 q^{83} + 23 q^{85} - 14 q^{86} - 4 q^{88} - 3 q^{89} + 42 q^{91} + 23 q^{92} + 29 q^{94} - 22 q^{95} + 51 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + q^2 - q^4 - 8 * q^5 + 8 * q^7 + q^8 - 3 * q^10 - 7 * q^11 + 3 * q^13 + 3 * q^14 - q^16 - 4 * q^17 + 3 * q^20 - 26 * q^22 + 12 * q^23 - 15 * q^25 - 3 * q^26 - 3 * q^28 + 25 * q^29 + 6 * q^31 + q^32 - 7 * q^34 - 2 * q^35 + 9 * q^37 - 11 * q^38 - 3 * q^40 - 24 * q^41 - 30 * q^43 - 7 * q^44 + 21 * q^46 + 48 * q^47 + 9 * q^49 - 7 * q^50 + 14 * q^52 - 15 * q^53 - 23 * q^55 - 8 * q^56 - 3 * q^58 - 5 * q^59 + 12 * q^61 - 28 * q^62 - q^64 + 13 * q^65 + 18 * q^67 + 18 * q^68 + 2 * q^70 - 28 * q^71 + 19 * q^73 - 9 * q^74 + 22 * q^76 + 12 * q^77 - 52 * q^79 - 8 * q^80 - 20 * q^82 - 7 * q^83 + 23 * q^85 - 14 * q^86 - 4 * q^88 - 3 * q^89 + 42 * q^91 + 23 * q^92 + 29 * q^94 - 22 * q^95 + 51 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$		0			0
$3$		0			0
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−1.69894	+	1.96068i	−0.759788	+	0.876843i	−0.995479	−	0.0949856i	$-0.969719\pi$
$5$	−1.69894	+	1.96068i	−0.759788	+	0.876843i	0.235690	+	0.971828i	$0.424265\pi$
$6$		0			0
$7$	−1.04019	+	0.668491i	−0.393156	+	0.252666i	−0.722251	−	0.691631i	$-0.756893\pi$
$7$	−1.04019	+	0.668491i	−0.393156	+	0.252666i	0.329096	+	0.944297i	$0.393256\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$		0			0
$10$	−2.18251	−	1.40261i	−0.690169	−	0.443545i
$11$	−0.0886578	+	0.616629i	−0.0267313	+	0.185921i	−0.998812	−	0.0487255i	$-0.984484\pi$
$11$	−0.0886578	+	0.616629i	−0.0267313	+	0.185921i	0.972081	+	0.234646i	$0.0753931\pi$
$12$		0			0
$13$	−1.11435	−	0.716152i	−0.309066	−	0.198625i	0.376908	−	0.926251i	$-0.376987\pi$
$13$	−1.11435	−	0.716152i	−0.309066	−	0.198625i	−0.685974	+	0.727626i	$0.740624\pi$
$14$	−0.809721	−	0.934468i	−0.216407	−	0.249747i
$15$		0			0
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−4.51691	−	1.32628i	−1.09551	−	0.321671i	−0.316444	−	0.948611i	$-0.602489\pi$
$17$	−4.51691	−	1.32628i	−1.09551	−	0.321671i	−0.779067	+	0.626940i	$0.784307\pi$
$18$		0			0
$19$	−3.63667	+	1.06782i	−0.834308	+	0.244975i	−0.670867	−	0.741578i	$-0.734078\pi$
$19$	−3.63667	+	1.06782i	−0.834308	+	0.244975i	−0.163442	+	0.986553i	$0.552260\pi$
$20$	1.07773	−	2.35990i	0.240988	−	0.527691i
$21$		0			0
$22$	−0.622970			−0.132818
$23$	−3.35197	−	3.42992i	−0.698933	−	0.715187i
$23$	−3.35197	−	3.42992i	−0.698933	−	0.715187i
$24$		0			0
$25$	−0.246298	−	1.71304i	−0.0492597	−	0.342608i
$26$	0.550273	−	1.20493i	0.107917	−	0.236306i
$27$		0			0
$28$	0.809721	−	0.934468i	0.153023	−	0.176598i
$29$	−1.06699	−	0.313298i	−0.198136	−	0.0581779i	0.181159	−	0.983454i	$-0.442015\pi$
$29$	−1.06699	−	0.313298i	−0.198136	−	0.0581779i	−0.379295	+	0.925276i	$0.623833\pi$
$30$		0			0
$31$	3.92849	+	8.60219i	0.705578	+	1.54500i	0.833075	+	0.553161i	$0.186578\pi$
$31$	3.92849	+	8.60219i	0.705578	+	1.54500i	−0.127497	+	0.991839i	$0.540694\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$		0			0
$34$	0.669961	−	4.65968i	0.114897	−	0.799129i
$35$	0.456526	−	3.17521i	0.0771670	−	0.536708i
$36$		0			0
$37$	1.06560	+	1.22977i	0.175183	+	0.202172i	0.836550	−	0.547890i	$-0.184569\pi$
$37$	1.06560	+	1.22977i	0.175183	+	0.202172i	−0.661367	+	0.750063i	$0.730023\pi$
$38$	−1.57450	−	3.44768i	−0.255418	−	0.559288i
$39$		0			0
$40$	2.48926	+	0.730913i	0.393587	+	0.115568i
$41$	−7.75992	+	8.95543i	−1.21190	+	1.39860i	−0.319357	+	0.947635i	$0.603467\pi$
$41$	−7.75992	+	8.95543i	−1.21190	+	1.39860i	−0.892540	+	0.450969i	$0.851079\pi$
$42$		0			0
$43$	−0.697393	+	1.52708i	−0.106351	+	0.232877i	−0.955324	−	0.295559i	$-0.904494\pi$
$43$	−0.697393	+	1.52708i	−0.106351	+	0.232877i	0.848973	+	0.528436i	$0.177221\pi$
$44$	−0.0886578	−	0.616629i	−0.0133657	−	0.0929603i
$45$		0			0
$46$	2.91797	−	3.80598i	0.430231	−	0.561161i
$47$	6.94494			1.01302			0.506512	−	0.862233i	$-0.330935\pi$
$47$	6.94494			1.01302			0.506512	+	0.862233i	$0.330935\pi$
$48$		0			0
$49$	−2.27279	+	4.97671i	−0.324684	+	0.710958i
$50$	1.66055	−	0.487583i	0.234838	−	0.0689546i
$51$		0			0
$52$	1.27098	+	0.373193i	0.176253	+	0.0517525i
$53$	9.46721	−	6.08421i	1.30042	−	0.835730i	0.307163	−	0.951657i	$-0.400620\pi$
$53$	9.46721	−	6.08421i	1.30042	−	0.835730i	0.993258	+	0.115927i	$0.0369838\pi$
$54$		0			0
$55$	−1.05839	−	1.22144i	−0.142713	−	0.164699i
$56$	1.04019	+	0.668491i	0.139002	+	0.0893309i
$57$		0			0
$58$	0.158260	−	1.10072i	0.0207805	−	0.144532i
$59$	8.19910	+	5.26924i	1.06743	+	0.685997i	0.951621	−	0.307274i	$-0.0994169\pi$
$59$	8.19910	+	5.26924i	1.06743	+	0.685997i	0.115811	+	0.993271i	$0.463053\pi$
$60$		0			0
$61$	−5.97099	−	13.0746i	−0.764507	−	1.67404i	−0.738386	−	0.674379i	$-0.764412\pi$
$61$	−5.97099	−	13.0746i	−0.764507	−	1.67404i	−0.0261214	−	0.999659i	$-0.508316\pi$
$62$	−7.95555	+	5.11272i	−1.01036	+	0.649317i
$63$		0			0
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	3.29736	−	0.968193i	0.408988	−	0.120090i
$66$		0			0
$67$	0.871145	+	6.05895i	0.106427	+	0.740218i	0.971236	+	0.238117i	$0.0765303\pi$
$67$	0.871145	+	6.05895i	0.106427	+	0.740218i	−0.864809	+	0.502101i	$0.832561\pi$
$68$	4.70760			0.570880
$69$		0			0
$70$	3.20786			0.383413
$71$	0.923986	+	6.42646i	0.109657	+	0.762681i	0.968243	+	0.250011i	$0.0804343\pi$
$71$	0.923986	+	6.42646i	0.109657	+	0.762681i	−0.858586	+	0.512669i	$0.828657\pi$
$72$		0			0
$73$	12.5598	−	3.68788i	1.47001	−	0.431634i	0.553907	−	0.832578i	$-0.313136\pi$
$73$	12.5598	−	3.68788i	1.47001	−	0.431634i	0.916102	+	0.400944i	$0.131318\pi$
$74$	−1.06560	+	1.22977i	−0.123873	+	0.142957i
$75$		0			0
$76$	3.18852	−	2.04913i	0.365748	−	0.235052i
$77$	−0.319990	−	0.700679i	−0.0364662	−	0.0798498i
$78$		0			0
$79$	−10.1643	−	6.53221i	−1.14357	−	0.734931i	−0.175225	−	0.984528i	$-0.556065\pi$
$79$	−10.1643	−	6.53221i	−1.14357	−	0.734931i	−0.968350	+	0.249598i	$0.919702\pi$
$80$	−0.369215	+	2.56794i	−0.0412795	+	0.287105i
$81$		0			0
$82$	−9.96863	−	6.40645i	−1.10085	−	0.707474i
$83$	4.83987	+	5.58551i	0.531245	+	0.613089i	0.956410	−	0.292027i	$-0.0943296\pi$
$83$	4.83987	+	5.58551i	0.531245	+	0.613089i	−0.425166	+	0.905116i	$0.639784\pi$
$84$		0			0
$85$	10.2744	−	6.60294i	1.11441	−	0.716189i
$86$	−1.61078	−	0.472968i	−0.173695	−	0.0510015i
$87$		0			0
$88$	0.597735	−	0.175511i	0.0637188	−	0.0187095i
$89$	−1.40618	+	3.07910i	−0.149055	+	0.326384i	−0.969401	−	0.245483i	$-0.921053\pi$
$89$	−1.40618	+	3.07910i	−0.149055	+	0.326384i	0.820346	+	0.571867i	$0.193781\pi$
$90$		0			0
$91$	1.63788			0.171697
$92$	4.18251	+	2.34662i	0.436057	+	0.244652i
$93$		0			0
$94$	0.988368	+	6.87425i	0.101942	+	0.709025i
$95$	4.08482	−	8.94450i	0.419093	−	0.917686i
$96$		0			0
$97$	−7.49539	+	8.65015i	−0.761042	+	0.878289i	−0.995590	−	0.0938155i	$-0.970094\pi$
$97$	−7.49539	+	8.65015i	−0.761042	+	0.878289i	0.234548	+	0.972105i	$0.424639\pi$
$98$	−5.24950	−	1.54139i	−0.530280	−	0.155704i
$99$		0			0
$100$	0.718941	+	1.57426i	0.0718941	+	0.157426i
$101$	−1.16810	−	1.34806i	−0.116230	−	0.134137i	0.694653	−	0.719345i	$-0.255558\pi$
$101$	−1.16810	−	1.34806i	−0.116230	−	0.134137i	−0.810883	+	0.585208i	$0.801013\pi$
$102$		0			0
$103$	−2.82502	+	19.6484i	−0.278357	+	1.93602i	0.0674723	+	0.997721i	$0.478507\pi$
$103$	−2.82502	+	19.6484i	−0.278357	+	1.93602i	−0.345830	+	0.938297i	$0.612403\pi$
$104$	−0.188515	+	1.31115i	−0.0184854	+	0.128569i
$105$		0			0
$106$	7.36960	+	8.50497i	0.715799	+	0.826076i
$107$	1.81089	+	3.96529i	0.175065	+	0.383339i	0.976742	−	0.214419i	$-0.0687858\pi$
