LMFDB - Embedded newform 504.3.e.c.251.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(251,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.251"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.37
Character	$\chi$	$=$	504.251
Dual form			504.3.e.c.251.39

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.64277 - 1.14075i) q^{2} +(1.39736 - 3.74798i) q^{4} +3.51431i q^{5} +(6.42922 + 2.76859i) q^{7} +(-1.97998 - 7.75111i) q^{8} +(4.00896 + 5.77318i) q^{10} -5.26675i q^{11} +9.36128 q^{13} +(13.7200 - 2.78601i) q^{14} +(-12.0948 - 10.4746i) q^{16} +12.3664 q^{17} +8.84770i q^{19} +(13.1716 + 4.91076i) q^{20} +(-6.00806 - 8.65204i) q^{22} -4.29743 q^{23} +12.6496 q^{25} +(15.3784 - 10.6789i) q^{26} +(19.3606 - 20.2279i) q^{28} +18.6786 q^{29} +52.1525 q^{31} +(-31.8178 - 3.41016i) q^{32} +(20.3151 - 14.1070i) q^{34} +(-9.72968 + 22.5943i) q^{35} -45.4695i q^{37} +(10.0930 + 14.5347i) q^{38} +(27.2398 - 6.95827i) q^{40} -42.0916 q^{41} -23.2557 q^{43} +(-19.7397 - 7.35956i) q^{44} +(-7.05967 + 4.90230i) q^{46} -28.5041i q^{47} +(33.6698 + 35.5998i) q^{49} +(20.7804 - 14.4301i) q^{50} +(13.0811 - 35.0859i) q^{52} -18.1585 q^{53} +18.5090 q^{55} +(8.72990 - 55.3154i) q^{56} +(30.6845 - 21.3076i) q^{58} -76.3857 q^{59} -3.84787 q^{61} +(85.6744 - 59.4932i) q^{62} +(-56.1593 + 30.6942i) q^{64} +32.8984i q^{65} +4.55636 q^{67} +(17.2803 - 46.3491i) q^{68} +(9.79088 + 48.2163i) q^{70} -40.3858 q^{71} +123.009i q^{73} +(-51.8695 - 74.6958i) q^{74} +(33.1610 + 12.3634i) q^{76} +(14.5815 - 33.8611i) q^{77} -107.545i q^{79} +(36.8109 - 42.5047i) q^{80} +(-69.1466 + 48.0161i) q^{82} -92.3016 q^{83} +43.4593i q^{85} +(-38.2036 + 26.5290i) q^{86} +(-40.8231 + 10.4281i) q^{88} -1.80053 q^{89} +(60.1857 + 25.9176i) q^{91} +(-6.00506 + 16.1067i) q^{92} +(-32.5161 - 46.8255i) q^{94} -31.0935 q^{95} +122.204i q^{97} +(95.9222 + 20.0732i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 144 q^{22} - 336 q^{25} - 232 q^{28} - 384 q^{43} + 736 q^{46} + 368 q^{49} - 432 q^{58} + 480 q^{64} - 896 q^{67} + 264 q^{70} - 48 q^{88} - 576 q^{91}+O(q^{100}) $ 48 * q + 144 * q^22 - 336 * q^25 - 232 * q^28 - 384 * q^43 + 736 * q^46 + 368 * q^49 - 432 * q^58 + 480 * q^64 - 896 * q^67 + 264 * q^70 - 48 * q^88 - 576 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.64277	−	1.14075i	0.821383	−	0.570377i
$2$	1.64277	−	1.14075i	0.821383	−	0.570377i
$3$		0			0
$3$		0			0
$4$	1.39736	−	3.74798i	0.349341	−	0.936996i
$5$			3.51431i			0.702861i	0.936214	+	0.351431i	$0.114305\pi$
$5$			3.51431i			0.702861i	−0.936214	+	0.351431i	$0.885695\pi$
$6$		0			0
$7$	6.42922	+	2.76859i	0.918460	+	0.395513i
$7$	6.42922	+	2.76859i	0.918460	+	0.395513i
$8$	−1.97998	−	7.75111i	−0.247498	−	0.968888i
$9$		0			0
$10$	4.00896	+	5.77318i	0.400896	+	0.577318i
$11$		−	5.26675i		−	0.478795i	−0.970922	−	0.239398i	$-0.923050\pi$
$11$		−	5.26675i		−	0.478795i	0.970922	−	0.239398i	$-0.0769499\pi$
$12$		0			0
$13$	9.36128			0.720098			0.360049	−	0.932933i	$-0.382760\pi$
$13$	9.36128			0.720098			0.360049	+	0.932933i	$0.382760\pi$
$14$	13.7200	−	2.78601i	0.979999	−	0.199000i
$15$		0			0
$16$	−12.0948	−	10.4746i	−0.755922	−	0.654661i
$17$	12.3664			0.727435			0.363718	−	0.931509i	$-0.381507\pi$
$17$	12.3664			0.727435			0.363718	+	0.931509i	$0.381507\pi$
$18$		0			0
$19$			8.84770i			0.465669i	0.972516	+	0.232834i	$0.0748000\pi$
$19$			8.84770i			0.465669i	−0.972516	+	0.232834i	$0.925200\pi$
$20$	13.1716	+	4.91076i	0.658578	+	0.245538i
$21$		0			0
$22$	−6.00806	−	8.65204i	−0.273094	−	0.393274i
$23$	−4.29743			−0.186845			−0.0934223	−	0.995627i	$-0.529781\pi$
$23$	−4.29743			−0.186845			−0.0934223	+	0.995627i	$0.529781\pi$
$24$		0			0
$25$	12.6496			0.505986
$26$	15.3784	−	10.6789i	0.591477	−	0.410727i
$27$		0			0
$28$	19.3606	−	20.2279i	0.691450	−	0.722425i
$29$	18.6786			0.644088			0.322044	−	0.946725i	$-0.395630\pi$
$29$	18.6786			0.644088			0.322044	+	0.946725i	$0.395630\pi$
$30$		0			0
$31$	52.1525			1.68234			0.841170	−	0.540771i	$-0.181867\pi$
$31$	52.1525			1.68234			0.841170	+	0.540771i	$0.181867\pi$
$32$	−31.8178	−	3.41016i	−0.994305	−	0.106567i
$33$		0			0
$34$	20.3151	−	14.1070i	0.597503	−	0.414912i
$35$	−9.72968	+	22.5943i	−0.277991	+	0.645550i
$36$		0			0
$37$		−	45.4695i		−	1.22891i	−0.788954	−	0.614453i	$-0.789377\pi$
$37$		−	45.4695i		−	1.22891i	0.788954	−	0.614453i	$-0.210623\pi$
$38$	10.0930	+	14.5347i	0.265607	+	0.382492i
$39$		0			0
$40$	27.2398	−	6.95827i	0.680994	−	0.173957i
$41$	−42.0916			−1.02662			−0.513312	−	0.858202i	$-0.671582\pi$
$41$	−42.0916			−1.02662			−0.513312	+	0.858202i	$0.671582\pi$
$42$		0			0
$43$	−23.2557			−0.540830			−0.270415	−	0.962744i	$-0.587161\pi$
$43$	−23.2557			−0.540830			−0.270415	+	0.962744i	$0.587161\pi$
$44$	−19.7397	−	7.35956i	−0.448629	−	0.167263i
$45$		0			0
$46$	−7.05967	+	4.90230i	−0.153471	+	0.106572i
$47$		−	28.5041i		−	0.606469i	−0.952916	−	0.303235i	$-0.901933\pi$
$47$		−	28.5041i		−	0.606469i	0.952916	−	0.303235i	$-0.0980666\pi$
$48$		0			0
$49$	33.6698	+	35.5998i	0.687139	+	0.726526i
$50$	20.7804	−	14.4301i	0.415608	−	0.288603i
$51$		0			0
$52$	13.0811	−	35.0859i	0.251560	−	0.674729i
$53$	−18.1585			−0.342614			−0.171307	−	0.985218i	$-0.554799\pi$
$53$	−18.1585			−0.342614			−0.171307	+	0.985218i	$0.554799\pi$
$54$		0			0
$55$	18.5090			0.336527
$56$	8.72990	−	55.3154i	0.155891	−	0.987774i
$57$		0			0
$58$	30.6845	−	21.3076i	0.529043	−	0.367373i
$59$	−76.3857			−1.29467			−0.647336	−	0.762205i	$-0.724117\pi$
$59$	−76.3857			−1.29467			−0.647336	+	0.762205i	$0.724117\pi$
$60$		0			0
$61$	−3.84787			−0.0630799			−0.0315400	−	0.999502i	$-0.510041\pi$
$61$	−3.84787			−0.0630799			−0.0315400	+	0.999502i	$0.510041\pi$
$62$	85.6744	−	59.4932i	1.38185	−	0.959568i
$63$		0			0
$64$	−56.1593	+	30.6942i	−0.877489	+	0.479596i
$65$			32.8984i			0.506129i
$66$		0			0
$67$	4.55636			0.0680054			0.0340027	−	0.999422i	$-0.489175\pi$
$67$	4.55636			0.0680054			0.0340027	+	0.999422i	$0.489175\pi$
$68$	17.2803	−	46.3491i	0.254123	−	0.681604i
$69$		0			0
$70$	9.79088	+	48.2163i	0.139870	+	0.688804i
$71$	−40.3858			−0.568814			−0.284407	−	0.958704i	$-0.591797\pi$
$71$	−40.3858			−0.568814			−0.284407	+	0.958704i	$0.591797\pi$
$72$		0			0
$73$			123.009i			1.68505i	0.538656	+	0.842526i	$0.318932\pi$
$73$			123.009i			1.68505i	−0.538656	+	0.842526i	$0.681068\pi$
$74$	−51.8695	−	74.6958i	−0.700939	−	1.00940i
$75$		0			0
$76$	33.1610	+	12.3634i	0.436330	+	0.162677i
$77$	14.5815	−	33.8611i	0.189370	−	0.439754i
$78$		0			0
$79$		−	107.545i		−	1.36133i	−0.732596	−	0.680663i	$-0.761692\pi$
$79$		−	107.545i		−	1.36133i	0.732596	−	0.680663i	$-0.238308\pi$
