LMFDB - Embedded newform 336.6.q.m.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,6,Mod(193,336)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$53.8889634572$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 1094 x^{8} - 12883 x^{7} + 1063781 x^{6} - 7555708 x^{5} + 199315216 x^{4} + \cdots + 37456183296 $ x^10 - x^9 + 1094x^8 - 12883x^7 + 1063781x^6 - 7555708x^5 + 199315216x^4 + 540268032x^3 + 20356706304x^2 - 26680098816x + 37456183296
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$8.89029 + 15.3984i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.6.q.m.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.50000 + 7.79423i) q^{3} +(9.56607 - 16.5689i) q^{5} +(126.222 + 29.5814i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(4.50000 + 7.79423i) q^{3} +(9.56607 - 16.5689i) q^{5} +(126.222 + 29.5814i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-316.141 - 547.572i) q^{11} -626.430 q^{13} +172.189 q^{15} +(461.921 + 800.071i) q^{17} +(-1201.93 + 2081.80i) q^{19} +(337.434 + 1116.92i) q^{21} +(-192.254 + 332.994i) q^{23} +(1379.48 + 2389.33i) q^{25} -729.000 q^{27} -2708.57 q^{29} +(-615.683 - 1066.39i) q^{31} +(2845.27 - 4928.15i) q^{33} +(1697.58 - 1808.38i) q^{35} +(-1691.60 + 2929.93i) q^{37} +(-2818.93 - 4882.54i) q^{39} +19008.0 q^{41} -21564.7 q^{43} +(774.851 + 1342.08i) q^{45} +(-4719.39 + 8174.22i) q^{47} +(15056.9 + 7467.64i) q^{49} +(-4157.29 + 7200.64i) q^{51} +(11475.1 + 19875.5i) q^{53} -12096.9 q^{55} -21634.7 q^{57} +(5572.36 + 9651.61i) q^{59} +(-16742.9 + 28999.5i) q^{61} +(-7187.06 + 7656.17i) q^{63} +(-5992.47 + 10379.3i) q^{65} +(-1497.16 - 2593.16i) q^{67} -3460.58 q^{69} -74926.3 q^{71} +(12840.0 + 22239.6i) q^{73} +(-12415.3 + 21504.0i) q^{75} +(-23705.9 - 78467.4i) q^{77} +(38053.4 - 65910.4i) q^{79} +(-3280.50 - 5681.99i) q^{81} +4059.07 q^{83} +17675.1 q^{85} +(-12188.6 - 21111.2i) q^{87} +(-56004.6 + 97002.9i) q^{89} +(-79069.1 - 18530.7i) q^{91} +(5541.14 - 9597.54i) q^{93} +(22995.4 + 39829.2i) q^{95} -100527. q^{97} +51214.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 45 q^{3} - 75 q^{5} + 113 q^{7} - 405 q^{9}+O(q^{10}) $ 10 * q + 45 * q^3 - 75 * q^5 + 113 * q^7 - 405 * q^9	$ 10 q + 45 q^{3} - 75 q^{5} + 113 q^{7} - 405 q^{9} - 91 q^{11} + 580 q^{13} - 1350 q^{15} - 1128 q^{17} - 282 q^{19} + 279 q^{21} + 1808 q^{23} - 202 q^{25} - 7290 q^{27} + 5026 q^{29} + 5069 q^{31} + 819 q^{33} + 884 q^{35} - 5010 q^{37} + 2610 q^{39} + 12872 q^{41} - 17328 q^{43} - 6075 q^{45} + 50 q^{47} + 29135 q^{49} + 10152 q^{51} + 1167 q^{53} - 97410 q^{55} - 5076 q^{57} + 42797 q^{59} - 26546 q^{61} - 6642 q^{63} - 2216 q^{65} + 13440 q^{67} + 32544 q^{69} + 39356 q^{71} - 27768 q^{73} + 1818 q^{75} + 125797 q^{77} + 123369 q^{79} - 32805 q^{81} - 334250 q^{83} - 324936 q^{85} + 22617 q^{87} - 59350 q^{89} - 113850 q^{91} - 45621 q^{93} - 41864 q^{95} + 525282 q^{97} + 14742 q^{99}+O(q^{100}) $ 10 * q + 45 * q^3 - 75 * q^5 + 113 * q^7 - 405 * q^9 - 91 * q^11 + 580 * q^13 - 1350 * q^15 - 1128 * q^17 - 282 * q^19 + 279 * q^21 + 1808 * q^23 - 202 * q^25 - 7290 * q^27 + 5026 * q^29 + 5069 * q^31 + 819 * q^33 + 884 * q^35 - 5010 * q^37 + 2610 * q^39 + 12872 * q^41 - 17328 * q^43 - 6075 * q^45 + 50 * q^47 + 29135 * q^49 + 10152 * q^51 + 1167 * q^53 - 97410 * q^55 - 5076 * q^57 + 42797 * q^59 - 26546 * q^61 - 6642 * q^63 - 2216 * q^65 + 13440 * q^67 + 32544 * q^69 + 39356 * q^71 - 27768 * q^73 + 1818 * q^75 + 125797 * q^77 + 123369 * q^79 - 32805 * q^81 - 334250 * q^83 - 324936 * q^85 + 22617 * q^87 - 59350 * q^89 - 113850 * q^91 - 45621 * q^93 - 41864 * q^95 + 525282 * q^97 + 14742 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$		0			0
$5$	9.56607	−	16.5689i	0.171123	−	0.296394i	−0.767690	−	0.640822i	$-0.778594\pi$
$5$	9.56607	−	16.5689i	0.171123	−	0.296394i	0.938813	+	0.344428i	$0.111927\pi$
$6$		0			0
$7$	126.222	+	29.5814i	0.973619	+	0.228178i
$7$	126.222	+	29.5814i	0.973619	+	0.228178i
$8$		0			0
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$		0			0
$11$	−316.141	−	547.572i	−0.787769	−	1.36446i	−0.927331	−	0.374242i	$-0.877903\pi$
$11$	−316.141	−	547.572i	−0.787769	−	1.36446i	0.139562	−	0.990213i	$-0.455430\pi$
$12$		0			0
$13$	−626.430			−1.02805			−0.514025	−	0.857775i	$-0.671846\pi$
$13$	−626.430			−1.02805			−0.514025	+	0.857775i	$0.671846\pi$
$14$		0			0
$15$	172.189			0.197596
$16$		0			0
$17$	461.921	+	800.071i	0.387655	+	0.671438i	0.992134	−	0.125183i	$-0.0399519\pi$
$17$	461.921	+	800.071i	0.387655	+	0.671438i	−0.604479	+	0.796621i	$0.706619\pi$
$18$		0			0
$19$	−1201.93	+	2081.80i	−0.763825	+	1.32298i	0.177040	+	0.984204i	$0.443348\pi$
$19$	−1201.93	+	2081.80i	−0.763825	+	1.32298i	−0.940866	+	0.338780i	$0.889986\pi$
$20$		0			0
$21$	337.434	+	1116.92i	0.166971	+	0.552679i
$22$		0			0
$23$	−192.254	+	332.994i	−0.0757803	+	0.131255i	−0.901425	−	0.432935i	$-0.857478\pi$
$23$	−192.254	+	332.994i	−0.0757803	+	0.131255i	0.825645	+	0.564190i	$0.190811\pi$
$24$		0			0
$25$	1379.48	+	2389.33i	0.441434	+	0.764586i
$26$		0			0
$27$	−729.000			−0.192450
$28$		0			0
$29$	−2708.57			−0.598061			−0.299030	−	0.954244i	$-0.596663\pi$
$29$	−2708.57			−0.598061			−0.299030	+	0.954244i	$0.596663\pi$
$30$		0			0
$31$	−615.683	−	1066.39i	−0.115068	−	0.199303i	0.802739	−	0.596330i	$-0.203375\pi$
$31$	−615.683	−	1066.39i	−0.115068	−	0.199303i	−0.917807	+	0.397027i	$0.870042\pi$
$32$		0			0
$33$	2845.27	−	4928.15i	0.454818	−	0.787769i
$34$		0			0
$35$	1697.58	−	1808.38i	0.234239	−	0.249528i
$36$		0			0
$37$	−1691.60	+	2929.93i	−0.203139	+	0.351847i	−0.949538	−	0.313652i	$-0.898448\pi$
$37$	−1691.60	+	2929.93i	−0.203139	+	0.351847i	0.746399	+	0.665498i	$0.231781\pi$
$38$		0			0
$39$	−2818.93	−	4882.54i	−0.296772	−	0.514025i
$40$		0			0
$41$	19008.0			1.76595			0.882974	−	0.469422i	$-0.155538\pi$
$41$	19008.0			1.76595			0.882974	+	0.469422i	$0.155538\pi$
$42$		0			0
$43$	−21564.7			−1.77858			−0.889289	−	0.457345i	$-0.848800\pi$
$43$	−21564.7			−1.77858			−0.889289	+	0.457345i	$0.848800\pi$
$44$		0			0
$45$	774.851	+	1342.08i	0.0570410	+	0.0987979i
$46$		0			0
$47$	−4719.39	+	8174.22i	−0.311631	+	0.539761i	−0.978716	−	0.205221i	$-0.934209\pi$
$47$	−4719.39	+	8174.22i	−0.311631	+	0.539761i	0.667085	+	0.744982i	$0.267542\pi$
$48$		0			0
$49$	15056.9	+	7467.64i	0.895869	+	0.444317i
$50$		0			0
$51$	−4157.29	+	7200.64i	−0.223813	+	0.387655i
$52$		0			0
$53$	11475.1	+	19875.5i	0.561134	+	0.971913i	0.997398	+	0.0720942i	$0.0229682\pi$
$53$	11475.1	+	19875.5i	0.561134	+	0.971913i	−0.436263	+	0.899819i	$0.643698\pi$
$54$		0			0
$55$	−12096.9			−0.539221
$56$		0			0
$57$	−21634.7			−0.881989
$58$		0			0
$59$	5572.36	+	9651.61i	0.208406	+	0.360969i	0.951212	−	0.308537i	$-0.0998393\pi$
$59$	5572.36	+	9651.61i	0.208406	+	0.360969i	−0.742807	+	0.669506i	$0.766506\pi$
$60$		0			0
