LMFDB - Embedded newform 441.2.bg.a.278.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			278.7
Character	$\chi$	$=$	441.278
Dual form			441.2.bg.a.395.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.811510 + 0.318494i) q^{2} +(-0.908993 + 0.843422i) q^{4} +(0.228773 - 0.155975i) q^{5} +(-2.58038 - 0.584516i) q^{7} +(1.22553 - 2.54484i) q^{8} +O(q^{10})$	\(q+(-0.811510 + 0.318494i) q^{2} +(-0.908993 + 0.843422i) q^{4} +(0.228773 - 0.155975i) q^{5} +(-2.58038 - 0.584516i) q^{7} +(1.22553 - 2.54484i) q^{8} +(-0.135974 + 0.199438i) q^{10} +(0.640710 - 4.25083i) q^{11} +(3.73796 + 2.98092i) q^{13} +(2.28017 - 0.347495i) q^{14} +(0.00131931 - 0.0176050i) q^{16} +(5.10459 - 1.57456i) q^{17} +(1.61087 + 0.930035i) q^{19} +(-0.0764004 + 0.334732i) q^{20} +(0.833924 + 3.65366i) q^{22} +(0.312885 - 1.01435i) q^{23} +(-1.79870 + 4.58300i) q^{25} +(-3.98280 - 1.22853i) q^{26} +(2.83854 - 1.64503i) q^{28} +(3.23196 + 0.737675i) q^{29} +(4.59195 - 2.65116i) q^{31} +(1.66964 + 5.41284i) q^{32} +(-3.64094 + 2.90355i) q^{34} +(-0.681490 + 0.268752i) q^{35} +(-5.88543 - 5.46088i) q^{37} +(-1.60345 - 0.241681i) q^{38} +(-0.116562 - 0.773341i) q^{40} +(5.58866 + 2.69136i) q^{41} +(9.74651 - 4.69367i) q^{43} +(3.00285 + 4.40437i) q^{44} +(0.0691548 + 0.922807i) q^{46} +(-3.78553 - 9.64538i) q^{47} +(6.31668 + 3.01654i) q^{49} -4.29203i q^{50} +(-5.91196 + 0.443040i) q^{52} +(2.18512 + 2.35500i) q^{53} +(-0.516445 - 1.07241i) q^{55} +(-4.64982 + 5.85029i) q^{56} +(-2.85772 + 0.430732i) q^{58} +(-10.0364 - 6.84272i) q^{59} +(5.45959 - 5.88404i) q^{61} +(-2.88203 + 3.61396i) q^{62} +(-3.05688 - 3.83320i) q^{64} +(1.32009 + 0.0989272i) q^{65} +(3.64950 + 6.32111i) q^{67} +(-3.31202 + 5.73658i) q^{68} +(0.467440 - 0.435146i) q^{70} +(4.23060 - 0.965606i) q^{71} +(-4.31759 - 1.69453i) q^{73} +(6.51535 + 2.55708i) q^{74} +(-2.24868 + 0.513247i) q^{76} +(-4.13795 + 10.5942i) q^{77} +(1.86308 - 3.22695i) q^{79} +(-0.00244411 - 0.00423332i) q^{80} +(-5.39244 - 0.404107i) q^{82} +(-0.641843 - 0.804845i) q^{83} +(0.922200 - 1.15640i) q^{85} +(-6.41449 + 6.91317i) q^{86} +(-10.0325 - 6.84002i) q^{88} +(-15.0504 + 2.26848i) q^{89} +(-7.90295 - 9.87680i) q^{91} +(0.571114 + 1.18593i) q^{92} +(6.14400 + 6.62166i) q^{94} +(0.513585 - 0.0384879i) q^{95} +10.6247i q^{97} +(-6.08681 - 0.436126i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{41}{42}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.811510	+	0.318494i	−0.573825	+	0.225210i	−0.634467	−	0.772950i	$-0.718780\pi$
$2$	−0.811510	+	0.318494i	−0.573825	+	0.225210i	0.0606424	+	0.998160i	$0.480685\pi$
$3$		0			0
$3$		0			0
$4$	−0.908993	+	0.843422i	−0.454497	+	0.421711i
$5$	0.228773	−	0.155975i	0.102310	−	0.0697540i	−0.511084	−	0.859531i	$-0.670756\pi$
$5$	0.228773	−	0.155975i	0.102310	−	0.0697540i	0.613395	+	0.789777i	$0.289804\pi$
$6$		0			0
$7$	−2.58038	−	0.584516i	−0.975291	−	0.220926i
$7$	−2.58038	−	0.584516i	−0.975291	−	0.220926i
$8$	1.22553	−	2.54484i	0.433290	−	0.899735i
$9$		0			0
$10$	−0.135974	+	0.199438i	−0.0429989	+	0.0630678i
$11$	0.640710	−	4.25083i	0.193181	−	1.28167i	−0.656479	−	0.754344i	$-0.727955\pi$
$11$	0.640710	−	4.25083i	0.193181	−	1.28167i	0.849660	−	0.527330i	$-0.176807\pi$
$12$		0			0
$13$	3.73796	+	2.98092i	1.03672	+	0.826760i	0.985113	−	0.171908i	$-0.0549931\pi$
$13$	3.73796	+	2.98092i	1.03672	+	0.826760i	0.0516106	+	0.998667i	$0.483565\pi$
$14$	2.28017	−	0.347495i	0.609400	−	0.0928719i
$15$		0			0
$16$	0.00131931	−	0.0176050i	0.000329828	−	0.00440124i
$17$	5.10459	−	1.57456i	1.23804	−	0.381886i	0.394475	−	0.918907i	$-0.370927\pi$
$17$	5.10459	−	1.57456i	1.23804	−	0.381886i	0.843569	+	0.537021i	$0.180450\pi$
$18$		0			0
$19$	1.61087	+	0.930035i	0.369558	+	0.213365i	0.673266	−	0.739401i	$-0.264891\pi$
$19$	1.61087	+	0.930035i	0.369558	+	0.213365i	−0.303707	+	0.952765i	$0.598224\pi$
$20$	−0.0764004	+	0.334732i	−0.0170837	+	0.0748484i
$21$		0			0
$22$	0.833924	+	3.65366i	0.177793	+	0.778963i
$23$	0.312885	−	1.01435i	0.0652411	−	0.211506i	−0.917082	−	0.398698i	$-0.869462\pi$
$23$	0.312885	−	1.01435i	0.0652411	−	0.211506i	0.982323	+	0.187191i	$0.0599385\pi$
$24$		0			0
$25$	−1.79870	+	4.58300i	−0.359739	+	0.916601i
$26$	−3.98280	−	1.22853i	−0.781092	−	0.240935i
$27$		0			0
$28$	2.83854	−	1.64503i	0.536433	−	0.310881i
$29$	3.23196	+	0.737675i	0.600161	+	0.136983i	0.511798	−	0.859106i	$-0.328980\pi$
$29$	3.23196	+	0.737675i	0.600161	+	0.136983i	0.0883624	+	0.996088i	$0.471837\pi$
$30$		0			0
$31$	4.59195	−	2.65116i	0.824738	−	0.476163i	−0.0273093	−	0.999627i	$-0.508694\pi$
$31$	4.59195	−	2.65116i	0.824738	−	0.476163i	0.852048	+	0.523464i	$0.175361\pi$
$32$	1.66964	+	5.41284i	0.295154	+	0.956864i
$33$		0			0
$34$	−3.64094	+	2.90355i	−0.624416	+	0.497955i
$35$	−0.681490	+	0.268752i	−0.115193	+	0.0454274i
$36$		0			0
$37$	−5.88543	−	5.46088i	−0.967558	−	0.897763i	0.0272397	−	0.999629i	$-0.491328\pi$
$37$	−5.88543	−	5.46088i	−0.967558	−	0.897763i	−0.994798	+	0.101866i	$0.967519\pi$
$38$	−1.60345	−	0.241681i	−0.260113	−	0.0392058i
$39$		0			0
$40$	−0.116562	−	0.773341i	−0.0184301	−	0.122276i
$41$	5.58866	+	2.69136i	0.872802	+	0.420319i	0.815990	−	0.578066i	$-0.196192\pi$
$41$	5.58866	+	2.69136i	0.872802	+	0.420319i	0.0568115	+	0.998385i	$0.481907\pi$
$42$		0			0
$43$	9.74651	−	4.69367i	1.48633	−	0.715778i	0.497867	−	0.867253i	$-0.334117\pi$
$43$	9.74651	−	4.69367i	1.48633	−	0.715778i	0.988461	+	0.151475i	$0.0484023\pi$
$44$	3.00285	+	4.40437i	0.452696	+	0.663983i
$45$		0			0
$46$	0.0691548	+	0.922807i	0.0101963	+	0.136060i
$47$	−3.78553	−	9.64538i	−0.552177	−	1.40692i	−0.885734	−	0.464194i	$-0.846344\pi$
$47$	−3.78553	−	9.64538i	−0.552177	−	1.40692i	0.333557	−	0.942730i	$-0.391751\pi$
$48$		0			0
$49$	6.31668	+	3.01654i	0.902383	+	0.430934i
$50$		−	4.29203i		−	0.606985i
$51$		0			0
$52$	−5.91196	+	0.443040i	−0.819841	+	0.0614386i
$53$	2.18512	+	2.35500i	0.300149	+	0.323484i	0.865060	−	0.501668i	$-0.167280\pi$
$53$	2.18512	+	2.35500i	0.300149	+	0.323484i	−0.564911	+	0.825152i	$0.691089\pi$
$54$		0			0
$55$	−0.516445	−	1.07241i	−0.0696375	−	0.144604i
$56$	−4.64982	+	5.85029i	−0.621358	+	0.781778i
$57$		0			0
$58$	−2.85772	+	0.430732i	−0.375237	+	0.0565578i
$59$	−10.0364	−	6.84272i	−1.30663	−	0.890847i	−0.308457	−	0.951238i	$-0.599813\pi$
$59$	−10.0364	−	6.84272i	−1.30663	−	0.890847i	−0.998175	+	0.0603916i	$0.980765\pi$
$60$		0			0
$61$	5.45959	−	5.88404i	0.699029	−	0.753374i	−0.279351	−	0.960189i	$-0.590119\pi$
$61$	5.45959	−	5.88404i	0.699029	−	0.753374i	0.978380	+	0.206815i	$0.0663098\pi$
$62$	−2.88203	+	3.61396i	−0.366019	+	0.458973i
$63$		0			0
$64$	−3.05688	−	3.83320i	−0.382109	−	0.479150i
$65$	1.32009	+	0.0989272i	0.163737	+	0.0122704i
$66$		0			0
$67$	3.64950	+	6.32111i	0.445857	+	0.772247i	0.998111	−	0.0614287i	$-0.0195657\pi$
$67$	3.64950	+	6.32111i	0.445857	+	0.772247i	−0.552255	+	0.833676i	$0.686232\pi$
$68$	−3.31202	+	5.73658i	−0.401641	+	0.695663i
$69$		0			0
$70$	0.467440	−	0.435146i	0.0558698	−	0.0520099i
$71$	4.23060	−	0.965606i	0.502080	−	0.114596i	0.0360224	−	0.999351i	$-0.488531\pi$
$71$	4.23060	−	0.965606i	0.502080	−	0.114596i	0.466057	+	0.884755i	$0.345674\pi$
$72$		0			0
$73$	−4.31759	−	1.69453i	−0.505336	−	0.198330i	0.0989576	−	0.995092i	$-0.468449\pi$
$73$	−4.31759	−	1.69453i	−0.505336	−	0.198330i	−0.604293	+	0.796762i	$0.706544\pi$
$74$	6.51535	+	2.55708i	0.757394	+	0.297255i
$75$		0			0
$76$	−2.24868	+	0.513247i	−0.257941	+	0.0588734i
$77$	−4.13795	+	10.5942i	−0.471563	+	1.20733i
$78$		0			0
$79$	1.86308	−	3.22695i	0.209613	−	0.363060i	−0.741980	−	0.670422i	$-0.766113\pi$
$79$	1.86308	−	3.22695i	0.209613	−	0.363060i	0.951593	+	0.307362i	$0.0994463\pi$