$80$	36.8109	−	42.5047i	0.460136	−	0.531309i
$81$		0			0
$82$	−69.1466	+	48.0161i	−0.843251	+	0.585562i
$83$	−92.3016			−1.11207			−0.556034	−	0.831160i	$-0.687677\pi$
$83$	−92.3016			−1.11207			−0.556034	+	0.831160i	$0.687677\pi$
$84$		0			0
$85$			43.4593i			0.511286i
$86$	−38.2036	+	26.5290i	−0.444228	+	0.308477i
$87$		0			0
$88$	−40.8231	+	10.4281i	−0.463899	+	0.118501i
$89$	−1.80053			−0.0202306			−0.0101153	−	0.999949i	$-0.503220\pi$
$89$	−1.80053			−0.0202306			−0.0101153	+	0.999949i	$0.503220\pi$
$90$		0			0
$91$	60.1857	+	25.9176i	0.661382	+	0.284808i
$92$	−6.00506	+	16.1067i	−0.0652724	+	0.175073i
$93$		0			0
$94$	−32.5161	−	46.8255i	−0.345916	−	0.498144i
$95$	−31.0935			−0.327300
$96$		0			0
$97$			122.204i			1.25984i	0.776660	+	0.629919i	$0.216912\pi$
$97$			122.204i			1.25984i	−0.776660	+	0.629919i	$0.783088\pi$
$98$	95.9222	+	20.0732i	0.978798	+	0.204829i
$99$		0			0
$100$	17.6761	−	47.4107i	0.176761	−	0.474107i
$101$			85.2602i			0.844160i	0.906559	+	0.422080i	$0.138700\pi$
$101$			85.2602i			0.844160i	−0.906559	+	0.422080i	$0.861300\pi$
$102$		0			0
$103$	27.4148			0.266164			0.133082	−	0.991105i	$-0.457513\pi$
$103$	27.4148			0.266164			0.133082	+	0.991105i	$0.457513\pi$
$104$	−18.5352	−	72.5603i	−0.178223	−	0.697695i
$105$		0			0
$106$	−29.8302	+	20.7144i	−0.281417	+	0.195419i
$107$			116.898i			1.09250i	0.837622	+	0.546250i	$0.183945\pi$
$107$			116.898i			1.09250i	−0.837622	+	0.546250i	$0.816055\pi$
$108$		0			0
$109$			109.910i			1.00835i	0.863602	+	0.504175i	$0.168203\pi$
$109$			109.910i			1.00835i	−0.863602	+	0.504175i	$0.831797\pi$
$110$	30.4059	−	21.1142i	0.276417	−	0.191947i
$111$		0			0
$112$	−48.7600	−	100.829i	−0.435357	−	0.900258i
$113$			91.9016i			0.813288i	0.913587	+	0.406644i	$0.133301\pi$
$113$			91.9016i			0.813288i	−0.913587	+	0.406644i	$0.866699\pi$
$114$		0			0
$115$		−	15.1025i		−	0.131326i
$116$	26.1007	−	70.0069i	0.225006	−	0.603508i
$117$		0			0
$118$	−125.484	+	87.1372i	−1.06342	+	0.738451i
$119$	79.5063	+	34.2375i	0.668120	+	0.287710i
$120$		0			0
$121$	93.2614			0.770755
$122$	−6.32116	+	4.38948i	−0.0518128	+	0.0359793i
$123$		0			0
$124$	72.8760	−	195.467i	0.587710	−	1.57635i
$125$			132.312i			1.05850i
$126$		0			0
$127$			54.4707i			0.428903i	0.976735	+	0.214452i	$0.0687964\pi$
$127$			54.4707i			0.428903i	−0.976735	+	0.214452i	$0.931204\pi$
$128$	−57.2422	+	114.487i	−0.447205	+	0.894432i
$129$		0			0
$130$	37.5290	+	54.0444i	0.288684	+	0.415726i
$131$	−229.881			−1.75481			−0.877407	−	0.479746i	$-0.840729\pi$
$131$	−229.881			−1.75481			−0.877407	+	0.479746i	$0.840729\pi$
$132$		0			0
$133$	−24.4957	+	56.8838i	−0.184178	+	0.427698i
$134$	7.48504	−	5.19769i	0.0558585	−	0.0387887i
$135$		0			0
$136$	−24.4853	−	95.8533i	−0.180039	−	0.704803i
$137$		−	218.060i		−	1.59168i	−0.605507	−	0.795840i	$-0.707030\pi$
$137$		−	218.060i		−	1.59168i	0.605507	−	0.795840i	$-0.292970\pi$
$138$		0			0
$139$		−	275.165i		−	1.97960i	−0.142458	−	0.989801i	$-0.545501\pi$
$139$		−	275.165i		−	1.97960i	0.142458	−	0.989801i	$-0.454499\pi$
$140$	71.0870	+	68.0391i	0.507764	+	0.485993i
$141$		0			0
$142$	−66.3444	+	46.0702i	−0.467214	+	0.324438i
$143$		−	49.3035i		−	0.344780i
$144$		0			0
$145$			65.6422i			0.452705i
$146$	140.323	+	202.075i	0.961115	+	1.38407i
$147$		0			0
$148$	−170.419	−	63.5374i	−1.15148	−	0.429307i
$149$	158.666			1.06487			0.532437	−	0.846469i	$-0.321276\pi$
$149$	158.666			1.06487			0.532437	+	0.846469i	$0.321276\pi$
$150$		0			0
$151$		−	62.5692i		−	0.414366i	−0.978302	−	0.207183i	$-0.933570\pi$
$151$		−	62.5692i		−	0.414366i	0.978302	−	0.207183i	$-0.0664295\pi$
$152$	68.5795	−	17.5183i	0.451181	−	0.115252i
$153$		0			0
$154$	−14.6732	−	72.2597i	−0.0952805	−	0.469219i
$155$			183.280i			1.18245i
$156$		0			0
$157$	−119.454			−0.760853			−0.380427	−	0.924811i	$-0.624223\pi$
$157$	−119.454			−0.760853			−0.380427	+	0.924811i	$0.624223\pi$
$158$	−122.682	−	176.671i	−0.776469	−	1.11817i
$159$		0			0
$160$	11.9843	−	111.817i	0.0749021	−	0.698859i
$161$	−27.6291	−	11.8978i	−0.171609	−	0.0738995i
$162$		0			0
$163$	−114.091			−0.699945			−0.349972	−	0.936760i	$-0.613809\pi$
$163$	−114.091			−0.699945			−0.349972	+	0.936760i	$0.613809\pi$
$164$	−58.8172	+	157.758i	−0.358641	+	0.961942i
$165$		0			0
$166$	−151.630	+	105.293i	−0.913434	+	0.634298i
$167$			7.52860i			0.0450814i	0.999746	+	0.0225407i	$0.00717554\pi$
$167$			7.52860i			0.0450814i	−0.999746	+	0.0225407i	$0.992824\pi$
$168$		0			0
$169$	−81.3664			−0.481458
$170$	49.5764	+	71.3935i	0.291626	+	0.419962i
$171$		0			0
$172$	−32.4966	+	87.1619i	−0.188934	+	0.506755i
$173$			247.124i			1.42846i	0.699910	+	0.714231i	$0.253223\pi$
$173$			247.124i			1.42846i	−0.699910	+	0.714231i	$0.746777\pi$
$174$		0			0
$175$	81.3274	+	35.0217i	0.464728	+	0.200124i
$176$	−55.1670	+	63.7000i	−0.313449	+	0.361932i
$177$		0			0
$178$	−2.95784	+	2.05396i	−0.0166171	+	0.0115391i
$179$		−	185.560i		−	1.03665i	−0.855184	−	0.518324i	$-0.826556\pi$
$179$		−	185.560i		−	1.03665i	0.855184	−	0.518324i	$-0.173444\pi$
$180$		0			0
$181$	−322.522			−1.78189			−0.890944	−	0.454113i	$-0.849956\pi$
$181$	−322.522			−1.78189			−0.890944	+	0.454113i	$0.849956\pi$
$182$	128.437	−	26.0806i	0.705696	−	0.143300i
$183$		0			0
$184$	8.50884	+	33.3098i	0.0462437	+	0.181032i
$185$	159.794			0.863750
$186$		0			0
$187$		−	65.1307i		−	0.348292i
$188$	−106.833	−	39.8305i	−0.568259	−	0.211864i
$189$		0			0
$190$	−51.0794	+	35.4701i	−0.268839	+	0.186685i
$191$	301.533			1.57871			0.789355	−	0.613937i	$-0.210415\pi$
$191$	301.533			1.57871			0.789355	+	0.613937i	$0.210415\pi$
$192$		0			0
$193$	−11.9190			−0.0617567			−0.0308783	−	0.999523i	$-0.509830\pi$
$193$	−11.9190			−0.0617567			−0.0308783	+	0.999523i	$0.509830\pi$
$194$	139.405	+	200.753i	0.718583	+	1.03481i
$195$		0			0
$196$	180.476	−	76.4480i	0.920798	−	0.390041i
$197$	−149.961			−0.761224			−0.380612	−	0.924735i	$-0.624287\pi$
$197$	−149.961			−0.761224			−0.380612	+	0.924735i	$0.624287\pi$
$198$		0			0
$199$	17.5356			0.0881185			0.0440593	−	0.999029i	$-0.485971\pi$
$199$	17.5356			0.0881185			0.0440593	+	0.999029i	$0.485971\pi$
$200$	−25.0461	−	98.0488i	−0.125231	−	0.490244i
$201$		0			0
$202$	97.2609	+	140.063i	0.481489	+	0.693379i
$203$	120.089	+	51.7133i	0.591570	+	0.254745i
$204$		0			0
$205$		−	147.923i		−	0.721574i
$206$	45.0362	−	31.2736i	0.218622	−	0.151813i
$207$		0			0
$208$	−113.222	−	98.0555i	−0.544338	−	0.471421i
$209$	46.5986			0.222960
$210$		0			0
$211$	−377.299			−1.78815			−0.894074	−	0.447919i	$-0.852165\pi$
$211$	−377.299			−1.78815			−0.894074	+	0.447919i	$0.852165\pi$
$212$	−25.3741	+	68.0579i	−0.119689	+	0.321028i
$213$		0			0
