LMFDB - Embedded newform 14.5.b.a.13.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,5,Mod(13,14)] 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("14.13"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	14.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.44717948317$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.1308672.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 72x^{2} + 1278 $ x^4 + 72*x^2 + 1278
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.1
Root			$6.34371i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.5.b.a.13.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.82843 q^{2} -12.6874i q^{3} +8.00000 q^{4} -23.1980i q^{5} +35.8854i q^{6} +(6.45584 + 48.5729i) q^{7} -22.6274 q^{8} -79.9706 q^{9} +65.6139i q^{10} +191.823 q^{11} -101.499i q^{12} -48.5729i q^{13} +(-18.2599 - 137.385i) q^{14} -294.323 q^{15} +64.0000 q^{16} -181.977i q^{17} +226.191 q^{18} +599.915i q^{19} -185.584i q^{20} +(616.264 - 81.9080i) q^{21} -542.558 q^{22} -469.529 q^{23} +287.083i q^{24} +86.8519 q^{25} +137.385i q^{26} -13.0609i q^{27} +(51.6468 + 388.583i) q^{28} -338.881 q^{29} +832.471 q^{30} +267.556i q^{31} -181.019 q^{32} -2433.74i q^{33} +514.710i q^{34} +(1126.79 - 149.763i) q^{35} -639.765 q^{36} -668.530 q^{37} -1696.82i q^{38} -616.264 q^{39} +524.911i q^{40} +1323.85i q^{41} +(-1743.06 + 231.671i) q^{42} +1940.23 q^{43} +1534.59 q^{44} +1855.16i q^{45} +1328.03 q^{46} +2936.89i q^{47} -811.995i q^{48} +(-2317.64 + 627.158i) q^{49} -245.654 q^{50} -2308.82 q^{51} -388.583i q^{52} -1460.94 q^{53} +36.9418i q^{54} -4449.92i q^{55} +(-146.079 - 1099.08i) q^{56} +7611.38 q^{57} +958.501 q^{58} -1730.83i q^{59} -2354.58 q^{60} +246.343i q^{61} -756.763i q^{62} +(-516.277 - 3884.40i) q^{63} +512.000 q^{64} -1126.79 q^{65} +6883.67i q^{66} -1076.59 q^{67} -1455.82i q^{68} +5957.11i q^{69} +(-3187.05 + 423.593i) q^{70} -2276.39 q^{71} +1809.53 q^{72} -7106.94i q^{73} +1890.89 q^{74} -1101.93i q^{75} +4799.32i q^{76} +(1238.38 + 9317.41i) q^{77} +1743.06 q^{78} +7012.38 q^{79} -1484.67i q^{80} -6643.32 q^{81} -3744.40i q^{82} -1448.36i q^{83} +(4930.11 - 655.264i) q^{84} -4221.52 q^{85} -5487.81 q^{86} +4299.53i q^{87} -4340.47 q^{88} -2133.73i q^{89} -5247.18i q^{90} +(2359.32 - 313.579i) q^{91} -3756.23 q^{92} +3394.60 q^{93} -8306.77i q^{94} +13916.8 q^{95} +2296.67i q^{96} -5898.76i q^{97} +(6555.29 - 1773.87i) q^{98} -15340.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{4} - 76 q^{7} - 252 q^{9} + 360 q^{11} - 288 q^{14} + 384 q^{15} + 256 q^{16} + 192 q^{18} + 768 q^{21} - 1152 q^{22} - 792 q^{23} - 2300 q^{25} - 608 q^{28} + 1224 q^{29} + 4416 q^{30} + 4032 q^{35}+ \cdots - 29592 q^{99}+O(q^{100}) $ 4 * q + 32 * q^4 - 76 * q^7 - 252 * q^9 + 360 * q^11 - 288 * q^14 + 384 * q^15 + 256 * q^16 + 192 * q^18 + 768 * q^21 - 1152 * q^22 - 792 * q^23 - 2300 * q^25 - 608 * q^28 + 1224 * q^29 + 4416 * q^30 + 4032 * q^35 - 2016 * q^36 - 3896 * q^37 - 768 * q^39 - 4800 * q^42 + 3688 * q^43 + 2880 * q^44 + 3072 * q^46 - 1532 * q^49 - 7488 * q^50 - 11136 * q^51 + 5832 * q^53 - 2304 * q^56 + 12864 * q^57 + 7296 * q^58 + 3072 * q^60 + 3060 * q^63 + 2048 * q^64 - 4032 * q^65 - 1048 * q^67 - 1344 * q^70 - 21528 * q^71 + 1536 * q^72 - 3456 * q^74 + 3528 * q^77 + 4800 * q^78 + 12776 * q^79 - 29628 * q^81 + 6144 * q^84 + 16512 * q^85 - 11520 * q^86 - 9216 * q^88 + 5568 * q^91 - 6336 * q^92 + 38016 * q^93 + 36864 * q^95 + 21888 * q^98 - 29592 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−2.82843			−0.707107
$2$	−2.82843			−0.707107
$3$		−	12.6874i		−	1.40971i	−0.709350	−	0.704857i	$-0.751011\pi$
$3$		−	12.6874i		−	1.40971i	0.709350	−	0.704857i	$-0.248989\pi$
$4$	8.00000			0.500000
$5$		−	23.1980i		−	0.927921i	−0.885856	−	0.463960i	$-0.846428\pi$
$5$		−	23.1980i		−	0.927921i	0.885856	−	0.463960i	$-0.153572\pi$
$6$			35.8854i			0.996818i
$7$	6.45584	+	48.5729i	0.131752	+	0.991283i
$7$	6.45584	+	48.5729i	0.131752	+	0.991283i
$8$	−22.6274			−0.353553
$9$	−79.9706			−0.987291
$10$			65.6139i			0.656139i
$11$	191.823			1.58532			0.792659	−	0.609666i	$-0.208696\pi$
$11$	191.823			1.58532			0.792659	+	0.609666i	$0.208696\pi$
$12$		−	101.499i		−	0.704857i
$13$		−	48.5729i		−	0.287413i	−0.989620	−	0.143707i	$-0.954098\pi$
$13$		−	48.5729i		−	0.287413i	0.989620	−	0.143707i	$-0.0459022\pi$
$14$	−18.2599	−	137.385i	−0.0931627	−	0.700943i
$15$	−294.323			−1.30810
$16$	64.0000			0.250000
$17$		−	181.977i		−	0.629680i	−0.949145	−	0.314840i	$-0.898049\pi$
$17$		−	181.977i		−	0.629680i	0.949145	−	0.314840i	$-0.101951\pi$
$18$	226.191			0.698120
$19$			599.915i			1.66182i	0.556410	+	0.830908i	$0.312178\pi$
$19$			599.915i			1.66182i	−0.556410	+	0.830908i	$0.687822\pi$
$20$		−	185.584i		−	0.463960i
$21$	616.264	−	81.9080i	1.39742	−	0.185732i
$22$	−542.558			−1.12099
$23$	−469.529			−0.887578			−0.443789	−	0.896131i	$-0.646366\pi$
$23$	−469.529			−0.887578			−0.443789	+	0.896131i	$0.646366\pi$
$24$			287.083i			0.498409i
$25$	86.8519			0.138963
$26$			137.385i			0.203232i
$27$		−	13.0609i		−	0.0179162i
$28$	51.6468	+	388.583i	0.0658760	+	0.495641i
$29$	−338.881			−0.402951			−0.201475	−	0.979494i	$-0.564574\pi$
$29$	−338.881			−0.402951			−0.201475	+	0.979494i	$0.564574\pi$
$30$	832.471			0.924968
$31$			267.556i			0.278414i	0.990263	+	0.139207i	$0.0444554\pi$
$31$			267.556i			0.278414i	−0.990263	+	0.139207i	$0.955545\pi$
$32$	−181.019			−0.176777
$33$		−	2433.74i		−	2.23484i
$34$			514.710i			0.445251i
$35$	1126.79	−	149.763i	0.919832	−	0.122255i
$36$	−639.765			−0.493645
$37$	−668.530			−0.488334			−0.244167	−	0.969733i	$-0.578515\pi$
$37$	−668.530			−0.488334			−0.244167	+	0.969733i	$0.578515\pi$
$38$		−	1696.82i		−	1.17508i
$39$	−616.264			−0.405170
$40$			524.911i			0.328070i
$41$			1323.85i			0.787534i	0.919210	+	0.393767i	$0.128828\pi$
$41$			1323.85i			0.787534i	−0.919210	+	0.393767i	$0.871172\pi$
$42$	−1743.06	+	231.671i	−0.988128	+	0.131333i
$43$	1940.23			1.04934			0.524671	−	0.851305i	$-0.324188\pi$
$43$	1940.23			1.04934			0.524671	+	0.851305i	$0.324188\pi$
$44$	1534.59			0.792659
$45$			1855.16i			0.916128i
$46$	1328.03			0.627613
$47$			2936.89i			1.32951i	0.747062	+	0.664755i	$0.231464\pi$
$47$			2936.89i			1.32951i	−0.747062	+	0.664755i	$0.768536\pi$
$48$		−	811.995i		−	0.352428i
$49$	−2317.64	+	627.158i	−0.965283	+	0.261207i
$50$	−245.654			−0.0982618
$51$	−2308.82			−0.887668
$52$		−	388.583i		−	0.143707i
$53$	−1460.94			−0.520091			−0.260046	−	0.965596i	$-0.583738\pi$
$53$	−1460.94			−0.520091			−0.260046	+	0.965596i	$0.583738\pi$
$54$			36.9418i			0.0126687i
$55$		−	4449.92i		−	1.47105i
$56$	−146.079	−	1099.08i	−0.0465813	−	0.350471i
$57$	7611.38			2.34268
$58$	958.501			0.284929
$59$		−	1730.83i		−	0.497223i	−0.968603	−	0.248612i	$-0.920026\pi$
$59$		−	1730.83i		−	0.497223i	0.968603	−	0.248612i	$-0.0799743\pi$
$60$	−2354.58			−0.654051
$61$			246.343i			0.0662034i	0.999452	+	0.0331017i	$0.0105385\pi$
$61$			246.343i			0.0662034i	−0.999452	+	0.0331017i	$0.989461\pi$