$61$	−16742.9	+	28999.5i	−0.576111	+	0.997853i	0.419809	+	0.907612i	$0.362097\pi$
$61$	−16742.9	+	28999.5i	−0.576111	+	0.997853i	−0.995920	+	0.0902408i	$0.971236\pi$
$62$		0			0
$63$	−7187.06	+	7656.17i	−0.228139	+	0.243030i
$64$		0			0
$65$	−5992.47	+	10379.3i	−0.175923	+	0.304707i
$66$		0			0
$67$	−1497.16	−	2593.16i	−0.0407456	−	0.0705735i	0.844933	−	0.534872i	$-0.179640\pi$
$67$	−1497.16	−	2593.16i	−0.0407456	−	0.0705735i	−0.885679	+	0.464298i	$0.846307\pi$
$68$		0			0
$69$	−3460.58			−0.0875036
$70$		0			0
$71$	−74926.3			−1.76396			−0.881979	−	0.471288i	$-0.843789\pi$
$71$	−74926.3			−1.76396			−0.881979	+	0.471288i	$0.843789\pi$
$72$		0			0
$73$	12840.0	+	22239.6i	0.282006	+	0.488449i	0.971879	−	0.235482i	$-0.0756668\pi$
$73$	12840.0	+	22239.6i	0.282006	+	0.488449i	−0.689873	+	0.723931i	$0.742333\pi$
$74$		0			0
$75$	−12415.3	+	21504.0i	−0.254862	+	0.441434i
$76$		0			0
$77$	−23705.9	−	78467.4i	−0.455648	−	1.50821i
$78$		0			0
$79$	38053.4	−	65910.4i	0.686002	−	1.18819i	−0.287118	−	0.957895i	$-0.592697\pi$
$79$	38053.4	−	65910.4i	0.686002	−	1.18819i	0.973121	−	0.230296i	$-0.0739694\pi$
$80$		0			0
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	4059.07			0.0646742			0.0323371	−	0.999477i	$-0.489705\pi$
$83$	4059.07			0.0646742			0.0323371	+	0.999477i	$0.489705\pi$
$84$		0			0
$85$	17675.1			0.265347
$86$		0			0
$87$	−12188.6	−	21111.2i	−0.172645	−	0.299030i
$88$		0			0
$89$	−56004.6	+	97002.9i	−0.749461	+	1.29810i	0.198621	+	0.980076i	$0.436354\pi$
$89$	−56004.6	+	97002.9i	−0.749461	+	1.29810i	−0.948081	+	0.318028i	$0.896980\pi$
$90$		0			0
$91$	−79069.1	−	18530.7i	−1.00093	−	0.234578i
$92$		0			0
$93$	5541.14	−	9597.54i	0.0664343	−	0.115068i
$94$		0			0
$95$	22995.4	+	39829.2i	0.261416	+	0.452786i
$96$		0			0
$97$	−100527.			−1.08481			−0.542405	−	0.840117i	$-0.682486\pi$
$97$	−100527.			−1.08481			−0.542405	+	0.840117i	$0.682486\pi$
$98$		0			0
$99$	51214.8			0.525179
$100$		0			0
$101$	−34826.8	−	60321.8i	−0.339711	−	0.588397i	0.644667	−	0.764464i	$-0.276996\pi$
$101$	−34826.8	−	60321.8i	−0.339711	−	0.588397i	−0.984378	+	0.176066i	$0.943663\pi$
$102$		0			0
$103$	−64512.6	+	111739.i	−0.599172	+	1.03780i	0.393772	+	0.919208i	$0.371170\pi$
$103$	−64512.6	+	111739.i	−0.599172	+	1.03780i	−0.992944	+	0.118588i	$0.962163\pi$
$104$		0			0
$105$	21734.0	+	5093.60i	0.192383	+	0.0450870i
$106$		0			0
$107$	−35463.8	+	61425.1i	−0.299451	+	0.518665i	−0.976011	−	0.217723i	$-0.930137\pi$
$107$	−35463.8	+	61425.1i	−0.299451	+	0.518665i	0.676559	+	0.736388i	$0.263470\pi$
$108$		0			0
$109$	9399.49	+	16280.4i	0.0757771	+	0.131250i	0.901424	−	0.432937i	$-0.142523\pi$
$109$	9399.49	+	16280.4i	0.0757771	+	0.131250i	−0.825647	+	0.564187i	$0.809190\pi$
$110$		0			0
$111$	−30448.8			−0.234565
$112$		0			0
$113$	−150561.			−1.10922			−0.554610	−	0.832110i	$-0.687133\pi$
$113$	−150561.			−1.10922			−0.554610	+	0.832110i	$0.687133\pi$
$114$		0			0
$115$	3678.23	+	6370.89i	0.0259355	+	0.0449216i
$116$		0			0
$117$	25370.4	−	43942.8i	0.171342	−	0.296772i
$118$		0			0
$119$	34637.3	+	114651.i	0.224221	+	0.742180i
$120$		0			0
$121$	−119364.	+	206745.i	−0.741159	+	1.28373i
$122$		0			0
$123$	85536.2	+	148153.i	0.509785	+	0.882974i
$124$		0			0
$125$	112573.			0.644404
$126$		0			0
$127$	290191.			1.59652			0.798259	−	0.602314i	$-0.205755\pi$
$127$	290191.			1.59652			0.798259	+	0.602314i	$0.205755\pi$
$128$		0			0
$129$	−97041.3	−	168080.i	−0.513431	−	0.889289i
$130$		0			0
$131$	9398.44	−	16278.6i	0.0478495	−	0.0828777i	−0.841109	−	0.540866i	$-0.818097\pi$
$131$	9398.44	−	16278.6i	0.0478495	−	0.0828777i	0.888958	+	0.457988i	$0.151430\pi$
$132$		0			0
$133$	−213292.	+	227214.i	−1.04555	+	1.11379i
$134$		0			0
$135$	−6973.66	+	12078.7i	−0.0329326	+	0.0570410i
$136$		0			0
$137$	−60282.9	−	104413.i	−0.274406	−	0.475284i	0.695579	−	0.718449i	$-0.255148\pi$
$137$	−60282.9	−	104413.i	−0.274406	−	0.475284i	−0.969985	+	0.243165i	$0.921814\pi$
$138$		0			0
$139$	−392984.			−1.72519			−0.862597	−	0.505892i	$-0.831163\pi$
$139$	−392984.			−1.72519			−0.862597	+	0.505892i	$0.831163\pi$
$140$		0			0
$141$	−84948.9			−0.359841
$142$		0			0
$143$	198040.	+	343015.i	0.809865	+	1.40273i
$144$		0			0
$145$	−25910.4	+	44878.1i	−0.102342	+	0.177261i
$146$		0			0
$147$	9551.46	+	150961.i	0.0364566	+	0.576198i
$148$		0			0
$149$	−68977.4	+	119472.i	−0.254531	+	0.440861i	−0.964768	−	0.263102i	$-0.915254\pi$
$149$	−68977.4	+	119472.i	−0.254531	+	0.440861i	0.710237	+	0.703963i	$0.248588\pi$
$150$		0			0
$151$	−251965.	−	436416.i	−0.899285	−	1.55761i	−0.828410	−	0.560123i	$-0.810754\pi$
$151$	−251965.	−	436416.i	−0.899285	−	1.55761i	−0.0708759	−	0.997485i	$-0.522579\pi$
$152$		0			0
$153$	−74831.2			−0.258437
$154$		0			0
$155$	−23558.6			−0.0787628
$156$		0			0
$157$	79373.8	+	137480.i	0.256997	+	0.445132i	0.965436	−	0.260640i	$-0.0839336\pi$
$157$	79373.8	+	137480.i	0.256997	+	0.445132i	−0.708439	+	0.705772i	$0.750600\pi$
$158$		0			0
$159$	−103276.	+	178879.i	−0.323971	+	0.561134i
$160$		0			0
$161$	−34117.1	+	36344.0i	−0.103731	+	0.110501i
$162$		0			0
$163$	206081.	−	356943.i	0.607531	−	1.05228i	−0.384115	−	0.923285i	$-0.625493\pi$
$163$	206081.	−	356943.i	0.607531	−	1.05228i	0.991646	−	0.128990i	$-0.0411734\pi$
$164$		0			0
$165$	−54436.0	−	94285.9i	−0.155660	−	0.269611i
$166$		0			0
$167$	441722.			1.22563			0.612813	−	0.790228i	$-0.290038\pi$
$167$	441722.			1.22563			0.612813	+	0.790228i	$0.290038\pi$
$168$		0			0
$169$	21121.2			0.0568854
$170$		0			0
$171$	−97356.0	−	168626.i	−0.254608	−	0.440995i
$172$		0			0
$173$	60596.3	−	104956.i	0.153933	−	0.266619i	−0.778737	−	0.627350i	$-0.784139\pi$
$173$	60596.3	−	104956.i	0.153933	−	0.266619i	0.932670	+	0.360731i	$0.117473\pi$
$174$		0			0
$175$	103441.	+	342393.i	0.255327	+	0.845141i
$176$		0			0
$177$	−50151.3	+	86864.5i	−0.120323	+	0.208406i
$178$		0			0
$179$	238119.	+	412435.i	0.555472	+	0.962106i	0.997867	+	0.0652854i	$0.0207958\pi$
$179$	238119.	+	412435.i	0.555472	+	0.962106i	−0.442395	+	0.896821i	$0.645871\pi$
$180$		0			0
$181$	296123.			0.671855			0.335927	−	0.941888i	$-0.390950\pi$
$181$	296123.			0.671855			0.335927	+	0.941888i	$0.390950\pi$
$182$		0			0
$183$	−301372.			−0.665235
$184$		0			0
$185$	32363.9	+	56055.9i	0.0695235	+	0.120418i
$186$		0			0
$187$	292064.	−	505870.i	0.610765	−	1.05788i
$188$		0			0
$189$	−92015.7	−	21564.9i	−0.187373	−	0.0439129i
$190$		0			0
$191$	50774.1	−	87943.4i	0.100707	−	0.174429i	−0.811269	−	0.584673i	$-0.801223\pi$
$191$	50774.1	−	87943.4i	0.100707	−	0.174429i	0.911976	+	0.410243i	$0.134556\pi$
$192$		0			0
$193$	−71891.3	−	124519.i	−0.138926	−	0.240627i	0.788164	−	0.615465i	$-0.211032\pi$
$193$	−71891.3	−	124519.i	−0.138926	−	0.240627i	−0.927090	+	0.374838i	$0.877698\pi$
$194$		0			0
$195$	−107864.			−0.203138
$196$		0			0
$197$	919041.			1.68721			0.843606	−	0.536963i	$-0.180429\pi$
