LMFDB - Embedded newform 576.2.bd.a.109.1

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			109.1
Character	$\chi$	$=$	576.109
Dual form			576.2.bd.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998819 - 1.00118i) q^{2} +(-0.00472188 + 1.99999i) q^{4} +(-0.0517508 - 0.260169i) q^{5} +(-0.515195 - 1.24379i) q^{7} +(2.00707 - 1.99290i) q^{8} +O(q^{10})$	\(q+(-0.998819 - 1.00118i) q^{2} +(-0.00472188 + 1.99999i) q^{4} +(-0.0517508 - 0.260169i) q^{5} +(-0.515195 - 1.24379i) q^{7} +(2.00707 - 1.99290i) q^{8} +(-0.208786 + 0.311673i) q^{10} +(4.11495 + 2.74952i) q^{11} +(-0.650168 + 3.26862i) q^{13} +(-0.730672 + 1.75812i) q^{14} +(-3.99996 - 0.0188875i) q^{16} +(-1.10212 - 1.10212i) q^{17} +(2.56547 + 0.510304i) q^{19} +(0.520580 - 0.102273i) q^{20} +(-1.35733 - 6.86609i) q^{22} +(-3.70792 - 1.53587i) q^{23} +(4.55439 - 1.88649i) q^{25} +(3.92187 - 2.61382i) q^{26} +(2.49001 - 1.02451i) q^{28} +(5.46390 - 3.65086i) q^{29} +8.22961i q^{31} +(3.97632 + 4.02354i) q^{32} +(-0.00260204 + 2.20424i) q^{34} +(-0.296934 + 0.198405i) q^{35} +(7.58710 - 1.50917i) q^{37} +(-2.05154 - 3.07820i) q^{38} +(-0.622359 - 0.419042i) q^{40} +(10.4659 + 4.33512i) q^{41} +(2.31618 - 3.46640i) q^{43} +(-5.51846 + 8.21690i) q^{44} +(2.16586 + 5.24635i) q^{46} +(-2.33317 - 2.33317i) q^{47} +(3.66816 - 3.66816i) q^{49} +(-6.43772 - 2.67550i) q^{50} +(-6.53414 - 1.31577i) q^{52} +(3.33837 + 2.23063i) q^{53} +(0.502388 - 1.21287i) q^{55} +(-3.51279 - 1.46964i) q^{56} +(-9.11262 - 1.82380i) q^{58} +(-1.16241 - 5.84382i) q^{59} +(-6.89488 - 10.3189i) q^{61} +(8.23932 - 8.21989i) q^{62} +(0.0566621 - 7.99980i) q^{64} +0.884038 q^{65} +(1.94793 + 2.91529i) q^{67} +(2.20944 - 2.19903i) q^{68} +(0.495222 + 0.0991136i) q^{70} +(5.39337 + 13.0208i) q^{71} +(-0.375531 + 0.906612i) q^{73} +(-9.08909 - 6.08867i) q^{74} +(-1.03272 + 5.12852i) q^{76} +(1.29983 - 6.53468i) q^{77} +(1.20158 - 1.20158i) q^{79} +(0.202087 + 1.04164i) q^{80} +(-6.11331 - 14.8083i) q^{82} +(-15.1088 - 3.00532i) q^{83} +(-0.229702 + 0.343773i) q^{85} +(-5.78393 + 1.14340i) q^{86} +(13.7385 - 2.68222i) q^{88} +(1.66533 - 0.689803i) q^{89} +(4.40044 - 0.875301i) q^{91} +(3.08924 - 7.40856i) q^{92} +(-0.00550847 + 4.66633i) q^{94} -0.693864i q^{95} +15.4207i q^{97} +(-7.33631 - 0.00866031i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{16}\right)$

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 $

$2$	−0.998819	−	1.00118i	−0.706272	−	0.707941i
$2$	−0.998819	−	1.00118i	−0.706272	−	0.707941i
$3$		0			0
$3$		0			0
$4$	−0.00472188	+	1.99999i	−0.00236094	+	0.999997i
$5$	−0.0517508	−	0.260169i	−0.0231436	−	0.116351i	0.967487	−	0.252922i	$-0.0813917\pi$
$5$	−0.0517508	−	0.260169i	−0.0231436	−	0.116351i	−0.990630	+	0.136571i	$0.956392\pi$
$6$		0			0
$7$	−0.515195	−	1.24379i	−0.194725	−	0.470109i	0.796115	−	0.605145i	$-0.206885\pi$
$7$	−0.515195	−	1.24379i	−0.194725	−	0.470109i	−0.990841	+	0.135036i	$0.956885\pi$
$8$	2.00707	−	1.99290i	0.709606	−	0.704598i
$9$		0			0
$10$	−0.208786	+	0.311673i	−0.0660239	+	0.0985597i
$11$	4.11495	+	2.74952i	1.24071	+	0.829013i	0.990275	−	0.139122i	$-0.0444280\pi$
$11$	4.11495	+	2.74952i	1.24071	+	0.829013i	0.250430	+	0.968135i	$0.419428\pi$
$12$		0			0
$13$	−0.650168	+	3.26862i	−0.180324	+	0.906551i	0.779597	+	0.626281i	$0.215424\pi$
$13$	−0.650168	+	3.26862i	−0.180324	+	0.906551i	−0.959921	+	0.280269i	$0.909576\pi$
$14$	−0.730672	+	1.75812i	−0.195280	+	0.469879i
$15$		0			0
$16$	−3.99996	−	0.0188875i	−0.999989	−	0.00472187i
$17$	−1.10212	−	1.10212i	−0.267304	−	0.267304i	0.560709	−	0.828013i	$-0.310529\pi$
$17$	−1.10212	−	1.10212i	−0.267304	−	0.267304i	−0.828013	+	0.560709i	$0.810529\pi$
$18$		0			0
$19$	2.56547	+	0.510304i	0.588560	+	0.117072i	0.480381	−	0.877060i	$-0.340498\pi$
$19$	2.56547	+	0.510304i	0.588560	+	0.117072i	0.108178	+	0.994132i	$0.465498\pi$
$20$	0.520580	−	0.102273i	0.116405	−	0.0228689i
$21$		0			0
$22$	−1.35733	−	6.86609i	−0.289383	−	1.46385i
$23$	−3.70792	−	1.53587i	−0.773154	−	0.320251i	−0.0390048	−	0.999239i	$-0.512419\pi$
$23$	−3.70792	−	1.53587i	−0.773154	−	0.320251i	−0.734149	+	0.678988i	$0.762419\pi$
$24$		0			0
$25$	4.55439	−	1.88649i	0.910878	−	0.377298i
$26$	3.92187	−	2.61382i	0.769142	−	0.512612i
$27$		0			0
$28$	2.49001	−	1.02451i	0.470567	−	0.193615i
$29$	5.46390	−	3.65086i	1.01462	−	0.677948i	0.0671349	−	0.997744i	$-0.478614\pi$
$29$	5.46390	−	3.65086i	1.01462	−	0.677948i	0.947487	+	0.319795i	$0.103614\pi$
$30$		0			0
$31$			8.22961i			1.47808i	0.673661	+	0.739041i	$0.264721\pi$
$31$			8.22961i			1.47808i	−0.673661	+	0.739041i	$0.735279\pi$
$32$	3.97632	+	4.02354i	0.702921	+	0.711268i
$33$		0			0
$34$	−0.00260204	+	2.20424i	−0.000446247	+	0.378024i
$35$	−0.296934	+	0.198405i	−0.0501909	+	0.0335365i
$36$		0			0
$37$	7.58710	−	1.50917i	1.24731	−	0.248106i	0.473087	−	0.881016i	$-0.343140\pi$
$37$	7.58710	−	1.50917i	1.24731	−	0.248106i	0.774225	+	0.632910i	$0.218140\pi$
$38$	−2.05154	−	3.07820i	−0.332803	−	0.499350i
$39$		0			0
$40$	−0.622359	−	0.419042i	−0.0984036	−	0.0662564i
$41$	10.4659	+	4.33512i	1.63450	+	0.677032i	0.995725	−	0.0923624i	$-0.0294418\pi$
$41$	10.4659	+	4.33512i	1.63450	+	0.677032i	0.638774	+	0.769394i	$0.279442\pi$
$42$		0			0
$43$	2.31618	−	3.46640i	0.353213	−	0.528621i	−0.611734	−	0.791063i	$-0.709528\pi$
$43$	2.31618	−	3.46640i	0.353213	−	0.528621i	0.964948	+	0.262442i	$0.0845278\pi$
$44$	−5.51846	+	8.21690i	−0.831940	+	1.23874i
$45$		0			0
$46$	2.16586	+	5.24635i	0.319338	+	0.773532i
$47$	−2.33317	−	2.33317i	−0.340328	−	0.340328i	0.516163	−	0.856490i	$-0.327360\pi$
$47$	−2.33317	−	2.33317i	−0.340328	−	0.340328i	−0.856490	+	0.516163i	$0.827360\pi$
$48$		0			0
$49$	3.66816	−	3.66816i	0.524023	−	0.524023i
$50$	−6.43772	−	2.67550i	−0.910432	−	0.378373i
$51$		0			0
$52$	−6.53414	−	1.31577i	−0.906122	−	0.182464i
$53$	3.33837	+	2.23063i	0.458560	+	0.306400i	0.763310	−	0.646032i	$-0.223573\pi$
$53$	3.33837	+	2.23063i	0.458560	+	0.306400i	−0.304750	+	0.952432i	$0.598573\pi$
$54$		0			0
$55$	0.502388	−	1.21287i	0.0677420	−	0.163544i
$56$	−3.51279	−	1.46964i	−0.469416	−	0.196389i
$57$		0			0
$58$	−9.11262	−	1.82380i	−1.19655	−	0.239476i
$59$	−1.16241	−	5.84382i	−0.151333	−	0.760800i	−0.979677	−	0.200581i	$-0.935717\pi$
$59$	−1.16241	−	5.84382i	−0.151333	−	0.760800i	0.828345	−	0.560219i	$-0.189283\pi$
$60$		0			0
$61$	−6.89488	−	10.3189i	−0.882799	−	1.32120i	−0.946323	−	0.323222i	$-0.895234\pi$
$61$	−6.89488	−	10.3189i	−0.882799	−	1.32120i	0.0635241	−	0.997980i	$-0.479766\pi$
$62$	8.23932	−	8.21989i	1.04639	−	1.04393i
$63$		0			0
$64$	0.0566621	−	7.99980i	0.00708277	−	0.999975i
$65$	0.884038			0.109651
$66$		0			0
$67$	1.94793	+	2.91529i	0.237978	+	0.356159i	0.931165	−	0.364599i	$-0.118794\pi$
$67$	1.94793	+	2.91529i	0.237978	+	0.356159i	−0.693187	+	0.720758i	$0.743794\pi$
$68$	2.20944	−	2.19903i	0.267934	−	0.266672i
$69$		0			0
$70$	0.495222	+	0.0991136i	0.0591903	+	0.0118463i
$71$	5.39337	+	13.0208i	0.640076	+	1.54528i	0.826577	+	0.562824i	$0.190285\pi$
$71$	5.39337	+	13.0208i	0.640076	+	1.54528i	−0.186501	+	0.982455i	$0.559715\pi$
$72$		0			0
$73$	−0.375531	+	0.906612i	−0.0439526	+	0.106111i	−0.944331	−	0.328996i	$-0.893290\pi$
$73$	−0.375531	+	0.906612i	−0.0439526	+	0.106111i	0.900379	+	0.435107i	$0.143290\pi$
$74$	−9.08909	−	6.08867i	−1.05659	−	0.707793i
$75$		0			0
$76$	−1.03272	+	5.12852i	−0.118461	+	0.588282i
$77$	1.29983	−	6.53468i	0.148129	−	0.744696i
$78$		0			0
$79$	1.20158	−	1.20158i	0.135189	−	0.135189i	−0.636274	−	0.771463i	$-0.719525\pi$
$79$	1.20158	−	1.20158i	0.135189	−	0.135189i	0.771463	+	0.636274i	$0.219525\pi$
