LMFDB - Embedded newform 294.3.g.a.19.2

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			19.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.19
Dual form			294.3.g.a.31.2

$q$-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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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	0.619090	−	0.785320i	$-0.287502\pi$
$5$	1.24264	+	0.717439i	0.248528	+	0.143488i	−0.370562	+	0.928808i	$0.620835\pi$
$6$			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	0.696832	−	0.717234i	$-0.254592\pi$
$11$	−3.00000	−	5.19615i	−0.272727	−	0.472377i	−0.969559	+	0.244857i	$0.921259\pi$
$12$	3.00000	+	1.73205i	0.250000	+	0.144338i
$13$		−	21.3280i		−	1.64061i	−0.571924	−	0.820306i	$-0.693803\pi$
$13$		−	21.3280i		−	1.64061i	0.571924	−	0.820306i	$-0.306197\pi$
$14$		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	−0.254178	−	0.967157i	$-0.581805\pi$
$17$	7.75736	−	4.47871i	0.456315	−	0.263454i	0.710494	+	0.703704i	$0.248472\pi$
$18$	−2.12132	−	3.67423i	−0.117851	−	0.204124i
$19$	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	$0.605772\pi$
$20$		−	2.86976i		−	0.143488i
$21$		0			0
$22$	−8.48528			−0.385695
$23$	18.7279	−	32.4377i	0.814257	−	1.41034i	−0.0956024	−	0.995420i	$-0.530478\pi$
$23$	18.7279	−	32.4377i	0.814257	−	1.41034i	0.909860	−	0.414916i	$-0.136189\pi$
$24$	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	−0.967687	−	0.252154i	$-0.918861\pi$
$31$	−38.2279	+	22.0709i	−1.23316	+	0.711965i	−0.265472	+	0.964119i	$0.585528\pi$
$32$	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	−0.612788	−	0.790248i	$-0.709952\pi$
$37$	13.9853	−	24.2232i	0.377981	−	0.654682i	0.990768	+	0.135566i	$0.0432853\pi$
$38$	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	$-0.766862\pi$
$41$		−	54.8313i		−	1.33735i	0.743556	−	0.668674i	$-0.233138\pi$
$42$		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	0.840806	−	0.541337i	$-0.182082\pi$
$47$	37.2426	+	21.5020i	0.792397	+	0.457490i	−0.0484090	+	0.998828i	$0.515415\pi$
$48$		−	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	0.915487	+	0.402348i	$0.131806\pi$
$53$	42.7279	+	74.0069i	0.806187	+	1.39636i	−0.109299	+	0.994009i	$0.534861\pi$
$54$	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	−0.165970	−	0.986131i	$-0.553076\pi$
$59$	35.6985	−	20.6105i	0.605059	−	0.349331i	0.771029	+	0.636800i	$0.219742\pi$
$60$	2.48528	+	4.30463i	0.0414214	+	0.0717439i
$61$	1.02944	+	0.594346i	0.0168760	+	0.00974337i	0.508414	−	0.861113i	$-0.330232\pi$
$61$	1.02944	+	0.594346i	0.0168760	+	0.00974337i	−0.491538	+	0.870856i	$0.663565\pi$
$62$			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	0.849152	−	0.528148i	$-0.177113\pi$
$67$	−2.19848	−	3.80789i	−0.0328132	−	0.0568341i	−0.881966	+	0.471314i	$0.843780\pi$
$68$	−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	−0.888811	−	0.458274i	$-0.848468\pi$
$73$	−68.3528	+	39.4635i	−0.936340	+	0.540596i	−0.0475288	+	0.998870i	$0.515135\pi$
$74$	−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	0.366646	+	0.930361i	$0.380506\pi$
$79$	−49.1690	+	85.1633i	−0.622393	+	1.07802i	−0.989039	+	0.147656i	$0.952827\pi$
$80$	−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	$0.231597\pi$
$83$			110.401i			1.33013i	−0.746784	+	0.665067i	$0.768403\pi$