$62$		−	756.763i		−	0.196869i
$63$	−516.277	−	3884.40i	−0.130077	−	0.978684i
$64$	512.000			0.125000
$65$	−1126.79			−0.266697
$66$			6883.67i			1.58027i
$67$	−1076.59			−0.239828			−0.119914	−	0.992784i	$-0.538262\pi$
$67$	−1076.59			−0.239828			−0.119914	+	0.992784i	$0.538262\pi$
$68$		−	1455.82i		−	0.314840i
$69$			5957.11i			1.25123i
$70$	−3187.05	+	423.593i	−0.650419	+	0.0864476i
$71$	−2276.39			−0.451574			−0.225787	−	0.974177i	$-0.572495\pi$
$71$	−2276.39			−0.451574			−0.225787	+	0.974177i	$0.572495\pi$
$72$	1809.53			0.349060
$73$		−	7106.94i		−	1.33363i	−0.745221	−	0.666817i	$-0.767656\pi$
$73$		−	7106.94i		−	1.33363i	0.745221	−	0.666817i	$-0.232344\pi$
$74$	1890.89			0.345305
$75$		−	1101.93i		−	0.195898i
$76$			4799.32i			0.830908i
$77$	1238.38	+	9317.41i	0.208869	+	1.57150i
$78$	1743.06			0.286499
$79$	7012.38			1.12360			0.561799	−	0.827274i	$-0.310109\pi$
$79$	7012.38			1.12360			0.561799	+	0.827274i	$0.310109\pi$
$80$		−	1484.67i		−	0.231980i
$81$	−6643.32			−1.01255
$82$		−	3744.40i		−	0.556871i
$83$		−	1448.36i		−	0.210243i	−0.994459	−	0.105121i	$-0.966477\pi$
$83$		−	1448.36i		−	0.210243i	0.994459	−	0.105121i	$-0.0335231\pi$
$84$	4930.11	−	655.264i	0.698712	−	0.0928662i
$85$	−4221.52			−0.584293
$86$	−5487.81			−0.741997
$87$			4299.53i			0.568045i
$88$	−4340.47			−0.560494
$89$		−	2133.73i		−	0.269376i	−0.990888	−	0.134688i	$-0.956997\pi$
$89$		−	2133.73i		−	0.269376i	0.990888	−	0.134688i	$-0.0430032\pi$
$90$		−	5247.18i		−	0.647800i
$91$	2359.32	−	313.579i	0.284908	−	0.0378673i
$92$	−3756.23			−0.443789
$93$	3394.60			0.392484
$94$		−	8306.77i		−	0.940105i
$95$	13916.8			1.54203
$96$			2296.67i			0.249204i
$97$		−	5898.76i		−	0.626928i	−0.949600	−	0.313464i	$-0.898511\pi$
$97$		−	5898.76i		−	0.626928i	0.949600	−	0.313464i	$-0.101489\pi$
$98$	6555.29	−	1773.87i	0.682558	−	0.184701i
$99$	−15340.2			−1.56517
$100$	694.816			0.0694816
$101$			9172.07i			0.899135i	0.893246	+	0.449567i	$0.148422\pi$
$101$			9172.07i			0.899135i	−0.893246	+	0.449567i	$0.851578\pi$
$102$	6530.34			0.627676
$103$			3906.46i			0.368222i	0.982905	+	0.184111i	$0.0589406\pi$
$103$			3906.46i			0.368222i	−0.982905	+	0.184111i	$0.941059\pi$
$104$			1099.08i			0.101616i
$105$	−1900.10	−	14296.1i	−0.172345	−	1.29670i
$106$	4132.15			0.367760
$107$	−12141.3			−1.06047			−0.530233	−	0.847852i	$-0.677896\pi$
$107$	−12141.3			−1.06047			−0.530233	+	0.847852i	$0.677896\pi$
$108$		−	104.487i		−	0.00895809i
$109$	6808.34			0.573044			0.286522	−	0.958074i	$-0.407501\pi$
$109$	6808.34			0.573044			0.286522	+	0.958074i	$0.407501\pi$
$110$			12586.3i			1.04019i
$111$			8481.92i			0.688411i
$112$	413.174	+	3108.66i	0.0329380	+	0.247821i
$113$	−4764.20			−0.373107			−0.186553	−	0.982445i	$-0.559732\pi$
$113$	−4764.20			−0.373107			−0.186553	+	0.982445i	$0.559732\pi$
$114$	−21528.2			−1.65653
$115$			10892.1i			0.823602i
$116$	−2711.05			−0.201475
$117$			3884.40i			0.283761i
$118$			4895.54i			0.351590i
$119$	8839.17	−	1174.82i	0.624191	−	0.0829615i
$120$	6659.77			0.462484
$121$	22155.2			1.51323
$122$		−	696.763i		−	0.0468129i
$123$	16796.2			1.11020
$124$			2140.45i			0.139207i
$125$		−	16513.6i		−	1.05687i
$126$	1460.25	+	10986.7i	0.0919787	+	0.692034i
$127$	−27968.9			−1.73408			−0.867038	−	0.498242i	$-0.833979\pi$
$127$	−27968.9			−1.73408			−0.867038	+	0.498242i	$0.833979\pi$
$128$	−1448.15			−0.0883883
$129$		−	24616.6i		−	1.47927i
$130$	3187.05			0.188583
$131$		−	24016.5i		−	1.39948i	−0.714397	−	0.699741i	$-0.753299\pi$
$131$		−	24016.5i		−	1.39948i	0.714397	−	0.699741i	$-0.246701\pi$
$132$		−	19469.9i		−	1.11742i
$133$	−29139.6	+	3872.96i	−1.64733	+	0.218947i
$134$	3045.05			0.169584
$135$	−302.987			−0.0166248
$136$			4117.68i			0.222625i
$137$	−4162.00			−0.221748			−0.110874	−	0.993834i	$-0.535365\pi$
$137$	−4162.00			−0.221748			−0.110874	+	0.993834i	$0.535365\pi$
$138$		−	16849.3i		−	0.884754i
$139$			26365.8i			1.36462i	0.731064	+	0.682309i	$0.239024\pi$
$139$			26365.8i			1.36462i	−0.731064	+	0.682309i	$0.760976\pi$
$140$	9014.35	−	1198.10i	0.459916	−	0.0611277i
$141$	37261.5			1.87423
$142$	6438.59			0.319311
$143$		−	9317.41i		−	0.455641i
$144$	−5118.12			−0.246823
$145$			7861.38i			0.373906i
$146$			20101.5i			0.943022i
$147$	7957.01	+	29404.9i	0.368227	+	1.36077i
$148$	−5348.24			−0.244167
$149$	−6576.57			−0.296229			−0.148114	−	0.988970i	$-0.547320\pi$
$149$	−6576.57			−0.296229			−0.148114	+	0.988970i	$0.547320\pi$
$150$			3116.72i			0.138521i
$151$	−22930.4			−1.00568			−0.502839	−	0.864380i	$-0.667711\pi$
$151$	−22930.4			−1.00568			−0.502839	+	0.864380i	$0.667711\pi$
$152$		−	13574.5i		−	0.587540i
$153$			14552.8i			0.621677i
$154$	−3502.67	−	26353.6i	−0.147692	−	1.11122i
$155$	6206.77			0.258346
$156$	−4930.11			−0.202585
$157$			37292.9i			1.51296i	0.654017	+	0.756480i	$0.273082\pi$
$157$			37292.9i			1.51296i	−0.654017	+	0.756480i	$0.726918\pi$
$158$	−19834.0			−0.794504
$159$			18535.5i			0.733180i
$160$			4199.29i			0.164035i
$161$	−3031.21	−	22806.4i	−0.116940	−	0.879841i
$162$	18790.2			0.715979
$163$	40854.0			1.53766			0.768828	−	0.639455i	$-0.220840\pi$
$163$	40854.0			1.53766			0.768828	+	0.639455i	$0.220840\pi$
$164$			10590.8i			0.393767i
$165$	−56458.0			−2.07376
$166$			4096.58i			0.148664i
$167$		−	34774.9i		−	1.24690i	−0.781862	−	0.623452i	$-0.785730\pi$
$167$		−	34774.9i		−	1.24690i	0.781862	−	0.623452i	$-0.214270\pi$
$168$	−13944.5	+	1853.37i	−0.494064	+	0.0656663i
$169$	26201.7			0.917394
$170$	11940.3			0.413158
$171$		−	47975.6i		−	1.64070i
$172$	15521.9			0.524671
$173$			31600.1i			1.05583i	0.849296	+	0.527917i	$0.177027\pi$
$173$			31600.1i			1.05583i	−0.849296	+	0.527917i	$0.822973\pi$
$174$		−	12160.9i		−	0.401668i
$175$	560.703	+	4218.65i	0.0183087	+	0.137752i
$176$	12276.7			0.396329
$177$	−21959.8			−0.700942
$178$			6035.09i			0.190478i
$179$	22750.7			0.710048			0.355024	−	0.934857i	$-0.384473\pi$
$179$	22750.7			0.710048			0.355024	+	0.934857i	$0.384473\pi$
$180$			14841.3i			0.458064i
$181$		−	55434.4i		−	1.69208i	−0.533116	−	0.846042i	$-0.678979\pi$
$181$		−	55434.4i		−	1.69208i	0.533116	−	0.846042i	$-0.321021\pi$
$182$	−6673.17	+	886.935i	−0.201460	+	0.0267762i
$183$	3125.45			0.0933278
$184$	10624.2			0.313806
$185$			15508.6i			0.453136i
$186$	−9601.37			−0.277528
$187$		−	34907.5i		−	0.998242i
$188$			23495.1i			0.664755i
$189$	634.405	−	84.3191i	0.0177600	−	0.00236049i
$190$	−39362.8			−1.09038
$191$	−50817.6			−1.39299			−0.696494	−	0.717562i	$-0.745258\pi$
$191$	−50817.6			−1.39299			−0.696494	+	0.717562i	$0.745258\pi$
$192$		−	6495.96i		−	0.176214i
$193$	−1248.34			−0.0335134			−0.0167567	−	0.999860i	$-0.505334\pi$
$193$	−1248.34			−0.0335134			−0.0167567	+	0.999860i	$0.505334\pi$
$194$			16684.2i			0.443305i
$195$			14296.1i			0.375966i
$196$	−18541.2	+	5017.26i	−0.482641	+	0.130603i
$197$	64454.6			1.66082			0.830408	−	0.557155i	$-0.188107\pi$
$197$	64454.6			1.66082			0.830408	+	0.557155i	$0.188107\pi$
$198$	43388.7			1.10674
