LMFDB - Embedded newform 162.5.f.a.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,5,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7459340196$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	162.17
Dual form			162.5.f.a.143.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-0.622849 - 0.109825i) q^{5} +(42.1999 - 35.4099i) q^{7} +(-19.5959 + 11.3137i) q^{8} +O(q^{10})$	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-0.622849 - 0.109825i) q^{5} +(42.1999 - 35.4099i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(-0.894430 + 1.54920i) q^{10} +(11.7899 - 2.07887i) q^{11} +(141.273 - 51.4193i) q^{13} +(-53.2910 - 146.416i) q^{14} +(11.1135 + 63.0277i) q^{16} +(-377.445 - 217.918i) q^{17} +(-37.3677 - 64.7228i) q^{19} +(3.25229 + 3.87593i) q^{20} +(5.87993 - 33.3468i) q^{22} +(269.539 - 321.224i) q^{23} +(-586.932 - 213.626i) q^{25} -425.226i q^{26} -440.704 q^{28} +(278.193 - 764.328i) q^{29} +(-1139.63 - 956.259i) q^{31} +(178.269 + 31.4337i) q^{32} +(-944.327 + 792.385i) q^{34} +(-30.1731 + 17.4204i) q^{35} +(143.349 - 248.287i) q^{37} +(-208.172 + 36.7064i) q^{38} +(13.4478 - 4.89461i) q^{40} +(151.071 + 415.063i) q^{41} +(465.619 + 2640.66i) q^{43} +(-82.9427 - 47.8870i) q^{44} +(-593.020 - 1027.14i) q^{46} +(-839.864 - 1000.91i) q^{47} +(110.040 - 624.065i) q^{49} +(-1135.57 + 1353.32i) q^{50} +(-1130.19 - 411.354i) q^{52} -3784.91i q^{53} -7.57162 q^{55} +(-426.328 + 1171.33i) q^{56} +(-1762.35 - 1478.79i) q^{58} +(4003.04 + 705.845i) q^{59} +(-1063.82 + 892.654i) q^{61} +(-3644.04 + 2103.89i) q^{62} +(256.000 - 443.405i) q^{64} +(-93.6391 + 16.5111i) q^{65} +(4668.88 - 1699.33i) q^{67} +(1192.52 + 3276.42i) q^{68} +(17.1121 + 97.0477i) q^{70} +(-4457.32 - 2573.43i) q^{71} +(1733.31 + 3002.18i) q^{73} +(-521.238 - 621.187i) q^{74} +(-103.821 + 588.800i) q^{76} +(423.918 - 505.206i) q^{77} +(5272.09 + 1918.88i) q^{79} -40.4773i q^{80} +1249.32 q^{82} +(-2319.64 + 6373.17i) q^{83} +(211.159 + 177.183i) q^{85} +(7468.91 + 1316.97i) q^{86} +(-207.513 + 174.124i) q^{88} +(12671.0 - 7315.60i) q^{89} +(4140.97 - 7172.37i) q^{91} +(-3303.66 + 582.525i) q^{92} +(-3472.74 + 1263.97i) q^{94} +(16.1663 + 44.4164i) q^{95} +(2192.78 + 12435.9i) q^{97} +(-1552.22 - 896.176i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{5}+O(q^{10}) $ 72 * q + 18 * q^5	$ 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) $ 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$3$		0			0
$3$		0			0
$4$	−6.12836	−	5.14230i	−0.383022	−	0.321394i
$5$	−0.622849	−	0.109825i	−0.0249140	−	0.00439300i	0.161177	−	0.986925i	$-0.448471\pi$
$5$	−0.622849	−	0.109825i	−0.0249140	−	0.00439300i	−0.186091	+	0.982532i	$0.559582\pi$
$6$		0			0
$7$	42.1999	−	35.4099i	0.861222	−	0.722651i	−0.101009	−	0.994886i	$-0.532207\pi$
$7$	42.1999	−	35.4099i	0.861222	−	0.722651i	0.962231	+	0.272234i	$0.0877626\pi$
$8$	−19.5959	+	11.3137i	−0.306186	+	0.176777i
$9$		0			0
$10$	−0.894430	+	1.54920i	−0.00894430	+	0.0154920i
$11$	11.7899	−	2.07887i	0.0974369	−	0.0171808i	−0.124717	−	0.992192i	$-0.539802\pi$
$11$	11.7899	−	2.07887i	0.0974369	−	0.0171808i	0.222154	+	0.975012i	$0.428691\pi$
$12$		0			0
$13$	141.273	−	51.4193i	0.835937	−	0.304256i	0.111644	−	0.993748i	$-0.464388\pi$
$13$	141.273	−	51.4193i	0.835937	−	0.304256i	0.724293	+	0.689492i	$0.242166\pi$
$14$	−53.2910	−	146.416i	−0.271893	−	0.747020i
$15$		0			0
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	−377.445	−	217.918i	−1.30604	−	0.754042i	−0.324607	−	0.945849i	$-0.605232\pi$
$17$	−377.445	−	217.918i	−1.30604	−	0.754042i	−0.981433	+	0.191807i	$0.938565\pi$
$18$		0			0
$19$	−37.3677	−	64.7228i	−0.103512	−	0.179287i	0.809617	−	0.586958i	$-0.199675\pi$
$19$	−37.3677	−	64.7228i	−0.103512	−	0.179287i	−0.913129	+	0.407670i	$0.866341\pi$
$20$	3.25229	+	3.87593i	0.00813072	+	0.00968981i
$21$		0			0
$22$	5.87993	−	33.3468i	0.0121486	−	0.0688983i
$23$	269.539	−	321.224i	0.509526	−	0.607229i	−0.448545	−	0.893760i	$-0.648058\pi$
$23$	269.539	−	321.224i	0.509526	−	0.607229i	0.958071	+	0.286531i	$0.0925021\pi$
$24$		0			0
$25$	−586.932	−	213.626i	−0.939091	−	0.341801i
$26$		−	425.226i		−	0.629032i
$27$		0			0
$28$	−440.704			−0.562123
$29$	278.193	−	764.328i	0.330788	−	0.908833i	−0.657119	−	0.753787i	$-0.728225\pi$
$29$	278.193	−	764.328i	0.330788	−	0.908833i	0.987907	−	0.155046i	$-0.0495526\pi$
$30$		0			0
$31$	−1139.63	−	956.259i	−1.18587	−	0.995067i	−0.999922	−	0.0125078i	$-0.996019\pi$
$31$	−1139.63	−	956.259i	−1.18587	−	0.995067i	−0.185952	−	0.982559i	$-0.559537\pi$
$32$	178.269	+	31.4337i	0.174091	+	0.0306970i
$33$		0			0
$34$	−944.327	+	792.385i	−0.816892	+	0.685454i
$35$	−30.1731	+	17.4204i	−0.0246311	+	0.0142208i
$36$		0			0
$37$	143.349	−	248.287i	0.104710	−	0.181364i	−0.808909	−	0.587933i	$-0.799942\pi$
$37$	143.349	−	248.287i	0.104710	−	0.181364i	0.913620	+	0.406570i	$0.133275\pi$
$38$	−208.172	+	36.7064i	−0.144164	+	0.0254199i
$39$		0			0
$40$	13.4478	−	4.89461i	0.00840489	−	0.00305913i
$41$	151.071	+	415.063i	0.0898694	+	0.246914i	0.976482	−	0.215598i	$-0.0691702\pi$
$41$	151.071	+	415.063i	0.0898694	+	0.246914i	−0.886613	+	0.462513i	$0.846948\pi$
$42$		0			0
$43$	465.619	+	2640.66i	0.251822	+	1.42815i	0.804100	+	0.594494i	$0.202648\pi$
$43$	465.619	+	2640.66i	0.251822	+	1.42815i	−0.552278	+	0.833660i	$0.686241\pi$
$44$	−82.9427	−	47.8870i	−0.0428423	−	0.0247350i
$45$		0			0
$46$	−593.020	−	1027.14i	−0.280255	−	0.485416i
$47$	−839.864	−	1000.91i	−0.380201	−	0.453106i	0.541677	−	0.840587i	$-0.317790\pi$
$47$	−839.864	−	1000.91i	−0.380201	−	0.453106i	−0.921878	+	0.387481i	$0.873345\pi$
$48$		0			0
$49$	110.040	−	624.065i	0.0458307	−	0.259919i
$50$	−1135.57	+	1353.32i	−0.454229	+	0.541329i
$51$		0			0
$52$	−1130.19	−	411.354i	−0.417969	−	0.152128i
$53$		−	3784.91i		−	1.34742i	−0.738994	−	0.673712i	$-0.764699\pi$
$53$		−	3784.91i		−	1.34742i	0.738994	−	0.673712i	$-0.235301\pi$
$54$		0			0
$55$	−7.57162			−0.00250301
$56$	−426.328	+	1171.33i	−0.135946	+	0.373510i
$57$		0			0
$58$	−1762.35	−	1478.79i	−0.523886	−	0.439593i
$59$	4003.04	+	705.845i	1.14997	+	0.202771i	0.715963	−	0.698139i	$-0.245988\pi$
$59$	4003.04	+	705.845i	1.14997	+	0.202771i	0.434007	+	0.900909i	$0.357099\pi$
$60$		0			0
$61$	−1063.82	+	892.654i	−0.285897	+	0.239896i	−0.774446	−	0.632641i	$-0.781971\pi$
$61$	−1063.82	+	892.654i	−0.285897	+	0.239896i	0.488548	+	0.872537i	$0.337527\pi$
$62$	−3644.04	+	2103.89i	−0.947982	+	0.547318i
$63$		0			0
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	−93.6391	+	16.5111i	−0.0221631	+	0.00390795i
$66$		0			0
$67$	4668.88	−	1699.33i	1.04007	−	0.378555i	0.235164	−	0.971956i	$-0.424437\pi$
$67$	4668.88	−	1699.33i	1.04007	−	0.378555i	0.804907	+	0.593401i	$0.202215\pi$
$68$	1192.52	+	3276.42i	0.257898	+	0.708568i
$69$		0			0
$70$	17.1121	+	97.0477i	0.00349227	+	0.0198057i
$71$	−4457.32	−	2573.43i	−0.884213	−	0.510501i	−0.0121678	−	0.999926i	$-0.503873\pi$
$71$	−4457.32	−	2573.43i	−0.884213	−	0.510501i	−0.872045	+	0.489425i	$0.837207\pi$
$72$		0			0
$73$	1733.31	+	3002.18i	0.325260	+	0.563366i	0.981565	−	0.191129i	$-0.0612150\pi$
$73$	1733.31	+	3002.18i	0.325260	+	0.563366i	−0.656305	+	0.754496i	$0.727882\pi$
$74$	−521.238	−	621.187i	−0.0951858	−	0.113438i
$75$		0			0
$76$	−103.821	+	588.800i	−0.0179746	+	0.101939i
$77$	423.918	−	505.206i	0.0714991	−	0.0852093i
$78$		0			0
$79$	5272.09	+	1918.88i	0.844751	+	0.307464i	0.727898	−	0.685685i	$-0.240497\pi$
$79$	5272.09	+	1918.88i	0.844751	+	0.307464i	0.116853	+	0.993149i	$0.462720\pi$