$197$	919041.			1.68721			0.843606	+	0.536963i	$0.180429\pi$
$198$		0			0
$199$	−328131.	−	568340.i	−0.587374	−	1.01736i	−0.994575	−	0.104023i	$-0.966828\pi$
$199$	−328131.	−	568340.i	−0.587374	−	1.01736i	0.407201	−	0.913339i	$-0.366505\pi$
$200$		0			0
$201$	13474.4	−	23338.4i	0.0235245	−	0.0407456i
$202$		0			0
$203$	−341881.	−	80123.4i	−0.582283	−	0.136464i
$204$		0			0
$205$	181832.	−	314943.i	0.302194	−	0.523416i
$206$		0			0
$207$	−15572.6	−	26972.5i	−0.0252601	−	0.0437518i
$208$		0			0
$209$	1.51991e6			2.40687
$210$		0			0
$211$	−910993.			−1.40867			−0.704334	−	0.709869i	$-0.748754\pi$
$211$	−910993.			−1.40867			−0.704334	+	0.709869i	$0.748754\pi$
$212$		0			0
$213$	−337168.	−	583993.i	−0.509211	−	0.881979i
$214$		0			0
$215$	−206290.	+	357304.i	−0.304356	+	0.527159i
$216$		0			0
$217$	−46167.1	−	152815.i	−0.0665554	−	0.220301i
$218$		0			0
$219$	−115560.	+	200156.i	−0.162816	+	0.282006i
$220$		0			0
$221$	−289361.	−	501188.i	−0.398528	−	0.690272i
$222$		0			0
$223$	−308436.			−0.415339			−0.207669	−	0.978199i	$-0.566588\pi$
$223$	−308436.			−0.415339			−0.207669	+	0.978199i	$0.566588\pi$
$224$		0			0
$225$	−223476.			−0.294289
$226$		0			0
$227$	−695369.	−	1.20441e6i	−0.895675	−	1.55135i	−0.832967	−	0.553323i	$-0.813360\pi$
$227$	−695369.	−	1.20441e6i	−0.895675	−	1.55135i	−0.0627082	−	0.998032i	$-0.519974\pi$
$228$		0			0
$229$	−204120.	+	353546.i	−0.257215	+	0.445510i	−0.965495	−	0.260422i	$-0.916138\pi$
$229$	−204120.	+	353546.i	−0.257215	+	0.445510i	0.708280	+	0.705932i	$0.249472\pi$
$230$		0			0
$231$	504916.	−	537872.i	0.622572	−	0.663207i
$232$		0			0
$233$	−281596.	+	487739.i	−0.339811	+	0.588570i	−0.984397	−	0.175962i	$-0.943696\pi$
$233$	−281596.	+	487739.i	−0.339811	+	0.588570i	0.644586	+	0.764532i	$0.277030\pi$
$234$		0			0
$235$	90291.9	+	156390.i	0.106654	+	0.184731i
$236$		0			0
$237$	684961.			0.792127
$238$		0			0
$239$	1.27512e6			1.44396			0.721982	−	0.691912i	$-0.243231\pi$
$239$	1.27512e6			1.44396			0.721982	+	0.691912i	$0.243231\pi$
$240$		0			0
$241$	483605.	+	837628.i	0.536350	+	0.928985i	0.999097	+	0.0424946i	$0.0135305\pi$
$241$	483605.	+	837628.i	0.536350	+	0.928985i	−0.462747	+	0.886490i	$0.653136\pi$
$242$		0			0
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$		0			0
$245$	267766.	−	178040.i	0.284997	−	0.189497i
$246$		0			0
$247$	752922.	−	1.30410e6i	0.785250	−	1.36009i
$248$		0			0
$249$	18265.8	+	31637.3i	0.0186698	+	0.0323371i
$250$		0			0
$251$	667056.			0.668310			0.334155	−	0.942518i	$-0.391549\pi$
$251$	667056.			0.668310			0.334155	+	0.942518i	$0.391549\pi$
$252$		0			0
$253$	243118.			0.238790
$254$		0			0
$255$	79537.8	+	137763.i	0.0765990	+	0.132673i
$256$		0			0
$257$	851312.	−	1.47452e6i	0.804000	−	1.39257i	−0.112964	−	0.993599i	$-0.536035\pi$
$257$	851312.	−	1.47452e6i	0.804000	−	1.39257i	0.916964	−	0.398969i	$-0.130632\pi$
$258$		0			0
$259$	−300188.	+	319782.i	−0.278064	+	0.296213i
$260$		0			0
$261$	109697.	−	190001.i	0.0996768	−	0.172645i
$262$		0			0
$263$	494441.	+	856397.i	0.440783	+	0.763459i	0.997748	−	0.0670774i	$-0.0213675\pi$
$263$	494441.	+	856397.i	0.440783	+	0.763459i	−0.556965	+	0.830536i	$0.688034\pi$
$264$		0			0
$265$	439086.			0.384092
$266$		0			0
$267$	−1.00808e6			−0.865403
$268$		0			0
$269$	626486.	+	1.08511e6i	0.527875	+	0.914306i	0.999472	+	0.0324917i	$0.0103442\pi$
$269$	626486.	+	1.08511e6i	0.527875	+	0.914306i	−0.471597	+	0.881814i	$0.656322\pi$
$270$		0			0
$271$	−358370.	+	620716.i	−0.296421	+	0.513416i	−0.975314	−	0.220821i	$-0.929126\pi$
$271$	−358370.	+	620716.i	−0.296421	+	0.513416i	0.678893	+	0.734237i	$0.262460\pi$
$272$		0			0
$273$	−211378.	−	699671.i	−0.171654	−	0.568181i
$274$		0			0
$275$	872220.	−	1.51073e6i	0.695496	−	1.20463i
$276$		0			0
$277$	−117008.	−	202664.i	−0.0916253	−	0.158700i	0.816570	−	0.577247i	$-0.195873\pi$
$277$	−117008.	−	202664.i	−0.0916253	−	0.158700i	−0.908195	+	0.418547i	$0.862540\pi$
$278$		0			0
$279$	99740.6			0.0767117
$280$		0			0
$281$	−350221.			−0.264592			−0.132296	−	0.991210i	$-0.542235\pi$
$281$	−350221.			−0.264592			−0.132296	+	0.991210i	$0.542235\pi$
$282$		0			0
$283$	−129044.	−	223510.i	−0.0957790	−	0.165894i	0.814154	−	0.580648i	$-0.197201\pi$
$283$	−129044.	−	223510.i	−0.0957790	−	0.165894i	−0.909933	+	0.414754i	$0.863868\pi$
$284$		0			0
$285$	−206959.	+	358463.i	−0.150929	+	0.261416i
$286$		0			0
$287$	2.39923e6	+	562285.i	1.71936	+	0.402951i
$288$		0			0
$289$	283187.	−	490493.i	0.199447	−	0.345453i
$290$		0			0
$291$	−452371.	−	783530.i	−0.313157	−	0.542405i
$292$		0			0
$293$	989248.			0.673187			0.336594	−	0.941650i	$-0.390725\pi$
$293$	989248.			0.673187			0.336594	+	0.941650i	$0.390725\pi$
$294$		0			0
$295$	213222.			0.142652
$296$		0			0
$297$	230467.	+	399180.i	0.151606	+	0.262590i
$298$		0			0
$299$	120434.	−	208597.i	0.0779059	−	0.134937i
$300$		0			0
$301$	−2.72194e6	−	637916.i	−1.73166	−	0.405833i
$302$		0			0
$303$	313441.	−	542896.i	0.196132	−	0.339711i
$304$		0			0
$305$	320327.	+	554823.i	0.197172	+	0.341511i
$306$		0			0
$307$	864946.			0.523773			0.261886	−	0.965099i	$-0.415655\pi$
$307$	864946.			0.523773			0.261886	+	0.965099i	$0.415655\pi$
$308$		0			0
$309$	−1.16123e6			−0.691864
$310$		0			0
$311$	441957.	+	765492.i	0.259107	+	0.448786i	0.966003	−	0.258531i	$-0.0832385\pi$
$311$	441957.	+	765492.i	0.259107	+	0.448786i	−0.706896	+	0.707317i	$0.749905\pi$
$312$		0			0
$313$	1.56263e6	−	2.70655e6i	0.901560	−	1.56155i	0.0760912	−	0.997101i	$-0.475756\pi$
$313$	1.56263e6	−	2.70655e6i	0.901560	−	1.56155i	0.825469	−	0.564447i	$-0.190911\pi$
$314$		0			0
$315$	58102.4	+	192321.i	0.0329927	+	0.109207i
$316$		0			0
$317$	−277957.	+	481435.i	−0.155356	+	0.269085i	−0.933189	−	0.359387i	$-0.882986\pi$
$317$	−277957.	+	481435.i	−0.155356	+	0.269085i	0.777832	+	0.628472i	$0.216319\pi$
$318$		0			0
$319$	856289.	+	1.48314e6i	0.471133	+	0.816027i
$320$		0			0
$321$	−638349.			−0.345777
$322$		0			0
$323$	−2.22078e6			−1.18440
$324$		0			0
$325$	−864148.	−	1.49675e6i	−0.453816	−	0.786032i
$326$		0			0
$327$	−84595.4	+	146524.i	−0.0437499	+	0.0757771i
$328$		0			0
$329$	−837494.	+	892158.i	−0.426572	+	0.454414i
$330$		0			0
$331$	70822.5	−	122668.i	0.0355305	−	0.0615407i	−0.847713	−	0.530455i	$-0.822021\pi$
$331$	70822.5	−	122668.i	0.0355305	−	0.0615407i	0.883244	+	0.468914i	$0.155355\pi$
$332$		0			0
$333$	−137019.	−	237325.i	−0.0677130	−	0.117282i
$334$		0			0
$335$	−57287.7			−0.0278901
$336$		0			0
$337$	−1.32051e6			−0.633384			−0.316692	−	0.948528i	$-0.602572\pi$
$337$	−1.32051e6			−0.633384			−0.316692	+	0.948528i	$0.602572\pi$
$338$		0			0
$339$	−677527.	−	1.17351e6i	−0.320204	−	0.554610i
$340$		0			0
$341$	−389285.	+	674261.i	−0.181293	+	0.314009i
$342$		0			0
$343$	1.67960e6	+	1.38798e6i	0.770852	+	0.637014i
$344$		0			0
