LMFDB - Embedded newform 441.2.bb.c.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			163.2
Character	$\chi$	$=$	441.163
Dual form			441.2.bb.c.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.293772 - 0.748519i) q^{2} +(0.992125 - 0.920558i) q^{4} +(1.11822 - 0.762387i) q^{5} +(1.80149 - 1.93768i) q^{7} +(-2.42946 - 1.16997i) q^{8} +O(q^{10})$	\(q+(-0.293772 - 0.748519i) q^{2} +(0.992125 - 0.920558i) q^{4} +(1.11822 - 0.762387i) q^{5} +(1.80149 - 1.93768i) q^{7} +(-2.42946 - 1.16997i) q^{8} +(-0.899162 - 0.613038i) q^{10} +(-1.27408 - 0.192037i) q^{11} +(-0.117007 + 0.146722i) q^{13} +(-1.97962 - 0.779214i) q^{14} +(0.0402476 - 0.537067i) q^{16} +(2.86041 - 0.882320i) q^{17} +(-2.34871 + 4.06809i) q^{19} +(0.407589 - 1.78577i) q^{20} +(0.230546 + 1.01009i) q^{22} +(2.09355 + 0.645775i) q^{23} +(-1.15753 + 2.94934i) q^{25} +(0.144197 + 0.0444790i) q^{26} +(0.00355656 - 3.58080i) q^{28} +(1.11979 - 4.90614i) q^{29} +(-1.06003 - 1.83602i) q^{31} +(-5.56722 + 1.71726i) q^{32} +(-1.50074 - 1.88187i) q^{34} +(0.537194 - 3.54019i) q^{35} +(-3.51631 - 3.26266i) q^{37} +(3.73503 + 0.562965i) q^{38} +(-3.60863 + 0.543913i) q^{40} +(9.47404 + 4.56246i) q^{41} +(1.77306 - 0.853859i) q^{43} +(-1.44083 + 0.982341i) q^{44} +(-0.131652 - 1.75677i) q^{46} +(-2.97700 - 7.58526i) q^{47} +(-0.509243 - 6.98145i) q^{49} +2.54769 q^{50} +(0.0189806 + 0.253278i) q^{52} +(-5.78671 + 5.36928i) q^{53} +(-1.57111 + 0.756605i) q^{55} +(-6.64368 + 2.59984i) q^{56} +(-4.00130 + 0.603099i) q^{58} +(-2.53525 - 1.72850i) q^{59} +(8.23220 + 7.63836i) q^{61} +(-1.06289 + 1.33282i) q^{62} +(2.24931 + 2.82054i) q^{64} +(-0.0189801 + 0.253271i) q^{65} +(6.34314 + 10.9866i) q^{67} +(2.02566 - 3.50854i) q^{68} +(-2.80771 + 0.637908i) q^{70} +(0.310774 + 1.36159i) q^{71} +(4.84618 - 12.3479i) q^{73} +(-1.40917 + 3.59050i) q^{74} +(1.41469 + 6.19818i) q^{76} +(-2.66736 + 2.12282i) q^{77} +(-6.97387 + 12.0791i) q^{79} +(-0.364447 - 0.631242i) q^{80} +(0.631878 - 8.43182i) q^{82} +(10.7654 + 13.4994i) q^{83} +(2.52589 - 3.16736i) q^{85} +(-1.16000 - 1.07633i) q^{86} +(2.87065 + 1.95718i) q^{88} +(-2.26094 + 0.340781i) q^{89} +(0.0735137 + 0.491041i) q^{91} +(2.67154 - 1.28654i) q^{92} +(-4.80315 + 4.45668i) q^{94} +(0.475090 + 6.33963i) q^{95} +14.5637 q^{97} +(-5.07615 + 2.43213i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{10}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.293772	−	0.748519i	−0.207728	−	0.529283i	0.788599	−	0.614907i	$-0.210807\pi$
$2$	−0.293772	−	0.748519i	−0.207728	−	0.529283i	−0.996327	+	0.0856246i	$0.972711\pi$
$3$		0			0
$3$		0			0
$4$	0.992125	−	0.920558i	0.496063	−	0.460279i
$5$	1.11822	−	0.762387i	0.500082	−	0.340950i	−0.286865	−	0.957971i	$-0.592613\pi$
$5$	1.11822	−	0.762387i	0.500082	−	0.340950i	0.786947	+	0.617021i	$0.211661\pi$
$6$		0			0
$7$	1.80149	−	1.93768i	0.680900	−	0.732376i
$7$	1.80149	−	1.93768i	0.680900	−	0.732376i
$8$	−2.42946	−	1.16997i	−0.858943	−	0.413645i
$9$		0			0
$10$	−0.899162	−	0.613038i	−0.284340	−	0.193860i
$11$	−1.27408	−	0.192037i	−0.384150	−	0.0579013i	−0.0458717	−	0.998947i	$-0.514607\pi$
$11$	−1.27408	−	0.192037i	−0.384150	−	0.0579013i	−0.338279	+	0.941046i	$0.609845\pi$
$12$		0			0
$13$	−0.117007	+	0.146722i	−0.0324518	+	0.0406933i	−0.797793	−	0.602932i	$-0.793999\pi$
$13$	−0.117007	+	0.146722i	−0.0324518	+	0.0406933i	0.765341	+	0.643625i	$0.222570\pi$
$14$	−1.97962	−	0.779214i	−0.529076	−	0.208254i
$15$		0			0
$16$	0.0402476	−	0.537067i	0.0100619	−	0.134267i
$17$	2.86041	−	0.882320i	0.693751	−	0.213994i	0.0722264	−	0.997388i	$-0.476990\pi$
$17$	2.86041	−	0.882320i	0.693751	−	0.213994i	0.621525	+	0.783394i	$0.286513\pi$
$18$		0			0
$19$	−2.34871	+	4.06809i	−0.538831	+	0.933283i	0.460136	+	0.887849i	$0.347801\pi$
$19$	−2.34871	+	4.06809i	−0.538831	+	0.933283i	−0.998967	+	0.0454349i	$0.985533\pi$
$20$	0.407589	−	1.78577i	0.0911398	−	0.399309i
$21$		0			0
$22$	0.230546	+	1.01009i	0.0491527	+	0.215352i
$23$	2.09355	+	0.645775i	0.436536	+	0.134653i	0.505231	−	0.862984i	$-0.331407\pi$
$23$	2.09355	+	0.645775i	0.436536	+	0.134653i	−0.0686952	+	0.997638i	$0.521884\pi$
$24$		0			0
$25$	−1.15753	+	2.94934i	−0.231506	+	0.589868i
$26$	0.144197	+	0.0444790i	0.0282794	+	0.00872305i
$27$		0			0
$28$	0.00355656	−	3.58080i	0.000672127	−	0.676708i
$29$	1.11979	−	4.90614i	0.207940	−	0.911046i	−0.757994	−	0.652261i	$-0.773821\pi$
$29$	1.11979	−	4.90614i	0.207940	−	0.911046i	0.965935	−	0.258785i	$-0.0833223\pi$
$30$		0			0
$31$	−1.06003	−	1.83602i	−0.190387	−	0.329759i	0.754992	−	0.655734i	$-0.227641\pi$
$31$	−1.06003	−	1.83602i	−0.190387	−	0.329759i	−0.945378	+	0.325975i	$0.894308\pi$
$32$	−5.56722	+	1.71726i	−0.984155	+	0.303572i
$33$		0			0
$34$	−1.50074	−	1.88187i	−0.257375	−	0.322738i
$35$	0.537194	−	3.54019i	0.0908023	−	0.598401i
$36$		0			0
$37$	−3.51631	−	3.26266i	−0.578078	−	0.536378i	0.336029	−	0.941852i	$-0.390916\pi$
$37$	−3.51631	−	3.26266i	−0.578078	−	0.536378i	−0.914107	+	0.405474i	$0.867107\pi$
$38$	3.73503	+	0.562965i	0.605901	+	0.0913249i
$39$		0			0
$40$	−3.60863	+	0.543913i	−0.570574	+	0.0860002i
$41$	9.47404	+	4.56246i	1.47960	+	0.712536i	0.987443	−	0.157973i	$-0.0504958\pi$
$41$	9.47404	+	4.56246i	1.47960	+	0.712536i	0.492153	+	0.870509i	$0.336210\pi$
$42$		0			0
$43$	1.77306	−	0.853859i	0.270388	−	0.130212i	−0.293777	−	0.955874i	$-0.594912\pi$
$43$	1.77306	−	0.853859i	0.270388	−	0.130212i	0.564165	+	0.825662i	$0.309198\pi$
$44$	−1.44083	+	0.982341i	−0.217213	+	0.148094i
$45$		0			0
$46$	−0.131652	−	1.75677i	−0.0194110	−	0.259022i
$47$	−2.97700	−	7.58526i	−0.434240	−	1.10642i	−0.965773	−	0.259387i	$-0.916479\pi$
$47$	−2.97700	−	7.58526i	−0.434240	−	1.10642i	0.531534	−	0.847037i	$-0.321616\pi$
$48$		0			0
$49$	−0.509243	−	6.98145i	−0.0727490	−	0.997350i
$50$	2.54769			0.360297
$51$		0			0
$52$	0.0189806	+	0.253278i	0.00263213	+	0.0351233i
$53$	−5.78671	+	5.36928i	−0.794865	+	0.737527i	−0.968964	−	0.247201i	$-0.920489\pi$
$53$	−5.78671	+	5.36928i	−0.794865	+	0.737527i	0.174099	+	0.984728i	$0.444299\pi$
$54$		0			0
$55$	−1.57111	+	0.756605i	−0.211848	+	0.102021i
$56$	−6.64368	+	2.59984i	−0.887799	+	0.347418i
$57$		0			0
$58$	−4.00130	+	0.603099i	−0.525396	+	0.0791908i
$59$	−2.53525	−	1.72850i	−0.330061	−	0.225032i	0.386938	−	0.922106i	$-0.373533\pi$
$59$	−2.53525	−	1.72850i	−0.330061	−	0.225032i	−0.716999	+	0.697074i	$0.754485\pi$
$60$		0			0
$61$	8.23220	+	7.63836i	1.05402	+	0.977992i	0.999789	−	0.0205362i	$-0.00653735\pi$
$61$	8.23220	+	7.63836i	1.05402	+	0.977992i	0.0542355	+	0.998528i	$0.482728\pi$
$62$	−1.06289	+	1.33282i	−0.134987	+	0.169269i
$63$		0			0
$64$	2.24931	+	2.82054i	0.281163	+	0.352568i
$65$	−0.0189801	+	0.253271i	−0.00235419	+	0.0314144i
$66$		0			0
$67$	6.34314	+	10.9866i	0.774937	+	1.34223i	0.934830	+	0.355096i	$0.115552\pi$
$67$	6.34314	+	10.9866i	0.774937	+	1.34223i	−0.159892	+	0.987134i	$0.551115\pi$
$68$	2.02566	−	3.50854i	0.245647	−	0.425473i
$69$		0			0
$70$	−2.80771	+	0.637908i	−0.335585	+	0.0762446i
$71$	0.310774	+	1.36159i	0.0368821	+	0.161591i	0.990015	−	0.140960i	$-0.0450189\pi$
$71$	0.310774	+	1.36159i	0.0368821	+	0.161591i	−0.953133	+	0.302551i	$0.902162\pi$
$72$		0			0
$73$	4.84618	−	12.3479i	0.567202	−	1.44521i	−0.303229	−	0.952918i	$-0.598065\pi$
$73$	4.84618	−	12.3479i	0.567202	−	1.44521i	0.870431	−	0.492290i	$-0.163840\pi$
$74$	−1.40917	+	3.59050i	−0.163813	+	0.417388i
$75$		0			0
$76$	1.41469	+	6.19818i	0.162276	+	0.710980i
$77$	−2.66736	+	2.12282i	−0.303974	+	0.241917i
$78$		0			0
$79$	−6.97387	+	12.0791i	−0.784621	+	1.35900i	0.144604	+	0.989490i	$0.453809\pi$
$79$	−6.97387	+	12.0791i	−0.784621	+	1.35900i	−0.929225	+	0.369514i	$0.879524\pi$
