LMFDB - Embedded newform 81.4.e.a.10.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,4,Mod(10,81)] 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("81.10"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.77915471046$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.2
Character	$\chi$	$=$	81.10
Dual form			81.4.e.a.73.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.640527 - 3.63261i) q^{2} +(-5.26804 + 1.91741i) q^{4} +(1.23763 + 1.03850i) q^{5} +(-31.9169 - 11.6168i) q^{7} +(-4.41508 - 7.64714i) q^{8} +(2.97972 - 5.16102i) q^{10} +(-18.8740 + 15.8372i) q^{11} +(5.35351 - 30.3613i) q^{13} +(-21.7557 + 123.382i) q^{14} +(-59.3074 + 49.7648i) q^{16} +(18.2417 - 31.5955i) q^{17} +(36.5170 + 63.2494i) q^{19} +(-8.51112 - 3.09779i) q^{20} +(69.6196 + 58.4178i) q^{22} +(62.9523 - 22.9128i) q^{23} +(-21.2528 - 120.530i) q^{25} -113.720 q^{26} +190.413 q^{28} +(-41.0688 - 232.913i) q^{29} +(-152.414 + 55.4740i) q^{31} +(164.650 + 138.158i) q^{32} +(-126.458 - 46.0271i) q^{34} +(-27.4374 - 47.5229i) q^{35} +(93.1046 - 161.262i) q^{37} +(206.370 - 173.165i) q^{38} +(2.47729 - 14.0494i) q^{40} +(37.9265 - 215.092i) q^{41} +(156.989 - 131.730i) q^{43} +(69.0627 - 119.620i) q^{44} +(-123.556 - 214.005i) q^{46} +(450.185 + 163.854i) q^{47} +(620.985 + 521.068i) q^{49} +(-424.227 + 154.406i) q^{50} +(30.0125 + 170.209i) q^{52} -736.254 q^{53} -39.8060 q^{55} +(52.0803 + 295.362i) q^{56} +(-819.775 + 298.374i) q^{58} +(-39.2313 - 32.9190i) q^{59} +(108.686 + 39.5585i) q^{61} +(299.141 + 518.127i) q^{62} +(86.7288 - 150.219i) q^{64} +(38.1558 - 32.0165i) q^{65} +(20.2242 - 114.697i) q^{67} +(-35.5163 + 201.423i) q^{68} +(-155.058 + 130.109i) q^{70} +(-118.488 + 205.227i) q^{71} +(-23.0477 - 39.9198i) q^{73} +(-645.437 - 234.920i) q^{74} +(-313.648 - 263.182i) q^{76} +(786.377 - 286.218i) q^{77} +(-130.778 - 741.681i) q^{79} -125.081 q^{80} -805.637 q^{82} +(59.3213 + 336.428i) q^{83} +(55.3883 - 20.1597i) q^{85} +(-579.078 - 485.904i) q^{86} +(204.439 + 74.4099i) q^{88} +(455.636 + 789.185i) q^{89} +(-523.568 + 906.847i) q^{91} +(-287.702 + 241.411i) q^{92} +(306.862 - 1740.30i) q^{94} +(-20.4896 + 116.202i) q^{95} +(-37.6866 + 31.6228i) q^{97} +(1495.08 - 2589.55i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{2} - 6 q^{4} - 6 q^{5} - 6 q^{7} + 75 q^{8} - 3 q^{10} - 57 q^{11} - 6 q^{13} - 51 q^{14} + 18 q^{16} + 207 q^{17} - 3 q^{19} + 597 q^{20} - 60 q^{22} - 402 q^{23} - 222 q^{25} - 1914 q^{26}+ \cdots + 4392 q^{98}+O(q^{100}) $ 48 * q + 6 * q^2 - 6 * q^4 - 6 * q^5 - 6 * q^7 + 75 * q^8 - 3 * q^10 - 57 * q^11 - 6 * q^13 - 51 * q^14 + 18 * q^16 + 207 * q^17 - 3 * q^19 + 597 * q^20 - 60 * q^22 - 402 * q^23 - 222 * q^25 - 1914 * q^26 - 12 * q^28 - 480 * q^29 - 60 * q^31 + 648 * q^32 + 288 * q^34 + 1257 * q^35 - 3 * q^37 + 1524 * q^38 + 561 * q^40 + 1731 * q^41 + 507 * q^43 + 2211 * q^44 - 3 * q^46 - 984 * q^47 - 600 * q^49 - 4359 * q^50 - 1431 * q^52 - 2736 * q^53 - 12 * q^55 - 5907 * q^56 - 897 * q^58 - 2238 * q^59 + 48 * q^61 + 2118 * q^62 - 195 * q^64 + 6990 * q^65 - 681 * q^67 + 11169 * q^68 - 33 * q^70 + 3105 * q^71 - 219 * q^73 - 3543 * q^74 + 3426 * q^76 - 4722 * q^77 + 2802 * q^79 - 9870 * q^80 - 12 * q^82 - 3468 * q^83 + 2529 * q^85 - 3624 * q^86 + 2850 * q^88 + 5202 * q^89 + 267 * q^91 + 18453 * q^92 - 1653 * q^94 + 10113 * q^95 - 3381 * q^97 + 4392 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.640527	−	3.63261i	−0.226461	−	1.28432i	−0.859873	−	0.510507i	$-0.829458\pi$
$2$	−0.640527	−	3.63261i	−0.226461	−	1.28432i	0.633413	−	0.773814i	$-0.281654\pi$
$3$		0			0
$3$		0			0
$4$	−5.26804	+	1.91741i	−0.658504	+	0.239676i
$5$	1.23763	+	1.03850i	0.110697	+	0.0928860i	0.696456	−	0.717599i	$-0.254759\pi$
$5$	1.23763	+	1.03850i	0.110697	+	0.0928860i	−0.585759	+	0.810485i	$0.699203\pi$
$6$		0			0
$7$	−31.9169	−	11.6168i	−1.72335	−	0.627248i	−0.725228	−	0.688508i	$-0.758266\pi$
$7$	−31.9169	−	11.6168i	−1.72335	−	0.627248i	−0.998122	+	0.0612602i	$0.980488\pi$
$8$	−4.41508	−	7.64714i	−0.195121	−	0.337959i
$9$		0			0
$10$	2.97972	−	5.16102i	0.0942269	−	0.163206i
$11$	−18.8740	+	15.8372i	−0.517339	+	0.434099i	−0.863703	−	0.504001i	$-0.831861\pi$
$11$	−18.8740	+	15.8372i	−0.517339	+	0.434099i	0.346364	+	0.938100i	$0.387416\pi$
$12$		0			0
$13$	5.35351	−	30.3613i	0.114215	−	0.647746i	−0.872921	−	0.487862i	$-0.837777\pi$
$13$	5.35351	−	30.3613i	0.114215	−	0.647746i	0.987136	−	0.159884i	$-0.0511121\pi$
$14$	−21.7557	+	123.382i	−0.415317	+	2.35538i
$15$		0			0
$16$	−59.3074	+	49.7648i	−0.926679	+	0.777576i
$17$	18.2417	−	31.5955i	0.260250	−	0.450766i	−0.706058	−	0.708154i	$-0.749528\pi$
$17$	18.2417	−	31.5955i	0.260250	−	0.450766i	0.966308	+	0.257387i	$0.0828617\pi$
$18$		0			0
$19$	36.5170	+	63.2494i	0.440925	+	0.763705i	0.997758	−	0.0669192i	$-0.0213170\pi$
$19$	36.5170	+	63.2494i	0.440925	+	0.763705i	−0.556833	+	0.830625i	$0.687984\pi$
$20$	−8.51112	−	3.09779i	−0.0951572	−	0.0346344i
$21$		0			0
$22$	69.6196	+	58.4178i	0.674680	+	0.566124i
$23$	62.9523	−	22.9128i	0.570716	−	0.207724i	−0.0405108	−	0.999179i	$-0.512899\pi$
$23$	62.9523	−	22.9128i	0.570716	−	0.207724i	0.611227	+	0.791455i	$0.290676\pi$
$24$		0			0
$25$	−21.2528	−	120.530i	−0.170022	−	0.964243i
$26$	−113.720			−0.857780
$27$		0			0
$28$	190.413			1.28517
$29$	−41.0688	−	232.913i	−0.262975	−	1.49141i	−0.774739	−	0.632281i	$-0.782119\pi$
$29$	−41.0688	−	232.913i	−0.262975	−	1.49141i	0.511764	−	0.859126i	$-0.328992\pi$
$30$		0			0
$31$	−152.414	+	55.4740i	−0.883042	+	0.321401i	−0.743437	−	0.668806i	$-0.766806\pi$
$31$	−152.414	+	55.4740i	−0.883042	+	0.321401i	−0.139605	+	0.990207i	$0.544583\pi$
$32$	164.650	+	138.158i	0.909571	+	0.763221i
$33$		0			0
$34$	−126.458	−	46.0271i	−0.637865	−	0.232164i
$35$	−27.4374	−	47.5229i	−0.132508	−	0.229510i
$36$		0			0
$37$	93.1046	−	161.262i	0.413684	−	0.716521i	−0.581605	−	0.813471i	$-0.697575\pi$
$37$	93.1046	−	161.262i	0.413684	−	0.716521i	0.995289	+	0.0969496i	$0.0309086\pi$
$38$	206.370	−	173.165i	0.880991	−	0.739239i
$39$		0			0
$40$	2.47729	−	14.0494i	0.00979234	−	0.0555351i
$41$	37.9265	−	215.092i	0.144466	−	0.819309i	−0.823328	−	0.567566i	$-0.807885\pi$
$41$	37.9265	−	215.092i	0.144466	−	0.819309i	0.967794	−	0.251743i	$-0.0810038\pi$
$42$		0			0
$43$	156.989	−	131.730i	0.556759	−	0.467176i	−0.320463	−	0.947261i	$-0.603839\pi$
$43$	156.989	−	131.730i	0.556759	−	0.467176i	0.877222	+	0.480085i	$0.159394\pi$
$44$	69.0627	−	119.620i	0.236627	−	0.409850i
$45$		0			0
$46$	−123.556	−	214.005i	−0.396029	−	0.685942i
$47$	450.185	+	163.854i	1.39715	+	0.508522i	0.927332	−	0.374239i	$-0.122096\pi$
$47$	450.185	+	163.854i	1.39715	+	0.508522i	0.469821	+	0.882762i	$0.344318\pi$
$48$		0			0
$49$	620.985	+	521.068i	1.81045	+	1.51915i
$50$	−424.227	+	154.406i	−1.19990	+	0.436726i
$51$		0			0
$52$	30.0125	+	170.209i	0.0800381	+	0.453919i
$53$	−736.254			−1.90816			−0.954078	−	0.299559i	$-0.903160\pi$
$53$	−736.254			−1.90816			−0.954078	+	0.299559i	$0.903160\pi$
$54$		0			0
$55$	−39.8060			−0.0975898
$56$	52.0803	+	295.362i	0.124277	+	0.704811i
$57$		0			0
$58$	−819.775	+	298.374i	−1.85589	+	0.675490i
$59$	−39.2313	−	32.9190i	−0.0865675	−	0.0726387i	0.598477	−	0.801140i	$-0.295773\pi$
$59$	−39.2313	−	32.9190i	−0.0865675	−	0.0726387i	−0.685044	+	0.728501i	$0.740217\pi$
$60$		0			0
$61$	108.686	+	39.5585i	0.228128	+	0.0830319i	0.453555	−	0.891228i	$-0.350155\pi$
$61$	108.686	+	39.5585i	0.228128	+	0.0830319i	−0.225427	+	0.974260i	$0.572378\pi$
$62$	299.141	+	518.127i	0.612756	+	1.06133i
$63$		0			0
$64$	86.7288	−	150.219i	0.169392	−	0.293396i
$65$	38.1558	−	32.0165i	0.0728099	−	0.0610947i
$66$		0			0
$67$	20.2242	−	114.697i	0.0368773	−	0.209142i	−0.960801	−	0.277237i	$-0.910581\pi$
