LMFDB - Embedded newform 108.5.f.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58866 - 3.04940i) q^{2} +(-2.59770 + 15.7877i) q^{4} +(5.51579 + 9.55363i) q^{5} +(10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +O(q^{10})$	\(q+(-2.58866 - 3.04940i) q^{2} +(-2.59770 + 15.7877i) q^{4} +(5.51579 + 9.55363i) q^{5} +(10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +(14.8544 - 41.5509i) q^{10} +(-189.995 - 109.694i) q^{11} +(18.5350 + 32.1036i) q^{13} +(-8.54488 - 46.8884i) q^{14} +(-242.504 - 82.0235i) q^{16} -284.021 q^{17} +45.4901i q^{19} +(-165.158 + 62.2643i) q^{20} +(157.332 + 863.330i) q^{22} +(-174.319 + 100.643i) q^{23} +(251.652 - 435.874i) q^{25} +(49.9160 - 139.626i) q^{26} +(-120.862 + 147.435i) q^{28} +(-614.153 + 1063.74i) q^{29} +(-1311.83 + 757.384i) q^{31} +(377.637 + 951.823i) q^{32} +(735.233 + 866.094i) q^{34} +131.443i q^{35} -1521.29 q^{37} +(138.718 - 117.758i) q^{38} +(617.407 + 342.453i) q^{40} +(-1316.97 - 2281.07i) q^{41} +(-34.6057 - 19.9796i) q^{43} +(2225.36 - 2714.63i) q^{44} +(758.153 + 271.038i) q^{46} +(2498.36 + 1442.43i) q^{47} +(-1129.51 - 1956.38i) q^{49} +(-1980.60 + 360.941i) q^{50} +(-554.991 + 209.230i) q^{52} -1415.13 q^{53} -2420.19i q^{55} +(762.458 - 13.1019i) q^{56} +(4833.61 - 880.870i) q^{58} +(-2453.33 + 1416.43i) q^{59} +(2628.64 - 4552.93i) q^{61} +(5705.44 + 2039.68i) q^{62} +(1924.92 - 3615.51i) q^{64} +(-204.471 + 354.154i) q^{65} +(805.917 - 465.296i) q^{67} +(737.801 - 4484.04i) q^{68} +(400.823 - 340.261i) q^{70} -1162.75i q^{71} -2162.87 q^{73} +(3938.11 + 4639.03i) q^{74} +(-718.185 - 118.170i) q^{76} +(-1307.02 - 2263.82i) q^{77} +(6482.54 + 3742.70i) q^{79} +(-553.978 - 2769.22i) q^{80} +(-3546.69 + 9920.88i) q^{82} +(966.756 + 558.157i) q^{83} +(-1566.60 - 2713.43i) q^{85} +(28.6565 + 157.247i) q^{86} +(-14038.7 + 241.238i) q^{88} +6739.71 q^{89} +441.696i q^{91} +(-1136.10 - 3013.54i) q^{92} +(-2068.85 - 11352.5i) q^{94} +(-434.596 + 250.914i) q^{95} +(-6023.28 + 10432.6i) q^{97} +(-3041.85 + 8508.73i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.58866	−	3.04940i	−0.647164	−	0.762350i
$2$	−2.58866	−	3.04940i	−0.647164	−	0.762350i
$3$		0			0
$3$		0			0
$4$	−2.59770	+	15.7877i	−0.162356	+	0.986732i
$5$	5.51579	+	9.55363i	0.220632	+	0.382145i	0.955000	−	0.296606i	$-0.0958548\pi$
$5$	5.51579	+	9.55363i	0.220632	+	0.382145i	−0.734368	+	0.678751i	$0.762521\pi$
$6$		0			0
$7$	10.3188	+	5.95759i	0.210589	+	0.121583i	0.601585	−	0.798809i	$-0.294536\pi$
$7$	10.3188	+	5.95759i	0.210589	+	0.121583i	−0.390996	+	0.920392i	$0.627869\pi$
$8$	54.8676	−	32.9476i	0.857307	−	0.514806i
$9$		0			0
$10$	14.8544	−	41.5509i	0.148544	−	0.415509i
$11$	−189.995	−	109.694i	−1.57021	−	0.906559i	−0.996143	−	0.0877473i	$-0.972033\pi$
$11$	−189.995	−	109.694i	−1.57021	−	0.906559i	−0.574063	−	0.818811i	$-0.694633\pi$
$12$		0			0
$13$	18.5350	+	32.1036i	0.109675	+	0.189962i	0.915639	−	0.402003i	$-0.131686\pi$
$13$	18.5350	+	32.1036i	0.109675	+	0.189962i	−0.805964	+	0.591965i	$0.798352\pi$
$14$	−8.54488	−	46.8884i	−0.0435963	−	0.239227i
$15$		0			0
$16$	−242.504	−	82.0235i	−0.947281	−	0.320404i
$17$	−284.021			−0.982771			−0.491386	−	0.870942i	$-0.663509\pi$
$17$	−284.021			−0.982771			−0.491386	+	0.870942i	$0.663509\pi$
$18$		0			0
$19$			45.4901i			0.126011i	0.998013	+	0.0630057i	$0.0200686\pi$
$19$			45.4901i			0.126011i	−0.998013	+	0.0630057i	$0.979931\pi$
$20$	−165.158	+	62.2643i	−0.412896	+	0.155661i
$21$		0			0
$22$	157.332	+	863.330i	0.325066	+	1.78374i
$23$	−174.319	+	100.643i	−0.329525	+	0.190252i	−0.655630	−	0.755082i	$-0.727597\pi$
$23$	−174.319	+	100.643i	−0.329525	+	0.190252i	0.326105	+	0.945334i	$0.394264\pi$
$24$		0			0
$25$	251.652	−	435.874i	0.402643	−	0.697399i
$26$	49.9160	−	139.626i	0.0738402	−	0.206547i
$27$		0			0
$28$	−120.862	+	147.435i	−0.154161	+	0.188055i
$29$	−614.153	+	1063.74i	−0.730265	+	1.26486i	0.226505	+	0.974010i	$0.427270\pi$
$29$	−614.153	+	1063.74i	−0.730265	+	1.26486i	−0.956770	+	0.290846i	$0.906063\pi$
$30$		0			0
$31$	−1311.83	+	757.384i	−1.36507	+	0.788121i	−0.990293	−	0.138996i	$-0.955613\pi$
$31$	−1311.83	+	757.384i	−1.36507	+	0.788121i	−0.374773	+	0.927117i	$0.622279\pi$
$32$	377.637	+	951.823i	0.368786	+	0.929514i
$33$		0			0
$34$	735.233	+	866.094i	0.636015	+	0.749216i
$35$			131.443i			0.107301i
$36$		0			0
$37$	−1521.29			−1.11124			−0.555622	−	0.831435i	$-0.687520\pi$
$37$	−1521.29			−1.11124			−0.555622	+	0.831435i	$0.687520\pi$
$38$	138.718	−	117.758i	0.0960648	−	0.0815501i
$39$		0			0
$40$	617.407	+	342.453i	0.385879	+	0.214033i
$41$	−1316.97	−	2281.07i	−0.783447	−	1.35697i	−0.929923	−	0.367755i	$-0.880126\pi$
$41$	−1316.97	−	2281.07i	−0.783447	−	1.35697i	0.146476	−	0.989214i	$-0.453207\pi$
$42$		0			0
$43$	−34.6057	−	19.9796i	−0.0187159	−	0.0108056i	0.490613	−	0.871378i	$-0.336773\pi$
$43$	−34.6057	−	19.9796i	−0.0187159	−	0.0108056i	−0.509329	+	0.860572i	$0.670106\pi$
$44$	2225.36	−	2714.63i	1.14946	−	1.40219i
$45$		0			0
$46$	758.153	+	271.038i	0.358295	+	0.128090i
$47$	2498.36	+	1442.43i	1.13099	+	0.652978i	0.944184	−	0.329419i	$-0.106853\pi$
$47$	2498.36	+	1442.43i	1.13099	+	0.652978i	0.186807	+	0.982397i	$0.440186\pi$
$48$		0			0
$49$	−1129.51	−	1956.38i	−0.470435	−	0.814817i
$50$	−1980.60	+	360.941i	−0.792239	+	0.144376i
$51$		0			0
$52$	−554.991	+	209.230i	−0.205248	+	0.0773780i
$53$	−1415.13			−0.503783			−0.251892	−	0.967755i	$-0.581053\pi$
$53$	−1415.13			−0.503783			−0.251892	+	0.967755i	$0.581053\pi$
$54$		0			0
$55$		−	2420.19i		−	0.800062i
$56$	762.458	−	13.1019i	0.243131	−	0.00417791i
$57$		0			0
$58$	4833.61	−	880.870i	1.43686	−	0.261852i
$59$	−2453.33	+	1416.43i	−0.704778	+	0.406904i	−0.809125	−	0.587637i	$-0.800058\pi$
$59$	−2453.33	+	1416.43i	−0.704778	+	0.406904i	0.104346	+	0.994541i	$0.466725\pi$
$60$		0			0
$61$	2628.64	−	4552.93i	0.706433	−	1.22358i	−0.259739	−	0.965679i	$-0.583637\pi$
$61$	2628.64	−	4552.93i	0.706433	−	1.22358i	0.966172	−	0.257899i	$-0.0830300\pi$
$62$	5705.44	+	2039.68i	1.48425	+	0.530614i
$63$		0			0
$64$	1924.92	−	3615.51i	0.469950	−	0.882693i
$65$	−204.471	+	354.154i	−0.0483954	+	0.0838233i
$66$		0			0
$67$	805.917	−	465.296i	0.179531	−	0.103653i	−0.407541	−	0.913187i	$-0.633614\pi$
$67$	805.917	−	465.296i	0.179531	−	0.103653i	0.587073	+	0.809534i	$0.300280\pi$
$68$	737.801	−	4484.04i	0.159559	−	0.969732i
$69$		0			0
$70$	400.823	−	340.261i	0.0818006	−	0.0694411i
$71$		−	1162.75i		−	0.230659i	−0.993327	−	0.115329i	$-0.963208\pi$
$71$		−	1162.75i		−	0.230659i	0.993327	−	0.115329i	$-0.0367923\pi$
$72$		0			0
$73$	−2162.87			−0.405867			−0.202934	−	0.979192i	$-0.565048\pi$
$73$	−2162.87			−0.405867			−0.202934	+	0.979192i	$0.565048\pi$
$74$	3938.11	+	4639.03i	0.719158	+	0.847157i
$75$		0			0
$76$	−718.185	−	118.170i	−0.124339	−	0.0204587i
$77$	−1307.02	−	2263.82i	−0.220445	−	0.381822i
$78$		0			0
$79$	6482.54	+	3742.70i	1.03870	+	0.599695i	0.919466	−	0.393171i	$-0.128622\pi$
$79$	6482.54	+	3742.70i	1.03870	+	0.599695i	0.119237	+	0.992866i	$0.461955\pi$
$80$	−553.978	−	2769.22i	−0.0865591	−	0.432690i
$81$		0			0
$82$	−3546.69	+	9920.88i	−0.527467	+	1.47544i
$83$	966.756	+	558.157i	0.140333	+	0.0810215i	0.568523	−	0.822667i	$-0.307515\pi$
$83$	966.756	+	558.157i	0.140333	+	0.0810215i	−0.428190	+	0.903689i	$0.640848\pi$