$107$	1.81089	+	3.96529i	0.175065	+	0.383339i	−0.801677	+	0.597758i	$0.796059\pi$
$108$		0			0
$109$	−6.20349	−	1.82151i	−0.594186	−	0.174469i	−0.0292063	−	0.999573i	$-0.509298\pi$
$109$	−6.20349	−	1.82151i	−0.594186	−	0.174469i	−0.564980	+	0.825105i	$0.691116\pi$
$110$	1.05839	−	1.22144i	0.100913	−	0.116460i
$111$		0			0
$112$	−0.513652	+	1.12474i	−0.0485355	+	0.106278i
$113$	−0.193894	−	1.34856i	−0.0182400	−	0.126862i	0.978667	−	0.205453i	$-0.0658669\pi$
$113$	−0.193894	−	1.34856i	−0.0182400	−	0.126862i	−0.996907	+	0.0785914i	$0.974958\pi$
$114$		0			0
$115$	12.4198	−	0.744916i	1.15815	−	0.0694638i
$116$	1.11204			0.103250
$117$		0			0
$118$	−4.04875	+	8.86554i	−0.372718	+	0.816139i
$119$	5.58506	−	1.63992i	0.511982	−	0.150331i
$120$		0			0
$121$	10.1821	+	2.98972i	0.925641	+	0.271793i
$122$	12.0918	−	7.77093i	1.09474	−	0.703547i
$123$		0			0
$124$	−6.19288	−	7.14696i	−0.556137	−	0.641816i
$125$	−7.13536	−	4.58562i	−0.638206	−	0.410150i
$126$		0			0
$127$	−0.491724	+	3.42002i	−0.0436335	+	0.303478i	0.956305	+	0.292371i	$0.0944444\pi$
$127$	−0.491724	+	3.42002i	−0.0436335	+	0.303478i	−0.999938	+	0.0111061i	$0.996465\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$		0			0
$130$	1.42760	+	3.12601i	0.125209	+	0.274169i
$131$	−15.9396	+	10.2437i	−1.39265	+	0.895000i	−0.999698	−	0.0245608i	$-0.992181\pi$
$131$	−15.9396	+	10.2437i	−1.39265	+	0.895000i	−0.392948	+	0.919561i	$0.628545\pi$
$132$		0			0
$133$	3.06900	−	3.54182i	0.266116	−	0.307115i
$134$	−5.87330	+	1.72456i	−0.507376	+	0.148979i
$135$		0			0
$136$	0.669961	+	4.65968i	0.0574487	+	0.399564i
$137$	11.3960			0.973629			0.486815	−	0.873505i	$-0.338159\pi$
$137$	11.3960			0.973629			0.486815	+	0.873505i	$0.338159\pi$
$138$		0			0
$139$	5.30267			0.449766			0.224883	−	0.974386i	$-0.427800\pi$
$139$	5.30267			0.449766			0.224883	+	0.974386i	$0.427800\pi$
$140$	0.456526	+	3.17521i	0.0385835	+	0.268354i
$141$		0			0
$142$	−6.22955	+	1.82916i	−0.522772	+	0.153500i
$143$	0.540396	−	0.623650i	0.0451902	−	0.0521522i
$144$		0			0
$145$	2.42703	−	1.55976i	0.201554	−	0.129531i
$146$	5.43779	+	11.9071i	0.450034	+	0.985438i
$147$		0			0
$148$	−1.36890	−	0.879739i	−0.112523	−	0.0723141i
$149$	1.96659	−	13.6779i	0.161109	−	1.12054i	−0.735439	−	0.677591i	$-0.763024\pi$
$149$	1.96659	−	13.6779i	0.161109	−	1.12054i	0.896548	−	0.442947i	$-0.146067\pi$
$150$		0			0
$151$	−4.57223	−	2.93840i	−0.372083	−	0.239123i	0.341213	−	0.939986i	$-0.389162\pi$
$151$	−4.57223	−	2.93840i	−0.372083	−	0.239123i	−0.713296	+	0.700863i	$0.752799\pi$
$152$	2.48205	+	2.86444i	0.201321	+	0.232337i
$153$		0			0
$154$	0.648008	−	0.416450i	0.0522180	−	0.0335585i
$155$	−23.5404	−	6.91209i	−1.89081	−	0.555192i
$156$		0			0
$157$	−5.06808	+	1.48812i	−0.404477	+	0.118765i	−0.477642	−	0.878555i	$-0.658508\pi$
$157$	−5.06808	+	1.48812i	−0.404477	+	0.118765i	0.0731647	+	0.997320i	$0.476690\pi$
$158$	5.01919	−	10.9905i	0.399305	−	0.874356i
$159$		0			0
$160$	−2.59435			−0.205101
$161$	5.77956	+	1.32701i	0.455493	+	0.104583i
$162$		0			0
$163$	−1.29373	−	8.99811i	−0.101333	−	0.704786i	−0.975634	−	0.219403i	$-0.929589\pi$
$163$	−1.29373	−	8.99811i	−0.101333	−	0.704786i	0.874301	−	0.485383i	$-0.161320\pi$
$164$	4.92256	−	10.7789i	0.384387	−	0.841690i
$165$		0			0
$166$	−4.83987	+	5.58551i	−0.375647	+	0.433519i
$167$	2.76133	+	0.810798i	0.213678	+	0.0627415i	0.386819	−	0.922155i	$-0.373574\pi$
$167$	2.76133	+	0.810798i	0.213678	+	0.0627415i	−0.173142	+	0.984897i	$0.555392\pi$
$168$		0			0
$169$	−4.67148	−	10.2291i	−0.359345	−	0.786856i
$170$	7.99792	+	9.23009i	0.613413	+	0.707916i
$171$		0			0
$172$	0.238916	−	1.66170i	0.0182172	−	0.126703i
$173$	1.94440	−	13.5236i	0.147830	−	1.02818i	−0.771932	−	0.635705i	$-0.780709\pi$
$173$	1.94440	−	13.5236i	0.147830	−	1.02818i	0.919762	−	0.392477i	$-0.128382\pi$
$174$		0			0
$175$	1.40135	+	1.61725i	0.105932	+	0.122252i
$176$	0.258791	+	0.566673i	0.0195071	+	0.0427146i
$177$		0			0
$178$	−3.24788	−	0.953664i	−0.243439	−	0.0714801i
$179$	−13.3589	+	15.4169i	−0.998488	+	1.15232i	−0.0101646	+	0.999948i	$0.503236\pi$
$179$	−13.3589	+	15.4169i	−0.998488	+	1.15232i	−0.988324	+	0.152369i	$0.951310\pi$
$180$		0			0
$181$	3.96163	−	8.67476i	0.294466	−	0.644790i	−0.703350	−	0.710843i	$-0.748313\pi$
$181$	3.96163	−	8.67476i	0.294466	−	0.644790i	0.997816	+	0.0660534i	$0.0210408\pi$
$182$	0.233095	+	1.62121i	0.0172782	+	0.120172i
$183$		0			0
$184$	−1.72750	+	4.47389i	−0.127353	+	0.329820i
$185$	−4.22157			−0.310376
$186$		0			0
$187$	1.21828	−	2.66767i	0.0890897	−	0.195079i
$188$	−6.66362	+	1.95662i	−0.485995	+	0.142701i
$189$		0			0
$190$	9.43479	+	2.77030i	0.684471	+	0.200979i
$191$	−1.34015	+	0.861261i	−0.0969697	+	0.0623186i	−0.588227	−	0.808696i	$-0.700174\pi$
$191$	−1.34015	+	0.861261i	−0.0969697	+	0.0623186i	0.491257	+	0.871014i	$0.336537\pi$
$192$		0			0
$193$	−11.5112	−	13.2847i	−0.828597	−	0.956252i	0.170982	−	0.985274i	$-0.445306\pi$
$193$	−11.5112	−	13.2847i	−0.828597	−	0.956252i	−0.999579	+	0.0290223i	$0.990761\pi$
$194$	−9.62880	−	6.18806i	−0.691308	−	0.444277i
$195$		0			0
$196$	0.778622	−	5.41543i	0.0556158	−	0.386817i
$197$	−1.02768	−	0.660450i	−0.0732191	−	0.0470551i	0.503519	−	0.863984i	$-0.332038\pi$
$197$	−1.02768	−	0.660450i	−0.0732191	−	0.0470551i	−0.576738	+	0.816929i	$0.695675\pi$
$198$		0			0
$199$	−0.0416361	−	0.0911703i	−0.00295150	−	0.00646289i	0.908151	−	0.418644i	$-0.137494\pi$
$199$	−0.0416361	−	0.0911703i	−0.00295150	−	0.00646289i	−0.911102	+	0.412181i	$0.864767\pi$
$200$	−1.45592	+	0.935664i	−0.102949	+	0.0661615i
$201$		0			0
$202$	1.16810	−	1.34806i	0.0821873	−	0.0948491i
$203$	1.31932	−	0.387386i	0.0925978	−	0.0271892i
$204$		0			0
$205$	−4.37510	−	30.4295i	−0.305570	−	2.12529i
$206$	−19.8505			−1.38305
$207$		0			0
$208$	−1.32463			−0.0918469
$209$	−0.336030	−	2.33714i	−0.0232437	−	0.161664i
$210$		0			0
$211$	16.0208	−	4.70412i	1.10291	−	0.323845i	0.320905	−	0.947111i	$-0.396013\pi$
$211$	16.0208	−	4.70412i	1.10291	−	0.323845i	0.782010	+	0.623266i	$0.214195\pi$
$212$	−7.36960	+	8.50497i	−0.506146	+	0.584124i
$213$		0			0
$214$	−3.66721	+	2.35677i	−0.250685	+	0.161106i
$215$	−1.80928	−	3.96177i	−0.123392	−	0.270191i
$216$		0			0
$217$	−9.83687	−	6.32178i	−0.667771	−	0.429150i
$218$	0.920120	−	6.39957i	0.0623184	−	0.433434i
$219$		0			0
$220$	1.35964	+	0.873785i	0.0916666	+	0.0589106i
$221$	4.08361	+	4.71274i	0.274694	+	0.317013i
$222$		0			0
$223$	15.3177	−	9.84407i	1.02575	−	0.659207i	0.0843248	−	0.996438i	$-0.473127\pi$
$223$	15.3177	−	9.84407i	1.02575	−	0.659207i	0.941422	+	0.337231i	$0.109490\pi$
$224$	−1.18639	−	0.348356i	−0.0792692	−	0.0232755i
$225$		0			0
$226$	1.30724	−	0.383840i	0.0869563	−	0.0255327i
$227$	−6.64052	+	14.5407i	−0.440747	+	0.965101i	0.550714	+	0.834694i	$0.314356\pi$
$227$	−6.64052	+	14.5407i	−0.440747	+	0.965101i	−0.991461	+	0.130407i	$0.958372\pi$
$228$		0			0
$229$	−17.7317			−1.17174			−0.585872	−	0.810404i	$-0.699248\pi$
$229$	−17.7317			−1.17174			−0.585872	+	0.810404i	$0.699248\pi$
$230$	2.50485	+	12.1873i	0.165165	+	0.803608i
$231$		0			0
$232$	0.158260	+	1.10072i	0.0103903	+	0.0722658i
$233$	3.88183	−	8.50002i	0.254307	−	0.556855i	−0.738819	−	0.673904i	$-0.764616\pi$
$233$	3.88183	−	8.50002i	0.254307	−	0.556855i	0.993126	+	0.117049i	$0.0373434\pi$
$234$		0			0
$235$	−11.7990	+	13.6168i	−0.769684	+	0.888263i
$236$	−9.35150	−	2.74585i	−0.608731	−	0.178739i
$237$		0			0
$238$	2.41807	+	5.29483i	0.156740	+	0.343213i
$239$	−3.28022	−	3.78558i	−0.212180	−	0.244869i	0.639676	−	0.768644i	$-0.279068\pi$
