LMFDB - Embedded newform 294.3.g.a.31.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,3,Mod(19,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	294.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-6,-4,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.01091977219$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.31
Dual form			294.3.g.a.19.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.24264 - 0.717439i) q^{5} -2.44949i q^{6} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.75736 + 1.01461i) q^{10} +(-3.00000 + 5.19615i) q^{11} +(3.00000 - 1.73205i) q^{12} +21.3280i q^{13} -2.48528 q^{15} +(-2.00000 - 3.46410i) q^{16} +(7.75736 + 4.47871i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(6.25736 - 3.61269i) q^{19} +2.86976i q^{20} -8.48528 q^{22} +(18.7279 + 32.4377i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-11.4706 + 19.8676i) q^{25} +(-26.1213 + 15.0812i) q^{26} -5.19615i q^{27} -33.9411 q^{29} +(-1.75736 - 3.04384i) q^{30} +(-38.2279 - 22.0709i) q^{31} +(2.82843 - 4.89898i) q^{32} +(9.00000 - 5.19615i) q^{33} +12.6677i q^{34} -6.00000 q^{36} +(13.9853 + 24.2232i) q^{37} +(8.84924 + 5.10911i) q^{38} +(18.4706 - 31.9920i) q^{39} +(-3.51472 + 2.02922i) q^{40} +54.8313i q^{41} -1.48528 q^{43} +(-6.00000 - 10.3923i) q^{44} +(3.72792 + 2.15232i) q^{45} +(-26.4853 + 45.8739i) q^{46} +(37.2426 - 21.5020i) q^{47} +6.92820i q^{48} -32.4437 q^{50} +(-7.75736 - 13.4361i) q^{51} +(-36.9411 - 21.3280i) q^{52} +(42.7279 - 74.0069i) q^{53} +(6.36396 - 3.67423i) q^{54} +8.60927i q^{55} -12.5147 q^{57} +(-24.0000 - 41.5692i) q^{58} +(35.6985 + 20.6105i) q^{59} +(2.48528 - 4.30463i) q^{60} +(1.02944 - 0.594346i) q^{61} -62.4259i q^{62} +8.00000 q^{64} +(15.3015 + 26.5030i) q^{65} +(12.7279 + 7.34847i) q^{66} +(-2.19848 + 3.80789i) q^{67} +(-15.5147 + 8.95743i) q^{68} -64.8754i q^{69} +137.397 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-68.3528 - 39.4635i) q^{73} +(-19.7782 + 34.2568i) q^{74} +(34.4117 - 19.8676i) q^{75} +14.4508i q^{76} +52.2426 q^{78} +(-49.1690 - 85.1633i) q^{79} +(-4.97056 - 2.86976i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-67.1543 + 38.7716i) q^{82} -110.401i q^{83} +12.8528 q^{85} +(-1.05025 - 1.81909i) q^{86} +(50.9117 + 29.3939i) q^{87} +(8.48528 - 14.6969i) q^{88} +(18.0000 - 10.3923i) q^{89} +6.08767i q^{90} -74.9117 q^{92} +(38.2279 + 66.2127i) q^{93} +(52.6690 + 30.4085i) q^{94} +(5.18377 - 8.97855i) q^{95} +(-8.48528 + 4.89898i) q^{96} +10.9867i q^{97} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 4 q^{4} - 12 q^{5} + 6 q^{9} + 24 q^{10} - 12 q^{11} + 12 q^{12} + 24 q^{15} - 8 q^{16} + 48 q^{17} + 42 q^{19} + 24 q^{23} + 22 q^{25} - 96 q^{26} - 24 q^{30} - 102 q^{31} + 36 q^{33} - 24 q^{36}+ \cdots - 72 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 4 * q^4 - 12 * q^5 + 6 * q^9 + 24 * q^10 - 12 * q^11 + 12 * q^12 + 24 * q^15 - 8 * q^16 + 48 * q^17 + 42 * q^19 + 24 * q^23 + 22 * q^25 - 96 * q^26 - 24 * q^30 - 102 * q^31 + 36 * q^33 - 24 * q^36 + 22 * q^37 - 24 * q^38 + 6 * q^39 - 48 * q^40 + 28 * q^43 - 24 * q^44 - 36 * q^45 - 72 * q^46 + 132 * q^47 - 192 * q^50 - 48 * q^51 - 12 * q^52 + 120 * q^53 - 84 * q^57 - 96 * q^58 + 24 * q^59 - 24 * q^60 + 72 * q^61 + 32 * q^64 + 180 * q^65 + 110 * q^67 - 96 * q^68 + 312 * q^71 + 66 * q^73 - 48 * q^74 - 66 * q^75 + 192 * q^78 - 10 * q^79 + 48 * q^80 - 18 * q^81 - 48 * q^82 - 288 * q^85 - 24 * q^86 + 72 * q^89 - 96 * q^92 + 102 * q^93 + 24 * q^94 - 132 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	1.24264	−	0.717439i	0.248528	−	0.143488i	−0.370562	−	0.928808i	$-0.620835\pi$
$5$	1.24264	−	0.717439i	0.248528	−	0.143488i	0.619090	+	0.785320i	$0.287502\pi$
$6$		−	2.44949i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	1.75736	+	1.01461i	0.175736	+	0.101461i
$11$	−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	$0.254592\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$			21.3280i			1.64061i	0.571924	+	0.820306i	$0.306197\pi$
$13$			21.3280i			1.64061i	−0.571924	+	0.820306i	$0.693803\pi$
$14$		0			0
$15$	−2.48528			−0.165685
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	7.75736	+	4.47871i	0.456315	+	0.263454i	0.710494	−	0.703704i	$-0.248472\pi$
$17$	7.75736	+	4.47871i	0.456315	+	0.263454i	−0.254178	+	0.967157i	$0.581805\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	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	$0.272439\pi$
$20$			2.86976i			0.143488i
$21$		0			0
$22$	−8.48528			−0.385695
$23$	18.7279	+	32.4377i	0.814257	+	1.41034i	0.909860	+	0.414916i	$0.136189\pi$
$23$	18.7279	+	32.4377i	0.814257	+	1.41034i	−0.0956024	+	0.995420i	$0.530478\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$	−11.4706	+	19.8676i	−0.458823	+	0.794704i
$26$	−26.1213	+	15.0812i	−1.00467	+	0.580044i
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−33.9411			−1.17038			−0.585192	−	0.810895i	$-0.698981\pi$
$29$	−33.9411			−1.17038			−0.585192	+	0.810895i	$0.698981\pi$
$30$	−1.75736	−	3.04384i	−0.0585786	−	0.101461i
$31$	−38.2279	−	22.0709i	−1.23316	−	0.711965i	−0.265472	−	0.964119i	$-0.585528\pi$
$31$	−38.2279	−	22.0709i	−1.23316	−	0.711965i	−0.967687	+	0.252154i	$0.918861\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	9.00000	−	5.19615i	0.272727	−	0.157459i
$34$			12.6677i			0.372580i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	13.9853	+	24.2232i	0.377981	+	0.654682i	0.990768	−	0.135566i	$-0.0432853\pi$
$37$	13.9853	+	24.2232i	0.377981	+	0.654682i	−0.612788	+	0.790248i	$0.709952\pi$
$38$	8.84924	+	5.10911i	0.232875	+	0.134450i
$39$	18.4706	−	31.9920i	0.473604	−	0.820306i
$40$	−3.51472	+	2.02922i	−0.0878680	+	0.0507306i
$41$			54.8313i			1.33735i	0.743556	+	0.668674i	$0.233138\pi$
$41$			54.8313i			1.33735i	−0.743556	+	0.668674i	$0.766862\pi$
$42$		0			0
$43$	−1.48528			−0.0345414			−0.0172707	−	0.999851i	$-0.505498\pi$
$43$	−1.48528			−0.0345414			−0.0172707	+	0.999851i	$0.505498\pi$
$44$	−6.00000	−	10.3923i	−0.136364	−	0.236189i
$45$	3.72792	+	2.15232i	0.0828427	+	0.0478293i
$46$	−26.4853	+	45.8739i	−0.575767	+	0.997258i
$47$	37.2426	−	21.5020i	0.792397	−	0.457490i	−0.0484090	−	0.998828i	$-0.515415\pi$
$47$	37.2426	−	21.5020i	0.792397	−	0.457490i	0.840806	+	0.541337i	$0.182082\pi$
$48$			6.92820i			0.144338i
$49$		0			0
$50$	−32.4437			−0.648873
$51$	−7.75736	−	13.4361i	−0.152105	−	0.263454i
$52$	−36.9411	−	21.3280i	−0.710406	−	0.410153i
$53$	42.7279	−	74.0069i	0.806187	−	1.39636i	−0.109299	−	0.994009i	$-0.534861\pi$
$53$	42.7279	−	74.0069i	0.806187	−	1.39636i	0.915487	−	0.402348i	$-0.131806\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$			8.60927i			0.156532i
$56$		0			0
$57$	−12.5147			−0.219556
$58$	−24.0000	−	41.5692i	−0.413793	−	0.716711i
$59$	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	$0.553076\pi$
$60$	2.48528	−	4.30463i	0.0414214	−	0.0717439i
$61$	1.02944	−	0.594346i	0.0168760	−	0.00974337i	−0.491538	−	0.870856i	$-0.663565\pi$
$61$	1.02944	−	0.594346i	0.0168760	−	0.00974337i	0.508414	+	0.861113i	$0.330232\pi$
$62$		−	62.4259i		−	1.00687i
$63$		0			0
$64$	8.00000			0.125000
$65$	15.3015	+	26.5030i	0.235408	+	0.407738i
$66$	12.7279	+	7.34847i	0.192847	+	0.111340i
$67$	−2.19848	+	3.80789i	−0.0328132	+	0.0568341i	−0.881966	−	0.471314i	$-0.843780\pi$
$67$	−2.19848	+	3.80789i	−0.0328132	+	0.0568341i	0.849152	+	0.528148i	$0.177113\pi$
$68$	−15.5147	+	8.95743i	−0.228158	+	0.131727i
$69$		−	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	$0.0812687\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	−68.3528	−	39.4635i	−0.936340	−	0.540596i	−0.0475288	−	0.998870i	$-0.515135\pi$
