LMFDB - Embedded newform 387.2.y.c.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			253.2
Character	$\chi$	$=$	387.253
Dual form			387.2.y.c.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.178150 - 0.780524i) q^{2} +(1.22446 + 0.589667i) q^{4} +(-0.511972 - 1.30448i) q^{5} +(-2.37928 - 4.12103i) q^{7} +(1.67671 - 2.10253i) q^{8} +O(q^{10})$	\(q+(0.178150 - 0.780524i) q^{2} +(1.22446 + 0.589667i) q^{4} +(-0.511972 - 1.30448i) q^{5} +(-2.37928 - 4.12103i) q^{7} +(1.67671 - 2.10253i) q^{8} +(-1.10939 + 0.167213i) q^{10} +(-2.39760 + 1.15462i) q^{11} +(0.611008 + 0.0920946i) q^{13} +(-3.64044 + 1.12293i) q^{14} +(0.352328 + 0.441805i) q^{16} +(2.15975 - 5.50296i) q^{17} +(-1.48286 + 1.01100i) q^{19} +(0.142323 - 1.89917i) q^{20} +(0.474081 + 2.07708i) q^{22} +(-0.178184 + 2.37770i) q^{23} +(2.22570 - 2.06515i) q^{25} +(0.180733 - 0.460500i) q^{26} +(-0.483287 - 6.44901i) q^{28} +(1.79980 - 0.555165i) q^{29} +(5.49565 + 5.09922i) q^{31} +(5.25345 - 2.52993i) q^{32} +(-3.91044 - 2.66609i) q^{34} +(-4.15769 + 5.21358i) q^{35} +(1.11406 - 1.92960i) q^{37} +(0.524936 + 1.33752i) q^{38} +(-3.60115 - 1.11081i) q^{40} +(0.583954 - 2.55847i) q^{41} +(-6.54183 - 0.452170i) q^{43} -3.61660 q^{44} +(1.82411 + 0.562664i) q^{46} +(8.07377 + 3.88812i) q^{47} +(-7.82195 + 13.5480i) q^{49} +(-1.21539 - 2.10512i) q^{50} +(0.693847 + 0.473057i) q^{52} +(-13.5894 + 2.04828i) q^{53} +(2.73369 + 2.53650i) q^{55} +(-12.6540 - 1.90728i) q^{56} +(-0.112686 - 1.50369i) q^{58} +(4.23034 + 5.30467i) q^{59} +(3.03226 - 2.81353i) q^{61} +(4.95912 - 3.38107i) q^{62} +(-0.787282 - 3.44931i) q^{64} +(-0.192683 - 0.844198i) q^{65} +(4.65539 - 3.17399i) q^{67} +(5.88944 - 5.46460i) q^{68} +(3.32864 + 4.17398i) q^{70} +(0.641465 + 8.55975i) q^{71} +(8.41561 + 1.26845i) q^{73} +(-1.30763 - 1.21331i) q^{74} +(-2.41185 + 0.363527i) q^{76} +(10.4628 + 7.13343i) q^{77} +(3.09616 + 5.36270i) q^{79} +(0.395945 - 0.685797i) q^{80} +(-1.89292 - 0.911581i) q^{82} +(1.21371 + 0.374380i) q^{83} -8.28425 q^{85} +(-1.51835 + 5.02550i) q^{86} +(-1.59246 + 6.97702i) q^{88} +(9.04506 + 2.79003i) q^{89} +(-1.07423 - 2.73710i) q^{91} +(-1.62023 + 2.80632i) q^{92} +(4.47311 - 5.60911i) q^{94} +(2.07801 + 1.41676i) q^{95} +(4.06114 - 1.95574i) q^{97} +(9.18108 + 8.51880i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{2}{21}\right)$	$1$

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 $

$2$	0.178150	−	0.780524i	0.125971	−	0.551914i	−0.872072	−	0.489378i	$-0.837224\pi$
$2$	0.178150	−	0.780524i	0.125971	−	0.551914i	0.998043	−	0.0625363i	$-0.0199189\pi$
$3$		0			0
$3$		0			0
$4$	1.22446	+	0.589667i	0.612228	+	0.294834i
$5$	−0.511972	−	1.30448i	−0.228961	−	0.583382i	0.769512	−	0.638632i	$-0.220500\pi$
$5$	−0.511972	−	1.30448i	−0.228961	−	0.583382i	−0.998473	+	0.0552503i	$0.982404\pi$
$6$		0			0
$7$	−2.37928	−	4.12103i	−0.899283	−	1.55760i	−0.828412	−	0.560119i	$-0.810755\pi$
$7$	−2.37928	−	4.12103i	−0.899283	−	1.55760i	−0.0708714	−	0.997485i	$-0.522578\pi$
$8$	1.67671	−	2.10253i	0.592808	−	0.743358i
$9$		0			0
$10$	−1.10939	+	0.167213i	−0.350819	+	0.0528775i
$11$	−2.39760	+	1.15462i	−0.722904	+	0.348132i	−0.758889	−	0.651220i	$-0.774258\pi$
$11$	−2.39760	+	1.15462i	−0.722904	+	0.348132i	0.0359847	+	0.999352i	$0.488543\pi$
$12$		0			0
$13$	0.611008	+	0.0920946i	0.169463	+	0.0255424i	0.233226	−	0.972423i	$-0.425072\pi$
$13$	0.611008	+	0.0920946i	0.169463	+	0.0255424i	−0.0637626	+	0.997965i	$0.520310\pi$
$14$	−3.64044	+	1.12293i	−0.972947	+	0.300115i
$15$		0			0
$16$	0.352328	+	0.441805i	0.0880820	+	0.110451i
$17$	2.15975	−	5.50296i	0.523817	−	1.33466i	−0.387086	−	0.922044i	$-0.626518\pi$
$17$	2.15975	−	5.50296i	0.523817	−	1.33466i	0.910903	−	0.412621i	$-0.135387\pi$
$18$		0			0
$19$	−1.48286	+	1.01100i	−0.340191	+	0.231938i	−0.721349	−	0.692572i	$-0.756478\pi$
$19$	−1.48286	+	1.01100i	−0.340191	+	0.231938i	0.381158	+	0.924510i	$0.375525\pi$
$20$	0.142323	−	1.89917i	0.0318245	−	0.424668i
$21$		0			0
$22$	0.474081	+	2.07708i	0.101074	+	0.442836i
$23$	−0.178184	+	2.37770i	−0.0371540	+	0.495785i	0.947324	+	0.320277i	$0.103776\pi$
$23$	−0.178184	+	2.37770i	−0.0371540	+	0.495785i	−0.984478	+	0.175508i	$0.943843\pi$
$24$		0			0
$25$	2.22570	−	2.06515i	0.445140	−	0.413030i
$26$	0.180733	−	0.460500i	0.0354446	−	0.0903114i
$27$		0			0
$28$	−0.483287	−	6.44901i	−0.0913326	−	1.21875i
$29$	1.79980	−	0.555165i	0.334215	−	0.103092i	−0.123106	−	0.992394i	$-0.539285\pi$
$29$	1.79980	−	0.555165i	0.334215	−	0.103092i	0.457320	+	0.889302i	$0.348809\pi$
$30$		0			0
$31$	5.49565	+	5.09922i	0.987048	+	0.915847i	0.996457	−	0.0841086i	$-0.0268043\pi$
$31$	5.49565	+	5.09922i	0.987048	+	0.915847i	−0.00940813	+	0.999956i	$0.502995\pi$
$32$	5.25345	−	2.52993i	0.928688	−	0.447232i
$33$		0			0
$34$	−3.91044	−	2.66609i	−0.670635	−	0.457231i
$35$	−4.15769	+	5.21358i	−0.702778	+	0.881256i
$36$		0			0
$37$	1.11406	−	1.92960i	0.183150	−	0.317225i	−0.759802	−	0.650155i	$-0.774704\pi$
$37$	1.11406	−	1.92960i	0.183150	−	0.317225i	0.942951	+	0.332930i	$0.108037\pi$
$38$	0.524936	+	1.33752i	0.0851559	+	0.216974i
$39$		0			0
$40$	−3.60115	−	1.11081i	−0.569391	−	0.175634i
$41$	0.583954	−	2.55847i	0.0911984	−	0.399566i	−0.908639	−	0.417582i	$-0.862878\pi$
$41$	0.583954	−	2.55847i	0.0911984	−	0.399566i	0.999838	+	0.0180157i	$0.00573487\pi$
$42$		0			0
$43$	−6.54183	−	0.452170i	−0.997620	−	0.0689553i
$43$	−6.54183	−	0.452170i	−0.997620	−	0.0689553i
$44$	−3.61660			−0.545224
$45$		0			0
$46$	1.82411	+	0.562664i	0.268951	+	0.0829603i
$47$	8.07377	+	3.88812i	1.17768	+	0.567141i	0.917235	−	0.398348i	$-0.130416\pi$
$47$	8.07377	+	3.88812i	1.17768	+	0.567141i	0.260446	+	0.965489i	$0.416131\pi$
$48$		0			0
$49$	−7.82195	+	13.5480i	−1.11742	+	1.93543i
$50$	−1.21539	−	2.10512i	−0.171882	−	0.297709i
$51$		0			0
$52$	0.693847	+	0.473057i	0.0962193	+	0.0656012i
$53$	−13.5894	+	2.04828i	−1.86665	+	0.281352i	−0.982558	−	0.185957i	$-0.940461\pi$
$53$	−13.5894	+	2.04828i	−1.86665	+	0.281352i	−0.884094	+	0.467310i	$0.845223\pi$
$54$		0			0
$55$	2.73369	+	2.53650i	0.368611	+	0.342021i
$56$	−12.6540	−	1.90728i	−1.69096	−	0.254871i
$57$		0			0
$58$	−0.112686	−	1.50369i	−0.0147964	−	0.197444i
$59$	4.23034	+	5.30467i	0.550743	+	0.690610i	0.976816	−	0.214079i	$-0.0686749\pi$
$59$	4.23034	+	5.30467i	0.550743	+	0.690610i	−0.426073	+	0.904689i	$0.640103\pi$
$60$		0			0
$61$	3.03226	−	2.81353i	0.388242	−	0.360236i	−0.461770	−	0.887000i	$-0.652785\pi$
$61$	3.03226	−	2.81353i	0.388242	−	0.360236i	0.850011	+	0.526764i	$0.176595\pi$
$62$	4.95912	−	3.38107i	0.629808	−	0.429396i
$63$		0			0
$64$	−0.787282	−	3.44931i	−0.0984103	−	0.431164i
$65$	−0.192683	−	0.844198i	−0.0238994	−	0.104710i
$66$		0			0
$67$	4.65539	−	3.17399i	0.568747	−	0.387765i	−0.244530	−	0.969642i	$-0.578634\pi$
$67$	4.65539	−	3.17399i	0.568747	−	0.387765i	0.813277	+	0.581877i	$0.197681\pi$
$68$	5.88944	−	5.46460i	0.714200	−	0.662681i
$69$		0			0
$70$	3.32864	+	4.17398i	0.397848	+	0.498886i
$71$	0.641465	+	8.55975i	0.0761278	+	1.01586i	0.896216	+	0.443618i	$0.146305\pi$
$71$	0.641465	+	8.55975i	0.0761278	+	1.01586i	−0.820088	+	0.572237i	$0.806076\pi$
$72$		0			0
$73$	8.41561	+	1.26845i	0.984972	+	0.148461i	0.621728	−	0.783233i	$-0.286431\pi$
$73$	8.41561	+	1.26845i	0.984972	+	0.148461i	0.363244	+	0.931694i	$0.381669\pi$
$74$	−1.30763	−	1.21331i	−0.152009	−	0.141044i
$75$		0			0
$76$	−2.41185	+	0.363527i	−0.276658	+	0.0416994i
$77$	10.4628	+	7.13343i	1.19235	+	0.812930i
$78$		0			0
$79$	3.09616	+	5.36270i	0.348345	+	0.603351i	0.985956	−	0.167007i	$-0.0534104\pi$
$79$	3.09616	+	5.36270i	0.348345	+	0.603351i	−0.637611	+	0.770359i	$0.720077\pi$
