LMFDB - Embedded newform 864.2.bk.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(37,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("864.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bk (of order $24$, degree $8$, not 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	864.37
Dual form			864.2.bk.a.397.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04770 + 0.949902i) q^{2} +(0.195371 - 1.99043i) q^{4} +(2.93870 - 2.25494i) q^{5} +(1.16359 - 4.34257i) q^{7} +(1.68603 + 2.27097i) q^{8} +O(q^{10})$	\(q+(-1.04770 + 0.949902i) q^{2} +(0.195371 - 1.99043i) q^{4} +(2.93870 - 2.25494i) q^{5} +(1.16359 - 4.34257i) q^{7} +(1.68603 + 2.27097i) q^{8} +(-0.936914 + 5.15400i) q^{10} +(3.80440 - 0.500859i) q^{11} +(-0.0873426 + 0.663433i) q^{13} +(2.90592 + 5.65503i) q^{14} +(-3.92366 - 0.777745i) q^{16} +2.24902i q^{17} +(1.79007 - 0.741472i) q^{19} +(-3.91418 - 6.28984i) q^{20} +(-3.51012 + 4.13856i) q^{22} +(0.487832 + 1.82061i) q^{23} +(2.25709 - 8.42358i) q^{25} +(-0.538687 - 0.778048i) q^{26} +(-8.41628 - 3.16446i) q^{28} +(-5.18509 + 6.75734i) q^{29} +(0.585159 - 1.01353i) q^{31} +(4.84962 - 2.91225i) q^{32} +(-2.13635 - 2.35631i) q^{34} +(-6.37282 - 15.3853i) q^{35} +(-2.64545 - 1.09578i) q^{37} +(-1.17114 + 2.47724i) q^{38} +(10.0756 + 2.87181i) q^{40} +(-1.96391 - 7.32940i) q^{41} +(3.60825 - 0.475035i) q^{43} +(-0.253658 - 7.67026i) q^{44} +(-2.24051 - 1.44407i) q^{46} +(-6.03021 + 3.48154i) q^{47} +(-11.4418 - 6.60594i) q^{49} +(5.63682 + 10.9694i) q^{50} +(1.30346 + 0.303465i) q^{52} +(-4.84541 + 11.6979i) q^{53} +(10.0506 - 10.0506i) q^{55} +(11.8237 - 4.67922i) q^{56} +(-0.986371 - 12.0050i) q^{58} +(4.00831 - 3.07569i) q^{59} +(-3.36120 + 4.38040i) q^{61} +(0.349676 + 1.61772i) q^{62} +(-2.31462 + 7.65784i) q^{64} +(1.23933 + 2.14658i) q^{65} +(7.17032 + 0.943991i) q^{67} +(4.47652 + 0.439392i) q^{68} +(21.2914 + 10.0657i) q^{70} +(10.6269 + 10.6269i) q^{71} +(-1.59954 + 1.59954i) q^{73} +(3.81254 - 1.36487i) q^{74} +(-1.12612 - 3.70788i) q^{76} +(2.25174 - 17.1037i) q^{77} +(-2.89618 + 1.67211i) q^{79} +(-13.2842 + 6.56208i) q^{80} +(9.01981 + 5.81353i) q^{82} +(-1.21803 - 0.934627i) q^{83} +(5.07141 + 6.60919i) q^{85} +(-3.32914 + 3.92518i) q^{86} +(7.55176 + 7.79522i) q^{88} +(-7.83449 - 7.83449i) q^{89} +(2.77937 + 1.15125i) q^{91} +(3.71912 - 0.615303i) q^{92} +(3.01075 - 9.37573i) q^{94} +(3.58851 - 6.21548i) q^{95} +(7.56906 + 13.1100i) q^{97} +(18.2626 - 3.94754i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.04770	+	0.949902i	−0.740839	+	0.671682i
$2$	−1.04770	+	0.949902i	−0.740839	+	0.671682i
$3$		0			0
$3$		0			0
$4$	0.195371	−	1.99043i	0.0976853	−	0.995217i
$5$	2.93870	−	2.25494i	1.31423	−	1.00844i	0.316010	−	0.948756i	$-0.397657\pi$
$5$	2.93870	−	2.25494i	1.31423	−	1.00844i	0.998217	−	0.0596858i	$-0.0190099\pi$
$6$		0			0
$7$	1.16359	−	4.34257i	0.439795	−	1.64134i	−0.289529	−	0.957169i	$-0.593499\pi$
$7$	1.16359	−	4.34257i	0.439795	−	1.64134i	0.729324	−	0.684169i	$-0.239835\pi$
$8$	1.68603	+	2.27097i	0.596101	+	0.802910i
$9$		0			0
$10$	−0.936914	+	5.15400i	−0.296278	+	1.62984i
$11$	3.80440	−	0.500859i	1.14707	−	0.151015i	0.467065	−	0.884223i	$-0.345311\pi$
$11$	3.80440	−	0.500859i	1.14707	−	0.151015i	0.680004	+	0.733208i	$0.261978\pi$
$12$		0			0
$13$	−0.0873426	+	0.663433i	−0.0242245	+	0.184003i	−0.999279	−	0.0379614i	$-0.987914\pi$
$13$	−0.0873426	+	0.663433i	−0.0242245	+	0.184003i	0.975055	+	0.221965i	$0.0712469\pi$
$14$	2.90592	+	5.65503i	0.776640	+	1.51137i
$15$		0			0
$16$	−3.92366	−	0.777745i	−0.980915	−	0.194436i
$17$			2.24902i			0.545467i	0.962090	+	0.272734i	$0.0879278\pi$
$17$			2.24902i			0.545467i	−0.962090	+	0.272734i	$0.912072\pi$
$18$		0			0
$19$	1.79007	−	0.741472i	0.410671	−	0.170105i	−0.167777	−	0.985825i	$-0.553659\pi$
$19$	1.79007	−	0.741472i	0.410671	−	0.170105i	0.578447	+	0.815720i	$0.303659\pi$
$20$	−3.91418	−	6.28984i	−0.875238	−	1.40645i
$21$		0			0
$22$	−3.51012	+	4.13856i	−0.748360	+	0.882344i
$23$	0.487832	+	1.82061i	0.101720	+	0.379624i	0.997952	−	0.0639605i	$-0.0203732\pi$
$23$	0.487832	+	1.82061i	0.101720	+	0.379624i	−0.896232	+	0.443585i	$0.853707\pi$
$24$		0			0
$25$	2.25709	−	8.42358i	0.451419	−	1.68472i
$26$	−0.538687	−	0.778048i	−0.105645	−	0.152588i
$27$		0			0
$28$	−8.41628	−	3.16446i	−1.59053	−	0.598026i
$29$	−5.18509	+	6.75734i	−0.962848	+	1.25481i	0.00414209	+	0.999991i	$0.498682\pi$
$29$	−5.18509	+	6.75734i	−0.962848	+	1.25481i	−0.966990	+	0.254816i	$0.917985\pi$
$30$		0			0
$31$	0.585159	−	1.01353i	0.105098	−	0.182035i	−0.808680	−	0.588248i	$-0.799818\pi$
$31$	0.585159	−	1.01353i	0.105098	−	0.182035i	0.913778	+	0.406214i	$0.133151\pi$
$32$	4.84962	−	2.91225i	0.857300	−	0.514817i
$33$		0			0
$34$	−2.13635	−	2.35631i	−0.366381	−	0.404103i
$35$	−6.37282	−	15.3853i	−1.07720	−	2.60060i
$36$		0			0
$37$	−2.64545	−	1.09578i	−0.434910	−	0.180145i	0.154477	−	0.987996i	$-0.450631\pi$
$37$	−2.64545	−	1.09578i	−0.434910	−	0.180145i	−0.589387	+	0.807851i	$0.700631\pi$
$38$	−1.17114	+	2.47724i	−0.189984	+	0.401861i
$39$		0			0
$40$	10.0756	+	2.87181i	1.59310	+	0.454072i
$41$	−1.96391	−	7.32940i	−0.306711	−	1.14466i	−0.931463	−	0.363837i	$-0.881467\pi$
$41$	−1.96391	−	7.32940i	−0.306711	−	1.14466i	0.624752	−	0.780823i	$-0.285200\pi$
$42$		0			0
$43$	3.60825	−	0.475035i	0.550253	−	0.0724422i	0.149727	−	0.988727i	$-0.452161\pi$
$43$	3.60825	−	0.475035i	0.550253	−	0.0724422i	0.400526	+	0.916285i	$0.368827\pi$
$44$	−0.253658	−	7.67026i	−0.0382404	−	1.15634i
$45$		0			0
$46$	−2.24051	−	1.44407i	−0.330345	−	0.212917i
$47$	−6.03021	+	3.48154i	−0.879596	+	0.507835i	−0.870525	−	0.492124i	$-0.836221\pi$
$47$	−6.03021	+	3.48154i	−0.879596	+	0.507835i	−0.00907070	+	0.999959i	$0.502887\pi$
$48$		0			0
$49$	−11.4418	−	6.60594i	−1.63455	−	0.943705i
$50$	5.63682	+	10.9694i	0.797166	+	1.55131i
$51$		0			0
$52$	1.30346	+	0.303465i	0.180757	+	0.0420830i
$53$	−4.84541	+	11.6979i	−0.665569	+	1.60682i	0.123376	+	0.992360i	$0.460628\pi$
$53$	−4.84541	+	11.6979i	−0.665569	+	1.60682i	−0.788944	+	0.614465i	$0.789372\pi$
$54$		0			0
$55$	10.0506	−	10.0506i	1.35522	−	1.35522i
$56$	11.8237	−	4.67922i	1.58001	−	0.625287i
$57$		0			0
$58$	−0.986371	−	12.0050i	−0.129517	−	1.57634i
$59$	4.00831	−	3.07569i	0.521838	−	0.400420i	−0.313978	−	0.949430i	$-0.601662\pi$
$59$	4.00831	−	3.07569i	0.521838	−	0.400420i	0.835816	+	0.549010i	$0.184995\pi$
$60$		0			0
$61$	−3.36120	+	4.38040i	−0.430357	+	0.560852i	−0.957318	−	0.289037i	$-0.906665\pi$
$61$	−3.36120	+	4.38040i	−0.430357	+	0.560852i	0.526961	+	0.849890i	$0.323331\pi$
$62$	0.349676	+	1.61772i	0.0444089	+	0.205451i
$63$		0			0
$64$	−2.31462	+	7.65784i	−0.289327	+	0.957230i
$65$	1.23933	+	2.14658i	0.153720	+	0.266251i
$66$		0			0
$67$	7.17032	+	0.943991i	0.875995	+	0.115327i	0.555096	−	0.831787i	$-0.312682\pi$
$67$	7.17032	+	0.943991i	0.875995	+	0.115327i	0.320899	+	0.947113i	$0.396015\pi$
$68$	4.47652	+	0.439392i	0.542858	+	0.0532841i
$69$		0			0
$70$	21.2914	+	10.0657i	2.54481	+	1.20309i
$71$	10.6269	+	10.6269i	1.26118	+	1.26118i	0.950521	+	0.310660i	$0.100550\pi$
$71$	10.6269	+	10.6269i	1.26118	+	1.26118i	0.310660	+	0.950521i	$0.399450\pi$
$72$		0			0
$73$	−1.59954	+	1.59954i	−0.187212	+	0.187212i	−0.794490	−	0.607277i	$-0.792262\pi$
$73$	−1.59954	+	1.59954i	−0.187212	+	0.187212i	0.607277	+	0.794490i	$0.292262\pi$
$74$	3.81254	−	1.36487i	0.443199	−	0.158662i
$75$		0			0
$76$	−1.12612	−	3.70788i	−0.129175	−	0.425323i
$77$	2.25174	−	17.1037i	0.256610	−	1.94914i
$78$		0			0
$79$	−2.89618	+	1.67211i	−0.325845	+	0.188127i	−0.653995	−	0.756499i	$-0.726908\pi$
