LMFDB - Embedded newform 441.2.bb.e.100.2

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:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.2
Character	$\chi$	$=$	441.100
Dual form			441.2.bb.e.172.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64310 - 0.506829i) q^{2} +(0.790427 + 0.538904i) q^{4} +(-1.86453 + 0.281032i) q^{5} +(-2.42176 + 1.06541i) q^{7} +(1.11855 + 1.40262i) q^{8} +O(q^{10})$	\(q+(-1.64310 - 0.506829i) q^{2} +(0.790427 + 0.538904i) q^{4} +(-1.86453 + 0.281032i) q^{5} +(-2.42176 + 1.06541i) q^{7} +(1.11855 + 1.40262i) q^{8} +(3.20604 + 0.483233i) q^{10} +(1.81867 - 1.68748i) q^{11} +(1.03337 + 4.52749i) q^{13} +(4.51917 - 0.523159i) q^{14} +(-1.82602 - 4.65262i) q^{16} +(-0.337576 - 4.50464i) q^{17} +(3.47696 - 6.02227i) q^{19} +(-1.62522 - 0.782665i) q^{20} +(-3.84353 + 1.85095i) q^{22} +(0.00580944 - 0.0775216i) q^{23} +(-1.38038 + 0.425792i) q^{25} +(0.596735 - 7.96287i) q^{26} +(-2.48837 - 0.462965i) q^{28} +(7.17006 + 3.45292i) q^{29} +(-1.90322 - 3.29647i) q^{31} +(0.374113 + 4.99219i) q^{32} +(-1.72841 + 7.57268i) q^{34} +(4.21601 - 2.66708i) q^{35} +(4.31449 - 2.94157i) q^{37} +(-8.76526 + 8.13297i) q^{38} +(-2.47976 - 2.30088i) q^{40} +(-5.50342 - 6.90107i) q^{41} +(5.23387 - 6.56306i) q^{43} +(2.34692 - 0.353741i) q^{44} +(-0.0488357 + 0.124431i) q^{46} +(1.10809 + 0.341801i) q^{47} +(4.72980 - 5.16033i) q^{49} +2.48391 q^{50} +(-1.62308 + 4.13554i) q^{52} +(-3.61329 - 2.46350i) q^{53} +(-2.91673 + 3.65746i) q^{55} +(-4.20323 - 2.20509i) q^{56} +(-10.0311 - 9.30750i) q^{58} +(3.13814 + 0.472998i) q^{59} +(4.28846 - 2.92382i) q^{61} +(1.45643 + 6.38103i) q^{62} +(-0.308888 + 1.35333i) q^{64} +(-3.19912 - 8.15122i) q^{65} +(3.35023 + 5.80277i) q^{67} +(2.16074 - 3.74251i) q^{68} +(-8.27909 + 2.24548i) q^{70} +(12.6006 - 6.06812i) q^{71} +(12.1181 - 3.73793i) q^{73} +(-8.58001 + 2.64658i) q^{74} +(5.99371 - 2.88642i) q^{76} +(-2.60652 + 6.02430i) q^{77} +(-2.61929 + 4.53675i) q^{79} +(4.71220 + 8.16177i) q^{80} +(5.54501 + 14.1285i) q^{82} +(-0.923121 + 4.04446i) q^{83} +(1.89537 + 8.30416i) q^{85} +(-11.9261 + 8.13109i) q^{86} +(4.40119 + 0.663372i) q^{88} +(-6.23812 - 5.78813i) q^{89} +(-7.32621 - 9.86352i) q^{91} +(0.0463686 - 0.0581444i) q^{92} +(-1.64747 - 1.12323i) q^{94} +(-4.79043 + 12.2058i) q^{95} -15.6775 q^{97} +(-10.3869 + 6.08173i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$1$

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 $

$2$	−1.64310	−	0.506829i	−1.16185	−	0.358383i	−0.346892	−	0.937905i	$-0.612763\pi$
$2$	−1.64310	−	0.506829i	−1.16185	−	0.358383i	−0.814956	+	0.579523i	$0.803239\pi$
$3$		0			0
$3$		0			0
$4$	0.790427	+	0.538904i	0.395213	+	0.269452i
$5$	−1.86453	+	0.281032i	−0.833842	+	0.125681i	−0.552068	−	0.833799i	$-0.686161\pi$
$5$	−1.86453	+	0.281032i	−0.833842	+	0.125681i	−0.281774	+	0.959481i	$0.590923\pi$
$6$		0			0
$7$	−2.42176	+	1.06541i	−0.915338	+	0.402687i
$7$	−2.42176	+	1.06541i	−0.915338	+	0.402687i
$8$	1.11855	+	1.40262i	0.395469	+	0.495902i
$9$		0			0
$10$	3.20604	+	0.483233i	1.01384	+	0.152812i
$11$	1.81867	−	1.68748i	0.548351	−	0.508795i	−0.356631	−	0.934245i	$-0.616075\pi$
$11$	1.81867	−	1.68748i	0.548351	−	0.508795i	0.904982	+	0.425450i	$0.139884\pi$
$12$		0			0
$13$	1.03337	+	4.52749i	0.286605	+	1.25570i	0.889150	+	0.457616i	$0.151296\pi$
$13$	1.03337	+	4.52749i	0.286605	+	1.25570i	−0.602545	+	0.798085i	$0.705846\pi$
$14$	4.51917	−	0.523159i	1.20780	−	0.139820i
$15$		0			0
$16$	−1.82602	−	4.65262i	−0.456505	−	1.16315i
$17$	−0.337576	−	4.50464i	−0.0818743	−	1.09254i	−0.875207	−	0.483748i	$-0.839275\pi$
$17$	−0.337576	−	4.50464i	−0.0818743	−	1.09254i	0.793333	−	0.608788i	$-0.208344\pi$
$18$		0			0
$19$	3.47696	−	6.02227i	0.797669	−	1.38160i	−0.123461	−	0.992349i	$-0.539399\pi$
$19$	3.47696	−	6.02227i	0.797669	−	1.38160i	0.921130	−	0.389254i	$-0.127267\pi$
$20$	−1.62522	−	0.782665i	−0.363411	−	0.175009i
$21$		0			0
$22$	−3.84353	+	1.85095i	−0.819443	+	0.394623i
$23$	0.00580944	−	0.0775216i	0.00121135	−	0.0161644i	−0.996565	−	0.0828098i	$-0.973611\pi$
$23$	0.00580944	−	0.0775216i	0.00121135	−	0.0161644i	0.997777	+	0.0666455i	$0.0212296\pi$
$24$		0			0
$25$	−1.38038	+	0.425792i	−0.276076	+	0.0851583i
$26$	0.596735	−	7.96287i	0.117029	−	1.56165i
$27$		0			0
$28$	−2.48837	−	0.462965i	−0.470259	−	0.0874921i
$29$	7.17006	+	3.45292i	1.33145	+	0.641191i	0.958082	−	0.286493i	$-0.0924895\pi$
$29$	7.17006	+	3.45292i	1.33145	+	0.641191i	0.373365	+	0.927684i	$0.378204\pi$
$30$		0			0
$31$	−1.90322	−	3.29647i	−0.341828	−	0.592063i	0.642944	−	0.765913i	$-0.277713\pi$
$31$	−1.90322	−	3.29647i	−0.341828	−	0.592063i	−0.984772	+	0.173850i	$0.944379\pi$
$32$	0.374113	+	4.99219i	0.0661345	+	0.882503i
$33$		0			0
$34$	−1.72841	+	7.57268i	−0.296421	+	1.29870i
$35$	4.21601	−	2.66708i	0.712637	−	0.450818i
$36$		0			0
$37$	4.31449	−	2.94157i	0.709298	−	0.483591i	−0.154138	−	0.988049i	$-0.549260\pi$
$37$	4.31449	−	2.94157i	0.709298	−	0.483591i	0.863436	+	0.504458i	$0.168308\pi$
$38$	−8.76526	+	8.13297i	−1.42191	+	1.31934i
$39$		0			0
$40$	−2.47976	−	2.30088i	−0.392084	−	0.363801i
$41$	−5.50342	−	6.90107i	−0.859490	−	1.07777i	−0.996195	−	0.0871548i	$-0.972223\pi$
$41$	−5.50342	−	6.90107i	−0.859490	−	1.07777i	0.136705	−	0.990612i	$-0.456349\pi$
$42$		0			0
$43$	5.23387	−	6.56306i	0.798157	−	1.00086i	−0.201614	−	0.979465i	$-0.564619\pi$
$43$	5.23387	−	6.56306i	0.798157	−	1.00086i	0.999771	−	0.0213925i	$-0.00680995\pi$
$44$	2.34692	−	0.353741i	0.353811	−	0.0533285i
$45$		0			0
$46$	−0.0488357	+	0.124431i	−0.00720044	+	0.0183464i
$47$	1.10809	+	0.341801i	0.161632	+	0.0498568i	0.374515	−	0.927221i	$-0.377809\pi$
$47$	1.10809	+	0.341801i	0.161632	+	0.0498568i	−0.212883	+	0.977078i	$0.568285\pi$
$48$		0			0
$49$	4.72980	−	5.16033i	0.675686	−	0.737189i
$50$	2.48391			0.351278
$51$		0			0
$52$	−1.62308	+	4.13554i	−0.225081	+	0.573496i
$53$	−3.61329	−	2.46350i	−0.496324	−	0.338388i	0.289149	−	0.957284i	$-0.406628\pi$
$53$	−3.61329	−	2.46350i	−0.496324	−	0.338388i	−0.785473	+	0.618896i	$0.787580\pi$
$54$		0			0
$55$	−2.91673	+	3.65746i	−0.393292	+	0.493172i
$56$	−4.20323	−	2.20509i	−0.561681	−	0.294668i
$57$		0			0
$58$	−10.0311	−	9.30750i	−1.31715	−	1.22213i
$59$	3.13814	+	0.472998i	0.408551	+	0.0615792i	0.350103	−	0.936711i	$-0.386147\pi$
$59$	3.13814	+	0.472998i	0.408551	+	0.0615792i	0.0584482	+	0.998290i	$0.481385\pi$
$60$		0			0
$61$	4.28846	−	2.92382i	0.549081	−	0.374357i	−0.256773	−	0.966472i	$-0.582659\pi$
$61$	4.28846	−	2.92382i	0.549081	−	0.374357i	0.805854	+	0.592115i	$0.201707\pi$
$62$	1.45643	+	6.38103i	0.184967	+	0.810392i
$63$		0			0
$64$	−0.308888	+	1.35333i	−0.0386110	+	0.169166i
$65$	−3.19912	−	8.15122i	−0.396802	−	1.01103i
$66$		0			0
$67$	3.35023	+	5.80277i	0.409296	+	0.708921i	0.994811	−	0.101740i	$-0.0324410\pi$
$67$	3.35023	+	5.80277i	0.409296	+	0.708921i	−0.585515	+	0.810662i	$0.699108\pi$
$68$	2.16074	−	3.74251i	0.262028	−	0.453846i
$69$		0			0
$70$	−8.27909	+	2.24548i	−0.989541	+	0.268386i
$71$	12.6006	−	6.06812i	1.49541	−	0.720154i	0.505634	−	0.862748i	$-0.331259\pi$
$71$	12.6006	−	6.06812i	1.49541	−	0.720154i	0.989781	+	0.142594i	$0.0455445\pi$
$72$		0			0
$73$	12.1181	−	3.73793i	1.41831	−	0.437492i	0.511594	−	0.859227i	$-0.329055\pi$
$73$	12.1181	−	3.73793i	1.41831	−	0.437492i	0.906719	+	0.421736i	$0.138579\pi$
$74$	−8.58001	+	2.64658i	−0.997406	+	0.307659i
$75$		0			0
$76$	5.99371	−	2.88642i	0.687525	−	0.331095i
$77$	−2.60652	+	6.02430i	−0.297041	+	0.686533i
$78$		0			0
$79$	−2.61929	+	4.53675i	−0.294694	+	0.510424i	−0.974914	−	0.222584i	$-0.928551\pi$
