LMFDB - Embedded newform 98.5.d.d.19.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,5,Mod(19,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.19"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-32,0,0,0,0,252] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1302563822$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1712622403584.28
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 24x^{6} + 434x^{4} + 3408x^{2} + 20164 $ x^8 + 24x^6 + 434x^4 + 3408*x^2 + 20164
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$1.83127 + 3.17185i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.5.d.d.31.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41421 - 2.44949i) q^{2} +(10.9876 - 6.34371i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-20.0901 - 11.5990i) q^{5} -35.8854i q^{6} -22.6274 q^{8} +(39.9853 - 69.2565i) q^{9} +(-56.8233 + 32.8070i) q^{10} +(-95.9117 - 166.124i) q^{11} +(-87.9010 - 50.7497i) q^{12} +48.5729i q^{13} -294.323 q^{15} +(-32.0000 + 55.4256i) q^{16} +(157.597 - 90.9887i) q^{17} +(-113.095 - 195.887i) q^{18} +(519.542 + 299.958i) q^{19} +185.584i q^{20} -542.558 q^{22} +(234.765 - 406.624i) q^{23} +(-248.622 + 143.542i) q^{24} +(-43.4260 - 75.2160i) q^{25} +(118.979 + 68.6924i) q^{26} +13.0609i q^{27} -338.881 q^{29} +(-416.235 + 720.941i) q^{30} +(-231.710 + 133.778i) q^{31} +(90.5097 + 156.767i) q^{32} +(-2107.68 - 1216.87i) q^{33} -514.710i q^{34} -639.765 q^{36} +(334.265 - 578.964i) q^{37} +(1469.49 - 848.408i) q^{38} +(308.132 + 533.700i) q^{39} +(454.586 + 262.456i) q^{40} -1323.85i q^{41} +1940.23 q^{43} +(-767.294 + 1328.99i) q^{44} +(-1606.61 + 927.579i) q^{45} +(-664.014 - 1150.11i) q^{46} +(2543.42 + 1468.44i) q^{47} +811.995i q^{48} -245.654 q^{50} +(1154.41 - 1999.50i) q^{51} +(336.523 - 194.291i) q^{52} +(730.468 + 1265.21i) q^{53} +(31.9925 + 18.4709i) q^{54} +4449.92i q^{55} +7611.38 q^{57} +(-479.251 + 830.086i) q^{58} +(1498.95 - 865.417i) q^{59} +(1177.29 + 2039.13i) q^{60} +(213.339 + 123.171i) q^{61} +756.763i q^{62} +512.000 q^{64} +(563.397 - 975.832i) q^{65} +(-5961.43 + 3441.83i) q^{66} +(538.294 + 932.352i) q^{67} +(-1260.78 - 727.910i) q^{68} -5957.11i q^{69} -2276.39 q^{71} +(-904.764 + 1567.10i) q^{72} +(6154.79 - 3553.47i) q^{73} +(-945.444 - 1637.56i) q^{74} +(-954.297 - 550.963i) q^{75} -4799.32i q^{76} +1743.06 q^{78} +(-3506.19 + 6072.90i) q^{79} +(1285.76 - 742.337i) q^{80} +(3321.66 + 5753.29i) q^{81} +(-3242.74 - 1872.20i) q^{82} +1448.36i q^{83} -4221.52 q^{85} +(2743.90 - 4752.58i) q^{86} +(-3723.50 + 2149.76i) q^{87} +(2170.23 + 3758.96i) q^{88} +(-1847.86 - 1066.86i) q^{89} +5247.18i q^{90} -3756.23 q^{92} +(-1697.30 + 2939.81i) q^{93} +(7193.87 - 4153.38i) q^{94} +(-6958.42 - 12052.3i) q^{95} +(1988.97 + 1148.33i) q^{96} +5898.76i q^{97} -15340.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 252 q^{9} - 360 q^{11} + 768 q^{15} - 256 q^{16} - 192 q^{18} - 2304 q^{22} + 792 q^{23} + 2300 q^{25} + 2448 q^{29} - 4416 q^{30} - 4032 q^{36} + 3896 q^{37} + 768 q^{39} + 7376 q^{43}+ \cdots - 59184 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 + 252 * q^9 - 360 * q^11 + 768 * q^15 - 256 * q^16 - 192 * q^18 - 2304 * q^22 + 792 * q^23 + 2300 * q^25 + 2448 * q^29 - 4416 * q^30 - 4032 * q^36 + 3896 * q^37 + 768 * q^39 + 7376 * q^43 - 2880 * q^44 - 3072 * q^46 - 14976 * q^50 + 11136 * q^51 - 5832 * q^53 + 25728 * q^57 - 7296 * q^58 - 3072 * q^60 + 4096 * q^64 + 4032 * q^65 + 1048 * q^67 - 43056 * q^71 - 1536 * q^72 + 3456 * q^74 + 9600 * q^78 - 12776 * q^79 + 29628 * q^81 + 33024 * q^85 + 11520 * q^86 + 9216 * q^88 - 12672 * q^92 - 38016 * q^93 - 36864 * q^95 - 59184 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.41421	−	2.44949i	0.353553	−	0.612372i
$2$	1.41421	−	2.44949i	0.353553	−	0.612372i
$3$	10.9876	−	6.34371i	1.22085	−	0.704857i	0.255749	−	0.966743i	$-0.417678\pi$
$3$	10.9876	−	6.34371i	1.22085	−	0.704857i	0.965099	+	0.261887i	$0.0843447\pi$
$4$	−4.00000	−	6.92820i	−0.250000	−	0.433013i
$5$	−20.0901	−	11.5990i	−0.803603	−	0.463960i	0.0411265	−	0.999154i	$-0.486905\pi$
$5$	−20.0901	−	11.5990i	−0.803603	−	0.463960i	−0.844729	+	0.535194i	$0.820239\pi$
$6$		−	35.8854i		−	0.996818i
$7$		0			0
$7$		0			0
$8$	−22.6274			−0.353553
$9$	39.9853	−	69.2565i	0.493645	−	0.855019i
$10$	−56.8233	+	32.8070i	−0.568233	+	0.328070i
$11$	−95.9117	−	166.124i	−0.792659	−	1.37292i	−0.924315	−	0.381630i	$-0.875363\pi$
$11$	−95.9117	−	166.124i	−0.792659	−	1.37292i	0.131657	−	0.991295i	$-0.457970\pi$
$12$	−87.9010	−	50.7497i	−0.610424	−	0.352428i
$13$			48.5729i			0.287413i	0.989620	+	0.143707i	$0.0459022\pi$
$13$			48.5729i			0.287413i	−0.989620	+	0.143707i	$0.954098\pi$
$14$		0			0
$15$	−294.323			−1.30810
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	157.597	−	90.9887i	0.545319	−	0.314840i	−0.201913	−	0.979403i	$-0.564716\pi$
$17$	157.597	−	90.9887i	0.545319	−	0.314840i	0.747232	+	0.664564i	$0.231382\pi$
$18$	−113.095	−	195.887i	−0.349060	−	0.604590i
$19$	519.542	+	299.958i	1.43917	+	0.830908i	0.997792	−	0.0664118i	$-0.0211551\pi$
$19$	519.542	+	299.958i	1.43917	+	0.830908i	0.441382	+	0.897319i	$0.354488\pi$
$20$			185.584i			0.463960i
$21$		0			0
$22$	−542.558			−1.12099
$23$	234.765	−	406.624i	0.443789	−	0.768665i	−0.554178	−	0.832398i	$-0.686967\pi$
$23$	234.765	−	406.624i	0.443789	−	0.768665i	0.997967	+	0.0637329i	$0.0203006\pi$
$24$	−248.622	+	143.542i	−0.431635	+	0.249204i
$25$	−43.4260	−	75.2160i	−0.0694816	−	0.120346i
$26$	118.979	+	68.6924i	0.176004	+	0.101616i
$27$			13.0609i			0.0179162i
$28$		0			0
$29$	−338.881			−0.402951			−0.201475	−	0.979494i	$-0.564574\pi$
$29$	−338.881			−0.402951			−0.201475	+	0.979494i	$0.564574\pi$
$30$	−416.235	+	720.941i	−0.462484	+	0.801046i
$31$	−231.710	+	133.778i	−0.241114	+	0.139207i	−0.615689	−	0.787990i	$-0.711122\pi$
$31$	−231.710	+	133.778i	−0.241114	+	0.139207i	0.374575	+	0.927197i	$0.377789\pi$
$32$	90.5097	+	156.767i	0.0883883	+	0.153093i
$33$	−2107.68	−	1216.87i	−1.93543	−	1.11742i
$34$		−	514.710i		−	0.445251i
$35$		0			0
$36$	−639.765			−0.493645
$37$	334.265	−	578.964i	0.244167	−	0.422910i	−0.717730	−	0.696322i	$-0.754819\pi$
$37$	334.265	−	578.964i	0.244167	−	0.422910i	0.961897	+	0.273412i	$0.0881521\pi$
$38$	1469.49	−	848.408i	1.01765	−	0.587540i
$39$	308.132	+	533.700i	0.202585	+	0.350888i
$40$	454.586	+	262.456i	0.284117	+	0.164035i
$41$		−	1323.85i		−	0.787534i	−0.919210	−	0.393767i	$-0.871172\pi$
$41$		−	1323.85i		−	0.787534i	0.919210	−	0.393767i	$-0.128828\pi$
$42$		0			0
$43$	1940.23			1.04934			0.524671	−	0.851305i	$-0.324188\pi$
$43$	1940.23			1.04934			0.524671	+	0.851305i	$0.324188\pi$
$44$	−767.294	+	1328.99i	−0.396329	+	0.686462i
$45$	−1606.61	+	927.579i	−0.793390	+	0.458064i
$46$	−664.014	−	1150.11i	−0.313806	−	0.543529i
$47$	2543.42	+	1468.44i	1.15139	+	0.664755i	0.949225	−	0.314597i	$-0.101869\pi$
$47$	2543.42	+	1468.44i	1.15139	+	0.664755i	0.202164	+	0.979352i	$0.435203\pi$
$48$			811.995i			0.352428i
$49$		0			0
$50$	−245.654			−0.0982618
$51$	1154.41	−	1999.50i	0.443834	−	0.768743i
$52$	336.523	−	194.291i	0.124454	−	0.0718533i
$53$	730.468	+	1265.21i	0.260046	+	0.450412i	0.966254	−	0.257592i	$-0.0829290\pi$
$53$	730.468	+	1265.21i	0.260046	+	0.450412i	−0.706208	+	0.708004i	$0.749596\pi$
$54$	31.9925	+	18.4709i	0.0109714	+	0.00633433i
$55$			4449.92i			1.47105i
$56$		0			0
$57$	7611.38			2.34268
$58$	−479.251	+	830.086i	−0.142465	+	0.246756i
$59$	1498.95	−	865.417i	0.430608	−	0.248612i	−0.268998	−	0.963141i	$-0.586692\pi$
$59$	1498.95	−	865.417i	0.430608	−	0.248612i	0.699606	+	0.714529i	$0.253359\pi$
$60$	1177.29	+	2039.13i	0.327025	+	0.566425i
$61$	213.339	+	123.171i	0.0573338	+	0.0331017i	0.528393	−	0.849000i	$-0.322795\pi$
$61$	213.339	+	123.171i	0.0573338	+	0.0331017i	−0.471059	+	0.882102i	$0.656128\pi$
$62$			756.763i			0.196869i
$63$		0			0
$64$	512.000			0.125000
$65$	563.397	−	975.832i	0.133348	−	0.230966i
$66$	−5961.43	+	3441.83i	−1.36856	+	0.790136i
$67$	538.294	+	932.352i	0.119914	+	0.207697i	0.919733	−	0.392544i	$-0.128405\pi$
