LMFDB - Embedded newform 490.3.d.a.489.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,3,Mod(489,490)] 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("490.489"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	490.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$13.3515329537$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 42x^{14} + 1322x^{12} + 17616x^{10} + 175407x^{8} + 205392x^{6} + 203018x^{4} + 23226x^{2} + 2401 $ x^16 + 42x^14 + 1322x^12 + 17616x^10 + 175407x^8 + 205392x^6 + 203018x^4 + 23226*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			489.6
Root			$-0.518845 + 0.898665i$ of defining polynomial
Character	$\chi$	$=$	490.489
Dual form			490.3.d.a.489.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} +1.03769 q^{3} -2.00000 q^{4} +(-4.96625 - 0.579969i) q^{5} -1.46751i q^{6} +2.82843i q^{8} -7.92320 q^{9} +(-0.820200 + 7.02334i) q^{10} +12.4741 q^{11} -2.07538 q^{12} +0.748223 q^{13} +(-5.15342 - 0.601827i) q^{15} +4.00000 q^{16} -11.5507 q^{17} +11.2051i q^{18} +15.1205i q^{19} +(9.93250 + 1.15994i) q^{20} -17.6410i q^{22} +36.3131i q^{23} +2.93503i q^{24} +(24.3273 + 5.76054i) q^{25} -1.05815i q^{26} -17.5610 q^{27} +50.5846 q^{29} +(-0.851113 + 7.28804i) q^{30} +46.7641i q^{31} -5.65685i q^{32} +12.9442 q^{33} +16.3351i q^{34} +15.8464 q^{36} -11.7383i q^{37} +21.3837 q^{38} +0.776423 q^{39} +(1.64040 - 14.0467i) q^{40} +12.7397i q^{41} +26.2604i q^{43} -24.9482 q^{44} +(39.3486 + 4.59521i) q^{45} +51.3545 q^{46} -40.4487 q^{47} +4.15076 q^{48} +(8.14664 - 34.4040i) q^{50} -11.9860 q^{51} -1.49645 q^{52} -26.3722i q^{53} +24.8350i q^{54} +(-61.9494 - 7.23458i) q^{55} +15.6904i q^{57} -71.5374i q^{58} +79.0852i q^{59} +(10.3068 + 1.20365i) q^{60} +52.2630i q^{61} +66.1344 q^{62} -8.00000 q^{64} +(-3.71586 - 0.433946i) q^{65} -18.3059i q^{66} -34.7009i q^{67} +23.1014 q^{68} +37.6817i q^{69} +14.6636 q^{71} -22.4102i q^{72} -101.166 q^{73} -16.6005 q^{74} +(25.2441 + 5.97765i) q^{75} -30.2411i q^{76} -1.09803i q^{78} -35.7249 q^{79} +(-19.8650 - 2.31988i) q^{80} +53.0859 q^{81} +18.0167 q^{82} +80.8664 q^{83} +(57.3636 + 6.69903i) q^{85} +37.1378 q^{86} +52.4911 q^{87} +35.2820i q^{88} -135.219i q^{89} +(6.49861 - 55.6473i) q^{90} -72.6263i q^{92} +48.5266i q^{93} +57.2031i q^{94} +(8.76944 - 75.0924i) q^{95} -5.87006i q^{96} -91.4185 q^{97} -98.8347 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4} + 24 q^{9} + 24 q^{11} - 28 q^{15} + 64 q^{16} + 84 q^{25} - 136 q^{29} - 64 q^{30} - 48 q^{36} - 624 q^{39} - 48 q^{44} + 136 q^{46} - 96 q^{50} + 152 q^{51} + 56 q^{60} - 128 q^{64} + 208 q^{65}+ \cdots + 176 q^{99}+O(q^{100}) $ 16 * q - 32 * q^4 + 24 * q^9 + 24 * q^11 - 28 * q^15 + 64 * q^16 + 84 * q^25 - 136 * q^29 - 64 * q^30 - 48 * q^36 - 624 * q^39 - 48 * q^44 + 136 * q^46 - 96 * q^50 + 152 * q^51 + 56 * q^60 - 128 * q^64 + 208 * q^65 - 384 * q^71 - 416 * q^74 - 296 * q^79 + 280 * q^81 + 580 * q^85 + 376 * q^86 + 620 * q^95 + 176 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	1.03769			0.345896			0.172948	−	0.984931i	$-0.444671\pi$
$3$	1.03769			0.345896			0.172948	+	0.984931i	$0.444671\pi$
$4$	−2.00000			−0.500000
$5$	−4.96625	−	0.579969i	−0.993250	−	0.115994i
$5$	−4.96625	−	0.579969i	−0.993250	−	0.115994i
$6$		−	1.46751i		−	0.244586i
$7$		0			0
$7$		0			0
$8$			2.82843i			0.353553i
$9$	−7.92320			−0.880356
$10$	−0.820200	+	7.02334i	−0.0820200	+	0.702334i
$11$	12.4741			1.13401			0.567004	−	0.823715i	$-0.308103\pi$
$11$	12.4741			1.13401			0.567004	+	0.823715i	$0.308103\pi$
$12$	−2.07538			−0.172948
$13$	0.748223			0.0575556			0.0287778	−	0.999586i	$-0.490838\pi$
$13$	0.748223			0.0575556			0.0287778	+	0.999586i	$0.490838\pi$
$14$		0			0
$15$	−5.15342	−	0.601827i	−0.343562	−	0.0401218i
$16$	4.00000			0.250000
$17$	−11.5507			−0.679452			−0.339726	−	0.940525i	$-0.610334\pi$
$17$	−11.5507			−0.679452			−0.339726	+	0.940525i	$0.610334\pi$
$18$			11.2051i			0.622505i
$19$			15.1205i			0.795818i	0.917425	+	0.397909i	$0.130264\pi$
$19$			15.1205i			0.795818i	−0.917425	+	0.397909i	$0.869736\pi$
$20$	9.93250	+	1.15994i	0.496625	+	0.0579969i
$21$		0			0
$22$		−	17.6410i		−	0.801864i
$23$			36.3131i			1.57883i	0.613859	+	0.789416i	$0.289616\pi$
$23$			36.3131i			1.57883i	−0.613859	+	0.789416i	$0.710384\pi$
$24$			2.93503i			0.122293i
$25$	24.3273	+	5.76054i	0.973091	+	0.230422i
$26$		−	1.05815i		−	0.0406980i
$27$	−17.5610			−0.650408
$28$		0			0
$29$	50.5846			1.74430			0.872148	−	0.489243i	$-0.162727\pi$
$29$	50.5846			1.74430			0.872148	+	0.489243i	$0.162727\pi$
$30$	−0.851113	+	7.28804i	−0.0283704	+	0.242935i
$31$			46.7641i			1.50852i	0.656577	+	0.754259i	$0.272004\pi$
$31$			46.7641i			1.50852i	−0.656577	+	0.754259i	$0.727996\pi$
$32$		−	5.65685i		−	0.176777i
$33$	12.9442			0.392249
$34$			16.3351i			0.480445i
$35$		0			0
$36$	15.8464			0.440178
$37$		−	11.7383i		−	0.317251i	−0.987339	−	0.158626i	$-0.949294\pi$
$37$		−	11.7383i		−	0.317251i	0.987339	−	0.158626i	$-0.0507063\pi$
$38$	21.3837			0.562728
$39$	0.776423			0.0199083
$40$	1.64040	−	14.0467i	0.0410100	−	0.351167i
$41$			12.7397i			0.310724i	0.987858	+	0.155362i	$0.0496545\pi$
$41$			12.7397i			0.310724i	−0.987858	+	0.155362i	$0.950346\pi$
$42$		0			0
$43$			26.2604i			0.610706i	0.952239	+	0.305353i	$0.0987745\pi$
$43$			26.2604i			0.610706i	−0.952239	+	0.305353i	$0.901226\pi$
$44$	−24.9482			−0.567004
$45$	39.3486	+	4.59521i	0.874413	+	0.102116i
$46$	51.3545			1.11640
$47$	−40.4487			−0.860611			−0.430305	−	0.902683i	$-0.641594\pi$
$47$	−40.4487			−0.860611			−0.430305	+	0.902683i	$0.641594\pi$
$48$	4.15076			0.0864741
$49$		0			0
$50$	8.14664	−	34.4040i	0.162933	−	0.688079i
$51$	−11.9860			−0.235020
$52$	−1.49645			−0.0287778
$53$		−	26.3722i		−	0.497588i	−0.968556	−	0.248794i	$-0.919966\pi$
$53$		−	26.3722i		−	0.497588i	0.968556	−	0.248794i	$-0.0800342\pi$
$54$			24.8350i			0.459908i
$55$	−61.9494	−	7.23458i	−1.12635	−	0.131538i
$56$		0			0
$57$			15.6904i			0.275270i
$58$		−	71.5374i		−	1.23340i
$59$			79.0852i			1.34043i	0.742168	+	0.670214i	$0.233798\pi$
$59$			79.0852i			1.34043i	−0.742168	+	0.670214i	$0.766202\pi$
$60$	10.3068	+	1.20365i	0.171781	+	0.0200609i
$61$			52.2630i			0.856770i	0.903596	+	0.428385i	$0.140917\pi$
$61$			52.2630i			0.856770i	−0.903596	+	0.428385i	$0.859083\pi$
$62$	66.1344			1.06668
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−3.71586	−	0.433946i	−0.0571671	−	0.00667609i
$66$		−	18.3059i		−	0.277362i
$67$		−	34.7009i		−	0.517924i	−0.965888	−	0.258962i	$-0.916620\pi$
$67$		−	34.7009i		−	0.517924i	0.965888	−	0.258962i	$-0.0833804\pi$
$68$	23.1014			0.339726
$69$			37.6817i			0.546112i
$70$		0			0
$71$	14.6636			0.206530			0.103265	−	0.994654i	$-0.467071\pi$
