LMFDB - Embedded newform 576.2.bd.a.181.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(37,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 9, 0]))

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

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

chi := DirichletCharacter("576.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, degree $8$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			181.5
Character	$\chi$	$=$	576.181
Dual form			576.2.bd.a.541.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11482 + 0.870162i) q^{2} +(0.485635 + 1.94014i) q^{4} +(0.153107 + 0.229142i) q^{5} +(-0.843108 - 0.349227i) q^{7} +(-1.14685 + 2.58549i) q^{8} +O(q^{10})$	\(q+(1.11482 + 0.870162i) q^{2} +(0.485635 + 1.94014i) q^{4} +(0.153107 + 0.229142i) q^{5} +(-0.843108 - 0.349227i) q^{7} +(-1.14685 + 2.58549i) q^{8} +(-0.0287035 + 0.388679i) q^{10} +(-0.575451 + 2.89299i) q^{11} +(-3.63027 + 5.43308i) q^{13} +(-0.636028 - 1.12297i) q^{14} +(-3.52832 + 1.88440i) q^{16} +(3.22910 - 3.22910i) q^{17} +(5.20741 + 3.47948i) q^{19} +(-0.370213 + 0.408330i) q^{20} +(-3.15889 + 2.72442i) q^{22} +(2.33779 + 5.64392i) q^{23} +(1.88435 - 4.54923i) q^{25} +(-8.77475 + 2.89797i) q^{26} +(0.268107 - 1.80535i) q^{28} +(-0.693313 - 3.48552i) q^{29} -3.92256i q^{31} +(-5.57317 - 0.969441i) q^{32} +(6.40970 - 0.790016i) q^{34} +(-0.0490638 - 0.246660i) q^{35} +(4.35133 - 2.90747i) q^{37} +(2.77760 + 8.41027i) q^{38} +(-0.768033 + 0.133068i) q^{40} +(0.653569 + 1.57786i) q^{41} +(-3.96655 - 0.788996i) q^{43} +(-5.89227 + 0.288479i) q^{44} +(-2.30492 + 8.32620i) q^{46} +(-3.42980 + 3.42980i) q^{47} +(-4.36088 - 4.36088i) q^{49} +(6.05928 - 3.43187i) q^{50} +(-12.3040 - 4.40475i) q^{52} +(0.321835 - 1.61797i) q^{53} +(-0.751009 + 0.311078i) q^{55} +(1.86984 - 1.77934i) q^{56} +(2.26005 - 4.48902i) q^{58} +(-3.43310 - 5.13800i) q^{59} +(11.5586 - 2.29915i) q^{61} +(3.41327 - 4.37294i) q^{62} +(-5.36949 - 5.93031i) q^{64} -1.80077 q^{65} +(6.90108 - 1.37271i) q^{67} +(7.83309 + 4.69676i) q^{68} +(0.159937 - 0.317675i) q^{70} +(-2.53894 - 1.05166i) q^{71} +(2.05602 - 0.851633i) q^{73} +(7.38090 + 0.545070i) q^{74} +(-4.22179 + 11.7929i) q^{76} +(1.49548 - 2.23814i) q^{77} +(4.21203 + 4.21203i) q^{79} +(-0.972007 - 0.519967i) q^{80} +(-0.644380 + 2.32773i) q^{82} +(8.64283 + 5.77496i) q^{83} +(1.23432 + 0.245522i) q^{85} +(-3.73542 - 4.33113i) q^{86} +(-6.81983 - 4.80563i) q^{88} +(3.87335 - 9.35109i) q^{89} +(4.95809 - 3.31289i) q^{91} +(-9.81471 + 7.27653i) q^{92} +(-6.80808 + 0.839118i) q^{94} +1.72597i q^{95} -1.83166i q^{97} +(-1.06691 - 8.65625i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$	1.11482	+	0.870162i	0.788295	+	0.615298i
$2$	1.11482	+	0.870162i	0.788295	+	0.615298i
$3$		0			0
$3$		0			0
$4$	0.485635	+	1.94014i	0.242818	+	0.970072i
$5$	0.153107	+	0.229142i	0.0684717	+	0.102475i	0.864125	−	0.503277i	$-0.167872\pi$
$5$	0.153107	+	0.229142i	0.0684717	+	0.102475i	−0.795654	+	0.605752i	$0.792872\pi$
$6$		0			0
$7$	−0.843108	−	0.349227i	−0.318665	−	0.131995i	0.217617	−	0.976034i	$-0.430172\pi$
$7$	−0.843108	−	0.349227i	−0.318665	−	0.131995i	−0.536282	+	0.844039i	$0.680172\pi$
$8$	−1.14685	+	2.58549i	−0.405471	+	0.914108i
$9$		0			0
$10$	−0.0287035	+	0.388679i	−0.00907683	+	0.122911i
$11$	−0.575451	+	2.89299i	−0.173505	+	0.872268i	0.791727	+	0.610875i	$0.209182\pi$
$11$	−0.575451	+	2.89299i	−0.173505	+	0.872268i	−0.965232	+	0.261394i	$0.915818\pi$
$12$		0			0
$13$	−3.63027	+	5.43308i	−1.00686	+	1.50687i	−0.151746	+	0.988419i	$0.548490\pi$
$13$	−3.63027	+	5.43308i	−1.00686	+	1.50687i	−0.855110	+	0.518447i	$0.826510\pi$
$14$	−0.636028	−	1.12297i	−0.169986	−	0.300125i
$15$		0			0
$16$	−3.52832	+	1.88440i	−0.882079	+	0.471101i
$17$	3.22910	−	3.22910i	0.783172	−	0.783172i	−0.197192	−	0.980365i	$-0.563182\pi$
$17$	3.22910	−	3.22910i	0.783172	−	0.783172i	0.980365	+	0.197192i	$0.0631824\pi$
$18$		0			0
$19$	5.20741	+	3.47948i	1.19466	+	0.798247i	0.983800	−	0.179269i	$-0.0573731\pi$
$19$	5.20741	+	3.47948i	1.19466	+	0.798247i	0.210861	+	0.977516i	$0.432373\pi$
$20$	−0.370213	+	0.408330i	−0.0827822	+	0.0913053i
$21$		0			0
$22$	−3.15889	+	2.72442i	−0.673478	+	0.580847i
$23$	2.33779	+	5.64392i	0.487463	+	1.17684i	0.955992	+	0.293391i	$0.0947839\pi$
$23$	2.33779	+	5.64392i	0.487463	+	1.17684i	−0.468530	+	0.883448i	$0.655216\pi$
$24$		0			0
$25$	1.88435	−	4.54923i	0.376871	−	0.909846i
$26$	−8.77475	+	2.89797i	−1.72087	+	0.568339i
$27$		0			0
$28$	0.268107	−	1.80535i	0.0506675	−	0.341179i
$29$	−0.693313	−	3.48552i	−0.128745	−	0.647245i	−0.990228	−	0.139458i	$-0.955464\pi$
$29$	−0.693313	−	3.48552i	−0.128745	−	0.647245i	0.861483	−	0.507787i	$-0.169536\pi$
$30$		0			0
$31$		−	3.92256i		−	0.704513i	−0.935904	−	0.352256i	$-0.885414\pi$
$31$		−	3.92256i		−	0.704513i	0.935904	−	0.352256i	$-0.114586\pi$
$32$	−5.57317	−	0.969441i	−0.985206	−	0.171375i
$33$		0			0
$34$	6.40970	−	0.790016i	1.09925	−	0.135487i
$35$	−0.0490638	−	0.246660i	−0.00829330	−	0.0416932i
$36$		0			0
$37$	4.35133	−	2.90747i	0.715354	−	0.477984i	−0.143862	−	0.989598i	$-0.545952\pi$
$37$	4.35133	−	2.90747i	0.715354	−	0.477984i	0.859216	+	0.511614i	$0.170952\pi$
$38$	2.77760	+	8.41027i	0.450586	+	1.36433i
$39$		0			0
$40$	−0.768033	+	0.133068i	−0.121437	+	0.0210398i
$41$	0.653569	+	1.57786i	0.102070	+	0.246420i	0.966662	−	0.256055i	$-0.0824229\pi$
$41$	0.653569	+	1.57786i	0.102070	+	0.246420i	−0.864592	+	0.502475i	$0.832423\pi$
$42$		0			0
$43$	−3.96655	−	0.788996i	−0.604893	−	0.120321i	−0.116864	−	0.993148i	$-0.537284\pi$
$43$	−3.96655	−	0.788996i	−0.604893	−	0.120321i	−0.488029	+	0.872827i	$0.662284\pi$
$44$	−5.89227	+	0.288479i	−0.888293	+	0.0434898i
$45$		0			0
$46$	−2.30492	+	8.32620i	−0.339842	+	1.22763i
$47$	−3.42980	+	3.42980i	−0.500288	+	0.500288i	−0.911527	−	0.411240i	$-0.865096\pi$
$47$	−3.42980	+	3.42980i	−0.500288	+	0.500288i	0.411240	+	0.911527i	$0.365096\pi$
$48$		0			0
$49$	−4.36088	−	4.36088i	−0.622982	−	0.622982i
$50$	6.05928	−	3.43187i	0.856911	−	0.485339i
$51$		0			0
$52$	−12.3040	−	4.40475i	−1.70625	−	0.610829i
$53$	0.321835	−	1.61797i	0.0442075	−	0.222246i	−0.952366	−	0.304957i	$-0.901358\pi$
$53$	0.321835	−	1.61797i	0.0442075	−	0.222246i	0.996574	+	0.0827111i	$0.0263579\pi$
$54$		0			0
$55$	−0.751009	+	0.311078i	−0.101266	+	0.0419458i
$56$	1.86984	−	1.77934i	0.249867	−	0.237774i
$57$		0			0
$58$	2.26005	−	4.48902i	0.296759	−	0.589437i
$59$	−3.43310	−	5.13800i	−0.446952	−	0.668910i	0.537761	−	0.843097i	$-0.319270\pi$
$59$	−3.43310	−	5.13800i	−0.446952	−	0.668910i	−0.984713	+	0.174187i	$0.944270\pi$
$60$		0			0
$61$	11.5586	−	2.29915i	1.47993	−	0.294376i	0.611917	−	0.790922i	$-0.290399\pi$
$61$	11.5586	−	2.29915i	1.47993	−	0.294376i	0.868010	+	0.496546i	$0.165399\pi$
$62$	3.41327	−	4.37294i	0.433485	−	0.555364i
$63$		0			0
$64$	−5.36949	−	5.93031i	−0.671186	−	0.741289i
$65$	−1.80077			−0.223358
$66$		0			0
$67$	6.90108	−	1.37271i	0.843101	−	0.167703i	0.245400	−	0.969422i	$-0.421081\pi$
$67$	6.90108	−	1.37271i	0.843101	−	0.167703i	0.597701	+	0.801719i	$0.296081\pi$
$68$	7.83309	+	4.69676i	0.949902	+	0.569565i
$69$		0			0
$70$	0.159937	−	0.317675i	0.0191162	−	0.0379694i
$71$	−2.53894	−	1.05166i	−0.301317	−	0.124809i	0.226903	−	0.973917i	$-0.427140\pi$
$71$	−2.53894	−	1.05166i	−0.301317	−	0.124809i	−0.528219	+	0.849108i	$0.677140\pi$
$72$		0			0
$73$	2.05602	−	0.851633i	0.240640	−	0.0996762i	−0.259105	−	0.965849i	$-0.583427\pi$
$73$	2.05602	−	0.851633i	0.240640	−	0.0996762i	0.499744	+	0.866173i	$0.333427\pi$
$74$	7.38090	+	0.545070i	0.858013	+	0.0633631i
$75$		0			0
$76$	−4.22179	+	11.7929i	−0.484272	+	1.35274i