$67$	538.294	+	932.352i	0.119914	+	0.207697i	−0.799819	+	0.600241i	$0.795071\pi$
$68$	−1260.78	−	727.910i	−0.272659	−	0.157420i
$69$		−	5957.11i		−	1.25123i
$70$		0			0
$71$	−2276.39			−0.451574			−0.225787	−	0.974177i	$-0.572495\pi$
$71$	−2276.39			−0.451574			−0.225787	+	0.974177i	$0.572495\pi$
$72$	−904.764	+	1567.10i	−0.174530	+	0.302295i
$73$	6154.79	−	3553.47i	1.15496	−	0.666817i	0.204870	−	0.978789i	$-0.434323\pi$
$73$	6154.79	−	3553.47i	1.15496	−	0.666817i	0.950091	+	0.311972i	$0.100989\pi$
$74$	−945.444	−	1637.56i	−0.172652	−	0.299043i
$75$	−954.297	−	550.963i	−0.169653	−	0.0979491i
$76$		−	4799.32i		−	0.830908i
$77$		0			0
$78$	1743.06			0.286499
$79$	−3506.19	+	6072.90i	−0.561799	+	0.973065i	0.435540	+	0.900169i	$0.356557\pi$
$79$	−3506.19	+	6072.90i	−0.561799	+	0.973065i	−0.997340	+	0.0728955i	$0.976776\pi$
$80$	1285.76	−	742.337i	0.200901	−	0.115990i
$81$	3321.66	+	5753.29i	0.506274	+	0.876892i
$82$	−3242.74	−	1872.20i	−0.482264	−	0.278435i
$83$			1448.36i			0.210243i	0.994459	+	0.105121i	$0.0335231\pi$
$83$			1448.36i			0.210243i	−0.994459	+	0.105121i	$0.966477\pi$
$84$		0			0
$85$	−4221.52			−0.584293
$86$	2743.90	−	4752.58i	0.370998	−	0.642588i
$87$	−3723.50	+	2149.76i	−0.491941	+	0.284022i
$88$	2170.23	+	3758.96i	0.280247	+	0.485402i
$89$	−1847.86	−	1066.86i	−0.233286	−	0.134688i	0.378801	−	0.925478i	$-0.376337\pi$
$89$	−1847.86	−	1066.86i	−0.233286	−	0.134688i	−0.612087	+	0.790790i	$0.709670\pi$
$90$			5247.18i			0.647800i
$91$		0			0
$92$	−3756.23			−0.443789
$93$	−1697.30	+	2939.81i	−0.196242	+	0.339901i
$94$	7193.87	−	4153.38i	0.814155	−	0.470053i
$95$	−6958.42	−	12052.3i	−0.771016	−	1.33544i
$96$	1988.97	+	1148.33i	0.215817	+	0.124602i
$97$			5898.76i			0.626928i	0.949600	+	0.313464i	$0.101489\pi$
$97$			5898.76i			0.626928i	−0.949600	+	0.313464i	$0.898511\pi$
$98$		0			0
$99$	−15340.2			−1.56517
$100$	−347.408	+	601.728i	−0.0347408	+	0.0601728i
$101$	−7943.25	+	4586.04i	−0.778674	+	0.449567i	−0.835960	−	0.548790i	$-0.815089\pi$
$101$	−7943.25	+	4586.04i	−0.778674	+	0.449567i	0.0572864	+	0.998358i	$0.481755\pi$
$102$	−3265.17	−	5655.44i	−0.313838	−	0.543583i
$103$	3383.10	+	1953.23i	0.318889	+	0.184111i	0.650897	−	0.759166i	$-0.274393\pi$
$103$	3383.10	+	1953.23i	0.318889	+	0.184111i	−0.332008	+	0.943277i	$0.607726\pi$
$104$		−	1099.08i		−	0.101616i
$105$		0			0
$106$	4132.15			0.367760
$107$	6070.64	−	10514.7i	0.530233	−	0.918391i	−0.469145	−	0.883121i	$-0.655438\pi$
$107$	6070.64	−	10514.7i	0.530233	−	0.918391i	0.999378	−	0.0352695i	$-0.0112290\pi$
$108$	90.4886	−	52.2436i	0.00775794	−	0.00447905i
$109$	−3404.17	−	5896.19i	−0.286522	−	0.496271i	0.686455	−	0.727172i	$-0.259166\pi$
$109$	−3404.17	−	5896.19i	−0.286522	−	0.496271i	−0.972977	+	0.230901i	$0.925833\pi$
$110$	10900.0	+	6293.14i	0.900830	+	0.520094i
$111$		−	8481.92i		−	0.688411i
$112$		0			0
$113$	−4764.20			−0.373107			−0.186553	−	0.982445i	$-0.559732\pi$
$113$	−4764.20			−0.373107			−0.186553	+	0.982445i	$0.559732\pi$
$114$	10764.1	−	18644.0i	0.828263	−	1.43459i
$115$	−9432.87	+	5446.07i	−0.713261	+	0.411801i
$116$	1355.53	+	2347.84i	0.100738	+	0.174483i
$117$	3363.99	+	1942.20i	0.245744	+	0.141880i
$118$		−	4895.54i		−	0.351590i
$119$		0			0
$120$	6659.77			0.462484
$121$	−11077.6	+	19187.0i	−0.756615	+	1.31050i
$122$	603.414	−	348.381i	0.0405411	−	0.0234064i
$123$	−8398.09	−	14545.9i	−0.555099	−	0.961459i
$124$	1853.68	+	1070.22i	0.120557	+	0.0696036i
$125$			16513.6i			1.05687i
$126$		0			0
$127$	−27968.9			−1.73408			−0.867038	−	0.498242i	$-0.833979\pi$
$127$	−27968.9			−1.73408			−0.867038	+	0.498242i	$0.833979\pi$
$128$	724.077	−	1254.14i	0.0441942	−	0.0765466i
$129$	21318.6	−	12308.3i	1.28109	−	0.739636i
$130$	−1593.53	−	2760.07i	−0.0942916	−	0.163318i
$131$	−20798.9	−	12008.3i	−1.21199	−	0.699741i	−0.248795	−	0.968556i	$-0.580035\pi$
$131$	−20798.9	−	12008.3i	−1.21199	−	0.699741i	−0.963192	+	0.268815i	$0.913368\pi$
$132$			19469.9i			1.11742i
$133$		0			0
$134$	3045.05			0.169584
$135$	151.494	−	262.394i	0.00831240	−	0.0143975i
$136$	−3566.02	+	2058.84i	−0.192799	+	0.111313i
$137$	2081.00	+	3604.39i	0.110874	+	0.192040i	0.916123	−	0.400897i	$-0.131302\pi$
$137$	2081.00	+	3604.39i	0.110874	+	0.192040i	−0.805249	+	0.592937i	$0.797968\pi$
$138$	−14591.9	−	8424.63i	−0.766219	−	0.442377i
$139$		−	26365.8i		−	1.36462i	−0.731064	−	0.682309i	$-0.760976\pi$
$139$		−	26365.8i		−	1.36462i	0.731064	−	0.682309i	$-0.239024\pi$
$140$		0			0
$141$	37261.5			1.87423
$142$	−3219.30	+	5575.99i	−0.159656	+	0.276532i
$143$	8069.11	−	4658.70i	0.394597	−	0.227821i
$144$	2559.06	+	4432.42i	0.123411	+	0.213755i
$145$	6808.15	+	3930.69i	0.323812	+	0.186953i
$146$		−	20101.5i		−	0.943022i
$147$		0			0
$148$	−5348.24			−0.244167
$149$	3288.28	−	5695.48i	0.148114	−	0.256541i	−0.782416	−	0.622756i	$-0.786013\pi$
$149$	3288.28	−	5695.48i	0.148114	−	0.256541i	0.930530	+	0.366214i	$0.119346\pi$
$150$	−2699.16	+	1558.36i	−0.119963	+	0.0692604i
$151$	11465.2	+	19858.3i	0.502839	+	0.870942i	0.999995	+	0.00328086i	$0.00104433\pi$
$151$	11465.2	+	19858.3i	0.502839	+	0.870942i	−0.497156	+	0.867661i	$0.665622\pi$
$152$	−11755.9	−	6787.27i	−0.508825	−	0.293770i
$153$		−	14552.8i		−	0.621677i
$154$		0			0
$155$	6206.77			0.258346
$156$	2465.06	−	4269.60i	0.101293	−	0.175444i
$157$	−32296.6	+	18646.5i	−1.31026	+	0.756480i	−0.982139	−	0.188156i	$-0.939749\pi$
$157$	−32296.6	+	18646.5i	−1.31026	+	0.756480i	−0.328122	+	0.944635i	$0.606416\pi$
$158$	9917.00	+	17176.7i	0.397252	+	0.688061i
$159$	16052.2	+	9267.76i	0.634952	+	0.366590i
$160$		−	4199.29i		−	0.164035i
$161$		0			0
$162$	18790.2			0.715979
$163$	−20427.0	+	35380.6i	−0.768828	+	1.33165i	0.169370	+	0.985553i	$0.445827\pi$
$163$	−20427.0	+	35380.6i	−0.768828	+	1.33165i	−0.938199	+	0.346097i	$0.887507\pi$
$164$	−9171.87	+	5295.38i	−0.341012	+	0.196884i
$165$	28229.0	+	48894.1i	1.03688	+	1.79593i
$166$	3547.75	+	2048.29i	0.128747	+	0.0743320i
$167$			34774.9i			1.24690i	0.781862	+	0.623452i	$0.214270\pi$
$167$			34774.9i			1.24690i	−0.781862	+	0.623452i	$0.785730\pi$
$168$		0			0
$169$	26201.7			0.917394
$170$	−5970.13	+	10340.6i	−0.206579	+	0.357805i
$171$	41548.1	−	23987.8i	1.42088	−	0.820348i
$172$	−7760.94	−	13442.3i	−0.262336	−	0.454379i
$173$	27366.5	+	15800.0i	0.914379	+	0.527917i	0.881838	−	0.471553i	$-0.156307\pi$
$173$	27366.5	+	15800.0i	0.914379	+	0.527917i	0.0325416	+	0.999470i	$0.489640\pi$
$174$			12160.9i			0.401668i
$175$		0			0
$176$	12276.7			0.396329
$177$	10979.9	−	19017.8i	0.350471	−	0.607034i
$178$	−5226.54	+	3017.55i	−0.164958	+	0.0952388i
$179$	−11375.3	−	19702.6i	−0.355024	−	0.614920i	0.632098	−	0.774888i	$-0.282194\pi$
$179$	−11375.3	−	19702.6i	−0.355024	−	0.614920i	−0.987122	+	0.159969i	$0.948861\pi$
$180$	12852.9	+	7420.63i	0.396695	+	0.229032i
$181$			55434.4i			1.69208i	0.533116	+	0.846042i	$0.321021\pi$
$181$			55434.4i			1.69208i	−0.533116	+	0.846042i	$0.678979\pi$
$182$		0			0
$183$	3125.45			0.0933278
$184$	−5312.11	+	9200.85i	−0.156903	+	0.271764i
$185$	−13430.8	+	7754.28i	−0.392427	+	0.226568i
$186$	4800.69	+	8315.03i	0.138764	+	0.240347i
$187$	−30230.8	−	17453.8i	−0.864503	−	0.499121i
$188$		−	23495.1i		−	0.664755i
$189$		0			0
$190$	−39362.8			−1.09038
$191$	25408.8	−	44009.3i	0.696494	−	1.20636i	−0.273180	−	0.961963i	$-0.588075\pi$
$191$	25408.8	−	44009.3i	0.696494	−	1.20636i	0.969674	−	0.244401i	$-0.0785912\pi$
$192$	5625.66	−	3247.98i	0.152606	−	0.0881071i
$193$	624.170	+	1081.09i	0.0167567	+	0.0290234i	0.874282	−	0.485418i	$-0.161333\pi$
$193$	624.170	+	1081.09i	0.0167567	+	0.0290234i	−0.857525	+	0.514442i	$0.827999\pi$
$194$	14449.0	+	8342.11i	0.383913	+	0.221652i
$195$		−	14296.1i		−	0.375966i
$196$		0			0
$197$	64454.6			1.66082			0.830408	−	0.557155i	$-0.188107\pi$
$197$	64454.6			1.66082			0.830408	+	0.557155i	$0.188107\pi$
$198$	−21694.4	+	37575.7i	−0.553371	+	0.958466i
$199$	2037.41	−	1176.30i	0.0514485	−	0.0297038i	−0.474055	−	0.880495i	$-0.657210\pi$
$199$	2037.41	−	1176.30i	0.0514485	−	0.0297038i	0.525504	+	0.850791i	$0.323877\pi$
$200$	982.618	+	1701.94i	0.0245654	+	0.0425486i
$201$	11829.1	+	6829.55i	0.292793	+	0.169044i