$84$		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	0.597703	−	0.801717i	$-0.296080\pi$
$89$	18.0000	+	10.3923i	0.202247	+	0.116767i	−0.395456	+	0.918485i	$0.629413\pi$
$90$		−	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	$-0.981964\pi$
$97$		−	10.9867i		−	0.113264i	0.998395	−	0.0566322i	$-0.0180362\pi$
$98$		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	0.0357136	−	0.999362i	$-0.488630\pi$
$101$	92.8234	−	53.5916i	0.919043	−	0.530610i	0.883330	+	0.468752i	$0.155296\pi$
$102$	10.9706	+	19.0016i	0.107555	+	0.186290i
$103$	−91.1102	−	52.6025i	−0.884565	−	0.510704i	−0.0124040	−	0.999923i	$-0.503948\pi$
$103$	−91.1102	−	52.6025i	−0.884565	−	0.510704i	−0.872161	+	0.489219i	$0.837282\pi$
$104$			60.3246i			0.580044i
$105$		0			0
$106$	120.853			1.14012
$107$	−59.2721	+	102.662i	−0.553945	+	0.959460i	0.444040	+	0.896007i	$0.353545\pi$
$107$	−59.2721	+	102.662i	−0.553945	+	0.959460i	−0.997985	+	0.0634534i	$0.979789\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	−55.5294	−	96.1798i	−0.509444	−	0.882384i	−0.999940	−	0.0109400i	$-0.996518\pi$
$109$	−55.5294	−	96.1798i	−0.509444	−	0.882384i	0.490496	−	0.871444i	$-0.336816\pi$
$110$	−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	0.686668	−	0.726971i	$-0.259073\pi$
$131$	52.4558	+	30.2854i	0.400426	+	0.231186i	−0.286242	+	0.958157i	$0.592406\pi$
$132$		−	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	0.717395	−	0.696666i	$-0.245334\pi$
$137$	−33.5147	−	58.0492i	−0.244633	−	0.423717i	−0.962028	+	0.272949i	$0.912001\pi$
$138$	79.4558	+	45.8739i	0.575767	+	0.332419i
$139$			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
$142$	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	−0.969402	−	0.245480i	$-0.921054\pi$
$149$	−40.5442	+	70.2245i	−0.272108	+	0.471306i	0.697293	+	0.716786i	$0.254388\pi$
$150$	48.6655	−	28.0970i	0.324437	−	0.187314i
$151$	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	$0.779100\pi$
$152$	−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	−0.917513	−	0.397705i	$-0.869807\pi$
$157$	−162.000	+	93.5307i	−1.03185	+	0.595737i	−0.114334	+	0.993442i	$0.536473\pi$
$158$	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	−0.965568	−	0.260149i	$-0.916228\pi$
$163$	−41.9706	+	72.6951i	−0.257488	+	0.445982i	0.708080	+	0.706132i	$0.249561\pi$
$164$	−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	$-0.875203\pi$
$167$		−	127.620i		−	0.764190i	0.924123	−	0.382095i	$-0.124797\pi$
$168$		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	0.813168	−	0.582029i	$-0.197741\pi$
$173$	123.816	+	71.4853i	0.715701	+	0.413210i	−0.0974675	+	0.995239i	$0.531074\pi$
$174$		−	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	0.526670	−	0.850070i	$-0.323440\pi$
$179$	−84.6396	−	146.600i	−0.472847	−	0.818995i	−0.999517	+	0.0310748i	$0.990107\pi$
$180$	−7.45584	−	4.30463i	−0.0414214	−	0.0239146i
$181$		−	209.969i		−	1.16005i	−0.814600	−	0.580024i	$-0.803043\pi$
$181$		−	209.969i		−	1.16005i	0.814600	−	0.580024i	$-0.196957\pi$
$182$		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	−0.939937	−	0.341347i	$-0.889117\pi$
$191$	−33.3015	+	57.6799i	−0.174353	+	0.301989i	0.765584	+	0.643336i	$0.222450\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	4.89697	+	8.48180i	0.0253729	+	0.0439472i	0.878433	−	0.477865i	$-0.158589\pi$