$77$	1.49548	−	2.23814i	0.170425	−	0.255059i
$78$		0			0
$79$	4.21203	+	4.21203i	0.473890	+	0.473890i	0.903171	−	0.429281i	$-0.141233\pi$
$79$	4.21203	+	4.21203i	0.473890	+	0.473890i	−0.429281	+	0.903171i	$0.641233\pi$
$80$	−0.972007	−	0.519967i	−0.108674	−	0.0581341i
$81$		0			0
$82$	−0.644380	+	2.32773i	−0.0711599	+	0.257055i
$83$	8.64283	+	5.77496i	0.948674	+	0.633884i	0.930633	−	0.365953i	$-0.119257\pi$
$83$	8.64283	+	5.77496i	0.948674	+	0.633884i	0.0180410	+	0.999837i	$0.494257\pi$
$84$		0			0
$85$	1.23432	+	0.245522i	0.133881	+	0.0266306i
$86$	−3.73542	−	4.33113i	−0.402801	−	0.467037i
$87$		0			0
$88$	−6.81983	−	4.80563i	−0.726996	−	0.512282i
$89$	3.87335	−	9.35109i	0.410574	−	0.991214i	−0.574410	−	0.818568i	$-0.694768\pi$
$89$	3.87335	−	9.35109i	0.410574	−	0.991214i	0.984984	−	0.172646i	$-0.0552316\pi$
$90$		0			0
$91$	4.95809	−	3.31289i	0.519749	−	0.347285i
$92$	−9.81471	+	7.27653i	−1.02325	+	0.758631i
$93$		0			0
$94$	−6.80808	+	0.839118i	−0.702200	+	0.0865484i
$95$			1.72597i			0.177081i
$96$		0			0
$97$		−	1.83166i		−	0.185977i	−0.995667	−	0.0929884i	$-0.970358\pi$
$97$		−	1.83166i		−	0.185977i	0.995667	−	0.0929884i	$-0.0296419\pi$
$98$	−1.06691	−	8.65625i	−0.107774	−	0.874413i
$99$		0			0
$100$	9.74127	+	1.44665i	0.974127	+	0.144665i
$101$	−0.569062	+	0.380235i	−0.0566238	+	0.0378348i	−0.583560	−	0.812070i	$-0.698341\pi$
$101$	−0.569062	+	0.380235i	−0.0566238	+	0.0378348i	0.526936	+	0.849905i	$0.323341\pi$
$102$		0			0
$103$	−1.03003	+	2.48672i	−0.101492	+	0.245024i	−0.966467	−	0.256792i	$-0.917334\pi$
$103$	−1.03003	+	2.48672i	−0.101492	+	0.245024i	0.864975	+	0.501816i	$0.167334\pi$
$104$	−9.88381	−	15.6169i	−0.969188	−	1.53137i
$105$		0			0
$106$	1.76669	−	1.52370i	0.171596	−	0.147995i
$107$	12.3947	+	2.46545i	1.19824	+	0.238344i	0.753580	−	0.657356i	$-0.228325\pi$
$107$	12.3947	+	2.46545i	1.19824	+	0.238344i	0.444658	+	0.895701i	$0.353325\pi$
$108$		0			0
$109$	−5.11373	−	3.41688i	−0.489806	−	0.327278i	0.286021	−	0.958223i	$-0.407667\pi$
$109$	−5.11373	−	3.41688i	−0.489806	−	0.327278i	−0.775827	+	0.630945i	$0.782667\pi$
$110$	−1.10793	−	0.306704i	−0.105637	−	0.0292431i
$111$		0			0
$112$	3.63284	−	0.356574i	0.343271	−	0.0336931i
$113$	−6.83631	−	6.83631i	−0.643106	−	0.643106i	0.308212	−	0.951318i	$-0.400270\pi$
$113$	−6.83631	−	6.83631i	−0.643106	−	0.643106i	−0.951318	+	0.308212i	$0.900270\pi$
$114$		0			0
$115$	−0.935324	+	1.39981i	−0.0872194	+	0.130533i
$116$	6.42572	−	3.03782i	0.596613	−	0.282054i
$117$		0			0
$118$	0.643612	−	8.71528i	0.0592493	−	0.802307i
$119$	−3.85017	+	1.59479i	−0.352945	+	0.146194i
$120$		0			0
$121$	2.12445	+	0.879976i	0.193132	+	0.0799978i
$122$	14.8864	+	7.49473i	1.34775	+	0.678541i
$123$		0			0
$124$	7.61034	−	1.90493i	0.683428	−	0.171068i
$125$	2.68238	−	0.533559i	0.239919	−	0.0477229i
$126$		0			0
$127$	−11.4576			−1.01669			−0.508347	−	0.861152i	$-0.669743\pi$
$127$	−11.4576			−1.01669			−0.508347	+	0.861152i	$0.669743\pi$
$128$	−0.825670	−	11.2835i	−0.0729796	−	0.997333i
$129$		0			0
$130$	−2.00753	−	1.56696i	−0.176072	−	0.137431i
$131$	−2.37921	+	0.473254i	−0.207872	+	0.0413484i	−0.297928	−	0.954588i	$-0.596296\pi$
$131$	−2.37921	+	0.473254i	−0.207872	+	0.0413484i	0.0900556	+	0.995937i	$0.471296\pi$
$132$		0			0
$133$	−3.17528	−	4.75215i	−0.275332	−	0.412063i
$134$	8.88792	+	4.47474i	0.767800	+	0.386559i
$135$		0			0
$136$	4.64552	+	12.0521i	0.398350	+	1.03346i
$137$	21.2383	−	8.79718i	1.81451	−	0.751594i	0.834983	−	0.550276i	$-0.185477\pi$
$137$	21.2383	−	8.79718i	1.81451	−	0.751594i	0.979526	−	0.201319i	$-0.0645227\pi$
$138$		0			0
$139$	−1.92573	+	9.68131i	−0.163338	+	0.821158i	0.809041	+	0.587752i	$0.199987\pi$
$139$	−1.92573	+	9.68131i	−0.163338	+	0.821158i	−0.972379	+	0.233406i	$0.925013\pi$
$140$	0.454730	−	0.214978i	0.0384317	−	0.0181689i
$141$		0			0
$142$	−1.91534	−	3.38170i	−0.160731	−	0.283786i
$143$	−13.6288	−	13.6288i	−1.13970	−	1.13970i
$144$		0			0
$145$	0.692526	−	0.692526i	0.0575112	−	0.0575112i
$146$	3.03315	+	0.839660i	0.251025	+	0.0694907i
$147$		0			0
$148$	7.75406	+	7.03024i	0.637380	+	0.577882i
$149$	−15.3683	−	3.05694i	−1.25902	−	0.250434i	−0.479906	−	0.877320i	$-0.659329\pi$
$149$	−15.3683	−	3.05694i	−1.25902	−	0.250434i	−0.779111	+	0.626886i	$0.784329\pi$
$150$		0			0
$151$	−4.19983	−	10.1393i	−0.341777	−	0.825123i	−0.997536	−	0.0701526i	$-0.977651\pi$
$151$	−4.19983	−	10.1393i	−0.341777	−	0.825123i	0.655759	−	0.754970i	$-0.272349\pi$
$152$	−14.9682	+	9.47327i	−1.21408	+	0.768383i
$153$		0			0
$154$	3.61473	−	1.19381i	0.291283	−	0.0961998i
$155$	0.898822	−	0.600574i	0.0721951	−	0.0482392i
$156$		0			0
$157$	4.25698	+	21.4013i	0.339744	+	1.70801i	0.652174	+	0.758069i	$0.273857\pi$
$157$	4.25698	+	21.4013i	0.339744	+	1.70801i	−0.312430	+	0.949941i	$0.601143\pi$
$158$	1.03049	+	8.36079i	0.0819816	+	0.665148i
$159$		0			0
$160$	−0.631154	−	1.42547i	−0.0498971	−	0.112694i
$161$		−	5.57486i		−	0.439360i
$162$		0			0
$163$	−0.0534145	−	0.268533i	−0.00418374	−	0.0210331i	0.978637	−	0.205596i	$-0.0659132\pi$
$163$	−0.0534145	−	0.268533i	−0.00418374	−	0.0210331i	−0.982821	+	0.184563i	$0.940913\pi$
$164$	−2.74387	+	2.03428i	−0.214260	+	0.158851i
$165$		0			0
$166$	4.61003	+	13.9587i	0.357808	+	1.08340i
$167$	−8.36818	+	20.2026i	−0.647549	+	1.56332i	0.168729	+	0.985662i	$0.446034\pi$
$167$	−8.36818	+	20.2026i	−0.647549	+	1.56332i	−0.816278	+	0.577659i	$0.803966\pi$
$168$		0			0
$169$	−11.3647	−	27.4367i	−0.874204	−	2.11052i
$170$	1.16240	+	1.34777i	0.0891519	+	0.103369i
$171$		0			0
$172$	−0.395531	−	8.07884i	−0.0301589	−	0.616006i
$173$	11.3220	+	7.56510i	0.860793	+	0.575164i	0.905744	−	0.423825i	$-0.139313\pi$
$173$	11.3220	+	7.56510i	0.860793	+	0.575164i	−0.0449505	+	0.998989i	$0.514313\pi$
$174$		0			0
$175$	−3.17743	+	3.17743i	−0.240191	+	0.240191i
$176$	−3.42118	−	11.2918i	−0.257881	−	0.851148i
$177$		0			0
$178$	12.4550	−	7.05432i	0.933545	−	0.528743i
$179$	−3.53996	+	5.29793i	−0.264589	+	0.395986i	−0.939847	−	0.341596i	$-0.889032\pi$
$179$	−3.53996	+	5.29793i	−0.264589	+	0.395986i	0.675258	+	0.737582i	$0.264032\pi$
$180$		0			0
$181$	−1.23356	+	6.20153i	−0.0916898	+	0.460956i	0.907475	+	0.420105i	$0.138007\pi$
$181$	−1.23356	+	6.20153i	−0.0916898	+	0.460956i	−0.999165	+	0.0408508i	$0.986993\pi$
$182$	8.41012	+	0.621076i	0.623399	+	0.0460372i
$183$		0			0
$184$	−17.2734	−	0.428382i	−1.27341	−	0.0315807i
$185$	1.33244	+	0.551916i	0.0979631	+	0.0405776i
$186$		0			0
$187$	7.48356	+	11.1999i	0.547252	+	0.819021i
$188$	−8.31994	−	4.98867i	−0.606794	−	0.363836i
$189$		0			0
$190$	−1.50187	+	1.92414i	−0.108957	+	0.139592i
$191$	12.7011			0.919021			0.459511	−	0.888172i	$-0.348025\pi$
$191$	12.7011			0.919021			0.459511	+	0.888172i	$0.348025\pi$
$192$		0			0
$193$	13.2427			0.953228			0.476614	−	0.879113i	$-0.341864\pi$
$193$	13.2427			0.953228			0.476614	+	0.879113i	$0.341864\pi$
$194$	1.59384	−	2.04197i	0.114431	−	0.146605i
$195$		0			0
$196$	6.34293	−	10.5785i	0.453066	−	0.755609i
$197$	−4.91763	−	7.35976i	−0.350367	−	0.524361i	0.613869	−	0.789408i	$-0.289612\pi$
$197$	−4.91763	−	7.35976i	−0.350367	−	0.524361i	−0.964235	+	0.265047i	$0.914612\pi$
$198$		0			0
$199$	1.07833	+	0.446660i	0.0764410	+	0.0316629i	0.420576	−	0.907257i	$-0.361828\pi$
$199$	1.07833	+	0.446660i	0.0764410	+	0.0316629i	−0.344135	+	0.938920i	$0.611828\pi$
$200$	9.60092	+	10.0892i	0.678887	+	0.713417i
$201$		0			0
$202$	−0.965267	−	0.0712837i	−0.0679160	−	0.00501550i
$203$	−0.632700	+	3.18080i	−0.0444068	+	0.223248i
$204$		0			0
$205$	−0.261486	+	0.391341i	−0.0182630	+	0.0273325i
$206$	−3.31215	+	1.87594i	−0.230768	+	0.130703i
$207$		0			0