$67$	20.2242	−	114.697i	0.0368773	−	0.209142i	0.997679	+	0.0680957i	$0.0216923\pi$
$68$	−35.5163	+	201.423i	−0.0633380	+	0.359207i
$69$		0			0
$70$	−155.058	+	130.109i	−0.264757	+	0.222157i
$71$	−118.488	+	205.227i	−0.198055	+	0.343042i	−0.947898	−	0.318575i	$-0.896796\pi$
$71$	−118.488	+	205.227i	−0.198055	+	0.343042i	0.749843	+	0.661616i	$0.230129\pi$
$72$		0			0
$73$	−23.0477	−	39.9198i	−0.0369524	−	0.0640035i	0.846958	−	0.531660i	$-0.178432\pi$
$73$	−23.0477	−	39.9198i	−0.0369524	−	0.0640035i	−0.883910	+	0.467657i	$0.845098\pi$
$74$	−645.437	−	234.920i	−1.01393	−	0.369039i
$75$		0			0
$76$	−313.648	−	263.182i	−0.473393	−	0.397224i
$77$	786.377	−	286.218i	1.16384	−	0.423605i
$78$		0			0
$79$	−130.778	−	741.681i	−0.186250	−	1.05627i	−0.924339	−	0.381572i	$-0.875383\pi$
$79$	−130.778	−	741.681i	−0.186250	−	1.05627i	0.738090	−	0.674703i	$-0.235728\pi$
$80$	−125.081			−0.174807
$81$		0			0
$82$	−805.637			−1.08497
$83$	59.3213	+	336.428i	0.0784501	+	0.444913i	0.998579	+	0.0532963i	$0.0169728\pi$
$83$	59.3213	+	336.428i	0.0784501	+	0.444913i	−0.920129	+	0.391616i	$0.871916\pi$
$84$		0			0
$85$	55.3883	−	20.1597i	0.0706789	−	0.0257250i
$86$	−579.078	−	485.904i	−0.726088	−	0.609260i
$87$		0			0
$88$	204.439	+	74.4099i	0.247651	+	0.0901377i
$89$	455.636	+	789.185i	0.542667	+	0.939926i	0.998750	+	0.0499890i	$0.0159186\pi$
$89$	455.636	+	789.185i	0.542667	+	0.939926i	−0.456083	+	0.889937i	$0.650748\pi$
$90$		0			0
$91$	−523.568	+	906.847i	−0.603131	+	1.04465i
$92$	−287.702	+	241.411i	−0.326033	+	0.273574i
$93$		0			0
$94$	306.862	−	1740.30i	0.336706	−	1.90955i
$95$	−20.4896	+	116.202i	−0.0221283	+	0.125496i
$96$		0			0
$97$	−37.6866	+	31.6228i	−0.0394484	+	0.0331011i	−0.662299	−	0.749240i	$-0.730419\pi$
$97$	−37.6866	+	31.6228i	−0.0394484	+	0.0331011i	0.622850	+	0.782341i	$0.285975\pi$
$98$	1495.08	−	2589.55i	1.54108	−	2.66923i
$99$		0			0
$100$	343.066	+	594.208i	0.343066	+	0.594208i
$101$	−1019.98	−	371.243i	−1.00487	−	0.365743i	−0.213410	−	0.976963i	$-0.568457\pi$
$101$	−1019.98	−	371.243i	−1.00487	−	0.365743i	−0.791461	+	0.611220i	$0.790679\pi$
$102$		0			0
$103$	−436.880	−	366.586i	−0.417933	−	0.350687i	0.409443	−	0.912336i	$-0.365723\pi$
$103$	−436.880	−	366.586i	−0.417933	−	0.350687i	−0.827376	+	0.561648i	$0.810167\pi$
$104$	−255.813	+	93.1084i	−0.241198	+	0.0877887i
$105$		0			0
$106$	471.591	+	2674.52i	0.432122	+	2.45068i
$107$	360.258			0.325490			0.162745	−	0.986668i	$-0.447965\pi$
$107$	360.258			0.325490			0.162745	+	0.986668i	$0.447965\pi$
$108$		0			0
$109$	895.448			0.786866			0.393433	−	0.919353i	$-0.371287\pi$
$109$	895.448			0.786866			0.393433	+	0.919353i	$0.371287\pi$
$110$	25.4968	+	144.600i	0.0221002	+	0.125337i
$111$		0			0
$112$	2471.02	−	899.377i	2.08472	−	0.758778i
$113$	41.0845	+	34.4740i	0.0342027	+	0.0286995i	0.659729	−	0.751504i	$-0.270671\pi$
$113$	41.0845	+	34.4740i	0.0342027	+	0.0286995i	−0.625526	+	0.780203i	$0.715116\pi$
$114$		0			0
$115$	101.707	+	37.0182i	0.0824713	+	0.0300171i
$116$	662.941	+	1148.25i	0.530625	+	0.919069i
$117$		0			0
$118$	−94.4530	+	163.597i	−0.0736874	+	0.127630i
$119$	−949.255	+	796.520i	−0.731244	+	0.613587i
$120$		0			0
$121$	−125.713	+	712.956i	−0.0944504	+	0.535655i
$122$	74.0842	−	420.153i	0.0549776	−	0.311794i
$123$		0			0
$124$	696.554	−	584.478i	0.504455	−	0.423288i
$125$	199.843	−	346.139i	0.142996	−	0.247677i
$126$		0			0
$127$	432.376	+	748.897i	0.302104	+	0.523259i	0.976612	−	0.215008i	$-0.0689778\pi$
$127$	432.376	+	748.897i	0.302104	+	0.523259i	−0.674509	+	0.738267i	$0.735644\pi$
$128$	1014.55	+	369.265i	0.700579	+	0.254990i
$129$		0			0
$130$	−140.743	−	118.098i	−0.0949539	−	0.0796757i
$131$	522.721	−	190.255i	0.348629	−	0.126891i	−0.161770	−	0.986829i	$-0.551720\pi$
$131$	522.721	−	190.255i	0.348629	−	0.126891i	0.510398	+	0.859938i	$0.329498\pi$
$132$		0			0
$133$	−430.755	−	2442.93i	−0.280836	−	1.59270i
$134$	−429.604			−0.276956
$135$		0			0
$136$	−322.153			−0.203121
$137$	−150.903	−	855.811i	−0.0941057	−	0.533700i	−0.995018	−	0.0996981i	$-0.968212\pi$
$137$	−150.903	−	855.811i	−0.0941057	−	0.533700i	0.900912	−	0.434002i	$-0.142899\pi$
$138$		0			0
$139$	−871.640	+	317.251i	−0.531882	+	0.193589i	−0.593978	−	0.804481i	$-0.702444\pi$
$139$	−871.640	+	317.251i	−0.531882	+	0.193589i	0.0620966	+	0.998070i	$0.480221\pi$
$140$	235.662	+	197.744i	0.142265	+	0.119374i
$141$		0			0
$142$	821.404	+	298.967i	0.485427	+	0.176681i
$143$	379.795	+	657.824i	0.222098	+	0.384685i
$144$		0			0
$145$	191.051	−	330.910i	0.109420	−	0.189521i
$146$	−130.250	+	109.293i	−0.0738328	+	0.0619531i
$147$		0			0
$148$	−181.273	+	1028.05i	−0.100680	+	0.570983i
$149$	291.432	−	1652.79i	0.160235	−	0.908739i	−0.793607	−	0.608431i	$-0.791799\pi$
$149$	291.432	−	1652.79i	0.160235	−	0.908739i	0.953842	−	0.300309i	$-0.0970896\pi$
$150$		0			0
$151$	−1885.95	+	1582.50i	−1.01640	+	0.852861i	−0.989171	−	0.146768i	$-0.953113\pi$
$151$	−1885.95	+	1582.50i	−1.01640	+	0.852861i	−0.0272292	+	0.999629i	$0.508668\pi$
$152$	322.451	−	558.502i	0.172067	−	0.298030i
$153$		0			0
$154$	−1543.41	−	2673.27i	−0.807609	−	1.39882i
$155$	−246.242	−	89.6247i	−0.127604	−	0.0464440i
$156$		0			0
$157$	−2134.05	−	1790.68i	−1.08481	−	0.910265i	−0.0884998	−	0.996076i	$-0.528207\pi$
$157$	−2134.05	−	1790.68i	−1.08481	−	0.910265i	−0.996311	+	0.0858116i	$0.972652\pi$
$158$	−2610.47	+	950.134i	−1.31442	+	0.478409i
$159$		0			0
$160$	60.2998	+	341.977i	0.0297945	+	0.168973i
$161$	−2275.42			−1.11384
$162$		0			0
$163$	−2058.86			−0.989337			−0.494669	−	0.869082i	$-0.664711\pi$
$163$	−2058.86			−0.989337			−0.494669	+	0.869082i	$0.664711\pi$
$164$	212.621	+	1205.83i	0.101237	+	0.574144i
$165$		0			0
$166$	1184.11	−	430.982i	0.553645	−	0.201510i
$167$	285.177	+	239.292i	0.132142	+	0.110880i	0.706463	−	0.707750i	$-0.250290\pi$
$167$	285.177	+	239.292i	0.132142	+	0.110880i	−0.574321	+	0.818630i	$0.694734\pi$
$168$		0			0
$169$	1171.36	+	426.339i	0.533162	+	0.194055i
$170$	−108.710	−	188.291i	−0.0490451	−	0.0849487i
$171$		0			0
$172$	−574.445	+	994.968i	−0.254657	+	0.441079i
$173$	1311.38	−	1100.38i	0.576316	−	0.483586i	−0.307419	−	0.951574i	$-0.599465\pi$
$173$	1311.38	−	1100.38i	0.576316	−	0.483586i	0.883735	+	0.467988i	$0.155021\pi$
$174$		0			0
$175$	−721.855	+	4093.85i	−0.311812	+	1.76837i
$176$	331.235	−	1878.53i	0.141862	−	0.804541i
$177$		0			0
$178$	2574.95	−	2160.64i	1.08427	−	0.909815i
$179$	−1512.45	+	2619.64i	−0.631540	+	1.09386i	0.355697	+	0.934601i	$0.384243\pi$
$179$	−1512.45	+	2619.64i	−0.631540	+	1.09386i	−0.987237	+	0.159258i	$0.949090\pi$
$180$		0			0
$181$	33.5721	+	58.1486i	0.0137867	+	0.0238793i	0.872836	−	0.488013i	$-0.162278\pi$
$181$	33.5721	+	58.1486i	0.0137867	+	0.0238793i	−0.859050	+	0.511892i	$0.828945\pi$
$182$	3629.58	+	1321.06i	1.47826	+	0.538041i
$183$		0			0
$184$	−453.157	−	380.244i	−0.181561	−	0.152347i
$185$	282.699	−	102.894i	0.112348	−	0.0408915i
$186$		0			0
$187$	156.090	+	885.230i	0.0610397	+	0.346173i
$188$	−2685.76			−1.04191
$189$		0			0
$190$	435.242			0.166188
$191$	−175.616	−	995.967i	−0.0665294	−	0.377307i	−0.999834	−	0.0182213i	$-0.994200\pi$
$191$	−175.616	−	995.967i	−0.0665294	−	0.377307i	0.933305	−	0.359086i	$-0.116911\pi$
$192$		0			0
$193$	−188.381	+	68.5652i	−0.0702590	+	0.0255722i	−0.376911	−	0.926250i	$-0.623014\pi$
$193$	−188.381	+	68.5652i	−0.0702590	+	0.0255722i	0.306652	+	0.951822i	$0.400791\pi$
$194$	139.013	+	116.645i	0.0514460	+	0.0431683i
$195$		0			0
$196$	−4270.47	−	1554.32i	−1.55629	−	0.566445i
$197$	1376.86	+	2384.79i	0.497954	+	0.862482i	0.999997	−	0.00236077i	$-0.000751458\pi$
$197$	1376.86	+	2384.79i	0.497954	+	0.862482i	−0.502043	+	0.864843i	$0.667418\pi$
$198$		0			0
$199$	2395.21	−	4148.63i	0.853227	−	1.47783i	−0.0250538	−	0.999686i	$-0.507976\pi$