$202$			25942.5i			0.635784i
$203$		0			0
$204$	−18470.6			−0.443834
$205$	−15355.3	+	26596.1i	−0.365385	+	0.632865i
$206$	9568.85	−	5524.58i	0.225489	−	0.130186i
$207$	−18774.2	−	32518.0i	−0.438149	−	0.758896i
$208$	−2692.18	−	1554.33i	−0.0622268	−	0.0359267i
$209$		−	115078.i		−	2.63450i
$210$		0			0
$211$	−65056.4			−1.46125			−0.730626	−	0.682778i	$-0.760772\pi$
$211$	−65056.4			−1.46125			−0.730626	+	0.682778i	$0.760772\pi$
$212$	5843.75	−	10121.7i	0.130023	−	0.225206i
$213$	−25012.1	+	14440.7i	−0.551304	+	0.318295i
$214$	−17170.4	−	29739.9i	−0.374931	−	0.649400i
$215$	−38979.4	−	22504.8i	−0.843254	−	0.486853i
$216$		−	295.534i		−	0.00633433i
$217$		0			0
$218$	−19256.9			−0.405203
$219$	45084.3	−	78088.4i	0.940021	−	1.62816i
$220$	30830.0	−	17799.7i	0.636983	−	0.367762i
$221$	4419.58	+	7654.94i	0.0904892	+	0.156732i
$222$	−20776.4	−	11995.2i	−0.421564	−	0.243390i
$223$		−	30412.4i		−	0.611563i	−0.952102	−	0.305781i	$-0.901082\pi$
$223$		−	30412.4i		−	0.611563i	0.952102	−	0.305781i	$-0.0989177\pi$
$224$		0			0
$225$	−6945.60			−0.137197
$226$	−6737.60	+	11669.9i	−0.131913	+	0.228480i
$227$	−45142.0	+	26062.7i	−0.876050	+	0.505788i	−0.869354	−	0.494190i	$-0.835465\pi$
$227$	−45142.0	+	26062.7i	−0.876050	+	0.505788i	−0.00669601	+	0.999978i	$0.502131\pi$
$228$	−30445.5	−	52733.2i	−0.585671	−	1.01441i
$229$	−70390.7	−	40640.1i	−1.34228	−	0.774968i	−0.355142	−	0.934812i	$-0.615568\pi$
$229$	−70390.7	−	40640.1i	−1.34228	−	0.774968i	−0.987142	+	0.159844i	$0.948901\pi$
$230$			30807.6i			0.582375i
$231$		0			0
$232$	7668.01			0.142465
$233$	20859.4	−	36129.6i	0.384229	−	0.665505i	−0.607433	−	0.794371i	$-0.707800\pi$
$233$	20859.4	−	36129.6i	0.384229	−	0.665505i	0.991662	+	0.128866i	$0.0411338\pi$
$234$	9514.79	−	5493.37i	0.173767	−	0.100325i
$235$	−34065.0	−	59002.3i	−0.616840	−	1.06840i
$236$	−11991.6	−	6923.34i	−0.215304	−	0.124306i
$237$			88968.9i			1.58395i
$238$		0			0
$239$	−3936.55			−0.0689160			−0.0344580	−	0.999406i	$-0.510970\pi$
$239$	−3936.55			−0.0689160			−0.0344580	+	0.999406i	$0.510970\pi$
$240$	9418.33	−	16313.0i	0.163513	−	0.283212i
$241$	61064.8	−	35255.8i	1.05137	−	0.607010i	0.128340	−	0.991730i	$-0.459035\pi$
$241$	61064.8	−	35255.8i	1.05137	−	0.607010i	0.923033	+	0.384720i	$0.125702\pi$
$242$	31332.2	+	54269.0i	0.535008	+	0.926661i
$243$	72078.2	+	41614.4i	1.22065	+	0.704743i
$244$		−	1970.74i		−	0.0331017i
$245$		0			0
$246$	−47506.8			−0.785028
$247$	−14569.8	+	25235.6i	−0.238814	+	0.413638i
$248$	5243.01	−	3027.05i	0.0852466	−	0.0492172i
$249$	9187.98	+	15914.1i	0.148191	+	0.256674i
$250$	40449.8	+	23353.7i	0.647197	+	0.373659i
$251$			72042.3i			1.14351i	0.820424	+	0.571755i	$0.193737\pi$
$251$			72042.3i			1.14351i	−0.820424	+	0.571755i	$0.806263\pi$
$252$		0			0
$253$	−90066.6			−1.40709
$254$	−39554.0	+	68509.6i	−0.613089	+	1.06190i
$255$	−46384.4	+	26780.1i	−0.713333	+	0.411843i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	56824.7	+	32807.7i	0.860341	+	0.496718i	0.864127	−	0.503275i	$-0.167872\pi$
$257$	56824.7	+	32807.7i	0.860341	+	0.496718i	−0.00378538	+	0.999993i	$0.501205\pi$
$258$		−	69626.1i		−	1.04600i
$259$		0			0
$260$	−9014.35			−0.133348
$261$	−13550.3	+	23469.8i	−0.198915	+	0.344530i
$262$	−58828.2	+	33964.5i	−0.857004	+	0.494792i
$263$	19353.1	+	33520.5i	0.279794	+	0.484617i	0.971333	−	0.237721i	$-0.0764005\pi$
$263$	19353.1	+	33520.5i	0.279794	+	0.484617i	−0.691539	+	0.722339i	$0.743067\pi$
$264$	47691.4	+	27534.7i	0.684278	+	0.395068i
$265$		−	33890.8i		−	0.482604i
$266$		0			0
$267$	−27071.5			−0.379743
$268$	4306.35	−	7458.81i	0.0599570	−	0.103848i
$269$	75540.7	−	43613.5i	1.04394	−	0.602721i	0.122995	−	0.992407i	$-0.460750\pi$
$269$	75540.7	−	43613.5i	1.04394	−	0.602721i	0.920948	+	0.389687i	$0.127417\pi$
$270$	−428.488	−	742.164i	−0.00587775	−	0.0101806i
$271$	91246.2	+	52681.0i	1.24244	+	0.717324i	0.969591	−	0.244732i	$-0.0786999\pi$
$271$	91246.2	+	52681.0i	1.24244	+	0.717324i	0.272851	+	0.962056i	$0.412033\pi$
$272$			11646.6i			0.157420i
$273$		0			0
$274$	11771.9			0.156800
$275$	−8330.12	+	14428.2i	−0.110150	+	0.190786i
$276$	−41272.1	+	23828.4i	−0.541799	+	0.312808i
$277$	−18089.4	−	31331.8i	−0.235758	−	0.408344i	0.723735	−	0.690078i	$-0.242424\pi$
$277$	−18089.4	−	31331.8i	−0.235758	−	0.408344i	−0.959493	+	0.281734i	$0.909090\pi$
$278$	−64582.7	−	37286.9i	−0.835655	−	0.482465i
$279$			21396.6i			0.274876i
$280$		0			0
$281$	99142.2			1.25558			0.627792	−	0.778381i	$-0.283959\pi$
$281$	99142.2			1.25558			0.627792	+	0.778381i	$0.283959\pi$
$282$	52695.7	−	91271.7i	0.662639	−	1.14772i
$283$	3596.84	−	2076.63i	0.0449105	−	0.0259291i	−0.477377	−	0.878699i	$-0.658412\pi$
$283$	3596.84	−	2076.63i	0.0449105	−	0.0259291i	0.522287	+	0.852770i	$0.325079\pi$
$284$	9105.55	+	15771.3i	0.112894	+	0.195537i
$285$	−152913.	−	88284.4i	−1.88259	−	1.08691i
$286$		−	26353.6i		−	0.322187i
$287$		0			0
$288$	14476.2			0.174530
$289$	−25202.6	+	43652.2i	−0.301752	+	0.522649i
$290$	19256.4	−	11117.7i	0.228970	−	0.132196i
$291$	37420.0	+	64813.4i	0.441894	+	0.765383i
$292$	−49238.3	−	28427.8i	−0.577481	−	0.333409i
$293$			20239.4i			0.235756i	0.993028	+	0.117878i	$0.0376092\pi$
$293$			20239.4i			0.235756i	−0.993028	+	0.117878i	$0.962391\pi$
$294$		0			0
$295$	−40151.9			−0.461384
$296$	−7563.55	+	13100.5i	−0.0863262	+	0.149521i
$297$	2169.73	−	1252.69i	0.0245976	−	0.0142014i
$298$	−9300.67	−	16109.2i	−0.104733	−	0.181402i
$299$	19750.9	+	11403.2i	0.220925	+	0.127551i
$300$			8815.42i			0.0979491i
$301$		0			0
$302$	64857.1			0.711121
$303$	−58185.0	+	100779.i	−0.633761	+	1.09771i
$304$	−33250.7	+	19197.3i	−0.359794	+	0.207727i
$305$	−2857.33	−	4949.04i	−0.0307157	−	0.0532012i
$306$	−35647.0	−	20580.8i	−0.380698	−	0.219796i
$307$		−	63269.8i		−	0.671305i	−0.941986	−	0.335652i	$-0.891043\pi$
$307$		−	63269.8i		−	0.671305i	0.941986	−	0.335652i	$-0.108957\pi$
$308$		0			0
$309$	49563.0			0.519087
$310$	8777.70	−	15203.4i	0.0913393	−	0.158204i
$311$	12449.4	−	7187.69i	0.128715	−	0.0743137i	−0.434260	−	0.900788i	$-0.642990\pi$
$311$	12449.4	−	7187.69i	0.128715	−	0.0743137i	0.562975	+	0.826474i	$0.309657\pi$
$312$	−6972.23	−	12076.3i	−0.0716247	−	0.124058i
$313$	31837.7	+	18381.5i	0.324978	+	0.187626i	0.653609	−	0.756832i	$-0.273254\pi$
$313$	31837.7	+	18381.5i	0.324978	+	0.187626i	−0.328632	+	0.944458i	$0.606587\pi$
$314$			105480.i			1.06982i
$315$		0			0
$316$	56099.0			0.561799
$317$	62778.0	−	108735.i	0.624726	−	1.08206i	−0.363868	−	0.931450i	$-0.618544\pi$
$317$	62778.0	−	108735.i	0.624726	−	1.08206i	0.988594	−	0.150606i	$-0.0481225\pi$
$318$	45402.6	−	26213.2i	0.448979	−	0.259218i
$319$	32502.7	+	56296.3i	0.319402	+	0.553221i
$320$	−10286.1	−	5938.69i	−0.100450	−	0.0579950i
$321$		−	154041.i		−	1.49495i
$322$		0			0
$323$	109171.			1.04641
$324$	26573.3	−	46026.3i	0.253137	−	0.438446i
$325$	3653.46	−	2109.32i	0.0345889	−	0.0199699i
$326$	57776.3	+	100071.i	0.543644	+	0.941619i
$327$	−74807.5	−	43190.1i	−0.699599	−	0.403914i
$328$			29955.2i			0.278435i
$329$		0			0
$330$	159687.			1.46637
$331$	−2688.27	+	4656.22i	−0.0245367	+	0.0424989i	−0.878033	−	0.478600i	$-0.841144\pi$
$331$	−2688.27	+	4656.22i	−0.0245367	+	0.0424989i	0.853496	+	0.521099i	$0.174478\pi$
$332$	10034.5	−	5793.44i	0.0910377	−	0.0525606i
$333$	−26731.4	−	46300.1i	−0.241064	−	0.417535i
$334$	85180.8	+	49179.1i	0.763569	+	0.440847i
$335$		−	24974.7i		−	0.222541i
$336$		0			0
$337$	2202.27			0.0193914			0.00969572	−	0.999953i	$-0.496914\pi$
$337$	2202.27			0.0193914			0.00969572	+	0.999953i	$0.496914\pi$
$338$	37054.8	−	64180.7i	0.324348	−	0.561787i
$339$	−52347.3	+	30222.7i	−0.455507	+	0.262987i
$340$	16886.1	+	29247.5i	0.146073	+	0.253006i
$341$	44447.5	+	25661.8i	0.382242	+	0.220688i
$342$		−	135695.i		−	1.16015i
$343$		0			0
$344$	−43902.5			−0.370998
$345$	−69096.6	+	119679.i	−0.580522	+	1.00549i
$346$	77404.0	−	44689.2i	0.646564	−	0.373294i
$347$	−111100.	−	192431.i	−0.922691	−	1.59815i	−0.795234	−	0.606303i	$-0.792652\pi$
$347$	−111100.	−	192431.i	−0.922691	−	1.59815i	−0.127457	−	0.991844i	$-0.540682\pi$