$80$	−0.00244411	−	0.00423332i	−0.000273259	−	0.000473299i
$81$		0			0
$82$	−5.39244	−	0.404107i	−0.595495	−	0.0446262i
$83$	−0.641843	−	0.804845i	−0.0704514	−	0.0883433i	0.745357	−	0.666666i	$-0.232279\pi$
$83$	−0.641843	−	0.804845i	−0.0704514	−	0.0883433i	−0.815808	+	0.578322i	$0.803708\pi$
$84$		0			0
$85$	0.922200	−	1.15640i	0.100027	−	0.125429i
$86$	−6.41449	+	6.91317i	−0.691692	+	0.745466i
$87$		0			0
$88$	−10.0325	−	6.84002i	−1.06946	−	0.729148i
$89$	−15.0504	+	2.26848i	−1.59534	+	0.240459i	−0.885752	−	0.464159i	$-0.846357\pi$
$89$	−15.0504	+	2.26848i	−1.59534	+	0.240459i	−0.709587	+	0.704617i	$0.751119\pi$
$90$		0			0
$91$	−7.90295	−	9.87680i	−0.828454	−	1.03537i
$92$	0.571114	+	1.18593i	0.0595427	+	0.123642i
$93$		0			0
$94$	6.14400	+	6.62166i	0.633705	+	0.682972i
$95$	0.513585	−	0.0384879i	0.0526927	−	0.00394877i
$96$		0			0
$97$			10.6247i			1.07877i	0.842059	+	0.539385i	$0.181343\pi$
$97$			10.6247i			1.07877i	−0.842059	+	0.539385i	$0.818657\pi$
$98$	−6.08681	−	0.436126i	−0.614860	−	0.0440554i
$99$		0			0
$100$	−2.23041	−	5.68298i	−0.223041	−	0.568298i
$101$	−1.24376	−	16.5969i	−0.123759	−	1.65145i	−0.620979	−	0.783827i	$-0.713265\pi$
$101$	−1.24376	−	16.5969i	−0.123759	−	1.65145i	0.497220	−	0.867624i	$-0.334354\pi$
$102$		0			0
$103$	1.06150	+	1.55694i	0.104593	+	0.153410i	0.874967	−	0.484183i	$-0.160883\pi$
$103$	1.06150	+	1.55694i	0.104593	+	0.153410i	−0.770374	+	0.637592i	$0.779931\pi$
$104$	12.1669	−	5.85929i	1.19307	−	0.574550i
$105$		0			0
$106$	−2.52330	−	1.21516i	−0.245085	−	0.118027i
$107$	2.47659	+	16.4311i	0.239421	+	1.58845i	0.708770	+	0.705439i	$0.249250\pi$
$107$	2.47659	+	16.4311i	0.239421	+	1.58845i	−0.469350	+	0.883012i	$0.655512\pi$
$108$		0			0
$109$	−14.3027	−	2.15578i	−1.36995	−	0.206487i	−0.577483	−	0.816402i	$-0.695965\pi$
$109$	−14.3027	−	2.15578i	−1.36995	−	0.206487i	−0.792466	+	0.609916i	$0.791203\pi$
$110$	0.760657	+	0.705787i	0.0725258	+	0.0672941i
$111$		0			0
$112$	−0.0136947	+	0.0446563i	−0.00129403	+	0.00421962i
$113$	9.63490	−	7.68357i	0.906375	−	0.722810i	−0.0548736	−	0.998493i	$-0.517476\pi$
$113$	9.63490	−	7.68357i	0.906375	−	0.722810i	0.961248	+	0.275683i	$0.0889042\pi$
$114$		0			0
$115$	−0.0866331	−	0.280858i	−0.00807858	−	0.0261901i
$116$	−3.56000	+	2.05537i	−0.330538	+	0.190836i
$117$		0			0
$118$	10.3240	+	2.35639i	0.950405	+	0.216924i
$119$	−14.0921	+	1.07924i	−1.29182	+	0.0989335i
$120$		0			0
$121$	−7.14777	−	2.20480i	−0.649798	−	0.200436i
$122$	−2.55648	+	6.51381i	−0.231453	+	0.589733i
$123$		0			0
$124$	−1.93800	+	6.28284i	−0.174038	+	0.564216i
$125$	0.611403	+	2.67873i	0.0546855	+	0.239593i
$126$		0			0
$127$	−2.70552	+	11.8537i	−0.240077	+	1.05184i	0.700870	+	0.713289i	$0.252795\pi$
$127$	−2.70552	+	11.8537i	−0.240077	+	1.05184i	−0.940947	+	0.338555i	$0.890062\pi$
$128$	−6.10966	−	3.52741i	−0.540023	−	0.311782i
$129$		0			0
$130$	−1.10278	+	0.340162i	−0.0967199	+	0.0298341i
$131$	−0.180600	+	2.40993i	−0.0157791	+	0.210557i	0.983741	+	0.179591i	$0.0574774\pi$
$131$	−0.180600	+	2.40993i	−0.0157791	+	0.210557i	−0.999520	+	0.0309660i	$0.990142\pi$
$132$		0			0
$133$	−3.61303	−	3.34142i	−0.313289	−	0.289738i
$134$	−4.97484	−	3.96731i	−0.429761	−	0.342723i
$135$		0			0
$136$	2.24883	−	14.9200i	0.192835	−	1.27938i
$137$	−5.24492	+	7.69289i	−0.448104	+	0.657248i	−0.982126	−	0.188222i	$-0.939727\pi$
$137$	−5.24492	+	7.69289i	−0.448104	+	0.657248i	0.534022	+	0.845470i	$0.320680\pi$
$138$		0			0
$139$	0.735987	−	1.52829i	0.0624256	−	0.129628i	−0.867422	−	0.497574i	$-0.834224\pi$
$139$	0.735987	−	1.52829i	0.0624256	−	0.129628i	0.929847	+	0.367946i	$0.119939\pi$
$140$	0.392798	−	0.819077i	0.0331975	−	0.0692247i
$141$		0			0
$142$	−3.12563	+	2.13102i	−0.262297	+	0.178831i
$143$	15.0664	−	13.9795i	1.25991	−	1.16903i
$144$		0			0
$145$	0.854444	−	0.335345i	0.0709577	−	0.0278489i
$146$	4.04347			0.334640
$147$		0			0
$148$	9.95564			0.818349
$149$	3.50677	−	1.37630i	0.287286	−	0.112751i	−0.217322	−	0.976100i	$-0.569732\pi$
$149$	3.50677	−	1.37630i	0.287286	−	0.112751i	0.504608	+	0.863349i	$0.331637\pi$
$150$		0			0
$151$	4.76478	−	4.42107i	0.387752	−	0.359782i	−0.462077	−	0.886840i	$-0.652896\pi$
$151$	4.76478	−	4.42107i	0.387752	−	0.359782i	0.849829	+	0.527058i	$0.176705\pi$
$152$	4.34095	−	2.95961i	0.352098	−	0.240056i
$153$		0			0
$154$	−0.0162164	−	9.91525i	−0.00130675	−	0.798994i
$155$	0.636999	−	1.32274i	0.0511650	−	0.106245i
$156$		0			0
$157$	−1.64517	+	2.41302i	−0.131299	+	0.192580i	−0.886258	−	0.463191i	$-0.846704\pi$
$157$	−1.64517	+	2.41302i	−0.131299	+	0.192580i	0.754959	+	0.655772i	$0.227657\pi$
$158$	−0.484144	+	3.21208i	−0.0385164	+	0.255540i
$159$		0			0
$160$	1.22623	+	0.977890i	0.0969424	+	0.0773090i
$161$	−1.40026	+	2.43451i	−0.110356	+	0.191867i
$162$		0			0
$163$	−0.954846	+	12.7415i	−0.0747893	+	0.997994i	0.825981	+	0.563698i	$0.190622\pi$
$163$	−0.954846	+	12.7415i	−0.0747893	+	0.997994i	−0.900770	+	0.434296i	$0.856997\pi$
$164$	−7.35000	+	2.26718i	−0.573939	+	0.177037i
$165$		0			0
$166$	0.777201	+	0.448717i	0.0603225	+	0.0348272i
$167$	1.13054	−	4.95320i	0.0874835	−	0.383290i	−0.912164	−	0.409824i	$-0.865590\pi$
$167$	1.13054	−	4.95320i	0.0874835	−	0.383290i	0.999648	+	0.0265343i	$0.00844713\pi$
$168$		0			0
$169$	2.19367	+	9.61109i	0.168744	+	0.739314i
$170$	−0.380067	+	1.23215i	−0.0291498	+	0.0945014i
$171$		0			0
$172$	−4.90076	+	12.4869i	−0.373680	+	0.952120i
$173$	−11.6361	−	3.58926i	−0.884676	−	0.272886i	−0.181065	−	0.983471i	$-0.557954\pi$
$173$	−11.6361	−	3.58926i	−0.884676	−	0.272886i	−0.703612	+	0.710585i	$0.748430\pi$
$174$		0			0
$175$	7.32015	−	10.7745i	0.553351	−	0.814476i
$176$	−0.0739905	−	0.0168878i	−0.00557724	−	0.00127297i
$177$		0			0
$178$	11.4911	−	6.63437i	0.861291	−	0.497267i
$179$	−3.24820	−	10.5304i	−0.242782	−	0.787081i	−0.992164	−	0.124942i	$-0.960125\pi$
$179$	−3.24820	−	10.5304i	−0.242782	−	0.787081i	0.749382	−	0.662138i	$-0.230351\pi$
$180$		0			0
$181$	5.36313	−	4.27695i	0.398638	−	0.317903i	−0.403569	−	0.914949i	$-0.632230\pi$
$181$	5.36313	−	4.27695i	0.398638	−	0.317903i	0.802207	+	0.597046i	$0.203659\pi$
$182$	9.55903	+	5.49808i	0.708562	+	0.407545i
$183$		0			0
$184$	−2.19790	−	2.03935i	−0.162031	−	0.150343i
$185$	−2.19818	−	0.331323i	−0.161614	−	0.0243594i
$186$		0			0
$187$	−3.42262	−	22.7076i	−0.250287	−	1.66054i
$188$	11.5762	+	5.57478i	0.844278	+	0.406583i
$189$		0			0
$190$	−0.404521	+	0.194807i	−0.0293471	+	0.0141328i
$191$	5.80719	+	8.51758i	0.420193	+	0.616311i	0.976720	−	0.214519i	$-0.0688185\pi$
$191$	5.80719	+	8.51758i	0.420193	+	0.616311i	−0.556526	+	0.830830i	$0.687866\pi$
$192$		0			0
$193$	1.73566	+	23.1608i	0.124936	+	1.66715i	0.609796	+	0.792558i	$0.291251\pi$
$193$	1.73566	+	23.1608i	0.124936	+	1.66715i	−0.484860	+	0.874592i	$0.661130\pi$
$194$	−3.38389	−	8.62202i	−0.242949	−	0.619025i
$195$		0			0
$196$	−8.28604	+	2.58562i	−0.591860	+	0.184687i
$197$			12.5738i			0.895847i	0.894072	+	0.447923i	$0.147836\pi$
$197$			12.5738i			0.895847i	−0.894072	+	0.447923i	$0.852164\pi$
$198$		0			0
$199$	22.3916	−	1.67802i	1.58730	−	0.118952i	0.748404	−	0.663243i	$-0.230821\pi$
$199$	22.3916	−	1.67802i	1.58730	−	0.118952i	0.838896	+	0.544292i	$0.183201\pi$
$200$	9.45864	+	10.1940i	0.668827	+	0.720824i
$201$		0			0
$202$	6.29534	+	13.0724i	0.442939	+	0.919772i
$203$	−7.90850	−	3.79261i	−0.555068	−	0.266189i
$204$		0			0
$205$	1.69832	−	0.255980i	0.118616	−	0.0178784i
$206$	−1.35730	−	0.925388i	−0.0945673	−	0.0644749i
$207$		0			0
$208$	0.0574106	−	0.0618739i	0.00398071	−	0.00429018i
$209$	4.98552	−	6.25165i	0.344856	−	0.432436i
$210$		0			0