$79$	−2.61929	+	4.53675i	−0.294694	+	0.510424i	0.680220	+	0.733008i	$0.261884\pi$
$80$	4.71220	+	8.16177i	0.526840	+	0.912513i
$81$		0			0
$82$	5.54501	+	14.1285i	0.612344	+	1.56023i
$83$	−0.923121	+	4.04446i	−0.101326	+	0.443937i	0.898660	+	0.438645i	$0.144542\pi$
$83$	−0.923121	+	4.04446i	−0.101326	+	0.443937i	−0.999986	+	0.00529163i	$0.998316\pi$
$84$		0			0
$85$	1.89537	+	8.30416i	0.205582	+	0.900713i
$86$	−11.9261	+	8.13109i	−1.28603	+	0.876798i
$87$		0			0
$88$	4.40119	+	0.663372i	0.469168	+	0.0707157i
$89$	−6.23812	−	5.78813i	−0.661240	−	0.613541i	0.276444	−	0.961030i	$-0.410844\pi$
$89$	−6.23812	−	5.78813i	−0.661240	−	0.613541i	−0.937684	+	0.347489i	$0.887034\pi$
$90$		0			0
$91$	−7.32621	−	9.86352i	−0.767995	−	1.03398i
$92$	0.0463686	−	0.0581444i	0.00483426	−	0.00606198i
$93$		0			0
$94$	−1.64747	−	1.12323i	−0.169924	−	0.115852i
$95$	−4.79043	+	12.2058i	−0.491488	+	1.25229i
$96$		0			0
$97$	−15.6775			−1.59180			−0.795902	−	0.605425i	$-0.793003\pi$
$97$	−15.6775			−1.59180			−0.795902	+	0.605425i	$0.793003\pi$
$98$	−10.3869	+	6.08173i	−1.04924	+	0.614348i
$99$		0			0
$100$	−1.32055	−	0.407336i	−0.132055	−	0.0407336i
$101$	−1.40125	+	3.57033i	−0.139430	+	0.355262i	−0.983484	−	0.180997i	$-0.942068\pi$
$101$	−1.40125	+	3.57033i	−0.139430	+	0.355262i	0.844054	+	0.536259i	$0.180163\pi$
$102$		0			0
$103$	6.34706	−	0.956665i	0.625394	−	0.0942630i	0.171303	−	0.985218i	$-0.445202\pi$
$103$	6.34706	−	0.956665i	0.625394	−	0.0942630i	0.454091	+	0.890955i	$0.349964\pi$
$104$	−5.19448	+	6.51368i	−0.509361	+	0.638719i
$105$		0			0
$106$	4.68843	+	5.87910i	0.455380	+	0.571029i
$107$	3.59757	+	3.33805i	0.347790	+	0.322702i	0.834653	−	0.550777i	$-0.185668\pi$
$107$	3.59757	+	3.33805i	0.347790	+	0.322702i	−0.486863	+	0.873478i	$0.661859\pi$
$108$		0			0
$109$	−5.30502	+	4.92234i	−0.508129	+	0.471475i	−0.892079	−	0.451879i	$-0.850754\pi$
$109$	−5.30502	+	4.92234i	−0.508129	+	0.471475i	0.383950	+	0.923354i	$0.374563\pi$
$110$	6.64619	−	4.53130i	0.633689	−	0.432042i
$111$		0			0
$112$	9.37912	+	9.32205i	0.886244	+	0.880851i
$113$	−2.10172	+	9.20825i	−0.197713	+	0.866239i	0.774580	+	0.632476i	$0.217961\pi$
$113$	−2.10172	+	9.20825i	−0.197713	+	0.866239i	−0.972294	+	0.233763i	$0.924896\pi$
$114$		0			0
$115$	0.0109542	+	0.146174i	0.00102149	+	0.0136308i
$116$	3.80662	+	6.59326i	0.353436	+	0.612168i
$117$		0			0
$118$	−4.91655	−	2.36769i	−0.452605	−	0.217963i
$119$	5.61682	+	10.5495i	0.514893	+	0.967070i
$120$		0			0
$121$	−0.362054	+	4.83128i	−0.0329140	+	0.439207i
$122$	−8.52825	+	2.63062i	−0.772112	+	0.238165i
$123$		0			0
$124$	0.272126	−	3.63127i	0.0244376	−	0.326097i
$125$	10.9484	−	5.27246i	0.979253	−	0.471583i
$126$		0			0
$127$	9.20996	+	4.43528i	0.817252	+	0.393568i	0.795319	−	0.606192i	$-0.207304\pi$
$127$	9.20996	+	4.43528i	0.817252	+	0.393568i	0.0219332	+	0.999759i	$0.493018\pi$
$128$	6.19963	−	10.7381i	0.547975	−	0.949121i
$129$		0			0
$130$	1.12520	+	15.0147i	0.0986862	+	1.31688i
$131$	−0.926848	−	2.36157i	−0.0809790	−	0.206331i	0.884650	−	0.466256i	$-0.154397\pi$
$131$	−0.926848	−	2.36157i	−0.0809790	−	0.206331i	−0.965629	+	0.259925i	$0.916302\pi$
$132$		0			0
$133$	−2.00416	+	18.2889i	−0.173783	+	1.58585i
$134$	−2.56375	−	11.2325i	−0.221475	−	0.970343i
$135$		0			0
$136$	5.94072	−	5.51218i	0.509412	−	0.472666i
$137$	21.3064	+	3.21142i	1.82033	+	0.274370i	0.968421	−	0.249321i	$-0.0802074\pi$
$137$	21.3064	+	3.21142i	1.82033	+	0.274370i	0.851908	+	0.523691i	$0.175445\pi$
$138$		0			0
$139$	−0.320312	−	0.401658i	−0.0271685	−	0.0340682i	0.768062	−	0.640376i	$-0.221221\pi$
$139$	−0.320312	−	0.401658i	−0.0271685	−	0.0340682i	−0.795230	+	0.606308i	$0.792650\pi$
$140$	4.76975	+	0.163897i	0.403117	+	0.0138518i
$141$		0			0
$142$	−23.7795	+	3.58419i	−1.99553	+	0.300778i
$143$	9.51943	+	6.49024i	0.796055	+	0.542741i
$144$		0			0
$145$	−14.3392	−	4.42305i	−1.19080	−	0.367314i
$146$	−21.8057			−1.80465
$147$		0			0
$148$	4.99551			0.410628
$149$	−13.4021	−	4.13399i	−1.09794	−	0.338670i	−0.307710	−	0.951480i	$-0.599563\pi$
$149$	−13.4021	−	4.13399i	−1.09794	−	0.338670i	−0.790230	+	0.612810i	$0.790039\pi$
$150$		0			0
$151$	−11.8029	−	8.04706i	−0.960503	−	0.654860i	−0.0218643	−	0.999761i	$-0.506960\pi$
$151$	−11.8029	−	8.04706i	−0.960503	−	0.654860i	−0.938639	+	0.344901i	$0.887913\pi$
$152$	12.3361	−	1.85937i	1.00059	−	0.150815i
$153$		0			0
$154$	7.33607	−	8.57748i	0.591158	−	0.691193i
$155$	4.47501	+	5.61149i	0.359442	+	0.450725i
$156$		0			0
$157$	−14.9383	−	2.25159i	−1.19221	−	0.179697i	−0.477189	−	0.878801i	$-0.658344\pi$
$157$	−14.9383	−	2.25159i	−1.19221	−	0.179697i	−0.715020	+	0.699104i	$0.753582\pi$
$158$	6.60313	−	6.12680i	0.525316	−	0.487422i
$159$		0			0
$160$	−2.10051	−	9.20294i	−0.166060	−	0.727556i
$161$	0.0685233	+	0.193928i	0.00540039	+	0.0152837i
$162$		0			0
$163$	−1.15814	−	2.95090i	−0.0907127	−	0.231132i	0.878316	−	0.478081i	$-0.158667\pi$
$163$	−1.15814	−	2.95090i	−0.0907127	−	0.231132i	−0.969029	+	0.246949i	$0.920572\pi$
$164$	−0.631037	−	8.42061i	−0.0492757	−	0.657539i
$165$		0			0
$166$	3.56663	−	6.17759i	0.276824	−	0.479474i
$167$	0.860992	+	0.414632i	0.0666256	+	0.0320852i	0.466900	−	0.884310i	$-0.345371\pi$
$167$	0.860992	+	0.414632i	0.0666256	+	0.0320852i	−0.400274	+	0.916395i	$0.631085\pi$
$168$		0			0
$169$	−7.71774	+	3.71667i	−0.593673	+	0.285898i
$170$	1.09451	−	14.6052i	0.0839450	−	1.12017i
$171$		0			0
$172$	7.67385	−	2.36707i	0.585125	−	0.180487i
$173$	1.27007	−	16.9479i	0.0965616	−	1.28853i	−0.712864	−	0.701302i	$-0.752602\pi$
$173$	1.27007	−	16.9479i	0.0965616	−	1.28853i	0.809425	−	0.587223i	$-0.199779\pi$
$174$		0			0
$175$	2.88931	−	2.50184i	0.218411	−	0.189121i
$176$	−11.1721	−	5.38022i	−0.842132	−	0.405550i
$177$		0			0
$178$	7.31627	+	12.6721i	0.548377	+	0.949818i
$179$	−0.888760	−	11.8597i	−0.0664290	−	0.886434i	−0.926509	−	0.376274i	$-0.877205\pi$
$179$	−0.888760	−	11.8597i	−0.0664290	−	0.886434i	0.860080	−	0.510160i	$-0.170414\pi$
$180$		0			0
$181$	0.919071	−	4.02671i	0.0683140	−	0.299303i	−0.929217	−	0.369535i	$-0.879517\pi$
$181$	0.919071	−	4.02671i	0.0683140	−	0.299303i	0.997531	+	0.0702321i	$0.0223740\pi$
$182$	7.03858	+	19.9199i	0.521734	+	1.47656i
$183$		0			0
$184$	0.115232	−	0.0785637i	0.00849500	−	0.00579179i
$185$	−7.21780	+	6.69714i	−0.530664	+	0.492384i
$186$		0			0
$187$	−8.21545	−	7.62282i	−0.600773	−	0.557436i
$188$	0.691667	+	0.867323i	0.0504450	+	0.0632560i
$189$		0			0
$190$	14.0574	−	17.6275i	1.01983	−	1.27883i
$191$	7.89260	−	1.18962i	0.571089	−	0.0860778i	0.142852	−	0.989744i	$-0.454373\pi$
$191$	7.89260	−	1.18962i	0.571089	−	0.0860778i	0.428237	+	0.903666i	$0.359135\pi$
$192$		0			0
$193$	8.13896	−	20.7377i	0.585855	−	1.49273i	−0.263366	−	0.964696i	$-0.584833\pi$
$193$	8.13896	−	20.7377i	0.585855	−	1.49273i	0.849221	−	0.528038i	$-0.177072\pi$
$194$	25.7596	+	7.94580i	1.84944	+	0.570475i
$195$		0			0
$196$	6.51948	−	1.52995i	0.465677	−	0.109282i
$197$	−18.8790			−1.34508			−0.672538	−	0.740062i	$-0.734796\pi$
$197$	−18.8790			−1.34508			−0.672538	+	0.740062i	$0.734796\pi$
$198$		0			0
$199$	−7.61381	+	19.3997i	−0.539729	+	1.37521i	0.357613	+	0.933870i	$0.383591\pi$
$199$	−7.61381	+	19.3997i	−0.539729	+	1.37521i	−0.897342	+	0.441337i	$0.854504\pi$
$200$	−2.14126	−	1.45988i	−0.151410	−	0.103229i
$201$		0			0
$202$	4.11195	−	5.15622i	0.289316	−	0.362791i
$203$	−21.0429	−	0.723073i	−1.47692	−	0.0507497i
$204$		0			0
$205$	12.2007	+	11.3206i	0.852134	+	0.790665i
$206$	−10.9137	−	1.64498i	−0.760395	−	0.114611i
$207$		0			0
$208$	19.1778	−	13.0752i	1.32974	−	0.906600i
$209$	−3.83902	−	16.8199i	−0.265551	−	1.16345i
$210$		0			0