$80$	−0.364447	−	0.631242i	−0.0407465	−	0.0705750i
$81$		0			0
$82$	0.631878	−	8.43182i	0.0697792	−	0.931139i
$83$	10.7654	+	13.4994i	1.18166	+	1.48176i	0.840551	+	0.541733i	$0.182232\pi$
$83$	10.7654	+	13.4994i	1.18166	+	1.48176i	0.341110	+	0.940023i	$0.389197\pi$
$84$		0			0
$85$	2.52589	−	3.16736i	0.273971	−	0.343549i
$86$	−1.16000	−	1.07633i	−0.125086	−	0.116063i
$87$		0			0
$88$	2.87065	+	1.95718i	0.306013	+	0.208636i
$89$	−2.26094	+	0.340781i	−0.239659	+	0.0361227i	−0.267773	−	0.963482i	$-0.586288\pi$
$89$	−2.26094	+	0.340781i	−0.239659	+	0.0361227i	0.0281145	+	0.999605i	$0.491050\pi$
$90$		0			0
$91$	0.0735137	+	0.491041i	0.00770633	+	0.0514750i
$92$	2.67154	−	1.28654i	0.278527	−	0.134132i
$93$		0			0
$94$	−4.80315	+	4.45668i	−0.495408	+	0.459671i
$95$	0.475090	+	6.33963i	0.0487432	+	0.650432i
$96$		0			0
$97$	14.5637			1.47871			0.739357	−	0.673313i	$-0.235129\pi$
$97$	14.5637			1.47871			0.739357	+	0.673313i	$0.235129\pi$
$98$	−5.07615	+	2.43213i	−0.512768	+	0.245683i
$99$		0			0
$100$	1.56662	+	3.99169i	0.156662	+	0.399169i
$101$	0.407052	+	5.43173i	0.0405032	+	0.540478i	0.980140	+	0.198305i	$0.0635437\pi$
$101$	0.407052	+	5.43173i	0.0405032	+	0.540478i	−0.939637	+	0.342173i	$0.888837\pi$
$102$		0			0
$103$	2.08752	−	1.42325i	0.205690	−	0.140237i	−0.456094	−	0.889931i	$-0.650752\pi$
$103$	2.08752	−	1.42325i	0.205690	−	0.140237i	0.661784	+	0.749695i	$0.269800\pi$
$104$	0.455923	−	0.219561i	0.0447069	−	0.0215297i
$105$		0			0
$106$	5.71898	+	2.75412i	0.555476	+	0.267503i
$107$	−9.47171	+	1.42763i	−0.915665	+	0.138014i	−0.589937	−	0.807449i	$-0.700847\pi$
$107$	−9.47171	+	1.42763i	−0.915665	+	0.138014i	−0.325728	+	0.945464i	$0.605609\pi$
$108$		0			0
$109$	−9.48370	−	1.42944i	−0.908374	−	0.136915i	−0.321797	−	0.946809i	$-0.604287\pi$
$109$	−9.48370	−	1.42944i	−0.908374	−	0.136915i	−0.586577	+	0.809893i	$0.699525\pi$
$110$	1.02788	+	0.953734i	0.0980046	+	0.0909349i
$111$		0			0
$112$	−0.968161	−	1.04551i	−0.0914826	−	0.0987914i
$113$	11.9924	+	15.0380i	1.12815	+	1.41466i	0.897160	+	0.441705i	$0.145626\pi$
$113$	11.9924	+	15.0380i	1.12815	+	1.41466i	0.230994	+	0.972955i	$0.425802\pi$
$114$		0			0
$115$	2.83337	−	0.873980i	0.264213	−	0.0814991i
$116$	−3.40540	−	5.89833i	−0.316184	−	0.547647i
$117$		0			0
$118$	−0.549032	+	2.40547i	−0.0505425	+	0.221441i
$119$	3.44335	−	7.13207i	0.315652	−	0.653795i
$120$		0			0
$121$	−8.92489	−	2.75296i	−0.811354	−	0.250270i
$122$	3.29907	−	8.40589i	0.298684	−	0.761034i
$123$		0			0
$124$	−2.74185	−	0.845747i	−0.246225	−	0.0759504i
$125$	2.45995	+	10.7777i	0.220024	+	0.963990i
$126$		0			0
$127$	2.63730	−	11.5547i	0.234022	−	1.02532i	−0.712245	−	0.701931i	$-0.752321\pi$
$127$	2.63730	−	11.5547i	0.234022	−	1.02532i	0.946267	−	0.323387i	$-0.104821\pi$
$128$	−4.37561	+	7.57878i	−0.386753	+	0.669876i
$129$		0			0
$130$	0.195154	−	0.0601971i	0.0171162	−	0.00527963i
$131$	−0.0746309	+	0.995881i	−0.00652053	+	0.0870105i	−0.999515	−	0.0311537i	$-0.990082\pi$
$131$	−0.0746309	+	0.995881i	−0.00652053	+	0.0870105i	0.992994	+	0.118164i	$0.0377009\pi$
$132$		0			0
$133$	3.65148	+	11.8797i	0.316624	+	1.03010i
$134$	6.36027	−	7.97552i	0.549443	−	0.688980i
$135$		0			0
$136$	−7.98153	−	1.20302i	−0.684411	−	0.103158i
$137$	18.9694	+	12.9331i	1.62067	+	1.10495i	0.920331	+	0.391141i	$0.127920\pi$
$137$	18.9694	+	12.9331i	1.62067	+	1.10495i	0.700338	+	0.713812i	$0.253033\pi$
$138$		0			0
$139$	−0.196185	−	0.0944777i	−0.0166402	−	0.00801349i	0.425545	−	0.904937i	$-0.360082\pi$
$139$	−0.196185	−	0.0944777i	−0.0166402	−	0.00801349i	−0.442185	+	0.896924i	$0.645797\pi$
$140$	−2.72598	−	4.00683i	−0.230388	−	0.338639i
$141$		0			0
$142$	0.927880	−	0.632618i	0.0778659	−	0.0530881i
$143$	0.177252	−	0.164466i	0.0148226	−	0.0137533i
$144$		0			0
$145$	−2.48820	−	6.33984i	−0.206634	−	0.526495i
$146$	−10.6663			−0.882748
$147$		0			0
$148$	−6.49209			−0.533646
$149$	−5.30056	−	13.5056i	−0.434239	−	1.10642i	−0.965774	−	0.259386i	$-0.916480\pi$
$149$	−5.30056	−	13.5056i	−0.434239	−	1.10642i	0.531535	−	0.847037i	$-0.321616\pi$
$150$		0			0
$151$	−13.0781	+	12.1347i	−1.06428	+	0.987511i	−0.999946	−	0.0104167i	$-0.996684\pi$
$151$	−13.0781	+	12.1347i	−1.06428	+	0.987511i	−0.0643385	+	0.997928i	$0.520494\pi$
$152$	10.4656	−	7.13534i	0.848874	−	0.578752i
$153$		0			0
$154$	2.37256	+	1.37294i	0.191187	+	0.110635i
$155$	−2.58510	−	1.24492i	−0.207640	−	0.0999943i
$156$		0			0
$157$	10.4812	+	7.14597i	0.836492	+	0.570311i	0.904061	−	0.427404i	$-0.140572\pi$
$157$	10.4812	+	7.14597i	0.836492	+	0.570311i	−0.0675687	+	0.997715i	$0.521524\pi$
$158$	11.0902	+	1.67157i	0.882285	+	0.132983i
$159$		0			0
$160$	−4.91614	+	6.16465i	−0.388655	+	0.487358i
$161$	5.02283	−	2.89328i	0.395854	−	0.228023i
$162$		0			0
$163$	0.640922	−	8.55251i	0.0502009	−	0.669884i	−0.914170	−	0.405331i	$-0.867156\pi$
$163$	0.640922	−	8.55251i	0.0502009	−	0.669884i	0.964371	−	0.264554i	$-0.0852246\pi$
$164$	13.5994	−	4.19487i	1.06194	−	0.327564i
$165$		0			0
$166$	6.94200	−	12.0239i	0.538804	−	0.933235i
$167$	2.14606	−	9.40250i	0.166067	−	0.727587i	−0.821477	−	0.570242i	$-0.806849\pi$
$167$	2.14606	−	9.40250i	0.166067	−	0.727587i	0.987544	−	0.157345i	$-0.0502934\pi$
$168$		0			0
$169$	2.88494	+	12.6397i	0.221918	+	0.972287i
$170$	−3.11287	−	0.960193i	−0.238746	−	0.0736434i
$171$		0			0
$172$	0.973067	−	2.47933i	0.0741957	−	0.189047i
$173$	−14.1985	−	4.37964i	−1.07949	−	0.332978i	−0.296512	−	0.955029i	$-0.595823\pi$
$173$	−14.1985	−	4.37964i	−1.07949	−	0.332978i	−0.782977	+	0.622051i	$0.786300\pi$
$174$		0			0
$175$	3.62961	+	7.55615i	0.274373	+	0.571191i
$176$	−0.154416	+	0.676539i	−0.0116395	+	0.0509960i
$177$		0			0
$178$	0.919281	+	1.59224i	0.0689030	+	0.119344i
$179$	−12.9153	+	3.98385i	−0.965336	+	0.297767i	−0.737058	−	0.675829i	$-0.763786\pi$
$179$	−12.9153	+	3.98385i	−0.965336	+	0.297767i	−0.228278	+	0.973596i	$0.573309\pi$
$180$		0			0
$181$	−4.10705	−	5.15008i	−0.305275	−	0.382802i	0.605404	−	0.795919i	$-0.293012\pi$
$181$	−4.10705	−	5.15008i	−0.305275	−	0.382802i	−0.910678	+	0.413116i	$0.864440\pi$
$182$	0.345957	−	0.199280i	0.0256440	−	0.0147717i
$183$		0			0
$184$	−4.33066	−	4.01827i	−0.319261	−	0.296230i
$185$	−6.41941	−	0.967570i	−0.471964	−	0.0711372i
$186$		0			0
$187$	−3.81384	+	0.574843i	−0.278895	+	0.0420367i
$188$	−9.93622	−	4.78503i	−0.724674	−	0.348984i
$189$		0			0
$190$	4.60577	−	2.21802i	0.334137	−	0.160912i
$191$	−14.0789	+	9.59883i	−1.01871	+	0.694547i	−0.952900	−	0.303285i	$-0.901917\pi$
$191$	−14.0789	+	9.59883i	−1.01871	+	0.694547i	−0.0658138	+	0.997832i	$0.520964\pi$
$192$		0			0
$193$	−1.59132	−	21.2346i	−0.114546	−	1.52850i	−0.697846	−	0.716247i	$-0.745858\pi$
$193$	−1.59132	−	21.2346i	−0.114546	−	1.52850i	0.583301	−	0.812256i	$-0.301761\pi$
$194$	−4.27839	−	10.9012i	−0.307171	−	0.782658i
$195$		0			0
$196$	−6.93206	−	6.45769i	−0.495147	−	0.461263i
$197$	13.6769			0.974437			0.487219	−	0.873280i	$-0.338012\pi$
$197$	13.6769			0.974437			0.487219	+	0.873280i	$0.338012\pi$
$198$		0			0
$199$	−0.00219167	−	0.0292458i	−0.000155363	−	0.00207318i	0.997126	−	0.0757666i	$-0.0241404\pi$
$199$	−0.00219167	−	0.0292458i	−0.000155363	−	0.00207318i	−0.997281	+	0.0736935i	$0.976521\pi$
$200$	6.26280	−	5.81103i	0.442847	−	0.410902i
$201$		0			0
$202$	3.94617	−	1.90038i	0.277652	−	0.133710i
$203$	−7.48924	−	11.0082i	−0.525642	−	0.772623i
$204$		0			0
$205$	14.0724	−	2.12107i	0.982858	−	0.148142i
$206$	−1.67858	−	1.14444i	−0.116952	−	0.0797368i
$207$		0			0
$208$	0.0740902	+	0.0687457i	0.00513723	+	0.00476666i
$209$	3.77368	−	4.73204i	0.261031	−	0.327322i
$210$		0			0
$211$	−9.97956	−	12.5140i	−0.687021	−	0.861498i	0.308958	−	0.951076i	$-0.400020\pi$