$214$	133.351	+	192.035i	0.623137	+	0.897361i
$215$		−	81.7276i		−	0.380128i
$216$		0			0
$217$	335.300	+	144.389i	1.54516	+	0.665388i
$218$	125.380	+	180.557i	0.575139	+	0.828241i
$219$		0			0
$220$	25.8637	−	69.3713i	0.117562	−	0.315324i
$221$	115.765			0.523825
$222$		0			0
$223$	191.043			0.856695			0.428348	−	0.903614i	$-0.359096\pi$
$223$	191.043			0.856695			0.428348	+	0.903614i	$0.359096\pi$
$224$	−195.122	−	110.015i	−0.871081	−	0.491139i
$225$		0			0
$226$	104.837	+	150.973i	0.463881	+	0.668021i
$227$	−54.0537			−0.238122			−0.119061	−	0.992887i	$-0.537988\pi$
$227$	−54.0537			−0.238122			−0.119061	+	0.992887i	$0.537988\pi$
$228$		0			0
$229$	−63.8040			−0.278620			−0.139310	−	0.990249i	$-0.544488\pi$
$229$	−63.8040			−0.278620			−0.139310	+	0.990249i	$0.544488\pi$
$230$	−17.2282	−	24.8098i	−0.0749052	−	0.107869i
$231$		0			0
$232$	−36.9833	−	144.780i	−0.159411	−	0.624050i
$233$		−	91.0939i		−	0.390961i	−0.980708	−	0.195480i	$-0.937373\pi$
$233$		−	91.0939i		−	0.390961i	0.980708	−	0.195480i	$-0.0626266\pi$
$234$		0			0
$235$	100.172			0.426264
$236$	−106.738	+	286.292i	−0.452282	+	1.21310i
$237$		0			0
$238$	169.667	−	34.4529i	0.712886	−	0.144760i
$239$	−390.181			−1.63256			−0.816279	−	0.577658i	$-0.803967\pi$
$239$	−390.181			−1.63256			−0.816279	+	0.577658i	$0.803967\pi$
$240$		0			0
$241$			66.2992i			0.275100i	0.990495	+	0.137550i	$0.0439228\pi$
$241$			66.2992i			0.275100i	−0.990495	+	0.137550i	$0.956077\pi$
$242$	153.207	−	106.388i	0.633085	−	0.439621i
$243$		0			0
$244$	−5.37688	+	14.4218i	−0.0220364	+	0.0591056i
$245$	−125.109	+	118.326i	−0.510647	+	0.482963i
$246$		0			0
$247$			82.8258i			0.335327i
$248$	−103.261	−	404.240i	−0.416376	−	1.63000i
$249$		0			0
$250$	150.936	+	217.358i	0.603743	+	0.869434i
$251$	72.6421			0.289411			0.144705	−	0.989475i	$-0.453777\pi$
$251$	72.6421			0.289411			0.144705	+	0.989475i	$0.453777\pi$
$252$		0			0
$253$			22.6335i			0.0894603i
$254$	62.1376	+	89.4826i	0.244636	+	0.352294i
$255$		0			0
$256$	36.5662	+	253.375i	0.142837	+	0.989746i
$257$	480.730			1.87055			0.935273	−	0.353927i	$-0.115154\pi$
$257$	480.730			1.87055			0.935273	+	0.353927i	$0.115154\pi$
$258$		0			0
$259$	125.887	−	292.334i	0.486048	−	1.12870i
$260$	123.303	+	45.9710i	0.474241	+	0.176812i
$261$		0			0
$262$	−377.640	+	262.237i	−1.44138	+	1.00091i
$263$	−221.781			−0.843274			−0.421637	−	0.906765i	$-0.638544\pi$
$263$	−221.781			−0.843274			−0.421637	+	0.906765i	$0.638544\pi$
$264$		0			0
$265$		−	63.8147i		−	0.240810i
$266$	24.6498	+	121.390i	0.0926683	+	0.456355i
$267$		0			0
$268$	6.36689	−	17.0772i	0.0237571	−	0.0637208i
$269$		−	65.8358i		−	0.244743i	−0.992484	−	0.122371i	$-0.960950\pi$
$269$		−	65.8358i		−	0.244743i	0.992484	−	0.122371i	$-0.0390499\pi$
$270$		0			0
$271$	−63.0008			−0.232475			−0.116238	−	0.993221i	$-0.537083\pi$
$271$	−63.0008			−0.232475			−0.116238	+	0.993221i	$0.537083\pi$
$272$	−149.569	−	129.533i	−0.549884	−	0.476224i
$273$		0			0
$274$	−248.753	−	358.222i	−0.907857	−	1.30738i
$275$		−	66.6225i		−	0.242264i
$276$		0			0
$277$			274.997i			0.992769i	0.868103	+	0.496385i	$0.165339\pi$
$277$			274.997i			0.992769i	−0.868103	+	0.496385i	$0.834661\pi$
$278$	−313.895	−	452.031i	−1.12912	−	1.62601i
$279$		0			0
$280$	194.395	+	30.6795i	0.694268	+	0.109570i
$281$			148.229i			0.527504i	0.964591	+	0.263752i	$0.0849600\pi$
$281$			148.229i			0.527504i	−0.964591	+	0.263752i	$0.915040\pi$
$282$		0			0
$283$		−	265.522i		−	0.938240i	−0.883134	−	0.469120i	$-0.844571\pi$
$283$		−	265.522i		−	0.938240i	0.883134	−	0.469120i	$-0.155429\pi$
$284$	−56.4336	+	151.365i	−0.198710	+	0.532976i
$285$		0			0
$286$	−56.2431	−	80.9941i	−0.196654	−	0.283196i
$287$	−270.616	−	116.534i	−0.942913	−	0.406043i
$288$		0			0
$289$	−136.072			−0.470838
$290$	74.8816	+	107.835i	0.258212	+	0.371844i
$291$		0			0
$292$	461.035	+	171.888i	1.57889	+	0.588657i
$293$		−	521.117i		−	1.77855i	−0.457368	−	0.889277i	$-0.651208\pi$
$293$		−	521.117i		−	1.77855i	0.457368	−	0.889277i	$-0.348792\pi$
$294$		0			0
$295$		−	268.443i		−	0.909975i
$296$	−352.439	+	90.0289i	−1.19067	+	0.304152i
$297$		0			0
$298$	260.652	−	180.999i	0.874670	−	0.607380i
$299$	−40.2294			−0.134546
$300$		0			0
$301$	−149.516	−	64.3855i	−0.496731	−	0.213905i
$302$	−71.3761	−	102.787i	−0.236345	−	0.340353i
$303$		0			0
$304$	92.6760	−	107.011i	0.304855	−	0.352009i
$305$		−	13.5226i		−	0.0443364i
$306$		0			0
$307$			120.087i			0.391162i	0.980688	+	0.195581i	$0.0626592\pi$
$307$			120.087i			0.391162i	−0.980688	+	0.195581i	$0.937341\pi$
$308$	−106.535	−	101.967i	−0.345893	−	0.331063i
$309$		0			0
$310$	209.077	+	301.086i	0.674443	+	0.971246i
$311$		−	351.784i		−	1.13114i	−0.824701	−	0.565570i	$-0.808656\pi$
$311$		−	351.784i		−	1.13114i	0.824701	−	0.565570i	$-0.191344\pi$
$312$		0			0
$313$		−	55.1841i		−	0.176307i	−0.996107	−	0.0881536i	$-0.971903\pi$
$313$		−	55.1841i		−	0.176307i	0.996107	−	0.0881536i	$-0.0280966\pi$
$314$	−196.235	+	136.268i	−0.624952	+	0.433973i
$315$		0			0
$316$	−403.076	−	150.279i	−1.27556	−	0.475567i
$317$	410.736			1.29570			0.647849	−	0.761769i	$-0.275669\pi$
$317$	410.736			1.29570			0.647849	+	0.761769i	$0.275669\pi$
$318$		0			0
$319$		−	98.3753i		−	0.308386i
$320$	−107.869	−	197.361i	−0.337090	−	0.616753i
$321$		0			0
$322$	−58.9606	+	11.9727i	−0.183108	+	0.0371822i
$323$			109.414i			0.338744i
$324$		0			0
$325$	118.417			0.364360
$326$	−187.425	+	130.150i	−0.574923	+	0.399232i
$327$		0			0
$328$	83.3407	+	326.256i	0.254087	+	0.994684i
$329$	78.9162	−	183.259i	0.239867	−	0.557018i
$330$		0			0
$331$	−284.206			−0.858629			−0.429314	−	0.903155i	$-0.641245\pi$
$331$	−284.206			−0.858629			−0.429314	+	0.903155i	$0.641245\pi$
$332$	−128.979	+	345.945i	−0.388490	+	1.04200i
$333$		0			0
$334$	8.58828	+	12.3677i	0.0257134	+	0.0370291i
$335$			16.0125i			0.0477984i
$336$		0			0
$337$	−459.374			−1.36313			−0.681564	−	0.731758i	$-0.738700\pi$
$337$	−459.374			−1.36313			−0.681564	+	0.731758i	$0.738700\pi$
$338$	−133.666	+	92.8191i	−0.395462	+	0.274613i
$339$		0			0
$340$	162.885	+	60.7284i	0.479073	+	0.178613i
$341$		−	274.674i		−	0.805496i
$342$		0			0
$343$	117.909	+	322.097i	0.343759	+	0.939058i
$344$	46.0459	+	180.257i	0.133854	+	0.524004i
$345$		0			0
$346$	281.908	+	405.967i	0.814762	+	1.17331i
$347$		−	460.926i		−	1.32832i	−0.747592	−	0.664159i	$-0.768790\pi$
$347$		−	460.926i		−	1.32832i	0.747592	−	0.664159i	$-0.231210\pi$
$348$		0			0
$349$	359.787			1.03091			0.515454	−	0.856917i	$-0.327623\pi$
$349$	359.787			1.03091			0.515454	+	0.856917i	$0.327623\pi$
$350$	173.553	−	35.2420i	0.495866	−	0.100691i
$351$		0			0
$352$	−17.9604	+	167.576i	−0.0510240	+	0.476069i
