LMFDB - Embedded newform 483.2.y.b.4.4

Newspace parameters

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.y (of order $33$, degree $20$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	483.4
Dual form			483.2.y.b.121.4

$q$-expansion

$f(q)$	$=$	$q+(-1.09595 + 1.53904i) q^{2} +(0.235759 - 0.971812i) q^{3} +(-0.513414 - 1.48341i) q^{4} +(-0.133721 + 2.80715i) q^{5} +(1.23728 + 1.42790i) q^{6} +(2.23077 + 1.42255i) q^{7} +(-0.779983 - 0.229024i) q^{8} +(-0.888835 - 0.458227i) q^{9} +O(q^{10})$	\(q+(-1.09595 + 1.53904i) q^{2} +(0.235759 - 0.971812i) q^{3} +(-0.513414 - 1.48341i) q^{4} +(-0.133721 + 2.80715i) q^{5} +(1.23728 + 1.42790i) q^{6} +(2.23077 + 1.42255i) q^{7} +(-0.779983 - 0.229024i) q^{8} +(-0.888835 - 0.458227i) q^{9} +(-4.17377 - 3.28229i) q^{10} +(-2.07040 - 2.90747i) q^{11} +(-1.56264 + 0.149214i) q^{12} +(-0.881180 + 6.12874i) q^{13} +(-4.63417 + 1.87421i) q^{14} +(2.69650 + 0.791763i) q^{15} +(3.67510 - 2.89013i) q^{16} +(-5.23725 + 1.00940i) q^{17} +(1.67935 - 0.865763i) q^{18} +(4.41889 + 0.851671i) q^{19} +(4.23281 - 1.24287i) q^{20} +(1.90838 - 1.83251i) q^{21} +6.74377 q^{22} +(2.77508 + 3.91138i) q^{23} +(-0.406456 + 0.704002i) q^{24} +(-2.88485 - 0.275470i) q^{25} +(-8.46666 - 8.07294i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(0.964924 - 4.03951i) q^{28} +(-2.23847 - 2.58333i) q^{29} +(-4.17377 + 3.28229i) q^{30} +(-1.70366 + 1.62443i) q^{31} +(0.342959 + 7.19959i) q^{32} +(-3.31363 + 1.32658i) q^{33} +(4.18624 - 9.16659i) q^{34} +(-4.29162 + 6.07189i) q^{35} +(-0.223398 + 1.55377i) q^{36} +(-10.2548 - 5.28670i) q^{37} +(-6.15362 + 5.86746i) q^{38} +(5.74823 + 2.30125i) q^{39} +(0.747204 - 2.15890i) q^{40} +(-4.59749 - 2.95463i) q^{41} +(0.728828 + 4.94541i) q^{42} +(-11.2004 + 3.28874i) q^{43} +(-3.25001 + 4.56400i) q^{44} +(1.40517 - 2.43382i) q^{45} +(-9.06112 - 0.0157046i) q^{46} +(1.95345 + 3.38348i) q^{47} +(-1.94223 - 4.25288i) q^{48} +(2.95268 + 6.34678i) q^{49} +(3.58560 - 4.13801i) q^{50} +(-0.253785 + 5.32760i) q^{51} +(9.54385 - 1.83943i) q^{52} +(11.2358 + 4.49814i) q^{53} +(-0.445438 - 1.83612i) q^{54} +(8.43858 - 5.42314i) q^{55} +(-1.41416 - 1.62047i) q^{56} +(1.86946 - 4.09354i) q^{57} +(6.42909 - 0.613904i) q^{58} +(1.07265 + 0.843543i) q^{59} +(-0.209908 - 4.40651i) q^{60} +(0.475186 + 1.95874i) q^{61} +(-0.632954 - 4.40229i) q^{62} +(-1.33094 - 2.28661i) q^{63} +(-3.58995 - 2.30712i) q^{64} +(-17.0865 - 3.29315i) q^{65} +(1.58991 - 6.55368i) q^{66} +(-3.03636 - 0.289937i) q^{67} +(4.18623 + 7.25076i) q^{68} +(4.45538 - 1.77471i) q^{69} +(-4.64149 - 13.2594i) q^{70} +(2.26087 + 4.95062i) q^{71} +(0.588332 + 0.560973i) q^{72} +(-2.16069 - 6.24291i) q^{73} +(19.3751 - 9.98858i) q^{74} +(-0.947835 + 2.73859i) q^{75} +(-1.00534 - 6.99229i) q^{76} +(-0.482558 - 9.43117i) q^{77} +(-9.84147 + 6.32473i) q^{78} +(1.61971 - 0.648432i) q^{79} +(7.62160 + 10.7030i) q^{80} +(0.580057 + 0.814576i) q^{81} +(9.58589 - 3.83761i) q^{82} +(11.9027 - 7.64938i) q^{83} +(-3.69815 - 1.89007i) q^{84} +(-2.13320 - 14.8367i) q^{85} +(7.21355 - 20.8422i) q^{86} +(-3.03825 + 1.56633i) q^{87} +(0.948999 + 2.74195i) q^{88} +(5.88277 + 5.60921i) q^{89} +(2.20576 + 4.82995i) q^{90} +(-10.6842 + 12.4183i) q^{91} +(4.37743 - 6.12474i) q^{92} +(1.17699 + 2.03861i) q^{93} +(-7.34820 - 0.701668i) q^{94} +(-2.98167 + 12.2906i) q^{95} +(7.07750 + 1.36408i) q^{96} +(10.5374 + 6.77197i) q^{97} +(-13.0039 - 2.41143i) q^{98} +(0.507966 + 3.53298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320q + 2q^{2} + 16q^{3} + 18q^{4} - 2q^{5} + 18q^{6} + 2q^{7} - 12q^{8} + 16q^{9} + O(q^{10}) $	\( 320q + 2q^{2} + 16q^{3} + 18q^{4} - 2q^{5} + 18q^{6} + 2q^{7} - 12q^{8} + 16q^{9} + 2q^{11} + 18q^{12} + 18q^{14} - 18q^{15} - 8q^{16} + 4q^{17} + 2q^{18} + 8q^{19} - 162q^{20} - 4q^{21} + 144q^{22} - 26q^{23} + 6q^{24} - 8q^{25} - 14q^{26} - 32q^{27} + 86q^{28} - 74q^{29} - 56q^{31} - 28q^{32} + 13q^{33} + 40q^{34} - 32q^{35} - 14q^{36} + 2q^{37} - 39q^{38} - 52q^{40} + 60q^{41} - 61q^{42} + 16q^{43} - 75q^{44} - 2q^{45} - 4q^{46} - 40q^{47} - 28q^{48} - 100q^{49} + 146q^{50} - 18q^{51} - 18q^{52} + 34q^{53} + 2q^{54} + 36q^{55} - 102q^{56} + 28q^{57} - 17q^{58} - 102q^{59} - 18q^{60} - 18q^{61} - 88q^{62} + 2q^{63} - 252q^{64} - 78q^{65} + 16q^{66} + 12q^{67} + 34q^{68} + 8q^{69} + 264q^{70} + 160q^{71} + 6q^{72} - 8q^{73} + 70q^{74} + 14q^{75} - 40q^{76} - 90q^{77} - 16q^{78} + 26q^{79} - 103q^{80} + 16q^{81} - 30q^{82} - 80q^{83} - 52q^{84} - 128q^{85} + 90q^{86} + 4q^{87} - 293q^{88} - 36q^{89} + 16q^{91} - 174q^{92} + 32q^{93} + 57q^{94} - 85q^{95} - 50q^{96} - 8q^{97} - 193q^{98} - 26q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{11}\right)$

Coefficient data

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

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

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

$2$	−1.09595	+	1.53904i	−0.774951	+	1.08827i	0.218703	+	0.975791i	$0.429817\pi$
$2$	−1.09595	+	1.53904i	−0.774951	+	1.08827i	−0.993655	+	0.112475i	$0.964122\pi$
$3$	0.235759	−	0.971812i	0.136115	−	0.561076i
$3$	0.235759	−	0.971812i	0.136115	−	0.561076i
$4$	−0.513414	−	1.48341i	−0.256707	−	0.741706i
$5$	−0.133721	+	2.80715i	−0.0598019	+	1.25540i	0.747100	+	0.664711i	$0.231445\pi$
$5$	−0.133721	+	2.80715i	−0.0598019	+	1.25540i	−0.806902	+	0.590685i	$0.798858\pi$
$6$	1.23728	+	1.42790i	0.505117	+	0.582936i
$7$	2.23077	+	1.42255i	0.843152	+	0.537675i
$7$	2.23077	+	1.42255i	0.843152	+	0.537675i
$8$	−0.779983	−	0.229024i	−0.275766	−	0.0809721i
$9$	−0.888835	−	0.458227i	−0.296278	−	0.152742i
$10$	−4.17377	−	3.28229i	−1.31986	−	1.03795i
$11$	−2.07040	−	2.90747i	−0.624250	−	0.876637i	0.374469	−	0.927240i	$-0.377825\pi$
$11$	−2.07040	−	2.90747i	−0.624250	−	0.876637i	−0.998719	+	0.0506029i	$0.983886\pi$
$12$	−1.56264	+	0.149214i	−0.451095	+	0.0430743i
$13$	−0.881180	+	6.12874i	−0.244395	+	1.69981i	0.385159	+	0.922850i	$0.374147\pi$
$13$	−0.881180	+	6.12874i	−0.244395	+	1.69981i	−0.629554	+	0.776956i	$0.716763\pi$
$14$	−4.63417	+	1.87421i	−1.23854	+	0.500903i
$15$	2.69650	+	0.791763i	0.696232	+	0.204432i
$16$	3.67510	−	2.89013i	0.918776	−	0.722533i
$17$	−5.23725	+	1.00940i	−1.27022	+	0.244815i	−0.779445	−	0.626471i	$-0.784499\pi$
$17$	−5.23725	+	1.00940i	−1.27022	+	0.244815i	−0.490776	+	0.871286i	$0.663287\pi$
$18$	1.67935	−	0.865763i	0.395826	−	0.204062i
$19$	4.41889	+	0.851671i	1.01376	+	0.195387i	0.668968	−	0.743292i	$-0.266736\pi$
$19$	4.41889	+	0.851671i	1.01376	+	0.195387i	0.344795	+	0.938678i	$0.387949\pi$
$20$	4.23281	−	1.24287i	0.946486	−	0.277913i
$21$	1.90838	−	1.83251i	0.416442	−	0.399886i
$22$	6.74377			1.43778
$23$	2.77508	+	3.91138i	0.578644	+	0.815580i
$23$	2.77508	+	3.91138i	0.578644	+	0.815580i
$24$	−0.406456	+	0.704002i	−0.0829674	+	0.143704i
$25$	−2.88485	−	0.275470i	−0.576971	−	0.0550940i
$26$	−8.46666	−	8.07294i	−1.66045	−	1.58323i
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$	0.964924	−	4.03951i	0.182353	−	0.763396i
$29$	−2.23847	−	2.58333i	−0.415673	−	0.479712i	0.508841	−	0.860861i	$-0.330074\pi$
$29$	−2.23847	−	2.58333i	−0.415673	−	0.479712i	−0.924514	+	0.381148i	$0.875529\pi$
$30$	−4.17377	+	3.28229i	−0.762023	+	0.599261i
$31$	−1.70366	+	1.62443i	−0.305986	+	0.291757i	−0.827477	−	0.561500i	$-0.810224\pi$
$31$	−1.70366	+	1.62443i	−0.305986	+	0.291757i	0.521491	+	0.853257i	$0.325376\pi$
$32$	0.342959	+	7.19959i	0.0606271	+	1.27272i
$33$	−3.31363	+	1.32658i	−0.576830	+	0.230928i
$34$	4.18624	−	9.16659i	0.717935	−	1.57206i
$35$	−4.29162	+	6.07189i	−0.725417	+	1.02634i
$36$	−0.223398	+	1.55377i	−0.0372330	+	0.258961i
$37$	−10.2548	−	5.28670i	−1.68587	−	0.869129i	−0.988283	−	0.152634i	$-0.951225\pi$
$37$	−10.2548	−	5.28670i	−1.68587	−	0.869129i	−0.697592	−	0.716495i	$-0.745745\pi$