$84$		0			0
$85$	−1566.60	−	2713.43i	−0.216830	−	0.375561i
$86$	28.6565	+	157.247i	0.00387459	+	0.0212611i
$87$		0			0
$88$	−14038.7	+	241.238i	−1.81285	+	0.0311516i
$89$	6739.71			0.850866			0.425433	−	0.904990i	$-0.360122\pi$
$89$	6739.71			0.850866			0.425433	+	0.904990i	$0.360122\pi$
$90$		0			0
$91$			441.696i			0.0533385i
$92$	−1136.10	−	3013.54i	−0.134227	−	0.356042i
$93$		0			0
$94$	−2068.85	−	11352.5i	−0.234139	−	1.28480i
$95$	−434.596	+	250.914i	−0.0481546	+	0.0278021i
$96$		0			0
$97$	−6023.28	+	10432.6i	−0.640161	+	1.10879i	0.345235	+	0.938516i	$0.387799\pi$
$97$	−6023.28	+	10432.6i	−0.640161	+	1.10879i	−0.985396	+	0.170276i	$0.945534\pi$
$98$	−3041.85	+	8508.73i	−0.316727	+	0.885957i
$99$		0			0
$100$	6227.74	+	5105.28i	0.622774	+	0.510528i
$101$	−4777.60	+	8275.04i	−0.468346	+	0.811199i	−0.999346	−	0.0361728i	$-0.988483\pi$
$101$	−4777.60	+	8275.04i	−0.468346	+	0.811199i	0.530999	+	0.847372i	$0.321817\pi$
$102$		0			0
$103$	−9962.26	+	5751.71i	−0.939039	+	0.542154i	−0.889659	−	0.456626i	$-0.849058\pi$
$103$	−9962.26	+	5751.71i	−0.939039	+	0.542154i	−0.0493798	+	0.998780i	$0.515724\pi$
$104$	2074.71	+	1150.77i	0.191819	+	0.106395i
$105$		0			0
$106$	3663.28	+	4315.29i	0.326031	+	0.384059i
$107$		−	6602.72i		−	0.576707i	−0.957524	−	0.288353i	$-0.906892\pi$
$107$		−	6602.72i		−	0.576707i	0.957524	−	0.288353i	$-0.0931078\pi$
$108$		0			0
$109$	12045.3			1.01383			0.506913	−	0.861997i	$-0.330786\pi$
$109$	12045.3			1.01383			0.506913	+	0.861997i	$0.330786\pi$
$110$	−7380.12	+	6265.04i	−0.609928	+	0.517772i
$111$		0			0
$112$	−2013.70	−	2291.13i	−0.160531	−	0.182647i
$113$	1865.35	+	3230.88i	0.146084	+	0.253025i	0.929777	−	0.368124i	$-0.120000\pi$
$113$	1865.35	+	3230.88i	0.146084	+	0.253025i	−0.783693	+	0.621149i	$0.786666\pi$
$114$		0			0
$115$	−1923.01	−	1110.25i	−0.145407	−	0.0839510i
$116$	−15198.7	−	12459.4i	−1.12951	−	0.925933i
$117$		0			0
$118$	10670.1	+	3814.54i	0.766311	+	0.273954i
$119$	−2930.77	−	1692.08i	−0.206960	−	0.119489i
$120$		0			0
$121$	16744.9	+	29003.0i	1.14370	+	1.98094i
$122$	−20688.4	+	3770.21i	−1.38997	+	0.253307i
$123$		0			0
$124$	−8549.63	−	22678.2i	−0.556037	−	1.47491i
$125$	12447.0			0.796607
$126$		0			0
$127$		−	26549.7i		−	1.64608i	−0.567980	−	0.823042i	$-0.692275\pi$
$127$		−	26549.7i		−	1.64608i	0.567980	−	0.823042i	$-0.307725\pi$
$128$	−16008.1	+	3489.47i	−0.977056	+	0.212981i
$129$		0			0
$130$	1609.26	−	293.269i	0.0952226	−	0.0173532i
$131$	1142.84	−	659.821i	0.0665954	−	0.0384489i	−0.466333	−	0.884609i	$-0.654425\pi$
$131$	1142.84	−	659.821i	0.0665954	−	0.0384489i	0.532928	+	0.846161i	$0.321092\pi$
$132$		0			0
$133$	−271.011	+	469.405i	−0.0153209	+	0.0265366i
$134$	−3505.12	−	1253.07i	−0.195206	−	0.0697856i
$135$		0			0
$136$	−15583.6	+	9357.79i	−0.842537	+	0.505936i
$137$	12906.5	−	22354.7i	0.687648	−	1.19104i	−0.284949	−	0.958543i	$-0.591977\pi$
$137$	12906.5	−	22354.7i	0.687648	−	1.19104i	0.972597	−	0.232499i	$-0.0746901\pi$
$138$		0			0
$139$	−11377.8	+	6569.00i	−0.588885	+	0.339993i	−0.764656	−	0.644438i	$-0.777091\pi$
$139$	−11377.8	+	6569.00i	−0.588885	+	0.339993i	0.175772	+	0.984431i	$0.443758\pi$
$140$	−2075.19	−	341.450i	−0.105877	−	0.0174209i
$141$		0			0
$142$	−3545.69	+	3009.96i	−0.175843	+	0.149274i
$143$		−	8132.70i		−	0.397706i
$144$		0			0
$145$	−13550.2			−0.644478
$146$	5598.92	+	6595.45i	0.262663	+	0.309413i
$147$		0			0
$148$	3951.86	−	24017.7i	0.180417	−	1.09650i
$149$	12968.2	+	22461.6i	0.584128	+	1.01174i	0.994984	+	0.100038i	$0.0318965\pi$
$149$	12968.2	+	22461.6i	0.584128	+	1.01174i	−0.410856	+	0.911700i	$0.634770\pi$
$150$		0			0
$151$	24591.2	+	14197.8i	1.07852	+	0.622681i	0.930496	−	0.366303i	$-0.119377\pi$
$151$	24591.2	+	14197.8i	1.07852	+	0.622681i	0.148020	+	0.988984i	$0.452710\pi$
$152$	1498.79	+	2495.93i	0.0648714	+	0.108030i
$153$		0			0
$154$	−3519.88	+	9845.88i	−0.148418	+	0.415158i
$155$	−14471.5	−	8355.15i	−0.602353	−	0.347769i
$156$		0			0
$157$	2760.19	+	4780.78i	0.111980	+	0.193954i	0.916568	−	0.399878i	$-0.130948\pi$
$157$	2760.19	+	4780.78i	0.111980	+	0.193954i	−0.804589	+	0.593832i	$0.797614\pi$
$158$	−5368.10	−	29456.4i	−0.215033	−	1.17996i
$159$		0			0
$160$	−7010.39	+	8857.86i	−0.273844	+	0.346010i
$161$	−2398.36			−0.0925257
$162$		0			0
$163$			407.281i			0.0153292i	0.999971	+	0.00766459i	$0.00243974\pi$
$163$			407.281i			0.0153292i	−0.999971	+	0.00766459i	$0.997560\pi$
$164$	39433.9	−	14866.5i	1.46616	−	0.552739i
$165$		0			0
$166$	−800.556	−	4392.91i	−0.0290520	−	0.159417i
$167$	20561.9	−	11871.4i	0.737277	−	0.425667i	−0.0838016	−	0.996482i	$-0.526706\pi$
$167$	20561.9	−	11871.4i	0.737277	−	0.425667i	0.821078	+	0.570816i	$0.193373\pi$
$168$		0			0
$169$	13593.4	−	23544.5i	0.475943	−	0.824357i
$170$	−4218.95	+	11801.3i	−0.145984	+	0.408351i
$171$		0			0
$172$	405.328	−	494.444i	0.0137009	−	0.0167132i
$173$	−1413.25	+	2447.82i	−0.0472200	+	0.0817874i	−0.888669	−	0.458549i	$-0.848370\pi$
$173$	−1413.25	+	2447.82i	−0.0472200	+	0.0817874i	0.841449	+	0.540336i	$0.181703\pi$
$174$		0			0
$175$	5193.52	−	2998.48i	0.169584	−	0.0979095i
$176$	37077.0	+	42185.2i	1.19696	+	1.36187i
$177$		0			0
$178$	−17446.8	−	20552.1i	−0.550650	−	0.648658i
$179$			45743.4i			1.42765i	0.700323	+	0.713826i	$0.253039\pi$
$179$			45743.4i			1.42765i	−0.700323	+	0.713826i	$0.746961\pi$
$180$		0			0
$181$	−24226.2			−0.739483			−0.369742	−	0.929135i	$-0.620554\pi$
$181$	−24226.2			−0.739483			−0.369742	+	0.929135i	$0.620554\pi$
$182$	1346.91	−	1143.40i	0.0406626	−	0.0345188i
$183$		0			0
$184$	−6248.52	+	11265.4i	−0.184562	+	0.332745i
$185$	−8391.13	−	14533.9i	−0.245176	−	0.424657i
$186$		0			0
$187$	53962.5	+	31155.3i	1.54315	+	0.890940i
$188$	−29262.6	+	35696.4i	−0.827938	+	1.00997i
$189$		0			0
$190$	1890.16	+	675.726i	0.0523589	+	0.0187182i
$191$	19504.6	+	11261.0i	0.534651	+	0.308681i	0.742908	−	0.669393i	$-0.233446\pi$
$191$	19504.6	+	11261.0i	0.534651	+	0.308681i	−0.208257	+	0.978074i	$0.566779\pi$
$192$		0			0
$193$	−9144.35	−	15838.5i	−0.245493	−	0.425205i	0.716777	−	0.697302i	$-0.245616\pi$
$193$	−9144.35	−	15838.5i	−0.245493	−	0.425205i	−0.962270	+	0.272097i	$0.912283\pi$
$194$	47405.5	−	8639.10i	1.25958	−	0.229544i
$195$		0			0
$196$	33820.9	−	12750.4i	0.880385	−	0.331903i
$197$	−36300.2			−0.935356			−0.467678	−	0.883899i	$-0.654909\pi$
$197$	−36300.2			−0.935356			−0.467678	+	0.883899i	$0.654909\pi$
$198$		0			0
$199$		−	47336.5i		−	1.19533i	−0.801744	−	0.597667i	$-0.796094\pi$
$199$		−	47336.5i		−	1.19533i	0.801744	−	0.597667i	$-0.203906\pi$
$200$	−553.433	−	32206.7i	−0.0138358	−	0.805168i
$201$		0			0
$202$	37601.5	−	6852.44i	0.921515	−	0.167935i
$203$	−12674.7	+	7317.73i	−0.307571	+	0.177576i
$204$		0			0
$205$	14528.3	−	25163.8i	0.345706	−	0.598781i
$206$	43328.2	+	15489.7i	1.02102	+	0.365014i
$207$		0			0
$208$	−1861.57	−	9305.56i	−0.0430280	−	0.215088i
$209$	4989.97	−	8642.89i	0.114237	−	0.197864i
$210$		0			0
$211$	−40261.7	+	23245.1i	−0.904330	+	0.522115i	−0.878602	−	0.477554i	$-0.841524\pi$
$211$	−40261.7	+	23245.1i	−0.904330	+	0.522115i	−0.0257275	+	0.999669i	$0.508190\pi$
$212$	3676.08	−	22341.6i	0.0817924	−	0.497099i
$213$		0			0
$214$	−20134.3	+	17092.2i	−0.439653	+	0.373224i
$215$		−	440.814i		−	0.00953626i
$216$		0			0