$345$	−33104.1	+	57338.0i	−0.0149739	+	0.0259355i
$346$		0			0
$347$	1.40059e6	+	2.42589e6i	0.624434	+	1.08155i	0.988650	+	0.150237i	$0.0480036\pi$
$347$	1.40059e6	+	2.42589e6i	0.624434	+	1.08155i	−0.364216	+	0.931314i	$0.618663\pi$
$348$		0			0
$349$	152194.			0.0668857			0.0334428	−	0.999441i	$-0.489353\pi$
$349$	152194.			0.0668857			0.0334428	+	0.999441i	$0.489353\pi$
$350$		0			0
$351$	456667.			0.197848
$352$		0			0
$353$	1.18661e6	+	2.05527e6i	0.506841	+	0.877875i	0.999969	+	0.00791770i	$0.00252031\pi$
$353$	1.18661e6	+	2.05527e6i	0.506841	+	0.877875i	−0.493127	+	0.869957i	$0.664146\pi$
$354$		0			0
$355$	−716750.	+	1.24145e6i	−0.301854	+	0.522826i
$356$		0			0
$357$	−737745.	+	785899.i	−0.306363	+	0.326359i
$358$		0			0
$359$	746669.	−	1.29327e6i	0.305768	−	0.529605i	−0.671664	−	0.740856i	$-0.734420\pi$
$359$	746669.	−	1.29327e6i	0.305768	−	0.529605i	0.977432	+	0.211250i	$0.0677535\pi$
$360$		0			0
$361$	−1.65121e6	−	2.85997e6i	−0.666858	−	1.15503i
$362$		0			0
$363$	−2.14856e6			−0.855817
$364$		0			0
$365$	491314.			0.193031
$366$		0			0
$367$	965730.	+	1.67269e6i	0.374275	+	0.648263i	0.990218	−	0.139527i	$-0.0445584\pi$
$367$	965730.	+	1.67269e6i	0.374275	+	0.648263i	−0.615943	+	0.787790i	$0.711225\pi$
$368$		0			0
$369$	−769826.	+	1.33338e6i	−0.294325	+	0.509785i
$370$		0			0
$371$	860463.	+	2.84817e6i	0.324562	+	1.07431i
$372$		0			0
$373$	−2.11238e6	+	3.65875e6i	−0.786140	+	1.36163i	0.142176	+	0.989841i	$0.454590\pi$
$373$	−2.11238e6	+	3.65875e6i	−0.786140	+	1.36163i	−0.928316	+	0.371793i	$0.878743\pi$
$374$		0			0
$375$	506577.	+	877418.i	0.186023	+	0.322202i
$376$		0			0
$377$	1.69673e6			0.614836
$378$		0			0
$379$	−3.71189e6			−1.32738			−0.663692	−	0.748006i	$-0.731012\pi$
$379$	−3.71189e6			−1.32738			−0.663692	+	0.748006i	$0.731012\pi$
$380$		0			0
$381$	1.30586e6	+	2.26181e6i	0.460875	+	0.798259i
$382$		0			0
$383$	2.12280e6	−	3.67680e6i	0.739456	−	1.28078i	−0.213284	−	0.976990i	$-0.568416\pi$
$383$	2.12280e6	−	3.67680e6i	0.739456	−	1.28078i	0.952740	−	0.303786i	$-0.0982507\pi$
$384$		0			0
$385$	−1.52689e6	−	357843.i	−0.524996	−	0.123039i
$386$		0			0
$387$	873372.	−	1.51272e6i	0.296430	−	0.513431i
$388$		0			0
$389$	−584412.	−	1.01223e6i	−0.195815	−	0.339161i	0.751353	−	0.659901i	$-0.229402\pi$
$389$	−584412.	−	1.01223e6i	−0.195815	−	0.339161i	−0.947167	+	0.320740i	$0.896068\pi$
$390$		0			0
$391$	−355225.			−0.117507
$392$		0			0
$393$	169172.			0.0552518
$394$		0			0
$395$	−728043.	−	1.26101e6i	−0.234782	−	0.406654i
$396$		0			0
$397$	1.88016e6	−	3.25654e6i	0.598713	−	1.03700i	−0.394298	−	0.918983i	$-0.629012\pi$
$397$	1.88016e6	−	3.25654e6i	0.598713	−	1.03700i	0.993011	−	0.118019i	$-0.0376545\pi$
$398$		0			0
$399$	−2.73077e6	−	639985.i	−0.858722	−	0.201251i
$400$		0			0
$401$	68122.3	−	117991.i	0.0211557	−	0.0366428i	−0.855254	−	0.518210i	$-0.826599\pi$
$401$	68122.3	−	117991.i	0.0211557	−	0.0366428i	0.876409	+	0.481567i	$0.159932\pi$
$402$		0			0
$403$	385682.	+	668021.i	0.118295	+	0.204893i
$404$		0			0
$405$	−125526.			−0.0380273
$406$		0			0
$407$	2.13913e6			0.640106
$408$		0			0
$409$	−1.44251e6	−	2.49851e6i	−0.426394	−	0.738537i	0.570155	−	0.821537i	$-0.306883\pi$
$409$	−1.44251e6	−	2.49851e6i	−0.426394	−	0.738537i	−0.996550	+	0.0830004i	$0.973550\pi$
$410$		0			0
$411$	542546.	−	939718.i	0.158428	−	0.274406i
$412$		0			0
$413$	417845.	+	1.38308e6i	0.120542	+	0.399000i
$414$		0			0
$415$	38829.3	−	67254.3i	0.0110672	−	0.0191690i
$416$		0			0
$417$	−1.76843e6	−	3.06301e6i	−0.498021	−	0.862597i
$418$		0			0
$419$	−2.99437e6			−0.833240			−0.416620	−	0.909081i	$-0.636785\pi$
$419$	−2.99437e6			−0.833240			−0.416620	+	0.909081i	$0.636785\pi$
$420$		0			0
$421$	−289582.			−0.0796281			−0.0398140	−	0.999207i	$-0.512677\pi$
$421$	−289582.			−0.0796281			−0.0398140	+	0.999207i	$0.512677\pi$
$422$		0			0
$423$	−382270.	−	662111.i	−0.103877	−	0.179920i
$424$		0			0
$425$	−1.27442e6	+	2.20736e6i	−0.342248	+	0.592791i
$426$		0			0
$427$	−2.97117e6	+	3.16510e6i	−0.788601	+	0.840073i
$428$		0			0
$429$	−1.78236e6	+	3.08714e6i	−0.467576	+	0.809865i
$430$		0			0
$431$	919056.	+	1.59185e6i	0.238314	+	0.412771i	0.960231	−	0.279208i	$-0.0900721\pi$
$431$	919056.	+	1.59185e6i	0.238314	+	0.412771i	−0.721917	+	0.691980i	$0.756739\pi$
$432$		0			0
$433$	−792550.			−0.203145			−0.101573	−	0.994828i	$-0.532387\pi$
$433$	−792550.			−0.203145			−0.101573	+	0.994828i	$0.532387\pi$
$434$		0			0
$435$	−466386.			−0.118174
$436$		0			0
$437$	−462151.	−	800469.i	−0.115766	−	0.200512i
$438$		0			0
$439$	−1.31265e6	+	2.27357e6i	−0.325077	+	0.563050i	−0.981528	−	0.191319i	$-0.938724\pi$
$439$	−1.31265e6	+	2.27357e6i	−0.325077	+	0.563050i	0.656451	+	0.754369i	$0.272057\pi$
$440$		0			0
$441$	−1.13364e6	+	753771.i	−0.277575	+	0.184562i
$442$		0			0
$443$	1.56458e6	−	2.70993e6i	0.378780	−	0.656067i	−0.612105	−	0.790777i	$-0.709677\pi$
$443$	1.56458e6	−	2.70993e6i	0.378780	−	0.656067i	0.990885	+	0.134710i	$0.0430103\pi$
$444$		0			0
$445$	1.07149e6	+	1.85587e6i	0.256500	+	0.444271i
$446$		0			0
$447$	−1.24159e6			−0.293907
$448$		0			0
$449$	2.95287e6			0.691239			0.345620	−	0.938375i	$-0.387669\pi$
$449$	2.95287e6			0.691239			0.345620	+	0.938375i	$0.387669\pi$
$450$		0			0
$451$	−6.00922e6	−	1.04083e7i	−1.39116	−	2.40956i
$452$		0			0
$453$	2.26768e6	−	3.92774e6i	0.519203	−	0.899285i
$454$		0			0
$455$	−1.06341e6	+	1.13282e6i	−0.240809	+	0.256527i
$456$		0			0
$457$	−3.24942e6	+	5.62815e6i	−0.727805	+	1.26059i	0.230005	+	0.973190i	$0.426126\pi$
$457$	−3.24942e6	+	5.62815e6i	−0.727805	+	1.26059i	−0.957809	+	0.287405i	$0.907207\pi$
$458$		0			0
$459$	−336740.	−	583251.i	−0.0746042	−	0.129218i
$460$		0			0
$461$	5.70443e6			1.25014			0.625072	−	0.780567i	$-0.285070\pi$
$461$	5.70443e6			1.25014			0.625072	+	0.780567i	$0.285070\pi$
$462$		0			0
$463$	−88200.8			−0.0191214			−0.00956071	−	0.999954i	$-0.503043\pi$
$463$	−88200.8			−0.0191214			−0.00956071	+	0.999954i	$0.503043\pi$
$464$		0			0
$465$	−106014.	−	183621.i	−0.0227369	−	0.0393814i
$466$		0			0
$467$	−2.29451e6	+	3.97421e6i	−0.486853	+	0.843254i	−0.999886	−	0.0151150i	$-0.995189\pi$
$467$	−2.29451e6	+	3.97421e6i	−0.486853	+	0.843254i	0.513033	+	0.858369i	$0.328522\pi$
$468$		0			0
$469$	−112265.	−	371601.i	−0.0235674	−	0.0780090i
$470$		0			0
$471$	−714365.	+	1.23732e6i	−0.148377	+	0.256997i
$472$		0			0
$473$	6.81749e6	+	1.18082e7i	1.40111	+	2.42679i
$474$		0			0
$475$	−6.63214e6			−1.34871
$476$		0			0
$477$	−1.85897e6			−0.374090
$478$		0			0
$479$	817814.	+	1.41649e6i	0.162860	+	0.282083i	0.935893	−	0.352283i	$-0.114595\pi$
$479$	817814.	+	1.41649e6i	0.162860	+	0.282083i	−0.773033	+	0.634366i	$0.781261\pi$
$480$		0			0
$481$	1.05967e6	−	1.83540e6i	0.208837	−	0.361716i
$482$		0			0
$483$	−436800.	−	102369.i	−0.0851952	−	0.0199664i
$484$		0			0
$485$	−961648.	+	1.66562e6i	−0.185636	+	0.321531i