$73$	−68.3528	−	39.4635i	−0.936340	−	0.540596i	−0.888811	+	0.458274i	$0.848468\pi$
$74$	−19.7782	+	34.2568i	−0.267273	+	0.462930i
$75$	34.4117	−	19.8676i	0.458823	−	0.264901i
$76$			14.4508i			0.190141i
$77$		0			0
$78$	52.2426			0.669777
$79$	−49.1690	−	85.1633i	−0.622393	−	1.07802i	−0.989039	−	0.147656i	$-0.952827\pi$
$79$	−49.1690	−	85.1633i	−0.622393	−	1.07802i	0.366646	−	0.930361i	$-0.380506\pi$
$80$	−4.97056	−	2.86976i	−0.0621320	−	0.0358719i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−67.1543	+	38.7716i	−0.818955	+	0.472824i
$83$		−	110.401i		−	1.33013i	−0.746784	−	0.665067i	$-0.768403\pi$
$83$		−	110.401i		−	1.33013i	0.746784	−	0.665067i	$-0.231597\pi$
$84$		0			0
$85$	12.8528			0.151210
$86$	−1.05025	−	1.81909i	−0.0122122	−	0.0211522i
$87$	50.9117	+	29.3939i	0.585192	+	0.337861i
$88$	8.48528	−	14.6969i	0.0964237	−	0.167011i
$89$	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	$0.296080\pi$
$90$			6.08767i			0.0676408i
$91$		0			0
$92$	−74.9117			−0.814257
$93$	38.2279	+	66.2127i	0.411053	+	0.711965i
$94$	52.6690	+	30.4085i	0.560309	+	0.323495i
$95$	5.18377	−	8.97855i	0.0545660	−	0.0945110i
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$			10.9867i			0.113264i	0.998395	+	0.0566322i	$0.0180362\pi$
$97$			10.9867i			0.113264i	−0.998395	+	0.0566322i	$0.981964\pi$
$98$		0			0
$99$	−18.0000			−0.181818
$100$	−22.9411	−	39.7352i	−0.229411	−	0.397352i
$101$	92.8234	+	53.5916i	0.919043	+	0.530610i	0.883330	−	0.468752i	$-0.155296\pi$
$101$	92.8234	+	53.5916i	0.919043	+	0.530610i	0.0357136	+	0.999362i	$0.488630\pi$
$102$	10.9706	−	19.0016i	0.107555	−	0.186290i
$103$	−91.1102	+	52.6025i	−0.884565	+	0.510704i	−0.872161	−	0.489219i	$-0.837282\pi$
$103$	−91.1102	+	52.6025i	−0.884565	+	0.510704i	−0.0124040	+	0.999923i	$0.503948\pi$
$104$		−	60.3246i		−	0.580044i
$105$		0			0
$106$	120.853			1.14012
$107$	−59.2721	−	102.662i	−0.553945	−	0.959460i	−0.997985	−	0.0634534i	$-0.979789\pi$
$107$	−59.2721	−	102.662i	−0.553945	−	0.959460i	0.444040	−	0.896007i	$-0.353545\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	−55.5294	+	96.1798i	−0.509444	+	0.882384i	0.490496	+	0.871444i	$0.336816\pi$
$109$	−55.5294	+	96.1798i	−0.509444	+	0.882384i	−0.999940	+	0.0109400i	$0.996518\pi$
$110$	−10.5442	+	6.08767i	−0.0958560	+	0.0553425i
$111$		−	48.4464i		−	0.436454i
$112$		0			0
$113$	101.397			0.897318			0.448659	−	0.893703i	$-0.351902\pi$
$113$	101.397			0.897318			0.448659	+	0.893703i	$0.351902\pi$
$114$	−8.84924	−	15.3273i	−0.0776249	−	0.134450i
$115$	46.5442	+	26.8723i	0.404732	+	0.233672i
$116$	33.9411	−	58.7878i	0.292596	−	0.506791i
$117$	−55.4117	+	31.9920i	−0.473604	+	0.273435i
$118$			58.2954i			0.494029i
$119$		0			0
$120$	7.02944			0.0585786
$121$	42.5000	+	73.6122i	0.351240	+	0.608365i
$122$	1.45584	+	0.840532i	0.0119331	+	0.00688961i
$123$	47.4853	−	82.2469i	0.386059	−	0.668674i
$124$	76.4558	−	44.1418i	0.616579	−	0.355982i
$125$			68.7897i			0.550317i
$126$		0			0
$127$	82.5736			0.650186			0.325093	−	0.945682i	$-0.394604\pi$
$127$	82.5736			0.650186			0.325093	+	0.945682i	$0.394604\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	2.22792	+	1.28629i	0.0172707	+	0.00997125i
$130$	−21.6396	+	37.4809i	−0.166459	+	0.288315i
$131$	52.4558	−	30.2854i	0.400426	−	0.231186i	−0.286242	−	0.958157i	$-0.592406\pi$
$131$	52.4558	−	30.2854i	0.400426	−	0.231186i	0.686668	+	0.726971i	$0.259073\pi$
$132$			20.7846i			0.157459i
$133$		0			0
$134$	−6.21825			−0.0464049
$135$	−3.72792	−	6.45695i	−0.0276142	−	0.0478293i
$136$	−21.9411	−	12.6677i	−0.161332	−	0.0931450i
$137$	−33.5147	+	58.0492i	−0.244633	+	0.423717i	−0.962028	−	0.272949i	$-0.912001\pi$
$137$	−33.5147	+	58.0492i	−0.244633	+	0.423717i	0.717395	+	0.696666i	$0.245334\pi$
$138$	79.4558	−	45.8739i	0.575767	−	0.332419i
$139$		−	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
$142$	97.1543	+	168.276i	0.684185	+	1.18504i
$143$	−110.823	−	63.9839i	−0.774989	−	0.447440i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$	−42.1766	+	24.3507i	−0.290873	+	0.167936i
$146$		−	111.620i		−	0.764518i
$147$		0			0
$148$	−55.9411			−0.377981
$149$	−40.5442	−	70.2245i	−0.272108	−	0.471306i	0.697293	−	0.716786i	$-0.254388\pi$
$149$	−40.5442	−	70.2245i	−0.272108	−	0.471306i	−0.969402	+	0.245480i	$0.921054\pi$
$150$	48.6655	+	28.0970i	0.324437	+	0.187314i
$151$	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	$0.112433\pi$
$152$	−17.6985	+	10.2182i	−0.116437	+	0.0672252i
$153$			26.8723i			0.175636i
$154$		0			0
$155$	−63.3381			−0.408633
$156$	36.9411	+	63.9839i	0.236802	+	0.410153i
$157$	−162.000	−	93.5307i	−1.03185	−	0.595737i	−0.114334	−	0.993442i	$-0.536473\pi$
$157$	−162.000	−	93.5307i	−1.03185	−	0.595737i	−0.917513	+	0.397705i	$0.869807\pi$
$158$	69.5355	−	120.439i	0.440098	−	0.762273i
$159$	−128.184	+	74.0069i	−0.806187	+	0.465452i
$160$		−	8.11689i		−	0.0507306i
$161$		0			0
$162$	−12.7279			−0.0785674
$163$	−41.9706	−	72.6951i	−0.257488	−	0.445982i	0.708080	−	0.706132i	$-0.249561\pi$
$163$	−41.9706	−	72.6951i	−0.257488	−	0.445982i	−0.965568	+	0.260149i	$0.916228\pi$
$164$	−94.9706	−	54.8313i	−0.579089	−	0.334337i
$165$	7.45584	−	12.9139i	0.0451869	−	0.0782661i
$166$	135.213	−	78.0654i	0.814537	−	0.470273i
$167$			127.620i			0.764190i	0.924123	+	0.382095i	$0.124797\pi$
$167$			127.620i			0.764190i	−0.924123	+	0.382095i	$0.875203\pi$
$168$		0			0
$169$	−285.882			−1.69161
$170$	9.08831	+	15.7414i	0.0534607	+	0.0925966i
$171$	18.7721	+	10.8381i	0.109778	+	0.0633805i
$172$	1.48528	−	2.57258i	0.00863536	−	0.0149569i
$173$	123.816	−	71.4853i	0.715701	−	0.413210i	−0.0974675	−	0.995239i	$-0.531074\pi$
$173$	123.816	−	71.4853i	0.715701	−	0.413210i	0.813168	+	0.582029i	$0.197741\pi$
$174$			83.1384i			0.477807i
$175$		0			0
$176$	24.0000			0.136364
$177$	−35.6985	−	61.8316i	−0.201686	−	0.349331i
$178$	25.4558	+	14.6969i	0.143010	+	0.0825671i
$179$	−84.6396	+	146.600i	−0.472847	+	0.818995i	−0.999517	−	0.0310748i	$-0.990107\pi$
$179$	−84.6396	+	146.600i	−0.472847	+	0.818995i	0.526670	+	0.850070i	$0.323440\pi$
$180$	−7.45584	+	4.30463i	−0.0414214	+	0.0239146i
$181$			209.969i			1.16005i	0.814600	+	0.580024i	$0.196957\pi$
$181$			209.969i			1.16005i	−0.814600	+	0.580024i	$0.803043\pi$
$182$		0			0
$183$	−2.05887			−0.0112507
$184$	−52.9706	−	91.7477i	−0.287883	−	0.498629i
$185$	34.7574	+	20.0672i	0.187878	+	0.108471i
$186$	−54.0624	+	93.6389i	−0.290658	+	0.503435i
$187$	−46.5442	+	26.8723i	−0.248899	+	0.143702i
$188$			86.0082i			0.457490i
$189$		0			0
$190$	14.6619			0.0771679
$191$	−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	$0.889117\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	4.89697	−	8.48180i	0.0253729	−	0.0439472i	−0.853060	−	0.521813i	$-0.825256\pi$
$193$	4.89697	−	8.48180i	0.0253729	−	0.0439472i	0.878433	+	0.477865i	$0.158589\pi$
$194$	−13.4558	+	7.76874i	−0.0693600	+	0.0400450i
$195$		−	53.0060i		−	0.271826i
$196$		0			0
$197$	−267.161			−1.35615			−0.678075	−	0.734993i	$-0.737185\pi$
$197$	−267.161			−1.35615			−0.678075	+	0.734993i	$0.737185\pi$
$198$	−12.7279	−	22.0454i	−0.0642824	−	0.111340i
$199$	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	$0.559957\pi$
$200$	32.4437	−	56.1941i	0.162218	−	0.280970i
$201$	6.59545	−	3.80789i	0.0328132	−	0.0189447i
$202$			151.580i			0.750396i
$203$		0			0
$204$	31.0294			0.152105
$205$	39.3381	+	68.1356i	0.191893	+	0.332369i
$206$	−128.849	−	74.3911i	−0.625482	−	0.361122i
$207$	−56.1838	+	97.3131i	−0.271419	+	0.470112i
$208$	73.8823	−	42.6559i	0.355203	−	0.205077i
$209$			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	$0.517424\pi$
$212$	85.4558	+	148.014i	0.403094	+	0.698179i
$213$	−206.095	−	118.989i	−0.967584	−	0.558635i