$38$	−6.15362	+	5.86746i	−0.998249	+	0.951828i
$39$	5.74823	+	2.30125i	0.920454	+	0.368494i
$40$	0.747204	−	2.15890i	0.118143	−	0.341353i
$41$	−4.59749	−	2.95463i	−0.718007	−	0.461435i	0.129936	−	0.991522i	$-0.458523\pi$
$41$	−4.59749	−	2.95463i	−0.718007	−	0.461435i	−0.847943	+	0.530087i	$0.822159\pi$
$42$	0.728828	+	4.94541i	0.112461	+	0.763093i
$43$	−11.2004	+	3.28874i	−1.70805	+	0.501528i	−0.982440	−	0.186580i	$-0.940260\pi$
$43$	−11.2004	+	3.28874i	−1.70805	+	0.501528i	−0.725608	+	0.688108i	$0.758441\pi$
$44$	−3.25001	+	4.56400i	−0.489957	+	0.688049i
$45$	1.40517	−	2.43382i	0.209470	−	0.362813i
$46$	−9.06112	−	0.0157046i	−1.33599	−	0.00231552i
$47$	1.95345	+	3.38348i	0.284941	+	0.493532i	0.972595	−	0.232507i	$-0.0746928\pi$
$47$	1.95345	+	3.38348i	0.284941	+	0.493532i	−0.687654	+	0.726038i	$0.741359\pi$
$48$	−1.94223	−	4.25288i	−0.280336	−	0.613851i
$49$	2.95268	+	6.34678i	0.421812	+	0.906683i
$50$	3.58560	−	4.13801i	0.507081	−	0.585203i
$51$	−0.253785	+	5.32760i	−0.0355370	+	0.746013i
$52$	9.54385	−	1.83943i	1.32349	−	0.255083i
$53$	11.2358	+	4.49814i	1.54336	+	0.617866i	0.978301	−	0.207187i	$-0.0664310\pi$
$53$	11.2358	+	4.49814i	1.54336	+	0.617866i	0.565054	+	0.825054i	$0.308855\pi$
$54$	−0.445438	−	1.83612i	−0.0606164	−	0.249864i
$55$	8.43858	−	5.42314i	1.13786	−	0.731257i
$56$	−1.41416	−	1.62047i	−0.188976	−	0.216544i
$57$	1.86946	−	4.09354i	0.247615	−	0.542202i
$58$	6.42909	−	0.613904i	0.844181	−	0.0806095i
$59$	1.07265	+	0.843543i	0.139647	+	0.109820i	0.685539	−	0.728036i	$-0.259567\pi$
$59$	1.07265	+	0.843543i	0.139647	+	0.109820i	−0.545892	+	0.837856i	$0.683809\pi$
$60$	−0.209908	−	4.40651i	−0.0270990	−	0.568879i
$61$	0.475186	+	1.95874i	0.0608414	+	0.250791i	0.994108	−	0.108392i	$-0.0345703\pi$
$61$	0.475186	+	1.95874i	0.0608414	+	0.250791i	−0.933267	+	0.359184i	$0.883055\pi$
$62$	−0.632954	−	4.40229i	−0.0803852	−	0.559091i
$63$	−1.33094	−	2.28661i	−0.167682	−	0.288086i
$64$	−3.58995	−	2.30712i	−0.448744	−	0.288390i
$65$	−17.0865	−	3.29315i	−2.11931	−	0.408464i
$66$	1.58991	−	6.55368i	0.195704	−	0.806702i
$67$	−3.03636	−	0.289937i	−0.370951	−	0.0354215i	−0.0920838	−	0.995751i	$-0.529353\pi$
$67$	−3.03636	−	0.289937i	−0.370951	−	0.0354215i	−0.278867	+	0.960330i	$0.589959\pi$
$68$	4.18623	+	7.25076i	0.507655	+	0.879284i
$69$	4.45538	−	1.77471i	0.536365	−	0.213650i
$70$	−4.64149	−	13.2594i	−0.554765	−	1.58481i
$71$	2.26087	+	4.95062i	0.268316	+	0.587530i	0.995049	−	0.0993905i	$-0.0316893\pi$
$71$	2.26087	+	4.95062i	0.268316	+	0.587530i	−0.726733	+	0.686921i	$0.758962\pi$
$72$	0.588332	+	0.560973i	0.0693355	+	0.0661113i
$73$	−2.16069	−	6.24291i	−0.252890	−	0.730677i	−0.997969	−	0.0637013i	$-0.979710\pi$
$73$	−2.16069	−	6.24291i	−0.252890	−	0.730677i	0.745079	−	0.666976i	$-0.232412\pi$
$74$	19.3751	−	9.98858i	2.25231	−	1.16115i
$75$	−0.947835	+	2.73859i	−0.109447	+	0.316225i
$76$	−1.00534	−	6.99229i	−0.115320	−	0.802070i
$77$	−0.482558	−	9.43117i	−0.0549926	−	1.07478i
$78$	−9.84147	+	6.32473i	−1.11433	+	0.716134i
$79$	1.61971	−	0.648432i	0.182231	−	0.0729543i	−0.278753	−	0.960363i	$-0.589921\pi$
$79$	1.61971	−	0.648432i	0.182231	−	0.0729543i	0.460984	+	0.887409i	$0.347497\pi$
$80$	7.62160	+	10.7030i	0.852121	+	1.19664i
$81$	0.580057	+	0.814576i	0.0644508	+	0.0905084i
$82$	9.58589	−	3.83761i	1.05858	−	0.423793i
$83$	11.9027	−	7.64938i	1.30649	−	0.839629i	0.312585	−	0.949890i	$-0.398805\pi$
$83$	11.9027	−	7.64938i	1.30649	−	0.839629i	0.993903	+	0.110261i	$0.0351686\pi$
$84$	−3.69815	−	1.89007i	−0.403502	−	0.206224i
$85$	−2.13320	−	14.8367i	−0.231378	−	1.60927i
$86$	7.21355	−	20.8422i	0.777857	−	2.24747i
$87$	−3.03825	+	1.56633i	−0.325734	+	0.167928i
$88$	0.948999	+	2.74195i	0.101164	+	0.292293i
$89$	5.88277	+	5.60921i	0.623572	+	0.594575i	0.934546	−	0.355844i	$-0.115806\pi$
$89$	5.88277	+	5.60921i	0.623572	+	0.594575i	−0.310973	+	0.950419i	$0.600655\pi$
$90$	2.20576	+	4.82995i	0.232508	+	0.509121i
$91$	−10.6842	+	12.4183i	−1.12001	+	1.30179i
$92$	4.37743	−	6.12474i	0.456379	−	0.638549i
$93$	1.17699	+	2.03861i	0.122048	+	0.211394i
$94$	−7.34820	−	0.701668i	−0.757909	−	0.0723716i
$95$	−2.98167	+	12.2906i	−0.305912	+	1.26099i
$96$	7.07750	+	1.36408i	0.722344	+	0.139220i
$97$	10.5374	+	6.77197i	1.06991	+	0.687590i	0.952205	−	0.305459i	$-0.0988098\pi$
$97$	10.5374	+	6.77197i	1.06991	+	0.687590i	0.117705	+	0.993049i	$0.462446\pi$
$98$	−13.0039	−	2.41143i	−1.31360	−	0.243592i
$99$	0.507966	+	3.53298i	0.0510525	+	0.355078i
$100$	1.07249	+	4.42086i	0.107249	+	0.442086i
$101$	0.181782	+	3.81606i	0.0180879	+	0.379713i	0.989702	+	0.143142i	$0.0457205\pi$
$101$	0.181782	+	3.81606i	0.0180879	+	0.379713i	−0.971614	+	0.236571i	$0.923976\pi$
$102$	−7.92126	−	6.22934i	−0.784321	−	0.616797i
$103$	8.58193	−	0.819475i	0.845602	−	0.0807452i	0.336745	−	0.941596i	$-0.390674\pi$
$103$	8.58193	−	0.819475i	0.845602	−	0.0807452i	0.508858	+	0.860851i	$0.330068\pi$
$104$	2.09093	−	4.57850i	0.205033	−	0.448959i
$105$	4.88894	+	5.60215i	0.477112	+	0.546714i
$106$	−19.2366	+	12.3626i	−1.86843	+	1.20077i
$107$	2.08016	+	8.57455i	0.201097	+	0.828933i	0.979545	+	0.201224i	$0.0644920\pi$
$107$	2.08016	+	8.57455i	0.201097	+	0.828933i	−0.778448	+	0.627709i	$0.783993\pi$
$108$	1.45730	+	0.583416i	0.140229	+	0.0561392i
$109$	14.7759	−	2.84781i	1.41527	−	0.272771i	0.576429	−	0.817147i	$-0.304446\pi$
$109$	14.7759	−	2.84781i	1.41527	−	0.272771i	0.838841	+	0.544376i	$0.183234\pi$
$110$	−0.901785	+	18.9308i	−0.0859818	+	1.80498i
$111$	−7.55534	+	8.71932i	−0.717121	+	0.827601i
$112$	12.3097	−	1.21920i	1.16316	−	0.115203i
$113$	7.12927	+	15.6109i	0.670665	+	1.46855i	0.872240	+	0.489078i	$0.162667\pi$
$113$	7.12927	+	15.6109i	0.670665	+	1.46855i	−0.201575	+	0.979473i	$0.564606\pi$
$114$	4.25130	+	7.36346i	0.398171	+	0.689652i
$115$	−11.3509	+	7.26703i	−1.05848	+	0.677654i
$116$	−2.68288	+	4.64688i	−0.249099	+	0.431452i
$117$	3.59157	−	5.04366i	0.332041	−	0.466287i
$118$	−2.47382	+	0.726378i	−0.227733	+	0.0668685i
$119$	−13.1190	−	5.19854i	−1.20262	−	0.476549i
$120$	−1.92189	−	1.23512i	−0.175444	−	0.112751i
$121$	−0.569091	+	1.64428i	−0.0517356	+	0.149480i
$122$	−3.53537	−	1.41535i	−0.320077	−	0.128140i
$123$	−3.95524	+	3.77131i	−0.356632	+	0.340048i
$124$	3.28438	+	1.69322i	0.294946	+	0.152055i
$125$	−0.840709	+	5.84726i	−0.0751953	+	0.522995i
$126$	4.97783	+	0.457640i	0.443460	+	0.0407698i
$127$	6.34506	−	13.8937i	0.563033	−	1.23287i	−0.387391	−	0.921915i	$-0.626624\pi$
$127$	6.34506	−	13.8937i	0.563033	−	1.23287i	0.950425	−	0.310955i	$-0.100649\pi$
$128$	−5.89774	+	2.36110i	−0.521292	+	0.208694i
$129$	0.555436	+	11.6600i	0.0489034	+	1.02661i
$130$	23.7941	−	22.6877i	2.08688	−	1.98984i
$131$	8.07442	−	6.34979i	0.705465	−	0.554784i	−0.199693	−	0.979858i	$-0.563995\pi$
$131$	8.07442	−	6.34979i	0.705465	−	0.554784i	0.905158	+	0.425075i	$0.139752\pi$
$132$	3.66913	+	4.23440i	0.319357	+	0.368557i
$133$	8.64598	+	8.18599i	0.749701	+	0.709815i
$134$	3.77392	−	4.35533i	0.326017	−	0.376243i
$135$	−2.03393	−	1.93935i	−0.175053	−	0.166913i
$136$	4.31614	+	0.412142i	0.370106	+	0.0353409i
$137$	3.86618	−	6.69642i	0.330310	−	0.572114i	−0.652262	−	0.757993i	$-0.726180\pi$
$137$	3.86618	−	6.69642i	0.330310	−	0.572114i	0.982573	+	0.185879i	$0.0595133\pi$
$138$	−2.15150	+	8.80200i	−0.183148	+	0.749276i
$139$	−0.399115			−0.0338525			−0.0169262	−	0.999857i	$-0.505388\pi$
$139$	−0.399115			−0.0338525			−0.0169262	+	0.999857i	$0.505388\pi$
$140$	11.2105	+	3.24885i	0.947459	+	0.274578i
$141$	3.74865	−	1.10070i	0.315694	−	0.0926960i
$142$	−10.0970	−	1.94604i	−0.847321	−	0.163308i
$143$	19.6436	−	10.1270i	1.64268	−	0.846859i
$144$	−4.59090	+	0.884823i	−0.382575	+	0.0737353i
$145$	7.55112	−	5.93827i	0.627087	−	0.493146i
$146$	11.9761	+	3.51650i	0.991149	+	0.291028i