$199$	2395.21	−	4148.63i	0.853227	−	1.47783i	0.878280	−	0.478146i	$-0.158691\pi$
$200$	−827.880	+	694.674i	−0.292700	+	0.245604i
$201$		0			0
$202$	−695.254	+	3942.98i	−0.242168	+	1.37340i
$203$	−1394.91	+	7910.94i	−0.482284	+	2.73517i
$204$		0			0
$205$	270.311	−	226.818i	0.0920944	−	0.0772763i
$206$	−1051.83	+	1821.82i	−0.355750	+	0.616177i
$207$		0			0
$208$	1193.42	+	2067.07i	0.397831	+	0.689064i
$209$	−1690.92	−	615.443i	−0.559632	−	0.203689i
$210$		0			0
$211$	751.352	+	630.459i	0.245143	+	0.205699i	0.757077	−	0.653325i	$-0.226627\pi$
$211$	751.352	+	630.459i	0.245143	+	0.205699i	−0.511934	+	0.859024i	$0.671071\pi$
$212$	3878.61	−	1411.70i	1.25653	−	0.457339i
$213$		0			0
$214$	−230.755	−	1308.68i	−0.0737107	−	0.418034i
$215$	331.096			0.105026
$216$		0			0
$217$	5509.00			1.72339
$218$	−573.559	−	3252.81i	−0.178194	−	1.01059i
$219$		0			0
$220$	209.699	−	76.3243i	0.0642633	−	0.0233899i
$221$	−861.622	−	722.987i	−0.262258	−	0.220060i
$222$		0			0
$223$	−437.380	−	159.193i	−0.131341	−	0.0478044i	0.275513	−	0.961297i	$-0.411152\pi$
$223$	−437.380	−	159.193i	−0.131341	−	0.0478044i	−0.406855	+	0.913493i	$0.633374\pi$
$224$	−3650.16	−	6322.27i	−1.08878	−	1.88582i
$225$		0			0
$226$	98.9147	−	171.325i	0.0291138	−	0.0504265i
$227$	3603.52	−	3023.71i	1.05363	−	0.884100i	0.0601584	−	0.998189i	$-0.480839\pi$
$227$	3603.52	−	3023.71i	1.05363	−	0.884100i	0.993471	+	0.114089i	$0.0363950\pi$
$228$		0			0
$229$	272.294	−	1544.26i	0.0785752	−	0.445622i	−0.919984	−	0.391956i	$-0.871798\pi$
$229$	272.294	−	1544.26i	0.0785752	−	0.445622i	0.998559	−	0.0536655i	$-0.0170905\pi$
$230$	69.3268	−	393.172i	0.0198751	−	0.112717i
$231$		0			0
$232$	−1599.79	+	1342.39i	−0.452723	+	0.379879i
$233$	2879.03	−	4986.62i	0.809491	−	1.40208i	−0.103727	−	0.994606i	$-0.533077\pi$
$233$	2879.03	−	4986.62i	0.809491	−	1.40208i	0.913217	−	0.407473i	$-0.133590\pi$
$234$		0			0
$235$	387.002	+	670.307i	0.107426	+	0.186068i
$236$	269.791	+	98.1959i	0.0744148	+	0.0270848i
$237$		0			0
$238$	3501.47	+	2938.08i	0.953641	+	0.800200i
$239$	3026.69	−	1101.62i	0.819164	−	0.298151i	0.101760	−	0.994809i	$-0.467553\pi$
$239$	3026.69	−	1101.62i	0.819164	−	0.298151i	0.717404	+	0.696658i	$0.245330\pi$
$240$		0			0
$241$	−472.252	−	2678.27i	−0.126226	−	0.715862i	−0.980572	−	0.196158i	$-0.937153\pi$
$241$	−472.252	−	2678.27i	−0.126226	−	0.715862i	0.854346	−	0.519704i	$-0.173958\pi$
$242$	2670.42			0.709342
$243$		0			0
$244$	−648.412			−0.170124
$245$	227.423	+	1289.78i	0.0593043	+	0.336331i
$246$		0			0
$247$	2115.83	−	770.098i	0.545048	−	0.198381i
$248$	1097.14	+	920.607i	0.280920	+	0.235720i
$249$		0			0
$250$	−1385.39	−	504.241i	−0.350480	−	0.127564i
$251$	−2711.14	−	4695.84i	−0.681777	−	1.18087i	−0.974438	−	0.224656i	$-0.927874\pi$
$251$	−2711.14	−	4695.84i	−0.681777	−	1.18087i	0.292661	−	0.956216i	$-0.405459\pi$
$252$		0			0
$253$	−825.290	+	1429.44i	−0.205081	+	0.355211i
$254$	2443.50	−	2050.34i	0.603618	−	0.506496i
$255$		0			0
$256$	932.515	−	5288.55i	0.227665	−	1.29115i
$257$	−183.660	+	1041.59i	−0.0445774	+	0.252811i	−0.998950	−	0.0458063i	$-0.985414\pi$
$257$	−183.660	+	1041.59i	−0.0445774	+	0.252811i	0.954373	+	0.298617i	$0.0965254\pi$
$258$		0			0
$259$	−4844.96	+	4065.40i	−1.16236	+	0.975335i
$260$	−139.617	+	241.824i	−0.0333027	+	0.0576819i
$261$		0			0
$262$	−1025.94	−	1776.98i	−0.241919	−	0.419016i
$263$	−4969.14	−	1808.62i	−1.16506	−	0.424046i	−0.314156	−	0.949371i	$-0.601722\pi$
$263$	−4969.14	−	1808.62i	−1.16506	−	0.424046i	−0.850902	+	0.525325i	$0.823944\pi$
$264$		0			0
$265$	−911.212	−	764.597i	−0.211228	−	0.177241i
$266$	−8598.32	+	3129.53i	−1.98194	+	0.721368i
$267$		0			0
$268$	113.379	+	643.007i	0.0258424	+	0.146559i
$269$	7352.28			1.66646			0.833228	−	0.552930i	$-0.186490\pi$
$269$	7352.28			1.66646			0.833228	+	0.552930i	$0.186490\pi$
$270$		0			0
$271$	3845.21			0.861917			0.430959	−	0.902372i	$-0.358175\pi$
$271$	3845.21			0.861917			0.430959	+	0.902372i	$0.358175\pi$
$272$	490.478	+	2781.64i	0.109337	+	0.620080i
$273$		0			0
$274$	−3012.17	+	1096.34i	−0.664131	+	0.241724i
$275$	2309.99	+	1938.31i	0.506536	+	0.425034i
$276$		0			0
$277$	3573.52	+	1300.65i	0.775133	+	0.282125i	0.699142	−	0.714983i	$-0.253566\pi$
$277$	3573.52	+	1300.65i	0.775133	+	0.282125i	0.0759911	+	0.997108i	$0.475788\pi$
$278$	1710.76	+	2963.12i	0.369081	+	0.639267i
$279$		0			0
$280$	−242.276	+	419.635i	−0.0517099	+	0.0895642i
$281$	−4191.24	+	3516.87i	−0.889781	+	0.746615i	−0.968166	−	0.250308i	$-0.919468\pi$
$281$	−4191.24	+	3516.87i	−0.889781	+	0.746615i	0.0783853	+	0.996923i	$0.475024\pi$
$282$		0			0
$283$	1071.49	−	6076.70i	0.225064	−	1.27640i	−0.637498	−	0.770452i	$-0.720030\pi$
$283$	1071.49	−	6076.70i	0.225064	−	1.27640i	0.862562	−	0.505951i	$-0.168858\pi$
$284$	230.694	−	1308.33i	0.0482014	−	0.273363i
$285$		0			0
$286$	2146.35	−	1801.00i	0.443763	−	0.372362i
$287$	−3709.17	+	6424.47i	−0.762876	+	1.32134i
$288$		0			0
$289$	1790.98	+	3102.08i	0.364540	+	0.631401i
$290$	−1324.44	−	482.057i	−0.268186	−	0.0976116i
$291$		0			0
$292$	197.959	+	166.107i	0.0396734	+	0.0332900i
$293$	1483.01	−	539.771i	0.295694	−	0.107624i	−0.189913	−	0.981801i	$-0.560821\pi$
$293$	1483.01	−	539.771i	0.295694	−	0.107624i	0.485607	+	0.874177i	$0.338598\pi$
$294$		0			0
$295$	−14.3677	−	81.4832i	−0.00283566	−	0.0160818i
$296$	−1644.26			−0.322873
$297$		0			0
$298$	−6190.63			−1.20340
$299$	−358.645	−	2033.98i	−0.0693678	−	0.393404i
$300$		0			0
$301$	−6540.88	+	2380.69i	−1.25253	+	0.455882i
$302$	6956.61	+	5837.29i	1.32552	+	1.11225i
$303$		0			0
$304$	−5313.33	−	1933.89i	−1.00243	−	0.364856i
$305$	93.4321	+	161.829i	0.0175407	+	0.0303813i
$306$		0			0
$307$	−2688.23	+	4656.16i	−0.499758	+	0.865606i	−1.00000		0.000279643i	$-0.999911\pi$
$307$	−2688.23	+	4656.16i	−0.499758	+	0.865606i	0.500242	+	0.865886i	$0.333244\pi$
$308$	−3593.87	+	3015.61i	−0.664869	+	0.557891i
$309$		0			0
$310$	−167.847	+	951.907i	−0.0307518	+	0.174402i
$311$	1068.47	−	6059.59i	0.194814	−	1.10485i	−0.717868	−	0.696179i	$-0.754882\pi$
$311$	1068.47	−	6059.59i	0.194814	−	1.10485i	0.912683	−	0.408669i	$-0.134007\pi$
$312$		0			0
$313$	5626.07	−	4720.84i	1.01599	−	0.852516i	0.0268706	−	0.999639i	$-0.491446\pi$
$313$	5626.07	−	4720.84i	1.01599	−	0.852516i	0.989118	+	0.147123i	$0.0470014\pi$
$314$	−5137.91	+	8899.13i	−0.923405	+	1.59939i
$315$		0			0
$316$	2111.05	+	3656.45i	0.375810	+	0.650922i
$317$	964.065	+	350.891i	0.170812	+	0.0621703i	0.426010	−	0.904718i	$-0.359919\pi$
$317$	964.065	+	350.891i	0.170812	+	0.0621703i	−0.255199	+	0.966889i	$0.582141\pi$
$318$		0			0
$319$	4463.81	+	3745.59i	0.783466	+	0.657406i
$320$	263.340	−	95.8479i	0.0460036	−	0.0167439i
$321$		0			0
$322$	1457.47	+	8265.70i	0.252240	+	1.43053i
$323$	2664.53			0.459004
$324$		0			0
$325$	−3773.23			−0.644004
$326$	1318.75	+	7479.02i	0.224046	+	1.27063i
$327$		0			0
$328$	−1812.28	+	659.618i	−0.305081	+	0.111041i
$329$	−12465.0	−	10459.4i	−2.08882	−	1.75272i
$330$		0			0
$331$	5414.80	+	1970.83i	0.899167	+	0.327270i	0.749919	−	0.661530i	$-0.230092\pi$
$331$	5414.80	+	1970.83i	0.899167	+	0.327270i	0.149248	+	0.988800i	$0.452315\pi$
$332$	−957.576	−	1658.57i	−0.158295	−	0.274174i
$333$		0			0
$334$	686.591	−	1189.21i	0.112481	−	0.194822i
$335$	144.143	−	120.950i	0.0235085	−	0.0197260i
$336$		0			0
$337$	557.882	−	3163.91i	0.0901774	−	0.511422i	−0.905941	−	0.423403i	$-0.860835\pi$
$337$	557.882	−	3163.91i	0.0901774	−	0.511422i	0.996119	−	0.0880185i	$-0.0280535\pi$
$338$	798.438	−	4528.17i	0.128489	−	0.728698i
$339$		0			0
$340$	−253.133	+	212.404i	−0.0403767	+	0.0338801i
$341$	1998.11	−	3460.82i	0.317312	−	0.549601i
$342$		0			0
$343$	−7941.72	−	13755.5i	−1.25018	−	2.16538i
