LMFDB - Embedded newform 336.6.q.f.289.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{9601})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2401x^{2} + 2400x + 5760000 $ x^4 - x^3 + 2401x^2 + 2400x + 5760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-24.2462 + 41.9956i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.6.q.f.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 - 7.79423i) q^{3} +(-11.2462 + 19.4789i) q^{5} +(96.4847 - 86.5893i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-4.50000 - 7.79423i) q^{3} +(-11.2462 + 19.4789i) q^{5} +(96.4847 - 86.5893i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(170.231 + 294.849i) q^{11} -728.416 q^{13} +202.431 q^{15} +(-404.923 - 701.348i) q^{17} +(513.101 - 888.717i) q^{19} +(-1109.08 - 362.372i) q^{21} +(711.015 - 1231.51i) q^{23} +(1309.55 + 2268.20i) q^{25} +729.000 q^{27} +5218.03 q^{29} +(-3518.87 - 6094.87i) q^{31} +(1532.08 - 2653.64i) q^{33} +(601.584 + 2853.22i) q^{35} +(-6396.05 + 11078.3i) q^{37} +(3277.87 + 5677.44i) q^{39} +1173.51 q^{41} -3664.17 q^{43} +(-910.940 - 1577.79i) q^{45} +(4656.60 - 8065.46i) q^{47} +(1811.59 - 16709.1i) q^{49} +(-3644.31 + 6312.13i) q^{51} +(-17821.4 - 30867.6i) q^{53} -7657.78 q^{55} -9235.81 q^{57} +(-15188.1 - 26306.5i) q^{59} +(-16093.1 + 27874.1i) q^{61} +(2166.44 + 10275.1i) q^{63} +(8191.89 - 14188.8i) q^{65} +(10675.5 + 18490.6i) q^{67} -12798.3 q^{69} -61153.7 q^{71} +(-20633.9 - 35739.0i) q^{73} +(11785.9 - 20413.8i) q^{75} +(41955.4 + 13708.2i) q^{77} +(-17500.2 + 30311.3i) q^{79} +(-3280.50 - 5681.99i) q^{81} -86193.0 q^{83} +18215.4 q^{85} +(-23481.1 - 40670.5i) q^{87} +(-38996.3 + 67543.6i) q^{89} +(-70281.0 + 63073.0i) q^{91} +(-31669.9 + 54853.8i) q^{93} +(11540.8 + 19989.3i) q^{95} -161765. q^{97} -27577.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{3} + 53 q^{5} - 6 q^{7} - 162 q^{9}+O(q^{10}) $ 4 * q - 18 * q^3 + 53 * q^5 - 6 * q^7 - 162 * q^9	$ 4 q - 18 q^{3} + 53 q^{5} - 6 q^{7} - 162 q^{9} + 191 q^{11} - 758 q^{13} - 954 q^{15} + 340 q^{17} - 1769 q^{19} - 27 q^{21} + 3236 q^{23} + 45 q^{25} + 2916 q^{27} + 8918 q^{29} + 1994 q^{31} + 1719 q^{33} + 4562 q^{35} - 20587 q^{37} + 3411 q^{39} + 17628 q^{41} - 31706 q^{43} + 4293 q^{45} + 33912 q^{47} + 9598 q^{49} + 3060 q^{51} - 49239 q^{53} - 37882 q^{55} + 31842 q^{57} - 56735 q^{59} - 67508 q^{61} + 729 q^{63} + 42762 q^{65} + 75723 q^{67} - 58248 q^{69} + 17984 q^{71} + 3201 q^{73} + 405 q^{75} + 120299 q^{77} + 26612 q^{79} - 