$193$	4.89697	+	8.48180i	0.0253729	+	0.0439472i	−0.853060	+	0.521813i	$0.825256\pi$
$194$	−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	−0.187249	−	0.982312i	$-0.559957\pi$
$199$	113.397	−	65.4698i	0.569834	−	0.328994i	0.757083	+	0.653319i	$0.226624\pi$
$200$	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	$0.171327\pi$
$223$			228.631i			1.02525i	−0.858613	+	0.512625i	$0.828673\pi$
$224$		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	−0.619912	−	0.784671i	$-0.712832\pi$
$227$	−56.8234	+	32.8070i	−0.250323	+	0.144524i	0.369589	+	0.929195i	$0.379498\pi$
$228$	12.5147	+	21.6761i	0.0548891	+	0.0950707i
$229$	−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	$0.732095\pi$
$230$		−	76.0063i		−	0.330462i
$231$		0			0
$232$	96.0000			0.413793
$233$	118.757	−	205.694i	0.509688	−	0.882806i	−0.490249	−	0.871583i	$-0.663094\pi$
$233$	118.757	−	205.694i	0.509688	−	0.882806i	0.999937	−	0.0112234i	$-0.00357259\pi$
$234$	−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	0.513049	−	0.858359i	$-0.328516\pi$
$241$	364.617	−	210.512i	1.51293	−	0.873493i	0.999885	−	0.0151343i	$-0.00481759\pi$
$242$	−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	$-0.905655\pi$
$251$		−	146.621i		−	0.584148i	0.956396	−	0.292074i	$-0.0943454\pi$
$252$		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	0.457132	−	0.889399i	$-0.348877\pi$
$257$	−21.7279	−	12.5446i	−0.0845444	−	0.0488118i	−0.541676	+	0.840587i	$0.682210\pi$
$258$		−	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	0.939254	−	0.343222i	$-0.111518\pi$
$263$	45.3381	+	78.5279i	0.172388	+	0.298585i	−0.766866	+	0.641807i	$0.778185\pi$
$264$	−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	−0.385839	−	0.922566i	$-0.626088\pi$
$269$	59.2355	−	34.1996i	0.220206	−	0.127136i	0.606046	+	0.795430i	$0.292755\pi$
$270$	5.27208	+	9.13151i	0.0195262	+	0.0338204i
$271$	106.971	+	61.7595i	0.394725	+	0.227895i	0.684206	−	0.729289i	$-0.260149\pi$
$271$	106.971	+	61.7595i	0.394725	+	0.227895i	−0.289480	+	0.957184i	$0.593482\pi$
$272$			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	0.999963	−	0.00856145i	$-0.00272523\pi$
$277$	136.441	+	236.323i	0.492567	+	0.853151i	−0.507396	+	0.861713i	$0.669392\pi$
$278$	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	−0.289882	−	0.957063i	$-0.593616\pi$
$283$	111.507	−	64.3787i	0.394018	−	0.227486i	0.683900	+	0.729576i	$0.260283\pi$
$284$	−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	$-0.823213\pi$
$293$		−	308.984i		−	1.05455i	0.849694	−	0.527276i	$-0.176787\pi$
$294$		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	$0.448850\pi$
$307$			606.090i			1.97423i	−0.160003	+	0.987117i	$0.551150\pi$
$308$		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	−0.189516	−	0.981878i	$-0.560692\pi$
$311$	176.044	−	101.639i	0.566057	−	0.326813i	0.755573	+	0.655064i	$0.227359\pi$
$312$	−52.2426	−	90.4869i	−0.167444	−	0.290022i
$313$	351.294	+	202.820i	1.12234	+	0.647986i	0.941999	−	0.335617i	$-0.108945\pi$
$313$	351.294	+	202.820i	1.12234	+	0.647986i	0.180346	+	0.983603i	$0.442278\pi$
$314$			264.545i			0.842500i
$315$		0			0
$316$	196.676			0.622393
$317$	13.0294	−	22.5676i	0.0411023	−	0.0711913i	−0.844742	−	0.535173i	$-0.820246\pi$