$353$	152.580			0.432238			0.216119	−	0.976367i	$-0.430660\pi$
$353$	152.580			0.432238			0.216119	+	0.976367i	$0.430660\pi$
$354$		0			0
$355$		−	141.928i		−	0.399797i
$356$	−2.51599	+	6.74834i	−0.00706738	+	0.0189560i
$357$		0			0
$358$	−211.678	−	304.832i	−0.591280	−	0.851486i
$359$	405.919			1.13069			0.565347	−	0.824853i	$-0.308742\pi$
$359$	405.919			1.13069			0.565347	+	0.824853i	$0.308742\pi$
$360$		0			0
$361$	282.718			0.783153
$362$	−529.828	+	367.918i	−1.46361	+	1.01635i
$363$		0			0
$364$	181.240	−	189.359i	0.497912	−	0.520217i
$365$	−432.291			−1.18436
$366$		0			0
$367$	−70.1579			−0.191166			−0.0955830	−	0.995421i	$-0.530472\pi$
$367$	−70.1579			−0.191166			−0.0955830	+	0.995421i	$0.530472\pi$
$368$	51.9763	+	45.0137i	0.141240	+	0.122320i
$369$		0			0
$370$	262.504	−	182.285i	0.709470	−	0.492663i
$371$	−116.745	−	50.2736i	−0.314677	−	0.135508i
$372$		0			0
$373$		−	330.205i		−	0.885268i	−0.896702	−	0.442634i	$-0.854044\pi$
$373$		−	330.205i		−	0.885268i	0.896702	−	0.442634i	$-0.145956\pi$
$374$	−74.2981	−	106.995i	−0.198658	−	0.286082i
$375$		0			0
$376$	−220.938	+	56.4376i	−0.587601	+	0.150100i
$377$	174.855			0.463807
$378$		0			0
$379$	−29.3602			−0.0774675			−0.0387337	−	0.999250i	$-0.512332\pi$
$379$	−29.3602			−0.0774675			−0.0387337	+	0.999250i	$0.512332\pi$
$380$	−43.4490	+	116.538i	−0.114339	+	0.306679i
$381$		0			0
$382$	495.349	−	343.975i	1.29673	−	0.900459i
$383$		−	328.601i		−	0.857966i	−0.903313	−	0.428983i	$-0.858872\pi$
$383$		−	328.601i		−	0.857966i	0.903313	−	0.428983i	$-0.141128\pi$
$384$		0			0
$385$	118.998	+	51.2438i	0.309086	+	0.133101i
$386$	−19.5802	+	13.5967i	−0.0507259	+	0.0352246i
$387$		0			0
$388$	458.020	+	170.764i	1.18046	+	0.440113i
$389$	397.533			1.02194			0.510968	−	0.859599i	$-0.329287\pi$
$389$	397.533			1.02194			0.510968	+	0.859599i	$0.329287\pi$
$390$		0			0
$391$	−53.1437			−0.135917
$392$	209.272	−	331.465i	0.533858	−	0.845574i
$393$		0			0
$394$	−246.351	+	171.069i	−0.625256	+	0.434184i
$395$	377.945			0.956824
$396$		0			0
$397$	192.561			0.485041			0.242520	−	0.970146i	$-0.422026\pi$
$397$	192.561			0.485041			0.242520	+	0.970146i	$0.422026\pi$
$398$	28.8069	−	20.0038i	0.0723791	−	0.0502608i
$399$		0			0
$400$	−152.994	−	132.500i	−0.382486	−	0.331249i
$401$		−	447.317i		−	1.11550i	−0.830008	−	0.557752i	$-0.811664\pi$
$401$		−	447.317i		−	1.11550i	0.830008	−	0.557752i	$-0.188336\pi$
$402$		0			0
$403$	488.215			1.21145
$404$	319.554	+	119.139i	0.790975	+	0.294899i
$405$		0			0
$406$	256.270	−	52.0386i	0.631206	−	0.128174i
$407$	−239.476			−0.588394
$408$		0			0
$409$		−	556.925i		−	1.36167i	−0.732435	−	0.680837i	$-0.761616\pi$
$409$		−	556.925i		−	1.36167i	0.732435	−	0.680837i	$-0.238384\pi$
$410$	−168.743	−	243.002i	−0.411569	−	0.592689i
$411$		0			0
$412$	38.3085	−	102.750i	0.0929817	−	0.249394i
$413$	−491.100	−	211.481i	−1.18911	−	0.512060i
$414$		0			0
$415$		−	324.376i		−	0.781629i
$416$	−297.855	−	31.9234i	−0.715998	−	0.0767390i
$417$		0			0
$418$	76.5506	−	53.1575i	0.183136	−	0.127171i
$419$	655.843			1.56526			0.782628	−	0.622489i	$-0.213879\pi$
$419$	655.843			1.56526			0.782628	+	0.622489i	$0.213879\pi$
$420$		0			0
$421$			358.380i			0.851258i	0.904898	+	0.425629i	$0.139947\pi$
$421$			358.380i			0.851258i	−0.904898	+	0.425629i	$0.860053\pi$
$422$	−619.815	+	430.405i	−1.46875	+	1.01992i
$423$		0			0
$424$	35.9536	+	140.749i	0.0847963	+	0.331955i
$425$	156.431			0.368072
$426$		0			0
$427$	−24.7388	−	10.6532i	−0.0579364	−	0.0249489i
$428$	438.130	+	163.348i	1.02367	+	0.381655i
$429$		0			0
$430$	−93.2310	−	134.259i	−0.216816	−	0.312231i
$431$	340.972			0.791117			0.395559	−	0.918441i	$-0.370551\pi$
$431$	340.972			0.791117			0.395559	+	0.918441i	$0.370551\pi$
$432$		0			0
$433$			213.233i			0.492454i	0.969212	+	0.246227i	$0.0791909\pi$
$433$			213.233i			0.492454i	−0.969212	+	0.246227i	$0.920809\pi$
$434$	715.532	−	145.297i	1.64869	−	0.334786i
$435$		0			0
$436$	411.941	+	153.584i	0.944819	+	0.352257i
$437$		−	38.0223i		−	0.0870077i
$438$		0			0
$439$	238.439			0.543140			0.271570	−	0.962419i	$-0.412457\pi$
$439$	238.439			0.543140			0.271570	+	0.962419i	$0.412457\pi$
$440$	−36.6475	−	143.465i	−0.0832897	−	0.326057i
$441$		0			0
$442$	190.175	−	132.060i	0.430261	−	0.298778i
$443$		−	112.783i		−	0.254589i	−0.991865	−	0.127295i	$-0.959371\pi$
$443$		−	112.783i		−	0.254589i	0.991865	−	0.127295i	$-0.0406294\pi$
$444$		0			0
$445$		−	6.32760i		−	0.0142193i
$446$	313.839	−	217.933i	0.703675	−	0.488639i
$447$		0			0
$448$	−446.040	+	41.8572i	−0.995626	+	0.0934313i
$449$			366.262i			0.815729i	0.913043	+	0.407864i	$0.133726\pi$
$449$			366.262i			0.815729i	−0.913043	+	0.407864i	$0.866274\pi$
$450$		0			0
$451$			221.686i			0.491543i
$452$	344.446	+	128.420i	0.762048	+	0.284115i
$453$		0			0
$454$	−88.7976	+	61.6619i	−0.195589	+	0.135819i
$455$	−91.0823	+	211.511i	−0.200181	+	0.464860i
$456$		0			0
$457$	−127.312			−0.278582			−0.139291	−	0.990252i	$-0.544482\pi$
$457$	−127.312			−0.278582			−0.139291	+	0.990252i	$0.544482\pi$
$458$	−104.815	+	72.7846i	−0.228854	+	0.158918i
$459$		0			0
$460$	−56.6038	−	21.1036i	−0.123052	−	0.0458775i
$461$			588.619i			1.27683i	0.769692	+	0.638415i	$0.220410\pi$
$461$			588.619i			1.27683i	−0.769692	+	0.638415i	$0.779590\pi$
$462$		0			0
$463$			269.281i			0.581601i	0.956784	+	0.290801i	$0.0939217\pi$
$463$			269.281i			0.581601i	−0.956784	+	0.290801i	$0.906078\pi$
$464$	−225.913	−	195.650i	−0.486881	−	0.421660i
$465$		0			0
$466$	−103.916	−	149.646i	−0.222995	−	0.321129i
$467$	357.434			0.765383			0.382692	−	0.923876i	$-0.374997\pi$
$467$	357.434			0.765383			0.382692	+	0.923876i	$0.374997\pi$
$468$		0			0
$469$	29.2939	+	12.6147i	0.0624603	+	0.0268970i
$470$	164.559	−	114.272i	0.350126	−	0.243131i
$471$		0			0
$472$	151.242	+	592.074i	0.320429	+	1.25439i
$473$			122.482i			0.258947i
$474$		0			0
$475$			111.920i			0.235622i
$476$	239.421	−	250.146i	0.502985	−	0.525517i
$477$		0			0
$478$	−640.977	+	445.101i	−1.34096	+	0.931173i
$479$			758.388i			1.58327i	0.610992	+	0.791637i	$0.290771\pi$
$479$			758.388i			1.58327i	−0.610992	+	0.791637i	$0.709229\pi$
$480$		0			0
$481$		−	425.653i		−	0.884933i
$482$	75.6310	+	108.914i	0.156911	+	0.225963i
$483$		0			0
$484$	130.320	−	349.542i	0.269256	−	0.722194i
$485$	−429.464			−0.885492
$486$		0			0
$487$		−	616.289i		−	1.26548i	−0.774364	−	0.632741i	$-0.781930\pi$
$487$		−	616.289i		−	1.26548i	0.774364	−	0.632741i	$-0.218070\pi$
$488$	7.61873	+	29.8253i	0.0156122	+	0.0611174i
$489$		0			0
$490$	−70.5434	+	337.100i	−0.143966	+	0.687959i
$491$			574.215i			1.16948i	0.811221	+	0.584740i	$0.198803\pi$