$71$	14.6636			0.206530			0.103265	+	0.994654i	$0.467071\pi$
$72$		−	22.4102i		−	0.311253i
$73$	−101.166			−1.38584			−0.692918	−	0.721016i	$-0.743675\pi$
$73$	−101.166			−1.38584			−0.692918	+	0.721016i	$0.743675\pi$
$74$	−16.6005			−0.224331
$75$	25.2441	+	5.97765i	0.336589	+	0.0797020i
$76$		−	30.2411i		−	0.397909i
$77$		0			0
$78$		−	1.09803i		−	0.0140773i
$79$	−35.7249			−0.452214			−0.226107	−	0.974102i	$-0.572600\pi$
$79$	−35.7249			−0.452214			−0.226107	+	0.974102i	$0.572600\pi$
$80$	−19.8650	−	2.31988i	−0.248312	−	0.0289984i
$81$	53.0859			0.655382
$82$	18.0167			0.219715
$83$	80.8664			0.974293			0.487147	−	0.873320i	$-0.338038\pi$
$83$	80.8664			0.974293			0.487147	+	0.873320i	$0.338038\pi$
$84$		0			0
$85$	57.3636	+	6.69903i	0.674865	+	0.0788122i
$86$	37.1378			0.431835
$87$	52.4911			0.603345
$88$			35.2820i			0.400932i
$89$		−	135.219i		−	1.51931i	−0.650326	−	0.759655i	$-0.725368\pi$
$89$		−	135.219i		−	1.51931i	0.650326	−	0.759655i	$-0.274632\pi$
$90$	6.49861	−	55.6473i	0.0722068	−	0.618304i
$91$		0			0
$92$		−	72.6263i		−	0.789416i
$93$			48.5266i			0.521791i
$94$			57.2031i			0.608544i
$95$	8.76944	−	75.0924i	0.0923099	−	0.790446i
$96$		−	5.87006i		−	0.0611464i
$97$	−91.4185			−0.942459			−0.471230	−	0.882011i	$-0.656190\pi$
$97$	−91.4185			−0.942459			−0.471230	+	0.882011i	$0.656190\pi$
$98$		0			0
$99$	−98.8347			−0.998330
$100$	−48.6545	−	11.5211i	−0.486545	−	0.115211i
$101$		−	88.0109i		−	0.871395i	−0.900093	−	0.435698i	$-0.856502\pi$
$101$		−	88.0109i		−	0.871395i	0.900093	−	0.435698i	$-0.143498\pi$
$102$			16.9508i			0.166184i
$103$	112.595			1.09316			0.546579	−	0.837408i	$-0.315930\pi$
$103$	112.595			1.09316			0.546579	+	0.837408i	$0.315930\pi$
$104$			2.11629i			0.0203490i
$105$		0			0
$106$	−37.2959			−0.351848
$107$			2.87289i			0.0268494i	0.999910	+	0.0134247i	$0.00427334\pi$
$107$			2.87289i			0.0268494i	−0.999910	+	0.0134247i	$0.995727\pi$
$108$	35.1220			0.325204
$109$	−85.2169			−0.781806			−0.390903	−	0.920432i	$-0.627837\pi$
$109$	−85.2169			−0.781806			−0.390903	+	0.920432i	$0.627837\pi$
$110$	−10.2312	+	87.6097i	−0.0930113	+	0.796452i
$111$		−	12.1807i		−	0.109736i
$112$		0			0
$113$			211.525i			1.87190i	0.352132	+	0.935950i	$0.385457\pi$
$113$			211.525i			1.87190i	−0.352132	+	0.935950i	$0.614543\pi$
$114$	22.1896			0.194646
$115$	21.0605	−	180.340i	0.183135	−	1.56817i
$116$	−101.169			−0.872148
$117$	−5.92832			−0.0506694
$118$	111.843			0.947825
$119$		0			0
$120$	1.70223	−	14.5761i	0.0141852	−	0.121467i
$121$	34.6027			0.285973
$122$	73.9110			0.605828
$123$			13.2199i			0.107478i
$124$		−	93.5281i		−	0.754259i
$125$	−117.474	−	42.7173i	−0.939795	−	0.341739i
$126$		0			0
$127$			52.2434i			0.411366i	0.978619	+	0.205683i	$0.0659415\pi$
$127$			52.2434i			0.411366i	−0.978619	+	0.205683i	$0.934058\pi$
$128$			11.3137i			0.0883883i
$129$			27.2501i			0.211241i
$130$	−0.613693	+	5.25502i	−0.00472071	+	0.0404233i
$131$			93.9167i			0.716921i	0.933545	+	0.358461i	$0.116698\pi$
$131$			93.9167i			0.716921i	−0.933545	+	0.358461i	$0.883302\pi$
$132$	−25.8884			−0.196125
$133$		0			0
$134$	−49.0745			−0.366227
$135$	87.2124	+	10.1848i	0.646018	+	0.0754433i
$136$		−	32.6703i		−	0.240222i
$137$			116.838i			0.852831i	0.904527	+	0.426415i	$0.140224\pi$
$137$			116.838i			0.852831i	−0.904527	+	0.426415i	$0.859776\pi$
$138$	53.2900			0.386160
$139$			67.8796i			0.488342i	0.969732	+	0.244171i	$0.0785159\pi$
$139$			67.8796i			0.488342i	−0.969732	+	0.244171i	$0.921484\pi$
$140$		0			0
$141$	−41.9732			−0.297682
$142$		−	20.7375i		−	0.146039i
$143$	9.33340			0.0652685
$144$	−31.6928			−0.220089
$145$	−251.216	−	29.3375i	−1.73252	−	0.202327i
$146$			143.070i			0.979934i
$147$		0			0
$148$			23.4766i			0.158626i
$149$	172.156			1.15541			0.577704	−	0.816246i	$-0.303949\pi$
$149$	172.156			1.15541			0.577704	+	0.816246i	$0.303949\pi$
$150$	8.45367	−	35.7006i	0.0563578	−	0.238004i
$151$	−110.216			−0.729908			−0.364954	−	0.931026i	$-0.618915\pi$
$151$	−110.216			−0.729908			−0.364954	+	0.931026i	$0.618915\pi$
$152$	−42.7673			−0.281364
$153$	91.5184			0.598159
$154$		0			0
$155$	27.1217	−	232.242i	0.174979	−	1.49834i
$156$	−1.55285			−0.00995414
$157$	−204.163			−1.30040			−0.650201	−	0.759762i	$-0.725315\pi$
$157$	−204.163			−1.30040			−0.650201	+	0.759762i	$0.725315\pi$
$158$			50.5227i			0.319764i
$159$		−	27.3661i		−	0.172114i
$160$	−3.28080	+	28.0934i	−0.0205050	+	0.175583i
$161$		0			0
$162$		−	75.0748i		−	0.463425i
$163$			97.8716i			0.600439i	0.953870	+	0.300220i	$0.0970600\pi$
$163$			97.8716i			0.600439i	−0.953870	+	0.300220i	$0.902940\pi$
$164$		−	25.4794i		−	0.155362i
$165$	−64.2842	−	7.50724i	−0.389601	−	0.0454985i
$166$		−	114.362i		−	0.688929i
$167$	−97.1736			−0.581878			−0.290939	−	0.956742i	$-0.593968\pi$
$167$	−97.1736			−0.581878			−0.290939	+	0.956742i	$0.593968\pi$
$168$		0			0
$169$	−168.440			−0.996687
$170$	9.47387	−	81.1243i	0.0557286	−	0.477202i
$171$		−	119.803i		−	0.700603i
$172$		−	52.5207i		−	0.305353i
$173$	61.8572			0.357556			0.178778	−	0.983889i	$-0.442786\pi$
$173$	61.8572			0.357556			0.178778	+	0.983889i	$0.442786\pi$
$174$		−	74.2336i		−	0.426630i
$175$		0			0
$176$	49.8963			0.283502
$177$			82.0659i			0.463649i
$178$	−191.228			−1.07431
$179$	−224.221			−1.25263			−0.626316	−	0.779569i	$-0.715438\pi$
$179$	−224.221			−1.25263			−0.626316	+	0.779569i	$0.715438\pi$
$180$	−78.6972	−	9.19042i	−0.437207	−	0.0510579i
$181$		−	329.246i		−	1.81904i	−0.415659	−	0.909520i	$-0.636449\pi$
$181$		−	329.246i		−	1.81904i	0.415659	−	0.909520i	$-0.363551\pi$
$182$		0			0
$183$			54.2327i			0.296354i
$184$	−102.709			−0.558201
$185$	−6.80785	+	58.2953i	−0.0367992	+	0.315110i
$186$	68.6269			0.368962
$187$	−144.084			−0.770503
$188$	80.8974			0.430305
$189$		0			0
$190$	−106.197	−	12.4019i	−0.558930	−	0.0652730i
$191$	−66.2350			−0.346780			−0.173390	−	0.984853i	$-0.555472\pi$
$191$	−66.2350			−0.346780			−0.173390	+	0.984853i	$0.555472\pi$
$192$	−8.30151			−0.0432370
$193$			253.457i			1.31325i	0.754219	+	0.656623i	$0.228016\pi$
$193$			253.457i			1.31325i	−0.754219	+	0.656623i	$0.771984\pi$
$194$			129.285i			0.666419i
$195$	−3.85591	−	0.450301i	−0.0197739	−	0.00230924i
$196$		0			0
$197$		−	191.330i		−	0.971217i	−0.874176	−	0.485608i	$-0.838598\pi$
$197$		−	191.330i		−	0.971217i	0.874176	−	0.485608i	$-0.161402\pi$
$198$			139.773i			0.705926i
$199$		−	225.870i		−	1.13502i	−0.823365	−	0.567512i	$-0.807906\pi$
$199$		−	225.870i		−	1.13502i	0.823365	−	0.567512i	$-0.192094\pi$
$200$	−16.2933	+	68.8079i	−0.0814664	+	0.344040i
$201$		−	36.0087i		−	0.179148i
$202$	−124.466			−0.616169
$203$		0			0
$204$	23.9720			0.117510
$205$	7.38863	−	63.2685i	0.0360421	−	0.308627i