$211$	4.69560	−	20.5728i	0.323258	−	1.41629i	−0.508458	−	0.861087i	$-0.669784\pi$
$211$	4.69560	−	20.5728i	0.323258	−	1.41629i	0.831716	−	0.555201i	$-0.187359\pi$
$212$	−1.52845	−	3.89443i	−0.104975	−	0.267471i
$213$		0			0
$214$	−4.21934	−	7.30811i	−0.288428	−	0.499572i
$215$	−7.91425	+	13.7079i	−0.539748	+	0.934870i
$216$		0			0
$217$	8.12121	+	5.95553i	0.551304	+	0.404288i
$218$	11.2115	−	5.39916i	0.759337	−	0.365677i
$219$		0			0
$220$	−4.27648	+	1.31912i	−0.288320	+	0.0889350i
$221$	20.0459	−	6.18334i	1.34843	−	0.415937i
$222$		0			0
$223$	8.14830	−	3.92402i	0.545651	−	0.262772i	−0.140687	−	0.990054i	$-0.544931\pi$
$223$	8.14830	−	3.92402i	0.545651	−	0.262772i	0.686338	+	0.727282i	$0.259217\pi$
$224$	−6.22474	−	11.6913i	−0.415908	−	0.781157i
$225$		0			0
$226$	8.12035	−	14.0649i	0.540158	−	0.935581i
$227$	−7.58138	−	13.1313i	−0.503194	−	0.871558i	−0.999993	−	0.00369200i	$-0.998825\pi$
$227$	−7.58138	−	13.1313i	−0.503194	−	0.871558i	0.496799	−	0.867866i	$-0.334509\pi$
$228$		0			0
$229$	−1.35262	−	3.44642i	−0.0893836	−	0.227746i	0.879191	−	0.476470i	$-0.158084\pi$
$229$	−1.35262	−	3.44642i	−0.0893836	−	0.227746i	−0.968574	+	0.248724i	$0.919989\pi$
$230$	0.0560863	−	0.245730i	0.00369822	−	0.0162030i
$231$		0			0
$232$	3.17696	+	13.9192i	0.208578	+	0.913839i
$233$	−8.08299	+	5.51089i	−0.529534	+	0.361030i	−0.798381	−	0.602153i	$-0.794310\pi$
$233$	−8.08299	+	5.51089i	−0.529534	+	0.361030i	0.268847	+	0.963183i	$0.413357\pi$
$234$		0			0
$235$	−2.16212	−	0.325888i	−0.141041	−	0.0212586i
$236$	2.22557	+	2.06503i	0.144872	+	0.134422i
$237$		0			0
$238$	−3.88221	−	20.1806i	−0.251646	−	1.30812i
$239$	18.6098	−	23.3360i	1.20377	−	1.50948i	0.397857	−	0.917447i	$-0.369754\pi$
$239$	18.6098	−	23.3360i	1.20377	−	1.50948i	0.805914	−	0.592033i	$-0.201675\pi$
$240$		0			0
$241$	−3.98761	−	2.71871i	−0.256864	−	0.175127i	0.428041	−	0.903759i	$-0.359204\pi$
$241$	−3.98761	−	2.71871i	−0.256864	−	0.175127i	−0.684905	+	0.728632i	$0.740156\pi$
$242$	3.04353	−	7.75478i	0.195645	−	0.498496i
$243$		0			0
$244$	4.96537			0.317875
$245$	−7.36863	+	10.9508i	−0.470764	+	0.699621i
$246$		0			0
$247$	30.8588	+	9.51867i	1.96350	+	0.605659i
$248$	2.49485	−	6.35677i	0.158423	−	0.403655i
$249$		0			0
$250$	−20.6615	+	3.11422i	−1.30675	+	0.196961i
$251$	0.363515	−	0.455833i	0.0229448	−	0.0287719i	−0.770227	−	0.637770i	$-0.779857\pi$
$251$	0.363515	−	0.455833i	0.0229448	−	0.0287719i	0.793172	+	0.608998i	$0.208428\pi$
$252$		0			0
$253$	−0.120251	−	0.150790i	−0.00756011	−	0.00948008i
$254$	−12.8850	−	11.9555i	−0.808474	−	0.750154i
$255$		0			0
$256$	−13.5939	+	12.6133i	−0.849616	+	0.788328i
$257$	−23.8343	+	16.2500i	−1.48674	+	1.01365i	−0.497486	+	0.867472i	$0.665743\pi$
$257$	−23.8343	+	16.2500i	−1.48674	+	1.01365i	−0.989259	+	0.146173i	$0.953304\pi$
$258$		0			0
$259$	−7.31466	+	11.7205i	−0.454511	+	0.728274i
$260$	1.86406	−	8.16696i	0.115604	−	0.506493i
$261$		0			0
$262$	0.325991	+	4.35005i	0.0201398	+	0.268747i
$263$	10.9822	+	19.0217i	0.677191	+	1.17293i	0.975823	+	0.218561i	$0.0701364\pi$
$263$	10.9822	+	19.0217i	0.677191	+	1.17293i	−0.298632	+	0.954368i	$0.596530\pi$
$264$		0			0
$265$	7.42940	+	3.57781i	0.456385	+	0.219783i
$266$	12.5624	−	29.0347i	0.770248	−	1.78023i
$267$		0			0
$268$	−0.479023	+	6.39212i	−0.0292610	+	0.390461i
$269$	10.6005	−	3.26983i	0.646327	−	0.199365i	0.0457755	−	0.998952i	$-0.485424\pi$
$269$	10.6005	−	3.26983i	0.646327	−	0.199365i	0.600551	+	0.799586i	$0.294948\pi$
$270$		0			0
$271$	0.701194	−	9.35679i	0.0425945	−	0.568384i	−0.934553	−	0.355823i	$-0.884200\pi$
$271$	0.701194	−	9.35679i	0.0425945	−	0.568384i	0.977148	−	0.212561i	$-0.0681805\pi$
$272$	−20.3420	+	9.79618i	−1.23341	+	0.593981i
$273$		0			0
$274$	−33.3809	−	16.0754i	−2.01662	−	0.971151i
$275$	−1.79195	+	3.10375i	−0.108059	+	0.187163i
$276$		0			0
$277$	0.518168	+	6.91447i	0.0311337	+	0.415450i	0.990895	+	0.134634i	$0.0429860\pi$
$277$	0.518168	+	6.91447i	0.0311337	+	0.415450i	−0.959762	+	0.280816i	$0.909395\pi$
$278$	0.322732	+	0.822308i	0.0193562	+	0.0493188i
$279$		0			0
$280$	8.45674	+	2.93021i	0.505387	+	0.175113i
$281$	2.80888	+	12.3065i	0.167564	+	0.734146i	0.986966	+	0.160927i	$0.0514483\pi$
$281$	2.80888	+	12.3065i	0.167564	+	0.734146i	−0.819402	+	0.573219i	$0.805695\pi$
$282$		0			0
$283$	−12.0507	+	11.1814i	−0.716341	+	0.664667i	−0.951626	−	0.307259i	$-0.900588\pi$
$283$	−12.0507	+	11.1814i	−0.716341	+	0.664667i	0.235285	+	0.971926i	$0.424398\pi$
$284$	13.2300	+	1.99410i	0.785055	+	0.118328i
$285$		0			0
$286$	−12.3519	−	15.4888i	−0.730386	−	0.915874i
$287$	20.6804	+	10.8493i	1.22073	+	0.640415i
$288$		0			0
$289$	−3.36773	+	0.507604i	−0.198102	+	0.0298591i
$290$	21.3190	+	14.5350i	1.25189	+	0.853526i
$291$		0			0
$292$	11.5928	+	3.57591i	0.678419	+	0.209265i
$293$	−6.02256			−0.351842			−0.175921	−	0.984404i	$-0.556290\pi$
$293$	−6.02256			−0.351842			−0.175921	+	0.984404i	$0.556290\pi$
$294$		0			0
$295$	−5.98407			−0.348406
$296$	8.95190	+	2.76130i	0.520319	+	0.160497i
$297$		0			0
$298$	19.9257	+	13.5851i	1.15427	+	0.786965i
$299$	0.356982	−	0.0538064i	0.0206448	−	0.00311170i
$300$		0			0
$301$	−5.68280	+	21.4703i	−0.327551	+	1.23753i
$302$	15.3148	+	19.2042i	0.881268	+	1.10508i
$303$		0			0
$304$	−34.3683	−	5.18019i	−1.97116	−	0.297104i
$305$	−7.17426	+	6.65674i	−0.410797	+	0.381164i
$306$		0			0
$307$	2.36721	+	10.3714i	0.135104	+	0.591930i	0.996470	+	0.0839453i	$0.0267521\pi$
$307$	2.36721	+	10.3714i	0.135104	+	0.591930i	−0.861366	+	0.507984i	$0.830391\pi$
$308$	−5.30679	+	3.35711i	−0.302382	+	0.191289i
$309$		0			0
$310$	−4.50883	−	11.4883i	−0.256084	−	0.652492i
$311$	−1.69345	−	22.5975i	−0.0960266	−	1.28139i	−0.812165	−	0.583428i	$-0.801711\pi$
$311$	−1.69345	−	22.5975i	−0.0960266	−	1.28139i	0.716138	−	0.697958i	$-0.245908\pi$
$312$		0			0
$313$	−12.6261	+	21.8691i	−0.713670	+	1.23611i	0.249800	+	0.968297i	$0.419635\pi$
$313$	−12.6261	+	21.8691i	−0.713670	+	1.23611i	−0.963470	+	0.267815i	$0.913698\pi$
$314$	23.4040	+	11.2708i	1.32077	+	0.636047i
$315$		0			0
$316$	−4.51523	+	2.17442i	−0.254002	+	0.122321i
$317$	1.53288	−	20.4548i	0.0860949	−	1.14886i	−0.772089	−	0.635515i	$-0.780788\pi$
$317$	1.53288	−	20.4548i	0.0860949	−	1.14886i	0.858184	−	0.513342i	$-0.171593\pi$
$318$		0			0
$319$	18.8668	−	5.81962i	1.05634	−	0.325836i
$320$	0.195602	−	2.61012i	0.0109345	−	0.145910i
$321$		0			0
$322$	−0.0143023	−	0.353373i	−0.000797035	−	0.0196927i
$323$	−28.3019	−	13.6295i	−1.57476	−	0.758365i
$324$		0			0
$325$	−3.35422	−	5.80967i	−0.186058	−	0.322263i
$326$	0.407342	+	5.43560i	0.0225606	+	0.301050i
$327$		0			0
$328$	3.52373	−	15.4385i	0.194565	−	0.852446i
$329$	−3.04768	+	0.352813i	−0.168024	+	0.0194512i
$330$		0			0
$331$	23.1445	−	15.7796i	1.27214	−	0.867327i	0.276533	−	0.961005i	$-0.410815\pi$
$331$	23.1445	−	15.7796i	1.27214	−	0.867327i	0.995603	+	0.0936775i	$0.0298623\pi$
$332$	−2.90923	+	2.69937i	−0.159665	+	0.148147i
$333$		0			0
$334$	−1.20455	−	1.11766i	−0.0659100	−	0.0611555i
$335$	−7.87736	−	9.87790i	−0.430386	−	0.539687i
$336$		0			0
$337$	13.8737	−	17.3970i	0.755747	−	0.947676i	−0.244009	−	0.969773i	$-0.578463\pi$
$337$	13.8737	−	17.3970i	0.755747	−	0.947676i	0.999756	+	0.0220966i	$0.00703413\pi$
$338$	14.5647	−	2.19528i	0.792218	−	0.119408i
$339$		0			0
$340$	−2.97699	+	7.58525i	−0.161450	+	0.411368i
$341$	−9.02406	−	2.78355i	−0.488680	−	0.150738i
$342$		0			0
$343$	−5.95656	+	17.5362i	−0.321624	+	0.946867i
$344$	15.0599			0.811973
$345$		0			0
$346$	−10.6765	+	27.2034i	−0.573975	+	1.46246i
$347$	5.98786	+	4.08245i	0.321445	+	0.219158i	0.713282	−	0.700877i	$-0.247208\pi$