$80$	0.395945	−	0.685797i	0.0442680	−	0.0766745i
$81$		0			0
$82$	−1.89292	−	0.911581i	−0.209038	−	0.100667i
$83$	1.21371	+	0.374380i	0.133222	+	0.0410935i	0.360649	−	0.932702i	$-0.382555\pi$
$83$	1.21371	+	0.374380i	0.133222	+	0.0410935i	−0.227427	+	0.973795i	$0.573031\pi$
$84$		0			0
$85$	−8.28425			−0.898553
$86$	−1.51835	+	5.02550i	−0.163728	+	0.541914i
$87$		0			0
$88$	−1.59246	+	6.97702i	−0.169757	+	0.743752i
$89$	9.04506	+	2.79003i	0.958774	+	0.295743i	0.734367	−	0.678753i	$-0.237479\pi$
$89$	9.04506	+	2.79003i	0.958774	+	0.295743i	0.224408	+	0.974495i	$0.427955\pi$
$90$		0			0
$91$	−1.07423	−	2.73710i	−0.112610	−	0.286926i
$92$	−1.62023	+	2.80632i	−0.168921	+	0.292579i
$93$		0			0
$94$	4.47311	−	5.60911i	0.461366	−	0.578535i
$95$	2.07801	+	1.41676i	0.213199	+	0.145357i
$96$		0			0
$97$	4.06114	−	1.95574i	0.412346	−	0.198575i	−0.216198	−	0.976350i	$-0.569366\pi$
$97$	4.06114	−	1.95574i	0.412346	−	0.198575i	0.628544	+	0.777774i	$0.283651\pi$
$98$	9.18108	+	8.51880i	0.927429	+	0.860528i
$99$		0			0
$100$	3.94302	−	1.21626i	0.394302	−	0.121626i
$101$	0.836983	+	11.1688i	0.0832829	+	1.11133i	0.869681	+	0.493614i	$0.164324\pi$
$101$	0.836983	+	11.1688i	0.0832829	+	1.11133i	−0.786398	+	0.617720i	$0.788057\pi$
$102$		0			0
$103$	−3.78337	+	9.63986i	−0.372786	+	0.949844i	0.614216	+	0.789138i	$0.289472\pi$
$103$	−3.78337	+	9.63986i	−0.372786	+	0.949844i	−0.987002	+	0.160706i	$0.948623\pi$
$104$	1.21812	−	1.13025i	0.119446	−	0.110830i
$105$		0			0
$106$	−0.822221	+	10.9718i	−0.0798612	+	1.06567i
$107$	−1.06717	−	4.67559i	−0.103168	−	0.452007i	−0.999954	−	0.00954399i	$-0.996962\pi$
$107$	−1.06717	−	4.67559i	−0.103168	−	0.452007i	0.896787	−	0.442463i	$-0.145895\pi$
$108$		0			0
$109$	1.33576	−	17.8244i	0.127942	−	1.70727i	−0.451511	−	0.892266i	$-0.649115\pi$
$109$	1.33576	−	17.8244i	0.127942	−	1.70727i	0.579453	−	0.815006i	$-0.303266\pi$
$110$	2.46680	−	1.68184i	0.235200	−	0.160357i
$111$		0			0
$112$	0.982408	−	2.50313i	0.0928288	−	0.236524i
$113$	−0.802598	−	1.00643i	−0.0755021	−	0.0946766i	0.742646	−	0.669684i	$-0.233571\pi$
$113$	−0.802598	−	1.00643i	−0.0755021	−	0.0946766i	−0.818148	+	0.575008i	$0.804999\pi$
$114$		0			0
$115$	3.19290	−	0.984878i	0.297739	−	0.0918403i
$116$	2.53114	+	0.381508i	0.235011	+	0.0354221i
$117$		0			0
$118$	4.89406	−	2.35686i	0.450535	−	0.216966i
$119$	−27.8166	+	4.19267i	−2.54994	+	0.384342i
$120$		0			0
$121$	−2.44305	+	3.06348i	−0.222095	+	0.278499i
$122$	−1.65583	−	2.86799i	−0.149912	−	0.259655i
$123$		0			0
$124$	3.72235	+	9.48438i	0.334276	+	0.851723i
$125$	−10.1463	−	4.88621i	−0.907514	−	0.437036i
$126$		0			0
$127$	−0.977712	+	4.28364i	−0.0867579	+	0.380111i	−0.999602	−	0.0281961i	$-0.991024\pi$
$127$	−0.977712	+	4.28364i	−0.0867579	+	0.380111i	0.912844	+	0.408307i	$0.133881\pi$
$128$	8.82926			0.780404
$129$		0			0
$130$	−0.693244			−0.0608015
$131$	3.14191	−	13.7656i	0.274510	−	1.20271i	−0.630116	−	0.776501i	$-0.716993\pi$
$131$	3.14191	−	13.7656i	0.274510	−	1.20271i	0.904626	−	0.426206i	$-0.140150\pi$
$132$		0			0
$133$	7.69448	+	3.70547i	0.667196	+	0.321305i
$134$	−1.64802	−	4.19909i	−0.142367	−	0.362746i
$135$		0			0
$136$	−7.94887	−	13.7679i	−0.681610	−	1.18058i
$137$	5.86675	−	7.35668i	0.501231	−	0.628523i	−0.465276	−	0.885166i	$-0.654045\pi$
$137$	5.86675	−	7.35668i	0.501231	−	0.628523i	0.966506	+	0.256642i	$0.0826163\pi$
$138$		0			0
$139$	−16.5348	+	2.49223i	−1.40247	+	0.211388i	−0.806316	−	0.591485i	$-0.798542\pi$
$139$	−16.5348	+	2.49223i	−1.40247	+	0.211388i	−0.596151	+	0.802873i	$0.703304\pi$
$140$	−8.16519	+	3.93215i	−0.690085	+	0.332327i
$141$		0			0
$142$	6.79537	+	1.02424i	0.570255	+	0.0859521i
$143$	−1.57129	+	0.484678i	−0.131398	+	0.0405308i
$144$		0			0
$145$	−1.64565	−	2.06358i	−0.136664	−	0.171371i
$146$	2.48929	−	6.34261i	0.206015	−	0.524918i
$147$		0			0
$148$	2.50194	−	1.70579i	0.205658	−	0.140215i
$149$	−0.871916	+	11.6349i	−0.0714302	+	0.953169i	0.840231	+	0.542228i	$0.182419\pi$
$149$	−0.871916	+	11.6349i	−0.0714302	+	0.953169i	−0.911662	+	0.410942i	$0.865200\pi$
$150$		0			0
$151$	−1.79030	−	7.84381i	−0.145692	−	0.638320i	−0.994053	−	0.108901i	$-0.965267\pi$
$151$	−1.79030	−	7.84381i	−0.145692	−	0.638320i	0.848360	−	0.529419i	$-0.177590\pi$
$152$	−0.360678	+	4.81291i	−0.0292548	+	0.390378i
$153$		0			0
$154$	7.43176	−	6.89567i	0.598868	−	0.555669i
$155$	3.83823	−	9.77964i	0.308294	−	0.785519i
$156$		0			0
$157$	0.566002	+	7.55278i	0.0451719	+	0.602777i	0.973154	+	0.230153i	$0.0739228\pi$
$157$	0.566002	+	7.55278i	0.0451719	+	0.602777i	−0.927982	+	0.372624i	$0.878458\pi$
$158$	4.73730	−	1.46126i	0.376879	−	0.116252i
$159$		0			0
$160$	−5.98987	−	5.55778i	−0.473540	−	0.439381i
$161$	10.2225	−	4.92292i	0.805649	−	0.387980i
$162$		0			0
$163$	5.09936	+	3.47669i	0.399413	+	0.272315i	0.746324	−	0.665583i	$-0.231817\pi$
$163$	5.09936	+	3.47669i	0.399413	+	0.272315i	−0.346911	+	0.937898i	$0.612769\pi$
$164$	2.22367	−	2.78840i	0.173640	−	0.217737i
$165$		0			0
$166$	0.508435	−	0.880635i	0.0394622	−	0.0683505i
$167$	3.21985	+	8.20404i	0.249159	+	0.634848i	0.999661	−	0.0260204i	$-0.00828347\pi$
$167$	3.21985	+	8.20404i	0.249159	+	0.634848i	−0.750502	+	0.660868i	$0.770188\pi$
$168$		0			0
$169$	−12.0576	−	3.71928i	−0.927508	−	0.286098i
$170$	−1.47584	+	6.46606i	−0.113191	+	0.495924i
$171$		0			0
$172$	−7.74356	−	4.41117i	−0.590441	−	0.336348i
$173$	−6.12350			−0.465561			−0.232780	−	0.972529i	$-0.574782\pi$
$173$	−6.12350			−0.465561			−0.232780	+	0.972529i	$0.574782\pi$
$174$		0			0
$175$	−13.8061	−	4.25862i	−1.04364	−	0.321922i
$176$	−1.35486	−	0.652467i	−0.102127	−	0.0491816i
$177$		0			0
$178$	3.78906	−	6.56285i	0.284002	−	0.491906i
$179$	−12.2987	−	21.3020i	−0.919250	−	1.59219i	−0.800557	−	0.599257i	$-0.795463\pi$
$179$	−12.2987	−	21.3020i	−0.919250	−	1.59219i	−0.118693	−	0.992931i	$-0.537870\pi$
$180$		0			0
$181$	−4.71852	−	3.21703i	−0.350725	−	0.239120i	0.375124	−	0.926975i	$-0.377600\pi$
$181$	−4.71852	−	3.21703i	−0.350725	−	0.239120i	−0.725848	+	0.687855i	$0.758553\pi$
$182$	−2.32775	+	0.350852i	−0.172544	+	0.0260069i
$183$		0			0
$184$	4.70043	+	4.36137i	0.346521	+	0.321524i
$185$	−3.08750	−	0.465365i	−0.226997	−	0.0342143i
$186$		0			0
$187$	1.17562	+	15.6876i	0.0859702	+	1.14719i
$188$	7.59328	+	9.52167i	0.553797	+	0.694439i
$189$		0			0
$190$	1.47601	−	1.36954i	0.107081	−	0.0993568i
$191$	−0.303915	+	0.207206i	−0.0219905	+	0.0149929i	−0.574265	−	0.818669i	$-0.694712\pi$
$191$	−0.303915	+	0.207206i	−0.0219905	+	0.0149929i	0.552275	+	0.833662i	$0.313760\pi$
$192$		0			0
$193$	1.96944	+	8.62869i	0.141764	+	0.621107i	0.995025	+	0.0996237i	$0.0317639\pi$
$193$	1.96944	+	8.62869i	0.141764	+	0.621107i	−0.853262	+	0.521483i	$0.825379\pi$
$194$	−0.803013	−	3.51823i	−0.0576530	−	0.252594i
$195$		0			0
$196$	−17.5665	+	11.9766i	−1.25475	+	0.855472i
$197$	−2.76426	+	2.56486i	−0.196945	+	0.182738i	−0.772480	−	0.635039i	$-0.780984\pi$
$197$	−2.76426	+	2.56486i	−0.196945	+	0.182738i	0.575535	+	0.817777i	$0.304794\pi$
$198$		0			0
$199$	7.05704	+	8.84925i	0.500260	+	0.627307i	0.966288	−	0.257464i	$-0.0828867\pi$
$199$	7.05704	+	8.84925i	0.500260	+	0.627307i	−0.466028	+	0.884770i	$0.654315\pi$
$200$	−0.610179	−	8.14227i	−0.0431462	−	0.575746i
$201$		0			0
$202$	8.86660	+	1.33642i	0.623852	+	0.0940305i
$203$	−6.57009	−	6.09615i	−0.461130	−	0.427866i
$204$		0			0
$205$	−3.63645	+	0.548106i	−0.253981	+	0.0382814i
$206$	6.85014	+	4.67035i	0.477272	+	0.325399i
$207$		0			0
$208$	0.174587	+	0.302394i	0.0121054	+	0.0209672i
$209$	2.38798	−	4.13611i	0.165180	−	0.286101i
$210$		0			0
$211$	2.57368	+	1.23942i	0.177180	+	0.0853253i	0.520371	−	0.853940i	$-0.325794\pi$