$217$	−18048.7			−0.383290
$218$	−31181.1	−	36730.9i	−0.656113	−	0.772891i
$219$		0			0
$220$	38209.2	+	6286.92i	0.789447	+	0.129895i
$221$	−5264.34	−	9118.10i	−0.107785	−	0.186689i
$222$		0			0
$223$	−71531.9	−	41298.9i	−1.43843	−	0.830480i	−0.440693	−	0.897658i	$-0.645267\pi$
$223$	−71531.9	−	41298.9i	−1.43843	−	0.830480i	−0.997741	+	0.0671780i	$0.978600\pi$
$224$	−1773.79	+	12071.5i	−0.0353514	+	0.240583i
$225$		0			0
$226$	5023.49	−	14051.8i	0.0983533	−	0.275116i
$227$	−25722.3	−	14850.8i	−0.499182	−	0.288203i	0.229194	−	0.973381i	$-0.426391\pi$
$227$	−25722.3	−	14850.8i	−0.499182	−	0.288203i	−0.728376	+	0.685178i	$0.759724\pi$
$228$		0			0
$229$	−22667.9	−	39262.0i	−0.432256	−	0.748690i	0.564811	−	0.825220i	$-0.308949\pi$
$229$	−22667.9	−	39262.0i	−0.432256	−	0.748690i	−0.997067	+	0.0765307i	$0.975616\pi$
$230$	1592.42	+	8738.10i	0.0301024	+	0.165182i
$231$		0			0
$232$	1350.64	+	78599.9i	0.0250937	+	1.46031i
$233$	−50931.3			−0.938151			−0.469075	−	0.883158i	$-0.655413\pi$
$233$	−50931.3			−0.938151			−0.469075	+	0.883158i	$0.655413\pi$
$234$		0			0
$235$			31824.5i			0.576270i
$236$	−15989.2	−	42412.0i	−0.287080	−	0.761491i
$237$		0			0
$238$	2426.92	+	13317.3i	0.0428452	+	0.235105i
$239$	31946.2	−	18444.1i	0.559272	−	0.322896i	−0.193581	−	0.981084i	$-0.562010\pi$
$239$	31946.2	−	18444.1i	0.559272	−	0.322896i	0.752853	+	0.658188i	$0.228677\pi$
$240$		0			0
$241$	−4193.64	+	7263.59i	−0.0722033	+	0.125060i	−0.899867	−	0.436165i	$-0.856336\pi$
$241$	−4193.64	+	7263.59i	−0.0722033	+	0.125060i	0.827663	+	0.561225i	$0.189670\pi$
$242$	45094.9	−	126141.i	0.770011	−	2.15389i
$243$		0			0
$244$	65052.0	+	53327.3i	1.09265	+	0.895715i
$245$	12460.3	−	21581.9i	0.207586	−	0.359549i
$246$		0			0
$247$	−1460.40	+	843.160i	−0.0239374	+	0.0138203i
$248$	−47023.0	+	84777.4i	−0.764551	+	1.37840i
$249$		0			0
$250$	−32221.0	−	37955.8i	−0.515536	−	0.607293i
$251$			1475.47i			0.0234198i	0.999931	+	0.0117099i	$0.00372746\pi$
$251$			1475.47i			0.0234198i	−0.999931	+	0.0117099i	$0.996273\pi$
$252$		0			0
$253$	44159.6			0.689897
$254$	−80960.7	+	68728.1i	−1.25489	+	1.06529i
$255$		0			0
$256$	52080.3	+	39782.1i	0.794682	+	0.607026i
$257$	17336.5	+	30027.8i	0.262480	+	0.454629i	0.966900	−	0.255154i	$-0.0821263\pi$
$257$	17336.5	+	30027.8i	0.262480	+	0.454629i	−0.704420	+	0.709783i	$0.748793\pi$
$258$		0			0
$259$	−15698.0	−	9063.23i	−0.234015	−	0.135109i
$260$	−5060.12	−	4148.11i	−0.0748539	−	0.0613626i
$261$		0			0
$262$	−4970.49	−	1776.94i	−0.0724097	−	0.0258863i
$263$	16482.5	+	9516.19i	0.238294	+	0.137579i	0.614392	−	0.789001i	$-0.289401\pi$
$263$	16482.5	+	9516.19i	0.238294	+	0.137579i	−0.376099	+	0.926580i	$0.622735\pi$
$264$		0			0
$265$	−7805.54	−	13519.6i	−0.111151	−	0.192518i
$266$	2132.96	−	388.707i	0.0301453	−	0.00549363i
$267$		0			0
$268$	5252.43	+	13932.3i	0.0731292	+	0.193978i
$269$	−58724.1			−0.811544			−0.405772	−	0.913974i	$-0.632997\pi$
$269$	−58724.1			−0.811544			−0.405772	+	0.913974i	$0.632997\pi$
$270$		0			0
$271$			31474.1i			0.428563i	0.976772	+	0.214281i	$0.0687409\pi$
$271$			31474.1i			0.428563i	−0.976772	+	0.214281i	$0.931259\pi$
$272$	68876.2	+	23296.4i	0.930960	+	0.314884i
$273$		0			0
$274$	−101579.	+	18511.6i	−1.35301	+	0.246571i
$275$	−95625.2	+	55209.2i	−1.26447	+	0.730040i
$276$		0			0
$277$	−33265.8	+	57618.0i	−0.433549	+	0.750929i	−0.997176	−	0.0751008i	$-0.976072\pi$
$277$	−33265.8	+	57618.0i	−0.433549	+	0.750929i	0.563627	+	0.826029i	$0.309405\pi$
$278$	49484.8	+	17690.7i	0.640299	+	0.228905i
$279$		0			0
$280$	4330.73	+	7211.98i	0.0552389	+	0.0919895i
$281$	−61859.9	+	107145.i	−0.783424	+	1.35693i	0.146512	+	0.989209i	$0.453195\pi$
$281$	−61859.9	+	107145.i	−0.783424	+	1.35693i	−0.929936	+	0.367721i	$0.880138\pi$
$282$		0			0
$283$	−47401.9	+	27367.5i	−0.591865	+	0.341713i	−0.765835	−	0.643038i	$-0.777674\pi$
$283$	−47401.9	+	27367.5i	−0.591865	+	0.341713i	0.173970	+	0.984751i	$0.444341\pi$
$284$	18357.2	+	3020.48i	0.227598	+	0.0374489i
$285$		0			0
$286$	−24799.9	+	21052.8i	−0.303192	+	0.257381i
$287$		−	31383.9i		−	0.381016i
$288$		0			0
$289$	−2853.15			−0.0341609
$290$	35076.7	+	41319.9i	0.417083	+	0.491318i
$291$		0			0
$292$	5618.48	−	34146.7i	0.0658951	−	0.400482i
$293$	−44309.0	−	76745.4i	−0.516127	−	0.893958i	−0.999825	−	0.0187226i	$-0.994040\pi$
$293$	−44309.0	−	76745.4i	−0.516127	−	0.893958i	0.483698	−	0.875235i	$-0.339293\pi$
$294$		0			0
$295$	−27064.1	−	15625.5i	−0.310993	−	0.179552i
$296$	−83469.8	+	50122.9i	−0.952677	+	0.572075i
$297$		0			0
$298$	34924.2	−	97690.7i	0.393273	−	1.10007i
$299$	−6462.01	−	3730.84i	−0.0722812	−	0.0417316i
$300$		0			0
$301$	−238.061	−	412.333i	−0.00262757	−	0.00455109i
$302$	−20363.6	−	111742.i	−0.223276	−	1.22518i
$303$		0			0
$304$	3731.26	−	11031.5i	0.0403746	−	0.119368i
$305$	57996.0			0.623446
$306$		0			0
$307$			123447.i			1.30980i	0.755716	+	0.654900i	$0.227289\pi$
$307$			123447.i			1.30980i	−0.755716	+	0.654900i	$0.772711\pi$
$308$	39135.8	−	14754.1i	0.412547	−	0.155529i
$309$		0			0
$310$	11983.7	+	65758.1i	0.124700	+	0.684268i
$311$	52431.9	−	30271.6i	0.542094	−	0.312978i	−0.203833	−	0.979006i	$-0.565340\pi$
$311$	52431.9	−	30271.6i	0.542094	−	0.312978i	0.745927	+	0.666027i	$0.232007\pi$
$312$		0			0
$313$	26193.1	−	45367.8i	0.267361	−	0.463083i	−0.700818	−	0.713340i	$-0.747182\pi$
$313$	26193.1	−	45367.8i	0.267361	−	0.463083i	0.968180	+	0.250257i	$0.0805150\pi$
$314$	7433.35	−	20792.7i	0.0753920	−	0.210888i
$315$		0			0
$316$	−75928.4	+	92622.1i	−0.760378	+	0.927557i
$317$	−12998.7	+	22514.4i	−0.129354	+	0.224048i	−0.923427	−	0.383775i	$-0.874624\pi$
$317$	−12998.7	+	22514.4i	−0.129354	+	0.224048i	0.794072	+	0.607823i	$0.207957\pi$
$318$		0			0
$319$	233372.	−	134737.i	2.29333	−	1.32406i
$320$	45158.7	−	1552.45i	0.441003	−	0.0151607i
$321$		0			0
$322$	6208.53	+	7313.56i	0.0598794	+	0.0705370i
$323$		−	12920.1i		−	0.123840i
$324$		0			0
$325$	18657.5			0.176639
$326$	1241.96	−	1054.31i	0.0116862	−	0.00992050i
$327$		0			0
$328$	−147415.	−	81765.6i	−1.37023	−	0.760017i
$329$	17186.8	+	29768.4i	0.158783	+	0.275019i
$330$		0			0
$331$	37439.2	+	21615.5i	0.341720	+	0.197292i	0.661032	−	0.750357i	$-0.270119\pi$
$331$	37439.2	+	21615.5i	0.341720	+	0.197292i	−0.319312	+	0.947650i	$0.603452\pi$
$332$	−11323.4	+	13812.9i	−0.102731	+	0.125317i
$333$		0			0
$334$	−89428.5	−	31970.5i	−0.801647	−	0.286587i
$335$	8890.54	+	5132.95i	0.0792206	+	0.0457381i
$336$		0			0
$337$	−5926.38	−	10264.8i	−0.0521831	−	0.0903837i	0.838754	−	0.544511i	$-0.183285\pi$
$337$	−5926.38	−	10264.8i	−0.0521831	−	0.0903837i	−0.890937	+	0.454127i	$0.849951\pi$
$338$	−106985.	+	19496.8i	−0.936462	+	0.170659i
$339$		0			0
$340$	46908.4	−	17684.3i	0.405782	−	0.152979i
$341$	332321.			2.85791
$342$		0			0
$343$		−	55525.0i		−	0.471955i
$344$	−2557.01	+	43.9392i	−0.0216081	+	0.000371309i
$345$		0			0
$346$	11122.8	−	2027.00i	0.0929098	−	0.0169317i
$347$	−25222.5	+	14562.2i	−0.209473	+	0.120940i	−0.601067	−	0.799199i	$-0.705257\pi$
$347$	−25222.5	+	14562.2i	−0.209473	+	0.120940i	0.391593	+	0.920138i	$0.371924\pi$
$348$		0			0
$349$	−59988.4	+	103903.i	−0.492512	+	0.853055i	−0.999963	−	0.00862528i	$-0.997254\pi$
$349$	−59988.4	+	103903.i	−0.492512	+	0.853055i	0.507451	+	0.861681i	$0.330588\pi$
$350$	−22587.8	−	8075.08i	−0.184390	−	0.0659191i