$211$	6.35501	+	7.96894i	0.437497	+	0.548604i	0.950882	−	0.309555i	$-0.100180\pi$
$211$	6.35501	+	7.96894i	0.437497	+	0.548604i	−0.513384	+	0.858159i	$0.671609\pi$
$212$	−3.97252	−	0.297699i	−0.272834	−	0.0204461i
$213$		0			0
$214$	−7.24298	−	12.5452i	−0.495120	−	0.857573i
$215$	1.49764	−	2.59399i	0.102138	−	0.176909i
$216$		0			0
$217$	−13.3986	+	4.15693i	−0.909556	+	0.282191i
$218$	12.2934	−	2.80589i	0.832613	−	0.190039i
$219$		0			0
$220$	1.37394	+	0.539232i	0.0926310	+	0.0363550i
$221$	23.7744	+	9.33075i	1.59924	+	0.627654i
$222$		0			0
$223$	−12.5054	+	2.85429i	−0.837426	+	0.191137i	−0.619666	−	0.784865i	$-0.712732\pi$
$223$	−12.5054	+	2.85429i	−0.837426	+	0.191137i	−0.217760	+	0.976002i	$0.569875\pi$
$224$	−1.14441	−	14.9431i	−0.0764641	−	0.998428i
$225$		0			0
$226$	−5.37164	+	9.30396i	−0.357316	+	0.618890i
$227$	−1.71216	−	2.96554i	−0.113640	−	0.196830i	0.803595	−	0.595176i	$-0.202918\pi$
$227$	−1.71216	−	2.96554i	−0.113640	−	0.196830i	−0.917235	+	0.398346i	$0.869584\pi$
$228$		0			0
$229$	19.3879	+	1.45292i	1.28119	+	0.0960118i	0.697866	−	0.716229i	$-0.254133\pi$
$229$	19.3879	+	1.45292i	1.28119	+	0.0960118i	0.583323	+	0.812241i	$0.301752\pi$
$230$	0.159755	+	0.200327i	0.0105339	+	0.0132092i
$231$		0			0
$232$	5.83812	−	7.32078i	0.383292	−	0.480633i
$233$	11.1624	−	12.0302i	0.731274	−	0.788126i	−0.252489	−	0.967600i	$-0.581249\pi$
$233$	11.1624	−	12.0302i	0.731274	−	0.788126i	0.983763	+	0.179474i	$0.0574396\pi$
$234$		0			0
$235$	−2.37046	−	1.61615i	−0.154632	−	0.105426i
$236$	14.8944	−	2.24496i	0.969540	−	0.146135i
$237$		0			0
$238$	11.0922	−	5.36407i	0.718998	−	0.347701i
$239$	−8.73850	−	18.1457i	−0.565247	−	1.17375i	−0.966235	−	0.257664i	$-0.917047\pi$
$239$	−8.73850	−	18.1457i	−0.565247	−	1.17375i	0.400988	−	0.916083i	$-0.368667\pi$
$240$		0			0
$241$	4.89741	+	5.27815i	0.315470	+	0.339996i	0.870803	−	0.491632i	$-0.163600\pi$
$241$	4.89741	+	5.27815i	0.315470	+	0.339996i	−0.555333	+	0.831628i	$0.687409\pi$
$242$	6.50271	−	0.487311i	0.418010	−	0.0313255i
$243$		0			0
$244$			9.95329i			0.637194i
$245$	1.91559	−	0.295140i	0.122383	−	0.0188558i
$246$		0			0
$247$	3.24900	+	8.27831i	0.206729	+	0.526736i
$248$	−1.11921	−	14.9348i	−0.0710700	−	0.948363i
$249$		0			0
$250$	−1.34932	−	1.97909i	−0.0853385	−	0.125169i
$251$	13.6920	−	6.59370i	0.864229	−	0.416191i	0.0513894	−	0.998679i	$-0.483635\pi$
$251$	13.6920	−	6.59370i	0.864229	−	0.416191i	0.812839	+	0.582488i	$0.197921\pi$
$252$		0			0
$253$	−4.11136	−	1.97993i	−0.258479	−	0.124477i
$254$	−1.57977	−	10.4811i	−0.0991235	−	0.657641i
$255$		0			0
$256$	15.7777	+	2.37810i	0.986106	+	0.148632i
$257$	11.8368	+	10.9830i	0.738361	+	0.685099i	0.956799	−	0.290752i	$-0.0939054\pi$
$257$	11.8368	+	10.9830i	0.738361	+	0.685099i	−0.218437	+	0.975851i	$0.570096\pi$
$258$		0			0
$259$	11.9946	+	17.5312i	0.745311	+	1.08934i
$260$	−1.28339	+	1.02347i	−0.0795926	+	0.0634730i
$261$		0			0
$262$	−0.620992	−	2.01321i	−0.0383650	−	0.124376i
$263$	−11.2661	+	6.50450i	−0.694699	+	0.401084i	−0.805370	−	0.592773i	$-0.798033\pi$
$263$	−11.2661	+	6.50450i	−0.694699	+	0.401084i	0.110671	+	0.993857i	$0.464700\pi$
$264$		0			0
$265$	0.867217	+	0.197937i	0.0532727	+	0.0121591i
$266$	3.99623	+	1.56087i	0.245025	+	0.0957029i
$267$		0			0
$268$	−8.64874	−	2.66778i	−0.528306	−	0.162961i
$269$	−2.21024	+	5.63160i	−0.134761	+	0.343365i	−0.982285	−	0.187391i	$-0.939997\pi$
$269$	−2.21024	+	5.63160i	−0.134761	+	0.343365i	0.847525	+	0.530756i	$0.178092\pi$
$270$		0			0
$271$	2.34986	−	7.61806i	0.142744	−	0.462764i	−0.855764	−	0.517366i	$-0.826913\pi$
$271$	2.34986	−	7.61806i	0.142744	−	0.462764i	0.998508	+	0.0546014i	$0.0173888\pi$
$272$	−0.0209855	−	0.0919434i	−0.00127243	−	0.00557489i
$273$		0			0
$274$	1.80617	−	7.91334i	0.109115	−	0.478062i
$275$	18.3291	+	10.5823i	1.10529	+	0.638139i
$276$		0			0
$277$	14.6743	−	4.52643i	0.881695	−	0.271967i	0.179334	−	0.983788i	$-0.442606\pi$
$277$	14.6743	−	4.52643i	0.881695	−	0.271967i	0.702360	+	0.711821i	$0.252129\pi$
$278$	−0.110509	+	1.47463i	−0.00662786	+	0.0884427i
$279$		0			0
$280$	−0.151255	+	2.06364i	−0.00903921	+	0.123326i
$281$	7.00086	+	5.58300i	0.417636	+	0.333054i	0.809658	−	0.586902i	$-0.199653\pi$
$281$	7.00086	+	5.58300i	0.417636	+	0.333054i	−0.392022	+	0.919956i	$0.628224\pi$
$282$		0			0
$283$	−2.90781	+	19.2921i	−0.172852	+	1.14680i	0.719181	+	0.694823i	$0.244517\pi$
$283$	−2.90781	+	19.2921i	−0.172852	+	1.14680i	−0.892032	+	0.451972i	$0.850721\pi$
$284$	−3.03117	+	4.44591i	−0.179867	+	0.263816i
$285$		0			0
$286$	−7.77410	+	16.1431i	−0.459692	+	0.954561i
$287$	−12.8477	−	10.2114i	−0.758376	−	0.602758i
$288$		0			0
$289$	9.53151	−	6.49847i	0.560677	−	0.382263i
$290$	−0.586585	+	0.544271i	−0.0344455	+	0.0319607i
$291$		0			0
$292$	5.35386	−	2.10124i	0.313311	−	0.122966i
$293$	−23.9976			−1.40195			−0.700977	−	0.713183i	$-0.747253\pi$
$293$	−23.9976			−1.40195			−0.700977	+	0.713183i	$0.747253\pi$
$294$		0			0
$295$	−3.36335			−0.195822
$296$	−21.1098	+	8.28499i	−1.22698	+	0.481555i
$297$		0			0
$298$	−2.40743	+	2.23377i	−0.139459	+	0.129399i
$299$	4.19325	−	2.85891i	0.242502	−	0.165335i
$300$		0			0
$301$	−27.8932	+	6.41445i	−1.60774	+	0.369723i
$302$	−2.45858	+	5.10530i	−0.141476	+	0.293777i
$303$		0			0
$304$	0.0184985	−	0.0271323i	0.00106096	−	0.00155614i
$305$	0.331245	−	2.19767i	0.0189670	−	0.125838i
$306$		0			0
$307$	−21.5006	−	17.1462i	−1.22711	−	0.978584i	−0.999989	−	0.00471621i	$-0.998499\pi$
$307$	−21.5006	−	17.1462i	−1.22711	−	0.978584i	−0.227116	−	0.973868i	$-0.572930\pi$
$308$	−5.17405	−	13.1201i	−0.294819	−	0.747589i
$309$		0			0
$310$	−0.0956454	+	1.27630i	−0.00543229	+	0.0724889i
$311$	−15.0023	+	4.62759i	−0.850701	+	0.262407i	−0.689294	−	0.724481i	$-0.742079\pi$
$311$	−15.0023	+	4.62759i	−0.850701	+	0.262407i	−0.161407	+	0.986888i	$0.551603\pi$
$312$		0			0
$313$	−15.8489	−	9.15035i	−0.895831	−	0.517209i	−0.0199860	−	0.999800i	$-0.506362\pi$
$313$	−15.8489	−	9.15035i	−0.895831	−	0.517209i	−0.875845	+	0.482592i	$0.839696\pi$
$314$	0.566539	−	2.48217i	0.0319717	−	0.140077i
$315$		0			0
$316$	1.02815	+	4.50464i	0.0578382	+	0.253406i
$317$	−4.14770	+	13.4465i	−0.232958	+	0.755231i	0.761317	+	0.648380i	$0.224553\pi$
$317$	−4.14770	+	13.4465i	−0.232958	+	0.755231i	−0.994275	+	0.106851i	$0.965923\pi$
$318$		0			0
$319$	5.20648	−	13.2659i	0.291507	−	0.742748i
$320$	−1.29721	−	0.400137i	−0.0725164	−	0.0223683i
$321$		0			0
$322$	0.360950	−	2.42161i	0.0201149	−	0.134951i
$323$	9.68721	+	2.21104i	0.539011	+	0.123026i
$324$		0			0
$325$	−20.3850	+	11.7693i	−1.13076	+	0.652844i
$326$	−3.28324	−	10.6440i	−0.181842	−	0.589517i
$327$		0			0
$328$	13.6981	−	10.9239i	0.756352	−	0.603171i
$329$	4.13022	+	27.1014i	0.227707	+	1.49415i
$330$		0			0
$331$	−5.68394	−	5.27393i	−0.312418	−	0.289881i	0.508341	−	0.861156i	$-0.330259\pi$
$331$	−5.68394	−	5.27393i	−0.312418	−	0.289881i	−0.820759	+	0.571274i	$0.806449\pi$
$332$	1.26226	+	0.190254i	0.0692753	+	0.0104416i
$333$		0			0
$334$	0.660125	+	4.37964i	0.0361204	+	0.239643i
$335$	1.82084	+	0.876870i	0.0994831	+	0.0479085i
$336$		0			0
$337$	−14.8709	+	7.16145i	−0.810070	+	0.390109i	−0.792603	−	0.609739i	$-0.791274\pi$
$337$	−14.8709	+	7.16145i	−0.810070	+	0.390109i	−0.0174669	+	0.999847i	$0.505560\pi$
$338$	−4.84126	−	7.10083i	−0.263330	−	0.386234i
$339$		0			0
$340$	0.137062	+	1.82897i	0.00743323	+	0.0991896i
$341$	−8.32754	−	21.2182i	−0.450962	−	1.14903i
$342$		0			0
$343$	−14.5362	−	11.4760i	−0.784881	−	0.619646i
$344$		−	30.5555i		−	1.64744i
$345$		0			0
$346$	10.5860	−	0.793309i	0.569105	−	0.0426486i
$347$	−4.50396	−	4.85411i	−0.241785	−	0.260582i	0.600488	−	0.799634i	$-0.294973\pi$