$80$	0.202087	+	1.04164i	0.0225940	+	0.116459i
$81$		0			0
$82$	−6.11331	−	14.8083i	−0.675102	−	1.63530i
$83$	−15.1088	−	3.00532i	−1.65840	−	0.329877i	−0.725012	−	0.688736i	$-0.758166\pi$
$83$	−15.1088	−	3.00532i	−1.65840	−	0.329877i	−0.933392	+	0.358859i	$0.883166\pi$
$84$		0			0
$85$	−0.229702	+	0.343773i	−0.0249147	+	0.0372874i
$86$	−5.78393	+	1.14340i	−0.623697	+	0.123296i
$87$		0			0
$88$	13.7385	−	2.68222i	1.46453	−	0.285926i
$89$	1.66533	−	0.689803i	0.176525	−	0.0731189i	−0.292671	−	0.956213i	$-0.594544\pi$
$89$	1.66533	−	0.689803i	0.176525	−	0.0731189i	0.469195	+	0.883094i	$0.344544\pi$
$90$		0			0
$91$	4.40044	−	0.875301i	0.461291	−	0.0917565i
$92$	3.08924	−	7.40856i	0.322075	−	0.772396i
$93$		0			0
$94$	−0.00550847	+	4.66633i	−0.000568156	+	0.481296i
$95$		−	0.693864i		−	0.0711889i
$96$		0			0
$97$			15.4207i			1.56574i	0.622188	+	0.782868i	$0.286244\pi$
$97$			15.4207i			1.56574i	−0.622188	+	0.782868i	$0.713756\pi$
$98$	−7.33631	−	0.00866031i	−0.741079	−	0.000874823i
$99$		0			0
$100$	3.75146	+	9.11766i	0.375146	+	0.911766i
$101$	−8.24786	+	1.64060i	−0.820692	+	0.163246i	−0.587541	−	0.809195i	$-0.699904\pi$
$101$	−8.24786	+	1.64060i	−0.820692	+	0.163246i	−0.233152	+	0.972440i	$0.574904\pi$
$102$		0			0
$103$	−9.41219	+	3.89866i	−0.927410	+	0.384146i	−0.794695	−	0.607008i	$-0.792369\pi$
$103$	−9.41219	+	3.89866i	−0.927410	+	0.384146i	−0.132715	+	0.991154i	$0.542369\pi$
$104$	5.20911	+	7.85606i	0.510795	+	0.770350i
$105$		0			0
$106$	−1.10117	−	5.57030i	−0.106955	−	0.541035i
$107$	−1.05984	+	1.58616i	−0.102459	+	0.153340i	−0.879156	−	0.476533i	$-0.841893\pi$
$107$	−1.05984	+	1.58616i	−0.102459	+	0.153340i	0.776698	+	0.629873i	$0.216893\pi$
$108$		0			0
$109$	4.24989	+	0.845355i	0.407065	+	0.0809704i	0.394376	−	0.918949i	$-0.370961\pi$
$109$	4.24989	+	0.845355i	0.407065	+	0.0809704i	0.0126894	+	0.999919i	$0.495961\pi$
$110$	−1.71610	+	0.708459i	−0.163623	+	0.0675489i
$111$		0			0
$112$	2.03727	+	4.98484i	0.192503	+	0.471023i
$113$	−1.13449	+	1.13449i	−0.106724	+	0.106724i	−0.758453	−	0.651728i	$-0.774044\pi$
$113$	−1.13449	+	1.13449i	−0.106724	+	0.106724i	0.651728	+	0.758453i	$0.274044\pi$
$114$		0			0
$115$	−0.207698	+	1.04417i	−0.0193679	+	0.0973690i
$116$	7.27591	+	10.9450i	0.675551	+	1.01622i
$117$		0			0
$118$	−4.68968	+	7.00069i	−0.431720	+	0.644466i
$119$	−0.803001	+	1.93862i	−0.0736110	+	0.177713i
$120$		0			0
$121$	5.16345	+	12.4657i	0.469404	+	1.13324i
$122$	−3.44436	+	17.2097i	−0.311837	+	1.55810i
$123$		0			0
$124$	−16.4592	−	0.0388592i	−1.47808	−	0.00348966i
$125$	−1.46337	−	2.19008i	−0.130888	−	0.195887i
$126$		0			0
$127$	−18.1894			−1.61405			−0.807025	−	0.590517i	$-0.798924\pi$
$127$	−18.1894			−1.61405			−0.807025	+	0.590517i	$0.798924\pi$
$128$	−8.06583	+	7.93362i	−0.712926	+	0.701240i
$129$		0			0
$130$	−0.882994	−	0.885081i	−0.0774437	−	0.0776267i
$131$	5.01304	+	7.50254i	0.437991	+	0.655500i	0.983143	−	0.182837i	$-0.0585281\pi$
$131$	5.01304	+	7.50254i	0.437991	+	0.655500i	−0.545152	+	0.838337i	$0.683528\pi$
$132$		0			0
$133$	−0.687007	−	3.45382i	−0.0595711	−	0.299484i
$134$	0.973095	−	4.86208i	0.0840626	−	0.420019i
$135$		0			0
$136$	−4.40846	−	0.0156122i	−0.378022	−	0.00133874i
$137$	2.99585	−	7.23263i	0.255953	−	0.617925i	−0.742710	−	0.669613i	$-0.766460\pi$
$137$	2.99585	−	7.23263i	0.255953	−	0.617925i	0.998663	+	0.0516877i	$0.0164600\pi$
$138$		0			0
$139$	2.95817	+	1.97658i	0.250908	+	0.167652i	0.674664	−	0.738125i	$-0.264288\pi$
$139$	2.95817	+	1.97658i	0.250908	+	0.167652i	−0.423756	+	0.905777i	$0.639288\pi$
$140$	−0.395406	−	0.594802i	−0.0334179	−	0.0502700i
$141$		0			0
$142$	7.64911	−	18.4051i	0.641899	−	1.54452i
$143$	−11.6625	+	11.6625i	−0.975271	+	0.975271i
$144$		0			0
$145$	−1.23260	−	1.23260i	−0.102362	−	0.102362i
$146$	1.28277	−	0.529567i	0.106163	−	0.0438273i
$147$		0			0
$148$	2.98250	+	15.1813i	0.245160	+	1.24789i
$149$	4.93832	−	7.39072i	0.404563	−	0.605472i	−0.572117	−	0.820172i	$-0.693878\pi$
$149$	4.93832	−	7.39072i	0.404563	−	0.605472i	0.976680	+	0.214701i	$0.0688776\pi$
$150$		0			0
$151$	−3.73549	−	1.54729i	−0.303990	−	0.125917i	0.225474	−	0.974249i	$-0.427607\pi$
$151$	−3.73549	−	1.54729i	−0.303990	−	0.125917i	−0.529464	+	0.848332i	$0.677607\pi$
$152$	6.16607	−	4.08853i	0.500134	−	0.331623i
$153$		0			0
$154$	−7.84069	+	5.22560i	−0.631821	+	0.421091i
$155$	2.14109	−	0.425888i	0.171976	−	0.0342082i
$156$		0			0
$157$	9.49118	−	6.34180i	0.757478	−	0.506131i	−0.115848	−	0.993267i	$-0.536958\pi$
$157$	9.49118	−	6.34180i	0.757478	−	0.506131i	0.873326	+	0.487136i	$0.161958\pi$
$158$	−2.40317	−	0.00283687i	−0.191186	−	0.000225689i
$159$		0			0
$160$	0.841021	−	1.24274i	0.0664886	−	0.0982468i
$161$			5.40314i			0.425827i
$162$		0			0
$163$	0.00315871	−	0.00211058i	0.000247409	−	0.000165314i	−0.555447	−	0.831552i	$-0.687453\pi$
$163$	0.00315871	−	0.00211058i	0.000247409	−	0.000165314i	0.555694	+	0.831387i	$0.312453\pi$
$164$	−8.71963	+	20.9113i	−0.680889	+	1.63290i
$165$		0			0
$166$	12.0821	+	18.1284i	0.937750	+	1.40704i
$167$	4.28839	−	1.77631i	0.331846	−	0.137455i	−0.210538	−	0.977586i	$-0.567522\pi$
$167$	4.28839	−	1.77631i	0.331846	−	0.137455i	0.542384	+	0.840131i	$0.317522\pi$
$168$		0			0
$169$	1.74931	+	0.724587i	0.134562	+	0.0557374i
$170$	0.573609	−	0.113394i	0.0439938	−	0.00869694i
$171$		0			0
$172$	6.92185	+	4.64871i	0.527786	+	0.354461i
$173$	−7.26821	−	1.44574i	−0.552592	−	0.109917i	−0.0891066	−	0.996022i	$-0.528401\pi$
$173$	−7.26821	−	1.44574i	−0.552592	−	0.109917i	−0.463485	+	0.886105i	$0.653401\pi$
$174$		0			0
$175$	−4.69280	−	4.69280i	−0.354742	−	0.354742i
$176$	−16.4077	−	11.0757i	−1.23678	−	0.834862i
$177$		0			0
$178$	−2.35398	−	0.978308i	−0.176438	−	0.0733273i
$179$	−2.46773	+	12.4061i	−0.184447	+	0.927277i	0.772056	+	0.635554i	$0.219228\pi$
$179$	−2.46773	+	12.4061i	−0.184447	+	0.927277i	−0.956503	+	0.291722i	$0.905772\pi$
$180$		0			0
$181$	−13.4674	−	8.99863i	−1.00102	−	0.668863i	−0.0568753	−	0.998381i	$-0.518114\pi$
$181$	−13.4674	−	8.99863i	−1.00102	−	0.668863i	−0.944149	+	0.329518i	$0.893114\pi$
$182$	−5.27157	−	3.53136i	−0.390755	−	0.261762i
$183$		0			0
$184$	−10.5029	+	4.30693i	−0.774283	+	0.317511i
$185$	−0.785277	−	1.89583i	−0.0577347	−	0.139384i
$186$		0			0
$187$	−1.50487	−	7.56549i	−0.110047	−	0.553244i
$188$	4.67734	−	4.65531i	0.341130	−	0.339523i
$189$		0			0
$190$	−0.694683	+	0.693044i	−0.0503976	+	0.0502787i
$191$	−17.2169			−1.24577			−0.622885	−	0.782313i	$-0.714040\pi$
$191$	−17.2169			−1.24577			−0.622885	+	0.782313i	$0.714040\pi$
$192$		0			0
$193$	−12.7608			−0.918541			−0.459270	−	0.888296i	$-0.651889\pi$
$193$	−12.7608			−0.918541			−0.459270	+	0.888296i	$0.651889\pi$
$194$	15.4389	−	15.4025i	1.10845	−	1.10583i
$195$		0			0
$196$	7.31897	+	7.35362i	0.522784	+	0.525258i
$197$	0.972213	+	4.88764i	0.0692673	+	0.348230i	0.999840	−	0.0178765i	$-0.00569056\pi$
$197$	0.972213	+	4.88764i	0.0692673	+	0.348230i	−0.930573	+	0.366107i	$0.880691\pi$
$198$		0			0
$199$	8.85562	+	21.3794i	0.627758	+	1.51554i	0.842402	+	0.538850i	$0.181141\pi$
$199$	8.85562	+	21.3794i	0.627758	+	1.51554i	−0.214643	+	0.976692i	$0.568859\pi$
$200$	5.38138	−	12.8628i	0.380521	−	0.909536i
$201$		0			0
$202$	9.88065	+	6.61892i	0.695200	+	0.465706i
$203$	−7.35589	−	4.91505i	−0.516282	−	0.344969i
$204$		0			0
$205$	0.586244	−	2.94725i	0.0409450	−	0.205845i
$206$	13.3043	+	5.52924i	0.926956	+	0.385240i
$207$		0			0
$208$	2.66238	−	13.0620i	0.184603	−	0.905689i
$209$	9.15371	+	9.15371i	0.633175	+	0.633175i
$210$		0			0
$211$	−3.65496	−	0.727017i	−0.251618	−	0.0500499i	0.0676697	−	0.997708i	$-0.478444\pi$