$206$		−	159.234i		−	0.772979i
$207$		−	287.716i		−	1.38993i
$208$	2.99289			0.0143889
$209$			188.615i			0.902463i
$210$		0			0
$211$	−186.816			−0.885386			−0.442693	−	0.896673i	$-0.645977\pi$
$211$	−186.816			−0.885386			−0.442693	+	0.896673i	$0.645977\pi$
$212$			52.7443i			0.248794i
$213$	15.2163			0.0714379
$214$	4.06287			0.0189854
$215$	15.2302	−	130.416i	0.0708381	−	0.606584i
$216$		−	49.6701i		−	0.229954i
$217$		0			0
$218$			120.515i			0.552821i
$219$	−104.979			−0.479356
$220$	123.899	+	14.4692i	0.563176	+	0.0657689i
$221$	−8.64249			−0.0391063
$222$	−17.2261			−0.0775951
$223$	194.106			0.870431			0.435215	−	0.900326i	$-0.356672\pi$
$223$	194.106			0.870431			0.435215	+	0.900326i	$0.356672\pi$
$224$		0			0
$225$	−192.750	−	45.6419i	−0.856666	−	0.202853i
$226$	299.141			1.32363
$227$	351.757			1.54959			0.774795	−	0.632212i	$-0.217853\pi$
$227$	351.757			1.54959			0.774795	+	0.632212i	$0.217853\pi$
$228$		−	31.3808i		−	0.137635i
$229$			188.208i			0.821870i	0.911665	+	0.410935i	$0.134798\pi$
$229$			188.208i			0.821870i	−0.911665	+	0.410935i	$0.865202\pi$
$230$	−255.039	−	29.7840i	−1.10887	−	0.129496i
$231$		0			0
$232$			143.075i			0.616702i
$233$		−	314.080i		−	1.34798i	−0.738740	−	0.673991i	$-0.764579\pi$
$233$		−	314.080i		−	1.34798i	0.738740	−	0.673991i	$-0.235421\pi$
$234$			8.38391i			0.0358287i
$235$	200.878	+	23.4590i	0.854802	+	0.0998255i
$236$		−	158.170i		−	0.670214i
$237$	−37.0714			−0.156419
$238$		0			0
$239$	336.269			1.40699			0.703493	−	0.710703i	$-0.251623\pi$
$239$	336.269			1.40699			0.703493	+	0.710703i	$0.251623\pi$
$240$	−20.6137	−	2.40731i	−0.0858904	−	0.0100305i
$241$			382.524i			1.58724i	0.608416	+	0.793619i	$0.291805\pi$
$241$			382.524i			1.58724i	−0.608416	+	0.793619i	$0.708195\pi$
$242$		−	48.9356i		−	0.202213i
$243$	213.136			0.877102
$244$		−	104.526i		−	0.428385i
$245$		0			0
$246$	18.6957			0.0759988
$247$			11.3135i			0.0458038i
$248$	−132.269			−0.533342
$249$	83.9141			0.337005
$250$	−60.4115	+	166.134i	−0.241646	+	0.664535i
$251$			302.072i			1.20347i	0.798695	+	0.601736i	$0.205524\pi$
$251$			302.072i			1.20347i	−0.798695	+	0.601736i	$0.794476\pi$
$252$		0			0
$253$			452.973i			1.79041i
$254$	73.8834			0.290879
$255$	59.5255	+	6.95152i	0.233433	+	0.0272608i
$256$	16.0000			0.0625000
$257$	204.679			0.796416			0.398208	−	0.917295i	$-0.369632\pi$
$257$	204.679			0.796416			0.398208	+	0.917295i	$0.369632\pi$
$258$	38.5375			0.149370
$259$		0			0
$260$	7.43173	+	0.867892i	0.0285836	+	0.00333805i
$261$	−400.792			−1.53560
$262$	132.818			0.506940
$263$		−	97.4309i		−	0.370460i	−0.982695	−	0.185230i	$-0.940697\pi$
$263$		−	97.4309i		−	0.370460i	0.982695	−	0.185230i	$-0.0593030\pi$
$264$			36.6118i			0.138681i
$265$	−15.2950	+	130.971i	−0.0577171	+	0.494229i
$266$		0			0
$267$		−	140.315i		−	0.525524i
$268$			69.4018i			0.258962i
$269$		−	96.5427i		−	0.358895i	−0.983768	−	0.179447i	$-0.942569\pi$
$269$		−	96.5427i		−	0.358895i	0.983768	−	0.179447i	$-0.0574309\pi$
$270$	14.4035	−	123.337i	0.0533465	−	0.456804i
$271$		−	83.6068i		−	0.308512i	−0.988031	−	0.154256i	$-0.950702\pi$
$271$		−	83.6068i		−	0.308512i	0.988031	−	0.154256i	$-0.0492981\pi$
$272$	−46.2027			−0.169863
$273$		0			0
$274$	165.234			0.603043
$275$	303.460	+	71.8575i	1.10349	+	0.261300i
$276$		−	75.3635i		−	0.273056i
$277$			385.734i			1.39254i	0.717779	+	0.696271i	$0.245159\pi$
$277$			385.734i			1.39254i	−0.717779	+	0.696271i	$0.754841\pi$
$278$	95.9962			0.345310
$279$		−	370.521i		−	1.32803i
$280$		0			0
$281$	243.459			0.866402			0.433201	−	0.901297i	$-0.357384\pi$
$281$	243.459			0.866402			0.433201	+	0.901297i	$0.357384\pi$
$282$			59.3590i			0.210493i
$283$	−102.831			−0.363359			−0.181680	−	0.983358i	$-0.558153\pi$
$283$	−102.831			−0.363359			−0.181680	+	0.983358i	$0.558153\pi$
$284$	−29.3272			−0.103265
$285$	9.09995	−	77.9225i	0.0319297	−	0.273412i
$286$		−	13.1994i		−	0.0461518i
$287$		0			0
$288$			44.8204i			0.155626i
$289$	−155.582			−0.538345
$290$	−41.4895	+	355.272i	−0.143067	+	1.22508i
$291$	−94.8640			−0.325993
$292$	202.332			0.692918
$293$	440.610			1.50379			0.751894	−	0.659284i	$-0.229141\pi$
$293$	440.610			1.50379			0.751894	+	0.659284i	$0.229141\pi$
$294$		0			0
$295$	45.8670	−	392.757i	0.155481	−	1.33138i
$296$	33.2009			0.112165
$297$	−219.058			−0.737568
$298$		−	243.465i		−	0.816997i
$299$			27.1703i			0.0908706i
$300$	−50.4883	−	11.9553i	−0.168294	−	0.0398510i
$301$		0			0
$302$			155.869i			0.516123i
$303$		−	91.3279i		−	0.301412i
$304$			60.4821i			0.198954i
$305$	30.3109	−	259.551i	0.0993800	−	0.850987i
$306$		−	129.427i		−	0.422962i
$307$	247.192			0.805185			0.402592	−	0.915379i	$-0.368109\pi$
$307$	247.192			0.805185			0.402592	+	0.915379i	$0.368109\pi$
$308$		0			0
$309$	116.839			0.378119
$310$	−328.440	−	38.3559i	−1.05948	−	0.123729i
$311$			426.219i			1.37048i	0.728317	+	0.685240i	$0.240303\pi$
$311$			426.219i			1.37048i	−0.728317	+	0.685240i	$0.759697\pi$
$312$			2.19606i			0.00703864i
$313$	133.974			0.428032			0.214016	−	0.976830i	$-0.431346\pi$
$313$	133.974			0.428032			0.214016	+	0.976830i	$0.431346\pi$
$314$			288.730i			0.919523i
$315$		0			0
$316$	71.4499			0.226107
$317$		−	321.966i		−	1.01567i	−0.861456	−	0.507833i	$-0.830447\pi$
$317$		−	321.966i		−	1.01567i	0.861456	−	0.507833i	$-0.169553\pi$
$318$	−38.7015			−0.121703
$319$	630.996			1.97804
$320$	39.7300	+	4.63975i	0.124156	+	0.0144992i
$321$			2.98116i			0.00928711i
$322$		0			0
$323$		−	174.652i		−	0.540720i
$324$	−106.172			−0.327691
$325$	18.2022	+	4.31017i	0.0560069	+	0.0132621i
$326$	138.411			0.424575
$327$	−88.4286			−0.270424
$328$	−36.0333			−0.109858
$329$		0			0
$330$	−10.6168	+	90.9116i	−0.0321723	+	0.275490i
$331$	−234.805			−0.709381			−0.354690	−	0.934984i	$-0.615414\pi$
$331$	−234.805			−0.709381			−0.354690	+	0.934984i	$0.615414\pi$
$332$	−161.733			−0.487147
$333$			93.0049i			0.279294i
$334$			137.424i			0.411450i
$335$	−20.1254	+	172.333i	−0.0600759	+	0.514428i
$336$		0			0
$337$		−	217.706i		−	0.646012i	−0.946397	−	0.323006i	$-0.895307\pi$
$337$		−	217.706i		−	0.646012i	0.946397	−	0.323006i	$-0.104693\pi$
$338$			238.210i			0.704764i
$339$			219.497i			0.647484i
$340$	−114.727	−	13.3981i	−0.337433	−	0.0394061i
$341$			583.339i			1.71067i
$342$	−169.427			−0.495401
$343$		0			0
$344$	−74.2755			−0.215917
$345$	21.8542	−	187.137i	0.0633456	−	0.542426i
$346$		−	87.4793i		−	0.252830i
$347$		−	186.231i		−	0.536690i	−0.963323	−	0.268345i	$-0.913523\pi$
$347$		−	186.231i		−	0.536690i	0.963323	−	0.268345i	$-0.0864767\pi$
$348$	−104.982			−0.301673
$349$		−	81.7368i		−	0.234203i	−0.993120	−	0.117101i	$-0.962640\pi$