$347$	−4.50396	−	4.85411i	−0.241785	−	0.260582i	−0.842273	+	0.539052i	$0.818783\pi$
$348$		0			0
$349$	−14.2030	−	29.4929i	−0.760270	−	1.57872i	−0.814483	−	0.580188i	$-0.802979\pi$
$349$	−14.2030	−	29.4929i	−0.760270	−	1.57872i	0.0542126	−	0.998529i	$-0.482735\pi$
$350$	−2.50876	+	11.0751i	−0.134099	+	0.591986i
$351$		0			0
$352$	24.0788	−	3.62930i	1.28341	−	0.193442i
$353$	21.2098	+	14.4606i	1.12889	+	0.769661i	0.975824	−	0.218556i	$-0.0701346\pi$
$353$	21.2098	+	14.4606i	1.12889	+	0.769661i	0.153061	+	0.988217i	$0.451087\pi$
$354$		0			0
$355$	0.817236	−	0.880771i	0.0433744	−	0.0467464i
$356$	11.7674	−	14.7559i	0.623672	−	0.782060i
$357$		0			0
$358$	5.98983	+	7.51101i	0.316572	+	0.396969i
$359$	−34.3431	−	2.57366i	−1.81256	−	0.135833i	−0.875103	−	0.483936i	$-0.839207\pi$
$359$	−34.3431	−	2.57366i	−1.81256	−	0.135833i	−0.937456	+	0.348103i	$0.886826\pi$
$360$		0			0
$361$	−7.77007	−	13.4582i	−0.408951	−	0.708324i
$362$	−2.99005	+	5.17892i	−0.157153	+	0.272198i
$363$		0			0
$364$	15.5140	+	2.31242i	0.813157	+	0.121204i
$365$	−1.25205	+	0.285772i	−0.0655353	+	0.0149580i
$366$		0			0
$367$	−1.39443	−	0.547272i	−0.0727885	−	0.0285674i	0.328667	−	0.944446i	$-0.393400\pi$
$367$	−1.39443	−	0.547272i	−0.0727885	−	0.0285674i	−0.401456	+	0.915878i	$0.631496\pi$
$368$	−0.0174448	−	0.00684657i	−0.000909372	−	0.000356902i
$369$		0			0
$370$	1.88937	−	0.431237i	0.0982239	−	0.0224190i
$371$	−4.26190	−	7.35402i	−0.221267	−	0.381802i
$372$		0			0
$373$	−7.15901	+	12.3998i	−0.370680	+	0.642036i	−0.989670	−	0.143362i	$-0.954209\pi$
$373$	−7.15901	+	12.3998i	−0.370680	+	0.642036i	0.618991	+	0.785398i	$0.287542\pi$
$374$	10.0097	+	17.3374i	0.517591	+	0.896493i
$375$		0			0
$376$	−29.1852	−	2.18713i	−1.50511	−	0.112792i
$377$	9.88200	+	12.3916i	0.508949	+	0.638202i
$378$		0			0
$379$	−12.2500	+	15.3610i	−0.629241	+	0.789043i	−0.989612	−	0.143766i	$-0.954079\pi$
$379$	−12.2500	+	15.3610i	−0.629241	+	0.789043i	0.360371	+	0.932809i	$0.382650\pi$
$380$	−0.434384	+	0.468154i	−0.0222834	+	0.0240158i
$381$		0			0
$382$	−7.42540	−	5.06255i	−0.379916	−	0.259023i
$383$	−38.4974	+	5.80256i	−1.96713	+	0.296497i	−0.968201	+	0.250175i	$0.919512\pi$
$383$	−38.4974	+	5.80256i	−1.96713	+	0.296497i	−0.998927	+	0.0463217i	$0.985250\pi$
$384$		0			0
$385$	0.705783	+	3.06909i	0.0359700	+	0.156415i
$386$	−8.78509	−	18.2424i	−0.447149	−	0.928515i
$387$		0			0
$388$	−8.96108	−	9.65774i	−0.454930	−	0.490298i
$389$	18.9964	−	1.42358i	0.963155	−	0.0721785i	0.416140	−	0.909301i	$-0.363383\pi$
$389$	18.9964	−	1.42358i	0.963155	−	0.0721785i	0.547016	+	0.837122i	$0.315764\pi$
$390$		0			0
$391$		−	5.67048i		−	0.286769i
$392$	15.4179	−	12.3781i	0.778720	−	0.625187i
$393$		0			0
$394$	−4.00469	−	10.2038i	−0.201753	−	0.514059i
$395$	−0.0771003	−	1.02883i	−0.00387934	−	0.0517662i
$396$		0			0
$397$	21.3628	+	31.3335i	1.07217	+	1.57258i	0.789886	+	0.613254i	$0.210140\pi$
$397$	21.3628	+	31.3335i	1.07217	+	1.57258i	0.282284	+	0.959331i	$0.408908\pi$
$398$	−17.6366	+	8.49334i	−0.884043	+	0.425733i
$399$		0			0
$400$	0.0783106	+	0.0377124i	0.00391553	+	0.00188562i
$401$	1.67231	+	11.0951i	0.0835112	+	0.554060i	0.990987	+	0.133957i	$0.0427683\pi$
$401$	1.67231	+	11.0951i	0.0835112	+	0.554060i	−0.907476	+	0.420104i	$0.861994\pi$
$402$		0			0
$403$	25.0674	+	3.77831i	1.24870	+	0.188211i
$404$	15.1288	+	14.0374i	0.752684	+	0.698388i
$405$		0			0
$406$	7.62576	+	0.558931i	0.378460	+	0.0277393i
$407$	−26.9841	+	21.5191i	−1.33755	+	1.06666i
$408$		0			0
$409$	−2.17430	−	7.04892i	−0.107512	−	0.348547i	0.885791	−	0.464085i	$-0.153617\pi$
$409$	−2.17430	−	7.04892i	−0.107512	−	0.348547i	−0.993303	+	0.115538i	$0.963141\pi$
$410$	−1.29667	+	0.748635i	−0.0640381	+	0.0369724i
$411$		0			0
$412$	−2.27805	−	0.519951i	−0.112232	−	0.0256161i
$413$	21.8981	+	23.5232i	1.07753	+	1.15750i
$414$		0			0
$415$	−0.272372	−	0.0840155i	−0.0133702	−	0.00412416i
$416$	−9.89422	+	25.2101i	−0.485104	+	1.23602i
$417$		0			0
$418$	−2.05469	+	6.66114i	−0.100498	+	0.325807i
$419$	−3.14968	−	13.7996i	−0.153872	−	0.674156i	−0.991738	−	0.128280i	$-0.959054\pi$
$419$	−3.14968	−	13.7996i	−0.153872	−	0.674156i	0.837866	−	0.545876i	$-0.183803\pi$
$420$		0			0
$421$	−0.174136	+	0.762941i	−0.00848688	+	0.0371835i	−0.978994	−	0.203889i	$-0.934642\pi$
$421$	−0.174136	+	0.762941i	−0.00848688	+	0.0371835i	0.970507	+	0.241072i	$0.0774991\pi$
$422$	−7.69522	−	4.44284i	−0.374598	−	0.216274i
$423$		0			0
$424$	8.67102	−	2.67465i	0.421102	−	0.129893i
$425$	−1.96540	+	26.2265i	−0.0953360	+	1.27217i
$426$		0			0
$427$	−17.5271	+	11.9918i	−0.848196	+	0.580325i
$428$	−16.1095	−	12.8469i	−0.778684	−	0.620980i
$429$		0			0
$430$	−0.389180	+	2.58204i	−0.0187679	+	0.124517i
$431$	−9.82949	+	14.4172i	−0.473470	+	0.694453i	−0.986471	−	0.163935i	$-0.947581\pi$
$431$	−9.82949	+	14.4172i	−0.473470	+	0.694453i	0.513001	+	0.858388i	$0.328534\pi$
$432$		0			0
$433$	13.1419	−	27.2894i	0.631558	−	1.31144i	−0.302100	−	0.953276i	$-0.597688\pi$
$433$	13.1419	−	27.2894i	0.631558	−	1.31144i	0.933658	−	0.358167i	$-0.116598\pi$
$434$	9.54915	−	7.64077i	0.458374	−	0.366769i
$435$		0			0
$436$	14.8193	−	10.1036i	0.709715	−	0.483876i
$437$	1.44740	−	1.34299i	0.0692384	−	0.0642438i
$438$		0			0
$439$	10.1890	−	3.99890i	0.486296	−	0.190857i	−0.109510	−	0.993986i	$-0.534928\pi$
$439$	10.1890	−	3.99890i	0.486296	−	0.190857i	0.595806	+	0.803129i	$0.296833\pi$
$440$	−3.36202			−0.160278
$441$		0			0
$442$	−22.2649			−1.05904
$443$	16.2878	−	6.39250i	0.773858	−	0.303717i	0.0546446	−	0.998506i	$-0.482597\pi$
$443$	16.2878	−	6.39250i	0.773858	−	0.303717i	0.719214	+	0.694789i	$0.244502\pi$
$444$		0			0
$445$	−3.08930	+	2.86645i	−0.146447	+	0.135883i
$446$	9.23922	−	6.29919i	0.437490	−	0.298276i
$447$		0			0
$448$	5.64732	+	11.6779i	0.266811	+	0.551729i
$449$	−8.43206	+	17.5094i	−0.397933	+	0.826317i	0.601686	+	0.798733i	$0.294496\pi$
$449$	−8.43206	+	17.5094i	−0.397933	+	0.826317i	−0.999619	+	0.0275846i	$0.991218\pi$
$450$		0			0
$451$	15.0212	−	22.0321i	0.707321	−	1.03745i
$452$	−2.27756	+	15.1106i	−0.107127	+	0.710743i
$453$		0			0
$454$	2.33394	+	1.86126i	0.109537	+	0.0873531i
$455$	−3.34851	−	1.02688i	−0.156981	−	0.0481411i
$456$		0			0
$457$	−0.462572	+	6.17260i	−0.0216382	+	0.288742i	0.975879	+	0.218314i	$0.0700556\pi$
$457$	−0.462572	+	6.17260i	−0.0216382	+	0.288742i	−0.997517	+	0.0704283i	$0.977563\pi$
$458$	−16.1962	+	4.99587i	−0.756800	+	0.233442i
$459$		0			0
$460$	0.315630	+	0.182229i	0.0147163	+	0.00849649i
$461$	−5.60182	+	24.5432i	−0.260903	+	1.14309i	0.659372	+	0.751817i	$0.270822\pi$
$461$	−5.60182	+	24.5432i	−0.260903	+	1.14309i	−0.920275	+	0.391273i	$0.872035\pi$
$462$		0			0
$463$	−6.45210	−	28.2685i	−0.299854	−	1.31375i	−0.870344	−	0.492443i	$-0.836104\pi$
$463$	−6.45210	−	28.2685i	−0.299854	−	1.31375i	0.570490	−	0.821304i	$-0.306753\pi$
$464$	0.0172507	−	0.0559254i	0.000800844	−	0.00259627i
$465$		0			0
$466$	−5.22686	+	13.3178i	−0.242129	+	0.616936i
$467$	30.4671	+	9.39786i	1.40985	+	0.434881i	0.903923	−	0.427695i	$-0.140674\pi$
$467$	30.4671	+	9.39786i	1.40985	+	0.434881i	0.505927	+	0.862576i	$0.331150\pi$
$468$		0			0
$469$	−5.72228	−	18.4440i	−0.264231	−	0.851667i
$470$	2.43839	+	0.556547i	0.112475	+	0.0256716i
$471$		0			0
$472$	−29.7135	+	17.1551i	−1.36768	+	0.789628i
$473$	−13.7073	−	44.4381i	−0.630264	−	2.04326i
$474$		0			0
$475$	−7.15982	+	5.70976i	−0.328515	+	0.261982i
$476$	11.8994	−	12.8666i	0.545407	−	0.589740i
$477$		0			0
$478$	12.8707	+	11.9423i	0.588692	+	0.546226i
$479$	13.8989	+	2.09492i	0.635057	+	0.0957195i	0.458678	−	0.888603i	$-0.348323\pi$
$479$	13.8989	+	2.09492i	0.635057	+	0.0957195i	0.176380	+	0.984322i	$0.443561\pi$