$211$	−3.65496	−	0.727017i	−0.251618	−	0.0500499i	−0.319288	+	0.947658i	$0.603444\pi$
$212$	−4.47700	+	6.66618i	−0.307482	+	0.457835i
$213$		0			0
$214$	2.64662	−	0.523199i	0.180919	−	0.0357651i
$215$	−1.02171	−	0.423207i	−0.0696802	−	0.0288625i
$216$		0			0
$217$	10.2359	−	4.23985i	0.694859	−	0.287820i
$218$	−3.39852	−	5.09926i	−0.230177	−	0.345365i
$219$		0			0
$220$	2.42337	+	1.01050i	0.163383	+	0.0681279i
$221$	4.31898	−	2.88585i	0.290526	−	0.194123i
$222$		0			0
$223$		−	23.7016i		−	1.58718i	−0.608456	−	0.793588i	$-0.708211\pi$
$223$		−	23.7016i		−	1.58718i	0.608456	−	0.793588i	$-0.291789\pi$
$224$	2.95586	−	7.01862i	0.197497	−	0.468951i
$225$		0			0
$226$	2.26899	+	0.00267847i	0.150931	+	0.000178169i
$227$	8.78436	−	5.86952i	0.583039	−	0.389574i	−0.228785	−	0.973477i	$-0.573475\pi$
$227$	8.78436	−	5.86952i	0.583039	−	0.389574i	0.811823	+	0.583903i	$0.198475\pi$
$228$		0			0
$229$	−14.0985	+	2.80436i	−0.931653	+	0.185317i	−0.637508	−	0.770444i	$-0.720035\pi$
$229$	−14.0985	+	2.80436i	−0.931653	+	0.185317i	−0.294145	+	0.955761i	$0.595035\pi$
$230$	1.25285	−	0.834990i	0.0826105	−	0.0550576i
$231$		0			0
$232$	3.69062	−	18.2166i	0.242301	−	1.19598i
$233$	−5.04386	−	2.08924i	−0.330435	−	0.136870i	0.211297	−	0.977422i	$-0.432231\pi$
$233$	−5.04386	−	2.08924i	−0.330435	−	0.136870i	−0.541732	+	0.840551i	$0.682231\pi$
$234$		0			0
$235$	−0.486274	+	0.727761i	−0.0317210	+	0.0474739i
$236$	11.6931	−	2.29721i	0.761155	−	0.149536i
$237$		0			0
$238$	2.74296	−	1.13238i	0.177799	−	0.0734012i
$239$	−13.6816	−	13.6816i	−0.884992	−	0.884992i	0.109045	−	0.994037i	$-0.465221\pi$
$239$	−13.6816	−	13.6816i	−0.884992	−	0.884992i	−0.994037	+	0.109045i	$0.965221\pi$
$240$		0			0
$241$	2.22031	−	2.22031i	0.143023	−	0.143023i	−0.631970	−	0.774993i	$-0.717753\pi$
$241$	2.22031	−	2.22031i	0.143023	−	0.143023i	0.774993	+	0.631970i	$0.217753\pi$
$242$	7.32302	−	17.6205i	0.470742	−	1.13269i
$243$		0			0
$244$	20.6703	−	13.7410i	1.32328	−	0.879677i
$245$	−1.14417	−	0.764510i	−0.0730983	−	0.0488427i
$246$		0			0
$247$	−3.33598	+	8.05376i	−0.212263	+	0.512448i
$248$	16.4008	+	16.5174i	1.04145	+	1.04886i
$249$		0			0
$250$	−0.731029	+	3.65259i	−0.0462343	+	0.231010i
$251$	−0.729724	−	3.66857i	−0.0460598	−	0.231558i	0.950898	−	0.309505i	$-0.100163\pi$
$251$	−0.729724	−	3.66857i	−0.0460598	−	0.231558i	−0.996957	+	0.0779471i	$0.975163\pi$
$252$		0			0
$253$	−11.0350	−	16.5150i	−0.693764	−	1.03829i
$254$	18.1679	+	18.2109i	1.13996	+	1.14265i
$255$		0			0
$256$	15.9993	+	0.151098i	0.999955	+	0.00944363i
$257$	−17.3864			−1.08453			−0.542267	−	0.840206i	$-0.682434\pi$
$257$	−17.3864			−1.08453			−0.542267	+	0.840206i	$0.682434\pi$
$258$		0			0
$259$	−5.78593	−	8.65925i	−0.359520	−	0.538060i
$260$	−0.00417432	+	1.76807i	−0.000258880	+	0.109651i
$261$		0			0
$262$	2.50428	−	12.5126i	0.154715	−	0.773033i
$263$	−0.656941	−	1.58600i	−0.0405087	−	0.0977967i	0.902330	−	0.431045i	$-0.141855\pi$
$263$	−0.656941	−	1.58600i	−0.0405087	−	0.0977967i	−0.942839	+	0.333249i	$0.891855\pi$
$264$		0			0
$265$	0.407576	−	0.983975i	0.0250372	−	0.0604451i
$266$	−2.77170	+	4.13755i	−0.169944	+	0.253690i
$267$		0			0
$268$	−5.83976	+	3.88209i	−0.356720	+	0.237136i
$269$	1.25541	−	6.31135i	0.0765434	−	0.384810i	−0.923456	−	0.383704i	$-0.874648\pi$
$269$	1.25541	−	6.31135i	0.0765434	−	0.384810i	0.999999	−	0.00110539i	$-0.000351857\pi$
$270$		0			0
$271$	−17.1048	+	17.1048i	−1.03904	+	1.03904i	−0.0398353	+	0.999206i	$0.512683\pi$
$271$	−17.1048	+	17.1048i	−1.03904	+	1.03904i	−0.999206	+	0.0398353i	$0.987317\pi$
$272$	4.38762	+	4.42925i	0.266039	+	0.268563i
$273$		0			0
$274$	−10.2335	+	4.22470i	−0.618227	+	0.255223i
$275$	23.9280	+	4.75958i	1.44292	+	0.287014i
$276$		0			0
$277$	−4.08114	+	6.10786i	−0.245212	+	0.366985i	−0.933576	−	0.358380i	$-0.883329\pi$
$277$	−4.08114	+	6.10786i	−0.245212	+	0.366985i	0.688364	+	0.725365i	$0.258329\pi$
$278$	−0.975757	−	4.93591i	−0.0585220	−	0.296036i
$279$		0			0
$280$	−0.200565	+	0.989973i	−0.0119861	+	0.0591622i
$281$	16.8252	−	6.96925i	1.00371	−	0.415750i	0.180554	−	0.983565i	$-0.442211\pi$
$281$	16.8252	−	6.96925i	1.00371	−	0.415750i	0.823156	+	0.567815i	$0.192211\pi$
$282$		0			0
$283$	22.3174	−	4.43920i	1.32663	−	0.263883i	0.519608	−	0.854405i	$-0.326078\pi$
$283$	22.3174	−	4.43920i	1.32663	−	0.263883i	0.807022	+	0.590522i	$0.201078\pi$
$284$	−26.0669	+	10.7252i	−1.54679	+	0.636425i
$285$		0			0
$286$	23.3251	+	0.0275346i	1.37924	+	0.00162815i
$287$		−	15.2508i		−	0.900228i
$288$		0			0
$289$		−	14.5707i		−	0.857097i
$290$	−0.00291010	+	2.46520i	−0.000170887	+	0.144762i
$291$		0			0
$292$	−1.81145	−	0.755341i	−0.106007	−	0.0442030i
$293$	23.6486	−	4.70399i	1.38156	−	0.274810i	0.552290	−	0.833652i	$-0.313754\pi$
$293$	23.6486	−	4.70399i	1.38156	−	0.274810i	0.829274	+	0.558842i	$0.188754\pi$
$294$		0			0
$295$	−1.46022	+	0.604844i	−0.0850174	+	0.0352154i
$296$	12.2202	−	18.1494i	0.710286	−	1.05491i
$297$		0			0
$298$	−12.3319	+	2.43784i	−0.714370	+	0.141220i
$299$	7.43093	−	11.1212i	0.429742	−	0.643154i
$300$		0			0
$301$	−5.50476	−	1.09497i	−0.317289	−	0.0631127i
$302$	2.18196	+	5.28536i	0.125558	+	0.304139i
$303$		0			0
$304$	−10.2521	−	2.08965i	−0.588000	−	0.119850i
$305$	−2.32784	+	2.32784i	−0.133292	+	0.133292i
$306$		0			0
$307$	1.72081	−	8.65108i	0.0982116	−	0.493743i	−0.900101	−	0.435681i	$-0.856508\pi$
$307$	1.72081	−	8.65108i	0.0982116	−	0.493743i	0.998313	−	0.0580626i	$-0.0184923\pi$
$308$	13.0632	+	2.63051i	0.744345	+	0.149887i
$309$		0			0
$310$	−2.56495	−	1.71823i	−0.145679	−	0.0975887i
$311$	−1.49356	+	3.60578i	−0.0846923	+	0.204465i	−0.960552	−	0.278101i	$-0.910295\pi$
$311$	−1.49356	+	3.60578i	−0.0846923	+	0.204465i	0.875860	+	0.482566i	$0.160295\pi$
$312$		0			0
$313$	8.26474	+	19.9529i	0.467151	+	1.12780i	0.965401	+	0.260769i	$0.0839760\pi$
$313$	8.26474	+	19.9529i	0.467151	+	1.12780i	−0.498250	+	0.867033i	$0.666024\pi$
$314$	−15.8292	−	3.16806i	−0.893296	−	0.178784i
$315$		0			0
$316$	2.39749	+	2.40884i	0.134869	+	0.135508i
$317$	−16.4821	−	24.6672i	−0.925727	−	1.38545i	−0.922728	−	0.385452i	$-0.874045\pi$
$317$	−16.4821	−	24.6672i	−0.925727	−	1.38545i	−0.00299906	−	0.999996i	$-0.500955\pi$
$318$		0			0
$319$	32.5219			1.82087
$320$	−2.08423	+	0.399254i	−0.116512	+	0.0223190i
$321$		0			0
$322$	5.40952	−	5.39676i	0.301461	−	0.300750i
$323$	−2.26505	−	3.38988i	−0.126030	−	0.188618i
$324$		0			0
$325$	3.20509	+	16.1131i	0.177786	+	0.893793i
$326$	−0.00526805	−	0.00105435i	−0.000291770	−	5.83949e-5i
$327$		0			0
$328$	29.6453	−	12.1567i	1.63689	−	0.671239i
$329$	−1.69994	+	4.10401i	−0.0937206	+	0.226261i
$330$		0			0
$331$	−0.162367	−	0.108490i	−0.00892448	−	0.00596315i	0.551100	−	0.834439i	$-0.314208\pi$
$331$	−0.162367	−	0.108490i	−0.00892448	−	0.00596315i	−0.560024	+	0.828476i	$0.689208\pi$
$332$	6.08197	−	30.2033i	0.333792	−	1.65762i
$333$		0			0
$334$	−6.06174	−	2.51924i	−0.331683	−	0.137847i
$335$	0.657660	−	0.657660i	0.0359318	−	0.0359318i
$336$		0			0
$337$	6.58517	+	6.58517i	0.358717	+	0.358717i	0.863340	−	0.504623i	$-0.168368\pi$
$337$	6.58517	+	6.58517i	0.358717	+	0.358717i	−0.504623	+	0.863340i	$0.668368\pi$
$338$	−1.02180	−	2.47510i	−0.0555786	−	0.134628i
$339$		0			0
$340$	−0.686460	−	0.461026i	−0.0372285	−	0.0250026i
$341$	−22.6275	+	33.8645i	−1.22535	+	1.83386i
$342$		0			0
$343$	−15.1588	−	6.27897i	−0.818497	−	0.339032i
$344$	−2.25948	−	11.5732i	−0.121823	−	0.623987i
$345$		0			0
$346$	5.81218	+	8.72081i	0.312465	+	0.468834i
$347$	24.8134	−	4.93570i	1.33206	−	0.264962i	0.522818	−	0.852444i	$-0.324881\pi$
$347$	24.8134	−	4.93570i	1.33206	−	0.264962i	0.809237	+	0.587482i	$0.199881\pi$