$80$		−	40.4773i		−	0.00632458i
$81$		0			0
$82$	1249.32			0.185800
$83$	−2319.64	+	6373.17i	−0.336717	+	0.925122i	0.649602	+	0.760274i	$0.274936\pi$
$83$	−2319.64	+	6373.17i	−0.336717	+	0.925122i	−0.986319	+	0.164848i	$0.947287\pi$
$84$		0			0
$85$	211.159	+	177.183i	0.0292261	+	0.0245236i
$86$	7468.91	+	1316.97i	1.00986	+	0.178065i
$87$		0			0
$88$	−207.513	+	174.124i	−0.0267967	+	0.0224851i
$89$	12671.0	−	7315.60i	1.59967	−	0.923570i	0.608121	−	0.793844i	$-0.291924\pi$
$89$	12671.0	−	7315.60i	1.59967	−	0.923570i	0.991550	−	0.129726i	$-0.0414098\pi$
$90$		0			0
$91$	4140.97	−	7172.37i	0.500056	−	0.866123i
$92$	−3303.66	+	582.525i	−0.390319	+	0.0688238i
$93$		0			0
$94$	−3472.74	+	1263.97i	−0.393022	+	0.143048i
$95$	16.1663	+	44.4164i	0.00179128	+	0.00492149i
$96$		0			0
$97$	2192.78	+	12435.9i	0.233051	+	1.32170i	0.846679	+	0.532104i	$0.178599\pi$
$97$	2192.78	+	12435.9i	0.233051	+	1.32170i	−0.613627	+	0.789596i	$0.710290\pi$
$98$	−1552.22	−	896.176i	−0.161623	−	0.0933128i
$99$		0			0
$100$	2498.40	+	4327.36i	0.249840	+	0.432736i
$101$	6036.65	+	7194.20i	0.591771	+	0.705245i	0.975945	−	0.218016i	$-0.0699583\pi$
$101$	6036.65	+	7194.20i	0.591771	+	0.705245i	−0.384175	+	0.923260i	$0.625514\pi$
$102$		0			0
$103$	3096.58	−	17561.6i	0.291882	−	1.65534i	−0.387730	−	0.921773i	$-0.626741\pi$
$103$	3096.58	−	17561.6i	0.291882	−	1.65534i	0.679612	−	0.733572i	$-0.262148\pi$
$104$	−2186.64	+	2605.93i	−0.202167	+	0.240933i
$105$		0			0
$106$	−10059.7	−	3661.45i	−0.895314	−	0.325867i
$107$			2169.63i			0.189504i	0.995501	+	0.0947520i	$0.0302058\pi$
$107$			2169.63i			0.189504i	−0.995501	+	0.0947520i	$0.969794\pi$
$108$		0			0
$109$	17743.1			1.49340			0.746700	−	0.665161i	$-0.231637\pi$
$109$	17743.1			1.49340			0.746700	+	0.665161i	$0.231637\pi$
$110$	−7.32462	+	20.1242i	−0.000605341	+	0.00166316i
$111$		0			0
$112$	2700.79	+	2266.23i	0.215306	+	0.180663i
$113$	16755.3	+	2954.40i	1.31218	+	0.231373i	0.785591	−	0.618746i	$-0.212359\pi$
$113$	16755.3	+	2954.40i	1.31218	+	0.231373i	0.526591	+	0.850119i	$0.323470\pi$
$114$		0			0
$115$	−203.161	+	170.472i	−0.0153619	+	0.0128901i
$116$	−5635.27	+	3253.53i	−0.418792	+	0.241790i
$117$		0			0
$118$	5748.49	−	9956.68i	0.412848	−	0.715073i
$119$	−23644.6	+	4169.18i	−1.66970	+	0.294413i
$120$		0			0
$121$	−13623.4	+	4958.50i	−0.930494	+	0.338672i
$122$	1343.42	+	3691.02i	0.0902595	+	0.247986i
$123$		0			0
$124$	2066.66	+	11720.6i	0.134408	+	0.762265i
$125$	684.436	+	395.160i	0.0438039	+	0.0252902i
$126$		0			0
$127$	13536.4	+	23445.8i	0.839260	+	1.45364i	0.890515	+	0.454955i	$0.150345\pi$
$127$	13536.4	+	23445.8i	0.839260	+	1.45364i	−0.0512550	+	0.998686i	$0.516322\pi$
$128$	−930.856	−	1109.35i	−0.0568149	−	0.0677094i
$129$		0			0
$130$	−46.7005	+	264.851i	−0.00276334	+	0.0156717i
$131$	−6166.75	+	7349.25i	−0.359347	+	0.428253i	−0.915183	−	0.403039i	$-0.867954\pi$
$131$	−6166.75	+	7349.25i	−0.359347	+	0.428253i	0.555836	+	0.831292i	$0.312398\pi$
$132$		0			0
$133$	−3868.74	−	1408.11i	−0.218709	−	0.0796035i
$134$		−	14053.1i		−	0.782640i
$135$		0			0
$136$	9861.85			0.533188
$137$	−9865.33	+	27104.8i	−0.525618	+	1.44412i	0.338563	+	0.940944i	$0.390059\pi$
$137$	−9865.33	+	27104.8i	−0.525618	+	1.44412i	−0.864181	+	0.503181i	$0.832163\pi$
$138$		0			0
$139$	−24147.9	−	20262.5i	−1.24983	−	1.04873i	−0.996690	−	0.0812987i	$-0.974093\pi$
$139$	−24147.9	−	20262.5i	−1.24983	−	1.04873i	−0.253137	−	0.967430i	$-0.581462\pi$
$140$	274.492	+	48.4004i	0.0140047	+	0.00246941i
$141$		0			0
$142$	−11151.7	+	9357.41i	−0.553051	+	0.464065i
$143$	1558.70	−	899.916i	0.0762237	−	0.0440078i
$144$		0			0
$145$	−257.215	+	445.509i	−0.0122337	+	0.0211895i
$146$	9656.11	−	1702.63i	0.452998	−	0.0798758i
$147$		0			0
$148$	−2155.26	+	784.449i	−0.0983956	+	0.0358131i
$149$	−11940.4	−	32805.9i	−0.537830	−	1.47768i	−0.849553	−	0.527504i	$-0.823128\pi$
$149$	−11940.4	−	32805.9i	−0.537830	−	1.47768i	0.311722	−	0.950173i	$-0.399094\pi$
$150$		0			0
$151$	−1978.86	−	11222.6i	−0.0867881	−	0.492200i	−0.996956	−	0.0779612i	$-0.975159\pi$
$151$	−1978.86	−	11222.6i	−0.0867881	−	0.492200i	0.910168	−	0.414239i	$-0.135952\pi$
$152$	1464.51	+	845.535i	0.0633877	+	0.0365969i
$153$		0			0
$154$	−932.673	−	1615.44i	−0.0393268	−	0.0681159i
$155$	604.793	+	720.765i	0.0251735	+	0.0300006i
$156$		0			0
$157$	764.678	−	4336.70i	0.0310227	−	0.175938i	−0.965360	−	0.260923i	$-0.915973\pi$
$157$	764.678	−	4336.70i	0.0310227	−	0.175938i	0.996382	+	0.0849849i	$0.0270842\pi$
$158$	10200.2	−	12156.1i	0.408597	−	0.486947i
$159$		0			0
$160$	−107.583	−	39.1569i	−0.00420245	−	0.00152957i
$161$		−	23100.0i		−	0.891169i
$162$		0			0
$163$	−45414.8			−1.70931			−0.854657	−	0.519193i	$-0.826232\pi$
$163$	−45414.8			−1.70931			−0.854657	+	0.519193i	$0.826232\pi$
$164$	1208.56	−	3320.50i	0.0449347	−	0.123457i
$165$		0			0
$166$	14695.0	+	12330.5i	0.533276	+	0.447472i
$167$	8159.14	+	1438.68i	0.292558	+	0.0515858i	0.318001	−	0.948090i	$-0.396989\pi$
$167$	8159.14	+	1438.68i	0.292558	+	0.0515858i	−0.0254430	+	0.999676i	$0.508100\pi$
$168$		0			0
$169$	−4564.78	+	3830.30i	−0.159826	+	0.134110i
$170$	675.197	−	389.825i	0.0233632	−	0.0134888i
$171$		0			0
$172$	10725.6	−	18577.2i	0.362546	−	0.627949i
$173$	−3962.96	+	698.776i	−0.132412	+	0.0233478i	−0.239461	−	0.970906i	$-0.576971\pi$
$173$	−3962.96	+	698.776i	−0.132412	+	0.0233478i	0.107049	+	0.994254i	$0.465860\pi$
$174$		0			0
$175$	−32332.9	+	11768.2i	−1.05577	+	0.384269i
$176$	262.053	+	719.984i	0.00845987	+	0.0232433i
$177$		0			0
$178$	−7186.13	−	40754.6i	−0.226806	−	1.28628i
$179$	2625.75	+	1515.98i	0.0819498	+	0.0473137i	0.540415	−	0.841399i	$-0.318267\pi$
$179$	2625.75	+	1515.98i	0.0819498	+	0.0473137i	−0.458465	+	0.888712i	$0.651601\pi$
$180$		0			0
$181$	9083.47	+	15733.0i	0.277265	+	0.480236i	0.970704	−	0.240279i	$-0.0772388\pi$
$181$	9083.47	+	15733.0i	0.277265	+	0.480236i	−0.693439	+	0.720515i	$0.743905\pi$
$182$	−15057.2	−	17944.5i	−0.454571	−	0.541736i
$183$		0			0
$184$	−1647.63	+	9344.17i	−0.0486658	+	0.275997i
$185$	−116.553	+	138.902i	−0.00340548	+	0.00405850i
$186$		0			0
$187$	−4903.05	−	1784.57i	−0.140211	−	0.0510328i
$188$			10452.8i			0.295744i
$189$		0			0
$190$	133.691			0.00370336
$191$	4030.85	−	11074.7i	0.110492	−	0.303574i	−0.872107	−	0.489316i	$-0.837247\pi$
$191$	4030.85	−	11074.7i	0.110492	−	0.303574i	0.982599	+	0.185742i	$0.0594689\pi$
$192$		0			0
$193$	−12047.3	−	10108.9i	−0.323427	−	0.271388i	0.466588	−	0.884475i	$-0.345483\pi$
$193$	−12047.3	−	10108.9i	−0.323427	−	0.271388i	−0.790015	+	0.613087i	$0.789927\pi$
$194$	35174.0	+	6202.12i	0.934583	+	0.164792i
$195$		0			0
$196$	−3883.49	+	3258.64i	−0.101090	+	0.0848250i
$197$	19126.4	−	11042.6i	0.492833	−	0.284537i	−0.232916	−	0.972497i	$-0.574827\pi$
$197$	19126.4	−	11042.6i	0.492833	−	0.284537i	0.725749	+	0.687960i	$0.241493\pi$
$198$		0			0
$199$	4861.66	−	8420.65i	0.122766	−	0.212637i	−0.798091	−	0.602536i	$-0.794157\pi$
$199$	4861.66	−	8420.65i	0.122766	−	0.212637i	0.920858	+	0.389899i	$0.127490\pi$
$200$	13918.4	−	2454.18i	0.347959	−	0.0613546i
$201$		0			0
$202$	24960.9	−	9085.01i	0.611726	−	0.222650i
$203$	−15325.1	−	42105.4i	−0.371887	−	1.02175i
$204$		0			0
$205$	−48.5098	−	275.113i	−0.00115431	−	0.00654641i
$206$	−43680.5	−	25218.9i	−1.02933	−	0.594281i
$207$		0			0
$208$	4810.88	+	8332.69i	0.111198	+	0.192601i
$209$	−575.111	−	685.390i	−0.0131661	−	0.0156908i
$210$		0			0
