LMFDB - Embedded newform 1050.3.q.e.649.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.4
Character	$\chi$	$=$	1050.649
Dual form			1050.3.q.e.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.72455 + 1.94434i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.72455 + 1.94434i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.263223 + 0.455915i) q^{11} +(-1.73205 + 3.00000i) q^{12} +4.22307 q^{13} +(9.61071 + 2.37366i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-16.6753 - 28.8825i) q^{17} +(3.67423 - 2.12132i) q^{18} +(-2.75133 - 1.58848i) q^{19} +(-8.74014 - 8.40298i) q^{21} -0.744507i q^{22} +(9.57744 + 5.52954i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-5.17218 - 2.98616i) q^{26} -5.19615 q^{27} +(-10.0922 - 9.70292i) q^{28} +56.1302 q^{29} +(-1.63817 + 0.945800i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-0.455915 + 0.789668i) q^{33} +47.1649i q^{34} -6.00000 q^{36} +(8.44690 + 4.87682i) q^{37} +(2.24645 + 3.89097i) q^{38} +(3.65729 + 6.33460i) q^{39} -4.07377i q^{41} +(4.76263 + 16.4717i) q^{42} -46.3519i q^{43} +(-0.526446 + 0.911831i) q^{44} +(-7.81995 - 13.5445i) q^{46} +(-31.6370 + 54.7969i) q^{47} -6.92820 q^{48} +(41.4391 - 26.1496i) q^{49} +(28.8825 - 50.0259i) q^{51} +(4.22307 + 7.31457i) q^{52} +(40.2885 - 23.2606i) q^{53} +(6.36396 + 3.67423i) q^{54} +(5.49942 + 19.0199i) q^{56} -5.50267i q^{57} +(-68.7452 - 39.6900i) q^{58} +(43.7614 - 25.2657i) q^{59} +(89.4583 + 51.6488i) q^{61} +2.67513 q^{62} +(5.03529 - 20.3874i) q^{63} -8.00000 q^{64} +(1.11676 - 0.644762i) q^{66} +(7.56816 - 4.36948i) q^{67} +(33.3506 - 57.7649i) q^{68} +19.1549i q^{69} +29.0608 q^{71} +(7.34847 + 4.24264i) q^{72} +(-8.36647 - 14.4912i) q^{73} +(-6.89686 - 11.9457i) q^{74} -6.35393i q^{76} +(-2.65651 - 2.55403i) q^{77} -10.3444i q^{78} +(-66.1473 + 114.571i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-2.88059 + 4.98933i) q^{82} -12.4838 q^{83} +(5.81425 - 23.5413i) q^{84} +(-32.7757 + 56.7692i) q^{86} +(48.6102 + 84.1953i) q^{87} +(1.28952 - 0.744507i) q^{88} +(59.1101 + 34.1272i) q^{89} +(-28.3982 + 8.21107i) q^{91} +22.1182i q^{92} +(-2.83740 - 1.63817i) q^{93} +(77.4945 - 44.7415i) q^{94} +(8.48528 + 4.89898i) q^{96} -149.281 q^{97} +(-69.2429 + 2.72468i) q^{98} -1.57934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 48 * q^9	$ 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	−6.72455	+	1.94434i	−0.960650	+	0.277762i
$7$	−6.72455	+	1.94434i	−0.960650	+	0.277762i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	0.263223	+	0.455915i	0.0239293	+	0.0414468i	0.877742	−	0.479133i	$-0.159049\pi$
$11$	0.263223	+	0.455915i	0.0239293	+	0.0414468i	−0.853813	+	0.520580i	$0.825716\pi$
$12$	−1.73205	+	3.00000i	−0.144338	+	0.250000i
$13$	4.22307			0.324851			0.162426	−	0.986721i	$-0.448068\pi$
$13$	4.22307			0.324851			0.162426	+	0.986721i	$0.448068\pi$
$14$	9.61071	+	2.37366i	0.686479	+	0.169547i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−16.6753	−	28.8825i	−0.980900	−	1.69897i	−0.658903	−	0.752228i	$-0.728979\pi$
$17$	−16.6753	−	28.8825i	−0.980900	−	1.69897i	−0.321997	−	0.946741i	$-0.604354\pi$
$18$	3.67423	−	2.12132i	0.204124	−	0.117851i
$19$	−2.75133	−	1.58848i	−0.144807	−	0.0836044i	0.425846	−	0.904796i	$-0.359977\pi$
$19$	−2.75133	−	1.58848i	−0.144807	−	0.0836044i	−0.570653	+	0.821191i	$0.693310\pi$
$20$		0			0
$21$	−8.74014	−	8.40298i	−0.416197	−	0.400142i
$22$		−	0.744507i		−	0.0338412i
$23$	9.57744	+	5.52954i	0.416410	+	0.240415i	0.693540	−	0.720418i	$-0.256050\pi$
$23$	9.57744	+	5.52954i	0.416410	+	0.240415i	−0.277130	+	0.960832i	$0.589383\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	−5.17218	−	2.98616i	−0.198930	−	0.114852i
$27$	−5.19615			−0.192450
$28$	−10.0922	−	9.70292i	−0.360437	−	0.346533i
$29$	56.1302			1.93552			0.967762	−	0.251866i	$-0.0810442\pi$
$29$	56.1302			1.93552			0.967762	+	0.251866i	$0.0810442\pi$
$30$		0			0
$31$	−1.63817	+	0.945800i	−0.0528443	+	0.0305097i	−0.526189	−	0.850367i	$-0.676380\pi$
$31$	−1.63817	+	0.945800i	−0.0528443	+	0.0305097i	0.473345	+	0.880877i	$0.343046\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	−0.455915	+	0.789668i	−0.0138156	+	0.0239293i
$34$			47.1649i			1.38720i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	8.44690	+	4.87682i	0.228294	+	0.131806i	0.609785	−	0.792567i	$-0.291256\pi$
$37$	8.44690	+	4.87682i	0.228294	+	0.131806i	−0.381491	+	0.924373i	$0.624589\pi$
$38$	2.24645	+	3.89097i	0.0591172	+	0.102394i
$39$	3.65729	+	6.33460i	0.0937765	+	0.162426i
$40$		0			0
$41$		−	4.07377i		−	0.0993603i	−0.998765	−	0.0496802i	$-0.984180\pi$
$41$		−	4.07377i		−	0.0993603i	0.998765	−	0.0496802i	$-0.0158202\pi$
$42$	4.76263	+	16.4717i	0.113396	+	0.392184i
$43$		−	46.3519i		−	1.07795i	−0.842322	−	0.538975i	$-0.818812\pi$
$43$		−	46.3519i		−	1.07795i	0.842322	−	0.538975i	$-0.181188\pi$
$44$	−0.526446	+	0.911831i	−0.0119647	+	0.0207234i
$45$		0			0
$46$	−7.81995	−	13.5445i	−0.169999	−	0.294447i
$47$	−31.6370	+	54.7969i	−0.673127	+	1.16589i	0.303885	+	0.952709i	$0.401716\pi$
$47$	−31.6370	+	54.7969i	−0.673127	+	1.16589i	−0.977012	+	0.213182i	$0.931617\pi$
$48$	−6.92820			−0.144338
$49$	41.4391	−	26.1496i	0.845696	−	0.533665i
$50$		0			0
$51$	28.8825	−	50.0259i	0.566323	−	0.980900i
$52$	4.22307	+	7.31457i	0.0812129	+	0.140665i
$53$	40.2885	−	23.2606i	0.760160	−	0.438878i	−0.0691934	−	0.997603i	$-0.522043\pi$
$53$	40.2885	−	23.2606i	0.760160	−	0.438878i	0.829353	+	0.558725i	$0.188709\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	5.49942	+	19.0199i	0.0982038	+	0.339641i
$57$		−	5.50267i		−	0.0965380i
$58$	−68.7452	−	39.6900i	−1.18526	−	0.684311i
$59$	43.7614	−	25.2657i	0.741719	−	0.428231i	−0.0809752	−	0.996716i	$-0.525803\pi$
$59$	43.7614	−	25.2657i	0.741719	−	0.428231i	0.822694	+	0.568485i	$0.192470\pi$
$60$		0			0
$61$	89.4583	+	51.6488i	1.46653	+	0.846702i	0.999299	−	0.0374335i	$-0.0119182\pi$
$61$	89.4583	+	51.6488i	1.46653	+	0.846702i	0.467231	+	0.884135i	$0.345252\pi$
$62$	2.67513			0.0431472
$63$	5.03529	−	20.3874i	0.0799252	−	0.323609i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	1.11676	−	0.644762i	0.0169206	−	0.00976912i
$67$	7.56816	−	4.36948i	0.112958	−	0.0652161i	−0.442457	−	0.896790i	$-0.645893\pi$
$67$	7.56816	−	4.36948i	0.112958	−	0.0652161i	0.555414	+	0.831574i	$0.312560\pi$
$68$	33.3506	−	57.7649i	0.490450	−	0.849484i
$69$			19.1549i			0.277607i
$70$		0			0
$71$	29.0608			0.409307			0.204653	−	0.978835i	$-0.434393\pi$
$71$	29.0608			0.409307			0.204653	+	0.978835i	$0.434393\pi$
$72$	7.34847	+	4.24264i	0.102062	+	0.0589256i
$73$	−8.36647	−	14.4912i	−0.114609	−	0.198509i	0.803014	−	0.595960i	$-0.203228\pi$
$73$	−8.36647	−	14.4912i	−0.114609	−	0.198509i	−0.917623	+	0.397451i	$0.869895\pi$
$74$	−6.89686	−	11.9457i	−0.0932008	−	0.161429i
$75$		0			0
$76$		−	6.35393i		−	0.0836044i
$77$	−2.65651	−	2.55403i	−0.0345001	−	0.0331692i
$78$		−	10.3444i		−	0.132620i
$79$	−66.1473	+	114.571i	−0.837308	+	1.45026i	0.0548297	+	0.998496i	$0.482538\pi$
$79$	−66.1473	+	114.571i	−0.837308	+	1.45026i	−0.892137	+	0.451764i	$0.850795\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−2.88059	+	4.98933i	−0.0351292	+	0.0608455i
$83$	−12.4838			−0.150407			−0.0752033	−	0.997168i	$-0.523961\pi$
$83$	−12.4838			−0.150407			−0.0752033	+	0.997168i	$0.523961\pi$
$84$	5.81425	−	23.5413i	0.0692173	−	0.280254i
$85$		0			0
$86$	−32.7757	+	56.7692i	−0.381113	+	0.660107i
$87$	48.6102	+	84.1953i	0.558738	+	0.967762i
$88$	1.28952	−	0.744507i	0.0146537	−	0.00846030i
$89$	59.1101	+	34.1272i	0.664158	+	0.383452i	0.793860	−	0.608101i	$-0.208069\pi$