$199$		−	2352.60i		−	0.0594076i	−0.999559	−	0.0297038i	$-0.990544\pi$
$199$		−	2352.60i		−	0.0594076i	0.999559	−	0.0297038i	$-0.00945641\pi$
$200$	−1965.24			−0.0491309
$201$			13659.1i			0.338088i
$202$		−	25942.5i		−	0.635784i
$203$	−2187.77	−	16460.4i	−0.0530895	−	0.399438i
$204$	−18470.6			−0.443834
$205$	30710.6			0.730769
$206$		−	11049.2i		−	0.260372i
$207$	37548.5			0.876298
$208$		−	3108.66i		−	0.0718533i
$209$			115078.i			2.63450i
$210$	5374.30	+	40435.5i	0.121866	+	0.916905i
$211$	−65056.4			−1.46125			−0.730626	−	0.682778i	$-0.760772\pi$
$211$	−65056.4			−1.46125			−0.730626	+	0.682778i	$0.760772\pi$
$212$	−11687.5			−0.260046
$213$			28881.5i			0.636590i
$214$	34340.7			0.749863
$215$		−	45009.6i		−	0.973706i
$216$			295.534i			0.00633433i
$217$	−12996.0	+	1727.30i	−0.275987	+	0.0366816i
$218$	−19256.9			−0.405203
$219$	−90168.7			−1.88004
$220$		−	35599.4i		−	0.735524i
$221$	−8839.17			−0.180978
$222$		−	23990.5i		−	0.486780i
$223$			30412.4i			0.611563i	0.952102	+	0.305781i	$0.0989177\pi$
$223$			30412.4i			0.611563i	−0.952102	+	0.305781i	$0.901082\pi$
$224$	−1168.63	−	8792.63i	−0.0232907	−	0.175236i
$225$	−6945.60			−0.137197
$226$	13475.2			0.263826
$227$			52125.5i			1.01158i	0.862658	+	0.505788i	$0.168798\pi$
$227$			52125.5i			1.01158i	−0.862658	+	0.505788i	$0.831202\pi$
$228$	60891.0			1.17134
$229$		−	81280.2i		−	1.54994i	−0.632000	−	0.774968i	$-0.717766\pi$
$229$		−	81280.2i		−	1.54994i	0.632000	−	0.774968i	$-0.282234\pi$
$230$		−	30807.6i		−	0.582375i
$231$	118214.	−	15711.9i	2.21536	−	0.294445i
$232$	7668.01			0.142465
$233$	−41718.9			−0.768459			−0.384229	−	0.923238i	$-0.625533\pi$
$233$	−41718.9			−0.768459			−0.384229	+	0.923238i	$0.625533\pi$
$234$		−	10986.7i		−	0.200649i
$235$	68129.9			1.23368
$236$		−	13846.7i		−	0.248612i
$237$		−	88968.9i		−	1.58395i
$238$	−25000.9	+	3322.89i	−0.441370	+	0.0586627i
$239$	−3936.55			−0.0689160			−0.0344580	−	0.999406i	$-0.510970\pi$
$239$	−3936.55			−0.0689160			−0.0344580	+	0.999406i	$0.510970\pi$
$240$	−18836.7			−0.327025
$241$		−	70511.5i		−	1.21402i	−0.794694	−	0.607010i	$-0.792369\pi$
$241$		−	70511.5i		−	1.21402i	0.794694	−	0.607010i	$-0.207631\pi$
$242$	−62664.4			−1.07002
$243$			83228.7i			1.40949i
$244$			1970.74i			0.0331017i
$245$	14548.8	+	53764.8i	0.242379	+	0.895706i
$246$	−47506.8			−0.785028
$247$	29139.6			0.477628
$248$		−	6054.11i		−	0.0984343i
$249$	−18376.0			−0.296382
$250$			46707.4i			0.747318i
$251$		−	72042.3i		−	1.14351i	−0.820424	−	0.571755i	$-0.806263\pi$
$251$		−	72042.3i		−	1.14351i	0.820424	−	0.571755i	$-0.193737\pi$
$252$	−4130.22	−	31075.2i	−0.0650387	−	0.489342i
$253$	−90066.6			−1.40709
$254$	79108.1			1.22618
$255$			53560.1i			0.823685i
$256$	4096.00			0.0625000
$257$			65615.5i			0.993436i	0.867912	+	0.496718i	$0.165462\pi$
$257$			65615.5i			0.993436i	−0.867912	+	0.496718i	$0.834538\pi$
$258$			69626.1i			1.04600i
$259$	−4315.92	−	32472.4i	−0.0643390	−	0.484078i
$260$	−9014.35			−0.133348
$261$	27100.5			0.397829
$262$			67929.0i			0.989583i
$263$	−38706.1			−0.559588			−0.279794	−	0.960060i	$-0.590266\pi$
$263$	−38706.1			−0.559588			−0.279794	+	0.960060i	$0.590266\pi$
$264$			55069.3i			0.790136i
$265$			33890.8i			0.482604i
$266$	82419.2	−	10954.4i	1.16484	−	0.154819i
$267$	−27071.5			−0.379743
$268$	−8612.70			−0.119914
$269$		−	87226.9i		−	1.20544i	−0.797952	−	0.602721i	$-0.794083\pi$
$269$		−	87226.9i		−	1.20544i	0.797952	−	0.602721i	$-0.205917\pi$
$270$	856.977			0.0117555
$271$			105362.i			1.43465i	0.696739	+	0.717324i	$0.254633\pi$
$271$			105362.i			1.43465i	−0.696739	+	0.717324i	$0.745367\pi$
$272$		−	11646.6i		−	0.157420i
$273$	−3978.50	−	29933.7i	−0.0533820	−	0.401638i
$274$	11771.9			0.156800
$275$	16660.2			0.220301
$276$			47656.9i			0.625615i
$277$	36178.9			0.471515			0.235758	−	0.971812i	$-0.424243\pi$
$277$	36178.9			0.471515			0.235758	+	0.971812i	$0.424243\pi$
$278$		−	74573.7i		−	0.964931i
$279$		−	21396.6i		−	0.274876i
$280$	−25496.4	+	3388.75i	−0.325210	+	0.0432238i
$281$	99142.2			1.25558			0.627792	−	0.778381i	$-0.283959\pi$
$281$	99142.2			1.25558			0.627792	+	0.778381i	$0.283959\pi$
$282$	−105391.			−1.32528
$283$		−	4153.27i		−	0.0518581i	−0.999664	−	0.0259291i	$-0.991746\pi$
$283$		−	4153.27i		−	0.0518581i	0.999664	−	0.0259291i	$-0.00825441\pi$
$284$	−18211.1			−0.225787
$285$		−	176569.i		−	2.17382i
$286$			26353.6i			0.322187i
$287$	−64302.9	+	8546.54i	−0.780669	+	0.103759i
$288$	14476.2			0.174530
$289$	50405.2			0.603503
$290$		−	22235.3i		−	0.264392i
$291$	−74840.1			−0.883788
$292$		−	56855.5i		−	0.666817i
$293$		−	20239.4i		−	0.235756i	−0.993028	−	0.117878i	$-0.962391\pi$
$293$		−	20239.4i		−	0.235756i	0.993028	−	0.117878i	$-0.0376092\pi$
$294$	−22505.8	−	83169.7i	−0.260376	−	0.962211i
$295$	−40151.9			−0.461384
$296$	15127.1			0.172652
$297$		−	2505.39i		−	0.0284028i
$298$	18601.3			0.209465
$299$			22806.4i			0.255102i
$300$		−	8815.42i		−	0.0979491i
$301$	12525.8	+	94242.7i	0.138253	+	1.04019i
$302$	64857.1			0.711121
$303$	116370.			1.26752
$304$			38394.6i			0.415454i
$305$	5714.66			0.0614315
$306$		−	41161.7i		−	0.439592i
$307$			63269.8i			0.671305i	0.941986	+	0.335652i	$0.108957\pi$
$307$			63269.8i			0.671305i	−0.941986	+	0.335652i	$0.891043\pi$
$308$	9907.05	+	74539.3i	0.104434	+	0.785749i
$309$	49563.0			0.519087
$310$	−17555.4			−0.182679
$311$		−	14375.4i		−	0.148627i	−0.997235	−	0.0743137i	$-0.976323\pi$
$311$		−	14375.4i		−	0.148627i	0.997235	−	0.0743137i	$-0.0236766\pi$
$312$	13944.5			0.143249
$313$			36763.0i			0.375252i	0.982241	+	0.187626i	$0.0600792\pi$
$313$			36763.0i			0.375252i	−0.982241	+	0.187626i	$0.939921\pi$
$314$		−	105480.i		−	1.06982i
$315$	−90110.3	+	11976.6i	−0.908142	+	0.120702i
$316$	56099.0			0.561799
$317$	−125556.			−1.24945			−0.624726	−	0.780844i	$-0.714789\pi$
$317$	−125556.			−1.24945			−0.624726	+	0.780844i	$0.714789\pi$
$318$		−	52426.4i		−	0.518436i
$319$	−65005.4			−0.638804
$320$		−	11877.4i		−	0.115990i
$321$			154041.i			1.49495i
$322$	8573.55	+	64506.1i	0.0826892	+	0.622142i
$323$	109171.			1.04641
$324$	−53146.6			−0.506274
$325$		−	4218.65i		−	0.0399399i
$326$	−115553.			−1.08729
$327$		−	86380.2i		−	0.807828i
$328$		−	29955.2i		−	0.278435i
$329$	−142653.	+	18960.1i	−1.31792	+	0.175165i
$330$	159687.			1.46637
$331$	5376.54			0.0490735			0.0245367	−	0.999699i	$-0.492189\pi$
$331$	5376.54			0.0490735			0.0245367	+	0.999699i	$0.492189\pi$
$332$		−	11586.9i		−	0.105121i
$333$	53462.7			0.482128
$334$			98358.3i			0.881694i
$335$			24974.7i			0.222541i
$336$	39440.9	−	5242.11i	0.349356	−	0.0464331i
$337$	2202.27			0.0193914			0.00969572	−	0.999953i	$-0.496914\pi$
$337$	2202.27			0.0193914			0.00969572	+	0.999953i	$0.496914\pi$
$338$	−74109.5			−0.648695
$339$			60445.4i			0.525974i
$340$	−33772.1			−0.292146
$341$			51323.5i			0.441375i
$342$			135695.i			1.16015i
$343$	−45425.2	−	108526.i	−0.386108	−	0.922454i
$344$	−43902.5			−0.370998
$345$	138193.			1.16104
$346$		−	89378.5i		−	0.746587i