$351$		0			0
$352$	32659.8	−	222266.i	0.263589	−	1.79385i
$353$	77379.0	−	134024.i	0.620975	−	1.07556i	−0.368330	−	0.929695i	$-0.620070\pi$
$353$	77379.0	−	134024.i	0.620975	−	1.07556i	0.989305	−	0.145865i	$-0.0465964\pi$
$354$		0			0
$355$	11108.5	−	6413.49i	0.0881451	−	0.0508906i
$356$	−17507.8	+	106405.i	−0.138144	+	0.839577i
$357$		0			0
$358$	139490.	−	118414.i	1.08837	−	0.923925i
$359$		−	66839.6i		−	0.518615i	−0.965795	−	0.259307i	$-0.916506\pi$
$359$		−	66839.6i		−	0.518615i	0.965795	−	0.259307i	$-0.0834942\pi$
$360$		0			0
$361$	128252.			0.984121
$362$	62713.4	+	73875.4i	0.478567	+	0.563745i
$363$		0			0
$364$	−6973.37	−	1147.39i	−0.0526308	−	0.00865984i
$365$	−11929.9	−	20663.2i	−0.0895472	−	0.155100i
$366$		0			0
$367$	−81901.3	−	47285.7i	−0.608077	−	0.351073i	0.164136	−	0.986438i	$-0.447517\pi$
$367$	−81901.3	−	47285.7i	−0.608077	−	0.351073i	−0.772212	+	0.635364i	$0.780850\pi$
$368$	50528.1	−	10108.1i	0.373110	−	0.0746403i
$369$		0			0
$370$	−22597.8	+	63211.2i	−0.165068	+	0.461732i
$371$	−14602.5	−	8430.74i	−0.106091	−	0.0612517i
$372$		0			0
$373$	90530.4	+	156803.i	0.650694	+	1.12704i	0.982955	+	0.183848i	$0.0588554\pi$
$373$	90530.4	+	156803.i	0.650694	+	1.12704i	−0.332260	+	0.943188i	$0.607811\pi$
$374$	−44685.5	−	245204.i	−0.319465	−	1.75301i
$375$		0			0
$376$	184604.	−	3172.19i	1.30576	−	0.0224379i
$377$	−45533.4			−0.320366
$378$		0			0
$379$		−	51191.3i		−	0.356384i	−0.983996	−	0.178192i	$-0.942975\pi$
$379$		−	51191.3i		−	0.356384i	0.983996	−	0.178192i	$-0.0570248\pi$
$380$	−2832.41	−	7513.07i	−0.0196150	−	0.0520296i
$381$		0			0
$382$	−16151.5	−	88628.2i	−0.110684	−	0.607359i
$383$	132128.	−	76284.0i	0.900734	−	0.520039i	0.0232957	−	0.999729i	$-0.492584\pi$
$383$	132128.	−	76284.0i	0.900734	−	0.520039i	0.877438	+	0.479690i	$0.159251\pi$
$384$		0			0
$385$	14418.5	−	24973.5i	0.0972742	−	0.168484i
$386$	−24626.3	+	68885.2i	−0.165282	+	0.462329i
$387$		0			0
$388$	−149061.	−	122195.i	−0.990147	−	0.811687i
$389$	33948.4	−	58800.3i	0.224347	−	0.388580i	−0.731776	−	0.681545i	$-0.761308\pi$
$389$	33948.4	−	58800.3i	0.224347	−	0.388580i	0.956123	+	0.292965i	$0.0946418\pi$
$390$		0			0
$391$	49510.2	−	28584.7i	0.323848	−	0.186974i
$392$	−126432.	−	70127.0i	−0.822780	−	0.456366i
$393$		0			0
$394$	93968.9	+	110694.i	0.605329	+	0.713069i
$395$			82575.7i			0.529247i
$396$		0			0
$397$	−126087.			−0.799998			−0.399999	−	0.916516i	$-0.630990\pi$
$397$	−126087.			−0.799998			−0.399999	+	0.916516i	$0.630990\pi$
$398$	−144348.	+	122538.i	−0.911264	+	0.773578i
$399$		0			0
$400$	−96778.6	+	85059.8i	−0.604866	+	0.531624i
$401$	35445.4	+	61393.2i	0.220430	+	0.381796i	0.954939	−	0.296803i	$-0.0959206\pi$
$401$	35445.4	+	61393.2i	0.220430	+	0.381796i	−0.734509	+	0.678599i	$0.762587\pi$
$402$		0			0
$403$	−48629.5	−	28076.3i	−0.299426	−	0.172874i
$404$	−118233.	−	96923.5i	−0.724398	−	0.593836i
$405$		0			0
$406$	55125.1	+	19707.1i	0.334424	+	0.119556i
$407$	289038.	+	166876.i	1.74488	+	1.00741i
$408$		0			0
$409$	−21772.1	−	37710.4i	−0.130153	−	0.225432i	0.793582	−	0.608463i	$-0.208214\pi$
$409$	−21772.1	−	37710.4i	−0.130153	−	0.225432i	−0.923735	+	0.383031i	$0.874880\pi$
$410$	−114343.	+	20837.7i	−0.680209	+	0.123960i
$411$		0			0
$412$	−64927.4	−	172223.i	−0.382502	−	1.01460i
$413$	−33754.1			−0.197891
$414$		0			0
$415$			12314.7i			0.0715036i
$416$	−23557.4	+	29765.6i	−0.136126	+	0.172000i
$417$		0			0
$418$	−39273.0	+	7157.04i	−0.224771	+	0.0409620i
$419$	−182385.	+	105300.i	−1.03887	+	0.599792i	−0.919513	−	0.393060i	$-0.871417\pi$
$419$	−182385.	+	105300.i	−1.03887	+	0.599792i	−0.119357	+	0.992851i	$0.538083\pi$
$420$		0			0
$421$	−42063.0	+	72855.3i	−0.237321	+	0.411052i	−0.959945	−	0.280190i	$-0.909603\pi$
$421$	−42063.0	+	72855.3i	−0.237321	+	0.411052i	0.722624	+	0.691242i	$0.242936\pi$
$422$	175107.	+	62600.4i	0.983285	+	0.351522i
$423$		0			0
$424$	−77644.7	+	46625.0i	−0.431897	+	0.259350i
$425$	−71474.4	+	123797.i	−0.395706	+	0.685383i
$426$		0			0
$427$	54249.0	−	31320.7i	0.297533	−	0.171781i
$428$	104242.	+	17151.9i	0.569055	+	0.0936320i
$429$		0			0
$430$	−1344.22	+	1141.12i	−0.00726997	+	0.00617153i
$431$		−	150083.i		−	0.807933i	−0.914774	−	0.403967i	$-0.867631\pi$
$431$		−	150083.i		−	0.807933i	0.914774	−	0.403967i	$-0.132369\pi$
$432$		0			0
$433$	71221.5			0.379871			0.189935	−	0.981797i	$-0.439172\pi$
$433$	71221.5			0.379871			0.189935	+	0.981797i	$0.439172\pi$
$434$	46722.0	+	55037.8i	0.248051	+	0.292201i
$435$		0			0
$436$	−31290.0	+	190167.i	−0.164601	+	1.00038i
$437$	−4578.26	−	7929.78i	−0.0239739	−	0.0415239i
$438$		0			0
$439$	−94609.3	−	54622.7i	−0.490913	−	0.283429i	0.234040	−	0.972227i	$-0.424805\pi$
$439$	−94609.3	−	54622.7i	−0.490913	−	0.283429i	−0.724953	+	0.688798i	$0.758139\pi$
$440$	−79739.3	−	132790.i	−0.411876	−	0.685899i
$441$		0			0
$442$	−14177.2	+	39656.7i	−0.0725680	+	0.202989i
$443$	−199756.	−	115329.i	−1.01787	−	0.587666i	−0.104382	−	0.994537i	$-0.533287\pi$
$443$	−199756.	−	115329.i	−1.01787	−	0.587666i	−0.913486	+	0.406871i	$0.866620\pi$
$444$		0			0
$445$	37174.8	+	64388.7i	0.187728	+	0.325154i
$446$	59234.5	+	325038.i	0.297786	+	1.63405i
$447$		0			0
$448$	41402.6	−	25840.0i	0.206287	−	0.128747i
$449$	9751.64			0.0483710			0.0241855	−	0.999707i	$-0.492301\pi$
$449$	9751.64			0.0483710			0.0241855	+	0.999707i	$0.492301\pi$
$450$		0			0
$451$			577854.i			2.84096i
$452$	−55853.8	+	21056.7i	−0.273386	+	0.103066i
$453$		0			0
$454$	21300.3	+	116881.i	0.103341	+	0.567066i
$455$	−4219.80	+	2436.30i	−0.0203831	+	0.0117682i
$456$		0			0
$457$	−33069.5	+	57278.1i	−0.158342	+	0.274256i	−0.934271	−	0.356564i	$-0.883948\pi$
$457$	−33069.5	+	57278.1i	−0.158342	+	0.274256i	0.775929	+	0.630820i	$0.217281\pi$
$458$	−61046.1	+	170760.i	−0.291023	+	0.814056i
$459$		0			0
$460$	22523.8	−	27475.9i	0.106445	−	0.129848i
$461$	−86994.6	+	150679.i	−0.409346	+	0.709008i	−0.994817	−	0.101686i	$-0.967576\pi$
$461$	−86994.6	+	150679.i	−0.409346	+	0.709008i	0.585471	+	0.810694i	$0.300910\pi$
$462$		0			0
$463$	−150682.	+	86996.3i	−0.702909	+	0.405825i	−0.808430	−	0.588592i	$-0.799682\pi$
$463$	−150682.	+	86996.3i	−0.702909	+	0.405825i	0.105521	+	0.994417i	$0.466349\pi$
$464$	236186.	−	207587.i	1.09703	−	0.964194i
$465$		0			0
$466$	131844.	+	155310.i	0.607138	+	0.715200i
$467$		−	172090.i		−	0.789080i	−0.918879	−	0.394540i	$-0.870904\pi$
$467$		−	172090.i		−	0.789080i	0.918879	−	0.394540i	$-0.129096\pi$
$468$		0			0
$469$	11088.2			0.0504097
$470$	97045.8	−	82382.8i	0.439320	−	0.372942i
$471$		0			0
$472$	−87940.6	+	158548.i	−0.394735	+	0.711665i
$473$	4383.27	+	7592.05i	0.0195919	+	0.0339341i
$474$		0			0
$475$	19828.0	+	11447.7i	0.0878802	+	0.0507376i
$476$	34327.3	−	41874.6i	0.151505	−	0.184815i
$477$		0			0
$478$	−138941.	−	49671.2i	−0.608101	−	0.217395i
$479$	−189138.	−	109199.i	−0.824343	−	0.475935i	0.0275690	−	0.999620i	$-0.491223\pi$
$479$	−189138.	−	109199.i	−0.824343	−	0.475935i	−0.851912	+	0.523685i	$0.824557\pi$
$480$		0			0
$481$	−28197.2	−	48839.0i	−0.121875	−	0.211094i
$482$	33005.5	−	6014.87i	0.142067	−	0.0258900i
$483$		0			0
$484$	−501389.	+	189022.i	−2.14034	+	0.806904i
$485$	−132893.			−0.564959
$486$		0			0
$487$		−	392112.i		−	1.65330i	−0.562716	−	0.826650i	$-0.690243\pi$