$348$	29788.0	+	17198.1i	0.245971	+	0.142011i
$349$			102679.i			0.843006i	0.906827	+	0.421503i	$0.138497\pi$
$349$			102679.i			0.843006i	−0.906827	+	0.421503i	$0.861503\pi$
$350$		0			0
$351$	−634.405			−0.00514935
$352$	17361.9	−	30071.6i	0.140124	−	0.242701i
$353$	−54209.4	+	31297.8i	−0.435036	+	0.251168i	−0.701490	−	0.712680i	$-0.747481\pi$
$353$	−54209.4	+	31297.8i	−0.435036	+	0.251168i	0.266454	+	0.963848i	$0.414148\pi$
$354$	−31055.9	−	53790.4i	−0.247821	−	0.429238i
$355$	45732.8	+	26403.8i	0.362887	+	0.209513i
$356$			17069.8i			0.134688i
$357$		0			0
$358$	−64348.6			−0.502080
$359$	−47753.0	+	82710.6i	−0.370520	+	0.641759i	−0.989646	−	0.143533i	$-0.954154\pi$
$359$	−47753.0	+	82710.6i	−0.370520	+	0.641759i	0.619126	+	0.785292i	$0.287487\pi$
$360$	36353.5	−	20988.7i	0.280506	−	0.161950i
$361$	114789.	+	198820.i	0.880815	+	1.52562i
$362$	135786.	+	78396.0i	1.03619	+	0.598242i
$363$			281092.i			2.13322i
$364$		0			0
$365$	−164867.			−1.23751
$366$	4420.06	−	7655.77i	0.0329963	−	0.0571514i
$367$	71300.6	−	41165.4i	0.529372	−	0.305633i	−0.211388	−	0.977402i	$-0.567798\pi$
$367$	71300.6	−	41165.4i	0.529372	−	0.305633i	0.740761	+	0.671769i	$0.234465\pi$
$368$	15024.9	+	26023.9i	0.110947	+	0.192166i
$369$	−91684.9	−	52934.3i	−0.673357	−	0.388763i
$370$			43864.9i			0.320415i
$371$		0			0
$372$	27156.8			0.196242
$373$	−65111.7	+	112777.i	−0.467995	+	0.810592i	−0.999331	−	0.0365697i	$-0.988357\pi$
$373$	−65111.7	+	112777.i	−0.467995	+	0.810592i	0.531336	+	0.847161i	$0.321690\pi$
$374$	−85505.6	+	49366.7i	−0.611296	+	0.352932i
$375$	104757.	+	181445.i	0.744940	+	1.29027i
$376$	−57551.0	−	33227.1i	−0.407077	−	0.235026i
$377$		−	16460.4i		−	0.115813i
$378$		0			0
$379$	192349.			1.33909			0.669546	−	0.742770i	$-0.266489\pi$
$379$	192349.			1.33909			0.669546	+	0.742770i	$0.266489\pi$
$380$	−55667.4	+	96418.7i	−0.385508	+	0.667720i
$381$	−307312.	+	177427.i	−2.11704	+	1.22228i
$382$	−71867.0	−	124477.i	−0.492496	−	0.853028i
$383$	−88276.5	−	50966.5i	−0.601794	−	0.347446i	0.167953	−	0.985795i	$-0.446284\pi$
$383$	−88276.5	−	50966.5i	−0.601794	−	0.347446i	−0.769747	+	0.638349i	$0.779618\pi$
$384$		−	18373.3i		−	0.124602i
$385$		0			0
$386$	3530.84			0.0236975
$387$	77580.8	−	134374.i	0.518003	−	0.897208i
$388$	40867.8	−	23595.1i	0.271468	−	0.156732i
$389$	−95537.0	−	165475.i	−0.631353	−	1.09354i	−0.987275	−	0.159020i	$-0.949167\pi$
$389$	−95537.0	−	165475.i	−0.631353	−	1.09354i	0.355922	−	0.934516i	$-0.384167\pi$
$390$	−35018.2	−	20217.7i	−0.230231	−	0.132924i
$391$		−	85443.7i		−	0.558890i
$392$		0			0
$393$	−304708.			−1.97287
$394$	91152.6	−	157881.i	0.587187	−	1.01704i
$395$	140879.	−	81336.6i	0.902927	−	0.521305i
$396$	61360.9	+	106280.i	0.391292	+	0.677738i
$397$	174195.	+	100572.i	1.10524	+	0.638108i	0.937591	−	0.347739i	$-0.113051\pi$
$397$	174195.	+	100572.i	1.10524	+	0.638108i	0.167644	+	0.985848i	$0.446384\pi$
$398$		−	6654.16i		−	0.0420076i
$399$		0			0
$400$	5558.52			0.0347408
$401$	19989.2	−	34622.3i	0.124310	−	0.215312i	−0.797153	−	0.603778i	$-0.793662\pi$
$401$	19989.2	−	34622.3i	0.124310	−	0.215312i	0.921463	+	0.388466i	$0.126995\pi$
$402$	33457.8	−	19316.9i	0.207036	−	0.119532i
$403$	−6497.98	−	11254.8i	−0.0400100	−	0.0692994i
$404$	63546.0	+	36688.3i	0.389337	+	0.224784i
$405$		−	154112.i		−	0.939564i
$406$		0			0
$407$	−128240.			−0.774165
$408$	−26121.4	+	45243.5i	−0.156919	+	0.271792i
$409$	69849.9	−	40327.9i	0.417560	−	0.241078i	−0.276473	−	0.961022i	$-0.589166\pi$
$409$	69849.9	−	40327.9i	0.417560	−	0.241078i	0.694033	+	0.719943i	$0.255832\pi$
$410$	43431.3	+	75225.3i	0.258366	+	0.447503i
$411$	45730.5	+	26402.5i	0.270721	+	0.156301i
$412$		−	31251.7i		−	0.184111i
$413$		0			0
$414$	−106203.			−0.619636
$415$	16799.6	−	29097.7i	0.0975442	−	0.168952i
$416$	−7614.64	+	4396.31i	−0.0440010	+	0.0254040i
$417$	−167257.	−	289697.i	−0.961860	−	1.66599i
$418$	−281882.	−	162745.i	−1.61330	−	0.931438i
$419$		−	252034.i		−	1.43559i	−0.696254	−	0.717795i	$-0.745151\pi$
$419$		−	252034.i		−	1.43559i	0.696254	−	0.717795i	$-0.254849\pi$
$420$		0			0
$421$	−84439.3			−0.476410			−0.238205	−	0.971215i	$-0.576559\pi$
$421$	−84439.3			−0.476410			−0.238205	+	0.971215i	$0.576559\pi$
$422$	−92003.6	+	159355.i	−0.516630	+	0.894830i
$423$	203399.	−	117432.i	1.13676	−	0.656306i
$424$	−16528.6	−	28628.4i	−0.0919400	−	0.159245i
$425$	−13687.6	−	7902.55i	−0.0757792	−	0.0437511i
$426$			81689.1i			0.450137i
$427$		0			0
$428$	−97130.2			−0.530233
$429$	59106.9	−	102376.i	0.321162	−	0.556268i
$430$	−110251.	+	63653.2i	−0.596271	+	0.344257i
$431$	63756.1	+	110429.i	0.343215	+	0.594467i	0.985028	−	0.172395i	$-0.0551506\pi$
$431$	63756.1	+	110429.i	0.343215	+	0.594467i	−0.641812	+	0.766862i	$0.721817\pi$
$432$	−723.909	−	417.949i	−0.00387897	−	0.00223952i
$433$			233539.i			1.24562i	0.782375	+	0.622808i	$0.214008\pi$
$433$			233539.i			1.24562i	−0.782375	+	0.622808i	$0.785992\pi$
$434$		0			0
$435$	99740.6			0.527100
$436$	−27233.4	+	47169.5i	−0.143261	+	0.248135i
$437$	243940.	−	140839.i	1.27738	−	0.737496i
$438$	−127518.	−	220867.i	−0.664695	−	1.15129i
$439$	−263478.	−	152119.i	−1.36715	−	0.789322i	−0.376583	−	0.926383i	$-0.622901\pi$
$439$	−263478.	−	152119.i	−1.36715	−	0.789322i	−0.990563	+	0.137061i	$0.956234\pi$
$440$		−	100690.i		−	0.520094i
$441$		0			0
$442$	25000.9			0.127971
$443$	43530.5	−	75397.1i	0.221813	−	0.384191i	−0.733546	−	0.679640i	$-0.762136\pi$
$443$	43530.5	−	75397.1i	0.221813	−	0.384191i	0.955358	+	0.295449i	$0.0954693\pi$
$444$	−58764.4	+	33927.7i	−0.298091	+	0.172103i
$445$	24749.1	+	42866.7i	0.124980	+	0.216471i
$446$	−74494.9	−	43009.6i	−0.374504	−	0.216220i
$447$		−	83439.7i		−	0.417597i
$448$		0			0
$449$	−91141.4			−0.452088			−0.226044	−	0.974117i	$-0.572579\pi$
$449$	−91141.4			−0.452088			−0.226044	+	0.974117i	$0.572579\pi$
$450$	−9822.56	+	17013.2i	−0.0485065	+	0.0840157i
$451$	−219922.	+	126972.i	−1.08123	+	0.624246i
$452$	19056.8	+	33007.4i	0.0932767	+	0.161560i
$453$	251951.	+	145464.i	1.22778	+	0.708858i
$454$			147433.i			0.715292i
$455$		0			0
$456$	−172226.			−0.828263
$457$	205964.	−	356741.i	0.986187	−	1.70813i	0.349651	−	0.936880i	$-0.386300\pi$
$457$	205964.	−	356741.i	0.986187	−	1.70813i	0.636537	−	0.771246i	$-0.280366\pi$
$458$	−199095.	+	114948.i	−0.949138	+	0.547985i
$459$	1188.39	+	2058.36i	0.00564073	+	0.00977003i
$460$	75463.0	+	43568.6i	0.356630	+	0.205901i
$461$			157397.i			0.740617i	0.928909	+	0.370309i	$0.120748\pi$
$461$			157397.i			0.740617i	−0.928909	+	0.370309i	$0.879252\pi$
$462$		0			0
$463$	245557.			1.14549			0.572745	−	0.819734i	$-0.305879\pi$
$463$	245557.			1.14549			0.572745	+	0.819734i	$0.305879\pi$
$464$	10844.2	−	18782.7i	0.0503688	−	0.0872413i
$465$	68197.7	−	39374.0i	0.315402	−	0.182097i
$466$	−58999.4	−	102190.i	−0.271691	−	0.470583i
$467$	−28638.8	−	16534.6i	−0.131317	−	0.0758158i	0.432903	−	0.901441i	$-0.357489\pi$
$467$	−28638.8	−	16534.6i	−0.131317	−	0.0758158i	−0.564219	+	0.825625i	$0.690823\pi$
$468$		−	31075.2i		−	0.141880i
$469$		0			0
$470$	−192701.			−0.872343
$471$	−236576.	+	409761.i	−1.06642	+	1.84709i
$472$	−33917.3	+	19582.2i	−0.152243	+	0.0878975i
$473$	−186091.	−	322319.i	−0.831770	−	1.44067i
$474$	217929.	+	125821.i	0.969968	+	0.560011i
$475$		−	52103.8i		−	0.230931i
$476$		0			0
$477$	116832.			0.513482
$478$	−5567.12	+	9642.54i	−0.0243655	+	0.0422022i
$479$	−332794.	+	192139.i	−1.45046	+	0.837421i	−0.998507	−	0.0546235i	$-0.982604\pi$
$479$	−332794.	+	192139.i	−1.45046	+	0.837421i	−0.451948	+	0.892044i	$0.649271\pi$
$480$	−26639.1	−	46140.2i	−0.115621	−	0.200261i
$481$	28121.9	+	16236.2i	0.121550	+	0.0701769i
$482$		−	199437.i		−	0.858442i
$483$		0			0
$484$	177242.			0.756615
$485$	68419.8	−	118507.i	0.290870	−	0.503801i
$486$	203868.	−	117703.i	0.863130	−	0.498328i
$487$	86763.2	+	150278.i	0.365829	+	0.633634i	0.988909	−	0.148524i	$-0.0474523\pi$
$487$	86763.2	+	150278.i	0.365829	+	0.633634i	−0.623080	+	0.782158i	$0.714119\pi$
$488$	−4827.31	−	2787.05i	−0.0202706	−	0.0117032i
$489$			518332.i			2.16765i
$490$		0			0