$89$	59.1101	+	34.1272i	0.664158	+	0.383452i	−0.129701	+	0.991553i	$0.541402\pi$
$90$		0			0
$91$	−28.3982	+	8.21107i	−0.312068	+	0.0902315i
$92$			22.1182i			0.240415i
$93$	−2.83740	−	1.63817i	−0.0305097	−	0.0176148i
$94$	77.4945	−	44.7415i	0.824409	−	0.475973i
$95$		0			0
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$	−149.281			−1.53898			−0.769490	−	0.638659i	$-0.779490\pi$
$97$	−149.281			−1.53898			−0.769490	+	0.638659i	$0.779490\pi$
$98$	−69.2429	+	2.72468i	−0.706560	+	0.0278029i
$99$	−1.57934			−0.0159529
$100$		0			0
$101$	83.7839	−	48.3726i	0.829543	−	0.478937i	−0.0241531	−	0.999708i	$-0.507689\pi$
$101$	83.7839	−	48.3726i	0.829543	−	0.478937i	0.853696	+	0.520771i	$0.174356\pi$
$102$	−70.7473	+	40.8460i	−0.693601	+	0.400451i
$103$	52.3811	−	90.7268i	0.508555	−	0.880843i	−0.491396	−	0.870936i	$-0.663513\pi$
$103$	52.3811	−	90.7268i	0.508555	−	0.880843i	0.999951	−	0.00990642i	$-0.00315336\pi$
$104$		−	11.9446i		−	0.114852i
$105$		0			0
$106$	−65.7908			−0.620668
$107$	107.911	+	62.3022i	1.00851	+	0.582263i	0.910755	−	0.412947i	$-0.135501\pi$
$107$	107.911	+	62.3022i	1.00851	+	0.582263i	0.0977548	+	0.995211i	$0.468834\pi$
$108$	−5.19615	−	9.00000i	−0.0481125	−	0.0833333i
$109$	42.3042	+	73.2731i	0.388112	+	0.672230i	0.992196	−	0.124691i	$-0.0397940\pi$
$109$	42.3042	+	73.2731i	0.388112	+	0.672230i	−0.604083	+	0.796921i	$0.706461\pi$
$110$		0			0
$111$			16.8938i			0.152196i
$112$	6.71372	−	27.1832i	0.0599439	−	0.242707i
$113$			116.241i			1.02868i	0.857586	+	0.514340i	$0.171963\pi$
$113$			116.241i			1.02868i	−0.857586	+	0.514340i	$0.828037\pi$
$114$	−3.89097	+	6.73936i	−0.0341313	+	0.0591172i
$115$		0			0
$116$	56.1302	+	97.2204i	0.483881	+	0.838107i
$117$	−6.33460	+	10.9719i	−0.0541419	+	0.0937765i
$118$	−71.4621			−0.605611
$119$	168.291	+	161.799i	1.41421	+	1.35966i
$120$		0			0
$121$	60.3614	−	104.549i	0.498855	−	0.864042i
$122$	−73.0424	−	126.513i	−0.598708	−	1.03699i
$123$	6.11066	−	3.52799i	0.0496802	−	0.0286829i
$124$	−3.27635	−	1.89160i	−0.0264222	−	0.0152548i
$125$		0			0
$126$	−20.5830	+	21.4089i	−0.163357	+	0.169912i
$127$		−	81.3744i		−	0.640743i	−0.947292	−	0.320372i	$-0.896192\pi$
$127$		−	81.3744i		−	0.640743i	0.947292	−	0.320372i	$-0.103808\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	69.5278	−	40.1419i	0.538975	−	0.311178i
$130$		0			0
$131$	208.389	+	120.313i	1.59075	+	0.918421i	0.993178	+	0.116608i	$0.0372020\pi$
$131$	208.389	+	120.313i	1.59075	+	0.918421i	0.597574	+	0.801814i	$0.296131\pi$
$132$	−1.82366			−0.0138156
$133$	21.5900	+	5.33231i	0.162331	+	0.0400926i
$134$	−12.3588			−0.0922295
$135$		0			0
$136$	−81.6919	+	47.1649i	−0.600676	+	0.346800i
$137$	202.357	−	116.831i	1.47706	−	0.852778i	0.477391	−	0.878691i	$-0.341582\pi$
$137$	202.357	−	116.831i	1.47706	−	0.852778i	0.999664	+	0.0259125i	$0.00824914\pi$
$138$	13.5445	−	23.4598i	0.0981489	−	0.169999i
$139$		−	211.491i		−	1.52152i	−0.649033	−	0.760760i	$-0.724826\pi$
$139$		−	211.491i		−	1.52152i	0.649033	−	0.760760i	$-0.275174\pi$
$140$		0			0
$141$	−109.594			−0.777261
$142$	−35.5920	−	20.5491i	−0.250648	−	0.144712i
$143$	1.11161	+	1.92536i	0.00777348	+	0.0134641i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$		0			0
$146$			23.6640i			0.162082i
$147$	75.1117	+	39.5125i	0.510964	+	0.268792i
$148$			19.5073i			0.131806i
$149$	72.0402	−	124.777i	0.483491	−	0.837431i	−0.516329	−	0.856390i	$-0.672702\pi$
$149$	72.0402	−	124.777i	0.483491	−	0.837431i	0.999820	+	0.0189590i	$0.00603520\pi$
$150$		0			0
$151$	−46.7563	−	80.9842i	−0.309644	−	0.536319i	0.668640	−	0.743586i	$-0.266877\pi$
$151$	−46.7563	−	80.9842i	−0.309644	−	0.536319i	−0.978285	+	0.207267i	$0.933543\pi$
$152$	−4.49291	+	7.78195i	−0.0295586	+	0.0511970i
$153$	100.052			0.653933
$154$	1.44757	+	5.00647i	0.00939982	+	0.0325095i
$155$		0			0
$156$	−7.31457	+	12.6692i	−0.0468883	+	0.0812129i
$157$	−85.6127	−	148.286i	−0.545304	−	0.944494i	−0.998588	−	0.0531280i	$-0.983081\pi$
$157$	−85.6127	−	148.286i	−0.545304	−	0.944494i	0.453284	−	0.891366i	$-0.350252\pi$
$158$	162.027	−	93.5464i	1.02549	−	0.592066i
$159$	69.7817	+	40.2885i	0.438878	+	0.253387i
$160$		0			0
$161$	−75.1553	−	18.5619i	−0.466803	−	0.115291i
$162$			12.7279i			0.0785674i
$163$	80.5515	+	46.5064i	0.494181	+	0.285316i	0.726307	−	0.687370i	$-0.241235\pi$
$163$	80.5515	+	46.5064i	0.494181	+	0.285316i	−0.232126	+	0.972686i	$0.574568\pi$
$164$	7.05598	−	4.07377i	0.0430243	−	0.0248401i
$165$		0			0
$166$	15.2894	+	8.82735i	0.0921049	+	0.0531768i
$167$	104.991			0.628688			0.314344	−	0.949309i	$-0.398216\pi$
$167$	104.991			0.628688			0.314344	+	0.949309i	$0.398216\pi$
$168$	−23.7672	+	24.7208i	−0.141471	+	0.147148i
$169$	−151.166			−0.894472
$170$		0			0
$171$	8.25400	−	4.76545i	0.0482690	−	0.0278681i
$172$	80.2838	−	46.3519i	0.466766	−	0.269488i
$173$	102.079	−	176.805i	0.590049	−	1.02200i	−0.404176	−	0.914681i	$-0.632442\pi$
$173$	102.079	−	176.805i	0.590049	−	1.02200i	0.994225	−	0.107314i	$-0.0342251\pi$
$174$		−	137.490i		−	0.790174i
$175$		0			0
$176$	−2.10578			−0.0119647
$177$	75.7970	+	43.7614i	0.428231	+	0.247240i
$178$	−48.2632	−	83.5943i	−0.271141	−	0.469631i
$179$	−97.9495	−	169.653i	−0.547204	−	0.947785i	−0.998465	−	0.0553926i	$-0.982359\pi$
$179$	−97.9495	−	169.653i	−0.547204	−	0.947785i	0.451261	−	0.892392i	$-0.350974\pi$
$180$		0			0
$181$		−	119.031i		−	0.657632i	−0.944394	−	0.328816i	$-0.893350\pi$
$181$		−	119.031i		−	0.657632i	0.944394	−	0.328816i	$-0.106650\pi$
$182$	40.5867	+	10.0241i	0.223004	+	0.0550776i
$183$			178.917i			0.977687i
$184$	15.6399	−	27.0891i	0.0849994	−	0.147223i
$185$		0			0
$186$	2.31673	+	4.01269i	0.0124555	+	0.0215736i
$187$	8.77864	−	15.2050i	0.0469446	−	0.0813104i
$188$	−126.548			−0.673127
$189$	34.9418	−	10.1031i	0.184877	−	0.0534554i
$190$		0			0
$191$	32.8657	−	56.9250i	0.172072	−	0.298037i	−0.767072	−	0.641561i	$-0.778287\pi$
$191$	32.8657	−	56.9250i	0.172072	−	0.298037i	0.939144	+	0.343524i	$0.111621\pi$
$192$	−6.92820	−	12.0000i	−0.0360844	−	0.0625000i
$193$	83.8919	−	48.4350i	0.434673	−	0.250959i	−0.266662	−	0.963790i	$-0.585921\pi$
$193$	83.8919	−	48.4350i	0.434673	−	0.250959i	0.701335	+	0.712831i	$0.252588\pi$
$194$	182.831	+	105.558i	0.942429	+	0.544112i
$195$		0			0
$196$	86.7315	+	45.6251i	0.442508	+	0.232781i
$197$			186.672i			0.947574i	0.880640	+	0.473787i	$0.157113\pi$
$197$			186.672i			0.947574i	−0.880640	+	0.473787i	$0.842887\pi$
$198$	1.93428	+	1.11676i	0.00976912	+	0.00564020i
$199$	−99.8454	+	57.6458i	−0.501736	+	0.289677i	−0.729430	−	0.684055i	$-0.760215\pi$
$199$	−99.8454	+	57.6458i	−0.501736	+	0.289677i	0.227694	+	0.973733i	$0.426881\pi$
$200$		0			0
$201$	13.1084	+	7.56816i	0.0652161	+	0.0376525i
$202$	−136.818			−0.677319
$203$	−377.450	+	109.136i	−1.85936	+	0.537616i
$204$	115.530			0.566323
$205$		0			0
$206$	−128.307	+	74.0781i	−0.622850	+	0.359602i
$207$	−28.7323	+	16.5886i	−0.138803	+	0.0801382i
$208$	−8.44614	+	14.6291i	−0.0406064	+	0.0703324i
$209$		−	1.67250i		−	0.00800239i
$210$		0			0
$211$	139.433			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$211$	139.433			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$212$	80.5769	+	46.5211i	0.380080	+	0.219439i
$213$	25.1674	+	43.5912i	0.118157	+	0.204653i
$214$	−88.1086	−	152.609i	−0.411722	−	0.713124i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	9.17703	−	9.54524i	0.0422905	−	0.0439873i
$218$		−	119.654i		−	0.548874i
$219$	14.4912	−	25.0994i	0.0661697	−	0.114609i
$220$		0			0
$221$	−70.4209	−	121.973i	−0.318647	−	0.551912i
$222$	11.9457	−	20.6906i	0.0538095	−	0.0932008i