$211$	2.57368	+	1.23942i	0.177180	+	0.0853253i	−0.343191	+	0.939266i	$0.611508\pi$
$212$	−17.8475	−	5.50521i	−1.22577	−	0.378100i
$213$		0			0
$214$	−3.83953			−0.262465
$215$	2.75938	+	8.76520i	0.188188	+	0.597782i
$216$		0			0
$217$	7.93837	−	34.7803i	0.538891	−	2.36104i
$218$	−13.6744	−	4.21801i	−0.926150	−	0.285679i
$219$		0			0
$220$	1.85160	+	4.71780i	0.124835	+	0.318074i
$221$	1.82642	−	3.16345i	0.122858	−	0.212797i
$222$		0			0
$223$	2.73391	−	3.42821i	0.183076	−	0.229570i	−0.681822	−	0.731519i	$-0.738812\pi$
$223$	2.73391	−	3.42821i	0.183076	−	0.229570i	0.864897	+	0.501949i	$0.167383\pi$
$224$	−22.9254	−	15.6302i	−1.53177	−	1.04434i
$225$		0			0
$226$	−0.928523	+	0.447153i	−0.0617644	+	0.0297442i
$227$	−9.09730	−	8.44106i	−0.603809	−	0.560253i	0.317905	−	0.948122i	$-0.397021\pi$
$227$	−9.09730	−	8.44106i	−0.603809	−	0.560253i	−0.921714	+	0.387870i	$0.873211\pi$
$228$		0			0
$229$	9.76205	−	3.01119i	0.645094	−	0.198985i	0.0450911	−	0.998983i	$-0.485642\pi$
$229$	9.76205	−	3.01119i	0.645094	−	0.198985i	0.600003	+	0.799998i	$0.295166\pi$
$230$	−0.199908	−	2.66759i	−0.0131816	−	0.175896i
$231$		0			0
$232$	1.85050	−	4.71500i	0.121491	−	0.309555i
$233$	14.9717	−	13.8917i	0.980830	−	0.910077i	−0.0151294	−	0.999886i	$-0.504816\pi$
$233$	14.9717	−	13.8917i	0.980830	−	0.910077i	0.995959	+	0.0898086i	$0.0286255\pi$
$234$		0			0
$235$	0.938446	−	12.5227i	0.0612175	−	0.816891i
$236$	2.05187	+	8.98984i	0.133565	+	0.585188i
$237$		0			0
$238$	−1.68303	+	22.4584i	−0.109094	+	1.45576i
$239$	−1.59638	+	1.08839i	−0.103261	+	0.0704022i	−0.613850	−	0.789423i	$-0.710380\pi$
$239$	−1.59638	+	1.08839i	−0.103261	+	0.0704022i	0.510589	+	0.859825i	$0.329428\pi$
$240$		0			0
$241$	5.18733	−	13.2171i	0.334145	−	0.851388i	−0.660762	−	0.750595i	$-0.729767\pi$
$241$	5.18733	−	13.2171i	0.334145	−	0.851388i	0.994907	−	0.100793i	$-0.0321380\pi$
$242$	1.95590	+	2.45262i	0.125730	+	0.157660i
$243$		0			0
$244$	5.37192	−	1.65702i	0.343902	−	0.106080i
$245$	21.6778	+	3.26740i	1.38494	+	0.208746i
$246$		0			0
$247$	−0.999145	+	0.481163i	−0.0635741	+	0.0306157i
$248$	19.9359	−	3.00486i	1.26593	−	0.190809i
$249$		0			0
$250$	−5.62137	+	7.04897i	−0.355527	+	0.445816i
$251$	4.31293	+	7.47021i	0.272230	+	0.471516i	0.969432	−	0.245358i	$-0.0789056\pi$
$251$	4.31293	+	7.47021i	0.272230	+	0.471516i	−0.697203	+	0.716874i	$0.745572\pi$
$252$		0			0
$253$	−2.31814	−	5.90652i	−0.145740	−	0.371340i
$254$	3.16930	+	1.52626i	0.198860	+	0.0957658i
$255$		0			0
$256$	3.14749	−	13.7901i	0.196718	−	0.861879i
$257$	−12.4670			−0.777670			−0.388835	−	0.921307i	$-0.627122\pi$
$257$	−12.4670			−0.777670			−0.388835	+	0.921307i	$0.627122\pi$
$258$		0			0
$259$	−10.6026			−0.658814
$260$	0.261864	−	1.14730i	0.0162401	−	0.0711527i
$261$		0			0
$262$	−10.1847	−	4.90468i	−0.629211	−	0.303012i
$263$	6.48661	+	16.5276i	0.399982	+	1.01914i	0.979007	+	0.203827i	$0.0653380\pi$
$263$	6.48661	+	16.5276i	0.399982	+	1.01914i	−0.579025	+	0.815310i	$0.696567\pi$
$264$		0			0
$265$	9.62934	+	16.6785i	0.591526	+	1.02455i
$266$	4.26298	−	5.34560i	0.261380	−	0.327760i
$267$		0			0
$268$	7.57193	−	1.14128i	0.462529	−	0.0697150i
$269$	25.8191	−	12.4338i	1.57422	−	0.758105i	0.575984	−	0.817461i	$-0.304619\pi$
$269$	25.8191	−	12.4338i	1.57422	−	0.758105i	0.998237	+	0.0593567i	$0.0189049\pi$
$270$		0			0
$271$	−18.1205	−	2.73123i	−1.10074	−	0.165910i	−0.426549	−	0.904464i	$-0.640271\pi$
$271$	−18.1205	−	2.73123i	−1.10074	−	0.165910i	−0.674194	+	0.738554i	$0.735509\pi$
$272$	3.19218	−	0.984657i	0.193554	−	0.0597036i
$273$		0			0
$274$	−4.69691	−	5.88973i	−0.283750	−	0.355812i
$275$	−2.95187	+	7.52125i	−0.178005	+	0.453549i
$276$		0			0
$277$	5.46901	−	3.72871i	0.328601	−	0.224036i	−0.387770	−	0.921756i	$-0.626754\pi$
$277$	5.46901	−	3.72871i	0.328601	−	0.224036i	0.716371	+	0.697720i	$0.245802\pi$
$278$	−1.00043	+	13.3498i	−0.0600019	+	0.800670i
$279$		0			0
$280$	3.99047	+	17.4834i	0.238476	+	1.04483i
$281$	0.962331	−	12.8414i	0.0574079	−	0.766055i	−0.892005	−	0.452025i	$-0.850702\pi$
$281$	0.962331	−	12.8414i	0.0574079	−	0.766055i	0.949413	−	0.314030i	$-0.101679\pi$
$282$		0			0
$283$	−0.459412	+	0.426272i	−0.0273092	+	0.0253393i	−0.693709	−	0.720255i	$-0.744025\pi$
$283$	−0.459412	+	0.426272i	−0.0273092	+	0.0253393i	0.666400	+	0.745594i	$0.267834\pi$
$284$	−4.26196	+	10.8593i	−0.252901	+	0.644380i
$285$		0			0
$286$	0.0983788	+	1.31277i	0.00581726	+	0.0776260i
$287$	−11.9329	+	3.68082i	−0.704379	+	0.217272i
$288$		0			0
$289$	−13.1562	−	12.2072i	−0.773893	−	0.718068i
$290$	−1.90385	+	0.916844i	−0.111798	+	0.0538389i
$291$		0			0
$292$	9.55658	+	6.51557i	0.559257	+	0.381295i
$293$	−13.5001	+	16.9285i	−0.788682	+	0.988976i	0.211251	+	0.977432i	$0.432246\pi$
$293$	−13.5001	+	16.9285i	−0.788682	+	0.988976i	−0.999933	+	0.0115444i	$0.996325\pi$
$294$		0			0
$295$	4.75404	−	8.23424i	0.276791	−	0.479416i
$296$	−2.18910	−	5.57773i	−0.127239	−	0.324199i
$297$		0			0
$298$	8.92600	+	2.75331i	0.517070	+	0.159495i
$299$	−0.327845	+	1.43638i	−0.0189598	+	0.0830683i
$300$		0			0
$301$	13.7014	+	28.0349i	0.789738	+	1.61591i
$302$	−6.44123			−0.370651
$303$		0			0
$304$	−0.969115	−	0.298932i	−0.0555826	−	0.0171450i
$305$	−5.22263	−	2.51509i	−0.299047	−	0.144013i
$306$		0			0
$307$	4.16103	−	7.20711i	0.237482	−	0.411332i	−0.722509	−	0.691362i	$-0.757011\pi$
$307$	4.16103	−	7.20711i	0.237482	−	0.411332i	0.959991	+	0.280030i	$0.0903445\pi$
$308$	8.60492	+	14.9042i	0.490311	+	0.849243i
$309$		0			0
$310$	−6.94947	−	4.73807i	−0.394703	−	0.269104i
$311$	13.6228	−	2.05331i	0.772481	−	0.116433i	0.249038	−	0.968494i	$-0.419886\pi$
$311$	13.6228	−	2.05331i	0.772481	−	0.116433i	0.523443	+	0.852061i	$0.324647\pi$
$312$		0			0
$313$	−3.60094	−	3.34119i	−0.203537	−	0.188855i	0.571818	−	0.820381i	$-0.306238\pi$
$313$	−3.60094	−	3.34119i	−0.203537	−	0.188855i	−0.775355	+	0.631526i	$0.782429\pi$
$314$	5.99596	+	0.903745i	0.338372	+	0.0510013i
$315$		0			0
$316$	0.628901	+	8.39210i	0.0353785	+	0.472093i
$317$	−11.7522	−	14.7368i	−0.660071	−	0.827703i	0.333280	−	0.942828i	$-0.391845\pi$
$317$	−11.7522	−	14.7368i	−0.660071	−	0.827703i	−0.993351	+	0.115125i	$0.963273\pi$
$318$		0			0
$319$	−3.67420	+	3.40916i	−0.205716	+	0.190876i
$320$	−4.09650	+	2.79294i	−0.229001	+	0.156130i
$321$		0			0
$322$	−2.02132	−	8.85596i	−0.112643	−	0.493523i
$323$	2.36086	+	10.3436i	0.131362	+	0.575534i
$324$		0			0
$325$	1.55011	−	1.05685i	0.0859846	−	0.0586233i
$326$	3.62209	−	3.36081i	0.200609	−	0.186138i
$327$		0			0
$328$	−4.40015	−	5.51761i	−0.242957	−	0.304659i
$329$	−3.18667	−	42.5232i	−0.175687	−	2.34438i
$330$		0			0
$331$	−3.20077	−	0.482439i	−0.175930	−	0.0265172i	0.0604862	−	0.998169i	$-0.480735\pi$
$331$	−3.20077	−	0.482439i	−0.175930	−	0.0265172i	−0.236416	+	0.971652i	$0.575973\pi$
$332$	1.26538	+	1.17410i	0.0694465	+	0.0644369i
$333$		0			0
$334$	6.97707	−	1.05162i	0.381768	−	0.0575423i
$335$	−6.52385	−	4.44788i	−0.356436	−	0.243014i
$336$		0			0
$337$	−4.83669	−	8.37738i	−0.263471	−	0.456345i	0.703691	−	0.710506i	$-0.251534\pi$
$337$	−4.83669	−	8.37738i	−0.263471	−	0.456345i	−0.967162	+	0.254161i	$0.918201\pi$
$338$	−5.05104	+	8.74866i	−0.274740	+	0.475864i
$339$		0			0
$340$	−10.1437	−	4.88495i	−0.550120	−	0.264924i
$341$	−19.0641	−	5.88049i	−1.03238	−	0.318446i
$342$		0			0
$343$	41.1325			2.22095
$344$	−11.9195	+	12.9963i	−0.642655	+	0.700711i
$345$		0			0
$346$	−1.09090	+	4.77954i	−0.0586471	+	0.256950i
$347$	−10.4815	−	3.23310i	−0.562674	−	0.173562i	0.000353651	−	1.00000i	$-0.499887\pi$
$347$	−10.4815	−	3.23310i	−0.562674	−	0.173562i	−0.563028	+	0.826438i	$0.690364\pi$