$347$	222201.			1.84538			0.922691	−	0.385541i	$-0.125985\pi$
$347$	222201.			1.84538			0.922691	+	0.385541i	$0.125985\pi$
$348$			34396.2i			0.284022i
$349$		−	102679.i		−	0.843006i	−0.906827	−	0.421503i	$-0.861503\pi$
$349$		−	102679.i		−	0.843006i	0.906827	−	0.421503i	$-0.138497\pi$
$350$	−1585.91	−	11932.1i	−0.0129462	−	0.0974052i
$351$	−634.405			−0.00514935
$352$	−34723.7			−0.280247
$353$			62595.6i			0.502336i	0.967943	+	0.251168i	$0.0808147\pi$
$353$			62595.6i			0.502336i	−0.967943	+	0.251168i	$0.919185\pi$
$354$	62111.8			0.495641
$355$			52807.7i			0.419025i
$356$		−	17069.8i		−	0.134688i
$357$	−14905.4	−	112146.i	−0.116952	−	0.879930i
$358$	−64348.6			−0.502080
$359$	95505.9			0.741040			0.370520	−	0.928825i	$-0.379180\pi$
$359$	95505.9			0.741040			0.370520	+	0.928825i	$0.379180\pi$
$360$		−	41977.4i		−	0.323900i
$361$	−229577.			−1.76163
$362$			156792.i			1.19648i
$363$		−	281092.i		−	2.13322i
$364$	18874.6	−	2508.63i	0.142454	−	0.0189336i
$365$	−164867.			−1.23751
$366$	−8840.12			−0.0659927
$367$		−	82330.9i		−	0.611267i	−0.952149	−	0.305633i	$-0.901132\pi$
$367$		−	82330.9i		−	0.611267i	0.952149	−	0.305633i	$-0.0988682\pi$
$368$	−30049.9			−0.221895
$369$		−	105869.i		−	0.777525i
$370$		−	43864.9i		−	0.320415i
$371$	−9431.58	−	70961.9i	−0.0685230	−	0.515558i
$372$	27156.8			0.196242
$373$	130223.			0.935991			0.467995	−	0.883731i	$-0.344976\pi$
$373$	130223.			0.935991			0.467995	+	0.883731i	$0.344976\pi$
$374$			98733.4i			0.705864i
$375$	−209514.			−1.48988
$376$		−	66454.2i		−	0.470053i
$377$			16460.4i			0.115813i
$378$	−1794.37	+	238.491i	−0.0125582	+	0.00166912i
$379$	192349.			1.33909			0.669546	−	0.742770i	$-0.266489\pi$
$379$	192349.			1.33909			0.669546	+	0.742770i	$0.266489\pi$
$380$	111335.			0.771016
$381$			354853.i			2.44455i
$382$	143734.			0.984992
$383$		−	101933.i		−	0.694891i	−0.937700	−	0.347446i	$-0.887049\pi$
$383$		−	101933.i		−	0.694891i	0.937700	−	0.347446i	$-0.112951\pi$
$384$			18373.3i			0.124602i
$385$	216145.	−	28728.0i	1.45823	−	0.193813i
$386$	3530.84			0.0236975
$387$	−155162.			−1.03601
$388$		−	47190.1i		−	0.313464i
$389$	191074.			1.26271			0.631353	−	0.775495i	$-0.282500\pi$
$389$	191074.			1.26271			0.631353	+	0.775495i	$0.282500\pi$
$390$		−	40435.5i		−	0.265848i
$391$			85443.7i			0.558890i
$392$	52442.3	−	14191.0i	0.341279	−	0.0923506i
$393$	−304708.			−1.97287
$394$	−182305.			−1.17437
$395$		−	162673.i		−	1.04261i
$396$	−122722.			−0.782585
$397$			201143.i			1.27622i	0.769947	+	0.638108i	$0.220283\pi$
$397$			201143.i			1.27622i	−0.769947	+	0.638108i	$0.779717\pi$
$398$			6654.16i			0.0420076i
$399$	49137.9	+	369706.i	0.308653	+	2.32226i
$400$	5558.52			0.0347408
$401$	−39978.4			−0.248621			−0.124310	−	0.992243i	$-0.539672\pi$
$401$	−39978.4			−0.248621			−0.124310	+	0.992243i	$0.539672\pi$
$402$		−	38633.8i		−	0.239065i
$403$	12996.0			0.0800200
$404$			73376.6i			0.449567i
$405$			154112.i			0.939564i
$406$	6187.93	+	46557.1i	0.0375399	+	0.282445i
$407$	−128240.			−0.774165
$408$	52242.7			0.313838
$409$		−	80655.7i		−	0.482157i	−0.970506	−	0.241078i	$-0.922499\pi$
$409$		−	80655.7i		−	0.482157i	0.970506	−	0.241078i	$-0.0775011\pi$
$410$	−86862.6			−0.516732
$411$			52805.0i			0.312602i
$412$			31251.7i			0.184111i
$413$	84071.6	−	11174.0i	0.492889	−	0.0655101i
$414$	−106203.			−0.619636
$415$	−33599.1			−0.195088
$416$			8792.63i			0.0508080i
$417$	334514.			1.92372
$418$		−	325489.i		−	1.86288i
$419$			252034.i			1.43559i	0.696254	+	0.717795i	$0.254849\pi$
$419$			252034.i			1.43559i	−0.696254	+	0.717795i	$0.745151\pi$
$420$	−15200.8	−	114369.i	−0.0861725	−	0.648349i
$421$	−84439.3			−0.476410			−0.238205	−	0.971215i	$-0.576559\pi$
$421$	−84439.3			−0.476410			−0.238205	+	0.971215i	$0.576559\pi$
$422$	184007.			1.03326
$423$		−	234864.i		−	1.31261i
$424$	33057.2			0.183880
$425$		−	15805.1i		−	0.0875023i
$426$		−	81689.1i		−	0.450137i
$427$	−11965.6	+	1590.35i	−0.0656263	+	0.00872242i
$428$	−97130.2			−0.530233
$429$	−118214.			−0.642323
$430$			127306.i			0.688514i
$431$	−127512.			−0.686431			−0.343215	−	0.939257i	$-0.611516\pi$
$431$	−127512.			−0.686431			−0.343215	+	0.939257i	$0.611516\pi$
$432$		−	835.898i		−	0.00447905i
$433$		−	233539.i		−	1.24562i	−0.782375	−	0.622808i	$-0.785992\pi$
$433$		−	233539.i		−	1.24562i	0.782375	−	0.622808i	$-0.214008\pi$
$434$	36758.2	−	4885.55i	0.195153	−	0.0259378i
$435$	99740.6			0.527100
$436$	54466.7			0.286522
$437$		−	281678.i		−	1.47499i
$438$	255036.			1.32939
$439$		−	304238.i		−	1.57864i	−0.613980	−	0.789322i	$-0.710432\pi$
$439$		−	304238.i		−	1.57864i	0.613980	−	0.789322i	$-0.289568\pi$
$440$			100690.i			0.520094i
$441$	185343.	−	50154.1i	0.953015	−	0.257887i
$442$	25000.9			0.127971
$443$	−87061.0			−0.443625			−0.221813	−	0.975089i	$-0.571197\pi$
$443$	−87061.0			−0.443625			−0.221813	+	0.975089i	$0.571197\pi$
$444$			67855.3i			0.344206i
$445$	−49498.2			−0.249960
$446$		−	86019.3i		−	0.432440i
$447$			83439.7i			0.417597i
$448$	3305.39	+	24869.3i	0.0164690	+	0.123910i
$449$	−91141.4			−0.452088			−0.226044	−	0.974117i	$-0.572579\pi$
$449$	−91141.4			−0.452088			−0.226044	+	0.974117i	$0.572579\pi$
$450$	19645.1			0.0970129
$451$			253944.i			1.24849i
$452$	−38113.6			−0.186553
$453$			290928.i			1.41772i
$454$		−	147433.i		−	0.715292i
$455$	−7274.41	−	54731.6i	−0.0351378	−	0.264372i
$456$	−172226.			−0.828263
$457$	−411928.			−1.97237			−0.986187	−	0.165634i	$-0.947033\pi$
$457$	−411928.			−1.97237			−0.986187	+	0.165634i	$0.947033\pi$
$458$			229895.i			1.09597i
$459$	−2376.79			−0.0112815
$460$			87137.1i			0.411801i
$461$		−	157397.i		−	0.740617i	−0.928909	−	0.370309i	$-0.879252\pi$
$461$		−	157397.i		−	0.740617i	0.928909	−	0.370309i	$-0.120748\pi$
$462$	−334359.	+	44439.9i	−1.56650	+	0.208204i
$463$	245557.			1.14549			0.572745	−	0.819734i	$-0.305879\pi$
$463$	245557.			1.14549			0.572745	+	0.819734i	$0.305879\pi$
$464$	−21688.4			−0.100738
$465$		−	78747.9i		−	0.364194i
$466$	117999.			0.543383
$467$		−	33069.2i		−	0.151632i	−0.997122	−	0.0758158i	$-0.975844\pi$
$467$		−	33069.2i		−	0.151632i	0.997122	−	0.0758158i	$-0.0241561\pi$
$468$			31075.2i			0.141880i
$469$	−6950.28	−	52292.9i	−0.0315978	−	0.237737i
$470$	−192701.			−0.872343
$471$	473151.			2.13284
$472$			39164.3i			0.175795i
$473$	372182.			1.66354
$474$			251642.i			1.12002i
$475$			52103.8i			0.230931i
$476$	70713.3	−	9398.55i	0.312095	−	0.0414808i
$477$	116832.			0.513482
$478$	11134.2			0.0487309
$479$			384277.i			1.67484i	0.546559	+	0.837421i	$0.315937\pi$
$479$			384277.i			1.67484i	−0.546559	+	0.837421i	$0.684063\pi$
$480$	53278.1			0.231242
$481$			32472.4i			0.140354i
$482$			199437.i			0.858442i
$483$	−289354.	+	38458.2i	−1.24032	+	0.164852i
$484$	177242.			0.756615
$485$	−136840.			−0.581739
$486$		−	235406.i		−	0.996657i
$487$	−173526.			−0.731657			−0.365829	−	0.930682i	$-0.619214\pi$
$487$	−173526.			−0.731657			−0.365829	+	0.930682i	$0.619214\pi$
$488$		−	5574.10i		−	0.0234064i
$489$		−	518332.i		−	2.16765i
