LMFDB - Embedded newform 336.6.q.m.193.5

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			193.5
Root			$-4.79197 + 8.29994i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.6.q.m.289.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.50000 - 7.79423i) q^{3} +(22.2576 + 38.5514i) q^{5} +(8.29943 + 129.376i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(4.50000 - 7.79423i) q^{3} +(22.2576 + 38.5514i) q^{5} +(8.29943 + 129.376i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(131.614 - 227.962i) q^{11} -208.220 q^{13} +400.637 q^{15} +(-750.577 + 1300.04i) q^{17} +(567.347 + 982.673i) q^{19} +(1045.73 + 517.504i) q^{21} +(609.477 + 1055.64i) q^{23} +(571.695 - 990.205i) q^{25} -729.000 q^{27} -350.738 q^{29} +(-2181.24 + 3778.02i) q^{31} +(-1184.53 - 2051.66i) q^{33} +(-4802.89 + 3199.56i) q^{35} +(-6436.97 - 11149.2i) q^{37} +(-936.992 + 1622.92i) q^{39} -18581.8 q^{41} -268.381 q^{43} +(1802.87 - 3122.66i) q^{45} +(4850.78 + 8401.80i) q^{47} +(-16669.2 + 2147.49i) q^{49} +(6755.19 + 11700.3i) q^{51} +(7861.76 - 13617.0i) q^{53} +11717.7 q^{55} +10212.2 q^{57} +(-16752.8 + 29016.7i) q^{59} +(-866.770 - 1501.29i) q^{61} +(8739.34 - 5821.91i) q^{63} +(-4634.50 - 8027.18i) q^{65} +(-16991.4 + 29430.0i) q^{67} +10970.6 q^{69} +15371.3 q^{71} +(-38204.0 + 66171.3i) q^{73} +(-5145.26 - 8911.85i) q^{75} +(30585.1 + 15135.7i) q^{77} +(41761.4 + 72333.0i) q^{79} +(-3280.50 + 5681.99i) q^{81} -14703.1 q^{83} -66824.3 q^{85} +(-1578.32 + 2733.73i) q^{87} +(13261.5 + 22969.6i) q^{89} +(-1728.11 - 26938.7i) q^{91} +(19631.2 + 34002.2i) q^{93} +(-25255.6 + 43744.0i) q^{95} -23955.2 q^{97} -21321.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	22.2576	+	38.5514i	0.398157	+	0.689628i	0.993499	−	0.113845i	$-0.0363167\pi$
$5$	22.2576	+	38.5514i	0.398157	+	0.689628i	−0.595342	+	0.803473i	$0.702983\pi$
$6$		0			0
$7$	8.29943	+	129.376i	0.0640182	+	0.997949i
$7$	8.29943	+	129.376i	0.0640182	+	0.997949i
$8$		0			0
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$		0			0
$11$	131.614	−	227.962i	0.327960	−	0.568043i	−0.654147	−	0.756367i	$-0.726972\pi$
$11$	131.614	−	227.962i	0.327960	−	0.568043i	0.982107	+	0.188324i	$0.0603057\pi$
$12$		0			0
$13$	−208.220			−0.341716			−0.170858	−	0.985296i	$-0.554654\pi$
$13$	−208.220			−0.341716			−0.170858	+	0.985296i	$0.554654\pi$
$14$		0			0
$15$	400.637			0.459752
$16$		0			0
$17$	−750.577	+	1300.04i	−0.629902	+	1.09102i	0.357669	+	0.933848i	$0.383572\pi$
$17$	−750.577	+	1300.04i	−0.629902	+	1.09102i	−0.987571	+	0.157174i	$0.949762\pi$
$18$		0			0
$19$	567.347	+	982.673i	0.360549	+	0.624490i	0.988051	−	0.154125i	$-0.0492559\pi$
$19$	567.347	+	982.673i	0.360549	+	0.624490i	−0.627502	+	0.778615i	$0.715923\pi$
$20$		0			0
$21$	1045.73	+	517.504i	0.517455	+	0.256074i
$22$		0			0
$23$	609.477	+	1055.64i	0.240236	+	0.416100i	0.960781	−	0.277307i	$-0.0894419\pi$
$23$	609.477	+	1055.64i	0.240236	+	0.416100i	−0.720546	+	0.693407i	$0.756109\pi$
$24$		0			0
$25$	571.695	−	990.205i	0.182942	−	0.316866i
$26$		0			0
$27$	−729.000			−0.192450
$28$		0			0
$29$	−350.738			−0.0774440			−0.0387220	−	0.999250i	$-0.512329\pi$
$29$	−350.738			−0.0774440			−0.0387220	+	0.999250i	$0.512329\pi$
$30$		0			0
$31$	−2181.24	+	3778.02i	−0.407662	+	0.706091i	−0.994627	−	0.103521i	$-0.966989\pi$
$31$	−2181.24	+	3778.02i	−0.407662	+	0.706091i	0.586966	+	0.809612i	$0.300322\pi$
$32$		0			0
$33$	−1184.53	−	2051.66i	−0.189348	−	0.327960i
$34$		0			0
$35$	−4802.89	+	3199.56i	−0.662724	+	0.441489i
$36$		0			0
$37$	−6436.97	−	11149.2i	−0.772996	−	1.33887i	−0.935914	−	0.352229i	$-0.885424\pi$
$37$	−6436.97	−	11149.2i	−0.772996	−	1.33887i	0.162918	−	0.986640i	$-0.447909\pi$
$38$		0			0
$39$	−936.992	+	1622.92i	−0.0986449	+	0.170858i
$40$		0			0
$41$	−18581.8			−1.72635			−0.863176	−	0.504903i	$-0.831528\pi$
$41$	−18581.8			−1.72635			−0.863176	+	0.504903i	$0.831528\pi$
$42$		0			0
$43$	−268.381			−0.0221351			−0.0110675	−	0.999939i	$-0.503523\pi$
$43$	−268.381			−0.0221351			−0.0110675	+	0.999939i	$0.503523\pi$
$44$		0			0
$45$	1802.87	−	3122.66i	0.132719	−	0.229876i
$46$		0			0
$47$	4850.78	+	8401.80i	0.320307	+	0.554789i	0.980551	−	0.196263i	$-0.0628805\pi$
$47$	4850.78	+	8401.80i	0.320307	+	0.554789i	−0.660244	+	0.751051i	$0.729547\pi$
$48$		0			0
$49$	−16669.2	+	2147.49i	−0.991803	+	0.127774i
$50$		0			0
$51$	6755.19	+	11700.3i	0.363674	+	0.629902i
$52$		0			0
$53$	7861.76	−	13617.0i	0.384441	−	0.665872i	−0.607250	−	0.794511i	$-0.707727\pi$
$53$	7861.76	−	13617.0i	0.384441	−	0.665872i	0.991692	+	0.128639i	$0.0410608\pi$
$54$		0			0
$55$	11717.7			0.522317
$56$		0			0
$57$	10212.2			0.416326
$58$		0			0
$59$	−16752.8	+	29016.7i	−0.626553	+	1.08522i	0.361685	+	0.932300i	$0.382201\pi$
$59$	−16752.8	+	29016.7i	−0.626553	+	1.08522i	−0.988238	+	0.152921i	$0.951132\pi$
$60$		0			0
$61$	−866.770	−	1501.29i	−0.0298249	−	0.0516583i	0.850728	−	0.525607i	$-0.176162\pi$
$61$	−866.770	−	1501.29i	−0.0298249	−	0.0516583i	−0.880553	+	0.473948i	$0.842828\pi$
$62$		0			0
$63$	8739.34	−	5821.91i	0.277413	−	0.184805i
$64$		0			0
$65$	−4634.50	−	8027.18i	−0.136056	−	0.235657i
$66$		0			0
$67$	−16991.4	+	29430.0i	−0.462427	+	0.800947i	−0.999081	−	0.0428550i	$-0.986355\pi$
$67$	−16991.4	+	29430.0i	−0.462427	+	0.800947i	0.536654	+	0.843802i	$0.319688\pi$
$68$		0			0
$69$	10970.6			0.277400
$70$		0			0
$71$	15371.3			0.361880			0.180940	−	0.983494i	$-0.442086\pi$
$71$	15371.3			0.361880			0.180940	+	0.983494i	$0.442086\pi$
$72$		0			0
$73$	−38204.0	+	66171.3i	−0.839078	+	1.45333i	0.0515890	+	0.998668i	$0.483571\pi$
$73$	−38204.0	+	66171.3i	−0.839078	+	1.45333i	−0.890667	+	0.454657i	$0.849762\pi$
$74$		0			0
$75$	−5145.26	−	8911.85i	−0.105622	−	0.182942i
$76$		0			0
$77$	30585.1	+	15135.7i	0.587873	+	0.290922i
$78$		0			0
$79$	41761.4	+	72333.0i	0.752849	+	1.30397i	0.946437	+	0.322890i	$0.104654\pi$
$79$	41761.4	+	72333.0i	0.752849	+	1.30397i	−0.193588	+	0.981083i	$0.562012\pi$
$80$		0			0
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−14703.1			−0.234268			−0.117134	−	0.993116i	$-0.537371\pi$
$83$	−14703.1			−0.234268			−0.117134	+	0.993116i	$0.537371\pi$
$84$		0			0
$85$	−66824.3			−1.00320
$86$		0			0
$87$	−1578.32	+	2733.73i	−0.0223562	+	0.0387220i
$88$		0			0
$89$	13261.5	+	22969.6i	0.177467	+	0.307381i	0.941012	−	0.338373i	$-0.109876\pi$
$89$	13261.5	+	22969.6i	0.177467	+	0.307381i	−0.763545	+	0.645754i	$0.776543\pi$