$147$	6.86400	−	1.37314i	0.566133	−	0.113255i
$148$	−2.57742	+	17.9263i	−0.211862	+	1.47353i
$149$	−11.8930	+	1.13565i	−0.974315	+	0.0930358i	−0.570054	−	0.821608i	$-0.693078\pi$
$149$	−11.8930	+	1.13565i	−0.974315	+	0.0930358i	−0.404262	+	0.914643i	$0.632471\pi$
$150$	−3.17603	−	4.46010i	−0.259321	−	0.364166i
$151$	−5.12831	−	4.03295i	−0.417336	−	0.328197i	0.387312	−	0.921949i	$-0.373404\pi$
$151$	−5.12831	−	4.03295i	−0.417336	−	0.328197i	−0.804648	+	0.593752i	$0.797646\pi$
$152$	−3.25160	−	1.67632i	−0.263740	−	0.135967i
$153$	5.11759	+	1.50266i	0.413732	+	0.121483i
$154$	15.0438	+	9.59338i	1.21227	+	0.773057i
$155$	−4.33221	−	4.99964i	−0.347972	−	0.401581i
$156$	0.462472	−	9.70849i	0.0370274	−	0.777301i
$157$	−1.98534	−	5.73626i	−0.158447	−	0.457803i	0.837635	−	0.546230i	$-0.183937\pi$
$157$	−1.98534	−	5.73626i	−0.158447	−	0.457803i	−0.996083	+	0.0884263i	$0.971816\pi$
$158$	−0.777146	+	3.20344i	−0.0618264	+	0.254852i
$159$	7.02028	−	9.85860i	0.556744	−	0.781838i
$160$	−20.2562			−1.60139
$161$	0.626415	+	12.6731i	0.0493684	+	0.998781i
$162$	−1.88938			−0.148443
$163$	−5.85099	+	8.21657i	−0.458285	+	0.643571i	−0.977466	−	0.211093i	$-0.932298\pi$
$163$	−5.85099	+	8.21657i	−0.458285	+	0.643571i	0.519181	+	0.854664i	$0.326237\pi$
$164$	−2.02251	+	8.33691i	−0.157932	+	0.651003i
$165$	−3.28080	−	9.47926i	−0.255410	−	0.737959i
$166$	−1.27197	+	26.7020i	−0.0987243	+	2.07248i
$167$	2.84630	+	3.28480i	0.220253	+	0.254186i	0.855113	−	0.518442i	$-0.173488\pi$
$167$	2.84630	+	3.28480i	0.220253	+	0.254186i	−0.634860	+	0.772627i	$0.718942\pi$
$168$	−1.90819	+	0.992262i	−0.147220	+	0.0765547i
$169$	−24.3116	−	7.13852i	−1.87012	−	0.549117i
$170$	25.1722	+	12.9772i	1.93062	+	0.995304i
$171$	−3.53741	−	2.78185i	−0.270512	−	0.212733i
$172$	10.6290	+	14.9263i	0.810454	+	1.13812i
$173$	−1.02865	+	0.0982238i	−0.0782065	+	0.00746781i	−0.134086	−	0.990970i	$-0.542810\pi$
$173$	−1.02865	+	0.0982238i	−0.0782065	+	0.00746781i	0.0558794	+	0.998438i	$0.482204\pi$
$174$	0.919117	−	6.39260i	0.0696781	−	0.484622i
$175$	−6.04358	−	4.71837i	−0.456852	−	0.356675i
$176$	−16.0119	−	4.70153i	−1.20695	−	0.354391i
$177$	1.07265	−	0.843543i	0.0806255	−	0.0634046i
$178$	−15.0800	+	2.90643i	−1.13029	+	0.217846i
$179$	4.18725	−	2.15868i	0.312970	−	0.161347i	−0.294584	−	0.955626i	$-0.595181\pi$
$179$	4.18725	−	2.15868i	0.312970	−	0.161347i	0.607554	+	0.794278i	$0.292151\pi$
$180$	−4.33179	−	0.834884i	−0.322873	−	0.0622286i
$181$	16.6787	−	4.89731i	1.23972	−	0.364015i	0.404810	−	0.914401i	$-0.367338\pi$
$181$	16.6787	−	4.89731i	1.23972	−	0.364015i	0.834910	+	0.550386i	$0.185520\pi$
$182$	−7.40299	−	30.0532i	−0.548746	−	2.22769i
$183$	2.01556			0.148994
$184$	−1.26872	−	3.68637i	−0.0935309	−	0.271763i
$185$	16.2119	−	28.0798i	1.19192	−	2.06446i
$186$	−4.42742	−	0.422767i	−0.324634	−	0.0309988i
$187$	13.7780	+	13.1373i	1.00755	+	0.960696i
$188$	4.01617	−	4.63490i	0.292909	−	0.338035i
$189$	−2.53594	+	0.754330i	−0.184462	+	0.0548694i
$190$	−15.6480	−	18.0587i	−1.13522	−	1.31012i
$191$	−4.65240	+	3.65869i	−0.336636	+	0.264733i	−0.772139	−	0.635454i	$-0.780813\pi$
$191$	−4.65240	+	3.65869i	−0.336636	+	0.264733i	0.435503	+	0.900187i	$0.356571\pi$
$192$	−3.08845	+	2.94483i	−0.222890	+	0.212525i
$193$	1.12791	+	23.6777i	0.0811885	+	1.70436i	0.561678	+	0.827356i	$0.310156\pi$
$193$	1.12791	+	23.6777i	0.0811885	+	1.70436i	−0.480489	+	0.877001i	$0.659541\pi$
$194$	−21.9708	+	8.79577i	−1.57741	+	0.631499i
$195$	−7.22860	+	15.8284i	−0.517651	+	1.13350i
$196$	7.89895	−	7.63857i	0.564210	−	0.545612i
$197$	1.90331	−	13.2378i	0.135605	−	0.943153i	−0.802463	−	0.596702i	$-0.796478\pi$
$197$	1.90331	−	13.2378i	0.135605	−	0.943153i	0.938068	−	0.346451i	$-0.112613\pi$
$198$	−5.99411	−	3.09018i	−0.425983	−	0.219609i
$199$	7.40661	−	7.06219i	0.525041	−	0.500625i	−0.380560	−	0.924756i	$-0.624269\pi$
$199$	7.40661	−	7.06219i	0.525041	−	0.500625i	0.905601	+	0.424131i	$0.139420\pi$
$200$	2.18705	+	0.875562i	0.154648	+	0.0619116i
$201$	−0.997614	+	2.88242i	−0.0703663	+	0.203310i
$202$	−6.07230	−	3.90243i	−0.427246	−	0.274574i
$203$	−1.31858	−	8.94716i	−0.0925465	−	0.627967i
$204$	8.03332	−	2.35879i	0.562445	−	0.165149i
$205$	8.90886	−	12.5107i	0.622222	−	0.873788i
$206$	−8.14413	+	14.1060i	−0.567428	+	0.982814i
$207$	−0.674290	−	4.74819i	−0.0468664	−	0.330022i
$208$	14.4745	+	25.0705i	1.00362	+	1.73833i
$209$	−6.67267	−	14.6111i	−0.461558	−	1.01067i
$210$	−13.9800	+	1.38462i	−0.964709	+	0.0955482i
$211$	−8.24617	+	9.51658i	−0.567689	+	0.655149i	−0.964912	−	0.262574i	$-0.915429\pi$
$211$	−8.24617	+	9.51658i	−0.567689	+	0.655149i	0.397222	+	0.917722i	$0.369974\pi$
$212$	0.903973	−	18.9767i	0.0620851	−	1.30333i
$213$	5.34409	−	1.02999i	0.366171	−	0.0705736i
$214$	−15.4763	−	6.19579i	−1.05794	−	0.423536i
$215$	−7.73425	−	31.8810i	−0.527472	−	2.17427i
$216$	0.683865	−	0.439493i	0.0465311	−	0.0299037i
$217$	−6.11131	+	1.20020i	−0.414863	+	0.0814746i
$218$	−11.8106	+	25.8617i	−0.799917	+	1.75157i
$219$	−6.57634	+	0.627964i	−0.444388	+	0.0424339i
$220$	−12.3772	−	9.73357i	−0.834473	−	0.656237i
$221$	−1.57137	−	32.9872i	−0.105702	−	2.21896i
$222$	−5.13915	−	21.1839i	−0.344917	−	1.42177i
$223$	2.95591	+	20.5588i	0.197942	+	1.37672i	0.810243	+	0.586094i	$0.199335\pi$
$223$	2.95591	+	20.5588i	0.197942	+	1.37672i	−0.612300	+	0.790625i	$0.709756\pi$
$224$	−9.47674	+	16.5485i	−0.633191	+	1.10569i
$225$	2.43793	+	1.56676i	0.162529	+	0.104451i
$226$	−31.8391	−	6.13649i	−2.11791	−	0.408193i
$227$	0.228763	−	0.942974i	0.0151835	−	0.0625874i	−0.963716	−	0.266930i	$-0.913991\pi$
$227$	0.228763	−	0.942974i	0.0151835	−	0.0625874i	0.978899	+	0.204343i	$0.0655058\pi$
$228$	−7.03220	−	0.671494i	−0.465719	−	0.0444708i
$229$	2.87850	+	4.98571i	0.190217	+	0.329465i	0.945322	−	0.326139i	$-0.105748\pi$
$229$	2.87850	+	4.98571i	0.190217	+	0.329465i	−0.755105	+	0.655604i	$0.772414\pi$
$230$	1.25575	−	25.4338i	0.0828016	−	1.67706i
$231$	−9.27909	−	1.75453i	−0.610519	−	0.115439i
$232$	1.15432	+	2.52761i	0.0757850	+	0.165946i
$233$	0.573603	+	0.546929i	0.0375780	+	0.0358305i	0.708635	−	0.705575i	$-0.249311\pi$
$233$	0.573603	+	0.546929i	0.0375780	+	0.0358305i	−0.671057	+	0.741405i	$0.734160\pi$
$234$	3.82623	+	11.0552i	0.250128	+	0.722699i
$235$	−9.75917	+	5.03120i	−0.636618	+	0.328199i
$236$	0.700607	−	2.02427i	0.0456056	−	0.131769i
$237$	−0.248294	−	1.72692i	−0.0161284	−	0.112176i
$238$	22.3785	−	14.4934i	1.45058	−	0.939469i
$239$	11.0218	−	7.08328i	0.712940	−	0.458179i	−0.133234	−	0.991085i	$-0.542536\pi$
$239$	11.0218	−	7.08328i	0.712940	−	0.458179i	0.846175	+	0.532906i	$0.178900\pi$
$240$	12.1982	−	4.88342i	0.787391	−	0.315224i
$241$	−6.73419	−	9.45685i	−0.433787	−	0.609169i	0.538594	−	0.842565i	$-0.318956\pi$
$241$	−6.73419	−	9.45685i	−0.433787	−	0.609169i	−0.972382	+	0.233396i	$0.925016\pi$
$242$	−1.90692	−	2.67790i	−0.122582	−	0.172142i
$243$	0.928368	−	0.371662i	0.0595548	−	0.0238422i
$244$	2.66166	−	1.71054i	0.170395	−	0.109506i
$245$	−18.2112	+	7.43993i	−1.16347	+	0.475319i
$246$	−1.46948	−	10.2204i	−0.0936904	−	0.651631i
$247$	−9.11350	+	26.3317i	−0.579878	+	1.67545i
$248$	1.70086	−	0.876852i	0.108004	−	0.0556802i
$249$	−4.62760	−	13.3706i	−0.293262	−	0.847325i
$250$	−8.07780	−	7.70217i	−0.510885	−	0.487128i
$251$	−4.92710	−	10.7888i	−0.310996	−	0.680986i	0.688004	−	0.725707i	$-0.258487\pi$
$251$	−4.92710	−	10.7888i	−0.310996	−	0.680986i	−0.998999	+	0.0447214i	$0.985760\pi$
$252$	−2.70867	+	3.14831i	−0.170630	+	0.198325i
$253$	5.62672	−	16.1666i	0.353749	−	1.01639i
$254$	14.4292	+	24.9921i	0.905369	+	1.56814i
$255$	−14.9214	−	1.42482i	−0.934416	−	0.0892259i
$256$	4.84193	−	19.9587i	0.302620	−	1.24742i
$257$	−1.72576	−	0.332613i	−0.107650	−	0.0207479i	0.135142	−	0.990826i	$-0.456851\pi$
$257$	−1.72576	−	0.332613i	−0.107650	−	0.0207479i	−0.242792	+	0.970078i	$0.578063\pi$