$487$		−	392112.i		−	1.65330i	0.562716	−	0.826650i	$-0.309757\pi$
$488$	−5780.89	−	336416.i	−0.0242748	−	1.41266i
$489$		0			0
$490$	−98067.5	+	17871.7i	−0.408444	+	0.0744343i
$491$	−181620.	+	104859.i	−0.753358	+	0.434951i	−0.826906	−	0.562340i	$-0.809901\pi$
$491$	−181620.	+	104859.i	−0.753358	+	0.434951i	0.0735480	+	0.997292i	$0.476568\pi$
$492$		0			0
$493$	174432.	−	302125.i	0.717683	−	1.24306i
$494$	6351.60	+	2270.68i	0.0260273	+	0.00930470i
$495$		0			0
$496$	380247.	−	76067.9i	1.54562	−	0.309199i
$497$	6927.19	−	11998.2i	0.0280443	−	0.0485741i
$498$		0			0
$499$	117681.	−	67943.0i	0.472611	−	0.272862i	−0.244721	−	0.969594i	$-0.578696\pi$
$499$	117681.	−	67943.0i	0.472611	−	0.272862i	0.717332	+	0.696731i	$0.245363\pi$
$500$	−32333.5	+	196509.i	−0.129334	+	0.786037i
$501$		0			0
$502$	4499.29	−	3819.48i	0.0178541	−	0.0151564i
$503$			232332.i			0.918275i	0.888365	+	0.459137i	$0.151841\pi$
$503$			232332.i			0.918275i	−0.888365	+	0.459137i	$0.848159\pi$
$504$		0			0
$505$	−105409.			−0.413328
$506$	−114314.	−	134660.i	−0.446477	−	0.525943i
$507$		0			0
$508$	419159.	+	68968.2i	1.62424	+	0.267252i
$509$	−72659.4	−	125850.i	−0.280451	−	0.485755i	0.691045	−	0.722812i	$-0.257151\pi$
$509$	−72659.4	−	125850.i	−0.280451	−	0.485755i	−0.971496	+	0.237057i	$0.923817\pi$
$510$		0			0
$511$	−22318.3	−	12885.5i	−0.0854711	−	0.0493467i
$512$	−13506.6	−	261796.i	−0.0515234	−	0.998672i
$513$		0			0
$514$	46688.3	−	130598.i	0.176719	−	0.494321i
$515$	−109899.	−	63450.5i	−0.414363	−	0.239233i
$516$		0			0
$517$	−316450.	−	548108.i	−1.18393	−	2.05062i
$518$	12999.3	+	71331.1i	0.0484461	+	0.265839i
$519$		0			0
$520$	449.672	+	26168.4i	0.00166299	+	0.0967766i
$521$	−443088.			−1.63235			−0.816177	−	0.577803i	$-0.803910\pi$
$521$	−443088.			−1.63235			−0.816177	+	0.577803i	$0.803910\pi$
$522$		0			0
$523$			73202.4i			0.267622i	0.991007	+	0.133811i	$0.0427215\pi$
$523$			73202.4i			0.267622i	−0.991007	+	0.133811i	$0.957278\pi$
$524$	7448.30	+	19756.9i	0.0271266	+	0.0719543i
$525$		0			0
$526$	−13648.9	−	74896.0i	−0.0493318	−	0.270699i
$527$	372587.	−	215113.i	1.34155	−	0.774543i
$528$		0			0
$529$	−119662.	+	207261.i	−0.427609	+	0.740640i
$530$	−21020.8	+	58799.9i	−0.0748338	+	0.209327i
$531$		0			0
$532$	−6706.83	−	5498.02i	−0.0236970	−	0.0194260i
$533$	48820.3	−	84559.2i	0.171849	−	0.297651i
$534$		0			0
$535$	63079.9	−	36419.2i	0.220386	−	0.127240i
$536$	28888.4	−	52082.7i	0.100553	−	0.181286i
$537$		0			0
$538$	152017.	+	179073.i	0.525202	+	0.618681i
$539$			495602.i			1.70591i
$540$		0			0
$541$	438165.			1.49707			0.748536	−	0.663094i	$-0.230757\pi$
$541$	438165.			1.49707			0.748536	+	0.663094i	$0.230757\pi$
$542$	95977.1	−	81475.6i	0.326715	−	0.277351i
$543$		0			0
$544$	−107257.	−	270337.i	−0.362432	−	0.913500i
$545$	66439.2	+	115076.i	0.223682	+	0.387429i
$546$		0			0
$547$	−270221.	−	156012.i	−0.903118	−	0.521416i	−0.0249077	−	0.999690i	$-0.507929\pi$
$547$	−270221.	−	156012.i	−0.903118	−	0.521416i	−0.878211	+	0.478274i	$0.841263\pi$
$548$	319402.	+	261834.i	1.06359	+	0.871898i
$549$		0			0
$550$	415896.	+	148682.i	1.37486	+	0.491510i
$551$	−48389.8	−	27937.9i	−0.159386	−	0.0920217i
$552$		0			0
$553$	44594.9	+	77240.6i	0.145826	+	0.252578i
$554$	261814.	−	47712.6i	0.853048	−	0.155458i
$555$		0			0
$556$	−74153.2	−	196694.i	−0.239873	−	0.636271i
$557$	−312549.			−1.00741			−0.503707	−	0.863874i	$-0.668031\pi$
$557$	−312549.			−1.00741			−0.503707	+	0.863874i	$0.668031\pi$
$558$		0			0
$559$		−	1481.29i		−	0.00474042i
$560$	10781.4	−	31875.5i	0.0343796	−	0.101644i
$561$		0			0
$562$	486861.	−	88724.8i	1.54146	−	0.280913i
$563$	74780.6	−	43174.6i	0.235924	−	0.136211i	−0.377378	−	0.926059i	$-0.623174\pi$
$563$	74780.6	−	43174.6i	0.235924	−	0.136211i	0.613302	+	0.789849i	$0.289841\pi$
$564$		0			0
$565$	−20577.7	+	35641.7i	−0.0644615	+	0.111651i
$566$	206162.	+	73702.3i	0.643539	+	0.230064i
$567$		0			0
$568$	−38309.8	−	63797.4i	−0.118744	−	0.197745i
$569$	277479.	−	480608.i	0.857049	−	1.48445i	−0.0176822	−	0.999844i	$-0.505629\pi$
$569$	277479.	−	480608.i	0.857049	−	1.48445i	0.874731	−	0.484609i	$-0.161038\pi$
$570$		0			0
$571$	−262848.	+	151755.i	−0.806181	+	0.465449i	−0.845628	−	0.533773i	$-0.820774\pi$
$571$	−262848.	+	151755.i	−0.806181	+	0.465449i	0.0394467	+	0.999222i	$0.487440\pi$
$572$	128397.	+	21126.3i	0.392430	+	0.0645701i
$573$		0			0
$574$	−95702.2	+	81242.3i	−0.290468	+	0.246580i
$575$			101308.i			0.306414i
$576$		0			0
$577$	−500884.			−1.50448			−0.752238	−	0.658892i	$-0.771026\pi$
$577$	−500884.			−1.50448			−0.752238	+	0.658892i	$0.771026\pi$
$578$	7385.83	+	8700.40i	0.0221077	+	0.0260426i
$579$		0			0
$580$	35199.2	−	213926.i	0.104635	−	0.635927i
$581$	6650.54	+	11519.1i	0.0197017	+	0.0341244i
$582$		0			0
$583$	268867.	+	155230.i	0.791043	+	0.456709i
$584$	−118671.	+	71261.2i	−0.347953	+	0.208943i
$585$		0			0
$586$	−119327.	+	333783.i	−0.347490	+	0.972007i
$587$	498580.	+	287855.i	1.44697	+	0.835406i	0.998300	−	0.0582932i	$-0.0185658\pi$
$587$	498580.	+	287855.i	1.44697	+	0.835406i	0.448666	+	0.893699i	$0.351899\pi$
$588$		0			0
$589$	−34453.5	−	59675.2i	−0.0993122	−	0.172014i
$590$	22411.4	+	122978.i	0.0643821	+	0.353285i
$591$		0			0
$592$	368919.	+	124782.i	1.05266	+	0.356048i
$593$	138143.			0.392843			0.196421	−	0.980520i	$-0.437068\pi$
$593$	138143.			0.392843			0.196421	+	0.980520i	$0.437068\pi$
$594$		0			0
$595$		−	37332.6i		−	0.105452i
$596$	−388305.	+	146390.i	−1.09315	+	0.412115i
$597$		0			0
$598$	5351.10	+	29363.2i	0.0149637	+	0.0821108i
$599$	165665.	−	95646.9i	0.461719	−	0.266574i	−0.251048	−	0.967975i	$-0.580775\pi$
$599$	165665.	−	95646.9i	0.461719	−	0.266574i	0.712767	+	0.701401i	$0.247442\pi$
$600$		0			0
$601$	203120.	−	351814.i	0.562346	−	0.974012i	−0.434945	−	0.900457i	$-0.643232\pi$
$601$	203120.	−	351814.i	0.562346	−	0.974012i	0.997291	−	0.0735551i	$-0.0234345\pi$
$602$	−641.112	+	1793.33i	−0.00176905	+	0.00494843i
$603$		0			0
$604$	−288031.	+	351358.i	−0.789524	+	0.963110i
$605$	−184722.	+	319948.i	−0.504671	+	0.874117i
$606$		0			0
$607$	59466.9	−	34333.2i	0.161398	−	0.0931831i	−0.417126	−	0.908849i	$-0.636962\pi$
$607$	59466.9	−	34333.2i	0.161398	−	0.0931831i	0.578523	+	0.815666i	$0.303629\pi$
$608$	−43298.5	+	17178.7i	−0.117129	+	0.0464712i
$609$		0			0
$610$	−150132.	−	176853.i	−0.403472	−	0.475284i
$611$			106942.i			0.286461i
$612$		0			0
$613$	−572114.			−1.52252			−0.761258	−	0.648450i	$-0.775418\pi$
$613$	−572114.			−1.52252			−0.761258	+	0.648450i	$0.775418\pi$
$614$	376440.	−	319563.i	0.998526	−	0.847655i
$615$		0			0
$616$	−146300.	−	81147.5i	−0.385553	−	0.213852i
$617$	10190.4	+	17650.3i	0.0267684	+	0.0463642i	0.879099	−	0.476639i	$-0.158145\pi$
$617$	10190.4	+	17650.3i	0.0267684	+	0.0463642i	−0.852331	+	0.523003i	$0.824812\pi$
$618$		0			0
$619$	388604.	+	224361.i	1.01421	+	0.585552i	0.912420	−	0.409254i	$-0.134211\pi$
$619$	388604.	+	224361.i	1.01421	+	0.585552i	0.101786	+	0.994806i	$0.467544\pi$
$620$	169501.	−	206768.i	0.440951	−	0.537899i
$621$		0			0
$622$	−228038.	−	81523.2i	−0.589423	−	0.210717i
$623$	69546.0	+	40152.4i	0.179183	+	0.103451i
$624$		0			0
$625$	−88627.6	−	153508.i	−0.226887	−	0.392979i
$626$	−206150.	+	37568.4i	−0.526058	+	0.0958680i
$627$		0			0
$628$	−82647.8	+	31158.0i	−0.209562	+	0.0790042i