$79$	−2.89618	+	1.67211i	−0.325845	+	0.188127i	0.328150	+	0.944626i	$0.393575\pi$
$80$	−13.2842	+	6.56208i	−1.48522	+	0.733662i
$81$		0			0
$82$	9.01981	+	5.81353i	0.996071	+	0.641997i
$83$	−1.21803	−	0.934627i	−0.133696	−	0.102589i	0.539749	−	0.841826i	$-0.318519\pi$
$83$	−1.21803	−	0.934627i	−0.133696	−	0.102589i	−0.673445	+	0.739238i	$0.735186\pi$
$84$		0			0
$85$	5.07141	+	6.60919i	0.550072	+	0.716868i
$86$	−3.32914	+	3.92518i	−0.358991	+	0.423263i
$87$		0			0
$88$	7.55176	+	7.79522i	0.805020	+	0.830973i
$89$	−7.83449	−	7.83449i	−0.830454	−	0.830454i	0.157125	−	0.987579i	$-0.449778\pi$
$89$	−7.83449	−	7.83449i	−0.830454	−	0.830454i	−0.987579	+	0.157125i	$0.949778\pi$
$90$		0			0
$91$	2.77937	+	1.15125i	0.291357	+	0.120684i
$92$	3.71912	−	0.615303i	0.387745	−	0.0641498i
$93$		0			0
$94$	3.01075	−	9.37573i	0.310535	−	0.967033i
$95$	3.58851	−	6.21548i	0.368173	−	0.637695i
$96$		0			0
$97$	7.56906	+	13.1100i	0.768521	+	1.33112i	0.938365	+	0.345647i	$0.112340\pi$
$97$	7.56906	+	13.1100i	0.768521	+	1.33112i	−0.169843	+	0.985471i	$0.554326\pi$
$98$	18.2626	−	3.94754i	1.84481	−	0.398762i
$99$		0			0
$100$	−16.3256	−	6.13832i	−1.63256	−	0.613832i
$101$	−0.640494	−	4.86503i	−0.0637315	−	0.484089i	−0.993311	−	0.115468i	$-0.963163\pi$
$101$	−0.640494	−	4.86503i	−0.0637315	−	0.484089i	0.929580	−	0.368621i	$-0.120170\pi$
$102$		0			0
$103$	2.38025	−	0.637787i	0.234533	−	0.0628430i	−0.139638	−	0.990203i	$-0.544594\pi$
$103$	2.38025	−	0.637787i	0.234533	−	0.0628430i	0.374171	+	0.927360i	$0.377927\pi$
$104$	−1.65390	+	0.920214i	−0.162178	+	0.0902344i
$105$		0			0
$106$	−6.03526	−	16.8586i	−0.586197	−	1.63745i
$107$	3.78147	−	9.12928i	0.365569	−	0.882561i	−0.628896	−	0.777490i	$-0.716493\pi$
$107$	3.78147	−	9.12928i	0.365569	−	0.882561i	0.994465	−	0.105072i	$-0.0335072\pi$
$108$		0			0
$109$	3.49584	−	1.44802i	0.334840	−	0.138695i	−0.208927	−	0.977931i	$-0.566997\pi$
$109$	3.49584	−	1.44802i	0.334840	−	0.138695i	0.543768	+	0.839236i	$0.316997\pi$
$110$	−0.982971	+	20.0771i	−0.0937226	+	1.91428i
$111$		0			0
$112$	−7.94294	+	16.1338i	−0.750537	+	1.52450i
$113$	3.86925	+	2.23391i	0.363989	+	0.210149i	0.670829	−	0.741612i	$-0.265938\pi$
$113$	3.86925	+	2.23391i	0.363989	+	0.210149i	−0.306840	+	0.951761i	$0.599272\pi$
$114$		0			0
$115$	5.53898	+	4.25021i	0.516512	+	0.396334i
$116$	12.4370	+	11.6408i	1.15475	+	1.08082i
$117$		0			0
$118$	−1.27793	+	7.02992i	−0.117643	+	0.647156i
$119$	9.76653	+	2.61693i	0.895296	+	0.239894i
$120$		0			0
$121$	3.59741	−	0.963924i	0.327038	−	0.0876295i
$122$	−0.639408	−	7.78217i	−0.0578892	−	0.704564i
$123$		0			0
$124$	−1.90303	−	1.36273i	−0.170898	−	0.122377i
$125$	−5.27421	−	12.7331i	−0.471739	−	1.13888i
$126$		0			0
$127$	−7.31929			−0.649482			−0.324741	−	0.945803i	$-0.605277\pi$
$127$	−7.31929			−0.649482			−0.324741	+	0.945803i	$0.605277\pi$
$128$	−4.84916	−	10.2218i	−0.428610	−	0.903490i
$129$		0			0
$130$	−3.33750	−	1.07174i	−0.292718	−	0.0939980i
$131$	1.12200	+	0.147714i	0.0980295	+	0.0129058i	0.179381	−	0.983780i	$-0.442590\pi$
$131$	1.12200	+	0.147714i	0.0980295	+	0.0129058i	−0.0813519	+	0.996685i	$0.525924\pi$
$132$		0			0
$133$	−1.13699	−	8.63629i	−0.0985894	−	0.748861i
$134$	−8.40908	+	5.82208i	−0.726434	+	0.502952i
$135$		0			0
$136$	−5.10746	+	3.79191i	−0.437961	+	0.325153i
$137$	−3.34773	−	0.897020i	−0.286016	−	0.0766376i	0.112959	−	0.993600i	$-0.463967\pi$
$137$	−3.34773	−	0.897020i	−0.286016	−	0.0766376i	−0.398974	+	0.916962i	$0.630634\pi$
$138$		0			0
$139$	−5.83812	−	7.60838i	−0.495183	−	0.645335i	0.477181	−	0.878805i	$-0.341659\pi$
$139$	−5.83812	−	7.60838i	−0.495183	−	0.645335i	−0.972364	+	0.233470i	$0.924992\pi$
$140$	−31.8686	+	9.67884i	−2.69339	+	0.818011i
$141$		0			0
$142$	−21.2284	−	1.03934i	−1.78145	−	0.0872191i
$143$			2.56771i			0.214723i
$144$		0			0
$145$			31.5499i			2.62008i
$146$	0.156439	−	3.19526i	0.0129470	−	0.264441i
$147$		0			0
$148$	−2.69793	+	5.05152i	−0.221768	+	0.415232i
$149$	0.112728	+	0.146910i	0.00923501	+	0.0120353i	0.797948	−	0.602726i	$-0.205919\pi$
$149$	0.112728	+	0.146910i	0.00923501	+	0.0120353i	−0.788713	+	0.614762i	$0.789252\pi$
$150$		0			0
$151$	11.0016	+	2.94788i	0.895300	+	0.239895i	0.676997	−	0.735986i	$-0.263281\pi$
$151$	11.0016	+	2.94788i	0.895300	+	0.239895i	0.218303	+	0.975881i	$0.429948\pi$
$152$	4.70197	+	2.81506i	0.381380	+	0.228331i
$153$		0			0
$154$	13.8877	+	20.0585i	1.11910	+	1.61636i
$155$	−0.565836	−	4.29795i	−0.0454490	−	0.345220i
$156$		0			0
$157$	−10.5028	−	1.38272i	−0.838215	−	0.110353i	−0.300817	−	0.953682i	$-0.597259\pi$
$157$	−10.5028	−	1.38272i	−0.838215	−	0.110353i	−0.537398	+	0.843329i	$0.680593\pi$
$158$	1.44600	−	4.50296i	0.115037	−	0.358237i
$159$		0			0
$160$	7.68463	−	19.4938i	0.607523	−	1.54112i
$161$	8.47378			0.667828
$162$		0			0
$163$	−5.98941	−	14.4597i	−0.469127	−	1.13257i	−0.964545	−	0.263918i	$-0.914985\pi$
$163$	−5.98941	−	14.4597i	−0.469127	−	1.13257i	0.495418	−	0.868654i	$-0.335015\pi$
$164$	−14.9724	+	2.47708i	−1.16915	+	0.193427i
$165$		0			0
$166$	2.16394	−	0.177796i	0.167954	−	0.0137996i
$167$	−24.6678	+	6.60972i	−1.90885	+	0.511476i	−0.914609	+	0.404339i	$0.867502\pi$
$167$	−24.6678	+	6.60972i	−1.90885	+	0.511476i	−0.994244	+	0.107137i	$0.965832\pi$
$168$		0			0
$169$	12.1245	+	3.24876i	0.932656	+	0.249904i
$170$	−11.5914	−	2.10714i	−0.889022	−	0.161610i
$171$		0			0
$172$	−0.240580	−	7.27479i	−0.0183441	−	0.554698i
$173$	14.1090	+	10.8262i	1.07269	+	0.823102i	0.984915	−	0.173038i	$-0.0553584\pi$
$173$	14.1090	+	10.8262i	1.07269	+	0.823102i	0.0877728	+	0.996141i	$0.472025\pi$
$174$		0			0
$175$	−33.9537	−	19.6032i	−2.56666	−	1.48186i
$176$	−15.3167	−	0.993654i	−1.15454	−	0.0748995i
$177$		0			0
$178$	15.6502	+	0.766231i	1.17303	+	0.0574315i
$179$	−4.60087	+	1.90574i	−0.343885	+	0.142442i	−0.547940	−	0.836518i	$-0.684588\pi$
$179$	−4.60087	+	1.90574i	−0.343885	+	0.142442i	0.204055	+	0.978959i	$0.434588\pi$
$180$		0			0
$181$	−0.346691	+	0.836985i	−0.0257693	+	0.0622126i	−0.936240	−	0.351360i	$-0.885719\pi$
$181$	−0.346691	+	0.836985i	−0.0257693	+	0.0622126i	0.910471	+	0.413573i	$0.135719\pi$
$182$	−4.00554	+	1.43396i	−0.296911	+	0.106292i
$183$		0			0
$184$	−3.31206	+	4.17746i	−0.244169	+	0.307966i
$185$	−10.2451	+	2.74517i	−0.753236	+	0.201829i
$186$		0			0
$187$	1.12644	+	8.55617i	0.0823735	+	0.625689i
$188$	5.75165	+	12.6829i	0.419482	+	0.924997i
$189$		0			0
$190$	2.14440	+	9.92072i	0.155571	+	0.719725i
$191$	1.79169	+	3.10331i	0.129642	+	0.224547i	0.923538	−	0.383507i	$-0.125284\pi$
$191$	1.79169	+	3.10331i	0.129642	+	0.224547i	−0.793896	+	0.608054i	$0.791950\pi$
$192$		0			0
$193$	−3.64200	+	6.30813i	−0.262157	+	0.454069i	−0.966815	−	0.255478i	$-0.917767\pi$
$193$	−3.64200	+	6.30813i	−0.262157	+	0.454069i	0.704658	+	0.709547i	$0.251100\pi$
$194$	−20.3833	−	6.54553i	−1.46344	−	0.469942i
$195$		0			0
$196$	−15.3841	+	21.4836i	−1.09886	+	1.53454i
$197$	−7.11203	−	2.94590i	−0.506711	−	0.209887i	0.114657	−	0.993405i	$-0.463423\pi$
$197$	−7.11203	−	2.94590i	−0.506711	−	0.209887i	−0.621368	+	0.783519i	$0.713423\pi$
$198$		0			0
$199$	−5.97203	−	5.97203i	−0.423346	−	0.423346i	0.463008	−	0.886354i	$-0.346770\pi$
$199$	−5.97203	−	5.97203i	−0.423346	−	0.423346i	−0.886354	+	0.463008i	$0.846770\pi$
$200$	22.9352	−	9.07661i	1.62177	−	0.641813i
$201$		0			0
$202$	5.29235	+	4.48871i	0.372369	+	0.315825i
$203$	23.3109	+	30.3794i	1.63611	+	2.13222i
$204$		0			0
$205$	−22.2987	−	17.1104i	−1.55741	−	1.19504i
$206$	−1.88797	+	2.92922i	−0.131541	+	0.204088i
$207$		0			0
$208$	0.858684	−	2.53515i	0.0595390	−	0.175781i
$209$	6.43878	−	3.71743i	0.445380	−	0.257140i
$210$		0			0