$239$	−3.28022	−	3.78558i	−0.212180	−	0.244869i	−0.851856	+	0.523776i	$0.824523\pi$
$240$		0			0
$241$	−2.07440	+	14.4278i	−0.133624	+	0.929375i	0.807151	+	0.590345i	$0.201008\pi$
$241$	−2.07440	+	14.4278i	−0.133624	+	0.929375i	−0.940775	+	0.339031i	$0.889901\pi$
$242$	−1.51023	+	10.5039i	−0.0970814	+	0.675216i
$243$		0			0
$244$	9.41268	+	10.8628i	0.602585	+	0.695420i
$245$	−5.89640	−	12.9113i	−0.376707	−	0.824874i
$246$		0			0
$247$	4.81725	+	1.41447i	0.306515	+	0.0900008i
$248$	6.19288	−	7.14696i	0.393248	−	0.453833i
$249$		0			0
$250$	3.52348	−	7.71534i	0.222844	−	0.487961i
$251$	−2.66634	−	18.5448i	−0.168298	−	1.17054i	−0.882401	−	0.470499i	$-0.844074\pi$
$251$	−2.66634	−	18.5448i	−0.168298	−	1.17054i	0.714103	−	0.700041i	$-0.246835\pi$
$252$		0			0
$253$	2.41216	−	1.76283i	0.151651	−	0.110828i
$254$	−3.45519			−0.216798
$255$		0			0
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−1.67895	+	0.492983i	−0.104730	+	0.0307514i	−0.333678	−	0.942687i	$-0.608290\pi$
$257$	−1.67895	+	0.492983i	−0.104730	+	0.0307514i	0.228948	+	0.973439i	$0.426471\pi$
$258$		0			0
$259$	−1.93052	−	0.566850i	−0.119956	−	0.0352224i
$260$	−2.89102	+	1.85795i	−0.179294	+	0.115225i
$261$		0			0
$262$	−12.4079	−	14.3195i	−0.766563	−	0.884661i
$263$	14.0110	+	9.00435i	0.863958	+	0.555232i	0.895899	−	0.444258i	$-0.146533\pi$
$263$	14.0110	+	9.00435i	0.863958	+	0.555232i	−0.0319412	+	0.999490i	$0.510169\pi$
$264$		0			0
$265$	−4.15503	+	28.8989i	−0.255241	+	1.77524i
$266$	3.94253	+	2.53371i	0.241732	+	0.155352i
$267$		0			0
$268$	−2.54286	−	5.56809i	−0.155330	−	0.340125i
$269$	22.4639	−	14.4367i	1.36965	−	0.880219i	0.370823	−	0.928703i	$-0.379076\pi$
$269$	22.4639	−	14.4367i	1.36965	−	0.880219i	0.998824	+	0.0484848i	$0.0154392\pi$
$270$		0			0
$271$	−17.6209	+	20.3356i	−1.07039	+	1.23530i	−0.0996919	+	0.995018i	$0.531786\pi$
$271$	−17.6209	+	20.3356i	−1.07039	+	1.23530i	−0.970703	+	0.240283i	$0.922760\pi$
$272$	−4.51691	+	1.32628i	−0.273878	+	0.0804178i
$273$		0			0
$274$	1.62183	+	11.2800i	0.0979781	+	0.681452i
$275$	1.07815			0.0650147
$276$		0			0
$277$	−2.13714			−0.128408			−0.0642042	−	0.997937i	$-0.520451\pi$
$277$	−2.13714			−0.128408			−0.0642042	+	0.997937i	$0.520451\pi$
$278$	0.754648	+	5.24869i	0.0452608	+	0.314796i
$279$		0			0
$280$	−3.07792	+	0.903759i	−0.183941	+	0.0540099i
$281$	−18.1958	+	20.9990i	−1.08547	+	1.25270i	−0.119833	+	0.992794i	$0.538236\pi$
$281$	−18.1958	+	20.9990i	−1.08547	+	1.25270i	−0.965635	+	0.259902i	$0.916310\pi$
$282$		0			0
$283$	19.7538	−	12.6950i	1.17424	−	0.754638i	0.199921	−	0.979812i	$-0.435931\pi$
$283$	19.7538	−	12.6950i	1.17424	−	0.754638i	0.974319	+	0.225174i	$0.0722950\pi$
$284$	−2.69710	−	5.90583i	−0.160043	−	0.350446i
$285$		0			0
$286$	0.694209	+	0.446141i	0.0410494	+	0.0263809i
$287$	2.08519	−	14.5028i	0.123085	−	0.856074i
$288$		0			0
$289$	4.34212	+	2.79051i	0.255419	+	0.164148i
$290$	1.88929	+	2.18035i	0.110943	+	0.128035i
$291$		0			0
$292$	−11.0120	+	7.07699i	−0.644429	+	0.414150i
$293$	−18.2115	−	5.34738i	−1.06393	−	0.312398i	−0.297496	−	0.954723i	$-0.596152\pi$
$293$	−18.2115	−	5.34738i	−1.06393	−	0.312398i	−0.766432	+	0.642325i	$0.777970\pi$
$294$		0			0
$295$	−24.2611	+	7.12369i	−1.41253	+	0.414757i
$296$	0.675969	−	1.48017i	0.0392899	−	0.0860329i
$297$		0			0
$298$	13.8186			0.800488
$299$	1.27894	+	6.22266i	0.0739628	+	0.359865i
$300$		0			0
$301$	−0.295415	−	2.05465i	−0.0170274	−	0.118428i
$302$	2.25779	−	4.94387i	0.129921	−	0.284488i
$303$		0			0
$304$	−2.48205	+	2.86444i	−0.142355	+	0.164287i
$305$	35.7796	+	10.5058i	2.04873	+	0.601562i
$306$		0			0
$307$	6.19445	+	13.5640i	0.353536	+	0.774136i	0.999938	+	0.0111390i	$0.00354572\pi$
$307$	6.19445	+	13.5640i	0.353536	+	0.774136i	−0.646402	+	0.762997i	$0.723727\pi$
$308$	0.504432	+	0.582145i	0.0287427	+	0.0331708i
$309$		0			0
$310$	3.49158	−	24.2845i	0.198309	−	1.37927i
$311$	−0.752614	+	5.23455i	−0.0426769	+	0.296824i	0.957293	+	0.289118i	$0.0933620\pi$
$311$	−0.752614	+	5.23455i	−0.0426769	+	0.296824i	−0.999970	+	0.00770598i	$0.997547\pi$
$312$		0			0
$313$	5.80888	+	6.70380i	0.328337	+	0.378921i	0.895785	−	0.444488i	$-0.146614\pi$
$313$	5.80888	+	6.70380i	0.328337	+	0.378921i	−0.567448	+	0.823410i	$0.692069\pi$
$314$	−2.19424	−	4.80472i	−0.123828	−	0.271146i
$315$		0			0
$316$	11.5929	+	3.40399i	0.652153	+	0.191489i
$317$	1.99059	−	2.29726i	0.111802	−	0.129027i	−0.697090	−	0.716984i	$-0.745522\pi$
$317$	1.99059	−	2.29726i	0.111802	−	0.129027i	0.808892	+	0.587957i	$0.200068\pi$
$318$		0			0
$319$	0.287786	−	0.630163i	0.0161129	−	0.0352823i
$320$	−0.369215	−	2.56794i	−0.0206397	−	0.143552i
$321$		0			0
$322$	−0.490989	+	5.90958i	−0.0273617	+	0.329328i
$323$	17.8427			0.992795
$324$		0			0
$325$	−0.952335	+	2.08532i	−0.0528260	+	0.115673i
$326$	8.72240	−	2.56113i	0.483089	−	0.141848i
$327$		0			0
$328$	11.3697	+	3.33846i	0.627789	+	0.184335i
$329$	−7.22407	+	4.64263i	−0.398276	+	0.255957i
$330$		0			0
$331$	−1.07480	−	1.24038i	−0.0590762	−	0.0681776i	0.725442	−	0.688283i	$-0.241635\pi$
$331$	−1.07480	−	1.24038i	−0.0590762	−	0.0681776i	−0.784518	+	0.620105i	$0.787090\pi$
$332$	−6.21744	−	3.99571i	−0.341226	−	0.219293i
$333$		0			0
$334$	−0.409568	+	2.84861i	−0.0224106	+	0.155869i
$335$	−13.3597	−	8.58574i	−0.729917	−	0.469089i
$336$		0			0
$337$	7.46526	+	16.3466i	0.406659	+	0.890458i	0.996551	+	0.0829766i	$0.0264427\pi$
$337$	7.46526	+	16.3466i	0.406659	+	0.890458i	−0.589893	+	0.807481i	$0.700830\pi$
$338$	9.46018	−	6.07969i	0.514566	−	0.330692i
$339$		0			0
$340$	−7.99792	+	9.23009i	−0.433748	+	0.500572i
$341$	−5.65265	+	1.65977i	−0.306108	+	0.0898815i
$342$		0			0
$343$	−2.19453	−	15.2633i	−0.118494	−	0.824142i
$344$	1.67879			0.0905140
$345$		0			0
$346$	13.6627			0.734511
$347$	0.0317652	+	0.220932i	0.00170524	+	0.0118602i	0.990656	−	0.136382i	$-0.0435475\pi$
$347$	0.0317652	+	0.220932i	0.00170524	+	0.0118602i	−0.988951	+	0.148242i	$0.952638\pi$
$348$		0			0
$349$	19.4199	−	5.70221i	1.03953	−	0.305232i	0.282947	−	0.959136i	$-0.408688\pi$
$349$	19.4199	−	5.70221i	1.03953	−	0.305232i	0.756578	+	0.653903i	$0.226870\pi$
$350$	−1.40135	+	1.61725i	−0.0749054	+	0.0864454i
$351$		0			0
$352$	−0.524075	+	0.336803i	−0.0279333	+	0.0179516i
$353$	−7.89861	−	17.2956i	−0.420401	−	0.920549i	−0.994788	−	0.101966i	$-0.967487\pi$
$353$	−7.89861	−	17.2956i	−0.420401	−	0.920549i	0.574387	−	0.818584i	$-0.305240\pi$
$354$		0			0
$355$	−14.1700	−	9.10652i	−0.752067	−	0.483324i
$356$	0.481735	−	3.35054i	0.0255319	−	0.177578i
$357$		0			0
$358$	−17.1612	−	11.0288i	−0.906997	−	0.582892i
$359$	3.36334	+	3.88150i	0.177510	+	0.204858i	0.837531	−	0.546389i	$-0.183998\pi$
$359$	3.36334	+	3.88150i	0.177510	+	0.204858i	−0.660021	+	0.751247i	$0.729453\pi$
$360$		0			0
$361$	−3.89872	+	2.50556i	−0.205196	+	0.131871i
$362$	9.15026	+	2.68676i	0.480927	+	0.141213i
$363$		0			0
$364$	−1.57154	+	0.461445i	−0.0823709	+	0.0241863i
$365$	−14.1075	+	30.8912i	−0.738422	+	1.61692i
$366$		0			0
$367$	24.7772			1.29336			0.646679	−	0.762762i	$-0.276157\pi$
$367$	24.7772			1.29336			0.646679	+	0.762762i	$0.276157\pi$
$368$	−4.67421	−	1.07322i	−0.243660	−	0.0559454i
$369$		0			0
$370$	−0.600791	−	4.17860i	−0.0312337	−	0.217235i
$371$	−5.78048	+	12.6575i	−0.300108	+	0.657144i
$372$		0			0
$373$	−24.3045	+	28.0489i	−1.25844	+	1.45231i	−0.419808	+	0.907613i	$0.637903\pi$
$373$	−24.3045	+	28.0489i	−1.25844	+	1.45231i	−0.838630	+	0.544702i	$0.816643\pi$
$374$	2.81390	+	0.826235i	0.145503	+	0.0427236i
$375$		0			0