13122 q^{81} + 1898 q^{83} + 210040 q^{85} - 40131 q^{87} - 176562 q^{89} - 210085 q^{91} + 17946 q^{93} + 234098 q^{95} - 258846 q^{97} - 30942 q^{99}+O(q^{100}) $ 4 * q - 18 * q^3 + 53 * q^5 - 6 * q^7 - 162 * q^9 + 191 * q^11 - 758 * q^13 - 954 * q^15 + 340 * q^17 - 1769 * q^19 - 27 * q^21 + 3236 * q^23 + 45 * q^25 + 2916 * q^27 + 8918 * q^29 + 1994 * q^31 + 1719 * q^33 + 4562 * q^35 - 20587 * q^37 + 3411 * q^39 + 17628 * q^41 - 31706 * q^43 + 4293 * q^45 + 33912 * q^47 + 9598 * q^49 + 3060 * q^51 - 49239 * q^53 - 37882 * q^55 + 31842 * q^57 - 56735 * q^59 - 67508 * q^61 + 729 * q^63 + 42762 * q^65 + 75723 * q^67 - 58248 * q^69 + 17984 * q^71 + 3201 * q^73 + 405 * q^75 + 120299 * q^77 + 26612 * q^79 - 13122 * q^81 + 1898 * q^83 + 210040 * q^85 - 40131 * q^87 - 176562 * q^89 - 210085 * q^91 + 17946 * q^93 + 234098 * q^95 - 258846 * q^97 - 30942 * 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
$5$	−11.2462	+	19.4789i	−0.201178	+	0.348450i	−0.948908	−	0.315552i	$-0.897810\pi$
$5$	−11.2462	+	19.4789i	−0.201178	+	0.348450i	0.747730	+	0.664002i	$0.231144\pi$
$6$		0			0
$7$	96.4847	−	86.5893i	0.744241	−	0.667912i
$7$	96.4847	−	86.5893i	0.744241	−	0.667912i
$8$		0			0
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$		0			0
$11$	170.231	+	294.849i	0.424186	+	0.734712i	0.996344	−	0.0854314i	$-0.0272268\pi$
$11$	170.231	+	294.849i	0.424186	+	0.734712i	−0.572158	+	0.820144i	$0.693894\pi$
$12$		0			0
$13$	−728.416			−1.19542			−0.597711	−	0.801712i	$-0.703923\pi$
$13$	−728.416			−1.19542			−0.597711	+	0.801712i	$0.703923\pi$
$14$		0			0
$15$	202.431			0.232300
$16$		0			0
$17$	−404.923	−	701.348i	−0.339821	−	0.588588i	0.644578	−	0.764539i	$-0.277033\pi$
$17$	−404.923	−	701.348i	−0.339821	−	0.588588i	−0.984399	+	0.175951i	$0.943700\pi$
$18$		0			0
$19$	513.101	−	888.717i	0.326076	−	0.564780i	−0.655654	−	0.755062i	$-0.727607\pi$
$19$	513.101	−	888.717i	0.326076	−	0.564780i	0.981730	+	0.190282i	$0.0609402\pi$
$20$		0			0
$21$	−1109.08	−	362.372i	−0.548800	−	0.179311i
$22$		0			0
$23$	711.015	−	1231.51i	0.280259	−	0.485423i	−0.691190	−	0.722674i	$-0.742913\pi$
$23$	711.015	−	1231.51i	0.280259	−	0.485423i	0.971448	+	0.237251i	$0.0762464\pi$
$24$		0			0
$25$	1309.55	+	2268.20i	0.419055	+	0.725825i
$26$		0			0
$27$	729.000			0.192450
$28$		0			0
$29$	5218.03			1.15216			0.576079	−	0.817394i	$-0.304582\pi$
$29$	5218.03			1.15216			0.576079	+	0.817394i	$0.304582\pi$
$30$		0			0
$31$	−3518.87	−	6094.87i	−0.657657	−	1.13909i	−0.981221	−	0.192889i	$-0.938214\pi$