$211$	−1458.71	+	8272.76i	−0.0327645	+	0.185817i	−0.996798	−	0.0799652i	$-0.974519\pi$
$211$	−1458.71	+	8272.76i	−0.0327645	+	0.185817i	0.964033	+	0.265782i	$0.0856302\pi$
$212$	−19463.2	+	23195.3i	−0.433054	+	0.516093i
$213$		0			0
$214$	5766.56	+	2098.86i	0.125918	+	0.0458306i
$215$		−	1695.87i		−	0.0366872i
$216$		0			0
$217$	−81953.1			−1.74039
$218$	17164.3	−	47158.5i	0.361171	−	0.992309i
$219$		0			0
$220$	46.4016	+	38.9355i	0.000958710	+	0.000804453i
$221$	−64528.2	−	11378.1i	−1.32119	−	0.232961i
$222$		0			0
$223$	8610.16	−	7224.78i	0.173142	−	0.145283i	−0.552099	−	0.833779i	$-0.686173\pi$
$223$	8610.16	−	7224.78i	0.173142	−	0.145283i	0.725241	+	0.688496i	$0.241729\pi$
$224$	8636.01	−	4986.00i	0.172114	−	0.0993702i
$225$		0			0
$226$	24061.1	−	41675.0i	0.471083	−	0.815940i
$227$	−39215.7	+	6914.79i	−0.761042	+	0.134192i	−0.540683	−	0.841227i	$-0.681834\pi$
$227$	−39215.7	+	6914.79i	−0.761042	+	0.134192i	−0.220359	+	0.975419i	$0.570723\pi$
$228$		0			0
$229$	83003.3	−	30210.7i	1.58279	−	0.576090i	0.606985	−	0.794713i	$-0.292379\pi$
$229$	83003.3	−	30210.7i	1.58279	−	0.576090i	0.975809	+	0.218623i	$0.0701565\pi$
$230$	256.556	+	704.882i	0.00484983	+	0.0133248i
$231$		0			0
$232$	3195.95	+	18125.1i	0.0593777	+	0.336748i
$233$	72284.3	+	41733.4i	1.33147	+	0.768726i	0.985525	−	0.169528i	$-0.0542243\pi$
$233$	72284.3	+	41733.4i	1.33147	+	0.768726i	0.345947	+	0.938254i	$0.387558\pi$
$234$		0			0
$235$	413.184	+	715.655i	0.00748182	+	0.0129589i
$236$	−20902.4	−	24910.5i	−0.375295	−	0.447259i
$237$		0			0
$238$	−11792.2	+	66877.1i	−0.208182	+	1.18066i
$239$	−52700.7	+	62806.2i	−0.922615	+	1.09953i	0.0721556	+	0.997393i	$0.477012\pi$
$239$	−52700.7	+	62806.2i	−0.922615	+	1.09953i	−0.994770	+	0.102136i	$0.967432\pi$
$240$		0			0
$241$	91147.8	+	33175.1i	1.56932	+	0.571187i	0.972848	−	0.231445i	$-0.0743454\pi$
$241$	91147.8	+	33175.1i	1.56932	+	0.571187i	0.596475	+	0.802632i	$0.296568\pi$
$242$			41005.6i			0.700185i
$243$		0			0
$244$	11109.8			0.186606
$245$	−137.076	+	376.613i	−0.00228365	+	0.00627428i
$246$		0			0
$247$	−8607.06	−	7222.18i	−0.141079	−	0.118379i
$248$	33150.8	+	5845.39i	0.539003	+	0.0950408i
$249$		0			0
$250$	1712.38	−	1436.86i	0.0273982	−	0.0229898i
$251$	−55015.2	+	31763.1i	−0.873244	+	0.504168i	−0.868425	−	0.495821i	$-0.834867\pi$
$251$	−55015.2	+	31763.1i	−0.873244	+	0.504168i	−0.00481907	+	0.999988i	$0.501534\pi$
$252$		0			0
$253$	2510.05	−	4347.53i	0.0392139	−	0.0679206i
$254$	75410.2	−	13296.9i	1.16886	−	0.206102i
$255$		0			0
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	23057.3	+	63349.5i	0.349094	+	0.959129i	0.982656	+	0.185437i	$0.0593701\pi$
$257$	23057.3	+	63349.5i	0.349094	+	0.959129i	−0.633562	+	0.773692i	$0.718408\pi$
$258$		0			0
$259$	−2742.53	−	15553.6i	−0.0408838	−	0.231864i
$260$	658.759	+	380.335i	0.00974495	+	0.00562625i
$261$		0			0
$262$	13567.6	+	23499.8i	0.197652	+	0.342344i
$263$	64777.0	+	77198.2i	0.936503	+	1.11608i	0.993051	+	0.117681i	$0.0375460\pi$
$263$	64777.0	+	77198.2i	0.936503	+	1.11608i	−0.0565486	+	0.998400i	$0.518010\pi$
$264$		0			0
$265$	−415.679	+	2357.43i	−0.00591924	+	0.0335697i
$266$	−7485.08	+	8920.37i	−0.105787	+	0.126072i
$267$		0			0
$268$	−37351.0	−	13594.7i	−0.520035	−	0.189277i
$269$			82135.3i			1.13508i	0.823347	+	0.567539i	$0.192104\pi$
$269$			82135.3i			1.13508i	−0.823347	+	0.567539i	$0.807896\pi$
$270$		0			0
$271$	−131533.			−1.79100			−0.895498	−	0.445065i	$-0.853181\pi$
$271$	−131533.			−1.79100			−0.895498	+	0.445065i	$0.853181\pi$
$272$	9540.15	−	26211.3i	0.128949	−	0.354284i
$273$		0			0
$274$	62497.0	+	52441.2i	0.832450	+	0.698508i
$275$	−7363.95	−	1298.46i	−0.0973745	−	0.0171698i
$276$		0			0
$277$	46112.9	−	38693.3i	0.600984	−	0.504286i	−0.290778	−	0.956791i	$-0.593914\pi$
$277$	46112.9	−	38693.3i	0.600984	−	0.504286i	0.891762	+	0.452505i	$0.149469\pi$
$278$	−77214.9	+	44580.0i	−0.999106	+	0.576834i
$279$		0			0
$280$	394.179	−	682.738i	0.00502780	−	0.00870840i
$281$	107029.	−	18872.1i	1.35546	−	0.239005i	0.551745	−	0.834013i	$-0.313962\pi$
$281$	107029.	−	18872.1i	1.35546	−	0.239005i	0.803720	+	0.595008i	$0.202851\pi$
$282$		0			0
$283$	19324.5	−	7033.55i	0.241288	−	0.0878217i	−0.218546	−	0.975827i	$-0.570131\pi$
$283$	19324.5	−	7033.55i	0.241288	−	0.0878217i	0.459834	+	0.888005i	$0.347909\pi$
$284$	14082.7	+	38691.8i	0.174601	+	0.479714i
$285$		0			0
$286$	−883.989	−	5013.35i	−0.0108072	−	0.0612909i
$287$	21072.5	+	12166.2i	0.255830	+	0.147704i
$288$		0			0
$289$	53216.2	+	92173.2i	0.637160	+	1.10359i
$290$	935.272	+	1114.61i	0.0111210	+	0.0132534i
$291$		0			0
$292$	4815.77	−	27311.6i	0.0564807	−	0.320318i
$293$	49560.6	−	59064.0i	0.577299	−	0.687999i	−0.395812	−	0.918331i	$-0.629537\pi$
$293$	49560.6	−	59064.0i	0.577299	−	0.687999i	0.973112	+	0.230333i	$0.0739814\pi$
$294$		0			0
$295$	−2415.77	−	879.270i	−0.0277595	−	0.0101036i
$296$			6487.21i			0.0740414i
$297$		0			0
$298$	−98744.1			−1.11193
$299$	21561.6	−	59239.9i	0.241178	−	0.662632i
$300$		0			0
$301$	113154.	+	94947.9i	1.24893	+	1.04798i
$302$	−31742.4	−	5597.05i	−0.348038	−	0.0613685i
$303$		0			0
$304$	3664.04	−	3074.50i	0.0396473	−	0.0332680i
$305$	760.638	−	439.154i	0.00817670	−	0.00472082i
$306$		0			0
$307$	31482.5	−	54529.2i	0.334035	−	0.578566i	−0.649264	−	0.760563i	$-0.724923\pi$
$307$	31482.5	−	54529.2i	0.334035	−	0.578566i	0.983299	+	0.181998i	$0.0582563\pi$
$308$	−5195.84	+	916.167i	−0.0547715	+	0.00965769i
$309$		0			0
$310$	2500.75	−	910.199i	0.0260224	−	0.00947137i
$311$	−46227.8	−	127010.i	−0.477950	−	1.31316i	−0.911230	−	0.411897i	$-0.864866\pi$
$311$	−46227.8	−	127010.i	−0.477950	−	1.31316i	0.433280	−	0.901259i	$-0.357356\pi$
$312$		0			0
$313$	2699.46	+	15309.4i	0.0275543	+	0.156268i	0.995480	−	0.0949668i	$-0.0302745\pi$
$313$	2699.46	+	15309.4i	0.0275543	+	0.156268i	−0.967926	+	0.251235i	$0.919163\pi$
$314$	−10786.6	−	6227.63i	−0.109402	−	0.0631632i
$315$		0			0
$316$	−22441.8	−	38870.3i	−0.224741	−	0.389263i
$317$	25226.5	+	30063.8i	0.251038	+	0.299175i	0.876816	−	0.480826i	$-0.159663\pi$
$317$	25226.5	+	30063.8i	0.251038	+	0.299175i	−0.625778	+	0.780001i	$0.715219\pi$
$318$		0			0
$319$	1690.91	−	9589.65i	0.0166165	−	0.0942370i
$320$	−208.146	+	248.059i	−0.00203268	+	0.00242245i
$321$		0			0
$322$	−61396.3	−	22346.4i	−0.592149	−	0.215524i
$323$			32572.4i			0.312209i
$324$		0			0
$325$	−93902.3			−0.889016
$326$	−43933.3	+	120706.i	−0.413389	+	1.13578i
$327$		0			0
$328$	−7656.27	−	6424.37i	−0.0711655	−	0.0597149i
$329$	−70884.4	−	12498.8i	−0.654875	−	0.115472i
$330$		0			0
$331$	71296.8	−	59825.1i	0.650750	−	0.546044i	−0.256549	−	0.966531i	$-0.582585\pi$
$331$	71296.8	−	59825.1i	0.650750	−	0.546044i	0.907298	+	0.420488i	$0.138141\pi$
$332$	46988.3	−	27128.7i	0.426299	−	0.246124i
$333$		0			0
$334$	11716.8	−	20294.1i	0.105030	−	0.181918i
$335$	−3094.64	+	545.668i	−0.0275753	+	0.00486227i
$336$		0			0
$337$	−14502.2	+	5278.38i	−0.127695	+	0.0464773i	−0.405077	−	0.914282i	$-0.632755\pi$
$337$	−14502.2	+	5278.38i	−0.127695	+	0.0464773i	0.277382	+	0.960760i	$0.410533\pi$
$338$	5764.51	+	15837.9i	0.0504579	+	0.138632i
$339$		0			0
$340$	−382.926	−	2171.68i	−0.00331251	−	0.0187862i
$341$	−15424.0	−	8905.03i	−0.132644	−	0.0765820i
$342$		0			0
$343$	48678.8	+	84314.1i	0.413763	+	0.716658i
$344$	−38999.9	−	46478.2i	−0.329569	−	0.392765i
$345$		0			0
$346$	−1976.44	+	11208.9i	−0.0165094	+	0.0936294i
$347$	−20646.4	+	24605.5i	−0.171469	+	0.204349i	−0.844935	−	0.534870i	$-0.820361\pi$