$344$	−1700.47	−	618.922i	−0.266522	−	0.0970059i
$345$		0			0
$346$	−4837.23	−	4058.92i	−0.751593	−	0.630661i
$347$	−3383.81	+	1231.60i	−0.523494	+	0.190536i	−0.590231	−	0.807235i	$-0.700963\pi$
$347$	−3383.81	+	1231.60i	−0.523494	+	0.190536i	0.0667373	+	0.997771i	$0.478741\pi$
$348$		0			0
$349$	−321.225	−	1821.76i	−0.0492686	−	0.279416i	0.950213	−	0.311600i	$-0.100865\pi$
$349$	−321.225	−	1821.76i	−0.0492686	−	0.279416i	−0.999482	+	0.0321837i	$0.989754\pi$
$350$	15333.7			2.34177
$351$		0			0
$352$	−5295.63			−0.801870
$353$	−540.224	−	3063.76i	−0.0814538	−	0.461948i	−0.998066	−	0.0621691i	$-0.980198\pi$
$353$	−540.224	−	3063.76i	−0.0814538	−	0.461948i	0.916612	−	0.399778i	$-0.130913\pi$
$354$		0			0
$355$	−359.772	+	130.946i	−0.0537879	+	0.0195772i
$356$	−3913.50	−	3283.81i	−0.582626	−	0.488881i
$357$		0			0
$358$	10484.9	+	3816.18i	1.54788	+	0.563384i
$359$	−3228.43	−	5591.80i	−0.474624	−	0.822072i	0.524954	−	0.851131i	$-0.324082\pi$
$359$	−3228.43	−	5591.80i	−0.474624	−	0.822072i	−0.999578	+	0.0290584i	$0.990749\pi$
$360$		0			0
$361$	762.511	−	1320.71i	0.111169	−	0.192551i
$362$	189.727	−	159.200i	0.0275465	−	0.0231143i
$363$		0			0
$364$	1019.38	−	5781.20i	0.146786	−	0.832464i
$365$	12.9320	−	73.3410i	0.00185450	−	0.0105174i
$366$		0			0
$367$	−3998.61	+	3355.23i	−0.568735	+	0.477226i	−0.881226	−	0.472695i	$-0.843281\pi$
$367$	−3998.61	+	3355.23i	−0.568735	+	0.477226i	0.312491	+	0.949921i	$0.398837\pi$
$368$	−2593.29	+	4491.71i	−0.367350	+	0.636268i
$369$		0			0
$370$	−554.851	−	961.030i	−0.0779603	−	0.135031i
$371$	23498.9	+	8552.91i	3.28842	+	1.19689i
$372$		0			0
$373$	4441.26	+	3726.66i	0.616515	+	0.517317i	0.896706	−	0.442627i	$-0.145953\pi$
$373$	4441.26	+	3726.66i	0.616515	+	0.517317i	−0.280191	+	0.959944i	$0.590398\pi$
$374$	3115.72	−	1134.03i	0.430775	−	0.156789i
$375$		0			0
$376$	−734.588	−	4166.06i	−0.100754	−	0.571404i
$377$	−7291.39			−0.996089
$378$		0			0
$379$	−12786.6			−1.73299			−0.866495	−	0.499185i	$-0.833633\pi$
$379$	−12786.6			−1.73299			−0.866495	+	0.499185i	$0.833633\pi$
$380$	−114.867	−	651.445i	−0.0155068	−	0.0879432i
$381$		0			0
$382$	−3505.47	+	1275.89i	−0.469517	+	0.170890i
$383$	−2864.04	−	2403.21i	−0.382103	−	0.320623i	0.431424	−	0.902149i	$-0.358011\pi$
$383$	−2864.04	−	2403.21i	−0.382103	−	0.320623i	−0.813527	+	0.581527i	$0.802456\pi$
$384$		0			0
$385$	1270.48	+	462.418i	0.168181	+	0.0612130i
$386$	369.734	+	640.398i	0.0487538	+	0.0844441i
$387$		0			0
$388$	137.900	−	238.851i	0.0180434	−	0.0312521i
$389$	−4350.72	+	3650.69i	−0.567070	+	0.475828i	−0.880672	−	0.473726i	$-0.842909\pi$
$389$	−4350.72	+	3650.69i	−0.567070	+	0.475828i	0.313602	+	0.949554i	$0.398464\pi$
$390$		0			0
$391$	424.415	−	2406.98i	0.0548941	−	0.311320i
$392$	1242.98	−	7049.31i	0.160154	−	0.908276i
$393$		0			0
$394$	7781.08	−	6529.10i	0.994937	−	0.834851i
$395$	608.378	−	1053.74i	0.0774958	−	0.134227i
$396$		0			0
$397$	3935.17	+	6815.91i	0.497482	+	0.861664i	0.999996	−	0.00290500i	$-0.000924692\pi$
$397$	3935.17	+	6815.91i	0.497482	+	0.861664i	−0.502514	+	0.864569i	$0.667591\pi$
$398$	−16604.5	−	6043.56i	−2.09123	−	0.761147i
$399$		0			0
$400$	7258.62	+	6090.71i	0.907328	+	0.761339i
$401$	11786.5	−	4289.92i	1.46780	−	0.534236i	0.520298	−	0.853985i	$-0.325821\pi$
$401$	11786.5	−	4289.92i	1.46780	−	0.534236i	0.947502	+	0.319749i	$0.103599\pi$
$402$		0			0
$403$	868.314	+	4924.46i	0.107330	+	0.608696i
$404$	6085.12			0.749371
$405$		0			0
$406$	29630.8			3.62205
$407$	796.676	+	4518.17i	0.0970265	+	0.550264i
$408$		0			0
$409$	7535.89	−	2742.84i	0.911065	−	0.331601i	0.156387	−	0.987696i	$-0.450015\pi$
$409$	7535.89	−	2742.84i	0.911065	−	0.331601i	0.754678	+	0.656095i	$0.227793\pi$
$410$	−997.083	−	836.652i	−0.120103	−	0.100779i
$411$		0			0
$412$	3004.39	+	1093.51i	0.359262	+	0.130761i
$413$	869.728	+	1506.41i	0.103624	+	0.179481i
$414$		0			0
$415$	−275.961	+	477.979i	−0.0326419	+	0.0565375i
$416$	5076.10	−	4259.35i	0.598260	−	0.502000i
$417$		0			0
$418$	−1152.59	+	6536.64i	−0.134868	+	0.764875i
$419$	−2688.55	+	15247.5i	−0.313471	+	1.77778i	0.267199	+	0.963641i	$0.413902\pi$
$419$	−2688.55	+	15247.5i	−0.313471	+	1.77778i	−0.580670	+	0.814139i	$0.697209\pi$
$420$		0			0
$421$	−2941.20	+	2467.96i	−0.340488	+	0.285703i	−0.796957	−	0.604036i	$-0.793558\pi$
$421$	−2941.20	+	2467.96i	−0.340488	+	0.285703i	0.456469	+	0.889739i	$0.349114\pi$
$422$	1808.95	−	3133.19i	0.208669	−	0.361425i
$423$		0			0
$424$	3250.62	+	5630.24i	0.372321	+	0.644878i
$425$	−4195.90	−	1527.18i	−0.478897	−	0.174304i
$426$		0			0
$427$	−3009.38	−	2525.17i	−0.341063	−	0.286186i
$428$	−1897.85	+	690.762i	−0.214337	+	0.0780122i
$429$		0			0
$430$	−212.076	−	1202.74i	−0.0237842	−	0.134887i
$431$	4322.86			0.483121			0.241560	−	0.970386i	$-0.422341\pi$
$431$	4322.86			0.483121			0.241560	+	0.970386i	$0.422341\pi$
$432$		0			0
$433$	−8167.34			−0.906460			−0.453230	−	0.891394i	$-0.649728\pi$
$433$	−8167.34			−0.906460			−0.453230	+	0.891394i	$0.649728\pi$
$434$	−3528.66	−	20012.1i	−0.390280	−	2.21339i
$435$		0			0
$436$	−4717.25	+	1716.94i	−0.518155	+	0.188593i
$437$	3748.05	+	3144.99i	0.410283	+	0.344268i
$438$		0			0
$439$	−6964.64	−	2534.92i	−0.757185	−	0.275593i	−0.0655591	−	0.997849i	$-0.520883\pi$
$439$	−6964.64	−	2534.92i	−0.757185	−	0.275593i	−0.691626	+	0.722256i	$0.743105\pi$
$440$	175.747	+	304.402i	0.0190418	+	0.0329813i
$441$		0			0
$442$	−2074.44	+	3593.03i	−0.223237	+	0.386658i
$443$	−5428.84	+	4555.34i	−0.582239	+	0.488556i	−0.885682	−	0.464293i	$-0.846308\pi$
$443$	−5428.84	+	4555.34i	−0.582239	+	0.488556i	0.303443	+	0.952850i	$0.401864\pi$
$444$		0			0
$445$	−255.656	+	1449.90i	−0.0272343	+	0.154453i
$446$	−298.134	+	1690.80i	−0.0316525	+	0.179510i
$447$		0			0
$448$	−4513.17	+	3787.00i	−0.475954	+	0.399373i
$449$	−5632.70	+	9756.13i	−0.592035	+	1.02543i	0.401923	+	0.915673i	$0.368342\pi$
$449$	−5632.70	+	9756.13i	−0.592035	+	1.02543i	−0.993958	+	0.109761i	$0.964991\pi$
$450$		0			0
$451$	2690.62	+	4660.29i	0.280923	+	0.486573i
$452$	−282.535	−	102.834i	−0.0294012	−	0.0107012i
$453$		0			0
$454$	−13292.1	−	11153.4i	−1.37407	−	1.15298i
$455$	−1589.74	+	578.619i	−0.163799	+	0.0596178i
$456$		0			0
$457$	349.551	+	1982.40i	0.0357797	+	0.202917i	0.997457	−	0.0712659i	$-0.0227039\pi$
$457$	349.551	+	1982.40i	0.0357797	+	0.202917i	−0.961678	+	0.274182i	$0.911593\pi$
$458$	−5784.10			−0.590116
$459$		0			0
$460$	−606.774			−0.0615021
$461$	2310.16	+	13101.6i	0.233395	+	1.32365i	0.845968	+	0.533233i	$0.179023\pi$
$461$	2310.16	+	13101.6i	0.233395	+	1.32365i	−0.612574	+	0.790414i	$0.709866\pi$
$462$		0			0
$463$	16771.8	−	6104.42i	1.68348	−	0.612735i	0.689697	−	0.724098i	$-0.257744\pi$
$463$	16771.8	−	6104.42i	1.68348	−	0.612735i	0.993780	+	0.111363i	$0.0355217\pi$
$464$	14026.6	+	11769.7i	1.40338	+	1.17757i
$465$		0			0
$466$	−19958.5	−	7264.31i	−1.98404	−	0.722131i
$467$	−5090.74	−	8817.42i	−0.504435	−	0.873708i	−0.999987	−	0.00512926i	$-0.998367\pi$
$467$	−5090.74	−	8817.42i	−0.504435	−	0.873708i	0.495551	−	0.868579i	$-0.334966\pi$
$468$		0			0
$469$	−1977.91	+	3425.84i	−0.194736	+	0.337293i
$470$	2187.08	−	1835.18i	0.214643	−	0.180107i
$471$		0			0
$472$	−78.5267	+	445.347i	−0.00765781	+	0.0434296i
$473$	−876.792	+	4972.53i	−0.0852324	+	0.483377i
$474$		0			0
$475$	6847.38	−	5745.64i	0.661431	−	0.555006i
$476$	3473.46	−	6016.20i	0.334466	−	0.579311i
$477$		0			0
$478$	−5940.44	−	10289.2i	−0.568430	−	0.984550i
$479$	−2896.89	−	1054.38i	−0.276330	−	0.100576i	0.200138	−	0.979768i	$-0.435861\pi$
$479$	−2896.89	−	1054.38i	−0.276330	−	0.100576i	−0.476468	+	0.879192i	$0.658083\pi$
$480$		0			0
$481$	−4397.68	−	3690.09i	−0.416875	−	0.349800i
$482$	−9426.63	+	3431.01i	−0.890812	+	0.324229i
$483$		0			0