$223$	258.055			1.15720			0.578599	−	0.815612i	$-0.303600\pi$
$223$	258.055			1.15720			0.578599	+	0.815612i	$0.303600\pi$
$224$	−27.4440	+	28.5452i	−0.122518	+	0.127434i
$225$		0			0
$226$	82.1947	−	142.365i	0.363693	−	0.629935i
$227$	165.516	+	286.682i	0.729146	+	1.26292i	0.957245	+	0.289280i	$0.0934158\pi$
$227$	165.516	+	286.682i	0.729146	+	1.26292i	−0.228099	+	0.973638i	$0.573251\pi$
$228$	9.53090	−	5.50267i	0.0418022	−	0.0241345i
$229$	−211.516	−	122.119i	−0.923653	−	0.533271i	−0.0388541	−	0.999245i	$-0.512371\pi$
$229$	−211.516	−	122.119i	−0.923653	−	0.533271i	−0.884799	+	0.465974i	$0.845704\pi$
$230$		0			0
$231$	1.53044	−	6.19662i	0.00662529	−	0.0268252i
$232$		−	158.760i		−	0.684311i
$233$	183.155	+	105.745i	0.786074	+	0.453840i	0.838579	−	0.544781i	$-0.183387\pi$
$233$	183.155	+	105.745i	0.786074	+	0.453840i	−0.0525044	+	0.998621i	$0.516720\pi$
$234$	15.5165	−	8.95848i	0.0663100	−	0.0382841i
$235$		0			0
$236$	87.5228	+	50.5313i	0.370859	+	0.214116i
$237$	−229.141			−0.966840
$238$	−91.7044	−	317.162i	−0.385313	−	1.33262i
$239$	−344.134			−1.43989			−0.719946	−	0.694030i	$-0.755833\pi$
$239$	−344.134			−1.43989			−0.719946	+	0.694030i	$0.755833\pi$
$240$		0			0
$241$	−148.392	+	85.6742i	−0.615735	+	0.355495i	−0.775207	−	0.631708i	$-0.782354\pi$
$241$	−148.392	+	85.6742i	−0.615735	+	0.355495i	0.159472	+	0.987203i	$0.449021\pi$
$242$	−147.855	+	85.3639i	−0.610970	+	0.352744i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$			206.595i			0.846702i
$245$		0			0
$246$	−9.97867			−0.0405637
$247$	−11.6191	−	6.70827i	−0.0470408	−	0.0271590i
$248$	2.67513	+	4.63346i	0.0107868	+	0.0186833i
$249$	−10.8112	−	18.7256i	−0.0434187	−	0.0752033i
$250$		0			0
$251$		−	327.538i		−	1.30493i	−0.757818	−	0.652467i	$-0.773734\pi$
$251$		−	327.538i		−	1.30493i	0.757818	−	0.652467i	$-0.226266\pi$
$252$	40.3473	−	11.6660i	0.160108	−	0.0462937i
$253$			5.82200i			0.0230119i
$254$	−57.5404	+	99.6629i	−0.226537	+	0.392374i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	110.179	−	190.836i	0.428713	−	0.742552i	−0.568046	−	0.822997i	$-0.692301\pi$
$257$	110.179	−	190.836i	0.428713	−	0.742552i	0.996759	+	0.0804442i	$0.0256339\pi$
$258$	−113.538			−0.440072
$259$	−66.2837	−	16.3708i	−0.255922	−	0.0632077i
$260$		0			0
$261$	−84.1953	+	145.831i	−0.322587	+	0.558738i
$262$	−170.149	−	294.706i	−0.649422	−	1.12483i
$263$	−115.350	+	66.5976i	−0.438594	+	0.253223i	−0.703001	−	0.711189i	$-0.748157\pi$
$263$	−115.350	+	66.5976i	−0.438594	+	0.253223i	0.264407	+	0.964411i	$0.414824\pi$
$264$	2.23352	+	1.28952i	0.00846030	+	0.00488456i
$265$		0			0
$266$	−22.6718	−	21.7972i	−0.0852322	−	0.0819443i
$267$			118.220i			0.442772i
$268$	15.1363	+	8.73896i	0.0564788	+	0.0326080i
$269$	22.9633	−	13.2578i	0.0853653	−	0.0492857i	−0.456710	−	0.889616i	$-0.650972\pi$
$269$	22.9633	−	13.2578i	0.0853653	−	0.0492857i	0.542075	+	0.840330i	$0.317639\pi$
$270$		0			0
$271$	−92.6776	−	53.5074i	−0.341984	−	0.197444i	0.319165	−	0.947699i	$-0.396598\pi$
$271$	−92.6776	−	53.5074i	−0.341984	−	0.197444i	−0.661149	+	0.750255i	$0.729931\pi$
$272$	133.402			0.490450
$273$	−36.9102	−	35.4864i	−0.135202	−	0.129987i
$274$	−330.447			−1.20601
$275$		0			0
$276$	−33.1772	+	19.1549i	−0.120207	+	0.0694017i
$277$	381.381	−	220.191i	1.37683	−	0.794912i	0.385052	−	0.922895i	$-0.374184\pi$
$277$	381.381	−	220.191i	1.37683	−	0.794912i	0.991776	+	0.127983i	$0.0408503\pi$
$278$	−149.547	+	259.023i	−0.537939	+	0.931737i
$279$		−	5.67480i		−	0.0203398i
$280$		0			0
$281$	322.069			1.14615			0.573076	−	0.819502i	$-0.305750\pi$
$281$	322.069			1.14615			0.573076	+	0.819502i	$0.305750\pi$
$282$	134.224	+	77.4945i	0.475973	+	0.274803i
$283$	34.2665	+	59.3514i	0.121083	+	0.209722i	0.920195	−	0.391460i	$-0.128030\pi$
$283$	34.2665	+	59.3514i	0.121083	+	0.209722i	−0.799112	+	0.601182i	$0.794697\pi$
$284$	29.0608	+	50.3347i	0.102327	+	0.177235i
$285$		0			0
$286$		−	3.14410i		−	0.0109934i
$287$	7.92079	+	27.3943i	0.0275986	+	0.0954505i
$288$			16.9706i			0.0589256i
$289$	−411.631	+	712.966i	−1.42433	+	2.46701i
$290$		0			0
$291$	−129.281	−	223.922i	−0.444265	−	0.769490i
$292$	16.7329	−	28.9823i	0.0573046	−	0.0992545i
$293$	147.510			0.503448			0.251724	−	0.967799i	$-0.419003\pi$
$293$	147.510			0.503448			0.251724	+	0.967799i	$0.419003\pi$
$294$	−64.0531	−	101.505i	−0.217868	−	0.345254i
$295$		0			0
$296$	13.7937	−	23.8914i	0.0466004	−	0.0807143i
$297$	−1.36775	−	2.36901i	−0.00460521	−	0.00797645i
$298$	−176.462	+	101.880i	−0.592153	+	0.341880i
$299$	40.4462	+	23.3516i	0.135272	+	0.0780991i
$300$		0			0
$301$	90.1237	+	311.695i	0.299414	+	1.03553i
$302$			132.247i			0.437903i
$303$	145.118	+	83.7839i	0.478937	+	0.276514i
$304$	11.0053	−	6.35393i	0.0362018	−	0.0209011i
$305$		0			0
$306$	−122.538	−	70.7473i	−0.400451	−	0.231200i
$307$	−376.010			−1.22479			−0.612394	−	0.790553i	$-0.709793\pi$
$307$	−376.010			−1.22479			−0.612394	+	0.790553i	$0.709793\pi$
$308$	1.76720	−	7.15524i	0.00573767	−	0.0232313i
$309$	181.454			0.587228
$310$		0			0
$311$	−337.599	+	194.913i	−1.08553	+	0.626730i	−0.932383	−	0.361473i	$-0.882274\pi$
$311$	−337.599	+	194.913i	−1.08553	+	0.626730i	−0.153146	+	0.988204i	$0.548941\pi$
$312$	17.9170	−	10.3444i	0.0574262	−	0.0331550i
$313$	−71.5282	+	123.890i	−0.228524	+	0.395816i	−0.957371	−	0.288861i	$-0.906723\pi$
$313$	−71.5282	+	123.890i	−0.228524	+	0.395816i	0.728847	+	0.684677i	$0.240057\pi$
$314$			242.149i			0.771176i
$315$		0			0
$316$	−264.589			−0.837308
$317$	−332.938	−	192.222i	−1.05028	−	0.606378i	−0.127551	−	0.991832i	$-0.540712\pi$
$317$	−332.938	−	192.222i	−1.05028	−	0.606378i	−0.922727	+	0.385454i	$0.874045\pi$
$318$	−56.9765	−	98.6862i	−0.179171	−	0.310334i
$319$	14.7747	+	25.5906i	0.0463158	+	0.0802214i
$320$		0			0
$321$			215.821i			0.672340i
$322$	78.9208	+	75.8764i	0.245096	+	0.235641i
$323$			105.954i			0.328030i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$		0			0
$326$	−65.7700	−	113.917i	−0.201749	−	0.349439i
$327$	−73.2731	+	126.913i	−0.224077	+	0.388112i
$328$	−11.5224			−0.0351292
$329$	106.201	−	429.997i	0.322799	−	1.30698i
$330$		0			0
$331$	−96.9539	+	167.929i	−0.292912	+	0.507338i	−0.974497	−	0.224400i	$-0.927958\pi$
$331$	−96.9539	+	167.929i	−0.292912	+	0.507338i	0.681585	+	0.731739i	$0.261291\pi$
$332$	−12.4838	−	21.6225i	−0.0376017	−	0.0651280i
$333$	−25.3407	+	14.6305i	−0.0760982	+	0.0439353i
$334$	−128.587	−	74.2397i	−0.384991	−	0.222275i
$335$		0			0
$336$	46.5890	−	13.4708i	0.138658	−	0.0400916i
$337$			125.477i			0.372337i	0.982518	+	0.186168i	$0.0596070\pi$
$337$			125.477i			0.372337i	−0.982518	+	0.186168i	$0.940393\pi$
$338$	185.139	+	106.890i	0.547750	+	0.316243i
$339$	−174.361	+	100.668i	−0.514340	+	0.296954i
$340$		0			0
$341$	−0.862410	−	0.497912i	−0.00252906	−	0.00146015i
$342$	−13.4787			−0.0394115
$343$	−227.816	+	256.416i	−0.664186	+	0.747568i
$344$	−131.103			−0.381113
$345$		0			0
$346$	−250.040	+	144.361i	−0.722660	+	0.417228i
$347$	−436.128	+	251.798i	−1.25685	+	0.725644i	−0.972461	−	0.233065i	$-0.925125\pi$
$347$	−436.128	+	251.798i	−1.25685	+	0.725644i	−0.284391	+	0.958708i	$0.591791\pi$
$348$	−97.2204	+	168.391i	−0.279369	+	0.483881i
$349$			47.7682i			0.136872i	0.997656	+	0.0684358i	$0.0218008\pi$
$349$			47.7682i			0.136872i	−0.997656	+	0.0684358i	$0.978199\pi$
$350$		0			0
$351$	−21.9437			−0.0625177
$352$	2.57905	+	1.48901i	0.00732684	+	0.00423015i
$353$	−16.4552	−	28.5012i	−0.0466152	−	0.0807399i	0.841776	−	0.539826i	$-0.181510\pi$
$353$	−16.4552	−	28.5012i	−0.0466152	−	0.0807399i	−0.888392	+	0.459087i	$0.848177\pi$
$354$	−61.8880	−	107.193i	−0.174825	−	0.302805i