$208$	2.57062	−	26.0105i	0.178240	−	1.80351i
$209$	−13.0627	+	13.0627i	−0.903565	+	0.903565i
$210$		0			0
$211$	9.00912	+	6.01970i	0.620213	+	0.414413i	0.825591	−	0.564270i	$-0.190842\pi$
$211$	9.00912	+	6.01970i	0.620213	+	0.414413i	−0.205377	+	0.978683i	$0.565842\pi$
$212$	3.29540	−	0.161339i	0.226329	−	0.0110808i
$213$		0			0
$214$	11.6724	+	13.5339i	0.797912	+	0.925158i
$215$	−0.426517	−	1.02970i	−0.0290882	−	0.0702251i
$216$		0			0
$217$	−1.36986	+	3.30714i	−0.0929924	+	0.224504i
$218$	−2.72763	−	8.25897i	−0.184738	−	0.559368i
$219$		0			0
$220$	−0.968253	−	1.30600i	−0.0652796	−	0.0880502i
$221$	5.82147	+	29.2665i	0.391594	+	1.96868i
$222$		0			0
$223$			13.6571i			0.914545i	0.889327	+	0.457273i	$0.151174\pi$
$223$			13.6571i			0.914545i	−0.889327	+	0.457273i	$0.848826\pi$
$224$	4.36023	+	2.76364i	0.291330	+	0.184654i
$225$		0			0
$226$	−1.67254	−	13.5699i	−0.111256	−	0.902659i
$227$	0.0149278	+	0.0750473i	0.000990796	+	0.00498107i	0.981278	−	0.192599i	$-0.0616917\pi$
$227$	0.0149278	+	0.0750473i	0.000990796	+	0.00498107i	−0.980287	+	0.197580i	$0.936692\pi$
$228$		0			0
$229$	−3.11926	+	2.08423i	−0.206127	+	0.137730i	−0.654349	−	0.756193i	$-0.727057\pi$
$229$	−3.11926	+	2.08423i	−0.206127	+	0.137730i	0.448222	+	0.893922i	$0.352057\pi$
$230$	−2.26078	+	0.746650i	−0.149071	+	0.0492326i
$231$		0			0
$232$	9.80690	+	2.20480i	0.643854	+	0.144752i
$233$	−5.43841	−	13.1295i	−0.356282	−	0.860141i	−0.995816	−	0.0913785i	$-0.970873\pi$
$233$	−5.43841	−	13.1295i	−0.356282	−	0.860141i	0.639534	−	0.768763i	$-0.279127\pi$
$234$		0			0
$235$	−1.31104	−	0.260782i	−0.0855226	−	0.0170115i
$236$	8.30122	−	9.15590i	0.540363	−	0.595998i
$237$		0			0
$238$	−5.67997	−	1.57237i	−0.368178	−	0.101922i
$239$	18.6031	−	18.6031i	1.20333	−	1.20333i	0.230186	−	0.973147i	$-0.426066\pi$
$239$	18.6031	−	18.6031i	1.20333	−	1.20333i	0.973147	−	0.230186i	$-0.0739335\pi$
$240$		0			0
$241$	−8.43324	−	8.43324i	−0.543233	−	0.543233i	0.381242	−	0.924475i	$-0.375496\pi$
$241$	−8.43324	−	8.43324i	−0.543233	−	0.543233i	−0.924475	+	0.381242i	$0.875496\pi$
$242$	1.60265	+	2.82963i	0.103022	+	0.181895i
$243$		0			0
$244$	10.0739	+	21.3088i	0.644918	+	1.36416i
$245$	0.331575	−	1.66694i	0.0211836	−	0.106497i
$246$		0			0
$247$	−37.8086	+	15.6608i	−2.40570	+	0.996475i
$248$	10.1417	+	4.49857i	0.644001	+	0.285660i
$249$		0			0
$250$	3.45465	+	1.73929i	0.218491	+	0.110002i
$251$	−3.56767	−	5.33939i	−0.225189	−	0.337019i	0.701621	−	0.712551i	$-0.252460\pi$
$251$	−3.56767	−	5.33939i	−0.225189	−	0.337019i	−0.926810	+	0.375532i	$0.877460\pi$
$252$		0			0
$253$	−17.6731	+	3.51539i	−1.11110	+	0.221011i
$254$	−12.7731	−	9.96994i	−0.801455	−	0.625570i
$255$		0			0
$256$	8.89804	−	13.2976i	0.556127	−	0.831097i
$257$	−22.6435			−1.41246			−0.706230	−	0.707982i	$-0.749606\pi$
$257$	−22.6435			−1.41246			−0.706230	+	0.707982i	$0.749606\pi$
$258$		0			0
$259$	−4.68401	+	0.931707i	−0.291050	+	0.0578934i
$260$	−0.874516	−	3.49375i	−0.0542352	−	0.216673i
$261$		0			0
$262$	−3.06419	−	1.54271i	−0.189306	−	0.0953086i
$263$	4.08591	+	1.69244i	0.251948	+	0.104360i	0.505083	−	0.863071i	$-0.331462\pi$
$263$	4.08591	+	1.69244i	0.251948	+	0.104360i	−0.253135	+	0.967431i	$0.581462\pi$
$264$		0			0
$265$	0.420021	−	0.173978i	0.0258017	−	0.0106874i
$266$	0.595278	−	8.06078i	0.0364989	−	0.494238i
$267$		0			0
$268$	6.01466	+	12.7225i	0.367404	+	0.777147i
$269$	−0.00106182	+	0.00158913i	−6.47403e−5	+	9.68908e-5i	−0.831502	−	0.555522i	$-0.812519\pi$
$269$	−0.00106182	+	0.00158913i	−6.47403e−5	+	9.68908e-5i	0.831437	+	0.555619i	$0.187519\pi$
$270$		0			0
$271$	−19.1266	−	19.1266i	−1.16186	−	1.16186i	−0.984069	−	0.177788i	$-0.943106\pi$
$271$	−19.1266	−	19.1266i	−1.16186	−	1.16186i	−0.177788	−	0.984069i	$-0.556894\pi$
$272$	−5.30836	+	17.4782i	−0.321867	+	1.05977i
$273$		0			0
$274$	31.3318	+	8.67350i	1.89282	+	0.523985i
$275$	12.0765	+	8.06927i	0.728241	+	0.486595i
$276$		0			0
$277$	−24.9785	−	4.96854i	−1.50082	−	0.298531i	−0.624789	−	0.780794i	$-0.714815\pi$
$277$	−24.9785	−	4.96854i	−1.50082	−	0.298531i	−0.876026	+	0.482263i	$0.839815\pi$
$278$	−10.5711	+	9.11719i	−0.634015	+	0.546813i
$279$		0			0
$280$	0.694006	+	0.156027i	0.0414748	+	0.00932443i
$281$	−8.84989	+	21.3655i	−0.527940	+	1.27456i	0.404930	+	0.914348i	$0.367296\pi$
$281$	−8.84989	+	21.3655i	−0.527940	+	1.27456i	−0.932870	+	0.360213i	$0.882704\pi$
$282$		0			0
$283$	0.552579	−	0.369221i	0.0328474	−	0.0219479i	−0.539038	−	0.842281i	$-0.681212\pi$
$283$	0.552579	−	0.369221i	0.0328474	−	0.0219479i	0.571886	+	0.820333i	$0.306212\pi$
$284$	0.807379	−	5.43663i	0.0479091	−	0.322605i
$285$		0			0
$286$	−3.33435	−	27.0529i	−0.197164	−	1.59967i
$287$		−	1.55855i		−	0.0919981i
$288$		0			0
$289$		−	3.85420i		−	0.226718i
$290$	1.37465	−	0.169430i	0.0807223	−	0.00994928i
$291$		0			0
$292$	2.65077	+	3.57540i	0.155125	+	0.209235i
$293$	14.0919	−	9.41592i	0.823259	−	0.550084i	−0.0710819	−	0.997470i	$-0.522645\pi$
$293$	14.0919	−	9.41592i	0.823259	−	0.550084i	0.894341	+	0.447387i	$0.147645\pi$
$294$		0			0
$295$	0.651695	−	1.57333i	0.0379432	−	0.0916029i
$296$	2.52691	+	14.5847i	0.146874	+	0.847720i
$297$		0			0
$298$	−14.4728	−	16.7808i	−0.838386	−	0.972087i
$299$	−39.1507	−	7.78756i	−2.26414	−	0.450366i
$300$		0			0
$301$	3.06869	+	2.05043i	0.176876	+	0.118185i
$302$	4.14078	−	14.9580i	0.238275	−	0.860735i
$303$		0			0
$304$	−24.9301	−	2.46384i	−1.42984	−	0.141311i
$305$	2.29654	+	2.29654i	0.131499	+	0.131499i
$306$		0			0
$307$	11.9514	−	17.8865i	0.682100	−	1.02083i	−0.315316	−	0.948987i	$-0.602110\pi$
$307$	11.9514	−	17.8865i	0.682100	−	1.02083i	0.997416	−	0.0718479i	$-0.0228896\pi$
$308$	5.06857	+	1.81452i	0.288808	+	0.103392i
$309$		0			0
$310$	1.52462	+	0.112591i	0.0865925	+	0.00639474i
$311$	−28.0762	+	11.6295i	−1.59205	+	0.659450i	−0.990264	−	0.139204i	$-0.955545\pi$
$311$	−28.0762	+	11.6295i	−1.59205	+	0.659450i	−0.601790	+	0.798655i	$0.705545\pi$
$312$		0			0
$313$	6.79018	+	2.81259i	0.383804	+	0.158977i	0.566239	−	0.824241i	$-0.308398\pi$
$313$	6.79018	+	2.81259i	0.383804	+	0.158977i	−0.182435	+	0.983218i	$0.558398\pi$
$314$	−13.8768	+	27.5628i	−0.783116	+	1.55546i
$315$		0			0
$316$	−6.12643	+	10.2174i	−0.344639	+	0.574776i
$317$	−19.5241	+	3.88359i	−1.09658	+	0.218124i	−0.710051	−	0.704151i	$-0.751328\pi$
$317$	−19.5241	+	3.88359i	−1.09658	+	0.218124i	−0.386534	+	0.922275i	$0.626328\pi$
$318$		0			0
$319$	10.4825			0.586909
$320$	0.536771	−	2.13835i	0.0300064	−	0.119537i
$321$		0			0
$322$	4.85103	−	6.21495i	0.270337	−	0.346345i
$323$	28.0509	−	5.57966i	1.56079	−	0.310461i
$324$		0			0
$325$	17.8756	+	26.7528i	0.991562	+	1.48398i
$326$	0.174120	−	0.345844i	0.00964360	−	0.0191545i
$327$		0			0
$328$	−4.82907	−	0.119762i	−0.266641	−	0.00661273i
$329$	4.08947	−	1.69391i	0.225460	−	0.0933885i
$330$		0			0
$331$	2.07742	−	10.4439i	0.114185	−	0.574049i	−0.880754	−	0.473574i	$-0.842964\pi$
$331$	2.07742	−	10.4439i	0.114185	−	0.574049i	0.994940	−	0.100475i	$-0.0320363\pi$
$332$	−7.00698	+	19.5729i	−0.384558	+	1.07420i
$333$		0			0
$334$	−26.9085	+	15.2405i	−1.47237	+	0.833923i
$335$	1.37115	+	1.37115i	0.0749140	+	0.0749140i
$336$		0			0
$337$	−9.26878	+	9.26878i	−0.504902	+	0.504902i	−0.912957	−	0.408055i	$-0.866207\pi$
$337$	−9.26878	+	9.26878i	−0.504902	+	0.504902i	0.408055	+	0.912957i	$0.366207\pi$
$338$	11.2049	−	40.4760i	0.609465	−	2.20160i
$339$		0			0
$340$	0.123082	+	2.51399i	0.00667508	+	0.136341i
$341$	11.3479	+	2.25724i	0.614524	+	0.122236i
$342$		0			0
$343$	4.59834	+	11.1014i	0.248287	+	0.599418i
$344$	6.58896	−	9.35061i	0.355253	−	0.504151i
$345$		0			0
$346$	6.03906	+	18.2857i	0.324662	+	0.983043i