$347$	5.98786	+	4.08245i	0.321445	+	0.219158i	−0.391837	+	0.920035i	$0.628160\pi$
$348$		0			0
$349$	−4.69989	+	5.89348i	−0.251580	+	0.315471i	−0.891544	−	0.452933i	$-0.850377\pi$
$349$	−4.69989	+	5.89348i	−0.251580	+	0.315471i	0.639965	+	0.768404i	$0.278949\pi$
$350$	−6.01543	+	2.64638i	−0.321538	+	0.141455i
$351$		0			0
$352$	9.10463	+	8.44786i	0.485278	+	0.450273i
$353$	−32.0804	−	4.83534i	−1.70747	−	0.257359i	−0.778533	−	0.627604i	$-0.784036\pi$
$353$	−32.0804	−	4.83534i	−1.70747	−	0.257359i	−0.928934	+	0.370245i	$0.879274\pi$
$354$		0			0
$355$	−21.7888	+	14.8554i	−1.15643	+	0.788440i
$356$	−1.81153	−	7.93684i	−0.0960110	−	0.420652i
$357$		0			0
$358$	−4.55051	+	19.9371i	−0.240502	+	1.05371i
$359$	7.02699	+	17.9045i	0.370870	+	0.944962i	0.987487	+	0.157699i	$0.0504074\pi$
$359$	7.02699	+	17.9045i	0.370870	+	0.944962i	−0.616617	+	0.787263i	$0.711497\pi$
$360$		0			0
$361$	−14.6785	−	25.4239i	−0.772552	−	1.33810i
$362$	−3.55098	+	6.15048i	−0.186636	+	0.323262i
$363$		0			0
$364$	−0.475343	−	11.7445i	−0.0249147	−	0.615580i
$365$	−21.5440	+	10.3750i	−1.12766	+	0.543054i
$366$		0			0
$367$	30.8804	−	9.52533i	1.61194	−	0.497218i	0.647623	−	0.761961i	$-0.275763\pi$
$367$	30.8804	−	9.52533i	1.61194	−	0.497218i	0.964319	+	0.264743i	$0.0852871\pi$
$368$	−0.371287	+	0.114527i	−0.0193547	+	0.00597012i
$369$		0			0
$370$	15.2539	−	7.34589i	0.793012	−	0.381894i
$371$	11.3751	+	2.11636i	0.590568	+	0.109876i
$372$		0			0
$373$	−9.61917	+	16.6609i	−0.498062	+	0.862668i	−0.999997	−	0.00223658i	$-0.999288\pi$
$373$	−9.61917	+	16.6609i	−0.498062	+	0.862668i	0.501936	+	0.864905i	$0.332621\pi$
$374$	9.63534	+	16.6889i	0.498232	+	0.862962i
$375$		0			0
$376$	0.760043	+	1.93656i	0.0391962	+	0.0998703i
$377$	−8.22374	+	36.0306i	−0.423544	+	1.85567i
$378$		0			0
$379$	6.88521	+	30.1661i	0.353670	+	1.54953i	0.768633	+	0.639690i	$0.220937\pi$
$379$	6.88521	+	30.1661i	0.353670	+	1.54953i	−0.414963	+	0.909838i	$0.636206\pi$
$380$	−10.3643	+	7.06623i	−0.531675	+	0.362490i
$381$		0			0
$382$	−13.5713	−	2.04554i	−0.694367	−	0.104659i
$383$	−6.03724	−	5.60174i	−0.308489	−	0.286236i	0.510701	−	0.859758i	$-0.329386\pi$
$383$	−6.03724	−	5.60174i	−0.308489	−	0.286236i	−0.819190	+	0.573523i	$0.805576\pi$
$384$		0			0
$385$	3.16691	−	11.9650i	0.161401	−	0.609793i
$386$	−23.8836	+	29.9491i	−1.21564	+	1.52437i
$387$		0			0
$388$	−12.3919	−	8.44864i	−0.629103	−	0.428915i
$389$	−2.06324	+	5.25705i	−0.104610	+	0.266543i	−0.973589	−	0.228306i	$-0.926681\pi$
$389$	−2.06324	+	5.25705i	−0.104610	+	0.266543i	0.868979	+	0.494849i	$0.164777\pi$
$390$		0			0
$391$	−0.351168			−0.0177593
$392$	12.5285	+	0.862024i	0.632786	+	0.0435388i
$393$		0			0
$394$	31.0202	+	9.56846i	1.56277	+	0.482052i
$395$	3.60877	−	9.19500i	0.181577	−	0.462651i
$396$		0			0
$397$	−3.86406	+	0.582414i	−0.193932	+	0.0292305i	−0.245290	−	0.969450i	$-0.578883\pi$
$397$	−3.86406	+	0.582414i	−0.193932	+	0.0292305i	0.0513580	+	0.998680i	$0.483645\pi$
$398$	22.3426	−	28.0167i	1.11993	−	1.40435i
$399$		0			0
$400$	4.50165	+	5.64489i	0.225083	+	0.282245i
$401$	22.4340	+	20.8157i	1.12030	+	1.03949i	0.998900	+	0.0468815i	$0.0149283\pi$
$401$	22.4340	+	20.8157i	1.12030	+	1.03949i	0.121398	+	0.992604i	$0.461262\pi$
$402$		0			0
$403$	12.9580	−	12.0233i	0.645484	−	0.598922i
$404$	−3.03165	+	2.06695i	−0.150830	+	0.102834i
$405$		0			0
$406$	34.2092	+	11.8533i	1.69777	+	0.588267i
$407$	2.88280	−	12.6304i	0.142895	−	0.626065i
$408$		0			0
$409$	−0.788617	−	10.5234i	−0.0389946	−	0.520347i	−0.982163	−	0.188032i	$-0.939789\pi$
$409$	−0.788617	−	10.5234i	−0.0389946	−	0.520347i	0.943168	−	0.332315i	$-0.107830\pi$
$410$	−14.3094	−	24.7846i	−0.706690	−	1.22402i
$411$		0			0
$412$	5.53243	+	2.66428i	0.272563	+	0.131260i
$413$	−8.10375	+	2.19792i	−0.398759	+	0.108153i
$414$		0			0
$415$	0.584561	−	7.80043i	0.0286950	−	0.382908i
$416$	−22.2155	+	6.85258i	−1.08921	+	0.335975i
$417$		0			0
$418$	−2.21690	+	29.5824i	−0.108432	+	1.44692i
$419$	23.1917	−	11.1685i	1.13299	−	0.545618i	0.229106	−	0.973401i	$-0.426420\pi$
$419$	23.1917	−	11.1685i	1.13299	−	0.545618i	0.903881	+	0.427784i	$0.140705\pi$
$420$		0			0
$421$	−25.6443	−	12.3497i	−1.24983	−	0.601885i	−0.312362	−	0.949963i	$-0.601120\pi$
$421$	−25.6443	−	12.3497i	−1.24983	−	0.601885i	−0.937466	+	0.348078i	$0.886835\pi$
$422$	−18.1422	+	31.4233i	−0.883150	+	1.52966i
$423$		0			0
$424$	−0.586301	−	7.82364i	−0.0284733	−	0.379950i
$425$	2.38402	+	6.07439i	0.115642	+	0.294651i
$426$		0			0
$427$	−7.27053	+	11.6498i	−0.351846	+	0.563771i
$428$	1.04472	+	4.57723i	0.0504986	+	0.221249i
$429$		0			0
$430$	19.9515	−	18.5123i	0.962146	−	0.892741i
$431$	−23.7126	−	3.57409i	−1.14219	−	0.172158i	−0.449425	−	0.893318i	$-0.648371\pi$
$431$	−23.7126	−	3.57409i	−1.14219	−	0.172158i	−0.692768	+	0.721160i	$0.743609\pi$
$432$		0			0
$433$	−22.1171	−	27.7340i	−1.06288	−	1.33281i	−0.940299	−	0.340350i	$-0.889454\pi$
$433$	−22.1171	−	27.7340i	−1.06288	−	1.33281i	−0.122581	−	0.992459i	$-0.539117\pi$
$434$	−10.3255	−	13.9016i	−0.495641	−	0.667299i
$435$		0			0
$436$	−6.84590	+	1.03185i	−0.327859	+	0.0494168i
$437$	−0.446657	−	0.304526i	−0.0213665	−	0.0145674i
$438$		0			0
$439$	2.53140	+	0.780832i	0.120817	+	0.0372671i	0.354574	−	0.935028i	$-0.384626\pi$
$439$	2.53140	+	0.780832i	0.120817	+	0.0372671i	−0.233757	+	0.972295i	$0.575102\pi$
$440$	−8.39256			−0.400100
$441$		0			0
$442$	−36.0713			−1.71574
$443$	21.1196	+	6.51453i	1.00342	+	0.309515i	0.752571	−	0.658511i	$-0.228813\pi$
$443$	21.1196	+	6.51453i	1.00342	+	0.309515i	0.250851	+	0.968026i	$0.419290\pi$
$444$		0			0
$445$	13.2578	+	9.03901i	0.628480	+	0.428490i
$446$	−15.3773	+	2.31775i	−0.728136	+	0.109749i
$447$		0			0
$448$	−0.693797	−	3.60652i	−0.0327788	−	0.170392i
$449$	1.58403	+	1.98631i	0.0747549	+	0.0937397i	0.817803	−	0.575499i	$-0.195192\pi$
$449$	1.58403	+	1.98631i	0.0747549	+	0.0937397i	−0.743048	+	0.669238i	$0.766621\pi$
$450$		0			0
$451$	−21.6544	−	3.26387i	−1.01966	−	0.153690i
$452$	−6.62362	+	6.14582i	−0.311549	+	0.289075i
$453$		0			0
$454$	5.80163	+	25.4186i	0.272284	+	1.19295i
$455$	16.4319	+	16.3319i	0.770338	+	0.765651i
$456$		0			0
$457$	−1.30899	−	3.33525i	−0.0612319	−	0.156016i	0.896983	−	0.442064i	$-0.145754\pi$
$457$	−1.30899	−	3.33525i	−0.0612319	−	0.156016i	−0.958215	+	0.286048i	$0.907658\pi$
$458$	0.475744	+	6.34836i	0.0222301	+	0.296639i
$459$		0			0
$460$	−0.0701151	+	0.121443i	−0.00326913	+	0.00566231i
$461$	3.47251	+	1.67227i	0.161731	+	0.0778856i	0.512998	−	0.858390i	$-0.328535\pi$
$461$	3.47251	+	1.67227i	0.161731	+	0.0778856i	−0.351267	+	0.936275i	$0.614249\pi$
$462$		0			0
$463$	23.8417	−	11.4816i	1.10802	−	0.533593i	0.211847	−	0.977303i	$-0.432052\pi$
$463$	23.8417	−	11.4816i	1.10802	−	0.533593i	0.896171	+	0.443709i	$0.146338\pi$
$464$	2.97246	−	39.6647i	0.137993	−	1.84139i
$465$		0			0
$466$	16.0742	−	4.95825i	0.744625	−	0.229686i
$467$	−1.28240	+	17.1124i	−0.0593424	+	0.791869i	0.885562	+	0.464522i	$0.153774\pi$
$467$	−1.28240	+	17.1124i	−0.0593424	+	0.791869i	−0.944904	+	0.327347i	$0.893845\pi$
$468$		0			0
$469$	−14.2958	−	10.4835i	−0.660118	−	0.484084i
$470$	3.38742	+	1.63129i	0.156250	+	0.0752460i
$471$		0			0
$472$	2.84674	+	4.93070i	0.131032	+	0.226954i
$473$	−1.55636	−	20.7681i	−0.0715613	−	0.954920i
$474$		0			0
$475$	−2.23530	+	9.79350i	−0.102563	+	0.449356i
$476$	−1.24548	+	11.3655i	−0.0570863	+	0.520938i
$477$		0			0
$478$	−42.4052	+	28.9114i	−1.93957	+	1.32238i
$479$	−1.21170	+	1.12429i	−0.0553638	+	0.0513701i	−0.707369	−	0.706844i	$-0.750118\pi$
$479$	−1.21170	+	1.12429i	−0.0553638	+	0.0513701i	0.652006	+	0.758214i	$0.273928\pi$
$480$		0			0