$484$	−704.766	−	3996.92i	−0.0661876	−	0.375369i
$485$	−79.4823			−0.00744146
$486$		0			0
$487$	1482.64			0.137956			0.0689782	−	0.997618i	$-0.478026\pi$
$487$	1482.64			0.137956			0.0689782	+	0.997618i	$0.478026\pi$
$488$	−177.348	−	1005.79i	−0.0164512	−	0.0932993i
$489$		0			0
$490$	4539.60	−	1652.28i	0.418527	−	0.152331i
$491$	−6066.55	−	5090.44i	−0.557596	−	0.467878i	0.319908	−	0.947449i	$-0.396348\pi$
$491$	−6066.55	−	5090.44i	−0.557596	−	0.467878i	−0.877503	+	0.479570i	$0.840793\pi$
$492$		0			0
$493$	−8108.15	−	2951.13i	−0.740716	−	0.269598i
$494$	−4152.71	−	7192.70i	−0.378217	−	0.655091i
$495$		0			0
$496$	6278.61	−	10874.9i	0.568383	−	0.984468i
$497$	6165.84	−	5173.76i	0.556491	−	0.466951i
$498$		0			0
$499$	−1417.01	+	8036.24i	−0.127122	+	0.720945i	0.852903	+	0.522070i	$0.174840\pi$
$499$	−1417.01	+	8036.24i	−0.127122	+	0.720945i	−0.980025	+	0.198875i	$0.936271\pi$
$500$	−389.092	+	2206.65i	−0.0348015	+	0.197369i
$501$		0			0
$502$	−15321.6	+	12856.3i	−1.36222	+	1.14304i
$503$	8812.36	−	15263.5i	0.781161	−	1.35301i	−0.150105	−	0.988670i	$-0.547961\pi$
$503$	8812.36	−	15263.5i	0.781161	−	1.35301i	0.931266	−	0.364340i	$-0.118705\pi$
$504$		0			0
$505$	−876.827	−	1518.71i	−0.0772640	−	0.133825i
$506$	5721.23	+	2082.36i	0.502648	+	0.182949i
$507$		0			0
$508$	−3713.71	−	3116.18i	−0.324349	−	0.272161i
$509$	−8361.44	+	3043.31i	−0.728122	+	0.265015i	−0.679370	−	0.733796i	$-0.737747\pi$
$509$	−8361.44	+	3043.31i	−0.728122	+	0.265015i	−0.0487523	+	0.998811i	$0.515524\pi$
$510$		0			0
$511$	271.871	+	1541.86i	0.0235359	+	0.133479i
$512$	−11171.3			−0.964269
$513$		0			0
$514$	3901.32			0.334786
$515$	−159.999	−	907.397i	−0.0136901	−	0.0776402i
$516$		0			0
$517$	−11091.8	+	4037.08i	−0.943551	+	0.343425i
$518$	17871.3	+	14995.8i	1.51587	+	1.27197i
$519$		0			0
$520$	−413.296	−	150.427i	−0.0348542	−	0.0126859i
$521$	9964.97	+	17259.8i	0.837953	+	1.45138i	0.891604	+	0.452817i	$0.149581\pi$
$521$	9964.97	+	17259.8i	0.837953	+	1.45138i	−0.0536508	+	0.998560i	$0.517086\pi$
$522$		0			0
$523$	894.732	−	1549.72i	0.0748067	−	0.129569i	−0.826195	−	0.563384i	$-0.809499\pi$
$523$	894.732	−	1549.72i	0.0748067	−	0.129569i	0.901002	+	0.433815i	$0.142833\pi$
$524$	−2388.92	+	2004.54i	−0.199161	+	0.167116i
$525$		0			0
$526$	−3387.14	+	19209.4i	−0.280772	+	1.59234i
$527$	−1027.55	+	5827.52i	−0.0849350	+	0.481690i
$528$		0			0
$529$	−5882.46	+	4935.97i	−0.483477	+	0.405685i
$530$	−2193.83	+	3799.82i	−0.179800	+	0.311422i
$531$		0			0
$532$	6953.34	+	12043.5i	0.566664	+	0.981491i
$533$	−6327.42	−	2302.99i	−0.514204	−	0.187155i
$534$		0			0
$535$	445.867	+	374.127i	0.0360309	+	0.0302335i
$536$	−966.397	+	351.740i	−0.0778768	+	0.0283448i
$537$		0			0
$538$	−4709.34	−	26708.0i	−0.377386	−	2.14027i
$539$	−19972.7			−1.59608
$540$		0			0
$541$	9074.21			0.721129			0.360564	−	0.932734i	$-0.382584\pi$
$541$	9074.21			0.721129			0.360564	+	0.932734i	$0.382584\pi$
$542$	−2462.96	−	13968.1i	−0.195190	−	1.10698i
$543$		0			0
$544$	7368.65	−	2681.97i	0.580750	−	0.211376i
$545$	1108.24	+	929.921i	0.0871039	+	0.0730888i
$546$		0			0
$547$	7530.92	+	2741.03i	0.588664	+	0.214256i	0.619142	−	0.785279i	$-0.287481\pi$
$547$	7530.92	+	2741.03i	0.588664	+	0.214256i	−0.0304779	+	0.999535i	$0.509703\pi$
$548$	2435.90	+	4219.10i	0.189884	+	0.328889i
$549$		0			0
$550$	5561.51	−	9632.82i	0.431170	−	0.746809i
$551$	13231.9	−	11102.9i	1.02304	−	0.858435i
$552$		0			0
$553$	−4441.92	+	25191.4i	−0.341573	+	1.93715i
$554$	2435.83	−	13814.3i	0.186802	−	1.05941i
$555$		0			0
$556$	3983.53	−	3342.58i	0.303848	−	0.254959i
$557$	−3679.68	+	6373.39i	−0.279915	+	0.484828i	−0.971363	−	0.237598i	$-0.923640\pi$
$557$	−3679.68	+	6373.39i	−0.279915	+	0.484828i	0.691448	+	0.722426i	$0.256973\pi$
$558$		0			0
$559$	−3159.03	−	5471.61i	−0.239021	−	0.413997i
$560$	3992.21	+	1453.05i	0.301253	+	0.109647i
$561$		0			0
$562$	15460.0	+	12972.5i	1.16039	+	0.973686i
$563$	1774.18	−	645.750i	0.132812	−	0.0483395i	−0.274759	−	0.961513i	$-0.588598\pi$
$563$	1774.18	−	645.750i	0.132812	−	0.0483395i	0.407571	+	0.913174i	$0.366376\pi$
$564$		0			0
$565$	15.0464	+	85.3322i	0.00112036	+	0.00635390i
$566$	−22760.6			−1.69028
$567$		0			0
$568$	2092.53			0.154579
$569$	4311.69	+	24452.8i	0.317672	+	1.80161i	0.556829	+	0.830627i	$0.312018\pi$
$569$	4311.69	+	24452.8i	0.317672	+	1.80161i	−0.239156	+	0.970981i	$0.576871\pi$
$570$		0			0
$571$	13261.5	−	4826.79i	0.971939	−	0.353757i	0.193238	−	0.981152i	$-0.438101\pi$
$571$	13261.5	−	4826.79i	0.971939	−	0.353757i	0.778701	+	0.627395i	$0.215879\pi$
$572$	−3262.09	−	2737.22i	−0.238453	−	0.200085i
$573$		0			0
$574$	25713.4	+	9358.92i	1.86979	+	0.680547i
$575$	−4099.60	−	7100.71i	−0.297330	−	0.514992i
$576$		0			0
$577$	−4690.34	+	8123.90i	−0.338408	+	0.586140i	−0.984133	−	0.177430i	$-0.943222\pi$
$577$	−4690.34	+	8123.90i	−0.338408	+	0.586140i	0.645726	+	0.763570i	$0.276555\pi$
$578$	10121.5	−	8492.91i	0.728368	−	0.611174i
$579$		0			0
$580$	−371.974	+	2109.57i	−0.0266300	+	0.151026i
$581$	2014.86	−	11426.9i	0.143874	−	0.815948i
$582$		0			0
$583$	13896.1	−	11660.2i	0.987164	−	0.828329i
$584$	−203.515	+	352.498i	−0.0144204	+	0.0249768i
$585$		0			0
$586$	−2910.69	−	5041.46i	−0.205187	−	0.355394i
$587$	3439.46	+	1251.86i	0.241843	+	0.0880236i	0.460098	−	0.887868i	$-0.347814\pi$
$587$	3439.46	+	1251.86i	0.241843	+	0.0880236i	−0.218255	+	0.975892i	$0.570037\pi$
$588$		0			0
$589$	−9074.39	−	7614.32i	−0.634811	−	0.532670i
$590$	−286.794	+	104.384i	−0.0200120	+	0.00728379i
$591$		0			0
$592$	2503.38	+	14197.4i	0.173798	+	0.985656i
$593$	21034.0			1.45660			0.728299	−	0.685260i	$-0.240311\pi$
$593$	21034.0			1.45660			0.728299	+	0.685260i	$0.240311\pi$
$594$		0			0
$595$	−2002.01			−0.137940
$596$	1633.81	+	9265.77i	0.112287	+	0.636814i
$597$		0			0
$598$	−7158.92	+	2605.63i	−0.489549	+	0.178181i
$599$	−13783.5	−	11565.7i	−0.940199	−	0.788921i	0.0374208	−	0.999300i	$-0.488086\pi$
$599$	−13783.5	−	11565.7i	−0.940199	−	0.788921i	−0.977620	+	0.210379i	$0.932530\pi$
$600$		0			0
$601$	−18472.2	−	6723.33i	−1.25374	−	0.456324i	−0.372075	−	0.928203i	$-0.621354\pi$
$601$	−18472.2	−	6723.33i	−1.25374	−	0.456324i	−0.881663	+	0.471879i	$0.843576\pi$
$602$	12837.7	+	22235.6i	0.869147	+	1.50541i
$603$		0			0
$604$	6900.95	−	11952.8i	0.464894	−	0.805220i
$605$	−895.990	+	751.825i	−0.0602102	+	0.0505224i
$606$		0			0
$607$	3505.49	−	19880.6i	0.234404	−	1.32937i	−0.609461	−	0.792816i	$-0.708614\pi$
$607$	3505.49	−	19880.6i	0.234404	−	1.32937i	0.843865	−	0.536555i	$-0.180275\pi$
$608$	−2725.86	+	15459.1i	−0.181823	+	1.03117i
$609$		0			0
$610$	528.016	−	443.058i	0.0350471	−	0.0294080i
$611$	7384.88	−	12791.0i	0.488970	−	0.846920i
$612$		0			0
$613$	−2360.70	−	4088.85i	−0.155543	−	0.269408i	0.777714	−	0.628619i	$-0.216379\pi$
$613$	−2360.70	−	4088.85i	−0.155543	−	0.269408i	−0.933257	+	0.359210i	$0.883046\pi$
$614$	18635.9	+	6782.91i	1.22489	+	0.445824i
$615$		0			0
$616$	−5660.67	−	4749.86i	−0.370251	−	0.310678i
$617$	25172.0	−	9161.84i	1.64244	−	0.597799i	0.654976	−	0.755650i	$-0.272679\pi$
$617$	25172.0	−	9161.84i	1.64244	−	0.597799i	0.987463	+	0.157851i	$0.0504566\pi$
$618$		0			0
$619$	4631.21	+	26264.9i	0.300717	+	1.70545i	0.643010	+	0.765858i	$0.277686\pi$
$619$	4631.21	+	26264.9i	0.300717	+	1.70545i	−0.342293	+	0.939593i	$0.611203\pi$
$620$	1469.06			0.0951593
$621$		0			0
$622$	−22696.5			−1.46310
$623$	−5374.69	−	30481.4i	−0.345638	−	1.96021i
$624$		0			0
$625$	−13769.3	+	5011.62i	−0.881235	+	0.320743i
$626$	−20752.6	−	17413.5i	−1.32499	−	1.11179i
$627$		0			0
$628$	14675.7	+	5341.51i	0.932522	+	0.339410i
$629$	−3396.76	−	5883.37i	−0.215323	−	0.372950i
$630$		0			0
$631$	8435.45	−	14610.6i	0.532187	−	0.921775i	−0.467107	−	0.884201i	$-0.654704\pi$