$355$		0			0
$356$			136.509i			0.383452i
$357$	−96.9543	+	392.559i	−0.271581	+	1.09960i
$358$			277.043i			0.773863i
$359$	133.898	−	231.919i	0.372976	−	0.646013i	−0.617046	−	0.786927i	$-0.711671\pi$
$359$	133.898	−	231.919i	0.372976	−	0.646013i	0.990022	+	0.140914i	$0.0450040\pi$
$360$		0			0
$361$	−175.453	−	303.894i	−0.486021	−	0.841812i
$362$	−84.1679	+	145.783i	−0.232508	+	0.402716i
$363$	209.098			0.576028
$364$	−42.6202	−	40.9761i	−0.117089	−	0.112572i
$365$		0			0
$366$	126.513	−	219.127i	0.345665	−	0.598708i
$367$	−79.3613	−	137.458i	−0.216243	−	0.374545i	0.737413	−	0.675442i	$-0.236047\pi$
$367$	−79.3613	−	137.458i	−0.216243	−	0.374545i	−0.953657	+	0.300897i	$0.902714\pi$
$368$	−38.3098	+	22.1182i	−0.104103	+	0.0601037i
$369$	10.5840	+	6.11066i	0.0286829	+	0.0165601i
$370$		0			0
$371$	−225.695	+	234.751i	−0.608343	+	0.632752i
$372$		−	6.55270i		−	0.0176148i
$373$	358.832	+	207.172i	0.962017	+	0.555421i	0.896793	−	0.442450i	$-0.145891\pi$
$373$	358.832	+	207.172i	0.962017	+	0.555421i	0.0652235	+	0.997871i	$0.479224\pi$
$374$	−21.5032	+	12.4149i	−0.0574951	+	0.0331948i
$375$		0			0
$376$	154.989	+	89.4829i	0.412205	+	0.237986i
$377$	237.042			0.628758
$378$	−49.9387	−	12.3339i	−0.132113	−	0.0326293i
$379$	72.8000			0.192084			0.0960422	−	0.995377i	$-0.469382\pi$
$379$	72.8000			0.192084			0.0960422	+	0.995377i	$0.469382\pi$
$380$		0			0
$381$	122.062	−	70.4723i	0.320372	−	0.184967i
$382$	−80.5042	+	46.4791i	−0.210744	+	0.121673i
$383$	−142.507	+	246.830i	−0.372082	+	0.644464i	−0.989886	−	0.141868i	$-0.954689\pi$
$383$	−142.507	+	246.830i	−0.372082	+	0.644464i	0.617804	+	0.786332i	$0.288023\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−136.995			−0.354909
$387$	120.426	+	69.5278i	0.311178	+	0.179658i
$388$	−149.281	−	258.562i	−0.384745	−	0.666398i
$389$	−48.5692	−	84.1242i	−0.124856	−	0.216258i	0.796820	−	0.604216i	$-0.206514\pi$
$389$	−48.5692	−	84.1242i	−0.124856	−	0.216258i	−0.921677	+	0.387959i	$0.873180\pi$
$390$		0			0
$391$		−	368.827i		−	0.943291i
$392$	−73.9622	−	117.207i	−0.188679	−	0.298999i
$393$			416.777i			1.06050i
$394$	131.997	−	228.626i	0.335018	−	0.580268i
$395$		0			0
$396$	−1.57934	−	2.73549i	−0.00398822	−	0.00690781i
$397$	395.852	−	685.636i	0.997108	−	1.72704i	0.432737	−	0.901520i	$-0.357548\pi$
$397$	395.852	−	685.636i	0.997108	−	1.72704i	0.564371	−	0.825522i	$-0.309119\pi$
$398$	163.047			0.409665
$399$	10.6990	+	37.0030i	0.0268146	+	0.0927392i
$400$		0			0
$401$	−251.613	+	435.807i	−0.627464	+	1.08680i	0.360594	+	0.932723i	$0.382574\pi$
$401$	−251.613	+	435.807i	−0.627464	+	1.08680i	−0.988059	+	0.154077i	$0.950759\pi$
$402$	−10.7030	−	18.5381i	−0.0266244	−	0.0461147i
$403$	−6.91812	+	3.99418i	−0.0171666	+	0.00991112i
$404$	167.568	+	96.7453i	0.414772	+	0.239468i
$405$		0			0
$406$	539.451	+	133.234i	1.32870	+	0.328162i
$407$			5.13476i			0.0126161i
$408$	−141.495	−	81.6919i	−0.346800	−	0.200225i
$409$	−649.395	+	374.928i	−1.58776	+	0.916696i	−0.594088	+	0.804400i	$0.702487\pi$
$409$	−649.395	+	374.928i	−1.58776	+	0.916696i	−0.993675	+	0.112296i	$0.964180\pi$
$410$		0			0
$411$	350.492	+	202.357i	0.852778	+	0.492352i
$412$	209.525			0.508555
$413$	−245.151	+	254.987i	−0.593585	+	0.617402i
$414$	46.9197			0.113333
$415$		0			0
$416$	20.6887	−	11.9446i	0.0497325	−	0.0287131i
$417$	317.237	−	183.157i	0.760760	−	0.439225i
$418$	−1.18264	+	2.04839i	−0.00282927	+	0.00490044i
$419$		−	465.759i		−	1.11160i	−0.831317	−	0.555799i	$-0.812413\pi$
$419$		−	465.759i		−	1.11160i	0.831317	−	0.555799i	$-0.187587\pi$
$420$		0			0
$421$	345.980			0.821805			0.410902	−	0.911679i	$-0.365214\pi$
$421$	345.980			0.821805			0.410902	+	0.911679i	$0.365214\pi$
$422$	−170.770	−	98.5939i	−0.404667	−	0.233635i
$423$	−94.9110	−	164.391i	−0.224376	−	0.388630i
$424$	−65.7908	−	113.953i	−0.155167	−	0.268757i
$425$		0			0
$426$		−	71.1841i		−	0.167099i
$427$	−701.990	−	173.378i	−1.64400	−	0.406037i
$428$			249.209i			0.582263i
$429$	−1.92536	+	3.33482i	−0.00448802	+	0.00777348i
$430$		0			0
$431$	−247.300	−	428.336i	−0.573782	−	0.993819i	−0.996173	−	0.0874056i	$-0.972142\pi$
$431$	−247.300	−	428.336i	−0.573782	−	0.993819i	0.422391	−	0.906414i	$-0.361191\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	−730.022			−1.68596			−0.842981	−	0.537943i	$-0.819201\pi$
$433$	−730.022			−1.68596			−0.842981	+	0.537943i	$0.819201\pi$
$434$	−17.9890	+	5.20135i	−0.0414494	+	0.0119847i
$435$		0			0
$436$	−84.6085	+	146.546i	−0.194056	+	0.336115i
$437$	−17.5672	−	30.4272i	−0.0401994	−	0.0696275i
$438$	−35.4959	+	20.4936i	−0.0810410	+	0.0467890i
$439$	321.631	+	185.694i	0.732645	+	0.422993i	0.819389	−	0.573238i	$-0.194313\pi$
$439$	321.631	+	185.694i	0.732645	+	0.422993i	−0.0867437	+	0.996231i	$0.527646\pi$
$440$		0			0
$441$	5.77993	+	146.886i	0.0131064	+	0.333076i
$442$			199.180i			0.450635i
$443$	353.951	+	204.354i	0.798987	+	0.461295i	0.843117	−	0.537731i	$-0.180718\pi$
$443$	353.951	+	204.354i	0.798987	+	0.461295i	−0.0441299	+	0.999026i	$0.514052\pi$
$444$	−29.2609	+	16.8938i	−0.0659029	+	0.0380491i
$445$		0			0
$446$	−316.052	−	182.473i	−0.708636	−	0.409131i
$447$	249.555			0.558288
$448$	53.7964	−	15.5547i	0.120081	−	0.0347203i
$449$	−725.469			−1.61574			−0.807872	−	0.589358i	$-0.799381\pi$
$449$	−725.469			−1.61574			−0.807872	+	0.589358i	$0.799381\pi$
$450$		0			0
$451$	1.85730	−	1.07231i	0.00411817	−	0.00237763i
$452$	−201.335	+	116.241i	−0.445432	+	0.257170i
$453$	80.9842	−	140.269i	0.178773	−	0.309644i
$454$		−	468.150i		−	1.03117i
$455$		0			0
$456$	−15.5639			−0.0341313
$457$	−347.736	−	200.765i	−0.760909	−	0.439311i	0.0687128	−	0.997636i	$-0.478111\pi$
$457$	−347.736	−	200.765i	−0.760909	−	0.439311i	−0.829622	+	0.558325i	$0.811444\pi$
$458$	172.702	+	299.129i	0.377080	+	0.653121i
$459$	86.6474	+	150.078i	0.188774	+	0.326967i
$460$		0			0
$461$		−	653.050i		−	1.41659i	−0.705915	−	0.708297i	$-0.749464\pi$
$461$		−	653.050i		−	1.41659i	0.705915	−	0.708297i	$-0.250536\pi$
$462$	−6.25607	+	6.50709i	−0.0135413	+	0.0140846i
$463$			869.580i			1.87814i	0.343722	+	0.939072i	$0.388312\pi$
$463$			869.580i			1.87814i	−0.343722	+	0.939072i	$0.611688\pi$
$464$	−112.260	+	194.441i	−0.241941	+	0.419053i
$465$		0			0
$466$	−149.546	−	259.021i	−0.320913	−	0.555838i
$467$	−369.601	+	640.168i	−0.791437	+	1.37081i	0.133641	+	0.991030i	$0.457333\pi$
$467$	−369.601	+	640.168i	−0.791437	+	1.37081i	−0.925077	+	0.379779i	$0.876000\pi$
$468$	−25.3384			−0.0541419
$469$	−42.3967	+	44.0978i	−0.0903981	+	0.0940252i
$470$		0			0
$471$	148.286	−	256.838i	0.314831	−	0.545304i
$472$	−71.4621	−	123.776i	−0.151403	−	0.262237i
$473$	21.1325	−	12.2009i	0.0446777	−	0.0257947i
$474$	280.639	+	162.027i	0.592066	+	0.341829i
$475$		0			0
$476$	−111.953	+	453.288i	−0.235196	+	0.952285i
$477$			139.563i			0.292586i
$478$	421.476	+	243.339i	0.881750	+	0.509078i
$479$	525.006	−	303.112i	1.09605	−	0.632802i	0.160866	−	0.986976i	$-0.448571\pi$
$479$	525.006	−	303.112i	1.09605	−	0.632802i	0.935180	+	0.354174i	$0.115238\pi$
$480$		0			0
$481$	35.6718	+	20.5951i	0.0741618	+	0.0428173i
$482$	242.323			0.502745
$483$	−37.2435	−	128.808i	−0.0771088	−	0.266683i
$484$	241.446			0.498855
$485$		0			0
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	562.549	−	324.788i	1.15513	−	0.666916i	0.205000	−	0.978762i	$-0.434281\pi$
$487$	562.549	−	324.788i	1.15513	−	0.666916i	0.950133	+	0.311846i	$0.100947\pi$
$488$	146.085	−	253.026i	0.299354	−	0.518497i
$489$			161.103i			0.329454i
$490$		0			0
$491$	266.629			0.543033			0.271516	−	0.962434i	$-0.412475\pi$
$491$	266.629			0.543033			0.271516	+	0.962434i	$0.412475\pi$