$491$	−20006.3			−0.0829858			−0.0414929	−	0.999139i	$-0.513211\pi$
$491$	−20006.3			−0.0829858			−0.0414929	+	0.999139i	$0.513211\pi$
$492$	−67184.7	+	116367.i	−0.277549	+	0.480730i
$493$	−53406.7	+	30834.4i	−0.219736	+	0.126865i
$494$	41209.6	+	71377.1i	0.168867	+	0.292486i
$495$	308186.	+	177931.i	1.25777	+	0.726176i
$496$		−	17123.6i		−	0.0696036i
$497$		0			0
$498$	51975.1			0.209574
$499$	214184.	−	370978.i	0.860174	−	1.48987i	−0.0115863	−	0.999933i	$-0.503688\pi$
$499$	214184.	−	370978.i	0.860174	−	1.48987i	0.871760	−	0.489932i	$-0.162979\pi$
$500$	114409.	−	66054.2i	0.457637	−	0.264217i
$501$	220602.	+	382094.i	0.878888	+	1.52228i
$502$	176467.	+	101883.i	0.700254	+	0.404292i
$503$		−	36793.4i		−	0.145423i	−0.997353	−	0.0727116i	$-0.976835\pi$
$503$		−	36793.4i		−	0.145423i	0.997353	−	0.0727116i	$-0.0231653\pi$
$504$		0			0
$505$	212774.			0.834326
$506$	−127373.	+	220617.i	−0.497483	+	0.861665i
$507$	287894.	−	166216.i	1.12000	−	0.646631i
$508$	111876.	+	193774.i	0.433519	+	0.750877i
$509$	−118934.	−	68666.9i	−0.459063	−	0.265040i	0.252587	−	0.967574i	$-0.418719\pi$
$509$	−118934.	−	68666.9i	−0.459063	−	0.265040i	−0.711650	+	0.702534i	$0.752052\pi$
$510$			151491.i			0.582434i
$511$		0			0
$512$	−11585.2			−0.0441942
$513$	−3917.72	+	6785.68i	−0.0148867	+	0.0257845i
$514$	160724.	−	92794.3i	0.608353	−	0.351233i
$515$	−45311.1	−	78481.2i	−0.170840	−	0.295904i
$516$	−170549.	−	98466.2i	−0.640543	−	0.369818i
$517$		−	563363.i		−	2.10769i
$518$		0			0
$519$	400923.			1.48842
$520$	−12748.2	+	22080.6i	−0.0471458	+	0.0816589i
$521$	−89006.2	+	51387.7i	−0.327902	+	0.189315i	−0.654909	−	0.755707i	$-0.727293\pi$
$521$	−89006.2	+	51387.7i	−0.327902	+	0.189315i	0.327007	+	0.945022i	$0.393960\pi$
$522$	38325.9	+	66382.5i	0.140654	+	0.243620i
$523$	−272100.	−	157097.i	−0.994776	−	0.574334i	−0.0880777	−	0.996114i	$-0.528072\pi$
$523$	−272100.	−	157097.i	−0.994776	−	0.574334i	−0.906699	+	0.421779i	$0.861406\pi$
$524$			192132.i			0.699741i
$525$		0			0
$526$	109478.			0.395689
$527$	−24344.6	+	42166.1i	−0.0876560	+	0.151825i
$528$	134892.	−	77879.8i	0.483858	−	0.279355i
$529$	29691.8	+	51427.6i	0.106102	+	0.183774i
$530$	−83015.3	−	47928.9i	−0.295533	−	0.170626i
$531$		−	138416.i		−	0.490904i
$532$		0			0
$533$	64302.9			0.226348
$534$	−38284.9	+	66311.3i	−0.134259	+	0.232544i
$535$	−243919.	+	140827.i	−0.852194	+	0.492014i
$536$	−12180.2	−	21096.7i	−0.0423960	−	0.0734320i
$537$	−249976.	−	144324.i	−0.866860	−	0.500482i
$538$		−	246715.i		−	0.852376i
$539$		0			0
$540$	−2423.90			−0.00831240
$541$	−149192.	+	258408.i	−0.509742	+	0.882899i	0.490194	+	0.871613i	$0.336926\pi$
$541$	−149192.	+	258408.i	−0.509742	+	0.882899i	−0.999936	+	0.0112862i	$0.996407\pi$
$542$	258083.	−	149004.i	0.878539	−	0.507225i
$543$	351659.	+	609092.i	1.19268	+	2.06578i
$544$	28528.1	+	16470.7i	0.0963996	+	0.0556564i
$545$			157940.i			0.531740i
$546$		0			0
$547$	361462.			1.20806			0.604029	−	0.796963i	$-0.293561\pi$
$547$	361462.			1.20806			0.604029	+	0.796963i	$0.293561\pi$
$548$	16648.0	−	28835.2i	0.0554371	−	0.0960199i
$549$	17060.8	−	9850.09i	0.0566051	−	0.0326810i
$550$	23561.1	+	40809.1i	0.0778880	+	0.134906i
$551$	−176063.	−	101650.i	−0.579916	−	0.334815i
$552$			134794.i			0.442377i
$553$		0			0
$554$	−102329.			−0.333412
$555$	−98381.8	+	170402.i	−0.319396	+	0.553209i
$556$	−182668.	+	105463.i	−0.590897	+	0.341155i
$557$	−56212.0	−	97362.0i	−0.181183	−	0.313819i	0.761100	−	0.648634i	$-0.224659\pi$
$557$	−56212.0	−	97362.0i	−0.181183	−	0.313819i	−0.942284	+	0.334815i	$0.891326\pi$
$558$	52410.8	+	30259.4i	0.168326	+	0.0971833i
$559$			94242.7i			0.301595i
$560$		0			0
$561$	−442886.			−1.40724
$562$	140208.	−	242848.i	0.443916	−	0.768885i
$563$	−382376.	+	220765.i	−1.20635	+	0.696488i	−0.961960	−	0.273189i	$-0.911922\pi$
$563$	−382376.	+	220765.i	−1.20635	+	0.696488i	−0.244392	+	0.969677i	$0.578588\pi$
$564$	−149046.	−	258155.i	−0.468557	−	0.811564i
$565$	95713.2	+	55260.0i	0.299830	+	0.173107i
$566$		−	11747.2i		−	0.0366692i
$567$		0			0
$568$	51508.8			0.159656
$569$	−198637.	+	344049.i	−0.613529	+	1.06266i	0.377112	+	0.926168i	$0.376917\pi$
$569$	−198637.	+	344049.i	−0.613529	+	1.06266i	−0.990641	+	0.136495i	$0.956416\pi$
$570$	−432504.	+	249706.i	−1.33119	+	0.768563i
$571$	33617.9	+	58227.9i	0.103109	+	0.178591i	0.912964	−	0.408040i	$-0.133787\pi$
$571$	33617.9	+	58227.9i	0.103109	+	0.178591i	−0.809855	+	0.586630i	$0.800454\pi$
$572$	−64552.9	−	37269.6i	−0.197298	−	0.113910i
$573$		−	644744.i		−	1.96371i
$574$		0			0
$575$	−40779.5			−0.123341
$576$	20472.5	−	35459.3i	0.0617057	−	0.106877i
$577$	56080.4	−	32378.1i	0.168446	−	0.0972521i	−0.413407	−	0.910546i	$-0.635661\pi$
$577$	56080.4	−	32378.1i	0.168446	−	0.0972521i	0.581853	+	0.813294i	$0.302328\pi$
$578$	71283.7	+	123467.i	0.213371	+	0.369569i
$579$	13716.3	+	7919.11i	0.0409147	+	0.0236221i
$580$		−	62891.0i		−	0.186953i
$581$		0			0
$582$	211680.			0.624933
$583$	140121.	−	242697.i	0.412255	−	0.714046i
$584$	−139267.	+	80405.8i	−0.408341	+	0.235756i
$585$	−45055.2	−	78037.8i	−0.131654	−	0.228031i
$586$	49576.3	+	28622.9i	0.144371	+	0.0833524i
$587$			338967.i			0.983741i	0.870668	+	0.491870i	$0.163687\pi$
$587$			338967.i			0.983741i	−0.870668	+	0.491870i	$0.836313\pi$
$588$		0			0
$589$	−160511.			−0.462673
$590$	−56783.4	+	98351.8i	−0.163124	+	0.282539i
$591$	708203.	−	408881.i	2.02760	−	1.17064i
$592$	21393.0	+	37053.7i	0.0610418	+	0.105728i
$593$	221415.	+	127834.i	0.629647	+	0.363527i	0.780615	−	0.625012i	$-0.214906\pi$
$593$	221415.	+	127834.i	0.629647	+	0.363527i	−0.150968	+	0.988539i	$0.548239\pi$
$594$		−	7086.30i		−	0.0200838i
$595$		0			0
$596$	−52612.6			−0.148114
$597$	14924.2	−	25849.5i	0.0418739	−	0.0725277i
$598$	55864.0	−	32253.1i	0.156217	−	0.0901921i
$599$	−64760.3	−	112168.i	−0.180491	−	0.312619i	0.761557	−	0.648098i	$-0.224435\pi$
$599$	−64760.3	−	112168.i	−0.180491	−	0.312619i	−0.942048	+	0.335479i	$0.891102\pi$
$600$	21593.3	+	12466.9i	0.0599813	+	0.0346302i
$601$			377277.i			1.04451i	0.852790	+	0.522254i	$0.174909\pi$
$601$			377277.i			1.04451i	−0.852790	+	0.522254i	$0.825091\pi$
$602$		0			0
$603$	86095.3			0.236780
$604$	91721.8	−	158867.i	0.251419	−	0.435471i
$605$	445100.	−	256978.i	1.21604	−	0.702079i
$606$	164572.	+	285047.i	0.448137	+	0.776196i
$607$	364676.	+	210546.i	0.989759	+	0.571437i	0.905202	−	0.424981i	$-0.139719\pi$
$607$	364676.	+	210546.i	0.989759	+	0.571437i	0.0845566	+	0.996419i	$0.473053\pi$
$608$			108596.i			0.293770i
$609$		0			0
$610$	−16163.5			−0.0434386
$611$	−71326.5	+	123541.i	−0.191059	+	0.330925i
$612$	−100825.	+	58211.4i	−0.269194	+	0.155419i
$613$	−206087.	−	356952.i	−0.548440	−	0.949925i	−0.998382	−	0.0568676i	$-0.981889\pi$
$613$	−206087.	−	356952.i	−0.548440	−	0.949925i	0.449942	−	0.893058i	$-0.351445\pi$
$614$	−154979.	−	89477.0i	−0.411089	−	0.237342i
$615$			389638.i			1.03018i
$616$		0			0
$617$	−262676.			−0.690002			−0.345001	−	0.938602i	$-0.612121\pi$
$617$	−262676.			−0.690002			−0.345001	+	0.938602i	$0.612121\pi$
$618$	70092.6	−	121404.i	0.183525	−	0.317875i
$619$	323872.	−	186988.i	0.845263	−	0.488013i	−0.0137865	−	0.999905i	$-0.504389\pi$
$619$	323872.	−	186988.i	0.845263	−	0.488013i	0.859050	+	0.511892i	$0.171055\pi$
$620$	−24827.1	−	43001.8i	−0.0645866	−	0.111867i
$621$	5310.88	+	3066.24i	0.0137716	+	0.00795101i
$622$		−	40659.7i		−	0.105095i
$623$		0			0
$624$	−39440.9			−0.101293
$625$	164400.	−	284749.i	0.420863	−	0.728956i
$626$	90050.7	−	51990.8i	0.229794	−	0.132672i
$627$	−730020.	−	1.26443e6i	−1.85695	−	3.21633i
$628$	258373.	+	149172.i	0.655131	+	0.378240i
$629$		−	121657.i		−	0.307494i
$630$		0			0
$631$	−408746.			−1.02659			−0.513293	−	0.858214i	$-0.671574\pi$
$631$	−408746.			−1.02659			−0.513293	+	0.858214i	$0.671574\pi$
$632$	79336.0	−	137414.i	0.198626	−	0.344030i
$633$	−714815.	+	412699.i	−1.78397	+	1.02997i
$634$	−177563.	−	307548.i	−0.441748	−	0.765129i
$635$	561898.	+	324412.i	1.39351	+	0.804543i
$636$		−	148284.i		−	0.366590i
$637$		0			0
$638$	183863.			0.451703
$639$	−91022.0	+	157655.i	−0.222918	+	0.386105i