$491$			574.215i			1.16948i	−0.811221	+	0.584740i	$0.801197\pi$
$492$		0			0
$493$	230.987			0.468532
$494$	94.4839	+	136.063i	0.191263	+	0.275432i
$495$		0			0
$496$	−630.772	−	546.276i	−1.27172	−	1.10136i
$497$	−259.649	−	111.812i	−0.522433	−	0.224973i
$498$		0			0
$499$	−613.646			−1.22975			−0.614875	−	0.788624i	$-0.710794\pi$
$499$	−613.646			−1.22975			−0.614875	+	0.788624i	$0.710794\pi$
$500$	495.905	+	184.888i	0.991809	+	0.369777i
$501$		0			0
$502$	119.334	−	82.8667i	0.237717	−	0.165073i
$503$			55.3348i			0.110010i	0.998486	+	0.0550048i	$0.0175174\pi$
$503$			55.3348i			0.110010i	−0.998486	+	0.0550048i	$0.982483\pi$
$504$		0			0
$505$	−299.630			−0.593328
$506$	25.8192	+	37.1815i	0.0510261	+	0.0734812i
$507$		0			0
$508$	204.155	+	76.1153i	0.401880	+	0.149833i
$509$			310.802i			0.610613i	0.952254	+	0.305307i	$0.0987589\pi$
$509$			310.802i			0.610613i	−0.952254	+	0.305307i	$0.901241\pi$
$510$		0			0
$511$	−340.561	+	790.851i	−0.666460	+	1.54765i
$512$	349.108	+	374.523i	0.681852	+	0.731490i
$513$		0			0
$514$	789.727	−	548.395i	1.53643	−	1.06692i
$515$			96.3442i			0.187076i
$516$		0			0
$517$	−150.124			−0.290375
$518$	−126.678	−	623.841i	−0.244553	−	1.20433i
$519$		0			0
$520$	254.999	−	65.1384i	0.490383	−	0.125266i
$521$	−774.806			−1.48715			−0.743576	−	0.668652i	$-0.766872\pi$
$521$	−774.806			−1.48715			−0.743576	+	0.668652i	$0.766872\pi$
$522$		0			0
$523$			440.022i			0.841342i	0.907213	+	0.420671i	$0.138205\pi$
$523$			440.022i			0.841342i	−0.907213	+	0.420671i	$0.861795\pi$
$524$	−321.227	+	861.589i	−0.613028	+	1.64425i
$525$		0			0
$526$	−364.334	+	252.997i	−0.692651	+	0.480984i
$527$	644.939			1.22379
$528$		0			0
$529$	−510.532			−0.965089
$530$	−72.7968	−	104.833i	−0.137353	−	0.197797i
$531$		0			0
$532$	178.970	+	171.297i	0.336410	+	0.321986i
$533$	−394.031			−0.739270
$534$		0			0
$535$	−410.814			−0.767876
$536$	−9.02153	−	35.3169i	−0.0168312	−	0.0658897i
$537$		0			0
$538$	−75.1024	−	108.153i	−0.139596	−	0.201028i
$539$	187.495	−	177.330i	0.347857	−	0.328999i
$540$		0			0
$541$		−	1012.28i		−	1.87113i	−0.353159	−	0.935563i	$-0.614893\pi$
$541$		−	1012.28i		−	1.87113i	0.353159	−	0.935563i	$-0.385107\pi$
$542$	−103.496	+	71.8684i	−0.190951	+	0.132599i
$543$		0			0
$544$	−393.471	−	42.1714i	−0.723293	−	0.0775209i
$545$	−386.258			−0.708730
$546$		0			0
$547$	588.492			1.07585			0.537927	−	0.842991i	$-0.319208\pi$
$547$	588.492			1.07585			0.537927	+	0.842991i	$0.319208\pi$
$548$	−817.286	−	304.709i	−1.49140	−	0.556038i
$549$		0			0
$550$	−75.9999	−	109.445i	−0.138182	−	0.198991i
$551$			165.262i			0.299932i
$552$		0			0
$553$	297.748	−	691.430i	0.538423	−	1.25032i
$554$	313.704	+	451.756i	0.566253	+	0.815444i
$555$		0			0
$556$	−1031.31	−	384.505i	−1.85488	−	0.691555i
$557$	1101.14			1.97691			0.988454	−	0.151520i	$-0.0484168\pi$
$557$	1101.14			1.97691			0.988454	+	0.151520i	$0.0484168\pi$
$558$		0			0
$559$	−217.703			−0.389451
$560$	354.344	−	171.358i	0.632756	−	0.305996i
$561$		0			0
$562$	169.092	+	243.505i	0.300876	+	0.433283i
$563$	−394.840			−0.701315			−0.350658	−	0.936504i	$-0.614042\pi$
$563$	−394.840			−0.701315			−0.350658	+	0.936504i	$0.614042\pi$
$564$		0			0
$565$	−322.970			−0.571629
$566$	−302.895	−	436.191i	−0.535150	−	0.770655i
$567$		0			0
$568$	79.9632	+	313.034i	0.140780	+	0.551117i
$569$		−	314.095i		−	0.552013i	−0.961156	−	0.276006i	$-0.910989\pi$
$569$		−	314.095i		−	0.552013i	0.961156	−	0.276006i	$-0.0890111\pi$
$570$		0			0
$571$	715.232			1.25260			0.626298	−	0.779584i	$-0.284569\pi$
$571$	715.232			1.25260			0.626298	+	0.779584i	$0.284569\pi$
$572$	−184.789	−	68.8949i	−0.323057	−	0.120446i
$573$		0			0
$574$	−577.496	+	117.267i	−1.00609	+	0.204299i
$575$	−54.3609			−0.0945407
$576$		0			0
$577$		−	250.055i		−	0.433371i	−0.976241	−	0.216685i	$-0.930475\pi$
$577$		−	250.055i		−	0.433371i	0.976241	−	0.216685i	$-0.0695246\pi$
$578$	−223.535	+	155.225i	−0.386738	+	0.268555i
$579$		0			0
$580$	246.026	+	91.7259i	0.424182	+	0.158148i
$581$	−593.428	−	255.546i	−1.02139	−	0.439837i
$582$		0			0
$583$			95.6365i			0.164042i
$584$	953.454	−	243.556i	1.63263	−	0.417047i
$585$		0			0
$586$	−594.466	−	856.073i	−1.01445	−	1.46087i
$587$	−608.274			−1.03624			−0.518121	−	0.855308i	$-0.673368\pi$
$587$	−608.274			−1.03624			−0.518121	+	0.855308i	$0.673368\pi$
$588$		0			0
$589$			461.430i			0.783413i
$590$	−306.227	−	440.989i	−0.519029	−	0.747438i
$591$		0			0
$592$	−476.274	+	549.943i	−0.804517	+	0.928957i
$593$	−1006.48			−1.69727			−0.848634	−	0.528980i	$-0.822575\pi$
$593$	−1006.48			−1.69727			−0.848634	+	0.528980i	$0.822575\pi$
$594$		0			0
$595$	−120.321	+	279.410i	−0.202220	+	0.469596i
$596$	221.714	−	594.679i	0.372004	−	0.997783i
$597$		0			0
$598$	−66.0875	+	45.8918i	−0.110514	+	0.0767422i
$599$	−81.6309			−0.136279			−0.0681393	−	0.997676i	$-0.521706\pi$
$599$	−81.6309			−0.136279			−0.0681393	+	0.997676i	$0.521706\pi$
$600$		0			0
$601$			84.9314i			0.141317i	0.997501	+	0.0706584i	$0.0225100\pi$
$601$			84.9314i			0.141317i	−0.997501	+	0.0706584i	$0.977490\pi$
$602$	−319.068	+	64.7905i	−0.530013	+	0.107625i
$603$		0			0
$604$	−234.508	−	87.4319i	−0.388259	−	0.144755i
$605$			327.749i			0.541734i
$606$		0			0
$607$	−964.122			−1.58834			−0.794170	−	0.607696i	$-0.792094\pi$
$607$	−964.122			−1.58834			−0.794170	+	0.607696i	$0.792094\pi$
$608$	30.1721	−	281.514i	0.0496251	−	0.463017i
$609$		0			0
$610$	−15.4260	−	22.2145i	−0.0252885	−	0.0364172i
$611$		−	266.835i		−	0.436718i
$612$		0			0
$613$			282.857i			0.461430i	0.973021	+	0.230715i	$0.0741065\pi$
$613$			282.857i			0.461430i	−0.973021	+	0.230715i	$0.925894\pi$
$614$	136.989	+	197.274i	0.223110	+	0.321294i
$615$		0			0
$616$	−291.332	−	45.9782i	−0.472942	−	0.0746399i
$617$			805.890i			1.30614i	0.757296	+	0.653071i	$0.226520\pi$
$617$			805.890i			1.30614i	−0.757296	+	0.653071i	$0.773480\pi$
$618$		0			0
$619$			970.057i			1.56714i	0.621306	+	0.783568i	$0.286602\pi$
$619$			970.057i			1.56714i	−0.621306	+	0.783568i	$0.713398\pi$
$620$	686.930	+	256.109i	1.10795	+	0.413078i
$621$		0			0
$622$	−401.299	−	577.899i	−0.645176	−	0.929099i
$623$	−11.5760	−	4.98492i	−0.0185810	−	0.00800148i
$624$		0			0
$625$	−148.745			−0.237992
$626$	−62.9515	−	90.6547i	−0.100562	−	0.144816i
$627$		0			0
$628$	−166.921	+	447.712i	−0.265797	+	0.712917i
$629$		−	562.294i		−	0.893949i
$630$		0			0
$631$			750.402i			1.18923i	0.804012	+	0.594613i	$0.202695\pi$
$631$			750.402i			1.18923i	−0.804012	+	0.594613i	$0.797305\pi$
$632$	−833.591	+	212.937i	−1.31897	+	0.336926i
$633$		0			0
$634$	674.744	−	468.549i	1.06427	−	0.739036i
$635$	−191.427			−0.301459
$636$		0			0
