LMFDB - Embedded newform 1050.3.q.a.649.3

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ 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			649.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1050.649
Dual form			1050.3.q.a.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.77962 + 1.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(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	$ 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}) $ 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

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
$7$	−6.77962	+	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	0.696832	−	0.717234i	$-0.254592\pi$
$11$	−3.00000	−	5.19615i	−0.272727	−	0.472377i	−0.969559	+	0.244857i	$0.921259\pi$
$12$	1.73205	−	3.00000i	0.144338	−	0.250000i
$13$	21.3280			1.64061			0.820306	−	0.571924i	$-0.193803\pi$
$13$	21.3280			1.64061			0.820306	+	0.571924i	$0.193803\pi$
$14$	−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	$-0.251528\pi$
$17$	−4.47871	−	7.75736i	−0.263454	−	0.456315i	−0.967157	+	0.254178i	$0.918195\pi$
$18$	−3.67423	+	2.12132i	−0.204124	+	0.117851i
$19$	6.25736	+	3.61269i	0.329335	+	0.190141i	0.655546	−	0.755156i	$-0.272439\pi$
$19$	6.25736	+	3.61269i	0.329335	+	0.190141i	−0.326211	+	0.945297i	$0.605772\pi$
$20$		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	$-0.636189\pi$
$23$	−32.4377	−	18.7279i	−1.41034	−	0.814257i	−0.995420	+	0.0956024i	$0.969522\pi$
$24$	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	0.265472	−	0.964119i	$-0.414472\pi$
$31$	38.2279	−	22.0709i	1.23316	−	0.711965i	0.967687	+	0.252154i	$0.0811390\pi$
$32$	−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	$-0.209952\pi$
$37$	24.2232	+	13.9853i	0.654682	+	0.377981i	−0.135566	+	0.990768i	$0.543285\pi$
$38$	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	$0.233138\pi$
$41$			54.8313i			1.33735i	−0.743556	+	0.668674i	$0.766862\pi$
$42$	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	$-0.682082\pi$
$47$	21.5020	−	37.2426i	0.457490	−	0.792397i	0.998828	+	0.0484090i	$0.0154151\pi$
$48$	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	$-0.368194\pi$
$53$	74.0069	−	42.7279i	1.39636	−	0.806187i	0.994009	+	0.109299i	$0.0348607\pi$
$54$	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	−0.165970	−	0.986131i	$-0.553076\pi$
$59$	35.6985	−	20.6105i	0.605059	−	0.349331i	0.771029	+	0.636800i	$0.219742\pi$
$60$		0			0
$61$	−1.02944	−	0.594346i	−0.0168760	−	0.00974337i	0.491538	−	0.870856i	$-0.336435\pi$
$61$	−1.02944	−	0.594346i	−0.0168760	−	0.00974337i	−0.508414	+	0.861113i	$0.669768\pi$
$62$	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	$-0.656220\pi$
$67$	3.80789	−	2.19848i	0.0568341	−	0.0328132i	0.528148	+	0.849152i	$0.322887\pi$
$68$	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	−0.998870	−	0.0475288i	$-0.984865\pi$
$73$	−39.4635	−	68.3528i	−0.540596	−	0.936340i	0.458274	−	0.888811i	$-0.348468\pi$
$74$	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	−0.366646	−	0.930361i	$-0.619494\pi$
$79$	49.1690	−	85.1633i	0.622393	−	1.07802i	0.989039	−	0.147656i	$-0.0471728\pi$
$80$		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	$-0.731597\pi$
$83$	−110.401			−1.33013			−0.665067	+	0.746784i	$0.731597\pi$
$84$	−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	0.597703	−	0.801717i	$-0.296080\pi$
$89$	18.0000	+	10.3923i	0.202247	+	0.116767i	−0.395456	+	0.918485i	$0.629413\pi$
$90$		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	$-0.518036\pi$
$97$	−10.9867			−0.113264			−0.0566322	+	0.998395i	$0.518036\pi$
$98$	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	−0.883330	−	0.468752i	$-0.844704\pi$
$101$	−92.8234	+	53.5916i	−0.919043	+	0.530610i	−0.0357136	+	0.999362i	$0.511370\pi$
$102$	−19.0016	+	10.9706i	−0.186290	+	0.107555i
$103$	52.6025	−	91.1102i	0.510704	−	0.884565i	−0.489219	−	0.872161i	$-0.662718\pi$
$103$	52.6025	−	91.1102i	0.510704	−	0.884565i	0.999923	−	0.0124040i	$-0.00394842\pi$
$104$			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	$-0.520211\pi$
$107$	−102.662	−	59.2721i	−0.959460	−	0.553945i	−0.896007	+	0.444040i	$0.853545\pi$