$317$	13.0294	−	22.5676i	0.0411023	−	0.0711913i	0.885845	+	0.463982i	$0.153580\pi$
$318$	−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	−0.772237	−	0.635335i	$-0.780862\pi$
$331$	54.3162	−	94.0785i	0.164097	−	0.284225i	0.936334	+	0.351110i	$0.114196\pi$
$332$	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	0.840341	−	0.542059i	$-0.182355\pi$
$347$	−17.0955	−	29.6102i	−0.0492664	−	0.0853320i	−0.889607	+	0.456727i	$0.849022\pi$
$348$	−101.823	−	58.7878i	−0.292596	−	0.168930i
$349$			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
$352$	16.9706	−	29.3939i	0.0482118	−	0.0835053i
$353$	−387.448	+	223.693i	−1.09759	+	0.633692i	−0.935586	−	0.353099i	$-0.885128\pi$
$353$	−387.448	+	223.693i	−1.09759	+	0.633692i	−0.162000	+	0.986791i	$0.551794\pi$
$354$	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	−0.994478	−	0.104941i	$-0.966534\pi$
$359$	−145.882	+	252.675i	−0.406357	+	0.703831i	0.588121	+	0.808773i	$0.299868\pi$
$360$	−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	0.0844183	−	0.996430i	$-0.473097\pi$
$367$	363.169	−	209.676i	0.989561	−	0.571324i	0.905143	+	0.425107i	$0.139763\pi$
$368$	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	−0.886292	−	0.463127i	$-0.846728\pi$
$373$	−15.6909	+	27.1775i	−0.0420668	+	0.0728618i	0.844225	+	0.535988i	$0.180061\pi$
$374$	−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	0.943265	−	0.332041i	$-0.107737\pi$
$383$	431.772	+	249.283i	1.12734	+	0.650871i	0.184076	+	0.982912i	$0.441071\pi$
$384$			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	0.895284	+	0.445496i	$0.146973\pi$
$389$	324.213	+	561.554i	0.833453	+	1.44358i	−0.0618308	+	0.998087i	$0.519694\pi$
$390$	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	0.415096	−	0.909777i	$-0.363748\pi$
$397$	−65.6026	−	37.8757i	−0.165246	−	0.0954047i	−0.580342	+	0.814373i	$0.697081\pi$
$398$		−	185.176i		−	0.465268i
$399$		0			0
$400$	91.7645			0.229411
$401$	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	$-0.0817377\pi$
$402$	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	−0.0713023	−	0.997455i	$-0.522716\pi$
$409$	309.559	−	178.724i	0.756868	−	0.436978i	0.828170	+	0.560477i	$0.189382\pi$
$410$	−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	$-0.795464\pi$
$419$		−	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	$0.487221\pi$
$422$	−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	−0.994955	−	0.100326i	$-0.968012\pi$
$431$	−251.860	−	436.234i	−0.584362	−	1.01214i	0.410593	−	0.911819i	$-0.365322\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$		−	837.548i		−	1.93429i	−0.254224	−	0.967145i	$-0.581820\pi$
$433$		−	837.548i		−	1.93429i	0.254224	−	0.967145i	$-0.418180\pi$
$434$		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	0.675575	−	0.737292i	$-0.263896\pi$
$439$	164.558	+	95.0079i	0.374848	+	0.216419i	−0.300726	+	0.953711i	$0.597229\pi$
$440$			24.3507i			0.0553425i
$441$		0			0
$442$	−270.177			−0.611259
$443$	84.7279	−	146.753i	0.191259	−	0.331271i	−0.754408	−	0.656405i	$-0.772076\pi$
$443$	84.7279	−	146.753i	0.191259	−	0.331271i	0.945668	+	0.325134i	$0.105409\pi$
$444$	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	−0.628158	−	0.778086i	$-0.716191\pi$
$457$	164.412	−	284.769i	0.359763	−	0.623128i	0.987921	+	0.154958i	$0.0495242\pi$