$637$	315.192	+	333.260i	0.494807	+	0.523171i
$638$	−112.222	−	161.608i	−0.175896	−	0.253303i
$639$		0			0
$640$	−402.343	−	201.167i	−0.628661	−	0.314323i
$641$			1031.35i			1.60897i	0.593974	+	0.804484i	$0.297558\pi$
$641$			1031.35i			1.60897i	−0.593974	+	0.804484i	$0.702442\pi$
$642$		0			0
$643$			545.671i			0.848634i	0.905514	+	0.424317i	$0.139486\pi$
$643$			545.671i			0.848634i	−0.905514	+	0.424317i	$0.860514\pi$
$644$	−83.2007	+	86.9278i	−0.129194	+	0.134981i
$645$		0			0
$646$	124.815	+	179.742i	0.193212	+	0.278238i
$647$			291.352i			0.450313i	0.974323	+	0.225156i	$0.0722893\pi$
$647$			291.352i			0.450313i	−0.974323	+	0.225156i	$0.927711\pi$
$648$		0			0
$649$			402.304i			0.619883i
$650$	194.531	−	135.085i	0.299279	−	0.207822i
$651$		0			0
$652$	−159.426	+	427.611i	−0.244519	+	0.655845i
$653$	383.246			0.586900			0.293450	−	0.955974i	$-0.405197\pi$
$653$	383.246			0.586900			0.293450	+	0.955974i	$0.405197\pi$
$654$		0			0
$655$		−	807.871i		−	1.23339i
$656$	509.087	+	440.892i	0.776048	+	0.672091i
$657$		0			0
$658$	−79.4125	−	391.076i	−0.120688	−	0.594340i
$659$			60.8502i			0.0923372i	0.998934	+	0.0461686i	$0.0147011\pi$
$659$			60.8502i			0.0923372i	−0.998934	+	0.0461686i	$0.985299\pi$
$660$		0			0
$661$	−519.891			−0.786523			−0.393261	−	0.919427i	$-0.628653\pi$
$661$	−519.891			−0.786523			−0.393261	+	0.919427i	$0.628653\pi$
$662$	−466.884	+	324.209i	−0.705263	+	0.489742i
$663$		0			0
$664$	182.756	+	715.440i	0.275235	+	1.07747i
$665$	−199.907	−	86.0854i	−0.300612	−	0.129452i
$666$		0			0
$667$	−80.2697			−0.120344
$668$	28.2171	+	10.5202i	0.0422411	+	0.0157488i
$669$		0			0
$670$	18.2663	+	26.3047i	0.0272631	+	0.0392608i
$671$			20.2658i			0.0302024i
$672$		0			0
$673$	871.592			1.29508			0.647542	−	0.762029i	$-0.275797\pi$
$673$	871.592			1.29508			0.647542	+	0.762029i	$0.275797\pi$
$674$	−754.645	+	524.033i	−1.11965	+	0.777497i
$675$		0			0
$676$	−113.698	+	304.960i	−0.168193	+	0.451124i
$677$		−	458.477i		−	0.677219i	−0.940927	−	0.338610i	$-0.890043\pi$
$677$		−	458.477i		−	0.677219i	0.940927	−	0.338610i	$-0.109957\pi$
$678$		0			0
$679$	−338.334	+	785.679i	−0.498283	+	1.15711i
$680$	336.858	−	86.0488i	0.495379	−	0.126542i
$681$		0			0
$682$	−313.336	−	451.226i	−0.459436	−	0.661621i
$683$		−	270.189i		−	0.395591i	−0.980243	−	0.197796i	$-0.936622\pi$
$683$		−	270.189i		−	0.395591i	0.980243	−	0.197796i	$-0.0633783\pi$
$684$		0			0
$685$	766.330			1.11873
$686$	561.130	+	394.625i	0.817974	+	0.575255i
$687$		0			0
$688$	281.272	+	243.593i	0.408825	+	0.354060i
$689$	−169.987			−0.246716
$690$		0			0
$691$			931.061i			1.34741i	0.739000	+	0.673705i	$0.235298\pi$
$691$			931.061i			1.34741i	−0.739000	+	0.673705i	$0.764702\pi$
$692$	926.217	+	345.322i	1.33846	+	0.499020i
$693$		0			0
$694$	−525.803	−	757.194i	−0.757641	−	1.09106i
$695$	967.013			1.39139
$696$		0			0
$697$	−520.521			−0.746802
$698$	591.046	−	410.429i	0.846771	−	0.588006i
$699$		0			0
$700$	244.905	−	255.876i	0.349864	−	0.365537i
$701$	421.119			0.600740			0.300370	−	0.953823i	$-0.402890\pi$
$701$	421.119			0.600740			0.300370	+	0.953823i	$0.402890\pi$
$702$		0			0
$703$	402.301			0.572263
$704$	161.658	+	295.777i	0.229628	+	0.420138i
$705$		0			0
$706$	250.654	−	174.056i	0.355033	−	0.246539i
$707$	−236.051	+	548.157i	−0.333877	+	0.775328i
$708$		0			0
$709$		−	1227.26i		−	1.73097i	−0.500931	−	0.865487i	$-0.667009\pi$
$709$		−	1227.26i		−	1.73097i	0.500931	−	0.865487i	$-0.332991\pi$
$710$	−161.905	−	233.155i	−0.228035	−	0.328387i
$711$		0			0
$712$	3.56501	+	13.9561i	0.00500704	+	0.0196012i
$713$	−224.122			−0.314336
$714$		0			0
$715$	173.268			0.242332
$716$	−695.476	−	259.295i	−0.971335	−	0.362143i
$717$		0			0
$718$	666.831	−	463.054i	0.928734	−	0.644922i
$719$			1202.04i			1.67182i	0.548869	+	0.835908i	$0.315059\pi$
$719$			1202.04i			1.67182i	−0.548869	+	0.835908i	$0.684941\pi$
$720$		0			0
$721$	176.256	+	75.9005i	0.244461	+	0.105271i
$722$	464.440	−	322.512i	0.643269	−	0.446692i
$723$		0			0
$724$	−450.680	+	1208.81i	−0.622486	+	1.66962i
$725$	236.277			0.325900
$726$		0			0
$727$	−725.480			−0.997910			−0.498955	−	0.866628i	$-0.666283\pi$
$727$	−725.480			−0.997910			−0.498955	+	0.866628i	$0.666283\pi$
$728$	81.7230	−	517.823i	0.112257	−	0.711295i
$729$		0			0
$730$	−710.153	+	493.137i	−0.972812	+	0.675530i
$731$	−287.589			−0.393418
$732$		0			0
$733$	1032.80			1.40900			0.704499	−	0.709705i	$-0.251172\pi$
$733$	1032.80			1.40900			0.704499	+	0.709705i	$0.251172\pi$
$734$	−115.253	+	80.0329i	−0.157021	+	0.109037i
$735$		0			0
$736$	136.735	+	14.6549i	0.185781	+	0.0199115i
$737$		−	23.9972i		−	0.0325607i
$738$		0			0
$739$	1062.50			1.43775			0.718877	−	0.695137i	$-0.244656\pi$
$739$	1062.50			1.43775			0.718877	+	0.695137i	$0.244656\pi$
$740$	223.290	−	598.904i	0.301743	−	0.809330i
$741$		0			0
$742$	−249.135	+	50.5898i	−0.335762	+	0.0681804i
$743$	−684.488			−0.921249			−0.460625	−	0.887595i	$-0.652375\pi$
$743$	−684.488			−0.921249			−0.460625	+	0.887595i	$0.652375\pi$
$744$		0			0
$745$			557.602i			0.748459i
$746$	−376.683	−	542.450i	−0.504936	−	0.727144i
$747$		0			0
$748$	−244.109	−	91.0112i	−0.326349	−	0.121673i
$749$	−323.642	+	751.560i	−0.432098	+	1.00342i
$750$		0			0
$751$			565.603i			0.753133i	0.926390	+	0.376567i	$0.122895\pi$
$751$			565.603i			0.753133i	−0.926390	+	0.376567i	$0.877105\pi$
$752$	−298.568	+	344.750i	−0.397032	+	0.458444i
$753$		0			0
$754$	287.246	−	199.467i	0.380963	−	0.264545i
$755$	219.887			0.291242
$756$		0			0
$757$			383.583i			0.506714i	0.967373	+	0.253357i	$0.0815348\pi$
$757$			383.583i			0.506714i	−0.967373	+	0.253357i	$0.918465\pi$
$758$	−48.2319	+	33.4927i	−0.0636305	+	0.0441856i
$759$		0			0
$760$	61.5647	+	241.009i	0.0810062	+	0.317118i
$761$	−1312.55			−1.72476			−0.862382	−	0.506258i	$-0.831028\pi$
$761$	−1312.55			−1.72476			−0.862382	+	0.506258i	$0.831028\pi$
$762$		0			0
$763$	−304.296	+	706.636i	−0.398816	+	0.926129i
$764$	421.352	−	1130.14i	0.551507	−	1.47924i
$765$		0			0
$766$	−374.853	−	539.815i	−0.489364	−	0.704719i
$767$	−715.068			−0.932292
$768$		0			0
$769$		−	1180.37i		−	1.53494i	−0.641086	−	0.767469i	$-0.721516\pi$
$769$		−	1180.37i		−	1.53494i	0.641086	−	0.767469i	$-0.278484\pi$
$770$	253.943	−	51.5661i	0.329796	−	0.0669690i
$771$		0			0
$772$	−16.6552	+	44.6724i	−0.0215741	+	0.0578657i
$773$		−	1269.43i		−	1.64221i	−0.570780	−	0.821103i	$-0.693359\pi$
$773$		−	1269.43i		−	1.64221i	0.570780	−	0.821103i	$-0.306641\pi$
$774$		0			0
$775$	659.711			0.851240
$776$	947.219	−	241.963i	1.22064	−	0.311808i
$777$		0			0
$778$	653.055	−	453.488i	0.839402	−	0.582889i
$779$		−	372.414i		−	0.478066i