$348$		0			0
$349$	7.84116	+	19.9790i	0.419728	+	1.06945i	0.971832	+	0.235674i	$0.0757297\pi$
$349$	7.84116	+	19.9790i	0.419728	+	1.06945i	−0.552104	+	0.833775i	$0.686175\pi$
$350$	−5.78351	+	10.0173i	−0.309142	+	0.535449i
$351$		0			0
$352$	−9.67457	+	12.1315i	−0.515656	+	0.646613i
$353$	27.5239	+	18.7655i	1.46495	+	0.998785i	0.993121	+	0.117095i	$0.0373581\pi$
$353$	27.5239	+	18.7655i	1.46495	+	0.998785i	0.471828	+	0.881690i	$0.343594\pi$
$354$		0			0
$355$	10.8376	−	5.21913i	0.575202	−	0.277003i
$356$	9.43009	+	8.74985i	0.499794	+	0.463741i
$357$		0			0
$358$	−18.8178	+	5.80451i	−0.994550	+	0.306778i
$359$	0.560334	+	7.47713i	0.0295733	+	0.394628i	0.992275	+	0.124061i	$0.0395920\pi$
$359$	0.560334	+	7.47713i	0.0295733	+	0.394628i	−0.962701	+	0.270567i	$0.912789\pi$
$360$		0			0
$361$	−5.76472	+	14.6883i	−0.303407	+	0.773067i
$362$	−3.35158	+	3.10981i	−0.176155	+	0.163448i
$363$		0			0
$364$	0.298627	−	3.98490i	0.0156523	−	0.208866i
$365$	−2.65388	−	11.6274i	−0.138911	−	0.608607i
$366$		0			0
$367$	−0.382393	+	5.10269i	−0.0199608	+	0.266358i	0.978290	+	0.207240i	$0.0664480\pi$
$367$	−0.382393	+	5.10269i	−0.0199608	+	0.266358i	−0.998251	+	0.0591184i	$0.981171\pi$
$368$	−1.11326	+	0.759008i	−0.0580327	+	0.0395660i
$369$		0			0
$370$	−0.913265	+	2.32696i	−0.0474784	+	0.120973i
$371$	40.7741	+	51.1291i	2.11688	+	2.65449i
$372$		0			0
$373$	−31.4395	+	9.69781i	−1.62788	+	0.502134i	−0.968360	−	0.249556i	$-0.919715\pi$
$373$	−31.4395	+	9.69781i	−1.62788	+	0.502134i	−0.659517	+	0.751690i	$0.729239\pi$
$374$	12.4540	+	1.87714i	0.643982	+	0.0970646i
$375$		0			0
$376$	21.7123	−	10.4561i	1.11973	−	0.539232i
$377$	1.15082	−	0.173458i	0.0592703	−	0.00893355i
$378$		0			0
$379$	−5.54243	+	6.94999i	−0.284695	+	0.356997i	−0.903530	−	0.428524i	$-0.859034\pi$
$379$	−5.54243	+	6.94999i	−0.284695	+	0.356997i	0.618835	+	0.785521i	$0.287605\pi$
$380$	1.70901	+	2.96009i	0.0876704	+	0.151850i
$381$		0			0
$382$	0.107587	+	0.274127i	0.00550463	+	0.0140256i
$383$	−12.2349	−	5.89201i	−0.625173	−	0.301067i	0.0943467	−	0.995539i	$-0.469924\pi$
$383$	−12.2349	−	5.89201i	−0.625173	−	0.301067i	−0.719520	+	0.694472i	$0.755638\pi$
$384$		0			0
$385$	3.94876	−	17.3007i	0.201248	−	0.881724i
$386$	7.08576			0.360656
$387$		0			0
$388$	6.12592			0.310997
$389$	−0.872197	+	3.82135i	−0.0442222	+	0.193750i	−0.992214	−	0.124545i	$-0.960253\pi$
$389$	−0.872197	+	3.82135i	−0.0442222	+	0.193750i	0.947992	+	0.318295i	$0.103110\pi$
$390$		0			0
$391$	12.6996	+	6.11579i	0.642245	+	0.309289i
$392$	15.3700	+	39.1621i	0.776301	+	1.97798i
$393$		0			0
$394$	1.50948	+	2.61450i	0.0760466	+	0.131717i
$395$	5.41041	−	6.78444i	0.272227	−	0.341362i
$396$		0			0
$397$	0.912545	−	0.137544i	0.0457993	−	0.00690313i	−0.126103	−	0.992017i	$-0.540247\pi$
$397$	0.912545	−	0.137544i	0.0457993	−	0.00690313i	0.171902	+	0.985114i	$0.445009\pi$
$398$	8.16426	−	3.93170i	0.409238	−	0.197078i
$399$		0			0
$400$	1.69657	+	0.255717i	0.0848285	+	0.0127858i
$401$	12.9927	−	4.00771i	0.648823	−	0.200136i	0.0471626	−	0.998887i	$-0.484982\pi$
$401$	12.9927	−	4.00771i	0.648823	−	0.200136i	0.601661	+	0.798752i	$0.294506\pi$
$402$		0			0
$403$	2.88828	+	3.62178i	0.143875	+	0.180414i
$404$	−5.56100	+	14.1692i	−0.276670	+	0.704944i
$405$		0			0
$406$	−5.92865	+	4.04209i	−0.294234	+	0.200605i
$407$	−0.443098	+	5.91274i	−0.0219636	+	0.293083i
$408$		0			0
$409$	−3.60394	−	15.7899i	−0.178204	−	0.780761i	−0.982459	−	0.186477i	$-0.940293\pi$
$409$	−3.60394	−	15.7899i	−0.178204	−	0.780761i	0.804256	−	0.594283i	$-0.202564\pi$
$410$	−0.220021	+	2.93598i	−0.0108661	+	0.144998i
$411$		0			0
$412$	−10.3169	+	9.57266i	−0.508276	+	0.471611i
$413$	11.7956	−	30.0547i	0.580423	−	1.47889i
$414$		0			0
$415$	−0.133013	−	1.77493i	−0.00652935	−	0.0871281i
$416$	3.44289	−	1.06199i	0.168802	−	0.0520684i
$417$		0			0
$418$	−2.80292	−	2.60073i	−0.137095	−	0.127206i
$419$	−22.4254	+	10.7995i	−1.09555	+	0.527590i	−0.892257	−	0.451527i	$-0.850879\pi$
$419$	−22.4254	+	10.7995i	−1.09555	+	0.527590i	−0.203295	+	0.979117i	$0.565165\pi$
$420$		0			0
$421$	25.5011	+	17.3863i	1.24285	+	0.847359i	0.992672	−	0.120842i	$-0.0385594\pi$
$421$	25.5011	+	17.3863i	1.24285	+	0.847359i	0.250175	+	0.968201i	$0.419512\pi$
$422$	1.42590	−	1.78802i	0.0694117	−	0.0870395i
$423$		0			0
$424$	−18.4790	+	32.0066i	−0.897421	+	1.55438i
$425$	−6.55747	−	16.7082i	−0.318084	−	0.810465i
$426$		0			0
$427$	−18.8093	−	5.80189i	−0.910244	−	0.280773i
$428$	1.45034	−	6.35434i	0.0701047	−	0.307149i
$429$		0			0
$430$	7.33304	−	0.592249i	0.353630	−	0.0285608i
$431$	2.13534			0.102856			0.0514278	−	0.998677i	$-0.483623\pi$
$431$	2.13534			0.102856			0.0514278	+	0.998677i	$0.483623\pi$
$432$		0			0
$433$	18.6448	+	5.75116i	0.896012	+	0.276383i	0.708359	−	0.705852i	$-0.249436\pi$
$433$	18.6448	+	5.75116i	0.896012	+	0.276383i	0.187653	+	0.982235i	$0.439912\pi$
$434$	−25.7326	−	12.3922i	−1.23521	−	0.594844i
$435$		0			0
$436$	12.1461	−	21.0376i	0.581691	−	1.00752i
$437$	−2.13962	−	3.70594i	−0.102352	−	0.177279i
$438$		0			0
$439$	11.8985	+	8.11229i	0.567887	+	0.387179i	0.812954	−	0.582327i	$-0.197858\pi$
$439$	11.8985	+	8.11229i	0.567887	+	0.387179i	−0.245068	+	0.969506i	$0.578810\pi$
$440$	9.91669	−	1.49470i	0.472759	−	0.0712570i
$441$		0			0
$442$	−2.14378	−	1.98913i	−0.101969	−	0.0946134i
$443$	20.4362	+	3.08026i	0.970951	+	0.146347i	0.615319	−	0.788278i	$-0.289027\pi$
$443$	20.4362	+	3.08026i	0.970951	+	0.146347i	0.355633	+	0.934626i	$0.384265\pi$
$444$		0			0
$445$	−0.991267	−	13.2275i	−0.0469906	−	0.627045i
$446$	−2.18876	−	2.74462i	−0.103641	−	0.129961i
$447$		0			0
$448$	−12.3416	+	11.4513i	−0.583084	+	0.541023i
$449$	−27.0107	+	18.4156i	−1.27471	+	0.869084i	−0.995829	−	0.0912409i	$-0.970917\pi$
$449$	−27.0107	+	18.4156i	−1.27471	+	0.869084i	−0.278883	+	0.960325i	$0.589964\pi$
$450$		0			0
$451$	1.55398	+	6.80845i	0.0731742	+	0.320597i
$452$	−0.389290	−	1.70559i	−0.0183107	−	0.0802243i
$453$		0			0
$454$	−8.20913	+	5.59689i	−0.385274	+	0.262675i
$455$	−3.02052	+	2.80264i	−0.141604	+	0.131390i
$456$		0			0
$457$	1.92198	+	2.41009i	0.0899066	+	0.112739i	0.824750	−	0.565497i	$-0.191316\pi$
$457$	1.92198	+	2.41009i	0.0899066	+	0.112739i	−0.734843	+	0.678237i	$0.762744\pi$
$458$	−0.611205	−	8.15596i	−0.0285597	−	0.381103i
$459$		0			0
$460$	4.49031	+	0.676806i	0.209362	+	0.0315562i
$461$	−15.8067	−	14.6665i	−0.736193	−	0.683087i	0.220107	−	0.975476i	$-0.429359\pi$
$461$	−15.8067	−	14.6665i	−0.736193	−	0.683087i	−0.956300	+	0.292389i	$0.905550\pi$
$462$		0			0
$463$	−27.1728	+	4.09564i	−1.26283	+	0.190340i	−0.746114	−	0.665818i	$-0.768083\pi$
$463$	−27.1728	+	4.09564i	−1.26283	+	0.190340i	−0.516713	+	0.856159i	$0.672844\pi$
$464$	0.879395	+	0.599562i	0.0408249	+	0.0278339i
$465$		0			0
$466$	−8.17562	−	14.1606i	−0.378728	−	0.655977i
$467$	−15.8517	+	27.4559i	−0.733529	+	1.27051i	0.221836	+	0.975084i	$0.428795\pi$
$467$	−15.8517	+	27.4559i	−0.733529	+	1.27051i	−0.955366	+	0.295426i	$0.904538\pi$
$468$		0			0
$469$	−24.1566	−	11.6332i	−1.11545	−	0.537172i
$470$	−9.60709	−	2.96339i	−0.443142	−	0.136691i
$471$		0			0
$472$	18.2463			0.839855
$473$	16.2068	−	6.46923i	0.745189	−	0.297456i
$474$		0			0
$475$	−1.21254	+	5.31249i	−0.0556352	+	0.243754i
$476$	−36.5325	−	11.2688i	−1.67446	−	0.516503i
$477$		0			0
$478$	0.565122	+	1.43991i	0.0258481	+	0.0658598i
$479$	1.49373	−	2.58721i	0.0682502	−	0.118213i	−0.829881	−	0.557941i	$-0.811592\pi$
$479$	1.49373	−	2.58721i	0.0682502	−	0.118213i	0.898131	+	0.439728i	$0.144925\pi$
$480$		0			0
$481$	0.858403	−	1.07640i	0.0391398	−	0.0490798i
$482$	−9.39215	−	6.40346i	−0.427801	−	0.291670i