$90$		0			0
$91$	−1728.11	−	26938.7i	−0.0218760	−	0.341015i
$92$		0			0
$93$	19631.2	+	34002.2i	0.235364	+	0.407662i
$94$		0			0
$95$	−25255.6	+	43744.0i	−0.287110	+	0.497289i
$96$		0			0
$97$	−23955.2			−0.258506			−0.129253	−	0.991612i	$-0.541258\pi$
$97$	−23955.2			−0.258506			−0.129253	+	0.991612i	$0.541258\pi$
$98$		0			0
$99$	−21321.5			−0.218640
$100$		0			0
$101$	−35494.3	+	61478.0i	−0.346223	+	0.599675i	−0.985575	−	0.169239i	$-0.945869\pi$
$101$	−35494.3	+	61478.0i	−0.346223	+	0.599675i	0.639352	+	0.768914i	$0.279202\pi$
$102$		0			0
$103$	−835.673	−	1447.43i	−0.00776146	−	0.0134432i	0.862119	−	0.506707i	$-0.169137\pi$
$103$	−835.673	−	1447.43i	−0.00776146	−	0.0134432i	−0.869880	+	0.493263i	$0.835804\pi$
$104$		0			0
$105$	3325.06	+	51832.8i	0.0294325	+	0.458809i
$106$		0			0
$107$	14629.8	+	25339.5i	0.123532	+	0.213963i	0.921158	−	0.389189i	$-0.127245\pi$
$107$	14629.8	+	25339.5i	0.123532	+	0.213963i	−0.797626	+	0.603152i	$0.793911\pi$
$108$		0			0
$109$	−25366.4	+	43935.9i	−0.204500	+	0.354204i	−0.949973	−	0.312331i	$-0.898890\pi$
$109$	−25366.4	+	43935.9i	−0.204500	+	0.354204i	0.745474	+	0.666535i	$0.232223\pi$
$110$		0			0
$111$	−115865.			−0.892579
$112$		0			0
$113$	76231.0			0.561611			0.280805	−	0.959765i	$-0.409398\pi$
$113$	76231.0			0.561611			0.280805	+	0.959765i	$0.409398\pi$
$114$		0			0
$115$	−27131.0	+	46992.3i	−0.191303	+	0.331346i
$116$		0			0
$117$	8432.93	+	14606.3i	0.0569526	+	0.0986449i
$118$		0			0
$119$	−174423.	−	86317.0i	−1.12911	−	0.558765i
$120$		0			0
$121$	45881.0	+	79468.2i	0.284885	+	0.493435i
$122$		0			0
$123$	−83618.3	+	144831.i	−0.498355	+	0.863176i
$124$		0			0
$125$	190009.			1.08767
$126$		0			0
$127$	22686.7			0.124814			0.0624068	−	0.998051i	$-0.480122\pi$
$127$	22686.7			0.124814			0.0624068	+	0.998051i	$0.480122\pi$
$128$		0			0
$129$	−1207.71	+	2091.82i	−0.00638984	+	0.0110675i
$130$		0			0
$131$	−135441.	−	234590.i	−0.689558	−	1.19435i	−0.971981	−	0.235060i	$-0.924471\pi$
$131$	−135441.	−	234590.i	−0.689558	−	1.19435i	0.282423	−	0.959290i	$-0.408862\pi$
$132$		0			0
$133$	−122426.	+	81556.6i	−0.600127	+	0.399788i
$134$		0			0
$135$	−16225.8	−	28103.9i	−0.0766253	−	0.132719i
$136$		0			0
$137$	−199041.	+	344749.i	−0.906026	+	1.56928i	−0.0864917	+	0.996253i	$0.527566\pi$
$137$	−199041.	+	344749.i	−0.906026	+	1.56928i	−0.819534	+	0.573030i	$0.805768\pi$
$138$		0			0
$139$	155651.			0.683306			0.341653	−	0.939826i	$-0.389013\pi$
$139$	155651.			0.683306			0.341653	+	0.939826i	$0.389013\pi$
$140$		0			0
$141$	87314.0			0.369859
$142$		0			0
$143$	−27404.7	+	47466.4i	−0.112069	+	0.194109i
$144$		0			0
$145$	−7806.60	−	13521.4i	−0.0308349	−	0.0534076i
$146$		0			0
$147$	−58273.5	+	139588.i	−0.222422	+	0.532787i
$148$		0			0
$149$	−76353.8	−	132249.i	−0.281751	−	0.488006i	0.690065	−	0.723747i	$-0.257582\pi$
$149$	−76353.8	−	132249.i	−0.281751	−	0.488006i	−0.971816	+	0.235741i	$0.924248\pi$
$150$		0			0
$151$	204779.	−	354688.i	0.730876	−	1.26591i	−0.225633	−	0.974212i	$-0.572445\pi$
$151$	204779.	−	354688.i	0.730876	−	1.26591i	0.956509	−	0.291702i	$-0.0942215\pi$
$152$		0			0
$153$	121593.			0.419935
$154$		0			0
$155$	−194197.			−0.649253
$156$		0			0
$157$	−263267.	+	455991.i	−0.852406	+	1.47641i	0.0266241	+	0.999646i	$0.491524\pi$
$157$	−263267.	+	455991.i	−0.852406	+	1.47641i	−0.879030	+	0.476766i	$0.841809\pi$
$158$		0			0
$159$	−70755.8	−	122553.i	−0.221957	−	0.384441i
$160$		0			0
$161$	−131517.	+	87612.8i	−0.399867	+	0.266381i
$162$		0			0
$163$	198694.	+	344148.i	0.585755	+	1.01456i	0.994781	+	0.102035i	$0.0325353\pi$
$163$	198694.	+	344148.i	0.585755	+	1.01456i	−0.409026	+	0.912523i	$0.634131\pi$
$164$		0			0
$165$	52729.5	−	91330.2i	0.150780	−	0.261159i
$166$		0			0
$167$	−519557.			−1.44159			−0.720795	−	0.693148i	$-0.756223\pi$
$167$	−519557.			−1.44159			−0.720795	+	0.693148i	$0.756223\pi$
$168$		0			0
$169$	−327937.			−0.883230
$170$		0			0
$171$	45955.1	−	79596.5i	0.120183	−	0.208163i
$172$		0			0
$173$	−289019.	−	500596.i	−0.734195	−	1.27166i	−0.955075	−	0.296363i	$-0.904226\pi$
$173$	−289019.	−	500596.i	−0.734195	−	1.27166i	0.220880	−	0.975301i	$-0.429107\pi$
$174$		0			0
$175$	132853.	+	65745.4i	0.327927	+	0.162282i
$176$		0			0
$177$	150775.	+	261151.i	0.361740	+	0.626553i
$178$		0			0
$179$	131661.	−	228043.i	0.307130	−	0.531966i	−0.670603	−	0.741817i	$-0.733965\pi$
$179$	131661.	−	228043.i	0.307130	−	0.531966i	0.977733	+	0.209851i	$0.0672979\pi$
$180$		0			0
$181$	456567.			1.03588			0.517938	−	0.855418i	$-0.326700\pi$
$181$	456567.			1.03588			0.517938	+	0.855418i	$0.326700\pi$
$182$		0			0
$183$	−15601.9			−0.0344389
$184$		0			0
$185$	286544.	−	496308.i	0.615547	−	1.06616i
$186$		0			0
$187$	197573.	+	342206.i	0.413165	+	0.715623i
$188$		0			0
$189$	−6050.29	−	94315.0i	−0.0123203	−	0.192055i
$190$		0			0
$191$	110601.	+	191566.i	0.219369	+	0.379958i	0.954615	−	0.297842i	$-0.0962668\pi$
$191$	110601.	+	191566.i	0.219369	+	0.379958i	−0.735246	+	0.677800i	$0.762933\pi$
$192$		0			0
$193$	139948.	−	242397.i	0.270442	−	0.468419i	−0.698533	−	0.715578i	$-0.746164\pi$
$193$	139948.	−	242397.i	0.270442	−	0.468419i	0.968975	+	0.247159i	$0.0794970\pi$
$194$		0			0
$195$	−83420.9			−0.157104
$196$		0			0
$197$	257685.			0.473068			0.236534	−	0.971623i	$-0.423989\pi$
$197$	257685.			0.473068			0.236534	+	0.971623i	$0.423989\pi$
$198$		0			0
$199$	−75572.4	+	130895.i	−0.135279	+	0.234310i	−0.925704	−	0.378249i	$-0.876526\pi$
$199$	−75572.4	+	130895.i	−0.135279	+	0.234310i	0.790425	+	0.612559i	$0.209860\pi$
$200$		0			0
$201$	152923.	+	264870.i	0.266982	+	0.462427i
$202$		0			0
$203$	−2910.93	−	45377.1i	−0.00495783	−	0.0772852i
$204$		0			0
$205$	−413588.	−	716355.i	−0.687358	−	1.19054i
$206$		0			0
$207$	49367.6	−	85507.2i	0.0800786	−	0.138700i
$208$		0			0
$209$	298683.			0.472982
$210$		0			0
$211$	1.06807e6			1.65155			0.825776	−	0.563998i	$-0.190737\pi$
$211$	1.06807e6			1.65155			0.825776	+	0.563998i	$0.190737\pi$
$212$		0			0
$213$	69170.7	−	119807.i	0.104466	−	0.180940i
$214$		0			0
$215$	−5973.53	−	10346.5i	−0.00881322	−	0.0152649i
$216$		0			0
$217$	−506888.	−	250845.i	−0.730740	−	0.361623i
$218$		0			0
$219$	343836.	+	595542.i	0.484442	+	0.839078i
$220$		0			0
$221$	156286.	−	270694.i	0.215247	−	0.372820i
$222$		0			0
$223$	587032.			0.790496			0.395248	−	0.918574i	$-0.370659\pi$
$223$	587032.			0.790496			0.395248	+	0.918574i	$0.370659\pi$