$376$	−2.88503	−	6.31734i	−0.148784	−	0.325792i
$377$	0.964640	+	1.11325i	0.0496815	+	0.0573355i
$378$		0			0
$379$	4.43761	−	30.8642i	0.227945	−	1.58539i	−0.478802	−	0.877923i	$-0.658929\pi$
$379$	4.43761	−	30.8642i	0.227945	−	1.58539i	0.706747	−	0.707467i	$-0.250162\pi$
$380$	−1.39940	+	9.73301i	−0.0717875	+	0.499293i
$381$		0			0
$382$	−1.04322	−	1.20394i	−0.0533756	−	0.0615988i
$383$	4.80062	+	10.5119i	0.245300	+	0.537132i	0.991732	−	0.128330i	$-0.0409617\pi$
$383$	4.80062	+	10.5119i	0.245300	+	0.537132i	−0.746431	+	0.665462i	$0.768234\pi$
$384$		0			0
$385$	1.91745	+	0.563014i	0.0977223	+	0.0286939i
$386$	11.5112	−	13.2847i	0.585907	−	0.676172i
$387$		0			0
$388$	4.75475	−	10.4114i	0.241386	−	0.528561i
$389$	3.38765	+	23.5616i	0.171761	+	1.19462i	0.875163	+	0.483829i	$0.160754\pi$
$389$	3.38765	+	23.5616i	0.171761	+	1.19462i	−0.703402	+	0.710792i	$0.748337\pi$
$390$		0			0
$391$	10.5915	+	19.9383i	0.535634	+	1.00832i
$392$	5.47112			0.276333
$393$		0			0
$394$	0.507473	−	1.11121i	0.0255661	−	0.0559820i
$395$	30.0761	−	8.83114i	1.51329	−	0.444343i
$396$		0			0
$397$	21.2291	+	6.23343i	1.06546	+	0.312847i	0.767047	−	0.641591i	$-0.221725\pi$
$397$	21.2291	+	6.23343i	1.06546	+	0.312847i	0.298411	+	0.954437i	$0.403543\pi$
$398$	0.0843169	−	0.0541872i	0.00422642	−	0.00271616i
$399$		0			0
$400$	−1.13334	−	1.30794i	−0.0566670	−	0.0653972i
$401$	8.99099	+	5.77816i	0.448989	+	0.288548i	0.745530	−	0.666473i	$-0.232197\pi$
$401$	8.99099	+	5.77816i	0.448989	+	0.288548i	−0.296541	+	0.955020i	$0.595833\pi$
$402$		0			0
$403$	1.78275	−	12.3993i	0.0888050	−	0.617652i
$404$	1.50058	+	0.964362i	0.0746565	+	0.0479788i
$405$		0			0
$406$	0.571201	+	1.25076i	0.0283482	+	0.0620740i
$407$	−0.852783	+	0.548050i	−0.0422709	+	0.0271658i
$408$		0			0
$409$	10.3992	−	12.0014i	0.514209	−	0.593429i	−0.437962	−	0.898993i	$-0.644300\pi$
$409$	10.3992	−	12.0014i	0.514209	−	0.593429i	0.952171	+	0.305564i	$0.0988451\pi$
$410$	29.4971	−	8.66113i	1.45676	−	0.427743i
$411$		0			0
$412$	−2.82502	−	19.6484i	−0.139179	−	0.968009i
$413$	−12.0511			−0.592995
$414$		0			0
$415$	−19.1740			−0.941216
$416$	−0.188515	−	1.31115i	−0.00924272	−	0.0642845i
$417$		0			0
$418$	2.26553	−	0.665220i	0.110811	−	0.0325370i
$419$	−3.03210	+	3.49923i	−0.148128	+	0.170948i	−0.824964	−	0.565185i	$-0.808805\pi$
$419$	−3.03210	+	3.49923i	−0.148128	+	0.170948i	0.676837	+	0.736133i	$0.263350\pi$
$420$		0			0
$421$	−8.84060	+	5.68151i	−0.430865	+	0.276900i	−0.738045	−	0.674751i	$-0.764251\pi$
$421$	−8.84060	+	5.68151i	−0.430865	+	0.276900i	0.307180	+	0.951651i	$0.400614\pi$
$422$	6.93623	+	15.1882i	0.337650	+	0.739351i
$423$		0			0
$424$	−9.46721	−	6.08421i	−0.459768	−	0.295475i
$425$	−1.15947	+	8.06432i	−0.0562427	+	0.391177i
$426$		0			0
$427$	14.9513	+	9.60859i	0.723542	+	0.464992i
$428$	−2.85468	−	3.29448i	−0.137986	−	0.159245i
$429$		0			0
$430$	3.66396	−	2.35468i	0.176692	−	0.113553i
$431$	13.0764	+	3.83957i	0.629867	+	0.184946i	0.581058	−	0.813862i	$-0.302639\pi$
$431$	13.0764	+	3.83957i	0.629867	+	0.184946i	0.0488095	+	0.998808i	$0.484457\pi$
$432$		0			0
$433$	8.26166	−	2.42584i	0.397030	−	0.116579i	−0.0771217	−	0.997022i	$-0.524573\pi$
$433$	8.26166	−	2.42584i	0.397030	−	0.116579i	0.474152	+	0.880443i	$0.342755\pi$
$434$	4.85750	−	10.6364i	0.233167	−	0.510565i
$435$		0			0
$436$	6.46538			0.309636
$437$	15.8525	+	8.89416i	0.758329	+	0.425465i
$438$		0			0
$439$	5.27024	+	36.6553i	0.251535	+	1.74946i	0.589007	+	0.808128i	$0.299519\pi$
$439$	5.27024	+	36.6553i	0.251535	+	1.74946i	−0.337472	+	0.941336i	$0.609572\pi$
$440$	−0.671395	+	1.47015i	−0.0320075	+	0.0700866i
$441$		0			0
$442$	−4.08361	+	4.71274i	−0.194238	+	0.224162i
$443$	13.8173	+	4.05713i	0.656481	+	0.192760i	0.592975	−	0.805221i	$-0.297953\pi$
$443$	13.8173	+	4.05713i	0.656481	+	0.192760i	0.0635066	+	0.997981i	$0.479772\pi$
$444$		0			0
$445$	−3.64812	−	7.98827i	−0.172938	−	0.378680i
$446$	11.9238	+	13.7608i	0.564608	+	0.651593i
$447$		0			0
$448$	0.175969	−	1.22389i	0.00831377	−	0.0578235i
$449$	2.10099	−	14.6127i	0.0991516	−	0.689615i	−0.878247	−	0.478208i	$-0.841286\pi$
$449$	2.10099	−	14.6127i	0.0991516	−	0.689615i	0.977398	−	0.211407i	$-0.0678044\pi$
$450$		0			0
$451$	−4.83420	−	5.57896i	−0.227633	−	0.262703i
$452$	0.565973	+	1.23931i	0.0266211	+	0.0582921i
$453$		0			0
$454$	−15.3378	−	4.50357i	−0.719836	−	0.211363i
$455$	−2.78266	+	3.21136i	−0.130453	+	0.150551i
$456$		0			0
$457$	2.75189	−	6.02580i	0.128728	−	0.281875i	−0.834283	−	0.551336i	$-0.814118\pi$
$457$	2.75189	−	6.02580i	0.128728	−	0.281875i	0.963011	+	0.269461i	$0.0868455\pi$
$458$	−2.52348	−	17.5512i	−0.117915	−	0.820114i
$459$		0			0
$460$	−11.7068	+	4.21379i	−0.545832	+	0.196469i
$461$	−7.35627			−0.342616			−0.171308	−	0.985218i	$-0.554799\pi$
$461$	−7.35627			−0.342616			−0.171308	+	0.985218i	$0.554799\pi$
$462$		0			0
$463$	14.3882	−	31.5059i	0.668678	−	1.46420i	−0.205530	−	0.978651i	$-0.565892\pi$
$463$	14.3882	−	31.5059i	0.668678	−	1.46420i	0.874209	−	0.485551i	$-0.161381\pi$
$464$	−1.06699	+	0.313298i	−0.0495340	+	0.0145445i
$465$		0			0
$466$	8.96595	+	2.63264i	0.415340	+	0.121955i
$467$	11.8642	−	7.62464i	0.549008	−	0.352826i	−0.236545	−	0.971621i	$-0.576015\pi$
$467$	11.8642	−	7.62464i	0.549008	−	0.352826i	0.785553	+	0.618794i	$0.212379\pi$
$468$		0			0
$469$	−4.95651	−	5.72012i	−0.228870	−	0.264131i
$470$	−15.1574	−	9.74106i	−0.699158	−	0.449322i
$471$		0			0
$472$	1.38704	−	9.64709i	0.0638438	−	0.444043i
$473$	−0.879810	−	0.565420i	−0.0404537	−	0.0259980i
$474$		0			0
$475$	2.72493	+	5.96676i	0.125028	+	0.273774i
$476$	−4.89681	+	3.14699i	−0.224445	+	0.144242i
$477$		0			0
$478$	3.28022	−	3.78558i	0.150034	−	0.173148i
$479$	−16.3570	+	4.80286i	−0.747372	+	0.219448i	−0.633174	−	0.774010i	$-0.718248\pi$
$479$	−16.3570	+	4.80286i	−0.747372	+	0.219448i	−0.114198	+	0.993458i	$0.536430\pi$
$480$		0			0
$481$	−0.306755	−	2.13353i	−0.0139868	−	0.0972804i
$482$	−14.5761			−0.663925
$483$		0			0
$484$	−10.6119			−0.482359
$485$	−4.22595	−	29.3921i	−0.191891	−	1.33463i
$486$		0			0
$487$	11.8285	−	3.47316i	0.536000	−	0.157384i	−0.00251946	−	0.999997i	$-0.500802\pi$
$487$	11.8285	−	3.47316i	0.536000	−	0.157384i	0.538520	+	0.842613i	$0.318984\pi$
$488$	−9.41268	+	10.8628i	−0.426092	+	0.491736i
$489$		0			0
$490$	11.9408	−	7.67386i	0.539428	−	0.346670i
$491$	2.69768	+	5.90709i	0.121744	+	0.266583i	0.960685	−	0.277639i	$-0.0895520\pi$
$491$	2.69768	+	5.90709i	0.121744	+	0.266583i	−0.838941	+	0.544223i	$0.816825\pi$
$492$		0			0
$493$	4.40399	+	2.83027i	0.198346	+	0.127469i
$494$	−0.714509	+	4.96952i	−0.0321473	+	0.223589i
$495$		0			0
$496$	7.95555	+	5.11272i	0.357215	+	0.229568i
$497$	−5.25715	−	6.06708i	−0.235816	−	0.272146i
$498$		0			0
$499$	−11.4414	+	7.35297i	−0.512189	+	0.329164i	−0.771076	−	0.636744i	$-0.780281\pi$
$499$	−11.4414	+	7.35297i	−0.512189	+	0.329164i	0.258886	+	0.965908i	$0.416645\pi$
$500$	8.13825	+	2.38961i	0.363954	+	0.106866i
$501$		0			0
$502$	17.9766	−	5.27841i	0.802336	−	0.235587i
$503$	−1.25141	+	2.74021i	−0.0557977	+	0.122180i	−0.935477	−	0.353387i	$-0.885030\pi$
$503$	−1.25141	+	2.74021i	−0.0557977	+	0.122180i	0.879679	+	0.475567i	$0.157757\pi$
$504$		0			0
$505$	4.62764			0.205927
$506$	2.08817	+	2.13673i	0.0928306	+	0.0949894i
$507$		0			0
$508$	−0.491724	−	3.42002i	−0.0218167	−	0.151739i
$509$	−17.8751	+	39.1410i	−0.792300	+	1.73490i	−0.122354	+	0.992486i	$0.539044\pi$
$509$	−17.8751	+	39.1410i	−0.792300	+	1.73490i	−0.669946	+	0.742410i	$0.733683\pi$
$510$		0			0