$347$	−6.76125	+	4.51772i	−0.362963	+	0.242524i	−0.723656	−	0.690160i	$-0.757540\pi$
$347$	−6.76125	+	4.51772i	−0.362963	+	0.242524i	0.360694	+	0.932684i	$0.382540\pi$
$348$		0			0
$349$	2.20654	+	11.0931i	0.118114	+	0.593797i	0.993825	+	0.110962i	$0.0353931\pi$
$349$	2.20654	+	11.0931i	0.118114	+	0.593797i	−0.875711	+	0.482836i	$0.839607\pi$
$350$	−6.30713	+	0.777374i	−0.337130	+	0.0415524i
$351$		0			0
$352$	6.01166	−	15.5652i	0.320423	−	0.829629i
$353$			2.13438i			0.113602i	0.998386	+	0.0568008i	$0.0180900\pi$
$353$			2.13438i			0.113602i	−0.998386	+	0.0568008i	$0.981910\pi$
$354$		0			0
$355$	−0.147751	−	0.742794i	−0.00784180	−	0.0394234i
$356$	20.0235	+	2.97363i	1.06124	+	0.157602i
$357$		0			0
$358$	−8.55647	+	2.82588i	−0.452223	+	0.149352i
$359$	1.13471	−	2.73943i	0.0598876	−	0.144581i	−0.891103	−	0.453801i	$-0.850068\pi$
$359$	1.13471	−	2.73943i	0.0598876	−	0.144581i	0.950991	+	0.309219i	$0.100068\pi$
$360$		0			0
$361$	7.73934	+	18.6844i	0.407334	+	0.983391i
$362$	−6.77153	+	5.84017i	−0.355904	+	0.306953i
$363$		0			0
$364$	8.83531	+	8.01055i	0.463096	+	0.419867i
$365$	0.509937	+	0.340729i	0.0266913	+	0.0178346i
$366$		0			0
$367$	8.53257	−	8.53257i	0.445396	−	0.445396i	−0.448424	−	0.893821i	$-0.648015\pi$
$367$	8.53257	−	8.53257i	0.445396	−	0.445396i	0.893821	+	0.448424i	$0.148015\pi$
$368$	−18.8839	−	15.5082i	−0.984391	−	0.808421i
$369$		0			0
$370$	1.00517	+	1.77473i	0.0522565	+	0.0922636i
$371$	−0.836382	+	1.25173i	−0.0434228	+	0.0649868i
$372$		0			0
$373$	1.44487	−	7.26383i	0.0748123	−	0.376107i	−0.925182	−	0.379524i	$-0.876088\pi$
$373$	1.44487	−	7.26383i	0.0748123	−	0.376107i	0.999994	+	0.00341725i	$0.00108775\pi$
$374$	−1.40296	+	18.9978i	−0.0725454	+	0.982353i
$375$		0			0
$376$	−4.93425	−	12.8012i	−0.254465	−	0.660169i
$377$	21.4540	+	8.88656i	1.10494	+	0.457681i
$378$		0			0
$379$	−18.0363	−	26.9933i	−0.926464	−	1.38655i	−0.922264	−	0.386560i	$-0.873663\pi$
$379$	−18.0363	−	26.9933i	−0.926464	−	1.38655i	−0.00420008	−	0.999991i	$-0.501337\pi$
$380$	−3.34863	+	0.838191i	−0.171781	+	0.0429983i
$381$		0			0
$382$	14.1594	+	11.0520i	0.724460	+	0.565471i
$383$	−34.5409			−1.76496			−0.882479	−	0.470351i	$-0.844127\pi$
$383$	−34.5409			−1.76496			−0.882479	+	0.470351i	$0.844127\pi$
$384$		0			0
$385$	0.741819			0.0378066
$386$	14.7631	+	11.5233i	0.751424	+	0.586519i
$387$		0			0
$388$	3.55368	−	0.889518i	0.180411	−	0.0451584i
$389$	−7.37213	−	11.0332i	−0.373782	−	0.559404i	0.596121	−	0.802894i	$-0.296708\pi$
$389$	−7.37213	−	11.0332i	−0.373782	−	0.559404i	−0.969903	+	0.243490i	$0.921708\pi$
$390$		0			0
$391$	25.7738	+	10.6758i	1.30344	+	0.539900i
$392$	16.2762	−	6.27374i	0.822074	−	0.316872i
$393$		0			0
$394$	0.921921	−	12.4839i	0.0464457	−	0.628931i
$395$	−0.320257	+	1.61004i	−0.0161139	+	0.0810100i
$396$		0			0
$397$	−2.85471	+	4.27237i	−0.143274	+	0.214424i	−0.896165	−	0.443720i	$-0.853658\pi$
$397$	−2.85471	+	4.27237i	−0.143274	+	0.214424i	0.752892	+	0.658144i	$0.228658\pi$
$398$	0.813478	+	1.43627i	0.0407760	+	0.0719937i
$399$		0			0
$400$	1.92400	+	19.6020i	0.0961998	+	0.980101i
$401$	−4.16307	+	4.16307i	−0.207894	+	0.207894i	−0.803372	−	0.595478i	$-0.796963\pi$
$401$	−4.16307	+	4.16307i	−0.207894	+	0.207894i	0.595478	+	0.803372i	$0.296963\pi$
$402$		0			0
$403$	21.3116	+	14.2400i	1.06161	+	0.709343i
$404$	−1.01407	−	0.919407i	−0.0504518	−	0.0457422i
$405$		0			0
$406$	−3.47315	+	2.99546i	−0.172370	+	0.148662i
$407$	5.90728	+	14.2614i	0.292813	+	0.706913i
$408$		0			0
$409$	1.24674	−	3.00991i	0.0616475	−	0.148830i	−0.890054	−	0.455855i	$-0.849333\pi$
$409$	1.24674	−	3.00991i	0.0616475	−	0.148830i	0.951701	+	0.307025i	$0.0993335\pi$
$410$	−0.632039	+	0.208739i	−0.0312142	+	0.0103089i
$411$		0			0
$412$	−5.32481	−	0.790773i	−0.262335	−	0.0389586i
$413$	1.10015	+	5.53082i	0.0541348	+	0.272154i
$414$		0			0
$415$			2.86462i			0.140619i
$416$	25.4992	−	26.7601i	1.25020	−	1.31202i
$417$		0			0
$418$	−25.9292	+	3.19585i	−1.26824	+	0.156314i
$419$	1.34847	+	6.77921i	0.0658771	+	0.331186i	0.999644	−	0.0266964i	$-0.00849875\pi$
$419$	1.34847	+	6.77921i	0.0658771	+	0.331186i	−0.933767	+	0.357883i	$0.883499\pi$
$420$		0			0
$421$	4.37453	−	2.92296i	0.213201	−	0.142457i	−0.444385	−	0.895836i	$-0.646578\pi$
$421$	4.37453	−	2.92296i	0.213201	−	0.142457i	0.657586	+	0.753380i	$0.271578\pi$
$422$	4.80540	+	14.5503i	0.233923	+	0.708295i
$423$		0			0
$424$	3.81416	+	2.68767i	0.185232	+	0.130525i
$425$	−8.60516	−	20.7747i	−0.417412	−	1.00772i
$426$		0			0
$427$	−10.5481	−	2.09814i	−0.510457	−	0.101536i
$428$	1.23595	+	25.2447i	0.0597421	+	1.22025i
$429$		0			0
$430$	0.420520	−	1.51907i	0.0202793	−	0.0732560i
$431$	14.3235	−	14.3235i	0.689941	−	0.689941i	−0.272278	−	0.962219i	$-0.587777\pi$
$431$	14.3235	−	14.3235i	0.689941	−	0.689941i	0.962219	+	0.272278i	$0.0877770\pi$
$432$		0			0
$433$	−8.31597	−	8.31597i	−0.399640	−	0.399640i	0.478466	−	0.878106i	$-0.341193\pi$
$433$	−8.31597	−	8.31597i	−0.399640	−	0.399640i	−0.878106	+	0.478466i	$0.841193\pi$
$434$	−4.40490	+	2.49486i	−0.211442	+	0.119757i
$435$		0			0
$436$	4.14584	−	11.5807i	0.198550	−	0.554616i
$437$	−7.46409	+	37.5245i	−0.357056	+	1.79504i
$438$		0			0
$439$	−14.3157	+	5.92976i	−0.683251	+	0.283012i	−0.697185	−	0.716891i	$-0.745564\pi$
$439$	−14.3157	+	5.92976i	−0.683251	+	0.283012i	0.0139342	+	0.999903i	$0.495564\pi$
$440$	0.0570027	−	2.29848i	0.00271750	−	0.109576i
$441$		0			0
$442$	−18.9767	+	37.6924i	−0.902631	+	1.79285i
$443$	−3.72766	−	5.57883i	−0.177106	−	0.265058i	0.732287	−	0.680997i	$-0.238453\pi$
$443$	−3.72766	−	5.57883i	−0.177106	−	0.265058i	−0.909393	+	0.415938i	$0.863453\pi$
$444$		0			0
$445$	2.73576	−	0.544177i	0.129688	−	0.0257965i
$446$	−11.8839	+	15.2251i	−0.562718	+	0.720931i
$447$		0			0
$448$	2.45604	+	6.87506i	0.116037	+	0.324816i
$449$	12.1738			0.574519			0.287259	−	0.957853i	$-0.407256\pi$
$449$	12.1738			0.574519			0.287259	+	0.957853i	$0.407256\pi$
$450$		0			0
$451$	−4.94081	+	0.982788i	−0.232654	+	0.0462777i
$452$	9.94348	−	16.5834i	0.467702	−	0.780017i
$453$		0			0
$454$	−0.0486615	+	0.0966537i	−0.00228380	+	0.00453618i
$455$	1.51824	+	0.628876i	0.0711763	+	0.0294822i
$456$		0			0
$457$	21.6386	−	8.96300i	1.01221	−	0.419271i	0.185950	−	0.982559i	$-0.440464\pi$
$457$	21.6386	−	8.96300i	1.01221	−	0.419271i	0.826261	+	0.563288i	$0.190464\pi$
$458$	−5.29103	−	0.390735i	−0.247233	−	0.0182579i
$459$		0			0
$460$	−3.17006	−	1.13487i	−0.147805	−	0.0529134i
$461$	−3.40229	+	5.09189i	−0.158461	+	0.237153i	−0.902201	−	0.431315i	$-0.858050\pi$
$461$	−3.40229	+	5.09189i	−0.158461	+	0.237153i	0.743741	+	0.668468i	$0.233050\pi$
$462$		0			0
$463$	−8.70982	−	8.70982i	−0.404780	−	0.404780i	0.475134	−	0.879914i	$-0.342400\pi$
$463$	−8.70982	−	8.70982i	−0.404780	−	0.404780i	−0.879914	+	0.475134i	$0.842400\pi$
$464$	9.01436	+	10.9915i	0.418481	+	0.510270i
$465$		0			0
$466$	5.36195	−	19.3693i	0.248388	−	0.897265i
$467$	5.86536	+	3.91911i	0.271416	+	0.181355i	0.683829	−	0.729643i	$-0.260314\pi$
$467$	5.86536	+	3.91911i	0.271416	+	0.181355i	−0.412412	+	0.910997i	$0.635314\pi$
$468$		0			0
$469$	−6.29775	−	1.25270i	−0.290803	−	0.0578443i
$470$	−1.23464	−	1.43154i	−0.0569499	−	0.0660320i
$471$		0			0
$472$	17.2215	−	2.98375i	0.792682	−	0.137338i
$473$	4.56511	−	11.0211i	0.209904	−	0.506753i
$474$		0			0
$475$	25.6416	−	17.1331i	1.17652	−	0.786122i
$476$	−4.96391	−	6.69540i	−0.227520	−	0.306883i
$477$		0			0
$478$	36.9267	−	4.55134i	1.68899	−	0.208173i
$479$		−	26.1701i		−	1.19574i	−0.801592	−	0.597871i	$-0.796013\pi$
$479$		−	26.1701i		−	1.19574i	0.801592	−	0.597871i	$-0.203987\pi$
$480$		0			0
$481$			34.1960i			1.55920i