$214$	83.8234	−	145.186i	0.391698	−	0.678441i
$215$	−1.84567	+	1.06560i	−0.00858452	+	0.00495627i
$216$			14.6969i			0.0680414i
$217$		0			0
$218$	−157.061			−0.720463
$219$	68.3528	+	118.391i	0.312113	+	0.540596i
$220$	−14.9117	−	8.60927i	−0.0677804	−	0.0391330i
$221$	−95.5219	+	165.449i	−0.432226	+	0.748637i
$222$	59.3345	−	34.2568i	0.267273	−	0.154310i
$223$		−	228.631i		−	1.02525i	−0.858613	−	0.512625i	$-0.828673\pi$
$223$		−	228.631i		−	1.02525i	0.858613	−	0.512625i	$-0.171327\pi$
$224$		0			0
$225$	−68.8234			−0.305882
$226$	71.6985	+	124.185i	0.317250	+	0.549493i
$227$	−56.8234	−	32.8070i	−0.250323	−	0.144524i	0.369589	−	0.929195i	$-0.379498\pi$
$227$	−56.8234	−	32.8070i	−0.250323	−	0.144524i	−0.619912	+	0.784671i	$0.712832\pi$
$228$	12.5147	−	21.6761i	0.0548891	−	0.0950707i
$229$	−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	$0.398761\pi$
$230$			76.0063i			0.330462i
$231$		0			0
$232$	96.0000			0.413793
$233$	118.757	+	205.694i	0.509688	+	0.882806i	0.999937	+	0.0112234i	$0.00357259\pi$
$233$	118.757	+	205.694i	0.509688	+	0.882806i	−0.490249	+	0.871583i	$0.663094\pi$
$234$	−78.3640	−	45.2435i	−0.334889	−	0.193348i
$235$	30.8528	−	53.4386i	0.131289	−	0.227398i
$236$	−71.3970	+	41.2211i	−0.302530	+	0.174666i
$237$			170.327i			0.718678i
$238$		0			0
$239$	366.853			1.53495			0.767475	−	0.641079i	$-0.221513\pi$
$239$	366.853			1.53495			0.767475	+	0.641079i	$0.221513\pi$
$240$	4.97056	+	8.60927i	0.0207107	+	0.0358719i
$241$	364.617	+	210.512i	1.51293	+	0.873493i	0.999885	+	0.0151343i	$0.00481759\pi$
$241$	364.617	+	210.512i	1.51293	+	0.873493i	0.513049	+	0.858359i	$0.328516\pi$
$242$	−60.1041	+	104.103i	−0.248364	+	0.430179i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$			2.37738i			0.00974337i
$245$		0			0
$246$	134.309			0.545970
$247$	77.0513	+	133.457i	0.311949	+	0.540311i
$248$	108.125	+	62.4259i	0.435987	+	0.251717i
$249$	−95.6102	+	165.602i	−0.383977	+	0.665067i
$250$	−84.2498	+	48.6416i	−0.336999	+	0.194567i
$251$			146.621i			0.584148i	0.956396	+	0.292074i	$0.0943454\pi$
$251$			146.621i			0.584148i	−0.956396	+	0.292074i	$0.905655\pi$
$252$		0			0
$253$	−224.735			−0.888281
$254$	58.3883	+	101.132i	0.229875	+	0.398156i
$255$	−19.2792	−	11.1309i	−0.0756048	−	0.0436504i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−21.7279	+	12.5446i	−0.0845444	+	0.0488118i	−0.541676	−	0.840587i	$-0.682210\pi$
$257$	−21.7279	+	12.5446i	−0.0845444	+	0.0488118i	0.457132	+	0.889399i	$0.348877\pi$
$258$			3.63818i			0.0141015i
$259$		0			0
$260$	−61.2061			−0.235408
$261$	−50.9117	−	88.1816i	−0.195064	−	0.337861i
$262$	74.1838	+	42.8300i	0.283144	+	0.163473i
$263$	45.3381	−	78.5279i	0.172388	−	0.298585i	−0.766866	−	0.641807i	$-0.778185\pi$
$263$	45.3381	−	78.5279i	0.172388	−	0.298585i	0.939254	+	0.343222i	$0.111518\pi$
$264$	−25.4558	+	14.6969i	−0.0964237	+	0.0556702i
$265$		−	122.619i		−	0.462712i
$266$		0			0
$267$	−36.0000			−0.134831
$268$	−4.39697	−	7.61577i	−0.0164066	−	0.0284171i
$269$	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	$0.626088\pi$
$270$	5.27208	−	9.13151i	0.0195262	−	0.0338204i
$271$	106.971	−	61.7595i	0.394725	−	0.227895i	−0.289480	−	0.957184i	$-0.593482\pi$
$271$	106.971	−	61.7595i	0.394725	−	0.227895i	0.684206	+	0.729289i	$0.260149\pi$
$272$		−	35.8297i		−	0.131727i
$273$		0			0
$274$	−94.7939			−0.345963
$275$	−68.8234	−	119.206i	−0.250267	−	0.433475i
$276$	112.368	+	64.8754i	0.407129	+	0.235056i
$277$	136.441	−	236.323i	0.492567	−	0.853151i	−0.507396	−	0.861713i	$-0.669392\pi$
$277$	136.441	−	236.323i	0.492567	−	0.853151i	0.999963	+	0.00856145i	$0.00272523\pi$
$278$	112.128	−	64.7374i	0.403340	−	0.232868i
$279$		−	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	$0.423889\pi$
$282$	−52.6690	−	91.2255i	−0.186770	−	0.323495i
$283$	111.507	+	64.3787i	0.394018	+	0.227486i	0.683900	−	0.729576i	$-0.260283\pi$
$283$	111.507	+	64.3787i	0.394018	+	0.227486i	−0.289882	+	0.957063i	$0.593616\pi$
$284$	−137.397	+	237.979i	−0.483792	+	0.837953i
$285$	−15.5513	+	8.97855i	−0.0545660	+	0.0315037i
$286$		−	180.974i		−	0.632776i
$287$		0			0
$288$	16.9706			0.0589256
$289$	−104.382	−	180.795i	−0.361184	−	0.625589i
$290$	−59.6468	−	34.4371i	−0.205678	−	0.118749i
$291$	9.51472	−	16.4800i	0.0326966	−	0.0566322i
$292$	136.706	−	78.9270i	0.468170	−	0.270298i
$293$			308.984i			1.05455i	0.849694	+	0.527276i	$0.176787\pi$
$293$			308.984i			1.05455i	−0.849694	+	0.527276i	$0.823213\pi$
$294$		0			0
$295$	59.1472			0.200499
$296$	−39.5563	−	68.5136i	−0.133636	−	0.231465i
$297$	27.0000	+	15.5885i	0.0909091	+	0.0524864i
$298$	57.3381	−	99.3125i	0.192410	−	0.333263i
$299$	−691.831	+	399.429i	−2.31381	+	1.33588i
$300$			79.4704i			0.264901i
$301$		0			0
$302$	72.4163			0.239789
$303$	−92.8234	−	160.775i	−0.306348	−	0.530610i
$304$	−25.0294	−	14.4508i	−0.0823337	−	0.0475354i
$305$	0.852814	−	1.47712i	0.00279611	−	0.00484301i
$306$	−32.9117	+	19.0016i	−0.107555	+	0.0620966i
$307$		−	606.090i		−	1.97423i	−0.160003	−	0.987117i	$-0.551150\pi$
$307$		−	606.090i		−	1.97423i	0.160003	−	0.987117i	$-0.448850\pi$
$308$		0			0
$309$	182.220			0.589710
$310$	−44.7868	−	77.5730i	−0.144474	−	0.250236i
$311$	176.044	+	101.639i	0.566057	+	0.326813i	0.755573	−	0.655064i	$-0.227359\pi$
$311$	176.044	+	101.639i	0.566057	+	0.326813i	−0.189516	+	0.981878i	$0.560692\pi$
$312$	−52.2426	+	90.4869i	−0.167444	+	0.290022i
$313$	351.294	−	202.820i	1.12234	−	0.647986i	0.180346	−	0.983603i	$-0.442278\pi$
$313$	351.294	−	202.820i	1.12234	−	0.647986i	0.941999	+	0.335617i	$0.108945\pi$
$314$		−	264.545i		−	0.842500i
$315$		0			0
$316$	196.676			0.622393
$317$	13.0294	+	22.5676i	0.0411023	+	0.0711913i	0.885845	−	0.463982i	$-0.153580\pi$
$317$	13.0294	+	22.5676i	0.0411023	+	0.0711913i	−0.844742	+	0.535173i	$0.820246\pi$
$318$	−181.279	−	104.662i	−0.570060	−	0.329125i
$319$	101.823	−	176.363i	0.319196	−	0.552863i
$320$	9.94113	−	5.73951i	0.0310660	−	0.0179360i
$321$			205.325i			0.639640i
$322$		0			0
$323$	64.7208			0.200374
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$	−423.735	−	244.644i	−1.30380	−	0.752750i
$326$	59.3553	−	102.806i	0.182072	−	0.315357i
$327$	166.588	−	96.1798i	0.509444	−	0.294128i
$328$		−	155.086i		−	0.472824i
$329$		0			0
$330$	21.0883			0.0639040
$331$	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	$0.780862\pi$
$332$	191.220	+	110.401i	0.575965	+	0.332533i
$333$	−41.9558	+	72.6697i	−0.125994	+	0.218227i
$334$	−156.302	+	90.2407i	−0.467969	+	0.270182i
$335$			6.30911i			0.0188332i
$336$		0			0
$337$	441.735			1.31079			0.655393	−	0.755288i	$-0.272503\pi$
$337$	441.735			1.31079			0.655393	+	0.755288i	$0.272503\pi$
$338$	−202.149	−	350.133i	−0.598075	−	1.03590i
$339$	−152.095	−	87.8124i	−0.448659	−	0.259033i
$340$	−12.8528	+	22.2617i	−0.0378024	+	0.0654757i
$341$	229.368	−	132.425i	0.672632	−	0.388344i
$342$			30.6547i			0.0896336i
$343$		0			0
$344$	4.20101			0.0122122
$345$	−46.5442	−	80.6168i	−0.134911	−	0.233672i
$346$	175.103	+	101.096i	0.506077	+	0.292184i
$347$	−17.0955	+	29.6102i	−0.0492664	+	0.0853320i	−0.889607	−	0.456727i	$-0.849022\pi$
$347$	−17.0955	+	29.6102i	−0.0492664	+	0.0853320i	0.840341	+	0.542059i	$0.182355\pi$
$348$	−101.823	+	58.7878i	−0.292596	+	0.168930i
$349$		−	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
$352$	16.9706	+	29.3939i	0.0482118	+	0.0835053i
$353$	−387.448	−	223.693i	−1.09759	−	0.633692i	−0.162000	−	0.986791i	$-0.551794\pi$
$353$	−387.448	−	223.693i	−1.09759	−	0.633692i	−0.935586	+	0.353099i	$0.885128\pi$
$354$	50.4853	−	87.4431i	0.142614	−	0.247014i
$355$	170.735	−	98.5739i	0.480944	−	0.277673i
$356$			41.5692i			0.116767i
$357$		0			0
$358$	−239.397			−0.668707
