LMFDB - Embedded newform 243.4.e.c.109.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,4,Mod(28,243)] 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("243.28"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,3,0,3,-21] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$14.3374641314$
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			109.7
Character	$\chi$	$=$	243.109
Dual form			243.4.e.c.136.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.82567 - 2.37102i) q^{2} +(0.973494 - 5.52096i) q^{4} +(1.51818 - 0.552573i) q^{5} +(5.89800 + 33.4492i) q^{7} +(4.41508 + 7.64714i) q^{8} +(2.97972 - 5.16102i) q^{10} +(-23.1524 - 8.42679i) q^{11} +(23.6169 + 19.8169i) q^{13} +(95.9745 + 80.5322i) q^{14} +(72.7513 + 26.4793i) q^{16} +(-18.2417 + 31.5955i) q^{17} +(36.5170 + 63.2494i) q^{19} +(-1.57279 - 8.91974i) q^{20} +(-85.4011 + 31.0835i) q^{22} +(11.6331 - 65.9747i) q^{23} +(-93.7560 + 78.6706i) q^{25} +113.720 q^{26} +190.413 q^{28} +(181.174 - 152.023i) q^{29} +(28.1649 - 159.731i) q^{31} +(201.973 - 73.5122i) q^{32} +(23.3685 + 132.530i) q^{34} +(27.4374 + 47.5229i) q^{35} +(93.1046 - 161.262i) q^{37} +(253.150 + 92.1392i) q^{38} +(10.9285 + 9.17009i) q^{40} +(-167.312 - 140.391i) q^{41} +(-192.576 - 70.0918i) q^{43} +(-69.0627 + 119.620i) q^{44} +(-123.556 - 214.005i) q^{46} +(83.1908 + 471.798i) q^{47} +(-761.751 + 277.255i) q^{49} +(-78.3940 + 444.594i) q^{50} +(132.399 - 111.096i) q^{52} +736.254 q^{53} -39.8060 q^{55} +(-229.751 + 192.784i) q^{56} +(151.488 - 859.133i) q^{58} +(-48.1243 + 17.5158i) q^{59} +(-20.0844 - 113.904i) q^{61} +(-299.141 - 518.127i) q^{62} +(86.7288 - 150.219i) q^{64} +(46.8050 + 17.0356i) q^{65} +(89.2186 + 74.8633i) q^{67} +(156.679 + 131.469i) q^{68} +(190.207 + 69.2296i) q^{70} +(118.488 - 205.227i) q^{71} +(-23.0477 - 39.9198i) q^{73} +(-119.272 - 676.425i) q^{74} +(384.746 - 140.036i) q^{76} +(145.317 - 824.132i) q^{77} +(-576.926 + 484.098i) q^{79} +125.081 q^{80} -805.637 q^{82} +(-261.694 + 219.588i) q^{83} +(-10.2353 + 58.0475i) q^{85} +(-710.344 + 258.544i) q^{86} +(-37.7789 - 214.255i) q^{88} +(-455.636 - 789.185i) q^{89} +(-523.568 + 906.847i) q^{91} +(-352.919 - 128.452i) q^{92} +(1353.71 + 1135.90i) q^{94} +(90.3894 + 75.8457i) q^{95} +(46.2294 + 16.8261i) q^{97} +(-1495.08 + 2589.55i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} - 159 q^{11} + 3 q^{13} - 336 q^{14} - 45 q^{16} - 207 q^{17} - 3 q^{19} + 681 q^{20} + 111 q^{22} + 33 q^{23} + 435 q^{25} + 1914 q^{26}+ \cdots - 4392 q^{98}+O(q^{100}) $ 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 - 159 * q^11 + 3 * q^13 - 336 * q^14 - 45 * q^16 - 207 * q^17 - 3 * q^19 + 681 * q^20 + 111 * q^22 + 33 * q^23 + 435 * q^25 + 1914 * q^26 - 12 * q^28 - 51 * q^29 + 111 * q^31 + 1647 * q^32 - 513 * q^34 - 1257 * q^35 - 3 * q^37 - 525 * q^38 - 6 * q^40 + 447 * q^41 + 516 * q^43 - 2211 * q^44 - 3 * q^46 + 2109 * q^47 - 591 * q^49 - 4938 * q^50 - 1350 * q^52 + 2736 * q^53 - 12 * q^55 - 7773 * q^56 - 888 * q^58 + 3048 * q^59 + 57 * q^61 - 2118 * q^62 - 195 * q^64 + 3297 * q^65 + 2082 * q^67 + 3573 * q^68 + 1524 * q^70 - 3105 * q^71 - 219 * q^73 + 9006 * q^74 - 1425 * q^76 - 8985 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 - 8511 * q^83 - 1827 * q^85 + 12507 * q^86 - 3693 * q^88 - 5202 * q^89 + 267 * q^91 + 5118 * q^92 - 2211 * q^94 + 5178 * q^95 + 1569 * q^97 - 4392 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	2.82567	−	2.37102i	0.999025	−	0.838281i	0.0121757	−	0.999926i	$-0.496124\pi$
$2$	2.82567	−	2.37102i	0.999025	−	0.838281i	0.986849	+	0.161645i	$0.0516798\pi$
$3$		0			0
$3$		0			0
$4$	0.973494	−	5.52096i	0.121687	−	0.690120i
$5$	1.51818	−	0.552573i	0.135790	−	0.0494236i	−0.273231	−	0.961948i	$-0.588092\pi$
$5$	1.51818	−	0.552573i	0.135790	−	0.0494236i	0.409021	+	0.912525i	$0.365870\pi$
$6$		0			0
$7$	5.89800	+	33.4492i	0.318462	+	1.80609i	0.552114	+	0.833769i	$0.313821\pi$
$7$	5.89800	+	33.4492i	0.318462	+	1.80609i	−0.233652	+	0.972320i	$0.575068\pi$
$8$	4.41508	+	7.64714i	0.195121	+	0.337959i
$9$		0			0
$10$	2.97972	−	5.16102i	0.0942269	−	0.163206i
$11$	−23.1524	−	8.42679i	−0.634610	−	0.230979i	0.00462630	−	0.999989i	$-0.498527\pi$
$11$	−23.1524	−	8.42679i	−0.634610	−	0.230979i	−0.639237	+	0.769010i	$0.720750\pi$
$12$		0			0
$13$	23.6169	+	19.8169i	0.503857	+	0.422786i	0.858961	−	0.512040i	$-0.171110\pi$
$13$	23.6169	+	19.8169i	0.503857	+	0.422786i	−0.355104	+	0.934827i	$0.615555\pi$
$14$	95.9745	+	80.5322i	1.83216	+	1.53737i
$15$		0			0
$16$	72.7513	+	26.4793i	1.13674	+	0.413739i
$17$	−18.2417	+	31.5955i	−0.260250	+	0.450766i	−0.966308	−	0.257387i	$-0.917138\pi$
$17$	−18.2417	+	31.5955i	−0.260250	+	0.450766i	0.706058	+	0.708154i	$0.250472\pi$
$18$		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	$0.687984\pi$
$20$	−1.57279	−	8.91974i	−0.0175843	−	0.0997257i
$21$		0			0
$22$	−85.4011	+	31.0835i	−0.827617	+	0.301228i
$23$	11.6331	−	65.9747i	0.105464	−	0.598116i	−0.885570	−	0.464506i	$-0.846232\pi$
$23$	11.6331	−	65.9747i	0.105464	−	0.598116i	0.991034	−	0.133610i	$-0.0426570\pi$
$24$		0			0
$25$	−93.7560	+	78.6706i	−0.750048	+	0.629365i
$26$	113.720			0.857780
$27$		0			0
$28$	190.413			1.28517
$29$	181.174	−	152.023i	1.16011	−	0.973447i	0.160202	−	0.987084i	$-0.448786\pi$
$29$	181.174	−	152.023i	1.16011	−	0.973447i	0.999907	+	0.0136374i	$0.00434106\pi$
$30$		0			0
$31$	28.1649	−	159.731i	0.163180	−	0.925437i	−0.787742	−	0.616005i	$-0.788750\pi$
$31$	28.1649	−	159.731i	0.163180	−	0.925437i	0.950922	−	0.309432i	$-0.100139\pi$
$32$	201.973	−	73.5122i	1.11575	−	0.406101i
$33$		0			0
$34$	23.3685	+	132.530i	0.117873	+	0.668490i
$35$	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	$0.0309086\pi$
$38$	253.150	+	92.1392i	1.08070	+	0.393341i
$39$		0			0
$40$	10.9285	+	9.17009i	0.0431987	+	0.0362480i
$41$	−167.312	−	140.391i	−0.637309	−	0.534766i	0.265881	−	0.964006i	$-0.414337\pi$
$41$	−167.312	−	140.391i	−0.637309	−	0.534766i	−0.903191	+	0.429240i	$0.858782\pi$
$42$		0			0
$43$	−192.576	−	70.0918i	−0.682966	−	0.248579i	−0.0228453	−	0.999739i	$-0.507273\pi$
$43$	−192.576	−	70.0918i	−0.682966	−	0.248579i	−0.660120	+	0.751160i	$0.729495\pi$
$44$	−69.0627	+	119.620i	−0.236627	+	0.409850i
$45$		0			0
$46$	−123.556	−	214.005i	−0.396029	−	0.685942i
$47$	83.1908	+	471.798i	0.258184	+	1.46423i	0.787767	+	0.615974i	$0.211237\pi$
$47$	83.1908	+	471.798i	0.258184	+	1.46423i	−0.529583	+	0.848258i	$0.677652\pi$
$48$		0			0
$49$	−761.751	+	277.255i	−2.22085	+	0.808322i
$50$	−78.3940	+	444.594i	−0.221732	+	1.25750i
$51$		0			0
$52$	132.399	−	111.096i	0.353086	−	0.296274i
$53$	736.254			1.90816			0.954078	−	0.299559i	$-0.0968396\pi$
$53$	736.254			1.90816			0.954078	+	0.299559i	$0.0968396\pi$
$54$		0			0
$55$	−39.8060			−0.0975898
$56$	−229.751	+	192.784i	−0.548246	+	0.460033i
$57$		0			0
$58$	151.488	−	859.133i	0.342955	−	1.94499i
$59$	−48.1243	+	17.5158i	−0.106191	+	0.0386503i	−0.394569	−	0.918866i	$-0.629106\pi$
$59$	−48.1243	+	17.5158i	−0.106191	+	0.0386503i	0.288378	+	0.957517i	$0.406884\pi$
$60$		0			0
$61$	−20.0844	−	113.904i	−0.0421564	−	0.239081i	0.956447	−	0.291905i	$-0.0942890\pi$
$61$	−20.0844	−	113.904i	−0.0421564	−	0.239081i	−0.998604	+	0.0528237i	$0.983178\pi$
$62$	−299.141	−	518.127i	−0.612756	−	1.06133i
$63$		0			0