$349$		−	81.7368i		−	0.234203i	0.993120	−	0.117101i	$-0.0373603\pi$
$350$		0			0
$351$	−13.1396			−0.0374347
$352$		−	70.5641i		−	0.200466i
$353$	−107.936			−0.305769			−0.152884	−	0.988244i	$-0.548856\pi$
$353$	−107.936			−0.305769			−0.152884	+	0.988244i	$0.548856\pi$
$354$	116.059			0.327849
$355$	−72.8232	−	8.50444i	−0.205136	−	0.0239562i
$356$			270.437i			0.759655i
$357$		0			0
$358$			317.097i			0.885745i
$359$	603.859			1.68206			0.841029	−	0.540989i	$-0.181950\pi$
$359$	603.859			1.68206			0.841029	+	0.540989i	$0.181950\pi$
$360$	−12.9972	+	111.295i	−0.0361034	+	0.309152i
$361$	132.369			0.366674
$362$	−465.625			−1.28626
$363$	35.9069			0.0989169
$364$		0			0
$365$	502.416	+	58.6732i	1.37648	+	0.160748i
$366$	76.6967			0.209554
$367$	543.529			1.48101			0.740503	−	0.672053i	$-0.234587\pi$
$367$	543.529			1.48101			0.740503	+	0.672053i	$0.234587\pi$
$368$			145.253i			0.394708i
$369$		−	100.939i		−	0.273548i
$370$	82.4421	+	9.62775i	0.222816	+	0.0260210i
$371$		0			0
$372$		−	97.0531i		−	0.260895i
$373$			83.2904i			0.223299i	0.993748	+	0.111649i	$0.0356134\pi$
$373$			83.2904i			0.223299i	−0.993748	+	0.111649i	$0.964387\pi$
$374$			203.766i			0.544828i
$375$	−121.902	−	44.3273i	−0.325072	−	0.118206i
$376$		−	114.406i		−	0.304272i
$377$	37.8485			0.100394
$378$		0			0
$379$	−30.4409			−0.0803189			−0.0401595	−	0.999193i	$-0.512787\pi$
$379$	−30.4409			−0.0803189			−0.0401595	+	0.999193i	$0.512787\pi$
$380$	−17.5389	+	150.185i	−0.0461549	+	0.395223i
$381$			54.2124i			0.142290i
$382$			93.6704i			0.245210i
$383$	295.517			0.771586			0.385793	−	0.922585i	$-0.373928\pi$
$383$	295.517			0.771586			0.385793	+	0.922585i	$0.373928\pi$
$384$			11.7401i			0.0305732i
$385$		0			0
$386$	358.442			0.928605
$387$		−	208.066i		−	0.537639i
$388$	182.837			0.471230
$389$	428.775			1.10225			0.551125	−	0.834423i	$-0.314199\pi$
$389$	428.775			1.10225			0.551125	+	0.834423i	$0.314199\pi$
$390$	−0.636822	+	5.45308i	−0.00163288	+	0.0139823i
$391$		−	419.441i		−	1.07274i
$392$		0			0
$393$			97.4563i			0.247980i
$394$	−270.581			−0.686754
$395$	177.419	+	20.7194i	0.449162	+	0.0524541i
$396$	197.669			0.499165
$397$	−320.783			−0.808019			−0.404009	−	0.914755i	$-0.632384\pi$
$397$	−320.783			−0.808019			−0.404009	+	0.914755i	$0.632384\pi$
$398$	−319.428			−0.802583
$399$		0			0
$400$	97.3091	+	23.0422i	0.243273	+	0.0576054i
$401$	−237.708			−0.592789			−0.296394	−	0.955066i	$-0.595784\pi$
$401$	−237.708			−0.592789			−0.296394	+	0.955066i	$0.595784\pi$
$402$	−50.9240			−0.126677
$403$			34.9900i			0.0868237i
$404$			176.022i			0.435698i
$405$	−263.638	−	30.7882i	−0.650958	−	0.0760202i
$406$		0			0
$407$		−	146.425i		−	0.359765i
$408$		−	33.9016i		−	0.0830921i
$409$		−	198.100i		−	0.484352i	−0.970232	−	0.242176i	$-0.922139\pi$
$409$		−	198.100i		−	0.484352i	0.970232	−	0.242176i	$-0.0778612\pi$
$410$	−89.4752	−	10.4491i	−0.218232	−	0.0254856i
$411$			121.241i			0.294991i
$412$	−225.191			−0.546579
$413$		0			0
$414$	−406.892			−0.982831
$415$	−401.603	−	46.9000i	−0.967717	−	0.113012i
$416$		−	4.23259i		−	0.0101745i
$417$			70.4379i			0.168916i
$418$	266.742			0.638138
$419$		−	56.6448i		−	0.135190i	−0.997713	−	0.0675952i	$-0.978467\pi$
$419$		−	56.6448i		−	0.135190i	0.997713	−	0.0675952i	$-0.0215326\pi$
$420$		0			0
$421$	−220.350			−0.523396			−0.261698	−	0.965150i	$-0.584282\pi$
$421$	−220.350			−0.523396			−0.261698	+	0.965150i	$0.584282\pi$
$422$			264.198i			0.626062i
$423$	320.483			0.757644
$424$	74.5917			0.175924
$425$	−280.997	−	66.5382i	−0.661168	−	0.156560i
$426$		−	21.5191i		−	0.0505142i
$427$		0			0
$428$		−	5.74577i		−	0.0134247i
$429$	9.68516			0.0225761
$430$	−184.435	−	21.5388i	−0.428920	−	0.0500901i
$431$	−273.322			−0.634158			−0.317079	−	0.948399i	$-0.602702\pi$
$431$	−273.322			−0.634158			−0.317079	+	0.948399i	$0.602702\pi$
$432$	−70.2441			−0.162602
$433$	−201.926			−0.466342			−0.233171	−	0.972436i	$-0.574910\pi$
$433$	−201.926			−0.466342			−0.233171	+	0.972436i	$0.574910\pi$
$434$		0			0
$435$	−260.684	−	30.4432i	−0.599273	−	0.0699843i
$436$	170.434			0.390903
$437$	−549.074			−1.25646
$438$			148.463i			0.338956i
$439$		−	608.739i		−	1.38665i	−0.720625	−	0.693325i	$-0.756145\pi$
$439$		−	608.739i		−	1.38665i	0.720625	−	0.693325i	$-0.243855\pi$
$440$	20.4625	−	175.219i	0.0465056	−	0.398226i
$441$		0			0
$442$			12.2223i			0.0276523i
$443$			779.369i			1.75930i	0.475622	+	0.879650i	$0.342223\pi$
$443$			779.369i			1.75930i	−0.475622	+	0.879650i	$0.657777\pi$
$444$			24.3614i			0.0548681i
$445$	−78.4226	+	671.529i	−0.176230	+	1.50905i
$446$		−	274.507i		−	0.615487i
$447$	178.644			0.399652
$448$		0			0
$449$	−8.03323			−0.0178914			−0.00894569	−	0.999960i	$-0.502848\pi$
$449$	−8.03323			−0.0178914			−0.00894569	+	0.999960i	$0.502848\pi$
$450$	−64.5474	+	272.589i	−0.143439	+	0.605754i
$451$			158.916i			0.352364i
$452$		−	423.049i		−	0.935950i
$453$	−114.370			−0.252473
$454$		−	497.459i		−	1.09573i
$455$		0			0
$456$	−44.3792			−0.0973228
$457$			499.308i			1.09258i	0.837597	+	0.546289i	$0.183960\pi$
$457$			499.308i			1.09258i	−0.837597	+	0.546289i	$0.816040\pi$
$458$	266.167			0.581150
$459$	202.842			0.441921
$460$	−42.1210	+	360.680i	−0.0915673	+	0.784087i
$461$			690.386i			1.49758i	0.662805	+	0.748792i	$0.269366\pi$
$461$			690.386i			1.49758i	−0.662805	+	0.748792i	$0.730634\pi$
$462$		0			0
$463$		−	615.045i		−	1.32839i	−0.747559	−	0.664195i	$-0.768774\pi$
$463$		−	615.045i		−	1.32839i	0.747559	−	0.664195i	$-0.231226\pi$
$464$	202.338			0.436074
$465$	28.1439	−	240.995i	0.0605245	−	0.518269i
$466$	−444.176			−0.953167
$467$	47.8680			0.102501			0.0512506	−	0.998686i	$-0.483679\pi$
$467$	47.8680			0.102501			0.0512506	+	0.998686i	$0.483679\pi$
$468$	11.8566			0.0253347
$469$		0			0
$470$	33.1760	−	284.085i	0.0705873	−	0.604436i
$471$	−211.858			−0.449805
$472$	−223.687			−0.473913
$473$			327.574i			0.692545i
$474$			52.4268i			0.110605i
$475$	−87.1025	+	367.841i	−0.183374	+	0.774403i
$476$		0			0
$477$			208.952i			0.438054i
$478$		−	475.557i		−	0.994889i
$479$		−	134.654i		−	0.281114i	−0.990073	−	0.140557i	$-0.955111\pi$
$479$		−	134.654i		−	0.281114i	0.990073	−	0.140557i	$-0.0448894\pi$
$480$	−3.40445	+	29.1522i	−0.00709260	+	0.0607337i
$481$		−	8.78287i		−	0.0182596i
$482$	540.971			1.12235
$483$		0			0
$484$	−69.2054			−0.142986
$485$	454.007	+	53.0199i	0.936098	+	0.109319i
$486$		−	301.420i		−	0.620205i
$487$		−	446.828i		−	0.917511i	−0.888563	−	0.458755i	$-0.848295\pi$
$487$		−	446.828i		−	0.917511i	0.888563	−	0.458755i	$-0.151705\pi$
$488$	−147.822			−0.302914
$489$			101.560i			0.207690i
$490$		0			0
$491$	−119.125			−0.242617			−0.121309	−	0.992615i	$-0.538709\pi$
$491$	−119.125			−0.242617			−0.121309	+	0.992615i	$0.538709\pi$