$211$	−9.97956	−	12.5140i	−0.687021	−	0.861498i	−0.995980	+	0.0895780i	$0.971448\pi$
$212$	−0.798406	+	10.6540i	−0.0548348	+	0.731719i
$213$		0			0
$214$	3.85113	+	6.67036i	0.263258	+	0.455976i
$215$	1.33169	−	2.30655i	0.0908205	−	0.157306i
$216$		0			0
$217$	−5.46727	−	1.25358i	−0.371142	−	0.0850987i
$218$	1.71609	+	7.51866i	0.116228	+	0.509228i
$219$		0			0
$220$	−0.862236	+	2.19694i	−0.0581319	+	0.148118i
$221$	−0.205232	+	0.522922i	−0.0138054	+	0.0351755i
$222$		0			0
$223$	1.53710	+	6.73448i	0.102932	+	0.450974i	0.999960	+	0.00899973i	$0.00286474\pi$
$223$	1.53710	+	6.73448i	0.102932	+	0.450974i	−0.897028	+	0.441975i	$0.854278\pi$
$224$	−6.70181	+	13.8812i	−0.447783	+	0.927474i
$225$		0			0
$226$	7.73322	−	13.3943i	0.514406	−	0.890977i
$227$	−11.4607	−	19.8505i	−0.760672	−	1.31752i	−0.942505	−	0.334192i	$-0.891536\pi$
$227$	−11.4607	−	19.8505i	−0.760672	−	1.31752i	0.181833	−	0.983329i	$-0.441797\pi$
$228$		0			0
$229$	0.0216703	−	0.289170i	0.00143201	−	0.0191089i	−0.996442	−	0.0842811i	$-0.973141\pi$
$229$	0.0216703	−	0.289170i	0.00143201	−	0.0191089i	0.997874	+	0.0651722i	$0.0207597\pi$
$230$	−1.48656	−	1.86408i	−0.0980206	−	0.122914i
$231$		0			0
$232$	−8.46050	+	10.6091i	−0.555459	+	0.696524i
$233$	−5.43994	−	5.04753i	−0.356383	−	0.330675i	0.481580	−	0.876402i	$-0.340063\pi$
$233$	−5.43994	−	5.04753i	−0.356383	−	0.330675i	−0.837963	+	0.545727i	$0.816253\pi$
$234$		0			0
$235$	−9.11183	−	6.21234i	−0.594390	−	0.405249i
$236$	−4.10647	+	0.618951i	−0.267308	+	0.0402903i
$237$		0			0
$238$	−6.35005	−	0.482213i	−0.411612	−	0.0312572i
$239$	−9.06542	+	4.36567i	−0.586393	+	0.282392i	−0.703463	−	0.710732i	$-0.748364\pi$
$239$	−9.06542	+	4.36567i	−0.586393	+	0.282392i	0.117070	+	0.993124i	$0.462650\pi$
$240$		0			0
$241$	−4.31303	+	4.00191i	−0.277827	+	0.257785i	−0.806762	−	0.590877i	$-0.798782\pi$
$241$	−4.31303	+	4.00191i	−0.277827	+	0.257785i	0.528935	+	0.848662i	$0.322591\pi$
$242$	0.561238	+	7.48920i	0.0360777	+	0.481424i
$243$		0			0
$244$	15.1989			0.973011
$245$	−5.89201	−	7.41853i	−0.376427	−	0.473953i
$246$		0			0
$247$	−0.322062	−	0.820601i	−0.0204923	−	0.0522136i
$248$	0.427211	+	5.70074i	0.0271279	+	0.361997i
$249$		0			0
$250$	7.34468	−	5.00752i	0.464518	−	0.316703i
$251$	−13.8146	+	6.65277i	−0.871970	+	0.419919i	−0.815685	−	0.578496i	$-0.803640\pi$
$251$	−13.8146	+	6.65277i	−0.871970	+	0.419919i	−0.0562852	+	0.998415i	$0.517926\pi$
$252$		0			0
$253$	−2.54334	−	1.22481i	−0.159899	−	0.0770031i
$254$	−9.42371	+	1.42040i	−0.591296	+	0.0891236i
$255$		0			0
$256$	14.0929	+	2.12417i	0.880808	+	0.132760i
$257$	13.7244	+	12.7344i	0.856105	+	0.794350i	0.980218	−	0.197919i	$-0.0634181\pi$
$257$	13.7244	+	12.7344i	0.856105	+	0.794350i	−0.124113	+	0.992268i	$0.539609\pi$
$258$		0			0
$259$	−12.6566	+	0.935842i	−0.786444	+	0.0581504i
$260$	0.214320	+	0.268749i	0.0132916	+	0.0166671i
$261$		0			0
$262$	0.767360	−	0.236699i	0.0474077	−	0.0146233i
$263$	−11.9603	−	20.7159i	−0.737505	−	1.27740i	−0.953616	−	0.301027i	$-0.902670\pi$
$263$	−11.9603	−	20.7159i	−0.737505	−	1.27740i	0.216111	−	0.976369i	$-0.430663\pi$
$264$		0			0
$265$	−2.37732	+	10.4157i	−0.146038	+	0.639833i
$266$	7.81948	−	6.22313i	0.479443	−	0.381564i
$267$		0			0
$268$	16.4070	+	5.06089i	1.00222	+	0.309143i
$269$	8.14570	−	20.7549i	0.496652	−	1.26545i	−0.434452	−	0.900695i	$-0.643058\pi$
$269$	8.14570	−	20.7549i	0.496652	−	1.26545i	0.931104	−	0.364754i	$-0.118847\pi$
$270$		0			0
$271$	−11.1173	−	3.42923i	−0.675328	−	0.208311i	−0.0619245	−	0.998081i	$-0.519724\pi$
$271$	−11.1173	−	3.42923i	−0.675328	−	0.208311i	−0.613403	+	0.789770i	$0.710200\pi$
$272$	−0.358740	−	1.57174i	−0.0217518	−	0.0953010i
$273$		0			0
$274$	4.10801	−	17.9984i	0.248174	−	1.08732i
$275$	2.04117	−	3.53541i	0.123087	−	0.213194i
$276$		0			0
$277$	1.02764	−	0.316984i	0.0617448	−	0.0190457i	−0.263729	−	0.964597i	$-0.584952\pi$
$277$	1.02764	−	0.316984i	0.0617448	−	0.0190457i	0.325474	+	0.945551i	$0.394476\pi$
$278$	−0.0130847	+	0.174603i	−0.000784767	+	0.0104720i
$279$		0			0
$280$	−5.44699	+	7.97224i	−0.325520	+	0.476432i
$281$	14.2933	−	17.9232i	0.852664	−	1.06921i	−0.144159	−	0.989555i	$-0.546048\pi$
$281$	14.2933	−	17.9232i	0.852664	−	1.06921i	0.996823	−	0.0796522i	$-0.0253810\pi$
$282$		0			0
$283$	19.5968	+	2.95374i	1.16491	+	0.175582i	0.702896	−	0.711292i	$-0.251890\pi$
$283$	19.5968	+	2.95374i	1.16491	+	0.175582i	0.462012	+	0.886874i	$0.347128\pi$
$284$	1.56175	+	1.06478i	0.0926728	+	0.0631832i
$285$		0			0
$286$	−0.175178	−	0.0843612i	−0.0103585	−	0.00498838i
$287$	25.9080	−	10.1385i	1.52930	−	0.598455i
$288$		0			0
$289$	−6.64260	+	4.52885i	−0.390741	+	0.266403i
$290$	−4.01452	+	3.72493i	−0.235741	+	0.218736i
$291$		0			0
$292$	−6.55890	−	16.7118i	−0.383831	−	0.977985i
$293$	−12.2307			−0.714525			−0.357263	−	0.934004i	$-0.616290\pi$
$293$	−12.2307			−0.714525			−0.357263	+	0.934004i	$0.616290\pi$
$294$		0			0
$295$	−4.15274			−0.241782
$296$	4.72553	+	12.0405i	0.274666	+	0.699838i
$297$		0			0
$298$	−8.55205	+	7.93514i	−0.495407	+	0.459671i
$299$	−0.339709	+	0.231610i	−0.0196459	+	0.0133943i
$300$		0			0
$301$	1.53964	−	4.97384i	0.0887433	−	0.286688i
$302$	12.9251	+	6.22439i	0.743755	+	0.358173i
$303$		0			0
$304$	2.09031	+	1.42515i	0.119887	+	0.0817378i
$305$	15.0288	+	2.26522i	0.860545	+	0.129706i
$306$		0			0
$307$	−6.96441	+	8.73310i	−0.397480	+	0.498424i	−0.939789	−	0.341755i	$-0.888979\pi$
$307$	−6.96441	+	8.73310i	−0.397480	+	0.498424i	0.542309	+	0.840179i	$0.317550\pi$
$308$	−0.692178	+	4.56156i	−0.0394405	+	0.259919i
$309$		0			0
$310$	−0.172415	+	2.30072i	−0.00979252	+	0.130672i
$311$	2.15425	−	0.664499i	0.122156	−	0.0376803i	−0.233074	−	0.972459i	$-0.574879\pi$
$311$	2.15425	−	0.664499i	0.122156	−	0.0376803i	0.355231	+	0.934779i	$0.384402\pi$
$312$		0			0
$313$	1.65632	−	2.86883i	0.0936206	−	0.162156i	−0.815411	−	0.578882i	$-0.803489\pi$
$313$	1.65632	−	2.86883i	0.0936206	−	0.162156i	0.909032	+	0.416726i	$0.136823\pi$
$314$	2.26981	−	9.94467i	0.128093	−	0.561210i
$315$		0			0
$316$	4.20055	+	18.4038i	0.236299	+	1.03530i
$317$	15.8424	+	4.88673i	0.889797	+	0.274466i	0.705758	−	0.708453i	$-0.250607\pi$
$317$	15.8424	+	4.88673i	0.889797	+	0.274466i	0.184039	+	0.982919i	$0.441083\pi$
$318$		0			0
$319$	−2.36887	+	6.03578i	−0.132631	+	0.337939i
$320$	4.66556	+	1.43913i	0.260813	+	0.0804500i
$321$		0			0
$322$	−3.64124	−	2.90972i	−0.202919	−	0.162152i
$323$	−3.12893	+	13.7087i	−0.174098	+	0.762773i
$324$		0			0
$325$	−0.297294	−	0.514928i	−0.0164909	−	0.0285631i
$326$	−6.59000	+	2.03275i	−0.364986	+	0.112583i
$327$		0			0
$328$	−17.6789	−	22.1686i	−0.976152	−	1.22406i
$329$	−20.0609	−	7.89632i	−1.10599	−	0.435338i
$330$		0			0
$331$	5.85336	+	5.43113i	0.321730	+	0.298522i	0.824458	−	0.565923i	$-0.191480\pi$
$331$	5.85336	+	5.43113i	0.321730	+	0.298522i	−0.502728	+	0.864444i	$0.667670\pi$
$332$	23.1077	+	3.48292i	1.26820	+	0.191150i
$333$		0			0
$334$	−7.66840	+	1.15583i	−0.419596	+	0.0632439i
$335$	15.4691	+	7.44951i	0.845165	+	0.407010i
$336$		0			0
$337$	9.44302	−	4.54752i	0.514394	−	0.247719i	−0.158632	−	0.987338i	$-0.550708\pi$
$337$	9.44302	−	4.54752i	0.514394	−	0.247719i	0.673026	+	0.739619i	$0.264994\pi$
$338$	8.61356	−	5.87263i	0.468516	−	0.319429i
$339$		0			0
$340$	−0.409744	−	5.46765i	−0.0222215	−	0.296525i
$341$	0.997979	+	2.54281i	0.0540436	+	0.137701i
$342$		0			0
$343$	−14.4453	−	11.5903i	−0.779970	−	0.625817i
$344$	−5.30655			−0.286110
$345$		0			0
$346$	0.892863	+	11.9144i	0.0480006	+	0.640524i
$347$	−8.73665	+	8.10642i	−0.469008	+	0.435176i	−0.878934	−	0.476943i	$-0.841745\pi$
$347$	−8.73665	+	8.10642i	−0.469008	+	0.435176i	0.409926	+	0.912119i	$0.365554\pi$