$347$	−20646.4	+	24605.5i	−0.171469	+	0.204349i	0.673465	+	0.739219i	$0.264805\pi$
$348$		0			0
$349$	96376.8	+	35078.3i	0.791264	+	0.287997i	0.705862	−	0.708350i	$-0.250560\pi$
$349$	96376.8	+	35078.3i	0.791264	+	0.287997i	0.0854029	+	0.996347i	$0.472782\pi$
$350$			97320.5i			0.794453i
$351$		0			0
$352$	2167.12			0.0174903
$353$	62753.7	−	172414.i	0.503605	−	1.38364i	−0.384127	−	0.923280i	$-0.625497\pi$
$353$	62753.7	−	172414.i	0.503605	−	1.38364i	0.887731	−	0.460362i	$-0.152280\pi$
$354$		0			0
$355$	2493.61	+	2092.39i	0.0197866	+	0.0166029i
$356$	−115271.	−	20325.5i	−0.909539	−	0.160376i
$357$		0			0
$358$	6569.34	−	5512.33i	0.0512573	−	0.0430100i
$359$	65929.7	−	38064.5i	0.511555	−	0.295346i	−0.221918	−	0.975065i	$-0.571232\pi$
$359$	65929.7	−	38064.5i	0.511555	−	0.295346i	0.733473	+	0.679719i	$0.237898\pi$
$360$		0			0
$361$	62367.8	−	108024.i	0.478571	−	0.828909i
$362$	50603.2	−	8922.71i	0.386154	−	0.0680894i
$363$		0			0
$364$	−62259.8	+	22660.7i	−0.469899	+	0.171029i
$365$	−749.875	−	2060.27i	−0.00562864	−	0.0154646i
$366$		0			0
$367$	−27502.4	−	155974.i	−0.204192	−	1.15803i	−0.898707	−	0.438550i	$-0.855492\pi$
$367$	−27502.4	−	155974.i	−0.204192	−	1.15803i	0.694515	−	0.719478i	$-0.255619\pi$
$368$	23241.5	+	13418.5i	0.171621	+	0.0990852i
$369$		0			0
$370$	256.431	+	444.151i	0.00187312	+	0.00324434i
$371$	−134023.	−	159723.i	−0.973718	−	1.16043i
$372$		0			0
$373$	1636.09	−	9278.74i	0.0117595	−	0.0666916i	−0.978363	−	0.206894i	$-0.933664\pi$
$373$	1636.09	−	9278.74i	0.0117595	−	0.0666916i	0.990123	+	0.140203i	$0.0447754\pi$
$374$	−9486.22	+	11305.2i	−0.0678188	+	0.0808233i
$375$		0			0
$376$	27781.9	+	10111.8i	0.196511	+	0.0715241i
$377$		−	122284.i		−	0.860371i
$378$		0			0
$379$	−8267.23			−0.0575548			−0.0287774	−	0.999586i	$-0.509161\pi$
$379$	−8267.23			−0.0575548			−0.0287774	+	0.999586i	$0.509161\pi$
$380$	129.330	−	355.332i	0.000895638	−	0.00246074i
$381$		0			0
$382$	−25535.5	−	21426.8i	−0.174992	−	0.146835i
$383$	−76016.4	−	13403.7i	−0.518215	−	0.0913753i	−0.0915774	−	0.995798i	$-0.529191\pi$
$383$	−76016.4	−	13403.7i	−0.518215	−	0.0913753i	−0.426638	+	0.904423i	$0.640302\pi$
$384$		0			0
$385$	−319.521	+	268.110i	−0.00215565	+	0.00180881i
$386$	−38522.3	+	22240.9i	−0.258546	+	0.149272i
$387$		0			0
$388$	50510.9	−	87487.4i	0.335522	−	0.581142i
$389$	−161798.	+	28529.3i	−1.06924	+	0.188535i	−0.680451	−	0.732793i	$-0.738216\pi$
$389$	−161798.	+	28529.3i	−1.06924	+	0.188535i	−0.388785	+	0.921329i	$0.627105\pi$
$390$		0			0
$391$	−171737.	+	62507.1i	−1.12334	+	0.408861i
$392$	4904.17	+	13474.1i	0.0319149	+	0.0876854i
$393$		0			0
$394$	−10847.2	−	61517.4i	−0.0698754	−	0.396283i
$395$	−3072.98	−	1774.18i	−0.0196954	−	0.0113711i
$396$		0			0
$397$	61887.7	+	107193.i	0.392666	+	0.680117i	0.992800	−	0.119782i	$-0.0382196\pi$
$397$	61887.7	+	107193.i	0.392666	+	0.680117i	−0.600134	+	0.799899i	$0.704886\pi$
$398$	−17677.8	−	21067.5i	−0.111599	−	0.132999i
$399$		0			0
$400$	6941.48	−	39367.1i	0.0433843	−	0.246044i
$401$	167515.	−	199637.i	1.04175	−	1.24151i	0.0720057	−	0.997404i	$-0.477060\pi$
$401$	167515.	−	199637.i	1.04175	−	1.24151i	0.969748	−	0.244109i	$-0.0784955\pi$
$402$		0			0
$403$	−210169.	−	76495.2i	−1.29407	−	0.471003i
$404$		−	75130.9i		−	0.460316i
$405$		0			0
$406$	−126735.			−0.768855
$407$	1173.90	−	3225.27i	0.00708669	−	0.0194705i
$408$		0			0
$409$	−33417.7	−	28040.8i	−0.199770	−	0.167627i	0.537415	−	0.843318i	$-0.319401\pi$
$409$	−33417.7	−	28040.8i	−0.199770	−	0.167627i	−0.737185	+	0.675691i	$0.763845\pi$
$410$	−778.137	−	137.207i	−0.00462901	−	0.000816220i
$411$		0			0
$412$	−109284.	+	91699.9i	−0.643815	+	0.540225i
$413$	193922.	−	111961.i	1.13691	−	0.656396i
$414$		0			0
$415$	2144.72	−	3714.77i	0.0124530	−	0.0215693i
$416$	26801.0	−	4725.74i	0.154869	−	0.0273076i
$417$		0			0
$418$	−2378.02	+	865.527i	−0.0136101	+	0.00495368i
$419$	40235.3	+	110545.i	0.229181	+	0.629670i	0.999972	−	0.00741780i	$-0.00236118\pi$
$419$	40235.3	+	110545.i	0.229181	+	0.629670i	−0.770791	+	0.637088i	$0.780139\pi$
$420$		0			0
$421$	36044.7	+	204420.i	0.203365	+	1.15334i	0.899991	+	0.435908i	$0.143573\pi$
$421$	36044.7	+	204420.i	0.203365	+	1.15334i	−0.696626	+	0.717435i	$0.745316\pi$
$422$	20576.6	+	11879.9i	0.115545	+	0.0667097i
$423$		0			0
$424$	42821.4	+	74168.9i	0.238193	+	0.412563i
$425$	174982.	+	208535.i	0.968758	+	1.15452i
$426$		0			0
$427$	−13284.4	+	75339.8i	−0.0728598	+	0.413208i
$428$	11156.9	−	13296.3i	0.0609054	−	0.0725843i
$429$		0			0
$430$	−4507.37	−	1640.55i	−0.0243773	−	0.00887262i
$431$			32980.8i			0.177544i	0.996052	+	0.0887720i	$0.0282943\pi$
$431$			32980.8i			0.177544i	−0.996052	+	0.0887720i	$0.971706\pi$
$432$		0			0
$433$	−201172.			−1.07298			−0.536490	−	0.843907i	$-0.680250\pi$
$433$	−201172.			−1.07298			−0.536490	+	0.843907i	$0.680250\pi$
$434$	−79279.7	+	217819.i	−0.420904	+	1.15642i
$435$		0			0
$436$	−108736.	−	91240.2i	−0.572005	−	0.479969i
$437$	−30862.6	−	5441.91i	−0.161610	−	0.0284963i
$438$		0			0
$439$	69333.7	−	58177.9i	0.359762	−	0.301876i	−0.444934	−	0.895563i	$-0.646773\pi$
$439$	69333.7	−	58177.9i	0.359762	−	0.301876i	0.804696	+	0.593687i	$0.202328\pi$
$440$	148.373	−	85.6631i	0.000766388	−	0.000442475i
$441$		0			0
$442$	−92664.4	+	160499.i	−0.474317	+	0.821541i
$443$	−108492.	+	19130.1i	−0.552829	+	0.0974787i	−0.443082	−	0.896481i	$-0.646115\pi$
$443$	−108492.	+	19130.1i	−0.552829	+	0.0974787i	−0.109747	+	0.993960i	$0.535004\pi$
$444$		0			0
$445$	−8695.55	+	3164.92i	−0.0439114	+	0.0159824i
$446$	−10873.1	−	29873.6i	−0.0546618	−	0.150182i
$447$		0			0
$448$	−4897.76	−	27776.6i	−0.0244029	−	0.138396i
$449$	16153.8	+	9326.40i	0.0801276	+	0.0462617i	0.539528	−	0.841967i	$-0.318603\pi$
$449$	16153.8	+	9326.40i	0.0801276	+	0.0462617i	−0.459401	+	0.888229i	$0.651936\pi$
$450$		0			0
$451$	2643.96	+	4579.48i	0.0129988	+	0.0225145i
$452$	−87489.7	−	104266.i	−0.428233	−	0.510348i
$453$		0			0
$454$	−19558.0	+	110919.i	−0.0948882	+	0.538138i
$455$	−3366.90	+	4012.52i	−0.0162633	+	0.0193818i
$456$		0			0
$457$	−252716.	−	91981.2i	−1.21004	−	0.440420i	−0.343325	−	0.939217i	$-0.611553\pi$
$457$	−252716.	−	91981.2i	−1.21004	−	0.440420i	−0.866719	+	0.498797i	$0.833775\pi$
$458$		−	249836.i		−	1.19103i
$459$		0			0
$460$	2121.66			0.0100267
$461$	−27214.5	+	74771.3i	−0.128056	+	0.351830i	−0.987108	−	0.160059i	$-0.948832\pi$
$461$	−27214.5	+	74771.3i	−0.128056	+	0.351830i	0.859052	+	0.511889i	$0.171054\pi$
$462$		0			0
$463$	−78139.4	−	65566.8i	−0.364509	−	0.305859i	0.442076	−	0.896978i	$-0.354242\pi$
$463$	−78139.4	−	65566.8i	−0.364509	−	0.305859i	−0.806585	+	0.591118i	$0.798687\pi$
$464$	51265.5	+	9039.50i	0.238117	+	0.0419864i
$465$		0			0
$466$	180847.	−	151749.i	0.832800	−	0.698802i
$467$	−283755.	+	163826.i	−1.30110	+	0.751188i	−0.980592	−	0.196060i	$-0.937185\pi$
$467$	−283755.	+	163826.i	−1.30110	+	0.751188i	−0.320503	+	0.947247i	$0.603852\pi$
$468$		0			0
$469$	136853.	−	237036.i	0.622169	−	1.07763i
$470$	2301.81	−	405.871i	0.0104201	−	0.00183735i
$471$		0			0
$472$	−86429.1	+	31457.6i	−0.387950	+	0.141202i
$473$	10979.2	+	30165.0i	0.0490735	+	0.134828i
$474$		0			0
$475$	8105.85	+	45970.6i	0.0359262	+	0.203748i
$476$	166342.	+	96037.5i	0.734155	+	0.423864i
$477$		0			0
$478$	115948.	+	200828.i	0.507467	+	0.878959i
$479$	128207.	+	152791.i	0.558780	+	0.665928i	0.969288	−	0.245929i	$-0.0790931\pi$
$479$	128207.	+	152791.i	0.558780	+	0.665928i	−0.410508	+	0.911857i	$0.634649\pi$
$480$		0			0