$483$		0			0
$484$	−4.79784	+	2.31052i	−0.218084	+	0.105024i
$485$	−4.63041	−	4.29640i	−0.210256	−	0.195089i
$486$		0			0
$487$	−30.1329	+	9.29475i	−1.36545	+	0.421186i	−0.888956	−	0.457992i	$-0.848569\pi$
$487$	−30.1329	+	9.29475i	−1.36545	+	0.421186i	−0.476494	+	0.879178i	$0.658093\pi$
$488$	−0.831300	−	11.0929i	−0.0376312	−	0.502153i
$489$		0			0
$490$	6.41217	−	16.3379i	0.289672	−	0.738073i
$491$	−13.8180	+	12.8213i	−0.623600	+	0.578616i	−0.927378	−	0.374127i	$-0.877942\pi$
$491$	−13.8180	+	12.8213i	−0.623600	+	0.578616i	0.303778	+	0.952743i	$0.401752\pi$
$492$		0			0
$493$	0.832074	−	11.1033i	0.0374747	−	0.500066i
$494$	0.197562	+	0.865576i	0.00888874	+	0.0389441i
$495$		0			0
$496$	−0.316591	+	4.22461i	−0.0142153	+	0.189690i
$497$	33.7488	−	23.0095i	1.51384	−	1.03212i
$498$		0			0
$499$	11.4840	−	29.2608i	0.514096	−	1.30989i	−0.404443	−	0.914563i	$-0.632535\pi$
$499$	11.4840	−	29.2608i	0.514096	−	1.30989i	0.918539	−	0.395331i	$-0.129370\pi$
$500$	−9.54249	−	11.9659i	−0.426753	−	0.535131i
$501$		0			0
$502$	6.59903	−	2.03553i	0.294529	−	0.0908502i
$503$	−22.4500	−	3.38379i	−1.00100	−	0.150876i	−0.371957	−	0.928250i	$-0.621313\pi$
$503$	−22.4500	−	3.38379i	−1.00100	−	0.150876i	−0.629039	+	0.777374i	$0.716551\pi$
$504$		0			0
$505$	14.1409	−	6.80992i	0.629263	−	0.303037i
$506$	−5.02316	+	0.757119i	−0.223307	+	0.0336581i
$507$		0			0
$508$	−3.72309	+	4.66860i	−0.165185	+	0.207136i
$509$	8.84121	+	15.3134i	0.391880	+	0.678755i	0.992697	−	0.120631i	$-0.0384917\pi$
$509$	8.84121	+	15.3134i	0.391880	+	0.678755i	−0.600818	+	0.799386i	$0.705158\pi$
$510$		0			0
$511$	−14.7958	−	37.6990i	−0.654526	−	1.66771i
$512$	5.70701	+	2.74835i	0.252217	+	0.121461i
$513$		0			0
$514$	−2.22099	+	9.73080i	−0.0979637	+	0.429207i
$515$	14.5120			0.639475
$516$		0			0
$517$	−23.8470			−1.04879
$518$	−1.88885	+	8.27560i	−0.0829913	+	0.363609i
$519$		0			0
$520$	−2.09803	−	1.01036i	−0.0920047	−	0.0443071i
$521$	12.4384	+	31.6925i	0.544936	+	1.38847i	0.892598	+	0.450854i	$0.148880\pi$
$521$	12.4384	+	31.6925i	0.544936	+	1.38847i	−0.347662	+	0.937620i	$0.613024\pi$
$522$		0			0
$523$	4.21809	+	7.30594i	0.184444	+	0.319466i	0.943389	−	0.331688i	$-0.107618\pi$
$523$	4.21809	+	7.30594i	0.184444	+	0.319466i	−0.758945	+	0.651155i	$0.774285\pi$
$524$	11.9643	−	15.0027i	0.522661	−	0.655397i
$525$		0			0
$526$	14.0558	−	2.11857i	0.612862	−	0.0923741i
$527$	39.9301	−	19.2293i	1.73938	−	0.837642i
$528$		0			0
$529$	17.1214	+	2.58063i	0.744408	+	0.112201i
$530$	14.7334	−	4.54467i	0.639980	−	0.197408i
$531$		0			0
$532$	7.23657	+	9.07437i	0.313745	+	0.393424i
$533$	0.592422	−	1.50947i	0.0256606	−	0.0653823i
$534$		0			0
$535$	−5.55287	+	3.78588i	−0.240071	+	0.163678i
$536$	1.13234	−	15.1100i	0.0489095	−	0.652652i
$537$		0			0
$538$	−5.10525	−	22.3675i	−0.220103	−	0.964333i
$539$	3.11106	−	41.5142i	0.134003	−	1.78814i
$540$		0			0
$541$	−7.39584	+	6.86234i	−0.317972	+	0.295035i	−0.822969	−	0.568086i	$-0.807684\pi$
$541$	−7.39584	+	6.86234i	−0.317972	+	0.295035i	0.504997	+	0.863121i	$0.331494\pi$
$542$	−5.35995	+	13.6569i	−0.230230	+	0.586616i
$543$		0			0
$544$	−2.57594	−	34.3736i	−0.110443	−	1.47375i
$545$	−23.9355	+	7.38313i	−1.02529	+	0.316259i
$546$		0			0
$547$	13.5257	+	12.5500i	0.578318	+	0.536600i	0.914179	−	0.405311i	$-0.132837\pi$
$547$	13.5257	+	12.5500i	0.578318	+	0.536600i	−0.335861	+	0.941911i	$0.609027\pi$
$548$	11.5216	−	5.54850i	0.492177	−	0.237020i
$549$		0			0
$550$	5.34465	+	3.64392i	0.227896	+	0.155377i
$551$	−2.10758	+	2.64282i	−0.0897859	+	0.112588i
$552$		0			0
$553$	14.7333	−	25.5188i	0.626522	−	1.08517i
$554$	−1.93605	−	4.93296i	−0.0822547	−	0.209582i
$555$		0			0
$556$	−21.7158	−	6.69843i	−0.920954	−	0.284077i
$557$	−0.981857	+	4.30180i	−0.0416026	+	0.182273i	−0.991460	−	0.130410i	$-0.958371\pi$
$557$	−0.981857	+	4.30180i	−0.0416026	+	0.182273i	0.949858	+	0.312683i	$0.101228\pi$
$558$		0			0
$559$	−3.95547	−	0.878747i	−0.167298	−	0.0371670i
$560$	−3.76826			−0.159238
$561$		0			0
$562$	−9.85160	−	3.03882i	−0.415565	−	0.128185i
$563$	−8.26616	−	3.98077i	−0.348377	−	0.167769i	0.251509	−	0.967855i	$-0.419073\pi$
$563$	−8.26616	−	3.98077i	−0.348377	−	0.167769i	−0.599886	+	0.800085i	$0.704787\pi$
$564$		0			0
$565$	−0.901958	+	1.56224i	−0.0379457	+	0.0657238i
$566$	0.250872	+	0.434523i	0.0105449	+	0.0182644i
$567$		0			0
$568$	19.0727	+	13.0036i	0.800273	+	0.545617i
$569$	−2.08305	+	0.313969i	−0.0873259	+	0.0131623i	−0.192560	−	0.981285i	$-0.561679\pi$
$569$	−2.08305	+	0.313969i	−0.0873259	+	0.0131623i	0.105234	+	0.994447i	$0.466441\pi$
$570$		0			0
$571$	21.4978	+	19.9470i	0.899654	+	0.834757i	0.986884	−	0.161431i	$-0.0516110\pi$
$571$	21.4978	+	19.9470i	0.899654	+	0.834757i	−0.0872298	+	0.996188i	$0.527801\pi$
$572$	−2.20977	−	0.333070i	−0.0923953	−	0.0139263i
$573$		0			0
$574$	0.747125	+	9.96969i	0.0311844	+	0.416127i
$575$	4.51372	+	5.66003i	0.188235	+	0.236040i
$576$		0			0
$577$	−12.2136	+	11.3326i	−0.508459	+	0.471781i	−0.892188	−	0.451665i	$-0.850830\pi$
$577$	−12.2136	+	11.3326i	−0.508459	+	0.471781i	0.383729	+	0.923446i	$0.374640\pi$
$578$	−11.8718	+	8.09402i	−0.493800	+	0.336667i
$579$		0			0
$580$	−0.798202	−	3.49715i	−0.0331435	−	0.145211i
$581$	−1.34492	−	5.89249i	−0.0557968	−	0.244462i
$582$		0			0
$583$	30.2171	−	20.6016i	1.25146	−	0.853233i
$584$	16.7775	−	15.5673i	0.694259	−	0.644178i
$585$		0			0
$586$	10.8081	+	13.5529i	0.446479	+	0.559867i
$587$	−1.69281	−	22.5890i	−0.0698698	−	0.932348i	−0.916466	−	0.400112i	$-0.868971\pi$
$587$	−1.69281	−	22.5890i	−0.0698698	−	0.932348i	0.846596	−	0.532236i	$-0.178648\pi$
$588$		0			0
$589$	−13.3046	−	2.00534i	−0.548205	−	0.0826286i
$590$	−5.58010	−	5.17757i	−0.229729	−	0.213157i
$591$		0			0
$592$	1.24502	−	0.187657i	0.0511701	−	0.00771265i
$593$	29.4226	+	20.0600i	1.20824	+	0.823765i	0.988415	−	0.151775i	$-0.0484988\pi$
$593$	29.4226	+	20.0600i	1.20824	+	0.823765i	0.219826	+	0.975539i	$0.429451\pi$
$594$		0			0
$595$	19.7106	+	34.1397i	0.808054	+	1.39959i
$596$	−7.92835	+	13.7323i	−0.324758	+	0.562497i
$597$		0			0
$598$	1.06273	+	0.511783i	0.0434582	+	0.0209283i
$599$	−29.6180	−	9.13596i	−1.21016	−	0.373285i	−0.376946	−	0.926235i	$-0.623026\pi$
$599$	−29.6180	−	9.13596i	−1.21016	−	0.373285i	−0.833214	+	0.552950i	$0.813502\pi$
$600$		0			0
$601$	21.0632			0.859187			0.429594	−	0.903022i	$-0.358657\pi$
$601$	21.0632			0.859187			0.429594	+	0.903022i	$0.358657\pi$
$602$	24.3229	−	5.69989i	0.991326	−	0.232310i
$603$		0			0
$604$	2.43310	−	10.6601i	0.0990012	−	0.433753i
$605$	5.24703	+	1.61849i	0.213322	+	0.0658012i
$606$		0			0
$607$	1.57042	+	4.00136i	0.0637413	+	0.162410i	0.959196	−	0.282743i	$-0.0912444\pi$
$607$	1.57042	+	4.00136i	0.0637413	+	0.162410i	−0.895454	+	0.445153i	$0.853149\pi$
$608$	−5.23238	+	9.06274i	−0.212201	+	0.367543i
$609$		0			0
$610$	−2.89350	+	3.62833i	−0.117154	+	0.146907i
$611$	4.57506	+	3.11922i	0.185087	+	0.126190i
$612$		0			0
$613$	0.154163	−	0.0742412i	0.00622660	−	0.00299857i	−0.430768	−	0.902463i	$-0.641757\pi$
$613$	0.154163	−	0.0742412i	0.00622660	−	0.00299857i	0.436994	+	0.899464i	$0.356043\pi$
$614$	−4.88404	−	4.53173i	−0.197104	−	0.182886i
$615$		0			0
$616$	32.5414	−	10.0377i	1.31113	−	0.404430i
$617$	−0.435808	−	5.81545i	−0.0175450	−	0.234121i	−0.999082	−	0.0428472i	$-0.986357\pi$
$617$	−0.435808	−	5.81545i	−0.0175450	−	0.234121i	0.981537	−	0.191274i	$-0.0612619\pi$
$618$		0			0
$619$	0.320011	−	0.815375i	0.0128623	−	0.0327727i	−0.924298	−	0.381671i	$-0.875349\pi$
$619$	0.320011	−	0.815375i	0.0128623	−	0.0327727i	0.937161	+	0.348898i	$0.113444\pi$
$620$	10.4665	−	9.71147i	0.420344	−	0.390022i
$621$		0			0