$348$		0			0
$349$	−10.7430	+	7.17827i	−0.575062	+	0.384244i	−0.808825	−	0.588050i	$-0.799896\pi$
$349$	−10.7430	+	7.17827i	−0.575062	+	0.384244i	0.233763	+	0.972294i	$0.424896\pi$
$350$	−0.0110794	+	9.38559i	−0.000592220	+	0.501681i
$351$		0			0
$352$	5.29956	+	27.4897i	0.282467	+	1.46520i
$353$			15.3080i			0.814764i	0.913258	+	0.407382i	$0.133558\pi$
$353$			15.3080i			0.814764i	−0.913258	+	0.407382i	$0.866442\pi$
$354$		0			0
$355$	3.10848	−	2.07702i	0.164981	−	0.110237i
$356$	1.37174	+	3.33391i	0.0727020	+	0.176697i
$357$		0			0
$358$	14.8856	−	9.92082i	0.786727	−	0.524332i
$359$	−7.28425	+	3.01723i	−0.384448	+	0.159243i	−0.566533	−	0.824039i	$-0.691715\pi$
$359$	−7.28425	+	3.01723i	−0.384448	+	0.159243i	0.182085	+	0.983283i	$0.441715\pi$
$360$		0			0
$361$	−11.2325	−	4.65264i	−0.591183	−	0.244876i
$362$	4.44225	+	22.4713i	0.233479	+	1.18107i
$363$		0			0
$364$	1.72982	+	8.80498i	0.0906672	+	0.461506i
$365$	0.255306	+	0.0507835i	0.0133633	+	0.00265813i
$366$		0			0
$367$	−9.38201	−	9.38201i	−0.489737	−	0.489737i	0.418486	−	0.908223i	$-0.362561\pi$
$367$	−9.38201	−	9.38201i	−0.489737	−	0.489737i	−0.908223	+	0.418486i	$0.862561\pi$
$368$	14.8025	+	6.21344i	0.771633	+	0.323898i
$369$		0			0
$370$	−1.11371	+	2.67979i	−0.0578992	+	0.139316i
$371$	1.05452	−	5.30144i	0.0547480	−	0.275237i
$372$		0			0
$373$	1.73641	+	1.16023i	0.0899078	+	0.0600745i	0.599712	−	0.800216i	$-0.295282\pi$
$373$	1.73641	+	1.16023i	0.0899078	+	0.0600745i	−0.509804	+	0.860291i	$0.670282\pi$
$374$	−6.07132	+	9.06320i	−0.313941	+	0.468647i
$375$		0			0
$376$	−9.33262	−	0.0330508i	−0.481293	−	0.00170446i
$377$	8.38081	+	20.2331i	0.431634	+	1.04206i
$378$		0			0
$379$	−6.02722	−	30.3009i	−0.309597	−	1.55645i	−0.751711	−	0.659492i	$-0.770771\pi$
$379$	−6.02722	−	30.3009i	−0.309597	−	1.55645i	0.442114	−	0.896959i	$-0.354229\pi$
$380$	1.38772	+	0.00327634i	0.0711887	+	0.000168073i
$381$		0			0
$382$	17.1966	+	17.2372i	0.879852	+	0.881932i
$383$	28.6473			1.46381			0.731904	−	0.681408i	$-0.238632\pi$
$383$	28.6473			1.46381			0.731904	+	0.681408i	$0.238632\pi$
$384$		0			0
$385$	−1.76739			−0.0900744
$386$	12.7457	+	12.7758i	0.648739	+	0.650273i
$387$		0			0
$388$	−30.8413	−	0.0728147i	−1.56573	−	0.00369661i
$389$	1.69036	+	8.49804i	0.0857049	+	0.430868i	0.999685	+	0.0251080i	$0.00799298\pi$
$389$	1.69036	+	8.49804i	0.0857049	+	0.430868i	−0.913980	+	0.405760i	$0.867007\pi$
$390$		0			0
$391$	2.39386	+	5.77929i	0.121063	+	0.292271i
$392$	0.0519617	−	14.6725i	0.00262446	−	0.741075i
$393$		0			0
$394$	3.92234	−	5.85523i	0.197605	−	0.294982i
$395$	−0.374798	−	0.250432i	−0.0188581	−	0.0126006i
$396$		0			0
$397$	3.77514	−	18.9789i	0.189469	−	0.952525i	−0.762653	−	0.646808i	$-0.776104\pi$
$397$	3.77514	−	18.9789i	0.189469	−	0.952525i	0.952122	−	0.305718i	$-0.0988963\pi$
$398$	12.5594	−	30.2202i	0.629547	−	1.51480i
$399$		0			0
$400$	−18.2530	+	7.45985i	−0.912649	+	0.372993i
$401$	−22.1086	−	22.1086i	−1.10405	−	1.10405i	−0.993917	−	0.110133i	$-0.964872\pi$
$401$	−22.1086	−	22.1086i	−1.10405	−	1.10405i	−0.110133	−	0.993917i	$-0.535128\pi$
$402$		0			0
$403$	−26.8994	−	5.35063i	−1.33996	−	0.266534i
$404$	−3.24225	−	16.5034i	−0.161308	−	0.821076i
$405$		0			0
$406$	2.42635	+	12.2738i	0.120418	+	0.609139i
$407$	35.3701	+	14.6508i	1.75323	+	0.726212i
$408$		0			0
$409$	−0.412610	+	0.170909i	−0.0204023	+	0.00845089i	−0.392861	−	0.919598i	$-0.628515\pi$
$409$	−0.412610	+	0.170909i	−0.0204023	+	0.00845089i	0.372459	+	0.928049i	$0.378515\pi$
$410$	−3.53627	+	2.35683i	−0.174644	+	0.116395i
$411$		0			0
$412$	−7.75285	−	18.8427i	−0.381955	−	0.928315i
$413$	−6.66962	+	4.45650i	−0.328191	+	0.219290i
$414$		0			0
$415$			4.08636i			0.200591i
$416$	−15.7367	+	10.3811i	−0.771554	+	0.508975i
$417$		0			0
$418$	0.0216114	−	18.3074i	0.00105705	−	0.895444i
$419$	−24.9030	+	16.6397i	−1.21659	+	0.812901i	−0.987052	−	0.160398i	$-0.948722\pi$
$419$	−24.9030	+	16.6397i	−1.21659	+	0.812901i	−0.229541	+	0.973299i	$0.573722\pi$
$420$		0			0
$421$	27.6476	−	5.49946i	1.34746	−	0.268027i	0.531955	−	0.846772i	$-0.321457\pi$
$421$	27.6476	−	5.49946i	1.34746	−	0.268027i	0.815508	+	0.578745i	$0.196457\pi$
$422$	2.92277	+	4.38543i	0.142278	+	0.213479i
$423$		0			0
$424$	11.1458	−	2.17602i	0.541286	−	0.105677i
$425$	−7.09863	−	2.94035i	−0.344334	−	0.142628i
$426$		0			0
$427$	−9.28237	+	13.8920i	−0.449205	+	0.672283i
$428$	−3.16731	−	2.12716i	−0.153098	−	0.102820i
$429$		0			0
$430$	0.596799	+	1.44563i	0.0287802	+	0.0697143i
$431$	−5.47861	−	5.47861i	−0.263896	−	0.263896i	0.562739	−	0.826635i	$-0.309748\pi$
$431$	−5.47861	−	5.47861i	−0.263896	−	0.263896i	−0.826635	+	0.562739i	$0.809748\pi$
$432$		0			0
$433$	−13.9653	+	13.9653i	−0.671130	+	0.671130i	−0.957977	−	0.286847i	$-0.907393\pi$
$433$	−13.9653	+	13.9653i	−0.671130	+	0.671130i	0.286847	+	0.957977i	$0.407393\pi$
$434$	−14.4687	−	6.01314i	−0.694519	−	0.288640i
$435$		0			0
$436$	−1.71077	+	8.49576i	−0.0819312	+	0.406873i
$437$	−8.72880	−	5.83240i	−0.417555	−	0.279001i
$438$		0			0
$439$	7.32429	−	17.6824i	0.349569	−	0.843935i	−0.647102	−	0.762404i	$-0.724019\pi$
$439$	7.32429	−	17.6824i	0.349569	−	0.843935i	0.996671	−	0.0815308i	$-0.0259809\pi$
$440$	−1.40881	−	3.43553i	−0.0671624	−	0.163783i
$441$		0			0
$442$	−7.20313	−	1.44163i	−0.342618	−	0.0685715i
$443$	−1.03061	−	5.18121i	−0.0489656	−	0.246167i	0.948549	−	0.316631i	$-0.102552\pi$
$443$	−1.03061	−	5.18121i	−0.0489656	−	0.246167i	−0.997514	+	0.0704647i	$0.977552\pi$
$444$		0			0
$445$	−0.265647	−	0.397569i	−0.0125929	−	0.0188466i
$446$	−23.7295	+	23.6736i	−1.12363	+	1.12098i
$447$		0			0
$448$	−9.97927	+	4.05098i	−0.471476	+	0.191391i
$449$	−25.4195			−1.19962			−0.599809	−	0.800143i	$-0.704757\pi$
$449$	−25.4195			−1.19962			−0.599809	+	0.800143i	$0.704757\pi$
$450$		0			0
$451$	31.1472	+	46.6151i	1.46666	+	2.19502i
$452$	−2.26362	−	2.27434i	−0.106472	−	0.106976i
$453$		0			0
$454$	−14.6504	−	2.93214i	−0.687579	−	0.137612i
$455$	−0.455452	−	1.09956i	−0.0213519	−	0.0515481i
$456$		0			0
$457$	0.410387	−	0.990763i	0.0191971	−	0.0463459i	−0.913990	−	0.405736i	$-0.867015\pi$
$457$	0.410387	−	0.990763i	0.0191971	−	0.0463459i	0.933187	+	0.359390i	$0.117015\pi$
$458$	16.8895	+	11.3140i	0.789193	+	0.528671i
$459$		0			0
$460$	−2.08735	−	0.420324i	−0.0973230	−	0.0195977i
$461$	0.499040	−	2.50885i	0.0232426	−	0.116849i	−0.967422	−	0.253168i	$-0.918527\pi$
$461$	0.499040	−	2.50885i	0.0232426	−	0.116849i	0.990665	+	0.136320i	$0.0435274\pi$
$462$		0			0
$463$	−23.9046	+	23.9046i	−1.11094	+	1.11094i	−0.117915	+	0.993024i	$0.537621\pi$
$463$	−23.9046	+	23.9046i	−1.11094	+	1.11094i	−0.993024	+	0.117915i	$0.962379\pi$
$464$	−21.9243	+	14.5001i	−1.01781	+	0.673150i
$465$		0			0
$466$	2.94620	+	7.13658i	0.136480	+	0.330596i
$467$	−32.9221	−	6.54862i	−1.52345	−	0.303034i	−0.638833	−	0.769345i	$-0.720583\pi$
$467$	−32.9221	−	6.54862i	−1.52345	−	0.303034i	−0.884621	+	0.466311i	$0.845583\pi$
$468$		0			0
$469$	2.62244	−	3.92476i	0.121093	−	0.181229i
$470$	1.21432	−	0.240053i	0.0560124	−	0.0110728i
$471$		0			0
$472$	−13.9792	−	9.41238i	−0.643445	−	0.433240i
$473$	19.0619	−	7.89570i	0.876468	−	0.363045i
$474$		0			0
$475$	12.6468	−	2.51561i	0.580277	−	0.115424i
$476$	−3.87343	−	1.61515i	−0.177538	−	0.0740304i
$477$		0			0
$478$	−0.0323016	+	27.3633i	−0.00147744	+	1.25157i
$479$			17.7201i			0.809654i	0.914393	+	0.404827i	$0.132668\pi$
$479$			17.7201i			0.809654i	−0.914393	+	0.404827i	$0.867332\pi$
$480$		0			0
$481$			25.7805i			1.17549i
$482$	−4.44062	−	0.00524203i	−0.202265	−	0.000238768i
$483$		0			0
$484$	−24.9556	+	10.2680i	−1.13435	+	0.466727i