$458$	−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	$0.330494\pi$
$461$			794.331i			1.72306i	−0.507706	+	0.861530i	$0.669506\pi$
$462$		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	0.502619	−	0.864508i	$-0.332370\pi$
$467$	2.44870	+	1.41376i	0.00524347	+	0.00302732i	−0.497376	+	0.867535i	$0.665703\pi$
$468$			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	−0.802171	−	0.597095i	$-0.796322\pi$
$479$	−328.669	+	189.757i	−0.686157	+	0.396153i	0.116014	+	0.993248i	$0.462988\pi$
$480$	−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	−0.994115	−	0.108333i	$-0.965449\pi$
$487$	−287.757	−	498.410i	−0.590877	−	1.02343i	0.403238	−	0.915095i	$-0.367885\pi$
$488$	−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	−0.685980	−	0.727620i	$-0.740626\pi$
$499$	143.287	−	248.180i	0.287148	−	0.497355i	0.973128	+	0.230266i	$0.0739595\pi$
$500$	−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	$-0.991950\pi$
$503$		−	25.4374i		−	0.0505714i	0.999680	−	0.0252857i	$-0.00804954\pi$
$504$		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	0.991066	−	0.133370i	$-0.0425800\pi$
$509$	697.889	+	402.926i	1.37110	+	0.791603i	0.380031	+	0.924974i	$0.375913\pi$
$510$			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	0.295068	−	0.955476i	$-0.404658\pi$
$521$	661.706	−	382.036i	1.27007	−	0.733274i	0.975001	+	0.222202i	$0.0713244\pi$
$522$	72.0000	+	124.708i	0.137931	+	0.238904i
$523$	153.096	+	88.3900i	0.292726	+	0.169006i	0.639171	−	0.769065i	$-0.279278\pi$
$523$	153.096	+	88.3900i	0.292726	+	0.169006i	−0.346444	+	0.938071i	$0.612611\pi$
$524$		−	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	−0.873854	−	0.486189i	$-0.838387\pi$
$541$	−8.58831	+	14.8754i	−0.0158749	+	0.0274961i	0.857979	+	0.513685i	$0.171720\pi$
$542$	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	0.925085	+	0.379760i	$0.123993\pi$
$557$	440.823	+	763.528i	0.791424	+	1.37079i	−0.133661	+	0.991027i	$0.542673\pi$
$558$	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	−0.955998	−	0.293372i	$-0.905223\pi$
$563$	−664.301	+	383.534i	−1.17993	+	0.681233i	−0.223932	+	0.974605i	$0.571889\pi$
$564$	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	−0.852868	−	0.522127i	$-0.825139\pi$
$569$	14.6468	−	25.3689i	0.0257412	−	0.0445851i	0.878609	+	0.477542i	$0.158472\pi$
$570$	−21.9929	+	12.6976i	−0.0385840	+	0.0222765i
$571$	−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	$-0.487094\pi$
$572$	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	−0.684300	−	0.729201i	$-0.739892\pi$
$577$	−227.883	+	131.568i	−0.394944	+	0.228021i	0.289356	+	0.957222i	$0.406559\pi$
$578$	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	$0.121254\pi$
$587$			436.477i			0.743572i	−0.928318	+	0.371786i	$0.878746\pi$
$588$		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	−0.104391	−	0.994536i	$-0.533289\pi$
$593$	−603.603	−	348.490i	−1.01788	−	0.587673i	−0.913489	+	0.406863i	$0.866623\pi$
$594$		−	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	0.650450	−	0.759549i	$-0.274581\pi$
$599$	−199.206	−	345.035i	−0.332564	−	0.576018i	−0.983014	+	0.183531i	$0.941247\pi$
$600$	−97.3310	−	56.1941i	−0.162218	−	0.0936568i
$601$			36.1691i			0.0601816i	0.999547	+	0.0300908i	$0.00957964\pi$
$601$			36.1691i			0.0601816i	−0.999547	+	0.0300908i	$0.990420\pi$