$224$		0			0
$225$	−92614.6			−0.121962
$226$		0			0
$227$	82623.5	−	143108.i	0.106424	−	0.184332i	−0.807895	−	0.589326i	$-0.799393\pi$
$227$	82623.5	−	143108.i	0.106424	−	0.184332i	0.914319	+	0.404995i	$0.132727\pi$
$228$		0			0
$229$	121458.	+	210372.i	0.153052	+	0.265094i	0.932348	−	0.361562i	$-0.117757\pi$
$229$	121458.	+	210372.i	0.153052	+	0.265094i	−0.779296	+	0.626656i	$0.784423\pi$
$230$		0			0
$231$	255604.	−	170277.i	0.315165	−	0.209955i
$232$		0			0
$233$	−456035.	−	789875.i	−0.550311	−	0.953166i	−0.998252	−	0.0591032i	$-0.981176\pi$
$233$	−456035.	−	789875.i	−0.550311	−	0.953166i	0.447941	−	0.894063i	$-0.352157\pi$
$234$		0			0
$235$	−215934.	+	374008.i	−0.255065	+	0.441786i
$236$		0			0
$237$	751706.			0.869315
$238$		0			0
$239$	−1.06926e6			−1.21085			−0.605423	−	0.795904i	$-0.706996\pi$
$239$	−1.06926e6			−1.21085			−0.605423	+	0.795904i	$0.706996\pi$
$240$		0			0
$241$	387365.	−	670936.i	0.429613	−	0.744112i	−0.567225	−	0.823563i	$-0.691983\pi$
$241$	387365.	−	670936.i	0.429613	−	0.744112i	0.996839	+	0.0794503i	$0.0253165\pi$
$242$		0			0
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−453807.	−	594824.i	−0.483009	−	0.633101i
$246$		0			0
$247$	−118133.	−	204613.i	−0.123205	−	0.213398i
$248$		0			0
$249$	−66164.0	+	114599.i	−0.0676275	+	0.117134i
$250$		0			0
$251$	1.16719e6			1.16938			0.584691	−	0.811256i	$-0.301216\pi$
$251$	1.16719e6			1.16938			0.584691	+	0.811256i	$0.301216\pi$
$252$		0			0
$253$	320863.			0.315150
$254$		0			0
$255$	−300709.	+	520844.i	−0.289599	+	0.501599i
$256$		0			0
$257$	−427023.	−	739625.i	−0.403291	−	0.698520i	0.590830	−	0.806796i	$-0.298800\pi$
$257$	−427023.	−	739625.i	−0.403291	−	0.698520i	−0.994121	+	0.108276i	$0.965467\pi$
$258$		0			0
$259$	1.38901e6	−	925321.i	1.28664	−	0.857122i
$260$		0			0
$261$	14204.9	+	24603.6i	0.0129073	+	0.0223562i
$262$		0			0
$263$	1.09823e6	−	1.90219e6i	0.979047	−	1.69576i	0.313172	−	0.949696i	$-0.398608\pi$
$263$	1.09823e6	−	1.90219e6i	0.979047	−	1.69576i	0.665875	−	0.746063i	$-0.268058\pi$
$264$		0			0
$265$	699937.			0.612272
$266$		0			0
$267$	238707.			0.204921
$268$		0			0
$269$	689235.	−	1.19379e6i	0.580746	−	1.00588i	−0.414645	−	0.909983i	$-0.636094\pi$
$269$	689235.	−	1.19379e6i	0.580746	−	1.00588i	0.995391	−	0.0958989i	$-0.0305726\pi$
$270$		0			0
$271$	−903523.	−	1.56495e6i	−0.747336	−	1.29442i	−0.949095	−	0.314989i	$-0.897999\pi$
$271$	−903523.	−	1.56495e6i	−0.747336	−	1.29442i	0.201759	−	0.979435i	$-0.435334\pi$
$272$		0			0
$273$	−217743.	−	107755.i	−0.176822	−	0.0875045i
$274$		0			0
$275$	−150486.	−	260650.i	−0.119996	−	0.207838i
$276$		0			0
$277$	−828234.	+	1.43454e6i	−0.648565	+	1.12335i	0.334901	+	0.942253i	$0.391297\pi$
$277$	−828234.	+	1.43454e6i	−0.648565	+	1.12335i	−0.983466	+	0.181094i	$0.942036\pi$
$278$		0			0
$279$	353361.			0.271774
$280$		0			0
$281$	−552799.			−0.417640			−0.208820	−	0.977954i	$-0.566962\pi$
$281$	−552799.			−0.417640			−0.208820	+	0.977954i	$0.566962\pi$
$282$		0			0
$283$	−1.10043e6	+	1.90599e6i	−0.816760	+	1.41467i	0.0912972	+	0.995824i	$0.470899\pi$
$283$	−1.10043e6	+	1.90599e6i	−0.816760	+	1.41467i	−0.908057	+	0.418846i	$0.862435\pi$
$284$		0			0
$285$	227300.	+	393696.i	0.165763	+	0.287110i
$286$		0			0
$287$	−154219.	−	2.40404e6i	−0.110518	−	1.72281i
$288$		0			0
$289$	−416803.	−	721925.i	−0.293553	−	0.508449i
$290$		0			0
$291$	−107799.	+	186713.i	−0.0746243	+	0.129253i
$292$		0			0
$293$	626936.			0.426633			0.213316	−	0.976983i	$-0.431574\pi$
$293$	626936.			0.426633			0.213316	+	0.976983i	$0.431574\pi$
$294$		0			0
$295$	−1.49151e6			−0.997865
$296$		0			0
$297$	−95946.6	+	166184.i	−0.0631159	+	0.109320i
$298$		0			0
$299$	−126906.	−	219807.i	−0.0820923	−	0.142188i
$300$		0			0
$301$	−2227.41	−	34722.0i	−0.00141705	−	0.0220897i
$302$		0			0
$303$	319449.	+	553302.i	0.199892	+	0.346223i
$304$		0			0
$305$	38584.5	−	66830.3i	0.0237500	−	0.0411362i
$306$		0			0
$307$	−1.71449e6			−1.03822			−0.519109	−	0.854708i	$-0.673736\pi$
$307$	−1.71449e6			−1.03822			−0.519109	+	0.854708i	$0.673736\pi$
$308$		0			0
$309$	−15042.1			−0.00896216
$310$		0			0
$311$	586169.	−	1.01527e6i	0.343654	−	0.595226i	−0.641454	−	0.767161i	$-0.721669\pi$
$311$	586169.	−	1.01527e6i	0.343654	−	0.595226i	0.985108	+	0.171935i	$0.0550019\pi$
$312$		0			0
$313$	1.30942e6	+	2.26798e6i	0.755470	+	1.30851i	0.945140	+	0.326665i	$0.105925\pi$
$313$	1.30942e6	+	2.26798e6i	0.755470	+	1.30851i	−0.189670	+	0.981848i	$0.560742\pi$
$314$		0			0
$315$	418960.	+	207331.i	0.237901	+	0.117730i
$316$		0			0
$317$	−242986.	−	420864.i	−0.135811	−	0.235231i	0.790096	−	0.612983i	$-0.210031\pi$
$317$	−242986.	−	420864.i	−0.135811	−	0.235231i	−0.925907	+	0.377752i	$0.876697\pi$
$318$		0			0
$319$	−46162.1	+	79955.0i	−0.0253985	+	0.0439915i
$320$		0			0
$321$	263336.			0.142642
$322$		0			0
$323$	−1.70335e6			−0.908443
$324$		0			0
$325$	−119039.	+	206181.i	−0.0625143	+	0.108278i
$326$		0			0
$327$	228298.	+	395423.i	0.118068	+	0.204500i
$328$		0			0
$329$	−1.04673e6	+	697304.i	−0.533145	+	0.355167i
$330$		0			0
$331$	1.33773e6	+	2.31702e6i	0.671120	+	1.16241i	0.977587	+	0.210532i	$0.0675196\pi$
$331$	1.33773e6	+	2.31702e6i	0.671120	+	1.16241i	−0.306467	+	0.951881i	$0.599147\pi$
$332$		0			0
$333$	−521395.	+	903082.i	−0.257665	+	0.446289i
$334$		0			0
$335$	−1.51276e6			−0.736474
$336$		0			0
$337$	3.92637e6			1.88328			0.941642	−	0.336615i	$-0.109282\pi$
$337$	3.92637e6			1.88328			0.941642	+	0.336615i	$0.109282\pi$
$338$		0			0
$339$	343039.	−	594162.i	0.162123	−	0.280805i
$340$		0			0
$341$	574164.	+	994482.i	0.267393	+	0.463138i
$342$		0			0
$343$	−416179.	−	2.13877e6i	−0.191005	−	0.981589i
$344$		0			0
$345$	244179.	+	422931.i	0.110449	+	0.191303i
$346$		0			0
$347$	717045.	−	1.24196e6i	0.319685	−	0.553711i	−0.660737	−	0.750618i	$-0.729756\pi$
$347$	717045.	−	1.24196e6i	0.319685	−	0.553711i	0.980422	+	0.196906i	$0.0630894\pi$
$348$		0			0
$349$	1.10644e6			0.486255			0.243128	−	0.969994i	$-0.421827\pi$
$349$	1.10644e6			0.486255			0.243128	+	0.969994i	$0.421827\pi$
$350$		0			0
$351$	151793.			0.0657632
$352$		0			0
$353$	513012.	−	888563.i	0.219124	−	0.379535i	−0.735416	−	0.677616i	$-0.763013\pi$
$353$	513012.	−	888563.i	0.219124	−	0.379535i	0.954541	+	0.298081i	$0.0963466\pi$
$354$		0			0
$355$	342128.	+	592583.i	0.144085	+	0.249562i
$356$		0			0
$357$	−1.45768e6	+	971065.i	−0.605328	+	0.403253i
$358$		0			0