$485$	4.01198	−	0.798033i	0.182175	−	0.0362368i
$486$		0			0
$487$	22.3630	−	9.26304i	1.01336	−	0.419749i	0.186682	−	0.982420i	$-0.440227\pi$
$487$	22.3630	−	9.26304i	1.01336	−	0.419749i	0.826680	+	0.562672i	$0.190227\pi$
$488$	−34.4031	−	6.96995i	−1.55736	−	0.315515i
$489$		0			0
$490$	0.377406	+	1.90913i	0.0170495	+	0.0862455i
$491$	16.5333	−	24.7438i	0.746136	−	1.11667i	−0.243051	−	0.970013i	$-0.578148\pi$
$491$	16.5333	−	24.7438i	0.746136	−	1.11667i	0.989187	−	0.146658i	$-0.0468517\pi$
$492$		0			0
$493$	−10.0456	−	1.99819i	−0.452430	−	0.0899940i
$494$	11.3953	−	4.70433i	0.512699	−	0.211658i
$495$		0			0
$496$	0.155436	−	32.9181i	0.00697930	−	1.47806i
$497$	13.4165	−	13.4165i	0.601810	−	0.601810i
$498$		0			0
$499$	−5.85555	+	29.4378i	−0.262130	+	1.31782i	0.595419	+	0.803416i	$0.296986\pi$
$499$	−5.85555	+	29.4378i	−0.262130	+	1.31782i	−0.857549	+	0.514402i	$0.828014\pi$
$500$	4.38706	−	2.91638i	0.196195	−	0.130425i
$501$		0			0
$502$	−2.94404	+	4.39482i	−0.131399	+	0.196151i
$503$	−2.73931	+	6.61328i	−0.122140	+	0.294871i	−0.973109	−	0.230343i	$-0.926015\pi$
$503$	−2.73931	+	6.61328i	−0.122140	+	0.294871i	0.850970	+	0.525215i	$0.176015\pi$
$504$		0			0
$505$	0.853666	+	2.06093i	0.0379876	+	0.0917102i
$506$	−5.51256	+	27.5435i	−0.245063	+	1.22446i
$507$		0			0
$508$	0.0858883	−	36.3788i	0.00381068	−	1.61405i
$509$	−3.41939	−	5.11748i	−0.151562	−	0.226829i	0.747917	−	0.663792i	$-0.231054\pi$
$509$	−3.41939	−	5.11748i	−0.151562	−	0.226829i	−0.899479	+	0.436963i	$0.856054\pi$
$510$		0			0
$511$	1.32111			0.0584423
$512$	−15.8291	−	16.1691i	−0.699555	−	0.714579i
$513$		0			0
$514$	17.3659	+	17.4069i	0.765976	+	0.767787i
$515$	1.50140	+	2.24700i	0.0661594	+	0.0990145i
$516$		0			0
$517$	−3.18578	−	16.0160i	−0.140110	−	0.704382i
$518$	−2.89038	+	14.4418i	−0.126996	+	0.634535i
$519$		0			0
$520$	1.77433	−	1.76180i	0.0778093	−	0.0772602i
$521$	−5.10532	+	12.3253i	−0.223668	+	0.539983i	−0.995383	−	0.0959866i	$-0.969399\pi$
$521$	−5.10532	+	12.3253i	−0.223668	+	0.539983i	0.771715	+	0.635969i	$0.219399\pi$
$522$		0			0
$523$	22.7053	+	15.1712i	0.992835	+	0.663391i	0.942104	−	0.335321i	$-0.108845\pi$
$523$	22.7053	+	15.1712i	0.992835	+	0.663391i	0.0507311	+	0.998712i	$0.483845\pi$
$524$	−15.0287	+	9.99062i	−0.656532	+	0.436442i
$525$		0			0
$526$	−0.931702	+	2.24184i	−0.0406241	+	0.0977488i
$527$	9.07003	−	9.07003i	0.395097	−	0.395097i
$528$		0			0
$529$	−4.87371	−	4.87371i	−0.211900	−	0.211900i
$530$	−1.39223	+	0.574756i	−0.0604746	+	0.0249658i
$531$		0			0
$532$	6.91086	−	1.35770i	0.299624	−	0.0588638i
$533$	−20.9744	+	31.3905i	−0.908504	+	1.35967i
$534$		0			0
$535$	0.467517	+	0.193652i	0.0202125	+	0.00837231i
$536$	9.71953	+	1.96914i	0.419820	+	0.0850540i
$537$		0			0
$538$	−7.57272	+	5.04701i	−0.326483	+	0.217592i
$539$	25.1800	−	5.00861i	1.08458	−	0.215736i
$540$		0			0
$541$	−1.36491	+	0.912006i	−0.0586822	+	0.0392102i	−0.584565	−	0.811347i	$-0.698735\pi$
$541$	−1.36491	+	0.912006i	−0.0586822	+	0.0392102i	0.525883	+	0.850557i	$0.323735\pi$
$542$	34.2095	+	0.0403834i	1.46943	+	0.00173462i
$543$		0			0
$544$	0.0520406	−	8.81682i	0.00223122	−	0.378018i
$545$		−	1.14944i		−	0.0492364i
$546$		0			0
$547$	35.6558	−	23.8244i	1.52453	−	1.01866i	0.540361	−	0.841434i	$-0.318288\pi$
$547$	35.6558	−	23.8244i	1.52453	−	1.01866i	0.984170	−	0.177225i	$-0.0567122\pi$
$548$	14.4511	+	6.02584i	0.617319	+	0.257411i
$549$		0			0
$550$	−19.1346	−	28.7102i	−0.815901	−	1.22421i
$551$	15.8805	−	6.57794i	0.676534	−	0.280230i
$552$		0			0
$553$	−2.11357	−	0.875469i	−0.0898782	−	0.0372287i
$554$	10.1914	−	2.01469i	0.432990	−	0.0855959i
$555$		0			0
$556$	−3.96713	+	5.90699i	−0.168244	+	0.250512i
$557$	2.38952	+	0.475305i	0.101247	+	0.0201393i	0.245454	−	0.969408i	$-0.421063\pi$
$557$	2.38952	+	0.475305i	0.101247	+	0.0201393i	−0.144207	+	0.989548i	$0.546063\pi$
$558$		0			0
$559$	9.82443	+	9.82443i	0.415529	+	0.415529i
$560$	1.19147	−	0.788002i	0.0503487	−	0.0332991i
$561$		0			0
$562$	−23.7828	−	9.88408i	−1.00322	−	0.416935i
$563$	−2.89115	+	14.5348i	−0.121847	+	0.612567i	0.870811	+	0.491617i	$0.163594\pi$
$563$	−2.89115	+	14.5348i	−0.121847	+	0.612567i	−0.992659	+	0.120950i	$0.961406\pi$
$564$		0			0
$565$	0.353871	+	0.236449i	0.0148874	+	0.00994748i
$566$	−26.7354	−	17.9097i	−1.12377	−	0.752802i
$567$		0			0
$568$	36.7740	+	15.3851i	1.54300	+	0.645544i
$569$	13.6164	+	32.8729i	0.570829	+	1.37810i	0.900851	+	0.434129i	$0.142944\pi$
$569$	13.6164	+	32.8729i	0.570829	+	1.37810i	−0.330022	+	0.943973i	$0.607056\pi$
$570$		0			0
$571$	−4.08279	−	20.5256i	−0.170859	−	0.858968i	−0.967180	−	0.254093i	$-0.918223\pi$
$571$	−4.08279	−	20.5256i	−0.170859	−	0.858968i	0.796321	−	0.604875i	$-0.206777\pi$
$572$	−23.2700	−	23.3801i	−0.972966	−	0.977571i
$573$		0			0
$574$	−15.2688	+	15.2328i	−0.637308	+	0.635805i
$575$	−19.7847			−0.825079
$576$		0			0
$577$	−13.2749			−0.552640			−0.276320	−	0.961066i	$-0.589115\pi$
$577$	−13.2749			−0.552640			−0.276320	+	0.961066i	$0.589115\pi$
$578$	−14.5878	+	14.5534i	−0.606774	+	0.605344i
$579$		0			0
$580$	2.47102	−	2.45938i	0.102603	−	0.102120i
$581$	4.04598	+	20.3405i	0.167855	+	0.843866i
$582$		0			0
$583$	7.60407	+	18.3578i	0.314928	+	0.760304i
$584$	1.05307	+	2.56803i	0.0435765	+	0.106266i
$585$		0			0
$586$	−28.3302	−	18.9780i	−1.17031	−	0.783975i
$587$	5.72679	+	3.82652i	0.236370	+	0.157937i	0.668114	−	0.744059i	$-0.267102\pi$
$587$	5.72679	+	3.82652i	0.236370	+	0.157937i	−0.431744	+	0.901996i	$0.642102\pi$
$588$		0			0
$589$	−4.19960	+	21.1128i	−0.173042	+	0.869939i
$590$	2.06406	+	0.857816i	0.0849758	+	0.0353157i
$591$		0			0
$592$	−30.3766	+	5.89331i	−1.24847	+	0.242213i
$593$	−5.93109	−	5.93109i	−0.243561	−	0.243561i	0.574761	−	0.818321i	$-0.305095\pi$
$593$	−5.93109	−	5.93109i	−0.243561	−	0.243561i	−0.818321	+	0.574761i	$0.805095\pi$
$594$		0			0
$595$	0.545923	+	0.108591i	0.0223807	+	0.00445179i
$596$	14.7581	+	9.91152i	0.604515	+	0.405991i
$597$		0			0
$598$	−18.5565	+	3.66834i	−0.758830	+	0.150010i
$599$	−8.60956	−	3.56620i	−0.351777	−	0.145711i	0.199796	−	0.979838i	$-0.435972\pi$
$599$	−8.60956	−	3.56620i	−0.351777	−	0.145711i	−0.551573	+	0.834127i	$0.685972\pi$
$600$		0			0
$601$	−9.04530	+	3.74668i	−0.368965	+	0.152830i	−0.559459	−	0.828858i	$-0.688991\pi$
$601$	−9.04530	+	3.74668i	−0.368965	+	0.152830i	0.190494	+	0.981688i	$0.438991\pi$
$602$	4.40200	+	6.60493i	0.179412	+	0.269197i
$603$		0			0
$604$	3.11221	−	7.46366i	0.126634	−	0.303692i
$605$	2.97596	−	1.98847i	0.120990	−	0.0808430i
$606$		0			0
$607$		−	34.8085i		−	1.41283i	−0.707796	−	0.706417i	$-0.750311\pi$
$607$		−	34.8085i		−	1.41283i	0.707796	−	0.706417i	$-0.249689\pi$
$608$	8.14791	+	12.3514i	0.330441	+	0.500916i
$609$		0			0
$610$	4.65568	+	0.00549590i	0.188503	+	0.000222523i
$611$	9.14318	−	6.10928i	0.369894	−	0.247155i
$612$		0			0
$613$	14.7093	−	2.92585i	0.594101	−	0.118174i	0.111123	−	0.993807i	$-0.464555\pi$
$613$	14.7093	−	2.92585i	0.594101	−	0.118174i	0.482978	+	0.875632i	$0.339555\pi$
$614$	−10.3801	+	6.91802i	−0.418905	+	0.279189i
$615$		0			0
$616$	−10.4142	−	15.7060i	−0.419598	−	0.632813i
$617$	−7.99200	−	3.31040i	−0.321746	−	0.133272i	0.215964	−	0.976401i	$-0.430711\pi$
$617$	−7.99200	−	3.31040i	−0.321746	−	0.133272i	−0.537710	+	0.843130i	$0.680711\pi$
$618$		0			0
$619$	−4.66067	+	6.97519i	−0.187328	+	0.280356i	−0.913232	−	0.407440i	$-0.866422\pi$
$619$	−4.66067	+	6.97519i	−0.187328	+	0.280356i	0.725904	+	0.687796i	$0.241422\pi$
$620$	0.841665	+	4.28417i	0.0338021	+	0.172056i
$621$		0			0
$622$	5.10184	−	2.10620i	0.204565	−	0.0844509i