$492$	12.2213	+	7.05598i	0.0248401	+	0.0143414i
$493$	−935.988	−	1621.18i	−1.89856	−	3.28839i
$494$	9.48693	+	16.4318i	0.0192043	+	0.0332628i
$495$		0			0
$496$		−	7.56640i		−	0.0152548i
$497$	−195.421	+	56.5039i	−0.393200	+	0.113690i
$498$			30.5788i			0.0614033i
$499$	−340.553	+	589.855i	−0.682471	+	1.18207i	0.291754	+	0.956493i	$0.405761\pi$
$499$	−340.553	+	589.855i	−0.682471	+	1.18207i	−0.974225	+	0.225581i	$0.927572\pi$
$500$		0			0
$501$	90.9247	+	157.486i	0.181487	+	0.314344i
$502$	−231.604	+	401.151i	−0.461364	+	0.799105i
$503$	−453.326			−0.901245			−0.450622	−	0.892715i	$-0.648798\pi$
$503$	−453.326			−0.901245			−0.450622	+	0.892715i	$0.648798\pi$
$504$	−57.6643	−	14.2419i	−0.114413	−	0.0282578i
$505$		0			0
$506$	4.11678	−	7.13047i	0.00813592	−	0.0140918i
$507$	−130.913	−	226.749i	−0.258212	−	0.447236i
$508$	140.945	−	81.3744i	0.277450	−	0.160186i
$509$	43.5300	+	25.1321i	0.0855206	+	0.0493754i	0.542150	−	0.840281i	$-0.317610\pi$
$509$	43.5300	+	25.1321i	0.0855206	+	0.0493754i	−0.456630	+	0.889657i	$0.650944\pi$
$510$		0			0
$511$	84.4364	+	81.1792i	0.165238	+	0.158863i
$512$			22.6274i			0.0441942i
$513$	14.2963	+	8.25400i	0.0278681	+	0.0160897i
$514$	−269.883	+	155.817i	−0.525064	+	0.303146i
$515$		0			0
$516$	139.056	+	80.2838i	0.269488	+	0.155589i
$517$	−33.3103			−0.0644300
$518$	69.6048	+	66.9197i	0.134372	+	0.129189i
$519$	353.610			0.681330
$520$		0			0
$521$	−89.2971	+	51.5557i	−0.171396	+	0.0989553i	−0.583244	−	0.812297i	$-0.698217\pi$
$521$	−89.2971	+	51.5557i	−0.171396	+	0.0989553i	0.411848	+	0.911252i	$0.364883\pi$
$522$	206.236	−	119.070i	0.395087	−	0.228104i
$523$	−183.434	+	317.716i	−0.350733	+	0.607488i	−0.986378	−	0.164494i	$-0.947401\pi$
$523$	−183.434	+	317.716i	−0.350733	+	0.607488i	0.635645	+	0.771982i	$0.280734\pi$
$524$			481.253i			0.918421i
$525$		0			0
$526$	188.366			0.358111
$527$	54.6341	+	31.5430i	0.103670	+	0.0598539i
$528$	−1.82366	−	3.15867i	−0.00345390	−	0.00598234i
$529$	−203.348	−	352.210i	−0.384402	−	0.665803i
$530$		0			0
$531$			151.594i			0.285488i
$532$	12.3542	+	42.7273i	0.0232222	+	0.0803145i
$533$		−	17.2038i		−	0.0322773i
$534$	83.5943	−	144.790i	0.156544	−	0.271141i
$535$		0			0
$536$	−12.3588	−	21.4060i	−0.0230574	−	0.0399365i
$537$	169.653	−	293.848i	0.315928	−	0.547204i
$538$	−37.4988			−0.0697005
$539$	22.8297	+	12.0096i	0.0423557	+	0.0222812i
$540$		0			0
$541$	266.559	−	461.693i	0.492714	−	0.853407i	−0.507250	−	0.861799i	$-0.669338\pi$
$541$	266.559	−	461.693i	0.492714	−	0.853407i	0.999965	+	0.00839227i	$0.00267137\pi$
$542$	75.6709	+	131.066i	0.139614	+	0.241819i
$543$	178.547	−	103.084i	0.328816	−	0.189842i
$544$	−163.384	−	94.3297i	−0.300338	−	0.173400i
$545$		0			0
$546$	20.1129	+	69.5612i	0.0368369	+	0.127401i
$547$			69.6218i			0.127279i	0.997973	+	0.0636396i	$0.0202708\pi$
$547$			69.6218i			0.127279i	−0.997973	+	0.0636396i	$0.979729\pi$
$548$	404.713	+	233.661i	0.738528	+	0.426389i
$549$	−268.375	+	154.946i	−0.488843	+	0.282234i
$550$		0			0
$551$	−154.433	−	89.1619i	−0.280277	−	0.161818i
$552$	54.1782			0.0981489
$553$	222.047	−	899.048i	0.401532	−	1.62576i
$554$	−622.793			−1.12418
$555$		0			0
$556$	366.314	−	211.491i	0.658838	−	0.380380i
$557$	14.6033	−	8.43122i	0.0262178	−	0.0151368i	−0.486834	−	0.873495i	$-0.661848\pi$
$557$	14.6033	−	8.43122i	0.0262178	−	0.0151368i	0.513052	+	0.858358i	$0.328515\pi$
$558$	−4.01269	+	6.95018i	−0.00719120	+	0.0124555i
$559$		−	195.747i		−	0.350174i
$560$		0			0
$561$	30.4101			0.0542069
$562$	−394.452	−	227.737i	−0.701872	−	0.405226i
$563$	−457.892	−	793.093i	−0.813308	−	1.40869i	−0.910537	−	0.413428i	$-0.864331\pi$
$563$	−457.892	−	793.093i	−0.813308	−	1.40869i	0.0972290	−	0.995262i	$-0.469002\pi$
$564$	−109.594	−	189.822i	−0.194315	−	0.336564i
$565$		0			0
$566$		−	96.9204i		−	0.171237i
$567$	45.4151	+	43.6632i	0.0800971	+	0.0770073i
$568$		−	82.1963i		−	0.144712i
$569$	203.828	−	353.040i	0.358221	−	0.620456i	−0.629443	−	0.777047i	$-0.716717\pi$
$569$	203.828	−	353.040i	0.358221	−	0.620456i	0.987664	+	0.156590i	$0.0500502\pi$
$570$		0			0
$571$	447.910	+	775.803i	0.784431	+	1.35867i	0.929339	+	0.369229i	$0.120378\pi$
$571$	447.910	+	775.803i	0.784431	+	1.35867i	−0.144908	+	0.989445i	$0.546289\pi$
$572$	−2.22322	+	3.85072i	−0.00388674	+	0.00673203i
$573$	113.850			0.198691
$574$	9.66974	−	39.1519i	0.0168462	−	0.0682088i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	340.703	+	590.115i	0.590473	+	1.02273i	0.994169	+	0.107836i	$0.0343922\pi$
$577$	340.703	+	590.115i	0.590473	+	1.02273i	−0.403695	+	0.914893i	$0.632274\pi$
$578$	1008.29	−	582.134i	1.74444	−	1.00715i
$579$	145.305	+	83.8919i	0.250959	+	0.144891i
$580$		0			0
$581$	83.9476	−	24.2726i	0.144488	−	0.0417773i
$582$			365.662i			0.628286i
$583$	21.2097	+	12.2454i	0.0363802	+	0.0210041i
$584$	−40.9872	+	23.6640i	−0.0701835	+	0.0405205i
$585$		0			0
$586$	−180.662	−	104.305i	−0.308297	−	0.177996i
$587$	833.001			1.41908			0.709541	−	0.704665i	$-0.248903\pi$
$587$	833.001			1.41908			0.709541	+	0.704665i	$0.248903\pi$
$588$	6.67408	+	169.610i	0.0113505	+	0.288452i
$589$	6.00955			0.0102030
$590$		0			0
$591$	−280.008	+	161.663i	−0.473787	+	0.273541i
$592$	−33.7876	+	19.5073i	−0.0570736	+	0.0329515i
$593$	156.371	−	270.842i	0.263694	−	0.456731i	−0.703527	−	0.710669i	$-0.748392\pi$
$593$	156.371	−	270.842i	0.263694	−	0.456731i	0.967221	+	0.253938i	$0.0817258\pi$
$594$			3.86857i			0.00651274i
$595$		0			0
$596$	288.161			0.483491
$597$	−172.937	−	99.8454i	−0.289677	−	0.167245i
$598$	−33.0242	−	57.1996i	−0.0552244	−	0.0956514i
$599$	107.121	+	185.540i	0.178834	+	0.309749i	0.941481	−	0.337065i	$-0.109434\pi$
$599$	107.121	+	185.540i	0.178834	+	0.309749i	−0.762648	+	0.646814i	$0.776101\pi$
$600$		0			0
$601$			176.849i			0.294257i	0.989117	+	0.147129i	$0.0470031\pi$
$601$			176.849i			0.294257i	−0.989117	+	0.147129i	$0.952997\pi$
$602$	110.023	−	445.474i	0.182763	−	0.739991i
$603$			26.2169i			0.0434774i
$604$	93.5125	−	161.968i	0.154822	−	0.268160i
$605$		0			0
$606$	−118.488	−	205.228i	−0.195525	−	0.338660i
$607$	−18.5505	+	32.1304i	−0.0305609	+	0.0529331i	−0.880901	−	0.473300i	$-0.843063\pi$
$607$	−18.5505	+	32.1304i	−0.0305609	+	0.0529331i	0.850340	+	0.526233i	$0.176396\pi$
$608$	−17.9716			−0.0295586
$609$	−490.586	−	471.661i	−0.805559	−	0.774484i
$610$		0			0
$611$	−133.605	+	231.411i	−0.218666	+	0.378741i
$612$	100.052	+	173.295i	0.163483	+	0.283161i
$613$	779.180	−	449.860i	1.27109	−	0.733866i	0.295899	−	0.955219i	$-0.404381\pi$
$613$	779.180	−	449.860i	1.27109	−	0.733866i	0.975194	+	0.221353i	$0.0710475\pi$
$614$	460.516	+	265.879i	0.750027	+	0.433028i
$615$		0			0
$616$	−7.22389	+	7.51374i	−0.0117271	+	0.0121976i
$617$		−	626.244i		−	1.01498i	−0.861657	−	0.507491i	$-0.830573\pi$
$617$		−	626.244i		−	1.01498i	0.861657	−	0.507491i	$-0.169427\pi$
$618$	−222.234	−	128.307i	−0.359602	−	0.207617i
$619$	776.375	−	448.240i	1.25424	−	0.724136i	0.282291	−	0.959329i	$-0.408906\pi$
$619$	776.375	−	448.240i	1.25424	−	0.724136i	0.971949	+	0.235193i	$0.0755722\pi$
$620$		0			0
$621$	−49.7658	−	28.7323i	−0.0801382	−	0.0462678i
$622$	551.298			0.886331
$623$	−463.843	−	114.560i	−0.744532	−	0.183885i
$624$	−29.2583			−0.0468883
$625$		0			0
$626$	175.207	−	101.156i	0.279884	−	0.161591i
$627$	2.50875	−	1.44843i	0.00400120	−	0.00231009i
$628$	171.225	−	296.571i	0.272652	−	0.472247i
$629$		−	325.290i		−	0.517153i
$630$		0			0
$631$	−500.730			−0.793550			−0.396775	−	0.917916i	$-0.629871\pi$
$631$	−500.730			−0.793550			−0.396775	+	0.917916i	$0.629871\pi$
$632$	324.054	+	187.093i	0.512744	+	0.296033i