$780$		0			0
$781$			212.702i			0.272345i
$782$	−87.3026	+	60.6238i	−0.111640	+	0.0775241i
$783$		0			0
$784$	−34.3349	−	783.248i	−0.0437945	−	0.999041i
$785$		−	419.798i		−	0.534774i
$786$		0			0
$787$		−	1159.82i		−	1.47372i	−0.676044	−	0.736861i	$-0.736307\pi$
$787$		−	1159.82i		−	1.47372i	0.676044	−	0.736861i	$-0.263693\pi$
$788$	−209.550	+	562.052i	−0.265926	+	0.713263i
$789$		0			0
$790$	620.876	−	431.143i	0.785919	−	0.545750i
$791$	−254.438	+	590.856i	−0.321666	+	0.746973i
$792$		0			0
$793$	−36.0210			−0.0454237
$794$	316.333	−	219.665i	0.398404	−	0.276656i
$795$		0			0
$796$	24.5036	−	65.7231i	0.0307834	−	0.0825667i
$797$			478.221i			0.600026i	0.953935	+	0.300013i	$0.0969910\pi$
$797$			478.221i			0.600026i	−0.953935	+	0.300013i	$0.903009\pi$
$798$		0			0
$799$		−	352.493i		−	0.441167i
$800$	−402.484	−	43.1373i	−0.503105	−	0.0539216i
$801$		0			0
$802$	−510.278	−	734.837i	−0.636257	−	0.916256i
$803$	647.856			0.806795
$804$		0			0
$805$	41.8126	−	97.0971i	0.0519411	−	0.120618i
$806$	802.022	−	556.932i	0.995065	−	0.690983i
$807$		0			0
$808$	660.861	−	168.814i	0.817897	−	0.208928i
$809$			1061.21i			1.31176i	0.754865	+	0.655881i	$0.227703\pi$
$809$			1061.21i			1.31176i	−0.754865	+	0.655881i	$0.772297\pi$
$810$		0			0
$811$			738.364i			0.910437i	0.890380	+	0.455218i	$0.150439\pi$
$811$			738.364i			0.910437i	−0.890380	+	0.455218i	$0.849561\pi$
$812$	361.628	−	377.828i	0.445355	−	0.465305i
$813$		0			0
$814$	−393.404	+	273.184i	−0.483297	+	0.335606i
$815$		−	400.951i		−	0.491964i
$816$		0			0
$817$		−	205.759i		−	0.251847i
$818$	−635.314	−	914.897i	−0.776667	−	1.11846i
$819$		0			0
$820$	−554.412	−	206.702i	−0.676112	−	0.252075i
$821$	448.627			0.546440			0.273220	−	0.961952i	$-0.411911\pi$
$821$	448.627			0.546440			0.273220	+	0.961952i	$0.411911\pi$
$822$		0			0
$823$		−	1327.80i		−	1.61337i	−0.590980	−	0.806686i	$-0.701259\pi$
$823$		−	1327.80i		−	1.61337i	0.590980	−	0.806686i	$-0.298741\pi$
$824$	−54.2810	−	212.495i	−0.0658750	−	0.257883i
$825$		0			0
$826$	−1048.01	+	212.811i	−1.26878	+	0.257640i
$827$		−	1315.08i		−	1.59018i	−0.606493	−	0.795089i	$-0.707424\pi$
$827$		−	1315.08i		−	1.59018i	0.606493	−	0.795089i	$-0.292576\pi$
$828$		0			0
$829$	1191.63			1.43744			0.718718	−	0.695302i	$-0.244729\pi$
$829$	1191.63			1.43744			0.718718	+	0.695302i	$0.244729\pi$
$830$	−370.033	−	532.874i	−0.445823	−	0.642017i
$831$		0			0
$832$	−525.723	+	287.337i	−0.631879	+	0.345356i
$833$	416.374	+	440.241i	0.499849	+	0.528501i
$834$		0			0
$835$	−26.4578			−0.0316860
$836$	65.1152	−	174.651i	0.0778890	−	0.208912i
$837$		0			0
$838$	1077.40	−	748.155i	1.28568	−	0.892786i
$839$			192.974i			0.230005i	0.993365	+	0.115002i	$0.0366876\pi$
$839$			192.974i			0.230005i	−0.993365	+	0.115002i	$0.963312\pi$
$840$		0			0
$841$	−492.111			−0.585150
$842$	408.823	+	588.734i	0.485538	+	0.699209i
$843$		0			0
$844$	−527.224	+	1414.11i	−0.624673	+	1.67549i
$845$		−	285.947i		−	0.338398i
$846$		0			0
$847$	599.598	+	258.203i	0.707908	+	0.304844i
$848$	219.623	+	190.203i	0.258990	+	0.224296i
$849$		0			0
$850$	256.979	−	178.449i	0.302328	−	0.209940i
$851$			195.402i			0.229614i
$852$		0			0
$853$	236.364			0.277097			0.138549	−	0.990356i	$-0.455756\pi$
$853$	236.364			0.277097			0.138549	+	0.990356i	$0.455756\pi$
$854$	−52.7928	+	10.7202i	−0.0618183	+	0.0125529i
$855$		0			0
$856$	906.085	−	231.455i	1.05851	−	0.270392i
$857$	464.302			0.541775			0.270888	−	0.962611i	$-0.412683\pi$
$857$	464.302			0.541775			0.270888	+	0.962611i	$0.412683\pi$
$858$		0			0
$859$		−	567.819i		−	0.661023i	−0.943802	−	0.330511i	$-0.892779\pi$
$859$		−	567.819i		−	0.661023i	0.943802	−	0.330511i	$-0.107221\pi$
$860$	−306.314	−	114.203i	−0.356179	−	0.132794i
$861$		0			0
$862$	560.137	−	388.965i	0.649810	−	0.451235i
$863$	610.907			0.707888			0.353944	−	0.935267i	$-0.384840\pi$
$863$	610.907			0.707888			0.353944	+	0.935267i	$0.384840\pi$
$864$		0			0
$865$	−868.469			−1.00401
$866$	243.246	+	350.291i	0.280884	+	0.404494i
$867$		0			0
$868$	1009.70	−	1054.94i	1.16325	−	1.21536i
$869$	−566.411			−0.651797
$870$		0			0
$871$	42.6534			0.0489706
$872$	851.925	−	217.620i	0.976978	−	0.249565i
$873$		0			0
$874$	−43.3741	−	62.4618i	−0.0496271	−	0.0714666i
$875$	−366.319	+	850.666i	−0.418651	+	0.972190i
$876$		0			0
$877$		−	780.619i		−	0.890101i	−0.895505	−	0.445050i	$-0.853186\pi$
$877$		−	780.619i		−	0.890101i	0.895505	−	0.445050i	$-0.146814\pi$
$878$	391.699	−	272.000i	0.446126	−	0.309795i
$879$		0			0
$880$	−223.861	−	193.874i	−0.254388	−	0.220311i
$881$	−539.433			−0.612296			−0.306148	−	0.951984i	$-0.599040\pi$
$881$	−539.433			−0.612296			−0.306148	+	0.951984i	$0.599040\pi$
$882$		0			0
$883$	797.997			0.903734			0.451867	−	0.892085i	$-0.350758\pi$
$883$	797.997			0.903734			0.451867	+	0.892085i	$0.350758\pi$
$884$	161.766	−	433.886i	0.182993	−	0.490822i
$885$		0			0
$886$	−128.658	−	185.276i	−0.145212	−	0.209115i
$887$			435.503i			0.490985i	0.969399	+	0.245492i	$0.0789496\pi$
$887$			435.503i			0.490985i	−0.969399	+	0.245492i	$0.921050\pi$
$888$		0			0
$889$	−150.807	+	350.204i	−0.169637	+	0.393931i
$890$	−7.21823	−	10.3948i	−0.00811037	−	0.0116795i
$891$		0			0
$892$	266.956	−	716.026i	0.299278	−	0.802720i
$893$	252.196			0.282414
$894$		0			0
$895$	652.115			0.728620
$896$	−684.991	+	577.584i	−0.764499	+	0.644625i
$897$		0			0
$898$	417.815	+	601.683i	0.465273	+	0.670026i
$899$	974.134			1.08358
$900$		0			0
$901$	−224.556			−0.249230
$902$	252.889	+	364.178i	0.280364	+	0.403745i
$903$		0			0
$904$	712.339	−	181.964i	0.787985	−	0.201287i
$905$		−	1133.44i		−	1.25242i
$906$		0			0
$907$	−834.673			−0.920257			−0.460128	−	0.887852i	$-0.652197\pi$
$907$	−834.673			−0.920257			−0.460128	+	0.887852i	$0.652197\pi$
$908$	−75.5326	+	202.592i	−0.0831857	+	0.223119i
$909$		0			0
$910$	91.6552	+	451.366i	0.100720	+	0.496006i
$911$	−543.809			−0.596937			−0.298468	−	0.954420i	$-0.596476\pi$
$911$	−543.809			−0.596937			−0.298468	+	0.954420i	$0.596476\pi$
$912$		0			0
$913$			486.129i			0.532453i
$914$	−209.144	+	145.231i	−0.228822	+	0.158897i
$915$		0			0
$916$	−89.1573	+	239.136i	−0.0973333	+	0.261066i
$917$	−1477.95	−	636.446i	−1.61173	−	0.694052i
$918$		0			0
$919$		−	257.470i		−	0.280163i	−0.990140	−	0.140082i	$-0.955264\pi$
$919$		−	257.470i		−	0.280163i	0.990140	−	0.140082i	$-0.0447365\pi$
$920$	−117.061	+	29.9027i	−0.127240	+	0.0325029i
$921$		0			0
$922$	671.469	+	966.963i	0.728274	+	1.04877i
$923$	−378.063			−0.409602
$924$		0			0
$925$		−	575.173i		−	0.621809i
$926$	307.184	+	442.366i	0.331732	+	0.477718i
$927$		0			0
$928$	−594.310	−	63.6968i	−0.640421	−	0.0686388i