$481$	7484.59	−	42447.2i	0.0323503	−	0.183467i
$482$	176349.	−	210165.i	0.759065	−	0.904618i
$483$		0			0
$484$	108987.	+	39668.0i	0.465247	+	0.169336i
$485$		−	7986.50i		−	0.0339526i
$486$		0			0
$487$	415581.			1.75226			0.876129	−	0.482076i	$-0.160117\pi$
$487$	415581.			1.75226			0.876129	+	0.482076i	$0.160117\pi$
$488$	10747.4	−	29528.2i	0.0451297	−	0.123993i
$489$		0			0
$490$	868.378	+	728.656i	0.00361674	+	0.00303480i
$491$	225929.	+	39837.4i	0.937151	+	0.165245i	0.621308	−	0.783567i	$-0.286602\pi$
$491$	225929.	+	39837.4i	0.937151	+	0.165245i	0.315843	+	0.948811i	$0.397713\pi$
$492$		0			0
$493$	−271564.	+	227869.i	−1.11732	+	0.937543i
$494$	−27521.8	+	15889.7i	−0.112778	+	0.0651122i
$495$		0			0
$496$	47605.6	−	82455.3i	0.193506	−	0.335162i
$497$	−279223.	+	49234.6i	−1.13042	+	0.199323i
$498$		0			0
$499$	215436.	−	78412.4i	0.865203	−	0.314908i	0.128980	−	0.991647i	$-0.458830\pi$
$499$	215436.	−	78412.4i	0.865203	−	0.314908i	0.736223	+	0.676739i	$0.236608\pi$
$500$	−2162.44	−	5941.26i	−0.00864976	−	0.0237650i
$501$		0			0
$502$	31200.9	+	176949.i	0.123811	+	0.702169i
$503$	−306210.	−	176790.i	−1.21027	−	0.698752i	−0.247454	−	0.968900i	$-0.579594\pi$
$503$	−306210.	−	176790.i	−1.21027	−	0.698752i	−0.962819	+	0.270148i	$0.912927\pi$
$504$		0			0
$505$	−2969.82	−	5143.88i	−0.0116452	−	0.0201701i
$506$	−9126.92	−	10877.0i	−0.0356470	−	0.0424824i
$507$		0			0
$508$	37609.2	−	213292.i	0.145736	−	0.826509i
$509$	−71276.8	+	84944.3i	−0.275114	+	0.327868i	−0.885855	−	0.463963i	$-0.846427\pi$
$509$	−71276.8	+	84944.3i	−0.275114	+	0.327868i	0.610741	+	0.791830i	$0.290872\pi$
$510$		0			0
$511$	179452.	+	65315.3i	0.687238	+	0.250134i
$512$			11585.2i			0.0441942i
$513$		0			0
$514$	190679.			0.721733
$515$	−3857.40	+	10598.1i	−0.0145439	+	0.0399590i
$516$		0			0
$517$	−11982.7	−	10054.6i	−0.0448303	−	0.0376171i
$518$	−43992.3	−	7757.04i	−0.163952	−	0.0289092i
$519$		0			0
$520$	1648.14	−	1382.96i	0.00609520	−	0.00511448i
$521$	118453.	−	68388.8i	0.436385	−	0.251947i	−0.265678	−	0.964062i	$-0.585596\pi$
$521$	118453.	−	68388.8i	0.436385	−	0.251947i	0.702063	+	0.712115i	$0.252262\pi$
$522$		0			0
$523$	152714.	−	264508.i	0.558308	−	0.967019i	−0.439329	−	0.898326i	$-0.644784\pi$
$523$	152714.	−	264508.i	0.558308	−	0.967019i	0.997638	−	0.0686925i	$-0.0218827\pi$
$524$	75584.1	−	13327.5i	0.275276	−	0.0485386i
$525$		0			0
$526$	267845.	−	97487.7i	0.968083	−	0.352353i
$527$	221760.	+	609281.i	0.798476	+	2.19380i
$528$		0			0
$529$	18060.2	+	102425.i	0.0645374	+	0.366010i
$530$	5863.58	+	3385.34i	0.0208743	+	0.0120518i
$531$		0			0
$532$	16468.1	+	28523.6i	0.0581863	+	0.100782i
$533$	42684.5	+	50869.4i	0.150250	+	0.179061i
$534$		0			0
$535$	238.280	−	1351.35i	0.000832492	−	0.00472130i
$536$	−72265.2	+	86122.3i	−0.251536	+	0.299768i
$537$		0			0
$538$	218304.	+	79456.0i	0.754217	+	0.274513i
$539$		−	7586.40i		−	0.0261131i
$540$		0			0
$541$	141556.			0.483654			0.241827	−	0.970319i	$-0.422253\pi$
$541$	141556.			0.483654			0.241827	+	0.970319i	$0.422253\pi$
$542$	−127242.	+	349594.i	−0.433143	+	1.19005i
$543$		0			0
$544$	−60436.9	−	50712.6i	−0.204223	−	0.171363i
$545$	−11051.3	−	1948.64i	−0.0372065	−	0.00656051i
$546$		0			0
$547$	−235279.	+	197422.i	−0.786335	+	0.659813i	−0.944835	−	0.327545i	$-0.893779\pi$
$547$	−235279.	+	197422.i	−0.786335	+	0.659813i	0.158500	+	0.987359i	$0.449334\pi$
$548$	199839.	−	115377.i	0.665456	−	0.384201i
$549$		0			0
$550$	−10574.9	+	18316.2i	−0.0349582	+	0.0605494i
$551$	−59864.9	+	10555.8i	−0.197183	+	0.0347686i
$552$		0			0
$553$	290429.	−	105708.i	0.949708	−	0.345665i
$554$	−58232.5	−	159992.i	−0.189734	−	0.521291i
$555$		0			0
$556$	43791.1	+	248352.i	0.141656	+	0.803373i
$557$	−182689.	−	105475.i	−0.588846	−	0.339970i	0.175795	−	0.984427i	$-0.443750\pi$
$557$	−182689.	−	105475.i	−0.588846	−	0.339970i	−0.764641	+	0.644457i	$0.777084\pi$
$558$		0			0
$559$	201560.	+	349113.i	0.645032	+	1.11723i
$560$	−1433.30	−	1708.14i	−0.00457046	−	0.00544687i
$561$		0			0
$562$	53378.3	−	302723.i	0.169002	−	0.958458i
$563$	140922.	−	167944.i	0.444592	−	0.529844i	−0.496481	−	0.868047i	$-0.665375\pi$
$563$	140922.	−	167944.i	0.444592	−	0.529844i	0.941073	+	0.338204i	$0.109819\pi$
$564$		0			0
$565$	−10111.5	−	3680.30i	−0.0316752	−	0.0115288i
$566$		−	58165.8i		−	0.181566i
$567$		0			0
$568$	116460.			0.360978
$569$	24998.3	−	68682.2i	0.0772121	−	0.212138i	−0.895081	−	0.445904i	$-0.852882\pi$
$569$	24998.3	−	68682.2i	0.0772121	−	0.212138i	0.972293	+	0.233765i	$0.0751047\pi$
$570$		0			0
$571$	−339405.	−	284794.i	−1.04099	−	0.873493i	−0.0488708	−	0.998805i	$-0.515562\pi$
$571$	−339405.	−	284794.i	−1.04099	−	0.873493i	−0.992117	+	0.125312i	$0.960007\pi$
$572$	−14179.9	−	2500.30i	−0.0433392	−	0.00764187i
$573$		0			0
$574$	52721.1	−	44238.2i	0.160015	−	0.134268i
$575$	−226823.	+	130956.i	−0.686043	+	0.396087i
$576$		0			0
$577$	4321.42	−	7484.92i	0.0129800	−	0.0224820i	−0.859462	−	0.511199i	$-0.829202\pi$
$577$	4321.42	−	7484.92i	0.0129800	−	0.0224820i	0.872442	+	0.488717i	$0.162535\pi$
$578$	296463.	−	52274.4i	0.887390	−	0.156471i
$579$		0			0
$580$	3867.24	−	1407.56i	0.0114960	−	0.00418419i
$581$	127785.	+	351085.i	0.378553	+	1.04006i
$582$		0			0
$583$	−7868.35	−	44623.6i	−0.0231498	−	0.131289i
$584$	−67931.6	−	39220.3i	−0.199180	−	0.114997i
$585$		0			0
$586$	−109040.	−	188862.i	−0.317533	−	0.549983i
$587$	−191776.	−	228550.i	−0.556568	−	0.663292i	0.412248	−	0.911072i	$-0.364744\pi$
$587$	−191776.	−	228550.i	−0.556568	−	0.663292i	−0.968817	+	0.247779i	$0.920299\pi$
$588$		0			0
$589$	−19306.6	+	109493.i	−0.0556512	+	0.315613i
$590$	−4673.94	+	5570.18i	−0.0134270	+	0.0160017i
$591$		0			0
$592$	17242.1	+	6275.60i	0.0491978	+	0.0179065i
$593$			37044.9i			0.105346i	0.998612	+	0.0526732i	$0.0167742\pi$
$593$			37044.9i			0.105346i	−0.998612	+	0.0526732i	$0.983226\pi$
$594$		0			0
$595$	15184.9			0.0428922
$596$	−95523.0	+	262447.i	−0.268915	+	0.738839i
$597$		0			0
$598$	−136593.	−	114615.i	−0.381967	−	0.320508i
$599$	674156.	+	118872.i	1.87891	+	0.331303i	0.991545	−	0.129760i	$-0.0414206\pi$
$599$	674156.	+	118872.i	1.87891	+	0.331303i	0.887368	+	0.461063i	$0.152532\pi$
$600$		0			0
$601$	−359910.	+	302000.i	−0.996426	+	0.836101i	−0.986485	−	0.163850i	$-0.947609\pi$
$601$	−359910.	+	302000.i	−0.996426	+	0.836101i	−0.00994093	+	0.999951i	$0.503164\pi$
$602$	361821.	−	208897.i	0.998391	−	0.576421i
$603$		0			0
$604$	−45583.1	+	78952.3i	−0.124948	+	0.216417i
$605$	9029.87	−	1592.21i	0.0246701	−	0.00435000i
$606$		0			0
$607$	−582959.	+	212180.i	−1.58220	+	0.575873i	−0.975680	−	0.219198i	$-0.929656\pi$
$607$	−582959.	+	212180.i	−1.58220	+	0.575873i	−0.606517	+	0.795070i	$0.707434\pi$
$608$	−4627.04	−	12712.7i	−0.0125169	−	0.0343898i
$609$		0			0
$610$	−431.382	−	2446.49i	−0.00115932	−	0.00657482i
$611$	−170117.	−	98216.9i	−0.455685	−	0.263090i
$612$		0			0
$613$	−281172.	−	487004.i	−0.748257	−	1.29602i	−0.948658	−	0.316305i	$-0.897558\pi$
$613$	−281172.	−	487004.i	−0.748257	−	1.29602i	0.200401	−	0.979714i	$-0.435776\pi$
$614$	−114475.	−	136426.i	−0.303651	−	0.361877i
$615$		0			0
$616$	−2591.31	+	14696.1i	−0.00682902	+	0.0387293i
$617$	−149496.	+	178163.i	−0.392699	+	0.468001i	−0.925779	−	0.378064i	$-0.876590\pi$
$617$	−149496.	+	178163.i	−0.392699	+	0.468001i	0.533080	+	0.846065i	$0.321034\pi$
$618$		0			0
$619$	140839.	+	51261.2i	0.367571	+	0.133785i	0.519201	−	0.854652i	$-0.326230\pi$
$619$	140839.	+	51261.2i	0.367571	+	0.133785i	−0.151629	+	0.988437i	$0.548452\pi$