$480$		0			0
$481$	−5.72103	−	37.9566i	−0.260857	−	1.73067i
$482$	−5.65536	−	2.72348i	−0.257595	−	0.124051i
$483$		0			0
$484$	8.35685	−	4.02445i	0.379857	−	0.182929i
$485$	1.65718	+	2.43063i	0.0752486	+	0.110369i
$486$		0			0
$487$	−1.41125	−	18.8319i	−0.0639500	−	0.853353i	−0.933286	−	0.359133i	$-0.883073\pi$
$487$	−1.41125	−	18.8319i	−0.0639500	−	0.853353i	0.869336	−	0.494221i	$-0.164547\pi$
$488$	−8.28303	−	21.1048i	−0.374955	−	0.955370i
$489$		0			0
$490$	−1.46052	+	0.849614i	−0.0659796	+	0.0383816i
$491$			23.3060i			1.05179i	0.850550	+	0.525894i	$0.176269\pi$
$491$			23.3060i			1.05179i	−0.850550	+	0.525894i	$0.823731\pi$
$492$		0			0
$493$	17.6593	−	1.32339i	0.795337	−	0.0596023i
$494$	−5.27319	−	5.68315i	−0.237252	−	0.255697i
$495$		0			0
$496$	−0.0406154	−	0.0843388i	−0.00182369	−	0.00378693i
$497$	−11.4809	+	0.0187771i	−0.514991	+	0.000842266i
$498$		0			0
$499$	1.48858	−	0.224367i	0.0666379	−	0.0100441i	−0.115639	−	0.993291i	$-0.536891\pi$
$499$	1.48858	−	0.224367i	0.0666379	−	0.0100441i	0.182277	+	0.983247i	$0.441653\pi$
$500$	−2.81506	−	1.91928i	−0.125893	−	0.0858327i
$501$		0			0
$502$	−9.01111	+	9.71167i	−0.402186	+	0.433453i
$503$	−26.3252	+	33.0107i	−1.17378	+	1.47187i	−0.322965	+	0.946411i	$0.604680\pi$
$503$	−26.3252	+	33.0107i	−1.17378	+	1.47187i	−0.850816	+	0.525464i	$0.823892\pi$
$504$		0			0
$505$	−2.87323	−	3.60292i	−0.127857	−	0.160328i
$506$	3.96701	+	0.297286i	0.176355	+	0.0132160i
$507$		0			0
$508$	−7.53836	−	13.0568i	−0.334460	−	0.579302i
$509$	7.79004	−	13.4927i	0.345287	−	0.598055i	−0.640118	−	0.768276i	$-0.721115\pi$
$509$	7.79004	−	13.4927i	0.345287	−	0.598055i	0.985406	+	0.170221i	$0.0544481\pi$
$510$		0			0
$511$	10.1505	+	6.89622i	0.449033	+	0.305071i
$512$	0.194726	−	0.0444450i	0.00860578	−	0.00196421i
$513$		0			0
$514$	−13.1037	−	5.14284i	−0.577981	−	0.226841i
$515$	0.485686	+	0.190618i	0.0214019	+	0.00839961i
$516$		0			0
$517$	−43.4263	+	9.91178i	−1.90989	+	0.435920i
$518$	−15.3174	−	10.4066i	−0.673007	−	0.457238i
$519$		0			0
$520$	1.86956	−	3.23818i	0.0819858	−	0.142004i
$521$	4.91771	+	8.51773i	0.215449	+	0.373168i	0.953411	−	0.301673i	$-0.0975452\pi$
$521$	4.91771	+	8.51773i	0.215449	+	0.373168i	−0.737962	+	0.674842i	$0.764212\pi$
$522$		0			0
$523$	4.35373	+	0.326267i	0.190375	+	0.0142667i	0.169577	−	0.985517i	$-0.445760\pi$
$523$	4.35373	+	0.326267i	0.190375	+	0.0142667i	0.0207989	+	0.999784i	$0.493379\pi$
$524$	−1.86843	−	2.34294i	−0.0816227	−	0.102352i
$525$		0			0
$526$	7.07093	−	8.86666i	0.308307	−	0.386605i
$527$	19.2656	−	20.7634i	0.839222	−	0.904467i
$528$		0			0
$529$	18.0725	+	12.3216i	0.785760	+	0.535722i
$530$	−0.766797	+	0.115576i	−0.0333075	+	0.00502030i
$531$		0			0
$532$	6.10244	−	0.00998053i	0.264574	−	0.000432711i
$533$	12.8675	+	26.7195i	0.557351	+	1.15735i
$534$		0			0
$535$	3.12941	+	3.37270i	0.135296	+	0.145814i
$536$	20.5588	−	1.54067i	0.888003	−	0.0665466i
$537$		0			0
$538$		−	5.27405i		−	0.227381i
$539$	16.8700	−	24.9184i	0.726641	−	1.07331i
$540$		0			0
$541$	8.74975	+	22.2940i	0.376181	+	0.958494i	0.986118	+	0.166044i	$0.0530995\pi$
$541$	8.74975	+	22.2940i	0.376181	+	0.958494i	−0.609937	+	0.792450i	$0.708805\pi$
$542$	0.519373	+	6.93056i	0.0223090	+	0.297693i
$543$		0			0
$544$	17.0456	+	25.0014i	0.730826	+	1.07192i
$545$	−3.60832	+	1.73767i	−0.154563	+	0.0744337i
$546$		0			0
$547$	6.46836	+	3.11500i	0.276567	+	0.133188i	0.567026	−	0.823700i	$-0.308094\pi$
$547$	6.46836	+	3.11500i	0.276567	+	0.133188i	−0.290459	+	0.956887i	$0.593808\pi$
$548$	−1.72076	−	11.4165i	−0.0735071	−	0.487688i
$549$		0			0
$550$	−18.2447	−	2.74995i	−0.777957	−	0.117258i
$551$	4.52020	+	4.19414i	0.192567	+	0.178676i
$552$		0			0
$553$	−6.69365	+	7.23775i	−0.284643	+	0.307780i
$554$	−10.4667	+	8.34693i	−0.444688	+	0.354627i
$555$		0			0
$556$	0.619990	+	2.00996i	0.0262934	+	0.0852411i
$557$	−24.1717	+	13.9555i	−1.02419	+	0.591315i	−0.915314	−	0.402741i	$-0.868058\pi$
$557$	−24.1717	+	13.9555i	−1.02419	+	0.591315i	−0.108873	+	0.994056i	$0.534724\pi$
$558$		0			0
$559$	50.4235	+	11.5088i	2.13269	+	0.486772i
$560$	0.00383228	+	0.0123522i	0.000161943	+	0.000521975i
$561$		0			0
$562$	−7.45942	−	2.30093i	−0.314657	−	0.0970588i
$563$	2.96369	−	7.55137i	0.124905	−	0.318252i	−0.854720	−	0.519090i	$-0.826271\pi$
$563$	2.96369	−	7.55137i	0.124905	−	0.318252i	0.979625	+	0.200837i	$0.0643663\pi$
$564$		0			0
$565$	1.00576	−	3.26059i	0.0423126	−	0.137174i
$566$	−3.78470	−	16.5818i	−0.159083	−	0.696987i
$567$		0			0
$568$	2.72741	−	11.9496i	0.114439	−	0.501392i
$569$	−25.8002	−	14.8957i	−1.08160	−	0.624462i	−0.150272	−	0.988645i	$-0.548015\pi$
$569$	−25.8002	−	14.8957i	−1.08160	−	0.624462i	−0.931328	+	0.364183i	$0.881348\pi$
$570$		0			0
$571$	23.9608	−	7.39093i	1.00273	−	0.309301i	0.250439	−	0.968132i	$-0.419425\pi$
$571$	23.9608	−	7.39093i	1.00273	−	0.309301i	0.752291	+	0.658832i	$0.228949\pi$
$572$	−1.90456	+	25.4146i	−0.0796337	+	1.06264i
$573$		0			0
$574$	13.6783	+	4.19471i	0.570921	+	0.175084i
$575$	4.08598	+	3.25846i	0.170397	+	0.135887i
$576$		0			0
$577$	−1.36164	+	9.03390i	−0.0566859	+	0.376086i	0.942443	+	0.334366i	$0.108522\pi$
$577$	−1.36164	+	9.03390i	−0.0566859	+	0.376086i	−0.999129	+	0.0417207i	$0.986716\pi$
$578$	−5.66519	+	8.30931i	−0.235641	+	0.345622i
$579$		0			0
$580$	−0.493847	+	1.02548i	−0.0205059	+	0.0425809i
$581$	1.18575	+	2.45197i	0.0491932	+	0.101725i
$582$		0			0
$583$	11.4107	−	7.77971i	0.472585	−	0.322203i
$584$	−9.60362	+	8.91086i	−0.397401	+	0.368734i
$585$		0			0
$586$	19.4743	−	7.64310i	0.804476	−	0.315734i
$587$	1.41804			0.0585289			0.0292645	−	0.999572i	$-0.490684\pi$
$587$	1.41804			0.0585289			0.0292645	+	0.999572i	$0.490684\pi$
$588$		0			0
$589$	9.86270			0.406385
$590$	2.72940	−	1.07121i	0.112367	−	0.0441010i
$591$		0			0
$592$	−0.103903	+	0.0964082i	−0.00427040	+	0.00396235i
$593$	36.0642	−	24.5882i	1.48098	−	1.00971i	0.490593	−	0.871389i	$-0.336780\pi$
$593$	36.0642	−	24.5882i	1.48098	−	1.00971i	0.990387	−	0.138326i	$-0.0441721\pi$
$594$		0			0
$595$	−3.05556	+	2.44491i	−0.125266	+	0.100232i
$596$	−2.02682	+	4.20874i	−0.0830218	+	0.172397i
$597$		0			0
$598$	−2.49232	+	3.65556i	−0.101918	+	0.149487i
$599$	6.45351	−	42.8162i	0.263683	−	1.74942i	−0.329315	−	0.944220i	$-0.606818\pi$
$599$	6.45351	−	42.8162i	0.263683	−	1.74942i	0.592999	−	0.805203i	$-0.297944\pi$
$600$		0			0
$601$	−2.02198	−	1.61248i	−0.0824784	−	0.0657743i	0.581383	−	0.813630i	$-0.302512\pi$
$601$	−2.02198	−	1.61248i	−0.0824784	−	0.0657743i	−0.663861	+	0.747856i	$0.731083\pi$
$602$	20.5926	−	14.0892i	0.839293	−	0.574234i
$603$		0			0
$604$	−0.602323	+	8.03745i	−0.0245082	+	0.327039i
$605$	−1.97911	+	0.610474i	−0.0804622	+	0.0248193i
$606$		0			0
$607$	−34.4840	−	19.9093i	−1.39966	−	0.808095i	−0.405304	−	0.914182i	$-0.632834\pi$
$607$	−34.4840	−	19.9093i	−1.39966	−	0.808095i	−0.994357	+	0.106087i	$0.966168\pi$
$608$	−2.34456	+	10.2722i	−0.0950846	+	0.416593i
$609$		0			0
$610$	0.431136	+	1.88893i	0.0174562	+	0.0764805i
$611$	14.6020	−	47.3384i	0.590733	−	1.91511i
$612$		0			0
$613$	−12.6903	+	32.3343i	−0.512555	+	1.30597i	0.407151	+	0.913361i	$0.366522\pi$
$613$	−12.6903	+	32.3343i	−0.512555	+	1.30597i	−0.919706	+	0.392607i	$0.871573\pi$
$614$	22.9089	+	7.06647i	0.924530	+	0.285180i
$615$		0			0
$616$	21.8894	+	23.5140i	0.881950	+	0.947404i
$617$	11.6915	+	2.66851i	0.470682	+	0.107430i	0.451282	−	0.892382i	$-0.350967\pi$
$617$	11.6915	+	2.66851i	0.470682	+	0.107430i	0.0194008	+	0.999812i	$0.493824\pi$
$618$		0			0
$619$	−30.5798	+	17.6553i	−1.22911	+	0.709625i	−0.966843	−	0.255372i	$-0.917802\pi$
$619$	−30.5798	+	17.6553i	−1.22911	+	0.709625i	−0.262263	+	0.964996i	$0.584469\pi$