$64$	86.7288	−	150.219i	0.169392	−	0.293396i
$65$	46.8050	+	17.0356i	0.0893145	+	0.0325078i
$66$		0			0
$67$	89.2186	+	74.8633i	0.162683	+	0.136507i	0.720495	−	0.693460i	$-0.243915\pi$
$67$	89.2186	+	74.8633i	0.162683	+	0.136507i	−0.557812	+	0.829967i	$0.688359\pi$
$68$	156.679	+	131.469i	0.279414	+	0.234456i
$69$		0			0
$70$	190.207	+	69.2296i	0.324772	+	0.118207i
$71$	118.488	−	205.227i	0.198055	−	0.343042i	−0.749843	−	0.661616i	$-0.769871\pi$
$71$	118.488	−	205.227i	0.198055	−	0.343042i	0.947898	+	0.318575i	$0.103204\pi$
$72$		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	$0.845098\pi$
$74$	−119.272	−	676.425i	−0.187366	−	1.06261i
$75$		0			0
$76$	384.746	−	140.036i	0.580703	−	0.211359i
$77$	145.317	−	824.132i	0.215070	−	1.21972i
$78$		0			0
$79$	−576.926	+	484.098i	−0.821635	+	0.689434i	−0.953354	−	0.301853i	$-0.902395\pi$
$79$	−576.926	+	484.098i	−0.821635	+	0.689434i	0.131719	+	0.991287i	$0.457950\pi$
$80$	125.081			0.174807
$81$		0			0
$82$	−805.637			−1.08497
$83$	−261.694	+	219.588i	−0.346081	+	0.290396i	−0.799214	−	0.601047i	$-0.794751\pi$
$83$	−261.694	+	219.588i	−0.346081	+	0.290396i	0.453133	+	0.891443i	$0.350306\pi$
$84$		0			0
$85$	−10.2353	+	58.0475i	−0.0130609	+	0.0740722i
$86$	−710.344	+	258.544i	−0.890679	+	0.324181i
$87$		0			0
$88$	−37.7789	−	214.255i	−0.0457641	−	0.259541i
$89$	−455.636	−	789.185i	−0.542667	−	0.939926i	−0.998750	−	0.0499890i	$-0.984081\pi$
$89$	−455.636	−	789.185i	−0.542667	−	0.939926i	0.456083	−	0.889937i	$-0.349252\pi$
$90$		0			0
$91$	−523.568	+	906.847i	−0.603131	+	1.04465i
$92$	−352.919	−	128.452i	−0.399938	−	0.145566i
$93$		0			0
$94$	1353.71	+	1135.90i	1.48537	+	1.24637i
$95$	90.3894	+	75.8457i	0.0976185	+	0.0819116i
$96$		0			0
$97$	46.2294	+	16.8261i	0.0483906	+	0.0176127i	0.366102	−	0.930575i	$-0.380692\pi$
$97$	46.2294	+	16.8261i	0.0483906	+	0.0176127i	−0.317711	+	0.948187i	$0.602914\pi$
$98$	−1495.08	+	2589.55i	−1.54108	+	2.66923i
$99$		0			0
$100$	343.066	+	594.208i	0.343066	+	0.594208i
$101$	−188.485	−	1068.95i	−0.185693	−	1.05311i	−0.925062	−	0.379815i	$-0.875988\pi$
$101$	−188.485	−	1068.95i	−0.185693	−	1.05311i	0.739370	−	0.673299i	$-0.235124\pi$
$102$		0			0
$103$	535.913	−	195.056i	0.512670	−	0.186597i	−0.0727137	−	0.997353i	$-0.523166\pi$
$103$	535.913	−	195.056i	0.512670	−	0.186597i	0.585384	+	0.810756i	$0.300944\pi$
$104$	−47.2724	+	268.095i	−0.0445715	+	0.252778i
$105$		0			0
$106$	2080.41	−	1745.67i	1.90629	−	1.59957i
$107$	−360.258			−0.325490			−0.162745	−	0.986668i	$-0.552035\pi$
$107$	−360.258			−0.325490			−0.162745	+	0.986668i	$0.552035\pi$
$108$		0			0
$109$	895.448			0.786866			0.393433	−	0.919353i	$-0.371287\pi$
$109$	895.448			0.786866			0.393433	+	0.919353i	$0.371287\pi$
$110$	−112.478	+	94.3807i	−0.0974946	+	0.0818077i
$111$		0			0
$112$	−456.626	+	2589.65i	−0.385242	+	2.18481i
$113$	50.3976	−	18.3432i	0.0419558	−	0.0152707i	−0.320957	−	0.947094i	$-0.604005\pi$
$113$	50.3976	−	18.3432i	0.0419558	−	0.0152707i	0.362913	+	0.931823i	$0.381782\pi$
$114$		0			0
$115$	−18.7946	−	106.590i	−0.0152401	−	0.0864308i
$116$	−662.941	−	1148.25i	−0.530625	−	0.919069i
$117$		0			0
$118$	−94.4530	+	163.597i	−0.0736874	+	0.127630i
$119$	−1164.43	−	423.819i	−0.897004	−	0.326483i
$120$		0			0
$121$	−554.582	−	465.349i	−0.416665	−	0.349624i
$122$	−326.821	−	274.235i	−0.242532	−	0.203509i
$123$		0			0
$124$	−854.450	−	310.994i	−0.618806	−	0.225227i
$125$	−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	$0.735644\pi$
$128$	187.481	+	1063.26i	0.129462	+	0.734214i
$129$		0			0
$130$	172.647	−	62.8384i	0.116478	−	0.0423946i
$131$	96.5950	−	547.817i	0.0644240	−	0.365367i	−0.935503	−	0.353318i	$-0.885053\pi$
$131$	96.5950	−	547.817i	0.0644240	−	0.365367i	0.999927	−	0.0120490i	$-0.00383541\pi$
$132$		0			0
$133$	−1900.27	+	1594.51i	−1.23890	+	1.03956i
$134$	429.604			0.276956
$135$		0			0
$136$	−322.153			−0.203121
$137$	665.703	−	558.591i	0.415145	−	0.348348i	−0.411168	−	0.911560i	$-0.634879\pi$
$137$	665.703	−	558.591i	0.415145	−	0.348348i	0.826312	+	0.563212i	$0.190435\pi$
$138$		0			0
$139$	161.073	−	913.488i	0.0982878	−	0.557418i	−0.895402	−	0.445258i	$-0.853112\pi$
$139$	161.073	−	913.488i	0.0982878	−	0.557418i	0.993690	−	0.112160i	$-0.0357769\pi$
$140$	289.082	−	105.217i	0.174514	−	0.0635177i
$141$		0			0
$142$	−151.789	−	860.840i	−0.0897033	−	0.508733i
$143$	−379.795	−	657.824i	−0.222098	−	0.384685i
$144$		0			0
$145$	191.051	−	330.910i	0.109420	−	0.189521i
$146$	−159.776	−	58.1536i	−0.0905693	−	0.0329645i
$147$		0			0
$148$	−799.683	−	671.014i	−0.444146	−	0.372682i
$149$	−1285.65	−	1078.78i	−0.706874	−	0.593138i	0.216846	−	0.976206i	$-0.430423\pi$
$149$	−1285.65	−	1078.78i	−0.706874	−	0.593138i	−0.923720	+	0.383068i	$0.874867\pi$
$150$		0			0
$151$	2313.46	+	842.031i	1.24680	+	0.453798i	0.879319	−	0.476233i	$-0.157998\pi$
$151$	2313.46	+	842.031i	1.24680	+	0.453798i	0.367480	+	0.930031i	$0.380220\pi$
$152$	−322.451	+	558.502i	−0.172067	+	0.298030i
$153$		0			0
$154$	−1543.41	−	2673.27i	−0.807609	−	1.39882i
$155$	−45.5036	−	258.064i	−0.0235803	−	0.133730i
$156$		0			0
$157$	2617.79	−	952.799i	1.33072	−	0.484342i	0.423841	−	0.905737i	$-0.360682\pi$
$157$	2617.79	−	952.799i	1.33072	−	0.484342i	0.906877	+	0.421395i	$0.138459\pi$
$158$	−482.396	+	2735.80i	−0.242894	+	1.37752i
$159$		0			0
$160$	266.011	−	223.210i	0.131438	−	0.110289i
$161$	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	$0.664711\pi$
$164$	−937.970	+	787.050i	−0.446605	+	0.374746i
$165$		0			0
$166$	−218.815	+	1240.96i	−0.102309	+	0.580226i
$167$	349.822	−	127.325i	0.162096	−	0.0589981i	−0.259698	−	0.965690i	$-0.583623\pi$
$167$	349.822	−	127.325i	0.162096	−	0.0589981i	0.421794	+	0.906692i	$0.361401\pi$
$168$		0			0
$169$	−216.458	−	1227.59i	−0.0985244	−	0.558760i
$170$	108.710	+	188.291i	0.0490451	+	0.0849487i
$171$		0			0
$172$	−574.445	+	994.968i	−0.254657	+	0.441079i
$173$	1608.65	+	585.501i	0.706956	+	0.257311i	0.670378	−	0.742020i	$-0.266132\pi$
$173$	1608.65	+	585.501i	0.706956	+	0.257311i	0.0365780	+	0.999331i	$0.488354\pi$
$174$		0			0
$175$	−3184.45	−	2672.07i	−1.37555	−	1.15422i
$176$	−1461.23	−	1226.12i	−0.625822	−	0.525127i
$177$		0			0
$178$	−3158.65	−	1149.65i	−1.33006	−	0.484102i
$179$	1512.45	−	2619.64i	0.631540	−	1.09386i	−0.355697	−	0.934601i	$-0.615757\pi$
$179$	1512.45	−	2619.64i	0.631540	−	1.09386i	0.987237	−	0.159258i	$-0.0509100\pi$
$180$		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	$0.828945\pi$
$182$	670.719	+	3803.84i	0.273171	+	1.54923i
$183$		0			0
$184$	555.879	−	202.323i	0.222717	−	0.0810624i
$185$	52.2407	−	296.272i	0.0207612	−	0.117742i
$186$		0			0
$187$	688.587	−	577.793i	0.269275	−	0.225949i
$188$	2685.76			1.04191
$189$		0			0
$190$	435.242			0.166188
$191$	774.725	−	650.071i	0.293493	−	0.246270i	−0.484137	−	0.874992i	$-0.660866\pi$
$191$	774.725	−	650.071i	0.293493	−	0.246270i	0.777630	+	0.628723i	$0.216422\pi$
$192$		0			0
$193$	34.8115	−	197.426i	0.0129833	−	0.0736322i	−0.977628	−	0.210343i	$-0.932542\pi$
$193$	34.8115	−	197.426i	0.0129833	−	0.0736322i	0.990611	+	0.136711i	$0.0436531\pi$
$194$	170.524	−	62.0657i	0.0631078	−	0.0229694i
$195$		0			0
$196$	789.151	+	4475.50i	0.287591	+	1.63101i
$197$	−1376.86	−	2384.79i	−0.497954	−	0.862482i	0.502043	−	0.864843i	$-0.332582\pi$