$108$	5.19615	+	9.00000i	0.0481125	+	0.0833333i
$109$	55.5294	+	96.1798i	0.509444	+	0.882384i	0.999940	+	0.0109400i	$0.00348237\pi$
$109$	55.5294	+	96.1798i	0.509444	+	0.882384i	−0.490496	+	0.871444i	$0.663184\pi$
$110$		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	0.286242	−	0.958157i	$-0.407594\pi$
$131$	−52.4558	−	30.2854i	−0.400426	−	0.231186i	−0.686668	+	0.726971i	$0.740927\pi$
$132$	−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	$-0.587999\pi$
$137$	58.0492	−	33.5147i	0.423717	−	0.244633i	0.696666	+	0.717395i	$0.254666\pi$
$138$	−45.8739	+	79.4558i	−0.332419	+	0.575767i
$139$			91.5525i			0.658651i	0.944216	+	0.329326i	$0.106821\pi$
$139$			91.5525i			0.658651i	−0.944216	+	0.329326i	$0.893179\pi$
$140$		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	−0.697293	−	0.716786i	$-0.745612\pi$
$149$	40.5442	−	70.2245i	0.272108	−	0.471306i	0.969402	+	0.245480i	$0.0789457\pi$
$150$		0			0
$151$	25.6030	+	44.3457i	0.169556	+	0.293680i	0.938264	−	0.345920i	$-0.112433\pi$
$151$	25.6030	+	44.3457i	0.169556	+	0.293680i	−0.768708	+	0.639600i	$0.779100\pi$
$152$	−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	0.993442	+	0.114334i	$0.0364734\pi$
$157$	93.5307	+	162.000i	0.595737	+	1.03185i	−0.397705	+	0.917513i	$0.630193\pi$
$158$	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	$-0.250439\pi$
$163$	72.6951	+	41.9706i	0.445982	+	0.257488i	−0.260149	+	0.965568i	$0.583772\pi$
$164$	−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	$-0.624797\pi$
$167$	−127.620			−0.764190			−0.382095	+	0.924123i	$0.624797\pi$
$168$	−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	$-0.968926\pi$
$173$	−71.4853	+	123.816i	−0.413210	+	0.715701i	0.582029	+	0.813168i	$0.302259\pi$
$174$		−	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	0.999517	−	0.0310748i	$-0.00989300\pi$
$179$	84.6396	+	146.600i	0.472847	+	0.818995i	−0.526670	+	0.850070i	$0.676560\pi$
$180$		0			0
$181$			209.969i			1.16005i	0.814600	+	0.580024i	$0.196957\pi$
$181$			209.969i			1.16005i	−0.814600	+	0.580024i	$0.803043\pi$
$182$	−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	−0.939937	−	0.341347i	$-0.889117\pi$
$191$	−33.3015	+	57.6799i	−0.174353	+	0.301989i	0.765584	+	0.643336i	$0.222450\pi$
$192$	6.92820	+	12.0000i	0.0360844	+	0.0625000i
$193$	8.48180	−	4.89697i	0.0439472	−	0.0253729i	−0.477865	−	0.878433i	$-0.658589\pi$
$193$	8.48180	−	4.89697i	0.0439472	−	0.0253729i	0.521813	+	0.853060i	$0.325256\pi$
$194$	−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	−0.187249	−	0.982312i	$-0.559957\pi$
$199$	113.397	−	65.4698i	0.569834	−	0.328994i	0.757083	+	0.653319i	$0.226624\pi$
$200$		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	$-0.671327\pi$
$223$	−228.631			−1.02525			−0.512625	+	0.858613i	$0.671327\pi$
$224$	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	$-0.120502\pi$
$227$	32.8070	+	56.8234i	0.144524	+	0.250323i	−0.784671	+	0.619912i	$0.787168\pi$
$228$	21.6761	−	12.5147i	0.0950707	−	0.0548891i
$229$	−80.9558	−	46.7399i	−0.353519	−	0.204104i	0.312715	−	0.949847i	$-0.398761\pi$
$229$	−80.9558	−	46.7399i	−0.353519	−	0.204104i	−0.666234	+	0.745743i	$0.732095\pi$
$230$		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	$-0.503573\pi$
$233$	−205.694	−	118.757i	−0.882806	−	0.509688i	−0.871583	+	0.490249i	$0.836906\pi$
$234$	−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	−0.513049	+	0.858359i	$0.671484\pi$
$241$	−364.617	+	210.512i	−1.51293	+	0.873493i	−0.999885	+	0.0151343i	$0.995182\pi$
$242$	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	$0.0943454\pi$
$251$			146.621i			0.584148i	−0.956396	+	0.292074i	$0.905655\pi$
$252$	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	$-0.848877\pi$
$257$	−12.5446	+	21.7279i	−0.0488118	+	0.0845444i	0.840587	+	0.541676i	$0.182210\pi$
$258$	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	$-0.611518\pi$
$263$	78.5279	−	45.3381i	0.298585	−	0.172388i	0.641807	+	0.766866i	$0.278185\pi$
$264$	−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	−0.385839	−	0.922566i	$-0.626088\pi$
$269$	59.2355	−	34.1996i	0.220206	−	0.127136i	0.606046	+	0.795430i	$0.292755\pi$
$270$		0			0