$622$	0.824243	−	10.9988i	0.0330491	−	0.441010i
$623$	−10.0229	−	43.9133i	−0.401560	−	1.75935i
$624$		0			0
$625$	−0.0448653	+	0.598685i	−0.00179461	+	0.0239474i
$626$	−3.24938	+	2.21539i	−0.129871	+	0.0885449i
$627$		0			0
$628$	−3.76058	+	9.58180i	−0.150063	+	0.382355i
$629$	−8.21244	−	10.2981i	−0.327452	−	0.410611i
$630$		0			0
$631$	−21.9032	+	6.75624i	−0.871953	+	0.268962i	−0.698265	−	0.715839i	$-0.746044\pi$
$631$	−21.9032	+	6.75624i	−0.871953	+	0.268962i	−0.173687	+	0.984801i	$0.555568\pi$
$632$	16.4666	+	2.48195i	0.655008	+	0.0987265i
$633$		0			0
$634$	−13.5961	+	6.54754i	−0.539970	+	0.260036i
$635$	6.08849	−	0.917692i	0.241614	−	0.0364175i
$636$		0			0
$637$	−6.02697	+	7.55758i	−0.238797	+	0.299442i
$638$	2.00638	+	3.47514i	0.0794332	+	0.137582i
$639$		0			0
$640$	−4.52033	−	11.5176i	−0.178682	−	0.455274i
$641$	−29.9739	−	14.4347i	−1.18390	−	0.570136i	−0.264854	−	0.964288i	$-0.585324\pi$
$641$	−29.9739	−	14.4347i	−1.18390	−	0.570136i	−0.919045	+	0.394153i	$0.871038\pi$
$642$		0			0
$643$	8.85495	−	38.7961i	0.349205	−	1.52997i	−0.429785	−	0.902931i	$-0.641410\pi$
$643$	8.85495	−	38.7961i	0.349205	−	1.52997i	0.778990	−	0.627037i	$-0.215732\pi$
$644$	15.4199			0.607631
$645$		0			0
$646$	8.49403			0.334193
$647$	1.59035	−	6.96776i	0.0625229	−	0.273931i	−0.933998	−	0.357279i	$-0.883704\pi$
$647$	1.59035	−	6.96776i	0.0625229	−	0.273931i	0.996520	+	0.0833487i	$0.0265615\pi$
$648$		0			0
$649$	−16.2676	−	7.83405i	−0.638558	−	0.307513i
$650$	−0.548743	−	1.39817i	−0.0215235	−	0.0548409i
$651$		0			0
$652$	4.19386	+	7.26398i	0.164244	+	0.284479i
$653$	−13.6325	+	17.0946i	−0.533482	+	0.668965i	−0.973411	−	0.229068i	$-0.926432\pi$
$653$	−13.6325	+	17.0946i	−0.533482	+	0.668965i	0.439929	+	0.898033i	$0.355004\pi$
$654$		0			0
$655$	−19.5656	+	2.94903i	−0.764490	+	0.115228i
$656$	1.33609	−	0.643427i	0.0521655	−	0.0251216i
$657$		0			0
$658$	−33.7581	−	5.08822i	−1.31603	−	0.198359i
$659$	−22.0315	+	6.79582i	−0.858225	+	0.264727i	−0.692476	−	0.721441i	$-0.743480\pi$
$659$	−22.0315	+	6.79582i	−0.858225	+	0.264727i	−0.165749	+	0.986168i	$0.553004\pi$
$660$		0			0
$661$	12.0427	+	15.1011i	0.468407	+	0.587364i	0.958780	−	0.284149i	$-0.0917109\pi$
$661$	12.0427	+	15.1011i	0.468407	+	0.587364i	−0.490373	+	0.871513i	$0.663139\pi$
$662$	−0.946771	+	2.41233i	−0.0367973	+	0.0937580i
$663$		0			0
$664$	2.82219	−	1.92414i	0.109522	−	0.0746710i
$665$	0.894360	−	11.9344i	0.0346818	−	0.462796i
$666$		0			0
$667$	0.999321	+	4.37831i	0.0386939	+	0.169529i
$668$	−0.895089	+	11.9441i	−0.0346320	+	0.462132i
$669$		0			0
$670$	−4.63390	+	4.29963i	−0.179023	+	0.166109i
$671$	−4.02159	+	10.2469i	−0.155252	+	0.395575i
$672$		0			0
$673$	−0.885315	−	11.8137i	−0.0341264	−	0.455385i	−0.987924	−	0.154936i	$-0.950483\pi$
$673$	−0.885315	−	11.8137i	−0.0341264	−	0.455385i	0.953798	−	0.300448i	$-0.0971363\pi$
$674$	−7.40041	+	2.28272i	−0.285053	+	0.0879272i
$675$		0			0
$676$	−12.5709	−	11.6641i	−0.483495	−	0.448618i
$677$	−39.6619	+	19.1002i	−1.52433	+	0.734079i	−0.993546	−	0.113428i	$-0.963817\pi$
$677$	−39.6619	+	19.1002i	−1.52433	+	0.734079i	−0.530785	+	0.847507i	$0.678103\pi$
$678$		0			0
$679$	−17.7223	−	12.0828i	−0.680118	−	0.463696i
$680$	−13.8903	+	17.4179i	−0.532670	+	0.667946i
$681$		0			0
$682$	−7.98612	+	13.8324i	−0.305804	+	0.529669i
$683$	3.21492	+	8.19149i	0.123016	+	0.313439i	0.979094	−	0.203407i	$-0.0652014\pi$
$683$	3.21492	+	8.19149i	0.123016	+	0.313439i	−0.856079	+	0.516845i	$0.827106\pi$
$684$		0			0
$685$	−12.6003	−	3.88667i	−0.481431	−	0.148502i
$686$	7.32774	−	32.1049i	0.279775	−	1.22577i
$687$		0			0
$688$	−2.10510	−	3.04953i	−0.0802561	−	0.116262i
$689$	−8.49188			−0.323515
$690$		0			0
$691$	−23.4565	−	7.23537i	−0.892327	−	0.275247i	−0.185510	−	0.982642i	$-0.559394\pi$
$691$	−23.4565	−	7.23537i	−0.892327	−	0.275247i	−0.706818	+	0.707396i	$0.749870\pi$
$692$	−7.49796	−	3.61083i	−0.285030	−	0.137263i
$693$		0			0
$694$	−4.39078	+	7.60506i	−0.166672	+	0.288684i
$695$	11.7164	+	20.2935i	0.444430	+	0.769775i
$696$		0			0
$697$	−12.8180	−	8.73915i	−0.485515	−	0.331019i
$698$	16.9910	−	2.56098i	0.643117	−	0.0969343i
$699$		0			0
$700$	−14.3938	−	13.3555i	−0.544035	−	0.504791i
$701$	7.74950	+	1.16805i	0.292695	+	0.0441166i	0.293748	−	0.955883i	$-0.405097\pi$
$701$	7.74950	+	1.16805i	0.292695	+	0.0441166i	−0.00105353	+	0.999999i	$0.500335\pi$
$702$		0			0
$703$	0.298832	+	3.98763i	0.0112707	+	0.150396i
$704$	5.87025	+	7.36106i	0.221243	+	0.277430i
$705$		0			0
$706$	19.5503	−	18.1400i	0.735784	−	0.682708i
$707$	44.0354	−	30.0228i	1.65612	−	1.12913i
$708$		0			0
$709$	−1.33852	−	5.86443i	−0.0502691	−	0.220243i	0.943554	−	0.331218i	$-0.107460\pi$
$709$	−1.33852	−	5.86443i	−0.0502691	−	0.220243i	−0.993823	+	0.110975i	$0.964603\pi$
$710$	−2.14294	−	9.38882i	−0.0804230	−	0.352356i
$711$		0			0
$712$	21.0321	−	14.3395i	0.788212	−	0.537394i
$713$	−13.1037	+	12.1584i	−0.490736	+	0.455337i
$714$		0			0
$715$	1.43671	+	1.80158i	0.0537299	+	0.0673751i
$716$	−2.49815	−	33.3356i	−0.0933604	−	1.24581i
$717$		0			0
$718$	5.93591	+	0.894694i	0.221526	+	0.0333897i
$719$	−10.4800	−	9.72406i	−0.390840	−	0.362646i	0.460139	−	0.887847i	$-0.347800\pi$
$719$	−10.4800	−	9.72406i	−0.390840	−	0.362646i	−0.850978	+	0.525201i	$0.823990\pi$
$720$		0			0
$721$	48.7279	−	7.34455i	1.81472	−	0.273525i
$722$	10.4376	+	7.11622i	0.388446	+	0.264838i
$723$		0			0
$724$	−3.88064	−	6.72147i	−0.144223	−	0.249802i
$725$	2.85932	−	4.95249i	0.106192	−	0.183931i
$726$		0			0
$727$	−6.01941	−	2.89879i	−0.223247	−	0.107510i	0.318917	−	0.947783i	$-0.396681\pi$
$727$	−6.01941	−	2.89879i	−0.223247	−	0.107510i	−0.542165	+	0.840272i	$0.682395\pi$
$728$	−7.55603	−	2.33073i	−0.280045	−	0.0863825i
$729$		0			0
$730$	−9.54827			−0.353397
$731$	−16.6170	+	35.0229i	−0.614603	+	1.29537i
$732$		0			0
$733$	−8.12555	+	35.6004i	−0.300124	+	1.31493i	0.569816	+	0.821772i	$0.307014\pi$
$733$	−8.12555	+	35.6004i	−0.300124	+	1.31493i	−0.869940	+	0.493157i	$0.835843\pi$
$734$	3.91465	+	1.20751i	0.144492	+	0.0445700i
$735$		0			0
$736$	5.07934	+	12.9419i	0.187227	+	0.477046i
$737$	−7.49701	+	12.9852i	−0.276156	+	0.478316i
$738$		0			0
$739$	−12.8940	+	16.1686i	−0.474313	+	0.594770i	−0.960221	−	0.279240i	$-0.909917\pi$
$739$	−12.8940	+	16.1686i	−0.474313	+	0.594770i	0.485908	+	0.874010i	$0.338489\pi$
$740$	−3.50610	−	2.39042i	−0.128887	−	0.0878734i
$741$		0			0
$742$	47.1714	−	22.7165i	1.73172	−	0.833950i
$743$	−4.99436	−	4.63408i	−0.183225	−	0.170008i	0.583228	−	0.812309i	$-0.301790\pi$
$743$	−4.99436	−	4.63408i	−0.183225	−	0.170008i	−0.766453	+	0.642301i	$0.777980\pi$
$744$		0			0
$745$	15.6239	−	4.81935i	0.572417	−	0.176567i
$746$	1.96844	+	26.2670i	0.0720696	+	0.961702i
$747$		0			0
$748$	−7.81098	+	19.9020i	−0.285598	+	0.727691i
$749$	−16.7292	+	15.5224i	−0.611271	+	0.567177i
$750$		0			0
$751$	−1.46930	+	19.6065i	−0.0536156	+	0.715450i	0.904024	+	0.427481i	$0.140599\pi$
$751$	−1.46930	+	19.6065i	−0.0536156	+	0.715450i	−0.957640	+	0.287969i	$0.907020\pi$
$752$	1.12682	+	4.93693i	0.0410910	+	0.180031i
$753$		0			0
$754$	0.0696298	−	0.929145i	0.00253577	−	0.0338375i
$755$	−9.31553	+	6.35122i	−0.339027	+	0.231145i
$756$		0			0
$757$	−14.3182	+	36.4821i	−0.520403	+	1.32597i	0.393235	+	0.919438i	$0.371356\pi$
$757$	−14.3182	+	36.4821i	−0.520403	+	1.32597i	−0.913638	+	0.406528i	$0.866739\pi$
$758$	4.43725	+	5.56414i	0.161168	+	0.202099i
$759$		0			0
$760$	6.46301	−	1.99357i	0.234438	−	0.0723145i
$761$	42.8441	+	6.45772i	1.55310	+	0.234092i	0.868820	−	0.495128i	$-0.164879\pi$
$761$	42.8441	+	6.45772i	1.55310	+	0.234092i	0.684279	+	0.729220i	$0.260117\pi$
$762$		0			0