$640$	−29093.5	+	16797.2i	−0.0710291	+	0.0410087i
$641$	264037.	+	457325.i	0.642612	+	1.11304i	0.984848	+	0.173422i	$0.0554825\pi$
$641$	264037.	+	457325.i	0.642612	+	1.11304i	−0.342236	+	0.939614i	$0.611184\pi$
$642$	−377323.	−	217848.i	−0.915468	−	0.528546i
$643$			323445.i			0.782310i	0.920325	+	0.391155i	$0.127924\pi$
$643$			323445.i			0.782310i	−0.920325	+	0.391155i	$0.872076\pi$
$644$		0			0
$645$	−571055.			−1.37265
$646$	154391.	−	267413.i	0.369962	−	0.640794i
$647$	−513009.	+	296186.i	−1.22551	+	0.707548i	−0.966087	−	0.258216i	$-0.916865\pi$
$647$	−513009.	+	296186.i	−1.22551	+	0.707548i	−0.259422	+	0.965764i	$0.583532\pi$
$648$	−75160.6	−	130182.i	−0.178995	−	0.310028i
$649$	−287533.	−	166007.i	−0.682650	−	0.394128i
$650$		−	11932.1i		−	0.0282417i
$651$		0			0
$652$	326832.			0.768828
$653$	164905.	−	285624.i	0.386730	−	0.669835i	−0.605278	−	0.796014i	$-0.706938\pi$
$653$	164905.	−	285624.i	0.386730	−	0.669835i	0.992007	+	0.126179i	$0.0402714\pi$
$654$	−211587.	+	122160.i	−0.494691	+	0.285610i
$655$	278568.	+	482493.i	0.649304	+	1.12463i
$656$	73374.9	+	42363.0i	0.170506	+	0.0984418i
$657$		−	568346.i		−	1.31669i
$658$		0			0
$659$	−526737.			−1.21290			−0.606448	−	0.795123i	$-0.707406\pi$
$659$	−526737.			−1.21290			−0.606448	+	0.795123i	$0.707406\pi$
$660$	225832.	−	391153.i	0.518439	−	0.897963i
$661$	124748.	−	72023.3i	0.285516	−	0.164843i	−0.350402	−	0.936599i	$-0.613955\pi$
$661$	124748.	−	72023.3i	0.285516	−	0.164843i	0.635918	+	0.771757i	$0.280622\pi$
$662$	7603.58	+	13169.8i	0.0173501	+	0.0300512i
$663$	97121.4	+	56073.1i	0.220947	+	0.127564i
$664$		−	32772.7i		−	0.0743320i
$665$		0			0
$666$	−151215.			−0.340916
$667$	−79557.3	+	137797.i	−0.178825	+	0.309734i
$668$	240928.	−	139100.i	0.539925	−	0.311726i
$669$	−192927.	−	334160.i	−0.431064	−	0.746625i
$670$	−61175.2	−	35319.5i	−0.136278	−	0.0786802i
$671$		−	47254.3i		−	0.104953i
$672$		0			0
$673$	620117.			1.36913			0.684563	−	0.728953i	$-0.259993\pi$
$673$	620117.			1.36913			0.684563	+	0.728953i	$0.259993\pi$
$674$	3114.48	−	5394.43i	0.00685591	−	0.0118748i
$675$	982.389	−	567.182i	0.00215613	−	0.00124484i
$676$	−104807.	−	181531.i	−0.229348	−	0.397243i
$677$	−542281.	−	313086.i	−1.18317	−	0.683103i	−0.226423	−	0.974029i	$-0.572703\pi$
$677$	−542281.	−	313086.i	−1.18317	−	0.683103i	−0.956746	+	0.290926i	$0.906037\pi$
$678$			170965.i			0.371920i
$679$		0			0
$680$	95522.0			0.206579
$681$	−330669.	+	572735.i	−0.713016	+	1.23498i
$682$	125716.	−	72582.4i	0.270286	−	0.156050i
$683$	−92778.8	−	160698.i	−0.198888	−	0.344483i	0.749280	−	0.662253i	$-0.230400\pi$
$683$	−92778.8	−	160698.i	−0.198888	−	0.344483i	−0.948168	+	0.317770i	$0.897066\pi$
$684$	−332384.	−	191902.i	−0.710442	−	0.410174i
$685$		−	96550.1i		−	0.205765i
$686$		0			0
$687$	−1.03124e6			−2.18497
$688$	−62087.5	+	107539.i	−0.131168	+	0.227189i
$689$	−61454.8	+	35480.9i	−0.129455	+	0.0747406i
$690$	195435.	+	338503.i	0.410491	+	0.710991i
$691$	−475345.	−	274440.i	−0.995526	−	0.574767i	−0.0886045	−	0.996067i	$-0.528241\pi$
$691$	−475345.	−	274440.i	−0.995526	−	0.574767i	−0.906921	+	0.421300i	$0.861574\pi$
$692$		−	252800.i		−	0.527917i
$693$		0			0
$694$	−628478.			−1.30488
$695$	−305817.	+	529691.i	−0.633129	+	1.09661i
$696$	84253.2	−	48643.6i	0.173927	−	0.100417i
$697$	−120455.	−	208634.i	−0.247947	−	0.429457i
$698$	251511.	+	145210.i	0.516234	+	0.298048i
$699$		−	529305.i		−	1.08331i
$700$		0			0
$701$	517501.			1.05311			0.526556	−	0.850140i	$-0.323483\pi$
$701$	517501.			1.05311			0.526556	+	0.850140i	$0.323483\pi$
$702$	−897.184	+	1553.97i	−0.00182057	+	0.00315332i
$703$	347329.	−	200531.i	0.702798	−	0.405761i
$704$	−49106.8	−	85055.4i	−0.0990823	−	0.171616i
$705$	−748586.	−	432197.i	−1.50613	−	0.869567i
$706$			177047.i			0.355205i
$707$		0			0
$708$	−175679.			−0.350471
$709$	−3017.98	+	5227.30i	−0.00600377	+	0.0103988i	−0.869012	−	0.494792i	$-0.835244\pi$
$709$	−3017.98	+	5227.30i	−0.00600377	+	0.0103988i	0.863008	+	0.505190i	$0.168578\pi$
$710$	129352.	−	74681.3i	0.256600	−	0.148148i
$711$	280392.	+	485653.i	0.554659	+	0.960698i
$712$	41812.3	+	24140.4i	0.0824792	+	0.0476194i
$713$			125625.i			0.247115i
$714$		0			0
$715$	−216145.			−0.422799
$716$	−91002.6	+	157621.i	−0.177512	+	0.307460i
$717$	−43253.3	+	24972.3i	−0.0841359	+	0.0485759i
$718$	135066.	+	233941.i	0.261997	+	0.453792i
$719$	648357.	+	374329.i	1.25417	+	0.724095i	0.971935	−	0.235250i	$-0.0755909\pi$
$719$	648357.	+	374329.i	1.25417	+	0.724095i	0.282235	+	0.959345i	$0.408924\pi$
$720$		−	118730.i		−	0.229032i
$721$		0			0
$722$	649343.			1.24566
$723$	447305.	−	774754.i	0.855711	−	1.48213i
$724$	384061.	−	221737.i	0.732694	−	0.423021i
$725$	14716.3	+	25489.3i	0.0279976	+	0.0484933i
$726$	688533.	+	397525.i	1.30633	+	0.754207i
$727$			370335.i			0.700691i	0.936621	+	0.350345i	$0.113936\pi$
$727$			370335.i			0.700691i	−0.936621	+	0.350345i	$0.886064\pi$
$728$		0			0
$729$	517848.			0.974422
$730$	−233157.	+	403840.i	−0.437525	+	0.757815i
$731$	305775.	−	176539.i	0.572226	−	0.330375i
$732$	−12501.8	−	21653.8i	−0.0233319	−	0.0404121i
$733$	125180.	+	72272.5i	0.232984	+	0.134513i	0.611948	−	0.790898i	$-0.290386\pi$
$733$	125180.	+	72272.5i	0.232984	+	0.134513i	−0.378964	+	0.925411i	$0.623720\pi$
$734$		−	232867.i		−	0.432231i
$735$		0			0
$736$	84993.8			0.156903
$737$	103257.	−	178847.i	0.190102	−	0.329266i
$738$	−259324.	+	149721.i	−0.476135	+	0.274897i
$739$	−2325.13	−	4027.24i	−0.00425753	−	0.00737426i	0.863889	−	0.503683i	$-0.168022\pi$
$739$	−2325.13	−	4027.24i	−0.00425753	−	0.00737426i	−0.868146	+	0.496308i	$0.834689\pi$
$740$	107447.	+	62034.3i	0.196213	+	0.113284i
$741$			369706.i			0.673318i
$742$		0			0
$743$	500204.			0.906087			0.453043	−	0.891489i	$-0.350338\pi$
$743$	500204.			0.906087			0.453043	+	0.891489i	$0.350338\pi$
$744$	38405.5	−	66520.3i	0.0693821	−	0.120173i
$745$	−132124.	+	76281.7i	−0.238050	+	0.137438i
$746$	184164.	+	318981.i	0.330923	+	0.573175i
$747$	100308.	+	57913.1i	0.179761	+	0.103785i
$748$			279260.i			0.499121i
$749$		0			0
$750$	592596.			1.05350
$751$	−472288.	+	818027.i	−0.837389	+	1.45040i	0.0546820	+	0.998504i	$0.482585\pi$
$751$	−472288.	+	818027.i	−0.837389	+	1.45040i	−0.892071	+	0.451896i	$0.850748\pi$
$752$	−162779.	+	93980.4i	−0.287847	+	0.166189i
$753$	457016.	+	791574.i	0.806011	+	1.39605i
$754$	−40319.7	−	23278.6i	−0.0709209	−	0.0409462i
$755$		−	531941.i		−	0.933189i
$756$		0			0
$757$	−654028.			−1.14131			−0.570656	−	0.821189i	$-0.693311\pi$
$757$	−654028.			−1.14131			−0.570656	+	0.821189i	$0.693311\pi$
$758$	272022.	−	471156.i	0.473441	−	0.820023i
$759$	−989619.	+	571357.i	−1.71785	+	0.991799i
$760$	157451.	+	272713.i	0.272595	+	0.472149i
$761$	557437.	+	321837.i	0.962557	+	0.555733i	0.896959	−	0.442113i	$-0.145771\pi$
$761$	557437.	+	321837.i	0.962557	+	0.555733i	0.0655982	+	0.997846i	$0.479104\pi$
$762$			1.00368e6i			1.72856i
$763$		0			0
$764$	−406541.			−0.696494
$765$	−168799.	+	292368.i	−0.288434	+	0.499582i
$766$	−249684.	+	144155.i	−0.425532	+	0.245681i
$767$	42035.8	+	72808.1i	0.0714543	+	0.123763i
$768$	−45005.3	−	25983.8i	−0.0763030	−	0.0440535i
$769$			103697.i			0.175354i	0.996149	+	0.0876768i	$0.0279443\pi$
$769$			103697.i			0.175354i	−0.996149	+	0.0876768i	$0.972056\pi$
$770$		0			0
$771$	832491.			1.40046
$772$	4993.36	−	8648.76i	0.00837835	−	0.0145117i
$773$	689685.	−	398190.i	1.15423	−	0.666394i	0.204315	−	0.978905i	$-0.434503\pi$
$773$	689685.	−	398190.i	1.15423	−	0.666394i	0.949914	+	0.312511i	$0.101170\pi$
$774$	−219432.	−	380067.i	−0.366283	−	0.634422i
$775$	20124.5	+	11618.9i	0.0335059	+	0.0193447i
$776$		−	133474.i		−	0.221652i
$777$		0			0
$778$	−540439.			−0.892868
$779$	397097.	−	687793.i	0.654368	−	1.13340i
$780$	−99046.3	+	57184.4i	−0.162798	+	0.0939915i
$781$	218332.	+	378162.i	0.357944	+	0.619978i
$782$	−209293.	−	120836.i	−0.342249	−	0.197598i
$783$		−	4426.10i		−	0.00721934i
$784$		0			0
$785$	865122.			1.40391
$786$	−430922.	+	746378.i	−0.697514	+	1.20813i
$787$	−1.01234e6	+	584476.i	−1.63447	+	0.943664i	−0.651785	+	0.758404i	$0.725979\pi$