$486$		0			0
$487$	4.59158e6	+	7.95284e6i	0.877282	+	1.51950i	0.854312	+	0.519761i	$0.173979\pi$
$487$	4.59158e6	+	7.95284e6i	0.877282	+	1.51950i	0.0229707	+	0.999736i	$0.492688\pi$
$488$		0			0
$489$	3.70946e6			0.701517
$490$		0			0
$491$	−8.19798e6			−1.53463			−0.767314	−	0.641271i	$-0.778407\pi$
$491$	−8.19798e6			−1.53463			−0.767314	+	0.641271i	$0.778407\pi$
$492$		0			0
$493$	−1.25115e6	−	2.16705e6i	−0.231841	−	0.401561i
$494$		0			0
$495$	489924.	−	848573.i	0.0898702	−	0.155660i
$496$		0			0
$497$	−9.45733e6	−	2.21643e6i	−1.71742	−	0.402497i
$498$		0			0
$499$	−3.38751e6	+	5.86734e6i	−0.609017	+	1.05485i	0.382386	+	0.924003i	$0.375102\pi$
$499$	−3.38751e6	+	5.86734e6i	−0.609017	+	1.05485i	−0.991403	+	0.130845i	$0.958231\pi$
$500$		0			0
$501$	1.98775e6	+	3.44288e6i	0.353808	+	0.612813i
$502$		0			0
$503$	−6.28394e6			−1.10742			−0.553710	−	0.832710i	$-0.686788\pi$
$503$	−6.28394e6			−1.10742			−0.553710	+	0.832710i	$0.686788\pi$
$504$		0			0
$505$	−1.33262e6			−0.232530
$506$		0			0
$507$	95045.2	+	164623.i	0.0164214	+	0.0284427i
$508$		0			0
$509$	1.71079e6	−	2.96317e6i	0.292686	−	0.506947i	−0.681758	−	0.731578i	$-0.738784\pi$
$509$	1.71079e6	−	2.96317e6i	0.292686	−	0.506947i	0.974444	+	0.224631i	$0.0721176\pi$
$510$		0			0
$511$	962812.	+	3.18694e6i	0.163113	+	0.539911i
$512$		0			0
$513$	876204.	−	1.51763e6i	0.146998	−	0.254608i
$514$		0			0
$515$	1.23426e6	+	2.13781e6i	0.205064	+	0.355182i
$516$		0			0
$517$	5.96796e6			0.981973
$518$		0			0
$519$	1.09073e6			0.177746
$520$		0			0
$521$	−117815.	−	204061.i	−0.0190154	−	0.0329356i	0.856361	−	0.516377i	$-0.172720\pi$
$521$	−117815.	−	204061.i	−0.0190154	−	0.0329356i	−0.875377	+	0.483442i	$0.839386\pi$
$522$		0			0
$523$	2.15285e6	−	3.72884e6i	0.344159	−	0.596100i	−0.641042	−	0.767506i	$-0.721498\pi$
$523$	2.15285e6	−	3.72884e6i	0.344159	−	0.596100i	0.985201	+	0.171406i	$0.0548308\pi$
$524$		0			0
$525$	−2.20320e6	+	2.34701e6i	−0.348864	+	0.371635i
$526$		0			0
$527$	568794.	−	985179.i	0.0892130	−	0.154521i
$528$		0			0
$529$	3.14425e6	+	5.44600e6i	0.488515	+	0.846132i
$530$		0			0
$531$	−902723.			−0.138937
$532$		0			0
$533$	−1.19072e7			−1.81548
$534$		0			0
$535$	678498.	+	1.17519e6i	0.102486	+	0.177511i
$536$		0			0
$537$	−2.14307e6	+	3.71191e6i	−0.320702	+	0.555472i
$538$		0			0
$539$	−671023.	−	1.06055e7i	−0.0994868	−	1.57239i
$540$		0			0
$541$	−1.46004e6	+	2.52887e6i	−0.214473	+	0.371478i	−0.953109	−	0.302626i	$-0.902137\pi$
$541$	−1.46004e6	+	2.52887e6i	−0.214473	+	0.371478i	0.738637	+	0.674104i	$0.235470\pi$
$542$		0			0
$543$	1.33255e6	+	2.30805e6i	0.193948	+	0.335927i
$544$		0			0
$545$	359665.			0.0518688
$546$		0			0
$547$	2.29174e6			0.327489			0.163745	−	0.986503i	$-0.447643\pi$
$547$	2.29174e6			0.327489			0.163745	+	0.986503i	$0.447643\pi$
$548$		0			0
$549$	−1.35617e6	−	2.34896e6i	−0.192037	−	0.332618i
$550$		0			0
$551$	3.25550e6	−	5.63870e6i	0.456814	−	0.791224i
$552$		0			0
$553$	6.75289e6	−	7.19366e6i	0.939025	−	1.00032i
$554$		0			0
$555$	−291275.	+	504503.i	−0.0401394	+	0.0695235i
$556$		0			0
$557$	−5.15335e6	−	8.92587e6i	−0.703805	−	1.21903i	−0.967121	−	0.254316i	$-0.918150\pi$
$557$	−5.15335e6	−	8.92587e6i	−0.703805	−	1.21903i	0.263317	−	0.964709i	$-0.415184\pi$
$558$		0			0
$559$	1.35088e7			1.82847
$560$		0			0
$561$	5.25715e6			0.705251
$562$		0			0
$563$	5.20845e6	+	9.02129e6i	0.692528	+	1.19949i	0.971007	+	0.239051i	$0.0768364\pi$
$563$	5.20845e6	+	9.02129e6i	0.692528	+	1.19949i	−0.278479	+	0.960442i	$0.589830\pi$
$564$		0			0
$565$	−1.44028e6	+	2.49464e6i	−0.189813	+	0.328766i
$566$		0			0
$567$	−245989.	−	814233.i	−0.0321335	−	0.106363i
$568$		0			0
$569$	576705.	−	998882.i	0.0746746	−	0.129340i	−0.826270	−	0.563274i	$-0.809542\pi$
$569$	576705.	−	998882.i	0.0746746	−	0.129340i	0.900945	+	0.433934i	$0.142875\pi$
$570$		0			0
$571$	−3.82936e6	−	6.63265e6i	−0.491514	−	0.851328i	0.508438	−	0.861099i	$-0.330223\pi$
$571$	−3.82936e6	−	6.63265e6i	−0.491514	−	0.851328i	−0.999952	+	0.00977096i	$0.996890\pi$
$572$		0			0
$573$	913934.			0.116286
$574$		0			0
$575$	−1.06084e6			−0.133808
$576$		0			0
$577$	2.30067e6	+	3.98488e6i	0.287683	+	0.498282i	0.973256	−	0.229722i	$-0.0737816\pi$
$577$	2.30067e6	+	3.98488e6i	0.287683	+	0.498282i	−0.685573	+	0.728004i	$0.740448\pi$
$578$		0			0
$579$	647022.	−	1.12067e6i	0.0802089	−	0.138926i
$580$		0			0
$581$	512342.	+	120073.i	0.0629680	+	0.0147572i
$582$		0			0
$583$	7.25549e6	−	1.25669e7i	0.884088	−	1.53129i
$584$		0			0
$585$	−485390.	−	840720.i	−0.0586410	−	0.101569i
$586$		0			0
$587$	−4.61040e6			−0.552260			−0.276130	−	0.961120i	$-0.589052\pi$
$587$	−4.61040e6			−0.552260			−0.276130	+	0.961120i	$0.589052\pi$
$588$		0			0
$589$	2.96002e6			0.351566
$590$		0			0
$591$	4.13569e6	+	7.16322e6i	0.487056	+	0.843606i
$592$		0			0
$593$	6.55104e6	−	1.13467e7i	0.765021	−	1.32505i	−0.175215	−	0.984530i	$-0.556062\pi$
$593$	6.55104e6	−	1.13467e7i	0.765021	−	1.32505i	0.940236	−	0.340525i	$-0.110605\pi$
$594$		0			0
$595$	2.23098e6	+	522854.i	0.258347	+	0.0605463i
$596$		0			0
$597$	2.95318e6	−	5.11506e6i	0.339121	−	0.587374i
$598$		0			0
$599$	6.77948e6	+	1.17424e7i	0.772021	+	1.33718i	0.936454	+	0.350791i	$0.114087\pi$
$599$	6.77948e6	+	1.17424e7i	0.772021	+	1.33718i	−0.164433	+	0.986388i	$0.552579\pi$
$600$		0			0
$601$	−7.77932e6			−0.878528			−0.439264	−	0.898358i	$-0.644761\pi$
$601$	−7.77932e6			−0.878528			−0.439264	+	0.898358i	$0.644761\pi$
$602$		0			0
$603$	242540.			0.0271638
$604$		0			0
$605$	2.28370e6	+	3.95548e6i	0.253659	+	0.439350i
$606$		0			0
$607$	3.65603e6	−	6.33242e6i	0.402752	−	0.697587i	−0.591305	−	0.806448i	$-0.701387\pi$
$607$	3.65603e6	−	6.33242e6i	0.402752	−	0.697587i	0.994057	+	0.108861i	$0.0347204\pi$
$608$		0			0
$609$	−913963.	−	3.02525e6i	−0.0998586	−	0.330536i
$610$		0			0
$611$	2.95636e6	−	5.12057e6i	0.320372	−	0.554901i
$612$		0			0
$613$	8.00829e6	+	1.38708e7i	0.860773	+	1.49090i	0.871184	+	0.490957i	$0.163353\pi$
$613$	8.00829e6	+	1.38708e7i	0.860773	+	1.49090i	−0.0104107	+	0.999946i	$0.503314\pi$
$614$		0			0
$615$	3.27298e6			0.348944
$616$		0			0
$617$	−1.37379e7			−1.45280			−0.726402	−	0.687270i	$-0.758809\pi$
$617$	−1.37379e7			−1.45280			−0.726402	+	0.687270i	$0.758809\pi$
$618$		0			0
$619$	−879322.	−	1.52303e6i	−0.0922404	−	0.159765i	0.816213	−	0.577751i	$-0.196069\pi$
$619$	−879322.	−	1.52303e6i	−0.0922404	−	0.159765i	−0.908454	+	0.417986i	$0.862736\pi$
$620$		0			0
$621$	140153.	−	242753.i	0.0145839	−	0.0252601i
$622$		0			0
$623$	−9.93849e6	+	1.05872e7i	−1.02589	+	1.09285i
$624$		0			0
$625$	−3.23400e6	+	5.60145e6i	−0.331162	+	0.573589i
$626$		0			0
$627$	6.83960e6	+	1.18465e7i	0.694804	+	1.20344i
$628$		0			0
$629$	−3.12554e6			−0.314991
$630$		0			0
$631$	−1.03422e7			−1.03404			−0.517022	−	0.855972i	$-0.672960\pi$
$631$	−1.03422e7			−1.03404			−0.517022	+	0.855972i	$0.672960\pi$