$348$		0			0
$349$	17.7998	−	8.57194i	0.952802	−	0.458845i	0.108134	−	0.994136i	$-0.465512\pi$
$349$	17.7998	−	8.57194i	0.952802	−	0.458845i	0.844668	+	0.535291i	$0.179798\pi$
$350$	4.58964	−	4.93662i	0.245327	−	0.263873i
$351$		0			0
$352$	7.42288	−	1.11882i	0.395641	−	0.0596333i
$353$	1.70438	+	1.16203i	0.0907151	+	0.0618485i	0.607828	−	0.794069i	$-0.292041\pi$
$353$	1.70438	+	1.16203i	0.0907151	+	0.0618485i	−0.517113	+	0.855917i	$0.672993\pi$
$354$		0			0
$355$	1.38557	+	1.28562i	0.0735385	+	0.0682338i
$356$	−1.92942	+	2.41942i	−0.102259	+	0.128229i
$357$		0			0
$358$	6.77614	+	8.49702i	0.358130	+	0.449081i
$359$	0.620663	−	8.28217i	0.0327573	−	0.437116i	−0.956580	−	0.291471i	$-0.905855\pi$
$359$	0.620663	−	8.28217i	0.0327573	−	0.437116i	0.989337	−	0.145645i	$-0.0465257\pi$
$360$		0			0
$361$	−1.53290	−	2.65505i	−0.0806787	−	0.139740i
$362$	−2.64840	+	4.58716i	−0.139197	+	0.241096i
$363$		0			0
$364$	0.524966	+	0.419500i	0.0275157	+	0.0219878i
$365$	−3.99477	−	17.5023i	−0.209096	−	0.916110i
$366$		0			0
$367$	2.85854	−	7.28343i	0.149214	−	0.380192i	−0.836650	−	0.547738i	$-0.815489\pi$
$367$	2.85854	−	7.28343i	0.149214	−	0.380192i	0.985864	+	0.167546i	$0.0535843\pi$
$368$	0.431085	−	1.09839i	0.0224719	−	0.0572574i
$369$		0			0
$370$	1.16160	+	5.08929i	0.0603886	+	0.264580i
$371$	−0.0207441	+	20.8855i	−0.00107698	+	1.08432i
$372$		0			0
$373$	−16.9959	+	29.4378i	−0.880015	+	1.52423i	−0.0286919	+	0.999588i	$0.509134\pi$
$373$	−16.9959	+	29.4378i	−0.880015	+	1.52423i	−0.851323	+	0.524642i	$0.824199\pi$
$374$	1.55068	+	2.68586i	0.0801837	+	0.138882i
$375$		0			0
$376$	−1.64201	+	21.9111i	−0.0846800	+	1.12998i
$377$	0.588814	+	0.738349i	0.0303255	+	0.0380269i
$378$		0			0
$379$	−2.14596	+	2.69095i	−0.110231	+	0.138225i	−0.833886	−	0.551936i	$-0.813889\pi$
$379$	−2.14596	+	2.69095i	−0.110231	+	0.138225i	0.723655	+	0.690161i	$0.242461\pi$
$380$	6.30734	+	5.85236i	0.323560	+	0.300220i
$381$		0			0
$382$	11.3209	+	7.71846i	0.579228	+	0.394911i
$383$	−31.8543	+	4.80126i	−1.62768	+	0.245333i	−0.898494	−	0.438986i	$-0.855338\pi$
$383$	−31.8543	+	4.80126i	−1.62768	+	0.245333i	−0.729183	+	0.684318i	$0.760100\pi$
$384$		0			0
$385$	−1.36428	+	4.40733i	−0.0695299	+	0.224618i
$386$	−15.4271	+	7.42928i	−0.785216	+	0.378140i
$387$		0			0
$388$	14.4490	−	13.4067i	0.733535	−	0.680621i
$389$	0.559740	+	7.46921i	0.0283799	+	0.378704i	0.993251	+	0.115981i	$0.0370013\pi$
$389$	0.559740	+	7.46921i	0.0283799	+	0.378704i	−0.964871	+	0.262722i	$0.915380\pi$
$390$		0			0
$391$	6.55820			0.331662
$392$	−6.93087	+	17.5569i	−0.350062	+	0.886759i
$393$		0			0
$394$	−4.01788	−	10.2374i	−0.202418	−	0.515753i
$395$	1.41065	+	18.8238i	0.0709775	+	0.947129i
$396$		0			0
$397$	2.45948	−	1.67685i	0.123438	−	0.0841585i	−0.500027	−	0.866010i	$-0.666677\pi$
$397$	2.45948	−	1.67685i	0.123438	−	0.0841585i	0.623465	+	0.781851i	$0.285724\pi$
$398$	−0.0212472	+	0.0102321i	−0.00106503	+	0.000512890i
$399$		0			0
$400$	1.53741	+	0.740376i	0.0768703	+	0.0370188i
$401$	15.7193	−	2.36931i	0.784986	−	0.118318i	0.255694	−	0.966758i	$-0.417696\pi$
$401$	15.7193	−	2.36931i	0.784986	−	0.118318i	0.529291	+	0.848440i	$0.322458\pi$
$402$		0			0
$403$	0.393415	+	0.0592978i	0.0195974	+	0.00295383i
$404$	5.40407	+	5.01424i	0.268862	+	0.249468i
$405$		0			0
$406$	−6.03970	+	8.83974i	−0.299745	+	0.438709i
$407$	3.85352	+	4.83216i	0.191012	+	0.239521i
$408$		0			0
$409$	−7.64712	+	2.35882i	−0.378126	+	0.116636i	−0.477991	−	0.878365i	$-0.658635\pi$
$409$	−7.64712	+	2.35882i	−0.378126	+	0.116636i	0.0998655	+	0.995001i	$0.468159\pi$
$410$	−5.72174	−	9.91034i	−0.282576	−	0.489437i
$411$		0			0
$412$	0.760901	−	3.33372i	0.0374869	−	0.164241i
$413$	−7.91652	+	1.79862i	−0.389547	+	0.0885045i
$414$		0			0
$415$	22.3299	+	6.88786i	1.09613	+	0.338112i
$416$	0.399443	−	1.01776i	0.0195843	−	0.0499000i
$417$		0			0
$418$	−4.65062	−	1.43453i	−0.227469	−	0.0701650i
$419$	5.97056	+	26.1588i	0.291681	+	1.27794i	0.882185	+	0.470904i	$0.156072\pi$
$419$	5.97056	+	26.1588i	0.291681	+	1.27794i	−0.590504	+	0.807035i	$0.701071\pi$
$420$		0			0
$421$	−2.83746	+	12.4317i	−0.138289	+	0.605886i	0.857521	+	0.514448i	$0.172003\pi$
$421$	−2.83746	+	12.4317i	−0.138289	+	0.605886i	−0.995811	+	0.0914373i	$0.970854\pi$
$422$	−6.43523	+	11.1461i	−0.313262	+	0.542586i
$423$		0			0
$424$	20.3404	−	6.27419i	0.987819	−	0.304702i
$425$	−0.708752	+	9.45764i	−0.0343795	+	0.458763i
$426$		0			0
$427$	29.6310	−	2.19094i	1.43394	−	0.106027i
$428$	−8.08291	+	10.1356i	−0.390702	+	0.489925i
$429$		0			0
$430$	−2.11771	−	0.319194i	−0.102125	−	0.0153929i
$431$	−11.1293	−	7.58784i	−0.536080	−	0.365493i	0.264814	−	0.964300i	$-0.414690\pi$
$431$	−11.1293	−	7.58784i	−0.536080	−	0.365493i	−0.800894	+	0.598806i	$0.795642\pi$
$432$		0			0
$433$	−25.3187	−	12.1929i	−1.21674	−	0.585952i	−0.288339	−	0.957528i	$-0.593103\pi$
$433$	−25.3187	−	12.1929i	−1.21674	−	0.585952i	−0.928402	+	0.371577i	$0.878817\pi$
$434$	0.667800	+	4.46062i	0.0320554	+	0.214117i
$435$		0			0
$436$	−10.7249	+	7.31211i	−0.513630	+	0.350187i
$437$	−7.54422	+	7.00001i	−0.360889	+	0.334856i
$438$		0			0
$439$	0.945958	+	2.41026i	0.0451481	+	0.115036i	0.951669	−	0.307125i	$-0.0993670\pi$
$439$	0.945958	+	2.41026i	0.0451481	+	0.115036i	−0.906521	+	0.422161i	$0.861272\pi$
$440$	4.70214			0.224166
$441$		0			0
$442$	0.451708			0.0214856
$443$	0.663795	+	1.69132i	0.0315379	+	0.0803572i	0.945775	−	0.324822i	$-0.105304\pi$
$443$	0.663795	+	1.69132i	0.0315379	+	0.0803572i	−0.914237	+	0.405179i	$0.867209\pi$
$444$		0			0
$445$	−2.26841	+	2.10478i	−0.107533	+	0.0997759i
$446$	4.58933	−	3.12895i	0.217311	−	0.148160i
$447$		0			0
$448$	9.51743	+	0.722740i	0.449656	+	0.0341462i
$449$	−23.2903	−	11.2160i	−1.09914	−	0.529317i	−0.205751	−	0.978604i	$-0.565964\pi$
$449$	−23.2903	−	11.2160i	−1.09914	−	0.529317i	−0.893387	+	0.449287i	$0.851678\pi$
$450$		0			0
$451$	−11.1945	−	7.63231i	−0.527131	−	0.359392i
$452$	25.7414	+	3.87989i	1.21077	+	0.182495i
$453$		0			0
$454$	−11.4916	+	14.4100i	−0.539329	+	0.676297i
$455$	0.456567	+	0.493044i	0.0214042	+	0.0231143i
$456$		0			0
$457$	0.348328	−	4.64812i	0.0162941	−	0.217430i	−0.983113	−	0.183000i	$-0.941419\pi$
$457$	0.348328	−	4.64812i	0.0162941	−	0.217430i	0.999407	−	0.0344302i	$-0.0109616\pi$
$458$	−0.222816	+	0.0687295i	−0.0104115	+	0.00321152i
$459$		0			0
$460$	2.00651	−	3.47538i	0.0935541	−	0.162040i
$461$	5.81447	−	25.4748i	0.270807	−	1.18648i	−0.638257	−	0.769824i	$-0.720344\pi$
$461$	5.81447	−	25.4748i	0.270807	−	1.18648i	0.909063	−	0.416658i	$-0.136799\pi$
$462$		0			0
$463$	−2.65090	−	11.6144i	−0.123198	−	0.539765i	−0.998428	−	0.0560573i	$-0.982147\pi$
$463$	−2.65090	−	11.6144i	−0.123198	−	0.539765i	0.875230	−	0.483707i	$-0.160710\pi$
$464$	−2.58985	−	0.798864i	−0.120231	−	0.0370864i
$465$		0			0
$466$	−2.18007	+	5.55472i	−0.100990	+	0.257318i
$467$	14.8926	+	4.59375i	0.689146	+	0.212573i	0.619498	−	0.784998i	$-0.287336\pi$
$467$	14.8926	+	4.59375i	0.689146	+	0.212573i	0.0696480	+	0.997572i	$0.477812\pi$
$468$		0			0
$469$	32.7157	+	7.50135i	1.51067	+	0.346380i
$470$	−1.97325	+	8.64539i	−0.0910194	+	0.398782i
$471$		0			0
$472$	4.13699	+	7.16548i	0.190420	+	0.329818i
$473$	−2.42299	+	0.747394i	−0.111409	+	0.0343652i
$474$		0			0
$475$	−9.27947	−	11.6361i	−0.425771	−	0.533900i
$476$	−3.14924	−	10.2457i	−0.144345	−	0.469611i
$477$		0			0
$478$	5.93096	+	5.50312i	0.271276	+	0.251707i
$479$	−34.4336	−	5.19003i	−1.57331	−	0.237139i	−0.696351	−	0.717701i	$-0.745194\pi$
$479$	−34.4336	−	5.19003i	−1.57331	−	0.237139i	−0.876960	+	0.480563i	$0.840432\pi$
$480$		0			0
$481$	0.890136	−	0.134166i	0.0405867	−	0.00611746i