$620$		−	7527.13i		−	0.0195815i
$621$		0			0
$622$	−382293.			−0.988134
$623$	275670.	−	757396.i	0.710253	−	1.95140i
$624$		0			0
$625$	298662.	+	250607.i	0.764574	+	0.641554i
$626$	43301.6	+	7635.23i	0.110498	+	0.0194838i
$627$		0			0
$628$	−26986.8	+	22644.6i	−0.0684278	+	0.0574178i
$629$	−108213.	+	62476.5i	−0.273512	+	0.157912i
$630$		0			0
$631$	−198524.	+	343854.i	−0.498602	+	0.863605i	−0.999999	−	0.00161303i	$-0.999487\pi$
$631$	−198524.	+	343854.i	−0.498602	+	0.863605i	0.501396	+	0.865218i	$0.332820\pi$
$632$	−125021.	+	22044.6i	−0.313004	+	0.0551910i
$633$		0			0
$634$	104309.	−	37965.3i	0.259503	−	0.0944513i
$635$	−5856.21	−	16089.8i	−0.0145234	−	0.0399028i
$636$		0			0
$637$	−16543.3	−	93821.9i	−0.0407703	−	0.231220i
$638$	−23852.1	−	13771.0i	−0.0585984	−	0.0338318i
$639$		0			0
$640$	457.948	+	793.190i	0.00111804	+	0.00193650i
$641$	286635.	+	341599.i	0.697612	+	0.831381i	0.992254	−	0.124226i	$-0.0396449\pi$
$641$	286635.	+	341599.i	0.697612	+	0.831381i	−0.294642	+	0.955608i	$0.595200\pi$
$642$		0			0
$643$	15317.3	−	86868.9i	0.0370477	−	0.210108i	−0.960665	−	0.277711i	$-0.910424\pi$
$643$	15317.3	−	86868.9i	0.0370477	−	0.210108i	0.997712	+	0.0676034i	$0.0215353\pi$
$644$	−118787.	+	141565.i	−0.286416	+	0.341337i
$645$		0			0
$646$	86572.7	+	31509.9i	0.207451	+	0.0755060i
$647$			34865.4i			0.0832887i	0.999132	+	0.0416444i	$0.0132596\pi$
$647$			34865.4i			0.0832887i	−0.999132	+	0.0416444i	$0.986740\pi$
$648$		0			0
$649$	48662.7			0.115533
$650$	−90839.2	+	249579.i	−0.215004	+	0.590718i
$651$		0			0
$652$	278318.	+	233536.i	0.654705	+	0.549363i
$653$	−428549.	−	75564.8i	−1.00502	−	0.177212i	−0.353169	−	0.935560i	$-0.614896\pi$
$653$	−428549.	−	75564.8i	−1.00502	−	0.177212i	−0.651850	+	0.758348i	$0.726007\pi$
$654$		0			0
$655$	4648.09	−	3900.21i	0.0108341	−	0.00909087i
$656$	−24481.5	+	14134.4i	−0.0568894	+	0.0328451i
$657$		0			0
$658$	−101792.	+	176309.i	−0.235105	+	0.407214i
$659$	−142541.	+	25133.8i	−0.328223	+	0.0578746i	−0.335332	−	0.942100i	$-0.608848\pi$
$659$	−142541.	+	25133.8i	−0.328223	+	0.0578746i	0.00710852	+	0.999975i	$0.497737\pi$
$660$		0			0
$661$	−37382.3	+	13606.1i	−0.0855586	+	0.0311408i	−0.384445	−	0.923148i	$-0.625607\pi$
$661$	−37382.3	+	13606.1i	−0.0855586	+	0.0311408i	0.298886	+	0.954289i	$0.403385\pi$
$662$	−90035.2	−	247370.i	−0.205445	−	0.564457i
$663$		0			0
$664$	−26648.6	−	151132.i	−0.0604420	−	0.342783i
$665$	2255.00	+	1301.92i	0.00509921	+	0.00294403i
$666$		0			0
$667$	−170537.	−	295379.i	−0.383325	−	0.663938i
$668$	−42604.0	−	50773.5i	−0.0954768	−	0.113785i
$669$		0			0
$670$	−1543.38	+	8752.95i	−0.00343814	+	0.0194987i
$671$	−10686.6	+	12735.8i	−0.0237353	+	0.0282867i
$672$		0			0
$673$	−454550.	−	165443.i	−1.00358	−	0.365273i	−0.212616	−	0.977136i	$-0.568198\pi$
$673$	−454550.	−	165443.i	−1.00358	−	0.365273i	−0.790964	+	0.611863i	$0.790421\pi$
$674$			43650.9i			0.0960890i
$675$		0			0
$676$	47671.2			0.104319
$677$	−97073.9	+	266708.i	−0.211800	+	0.581915i	−0.999413	−	0.0342549i	$-0.989094\pi$
$677$	−97073.9	+	266708.i	−0.211800	+	0.581915i	0.787614	+	0.616170i	$0.211316\pi$
$678$		0			0
$679$	532888.	+	447146.i	1.15584	+	0.969863i
$680$	−6142.45	−	1083.08i	−0.0132838	−	0.00234230i
$681$		0			0
$682$	−38589.1	+	32380.1i	−0.0829651	+	0.0696160i
$683$	−429620.	+	248041.i	−0.920964	+	0.531719i	−0.883943	−	0.467596i	$-0.845120\pi$
$683$	−429620.	+	248041.i	−0.920964	+	0.531719i	−0.0370216	+	0.999314i	$0.511787\pi$
$684$		0			0
$685$	9121.40	−	15798.7i	0.0194393	−	0.0336698i
$686$	271185.	−	47817.3i	0.576259	−	0.101610i
$687$		0			0
$688$	−161260.	+	58693.8i	−0.340682	+	0.123998i
$689$	−194618.	−	534708.i	−0.409962	−	1.12636i
$690$		0			0
$691$	−69234.6	−	392649.i	−0.145000	−	0.822334i	−0.967367	−	0.253378i	$-0.918458\pi$
$691$	−69234.6	−	392649.i	−0.145000	−	0.822334i	0.822368	−	0.568956i	$-0.192653\pi$
$692$	27879.7	+	16096.4i	0.0582205	+	0.0336136i
$693$		0			0
$694$	45424.8	+	78678.0i	0.0943135	+	0.163356i
$695$	12815.2	+	15272.5i	0.0265311	+	0.0316185i
$696$		0			0
$697$	33428.9	−	189585.i	0.0688108	−	0.390245i
$698$	186466.	−	222221.i	0.382726	−	0.456115i
$699$		0			0
$700$	258663.	+	94145.8i	0.527885	+	0.192134i
$701$		−	745502.i		−	1.51709i	−0.651618	−	0.758547i	$-0.725910\pi$
$701$		−	745502.i		−	1.51709i	0.651618	−	0.758547i	$-0.274090\pi$
$702$		0			0
$703$	−21426.4			−0.0433550
$704$	2096.42	−	5759.88i	0.00422993	−	0.0116216i
$705$		0			0
$706$	−397545.	−	333580.i	−0.797585	−	0.669253i
$707$	509492.	+	89837.2i	1.01929	+	0.179729i
$708$		0			0
$709$	166931.	−	140072.i	0.332081	−	0.278649i	−0.461466	−	0.887158i	$-0.652676\pi$
$709$	166931.	−	140072.i	0.332081	−	0.278649i	0.793547	+	0.608509i	$0.208232\pi$
$710$	7973.52	−	4603.51i	0.0158173	−	0.00913214i
$711$		0			0
$712$	−165533.	+	286712.i	−0.326531	+	0.565569i
$713$	−614347.	+	108326.i	−1.20847	+	0.213085i
$714$		0			0
$715$	−1069.67	+	389.327i	−0.00209236	+	0.000761558i
$716$	−8295.92	−	22792.9i	−0.0161822	−	0.0444603i
$717$		0			0
$718$	−37390.9	−	212054.i	−0.0725299	−	0.411337i
$719$	536209.	+	309580.i	1.03723	+	0.598846i	0.919048	−	0.394145i	$-0.128959\pi$
$719$	536209.	+	309580.i	1.03723	+	0.598846i	0.118184	+	0.992992i	$0.462293\pi$
$720$		0			0
$721$	−491178.	−	850745.i	−0.944862	−	1.63655i
$722$	−226779.	−	270265.i	−0.435039	−	0.518460i
$723$		0			0
$724$	25237.2	−	143127.i	0.0481465	−	0.273052i
$725$	−326560.	+	389180.i	−0.621280	+	0.740413i
$726$		0			0
$727$	−55997.4	−	20381.4i	−0.105950	−	0.0385625i	0.288501	−	0.957479i	$-0.406843\pi$
$727$	−55997.4	−	20381.4i	−0.105950	−	0.0385625i	−0.394451	+	0.918917i	$0.629065\pi$
$728$			187399.i			0.353593i
$729$		0			0
$730$	−6201.29			−0.0116369
$731$	399701.	−	1.09817e6i	0.747999	−	2.05511i
$732$		0			0
$733$	−143087.	−	120064.i	−0.266313	−	0.223463i	0.499846	−	0.866114i	$-0.333390\pi$
$733$	−143087.	−	120064.i	−0.266313	−	0.223463i	−0.766159	+	0.642651i	$0.777834\pi$
$734$	−441160.	−	77788.5i	−0.818850	−	0.144385i
$735$		0			0
$736$	58147.8	−	48791.8i	0.107344	−	0.0900723i
$737$	51512.7	−	29740.9i	0.0948374	−	0.0547544i
$738$		0			0
$739$	−165525.	+	286698.i	−0.303093	+	0.524972i	−0.976835	−	0.213995i	$-0.931353\pi$
$739$	−165525.	+	286698.i	−0.303093	+	0.524972i	0.673742	+	0.738967i	$0.264686\pi$
$740$	1428.55	−	251.892i	0.00260875	−	0.000459993i
$741$		0			0
$742$	−554172.	+	201702.i	−1.00655	+	0.366355i
$743$	−184250.	−	506222.i	−0.333756	−	0.916988i	−0.987125	−	0.159949i	$-0.948867\pi$
$743$	−184250.	−	506222.i	−0.333756	−	0.916988i	0.653369	−	0.757040i	$-0.273355\pi$
$744$		0			0
$745$	3834.14	+	21744.5i	0.00690805	+	0.0391775i
$746$	−23078.8	−	13324.6i	−0.0414701	−	0.0239428i
$747$		0			0
$748$	20870.9	+	36149.4i	0.0373025	+	0.0646098i
$749$	76826.5	+	91558.2i	0.136945	+	0.163205i
$750$		0			0
$751$	−56383.0	+	319764.i	−0.0999697	+	0.566956i	0.893141	+	0.449777i	$0.148496\pi$
$751$	−56383.0	+	319764.i	−0.0999697	+	0.566956i	−0.993111	+	0.117180i	$0.962615\pi$
$752$	53751.3	−	64058.3i	0.0950503	−	0.113277i
$753$		0			0
$754$	−325012.	−	118295.i	−0.571685	−	0.208076i
$755$			7207.35i			0.0126439i
$756$		0			0
$757$	492888.			0.860114			0.430057	−	0.902802i	$-0.358493\pi$
$757$	492888.			0.860114			0.430057	+	0.902802i	$0.358493\pi$
$758$	−7997.54	+	21973.1i	−0.0139193	+	0.0382430i
$759$		0			0
$760$	−819.307	−	687.481i	−0.00141847	−	0.00119024i
$761$	−479327.	−	84518.2i	−0.827680	−	0.145942i	−0.256268	−	0.966606i	$-0.582493\pi$