$197$	−1376.86	−	2384.79i	−0.497954	−	0.862482i	−0.999997	+	0.00236077i	$0.999249\pi$
$198$		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	$-0.158691\pi$
$200$	−1015.55	−	369.628i	−0.359050	−	0.130683i
$201$		0			0
$202$	−3067.10	−	2573.60i	−1.06832	−	0.896425i
$203$	6153.62	+	5163.50i	2.12758	+	1.78525i
$204$		0			0
$205$	−331.586	−	120.687i	−0.112970	−	0.0411179i
$206$	1051.83	−	1821.82i	0.355750	−	0.616177i
$207$		0			0
$208$	1193.42	+	2067.07i	0.397831	+	0.689064i
$209$	−312.469	−	1772.10i	−0.103416	−	0.586500i
$210$		0			0
$211$	−921.669	+	335.460i	−0.300712	+	0.109450i	−0.487970	−	0.872861i	$-0.662262\pi$
$211$	−921.669	+	335.460i	−0.300712	+	0.109450i	0.187257	+	0.982311i	$0.440040\pi$
$212$	716.738	−	4064.83i	0.232197	−	1.31686i
$213$		0			0
$214$	−1017.97	+	854.178i	−0.325173	+	0.272852i
$215$	−331.096			−0.105026
$216$		0			0
$217$	5509.00			1.72339
$218$	2530.24	−	2123.12i	0.786099	−	0.659615i
$219$		0			0
$220$	−38.7509	+	219.767i	−0.0118754	+	0.0673486i
$221$	−1056.94	+	384.693i	−0.321707	+	0.117092i
$222$		0			0
$223$	80.8246	+	458.379i	0.0242709	+	0.137647i	0.994535	−	0.104400i	$-0.0332922\pi$
$223$	80.8246	+	458.379i	0.0242709	+	0.137647i	−0.970264	+	0.242047i	$0.922181\pi$
$224$	3650.16	+	6322.27i	1.08878	+	1.88582i
$225$		0			0
$226$	98.9147	−	171.325i	0.0291138	−	0.0504265i
$227$	4420.37	+	1608.88i	1.29247	+	0.470420i	0.894536	−	0.446996i	$-0.147506\pi$
$227$	4420.37	+	1608.88i	1.29247	+	0.470420i	0.397931	+	0.917415i	$0.369728\pi$
$228$		0			0
$229$	1201.22	+	1007.94i	0.346632	+	0.290859i	0.799436	−	0.600751i	$-0.205132\pi$
$229$	1201.22	+	1007.94i	0.346632	+	0.290859i	−0.452804	+	0.891610i	$0.649576\pi$
$230$	−305.833	−	256.625i	−0.0876785	−	0.0735710i
$231$		0			0
$232$	1962.44	+	714.269i	0.555347	+	0.202130i
$233$	−2879.03	+	4986.62i	−0.809491	+	1.40208i	0.103727	+	0.994606i	$0.466923\pi$
$233$	−2879.03	+	4986.62i	−0.809491	+	1.40208i	−0.913217	+	0.407473i	$0.866410\pi$
$234$		0			0
$235$	387.002	+	670.307i	0.107426	+	0.186068i
$236$	49.8554	+	282.744i	0.0137513	+	0.0779875i
$237$		0			0
$238$	−4295.19	+	1563.32i	−1.16981	+	0.425777i
$239$	559.309	−	3172.00i	0.151375	−	0.858492i	−0.810650	−	0.585531i	$-0.800886\pi$
$239$	559.309	−	3172.00i	0.151375	−	0.858492i	0.962025	−	0.272961i	$-0.0880029\pi$
$240$		0			0
$241$	−2083.33	+	1748.12i	−0.556842	+	0.467246i	−0.877250	−	0.480034i	$-0.840624\pi$
$241$	−2083.33	+	1748.12i	−0.556842	+	0.467246i	0.320408	+	0.947280i	$0.396180\pi$
$242$	−2670.42			−0.709342
$243$		0			0
$244$	−648.412			−0.170124
$245$	−1003.27	+	841.845i	−0.261619	+	0.219525i
$246$		0			0
$247$	−390.989	+	2217.41i	−0.100721	+	0.571216i
$248$	1345.84	−	489.845i	0.344600	−	0.125424i
$249$		0			0
$250$	256.010	+	1451.91i	0.0647660	+	0.367306i
$251$	2711.14	+	4695.84i	0.681777	+	1.18087i	0.974438	+	0.224656i	$0.0721258\pi$
$251$	2711.14	+	4695.84i	0.681777	+	1.18087i	−0.292661	+	0.956216i	$0.594541\pi$
$252$		0			0
$253$	−825.290	+	1429.44i	−0.205081	+	0.355211i
$254$	2997.40	+	1090.96i	0.740447	+	0.269501i
$255$		0			0
$256$	4113.76	+	3451.86i	1.00434	+	0.842739i
$257$	810.211	+	679.848i	0.196652	+	0.165011i	0.735797	−	0.677203i	$-0.236808\pi$
$257$	810.211	+	679.848i	0.196652	+	0.165011i	−0.539145	+	0.842213i	$0.681252\pi$
$258$		0			0
$259$	5943.22	+	2163.15i	1.42584	+	0.518965i
$260$	139.617	−	241.824i	0.0333027	−	0.0576819i
$261$		0			0
$262$	−1025.94	−	1776.98i	−0.241919	−	0.419016i
$263$	−918.260	−	5207.71i	−0.215294	−	1.22099i	−0.880396	−	0.474240i	$-0.842723\pi$
$263$	−918.260	−	5207.71i	−0.215294	−	1.22099i	0.665101	−	0.746753i	$-0.268388\pi$
$264$		0			0
$265$	1117.77	−	406.834i	0.259109	−	0.0943079i
$266$	−1588.90	+	9011.13i	−0.366248	+	2.07710i
$267$		0			0
$268$	500.170	−	419.693i	0.114003	−	0.0956598i
$269$	−7352.28			−1.66646			−0.833228	−	0.552930i	$-0.813510\pi$
$269$	−7352.28			−1.66646			−0.833228	+	0.552930i	$0.813510\pi$
$270$		0			0
$271$	3845.21			0.861917			0.430959	−	0.902372i	$-0.358175\pi$
$271$	3845.21			0.861917			0.430959	+	0.902372i	$0.358175\pi$
$272$	−2163.73	+	1815.59i	−0.482336	+	0.404728i
$273$		0			0
$274$	556.626	−	3156.79i	0.122726	−	0.696016i
$275$	2833.62	−	1031.35i	0.621359	−	0.226156i
$276$		0			0
$277$	−660.359	−	3745.08i	−0.143239	−	0.812347i	−0.968764	−	0.247983i	$-0.920232\pi$
$277$	−660.359	−	3745.08i	−0.143239	−	0.812347i	0.825526	−	0.564364i	$-0.190879\pi$
$278$	−1710.76	−	2963.12i	−0.369081	−	0.639267i
$279$		0			0
$280$	−242.276	+	419.635i	−0.0517099	+	0.0895642i
$281$	−5141.32	−	1871.29i	−1.09148	−	0.397265i	−0.267310	−	0.963611i	$-0.586135\pi$
$281$	−5141.32	−	1871.29i	−1.09148	−	0.397265i	−0.824168	+	0.566345i	$0.808357\pi$
$282$		0			0
$283$	4726.83	+	3966.28i	0.992866	+	0.833113i	0.985980	−	0.166863i	$-0.0533638\pi$
$283$	4726.83	+	3966.28i	0.992866	+	0.833113i	0.00688565	+	0.999976i	$0.497808\pi$
$284$	−1017.70	−	853.953i	−0.212639	−	0.178425i
$285$		0			0
$286$	−2632.89	−	958.292i	−0.544356	−	0.198129i
$287$	3709.17	−	6424.47i	0.762876	−	1.32134i
$288$		0			0
$289$	1790.98	+	3102.08i	0.364540	+	0.631401i
$290$	−244.747	−	1388.03i	−0.0495587	−	0.281061i
$291$		0			0
$292$	−242.832	+	88.3836i	−0.0486667	+	0.0177132i
$293$	274.049	−	1554.21i	0.0546420	−	0.309890i	−0.945221	−	0.326431i	$-0.894154\pi$
$293$	274.049	−	1554.21i	0.0546420	−	0.309890i	0.999863	+	0.0165402i	$0.00526515\pi$
$294$		0			0
$295$	−63.3827	+	53.1844i	−0.0125094	+	0.0104967i
$296$	1644.26			0.322873
$297$		0			0
$298$	−6190.63			−1.20340
$299$	1582.15	−	1327.58i	0.306014	−	0.256777i
$300$		0			0
$301$	1208.71	−	6854.91i	0.231457	−	1.31266i
$302$	8533.54	−	3105.95i	1.62599	−	0.591813i
$303$		0			0
$304$	981.863	+	5568.42i	0.185242	+	1.05056i
$305$	−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	$0.333244\pi$
$308$	−4408.53	−	1604.57i	−0.815582	−	0.296848i
$309$		0			0
$310$	−740.452	−	621.313i	−0.135661	−	0.113833i
$311$	−4713.52	−	3955.11i	−0.859419	−	0.721138i	0.102424	−	0.994741i	$-0.467340\pi$
$311$	−4713.52	−	3955.11i	−0.859419	−	0.721138i	−0.961843	+	0.273603i	$0.911785\pi$
$312$		0			0
$313$	−6901.40	−	2511.90i	−1.24629	−	0.453614i	−0.367147	−	0.930163i	$-0.619665\pi$
$313$	−6901.40	−	2511.90i	−1.24629	−	0.453614i	−0.879148	+	0.476549i	$0.841888\pi$
$314$	5137.91	−	8899.13i	0.923405	−	1.59939i
$315$		0			0
$316$	2111.05	+	3656.45i	0.375810	+	0.650922i
$317$	178.152	+	1010.35i	0.0315647	+	0.179012i	0.996514	−	0.0834233i	$-0.0265854\pi$
$317$	178.152	+	1010.35i	0.0315647	+	0.179012i	−0.964949	+	0.262436i	$0.915474\pi$
$318$		0			0
$319$	−5475.68	+	1992.98i	−0.961063	+	0.349798i
$320$	48.6633	−	275.983i	0.00850112	−	0.0482123i
$321$		0			0
$322$	6429.57	−	5395.05i	1.11275	−	0.933709i
$323$	−2664.53			−0.459004
$324$		0			0
$325$	−3773.23			−0.644004
$326$	−5817.64	+	4881.58i	−0.988372	+	0.829343i
$327$		0			0
$328$	334.897	−	1899.29i	0.0563767	−	0.319728i
$329$	−15290.6	+	5565.34i	−2.56231	+	0.932605i
$330$		0			0
$331$	−1000.61	−	5674.77i	−0.166159	−	0.942336i	−0.947861	−	0.318684i	$-0.896759\pi$
$331$	−1000.61	−	5674.77i	−0.166159	−	0.942336i	0.781702	−	0.623652i	$-0.214352\pi$
$332$	957.576	+	1658.57i	0.158295	+	0.274174i
$333$		0			0
$334$	686.591	−	1189.21i	0.112481	−	0.194822i
$335$	176.817	+	64.3562i	0.0288375	+	0.0104960i
$336$		0			0
$337$	2461.08	+	2065.09i	0.397815	+	0.333807i	0.819649	−	0.572867i	$-0.194169\pi$