$482$	4.26255	+	2.05274i	0.194154	+	0.0934995i
$483$		0			0
$484$	−11.3889	+	5.48459i	−0.517676	+	0.249300i
$485$	16.2853	−	11.1031i	0.739478	−	0.504168i
$486$		0			0
$487$	−1.40347	−	18.7280i	−0.0635973	−	0.848647i	−0.934220	−	0.356696i	$-0.883903\pi$
$487$	−1.40347	−	18.7280i	−0.0635973	−	0.848647i	0.870623	−	0.491950i	$-0.163716\pi$
$488$	−11.0632	−	28.1885i	−0.500806	−	1.27603i
$489$		0			0
$490$	−3.82200	+	6.58964i	−0.172661	+	0.297690i
$491$	−23.9410			−1.08044			−0.540220	−	0.841524i	$-0.681659\pi$
$491$	−23.9410			−1.08044			−0.540220	+	0.841524i	$0.681659\pi$
$492$		0			0
$493$	−1.12571	−	15.0216i	−0.0506995	−	0.676538i
$494$	−0.519623	+	0.482139i	−0.0233789	+	0.0216925i
$495$		0			0
$496$	−1.02873	+	0.495411i	−0.0461914	+	0.0222446i
$497$	3.19819	+	1.85071i	0.143458	+	0.0830159i
$498$		0			0
$499$	−10.3992	+	1.56743i	−0.465532	+	0.0701677i	−0.377620	−	0.925961i	$-0.623257\pi$
$499$	−10.3992	+	1.56743i	−0.465532	+	0.0701677i	−0.0879119	+	0.996128i	$0.528019\pi$
$500$	12.3621	+	8.42834i	0.552850	+	0.376927i
$501$		0			0
$502$	9.03807	+	8.38610i	0.403389	+	0.374290i
$503$	9.12194	−	11.4385i	0.406727	−	0.510020i	−0.535711	−	0.844402i	$-0.679956\pi$
$503$	9.12194	−	11.4385i	0.406727	−	0.510020i	0.942438	+	0.334382i	$0.108528\pi$
$504$		0			0
$505$	4.59626	+	5.76352i	0.204531	+	0.256473i
$506$	−0.169630	+	2.26356i	−0.00754098	+	0.100627i
$507$		0			0
$508$	−8.02028	−	13.8915i	−0.355842	−	0.616337i
$509$	−8.51507	+	14.7485i	−0.377424	+	0.653717i	−0.990687	−	0.136162i	$-0.956523\pi$
$509$	−8.51507	+	14.7485i	−0.377424	+	0.653717i	0.613263	+	0.789879i	$0.289857\pi$
$510$		0			0
$511$	−15.1959	−	31.6350i	−0.672227	−	1.39945i
$512$	1.34453	+	5.89079i	0.0594205	+	0.260338i
$513$		0			0
$514$	5.50009	−	14.0140i	0.242598	−	0.618131i
$515$	1.24924	−	3.18300i	0.0550479	−	0.140260i
$516$		0			0
$517$	2.33629	+	10.2359i	0.102750	+	0.450176i
$518$	4.41866	+	9.19880i	0.194145	+	0.404172i
$519$		0			0
$520$	0.342430	−	0.593106i	0.0150165	−	0.0260094i
$521$	9.69558	+	16.7932i	0.424771	+	0.735725i	0.996399	−	0.0847880i	$-0.0270213\pi$
$521$	9.69558	+	16.7932i	0.424771	+	0.735725i	−0.571628	+	0.820513i	$0.693688\pi$
$522$		0			0
$523$	−2.88649	+	38.5175i	−0.126217	+	1.68425i	0.470968	+	0.882150i	$0.343905\pi$
$523$	−2.88649	+	38.5175i	−0.126217	+	1.68425i	−0.597185	+	0.802103i	$0.703714\pi$
$524$	0.842722	+	1.05674i	0.0368145	+	0.0461639i
$525$		0			0
$526$	−11.9926	+	15.0383i	−0.522903	+	0.655700i
$527$	−4.65208	−	4.31650i	−0.202648	−	0.188029i
$528$		0			0
$529$	−15.0376	−	10.2524i	−0.653807	−	0.445758i
$530$	8.49476	−	1.28038i	0.368989	−	0.0556161i
$531$		0			0
$532$	14.5587	+	8.42475i	0.631199	+	0.365259i
$533$	−1.77794	+	0.856210i	−0.0770111	+	0.0370866i
$534$		0			0
$535$	−9.50302	+	8.81751i	−0.410851	+	0.381214i
$536$	−2.55640	−	34.1128i	−0.110420	−	1.47345i
$537$		0			0
$538$	−17.9284			−0.772949
$539$	−0.691879	+	8.99274i	−0.0298014	+	0.387345i
$540$		0			0
$541$	−11.0871	−	28.2494i	−0.476671	−	1.21454i	−0.943850	−	0.330374i	$-0.892825\pi$
$541$	−11.0871	−	28.2494i	−0.476671	−	1.21454i	0.467179	−	0.884163i	$-0.345270\pi$
$542$	0.699106	+	9.32892i	0.0300292	+	0.400712i
$543$		0			0
$544$	−14.4094	+	9.82414i	−0.617797	+	0.421207i
$545$	−11.6946	+	5.63183i	−0.500942	+	0.241241i
$546$		0			0
$547$	−0.735986	−	0.354432i	−0.0314685	−	0.0151544i	0.418083	−	0.908409i	$-0.362702\pi$
$547$	−0.735986	−	0.354432i	−0.0314685	−	0.0151544i	−0.449552	+	0.893254i	$0.648416\pi$
$548$	30.7258	−	4.63116i	1.31254	−	0.197833i
$549$		0			0
$550$	−3.24596	−	0.489250i	−0.138408	−	0.0208617i
$551$	17.3285	+	16.0785i	0.738220	+	0.684968i
$552$		0			0
$553$	10.8421	+	35.2736i	0.461053	+	1.49998i
$554$	−0.539160	−	0.676085i	−0.0229067	−	0.0287241i
$555$		0			0
$556$	−0.281612	+	0.0868658i	−0.0119430	+	0.00368393i
$557$	−17.5977	−	30.4801i	−0.745637	−	1.29148i	−0.949897	−	0.312565i	$-0.898812\pi$
$557$	−17.5977	−	30.4801i	−0.745637	−	1.29148i	0.204259	−	0.978917i	$-0.434521\pi$
$558$		0			0
$559$	−0.0821798	+	0.360053i	−0.00347584	+	0.0152286i
$560$	−1.87970	−	0.430993i	−0.0794317	−	0.0182128i
$561$		0			0
$562$	−17.6148	−	5.43344i	−0.743035	−	0.229196i
$563$	−7.20470	+	18.3573i	−0.303642	+	0.773667i	0.694870	+	0.719135i	$0.255462\pi$
$563$	−7.20470	+	18.3573i	−0.303642	+	0.773667i	−0.998512	+	0.0545318i	$0.982633\pi$
$564$		0			0
$565$	24.8750	+	7.67291i	1.04650	+	0.322802i
$566$	−3.54606	−	15.5363i	−0.149052	−	0.653039i
$567$		0			0
$568$	0.838001	−	3.67152i	0.0351617	−	0.154054i
$569$	10.4591	−	18.1157i	0.438468	−	0.759448i	−0.559104	−	0.829098i	$-0.688855\pi$
$569$	10.4591	−	18.1157i	0.438468	−	0.759448i	0.997572	+	0.0696494i	$0.0221881\pi$
$570$		0			0
$571$	40.1707	−	12.3910i	1.68109	−	0.518548i	0.700341	−	0.713809i	$-0.253031\pi$
$571$	40.1707	−	12.3910i	1.68109	−	0.518548i	0.980751	+	0.195260i	$0.0625551\pi$
$572$	0.0244559	−	0.326342i	0.00102255	−	0.0136450i
$573$		0			0
$574$	−15.1999	−	16.4142i	−0.634431	−	0.685118i
$575$	−4.32796	+	5.42709i	−0.180488	+	0.226325i
$576$		0			0
$577$	−23.6485	−	3.56444i	−0.984502	−	0.148390i	−0.362989	−	0.931794i	$-0.618244\pi$
$577$	−23.6485	−	3.56444i	−0.984502	−	0.148390i	−0.621513	+	0.783404i	$0.713482\pi$
$578$	5.34134	+	3.64166i	0.222170	+	0.151473i
$579$		0			0
$580$	−8.30479	−	3.99938i	−0.344838	−	0.166065i
$581$	45.5515	+	3.45912i	1.88980	+	0.143508i
$582$		0			0
$583$	8.40384	−	5.72964i	0.348052	−	0.237298i
$584$	−26.2202	+	24.3288i	−1.08500	+	1.00673i
$585$		0			0
$586$	3.59304	+	9.15491i	0.148427	+	0.378186i
$587$	13.7386			0.567053			0.283526	−	0.958964i	$-0.408496\pi$
$587$	13.7386			0.567053			0.283526	+	0.958964i	$0.408496\pi$
$588$		0			0
$589$	9.95880			0.410345
$590$	1.21996	+	3.10841i	0.0502250	+	0.127971i
$591$		0			0
$592$	−1.89379	+	1.75718i	−0.0778343	+	0.0722197i
$593$	18.4223	−	12.5601i	0.756512	−	0.515781i	−0.122565	−	0.992460i	$-0.539112\pi$
$593$	18.4223	−	12.5601i	0.756512	−	0.515781i	0.879077	+	0.476679i	$0.158160\pi$
$594$		0			0
$595$	−1.58698	−	10.6004i	−0.0650599	−	0.434572i
$596$	−17.6915	−	8.51979i	−0.724673	−	0.348984i
$597$		0			0
$598$	0.273161	+	0.186238i	0.0111704	+	0.00761584i
$599$	10.9853	+	1.65576i	0.448846	+	0.0676526i	0.369576	−	0.929201i	$-0.379503\pi$
$599$	10.9853	+	1.65576i	0.448846	+	0.0676526i	0.0792699	+	0.996853i	$0.474741\pi$
$600$		0			0
$601$	17.5693	−	22.0312i	0.716665	−	0.898670i	−0.281479	−	0.959567i	$-0.590825\pi$
$601$	17.5693	−	22.0312i	0.716665	−	0.898670i	0.998144	+	0.0608976i	$0.0193963\pi$
$602$	−4.17532	+	0.308727i	−0.170173	+	0.0125828i
$603$		0			0
$604$	−1.80442	+	24.0784i	−0.0734210	+	0.979735i
$605$	−12.0788	+	3.72581i	−0.491073	+	0.151476i
$606$		0			0
$607$	−3.99431	+	6.91835i	−0.162124	+	0.280807i	−0.935630	−	0.352982i	$-0.885168\pi$
$607$	−3.99431	+	6.91835i	−0.162124	+	0.280807i	0.773506	+	0.633789i	$0.218501\pi$
$608$	6.08983	−	26.6813i	0.246975	−	1.08207i
$609$		0			0
$610$	−2.71947	−	11.9148i	−0.110108	−	0.482415i
$611$	1.46125	+	0.450737i	0.0591159	+	0.0182349i
$612$		0			0
$613$	−2.01207	+	5.12667i	−0.0812667	+	0.207064i	−0.965732	−	0.259542i	$-0.916428\pi$
$613$	−2.01207	+	5.12667i	−0.0812667	+	0.207064i	0.884465	+	0.466606i	$0.154524\pi$
$614$	8.58284	+	2.64746i	0.346375	+	0.106843i
$615$		0			0
$616$	8.96386	−	2.03658i	0.361164	−	0.0820560i
$617$	5.59395	−	24.5087i	0.225204	−	0.986683i	−0.728289	−	0.685270i	$-0.759684\pi$
$617$	5.59395	−	24.5087i	0.225204	−	0.986683i	0.953493	−	0.301414i	$-0.0974585\pi$
$618$		0			0
$619$	−22.4733	−	38.9249i	−0.903279	−	1.56453i	−0.823211	−	0.567736i	$-0.807820\pi$
$619$	−22.4733	−	38.9249i	−0.903279	−	1.56453i	−0.0800680	−	0.996789i	$-0.525514\pi$
$620$	−3.71076	+	1.14462i	−0.149028	+	0.0459690i