$620$	0.536602	+	1.73962i	0.0215505	+	0.0698649i
$621$		0			0
$622$	10.7006	−	8.53348i	0.429057	−	0.342161i
$623$	40.1617	+	2.94366i	1.60904	+	0.117935i
$624$		0			0
$625$	−17.4876	−	16.2261i	−0.699505	−	0.649045i
$626$	15.7759	+	2.37783i	0.630530	+	0.0950372i
$627$		0			0
$628$	−0.539748	−	3.58100i	−0.0215383	−	0.142897i
$629$	−38.6411	−	18.6086i	−1.54072	−	0.741973i
$630$		0			0
$631$	−10.0804	+	4.85448i	−0.401295	+	0.193254i	−0.623635	−	0.781716i	$-0.714345\pi$
$631$	−10.0804	+	4.85448i	−0.401295	+	0.193254i	0.222340	+	0.974969i	$0.428631\pi$
$632$	−5.92880	−	8.69595i	−0.235835	−	0.345906i
$633$		0			0
$634$	−0.916736	−	12.2330i	−0.0364083	−	0.485834i
$635$	1.22992	+	3.13379i	0.0488080	+	0.124361i
$636$		0			0
$637$	14.6194	+	30.1053i	0.579243	+	1.19281i
$638$			12.4237i			0.491857i
$639$		0			0
$640$	−1.94791	+	0.145976i	−0.0769980	+	0.00577020i
$641$	−27.6812	−	29.8332i	−1.09334	−	1.17834i	−0.982839	−	0.184466i	$-0.940944\pi$
$641$	−27.6812	−	29.8332i	−1.09334	−	1.17834i	−0.110503	−	0.993876i	$-0.535246\pi$
$642$		0			0
$643$	2.78693	+	5.78711i	0.109906	+	0.228221i	0.948666	−	0.316279i	$-0.102434\pi$
$643$	2.78693	+	5.78711i	0.109906	+	0.228221i	−0.838761	+	0.544500i	$0.816719\pi$
$644$	−0.780494	−	3.39397i	−0.0307558	−	0.133741i
$645$		0			0
$646$	−8.56547	+	1.29104i	−0.337004	+	0.0507952i
$647$	0.889227	+	0.606265i	0.0349591	+	0.0238347i	0.580674	−	0.814136i	$-0.302789\pi$
$647$	0.889227	+	0.606265i	0.0349591	+	0.0238347i	−0.545714	+	0.837971i	$0.683742\pi$
$648$		0			0
$649$	−35.5177	+	38.2790i	−1.39419	+	1.50258i
$650$	12.7942	−	16.0434i	0.501830	−	0.629275i
$651$		0			0
$652$	−9.87855	−	12.3873i	−0.386874	−	0.485125i
$653$	28.3505	+	2.12457i	1.10944	+	0.0831410i	0.616820	−	0.787104i	$-0.288421\pi$
$653$	28.3505	+	2.12457i	1.10944	+	0.0831410i	0.492619	+	0.870245i	$0.336040\pi$
$654$		0			0
$655$	0.334572	+	0.579496i	0.0130728	+	0.0226428i
$656$	0.0547544	−	0.0948374i	0.00213780	−	0.00370278i
$657$		0			0
$658$	−11.9834	−	20.6776i	−0.467160	−	0.806098i
$659$	−21.2058	+	4.84008i	−0.826060	+	0.188543i	−0.614595	−	0.788843i	$-0.710681\pi$
$659$	−21.2058	+	4.84008i	−0.826060	+	0.188543i	−0.211465	+	0.977386i	$0.567823\pi$
$660$		0			0
$661$	−15.9421	−	6.25682i	−0.620077	−	0.243362i	0.0344436	−	0.999407i	$-0.489034\pi$
$661$	−15.9421	−	6.25682i	−0.620077	−	0.243362i	−0.654520	+	0.756044i	$0.727129\pi$
$662$	6.29230	+	2.46954i	0.244557	+	0.0959816i
$663$		0			0
$664$	−2.83480	+	0.647024i	−0.110011	+	0.0251094i
$665$	−1.34774	−	0.200885i	−0.0522631	−	0.00778999i
$666$		0			0
$667$	1.75949	−	3.04753i	0.0681278	−	0.118001i
$668$	3.14999	+	5.45594i	0.121877	+	0.211097i
$669$		0			0
$670$	−1.75691	−	0.131662i	−0.0678753	−	0.00508655i
$671$	−21.5141	−	26.9778i	−0.830541	−	1.04147i
$672$		0			0
$673$	−2.48969	+	3.12198i	−0.0959706	+	0.120343i	−0.827498	−	0.561469i	$-0.810236\pi$
$673$	−2.48969	+	3.12198i	−0.0959706	+	0.120343i	0.731527	+	0.681812i	$0.238808\pi$
$674$	9.78701	−	10.5479i	0.376982	−	0.406289i
$675$		0			0
$676$	−10.1002	−	6.88622i	−0.388471	−	0.264855i
$677$	19.0605	−	2.87290i	0.732553	−	0.110415i	0.227836	−	0.973699i	$-0.426835\pi$
$677$	19.0605	−	2.87290i	0.732553	−	0.110415i	0.504717	+	0.863285i	$0.331597\pi$
$678$		0			0
$679$	6.21028	−	27.4156i	0.238329	−	1.05211i
$680$	−1.81267	−	3.76405i	−0.0695127	−	0.144345i
$681$		0			0
$682$	13.5158	+	14.5665i	0.517546	+	0.557782i
$683$	−16.0986	+	1.20642i	−0.615994	+	0.0461624i	−0.379074	−	0.925367i	$-0.623757\pi$
$683$	−16.0986	+	1.20642i	−0.615994	+	0.0461624i	−0.236921	+	0.971529i	$0.576138\pi$
$684$		0			0
$685$			2.57800i			0.0985003i
$686$	15.4513	+	4.68320i	0.589934	+	0.178806i
$687$		0			0
$688$	−0.0697733	−	0.177779i	−0.00266008	−	0.00677778i
$689$	1.14782	+	15.3166i	0.0437284	+	0.583515i
$690$		0			0
$691$	18.8400	+	27.6332i	0.716708	+	1.05122i	0.995854	+	0.0909687i	$0.0289963\pi$
$691$	18.8400	+	27.6332i	0.716708	+	1.05122i	−0.279146	+	0.960249i	$0.590051\pi$
$692$	13.6044	−	6.55153i	0.517162	−	0.249052i
$693$		0			0
$694$	5.20101	+	2.50468i	0.197428	+	0.0950762i
$695$	−0.0700012	−	0.464427i	−0.00265530	−	0.0176167i
$696$		0			0
$697$	32.7655	+	4.93860i	1.24108	+	0.187063i
$698$	20.9192	+	19.4102i	0.791804	+	0.734687i
$699$		0			0
$700$	2.43349	+	15.9679i	0.0919774	+	0.603531i
$701$	26.7063	−	21.2976i	1.00868	−	0.804398i	0.0279223	−	0.999610i	$-0.491111\pi$
$701$	26.7063	−	21.2976i	1.00868	−	0.804398i	0.980761	+	0.195212i	$0.0625395\pi$
$702$		0			0
$703$	−4.40184	−	14.2704i	−0.166018	−	0.538219i
$704$	−18.2529	+	10.5383i	−0.687931	+	0.397177i
$705$		0			0
$706$	−21.8176	−	4.97973i	−0.821117	−	0.187415i
$707$	−6.49176	+	43.5532i	−0.244148	+	1.63799i
$708$		0			0
$709$	19.0917	+	5.88901i	0.717004	+	0.221167i	0.631727	−	0.775191i	$-0.282346\pi$
$709$	19.0917	+	5.88901i	0.717004	+	0.221167i	0.0852770	+	0.996357i	$0.472822\pi$
$710$	−0.382675	+	0.975039i	−0.0143615	+	0.0365926i
$711$		0			0
$712$	−12.6718	+	41.0809i	−0.474895	+	1.53957i
$713$	−1.25245	−	5.48735i	−0.0469047	−	0.205503i
$714$		0			0
$715$	1.26632	−	5.54811i	0.0473577	−	0.207488i
$716$	11.8342	+	6.83247i	0.442264	+	0.255341i
$717$		0			0
$718$	28.6895	−	8.84953i	1.07068	−	0.330262i
$719$	−0.768305	+	10.2523i	−0.0286529	+	0.382347i	0.964381	+	0.264517i	$0.0852126\pi$
$719$	−0.768305	+	10.2523i	−0.0286529	+	0.382347i	−0.993034	+	0.117829i	$0.962406\pi$
$720$		0			0
$721$	−1.82902	−	4.63795i	−0.0681163	−	0.172726i
$722$	10.5918	+	8.44671i	0.394187	+	0.314354i
$723$		0			0
$724$	−1.26777	+	8.41110i	−0.0471163	+	0.312596i
$725$	−9.19409	+	13.4852i	−0.341460	+	0.500830i
$726$		0			0
$727$	8.03723	−	16.6895i	0.298084	−	0.618978i	−0.697103	−	0.716971i	$-0.745528\pi$
$727$	8.03723	−	16.6895i	0.298084	−	0.618978i	0.995187	+	0.0979928i	$0.0312422\pi$
$728$	−34.8201	+	8.00740i	−1.29052	+	0.296774i
$729$		0			0
$730$	0.925035	−	0.630678i	0.0342371	−	0.0233425i
$731$	42.3614	−	39.3057i	1.56679	−	1.45377i
$732$		0			0
$733$	2.10783	−	0.827261i	0.0778544	−	0.0305556i	−0.326094	−	0.945337i	$-0.605733\pi$
$733$	2.10783	−	0.827261i	0.0778544	−	0.0305556i	0.403949	+	0.914782i	$0.367637\pi$
$734$	1.30590			0.0482015
$735$		0			0
$736$	6.01291			0.221639
$737$	29.2083	−	11.4634i	1.07590	−	0.422260i
$738$		0			0
$739$	−2.56600	+	2.38090i	−0.0943920	+	0.0875830i	−0.725958	−	0.687739i	$-0.758603\pi$
$739$	−2.56600	+	2.38090i	−0.0943920	+	0.0875830i	0.631566	+	0.775322i	$0.282413\pi$
$740$	2.27758	−	1.55283i	0.0837255	−	0.0570831i
$741$		0			0
$742$	5.80079	+	4.61048i	0.212954	+	0.169256i
$743$	−7.79526	+	16.1870i	−0.285980	+	0.593844i	−0.993626	−	0.112723i	$-0.964043\pi$
$743$	−7.79526	+	16.1870i	−0.285980	+	0.593844i	0.707646	+	0.706567i	$0.249757\pi$
$744$		0			0
$745$	0.587584	−	0.861828i	0.0215274	−	0.0315749i
$746$	1.86036	−	12.3427i	0.0681124	−	0.451897i
$747$		0			0
$748$	22.2632	+	17.7543i	0.814024	+	0.649162i
$749$	3.21370	−	43.8459i	0.117426	−	1.60210i
$750$		0			0
$751$	−2.07448	+	27.6821i	−0.0756990	+	1.01013i	0.821990	+	0.569502i	$0.192864\pi$
$751$	−2.07448	+	27.6821i	−0.0756990	+	1.01013i	−0.897689	+	0.440630i	$0.854755\pi$
$752$	−0.174801	+	0.0539189i	−0.00637433	+	0.00196622i
$753$		0			0
$754$	−11.9660	−	6.90858i	−0.435777	−	0.251596i
$755$	0.400477	−	1.75461i	0.0145749	−	0.0638566i
$756$		0			0
$757$	4.94805	+	21.6788i	0.179840	+	0.787930i	0.981702	+	0.190421i	$0.0609854\pi$
$757$	4.94805	+	21.6788i	0.179840	+	0.787930i	−0.801863	+	0.597508i	$0.796157\pi$
$758$	5.04861	−	16.3672i	0.183374	−	0.594483i
$759$		0			0
$760$	0.531467	−	1.35416i	0.0192783	−	0.0491204i
$761$	−30.5910	−	9.43607i	−1.10892	−	0.342057i	−0.314399	−	0.949291i	$-0.601803\pi$