$631$	8435.45	−	14610.6i	0.532187	−	0.921775i	0.999294	−	0.0375740i	$-0.0119630\pi$
$632$	−5094.34	+	4274.66i	−0.320636	+	0.269046i
$633$		0			0
$634$	657.140	−	3726.83i	0.0411646	−	0.233456i
$635$	−242.605	+	1375.88i	−0.0151614	+	0.0859845i
$636$		0			0
$637$	19144.7	−	16064.3i	1.19080	−	0.999203i
$638$	10747.1	−	18614.4i	0.666897	−	1.15510i
$639$		0			0
$640$	872.156	+	1510.62i	0.0538671	+	0.0933006i
$641$	−13203.2	−	4805.57i	−0.813564	−	0.296113i	−0.0984690	−	0.995140i	$-0.531395\pi$
$641$	−13203.2	−	4805.57i	−0.813564	−	0.296113i	−0.715095	+	0.699027i	$0.753617\pi$
$642$		0			0
$643$	3488.66	+	2927.33i	0.213965	+	0.179538i	0.743471	−	0.668768i	$-0.233178\pi$
$643$	3488.66	+	2927.33i	0.213965	+	0.179538i	−0.529506	+	0.848306i	$0.677623\pi$
$644$	11987.0	−	4362.90i	0.733467	−	0.266960i
$645$		0			0
$646$	−1706.70	−	9679.18i	−0.103946	−	0.589508i
$647$	−23937.2			−1.45451			−0.727257	−	0.686366i	$-0.759205\pi$
$647$	−23937.2			−1.45451			−0.727257	+	0.686366i	$0.759205\pi$
$648$		0			0
$649$	1261.80			0.0763171
$650$	2416.86	+	13706.7i	0.145842	+	0.827108i
$651$		0			0
$652$	10846.1	−	3947.67i	0.651483	−	0.237120i
$653$	−9215.63	−	7732.83i	−0.552275	−	0.463414i	0.323436	−	0.946250i	$-0.395162\pi$
$653$	−9215.63	−	7732.83i	−0.552275	−	0.463414i	−0.875711	+	0.482836i	$0.839607\pi$
$654$		0			0
$655$	844.516	+	307.379i	0.0503786	+	0.0183363i
$656$	8454.68	+	14643.9i	0.503201	+	0.871570i
$657$		0			0
$658$	−30010.8	+	51980.2i	−1.77803	+	3.07963i
$659$	2768.22	−	2322.81i	0.163633	−	0.137305i	−0.557294	−	0.830315i	$-0.688160\pi$
$659$	2768.22	−	2322.81i	0.163633	−	0.137305i	0.720928	+	0.693010i	$0.243716\pi$
$660$		0			0
$661$	3903.14	−	22135.8i	0.229674	−	1.30254i	−0.623872	−	0.781527i	$-0.714441\pi$
$661$	3903.14	−	22135.8i	0.229674	−	1.30254i	0.853546	−	0.521018i	$-0.174448\pi$
$662$	3690.91	−	20932.2i	0.216694	−	1.22893i
$663$		0			0
$664$	2310.80	−	1938.99i	0.135055	−	0.113325i
$665$	2003.86	−	3470.79i	0.116852	−	0.202393i
$666$		0			0
$667$	−7922.05	−	13721.4i	−0.459885	−	0.796544i
$668$	−1961.14	−	713.798i	−0.113591	−	0.0413438i
$669$		0			0
$670$	−531.692	−	446.143i	−0.0306583	−	0.0257254i
$671$	−2677.84	+	974.654i	−0.154064	+	0.0560747i
$672$		0			0
$673$	816.402	+	4630.05i	0.0467608	+	0.265193i	0.999221	−	0.0394703i	$-0.0125670\pi$
$673$	816.402	+	4630.05i	0.0467608	+	0.265193i	−0.952460	+	0.304664i	$0.901456\pi$
$674$	−11850.6			−0.677251
$675$		0			0
$676$	−6988.22			−0.397600
$677$	−1514.97	−	8591.82i	−0.0860045	−	0.487756i	−0.997135	−	0.0756384i	$-0.975901\pi$
$677$	−1514.97	−	8591.82i	−0.0860045	−	0.487756i	0.911131	−	0.412117i	$-0.135211\pi$
$678$		0			0
$679$	1570.19	−	571.504i	0.0887460	−	0.0323009i
$680$	−398.708	−	334.555i	−0.0224849	−	0.0188671i
$681$		0			0
$682$	−13851.7	−	5041.59i	−0.777723	−	0.283068i
$683$	12790.4	+	22153.6i	0.716559	+	1.24112i	0.962355	+	0.271795i	$0.0876173\pi$
$683$	12790.4	+	22153.6i	0.716559	+	1.24112i	−0.245796	+	0.969322i	$0.579049\pi$
$684$		0			0
$685$	701.995	−	1215.89i	0.0391560	−	0.0678202i
$686$	−44881.3	+	37659.9i	−2.49793	+	2.09601i
$687$		0			0
$688$	−2755.12	+	15625.1i	−0.152672	+	0.865844i
$689$	−3941.54	+	22353.6i	−0.217940	+	1.23600i
$690$		0			0
$691$	−25192.3	+	21138.8i	−1.38692	+	1.16376i	−0.420346	+	0.907364i	$0.638091\pi$
$691$	−25192.3	+	21138.8i	−1.38692	+	1.16376i	−0.966571	+	0.256398i	$0.917464\pi$
$692$	−4798.53	+	8311.30i	−0.263602	+	0.456573i
$693$		0			0
$694$	6641.36	+	11503.2i	0.363260	+	0.629185i
$695$	−1408.24	−	512.556i	−0.0768596	−	0.0279746i
$696$		0			0
$697$	−6104.08	−	5121.93i	−0.331720	−	0.278346i
$698$	−6411.97	+	2333.77i	−0.347703	+	0.126554i
$699$		0			0
$700$	−4046.81	−	22950.6i	−0.218507	−	1.23922i
$701$	27261.0			1.46881			0.734404	−	0.678713i	$-0.237462\pi$
$701$	27261.0			1.46881			0.734404	+	0.678713i	$0.237462\pi$
$702$		0			0
$703$	13599.6			0.729615
$704$	742.120	+	4208.77i	0.0397297	+	0.225318i
$705$		0			0
$706$	−10783.4	+	3924.84i	−0.574843	+	0.209226i
$707$	28242.0	+	23697.8i	1.50233	+	1.26061i
$708$		0			0
$709$	15803.5	+	5752.02i	0.837115	+	0.304685i	0.724776	−	0.688985i	$-0.241943\pi$
$709$	15803.5	+	5752.02i	0.837115	+	0.304685i	0.112339	+	0.993670i	$0.464166\pi$
$710$	706.120	+	1223.04i	0.0373243	+	0.0646475i
$711$		0			0
$712$	4023.34	−	6968.63i	0.211771	−	0.366798i
$713$	−8323.73	+	6984.44i	−0.437204	+	0.366857i
$714$		0			0
$715$	−213.102	+	1208.56i	−0.0111462	+	0.0632134i
$716$	2944.72	−	16700.3i	0.153700	−	0.871676i
$717$		0			0
$718$	−18244.9	+	15309.3i	−0.948321	+	0.795736i
$719$	8119.01	−	14062.5i	0.421124	−	0.729408i	−0.574926	−	0.818206i	$-0.694969\pi$
$719$	8119.01	−	14062.5i	0.421124	−	0.729408i	0.996050	+	0.0887976i	$0.0283024\pi$
$720$		0			0
$721$	9685.30	+	16775.4i	0.500277	+	0.866504i
$722$	−5286.03	−	1923.96i	−0.272473	−	0.0991721i
$723$		0			0
$724$	−288.353	−	241.957i	−0.0148019	−	0.0124203i
$725$	−27200.2	+	9900.08i	−1.39337	+	0.507144i
$726$		0			0
$727$	946.455	+	5367.62i	0.0482835	+	0.273829i	0.999386	−	0.0350472i	$-0.0111582\pi$
$727$	946.455	+	5367.62i	0.0482835	+	0.273829i	−0.951102	+	0.308876i	$0.900047\pi$
$728$	9246.38			0.470733
$729$		0			0
$730$	−274.702			−0.0139277
$731$	−1298.32	−	7363.11i	−0.0656907	−	0.372551i
$732$		0			0
$733$	−9511.13	+	3461.77i	−0.479266	+	0.174438i	−0.570345	−	0.821405i	$-0.693190\pi$
$733$	−9511.13	+	3461.77i	−0.479266	+	0.174438i	0.0910795	+	0.995844i	$0.470968\pi$
$734$	14749.5	+	12376.3i	0.741707	+	0.622366i
$735$		0			0
$736$	13530.7	+	4924.76i	0.677646	+	0.246643i
$737$	1434.77	+	2485.09i	0.0717101	+	0.124206i
$738$		0			0
$739$	458.883	−	794.808i	0.0228421	−	0.0395636i	−0.854378	−	0.519651i	$-0.826062\pi$
$739$	458.883	−	794.808i	0.0228421	−	0.0395636i	0.877220	+	0.480088i	$0.159395\pi$
$740$	−1291.98	+	1084.10i	−0.0641813	+	0.0538545i
$741$		0			0
$742$	16017.7	−	90840.8i	0.792490	−	4.49444i
$743$	−2387.92	+	13542.6i	−0.117906	+	0.668680i	0.867364	+	0.497674i	$0.165813\pi$
$743$	−2387.92	+	13542.6i	−0.117906	+	0.668680i	−0.985270	+	0.171005i	$0.945299\pi$
$744$		0			0
$745$	2077.11	−	1742.90i	0.102147	−	0.0857113i
$746$	10692.8	−	18520.4i	0.524785	−	0.908955i
$747$		0			0
$748$	−2519.63	−	4364.14i	−0.123164	−	0.213327i
$749$	−11498.3	−	4185.04i	−0.560934	−	0.204163i
$750$		0			0
$751$	17179.0	+	14414.9i	0.834713	+	0.700407i	0.956368	−	0.292165i	$-0.0943758\pi$
$751$	17179.0	+	14414.9i	0.834713	+	0.700407i	−0.121655	+	0.992572i	$0.538820\pi$
$752$	−34853.5	+	12685.6i	−1.69013	+	0.615156i
$753$		0			0
$754$	4670.33	+	26486.8i	0.225575	+	1.27930i
$755$	−3977.53			−0.191732
$756$		0			0
$757$	5900.33			0.283291			0.141645	−	0.989917i	$-0.454761\pi$
$757$	5900.33			0.283291			0.141645	+	0.989917i	$0.454761\pi$
$758$	8190.16	+	46448.7i	0.392454	+	2.22572i
$759$		0			0
$760$	979.079	−	356.356i	0.0467302	−	0.0170084i
$761$	−8512.89	−	7143.17i	−0.405509	−	0.340262i	0.417110	−	0.908856i	$-0.363043\pi$
$761$	−8512.89	−	7143.17i	−0.405509	−	0.340262i	−0.822618	+	0.568594i	$0.807488\pi$
$762$		0			0
$763$	−28579.9	−	10402.2i	−1.35605	−	0.493560i
$764$	2834.83	+	4910.06i	0.134241	+	0.232513i
$765$		0			0
$766$	−6895.44	+	11943.3i	−0.325251	+	0.563352i
$767$	−1209.49	+	1014.88i	−0.0569388	+	0.0477773i
$768$		0			0
$769$	1394.16	−	7906.68i	0.0653767	−	0.370770i	−0.934513	−	0.355929i	$-0.884165\pi$
$769$	1394.16	−	7906.68i	0.0653767	−	0.370770i	0.999890	−	0.0148412i	$-0.00472428\pi$
$770$	866.005	−	4911.36i	0.0405307	−	0.229861i
$771$		0			0
$772$	860.932	−	722.408i	0.0401368	−	0.0336788i
$773$	−661.004	+	1144.89i	−0.0307564	+	0.0532716i	−0.880994	−	0.473128i	$-0.843125\pi$
$773$	−661.004	+	1144.89i	−0.0307564	+	0.0532716i	0.850238	+	0.526399i	$0.176458\pi$
$774$		0			0
$775$	9925.52	+	17191.5i	0.460045	+	0.796822i
$776$	408.213	+	148.577i	0.0188840	+	0.00687322i