$629$	432079.			1.09210
$630$		0			0
$631$		−	402529.i		−	1.01097i	−0.862835	−	0.505486i	$-0.831313\pi$
$631$		−	402529.i		−	1.01097i	0.862835	−	0.505486i	$-0.168687\pi$
$632$	478995.	−	8230.94i	1.19921	−	0.0206070i
$633$		0			0
$634$	102304.	−	18643.8i	0.254517	−	0.0463827i
$635$	253646.	−	146443.i	0.629043	−	0.363178i
$636$		0			0
$637$	41871.2	−	72523.0i	0.103190	−	0.178730i
$638$	−1.01499e6	−	362856.i	−2.49356	−	0.891441i
$639$		0			0
$640$	−121634.	−	133688.i	−0.296959	−	0.326387i
$641$	176906.	−	306411.i	0.430554	−	0.745741i	−0.566367	−	0.824153i	$-0.691652\pi$
$641$	176906.	−	306411.i	0.430554	−	0.745741i	0.996921	+	0.0784117i	$0.0249849\pi$
$642$		0			0
$643$	−227886.	+	131570.i	−0.551184	+	0.318226i	−0.749599	−	0.661892i	$-0.769754\pi$
$643$	−227886.	+	131570.i	−0.551184	+	0.318226i	0.198415	+	0.980118i	$0.436420\pi$
$644$	6230.22	−	37864.6i	0.0150221	−	0.0912981i
$645$		0			0
$646$	−39398.7	+	33445.8i	−0.0944097	+	0.0801451i
$647$		−	265174.i		−	0.633464i	−0.948515	−	0.316732i	$-0.897414\pi$
$647$		−	265174.i		−	0.633464i	0.948515	−	0.316732i	$-0.102586\pi$
$648$		0			0
$649$	621494.			1.47553
$650$	−48297.9	−	56894.3i	−0.114315	−	0.134661i
$651$		0			0
$652$	−6430.04	−	1057.99i	−0.0151258	−	0.00248879i
$653$	−2938.96	−	5090.43i	−0.00689235	−	0.0119379i	0.862559	−	0.505957i	$-0.168861\pi$
$653$	−2938.96	−	5090.43i	−0.00689235	−	0.0119379i	−0.869451	+	0.494019i	$0.835527\pi$
$654$		0			0
$655$	12607.4	+	7278.87i	0.0293861	+	0.0169661i
$656$	132270.	+	661190.i	0.307365	+	1.53645i
$657$		0			0
$658$	46285.0	−	129470.i	0.106903	−	0.299031i
$659$	−480334.	−	277321.i	−1.10604	−	0.638575i	−0.168242	−	0.985746i	$-0.553809\pi$
$659$	−480334.	−	277321.i	−1.10604	−	0.638575i	−0.937802	+	0.347171i	$0.887142\pi$
$660$		0			0
$661$	410614.	+	711204.i	0.939789	+	1.62776i	0.765863	+	0.643004i	$0.222312\pi$
$661$	410614.	+	711204.i	0.939789	+	1.62776i	0.173926	+	0.984759i	$0.444355\pi$
$662$	−31002.8	−	170122.i	−0.0707433	−	0.388191i
$663$		0			0
$664$	71433.6	−	1227.50i	0.162019	−	0.00278410i
$665$	−5979.36			−0.0135211
$666$		0			0
$667$		−	247241.i		−	0.555736i
$668$	134009.	+	355464.i	0.300318	+	0.796604i
$669$		0			0
$670$	−7362.12	−	40398.3i	−0.0164004	−	0.0899939i
$671$	−998855.	+	576689.i	−2.21849	+	1.28085i
$672$		0			0
$673$	−258432.	+	447618.i	−0.570580	+	0.988274i	0.425926	+	0.904758i	$0.359948\pi$
$673$	−258432.	+	447618.i	−0.570580	+	0.988274i	−0.996506	+	0.0835158i	$0.973385\pi$
$674$	−15960.1	+	44643.9i	−0.0351330	+	0.0982749i
$675$		0			0
$676$	336402.	+	275770.i	0.736148	+	0.603468i
$677$	−345343.	+	598152.i	−0.753483	+	1.30507i	0.192642	+	0.981269i	$0.438294\pi$
$677$	−345343.	+	598152.i	−0.753483	+	1.30507i	−0.946125	+	0.323801i	$0.895039\pi$
$678$		0			0
$679$	−124307.	+	71768.4i	−0.269621	+	0.155666i
$680$	−175357.	−	97263.9i	−0.379231	−	0.210346i
$681$		0			0
$682$	−860265.	−	1.01338e6i	−1.84954	−	2.17873i
$683$		−	764551.i		−	1.63895i	−0.573117	−	0.819474i	$-0.694266\pi$
$683$		−	764551.i		−	1.63895i	0.573117	−	0.819474i	$-0.305734\pi$
$684$		0			0
$685$	284757.			0.606868
$686$	−169318.	+	143735.i	−0.359795	+	0.305433i
$687$		0			0
$688$	6753.22	+	7683.62i	0.0142671	+	0.0162326i
$689$	−26229.4	−	45430.7i	−0.0552523	−	0.0956998i
$690$		0			0
$691$	278107.	+	160565.i	0.582445	+	0.336275i	0.762105	−	0.647454i	$-0.224166\pi$
$691$	278107.	+	160565.i	0.582445	+	0.336275i	−0.179659	+	0.983729i	$0.557500\pi$
$692$	−34974.2	−	28670.6i	−0.0730358	−	0.0598722i
$693$		0			0
$694$	109698.	+	39216.9i	0.227762	+	0.0814244i
$695$	−125516.	−	72466.4i	−0.259853	−	0.150026i
$696$		0			0
$697$	374048.	+	647870.i	0.769949	+	1.33359i
$698$	472131.	−	86040.5i	0.969063	−	0.176601i
$699$		0			0
$700$	33847.9	+	89782.9i	0.0690774	+	0.183230i
$701$	621799.			1.26536			0.632680	−	0.774413i	$-0.281955\pi$
$701$	621799.			1.26536			0.632680	+	0.774413i	$0.281955\pi$
$702$		0			0
$703$		−	69203.8i		−	0.140029i
$704$	−762323.	+	475777.i	−1.53813	+	0.959972i
$705$		0			0
$706$	−609002.	+	110984.i	−1.22183	+	0.222664i
$707$	−98598.6	+	56925.9i	−0.197257	+	0.113886i
$708$		0			0
$709$	262435.	−	454550.i	0.522070	−	0.904252i	−0.477600	−	0.878577i	$-0.658493\pi$
$709$	262435.	−	454550.i	0.522070	−	0.904252i	0.999670	−	0.0256748i	$-0.00817343\pi$
$710$	−48313.4	−	17271.9i	−0.0958409	−	0.0342629i
$711$		0			0
$712$	369792.	−	222057.i	0.729454	−	0.438031i
$713$	152451.	−	264053.i	0.299882	−	0.519412i
$714$		0			0
$715$	77696.8	−	44858.2i	0.151982	−	0.0877466i
$716$	−722183.	−	118828.i	−1.40871	−	0.231788i
$717$		0			0
$718$	−203821.	+	173025.i	−0.395366	+	0.335629i
$719$		−	348658.i		−	0.674438i	−0.941426	−	0.337219i	$-0.890514\pi$
$719$		−	348658.i		−	0.674438i	0.941426	−	0.337219i	$-0.109486\pi$
$720$		0			0
$721$	−137065.			−0.263668
$722$	−332000.	−	391091.i	−0.636888	−	0.750245i
$723$		0			0
$724$	62932.5	−	382476.i	0.120060	−	0.729672i
$725$	309106.	+	535387.i	0.588073	+	1.01857i
$726$		0			0
$727$	523789.	+	302410.i	0.991032	+	0.572173i	0.905583	−	0.424170i	$-0.139434\pi$
$727$	523789.	+	302410.i	0.991032	+	0.572173i	0.0854497	+	0.996342i	$0.472767\pi$
$728$	14552.8	+	24234.8i	0.0274590	+	0.0457275i
$729$		0			0
$730$	−32128.0	+	89869.2i	−0.0602890	+	0.168642i
$731$	9828.75	+	5674.63i	0.0183935	+	0.0106195i
$732$		0			0
$733$	237805.	+	411891.i	0.442602	+	0.766609i	0.997882	−	0.0650546i	$-0.0207222\pi$
$733$	237805.	+	411891.i	0.442602	+	0.766609i	−0.555280	+	0.831664i	$0.687389\pi$
$734$	67821.2	+	372156.i	0.125885	+	0.690770i
$735$		0			0
$736$	−161624.	−	127914.i	−0.298366	−	0.236136i
$737$	−204160.			−0.375868
$738$		0			0
$739$		−	844449.i		−	1.54627i	−0.634244	−	0.773133i	$-0.718688\pi$
$739$		−	844449.i		−	1.54627i	0.634244	−	0.773133i	$-0.281312\pi$
$740$	251254.	−	94722.2i	0.458828	−	0.172977i
$741$		0			0
$742$	12092.1	+	66353.1i	0.0219631	+	0.120518i
$743$	537216.	−	310162.i	0.973131	−	0.561837i	0.0729415	−	0.997336i	$-0.476761\pi$
$743$	537216.	−	310162.i	0.973131	−	0.561837i	0.900189	+	0.435499i	$0.143428\pi$
$744$		0			0
$745$	−143060.	+	247787.i	−0.257754	+	0.446443i
$746$	243804.	−	681974.i	0.438090	−	1.22543i
$747$		0			0
$748$	−632049.	+	771013.i	−1.12966	+	1.37803i
$749$	39336.3	−	68132.4i	0.0701180	−	0.121448i
$750$		0			0
$751$	−632847.	+	365374.i	−1.12207	+	0.647825i	−0.941928	−	0.335816i	$-0.890988\pi$
$751$	−632847.	+	365374.i	−1.12207	+	0.647825i	−0.180139	+	0.983641i	$0.557655\pi$
$752$	−487549.	−	554719.i	−0.862149	−	0.980928i
$753$		0			0
$754$	117870.	+	138849.i	0.207330	+	0.244231i
$755$			313247.i			0.549533i
$756$		0			0
$757$	−769023.			−1.34198			−0.670992	−	0.741465i	$-0.734132\pi$
$757$	−769023.			−1.34198			−0.670992	+	0.741465i	$0.734132\pi$
$758$	−156103.	+	132517.i	−0.271689	+	0.230639i
$759$		0			0
$760$	−15578.2	+	28085.9i	−0.0269706	+	0.0486252i
$761$	137697.	+	238498.i	0.237769	+	0.411828i	0.960074	−	0.279747i	$-0.0902505\pi$
$761$	137697.	+	238498.i	0.237769	+	0.411828i	−0.722305	+	0.691575i	$0.756917\pi$
$762$		0			0
$763$	124293.	+	71760.8i	0.213500	+	0.123264i
$764$	−228452.	+	278680.i	−0.391389	+	0.477441i
$765$		0			0
$766$	−574654.	−	205437.i	−0.979375	−	0.350124i
$767$	−90945.2	−	52507.2i	−0.154593	−	0.0892541i
$768$		0			0
$769$	26421.1	+	45762.6i	0.0446784	+	0.0773853i	0.887500	−	0.460808i	$-0.152440\pi$