$258$	−18.5540	−	11.9239i	−1.15512	−	0.742352i
$259$	−15.3554	−	26.3814i	−0.954141	−	1.63926i
$260$	3.88733	+	27.0370i	0.241082	+	1.67676i
$261$	0.805879	+	3.32188i	0.0498827	+	0.205619i
$262$	0.923464	+	19.3859i	0.0570518	+	1.19766i
$263$	16.3236	+	12.8370i	1.00655	+	0.791563i	0.978122	−	0.208032i	$-0.0667059\pi$
$263$	16.3236	+	12.8370i	1.00655	+	0.791563i	0.0284327	+	0.999596i	$0.490948\pi$
$264$	2.88839	−	0.275808i	0.177768	−	0.0169748i
$265$	−14.1294	+	30.9391i	−0.867963	+	1.90057i
$266$	−22.0741	+	4.33512i	−1.35345	+	0.265803i
$267$	6.83801	−	4.39452i	0.418479	−	0.268940i
$268$	1.12881	+	4.65303i	0.0689533	+	0.284229i
$269$	19.7216	+	7.89536i	1.20245	+	0.481388i	0.884420	−	0.466692i	$-0.154554\pi$
$269$	19.7216	+	7.89536i	1.20245	+	0.481388i	0.318030	+	0.948081i	$0.396979\pi$
$270$	5.21383	−	1.00488i	0.317303	−	0.0611552i
$271$	−0.395789	+	8.30863i	−0.0240425	+	0.504713i	0.954442	+	0.298395i	$0.0964512\pi$
$271$	−0.395789	+	8.30863i	−0.0240425	+	0.504713i	−0.978485	+	0.206318i	$0.933852\pi$
$272$	−16.3302	+	18.8460i	−0.990161	+	1.14271i
$273$	9.54935	+	13.3107i	0.577953	+	0.805602i
$274$	6.06894	+	13.2891i	0.366638	+	0.802826i
$275$	5.17189	+	8.95797i	0.311877	+	0.540186i
$276$	−4.92008	−	5.69800i	−0.296154	−	0.342979i
$277$	6.64923	−	11.5168i	0.399514	−	0.691978i	−0.594152	−	0.804353i	$-0.702512\pi$
$277$	6.64923	−	11.5168i	0.399514	−	0.691978i	0.993666	+	0.112375i	$0.0358457\pi$
$278$	0.437409	−	0.614254i	0.0262340	−	0.0368405i
$279$	2.25863	−	0.663193i	0.135221	−	0.0397043i
$280$	4.73800	−	3.75308i	0.283150	−	0.224290i
$281$	0.526820	+	0.338567i	0.0314275	+	0.0201972i	0.556260	−	0.831008i	$-0.312236\pi$
$281$	0.526820	+	0.338567i	0.0314275	+	0.0201972i	−0.524833	+	0.851205i	$0.675872\pi$
$282$	−2.41429	+	6.97564i	−0.143769	+	0.415394i
$283$	12.5381	+	5.01951i	0.745315	+	0.298379i	0.713062	−	0.701101i	$-0.247308\pi$
$283$	12.5381	+	5.01951i	0.745315	+	0.298379i	0.0322528	+	0.999480i	$0.489732\pi$
$284$	6.18304	−	5.89552i	0.366896	−	0.349835i
$285$	11.2412	+	5.79523i	0.665870	+	0.343280i
$286$	−5.94248	+	41.3308i	−0.351386	+	2.44394i
$287$	−6.05283	−	13.1313i	−0.357287	−	0.775114i
$288$	2.99421	−	6.55640i	0.176435	−	0.386340i
$289$	10.6277	−	4.25468i	0.625157	−	0.250275i
$290$	0.863615	+	18.1295i	0.0507132	+	1.06460i
$291$	9.06537	−	8.64381i	0.531421	−	0.506709i
$292$	−8.15148	+	6.41039i	−0.477029	+	0.375140i
$293$	−12.7799	−	14.7488i	−0.746610	−	0.861634i	0.247625	−	0.968856i	$-0.420350\pi$
$293$	−12.7799	−	14.7488i	−0.746610	−	0.861634i	−0.994235	+	0.107222i	$0.965805\pi$
$294$	−5.40926	+	12.0689i	−0.315474	+	0.703871i
$295$	−2.51139	+	2.89830i	−0.146219	+	0.168745i
$296$	6.78777	+	6.47212i	0.394531	+	0.376185i
$297$	3.55315	+	0.339285i	0.206175	+	0.0196873i
$298$	11.2863	−	19.5485i	0.653799	−	1.13241i
$299$	−26.4172	+	13.5611i	−1.52775	+	0.784259i
$300$	4.54909			0.262642
$301$	−29.6640	−	8.59677i	−1.70980	−	0.495509i
$302$	11.8272	−	3.47279i	0.680581	−	0.199837i
$303$	3.75135	+	0.723014i	0.215510	+	0.0415361i
$304$	18.7013	−	9.64120i	1.07259	−	0.552960i
$305$	−5.56203	+	1.07199i	−0.318481	+	0.0613822i
$306$	−7.92126	+	6.22934i	−0.452828	+	0.356108i
$307$	−15.1453	−	4.44707i	−0.864390	−	0.253808i	−0.180662	−	0.983545i	$-0.557824\pi$
$307$	−15.1453	−	4.44707i	−0.864390	−	0.253808i	−0.683727	+	0.729737i	$0.739642\pi$
$308$	−13.7426	+	5.55793i	−0.783055	+	0.316692i
$309$	1.22689	−	8.53322i	0.0697954	−	0.485438i
$310$	12.4425	−	1.18812i	0.706688	−	0.0674805i
$311$	9.77823	+	13.7316i	0.554473	+	0.778648i	0.992751	−	0.120192i	$-0.0383509\pi$
$311$	9.77823	+	13.7316i	0.554473	+	0.778648i	−0.438278	+	0.898839i	$0.644411\pi$
$312$	−3.95648	−	3.11141i	−0.223992	−	0.176149i
$313$	−21.0065	−	10.8296i	−1.18736	−	0.612126i	−0.252656	−	0.967556i	$-0.581304\pi$
$313$	−21.0065	−	10.8296i	−1.18736	−	0.612126i	−0.934703	+	0.355431i	$0.884334\pi$
$314$	11.0042	+	3.23111i	0.621001	+	0.182342i
$315$	6.59685	−	3.43037i	0.371690	−	0.193280i
$316$	−1.79347	−	2.06978i	−0.100891	−	0.116434i
$317$	−0.190323	+	3.99536i	−0.0106896	+	0.224402i	0.987201	+	0.159482i	$0.0509823\pi$
$317$	−0.190323	+	3.99536i	−0.0106896	+	0.224402i	−0.997890	+	0.0649202i	$0.979321\pi$
$318$	7.47895	+	21.6090i	0.419399	+	1.21177i
$319$	−2.87643	+	11.8568i	−0.161049	+	0.663854i
$320$	6.95649	−	9.76902i	0.388880	−	0.546105i
$321$	8.82327			0.492467
$322$	−20.1910	−	12.9250i	−1.12520	−	0.720280i
$323$	−24.0025			−1.33553
$324$	0.910542	−	1.27868i	0.0505857	−	0.0710376i
$325$	4.23036	−	17.4378i	0.234658	−	0.967274i
$326$	−6.23327	−	18.0098i	−0.345229	−	0.997473i
$327$	0.716002	−	15.0307i	0.0395950	−	0.831202i
$328$	2.90928	+	3.35749i	0.160638	+	0.185386i
$329$	−0.455475	+	10.3267i	−0.0251111	+	0.569328i
$330$	18.1846	+	5.33947i	1.00103	+	0.293928i
$331$	−18.0173	−	9.28855i	−0.990318	−	0.510545i	−0.114623	−	0.993409i	$-0.536566\pi$
$331$	−18.0173	−	9.28855i	−0.990318	−	0.510545i	−0.875695	+	0.482864i	$0.839596\pi$
$332$	−17.4582	−	13.7293i	−0.958142	−	0.753491i
$333$	6.69230	+	9.39802i	0.366736	+	0.515008i
$334$	−8.17484	+	0.780602i	−0.447307	+	0.0427126i
$335$	1.21992	−	8.48476i	0.0666516	−	0.463572i
$336$	1.71729	−	12.2501i	0.0936859	−	0.668300i
$337$	26.2787	+	7.71611i	1.43149	+	0.420323i	0.903376	−	0.428850i	$-0.141081\pi$
$337$	26.2787	+	7.71611i	1.43149	+	0.420323i	0.528114	+	0.849174i	$0.322899\pi$
$338$	37.6306	−	29.5931i	2.04684	−	1.60965i
$339$	16.8517	−	3.24789i	0.915256	−	0.176401i
$340$	−20.9138	+	10.7818i	−1.13421	+	0.584725i
$341$	8.25025	+	1.59011i	0.446776	+	0.0861091i
$342$	8.15818	−	2.39546i	0.441144	−	0.129532i
$343$	−2.44188	+	18.3586i	−0.131849	+	0.991270i
$344$	9.48933			0.511630
$345$	4.38610	+	12.7442i	0.236140	+	0.686127i
$346$	0.976170	−	1.69078i	0.0524792	−	0.0908967i
$347$	−4.29618	−	0.410236i	−0.230631	−	0.0220226i	−0.0208995	−	0.999782i	$-0.506653\pi$
$347$	−4.29618	−	0.410236i	−0.230631	−	0.0220226i	−0.209732	+	0.977759i	$0.567259\pi$
$348$	3.88338	+	3.70280i	0.208171	+	0.198491i
$349$	−1.53290	+	1.76906i	−0.0820543	+	0.0946958i	−0.795292	−	0.606226i	$-0.792683\pi$
$349$	−1.53290	+	1.76906i	−0.0820543	+	0.0946958i	0.713238	+	0.700922i	$0.247228\pi$
$350$	13.8852	−	4.13024i	0.742195	−	0.220770i
$351$	−4.05474	−	4.67942i	−0.216426	−	0.249769i
$352$	20.2226	−	15.9032i	1.07787	−	0.847643i
$353$	−17.1791	+	16.3803i	−0.914354	+	0.871835i	−0.992140	−	0.125136i	$-0.960063\pi$
$353$	−17.1791	+	16.3803i	−0.914354	+	0.871835i	0.0777859	+	0.996970i	$0.475215\pi$
$354$	0.122678	+	2.57533i	0.00652028	+	0.136877i
$355$	−14.1995	+	5.68460i	−0.753629	+	0.301707i
$356$	5.30047	−	11.6064i	0.280924	−	0.615139i
$357$	−8.14493	+	11.5236i	−0.431075	+	0.609895i
$358$	−1.26671	+	8.81015i	−0.0669476	+	0.465631i
$359$	8.25306	+	4.25475i	0.435580	+	0.224557i	0.662048	−	0.749462i	$-0.269688\pi$
$359$	8.25306	+	4.25475i	0.435580	+	0.224557i	−0.226468	+	0.974019i	$0.572718\pi$
$360$	−1.65341	+	1.57652i	−0.0871423	+	0.0830900i
$361$	1.16223	+	0.465285i	0.0611698	+	0.0244887i
$362$	−10.7418	+	31.0364i	−0.564577	+	1.63124i
$363$	1.46376	+	0.940704i	0.0768277	+	0.0493741i
$364$	23.9068	+	9.47330i	1.25306	+	0.496536i
$365$	17.8137	−	5.23058i	0.932413	−	0.273781i
$366$	−2.20895	+	3.10203i	−0.115463	+	0.162146i
$367$	−2.03504	+	3.52480i	−0.106228	+	0.183993i	−0.914239	−	0.405174i	$-0.867211\pi$
$367$	−2.03504	+	3.52480i	−0.106228	+	0.183993i	0.808011	+	0.589167i	$0.200544\pi$
$368$	21.5031	+	6.35439i	1.12093	+	0.331246i
$369$	2.73252	+	4.73287i	0.142249	+	0.246383i
$370$	25.4486	+	55.7246i	1.32301	+	2.89699i
$371$	18.6657	+	26.0178i	0.969073	+	1.35078i
$372$	2.41981	−	2.79261i	0.125461	−	0.144790i
$373$	1.58981	−	33.3742i	0.0823172	−	1.72805i	−0.460037	−	0.887900i	$-0.652164\pi$
$373$	1.58981	−	33.3742i	0.0823172	−	1.72805i	0.542354	−	0.840150i	$-0.317533\pi$