$490$	−41150.3	−	152070.i	−0.171388	−	0.633360i
$491$	−20006.3			−0.0829858			−0.0414929	−	0.999139i	$-0.513211\pi$
$491$	−20006.3			−0.0829858			−0.0414929	+	0.999139i	$0.513211\pi$
$492$	134369.			0.555099
$493$			61668.8i			0.253730i
$494$	−82419.2			−0.337734
$495$			355863.i			1.45235i
$496$			17123.6i			0.0696036i
$497$	−14696.0	−	110571.i	−0.0594958	−	0.447638i
$498$	51975.1			0.209574
$499$	−428368.			−1.72035			−0.860174	−	0.510000i	$-0.829645\pi$
$499$	−428368.			−1.72035			−0.860174	+	0.510000i	$0.829645\pi$
$500$		−	132108.i		−	0.528434i
$501$	−441204.			−1.75778
$502$			203766.i			0.808584i
$503$			36793.4i			0.145423i	0.997353	+	0.0727116i	$0.0231653\pi$
$503$			36793.4i			0.145423i	−0.997353	+	0.0727116i	$0.976835\pi$
$504$	11682.0	+	87893.9i	0.0459893	+	0.346017i
$505$	212774.			0.834326
$506$	254747.			0.994965
$507$		−	332432.i		−	1.29326i
$508$	−223751.			−0.867038
$509$		−	137334.i		−	0.530080i	−0.964237	−	0.265040i	$-0.914615\pi$
$509$		−	137334.i		−	0.530080i	0.964237	−	0.265040i	$-0.0853852\pi$
$510$		−	151491.i		−	0.582434i
$511$	345204.	−	45881.3i	1.32201	−	0.175709i
$512$	−11585.2			−0.0441942
$513$	7835.43			0.0297734
$514$		−	185589.i		−	0.702466i
$515$	90622.2			0.341681
$516$		−	196932.i		−	0.739636i
$517$			563363.i			2.10769i
$518$	12207.3	+	91845.8i	0.0454945	+	0.342294i
$519$	400923.			1.48842
$520$	25496.4			0.0942916
$521$			102775.i			0.378629i	0.981916	+	0.189315i	$0.0606266\pi$
$521$			102775.i			0.378629i	−0.981916	+	0.189315i	$0.939373\pi$
$522$	−76651.9			−0.281308
$523$		−	314194.i		−	1.14867i	−0.818621	−	0.574334i	$-0.805261\pi$
$523$		−	314194.i		−	1.14867i	0.818621	−	0.574334i	$-0.194739\pi$
$524$		−	192132.i		−	0.699741i
$525$	53523.7	−	7113.87i	0.194190	−	0.0258100i
$526$	109478.			0.395689
$527$	48689.2			0.175312
$528$		−	155760.i		−	0.558711i
$529$	−59383.5			−0.212204
$530$		−	95857.8i		−	0.341252i
$531$			138416.i			0.490904i
$532$	−233117.	+	30983.7i	−0.823664	+	0.109474i
$533$	64302.9			0.226348
$534$	76569.7			0.268519
$535$			281654.i			0.984029i
$536$	24360.4			0.0847919
$537$		−	288647.i		−	1.00096i
$538$			246715.i			0.852376i
$539$	−444578.	+	120303.i	−1.53028	+	0.414096i
$540$	−2423.90			−0.00831240
$541$	298384.			1.01948			0.509742	−	0.860327i	$-0.329741\pi$
$541$	298384.			1.01948			0.509742	+	0.860327i	$0.329741\pi$
$542$		−	298009.i		−	1.01445i
$543$	−703319.			−2.38535
$544$			32941.4i			0.111313i
$545$		−	157940.i		−	0.531740i
$546$	11252.9	+	84665.3i	0.0377468	+	0.284001i
$547$	361462.			1.20806			0.604029	−	0.796963i	$-0.293561\pi$
$547$	361462.			1.20806			0.604029	+	0.796963i	$0.293561\pi$
$548$	−33296.0			−0.110874
$549$		−	19700.2i		−	0.0653620i
$550$	−47122.3			−0.155776
$551$		−	203300.i		−	0.669629i
$552$		−	134794.i		−	0.442377i
$553$	45270.8	+	340611.i	0.148036	+	1.11380i
$554$	−102329.			−0.333412
$555$	196764.			0.638791
$556$			210926.i			0.682309i
$557$	112424.			0.362367			0.181183	−	0.983449i	$-0.442007\pi$
$557$	112424.			0.362367			0.181183	+	0.983449i	$0.442007\pi$
$558$			60518.8i			0.194367i
$559$		−	94242.7i		−	0.301595i
$560$	72114.8	−	9584.82i	0.229958	−	0.0305638i
$561$	−442886.			−1.40724
$562$	−280416.			−0.887832
$563$			441530.i			1.39298i	0.717569	+	0.696488i	$0.245255\pi$
$563$			441530.i			1.39298i	−0.717569	+	0.696488i	$0.754745\pi$
$564$	298092.			0.937113
$565$			110520.i			0.346214i
$566$			11747.2i			0.0366692i
$567$	−42888.3	−	322685.i	−0.133405	−	1.00372i
$568$	51508.8			0.159656
$569$	397273.			1.22706			0.613529	−	0.789673i	$-0.289750\pi$
$569$	397273.			1.22706			0.613529	+	0.789673i	$0.289750\pi$
$570$			499412.i			1.53713i
$571$	−67235.8			−0.206219			−0.103109	−	0.994670i	$-0.532879\pi$
$571$	−67235.8			−0.206219			−0.103109	+	0.994670i	$0.532879\pi$
$572$		−	74539.3i		−	0.227821i
$573$			644744.i			1.96371i
$574$	181876.	−	24173.3i	0.552016	−	0.0733688i
$575$	−40779.5			−0.123341
$576$	−40944.9			−0.123411
$577$		−	64756.1i		−	0.194504i	−0.995260	−	0.0972521i	$-0.968995\pi$
$577$		−	64756.1i		−	0.194504i	0.995260	−	0.0972521i	$-0.0310053\pi$
$578$	−142567.			−0.426741
$579$			15838.2i			0.0472443i
$580$			62891.0i			0.186953i
$581$	70351.0	−	9350.39i	0.208410	−	0.0276999i
$582$	211680.			0.624933
$583$	−280242.			−0.824510
$584$			160812.i			0.471511i
$585$	90110.3			0.263307
$586$			57245.8i			0.166705i
$587$		−	338967.i		−	0.983741i	−0.870668	−	0.491870i	$-0.836313\pi$
$587$		−	338967.i		−	0.983741i	0.870668	−	0.491870i	$-0.163687\pi$
$588$	63656.1	+	235239.i	0.184113	+	0.680386i
$589$	−160511.			−0.462673
$590$	113567.			0.326248
$591$		−	817763.i		−	2.34128i
$592$	−42785.9			−0.122084
$593$			255668.i			0.727054i	0.931584	+	0.363527i	$0.118428\pi$
$593$			255668.i			0.727054i	−0.931584	+	0.363527i	$0.881572\pi$
$594$			7086.30i			0.0200838i
$595$	−27253.5	−	205051.i	−0.0769817	−	0.579200i
$596$	−52612.6			−0.148114
$597$	−29848.4			−0.0837477
$598$		−	64506.1i		−	0.180384i
$599$	129521.			0.360982			0.180491	−	0.983577i	$-0.442231\pi$
$599$	129521.			0.360982			0.180491	+	0.983577i	$0.442231\pi$
$600$			24933.8i			0.0692604i
$601$		−	377277.i		−	1.04451i	−0.852790	−	0.522254i	$-0.825091\pi$
$601$		−	377277.i		−	1.04451i	0.852790	−	0.522254i	$-0.174909\pi$
$602$	−35428.4	−	266559.i	−0.0977595	−	0.735529i
$603$	86095.3			0.236780
$604$	−183444.			−0.502839
$605$		−	513957.i		−	1.40416i
$606$	−329144.			−0.896274
$607$			421091.i			1.14287i	0.820646	+	0.571437i	$0.193614\pi$
$607$			421091.i			1.14287i	−0.820646	+	0.571437i	$0.806386\pi$
$608$		−	108596.i		−	0.293770i
$609$	−208840.	+	27757.1i	−0.563093	+	0.0748410i
$610$	−16163.5			−0.0434386
$611$	142653.			0.382119
$612$			116423.i			0.310839i
$613$	412173.			1.09688			0.548440	−	0.836190i	$-0.315222\pi$
$613$	412173.			1.09688			0.548440	+	0.836190i	$0.315222\pi$
$614$		−	178954.i		−	0.474684i
$615$		−	389638.i		−	1.03018i
$616$	−28021.4	−	210829.i	−0.0738462	−	0.555608i
$617$	−262676.			−0.690002			−0.345001	−	0.938602i	$-0.612121\pi$
$617$	−262676.			−0.690002			−0.345001	+	0.938602i	$0.612121\pi$
$618$	−140185.			−0.367050
$619$		−	373975.i		−	0.976026i	−0.872836	−	0.488013i	$-0.837722\pi$
$619$		−	373975.i		−	0.976026i	0.872836	−	0.488013i	$-0.162278\pi$
$620$	49654.2			0.129173
$621$			6132.47i			0.0159020i
$622$			40659.7i			0.105095i
$623$	103641.	−	13775.0i	0.267028	−	0.0354908i
$624$	−39440.9			−0.101293
$625$	−328799.			−0.841726
$626$		−	103982.i		−	0.265343i
$627$	1.46004e6			3.71389
$628$			298344.i			0.756480i
$629$			121657.i			0.307494i
$630$	254871.	−	33875.0i	0.642153	−	0.0853489i
$631$	−408746.			−1.02659			−0.513293	−	0.858214i	$-0.671574\pi$
$631$	−408746.			−1.02659			−0.513293	+	0.858214i	$0.671574\pi$
$632$	−158672.			−0.397252
$633$			825397.i			2.05995i
$634$	355126.			0.883495
$635$			648824.i			1.60909i
$636$			148284.i			0.366590i
$637$	30462.8	+	112575.i	0.0750743	+	0.277435i
$638$	183863.			0.451703
$639$	182044.			0.445835
$640$			33594.3i			0.0820174i
$641$	−528074.			−1.28522			−0.642612	−	0.766192i	$-0.722149\pi$