$481$	17.7764	+	16.4941i	0.810534	+	0.752066i
$482$	5.17412	+	6.48814i	0.235675	+	0.295527i
$483$		0			0
$484$	−2.88977	+	3.62366i	−0.131353	+	0.164712i
$485$	29.2310	−	4.40587i	1.32731	−	0.200060i
$486$		0			0
$487$	5.23371	−	13.3353i	0.237162	−	0.604279i	−0.761895	−	0.647701i	$-0.775731\pi$
$487$	5.23371	−	13.3353i	0.237162	−	0.604279i	0.999057	+	0.0434219i	$0.0138260\pi$
$488$	8.89790	+	2.74464i	0.402789	+	0.124244i
$489$		0			0
$490$	17.6576	−	14.2586i	0.797688	−	0.644139i
$491$	−16.4881			−0.744096			−0.372048	−	0.928213i	$-0.621344\pi$
$491$	−16.4881			−0.744096			−0.372048	+	0.928213i	$0.621344\pi$
$492$		0			0
$493$	13.1337	−	33.4642i	0.591514	−	1.50715i
$494$	−45.8797	−	31.2803i	−2.06423	−	1.40737i
$495$		0			0
$496$	−11.8619	+	14.8744i	−0.532615	+	0.667878i
$497$	−24.0505	+	28.1203i	−1.07881	+	1.26137i
$498$		0			0
$499$	−16.8049	−	15.5926i	−0.752289	−	0.698023i	0.207658	−	0.978201i	$-0.433416\pi$
$499$	−16.8049	−	15.5926i	−0.752289	−	0.698023i	−0.959948	+	0.280179i	$0.909606\pi$
$500$	11.4952	+	1.73263i	0.514083	+	0.0774855i
$501$		0			0
$502$	−0.828321	+	0.564740i	−0.0369698	+	0.0252056i
$503$	1.98101	+	8.67939i	0.0883290	+	0.386995i	0.999697	−	0.0245967i	$-0.00783018\pi$
$503$	1.98101	+	8.67939i	0.0883290	+	0.386995i	−0.911368	+	0.411592i	$0.864973\pi$
$504$		0			0
$505$	1.60929	−	7.05078i	0.0716127	−	0.313756i
$506$	0.121160	+	0.308710i	0.00538620	+	0.0137238i
$507$		0			0
$508$	4.88961	+	8.46905i	0.216941	+	0.375753i
$509$	−0.759864	+	1.31612i	−0.0336804	+	0.0583362i	−0.882374	−	0.470548i	$-0.844056\pi$
$509$	−0.759864	+	1.31612i	−0.0336804	+	0.0583362i	0.848694	+	0.528884i	$0.177389\pi$
$510$		0			0
$511$	−25.3646	+	21.9631i	−1.12206	+	0.971589i
$512$	6.38613	−	3.07540i	0.282230	−	0.135915i
$513$		0			0
$514$	47.3982	−	14.6204i	2.09064	−	0.644878i
$515$	−11.5654	+	3.56745i	−0.509633	+	0.157201i
$516$		0			0
$517$	2.59204	−	1.24826i	0.113998	−	0.0548984i
$518$	17.9590	−	15.5506i	0.789073	−	0.683255i
$519$		0			0
$520$	7.85470	−	13.6047i	0.344451	−	0.596607i
$521$	2.57347	+	4.45737i	0.112746	+	0.195281i	0.916876	−	0.399171i	$-0.130702\pi$
$521$	2.57347	+	4.45737i	0.112746	+	0.195281i	−0.804131	+	0.594453i	$0.797369\pi$
$522$		0			0
$523$	−0.0873485	−	0.222560i	−0.00381948	−	0.00973189i	0.928951	−	0.370202i	$-0.120712\pi$
$523$	−0.0873485	−	0.222560i	−0.00381948	−	0.00973189i	−0.932771	+	0.360470i	$0.882616\pi$
$524$	0.540053	−	2.36613i	0.0235923	−	0.103365i
$525$		0			0
$526$	−8.40409	−	36.8207i	−0.366436	−	1.60546i
$527$	−14.2069	+	9.68612i	−0.618863	+	0.421934i
$528$		0			0
$529$	22.7371	+	3.42707i	0.988571	+	0.149003i
$530$	−10.3939	−	9.64414i	−0.451483	−	0.418915i
$531$		0			0
$532$	−11.4401	+	13.3760i	−0.495990	+	0.579921i
$533$	25.5575	−	32.0481i	1.10702	−	1.38816i
$534$		0			0
$535$	−7.64586	−	5.21286i	−0.330559	−	0.225372i
$536$	−4.39168	+	11.1898i	−0.189692	+	0.483327i
$537$		0			0
$538$	−19.0750			−0.822382
$539$	−0.105993	−	17.3664i	−0.00456545	−	0.748024i
$540$		0			0
$541$	−7.82390	−	2.41335i	−0.336376	−	0.103758i	0.121966	−	0.992534i	$-0.461080\pi$
$541$	−7.82390	−	2.41335i	−0.336376	−	0.103758i	−0.458342	+	0.888776i	$0.651556\pi$
$542$	−5.89443	+	15.0188i	−0.253187	+	0.645111i
$543$		0			0
$544$	22.3618	−	3.37049i	0.958753	−	0.144509i
$545$	8.50802	−	10.6687i	0.364444	−	0.456998i
$546$		0			0
$547$	9.42201	+	11.8148i	0.402856	+	0.505165i	0.941335	−	0.337474i	$-0.109572\pi$
$547$	9.42201	+	11.8148i	0.402856	+	0.505165i	−0.538479	+	0.842639i	$0.681001\pi$
$548$	15.1105	+	14.0205i	0.645489	+	0.598926i
$549$		0			0
$550$	4.51742	−	4.19156i	0.192624	−	0.178729i
$551$	45.7245	−	31.1744i	1.94793	−	1.32807i
$552$		0			0
$553$	1.50979	−	13.7775i	0.0642029	−	0.585880i
$554$	2.65305	−	11.6238i	0.112717	−	0.493847i
$555$		0			0
$556$	−0.0367278	−	0.490098i	−0.00155761	−	0.0207848i
$557$	−9.53123	−	16.5086i	−0.403851	−	0.699491i	0.590336	−	0.807158i	$-0.298995\pi$
$557$	−9.53123	−	16.5086i	−0.403851	−	0.699491i	−0.994187	+	0.107667i	$0.965662\pi$
$558$		0			0
$559$	35.1227	+	16.9142i	1.48553	+	0.715395i
$560$	−20.1074	−	14.7454i	−0.849694	−	0.623106i
$561$		0			0
$562$	1.62203	−	21.6445i	0.0684212	−	0.913017i
$563$	−5.87668	+	1.81271i	−0.247672	+	0.0763968i	−0.416106	−	0.909316i	$-0.636605\pi$
$563$	−5.87668	+	1.81271i	−0.247672	+	0.0763968i	0.168433	+	0.985713i	$0.446129\pi$
$564$		0			0
$565$	1.33090	−	17.7597i	0.0559915	−	0.747155i
$566$	25.4676	−	12.2646i	1.07048	−	0.515518i
$567$		0			0
$568$	22.6057	+	10.8863i	0.948515	+	0.456781i
$569$	−17.3797	+	30.1026i	−0.728596	+	1.26196i	0.228881	+	0.973454i	$0.426493\pi$
$569$	−17.3797	+	30.1026i	−0.728596	+	1.26196i	−0.957477	+	0.288510i	$0.906840\pi$
$570$		0			0
$571$	0.435329	+	5.80906i	0.0182179	+	0.243102i	0.998877	+	0.0473780i	$0.0150865\pi$
$571$	0.435329	+	5.80906i	0.0182179	+	0.243102i	−0.980659	+	0.195724i	$0.937294\pi$
$572$	4.02680	+	10.2601i	0.168369	+	0.428997i
$573$		0			0
$574$	−28.4813	−	28.3080i	−1.18879	−	1.18155i
$575$	0.0249888	+	0.109483i	0.00104211	+	0.00456576i
$576$		0			0
$577$	−1.86484	+	1.73032i	−0.0776343	+	0.0720341i	−0.718036	−	0.696006i	$-0.754959\pi$
$577$	−1.86484	+	1.73032i	−0.0776343	+	0.0720341i	0.640401	+	0.768040i	$0.278768\pi$
$578$	5.79079	+	0.872821i	0.240865	+	0.0363046i
$579$		0			0
$580$	−8.95046	−	11.2235i	−0.371648	−	0.466031i
$581$	−2.07343	−	10.7782i	−0.0860205	−	0.447155i
$582$		0			0
$583$	−10.7285	+	1.61706i	−0.444330	+	0.0669719i
$584$	18.7976	+	12.8160i	0.777851	+	0.530330i
$585$		0			0
$586$	9.89568	+	3.05241i	0.408787	+	0.126094i
$587$	0.649728			0.0268171			0.0134086	−	0.999910i	$-0.495732\pi$
$587$	0.649728			0.0268171			0.0134086	+	0.999910i	$0.495732\pi$
$588$		0			0
$589$	−26.4696			−1.09066
$590$	9.83244	+	3.03290i	0.404795	+	0.124863i
$591$		0			0
$592$	−21.5643	−	14.7023i	−0.886289	−	0.604261i
$593$	−30.3672	+	4.57712i	−1.24703	+	0.187960i	−0.739193	−	0.673493i	$-0.764793\pi$
$593$	−30.3672	+	4.57712i	−1.24703	+	0.187960i	−0.507838	+	0.861453i	$0.669555\pi$
$594$		0			0
$595$	−13.4375	−	18.0913i	−0.550882	−	0.741671i
$596$	−8.36553	−	10.4900i	−0.342665	−	0.429689i
$597$		0			0
$598$	−0.613828	−	0.0925197i	−0.0251013	−	0.00378341i
$599$	4.08087	−	3.78650i	0.166740	−	0.154712i	−0.592390	−	0.805652i	$-0.701815\pi$
$599$	4.08087	−	3.78650i	0.166740	−	0.154712i	0.759130	+	0.650940i	$0.225625\pi$
$600$		0			0
$601$	−2.37395	−	10.4009i	−0.0968352	−	0.424263i	0.903152	−	0.429321i	$-0.141247\pi$
$601$	−2.37395	−	10.4009i	−0.0968352	−	0.424263i	−0.999987	+	0.00505808i	$0.998390\pi$
$602$	20.2192	−	32.3977i	0.824074	−	1.32043i
$603$		0			0
$604$	−4.99271	−	12.7212i	−0.203150	−	0.517619i
$605$	−0.682685	−	9.10980i	−0.0277551	−	0.370366i
$606$		0			0
$607$	−22.3394	+	38.6929i	−0.906727	+	1.57050i	−0.0881447	+	0.996108i	$0.528094\pi$
$607$	−22.3394	+	38.6929i	−0.906727	+	1.57050i	−0.818582	+	0.574389i	$0.805240\pi$
$608$	31.3651	+	15.1046i	1.27202	+	0.612574i
$609$		0			0
$610$	15.1619	−	7.30157i	0.613886	−	0.295632i
$611$	−0.402432	+	5.37008i	−0.0162807	+	0.217250i
$612$		0			0
$613$	−33.3372	+	10.2832i	−1.34648	+	0.415333i	−0.882416	−	0.470470i	$-0.844084\pi$
$613$	−33.3372	+	10.2832i	−1.34648	+	0.415333i	−0.464061	+	0.885803i	$0.653608\pi$
$614$	1.36698	−	18.2411i	0.0551669	−	0.736151i
$615$		0			0
$616$	−11.3654	+	3.08254i	−0.457924	+	0.124199i
$617$	27.7523	+	13.3648i	1.11726	+	0.538046i	0.899046	−	0.437854i	$-0.144261\pi$
$617$	27.7523	+	13.3648i	1.11726	+	0.538046i	0.218218	+	0.975900i	$0.429975\pi$
$618$		0			0
$619$	7.51631	+	13.0186i	0.302106	+	0.523263i	0.976613	−	0.215006i	$-0.0689770\pi$
$619$	7.51631	+	13.0186i	0.302106	+	0.523263i	−0.674507	+	0.738269i	$0.735644\pi$
