LMFDB - Embedded newform 1050.3.q.a.199.2

Newspace parameters

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
Defining polynomial:	$x^{8} - x^{4} + 1$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.a.649.2

$q$-expansion

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.77962 + 1.74264i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.77962 + 1.74264i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(-1.73205 - 3.00000i) q^{12} -21.3280 q^{13} +(-9.53553 + 2.65962i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(4.47871 - 7.75736i) q^{17} +(3.67423 + 2.12132i) q^{18} +(6.25736 - 3.61269i) q^{19} +(8.48528 - 8.66025i) q^{21} -8.48528i q^{22} +(32.4377 - 18.7279i) q^{23} +(4.24264 + 2.44949i) q^{24} +(26.1213 - 15.0812i) q^{26} -5.19615 q^{27} +(9.79796 - 10.0000i) q^{28} +33.9411 q^{29} +(38.2279 + 22.0709i) q^{31} +(4.89898 + 2.82843i) q^{32} +(5.19615 + 9.00000i) q^{33} +12.6677i q^{34} -6.00000 q^{36} +(-24.2232 + 13.9853i) q^{37} +(-5.10911 + 8.84924i) q^{38} +(-18.4706 + 31.9920i) q^{39} -54.8313i q^{41} +(-4.26858 + 16.6066i) q^{42} +1.48528i q^{43} +(6.00000 + 10.3923i) q^{44} +(-26.4853 + 45.8739i) q^{46} +(-21.5020 - 37.2426i) q^{47} -6.92820 q^{48} +(42.9264 + 23.6289i) q^{49} +(-7.75736 - 13.4361i) q^{51} +(-21.3280 + 36.9411i) q^{52} +(-74.0069 - 42.7279i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-4.92893 + 19.1757i) q^{56} -12.5147i q^{57} +(-41.5692 + 24.0000i) q^{58} +(35.6985 + 20.6105i) q^{59} +(-1.02944 + 0.594346i) q^{61} -62.4259 q^{62} +(-5.64191 - 20.2279i) q^{63} -8.00000 q^{64} +(-12.7279 - 7.34847i) q^{66} +(-3.80789 - 2.19848i) q^{67} +(-8.95743 - 15.5147i) q^{68} -64.8754i q^{69} +137.397 q^{71} +(7.34847 - 4.24264i) q^{72} +(39.4635 - 68.3528i) q^{73} +(19.7782 - 34.2568i) q^{74} -14.4508i q^{76} +(-29.3939 + 30.0000i) q^{77} -52.2426i q^{78} +(49.1690 + 85.1633i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(38.7716 + 67.1543i) q^{82} +110.401 q^{83} +(-6.51472 - 23.3572i) q^{84} +(-1.05025 - 1.81909i) q^{86} +(29.3939 - 50.9117i) q^{87} +(-14.6969 - 8.48528i) q^{88} +(18.0000 - 10.3923i) q^{89} +(-144.595 - 37.1670i) q^{91} -74.9117i q^{92} +(66.2127 - 38.2279i) q^{93} +(52.6690 + 30.4085i) q^{94} +(8.48528 - 4.89898i) q^{96} +10.9867 q^{97} +(-69.2820 + 1.41421i) q^{98} +18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 12 q^{9} + O(q^{10}) $	$ 8 q + 8 q^{4} - 12 q^{9} - 24 q^{11} - 48 q^{14} - 16 q^{16} + 84 q^{19} + 192 q^{26} + 204 q^{31} - 48 q^{36} - 12 q^{39} + 48 q^{44} - 144 q^{46} + 4 q^{49} - 96 q^{51} - 96 q^{56} + 48 q^{59} - 144 q^{61} - 64 q^{64} + 624 q^{71} + 96 q^{74} + 20 q^{79} - 36 q^{81} - 120 q^{84} - 48 q^{86} + 144 q^{89} - 444 q^{91} + 48 q^{94} + 144 q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	6.77962	+	1.74264i	0.968517	+	0.248949i
$7$	6.77962	+	1.74264i	0.968517	+	0.248949i
$8$			2.82843i			0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.272727	+	0.472377i	−0.969559	−	0.244857i	$-0.921259\pi$
$11$	−3.00000	+	5.19615i	−0.272727	+	0.472377i	0.696832	+	0.717234i	$0.254592\pi$
$12$	−1.73205	−	3.00000i	−0.144338	−	0.250000i
$13$	−21.3280			−1.64061			−0.820306	−	0.571924i	$-0.806197\pi$
$13$	−21.3280			−1.64061			−0.820306	+	0.571924i	$0.806197\pi$
$14$	−9.53553	+	2.65962i	−0.681110	+	0.189973i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	4.47871	−	7.75736i	0.263454	−	0.456315i	−0.703704	−	0.710494i	$-0.748472\pi$
$17$	4.47871	−	7.75736i	0.263454	−	0.456315i	0.967157	+	0.254178i	$0.0818050\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	6.25736	−	3.61269i	0.329335	−	0.190141i	−0.326211	−	0.945297i	$-0.605772\pi$
$19$	6.25736	−	3.61269i	0.329335	−	0.190141i	0.655546	+	0.755156i	$0.272439\pi$
$20$		0			0
$21$	8.48528	−	8.66025i	0.404061	−	0.412393i
$22$		−	8.48528i		−	0.385695i
$23$	32.4377	−	18.7279i	1.41034	−	0.814257i	0.414916	−	0.909860i	$-0.363811\pi$
$23$	32.4377	−	18.7279i	1.41034	−	0.814257i	0.995420	+	0.0956024i	$0.0304777\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	26.1213	−	15.0812i	1.00467	−	0.580044i
$27$	−5.19615			−0.192450
$28$	9.79796	−	10.0000i	0.349927	−	0.357143i
$29$	33.9411			1.17038			0.585192	−	0.810895i	$-0.301019\pi$
$29$	33.9411			1.17038			0.585192	+	0.810895i	$0.301019\pi$
$30$		0			0
$31$	38.2279	+	22.0709i	1.23316	+	0.711965i	0.967687	−	0.252154i	$-0.0811390\pi$
$31$	38.2279	+	22.0709i	1.23316	+	0.711965i	0.265472	+	0.964119i	$0.414472\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	5.19615	+	9.00000i	0.157459	+	0.272727i
$34$			12.6677i			0.372580i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−24.2232	+	13.9853i	−0.654682	+	0.377981i	−0.790248	−	0.612788i	$-0.790048\pi$
$37$	−24.2232	+	13.9853i	−0.654682	+	0.377981i	0.135566	+	0.990768i	$0.456715\pi$
$38$	−5.10911	+	8.84924i	−0.134450	+	0.232875i
$39$	−18.4706	+	31.9920i	−0.473604	+	0.820306i
$40$		0			0
$41$		−	54.8313i		−	1.33735i	−0.743556	−	0.668674i	$-0.766862\pi$
$41$		−	54.8313i		−	1.33735i	0.743556	−	0.668674i	$-0.233138\pi$
$42$	−4.26858	+	16.6066i	−0.101633	+	0.395395i
$43$			1.48528i			0.0345414i	0.999851	+	0.0172707i	$0.00549771\pi$
$43$			1.48528i			0.0345414i	−0.999851	+	0.0172707i	$0.994502\pi$
$44$	6.00000	+	10.3923i	0.136364	+	0.236189i
$45$		0			0
$46$	−26.4853	+	45.8739i	−0.575767	+	0.997258i
$47$	−21.5020	−	37.2426i	−0.457490	−	0.792397i	0.541337	−	0.840806i	$-0.317918\pi$
$47$	−21.5020	−	37.2426i	−0.457490	−	0.792397i	−0.998828	+	0.0484090i	$0.984585\pi$
$48$	−6.92820			−0.144338
$49$	42.9264	+	23.6289i	0.876049	+	0.482222i
$50$		0			0
$51$	−7.75736	−	13.4361i	−0.152105	−	0.263454i
$52$	−21.3280	+	36.9411i	−0.410153	+	0.710406i
$53$	−74.0069	−	42.7279i	−1.39636	−	0.806187i	−0.402348	−	0.915487i	$-0.631806\pi$
$53$	−74.0069	−	42.7279i	−1.39636	−	0.806187i	−0.994009	+	0.109299i	$0.965139\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	−4.92893	+	19.1757i	−0.0880166	+	0.342422i
$57$		−	12.5147i		−	0.219556i
$58$	−41.5692	+	24.0000i	−0.716711	+	0.413793i
$59$	35.6985	+	20.6105i	0.605059	+	0.349331i	0.771029	−	0.636800i	$-0.219742\pi$