$31$	−3518.87	−	6094.87i	−0.657657	−	1.13909i	0.323564	−	0.946206i	$-0.395119\pi$
$32$		0			0
$33$	1532.08	−	2653.64i	0.244904	−	0.424186i
$34$		0			0
$35$	601.584	+	2853.22i	0.0830092	+	0.393699i
$36$		0			0
$37$	−6396.05	+	11078.3i	−0.768082	+	1.33036i	0.170519	+	0.985354i	$0.445456\pi$
$37$	−6396.05	+	11078.3i	−0.768082	+	1.33036i	−0.938601	+	0.345004i	$0.887878\pi$
$38$		0			0
$39$	3277.87	+	5677.44i	0.345088	+	0.597711i
$40$		0			0
$41$	1173.51			0.109025			0.0545124	−	0.998513i	$-0.482640\pi$
$41$	1173.51			0.109025			0.0545124	+	0.998513i	$0.482640\pi$
$42$		0			0
$43$	−3664.17			−0.302207			−0.151103	−	0.988518i	$-0.548283\pi$
$43$	−3664.17			−0.302207			−0.151103	+	0.988518i	$0.548283\pi$
$44$		0			0
$45$	−910.940	−	1577.79i	−0.0670592	−	0.116150i
$46$		0			0
$47$	4656.60	−	8065.46i	0.307485	−	0.532580i	−0.670326	−	0.742066i	$-0.733846\pi$
$47$	4656.60	−	8065.46i	0.307485	−	0.532580i	0.977812	+	0.209487i	$0.0671793\pi$
$48$		0			0
$49$	1811.59	−	16709.1i	0.107788	−	0.994174i
$50$		0			0
$51$	−3644.31	+	6312.13i	−0.196196	+	0.339821i
$52$		0			0
$53$	−17821.4	−	30867.6i	−0.871469	−	1.50943i	−0.860477	−	0.509489i	$-0.829835\pi$
$53$	−17821.4	−	30867.6i	−0.871469	−	1.50943i	−0.0109916	−	0.999940i	$-0.503499\pi$
$54$		0			0
$55$	−7657.78			−0.341347
$56$		0			0
$57$	−9235.81			−0.376520
$58$		0			0
$59$	−15188.1	−	26306.5i	−0.568033	−	0.983861i	−0.996760	−	0.0804276i	$-0.974371\pi$
$59$	−15188.1	−	26306.5i	−0.568033	−	0.983861i	0.428728	−	0.903434i	$-0.358962\pi$
$60$		0			0
$61$	−16093.1	+	27874.1i	−0.553753	+	0.959128i	0.444247	+	0.895904i	$0.353471\pi$
$61$	−16093.1	+	27874.1i	−0.553753	+	0.959128i	−0.997999	+	0.0632231i	$0.979862\pi$
$62$		0			0
$63$	2166.44	+	10275.1i	0.0687694	+	0.326162i
$64$		0			0
$65$	8191.89	−	14188.8i	0.240492	−	0.416544i
$66$		0			0
$67$	10675.5	+	18490.6i	0.290538	+	0.503226i	0.973937	−	0.226819i	$-0.0728324\pi$
$67$	10675.5	+	18490.6i	0.290538	+	0.503226i	−0.683399	+	0.730045i	$0.739499\pi$
$68$		0			0
$69$	−12798.3			−0.323615
$70$		0			0
$71$	−61153.7			−1.43972			−0.719859	−	0.694121i	$-0.755793\pi$
$71$	−61153.7			−1.43972			−0.719859	+	0.694121i	$0.755793\pi$
$72$		0			0
$73$	−20633.9	−	35739.0i	−0.453184	−	0.784937i	0.545398	−	0.838177i	$-0.316378\pi$
$73$	−20633.9	−	35739.0i	−0.453184	−	0.784937i	−0.998582	+	0.0532401i	$0.983045\pi$
$74$		0			0
$75$	11785.9	−	20413.8i	0.241942	−	0.419055i
$76$		0			0
$77$	41955.4	+	13708.2i	0.806419	+	0.263484i
$78$		0			0