$623$	−1.71594	−	1.71594i	−0.0687477	−	0.0687477i
$624$		0			0
$625$	16.9348	−	16.9348i	0.677393	−	0.677393i
$626$	11.7214	−	28.2038i	0.468482	−	1.12725i
$627$		0			0
$628$	12.6387	+	19.0122i	0.504341	+	0.758671i
$629$	−10.0252	−	6.69862i	−0.399731	−	0.267092i
$630$		0			0
$631$	12.6693	−	30.5864i	0.504358	−	1.21763i	−0.442731	−	0.896654i	$-0.645990\pi$
$631$	12.6693	−	30.5864i	0.504358	−	1.21763i	0.947089	−	0.320972i	$-0.104010\pi$
$632$	0.0170212	−	4.80631i	0.000677067	−	0.191185i
$633$		0			0
$634$	−8.23367	+	41.1396i	−0.327001	+	1.63386i
$635$	0.941317	+	4.73232i	0.0373550	+	0.187796i
$636$		0			0
$637$	9.60488	+	14.3747i	0.380559	+	0.569547i
$638$	−32.4834	−	32.5602i	−1.28603	−	1.28907i
$639$		0			0
$640$	2.48149	+	1.68791i	0.0980896	+	0.0667203i
$641$	−10.2292			−0.404030			−0.202015	−	0.979382i	$-0.564749\pi$
$641$	−10.2292			−0.404030			−0.202015	+	0.979382i	$0.564749\pi$
$642$		0			0
$643$	−4.22568	−	6.32418i	−0.166645	−	0.249401i	0.738743	−	0.673987i	$-0.235420\pi$
$643$	−4.22568	−	6.32418i	−0.166645	−	0.249401i	−0.905388	+	0.424586i	$0.860420\pi$
$644$	−10.8063	−	0.0255130i	−0.425826	−	0.00100535i
$645$		0			0
$646$	−1.13151	+	5.65359i	−0.0445186	+	0.222438i
$647$	7.05188	+	17.0247i	0.277238	+	0.669311i	0.999757	−	0.0220394i	$-0.00701594\pi$
$647$	7.05188	+	17.0247i	0.277238	+	0.669311i	−0.722519	+	0.691351i	$0.757016\pi$
$648$		0			0
$649$	11.2845	−	27.2431i	0.442954	−	1.06939i
$650$	12.9308	−	19.3029i	0.507187	−	0.757123i
$651$		0			0
$652$	0.00420624	+	0.00632737i	0.000164729	+	0.000247799i
$653$	−5.75170	+	28.9158i	−0.225081	+	1.13156i	0.688604	+	0.725138i	$0.258224\pi$
$653$	−5.75170	+	28.9158i	−0.225081	+	1.13156i	−0.913685	+	0.406423i	$0.866776\pi$
$654$		0			0
$655$	1.69250	−	1.69250i	0.0661314	−	0.0661314i
$656$	−41.7813	−	17.5380i	−1.63128	−	0.684742i
$657$		0			0
$658$	5.80678	−	2.39722i	0.226372	−	0.0934534i
$659$	4.76397	+	0.947613i	0.185578	+	0.0369138i	0.287004	−	0.957929i	$-0.407341\pi$
$659$	4.76397	+	0.947613i	0.185578	+	0.0369138i	−0.101426	+	0.994843i	$0.532341\pi$
$660$		0			0
$661$	−14.3165	+	21.4261i	−0.556846	+	0.833378i	−0.997945	−	0.0640799i	$-0.979589\pi$
$661$	−14.3165	+	21.4261i	−0.556846	+	0.833378i	0.441099	+	0.897458i	$0.354589\pi$
$662$	0.0535570	+	0.270920i	0.00208155	+	0.0105296i
$663$		0			0
$664$	−36.3137	+	24.0785i	−1.40925	+	0.934426i
$665$	−0.863022	+	0.357475i	−0.0334665	+	0.0138623i
$666$		0			0
$667$	−25.8670	+	5.14526i	−1.00157	+	0.199225i
$668$	3.53236	+	8.58515i	0.136671	+	0.332169i
$669$		0			0
$670$	−1.31532	−	0.00155270i	−0.0508152	−	5.99859e-5i
$671$		−	61.4195i		−	2.37107i
$672$		0			0
$673$			7.18022i			0.276777i	0.990378	+	0.138389i	$0.0441923\pi$
$673$			7.18022i			0.276777i	−0.990378	+	0.138389i	$0.955808\pi$
$674$	0.0155472	−	13.1703i	0.000598856	−	0.507302i
$675$		0			0
$676$	−1.45743	+	3.49518i	−0.0560550	+	0.134430i
$677$	−0.516673	+	0.102773i	−0.0198574	+	0.00394987i	−0.205009	−	0.978760i	$-0.565722\pi$
$677$	−0.516673	+	0.102773i	−0.0198574	+	0.00394987i	0.185152	+	0.982710i	$0.440722\pi$
$678$		0			0
$679$	19.1801	−	7.94467i	0.736066	−	0.304888i
$680$	0.224079	+	1.14775i	0.00859305	+	0.0440142i
$681$		0			0
$682$	56.5052	−	11.1703i	2.16370	−	0.427731i
$683$	−10.6617	+	15.9564i	−0.407960	+	0.610555i	−0.977380	−	0.211492i	$-0.932168\pi$
$683$	−10.6617	+	15.9564i	−0.407960	+	0.610555i	0.569420	+	0.822047i	$0.307168\pi$
$684$		0			0
$685$	−2.03674	−	0.405133i	−0.0778199	−	0.0154793i
$686$	8.85449	+	21.4482i	0.338066	+	0.818896i
$687$		0			0
$688$	−9.33007	+	13.8217i	−0.355706	+	0.526948i
$689$	−9.46156	+	9.46156i	−0.360457	+	0.360457i
$690$		0			0
$691$	8.09941	−	40.7185i	0.308116	−	1.54901i	−0.447677	−	0.894195i	$-0.647749\pi$
$691$	8.09941	−	40.7185i	0.308116	−	1.54901i	0.755794	−	0.654810i	$-0.227251\pi$
$692$	2.92578	−	14.5295i	0.111222	−	0.552331i
$693$		0			0
$694$	−29.7257	−	19.9128i	−1.12837	−	0.755881i
$695$	0.361158	−	0.871912i	0.0136995	−	0.0330735i
$696$		0			0
$697$	−6.75687	−	16.3125i	−0.255935	−	0.617881i
$698$	17.9171	+	3.58592i	0.678172	+	0.135729i
$699$		0			0
$700$	9.40773	−	9.36341i	0.355579	−	0.353904i
$701$	−2.87333	−	4.30025i	−0.108524	−	0.162418i	0.773232	−	0.634123i	$-0.218639\pi$
$701$	−2.87333	−	4.30025i	−0.108524	−	0.162418i	−0.881756	+	0.471705i	$0.843639\pi$
$702$		0			0
$703$	20.2346			0.763164
$704$	22.2288	−	32.7630i	0.837780	−	1.23480i
$705$		0			0
$706$	15.3261	−	15.2899i	0.576805	−	0.575445i
$707$	6.28982	+	9.41338i	0.236553	+	0.354027i
$708$		0			0
$709$	8.49385	+	42.7015i	0.318993	+	1.60369i	0.724286	+	0.689500i	$0.242170\pi$
$709$	8.49385	+	42.7015i	0.318993	+	1.60369i	−0.405292	+	0.914187i	$0.632830\pi$
$710$	−5.18428	−	1.03758i	−0.194563	−	0.0389397i
$711$		0			0
$712$	1.96773	−	4.70333i	0.0737436	−	0.176265i
$713$	12.6396	−	30.5147i	0.473357	−	1.14278i
$714$		0			0
$715$	3.63778	+	2.43068i	0.136045	+	0.0909024i
$716$	−24.8005	−	4.99403i	−0.926838	−	0.186635i
$717$		0			0
$718$	10.2964	+	4.27917i	0.384260	+	0.159697i
$719$	−4.80412	+	4.80412i	−0.179163	+	0.179163i	−0.790991	−	0.611828i	$-0.790435\pi$
$719$	−4.80412	+	4.80412i	−0.179163	+	0.179163i	0.611828	+	0.790991i	$0.290435\pi$
$720$		0			0
$721$	9.69822	+	9.69822i	0.361181	+	0.361181i
$722$	6.56107	+	15.8929i	0.244178	+	0.591472i
$723$		0			0
$724$	18.0608	−	26.8923i	0.671225	−	0.999443i
$725$	17.9974	−	26.9350i	0.668408	−	1.00034i
$726$		0			0
$727$	3.79111	+	1.57033i	0.140604	+	0.0582402i	0.451876	−	0.892081i	$-0.350755\pi$
$727$	3.79111	+	1.57033i	0.140604	+	0.0582402i	−0.311272	+	0.950321i	$0.600755\pi$
$728$	7.08759	−	10.5264i	0.262684	−	0.390136i
$729$		0			0
$730$	−0.204161	−	0.306331i	−0.00755634	−	0.0113378i
$731$	−6.37310	+	1.26769i	−0.235718	+	0.0468872i
$732$		0			0
$733$	37.2568	−	24.8942i	1.37611	−	0.919488i	0.376136	−	0.926564i	$-0.377253\pi$
$733$	37.2568	−	24.8942i	1.37611	−	0.919488i	0.999975	+	0.00707651i	$0.00225254\pi$
$734$	−0.0221504	+	18.7640i	−0.000817585	+	0.692592i
$735$		0			0
$736$	−8.56424	−	21.0261i	−0.315682	−	0.775031i
$737$			17.3522i			0.639175i
$738$		0			0
$739$	−29.8791	+	19.9646i	−1.09912	+	0.734409i	−0.966477	−	0.256754i	$-0.917347\pi$
$739$	−29.8791	+	19.9646i	−1.09912	+	0.734409i	−0.132645	+	0.991164i	$0.542347\pi$
$740$	3.79535	−	1.56160i	0.139520	−	0.0574055i
$741$		0			0
$742$	−6.36097	+	4.23941i	−0.233518	+	0.155634i
$743$	18.9414	−	7.84578i	0.694892	−	0.287834i	−0.00714476	−	0.999974i	$-0.502274\pi$
$743$	18.9414	−	7.84578i	0.694892	−	0.287834i	0.702037	+	0.712141i	$0.252274\pi$
$744$		0			0
$745$	−2.17840	−	0.902321i	−0.0798102	−	0.0330585i
$746$	−0.572757	−	2.89732i	−0.0209701	−	0.106078i
$747$		0			0
$748$	15.1380	−	2.97401i	0.553502	−	0.108740i
$749$	2.51888	+	0.501036i	0.0920379	+	0.0183075i
$750$		0			0
$751$	−5.62839	−	5.62839i	−0.205383	−	0.205383i	0.596919	−	0.802302i	$-0.296391\pi$
$751$	−5.62839	−	5.62839i	−0.205383	−	0.205383i	−0.802302	+	0.596919i	$0.796391\pi$
$752$	9.28850	+	9.37664i	0.338717	+	0.341931i
$753$		0			0
$754$	11.8860	−	28.5999i	0.432864	−	1.04155i
$755$	−0.209242	+	1.05193i	−0.00761510	+	0.0382837i
$756$		0			0
$757$	−17.5865	−	11.7509i	−0.639192	−	0.427095i	0.193293	−	0.981141i	$-0.438083\pi$
$757$	−17.5865	−	11.7509i	−0.639192	−	0.427095i	−0.832486	+	0.554046i	$0.813083\pi$
$758$	−24.3165	+	36.2994i	−0.883216	+	1.31845i
$759$		0			0
$760$	−1.38280	−	1.39263i	−0.0501596	−	0.0505161i
$761$	−8.96561	−	21.6449i	−0.325003	−	0.784627i	−0.998949	−	0.0458456i	$-0.985402\pi$
$761$	−8.96561	−	21.6449i	−0.325003	−	0.784627i	0.673946	−	0.738781i	$-0.264598\pi$
$762$		0			0
$763$	−1.13808	−	5.72150i	−0.0412011	−	0.207132i
$764$	0.0812961	−	34.4337i	0.00294119	−	1.24577i