$59$	35.6985	+	20.6105i	0.605059	+	0.349331i	−0.165970	+	0.986131i	$0.553076\pi$
$60$		0			0
$61$	−1.02944	+	0.594346i	−0.0168760	+	0.00974337i	−0.508414	−	0.861113i	$-0.669768\pi$
$61$	−1.02944	+	0.594346i	−0.0168760	+	0.00974337i	0.491538	+	0.870856i	$0.336435\pi$
$62$	−62.4259			−1.00687
$63$	−5.64191	−	20.2279i	−0.0895542	−	0.321078i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−12.7279	−	7.34847i	−0.192847	−	0.111340i
$67$	−3.80789	−	2.19848i	−0.0568341	−	0.0328132i	0.471314	−	0.881966i	$-0.343780\pi$
$67$	−3.80789	−	2.19848i	−0.0568341	−	0.0328132i	−0.528148	+	0.849152i	$0.677113\pi$
$68$	−8.95743	−	15.5147i	−0.131727	−	0.228158i
$69$		−	64.8754i		−	0.940224i
$70$		0			0
$71$	137.397			1.93517			0.967584	−	0.252548i	$-0.0812687\pi$
$71$	137.397			1.93517			0.967584	+	0.252548i	$0.0812687\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	39.4635	−	68.3528i	0.540596	−	0.936340i	−0.458274	−	0.888811i	$-0.651532\pi$
$73$	39.4635	−	68.3528i	0.540596	−	0.936340i	0.998870	−	0.0475288i	$-0.0151346\pi$
$74$	19.7782	−	34.2568i	0.267273	−	0.462930i
$75$		0			0
$76$		−	14.4508i		−	0.190141i
$77$	−29.3939	+	30.0000i	−0.381739	+	0.389610i
$78$		−	52.2426i		−	0.669777i
$79$	49.1690	+	85.1633i	0.622393	+	1.07802i	0.989039	+	0.147656i	$0.0471728\pi$
$79$	49.1690	+	85.1633i	0.622393	+	1.07802i	−0.366646	+	0.930361i	$0.619494\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	38.7716	+	67.1543i	0.472824	+	0.818955i
$83$	110.401			1.33013			0.665067	−	0.746784i	$-0.268403\pi$
$83$	110.401			1.33013			0.665067	+	0.746784i	$0.268403\pi$
$84$	−6.51472	−	23.3572i	−0.0775562	−	0.278062i
$85$		0			0
$86$	−1.05025	−	1.81909i	−0.0122122	−	0.0211522i
$87$	29.3939	−	50.9117i	0.337861	−	0.585192i
$88$	−14.6969	−	8.48528i	−0.167011	−	0.0964237i
$89$	18.0000	−	10.3923i	0.202247	−	0.116767i	−0.395456	−	0.918485i	$-0.629413\pi$
$89$	18.0000	−	10.3923i	0.202247	−	0.116767i	0.597703	+	0.801717i	$0.296080\pi$
$90$		0			0
$91$	−144.595	−	37.1670i	−1.58896	−	0.408428i
$92$		−	74.9117i		−	0.814257i
$93$	66.2127	−	38.2279i	0.711965	−	0.411053i
$94$	52.6690	+	30.4085i	0.560309	+	0.323495i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$	10.9867			0.113264			0.0566322	−	0.998395i	$-0.481964\pi$
$97$	10.9867			0.113264			0.0566322	+	0.998395i	$0.481964\pi$
$98$	−69.2820	+	1.41421i	−0.706960	+	0.0144308i
$99$	18.0000			0.181818
$100$		0			0
$101$	−92.8234	−	53.5916i	−0.919043	−	0.530610i	−0.0357136	−	0.999362i	$-0.511370\pi$
$101$	−92.8234	−	53.5916i	−0.919043	−	0.530610i	−0.883330	+	0.468752i	$0.844704\pi$
$102$	19.0016	+	10.9706i	0.186290	+	0.107555i
$103$	−52.6025	−	91.1102i	−0.510704	−	0.884565i	−0.999923	−	0.0124040i	$-0.996052\pi$
$103$	−52.6025	−	91.1102i	−0.510704	−	0.884565i	0.489219	−	0.872161i	$-0.337282\pi$
$104$		−	60.3246i		−	0.580044i
$105$		0			0
$106$	120.853			1.14012
$107$	102.662	−	59.2721i	0.959460	−	0.553945i	0.0634534	−	0.997985i	$-0.479789\pi$
$107$	102.662	−	59.2721i	0.959460	−	0.553945i	0.896007	+	0.444040i	$0.146455\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	55.5294	−	96.1798i	0.509444	−	0.882384i	−0.490496	−	0.871444i	$-0.663184\pi$
$109$	55.5294	−	96.1798i	0.509444	−	0.882384i	0.999940	−	0.0109400i	$-0.00348237\pi$
$110$		0			0
$111$			48.4464i			0.436454i
$112$	−7.52255	−	26.9706i	−0.0671656	−	0.240809i
$113$		−	101.397i		−	0.897318i	−0.893703	−	0.448659i	$-0.851902\pi$
$113$		−	101.397i		−	0.897318i	0.893703	−	0.448659i	$-0.148098\pi$
$114$	8.84924	+	15.3273i	0.0776249	+	0.134450i
$115$		0			0
$116$	33.9411	−	58.7878i	0.292596	−	0.506791i
$117$	31.9920	+	55.4117i	0.273435	+	0.473604i
$118$	−58.2954			−0.494029
$119$	43.8823	−	44.7871i	0.368758	−	0.376362i
$120$		0			0
$121$	42.5000	+	73.6122i	0.351240	+	0.608365i
$122$	0.840532	−	1.45584i	0.00688961	−	0.0119331i
$123$	−82.2469	−	47.4853i	−0.668674	−	0.386059i
$124$	76.4558	−	44.1418i	0.616579	−	0.355982i
$125$		0			0
$126$	21.2132	+	20.7846i	0.168359	+	0.164957i
$127$			82.5736i			0.650186i	0.945682	+	0.325093i	$0.105396\pi$
$127$			82.5736i			0.650186i	−0.945682	+	0.325093i	$0.894604\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	2.22792	+	1.28629i	0.0172707	+	0.00997125i
$130$		0			0
$131$	−52.4558	+	30.2854i	−0.400426	+	0.231186i	−0.686668	−	0.726971i	$-0.740927\pi$
$131$	−52.4558	+	30.2854i	−0.400426	+	0.231186i	0.286242	+	0.958157i	$0.407594\pi$
$132$	20.7846			0.157459
$133$	48.7181	−	13.5883i	0.366302	−	0.102168i
$134$	6.21825			0.0464049
$135$		0			0
$136$	21.9411	+	12.6677i	0.161332	+	0.0931450i
$137$	−58.0492	−	33.5147i	−0.423717	−	0.244633i	0.272949	−	0.962028i	$-0.412001\pi$
$137$	−58.0492	−	33.5147i	−0.423717	−	0.244633i	−0.696666	+	0.717395i	$0.745334\pi$
$138$	45.8739	+	79.4558i	0.332419	+	0.575767i
$139$		−	91.5525i		−	0.658651i	−0.944216	−	0.329326i	$-0.893179\pi$
$139$		−	91.5525i		−	0.658651i	0.944216	−	0.329326i	$-0.106821\pi$
$140$		0			0
$141$	−74.4853			−0.528264
$142$	−168.276	+	97.1543i	−1.18504	+	0.684185i
$143$	63.9839	−	110.823i	0.447440	−	0.774989i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			111.620i			0.764518i
$147$	72.6187	−	43.9264i	0.494005	−	0.298819i
$148$			55.9411i			0.377981i
$149$	40.5442	+	70.2245i	0.272108	+	0.471306i	0.969402	−	0.245480i	$-0.0789457\pi$
$149$	40.5442	+	70.2245i	0.272108	+	0.471306i	−0.697293	+	0.716786i	$0.745612\pi$
$150$		0			0
$151$	25.6030	−	44.3457i	0.169556	−	0.293680i	−0.768708	−	0.639600i	$-0.779100\pi$
$151$	25.6030	−	44.3457i	0.169556	−	0.293680i	0.938264	+	0.345920i	$0.112433\pi$
$152$	10.2182	+	17.6985i	0.0672252	+	0.116437i
$153$	−26.8723			−0.175636
$154$	14.7868	−	57.5270i	0.0960182	−	0.373552i
$155$		0			0
$156$	36.9411	+	63.9839i	0.236802	+	0.410153i
$157$	−93.5307	+	162.000i	−0.595737	+	1.03185i	0.397705	+	0.917513i	$0.369807\pi$
$157$	−93.5307	+	162.000i	−0.595737	+	1.03185i	−0.993442	+	0.114334i	$0.963527\pi$
$158$	−120.439	−	69.5355i	−0.762273	−	0.440098i
$159$	−128.184	+	74.0069i	−0.806187	+	0.465452i
$160$		0			0
$161$	252.551	−	70.4409i	1.56864	−	0.437521i
$162$		−	12.7279i		−	0.0785674i
$163$	−72.6951	+	41.9706i	−0.445982	+	0.257488i	−0.706132	−	0.708080i	$-0.749561\pi$