$337$	2461.08	+	2065.09i	0.397815	+	0.333807i	−0.421833	+	0.906673i	$0.638613\pi$
$338$	−3522.29	−	2955.55i	−0.566826	−	0.475624i
$339$		0			0
$340$	310.514	+	113.018i	0.0495293	+	0.0180272i
$341$	−1998.11	+	3460.82i	−0.317312	+	0.549601i
$342$		0			0
$343$	−7941.72	−	13755.5i	−1.25018	−	2.16538i
$344$	−314.235	−	1782.11i	−0.0492512	−	0.279317i
$345$		0			0
$346$	5933.74	−	2159.71i	0.921965	−	0.335568i
$347$	−625.302	+	3546.27i	−0.0967377	+	0.548627i	0.897463	+	0.441089i	$0.145408\pi$
$347$	−625.302	+	3546.27i	−0.0967377	+	0.548627i	−0.994201	+	0.107538i	$0.965703\pi$
$348$		0			0
$349$	−1417.07	+	1189.07i	−0.217347	+	0.182376i	−0.744960	−	0.667109i	$-0.767532\pi$
$349$	−1417.07	+	1189.07i	−0.217347	+	0.182376i	0.527613	+	0.849485i	$0.323087\pi$
$350$	−15333.7			−2.34177
$351$		0			0
$352$	−5295.63			−0.801870
$353$	2383.18	−	1999.73i	0.359331	−	0.301515i	−0.445193	−	0.895435i	$-0.646865\pi$
$353$	2383.18	−	1999.73i	0.359331	−	0.301515i	0.804524	+	0.593920i	$0.202420\pi$
$354$		0			0
$355$	66.4832	−	377.045i	0.00993961	−	0.0563703i
$356$	−4800.61	+	1747.28i	−0.714697	+	0.260128i
$357$		0			0
$358$	−1937.53	−	10988.3i	−0.286038	−	1.62220i
$359$	3228.43	+	5591.80i	0.474624	+	0.822072i	0.999578	−	0.0290584i	$-0.00925087\pi$
$359$	3228.43	+	5591.80i	0.474624	+	0.822072i	−0.524954	+	0.851131i	$0.675918\pi$
$360$		0			0
$361$	762.511	−	1320.71i	0.111169	−	0.192551i
$362$	232.735	+	84.7085i	0.0337908	+	0.0122988i
$363$		0			0
$364$	4496.97	+	3773.41i	0.647542	+	0.543353i
$365$	−57.0491	−	47.8699i	−0.00818106	−	0.00686473i
$366$		0			0
$367$	4905.02	+	1785.28i	0.697657	+	0.253926i	0.666410	−	0.745585i	$-0.267830\pi$
$367$	4905.02	+	1785.28i	0.697657	+	0.253926i	0.0312469	+	0.999512i	$0.490052\pi$
$368$	2593.29	−	4491.71i	0.367350	−	0.636268i
$369$		0			0
$370$	−554.851	−	961.030i	−0.0779603	−	0.135031i
$371$	4342.43	+	24627.1i	0.607675	+	3.44630i
$372$		0			0
$373$	−5448.02	+	1982.92i	−0.756267	+	0.275259i	−0.691241	−	0.722625i	$-0.742935\pi$
$373$	−5448.02	+	1982.92i	−0.756267	+	0.275259i	−0.0650267	+	0.997884i	$0.520713\pi$
$374$	575.761	−	3265.30i	0.0796040	−	0.451457i
$375$		0			0
$376$	−3240.62	+	2719.20i	−0.444473	+	0.372957i
$377$	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	$0.833633\pi$
$380$	506.734	−	425.201i	0.0684077	−	0.0574009i
$381$		0			0
$382$	647.785	−	3673.77i	0.0867633	−	0.492059i
$383$	−3513.26	+	1278.72i	−0.468719	+	0.170600i	−0.565572	−	0.824699i	$-0.691345\pi$
$383$	−3513.26	+	1278.72i	−0.468719	+	0.170600i	0.0968530	+	0.995299i	$0.469122\pi$
$384$		0			0
$385$	−234.776	−	1331.48i	−0.0310787	−	0.176256i
$386$	−369.734	−	640.398i	−0.0487538	−	0.0844441i
$387$		0			0
$388$	137.900	−	238.851i	0.0180434	−	0.0312521i
$389$	−5336.94	−	1942.49i	−0.695614	−	0.253183i	−0.0300769	−	0.999548i	$-0.509575\pi$
$389$	−5336.94	−	1942.49i	−0.695614	−	0.253183i	−0.665537	+	0.746365i	$0.731797\pi$
$390$		0			0
$391$	1872.29	+	1571.04i	0.242164	+	0.203200i
$392$	−5483.39	−	4601.11i	−0.706513	−	0.592835i
$393$		0			0
$394$	−9544.91	−	3474.06i	−1.22047	−	0.444215i
$395$	−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	$0.667591\pi$
$398$	−3068.40	−	17401.7i	−0.386444	−	2.19163i
$399$		0			0
$400$	−8904.02	+	3240.80i	−1.11300	+	0.405100i
$401$	2178.05	−	12352.3i	0.271239	−	1.53827i	−0.479423	−	0.877584i	$-0.659154\pi$
$401$	2178.05	−	12352.3i	0.271239	−	1.53827i	0.750662	−	0.660687i	$-0.229735\pi$
$402$		0			0
$403$	3830.55	−	3214.21i	0.473482	−	0.397298i
$404$	−6085.12			−0.749371
$405$		0			0
$406$	29630.8			3.62205
$407$	−3514.52	+	2949.03i	−0.428030	+	0.359160i
$408$		0			0
$409$	−1392.58	+	7897.69i	−0.168358	+	0.954806i	0.777176	+	0.629283i	$0.216651\pi$
$409$	−1392.58	+	7897.69i	−0.168358	+	0.954806i	−0.945534	+	0.325523i	$0.894460\pi$
$410$	−1223.10	+	445.173i	−0.147329	+	0.0536232i
$411$		0			0
$412$	−555.190	−	3148.64i	−0.0663889	−	0.376510i
$413$	−869.728	−	1506.41i	−0.103624	−	0.179481i
$414$		0			0
$415$	−275.961	+	477.979i	−0.0326419	+	0.0565375i
$416$	6226.76	+	2266.35i	0.733875	+	0.267109i
$417$		0			0
$418$	−5084.61	−	4266.49i	−0.594967	−	0.499237i
$419$	11860.5	+	9952.11i	1.38287	+	1.16036i	0.968138	+	0.250419i	$0.0805684\pi$
$419$	11860.5	+	9952.11i	1.38287	+	1.16036i	0.414730	+	0.909945i	$0.363876\pi$
$420$		0			0
$421$	3607.92	+	1313.18i	0.417671	+	0.152020i	0.542302	−	0.840183i	$-0.317553\pi$
$421$	3607.92	+	1313.18i	0.417671	+	0.152020i	−0.124632	+	0.992203i	$0.539775\pi$
$422$	−1808.95	+	3133.19i	−0.208669	+	0.361425i
$423$		0			0
$424$	3250.62	+	5630.24i	0.372321	+	0.644878i
$425$	−775.371	−	4397.35i	−0.0884965	−	0.501889i
$426$		0			0
$427$	3691.55	−	1343.61i	0.418376	−	0.152277i
$428$	−350.709	+	1988.97i	−0.0396078	+	0.224627i
$429$		0			0
$430$	−935.567	+	785.034i	−0.104923	+	0.0880411i
$431$	−4322.86			−0.483121			−0.241560	−	0.970386i	$-0.577659\pi$
$431$	−4322.86			−0.483121			−0.241560	+	0.970386i	$0.577659\pi$
$432$		0			0
$433$	−8167.34			−0.906460			−0.453230	−	0.891394i	$-0.649728\pi$
$433$	−8167.34			−0.906460			−0.453230	+	0.891394i	$0.649728\pi$
$434$	15566.6	−	13061.9i	1.72171	−	1.44468i
$435$		0			0
$436$	871.713	−	4943.73i	0.0957511	−	0.543032i
$437$	4597.67	−	1673.41i	0.503286	−	0.183181i
$438$		0			0
$439$	1287.01	+	7299.02i	0.139922	+	0.793538i	0.971305	+	0.237838i	$0.0764386\pi$
$439$	1287.01	+	7299.02i	0.139922	+	0.793538i	−0.831383	+	0.555700i	$0.812450\pi$
$440$	−175.747	−	304.402i	−0.0190418	−	0.0329813i
$441$		0			0
$442$	−2074.44	+	3593.03i	−0.223237	+	0.386658i
$443$	−6659.45	−	2423.84i	−0.714222	−	0.259955i	−0.0407510	−	0.999169i	$-0.512975\pi$
$443$	−6659.45	−	2423.84i	−0.714222	−	0.259955i	−0.673471	+	0.739214i	$0.735197\pi$
$444$		0			0
$445$	−1127.82	−	946.354i	−0.120143	−	0.100812i
$446$	1315.21	+	1103.59i	0.139634	+	0.117167i
$447$		0			0
$448$	5536.23	+	2015.02i	0.583844	+	0.212502i
$449$	5632.70	−	9756.13i	0.592035	−	1.02543i	−0.401923	−	0.915673i	$-0.631658\pi$
$449$	5632.70	−	9756.13i	0.592035	−	1.02543i	0.993958	−	0.109761i	$-0.0350085\pi$
$450$		0			0
$451$	2690.62	+	4660.29i	0.280923	+	0.486573i
$452$	−52.2104	−	296.100i	−0.00543312	−	0.0308128i
$453$		0			0
$454$	16305.2	−	5934.60i	1.68555	−	0.613490i
$455$	−293.773	+	1666.07i	−0.0302687	+	0.171663i
$456$		0			0
$457$	1542.04	−	1293.92i	0.157841	−	0.132444i	−0.560447	−	0.828190i	$-0.689371\pi$
$457$	1542.04	−	1293.92i	0.157841	−	0.132444i	0.718288	+	0.695746i	$0.244926\pi$
$458$	5784.10			0.590116
$459$		0			0
$460$	−606.774			−0.0615021
$461$	−10191.2	+	8551.45i	−1.02961	+	0.863949i	−0.990805	−	0.135298i	$-0.956801\pi$
$461$	−10191.2	+	8551.45i	−1.02961	+	0.863949i	−0.0388094	+	0.999247i	$0.512357\pi$
$462$		0			0
$463$	−3099.30	+	17577.0i	−0.311094	+	1.76430i	0.282239	+	0.959344i	$0.408923\pi$
$463$	−3099.30	+	17577.0i	−0.311094	+	1.76430i	−0.593333	+	0.804957i	$0.702188\pi$
$464$	17206.1	−	6262.51i	1.72150	−	0.626573i
$465$		0			0
$466$	3688.19	+	20916.8i	0.366635	+	2.07929i
$467$	5090.74	+	8817.42i	0.504435	+	0.873708i	0.999987	+	0.00512926i	$0.00163270\pi$
$467$	5090.74	+	8817.42i	0.504435	+	0.873708i	−0.495551	+	0.868579i	$0.665034\pi$
$468$		0			0
$469$	−1977.91	+	3425.84i	−0.194736	+	0.337293i
$470$	2682.85	+	976.477i	0.263299	+	0.0958330i
$471$		0			0
$472$	−346.419	−	290.680i	−0.0337822	−	0.0283466i
$473$	3867.94	+	3245.59i	0.376001	+	0.315502i
$474$		0			0