$761$	−30.5910	−	9.43607i	−1.10892	−	0.342057i	−0.794523	+	0.607234i	$0.792279\pi$
$762$		0			0
$763$	35.6462	+	13.9229i	1.29048	+	0.504042i
$764$	−12.4626	−	2.84451i	−0.450882	−	0.102911i
$765$		0			0
$766$	29.3930	−	16.9701i	1.06201	−	0.613153i
$767$	−17.1181	−	55.4957i	−0.618100	−	2.00383i
$768$		0			0
$769$	7.26818	−	5.79618i	0.262097	−	0.209016i	−0.483620	−	0.875278i	$-0.660678\pi$
$769$	7.26818	−	5.79618i	0.262097	−	0.209016i	0.745717	+	0.666262i	$0.232107\pi$
$770$	−1.55024	−	2.26581i	−0.0558667	−	0.0816542i
$771$		0			0
$772$	−21.1120	−	19.5891i	−0.759839	−	0.705027i
$773$	16.0242	+	2.41526i	0.576350	+	0.0868708i	0.430748	−	0.902472i	$-0.358250\pi$
$773$	16.0242	+	2.41526i	0.576350	+	0.0868708i	0.145602	+	0.989343i	$0.453488\pi$
$774$		0			0
$775$	3.89077	+	25.8136i	0.139760	+	0.927250i
$776$	27.0380	+	13.0208i	0.970608	+	0.467420i
$777$		0			0
$778$	−14.9624	+	7.20550i	−0.536427	+	0.258330i
$779$	6.49954	+	9.53307i	0.232870	+	0.341558i
$780$		0			0
$781$	−1.39405	−	18.6022i	−0.0498829	−	0.665640i
$782$	1.80602	+	4.60166i	0.0645830	+	0.164555i
$783$		0			0
$784$	0.0614398	−	0.107225i	0.00219428	−	0.00382947i
$785$			0.808639i			0.0288616i
$786$		0			0
$787$	−22.4776	+	1.68446i	−0.801239	+	0.0600446i	−0.469054	−	0.883170i	$-0.655405\pi$
$787$	−22.4776	+	1.68446i	−0.801239	+	0.0600446i	−0.332185	+	0.943214i	$0.607786\pi$
$788$	−10.6050	−	11.4295i	−0.377789	−	0.407159i
$789$		0			0
$790$	0.390245	+	0.810352i	0.0138843	+	0.0288310i
$791$	−29.3528	+	14.1948i	−1.04367	+	0.504708i
$792$		0			0
$793$	37.9476	−	5.71968i	1.34756	−	0.203112i
$794$	−27.3157	−	18.6235i	−0.969399	−	0.660925i
$795$		0			0
$796$	−18.9386	+	20.4109i	−0.671259	+	0.723445i
$797$	−17.3219	+	21.7209i	−0.613572	+	0.769395i	−0.987424	−	0.158093i	$-0.949465\pi$
$797$	−17.3219	+	21.7209i	−0.613572	+	0.769395i	0.373852	+	0.927488i	$0.378037\pi$
$798$		0			0
$799$	−34.5108	−	43.2751i	−1.22090	−	1.53096i
$800$	−27.8102	−	2.08409i	−0.983241	−	0.0736837i
$801$		0			0
$802$	−4.89081	−	8.47113i	−0.172700	−	0.299126i
$803$	−9.96948	+	17.2676i	−0.351815	+	0.609362i
$804$		0			0
$805$	0.0593803	+	0.775357i	0.00209288	+	0.0273277i
$806$	−21.5459	+	4.91770i	−0.758920	+	0.173219i
$807$		0			0
$808$	−43.7606	−	17.1748i	−1.53949	−	0.604206i
$809$	37.0259	+	14.5316i	1.30176	+	0.510904i	0.912068	−	0.410040i	$-0.134485\pi$
$809$	37.0259	+	14.5316i	1.30176	+	0.510904i	0.389695	+	0.920944i	$0.372580\pi$
$810$		0			0
$811$	44.2970	−	10.1105i	1.55548	−	0.355028i	0.643558	−	0.765397i	$-0.277457\pi$
$811$	44.2970	−	10.1105i	1.55548	−	0.355028i	0.911919	+	0.410369i	$0.134600\pi$
$812$	10.3875	−	3.22275i	0.364531	−	0.113096i
$813$		0			0
$814$	15.0442	−	26.0573i	0.527299	−	0.913308i
$815$	1.76891	+	3.06385i	0.0619624	+	0.107322i
$816$		0			0
$817$	20.0656	+	1.50371i	0.702007	+	0.0526082i
$818$	4.00951	+	5.02777i	0.140189	+	0.175792i
$819$		0			0
$820$	−1.32786	+	1.66508i	−0.0463708	+	0.0581472i
$821$	−3.13956	+	3.38364i	−0.109571	+	0.118090i	−0.785456	−	0.618918i	$-0.787571\pi$
$821$	−3.13956	+	3.38364i	−0.109571	+	0.118090i	0.675884	+	0.737008i	$0.263762\pi$
$822$		0			0
$823$	−38.5438	−	26.2787i	−1.34355	−	0.916018i	−0.343817	−	0.939037i	$-0.611720\pi$
$823$	−38.5438	−	26.2787i	−1.34355	−	0.916018i	−0.999735	+	0.0230186i	$0.992672\pi$
$824$	5.26305	−	0.793277i	0.183347	−	0.0276351i
$825$		0			0
$826$	−25.2626	−	12.1149i	−0.878997	−	0.421533i
$827$	22.4671	+	46.6534i	0.781257	+	1.62230i	0.782780	+	0.622299i	$0.213801\pi$
$827$	22.4671	+	46.6534i	0.781257	+	1.62230i	−0.00152245	+	0.999999i	$0.500485\pi$
$828$		0			0
$829$	4.19087	+	4.51668i	0.145555	+	0.156871i	0.801621	−	0.597833i	$-0.203971\pi$
$829$	4.19087	+	4.51668i	0.145555	+	0.156871i	−0.656066	+	0.754703i	$0.727781\pi$
$830$	0.247791	−	0.0185694i	0.00860095	−	0.000644552i
$831$		0			0
$832$		−	23.4407i		−	0.812659i
$833$	36.9938	+	5.45222i	1.28176	+	0.188908i
$834$		0			0
$835$	−0.513938	−	1.30949i	−0.0177856	−	0.0453168i
$836$	0.740974	+	9.88761i	0.0256271	+	0.341970i
$837$		0			0
$838$	6.95110	+	10.1954i	0.240122	+	0.352194i
$839$	−19.9513	+	9.60804i	−0.688796	+	0.331706i	−0.745331	−	0.666694i	$-0.767709\pi$
$839$	−19.9513	+	9.60804i	−0.688796	+	0.331706i	0.0565359	+	0.998401i	$0.481994\pi$
$840$		0			0
$841$	−16.2267	−	7.81435i	−0.559540	−	0.269460i
$842$	−0.101679	−	0.674596i	−0.00350409	−	0.0232481i
$843$		0			0
$844$	−12.4978	−	1.88375i	−0.430194	−	0.0648412i
$845$	2.00094	+	1.85660i	0.0688343	+	0.0638689i
$846$		0			0
$847$	17.1552	+	9.86719i	0.589460	+	0.339041i
$848$	0.0443426	−	0.0353620i	0.00152273	−	0.00121434i
$849$		0			0
$850$	−6.75804	−	21.9090i	−0.231799	−	0.751474i
$851$	−7.38070	+	4.26125i	−0.253007	+	0.146074i
$852$		0			0
$853$	−7.76088	−	1.77137i	−0.265727	−	0.0606506i	0.0875812	−	0.996157i	$-0.472086\pi$
$853$	−7.76088	−	1.77137i	−0.265727	−	0.0606506i	−0.353309	+	0.935507i	$0.614943\pi$
$854$	10.4041	−	15.3138i	0.356021	−	0.524027i
$855$		0			0
$856$	44.8495	+	13.8342i	1.53292	+	0.472845i
$857$	−17.6938	+	45.0832i	−0.604410	+	1.54001i	0.220878	+	0.975301i	$0.429108\pi$
$857$	−17.6938	+	45.0832i	−0.604410	+	1.54001i	−0.825289	+	0.564711i	$0.808988\pi$
$858$		0			0
$859$	−4.62637	+	14.9983i	−0.157850	+	0.511737i	−0.999604	−	0.0281237i	$-0.991047\pi$
$859$	−4.62637	+	14.9983i	−0.157850	+	0.511737i	0.841755	+	0.539860i	$0.181523\pi$
$860$	0.826485	+	3.62107i	0.0281829	+	0.123477i
$861$		0			0
$862$	3.38493	−	14.8304i	0.115291	−	0.505124i
$863$	−1.05962	−	0.611770i	−0.0360698	−	0.0208249i	0.481857	−	0.876250i	$-0.339963\pi$
$863$	−1.05962	−	0.611770i	−0.0360698	−	0.0208249i	−0.517926	+	0.855425i	$0.673296\pi$
$864$		0			0
$865$	−3.22186	+	0.993811i	−0.109546	+	0.0337906i
$866$	−1.97325	+	26.3312i	−0.0670538	+	0.894771i
$867$		0			0
$868$	8.67319	−	15.0793i	0.294387	−	0.511825i
$869$	−12.5235	−	9.98719i	−0.424832	−	0.338792i
$870$		0			0
$871$	−5.20108	+	34.5069i	−0.176232	+	1.16922i
$872$	−23.0145	+	33.7560i	−0.779368	+	1.14312i
$873$		0			0
$874$	−0.746843	+	1.55084i	−0.0252624	+	0.0524578i
$875$	−0.0118893	−	7.26951i	−0.000401930	−	0.245754i
$876$		0			0
$877$	6.32167	−	4.31004i	0.213468	−	0.145540i	−0.451866	−	0.892086i	$-0.649242\pi$
$877$	6.32167	−	4.31004i	0.213468	−	0.145540i	0.665334	+	0.746546i	$0.268289\pi$
$878$	−6.99488	+	6.49030i	−0.236066	+	0.219037i
$879$		0			0
$880$	−0.0195611	+	0.00767716i	−0.000659404	+	0.000258797i
$881$	−48.1263			−1.62142			−0.810709	−	0.585449i	$-0.800918\pi$
$881$	−48.1263			−1.62142			−0.810709	+	0.585449i	$0.800918\pi$
$882$		0			0
$883$	−42.3669			−1.42576			−0.712880	−	0.701286i	$-0.752609\pi$
$883$	−42.3669			−1.42576			−0.712880	+	0.701286i	$0.752609\pi$
$884$	−29.4805	+	11.5702i	−0.991537	+	0.389149i
$885$		0			0
$886$	−11.1818	+	10.3752i	−0.375659	+	0.348561i
$887$	−6.80738	+	4.64119i	−0.228569	+	0.155836i	−0.672190	−	0.740379i	$-0.734646\pi$
$887$	−6.80738	+	4.64119i	−0.228569	+	0.155836i	0.443621	+	0.896215i	$0.353694\pi$
$888$		0			0
$889$	13.9099	−	29.0055i	0.466524	−	0.972814i
$890$	1.59405	−	3.31008i	0.0534326	−	0.110954i
$891$		0			0
$892$	8.95999	−	13.1419i	0.300003	−	0.440023i
$893$	2.87255	−	19.0581i	0.0961262	−	0.637756i
$894$		0			0
$895$	−2.38558	−	1.90244i	−0.0797411	−	0.0635914i
$896$	13.7034	+	12.6732i	0.457798	+	0.423384i
$897$		0			0
$898$	1.26607	−	16.8946i	0.0422494	−	0.563780i
$899$	16.7967	−	5.18110i	0.560202	−	0.172799i
$900$		0			0
$901$	14.8622	+	8.58070i	0.495132	+	0.285865i
$902$	−5.17278	+	22.6634i	−0.172235	+	0.754610i
$903$		0			0
$904$	−7.74559	−	33.9357i	−0.257615	−	1.12868i
$905$	0.559842	−	1.81496i	0.0186098	−	0.0603314i
$906$		0			0
$907$	−4.69227	+	11.9557i	−0.155804	+	0.396982i	−0.987367	−	0.158448i	$-0.949351\pi$