$163$	−72.6951	+	41.9706i	−0.445982	+	0.257488i	0.260149	+	0.965568i	$0.416228\pi$
$164$	−94.9706	−	54.8313i	−0.579089	−	0.334337i
$165$		0			0
$166$	−135.213	+	78.0654i	−0.814537	+	0.470273i
$167$	127.620			0.764190			0.382095	−	0.924123i	$-0.375203\pi$
$167$	127.620			0.764190			0.382095	+	0.924123i	$0.375203\pi$
$168$	24.4949	+	24.0000i	0.145803	+	0.142857i
$169$	285.882			1.69161
$170$		0			0
$171$	−18.7721	−	10.8381i	−0.109778	−	0.0633805i
$172$	2.57258	+	1.48528i	0.0149569	+	0.00863536i
$173$	71.4853	+	123.816i	0.413210	+	0.715701i	0.995239	−	0.0974675i	$-0.0310742\pi$
$173$	71.4853	+	123.816i	0.413210	+	0.715701i	−0.582029	+	0.813168i	$0.697741\pi$
$174$			83.1384i			0.477807i
$175$		0			0
$176$	24.0000			0.136364
$177$	61.8316	−	35.6985i	0.349331	−	0.201686i
$178$	−14.6969	+	25.4558i	−0.0825671	+	0.143010i
$179$	84.6396	−	146.600i	0.472847	−	0.818995i	−0.526670	−	0.850070i	$-0.676560\pi$
$179$	84.6396	−	146.600i	0.472847	−	0.818995i	0.999517	+	0.0310748i	$0.00989300\pi$
$180$		0			0
$181$		−	209.969i		−	1.16005i	−0.814600	−	0.580024i	$-0.803043\pi$
$181$		−	209.969i		−	1.16005i	0.814600	−	0.580024i	$-0.196957\pi$
$182$	203.374	−	56.7244i	1.11744	−	0.311672i
$183$			2.05887i			0.0112507i
$184$	52.9706	+	91.7477i	0.287883	+	0.498629i
$185$		0			0
$186$	−54.0624	+	93.6389i	−0.290658	+	0.503435i
$187$	26.8723	+	46.5442i	0.143702	+	0.248899i
$188$	−86.0082			−0.457490
$189$	−35.2279	−	9.05503i	−0.186391	−	0.0479102i
$190$		0			0
$191$	−33.3015	−	57.6799i	−0.174353	−	0.301989i	0.765584	−	0.643336i	$-0.222450\pi$
$191$	−33.3015	−	57.6799i	−0.174353	−	0.301989i	−0.939937	+	0.341347i	$0.889117\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	−8.48180	−	4.89697i	−0.0439472	−	0.0253729i	0.477865	−	0.878433i	$-0.341411\pi$
$193$	−8.48180	−	4.89697i	−0.0439472	−	0.0253729i	−0.521813	+	0.853060i	$0.674744\pi$
$194$	−13.4558	+	7.76874i	−0.0693600	+	0.0400450i
$195$		0			0
$196$	83.8528	−	50.7218i	0.427820	−	0.258785i
$197$		−	267.161i		−	1.35615i	−0.734993	−	0.678075i	$-0.762815\pi$
$197$		−	267.161i		−	1.35615i	0.734993	−	0.678075i	$-0.237185\pi$
$198$	−22.0454	+	12.7279i	−0.111340	+	0.0642824i
$199$	113.397	+	65.4698i	0.569834	+	0.328994i	0.757083	−	0.653319i	$-0.226624\pi$
$199$	113.397	+	65.4698i	0.569834	+	0.328994i	−0.187249	+	0.982312i	$0.559957\pi$
$200$		0			0
$201$	−6.59545	+	3.80789i	−0.0328132	+	0.0189447i
$202$	151.580			0.750396
$203$	230.108	+	59.1472i	1.13354	+	0.291365i
$204$	−31.0294			−0.152105
$205$		0			0
$206$	128.849	+	74.3911i	0.625482	+	0.361122i
$207$	−97.3131	−	56.1838i	−0.470112	−	0.271419i
$208$	42.6559	+	73.8823i	0.205077	+	0.355203i
$209$			43.3523i			0.207427i
$210$		0			0
$211$	−23.0883			−0.109423			−0.0547116	−	0.998502i	$-0.517424\pi$
$211$	−23.0883			−0.109423			−0.0547116	+	0.998502i	$0.517424\pi$
$212$	−148.014	+	85.4558i	−0.698179	+	0.403094i
$213$	118.989	−	206.095i	0.558635	−	0.967584i
$214$	−83.8234	+	145.186i	−0.391698	+	0.678441i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	220.709	+	216.250i	1.01709	+	0.996543i
$218$			157.061i			0.720463i
$219$	−68.3528	−	118.391i	−0.312113	−	0.540596i
$220$		0			0
$221$	−95.5219	+	165.449i	−0.432226	+	0.748637i
$222$	−34.2568	−	59.3345i	−0.154310	−	0.267273i
$223$	228.631			1.02525			0.512625	−	0.858613i	$-0.328673\pi$
$223$	228.631			1.02525			0.512625	+	0.858613i	$0.328673\pi$
$224$	28.2843	+	27.7128i	0.126269	+	0.123718i
$225$		0			0
$226$	71.6985	+	124.185i	0.317250	+	0.549493i
$227$	−32.8070	+	56.8234i	−0.144524	+	0.250323i	−0.929195	−	0.369589i	$-0.879498\pi$
$227$	−32.8070	+	56.8234i	−0.144524	+	0.250323i	0.784671	+	0.619912i	$0.212832\pi$
$228$	−21.6761	−	12.5147i	−0.0950707	−	0.0548891i
$229$	−80.9558	+	46.7399i	−0.353519	+	0.204104i	−0.666234	−	0.745743i	$-0.732095\pi$
$229$	−80.9558	+	46.7399i	−0.353519	+	0.204104i	0.312715	+	0.949847i	$0.398761\pi$
$230$		0			0
$231$	19.5442	+	70.0716i	0.0846067	+	0.303340i
$232$			96.0000i			0.413793i
$233$	205.694	−	118.757i	0.882806	−	0.509688i	0.0112234	−	0.999937i	$-0.496427\pi$
$233$	205.694	−	118.757i	0.882806	−	0.509688i	0.871583	+	0.490249i	$0.163094\pi$
$234$	−78.3640	−	45.2435i	−0.334889	−	0.193348i
$235$		0			0
$236$	71.3970	−	41.2211i	0.302530	−	0.174666i
$237$	170.327			0.718678
$238$	−22.0753	+	85.8823i	−0.0927533	+	0.360850i
$239$	−366.853			−1.53495			−0.767475	−	0.641079i	$-0.778487\pi$
$239$	−366.853			−1.53495			−0.767475	+	0.641079i	$0.778487\pi$
$240$		0			0
$241$	−364.617	−	210.512i	−1.51293	−	0.873493i	−0.999885	−	0.0151343i	$-0.995182\pi$
$241$	−364.617	−	210.512i	−1.51293	−	0.873493i	−0.513049	−	0.858359i	$-0.671484\pi$
$242$	−104.103	−	60.1041i	−0.430179	−	0.248364i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$			2.37738i			0.00974337i
$245$		0			0
$246$	134.309			0.545970
$247$	−133.457	+	77.0513i	−0.540311	+	0.311949i
$248$	−62.4259	+	108.125i	−0.251717	+	0.435987i
$249$	95.6102	−	165.602i	0.383977	−	0.665067i
$250$		0			0
$251$		−	146.621i		−	0.584148i	−0.956396	−	0.292074i	$-0.905655\pi$
$251$		−	146.621i		−	0.584148i	0.956396	−	0.292074i	$-0.0943454\pi$
$252$	−40.6777	−	10.4558i	−0.161419	−	0.0414914i
$253$			224.735i			0.888281i
$254$	−58.3883	−	101.132i	−0.229875	−	0.398156i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	12.5446	+	21.7279i	0.0488118	+	0.0845444i	0.889399	−	0.457132i	$-0.151123\pi$
$257$	12.5446	+	21.7279i	0.0488118	+	0.0845444i	−0.840587	+	0.541676i	$0.817790\pi$
$258$	−3.63818			−0.0141015
$259$	−188.595	+	52.6025i	−0.728168	+	0.203098i
$260$		0			0
$261$	−50.9117	−	88.1816i	−0.195064	−	0.337861i
$262$	42.8300	−	74.1838i	0.163473	−	0.283144i
$263$	−78.5279	−	45.3381i	−0.298585	−	0.172388i	0.343222	−	0.939254i	$-0.388482\pi$
$263$	−78.5279	−	45.3381i	−0.298585	−	0.172388i	−0.641807	+	0.766866i	$0.721815\pi$
$264$	−25.4558	+	14.6969i	−0.0964237	+	0.0556702i
$265$		0			0
$266$	−50.0589	+	51.0911i	−0.188191	+	0.192072i
$267$		−	36.0000i		−	0.134831i
$268$	−7.61577	+	4.39697i	−0.0284171	+	0.0164066i
$269$	59.2355	+	34.1996i	0.220206	+	0.127136i	0.606046	−	0.795430i	$-0.292755\pi$