$79$	−17500.2	+	30311.3i	−0.315483	+	0.546433i	−0.979540	−	0.201249i	$-0.935500\pi$
$79$	−17500.2	+	30311.3i	−0.315483	+	0.546433i	0.664057	+	0.747682i	$0.268833\pi$
$80$		0			0
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−86193.0			−1.37334			−0.686668	−	0.726972i	$-0.740927\pi$
$83$	−86193.0			−1.37334			−0.686668	+	0.726972i	$0.740927\pi$
$84$		0			0
$85$	18215.4			0.273458
$86$		0			0
$87$	−23481.1	−	40670.5i	−0.332599	−	0.576079i
$88$		0			0
$89$	−38996.3	+	67543.6i	−0.521853	+	0.903876i	0.477824	+	0.878456i	$0.341426\pi$
$89$	−38996.3	+	67543.6i	−0.521853	+	0.903876i	−0.999677	+	0.0254206i	$0.991908\pi$
$90$		0			0
$91$	−70281.0	+	63073.0i	−0.889681	+	0.798436i
$92$		0			0
$93$	−31669.9	+	54853.8i	−0.379698	+	0.657657i
$94$		0			0
$95$	11540.8	+	19989.3i	0.131198	+	0.227242i
$96$		0			0
$97$	−161765.			−1.74565			−0.872823	−	0.488037i	$-0.837713\pi$
$97$	−161765.			−1.74565			−0.872823	+	0.488037i	$0.837713\pi$
$98$		0			0
$99$	−27577.4			−0.282791
$100$		0			0
$101$	32927.2	+	57031.6i	0.321182	+	0.556304i	0.980732	−	0.195357i	$-0.0625865\pi$
$101$	32927.2	+	57031.6i	0.321182	+	0.556304i	−0.659550	+	0.751661i	$0.729253\pi$
$102$		0			0
$103$	65099.0	−	112755.i	0.604619	−	1.04723i	−0.387493	−	0.921873i	$-0.626659\pi$
$103$	65099.0	−	112755.i	0.604619	−	1.04723i	0.992112	−	0.125358i	$-0.0400078\pi$
$104$		0			0
$105$	19531.5	−	17528.4i	0.172887	−	0.155156i
$106$		0			0
$107$	1295.48	−	2243.83i	0.0109388	−	0.0189466i	−0.860504	−	0.509443i	$-0.829851\pi$
$107$	1295.48	−	2243.83i	0.0109388	−	0.0189466i	0.871443	+	0.490497i	$0.163185\pi$
$108$		0			0
$109$	−55326.9	−	95828.9i	−0.446036	−	0.772557i	0.552088	−	0.833786i	$-0.313831\pi$
$109$	−55326.9	−	95828.9i	−0.446036	−	0.772557i	−0.998124	+	0.0612291i	$0.980498\pi$
$110$		0			0
$111$	115129.			0.886905
$112$		0			0
$113$	−193910.			−1.42858			−0.714291	−	0.699849i	$-0.753251\pi$
$113$	−193910.			−1.42858			−0.714291	+	0.699849i	$0.753251\pi$
$114$		0			0
$115$	15992.4	+	27699.7i	0.112764	+	0.195312i
$116$		0			0
$117$	29500.8	−	51097.0i	0.199237	−	0.345088i
$118$		0			0
$119$	−99798.1	−	32607.3i	−0.646033	−	0.211080i
$120$		0			0
$121$	22568.4	−	39089.6i	0.140132	−	0.242716i
$122$		0			0
$123$	−5280.77	−	9146.57i	−0.0314728	−	0.0545124i
$124$		0			0
$125$	−129198.			−0.739573
$126$		0			0
$127$	−27429.2			−0.150905			−0.0754526	−	0.997149i	$-0.524040\pi$
$127$	−27429.2			−0.150905			−0.0754526	+	0.997149i	$0.524040\pi$
$128$		0			0
$129$	16488.7	+	28559.3i	0.0872395	+	0.151103i
$130$		0			0