$763$	−76.6333	+	36.9046i	−2.77431	+	1.33604i
$764$	−0.494314	+	0.0745058i	−0.0178836	+	0.00269553i
$765$		0			0
$766$	−6.77849	+	8.49996i	−0.244917	+	0.307116i
$767$	2.09624	+	3.63079i	0.0756907	+	0.131100i
$768$		0			0
$769$	17.9092	+	45.6318i	0.645821	+	1.64553i	0.758327	+	0.651875i	$0.226017\pi$
$769$	17.9092	+	45.6318i	0.645821	+	1.64553i	−0.112505	+	0.993651i	$0.535888\pi$
$770$	−12.8001	−	6.16422i	−0.461284	−	0.222143i
$771$		0			0
$772$	−2.67656	+	11.7268i	−0.0963315	+	0.422056i
$773$	45.8099			1.64767			0.823833	−	0.566832i	$-0.191831\pi$
$773$	45.8099			1.64767			0.823833	+	0.566832i	$0.191831\pi$
$774$		0			0
$775$	22.7623			0.817647
$776$	2.69736	−	11.8179i	0.0968295	−	0.424238i
$777$		0			0
$778$	2.82727	+	1.36154i	0.101363	+	0.0488137i
$779$	1.72068	+	4.38422i	0.0616498	+	0.157081i
$780$		0			0
$781$	−11.4213	−	19.7822i	−0.408685	−	0.707864i
$782$	7.03595	−	8.82280i	0.251605	−	0.315503i
$783$		0			0
$784$	−8.74148	+	1.31757i	−0.312196	+	0.0470559i
$785$	9.56269	−	4.60515i	0.341307	−	0.164365i
$786$		0			0
$787$	47.1951	+	7.11352i	1.68233	+	0.253570i	0.919516	−	0.393053i	$-0.128581\pi$
$787$	47.1951	+	7.11352i	1.68233	+	0.253570i	0.762810	+	0.646623i	$0.223819\pi$
$788$	−4.89713	+	1.51056i	−0.174453	+	0.0538116i
$789$		0			0
$790$	−4.33156	−	5.43160i	−0.154110	−	0.193248i
$791$	−2.23791	+	5.70211i	−0.0795710	+	0.202744i
$792$		0			0
$793$	2.11185	−	1.43983i	0.0749939	−	0.0511300i
$794$	0.0552130	−	0.736767i	0.00195944	−	0.0261469i
$795$		0			0
$796$	3.42293	+	14.9968i	0.121322	+	0.531548i
$797$	−2.36014	+	31.4939i	−0.0836004	+	1.11557i	0.784814	+	0.619731i	$0.212758\pi$
$797$	−2.36014	+	31.4939i	−0.0836004	+	1.11557i	−0.868415	+	0.495839i	$0.834861\pi$
$798$		0			0
$799$	38.8335	−	36.0323i	1.37383	−	1.27473i
$800$	6.46793	−	16.4800i	0.228676	−	0.582657i
$801$		0			0
$802$	−0.813475	−	10.8551i	−0.0287248	−	0.383306i
$803$	−21.6419	+	6.67563i	−0.763725	+	0.235578i
$804$		0			0
$805$	−11.6555	−	10.8147i	−0.410803	−	0.381169i
$806$	3.34144	−	1.60915i	0.117697	−	0.0566799i
$807$		0			0
$808$	24.8861	+	16.9670i	0.875489	+	0.596898i
$809$	−31.3024	+	39.2520i	−1.10054	+	1.38003i	−0.182652	+	0.983178i	$0.558468\pi$
$809$	−31.3024	+	39.2520i	−1.10054	+	1.38003i	−0.917883	+	0.396850i	$0.870103\pi$
$810$		0			0
$811$	−18.3687	+	31.8155i	−0.645012	+	1.11719i	0.339287	+	0.940683i	$0.389814\pi$
$811$	−18.3687	+	31.8155i	−0.645012	+	1.11719i	−0.984299	+	0.176511i	$0.943519\pi$
$812$	−4.45009	−	11.3386i	−0.156167	−	0.397908i
$813$		0			0
$814$	4.53610	+	1.39920i	0.158990	+	0.0490420i
$815$	1.92455	−	8.43199i	0.0674140	−	0.295360i
$816$		0			0
$817$	10.1577	−	5.94326i	0.355375	−	0.207928i
$818$	−12.9664			−0.453361
$819$		0			0
$820$	−4.77587	−	1.47316i	−0.166781	−	0.0514450i
$821$	8.74383	+	4.21081i	0.305162	+	0.146958i	0.580197	−	0.814476i	$-0.302975\pi$
$821$	8.74383	+	4.21081i	0.305162	+	0.146958i	−0.275036	+	0.961434i	$0.588690\pi$
$822$		0			0
$823$	5.78962	−	10.0279i	0.201814	−	0.349551i	−0.747299	−	0.664488i	$-0.768650\pi$
$823$	5.78962	−	10.0279i	0.201814	−	0.349551i	0.949113	+	0.314936i	$0.101983\pi$
$824$	13.9245	+	24.1179i	0.485083	+	0.840188i
$825$		0			0
$826$	−21.3570	−	14.5610i	−0.743106	−	0.506641i
$827$	−13.5650	+	2.04459i	−0.471701	+	0.0710974i	−0.380591	−	0.924743i	$-0.624279\pi$
$827$	−13.5650	+	2.04459i	−0.471701	+	0.0710974i	−0.0911095	+	0.995841i	$0.529041\pi$
$828$		0			0
$829$	−25.3708	−	23.5407i	−0.881166	−	0.817602i	0.103031	−	0.994678i	$-0.467146\pi$
$829$	−25.3708	−	23.5407i	−0.881166	−	0.817602i	−0.984197	+	0.177076i	$0.943336\pi$
$830$	−1.40908	−	0.212384i	−0.0489097	−	0.00737196i
$831$		0			0
$832$	−0.163373	−	2.18006i	−0.00566393	−	0.0755799i
$833$	57.6607	+	72.3043i	1.99783	+	2.50519i
$834$		0			0
$835$	9.05356	−	8.40047i	0.313311	−	0.290710i
$836$	5.36291	−	3.65637i	0.185480	−	0.126458i
$837$		0			0
$838$	4.43420	+	19.4275i	0.153177	+	0.671112i
$839$	−5.36544	−	23.5075i	−0.185235	−	0.811570i	−0.979084	−	0.203455i	$-0.934783\pi$
$839$	−5.36544	−	23.5075i	−0.185235	−	0.811570i	0.793849	−	0.608115i	$-0.208074\pi$
$840$		0			0
$841$	−21.0298	+	14.3379i	−0.725167	+	0.494411i
$842$	18.1135	−	16.8069i	0.624232	−	0.579202i
$843$		0			0
$844$	2.42052	+	3.03523i	0.0833177	+	0.104477i
$845$	1.32142	+	17.6331i	0.0454581	+	0.606597i
$846$		0			0
$847$	18.4374	+	2.77899i	0.633517	+	0.0954874i
$848$	−5.69287	−	5.28222i	−0.195494	−	0.181392i
$849$		0			0
$850$	−14.2093	+	2.14171i	−0.487376	+	0.0734601i
$851$	4.38951	+	2.99272i	0.150471	+	0.102589i
$852$		0			0
$853$	−7.47416	−	12.9456i	−0.255911	−	0.443250i	0.709232	−	0.704975i	$-0.249042\pi$
$853$	−7.47416	−	12.9456i	−0.255911	−	0.443250i	−0.965142	+	0.261725i	$0.915709\pi$
$854$	−7.87938	+	13.6475i	−0.269627	+	0.467007i
$855$		0			0
$856$	−11.6199	−	5.59587i	−0.397161	−	0.191263i
$857$	33.2780	+	10.2649i	1.13675	+	0.350642i	0.805322	−	0.592837i	$-0.201992\pi$
$857$	33.2780	+	10.2649i	1.13675	+	0.350642i	0.331431	+	0.943479i	$0.392469\pi$
$858$		0			0
$859$	−34.5111			−1.17750			−0.588752	−	0.808314i	$-0.700381\pi$
$859$	−34.5111			−1.17750			−0.588752	+	0.808314i	$0.700381\pi$
$860$	−1.78981	+	12.3597i	−0.0610319	+	0.421463i
$861$		0			0
$862$	0.380410	−	1.66668i	0.0129568	−	0.0567675i
$863$	19.4875	+	6.01110i	0.663363	+	0.204620i	0.608111	−	0.793852i	$-0.291928\pi$
$863$	19.4875	+	6.01110i	0.663363	+	0.204620i	0.0552518	+	0.998472i	$0.482404\pi$
$864$		0			0
$865$	3.13506	+	7.98799i	0.106595	+	0.271600i
$866$	7.81049	−	13.5282i	0.265411	−	0.459706i
$867$		0			0
$868$	30.2290	−	37.9059i	1.02604	−	1.28661i
$869$	−13.6153	−	9.28273i	−0.461866	−	0.314895i
$870$		0			0
$871$	3.13679	−	1.51060i	0.106286	−	0.0511846i
$872$	−35.2368	−	32.6950i	−1.19327	−	1.10719i
$873$		0			0
$874$	−3.27375	+	1.00982i	−0.110736	+	0.0341576i
$875$	4.00470	+	53.4390i	0.135384	+	1.80657i
$876$		0			0
$877$	12.4401	−	31.6968i	0.420072	−	1.07032i	−0.551625	−	0.834092i	$-0.685992\pi$
$877$	12.4401	−	31.6968i	0.420072	−	1.07032i	0.971697	−	0.236233i	$-0.0759128\pi$
$878$	8.45156	−	7.84191i	0.285226	−	0.264651i
$879$		0			0
$880$	−0.157481	+	2.10144i	−0.00530868	+	0.0708394i
$881$	6.70780	+	29.3888i	0.225991	+	0.990133i	0.952873	+	0.303370i	$0.0981119\pi$
$881$	6.70780	+	29.3888i	0.225991	+	0.990133i	−0.726881	+	0.686763i	$0.759031\pi$
$882$		0			0
$883$	3.54420	−	47.2941i	0.119272	−	1.59157i	−0.541313	−	0.840821i	$-0.682073\pi$
$883$	3.54420	−	47.2941i	0.119272	−	1.59157i	0.660585	−	0.750751i	$-0.270308\pi$
$884$	4.10175	−	2.79653i	0.137957	−	0.0940575i
$885$		0			0
$886$	6.04491	−	15.4022i	0.203083	−	0.517446i
$887$	5.58398	+	7.00209i	0.187492	+	0.235107i	0.866689	−	0.498848i	$-0.166244\pi$
$887$	5.58398	+	7.00209i	0.187492	+	0.235107i	−0.679198	+	0.733955i	$0.737672\pi$
$888$		0			0
$889$	19.9793	−	6.16279i	0.670083	−	0.206693i
$890$	−10.5010	−	1.58277i	−0.351995	−	0.0530547i
$891$		0			0
$892$	5.36905	−	2.58560i	0.179769	−	0.0865723i
$893$	−15.9031	+	2.39701i	−0.532178	+	0.0802129i
$894$		0			0
$895$	−21.4915	+	26.9495i	−0.718382	+	0.900822i
$896$	−21.0073	−	36.3857i	−0.701804	−	1.21556i
$897$		0			0
$898$	9.56186	+	24.3632i	0.319083	+	0.813011i
$899$	12.7220	+	6.12659i	0.424302	+	0.204333i
$900$		0			0
$901$	−18.0782	+	79.2059i	−0.602273	+	2.63873i
$902$	5.59100			0.186160
$903$		0			0
$904$	−3.46177			−0.115137
$905$	−1.78081	+	7.80225i	−0.0591963	+	0.259356i
$906$		0			0
$907$	17.1208	+	8.24496i	0.568488	+	0.273769i	0.695969	−	0.718072i	$-0.254975\pi$
$907$	17.1208	+	8.24496i	0.568488	+	0.273769i	−0.127481	+	0.991841i	$0.540689\pi$
$908$	−6.16183	−	15.7001i	−0.204488	−	0.521026i
$909$		0			0
$910$	1.64942	+	2.85688i	0.0546778	+	0.0947047i