$777$		0			0
$778$	16048.3	+	13466.1i	0.739535	+	0.620544i
$779$	14989.4	−	5455.69i	0.689410	−	0.250925i
$780$		0			0
$781$	−1013.87	−	5749.97i	−0.0464524	−	0.263444i
$782$	−9015.45			−0.412266
$783$		0			0
$784$	−62759.9			−2.85896
$785$	−781.552	−	4432.40i	−0.0355347	−	0.201528i
$786$		0			0
$787$	−10920.8	+	3974.85i	−0.494644	+	0.180036i	−0.577284	−	0.816544i	$-0.695887\pi$
$787$	−10920.8	+	3974.85i	−0.494644	+	0.180036i	0.0826393	+	0.996580i	$0.473665\pi$
$788$	−11825.9	−	9923.14i	−0.534621	−	0.448600i
$789$		0			0
$790$	−4217.52	−	1535.05i	−0.189940	−	0.0691324i
$791$	−910.812	−	1577.57i	−0.0409415	−	0.0709128i
$792$		0			0
$793$	1782.90	−	3088.07i	0.0798394	−	0.138286i
$794$	22239.0	−	18660.7i	0.993994	−	0.834060i
$795$		0			0
$796$	−4663.45	+	26447.7i	−0.207653	+	1.17766i
$797$	5708.00	−	32371.7i	0.253686	−	1.43872i	−0.545737	−	0.837956i	$-0.683750\pi$
$797$	5708.00	−	32371.7i	0.253686	−	1.43872i	0.799423	−	0.600768i	$-0.205139\pi$
$798$		0			0
$799$	13389.2	−	11234.8i	0.592834	−	0.497447i
$800$	13152.9	−	22781.6i	0.581283	−	1.00681i
$801$		0			0
$802$	−23133.2	−	40067.8i	−1.01853	−	1.76414i
$803$	1067.22	+	388.436i	0.0469008	+	0.0170705i
$804$		0			0
$805$	−2816.13	−	2363.01i	−0.123299	−	0.103460i
$806$	17332.4	−	6308.49i	0.757456	−	0.275691i
$807$		0			0
$808$	1664.35	+	9439.00i	0.0724649	+	0.410969i
$809$	19325.6			0.839865			0.419932	−	0.907555i	$-0.362054\pi$
$809$	19325.6			0.839865			0.419932	+	0.907555i	$0.362054\pi$
$810$		0			0
$811$	20360.2			0.881556			0.440778	−	0.897616i	$-0.354703\pi$
$811$	20360.2			0.881556			0.440778	+	0.897616i	$0.354703\pi$
$812$	−7820.05	−	44349.7i	−0.337968	−	1.91671i
$813$		0			0
$814$	15902.5	−	5788.03i	0.684744	−	0.249226i
$815$	−2548.11	−	2138.12i	−0.109517	−	0.0918956i
$816$		0			0
$817$	14064.6	+	5119.09i	0.602274	+	0.219210i
$818$	−14790.6	−	25618.1i	−0.632202	−	1.09501i
$819$		0			0
$820$	−989.106	+	1713.18i	−0.0421233	+	0.0729596i
$821$	−15151.1	+	12713.3i	−0.644064	+	0.540434i	−0.905263	−	0.424851i	$-0.860326\pi$
$821$	−15151.1	+	12713.3i	−0.644064	+	0.540434i	0.261200	+	0.965285i	$0.415882\pi$
$822$		0			0
$823$	4602.09	−	26099.8i	0.194920	−	1.10544i	−0.717613	−	0.696442i	$-0.754765\pi$
$823$	4602.09	−	26099.8i	0.194920	−	1.10544i	0.912533	−	0.409003i	$-0.134123\pi$
$824$	−874.474	+	4959.39i	−0.0369706	+	0.209671i
$825$		0			0
$826$	4915.13	−	4124.28i	0.207045	−	0.173731i
$827$	−9829.63	+	17025.4i	−0.413313	+	0.715879i	−0.995250	−	0.0973550i	$-0.968962\pi$
$827$	−9829.63	+	17025.4i	−0.413313	+	0.715879i	0.581937	+	0.813234i	$0.302295\pi$
$828$		0			0
$829$	23296.2	+	40350.2i	0.976007	+	1.69049i	0.676571	+	0.736378i	$0.263465\pi$
$829$	23296.2	+	40350.2i	0.976007	+	1.69049i	0.299436	+	0.954116i	$0.403201\pi$
$830$	1913.07	+	696.301i	0.0800044	+	0.0291192i
$831$		0			0
$832$	−4096.53	−	3437.39i	−0.170699	−	0.143233i
$833$	27791.2	−	10115.2i	1.15595	−	0.420732i
$834$		0			0
$835$	104.440	+	592.311i	0.00432852	+	0.0245482i
$836$	10087.9			0.417340
$837$		0			0
$838$	57110.4			2.35423
$839$	−5314.48	−	30139.9i	−0.218684	−	1.24022i	−0.874397	−	0.485211i	$-0.838743\pi$
$839$	−5314.48	−	30139.9i	−0.218684	−	1.24022i	0.655713	−	0.755010i	$-0.272368\pi$
$840$		0			0
$841$	−29643.5	+	10789.4i	−1.21545	+	0.442386i
$842$	10849.1	+	9103.45i	0.444042	+	0.372596i
$843$		0			0
$844$	−5166.99	−	1880.63i	−0.210729	−	0.0766991i
$845$	1006.96	+	1744.10i	0.0409946	+	0.0710047i
$846$		0			0
$847$	12294.7	−	21295.0i	0.498760	−	0.863877i
$848$	43665.3	−	36639.6i	1.76825	−	1.48374i
$849$		0			0
$850$	−2860.07	+	16220.3i	−0.115411	+	0.654530i
$851$	2166.19	−	12285.1i	0.0872576	−	0.494862i
$852$		0			0
$853$	27195.3	−	22819.6i	1.09162	−	0.915977i	0.0947855	−	0.995498i	$-0.469783\pi$
$853$	27195.3	−	22819.6i	1.09162	−	0.915977i	0.996833	+	0.0795209i	$0.0253390\pi$
$854$	−7245.37	+	12549.3i	−0.290318	+	0.502845i
$855$		0			0
$856$	−1590.57	−	2754.94i	−0.0635099	−	0.110002i
$857$	−4997.32	−	1818.88i	−0.199189	−	0.0724990i	0.240499	−	0.970649i	$-0.422689\pi$
$857$	−4997.32	−	1818.88i	−0.199189	−	0.0724990i	−0.439688	+	0.898150i	$0.644911\pi$
$858$		0			0
$859$	18040.0	+	15137.3i	0.716549	+	0.601256i	0.926428	−	0.376471i	$-0.122863\pi$
$859$	18040.0	+	15137.3i	0.716549	+	0.601256i	−0.209879	+	0.977727i	$0.567307\pi$
$860$	−1744.22	+	634.846i	−0.0691599	+	0.0251722i
$861$		0			0
$862$	−2768.91	−	15703.3i	−0.109408	−	0.620482i
$863$	−41574.3			−1.63987			−0.819934	−	0.572459i	$-0.805990\pi$
$863$	−41574.3			−1.63987			−0.819934	+	0.572459i	$0.805990\pi$
$864$		0			0
$865$	2765.75			0.108715
$866$	5231.40	+	29668.7i	0.205277	+	1.16419i
$867$		0			0
$868$	−29021.6	+	10563.0i	−1.13486	+	0.413055i
$869$	14214.5	+	11927.3i	0.554882	+	0.465601i
$870$		0			0
$871$	−3374.08	−	1228.07i	−0.131259	−	0.0477743i
$872$	−3953.48	−	6847.62i	−0.153534	−	0.265929i
$873$		0			0
$874$	9023.79	−	15629.7i	0.349238	−	0.604898i
$875$	−10399.4	+	8726.13i	−0.401787	+	0.337140i
$876$		0			0
$877$	−7829.92	+	44405.7i	−0.301480	+	1.70978i	0.338149	+	0.941093i	$0.390199\pi$
$877$	−7829.92	+	44405.7i	−0.301480	+	1.70978i	−0.639629	+	0.768684i	$0.720912\pi$
$878$	−4747.34	+	26923.5i	−0.182477	+	1.03488i
$879$		0			0
$880$	2360.79	−	1980.94i	0.0904343	−	0.0758834i
$881$	−24958.3	+	43229.1i	−0.954446	+	1.65315i	−0.218815	+	0.975766i	$0.570219\pi$
$881$	−24958.3	+	43229.1i	−0.954446	+	1.65315i	−0.735631	+	0.677382i	$0.763114\pi$
$882$		0			0
$883$	−17926.2	−	31049.0i	−0.683197	−	1.18333i	−0.974000	−	0.226549i	$-0.927256\pi$
$883$	−17926.2	−	31049.0i	−0.683197	−	1.18333i	0.290803	−	0.956783i	$-0.406078\pi$
$884$	5925.32	+	2156.64i	0.225441	+	0.0820539i
$885$		0			0
$886$	20025.1	+	16803.0i	0.759318	+	0.637143i
$887$	8119.60	−	2955.29i	0.307361	−	0.111870i	−0.183734	−	0.982976i	$-0.558819\pi$
$887$	8119.60	−	2955.29i	0.307361	−	0.111870i	0.491096	+	0.871105i	$0.336596\pi$
$888$		0			0
$889$	−5100.31	−	28925.3i	−0.192417	−	1.09125i
$890$	5430.67			0.204535
$891$		0			0
$892$	2609.37			0.0979465
$893$	6075.76	+	34457.4i	0.227679	+	1.29123i
$894$		0			0
$895$	−4592.34	+	1671.47i	−0.171514	+	0.0624259i
$896$	−28091.5	−	23571.6i	−1.04740	−	0.878874i
$897$		0			0
$898$	39048.1	+	14212.3i	1.45106	+	0.528143i
$899$	19180.1	+	33220.8i	0.711558	+	1.23245i
$900$		0			0
$901$	−13430.5	+	23262.3i	−0.496598	+	0.860132i
$902$	15205.6	−	12759.0i	0.561299	−	0.470985i
$903$		0			0
$904$	82.2361	−	466.384i	0.00302559	−	0.0171590i
$905$	−18.8372	+	106.831i	−0.000691900	+	0.00392396i
$906$		0			0
$907$	−17043.7	+	14301.3i	−0.623953	+	0.523559i	−0.899043	−	0.437860i	$-0.855737\pi$
$907$	−17043.7	+	14301.3i	−0.623953	+	0.523559i	0.275090	+	0.961418i	$0.411292\pi$
$908$	−13185.8	+	22838.4i	−0.481922	+	0.834713i
$909$		0			0
$910$	3120.17	+	5404.30i	0.113662	+	0.196869i
$911$	29787.0	+	10841.6i	1.08330	+	0.394289i	0.821135	−	0.570734i	$-0.193341\pi$
$911$	29787.0	+	10841.6i	1.08330	+	0.394289i	0.262165	+	0.965023i	$0.415564\pi$
$912$		0			0
$913$	−6447.70	−	5410.26i	−0.233721	−	0.196116i
$914$	6977.40	−	2539.56i	0.252507	−	0.0919052i
$915$		0			0
$916$	1526.52	+	8657.30i	0.0550628	+	0.312277i
$917$	−18893.8			−0.680401
$918$		0			0
$919$	−47605.4			−1.70877			−0.854384	−	0.519642i	$-0.826065\pi$
$919$	−47605.4			−1.70877			−0.854384	+	0.519642i	$0.826065\pi$
$920$	−165.960	−	941.204i	−0.00594731	−	0.0337289i
$921$		0			0
$922$	46113.2	−	16783.8i	1.64713	−	0.599507i
$923$	5596.63	+	4696.13i	0.199583	+	0.167470i
$924$		0			0
$925$	−21415.7	−	7794.67i	−0.761236	−	0.277067i
$926$	−32917.7	−	57015.2i	−1.16819	−	2.02336i
$927$		0			0
$928$	25416.7	−	44023.0i	0.899078	−	1.55725i
$929$	33532.8	−	28137.3i	1.18426	−	0.993709i	0.184315	−	0.982867i	$-0.440993\pi$
$929$	33532.8	−	28137.3i	1.18426	−	0.993709i	0.999941	−	0.0108420i	$-0.00345117\pi$