$359$	413510.	+	716221.i	0.169336	+	0.293299i	0.938187	−	0.346130i	$-0.112504\pi$
$359$	413510.	+	716221.i	0.169336	+	0.293299i	−0.768850	+	0.639429i	$0.779171\pi$
$360$		0			0
$361$	594285.	−	1.02933e6i	0.240009	−	0.415707i
$362$		0			0
$363$	825858.			0.328957
$364$		0			0
$365$	−3.40133e6			−1.33634
$366$		0			0
$367$	−132027.	+	228677.i	−0.0511677	+	0.0886251i	−0.890475	−	0.455032i	$-0.849628\pi$
$367$	−132027.	+	228677.i	−0.0511677	+	0.0886251i	0.839307	+	0.543658i	$0.182961\pi$
$368$		0			0
$369$	752565.	+	1.30348e6i	0.287725	+	0.498355i
$370$		0			0
$371$	1.82696e6	+	904109.i	0.689117	+	0.341025i
$372$		0			0
$373$	557515.	+	965645.i	0.207484	+	0.359373i	0.950921	−	0.309433i	$-0.100139\pi$
$373$	557515.	+	965645.i	0.207484	+	0.359373i	−0.743437	+	0.668806i	$0.766806\pi$
$374$		0			0
$375$	855039.	−	1.48097e6i	0.313984	−	0.543836i
$376$		0			0
$377$	73030.9			0.0264639
$378$		0			0
$379$	−1.68943e6			−0.604145			−0.302073	−	0.953285i	$-0.597678\pi$
$379$	−1.68943e6			−0.604145			−0.302073	+	0.953285i	$0.597678\pi$
$380$		0			0
$381$	102090.	−	176825.i	0.0360306	−	0.0624068i
$382$		0			0
$383$	−1.73368e6	−	3.00282e6i	−0.603910	−	1.04600i	−0.992223	−	0.124475i	$-0.960275\pi$
$383$	−1.73368e6	−	3.00282e6i	−0.603910	−	1.04600i	0.388313	−	0.921528i	$-0.373058\pi$
$384$		0			0
$385$	97250.0	+	1.51598e6i	0.0334378	+	0.521246i
$386$		0			0
$387$	10869.4	+	18826.4i	0.00368918	+	0.00638984i
$388$		0			0
$389$	−934501.	+	1.61860e6i	−0.313116	+	0.542333i	−0.979035	−	0.203691i	$-0.934706\pi$
$389$	−934501.	+	1.61860e6i	−0.313116	+	0.542333i	0.665919	+	0.746024i	$0.268040\pi$
$390$		0			0
$391$	−1.82984e6			−0.605300
$392$		0			0
$393$	−2.43793e6			−0.796233
$394$		0			0
$395$	−1.85902e6	+	3.21992e6i	−0.599504	+	1.03837i
$396$		0			0
$397$	2.15146e6	+	3.72644e6i	0.685106	+	1.18664i	0.973403	+	0.229097i	$0.0735775\pi$
$397$	2.15146e6	+	3.72644e6i	0.685106	+	1.18664i	−0.288298	+	0.957541i	$0.593089\pi$
$398$		0			0
$399$	84755.8	+	1.32122e6i	0.0266525	+	0.415472i
$400$		0			0
$401$	−2.40533e6	−	4.16616e6i	−0.746989	−	1.29382i	−0.949260	−	0.314493i	$-0.898165\pi$
$401$	−2.40533e6	−	4.16616e6i	−0.746989	−	1.29382i	0.202271	−	0.979330i	$-0.435168\pi$
$402$		0			0
$403$	454179.	−	786662.i	0.139304	−	0.241282i
$404$		0			0
$405$	−292065.			−0.0884793
$406$		0			0
$407$	−3.38878e6			−1.01405
$408$		0			0
$409$	199699.	−	345889.i	0.0590293	−	0.102242i	−0.835001	−	0.550249i	$-0.814533\pi$
$409$	199699.	−	345889.i	0.0590293	−	0.102242i	0.894030	+	0.448007i	$0.147866\pi$
$410$		0			0
$411$	1.79137e6	+	3.10274e6i	0.523094	+	0.906026i
$412$		0			0
$413$	−3.89310e6	−	1.92659e6i	−1.12311	−	0.555794i
$414$		0			0
$415$	−327256.	−	566824.i	−0.0932755	−	0.161558i
$416$		0			0
$417$	700430.	−	1.21318e6i	0.197253	−	0.341653i
$418$		0			0
$419$	−3.24119e6			−0.901922			−0.450961	−	0.892544i	$-0.648919\pi$
$419$	−3.24119e6			−0.901922			−0.450961	+	0.892544i	$0.648919\pi$
$420$		0			0
$421$	1.17199e6			0.322268			0.161134	−	0.986933i	$-0.448485\pi$
$421$	1.17199e6			0.322268			0.161134	+	0.986933i	$0.448485\pi$
$422$		0			0
$423$	392913.	−	680546.i	0.106769	−	0.184930i
$424$		0			0
$425$	858203.	+	1.48645e6i	0.230472	+	0.399189i
$426$		0			0
$427$	187037.	−	124599.i	0.0496430	−	0.0330708i
$428$		0			0
$429$	246643.	+	427198.i	0.0647031	+	0.112069i
$430$		0			0
$431$	2.10370e6	−	3.64372e6i	0.545495	−	0.944826i	−0.453080	−	0.891470i	$-0.649675\pi$
$431$	2.10370e6	−	3.64372e6i	0.545495	−	0.944826i	0.998576	−	0.0533561i	$-0.0169918\pi$
$432$		0			0
$433$	2.35252e6			0.602994			0.301497	−	0.953467i	$-0.402514\pi$
$433$	2.35252e6			0.602994			0.301497	+	0.953467i	$0.402514\pi$
$434$		0			0
$435$	−140519.			−0.0356050
$436$		0			0
$437$	−691569.	+	1.19783e6i	−0.173234	+	0.300049i
$438$		0			0
$439$	2.79766e6	+	4.84570e6i	0.692842	+	1.20004i	0.970903	+	0.239474i	$0.0769751\pi$
$439$	2.79766e6	+	4.84570e6i	0.692842	+	1.20004i	−0.278060	+	0.960564i	$0.589692\pi$
$440$		0			0
$441$	825747.	+	1.08234e6i	0.202186	+	0.265013i
$442$		0			0
$443$	3.54479e6	+	6.13976e6i	0.858186	+	1.48642i	0.873657	+	0.486542i	$0.161742\pi$
$443$	3.54479e6	+	6.13976e6i	0.858186	+	1.48642i	−0.0154711	+	0.999880i	$0.504925\pi$
$444$		0			0
$445$	−590338.	+	1.02250e6i	−0.141319	+	0.244772i
$446$		0			0
$447$	−1.37437e6			−0.325338
$448$		0			0
$449$	−7.81355e6			−1.82908			−0.914540	−	0.404495i	$-0.867447\pi$
$449$	−7.81355e6			−1.82908			−0.914540	+	0.404495i	$0.867447\pi$
$450$		0			0
$451$	−2.44563e6	+	4.23596e6i	−0.566174	+	0.980642i
$452$		0			0
$453$	−1.84301e6	−	3.19219e6i	−0.421971	−	0.730876i
$454$		0			0
$455$	1.00006e6	−	666213.i	0.226463	−	0.150864i
$456$		0			0
$457$	−1.32148e6	−	2.28887e6i	−0.295985	−	0.512661i	0.679229	−	0.733927i	$-0.262314\pi$
$457$	−1.32148e6	−	2.28887e6i	−0.295985	−	0.512661i	−0.975213	+	0.221266i	$0.928981\pi$
$458$		0			0
$459$	547171.	−	947727.i	0.121225	−	0.209967i
$460$		0			0
$461$	5.51119e6			1.20780			0.603898	−	0.797062i	$-0.293614\pi$
$461$	5.51119e6			1.20780			0.603898	+	0.797062i	$0.293614\pi$
$462$		0			0
$463$	−263372.			−0.0570975			−0.0285488	−	0.999592i	$-0.509089\pi$
$463$	−263372.			−0.0570975			−0.0285488	+	0.999592i	$0.509089\pi$
$464$		0			0
$465$	−873888.	+	1.51362e6i	−0.187423	+	0.324626i
$466$		0			0
$467$	3.55469e6	+	6.15691e6i	0.754241	+	1.30638i	0.945751	+	0.324893i	$0.105328\pi$
$467$	3.55469e6	+	6.15691e6i	0.754241	+	1.30638i	−0.191510	+	0.981491i	$0.561338\pi$
$468$		0			0
$469$	−3.94856e6	−	1.95403e6i	−0.828908	−	0.410203i
$470$		0			0
$471$	2.36940e6	+	4.10392e6i	0.492137	+	0.852406i
$472$		0			0
$473$	−35322.7	+	61180.7i	−0.00725941	+	0.0125737i
$474$		0			0
$475$	1.29740e6			0.263839
$476$		0			0
$477$	−1.27361e6			−0.256294
$478$		0			0
$479$	435791.	−	754812.i	0.0867839	−	0.150314i	−0.819366	−	0.573271i	$-0.805674\pi$
$479$	435791.	−	754812.i	0.0867839	−	0.150314i	0.906150	+	0.422956i	$0.139008\pi$
$480$		0			0
$481$	1.34031e6	+	2.32148e6i	0.264145	+	0.457512i
$482$		0			0
$483$	91049.6	+	1.41933e6i	0.0177587	+	0.276831i
$484$		0			0
$485$	−533187.	−	923507.i	−0.102926	−	0.178273i
$486$		0			0
$487$	−1.52122e6	+	2.63482e6i	−0.290649	+	0.503418i	−0.973963	−	0.226706i	$-0.927204\pi$
$487$	−1.52122e6	+	2.63482e6i	−0.290649	+	0.503418i	0.683315	+	0.730124i	$0.260538\pi$
$488$		0			0
$489$	3.57649e6			0.676372
$490$		0			0
$491$	4.70685e6			0.881104			0.440552	−	0.897727i	$-0.354783\pi$
$491$	4.70685e6			0.881104			0.440552	+	0.897727i	$0.354783\pi$