$620$	0.513117	+	6.84707i	0.0206073	+	0.274985i
$621$		0			0
$622$	−8.67057	+	37.9882i	−0.347658	+	1.52319i
$623$	21.2739	+	7.37128i	0.852322	+	0.295324i
$624$		0			0
$625$	−12.9641	+	8.83874i	−0.518562	+	0.353550i
$626$	31.8299	−	29.5338i	1.27218	−	1.18041i
$627$		0			0
$628$	−10.5943	−	9.83004i	−0.422757	−	0.392261i
$629$	−14.7072	−	18.4422i	−0.586414	−	0.735340i
$630$		0			0
$631$	−17.4879	+	21.9292i	−0.696183	+	0.872986i	−0.996732	−	0.0807802i	$-0.974259\pi$
$631$	−17.4879	+	21.9292i	−0.696183	+	0.872986i	0.300549	+	0.953767i	$0.402830\pi$
$632$	−9.29318	+	1.40072i	−0.369663	+	0.0557177i
$633$		0			0
$634$	−12.8858	+	32.8324i	−0.511760	+	1.30394i
$635$	−18.4187	−	5.68141i	−0.730923	−	0.225460i
$636$		0			0
$637$	28.2510	+	16.0816i	1.11934	+	0.637177i
$638$	−33.9495			−1.34407
$639$		0			0
$640$	−8.54164	+	21.7637i	−0.337638	+	0.860287i
$641$	29.1116	+	19.8479i	1.14984	+	0.783946i	0.979501	−	0.201440i	$-0.0645622\pi$
$641$	29.1116	+	19.8479i	1.14984	+	0.783946i	0.170336	+	0.985386i	$0.445515\pi$
$642$		0			0
$643$	24.8703	−	31.1864i	0.980789	−	1.22987i	0.00757464	−	0.999971i	$-0.497589\pi$
$643$	24.8703	−	31.1864i	0.980789	−	1.22987i	0.973214	−	0.229899i	$-0.0738397\pi$
$644$	−0.0503459	+	0.190213i	−0.00198390	+	0.00749545i
$645$		0			0
$646$	39.5951	+	36.7389i	1.55785	+	1.44547i
$647$	19.2454	+	2.90077i	0.756614	+	0.114041i	0.516011	−	0.856582i	$-0.327417\pi$
$647$	19.2454	+	2.90077i	0.756614	+	0.114041i	0.240604	+	0.970623i	$0.422655\pi$
$648$		0			0
$649$	6.50543	−	4.43533i	0.255360	−	0.174102i
$650$	2.56680	+	11.2459i	0.100678	+	0.441100i
$651$		0			0
$652$	0.674824	−	2.95660i	0.0264281	−	0.115789i
$653$	8.82074	+	22.4749i	0.345182	+	0.879510i	0.993043	+	0.117751i	$0.0375685\pi$
$653$	8.82074	+	22.4749i	0.345182	+	0.879510i	−0.647861	+	0.761759i	$0.724336\pi$
$654$		0			0
$655$	2.39181	+	4.14273i	0.0934557	+	0.161870i
$656$	−22.0587	+	38.2068i	−0.861248	+	1.49173i
$657$		0			0
$658$	5.18647	+	0.964949i	0.202190	+	0.0376176i
$659$	−21.7133	+	10.4566i	−0.845830	+	0.407330i	−0.806028	−	0.591877i	$-0.798387\pi$
$659$	−21.7133	+	10.4566i	−0.845830	+	0.407330i	−0.0398023	+	0.999208i	$0.512673\pi$
$660$		0			0
$661$	33.6229	−	10.3713i	1.30778	−	0.403396i	0.438950	−	0.898511i	$-0.355350\pi$
$661$	33.6229	−	10.3713i	1.30778	−	0.403396i	0.868827	+	0.495115i	$0.164874\pi$
$662$	−46.0263	+	14.1972i	−1.78886	+	0.551791i
$663$		0			0
$664$	−6.70541	+	3.22915i	−0.260220	+	0.125316i
$665$	−1.40295	−	34.6633i	−0.0544040	−	1.34419i
$666$		0			0
$667$	0.309330	−	0.535775i	0.0119773	−	0.0207453i
$668$	0.457104	+	0.791728i	0.0176859	+	0.0306329i
$669$		0			0
$670$	7.93689	+	20.2229i	0.306629	+	0.781278i
$671$	2.86541	−	12.5542i	0.110618	−	0.484649i
$672$		0			0
$673$	3.56115	+	15.6024i	0.137272	+	0.601428i	0.996028	+	0.0890431i	$0.0283809\pi$
$673$	3.56115	+	15.6024i	0.137272	+	0.601428i	−0.858756	+	0.512385i	$0.828762\pi$
$674$	−31.6132	+	21.5535i	−1.21769	+	0.830209i
$675$		0			0
$676$	−8.10324	−	1.22137i	−0.311663	−	0.0469756i
$677$	−10.7026	−	9.93061i	−0.411336	−	0.381664i	0.447186	−	0.894441i	$-0.352426\pi$
$677$	−10.7026	−	9.93061i	−0.411336	−	0.381664i	−0.858522	+	0.512777i	$0.828617\pi$
$678$		0			0
$679$	37.9670	−	16.7029i	1.45704	−	0.640999i
$680$	−9.52753	+	11.9471i	−0.365364	+	0.458152i
$681$		0			0
$682$	13.4167	+	9.14732i	0.513750	+	0.350269i
$683$	2.09727	−	5.34375i	0.0802497	−	0.204473i	−0.885118	−	0.465367i	$-0.845922\pi$
$683$	2.09727	−	5.34375i	0.0802497	−	0.204473i	0.965367	+	0.260895i	$0.0840175\pi$
$684$		0			0
$685$	−40.6289			−1.55235
$686$	18.6751	−	25.7948i	0.713019	−	0.984851i
$687$		0			0
$688$	−40.0926	−	12.3669i	−1.52851	−	0.471484i
$689$	7.41961	−	18.9049i	0.282665	−	0.720218i
$690$		0			0
$691$	3.03027	−	0.456740i	0.115277	−	0.0173752i	−0.0911503	−	0.995837i	$-0.529054\pi$
$691$	3.03027	−	0.456740i	0.115277	−	0.0173752i	0.206427	+	0.978462i	$0.433816\pi$
$692$	10.1372	−	12.7116i	0.385358	−	0.483224i
$693$		0			0
$694$	−7.76955	−	9.74270i	−0.294928	−	0.369828i
$695$	0.710108	+	0.658884i	0.0269359	+	0.0249929i
$696$		0			0
$697$	−29.2291	+	27.1206i	−1.10713	+	1.02727i
$698$	10.7094	−	7.30154i	0.405356	−	0.276367i
$699$		0			0
$700$	3.63203	−	0.420460i	0.137278	−	0.0158919i
$701$	−3.95578	+	17.3314i	−0.149408	+	0.654599i	0.843642	+	0.536906i	$0.180407\pi$
$701$	−3.95578	+	17.3314i	−0.149408	+	0.654599i	−0.993050	+	0.117693i	$0.962450\pi$
$702$		0			0
$703$	−2.71362	−	36.2107i	−0.102346	−	1.36571i
$704$	1.72195	+	2.98251i	0.0648984	+	0.112407i
$705$		0			0
$706$	50.2606	+	24.2042i	1.89158	+	0.910939i
$707$	−0.410378	−	10.1394i	−0.0154338	−	0.381331i
$708$		0			0
$709$	−1.56692	+	20.9092i	−0.0588471	+	0.785260i	0.887232	+	0.461324i	$0.152625\pi$
$709$	−1.56692	+	20.9092i	−0.0588471	+	0.785260i	−0.946079	+	0.323936i	$0.894994\pi$
$710$	43.3303	−	13.3656i	1.62616	−	0.501603i
$711$		0			0
$712$	1.14089	−	15.2241i	0.0427565	−	0.570546i
$713$	−0.266604	+	0.128390i	−0.00998440	+	0.00480823i
$714$		0			0
$715$	−19.5732	−	9.42596i	−0.731996	−	0.352511i
$716$	5.68872	−	9.85316i	0.212598	−	0.368230i
$717$		0			0
$718$	−2.47153	−	32.9803i	−0.0922368	−	1.23082i
$719$	14.5248	+	37.0087i	0.541685	+	1.38019i	0.895578	+	0.444905i	$0.146763\pi$
$719$	14.5248	+	37.0087i	0.541685	+	1.38019i	−0.353892	+	0.935286i	$0.615142\pi$
$720$		0			0
$721$	−14.3518	+	9.07903i	−0.534488	+	0.338121i
$722$	11.2327	+	49.2135i	0.418037	+	1.83154i
$723$		0			0
$724$	2.89647	−	2.68753i	0.107646	−	0.0998813i
$725$	−11.3677	−	1.71340i	−0.422184	−	0.0636340i
$726$		0			0
$727$	31.6753	+	39.7195i	1.17477	+	1.47312i	0.849573	+	0.527470i	$0.176859\pi$
$727$	31.6753	+	39.7195i	1.17477	+	1.47312i	0.325198	+	0.945646i	$0.394569\pi$
$728$	5.64003	−	21.3088i	0.209034	−	0.789756i
$729$		0			0
$730$	40.6573	−	6.12810i	1.50479	−	0.226811i
$731$	−31.3311	−	21.3612i	−1.15882	−	0.790071i
$732$		0			0
$733$	26.2834	+	8.10737i	0.970801	+	0.299452i	0.739296	−	0.673381i	$-0.235159\pi$
$733$	26.2834	+	8.10737i	0.970801	+	0.299452i	0.231506	+	0.972834i	$0.425635\pi$
$734$	−55.5673			−2.05103
$735$		0			0
$736$	0.389176			0.0143452
$737$	15.8851	+	4.89989i	0.585134	+	0.180490i
$738$		0			0
$739$	19.4989	+	13.2941i	0.717279	+	0.489032i	0.866125	−	0.499828i	$-0.166603\pi$
$739$	19.4989	+	13.2941i	0.717279	+	0.489032i	−0.148846	+	0.988860i	$0.547556\pi$
$740$	−9.31426	+	1.40390i	−0.342399	+	0.0516084i
$741$		0			0
$742$	−17.6179	−	9.24265i	−0.646773	−	0.339308i
$743$	−16.4261	−	20.5977i	−0.602616	−	0.755656i	0.383167	−	0.923679i	$-0.374833\pi$
$743$	−16.4261	−	20.5977i	−0.602616	−	0.755656i	−0.985783	+	0.168023i	$0.946262\pi$
$744$		0			0
$745$	26.1503	+	3.94152i	0.958073	+	0.144406i
$746$	24.2495	−	22.5002i	0.887837	−	0.823793i
$747$		0			0
$748$	−2.38574	−	10.4526i	−0.0872314	−	0.382186i
$749$	−12.2688	−	4.25107i	−0.448293	−	0.155331i
$750$		0			0
$751$	−11.4064	−	29.0631i	−0.416226	−	1.06053i	−0.973193	−	0.229992i	$-0.926130\pi$
$751$	−11.4064	−	29.0631i	−0.416226	−	1.06053i	0.556966	−	0.830535i	$-0.311965\pi$
$752$	−0.433126	−	5.77966i	−0.0157945	−	0.210763i
$753$		0			0
$754$	31.7738	−	55.0338i	1.15713	−	2.00421i
$755$	24.2682	+	11.6870i	0.883212	+	0.425332i
$756$		0			0
$757$	14.4858	−	6.97598i	0.526495	−	0.253546i	−0.151703	−	0.988426i	$-0.548476\pi$
$757$	14.4858	−	6.97598i	0.526495	−	0.253546i	0.678198	+	0.734880i	$0.262761\pi$
$758$	3.97596	−	53.0556i	0.144414	−	1.92706i
$759$		0			0
$760$	−22.4785	+	6.93371i	−0.815382	+	0.251512i
$761$	−1.21379	+	16.1970i	−0.0440000	+	0.587140i	0.931012	+	0.364988i	$0.118927\pi$
$761$	−1.21379	+	16.1970i	−0.0440000	+	0.587140i	−0.975012	+	0.222151i	$0.928692\pi$