$511$	−10.5993	+	12.2322i	−0.468884	+	0.541121i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$		0			0
$514$	−0.726904	−	1.59170i	−0.0320623	−	0.0702068i
$515$	−33.7248	−	38.9205i	−1.48609	−	1.71504i
$516$		0			0
$517$	−0.615723	+	4.28245i	−0.0270795	+	0.188342i
$518$	0.286340	−	1.99154i	0.0125810	−	0.0875031i
$519$		0			0
$520$	−2.25047	−	2.59718i	−0.0986898	−	0.113894i
$521$	6.29609	+	13.7865i	0.275837	+	0.603998i	0.995955	−	0.0898530i	$-0.0286397\pi$
$521$	6.29609	+	13.7865i	0.275837	+	0.603998i	−0.720118	+	0.693851i	$0.755912\pi$
$522$		0			0
$523$	−15.0544	−	4.42038i	−0.658284	−	0.193290i	−0.0645043	−	0.997917i	$-0.520547\pi$
$523$	−15.0544	−	4.42038i	−0.658284	−	0.193290i	−0.593779	+	0.804628i	$0.702365\pi$
$524$	12.4079	−	14.3195i	0.542042	−	0.625550i
$525$		0			0
$526$	−6.91872	+	15.1499i	−0.301670	+	0.660566i
$527$	−6.33568	−	44.0656i	−0.275987	−	1.91953i
$528$		0			0
$529$	−0.528643	+	22.9939i	−0.0229845	+	0.999736i
$530$	−29.1960			−1.26819
$531$		0			0
$532$	−1.94684	+	4.26299i	−0.0844063	+	0.184824i
$533$	15.0607	−	4.42223i	0.652353	−	0.191548i
$534$		0			0
$535$	−10.8512	−	3.18621i	−0.469140	−	0.137752i
$536$	5.14953	−	3.30940i	0.222426	−	0.142944i
$537$		0			0
$538$	17.4867	+	20.1807i	0.753903	+	0.870051i
$539$	−2.86728	−	1.84269i	−0.123502	−	0.0793702i
$540$		0			0
$541$	3.09092	−	21.4978i	0.132889	−	0.924265i	−0.808873	−	0.587984i	$-0.799922\pi$
$541$	3.09092	−	21.4978i	0.132889	−	0.924265i	0.941762	−	0.336281i	$-0.109169\pi$
$542$	−22.6364	−	14.5475i	−0.972315	−	0.624869i
$543$		0			0
$544$	−1.95561	−	4.28218i	−0.0838460	−	0.183597i
$545$	14.1107	−	9.06842i	0.604438	−	0.388449i
$546$		0			0
$547$	−7.99651	+	9.22846i	−0.341906	+	0.394581i	−0.900497	−	0.434863i	$-0.856797\pi$
$547$	−7.99651	+	9.22846i	−0.341906	+	0.394581i	0.558591	+	0.829443i	$0.311342\pi$
$548$	−10.9344	+	3.21064i	−0.467095	+	0.137152i
$549$		0			0
$550$	0.153436	+	1.06717i	0.00654255	+	0.0455044i
$551$	4.21485			0.179559
$552$		0			0
$553$	14.9396			0.635295
$554$	−0.304147	−	2.11539i	−0.0129220	−	0.0898742i
$555$		0			0
$556$	−5.08787	+	1.49393i	−0.215774	+	0.0633569i
$557$	10.6515	−	12.2924i	0.451317	−	0.520848i	−0.483804	−	0.875176i	$-0.660745\pi$
$557$	10.6515	−	12.2924i	0.451317	−	0.520848i	0.935121	+	0.354329i	$0.115291\pi$
$558$		0			0
$559$	1.87076	−	1.20226i	0.0791247	−	0.0508504i
$560$	−1.33259	−	2.91797i	−0.0563123	−	0.123307i
$561$		0			0
$562$	−23.3748	−	15.0221i	−0.986007	−	0.633668i
$563$	4.50622	−	31.3414i	0.189914	−	1.32088i	−0.642310	−	0.766445i	$-0.722024\pi$
$563$	4.50622	−	31.3414i	0.189914	−	1.32088i	0.832224	−	0.554439i	$-0.187067\pi$
$564$		0			0
$565$	2.97351	+	1.91096i	0.125096	+	0.0803946i
$566$	15.3770	+	17.7460i	0.646344	+	0.745921i
$567$		0			0
$568$	5.46188	−	3.51014i	0.229175	−	0.147282i
$569$	35.3667	+	10.3846i	1.48265	+	0.435345i	0.920187	−	0.391479i	$-0.128036\pi$
$569$	35.3667	+	10.3846i	1.48265	+	0.435345i	0.562461	+	0.826824i	$0.309855\pi$
$570$		0			0
$571$	−29.6036	+	8.69239i	−1.23887	+	0.363765i	−0.834591	−	0.550870i	$-0.814296\pi$
$571$	−29.6036	+	8.69239i	−1.23887	+	0.363765i	−0.404280	+	0.914635i	$0.632478\pi$
$572$	−0.342803	+	0.750635i	−0.0143333	+	0.0313856i
$573$		0			0
$574$	14.6519			0.611560
$575$	−5.05001	+	6.58684i	−0.210600	+	0.274690i
$576$		0			0
$577$	6.50139	+	45.2182i	0.270657	+	1.88246i	0.441652	+	0.897186i	$0.354392\pi$
$577$	6.50139	+	45.2182i	0.270657	+	1.88246i	−0.170996	+	0.985272i	$0.554698\pi$
$578$	−2.14416	+	4.69505i	−0.0891853	+	0.195288i
$579$		0			0
$580$	−1.88929	+	2.18035i	−0.0784484	+	0.0905342i
$581$	−8.76825	−	2.57459i	−0.363769	−	0.106812i
$582$		0			0
$583$	2.91235	+	6.37716i	0.120617	+	0.264115i
$584$	−8.57213	−	9.89277i	−0.354717	−	0.409366i
$585$		0			0
$586$	2.70119	−	18.7872i	0.111585	−	0.776091i
$587$	−4.32880	+	30.1075i	−0.178669	+	1.24267i	0.681179	+	0.732117i	$0.261468\pi$
$587$	−4.32880	+	30.1075i	−0.178669	+	1.24267i	−0.859848	+	0.510551i	$0.829442\pi$
$588$		0			0
$589$	−23.4722	−	27.0884i	−0.967156	−	1.11616i
$590$	−10.5039	−	23.0003i	−0.432438	−	0.946908i
$591$		0			0
$592$	1.56130	+	0.458439i	0.0641691	+	0.0188417i
$593$	−18.2190	+	21.0258i	−0.748163	+	0.863426i	−0.994389	−	0.105786i	$-0.966264\pi$
$593$	−18.2190	+	21.0258i	−0.748163	+	0.863426i	0.246226	+	0.969213i	$0.420810\pi$
$594$		0			0
$595$	−6.27332	+	13.7366i	−0.257181	+	0.563147i
$596$	1.96659	+	13.6779i	0.0805545	+	0.560269i
$597$		0			0
$598$	−5.97731	+	2.15149i	−0.244430	+	0.0879812i
$599$	11.1914			0.457270			0.228635	−	0.973512i	$-0.426574\pi$
$599$	11.1914			0.457270			0.228635	+	0.973512i	$0.426574\pi$
$600$		0			0
$601$	−17.0438	+	37.3206i	−0.695229	+	1.52234i	0.150432	+	0.988620i	$0.451934\pi$
$601$	−17.0438	+	37.3206i	−0.695229	+	1.52234i	−0.845661	+	0.533720i	$0.820794\pi$
$602$	1.99170	−	0.584816i	0.0811756	−	0.0238353i
$603$		0			0
$604$	5.21487	+	1.53122i	0.212190	+	0.0623046i
$605$	−23.1606	+	14.8844i	−0.941611	+	0.605137i
$606$		0			0
$607$	−24.0132	−	27.7127i	−0.974667	−	1.12483i	−0.992159	−	0.124979i	$-0.960114\pi$
$607$	−24.0132	−	27.7127i	−0.974667	−	1.12483i	0.0174926	−	0.999847i	$-0.494432\pi$
$608$	−3.18852	−	2.04913i	−0.129311	−	0.0831034i
$609$		0			0
$610$	−5.30693	+	36.9105i	−0.214871	+	1.49446i
$611$	−7.73912	−	4.97363i	−0.313091	−	0.201212i
$612$		0			0
$613$	−0.0971676	−	0.212767i	−0.00392456	−	0.00859360i	0.907660	−	0.419707i	$-0.137867\pi$
$613$	−0.0971676	−	0.212767i	−0.00392456	−	0.00859360i	−0.911584	+	0.411114i	$0.865140\pi$
$614$	−12.5443	+	8.06176i	−0.506248	+	0.325346i
$615$		0			0
$616$	−0.504432	+	0.582145i	−0.0203241	+	0.0234553i
$617$	−41.8810	+	12.2974i	−1.68606	+	0.495073i	−0.977564	−	0.210637i	$-0.932446\pi$
$617$	−41.8810	+	12.2974i	−1.68606	+	0.495073i	−0.708500	+	0.705711i	$0.750628\pi$
$618$		0			0
$619$	0.169206	+	1.17685i	0.00680096	+	0.0473017i	0.992939	−	0.118623i	$-0.0378481\pi$
$619$	0.169206	+	1.17685i	0.00680096	+	0.0473017i	−0.986138	+	0.165925i	$0.946939\pi$
$620$	24.5342			0.985318
$621$		0			0
$622$	−5.28838			−0.212045
$623$	−0.595655	−	4.14287i	−0.0238644	−	0.165981i
$624$		0			0
$625$	29.4162	−	8.63739i	1.17665	−	0.345496i
$626$	−5.80888	+	6.70380i	−0.232169	+	0.267938i
$627$		0			0
$628$	4.44354	−	2.85569i	0.177316	−	0.113954i
$629$	−3.18219	−	6.96803i	−0.126882	−	0.277834i
$630$		0			0
$631$	14.0184	+	9.00907i	0.558063	+	0.358646i	0.789067	−	0.614307i	$-0.210565\pi$
$631$	14.0184	+	9.00907i	0.558063	+	0.358646i	−0.231003	+	0.972953i	$0.574201\pi$
$632$	−1.71950	+	11.9594i	−0.0683979	+	0.475718i
$633$		0			0
$634$	2.55717	+	1.64339i	0.101558	+	0.0652674i
$635$	−5.87015	−	6.77452i	−0.232950	−	0.268838i
$636$		0			0
$637$	6.09676	−	3.91815i	0.241563	−	0.155243i
$638$	0.664705	+	0.195175i	0.0263159	+	0.00772705i
$639$		0			0
$640$	2.48926	−	0.730913i	0.0983967	−	0.0288919i
$641$	12.3967	−	27.1451i	0.489641	−	1.07217i	−0.490057	−	0.871690i	$-0.663024\pi$
$641$	12.3967	−	27.1451i	0.489641	−	1.07217i	0.979699	−	0.200475i	$-0.0642485\pi$
$642$		0			0
$643$	−36.9937			−1.45889			−0.729445	−	0.684040i	$-0.760221\pi$
$643$	−36.9937			−1.45889			−0.729445	+	0.684040i	$0.760221\pi$
$644$	−5.91931	+	0.355030i	−0.233253	+	0.0139902i
$645$		0			0
$646$	2.53928	+	17.6611i	0.0999068	+	0.694867i
$647$	−12.8336	+	28.1016i	−0.504540	+	1.10479i	0.470427	+	0.882439i	$0.344100\pi$
$647$	−12.8336	+	28.1016i	−0.504540	+	1.10479i	−0.974967	+	0.222349i	$0.928627\pi$
$648$		0			0
$649$	−3.97608	+	4.58864i	−0.156075	+	0.180120i
$650$	−2.19963	−	0.645869i	−0.0862765	−	0.0253331i
$651$		0			0