$492$		0			0
$493$	263256.	−	455973.i	0.0487822	−	0.0844932i
$494$		0			0
$495$	−474566.	−	821972.i	−0.0870529	−	0.150780i
$496$		0			0
$497$	127573.	+	1.98867e6i	0.0231669	+	0.361137i
$498$		0			0
$499$	4.89328e6	+	8.47541e6i	0.879729	+	1.52373i	0.851639	+	0.524129i	$0.175609\pi$
$499$	4.89328e6	+	8.47541e6i	0.879729	+	1.52373i	0.0280897	+	0.999605i	$0.491058\pi$
$500$		0			0
$501$	−2.33801e6	+	4.04955e6i	−0.416151	+	0.720795i
$502$		0			0
$503$	−5.16799e6			−0.910756			−0.455378	−	0.890298i	$-0.650496\pi$
$503$	−5.16799e6			−0.910756			−0.455378	+	0.890298i	$0.650496\pi$
$504$		0			0
$505$	−3.16008e6			−0.551403
$506$		0			0
$507$	−1.47572e6	+	2.55602e6i	−0.254967	+	0.441615i
$508$		0			0
$509$	550457.	+	953419.i	0.0941735	+	0.163113i	0.909263	−	0.416221i	$-0.136646\pi$
$509$	550457.	+	953419.i	0.0941735	+	0.163113i	−0.815090	+	0.579335i	$0.803312\pi$
$510$		0			0
$511$	−8.87805e6	−	4.39350e6i	−1.50406	−	0.744317i
$512$		0			0
$513$	−413596.	−	716369.i	−0.0693877	−	0.120183i
$514$		0			0
$515$	37200.2	−	64432.7i	0.00618055	−	0.0107050i
$516$		0			0
$517$	2.55372e6			0.420192
$518$		0			0
$519$	−5.20235e6			−0.847776
$520$		0			0
$521$	−1.16154e6	+	2.01185e6i	−0.187473	+	0.324714i	−0.944407	−	0.328778i	$-0.893363\pi$
$521$	−1.16154e6	+	2.01185e6i	−0.187473	+	0.324714i	0.756934	+	0.653492i	$0.226697\pi$
$522$		0			0
$523$	1.65323e6	+	2.86347e6i	0.264288	+	0.457761i	0.967377	−	0.253341i	$-0.0815296\pi$
$523$	1.65323e6	+	2.86347e6i	0.264288	+	0.457761i	−0.703089	+	0.711102i	$0.748196\pi$
$524$		0			0
$525$	1.11028e6	−	739636.i	0.175806	−	0.117117i
$526$		0			0
$527$	−3.27438e6	−	5.67140e6i	−0.513574	−	0.889536i
$528$		0			0
$529$	2.47525e6	−	4.28726e6i	0.384574	−	0.666101i
$530$		0			0
$531$	2.71396e6			0.417702
$532$		0			0
$533$	3.86912e6			0.589922
$534$		0			0
$535$	−651248.	+	1.12800e6i	−0.0983699	+	0.170382i
$536$		0			0
$537$	−1.18494e6	−	2.05238e6i	−0.177322	−	0.307130i
$538$		0			0
$539$	−1.70436e6	+	4.08260e6i	−0.252691	+	0.605291i
$540$		0			0
$541$	−4.63443e6	−	8.02707e6i	−0.680774	−	1.17914i	−0.974745	−	0.223321i	$-0.928310\pi$
$541$	−4.63443e6	−	8.02707e6i	−0.680774	−	1.17914i	0.293971	−	0.955814i	$-0.405023\pi$
$542$		0			0
$543$	2.05455e6	−	3.55858e6i	0.299032	−	0.517938i
$544$		0			0
$545$	−2.25838e6			−0.325692
$546$		0			0
$547$	−4.75237e6			−0.679113			−0.339557	−	0.940586i	$-0.610277\pi$
$547$	−4.75237e6			−0.679113			−0.339557	+	0.940586i	$0.610277\pi$
$548$		0			0
$549$	−70208.4	+	121605.i	−0.00994164	+	0.0172194i
$550$		0			0
$551$	−198990.	−	344661.i	−0.0279224	−	0.0483630i
$552$		0			0
$553$	−9.01154e6	+	6.00325e6i	−1.25310	+	0.834783i
$554$		0			0
$555$	−2.57889e6	−	4.46677e6i	−0.355386	−	0.615547i
$556$		0			0
$557$	4.81393e6	−	8.33797e6i	0.657449	−	1.13873i	−0.323825	−	0.946117i	$-0.604969\pi$
$557$	4.81393e6	−	8.33797e6i	0.657449	−	1.13873i	0.981274	−	0.192617i	$-0.0616976\pi$
$558$		0			0
$559$	55882.4			0.00756390
$560$		0			0
$561$	3.55631e6			0.477082
$562$		0			0
$563$	1.97613e6	−	3.42275e6i	0.262751	−	0.455098i	−0.704221	−	0.709981i	$-0.748704\pi$
$563$	1.97613e6	−	3.42275e6i	0.262751	−	0.455098i	0.966972	+	0.254883i	$0.0820370\pi$
$564$		0			0
$565$	1.69672e6	+	2.93881e6i	0.223609	+	0.387302i
$566$		0			0
$567$	−762339.	−	377260.i	−0.0995842	−	0.0492814i
$568$		0			0
$569$	1.58941e6	+	2.75295e6i	0.205805	+	0.356465i	0.950389	−	0.311064i	$-0.100685\pi$
$569$	1.58941e6	+	2.75295e6i	0.205805	+	0.356465i	−0.744584	+	0.667529i	$0.767352\pi$
$570$		0			0
$571$	7.53900e6	−	1.30579e7i	0.967662	−	1.67604i	0.265376	−	0.964145i	$-0.414504\pi$
$571$	7.53900e6	−	1.30579e7i	0.967662	−	1.67604i	0.702286	−	0.711895i	$-0.252163\pi$
$572$		0			0
$573$	1.99082e6			0.253306
$574$		0			0
$575$	1.39374e6			0.175797
$576$		0			0
$577$	−5.39207e6	+	9.33934e6i	−0.674242	+	1.16782i	0.302447	+	0.953166i	$0.402196\pi$
$577$	−5.39207e6	+	9.33934e6i	−0.674242	+	1.16782i	−0.976690	+	0.214656i	$0.931137\pi$
$578$		0			0
$579$	−1.25953e6	−	2.18157e6i	−0.156140	−	0.270442i
$580$		0			0
$581$	−122027.	−	1.90223e6i	−0.0149974	−	0.233788i
$582$		0			0
$583$	−2.06944e6	−	3.58437e6i	−0.252163	−	0.436758i
$584$		0			0
$585$	−375394.	+	650202.i	−0.0453521	+	0.0785522i
$586$		0			0
$587$	3.07522e6			0.368367			0.184183	−	0.982892i	$-0.441036\pi$
$587$	3.07522e6			0.368367			0.184183	+	0.982892i	$0.441036\pi$
$588$		0			0
$589$	−4.95008e6			−0.587928
$590$		0			0
$591$	1.15958e6	−	2.00846e6i	0.136563	−	0.236534i
$592$		0			0
$593$	2.78728e6	+	4.82772e6i	0.325495	+	0.563774i	0.981612	−	0.190885i	$-0.0611357\pi$
$593$	2.78728e6	+	4.82772e6i	0.325495	+	0.563774i	−0.656117	+	0.754659i	$0.727802\pi$
$594$		0			0
$595$	−554604.	−	8.64545e6i	−0.0642229	−	1.00114i
$596$		0			0
$597$	680152.	+	1.17806e6i	0.0781034	+	0.135279i
$598$		0			0
$599$	1.61959e6	−	2.80521e6i	0.184433	−	0.319447i	−0.758952	−	0.651146i	$-0.774289\pi$
$599$	1.61959e6	−	2.80521e6i	0.184433	−	0.319447i	0.943385	+	0.331699i	$0.107622\pi$
$600$		0			0
$601$	−1.58656e7			−1.79172			−0.895858	−	0.444340i	$-0.853438\pi$
$601$	−1.58656e7			−1.79172			−0.895858	+	0.444340i	$0.853438\pi$
$602$		0			0
$603$	2.75261e6			0.308285
$604$		0			0
$605$	−2.04241e6	+	3.53755e6i	−0.226858	+	0.392929i
$606$		0			0
$607$	−4.90510e6	−	8.49589e6i	−0.540352	−	0.935916i	−0.998884	−	0.0472386i	$-0.984958\pi$
$607$	−4.90510e6	−	8.49589e6i	−0.540352	−	0.935916i	0.458532	−	0.888678i	$-0.348375\pi$
$608$		0			0
$609$	−366778.	−	181508.i	−0.0400738	−	0.0198314i
$610$		0			0
$611$	−1.01003e6	−	1.74943e6i	−0.109454	−	0.189580i
$612$		0			0
$613$	6.49079e6	−	1.12424e7i	0.697664	−	1.20839i	−0.271611	−	0.962407i	$-0.587556\pi$
$613$	6.49079e6	−	1.12424e7i	0.697664	−	1.20839i	0.969274	−	0.245982i	$-0.0791104\pi$
$614$		0			0
$615$	−7.44458e6			−0.793693
$616$		0			0
$617$	8.80430e6			0.931069			0.465534	−	0.885030i	$-0.345862\pi$
$617$	8.80430e6			0.931069			0.465534	+	0.885030i	$0.345862\pi$
$618$		0			0
$619$	−2.44030e6	+	4.22672e6i	−0.255986	+	0.443381i	−0.965163	−	0.261650i	$-0.915733\pi$
$619$	−2.44030e6	+	4.22672e6i	−0.255986	+	0.443381i	0.709177	+	0.705031i	$0.249067\pi$
$620$		0			0
$621$	−444309.	−	769565.i	−0.0462334	−	0.0800786i
$622$		0			0
$623$	−2.86164e6	+	1.90635e6i	−0.295390	+	0.196781i
$624$		0			0
$625$	2.44259e6	+	4.23070e6i	0.250122	+	0.433223i
$626$		0			0
$627$	1.34407e6	−	2.32800e6i	0.136538	−	0.236491i
$628$		0			0
$629$	1.93258e7			1.94765