$621$		0			0
$622$	−1.13025	−	1.41729i	−0.0453189	−	0.0568281i
$623$	−3.41273	+	4.99490i	−0.136728	+	0.200116i
$624$		0			0
$625$	−0.645290	−	0.598742i	−0.0258116	−	0.0239497i
$626$	−2.63395	−	0.397004i	−0.105274	−	0.0158675i
$627$		0			0
$628$	16.9770	−	2.55886i	0.677454	−	0.102110i
$629$	−12.9368	−	6.23004i	−0.515824	−	0.248408i
$630$		0			0
$631$	−5.58329	+	2.68877i	−0.222267	+	0.107038i	−0.541704	−	0.840569i	$-0.682221\pi$
$631$	−5.58329	+	2.68877i	−0.222267	+	0.107038i	0.319437	+	0.947608i	$0.396506\pi$
$632$	31.0748	−	21.1865i	1.23609	−	0.842752i
$633$		0			0
$634$	−0.996241	−	13.2939i	−0.0395658	−	0.527969i
$635$	−5.86012	−	14.9313i	−0.232552	−	0.592532i
$636$		0			0
$637$	1.08392	+	0.742160i	0.0429463	+	0.0294055i
$638$	5.21380			0.206416
$639$		0			0
$640$	0.885085	+	11.8106i	0.0349860	+	0.466856i
$641$	−28.2680	+	26.2288i	−1.11652	+	1.03598i	−0.117438	+	0.993080i	$0.537468\pi$
$641$	−28.2680	+	26.2288i	−1.11652	+	1.03598i	−0.999080	+	0.0428965i	$0.986341\pi$
$642$		0			0
$643$	−23.1540	+	11.1504i	−0.913105	+	0.439728i	−0.830604	−	0.556863i	$-0.812005\pi$
$643$	−23.1540	+	11.1504i	−0.913105	+	0.439728i	−0.0825005	+	0.996591i	$0.526291\pi$
$644$	2.31984	−	7.49430i	0.0914145	−	0.295317i
$645$		0			0
$646$	11.1804	−	1.68518i	0.439888	−	0.0663024i
$647$	11.5770	+	7.89309i	0.455140	+	0.310309i	0.769102	−	0.639126i	$-0.220704\pi$
$647$	11.5770	+	7.89309i	0.455140	+	0.310309i	−0.313962	+	0.949436i	$0.601656\pi$
$648$		0			0
$649$	2.89818	+	2.68912i	0.113763	+	0.105557i
$650$	−0.298097	+	0.373801i	−0.0116923	+	0.0146617i
$651$		0			0
$652$	−7.23720	−	9.07517i	−0.283431	−	0.355411i
$653$	1.76323	−	23.5286i	0.0690004	−	0.920746i	−0.850074	−	0.526663i	$-0.823443\pi$
$653$	1.76323	−	23.5286i	0.0690004	−	0.920746i	0.919075	−	0.394084i	$-0.128938\pi$
$654$		0			0
$655$	0.675793	+	1.17051i	0.0264054	+	0.0457355i
$656$	2.83165	−	4.90457i	0.110557	−	0.191491i
$657$		0			0
$658$	−0.0172183	+	17.3357i	−0.000671239	+	0.675815i
$659$	−8.56561	−	37.5284i	−0.333669	−	1.46190i	−0.811968	−	0.583702i	$-0.801604\pi$
$659$	−8.56561	−	37.5284i	−0.333669	−	1.46190i	0.478299	−	0.878197i	$-0.341254\pi$
$660$		0			0
$661$	−18.2976	+	46.6215i	−0.711693	+	1.81336i	−0.145007	+	0.989431i	$0.546320\pi$
$661$	−18.2976	+	46.6215i	−0.711693	+	1.81336i	−0.566686	+	0.823934i	$0.691775\pi$
$662$	2.34575	−	5.97687i	0.0911701	−	0.232298i
$663$		0			0
$664$	−10.3603	−	45.3915i	−0.402058	−	1.76153i
$665$	13.1401	+	10.5002i	0.509550	+	0.407181i
$666$		0			0
$667$	5.51260	−	9.54811i	0.213449	−	0.369704i
$668$	−6.52638	−	11.3040i	−0.252513	−	0.437366i
$669$		0			0
$670$	1.03172	−	13.7673i	0.0398588	−	0.531879i
$671$	−9.02165	−	11.3128i	−0.348277	−	0.436725i
$672$		0			0
$673$	−0.241703	+	0.303086i	−0.00931697	+	0.0116831i	−0.786468	−	0.617631i	$-0.788093\pi$
$673$	−0.241703	+	0.303086i	−0.00931697	+	0.0116831i	0.777151	+	0.629314i	$0.216664\pi$
$674$	−6.17800	−	5.73234i	−0.237968	−	0.220802i
$675$		0			0
$676$	14.4978	+	9.88444i	0.557608	+	0.380171i
$677$	−15.0492	+	2.26831i	−0.578389	+	0.0871781i	−0.431720	−	0.902008i	$-0.642093\pi$
$677$	−15.0492	+	2.26831i	−0.578389	+	0.0871781i	−0.146669	+	0.989186i	$0.546855\pi$
$678$		0			0
$679$	26.2363	−	28.2198i	1.00686	−	1.08298i
$680$	−9.84225	+	4.73978i	−0.377433	+	0.181762i
$681$		0			0
$682$	1.61016	−	1.49401i	0.0616563	−	0.0572087i
$683$	−3.56389	−	47.5568i	−0.136368	−	1.81971i	−0.476325	−	0.879269i	$-0.658031\pi$
$683$	−3.56389	−	47.5568i	−0.136368	−	1.81971i	0.339957	−	0.940441i	$-0.389588\pi$
$684$		0			0
$685$	31.0720			1.18720
$686$	−4.43194	+	14.2174i	−0.169212	+	0.542825i
$687$		0			0
$688$	−0.387218	−	0.986616i	−0.0147626	−	0.0376144i
$689$	−0.110707	−	1.47728i	−0.00421759	−	0.0562798i
$690$		0			0
$691$	−16.3738	+	11.1635i	−0.622890	+	0.424679i	−0.833212	−	0.552953i	$-0.813501\pi$
$691$	−16.3738	+	11.1635i	−0.622890	+	0.424679i	0.210323	+	0.977632i	$0.432549\pi$
$692$	−18.1184	+	8.72534i	−0.688757	+	0.331688i
$693$		0			0
$694$	8.63440	+	4.15811i	0.327757	+	0.157840i
$695$	−0.291406	+	0.0439223i	−0.0110536	+	0.00166607i
$696$		0			0
$697$	31.1252	+	4.69137i	1.17895	+	0.177698i
$698$	−11.6453	−	10.8053i	−0.440783	−	0.408987i
$699$		0			0
$700$	10.5569	+	4.15538i	0.399013	+	0.157059i
$701$	−13.4953	−	16.9226i	−0.509710	−	0.639156i	0.458679	−	0.888602i	$-0.348323\pi$
$701$	−13.4953	−	16.9226i	−0.509710	−	0.639156i	−0.968389	+	0.249446i	$0.919751\pi$
$702$		0			0
$703$	21.5316	−	6.64162i	0.812079	−	0.250493i
$704$	−2.32415	−	4.02555i	−0.0875949	−	0.151719i
$705$		0			0
$706$	0.369100	−	1.61713i	0.0138913	−	0.0608617i
$707$	11.2583	+	8.99649i	0.423411	+	0.338348i
$708$		0			0
$709$	18.1392	+	5.59521i	0.681233	+	0.210133i	0.616010	−	0.787738i	$-0.288748\pi$
$709$	18.1392	+	5.59521i	0.681233	+	0.210133i	0.0652230	+	0.997871i	$0.479224\pi$
$710$	0.555271	−	1.41481i	0.0208389	−	0.0530968i
$711$		0			0
$712$	5.89155	+	1.81730i	0.220795	+	0.0681063i
$713$	−1.03357	−	4.52835i	−0.0387073	−	0.169588i
$714$		0			0
$715$	0.0728196	−	0.319044i	0.00272330	−	0.0119316i
$716$	−9.14625	+	15.8418i	−0.341811	+	0.592035i
$717$		0			0
$718$	−6.38169	+	1.96849i	−0.238163	+	0.0734634i
$719$	−3.55591	+	47.4503i	−0.132613	+	1.76960i	0.393634	+	0.919267i	$0.371218\pi$
$719$	−3.55591	+	47.4503i	−0.132613	+	1.76960i	−0.526247	+	0.850332i	$0.676401\pi$
$720$		0			0
$721$	1.00285	−	6.60893i	0.0373481	−	0.246129i
$722$	−1.53704	+	1.92738i	−0.0572025	+	0.0717297i
$723$		0			0
$724$	−8.81565	−	1.32875i	−0.327631	−	0.0493825i
$725$	13.1737	+	8.98166i	0.489258	+	0.333570i
$726$		0			0
$727$	13.4492	+	6.47678i	0.498802	+	0.240210i	0.666330	−	0.745657i	$-0.267864\pi$
$727$	13.4492	+	6.47678i	0.498802	+	0.240210i	−0.167528	+	0.985867i	$0.553579\pi$
$728$	0.395902	−	1.27897i	0.0146731	−	0.0474018i
$729$		0			0
$730$	−11.9272	+	8.13184i	−0.441446	+	0.300973i
$731$	4.31829	−	4.00679i	0.159718	−	0.148196i
$732$		0			0
$733$	−13.0422	−	33.2310i	−0.481725	−	1.22741i	−0.940783	−	0.339008i	$-0.889908\pi$
$733$	−13.0422	−	33.2310i	−0.481725	−	1.22741i	0.459059	−	0.888406i	$-0.348187\pi$
$734$	−6.29155			−0.232225
$735$		0			0
$736$	−12.7642			−0.470496
$737$	−5.97184	−	15.2160i	−0.219975	−	0.560488i
$738$		0			0
$739$	−21.3776	+	19.8355i	−0.786388	+	0.729661i	−0.967244	−	0.253848i	$-0.918304\pi$
$739$	−21.3776	+	19.8355i	−0.786388	+	0.729661i	0.180856	+	0.983510i	$0.442113\pi$
$740$	−7.25956	+	4.94948i	−0.266867	+	0.181947i
$741$		0			0
$742$	15.6393	−	6.12006i	0.574137	−	0.224674i
$743$	−9.37912	−	4.51675i	−0.344087	−	0.165703i	0.253857	−	0.967242i	$-0.418301\pi$
$743$	−9.37912	−	4.51675i	−0.344087	−	0.165703i	−0.597943	+	0.801538i	$0.704015\pi$
$744$		0			0
$745$	−16.2237	−	11.0611i	−0.594390	−	0.405248i
$746$	27.0277	+	4.07376i	0.989553	+	0.149151i
$747$		0			0
$748$	−3.25463	+	4.08117i	−0.119001	+	0.149222i
$749$	−14.2969	+	20.9251i	−0.522398	+	0.764585i
$750$		0			0
$751$	2.48862	−	33.2084i	0.0908112	−	1.21179i	−0.746621	−	0.665250i	$-0.768325\pi$
$751$	2.48862	−	33.2084i	0.0908112	−	1.21179i	0.837432	−	0.546541i	$-0.184056\pi$
$752$	−4.19361	+	1.29356i	−0.152925	+	0.0471712i
$753$		0			0
$754$	0.379691	−	0.657645i	0.0138275	−	0.0239500i
$755$	−5.37282	+	23.5399i	−0.195537	+	0.856704i
$756$		0			0
$757$	3.16987	+	13.8881i	0.115211	+	0.504772i	0.999298	+	0.0374507i	$0.0119237\pi$
$757$	3.16987	+	13.8881i	0.115211	+	0.504772i	−0.884088	+	0.467321i	$0.845219\pi$
$758$	2.64465	+	0.815768i	0.0960582	+	0.0296300i
$759$		0			0
$760$	6.26294	−	15.9577i	0.227181	−	0.578847i
$761$	35.6567	+	10.9986i	1.29256	+	0.398701i	0.863396	−	0.504528i	$-0.168333\pi$
$761$	35.6567	+	10.9986i	1.29256	+	0.398701i	0.429160	+	0.903228i	$0.358810\pi$