$211$	3.63729	−	27.6280i	0.250402	−	1.90199i	−0.155106	−	0.987898i	$-0.549572\pi$
$211$	3.63729	−	27.6280i	0.250402	−	1.90199i	0.405508	−	0.914092i	$-0.367095\pi$
$212$	22.3372	+	11.9299i	1.53412	+	0.819349i
$213$		0			0
$214$	4.71006	+	13.1568i	0.321973	+	0.899382i
$215$	9.53239	−	9.53239i	0.650103	−	0.650103i
$216$		0			0
$217$	−3.72042	−	3.72042i	−0.252559	−	0.252559i
$218$	−2.28712	+	4.83780i	−0.154904	+	0.327657i
$219$		0			0
$220$	−18.0414	−	21.9686i	−1.21635	−	1.48112i
$221$	−1.49207	−	0.196435i	−0.100368	−	0.0132137i
$222$		0			0
$223$	11.2438	+	19.4748i	0.752938	+	1.30413i	0.946393	+	0.323017i	$0.104697\pi$
$223$	11.2438	+	19.4748i	0.752938	+	1.30413i	−0.193455	+	0.981109i	$0.561969\pi$
$224$	−7.00368	−	24.4485i	−0.467953	−	1.63353i
$225$		0			0
$226$	−6.17583	+	1.33493i	−0.410810	+	0.0887982i
$227$	1.59935	−	2.08432i	0.106153	−	0.138341i	−0.737256	−	0.675614i	$-0.763879\pi$
$227$	1.59935	−	2.08432i	0.106153	−	0.138341i	0.843409	+	0.537273i	$0.180545\pi$
$228$		0			0
$229$	16.6569	−	12.7813i	1.10072	−	0.844611i	0.111898	−	0.993720i	$-0.464307\pi$
$229$	16.6569	−	12.7813i	1.10072	−	0.844611i	0.988821	+	0.149108i	$0.0476403\pi$
$230$	−9.84049	+	0.808526i	−0.648863	+	0.0533126i
$231$		0			0
$232$	−24.0879	−	0.382124i	−1.58145	−	0.0250877i
$233$	−7.64833	+	7.64833i	−0.501059	+	0.501059i	−0.911767	−	0.410708i	$-0.865282\pi$
$233$	−7.64833	+	7.64833i	−0.501059	+	0.501059i	0.410708	+	0.911767i	$0.365282\pi$
$234$		0			0
$235$	−9.87029	+	23.8290i	−0.643867	+	1.55443i
$236$	−5.33884	−	8.57918i	−0.347529	−	0.558457i
$237$		0			0
$238$	−12.7183	+	6.53547i	−0.824403	+	0.423632i
$239$	−0.250015	−	0.144346i	−0.0161721	−	0.00933699i	0.491892	−	0.870656i	$-0.336305\pi$
$239$	−0.250015	−	0.144346i	−0.0161721	−	0.00933699i	−0.508064	+	0.861319i	$0.669639\pi$
$240$		0			0
$241$	5.14620	−	2.97116i	0.331496	−	0.191389i	−0.325009	−	0.945711i	$-0.605367\pi$
$241$	5.14620	−	2.97116i	0.331496	−	0.191389i	0.656505	+	0.754322i	$0.272034\pi$
$242$	−2.85339	+	4.42710i	−0.183423	+	0.284585i
$243$		0			0
$244$	8.06221	+	7.54604i	0.516130	+	0.483086i
$245$	−48.5201	+	6.38779i	−3.09983	+	0.408101i
$246$		0			0
$247$	0.335567	+	1.25235i	0.0213516	+	0.0796854i
$248$	3.28828	−	0.379953i	0.208806	−	0.0241270i
$249$		0			0
$250$	17.6210	+	8.33051i	1.11445	+	0.526868i
$251$	−5.46410	−	2.26331i	−0.344891	−	0.142859i	0.203513	−	0.979072i	$-0.434764\pi$
$251$	−5.46410	−	2.26331i	−0.344891	−	0.142859i	−0.548404	+	0.836214i	$0.684764\pi$
$252$		0			0
$253$	2.76778	+	6.68201i	0.174009	+	0.420094i
$254$	7.66845	−	6.95261i	0.481162	−	0.436246i
$255$		0			0
$256$	14.7902	+	6.10322i	0.924389	+	0.381451i
$257$	4.85036	−	8.40107i	0.302557	−	0.524044i	−0.674157	−	0.738588i	$-0.735493\pi$
$257$	4.85036	−	8.40107i	0.302557	−	0.524044i	0.976714	+	0.214544i	$0.0688264\pi$
$258$		0			0
$259$	−7.83673	+	10.2130i	−0.486951	+	0.634607i
$260$	4.51476	−	2.04743i	0.279994	−	0.126976i
$261$		0			0
$262$	−1.31584	+	0.911028i	−0.0812927	+	0.0562835i
$263$	−1.15767	+	4.32047i	−0.0713848	+	0.266412i	−0.992389	−	0.123140i	$-0.960703\pi$
$263$	−1.15767	+	4.32047i	−0.0713848	+	0.266412i	0.921004	+	0.389552i	$0.127370\pi$
$264$		0			0
$265$	12.1388	+	45.3026i	0.745681	+	2.78292i
$266$	9.39486	+	7.96825i	0.576036	+	0.488565i
$267$		0			0
$268$	3.27982	−	14.0876i	0.200347	−	0.860539i
$269$	−9.30640	+	3.85484i	−0.567421	+	0.235033i	−0.647903	−	0.761723i	$-0.724354\pi$
$269$	−9.30640	+	3.85484i	−0.567421	+	0.235033i	0.0804824	+	0.996756i	$0.474354\pi$
$270$		0			0
$271$		−	15.2975i		−	0.929259i	−0.885505	−	0.464629i	$-0.846188\pi$
$271$		−	15.2975i		−	0.929259i	0.885505	−	0.464629i	$-0.153812\pi$
$272$	1.74916	−	8.82439i	0.106059	−	0.535057i
$273$		0			0
$274$	4.35951	−	2.24020i	0.263368	−	0.135335i
$275$	4.36786	−	33.1772i	0.263392	−	2.00066i
$276$		0			0
$277$	−22.8665	+	3.01043i	−1.37391	+	0.180879i	−0.781073	−	0.624440i	$-0.785327\pi$
$277$	−22.8665	+	3.01043i	−1.37391	+	0.180879i	−0.592842	+	0.805319i	$0.701994\pi$
$278$	13.3438	+	2.42570i	0.800311	+	0.145484i
$279$		0			0
$280$	24.1949	−	40.4126i	1.44592	−	2.41512i
$281$	−5.81072	+	21.6859i	−0.346639	+	1.29367i	0.544047	+	0.839055i	$0.316891\pi$
$281$	−5.81072	+	21.6859i	−0.346639	+	1.29367i	−0.890686	+	0.454619i	$0.849775\pi$
$282$		0			0
$283$	11.0250	−	8.45975i	0.655366	−	0.502880i	−0.226725	−	0.973959i	$-0.572802\pi$
$283$	11.0250	−	8.45975i	0.655366	−	0.502880i	0.882091	+	0.471079i	$0.156135\pi$
$284$	23.2283	−	19.0760i	1.37835	−	1.13195i
$285$		0			0
$286$	−2.43907	−	2.69020i	−0.144225	−	0.159075i
$287$	−34.1136			−2.01366
$288$		0			0
$289$	11.9419			0.702466
$290$	−29.9693	−	33.0550i	−1.75986	−	1.94106i
$291$		0			0
$292$	2.87128	+	3.49629i	0.168029	+	0.204605i
$293$	−4.89927	+	3.75934i	−0.286218	+	0.219623i	−0.741884	−	0.670528i	$-0.766068\pi$
$293$	−4.89927	+	3.75934i	−0.286218	+	0.219623i	0.455666	+	0.890151i	$0.349401\pi$
$294$		0			0
$295$	4.84373	−	18.0770i	0.282013	−	1.05249i
$296$	−1.97182	−	7.85527i	−0.114610	−	0.456578i
$297$		0			0
$298$	−0.257655	−	0.0468376i	−0.0149256	−	0.00271323i
$299$	−1.25046	+	0.164627i	−0.0723162	+	0.00952060i
$300$		0			0
$301$	2.13564	−	16.2218i	0.123096	−	0.935011i
$302$	−14.3267	+	7.36197i	−0.824406	+	0.423634i
$303$		0			0
$304$	−7.60031	+	1.51707i	−0.435908	+	0.0870097i
$305$			20.4520i			1.17108i
$306$		0			0
$307$	−15.5404	+	6.43703i	−0.886936	+	0.367381i	−0.779183	−	0.626797i	$-0.784366\pi$
$307$	−15.5404	+	6.43703i	−0.886936	+	0.367381i	−0.107753	+	0.994178i	$0.534366\pi$
$308$	−33.6038	−	7.82350i	−1.91476	−	0.445785i
$309$		0			0
$310$	4.67546	+	3.96550i	0.265548	+	0.225225i
$311$	−0.914105	−	3.41149i	−0.0518341	−	0.193448i	0.935154	−	0.354242i	$-0.115261\pi$
$311$	−0.914105	−	3.41149i	−0.0518341	−	0.193448i	−0.986988	+	0.160794i	$0.948594\pi$
$312$		0			0
$313$	−4.19852	+	15.6691i	−0.237314	+	0.885669i	0.739778	+	0.672851i	$0.234931\pi$
$313$	−4.19852	+	15.6691i	−0.237314	+	0.885669i	−0.977092	+	0.212817i	$0.931736\pi$
$314$	12.3173	−	8.52795i	0.695105	−	0.481260i
$315$		0			0
$316$	2.76240	+	6.09133i	0.155397	+	0.342664i
$317$	0.115554	−	0.150593i	0.00649018	−	0.00845817i	−0.790097	−	0.612982i	$-0.789970\pi$
$317$	0.115554	−	0.150593i	0.00649018	−	0.00845817i	0.796587	+	0.604524i	$0.206637\pi$
$318$		0			0
$319$	−16.3417	+	28.3046i	−0.914959	+	1.58476i
$320$	10.4660	+	27.7234i	0.585069	+	1.54979i
$321$		0			0
$322$	−8.87802	+	8.04927i	−0.494753	+	0.448568i
$323$	1.66758	+	4.02591i	0.0927869	+	0.224007i
$324$		0			0
$325$	5.39134	+	2.23317i	0.299058	+	0.123874i
$326$	20.0105	+	9.46016i	1.10828	+	0.523950i
$327$		0			0
$328$	13.3337	−	16.8175i	0.736228	−	0.928594i
$329$	8.10216	+	30.2377i	0.446687	+	1.66706i
$330$		0			0
$331$	29.0537	−	3.82499i	1.59693	−	0.210240i	0.721092	−	0.692839i	$-0.243640\pi$
$331$	29.0537	−	3.82499i	1.59693	−	0.210240i	0.875841	+	0.482599i	$0.160307\pi$
$332$	−2.09828	+	2.24181i	−0.115158	+	0.123035i
$333$		0			0
$334$	19.5660	−	30.3571i	1.07060	−	1.66106i
$335$	23.2001	−	13.3946i	1.26756	−	0.731824i
$336$		0			0
$337$	11.5917	+	6.69246i	0.631439	+	0.364562i	0.781309	−	0.624144i	$-0.214552\pi$
$337$	11.5917	+	6.69246i	0.631439	+	0.364562i	−0.149870	+	0.988706i	$0.547885\pi$
$338$	−15.7889	+	8.11338i	−0.858804	+	0.441309i
$339$		0			0
$340$	14.1460	−	8.80307i	0.767173	−	0.477414i
$341$	1.71855	−	4.14894i	0.0930645	−	0.224678i
$342$		0			0
$343$	−19.7474	+	19.7474i	−1.06626	+	1.06626i
$344$	7.16240	+	7.39331i	0.386171	+	0.398620i
$345$		0			0
$346$	−25.0659	+	2.05950i	−1.34755	+	0.110719i
$347$	10.6523	−	8.17380i	0.571846	−	0.438793i	−0.281929	−	0.959435i	$-0.590974\pi$
$347$	10.6523	−	8.17380i	0.571846	−	0.438793i	0.853775	+	0.520643i	$0.174308\pi$