$492$		−	26.4397i		−	0.0537392i
$493$	−584.286			−1.18516
$494$	15.9998			0.0323882
$495$	490.838	+	57.3210i	0.991591	+	0.115800i
$496$			187.056i			0.377130i
$497$		0			0
$498$		−	118.673i		−	0.238298i
$499$	84.2421			0.168822			0.0844109	−	0.996431i	$-0.473099\pi$
$499$	84.2421			0.168822			0.0844109	+	0.996431i	$0.473099\pi$
$500$	234.949	+	85.4347i	0.469897	+	0.170869i
$501$	−100.836			−0.201269
$502$	427.194			0.850984
$503$	388.428			0.772223			0.386111	−	0.922452i	$-0.373818\pi$
$503$	388.428			0.772223			0.386111	+	0.922452i	$0.373818\pi$
$504$		0			0
$505$	−51.0436	+	437.084i	−0.101076	+	0.865513i
$506$	640.600			1.26601
$507$	−174.789			−0.344751
$508$		−	104.487i		−	0.205683i
$509$			79.5033i			0.156195i	0.996946	+	0.0780975i	$0.0248845\pi$
$509$			79.5033i			0.156195i	−0.996946	+	0.0780975i	$0.975115\pi$
$510$	9.83093	−	84.1818i	0.0192763	−	0.165062i
$511$		0			0
$512$		−	22.6274i		−	0.0441942i
$513$		−	265.532i		−	0.517606i
$514$		−	289.460i		−	0.563151i
$515$	−559.176	−	65.3018i	−1.08578	−	0.126800i
$516$		−	54.5002i		−	0.105621i
$517$	−504.561			−0.975939
$518$		0			0
$519$	64.1885			0.123677
$520$	1.22739	−	10.5100i	0.00236036	−	0.0202116i
$521$		−	80.5118i		−	0.154533i	−0.997010	−	0.0772666i	$-0.975381\pi$
$521$		−	80.5118i		−	0.154533i	0.997010	−	0.0772666i	$-0.0246192\pi$
$522$			566.805i			1.08583i
$523$	−812.363			−1.55328			−0.776638	−	0.629947i	$-0.783077\pi$
$523$	−812.363			−1.55328			−0.776638	+	0.629947i	$0.783077\pi$
$524$		−	187.833i		−	0.358461i
$525$		0			0
$526$	−137.788			−0.261955
$527$		−	540.157i		−	1.02497i
$528$	51.7769			0.0980623
$529$	−789.643			−1.49271
$530$	185.221	+	21.6304i	0.349473	+	0.0408122i
$531$		−	626.608i		−	1.18005i
$532$		0			0
$533$			9.53214i			0.0178839i
$534$	−198.435			−0.371601
$535$	1.66618	−	14.2675i	0.00311436	−	0.0266682i
$536$	98.1489			0.183114
$537$	−232.672			−0.433281
$538$	−136.532			−0.253777
$539$		0			0
$540$	−174.425	−	20.3697i	−0.323009	−	0.0377217i
$541$	283.329			0.523713			0.261857	−	0.965107i	$-0.415665\pi$
$541$	283.329			0.523713			0.261857	+	0.965107i	$0.415665\pi$
$542$	−118.238			−0.218151
$543$		−	341.655i		−	0.629200i
$544$			65.3405i			0.120111i
$545$	423.208	+	49.4231i	0.776529	+	0.0906847i
$546$		0			0
$547$			51.6110i			0.0943529i	0.998887	+	0.0471764i	$0.0150223\pi$
$547$			51.6110i			0.0943529i	−0.998887	+	0.0471764i	$0.984978\pi$
$548$		−	233.676i		−	0.426415i
$549$		−	414.090i		−	0.754263i
$550$	101.622	−	429.158i	0.184767	−	0.780287i
$551$			764.866i			1.38814i
$552$	−106.580			−0.193080
$553$		0			0
$554$	545.510			0.984675
$555$	−7.06443	+	60.4924i	−0.0127287	+	0.108995i
$556$		−	135.759i		−	0.244171i
$557$			235.757i			0.423262i	0.977350	+	0.211631i	$0.0678774\pi$
$557$			235.757i			0.423262i	−0.977350	+	0.211631i	$0.932123\pi$
$558$	−523.996			−0.939061
$559$			19.6486i			0.0351496i
$560$		0			0
$561$	−149.515			−0.266514
$562$		−	344.303i		−	0.612639i
$563$	265.632			0.471815			0.235907	−	0.971776i	$-0.424194\pi$
$563$	265.632			0.471815			0.235907	+	0.971776i	$0.424194\pi$
$564$	83.9464			0.148841
$565$	122.678	−	1050.48i	0.217129	−	1.85926i
$566$			145.425i			0.256934i
$567$		0			0
$568$			41.4750i			0.0730193i
$569$	−26.0762			−0.0458281			−0.0229141	−	0.999737i	$-0.507294\pi$
$569$	−26.0762			−0.0458281			−0.0229141	+	0.999737i	$0.507294\pi$
$570$	−110.199	−	12.8693i	−0.193332	−	0.0225777i
$571$	294.624			0.515979			0.257989	−	0.966148i	$-0.416940\pi$
$571$	294.624			0.515979			0.257989	+	0.966148i	$0.416940\pi$
$572$	−18.6668			−0.0326343
$573$	−68.7313			−0.119950
$574$		0			0
$575$	−209.183	+	883.399i	−0.363797	+	1.53635i
$576$	63.3856			0.110044
$577$	575.097			0.996702			0.498351	−	0.866975i	$-0.333939\pi$
$577$	575.097			0.996702			0.498351	+	0.866975i	$0.333939\pi$
$578$			220.026i			0.380668i
$579$			263.009i			0.454247i
$580$	502.431	+	58.6750i	0.866261	+	0.101164i
$581$		0			0
$582$			134.158i			0.230512i
$583$		−	328.968i		−	0.564268i
$584$		−	286.141i		−	0.489967i
$585$	29.4415	+	3.43824i	0.0503274	+	0.00587734i
$586$		−	623.116i		−	1.06334i
$587$	−509.360			−0.867734			−0.433867	−	0.900977i	$-0.642851\pi$
$587$	−509.360			−0.867734			−0.433867	+	0.900977i	$0.642851\pi$
$588$		0			0
$589$	−707.098			−1.20051
$590$	−555.442	−	64.8657i	−0.941427	−	0.109942i
$591$		−	198.541i		−	0.335940i
$592$		−	46.9532i		−	0.0793128i
$593$	214.746			0.362135			0.181067	−	0.983471i	$-0.442045\pi$
$593$	214.746			0.362135			0.181067	+	0.983471i	$0.442045\pi$
$594$			309.794i			0.521539i
$595$		0			0
$596$	−344.312			−0.577704
$597$		−	234.383i		−	0.392601i
$598$	38.4246			0.0642552
$599$	−954.499			−1.59349			−0.796744	−	0.604317i	$-0.793446\pi$
$599$	−954.499			−1.59349			−0.796744	+	0.604317i	$0.793446\pi$
$600$	−16.9073	+	71.4012i	−0.0281789	+	0.119002i
$601$		−	851.298i		−	1.41647i	−0.705977	−	0.708234i	$-0.749492\pi$
$601$		−	851.298i		−	1.41647i	0.705977	−	0.708234i	$-0.250508\pi$
$602$		0			0
$603$			274.942i			0.455957i
$604$	220.432			0.364954
$605$	−171.846	−	20.0685i	−0.284042	−	0.0331711i
$606$	−129.157			−0.213131
$607$	1050.57			1.73075			0.865377	−	0.501122i	$-0.167079\pi$
$607$	1050.57			1.73075			0.865377	+	0.501122i	$0.167079\pi$
$608$	85.5347			0.140682
$609$		0			0
$610$	−367.061	−	42.8661i	−0.601739	−	0.0702723i
$611$	−30.2647			−0.0495330
$612$	−183.037			−0.299080
$613$		−	1012.11i		−	1.65108i	−0.564341	−	0.825542i	$-0.690870\pi$
$613$		−	1012.11i		−	1.65108i	0.564341	−	0.825542i	$-0.309130\pi$
$614$		−	349.582i		−	0.569352i
$615$	7.66710	−	65.6531i	0.0124668	−	0.106753i
$616$		0			0
$617$			706.409i			1.14491i	0.819937	+	0.572454i	$0.194009\pi$
$617$			706.409i			1.14491i	−0.819937	+	0.572454i	$0.805991\pi$
$618$		−	165.235i		−	0.267371i
$619$		−	786.823i		−	1.27112i	−0.772051	−	0.635560i	$-0.780769\pi$
$619$		−	786.823i		−	1.27112i	0.772051	−	0.635560i	$-0.219231\pi$
$620$	−54.2434	+	464.484i	−0.0874894	+	0.749168i
$621$		−	637.696i		−	1.02689i
$622$	602.765			0.969076
$623$		0			0
$624$	3.10569			0.00497707
$625$	558.632	+	280.276i	0.893812	+	0.448442i
$626$		−	189.468i		−	0.302664i
$627$			195.723i			0.312159i
$628$	408.326			0.650201
$629$			135.585i			0.215557i
$630$		0			0
$631$	−218.755			−0.346680			−0.173340	−	0.984862i	$-0.555456\pi$
$631$	−218.755			−0.346680			−0.173340	+	0.984862i	$0.555456\pi$
$632$		−	101.045i		−	0.159882i
$633$	−193.857			−0.306252
$634$	−455.329			−0.718184
$635$	30.2996	−	259.454i	0.0477158	−	0.408589i
$636$			54.7322i			0.0860569i
$637$		0			0
$638$		−	892.363i		−	1.39869i
$639$	−116.183			−0.181820
$640$	6.56160	−	56.1867i	0.0102525	−	0.0877917i
$641$	−608.671			−0.949565			−0.474783	−	0.880103i	$-0.657473\pi$