$762$		0			0
$763$	7.60316	−	17.5727i	0.275253	−	0.636176i
$764$	6.87961	+	3.31305i	0.248896	+	0.119862i
$765$		0			0
$766$	7.08067	+	12.2641i	0.255835	+	0.443119i
$767$	1.10136	+	14.6967i	0.0397680	+	0.530667i
$768$		0			0
$769$	8.92545	−	39.1050i	0.321860	−	1.41016i	−0.512379	−	0.858759i	$-0.671236\pi$
$769$	8.92545	−	39.1050i	0.321860	−	1.41016i	0.834240	−	0.551402i	$-0.185907\pi$
$770$	−11.2678	+	18.0546i	−0.406062	+	0.650643i
$771$		0			0
$772$	17.6089	−	12.0055i	0.633758	−	0.432089i
$773$	−10.2125	+	9.47583i	−0.367319	+	0.340822i	−0.842139	−	0.539261i	$-0.818704\pi$
$773$	−10.2125	+	9.47583i	−0.367319	+	0.340822i	0.474820	+	0.880083i	$0.342513\pi$
$774$		0			0
$775$	4.03077	+	3.74001i	0.144790	+	0.134345i
$776$	−17.5361	−	21.9896i	−0.629509	−	0.789379i
$777$		0			0
$778$	6.05454	−	7.59216i	0.217066	−	0.272192i
$779$	−60.6953	+	9.14835i	−2.17464	+	0.327774i
$780$		0			0
$781$	12.6765	−	32.2992i	0.453601	−	1.15576i
$782$	0.577005	+	0.177983i	0.0206337	+	0.00636464i
$783$		0			0
$784$	−32.6457	−	12.5831i	−1.16592	−	0.449397i
$785$	28.4857			1.01670
$786$		0			0
$787$	−10.2475	+	26.1101i	−0.365283	+	0.930726i	0.623561	+	0.781774i	$0.285685\pi$
$787$	−10.2475	+	26.1101i	−0.365283	+	0.930726i	−0.988844	+	0.148952i	$0.952410\pi$
$788$	−14.9225	−	10.1740i	−0.531592	−	0.362433i
$789$		0			0
$790$	−10.5899	+	13.2793i	−0.376771	+	0.472456i
$791$	−4.72070	−	24.5393i	−0.167849	−	0.872518i
$792$		0			0
$793$	17.6692	+	16.3946i	0.627450	+	0.582189i
$794$	6.64423	+	1.00146i	0.235795	+	0.0355404i
$795$		0			0
$796$	−16.4727	+	11.2309i	−0.583860	+	0.398069i
$797$	1.16864	+	5.12013i	0.0413952	+	0.181364i	0.991399	−	0.130874i	$-0.0417784\pi$
$797$	1.16864	+	5.12013i	0.0413952	+	0.181364i	−0.950004	+	0.312238i	$0.898921\pi$
$798$		0			0
$799$	1.16563	−	5.10694i	0.0412369	−	0.180671i
$800$	−2.64205	−	6.73184i	−0.0934107	−	0.238007i
$801$		0			0
$802$	−26.3113	−	45.5725i	−0.929083	−	1.60922i
$803$	15.7311	−	27.2471i	0.555139	−	0.961529i
$804$		0			0
$805$	−0.182263	−	0.342327i	−0.00642394	−	0.0120654i
$806$	−27.3851	+	13.1879i	−0.964597	+	0.464526i
$807$		0			0
$808$	−6.57521	+	2.02818i	−0.231315	+	0.0713512i
$809$	14.5708	−	4.49449i	0.512281	−	0.158018i	−0.0278281	−	0.999613i	$-0.508859\pi$
$809$	14.5708	−	4.49449i	0.512281	−	0.158018i	0.540109	+	0.841595i	$0.318383\pi$
$810$		0			0
$811$	8.53541	−	4.11044i	0.299719	−	0.144337i	−0.277980	−	0.960587i	$-0.589665\pi$
$811$	8.53541	−	4.11044i	0.299719	−	0.144337i	0.577699	+	0.816250i	$0.303951\pi$
$812$	−16.2432	−	11.9116i	−0.570025	−	0.418017i
$813$		0			0
$814$	−11.1382	+	19.2919i	−0.390393	+	0.676181i
$815$	2.98868	+	5.17655i	0.104689	+	0.181327i
$816$		0			0
$817$	−21.3266	−	54.3393i	−0.746123	−	1.90109i
$818$	−4.03777	+	17.6906i	−0.141177	+	0.618539i
$819$		0			0
$820$	3.54305	+	15.5231i	0.123729	+	0.542091i
$821$	−3.20499	+	2.18512i	−0.111855	+	0.0762614i	−0.617956	−	0.786213i	$-0.712039\pi$
$821$	−3.20499	+	2.18512i	−0.111855	+	0.0762614i	0.506101	+	0.862474i	$0.331086\pi$
$822$		0			0
$823$	−21.3534	−	3.21851i	−0.744333	−	0.112190i	−0.234084	−	0.972216i	$-0.575209\pi$
$823$	−21.3534	−	3.21851i	−0.744333	−	0.112190i	−0.510250	+	0.860026i	$0.670447\pi$
$824$	8.44137	+	7.83244i	0.294069	+	0.272856i
$825$		0			0
$826$	14.4292	+	0.495815i	0.502057	+	0.0172516i
$827$	12.6686	−	15.8859i	0.440531	−	0.552408i	−0.511152	−	0.859490i	$-0.670781\pi$
$827$	12.6686	−	15.8859i	0.440531	−	0.552408i	0.951683	+	0.307082i	$0.0993527\pi$
$828$		0			0
$829$	20.5051	+	13.9802i	0.712173	+	0.485551i	0.864407	−	0.502793i	$-0.167694\pi$
$829$	20.5051	+	13.9802i	0.712173	+	0.485551i	−0.152234	+	0.988344i	$0.548647\pi$
$830$	−4.91398	+	12.5206i	−0.170567	+	0.434597i
$831$		0			0
$832$	−6.44638			−0.223488
$833$	−24.8421	−	19.5641i	−0.860728	−	0.677855i
$834$		0			0
$835$	−1.72187	−	0.531126i	−0.0595877	−	0.0183804i
$836$	6.02982	−	15.3637i	0.208546	−	0.531366i
$837$		0			0
$838$	−43.7668	+	6.59678i	−1.51190	+	0.227882i
$839$	1.31954	−	1.65465i	0.0455555	−	0.0571248i	−0.758532	−	0.651636i	$-0.774083\pi$
$839$	1.31954	−	1.65465i	0.0455555	−	0.0571248i	0.804087	+	0.594511i	$0.202654\pi$
$840$		0			0
$841$	21.4060	+	26.8422i	0.738136	+	0.925594i
$842$	35.8770	+	33.2890i	1.23640	+	1.14722i
$843$		0			0
$844$	14.7983	−	13.7308i	0.509377	−	0.472633i
$845$	13.3454	−	9.09876i	0.459097	−	0.313007i
$846$		0			0
$847$	−4.27049	−	12.0859i	−0.146736	−	0.415277i
$848$	−4.86379	+	21.3097i	−0.167023	+	0.731777i
$849$		0			0
$850$	−0.838510	−	11.1891i	−0.0287606	−	0.383784i
$851$	−0.202970	−	0.351555i	−0.00695774	−	0.0120512i
$852$		0			0
$853$	3.43398	+	1.65372i	0.117577	+	0.0566223i	0.491748	−	0.870738i	$-0.336358\pi$
$853$	3.43398	+	1.65372i	0.117577	+	0.0566223i	−0.374170	+	0.927360i	$0.622072\pi$
$854$	17.8507	−	15.4568i	0.610837	−	0.528921i
$855$		0			0
$856$	−0.657957	+	8.77982i	−0.0224885	+	0.300088i
$857$	29.2715	−	9.02905i	0.999894	−	0.308426i	0.248752	−	0.968567i	$-0.419980\pi$
$857$	29.2715	−	9.02905i	0.999894	−	0.308426i	0.751142	+	0.660141i	$0.229503\pi$
$858$		0			0
$859$	2.17939	−	29.0819i	0.0743597	−	0.992261i	−0.827846	−	0.560955i	$-0.810434\pi$
$859$	2.17939	−	29.0819i	0.0743597	−	0.992261i	0.902206	−	0.431306i	$-0.141947\pi$
$860$	−13.6429	+	6.57006i	−0.465218	+	0.224037i
$861$		0			0
$862$	37.1507	+	17.8908i	1.26536	+	0.609364i
$863$	11.7558	−	20.3617i	0.400173	−	0.693121i	−0.593573	−	0.804780i	$-0.702283\pi$
$863$	11.7558	−	20.3617i	0.400173	−	0.693121i	0.993747	+	0.111659i	$0.0356166\pi$
$864$		0			0
$865$	2.39483	+	31.9567i	0.0814266	+	1.08656i
$866$	22.2842	+	56.7793i	0.757249	+	1.92944i
$867$		0			0
$868$	3.20977	+	9.08396i	0.108947	+	0.308330i
$869$	2.89205	+	12.6709i	0.0981060	+	0.429830i
$870$		0			0
$871$	−22.8100	+	21.1646i	−0.772887	+	0.717134i
$872$	−12.8381	−	1.93504i	−0.434755	−	0.0655287i
$873$		0			0
$874$	0.579560	+	0.726745i	0.0196039	+	0.0245825i
$875$	−20.8970	+	24.4331i	−0.706446	+	0.825990i
$876$		0			0
$877$	−23.8141	+	3.58940i	−0.804145	+	0.121205i	−0.538238	−	0.842793i	$-0.680910\pi$
$877$	−23.8141	+	3.58940i	−0.804145	+	0.121205i	−0.265908	+	0.963999i	$0.585672\pi$
$878$	−3.76359	−	2.56597i	−0.127015	−	0.0865974i
$879$		0			0
$880$	22.3428	+	6.89184i	0.753175	+	0.232324i
$881$	49.0628			1.65297			0.826484	−	0.562960i	$-0.190338\pi$
$881$	49.0628			1.65297			0.826484	+	0.562960i	$0.190338\pi$
$882$		0			0
$883$	−44.2159			−1.48798			−0.743991	−	0.668189i	$-0.767070\pi$
$883$	−44.2159			−1.48798			−0.743991	+	0.668189i	$0.767070\pi$
$884$	19.1770	+	5.91533i	0.644994	+	0.198954i
$885$		0			0
$886$	−31.3998	−	21.4081i	−1.05490	−	0.719218i
$887$	−20.0288	+	3.01886i	−0.672502	+	0.101363i	−0.476411	−	0.879223i	$-0.658063\pi$
$887$	−20.0288	+	3.01886i	−0.672502	+	0.101363i	−0.196090	+	0.980586i	$0.562825\pi$
$888$		0			0
$889$	−27.0297	−	0.928788i	−0.906546	−	0.0311505i
$890$	−17.2027	−	21.5715i	−0.576634	−	0.723077i
$891$		0			0
$892$	8.55531	+	1.28950i	0.286453	+	0.0431758i
$893$	5.91121	−	5.48480i	0.197811	−	0.183542i
$894$		0			0
$895$	4.99007	+	21.8629i	0.166800	+	0.730797i
$896$	−3.57354	+	32.6102i	−0.119384	+	1.08943i
$897$		0			0
$898$	−1.59600	−	4.06654i	−0.0532592	−	0.135702i
$899$	−2.26374	−	30.2075i	−0.0755000	−	1.00748i
$900$		0			0
$901$	−9.87743	+	17.1082i	−0.329065	+	0.569957i
$902$	33.9261	+	16.3379i	1.12962	+	0.543994i
$903$		0			0
$904$	−15.2666	+	7.35200i	−0.507759	+	0.244524i
$905$	−0.581996	+	7.76620i	−0.0193462	+	0.258157i
$906$		0			0
$907$	−6.36050	+	1.96195i	−0.211197	+	0.0651456i	−0.398548	−	0.917147i	$-0.630486\pi$
$907$	−6.36050	+	1.96195i	−0.211197	+	0.0651456i	0.187351	+	0.982293i	$0.440010\pi$