$374$	−35.3188	+	6.80715i	−1.82629	+	0.351989i
$375$	5.48423	+	2.19555i	0.283204	+	0.113378i
$376$	−0.748764	−	3.08645i	−0.0386145	−	0.159171i
$377$	17.8050	−	11.4426i	0.917006	−	0.589324i
$378$	1.61831	−	4.72962i	0.0832368	−	0.243265i
$379$	−5.08517	+	11.1350i	−0.261208	+	0.571965i	−0.994111	−	0.108368i	$-0.965438\pi$
$379$	−5.08517	+	11.1350i	−0.261208	+	0.571965i	0.732903	+	0.680333i	$0.238165\pi$
$380$	19.7628	−	1.88712i	1.01381	−	0.0968073i
$381$	−12.0062	−	9.44178i	−0.615096	−	0.483717i
$382$	−0.532091	−	11.1700i	−0.0272241	−	0.571505i
$383$	−0.843901	−	3.47861i	−0.0431213	−	0.177748i	0.946179	−	0.323645i	$-0.104908\pi$
$383$	−0.843901	−	3.47861i	−0.0431213	−	0.177748i	−0.989300	+	0.145897i	$0.953393\pi$
$384$	0.904099	+	6.28814i	0.0461371	+	0.320891i
$385$	26.5392	−	0.0934669i	1.35257	−	0.00476351i
$386$	−37.6771	−	24.2136i	−1.91771	−	1.23244i
$387$	11.4623	+	2.20918i	0.582662	+	0.112299i
$388$	4.63558	−	19.1081i	0.235336	−	0.970068i
$389$	−16.7473	−	1.59917i	−0.849122	−	0.0810813i	−0.338584	−	0.940936i	$-0.609948\pi$
$389$	−16.7473	−	1.59917i	−0.849122	−	0.0810813i	−0.510538	+	0.859855i	$0.670554\pi$
$390$	−16.4385	−	28.4722i	−0.832393	−	1.44175i
$391$	−18.4819	−	17.6837i	−0.934672	−	0.894306i
$392$	−0.849478	−	5.62662i	−0.0429051	−	0.284187i
$393$	−4.26719	−	9.34383i	−0.215251	−	0.471334i
$394$	18.2876	+	17.4372i	0.921314	+	0.878471i
$395$	1.60366	+	4.63347i	0.0806888	+	0.233135i
$396$	4.98007	−	2.56740i	0.250258	−	0.129017i
$397$	−8.78873	+	25.3934i	−0.441094	+	1.27446i	0.477283	+	0.878750i	$0.341622\pi$
$397$	−8.78873	+	25.3934i	−0.441094	+	1.27446i	−0.918377	+	0.395707i	$0.870499\pi$
$398$	2.75175	+	19.1389i	0.137933	+	0.959345i
$399$	9.99360	−	6.47234i	0.500306	−	0.324022i
$400$	−11.3983	+	7.32523i	−0.569914	+	0.366262i
$401$	29.1145	−	11.6557i	1.45391	−	0.582058i	0.495795	−	0.868439i	$-0.334877\pi$
$401$	29.1145	−	11.6557i	1.45391	−	0.582058i	0.958116	+	0.286381i	$0.0924524\pi$
$402$	−3.34283	−	4.69434i	−0.166725	−	0.234133i
$403$	−8.45450	−	11.8727i	−0.421149	−	0.591420i
$404$	5.56747	−	2.22888i	0.276992	−	0.110891i
$405$	−2.36420	+	1.51938i	−0.117478	+	0.0754987i
$406$	15.2151	+	7.77625i	0.755115	+	0.385929i
$407$	5.86056	+	40.7611i	0.290497	+	2.02045i
$408$	1.41809	−	4.09731i	0.0702061	−	0.202847i
$409$	−0.712306	+	0.367219i	−0.0352213	+	0.0181578i	−0.475747	−	0.879582i	$-0.657822\pi$
$409$	−0.712306	+	0.367219i	−0.0352213	+	0.0181578i	0.440526	+	0.897740i	$0.354792\pi$
$410$	9.49092	+	27.4222i	0.468723	+	1.35429i
$411$	−5.59617	−	5.33594i	−0.276039	−	0.263203i
$412$	−5.62170	−	12.3098i	−0.276961	−	0.606460i
$413$	1.19286	+	3.40766i	0.0586966	+	0.167680i
$414$	8.04665	+	4.16600i	0.395471	+	0.204748i
$415$	19.8813	+	34.4355i	0.975936	+	1.69037i
$416$	−44.4266	−	4.24223i	−2.17819	−	0.207992i
$417$	−0.0940949	+	0.387864i	−0.00460785	+	0.0189938i
$418$	29.8000	+	5.74347i	1.45756	+	0.280923i
$419$	−17.5723	−	11.2930i	−0.858462	−	0.551700i	0.0357411	−	0.999361i	$-0.488621\pi$
$419$	−17.5723	−	11.2930i	−0.858462	−	0.551700i	−0.894203	+	0.447661i	$0.852257\pi$
$420$	5.80025	−	10.1285i	0.283023	−	0.494222i
$421$	−2.40962	−	16.7593i	−0.117438	−	0.816798i	−0.960360	−	0.278763i	$-0.910076\pi$
$421$	−2.40962	−	16.7593i	−0.117438	−	0.816798i	0.842922	−	0.538036i	$-0.180833\pi$
$422$	−5.60906	−	23.1209i	−0.273045	−	1.12551i
$423$	−0.185898	−	3.90248i	−0.00903868	−	0.189745i
$424$	−7.73355	−	6.08173i	−0.375574	−	0.295355i
$425$	15.3868	−	1.46926i	0.746368	−	0.0712695i
$426$	−4.27164	+	9.35358i	−0.206962	+	0.453183i
$427$	−1.72639	+	5.04549i	−0.0835457	+	0.244168i
$428$	11.6516	−	7.48803i	0.563202	−	0.361948i
$429$	−5.21035	−	21.4774i	−0.251558	−	1.03694i
$430$	57.5426	+	23.0366i	2.77495	+	1.11092i
$431$	−39.9982	+	7.70903i	−1.92665	+	0.371331i	−0.999990	−	0.00457440i	$-0.998544\pi$
$431$	−39.9982	+	7.70903i	−1.92665	+	0.371331i	−0.926658	+	0.375905i	$0.877332\pi$
$432$	−0.222464	+	4.67009i	−0.0107033	+	0.224690i
$433$	16.2737	−	18.7809i	0.782065	−	0.902552i	−0.215191	−	0.976572i	$-0.569038\pi$
$433$	16.2737	−	18.7809i	0.782065	−	0.902552i	0.997257	+	0.0740204i	$0.0235830\pi$
$434$	4.85052	−	10.7209i	0.232832	−	0.514620i
$435$	−3.99063	−	8.73827i	−0.191336	−	0.418968i
$436$	−11.8106	−	20.4566i	−0.565625	−	0.979692i
$437$	8.93155	+	19.6474i	0.427254	+	0.939864i
$438$	6.24085	−	10.8095i	0.298199	−	0.516496i
$439$	−6.36864	+	8.94350i	−0.303958	+	0.426850i	−0.938099	−	0.346368i	$-0.887415\pi$
$439$	−6.36864	+	8.94350i	−0.303958	+	0.426850i	0.634140	+	0.773218i	$0.281354\pi$
$440$	−7.82397	+	2.29733i	−0.372993	+	0.109521i
$441$	0.283816	−	6.99424i	0.0135150	−	0.333059i
$442$	52.4908	+	33.7338i	2.49673	+	1.60455i
$443$	9.24262	−	26.7048i	0.439130	−	1.26878i	−0.480844	−	0.876806i	$-0.659670\pi$
$443$	9.24262	−	26.7048i	0.439130	−	1.26878i	0.919975	−	0.391978i	$-0.128209\pi$
$444$	16.8134	+	6.73105i	0.797927	+	0.319442i
$445$	−16.5325	+	15.7638i	−0.783718	+	0.747274i
$446$	−34.8804	−	17.9821i	−1.65163	−	0.851476i
$447$	−1.70025	+	11.8255i	−0.0804192	+	0.559328i
$448$	−4.72636	−	10.2536i	−0.223299	−	0.484435i
$449$	−4.34352	+	9.51098i	−0.204983	+	0.448851i	−0.984004	−	0.178148i	$-0.942990\pi$
$449$	−4.34352	+	9.51098i	−0.204983	+	0.448851i	0.779020	+	0.626999i	$0.215717\pi$
$450$	−5.08316	+	2.03499i	−0.239622	+	0.0959303i
$451$	0.928154	+	19.4843i	0.0437050	+	0.917482i
$452$	19.4971	−	18.5905i	0.917069	−	0.874423i
$453$	−5.12831	+	4.03295i	−0.240949	+	0.189485i
$454$	1.20056	+	1.38553i	0.0563453	+	0.0650259i
$455$	−33.4313	−	31.6527i	−1.56728	−	1.48390i
$456$	−2.39566	+	2.76474i	−0.112187	+	0.129471i
$457$	1.49681	+	1.42721i	0.0700179	+	0.0667619i	0.724280	−	0.689506i	$-0.242172\pi$
$457$	1.49681	+	1.42721i	0.0700179	+	0.0667619i	−0.654262	+	0.756268i	$0.727021\pi$
$458$	−10.8279	−	1.03394i	−0.505954	−	0.0483128i
$459$	2.66682	−	4.61907i	0.124476	−	0.215600i
$460$	16.6077	+	13.1071i	0.774339	+	0.611122i
$461$	−15.4111			−0.717767			−0.358883	−	0.933382i	$-0.616842\pi$
$461$	−15.4111			−0.717767			−0.358883	+	0.933382i	$0.616842\pi$
$462$	12.8697	−	12.3580i	0.598751	−	0.574948i
$463$	−4.96849	+	1.45888i	−0.230905	+	0.0677999i	−0.395138	−	0.918622i	$-0.629303\pi$
$463$	−4.96849	+	1.45888i	−0.230905	+	0.0677999i	0.164233	+	0.986422i	$0.447485\pi$
$464$	−15.6928	−	3.02453i	−0.728518	−	0.140410i
$465$	−5.88007	+	3.03138i	−0.272682	+	0.140577i
$466$	−1.47038	+	0.283393i	−0.0681142	+	0.0131279i
$467$	−9.01242	+	7.08744i	−0.417045	+	0.327968i	−0.804534	−	0.593906i	$-0.797585\pi$
$467$	−9.01242	+	7.08744i	−0.417045	+	0.327968i	0.387489	+	0.921874i	$0.373342\pi$
$468$	−9.32579	−	2.73830i	−0.431085	−	0.126578i
$469$	−6.36098	−	4.96617i	−0.293723	−	0.229317i
$470$	2.95230	−	20.5337i	0.136179	−	0.947148i
$471$	−6.04262	+	0.577001i	−0.278429	+	0.0265868i
$472$	−0.643459	−	0.903612i	−0.0296176	−	0.0415921i
$473$	32.7513	+	25.7559i	1.50591	+	1.18426i
$474$	2.92992	+	1.51048i	0.134576	+	0.0693786i
$475$	−12.5132	−	3.67422i	−0.574146	−	0.168585i
$476$	−0.976077	+	22.1299i	−0.0447384	+	1.01432i
$477$	−7.92561	−	9.14664i	−0.362889	−	0.418796i
$478$	−1.17784	+	24.7259i	−0.0538731	+	1.13094i
$479$	−6.20785	−	17.9364i	−0.283644	−	0.819536i	−0.993360	−	0.115048i	$-0.963298\pi$
$479$	−6.20785	−	17.9364i	−0.283644	−	0.819536i	0.709716	−	0.704488i	$-0.248823\pi$
$480$	−4.77558	+	19.6852i	−0.217974	+	0.898502i
$481$	41.4371	−	58.1903i	1.88937	−	2.65325i
$482$	21.9348			0.999103
$483$	12.4636	+	2.37904i	0.567111	+	0.108250i
$484$	2.73133			0.124151
$485$	−20.4190	+	28.6745i	−0.927180	+	1.30204i
$486$	−0.445438	+	1.83612i	−0.0202055	+	0.0832880i
$487$	2.72855	+	7.88363i	0.123642	+	0.357241i	0.989787	−	0.142551i	$-0.0455306\pi$
$487$	2.72855	+	7.88363i	0.123642	+	0.357241i	−0.866145	+	0.499793i	$0.833409\pi$
$488$	0.0779616	−	1.63662i	0.00352916	−	0.0740861i