$482$	−2.06323	−	16.7398i	−0.0939778	−	0.762477i
$483$		0			0
$484$	−0.675572	+	4.54908i	−0.0307078	+	0.206777i
$485$	0.419709	−	0.280441i	0.0190580	−	0.0127342i
$486$		0			0
$487$	11.8872	−	28.6983i	0.538662	−	1.30044i	−0.386996	−	0.922082i	$-0.626487\pi$
$487$	11.8872	−	28.6983i	0.538662	−	1.30044i	0.925657	−	0.378363i	$-0.123513\pi$
$488$	−7.31151	+	32.5214i	−0.330976	+	1.47217i
$489$		0			0
$490$	1.82015	−	1.56981i	0.0822262	−	0.0709168i
$491$	26.5981	+	5.29070i	1.20036	+	0.238766i	0.754476	−	0.656327i	$-0.227891\pi$
$491$	26.5981	+	5.29070i	1.20036	+	0.238766i	0.445880	+	0.895093i	$0.352891\pi$
$492$		0			0
$493$	−13.4939	−	9.01633i	−0.607734	−	0.406075i
$494$	−55.7772	−	15.4407i	−2.50953	−	0.694708i
$495$		0			0
$496$	7.39169	+	13.8400i	0.331897	+	0.621436i
$497$	1.77333	+	1.77333i	0.0795448	+	0.0795448i
$498$		0			0
$499$	11.9390	−	17.8680i	0.534462	−	0.799879i	−0.461734	−	0.887019i	$-0.652772\pi$
$499$	11.9390	−	17.8680i	0.534462	−	0.799879i	0.996196	+	0.0871391i	$0.0277725\pi$
$500$	2.33784	+	4.94509i	0.104551	+	0.221151i
$501$		0			0
$502$	0.668839	−	9.05689i	0.0298518	−	0.404229i
$503$	28.1800	−	11.6725i	1.25649	−	0.520453i	0.347656	−	0.937622i	$-0.386978\pi$
$503$	28.1800	−	11.6725i	1.25649	−	0.520453i	0.908829	+	0.417169i	$0.136978\pi$
$504$		0			0
$505$	−0.174255	−	0.0721790i	−0.00775427	−	0.00321192i
$506$	−22.7612	−	11.4594i	−1.01186	−	0.509433i
$507$		0			0
$508$	−5.56420	−	22.2293i	−0.246871	−	0.986266i
$509$	23.3694	−	4.64846i	1.03583	−	0.206039i	0.352243	−	0.935908i	$-0.385419\pi$
$509$	23.3694	−	4.64846i	1.03583	−	0.206039i	0.683587	+	0.729869i	$0.260419\pi$
$510$		0			0
$511$	−2.03087			−0.0898402
$512$	21.4907	−	7.08160i	0.949764	−	0.312966i
$513$		0			0
$514$	−25.2433	−	19.7035i	−1.11344	−	0.869083i
$515$	−0.727516	+	0.144712i	−0.0320582	+	0.00637677i
$516$		0			0
$517$	−7.94868	−	11.8960i	−0.349583	−	0.523187i
$518$	−6.03255	−	3.03716i	−0.265055	−	0.133445i
$519$		0			0
$520$	2.06520	−	4.65586i	0.0905651	−	0.204173i
$521$	−5.84704	+	2.42192i	−0.256163	+	0.106106i	−0.507070	−	0.861905i	$-0.669271\pi$
$521$	−5.84704	+	2.42192i	−0.256163	+	0.106106i	0.250906	+	0.968011i	$0.419271\pi$
$522$		0			0
$523$	−5.95365	+	29.9310i	−0.260335	+	1.30879i	0.600384	+	0.799712i	$0.295014\pi$
$523$	−5.95365	+	29.9310i	−0.260335	+	1.30879i	−0.860719	+	0.509080i	$0.829986\pi$
$524$	−2.07361	−	4.38618i	−0.0905860	−	0.191611i
$525$		0			0
$526$	3.08234	+	5.44216i	0.134397	+	0.237289i
$527$	−12.6664	−	12.6664i	−0.551755	−	0.551755i
$528$		0			0
$529$	−10.1251	+	10.1251i	−0.440223	+	0.440223i
$530$	0.619635	+	0.171532i	0.0269152	+	0.00745088i
$531$		0			0
$532$	7.67782	−	8.46831i	0.332876	−	0.367148i
$533$	−10.9453	−	2.17715i	−0.474092	−	0.0943027i
$534$		0			0
$535$	1.33278	+	3.21761i	0.0576210	+	0.139109i
$536$	−4.36535	+	19.4169i	−0.188554	+	0.838684i
$537$		0			0
$538$	−0.00256653		0.000847630i	−0.000110651		3.65439e-5i
$539$	15.1254	−	10.1065i	0.651498	−	0.435317i
$540$		0			0
$541$	3.06081	+	15.3877i	0.131594	+	0.661570i	0.989118	+	0.147125i	$0.0470020\pi$
$541$	3.06081	+	15.3877i	0.131594	+	0.661570i	−0.857523	+	0.514445i	$0.827998\pi$
$542$	−4.67941	−	37.9659i	−0.200998	−	1.63077i
$543$		0			0
$544$	−21.1268	+	14.8659i	−0.905802	+	0.637370i
$545$		−	1.69492i		−	0.0726023i
$546$		0			0
$547$	3.60776	+	18.1374i	0.154257	+	0.775500i	0.978011	+	0.208553i	$0.0668755\pi$
$547$	3.60776	+	18.1374i	0.154257	+	0.775500i	−0.823754	+	0.566947i	$0.808125\pi$
$548$	27.3819	+	36.9331i	1.16970	+	1.57770i
$549$		0			0
$550$	6.44153	+	19.5043i	0.274668	+	0.831665i
$551$	8.51743	−	20.5629i	0.362855	−	0.876009i
$552$		0			0
$553$	−2.08024	−	5.02215i	−0.0884609	−	0.213563i
$554$	−23.5231	−	27.2744i	−0.999400	−	1.15878i
$555$		0			0
$556$	−19.7183	+	0.965387i	−0.836244	+	0.0409415i
$557$	3.89299	+	2.60121i	0.164951	+	0.110217i	0.635306	−	0.772261i	$-0.280874\pi$
$557$	3.89299	+	2.60121i	0.164951	+	0.110217i	−0.470355	+	0.882477i	$0.655874\pi$
$558$		0			0
$559$	18.6863	−	18.6863i	0.790347	−	0.790347i
$560$	0.637921	+	0.777840i	0.0269571	+	0.0328697i
$561$		0			0
$562$	−28.4575	+	16.1178i	−1.20041	+	0.679889i
$563$	11.9617	−	17.9019i	0.504124	−	0.754475i	−0.488906	−	0.872336i	$-0.662604\pi$
$563$	11.9617	−	17.9019i	0.504124	−	0.754475i	0.993030	+	0.117862i	$0.0376039\pi$
$564$		0			0
$565$	0.519793	−	2.61317i	0.0218678	−	0.109937i
$566$	0.937307	+	0.0692189i	0.0393980	+	0.00290949i
$567$		0			0
$568$	5.63083	−	5.35830i	0.236264	−	0.224829i
$569$	−3.57864	−	1.48232i	−0.150024	−	0.0621422i	0.306408	−	0.951900i	$-0.400873\pi$
$569$	−3.57864	−	1.48232i	−0.150024	−	0.0621422i	−0.456432	+	0.889758i	$0.650873\pi$
$570$		0			0
$571$	−3.89635	−	5.83130i	−0.163057	−	0.244032i	0.740940	−	0.671572i	$-0.234381\pi$
$571$	−3.89635	−	5.83130i	−0.163057	−	0.244032i	−0.903997	+	0.427539i	$0.859381\pi$
$572$	19.8232	−	33.0604i	0.828850	−	1.38233i
$573$		0			0
$574$	1.35619	−	1.73750i	0.0566062	−	0.0725216i
$575$	30.0807			1.25445
$576$		0			0
$577$	11.5627			0.481361			0.240680	−	0.970604i	$-0.422629\pi$
$577$	11.5627			0.481361			0.240680	+	0.970604i	$0.422629\pi$
$578$	3.35378	−	4.29673i	0.139499	−	0.178721i
$579$		0			0
$580$	1.67992	+	1.00729i	0.0697547	+	0.0418253i
$581$	−5.27007	−	7.88722i	−0.218640	−	0.327217i
$582$		0			0
$583$	4.49558	+	1.86213i	0.186188	+	0.0771215i
$584$	−0.156055	+	6.29252i	−0.00645761	+	0.260386i
$585$		0			0
$586$	23.9033	+	1.76523i	0.987436	+	0.0729208i
$587$	2.87452	−	14.4512i	0.118644	−	0.596464i	−0.875021	−	0.484084i	$-0.839153\pi$
$587$	2.87452	−	14.4512i	0.118644	−	0.596464i	0.993665	−	0.112380i	$-0.0358473\pi$
$588$		0			0
$589$	13.6485	−	20.4264i	0.562376	−	0.841655i
$590$	2.09558	−	1.18690i	0.0862735	−	0.0488638i
$591$		0			0
$592$	−9.87403	+	18.4581i	−0.405820	+	0.758624i
$593$	−25.9026	+	25.9026i	−1.06369	+	1.06369i	−0.0658644	+	0.997829i	$0.520980\pi$
$593$	−25.9026	+	25.9026i	−1.06369	+	1.06369i	−0.997829	+	0.0658644i	$0.979020\pi$
$594$		0			0
$595$	−0.954924	−	0.638060i	−0.0391481	−	0.0261579i
$596$	−1.53247	−	31.3012i	−0.0627725	−	1.28215i
$597$		0			0
$598$	−36.8694	−	42.7492i	−1.50770	−	1.74814i
$599$	−15.4679	−	37.3427i	−0.632000	−	1.52578i	−0.837105	−	0.547043i	$-0.815754\pi$
$599$	−15.4679	−	37.3427i	−0.632000	−	1.52578i	0.205105	−	0.978740i	$-0.434246\pi$
$600$		0			0
$601$	1.55993	−	3.76600i	0.0636308	−	0.153618i	−0.888866	−	0.458168i	$-0.848506\pi$
$601$	1.55993	−	3.76600i	0.0636308	−	0.153618i	0.952497	+	0.304549i	$0.0985059\pi$
$602$	1.63682	+	4.95612i	0.0667118	+	0.201996i
$603$		0			0
$604$	17.6321	−	13.0723i	0.717439	−	0.531903i
$605$	0.123630	+	0.621530i	0.00502628	+	0.0252688i
$606$		0			0
$607$		−	23.7080i		−	0.962278i	−0.876644	−	0.481139i	$-0.840223\pi$
$607$		−	23.7080i		−	0.962278i	0.876644	−	0.481139i	$-0.159777\pi$
$608$	−25.6486	−	24.4400i	−1.04019	−	0.991173i
$609$		0			0
$610$	0.561860	+	4.55858i	0.0227490	+	0.184572i
$611$	−6.18329	−	31.0855i	−0.250149	−	1.25758i
$612$		0			0
$613$	20.1792	−	13.4833i	0.815031	−	0.544587i	−0.0767514	−	0.997050i	$-0.524455\pi$
$613$	20.1792	−	13.4833i	0.815031	−	0.544587i	0.891783	+	0.452464i	$0.149455\pi$
$614$	28.8877	−	9.54053i	1.16581	−	0.385024i
$615$		0			0
$616$	4.07160	+	6.43333i	0.164049	+	0.259206i
$617$	5.64022	+	13.6167i	0.227067	+	0.548187i	0.995818	−	0.0913607i	$-0.0291216\pi$
$617$	5.64022	+	13.6167i	0.227067	+	0.548187i	−0.768751	+	0.639548i	$0.779122\pi$
$618$		0			0
$619$	−22.0029	−	4.37665i	−0.884371	−	0.175912i	−0.268048	−	0.963406i	$-0.586379\pi$
$619$	−22.0029	−	4.37665i	−0.884371	−	0.175912i	−0.616323	+	0.787493i	$0.711379\pi$
$620$	1.60170	+	1.45218i	0.0643258	+	0.0583211i
$621$		0			0