$907$	−4.69227	+	11.9557i	−0.155804	+	0.396982i	0.831563	+	0.555430i	$0.187446\pi$
$908$	4.05755	+	1.25159i	0.134654	+	0.0415354i
$909$		0			0
$910$	3.04441	−	0.233155i	0.100921	−	0.00772900i
$911$	−46.3147	−	10.5710i	−1.53448	−	0.350234i	−0.629944	−	0.776641i	$-0.716922\pi$
$911$	−46.3147	−	10.5710i	−1.53448	−	0.350234i	−0.904532	+	0.426406i	$0.859779\pi$
$912$		0			0
$913$	−3.83250	+	2.21269i	−0.126837	+	0.0732295i
$914$	−1.59056	−	5.15646i	−0.0526109	−	0.170560i
$915$		0			0
$916$	−18.8489	+	15.0315i	−0.622785	+	0.496654i
$917$	1.87466	−	6.11297i	0.0619067	−	0.201868i
$918$		0			0
$919$	22.4031	+	20.7871i	0.739011	+	0.685702i	0.956948	−	0.290261i	$-0.0937421\pi$
$919$	22.4031	+	20.7871i	0.739011	+	0.685702i	−0.217937	+	0.975963i	$0.569933\pi$
$920$	−0.820908	−	0.123732i	−0.0270645	−	0.00407932i
$921$		0			0
$922$	−3.27093	−	21.7012i	−0.107722	−	0.714691i
$923$	18.6922	+	9.00169i	0.615261	+	0.296294i
$924$		0			0
$925$	35.6133	−	17.1505i	1.17096	−	0.563904i
$926$	14.2393	+	20.8852i	0.467932	+	0.686331i
$927$		0			0
$928$	1.40330	+	18.7258i	0.0460656	+	0.614703i
$929$	−19.8187	−	50.4973i	−0.650232	−	1.65676i	−0.749745	−	0.661727i	$-0.769824\pi$
$929$	−19.8187	−	50.4973i	−0.650232	−	1.65676i	0.0995136	−	0.995036i	$-0.468271\pi$
$930$		0			0
$931$	7.36985	+	10.7340i	0.241537	+	0.351792i
$932$			20.3500i			0.666587i
$933$		0			0
$934$	−27.7176	+	2.07714i	−0.906946	+	0.0679662i
$935$	−4.32481	−	4.66104i	−0.141436	−	0.152432i
$936$		0			0
$937$	−25.2650	−	52.4632i	−0.825370	−	1.71390i	−0.690862	−	0.722987i	$-0.742769\pi$
$937$	−25.2650	−	52.4632i	−0.825370	−	1.71390i	−0.134508	−	0.990912i	$-0.542945\pi$
$938$	10.5180	+	13.1450i	0.343425	+	0.429200i
$939$		0			0
$940$	3.51783	−	0.530228i	0.114739	−	0.0172941i
$941$	−46.5259	−	31.7208i	−1.51670	−	1.03407i	−0.981968	−	0.189047i	$-0.939460\pi$
$941$	−46.5259	−	31.7208i	−1.51670	−	1.03407i	−0.534732	−	0.845022i	$-0.679587\pi$
$942$		0			0
$943$	4.47858	−	4.82676i	0.145843	−	0.157181i
$944$	−0.133707	+	0.167663i	−0.00435180	+	0.00545698i
$945$		0			0
$946$	25.2769	+	31.6962i	0.821823	+	1.03053i
$947$	37.8307	+	2.83502i	1.22933	+	0.0921257i	0.673512	−	0.739177i	$-0.264785\pi$
$947$	37.8307	+	2.83502i	1.22933	+	0.0921257i	0.555821	+	0.831302i	$0.312404\pi$
$948$		0			0
$949$	−11.0877	−	19.2045i	−0.359922	−	0.623404i
$950$	3.99174	−	6.91389i	0.129509	−	0.224316i
$951$		0			0
$952$	−14.5238	+	37.1847i	−0.470719	+	1.20516i
$953$	13.4026	−	3.05906i	0.434153	−	0.0990927i	0.000141795	−	1.00000i	$-0.499955\pi$
$953$	13.4026	−	3.05906i	0.434153	−	0.0990927i	0.434011	+	0.900907i	$0.357098\pi$
$954$		0			0
$955$	2.65705	+	1.04282i	0.0859803	+	0.0337448i
$956$	23.2477	+	9.12406i	0.751885	+	0.295093i
$957$		0			0
$958$	−11.9463	+	2.72667i	−0.385968	+	0.0880948i
$959$	18.0305	−	16.7848i	0.582235	−	0.542010i
$960$		0			0
$961$	−1.44267	+	2.49878i	−0.0465377	+	0.0806057i
$962$	16.7316	+	28.9800i	0.539449	+	0.934354i
$963$		0			0
$964$	−8.90343	−	0.667219i	−0.286760	−	0.0214897i
$965$	4.00957	+	5.02784i	0.129073	+	0.161852i
$966$		0			0
$967$	11.3125	−	14.1855i	0.363787	−	0.456174i	−0.565928	−	0.824455i	$-0.691482\pi$
$967$	11.3125	−	14.1855i	0.363787	−	0.456174i	0.929715	+	0.368281i	$0.120053\pi$
$968$	−14.3706	+	15.4879i	−0.461890	+	0.497799i
$969$		0			0
$970$	−2.11896	−	1.44468i	−0.0680357	−	0.0463860i
$971$	−57.3740	+	8.64775i	−1.84122	+	0.277519i	−0.975010	−	0.222160i	$-0.928689\pi$
$971$	−57.3740	+	8.64775i	−1.84122	+	0.277519i	−0.866210	+	0.499679i	$0.833451\pi$
$972$		0			0
$973$	−2.79244	+	3.51338i	−0.0895214	+	0.112634i
$974$	7.14309	+	14.8328i	0.228879	+	0.475273i
$975$		0			0
$976$	−0.0963855	−	0.103879i	−0.00308522	−	0.00332508i
$977$	30.0970	−	2.25546i	0.962889	−	0.0721585i	0.416001	−	0.909364i	$-0.363431\pi$
$977$	30.0970	−	2.25546i	0.962889	−	0.0721585i	0.546888	+	0.837206i	$0.315812\pi$
$978$		0			0
$979$			65.4302i			2.09116i
$980$	−1.49233	+	1.88393i	−0.0476707	+	0.0601800i
$981$		0			0
$982$	−7.42284	−	18.9131i	−0.236872	−	0.603541i
$983$	−2.83552	−	37.8374i	−0.0904390	−	1.20682i	−0.839139	−	0.543916i	$-0.816941\pi$
$983$	−2.83552	−	37.8374i	−0.0904390	−	1.20682i	0.748700	−	0.662909i	$-0.230678\pi$
$984$		0			0
$985$	1.96120	+	2.87655i	0.0624889	+	0.0916544i
$986$	−13.9093	+	6.69834i	−0.442961	+	0.213319i
$987$		0			0
$988$	−9.93543	−	4.78465i	−0.316088	−	0.152220i
$989$	−1.71148	−	11.3549i	−0.0544219	−	0.361066i
$990$		0			0
$991$	11.6432	+	1.75492i	0.369857	+	0.0557470i	0.331341	−	0.943511i	$-0.392499\pi$
$991$	11.6432	+	1.75492i	0.369857	+	0.0557470i	0.0385160	+	0.999258i	$0.487737\pi$
$992$	22.0172	+	20.4290i	0.699048	+	0.648622i
$993$		0			0
$994$	9.31093	−	3.67185i	0.295325	−	0.116464i
$995$	4.86087	−	3.87641i	0.154100	−	0.122891i
$996$		0			0
$997$	−2.18162	−	7.07264i	−0.0690926	−	0.223993i	0.914441	−	0.404720i	$-0.132631\pi$
$997$	−2.18162	−	7.07264i	−0.0690926	−	0.223993i	−0.983533	+	0.180727i	$0.942155\pi$
$998$	−1.13654	+	0.656180i	−0.0359765	+	0.0207710i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.278.7	✓	216
3.2	odd	2	inner	441.2.bg.a.278.12	yes	216
49.3	odd	42	inner	441.2.bg.a.395.12	yes	216
147.101	even	42	inner	441.2.bg.a.395.7	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.7	✓	216	1.1	even	1	trivial
441.2.bg.a.278.12	yes	216	3.2	odd	2	inner
441.2.bg.a.395.7	yes	216	147.101	even	42	inner
441.2.bg.a.395.12	yes	216	49.3	odd	42	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.811510 + 0.318494i) q^{2} +(-0.908993 + 0.843422i) q^{4} +(0.228773 - 0.155975i) q^{5} +(-2.58038 - 0.584516i) q^{7} +(1.22553 - 2.54484i) q^{8} +O(q^{10})\)	\(q+(-0.811510 + 0.318494i) q^{2} +(-0.908993 + 0.843422i) q^{4} +(0.228773 - 0.155975i) q^{5} +(-2.58038 - 0.584516i) q^{7} +(1.22553 - 2.54484i) q^{8} +(-0.135974 + 0.199438i) q^{10} +(0.640710 - 4.25083i) q^{11} +(3.73796 + 2.98092i) q^{13} +(2.28017 - 0.347495i) q^{14} +(0.00131931 - 0.0176050i) q^{16} +(5.10459 - 1.57456i) q^{17} +(1.61087 + 0.930035i) q^{19} +(-0.0764004 + 0.334732i) q^{20} +(0.833924 + 3.65366i) q^{22} +(0.312885 - 1.01435i) q^{23} +(-1.79870 + 4.58300i) q^{25} +(-3.98280 - 1.22853i) q^{26} +(2.83854 - 1.64503i) q^{28} +(3.23196 + 0.737675i) q^{29} +(4.59195 - 2.65116i) q^{31} +(1.66964 + 5.41284i) q^{32} +(-3.64094 + 2.90355i) q^{34} +(-0.681490 + 0.268752i) q^{35} +(-5.88543 - 5.46088i) q^{37} +(-1.60345 - 0.241681i) q^{38} +(-0.116562 - 0.773341i) q^{40} +(5.58866 + 2.69136i) q^{41} +(9.74651 - 4.69367i) q^{43} +(3.00285 + 4.40437i) q^{44} +(0.0691548 + 0.922807i) q^{46} +(-3.78553 - 9.64538i) q^{47} +(6.31668 + 3.01654i) q^{49} -4.29203i q^{50} +(-5.91196 + 0.443040i) q^{52} +(2.18512 + 2.35500i) q^{53} +(-0.516445 - 1.07241i) q^{55} +(-4.64982 + 5.85029i) q^{56} +(-2.85772 + 0.430732i) q^{58} +(-10.0364 - 6.84272i) q^{59} +(5.45959 - 5.88404i) q^{61} +(-2.88203 + 3.61396i) q^{62} +(-3.05688 - 3.83320i) q^{64} +(1.32009 + 0.0989272i) q^{65} +(3.64950 + 6.32111i) q^{67} +(-3.31202 + 5.73658i) q^{68} +(0.467440 - 0.435146i) q^{70} +(4.23060 - 0.965606i) q^{71} +(-4.31759 - 1.69453i) q^{73} +(6.51535 + 2.55708i) q^{74} +(-2.24868 + 0.513247i) q^{76} +(-4.13795 + 10.5942i) q^{77} +(1.86308 - 3.22695i) q^{79} +(-0.00244411 - 0.00423332i) q^{80} +(-5.39244 - 0.404107i) q^{82} +(-0.641843 - 0.804845i) q^{83} +(0.922200 - 1.15640i) q^{85} +(-6.41449 + 6.91317i) q^{86} +(-10.0325 - 6.84002i) q^{88} +(-15.0504 + 2.26848i) q^{89} +(-7.90295 - 9.87680i) q^{91} +(0.571114 + 1.18593i) q^{92} +(6.14400 + 6.62166i) q^{94} +(0.513585 - 0.0384879i) q^{95} +10.6247i q^{97} +(-6.08681 - 0.436126i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

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