$348$		0			0
$349$	9.80923	−	12.7836i	0.525076	−	0.684293i	−0.453245	−	0.891386i	$-0.649734\pi$
$349$	9.80923	−	12.7836i	0.525076	−	0.684293i	0.978321	+	0.207093i	$0.0664004\pi$
$350$	54.1946	−	11.7144i	2.89682	−	0.626159i
$351$		0			0
$352$	16.9913	−	13.5083i	0.905638	−	0.719996i
$353$	11.6659	+	20.2059i	0.620913	+	1.07545i	0.989316	+	0.145787i	$0.0465715\pi$
$353$	11.6659	+	20.2059i	0.620913	+	1.07545i	−0.368403	+	0.929666i	$0.620095\pi$
$354$		0			0
$355$	55.1924	+	7.26621i	2.92931	+	0.385650i
$356$	−17.1247	+	14.0634i	−0.907605	+	0.745359i
$357$		0			0
$358$	3.01008	−	6.36703i	0.159088	−	0.336508i
$359$	26.0768	+	26.0768i	1.37628	+	1.37628i	0.850815	+	0.525465i	$0.176109\pi$
$359$	26.0768	+	26.0768i	1.37628	+	1.37628i	0.525465	+	0.850815i	$0.323891\pi$
$360$		0			0
$361$	−10.7805	+	10.7805i	−0.567392	+	0.567392i
$362$	−0.431825	−	1.20624i	−0.0226962	−	0.0633983i
$363$		0			0
$364$	2.83450	−	5.30724i	0.148568	−	0.278175i
$365$	−1.09370	+	8.30746i	−0.0572467	+	0.434832i
$366$		0			0
$367$	−17.4198	+	10.0573i	−0.909307	+	0.524989i	−0.880208	−	0.474588i	$-0.842597\pi$
$367$	−17.4198	+	10.0573i	−0.909307	+	0.524989i	−0.0290988	+	0.999577i	$0.509264\pi$
$368$	−0.498114	−	7.52288i	−0.0259660	−	0.392157i
$369$		0			0
$370$	8.12622	−	12.6080i	0.422462	−	0.655458i
$371$	45.1607	+	34.6530i	2.34463	+	1.79910i
$372$		0			0
$373$	14.1274	+	18.4112i	0.731489	+	0.953295i	0.999950	−	0.00999548i	$-0.00318171\pi$
$373$	14.1274	+	18.4112i	0.731489	+	0.953295i	−0.268461	+	0.963291i	$0.586515\pi$
$374$	−9.30770	−	7.89433i	−0.481290	−	0.408206i
$375$		0			0
$376$	−18.0736	−	7.82445i	−0.932073	−	0.403515i
$377$	−4.03016	−	4.03016i	−0.207564	−	0.207564i
$378$		0			0
$379$	0.950079	+	0.393536i	0.0488023	+	0.0202146i	0.406951	−	0.913450i	$-0.366592\pi$
$379$	0.950079	+	0.393536i	0.0488023	+	0.0202146i	−0.358149	+	0.933665i	$0.616592\pi$
$380$	−11.6704	−	8.35701i	−0.598680	−	0.428706i
$381$		0			0
$382$	−4.82501	−	1.54941i	−0.246869	−	0.0792749i
$383$	−4.40895	+	7.63653i	−0.225287	+	0.390208i	−0.956405	−	0.292042i	$-0.905665\pi$
$383$	−4.40895	+	7.63653i	−0.225287	+	0.390208i	0.731119	+	0.682250i	$0.238999\pi$
$384$		0			0
$385$	−31.9506	−	55.3401i	−1.62836	−	2.82039i
$386$	−2.17637	−	10.0686i	−0.110774	−	0.512478i
$387$		0			0
$388$	27.5734	−	12.5044i	1.39982	−	0.634815i
$389$	−4.69698	−	35.6771i	−0.238147	−	1.80890i	−0.525190	−	0.850985i	$-0.676006\pi$
$389$	−4.69698	−	35.6771i	−0.238147	−	1.80890i	0.287043	−	0.957918i	$-0.407328\pi$
$390$		0			0
$391$	−4.09459	+	1.09714i	−0.207073	+	0.0554849i
$392$	−4.28933	−	37.1218i	−0.216644	−	1.87494i
$393$		0			0
$394$	10.2496	−	3.66930i	0.516368	−	0.184857i
$395$	−4.74049	+	11.4445i	−0.238520	+	0.575838i
$396$		0			0
$397$	29.4064	−	12.1805i	1.47587	−	0.611323i	0.507677	−	0.861547i	$-0.330504\pi$
$397$	29.4064	−	12.1805i	1.47587	−	0.611323i	0.968188	+	0.250224i	$0.0805042\pi$
$398$	11.9298	+	0.584079i	0.597986	+	0.0292772i
$399$		0			0
$400$	−15.4075	+	31.2958i	−0.770373	+	1.56479i
$401$	−21.5375	−	12.4347i	−1.07553	−	0.620958i	−0.145843	−	0.989308i	$-0.546589\pi$
$401$	−21.5375	−	12.4347i	−1.07553	−	0.620958i	−0.929687	+	0.368350i	$0.879923\pi$
$402$		0			0
$403$	0.621297	+	0.476738i	0.0309490	+	0.0237480i
$404$	−9.80866	+	0.324376i	−0.487999	+	0.0161383i
$405$		0			0
$406$	−53.2805	−	9.68553i	−2.64426	−	0.480685i
$407$	−10.6132	−	2.84380i	−0.526076	−	0.140962i
$408$		0			0
$409$	−29.0981	+	7.79682i	−1.43881	+	0.385528i	−0.892117	−	0.451805i	$-0.850780\pi$
$409$	−29.0981	+	7.79682i	−1.43881	+	0.385528i	−0.546693	+	0.837333i	$0.684114\pi$
$410$	39.6157	−	3.25495i	1.95648	−	0.160751i
$411$		0			0
$412$	−0.804441	−	4.86234i	−0.0396320	−	0.239550i
$413$	−8.69236	−	20.9852i	−0.427723	−	1.03261i
$414$		0			0
$415$	−5.68695			−0.279162
$416$	1.50850	+	3.47176i	0.0739604	+	0.170217i
$417$		0			0
$418$	−3.21474	+	10.0110i	−0.157238	+	0.489653i
$419$	26.3980	+	3.47536i	1.28962	+	0.169782i	0.743961	−	0.668223i	$-0.232945\pi$
$419$	26.3980	+	3.47536i	1.28962	+	0.169782i	0.545663	+	0.838005i	$0.316278\pi$
$420$		0			0
$421$	4.36422	+	33.1495i	0.212699	+	1.61561i	0.681167	+	0.732128i	$0.261473\pi$
$421$	4.36422	+	33.1495i	0.212699	+	1.61561i	−0.468468	+	0.883480i	$0.655194\pi$
$422$	22.4331	+	32.4011i	1.09203	+	1.57726i
$423$		0			0
$424$	−34.7350	+	8.71913i	−1.68688	+	0.423438i
$425$	18.9448	+	5.07624i	0.918958	+	0.246234i
$426$		0			0
$427$	15.1111	+	19.6932i	0.731279	+	0.953021i
$428$	−17.4325	−	9.31037i	−0.842630	−	0.450034i
$429$		0			0
$430$	−0.932290	+	19.0420i	−0.0449590	+	0.918285i
$431$		−	23.9549i		−	1.15387i	−0.816792	−	0.576933i	$-0.804249\pi$
$431$		−	23.9549i		−	1.15387i	0.816792	−	0.576933i	$-0.195751\pi$
$432$		0			0
$433$		−	18.3804i		−	0.883304i	−0.897186	−	0.441652i	$-0.854393\pi$
$433$		−	18.3804i		−	0.883304i	0.897186	−	0.441652i	$-0.145607\pi$
$434$	7.43195	+	0.363866i	0.356745	+	0.0174661i
$435$		0			0
$436$	−2.19921	−	7.24113i	−0.105323	−	0.346787i
$437$	2.22319	+	2.89732i	0.106350	+	0.138597i
$438$		0			0
$439$	−25.9425	−	6.95126i	−1.23817	−	0.331765i	−0.420412	−	0.907333i	$-0.638114\pi$
$439$	−25.9425	−	6.95126i	−1.23817	−	0.331765i	−0.817754	+	0.575568i	$0.804781\pi$
$440$	39.7701	+	5.87902i	1.89597	+	0.280271i
$441$		0			0
$442$	1.74985	−	1.21152i	0.0832317	−	0.0576260i
$443$	−0.00475586	−	0.0361243i	−0.000225958	−	0.00171632i	0.991332	−	0.131384i	$-0.0419422\pi$
$443$	−0.00475586	−	0.0361243i	−0.000225958	−	0.00171632i	−0.991557	+	0.129668i	$0.958609\pi$
$444$		0			0
$445$	−40.6895	−	5.35688i	−1.92887	−	0.253940i
$446$	−30.2793	−	9.72333i	−1.43376	−	0.460413i
$447$		0			0
$448$	30.5615	+	18.9620i	1.44389	+	0.895869i
$449$	15.1143			0.713286			0.356643	−	0.934241i	$-0.383921\pi$
$449$	15.1143			0.713286			0.356643	+	0.934241i	$0.383921\pi$
$450$		0			0
$451$	−11.1425	−	26.9003i	−0.524679	−	1.26669i
$452$	5.20240	−	7.26505i	0.244700	−	0.341719i
$453$		0			0
$454$	0.304248	+	3.70297i	0.0142791	+	0.173789i
$455$	10.7638	−	2.88414i	0.504613	−	0.135211i
$456$		0			0
$457$	−13.2993	−	3.56354i	−0.622115	−	0.166695i	−0.0660261	−	0.997818i	$-0.521032\pi$
$457$	−13.2993	−	3.56354i	−0.622115	−	0.166695i	−0.556089	+	0.831123i	$0.687699\pi$
$458$	−5.31054	+	29.2135i	−0.248145	+	1.36505i
$459$		0			0
$460$	9.54191	−	10.1946i	0.444894	−	0.475326i
$461$	−16.7511	−	12.8536i	−0.780176	−	0.598650i	0.140001	−	0.990151i	$-0.455289\pi$
$461$	−16.7511	−	12.8536i	−0.780176	−	0.598650i	−0.920178	+	0.391501i	$0.871956\pi$
$462$		0			0
$463$	27.5357	+	15.8977i	1.27969	+	0.738830i	0.976792	−	0.214192i	$-0.0687119\pi$
$463$	27.5357	+	15.8977i	1.27969	+	0.738830i	0.302900	+	0.953022i	$0.402045\pi$
$464$	25.6000	−	22.4808i	1.18845	−	1.04365i
$465$		0			0
$466$	0.748025	−	15.2784i	0.0346516	−	0.707756i
$467$	−8.15123	+	3.37635i	−0.377194	+	0.156239i	−0.563222	−	0.826306i	$-0.690438\pi$
$467$	−8.15123	+	3.37635i	−0.377194	+	0.156239i	0.186028	+	0.982544i	$0.440438\pi$
$468$		0			0
$469$	12.4427	−	30.0392i	0.574549	−	1.38708i
$470$	−12.2941	−	34.3416i	−0.567083	−	1.58406i
$471$		0			0
$472$	13.7429	+	3.91707i	0.632569	+	0.180298i
$473$	13.4893	−	3.61445i	0.620238	−	0.166192i
$474$		0			0
$475$	−2.20549	−	16.7524i	−0.101195	−	0.768653i
$476$	7.11693	−	18.9284i	0.326204	−	0.867580i
$477$		0			0
$478$	0.399057	−	0.0862577i	0.0182524	−	0.00394533i
$479$	1.94918	+	3.37608i	0.0890603	+	0.154257i	0.907114	−	0.420885i	$-0.138280\pi$
$479$	1.94918	+	3.37608i	0.0890603	+	0.154257i	−0.818054	+	0.575142i	$0.804947\pi$
$480$		0			0
$481$	0.958038	−	1.65937i	0.0436828	−	0.0756608i
$482$	−2.56938	+	8.00128i	−0.117032	+	0.364448i
$483$		0			0
$484$	−1.21580	−	7.34874i	−0.0552636	−	0.334034i