$622$	−41.4194	−	11.4660i	−1.66077	−	0.459746i
$623$	−6.53131	+	6.53131i	−0.261671	+	0.261671i
$624$		0			0
$625$	−16.8762	−	16.8762i	−0.675048	−	0.675048i
$626$	5.12241	+	9.04408i	0.204733	+	0.361474i
$627$		0			0
$628$	−39.4543	+	18.6524i	−1.57440	+	0.744311i
$629$	4.66238	−	23.4394i	0.185901	−	0.934590i
$630$		0			0
$631$	−4.18674	+	1.73421i	−0.166672	+	0.0690376i	−0.464459	−	0.885595i	$-0.653751\pi$
$631$	−4.18674	+	1.73421i	−0.166672	+	0.0690376i	0.297788	+	0.954632i	$0.403751\pi$
$632$	−15.7207	+	6.05960i	−0.625335	+	0.241038i
$633$		0			0
$634$	−25.1452	−	12.6597i	−0.998644	−	0.502780i
$635$	−1.75424	−	2.62540i	−0.0696148	−	0.104186i
$636$		0			0
$637$	39.5242	−	7.86184i	1.56600	−	0.311498i
$638$	11.6861	+	9.12151i	0.462658	+	0.361124i
$639$		0			0
$640$	2.45911	−	1.91679i	0.0972049	−	0.0757678i
$641$	34.6244			1.36758			0.683791	−	0.729678i	$-0.260330\pi$
$641$	34.6244			1.36758			0.683791	+	0.729678i	$0.260330\pi$
$642$		0			0
$643$	−28.9603	+	5.76055i	−1.14208	+	0.227174i	−0.729654	−	0.683817i	$-0.760319\pi$
$643$	−28.9603	+	5.76055i	−1.14208	+	0.227174i	−0.412427	+	0.910991i	$0.635319\pi$
$644$	10.8160	−	2.70735i	0.426211	−	0.106684i
$645$		0			0
$646$	36.1268	+	18.1885i	1.42139	+	0.715617i
$647$	4.00964	+	1.66085i	0.157635	+	0.0652946i	0.460106	−	0.887864i	$-0.347811\pi$
$647$	4.00964	+	1.66085i	0.157635	+	0.0652946i	−0.302471	+	0.953159i	$0.597811\pi$
$648$		0			0
$649$	16.8397	−	6.97525i	0.661018	−	0.273802i
$650$	−3.35119	+	45.3792i	−0.131445	+	1.77992i
$651$		0			0
$652$	0.495052	−	0.234041i	0.0193877	−	0.00916574i
$653$	−17.9859	+	26.9178i	−0.703843	+	1.05338i	0.291461	+	0.956583i	$0.405859\pi$
$653$	−17.9859	+	26.9178i	−0.703843	+	1.05338i	−0.995305	+	0.0967932i	$0.969141\pi$
$654$		0			0
$655$	−0.472717	−	0.472717i	−0.0184706	−	0.0184706i
$656$	−5.27932	−	4.33559i	−0.206123	−	0.169276i
$657$		0			0
$658$	6.03299	+	1.67010i	0.235191	+	0.0651072i
$659$	0.730386	+	0.488029i	0.0284518	+	0.0190109i	0.569715	−	0.821842i	$-0.307054\pi$
$659$	0.730386	+	0.488029i	0.0284518	+	0.0190109i	−0.541263	+	0.840853i	$0.682054\pi$
$660$		0			0
$661$	0.894601	+	0.177947i	0.0347959	+	0.00692134i	0.212458	−	0.977170i	$-0.431853\pi$
$661$	0.894601	+	0.177947i	0.0347959	+	0.00692134i	−0.177662	+	0.984092i	$0.556853\pi$
$662$	11.4038	−	9.83535i	0.443223	−	0.382262i
$663$		0			0
$664$	−24.8431	+	15.7230i	−0.964098	+	0.610169i
$665$	0.602754	−	1.45518i	0.0233738	−	0.0564294i
$666$		0			0
$667$	18.0512	−	12.0614i	0.698945	−	0.467020i
$668$	−43.2598	−	6.42439i	−1.67377	−	0.248567i
$669$		0			0
$670$	0.335459	+	2.72171i	0.0129599	+	0.105149i
$671$			34.7619i			1.34197i
$672$		0			0
$673$		−	8.15010i		−	0.314163i	−0.987586	−	0.157082i	$-0.949791\pi$
$673$		−	8.15010i		−	0.314163i	0.987586	−	0.157082i	$-0.0502086\pi$
$674$	−18.3983	+	2.26765i	−0.708677	+	0.0873467i
$675$		0			0
$676$	47.7121	−	35.3733i	1.83508	−	1.36051i
$677$	14.3667	−	9.59953i	0.552158	−	0.368940i	−0.247972	−	0.968767i	$-0.579764\pi$
$677$	14.3667	−	9.59953i	0.552158	−	0.368940i	0.800130	+	0.599827i	$0.204764\pi$
$678$		0			0
$679$	−0.639665	+	1.54429i	−0.0245481	+	0.0592643i
$680$	−2.05037	+	2.90975i	−0.0786281	+	0.111584i
$681$		0			0
$682$	10.6867	+	12.3909i	0.409214	+	0.474474i
$683$	−47.8740	−	9.52274i	−1.83185	−	0.364377i	−0.846157	−	0.532933i	$-0.821090\pi$
$683$	−47.8740	−	9.52274i	−1.83185	−	0.364377i	−0.985692	+	0.168556i	$0.946090\pi$
$684$		0			0
$685$	5.26754	+	3.51966i	0.201262	+	0.134479i
$686$	−4.53369	+	16.3773i	−0.173097	+	0.625289i
$687$		0			0
$688$	15.4820	−	4.69076i	0.590247	−	0.178833i
$689$	7.62224	+	7.62224i	0.290384	+	0.290384i
$690$		0			0
$691$	−12.9075	+	19.3174i	−0.491023	+	0.734868i	−0.991390	−	0.130946i	$-0.958199\pi$
$691$	−12.9075	+	19.3174i	−0.491023	+	0.734868i	0.500366	+	0.865814i	$0.333199\pi$
$692$	−9.17903	+	25.6401i	−0.348934	+	0.974691i
$693$		0			0
$694$	−11.4687	−	0.846949i	−0.435346	−	0.0321497i
$695$	−2.51323	+	1.04102i	−0.0953324	+	0.0394880i
$696$		0			0
$697$	7.20550	+	2.98462i	0.272928	+	0.113050i
$698$	−7.19286	+	14.2868i	−0.272254	+	0.540762i
$699$		0			0
$700$	−7.70774	−	4.62160i	−0.291325	−	0.174680i
$701$	30.2742	−	6.02192i	1.14344	−	0.227445i	0.413204	−	0.910638i	$-0.364409\pi$
$701$	30.2742	−	6.02192i	1.14344	−	0.227445i	0.730237	+	0.683194i	$0.239409\pi$
$702$		0			0
$703$	32.7756			1.23616
$704$	20.2462	−	12.1213i	0.763057	−	0.456837i
$705$		0			0
$706$	−1.85726	+	2.37944i	−0.0698988	+	0.0895516i
$707$	0.612570	−	0.121848i	0.0230381	−	0.00458255i
$708$		0			0
$709$	−21.3782	−	31.9948i	−0.802876	−	1.20159i	−0.976232	−	0.216730i	$-0.930461\pi$
$709$	−21.3782	−	31.9948i	−0.802876	−	1.20159i	0.173355	−	0.984859i	$-0.444539\pi$
$710$	0.481636	−	0.956646i	0.0180755	−	0.0359023i
$711$		0			0
$712$	19.7350	+	20.7388i	0.739600	+	0.777218i
$713$	22.1386	−	9.17012i	0.829098	−	0.343424i
$714$		0			0
$715$	1.03625	−	5.20959i	0.0387537	−	0.194828i
$716$	−11.9979	−	4.29518i	−0.448382	−	0.160518i
$717$		0			0
$718$	3.64874	−	2.06658i	0.136170	−	0.0771241i
$719$	18.4708	+	18.4708i	0.688844	+	0.688844i	0.961976	−	0.273133i	$-0.0880598\pi$
$719$	18.4708	+	18.4708i	0.688844	+	0.688844i	−0.273133	+	0.961976i	$0.588060\pi$
$720$		0			0
$721$	1.73686	−	1.73686i	0.0646840	−	0.0646840i
$722$	−7.63053	+	27.5642i	−0.283979	+	1.02583i
$723$		0			0
$724$	−12.6309	+	0.618395i	−0.469424	+	0.0229825i
$725$	−17.1629	−	3.41391i	−0.637414	−	0.126789i
$726$		0			0
$727$	13.4323	+	32.4285i	0.498177	+	1.20271i	0.950464	+	0.310834i	$0.100608\pi$
$727$	13.4323	+	32.4285i	0.498177	+	1.20271i	−0.452287	+	0.891872i	$0.649392\pi$
$728$	2.87927	+	16.6185i	0.106713	+	0.615921i
$729$		0			0
$730$	0.271997	+	0.823579i	0.0100671	+	0.0304820i
$731$	−15.3561	+	10.2606i	−0.567967	+	0.379504i
$732$		0			0
$733$	4.74446	+	23.8520i	0.175241	+	0.880995i	0.963920	+	0.266190i	$0.0857650\pi$
$733$	4.74446	+	23.8520i	0.175241	+	0.880995i	−0.788680	+	0.614804i	$0.789235\pi$
$734$	16.9370	−	2.08754i	0.625155	−	0.0770523i
$735$		0			0
$736$	−7.55743	−	33.7209i	−0.278571	−	1.24297i
$737$			20.7547i			0.764508i
$738$		0			0
$739$	−8.14420	−	40.9437i	−0.299589	−	1.50614i	−0.778148	−	0.628081i	$-0.783840\pi$
$739$	−8.14420	−	40.9437i	−0.299589	−	1.50614i	0.478558	−	0.878056i	$-0.341160\pi$
$740$	−0.423715	+	2.85316i	−0.0155761	+	0.104884i
$741$		0			0
$742$	−2.02163	+	0.667667i	−0.0742162	+	0.0245108i
$743$	−11.5706	+	27.9339i	−0.424485	+	1.02480i	0.556524	+	0.830832i	$0.312135\pi$
$743$	−11.5706	+	27.9339i	−0.424485	+	1.02480i	−0.981008	+	0.193965i	$0.937865\pi$
$744$		0			0
$745$	−1.65253	−	3.98955i	−0.0605438	−	0.146166i
$746$	7.93147	−	6.84058i	0.290392	−	0.250451i
$747$		0			0
$748$	−18.0952	+	19.9583i	−0.661626	+	0.729746i
$749$	−9.58904	−	6.40719i	−0.350376	−	0.234114i
$750$		0			0
$751$	14.1774	−	14.1774i	0.517342	−	0.517342i	−0.399424	−	0.916766i	$-0.630790\pi$
$751$	14.1774	−	14.1774i	0.517342	−	0.517342i	0.916766	+	0.399424i	$0.130790\pi$
$752$	5.63829	−	18.5645i	0.205607	−	0.676979i
$753$		0			0
$754$	16.1846	+	28.5754i	0.589408	+	1.04065i
$755$	1.68030	−	2.51475i	0.0611525	−	0.0915213i
$756$		0			0
$757$	−6.49319	+	32.6435i	−0.235999	+	1.18645i	0.663042	+	0.748582i	$0.269265\pi$
$757$	−6.49319	+	32.6435i	−0.235999	+	1.18645i	−0.899041	+	0.437864i	$0.855735\pi$
$758$	3.38132	−	45.7871i	0.122815	−	1.66306i
$759$		0			0
$760$	−4.46247	−	1.97942i	−0.161871	−	0.0718011i
$761$	−20.5439	−	8.50957i	−0.744717	−	0.308472i	−0.0221328	−	0.999755i	$-0.507046\pi$
$761$	−20.5439	−	8.50957i	−0.744717	−	0.308472i	−0.722584	+	0.691283i	$0.757046\pi$
$762$		0			0
$763$	3.11816	+	4.66665i	0.112885	+	0.168944i
$764$	6.16811	+	24.6420i	0.223155	+	0.891517i