$131$	75188.0	−	130229.i	0.382798	−	0.663026i	−0.608663	−	0.793429i	$-0.708294\pi$
$131$	75188.0	−	130229.i	0.382798	−	0.663026i	0.991461	+	0.130403i	$0.0416271\pi$
$132$		0			0
$133$	−27447.0	−	130177.i	−0.134544	−	0.638122i
$134$		0			0
$135$	−8198.46	+	14200.1i	−0.0387167	+	0.0670592i
$136$		0			0
$137$	−48051.0	−	83226.8i	−0.218726	−	0.378845i	0.735693	−	0.677316i	$-0.236857\pi$
$137$	−48051.0	−	83226.8i	−0.218726	−	0.378845i	−0.954419	+	0.298471i	$0.903524\pi$
$138$		0			0
$139$	−100854.			−0.442749			−0.221375	−	0.975189i	$-0.571054\pi$
$139$	−100854.			−0.442749			−0.221375	+	0.975189i	$0.571054\pi$
$140$		0			0
$141$	−83818.7			−0.355053
$142$		0			0
$143$	−123999.	−	214772.i	−0.507081	−	0.878291i
$144$		0			0
$145$	−58682.9	+	101642.i	−0.231788	+	0.401469i
$146$		0			0
$147$	−138387.	+	61070.9i	−0.528203	+	0.233099i
$148$		0			0
$149$	180472.	−	312587.i	0.665954	−	1.15347i	−0.313071	−	0.949730i	$-0.601358\pi$
$149$	180472.	−	312587.i	0.665954	−	1.15347i	0.979026	−	0.203737i	$-0.0653087\pi$
$150$		0			0
$151$	−217028.	−	375903.i	−0.774592	−	1.34163i	−0.935023	−	0.354586i	$-0.884622\pi$
$151$	−217028.	−	375903.i	−0.774592	−	1.34163i	0.160431	−	0.987047i	$-0.448712\pi$
$152$		0			0
$153$	65597.6			0.226548
$154$		0			0
$155$	158295.			0.529223
$156$		0			0
$157$	255798.	+	443055.i	0.828225	+	1.43453i	0.899430	+	0.437066i	$0.143982\pi$
$157$	255798.	+	443055.i	0.828225	+	1.43453i	−0.0712046	+	0.997462i	$0.522684\pi$
$158$		0			0
$159$	−160393.	+	277808.i	−0.503143	+	0.871469i
$160$		0			0
$161$	−38033.9	−	180389.i	−0.115639	−	0.548459i
$162$		0			0
$163$	−125635.	+	217606.i	−0.370374	+	0.641507i	−0.989623	−	0.143688i	$-0.954104\pi$
$163$	−125635.	+	217606.i	−0.370374	+	0.641507i	0.619249	+	0.785195i	$0.287437\pi$
$164$		0			0
$165$	34460.0	+	59686.5i	0.0985384	+	0.170674i
$166$		0			0
$167$	−419277.			−1.16335			−0.581674	−	0.813422i	$-0.697602\pi$
$167$	−419277.			−1.16335			−0.581674	+	0.813422i	$0.697602\pi$
$168$		0			0
$169$	159297.			0.429032
$170$		0			0
$171$	41561.2	+	71986.0i	0.108692	+	0.188260i
$172$		0			0
$173$	230688.	−	399564.i	0.586017	−	1.01501i	−0.408731	−	0.912655i	$-0.634029\pi$
$173$	230688.	−	399564.i	0.586017	−	1.01501i	0.994748	−	0.102356i	$-0.0326381\pi$
$174$		0			0
$175$	322753.	+	105454.i	0.796665	+	0.260296i
$176$		0			0
$177$	−136693.	+	236759.i	−0.327954	+	0.568033i
$178$		0			0
$179$	370853.	+	642336.i	0.865105	+	1.49841i	0.866942	+	0.498408i	$0.166082\pi$
$179$	370853.	+	642336.i	0.865105	+	1.49841i	−0.00183697	+	0.999998i	$0.500585\pi$