$641$	−608.671			−0.949565			−0.474783	+	0.880103i	$0.657473\pi$
$642$	4.21600			0.00656698
$643$	−1184.38			−1.84196			−0.920978	−	0.389614i	$-0.872608\pi$
$643$	−1184.38			−1.84196			−0.920978	+	0.389614i	$0.872608\pi$
$644$		0			0
$645$	15.8042	−	135.331i	0.0245027	−	0.209815i
$646$	−246.996			−0.382347
$647$	−227.604			−0.351784			−0.175892	−	0.984410i	$-0.556281\pi$
$647$	−227.604			−0.351784			−0.175892	+	0.984410i	$0.556281\pi$
$648$			150.150i			0.231712i
$649$			986.515i			1.52005i
$650$	6.09550	−	25.7418i	0.00937769	−	0.0396028i
$651$		0			0
$652$		−	195.743i		−	0.300220i
$653$		−	230.664i		−	0.353237i	−0.984279	−	0.176619i	$-0.943484\pi$
$653$		−	230.664i		−	0.353237i	0.984279	−	0.176619i	$-0.0565159\pi$
$654$			125.057i			0.191219i
$655$	54.4688	−	466.414i	0.0831584	−	0.712082i
$656$			50.9588i			0.0776811i
$657$	801.559			1.22003
$658$		0			0
$659$	726.539			1.10249			0.551244	−	0.834344i	$-0.314153\pi$
$659$	726.539			1.10249			0.551244	+	0.834344i	$0.314153\pi$
$660$	128.568	+	15.0145i	0.194801	+	0.0227492i
$661$			248.180i			0.375461i	0.982221	+	0.187731i	$0.0601132\pi$
$661$			248.180i			0.375461i	−0.982221	+	0.187731i	$0.939887\pi$
$662$			332.064i			0.501608i
$663$	−8.96821			−0.0135267
$664$			228.725i			0.344465i
$665$		0			0
$666$	131.529			0.197491
$667$			1836.88i			2.75395i
$668$	194.347			0.290939
$669$	201.422			0.301079
$670$	243.716	+	28.4617i	0.363755	+	0.0424801i
$671$			651.933i			0.971584i
$672$		0			0
$673$		−	835.990i		−	1.24218i	−0.783738	−	0.621092i	$-0.786689\pi$
$673$		−	835.990i		−	1.24218i	0.783738	−	0.621092i	$-0.213311\pi$
$674$	−307.883			−0.456799
$675$	−427.212	−	101.161i	−0.632906	−	0.149868i
$676$	336.880			0.498344
$677$	378.127			0.558533			0.279267	−	0.960214i	$-0.409909\pi$
$677$	378.127			0.558533			0.279267	+	0.960214i	$0.409909\pi$
$678$	310.416			0.457840
$679$		0			0
$680$	−18.9477	+	162.249i	−0.0278643	+	0.238601i
$681$	365.014			0.535998
$682$	824.966			1.20963
$683$			193.330i			0.283060i	0.989934	+	0.141530i	$0.0452021\pi$
$683$			193.330i			0.283060i	−0.989934	+	0.141530i	$0.954798\pi$
$684$			239.606i			0.350301i
$685$	67.7623	−	580.246i	0.0989231	−	0.847074i
$686$		0			0
$687$			195.302i			0.284282i
$688$			105.041i			0.152677i
$689$		−	19.7323i		−	0.0286390i
$690$	−264.652	−	30.9066i	−0.383553	−	0.0447921i
$691$			579.085i			0.838039i	0.907977	+	0.419019i	$0.137626\pi$
$691$			579.085i			0.838039i	−0.907977	+	0.419019i	$0.862374\pi$
$692$	−123.714			−0.178778
$693$		0			0
$694$	−263.371			−0.379497
$695$	39.3680	−	337.107i	0.0566447	−	0.485046i
$696$			148.467i			0.213315i
$697$		−	147.152i		−	0.211122i
$698$	−115.593			−0.165606
$699$		−	325.917i		−	0.466262i
$700$		0			0
$701$	−516.871			−0.737334			−0.368667	−	0.929562i	$-0.620186\pi$
$701$	−516.871			−0.737334			−0.368667	+	0.929562i	$0.620186\pi$
$702$			18.5821i			0.0264703i
$703$	177.489			0.252474
$704$	−99.7927			−0.141751
$705$	208.449	+	24.3431i	0.295673	+	0.0345293i
$706$			152.645i			0.216211i
$707$		0			0
$708$		−	164.132i		−	0.231824i
$709$	59.8751			0.0844500			0.0422250	−	0.999108i	$-0.486555\pi$
$709$	59.8751			0.0844500			0.0422250	+	0.999108i	$0.486555\pi$
$710$	−12.0271	+	102.988i	−0.0169396	+	0.145053i
$711$	283.056			0.398109
$712$	382.456			0.537157
$713$	−1698.15			−2.38170
$714$		0			0
$715$	−46.3520	−	5.41308i	−0.0648279	−	0.00757074i
$716$	448.443			0.626316
$717$	348.943			0.486671
$718$		−	853.986i		−	1.18940i
$719$		−	1238.46i		−	1.72247i	−0.508207	−	0.861235i	$-0.669692\pi$
$719$		−	1238.46i		−	1.72247i	0.508207	−	0.861235i	$-0.330308\pi$
$720$	157.394	+	18.3808i	0.218603	+	0.0255289i
$721$		0			0
$722$		−	187.199i		−	0.259278i
$723$			396.941i			0.549020i
$724$			658.493i			0.909520i
$725$	1230.58	+	291.394i	1.69736	+	0.401923i
$726$		−	50.7800i		−	0.0699448i
$727$	387.549			0.533080			0.266540	−	0.963824i	$-0.414120\pi$
$727$	387.549			0.533080			0.266540	+	0.963824i	$0.414120\pi$
$728$		0			0
$729$	−256.605			−0.351995
$730$	82.9764	−	710.523i	0.113666	−	0.973320i
$731$		−	303.325i		−	0.414945i
$732$		−	108.465i		−	0.148177i
$733$	−1053.10			−1.43670			−0.718350	−	0.695682i	$-0.755102\pi$
$733$	−1053.10			−1.43670			−0.718350	+	0.695682i	$0.755102\pi$
$734$		−	768.667i		−	1.04723i
$735$		0			0
$736$	205.418			0.279101
$737$		−	432.862i		−	0.587329i
$738$	−142.750			−0.193428
$739$	247.121			0.334399			0.167199	−	0.985923i	$-0.446528\pi$
$739$	247.121			0.334399			0.167199	+	0.985923i	$0.446528\pi$
$740$	13.6157	−	116.591i	0.0183996	−	0.157555i
$741$			11.7399i			0.0158434i
$742$		0			0
$743$			189.686i			0.255298i	0.991819	+	0.127649i	$0.0407431\pi$
$743$			189.686i			0.255298i	−0.991819	+	0.127649i	$0.959257\pi$
$744$	−137.254			−0.184481
$745$	−854.969	−	99.8451i	−1.14761	−	0.134020i
$746$	117.790			0.157896
$747$	−640.720			−0.857725
$748$	288.168			0.385252
$749$		0			0
$750$	−62.6883	+	172.395i	−0.0835844	+	0.229860i
$751$	−800.638			−1.06610			−0.533048	−	0.846085i	$-0.678954\pi$
$751$	−800.638			−1.06610			−0.533048	+	0.846085i	$0.678954\pi$
$752$	−161.795			−0.215153
$753$			313.456i			0.416277i
$754$		−	53.5259i		−	0.0709893i
$755$	547.361	+	63.9219i	0.724981	+	0.0846648i
$756$		0			0
$757$			809.069i			1.06878i	0.845237	+	0.534392i	$0.179459\pi$
$757$			809.069i			1.06878i	−0.845237	+	0.534392i	$0.820541\pi$
$758$			43.0499i			0.0567941i
$759$			470.045i			0.619295i
$760$	212.393	+	24.8037i	0.279465	+	0.0326365i
$761$		−	246.698i		−	0.324176i	−0.986776	−	0.162088i	$-0.948177\pi$
$761$		−	246.698i		−	0.324176i	0.986776	−	0.162088i	$-0.0518229\pi$
$762$	76.6680			0.100614
$763$		0			0
$764$	132.470			0.173390
$765$	−454.503	−	53.0778i	−0.594122	−	0.0693827i
$766$		−	417.925i		−	0.545593i
$767$			59.1734i			0.0771491i
$768$	16.6030			0.0216185
$769$			851.221i			1.10692i	0.832876	+	0.553460i	$0.186693\pi$
$769$			851.221i			1.10692i	−0.832876	+	0.553460i	$0.813307\pi$
$770$		0			0
$771$	212.393			0.275478
$772$		−	506.913i		−	0.656623i
$773$	891.064			1.15274			0.576368	−	0.817191i	$-0.304470\pi$
$773$	891.064			1.15274			0.576368	+	0.817191i	$0.304470\pi$
$774$	−294.250			−0.380168
$775$	−269.386	+	1137.64i	−0.347595	+	1.46793i
$776$		−	258.571i		−	0.333210i
$777$		0			0
$778$		−	606.380i		−	0.779409i
$779$	−192.631			−0.247280
$780$	7.71182	+	0.900602i	0.00988695	+	0.00115462i
$781$	182.915			0.234206
$782$	−593.180			−0.758542
$783$	−888.317			−1.13450
$784$		0			0
$785$	1013.93	+	118.408i	1.29162	+	0.150839i
$786$	137.824			0.175349
$787$	−491.351			−0.624334			−0.312167	−	0.950027i	$-0.601055\pi$
$787$	−491.351			−0.624334			−0.312167	+	0.950027i	$0.601055\pi$
$788$			382.659i			0.485608i
$789$		−	101.103i		−	0.128141i