$359$	−145.882	−	252.675i	−0.406357	−	0.703831i	0.588121	−	0.808773i	$-0.299868\pi$
$359$	−145.882	−	252.675i	−0.406357	−	0.703831i	−0.994478	+	0.104941i	$0.966534\pi$
$360$	−10.5442	−	6.08767i	−0.0292893	−	0.0169102i
$361$	−154.397	+	267.423i	−0.427692	+	0.740785i
$362$	−257.158	+	148.470i	−0.710381	+	0.410139i
$363$		−	147.224i		−	0.405577i
$364$		0			0
$365$	−113.251			−0.310276
$366$	−1.45584	−	2.52160i	−0.00397772	−	0.00688961i
$367$	363.169	+	209.676i	0.989561	+	0.571324i	0.905143	−	0.425107i	$-0.139763\pi$
$367$	363.169	+	209.676i	0.989561	+	0.571324i	0.0844183	+	0.996430i	$0.473097\pi$
$368$	74.9117	−	129.751i	0.203564	−	0.352584i
$369$	−142.456	+	82.2469i	−0.386059	+	0.222891i
$370$			56.7585i			0.153401i
$371$		0			0
$372$	−152.912			−0.411053
$373$	−15.6909	−	27.1775i	−0.0420668	−	0.0728618i	0.844225	−	0.535988i	$-0.180061\pi$
$373$	−15.6909	−	27.1775i	−0.0420668	−	0.0728618i	−0.886292	+	0.463127i	$0.846728\pi$
$374$	−65.8234	−	38.0031i	−0.175998	−	0.101613i
$375$	59.5736	−	103.184i	0.158863	−	0.275159i
$376$	−105.338	+	60.8170i	−0.280155	+	0.161747i
$377$		−	723.895i		−	1.92015i
$378$		0			0
$379$	206.779			0.545590			0.272795	−	0.962072i	$-0.412052\pi$
$379$	206.779			0.545590			0.272795	+	0.962072i	$0.412052\pi$
$380$	10.3675	+	17.9571i	0.0272830	+	0.0472555i
$381$	−123.860	−	71.5108i	−0.325093	−	0.187692i
$382$	47.0955	−	81.5717i	0.123287	−	0.213539i
$383$	431.772	−	249.283i	1.12734	−	0.650871i	0.184076	−	0.982912i	$-0.441071\pi$
$383$	431.772	−	249.283i	1.12734	−	0.650871i	0.943265	+	0.332041i	$0.107737\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	13.8507			0.0358827
$387$	−2.22792	−	3.85887i	−0.00575690	−	0.00997125i
$388$	−19.0294	−	10.9867i	−0.0490449	−	0.0283161i
$389$	324.213	−	561.554i	0.833453	−	1.44358i	−0.0618308	−	0.998087i	$-0.519694\pi$
$389$	324.213	−	561.554i	0.833453	−	1.44358i	0.895284	−	0.445496i	$-0.146973\pi$
$390$	64.9188	−	37.4809i	0.166459	−	0.0961049i
$391$			335.508i			0.858077i
$392$		0			0
$393$	−104.912			−0.266951
$394$	−188.912	−	327.205i	−0.479471	−	0.830469i
$395$	−122.199	−	70.5516i	−0.309364	−	0.178612i
$396$	18.0000	−	31.1769i	0.0454545	−	0.0787296i
$397$	−65.6026	+	37.8757i	−0.165246	+	0.0954047i	−0.580342	−	0.814373i	$-0.697081\pi$
$397$	−65.6026	+	37.8757i	−0.165246	+	0.0954047i	0.415096	+	0.909777i	$0.363748\pi$
$398$			185.176i			0.465268i
$399$		0			0
$400$	91.7645			0.229411
$401$	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	$0.584929\pi$
$402$	9.32738	+	5.38517i	0.0232024	+	0.0133959i
$403$	470.727	−	815.324i	1.16806	−	2.02314i
$404$	−185.647	+	107.183i	−0.459522	+	0.265305i
$405$			12.9139i			0.0318862i
$406$		0			0
$407$	−167.823			−0.412342
$408$	21.9411	+	38.0031i	0.0537773	+	0.0931450i
$409$	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	$0.522716\pi$
$410$	−55.6325	+	96.3583i	−0.135689	+	0.235020i
$411$	100.544	−	58.0492i	0.244633	−	0.141239i
$412$		−	210.410i		−	0.510704i
$413$		0			0
$414$	−158.912			−0.383845
$415$	−79.2061	−	137.189i	−0.190858	−	0.330576i
$416$	104.485	+	60.3246i	0.251167	+	0.145011i
$417$	−79.2868	+	137.329i	−0.190136	+	0.329326i
$418$	−53.0955	+	30.6547i	−0.127023	+	0.0733365i
$419$			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	$0.487221\pi$
$422$	−16.3259	−	28.2773i	−0.0386870	−	0.0670078i
$423$	111.728	+	64.5061i	0.264132	+	0.152497i
$424$	−120.853	+	209.323i	−0.285030	+	0.493687i
$425$	−177.963	+	102.747i	−0.418735	+	0.241757i
$426$		−	336.552i		−	0.790029i
$427$		0			0
$428$	237.088			0.553945
$429$	110.823	+	191.952i	0.258330	+	0.447440i
$430$	−2.61017	−	1.50698i	−0.00607017	−	0.00350461i
$431$	−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	$0.968012\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$			837.548i			1.93429i	0.254224	+	0.967145i	$0.418180\pi$
$433$			837.548i			1.93429i	−0.254224	+	0.967145i	$0.581820\pi$
$434$		0			0
$435$	84.3532			0.193916
$436$	−111.059	−	192.360i	−0.254722	−	0.441192i
$437$	234.375	+	135.316i	0.536326	+	0.309648i
$438$	−96.6655	+	167.430i	−0.220697	+	0.382259i
$439$	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	$0.263896\pi$
$440$		−	24.3507i		−	0.0553425i
$441$		0			0
$442$	−270.177			−0.611259
$443$	84.7279	+	146.753i	0.191259	+	0.331271i	0.945668	−	0.325134i	$-0.105409\pi$
$443$	84.7279	+	146.753i	0.191259	+	0.331271i	−0.754408	+	0.656405i	$0.772076\pi$
$444$	83.9117	+	48.4464i	0.188990	+	0.109114i
$445$	14.9117	−	25.8278i	0.0335094	−	0.0580400i
$446$	280.014	−	161.666i	0.627835	−	0.362481i
$447$			140.449i			0.314204i
$448$		0			0
$449$	18.1035			0.0403195			0.0201598	−	0.999797i	$-0.493583\pi$
$449$	18.1035			0.0403195			0.0201598	+	0.999797i	$0.493583\pi$
$450$	−48.6655	−	84.2911i	−0.108146	−	0.187314i
$451$	−284.912	−	164.494i	−0.631733	−	0.364731i
$452$	−101.397	+	175.625i	−0.224330	+	0.388550i
$453$	−76.8091	+	44.3457i	−0.169556	+	0.0978935i
$454$		−	92.7922i		−	0.204388i
$455$		0			0
$456$	35.3970			0.0776249
$457$	164.412	+	284.769i	0.359763	+	0.623128i	0.987921	−	0.154958i	$-0.0495242\pi$
$457$	164.412	+	284.769i	0.359763	+	0.623128i	−0.628158	+	0.778086i	$0.716191\pi$
$458$	−114.489	−	66.1002i	−0.249976	−	0.144324i
$459$	23.2721	−	40.3084i	0.0507017	−	0.0878179i
$460$	−93.0883	+	53.7446i	−0.202366	+	0.116836i
$461$		−	794.331i		−	1.72306i	−0.507706	−	0.861530i	$-0.669506\pi$
$461$		−	794.331i		−	1.72306i	0.507706	−	0.861530i	$-0.330494\pi$
$462$		0			0
$463$	−403.396			−0.871266			−0.435633	−	0.900124i	$-0.643475\pi$
$463$	−403.396			−0.871266			−0.435633	+	0.900124i	$0.643475\pi$
$464$	67.8823	+	117.576i	0.146298	+	0.253395i
$465$	95.0071	+	54.8524i	0.204316	+	0.117962i
$466$	−167.948	+	290.895i	−0.360404	+	0.624238i
$467$	2.44870	−	1.41376i	0.00524347	−	0.00302732i	−0.497376	−	0.867535i	$-0.665703\pi$
$467$	2.44870	−	1.41376i	0.00524347	−	0.00302732i	0.502619	+	0.864508i	$0.332370\pi$
$468$		−	127.968i		−	0.273435i
$469$		0			0
$470$	87.2649			0.185670
$471$	162.000	+	280.592i	0.343949	+	0.595737i
$472$	−100.971	−	58.2954i	−0.213921	−	0.123507i
$473$	4.45584	−	7.71775i	0.00942039	−	0.0163166i
$474$	−208.607	+	120.439i	−0.440098	+	0.254091i
$475$			165.758i			0.348965i
$476$		0			0
$477$	256.368			0.537458
$478$	259.404	+	449.301i	0.542686	+	0.939960i
$479$	−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	$0.796322\pi$
$480$	−7.02944	+	12.1753i	−0.0146447	+	0.0253653i
$481$	−516.632	+	298.278i	−1.07408	+	0.620120i
$482$			595.418i			1.23531i
$483$		0			0
$484$	−170.000			−0.351240
$485$	7.88225	+	13.6525i	0.0162521	+	0.0281494i
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	−287.757	+	498.410i	−0.590877	+	1.02343i	0.403238	+	0.915095i	$0.367885\pi$
$487$	−287.757	+	498.410i	−0.590877	+	1.02343i	−0.994115	+	0.108333i	$0.965449\pi$
$488$	−2.91169	+	1.68106i	−0.00596657	+	0.00344480i
$489$			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	$0.421930\pi$
$492$	94.9706	+	164.494i	0.193030	+	0.334337i
$493$	−263.294	−	152.013i	−0.534064	−	0.308342i
$494$	−108.967	+	188.736i	−0.220581	+	0.382057i
$495$	−22.3675	+	12.9139i	−0.0451869	+	0.0260887i
$496$			176.567i			0.355982i
$497$		0			0
$498$	−270.426			−0.543025
$499$	143.287	+	248.180i	0.287148	+	0.497355i	0.973128	−	0.230266i	$-0.0739595\pi$
$499$	143.287	+	248.180i	0.287148	+	0.497355i	−0.685980	+	0.727620i	$0.740626\pi$
$500$	−119.147	−	68.7897i	−0.238294	−	0.137579i
$501$	110.522	−	191.429i	0.220603	−	0.382095i
$502$	−179.574	+	103.677i	−0.357716	+	0.206528i
$503$			25.4374i			0.0505714i	0.999680	+	0.0252857i	$0.00804954\pi$
$503$			25.4374i			0.0505714i	−0.999680	+	0.0252857i	$0.991950\pi$
$504$		0			0
$505$	153.795			0.304544