$630$		0			0
$631$	1.20644e7			1.20624			0.603120	−	0.797650i	$-0.293924\pi$
$631$	1.20644e7			1.20624			0.603120	+	0.797650i	$0.293924\pi$
$632$		0			0
$633$	4.80630e6	−	8.32476e6i	0.476762	−	0.825776i
$634$		0			0
$635$	504952.	+	874602.i	0.0496953	+	0.0860749i
$636$		0			0
$637$	3.47088e6	−	447152.i	0.338915	−	0.0436623i
$638$		0			0
$639$	−622537.	−	1.07827e6i	−0.0603133	−	0.104466i
$640$		0			0
$641$	6.18280e6	−	1.07089e7i	0.594347	−	1.02944i	−0.399292	−	0.916824i	$-0.630744\pi$
$641$	6.18280e6	−	1.07089e7i	0.594347	−	1.02944i	0.993639	−	0.112615i	$-0.0359228\pi$
$642$		0			0
$643$	1.43574e7			1.36945			0.684727	−	0.728799i	$-0.259921\pi$
$643$	1.43574e7			1.36945			0.684727	+	0.728799i	$0.259921\pi$
$644$		0			0
$645$	−107524.			−0.0101766
$646$		0			0
$647$	−220051.	+	381140.i	−0.0206663	+	0.0357952i	−0.876174	−	0.481996i	$-0.839912\pi$
$647$	−220051.	+	381140.i	−0.0206663	+	0.0357952i	0.855507	+	0.517791i	$0.173245\pi$
$648$		0			0
$649$	4.40981e6	+	7.63802e6i	0.410968	+	0.711818i
$650$		0			0
$651$	−4.23614e6	+	2.82200e6i	−0.391758	+	0.260978i
$652$		0			0
$653$	7.57819e6	+	1.31258e7i	0.695477	+	1.20460i	0.970020	+	0.243026i	$0.0781401\pi$
$653$	7.57819e6	+	1.31258e7i	0.695477	+	1.20460i	−0.274543	+	0.961575i	$0.588527\pi$
$654$		0			0
$655$	6.02918e6	−	1.04428e7i	0.549104	−	0.951077i
$656$		0			0
$657$	6.18906e6			0.559385
$658$		0			0
$659$	−1.07235e7			−0.961883			−0.480941	−	0.876753i	$-0.659705\pi$
$659$	−1.07235e7			−0.961883			−0.480941	+	0.876753i	$0.659705\pi$
$660$		0			0
$661$	2.22900e6	−	3.86075e6i	0.198430	−	0.343691i	−0.749590	−	0.661903i	$-0.769749\pi$
$661$	2.22900e6	−	3.86075e6i	0.198430	−	0.343691i	0.948019	+	0.318212i	$0.103082\pi$
$662$		0			0
$663$	−1.40657e6	−	2.43625e6i	−0.124273	−	0.215247i
$664$		0			0
$665$	−5.86902e6	−	2.90441e6i	−0.514650	−	0.254686i
$666$		0			0
$667$	−213767.	−	370255.i	−0.0186048	−	0.0322245i
$668$		0			0
$669$	2.64165e6	−	4.57546e6i	0.228197	−	0.395248i
$670$		0			0
$671$	−456316.			−0.0391255
$672$		0			0
$673$	1.73680e7			1.47813			0.739064	−	0.673635i	$-0.235268\pi$
$673$	1.73680e7			1.47813			0.739064	+	0.673635i	$0.235268\pi$
$674$		0			0
$675$	−416766.	+	721860.i	−0.0352073	+	0.0609808i
$676$		0			0
$677$	7.98147e6	+	1.38243e7i	0.669285	+	1.15924i	0.978104	+	0.208115i	$0.0667328\pi$
$677$	7.98147e6	+	1.38243e7i	0.669285	+	1.15924i	−0.308819	+	0.951121i	$0.599934\pi$
$678$		0			0
$679$	−198815.	−	3.09923e6i	−0.0165491	−	0.257976i
$680$		0			0
$681$	−743612.	−	1.28797e6i	−0.0614439	−	0.106424i
$682$		0			0
$683$	2.44780e6	−	4.23971e6i	0.200782	−	0.347764i	−0.747999	−	0.663700i	$-0.768985\pi$
$683$	2.44780e6	−	4.23971e6i	0.200782	−	0.347764i	0.948780	+	0.315936i	$0.102318\pi$
$684$		0			0
$685$	−1.77207e7			−1.44296
$686$		0			0
$687$	2.18625e6			0.176729
$688$		0			0
$689$	−1.63698e6	+	2.83533e6i	−0.131370	+	0.227539i
$690$		0			0
$691$	2.28107e6	+	3.95093e6i	0.181737	+	0.314778i	0.942472	−	0.334285i	$-0.108495\pi$
$691$	2.28107e6	+	3.95093e6i	0.181737	+	0.314778i	−0.760735	+	0.649062i	$0.775161\pi$
$692$		0			0
$693$	−176956.	−	2.75848e6i	−0.0139969	−	0.218191i
$694$		0			0
$695$	3.46443e6	+	6.00056e6i	0.272063	+	0.471227i
$696$		0			0
$697$	1.39471e7	−	2.41571e7i	1.08743	−	1.88349i
$698$		0			0
$699$	−8.20862e6			−0.635444
$700$		0			0
$701$	−1.19910e7			−0.921640			−0.460820	−	0.887494i	$-0.652445\pi$
$701$	−1.19910e7			−0.921640			−0.460820	+	0.887494i	$0.652445\pi$
$702$		0			0
$703$	7.30399e6	−	1.26509e7i	0.557406	−	0.965456i
$704$		0			0
$705$	1.94340e6	+	3.36607e6i	0.147262	+	0.255065i
$706$		0			0
$707$	−8.24835e6	−	4.08188e6i	−0.620610	−	0.307122i
$708$		0			0
$709$	−4.84550e6	−	8.39266e6i	−0.362012	−	0.627024i	0.626280	−	0.779598i	$-0.284577\pi$
$709$	−4.84550e6	−	8.39266e6i	−0.362012	−	0.627024i	−0.988292	+	0.152575i	$0.951243\pi$
$710$		0			0
$711$	3.38268e6	−	5.85897e6i	0.250950	−	0.434658i
$712$		0			0
$713$	−5.31767e6			−0.391739
$714$		0			0
$715$	−2.43986e6			−0.178484
$716$		0			0
$717$	−4.81167e6	+	8.33406e6i	−0.349541	+	0.605423i
$718$		0			0
$719$	1.29116e7	+	2.23636e7i	0.931448	+	1.61332i	0.780848	+	0.624721i	$0.214787\pi$
$719$	1.29116e7	+	2.23636e7i	0.931448	+	1.61332i	0.150600	+	0.988595i	$0.451879\pi$
$720$		0			0
$721$	180327.	−	120129.i	0.0129188	−	0.00860615i
$722$		0			0
$723$	−3.48629e6	−	6.03842e6i	−0.248037	−	0.429613i
$724$		0			0
$725$	−200515.	+	347303.i	−0.0141678	+	0.0245394i
$726$		0			0
$727$	2.52983e7			1.77523			0.887617	−	0.460582i	$-0.152359\pi$
$727$	2.52983e7			1.77523			0.887617	+	0.460582i	$0.152359\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	201441.	−	348905.i	0.0139429	−	0.0241498i
$732$		0			0
$733$	−5.07195e6	−	8.78488e6i	−0.348671	−	0.603915i	0.637343	−	0.770580i	$-0.280033\pi$
$733$	−5.07195e6	−	8.78488e6i	−0.348671	−	0.603915i	−0.986014	+	0.166665i	$0.946700\pi$
$734$		0			0
$735$	−6.67832e6	+	860366.i	−0.455983	+	0.0587442i
$736$		0			0
$737$	4.47262e6	+	7.74681e6i	0.303315	+	0.525357i
$738$		0			0
$739$	−902329.	+	1.56288e6i	−0.0607790	+	0.105272i	−0.894814	−	0.446439i	$-0.852692\pi$
$739$	−902329.	+	1.56288e6i	−0.0607790	+	0.105272i	0.834035	+	0.551712i	$0.186025\pi$
$740$		0			0
$741$	−2.12640e6			−0.142265
$742$		0			0
$743$	−2.19536e6			−0.145893			−0.0729464	−	0.997336i	$-0.523240\pi$
$743$	−2.19536e6			−0.145893			−0.0729464	+	0.997336i	$0.523240\pi$
$744$		0			0
$745$	3.39891e6	−	5.88708e6i	0.224362	−	0.388606i
$746$		0			0
$747$	595476.	+	1.03139e6i	0.0390447	+	0.0676275i
$748$		0			0
$749$	−3.15690e6	+	2.10304e6i	−0.205616	+	0.136976i
$750$		0			0
$751$	990979.	+	1.71643e6i	0.0641157	+	0.111052i	0.896301	−	0.443445i	$-0.146244\pi$
$751$	990979.	+	1.71643e6i	0.0641157	+	0.111052i	−0.832186	+	0.554497i	$0.812911\pi$
$752$		0			0
$753$	5.25234e6	−	9.09732e6i	0.337571	−	0.584691i
$754$		0			0
$755$	1.82316e7			1.16401
$756$		0			0
$757$	−1.57770e7			−1.00066			−0.500328	−	0.865836i	$-0.666787\pi$
$757$	−1.57770e7			−1.00066			−0.500328	+	0.865836i	$0.666787\pi$
$758$		0			0
$759$	1.44388e6	−	2.50088e6i	0.0909761	−	0.157575i
$760$		0			0
$761$	1.69391e6	+	2.93394e6i	0.106030	+	0.183649i	0.914159	−	0.405357i	$-0.132853\pi$
$761$	1.69391e6	+	2.93394e6i	0.106030	+	0.183649i	−0.808129	+	0.589006i	$0.799519\pi$
$762$		0			0
$763$	−5.89477e6	−	2.91716e6i	−0.366569	−	0.181405i
$764$		0			0
$765$	2.70638e6	+	4.68759e6i	0.167200	+	0.289599i
$766$		0			0
$767$	3.48828e6	−	6.04188e6i	0.214103	−	0.370837i