$761$	−479327.	−	84518.2i	−0.827680	−	0.145942i	−0.571412	+	0.820664i	$0.693604\pi$
$762$		0			0
$763$	748756.	−	628281.i	1.28615	−	1.07921i
$764$	−81651.7	+	47141.7i	−0.139887	+	0.0807641i
$765$		0			0
$766$	−109162.	+	189074.i	−0.186043	+	0.322236i
$767$	601818.	−	106117.i	1.02300	−	0.180382i
$768$		0			0
$769$	200750.	−	73067.0i	0.339471	−	0.123557i	−0.166659	−	0.986015i	$-0.553298\pi$
$769$	200750.	−	73067.0i	0.339471	−	0.123557i	0.506130	+	0.862457i	$0.331076\pi$
$770$	403.499	+	1108.61i	0.000680552	+	0.00186980i
$771$		0			0
$772$	21847.3	+	123902.i	0.0366575	+	0.207895i
$773$	95275.9	+	55007.6i	0.159450	+	0.0920584i	0.577602	−	0.816319i	$-0.303989\pi$
$773$	95275.9	+	55007.6i	0.159450	+	0.0920584i	−0.418152	+	0.908377i	$0.637322\pi$
$774$		0			0
$775$	464601.	+	804712.i	0.773529	+	1.33979i
$776$	−183665.	−	218884.i	−0.305003	−	0.363488i
$777$		0			0
$778$	−80693.1	+	457633.i	−0.133314	+	0.756064i
$779$	21218.9	−	25287.7i	0.0349661	−	0.0416710i
$780$		0			0
$781$	−57901.0	−	21074.2i	−0.0949257	−	0.0345501i
$782$			516919.i			0.845297i
$783$		0			0
$784$	40556.3			0.0659821
$785$	−952.557	+	2617.13i	−0.00154579	+	0.00424704i
$786$		0			0
$787$	251295.	+	210862.i	0.405728	+	0.340446i	0.822703	−	0.568472i	$-0.192465\pi$
$787$	251295.	+	210862.i	0.405728	+	0.340446i	−0.416975	+	0.908918i	$0.636910\pi$
$788$	−173997.	−	30680.5i	−0.280214	−	0.0494094i
$789$		0			0
$790$	−7688.25	+	6451.21i	−0.0123189	+	0.0103368i
$791$	811685.	−	468627.i	1.29728	−	0.748987i
$792$		0			0
$793$	−104390.	+	180809.i	−0.166002	+	0.287524i
$794$	344771.	−	60792.4i	0.546877	−	0.0964292i
$795$		0			0
$796$	−73095.5	+	26604.6i	−0.115362	+	0.0419885i
$797$	−419233.	−	1.15183e6i	−0.659992	−	1.81331i	−0.576971	−	0.816765i	$-0.695765\pi$
$797$	−419233.	−	1.15183e6i	−0.659992	−	1.81331i	−0.0830213	−	0.996548i	$-0.526457\pi$
$798$		0			0
$799$	98886.1	+	560811.i	0.154897	+	0.878462i
$800$	−97916.9	−	56532.3i	−0.152995	−	0.0883318i
$801$		0			0
$802$	−368554.	−	638354.i	−0.572997	−	0.992460i
$803$	26676.6	+	31792.0i	0.0413713	+	0.0493044i
$804$		0			0
$805$	−2536.96	+	14387.8i	−0.00391491	+	0.0222025i
$806$	−406626.	+	484598.i	−0.625929	+	0.745953i
$807$		0			0
$808$	−199687.	−	72680.1i	−0.305863	−	0.111325i
$809$			1.04887e6i			1.60260i	0.598261	+	0.801301i	$0.295858\pi$
$809$			1.04887e6i			1.60260i	−0.598261	+	0.801301i	$0.704142\pi$
$810$		0			0
$811$	587821.			0.893724			0.446862	−	0.894603i	$-0.352541\pi$
$811$	587821.			0.893724			0.446862	+	0.894603i	$0.352541\pi$
$812$	−122601.	+	336843.i	−0.185944	+	0.510876i
$813$		0			0
$814$	−7436.69	−	6240.12i	−0.0112236	−	0.00941769i
$815$	28286.5	+	4987.68i	0.0425858	+	0.00750902i
$816$		0			0
$817$	153512.	−	128811.i	0.229984	−	0.192979i
$818$	−106856.	+	61693.3i	−0.159695	+	0.0922001i
$819$		0			0
$820$	−1117.43	+	1935.44i	−0.00166185	+	0.00287841i
$821$	464653.	−	81930.8i	0.689354	−	0.121552i	0.182012	−	0.983296i	$-0.441739\pi$
$821$	464653.	−	81930.8i	0.689354	−	0.121552i	0.507342	+	0.861745i	$0.330628\pi$
$822$		0			0
$823$	−111911.	+	40732.4i	−0.165225	+	0.0601369i	−0.423308	−	0.905986i	$-0.639131\pi$
$823$	−111911.	+	40732.4i	−0.165225	+	0.0601369i	0.258084	+	0.966123i	$0.416909\pi$
$824$	138006.	+	379169.i	0.203256	+	0.558442i
$825$		0			0
$826$	−109979.	−	623724.i	−0.161195	−	0.914182i
$827$	633347.	+	365663.i	0.926041	+	0.534650i	0.885557	−	0.464530i	$-0.153777\pi$
$827$	633347.	+	365663.i	0.926041	+	0.534650i	0.0404839	+	0.999180i	$0.487110\pi$
$828$		0			0
$829$	−546295.	−	946210.i	−0.794910	−	1.37682i	−0.922896	−	0.385049i	$-0.874185\pi$
$829$	−546295.	−	946210.i	−0.794910	−	1.37682i	0.127986	−	0.991776i	$-0.459149\pi$
$830$	−7798.54	−	9293.94i	−0.0113203	−	0.0134910i
$831$		0			0
$832$	13366.4	−	75804.7i	0.0193094	−	0.109509i
$833$	−177529.	+	211571.i	−0.255847	+	0.304906i
$834$		0			0
$835$	−4923.91	−	1792.16i	−0.00706216	−	0.00257042i
$836$			7157.71i			0.0102414i
$837$		0			0
$838$	332736.			0.473819
$839$	−55677.5	+	152973.i	−0.0790962	+	0.217315i	−0.972938	−	0.231068i	$-0.925778\pi$
$839$	−55677.5	+	152973.i	−0.0790962	+	0.217315i	0.893841	+	0.448384i	$0.148000\pi$
$840$		0			0
$841$	35002.0	+	29370.2i	0.0494882	+	0.0415255i
$842$	578186.	+	101950.i	0.815536	+	0.143801i
$843$		0			0
$844$	51480.5	−	43197.3i	0.0722700	−	0.0606417i
$845$	3263.83	−	1884.37i	0.00457103	−	0.00263909i
$846$		0			0
$847$	−399324.	+	691650.i	−0.556620	+	0.964094i
$848$	238554.	−	42063.6i	0.331738	−	0.0584944i
$849$		0			0
$850$	723530.	−	263343.i	1.00143	−	0.364489i
$851$	−41117.7	−	112970.i	−0.0567767	−	0.155993i
$852$		0			0
$853$	−115002.	−	652207.i	−0.158054	−	0.896371i	−0.955940	−	0.293562i	$-0.905159\pi$
$853$	−115002.	−	652207.i	−0.158054	−	0.896371i	0.797886	−	0.602809i	$-0.205952\pi$
$854$	187391.	+	108190.i	0.256941	+	0.148345i
$855$		0			0
$856$	−24546.6	−	42515.9i	−0.0334999	−	0.0580235i
$857$	296945.	+	353885.i	0.404310	+	0.481838i	0.929329	−	0.369252i	$-0.120386\pi$
$857$	296945.	+	353885.i	0.404310	+	0.481838i	−0.525019	+	0.851091i	$0.675942\pi$
$858$		0			0
$859$	−199075.	+	1.12901e6i	−0.269793	+	1.53007i	0.485237	+	0.874383i	$0.338733\pi$
$859$	−199075.	+	1.12901e6i	−0.269793	+	1.53007i	−0.755030	+	0.655690i	$0.772378\pi$
$860$	−8720.66	+	10392.9i	−0.0117911	+	0.0140520i
$861$		0			0
$862$	87658.0	+	31904.9i	0.117971	+	0.0429381i
$863$			497524.i			0.668024i	0.942569	+	0.334012i	$0.108403\pi$
$863$			497524.i			0.668024i	−0.942569	+	0.334012i	$0.891597\pi$
$864$		0			0
$865$	2545.07			0.00340147
$866$	−194610.	+	534685.i	−0.259495	+	0.712956i
$867$		0			0
$868$	502238.	+	421427.i	0.666607	+	0.559350i
$869$	66146.3	+	11663.4i	0.0875923	+	0.0154449i
$870$		0			0
$871$	572209.	−	480141.i	0.754256	−	0.632896i
$872$	−347692.	+	200740.i	−0.457258	+	0.263998i
$873$		0			0
$874$	−44319.6	+	76763.8i	−0.0580194	+	0.100492i
$875$	42875.7	−	7560.14i	0.0560009	−	0.00987447i
$876$		0			0
$877$	943703.	−	343480.i	1.22698	−	0.446583i	0.354415	−	0.935088i	$-0.384680\pi$
$877$	943703.	−	343480.i	1.22698	−	0.446583i	0.872561	+	0.488505i	$0.162458\pi$
$878$	−87556.2	−	240559.i	−0.113579	−	0.312056i
$879$		0			0
$880$	−84.1471	−	477.222i	−0.000108661	−	0.000616247i
$881$	−88277.9	−	50967.2i	−0.113737	−	0.0656658i	0.442053	−	0.896989i	$-0.354250\pi$
$881$	−88277.9	−	50967.2i	−0.113737	−	0.0656658i	−0.555789	+	0.831323i	$0.687584\pi$
$882$		0			0
$883$	180204.	+	312123.i	0.231123	+	0.400318i	0.958139	−	0.286303i	$-0.0924265\pi$
$883$	180204.	+	312123.i	0.231123	+	0.400318i	−0.727016	+	0.686621i	$0.759093\pi$
$884$	336942.	+	401552.i	0.431172	+	0.513851i
$885$		0			0
$886$	−54108.1	+	306862.i	−0.0689279	+	0.390909i
$887$	317087.	−	377889.i	0.403024	−	0.480305i	−0.525916	−	0.850537i	$-0.676277\pi$
$887$	317087.	−	377889.i	0.403024	−	0.480305i	0.928939	+	0.370232i	$0.120722\pi$
$888$		0			0
$889$	1.40145e6	+	510085.i	1.77326	+	0.645415i
$890$			26173.2i			0.0330428i
$891$		0			0
$892$	−89918.1			−0.113010
$893$	−33398.0	+	91760.1i	−0.0418810	+	0.115067i
$894$		0			0
$895$	−1468.95	−	1232.60i	−0.00183384	−	0.00153878i
$896$	−78564.0	−	13853.0i	−0.0978606	−	0.0172555i
$897$		0			0
$898$	40415.0	−	33912.2i	0.0501176	−	0.0420537i
$899$	−1.04793e6	+	605023.i	−1.29662	+	0.748605i
$900$		0			0
$901$	−824802.	+	1.42860e6i	−1.01601	+	1.75979i
$902$	14729.3	−	2597.17i	0.0181038	−	0.00319218i
$903$		0			0
$904$	−361760.	+	131670.i	−0.442674	+	0.161120i
$905$	−3929.75	−	10796.9i	−0.00479808	−	0.0131826i
$906$		0			0
$907$	−212145.	−	1.20314e6i	−0.257881	−	1.46252i	−0.788568	−	0.614948i	$-0.789177\pi$