$485$	51.8055	+	21.4585i	2.35237	+	0.974382i
$486$		0			0
$487$	17.4074	+	17.4074i	0.788803	+	0.788803i	0.981298	−	0.192495i	$-0.0616580\pi$
$487$	17.4074	+	17.4074i	0.788803	+	0.788803i	−0.192495	+	0.981298i	$0.561658\pi$
$488$	−15.6148	−	0.247709i	−0.706850	−	0.0112132i
$489$		0			0
$490$	44.7670	−	52.7819i	2.02236	−	2.38444i
$491$	−8.69368	−	11.3298i	−0.392340	−	0.511308i	0.554863	−	0.831942i	$-0.312771\pi$
$491$	−8.69368	−	11.3298i	−0.392340	−	0.511308i	−0.947203	+	0.320634i	$0.896104\pi$
$492$		0			0
$493$	−15.1974	−	11.6614i	−0.684456	−	0.525202i
$494$	−1.54119	−	0.993341i	−0.0693414	−	0.0446925i
$495$		0			0
$496$	−3.08423	+	3.52163i	−0.138486	+	0.158126i
$497$	58.5134	−	33.7827i	2.62469	−	1.51536i
$498$		0			0
$499$	3.01505	−	22.9016i	0.134972	−	1.02522i	−0.781158	−	0.624334i	$-0.785370\pi$
$499$	3.01505	−	22.9016i	0.134972	−	1.02522i	0.916130	−	0.400882i	$-0.131296\pi$
$500$	−26.3748	+	8.01030i	−1.17952	+	0.358231i
$501$		0			0
$502$	7.87469	−	2.81909i	0.351464	−	0.125822i
$503$	−26.4566	+	26.4566i	−1.17964	+	1.17964i	−0.199804	+	0.979836i	$0.564030\pi$
$503$	−26.4566	+	26.4566i	−1.17964	+	1.17964i	−0.979836	+	0.199804i	$0.935970\pi$
$504$		0			0
$505$	−12.8526	−	12.8526i	−0.571933	−	0.571933i
$506$	−9.24707	−	4.37165i	−0.411082	−	0.194344i
$507$		0			0
$508$	−1.42997	+	14.5686i	−0.0634449	+	0.646376i
$509$	34.8862	+	4.59285i	1.54630	+	0.203574i	0.854860	−	0.518858i	$-0.173643\pi$
$509$	34.8862	+	4.59285i	1.54630	+	0.203574i	0.691441	+	0.722433i	$0.256976\pi$
$510$		0			0
$511$	5.08492	+	8.80734i	0.224944	+	0.389614i
$512$	−21.2932	+	7.65490i	−0.941038	+	0.338302i
$513$		0			0
$514$	2.89845	+	13.4092i	0.127845	+	0.591455i
$515$	5.55668	−	7.24160i	0.244856	−	0.319103i
$516$		0			0
$517$	−21.1976	+	16.2655i	−0.932267	+	0.715354i
$518$	−1.49080	−	18.1444i	−0.0655019	−	0.797218i
$519$		0			0
$520$	−2.78528	+	6.43368i	−0.122143	+	0.282136i
$521$	−5.19845	+	5.19845i	−0.227748	+	0.227748i	−0.811751	−	0.584003i	$-0.801486\pi$
$521$	−5.19845	+	5.19845i	−0.227748	+	0.227748i	0.584003	+	0.811751i	$0.301486\pi$
$522$		0			0
$523$	−8.15821	+	19.6957i	−0.356734	+	0.861231i	0.639021	+	0.769189i	$0.279340\pi$
$523$	−8.15821	+	19.6957i	−0.356734	+	0.861231i	−0.995755	+	0.0920424i	$0.970660\pi$
$524$	0.513220	−	2.20441i	0.0224201	−	0.0962999i
$525$		0			0
$526$	−2.89113	−	5.62625i	−0.126059	−	0.245316i
$527$	2.27944	+	1.31603i	0.0992939	+	0.0573274i
$528$		0			0
$529$	16.8419	−	9.72369i	0.732258	−	0.422769i
$530$	−55.7510	−	35.9331i	−2.42167	−	1.56083i
$531$		0			0
$532$	−17.4121	+	0.575825i	−0.754910	+	0.0249652i
$533$	5.03409	−	0.662751i	0.218051	−	0.0287069i
$534$		0			0
$535$	−9.47341	−	35.3552i	−0.409571	−	1.52854i
$536$	9.94559	+	17.8752i	0.429584	+	0.772091i
$537$		0			0
$538$	6.08864	−	12.8789i	0.262500	−	0.555249i
$539$	−46.8379	−	19.4009i	−2.01745	−	0.835655i
$540$		0			0
$541$	1.08226	+	2.61281i	0.0465300	+	0.112333i	0.945436	−	0.325809i	$-0.105637\pi$
$541$	1.08226	+	2.61281i	0.0465300	+	0.112333i	−0.898906	+	0.438142i	$0.855637\pi$
$542$	14.5312	+	16.0273i	0.624167	+	0.688431i
$543$		0			0
$544$	6.54970	+	10.9069i	0.280816	+	0.467629i
$545$	7.00801	−	12.1382i	0.300190	−	0.519944i
$546$		0			0
$547$	7.16518	−	9.33784i	0.306361	−	0.399257i	−0.614646	−	0.788803i	$-0.710701\pi$
$547$	7.16518	−	9.33784i	0.306361	−	0.399257i	0.921007	+	0.389545i	$0.127368\pi$
$548$	−2.43951	+	6.48818i	−0.104211	+	0.277161i
$549$		0			0
$550$	26.9388	+	38.9089i	1.14868	+	1.65908i
$551$	−4.27131	+	15.9407i	−0.181964	+	0.679098i
$552$		0			0
$553$	3.89129	+	14.5225i	0.165475	+	0.617560i
$554$	21.0977	−	24.8750i	0.896357	−	1.05684i
$555$		0			0
$556$	−16.2846	+	10.1339i	−0.690620	+	0.429775i
$557$	−5.55281	+	2.30005i	−0.235280	+	0.0974562i	−0.497208	−	0.867631i	$-0.665642\pi$
$557$	−5.55281	+	2.30005i	−0.235280	+	0.0974562i	0.261928	+	0.965087i	$0.415642\pi$
$558$		0			0
$559$			2.43532i			0.103003i
$560$	13.0389	+	65.3233i	0.550994	+	2.76041i
$561$		0			0
$562$	−14.5116	−	28.2401i	−0.612134	−	1.19124i
$563$	2.77543	−	21.0815i	0.116970	−	0.888479i	−0.827864	−	0.560929i	$-0.810444\pi$
$563$	2.77543	−	21.0815i	0.116970	−	0.888479i	0.944834	−	0.327549i	$-0.106223\pi$
$564$		0			0
$565$	16.4079	−	2.16014i	0.690287	−	0.0908779i
$566$	−3.51497	+	19.3359i	−0.147745	+	0.812751i
$567$		0			0
$568$	−6.21613	+	42.0506i	−0.260823	+	1.76441i
$569$	1.97455	−	7.36913i	0.0827776	−	0.308930i	−0.912107	−	0.409953i	$-0.865545\pi$
$569$	1.97455	−	7.36913i	0.0827776	−	0.308930i	0.994884	+	0.101023i	$0.0322117\pi$
$570$		0			0
$571$	−28.1828	+	21.6254i	−1.17941	+	0.904996i	−0.996937	−	0.0782145i	$-0.975078\pi$
$571$	−28.1828	+	21.6254i	−1.17941	+	0.904996i	−0.182477	+	0.983210i	$0.558411\pi$
$572$	5.11086	+	0.501655i	0.213696	+	0.0209753i
$573$		0			0
$574$	35.7410	−	32.4046i	1.49180	−	1.35254i
$575$	16.4372			0.685478
$576$		0			0
$577$	−1.10962			−0.0461943			−0.0230971	−	0.999733i	$-0.507353\pi$
$577$	−1.10962			−0.0461943			−0.0230971	+	0.999733i	$0.507353\pi$
$578$	−12.5116	+	11.3437i	−0.520414	+	0.471834i
$579$		0			0
$580$	62.7980	+	6.16393i	2.60755	+	0.255943i
$581$	−5.47597	+	4.20186i	−0.227181	+	0.174322i
$582$		0			0
$583$	−12.5749	+	46.9302i	−0.520800	+	1.94365i
$584$	−6.32939	−	0.935641i	−0.261912	−	0.0387171i
$585$		0			0
$586$	1.56198	−	8.59250i	0.0645248	−	0.354953i
$587$	−20.1667	+	2.65500i	−0.832370	+	0.109584i	−0.534654	−	0.845071i	$-0.679558\pi$
$587$	−20.1667	+	2.65500i	−0.832370	+	0.109584i	−0.297716	+	0.954654i	$0.596225\pi$
$588$		0			0
$589$	0.295976	−	2.24816i	0.0121955	−	0.0926340i
$590$	12.0966	+	23.5405i	0.498010	+	0.969146i
$591$		0			0
$592$	9.52762	+	6.35697i	0.391583	+	0.261270i
$593$		−	1.20887i		−	0.0496424i	−0.999692	−	0.0248212i	$-0.992098\pi$
$593$		−	1.20887i		−	0.0496424i	0.999692	−	0.0248212i	$-0.00790165\pi$
$594$		0			0
$595$	34.6019	−	14.3326i	1.41854	−	0.587579i
$596$	0.314438	−	0.195675i	0.0128799	−	0.00801517i
$597$		0			0
$598$	1.15374	−	1.36030i	0.0471798	−	0.0556267i
$599$	1.22515	+	4.57232i	0.0500583	+	0.186820i	0.986428	−	0.164196i	$-0.0525029\pi$
$599$	1.22515	+	4.57232i	0.0500583	+	0.186820i	−0.936369	+	0.351016i	$0.885836\pi$
$600$		0			0
$601$	−7.23779	+	27.0118i	−0.295235	+	1.10183i	0.645795	+	0.763511i	$0.276526\pi$
$601$	−7.23779	+	27.0118i	−0.295235	+	1.10183i	−0.941030	+	0.338323i	$0.890140\pi$
$602$	13.1716	+	19.0243i	0.536835	+	0.775374i
$603$		0			0
$604$	8.01695	−	21.3221i	0.326205	−	0.867584i
$605$	8.39813	−	10.9447i	0.341432	−	0.444963i
$606$		0			0
$607$	1.71529	−	2.97097i	0.0696215	−	0.120588i	−0.829113	−	0.559081i	$-0.811154\pi$
$607$	1.71529	−	2.97097i	0.0696215	−	0.120588i	0.898735	+	0.438493i	$0.144488\pi$
$608$	6.52182	−	8.80899i	0.264495	−	0.357252i
$609$		0			0
$610$	−19.4274	−	21.4276i	−0.786592	−	0.867580i
$611$	−1.78307	−	4.30472i	−0.0721355	−	0.174150i
$612$		0			0
$613$	32.4868	+	13.4565i	1.31213	+	0.543502i	0.925505	−	0.378736i	$-0.123641\pi$
$613$	32.4868	+	13.4565i	1.31213	+	0.543502i	0.386624	+	0.922237i	$0.373641\pi$
$614$	10.1672	−	21.5059i	0.410313	−	0.867909i
$615$		0			0
$616$	42.6384	−	23.7236i	1.71795	−	0.955852i
$617$	−2.52850	−	9.43647i	−0.101793	−	0.379898i	0.896168	−	0.443714i	$-0.146340\pi$
$617$	−2.52850	−	9.43647i	−0.101793	−	0.379898i	−0.997962	+	0.0638163i	$0.979673\pi$
$618$		0			0
$619$	−9.10807	+	1.19910i	−0.366084	+	0.0481959i	−0.311325	−	0.950304i	$-0.600773\pi$
$619$	−9.10807	+	1.19910i	−0.366084	+	0.0481959i	−0.0547597	+	0.998500i	$0.517439\pi$
$620$	−8.66534	+	0.286566i	−0.348008	+	0.0115088i
$621$		0			0
$622$	4.19829	+	2.70592i	0.168336	+	0.108498i
$623$	−43.1379	+	24.9057i	−1.72829	+	0.997826i
$624$		0			0