$652$	3.77639	+	8.26913i	0.147895	+	0.323844i
$653$	−16.9793	−	19.5952i	−0.664452	−	0.766819i	0.319045	−	0.947739i	$-0.396638\pi$
$653$	−16.9793	−	19.5952i	−0.664452	−	0.766819i	−0.983498	+	0.180921i	$0.942092\pi$
$654$		0			0
$655$	6.99566	−	48.6559i	0.273343	−	1.90114i
$656$	−1.68639	+	11.7291i	−0.0658426	+	0.457945i
$657$		0			0
$658$	−5.62347	−	6.48983i	−0.219226	−	0.253000i
$659$	8.46149	+	18.5281i	0.329613	+	0.721752i	0.999791	−	0.0204488i	$-0.00650950\pi$
$659$	8.46149	+	18.5281i	0.329613	+	0.721752i	−0.670178	+	0.742200i	$0.733782\pi$
$660$		0			0
$661$	−40.3726	−	11.8545i	−1.57031	−	0.461085i	−0.623220	−	0.782047i	$-0.714176\pi$
$661$	−40.3726	−	11.8545i	−1.57031	−	0.461085i	−0.947092	+	0.320962i	$0.895994\pi$
$662$	1.07480	−	1.24038i	0.0417732	−	0.0482088i
$663$		0			0
$664$	3.07020	−	6.72280i	0.119147	−	0.260895i
$665$	1.73032	+	12.0347i	0.0670991	+	0.466684i
$666$		0			0
$667$	2.50194	+	4.70986i	0.0968756	+	0.182367i
$668$	−2.87790			−0.111349
$669$		0			0
$670$	6.59707	−	14.4456i	0.254867	−	0.558081i
$671$	8.59158	−	2.52272i	0.331674	−	0.0973883i
$672$		0			0
$673$	−19.5196	−	5.73148i	−0.752426	−	0.220932i	−0.117040	−	0.993127i	$-0.537341\pi$
$673$	−19.5196	−	5.73148i	−0.752426	−	0.220932i	−0.635386	+	0.772195i	$0.719159\pi$
$674$	−15.1178	+	9.71564i	−0.582317	+	0.374233i
$675$		0			0
$676$	7.36413	+	8.49866i	0.283236	+	0.326872i
$677$	−9.29082	−	5.97085i	−0.357075	−	0.229478i	0.349788	−	0.936829i	$-0.386254\pi$
$677$	−9.29082	−	5.97085i	−0.357075	−	0.229478i	−0.706863	+	0.707351i	$0.749890\pi$
$678$		0			0
$679$	2.01411	−	14.0084i	0.0772943	−	0.537594i
$680$	−10.2744	−	6.60294i	−0.394004	−	0.253211i
$681$		0			0
$682$	−2.44733	−	5.35891i	−0.0937131	−	0.205203i
$683$	9.04131	−	5.81050i	0.345956	−	0.222332i	−0.356110	−	0.934444i	$-0.615897\pi$
$683$	9.04131	−	5.81050i	0.345956	−	0.222332i	0.702066	+	0.712111i	$0.252261\pi$
$684$		0			0
$685$	−19.3612	+	22.3440i	−0.739752	+	0.853720i
$686$	14.7956	−	4.34439i	0.564900	−	0.165870i
$687$		0			0
$688$	0.238916	+	1.66170i	0.00910859	+	0.0633516i
$689$	−14.9070			−0.567913
$690$		0			0
$691$	−21.3444			−0.811980			−0.405990	−	0.913878i	$-0.633073\pi$
$691$	−21.3444			−0.811980			−0.405990	+	0.913878i	$0.633073\pi$
$692$	1.94440	+	13.5236i	0.0739151	+	0.514091i
$693$		0			0
$694$	−0.214162	+	0.0628837i	−0.00812948	+	0.00238703i
$695$	−9.00891	+	10.3968i	−0.341727	+	0.394374i
$696$		0			0
$697$	46.9283	−	30.1590i	1.77754	−	1.14235i
$698$	8.40791	+	18.4108i	0.318244	+	0.696857i
$699$		0			0
$700$	−1.80022	−	1.15693i	−0.0680418	−	0.0437278i
$701$	−4.68799	+	32.6057i	−0.177063	+	1.23150i	0.686452	+	0.727175i	$0.259167\pi$
$701$	−4.68799	+	32.6057i	−0.177063	+	1.23150i	−0.863515	+	0.504324i	$0.831742\pi$
$702$		0			0
$703$	−5.18840	−	3.33438i	−0.195684	−	0.125759i
$704$	−0.407958	−	0.470809i	−0.0153755	−	0.0177443i
$705$		0			0
$706$	15.9954	−	10.2796i	0.601996	−	0.386879i
$707$	2.11621	+	0.621377i	0.0795884	+	0.0233693i
$708$		0			0
$709$	39.8126	−	11.6900i	1.49519	−	0.439028i	0.570998	−	0.820951i	$-0.306556\pi$
$709$	39.8126	−	11.6900i	1.49519	−	0.439028i	0.924194	+	0.381923i	$0.124738\pi$
$710$	6.99723	−	15.3218i	0.262601	−	0.575017i
$711$		0			0
$712$	3.38500			0.126858
$713$	16.3366	−	42.3087i	0.611812	−	1.58447i
$714$		0			0
$715$	0.304679	+	2.11909i	0.0113943	+	0.0792493i
$716$	8.47428	−	18.5561i	0.316699	−	0.693473i
$717$		0			0
$718$	−3.36334	+	3.88150i	−0.125519	+	0.144856i
$719$	−26.8918	−	7.89614i	−1.00289	−	0.294476i	−0.261251	−	0.965271i	$-0.584135\pi$
$719$	−26.8918	−	7.89614i	−1.00289	−	0.294476i	−0.741643	+	0.670795i	$0.765953\pi$
$720$		0			0
$721$	−10.1962	−	22.3267i	−0.379728	−	0.831488i
$722$	−3.03490	−	3.50246i	−0.112947	−	0.130348i
$723$		0			0
$724$	−1.35719	+	9.43949i	−0.0504397	+	0.350816i
$725$	−0.273893	+	1.90497i	−0.0101721	+	0.0707488i
$726$		0			0
$727$	−6.50261	−	7.50441i	−0.241168	−	0.278323i	0.622242	−	0.782825i	$-0.286222\pi$
$727$	−6.50261	−	7.50441i	−0.241168	−	0.278323i	−0.863411	+	0.504501i	$0.831676\pi$
$728$	−0.680401	−	1.48987i	−0.0252173	−	0.0552183i
$729$		0			0
$730$	−32.5845	−	9.56766i	−1.20600	−	0.354115i
$731$	5.17540	−	5.97273i	0.191419	−	0.220909i
$732$		0			0
$733$	7.39687	−	16.1969i	0.273209	−	0.598245i	−0.722439	−	0.691435i	$-0.756979\pi$
$733$	7.39687	−	16.1969i	0.273209	−	0.598245i	0.995648	+	0.0931894i	$0.0297062\pi$
$734$	3.52616	+	24.5250i	0.130153	+	0.905234i
$735$		0			0
$736$	0.397086	−	4.77936i	0.0146368	−	0.176170i
$737$	−3.81336			−0.140467
$738$		0			0
$739$	9.04059	−	19.7961i	0.332564	−	0.728213i	−0.667299	−	0.744790i	$-0.732550\pi$
$739$	9.04059	−	19.7961i	0.332564	−	0.728213i	0.999863	+	0.0165773i	$0.00527697\pi$
$740$	4.05056	−	1.18935i	0.148902	−	0.0437215i
$741$		0			0
$742$	−13.3513	−	3.92030i	−0.490142	−	0.143919i
$743$	13.9637	−	8.97393i	0.512279	−	0.329222i	−0.258832	−	0.965922i	$-0.583338\pi$
$743$	13.9637	−	8.97393i	0.512279	−	0.329222i	0.771111	+	0.636701i	$0.219701\pi$
$744$		0			0
$745$	23.4769	+	27.0938i	0.860126	+	0.992639i
$746$	−31.2222	−	20.0653i	−1.14313	−	0.734644i
$747$		0			0
$748$	−0.417365	+	2.90284i	−0.0152604	+	0.106138i
$749$	−4.53443	−	2.91410i	−0.165684	−	0.106479i
$750$		0			0
$751$	−1.69926	−	3.72086i	−0.0620068	−	0.135776i	0.876092	−	0.482144i	$-0.160142\pi$
$751$	−1.69926	−	3.72086i	−0.0620068	−	0.135776i	−0.938099	+	0.346368i	$0.887415\pi$
$752$	5.84246	−	3.75472i	0.213052	−	0.136921i
$753$		0			0
$754$	−0.964640	+	1.11325i	−0.0351301	+	0.0405423i
$755$	13.5292	−	3.97253i	0.492378	−	0.144575i
$756$		0			0
$757$	−1.41901	−	9.86945i	−0.0515749	−	0.358711i	−0.999224	−	0.0393966i	$-0.987456\pi$
$757$	−1.41901	−	9.86945i	−0.0515749	−	0.358711i	0.947649	−	0.319315i	$-0.103453\pi$
$758$	31.1816			1.13257
$759$		0			0
$760$	−9.83310			−0.356684
$761$	6.54762	+	45.5397i	0.237351	+	1.65081i	0.664983	+	0.746859i	$0.268439\pi$
$761$	6.54762	+	45.5397i	0.237351	+	1.65081i	−0.427632	+	0.903953i	$0.640652\pi$
$762$		0			0
$763$	7.67048	−	2.25226i	0.277690	−	0.0815372i
$764$	1.04322	−	1.20394i	0.0377423	−	0.0435569i
$765$		0			0
$766$	−9.72169	+	6.24775i	−0.351259	+	0.225740i
$767$	−5.36312	−	11.7436i	−0.193651	−	0.424037i
$768$		0			0
$769$	23.0960	+	14.8429i	0.832863	+	0.535249i	0.886187	−	0.463329i	$-0.153345\pi$
$769$	23.0960	+	14.8429i	0.832863	+	0.535249i	−0.0533232	+	0.998577i	$0.516981\pi$
$770$	−0.284402	+	1.97806i	−0.0102491	+	0.0712843i
$771$		0			0
$772$	14.7877	+	9.50346i	0.532220	+	0.342037i
$773$	5.94154	+	6.85690i	0.213702	+	0.246626i	0.852473	−	0.522772i	$-0.175102\pi$
$773$	5.94154	+	6.85690i	0.213702	+	0.246626i	−0.638770	+	0.769398i	$0.720557\pi$
$774$		0			0
$775$	13.7683	−	8.84838i	0.494573	−	0.317843i
$776$	10.9821	+	3.22465i	0.394236	+	0.115758i
$777$		0			0
$778$	−22.8397	+	6.70634i	−0.818842	+	0.240434i
$779$	18.6575	−	40.8541i	0.668473	−	1.46375i
$780$		0			0
$781$	−4.04466			−0.144729
$782$	−18.2280	+	13.3212i	−0.651832	+	0.476365i
$783$		0			0
$784$	0.778622	+	5.41543i	0.0278079	+	0.193408i
$785$	5.69263	−	12.4651i	0.203179	−	0.444899i
$786$		0			0
$787$	34.0644	−	39.3125i	1.21427	−	1.40134i	0.323901	−	0.946091i	$-0.395006\pi$
$787$	34.0644	−	39.3125i	1.21427	−	1.40134i	0.890365	−	0.455247i	$-0.150449\pi$
$788$	1.17212	+	0.344166i	0.0417551	+	0.0122604i
$789$		0			0
$790$	13.0215	+	28.5132i	0.463285	+	1.01445i
$791$	1.10319	+	1.27315i	0.0392248	+	0.0452679i
$792$		0			0
$793$	−2.70963	+	18.8459i	−0.0962219	+	0.669238i
$794$	−3.14876	+	21.9001i	−0.111745	+	0.777207i
$795$		0			0
$796$	0.0656352	+	0.0757470i	0.00232638	+	0.00268478i