$765$		0			0
$766$	−38.5068	−	30.0562i	−1.39131	−	1.08598i
$767$	40.3783			1.45797
$768$		0			0
$769$	−7.22636			−0.260589			−0.130295	−	0.991475i	$-0.541592\pi$
$769$	−7.22636			−0.260589			−0.130295	+	0.991475i	$0.541592\pi$
$770$	0.826993	+	0.645503i	0.0298027	+	0.0232623i
$771$		0			0
$772$	6.43110	+	25.6927i	0.231460	+	0.924699i
$773$	−12.0788	−	18.0772i	−0.434444	−	0.650192i	0.548059	−	0.836440i	$-0.315367\pi$
$773$	−12.0788	−	18.0772i	−0.434444	−	0.650192i	−0.982503	+	0.186248i	$0.940367\pi$
$774$		0			0
$775$	−17.8446	−	7.39149i	−0.640998	−	0.265510i
$776$	4.73573	+	2.10063i	0.170003	+	0.0754082i
$777$		0			0
$778$	1.38207	−	18.7149i	0.0495497	−	0.670963i
$779$	−2.08671	+	10.4906i	−0.0747643	+	0.375865i
$780$		0			0
$781$	4.50348	−	6.73993i	0.161147	−	0.241174i
$782$	19.4433	+	34.3290i	0.695292	+	1.22760i
$783$		0			0
$784$	23.6042	+	7.16890i	0.843007	+	0.256032i
$785$	−4.25215	+	4.25215i	−0.151766	+	0.151766i
$786$		0			0
$787$	16.3647	+	10.9345i	0.583337	+	0.389773i	0.811935	−	0.583748i	$-0.198414\pi$
$787$	16.3647	+	10.9345i	0.583337	+	0.389773i	−0.228598	+	0.973521i	$0.573414\pi$
$788$	11.8908	−	13.1151i	0.423593	−	0.467205i
$789$		0			0
$790$	−1.75803	+	1.51623i	−0.0625478	+	0.0539450i
$791$	3.37633	+	8.15118i	0.120048	+	0.289823i
$792$		0			0
$793$	−29.4694	+	71.1454i	−1.04649	+	2.52645i
$794$	−6.90013	+	2.27885i	−0.244876	+	0.0808735i
$795$		0			0
$796$	−0.342909	+	2.30904i	−0.0121541	+	0.0818416i
$797$	9.67446	+	48.6368i	0.342687	+	1.72280i	0.640307	+	0.768119i	$0.278807\pi$
$797$	9.67446	+	48.6368i	0.342687	+	1.72280i	−0.297620	+	0.954684i	$0.596193\pi$
$798$		0			0
$799$			22.1503i			0.783623i
$800$	−14.9120	+	23.5269i	−0.527220	+	0.831800i
$801$		0			0
$802$	−8.26361	+	1.01852i	−0.291798	+	0.0359651i
$803$	1.28062	+	6.43812i	0.0451922	+	0.227196i
$804$		0			0
$805$	1.27743	−	0.853552i	0.0450235	−	0.0300838i
$806$	11.3675	+	34.4195i	0.400402	+	1.21238i
$807$		0			0
$808$	−0.330467	−	1.90738i	−0.0116258	−	0.0671012i
$809$	7.10619	+	17.1558i	0.249840	+	0.603168i	0.998190	−	0.0601366i	$-0.0191536\pi$
$809$	7.10619	+	17.1558i	0.249840	+	0.603168i	−0.748350	+	0.663304i	$0.769154\pi$
$810$		0			0
$811$	8.30457	+	1.65188i	0.291613	+	0.0580054i	0.338729	−	0.940884i	$-0.390003\pi$
$811$	8.30457	+	1.65188i	0.291613	+	0.0580054i	−0.0471161	+	0.998889i	$0.515003\pi$
$812$	−6.47846	+	0.317178i	−0.227349	+	0.0111308i
$813$		0			0
$814$	−5.82423	+	21.0392i	−0.204139	+	0.737423i
$815$	0.0533538	−	0.0533538i	0.00186890	−	0.00186890i
$816$		0			0
$817$	−17.9101	−	17.9101i	−0.626597	−	0.626597i
$818$	4.00900	−	2.27063i	0.140171	−	0.0793906i
$819$		0			0
$820$	−0.886245	−	0.317271i	−0.0309490	−	0.0110796i
$821$	6.55278	−	32.9430i	0.228694	−	1.14972i	−0.680308	−	0.732927i	$-0.738154\pi$
$821$	6.55278	−	32.9430i	0.228694	−	1.14972i	0.909001	−	0.416793i	$-0.136846\pi$
$822$		0			0
$823$	35.1942	−	14.5779i	1.22679	−	0.508155i	0.327230	−	0.944945i	$-0.393885\pi$
$823$	35.1942	−	14.5779i	1.22679	−	0.508155i	0.899563	+	0.436790i	$0.143885\pi$
$824$	−5.24809	−	5.51502i	−0.182826	−	0.192125i
$825$		0			0
$826$	−3.58625	+	7.12316i	−0.124781	+	0.247847i
$827$	−20.6833	−	30.9547i	−0.719229	−	1.07640i	−0.993398	−	0.114720i	$-0.963403\pi$
$827$	−20.6833	−	30.9547i	−0.719229	−	1.07640i	0.274169	−	0.961681i	$-0.411597\pi$
$828$		0			0
$829$	14.0046	−	2.78569i	0.486400	−	0.0967509i	0.0542024	−	0.998530i	$-0.482738\pi$
$829$	14.0046	−	2.78569i	0.486400	−	0.0967509i	0.432197	+	0.901779i	$0.357738\pi$
$830$	−2.49269	+	3.19353i	−0.0865224	+	0.110849i
$831$		0			0
$832$	51.7126	−	7.64427i	1.79281	−	0.265017i
$833$	−28.1634			−0.975805
$834$		0			0
$835$	−5.91048	+	1.17567i	−0.204541	+	0.0406856i
$836$	−31.6872	−	18.9998i	−1.09593	−	0.657122i
$837$		0			0
$838$	−4.39572	+	8.73097i	−0.151848	+	0.301606i
$839$	−1.76824	−	0.732431i	−0.0610466	−	0.0252863i	0.351951	−	0.936018i	$-0.385518\pi$
$839$	−1.76824	−	0.732431i	−0.0610466	−	0.0252863i	−0.412998	+	0.910732i	$0.635518\pi$
$840$		0			0
$841$	15.1243	−	6.26470i	0.521529	−	0.216024i
$842$	7.42025	+	0.547976i	0.255719	+	0.0188845i
$843$		0			0
$844$	−7.30394	+	20.4024i	−0.251412	+	0.702278i
$845$	4.54687	−	6.80488i	0.156417	−	0.234095i
$846$		0			0
$847$	−1.48383	−	1.48383i	−0.0509850	−	0.0509850i
$848$	1.91338	+	6.31520i	0.0657058	+	0.216865i
$849$		0			0
$850$	8.48418	−	30.6479i	0.291005	−	1.05121i
$851$	26.5820	+	17.7615i	0.911219	+	0.608857i
$852$		0			0
$853$	−6.56372	−	1.30561i	−0.224738	−	0.0447031i	0.0814369	−	0.996678i	$-0.474049\pi$
$853$	−6.56372	−	1.30561i	−0.224738	−	0.0447031i	−0.306174	+	0.951975i	$0.599049\pi$
$854$	−9.93345	−	11.5176i	−0.339916	−	0.394124i
$855$		0			0
$856$	−20.5892	+	29.2188i	−0.703723	+	0.998677i
$857$	−13.4560	+	32.4856i	−0.459647	+	1.10969i	0.508893	+	0.860830i	$0.330055\pi$
$857$	−13.4560	+	32.4856i	−0.459647	+	1.10969i	−0.968540	+	0.248857i	$0.919945\pi$
$858$		0			0
$859$	2.78301	−	1.85955i	0.0949550	−	0.0634469i	−0.507186	−	0.861836i	$-0.669314\pi$
$859$	2.78301	−	1.85955i	0.0949550	−	0.0634469i	0.602141	+	0.798390i	$0.294314\pi$
$860$	1.79064	−	1.32756i	0.0610603	−	0.0452695i
$861$		0			0
$862$	28.4319	−	3.50433i	0.968396	−	0.119358i
$863$			10.8105i			0.367993i	0.982927	+	0.183997i	$0.0589036\pi$
$863$			10.8105i			0.367993i	−0.982927	+	0.183997i	$0.941096\pi$
$864$		0			0
$865$			3.75261i			0.127592i
$866$	−2.03454	−	16.5070i	−0.0691366	−	0.560932i
$867$		0			0
$868$	−7.08159	−	1.05167i	−0.240365	−	0.0356959i
$869$	−14.6091	+	9.76152i	−0.495581	+	0.331137i
$870$		0			0
$871$	−17.5947	+	42.4775i	−0.596175	+	1.43929i
$872$	14.6990	−	9.30284i	0.497770	−	0.315034i
$873$		0			0
$874$	−40.9735	+	35.3380i	−1.38595	+	1.19533i
$875$	−2.44787	−	0.486912i	−0.0827531	−	0.0164606i
$876$		0			0
$877$	−31.4200	−	20.9942i	−1.06098	−	0.708924i	−0.102687	−	0.994714i	$-0.532744\pi$
$877$	−31.4200	−	20.9942i	−1.06098	−	0.708924i	−0.958292	+	0.285790i	$0.907744\pi$
$878$	−21.1192	−	5.84639i	−0.712740	−	0.197306i
$879$		0			0
$880$	2.06360	−	2.51279i	0.0695640	−	0.0847060i
$881$	−30.5938	−	30.5938i	−1.03073	−	1.03073i	−0.999513	−	0.0312196i	$-0.990061\pi$
$881$	−30.5938	−	30.5938i	−1.03073	−	1.03073i	−0.0312196	−	0.999513i	$-0.509939\pi$
$882$		0			0
$883$	−24.8141	+	37.1370i	−0.835062	+	1.24976i	0.130983	+	0.991385i	$0.458187\pi$
$883$	−24.8141	+	37.1370i	−0.835062	+	1.24976i	−0.966045	+	0.258374i	$0.916813\pi$
$884$	−53.9541	+	25.5073i	−1.81467	+	0.857904i
$885$		0			0
$886$	0.698833	−	9.46304i	0.0234778	−	0.317917i
$887$	−11.6990	+	4.84589i	−0.392814	+	0.162709i	−0.570343	−	0.821407i	$-0.693190\pi$
$887$	−11.6990	+	4.84589i	−0.392814	+	0.162709i	0.177529	+	0.984116i	$0.443190\pi$
$888$		0			0
$889$	9.65997	+	4.00129i	0.323985	+	0.134199i
$890$	3.52340	+	1.77390i	0.118105	+	0.0594612i
$891$		0			0
$892$	−26.4967	+	6.63236i	−0.887175	+	0.222068i
$893$	−29.7943	+	5.92645i	−0.997028	+	0.198321i
$894$		0			0
$895$	−1.75597			−0.0586956
$896$	−3.24439	+	9.80159i	−0.108387	+	0.327448i
$897$		0			0
$898$	13.5716	+	10.5932i	0.452890	+	0.353500i
$899$	−13.6722	+	2.71956i	−0.455993	+	0.0907026i
$900$		0			0
$901$	−4.18537	−	6.26384i	−0.139435	−	0.208679i
$902$	−6.36329	−	3.20368i	−0.211874	−	0.106671i
$903$		0			0
$904$	25.5154	−	9.83501i	0.848630	−	0.327108i
$905$	−1.60989	+	0.666840i	−0.0535147	+	0.0221665i
$906$		0			0
$907$	−10.1511	+	51.0331i	−0.337062	+	1.69453i	0.325519	+	0.945536i	$0.394461\pi$
$907$	−10.1511	+	51.0331i	−0.337062	+	1.69453i	−0.662581	+	0.748990i	$0.730539\pi$
$908$	−0.138353	+	0.0654078i	−0.00459141	+	0.00217063i
$909$		0			0
$910$	1.14534	+	2.02220i	0.0379676	+	0.0670352i