$489$	6.60553	+	7.62319i	0.298713	+	0.344733i
$490$	8.50816	−	36.1816i	0.384360	−	1.63452i
$491$	−27.1842	−	7.98201i	−1.22681	−	0.360223i	−0.396763	−	0.917921i	$-0.629866\pi$
$491$	−27.1842	−	7.98201i	−1.22681	−	0.360223i	−0.830044	+	0.557698i	$0.811685\pi$
$492$	7.62508	+	3.93100i	0.343765	+	0.177223i
$493$	14.3310	+	11.2700i	0.645437	+	0.507577i
$494$	−30.5377	−	42.8842i	−1.37396	−	1.92945i
$495$	−9.98553	+	0.953503i	−0.448816	+	0.0428568i
$496$	−1.56629	+	10.8938i	−0.0703283	+	0.489144i
$497$	−1.99903	+	14.2599i	−0.0896688	+	0.639644i
$498$	25.6494	+	7.53136i	1.14938	+	0.337488i
$499$	2.66644	−	2.09691i	0.119366	−	0.0938708i	−0.556691	−	0.830719i	$-0.687929\pi$
$499$	2.66644	−	2.09691i	0.119366	−	0.0938708i	0.676058	+	0.736849i	$0.263687\pi$
$500$	9.10553	−	1.75495i	0.407211	−	0.0784836i
$501$	3.86325	−	1.99164i	0.172597	−	0.0889801i
$502$	22.0043	+	4.24098i	0.982101	+	0.189284i
$503$	8.14608	−	2.39191i	0.363216	−	0.106650i	−0.0950321	−	0.995474i	$-0.530295\pi$
$503$	8.14608	−	2.39191i	0.363216	−	0.106650i	0.458248	+	0.888824i	$0.348477\pi$
$504$	0.514419	+	2.08834i	0.0229140	+	0.0930219i
$505$	−10.7366			−0.477771
$506$	18.7145	+	26.3775i	0.831962	+	1.17262i
$507$	−12.6690	+	21.9433i	−0.562648	+	0.974536i
$508$	−23.8678	−	2.27910i	−1.05896	−	0.101119i
$509$	4.33846	+	4.13672i	0.192299	+	0.183357i	0.780112	−	0.625640i	$-0.215162\pi$
$509$	4.33846	+	4.13672i	0.192299	+	0.183357i	−0.587813	+	0.808997i	$0.700011\pi$
$510$	18.5459	−	21.4032i	0.821228	−	0.947748i
$511$	4.06086	−	17.0002i	0.179642	−	0.752045i
$512$	17.0903	+	19.7233i	0.755294	+	0.871656i
$513$	−3.53741	+	2.78185i	−0.156180	+	0.122822i
$514$	2.40325	−	2.29149i	0.106003	−	0.101073i
$515$	1.15280	+	24.2003i	0.0507986	+	1.06639i
$516$	17.0115	−	6.81037i	0.748889	−	0.299810i
$517$	5.79295	−	12.6848i	0.254774	−	0.557877i
$518$	57.4308	+	5.27994i	2.52336	+	0.231987i
$519$	−0.147057	+	1.02281i	−0.00645511	+	0.0448962i
$520$	12.5729	+	6.48180i	0.551360	+	0.284246i
$521$	29.0680	−	27.7163i	1.27349	−	1.21427i	0.308730	−	0.951150i	$-0.400096\pi$
$521$	29.0680	−	27.7163i	1.27349	−	1.21427i	0.964762	−	0.263123i	$-0.0847523\pi$
$522$	−5.99571	−	2.40032i	−0.262425	−	0.105059i
$523$	4.31157	−	12.4575i	0.188532	−	0.544727i	−0.810635	−	0.585552i	$-0.800878\pi$
$523$	4.31157	−	12.4575i	0.188532	−	0.544727i	0.999166	+	0.0408257i	$0.0129988\pi$
$524$	−13.5649	−	8.71761i	−0.592584	−	0.380831i
$525$	−6.01019	+	4.76082i	−0.262306	+	0.207779i
$526$	−37.6464	+	11.0540i	−1.64146	+	0.481977i
$527$	7.28278	−	10.2272i	0.317243	−	0.445505i
$528$	−8.34396	+	14.4522i	−0.363124	+	0.628950i
$529$	−7.59786	+	21.7088i	−0.330342	+	0.943861i
$530$	−32.1315	−	55.6533i	−1.39570	−	2.41743i
$531$	−0.566877	−	1.24129i	−0.0246004	−	0.0538673i
$532$	7.70422	−	17.0283i	0.334020	−	0.738272i
$533$	22.1593	−	25.5732i	0.959828	−	1.10770i
$534$	−0.730741	+	15.3401i	−0.0316223	+	0.663833i
$535$	−24.3482	+	4.69274i	−1.05267	+	0.202885i
$536$	2.30191	+	0.921545i	0.0994273	+	0.0398047i
$537$	−1.11065	−	4.57815i	−0.0479280	−	0.197562i
$538$	−33.7651	+	21.6995i	−1.45572	+	0.935534i
$539$	12.3399	−	21.7253i	0.531516	−	0.935773i
$540$	−1.83261	+	4.01285i	−0.0788629	+	0.172686i
$541$	−33.8236	+	3.22976i	−1.45419	+	0.138858i	−0.792020	−	0.610496i	$-0.790970\pi$
$541$	−33.8236	+	3.22976i	−1.45419	+	0.138858i	−0.662170	+	0.749354i	$0.730364\pi$
$542$	−12.3536	−	9.71494i	−0.530631	−	0.417293i
$543$	−0.827109	−	17.3632i	−0.0354947	−	0.745125i
$544$	−9.06341	−	37.3599i	−0.388590	−	1.60179i
$545$	6.01839	+	41.8589i	0.257800	+	1.79304i
$546$	−30.9513	+	0.109006i	−1.32459	+	0.00466501i
$547$	−9.25827	−	5.94993i	−0.395855	−	0.254401i	0.327537	−	0.944838i	$-0.393781\pi$
$547$	−9.25827	−	5.94993i	−0.395855	−	0.254401i	−0.723392	+	0.690438i	$0.757418\pi$
$548$	−11.9185	−	2.29710i	−0.509133	−	0.0981274i
$549$	0.475186	−	1.95874i	0.0202805	−	0.0835972i
$550$	−19.4548	−	1.85771i	−0.829556	−	0.0792130i
$551$	−7.69139	−	13.3219i	−0.327664	−	0.567531i
$552$	−3.88157	+	0.363857i	−0.165211	+	0.0154868i
$553$	4.53562	+	0.857614i	0.192874	+	0.0364694i
$554$	10.4376	+	22.8552i	0.443453	+	0.971026i
$555$	−23.4661	−	22.3749i	−0.996082	−	0.949763i
$556$	0.204911	+	0.592052i	0.00869017	+	0.0251086i
$557$	−14.9763	+	7.72080i	−0.634564	+	0.327141i	−0.745320	−	0.666707i	$-0.767703\pi$
$557$	−14.9763	+	7.72080i	−0.634564	+	0.327141i	0.110756	+	0.993848i	$0.464673\pi$
$558$	−1.45465	+	4.20295i	−0.0615804	+	0.177925i
$559$	−10.2862	−	71.5424i	−0.435062	−	3.02592i
$560$	1.77640	+	34.7182i	0.0750666	+	1.46711i
$561$	16.0153	−	10.2924i	0.676166	−	0.434546i
$562$	−1.09843	+	0.439747i	−0.0463347	+	0.0185496i
$563$	3.40051	+	4.77534i	0.143314	+	0.201257i	0.879994	−	0.474985i	$-0.157547\pi$
$563$	3.40051	+	4.77534i	0.143314	+	0.201257i	−0.736679	+	0.676242i	$0.763607\pi$
$564$	−3.55741	−	4.99568i	−0.149794	−	0.210356i
$565$	−44.7755	+	17.9254i	−1.88372	+	0.754128i
$566$	−21.4664	+	13.7956i	−0.902299	+	0.579872i
$567$	0.135196	+	2.64229i	0.00567772	+	0.110966i
$568$	−0.629632	−	4.37919i	−0.0264188	−	0.183747i
$569$	0.704674	−	2.03602i	0.0295415	−	0.0853544i	−0.929266	−	0.369411i	$-0.879559\pi$
$569$	0.704674	−	2.03602i	0.0295415	−	0.0853544i	0.958807	+	0.284057i	$0.0916805\pi$
$570$	−21.2388	+	10.9494i	−0.889597	+	0.458619i
$571$	11.2606	+	32.5354i	0.471242	+	1.36156i	0.891031	+	0.453943i	$0.149983\pi$
$571$	11.2606	+	32.5354i	0.471242	+	1.36156i	−0.419789	+	0.907622i	$0.637896\pi$
$572$	−25.1077	−	23.9402i	−1.04981	−	1.00099i
$573$	2.45871	+	5.38382i	0.102714	+	0.224912i
$574$	26.8431	+	5.07561i	1.12041	+	0.211852i
$575$	−6.92823	−	12.0482i	−0.288927	−	0.502446i
$576$	2.13369	+	3.69566i	0.0889038	+	0.153986i
$577$	16.1180	+	1.53908i	0.671000	+	0.0640727i	0.424995	−	0.905196i	$-0.360276\pi$
$577$	16.1180	+	1.53908i	0.671000	+	0.0640727i	0.246005	+	0.969269i	$0.420882\pi$
$578$	−5.09923	+	21.0193i	−0.212100	+	0.874288i
$579$	23.2762	+	4.48611i	0.967324	+	0.186436i
$580$	−12.6857	−	8.15264i	−0.526747	−	0.338520i
$581$	37.4338	−	0.131836i	1.55302	−	0.00546947i
$582$	3.36803	+	23.4251i	0.139609	+	0.971003i
$583$	−10.1844	−	41.9808i	−0.421796	−	1.73867i
$584$	0.255529	+	5.36421i	0.0105739	+	0.221973i
$585$	13.6780	+	10.7565i	0.565518	+	0.444728i
$586$	36.7051	−	3.50491i	1.51627	−	0.144787i
$587$	6.73975	−	14.7580i	0.278179	−	0.609128i	−0.718040	−	0.696002i	$-0.754961\pi$
$587$	6.73975	−	14.7580i	0.278179	−	0.609128i	0.996219	+	0.0868741i	$0.0276878\pi$
$588$	−5.56100	−	9.47715i	−0.229332	−	0.390831i
$589$	−8.91175	+	5.72723i	−0.367202	+	0.235986i
$590$	−1.70825	−	7.04151i	−0.0703276	−	0.289894i
$591$	−12.4159	−	4.97058i	−0.510722	−	0.204462i
$592$	−52.9667	+	10.2085i	−2.17692	+	0.419566i
$593$	−0.232065	+	4.87164i	−0.00952977	+	0.200054i	0.989081	+	0.147370i	$0.0470808\pi$
$593$	−0.232065	+	4.87164i	−0.00952977	+	0.200054i	−0.998611	+	0.0526845i	$0.983222\pi$
$594$	−4.41623	+	5.09660i	−0.181200	+	0.209116i
$595$	16.3474	−	36.1320i	0.670177	−	1.48127i
$596$	7.79068	+	17.0592i	0.319119	+	0.698772i
$597$	−5.11694	−	8.86281i	−0.209423	−	0.362731i
$598$	8.08073	−	55.5194i	0.330445	−	2.27036i
$599$	0.934914	−	1.61932i	0.0381995	−	0.0661635i	−0.846294	−	0.532717i	$-0.821171\pi$
$599$	0.934914	−	1.61932i	0.0381995	−	0.0661635i	0.884493	+	0.466553i	$0.154504\pi$
$600$	1.36650	−	1.91898i	0.0557870	−	0.0783419i
$601$	1.55555	−	0.456750i	0.0634522	−	0.0186312i	−0.249852	−	0.968284i	$-0.580382\pi$
$601$	1.55555	−	0.456750i	0.0634522	−	0.0186312i	0.313305	+	0.949653i	$0.398564\pi$
$602$	45.7409	−	36.2325i	1.86426	−	1.47673i
$603$	2.56597	+	1.64905i	0.104494	+	0.0671545i
$604$	−3.34958	+	9.67797i	−0.136292	+	0.393791i
$605$	−4.53965	−	1.81740i	−0.184563	−	0.0738878i
$606$	−5.22403	+	4.98110i	−0.212212	+	0.202343i
$607$	43.5184	+	22.4353i	1.76636	+	0.910621i	0.934792	+	0.355195i	$0.115586\pi$