$269$	59.2355	+	34.1996i	0.220206	+	0.127136i	−0.385839	+	0.922566i	$0.626088\pi$
$270$		0			0
$271$	−106.971	+	61.7595i	−0.394725	+	0.227895i	−0.684206	−	0.729289i	$-0.739851\pi$
$271$	−106.971	+	61.7595i	−0.394725	+	0.227895i	0.289480	+	0.957184i	$0.406518\pi$
$272$	−35.8297			−0.131727
$273$	−180.974	+	184.706i	−0.662908	+	0.676577i
$274$	94.7939			0.345963
$275$		0			0
$276$	−112.368	−	64.8754i	−0.407129	−	0.235056i
$277$	236.323	+	136.441i	0.853151	+	0.492567i	0.861713	−	0.507396i	$-0.169392\pi$
$277$	236.323	+	136.441i	0.853151	+	0.492567i	−0.00856145	+	0.999963i	$0.502725\pi$
$278$	64.7374	+	112.128i	0.232868	+	0.403340i
$279$		−	132.425i		−	0.474643i
$280$		0			0
$281$	133.103			0.473675			0.236837	−	0.971549i	$-0.423889\pi$
$281$	133.103			0.473675			0.236837	+	0.971549i	$0.423889\pi$
$282$	91.2255	−	52.6690i	0.323495	−	0.186770i
$283$	−64.3787	+	111.507i	−0.227486	+	0.394018i	−0.957063	−	0.289882i	$-0.906384\pi$
$283$	−64.3787	+	111.507i	−0.227486	+	0.394018i	0.729576	+	0.683900i	$0.239717\pi$
$284$	137.397	−	237.979i	0.483792	−	0.837953i
$285$		0			0
$286$			180.974i			0.632776i
$287$	95.5512	−	371.735i	0.332931	−	1.29524i
$288$		−	16.9706i		−	0.0589256i
$289$	104.382	+	180.795i	0.361184	+	0.625589i
$290$		0			0
$291$	9.51472	−	16.4800i	0.0326966	−	0.0566322i
$292$	−78.9270	−	136.706i	−0.270298	−	0.468170i
$293$	−308.984			−1.05455			−0.527276	−	0.849694i	$-0.676787\pi$
$293$	−308.984			−1.05455			−0.527276	+	0.849694i	$0.676787\pi$
$294$	−57.8787	+	105.148i	−0.196866	+	0.357646i
$295$		0			0
$296$	−39.5563	−	68.5136i	−0.133636	−	0.231465i
$297$	15.5885	−	27.0000i	0.0524864	−	0.0909091i
$298$	−99.3125	−	57.3381i	−0.333263	−	0.192410i
$299$	−691.831	+	399.429i	−2.31381	+	1.33588i
$300$		0			0
$301$	−2.58831	+	10.0696i	−0.00859904	+	0.0334539i
$302$			72.4163i			0.239789i
$303$	−160.775	+	92.8234i	−0.530610	+	0.306348i
$304$	−25.0294	−	14.4508i	−0.0823337	−	0.0475354i
$305$		0			0
$306$	32.9117	−	19.0016i	0.107555	−	0.0620966i
$307$	−606.090			−1.97423			−0.987117	−	0.160003i	$-0.948850\pi$
$307$	−606.090			−1.97423			−0.987117	+	0.160003i	$0.948850\pi$
$308$	22.5676	+	80.9117i	0.0732716	+	0.262700i
$309$	−182.220			−0.589710
$310$		0			0
$311$	−176.044	−	101.639i	−0.566057	−	0.326813i	0.189516	−	0.981878i	$-0.439308\pi$
$311$	−176.044	−	101.639i	−0.566057	−	0.326813i	−0.755573	+	0.655064i	$0.772641\pi$
$312$	−90.4869	−	52.2426i	−0.290022	−	0.167444i
$313$	202.820	+	351.294i	0.647986	+	1.12234i	0.983603	+	0.180346i	$0.0577219\pi$
$313$	202.820	+	351.294i	0.647986	+	1.12234i	−0.335617	+	0.941999i	$0.608945\pi$
$314$		−	264.545i		−	0.842500i
$315$		0			0
$316$	196.676			0.622393
$317$	−22.5676	+	13.0294i	−0.0711913	+	0.0411023i	−0.535173	−	0.844742i	$-0.679754\pi$
$317$	−22.5676	+	13.0294i	−0.0711913	+	0.0411023i	0.463982	+	0.885845i	$0.346420\pi$
$318$	104.662	−	181.279i	0.329125	−	0.570060i
$319$	−101.823	+	176.363i	−0.319196	+	0.552863i
$320$		0			0
$321$		−	205.325i		−	0.639640i
$322$	−259.502	+	264.853i	−0.805906	+	0.822524i
$323$		−	64.7208i		−	0.200374i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	59.3553	−	102.806i	0.182072	−	0.315357i
$327$	−96.1798	−	166.588i	−0.294128	−	0.509444i
$328$	155.086			0.472824
$329$	−80.8751	−	289.961i	−0.245821	−	0.881341i
$330$		0			0
$331$	54.3162	+	94.0785i	0.164097	+	0.284225i	0.936334	−	0.351110i	$-0.114196\pi$
$331$	54.3162	+	94.0785i	0.164097	+	0.284225i	−0.772237	+	0.635335i	$0.780862\pi$
$332$	110.401	−	191.220i	0.332533	−	0.575965i
$333$	72.6697	+	41.9558i	0.218227	+	0.125994i
$334$	−156.302	+	90.2407i	−0.467969	+	0.270182i
$335$		0			0
$336$	−46.9706	−	12.0734i	−0.139793	−	0.0359326i
$337$			441.735i			1.31079i	0.755288	+	0.655393i	$0.227497\pi$
$337$			441.735i			1.31079i	−0.755288	+	0.655393i	$0.772503\pi$
$338$	−350.133	+	202.149i	−1.03590	+	0.598075i
$339$	−152.095	−	87.8124i	−0.448659	−	0.259033i
$340$		0			0
$341$	−229.368	+	132.425i	−0.672632	+	0.388344i
$342$	30.6547			0.0896336
$343$	249.848	+	235.000i	0.728420	+	0.685131i
$344$	−4.20101			−0.0122122
$345$		0			0
$346$	−175.103	−	101.096i	−0.506077	−	0.292184i
$347$	−29.6102	−	17.0955i	−0.0853320	−	0.0492664i	0.456727	−	0.889607i	$-0.349022\pi$
$347$	−29.6102	−	17.0955i	−0.0853320	−	0.0492664i	−0.542059	+	0.840341i	$0.682355\pi$
$348$	−58.7878	−	101.823i	−0.168930	−	0.292596i
$349$		−	221.787i		−	0.635493i	−0.948176	−	0.317746i	$-0.897074\pi$
$349$		−	221.787i		−	0.635493i	0.948176	−	0.317746i	$-0.102926\pi$
$350$		0			0
$351$	110.823			0.315736
$352$	−29.3939	+	16.9706i	−0.0835053	+	0.0482118i
$353$	223.693	−	387.448i	0.633692	−	1.09759i	−0.353099	−	0.935586i	$-0.614872\pi$
$353$	223.693	−	387.448i	0.633692	−	1.09759i	0.986791	−	0.162000i	$-0.0517945\pi$
$354$	−50.4853	+	87.4431i	−0.142614	+	0.247014i
$355$		0			0
$356$		−	41.5692i		−	0.116767i
$357$	−29.1776	−	104.610i	−0.0817299	−	0.293026i
$358$			239.397i			0.668707i
$359$	145.882	+	252.675i	0.406357	+	0.703831i	0.994478	−	0.104941i	$-0.0334655\pi$
$359$	145.882	+	252.675i	0.406357	+	0.703831i	−0.588121	+	0.808773i	$0.700132\pi$
$360$		0			0
$361$	−154.397	+	267.423i	−0.427692	+	0.740785i
$362$	148.470	+	257.158i	0.410139	+	0.710381i
$363$	147.224			0.405577
$364$	−208.971	+	213.280i	−0.574095	+	0.585933i
$365$		0			0
$366$	−1.45584	−	2.52160i	−0.00397772	−	0.00688961i
$367$	209.676	−	363.169i	0.571324	−	0.989561i	−0.425107	−	0.905143i	$-0.639763\pi$
$367$	209.676	−	363.169i	0.571324	−	0.989561i	0.996430	−	0.0844183i	$-0.0269032\pi$
$368$	−129.751	−	74.9117i	−0.352584	−	0.203564i
$369$	−142.456	+	82.2469i	−0.386059	+	0.222891i
$370$		0			0
$371$	−427.279	−	418.646i	−1.15170	−	1.12843i
$372$		−	152.912i		−	0.411053i
$373$	−27.1775	+	15.6909i	−0.0728618	+	0.0420668i	−0.535988	−	0.844225i	$-0.680061\pi$
$373$	−27.1775	+	15.6909i	−0.0728618	+	0.0420668i	0.463127	+	0.886292i	$0.346728\pi$
$374$	−65.8234	−	38.0031i	−0.175998	−	0.101613i
$375$		0			0
$376$	105.338	−	60.8170i	0.280155	−	0.161747i
$377$	−723.895			−1.92015
$378$	49.5481	−	13.8198i	0.131080	−	0.0365603i
$379$	−206.779			−0.545590			−0.272795	−	0.962072i	$-0.587948\pi$
$379$	−206.779			−0.545590			−0.272795	+	0.962072i	$0.587948\pi$