$625$	−6.44977	−	3.72378i	−0.257991	−	0.148951i
$626$	−10.4853	−	20.4048i	−0.419077	−	0.815538i
$627$		0			0
$628$	−4.80415	+	20.6350i	−0.191707	+	0.823426i
$629$	2.46443	−	5.94967i	0.0982634	−	0.237229i
$630$		0			0
$631$	−11.5682	+	11.5682i	−0.460524	+	0.460524i	−0.898827	−	0.438304i	$-0.855580\pi$
$631$	−11.5682	+	11.5682i	−0.460524	+	0.460524i	0.438304	+	0.898827i	$0.355580\pi$
$632$	−8.68035	−	3.75791i	−0.345286	−	0.149482i
$633$		0			0
$634$	0.0219822	+	0.267543i	0.000873023	+	0.0106255i
$635$	−21.5092	+	16.5046i	−0.853567	+	0.654965i
$636$		0			0
$637$	5.38195	−	7.01390i	0.213241	−	0.277901i
$638$	−9.76538	−	45.1779i	−0.386615	−	1.78861i
$639$		0			0
$640$	−37.2999	−	19.1043i	−1.47441	−	0.755163i
$641$	9.87216	+	17.0991i	0.389927	+	0.675373i	0.992439	−	0.122736i	$-0.0391670\pi$
$641$	9.87216	+	17.0991i	0.389927	+	0.675373i	−0.602513	+	0.798109i	$0.705834\pi$
$642$		0			0
$643$	−41.3154	−	5.43928i	−1.62932	−	0.214504i	−0.740269	−	0.672311i	$-0.765302\pi$
$643$	−41.3154	−	5.43928i	−1.62932	−	0.214504i	−0.889052	+	0.457806i	$0.848635\pi$
$644$	1.65553	−	16.8665i	0.0652370	−	0.664634i
$645$		0			0
$646$	−5.57135	−	2.63392i	−0.219202	−	0.103630i
$647$	10.6626	+	10.6626i	0.419191	+	0.419191i	0.884925	−	0.465734i	$-0.154210\pi$
$647$	10.6626	+	10.6626i	0.419191	+	0.419191i	−0.465734	+	0.884925i	$0.654210\pi$
$648$		0			0
$649$	13.7087	−	13.7087i	0.538115	−	0.538115i
$650$	−7.76982	+	2.78155i	−0.304758	+	0.109101i
$651$		0			0
$652$	−29.9513	+	9.09652i	−1.17298	+	0.356247i
$653$	−4.54840	+	34.5485i	−0.177993	+	1.35199i	0.636259	+	0.771476i	$0.280481\pi$
$653$	−4.54840	+	34.5485i	−0.177993	+	1.35199i	−0.814251	+	0.580513i	$0.802852\pi$
$654$		0			0
$655$	3.63030	−	2.09596i	0.141848	−	0.0818958i
$656$	2.00530	+	30.2855i	0.0782937	+	1.18245i
$657$		0			0
$658$	−37.2115	−	23.9839i	−1.45066	−	0.934990i
$659$	−37.6173	−	28.8647i	−1.46536	−	1.12441i	−0.966166	−	0.257921i	$-0.916963\pi$
$659$	−37.6173	−	28.8647i	−1.46536	−	1.12441i	−0.499194	−	0.866490i	$-0.666371\pi$
$660$		0			0
$661$	12.0599	+	15.7167i	0.469075	+	0.611311i	0.966647	−	0.256112i	$-0.0824416\pi$
$661$	12.0599	+	15.7167i	0.469075	+	0.611311i	−0.497572	+	0.867423i	$0.665775\pi$
$662$	−26.8063	+	31.6056i	−1.04186	+	1.22839i
$663$		0			0
$664$	0.0688788	−	4.34192i	0.00267302	−	0.168499i
$665$	−22.8156	−	22.8156i	−0.884752	−	0.884752i
$666$		0			0
$667$	−14.8320	−	6.14360i	−0.574296	−	0.237881i
$668$	8.33685	+	50.3910i	0.322563	+	1.94969i
$669$		0			0
$670$	−11.5833	+	36.0714i	−0.447502	+	1.39356i
$671$	−10.5934	+	18.3483i	−0.408953	+	0.708327i
$672$		0			0
$673$	−6.09021	−	10.5486i	−0.234760	−	0.406617i	0.724443	−	0.689335i	$-0.242097\pi$
$673$	−6.09021	−	10.5486i	−0.234760	−	0.406617i	−0.959203	+	0.282718i	$0.908764\pi$
$674$	−18.5019	+	3.99925i	−0.712665	+	0.154045i
$675$		0			0
$676$	8.83521	−	23.4984i	0.339816	−	0.903783i
$677$	2.72912	+	20.7297i	0.104889	+	0.796708i	0.960341	+	0.278827i	$0.0899456\pi$
$677$	2.72912	+	20.7297i	0.104889	+	0.796708i	−0.855453	+	0.517881i	$0.826721\pi$
$678$		0			0
$679$	65.7384	−	17.6145i	2.52281	−	0.675984i
$680$	−6.45874	+	22.6603i	−0.247681	+	0.868983i
$681$		0			0
$682$	2.14056	+	5.97932i	0.0819662	+	0.228960i
$683$	−10.6300	+	25.6632i	−0.406747	+	0.981974i	0.579241	+	0.815157i	$0.303349\pi$
$683$	−10.6300	+	25.6632i	−0.406747	+	0.981974i	−0.985988	+	0.166818i	$0.946651\pi$
$684$		0			0
$685$	−11.8607	+	4.91286i	−0.453174	+	0.187711i
$686$	1.93135	−	39.4476i	0.0737391	−	1.50612i
$687$		0			0
$688$	−14.5270	−	0.942422i	−0.553837	−	0.0359295i
$689$	−7.33753	−	4.23633i	−0.279538	−	0.161391i
$690$		0			0
$691$	−8.18871	−	6.28341i	−0.311513	−	0.239032i	0.441158	−	0.897430i	$-0.354568\pi$
$691$	−8.18871	−	6.28341i	−0.311513	−	0.239032i	−0.752671	+	0.658397i	$0.771235\pi$
$692$	24.3054	−	25.9679i	0.923952	−	0.987153i
$693$		0			0
$694$	−3.39616	+	18.6824i	−0.128916	+	0.709174i
$695$	−34.3130	−	9.19413i	−1.30156	−	0.348753i
$696$		0			0
$697$	16.4840	−	4.41686i	0.624374	−	0.167301i
$698$	1.86603	+	22.7113i	0.0706303	+	0.859635i
$699$		0			0
$700$	−45.6524	+	63.7527i	−1.72550	+	2.40963i
$701$	−7.10409	−	17.1508i	−0.268318	−	0.647776i	0.731087	−	0.682285i	$-0.239013\pi$
$701$	−7.10409	−	17.1508i	−0.268318	−	0.647776i	−0.999404	+	0.0345084i	$0.989013\pi$
$702$		0			0
$703$	−5.54804			−0.209248
$704$	−4.97024	+	30.2928i	−0.187323	+	1.14170i
$705$		0			0
$706$	−31.4161	−	10.0884i	−1.18236	−	0.379681i
$707$	−21.8720	−	2.87951i	−0.822582	−	0.108295i
$708$		0			0
$709$	−5.82694	−	44.2600i	−0.218835	−	1.66222i	−0.649991	−	0.759942i	$-0.725227\pi$
$709$	−5.82694	−	44.2600i	−0.218835	−	1.66222i	0.431155	−	0.902278i	$-0.358106\pi$
$710$	−64.7275	+	44.8145i	−2.42918	+	1.68186i
$711$		0			0
$712$	4.58273	−	31.0011i	0.171745	−	1.16181i
$713$	2.13070	+	0.570919i	0.0797953	+	0.0213811i
$714$		0			0
$715$	5.79004	+	7.54573i	0.216535	+	0.282194i
$716$	2.89438	+	9.53005i	0.108168	+	0.356155i
$717$		0			0
$718$	−52.0912	−	2.55037i	−1.94403	−	0.0951790i
$719$		−	34.8111i		−	1.29823i	−0.760689	−	0.649117i	$-0.775139\pi$
$719$		−	34.8111i		−	1.29823i	0.760689	−	0.649117i	$-0.224861\pi$
$720$		0			0
$721$		−	11.0785i		−	0.412586i
$722$	1.05435	−	21.5351i	0.0392390	−	0.801454i
$723$		0			0
$724$	1.59823	+	0.853587i	0.0593978	+	0.0317233i
$725$	45.2178	+	58.9290i	1.67935	+	2.18857i
$726$		0			0
$727$	−24.8684	−	6.66347i	−0.922319	−	0.247135i	−0.233743	−	0.972299i	$-0.575097\pi$
$727$	−24.8684	−	6.66347i	−0.922319	−	0.247135i	−0.688576	+	0.725164i	$0.741764\pi$
$728$	2.07164	+	8.25292i	0.0767800	+	0.305874i
$729$		0			0
$730$	−6.74540	−	9.74267i	−0.249659	−	0.360592i
$731$	1.06836	+	8.11502i	0.0395148	+	0.300145i
$732$		0			0
$733$	−7.13333	−	0.939121i	−0.263476	−	0.0346872i	−0.00236898	−	0.999997i	$-0.500754\pi$
$733$	−7.13333	−	0.939121i	−0.263476	−	0.0346872i	−0.261107	+	0.965310i	$0.584087\pi$
$734$	8.69734	−	27.0842i	0.321025	−	0.999698i
$735$		0			0
$736$	7.66788	+	7.40860i	0.282642	+	0.273085i
$737$	27.7516			1.02224
$738$		0			0
$739$	12.0153	+	29.0076i	0.441992	+	1.06706i	0.975249	+	0.221109i	$0.0709678\pi$
$739$	12.0153	+	29.0076i	0.441992	+	1.06706i	−0.533257	+	0.845953i	$0.679032\pi$
$740$	3.46249	+	20.9286i	0.127284	+	0.769350i
$741$		0			0
$742$	−80.2321	+	6.59212i	−2.94541	+	0.242005i
$743$	1.56001	−	0.418002i	0.0572311	−	0.0153350i	−0.230090	−	0.973169i	$-0.573902\pi$
$743$	1.56001	−	0.418002i	0.0572311	−	0.0153350i	0.287321	+	0.957834i	$0.407235\pi$
$744$		0			0
$745$	0.662546	+	0.177529i	0.0242738	+	0.00650414i
$746$	−32.2902	−	5.86984i	−1.18223	−	0.214910i
$747$		0			0
$748$	17.2506	−	0.570483i	0.630743	−	0.0208589i
$749$	−35.2445	−	27.0441i	−1.28781	−	0.988168i
$750$		0			0
$751$	−10.8610	−	6.27060i	−0.396323	−	0.228817i	0.288573	−	0.957458i	$-0.406819\pi$
$751$	−10.8610	−	6.27060i	−0.396323	−	0.228817i	−0.684896	+	0.728641i	$0.740153\pi$
$752$	26.3682	−	8.97042i	0.961550	−	0.327118i
$753$		0			0
$754$	8.05068	+	0.394159i	0.293189	+	0.0143544i
$755$	38.9778	−	16.1451i	1.41855	−	0.587581i
$756$		0			0
$757$	−9.65900	+	23.3189i	−0.351062	+	0.847540i	0.645427	+	0.763822i	$0.276679\pi$
$757$	−9.65900	+	23.3189i	−0.351062	+	0.847540i	−0.996490	+	0.0837177i	$0.973321\pi$
$758$	−1.36922	+	0.490173i	−0.0497324	+	0.0178039i
$759$		0			0
$760$	20.1655	−	2.33007i	0.731479	−	0.0845206i
$761$	22.4652	−	6.01954i	0.814363	−	0.218208i	0.172483	−	0.985013i	$-0.444821\pi$
$761$	22.4652	−	6.01954i	0.814363	−	0.218208i	0.641881	+	0.766804i	$0.278154\pi$
$762$		0			0
$763$	−2.22043	−	16.8658i	−0.0803849	−	0.610584i
$764$	6.52697	−	2.95996i	0.236138	−	0.107087i
$765$		0			0
$766$	−2.63468	−	12.1889i	−0.0951947	−	0.440403i