$271$	−106.971	−	61.7595i	−0.394725	−	0.227895i	0.289480	−	0.957184i	$-0.406518\pi$
$271$	−106.971	−	61.7595i	−0.394725	−	0.227895i	−0.684206	+	0.729289i	$0.739851\pi$
$272$	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	$-0.830608\pi$
$277$	−236.323	+	136.441i	−0.853151	+	0.492567i	0.00856145	+	0.999963i	$0.497275\pi$
$278$	−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	$-0.0936159\pi$
$283$	64.3787	+	111.507i	0.227486	+	0.394018i	−0.729576	+	0.683900i	$0.760283\pi$
$284$	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	$-0.323213\pi$
$293$	308.984			1.05455			0.527276	+	0.849694i	$0.323213\pi$
$294$	−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	$-0.0511503\pi$
$307$	606.090			1.97423			0.987117	+	0.160003i	$0.0511503\pi$
$308$	−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	−0.755573	−	0.655064i	$-0.772641\pi$
$311$	−176.044	+	101.639i	−0.566057	+	0.326813i	0.189516	+	0.981878i	$0.439308\pi$
$312$	90.4869	−	52.2426i	0.290022	−	0.167444i
$313$	−202.820	+	351.294i	−0.647986	+	1.12234i	0.335617	+	0.941999i	$0.391055\pi$
$313$	−202.820	+	351.294i	−0.647986	+	1.12234i	−0.983603	+	0.180346i	$0.942278\pi$
$314$			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	$-0.320246\pi$
$317$	22.5676	+	13.0294i	0.0711913	+	0.0411023i	−0.463982	+	0.885845i	$0.653580\pi$
$318$	−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	−0.772237	−	0.635335i	$-0.780862\pi$
$331$	54.3162	−	94.0785i	0.164097	−	0.284225i	0.936334	+	0.351110i	$0.114196\pi$
$332$	−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	$-0.650978\pi$
$347$	29.6102	−	17.0955i	0.0853320	−	0.0492664i	0.542059	+	0.840341i	$0.317645\pi$
$348$	58.7878	−	101.823i	0.168930	−	0.292596i
$349$			221.787i			0.635493i	0.948176	+	0.317746i	$0.102926\pi$
$349$			221.787i			0.635493i	−0.948176	+	0.317746i	$0.897074\pi$
$350$		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	−0.986791	−	0.162000i	$-0.948206\pi$
$353$	−223.693	−	387.448i	−0.633692	−	1.09759i	0.353099	−	0.935586i	$-0.385128\pi$
$354$	−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	−0.588121	−	0.808773i	$-0.700132\pi$
$359$	145.882	−	252.675i	0.406357	−	0.703831i	0.994478	+	0.104941i	$0.0334655\pi$
$360$		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	−0.996430	−	0.0844183i	$-0.973097\pi$
$367$	−209.676	−	363.169i	−0.571324	−	0.989561i	0.425107	−	0.905143i	$-0.360237\pi$
$368$	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	$-0.319939\pi$
$373$	27.1775	+	15.6909i	0.0728618	+	0.0420668i	−0.463127	+	0.886292i	$0.653272\pi$
$374$	−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	0.332041	+	0.943265i	$0.392263\pi$
$383$	−249.283	+	431.772i	−0.650871	+	1.12734i	−0.982912	+	0.184076i	$0.941071\pi$
$384$			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	−0.895284	−	0.445496i	$-0.853027\pi$
$389$	−324.213	−	561.554i	−0.833453	−	1.44358i	0.0618308	−	0.998087i	$-0.480306\pi$
$390$		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	$-0.863748\pi$
$397$	−37.8757	+	65.6026i	−0.0954047	+	0.165246i	0.814373	+	0.580342i	$0.197081\pi$
$398$	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	−0.263658	−	0.964616i	$-0.584929\pi$
$401$	282.125	−	488.655i	0.703553	−	1.21859i	0.967211	−	0.253974i	$-0.0817377\pi$
$402$	−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	−0.0713023	−	0.997455i	$-0.522716\pi$
$409$	309.559	−	178.724i	0.756868	−	0.436978i	0.828170	+	0.560477i	$0.189382\pi$
$410$		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	$-0.795464\pi$
$419$		−	502.175i		−	1.19851i	0.800559	−	0.599254i	$-0.204536\pi$
$420$		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	−0.994955	−	0.100326i	$-0.968012\pi$
$431$	−251.860	−	436.234i	−0.584362	−	1.01214i	0.410593	−	0.911819i	$-0.365322\pi$
$432$	−10.3923	+	18.0000i	−0.0240563	+	0.0416667i
$433$	837.548			1.93429			0.967145	−	0.254224i	$-0.0818202\pi$
$433$	837.548			1.93429			0.967145	+	0.254224i	$0.0818202\pi$
$434$	−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	0.675575	−	0.737292i	$-0.263896\pi$
$439$	164.558	+	95.0079i	0.374848	+	0.216419i	−0.300726	+	0.953711i	$0.597229\pi$
$440$		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	$-0.394591\pi$