$641$	−528074.			−1.28522			−0.642612	+	0.766192i	$0.722149\pi$
$642$		−	435695.i		−	1.05709i
$643$		−	323445.i		−	0.782310i	−0.920325	−	0.391155i	$-0.872076\pi$
$643$		−	323445.i		−	0.782310i	0.920325	−	0.391155i	$-0.127924\pi$
$644$	−24249.6	−	182451.i	−0.0584701	−	0.439921i
$645$	−571055.			−1.37265
$646$	−308782.			−0.739925
$647$			592372.i			1.41510i	0.706665	+	0.707548i	$0.250199\pi$
$647$			592372.i			1.41510i	−0.706665	+	0.707548i	$0.749801\pi$
$648$	150321.			0.357990
$649$		−	332015.i		−	0.788257i
$650$			11932.1i			0.0282417i
$651$	21915.0	+	164885.i	0.0517106	+	0.389063i
$652$	326832.			0.768828
$653$	−329810.			−0.773459			−0.386730	−	0.922193i	$-0.626395\pi$
$653$	−329810.			−0.773459			−0.386730	+	0.922193i	$0.626395\pi$
$654$			244320.i			0.571221i
$655$	−557135.			−1.29861
$656$			84726.1i			0.196884i
$657$			568346.i			1.31669i
$658$	403483.	−	53627.2i	0.931910	−	0.123861i
$659$	−526737.			−1.21290			−0.606448	−	0.795123i	$-0.707406\pi$
$659$	−526737.			−1.21290			−0.606448	+	0.795123i	$0.707406\pi$
$660$	−451664.			−1.03688
$661$		−	144047.i		−	0.329686i	−0.986320	−	0.164843i	$-0.947288\pi$
$661$		−	144047.i		−	0.329686i	0.986320	−	0.164843i	$-0.0527117\pi$
$662$	−15207.2			−0.0347002
$663$			112146.i			0.255128i
$664$			32772.7i			0.0743320i
$665$	89845.0	+	675981.i	0.203166	+	1.52859i
$666$	−151215.			−0.340916
$667$	159115.			0.357650
$668$		−	278199.i		−	0.623452i
$669$	385855.			0.862128
$670$		−	70639.1i		−	0.157360i
$671$			47254.3i			0.104953i
$672$	−111556.	+	14826.9i	−0.247032	+	0.0328332i
$673$	620117.			1.36913			0.684563	−	0.728953i	$-0.259993\pi$
$673$	620117.			1.36913			0.684563	+	0.728953i	$0.259993\pi$
$674$	−6228.95			−0.0137118
$675$		−	1134.36i		−	0.00248969i
$676$	209613.			0.458697
$677$		−	626172.i		−	1.36621i	−0.730322	−	0.683103i	$-0.760630\pi$
$677$		−	626172.i		−	1.36621i	0.730322	−	0.683103i	$-0.239370\pi$
$678$		−	170965.i		−	0.371920i
$679$	286520.	−	38081.5i	0.621463	−	0.0825989i
$680$	95522.0			0.206579
$681$	661338.			1.42603
$682$		−	145165.i		−	0.312099i
$683$	185558.			0.397775			0.198888	−	0.980022i	$-0.436267\pi$
$683$	185558.			0.397775			0.198888	+	0.980022i	$0.436267\pi$
$684$		−	383805.i		−	0.820348i
$685$			96550.1i			0.205765i
$686$	128482.	+	306957.i	0.273019	+	0.652273i
$687$	−1.03124e6			−2.18497
$688$	124175.			0.262336
$689$			70961.9i			0.149481i
$690$	−390869.			−0.820981
$691$		−	548881.i		−	1.14953i	−0.818317	−	0.574767i	$-0.805093\pi$
$691$		−	548881.i		−	1.14953i	0.818317	−	0.574767i	$-0.194907\pi$
$692$			252800.i			0.527917i
$693$	−99034.1	−	745118.i	−0.206214	−	1.55153i
$694$	−628478.			−1.30488
$695$	611634.			1.26626
$696$		−	97287.2i		−	0.200834i
$697$	240910.			0.495894
$698$			290420.i			0.596095i
$699$			529305.i			1.08331i
$700$	4485.62	+	33749.2i	0.00915433	+	0.0688759i
$701$	517501.			1.05311			0.526556	−	0.850140i	$-0.323483\pi$
$701$	517501.			1.05311			0.526556	+	0.850140i	$0.323483\pi$
$702$	1794.37			0.00364114
$703$		−	401061.i		−	0.811522i
$704$	98213.6			0.198165
$705$		−	864393.i		−	1.73913i
$706$		−	177047.i		−	0.355205i
$707$	−445514.	+	59213.5i	−0.891297	+	0.118463i
$708$	−175679.			−0.350471
$709$	6035.96			0.0120075			0.00600377	−	0.999982i	$-0.498089\pi$
$709$	6035.96			0.0120075			0.00600377	+	0.999982i	$0.498089\pi$
$710$		−	149363.i		−	0.296296i
$711$	−560784.			−1.10932
$712$			48280.7i			0.0952388i
$713$		−	125625.i		−	0.247115i
$714$	42158.9	+	317197.i	0.0826975	+	0.622204i
$715$	−216145.			−0.422799
$716$	182005.			0.355024
$717$			49944.6i			0.0971517i
$718$	−270132.			−0.523994
$719$			748658.i			1.44819i	0.689700	+	0.724095i	$0.257742\pi$
$719$			748658.i			1.44819i	−0.689700	+	0.724095i	$0.742258\pi$
$720$			118730.i			0.229032i
$721$	−189748.	+	25219.5i	−0.365012	+	0.0485139i
$722$	649343.			1.24566
$723$	−894609.			−1.71142
$724$		−	443475.i		−	0.846042i
$725$	−29432.5			−0.0559953
$726$			795049.i			1.50841i
$727$		−	370335.i		−	0.700691i	−0.936621	−	0.350345i	$-0.886064\pi$
$727$		−	370335.i		−	0.700691i	0.936621	−	0.350345i	$-0.113936\pi$
$728$	−53385.4	+	7095.48i	−0.100730	+	0.0133881i
$729$	517848.			0.974422
$730$	466314.			0.875050
$731$		−	353079.i		−	0.660750i
$732$	25003.6			0.0466639
$733$			144545.i			0.269027i	0.990912	+	0.134513i	$0.0429471\pi$
$733$			144545.i			0.269027i	−0.990912	+	0.134513i	$0.957053\pi$
$734$			232867.i			0.432231i
$735$	682136.	−	184587.i	1.26269	−	0.341685i
$736$	84993.8			0.156903
$737$	−206515.			−0.380203
$738$			299442.i			0.549793i
$739$	4650.26			0.00851506			0.00425753	−	0.999991i	$-0.498645\pi$
$739$	4650.26			0.00851506			0.00425753	+	0.999991i	$0.498645\pi$
$740$			124069.i			0.226568i
$741$		−	369706.i		−	0.673318i
$742$	26676.5	+	200710.i	0.0484531	+	0.364554i
$743$	500204.			0.906087			0.453043	−	0.891489i	$-0.350338\pi$
$743$	500204.			0.906087			0.453043	+	0.891489i	$0.350338\pi$
$744$	−76811.0			−0.138764
$745$			152563.i			0.274877i
$746$	−368327.			−0.661845
$747$			115826.i			0.207571i
$748$		−	279260.i		−	0.499121i
$749$	−78382.2	−	589737.i	−0.139718	−	1.05122i
$750$	592596.			1.05350
$751$	944576.			1.67478			0.837389	−	0.546608i	$-0.184081\pi$
$751$	944576.			1.67478			0.837389	+	0.546608i	$0.184081\pi$
$752$			187961.i			0.332377i
$753$	−914031.			−1.61202
$754$		−	46557.1i		−	0.0818924i
$755$			531941.i			0.933189i
$756$	5075.24	−	674.553i	0.00888000	−	0.00118025i
$757$	−654028.			−1.14131			−0.570656	−	0.821189i	$-0.693311\pi$
$757$	−654028.			−1.14131			−0.570656	+	0.821189i	$0.693311\pi$
$758$	−544044.			−0.946881
$759$			1.14271e6i			1.98360i
$760$	−314902.			−0.545191
$761$			643673.i			1.11147i	0.831361	+	0.555733i	$0.187562\pi$
$761$			643673.i			1.11147i	−0.831361	+	0.555733i	$0.812438\pi$
$762$		−	1.00368e6i		−	1.72856i
$763$	43953.6	+	330700.i	0.0754997	+	0.568049i
$764$	−406541.			−0.696494
$765$	337597.			0.576867
$766$			288310.i			0.491362i
$767$	−84071.6			−0.142909
$768$		−	51967.7i		−	0.0881071i
$769$		−	103697.i		−	0.175354i	−0.996149	−	0.0876768i	$-0.972056\pi$
$769$		−	103697.i		−	0.175354i	0.996149	−	0.0876768i	$-0.0279443\pi$
$770$	−611352.	+	81255.1i	−1.03112	+	0.137047i
$771$	832491.			1.40046
$772$	−9986.72			−0.0167567
$773$		−	796380.i		−	1.33279i	−0.745599	−	0.666394i	$-0.767837\pi$
$773$		−	796380.i		−	1.33279i	0.745599	−	0.666394i	$-0.232163\pi$
$774$	438863.			0.732567
$775$			23237.8i			0.0386893i
$776$			133474.i			0.221652i
$777$	−411991.	+	54757.9i	−0.682410	+	0.0906995i
$778$	−540439.			−0.892868
$779$	−794195.			−1.30874
$780$			114369.i			0.187983i
$781$	−436664.			−0.715889
$782$		−	241671.i		−	0.395195i
$783$			4426.10i			0.00721934i
$784$	−148329.	+	40138.1i	−0.241321	+	0.0653017i
$785$	865122.			1.40391
$786$	861843.			1.39503
$787$			1.16895e6i			1.88733i	0.330905	+	0.943664i	$0.392646\pi$
$787$			1.16895e6i			1.88733i	−0.330905	+	0.943664i	$0.607354\pi$
$788$	515637.			0.830408
$789$			491081.i			0.788859i
$790$			460109.i			0.737237i
$791$	−30756.9	−	231411.i	−0.0491575	−	0.369854i