$767$	1.69041	+	2.92788i	0.0610373	+	0.105720i
$768$		0			0
$769$	−5.43493	+	9.41358i	−0.195989	+	0.339462i	−0.947224	−	0.320572i	$-0.896125\pi$
$769$	−5.43493	+	9.41358i	−0.195989	+	0.339462i	0.751236	+	0.660034i	$0.229458\pi$
$770$	86.0426	+	27.6301i	3.10076	+	0.995721i
$771$		0			0
$772$	11.8444	+	8.48159i	0.426288	+	0.305259i
$773$	−4.42050	−	1.83103i	−0.158994	−	0.0658576i	0.301767	−	0.953382i	$-0.402424\pi$
$773$	−4.42050	−	1.83103i	−0.158994	−	0.0658576i	−0.460761	+	0.887524i	$0.652424\pi$
$774$		0			0
$775$	−7.21676	−	7.21676i	−0.259234	−	0.259234i
$776$	−17.0108	+	39.2929i	−0.610651	+	1.41053i
$777$		0			0
$778$	38.8109	+	32.9174i	1.39144	+	1.18015i
$779$	−8.95008	−	11.6640i	−0.320670	−	0.417905i
$780$		0			0
$781$	45.7516	+	35.1064i	1.63712	+	1.25621i
$782$	3.24775	−	5.03895i	0.116139	−	0.180192i
$783$		0			0
$784$	39.7561	+	34.8183i	1.41986	+	1.24351i
$785$	−33.9825	+	19.6198i	−1.21289	+	0.700262i
$786$		0			0
$787$	−6.38212	+	48.4770i	−0.227498	+	1.72802i	0.372512	+	0.928027i	$0.378497\pi$
$787$	−6.38212	+	48.4770i	−0.227498	+	1.72802i	−0.600010	+	0.799993i	$0.704837\pi$
$788$	−7.25310	+	13.5805i	−0.258381	+	0.483785i
$789$		0			0
$790$	−5.90457	−	16.4935i	−0.210075	−	0.586813i
$791$	14.2031	−	14.2031i	0.505006	−	0.505006i
$792$		0			0
$793$	−2.61252	−	2.61252i	−0.0927734	−	0.0927734i
$794$	−19.2389	+	40.6948i	−0.682764	+	1.44421i
$795$		0			0
$796$	−13.0537	+	10.7202i	−0.462676	+	0.379967i
$797$	−53.7073	−	7.07070i	−1.90241	−	0.250457i	−0.914395	−	0.404822i	$-0.867333\pi$
$797$	−53.7073	−	7.07070i	−1.90241	−	0.250457i	−0.988014	+	0.154366i	$0.950667\pi$
$798$		0			0
$799$	−7.83005	−	13.5620i	−0.277007	−	0.479791i
$800$	−13.5855	−	47.4244i	−0.480321	−	1.67671i
$801$		0			0
$802$	34.3766	−	7.43064i	1.21388	−	0.262385i
$803$	−5.28415	+	6.88644i	−0.186474	+	0.243017i
$804$		0			0
$805$	24.9019	−	19.1079i	0.877677	−	0.673465i
$806$	−1.10379	+	0.0906909i	−0.0388793	+	0.00319445i
$807$		0			0
$808$	9.96846	−	9.65712i	0.350689	−	0.339736i
$809$	−5.74345	+	5.74345i	−0.201929	+	0.201929i	−0.800826	−	0.598897i	$-0.795606\pi$
$809$	−5.74345	+	5.74345i	−0.201929	+	0.201929i	0.598897	+	0.800826i	$0.295606\pi$
$810$		0			0
$811$	10.1598	−	24.5280i	0.356760	−	0.861295i	−0.638992	−	0.769214i	$-0.720648\pi$
$811$	10.1598	−	24.5280i	0.356760	−	0.861295i	0.995752	−	0.0920809i	$-0.0293518\pi$
$812$	65.0225	−	40.4637i	2.28184	−	1.42000i
$813$		0			0
$814$	13.8208	−	7.10204i	0.484419	−	0.248926i
$815$	−50.2069	−	28.9870i	−1.75867	−	1.01537i
$816$		0			0
$817$	6.10680	−	3.52576i	0.213650	−	0.123351i
$818$	23.0800	−	35.8091i	0.806974	−	1.25204i
$819$		0			0
$820$	−38.4137	+	41.0413i	−1.34146	+	1.43322i
$821$	−2.53764	+	0.334086i	−0.0885642	+	0.0116597i	−0.174678	−	0.984626i	$-0.555888\pi$
$821$	−2.53764	+	0.334086i	−0.0885642	+	0.0116597i	0.0861139	+	0.996285i	$0.472555\pi$
$822$		0			0
$823$	3.94176	+	14.7108i	0.137401	+	0.512787i	0.999976	+	0.00685900i	$0.00218331\pi$
$823$	3.94176	+	14.7108i	0.137401	+	0.512787i	−0.862576	+	0.505928i	$0.831150\pi$
$824$	5.46157	+	4.33016i	0.190263	+	0.150848i
$825$		0			0
$826$	29.0409	+	13.7294i	1.01046	+	0.477707i
$827$	−18.5848	−	7.69809i	−0.646258	−	0.267689i	0.0353850	−	0.999374i	$-0.488734\pi$
$827$	−18.5848	−	7.69809i	−0.646258	−	0.267689i	−0.681643	+	0.731685i	$0.738734\pi$
$828$		0			0
$829$	−5.70138	−	13.7643i	−0.198017	−	0.478055i	0.793415	−	0.608681i	$-0.208301\pi$
$829$	−5.70138	−	13.7643i	−0.198017	−	0.478055i	−0.991432	+	0.130626i	$0.958301\pi$
$830$	5.95825	−	5.40205i	0.206814	−	0.187508i
$831$		0			0
$832$	−4.87830	−	2.20445i	−0.169125	−	0.0764255i
$833$	14.8569	−	25.7329i	0.514760	−	0.891591i
$834$		0			0
$835$	−57.5868	+	75.0486i	−1.99287	+	2.59716i
$836$	−6.14135	−	13.5422i	−0.212403	−	0.468368i
$837$		0			0
$838$	−30.9585	+	21.4343i	−1.06944	+	0.740437i
$839$	7.86090	−	29.3373i	0.271388	−	1.01284i	−0.686835	−	0.726814i	$-0.741000\pi$
$839$	7.86090	−	29.3373i	0.271388	−	1.01284i	0.958223	−	0.286022i	$-0.0923329\pi$
$840$		0			0
$841$	−11.2708	−	42.0631i	−0.388647	−	1.45045i
$842$	−36.0612	−	30.5853i	−1.24275	−	1.05404i
$843$		0			0
$844$	−54.2811	−	12.6375i	−1.86843	−	0.435001i
$845$	42.9561	−	17.7930i	1.47773	−	0.612098i
$846$		0			0
$847$		−	16.7436i		−	0.575318i
$848$	28.1097	−	42.1299i	0.965291	−	1.44675i
$849$		0			0
$850$	−24.6705	+	12.6773i	−0.846191	+	0.434828i
$851$	0.704460	−	5.35091i	0.0241486	−	0.183427i
$852$		0			0
$853$	47.2823	−	6.22483i	1.61892	−	0.213134i	0.734088	−	0.679054i	$-0.237610\pi$
$853$	47.2823	−	6.22483i	1.61892	−	0.213134i	0.884827	+	0.465920i	$0.154276\pi$
$854$	−34.5386	−	6.27857i	−1.18189	−	0.214848i
$855$		0			0
$856$	27.1080	−	6.80461i	0.926533	−	0.232577i
$857$	2.74930	−	10.2605i	0.0939142	−	0.350492i	−0.902938	−	0.429770i	$-0.858595\pi$
$857$	2.74930	−	10.2605i	0.0939142	−	0.350492i	0.996853	+	0.0792775i	$0.0252613\pi$
$858$		0			0
$859$	13.1682	−	10.1043i	0.449293	−	0.344755i	−0.359200	−	0.933261i	$-0.616950\pi$
$859$	13.1682	−	10.1043i	0.449293	−	0.344755i	0.808493	+	0.588506i	$0.200284\pi$
$860$	−17.1112	−	20.8359i	−0.583489	−	0.710500i
$861$		0			0
$862$	22.7548	+	25.0976i	0.775031	+	0.854829i
$863$	24.7712			0.843221			0.421611	−	0.906777i	$-0.361465\pi$
$863$	24.7712			0.843221			0.421611	+	0.906777i	$0.361465\pi$
$864$		0			0
$865$	65.8747			2.23981
$866$	17.4596	+	19.2572i	0.593300	+	0.654386i
$867$		0			0
$868$	−8.13212	+	6.67840i	−0.276022	+	0.226680i
$869$	−10.1807	+	7.81195i	−0.345358	+	0.265002i
$870$		0			0
$871$	−1.25255	+	4.67458i	−0.0424410	+	0.158392i
$872$	9.18250	+	5.49754i	0.310959	+	0.186170i
$873$		0			0
$874$	−5.08141	−	0.923720i	−0.171881	−	0.0312453i
$875$	−61.4313	+	8.08758i	−2.07676	+	0.273410i
$876$		0			0
$877$	5.58687	−	42.4365i	0.188655	−	1.43298i	−0.590950	−	0.806708i	$-0.701247\pi$
$877$	5.58687	−	42.4365i	0.188655	−	1.43298i	0.779605	−	0.626271i	$-0.215420\pi$
$878$	33.7830	−	17.3599i	1.14012	−	0.585869i
$879$		0			0
$880$	−47.2519	+	31.6183i	−1.59286	+	1.06585i
$881$		−	44.7683i		−	1.50828i	−0.656712	−	0.754141i	$-0.728053\pi$
$881$		−	44.7683i		−	1.50828i	0.656712	−	0.754141i	$-0.271947\pi$
$882$		0			0
$883$	−7.12904	+	2.95294i	−0.239911	+	0.0993745i	−0.499400	−	0.866372i	$-0.666446\pi$
$883$	−7.12904	+	2.95294i	−0.239911	+	0.0993745i	0.259488	+	0.965746i	$0.416446\pi$
$884$	−0.682498	+	2.93149i	−0.0229549	+	0.0985968i
$885$		0			0
$886$	0.0392973	+	0.0333300i	0.00132022	+	0.00111974i
$887$	−5.81512	−	21.7023i	−0.195253	−	0.728693i	−0.992201	−	0.124646i	$-0.960221\pi$
$887$	−5.81512	−	21.7023i	−0.195253	−	0.728693i	0.796949	−	0.604047i	$-0.206446\pi$
$888$		0			0
$889$	−8.51664	+	31.7845i	−0.285639	+	1.06602i
$890$	47.7191	−	33.0387i	1.59955	−	1.10746i
$891$		0			0
$892$	40.9599	−	18.5752i	1.37144	−	0.621943i
$893$	−8.21304	+	10.7034i	−0.274839	+	0.358177i
$894$		0			0
$895$	−9.22323	+	15.9751i	−0.308299	+	0.533989i
$896$	−50.0314	+	9.16385i	−1.67143	+	0.306143i
$897$		0			0
$898$	−15.8353	+	14.3571i	−0.528430	+	0.479102i
$899$	3.81464	+	9.20935i	0.127225	+	0.307149i
$900$		0			0
$901$	−26.3087	−	10.8974i	−0.876470	−	0.363046i
$902$	37.2267	+	17.5993i	1.23951	+	0.585994i
$903$		0			0
$904$	1.45051	+	12.5534i	0.0482434	+	0.417520i
$905$	0.868535	+	3.24142i	0.0288711	+	0.107748i
$906$		0			0
$907$	37.7665	−	4.97205i	1.25402	−	0.165094i	0.525899	−	0.850547i	$-0.323729\pi$
$907$	37.7665	−	4.97205i	1.25402	−	0.165094i	0.728117	+	0.685453i	$0.240396\pi$
$908$	−3.83623	−	3.59062i	−0.127310	−	0.119159i
$909$		0			0
$910$	−8.53759	+	13.2463i	−0.283018	+	0.439109i
$911$	28.5349	−	16.4746i	0.945404	−	0.545829i	0.0537540	−	0.998554i	$-0.482881\pi$