$380$		0			0
$381$	123.860	+	71.5108i	0.325093	+	0.187692i
$382$	81.5717	+	47.0955i	0.213539	+	0.123287i
$383$	249.283	+	431.772i	0.650871	+	1.12734i	0.982912	+	0.184076i	$0.0589293\pi$
$383$	249.283	+	431.772i	0.650871	+	1.12734i	−0.332041	+	0.943265i	$0.607737\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	13.8507			0.0358827
$387$	3.85887	−	2.22792i	0.00997125	−	0.00575690i
$388$	10.9867	−	19.0294i	0.0283161	−	0.0490449i
$389$	−324.213	+	561.554i	−0.833453	+	1.44358i	0.0618308	+	0.998087i	$0.480306\pi$
$389$	−324.213	+	561.554i	−0.833453	+	1.44358i	−0.895284	+	0.445496i	$0.853027\pi$
$390$		0			0
$391$		−	335.508i		−	0.858077i
$392$	−66.8325	+	121.414i	−0.170491	+	0.309730i
$393$			104.912i			0.266951i
$394$	188.912	+	327.205i	0.479471	+	0.830469i
$395$		0			0
$396$	18.0000	−	31.1769i	0.0454545	−	0.0787296i
$397$	37.8757	+	65.6026i	0.0954047	+	0.165246i	0.909777	−	0.415096i	$-0.136252\pi$
$397$	37.8757	+	65.6026i	0.0954047	+	0.165246i	−0.814373	+	0.580342i	$0.802919\pi$
$398$	−185.176			−0.465268
$399$	21.8087	−	84.8450i	0.0546583	−	0.212644i
$400$		0			0
$401$	282.125	+	488.655i	0.703553	+	1.21859i	0.967211	+	0.253974i	$0.0817377\pi$
$401$	282.125	+	488.655i	0.703553	+	1.21859i	−0.263658	+	0.964616i	$0.584929\pi$
$402$	5.38517	−	9.32738i	0.0133959	−	0.0232024i
$403$	−815.324	−	470.727i	−2.02314	−	1.16806i
$404$	−185.647	+	107.183i	−0.459522	+	0.265305i
$405$		0			0
$406$	−323.647	+	90.2706i	−0.797159	+	0.222341i
$407$		−	167.823i		−	0.412342i
$408$	38.0031	−	21.9411i	0.0931450	−	0.0537773i
$409$	309.559	+	178.724i	0.756868	+	0.436978i	0.828170	−	0.560477i	$-0.189382\pi$
$409$	309.559	+	178.724i	0.756868	+	0.436978i	−0.0713023	+	0.997455i	$0.522716\pi$
$410$		0			0
$411$	−100.544	+	58.0492i	−0.244633	+	0.141239i
$412$	−210.410			−0.510704
$413$	206.105	+	201.941i	0.499044	+	0.488962i
$414$	158.912			0.383845
$415$		0			0
$416$	−104.485	−	60.3246i	−0.251167	−	0.145011i
$417$	−137.329	−	79.2868i	−0.329326	−	0.190136i
$418$	−30.6547	−	53.0955i	−0.0733365	−	0.127023i
$419$			502.175i			1.19851i	0.800559	+	0.599254i	$0.204536\pi$
$419$			502.175i			1.19851i	−0.800559	+	0.599254i	$0.795464\pi$
$420$		0			0
$421$	33.7939			0.0802706			0.0401353	−	0.999194i	$-0.487221\pi$
$421$	33.7939			0.0802706			0.0401353	+	0.999194i	$0.487221\pi$
$422$	28.2773	−	16.3259i	0.0670078	−	0.0386870i
$423$	−64.5061	+	111.728i	−0.152497	+	0.264132i
$424$	120.853	−	209.323i	0.285030	−	0.493687i
$425$		0			0
$426$			336.552i			0.790029i
$427$	−8.01492	+	2.23550i	−0.0187703	+	0.00523536i
$428$		−	237.088i		−	0.553945i
$429$	−110.823	−	191.952i	−0.258330	−	0.447440i
$430$		0			0
$431$	−251.860	+	436.234i	−0.584362	+	1.01214i	0.410593	+	0.911819i	$0.365322\pi$
$431$	−251.860	+	436.234i	−0.584362	+	1.01214i	−0.994955	+	0.100326i	$0.968012\pi$
$432$	10.3923	+	18.0000i	0.0240563	+	0.0416667i
$433$	−837.548			−1.93429			−0.967145	−	0.254224i	$-0.918180\pi$
$433$	−837.548			−1.93429			−0.967145	+	0.254224i	$0.918180\pi$
$434$	−423.224	−	108.786i	−0.975170	−	0.250659i
$435$		0			0
$436$	−111.059	−	192.360i	−0.254722	−	0.441192i
$437$	135.316	−	234.375i	0.309648	−	0.536326i
$438$	167.430	+	96.6655i	0.382259	+	0.220697i
$439$	164.558	−	95.0079i	0.374848	−	0.216419i	−0.300726	−	0.953711i	$-0.597229\pi$
$439$	164.558	−	95.0079i	0.374848	−	0.216419i	0.675575	+	0.737292i	$0.263896\pi$
$440$		0			0
$441$	−3.00000	−	146.969i	−0.00680272	−	0.333264i
$442$		−	270.177i		−	0.611259i
$443$	146.753	−	84.7279i	0.331271	−	0.191259i	−0.325134	−	0.945668i	$-0.605409\pi$
$443$	146.753	−	84.7279i	0.331271	−	0.191259i	0.656405	+	0.754408i	$0.272076\pi$
$444$	83.9117	+	48.4464i	0.188990	+	0.109114i
$445$		0			0
$446$	−280.014	+	161.666i	−0.627835	+	0.362481i
$447$	140.449			0.314204
$448$	−54.2369	−	13.9411i	−0.121065	−	0.0311186i
$449$	−18.1035			−0.0403195			−0.0201598	−	0.999797i	$-0.506417\pi$
$449$	−18.1035			−0.0403195			−0.0201598	+	0.999797i	$0.506417\pi$
$450$		0			0
$451$	284.912	+	164.494i	0.631733	+	0.364731i
$452$	−175.625	−	101.397i	−0.388550	−	0.224330i
$453$	−44.3457	−	76.8091i	−0.0978935	−	0.169556i
$454$		−	92.7922i		−	0.204388i
$455$		0			0
$456$	35.3970			0.0776249
$457$	−284.769	+	164.412i	−0.623128	+	0.359763i	−0.778086	−	0.628158i	$-0.783809\pi$
$457$	−284.769	+	164.412i	−0.623128	+	0.359763i	0.154958	+	0.987921i	$0.450476\pi$
$458$	66.1002	−	114.489i	0.144324	−	0.249976i
$459$	−23.2721	+	40.3084i	−0.0507017	+	0.0878179i
$460$		0			0
$461$			794.331i			1.72306i	0.507706	+	0.861530i	$0.330494\pi$
$461$			794.331i			1.72306i	−0.507706	+	0.861530i	$0.669506\pi$
$462$	−73.4847	−	72.0000i	−0.159058	−	0.155844i
$463$			403.396i			0.871266i	0.900124	+	0.435633i	$0.143475\pi$
$463$			403.396i			0.871266i	−0.900124	+	0.435633i	$0.856525\pi$
$464$	−67.8823	−	117.576i	−0.146298	−	0.253395i
$465$		0			0
$466$	−167.948	+	290.895i	−0.360404	+	0.624238i
$467$	−1.41376	−	2.44870i	−0.00302732	−	0.00524347i	0.864508	−	0.502619i	$-0.167630\pi$
$467$	−1.41376	−	2.44870i	−0.00302732	−	0.00524347i	−0.867535	+	0.497376i	$0.834297\pi$
$468$	127.968			0.273435
$469$	−21.9848	−	21.5407i	−0.0468760	−	0.0459289i
$470$		0			0
$471$	162.000	+	280.592i	0.343949	+	0.595737i
$472$	−58.2954	+	100.971i	−0.123507	+	0.213921i
$473$	−7.71775	−	4.45584i	−0.0163166	−	0.00942039i
$474$	−208.607	+	120.439i	−0.440098	+	0.254091i
$475$		0			0
$476$	−33.6913	−	120.793i	−0.0707801	−	0.253768i
$477$			256.368i			0.537458i
$478$	449.301	−	259.404i	0.939960	−	0.542686i
$479$	−328.669	−	189.757i	−0.686157	−	0.396153i	0.116014	−	0.993248i	$-0.462988\pi$
$479$	−328.669	−	189.757i	−0.686157	−	0.396153i	−0.802171	+	0.597095i	$0.796322\pi$
$480$		0			0
$481$	516.632	−	298.278i	1.07408	−	0.620120i
$482$	595.418			1.23531
$483$	113.055	−	439.831i	0.234067	−	0.910622i
$484$	170.000			0.351240
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	−498.410	−	287.757i	−1.02343	−	0.590877i	−0.108333	−	0.994115i	$-0.534551\pi$
$487$	−498.410	−	287.757i	−1.02343	−	0.590877i	−0.915095	+	0.403238i	$0.867885\pi$
$488$	−1.68106	−	2.91169i	−0.00344480	−	0.00596657i
$489$			145.390i			0.297322i