$607$	43.5184	+	22.4353i	1.76636	+	0.910621i	0.831566	+	0.555426i	$0.187445\pi$
$608$	−4.61618	+	32.1062i	−0.187211	+	1.30208i
$609$	−9.00582	−	0.827956i	−0.364934	−	0.0335505i
$610$	4.44585	−	9.73505i	0.180007	−	0.394160i
$611$	−22.4578	+	8.99076i	−0.908547	+	0.363727i
$612$	−0.398378	−	8.36298i	−0.0161035	−	0.338053i
$613$	−1.80808	+	1.72400i	−0.0730278	+	0.0696318i	−0.725714	−	0.687996i	$-0.758490\pi$
$613$	−1.80808	+	1.72400i	−0.0730278	+	0.0696318i	0.652686	+	0.757628i	$0.273642\pi$
$614$	23.4427	−	18.4355i	0.946070	−	0.743998i
$615$	−10.0577	−	11.6073i	−0.405567	−	0.468050i
$616$	−1.78357	+	7.46667i	−0.0718622	+	0.300841i
$617$	−0.303501	+	0.350259i	−0.0122185	+	0.0141009i	−0.761826	−	0.647782i	$-0.775697\pi$
$617$	−0.303501	+	0.350259i	−0.0122185	+	0.0141009i	0.749607	+	0.661883i	$0.230242\pi$
$618$	11.7884	+	11.2402i	0.474198	+	0.452146i
$619$	16.7059	+	1.59522i	0.671467	+	0.0641174i	0.425220	−	0.905090i	$-0.360197\pi$
$619$	16.7059	+	1.59522i	0.671467	+	0.0641174i	0.246247	+	0.969207i	$0.420803\pi$
$620$	−5.19231	+	8.99334i	−0.208528	+	0.361181i
$621$	−4.77332	−	0.464147i	−0.191547	−	0.0186256i
$622$	−31.8499			−1.27707
$623$	5.14371	+	20.8814i	0.206079	+	0.836596i
$624$	27.7763	−	8.15585i	1.11194	−	0.326495i
$625$	−30.5297	−	5.88413i	−1.22119	−	0.235365i
$626$	39.6892	−	20.4612i	1.58630	−	0.817795i
$627$	−15.7724	+	3.03988i	−0.629888	+	0.121401i
$628$	−7.48993	+	5.89015i	−0.298881	+	0.235043i
$629$	59.0432	+	17.3367i	2.35421	+	0.691258i
$630$	−1.95031	+	13.9123i	−0.0777020	+	0.554280i
$631$	1.42875	−	9.93718i	0.0568777	−	0.395593i	−0.941418	−	0.337241i	$-0.890506\pi$
$631$	1.42875	−	9.93718i	0.0568777	−	0.395593i	0.998296	−	0.0583521i	$-0.0185846\pi$
$632$	−1.41185	+	0.134815i	−0.0561603	+	0.00536266i
$633$	7.30422	+	10.2573i	0.290317	+	0.407693i
$634$	−5.94045	−	4.67162i	−0.235925	−	0.185534i
$635$	38.1534	+	19.6694i	1.51407	+	0.780558i
$636$	−18.2287	−	5.35242i	−0.722814	−	0.212237i
$637$	−41.4996	+	12.5036i	−1.64428	+	0.495409i
$638$	−15.0957	−	17.4214i	−0.597645	−	0.689719i
$639$	0.258962	−	5.43627i	0.0102444	−	0.215056i
$640$	−5.83931	−	16.8716i	−0.230819	−	0.666908i
$641$	7.43448	−	30.6453i	0.293644	−	1.21042i	−0.613533	−	0.789669i	$-0.710252\pi$
$641$	7.43448	−	30.6453i	0.293644	−	1.21042i	0.907177	−	0.420749i	$-0.138233\pi$
$642$	−9.66983	+	13.5794i	−0.381638	+	0.535935i
$643$	17.2520			0.680352			0.340176	−	0.940362i	$-0.389513\pi$
$643$	17.2520			0.680352			0.340176	+	0.940362i	$0.389513\pi$
$644$	18.4778	−	7.43578i	0.728128	−	0.293011i
$645$	−32.8058			−1.29173
$646$	26.3054	−	36.9408i	1.03497	−	1.45342i
$647$	−0.287040	+	1.18319i	−0.0112847	+	0.0465161i	−0.977176	−	0.212433i	$-0.931861\pi$
$647$	−0.287040	+	1.18319i	−0.0112847	+	0.0465161i	0.965891	+	0.258949i	$0.0833763\pi$
$648$	−0.265877	−	0.768202i	−0.0104446	−	0.0301778i
$649$	0.231757	−	4.86518i	0.00909727	−	0.190975i
$650$	22.2012	+	25.6216i	0.870803	+	1.00496i
$651$	−0.274431	+	6.22200i	−0.0107558	+	0.243859i
$652$	15.1925	+	4.46093i	0.594986	+	0.174704i
$653$	1.35995	+	0.701103i	0.0532189	+	0.0274363i	0.484631	−	0.874719i	$-0.338954\pi$
$653$	1.35995	+	0.701103i	0.0532189	+	0.0274363i	−0.431412	+	0.902155i	$0.641984\pi$
$654$	22.3482	+	17.5748i	0.873885	+	0.687231i
$655$	16.7451	+	23.5152i	0.654285	+	0.918815i
$656$	−25.4355	+	2.42880i	−0.993090	+	0.0948286i
$657$	−0.940167	+	6.53901i	−0.0366794	+	0.255111i
$658$	−15.3940	−	12.0185i	−0.600121	−	0.468529i
$659$	−0.468105	−	0.137448i	−0.0182348	−	0.00535421i	0.272602	−	0.962127i	$-0.412116\pi$
$659$	−0.468105	−	0.137448i	−0.0182348	−	0.00535421i	−0.290837	+	0.956773i	$0.593934\pi$
$660$	−12.3772	+	9.73357i	−0.481783	+	0.378879i
$661$	25.7002	−	4.95330i	0.999621	−	0.192661i	0.336910	−	0.941537i	$-0.390618\pi$
$661$	25.7002	−	4.95330i	0.999621	−	0.192661i	0.662711	+	0.748876i	$0.269406\pi$
$662$	34.0414	−	17.5496i	1.32306	−	0.682083i
$663$	−32.4278	−	6.24995i	−1.25939	−	0.242728i
$664$	−11.0358	+	3.24039i	−0.428271	+	0.125752i
$665$	−24.1354	+	23.1759i	−0.935932	+	0.898724i
$666$	−21.7983			−0.844669
$667$	3.89247	−	15.9245i	0.150717	−	0.616597i
$668$	3.41139	−	5.90869i	0.131990	−	0.228614i
$669$	20.6762	+	1.97433i	0.799387	+	0.0763322i
$670$	11.7214	+	11.1764i	0.452838	+	0.431780i
$671$	4.71117	−	5.43698i	0.181873	−	0.209892i
$672$	13.8478	+	13.1111i	0.534191	+	0.505770i
$673$	−27.3573	−	31.5721i	−1.05455	−	1.21701i	−0.975467	−	0.220145i	$-0.929347\pi$
$673$	−27.3573	−	31.5721i	−1.05455	−	1.21701i	−0.0790808	−	0.996868i	$-0.525199\pi$
$674$	−40.6754	+	31.9875i	−1.56676	+	1.23211i
$675$	2.09736	−	1.99983i	0.0807276	−	0.0769736i
$676$	1.89253	+	39.7291i	0.0727896	+	1.52804i
$677$	−16.9598	+	6.78969i	−0.651819	+	0.260949i	−0.673917	−	0.738807i	$-0.735390\pi$
$677$	−16.9598	+	6.78969i	−0.651819	+	0.260949i	0.0220983	+	0.999756i	$0.492965\pi$
$678$	−13.4699	+	29.4949i	−0.517307	+	1.13274i
$679$	13.8730	+	30.0967i	0.532398	+	1.15501i
$680$	−1.73410	+	12.0609i	−0.0664998	+	0.462516i
$681$	−0.862460	−	0.444629i	−0.0330496	−	0.0170382i
$682$	−11.4891	+	10.9548i	−0.439939	+	0.419481i
$683$	−16.3650	−	6.55154i	−0.626188	−	0.250688i	0.0367945	−	0.999323i	$-0.488285\pi$
$683$	−16.3650	−	6.55154i	−0.626188	−	0.250688i	−0.662982	+	0.748635i	$0.730710\pi$
$684$	−2.31047	+	6.67567i	−0.0883430	+	0.255250i
$685$	18.2809	+	11.7484i	0.698476	+	0.448884i
$686$	−25.5784	−	23.8782i	−0.976589	−	0.911673i
$687$	5.52380	−	1.62193i	0.210746	−	0.0618807i
$688$	−31.6578	+	44.4572i	−1.20694	+	1.69491i
$689$	−37.4687	+	64.8976i	−1.42744	+	2.47240i
$690$	−24.4208	−	7.21660i	−0.929685	−	0.274731i
$691$	16.4684	+	28.5242i	0.626489	+	1.08511i	0.988251	+	0.152841i	$0.0488421\pi$
$691$	16.4684	+	28.5242i	0.626489	+	1.08511i	−0.361762	+	0.932271i	$0.617825\pi$
$692$	0.673827	+	1.47548i	0.0256151	+	0.0560892i
$693$	−3.89270	+	8.60388i	−0.147871	+	0.326834i
$694$	5.33976	−	6.16241i	0.202694	−	0.233922i
$695$	0.0533701	−	1.12038i	0.00202444	−	0.0424983i
$696$	2.72851	−	0.525876i	0.103424	−	0.0199333i
$697$	27.0606	+	10.8334i	1.02499	+	0.410345i
$698$	−1.04268	−	4.29800i	−0.0394661	−	0.162682i
$699$	0.666744	−	0.428490i	0.0252186	−	0.0162070i
$700$	−3.89643	+	11.3876i	−0.147271	+	0.430410i
$701$	2.43188	−	5.32508i	0.0918509	−	0.201126i	−0.858131	−	0.513431i	$-0.828374\pi$
$701$	2.43188	−	5.32508i	0.0918509	−	0.201126i	0.949982	+	0.312306i	$0.101101\pi$
$702$	11.6456	−	1.11202i	0.439535	−	0.0419705i
$703$	−40.8122	−	32.0950i	−1.53926	−	1.21049i
$704$	0.724749	+	15.2144i	0.0273150	+	0.573413i
$705$	2.58857	+	10.6702i	0.0974911	+	0.401864i
$706$	−6.38251	−	44.3913i	−0.240209	−	1.67069i
$707$	−5.02304	+	8.77136i	−0.188911	+	0.329881i
$708$	−1.80204	−	1.15810i	−0.0677246	−	0.0435240i
$709$	22.2327	+	4.28499i	0.834965	+	0.160926i	0.588777	−	0.808296i	$-0.299610\pi$
$709$	22.2327	+	4.28499i	0.834965	+	0.160926i	0.246188	+	0.969222i	$0.420822\pi$
$710$	6.81300	−	28.0836i	0.255687	−	1.05396i
$711$	−1.73678	−	0.165842i	−0.0651343	−	0.00621958i
$712$	−3.30382	−	5.72238i	−0.123816	−	0.214455i
$713$	−11.0816	−	2.15572i	−0.415008	−	0.0807325i
$714$	−8.80894	−	25.1647i	−0.329666	−	0.941764i
$715$	25.8011	+	56.4966i	0.964908	+	2.11285i
$716$	−5.35200	−	5.10312i	−0.200014	−	0.190713i
$717$	−4.28512	−	12.3810i	−0.160031	−	0.462379i
$718$	−15.5931	+	8.03883i	−0.581931	+	0.300006i
$719$	−9.44651	+	27.2939i	−0.352295	+	1.01789i	0.620094	+	0.784527i	$0.287094\pi$
$719$	−9.44651	+	27.2939i	−0.352295	+	1.01789i	−0.972390	+	0.233363i	$0.925027\pi$
$720$	−1.86993	−	13.0057i	−0.0696883	−	0.484692i
$721$	20.3101	+	10.3802i	0.756386	+	0.386579i
$722$	−1.98983	+	1.27879i	−0.0740538	+	0.0475915i
$723$	−10.7779	+	4.31483i	−0.400835	+	0.160470i
$724$	−15.8278	−	22.2271i	−0.588236	−	0.826062i
$725$	5.74602	+	8.06916i	0.213402	+	0.299681i