$602$		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	0.477306	−	0.878737i	$-0.341613\pi$
$607$	−27.3457	−	15.7880i	−0.0450505	−	0.0260099i	−0.522356	+	0.852727i	$0.674947\pi$
$608$			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	0.983258	−	0.182220i	$-0.0583285\pi$
$613$	204.632	+	354.434i	0.333821	+	0.578195i	−0.649436	+	0.760416i	$0.724995\pi$
$614$	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	−0.794417	−	0.607373i	$-0.792223\pi$
$619$	−412.022	+	237.881i	−0.665625	+	0.384299i	0.128792	+	0.991672i	$0.458890\pi$
$620$	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	0.941438	−	0.337186i	$-0.109475\pi$
$641$	114.551	+	198.409i	0.178707	+	0.309530i	−0.762731	+	0.646716i	$0.776142\pi$
$642$	−251.470	−	145.186i	−0.391698	−	0.226147i
$643$		−	854.640i		−	1.32914i	−0.747224	−	0.664572i	$-0.768614\pi$
$643$		−	854.640i		−	1.32914i	0.747224	−	0.664572i	$-0.231386\pi$
$644$		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	−0.987182	−	0.159601i	$-0.948979\pi$
$647$	−868.632	+	501.505i	−1.34255	+	0.775124i	−0.355372	+	0.934725i	$0.615646\pi$
$648$	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	−0.286698	+	0.958021i	$0.592558\pi$
$653$	−635.382	+	1100.51i	−0.973020	+	1.68532i	−0.686321	+	0.727299i	$0.740776\pi$
$654$	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	−0.553881	−	0.832596i	$-0.686854\pi$
$661$	−72.5589	+	41.8919i	−0.109771	+	0.0633765i	0.444109	+	0.895973i	$0.353520\pi$
$662$	−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	−0.100386	−	0.994949i	$-0.532008\pi$
$677$	−685.279	−	395.646i	−1.01223	−	0.584411i	−0.911844	+	0.410538i	$0.865341\pi$
$678$			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	0.960781	−	0.277308i	$-0.0894423\pi$
$683$	164.080	+	284.195i	0.240235	+	0.416099i	−0.720546	+	0.693407i	$0.756109\pi$
$684$	−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	−0.292212	−	0.956353i	$-0.594391\pi$
$691$	−875.182	−	505.287i	−1.26654	−	0.731240i	−0.974333	+	0.225113i	$0.927725\pi$
$692$		−	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	0.0313734	+	0.999508i	$0.490012\pi$
$709$	−602.588	+	1043.71i	−0.849912	+	1.47209i	−0.881286	+	0.472584i	$0.843321\pi$
$710$	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	−0.226666	−	0.973973i	$-0.572783\pi$
$719$	−850.925	−	491.282i	−1.18348	−	0.683285i	−0.956818	+	0.290688i	$0.906116\pi$
$720$			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	$-0.857247\pi$
$727$		−	630.440i		−	0.867181i	0.901110	−	0.433590i	$-0.142753\pi$
$728$		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	0.313207	−	0.949685i	$-0.398597\pi$
$733$	−258.486	−	149.237i	−0.352641	−	0.203597i	−0.665848	+	0.746088i	$0.731930\pi$
$734$		−	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	0.725214	−	0.688524i	$-0.241741\pi$
$739$	−172.684	−	299.097i	−0.233672	−	0.404732i	−0.958886	+	0.283792i	$0.908408\pi$
$740$	−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	−0.606730	−	0.794908i	$-0.707519\pi$
$751$	289.169	−	500.855i	0.385045	−	0.666918i	0.991775	+	0.127990i	$0.0408525\pi$
$752$	−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	0.627214	−	0.778847i	$-0.284195\pi$
$761$	202.669	+	117.011i	0.266319	+	0.153760i	−0.360894	+	0.932607i	$0.617529\pi$