$443$	−146.753	−	84.7279i	−0.331271	−	0.191259i	−0.656405	+	0.754408i	$0.727924\pi$
$444$	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	$-0.216191\pi$
$457$	284.769	+	164.412i	0.623128	+	0.359763i	−0.154958	+	0.987921i	$0.549524\pi$
$458$	−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	$-0.669506\pi$
$461$		−	794.331i		−	1.72306i	0.507706	−	0.861530i	$-0.330494\pi$
$462$	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	$-0.832370\pi$
$467$	1.41376	−	2.44870i	0.00302732	−	0.00524347i	0.867535	+	0.497376i	$0.165703\pi$
$468$	−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	−0.802171	−	0.597095i	$-0.796322\pi$
$479$	−328.669	+	189.757i	−0.686157	+	0.396153i	0.116014	+	0.993248i	$0.462988\pi$
$480$		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	$-0.465449\pi$
$487$	498.410	−	287.757i	1.02343	−	0.590877i	0.915095	+	0.403238i	$0.132115\pi$
$488$	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	−0.973128	−	0.230266i	$-0.926040\pi$
$499$	−143.287	+	248.180i	−0.287148	+	0.497355i	0.685980	+	0.727620i	$0.259374\pi$
$500$		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	$-0.491950\pi$
$503$	25.4374			0.0505714			0.0252857	+	0.999680i	$0.491950\pi$
$504$	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	0.991066	−	0.133370i	$-0.0425800\pi$
$509$	697.889	+	402.926i	1.37110	+	0.791603i	0.380031	+	0.924974i	$0.375913\pi$
$510$		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	−0.975001	−	0.222202i	$-0.928676\pi$
$521$	−661.706	+	382.036i	−1.27007	+	0.733274i	−0.295068	+	0.955476i	$0.595342\pi$
$522$	−124.708	+	72.0000i	−0.238904	+	0.137931i
$523$	−88.3900	+	153.096i	−0.169006	+	0.292726i	−0.938071	−	0.346444i	$-0.887389\pi$
$523$	−88.3900	+	153.096i	−0.169006	+	0.292726i	0.769065	+	0.639171i	$0.220722\pi$
$524$		−	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	−0.873854	−	0.486189i	$-0.838387\pi$
$541$	−8.58831	+	14.8754i	−0.0158749	+	0.0274961i	0.857979	+	0.513685i	$0.171720\pi$
$542$	−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	$-0.957327\pi$
$557$	−763.528	+	440.823i	−1.37079	+	0.791424i	−0.379760	+	0.925085i	$0.623993\pi$
$558$	−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	−0.974605	−	0.223932i	$-0.928111\pi$
$563$	−383.534	−	664.301i	−0.681233	−	1.17993i	0.293372	−	0.955998i	$-0.405223\pi$
$564$	−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	−0.878609	−	0.477542i	$-0.841528\pi$
$569$	−14.6468	+	25.3689i	−0.0257412	+	0.0445851i	0.852868	+	0.522127i	$0.174861\pi$
$570$		0			0
$571$	−482.521	−	835.752i	−0.845046	−	1.46366i	−0.885581	−	0.464485i	$-0.846239\pi$
$571$	−482.521	−	835.752i	−0.845046	−	1.46366i	0.0405347	−	0.999178i	$-0.487094\pi$
$572$	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	$-0.0934412\pi$
$577$	131.568	+	227.883i	0.228021	+	0.394944i	−0.729201	+	0.684300i	$0.760108\pi$
$578$	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	$-0.378746\pi$
$587$	436.477			0.743572			0.371786	+	0.928318i	$0.378746\pi$
$588$	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	−0.406863	−	0.913489i	$-0.633377\pi$
$593$	348.490	−	603.603i	0.587673	−	1.01788i	0.994536	−	0.104391i	$-0.0332894\pi$
$594$		−	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	0.983014	−	0.183531i	$-0.0587528\pi$
$599$	199.206	+	345.035i	0.332564	+	0.576018i	−0.650450	+	0.759549i	$0.725419\pi$
$600$		0			0
$601$		−	36.1691i		−	0.0601816i	−0.999547	−	0.0300908i	$-0.990420\pi$
$601$		−	36.1691i		−	0.0601816i	0.999547	−	0.0300908i	$-0.00957964\pi$
$602$	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	$-0.841613\pi$
$607$	−15.7880	+	27.3457i	−0.0260099	+	0.0450505i	0.852727	+	0.522356i	$0.174947\pi$
$608$	−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	$-0.558328\pi$
$613$	354.434	−	204.632i	0.578195	−	0.333821i	0.760416	+	0.649436i	$0.224995\pi$
$614$	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	−0.794417	−	0.607373i	$-0.792223\pi$
$619$	−412.022	+	237.881i	−0.665625	+	0.384299i	0.128792	+	0.991672i	$0.458890\pi$
$620$		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	0.941438	−	0.337186i	$-0.109475\pi$