$907$	−212145.	−	1.20314e6i	−0.257881	−	1.46252i	0.530687	−	0.847568i	$-0.321934\pi$
$908$	275886.	+	159283.i	0.334624	+	0.193196i
$909$		0			0
$910$	7407.61	+	12830.4i	0.00894531	+	0.0154937i
$911$	444391.	+	529605.i	0.535462	+	0.638139i	0.964164	−	0.265307i	$-0.0854733\pi$
$911$	444391.	+	529605.i	0.535462	+	0.638139i	−0.428702	+	0.903446i	$0.641029\pi$
$912$		0			0
$913$	−14099.3	+	79961.0i	−0.0169144	+	0.0959261i
$914$	−488945.	+	582702.i	−0.585285	+	0.697516i
$915$		0			0
$916$	−664027.	−	241686.i	−0.791397	−	0.288045i
$917$			528502.i			0.628504i
$918$		0			0
$919$	1.11234e6			1.31706			0.658529	−	0.752556i	$-0.271179\pi$
$919$	1.11234e6			1.31706			0.658529	+	0.752556i	$0.271179\pi$
$920$	2052.45	−	5639.06i	0.00242492	−	0.00666240i
$921$		0			0
$922$	172404.	+	144664.i	0.202808	+	0.170177i
$923$	−762024.	−	134365.i	−0.894469	−	0.157719i
$924$		0			0
$925$	−137176.	+	115105.i	−0.160323	+	0.134527i
$926$	−249857.	+	144255.i	−0.291387	+	0.168232i
$927$		0			0
$928$	73618.9	−	127512.i	0.0854856	−	0.148065i
$929$	−1.25847e6	+	221901.i	−1.45818	+	0.257116i	−0.845821	−	0.533467i	$-0.820889\pi$
$929$	−1.25847e6	+	221901.i	−1.45818	+	0.257116i	−0.612355	+	0.790583i	$0.709778\pi$
$930$		0			0
$931$	−44503.2	+	16197.8i	−0.0513442	+	0.0186878i
$932$	−228378.	−	627465.i	−0.262920	−	0.722366i
$933$		0			0
$934$	160926.	+	912659.i	0.184473	+	1.04620i
$935$	2857.87	+	1649.99i	0.00326904	+	0.00188738i
$936$		0			0
$937$	−256405.	−	444107.i	−0.292043	−	0.505834i	0.682249	−	0.731120i	$-0.261002\pi$
$937$	−256405.	−	444107.i	−0.292043	−	0.505834i	−0.974293	+	0.225285i	$0.927669\pi$
$938$	−497618.	−	593039.i	−0.565576	−	0.674027i
$939$		0			0
$940$	1147.98	−	6510.50i	0.00129920	−	0.00736816i
$941$	−404158.	+	481657.i	−0.456428	+	0.543950i	−0.944352	−	0.328936i	$-0.893310\pi$
$941$	−404158.	+	481657.i	−0.456428	+	0.543950i	0.487924	+	0.872886i	$0.337754\pi$
$942$		0			0
$943$	174048.	+	63348.2i	0.195724	+	0.0712378i
$944$			260147.i			0.291927i
$945$		0			0
$946$	90795.2			0.101457
$947$	196341.	−	539442.i	0.218933	−	0.601513i	−0.780796	−	0.624786i	$-0.785186\pi$
$947$	196341.	−	539442.i	0.218933	−	0.601513i	0.999729	+	0.0232725i	$0.00740855\pi$
$948$		0			0
$949$	399240.	+	335002.i	0.443304	+	0.371976i
$950$	130024.	+	22926.8i	0.144071	+	0.0254037i
$951$		0			0
$952$	416169.	−	349207.i	0.459194	−	0.385309i
$953$	959412.	−	553917.i	1.05638	−	0.609900i	0.131950	−	0.991256i	$-0.457876\pi$
$953$	959412.	−	553917.i	1.05638	−	0.609900i	0.924428	+	0.381356i	$0.124543\pi$
$954$		0			0
$955$	−3726.89	+	6455.16i	−0.00408639	+	0.00707783i
$956$	645937.	−	113896.i	0.706764	−	0.124622i
$957$		0			0
$958$	530121.	−	192948.i	0.577622	−	0.210237i
$959$	543462.	+	1.49315e6i	0.590924	+	1.62355i
$960$		0			0
$961$	223946.	+	1.27006e6i	0.242492	+	1.37524i
$962$	−105578.	−	60955.5i	−0.114084	−	0.0658662i
$963$		0			0
$964$	−387990.	−	672018.i	−0.417510	−	0.723148i
$965$	6393.46	+	7619.43i	0.00686564	+	0.00818216i
$966$		0			0
$967$	−36107.6	+	204777.i	−0.0386141	+	0.218991i	−0.998009	−	0.0630758i	$-0.979909\pi$
$967$	−36107.6	+	204777.i	−0.0386141	+	0.218991i	0.959395	+	0.282067i	$0.0910201\pi$
$968$	210863.	−	251297.i	0.225035	−	0.268186i
$969$		0			0
$970$	−21226.9	−	7725.97i	−0.0225602	−	0.00821125i
$971$		−	1.03221e6i		−	1.09478i	−0.836876	−	0.547392i	$-0.815621\pi$
$971$		−	1.03221e6i		−	1.09478i	0.836876	−	0.547392i	$-0.184379\pi$
$972$		0			0
$973$	−1.73653e6			−1.83424
$974$	402025.	−	1.10455e6i	0.423775	−	1.16431i
$975$		0			0
$976$	−68084.7	−	57129.9i	−0.0714743	−	0.0599741i
$977$	−167825.	−	29592.1i	−0.175820	−	0.0310018i	0.0850451	−	0.996377i	$-0.472897\pi$
$977$	−167825.	−	29592.1i	−0.175820	−	0.0310018i	−0.260865	+	0.965375i	$0.584008\pi$
$978$		0			0
$979$	134181.	−	112591.i	0.139999	−	0.117473i
$980$	2776.71	−	1603.13i	0.00289120	−	0.00166924i
$981$		0			0
$982$	324441.	−	561949.i	0.336444	−	0.582738i
$983$	133483.	−	23536.7i	0.138140	−	0.0243579i	−0.104150	−	0.994562i	$-0.533212\pi$
$983$	133483.	−	23536.7i	0.138140	−	0.0243579i	0.242291	+	0.970204i	$0.422101\pi$
$984$		0			0
$985$	−13125.6	+	4777.32i	−0.0135284	+	0.00492393i
$986$	342937.	+	942212.i	0.352745	+	0.969158i
$987$		0			0
$988$	15608.5	+	88520.2i	0.0159900	+	0.0906836i
$989$	973746.	+	562192.i	0.995527	+	0.574768i
$990$		0			0
$991$	−742219.	−	1.28556e6i	−0.755761	−	1.30902i	−0.944995	−	0.327085i	$-0.893934\pi$
$991$	−742219.	−	1.28556e6i	−0.755761	−	1.30902i	0.189234	−	0.981932i	$-0.439400\pi$
$992$	−173101.	−	206294.i	−0.175905	−	0.209635i
$993$		0			0
$994$	−139257.	+	789763.i	−0.140943	+	0.799326i
$995$	−3952.88	+	4710.86i	−0.00399271	+	0.00475833i
$996$		0			0
$997$	−955369.	−	347726.i	−0.961127	−	0.349822i	−0.186652	−	0.982426i	$-0.559764\pi$
$997$	−955369.	−	347726.i	−0.961127	−	0.349822i	−0.774475	+	0.632605i	$0.781986\pi$
$998$		−	648452.i		−	0.651054i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.17.11		72
3.2	odd	2		54.5.f.a.23.5	✓	72
27.7	even	9		54.5.f.a.47.5	yes	72
27.20	odd	18	inner	162.5.f.a.143.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.5	✓	72	3.2	odd	2
54.5.f.a.47.5	yes	72	27.7	even	9
162.5.f.a.17.11		72	1.1	even	1	trivial
162.5.f.a.143.11		72	27.20	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-0.622849 - 0.109825i) q^{5} +(42.1999 - 35.4099i) q^{7} +(-19.5959 + 11.3137i) q^{8} +O(q^{10})\)	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-0.622849 - 0.109825i) q^{5} +(42.1999 - 35.4099i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(-0.894430 + 1.54920i) q^{10} +(11.7899 - 2.07887i) q^{11} +(141.273 - 51.4193i) q^{13} +(-53.2910 - 146.416i) q^{14} +(11.1135 + 63.0277i) q^{16} +(-377.445 - 217.918i) q^{17} +(-37.3677 - 64.7228i) q^{19} +(3.25229 + 3.87593i) q^{20} +(5.87993 - 33.3468i) q^{22} +(269.539 - 321.224i) q^{23} +(-586.932 - 213.626i) q^{25} -425.226i q^{26} -440.704 q^{28} +(278.193 - 764.328i) q^{29} +(-1139.63 - 956.259i) q^{31} +(178.269 + 31.4337i) q^{32} +(-944.327 + 792.385i) q^{34} +(-30.1731 + 17.4204i) q^{35} +(143.349 - 248.287i) q^{37} +(-208.172 + 36.7064i) q^{38} +(13.4478 - 4.89461i) q^{40} +(151.071 + 415.063i) q^{41} +(465.619 + 2640.66i) q^{43} +(-82.9427 - 47.8870i) q^{44} +(-593.020 - 1027.14i) q^{46} +(-839.864 - 1000.91i) q^{47} +(110.040 - 624.065i) q^{49} +(-1135.57 + 1353.32i) q^{50} +(-1130.19 - 411.354i) q^{52} -3784.91i q^{53} -7.57162 q^{55} +(-426.328 + 1171.33i) q^{56} +(-1762.35 - 1478.79i) q^{58} +(4003.04 + 705.845i) q^{59} +(-1063.82 + 892.654i) q^{61} +(-3644.04 + 2103.89i) q^{62} +(256.000 - 443.405i) q^{64} +(-93.6391 + 16.5111i) q^{65} +(4668.88 - 1699.33i) q^{67} +(1192.52 + 3276.42i) q^{68} +(17.1121 + 97.0477i) q^{70} +(-4457.32 - 2573.43i) q^{71} +(1733.31 + 3002.18i) q^{73} +(-521.238 - 621.187i) q^{74} +(-103.821 + 588.800i) q^{76} +(423.918 - 505.206i) q^{77} +(5272.09 + 1918.88i) q^{79} -40.4773i q^{80} +1249.32 q^{82} +(-2319.64 + 6373.17i) q^{83} +(211.159 + 177.183i) q^{85} +(7468.91 + 1316.97i) q^{86} +(-207.513 + 174.124i) q^{88} +(12671.0 - 7315.60i) q^{89} +(4140.97 - 7172.37i) q^{91} +(-3303.66 + 582.525i) q^{92} +(-3472.74 + 1263.97i) q^{94} +(16.1663 + 44.4164i) q^{95} +(2192.78 + 12435.9i) q^{97} +(-1552.22 - 896.176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 72 * q + 18 * q^5	\( 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) \) 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Introduction

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