$475$	−8399.56	−	3057.19i	−0.811365	−	0.295313i
$476$	−3473.46	+	6016.20i	−0.334466	+	0.579311i
$477$		0			0
$478$	−5940.44	−	10289.2i	−0.568430	−	0.984550i
$479$	−535.323	−	3035.97i	−0.0510637	−	0.289597i	0.948573	−	0.316559i	$-0.102528\pi$
$479$	−535.323	−	3035.97i	−0.0510637	−	0.289597i	−0.999636	+	0.0269625i	$0.991417\pi$
$480$		0			0
$481$	5394.55	−	1963.46i	0.511373	−	0.186125i
$482$	−1741.97	+	9879.21i	−0.164615	+	0.933580i
$483$		0			0
$484$	−3109.06	+	2608.81i	−0.291985	+	0.245004i
$485$	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	$0.478026\pi$
$488$	782.367	−	656.484i	0.0725740	−	0.0608968i
$489$		0			0
$490$	−838.885	+	4757.55i	−0.0773407	+	0.438621i
$491$	−7441.72	+	2708.57i	−0.683992	+	0.248953i	−0.660561	−	0.750773i	$-0.729681\pi$
$491$	−7441.72	+	2708.57i	−0.683992	+	0.248953i	−0.0234316	+	0.999725i	$0.507459\pi$
$492$		0			0
$493$	1498.33	+	8497.43i	0.136879	+	0.776278i
$494$	4152.71	+	7192.70i	0.378217	+	0.655091i
$495$		0			0
$496$	6278.61	−	10874.9i	0.568383	−	0.984468i
$497$	7563.52	+	2752.90i	0.682637	+	0.248459i
$498$		0			0
$499$	−6251.08	−	5245.28i	−0.560796	−	0.470563i	0.317782	−	0.948164i	$-0.397062\pi$
$499$	−6251.08	−	5245.28i	−0.560796	−	0.470563i	−0.878577	+	0.477601i	$0.841507\pi$
$500$	1716.47	+	1440.29i	0.153526	+	0.128823i
$501$		0			0
$502$	18794.7	+	6840.72i	1.67101	+	0.608200i
$503$	−8812.36	+	15263.5i	−0.781161	+	1.35301i	0.150105	+	0.988670i	$0.452039\pi$
$503$	−8812.36	+	15263.5i	−0.781161	+	1.35301i	−0.931266	+	0.364340i	$0.881295\pi$
$504$		0			0
$505$	−876.827	−	1518.71i	−0.0772640	−	0.133825i
$506$	1057.24	+	5995.91i	0.0928856	+	0.526780i
$507$		0			0
$508$	4555.54	−	1658.08i	0.397873	−	0.144814i
$509$	−1545.13	+	8762.87i	−0.134552	+	0.763080i	0.840619	+	0.541626i	$0.182191\pi$
$509$	−1545.13	+	8762.87i	−0.134552	+	0.763080i	−0.975171	+	0.221453i	$0.928920\pi$
$510$		0			0
$511$	1199.35	−	1006.37i	0.103828	−	0.0871221i
$512$	11171.3			0.964269
$513$		0			0
$514$	3901.32			0.334786
$515$	705.830	−	592.262i	0.0603934	−	0.0506760i
$516$		0			0
$517$	2049.68	−	11624.3i	0.174361	−	0.988852i
$518$	21922.4	−	7979.12i	1.85949	−	0.676800i
$519$		0			0
$520$	76.3739	+	433.138i	0.00644080	+	0.0365276i
$521$	−9964.97	−	17259.8i	−0.837953	−	1.45138i	−0.891604	−	0.452817i	$-0.850419\pi$
$521$	−9964.97	−	17259.8i	−0.837953	−	1.45138i	0.0536508	−	0.998560i	$-0.482914\pi$
$522$		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	$0.142833\pi$
$524$	−2930.44	−	1066.59i	−0.244307	−	0.0889205i
$525$		0			0
$526$	−14942.3	−	12538.1i	−1.23862	−	1.03933i
$527$	4533.01	+	3803.64i	0.374689	+	0.314401i
$528$		0			0
$529$	7215.91	+	2626.38i	0.593072	+	0.215861i
$530$	2193.83	−	3799.82i	0.179800	−	0.311422i
$531$		0			0
$532$	6953.34	+	12043.5i	0.566664	+	0.981491i
$533$	−1169.26	−	6631.20i	−0.0950211	−	0.538892i
$534$		0			0
$535$	−546.937	+	199.069i	−0.0441984	+	0.0160869i
$536$	−178.583	+	1012.79i	−0.0143911	+	0.0816157i
$537$		0			0
$538$	−20775.1	+	17432.4i	−1.66483	+	1.39696i
$539$	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	$0.382584\pi$
$542$	10865.3	−	9117.05i	0.861077	−	0.722529i
$543$		0			0
$544$	−1361.67	+	7722.42i	−0.107318	+	0.608632i
$545$	1359.45	−	494.800i	0.106849	−	0.0388898i
$546$		0			0
$547$	−1391.66	−	7892.49i	−0.108781	−	0.616926i	−0.989643	−	0.143553i	$-0.954147\pi$
$547$	−1391.66	−	7892.49i	−0.108781	−	0.616926i	0.880862	−	0.473373i	$-0.156964\pi$
$548$	−2435.90	−	4219.10i	−0.189884	−	0.328889i
$549$		0			0
$550$	5561.51	−	9632.82i	0.431170	−	0.746809i
$551$	16231.3	+	5907.71i	1.25495	+	0.456764i
$552$		0			0
$553$	−19595.4	−	16442.5i	−1.50684	−	1.26439i
$554$	−10745.6	−	9016.64i	−0.824074	−	0.691480i
$555$		0			0
$556$	−4886.53	−	1778.55i	−0.372725	−	0.135661i
$557$	3679.68	−	6373.39i	0.279915	−	0.484828i	−0.691448	−	0.722426i	$-0.743027\pi$
$557$	3679.68	−	6373.39i	0.279915	−	0.484828i	0.971363	+	0.237598i	$0.0763602\pi$
$558$		0			0
$559$	−3159.03	−	5471.61i	−0.239021	−	0.413997i
$560$	737.731	+	4183.88i	0.0556693	+	0.315716i
$561$		0			0
$562$	−18964.5	+	6902.52i	−1.42343	+	0.518087i
$563$	327.856	−	1859.36i	0.0245426	−	0.139188i	−0.970074	−	0.242808i	$-0.921931\pi$
$563$	327.856	−	1859.36i	0.0245426	−	0.139188i	0.994617	+	0.103620i	$0.0330426\pi$
$564$		0			0
$565$	66.3767	−	55.6967i	0.00494246	−	0.00414721i
$566$	22760.6			1.69028
$567$		0			0
$568$	2092.53			0.154579
$569$	−19020.9	+	15960.4i	−1.40140	+	1.17592i	−0.440930	+	0.897541i	$0.645351\pi$
$569$	−19020.9	+	15960.4i	−1.40140	+	1.17592i	−0.960472	+	0.278375i	$0.910204\pi$
$570$		0			0
$571$	−2450.63	+	13898.2i	−0.179607	+	1.01860i	0.753084	+	0.657925i	$0.228565\pi$
$571$	−2450.63	+	13898.2i	−0.179607	+	1.01860i	−0.932691	+	0.360677i	$0.882546\pi$
$572$	−4001.55	+	1456.44i	−0.292505	+	0.106463i
$573$		0			0
$574$	−4751.65	−	26947.9i	−0.345523	−	1.95956i
$575$	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	$0.276555\pi$
$578$	12415.8	+	4518.98i	0.893476	+	0.325199i
$579$		0			0
$580$	−1640.95	−	1376.92i	−0.117477	−	0.0985753i
$581$	−8888.51	−	7458.35i	−0.634695	−	0.532572i
$582$		0			0
$583$	−17046.1	−	6204.26i	−1.21094	−	0.440744i
$584$	203.515	−	352.498i	0.0144204	−	0.0249768i
$585$		0			0
$586$	−2910.69	−	5041.46i	−0.205187	−	0.355394i
$587$	635.586	+	3604.59i	0.0446907	+	0.253454i	0.998965	−	0.0454776i	$-0.0144810\pi$
$587$	635.586	+	3604.59i	0.0446907	+	0.253454i	−0.954275	+	0.298931i	$0.903370\pi$
$588$		0			0
$589$	11131.4	−	4051.50i	0.778711	−	0.283428i
$590$	−52.9973	+	300.563i	−0.00369808	+	0.0209728i
$591$		0			0
$592$	11043.6	−	9266.67i	0.766704	−	0.643341i
$593$	−21034.0			−1.45660			−0.728299	−	0.685260i	$-0.759689\pi$
$593$	−21034.0			−1.45660			−0.728299	+	0.685260i	$0.759689\pi$
$594$		0			0
$595$	−2002.01			−0.137940
$596$	−7207.49	+	6047.80i	−0.495353	+	0.415651i
$597$		0			0
$598$	1322.92	−	7502.63i	0.0904649	−	0.513052i
$599$	−16908.0	+	6154.00i	−1.15332	+	0.419776i	−0.846708	−	0.532057i	$-0.821419\pi$
$599$	−16908.0	+	6154.00i	−1.15332	+	0.419776i	−0.306617	+	0.951833i	$0.599197\pi$
$600$		0			0
$601$	3413.53	+	19359.1i	0.231682	+	1.31393i	0.849491	+	0.527603i	$0.176909\pi$
$601$	3413.53	+	19359.1i	0.231682	+	1.31393i	−0.617809	+	0.786328i	$0.711980\pi$
$602$	−12837.7	−	22235.6i	−0.869147	−	1.50541i
$603$		0			0
$604$	6900.95	−	11952.8i	0.464894	−	0.805220i
$605$	−1099.09	−	400.038i	−0.0738588	−	0.0268824i
$606$		0			0
$607$	15464.4	+	12976.1i	1.03407	+	0.867686i	0.991329	−	0.131401i	$-0.0419474\pi$
$607$	15464.4	+	12976.1i	1.03407	+	0.867686i	0.0427382	+	0.999086i	$0.486392\pi$
$608$	12025.1	+	10090.2i	0.802106	+	0.673047i
$609$		0			0
$610$	−647.708	−	235.746i	−0.0429917	−	0.0156477i
$611$	−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	$0.883046\pi$
$614$	3443.77	+	19530.6i	0.226351	+	1.28370i
$615$		0			0
$616$	6943.84	−	2527.35i	0.454180	−	0.165308i
$617$	4651.59	−	26380.5i	0.303510	−	1.72129i	−0.326924	−	0.945051i	$-0.606012\pi$
$617$	4651.59	−	26380.5i	0.303510	−	1.72129i	0.630435	−	0.776242i	$-0.282877\pi$
$618$		0			0
$619$	20430.4	−	17143.2i	1.32661	−	1.11315i	0.341748	−	0.939792i	$-0.388981\pi$
$619$	20430.4	−	17143.2i	1.32661	−	1.11315i	0.984858	−	0.173363i	$-0.0554633\pi$
$620$	−1469.06			−0.0951593
$621$		0			0
$622$	−22696.5			−1.46310
$623$	23710.3	−	19895.3i	1.52477	−	1.27944i
$624$		0			0