$633$	120.752	+	209.149i	0.190762	+	0.330409i
$634$	271.843	+	470.846i	0.428774	+	0.742659i
$635$		0			0
$636$			161.154i			0.253387i
$637$	175.000	−	110.431i	0.274726	−	0.173362i
$638$		−	41.7893i		−	0.0655005i
$639$	−43.5912	+	75.5021i	−0.0682178	+	0.118157i
$640$		0			0
$641$	−310.289	−	537.436i	−0.484070	−	0.838434i	0.515763	−	0.856732i	$-0.327509\pi$
$641$	−310.289	−	537.436i	−0.484070	−	0.838434i	−0.999833	+	0.0182978i	$0.994175\pi$
$642$	152.609	−	264.326i	0.237708	−	0.411722i
$643$	1127.93			1.75417			0.877086	−	0.480334i	$-0.159484\pi$
$643$	1127.93			1.75417			0.877086	+	0.480334i	$0.159484\pi$
$644$	−43.0051	−	148.735i	−0.0667782	−	0.230954i
$645$		0			0
$646$	74.9206	−	129.766i	0.115976	−	0.200877i
$647$	−67.6248	−	117.130i	−0.104521	−	0.181035i	0.809022	−	0.587779i	$-0.199997\pi$
$647$	−67.6248	−	117.130i	−0.104521	−	0.181035i	−0.913542	+	0.406744i	$0.866664\pi$
$648$	−22.0454	+	12.7279i	−0.0340207	+	0.0196419i
$649$	23.0380	+	13.3010i	0.0354977	+	0.0204946i
$650$		0			0
$651$	22.2654	+	5.49912i	0.0342018	+	0.00844719i
$652$			186.026i			0.285316i
$653$	−338.001	−	195.145i	−0.517612	−	0.298843i	0.218345	−	0.975872i	$-0.429934\pi$
$653$	−338.001	−	195.145i	−0.517612	−	0.298843i	−0.735957	+	0.677028i	$0.763267\pi$
$654$	179.482	−	103.624i	0.274437	−	0.158446i
$655$		0			0
$656$	14.1120	+	8.14755i	0.0215121	+	0.0124200i
$657$	50.1988			0.0764061
$658$	−434.123	+	451.542i	−0.659761	+	0.686233i
$659$	864.853			1.31237			0.656186	−	0.754599i	$-0.272169\pi$
$659$	864.853			1.31237			0.656186	+	0.754599i	$0.272169\pi$
$660$		0			0
$661$	−873.134	+	504.104i	−1.32093	+	0.762638i	−0.983877	−	0.178848i	$-0.942763\pi$
$661$	−873.134	+	504.104i	−1.32093	+	0.762638i	−0.337052	+	0.941486i	$0.609430\pi$
$662$	237.487	−	137.113i	0.358742	−	0.207120i
$663$	121.973	−	211.263i	0.183971	−	0.318647i
$664$			35.3094i			0.0531768i
$665$		0			0
$666$	41.3812			0.0621339
$667$	537.584	+	310.374i	0.805973	+	0.465328i
$668$	104.991	+	181.849i	0.157172	+	0.272230i
$669$	223.482	+	387.083i	0.334054	+	0.578599i
$670$		0			0
$671$			54.3806i			0.0810441i
$672$	−66.5850	−	16.4452i	−0.0990848	−	0.0244720i
$673$			109.959i			0.163386i	0.996658	+	0.0816928i	$0.0260327\pi$
$673$			109.959i			0.163386i	−0.996658	+	0.0816928i	$0.973967\pi$
$674$	88.7259	−	153.678i	0.131641	−	0.228009i
$675$		0			0
$676$	−151.166	−	261.827i	−0.223618	−	0.387318i
$677$	−84.4163	+	146.213i	−0.124692	+	0.215972i	−0.921612	−	0.388112i	$-0.873128\pi$
$677$	−84.4163	+	146.213i	−0.124692	+	0.215972i	0.796921	+	0.604084i	$0.206461\pi$
$678$	284.731			0.419957
$679$	1003.85	−	290.253i	1.47842	−	0.427471i
$680$		0			0
$681$	−286.682	+	496.548i	−0.420973	+	0.729146i
$682$	0.704155	+	1.21963i	0.00103248	+	0.00178832i
$683$	377.700	−	218.065i	0.553002	−	0.319276i	−0.197330	−	0.980337i	$-0.563227\pi$
$683$	377.700	−	218.065i	0.553002	−	0.319276i	0.750332	+	0.661061i	$0.229894\pi$
$684$	16.5080	+	9.53090i	0.0241345	+	0.0139341i
$685$		0			0
$686$	460.329	−	152.954i	0.671034	−	0.222965i
$687$		−	423.033i		−	0.615768i
$688$	160.568	+	92.7038i	0.233383	+	0.134744i
$689$	170.141	−	98.2309i	0.246939	−	0.142570i
$690$		0			0
$691$	−59.2770	−	34.2236i	−0.0857843	−	0.0495276i	0.456494	−	0.889726i	$-0.349105\pi$
$691$	−59.2770	−	34.2236i	−0.0857843	−	0.0495276i	−0.542279	+	0.840199i	$0.682438\pi$
$692$	408.314			0.590049
$693$	10.6203	−	3.07076i	0.0153251	−	0.00443112i
$694$	712.193			1.02622
$695$		0			0
$696$	238.140	−	137.490i	0.342156	−	0.197544i
$697$	−117.661	+	67.9314i	−0.168810	+	0.0974625i
$698$	33.7772	−	58.5039i	0.0483914	−	0.0838164i
$699$			366.311i			0.524050i
$700$		0			0
$701$	1283.41			1.83083			0.915414	−	0.402514i	$-0.131864\pi$
$701$	1283.41			1.83083			0.915414	+	0.402514i	$0.131864\pi$
$702$	26.8754	+	15.5165i	0.0382841	+	0.0221033i
$703$	−15.4935	−	26.8355i	−0.0220391	−	0.0381728i
$704$	−2.10578	−	3.64732i	−0.00299117	−	0.00518086i
$705$		0			0
$706$			46.5422i			0.0659238i
$707$	−469.356	+	488.188i	−0.663870	+	0.690507i
$708$			175.046i			0.247240i
$709$	86.2000	−	149.303i	0.121580	−	0.210582i	−0.798811	−	0.601582i	$-0.794537\pi$
$709$	86.2000	−	149.303i	0.121580	−	0.210582i	0.920391	+	0.391000i	$0.127871\pi$
$710$		0			0
$711$	−198.442	−	343.712i	−0.279103	−	0.483420i
$712$	96.5264	−	167.189i	0.135571	−	0.234815i
$713$	−20.9194			−0.0293399
$714$	396.325	−	412.227i	0.555077	−	0.577349i
$715$		0			0
$716$	195.899	−	339.307i	0.273602	−	0.473892i
$717$	−298.029	−	516.201i	−0.415661	−	0.719946i
$718$	−327.983	+	189.361i	−0.456801	+	0.263734i
$719$	435.015	+	251.156i	0.605028	+	0.349313i	0.771017	−	0.636815i	$-0.219748\pi$
$719$	435.015	+	251.156i	0.605028	+	0.349313i	−0.165989	+	0.986128i	$0.553082\pi$
$720$		0			0
$721$	−175.836	+	711.943i	−0.243878	+	0.987439i
$722$			496.257i			0.687337i
$723$	−257.023	−	148.392i	−0.355495	−	0.205245i
$724$	206.168	−	119.031i	0.284763	−	0.164408i
$725$		0			0
$726$	−256.092	−	147.855i	−0.352744	−	0.203657i
$727$	−748.693			−1.02984			−0.514920	−	0.857238i	$-0.672178\pi$
$727$	−748.693			−1.02984			−0.514920	+	0.857238i	$0.672178\pi$
$728$	23.2244	+	80.3223i	0.0319017	+	0.110333i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−1338.76	+	772.931i	−1.83140	+	1.05736i
$732$	−309.893	+	178.917i	−0.423351	+	0.244422i
$733$	−469.248	+	812.761i	−0.640175	+	1.10881i	0.345219	+	0.938522i	$0.387805\pi$
$733$	−469.248	+	812.761i	−0.640175	+	1.10881i	−0.985394	+	0.170293i	$0.945529\pi$
$734$			224.468i			0.305814i
$735$		0			0
$736$	62.5596			0.0849994
$737$	3.98422	+	2.30029i	0.00540600	+	0.00312116i
$738$	−8.64178	−	14.9680i	−0.0117097	−	0.0202818i
$739$	106.820	+	185.018i	0.144547	+	0.250363i	0.929204	−	0.369567i	$-0.120494\pi$
$739$	106.820	+	185.018i	0.144547	+	0.250363i	−0.784657	+	0.619931i	$0.787161\pi$
$740$		0			0
$741$		−	23.2381i		−	0.0313605i
$742$	442.413	−	127.919i	0.596244	−	0.172398i
$743$		−	544.013i		−	0.732184i	−0.930579	−	0.366092i	$-0.880696\pi$
$743$		−	544.013i		−	0.732184i	0.930579	−	0.366092i	$-0.119304\pi$
$744$	−4.63346	+	8.02538i	−0.00622776	+	0.0107868i
$745$		0			0
$746$	−292.985	−	507.465i	−0.392742	−	0.680249i
$747$	18.7256	−	32.4337i	0.0250678	−	0.0434187i
$748$	35.1146			0.0469446
$749$	−846.786	−	209.140i	−1.13056	−	0.279225i
$750$		0			0
$751$	−294.705	+	510.443i	−0.392416	+	0.679685i	−0.992768	−	0.120051i	$-0.961694\pi$
$751$	−294.705	+	510.443i	−0.392416	+	0.679685i	0.600351	+	0.799736i	$0.295027\pi$
$752$	−126.548	−	219.187i	−0.168282	−	0.291473i
$753$	491.307	−	283.656i	0.652467	−	0.376702i
$754$	−290.316	−	167.614i	−0.385034	−	0.222299i
$755$		0			0
$756$	52.4408	+	50.4179i	0.0693662	+	0.0666903i
$757$		−	448.997i		−	0.593127i	−0.955013	−	0.296564i	$-0.904159\pi$
$757$		−	448.997i		−	0.593127i	0.955013	−	0.296564i	$-0.0958406\pi$
$758$	−89.1614	−	51.4774i	−0.117627	−	0.0679121i
$759$	−8.73300	+	5.04200i	−0.0115059	+	0.00664295i
$760$		0			0
$761$	371.914	+	214.725i	0.488718	+	0.282161i	0.724042	−	0.689756i	$-0.242282\pi$
$761$	371.914	+	214.725i	0.488718	+	0.282161i	−0.235325	+	0.971917i	$0.575615\pi$
$762$	−199.326			−0.261582
$763$	−426.944	−	410.475i	−0.559560	−	0.537975i
$764$	131.463			0.172072
$765$		0			0
$766$	349.070	−	201.536i	0.455705	−	0.263101i
$767$	184.807	−	106.699i	0.240948	−	0.139112i
$768$	13.8564	−	24.0000i	0.0180422	−	0.0312500i
$769$			32.5790i			0.0423655i	0.999776	+	0.0211827i	$0.00674318\pi$
$769$			32.5790i			0.0423655i	−0.999776	+	0.0211827i	$0.993257\pi$
$770$		0			0
$771$	381.672			0.495035
$772$	167.784	+	96.8700i	0.217337	+	0.125479i
$773$	−621.768	−	1076.93i	−0.804357	−	1.39319i	−0.916724	−	0.399520i	$-0.869177\pi$