$762$			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	$0.316774\pi$
$769$			1290.16i			1.67771i	−0.544358	+	0.838853i	$0.683226\pi$
$770$		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	−0.706625	−	0.707588i	$-0.749783\pi$
$773$	−345.646	+	199.559i	−0.447149	+	0.258161i	0.259477	+	0.965749i	$0.416450\pi$
$774$	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	0.782637	−	0.622478i	$-0.213874\pi$
$787$	1348.16	−	778.361i	1.71304	−	0.989023i	0.930401	−	0.366544i	$-0.119459\pi$
$788$	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	$0.122892\pi$
$797$			600.232i			0.753114i	−0.926393	+	0.376557i	$0.877108\pi$
$798$		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	0.928139	−	0.372234i	$-0.121408\pi$
$809$	114.640	+	198.562i	0.141705	+	0.245441i	−0.786434	+	0.617675i	$0.788075\pi$
$810$	−15.8162	−	9.13151i	−0.0195262	−	0.0112735i
$811$			529.955i			0.653459i	0.945118	+	0.326729i	$0.105947\pi$
$811$			529.955i			0.653459i	−0.945118	+	0.326729i	$0.894053\pi$
$812$		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	−0.758751	−	0.651381i	$-0.774190\pi$
$821$	151.669	−	262.698i	0.184737	−	0.319974i	0.943488	+	0.331407i	$0.107523\pi$
$822$	142.191	−	82.0940i	0.172982	−	0.0998710i
$823$	564.955	+	978.531i	0.686459	+	1.18898i	0.972976	+	0.230906i	$0.0741690\pi$
$823$	564.955	+	978.531i	0.686459	+	1.18898i	−0.286517	+	0.958075i	$0.592498\pi$
$824$	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	−0.606962	+	0.794731i	$0.707612\pi$
$829$	−1325.32	+	765.175i	−1.59870	+	0.923010i	−0.991738	+	0.128279i	$0.959055\pi$
$830$	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	$-0.958409\pi$
$839$		−	218.629i		−	0.260583i	0.991476	−	0.130291i	$-0.0415913\pi$
$840$		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	$0.147539\pi$
$853$			762.730i			0.894174i	−0.894491	+	0.447087i	$0.852461\pi$
$854$		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	0.0415977	−	0.999134i	$-0.486755\pi$
$857$	795.015	−	459.002i	0.927672	−	0.535592i	0.886075	+	0.463543i	$0.153422\pi$
$858$	−156.728	−	271.461i	−0.182667	−	0.316388i
$859$	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	$0.495672\pi$
$860$			4.26239i			0.00495627i
$861$		0			0
$862$	−712.368			−0.826412
$863$	−175.294	+	303.619i	−0.203122	+	0.351818i	−0.949533	−	0.313668i	$-0.898442\pi$
$863$	−175.294	+	303.619i	−0.203122	+	0.351818i	0.746411	+	0.665486i	$0.231776\pi$
$864$	−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	−0.867038	−	0.498242i	$-0.833979\pi$
$877$	−1.77965	+	3.08245i	−0.00202925	+	0.00351477i	0.865009	+	0.501756i	$0.167313\pi$
$878$	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	$-0.910567\pi$
$881$		−	488.565i		−	0.554557i	0.960790	−	0.277279i	$-0.0894325\pi$
$882$		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	0.456964	−	0.889485i	$-0.348937\pi$
$887$	−75.2801	−	43.4630i	−0.0848704	−	0.0490000i	−0.541835	+	0.840485i	$0.682270\pi$
$888$		−	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	0.964645	−	0.263554i	$-0.0848948\pi$
$907$	230.448	+	399.148i	0.254077	+	0.440075i	−0.710567	+	0.703629i	$0.751562\pi$
$908$	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	−0.680140	−	0.733082i	$-0.738081\pi$
$919$	270.919	−	469.246i	0.294798	−	0.510605i	0.974938	+	0.222477i	$0.0714143\pi$