$506$	−158.912	−	275.243i	−0.314055	−	0.543959i
$507$	428.823	+	247.581i	0.845805	+	0.488326i
$508$	−82.5736	+	143.022i	−0.162546	+	0.281539i
$509$	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	$0.0425800\pi$
$510$		−	31.4828i		−	0.0617310i
$511$		0			0
$512$	−22.6274			−0.0441942
$513$	−18.7721	−	32.5142i	−0.0365927	−	0.0633805i
$514$	−30.7279	−	17.7408i	−0.0597819	−	0.0345151i
$515$	−75.4781	+	130.732i	−0.146559	+	0.253848i
$516$	−4.45584	+	2.57258i	−0.00863536	+	0.00498563i
$517$			258.025i			0.499080i
$518$		0			0
$519$	−247.632			−0.477134
$520$	−43.2792	−	74.9618i	−0.0832293	−	0.144157i
$521$	661.706	+	382.036i	1.27007	+	0.733274i	0.975001	−	0.222202i	$-0.0713244\pi$
$521$	661.706	+	382.036i	1.27007	+	0.733274i	0.295068	+	0.955476i	$0.404658\pi$
$522$	72.0000	−	124.708i	0.137931	−	0.238904i
$523$	153.096	−	88.3900i	0.292726	−	0.169006i	−0.346444	−	0.938071i	$-0.612611\pi$
$523$	153.096	−	88.3900i	0.292726	−	0.169006i	0.639171	+	0.769065i	$0.279278\pi$
$524$			121.142i			0.231186i
$525$		0			0
$526$	128.235			0.243794
$527$	−197.698	−	342.424i	−0.375139	−	0.649761i
$528$	−36.0000	−	20.7846i	−0.0681818	−	0.0393648i
$529$	−436.970	+	756.854i	−0.826030	+	1.43073i
$530$	150.177	−	86.7045i	0.283352	−	0.163593i
$531$			123.663i			0.232887i
$532$		0			0
$533$	−1169.44			−2.19407
$534$	−25.4558	−	44.0908i	−0.0476701	−	0.0825671i
$535$	−147.308	−	85.0482i	−0.275342	−	0.158969i
$536$	6.21825	−	10.7703i	0.0116012	−	0.0200939i
$537$	253.919	−	146.600i	0.472847	−	0.272998i
$538$			96.7312i			0.179798i
$539$		0			0
$540$	14.9117			0.0276142
$541$	−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	$0.838387\pi$
$542$	151.279	+	87.3411i	0.279113	+	0.161146i
$543$	181.838	−	314.953i	0.334877	−	0.580024i
$544$	43.8823	−	25.3354i	0.0806659	−	0.0465725i
$545$			159.356i			0.292396i
$546$		0			0
$547$	212.676			0.388805			0.194402	−	0.980922i	$-0.437723\pi$
$547$	212.676			0.388805			0.194402	+	0.980922i	$0.437723\pi$
$548$	−67.0294	−	116.098i	−0.122316	−	0.211858i
$549$	3.08831	+	1.78304i	0.00562534	+	0.00324779i
$550$	97.3310	−	168.582i	0.176965	−	0.306513i
$551$	−212.382	+	122.619i	−0.385448	+	0.222538i
$552$			183.495i			0.332419i
$553$		0			0
$554$	385.914			0.696595
$555$	−34.7574	−	60.2015i	−0.0626259	−	0.108471i
$556$	158.574	+	91.5525i	0.285204	+	0.164663i
$557$	440.823	−	763.528i	0.791424	−	1.37079i	−0.133661	−	0.991027i	$-0.542673\pi$
$557$	440.823	−	763.528i	0.791424	−	1.37079i	0.925085	−	0.379760i	$-0.123993\pi$
$558$	162.187	−	93.6389i	0.290658	−	0.167812i
$559$		−	31.6780i		−	0.0566691i
$560$		0			0
$561$	93.0883			0.165933
$562$	94.1177	+	163.017i	0.167469	+	0.290065i
$563$	−664.301	−	383.534i	−1.17993	−	0.681233i	−0.223932	−	0.974605i	$-0.571889\pi$
$563$	−664.301	−	383.534i	−1.17993	−	0.681233i	−0.955998	+	0.293372i	$0.905223\pi$
$564$	74.4853	−	129.012i	0.132066	−	0.228745i
$565$	126.000	−	72.7461i	0.223009	−	0.128754i
$566$			182.090i			0.321714i
$567$		0			0
$568$	−388.617			−0.684185
$569$	14.6468	+	25.3689i	0.0257412	+	0.0445851i	0.878609	−	0.477542i	$-0.158472\pi$
$569$	14.6468	+	25.3689i	0.0257412	+	0.0445851i	−0.852868	+	0.522127i	$0.825139\pi$
$570$	−21.9929	−	12.6976i	−0.0385840	−	0.0222765i
$571$	−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	$0.846239\pi$
$572$	221.647	−	127.968i	0.387494	−	0.223720i
$573$			115.360i			0.201326i
$574$		0			0
$575$	−859.279			−1.49440
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−227.883	−	131.568i	−0.394944	−	0.228021i	0.289356	−	0.957222i	$-0.406559\pi$
$577$	−227.883	−	131.568i	−0.394944	−	0.228021i	−0.684300	+	0.729201i	$0.739892\pi$
$578$	147.619	−	255.683i	0.255396	−	0.442359i
$579$	−14.6909	+	8.48180i	−0.0253729	+	0.0146491i
$580$		−	97.4027i		−	0.167936i
$581$		0			0
$582$	26.9117			0.0462400
$583$	256.368	+	444.042i	0.439738	+	0.761649i
$584$	193.331	+	111.620i	0.331046	+	0.191130i
$585$	−45.9045	+	79.5090i	−0.0784693	+	0.135913i
$586$	−378.426	+	218.485i	−0.645779	+	0.372841i
$587$		−	436.477i		−	0.743572i	−0.928318	−	0.371786i	$-0.878746\pi$
$587$		−	436.477i		−	0.743572i	0.928318	−	0.371786i	$-0.121254\pi$
$588$		0			0
$589$	−318.941			−0.541496
$590$	41.8234	+	72.4402i	0.0708871	+	0.122780i
$591$	400.742	+	231.369i	0.678075	+	0.391487i
$592$	55.9411	−	96.8929i	0.0944951	−	0.163670i
$593$	−603.603	+	348.490i	−1.01788	+	0.587673i	−0.913489	−	0.406863i	$-0.866623\pi$
$593$	−603.603	+	348.490i	−1.01788	+	0.587673i	−0.104391	+	0.994536i	$0.533289\pi$
$594$			44.0908i			0.0742270i
$595$		0			0
$596$	162.177			0.272108
$597$	−113.397	−	196.409i	−0.189945	−	0.328994i
$598$	−978.396	−	564.877i	−1.63611	−	0.944611i
$599$	−199.206	+	345.035i	−0.332564	+	0.576018i	−0.983014	−	0.183531i	$-0.941247\pi$
$599$	−199.206	+	345.035i	−0.332564	+	0.576018i	0.650450	+	0.759549i	$0.274581\pi$
$600$	−97.3310	+	56.1941i	−0.162218	+	0.0936568i
$601$		−	36.1691i		−	0.0601816i	−0.999547	−	0.0300908i	$-0.990420\pi$
$601$		−	36.1691i		−	0.0601816i	0.999547	−	0.0300908i	$-0.00957964\pi$
$602$		0			0
$603$	−13.1909			−0.0218755
$604$	51.2061	+	88.6915i	0.0847782	+	0.146840i
$605$	105.624	+	60.9823i	0.174586	+	0.100797i
$606$	131.272	−	227.370i	0.216621	−	0.375198i
$607$	−27.3457	+	15.7880i	−0.0450505	+	0.0260099i	−0.522356	−	0.852727i	$-0.674947\pi$
$607$	−27.3457	+	15.7880i	−0.0450505	+	0.0260099i	0.477306	+	0.878737i	$0.341613\pi$
$608$		−	40.8729i		−	0.0672252i
$609$		0			0
$610$	2.41212			0.00395430
$611$	458.595	+	794.310i	0.750565	+	1.30002i
$612$	−46.5442	−	26.8723i	−0.0760525	−	0.0439090i
$613$	204.632	−	354.434i	0.333821	−	0.578195i	−0.649436	−	0.760416i	$-0.724995\pi$
$613$	204.632	−	354.434i	0.333821	−	0.578195i	0.983258	+	0.182220i	$0.0583285\pi$
$614$	742.305	−	428.570i	1.20897	−	0.697997i
$615$		−	136.271i		−	0.221579i
$616$		0			0
$617$	1227.38			1.98927			0.994636	−	0.103436i	$-0.0329837\pi$
$617$	1227.38			1.98927			0.994636	+	0.103436i	$0.0329837\pi$
$618$	128.849	+	223.173i	0.208494	+	0.361122i
$619$	−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	$0.792223\pi$
$620$	63.3381	−	109.705i	0.102158	−	0.176943i
$621$	168.551	−	97.3131i	0.271419	−	0.156704i
$622$			287.478i			0.462184i
$623$		0			0
$624$	−147.765			−0.236802
$625$	−237.412	−	411.209i	−0.379859	−	0.657935i
$626$	496.805	+	286.830i	0.793618	+	0.458195i
$627$	37.5442	−	65.0284i	0.0598790	−	0.103714i
$628$	324.000	−	187.061i	0.515924	−	0.297869i
$629$			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	$0.513862\pi$
$632$	139.071	+	240.878i	0.220049	+	0.381136i
$633$	34.6325	+	19.9951i	0.0547116	+	0.0315878i
$634$	−18.4264	+	31.9155i	−0.0290637	+	0.0503399i
$635$	102.609	−	59.2415i	0.161589	−	0.0932937i
$636$		−	296.028i		−	0.465452i
$637$		0			0
$638$	288.000			0.451411
$639$	206.095	+	356.968i	0.322528	+	0.558635i
$640$	14.0589	+	8.11689i	0.0219670	+	0.0126826i
$641$	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	$0.109475\pi$
$642$	−251.470	+	145.186i	−0.391698	+	0.226147i
$643$			854.640i			1.32914i	0.747224	+	0.664572i	$0.231386\pi$
$643$			854.640i			1.32914i	−0.747224	+	0.664572i	$0.768614\pi$
$644$		0			0
$645$	3.69134			0.00572301
$646$	45.7645	+	79.2664i	0.0708429	+	0.122703i
$647$	−868.632	−	501.505i	−1.34255	−	0.775124i	−0.355372	−	0.934725i	$-0.615646\pi$
$647$	−868.632	−	501.505i	−1.34255	−	0.775124i	−0.987182	+	0.159601i	$0.948979\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	−214.191	+	123.663i	−0.330032	+	0.190544i
$650$		−	691.957i		−	1.06455i
$651$		0			0
$652$	167.882			0.257488
$653$	−635.382	−	1100.51i	−0.973020	−	1.68532i	−0.686321	−	0.727299i	$-0.740776\pi$
$653$	−635.382	−	1100.51i	−0.973020	−	1.68532i	−0.286698	−	0.958021i	$-0.592558\pi$