$762$		0			0
$763$	−19.8546	+	15.8013i	−0.718786	+	0.572046i
$764$	−5.13175	+	22.4837i	−0.185660	+	0.813431i
$765$		0			0
$766$	12.9517	+	22.4331i	0.467965	+	0.810539i
$767$	0.550250	−	0.169730i	0.0198684	−	0.00612858i
$768$		0			0
$769$	17.2379	+	21.6156i	0.621613	+	0.779478i	0.988570	−	0.150760i	$-0.0481720\pi$
$769$	17.2379	+	21.6156i	0.621613	+	0.779478i	−0.366958	+	0.930238i	$0.619601\pi$
$770$	3.69975	−	0.273563i	0.133330	−	0.00985853i
$771$		0			0
$772$	−21.1265	−	19.6025i	−0.760359	−	0.705510i
$773$	−35.4003	−	5.33574i	−1.27326	−	0.191913i	−0.522587	−	0.852586i	$-0.675033\pi$
$773$	−35.4003	−	5.33574i	−1.27326	−	0.191913i	−0.750674	+	0.660673i	$0.770271\pi$
$774$		0			0
$775$	6.64207	−	1.00113i	0.238590	−	0.0359617i
$776$	−35.3818	−	17.0390i	−1.27013	−	0.611663i
$777$		0			0
$778$	5.42641	−	2.61322i	0.194546	−	0.0936885i
$779$	−40.8123	+	27.8253i	−1.46225	+	0.996946i
$780$		0			0
$781$	−0.134476	−	1.79446i	−0.00481193	−	0.0642108i
$782$	−1.92661	−	4.90893i	−0.0688956	−	0.175543i
$783$		0			0
$784$	−3.77000	−	0.00748896i	−0.134643	−	0.000267463i
$785$	17.1683			0.612762
$786$		0			0
$787$	3.47399	+	46.3571i	0.123834	+	1.65245i	0.620277	+	0.784383i	$0.287020\pi$
$787$	3.47399	+	46.3571i	0.123834	+	1.65245i	−0.496442	+	0.868070i	$0.665361\pi$
$788$	13.5692	−	12.5904i	0.483382	−	0.448513i
$789$		0			0
$790$	13.6756	−	6.58581i	0.486555	−	0.234313i
$791$	50.7433	+	3.85337i	1.80422	+	0.137010i
$792$		0			0
$793$	−2.08394	+	0.314103i	−0.0740028	+	0.0111541i
$794$	−1.97768	−	1.34836i	−0.0701852	−	0.0478514i
$795$		0			0
$796$	−0.0290969	−	0.0269980i	−0.00103131	−	0.000956917i
$797$	2.44468	−	3.06553i	0.0865949	−	0.108587i	−0.736647	−	0.676278i	$-0.763592\pi$
$797$	2.44468	−	3.06553i	0.0865949	−	0.108587i	0.823241	+	0.567691i	$0.192163\pi$
$798$		0			0
$799$	−15.2081	−	19.0703i	−0.538022	−	0.674659i
$800$	1.37945	−	18.4074i	0.0487708	−	0.650801i
$801$		0			0
$802$	−6.39137	−	11.0702i	−0.225687	−	0.390902i
$803$	−8.54568	+	14.8016i	−0.301570	+	0.522335i
$804$		0			0
$805$	3.41081	−	7.06465i	0.120215	−	0.248996i
$806$	−0.0711889	−	0.311899i	−0.00250752	−	0.0109862i
$807$		0			0
$808$	5.36602	−	13.6724i	0.188776	−	0.480994i
$809$	−15.5848	+	39.7095i	−0.547934	+	1.39611i	0.341861	+	0.939751i	$0.388943\pi$
$809$	−15.5848	+	39.7095i	−0.547934	+	1.39611i	−0.889795	+	0.456361i	$0.849152\pi$
$810$		0			0
$811$	3.01042	+	13.1895i	0.105710	+	0.463147i	0.999881	+	0.0154210i	$0.00490884\pi$
$811$	3.01042	+	13.1895i	0.105710	+	0.463147i	−0.894171	+	0.447726i	$0.852234\pi$
$812$	−17.5639	−	4.02721i	−0.616373	−	0.141327i
$813$		0			0
$814$	2.48491	−	4.30399i	0.0870960	−	0.150855i
$815$	−5.80363	−	10.0522i	−0.203292	−	0.352113i
$816$		0			0
$817$	−0.690825	+	9.21841i	−0.0241689	+	0.322512i
$818$	4.01214	+	5.03106i	0.140281	+	0.175907i
$819$		0			0
$820$	12.0090	−	15.0588i	0.419372	−	0.525876i
$821$	6.02215	+	5.58774i	0.210174	+	0.195013i	0.778235	−	0.627974i	$-0.216115\pi$
$821$	6.02215	+	5.58774i	0.210174	+	0.195013i	−0.568060	+	0.822987i	$0.692306\pi$
$822$		0			0
$823$	3.51974	+	2.39972i	0.122690	+	0.0836490i	0.623111	−	0.782134i	$-0.285869\pi$
$823$	3.51974	+	2.39972i	0.122690	+	0.0836490i	−0.500420	+	0.865783i	$0.666821\pi$
$824$	−6.73670	+	1.01539i	−0.234684	+	0.0353729i
$825$		0			0
$826$	3.67196	+	5.39728i	0.127764	+	0.187795i
$827$	25.5213	−	12.2904i	0.887462	−	0.427379i	0.0661177	−	0.997812i	$-0.478939\pi$
$827$	25.5213	−	12.2904i	0.887462	−	0.427379i	0.821344	+	0.570433i	$0.193224\pi$
$828$		0			0
$829$	−34.1108	+	31.6502i	−1.18472	+	1.09926i	−0.191678	+	0.981458i	$0.561393\pi$
$829$	−34.1108	+	31.6502i	−1.18472	+	1.09926i	−0.993038	+	0.117798i	$0.962417\pi$
$830$	−1.40420	−	18.7378i	−0.0487407	−	0.650399i
$831$		0			0
$832$	−0.677019			−0.0234714
$833$	−7.61652	−	19.5205i	−0.263897	−	0.676345i
$834$		0			0
$835$	−4.76858	−	12.1502i	−0.165024	−	0.420473i
$836$	−0.612157	−	8.16866i	−0.0211719	−	0.282519i
$837$		0			0
$838$	17.8263	−	12.1538i	0.615801	−	0.419846i
$839$	27.2173	−	13.1072i	0.939647	−	0.452510i	0.0996020	−	0.995027i	$-0.468243\pi$
$839$	27.2173	−	13.1072i	0.939647	−	0.452510i	0.840045	+	0.542517i	$0.182529\pi$
$840$		0			0
$841$	3.31187	+	1.59491i	0.114202	+	0.0549970i
$842$	10.1390	−	1.52820i	0.349412	−	0.0526653i
$843$		0			0
$844$	−21.4208	−	3.22867i	−0.737335	−	0.111135i
$845$	12.8623	+	11.9345i	0.442478	+	0.410560i
$846$		0			0
$847$	−21.4125	+	12.3342i	−0.735743	+	0.423807i
$848$	2.65076	+	3.32395i	0.0910275	+	0.114145i
$849$		0			0
$850$	7.28743	−	2.24788i	0.249957	−	0.0771015i
$851$	−5.25463	−	9.10129i	−0.180127	−	0.311988i
$852$		0			0
$853$	2.91443	−	12.7689i	0.0997881	−	0.437200i	−0.900210	−	0.435455i	$-0.856587\pi$
$853$	2.91443	−	12.7689i	0.0997881	−	0.437200i	0.999998	−	0.00174493i	$-0.000555427\pi$
$854$	−10.3447	−	21.5357i	−0.353989	−	0.736937i
$855$		0			0
$856$	24.6814	+	7.61321i	0.843593	+	0.260214i
$857$	6.52127	−	16.6159i	0.222762	−	0.567589i	−0.775178	−	0.631743i	$-0.782340\pi$
$857$	6.52127	−	16.6159i	0.222762	−	0.567589i	0.997940	+	0.0641542i	$0.0204350\pi$
$858$		0			0
$859$	−23.2206	−	7.16262i	−0.792278	−	0.244385i	−0.127905	−	0.991786i	$-0.540825\pi$
$859$	−23.2206	−	7.16262i	−0.792278	−	0.244385i	−0.664373	+	0.747401i	$0.731301\pi$
$860$	−0.802113	−	3.51429i	−0.0273518	−	0.119836i
$861$		0			0
$862$	−2.41016	+	10.5596i	−0.0820904	+	0.359661i
$863$	7.17397	−	12.4257i	0.244205	−	0.422975i	−0.717703	−	0.696349i	$-0.754806\pi$
$863$	7.17397	−	12.4257i	0.244205	−	0.422975i	0.961908	+	0.273374i	$0.0881397\pi$
$864$		0			0
$865$	−19.2159	+	5.92733i	−0.653361	+	0.201535i
$866$	−1.68865	+	22.5335i	−0.0573827	+	0.765719i
$867$		0			0
$868$	−6.57821	+	3.78922i	−0.223279	+	0.128615i
$869$	11.2049	−	14.0505i	0.380101	−	0.476631i
$870$		0			0
$871$	−2.35417	−	0.354834i	−0.0797680	−	0.0120231i
$872$	21.3679	+	14.5684i	0.723607	+	0.493347i
$873$		0			0
$874$	7.45592	+	3.59058i	0.252200	+	0.121453i
$875$	25.3154	+	14.6494i	0.855818	+	0.495241i
$876$		0			0
$877$	1.07311	−	0.731635i	0.0362364	−	0.0247056i	−0.545066	−	0.838393i	$-0.683496\pi$
$877$	1.07311	−	0.731635i	0.0362364	−	0.0247056i	0.581303	+	0.813687i	$0.302543\pi$
$878$	1.52623	−	1.41614i	0.0515078	−	0.0477923i
$879$		0			0
$880$	0.343114	+	0.874241i	0.0115664	+	0.0294707i
$881$	−23.2900			−0.784660			−0.392330	−	0.919825i	$-0.628331\pi$
$881$	−23.2900			−0.784660			−0.392330	+	0.919825i	$0.628331\pi$
$882$		0			0
$883$	−38.4637			−1.29441			−0.647203	−	0.762318i	$-0.724061\pi$
$883$	−38.4637			−1.29441			−0.647203	+	0.762318i	$0.724061\pi$
$884$	0.277764	+	0.707732i	0.00934222	+	0.0238036i
$885$		0			0
$886$	1.07098	−	0.993727i	0.0359804	−	0.0333849i
$887$	31.2470	−	21.3039i	1.04917	−	0.715313i	0.0893721	−	0.995998i	$-0.471514\pi$
$887$	31.2470	−	21.3039i	1.04917	−	0.715313i	0.959800	+	0.280685i	$0.0905616\pi$
$888$		0			0
$889$	−17.6384	−	25.9260i	−0.591572	−	0.869532i
$890$	2.24186	+	1.07962i	0.0751473	+	0.0361890i
$891$		0			0
$892$	7.72448	+	5.26646i	0.258635	+	0.176334i
$893$	37.8496	+	5.70491i	1.26659	+	0.190908i
$894$		0			0
$895$	−11.4049	+	14.3013i	−0.381223	+	0.478039i
$896$	6.80266	+	22.1317i	0.227261	+	0.739368i
$897$		0			0
$898$	−1.55336	+	20.7282i	−0.0518365	+	0.691709i
$899$	−10.1948	+	3.14468i	−0.340015	+	0.104881i
$900$		0			0
$901$	−11.8149	+	20.4641i	−0.393613	+	0.681757i
$902$	−2.42429	+	10.6215i	−0.0807199	+	0.353657i
$903$		0			0
$904$	−11.5411	−	50.5650i	−0.383853	−	1.68177i
$905$	−8.51893	−	2.62774i	−0.283179	−	0.0873491i
$906$		0			0
$907$	−10.1878	+	25.9580i	−0.338279	+	0.861922i	0.655965	+	0.754791i	$0.272262\pi$
$907$	−10.1878	+	25.9580i	−0.338279	+	0.861922i	−0.994245	+	0.107131i	$0.965834\pi$