$792$	347110.			0.553371
$793$	11965.6			0.0190277
$794$		−	568919.i		−	0.902421i
$795$	429987.			0.680333
$796$		−	18820.8i		−	0.0297038i
$797$		−	808048.i		−	1.27210i	−0.771649	−	0.636049i	$-0.780568\pi$
$797$		−	808048.i		−	1.27210i	0.771649	−	0.636049i	$-0.219432\pi$
$798$	−138983.	−	1.04569e6i	−0.218251	−	1.64209i
$799$	534447.			0.837165
$800$	−15721.9			−0.0245654
$801$			170635.i			0.265952i
$802$	113076.			0.175801
$803$		−	1.36328e6i		−	2.11423i
$804$			109273.i			0.169044i
$805$	−529062.	+	70318.0i	−0.816423	+	0.108511i
$806$	−36758.2			−0.0565827
$807$	−1.10668e6			−1.69933
$808$		−	207540.i		−	0.317892i
$809$	−692708.			−1.05841			−0.529204	−	0.848495i	$-0.677509\pi$
$809$	−692708.			−1.05841			−0.529204	+	0.848495i	$0.677509\pi$
$810$		−	435894.i		−	0.664372i
$811$			382267.i			0.581200i	0.956845	+	0.290600i	$0.0938548\pi$
$811$			382267.i			0.581200i	−0.956845	+	0.290600i	$0.906145\pi$
$812$	−17502.1	−	131683.i	−0.0265448	−	0.199719i
$813$	1.33677e6			2.02244
$814$	362717.			0.547417
$815$		−	947732.i		−	1.42682i
$816$	−147765.			−0.221917
$817$			1.16398e6i			1.74381i
$818$			228129.i			0.340936i
$819$	−188676.	+	25077.1i	−0.281287	+	0.0373860i
$820$	245685.			0.365385
$821$	116392.			0.172678			0.0863392	−	0.996266i	$-0.472483\pi$
$821$	116392.			0.172678			0.0863392	+	0.996266i	$0.472483\pi$
$822$		−	149355.i		−	0.221043i
$823$	640526.			0.945665			0.472832	−	0.881152i	$-0.343232\pi$
$823$	640526.			0.945665			0.472832	+	0.881152i	$0.343232\pi$
$824$		−	88393.2i		−	0.130186i
$825$		−	211375.i		−	0.310561i
$826$	−237790.	+	31604.8i	−0.348525	+	0.0463227i
$827$	−158299.			−0.231455			−0.115727	−	0.993281i	$-0.536920\pi$
$827$	−158299.			−0.231455			−0.115727	+	0.993281i	$0.536920\pi$
$828$	300388.			0.438149
$829$		−	680501.i		−	0.990192i	−0.868838	−	0.495096i	$-0.835133\pi$
$829$		−	680501.i		−	0.990192i	0.868838	−	0.495096i	$-0.164867\pi$
$830$	95032.6			0.137948
$831$		−	459017.i		−	0.664701i
$832$		−	24869.3i		−	0.0359267i
$833$	114129.	+	421759.i	0.164477	+	0.607819i
$834$	−946148.			−1.36028
$835$	−806709.			−1.15703
$836$			920622.i			1.31725i
$837$	3494.53			0.00498812
$838$		−	712859.i		−	1.01512i
$839$			622397.i			0.884186i	0.896969	+	0.442093i	$0.145764\pi$
$839$			622397.i			0.884186i	−0.896969	+	0.442093i	$0.854236\pi$
$840$	42994.4	+	323484.i	0.0609331	+	0.458452i
$841$	−592440.			−0.837631
$842$	238831.			0.336873
$843$		−	1.25786e6i		−	1.77001i
$844$	−520451.			−0.730626
$845$		−	607827.i		−	0.851269i
$846$			664297.i			0.928157i
$847$	143031.	+	1.07614e6i	0.199371	+	1.50004i
$848$	−93500.0			−0.130023
$849$	−52694.2			−0.0731051
$850$			44703.6i			0.0618735i
$851$	313894.			0.433435
$852$			231052.i			0.318295i
$853$			826596.i			1.13604i	0.823013	+	0.568022i	$0.192291\pi$
$853$			826596.i			1.13604i	−0.823013	+	0.568022i	$0.807709\pi$
$854$	33843.7	−	4498.19i	0.0464048	−	0.00616768i
$855$	−1.11294e6			−1.52243
$856$	274726.			0.374931
$857$			539076.i			0.733987i	0.930223	+	0.366994i	$0.119613\pi$
$857$			539076.i			0.733987i	−0.930223	+	0.366994i	$0.880387\pi$
$858$	334359.			0.454191
$859$			499964.i			0.677567i	0.940864	+	0.338783i	$0.110015\pi$
$859$			499964.i			0.677567i	−0.940864	+	0.338783i	$0.889985\pi$
$860$		−	360077.i		−	0.486853i
$861$	108433.	+	815838.i	0.146271	+	1.10052i
$862$	360659.			0.485380
$863$	1.16944e6			1.57021			0.785103	−	0.619365i	$-0.212610\pi$
$863$	1.16944e6			1.57021			0.785103	+	0.619365i	$0.212610\pi$
$864$			2364.28i			0.00316716i
$865$	733059.			0.979730
$866$			660548.i			0.880783i
$867$		−	639512.i		−	0.850766i
$868$	−103968.	+	13818.4i	−0.137994	+	0.0183408i
$869$	1.34514e6			1.78126
$870$	−282109.			−0.372716
$871$			52292.9i			0.0689297i
$872$	−154055.			−0.202602
$873$			471727.i			0.618960i
$874$			796705.i			1.04298i
$875$	802110.	−	106609.i	1.04765	−	0.139244i
$876$	−721350.			−0.940021
$877$	187496.			0.243777			0.121888	−	0.992544i	$-0.461105\pi$
$877$	187496.			0.243777			0.121888	+	0.992544i	$0.461105\pi$
$878$			860515.i			1.11627i
$879$	−256786.			−0.332349
$880$		−	284795.i		−	0.367762i
$881$		−	179673.i		−	0.231489i	−0.993279	−	0.115745i	$-0.963075\pi$
$881$		−	179673.i		−	0.231489i	0.993279	−	0.115745i	$-0.0369254\pi$
$882$	−524230.	+	141857.i	−0.673883	+	0.182354i
$883$	−1.04658e6			−1.34231			−0.671155	−	0.741317i	$-0.734201\pi$
$883$	−1.04658e6			−1.34231			−0.671155	+	0.741317i	$0.734201\pi$
$884$	−70713.3			−0.0904892
$885$			509424.i			0.650419i
$886$	246246.			0.313691
$887$		−	1.30029e6i		−	1.65270i	−0.563158	−	0.826349i	$-0.690414\pi$
$887$		−	1.30029e6i		−	1.65270i	0.563158	−	0.826349i	$-0.309586\pi$
$888$		−	191924.i		−	0.243390i
$889$	−180563.	−	1.35853e6i	−0.228468	−	1.71896i
$890$	140002.			0.176748
$891$	−1.27434e6			−1.60521
$892$			243299.i			0.305781i
$893$	−1.76188e6			−2.20940
$894$		−	236003.i		−	0.295286i
$895$		−	527770.i		−	0.658868i
$896$	−9349.06	−	70341.0i	−0.0116453	−	0.0876178i
$897$	289354.			0.359620
$898$	257787.			0.319675
$899$		−	90669.8i		−	0.112187i
$900$	−55564.8			−0.0685985
$901$			265858.i			0.327491i
$902$		−	718263.i		−	0.882817i
$903$	1.19570e6	−	158921.i	1.46638	−	0.194897i
$904$	107802.			0.131913
$905$	−1.28597e6			−1.57012
$906$		−	822869.i		−	1.00248i
$907$	1.18388e6			1.43911			0.719556	−	0.694435i	$-0.244346\pi$
$907$	1.18388e6			1.43911			0.719556	+	0.694435i	$0.244346\pi$
$908$			417004.i			0.505788i
$909$		−	733496.i		−	0.887708i
$910$	20575.1	+	154804.i	0.0248462	+	0.186939i
$911$	−1.30731e6			−1.57522			−0.787612	−	0.616172i	$-0.788683\pi$
$911$	−1.30731e6			−1.57522			−0.787612	+	0.616172i	$0.788683\pi$
$912$	487128.			0.585671
$913$		−	277830.i		−	0.333301i
$914$	1.16511e6			1.39468
$915$		−	72504.3i		−	0.0866008i
$916$		−	650242.i		−	0.774968i
$917$	1.16655e6	−	155047.i	1.38728	−	0.184384i
$918$	6722.58			0.00797720
$919$	698775.			0.827382			0.413691	−	0.910417i	$-0.364239\pi$
$919$	698775.			0.827382			0.413691	+	0.910417i	$0.364239\pi$
$920$		−	246461.i		−	0.291187i
$921$	802730.			0.946347
$922$			445185.i			0.523696i
$923$			110571.i			0.129789i
$924$	945711.	−	125695.i	1.10768	−	0.147222i
$925$	−58063.1			−0.0678605
$926$	−694541.			−0.809984
$927$		−	312402.i		−	0.363542i
$928$	61344.1			0.0712323
$929$			1.39460e6i			1.61591i	0.589244	+	0.807955i	$0.299426\pi$
$929$			1.39460e6i			1.61591i	−0.589244	+	0.807955i	$0.700574\pi$
$930$			222733.i			0.257524i
$931$	−376241.	−	1.39039e6i	−0.434077	−	1.60412i
$932$	−333751.			−0.384229
$933$	−182387.			−0.209522
$934$			93533.8i			0.107220i
$935$	−809786.			−0.926290
$936$		−	87893.9i		−	0.100325i
$937$			509380.i			0.580180i	0.956999	+	0.290090i	$0.0936852\pi$
$937$			509380.i			0.580180i	−0.956999	+	0.290090i	$0.906315\pi$
$938$	19658.4	+	147907.i	0.0223430	+	0.168106i
$939$	466428.			0.528997
$940$	545040.			0.616840
$941$			1.62505e6i			1.83522i	0.397486	+	0.917608i	$0.369883\pi$
$941$			1.62505e6i			1.83522i	−0.397486	+	0.917608i	$0.630117\pi$
$942$	−1.33827e6			−1.50814