$632$		0			0
$633$	−4.09947e6	−	7.10049e6i	−0.406648	−	0.704334i
$634$		0			0
$635$	2.77598e6	−	4.80814e6i	0.273201	−	0.473198i
$636$		0			0
$637$	−9.43208e6	−	4.67795e6i	−0.920998	−	0.456780i
$638$		0			0
$639$	3.03452e6	−	5.25594e6i	0.293993	−	0.509211i
$640$		0			0
$641$	−1.63134e6	−	2.82557e6i	−0.156819	−	0.271619i	0.776901	−	0.629623i	$-0.216791\pi$
$641$	−1.63134e6	−	2.82557e6i	−0.156819	−	0.271619i	−0.933720	+	0.358004i	$0.883457\pi$
$642$		0			0
$643$	1.73029e7			1.65041			0.825204	−	0.564835i	$-0.191060\pi$
$643$	1.73029e7			1.65041			0.825204	+	0.564835i	$0.191060\pi$
$644$		0			0
$645$	−3.71321e6			−0.351440
$646$		0			0
$647$	−3.71276e6	−	6.43069e6i	−0.348687	−	0.603944i	0.637329	−	0.770592i	$-0.280039\pi$
$647$	−3.71276e6	−	6.43069e6i	−0.348687	−	0.603944i	−0.986017	+	0.166647i	$0.946706\pi$
$648$		0			0
$649$	3.52330e6	−	6.10254e6i	0.328351	−	0.568720i
$650$		0			0
$651$	983322.	−	1.04750e6i	0.0909376	−	0.0968731i
$652$		0			0
$653$	5.09193e6	−	8.81947e6i	0.467304	−	0.809394i	−0.531999	−	0.846745i	$-0.678559\pi$
$653$	5.09193e6	−	8.81947e6i	0.467304	−	0.809394i	0.999302	+	0.0373517i	$0.0118922\pi$
$654$		0			0
$655$	−179812.	−	311444.i	−0.0163763	−	0.0283646i
$656$		0			0
$657$	−2.08008e6			−0.188004
$658$		0			0
$659$	5.22998e6			0.469123			0.234562	−	0.972101i	$-0.424635\pi$
$659$	5.22998e6			0.469123			0.234562	+	0.972101i	$0.424635\pi$
$660$		0			0
$661$	−1.67009e6	−	2.89269e6i	−0.148675	−	0.257512i	0.782063	−	0.623199i	$-0.214167\pi$
$661$	−1.67009e6	−	2.89269e6i	−0.148675	−	0.257512i	−0.930738	+	0.365687i	$0.880834\pi$
$662$		0			0
$663$	2.60425e6	−	4.51069e6i	0.230091	−	0.398528i
$664$		0			0
$665$	1.72432e6	+	5.70755e6i	0.151204	+	0.500491i
$666$		0			0
$667$	520734.	−	901938.i	0.0453212	−	0.0784987i
$668$		0			0
$669$	−1.38796e6	−	2.40402e6i	−0.119898	−	0.207669i
$670$		0			0
$671$	2.11724e7			1.81537
$672$		0			0
$673$	2.03769e6			0.173421			0.0867103	−	0.996234i	$-0.472365\pi$
$673$	2.03769e6			0.173421			0.0867103	+	0.996234i	$0.472365\pi$
$674$		0			0
$675$	−1.00564e6	−	1.74182e6i	−0.0849540	−	0.147145i
$676$		0			0
$677$	1.06779e7	−	1.84947e7i	0.895398	−	1.55087i	0.0620863	−	0.998071i	$-0.480225\pi$
$677$	1.06779e7	−	1.84947e7i	0.895398	−	1.55087i	0.833312	−	0.552804i	$-0.186442\pi$
$678$		0			0
$679$	−1.26887e7	−	2.97373e6i	−1.05619	−	0.247530i
$680$		0			0
$681$	6.25832e6	−	1.08397e7i	0.517118	−	0.895675i
$682$		0			0
$683$	353294.	+	611923.i	0.0289791	+	0.0501932i	0.880151	−	0.474693i	$-0.157441\pi$
$683$	353294.	+	611923.i	0.0289791	+	0.0501932i	−0.851172	+	0.524887i	$0.824108\pi$
$684$		0			0
$685$	−2.30668e6			−0.187828
$686$		0			0
$687$	−3.67416e6			−0.297007
$688$		0			0
$689$	−7.18834e6	−	1.24506e7i	−0.576874	−	0.999175i
$690$		0			0
$691$	927591.	−	1.60663e6i	0.0739029	−	0.128004i	−0.826706	−	0.562634i	$-0.809788\pi$
$691$	927591.	−	1.60663e6i	0.0739029	−	0.128004i	0.900609	+	0.434631i	$0.143121\pi$
$692$		0			0
$693$	6.46442e6	+	1.51501e6i	0.511325	+	0.119834i
$694$		0			0
$695$	−3.75931e6	+	6.51132e6i	−0.295220	+	0.511337i
$696$		0			0
$697$	8.78022e6	+	1.52078e7i	0.684579	+	1.18572i
$698$		0			0
$699$	−5.06874e6			−0.392380
$700$		0			0
$701$	4.91887e6			0.378068			0.189034	−	0.981971i	$-0.439464\pi$
$701$	4.91887e6			0.378068			0.189034	+	0.981971i	$0.439464\pi$
$702$		0			0
$703$	−4.06635e6	−	7.04313e6i	−0.310325	−	0.537499i
$704$		0			0
$705$	−812627.	+	1.40751e6i	−0.0615770	+	0.106654i
$706$		0			0
$707$	−2.61150e6	−	8.64415e6i	−0.196490	−	0.650390i
$708$		0			0
$709$	1.21845e7	−	2.11042e7i	0.910317	−	1.57672i	0.0967004	−	0.995314i	$-0.469171\pi$
$709$	1.21845e7	−	2.11042e7i	0.910317	−	1.57672i	0.813617	−	0.581402i	$-0.197496\pi$
$710$		0			0
$711$	3.08233e6	+	5.33874e6i	0.228667	+	0.396064i
$712$		0			0
$713$	473471.			0.0348794
$714$		0			0
$715$	7.57785e6			0.554346
$716$		0			0
$717$	5.73804e6	+	9.93858e6i	0.416837	+	0.721982i
$718$		0			0
$719$	5.99893e6	−	1.03904e7i	0.432764	−	0.749569i	−0.564346	−	0.825538i	$-0.690872\pi$
$719$	5.99893e6	−	1.03904e7i	0.432764	−	0.749569i	0.997110	+	0.0759689i	$0.0242050\pi$
$720$		0			0
$721$	−1.14483e7	+	1.21955e7i	−0.820168	+	0.873701i
$722$		0			0
$723$	−4.35244e6	+	7.53865e6i	−0.309662	+	0.536350i
$724$		0			0
$725$	−3.73642e6	−	6.47167e6i	−0.264004	−	0.457269i
$726$		0			0
$727$	−4.39123e6			−0.308141			−0.154071	−	0.988060i	$-0.549238\pi$
$727$	−4.39123e6			−0.308141			−0.154071	+	0.988060i	$0.549238\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	−9.96120e6	−	1.72533e7i	−0.689475	−	1.19421i
$732$		0			0
$733$	36433.4	−	63104.5i	0.00250461	−	0.00433811i	−0.864770	−	0.502167i	$-0.832536\pi$
$733$	36433.4	−	63104.5i	0.00250461	−	0.00433811i	0.867275	+	0.497829i	$0.165869\pi$
$734$		0			0
$735$	2.59263e6	+	1.28585e6i	0.177020	+	0.0877952i
$736$		0			0
$737$	−946626.	+	1.63960e6i	−0.0641963	+	0.111191i
$738$		0			0
$739$	−164098.	−	284226.i	−0.0110533	−	0.0191449i	0.860446	−	0.509542i	$-0.170185\pi$
$739$	−164098.	−	284226.i	−0.0110533	−	0.0191449i	−0.871499	+	0.490397i	$0.836852\pi$
$740$		0			0
$741$	1.35526e7			0.906728
$742$		0			0
$743$	7.90142e6			0.525090			0.262545	−	0.964920i	$-0.415438\pi$
$743$	7.90142e6			0.525090			0.262545	+	0.964920i	$0.415438\pi$
$744$		0			0
$745$	1.31968e6	+	2.28576e6i	0.0871123	+	0.150883i
$746$		0			0
$747$	−164392.	+	284736.i	−0.0107790	+	0.0186698i
$748$		0			0
$749$	−6.29335e6	+	6.70412e6i	−0.409899	+	0.436654i
$750$		0			0
$751$	1.02088e7	−	1.76821e7i	0.660501	−	1.14402i	−0.319984	−	0.947423i	$-0.603677\pi$
$751$	1.02088e7	−	1.76821e7i	0.660501	−	1.14402i	0.980484	−	0.196597i	$-0.0629892\pi$
$752$		0			0
$753$	3.00175e6	+	5.19918e6i	0.192924	+	0.334155i
$754$		0			0
$755$	−9.64125e6			−0.615554
$756$		0			0
$757$	2.08381e7			1.32165			0.660827	−	0.750538i	$-0.270206\pi$
$757$	2.08381e7			1.32165			0.660827	+	0.750538i	$0.270206\pi$
$758$		0			0
$759$	1.09403e6	+	1.89491e6i	0.0689326	+	0.119395i
$760$		0			0
$761$	−1.02298e7	+	1.77186e7i	−0.640334	+	1.10909i	0.345024	+	0.938594i	$0.387871\pi$
$761$	−1.02298e7	+	1.77186e7i	−0.640334	+	1.10909i	−0.985358	+	0.170497i	$0.945463\pi$
$762$		0			0
$763$	704823.	+	2.33299e6i	0.0438297	+	0.145078i
$764$		0			0
$765$	−715840.	+	1.23987e6i	−0.0442245	+	0.0765990i
$766$		0			0
$767$	−3.49069e6	−	6.04606e6i	−0.214251	−	0.371094i
$768$		0			0
$769$	−9.31076e6			−0.567766			−0.283883	−	0.958859i	$-0.591623\pi$
$769$	−9.31076e6			−0.567766			−0.283883	+	0.958859i	$0.591623\pi$
$770$		0			0
$771$	1.53236e7			0.928379
$772$		0			0
$773$	−1.12337e7	−	1.94574e7i	−0.676199	−	1.17121i	−0.976117	−	0.217246i	$-0.930293\pi$
$773$	−1.12337e7	−	1.94574e7i	−0.676199	−	1.17121i	0.299918	−	0.953965i	$-0.403041\pi$
$774$		0			0
$775$	1.69865e6	−	2.94214e6i	0.101589	−	0.175958i
$776$		0			0
$777$	−3.84330e6	−	900718.i	−0.228377	−	0.0535225i