$654$	235.591	+	136.019i	0.360232	+	0.207980i
$655$	43.4558	−	75.2677i	0.0663448	−	0.114913i
$656$	189.941	−	109.663i	0.289544	−	0.167169i
$657$		−	236.781i		−	0.360397i
$658$		0			0
$659$	−783.308			−1.18863			−0.594315	−	0.804232i	$-0.702577\pi$
$659$	−783.308			−1.18863			−0.594315	+	0.804232i	$0.702577\pi$
$660$	14.9117	+	25.8278i	0.0225935	+	0.0391330i
$661$	−72.5589	−	41.8919i	−0.109771	−	0.0633765i	0.444109	−	0.895973i	$-0.353520\pi$
$661$	−72.5589	−	41.8919i	−0.109771	−	0.0633765i	−0.553881	+	0.832596i	$0.686854\pi$
$662$	−76.8148	+	133.047i	−0.116034	+	0.200977i
$663$	286.566	−	165.449i	0.432226	−	0.249546i
$664$			312.262i			0.470273i
$665$		0			0
$666$	−118.669			−0.178182
$667$	−635.647	−	1100.97i	−0.952994	−	1.65063i
$668$	−221.044	−	127.620i	−0.330904	−	0.191047i
$669$	−198.000	+	342.946i	−0.295964	+	0.512625i
$670$	−7.72706	+	4.46122i	−0.0115329	+	0.00665853i
$671$			7.13215i			0.0106291i
$672$		0			0
$673$	415.676			0.617647			0.308823	−	0.951119i	$-0.400065\pi$
$673$	415.676			0.617647			0.308823	+	0.951119i	$0.400065\pi$
$674$	312.354	+	541.013i	0.463433	+	0.802690i
$675$	103.235	+	59.6028i	0.152941	+	0.0883004i
$676$	285.882	−	495.163i	0.422903	−	0.732489i
$677$	−685.279	+	395.646i	−1.01223	+	0.584411i	−0.911844	−	0.410538i	$-0.865341\pi$
$677$	−685.279	+	395.646i	−1.01223	+	0.584411i	−0.100386	+	0.994949i	$0.532008\pi$
$678$		−	248.371i		−	0.366329i
$679$		0			0
$680$	−36.3532			−0.0534607
$681$	56.8234	+	98.4210i	0.0834411	+	0.144524i
$682$	324.375	+	187.278i	0.475623	+	0.274601i
$683$	164.080	−	284.195i	0.240235	−	0.416099i	−0.720546	−	0.693407i	$-0.756109\pi$
$683$	164.080	−	284.195i	0.240235	−	0.416099i	0.960781	+	0.277308i	$0.0894423\pi$
$684$	−37.5442	+	21.6761i	−0.0548891	+	0.0316902i
$685$			96.1791i			0.140407i
$686$		0			0
$687$	161.912			0.235679
$688$	2.97056	+	5.14517i	0.00431768	+	0.00747844i
$689$	1578.42	+	911.300i	2.29088	+	1.32264i
$690$	65.8234	−	114.009i	0.0953962	−	0.165231i
$691$	−875.182	+	505.287i	−1.26654	+	0.731240i	−0.974333	−	0.225113i	$-0.927725\pi$
$691$	−875.182	+	505.287i	−1.26654	+	0.731240i	−0.292212	+	0.956353i	$0.594391\pi$
$692$			285.941i			0.413210i
$693$		0			0
$694$	−48.3532			−0.0696733
$695$	−65.6833	−	113.767i	−0.0945084	−	0.163693i
$696$	−144.000	−	83.1384i	−0.206897	−	0.119452i
$697$	−245.574	+	425.346i	−0.352329	+	0.610252i
$698$	271.632	−	156.827i	0.389158	−	0.224681i
$699$		−	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	$0.500023\pi$
$702$	78.3640	+	135.730i	0.111630	+	0.193348i
$703$	175.022	+	101.049i	0.248964	+	0.143740i
$704$	−24.0000	+	41.5692i	−0.0340909	+	0.0590472i
$705$	−92.5584	+	53.4386i	−0.131289	+	0.0757995i
$706$		−	632.700i		−	0.896175i
$707$		0			0
$708$	142.794			0.201686
$709$	−602.588	−	1043.71i	−0.849912	−	1.47209i	−0.881286	−	0.472584i	$-0.843321\pi$
$709$	−602.588	−	1043.71i	−0.849912	−	1.47209i	0.0313734	−	0.999508i	$-0.490012\pi$
$710$	241.456	+	139.405i	0.340079	+	0.196345i
$711$	147.507	−	255.490i	0.207464	−	0.359339i
$712$	−50.9117	+	29.3939i	−0.0715052	+	0.0412835i
$713$		−	1653.37i		−	2.31889i
$714$		0			0
$715$	−183.618			−0.256809
$716$	−169.279	−	293.200i	−0.236423	−	0.409498i
$717$	−550.279	−	317.704i	−0.767475	−	0.443102i
$718$	206.309	−	357.337i	0.287338	−	0.497684i
$719$	−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	$0.572783\pi$
$720$		−	17.2185i		−	0.0239146i
$721$		0			0
$722$	−436.701			−0.604848
$723$	−364.617	−	631.536i	−0.504312	−	0.873493i
$724$	−363.676	−	209.969i	−0.502315	−	0.290012i
$725$	389.324	−	674.329i	0.536998	−	0.930108i
$726$	180.312	−	104.103i	0.248364	−	0.143393i
$727$			630.440i			0.867181i	0.901110	+	0.433590i	$0.142753\pi$
$727$			630.440i			0.867181i	−0.901110	+	0.433590i	$0.857247\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	−80.0803	−	138.703i	−0.109699	−	0.190004i
$731$	−11.5219	−	6.65215i	−0.0157618	−	0.00910007i
$732$	2.05887	−	3.56608i	0.00281267	−	0.00487169i
$733$	−258.486	+	149.237i	−0.352641	+	0.203597i	−0.665848	−	0.746088i	$-0.731930\pi$
$733$	−258.486	+	149.237i	−0.352641	+	0.203597i	0.313207	+	0.949685i	$0.398597\pi$
$734$			593.053i			0.807974i
$735$		0			0
$736$	211.882			0.287883
$737$	−13.1909	−	22.8473i	−0.0178981	−	0.0310004i
$738$	−201.463	−	116.315i	−0.272985	−	0.157608i
$739$	−172.684	+	299.097i	−0.233672	+	0.404732i	−0.958886	−	0.283792i	$-0.908408\pi$
$739$	−172.684	+	299.097i	−0.233672	+	0.404732i	0.725214	+	0.688524i	$0.241741\pi$
$740$	−69.5147	+	40.1343i	−0.0939388	+	0.0542356i
$741$		−	266.914i		−	0.360207i
$742$		0			0
$743$	683.616			0.920076			0.460038	−	0.887899i	$-0.347836\pi$
$743$	683.616			0.920076			0.460038	+	0.887899i	$0.347836\pi$
$744$	−108.125	−	187.278i	−0.145329	−	0.251717i
$745$	−100.764	−	58.1759i	−0.135253	−	0.0780885i
$746$	22.1903	−	38.4347i	0.0297457	−	0.0515211i
$747$	286.831	−	165.602i	0.383977	−	0.221689i
$748$		−	107.489i		−	0.143702i
$749$		0			0
$750$	168.500			0.224666
$751$	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	$0.707519\pi$
$752$	−148.971	−	86.0082i	−0.198099	−	0.114373i
$753$	126.978	−	219.932i	0.168629	−	0.292074i
$754$	886.587	−	511.871i	1.17584	−	0.678874i
$755$		−	73.4744i		−	0.0973171i
$756$		0			0
$757$	1204.82			1.59158			0.795788	−	0.605576i	$-0.207057\pi$
$757$	1204.82			1.59158			0.795788	+	0.605576i	$0.207057\pi$
$758$	146.215	+	253.251i	0.192895	+	0.334105i
$759$	337.103	+	194.626i	0.444140	+	0.256425i
$760$	−14.6619	+	25.3952i	−0.0192920	+	0.0334147i
$761$	202.669	−	117.011i	0.266319	−	0.153760i	−0.360894	−	0.932607i	$-0.617529\pi$
$761$	202.669	−	117.011i	0.266319	−	0.153760i	0.627214	+	0.778847i	$0.284195\pi$
$762$		−	202.263i		−	0.265437i
$763$		0			0
$764$	133.206			0.174353
$765$	19.2792	+	33.3926i	0.0252016	+	0.0436504i
$766$	610.617	+	352.540i	0.797151	+	0.460235i
$767$	−439.581	+	761.376i	−0.573117	+	0.992668i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$		−	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
$772$	9.79394	+	16.9636i	0.0126864	+	0.0219736i
$773$	−345.646	−	199.559i	−0.447149	−	0.258161i	0.259477	−	0.965749i	$-0.416450\pi$
$773$	−345.646	−	199.559i	−0.447149	−	0.258161i	−0.706625	+	0.707588i	$0.749783\pi$
$774$	3.15076	−	5.45727i	0.00407075	−	0.00705074i
$775$	876.992	−	506.331i	1.13160	−	0.653331i
$776$		−	31.0749i		−	0.0400450i
$777$		0			0
$778$	917.013			1.17868
$779$	198.088	+	343.099i	0.254285	+	0.440435i
$780$	91.8091	+	53.0060i	0.117704	+	0.0679564i
$781$	−412.191	+	713.936i	−0.527773	+	0.914130i
$782$	−410.912	+	237.240i	−0.525463	+	0.303376i
$783$			176.363i			0.225240i
$784$		0			0
$785$	−268.410			−0.341924
$786$	−74.1838	−	128.490i	−0.0943814	−	0.163473i
$787$	1348.16	+	778.361i	1.71304	+	0.989023i	0.930401	+	0.366544i	$0.119459\pi$
$787$	1348.16	+	778.361i	1.71304	+	0.989023i	0.782637	+	0.622478i	$0.213874\pi$
$788$	267.161	−	462.737i	0.339037	−	0.587230i
$789$	−136.014	+	78.5279i	−0.172388	+	0.0995284i
$790$		−	199.550i		−	0.252595i
$791$		0			0
$792$	50.9117			0.0642824
$793$	12.6762	+	21.9558i	0.0159851	+	0.0276870i
$794$	−92.7761	−	53.5643i	−0.116846	−	0.0674613i
$795$	−106.191	+	183.928i	−0.133573	+	0.231356i
$796$	−226.794	+	130.940i	−0.284917	+	0.164497i
$797$		−	600.232i		−	0.753114i	−0.926393	−	0.376557i	$-0.877108\pi$
$797$		−	600.232i		−	0.753114i	0.926393	−	0.376557i	$-0.122892\pi$
$798$		0			0
$799$	385.206			0.482110
$800$	64.8873	+	112.388i	0.0811091	+	0.140485i
$801$	54.0000	+	31.1769i	0.0674157	+	0.0389225i
$802$	−398.985	+	691.062i	−0.497487	+	0.861673i
$803$	410.117	−	236.781i	0.510731	−	0.294871i
$804$			15.2315i			0.0189447i
$805$		0			0
$806$	1331.42			1.65188
$807$	−59.2355	−	102.599i	−0.0734021	−	0.127136i