$787$	−1.01234e6	+	584476.i	−1.63447	+	0.943664i	−0.982690	+	0.185260i	$0.940687\pi$
$788$	−257819.	−	446555.i	−0.415204	−	0.719155i
$789$	425289.	+	245541.i	0.683172	+	0.394429i
$790$		−	460109.i		−	0.737237i
$791$		0			0
$792$	347110.			0.553371
$793$	−5982.79	+	10362.5i	−0.00951387	+	0.0164785i
$794$	492698.	−	284459.i	0.781520	−	0.451211i
$795$	−214994.	−	372380.i	−0.340166	−	0.589185i
$796$	−16299.3	−	9410.41i	−0.0257243	−	0.0148519i
$797$			808048.i			1.27210i	0.771649	+	0.636049i	$0.219432\pi$
$797$			808048.i			1.27210i	−0.771649	+	0.636049i	$0.780568\pi$
$798$		0			0
$799$	534447.			0.837165
$800$	7860.94	−	13615.5i	0.0122827	−	0.0212743i
$801$	−147775.	+	85317.7i	−0.230322	+	0.132976i
$802$	−56538.1	−	97926.8i	−0.0879007	−	0.152248i
$803$	−1.18063e6	−	681638.i	−1.83098	−	1.05712i
$804$		−	109273.i		−	0.169044i
$805$		0			0
$806$	−36758.2			−0.0565827
$807$	553342.	−	958417.i	0.849663	−	1.47166i
$808$	179735.	−	103770.i	0.275303	−	0.158946i
$809$	346354.	+	599903.i	0.529204	+	0.916608i	0.999420	+	0.0340569i	$0.0108427\pi$
$809$	346354.	+	599903.i	0.529204	+	0.916608i	−0.470216	+	0.882551i	$0.655824\pi$
$810$	−377496.	−	217947.i	−0.575363	−	0.332186i
$811$		−	382267.i		−	0.581200i	−0.956845	−	0.290600i	$-0.906145\pi$
$811$		−	382267.i		−	0.581200i	0.956845	−	0.290600i	$-0.0938548\pi$
$812$		0			0
$813$	1.33677e6			2.02244
$814$	−181358.	+	314122.i	−0.273709	+	0.474077i
$815$	820760.	−	473866.i	1.23567	−	0.713412i
$816$	73882.4	+	127968.i	0.110958	+	0.192186i
$817$	1.00803e6	+	581988.i	1.51019	+	0.871906i
$818$		−	228129.i		−	0.340936i
$819$		0			0
$820$	245685.			0.365385
$821$	−58196.2	+	100799.i	−0.0863392	+	0.149544i	−0.905961	−	0.423361i	$-0.860850\pi$
$821$	−58196.2	+	100799.i	−0.0863392	+	0.149544i	0.819622	+	0.572905i	$0.194184\pi$
$822$	129345.	−	74677.5i	0.191429	−	0.110521i
$823$	−320263.	−	554712.i	−0.472832	−	0.818969i	0.526684	−	0.850061i	$-0.323435\pi$
$823$	−320263.	−	554712.i	−0.472832	−	0.818969i	−0.999517	+	0.0310915i	$0.990102\pi$
$824$	−76550.8	−	44196.6i	−0.112744	−	0.0650930i
$825$			211375.i			0.310561i
$826$		0			0
$827$	−158299.			−0.231455			−0.115727	−	0.993281i	$-0.536920\pi$
$827$	−158299.			−0.231455			−0.115727	+	0.993281i	$0.536920\pi$
$828$	−150194.	+	260144.i	−0.219075	+	0.379448i
$829$	589331.	−	340250.i	0.857532	−	0.495096i	−0.00565332	−	0.999984i	$-0.501800\pi$
$829$	589331.	−	340250.i	0.857532	−	0.495096i	0.863185	+	0.504888i	$0.168466\pi$
$830$	−47516.3	−	82300.7i	−0.0689742	−	0.119467i
$831$	−397520.	−	229508.i	−0.575648	−	0.332351i
$832$			24869.3i			0.0359267i
$833$		0			0
$834$	−946148.			−1.36028
$835$	403354.	−	698630.i	0.578514	−	1.00202i
$836$	−797282.	+	460311.i	−1.14077	+	0.658626i
$837$	−1747.26	−	3026.35i	−0.00249406	−	0.00431984i
$838$	−617354.	−	356430.i	−0.879116	−	0.507558i
$839$		−	622397.i		−	0.884186i	−0.896969	−	0.442093i	$-0.854236\pi$
$839$		−	622397.i		−	0.884186i	0.896969	−	0.442093i	$-0.145764\pi$
$840$		0			0
$841$	−592440.			−0.837631
$842$	−119415.	+	206833.i	−0.168436	+	0.291740i
$843$	1.08934e6	−	628929.i	1.53288	−	0.885007i
$844$	260226.	+	450724.i	0.365313	+	0.632740i
$845$	−526394.	−	303914.i	−0.737220	−	0.425634i
$846$		−	664297.i		−	0.928157i
$847$		0			0
$848$	−93500.0			−0.130023
$849$	26347.1	−	45634.5i	0.0365526	−	0.0633109i
$850$	−38714.4	+	22351.8i	−0.0535840	+	0.0309367i
$851$	−156947.	−	271840.i	−0.216718	−	0.375366i
$852$	200097.	+	115526.i	0.275652	+	0.159148i
$853$		−	826596.i		−	1.13604i	−0.823013	−	0.568022i	$-0.807709\pi$
$853$		−	826596.i		−	1.13604i	0.823013	−	0.568022i	$-0.192291\pi$
$854$		0			0
$855$	−1.11294e6			−1.52243
$856$	−137363.	+	237920.i	−0.187466	+	0.324700i
$857$	−466854.	+	269538.i	−0.635652	+	0.366994i	−0.782938	−	0.622100i	$-0.786280\pi$
$857$	−466854.	+	269538.i	−0.635652	+	0.366994i	0.147286	+	0.989094i	$0.452946\pi$
$858$	−167180.	−	289564.i	−0.227096	−	0.393341i
$859$	432981.	+	249982.i	0.586790	+	0.338783i	0.763827	−	0.645421i	$-0.223318\pi$
$859$	432981.	+	249982.i	0.586790	+	0.338783i	−0.177037	+	0.984204i	$0.556651\pi$
$860$			360077.i			0.486853i
$861$		0			0
$862$	360659.			0.485380
$863$	−584720.	+	1.01277e6i	−0.785103	+	1.35984i	0.143834	+	0.989602i	$0.454057\pi$
$863$	−584720.	+	1.01277e6i	−0.785103	+	1.35984i	−0.928938	+	0.370237i	$0.879277\pi$
$864$	−2047.52	+	1182.14i	−0.00274284	+	0.00158358i
$865$	−366529.	−	634847.i	−0.489865	−	0.848471i
$866$	572052.	+	330274.i	0.762780	+	0.440392i
$867$			639512.i			0.850766i
$868$		0			0
$869$	1.34514e6			1.78126
$870$	141054.	−	244313.i	0.186358	−	0.322782i
$871$	−45287.0	+	26146.5i	−0.0596949	+	0.0344649i
$872$	77027.5	+	133416.i	0.101301	+	0.175458i
$873$	408528.	+	235864.i	0.536035	+	0.309480i
$874$		−	796705.i		−	1.04298i
$875$		0			0
$876$	−721350.			−0.940021
$877$	−93747.8	+	162376.i	−0.121888	+	0.211117i	−0.920512	−	0.390714i	$-0.872228\pi$
$877$	−93747.8	+	162376.i	−0.121888	+	0.211117i	0.798624	+	0.601830i	$0.205562\pi$
$878$	−745227.	+	430257.i	−0.966718	+	0.558135i
$879$	128393.	+	222383.i	0.166174	+	0.287822i
$880$	−246640.	−	142398.i	−0.318491	−	0.183881i
$881$			179673.i			0.231489i	0.993279	+	0.115745i	$0.0369254\pi$
$881$			179673.i			0.231489i	−0.993279	+	0.115745i	$0.963075\pi$
$882$		0			0
$883$	−1.04658e6			−1.34231			−0.671155	−	0.741317i	$-0.734201\pi$
$883$	−1.04658e6			−1.34231			−0.671155	+	0.741317i	$0.734201\pi$
$884$	35356.7	−	61239.5i	0.0452446	−	0.0783659i
$885$	−441174.	+	254712.i	−0.563279	+	0.325209i
$886$	−123123.	−	213255.i	−0.156845	−	0.271664i
$887$	−1.12609e6	−	650146.i	−1.43128	−	0.826349i	−0.434061	−	0.900884i	$-0.642920\pi$
$887$	−1.12609e6	−	650146.i	−1.43128	−	0.826349i	−0.997218	+	0.0745342i	$0.976253\pi$
$888$			191924.i			0.243390i
$889$		0			0
$890$	140002.			0.176748
$891$	637172.	−	1.10362e6i	0.802605	−	1.39015i
$892$	−210703.	+	121650.i	−0.264814	+	0.152891i
$893$	880942.	+	1.52584e6i	1.10470	+	1.91340i
$894$	−204385.	−	118002.i	−0.255725	−	0.147643i
$895$			527770.i			0.658868i
$896$		0			0
$897$	289354.			0.359620
$898$	−128893.	+	223250.i	−0.159837	+	0.276846i
$899$	78522.4	−	45334.9i	0.0971570	−	0.0560936i
$900$	27782.4	+	48120.5i	0.0342993	+	0.0594081i
$901$	230239.	+	132929.i	0.283616	+	0.163746i
$902$			718263.i			0.882817i
$903$		0			0
$904$	107802.			0.131913
$905$	642984.	−	1.11368e6i	0.785060	−	1.35976i
$906$	712626.	−	411435.i	0.868170	−	0.501238i
$907$	−591942.	−	1.02527e6i	−0.719556	−	1.24631i	−0.961176	−	0.275936i	$-0.911012\pi$
$907$	−591942.	−	1.02527e6i	−0.719556	−	1.24631i	0.241620	−	0.970371i	$-0.422321\pi$
$908$	361136.	+	208502.i	0.438025	+	0.252894i
$909$			733496.i			0.887708i
$910$		0			0
$911$	−1.30731e6			−1.57522			−0.787612	−	0.616172i	$-0.788683\pi$
$911$	−1.30731e6			−1.57522			−0.787612	+	0.616172i	$0.788683\pi$
$912$	−243564.	+	421865.i	−0.292835	+	0.507206i
$913$	240607.	−	138915.i	0.288647	−	0.166651i
$914$	−582555.	−	1.00901e6i	−0.697340	−	1.20783i
$915$	−62790.6	−	36252.2i	−0.0749985	−	0.0433004i
$916$			650242.i			0.774968i
$917$		0			0
$918$	6722.58			0.00797720
$919$	−349387.	+	605157.i	−0.413691	+	0.716534i	−0.995290	−	0.0969417i	$-0.969094\pi$
$919$	−349387.	+	605157.i	−0.413691	+	0.716534i	0.581599	+	0.813476i	$0.302427\pi$
$920$	213442.	−	123231.i	0.252176	−	0.145594i
$921$	−401365.	−	695185.i	−0.473174	−	0.819561i
$922$	385542.	+	222593.i	0.453534	+	0.261848i
$923$		−	110571.i		−	0.129789i
$924$		0			0
$925$	−58063.1			−0.0678605
$926$	347271.	−	601491.i	0.404992	−	0.701466i
$927$	270548.	−	156201.i	0.314837	−	0.181771i
$928$	−30672.0	−	53125.5i	−0.0356161	−	0.0616889i
$929$	1.20776e6	+	697298.i	1.39942	+	0.807955i	0.994332	−	0.106323i	$-0.0339078\pi$
$929$	1.20776e6	+	697298.i	1.39942	+	0.807955i	0.405087	+	0.914278i	$0.367241\pi$
$930$		−	222733.i		−	0.257524i
$931$		0			0
$932$	−333751.			−0.384229
$933$	91193.3	−	157951.i	0.104761	−	0.181451i
$934$	−81002.6	+	46766.9i	−0.0928550	+	0.0536099i
$935$	404893.	+	701295.i	0.463145	+	0.802190i
$936$	−76118.4	−	43947.0i	−0.0868836	−	0.0501623i
$937$		−	509380.i		−	0.580180i	−0.956999	−	0.290090i	$-0.906315\pi$
$937$		−	509380.i		−	0.580180i	0.956999	−	0.290090i	$-0.0936852\pi$