$778$		0			0
$779$	−2.28463e7	+	3.95709e7i	−1.34888	+	2.33632i
$780$		0			0
$781$	2.36873e7	+	4.10275e7i	1.38959	+	2.40684i
$782$		0			0
$783$	1.97455e6			0.115097
$784$		0			0
$785$	3.03718e6			0.175912
$786$		0			0
$787$	5.63605e6	+	9.76193e6i	0.324368	+	0.561822i	0.981384	−	0.192055i	$-0.0615150\pi$
$787$	5.63605e6	+	9.76193e6i	0.324368	+	0.561822i	−0.657016	+	0.753876i	$0.728182\pi$
$788$		0			0
$789$	−4.44997e6	+	7.70757e6i	−0.254486	+	0.440783i
$790$		0			0
$791$	−1.90041e7	−	4.45382e6i	−1.07996	−	0.253100i
$792$		0			0
$793$	1.04882e7	−	1.81662e7i	0.592270	−	1.02584i
$794$		0			0
$795$	1.97589e6	+	3.42234e6i	0.110878	+	0.192046i
$796$		0			0
$797$	−8.46196e6			−0.471873			−0.235937	−	0.971768i	$-0.575816\pi$
$797$	−8.46196e6			−0.471873			−0.235937	+	0.971768i	$0.575816\pi$
$798$		0			0
$799$	−8.71993e6			−0.483221
$800$		0			0
$801$	−4.53637e6	−	7.85723e6i	−0.249820	−	0.432701i
$802$		0			0
$803$	8.11851e6	−	1.40617e7i	0.444311	−	0.769570i
$804$		0			0
$805$	275813.	+	912953.i	0.0150012	+	0.0496545i
$806$		0			0
$807$	−5.63838e6	+	9.76595e6i	−0.304769	+	0.527875i
$808$		0			0
$809$	1.76577e7	+	3.05840e7i	0.948555	+	1.64294i	0.748472	+	0.663166i	$0.230788\pi$
$809$	1.76577e7	+	3.05840e7i	0.948555	+	1.64294i	0.200082	+	0.979779i	$0.435879\pi$
$810$		0			0
$811$	3.32554e7			1.77545			0.887727	−	0.460370i	$-0.152283\pi$
$811$	3.32554e7			1.77545			0.887727	+	0.460370i	$0.152283\pi$
$812$		0			0
$813$	−6.45067e6			−0.342277
$814$		0			0
$815$	−3.94277e6	−	6.82907e6i	−0.207925	−	0.360137i
$816$		0			0
$817$	2.59192e7	−	4.48934e7i	1.35852	−	2.35303i
$818$		0			0
$819$	4.50219e6	−	4.79605e6i	0.234538	−	0.249847i
$820$		0			0
$821$	2.62772e6	−	4.55134e6i	0.136057	−	0.235658i	−0.789944	−	0.613179i	$-0.789890\pi$
$821$	2.62772e6	−	4.55134e6i	0.136057	−	0.235658i	0.926001	+	0.377522i	$0.123224\pi$
$822$		0			0
$823$	−7.92558e6	−	1.37275e7i	−0.407879	−	0.706467i	0.586773	−	0.809752i	$-0.300398\pi$
$823$	−7.92558e6	−	1.37275e7i	−0.407879	−	0.706467i	−0.994652	+	0.103284i	$0.967065\pi$
$824$		0			0
$825$	1.57000e7			0.803089
$826$		0			0
$827$	−3.49430e7			−1.77663			−0.888315	−	0.459235i	$-0.848124\pi$
$827$	−3.49430e7			−1.77663			−0.888315	+	0.459235i	$0.848124\pi$
$828$		0			0
$829$	1.17919e7	+	2.04242e7i	0.595935	+	1.03219i	0.993414	+	0.114579i	$0.0365518\pi$
$829$	1.17919e7	+	2.04242e7i	0.595935	+	1.03219i	−0.397479	+	0.917611i	$0.630115\pi$
$830$		0			0
$831$	1.05307e6	−	1.82397e6i	0.0528999	−	0.0916253i
$832$		0			0
$833$	980448.	+	1.54960e7i	0.0489567	+	0.773763i
$834$		0			0
$835$	4.22554e6	−	7.31885e6i	0.209733	−	0.363268i
$836$		0			0
$837$	448833.	+	777401.i	0.0221448	+	0.0383558i
$838$		0			0
$839$	−2.44436e7			−1.19884			−0.599420	−	0.800435i	$-0.704602\pi$
$839$	−2.44436e7			−1.19884			−0.599420	+	0.800435i	$0.704602\pi$
$840$		0			0
$841$	−1.31748e7			−0.642324
$842$		0			0
$843$	−1.57599e6	−	2.72970e6i	−0.0763811	−	0.132296i
$844$		0			0
$845$	202046.	−	349955.i	0.00973440	−	0.0168605i
$846$		0			0
$847$	−2.11822e7	+	2.25648e7i	−1.01452	+	1.08074i
$848$		0			0
$849$	1.16139e6	−	2.01159e6i	0.0552980	−	0.0957790i
$850$		0			0
$851$	−650434.	−	1.12659e6i	−0.0307879	−	0.0533261i
$852$		0			0
$853$	−2.84114e7			−1.33696			−0.668481	−	0.743729i	$-0.733055\pi$
$853$	−2.84114e7			−1.33696			−0.668481	+	0.743729i	$0.733055\pi$
$854$		0			0
$855$	−3.72526e6			−0.174277
$856$		0			0
$857$	−4.94487e6	−	8.56477e6i	−0.229987	−	0.398349i	0.727817	−	0.685771i	$-0.240535\pi$
$857$	−4.94487e6	−	8.56477e6i	−0.229987	−	0.398349i	−0.957804	+	0.287422i	$0.907202\pi$
$858$		0			0
$859$	−2.49822e6	+	4.32705e6i	−0.115518	+	0.200082i	−0.917987	−	0.396612i	$-0.870186\pi$
$859$	−2.49822e6	+	4.32705e6i	−0.115518	+	0.200082i	0.802469	+	0.596694i	$0.203519\pi$
$860$		0			0
$861$	6.41396e6	+	2.12304e7i	0.294861	+	0.976002i
$862$		0			0
$863$	−2.00041e7	+	3.46482e7i	−0.914308	+	1.58363i	−0.106396	+	0.994324i	$0.533931\pi$
$863$	−2.00041e7	+	3.46482e7i	−0.914308	+	1.58363i	−0.807911	+	0.589304i	$0.799402\pi$
$864$		0			0
$865$	−1.15934e6	−	2.00803e6i	−0.0526828	−	0.0912493i
$866$		0			0
$867$	5.09736e6			0.230302
$868$		0			0
$869$	−4.81209e7			−2.16165
$870$		0			0
$871$	937865.	+	1.62443e6i	0.0418885	+	0.0725530i
$872$		0			0
$873$	4.07134e6	−	7.05177e6i	0.180802	−	0.313157i
$874$		0			0
$875$	1.42091e7	+	3.33006e6i	0.627404	+	0.147039i
$876$		0			0
$877$	−1.26956e7	+	2.19894e7i	−0.557382	+	0.965414i	0.440332	+	0.897835i	$0.354861\pi$
$877$	−1.26956e7	+	2.19894e7i	−0.557382	+	0.965414i	−0.997714	+	0.0675791i	$0.978472\pi$
$878$		0			0
$879$	4.45161e6	+	7.71042e6i	0.194332	+	0.336594i
$880$		0			0
$881$	1.65856e7			0.719930			0.359965	−	0.932966i	$-0.382789\pi$
$881$	1.65856e7			0.719930			0.359965	+	0.932966i	$0.382789\pi$
$882$		0			0
$883$	−2.74696e7			−1.18563			−0.592817	−	0.805337i	$-0.701984\pi$
$883$	−2.74696e7			−1.18563			−0.592817	+	0.805337i	$0.701984\pi$
$884$		0			0
$885$	959500.	+	1.66190e6i	0.0411801	+	0.0713260i
$886$		0			0
$887$	1.13781e7	−	1.97074e7i	0.485579	−	0.841048i	−0.514283	−	0.857620i	$-0.671942\pi$
$887$	1.13781e7	−	1.97074e7i	0.485579	−	0.841048i	0.999863	+	0.0165724i	$0.00527539\pi$
$888$		0			0
$889$	3.66284e7	+	8.58425e6i	1.55440	+	0.364291i
$890$		0			0
$891$	−2.07420e6	+	3.59262e6i	−0.0875299	+	0.151606i
$892$		0			0
$893$	−1.13447e7	−	1.96496e7i	−0.476063	−	0.824566i
$894$		0			0
$895$	9.11146e6			0.380216
$896$		0			0
$897$	2.16781e6			0.0899580
$898$		0			0
$899$	1.66762e6	+	2.88840e6i	0.0688173	+	0.119195i
$900$		0			0
$901$	−1.06012e7	+	1.83618e7i	−0.435053	+	0.753534i
$902$		0			0
$903$	−7.27667e6	−	2.40860e7i	−0.296970	−	0.982983i
$904$		0			0
$905$	2.83273e6	−	4.90643e6i	0.114970	−	0.199133i
$906$		0			0
$907$	1.85188e7	+	3.20754e7i	0.747470	+	1.29466i	0.949032	+	0.315180i	$0.102065\pi$
$907$	1.85188e7	+	3.20754e7i	0.747470	+	1.29466i	−0.201562	+	0.979476i	$0.564602\pi$
$908$		0			0
$909$	5.64194e6			0.226474
$910$		0			0
$911$	−3.66081e7			−1.46144			−0.730721	−	0.682677i	$-0.760816\pi$
$911$	−3.66081e7			−1.46144			−0.730721	+	0.682677i	$0.760816\pi$
$912$		0			0
$913$	−1.28324e6	−	2.22263e6i	−0.0509483	−	0.0882450i
$914$		0			0
$915$	−2.88295e6	+	4.99341e6i	−0.113837	+	0.197172i
$916$		0			0
$917$	1.66783e6	−	1.77669e6i	0.0654981	−	0.0697732i
$918$		0			0
$919$	−2.24693e7	+	3.89180e7i	−0.877609	+	1.52006i	−0.0236508	+	0.999720i	$0.507529\pi$
$919$	−2.24693e7	+	3.89180e7i	−0.877609	+	1.52006i	−0.853958	+	0.520342i	$0.825804\pi$
$920$		0			0
$921$	3.89226e6	+	6.74158e6i	0.151200	+	0.261886i
$922$		0			0
$923$	4.69361e7			1.81344
$924$		0			0
$925$	−9.33411e6			−0.358689
$926$		0			0
$927$	−5.22552e6	−	9.05087e6i	−0.199724	−	0.345932i
$928$		0			0
$929$	−1.86787e7	+	3.23525e7i	−0.710082	+	1.22990i	0.254744	+	0.967008i	$0.418009\pi$
$929$	−1.86787e7	+	3.23525e7i	−0.710082	+	1.22990i	−0.964826	+	0.262889i	$0.915325\pi$