$908$	−29.6439	−	9.14394i	−0.983768	−	0.303452i
$909$		0			0
$910$	0.234926	−	0.486592i	0.00778772	−	0.0161304i
$911$	0.503664	−	2.20670i	0.0166871	−	0.0731111i	−0.965899	−	0.258920i	$-0.916633\pi$
$911$	0.503664	−	2.20670i	0.0166871	−	0.0731111i	0.982586	+	0.185809i	$0.0594905\pi$
$912$		0			0
$913$	−11.1237	−	19.2668i	−0.368140	−	0.637637i
$914$	−3.58153	+	1.10476i	−0.118467	+	0.0365421i
$915$		0			0
$916$	−0.244698	−	0.306842i	−0.00808506	−	0.0101383i
$917$	1.79526	+	1.93868i	0.0592846	+	0.0640210i
$918$		0			0
$919$	12.4666	+	11.5673i	0.411235	+	0.381571i	0.858485	−	0.512838i	$-0.171406\pi$
$919$	12.4666	+	11.5673i	0.411235	+	0.381571i	−0.447250	+	0.894409i	$0.647597\pi$
$920$	−7.90609	−	1.19165i	−0.260656	−	0.0392876i
$921$		0			0
$922$	−20.7765	+	3.13156i	−0.684239	+	0.103132i
$923$	−0.236138	−	0.113718i	−0.00777257	−	0.00374307i
$924$		0			0
$925$	13.6929	−	6.59417i	0.450221	−	0.216815i
$926$	−7.91480	+	5.39622i	−0.260097	+	0.177331i
$927$		0			0
$928$	2.19097	+	29.2365i	0.0719223	+	0.959736i
$929$	10.9319	+	27.8541i	0.358664	+	0.913862i	0.990344	+	0.138632i	$0.0442706\pi$
$929$	10.9319	+	27.8541i	0.358664	+	0.913862i	−0.631680	+	0.775230i	$0.717634\pi$
$930$		0			0
$931$	29.5972	+	14.3258i	0.970010	+	0.469508i
$932$	−10.0436			−0.328991
$933$		0			0
$934$	−0.936512	−	12.4969i	−0.0306436	−	0.408911i
$935$	−3.82644	+	3.55042i	−0.125138	+	0.116111i
$936$		0			0
$937$	−18.9856	+	9.14298i	−0.620232	+	0.298688i	−0.717488	−	0.696571i	$-0.754708\pi$
$937$	−18.9856	+	9.14298i	−0.620232	+	0.298688i	0.0972552	+	0.995259i	$0.468994\pi$
$938$	−3.99607	−	26.6920i	−0.130476	−	0.871526i
$939$		0			0
$940$	−14.7589	+	2.22455i	−0.481382	+	0.0725567i
$941$	36.5858	+	24.9438i	1.19266	+	0.813145i	0.986240	−	0.165318i	$-0.0528650\pi$
$941$	36.5858	+	24.9438i	1.19266	+	0.813145i	0.206424	+	0.978463i	$0.433817\pi$
$942$		0			0
$943$	16.8881	+	15.6698i	0.549951	+	0.510280i
$944$	−1.03036	+	1.29203i	−0.0335353	+	0.0420520i
$945$		0			0
$946$	1.27125	+	1.59409i	0.0413318	+	0.0518284i
$947$	−3.33947	+	44.5622i	−0.108518	+	1.44808i	0.631441	+	0.775424i	$0.282464\pi$
$947$	−3.33947	+	44.5622i	−0.108518	+	1.44808i	−0.739959	+	0.672652i	$0.765155\pi$
$948$		0			0
$949$	1.24467	+	2.15582i	0.0404036	+	0.0699810i
$950$	−5.98379	+	10.3642i	−0.194140	+	0.336260i
$951$		0			0
$952$	−16.7098	+	13.2985i	−0.541566	+	0.431005i
$953$	11.5401	+	50.5606i	0.373821	+	1.63782i	0.715940	+	0.698162i	$0.245998\pi$
$953$	11.5401	+	50.5606i	0.373821	+	1.63782i	−0.342118	+	0.939657i	$0.611144\pi$
$954$		0			0
$955$	−8.42524	+	21.4672i	−0.272634	+	0.694661i
$956$	−4.97517	+	12.6765i	−0.160909	+	0.409988i
$957$		0			0
$958$	6.23079	+	27.2989i	0.201308	+	0.881987i
$959$	59.2337	−	13.4578i	1.91275	−	0.434575i
$960$		0			0
$961$	13.2527	−	22.9543i	0.427506	−	0.740462i
$962$	−0.361923	−	0.626869i	−0.0116689	−	0.0202111i
$963$		0			0
$964$	−0.595079	+	7.94078i	−0.0191662	+	0.255755i
$965$	−17.9685	−	22.5317i	−0.578425	−	0.725322i
$966$		0			0
$967$	34.0053	−	42.6413i	1.09354	−	1.37125i	0.171031	−	0.985266i	$-0.445290\pi$
$967$	34.0053	−	42.6413i	1.09354	−	1.37125i	0.922505	−	0.385985i	$-0.126138\pi$
$968$	18.4618	+	17.1300i	0.593384	+	0.550580i
$969$		0			0
$970$	−13.0951	−	8.92808i	−0.420458	−	0.286663i
$971$	−25.4384	+	3.83422i	−0.816358	+	0.123046i	−0.543930	−	0.839130i	$-0.683064\pi$
$971$	−25.4384	+	3.83422i	−0.816358	+	0.123046i	−0.272427	+	0.962176i	$0.587826\pi$
$972$		0			0
$973$	−0.536494	+	0.209944i	−0.0171992	+	0.00673048i
$974$	−13.6060	+	6.55229i	−0.435963	+	0.209949i
$975$		0			0
$976$	4.43364	−	4.11382i	0.141917	−	0.131680i
$977$	0.126331	+	1.68576i	0.00404167	+	0.0539324i	0.998860	−	0.0477366i	$-0.0152008\pi$
$977$	0.126331	+	1.68576i	0.00404167	+	0.0539324i	−0.994818	+	0.101669i	$0.967582\pi$
$978$		0			0
$979$	2.94606			0.0941565
$980$	−12.6748	−	1.93618i	−0.404882	−	0.0618489i
$981$		0			0
$982$	7.03318	+	17.9203i	0.224438	+	0.571859i
$983$	0.960163	+	12.8125i	0.0306244	+	0.408655i	0.991358	+	0.131183i	$0.0418775\pi$
$983$	0.960163	+	12.8125i	0.0306244	+	0.408655i	−0.960734	+	0.277472i	$0.910503\pi$
$984$		0			0
$985$	15.2937	−	10.4271i	0.487298	−	0.332234i
$986$	−10.9132	+	5.25554i	−0.347548	+	0.167370i
$987$		0			0
$988$	−1.07494	−	0.517662i	−0.0341983	−	0.0164690i
$989$	4.26338	−	0.642602i	0.135568	−	0.0204335i
$990$		0			0
$991$	22.4820	+	3.38861i	0.714164	+	0.107643i	0.496067	−	0.868284i	$-0.334777\pi$
$991$	22.4820	+	3.38861i	0.714164	+	0.107643i	0.218097	+	0.975927i	$0.430015\pi$
$992$	9.05435	+	8.40120i	0.287476	+	0.266739i
$993$		0			0
$994$	0.445756	−	2.93759i	0.0141385	−	0.0931749i
$995$	−0.0247474	−	0.0310323i	−0.000784546	−	0.000983789i
$996$		0			0
$997$	−4.70676	+	1.45184i	−0.149065	+	0.0459804i	−0.368390	−	0.929672i	$-0.620091\pi$
$997$	−4.70676	+	1.45184i	−0.149065	+	0.0459804i	0.219325	+	0.975652i	$0.429615\pi$
$998$	4.22824	+	7.32353i	0.133843	+	0.231822i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.163.2		48
3.2	odd	2		147.2.m.a.16.3	✓	48
49.46	even	21	inner	441.2.bb.c.46.2		48
147.86	odd	42		7203.2.a.i.1.17		24
147.95	odd	42		147.2.m.a.46.3	yes	48
147.110	even	42		7203.2.a.k.1.17		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.16.3	✓	48	3.2	odd	2
147.2.m.a.46.3	yes	48	147.95	odd	42
441.2.bb.c.46.2		48	49.46	even	21	inner
441.2.bb.c.163.2		48	1.1	even	1	trivial
7203.2.a.i.1.17		24	147.86	odd	42
7203.2.a.k.1.17		24	147.110	even	42

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.293772 - 0.748519i) q^{2} +(0.992125 - 0.920558i) q^{4} +(1.11822 - 0.762387i) q^{5} +(1.80149 - 1.93768i) q^{7} +(-2.42946 - 1.16997i) q^{8} +O(q^{10})\)	\(q+(-0.293772 - 0.748519i) q^{2} +(0.992125 - 0.920558i) q^{4} +(1.11822 - 0.762387i) q^{5} +(1.80149 - 1.93768i) q^{7} +(-2.42946 - 1.16997i) q^{8} +(-0.899162 - 0.613038i) q^{10} +(-1.27408 - 0.192037i) q^{11} +(-0.117007 + 0.146722i) q^{13} +(-1.97962 - 0.779214i) q^{14} +(0.0402476 - 0.537067i) q^{16} +(2.86041 - 0.882320i) q^{17} +(-2.34871 + 4.06809i) q^{19} +(0.407589 - 1.78577i) q^{20} +(0.230546 + 1.01009i) q^{22} +(2.09355 + 0.645775i) q^{23} +(-1.15753 + 2.94934i) q^{25} +(0.144197 + 0.0444790i) q^{26} +(0.00355656 - 3.58080i) q^{28} +(1.11979 - 4.90614i) q^{29} +(-1.06003 - 1.83602i) q^{31} +(-5.56722 + 1.71726i) q^{32} +(-1.50074 - 1.88187i) q^{34} +(0.537194 - 3.54019i) q^{35} +(-3.51631 - 3.26266i) q^{37} +(3.73503 + 0.562965i) q^{38} +(-3.60863 + 0.543913i) q^{40} +(9.47404 + 4.56246i) q^{41} +(1.77306 - 0.853859i) q^{43} +(-1.44083 + 0.982341i) q^{44} +(-0.131652 - 1.75677i) q^{46} +(-2.97700 - 7.58526i) q^{47} +(-0.509243 - 6.98145i) q^{49} +2.54769 q^{50} +(0.0189806 + 0.253278i) q^{52} +(-5.78671 + 5.36928i) q^{53} +(-1.57111 + 0.756605i) q^{55} +(-6.64368 + 2.59984i) q^{56} +(-4.00130 + 0.603099i) q^{58} +(-2.53525 - 1.72850i) q^{59} +(8.23220 + 7.63836i) q^{61} +(-1.06289 + 1.33282i) q^{62} +(2.24931 + 2.82054i) q^{64} +(-0.0189801 + 0.253271i) q^{65} +(6.34314 + 10.9866i) q^{67} +(2.02566 - 3.50854i) q^{68} +(-2.80771 + 0.637908i) q^{70} +(0.310774 + 1.36159i) q^{71} +(4.84618 - 12.3479i) q^{73} +(-1.40917 + 3.59050i) q^{74} +(1.41469 + 6.19818i) q^{76} +(-2.66736 + 2.12282i) q^{77} +(-6.97387 + 12.0791i) q^{79} +(-0.364447 - 0.631242i) q^{80} +(0.631878 - 8.43182i) q^{82} +(10.7654 + 13.4994i) q^{83} +(2.52589 - 3.16736i) q^{85} +(-1.16000 - 1.07633i) q^{86} +(2.87065 + 1.95718i) q^{88} +(-2.26094 + 0.340781i) q^{89} +(0.0735137 + 0.491041i) q^{91} +(2.67154 - 1.28654i) q^{92} +(-4.80315 + 4.45668i) q^{94} +(0.475090 + 6.33963i) q^{95} +14.5637 q^{97} +(-5.07615 + 2.43213i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

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