$929$	943.723			1.01585			0.507924	−	0.861402i	$-0.330413\pi$
$929$	943.723			1.01585			0.507924	+	0.861402i	$0.330413\pi$
$930$		0			0
$931$	−314.976	+	297.900i	−0.338321	+	0.319979i
$932$	−341.418	−	127.291i	−0.366329	−	0.136579i
$933$		0			0
$934$	587.181	−	407.744i	0.628673	−	0.436557i
$935$	228.889			0.244801
$936$		0			0
$937$		−	468.548i		−	0.500052i	−0.968239	−	0.250026i	$-0.919561\pi$
$937$		−	468.548i		−	0.500052i	0.968239	−	0.250026i	$-0.0804391\pi$
$938$	62.5133	−	12.6941i	0.0666453	−	0.0135331i
$939$		0			0
$940$	139.977	−	375.443i	0.148911	−	0.399408i
$941$			1430.10i			1.51977i	0.650058	+	0.759885i	$0.274745\pi$
$941$			1430.10i			1.51977i	−0.650058	+	0.759885i	$0.725255\pi$
$942$		0			0
$943$	180.885			0.191819
$944$	923.866	+	800.108i	0.978672	+	0.847572i
$945$		0			0
$946$	139.722	+	201.209i	0.147697	+	0.212694i
$947$			782.150i			0.825924i	0.910748	+	0.412962i	$0.135506\pi$
$947$			782.150i			0.825924i	−0.910748	+	0.412962i	$0.864494\pi$
$948$		0			0
$949$			1151.52i			1.21340i
$950$	127.674	+	183.859i	0.134393	+	0.193536i
$951$		0			0
$952$	107.957	−	684.052i	0.113401	−	0.718542i
$953$			200.954i			0.210864i	0.994427	+	0.105432i	$0.0336226\pi$
$953$			200.954i			0.210864i	−0.994427	+	0.105432i	$0.966377\pi$
$954$		0			0
$955$			1059.68i			1.10961i
$956$	−545.225	+	1462.39i	−0.570319	+	1.52970i
$957$		0			0
$958$	865.134	+	1245.85i	0.903062	+	1.30047i
$959$	603.720	−	1401.96i	0.629530	−	1.46189i
$960$		0			0
$961$	1758.89			1.83027
$962$	−485.565	−	699.248i	−0.504745	−	0.726869i
$963$		0			0
$964$	248.488	+	92.6440i	0.257768	+	0.0961037i
$965$		−	41.8872i		−	0.0434064i
$966$		0			0
$967$			297.101i			0.307240i	0.988130	+	0.153620i	$0.0490931\pi$
$967$			297.101i			0.307240i	−0.988130	+	0.153620i	$0.950907\pi$
$968$	−184.656	−	722.879i	−0.190760	−	0.746776i
$969$		0			0
$970$	−705.508	+	489.912i	−0.727328	+	0.505064i
$971$	534.138			0.550090			0.275045	−	0.961431i	$-0.411307\pi$
$971$	534.138			0.550090			0.275045	+	0.961431i	$0.411307\pi$
$972$		0			0
$973$	761.819	−	1769.09i	0.782959	−	1.81819i
$974$	−703.034	−	1012.42i	−0.721801	−	1.03945i
$975$		0			0
$976$	46.5391	+	40.3049i	0.0476835	+	0.0412960i
$977$		−	631.207i		−	0.646066i	−0.946388	−	0.323033i	$-0.895298\pi$
$977$		−	631.207i		−	0.646066i	0.946388	−	0.323033i	$-0.104702\pi$
$978$		0			0
$979$			9.48292i			0.00968633i
$980$	268.662	+	634.249i	0.274145	+	0.647193i
$981$		0			0
$982$	655.037	+	943.301i	0.667044	+	0.960591i
$983$		−	1569.91i		−	1.59706i	−0.601955	−	0.798530i	$-0.705611\pi$
$983$		−	1569.91i		−	1.59706i	0.601955	−	0.798530i	$-0.294389\pi$
$984$		0			0
$985$		−	527.009i		−	0.535035i
$986$	379.457	−	263.499i	0.384845	−	0.267240i
$987$		0			0
$988$	310.430	+	115.738i	0.314200	+	0.117143i
$989$	99.9395			0.101051
$990$		0			0
$991$		−	890.354i		−	0.898440i	−0.893421	−	0.449220i	$-0.851702\pi$
$991$		−	890.354i		−	0.898440i	0.893421	−	0.449220i	$-0.148298\pi$
$992$	−1659.38	−	177.848i	−1.67276	−	0.179283i
$993$		0			0
$994$	−554.093	+	112.515i	−0.557437	+	0.113194i
$995$			61.6254i			0.0619351i
$996$		0			0
$997$	−918.467			−0.921230			−0.460615	−	0.887600i	$-0.652371\pi$
$997$	−918.467			−0.921230			−0.460615	+	0.887600i	$0.652371\pi$
$998$	−1008.08	+	700.018i	−1.01010	+	0.701421i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.e.c.251.37	yes	48
3.2	odd	2	inner	504.3.e.c.251.12	yes	48
4.3	odd	2		2016.3.e.c.1007.16		48
7.6	odd	2	inner	504.3.e.c.251.38	yes	48
8.3	odd	2	inner	504.3.e.c.251.9	✓	48
8.5	even	2		2016.3.e.c.1007.27		48
12.11	even	2		2016.3.e.c.1007.29		48
21.20	even	2	inner	504.3.e.c.251.11	yes	48
24.5	odd	2		2016.3.e.c.1007.18		48
24.11	even	2	inner	504.3.e.c.251.40	yes	48
28.27	even	2		2016.3.e.c.1007.17		48
56.13	odd	2		2016.3.e.c.1007.30		48
56.27	even	2	inner	504.3.e.c.251.10	yes	48
84.83	odd	2		2016.3.e.c.1007.28		48
168.83	odd	2	inner	504.3.e.c.251.39	yes	48
168.125	even	2		2016.3.e.c.1007.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.3.e.c.251.9	✓	48	8.3	odd	2	inner
504.3.e.c.251.10	yes	48	56.27	even	2	inner
504.3.e.c.251.11	yes	48	21.20	even	2	inner
504.3.e.c.251.12	yes	48	3.2	odd	2	inner
504.3.e.c.251.37	yes	48	1.1	even	1	trivial
504.3.e.c.251.38	yes	48	7.6	odd	2	inner
504.3.e.c.251.39	yes	48	168.83	odd	2	inner
504.3.e.c.251.40	yes	48	24.11	even	2	inner
2016.3.e.c.1007.15		48	168.125	even	2
2016.3.e.c.1007.16		48	4.3	odd	2
2016.3.e.c.1007.17		48	28.27	even	2
2016.3.e.c.1007.18		48	24.5	odd	2
2016.3.e.c.1007.27		48	8.5	even	2
2016.3.e.c.1007.28		48	84.83	odd	2
2016.3.e.c.1007.29		48	12.11	even	2
2016.3.e.c.1007.30		48	56.13	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64277 - 1.14075i) q^{2} +(1.39736 - 3.74798i) q^{4} +3.51431i q^{5} +(6.42922 + 2.76859i) q^{7} +(-1.97998 - 7.75111i) q^{8} +(4.00896 + 5.77318i) q^{10} -5.26675i q^{11} +9.36128 q^{13} +(13.7200 - 2.78601i) q^{14} +(-12.0948 - 10.4746i) q^{16} +12.3664 q^{17} +8.84770i q^{19} +(13.1716 + 4.91076i) q^{20} +(-6.00806 - 8.65204i) q^{22} -4.29743 q^{23} +12.6496 q^{25} +(15.3784 - 10.6789i) q^{26} +(19.3606 - 20.2279i) q^{28} +18.6786 q^{29} +52.1525 q^{31} +(-31.8178 - 3.41016i) q^{32} +(20.3151 - 14.1070i) q^{34} +(-9.72968 + 22.5943i) q^{35} -45.4695i q^{37} +(10.0930 + 14.5347i) q^{38} +(27.2398 - 6.95827i) q^{40} -42.0916 q^{41} -23.2557 q^{43} +(-19.7397 - 7.35956i) q^{44} +(-7.05967 + 4.90230i) q^{46} -28.5041i q^{47} +(33.6698 + 35.5998i) q^{49} +(20.7804 - 14.4301i) q^{50} +(13.0811 - 35.0859i) q^{52} -18.1585 q^{53} +18.5090 q^{55} +(8.72990 - 55.3154i) q^{56} +(30.6845 - 21.3076i) q^{58} -76.3857 q^{59} -3.84787 q^{61} +(85.6744 - 59.4932i) q^{62} +(-56.1593 + 30.6942i) q^{64} +32.8984i q^{65} +4.55636 q^{67} +(17.2803 - 46.3491i) q^{68} +(9.79088 + 48.2163i) q^{70} -40.3858 q^{71} +123.009i q^{73} +(-51.8695 - 74.6958i) q^{74} +(33.1610 + 12.3634i) q^{76} +(14.5815 - 33.8611i) q^{77} -107.545i q^{79} +(36.8109 - 42.5047i) q^{80} +(-69.1466 + 48.0161i) q^{82} -92.3016 q^{83} +43.4593i q^{85} +(-38.2036 + 26.5290i) q^{86} +(-40.8231 + 10.4281i) q^{88} -1.80053 q^{89} +(60.1857 + 25.9176i) q^{91} +(-6.00506 + 16.1067i) q^{92} +(-32.5161 - 46.8255i) q^{94} -31.0935 q^{95} +122.204i q^{97} +(95.9222 + 20.0732i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 144 q^{22} - 336 q^{25} - 232 q^{28} - 384 q^{43} + 736 q^{46} + 368 q^{49} - 432 q^{58} + 480 q^{64} - 896 q^{67} + 264 q^{70} - 48 q^{88} - 576 q^{91}+O(q^{100}) \) 48 * q + 144 * q^22 - 336 * q^25 - 232 * q^28 - 384 * q^43 + 736 * q^46 + 368 * q^49 - 432 * q^58 + 480 * q^64 - 896 * q^67 + 264 * q^70 - 48 * q^88 - 576 * q^91

Introduction

L-functions

Modular forms

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