$773$	−621.768	−	1076.93i	−0.804357	−	1.39319i	0.112367	−	0.993667i	$-0.464157\pi$
$774$	−98.3272	−	170.308i	−0.127038	−	0.220036i
$775$		0			0
$776$			422.231i			0.544112i
$777$	−32.8472	−	113.603i	−0.0422744	−	0.146207i
$778$			137.374i			0.176574i
$779$	−6.47112	+	11.2083i	−0.00830696	+	0.0143881i
$780$		0			0
$781$	7.64946	+	13.2493i	0.00979444	+	0.0169645i
$782$	−260.800	+	451.719i	−0.333504	+	0.577645i
$783$	−291.661			−0.372492
$784$	7.70657	+	195.848i	0.00982981	+	0.249807i
$785$		0			0
$786$	294.706	−	510.446i	0.374944	−	0.649422i
$787$	95.3138	+	165.088i	0.121110	+	0.209769i	0.920206	−	0.391435i	$-0.128021\pi$
$787$	95.3138	+	165.088i	0.121110	+	0.209769i	−0.799096	+	0.601204i	$0.794688\pi$
$788$	−323.325	+	186.672i	−0.410311	+	0.236893i
$789$	−199.793	−	115.350i	−0.253223	−	0.146198i
$790$		0			0
$791$	−226.011	−	781.667i	−0.285729	−	0.988202i
$792$			4.46704i			0.00564020i
$793$	377.789	+	218.116i	0.476405	+	0.275052i
$794$	−969.635	+	559.819i	−1.22120	+	0.705062i
$795$		0			0
$796$	−199.691	−	115.292i	−0.250868	−	0.144839i
$797$	387.796			0.486570			0.243285	−	0.969955i	$-0.421775\pi$
$797$	387.796			0.486570			0.243285	+	0.969955i	$0.421775\pi$
$798$	13.0614	−	52.8845i	0.0163677	−	0.0662713i
$799$	2110.23			2.64108
$800$		0			0
$801$	−177.330	+	102.382i	−0.221386	+	0.127817i
$802$	616.324	−	355.835i	0.768484	−	0.443684i
$803$	4.40449	−	7.62881i	0.00548505	−	0.00950038i
$804$			30.2726i			0.0376525i
$805$		0			0
$806$	11.2972			0.0140164
$807$	39.7735	+	22.9633i	0.0492857	+	0.0284551i
$808$	−136.818	−	236.977i	−0.169330	−	0.293288i
$809$	182.613	+	316.295i	0.225727	+	0.390970i	0.956537	−	0.291610i	$-0.0941911\pi$
$809$	182.613	+	316.295i	0.225727	+	0.390970i	−0.730811	+	0.682580i	$0.760858\pi$
$810$		0			0
$811$			944.189i			1.16423i	0.813107	+	0.582114i	$0.197774\pi$
$811$			944.189i			1.16423i	−0.813107	+	0.582114i	$0.802226\pi$
$812$	−566.479	−	544.627i	−0.697635	−	0.670723i
$813$		−	185.355i		−	0.227989i
$814$	3.63082	−	6.28877i	0.00446047	−	0.00772576i
$815$		0			0
$816$	115.530	+	200.104i	0.141581	+	0.245225i
$817$	−73.6292	+	127.529i	−0.0901214	+	0.156095i
$818$	1060.46			1.29640
$819$	21.2644	−	86.0974i	0.0259638	−	0.105125i
$820$		0			0
$821$	342.337	−	592.946i	0.416976	−	0.722224i	−0.578657	−	0.815571i	$-0.696423\pi$
$821$	342.337	−	592.946i	0.416976	−	0.722224i	0.995634	+	0.0933467i	$0.0297565\pi$
$822$	−286.175	−	495.670i	−0.348145	−	0.603005i
$823$	905.578	−	522.835i	1.10034	−	0.635280i	0.164028	−	0.986456i	$-0.447551\pi$
$823$	905.578	−	522.835i	1.10034	−	0.635280i	0.936310	+	0.351176i	$0.114218\pi$
$824$	−256.614	−	148.156i	−0.311425	−	0.179801i
$825$		0			0
$826$	480.550	−	138.946i	0.581780	−	0.168216i
$827$			830.505i			1.00424i	0.864798	+	0.502119i	$0.167446\pi$
$827$			830.505i			1.00424i	−0.864798	+	0.502119i	$0.832554\pi$
$828$	−57.4646	−	33.1772i	−0.0694017	−	0.0400691i
$829$	621.983	−	359.102i	0.750280	−	0.433175i	−0.0755148	−	0.997145i	$-0.524060\pi$
$829$	621.983	−	359.102i	0.750280	−	0.433175i	0.825795	+	0.563970i	$0.190727\pi$
$830$		0			0
$831$	660.572	+	381.381i	0.794912	+	0.458943i
$832$	−33.7846			−0.0406064
$833$	−1446.27	−	760.812i	−1.73622	−	0.913339i
$834$	−518.046			−0.621158
$835$		0			0
$836$	2.89685	−	1.67250i	0.00346514	−	0.00200060i
$837$	8.51220	−	4.91452i	0.0101699	−	0.00587159i
$838$	−329.342	+	570.436i	−0.393009	+	0.680712i
$839$			55.2900i			0.0658999i	0.999457	+	0.0329499i	$0.0104902\pi$
$839$			55.2900i			0.0658999i	−0.999457	+	0.0329499i	$0.989510\pi$
$840$		0			0
$841$	2309.60			2.74625
$842$	−423.737	−	244.645i	−0.503251	−	0.290552i
$843$	278.920	+	483.103i	0.330866	+	0.573076i
$844$	139.433	+	241.505i	0.165205	+	0.286143i
$845$		0			0
$846$			268.449i			0.317315i
$847$	−202.625	+	820.408i	−0.239226	+	0.968605i
$848$			186.084i			0.219439i
$849$	−59.3514	+	102.800i	−0.0699074	+	0.121083i
$850$		0			0
$851$	53.9331	+	93.4149i	0.0633761	+	0.109771i
$852$	−50.3347	+	87.1823i	−0.0590783	+	0.102327i
$853$	−21.9601			−0.0257445			−0.0128723	−	0.999917i	$-0.504097\pi$
$853$	−21.9601			−0.0257445			−0.0128723	+	0.999917i	$0.504097\pi$
$854$	737.162	+	708.725i	0.863187	+	0.829889i
$855$		0			0
$856$	176.217	−	305.217i	0.205861	−	0.356562i
$857$	−807.903	−	1399.33i	−0.942711	−	1.63282i	−0.760271	−	0.649607i	$-0.774934\pi$
$857$	−807.903	−	1399.33i	−0.942711	−	1.63282i	−0.182441	−	0.983217i	$-0.558400\pi$
$858$	4.71615	−	2.72287i	0.00549668	−	0.00317351i
$859$	−772.149	−	445.801i	−0.898893	−	0.518976i	−0.0220523	−	0.999757i	$-0.507020\pi$
$859$	−772.149	−	445.801i	−0.898893	−	0.518976i	−0.876841	+	0.480781i	$0.840353\pi$
$860$		0			0
$861$	−34.2318	+	35.6053i	−0.0397582	+	0.0413535i
$862$			699.470i			0.811450i
$863$	−776.259	−	448.173i	−0.899489	−	0.519320i	−0.0224544	−	0.999748i	$-0.507148\pi$
$863$	−776.259	−	448.173i	−0.899489	−	0.519320i	−0.877034	+	0.480428i	$0.840481\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	894.090	+	516.203i	1.03244	+	0.596078i
$867$	−1425.93			−1.64467
$868$	25.7099	+	6.34984i	0.0296197	+	0.00731548i
$869$	−69.6459			−0.0801449
$870$		0			0
$871$	31.9609	−	18.4526i	0.0366944	−	0.0211855i
$872$	207.248	−	119.654i	0.237669	−	0.137218i
$873$	223.922	−	387.844i	0.256497	−	0.444265i
$874$			49.6874i			0.0568506i
$875$		0			0
$876$	57.9646			0.0661697
$877$	292.517	+	168.885i	0.333543	+	0.192571i	0.657413	−	0.753530i	$-0.271651\pi$
$877$	292.517	+	168.885i	0.333543	+	0.192571i	−0.323870	+	0.946102i	$0.604984\pi$
$878$	−262.611	−	454.855i	−0.299101	−	0.518059i
$879$	127.748	+	221.265i	0.145333	+	0.251724i
$880$		0			0
$881$			301.377i			0.342085i	0.985264	+	0.171042i	$0.0547135\pi$
$881$			301.377i			0.342085i	−0.985264	+	0.171042i	$0.945287\pi$
$882$	96.7854	−	183.985i	0.109734	−	0.208600i
$883$		−	38.3679i		−	0.0434518i	−0.999764	−	0.0217259i	$-0.993084\pi$
$883$		−	38.3679i		−	0.0434518i	0.999764	−	0.0217259i	$-0.00691611\pi$
$884$	140.842	−	243.945i	0.159323	−	0.275956i
$885$		0			0
$886$	−289.000	−	500.563i	−0.326185	−	0.564969i
$887$	−330.726	+	572.834i	−0.372859	+	0.645811i	−0.990004	−	0.141038i	$-0.954956\pi$
$887$	−330.726	+	572.834i	−0.372859	+	0.645811i	0.617145	+	0.786849i	$0.288289\pi$
$888$	47.7829			0.0538095
$889$	158.219	+	547.206i	0.177974	+	0.615530i
$890$		0			0
$891$	2.36901	−	4.10324i	0.00265882	−	0.00460521i
$892$	258.055	+	446.965i	0.289300	+	0.501082i
$893$	174.088	−	100.510i	0.194947	−	0.112553i
$894$	−305.641	−	176.462i	−0.341880	−	0.197384i
$895$		0			0
$896$	−76.8857	−	18.9893i	−0.0858099	−	0.0211934i
$897$			80.8924i			0.0901810i
$898$	888.515	+	512.984i	0.989437	+	0.571252i
$899$	−91.9510	+	53.0880i	−0.102281	+	0.0590522i
$900$		0			0
$901$	−1343.64	−	775.753i	−1.49128	−	0.860991i
$902$	−3.03295			−0.00336247
$903$	−389.494	+	405.122i	−0.431333	+	0.448640i
$904$	328.779			0.363693
$905$		0			0
$906$	−198.370	+	114.529i	−0.218951	+	0.126412i
$907$	−838.576	+	484.152i	−0.924560	+	0.533795i	−0.885087	−	0.465426i	$-0.845901\pi$
$907$	−838.576	+	484.152i	−0.924560	+	0.533795i	−0.0394729	+	0.999221i	$0.512568\pi$
$908$	−331.032	+	573.365i	−0.364573	+	0.631459i
$909$			290.236i			0.319291i
$910$		0			0
$911$	220.674			0.242233			0.121116	−	0.992638i	$-0.461353\pi$
$911$	220.674			0.242233			0.121116	+	0.992638i	$0.461353\pi$
$912$	19.0618	+	11.0053i	0.0209011	+	0.0120673i
$913$	−3.28601	−	5.69153i	−0.00359913	−	0.00623388i
$914$	283.925	+	491.772i	0.310640	+	0.538044i
$915$		0			0
$916$		−	488.476i		−	0.533271i
$917$	−1635.25	−	403.874i	−1.78326	−	0.440430i
$918$		−	245.076i		−	0.266967i