$911$	−28.0572	−	28.0572i	−0.929578	−	0.929578i	0.0681006	−	0.997678i	$-0.478306\pi$
$911$	−28.0572	−	28.0572i	−0.929578	−	0.929578i	−0.997678	+	0.0681006i	$0.978306\pi$
$912$		0			0
$913$	−21.6804	+	21.6804i	−0.717516	+	0.717516i
$914$	31.9223	+	8.83698i	1.05590	+	0.292301i
$915$		0			0
$916$	−5.55852	−	5.03965i	−0.183659	−	0.166515i
$917$	2.17120	+	0.431879i	0.0716994	+	0.0142619i
$918$		0			0
$919$	−22.6448	−	54.6694i	−0.746984	−	1.80338i	−0.574764	−	0.818319i	$-0.694906\pi$
$919$	−22.6448	−	54.6694i	−0.746984	−	1.80338i	−0.172219	−	0.985059i	$-0.555094\pi$
$920$	−2.54652	−	4.02363i	−0.0839563	−	0.132655i
$921$		0			0
$922$	−8.22371	+	2.71598i	−0.270833	+	0.0894461i
$923$	14.9308	−	9.97645i	0.491454	−	0.328379i
$924$		0			0
$925$	−5.02729	−	25.2739i	−0.165296	−	0.831000i
$926$	−2.13090	−	17.2888i	−0.0700258	−	0.568146i
$927$		0			0
$928$	0.484942	+	20.0975i	0.0159190	+	0.659733i
$929$			56.6874i			1.85985i	0.367744	+	0.929927i	$0.380130\pi$
$929$			56.6874i			1.85985i	−0.367744	+	0.929927i	$0.619870\pi$
$930$		0			0
$931$	−7.53528	−	37.8824i	−0.246959	−	1.24155i
$932$	22.8320	−	16.9274i	0.747887	−	0.554477i
$933$		0			0
$934$	3.12854	+	9.47290i	0.102369	+	0.309963i
$935$	−1.42058	+	3.42959i	−0.0464580	+	0.112160i
$936$		0			0
$937$	3.54560	+	8.55984i	0.115830	+	0.279638i	0.971153	−	0.238457i	$-0.0766415\pi$
$937$	3.54560	+	8.55984i	0.115830	+	0.279638i	−0.855323	+	0.518095i	$0.826642\pi$
$938$	−5.93078	−	6.87659i	−0.193647	−	0.224529i
$939$		0			0
$940$	−0.130732	−	2.67025i	−0.00426402	−	0.0870938i
$941$	−25.5011	−	17.0393i	−0.831312	−	0.555465i	0.0655122	−	0.997852i	$-0.479132\pi$
$941$	−25.5011	−	17.0393i	−0.831312	−	0.555465i	−0.896824	+	0.442387i	$0.854132\pi$
$942$		0			0
$943$	−7.37739	+	7.37739i	−0.240241	+	0.240241i
$944$	21.7951	+	11.6591i	0.709371	+	0.379473i
$945$		0			0
$946$	14.6794	−	8.31418i	0.477270	−	0.270317i
$947$	−13.9505	+	20.8784i	−0.453331	+	0.678458i	−0.985787	−	0.168000i	$-0.946269\pi$
$947$	−13.9505	+	20.8784i	−0.453331	+	0.678458i	0.532456	+	0.846458i	$0.321269\pi$
$948$		0			0
$949$	−2.83693	+	14.2622i	−0.0920907	+	0.462971i
$950$	43.4943	+	3.21199i	1.41114	+	0.104211i
$951$		0			0
$952$	0.292234	−	11.7836i	0.00947135	−	0.381907i
$953$	20.3987	+	8.44942i	0.660779	+	0.273704i	0.687766	−	0.725932i	$-0.258591\pi$
$953$	20.3987	+	8.44942i	0.660779	+	0.273704i	−0.0269874	+	0.999636i	$0.508591\pi$
$954$		0			0
$955$	1.94464	+	2.91035i	0.0629270	+	0.0941769i
$956$	45.1269	+	27.0583i	1.45951	+	0.875129i
$957$		0			0
$958$	22.7722	−	29.1749i	0.735738	−	0.942598i
$959$	−20.9784			−0.677427
$960$		0			0
$961$	15.6135			0.503661
$962$	−29.7561	+	38.1223i	−0.959375	+	1.22911i
$963$		0			0
$964$	12.2662	−	20.4572i	0.395068	−	0.658881i
$965$	2.02755	+	3.03444i	0.0652692	+	0.0976822i
$966$		0			0
$967$	38.1280	+	15.7931i	1.22611	+	0.507873i	0.899349	−	0.437232i	$-0.144041\pi$
$967$	38.1280	+	15.7931i	1.22611	+	0.507873i	0.326766	+	0.945105i	$0.394041\pi$
$968$	−4.71158	+	4.48354i	−0.151436	+	0.144106i
$969$		0			0
$970$	0.711928	+	0.0525749i	0.0228586	+	0.00168808i
$971$	−5.64453	+	28.3769i	−0.181141	+	0.910660i	0.778115	+	0.628122i	$0.216176\pi$
$971$	−5.64453	+	28.3769i	−0.181141	+	0.910660i	−0.959256	+	0.282537i	$0.908824\pi$
$972$		0			0
$973$	5.00457	−	7.48987i	0.160439	−	0.240114i
$974$	38.2243	−	21.6496i	1.22478	−	0.693696i
$975$		0			0
$976$	−36.4499	+	29.8932i	−1.16673	+	0.956858i
$977$	33.6554	−	33.6554i	1.07673	−	1.07673i	0.0799325	−	0.996800i	$-0.474530\pi$
$977$	33.6554	−	33.6554i	1.07673	−	1.07673i	0.996800	−	0.0799325i	$-0.0254705\pi$
$978$		0			0
$979$	24.8237	+	16.5866i	0.793368	+	0.530111i
$980$	3.39513	−	0.166222i	0.108453	−	0.00530976i
$981$		0			0
$982$	25.0483	+	29.0428i	0.799323	+	0.926794i
$983$	19.1346	+	46.1950i	0.610299	+	1.47339i	0.862673	+	0.505762i	$0.168789\pi$
$983$	19.1346	+	46.1950i	0.610299	+	1.47339i	−0.252374	+	0.967630i	$0.581211\pi$
$984$		0			0
$985$	0.933500	−	2.25367i	0.0297438	−	0.0718078i
$986$	−7.19755	−	21.7934i	−0.229217	−	0.694044i
$987$		0			0
$988$	−48.7455	−	65.7487i	−1.55080	−	2.09174i
$989$	−4.81992	−	24.2314i	−0.153265	−	0.770514i
$990$		0			0
$991$			49.7101i			1.57909i	0.613691	+	0.789547i	$0.289684\pi$
$991$			49.7101i			1.57909i	−0.613691	+	0.789547i	$0.710316\pi$
$992$	−3.80269	+	21.8611i	−0.120736	+	0.694090i
$993$		0			0
$994$	0.433854	+	3.52003i	0.0137610	+	0.111648i
$995$	0.0627525	+	0.315478i	0.00198939	+	0.0100013i
$996$		0			0
$997$	42.0865	−	28.1213i	1.33289	−	0.890611i	0.334240	−	0.942488i	$-0.391521\pi$
$997$	42.0865	−	28.1213i	1.33289	−	0.890611i	0.998653	+	0.0518774i	$0.0165205\pi$
$998$	28.8578	−	9.53065i	0.913478	−	0.301687i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.a.181.5		56
3.2	odd	2		64.2.i.a.53.3	yes	56
12.11	even	2		256.2.i.a.49.1		56
24.5	odd	2		512.2.i.b.353.1		56
24.11	even	2		512.2.i.a.353.7		56
64.29	even	16	inner	576.2.bd.a.541.5		56
192.29	odd	16		64.2.i.a.29.3	✓	56
192.35	even	16		256.2.i.a.209.1		56
192.125	odd	16		512.2.i.b.161.1		56
192.131	even	16		512.2.i.a.161.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.3	✓	56	192.29	odd	16
64.2.i.a.53.3	yes	56	3.2	odd	2
256.2.i.a.49.1		56	12.11	even	2
256.2.i.a.209.1		56	192.35	even	16
512.2.i.a.161.7		56	192.131	even	16
512.2.i.a.353.7		56	24.11	even	2
512.2.i.b.161.1		56	192.125	odd	16
512.2.i.b.353.1		56	24.5	odd	2
576.2.bd.a.181.5		56	1.1	even	1	trivial
576.2.bd.a.541.5		56	64.29	even	16	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11482 + 0.870162i) q^{2} +(0.485635 + 1.94014i) q^{4} +(0.153107 + 0.229142i) q^{5} +(-0.843108 - 0.349227i) q^{7} +(-1.14685 + 2.58549i) q^{8} +O(q^{10})\)	\(q+(1.11482 + 0.870162i) q^{2} +(0.485635 + 1.94014i) q^{4} +(0.153107 + 0.229142i) q^{5} +(-0.843108 - 0.349227i) q^{7} +(-1.14685 + 2.58549i) q^{8} +(-0.0287035 + 0.388679i) q^{10} +(-0.575451 + 2.89299i) q^{11} +(-3.63027 + 5.43308i) q^{13} +(-0.636028 - 1.12297i) q^{14} +(-3.52832 + 1.88440i) q^{16} +(3.22910 - 3.22910i) q^{17} +(5.20741 + 3.47948i) q^{19} +(-0.370213 + 0.408330i) q^{20} +(-3.15889 + 2.72442i) q^{22} +(2.33779 + 5.64392i) q^{23} +(1.88435 - 4.54923i) q^{25} +(-8.77475 + 2.89797i) q^{26} +(0.268107 - 1.80535i) q^{28} +(-0.693313 - 3.48552i) q^{29} -3.92256i q^{31} +(-5.57317 - 0.969441i) q^{32} +(6.40970 - 0.790016i) q^{34} +(-0.0490638 - 0.246660i) q^{35} +(4.35133 - 2.90747i) q^{37} +(2.77760 + 8.41027i) q^{38} +(-0.768033 + 0.133068i) q^{40} +(0.653569 + 1.57786i) q^{41} +(-3.96655 - 0.788996i) q^{43} +(-5.89227 + 0.288479i) q^{44} +(-2.30492 + 8.32620i) q^{46} +(-3.42980 + 3.42980i) q^{47} +(-4.36088 - 4.36088i) q^{49} +(6.05928 - 3.43187i) q^{50} +(-12.3040 - 4.40475i) q^{52} +(0.321835 - 1.61797i) q^{53} +(-0.751009 + 0.311078i) q^{55} +(1.86984 - 1.77934i) q^{56} +(2.26005 - 4.48902i) q^{58} +(-3.43310 - 5.13800i) q^{59} +(11.5586 - 2.29915i) q^{61} +(3.41327 - 4.37294i) q^{62} +(-5.36949 - 5.93031i) q^{64} -1.80077 q^{65} +(6.90108 - 1.37271i) q^{67} +(7.83309 + 4.69676i) q^{68} +(0.159937 - 0.317675i) q^{70} +(-2.53894 - 1.05166i) q^{71} +(2.05602 - 0.851633i) q^{73} +(7.38090 + 0.545070i) q^{74} +(-4.22179 + 11.7929i) q^{76} +(1.49548 - 2.23814i) q^{77} +(4.21203 + 4.21203i) q^{79} +(-0.972007 - 0.519967i) q^{80} +(-0.644380 + 2.32773i) q^{82} +(8.64283 + 5.77496i) q^{83} +(1.23432 + 0.245522i) q^{85} +(-3.73542 - 4.33113i) q^{86} +(-6.81983 - 4.80563i) q^{88} +(3.87335 - 9.35109i) q^{89} +(4.95809 - 3.31289i) q^{91} +(-9.81471 + 7.27653i) q^{92} +(-6.80808 + 0.839118i) q^{94} +1.72597i q^{95} -1.83166i q^{97} +(-1.06691 - 8.65625i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

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