$490$		0			0
$491$	238.441			0.485623			0.242811	−	0.970074i	$-0.421930\pi$
$491$	238.441			0.485623			0.242811	+	0.970074i	$0.421930\pi$
$492$	−164.494	+	94.9706i	−0.334337	+	0.193030i
$493$	152.013	−	263.294i	0.308342	−	0.534064i
$494$	108.967	−	188.736i	0.220581	−	0.382057i
$495$		0			0
$496$		−	176.567i		−	0.355982i
$497$	931.499	+	239.434i	1.87424	+	0.481758i
$498$			270.426i			0.543025i
$499$	−143.287	−	248.180i	−0.287148	−	0.497355i	0.685980	−	0.727620i	$-0.259374\pi$
$499$	−143.287	−	248.180i	−0.287148	−	0.497355i	−0.973128	+	0.230266i	$0.926040\pi$
$500$		0			0
$501$	110.522	−	191.429i	0.220603	−	0.382095i
$502$	103.677	+	179.574i	0.206528	+	0.357716i
$503$	−25.4374			−0.0505714			−0.0252857	−	0.999680i	$-0.508050\pi$
$503$	−25.4374			−0.0505714			−0.0252857	+	0.999680i	$0.508050\pi$
$504$	57.2132	−	15.9577i	0.113518	−	0.0316622i
$505$		0			0
$506$	−158.912	−	275.243i	−0.314055	−	0.543959i
$507$	247.581	−	428.823i	0.488326	−	0.845805i
$508$	143.022	+	82.5736i	0.281539	+	0.162546i
$509$	697.889	−	402.926i	1.37110	−	0.791603i	0.380031	−	0.924974i	$-0.375913\pi$
$509$	697.889	−	402.926i	1.37110	−	0.791603i	0.991066	+	0.133370i	$0.0425800\pi$
$510$		0			0
$511$	386.662	−	394.635i	0.756677	−	0.772280i
$512$		−	22.6274i		−	0.0441942i
$513$	−32.5142	+	18.7721i	−0.0633805	+	0.0365927i
$514$	−30.7279	−	17.7408i	−0.0597819	−	0.0345151i
$515$		0			0
$516$	4.45584	−	2.57258i	0.00863536	−	0.00498563i
$517$	258.025			0.499080
$518$	193.786	−	197.782i	0.374104	−	0.381818i
$519$	247.632			0.477134
$520$		0			0
$521$	−661.706	−	382.036i	−1.27007	−	0.733274i	−0.295068	−	0.955476i	$-0.595342\pi$
$521$	−661.706	−	382.036i	−1.27007	−	0.733274i	−0.975001	+	0.222202i	$0.928676\pi$
$522$	124.708	+	72.0000i	0.238904	+	0.137931i
$523$	88.3900	+	153.096i	0.169006	+	0.292726i	0.938071	−	0.346444i	$-0.112611\pi$
$523$	88.3900	+	153.096i	0.169006	+	0.292726i	−0.769065	+	0.639171i	$0.779278\pi$
$524$			121.142i			0.231186i
$525$		0			0
$526$	128.235			0.243794
$527$	342.424	−	197.698i	0.649761	−	0.375139i
$528$	20.7846	−	36.0000i	0.0393648	−	0.0681818i
$529$	436.970	−	756.854i	0.826030	−	1.43073i
$530$		0			0
$531$		−	123.663i		−	0.232887i
$532$	25.1825	−	97.9706i	0.0473355	−	0.184155i
$533$			1169.44i			2.19407i
$534$	25.4558	+	44.0908i	0.0476701	+	0.0825671i
$535$		0			0
$536$	6.21825	−	10.7703i	0.0116012	−	0.0200939i
$537$	−146.600	−	253.919i	−0.272998	−	0.472847i
$538$	−96.7312			−0.179798
$539$	−251.558	+	152.166i	−0.466713	+	0.282311i
$540$		0			0
$541$	−8.58831	−	14.8754i	−0.0158749	−	0.0274961i	0.857979	−	0.513685i	$-0.171720\pi$
$541$	−8.58831	−	14.8754i	−0.0158749	−	0.0274961i	−0.873854	+	0.486189i	$0.838387\pi$
$542$	87.3411	−	151.279i	0.161146	−	0.279113i
$543$	−314.953	−	181.838i	−0.580024	−	0.334877i
$544$	43.8823	−	25.3354i	0.0806659	−	0.0465725i
$545$		0			0
$546$	91.0402	−	354.185i	0.166740	−	0.648691i
$547$			212.676i			0.388805i	0.980922	+	0.194402i	$0.0622767\pi$
$547$			212.676i			0.388805i	−0.980922	+	0.194402i	$0.937723\pi$
$548$	−116.098	+	67.0294i	−0.211858	+	0.122316i
$549$	3.08831	+	1.78304i	0.00562534	+	0.00324779i
$550$		0			0
$551$	212.382	−	122.619i	0.385448	−	0.222538i
$552$	183.495			0.332419
$553$	184.938	+	663.058i	0.334427	+	1.19902i
$554$	−385.914			−0.696595
$555$		0			0
$556$	−158.574	−	91.5525i	−0.285204	−	0.164663i
$557$	763.528	+	440.823i	1.37079	+	0.791424i	0.991027	−	0.133661i	$-0.0426732\pi$
$557$	763.528	+	440.823i	1.37079	+	0.791424i	0.379760	+	0.925085i	$0.376007\pi$
$558$	93.6389	+	162.187i	0.167812	+	0.290658i
$559$		−	31.6780i		−	0.0566691i
$560$		0			0
$561$	93.0883			0.165933
$562$	−163.017	+	94.1177i	−0.290065	+	0.167469i
$563$	383.534	−	664.301i	0.681233	−	1.17993i	−0.293372	−	0.955998i	$-0.594777\pi$
$563$	383.534	−	664.301i	0.681233	−	1.17993i	0.974605	−	0.223932i	$-0.0718893\pi$
$564$	−74.4853	+	129.012i	−0.132066	+	0.228745i
$565$		0			0
$566$		−	182.090i		−	0.321714i
$567$	−44.0908	+	45.0000i	−0.0777616	+	0.0793651i
$568$			388.617i			0.684185i
$569$	−14.6468	−	25.3689i	−0.0257412	−	0.0445851i	0.852868	−	0.522127i	$-0.174861\pi$
$569$	−14.6468	−	25.3689i	−0.0257412	−	0.0445851i	−0.878609	+	0.477542i	$0.841528\pi$
$570$		0			0
$571$	−482.521	+	835.752i	−0.845046	+	1.46366i	0.0405347	+	0.999178i	$0.487094\pi$
$571$	−482.521	+	835.752i	−0.845046	+	1.46366i	−0.885581	+	0.464485i	$0.846239\pi$
$572$	−127.968	−	221.647i	−0.223720	−	0.387494i
$573$	−115.360			−0.201326
$574$	145.831	+	522.846i	0.254060	+	0.910881i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−131.568	+	227.883i	−0.228021	+	0.394944i	−0.957222	−	0.289356i	$-0.906559\pi$
$577$	−131.568	+	227.883i	−0.228021	+	0.394944i	0.729201	+	0.684300i	$0.239892\pi$
$578$	−255.683	−	147.619i	−0.442359	−	0.255396i
$579$	−14.6909	+	8.48180i	−0.0253729	+	0.0146491i
$580$		0			0
$581$	748.477	+	192.389i	1.28826	+	0.331135i
$582$			26.9117i			0.0462400i
$583$	444.042	−	256.368i	0.761649	−	0.439738i
$584$	193.331	+	111.620i	0.331046	+	0.191130i
$585$		0			0
$586$	378.426	−	218.485i	0.645779	−	0.372841i
$587$	−436.477			−0.743572			−0.371786	−	0.928318i	$-0.621254\pi$
$587$	−436.477			−0.743572			−0.371786	+	0.928318i	$0.621254\pi$
$588$	−3.46410	−	169.706i	−0.00589133	−	0.288615i
$589$	318.941			0.541496
$590$		0			0
$591$	−400.742	−	231.369i	−0.678075	−	0.391487i
$592$	96.8929	+	55.9411i	0.163670	+	0.0944951i
$593$	−348.490	−	603.603i	−0.587673	−	1.01788i	−0.994536	−	0.104391i	$-0.966711\pi$
$593$	−348.490	−	603.603i	−0.587673	−	1.01788i	0.406863	−	0.913489i	$-0.366623\pi$
$594$			44.0908i			0.0742270i
$595$		0			0
$596$	162.177			0.272108
$597$	196.409	−	113.397i	0.328994	−	0.189945i
$598$	564.877	−	978.396i	0.944611	−	1.63611i
$599$	199.206	−	345.035i	0.332564	−	0.576018i	−0.650450	−	0.759549i	$-0.725419\pi$
$599$	199.206	−	345.035i	0.332564	−	0.576018i	0.983014	+	0.183531i	$0.0587528\pi$
$600$		0			0
$601$			36.1691i			0.0601816i	0.999547	+	0.0300908i	$0.00957964\pi$
$601$			36.1691i			0.0601816i	−0.999547	+	0.0300908i	$0.990420\pi$
$602$	−3.95029	−	14.1630i	−0.00656194	−	0.0235265i
$603$			13.1909i			0.0218755i