$641$	114.551	+	198.409i	0.178707	+	0.309530i	−0.762731	+	0.646716i	$0.776142\pi$
$642$	−145.186	+	251.470i	−0.226147	+	0.391698i
$643$	854.640			1.32914			0.664572	−	0.747224i	$-0.268614\pi$
$643$	854.640			1.32914			0.664572	+	0.747224i	$0.268614\pi$
$644$	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	0.934725	+	0.355372i	$0.115646\pi$
$647$	501.505	+	868.632i	0.775124	+	1.34255i	−0.159601	+	0.987182i	$0.551021\pi$
$648$	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	0.958021	+	0.286698i	$0.0925578\pi$
$653$	1100.51	+	635.382i	1.68532	+	0.973020i	0.727299	+	0.686321i	$0.240776\pi$
$654$	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	−0.444109	−	0.895973i	$-0.646480\pi$
$661$	72.5589	−	41.8919i	0.109771	−	0.0633765i	0.553881	+	0.832596i	$0.313146\pi$
$662$	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	0.410538	+	0.911844i	$0.365341\pi$
$677$	−395.646	+	685.279i	−0.584411	+	1.01223i	−0.994949	+	0.100386i	$0.967992\pi$
$678$	−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	$-0.589442\pi$
$683$	284.195	−	164.080i	0.416099	−	0.240235i	0.693407	+	0.720546i	$0.256109\pi$
$684$	−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	0.974333	−	0.225113i	$-0.0722753\pi$
$691$	875.182	+	505.287i	1.26654	+	0.731240i	0.292212	+	0.956353i	$0.405609\pi$
$692$	−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	−0.0313734	−	0.999508i	$-0.509988\pi$
$709$	602.588	−	1043.71i	0.849912	−	1.47209i	0.881286	−	0.472584i	$-0.156679\pi$
$710$		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	−0.226666	−	0.973973i	$-0.572783\pi$
$719$	−850.925	−	491.282i	−1.18348	−	0.683285i	−0.956818	+	0.290688i	$0.906116\pi$
$720$		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	$-0.642753\pi$
$727$	−630.440			−0.867181			−0.433590	+	0.901110i	$0.642753\pi$
$728$	−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	$-0.768070\pi$
$733$	149.237	−	258.486i	0.203597	−	0.352641i	0.949685	+	0.313207i	$0.101403\pi$
$734$		−	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	0.958886	−	0.283792i	$-0.0915924\pi$
$739$	172.684	+	299.097i	0.233672	+	0.404732i	−0.725214	+	0.688524i	$0.758259\pi$
$740$		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	−0.606730	−	0.794908i	$-0.707519\pi$
$751$	289.169	−	500.855i	0.385045	−	0.666918i	0.991775	+	0.127990i	$0.0408525\pi$
$752$	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	0.360894	−	0.932607i	$-0.382471\pi$
$761$	−202.669	−	117.011i	−0.266319	−	0.153760i	−0.627214	+	0.778847i	$0.715805\pi$
$762$	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	$0.316774\pi$
$769$			1290.16i			1.67771i	−0.544358	+	0.838853i	$0.683226\pi$
$770$		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	$-0.249783\pi$
$773$	−199.559	−	345.646i	−0.258161	−	0.447149i	−0.965749	+	0.259477i	$0.916450\pi$
$774$	−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	−0.303376	+	0.525463i
$783$	176.363			0.225240
$784$	−4.00000	+	195.959i	−0.00510204	+	0.249948i
$785$		0			0
$786$	−74.1838	+	128.490i	−0.0943814	+	0.163473i
$787$	−778.361	−	1348.16i	−0.989023	−	1.71304i	−0.622478	−	0.782637i	$-0.713874\pi$
$787$	−778.361	−	1348.16i	−0.989023	−	1.71304i	−0.366544	−	0.930401i	$-0.619459\pi$
$788$	462.737	−	267.161i	0.587230	−	0.339037i
$789$	−136.014	−	78.5279i	−0.172388	−	0.0995284i
$790$		0			0
$791$	176.698	+	687.433i	0.223386	+	0.869068i
$792$			50.9117i			0.0642824i
$793$	−21.9558	−	12.6762i	−0.0276870	−	0.0159851i
$794$	−92.7761	+	53.5643i	−0.116846	+	0.0674613i
$795$		0			0
$796$	226.794	+	130.940i	0.284917	+	0.164497i
$797$	600.232			0.753114			0.376557	−	0.926393i	$-0.377108\pi$
$797$	600.232			0.753114			0.376557	+	0.926393i	$0.377108\pi$
$798$	−33.2844	+	119.335i	−0.0417098	+	0.149542i
$799$	−385.206			−0.482110
$800$		0			0
$801$	−54.0000	+	31.1769i	−0.0674157	+	0.0389225i
$802$	691.062	−	398.985i	0.861673	−	0.497487i
$803$	−236.781	+	410.117i	−0.294871	+	0.510731i
$804$		−	15.2315i		−	0.0189447i
$805$		0			0
$806$	1331.42			1.65188
$807$	−102.599	−	59.2355i	−0.127136	−	0.0734021i
$808$	−151.580	−	262.544i	−0.187599	−	0.324931i
$809$	−114.640	−	198.562i	−0.141705	−	0.245441i	0.786434	−	0.617675i	$-0.211925\pi$