$790$	29.3016	−	250.908i	0.0370906	−	0.317605i
$791$		0			0
$792$		−	279.547i		−	0.352963i
$793$			39.1044i			0.0493120i
$794$			453.656i			0.571355i
$795$	−15.8715	+	135.907i	−0.0199641	+	0.170952i
$796$			451.740i			0.567512i
$797$	68.9206			0.0864751			0.0432375	−	0.999065i	$-0.486233\pi$
$797$	68.9206			0.0864751			0.0432375	+	0.999065i	$0.486233\pi$
$798$		0			0
$799$	467.210			0.584744
$800$	32.5865	−	137.616i	0.0407332	−	0.172020i
$801$			1071.36i			1.33753i
$802$			336.170i			0.419165i
$803$	−1261.95			−1.57155
$804$			72.0175i			0.0895740i
$805$		0			0
$806$	49.4833			0.0613936
$807$		−	100.181i		−	0.124140i
$808$	248.932			0.308085
$809$	−38.1526			−0.0471602			−0.0235801	−	0.999722i	$-0.507506\pi$
$809$	−38.1526			−0.0471602			−0.0235801	+	0.999722i	$0.507506\pi$
$810$	−43.5411	+	372.840i	−0.0537544	+	0.460297i
$811$			763.676i			0.941648i	0.882227	+	0.470824i	$0.156043\pi$
$811$			763.676i			0.941648i	−0.882227	+	0.470824i	$0.843957\pi$
$812$		0			0
$813$		−	86.7579i		−	0.106713i
$814$	−207.076			−0.254393
$815$	56.7625	−	486.055i	0.0696472	−	0.596386i
$816$	−47.9441			−0.0587550
$817$	−397.071			−0.486011
$818$	−280.156			−0.342489
$819$		0			0
$820$	−14.7773	+	126.537i	−0.0180211	+	0.154314i
$821$	−408.879			−0.498025			−0.249013	−	0.968500i	$-0.580106\pi$
$821$	−408.879			−0.498025			−0.249013	+	0.968500i	$0.580106\pi$
$822$	171.461			0.208590
$823$			153.706i			0.186763i	0.995630	+	0.0933814i	$0.0297676\pi$
$823$			153.706i			0.186763i	−0.995630	+	0.0933814i	$0.970232\pi$
$824$			318.468i			0.386490i
$825$	314.898	+	74.5657i	0.381694	+	0.0903827i
$826$		0			0
$827$		−	571.706i		−	0.691301i	−0.938363	−	0.345650i	$-0.887658\pi$
$827$		−	571.706i		−	0.691301i	0.938363	−	0.345650i	$-0.112342\pi$
$828$			575.432i			0.694967i
$829$			1269.81i			1.53174i	0.642997	+	0.765869i	$0.277691\pi$
$829$			1269.81i			1.53174i	−0.642997	+	0.765869i	$0.722309\pi$
$830$	−66.3266	+	567.952i	−0.0799115	+	0.684279i
$831$			400.272i			0.481675i
$832$	−5.98578			−0.00719445
$833$		0			0
$834$	99.6142			0.119442
$835$	482.588	+	56.3576i	0.577950	+	0.0674942i
$836$		−	377.230i		−	0.451232i
$837$		−	821.225i		−	0.981153i
$838$	−80.1078			−0.0955940
$839$			732.075i			0.872556i	0.899812	+	0.436278i	$0.143704\pi$
$839$			732.075i			0.872556i	−0.899812	+	0.436278i	$0.856296\pi$
$840$		0			0
$841$	1717.80			2.04257
$842$			311.621i			0.370097i
$843$	252.635			0.299685
$844$	373.633			0.442693
$845$	836.516	+	97.6901i	0.989960	+	0.115610i
$846$		−	453.232i		−	0.535735i
$847$		0			0
$848$		−	105.489i		−	0.124397i
$849$	−106.706			−0.125685
$850$	−94.0992	+	397.389i	−0.110705	+	0.467517i
$851$	426.254			0.500887
$852$	−30.4325			−0.0357190
$853$	193.304			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$853$	193.304			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$854$		0			0
$855$	−69.4820	+	594.972i	−0.0812655	+	0.695873i
$856$	−8.12575			−0.00949270
$857$	−473.815			−0.552876			−0.276438	−	0.961032i	$-0.589154\pi$
$857$	−473.815			−0.552876			−0.276438	+	0.961032i	$0.589154\pi$
$858$		−	13.6969i		−	0.0159637i
$859$		−	877.623i		−	1.02168i	−0.859676	−	0.510840i	$-0.829334\pi$
$859$		−	877.623i		−	1.02168i	0.859676	−	0.510840i	$-0.170666\pi$
$860$	−30.4604	+	260.831i	−0.0354191	+	0.303292i
$861$		0			0
$862$			386.536i			0.448417i
$863$		−	903.594i		−	1.04704i	−0.852014	−	0.523519i	$-0.824619\pi$
$863$		−	903.594i		−	1.04704i	0.852014	−	0.523519i	$-0.175381\pi$
$864$			99.3401i			0.114977i
$865$	−307.198	−	35.8752i	−0.355142	−	0.0414743i
$866$			285.567i			0.329754i
$867$	−161.446			−0.186212
$868$		0			0
$869$	−445.636			−0.512814
$870$	−43.0532	+	368.662i	−0.0494864	+	0.423750i
$871$		−	25.9640i		−	0.0298094i
$872$		−	241.030i		−	0.276410i
$873$	724.328			0.829699
$874$			776.508i			0.888453i
$875$		0			0
$876$	209.958			0.239678
$877$			1303.73i			1.48658i	0.668967	+	0.743292i	$0.266737\pi$
$877$			1303.73i			1.48658i	−0.668967	+	0.743292i	$0.733263\pi$
$878$	−860.887			−0.980509
$879$	457.216			0.520155
$880$	−247.798	−	28.9383i	−0.281588	−	0.0328845i
$881$		−	796.338i		−	0.903902i	−0.892043	−	0.451951i	$-0.850728\pi$
$881$		−	796.338i		−	0.903902i	0.892043	−	0.451951i	$-0.149272\pi$
$882$		0			0
$883$		−	1253.73i		−	1.41985i	−0.704276	−	0.709927i	$-0.748728\pi$
$883$		−	1253.73i		−	1.41985i	0.704276	−	0.709927i	$-0.251272\pi$
$884$	17.2850			0.0195531
$885$	47.5956	−	407.560i	0.0537804	−	0.460519i
$886$	1102.19			1.24401
$887$	979.226			1.10397			0.551987	−	0.833852i	$-0.313870\pi$
$887$	979.226			1.10397			0.551987	+	0.833852i	$0.313870\pi$
$888$	34.4522			0.0387976
$889$		0			0
$890$	949.686	+	110.906i	1.06706	+	0.124614i
$891$	662.198			0.743208
$892$	−388.212			−0.435215
$893$		−	611.606i		−	0.684889i
$894$		−	252.641i		−	0.282596i
$895$	1113.54	+	130.041i	1.24418	+	0.145298i
$896$		0			0
$897$			28.1943i			0.0314318i
$898$			11.3607i			0.0126511i
$899$			2365.54i			2.63130i
$900$	385.500	+	91.2839i	0.428333	+	0.101427i
$901$			304.616i			0.338087i
$902$	224.741			0.249159
$903$		0			0
$904$	−598.282			−0.661817
$905$	−190.953	+	1635.12i	−0.210997	+	1.80676i
$906$			161.744i			0.178525i
$907$			1650.77i			1.82003i	0.414570	+	0.910017i	$0.363932\pi$
$907$			1650.77i			1.82003i	−0.414570	+	0.910017i	$0.636068\pi$
$908$	−703.514			−0.774795
$909$			697.328i			0.767138i
$910$		0			0
$911$	−736.949			−0.808945			−0.404472	−	0.914550i	$-0.632545\pi$
$911$	−736.949			−0.808945			−0.404472	+	0.914550i	$0.632545\pi$
$912$			62.7617i			0.0688176i
$913$	1008.73			1.10486
$914$	706.128			0.772569
$915$	31.4533	−	269.333i	0.0343752	−	0.294353i
$916$		−	376.416i		−	0.410935i
$917$		0			0
$918$		−	286.862i		−	0.312485i
$919$	864.452			0.940644			0.470322	−	0.882495i	$-0.344138\pi$
$919$	864.452			0.940644			0.470322	+	0.882495i	$0.344138\pi$
$920$	510.079	+	59.5680i	0.554433	+	0.0647479i
$921$	256.508			0.278510
$922$	976.354			1.05895
$923$	10.9717			0.0118870
$924$		0			0
$925$	67.6190	−	285.561i	0.0731016	−	0.308714i
$926$	−869.805			−0.939314
$927$	−892.115			−0.962368
$928$		−	286.150i		−	0.308351i
$929$			594.739i			0.640193i	0.947385	+	0.320096i	$0.103715\pi$
$929$			594.739i			0.640193i	−0.947385	+	0.320096i	$0.896285\pi$
$930$	−340.818	−	39.8015i	−0.366471	−	0.0427973i
$931$		0			0
$932$			628.160i			0.673991i
$933$			442.283i			0.474044i
$934$		−	67.6956i		−	0.0724793i
$935$	715.558	+	83.5643i	0.765302	+	0.0893736i
$936$		−	16.7678i		−	0.0179143i
$937$	−312.979			−0.334022			−0.167011	−	0.985955i	$-0.553412\pi$
$937$	−312.979			−0.334022			−0.167011	+	0.985955i	$0.553412\pi$
$938$		0			0
$939$	139.023			0.148055
$940$	−401.757	−	46.9180i	−0.427401	−	0.0499128i
$941$		−	52.2357i		−	0.0555109i	−0.999615	−	0.0277554i	$-0.991164\pi$