$919$	−574.019	+	994.231i	−0.624613	+	1.08186i	0.364002	+	0.931398i	$0.381410\pi$
$919$	−574.019	+	994.231i	−0.624613	+	1.08186i	−0.988616	+	0.150464i	$0.951923\pi$
$920$		0			0
$921$	−325.634	−	564.015i	−0.353566	−	0.612394i
$922$	−461.776	+	799.819i	−0.500841	+	0.867483i
$923$	122.726			0.132964
$924$	12.2633	−	3.54581i	0.0132720	−	0.00383746i
$925$		0			0
$926$	614.886	−	1065.01i	0.664024	−	1.15012i
$927$	157.143	+	272.180i	0.169518	+	0.293614i
$928$	274.981	−	158.760i	0.296315	−	0.171078i
$929$	264.398	+	152.650i	0.284605	+	0.164317i	0.635506	−	0.772096i	$-0.280791\pi$
$929$	264.398	+	152.650i	0.284605	+	0.164317i	−0.350901	+	0.936412i	$0.614125\pi$
$930$		0			0
$931$	−155.551	+	6.12088i	−0.167079	+	0.00657452i
$932$			422.979i			0.453840i
$933$	−584.739	−	337.599i	−0.626730	−	0.361843i
$934$	905.334	−	522.695i	0.969308	−	0.559630i
$935$		0			0
$936$	31.0331	+	17.9170i	0.0331550	+	0.0191421i
$937$	12.4049			0.0132390			0.00661948	−	0.999978i	$-0.497893\pi$
$937$	12.4049			0.0132390			0.00661948	+	0.999978i	$0.497893\pi$
$938$	83.1070	−	24.0296i	0.0886002	−	0.0256179i
$939$	−247.781			−0.263877
$940$		0			0
$941$	−250.409	+	144.573i	−0.266109	+	0.153638i	−0.627118	−	0.778924i	$-0.715766\pi$
$941$	−250.409	+	144.573i	−0.266109	+	0.153638i	0.361009	+	0.932562i	$0.382432\pi$
$942$	−363.224	+	209.708i	−0.385588	+	0.222619i
$943$	22.5261	−	39.0163i	0.0238877	−	0.0413747i
$944$			202.125i			0.214116i
$945$		0			0
$946$	−34.5093			−0.0364792
$947$	1235.78	+	713.478i	1.30494	+	0.753409i	0.981247	−	0.192752i	$-0.0617414\pi$
$947$	1235.78	+	713.478i	1.30494	+	0.753409i	0.323695	+	0.946161i	$0.395075\pi$
$948$	−229.141	−	396.884i	−0.241710	−	0.418654i
$949$	−35.3322	−	61.1972i	−0.0372310	−	0.0644859i
$950$		0			0
$951$		−	665.876i		−	0.700186i
$952$	457.637	−	475.999i	0.480711	−	0.499999i
$953$			668.525i			0.701495i	0.936470	+	0.350747i	$0.114072\pi$
$953$			668.525i			0.701495i	−0.936470	+	0.350747i	$0.885928\pi$
$954$	98.6862	−	170.929i	0.103445	−	0.179171i
$955$		0			0
$956$	−344.134	−	596.058i	−0.359973	−	0.623491i
$957$	−25.5906	+	44.3242i	−0.0267405	+	0.0463158i
$958$	−857.331			−0.894918
$959$	−1133.60	+	1179.08i	−1.18206	+	1.22949i
$960$		0			0
$961$	−478.711	+	829.152i	−0.498138	+	0.862801i
$962$	−29.1259	−	50.4476i	−0.0302764	−	0.0524403i
$963$	−323.732	+	186.907i	−0.336170	+	0.194088i
$964$	−296.784	−	171.348i	−0.307867	−	0.177747i
$965$		0			0
$966$	−45.4671	+	184.092i	−0.0470674	+	0.190571i
$967$			1647.14i			1.70335i	0.524069	+	0.851676i	$0.324414\pi$
$967$			1647.14i			1.70335i	−0.524069	+	0.851676i	$0.675586\pi$
$968$	−295.709	−	170.728i	−0.305485	−	0.176372i
$969$	−158.931	+	91.7586i	−0.164015	+	0.0946941i
$970$		0			0
$971$	1138.76	+	657.466i	1.17277	+	0.677102i	0.954332	−	0.298748i	$-0.0965690\pi$
$971$	1138.76	+	657.466i	1.17277	+	0.677102i	0.218443	+	0.975850i	$0.429902\pi$
$972$	31.1769			0.0320750
$973$	411.210	+	1422.18i	0.422621	+	1.46165i
$974$	−918.639			−0.943161
$975$		0			0
$976$	−357.833	+	206.595i	−0.366633	+	0.211675i
$977$	1347.57	−	778.021i	1.37930	−	0.796337i	0.387221	−	0.921987i	$-0.373435\pi$
$977$	1347.57	−	778.021i	1.37930	−	0.796337i	0.992075	+	0.125650i	$0.0401017\pi$
$978$	113.917	−	197.310i	0.116480	−	0.201749i
$979$			35.9323i			0.0367030i
$980$		0			0
$981$	−253.825			−0.258741
$982$	−326.553	−	188.535i	−0.332538	−	0.191991i
$983$	686.397	+	1188.87i	0.698268	+	1.20944i	0.969067	+	0.246799i	$0.0793788\pi$
$983$	686.397	+	1188.87i	0.698268	+	1.20944i	−0.270799	+	0.962636i	$0.587288\pi$
$984$	−9.97867	−	17.2836i	−0.0101409	−	0.0175646i
$985$		0			0
$986$			2647.37i			2.68496i
$987$	736.968	−	213.087i	0.746675	−	0.215894i
$988$		−	26.8331i		−	0.0271590i
$989$	256.304	−	443.932i	0.259155	−	0.448870i
$990$		0			0
$991$	−321.812	−	557.395i	−0.324735	−	0.562457i	0.656724	−	0.754131i	$-0.271942\pi$
$991$	−321.812	−	557.395i	−0.324735	−	0.562457i	−0.981459	+	0.191674i	$0.938608\pi$
$992$	−5.35025	+	9.26691i	−0.00539340	+	0.00934165i
$993$	−335.858			−0.338226
$994$	279.295	+	68.9803i	0.280981	+	0.0693967i
$995$		0			0
$996$	21.6225	−	37.4513i	0.0217093	−	0.0376017i
$997$	352.433	+	610.431i	0.353493	+	0.612268i	0.986859	−	0.161584i	$-0.0516604\pi$
$997$	352.433	+	610.431i	0.353493	+	0.612268i	−0.633366	+	0.773853i	$0.718327\pi$
$998$	834.181	−	481.615i	0.835853	−	0.482580i
$999$	−43.8914	−	25.3407i	−0.0439353	−	0.0253661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.e.649.4		32
5.2	odd	4		1050.3.p.i.901.6		16
5.3	odd	4		210.3.o.b.61.4	yes	16
5.4	even	2	inner	1050.3.q.e.649.12		32
7.3	odd	6	inner	1050.3.q.e.199.12		32
15.8	even	4		630.3.v.c.271.6		16
35.3	even	12		210.3.o.b.31.4	✓	16
35.17	even	12		1050.3.p.i.451.6		16
35.23	odd	12		1470.3.f.d.391.9		16
35.24	odd	6	inner	1050.3.q.e.199.4		32
35.33	even	12		1470.3.f.d.391.15		16
105.38	odd	12		630.3.v.c.451.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.4	✓	16	35.3	even	12
210.3.o.b.61.4	yes	16	5.3	odd	4
630.3.v.c.271.6		16	15.8	even	4
630.3.v.c.451.6		16	105.38	odd	12
1050.3.p.i.451.6		16	35.17	even	12
1050.3.p.i.901.6		16	5.2	odd	4
1050.3.q.e.199.4		32	35.24	odd	6	inner
1050.3.q.e.199.12		32	7.3	odd	6	inner
1050.3.q.e.649.4		32	1.1	even	1	trivial
1050.3.q.e.649.12		32	5.4	even	2	inner
1470.3.f.d.391.9		16	35.23	odd	12
1470.3.f.d.391.15		16	35.33	even	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.72455 + 1.94434i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.72455 + 1.94434i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.263223 + 0.455915i) q^{11} +(-1.73205 + 3.00000i) q^{12} +4.22307 q^{13} +(9.61071 + 2.37366i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-16.6753 - 28.8825i) q^{17} +(3.67423 - 2.12132i) q^{18} +(-2.75133 - 1.58848i) q^{19} +(-8.74014 - 8.40298i) q^{21} -0.744507i q^{22} +(9.57744 + 5.52954i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-5.17218 - 2.98616i) q^{26} -5.19615 q^{27} +(-10.0922 - 9.70292i) q^{28} +56.1302 q^{29} +(-1.63817 + 0.945800i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-0.455915 + 0.789668i) q^{33} +47.1649i q^{34} -6.00000 q^{36} +(8.44690 + 4.87682i) q^{37} +(2.24645 + 3.89097i) q^{38} +(3.65729 + 6.33460i) q^{39} -4.07377i q^{41} +(4.76263 + 16.4717i) q^{42} -46.3519i q^{43} +(-0.526446 + 0.911831i) q^{44} +(-7.81995 - 13.5445i) q^{46} +(-31.6370 + 54.7969i) q^{47} -6.92820 q^{48} +(41.4391 - 26.1496i) q^{49} +(28.8825 - 50.0259i) q^{51} +(4.22307 + 7.31457i) q^{52} +(40.2885 - 23.2606i) q^{53} +(6.36396 + 3.67423i) q^{54} +(5.49942 + 19.0199i) q^{56} -5.50267i q^{57} +(-68.7452 - 39.6900i) q^{58} +(43.7614 - 25.2657i) q^{59} +(89.4583 + 51.6488i) q^{61} +2.67513 q^{62} +(5.03529 - 20.3874i) q^{63} -8.00000 q^{64} +(1.11676 - 0.644762i) q^{66} +(7.56816 - 4.36948i) q^{67} +(33.3506 - 57.7649i) q^{68} +19.1549i q^{69} +29.0608 q^{71} +(7.34847 + 4.24264i) q^{72} +(-8.36647 - 14.4912i) q^{73} +(-6.89686 - 11.9457i) q^{74} -6.35393i q^{76} +(-2.65651 - 2.55403i) q^{77} -10.3444i q^{78} +(-66.1473 + 114.571i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-2.88059 + 4.98933i) q^{82} -12.4838 q^{83} +(5.81425 - 23.5413i) q^{84} +(-32.7757 + 56.7692i) q^{86} +(48.6102 + 84.1953i) q^{87} +(1.28952 - 0.744507i) q^{88} +(59.1101 + 34.1272i) q^{89} +(-28.3982 + 8.21107i) q^{91} +22.1182i q^{92} +(-2.83740 - 1.63817i) q^{93} +(77.4945 - 44.7415i) q^{94} +(8.48528 + 4.89898i) q^{96} -149.281 q^{97} +(-69.2429 + 2.72468i) q^{98} -1.57934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 48 * q^9	\( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Introduction

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