$809$	−114.640	−	198.562i	−0.141705	−	0.245441i	−0.928139	+	0.372234i	$0.878592\pi$
$810$		0			0
$811$		−	529.955i		−	0.653459i	−0.945118	−	0.326729i	$-0.894053\pi$
$811$		−	529.955i		−	0.653459i	0.945118	−	0.326729i	$-0.105947\pi$
$812$	−332.554	−	339.411i	−0.409549	−	0.417994i
$813$			213.941i			0.263150i
$814$	118.669	−	205.541i	0.145785	−	0.252507i
$815$		0			0
$816$	−31.0294	−	53.7446i	−0.0380263	−	0.0658634i
$817$	−5.36586	+	9.29394i	−0.00656776	+	0.0113757i
$818$	505.508			0.617980
$819$	120.331	−	431.420i	0.146924	−	0.526765i
$820$		0			0
$821$	151.669	−	262.698i	0.184737	−	0.319974i	−0.758751	−	0.651381i	$-0.774190\pi$
$821$	151.669	−	262.698i	0.184737	−	0.319974i	0.943488	+	0.331407i	$0.107523\pi$
$822$	−82.0940	−	142.191i	−0.0998710	−	0.172982i
$823$	978.531	−	564.955i	1.18898	−	0.686459i	0.230906	−	0.972976i	$-0.425831\pi$
$823$	978.531	−	564.955i	1.18898	−	0.686459i	0.958075	+	0.286517i	$0.0924976\pi$
$824$	257.698	+	148.782i	0.312741	+	0.180561i
$825$		0			0
$826$	−395.220	+	101.588i	−0.478475	+	0.122988i
$827$		−	161.604i		−	0.195410i	−0.995215	−	0.0977049i	$-0.968850\pi$
$827$		−	161.604i		−	0.195410i	0.995215	−	0.0977049i	$-0.0311501\pi$
$828$	194.626	+	112.368i	0.235056	+	0.135710i
$829$	−1325.32	+	765.175i	−1.59870	+	0.923010i	−0.606962	+	0.794731i	$0.707612\pi$
$829$	−1325.32	+	765.175i	−1.59870	+	0.923010i	−0.991738	+	0.128279i	$0.959055\pi$
$830$		0			0
$831$	409.323	+	236.323i	0.492567	+	0.284384i
$832$	−170.624			−0.205077
$833$	−375.553	−	227.169i	−0.450844	−	0.272711i
$834$	224.257			0.268893
$835$		0			0
$836$	75.0883	−	43.3523i	0.0898186	−	0.0518568i
$837$	198.638	−	114.684i	0.237322	−	0.137018i
$838$	355.092	−	615.037i	0.423737	−	0.733934i
$839$		−	218.629i		−	0.260583i	−0.991476	−	0.130291i	$-0.958409\pi$
$839$		−	218.629i		−	0.260583i	0.991476	−	0.130291i	$-0.0415913\pi$
$840$		0			0
$841$	311.000			0.369798
$842$	41.3890	+	23.8959i	0.0491555	+	0.0283800i
$843$	−115.270	−	199.654i	−0.136738	−	0.236837i
$844$	−23.0883	−	39.9901i	−0.0273558	−	0.0473817i
$845$		0			0
$846$			182.451i			0.215663i
$847$	−159.854	+	573.124i	−0.188730	+	0.676652i
$848$			341.823i			0.403094i
$849$	111.507	−	193.136i	0.131339	−	0.227486i
$850$		0			0
$851$	−523.831	−	907.301i	−0.615547	−	1.06616i
$852$	237.979	−	412.191i	0.279318	−	0.483792i
$853$	−762.730			−0.894174			−0.447087	−	0.894491i	$-0.647539\pi$
$853$	−762.730			−0.894174			−0.447087	+	0.894491i	$0.647539\pi$
$854$	8.23550	+	8.40532i	0.00964344	+	0.00984230i
$855$		0			0
$856$	167.647	−	290.373i	0.195849	−	0.339220i
$857$	−459.002	−	795.015i	−0.535592	−	0.927672i	−0.999134	−	0.0415977i	$-0.986755\pi$
$857$	−459.002	−	795.015i	−0.535592	−	0.927672i	0.463543	−	0.886075i	$-0.346578\pi$
$858$	−271.461	+	156.728i	−0.316388	+	0.182667i
$859$	761.367	+	439.575i	0.886341	+	0.511729i	0.872744	−	0.488179i	$-0.162339\pi$
$859$	761.367	+	439.575i	0.886341	+	0.511729i	0.0135969	+	0.999908i	$0.495672\pi$
$860$		0			0
$861$	−474.853	+	465.259i	−0.551513	+	0.540370i
$862$		−	712.368i		−	0.826412i
$863$	303.619	+	175.294i	0.351818	+	0.203122i	0.665486	−	0.746411i	$-0.268224\pi$
$863$	303.619	+	175.294i	0.351818	+	0.203122i	−0.313668	+	0.949533i	$0.601558\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	1025.78	+	592.236i	1.18451	+	0.683875i
$867$	−361.591			−0.417060
$868$	−595.265	−	166.029i	−0.685789	−	0.191278i
$869$	−590.029			−0.678974
$870$		0			0
$871$	81.2145	−	46.8892i	0.0932428	−	0.0538338i
$872$	−272.038	+	157.061i	−0.311970	+	0.180116i
$873$	16.4800	−	28.5442i	0.0188774	−	0.0326966i
$874$		−	382.732i		−	0.437909i
$875$		0			0
$876$	−273.411			−0.312113
$877$	−3.08245	−	1.77965i	−0.00351477	−	0.00202925i	0.498242	−	0.867038i	$-0.333979\pi$
$877$	−3.08245	−	1.77965i	−0.00351477	−	0.00202925i	−0.501756	+	0.865009i	$0.667313\pi$
$878$	134.361	+	232.721i	0.153031	+	0.265058i
$879$	−267.588	−	463.476i	−0.304423	−	0.527276i
$880$		0			0
$881$			488.565i			0.554557i	0.960790	+	0.277279i	$0.0894325\pi$
$881$			488.565i			0.554557i	−0.960790	+	0.277279i	$0.910567\pi$
$882$	−107.597	+	177.879i	−0.121992	+	0.201677i
$883$			1162.16i			1.31615i	0.752953	+	0.658075i	$0.228629\pi$
$883$			1162.16i			1.31615i	−0.752953	+	0.658075i	$0.771371\pi$