$604$	−51.2061	−	88.6915i	−0.0847782	−	0.146840i
$605$		0			0
$606$	131.272	−	227.370i	0.216621	−	0.375198i
$607$	15.7880	+	27.3457i	0.0260099	+	0.0450505i	0.878737	−	0.477306i	$-0.158387\pi$
$607$	15.7880	+	27.3457i	0.0260099	+	0.0450505i	−0.852727	+	0.522356i	$0.825053\pi$
$608$	40.8729			0.0672252
$609$	288.000	−	293.939i	0.472906	−	0.482658i
$610$		0			0
$611$	458.595	+	794.310i	0.750565	+	1.30002i
$612$	−26.8723	+	46.5442i	−0.0439090	+	0.0760525i
$613$	−354.434	−	204.632i	−0.578195	−	0.333821i	0.182220	−	0.983258i	$-0.441672\pi$
$613$	−354.434	−	204.632i	−0.578195	−	0.333821i	−0.760416	+	0.649436i	$0.775005\pi$
$614$	742.305	−	428.570i	1.20897	−	0.697997i
$615$		0			0
$616$	−84.8528	−	83.1384i	−0.137748	−	0.134965i
$617$			1227.38i			1.98927i	0.103436	+	0.994636i	$0.467016\pi$
$617$			1227.38i			1.98927i	−0.103436	+	0.994636i	$0.532984\pi$
$618$	223.173	−	128.849i	0.361122	−	0.208494i
$619$	−412.022	−	237.881i	−0.665625	−	0.384299i	0.128792	−	0.991672i	$-0.458890\pi$
$619$	−412.022	−	237.881i	−0.665625	−	0.384299i	−0.794417	+	0.607373i	$0.792223\pi$
$620$		0			0
$621$	−168.551	+	97.3131i	−0.271419	+	0.156704i
$622$	287.478			0.462184
$623$	140.143	−	39.0883i	0.224949	−	0.0627421i
$624$	147.765			0.236802
$625$		0			0
$626$	−496.805	−	286.830i	−0.793618	−	0.458195i
$627$	65.0284	+	37.5442i	0.103714	+	0.0598790i
$628$	187.061	+	324.000i	0.297869	+	0.515924i
$629$			250.544i			0.398322i
$630$		0			0
$631$	−54.9420			−0.0870713			−0.0435357	−	0.999052i	$-0.513862\pi$
$631$	−54.9420			−0.0870713			−0.0435357	+	0.999052i	$0.513862\pi$
$632$	−240.878	+	139.071i	−0.381136	+	0.220049i
$633$	−19.9951	+	34.6325i	−0.0315878	+	0.0547116i
$634$	18.4264	−	31.9155i	0.0290637	−	0.0503399i
$635$		0			0
$636$			296.028i			0.465452i
$637$	−915.533	−	503.956i	−1.43726	−	0.791139i
$638$		−	288.000i		−	0.451411i
$639$	−206.095	−	356.968i	−0.322528	−	0.558635i
$640$		0			0
$641$	114.551	−	198.409i	0.178707	−	0.309530i	−0.762731	−	0.646716i	$-0.776142\pi$
$641$	114.551	−	198.409i	0.178707	−	0.309530i	0.941438	+	0.337186i	$0.109475\pi$
$642$	145.186	+	251.470i	0.226147	+	0.391698i
$643$	−854.640			−1.32914			−0.664572	−	0.747224i	$-0.731386\pi$
$643$	−854.640			−1.32914			−0.664572	+	0.747224i	$0.731386\pi$
$644$	130.544	−	507.873i	0.202708	−	0.788622i
$645$		0			0
$646$	45.7645	+	79.2664i	0.0708429	+	0.122703i
$647$	−501.505	+	868.632i	−0.775124	+	1.34255i	0.159601	+	0.987182i	$0.448979\pi$
$647$	−501.505	+	868.632i	−0.775124	+	1.34255i	−0.934725	+	0.355372i	$0.884354\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	−214.191	+	123.663i	−0.330032	+	0.190544i
$650$		0			0
$651$	515.514	−	143.786i	0.791881	−	0.220869i
$652$			167.882i			0.257488i
$653$	−1100.51	+	635.382i	−1.68532	+	0.973020i	−0.727299	+	0.686321i	$0.759224\pi$
$653$	−1100.51	+	635.382i	−1.68532	+	0.973020i	−0.958021	+	0.286698i	$0.907442\pi$
$654$	235.591	+	136.019i	0.360232	+	0.207980i
$655$		0			0
$656$	−189.941	+	109.663i	−0.289544	+	0.167169i
$657$	−236.781			−0.360397
$658$	304.085	+	297.941i	0.462135	+	0.452798i
$659$	783.308			1.18863			0.594315	−	0.804232i	$-0.297423\pi$
$659$	783.308			1.18863			0.594315	+	0.804232i	$0.297423\pi$
$660$		0			0
$661$	72.5589	+	41.8919i	0.109771	+	0.0633765i	0.553881	−	0.832596i	$-0.313146\pi$
$661$	72.5589	+	41.8919i	0.109771	+	0.0633765i	−0.444109	+	0.895973i	$0.646480\pi$
$662$	−133.047	−	76.8148i	−0.200977	−	0.116034i
$663$	165.449	+	286.566i	0.249546	+	0.432226i
$664$			312.262i			0.470273i
$665$		0			0
$666$	−118.669			−0.178182
$667$	1100.97	−	635.647i	1.65063	−	0.952994i
$668$	127.620	−	221.044i	0.191047	−	0.330904i
$669$	198.000	−	342.946i	0.295964	−	0.512625i
$670$		0			0
$671$		−	7.13215i		−	0.0106291i
$672$	66.0641	−	18.4264i	0.0983097	−	0.0274202i
$673$		−	415.676i		−	0.617647i	−0.951119	−	0.308823i	$-0.900065\pi$
$673$		−	415.676i		−	0.617647i	0.951119	−	0.308823i	$-0.0999352\pi$
$674$	−312.354	−	541.013i	−0.463433	−	0.802690i
$675$		0			0
$676$	285.882	−	495.163i	0.422903	−	0.732489i
$677$	395.646	+	685.279i	0.584411	+	1.01223i	0.994949	+	0.100386i	$0.0320077\pi$
$677$	395.646	+	685.279i	0.584411	+	1.01223i	−0.410538	+	0.911844i	$0.634659\pi$
$678$	248.371			0.366329
$679$	74.4853	+	19.1458i	0.109698	+	0.0281970i
$680$		0			0
$681$	56.8234	+	98.4210i	0.0834411	+	0.144524i
$682$	187.278	−	324.375i	0.274601	−	0.475623i
$683$	−284.195	−	164.080i	−0.416099	−	0.240235i	0.277308	−	0.960781i	$-0.410558\pi$
$683$	−284.195	−	164.080i	−0.416099	−	0.240235i	−0.693407	+	0.720546i	$0.743891\pi$
$684$	−37.5442	+	21.6761i	−0.0548891	+	0.0316902i
$685$		0			0
$686$	−472.170	−	111.146i	−0.688295	−	0.162020i
$687$			161.912i			0.235679i
$688$	5.14517	−	2.97056i	0.00747844	−	0.00431768i
$689$	1578.42	+	911.300i	2.29088	+	1.32264i
$690$		0			0
$691$	875.182	−	505.287i	1.26654	−	0.731240i	0.292212	−	0.956353i	$-0.405609\pi$
$691$	875.182	−	505.287i	1.26654	−	0.731240i	0.974333	+	0.225113i	$0.0722753\pi$
$692$	285.941			0.413210
$693$	122.033	+	31.3675i	0.176094	+	0.0452634i
$694$	48.3532			0.0696733
$695$		0			0
$696$	144.000	+	83.1384i	0.206897	+	0.119452i
$697$	−425.346	−	245.574i	−0.610252	−	0.352329i
$698$	156.827	+	271.632i	0.224681	+	0.389158i
$699$		−	411.388i		−	0.588537i
$700$		0			0
$701$	−0.103464			−0.000147594			−7.37972e−5	−	1.00000i	$-0.500023\pi$
$701$	−0.103464			−0.000147594			−7.37972e−5		1.00000i	$0.500023\pi$
$702$	−135.730	+	78.3640i	−0.193348	+	0.111630i
$703$	−101.049	+	175.022i	−0.143740	+	0.248964i
$704$	24.0000	−	41.5692i	0.0340909	−	0.0590472i
$705$		0			0
$706$			632.700i			0.896175i
$707$	−535.916	−	525.088i	−0.758014	−	0.742699i
$708$		−	142.794i		−	0.201686i
$709$	602.588	+	1043.71i	0.849912	+	1.47209i	0.881286	+	0.472584i	$0.156679\pi$
$709$	602.588	+	1043.71i	0.849912	+	1.47209i	−0.0313734	+	0.999508i	$0.509988\pi$
$710$		0			0
$711$	147.507	−	255.490i	0.207464	−	0.359339i
$712$	29.3939	+	50.9117i	0.0412835	+	0.0715052i
$713$	1653.37			2.31889
$714$	109.706	+	107.489i	0.153649	+	0.150545i
$715$		0			0
$716$	−169.279	−	293.200i	−0.236423	−	0.409498i
$717$	−317.704	+	550.279i	−0.443102	+	0.767475i