$765$		0			0
$766$	−28.6135	−	28.6811i	−1.03385	−	1.03629i
$767$	19.8570			0.716993
$768$		0			0
$769$	6.14218			0.221493			0.110746	−	0.993849i	$-0.464676\pi$
$769$	6.14218			0.221493			0.110746	+	0.993849i	$0.464676\pi$
$770$	1.76530	+	1.76947i	0.0636170	+	0.0637673i
$771$		0			0
$772$	0.0602549	−	25.5215i	0.00216862	−	0.918538i
$773$	−3.65565	−	18.3782i	−0.131485	−	0.661018i	−0.989162	−	0.146830i	$-0.953093\pi$
$773$	−3.65565	−	18.3782i	−0.131485	−	0.661018i	0.857677	−	0.514189i	$-0.171907\pi$
$774$		0			0
$775$	15.5251	+	37.4808i	0.557677	+	1.34635i
$776$	30.7320	+	30.9504i	1.10321	+	1.11106i
$777$		0			0
$778$	6.81970	−	10.1804i	0.244498	−	0.364984i
$779$	24.6378	+	16.4624i	0.882739	+	0.589827i
$780$		0			0
$781$	−13.6074	+	68.4090i	−0.486911	+	2.44787i
$782$	3.39508	−	8.16915i	0.121408	−	0.292128i
$783$		0			0
$784$	−14.7417	+	14.6032i	−0.526491	+	0.521542i
$785$	−2.14111	−	2.14111i	−0.0764196	−	0.0764196i
$786$		0			0
$787$	−43.2635	−	8.60564i	−1.54218	−	0.306758i	−0.650526	−	0.759484i	$-0.725452\pi$
$787$	−43.2635	−	8.60564i	−1.54218	−	0.306758i	−0.891650	+	0.452726i	$0.850452\pi$
$788$	−9.77985	+	1.92134i	−0.348393	+	0.0684449i
$789$		0			0
$790$	0.123628	+	0.625376i	0.00439848	+	0.0222499i
$791$	1.99556	+	0.826587i	0.0709539	+	0.0293901i
$792$		0			0
$793$	38.2114	−	15.8277i	1.35693	−	0.562058i
$794$	−22.7720	+	15.1769i	−0.808148	+	0.538609i
$795$		0			0
$796$	−42.8004	+	17.6102i	−1.51702	+	0.624178i
$797$	39.2600	−	26.2327i	1.39066	−	0.929211i	0.390700	−	0.920518i	$-0.372233\pi$
$797$	39.2600	−	26.2327i	1.39066	−	0.929211i	0.999962	−	0.00869271i	$-0.00276701\pi$
$798$		0			0
$799$			5.14287i			0.181942i
$800$	25.7001	+	10.8235i	0.908635	+	0.382668i
$801$		0			0
$802$	−0.0521970	+	44.2171i	−0.00184314	+	1.56136i
$803$	−4.03804	+	2.69813i	−0.142499	+	0.0952151i
$804$		0			0
$805$	1.40573	−	0.279617i	0.0495454	−	0.00985520i
$806$	21.5107	+	32.2755i	0.757682	+	1.13685i
$807$		0			0
$808$	−13.2845	+	19.7300i	−0.467346	+	0.694099i
$809$	14.5037	+	6.00764i	0.509924	+	0.211217i	0.622784	−	0.782394i	$-0.286001\pi$
$809$	14.5037	+	6.00764i	0.509924	+	0.211217i	−0.112861	+	0.993611i	$0.536001\pi$
$810$		0			0
$811$	−15.8735	+	23.7564i	−0.557395	+	0.834200i	−0.997981	−	0.0635100i	$-0.979771\pi$
$811$	−15.8735	+	23.7564i	−0.557395	+	0.834200i	0.440586	+	0.897710i	$0.354771\pi$
$812$	9.86480	−	14.6885i	0.346187	−	0.515466i
$813$		0			0
$814$	−20.6603	−	50.0453i	−0.724141	−	1.75409i
$815$	−0.000712573	0	0.000712573i	−2.49603e−5	0	2.49603e-5i
$816$		0			0
$817$	7.71100	−	7.71100i	0.269774	−	0.269774i
$818$	0.583233	+	0.242390i	0.0203923	+	0.00847497i
$819$		0			0
$820$	5.89171	+	1.18640i	0.205747	+	0.0414309i
$821$	10.7690	+	7.19563i	0.375842	+	0.251129i	0.729116	−	0.684391i	$-0.239932\pi$
$821$	10.7690	+	7.19563i	0.375842	+	0.251129i	−0.353274	+	0.935520i	$0.614932\pi$
$822$		0			0
$823$	−5.78447	+	13.9649i	−0.201634	+	0.486788i	−0.992059	−	0.125771i	$-0.959860\pi$
$823$	−5.78447	+	13.9649i	−0.201634	+	0.486788i	0.790425	+	0.612558i	$0.209860\pi$
$824$	−11.1213	+	26.5825i	−0.387428	+	0.926044i
$825$		0			0
$826$	11.1235	+	2.22625i	0.387036	+	0.0774613i
$827$	−6.95283	−	34.9542i	−0.241774	−	1.21548i	−0.890687	−	0.454616i	$-0.849776\pi$
$827$	−6.95283	−	34.9542i	−0.241774	−	1.21548i	0.648914	−	0.760862i	$-0.275224\pi$
$828$		0			0
$829$	−15.3694	−	23.0020i	−0.533802	−	0.798891i	0.462335	−	0.886705i	$-0.347012\pi$
$829$	−15.3694	−	23.0020i	−0.533802	−	0.798891i	−0.996137	+	0.0878145i	$0.972012\pi$
$830$	4.09118	−	4.08153i	0.142007	−	0.141672i
$831$		0			0
$832$	26.1114	+	5.38642i	0.905251	+	0.186741i
$833$	−8.08551			−0.280146
$834$		0			0
$835$	−0.684068	−	1.02378i	−0.0236732	−	0.0354294i
$836$	−18.3506	+	18.2641i	−0.634668	+	0.631678i
$837$		0			0
$838$	41.5329	+	8.31239i	1.43473	+	0.287147i
$839$	11.8401	+	28.5844i	0.408764	+	0.986844i	0.985463	+	0.169887i	$0.0543404\pi$
$839$	11.8401	+	28.5844i	0.408764	+	0.986844i	−0.576699	+	0.816956i	$0.695660\pi$
$840$		0			0
$841$	5.42762	−	13.1034i	0.187159	−	0.451843i
$842$	−33.1209	−	22.1873i	−1.14142	−	0.764625i
$843$		0			0
$844$	1.47129	−	7.30647i	0.0506438	−	0.251499i
$845$	0.0979868	−	0.492613i	0.00337085	−	0.0169464i
$846$		0			0
$847$	12.8445	−	12.8445i	0.441342	−	0.441342i
$848$	−13.3112	−	8.98546i	−0.457108	−	0.308562i
$849$		0			0
$850$	4.14643	+	10.0439i	0.142221	+	0.344502i
$851$	−30.4502	−	6.05693i	−1.04382	−	0.207629i
$852$		0			0
$853$	−25.8867	+	38.7421i	−0.886343	+	1.32651i	0.0582640	+	0.998301i	$0.481443\pi$
$853$	−25.8867	+	38.7421i	−0.886343	+	1.32651i	−0.944607	+	0.328204i	$0.893557\pi$
$854$	23.1798	−	4.58232i	0.793198	−	0.156804i
$855$		0			0
$856$	1.03390	+	5.29570i	0.0353379	+	0.181003i
$857$	−11.6236	+	4.81466i	−0.397055	+	0.164466i	−0.572271	−	0.820064i	$-0.693938\pi$
$857$	−11.6236	+	4.81466i	−0.397055	+	0.164466i	0.175216	+	0.984530i	$0.443938\pi$
$858$		0			0
$859$	7.21770	−	1.43569i	0.246265	−	0.0489851i	−0.0704144	−	0.997518i	$-0.522432\pi$
$859$	7.21770	−	1.43569i	0.246265	−	0.0489851i	0.316679	+	0.948533i	$0.397432\pi$
$860$	0.851237	−	2.04142i	0.0290269	−	0.0696119i
$861$		0			0
$862$	−0.0129347	+	10.9572i	−0.000440557	+	0.373204i
$863$			51.3234i			1.74707i	0.486761	+	0.873535i	$0.338178\pi$
$863$			51.3234i			1.74707i	−0.486761	+	0.873535i	$0.661822\pi$
$864$		0			0
$865$			1.96578i			0.0668384i
$866$	27.9306	+	0.0329713i	0.949121	+	0.00112041i
$867$		0			0
$868$	8.43135	+	20.4918i	0.286179	+	0.695536i
$869$	8.24825	−	1.64068i	0.279803	−	0.0556562i
$870$		0			0
$871$	−10.7954	+	4.47162i	−0.365790	+	0.151515i
$872$	10.2145	−	6.77294i	0.345908	−	0.229361i
$873$		0			0
$874$	2.87921	+	14.5646i	0.0973907	+	0.492655i
$875$	−1.97009	+	2.94844i	−0.0666011	+	0.0996755i
$876$		0			0
$877$	41.5765	+	8.27007i	1.40394	+	0.279260i	0.838217	−	0.545337i	$-0.183598\pi$
$877$	41.5765	+	8.27007i	1.40394	+	0.279260i	0.565720	+	0.824597i	$0.308598\pi$
$878$	−25.0189	+	10.3286i	−0.844347	+	0.348573i
$879$		0			0
$880$	−2.03244	+	4.84195i	−0.0685135	+	0.163222i
$881$	−19.0362	+	19.0362i	−0.641347	+	0.641347i	−0.950887	−	0.309539i	$-0.899825\pi$
$881$	−19.0362	+	19.0362i	−0.641347	+	0.641347i	0.309539	+	0.950887i	$0.399825\pi$
$882$		0			0
$883$	−6.24157	+	31.3785i	−0.210046	+	1.05597i	0.721519	+	0.692395i	$0.243444\pi$
$883$	−6.24157	+	31.3785i	−0.210046	+	1.05597i	−0.931565	+	0.363576i	$0.881556\pi$
$884$	5.75129	+	8.65155i	0.193437	+	0.290983i
$885$		0			0
$886$	−4.15793	+	6.20691i	−0.139688	+	0.208525i
$887$	17.9162	−	43.2535i	0.601567	−	1.45231i	−0.270401	−	0.962748i	$-0.587156\pi$
$887$	17.9162	−	43.2535i	0.601567	−	1.45231i	0.871968	−	0.489563i	$-0.162844\pi$
$888$		0			0
$889$	9.37110	+	22.6238i	0.314297	+	0.758779i
$890$	−0.132705	+	0.663060i	−0.00444827	+	0.0222258i
$891$		0			0
$892$	47.4030	+	0.111916i	1.58717	+	0.00374723i
$893$	−4.79505	−	7.17630i	−0.160460	−	0.240146i
$894$		0			0
$895$	3.35539			0.112158
$896$	14.0232	+	5.94485i	0.468484	+	0.198603i
$897$		0			0
$898$	25.3894	+	25.4495i	0.847257	+	0.849259i
$899$	30.0452	+	44.9658i	1.00206	+	1.49969i
$900$		0			0
$901$	−1.22087	−	6.13771i	−0.0406729	−	0.204477i
$902$	15.5597	−	77.7440i	0.518080	−	2.58859i
$903$		0			0
$904$	−0.0160708	+	4.53795i	−0.000534507	+	0.150930i
$905$	−1.64421	+	3.96948i	−0.0546555	+	0.131950i
$906$		0			0
$907$	−6.59470	−	4.40644i	−0.218974	−	0.146313i	0.441246	−	0.897386i	$-0.354537\pi$
$907$	−6.59470	−	4.40644i	−0.218974	−	0.146313i	−0.660219	+	0.751073i	$0.729537\pi$
$908$	11.6975	+	17.5964i	0.388196	+	0.583957i
$909$		0			0
$910$	−0.645941	+	1.55425i	−0.0214128	+	0.0515228i