$625$	2544.46	−	14430.4i	0.162846	−	0.923544i
$626$	−25456.8	+	9265.53i	−1.62534	+	0.591574i
$627$		0			0
$628$	−2711.96	−	15380.3i	−0.172323	−	0.977292i
$629$	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	$-0.0119630\pi$
$632$	−6249.14	−	2274.50i	−0.393319	−	0.143156i
$633$		0			0
$634$	2898.96	+	2432.51i	0.181597	+	0.152378i
$635$	1070.25	+	898.042i	0.0668841	+	0.0561224i
$636$		0			0
$637$	−23484.5	−	8547.66i	−1.46074	−	0.531665i
$638$	−10747.1	+	18614.4i	−0.666897	+	1.15510i
$639$		0			0
$640$	872.156	+	1510.62i	0.0538671	+	0.0933006i
$641$	−2439.85	−	13837.1i	−0.150341	−	0.852624i	−0.962923	−	0.269777i	$-0.913050\pi$
$641$	−2439.85	−	13837.1i	−0.150341	−	0.852624i	0.812582	−	0.582847i	$-0.198061\pi$
$642$		0			0
$643$	−4279.48	+	1557.60i	−0.262467	+	0.0955301i	−0.469902	−	0.882719i	$-0.655711\pi$
$643$	−4279.48	+	1557.60i	−0.262467	+	0.0955301i	0.207435	+	0.978249i	$0.433488\pi$
$644$	2215.10	−	12562.5i	0.135539	−	0.768681i
$645$		0			0
$646$	−7529.07	+	6317.64i	−0.458556	+	0.384774i
$647$	23937.2			1.45451			0.727257	−	0.686366i	$-0.240795\pi$
$647$	23937.2			1.45451			0.727257	+	0.686366i	$0.240795\pi$
$648$		0			0
$649$	1261.80			0.0763171
$650$	−10661.9	+	8946.41i	−0.643376	+	0.539857i
$651$		0			0
$652$	−2004.28	+	11366.9i	−0.120389	+	0.682761i
$653$	−11304.6	+	4114.56i	−0.677466	+	0.246577i	−0.657759	−	0.753228i	$-0.728495\pi$
$653$	−11304.6	+	4114.56i	−0.677466	+	0.246577i	−0.0197066	+	0.999806i	$0.506273\pi$
$654$		0			0
$655$	−156.060	−	885.062i	−0.00930959	−	0.0527973i
$656$	−8454.68	−	14643.9i	−0.503201	−	0.871570i
$657$		0			0
$658$	−30010.8	+	51980.2i	−1.77803	+	3.07963i
$659$	3395.72	+	1235.94i	0.200726	+	0.0730583i	0.440427	−	0.897789i	$-0.354827\pi$
$659$	3395.72	+	1235.94i	0.200726	+	0.0730583i	−0.239701	+	0.970847i	$0.577049\pi$
$660$		0			0
$661$	17218.6	+	14448.1i	1.01320	+	0.850176i	0.988758	−	0.149525i	$-0.0477746\pi$
$661$	17218.6	+	14448.1i	1.01320	+	0.850176i	0.0244422	+	0.999701i	$0.492219\pi$
$662$	−16282.4	−	13662.5i	−0.955940	−	0.802129i
$663$		0			0
$664$	−2834.62	−	1031.72i	−0.165669	−	0.0602988i
$665$	−2003.86	+	3470.79i	−0.116852	+	0.202393i
$666$		0			0
$667$	−7922.05	−	13721.4i	−0.459885	−	0.796544i
$668$	−362.405	−	2055.30i	−0.0209908	−	0.119045i
$669$		0			0
$670$	652.217	−	237.388i	0.0376080	−	0.0136882i
$671$	−494.845	+	2806.40i	−0.0284698	+	0.161461i
$672$		0			0
$673$	3601.54	−	3022.05i	0.206284	−	0.173093i	−0.533793	−	0.845615i	$-0.679234\pi$
$673$	3601.54	−	3022.05i	0.206284	−	0.173093i	0.740077	+	0.672523i	$0.234789\pi$
$674$	11850.6			0.677251
$675$		0			0
$676$	−6988.22			−0.397600
$677$	6683.25	−	5607.91i	0.379406	−	0.318360i	−0.433063	−	0.901364i	$-0.642567\pi$
$677$	6683.25	−	5607.91i	0.379406	−	0.318360i	0.812469	+	0.583004i	$0.198123\pi$
$678$		0			0
$679$	−290.160	+	1645.58i	−0.0163996	+	0.0930067i
$680$	−489.087	+	178.013i	−0.0275818	+	0.0100390i
$681$		0			0
$682$	2559.68	+	14516.7i	0.143717	+	0.815062i
$683$	−12790.4	−	22153.6i	−0.716559	−	1.24112i	−0.962355	−	0.271795i	$-0.912383\pi$
$683$	−12790.4	−	22153.6i	−0.716559	−	1.24112i	0.245796	−	0.969322i	$-0.420951\pi$
$684$		0			0
$685$	701.995	−	1215.89i	0.0391560	−	0.0678202i
$686$	−55055.1	−	20038.4i	−3.06416	−	1.11526i
$687$		0			0
$688$	−12154.2	−	10198.5i	−0.673507	−	0.565140i
$689$	17388.0	+	14590.3i	0.961438	+	0.806742i
$690$		0			0
$691$	30902.9	+	11247.7i	1.70131	+	0.619225i	0.995973	−	0.0896521i	$-0.0285755\pi$
$691$	30902.9	+	11247.7i	1.70131	+	0.619225i	0.705332	+	0.708877i	$0.250798\pi$
$692$	4798.53	−	8311.30i	0.263602	−	0.456573i
$693$		0			0
$694$	6641.36	+	11503.2i	0.363260	+	0.629185i
$695$	−260.231	−	1475.85i	−0.0142031	−	0.0805496i
$696$		0			0
$697$	7487.76	−	2725.32i	0.406914	−	0.148105i
$698$	−1184.88	+	6719.81i	−0.0642529	+	0.364396i
$699$		0			0
$700$	−17852.4	+	14979.9i	−0.963939	+	0.808841i
$701$	−27261.0			−1.46881			−0.734404	−	0.678713i	$-0.762538\pi$
$701$	−27261.0			−1.46881			−0.734404	+	0.678713i	$0.762538\pi$
$702$		0			0
$703$	13599.6			0.729615
$704$	−3273.84	+	2747.08i	−0.175266	+	0.147066i
$705$		0			0
$706$	1992.69	−	11301.1i	0.106227	−	0.602442i
$707$	34643.9	−	12609.4i	1.84288	−	0.670755i
$708$		0			0
$709$	−2920.38	−	16562.3i	−0.154693	−	0.877305i	−0.959066	−	0.283181i	$-0.908610\pi$
$709$	−2920.38	−	16562.3i	−0.154693	−	0.877305i	0.804374	−	0.594124i	$-0.202501\pi$
$710$	−706.120	−	1223.04i	−0.0373243	−	0.0646475i
$711$		0			0
$712$	4023.34	−	6968.63i	0.211771	−	0.366798i
$713$	−10210.6	−	3716.34i	−0.536310	−	0.195201i
$714$		0			0
$715$	−940.093	−	788.832i	−0.0491713	−	0.0412596i
$716$	−12990.5	−	10900.4i	−0.678043	−	0.568946i
$717$		0			0
$718$	22380.7	+	8145.92i	1.16329	+	0.423402i
$719$	−8119.01	+	14062.5i	−0.421124	+	0.729408i	−0.996050	−	0.0887976i	$-0.971698\pi$
$719$	−8119.01	+	14062.5i	−0.421124	+	0.729408i	0.574926	+	0.818206i	$0.305031\pi$
$720$		0			0
$721$	9685.30	+	16775.4i	0.500277	+	0.866504i
$722$	−976.818	−	5539.81i	−0.0503510	−	0.285555i
$723$		0			0
$724$	353.718	−	128.743i	0.0181572	−	0.00660868i
$725$	−5026.40	+	28506.1i	−0.257484	+	1.46026i
$726$		0			0
$727$	4175.26	−	3503.46i	0.213001	−	0.178729i	−0.530045	−	0.847970i	$-0.677825\pi$
$727$	4175.26	−	3503.46i	0.213001	−	0.178729i	0.743046	+	0.669240i	$0.233380\pi$
$728$	−9246.38			−0.470733
$729$		0			0
$730$	−274.702			−0.0139277
$731$	5727.49	−	4805.93i	0.289793	−	0.243165i
$732$		0			0
$733$	1757.59	−	9967.76i	0.0885647	−	0.502275i	−0.907966	−	0.419045i	$-0.862365\pi$
$733$	1757.59	−	9967.76i	0.0885647	−	0.502275i	0.996530	−	0.0832306i	$-0.0265238\pi$
$734$	18092.9	−	6585.28i	0.909838	−	0.331154i
$735$		0			0
$736$	−2500.37	−	14180.3i	−0.125224	−	0.710180i
$737$	−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	$0.159395\pi$
$740$	−1584.85	−	576.838i	−0.0787300	−	0.0286554i
$741$		0			0
$742$	70661.6	+	59292.1i	3.49605	+	2.93353i
$743$	10534.3	+	8839.29i	0.520140	+	0.436450i	0.864681	−	0.502322i	$-0.167521\pi$
$743$	10534.3	+	8839.29i	0.520140	+	0.436450i	−0.344540	+	0.938772i	$0.611965\pi$
$744$		0			0
$745$	−2547.95	−	927.378i	−0.125302	−	0.0456060i
$746$	−10692.8	+	18520.4i	−0.524785	+	0.908955i
$747$		0			0
$748$	−2519.63	−	4364.14i	−0.123164	−	0.213327i
$749$	−2124.80	−	12050.4i	−0.103656	−	0.587864i
$750$		0			0
$751$	−21073.1	+	7669.99i	−1.02393	+	0.372679i	−0.798765	−	0.601643i	$-0.794513\pi$
$751$	−21073.1	+	7669.99i	−1.02393	+	0.372679i	−0.225161	+	0.974322i	$0.572291\pi$
$752$	−6440.66	+	36526.8i	−0.312323	+	1.77127i
$753$		0			0
$754$	20603.1	−	17288.0i	0.995118	−	0.835003i
$755$	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	$0.454761\pi$
$758$	−36130.7	+	30317.3i	−1.73130	+	1.45273i
$759$		0			0
$760$	−180.926	+	1026.08i	−0.00863538	+	0.0489737i
$761$	−10442.6	+	3800.80i	−0.497430	+	0.181050i	−0.578538	−	0.815656i	$-0.696376\pi$
$761$	−10442.6	+	3800.80i	−0.497430	+	0.181050i	0.0811077	+	0.996705i	$0.474154\pi$
$762$		0			0
$763$	5281.36	+	29952.1i	0.250587	+	1.42115i
$764$	−2834.83	−	4910.06i	−0.134241	−	0.232513i
$765$		0			0
$766$	−6895.44	+	11943.3i	−0.325251	+	0.563352i
$767$	−1483.66	−	540.007i	−0.0698458	−	0.0254218i
$768$		0			0
$769$	6150.30	+	5160.72i	0.288408	+	0.242003i	0.775500	−	0.631348i	$-0.217498\pi$
$769$	6150.30	+	5160.72i	0.288408	+	0.242003i	−0.487092	+	0.873351i	$0.661942\pi$
$770$	−3820.36	−	3205.66i	−0.178800	−	0.150031i