$718$	−357.337	−	206.309i	−0.497684	−	0.287338i
$719$	−850.925	+	491.282i	−1.18348	+	0.683285i	−0.956818	−	0.290688i	$-0.906116\pi$
$719$	−850.925	+	491.282i	−1.18348	+	0.683285i	−0.226666	+	0.973973i	$0.572783\pi$
$720$		0			0
$721$	−197.852	−	709.359i	−0.274414	−	0.983855i
$722$		−	436.701i		−	0.604848i
$723$	−631.536	+	364.617i	−0.873493	+	0.504312i
$724$	−363.676	−	209.969i	−0.502315	−	0.290012i
$725$		0			0
$726$	−180.312	+	104.103i	−0.248364	+	0.143393i
$727$	630.440			0.867181			0.433590	−	0.901110i	$-0.357247\pi$
$727$	630.440			0.867181			0.433590	+	0.901110i	$0.357247\pi$
$728$	105.124	−	408.978i	0.144401	−	0.561783i
$729$	27.0000			0.0370370
$730$		0			0
$731$	11.5219	+	6.65215i	0.0157618	+	0.00910007i
$732$	3.56608	+	2.05887i	0.00487169	+	0.00281267i
$733$	−149.237	−	258.486i	−0.203597	−	0.352641i	0.746088	−	0.665848i	$-0.231930\pi$
$733$	−149.237	−	258.486i	−0.203597	−	0.352641i	−0.949685	+	0.313207i	$0.898597\pi$
$734$			593.053i			0.807974i
$735$		0			0
$736$	211.882			0.287883
$737$	22.8473	−	13.1909i	0.0310004	−	0.0178981i
$738$	116.315	−	201.463i	0.157608	−	0.272985i
$739$	172.684	−	299.097i	0.233672	−	0.404732i	−0.725214	−	0.688524i	$-0.758259\pi$
$739$	172.684	−	299.097i	0.233672	−	0.404732i	0.958886	+	0.283792i	$0.0915924\pi$
$740$		0			0
$741$			266.914i			0.360207i
$742$	819.336	+	210.603i	1.10423	+	0.283832i
$743$		−	683.616i		−	0.920076i	−0.887899	−	0.460038i	$-0.847836\pi$
$743$		−	683.616i		−	0.920076i	0.887899	−	0.460038i	$-0.152164\pi$
$744$	108.125	+	187.278i	0.145329	+	0.251717i
$745$		0			0
$746$	22.1903	−	38.4347i	0.0297457	−	0.0515211i
$747$	−165.602	−	286.831i	−0.221689	−	0.383977i
$748$	107.489			0.143702
$749$	799.301	−	222.939i	1.06716	−	0.297648i
$750$		0			0
$751$	289.169	+	500.855i	0.385045	+	0.666918i	0.991775	−	0.127990i	$-0.0408525\pi$
$751$	289.169	+	500.855i	0.385045	+	0.666918i	−0.606730	+	0.794908i	$0.707519\pi$
$752$	−86.0082	+	148.971i	−0.114373	+	0.198099i
$753$	−219.932	−	126.978i	−0.292074	−	0.168629i
$754$	886.587	−	511.871i	1.17584	−	0.678874i
$755$		0			0
$756$	−50.9117	+	51.9615i	−0.0673435	+	0.0687322i
$757$			1204.82i			1.59158i	0.605576	+	0.795788i	$0.292943\pi$
$757$			1204.82i			1.59158i	−0.605576	+	0.795788i	$0.707057\pi$
$758$	253.251	−	146.215i	0.334105	−	0.192895i
$759$	337.103	+	194.626i	0.444140	+	0.256425i
$760$		0			0
$761$	−202.669	+	117.011i	−0.266319	+	0.153760i	−0.627214	−	0.778847i	$-0.715805\pi$
$761$	−202.669	+	117.011i	−0.266319	+	0.153760i	0.360894	+	0.932607i	$0.382471\pi$
$762$	−202.263			−0.265437
$763$	544.075	−	555.294i	0.713074	−	0.727778i
$764$	−133.206			−0.174353
$765$		0			0
$766$	−610.617	−	352.540i	−0.797151	−	0.460235i
$767$	−761.376	−	439.581i	−0.992668	−	0.573117i
$768$	13.8564	+	24.0000i	0.0180422	+	0.0312500i
$769$		−	1290.16i		−	1.67771i	−0.544358	−	0.838853i	$-0.683226\pi$
$769$		−	1290.16i		−	1.67771i	0.544358	−	0.838853i	$-0.316774\pi$
$770$		0			0
$771$	43.4558			0.0563630
$772$	−16.9636	+	9.79394i	−0.0219736	+	0.0126864i
$773$	199.559	−	345.646i	0.258161	−	0.447149i	−0.707588	−	0.706625i	$-0.750217\pi$
$773$	199.559	−	345.646i	0.258161	−	0.447149i	0.965749	+	0.259477i	$0.0835500\pi$
$774$	−3.15076	+	5.45727i	−0.00407075	+	0.00705074i
$775$		0			0
$776$			31.0749i			0.0400450i
$777$	−84.4247	+	328.448i	−0.108655	+	0.422713i
$778$		−	917.013i		−	1.17868i
$779$	−198.088	−	343.099i	−0.254285	−	0.440435i
$780$		0			0
$781$	−412.191	+	713.936i	−0.527773	+	0.914130i
$782$	237.240	+	410.912i

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)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.77962 + 1.74264i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.77962 + 1.74264i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(-1.73205 - 3.00000i) q^{12} -21.3280 q^{13} +(-9.53553 + 2.65962i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(4.47871 - 7.75736i) q^{17} +(3.67423 + 2.12132i) q^{18} +(6.25736 - 3.61269i) q^{19} +(8.48528 - 8.66025i) q^{21} -8.48528i q^{22} +(32.4377 - 18.7279i) q^{23} +(4.24264 + 2.44949i) q^{24} +(26.1213 - 15.0812i) q^{26} -5.19615 q^{27} +(9.79796 - 10.0000i) q^{28} +33.9411 q^{29} +(38.2279 + 22.0709i) q^{31} +(4.89898 + 2.82843i) q^{32} +(5.19615 + 9.00000i) q^{33} +12.6677i q^{34} -6.00000 q^{36} +(-24.2232 + 13.9853i) q^{37} +(-5.10911 + 8.84924i) q^{38} +(-18.4706 + 31.9920i) q^{39} -54.8313i q^{41} +(-4.26858 + 16.6066i) q^{42} +1.48528i q^{43} +(6.00000 + 10.3923i) q^{44} +(-26.4853 + 45.8739i) q^{46} +(-21.5020 - 37.2426i) q^{47} -6.92820 q^{48} +(42.9264 + 23.6289i) q^{49} +(-7.75736 - 13.4361i) q^{51} +(-21.3280 + 36.9411i) q^{52} +(-74.0069 - 42.7279i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-4.92893 + 19.1757i) q^{56} -12.5147i q^{57} +(-41.5692 + 24.0000i) q^{58} +(35.6985 + 20.6105i) q^{59} +(-1.02944 + 0.594346i) q^{61} -62.4259 q^{62} +(-5.64191 - 20.2279i) q^{63} -8.00000 q^{64} +(-12.7279 - 7.34847i) q^{66} +(-3.80789 - 2.19848i) q^{67} +(-8.95743 - 15.5147i) q^{68} -64.8754i q^{69} +137.397 q^{71} +(7.34847 - 4.24264i) q^{72} +(39.4635 - 68.3528i) q^{73} +(19.7782 - 34.2568i) q^{74} -14.4508i q^{76} +(-29.3939 + 30.0000i) q^{77} -52.2426i q^{78} +(49.1690 + 85.1633i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(38.7716 + 67.1543i) q^{82} +110.401 q^{83} +(-6.51472 - 23.3572i) q^{84} +(-1.05025 - 1.81909i) q^{86} +(29.3939 - 50.9117i) q^{87} +(-14.6969 - 8.48528i) q^{88} +(18.0000 - 10.3923i) q^{89} +(-144.595 - 37.1670i) q^{91} -74.9117i q^{92} +(66.2127 - 38.2279i) q^{93} +(52.6690 + 30.4085i) q^{94} +(8.48528 - 4.89898i) q^{96} +10.9867 q^{97} +(-69.2820 + 1.41421i) q^{98} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 12 q^{9} + O(q^{10}) \)	\( 8 q + 8 q^{4} - 12 q^{9} - 24 q^{11} - 48 q^{14} - 16 q^{16} + 84 q^{19} + 192 q^{26} + 204 q^{31} - 48 q^{36} - 12 q^{39} + 48 q^{44} - 144 q^{46} + 4 q^{49} - 96 q^{51} - 96 q^{56} + 48 q^{59} - 144 q^{61} - 64 q^{64} + 624 q^{71} + 96 q^{74} + 20 q^{79} - 36 q^{81} - 120 q^{84} - 48 q^{86} + 144 q^{89} - 444 q^{91} + 48 q^{94} + 144 q^{99} + O(q^{100}) \)

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