$768$		0			0
$769$	−1.57463e7			−0.960203			−0.480102	−	0.877213i	$-0.659400\pi$
$769$	−1.57463e7			−0.960203			−0.480102	+	0.877213i	$0.659400\pi$
$770$		0			0
$771$	−7.68641e6			−0.465680
$772$		0			0
$773$	7.92274e6	−	1.37226e7i	0.476899	−	0.826014i	−0.522750	−	0.852486i	$-0.675094\pi$
$773$	7.92274e6	−	1.37226e7i	0.476899	−	0.826014i	0.999650	+	0.0264719i	$0.00842725\pi$
$774$		0			0
$775$	2.49401e6	+	4.31976e6i	0.149157	+	0.258348i
$776$		0			0
$777$	−961618.	−	1.49902e7i	−0.0571413	−	0.890748i
$778$		0			0
$779$	−1.05424e7	−	1.82599e7i	−0.622435	−	1.07809i
$780$		0			0
$781$	2.02308e6	−	3.50407e6i	0.118682	−	0.205563i
$782$		0			0
$783$	255688.			0.0149041
$784$		0			0
$785$	−2.34388e7			−1.35757
$786$		0			0
$787$	−8.46781e6	+	1.46667e7i	−0.487343	+	0.844102i	−0.999894	−	0.0145542i	$-0.995367\pi$
$787$	−8.46781e6	+	1.46667e7i	−0.487343	+	0.844102i	0.512551	+	0.858657i	$0.328700\pi$
$788$		0			0
$789$	−9.88406e6	−	1.71197e7i	−0.565253	−	0.979047i
$790$		0			0
$791$	632674.	+	9.86245e6i	0.0359533	+	0.560459i
$792$		0			0
$793$	180479.	+	312599.i	0.0101917	+	0.0176525i
$794$		0			0
$795$	3.14972e6	−	5.45547e6i	0.176748	−	0.306136i
$796$		0			0
$797$	1.91866e7			1.06992			0.534960	−	0.844878i	$-0.320327\pi$
$797$	1.91866e7			1.06992			0.534960	+	0.844878i	$0.320327\pi$
$798$		0			0
$799$	−1.45635e7			−0.807049
$800$		0			0
$801$	1.07418e6	−	1.86053e6i	0.0591556	−	0.102460i
$802$		0			0
$803$	1.00564e7	+	1.74182e7i	0.550367	+	0.953264i
$804$		0			0
$805$	−6.30484e6	−	3.12009e6i	−0.342914	−	0.169698i
$806$		0			0
$807$	−6.20311e6	−	1.07441e7i	−0.335294	−	0.580746i
$808$		0			0
$809$	−3.88270e6	+	6.72503e6i	−0.208575	+	0.361262i	−0.951266	−	0.308372i	$-0.900216\pi$
$809$	−3.88270e6	+	6.72503e6i	−0.208575	+	0.361262i	0.742691	+	0.669634i	$0.233549\pi$
$810$		0			0
$811$	2.53666e7			1.35428			0.677141	−	0.735853i	$-0.263219\pi$
$811$	2.53666e7			1.35428			0.677141	+	0.735853i	$0.263219\pi$
$812$		0			0
$813$	−1.62634e7			−0.862949
$814$		0			0
$815$	−8.84492e6	+	1.53199e7i	−0.466445	+	0.807906i
$816$		0			0
$817$	−152265.	−	263731.i	−0.00798078	−	0.0138231i
$818$		0			0
$819$	−1.81971e6	+	1.21224e6i	−0.0947965	+	0.0631509i
$820$		0			0
$821$	9.12996e6	+	1.58136e7i	0.472728	+	0.818788i	0.999513	−	0.0312102i	$-0.00993613\pi$
$821$	9.12996e6	+	1.58136e7i	0.472728	+	0.818788i	−0.526785	+	0.849998i	$0.676603\pi$
$822$		0			0
$823$	−1.54570e7	+	2.67724e7i	−0.795476	+	1.37780i	0.127061	+	0.991895i	$0.459446\pi$
$823$	−1.54570e7	+	2.67724e7i	−0.795476	+	1.37780i	−0.922537	+	0.385909i	$0.873888\pi$
$824$		0			0
$825$	−2.70875e6			−0.138559
$826$		0			0
$827$	−1.22844e7			−0.624584			−0.312292	−	0.949986i	$-0.601097\pi$
$827$	−1.22844e7			−0.624584			−0.312292	+	0.949986i	$0.601097\pi$
$828$		0			0
$829$	−8.14441e6	+	1.41065e7i	−0.411598	+	0.712908i	−0.995065	−	0.0992286i	$-0.968362\pi$
$829$	−8.14441e6	+	1.41065e7i	−0.411598	+	0.712908i	0.583467	+	0.812137i	$0.301696\pi$
$830$		0			0
$831$	7.45411e6	+	1.29109e7i	0.374449	+	0.648565i
$832$		0			0
$833$	9.71973e6	−	2.32825e7i	0.485335	−	1.16256i
$834$		0			0
$835$	−1.15641e7	−	2.00296e7i	−0.573979	−	0.994161i
$836$		0			0
$837$	1.59013e6	−	2.75418e6i	0.0784545	−	0.135887i
$838$		0			0
$839$	3.04940e6			0.149558			0.0747790	−	0.997200i	$-0.476175\pi$
$839$	3.04940e6			0.149558			0.0747790	+	0.997200i	$0.476175\pi$
$840$		0			0
$841$	−2.03881e7			−0.994002
$842$		0			0
$843$	−2.48760e6	+	4.30865e6i	−0.120562	+	0.208820i
$844$		0			0
$845$	−7.29911e6	−	1.26424e7i	−0.351664	−	0.609100i
$846$		0			0
$847$	−9.90049e6	+	6.59544e6i	−0.474185	+	0.315889i
$848$		0			0
$849$	9.90383e6	+	1.71539e7i	0.471557	+	0.816760i
$850$		0			0
$851$	7.84637e6	−	1.35903e7i	0.371402	−	0.643288i
$852$		0			0
$853$	1.35001e6			0.0635278			0.0317639	−	0.999495i	$-0.489888\pi$
$853$	1.35001e6			0.0635278			0.0317639	+	0.999495i	$0.489888\pi$
$854$		0			0
$855$	4.09141e6			0.191407
$856$		0			0
$857$	−4.32888e6	+	7.49784e6i	−0.201337	+	0.348726i	−0.948959	−	0.315398i	$-0.897862\pi$
$857$	−4.32888e6	+	7.49784e6i	−0.201337	+	0.348726i	0.747623	+	0.664124i	$0.231195\pi$
$858$		0			0
$859$	−9.31907e6	−	1.61411e7i	−0.430913	−	0.746364i	0.566039	−	0.824378i	$-0.308475\pi$
$859$	−9.31907e6	−	1.61411e7i	−0.430913	−	0.746364i	−0.996952	+	0.0780149i	$0.975142\pi$
$860$		0			0
$861$	−1.94316e7	−	9.61618e6i	−0.893309	−	0.442074i
$862$		0			0
$863$	1.79236e7	+	3.10446e7i	0.819215	+	1.41892i	0.906261	+	0.422718i	$0.138924\pi$
$863$	1.79236e7	+	3.10446e7i	0.819215	+	1.41892i	−0.0870457	+	0.996204i	$0.527743\pi$
$864$		0			0
$865$	1.28658e7	−	2.22842e7i	0.584650	−	1.01264i
$866$		0			0
$867$	−7.50246e6			−0.338966
$868$		0			0
$869$	2.19856e7			0.987616
$870$		0			0
$871$	3.53797e6	−	6.12794e6i	0.158019	−	0.273696i
$872$		0			0
$873$	970187.	+	1.68041e6i	0.0430844	+	0.0746243i
$874$		0			0
$875$	1.57696e6	+	2.45825e7i	0.0696308	+	1.08544i
$876$		0			0
$877$	1.35730e7	+	2.35091e7i	0.595905	+	1.03214i	0.993418	+	0.114542i	$0.0365400\pi$
$877$	1.35730e7	+	2.35091e7i	0.595905	+	1.03214i	−0.397513	+	0.917596i	$0.630127\pi$
$878$		0			0
$879$	2.82121e6	−	4.88648e6i	0.123158	−	0.213316i
$880$		0			0
$881$	−2.96350e7			−1.28637			−0.643183	−	0.765712i	$-0.722387\pi$
$881$	−2.96350e7			−1.28637			−0.643183	+	0.765712i	$0.722387\pi$
$882$		0			0
$883$	−2.33752e7			−1.00891			−0.504456	−	0.863438i	$-0.668307\pi$
$883$	−2.33752e7			−1.00891			−0.504456	+	0.863438i	$0.668307\pi$
$884$		0			0
$885$	−6.71180e6	+	1.16252e7i	−0.288059	+	0.498932i
$886$		0			0
$887$	2.19794e7	+	3.80694e7i	0.938008	+	1.62468i	0.769180	+	0.639032i	$0.220665\pi$
$887$	2.19794e7	+	3.80694e7i	0.938008	+	1.62468i	0.168828	+	0.985646i	$0.446002\pi$
$888$		0			0
$889$	188287.	+	2.93511e6i	0.00799033	+	0.124558i
$890$		0			0
$891$	863520.	+	1.49566e6i	0.0364400	+	0.0631159i
$892$		0			0
$893$	−5.50415e6	+	9.53346e6i	−0.230973	+	0.400057i
$894$		0			0
$895$	1.17218e7			0.489144
$896$		0			0
$897$	−2.28430e6			−0.0947921
$898$		0			0
$899$	765045.	−	1.32510e6i	0.0315710	−	0.0546825i
$900$		0			0
$901$	1.18017e7	+	2.04412e7i	0.484321	+	0.838868i
$902$		0			0
$903$	−280655.	−	138888.i	−0.0114539	−	0.00566821i
$904$		0			0
$905$	1.01621e7	+	1.76013e7i	0.412441	+	0.714368i
$906$		0			0
$907$	−9.22045e6	+	1.59703e7i	−0.372164	+	0.644606i	−0.989898	−	0.141780i	$-0.954717\pi$
$907$	−9.22045e6	+	1.59703e7i	−0.372164	+	0.644606i	0.617735	+	0.786387i	$0.288051\pi$