$771$		0			0
$772$	−1056.09	−	384.385i	−0.0492351	−	0.0179201i
$773$	661.004	−	1144.89i	0.0307564	−	0.0532716i	−0.850238	−	0.526399i	$-0.823542\pi$
$773$	661.004	−	1144.89i	0.0307564	−	0.0532716i	0.880994	+	0.473128i	$0.156875\pi$
$774$		0			0
$775$	9925.52	+	17191.5i	0.460045	+	0.796822i
$776$	75.4348	+	427.812i	0.00348963	+	0.0197907i
$777$		0			0
$778$	−19686.1	+	7165.16i	−0.907174	+	0.330184i
$779$	2769.92	−	15709.0i	0.127398	−	0.722508i
$780$		0			0
$781$	−4472.68	+	3753.03i	−0.204923	+	0.171951i
$782$	9015.45			0.412266
$783$		0			0
$784$	−62759.9			−2.85896
$785$	3447.79	−	2893.04i	0.156761	−	0.131538i
$786$		0			0
$787$	2018.09	−	11445.1i	0.0914066	−	0.518392i	−0.904383	−	0.426722i	$-0.859668\pi$
$787$	2018.09	−	11445.1i	0.0914066	−	0.518392i	0.995789	−	0.0916704i	$-0.0292206\pi$
$788$	−14506.7	+	5279.99i	−0.655810	+	0.238695i
$789$		0			0
$790$	779.365	+	4420.00i	0.0350995	+	0.199059i
$791$	910.812	+	1577.57i	0.0409415	+	0.0709128i
$792$		0			0
$793$	1782.90	−	3088.07i	0.0798394	−	0.138286i
$794$	27280.1	+	9929.15i	1.21931	+	0.443794i
$795$		0			0
$796$	−20572.7	−	17262.5i	−0.916054	−	0.768661i
$797$	−25180.7	−	21129.1i	−1.11913	−	0.939061i	−0.120569	−	0.992705i	$-0.538472\pi$
$797$	−25180.7	−	21129.1i	−1.11913	−	0.939061i	−0.998560	+	0.0536440i	$0.982916\pi$
$798$		0			0
$799$	−16424.2	−	5977.93i	−0.727219	−	0.264686i
$800$	−13152.9	+	22781.6i	−0.581283	+	1.00681i
$801$		0			0
$802$	−23133.2	−	40067.8i	−1.01853	−	1.76414i
$803$	197.214	+	1118.46i	0.00866692	+	0.0491525i
$804$		0			0
$805$	3454.49	−	1257.33i	0.151248	−	0.0550499i
$806$	3202.91	−	18164.6i	0.139972	−	0.793822i
$807$		0			0
$808$	7342.24	−	6160.87i	0.319677	−	0.268241i
$809$	−19325.6			−0.839865			−0.419932	−	0.907555i	$-0.637946\pi$
$809$	−19325.6			−0.839865			−0.419932	+	0.907555i	$0.637946\pi$
$810$		0			0
$811$	20360.2			0.881556			0.440778	−	0.897616i	$-0.354703\pi$
$811$	20360.2			0.881556			0.440778	+	0.897616i	$0.354703\pi$
$812$	34498.0	−	28947.2i	1.49094	−	1.25104i
$813$		0			0
$814$	−2938.66	+	16666.0i	−0.126536	+	0.717619i
$815$	−3125.72	+	1137.67i	−0.134342	+	0.0488966i
$816$		0			0
$817$	−2599.03	−	14739.8i	−0.111296	−	0.631189i
$818$	14790.6	+	25618.1i	0.632202	+	1.09501i
$819$		0			0
$820$	−989.106	+	1713.18i	−0.0421233	+	0.0729596i
$821$	−18585.5	−	6764.59i	−0.790061	−	0.287559i	−0.0846996	−	0.996407i	$-0.526993\pi$
$821$	−18585.5	−	6764.59i	−0.790061	−	0.287559i	−0.705361	+	0.708848i	$0.749215\pi$
$822$		0			0
$823$	20302.0	+	17035.4i	0.859883	+	0.721528i	0.961943	−	0.273251i	$-0.0880988\pi$
$823$	20302.0	+	17035.4i	0.859883	+	0.721528i	−0.102060	+	0.994778i	$0.532543\pi$
$824$	3857.72	+	3237.01i	0.163095	+	0.136853i
$825$		0			0
$826$	−6029.30	−	2194.48i	−0.253978	−	0.0924405i
$827$	9829.63	−	17025.4i	0.413313	−	0.715879i	−0.581937	−	0.813234i	$-0.697705\pi$
$827$	9829.63	−	17025.4i	0.413313	−	0.715879i	0.995250	+	0.0973550i	$0.0310382\pi$
$828$		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	$0.403201\pi$
$830$	353.521	+	2004.92i	0.0147842	+	0.0838455i
$831$		0			0
$832$	5025.13	−	1829.00i	0.209393	−	0.0762129i
$833$	5135.60	−	29125.5i	0.213611	−	1.21145i
$834$		0			0
$835$	460.736	−	386.604i	0.0190951	−	0.0160227i
$836$	−10087.9			−0.417340
$837$		0			0
$838$	57110.4			2.35423
$839$	23444.7	−	19672.4i	0.964721	−	0.809497i	−0.0169939	−	0.999856i	$-0.505410\pi$
$839$	23444.7	−	19672.4i	0.964721	−	0.809497i	0.981715	+	0.190359i	$0.0609651\pi$
$840$		0			0
$841$	5477.90	−	31066.7i	0.224605	−	1.27380i
$842$	13308.3	−	4843.84i	0.544698	−	0.198254i
$843$		0			0
$844$	954.822	+	5415.06i	0.0389411	+	0.220846i
$845$	−1006.96	−	1744.10i	−0.0409946	−	0.0710047i
$846$		0			0
$847$	12294.7	−	21295.0i	0.498760	−	0.863877i
$848$	53563.5	+	19495.5i	2.16908	+	0.789479i
$849$		0			0
$850$	−12617.1	−	10587.0i	−0.509134	−	0.427214i
$851$	−9556.11	−	8018.53i	−0.384934	−	0.322998i
$852$		0			0
$853$	−33360.0	−	12142.1i	−1.33907	−	0.487381i	−0.429549	−	0.903043i	$-0.641328\pi$
$853$	−33360.0	−	12142.1i	−1.33907	−	0.487381i	−0.909519	+	0.415662i	$0.863550\pi$
$854$	7245.37	−	12549.3i	0.290318	−	0.502845i
$855$		0			0
$856$	−1590.57	−	2754.94i	−0.0635099	−	0.110002i
$857$	−923.468	−	5237.25i	−0.0368087	−	0.208753i	0.960857	−	0.277046i	$-0.0893556\pi$
$857$	−923.468	−	5237.25i	−0.0368087	−	0.208753i	−0.997665	+	0.0682938i	$0.978244\pi$
$858$		0			0
$859$	−22129.3	+	8054.40i	−0.878977	+	0.319922i	−0.741797	−	0.670624i	$-0.766026\pi$
$859$	−22129.3	+	8054.40i	−0.878977	+	0.319922i	−0.137180	+	0.990546i	$0.543804\pi$
$860$	−322.320	+	1827.97i	−0.0127802	+	0.0724803i
$861$		0			0
$862$	−12215.0	+	10249.6i	−0.482649	+	0.404991i
$863$	41574.3			1.63987			0.819934	−	0.572459i	$-0.194010\pi$
$863$	41574.3			1.63987			0.819934	+	0.572459i	$0.194010\pi$
$864$		0			0
$865$	2765.75			0.108715
$866$	−23078.2	+	19364.9i	−0.905576	+	0.759868i
$867$		0			0
$868$	5362.98	−	30415.0i	0.209714	−	1.18934i
$869$	17436.6	−	6346.41i	0.680663	−	0.247741i
$870$		0			0
$871$	623.505	+	3536.07i	0.0242556	+	0.137561i
$872$	3953.48	+	6847.62i	0.153534	+	0.265929i
$873$		0			0
$874$	9023.79	−	15629.7i	0.349238	−	0.604898i
$875$	−12756.8	−	4643.08i	−0.492865	−	0.179388i
$876$		0			0
$877$	−34541.5	−	28983.8i	−1.32997	−	1.11598i	−0.984085	−	0.177700i	$-0.943134\pi$
$877$	−34541.5	−	28983.8i	−1.32997	−	1.11598i	−0.345885	−	0.938277i	$-0.612421\pi$
$878$	20942.8	+	17573.1i	0.804994	+	0.675470i
$879$		0			0
$880$	−2895.94	−	1054.04i	−0.110934	−	0.0403767i
$881$	24958.3	−	43229.1i	0.954446	−	1.65315i	0.218815	−	0.975766i	$-0.429781\pi$
$881$	24958.3	−	43229.1i	0.954446	−	1.65315i	0.735631	−	0.677382i	$-0.236886\pi$
$882$		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	$-0.406078\pi$
$884$	1094.95	+	6209.79i	0.0416598	+	0.236265i
$885$		0			0
$886$	−24564.4	+	8940.71i	−0.931441	+	0.339017i
$887$	1500.44	−	8509.43i	0.0567981	−	0.322118i	−0.943149	−	0.332369i	$-0.892152\pi$
$887$	1500.44	−	8509.43i	0.0567981	−	0.322118i	0.999947	+	0.0102512i	$0.00326311\pi$
$888$		0			0
$889$	−22499.9	+	18879.6i	−0.848843	+	0.712264i
$890$	−5430.67			−0.204535
$891$		0			0
$892$	2609.37			0.0979465
$893$	−26803.1	+	22490.5i	−1.00440	+	0.842793i
$894$		0			0
$895$	848.630	−	4812.82i	0.0316945	−	0.179748i
$896$	−34459.3	+	12542.2i	−1.28483	+	0.467639i
$897$		0			0
$898$	−7215.80	−	40922.8i	−0.268145	−	1.52073i
$899$	−19180.1	−	33220.8i	−0.711558	−	1.23245i
$900$		0			0
$901$	−13430.5	+	23262.3i	−0.496598	+	0.860132i
$902$	18652.4	+	6788.93i	0.688535	+	0.250606i
$903$		0			0
$904$	362.782	+	304.411i	0.0133473	+	0.0111997i
$905$	83.0998	+	69.7290i	0.00305230	+	0.00256118i
$906$		0			0
$907$	20907.1	+	7609.58i	0.765392	+	0.278580i	0.695068	−	0.718944i	$-0.255374\pi$
$907$	20907.1	+	7609.58i	0.765392	+	0.278580i	0.0703241	+	0.997524i	$0.477597\pi$
$908$	13185.8	−	22838.4i	0.481922	−	0.834713i
$909$		0			0
$910$	3120.17	+	5404.30i	0.113662	+	0.196869i
$911$	5504.41	+	31217.0i	0.200186	+	1.13531i	0.904838	+	0.425756i	$0.139992\pi$
$911$	5504.41	+	31217.0i	0.200186	+	1.13531i	−0.704652	+	0.709553i	$0.748897\pi$
$912$		0			0
$913$	7909.27	−	2878.74i	0.286702	−	0.104351i
$914$	1289.37	−	7312.38i	0.0466615	−	0.264630i
$915$		0			0
$916$	6734.19	−	5650.65i	0.242908	−	0.203824i
$917$	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	$0.826065\pi$