$769$	26421.1	+	45762.6i	0.0446784	+	0.0773853i	−0.842821	+	0.538193i	$0.819107\pi$
$770$	−113479.	+	20680.2i	−0.191396	+	0.0348798i
$771$		0			0
$772$	273808.	−	103225.i	0.459421	−	0.173201i
$773$	195309.			0.326861			0.163430	−	0.986555i	$-0.447744\pi$
$773$	195309.			0.326861			0.163430	+	0.986555i	$0.447744\pi$
$774$		0			0
$775$			762389.i			1.26933i
$776$	13246.4	+	770866.i	0.0219975	+	1.28013i
$777$		0			0
$778$	−267187.	+	48691.7i	−0.441423	+	0.0804443i
$779$	103766.	−	59909.3i	0.170994	−	0.0987232i
$780$		0			0
$781$	−127546.	+	220917.i	−0.209106	+	0.362182i
$782$	−215331.	−	76980.4i	−0.352122	−	0.125883i
$783$		0			0
$784$	113443.	+	567076.i	0.184563	+	0.922590i
$785$	−30449.2	+	52739.6i	−0.0494125	+	0.0855849i
$786$		0			0
$787$	−677438.	+	391119.i	−1.09375	+	0.631480i	−0.934574	−	0.355770i	$-0.884219\pi$
$787$	−677438.	+	391119.i	−1.09375	+	0.631480i	−0.159181	+	0.987249i	$0.550885\pi$
$788$	94297.2	−	573098.i	0.151861	−	0.922946i
$789$		0			0
$790$	251807.	−	213760.i	0.403472	−	0.342510i
$791$			44451.9i			0.0710456i
$792$		0			0
$793$	194887.			0.309911
$794$	326396.	+	384490.i	0.517730	+	0.609879i
$795$		0			0
$796$	747335.	+	122966.i	1.17948	+	0.194070i
$797$	−586714.	−	1.01622e6i	−0.923655	−	1.59982i	−0.793711	−	0.608296i	$-0.791854\pi$
$797$	−586714.	−	1.01622e6i	−0.923655	−	1.59982i	−0.129944	−	0.991521i	$-0.541480\pi$
$798$		0			0
$799$	−709586.	−	409680.i	−1.11151	−	0.641728i
$800$	509908.	+	74926.0i	0.796731	+	0.117072i
$801$		0			0
$802$	95456.6	−	267013.i	0.148408	−	0.415130i
$803$	410934.	+	237253.i	0.637295	+	0.367943i
$804$		0			0
$805$	−13228.8	−	22913.0i	−0.0204141	−	0.0353583i
$806$	40269.4	+	220971.i	0.0619876	+	0.340146i
$807$		0			0
$808$	10506.9	+	611442.i	0.0160935	+	0.936554i
$809$	421614.			0.644196			0.322098	−	0.946706i	$-0.395612\pi$
$809$	421614.			0.644196			0.322098	+	0.946706i	$0.395612\pi$
$810$		0			0
$811$		−	504037.i		−	0.766339i	−0.923678	−	0.383169i	$-0.874833\pi$
$811$		−	504037.i		−	0.766339i	0.923678	−	0.383169i	$-0.125167\pi$
$812$	−82605.3	−	219114.i	−0.125284	−	0.332321i
$813$		0			0
$814$	−239348.	−	1.31338e6i	−0.361228	−	1.98217i
$815$	−3891.01	+	2246.48i	−0.00585797	+	0.00338210i
$816$		0			0
$817$	908.875	−	1574.22i	0.00136163	−	0.00235842i
$818$	−58633.6	+	164011.i	−0.0876275	+	0.245113i
$819$		0			0
$820$	359538.	+	294737.i	0.534709	+	0.438335i
$821$	−35777.1	+	61967.7i	−0.0530785	+	0.0919346i	−0.891344	−	0.453328i	$-0.850237\pi$
$821$	−35777.1	+	61967.7i	−0.0530785	+	0.0919346i	0.838265	+	0.545262i	$0.183570\pi$
$822$		0			0
$823$	703826.	−	406354.i	1.03912	−	0.599936i	0.119536	−	0.992830i	$-0.461859\pi$
$823$	703826.	−	406354.i	1.03912	−	0.599936i	0.919584	+	0.392893i	$0.128526\pi$
$824$	−357101.	+	643815.i	−0.525940	+	0.948215i
$825$		0			0
$826$	87377.7	+	102930.i	0.128068	+	0.150862i
$827$			375951.i			0.549693i	0.961488	+	0.274847i	$0.0886271\pi$
$827$			375951.i			0.549693i	−0.961488	+	0.274847i	$0.911373\pi$
$828$		0			0
$829$	423699.			0.616522			0.308261	−	0.951302i	$-0.400253\pi$
$829$	423699.			0.616522			0.308261	+	0.951302i	$0.400253\pi$
$830$	37552.5	−	31878.6i	0.0545108	−	0.0462746i
$831$		0			0
$832$	151749.	−	5216.79i	0.219220	−	0.00753628i
$833$	320806.	+	555652.i	0.462330	+	0.800779i
$834$		0			0
$835$	226830.	+	130961.i	0.325333	+	0.187831i
$836$	123489.	+	101232.i	0.176691	+	0.144845i
$837$		0			0
$838$	793234.	+	283579.i	1.12957	+	0.403819i
$839$	959899.	+	554198.i	1.36365	+	0.787302i	0.990107	−	0.140313i	$-0.0448108\pi$
$839$	959899.	+	554198.i	1.36365	+	0.787302i	0.373539	+	0.927614i	$0.378144\pi$
$840$		0			0
$841$	−400727.	−	694079.i	−0.566573	−	0.981334i
$842$	331052.	−	60330.3i	0.466951	−	0.0850965i
$843$		0			0
$844$	−262399.	−	696024.i	−0.368364	−	0.977100i
$845$	299914.			0.420032
$846$		0			0
$847$			399036.i			0.556218i
$848$	343174.	+	116074.i	0.477224	+	0.161414i
$849$		0			0
$850$	562531.	−	102515.i	0.778589	−	0.141889i
$851$	265190.	−	153108.i	0.366183	−	0.211416i
$852$		0			0
$853$	254659.	−	441083.i	0.349995	−	0.606209i	−0.636253	−	0.771480i	$-0.719517\pi$
$853$	254659.	−	441083.i	0.349995	−	0.606209i	0.986248	+	0.165272i	$0.0528501\pi$
$854$	−235941.	−	84348.4i	−0.323510	−	0.115654i
$855$		0			0
$856$	−217543.	−	362276.i	−0.296892	−	0.494415i
$857$	−328394.	+	568795.i	−0.447130	+	0.774452i	−0.998198	−	0.0600088i	$-0.980887\pi$
$857$	−328394.	+	568795.i	−0.447130	+	0.774452i	0.551068	+	0.834460i	$0.314220\pi$
$858$		0			0
$859$	916830.	−	529332.i	1.24252	−	0.717368i	0.272912	−	0.962039i	$-0.412013\pi$
$859$	916830.	−	529332.i	1.24252	−	0.717368i	0.969606	+	0.244671i	$0.0786799\pi$
$860$	6959.44	+	1145.10i	0.00940974	+	0.00154827i
$861$		0			0
$862$	−457662.	+	388512.i	−0.615928	+	0.522866i
$863$			676878.i			0.908844i	0.890787	+	0.454422i	$0.150154\pi$
$863$			676878.i			0.908844i	−0.890787	+	0.454422i	$0.849846\pi$
$864$		0			0
$865$	−31180.7			−0.0416729
$866$	−184368.	−	217183.i	−0.245839	−	0.289594i
$867$		0			0
$868$	46885.2	−	284948.i	0.0622295	−	0.378204i
$869$	−821100.	−	1.42219e6i	−1.08732	−	1.88329i
$870$		0			0
$871$	29875.4	+	17248.6i	0.0393801	+	0.0227361i
$872$	660896.	−	396862.i	0.869161	−	0.521924i
$873$		0			0
$874$	−12329.5	+	34488.5i	−0.0161408	+	0.0451493i
$875$	128438.	+	74154.0i	0.167756	+	0.0968541i
$876$		0			0
$877$	−737914.	−	1.27810e6i	−0.959415	−	1.66176i	−0.723925	−	0.689879i	$-0.757664\pi$
$877$	−737914.	−	1.27810e6i	−0.959415	−	1.66176i	−0.235490	−	0.971877i	$-0.575669\pi$
$878$	78344.6	+	429901.i	0.101629	+	0.557673i
$879$		0			0
$880$	−198512.	+	586905.i	−0.256343	+	0.757883i
$881$	−599513.			−0.772408			−0.386204	−	0.922413i	$-0.626214\pi$
$881$	−599513.			−0.772408			−0.386204	+	0.922413i	$0.626214\pi$
$882$		0			0
$883$		−	729187.i		−	0.935229i	−0.883933	−	0.467614i	$-0.845114\pi$
$883$		−	729187.i		−	0.935229i	0.883933	−	0.467614i	$-0.154886\pi$
$884$	157629.	−	59425.7i	0.201712	−	0.0760449i
$885$		0			0
$886$	165415.	+	907682.i	0.210720	+	1.15629i
$887$	−1.26218e6	+	728722.i	−1.60426	+	0.926221i	−0.613641	+	0.789585i	$0.710296\pi$
$887$	−1.26218e6	+	728722.i	−1.60426	+	0.926221i	−0.990621	+	0.136636i	$0.956371\pi$
$888$		0			0
$889$	158172.	−	273962.i	0.200137	−	0.346647i
$890$	100114.	−	280041.i	0.126391	−	0.353543i
$891$		0			0
$892$	837834.	−	1.02204e6i	1.05300	−	1.28452i
$893$	−65616.2	+	113651.i	−0.0822826	+	0.142518i
$894$		0			0
$895$	−437015.	+	252311.i	−0.545570	+	0.314985i
$896$	−185974.	−	59362.3i	−0.231652	−	0.0739426i
$897$		0			0
$898$	−25243.7	−	29736.7i	−0.0313040	−	0.0368757i
$899$		−	1.86060e6i		−	2.30215i
$900$		0			0
$901$	401926.			0.495104
$902$	1.76211e6	−	1.49587e6i	2.16581	−	1.83857i
$903$		0			0
$904$	208797.	+	115812.i	0.255498	+	0.141715i
$905$	−133627.	−	231448.i	−0.163153	−	0.282590i
$906$		0			0
$907$	3010.76	+	1738.27i	0.00365984	+	0.00211301i	0.501829	−	0.864967i	$-0.332661\pi$
$907$	3010.76	+	1738.27i	0.00365984	+	0.00211301i	−0.498169	+	0.867080i	$0.665994\pi$
$908$	301279.	−	367519.i	0.365424	−	0.445767i
$909$		0			0
$910$	18352.9	+	6561.11i	0.0221627	+	0.00792309i
$911$	−712683.	−	411468.i	−0.858736	−	0.495791i	0.00485282	−	0.999988i	$-0.498455\pi$
$911$	−712683.	−	411468.i	−0.858736	−	0.495791i	−0.863589	+	0.504197i	$0.831789\pi$
$912$		0			0