$884$	191.044	−	330.897i	0.216113	−	0.374318i
$885$		0			0
$886$	−119.823	−	207.540i	−0.135241	−	0.234244i
$887$	−43.4630	+	75.2801i	−0.0490000	+	0.0848704i	−0.889485	−	0.456964i	$-0.848937\pi$
$887$	−43.4630	+	75.2801i	−0.0490000	+	0.0848704i	0.840485	+	0.541835i	$0.182270\pi$
$888$	137.027			0.154310
$889$	−143.896	−	559.817i	−0.161863	−	0.629716i
$890$		0			0
$891$	−27.0000	+	46.7654i	−0.0303030	+	0.0524864i
$892$	−228.631	−	396.000i	−0.256312	−	0.443946i
$893$	269.092	−	155.360i	0.301335	−	0.173976i
$894$	−172.014	−	99.3125i	−0.192410	−	0.111088i
$895$		0			0
$896$	76.2843	+	21.2770i	0.0851387	+	0.0237466i
$897$			1383.66i			1.54254i
$898$	−22.1721	−	12.8011i	−0.0246906	−	0.0142551i
$899$	1297.50	−	749.111i	1.44327	−	0.833272i
$900$		0			0
$901$	−662.912	−	382.732i	−0.735751	−	0.424786i
$902$	465.259			0.515808
$903$	−12.8629	+	12.6030i	−0.0142446	+	0.0139568i
$904$	286.794			0.317250
$905$		0			0
$906$	108.624	−	62.7144i	0.119895	−	0.0692211i
$907$	−399.148	+	230.448i	−0.440075	+	0.254077i	−0.703629	−	0.710567i	$-0.748438\pi$
$907$	−399.148	+	230.448i	−0.440075	+	0.254077i	0.263554	+	0.964645i	$0.415105\pi$
$908$	−65.6140	+	113.647i	−0.0722621	+	0.125162i
$909$		−	321.550i		−	0.353740i
$910$		0			0
$911$	−1184.28			−1.29998			−0.649988	−	0.759944i	$-0.725226\pi$
$911$	−1184.28			−1.29998			−0.649988	+	0.759944i	$0.725226\pi$
$912$	43.3523	+	25.0294i	0.0475354	+	0.0274446i
$913$	331.203	+	573.661i	0.362764	+	0.628325i
$914$	232.513	+	402.725i	0.254391	+	0.440618i
$915$		0			0
$916$		−	186.960i		−	0.204104i
$917$	408.407	+	113.912i	0.445373	+	0.124222i
$918$		−	65.8234i		−	0.0717030i
$919$	−270.919	+	469.246i	−0.294798	+	0.510605i	−0.974938	−	0.222477i	$-0.928586\pi$
$919$	−270.919	+	469.246i	−0.294798	+	0.510605i	0.680140	+	0.733082i	$0.261919\pi$
$920$		0			0
$921$	−524.889	−	909.134i	−0.569912	−	0.987117i
$922$	561.677	−	972.853i	0.609194	−	1.05515i
$923$	2930.40			3.17486
$924$	140.912	−	36.2201i	0.152502	−	0.0391992i
$925$		0			0
$926$	−285.244	+	494.057i	−0.308039	+	0.533539i
$927$	157.807	+	273.331i	0.170235	+	0.294855i
$928$	−166.277	+	96.0000i	−0.179178	+	0.103448i
$929$	779.610	+	450.108i	0.839193	+	0.484508i	0.856990	−	0.515333i	$-0.172332\pi$
$929$	779.610	+	450.108i	0.839193	+	0.484508i	−0.0177969	+	0.999842i	$0.505665\pi$
$930$		0			0
$931$	353.970	+	7.22538i	0.380204	+	0.00776088i
$932$		−	475.029i		−	0.509688i
$933$	304.917	+	176.044i	0.326813	+	0.188686i
$934$	3.46299	−	1.99936i	0.00370769	−	0.00214064i
$935$		0			0
$936$	−156.728	−	90.4869i	−0.167444	−	0.0966740i
$937$	233.964			0.249695			0.124847	−	0.992176i	$-0.460156\pi$
$937$	233.964			0.249695			0.124847	+	0.992176i	$0.460156\pi$
$938$	−42.1574	+	10.8362i	−0.0449439	+	0.0115524i
$939$	702.588			0.748230
$940$		0			0
$941$	1132.49	−	653.845i	1.20350	−	0.694840i	0.242167	−	0.970234i	$-0.422142\pi$
$941$	1132.49	−	653.845i	1.20350	−	0.694840i	0.961331	+	0.275394i	$0.0888083\pi$
$942$	396.817	−	229.103i	0.421250	−	0.243209i
$943$	1026.88	−	1778.60i	1.08895	−	1.88611i
$944$			164.884i			0.174666i
$945$		0			0
$946$	12.6030			0.0133224
$947$	976.671	+	563.881i	1.03133	+	0.595440i	0.917366	−	0.398045i	$-0.130311\pi$
$947$	976.671	+	563.881i	1.03133	+	0.595440i	0.113966	+	0.993485i	$0.463645\pi$
$948$	−170.327	−	295.014i	−0.179669	−	0.311197i
$949$	−841.677	−	1457.83i	−0.886909	−	1.53617i
$950$		0			0
$951$		−	45.1353i		−	0.0474609i
$952$	−126.677	+	124.118i	−0.133064	+	0.130376i
$953$			91.4255i			0.0959345i	0.998849	+	0.0479672i	$0.0152743\pi$
$953$			91.4255i			0.0959345i	−0.998849	+	0.0479672i	$0.984726\pi$
$954$	−181.279	+	313.985i	−0.190020	+	0.329125i
$955$		0			0
$956$	−366.853	−	635.408i	−0.383737	−	0.664652i
$957$	−176.363	+	305.470i	−0.184288	+	0.319196i
$958$	−536.714			−0.560245
$959$	−335.147	+	328.376i	−0.349476	+	0.342415i
$960$		0			0
$961$	493.749	−	855.199i	0.513787	−	0.889905i
$962$	421.828	+	730.628i	0.438491	+	0.759489i
$963$	307.987	−	177.816i	0.319820	−	0.184648i
$964$	−729.235	−	421.024i	−0.756467	−	0.436747i
$965$		0			0
$966$	172.544	−	618.622i	0.178617	−	0.640395i
$967$		−	1098.19i		−	1.13567i	−0.823143	−	0.567834i	$-0.807782\pi$