$797$	−11.0146	−	24.1187i	−0.390158	−	0.854328i	−0.998174	−	0.0604028i	$-0.980761\pi$
$797$	−11.0146	−	24.1187i	−0.390158	−	0.854328i	0.608016	−	0.793925i	$-0.291966\pi$
$798$		0			0
$799$	−31.3697	−	9.21096i	−1.10978	−	0.325861i
$800$	1.13334	−	1.30794i	0.0400696	−	0.0462428i
$801$		0			0
$802$	−4.43980	+	9.72180i	−0.156775	+	0.343289i
$803$	1.16053	+	8.07167i	0.0409543	+	0.284843i
$804$		0			0
$805$	−12.4210	+	9.07735i	−0.437781	+	0.319934i
$806$	12.5268			0.441237
$807$		0			0
$808$	−0.740992	+	1.62255i	−0.0260680	+	0.0570810i
$809$	−20.2221	+	5.93775i	−0.710972	+	0.208760i	−0.617169	−	0.786831i	$-0.711720\pi$
$809$	−20.2221	+	5.93775i	−0.710972	+	0.208760i	−0.0938028	+	0.995591i	$0.529902\pi$
$810$		0			0
$811$	33.9380	+	9.96510i	1.19173	+	0.349922i	0.816684	−	0.577086i	$-0.195810\pi$
$811$	33.9380	+	9.96510i	1.19173	+	0.349922i	0.375042	+	0.927008i	$0.377628\pi$
$812$	−1.15673	+	0.743388i	−0.0405934	+	0.0260878i
$813$		0			0
$814$	−0.663836	−	0.766107i	−0.0232674	−	0.0268520i
$815$	19.8404	+	12.7506i	0.694978	+	0.446635i
$816$		0			0
$817$	0.905539	−	6.29816i	0.0316808	−	0.220345i
$818$	13.3592	+	8.58542i	0.467093	+	0.300182i
$819$		0			0
$820$	12.7708	+	27.9642i	0.445977	+	0.976554i
$821$	41.4714	−	26.6520i	1.44736	−	0.930163i	0.448015	−	0.894026i	$-0.352131\pi$
$821$	41.4714	−	26.6520i	1.44736	−	0.930163i	0.999347	−	0.0361365i	$-0.0115051\pi$
$822$		0			0
$823$	8.11057	−	9.36009i	0.282717	−	0.326272i	−0.596574	−	0.802558i	$-0.703472\pi$
$823$	8.11057	−	9.36009i	0.282717	−	0.326272i	0.879291	+	0.476286i	$0.158017\pi$
$824$	19.0464	−	5.59253i	0.663513	−	0.194825i
$825$		0			0
$826$	−1.71505	−	11.9284i	−0.0596741	−	0.415043i
$827$	−30.0768			−1.04587			−0.522936	−	0.852372i	$-0.675163\pi$
$827$	−30.0768			−1.04587			−0.522936	+	0.852372i	$0.675163\pi$
$828$		0			0
$829$	48.4553			1.68292			0.841462	−	0.540317i	$-0.181696\pi$
$829$	48.4553			1.68292			0.841462	+	0.540317i	$0.181696\pi$
$830$	−2.72875	−	18.9789i	−0.0947163	−	0.658766i
$831$		0			0
$832$	1.27098	−	0.373193i	0.0440632	−	0.0129381i
$833$	16.8665	−	19.4650i	0.584389	−	0.674421i
$834$		0			0
$835$	−6.28104	+	4.03658i	−0.217364	+	0.139692i
$836$	0.980868	+	2.14780i	0.0339240	+	0.0742833i
$837$		0			0
$838$	−3.89512	−	2.50324i	−0.134555	−	0.0864731i
$839$	−6.45239	+	44.8773i	−0.222761	+	1.54934i	0.504764	+	0.863257i	$0.331579\pi$
$839$	−6.45239	+	44.8773i	−0.222761	+	1.54934i	−0.727525	+	0.686081i	$0.759330\pi$
$840$		0			0
$841$	−23.3560	−	15.0100i	−0.805380	−	0.517587i
$842$	−6.88183	−	7.94206i	−0.237164	−	0.273701i
$843$		0			0
$844$	−14.0465	+	9.02714i	−0.483501	+	0.310727i
$845$	27.9926	+	8.21937i	0.962975	+	0.282755i
$846$		0			0
$847$	−12.5899	+	3.69673i	−0.432594	+	0.127021i
$848$	4.67495	−	10.2367i	0.160539	−	0.351530i
$849$		0			0
$850$	−8.14724			−0.279448
$851$	0.646144	−	7.77705i	0.0221495	−	0.266594i
$852$		0			0
$853$	2.06419	+	14.3568i	0.0706765	+	0.491566i	0.994159	+	0.107925i	$0.0344207\pi$
$853$	2.06419	+	14.3568i	0.0706765	+	0.491566i	−0.923482	+	0.383641i	$0.874670\pi$
$854$	−7.38301	+	16.1665i	−0.252641	+	0.553207i
$855$		0			0
$856$	2.85468	−	3.29448i	0.0975710	−	0.112603i
$857$	47.8893	+	14.0616i	1.63587	+	0.480334i	0.965219	−	0.261442i	$-0.0841979\pi$
$857$	47.8893	+	14.0616i	1.63587	+	0.480334i	0.670648	+	0.741776i	$0.266016\pi$
$858$		0			0
$859$	22.8565	+	50.0487i	0.779853	+	1.70764i	0.703650	+	0.710547i	$0.251552\pi$
$859$	22.8565	+	50.0487i	0.779853	+	1.70764i	0.0762029	+	0.997092i	$0.475720\pi$
$860$	2.85215	+	3.29156i	0.0972576	+	0.112241i
$861$		0			0
$862$	−1.93953	+	13.4897i	−0.0660606	+	0.459461i
$863$	5.67710	−	39.4851i	0.193251	−	1.34409i	−0.630081	−	0.776529i	$-0.716978\pi$
$863$	5.67710	−	39.4851i	0.193251	−	1.34409i	0.823332	−	0.567560i	$-0.192112\pi$
$864$		0			0
$865$	23.2121	+	26.7882i	0.789234	+	0.910825i
$866$	3.57691	+	7.83233i	0.121548	+	0.266154i
$867$		0			0
$868$	11.2195	+	3.29433i	0.380813	+	0.111817i
$869$	4.92909	−	5.68848i	0.167208	−	0.192968i
$870$		0			0
$871$	3.36836	−	7.37568i	0.114133	−	0.249916i
$872$	0.920120	+	6.39957i	0.0311592	+	0.216717i
$873$		0			0
$874$	−6.54758	+	16.9569i	−0.221475	+	0.573577i
$875$	10.4876			0.354545
$876$		0			0
$877$	1.58544	−	3.47164i	0.0535366	−	0.117229i	−0.880973	−	0.473166i	$-0.843111\pi$
$877$	1.58544	−	3.47164i	0.0535366	−	0.117229i	0.934510	+	0.355937i	$0.115838\pi$
$878$	−35.5322	+	10.4332i	−1.19915	+	0.352103i
$879$		0			0
$880$	−1.55073	−	0.455337i	−0.0522752	−	0.0153494i
$881$	−17.4153	+	11.1921i	−0.586736	+	0.377072i	−0.800070	−	0.599907i	$-0.795204\pi$
$881$	−17.4153	+	11.1921i	−0.586736	+	0.377072i	0.213334	+	0.976979i	$0.431568\pi$
$882$		0			0
$883$	−11.8661	−	13.6942i	−0.399327	−	0.460848i	0.520102	−	0.854104i	$-0.325894\pi$
$883$	−11.8661	−	13.6942i	−0.399327	−	0.460848i	−0.919429	+	0.393257i	$0.871348\pi$
$884$	−5.24593	−	3.37135i	−0.176440	−	0.113391i
$885$		0			0
$886$	−2.04943	+	14.2541i	−0.0688519	+	0.478875i
$887$	23.7101	+	15.2376i	0.796109	+	0.511628i	0.874344	−	0.485307i	$-0.161292\pi$
$887$	23.7101	+	15.2376i	0.796109	+	0.511628i	−0.0782352	+	0.996935i	$0.524929\pi$
$888$		0			0
$889$	−1.77476	−	3.88619i	−0.0595237	−	0.130339i
$890$	7.38778	−	4.74784i	0.247639	−	0.159148i
$891$		0			0
$892$	−11.9238	+	13.7608i	−0.399238	+	0.460746i
$893$	−25.2564	+	7.41596i	−0.845174	+	0.248166i
$894$		0			0
$895$	−7.53181	−	52.3849i	−0.251761	−	1.75103i
$896$	1.23648			0.0413079
$897$		0			0
$898$	14.7629			0.492646
$899$	−1.49663	−	10.4093i	−0.0499153	−	0.347169i
$900$		0			0
$901$	−50.8319	+	14.9256i	−1.69346	+	0.497244i
$902$	4.83420	−	5.57896i	0.160961	−	0.185759i
$903$		0			0
$904$	−1.14615	+	0.736584i	−0.0381203	+	0.0244984i
$905$	10.2779	+	22.5054i	0.341648	+	0.748104i
$906$		0			0
$907$	20.8735	+	13.4146i	0.693092	+	0.445423i	0.839184	−	0.543848i	$-0.183033\pi$
$907$	20.8735	+	13.4146i	0.693092	+	0.445423i	−0.146092	+	0.989271i	$0.546670\pi$
$908$	2.27494	−	15.8226i	0.0754966	−	0.525090i
$909$		0			0
$910$	−3.57469	−	2.29731i	−0.118500	−	0.0761552i
$911$	−24.6656	−	28.4657i	−0.817209	−	0.943110i	0.181983	−	0.983302i	$-0.441749\pi$
$911$	−24.6656	−	28.4657i	−0.817209	−	0.943110i	−0.999192	+	0.0401918i	$0.987203\pi$
$912$		0			0
$913$	−3.87328	+	2.48920i	−0.128187	+	0.0823806i
$914$	6.35610	+	1.86632i	0.210241	+	0.0617324i
$915$		0			0
$916$	17.0134	−	4.99560i	0.562140	−	0.165059i
$917$	9.73237	−	21.3109i	0.321391	−	0.703749i
$918$		0			0
$919$	51.5748			1.70129			0.850647	−	0.525737i	$-0.176210\pi$
$919$	51.5748			1.70129			0.850647	+	0.525737i	$0.176210\pi$
$920$	−5.83695	−	10.9880i	−0.192439	−	0.362262i
$921$		0			0
$922$	−1.04691	−	7.28139i	−0.0344780	−	0.239800i
$923$	3.57267	−	7.82306i	0.117596	−	0.257499i
$924$		0			0
$925$	1.84419	−	2.12831i	0.0606365	−	0.0699782i
$926$	33.2328	+	9.75804i	1.09210	+	0.320669i
$927$		0			0
$928$	−0.461958	−	1.01155i	−0.0151645	−	0.0332056i
$929$	−8.90537	−	10.2773i	−0.292176	−	0.337189i	0.590617	−	0.806952i	$-0.298885\pi$
$929$	−8.90537	−	10.2773i	−0.292176	−	0.337189i	−0.882792	+	0.469764i	$0.844339\pi$
$930$		0			0
$931$	2.95113	−	20.5255i	0.0967193	−	0.672698i
$932$	−1.32986	+	9.24935i	−0.0435609	+	0.302973i
$933$		0			0
$934$	9.23548	+	10.6583i	0.302194	+	0.348751i
$935$	3.16066	+	6.92087i	0.103365	+	0.226337i
$936$		0			0
$937$	10.0520	+	2.95153i	0.328385	+	0.0964224i	0.441769	−	0.897129i	$-0.354351\pi$
$937$	10.0520	+	2.95153i	0.328385	+	0.0964224i	−0.113385	+	0.993551i	$0.536169\pi$
$938$	4.95651	−	5.72012i	0.161836	−	0.186768i
$939$		0			0
$940$	7.48479	−	16.3894i	0.244127	−	0.534563i