$913$	−122453.	−	212094.i	−0.146901	−	0.254441i
$914$	260270.	−	47431.1i	0.311552	−	0.0567768i
$915$		0			0
$916$	678742.	−	255884.i	0.808936	−	0.304967i
$917$	15723.8			0.0186990
$918$		0			0
$919$			873279.i			1.03400i	0.855984	+	0.517002i	$0.172952\pi$
$919$			873279.i			1.03400i	−0.855984	+	0.517002i	$0.827048\pi$
$920$	−142091.	+	2441.67i	−0.167877	+	0.00288477i
$921$		0			0
$922$	684680.	−	124775.i	0.805427	−	0.146780i
$923$	37328.5	−	21551.6i	0.0438164	−	0.0252974i
$924$		0			0
$925$	−382837.	+	663092.i	−0.447435	+	0.774980i
$926$	655351.	+	234286.i	0.764279	+	0.273228i
$927$		0			0
$928$	−1.24442e6	−	182856.i	−1.44501	−	0.212330i
$929$	172980.	−	299611.i	0.200431	−	0.347157i	−0.748236	−	0.663433i	$-0.769099\pi$
$929$	172980.	−	299611.i	0.200431	−	0.347157i	0.948667	+	0.316275i	$0.102432\pi$
$930$		0			0
$931$	88995.8	−	51381.7i	0.102676	−	0.0592802i
$932$	132304.	−	804088.i	0.152315	−	0.925704i
$933$		0			0
$934$	−524771.	+	445481.i	−0.601556	+	0.510665i
$935$			687384.i			0.786278i
$936$		0			0
$937$	−1.10958e6			−1.26380			−0.631901	−	0.775049i	$-0.717725\pi$
$937$	−1.10958e6			−1.26380			−0.631901	+	0.775049i	$0.717725\pi$
$938$	−28703.5	−	33812.3i	−0.0326234	−	0.0384299i
$939$		0			0
$940$	−502437.	−	82670.6i	−0.568624	−	0.0935611i
$941$	161271.	+	279330.i	0.182129	+	0.315456i	0.942605	−	0.333909i	$-0.108368\pi$
$941$	161271.	+	279330.i	0.182129	+	0.315456i	−0.760477	+	0.649365i	$0.775035\pi$
$942$		0			0
$943$	459147.	+	265089.i	0.516331	+	0.298104i
$944$	711124.	−	142259.i	0.797997	−	0.159638i
$945$		0			0
$946$	11804.4	−	33019.6i	0.0131905	−	0.0368969i
$947$	−120742.	−	69710.2i	−0.134635	−	0.0777314i	0.431170	−	0.902271i	$-0.358101\pi$
$947$	−120742.	−	69710.2i	−0.134635	−	0.0777314i	−0.565805	+	0.824539i	$0.691434\pi$
$948$		0			0
$949$	−40088.8	−	69435.9i	−0.0445134	−	0.0770995i
$950$	−16419.2	−	90097.6i	−0.0181931	−	0.0998311i
$951$		0			0
$952$	−216554.	+	3721.22i	−0.238942	+	0.00410593i
$953$	−1.68438e6			−1.85462			−0.927308	−	0.374300i	$-0.877883\pi$
$953$	−1.68438e6			−1.85462			−0.927308	+	0.374300i	$0.877883\pi$
$954$		0			0
$955$			248453.i			0.272419i
$956$	208204.	+	552270.i	0.227811	+	0.604276i
$957$		0			0
$958$	156622.	+	859436.i	0.170656	+	0.936446i
$959$	266360.	−	153783.i	0.289622	−	0.167213i
$960$		0			0
$961$	685501.	−	1.18732e6i	0.742269	−	1.28565i
$962$	−75936.8	+	212412.i	−0.0820545	+	0.229525i
$963$		0			0
$964$	−103782.	−	85076.6i	−0.111678	−	0.0915495i
$965$	100877.	−	174723.i	0.108327	−	0.187628i
$966$		0			0
$967$	39280.8	−	22678.8i	0.0420075	−	0.0242530i	−0.478849	−	0.877897i	$-0.658946\pi$
$967$	39280.8	−	22678.8i	0.0420075	−	0.0242530i	0.520857	+	0.853644i	$0.325613\pi$
$968$	1.87433e6	+	1.03962e6i	2.00030	+	1.10949i
$969$		0			0
$970$	344013.	+	405243.i	0.365622	+	0.430697i
$971$			1.18319e6i			1.25492i	0.778648	+	0.627461i	$0.215906\pi$
$971$			1.18319e6i			1.25492i	−0.778648	+	0.627461i	$0.784094\pi$
$972$		0			0
$973$	−156541.			−0.165350
$974$	−1.19571e6	+	1.01504e6i	−1.26039	+	1.06996i
$975$		0			0
$976$	−1.01090e6	+	888494.i	−1.06123	+	0.932727i
$977$	562965.	+	975083.i	0.589783	+	1.02153i	0.994261	+	0.106986i	$0.0341199\pi$
$977$	562965.	+	975083.i	0.589783	+	1.02153i	−0.404478	+	0.914548i	$0.632547\pi$
$978$		0			0
$979$	−1.28051e6	−	739303.i	−1.33604	−	0.771360i
$980$	308361.	+	252784.i	0.321076	+	0.263206i
$981$		0			0
$982$	789909.	+	282390.i	0.819132	+	0.292838i
$983$	−1.17197e6	−	676638.i	−1.21286	−	0.700243i	−0.249476	−	0.968381i	$-0.580259\pi$
$983$	−1.17197e6	−	676638.i	−1.21286	−	0.700243i	−0.963381	+	0.268137i	$0.913592\pi$
$984$		0			0
$985$	−200225.	−	346799.i	−0.206369	−	0.357442i
$986$	−1.37285e6	+	250185.i	−1.41211	+	0.257341i
$987$		0			0
$988$	−9517.90	−	25246.6i	−0.00975051	−	0.0258636i
$989$	8043.24			0.00822316
$990$		0			0
$991$			1.02847e6i			1.04724i	0.851953	+	0.523619i	$0.175418\pi$
$991$			1.02847e6i			1.04724i	−0.851953	+	0.523619i	$0.824582\pi$
$992$	−1.21629e6	−	962611.i	−1.23599	−	0.978200i
$993$		0			0
$994$	−54519.6	+	9935.56i	−0.0551797	+	0.0100559i
$995$	452235.	−	261098.i	0.456791	−	0.263729i
$996$		0			0
$997$	−564030.	+	976929.i	−0.567430	+	0.982817i	0.429389	+	0.903119i	$0.358729\pi$
$997$	−564030.	+	976929.i	−0.567430	+	0.982817i	−0.996819	+	0.0796977i	$0.974605\pi$
$998$	−511821.	−	182975.i	−0.513874	−	0.183709i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.19.7		44
3.2	odd	2		36.5.f.a.7.16	yes	44
4.3	odd	2	inner	108.5.f.a.19.21		44
9.2	odd	6		324.5.d.f.163.13		22
9.4	even	3	inner	108.5.f.a.91.21		44
9.5	odd	6		36.5.f.a.31.2	yes	44
9.7	even	3		324.5.d.e.163.10		22
12.11	even	2		36.5.f.a.7.2	✓	44
36.7	odd	6		324.5.d.e.163.9		22
36.11	even	6		324.5.d.f.163.14		22
36.23	even	6		36.5.f.a.31.16	yes	44
36.31	odd	6	inner	108.5.f.a.91.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.2	✓	44	12.11	even	2
36.5.f.a.7.16	yes	44	3.2	odd	2
36.5.f.a.31.2	yes	44	9.5	odd	6
36.5.f.a.31.16	yes	44	36.23	even	6
108.5.f.a.19.7		44	1.1	even	1	trivial
108.5.f.a.19.21		44	4.3	odd	2	inner
108.5.f.a.91.7		44	36.31	odd	6	inner
108.5.f.a.91.21		44	9.4	even	3	inner
324.5.d.e.163.9		22	36.7	odd	6
324.5.d.e.163.10		22	9.7	even	3
324.5.d.f.163.13		22	9.2	odd	6
324.5.d.f.163.14		22	36.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.58866 - 3.04940i) q^{2} +(-2.59770 + 15.7877i) q^{4} +(5.51579 + 9.55363i) q^{5} +(10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +O(q^{10})\)	\(q+(-2.58866 - 3.04940i) q^{2} +(-2.59770 + 15.7877i) q^{4} +(5.51579 + 9.55363i) q^{5} +(10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +(14.8544 - 41.5509i) q^{10} +(-189.995 - 109.694i) q^{11} +(18.5350 + 32.1036i) q^{13} +(-8.54488 - 46.8884i) q^{14} +(-242.504 - 82.0235i) q^{16} -284.021 q^{17} +45.4901i q^{19} +(-165.158 + 62.2643i) q^{20} +(157.332 + 863.330i) q^{22} +(-174.319 + 100.643i) q^{23} +(251.652 - 435.874i) q^{25} +(49.9160 - 139.626i) q^{26} +(-120.862 + 147.435i) q^{28} +(-614.153 + 1063.74i) q^{29} +(-1311.83 + 757.384i) q^{31} +(377.637 + 951.823i) q^{32} +(735.233 + 866.094i) q^{34} +131.443i q^{35} -1521.29 q^{37} +(138.718 - 117.758i) q^{38} +(617.407 + 342.453i) q^{40} +(-1316.97 - 2281.07i) q^{41} +(-34.6057 - 19.9796i) q^{43} +(2225.36 - 2714.63i) q^{44} +(758.153 + 271.038i) q^{46} +(2498.36 + 1442.43i) q^{47} +(-1129.51 - 1956.38i) q^{49} +(-1980.60 + 360.941i) q^{50} +(-554.991 + 209.230i) q^{52} -1415.13 q^{53} -2420.19i q^{55} +(762.458 - 13.1019i) q^{56} +(4833.61 - 880.870i) q^{58} +(-2453.33 + 1416.43i) q^{59} +(2628.64 - 4552.93i) q^{61} +(5705.44 + 2039.68i) q^{62} +(1924.92 - 3615.51i) q^{64} +(-204.471 + 354.154i) q^{65} +(805.917 - 465.296i) q^{67} +(737.801 - 4484.04i) q^{68} +(400.823 - 340.261i) q^{70} -1162.75i q^{71} -2162.87 q^{73} +(3938.11 + 4639.03i) q^{74} +(-718.185 - 118.170i) q^{76} +(-1307.02 - 2263.82i) q^{77} +(6482.54 + 3742.70i) q^{79} +(-553.978 - 2769.22i) q^{80} +(-3546.69 + 9920.88i) q^{82} +(966.756 + 558.157i) q^{83} +(-1566.60 - 2713.43i) q^{85} +(28.6565 + 157.247i) q^{86} +(-14038.7 + 241.238i) q^{88} +6739.71 q^{89} +441.696i q^{91} +(-1136.10 - 3013.54i) q^{92} +(-2068.85 - 11352.5i) q^{94} +(-434.596 + 250.914i) q^{95} +(-6023.28 + 10432.6i) q^{97} +(-3041.85 + 8508.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more