$808$	−262.544	−	151.580i	−0.324931	−	0.187599i
$809$	114.640	−	198.562i	0.141705	−	0.245441i	−0.786434	−	0.617675i	$-0.788075\pi$
$809$	114.640	−	198.562i	0.141705	−	0.245441i	0.928139	+	0.372234i	$0.121408\pi$
$810$	−15.8162	+	9.13151i	−0.0195262	+	0.0112735i
$811$		−	529.955i		−	0.653459i	−0.945118	−	0.326729i	$-0.894053\pi$
$811$		−	529.955i		−	0.653459i	0.945118	−	0.326729i	$-0.105947\pi$
$812$		0			0
$813$	−213.941			−0.263150
$814$	−118.669	−	205.541i	−0.145785	−	0.252507i
$815$	−104.309	−	60.2226i	−0.127986	−	0.0738928i
$816$	−31.0294	+	53.7446i	−0.0380263	+	0.0658634i
$817$	−9.29394	+	5.36586i	−0.0113757	+	0.00656776i
$818$			505.508i			0.617980i
$819$		0			0
$820$	−157.352			−0.191893
$821$	151.669	+	262.698i	0.184737	+	0.319974i	0.943488	−	0.331407i	$-0.107523\pi$
$821$	151.669	+	262.698i	0.184737	+	0.319974i	−0.758751	+	0.651381i	$0.774190\pi$
$822$	142.191	+	82.0940i	0.172982	+	0.0998710i
$823$	564.955	−	978.531i	0.686459	−	1.18898i	−0.286517	−	0.958075i	$-0.592498\pi$
$823$	564.955	−	978.531i	0.686459	−	1.18898i	0.972976	−	0.230906i	$-0.0741690\pi$
$824$	257.698	−	148.782i	0.312741	−	0.180561i
$825$			238.411i			0.288983i
$826$		0			0
$827$	−161.604			−0.195410			−0.0977049	−	0.995215i	$-0.531150\pi$
$827$	−161.604			−0.195410			−0.0977049	+	0.995215i	$0.531150\pi$
$828$	−112.368	−	194.626i	−0.135710	−	0.235056i
$829$	−1325.32	−	765.175i	−1.59870	−	0.923010i	−0.991738	−	0.128279i	$-0.959055\pi$
$829$	−1325.32	−	765.175i	−1.59870	−	0.923010i	−0.606962	−	0.794731i	$-0.707612\pi$
$830$	112.014	−	194.014i	0.134957	−	0.233752i
$831$	−409.323	+	236.323i	−0.492567	+	0.284384i
$832$			170.624i			0.205077i
$833$		0			0
$834$	−224.257			−0.268893
$835$	91.5593	+	158.585i	0.109652	+	0.189923i
$836$	−75.0883	−	43.3523i	−0.0898186	−	0.0518568i
$837$	−114.684	+	198.638i	−0.137018	+	0.237322i
$838$	−615.037	+	355.092i	−0.733934	+	0.423737i
$839$			218.629i			0.260583i	0.991476	+	0.130291i	$0.0415913\pi$
$839$			218.629i			0.260583i	−0.991476	+	0.130291i	$0.958409\pi$
$840$		0			0
$841$	311.000			0.369798
$842$	23.8959	+	41.3890i	0.0283800	+	0.0491555i
$843$	−199.654	−	115.270i	−0.236837	−	0.136738i
$844$	23.0883	−	39.9901i	0.0273558	−	0.0473817i
$845$	−355.249	+	205.103i	−0.420413	+	0.242726i
$846$			182.451i			0.215663i
$847$		0			0
$848$	−341.823			−0.403094
$849$	−111.507	−	193.136i	−0.131339	−	0.227486i
$850$	−251.677	−	145.306i	−0.296091	−	0.170948i
$851$	−523.831	+	907.301i	−0.615547	+	1.06616i
$852$	412.191	−	237.979i	0.483792	−	0.279318i
$853$		−	762.730i		−	0.894174i	−0.894491	−	0.447087i	$-0.852461\pi$
$853$		−	762.730i		−	0.894174i	0.894491	−	0.447087i	$-0.147539\pi$
$854$		0			0
$855$	31.1026			0.0363773
$856$	167.647	+	290.373i	0.195849	+	0.339220i
$857$	795.015	+	459.002i	0.927672	+	0.535592i	0.886075	−	0.463543i	$-0.153422\pi$
$857$	795.015	+	459.002i	0.927672	+	0.535592i	0.0415977	+	0.999134i	$0.486755\pi$
$858$	−156.728	+	271.461i	−0.182667	+	0.316388i
$859$	761.367	−	439.575i	0.886341	−	0.511729i	0.0135969	−	0.999908i	$-0.495672\pi$
$859$	761.367	−	439.575i	0.886341	−	0.511729i	0.872744	+	0.488179i	$0.162339\pi$
$860$		−	4.26239i		−	0.00495627i
$861$		0			0
$862$	−712.368			−0.826412
$863$	−175.294	−	303.619i	−0.203122	−	0.351818i	0.746411	−	0.665486i	$-0.231776\pi$
$863$	−175.294	−	303.619i	−0.203122	−	0.351818i	−0.949533	+	0.313668i	$0.898442\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$	102.573	−	177.661i	0.118581	−	0.205389i
$866$	−1025.78	+	592.236i	−1.18451	+	0.683875i
$867$			361.591i			0.417060i
$868$		0			0
$869$	590.029			0.678974
$870$	59.6468	+	103.311i	0.0685595	+	0.118749i
$871$	−81.2145	−	46.8892i	−0.0932428	−	0.0538338i
$872$	157.061	−	272.038i	0.180116	−	0.311970i
$873$	−28.5442	+	16.4800i	−0.0326966	+	0.0188774i
$874$			382.732i			0.437909i
$875$		0			0
$876$	−273.411			−0.312113
$877$	−1.77965	−	3.08245i	−0.00202925	−	0.00351477i	0.865009	−	0.501756i	$-0.167313\pi$
$877$	−1.77965	−	3.08245i	−0.00202925	−	0.00351477i	−0.867038	+	0.498242i	$0.833979\pi$
$878$	232.721	+	134.361i	0.265058	+	0.153031i
$879$	267.588	−	463.476i	0.304423	−	0.527276i
$880$	29.8234	−	17.2185i	0.0338902	−	0.0195665i
$881$			488.565i			0.554557i	0.960790	+	0.277279i	$0.0894325\pi$
$881$			488.565i			0.554557i	−0.960790	+	0.277279i	$0.910567\pi$
$882$		0			0
$883$	−1162.16			−1.31615			−0.658075	−	0.752953i	$-0.728629\pi$
$883$	−1162.16			−1.31615			−0.658075	+	0.752953i	$0.728629\pi$
$884$	−191.044	−	330.897i	−0.216113	−	0.374318i
$885$	−88.7208	−	51.2230i	−0.100249	−	0.0578791i
$886$	−119.823	+	207.540i	−0.135241	+	0.234244i
$887$	−75.2801	+	43.4630i	−0.0848704	+	0.0490000i	−0.541835	−	0.840485i	$-0.682270\pi$
$887$	−75.2801	+	43.4630i	−0.0848704	+	0.0490000i	0.456964	+	0.889485i	$0.348937\pi$
$888$			137.027i			0.154310i
$889$		0			0
$890$	42.1766			0.0473895
$891$	−27.0000	−	46.7654i	−0.0303030	−	0.0524864i
$892$	396.000	+	228.631i	0.443946	+	0.256312i
$893$	155.360	−	269.092i	0.173976	−	0.301335i
$894$	−172.014	+	99.3125i	−0.192410	+	0.111088i
$895$			242.895i			0.271391i
$896$		0			0
$897$	1383.66			1.54254
$898$	12.8011	+	22.1721i	0.0142551	+	0.0246906i
$899$	1297.50	+	749.111i	1.44327	+	0.833272i
$900$	68.8234	−	119.206i	0.0764704	−	0.132451i
$901$	662.912	−	382.732i	0.735751	−	0.424786i
$902$		−	465.259i		−	0.515808i
$903$		0			0
$904$	−286.794			−0.317250
$905$	150.640	+	260.915i	0.166453	+	0.288304i
$906$	−108.624	−	62.7144i	−0.119895	−	0.0692211i
$907$	230.448	−	399.148i	0.254077	−	0.440075i	−0.710567	−	0.703629i	$-0.751562\pi$
$907$	230.448	−	399.148i	0.254077	−	0.440075i	0.964645	+	0.263554i	$0.0848948\pi$
$908$	113.647	−	65.6140i	0.125162	−	0.0722621i
$909$			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	$0.725226\pi$
$912$	25.0294	+	43.3523i	0.0274446	+	0.0475354i
$913$	573.661	+	331.203i	0.628325	+	0.362764i
$914$	−232.513	+	402.725i	−0.254391	+	0.440618i
$915$	−2.55844	+	1.47712i	−0.00279611	+	0.00161434i
$916$		−	186.960i		−	0.204104i
$917$		0			0
$918$	65.8234			0.0717030
$919$	270.919	+	469.246i	0.294798	+	0.510605i	0.974938	−	0.222477i	$-0.0714143\pi$
$919$	270.919	+	469.246i	0.294798	+	0.510605i	−0.680140	+	0.733082i	$0.738081\pi$
$920$	−131.647	−	76.0063i	−0.143094	−	0.0826155i
$921$	−524.889	+	909.134i	−0.569912	+	0.987117i
$922$	972.853	−	561.677i	1.05515	−	0.609194i
$923$			2930.40i			3.17486i
$924$		0			0
$925$	−641.676			−0.693704
$926$	−285.244	−	494.057i	−0.308039	−	0.533539i
$927$	−273.331	−	157.807i	−0.294855	−	0.170235i
$928$	−96.0000	+	166.277i	−0.103448	+	0.179178i
$929$	779.610	−	450.108i	0.839193	−	0.484508i	−0.0177969	−	0.999842i	$-0.505665\pi$
$929$	779.610	−	450.108i	0.839193	−	0.484508i	0.856990	+	0.515333i	$0.172332\pi$
$930$			155.146i			0.166824i
$931$		0			0
$932$	−475.029			−0.509688
$933$	−176.044	−	304.917i	−0.188686	−	0.326813i
$934$	3.46299	+	1.99936i	0.00370769	+	0.00214064i
$935$	−38.5584	+	66.7852i	−0.0412390	+	0.0714280i
$936$	156.728	−	90.4869i	0.167444	−	0.0966740i
$937$		−	233.964i		−	0.249695i	−0.992176	−	0.124847i	$-0.960156\pi$
$937$		−	233.964i		−	0.249695i	0.992176	−	0.124847i	$-0.0398441\pi$
$938$		0			0
$939$	−702.588			−0.748230
$940$	61.7056	+	106.877i	0.0656443	+	0.113699i
$941$	−1132.49	−	653.845i	−1.20350	−	0.694840i	−0.242167	−	0.970234i	$-0.577858\pi$
$941$	−1132.49	−	653.845i	−1.20350	−	0.694840i	−0.961331	+	0.275394i	$0.911192\pi$
$942$	−229.103	+	396.817i	−0.243209	+	0.421250i
$943$	−1778.60	+	1026.88i	−1.88611	+	1.08895i
$944$		−	164.884i		−	0.174666i
$945$		0			0
$946$	12.6030			0.0133224
$947$	563.881	+	976.671i	0.595440	+	1.03133i	0.993485	+	0.113966i	$0.0363555\pi$
$947$	563.881	+	976.671i	0.595440	+	1.03133i	−0.398045	+	0.917366i	$0.630311\pi$