$920$	732.127	−	614.327i	0.0262364	−	0.0220150i
$921$		0			0
$922$	−8521.37	+	48327.1i	−0.304378	+	1.72621i
$923$	6865.28	−	2498.76i	0.244825	−	0.0891090i
$924$		0			0
$925$	3957.46	+	22443.9i	0.140671	+	0.797784i
$926$	32917.7	+	57015.2i	1.16819	+	2.02336i
$927$		0			0
$928$	25416.7	−	44023.0i	0.899078	−	1.55725i
$929$	41134.0	+	14971.6i	1.45271	+	0.528742i	0.943346	−	0.331812i	$-0.107660\pi$
$929$	41134.0	+	14971.6i	1.45271	+	0.528742i	0.509360	+	0.860554i	$0.329882\pi$
$930$		0			0
$931$	−45353.1	−	38055.7i	−1.59655	−	1.33966i
$932$	24728.2	+	20749.4i	0.869098	+	0.729260i
$933$		0			0
$934$	35291.0	+	12844.9i	1.23636	+	0.449997i
$935$	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	$-0.334998\pi$
$938$	2533.81	+	14369.9i	0.0882001	+	0.500208i
$939$		0			0
$940$	4077.48	−	1484.08i	0.141482	−	0.0514951i
$941$	−7567.14	+	42915.4i	−0.262148	+	1.48672i	0.514886	+	0.857259i	$0.327834\pi$
$941$	−7567.14	+	42915.4i	−0.262148	+	1.48672i	−0.777034	+	0.629459i	$0.783277\pi$
$942$		0			0
$943$	−11208.6	+	9405.15i	−0.387066	+	0.324787i
$944$	−3964.92			−0.136702
$945$		0			0
$946$	18624.9			0.640113
$947$	−2963.09	+	2486.33i	−0.101676	+	0.0853166i	−0.692209	−	0.721697i	$-0.743362\pi$
$947$	−2963.09	+	2486.33i	−0.101676	+	0.0853166i	0.590532	+	0.807014i	$0.298918\pi$
$948$		0			0
$949$	246.772	−	1399.51i	0.00844106	−	0.0478716i
$950$	−30983.0	+	11276.9i	−1.05813	+	0.385127i
$951$		0			0
$952$	−1900.06	−	10775.8i	−0.0646863	−	0.366854i
$953$	15695.5	+	27185.4i	0.533502	+	0.924053i	0.999234	+	0.0391271i	$0.0124577\pi$
$953$	15695.5	+	27185.4i	0.533502	+	0.924053i	−0.465732	+	0.884926i	$0.654209\pi$
$954$		0			0
$955$	816.961	−	1415.02i	0.0276819	−	0.0479465i
$956$	−16968.0	−	6175.84i	−0.574042	−	0.208934i
$957$		0			0
$958$	−8710.98	−	7309.38i	−0.293778	−	0.246509i
$959$	22610.8	+	18972.7i	0.761355	+	0.638853i
$960$		0			0
$961$	3273.61	+	1191.50i	0.109886	+	0.0399952i
$962$	10587.8	−	18338.7i	0.354850	−	0.614618i
$963$		0			0
$964$	7623.18	+	13203.7i	0.254695	+	0.441145i
$965$	−56.2419	−	318.964i	−0.00187616	−	0.0106402i
$966$		0			0
$967$	24196.3	−	8806.74i	0.804655	−	0.292870i	0.0932407	−	0.995644i	$-0.470277\pi$
$967$	24196.3	−	8806.74i	0.804655	−	0.292870i	0.711414	+	0.702773i	$0.248055\pi$
$968$	1110.07	−	6295.52i	0.0368585	−	0.209035i
$969$		0			0
$970$	224.591	−	188.454i	0.00743420	−	0.00623804i
$971$	−28752.1			−0.950258			−0.475129	−	0.879916i	$-0.657599\pi$
$971$	−28752.1			−0.950258			−0.475129	+	0.879916i	$0.657599\pi$
$972$		0			0
$973$	31505.5			1.03805
$974$	4189.45	−	3515.36i	0.137822	−	0.115646i
$975$		0			0
$976$	1554.94	−	8818.50i	0.0509963	−	0.289215i
$977$	3882.50	−	1413.11i	0.127136	−	0.0462738i	−0.277669	−	0.960677i	$-0.589562\pi$
$977$	3882.50	−	1413.11i	0.127136	−	0.0462738i	0.404805	+	0.914403i	$0.367339\pi$
$978$		0			0
$979$	3898.78	+	22111.1i	0.127278	+	0.721832i
$980$	3671.11	+	6358.55i	0.119663	+	0.207262i
$981$		0			0
$982$	−14605.8	+	25298.0i	−0.474633	+	0.822088i
$983$	−6566.55	−	2390.03i	−0.213062	−	0.0775484i	0.233284	−	0.972409i	$-0.425053\pi$
$983$	−6566.55	−	2390.03i	−0.213062	−	0.0775484i	−0.446346	+	0.894860i	$0.647275\pi$
$984$		0			0
$985$	−3408.09	−	2859.72i	−0.110244	−	0.0925059i
$986$	24381.3	+	20458.4i	0.787484	+	0.660778i
$987$		0			0
$988$	11861.6	+	4317.27i	0.381951	+	0.139019i
$989$	−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	$0.953311\pi$
$992$	−6053.63	−	34331.8i	−0.193753	−	1.09883i
$993$		0			0
$994$	27899.2	−	10154.5i	0.890250	−	0.324024i
$995$	1343.95	−	7621.90i	0.0428201	−	0.242845i
$996$		0			0
$997$	1360.86	−	1141.90i	0.0432285	−	0.0362730i	−0.620917	−	0.783876i	$-0.713240\pi$
$997$	1360.86	−	1141.90i	0.0432285	−	0.0362730i	0.664146	+	0.747603i	$0.268795\pi$
$998$	−30100.1			−0.954713
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.7	✓	48	9.4	even	3
27.4.e.a.25.7	yes	48	27.7	even	9
81.4.e.a.10.2		48	9.5	odd	6
81.4.e.a.73.2		48	27.20	odd	18
243.4.e.a.55.7		48	27.2	odd	18
243.4.e.a.190.7		48	9.2	odd	6
243.4.e.b.109.2		48	3.2	odd	2
243.4.e.b.136.2		48	27.11	odd	18
243.4.e.c.109.7		48	1.1	even	1	trivial
243.4.e.c.136.7		48	27.16	even	9	inner
243.4.e.d.55.2		48	27.25	even	9
243.4.e.d.190.2		48	9.7	even	3
729.4.a.c.1.5		24	27.23	odd	18
729.4.a.d.1.20		24	27.4	even	9

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.82567 - 2.37102i) q^{2} +(0.973494 - 5.52096i) q^{4} +(1.51818 - 0.552573i) q^{5} +(5.89800 + 33.4492i) q^{7} +(4.41508 + 7.64714i) q^{8} +(2.97972 - 5.16102i) q^{10} +(-23.1524 - 8.42679i) q^{11} +(23.6169 + 19.8169i) q^{13} +(95.9745 + 80.5322i) q^{14} +(72.7513 + 26.4793i) q^{16} +(-18.2417 + 31.5955i) q^{17} +(36.5170 + 63.2494i) q^{19} +(-1.57279 - 8.91974i) q^{20} +(-85.4011 + 31.0835i) q^{22} +(11.6331 - 65.9747i) q^{23} +(-93.7560 + 78.6706i) q^{25} +113.720 q^{26} +190.413 q^{28} +(181.174 - 152.023i) q^{29} +(28.1649 - 159.731i) q^{31} +(201.973 - 73.5122i) q^{32} +(23.3685 + 132.530i) q^{34} +(27.4374 + 47.5229i) q^{35} +(93.1046 - 161.262i) q^{37} +(253.150 + 92.1392i) q^{38} +(10.9285 + 9.17009i) q^{40} +(-167.312 - 140.391i) q^{41} +(-192.576 - 70.0918i) q^{43} +(-69.0627 + 119.620i) q^{44} +(-123.556 - 214.005i) q^{46} +(83.1908 + 471.798i) q^{47} +(-761.751 + 277.255i) q^{49} +(-78.3940 + 444.594i) q^{50} +(132.399 - 111.096i) q^{52} +736.254 q^{53} -39.8060 q^{55} +(-229.751 + 192.784i) q^{56} +(151.488 - 859.133i) q^{58} +(-48.1243 + 17.5158i) q^{59} +(-20.0844 - 113.904i) q^{61} +(-299.141 - 518.127i) q^{62} +(86.7288 - 150.219i) q^{64} +(46.8050 + 17.0356i) q^{65} +(89.2186 + 74.8633i) q^{67} +(156.679 + 131.469i) q^{68} +(190.207 + 69.2296i) q^{70} +(118.488 - 205.227i) q^{71} +(-23.0477 - 39.9198i) q^{73} +(-119.272 - 676.425i) q^{74} +(384.746 - 140.036i) q^{76} +(145.317 - 824.132i) q^{77} +(-576.926 + 484.098i) q^{79} +125.081 q^{80} -805.637 q^{82} +(-261.694 + 219.588i) q^{83} +(-10.2353 + 58.0475i) q^{85} +(-710.344 + 258.544i) q^{86} +(-37.7789 - 214.255i) q^{88} +(-455.636 - 789.185i) q^{89} +(-523.568 + 906.847i) q^{91} +(-352.919 - 128.452i) q^{92} +(1353.71 + 1135.90i) q^{94} +(90.3894 + 75.8457i) q^{95} +(46.2294 + 16.8261i) q^{97} +(-1495.08 + 2589.55i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} - 159 q^{11} + 3 q^{13} - 336 q^{14} - 45 q^{16} - 207 q^{17} - 3 q^{19} + 681 q^{20} + 111 q^{22} + 33 q^{23} + 435 q^{25} + 1914 q^{26}+ \cdots - 4392 q^{98}+O(q^{100}) \) 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 - 159 * q^11 + 3 * q^13 - 336 * q^14 - 45 * q^16 - 207 * q^17 - 3 * q^19 + 681 * q^20 + 111 * q^22 + 33 * q^23 + 435 * q^25 + 1914 * q^26 - 12 * q^28 - 51 * q^29 + 111 * q^31 + 1647 * q^32 - 513 * q^34 - 1257 * q^35 - 3 * q^37 - 525 * q^38 - 6 * q^40 + 447 * q^41 + 516 * q^43 - 2211 * q^44 - 3 * q^46 + 2109 * q^47 - 591 * q^49 - 4938 * q^50 - 1350 * q^52 + 2736 * q^53 - 12 * q^55 - 7773 * q^56 - 888 * q^58 + 3048 * q^59 + 57 * q^61 - 2118 * q^62 - 195 * q^64 + 3297 * q^65 + 2082 * q^67 + 3573 * q^68 + 1524 * q^70 - 3105 * q^71 - 219 * q^73 + 9006 * q^74 - 1425 * q^76 - 8985 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 - 8511 * q^83 - 1827 * q^85 + 12507 * q^86 - 3693 * q^88 - 5202 * q^89 + 267 * q^91 + 5118 * q^92 - 2211 * q^94 + 5178 * q^95 + 1569 * q^97 - 4392 * q^98

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