$967$		−	1098.19i		−	1.13567i	0.823143	−	0.567834i	$-0.192218\pi$
$968$	208.207	+	120.208i	0.215089	+	0.124182i
$969$	−97.0812	+	56.0498i	−0.100187	+	0.0578430i
$970$		0			0
$971$	114.405	+	66.0517i	0.117822	+	0.0680245i	0.557753	−	0.830007i	$-0.311664\pi$
$971$	114.405	+	66.0517i	0.117822	+	0.0680245i	−0.439931	+	0.898032i	$0.644997\pi$
$972$	−31.1769			−0.0320750
$973$	−159.543	−	620.691i	−0.163970	−	0.637915i
$974$	813.899			0.835626
$975$		0			0
$976$	4.11775	−	2.37738i	0.00421901	−	0.00243584i
$977$	388.182	−	224.117i	0.397320	−	0.229393i	−0.288007	−	0.957628i	$-0.592993\pi$
$977$	388.182	−	224.117i	0.397320	−	0.229393i	0.685327	+	0.728235i	$0.259659\pi$
$978$	102.806	−	178.066i	0.105119	−	0.182072i
$979$		−	124.708i		−	0.127383i
$980$		0			0
$981$	−333.177			−0.339630
$982$	292.029	+	168.603i	0.297382	+	0.171694i
$983$	−823.382	−	1426.14i	−0.837621	−	1.45080i	−0.891878	−	0.452276i	$-0.850612\pi$
$983$	−823.382	−	1426.14i	−0.837621	−	1.45080i	0.0542567	−	0.998527i	$-0.482721\pi$
$984$	134.309	+	232.629i	0.136493	+	0.236412i
$985$		0			0
$986$		−	429.956i		−	0.436061i
$987$	504.982	−	129.801i	0.511633	−	0.131511i
$988$			308.205i			0.311949i
$989$	27.8162	−	48.1791i	0.0281256	−	0.0487150i
$990$		0			0
$991$	314.448	+	544.640i	0.317304	+	0.549587i	0.979925	−	0.199369i	$-0.0638891\pi$
$991$	314.448	+	544.640i	0.317304	+	0.549587i	−0.662621	+	0.748955i	$0.730556\pi$
$992$	−124.852	+	216.250i	−0.125859	+	0.217994i
$993$	−188.157			−0.189483
$994$	−1310.15	−	365.424i	−1.31806	−	0.367630i
$995$		0			0
$996$	−191.220	+	331.203i	−0.191988	+	0.332533i
$997$	−502.090	−	869.645i	−0.503601	−	0.872262i	−0.999991	−	0.00416289i	$-0.998675\pi$
$997$	−502.090	−	869.645i	−0.503601	−	0.872262i	0.496390	−	0.868099i	$-0.334658\pi$
$998$	−350.980	+	202.638i	−0.351683	+	0.203044i
$999$	125.868	+	72.6697i	0.125994	+	0.0727424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.a.649.3		8
5.2	odd	4		1050.3.p.a.901.1		4
5.3	odd	4		42.3.g.a.19.2	✓	4
5.4	even	2	inner	1050.3.q.a.649.2		8
7.3	odd	6	inner	1050.3.q.a.199.2		8
15.8	even	4		126.3.n.a.19.1		4
20.3	even	4		336.3.bh.e.145.1		4
35.3	even	12		42.3.g.a.31.2	yes	4
35.13	even	4		294.3.g.a.19.2		4
35.17	even	12		1050.3.p.a.451.1		4
35.18	odd	12		294.3.g.a.31.2		4
35.23	odd	12		294.3.c.a.97.2		4
35.24	odd	6	inner	1050.3.q.a.199.3		8
35.33	even	12		294.3.c.a.97.1		4
60.23	odd	4		1008.3.cg.h.145.2		4
105.23	even	12		882.3.c.b.685.3		4
105.38	odd	12		126.3.n.a.73.1		4
105.53	even	12		882.3.n.e.325.1		4
105.68	odd	12		882.3.c.b.685.4		4
105.83	odd	4		882.3.n.e.19.1		4
140.3	odd	12		336.3.bh.e.241.1		4
140.23	even	12		2352.3.f.e.97.2		4
140.103	odd	12		2352.3.f.e.97.3		4
420.143	even	12		1008.3.cg.h.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.2	✓	4	5.3	odd	4
42.3.g.a.31.2	yes	4	35.3	even	12
126.3.n.a.19.1		4	15.8	even	4
126.3.n.a.73.1		4	105.38	odd	12
294.3.c.a.97.1		4	35.33	even	12
294.3.c.a.97.2		4	35.23	odd	12
294.3.g.a.19.2		4	35.13	even	4
294.3.g.a.31.2		4	35.18	odd	12
336.3.bh.e.145.1		4	20.3	even	4
336.3.bh.e.241.1		4	140.3	odd	12
882.3.c.b.685.3		4	105.23	even	12
882.3.c.b.685.4		4	105.68	odd	12
882.3.n.e.19.1		4	105.83	odd	4
882.3.n.e.325.1		4	105.53	even	12
1008.3.cg.h.145.2		4	60.23	odd	4
1008.3.cg.h.577.2		4	420.143	even	12
1050.3.p.a.451.1		4	35.17	even	12
1050.3.p.a.901.1		4	5.2	odd	4
1050.3.q.a.199.2		8	7.3	odd	6	inner
1050.3.q.a.199.3		8	35.24	odd	6	inner
1050.3.q.a.649.2		8	5.4	even	2	inner
1050.3.q.a.649.3		8	1.1	even	1	trivial
2352.3.f.e.97.2		4	140.23	even	12
2352.3.f.e.97.3		4	140.103	odd	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)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.77962 + 1.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(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	\( 8 q + 8 q^{4} - 12 q^{9} - 24 q^{11} - 48 q^{14} - 16 q^{16} + 84 q^{19} + 192 q^{26} + 204 q^{31} - 48 q^{36} - 12 q^{39} + 48 q^{44} - 144 q^{46} + 4 q^{49} - 96 q^{51} - 96 q^{56} + 48 q^{59} - 144 q^{61} - 64 q^{64} + 624 q^{71} + 96 q^{74} + 20 q^{79} - 36 q^{81} - 120 q^{84} - 48 q^{86} + 144 q^{89} - 444 q^{91} + 48 q^{94} + 144 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more