$930$		0			0
$931$	−10280.7	+	58304.8i	−0.361908	+	2.05248i
$932$	−5605.43	+	31790.0i	−0.197008	+	1.11729i
$933$		0			0
$934$	−28769.5	+	24140.5i	−1.00789	+	0.845718i
$935$	−726.127	+	1257.69i	−0.0253977	+	0.0439902i
$936$		0			0
$937$	−14470.7	−	25064.0i	−0.504522	−	0.873857i	−0.999986	−	0.00522921i	$-0.998335\pi$
$937$	−14470.7	−	25064.0i	−0.504522	−	0.873857i	0.495465	−	0.868628i	$-0.334998\pi$
$938$	13711.6	+	4990.62i	0.477293	+	0.173720i
$939$		0			0
$940$	−3323.99	−	2789.16i	−0.115337	−	0.0967791i
$941$	−40949.4	+	14904.4i	−1.41861	+	0.516332i	−0.933644	−	0.358202i	$-0.883390\pi$
$941$	−40949.4	+	14904.4i	−1.41861	+	0.516332i	−0.484965	+	0.874533i	$0.661168\pi$
$942$		0			0
$943$	−2540.79	−	14409.5i	−0.0877406	−	0.497602i
$944$	3964.92			0.136702
$945$		0			0
$946$	18624.9			0.640113
$947$	671.678	+	3809.28i	0.0230482	+	0.130713i	0.994161	−	0.107909i	$-0.0344155\pi$
$947$	671.678	+	3809.28i	0.0230482	+	0.130713i	−0.971113	+	0.238622i	$0.923304\pi$
$948$		0			0
$949$	−1335.40	+	486.046i	−0.0456786	+	0.0166256i
$950$	−25257.6	−	21193.6i	−0.862594	−	0.723803i
$951$		0			0
$952$	10282.1	+	3742.39i	0.350048	+	0.127407i
$953$	−15695.5	−	27185.4i	−0.533502	−	0.924053i	−0.999234	−	0.0391271i	$-0.987542\pi$
$953$	−15695.5	−	27185.4i	−0.533502	−	0.924053i	0.465732	−	0.884926i	$-0.345791\pi$
$954$		0			0
$955$	816.961	−	1415.02i	0.0276819	−	0.0479465i
$956$	−13832.4	+	11606.8i	−0.467963	+	0.392668i
$957$		0			0
$958$	−1974.62	+	11198.6i	−0.0665940	+	0.377673i
$959$	−5125.44	+	29067.8i	−0.172585	+	0.978779i
$960$		0			0
$961$	−2668.67	+	2239.28i	−0.0895798	+	0.0751664i
$962$	−10587.8	+	18338.7i	−0.354850	+	0.614618i
$963$		0			0
$964$	7623.18	+	13203.7i	0.254695	+	0.441145i
$965$	−304.352	−	110.775i	−0.0101528	−	0.00369531i
$966$		0			0
$967$	−19725.0	−	16551.3i	−0.655960	−	0.550416i	0.252913	−	0.967489i	$-0.418612\pi$
$967$	−19725.0	−	16551.3i	−0.655960	−	0.550416i	−0.908873	+	0.417073i	$0.863056\pi$
$968$	6007.11	−	2186.41i	0.199459	−	0.0725970i
$969$		0			0
$970$	50.9106	+	288.728i	0.00168520	+	0.00955722i
$971$	28752.1			0.950258			0.475129	−	0.879916i	$-0.342401\pi$
$971$	28752.1			0.950258			0.475129	+	0.879916i	$0.342401\pi$
$972$		0			0
$973$	31505.5			1.03805
$974$	−949.670	−	5385.85i	−0.0312417	−	0.177180i
$975$		0			0
$976$	−8414.52	+	3062.63i	−0.275965	+	0.100443i
$977$	3165.04	+	2655.78i	0.103642	+	0.0869663i	0.693136	−	0.720806i	$-0.256228\pi$
$977$	3165.04	+	2655.78i	0.103642	+	0.0869663i	−0.589494	+	0.807773i	$0.700673\pi$
$978$		0			0
$979$	−21098.2	−	7679.10i	−0.688764	−	0.250690i
$980$	−3671.11	−	6358.55i	−0.119663	−	0.207262i
$981$		0			0
$982$	−14605.8	+	25298.0i	−0.474633	+	0.822088i
$983$	−5353.10	+	4491.78i	−0.173690	+	0.145743i	−0.725489	−	0.688234i	$-0.758386\pi$
$983$	−5353.10	+	4491.78i	−0.173690	+	0.145743i	0.551799	+	0.833977i	$0.313942\pi$
$984$		0			0
$985$	−772.550	+	4381.35i	−0.0249904	+	0.141727i
$986$	−5526.80	+	31344.0i	−0.178508	+	1.01237i
$987$		0			0
$988$	−9669.66	+	8113.81i	−0.311369	+	0.261270i
$989$	6864.55	−	11889.7i	0.220708	−	0.382277i
$990$		0			0
$991$	−11482.3	−	19888.0i	−0.368060	−	0.637499i	0.621202	−	0.783651i	$-0.286645\pi$
$991$	−11482.3	−	19888.0i	−0.368060	−	0.637499i	−0.989262	+	0.146151i	$0.953311\pi$
$992$	−32759.1	−	11923.3i	−1.04849	−	0.381619i
$993$		0			0
$994$	−22743.6	−	19084.2i	−0.725738	−	0.608967i
$995$	7272.73	−	2647.06i	0.231720	−	0.0843391i
$996$		0			0
$997$	308.481	+	1749.48i	0.00979910	+	0.0555735i	0.989315	−	0.145792i	$-0.0465731\pi$
$997$	308.481	+	1749.48i	0.00979910	+	0.0555735i	−0.979516	+	0.201366i	$0.935462\pi$
$998$	30100.1			0.954713
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.4.e.a.10.2		48
3.2	odd	2		27.4.e.a.13.7	✓	48
9.2	odd	6		243.4.e.c.109.7		48
9.4	even	3		243.4.e.a.190.7		48
9.5	odd	6		243.4.e.d.190.2		48
9.7	even	3		243.4.e.b.109.2		48
27.2	odd	18		27.4.e.a.25.7	yes	48
27.5	odd	18		729.4.a.d.1.20		24
27.7	even	9		243.4.e.b.136.2		48
27.11	odd	18		243.4.e.d.55.2		48
27.16	even	9		243.4.e.a.55.7		48
27.20	odd	18		243.4.e.c.136.7		48
27.22	even	9		729.4.a.c.1.5		24
27.25	even	9	inner	81.4.e.a.73.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.7	✓	48	3.2	odd	2
27.4.e.a.25.7	yes	48	27.2	odd	18
81.4.e.a.10.2		48	1.1	even	1	trivial
81.4.e.a.73.2		48	27.25	even	9	inner
243.4.e.a.55.7		48	27.16	even	9
243.4.e.a.190.7		48	9.4	even	3
243.4.e.b.109.2		48	9.7	even	3
243.4.e.b.136.2		48	27.7	even	9
243.4.e.c.109.7		48	9.2	odd	6
243.4.e.c.136.7		48	27.20	odd	18
243.4.e.d.55.2		48	27.11	odd	18
243.4.e.d.190.2		48	9.5	odd	6
729.4.a.c.1.5		24	27.22	even	9
729.4.a.d.1.20		24	27.5	odd	18

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.640527 - 3.63261i) q^{2} +(-5.26804 + 1.91741i) q^{4} +(1.23763 + 1.03850i) q^{5} +(-31.9169 - 11.6168i) q^{7} +(-4.41508 - 7.64714i) q^{8} +(2.97972 - 5.16102i) q^{10} +(-18.8740 + 15.8372i) q^{11} +(5.35351 - 30.3613i) q^{13} +(-21.7557 + 123.382i) q^{14} +(-59.3074 + 49.7648i) q^{16} +(18.2417 - 31.5955i) q^{17} +(36.5170 + 63.2494i) q^{19} +(-8.51112 - 3.09779i) q^{20} +(69.6196 + 58.4178i) q^{22} +(62.9523 - 22.9128i) q^{23} +(-21.2528 - 120.530i) q^{25} -113.720 q^{26} +190.413 q^{28} +(-41.0688 - 232.913i) q^{29} +(-152.414 + 55.4740i) q^{31} +(164.650 + 138.158i) q^{32} +(-126.458 - 46.0271i) q^{34} +(-27.4374 - 47.5229i) q^{35} +(93.1046 - 161.262i) q^{37} +(206.370 - 173.165i) q^{38} +(2.47729 - 14.0494i) q^{40} +(37.9265 - 215.092i) q^{41} +(156.989 - 131.730i) q^{43} +(69.0627 - 119.620i) q^{44} +(-123.556 - 214.005i) q^{46} +(450.185 + 163.854i) q^{47} +(620.985 + 521.068i) q^{49} +(-424.227 + 154.406i) q^{50} +(30.0125 + 170.209i) q^{52} -736.254 q^{53} -39.8060 q^{55} +(52.0803 + 295.362i) q^{56} +(-819.775 + 298.374i) q^{58} +(-39.2313 - 32.9190i) q^{59} +(108.686 + 39.5585i) q^{61} +(299.141 + 518.127i) q^{62} +(86.7288 - 150.219i) q^{64} +(38.1558 - 32.0165i) q^{65} +(20.2242 - 114.697i) q^{67} +(-35.5163 + 201.423i) q^{68} +(-155.058 + 130.109i) q^{70} +(-118.488 + 205.227i) q^{71} +(-23.0477 - 39.9198i) q^{73} +(-645.437 - 234.920i) q^{74} +(-313.648 - 263.182i) q^{76} +(786.377 - 286.218i) q^{77} +(-130.778 - 741.681i) q^{79} -125.081 q^{80} -805.637 q^{82} +(59.3213 + 336.428i) q^{83} +(55.3883 - 20.1597i) q^{85} +(-579.078 - 485.904i) q^{86} +(204.439 + 74.4099i) q^{88} +(455.636 + 789.185i) q^{89} +(-523.568 + 906.847i) q^{91} +(-287.702 + 241.411i) q^{92} +(306.862 - 1740.30i) q^{94} +(-20.4896 + 116.202i) q^{95} +(-37.6866 + 31.6228i) q^{97} +(1495.08 - 2589.55i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{2} - 6 q^{4} - 6 q^{5} - 6 q^{7} + 75 q^{8} - 3 q^{10} - 57 q^{11} - 6 q^{13} - 51 q^{14} + 18 q^{16} + 207 q^{17} - 3 q^{19} + 597 q^{20} - 60 q^{22} - 402 q^{23} - 222 q^{25} - 1914 q^{26}+ \cdots + 4392 q^{98}+O(q^{100}) \) 48 * q + 6 * q^2 - 6 * q^4 - 6 * q^5 - 6 * q^7 + 75 * q^8 - 3 * q^10 - 57 * q^11 - 6 * q^13 - 51 * q^14 + 18 * q^16 + 207 * q^17 - 3 * q^19 + 597 * q^20 - 60 * q^22 - 402 * q^23 - 222 * q^25 - 1914 * q^26 - 12 * q^28 - 480 * q^29 - 60 * q^31 + 648 * q^32 + 288 * q^34 + 1257 * q^35 - 3 * q^37 + 1524 * q^38 + 561 * q^40 + 1731 * q^41 + 507 * q^43 + 2211 * q^44 - 3 * q^46 - 984 * q^47 - 600 * q^49 - 4359 * q^50 - 1431 * q^52 - 2736 * q^53 - 12 * q^55 - 5907 * q^56 - 897 * q^58 - 2238 * q^59 + 48 * q^61 + 2118 * q^62 - 195 * q^64 + 6990 * q^65 - 681 * q^67 + 11169 * q^68 - 33 * q^70 + 3105 * q^71 - 219 * q^73 - 3543 * q^74 + 3426 * q^76 - 4722 * q^77 + 2802 * q^79 - 9870 * q^80 - 12 * q^82 - 3468 * q^83 + 2529 * q^85 - 3624 * q^86 + 2850 * q^88 + 5202 * q^89 + 267 * q^91 + 18453 * q^92 - 1653 * q^94 + 10113 * q^95 - 3381 * q^97 + 4392 * q^98

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