$941$	2.04257	+	14.2064i	0.0665858	+	0.463114i	0.995648	+	0.0931913i	$0.0297068\pi$
$941$	2.04257	+	14.2064i	0.0665858	+	0.463114i	−0.929062	+	0.369923i	$0.879384\pi$
$942$		0			0
$943$	56.7274	−	3.40241i	1.84730	−	0.110798i
$944$	9.74629			0.317215
$945$		0			0
$946$	0.434454	−	0.951323i	0.0141253	−	0.0309302i
$947$	−2.12191	+	0.623050i	−0.0689529	+	0.0202464i	−0.316027	−	0.948750i	$-0.602349\pi$
$947$	−2.12191	+	0.623050i	−0.0689529	+	0.0202464i	0.247074	+	0.968997i	$0.420531\pi$
$948$		0			0
$949$	−16.6371	−	4.88510i	−0.540063	−	0.158577i
$950$	−5.51823	+	3.54635i	−0.179035	+	0.115059i
$951$		0			0
$952$	−3.81184	−	4.39910i	−0.123543	−	0.142576i
$953$	−19.3483	−	12.4344i	−0.626753	−	0.402790i	0.188353	−	0.982101i	$-0.439685\pi$
$953$	−19.3483	−	12.4344i	−0.626753	−	0.402790i	−0.815106	+	0.579312i	$0.803321\pi$
$954$		0			0
$955$	0.588172	−	4.09083i	0.0190328	−	0.132376i
$956$	4.21387	+	2.70809i	0.136286	+	0.0875859i
$957$		0			0
$958$	−7.08182	−	15.5070i	−0.228803	−	0.501009i
$959$	−11.8541	+	7.61815i	−0.382788	+	0.246003i
$960$		0			0
$961$	−38.2640	+	44.1590i	−1.23432	+	1.42449i
$962$	2.06815	−	0.607265i	0.0666799	−	0.0195790i
$963$		0			0
$964$	−2.07440	−	14.4278i	−0.0668120	−	0.464688i
$965$	45.6039			1.46804
$966$		0			0
$967$	−8.31090			−0.267261			−0.133630	−	0.991031i	$-0.542663\pi$
$967$	−8.31090			−0.267261			−0.133630	+	0.991031i	$0.542663\pi$
$968$	−1.51023	−	10.5039i	−0.0485407	−	0.337608i
$969$		0			0
$970$	28.4915	−	8.36587i	0.914808	−	0.268612i
$971$	9.81765	−	11.3302i	0.315063	−	0.363602i	−0.576025	−	0.817432i	$-0.695397\pi$
$971$	9.81765	−	11.3302i	0.315063	−	0.363602i	0.891089	+	0.453829i	$0.149942\pi$
$972$		0			0
$973$	−5.51579	+	3.54479i	−0.176828	+	0.113641i
$974$	5.12118	+	11.2138i	0.164093	+	0.359314i
$975$		0			0
$976$	−12.0918	−	7.77093i	−0.387049	−	0.248741i
$977$	−7.45385	+	51.8426i	−0.238470	+	1.65859i	0.421148	+	0.906992i	$0.361627\pi$
$977$	−7.45385	+	51.8426i	−0.238470	+	1.65859i	−0.659618	+	0.751601i	$0.729282\pi$
$978$		0			0
$979$	−1.77399	−	1.14008i	−0.0566971	−	0.0364370i
$980$	9.29510	+	10.7271i	0.296921	+	0.342665i
$981$		0			0
$982$	−5.46304	+	3.51089i	−0.174333	+	0.112037i
$983$	−28.9296	−	8.49451i	−0.922712	−	0.270933i	−0.214329	−	0.976761i	$-0.568757\pi$
$983$	−28.9296	−	8.49451i	−0.922712	−	0.270933i	−0.708382	+	0.705829i	$0.750575\pi$
$984$		0			0
$985$	3.04090	−	0.892887i	0.0968910	−	0.0284498i
$986$	−2.17471	+	4.76196i	−0.0692570	+	0.151652i
$987$		0			0
$988$	−5.02062			−0.159727
$989$	7.57538	−	2.72671i	0.240883	−	0.0867044i
$990$		0			0
$991$	−0.384388	−	2.67348i	−0.0122105	−	0.0849258i	0.982805	−	0.184647i	$-0.0591141\pi$
$991$	−0.384388	−	2.67348i	−0.0122105	−	0.0849258i	−0.995015	+	0.0997209i	$0.968205\pi$
$992$	−3.92849	+	8.60219i	−0.124730	+	0.273120i
$993$		0			0
$994$	5.25715	−	6.06708i	0.166747	−	0.192436i
$995$	0.249493	+	0.0732577i	0.00790946	+	0.00232243i
$996$		0			0
$997$	3.76854	+	8.25196i	0.119351	+	0.261342i	0.959873	−	0.280435i	$-0.0904788\pi$
$997$	3.76854	+	8.25196i	0.119351	+	0.261342i	−0.840522	+	0.541778i	$0.817752\pi$
$998$	−8.90642	−	10.2786i	−0.281928	−	0.325362i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.d.325.1		10
3.2	odd	2		138.2.e.a.49.1	yes	10
23.8	even	11	inner	414.2.i.d.307.1		10
23.10	odd	22		9522.2.a.bq.1.2		5
23.13	even	11		9522.2.a.bt.1.4		5
69.8	odd	22		138.2.e.a.31.1	✓	10
69.56	even	22		3174.2.a.bd.1.4		5
69.59	odd	22		3174.2.a.bc.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.a.31.1	✓	10	69.8	odd	22
138.2.e.a.49.1	yes	10	3.2	odd	2
414.2.i.d.307.1		10	23.8	even	11	inner
414.2.i.d.325.1		10	1.1	even	1	trivial
3174.2.a.bc.1.2		5	69.59	odd	22
3174.2.a.bd.1.4		5	69.56	even	22
9522.2.a.bq.1.2		5	23.10	odd	22
9522.2.a.bt.1.4		5	23.13	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(-1.69894 + 1.96068i) q^{5} +(-1.04019 + 0.668491i) q^{7} +(-0.415415 - 0.909632i) q^{8} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(-1.69894 + 1.96068i) q^{5} +(-1.04019 + 0.668491i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.18251 - 1.40261i) q^{10} +(-0.0886578 + 0.616629i) q^{11} +(-1.11435 - 0.716152i) q^{13} +(-0.809721 - 0.934468i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-4.51691 - 1.32628i) q^{17} +(-3.63667 + 1.06782i) q^{19} +(1.07773 - 2.35990i) q^{20} -0.622970 q^{22} +(-3.35197 - 3.42992i) q^{23} +(-0.246298 - 1.71304i) q^{25} +(0.550273 - 1.20493i) q^{26} +(0.809721 - 0.934468i) q^{28} +(-1.06699 - 0.313298i) q^{29} +(3.92849 + 8.60219i) q^{31} +(0.654861 + 0.755750i) q^{32} +(0.669961 - 4.65968i) q^{34} +(0.456526 - 3.17521i) q^{35} +(1.06560 + 1.22977i) q^{37} +(-1.57450 - 3.44768i) q^{38} +(2.48926 + 0.730913i) q^{40} +(-7.75992 + 8.95543i) q^{41} +(-0.697393 + 1.52708i) q^{43} +(-0.0886578 - 0.616629i) q^{44} +(2.91797 - 3.80598i) q^{46} +6.94494 q^{47} +(-2.27279 + 4.97671i) q^{49} +(1.66055 - 0.487583i) q^{50} +(1.27098 + 0.373193i) q^{52} +(9.46721 - 6.08421i) q^{53} +(-1.05839 - 1.22144i) q^{55} +(1.04019 + 0.668491i) q^{56} +(0.158260 - 1.10072i) q^{58} +(8.19910 + 5.26924i) q^{59} +(-5.97099 - 13.0746i) q^{61} +(-7.95555 + 5.11272i) q^{62} +(-0.654861 + 0.755750i) q^{64} +(3.29736 - 0.968193i) q^{65} +(0.871145 + 6.05895i) q^{67} +4.70760 q^{68} +3.20786 q^{70} +(0.923986 + 6.42646i) q^{71} +(12.5598 - 3.68788i) q^{73} +(-1.06560 + 1.22977i) q^{74} +(3.18852 - 2.04913i) q^{76} +(-0.319990 - 0.700679i) q^{77} +(-10.1643 - 6.53221i) q^{79} +(-0.369215 + 2.56794i) q^{80} +(-9.96863 - 6.40645i) q^{82} +(4.83987 + 5.58551i) q^{83} +(10.2744 - 6.60294i) q^{85} +(-1.61078 - 0.472968i) q^{86} +(0.597735 - 0.175511i) q^{88} +(-1.40618 + 3.07910i) q^{89} +1.63788 q^{91} +(4.18251 + 2.34662i) q^{92} +(0.988368 + 6.87425i) q^{94} +(4.08482 - 8.94450i) q^{95} +(-7.49539 + 8.65015i) q^{97} +(-5.24950 - 1.54139i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8}+O(q^{10}) \) 10 * q + q^2 - q^4 - 8 * q^5 + 8 * q^7 + q^8	\( 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8} - 3 q^{10} - 7 q^{11} + 3 q^{13} + 3 q^{14} - q^{16} - 4 q^{17} + 3 q^{20} - 26 q^{22} + 12 q^{23} - 15 q^{25} - 3 q^{26} - 3 q^{28} + 25 q^{29} + 6 q^{31} + q^{32} - 7 q^{34} - 2 q^{35} + 9 q^{37} - 11 q^{38} - 3 q^{40} - 24 q^{41} - 30 q^{43} - 7 q^{44} + 21 q^{46} + 48 q^{47} + 9 q^{49} - 7 q^{50} + 14 q^{52} - 15 q^{53} - 23 q^{55} - 8 q^{56} - 3 q^{58} - 5 q^{59} + 12 q^{61} - 28 q^{62} - q^{64} + 13 q^{65} + 18 q^{67} + 18 q^{68} + 2 q^{70} - 28 q^{71} + 19 q^{73} - 9 q^{74} + 22 q^{76} + 12 q^{77} - 52 q^{79} - 8 q^{80} - 20 q^{82} - 7 q^{83} + 23 q^{85} - 14 q^{86} - 4 q^{88} - 3 q^{89} + 42 q^{91} + 23 q^{92} + 29 q^{94} - 22 q^{95} + 51 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + q^2 - q^4 - 8 * q^5 + 8 * q^7 + q^8 - 3 * q^10 - 7 * q^11 + 3 * q^13 + 3 * q^14 - q^16 - 4 * q^17 + 3 * q^20 - 26 * q^22 + 12 * q^23 - 15 * q^25 - 3 * q^26 - 3 * q^28 + 25 * q^29 + 6 * q^31 + q^32 - 7 * q^34 - 2 * q^35 + 9 * q^37 - 11 * q^38 - 3 * q^40 - 24 * q^41 - 30 * q^43 - 7 * q^44 + 21 * q^46 + 48 * q^47 + 9 * q^49 - 7 * q^50 + 14 * q^52 - 15 * q^53 - 23 * q^55 - 8 * q^56 - 3 * q^58 - 5 * q^59 + 12 * q^61 - 28 * q^62 - q^64 + 13 * q^65 + 18 * q^67 + 18 * q^68 + 2 * q^70 - 28 * q^71 + 19 * q^73 - 9 * q^74 + 22 * q^76 + 12 * q^77 - 52 * q^79 - 8 * q^80 - 20 * q^82 - 7 * q^83 + 23 * q^85 - 14 * q^86 - 4 * q^88 - 3 * q^89 + 42 * q^91 + 23 * q^92 + 29 * q^94 - 22 * q^95 + 51 * q^97 + 2 * q^98

Introduction

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