$911$	21.2968	−	26.7054i	0.705595	−	0.884788i	−0.291832	−	0.956469i	$-0.594265\pi$
$911$	21.2968	−	26.7054i	0.705595	−	0.884788i	0.997428	+	0.0716811i	$0.0228364\pi$
$912$		0			0
$913$	−3.34226	+	0.503765i	−0.110613	+	0.0166722i
$914$	2.22354	−	1.07080i	0.0735481	−	0.0354189i
$915$		0			0
$916$	13.7288	+	2.06928i	0.453612	+	0.0683711i
$917$	−64.2040	+	19.8043i	−2.12020	+	0.653996i
$918$		0			0
$919$	28.1861	+	35.3443i	0.929774	+	1.16590i	0.985876	+	0.167475i	$0.0535613\pi$
$919$	28.1861	+	35.3443i	0.929774	+	1.16590i	−0.0561022	+	0.998425i	$0.517867\pi$
$920$	3.28284	−	8.36453i	0.108232	−	0.275770i
$921$		0			0
$922$	−14.2635	+	9.72471i	−0.469744	+	0.320266i
$923$	−0.396367	+	5.28915i	−0.0130466	+	0.174094i
$924$		0			0
$925$	−1.50536	−	6.59541i	−0.0494959	−	0.216856i
$926$	−1.64408	+	21.9387i	−0.0540277	+	0.720949i
$927$		0			0
$928$	8.05064	−	7.46990i	0.264275	−	0.245212i
$929$	7.73067	−	19.6974i	0.253635	−	0.646251i	−0.746175	−	0.665750i	$-0.768112\pi$
$929$	7.73067	−	19.6974i	0.253635	−	0.646251i	0.999810	+	0.0194985i	$0.00620696\pi$
$930$		0			0
$931$	−2.09814	−	27.9977i	−0.0687638	−	0.917589i
$932$	26.5237	−	8.18148i	0.868813	−	0.267993i
$933$		0			0
$934$	18.6061	+	17.2639i	0.608809	+	0.564892i
$935$	19.8623	−	9.56520i	0.649568	−	0.312815i
$936$		0			0
$937$	−41.6658	−	28.4073i	−1.36116	−	0.928025i	−0.361173	−	0.932499i	$-0.617624\pi$
$937$	−41.6658	−	28.4073i	−1.36116	−	0.928025i	−0.999990	+	0.00447367i	$0.998576\pi$
$938$	−13.3835	+	16.7824i	−0.436987	+	0.547964i
$939$		0			0
$940$	8.53331	−	14.7801i	0.278326	−	0.482075i
$941$	7.34488	+	18.7144i	0.239436	+	0.610074i	0.999194	−	0.0401322i	$-0.0127779\pi$
$941$	7.34488	+	18.7144i	0.239436	+	0.610074i	−0.759758	+	0.650206i	$0.774683\pi$
$942$		0			0
$943$	5.97923	+	1.84435i	0.194711	+	0.0600603i
$944$	−0.853167	+	3.73797i	−0.0277682	+	0.121661i
$945$		0			0
$946$	−2.16216	−	13.8023i	−0.0702979	−	0.448751i
$947$	−11.6359			−0.378117			−0.189059	−	0.981966i	$-0.560544\pi$
$947$	−11.6359			−0.378117			−0.189059	+	0.981966i	$0.560544\pi$
$948$		0			0
$949$	5.02518	+	1.55006i	0.163124	+	0.0503172i
$950$	3.93052	+	1.89284i	0.127523	+	0.0614118i
$951$		0			0
$952$	−37.8252	+	65.5152i	−1.22592	+	2.12336i
$953$	−21.3921	−	37.0523i	−0.692959	−	1.20024i	−0.970864	−	0.239632i	$-0.922973\pi$
$953$	−21.3921	−	37.0523i	−0.692959	−	1.20024i	0.277905	−	0.960609i	$-0.410360\pi$
$954$		0			0
$955$	0.425893	+	0.290369i	0.0137816	+	0.00939611i
$956$	−2.59648	+	0.391357i	−0.0839762	+	0.0126574i
$957$		0			0
$958$	−1.75328	−	1.62680i	−0.0566458	−	0.0525596i
$959$	−44.2758	−	6.67350i	−1.42974	−	0.215499i
$960$		0			0
$961$	1.88352	+	25.1338i	0.0607586	+	0.810767i
$962$	−0.687235	−	0.861765i	−0.0221573	−	0.0277844i
$963$		0			0
$964$	14.1454	−	13.1250i	0.455591	−	0.422727i
$965$	10.2477	−	6.98675i	0.329884	−	0.224911i
$966$		0			0
$967$	−11.0286	−	48.3194i	−0.354655	−	1.55385i	−0.766289	−	0.642497i	$-0.777899\pi$
$967$	−11.0286	−	48.3194i	−0.354655	−	1.55385i	0.411633	−	0.911350i	$-0.364958\pi$
$968$	2.34479	+	10.2732i	0.0753643	+	0.330192i
$969$		0			0
$970$	−4.17835	+	2.84875i	−0.134159	+	0.0914679i
$971$	16.0648	−	14.9060i	0.515544	−	0.478355i	−0.378961	−	0.925413i	$-0.623719\pi$
$971$	16.0648	−	14.9060i	0.515544	−	0.478355i	0.894505	+	0.447058i	$0.147528\pi$
$972$		0			0
$973$	49.6116	+	62.2109i	1.59047	+	1.99439i
$974$	1.88663	+	25.1753i	0.0604514	+	0.806668i
$975$		0			0
$976$	2.31138	+	0.348385i	0.0739856	+	0.0111515i
$977$	−21.5917	−	20.0342i	−0.690781	−	0.640951i	0.254551	−	0.967059i	$-0.418072\pi$
$977$	−21.5917	−	20.0342i	−0.690781	−	0.640951i	−0.945333	+	0.326108i	$0.894263\pi$
$978$		0			0
$979$	−24.9079	+	3.75426i	−0.796060	+	0.119987i
$980$	24.6168	+	16.7835i	0.786355	+	0.536128i
$981$		0			0
$982$	7.54564	+	13.0694i	0.240791	+	0.417062i
$983$	2.13856	−	3.70410i	0.0682095	−	0.118142i	−0.829904	−	0.557907i	$-0.811605\pi$
$983$	2.13856	−	3.70410i	0.0682095	−	0.118142i	0.898113	+	0.439764i	$0.144938\pi$
$984$		0			0
$985$	4.76103	+	2.29279i	0.151699	+	0.0730544i
$986$	−8.51813	−	2.62750i	−0.271273	−	0.0836765i
$987$		0			0
$988$	−1.50714			−0.0479484
$989$	2.24078	−	15.4740i	0.0712525	−	0.492043i
$990$		0			0
$991$	11.3481	−	49.7191i	0.360483	−	1.57938i	−0.391487	−	0.920183i	$-0.628039\pi$
$991$	11.3481	−	49.7191i	0.360483	−	1.57938i	0.751971	−	0.659197i	$-0.229103\pi$
$992$	41.7718	+	12.8849i	1.32626	+	0.409096i
$993$		0			0
$994$	−11.9472	−	30.4409i	−0.378941	−	0.965527i
$995$	7.93068	−	13.7363i	0.251420	−	0.435471i
$996$		0			0
$997$	25.9035	−	32.4820i	0.820373	−	1.02872i	−0.178623	−	0.983918i	$-0.557164\pi$
$997$	25.9035	−	32.4820i	0.820373	−	1.02872i	0.998996	−	0.0447976i	$-0.0142643\pi$
$998$	−20.7929	−	14.1764i	−0.658188	−	0.448745i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.253.2		36
3.2	odd	2		43.2.g.a.38.2	yes	36
12.11	even	2		688.2.bg.c.81.2		36
43.17	even	21	inner	387.2.y.c.361.2		36
129.17	odd	42		43.2.g.a.17.2	✓	36
129.62	even	42		1849.2.a.o.1.7		18
129.110	odd	42		1849.2.a.n.1.12		18
516.275	even	42		688.2.bg.c.17.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.17.2	✓	36	129.17	odd	42
43.2.g.a.38.2	yes	36	3.2	odd	2
387.2.y.c.253.2		36	1.1	even	1	trivial
387.2.y.c.361.2		36	43.17	even	21	inner
688.2.bg.c.17.2		36	516.275	even	42
688.2.bg.c.81.2		36	12.11	even	2
1849.2.a.n.1.12		18	129.110	odd	42
1849.2.a.o.1.7		18	129.62	even	42

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.178150 - 0.780524i) q^{2} +(1.22446 + 0.589667i) q^{4} +(-0.511972 - 1.30448i) q^{5} +(-2.37928 - 4.12103i) q^{7} +(1.67671 - 2.10253i) q^{8} +O(q^{10})\)	\(q+(0.178150 - 0.780524i) q^{2} +(1.22446 + 0.589667i) q^{4} +(-0.511972 - 1.30448i) q^{5} +(-2.37928 - 4.12103i) q^{7} +(1.67671 - 2.10253i) q^{8} +(-1.10939 + 0.167213i) q^{10} +(-2.39760 + 1.15462i) q^{11} +(0.611008 + 0.0920946i) q^{13} +(-3.64044 + 1.12293i) q^{14} +(0.352328 + 0.441805i) q^{16} +(2.15975 - 5.50296i) q^{17} +(-1.48286 + 1.01100i) q^{19} +(0.142323 - 1.89917i) q^{20} +(0.474081 + 2.07708i) q^{22} +(-0.178184 + 2.37770i) q^{23} +(2.22570 - 2.06515i) q^{25} +(0.180733 - 0.460500i) q^{26} +(-0.483287 - 6.44901i) q^{28} +(1.79980 - 0.555165i) q^{29} +(5.49565 + 5.09922i) q^{31} +(5.25345 - 2.52993i) q^{32} +(-3.91044 - 2.66609i) q^{34} +(-4.15769 + 5.21358i) q^{35} +(1.11406 - 1.92960i) q^{37} +(0.524936 + 1.33752i) q^{38} +(-3.60115 - 1.11081i) q^{40} +(0.583954 - 2.55847i) q^{41} +(-6.54183 - 0.452170i) q^{43} -3.61660 q^{44} +(1.82411 + 0.562664i) q^{46} +(8.07377 + 3.88812i) q^{47} +(-7.82195 + 13.5480i) q^{49} +(-1.21539 - 2.10512i) q^{50} +(0.693847 + 0.473057i) q^{52} +(-13.5894 + 2.04828i) q^{53} +(2.73369 + 2.53650i) q^{55} +(-12.6540 - 1.90728i) q^{56} +(-0.112686 - 1.50369i) q^{58} +(4.23034 + 5.30467i) q^{59} +(3.03226 - 2.81353i) q^{61} +(4.95912 - 3.38107i) q^{62} +(-0.787282 - 3.44931i) q^{64} +(-0.192683 - 0.844198i) q^{65} +(4.65539 - 3.17399i) q^{67} +(5.88944 - 5.46460i) q^{68} +(3.32864 + 4.17398i) q^{70} +(0.641465 + 8.55975i) q^{71} +(8.41561 + 1.26845i) q^{73} +(-1.30763 - 1.21331i) q^{74} +(-2.41185 + 0.363527i) q^{76} +(10.4628 + 7.13343i) q^{77} +(3.09616 + 5.36270i) q^{79} +(0.395945 - 0.685797i) q^{80} +(-1.89292 - 0.911581i) q^{82} +(1.21371 + 0.374380i) q^{83} -8.28425 q^{85} +(-1.51835 + 5.02550i) q^{86} +(-1.59246 + 6.97702i) q^{88} +(9.04506 + 2.79003i) q^{89} +(-1.07423 - 2.73710i) q^{91} +(-1.62023 + 2.80632i) q^{92} +(4.47311 - 5.60911i) q^{94} +(2.07801 + 1.41676i) q^{95} +(4.06114 - 1.95574i) q^{97} +(9.18108 + 8.51880i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

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