$908$		0			0
$909$	5.75008e6			0.230815
$910$		0			0
$911$	1.78981e7			0.714515			0.357257	−	0.934006i	$-0.383712\pi$
$911$	1.78981e7			0.714515			0.357257	+	0.934006i	$0.383712\pi$
$912$		0			0
$913$	−1.93513e6	+	3.35175e6i	−0.0768306	+	0.133074i
$914$		0			0
$915$	−347261.	−	601473.i	−0.0137121	−	0.0237500i
$916$		0			0
$917$	2.92262e7	−	1.94697e7i	1.14776	−	0.764604i
$918$		0			0
$919$	1.06153e7	+	1.83862e7i	0.414613	+	0.718131i	0.995388	−	0.0959335i	$-0.0305836\pi$
$919$	1.06153e7	+	1.83862e7i	0.414613	+	0.718131i	−0.580775	+	0.814064i	$0.697250\pi$
$920$		0			0
$921$	−7.71520e6	+	1.33631e7i	−0.299708	+	0.519109i
$922$		0			0
$923$	−3.20061e6			−0.123660
$924$		0			0
$925$	−1.47199e7			−0.565655
$926$		0			0
$927$	−67689.5	+	117242.i	−0.00258715	+	0.00448108i
$928$		0			0
$929$	1.23910e7	+	2.14618e7i	0.471050	+	0.815882i	0.999452	−	0.0331122i	$-0.0105419\pi$
$929$	1.23910e7	+	2.14618e7i	0.471050	+	0.815882i	−0.528402	+	0.848994i	$0.677209\pi$
$930$		0			0
$931$	−1.15675e7	−	1.51620e7i	−0.437387	−	0.573302i
$932$		0			0
$933$	−5.27552e6	−	9.13747e6i	−0.198409	−	0.343654i
$934$		0			0
$935$	−8.79501e6	+	1.52334e7i	−0.329009	+	0.569860i
$936$		0			0
$937$	2.29071e7			0.852357			0.426179	−	0.904639i	$-0.359859\pi$
$937$	2.29071e7			0.852357			0.426179	+	0.904639i	$0.359859\pi$
$938$		0			0
$939$	2.35695e7			0.872342
$940$		0			0
$941$	−2.11502e7	+	3.66333e7i	−0.778648	+	1.34866i	0.154073	+	0.988059i	$0.450761\pi$
$941$	−2.11502e7	+	3.66333e7i	−0.778648	+	1.34866i	−0.932721	+	0.360599i	$0.882572\pi$
$942$		0			0
$943$	−1.13252e7	−	1.96158e7i	−0.414731	−	0.718336i
$944$		0			0
$945$	3.50131e6	−	2.33248e6i	0.127541	−	0.0849645i
$946$		0			0
$947$	−2.25484e7	−	3.90550e7i	−0.817036	−	1.41515i	−0.907857	−	0.419281i	$-0.862282\pi$
$947$	−2.25484e7	−	3.90550e7i	−0.817036	−	1.41515i	0.0908205	−	0.995867i	$-0.471051\pi$
$948$		0			0
$949$	7.95486e6	−	1.37782e7i	0.286726	−	0.496624i
$950$		0			0
$951$	−4.37375e6			−0.156821
$952$		0			0
$953$	−4.78979e7			−1.70838			−0.854189	−	0.519962i	$-0.825946\pi$
$953$	−4.78979e7			−1.70838			−0.854189	+	0.519962i	$0.825946\pi$
$954$		0			0
$955$	−4.92343e6	+	8.52763e6i	−0.174687	+	0.302566i
$956$		0			0
$957$	415459.	+	719595.i	0.0146638	+	0.0253985i
$958$		0			0
$959$	−4.62541e7	−	2.28899e7i	−1.62407	−	0.803705i
$960$		0			0
$961$	4.79893e6	+	8.31200e6i	0.167624	+	0.290333i
$962$		0			0
$963$	1.18501e6	−	2.05250e6i	0.0411772	−	0.0713210i
$964$		0			0
$965$	1.24596e7			0.430713
$966$		0			0
$967$	−3.86466e7			−1.32906			−0.664531	−	0.747261i	$-0.731368\pi$
$967$	−3.86466e7			−1.32906			−0.664531	+	0.747261i	$0.731368\pi$
$968$		0			0
$969$	−7.66507e6	+	1.32763e7i	−0.262245	+	0.454221i
$970$		0			0
$971$	1.65267e7	+	2.86250e7i	0.562519	+	0.974312i	0.997276	+	0.0737638i	$0.0235011\pi$
$971$	1.65267e7	+	2.86250e7i	0.562519	+	0.974312i	−0.434757	+	0.900548i	$0.643166\pi$
$972$		0			0
$973$	1.29182e6	+	2.01375e7i	0.0437440	+	0.681904i
$974$		0			0
$975$	1.07135e6	+	1.85563e6i	0.0360927	+	0.0625143i
$976$		0			0
$977$	−1.34603e7	+	2.33139e7i	−0.451147	+	0.781409i	−0.998458	−	0.0555203i	$-0.982318\pi$
$977$	−1.34603e7	+	2.33139e7i	−0.451147	+	0.781409i	0.547311	+	0.836929i	$0.315652\pi$
$978$		0			0
$979$	6.98159e6			0.232808
$980$		0			0
$981$	4.10936e6			0.136333
$982$		0			0
$983$	1.77826e7	−	3.08004e7i	0.586964	−	1.01665i	−0.407663	−	0.913132i	$-0.633656\pi$
$983$	1.77826e7	−	3.08004e7i	0.586964	−	1.01665i	0.994627	−	0.103519i	$-0.0330103\pi$
$984$		0			0
$985$	5.73546e6	+	9.93411e6i	0.188355	+	0.326241i
$986$		0			0
$987$	724657.	+	1.12963e7i	0.0236777	+	0.369100i
$988$		0			0
$989$	−163572.	−	283315.i	−0.00531763	−	0.00921041i
$990$		0			0
$991$	−2.13709e7	+	3.70154e7i	−0.691254	+	1.19729i	0.280173	+	0.959950i	$0.409608\pi$
$991$	−2.13709e7	+	3.70154e7i	−0.691254	+	1.19729i	−0.971427	+	0.237338i	$0.923725\pi$
$992$		0			0
$993$	2.40792e7			0.774942
$994$		0			0
$995$	−6.72825e6			−0.215449
$996$		0			0
$997$	1.89893e6	−	3.28904e6i	0.0605022	−	0.104793i	−0.834188	−	0.551480i	$-0.814063\pi$
$997$	1.89893e6	−	3.28904e6i	0.0605022	−	0.104793i	0.894690	+	0.446688i	$0.147396\pi$
$998$		0			0
$999$	4.69255e6	+	8.12774e6i	0.148763	+	0.257665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.m.193.5		10
4.3	odd	2		168.6.q.b.25.5	✓	10
7.2	even	3	inner	336.6.q.m.289.5		10
12.11	even	2		504.6.s.e.361.1		10
28.23	odd	6		168.6.q.b.121.5	yes	10
84.23	even	6		504.6.s.e.289.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.6.q.b.25.5	✓	10	4.3	odd	2
168.6.q.b.121.5	yes	10	28.23	odd	6
336.6.q.m.193.5		10	1.1	even	1	trivial
336.6.q.m.289.5		10	7.2	even	3	inner
504.6.s.e.289.1		10	84.23	even	6
504.6.s.e.361.1		10	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(4.50000 - 7.79423i) q^{3} +(22.2576 + 38.5514i) q^{5} +(8.29943 + 129.376i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.50000 - 7.79423i) q^{3} +(22.2576 + 38.5514i) q^{5} +(8.29943 + 129.376i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(131.614 - 227.962i) q^{11} -208.220 q^{13} +400.637 q^{15} +(-750.577 + 1300.04i) q^{17} +(567.347 + 982.673i) q^{19} +(1045.73 + 517.504i) q^{21} +(609.477 + 1055.64i) q^{23} +(571.695 - 990.205i) q^{25} -729.000 q^{27} -350.738 q^{29} +(-2181.24 + 3778.02i) q^{31} +(-1184.53 - 2051.66i) q^{33} +(-4802.89 + 3199.56i) q^{35} +(-6436.97 - 11149.2i) q^{37} +(-936.992 + 1622.92i) q^{39} -18581.8 q^{41} -268.381 q^{43} +(1802.87 - 3122.66i) q^{45} +(4850.78 + 8401.80i) q^{47} +(-16669.2 + 2147.49i) q^{49} +(6755.19 + 11700.3i) q^{51} +(7861.76 - 13617.0i) q^{53} +11717.7 q^{55} +10212.2 q^{57} +(-16752.8 + 29016.7i) q^{59} +(-866.770 - 1501.29i) q^{61} +(8739.34 - 5821.91i) q^{63} +(-4634.50 - 8027.18i) q^{65} +(-16991.4 + 29430.0i) q^{67} +10970.6 q^{69} +15371.3 q^{71} +(-38204.0 + 66171.3i) q^{73} +(-5145.26 - 8911.85i) q^{75} +(30585.1 + 15135.7i) q^{77} +(41761.4 + 72333.0i) q^{79} +(-3280.50 + 5681.99i) q^{81} -14703.1 q^{83} -66824.3 q^{85} +(-1578.32 + 2733.73i) q^{87} +(13261.5 + 22969.6i) q^{89} +(-1728.11 - 26938.7i) q^{91} +(19631.2 + 34002.2i) q^{93} +(-25255.6 + 43744.0i) q^{95} -23955.2 q^{97} -21321.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 45 q^{3} - 75 q^{5} + 113 q^{7} - 405 q^{9}+O(q^{10}) \) 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

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Database

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