$948$	−295.014	−	170.327i	−0.311197	−	0.179669i
$949$	841.677	−	1457.83i	0.886909	−	1.53617i
$950$	−203.012	+	117.209i	−0.213696	+	0.123378i
$951$		−	45.1353i		−	0.0474609i
$952$		0			0
$953$	−91.4255			−0.0959345			−0.0479672	−	0.998849i	$-0.515274\pi$
$953$	−91.4255			−0.0959345			−0.0479672	+	0.998849i	$0.515274\pi$
$954$	181.279	+	313.985i	0.190020	+	0.329125i
$955$	−82.7636	−	47.7836i	−0.0866635	−	0.0500352i
$956$	−366.853	+	635.408i	−0.383737	+	0.664652i
$957$	−305.470	+	176.363i	−0.319196	+	0.184288i
$958$		−	536.714i		−	0.560245i
$959$		0			0
$960$	−19.8823			−0.0207107
$961$	493.749	+	855.199i	0.513787	+	0.889905i
$962$	−730.628	−	421.828i	−0.759489	−	0.438491i
$963$	177.816	−	307.987i	0.184648	−	0.319820i
$964$	−729.235	+	421.024i	−0.756467	+	0.436747i
$965$		−	14.0531i		−	0.0145628i
$966$		0			0
$967$	−1098.19			−1.13567			−0.567834	−	0.823143i	$-0.692218\pi$
$967$	−1098.19			−1.13567			−0.567834	+	0.823143i	$0.692218\pi$
$968$	−120.208	−	208.207i	−0.124182	−	0.215089i
$969$	−97.0812	−	56.0498i	−0.100187	−	0.0578430i
$970$	−11.1472	+	19.3075i	−0.0114919	+	0.0199046i
$971$	−114.405	+	66.0517i	−0.117822	+	0.0680245i	−0.557753	−	0.830007i	$-0.688336\pi$
$971$	−114.405	+	66.0517i	−0.117822	+	0.0680245i	0.439931	+	0.898032i	$0.355003\pi$
$972$			31.1769i			0.0320750i
$973$		0			0
$974$	−813.899			−0.835626
$975$	423.735	+	733.931i	0.434601	+	0.752750i
$976$	−4.11775	−	2.37738i	−0.00421901	−	0.00243584i
$977$	−224.117	+	388.182i	−0.229393	+	0.397320i	−0.957628	−	0.288007i	$-0.907007\pi$
$977$	−224.117	+	388.182i	−0.229393	+	0.397320i	0.728235	+	0.685327i	$0.240341\pi$
$978$	−178.066	+	102.806i	−0.182072	+	0.105119i
$979$			124.708i			0.127383i
$980$		0			0
$981$	−333.177			−0.339630
$982$	168.603	+	292.029i	0.171694	+	0.297382i
$983$	−1426.14	−	823.382i	−1.45080	−	0.837621i	−0.452276	−	0.891878i	$-0.649388\pi$
$983$	−1426.14	−	823.382i	−1.45080	−	0.837621i	−0.998527	+	0.0542567i	$0.982721\pi$
$984$	−134.309	+	232.629i	−0.136493	+	0.236412i
$985$	−331.986	+	191.672i	−0.337041	+	0.194591i
$986$		−	429.956i		−	0.436061i
$987$		0			0
$988$	−308.205			−0.311949
$989$	−27.8162	−	48.1791i	−0.0281256	−	0.0487150i
$990$	−31.6325	−	18.2630i	−0.0319520	−	0.0184475i
$991$	314.448	−	544.640i	0.317304	−	0.549587i	−0.662621	−	0.748955i	$-0.730556\pi$
$991$	314.448	−	544.640i	0.317304	−	0.549587i	0.979925	+	0.199369i	$0.0638891\pi$
$992$	−216.250	+	124.852i	−0.217994	+	0.125859i
$993$		−	188.157i		−	0.189483i
$994$		0			0
$995$	187.882			0.188826
$996$	−191.220	−	331.203i	−0.191988	−	0.332533i
$997$	869.645	+	502.090i	0.872262	+	0.503601i	0.868099	−	0.496390i	$-0.165342\pi$
$997$	869.645	+	502.090i	0.872262	+	0.503601i	0.00416289	+	0.999991i	$0.498675\pi$
$998$	−202.638	+	350.980i	−0.203044	+	0.351683i
$999$	125.868	−	72.6697i	0.125994	−	0.0727424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.g.a.31.2		4
3.2	odd	2		882.3.n.e.325.1		4
7.2	even	3		42.3.g.a.19.2	✓	4
7.3	odd	6		294.3.c.a.97.1		4
7.4	even	3		294.3.c.a.97.2		4
7.5	odd	6	inner	294.3.g.a.19.2		4
7.6	odd	2		42.3.g.a.31.2	yes	4
21.2	odd	6		126.3.n.a.19.1		4
21.5	even	6		882.3.n.e.19.1		4
21.11	odd	6		882.3.c.b.685.3		4
21.17	even	6		882.3.c.b.685.4		4
21.20	even	2		126.3.n.a.73.1		4
28.3	even	6		2352.3.f.e.97.3		4
28.11	odd	6		2352.3.f.e.97.2		4
28.23	odd	6		336.3.bh.e.145.1		4
28.27	even	2		336.3.bh.e.241.1		4
35.2	odd	12		1050.3.q.a.649.3		8
35.9	even	6		1050.3.p.a.901.1		4
35.13	even	4		1050.3.q.a.199.3		8
35.23	odd	12		1050.3.q.a.649.2		8
35.27	even	4		1050.3.q.a.199.2		8
35.34	odd	2		1050.3.p.a.451.1		4
84.23	even	6		1008.3.cg.h.145.2		4
84.83	odd	2		1008.3.cg.h.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.2	✓	4	7.2	even	3
42.3.g.a.31.2	yes	4	7.6	odd	2
126.3.n.a.19.1		4	21.2	odd	6
126.3.n.a.73.1		4	21.20	even	2
294.3.c.a.97.1		4	7.3	odd	6
294.3.c.a.97.2		4	7.4	even	3
294.3.g.a.19.2		4	7.5	odd	6	inner
294.3.g.a.31.2		4	1.1	even	1	trivial
336.3.bh.e.145.1		4	28.23	odd	6
336.3.bh.e.241.1		4	28.27	even	2
882.3.c.b.685.3		4	21.11	odd	6
882.3.c.b.685.4		4	21.17	even	6
882.3.n.e.19.1		4	21.5	even	6
882.3.n.e.325.1		4	3.2	odd	2
1008.3.cg.h.145.2		4	84.23	even	6
1008.3.cg.h.577.2		4	84.83	odd	2
1050.3.p.a.451.1		4	35.34	odd	2
1050.3.p.a.901.1		4	35.9	even	6
1050.3.q.a.199.2		8	35.27	even	4
1050.3.q.a.199.3		8	35.13	even	4
1050.3.q.a.649.2		8	35.23	odd	12
1050.3.q.a.649.3		8	35.2	odd	12
2352.3.f.e.97.2		4	28.11	odd	6
2352.3.f.e.97.3		4	28.3	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.24264 - 0.717439i) q^{5} -2.44949i q^{6} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.75736 + 1.01461i) q^{10} +(-3.00000 + 5.19615i) q^{11} +(3.00000 - 1.73205i) q^{12} +21.3280i q^{13} -2.48528 q^{15} +(-2.00000 - 3.46410i) q^{16} +(7.75736 + 4.47871i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(6.25736 - 3.61269i) q^{19} +2.86976i q^{20} -8.48528 q^{22} +(18.7279 + 32.4377i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-11.4706 + 19.8676i) q^{25} +(-26.1213 + 15.0812i) q^{26} -5.19615i q^{27} -33.9411 q^{29} +(-1.75736 - 3.04384i) q^{30} +(-38.2279 - 22.0709i) q^{31} +(2.82843 - 4.89898i) q^{32} +(9.00000 - 5.19615i) q^{33} +12.6677i q^{34} -6.00000 q^{36} +(13.9853 + 24.2232i) q^{37} +(8.84924 + 5.10911i) q^{38} +(18.4706 - 31.9920i) q^{39} +(-3.51472 + 2.02922i) q^{40} +54.8313i q^{41} -1.48528 q^{43} +(-6.00000 - 10.3923i) q^{44} +(3.72792 + 2.15232i) q^{45} +(-26.4853 + 45.8739i) q^{46} +(37.2426 - 21.5020i) q^{47} +6.92820i q^{48} -32.4437 q^{50} +(-7.75736 - 13.4361i) q^{51} +(-36.9411 - 21.3280i) q^{52} +(42.7279 - 74.0069i) q^{53} +(6.36396 - 3.67423i) q^{54} +8.60927i q^{55} -12.5147 q^{57} +(-24.0000 - 41.5692i) q^{58} +(35.6985 + 20.6105i) q^{59} +(2.48528 - 4.30463i) q^{60} +(1.02944 - 0.594346i) q^{61} -62.4259i q^{62} +8.00000 q^{64} +(15.3015 + 26.5030i) q^{65} +(12.7279 + 7.34847i) q^{66} +(-2.19848 + 3.80789i) q^{67} +(-15.5147 + 8.95743i) q^{68} -64.8754i q^{69} +137.397 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-68.3528 - 39.4635i) q^{73} +(-19.7782 + 34.2568i) q^{74} +(34.4117 - 19.8676i) q^{75} +14.4508i q^{76} +52.2426 q^{78} +(-49.1690 - 85.1633i) q^{79} +(-4.97056 - 2.86976i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-67.1543 + 38.7716i) q^{82} -110.401i q^{83} +12.8528 q^{85} +(-1.05025 - 1.81909i) q^{86} +(50.9117 + 29.3939i) q^{87} +(8.48528 - 14.6969i) q^{88} +(18.0000 - 10.3923i) q^{89} +6.08767i q^{90} -74.9117 q^{92} +(38.2279 + 66.2127i) q^{93} +(52.6690 + 30.4085i) q^{94} +(5.18377 - 8.97855i) q^{95} +(-8.48528 + 4.89898i) q^{96} +10.9867i q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 4 q^{4} - 12 q^{5} + 6 q^{9} + 24 q^{10} - 12 q^{11} + 12 q^{12} + 24 q^{15} - 8 q^{16} + 48 q^{17} + 42 q^{19} + 24 q^{23} + 22 q^{25} - 96 q^{26} - 24 q^{30} - 102 q^{31} + 36 q^{33} - 24 q^{36}+ \cdots - 72 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 4 * q^4 - 12 * q^5 + 6 * q^9 + 24 * q^10 - 12 * q^11 + 12 * q^12 + 24 * q^15 - 8 * q^16 + 48 * q^17 + 42 * q^19 + 24 * q^23 + 22 * q^25 - 96 * q^26 - 24 * q^30 - 102 * q^31 + 36 * q^33 - 24 * q^36 + 22 * q^37 - 24 * q^38 + 6 * q^39 - 48 * q^40 + 28 * q^43 - 24 * q^44 - 36 * q^45 - 72 * q^46 + 132 * q^47 - 192 * q^50 - 48 * q^51 - 12 * q^52 + 120 * q^53 - 84 * q^57 - 96 * q^58 + 24 * q^59 - 24 * q^60 + 72 * q^61 + 32 * q^64 + 180 * q^65 + 110 * q^67 - 96 * q^68 + 312 * q^71 + 66 * q^73 - 48 * q^74 - 66 * q^75 + 192 * q^78 - 10 * q^79 + 48 * q^80 - 18 * q^81 - 48 * q^82 - 288 * q^85 - 24 * q^86 + 72 * q^89 - 96 * q^92 + 102 * q^93 + 24 * q^94 - 132 * q^95 - 72 * q^99

Introduction

L-functions

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