$911$	0.693019	−	0.693019i	0.0229608	−	0.0229608i	−0.695533	−	0.718494i	$-0.744832\pi$
$911$	0.693019	−	0.693019i	0.0229608	−	0.0229608i	0.718494	+	0.695533i	$0.244832\pi$
$912$		0			0
$913$	−53.9087	−	53.9087i	−1.78412	−	1.78412i
$914$	−1.40183	+	0.578721i	−0.0463686	+	0.0191424i
$915$		0			0
$916$	−5.54213	−	28.2101i	−0.183117	−	0.932088i
$917$	6.74890	−	10.1004i	0.222868	−	0.333546i
$918$		0			0
$919$	24.9456	+	10.3328i	0.822879	+	0.340848i	0.754080	−	0.656783i	$-0.228083\pi$
$919$	24.9456	+	10.3328i	0.822879	+	0.340848i	0.0687992	+	0.997631i	$0.478083\pi$
$920$	1.66406	+	2.50964i	0.0548624	+	0.0827402i
$921$		0			0
$922$	−3.01026	+	2.00625i	−0.0991375	+	0.0660724i
$923$	−46.0664	+	9.16318i	−1.51630	+	0.301610i
$924$		0			0
$925$	31.7076	−	21.1863i	1.04254	−	0.696602i
$926$	47.8091	+	0.0564373i	1.57110	+	0.00185464i
$927$		0			0
$928$	36.4156	+	7.46723i	1.19540	+	0.245124i
$929$		−	12.4630i		−	0.408898i	−0.978877	−	0.204449i	$-0.934460\pi$
$929$		−	12.4630i		−	0.408898i	0.978877	−	0.204449i	$-0.0655402\pi$
$930$		0			0
$931$	11.2824	−	7.53868i	0.369767	−	0.247070i
$932$	4.20228	−	10.0778i	0.137650	−	0.330110i
$933$		0			0
$934$	26.3269	+	39.5018i	0.861442	+	1.29254i
$935$	−1.89043	+	0.783040i	−0.0618235	+	0.0256081i
$936$		0			0
$937$	−53.2713	−	22.0657i	−1.74030	−	0.720855i	−0.998752	−	0.0499537i	$-0.984093\pi$
$937$	−53.2713	−	22.0657i	−1.74030	−	0.720855i	−0.741547	−	0.670901i	$-0.765907\pi$
$938$	−6.54874	+	1.29459i	−0.213824	+	0.0422699i
$939$		0			0
$940$	−1.45322	−	0.975982i	−0.0473988	−	0.0318330i
$941$	15.5300	+	3.08911i	0.506264	+	0.100702i	0.441613	−	0.897206i	$-0.354407\pi$
$941$	15.5300	+	3.08911i	0.506264	+	0.100702i	0.0646512	+	0.997908i	$0.479407\pi$
$942$		0			0
$943$	−32.1485	−	32.1485i	−1.04690	−	1.04690i
$944$	4.53920	+	23.3970i	0.147738	+	0.761506i
$945$		0			0
$946$	−26.9444	−	11.1980i	−0.876039	−	0.364079i
$947$	2.16365	−	10.8774i	0.0703092	−	0.353468i	−0.929576	−	0.368631i	$-0.879827\pi$
$947$	2.16365	−	10.8774i	0.0703092	−	0.353468i	0.999885	+	0.0151628i	$0.00482666\pi$
$948$		0			0
$949$	−2.71921	−	1.81692i	−0.0882692	−	0.0589796i
$950$	−15.1505	−	10.1491i	−0.491547	−	0.329281i
$951$		0			0
$952$	2.25180	+	5.49124i	0.0729812	+	0.177972i
$953$	−13.7909	−	33.2942i	−0.446731	−	1.07850i	−0.973539	−	0.228520i	$-0.926611\pi$
$953$	−13.7909	−	33.2942i	−0.446731	−	1.07850i	0.526808	−	0.849984i	$-0.323389\pi$
$954$		0			0
$955$	0.890987	+	4.47929i	0.0288317	+	0.144947i
$956$	27.4278	−	27.2986i	0.887079	−	0.882900i
$957$		0			0
$958$	17.7410	−	17.6992i	0.573187	−	0.571835i
$959$	−10.5393			−0.340333
$960$		0			0
$961$	−36.7264			−1.18472
$962$	25.8110	−	25.7501i	0.832178	−	0.830216i
$963$		0			0
$964$	4.43013	+	4.45110i	0.142685	+	0.143360i
$965$	0.660380	+	3.31995i	0.0212584	+	0.106873i
$966$		0			0
$967$	−9.21382	−	22.2441i	−0.296296	−	0.715323i	−0.999988	−	0.00481755i	$-0.998467\pi$
$967$	−9.21382	−	22.2441i	−0.296296	−	0.715323i	0.703692	−	0.710505i	$-0.251533\pi$
$968$	35.2063	+	14.7292i	1.13157	+	0.473414i
$969$		0			0
$970$	−4.80622	−	3.21963i	−0.154318	−	0.103376i
$971$	−11.1713	−	7.46439i	−0.358503	−	0.239544i	0.363255	−	0.931690i	$-0.381665\pi$
$971$	−11.1713	−	7.46439i	−0.358503	−	0.239544i	−0.721757	+	0.692146i	$0.756665\pi$
$972$		0			0
$973$	0.934424	−	4.69767i	0.0299563	−	0.150600i
$974$	−31.6105	−	13.1372i	−1.01287	−	0.420944i
$975$		0			0
$976$	27.3843	+	41.4054i	0.876551	+	1.32536i
$977$	7.40597	+	7.40597i	0.236938	+	0.236938i	0.815581	−	0.578643i	$-0.196418\pi$
$977$	7.40597	+	7.40597i	0.236938	+	0.236938i	−0.578643	+	0.815581i	$0.696418\pi$
$978$		0			0
$979$	8.74939	+	1.74036i	0.279632	+	0.0556222i
$980$	1.53442	−	2.28472i	0.0490152	−	0.0729828i
$981$		0			0
$982$	−41.2867	+	8.16179i	−1.31751	+	0.260453i
$983$	−46.6330	−	19.3160i	−1.48736	−	0.616085i	−0.516620	−	0.856215i	$-0.672810\pi$
$983$	−46.6330	−	19.3160i	−1.48736	−	0.616085i	−0.970741	+	0.240129i	$0.922810\pi$
$984$		0			0
$985$	1.22130	−	0.505878i	0.0389138	−	0.0161186i
$986$	8.03317	+	12.0533i	0.255828	+	0.383854i
$987$		0			0
$988$	−16.0917	−	6.70996i	−0.511946	−	0.213472i
$989$	−13.9121	+	9.29579i	−0.442380	+	0.295589i
$990$		0			0
$991$			12.4779i			0.396374i	0.980164	+	0.198187i	$0.0635053\pi$
$991$			12.4779i			0.396374i	−0.980164	+	0.198187i	$0.936495\pi$
$992$	−33.1122	+	32.7236i	−1.05131	+	1.03897i
$993$		0			0
$994$	−26.8329	−	0.0316755i	−0.851088	−	0.00100468i
$995$	5.10395	−	3.41035i	0.161806	−	0.108115i
$996$		0			0
$997$	1.42739	−	0.283926i	0.0452060	−	0.00899203i	−0.172436	−	0.985021i	$-0.555164\pi$
$997$	1.42739	−	0.283926i	0.0452060	−	0.00899203i	0.217642	+	0.976029i	$0.430164\pi$
$998$	35.3212	−	23.5406i	1.11807	−	0.745165i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.a.109.1		56
3.2	odd	2		64.2.i.a.45.7	yes	56
12.11	even	2		256.2.i.a.17.4		56
24.5	odd	2		512.2.i.b.289.4		56
24.11	even	2		512.2.i.a.289.4		56
64.37	even	16	inner	576.2.bd.a.37.1		56
192.5	odd	16		512.2.i.b.225.4		56
192.59	even	16		512.2.i.a.225.4		56
192.101	odd	16		64.2.i.a.37.7	✓	56
192.155	even	16		256.2.i.a.241.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.7	✓	56	192.101	odd	16
64.2.i.a.45.7	yes	56	3.2	odd	2
256.2.i.a.17.4		56	12.11	even	2
256.2.i.a.241.4		56	192.155	even	16
512.2.i.a.225.4		56	192.59	even	16
512.2.i.a.289.4		56	24.11	even	2
512.2.i.b.225.4		56	192.5	odd	16
512.2.i.b.289.4		56	24.5	odd	2
576.2.bd.a.37.1		56	64.37	even	16	inner
576.2.bd.a.109.1		56	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.998819 - 1.00118i) q^{2} +(-0.00472188 + 1.99999i) q^{4} +(-0.0517508 - 0.260169i) q^{5} +(-0.515195 - 1.24379i) q^{7} +(2.00707 - 1.99290i) q^{8} +O(q^{10})\)	\(q+(-0.998819 - 1.00118i) q^{2} +(-0.00472188 + 1.99999i) q^{4} +(-0.0517508 - 0.260169i) q^{5} +(-0.515195 - 1.24379i) q^{7} +(2.00707 - 1.99290i) q^{8} +(-0.208786 + 0.311673i) q^{10} +(4.11495 + 2.74952i) q^{11} +(-0.650168 + 3.26862i) q^{13} +(-0.730672 + 1.75812i) q^{14} +(-3.99996 - 0.0188875i) q^{16} +(-1.10212 - 1.10212i) q^{17} +(2.56547 + 0.510304i) q^{19} +(0.520580 - 0.102273i) q^{20} +(-1.35733 - 6.86609i) q^{22} +(-3.70792 - 1.53587i) q^{23} +(4.55439 - 1.88649i) q^{25} +(3.92187 - 2.61382i) q^{26} +(2.49001 - 1.02451i) q^{28} +(5.46390 - 3.65086i) q^{29} +8.22961i q^{31} +(3.97632 + 4.02354i) q^{32} +(-0.00260204 + 2.20424i) q^{34} +(-0.296934 + 0.198405i) q^{35} +(7.58710 - 1.50917i) q^{37} +(-2.05154 - 3.07820i) q^{38} +(-0.622359 - 0.419042i) q^{40} +(10.4659 + 4.33512i) q^{41} +(2.31618 - 3.46640i) q^{43} +(-5.51846 + 8.21690i) q^{44} +(2.16586 + 5.24635i) q^{46} +(-2.33317 - 2.33317i) q^{47} +(3.66816 - 3.66816i) q^{49} +(-6.43772 - 2.67550i) q^{50} +(-6.53414 - 1.31577i) q^{52} +(3.33837 + 2.23063i) q^{53} +(0.502388 - 1.21287i) q^{55} +(-3.51279 - 1.46964i) q^{56} +(-9.11262 - 1.82380i) q^{58} +(-1.16241 - 5.84382i) q^{59} +(-6.89488 - 10.3189i) q^{61} +(8.23932 - 8.21989i) q^{62} +(0.0566621 - 7.99980i) q^{64} +0.884038 q^{65} +(1.94793 + 2.91529i) q^{67} +(2.20944 - 2.19903i) q^{68} +(0.495222 + 0.0991136i) q^{70} +(5.39337 + 13.0208i) q^{71} +(-0.375531 + 0.906612i) q^{73} +(-9.08909 - 6.08867i) q^{74} +(-1.03272 + 5.12852i) q^{76} +(1.29983 - 6.53468i) q^{77} +(1.20158 - 1.20158i) q^{79} +(0.202087 + 1.04164i) q^{80} +(-6.11331 - 14.8083i) q^{82} +(-15.1088 - 3.00532i) q^{83} +(-0.229702 + 0.343773i) q^{85} +(-5.78393 + 1.14340i) q^{86} +(13.7385 - 2.68222i) q^{88} +(1.66533 - 0.689803i) q^{89} +(4.40044 - 0.875301i) q^{91} +(3.08924 - 7.40856i) q^{92} +(-0.00550847 + 4.66633i) q^{94} -0.693864i q^{95} +15.4207i q^{97} +(-7.33631 - 0.00866031i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more