$941$		−	52.2357i		−	0.0555109i	0.999615	−	0.0277554i	$-0.00883596\pi$
$942$			299.612i			0.318060i
$943$	−462.618			−0.490582
$944$			316.341i			0.335107i
$945$		0			0
$946$	463.260			0.489704
$947$		−	562.494i		−	0.593975i	−0.954881	−	0.296987i	$-0.904018\pi$
$947$		−	562.494i		−	0.593975i	0.954881	−	0.296987i	$-0.0959820\pi$
$948$	74.1427			0.0782097
$949$	−75.6948			−0.0797627
$950$	520.206	+	123.181i	0.547586	+	0.129665i
$951$		−	334.101i		−	0.351315i
$952$		0			0
$953$		−	786.616i		−	0.825411i	−0.910865	−	0.412705i	$-0.864584\pi$
$953$		−	786.616i		−	0.825411i	0.910865	−	0.412705i	$-0.135416\pi$
$954$	295.503			0.309751
$955$	328.939	+	38.4142i	0.344439	+	0.0402243i
$956$	−672.539			−0.703493
$957$	654.778			0.684198
$958$	−190.429			−0.198778
$959$		0			0
$960$	41.2274	+	4.81462i	0.0429452	+	0.00501523i
$961$	−1225.88			−1.27563
$962$	−12.4209			−0.0129115
$963$		−	22.7625i		−	0.0236370i
$964$		−	765.048i		−	0.793619i
$965$	146.997	−	1258.73i	0.152328	−	1.30438i
$966$		0			0
$967$			372.034i			0.384730i	0.981323	+	0.192365i	$0.0616157\pi$
$967$			372.034i			0.384730i	−0.981323	+	0.192365i	$0.938384\pi$
$968$			97.8712i			0.101107i
$969$		−	181.235i		−	0.187033i
$970$	74.9815	−	642.063i	0.0773005	−	0.661921i
$971$		−	535.098i		−	0.551079i	−0.961290	−	0.275539i	$-0.911144\pi$
$971$		−	535.098i		−	0.551079i	0.961290	−	0.275539i	$-0.0888565\pi$
$972$	−426.272			−0.438551
$973$		0			0
$974$	−631.910			−0.648778
$975$	18.8883	+	4.47262i	0.0193726	+	0.00458730i
$976$			209.052i			0.214193i
$977$		−	803.913i		−	0.822838i	−0.911446	−	0.411419i	$-0.865033\pi$
$977$		−	803.913i		−	0.822838i	0.911446	−	0.411419i	$-0.134967\pi$
$978$	143.628			0.146859
$979$		−	1686.73i		−	1.72291i
$980$		0			0
$981$	675.191			0.688268
$982$			168.468i			0.171556i
$983$	−237.085			−0.241185			−0.120592	−	0.992702i	$-0.538479\pi$
$983$	−237.085			−0.241185			−0.120592	+	0.992702i	$0.538479\pi$
$984$	−37.3914			−0.0379994
$985$	−110.965	+	950.191i	−0.112655	+	0.964661i
$986$			826.305i			0.838038i
$987$		0			0
$988$		−	22.6271i		−	0.0229019i
$989$	−953.596			−0.964202
$990$	81.0642	−	694.149i	0.0818830	−	0.701161i
$991$	−422.184			−0.426018			−0.213009	−	0.977050i	$-0.568326\pi$
$991$	−422.184			−0.426018			−0.213009	+	0.977050i	$0.568326\pi$
$992$	264.538			0.266671
$993$	−243.655			−0.245372
$994$		0			0
$995$	−130.997	+	1121.73i	−0.131656	+	1.12736i
$996$	−167.828			−0.168502
$997$	1552.94			1.55761			0.778806	−	0.627265i	$-0.215826\pi$
$997$	1552.94			1.55761			0.778806	+	0.627265i	$0.215826\pi$
$998$		−	119.136i		−	0.119375i
$999$			206.137i			0.206343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.3.d.a.489.6		16
5.4	even	2	inner	490.3.d.a.489.11		16
7.2	even	3		70.3.h.a.59.2	yes	16
7.3	odd	6		70.3.h.a.19.7	yes	16
7.4	even	3		490.3.h.b.19.6		16
7.5	odd	6		490.3.h.b.129.3		16
7.6	odd	2	inner	490.3.d.a.489.3		16
21.2	odd	6		630.3.bc.a.199.6		16
21.17	even	6		630.3.bc.a.19.4		16
28.3	even	6		560.3.br.b.369.3		16
28.23	odd	6		560.3.br.b.129.6		16
35.2	odd	12		350.3.k.e.101.3		16
35.3	even	12		350.3.k.e.201.6		16
35.4	even	6		490.3.h.b.19.3		16
35.9	even	6		70.3.h.a.59.7	yes	16
35.17	even	12		350.3.k.e.201.3		16
35.19	odd	6		490.3.h.b.129.6		16
35.23	odd	12		350.3.k.e.101.6		16
35.24	odd	6		70.3.h.a.19.2	✓	16
35.34	odd	2	inner	490.3.d.a.489.14		16
105.44	odd	6		630.3.bc.a.199.4		16
105.59	even	6		630.3.bc.a.19.6		16
140.59	even	6		560.3.br.b.369.6		16
140.79	odd	6		560.3.br.b.129.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.h.a.19.2	✓	16	35.24	odd	6
70.3.h.a.19.7	yes	16	7.3	odd	6
70.3.h.a.59.2	yes	16	7.2	even	3
70.3.h.a.59.7	yes	16	35.9	even	6
350.3.k.e.101.3		16	35.2	odd	12
350.3.k.e.101.6		16	35.23	odd	12
350.3.k.e.201.3		16	35.17	even	12
350.3.k.e.201.6		16	35.3	even	12
490.3.d.a.489.3		16	7.6	odd	2	inner
490.3.d.a.489.6		16	1.1	even	1	trivial
490.3.d.a.489.11		16	5.4	even	2	inner
490.3.d.a.489.14		16	35.34	odd	2	inner
490.3.h.b.19.3		16	35.4	even	6
490.3.h.b.19.6		16	7.4	even	3
490.3.h.b.129.3		16	7.5	odd	6
490.3.h.b.129.6		16	35.19	odd	6
560.3.br.b.129.3		16	140.79	odd	6
560.3.br.b.129.6		16	28.23	odd	6
560.3.br.b.369.3		16	28.3	even	6
560.3.br.b.369.6		16	140.59	even	6
630.3.bc.a.19.4		16	21.17	even	6
630.3.bc.a.19.6		16	105.59	even	6
630.3.bc.a.199.4		16	105.44	odd	6
630.3.bc.a.199.6		16	21.2	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	490.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +1.03769 q^{3} -2.00000 q^{4} +(-4.96625 - 0.579969i) q^{5} -1.46751i q^{6} +2.82843i q^{8} -7.92320 q^{9} +(-0.820200 + 7.02334i) q^{10} +12.4741 q^{11} -2.07538 q^{12} +0.748223 q^{13} +(-5.15342 - 0.601827i) q^{15} +4.00000 q^{16} -11.5507 q^{17} +11.2051i q^{18} +15.1205i q^{19} +(9.93250 + 1.15994i) q^{20} -17.6410i q^{22} +36.3131i q^{23} +2.93503i q^{24} +(24.3273 + 5.76054i) q^{25} -1.05815i q^{26} -17.5610 q^{27} +50.5846 q^{29} +(-0.851113 + 7.28804i) q^{30} +46.7641i q^{31} -5.65685i q^{32} +12.9442 q^{33} +16.3351i q^{34} +15.8464 q^{36} -11.7383i q^{37} +21.3837 q^{38} +0.776423 q^{39} +(1.64040 - 14.0467i) q^{40} +12.7397i q^{41} +26.2604i q^{43} -24.9482 q^{44} +(39.3486 + 4.59521i) q^{45} +51.3545 q^{46} -40.4487 q^{47} +4.15076 q^{48} +(8.14664 - 34.4040i) q^{50} -11.9860 q^{51} -1.49645 q^{52} -26.3722i q^{53} +24.8350i q^{54} +(-61.9494 - 7.23458i) q^{55} +15.6904i q^{57} -71.5374i q^{58} +79.0852i q^{59} +(10.3068 + 1.20365i) q^{60} +52.2630i q^{61} +66.1344 q^{62} -8.00000 q^{64} +(-3.71586 - 0.433946i) q^{65} -18.3059i q^{66} -34.7009i q^{67} +23.1014 q^{68} +37.6817i q^{69} +14.6636 q^{71} -22.4102i q^{72} -101.166 q^{73} -16.6005 q^{74} +(25.2441 + 5.97765i) q^{75} -30.2411i q^{76} -1.09803i q^{78} -35.7249 q^{79} +(-19.8650 - 2.31988i) q^{80} +53.0859 q^{81} +18.0167 q^{82} +80.8664 q^{83} +(57.3636 + 6.69903i) q^{85} +37.1378 q^{86} +52.4911 q^{87} +35.2820i q^{88} -135.219i q^{89} +(6.49861 - 55.6473i) q^{90} -72.6263i q^{92} +48.5266i q^{93} +57.2031i q^{94} +(8.76944 - 75.0924i) q^{95} -5.87006i q^{96} -91.4185 q^{97} -98.8347 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 24 q^{9} + 24 q^{11} - 28 q^{15} + 64 q^{16} + 84 q^{25} - 136 q^{29} - 64 q^{30} - 48 q^{36} - 624 q^{39} - 48 q^{44} + 136 q^{46} - 96 q^{50} + 152 q^{51} + 56 q^{60} - 128 q^{64} + 208 q^{65}+ \cdots + 176 q^{99}+O(q^{100}) \) 16 * q - 32 * q^4 + 24 * q^9 + 24 * q^11 - 28 * q^15 + 64 * q^16 + 84 * q^25 - 136 * q^29 - 64 * q^30 - 48 * q^36 - 624 * q^39 - 48 * q^44 + 136 * q^46 - 96 * q^50 + 152 * q^51 + 56 * q^60 - 128 * q^64 + 208 * q^65 - 384 * q^71 - 416 * q^74 - 296 * q^79 + 280 * q^81 + 580 * q^85 + 376 * q^86 + 620 * q^95 + 176 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more