$943$		−	621584.i		−	0.698998i
$944$		−	110773.i		−	0.124306i
$945$	−1956.04	−	14716.9i	−0.00219035	−	0.0164799i
$946$	−1.05269e6			−1.17630
$947$	1.22462e6			1.36553			0.682763	−	0.730640i	$-0.260778\pi$
$947$	1.22462e6			1.36553			0.682763	+	0.730640i	$0.260778\pi$
$948$		−	711752.i		−	0.791976i
$949$	−345204.			−0.383304
$950$		−	147372.i		−	0.163293i
$951$			1.59298e6i			1.76137i
$952$	−200007.	+	26583.1i	−0.220685	+	0.0293313i
$953$	−1.14847e6			−1.26454			−0.632269	−	0.774749i	$-0.717876\pi$
$953$	−1.14847e6			−1.26454			−0.632269	+	0.774749i	$0.717876\pi$
$954$	−330451.			−0.363086
$955$			1.17887e6i			1.29258i
$956$	−31492.4			−0.0344580
$957$			824750.i			0.900531i
$958$		−	1.08690e6i		−	1.18429i
$959$	−26869.2	−	202160.i	−0.0292158	−	0.219815i
$960$	−150693.			−0.163513
$961$	851935.			0.922485
$962$		−	91845.8i		−	0.0992451i
$963$	970945.			1.04699
$964$		−	564092.i		−	0.607010i
$965$			28959.0i			0.0310978i
$966$	818416.	−	108776.i	0.877041	−	0.116568i
$967$	−733668.			−0.784597			−0.392298	−	0.919838i	$-0.628320\pi$
$967$	−733668.			−0.784597			−0.392298	+	0.919838i	$0.628320\pi$
$968$	−501315.			−0.535008
$969$		−	1.38510e6i		−	1.47514i
$970$	387041.			0.411352
$971$			786749.i			0.834445i	0.908804	+	0.417223i	$0.136996\pi$
$971$			786749.i			0.834445i	−0.908804	+	0.417223i	$0.863004\pi$
$972$			665830.i			0.704743i
$973$	−1.28066e6	+	170213.i	−1.35272	+	0.179791i
$974$	490807.			0.517360
$975$	−53523.7			−0.0563037
$976$			15765.9i			0.0165508i
$977$	837039.			0.876913			0.438457	−	0.898752i	$-0.355525\pi$
$977$	837039.			0.876913			0.438457	+	0.898752i	$0.355525\pi$
$978$			1.46606e6i			1.53276i
$979$		−	409299.i		−	0.427046i
$980$	116390.	+	430118.i	0.121190	+	0.447853i
$981$	−544467.			−0.565761
$982$	56586.3			0.0586798
$983$			644129.i			0.666600i	0.942821	+	0.333300i	$0.108162\pi$
$983$			644129.i			0.666600i	−0.942821	+	0.333300i	$0.891838\pi$
$984$	−380054.			−0.392514
$985$		−	1.49522e6i		−	1.54111i
$986$		−	174426.i		−	0.179414i
$987$	240554.	+	1.80990e6i	0.246933	+	1.85789i
$988$	233117.			0.238814
$989$	−910996.			−0.931374
$990$		−	1.00653e6i		−	1.02697i
$991$	92517.5			0.0942056			0.0471028	−	0.998890i	$-0.485001\pi$
$991$	92517.5			0.0942056			0.0471028	+	0.998890i	$0.485001\pi$
$992$		−	48432.8i		−	0.0492172i
$993$		−	68214.4i		−	0.0691795i
$994$	41566.6	+	312741.i	0.0420699	+	0.316528i
$995$	−54575.7			−0.0551256
$996$	−147008.			−0.148191
$997$			366383.i			0.368591i	0.982871	+	0.184295i	$0.0590003\pi$
$997$			366383.i			0.368591i	−0.982871	+	0.184295i	$0.941000\pi$
$998$	1.21161e6			1.21647
$999$			8731.60i			0.00874909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.5.b.a.13.1	✓	4
3.2	odd	2		126.5.c.a.55.4		4
4.3	odd	2		112.5.c.c.97.4		4
5.2	odd	4		350.5.d.a.349.1		8
5.3	odd	4		350.5.d.a.349.8		8
5.4	even	2		350.5.b.a.251.4		4
7.2	even	3		98.5.d.d.31.4		8
7.3	odd	6		98.5.d.d.19.4		8
7.4	even	3		98.5.d.d.19.3		8
7.5	odd	6		98.5.d.d.31.3		8
7.6	odd	2	inner	14.5.b.a.13.2	yes	4
8.3	odd	2		448.5.c.f.321.1		4
8.5	even	2		448.5.c.e.321.4		4
12.11	even	2		1008.5.f.h.433.3		4
21.20	even	2		126.5.c.a.55.3		4
28.27	even	2		112.5.c.c.97.1		4
35.13	even	4		350.5.d.a.349.5		8
35.27	even	4		350.5.d.a.349.4		8
35.34	odd	2		350.5.b.a.251.3		4
56.13	odd	2		448.5.c.e.321.1		4
56.27	even	2		448.5.c.f.321.4		4
84.83	odd	2		1008.5.f.h.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.b.a.13.1	✓	4	1.1	even	1	trivial
14.5.b.a.13.2	yes	4	7.6	odd	2	inner
98.5.d.d.19.3		8	7.4	even	3
98.5.d.d.19.4		8	7.3	odd	6
98.5.d.d.31.3		8	7.5	odd	6
98.5.d.d.31.4		8	7.2	even	3
112.5.c.c.97.1		4	28.27	even	2
112.5.c.c.97.4		4	4.3	odd	2
126.5.c.a.55.3		4	21.20	even	2
126.5.c.a.55.4		4	3.2	odd	2
350.5.b.a.251.3		4	35.34	odd	2
350.5.b.a.251.4		4	5.4	even	2
350.5.d.a.349.1		8	5.2	odd	4
350.5.d.a.349.4		8	35.27	even	4
350.5.d.a.349.5		8	35.13	even	4
350.5.d.a.349.8		8	5.3	odd	4
448.5.c.e.321.1		4	56.13	odd	2
448.5.c.e.321.4		4	8.5	even	2
448.5.c.f.321.1		4	8.3	odd	2
448.5.c.f.321.4		4	56.27	even	2
1008.5.f.h.433.2		4	84.83	odd	2
1008.5.f.h.433.3		4	12.11	even	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843 q^{2} -12.6874i q^{3} +8.00000 q^{4} -23.1980i q^{5} +35.8854i q^{6} +(6.45584 + 48.5729i) q^{7} -22.6274 q^{8} -79.9706 q^{9} +65.6139i q^{10} +191.823 q^{11} -101.499i q^{12} -48.5729i q^{13} +(-18.2599 - 137.385i) q^{14} -294.323 q^{15} +64.0000 q^{16} -181.977i q^{17} +226.191 q^{18} +599.915i q^{19} -185.584i q^{20} +(616.264 - 81.9080i) q^{21} -542.558 q^{22} -469.529 q^{23} +287.083i q^{24} +86.8519 q^{25} +137.385i q^{26} -13.0609i q^{27} +(51.6468 + 388.583i) q^{28} -338.881 q^{29} +832.471 q^{30} +267.556i q^{31} -181.019 q^{32} -2433.74i q^{33} +514.710i q^{34} +(1126.79 - 149.763i) q^{35} -639.765 q^{36} -668.530 q^{37} -1696.82i q^{38} -616.264 q^{39} +524.911i q^{40} +1323.85i q^{41} +(-1743.06 + 231.671i) q^{42} +1940.23 q^{43} +1534.59 q^{44} +1855.16i q^{45} +1328.03 q^{46} +2936.89i q^{47} -811.995i q^{48} +(-2317.64 + 627.158i) q^{49} -245.654 q^{50} -2308.82 q^{51} -388.583i q^{52} -1460.94 q^{53} +36.9418i q^{54} -4449.92i q^{55} +(-146.079 - 1099.08i) q^{56} +7611.38 q^{57} +958.501 q^{58} -1730.83i q^{59} -2354.58 q^{60} +246.343i q^{61} -756.763i q^{62} +(-516.277 - 3884.40i) q^{63} +512.000 q^{64} -1126.79 q^{65} +6883.67i q^{66} -1076.59 q^{67} -1455.82i q^{68} +5957.11i q^{69} +(-3187.05 + 423.593i) q^{70} -2276.39 q^{71} +1809.53 q^{72} -7106.94i q^{73} +1890.89 q^{74} -1101.93i q^{75} +4799.32i q^{76} +(1238.38 + 9317.41i) q^{77} +1743.06 q^{78} +7012.38 q^{79} -1484.67i q^{80} -6643.32 q^{81} -3744.40i q^{82} -1448.36i q^{83} +(4930.11 - 655.264i) q^{84} -4221.52 q^{85} -5487.81 q^{86} +4299.53i q^{87} -4340.47 q^{88} -2133.73i q^{89} -5247.18i q^{90} +(2359.32 - 313.579i) q^{91} -3756.23 q^{92} +3394.60 q^{93} -8306.77i q^{94} +13916.8 q^{95} +2296.67i q^{96} -5898.76i q^{97} +(6555.29 - 1773.87i) q^{98} -15340.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{4} - 76 q^{7} - 252 q^{9} + 360 q^{11} - 288 q^{14} + 384 q^{15} + 256 q^{16} + 192 q^{18} + 768 q^{21} - 1152 q^{22} - 792 q^{23} - 2300 q^{25} - 608 q^{28} + 1224 q^{29} + 4416 q^{30} + 4032 q^{35}+ \cdots - 29592 q^{99}+O(q^{100}) \) 4 * q + 32 * q^4 - 76 * q^7 - 252 * q^9 + 360 * q^11 - 288 * q^14 + 384 * q^15 + 256 * q^16 + 192 * q^18 + 768 * q^21 - 1152 * q^22 - 792 * q^23 - 2300 * q^25 - 608 * q^28 + 1224 * q^29 + 4416 * q^30 + 4032 * q^35 - 2016 * q^36 - 3896 * q^37 - 768 * q^39 - 4800 * q^42 + 3688 * q^43 + 2880 * q^44 + 3072 * q^46 - 1532 * q^49 - 7488 * q^50 - 11136 * q^51 + 5832 * q^53 - 2304 * q^56 + 12864 * q^57 + 7296 * q^58 + 3072 * q^60 + 3060 * q^63 + 2048 * q^64 - 4032 * q^65 - 1048 * q^67 - 1344 * q^70 - 21528 * q^71 + 1536 * q^72 - 3456 * q^74 + 3528 * q^77 + 4800 * q^78 + 12776 * q^79 - 29628 * q^81 + 6144 * q^84 + 16512 * q^85 - 11520 * q^86 - 9216 * q^88 + 5568 * q^91 - 6336 * q^92 + 38016 * q^93 + 36864 * q^95 + 21888 * q^98 - 29592 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more