$938$		0			0
$939$	466428.			0.528997
$940$	−272520.	+	472018.i	−0.308420	+	0.534199i
$941$	−1.40733e6	+	812525.i	−1.58934	+	0.917608i	−0.595929	+	0.803037i	$0.703216\pi$
$941$	−1.40733e6	+	812525.i	−1.58934	+	0.917608i	−0.993415	+	0.114572i	$0.963450\pi$
$942$	669137.	+	1.15898e6i	0.754072	+	1.30609i
$943$	−538307.	−	310792.i	−0.605350	−	0.349499i
$944$			110773.i			0.124306i
$945$		0			0
$946$	−1.05269e6			−1.17630
$947$	−612308.	+	1.06055e6i	−0.682763	+	1.18258i	0.291371	+	0.956610i	$0.405889\pi$
$947$	−612308.	+	1.06055e6i	−0.682763	+	1.18258i	−0.974134	+	0.225970i	$0.927445\pi$
$948$	616395.	−	355876.i	0.685871	−	0.395988i
$949$	172602.	+	298956.i	0.191652	+	0.331951i
$950$	−127628.	−	73685.9i	−0.141416	−	0.0816464i
$951$		−	1.59298e6i		−	1.76137i
$952$		0			0
$953$	−1.14847e6			−1.26454			−0.632269	−	0.774749i	$-0.717876\pi$
$953$	−1.14847e6			−1.26454			−0.632269	+	0.774749i	$0.717876\pi$
$954$	165225.	−	286179.i	0.181543	−	0.314442i
$955$	−1.02093e6	+	589434.i	−1.11941	+	0.646292i
$956$	15746.2	+	27273.2i	0.0172290	+	0.0298415i
$957$	714255.	+	412375.i	0.779883	+	0.450265i
$958$			1.08690e6i			1.18429i
$959$		0			0
$960$	−150693.			−0.163513
$961$	−425967.	+	737797.i	−0.461243	+	0.798896i
$962$	79540.8	−	45922.9i	0.0859488	−	0.0496226i
$963$	−485472.	−	840863.i	−0.523494	−	0.906719i
$964$	−488518.	−	282046.i	−0.525686	−	0.303505i
$965$		−	28959.0i		−	0.0310978i
$966$		0			0
$967$	−733668.			−0.784597			−0.392298	−	0.919838i	$-0.628320\pi$
$967$	−733668.			−0.784597			−0.392298	+	0.919838i	$0.628320\pi$
$968$	250658.	−	434152.i	0.267504	−	0.463330i
$969$	1.19953e6	−	692549.i	1.27751	−	0.737570i
$970$	−193520.	−	335187.i	−0.205676	−	0.356241i
$971$	681345.	+	393375.i	0.722651	+	0.417223i	0.815728	−	0.578436i	$-0.196337\pi$
$971$	681345.	+	393375.i	0.722651	+	0.417223i	−0.0930768	+	0.995659i	$0.529670\pi$
$972$		−	665830.i		−	0.704743i
$973$		0			0
$974$	490807.			0.517360
$975$	26761.9	−	46352.9i	0.0281519	−	0.0487605i
$976$	−13653.7	+	7882.97i	−0.0143335	+	0.00827542i
$977$	−418520.	−	724897.i	−0.438457	−	0.759429i	0.559114	−	0.829091i	$-0.311141\pi$
$977$	−418520.	−	724897.i	−0.438457	−	0.759429i	−0.997571	+	0.0696616i	$0.977808\pi$
$978$	1.26965e6	+	733032.i	1.32741	+	0.766382i
$979$			409299.i			0.427046i
$980$		0			0
$981$	−544467.			−0.565761
$982$	−28293.2	+	49005.2i	−0.0293399	+	0.0508182i
$983$	−557832.	+	322064.i	−0.577293	+	0.333300i	−0.760057	−	0.649857i	$-0.774829\pi$
$983$	−557832.	+	322064.i	−0.577293	+	0.333300i	0.182764	+	0.983157i	$0.441496\pi$
$984$	190027.	+	329136.i	0.196257	+	0.339927i
$985$	−1.29490e6	−	747610.i	−1.33464	−	0.770553i
$986$			174426.i			0.179414i
$987$		0			0
$988$	233117.			0.238814
$989$	455498.	−	788946.i	0.465687	−	0.806593i
$990$	871682.	−	503266.i	0.889381	−	0.513484i
$991$	−46258.8	−	80122.5i	−0.0471028	−	0.0815844i	0.841513	−	0.540237i	$-0.181665\pi$
$991$	−46258.8	−	80122.5i	−0.0471028	−	0.0815844i	−0.888616	+	0.458653i	$0.848332\pi$
$992$	−41944.1	−	24216.4i	−0.0426233	−	0.0246086i
$993$			68214.4i			0.0691795i
$994$		0			0
$995$	−54575.7			−0.0551256
$996$	73503.9	−	127312.i	0.0740954	−	0.128337i
$997$	−317297.	+	183191.i	−0.319209	+	0.184295i	−0.651040	−	0.759043i	$-0.725667\pi$
$997$	−317297.	+	183191.i	−0.319209	+	0.184295i	0.331831	+	0.943339i	$0.392334\pi$
$998$	−605804.	−	1.04928e6i	−0.608235	−	1.05349i
$999$	7561.79	+	4365.80i	0.00757694	+	0.00437455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.5.d.d.19.4		8
7.2	even	3		14.5.b.a.13.2	yes	4
7.3	odd	6	inner	98.5.d.d.31.4		8
7.4	even	3	inner	98.5.d.d.31.3		8
7.5	odd	6		14.5.b.a.13.1	✓	4
7.6	odd	2	inner	98.5.d.d.19.3		8
21.2	odd	6		126.5.c.a.55.3		4
21.5	even	6		126.5.c.a.55.4		4
28.19	even	6		112.5.c.c.97.4		4
28.23	odd	6		112.5.c.c.97.1		4
35.2	odd	12		350.5.d.a.349.4		8
35.9	even	6		350.5.b.a.251.3		4
35.12	even	12		350.5.d.a.349.1		8
35.19	odd	6		350.5.b.a.251.4		4
35.23	odd	12		350.5.d.a.349.5		8
35.33	even	12		350.5.d.a.349.8		8
56.5	odd	6		448.5.c.e.321.4		4
56.19	even	6		448.5.c.f.321.1		4
56.37	even	6		448.5.c.e.321.1		4
56.51	odd	6		448.5.c.f.321.4		4
84.23	even	6		1008.5.f.h.433.2		4
84.47	odd	6		1008.5.f.h.433.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.b.a.13.1	✓	4	7.5	odd	6
14.5.b.a.13.2	yes	4	7.2	even	3
98.5.d.d.19.3		8	7.6	odd	2	inner
98.5.d.d.19.4		8	1.1	even	1	trivial
98.5.d.d.31.3		8	7.4	even	3	inner
98.5.d.d.31.4		8	7.3	odd	6	inner
112.5.c.c.97.1		4	28.23	odd	6
112.5.c.c.97.4		4	28.19	even	6
126.5.c.a.55.3		4	21.2	odd	6
126.5.c.a.55.4		4	21.5	even	6
350.5.b.a.251.3		4	35.9	even	6
350.5.b.a.251.4		4	35.19	odd	6
350.5.d.a.349.1		8	35.12	even	12
350.5.d.a.349.4		8	35.2	odd	12
350.5.d.a.349.5		8	35.23	odd	12
350.5.d.a.349.8		8	35.33	even	12
448.5.c.e.321.1		4	56.37	even	6
448.5.c.e.321.4		4	56.5	odd	6
448.5.c.f.321.1		4	56.19	even	6
448.5.c.f.321.4		4	56.51	odd	6
1008.5.f.h.433.2		4	84.23	even	6
1008.5.f.h.433.3		4	84.47	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 - 2.44949i) q^{2} +(10.9876 - 6.34371i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-20.0901 - 11.5990i) q^{5} -35.8854i q^{6} -22.6274 q^{8} +(39.9853 - 69.2565i) q^{9} +(-56.8233 + 32.8070i) q^{10} +(-95.9117 - 166.124i) q^{11} +(-87.9010 - 50.7497i) q^{12} +48.5729i q^{13} -294.323 q^{15} +(-32.0000 + 55.4256i) q^{16} +(157.597 - 90.9887i) q^{17} +(-113.095 - 195.887i) q^{18} +(519.542 + 299.958i) q^{19} +185.584i q^{20} -542.558 q^{22} +(234.765 - 406.624i) q^{23} +(-248.622 + 143.542i) q^{24} +(-43.4260 - 75.2160i) q^{25} +(118.979 + 68.6924i) q^{26} +13.0609i q^{27} -338.881 q^{29} +(-416.235 + 720.941i) q^{30} +(-231.710 + 133.778i) q^{31} +(90.5097 + 156.767i) q^{32} +(-2107.68 - 1216.87i) q^{33} -514.710i q^{34} -639.765 q^{36} +(334.265 - 578.964i) q^{37} +(1469.49 - 848.408i) q^{38} +(308.132 + 533.700i) q^{39} +(454.586 + 262.456i) q^{40} -1323.85i q^{41} +1940.23 q^{43} +(-767.294 + 1328.99i) q^{44} +(-1606.61 + 927.579i) q^{45} +(-664.014 - 1150.11i) q^{46} +(2543.42 + 1468.44i) q^{47} +811.995i q^{48} -245.654 q^{50} +(1154.41 - 1999.50i) q^{51} +(336.523 - 194.291i) q^{52} +(730.468 + 1265.21i) q^{53} +(31.9925 + 18.4709i) q^{54} +4449.92i q^{55} +7611.38 q^{57} +(-479.251 + 830.086i) q^{58} +(1498.95 - 865.417i) q^{59} +(1177.29 + 2039.13i) q^{60} +(213.339 + 123.171i) q^{61} +756.763i q^{62} +512.000 q^{64} +(563.397 - 975.832i) q^{65} +(-5961.43 + 3441.83i) q^{66} +(538.294 + 932.352i) q^{67} +(-1260.78 - 727.910i) q^{68} -5957.11i q^{69} -2276.39 q^{71} +(-904.764 + 1567.10i) q^{72} +(6154.79 - 3553.47i) q^{73} +(-945.444 - 1637.56i) q^{74} +(-954.297 - 550.963i) q^{75} -4799.32i q^{76} +1743.06 q^{78} +(-3506.19 + 6072.90i) q^{79} +(1285.76 - 742.337i) q^{80} +(3321.66 + 5753.29i) q^{81} +(-3242.74 - 1872.20i) q^{82} +1448.36i q^{83} -4221.52 q^{85} +(2743.90 - 4752.58i) q^{86} +(-3723.50 + 2149.76i) q^{87} +(2170.23 + 3758.96i) q^{88} +(-1847.86 - 1066.86i) q^{89} +5247.18i q^{90} -3756.23 q^{92} +(-1697.30 + 2939.81i) q^{93} +(7193.87 - 4153.38i) q^{94} +(-6958.42 - 12052.3i) q^{95} +(1988.97 + 1148.33i) q^{96} +5898.76i q^{97} -15340.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 252 q^{9} - 360 q^{11} + 768 q^{15} - 256 q^{16} - 192 q^{18} - 2304 q^{22} + 792 q^{23} + 2300 q^{25} + 2448 q^{29} - 4416 q^{30} - 4032 q^{36} + 3896 q^{37} + 768 q^{39} + 7376 q^{43}+ \cdots - 59184 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 + 252 * q^9 - 360 * q^11 + 768 * q^15 - 256 * q^16 - 192 * q^18 - 2304 * q^22 + 792 * q^23 + 2300 * q^25 + 2448 * q^29 - 4416 * q^30 - 4032 * q^36 + 3896 * q^37 + 768 * q^39 + 7376 * q^43 - 2880 * q^44 - 3072 * q^46 - 14976 * q^50 + 11136 * q^51 - 5832 * q^53 + 25728 * q^57 - 7296 * q^58 - 3072 * q^60 + 4096 * q^64 + 4032 * q^65 + 1048 * q^67 - 43056 * q^71 - 1536 * q^72 + 3456 * q^74 + 9600 * q^78 - 12776 * q^79 + 29628 * q^81 + 33024 * q^85 + 11520 * q^86 + 9216 * q^88 - 12672 * q^92 - 38016 * q^93 - 36864 * q^95 - 59184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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