$930$		0			0
$931$	−3.36434e7	+	2.23698e7i	−1.27211	+	0.845840i
$932$		0			0
$933$	−3.97761e6	+	6.88943e6i	−0.149595	+	0.259107i
$934$		0			0
$935$	−5.58781e6	−	9.67837e6i	−0.209032	−	0.362054i
$936$		0			0
$937$	−4.73101e7			−1.76037			−0.880186	−	0.474629i	$-0.842582\pi$
$937$	−4.73101e7			−1.76037			−0.880186	+	0.474629i	$0.842582\pi$
$938$		0			0
$939$	2.81273e7			1.04103
$940$		0			0
$941$	−6.32640e6	−	1.09577e7i	−0.232907	−	0.403407i	0.725755	−	0.687953i	$-0.241490\pi$
$941$	−6.32640e6	−	1.09577e7i	−0.232907	−	0.403407i	−0.958662	+	0.284546i	$0.908157\pi$
$942$		0			0
$943$	−3.65438e6	+	6.32957e6i	−0.133824	+	0.231790i
$944$		0			0
$945$	−1.23753e6	+	1.31831e6i	−0.0450794	+	0.0480217i
$946$		0			0
$947$	8.72722e6	−	1.51160e7i	0.316229	−	0.547724i	−0.663469	−	0.748203i	$-0.730917\pi$
$947$	8.72722e6	−	1.51160e7i	0.316229	−	0.547724i	0.979698	+	0.200480i	$0.0642500\pi$
$948$		0			0
$949$	−8.04337e6	−	1.39315e7i	−0.289916	−	0.502150i
$950$		0			0
$951$	−5.00322e6			−0.179390
$952$		0			0
$953$	−6.91288e6			−0.246562			−0.123281	−	0.992372i	$-0.539342\pi$
$953$	−6.91288e6			−0.246562			−0.123281	+	0.992372i	$0.539342\pi$
$954$		0			0
$955$	−971417.	−	1.68254e6i	−0.0344665	−	0.0596978i
$956$		0			0
$957$	−7.70660e6	+	1.33482e7i	−0.272009	+	0.471133i
$958$		0			0
$959$	−4.52033e6	−	1.49625e7i	−0.158717	−	0.525359i
$960$		0			0
$961$	1.35564e7	−	2.34805e7i	0.473519	−	0.820159i
$962$		0			0
$963$	−2.87257e6	−	4.97544e6i	−0.0998171	−	0.172888i
$964$		0			0
$965$	−2.75087e6			−0.0950937
$966$		0			0
$967$	2.17201e7			0.746958			0.373479	−	0.927639i	$-0.378165\pi$
$967$	2.17201e7			0.746958			0.373479	+	0.927639i	$0.378165\pi$
$968$		0			0
$969$	−9.99351e6	−	1.73093e7i	−0.341908	−	0.592201i
$970$		0			0
$971$	2.31666e7	−	4.01258e7i	0.788524	−	1.36576i	−0.138347	−	0.990384i	$-0.544179\pi$
$971$	2.31666e7	−	4.01258e7i	0.788524	−	1.36576i	0.926871	−	0.375379i	$-0.122488\pi$
$972$		0			0
$973$	−4.96031e7	−	1.16250e7i	−1.67968	−	0.393651i
$974$		0			0
$975$	7.77733e6	−	1.34707e7i	0.262011	−	0.453816i
$976$		0			0
$977$	−1.48575e7	−	2.57339e7i	−0.497976	−	0.862520i	0.502021	−	0.864855i	$-0.332590\pi$
$977$	−1.48575e7	−	2.57339e7i	−0.497976	−	0.862520i	−0.999997	+	0.00233515i	$0.999257\pi$
$978$		0			0
$979$	7.08214e7			2.36161
$980$		0			0
$981$	−1.52272e6			−0.0505181
$982$		0			0
$983$	1.53252e7	+	2.65440e7i	0.505849	+	0.876157i	0.999977	+	0.00676744i	$0.00215416\pi$
$983$	1.53252e7	+	2.65440e7i	0.505849	+	0.876157i	−0.494128	+	0.869389i	$0.664513\pi$
$984$		0			0
$985$	8.79161e6	−	1.52275e7i	0.288721	−	0.500079i
$986$		0			0
$987$	−1.07224e7	−	2.51291e6i	−0.350348	−	0.0821078i
$988$		0			0
$989$	4.14591e6	−	7.18093e6i	0.134781	−	0.233448i
$990$		0			0
$991$	−1.17648e7	−	2.03772e7i	−0.380539	−	0.659113i	0.610600	−	0.791939i	$-0.290928\pi$
$991$	−1.17648e7	−	2.03772e7i	−0.380539	−	0.659113i	−0.991139	+	0.132826i	$0.957595\pi$
$992$		0			0
$993$	1.27481e6			0.0410271
$994$		0			0
$995$	−1.25557e7			−0.402053
$996$		0			0
$997$	−2.39948e7	−	4.15601e7i	−0.764502	−	1.32416i	−0.940510	−	0.339767i	$-0.889652\pi$
$997$	−2.39948e7	−	4.15601e7i	−0.764502	−	1.32416i	0.176008	−	0.984389i	$-0.443682\pi$
$998$		0			0
$999$	1.23318e6	−	2.13592e6i	0.0390941	−	0.0677130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.m.289.3		10
4.3	odd	2		168.6.q.b.121.3	yes	10
7.4	even	3	inner	336.6.q.m.193.3		10
12.11	even	2		504.6.s.e.289.3		10
28.11	odd	6		168.6.q.b.25.3	✓	10
84.11	even	6		504.6.s.e.361.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.6.q.b.25.3	✓	10	28.11	odd	6
168.6.q.b.121.3	yes	10	4.3	odd	2
336.6.q.m.193.3		10	7.4	even	3	inner
336.6.q.m.289.3		10	1.1	even	1	trivial
504.6.s.e.289.3		10	12.11	even	2
504.6.s.e.361.3		10	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.50000 + 7.79423i) q^{3} +(9.56607 - 16.5689i) q^{5} +(126.222 + 29.5814i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.50000 + 7.79423i) q^{3} +(9.56607 - 16.5689i) q^{5} +(126.222 + 29.5814i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-316.141 - 547.572i) q^{11} -626.430 q^{13} +172.189 q^{15} +(461.921 + 800.071i) q^{17} +(-1201.93 + 2081.80i) q^{19} +(337.434 + 1116.92i) q^{21} +(-192.254 + 332.994i) q^{23} +(1379.48 + 2389.33i) q^{25} -729.000 q^{27} -2708.57 q^{29} +(-615.683 - 1066.39i) q^{31} +(2845.27 - 4928.15i) q^{33} +(1697.58 - 1808.38i) q^{35} +(-1691.60 + 2929.93i) q^{37} +(-2818.93 - 4882.54i) q^{39} +19008.0 q^{41} -21564.7 q^{43} +(774.851 + 1342.08i) q^{45} +(-4719.39 + 8174.22i) q^{47} +(15056.9 + 7467.64i) q^{49} +(-4157.29 + 7200.64i) q^{51} +(11475.1 + 19875.5i) q^{53} -12096.9 q^{55} -21634.7 q^{57} +(5572.36 + 9651.61i) q^{59} +(-16742.9 + 28999.5i) q^{61} +(-7187.06 + 7656.17i) q^{63} +(-5992.47 + 10379.3i) q^{65} +(-1497.16 - 2593.16i) q^{67} -3460.58 q^{69} -74926.3 q^{71} +(12840.0 + 22239.6i) q^{73} +(-12415.3 + 21504.0i) q^{75} +(-23705.9 - 78467.4i) q^{77} +(38053.4 - 65910.4i) q^{79} +(-3280.50 - 5681.99i) q^{81} +4059.07 q^{83} +17675.1 q^{85} +(-12188.6 - 21111.2i) q^{87} +(-56004.6 + 97002.9i) q^{89} +(-79069.1 - 18530.7i) q^{91} +(5541.14 - 9597.54i) q^{93} +(22995.4 + 39829.2i) q^{95} -100527. q^{97} +51214.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 45 q^{3} - 75 q^{5} + 113 q^{7} - 405 q^{9}+O(q^{10}) \) 10 * q + 45 * q^3 - 75 * q^5 + 113 * q^7 - 405 * q^9	\( 10 q + 45 q^{3} - 75 q^{5} + 113 q^{7} - 405 q^{9} - 91 q^{11} + 580 q^{13} - 1350 q^{15} - 1128 q^{17} - 282 q^{19} + 279 q^{21} + 1808 q^{23} - 202 q^{25} - 7290 q^{27} + 5026 q^{29} + 5069 q^{31} + 819 q^{33} + 884 q^{35} - 5010 q^{37} + 2610 q^{39} + 12872 q^{41} - 17328 q^{43} - 6075 q^{45} + 50 q^{47} + 29135 q^{49} + 10152 q^{51} + 1167 q^{53} - 97410 q^{55} - 5076 q^{57} + 42797 q^{59} - 26546 q^{61} - 6642 q^{63} - 2216 q^{65} + 13440 q^{67} + 32544 q^{69} + 39356 q^{71} - 27768 q^{73} + 1818 q^{75} + 125797 q^{77} + 123369 q^{79} - 32805 q^{81} - 334250 q^{83} - 324936 q^{85} + 22617 q^{87} - 59350 q^{89} - 113850 q^{91} - 45621 q^{93} - 41864 q^{95} + 525282 q^{97} + 14742 q^{99}+O(q^{100}) \) 10 * q + 45 * q^3 - 75 * q^5 + 113 * q^7 - 405 * q^9 - 91 * q^11 + 580 * q^13 - 1350 * q^15 - 1128 * q^17 - 282 * q^19 + 279 * q^21 + 1808 * q^23 - 202 * q^25 - 7290 * q^27 + 5026 * q^29 + 5069 * q^31 + 819 * q^33 + 884 * q^35 - 5010 * q^37 + 2610 * q^39 + 12872 * q^41 - 17328 * q^43 - 6075 * q^45 + 50 * q^47 + 29135 * q^49 + 10152 * q^51 + 1167 * q^53 - 97410 * q^55 - 5076 * q^57 + 42797 * q^59 - 26546 * q^61 - 6642 * q^63 - 2216 * q^65 + 13440 * q^67 + 32544 * q^69 + 39356 * q^71 - 27768 * q^73 + 1818 * q^75 + 125797 * q^77 + 123369 * q^79 - 32805 * q^81 - 334250 * q^83 - 324936 * q^85 + 22617 * q^87 - 59350 * q^89 - 113850 * q^91 - 45621 * q^93 - 41864 * q^95 + 525282 * q^97 + 14742 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more