$911$	28.5349	−	16.4746i	0.945404	−	0.545829i	0.891650	+	0.452725i	$0.149548\pi$
$912$		0			0
$913$	−5.10199	−	2.94563i	−0.168851	−	0.0974862i
$914$	17.3188	−	8.89951i	0.572854	−	0.294370i
$915$		0			0
$916$	−22.1861	−	35.6516i	−0.733048	−	1.17796i
$917$	1.94700	−	4.70048i	0.0642957	−	0.155224i
$918$		0			0
$919$	−7.59597	+	7.59597i	−0.250568	+	0.250568i	−0.821203	−	0.570636i	$-0.806697\pi$
$919$	−7.59597	+	7.59597i	−0.250568	+	0.250568i	0.570636	+	0.821203i	$0.306697\pi$
$920$	−0.313226	+	19.7448i	−0.0103267	+	0.650967i
$921$		0			0
$922$	29.7598	−	2.44516i	0.980088	−	0.0805271i
$923$	−7.97841	+	6.12205i	−0.262613	+	0.201510i
$924$		0			0
$925$	−15.2014	+	19.8109i	−0.499820	+	0.651379i
$926$	−43.9506	+	9.50008i	−1.44430	+	0.312192i
$927$		0			0
$928$	−5.46667	+	47.8708i	−0.179452	+	1.57144i
$929$	27.2957	+	47.2775i	0.895542	+	1.55112i	0.833133	+	0.553073i	$0.186545\pi$
$929$	27.2957	+	47.2775i	0.895542	+	1.55112i	0.0624089	+	0.998051i	$0.480122\pi$
$930$		0			0
$931$	−25.3798	−	3.34131i	−0.831789	−	0.109507i
$932$	13.7292	+	16.7178i	0.449716	+	0.547608i
$933$		0			0
$934$	5.33288	−	11.2803i	0.174497	−	0.369102i
$935$	22.6039	+	22.6039i	0.739228	+	0.739228i
$936$		0			0
$937$	28.7721	−	28.7721i	0.939943	−	0.939943i	−0.0583530	−	0.998296i	$-0.518585\pi$
$937$	28.7721	−	28.7721i	0.939943	−	0.939943i	0.998296	+	0.0583530i	$0.0185849\pi$
$938$	15.4981	+	43.2916i	0.506031	+	1.41352i
$939$		0			0
$940$	45.5017	+	24.3016i	1.48410	+	0.792632i
$941$	5.68578	−	43.1878i	0.185351	−	1.40788i	−0.605486	−	0.795856i	$-0.707021\pi$
$941$	5.68578	−	43.1878i	0.185351	−	1.40788i	0.790837	−	0.612026i	$-0.209645\pi$
$942$		0			0
$943$	12.3859	−	7.15103i	0.403342	−	0.232870i
$944$	−18.1194	+	8.95050i	−0.589735	+	0.291314i
$945$		0			0
$946$	−10.6994	+	16.6004i	−0.347868	+	0.539725i
$947$	40.1144	+	30.7809i	1.30354	+	1.00024i	0.998857	+	0.0477909i	$0.0152181\pi$
$947$	40.1144	+	30.7809i	1.30354	+	1.00024i	0.304686	+	0.952453i	$0.401449\pi$
$948$		0			0
$949$	−0.921481	−	1.20090i	−0.0299125	−	0.0389828i
$950$	18.2238	+	15.4566i	0.591260	+	0.501477i
$951$		0			0
$952$	10.5237	+	26.5917i	0.341074	+	0.861843i
$953$	27.4133	+	27.4133i	0.888003	+	0.888003i	0.994331	−	0.106328i	$-0.0339093\pi$
$953$	27.4133	+	27.4133i	0.888003	+	0.888003i	−0.106328	+	0.994331i	$0.533909\pi$
$954$		0			0
$955$	12.2630	+	5.07952i	0.396823	+	0.164369i
$956$	−0.336158	+	0.469438i	−0.0108721	+	0.0151827i
$957$		0			0
$958$	−5.24911	−	1.68560i	−0.169591	−	0.0544594i
$959$	−7.79075	+	13.4940i	−0.251577	+	0.435743i
$960$		0			0
$961$	14.8152	+	25.6606i	0.477909	+	0.827763i
$962$	0.572499	+	2.64857i	0.0184581	+	0.0853935i
$963$		0			0
$964$	−4.90848	−	10.8236i	−0.158091	−	0.348606i
$965$	3.52173	+	26.7502i	0.113369	+	0.861120i
$966$		0			0
$967$	20.8926	−	5.59817i	0.671862	−	0.180025i	0.0932685	−	0.995641i	$-0.470268\pi$
$967$	20.8926	−	5.59817i	0.671862	−	0.180025i	0.578593	+	0.815616i	$0.303602\pi$
$968$	8.25438	+	6.54442i	0.265306	+	0.210346i
$969$		0			0
$970$	−74.6604	+	26.7280i	−2.39720	+	0.858183i
$971$	−6.88956	+	16.6329i	−0.221096	+	0.533774i	−0.995039	−	0.0994812i	$-0.968282\pi$
$971$	−6.88956	+	16.6329i	−0.221096	+	0.533774i	0.773943	+	0.633255i	$0.218282\pi$
$972$		0			0
$973$	−39.8331	+	16.4994i	−1.27699	+	0.528947i
$974$	−34.7731	−	1.70248i	−1.11420	−	0.0545510i
$975$		0			0
$976$	16.5950	−	14.5730i	0.531194	−	0.466471i
$977$	−42.5194	−	24.5486i	−1.36032	−	0.785379i	−0.370650	−	0.928772i	$-0.620865\pi$
$977$	−42.5194	−	24.5486i	−1.36032	−	0.785379i	−0.989666	+	0.143394i	$0.954199\pi$
$978$		0			0
$979$	−33.7295	−	25.8815i	−1.07800	−	0.827178i
$980$	3.23508	+	97.8241i	0.103341	+	3.12487i
$981$		0			0
$982$	19.8706	+	3.61216i	0.634097	+	0.115269i
$983$	25.3681	+	6.79737i	0.809117	+	0.216802i	0.639583	−	0.768722i	$-0.279107\pi$
$983$	25.3681	+	6.79737i	0.809117	+	0.216802i	0.169534	+	0.985524i	$0.445774\pi$
$984$		0			0
$985$	−27.5430	+	7.38011i	−0.877592	+	0.235150i
$986$	26.9995	−	2.21837i	0.859841	−	0.0706472i
$987$		0			0
$988$	2.55829	−	0.423252i	0.0813900	−	0.0134654i
$989$	2.62507	+	6.33749i	0.0834725	+	0.201520i
$990$		0			0
$991$	14.4716			0.459706			0.229853	−	0.973225i	$-0.426175\pi$
$991$	14.4716			0.459706			0.229853	+	0.973225i	$0.426175\pi$
$992$	−0.113837	−	6.61934i	−0.00361434	−	0.210164i
$993$		0			0
$994$	−29.2145	+	90.9764i	−0.926627	+	2.88560i
$995$	−31.0166	−	4.08342i	−0.983293	−	0.129453i
$996$		0			0
$997$	−3.18984	−	24.2293i	−0.101023	−	0.767349i	−0.964709	−	0.263318i	$-0.915183\pi$
$997$	−3.18984	−	24.2293i	−0.101023	−	0.767349i	0.863686	−	0.504031i	$-0.168150\pi$
$998$	18.5954	+	26.8581i	0.588627	+	0.850178i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bk.a.37.10		368
3.2	odd	2		288.2.bc.a.229.37	yes	368
9.2	odd	6		288.2.bc.a.133.5	yes	368
9.7	even	3	inner	864.2.bk.a.613.42		368
32.13	even	8	inner	864.2.bk.a.685.42		368
96.77	odd	8		288.2.bc.a.13.5	✓	368
288.173	odd	24		288.2.bc.a.205.37	yes	368
288.205	even	24	inner	864.2.bk.a.397.10		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.5	✓	368	96.77	odd	8
288.2.bc.a.133.5	yes	368	9.2	odd	6
288.2.bc.a.205.37	yes	368	288.173	odd	24
288.2.bc.a.229.37	yes	368	3.2	odd	2
864.2.bk.a.37.10		368	1.1	even	1	trivial
864.2.bk.a.397.10		368	288.205	even	24	inner
864.2.bk.a.613.42		368	9.7	even	3	inner
864.2.bk.a.685.42		368	32.13	even	8	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bk (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.04770 + 0.949902i) q^{2} +(0.195371 - 1.99043i) q^{4} +(2.93870 - 2.25494i) q^{5} +(1.16359 - 4.34257i) q^{7} +(1.68603 + 2.27097i) q^{8} +O(q^{10})\)	\(q+(-1.04770 + 0.949902i) q^{2} +(0.195371 - 1.99043i) q^{4} +(2.93870 - 2.25494i) q^{5} +(1.16359 - 4.34257i) q^{7} +(1.68603 + 2.27097i) q^{8} +(-0.936914 + 5.15400i) q^{10} +(3.80440 - 0.500859i) q^{11} +(-0.0873426 + 0.663433i) q^{13} +(2.90592 + 5.65503i) q^{14} +(-3.92366 - 0.777745i) q^{16} +2.24902i q^{17} +(1.79007 - 0.741472i) q^{19} +(-3.91418 - 6.28984i) q^{20} +(-3.51012 + 4.13856i) q^{22} +(0.487832 + 1.82061i) q^{23} +(2.25709 - 8.42358i) q^{25} +(-0.538687 - 0.778048i) q^{26} +(-8.41628 - 3.16446i) q^{28} +(-5.18509 + 6.75734i) q^{29} +(0.585159 - 1.01353i) q^{31} +(4.84962 - 2.91225i) q^{32} +(-2.13635 - 2.35631i) q^{34} +(-6.37282 - 15.3853i) q^{35} +(-2.64545 - 1.09578i) q^{37} +(-1.17114 + 2.47724i) q^{38} +(10.0756 + 2.87181i) q^{40} +(-1.96391 - 7.32940i) q^{41} +(3.60825 - 0.475035i) q^{43} +(-0.253658 - 7.67026i) q^{44} +(-2.24051 - 1.44407i) q^{46} +(-6.03021 + 3.48154i) q^{47} +(-11.4418 - 6.60594i) q^{49} +(5.63682 + 10.9694i) q^{50} +(1.30346 + 0.303465i) q^{52} +(-4.84541 + 11.6979i) q^{53} +(10.0506 - 10.0506i) q^{55} +(11.8237 - 4.67922i) q^{56} +(-0.986371 - 12.0050i) q^{58} +(4.00831 - 3.07569i) q^{59} +(-3.36120 + 4.38040i) q^{61} +(0.349676 + 1.61772i) q^{62} +(-2.31462 + 7.65784i) q^{64} +(1.23933 + 2.14658i) q^{65} +(7.17032 + 0.943991i) q^{67} +(4.47652 + 0.439392i) q^{68} +(21.2914 + 10.0657i) q^{70} +(10.6269 + 10.6269i) q^{71} +(-1.59954 + 1.59954i) q^{73} +(3.81254 - 1.36487i) q^{74} +(-1.12612 - 3.70788i) q^{76} +(2.25174 - 17.1037i) q^{77} +(-2.89618 + 1.67211i) q^{79} +(-13.2842 + 6.56208i) q^{80} +(9.01981 + 5.81353i) q^{82} +(-1.21803 - 0.934627i) q^{83} +(5.07141 + 6.60919i) q^{85} +(-3.32914 + 3.92518i) q^{86} +(7.55176 + 7.79522i) q^{88} +(-7.83449 - 7.83449i) q^{89} +(2.77937 + 1.15125i) q^{91} +(3.71912 - 0.615303i) q^{92} +(3.01075 - 9.37573i) q^{94} +(3.58851 - 6.21548i) q^{95} +(7.56906 + 13.1100i) q^{97} +(18.2626 - 3.94754i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

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