$920$	−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	0.856990	−	0.515333i	$-0.172332\pi$
$929$	779.610	+	450.108i	0.839193	+	0.484508i	−0.0177969	+	0.999842i	$0.505665\pi$
$930$		−	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	$0.0398441\pi$
$937$			233.964i			0.249695i	−0.992176	+	0.124847i	$0.960156\pi$
$938$		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	−0.961331	−	0.275394i	$-0.911192\pi$
$941$	−1132.49	+	653.845i	−1.20350	+	0.694840i	−0.242167	+	0.970234i	$0.577858\pi$
$942$	−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	−0.398045	−	0.917366i	$-0.630311\pi$
$947$	563.881	−	976.671i	0.595440	−	1.03133i	0.993485	−	0.113966i	$-0.0363555\pi$
$948$	−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	0.439931	−	0.898032i	$-0.355003\pi$
$971$	−114.405	−	66.0517i	−0.117822	−	0.0680245i	−0.557753	+	0.830007i	$0.688336\pi$
$972$		−	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	0.728235	−	0.685327i	$-0.240341\pi$
$977$	−224.117	−	388.182i	−0.229393	−	0.397320i	−0.957628	+	0.288007i	$0.907007\pi$
$978$	−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	−0.998527	−	0.0542567i	$-0.982721\pi$
$983$	−1426.14	+	823.382i	−1.45080	+	0.837621i	−0.452276	+	0.891878i	$0.649388\pi$
$984$	−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	0.979925	−	0.199369i	$-0.0638891\pi$
$991$	314.448	+	544.640i	0.317304	+	0.549587i	−0.662621	+	0.748955i	$0.730556\pi$
$992$	−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	0.00416289	−	0.999991i	$-0.498675\pi$
$997$	869.645	−	502.090i	0.872262	−	0.503601i	0.868099	+	0.496390i	$0.165342\pi$
$998$	−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.19.2		4
3.2	odd	2		882.3.n.e.19.1		4
7.2	even	3		294.3.c.a.97.1		4
7.3	odd	6	inner	294.3.g.a.31.2		4
7.4	even	3		42.3.g.a.31.2	yes	4
7.5	odd	6		294.3.c.a.97.2		4
7.6	odd	2		42.3.g.a.19.2	✓	4
21.2	odd	6		882.3.c.b.685.4		4
21.5	even	6		882.3.c.b.685.3		4
21.11	odd	6		126.3.n.a.73.1		4
21.17	even	6		882.3.n.e.325.1		4
21.20	even	2		126.3.n.a.19.1		4
28.11	odd	6		336.3.bh.e.241.1		4
28.19	even	6		2352.3.f.e.97.2		4
28.23	odd	6		2352.3.f.e.97.3		4
28.27	even	2		336.3.bh.e.145.1		4
35.4	even	6		1050.3.p.a.451.1		4
35.13	even	4		1050.3.q.a.649.2		8
35.18	odd	12		1050.3.q.a.199.3		8
35.27	even	4		1050.3.q.a.649.3		8
35.32	odd	12		1050.3.q.a.199.2		8
35.34	odd	2		1050.3.p.a.901.1		4
84.11	even	6		1008.3.cg.h.577.2		4
84.83	odd	2		1008.3.cg.h.145.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.2	✓	4	7.6	odd	2
42.3.g.a.31.2	yes	4	7.4	even	3
126.3.n.a.19.1		4	21.20	even	2
126.3.n.a.73.1		4	21.11	odd	6
294.3.c.a.97.1		4	7.2	even	3
294.3.c.a.97.2		4	7.5	odd	6
294.3.g.a.19.2		4	1.1	even	1	trivial
294.3.g.a.31.2		4	7.3	odd	6	inner
336.3.bh.e.145.1		4	28.27	even	2
336.3.bh.e.241.1		4	28.11	odd	6
882.3.c.b.685.3		4	21.5	even	6
882.3.c.b.685.4		4	21.2	odd	6
882.3.n.e.19.1		4	3.2	odd	2
882.3.n.e.325.1		4	21.17	even	6
1008.3.cg.h.145.2		4	84.83	odd	2
1008.3.cg.h.577.2		4	84.11	even	6
1050.3.p.a.451.1		4	35.4	even	6
1050.3.p.a.901.1		4	35.34	odd	2
1050.3.q.a.199.2		8	35.32	odd	12
1050.3.q.a.199.3		8	35.18	odd	12
1050.3.q.a.649.2		8	35.13	even	4
1050.3.q.a.649.3		8	35.27	even	4
2352.3.f.e.97.2		4	28.19	even	6
2352.3.f.e.97.3		4	28.23	odd	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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