$726$	−3.05199	+	1.22183i	−0.113270	+	0.0453464i
$727$	12.4087	−	7.97460i	0.460214	−	0.295761i	−0.289916	−	0.957052i	$-0.593627\pi$
$727$	12.4087	−	7.97460i	0.460214	−	0.295761i	0.750130	+	0.661291i	$0.229991\pi$
$728$	11.1776	−	7.23913i	0.414268	−	0.268300i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−11.4728	+	33.1485i	−0.424627	+	1.22688i
$731$	55.3398	−	28.5296i	2.04681	−	1.05521i
$732$	−1.03482	−	2.98990i	−0.0382479	−	0.110510i
$733$	−25.6765	−	24.4825i	−0.948382	−	0.904280i	0.0471328	−	0.998889i	$-0.484992\pi$
$733$	−25.6765	−	24.4825i	−0.948382	−	0.904280i	−0.995515	+	0.0946084i	$0.969840\pi$
$734$	−3.19451	−	6.99500i	−0.117912	−	0.258190i
$735$	2.93675	+	19.4519i	0.108324	+	0.717494i
$736$	−27.2086	+	21.3209i	−1.00292	+	0.785898i
$737$	5.44351	+	9.42844i	0.200514	+	0.347301i
$738$	−10.2788	−	0.981504i	−0.378367	−	0.0361297i
$739$	−0.0116869	+	0.0481741i	−0.000429910	+	0.00177211i	−0.972026	−	0.234873i	$-0.924533\pi$
$739$	−0.0116869	+	0.0481741i	−0.000429910	+	0.00177211i	0.971596	+	0.236645i	$0.0760478\pi$
$740$	−49.9772	−	9.63232i	−1.83720	−	0.354091i
$741$	23.4409	+	15.0645i	0.861123	+	0.553410i
$742$	−60.4991	+	0.213068i	−2.22099	+	0.00782197i
$743$	2.37864	+	16.5438i	0.0872639	+	0.606934i	0.985786	+	0.168006i	$0.0537327\pi$
$743$	2.37864	+	16.5438i	0.0872639	+	0.606934i	−0.898522	+	0.438928i	$0.855358\pi$
$744$	−0.451143	−	1.85964i	−0.0165397	−	0.0681776i
$745$	−1.59758	−	33.5374i	−0.0585309	−	1.22872i
$746$	49.6219	+	39.0231i	1.81679	+	1.42874i
$747$	−14.0847	+	1.34492i	−0.515331	+	0.0492081i
$748$	12.4142	−	27.1834i	0.453909	−	0.993922i
$749$	−7.55739	+	22.0870i	−0.276141	+	0.807042i
$750$	−9.38947	+	6.03425i	−0.342855	+	0.220340i
$751$	7.48179	+	30.8404i	0.273014	+	1.12538i	0.928844	+	0.370472i	$0.120804\pi$
$751$	7.48179	+	30.8404i	0.273014	+	1.12538i	−0.655829	+	0.754909i	$0.727681\pi$
$752$	16.9579	+	6.78891i	0.618390	+	0.247566i
$753$	−11.6463	+	2.24465i	−0.424416	+	0.0817995i
$754$	−1.90273	+	39.9432i	−0.0692933	+	1.45464i
$755$	12.0069	−	13.8567i	0.436974	−	0.504295i
$756$	2.42097	+	3.37456i	0.0880498	+	0.122731i
$757$	−4.34533	−	9.51494i	−0.157934	−	0.345826i	0.814079	−	0.580754i	$-0.197242\pi$
$757$	−4.34533	−	9.51494i	−0.157934	−	0.345826i	−0.972013	+	0.234927i	$0.924515\pi$
$758$	−11.5641	−	20.0296i	−0.420028	−	0.727509i
$759$	−14.3844	−	9.27953i	−0.522119	−	0.336826i
$760$	5.14048	−	8.90358i	0.186465	−	0.322967i
$761$	28.4383	−	39.9360i	1.03089	−	1.44768i	0.141827	−	0.989891i	$-0.454702\pi$
$761$	28.4383	−	39.9360i	1.03089	−	1.44768i	0.889061	−	0.457789i	$-0.151358\pi$
$762$	27.6894	−	8.13035i	1.00308	−	0.294532i
$763$	37.0127	+	14.6666i	1.33995	+	0.530967i
$764$	7.81594	+	5.02300i	0.282771	+	0.181726i
$765$	−4.90252	+	14.1649i	−0.177251	+	0.512133i
$766$	6.27859	+	2.51357i	0.226855	+	0.0908189i
$767$	−6.11505	+	5.83069i	−0.220802	+	0.210534i
$768$	−18.2546	−	9.41088i	−0.658705	−	0.339586i
$769$	1.76708	−	12.2903i	0.0637227	−	0.443201i	−0.932835	−	0.360303i	$-0.882673\pi$
$769$	1.76708	−	12.2903i	0.0637227	−	0.443201i	0.996558	−	0.0828979i	$-0.0264175\pi$
$770$	−28.9417	+	40.9474i	−1.04299	+	1.47564i
$771$	−0.730101	+	1.59870i	−0.0262940	+	0.0575757i
$772$	34.5447	−	13.8296i	1.24329	−	0.497738i
$773$	−0.137186	−	2.87989i

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09595 + 1.53904i) q^{2} +(0.235759 - 0.971812i) q^{3} +(-0.513414 - 1.48341i) q^{4} +(-0.133721 + 2.80715i) q^{5} +(1.23728 + 1.42790i) q^{6} +(2.23077 + 1.42255i) q^{7} +(-0.779983 - 0.229024i) q^{8} +(-0.888835 - 0.458227i) q^{9} +O(q^{10})\)	\(q+(-1.09595 + 1.53904i) q^{2} +(0.235759 - 0.971812i) q^{3} +(-0.513414 - 1.48341i) q^{4} +(-0.133721 + 2.80715i) q^{5} +(1.23728 + 1.42790i) q^{6} +(2.23077 + 1.42255i) q^{7} +(-0.779983 - 0.229024i) q^{8} +(-0.888835 - 0.458227i) q^{9} +(-4.17377 - 3.28229i) q^{10} +(-2.07040 - 2.90747i) q^{11} +(-1.56264 + 0.149214i) q^{12} +(-0.881180 + 6.12874i) q^{13} +(-4.63417 + 1.87421i) q^{14} +(2.69650 + 0.791763i) q^{15} +(3.67510 - 2.89013i) q^{16} +(-5.23725 + 1.00940i) q^{17} +(1.67935 - 0.865763i) q^{18} +(4.41889 + 0.851671i) q^{19} +(4.23281 - 1.24287i) q^{20} +(1.90838 - 1.83251i) q^{21} +6.74377 q^{22} +(2.77508 + 3.91138i) q^{23} +(-0.406456 + 0.704002i) q^{24} +(-2.88485 - 0.275470i) q^{25} +(-8.46666 - 8.07294i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(0.964924 - 4.03951i) q^{28} +(-2.23847 - 2.58333i) q^{29} +(-4.17377 + 3.28229i) q^{30} +(-1.70366 + 1.62443i) q^{31} +(0.342959 + 7.19959i) q^{32} +(-3.31363 + 1.32658i) q^{33} +(4.18624 - 9.16659i) q^{34} +(-4.29162 + 6.07189i) q^{35} +(-0.223398 + 1.55377i) q^{36} +(-10.2548 - 5.28670i) q^{37} +(-6.15362 + 5.86746i) q^{38} +(5.74823 + 2.30125i) q^{39} +(0.747204 - 2.15890i) q^{40} +(-4.59749 - 2.95463i) q^{41} +(0.728828 + 4.94541i) q^{42} +(-11.2004 + 3.28874i) q^{43} +(-3.25001 + 4.56400i) q^{44} +(1.40517 - 2.43382i) q^{45} +(-9.06112 - 0.0157046i) q^{46} +(1.95345 + 3.38348i) q^{47} +(-1.94223 - 4.25288i) q^{48} +(2.95268 + 6.34678i) q^{49} +(3.58560 - 4.13801i) q^{50} +(-0.253785 + 5.32760i) q^{51} +(9.54385 - 1.83943i) q^{52} +(11.2358 + 4.49814i) q^{53} +(-0.445438 - 1.83612i) q^{54} +(8.43858 - 5.42314i) q^{55} +(-1.41416 - 1.62047i) q^{56} +(1.86946 - 4.09354i) q^{57} +(6.42909 - 0.613904i) q^{58} +(1.07265 + 0.843543i) q^{59} +(-0.209908 - 4.40651i) q^{60} +(0.475186 + 1.95874i) q^{61} +(-0.632954 - 4.40229i) q^{62} +(-1.33094 - 2.28661i) q^{63} +(-3.58995 - 2.30712i) q^{64} +(-17.0865 - 3.29315i) q^{65} +(1.58991 - 6.55368i) q^{66} +(-3.03636 - 0.289937i) q^{67} +(4.18623 + 7.25076i) q^{68} +(4.45538 - 1.77471i) q^{69} +(-4.64149 - 13.2594i) q^{70} +(2.26087 + 4.95062i) q^{71} +(0.588332 + 0.560973i) q^{72} +(-2.16069 - 6.24291i) q^{73} +(19.3751 - 9.98858i) q^{74} +(-0.947835 + 2.73859i) q^{75} +(-1.00534 - 6.99229i) q^{76} +(-0.482558 - 9.43117i) q^{77} +(-9.84147 + 6.32473i) q^{78} +(1.61971 - 0.648432i) q^{79} +(7.62160 + 10.7030i) q^{80} +(0.580057 + 0.814576i) q^{81} +(9.58589 - 3.83761i) q^{82} +(11.9027 - 7.64938i) q^{83} +(-3.69815 - 1.89007i) q^{84} +(-2.13320 - 14.8367i) q^{85} +(7.21355 - 20.8422i) q^{86} +(-3.03825 + 1.56633i) q^{87} +(0.948999 + 2.74195i) q^{88} +(5.88277 + 5.60921i) q^{89} +(2.20576 + 4.82995i) q^{90} +(-10.6842 + 12.4183i) q^{91} +(4.37743 - 6.12474i) q^{92} +(1.17699 + 2.03861i) q^{93} +(-7.34820 - 0.701668i) q^{94} +(-2.98167 + 12.2906i) q^{95} +(7.07750 + 1.36408i) q^{96} +(10.5374 + 6.77197i) q^{97} +(-13.0039 - 2.41143i) q^{98} +(0.507966 + 3.53298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320q + 2q^{2} + 16q^{3} + 18q^{4} - 2q^{5} + 18q^{6} + 2q^{7} - 12q^{8} + 16q^{9} + O(q^{10}) \)	\( 320q + 2q^{2} + 16q^{3} + 18q^{4} - 2q^{5} + 18q^{6} + 2q^{7} - 12q^{8} + 16q^{9} + 2q^{11} + 18q^{12} + 18q^{14} - 18q^{15} - 8q^{16} + 4q^{17} + 2q^{18} + 8q^{19} - 162q^{20} - 4q^{21} + 144q^{22} - 26q^{23} + 6q^{24} - 8q^{25} - 14q^{26} - 32q^{27} + 86q^{28} - 74q^{29} - 56q^{31} - 28q^{32} + 13q^{33} + 40q^{34} - 32q^{35} - 14q^{36} + 2q^{37} - 39q^{38} - 52q^{40} + 60q^{41} - 61q^{42} + 16q^{43} - 75q^{44} - 2q^{45} - 4q^{46} - 40q^{47} - 28q^{48} - 100q^{49} + 146q^{50} - 18q^{51} - 18q^{52} + 34q^{53} + 2q^{54} + 36q^{55} - 102q^{56} + 28q^{57} - 17q^{58} - 102q^{59} - 18q^{60} - 18q^{61} - 88q^{62} + 2q^{63} - 252q^{64} - 78q^{65} + 16q^{66} + 12q^{67} + 34q^{68} + 8q^{69} + 264q^{70} + 160q^{71} + 6q^{72} - 8q^{73} + 70q^{74} + 14q^{75} - 40q^{76} - 90q^{77} - 16q^{78} + 26q^{79} - 103q^{80} + 16q^{81} - 30q^{82} - 80q^{83} - 52q^{84} - 128q^{85} + 90q^{86} + 4q^{87} - 293q^{88} - 36q^{89} + 16q^{91} - 174q^{92} + 32q^{93} + 57q^{94} - 85q^{95} - 50q^{96} - 8q^{97} - 193q^{98} - 26q^{99} + O(q^{100}) \)

Introduction

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