$908$	1.08400	−	14.4650i	0.0359739	−	0.480038i
$909$		0			0
$910$	−18.7217	−	35.1631i	−0.620620	−	1.16565i
$911$	6.85855	+	3.30290i	0.227234	+	0.109430i	0.544037	−	0.839061i	$-0.316895\pi$
$911$	6.85855	+	3.30290i	0.227234	+	0.109430i	−0.316803	+	0.948491i	$0.602609\pi$
$912$		0			0
$913$	5.14610	+	8.91330i	0.170311	+	0.294987i
$914$	0.460398	+	6.14358i	0.0152286	+	0.203212i
$915$		0			0
$916$	0.788142	−	3.45307i	0.0260409	−	0.114093i
$917$	4.76064	+	4.73167i	0.157210	+	0.156254i
$918$		0			0
$919$	−17.4868	+	11.9223i	−0.576837	+	0.393281i	−0.816303	−	0.577624i	$-0.803980\pi$
$919$	−17.4868	+	11.9223i	−0.576837	+	0.393281i	0.239466	+	0.970905i	$0.423028\pi$
$920$	−0.192774	+	0.178868i	−0.00635556	+	0.00589710i
$921$		0			0
$922$	−4.85813	−	4.50769i	−0.159994	−	0.148453i
$923$	40.4945	+	50.7785i	1.33289	+	1.67139i
$924$		0			0
$925$	−4.70315	+	5.89756i	−0.154639	+	0.193911i
$926$	−44.9935	+	6.78168i	−1.47858	+	0.222860i
$927$		0			0
$928$	−14.5552	+	37.0861i	−0.477799	+	1.21741i
$929$	−18.1712	−	5.60509i	−0.596179	−	0.183897i	−0.0180431	−	0.999837i	$-0.505744\pi$
$929$	−18.1712	−	5.60509i	−0.596179	−	0.183897i	−0.578136	+	0.815940i	$0.696220\pi$
$930$		0			0
$931$	−14.6315	−	46.4264i	−0.479530	−	1.52156i
$932$	−9.35885			−0.306559
$933$		0			0
$934$	10.7802	−	27.4675i	0.352739	−	0.898764i
$935$	17.4602	+	11.9042i	0.571009	+	0.389307i
$936$		0			0
$937$	−4.69575	+	5.88828i	−0.153403	+	0.192362i	−0.852595	−	0.522573i	$-0.824972\pi$
$937$	−4.69575	+	5.88828i	−0.153403	+	0.192362i	0.699191	+	0.714935i	$0.253544\pi$
$938$	18.1760	+	24.4710i	0.593469	+	0.799007i
$939$		0			0
$940$	−1.53338	−	1.42277i	−0.0500133	−	0.0464055i
$941$	20.1686	+	3.03993i	0.657479	+	0.0990990i	0.469304	−	0.883037i	$-0.344505\pi$
$941$	20.1686	+	3.03993i	0.657479	+	0.0990990i	0.188175	+	0.982136i	$0.439743\pi$
$942$		0			0
$943$	−0.566954	+	0.386543i	−0.0184626	+	0.0125876i
$944$	−3.52962	−	15.4643i	−0.114879	−	0.503319i
$945$		0			0
$946$	−7.96865	+	34.9129i	−0.259083	+	1.13512i
$947$	−19.8549	−	50.5895i	−0.645198	−	1.64394i	−0.759512	−	0.650494i	$-0.774562\pi$
$947$	−19.8549	−	50.5895i	−0.645198	−	1.64394i	0.114313	−	0.993445i	$-0.463533\pi$
$948$		0			0
$949$	29.4459	+	51.0018i	0.955855	+	1.65559i
$950$	8.63646	−	14.9588i	0.280204	−	0.485327i
$951$		0			0
$952$	−8.51424	+	19.6785i	−0.275948	+	0.637782i
$953$	−23.7265	+	11.4261i	−0.768578	+	0.370127i	−0.776725	−	0.629839i	$-0.783121\pi$
$953$	−23.7265	+	11.4261i	−0.768578	+	0.370127i	0.00814789	+	0.999967i	$0.497406\pi$
$954$		0			0
$955$	−14.3817	+	4.43615i	−0.465379	+	0.143550i
$956$	27.2856	−	8.41649i	0.882479	−	0.272209i
$957$		0			0
$958$	2.56076	−	1.23320i	0.0827344	−	0.0398428i
$959$	−55.0204	+	14.9228i	−1.77670	+	0.481882i
$960$		0			0
$961$	8.25554	−	14.2990i	0.266308	−	0.461258i
$962$	−20.8487	−	36.1110i	−0.672190	−	1.16427i
$963$		0			0
$964$	−1.68679	−	4.29787i	−0.0543279	−	0.138425i
$965$	−9.34733	+	40.9533i	−0.300901	+	1.31833i
$966$		0			0
$967$	0.979267	+	4.29045i	0.0314911	+	0.137972i	0.988230	−	0.152977i	$-0.0488862\pi$
$967$	0.979267	+	4.29045i	0.0314911	+	0.137972i	−0.956739	+	0.290949i	$0.906029\pi$
$968$	−7.18144	+	4.89622i	−0.230820	+	0.157371i
$969$		0			0
$970$	−50.2626	−	7.57587i	−1.61383	−	0.243246i
$971$	22.1024	+	20.5080i	0.709300	+	0.658134i	0.949923	−	0.312485i	$-0.101161\pi$
$971$	22.1024	+	20.5080i	0.709300	+	0.658134i	−0.240623	+	0.970619i	$0.577352\pi$
$972$		0			0
$973$	1.20365	+	0.631454i	0.0385872	+	0.0202435i
$974$	−15.3582	+	19.2586i	−0.492109	+	0.617085i
$975$		0			0
$976$	−21.4342	−	14.6136i	−0.686094	−	0.467771i
$977$	15.8176	−	40.3025i	0.506049	−	1.28939i	−0.418462	−	0.908234i	$-0.637431\pi$
$977$	15.8176	−	40.3025i	0.506049	−	1.28939i	0.924511	−	0.381156i	$-0.124474\pi$
$978$		0			0
$979$	−21.1125			−0.674758
$980$	−11.7258	+	4.68482i	−0.374566	+	0.149651i
$981$		0			0
$982$	27.0916	+	8.35664i	0.864527	+	0.266671i
$983$	−9.29604	+	23.6859i	−0.296498	+	0.755464i	0.702542	+	0.711642i	$0.252048\pi$
$983$	−9.29604	+	23.6859i	−0.296498	+	0.755464i	−0.999039	+	0.0438211i	$0.986047\pi$
$984$		0			0
$985$	35.2005	−	5.30562i	1.12158	−	0.169051i
$986$	−38.5407	+	48.3285i	−1.22739	+	1.53909i
$987$		0			0
$988$	19.2620	+	24.1537i	0.612804	+	0.768432i
$989$	−0.478373	−	0.443866i	−0.0152114	−	0.0141141i
$990$		0			0
$991$	−12.7875	+	11.8650i	−0.406207	+	0.376905i	−0.856648	−	0.515901i	$-0.827457\pi$
$991$	−12.7875	+	11.8650i	−0.406207	+	0.376905i	0.450441	+	0.892806i	$0.351267\pi$
$992$	15.7446	−	10.7345i	0.499891	−	0.340820i
$993$		0			0
$994$	53.7696	−	34.0150i	1.70547	−	1.07889i
$995$	8.74422	−	38.3109i	0.277211	−	1.21454i
$996$		0			0
$997$	−2.27335	−	30.3357i	−0.0719976	−	0.960741i	−0.909875	−	0.414883i	$-0.863823\pi$
$997$	−2.27335	−	30.3357i	−0.0719976	−	0.960741i	0.837877	−	0.545859i	$-0.183796\pi$
$998$	19.7093	+	34.1375i	0.623887	+	1.08060i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.100.2		60
3.2	odd	2		147.2.m.b.100.4	yes	60
49.25	even	21	inner	441.2.bb.e.172.2		60
147.5	even	42		7203.2.a.m.1.23		30
147.44	odd	42		7203.2.a.n.1.23		30
147.74	odd	42		147.2.m.b.25.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.25.4	✓	60	147.74	odd	42
147.2.m.b.100.4	yes	60	3.2	odd	2
441.2.bb.e.100.2		60	1.1	even	1	trivial
441.2.bb.e.172.2		60	49.25	even	21	inner
7203.2.a.m.1.23		30	147.5	even	42
7203.2.a.n.1.23		30	147.44	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.64310 - 0.506829i) q^{2} +(0.790427 + 0.538904i) q^{4} +(-1.86453 + 0.281032i) q^{5} +(-2.42176 + 1.06541i) q^{7} +(1.11855 + 1.40262i) q^{8} +O(q^{10})\)	\(q+(-1.64310 - 0.506829i) q^{2} +(0.790427 + 0.538904i) q^{4} +(-1.86453 + 0.281032i) q^{5} +(-2.42176 + 1.06541i) q^{7} +(1.11855 + 1.40262i) q^{8} +(3.20604 + 0.483233i) q^{10} +(1.81867 - 1.68748i) q^{11} +(1.03337 + 4.52749i) q^{13} +(4.51917 - 0.523159i) q^{14} +(-1.82602 - 4.65262i) q^{16} +(-0.337576 - 4.50464i) q^{17} +(3.47696 - 6.02227i) q^{19} +(-1.62522 - 0.782665i) q^{20} +(-3.84353 + 1.85095i) q^{22} +(0.00580944 - 0.0775216i) q^{23} +(-1.38038 + 0.425792i) q^{25} +(0.596735 - 7.96287i) q^{26} +(-2.48837 - 0.462965i) q^{28} +(7.17006 + 3.45292i) q^{29} +(-1.90322 - 3.29647i) q^{31} +(0.374113 + 4.99219i) q^{32} +(-1.72841 + 7.57268i) q^{34} +(4.21601 - 2.66708i) q^{35} +(4.31449 - 2.94157i) q^{37} +(-8.76526 + 8.13297i) q^{38} +(-2.47976 - 2.30088i) q^{40} +(-5.50342 - 6.90107i) q^{41} +(5.23387 - 6.56306i) q^{43} +(2.34692 - 0.353741i) q^{44} +(-0.0488357 + 0.124431i) q^{46} +(1.10809 + 0.341801i) q^{47} +(4.72980 - 5.16033i) q^{49} +2.48391 q^{50} +(-1.62308 + 4.13554i) q^{52} +(-3.61329 - 2.46350i) q^{53} +(-2.91673 + 3.65746i) q^{55} +(-4.20323 - 2.20509i) q^{56} +(-10.0311 - 9.30750i) q^{58} +(3.13814 + 0.472998i) q^{59} +(4.28846 - 2.92382i) q^{61} +(1.45643 + 6.38103i) q^{62} +(-0.308888 + 1.35333i) q^{64} +(-3.19912 - 8.15122i) q^{65} +(3.35023 + 5.80277i) q^{67} +(2.16074 - 3.74251i) q^{68} +(-8.27909 + 2.24548i) q^{70} +(12.6006 - 6.06812i) q^{71} +(12.1181 - 3.73793i) q^{73} +(-8.58001 + 2.64658i) q^{74} +(5.99371 - 2.88642i) q^{76} +(-2.60652 + 6.02430i) q^{77} +(-2.61929 + 4.53675i) q^{79} +(4.71220 + 8.16177i) q^{80} +(5.54501 + 14.1285i) q^{82} +(-0.923121 + 4.04446i) q^{83} +(1.89537 + 8.30416i) q^{85} +(-11.9261 + 8.13109i) q^{86} +(4.40119 + 0.663372i) q^{88} +(-6.23812 - 5.78813i) q^{89} +(-7.32621 - 9.86352i) q^{91} +(0.0463686 - 0.0581444i) q^{92} +(-1.64747 - 1.12323i) q^{94} +(-4.79043 + 12.2058i) q^{95} -15.6775 q^{97} +(-10.3869 + 6.08173i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

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