$180$		0			0
$181$	301371.			0.683762			0.341881	−	0.939743i	$-0.388936\pi$
$181$	301371.			0.683762			0.341881	+	0.939743i	$0.388936\pi$
$182$		0			0
$183$	289676.			0.639418
$184$		0			0
$185$	−143862.	−	249177.i	−0.309042	−	0.535277i
$186$		0			0
$187$	137861.	−	238782.i	0.288295	−	0.499342i
$188$		0			0
$189$	70337.3	−	63123.6i	0.143229	−	0.128540i
$190$		0			0
$191$	131591.	−	227923.i	0.261002	−	0.452069i	−0.705507	−	0.708703i	$-0.749280\pi$
$191$	131591.	−	227923.i	0.261002	−	0.452069i	0.966508	+	0.256635i	$0.0826138\pi$
$192$		0			0
$193$	415563.	+	719777.i	0.803053	+	1.39093i	0.917598	+	0.397510i	$0.130126\pi$
$193$	415563.	+	719777.i	0.803053	+	1.39093i	−0.114545	+	0.993418i	$0.536541\pi$
$194$		0			0
$195$	−147454.			−0.277696
$196$		0			0
$197$	−1.05421e6			−1.93536			−0.967681	−	0.252178i	$-0.918853\pi$
$197$	−1.05421e6			−1.93536			−0.967681	+	0.252178i	$0.918853\pi$
$198$		0			0
$199$	349284.	+	604977.i	0.625239	+	1.08295i	0.988495	+	0.151256i	$0.0483317\pi$
$199$	349284.	+	604977.i	0.625239	+	1.08295i	−0.363256	+	0.931689i	$0.618335\pi$
$200$		0			0
$201$	96079.9	−	166415.i	0.167742	−	0.290538i
$202$		0			0
$203$	503460.	−	451826.i	0.857482	−	0.769539i
$204$		0			0
$205$	−13197.4	+	22858.6i	−0.0219334	+	0.0379897i
$206$		0			0
$207$	57592.2	+	99752.7i	0.0934196	+	0.161808i
$208$		0			0
$209$	349382.			0.553268
$210$		0			0
$211$	99693.6			0.154156			0.0770781	−	0.997025i	$-0.475441\pi$
$211$	99693.6			0.154156			0.0770781	+	0.997025i	$0.475441\pi$
$212$		0			0
$213$	275192.	+	476646.i	0.415611	+	0.719859i
$214$		0			0
$215$	41207.8	−	71374.1i	0.0607972	−	0.105304i
$216$		0			0
$217$	−867267.	−	283365.i	−1.25027	−	0.408504i
$218$		0			0
$219$	−185705.	+	321651.i	−0.261646	+	0.453184i
$220$		0			0
$221$	294953.	+	510873.i	0.406230	+	0.703610i
$222$		0			0
$223$	−526194.			−0.708572			−0.354286	−	0.935137i	$-0.615276\pi$
$223$	−526194.			−0.708572			−0.354286	+	0.935137i	$0.615276\pi$
$224$		0			0
$225$	−212147.			−0.279370
$226$		0			0
$227$	−490802.	−	850095.i	−0.632182	−	1.09497i	−0.987105	−	0.160076i	$-0.948826\pi$
$227$	−490802.	−	850095.i	−0.632182	−	1.09497i	0.354923	−	0.934896i	$-0.384507\pi$
$228$		0			0
$229$	42540.5	−	73682.3i	0.0536061	−	0.0928484i	−0.837977	−	0.545705i	$-0.816262\pi$
$229$	42540.5	−	73682.3i	0.0536061	−	0.0928484i	0.891583	+	0.452857i	$0.149595\pi$
$230$		0			0
$231$	−81954.4	−	388697.i	−0.101051	−	0.479271i
$232$		0			0
$233$	−56561.4	+	97967.3i	−0.0682544	+	0.118220i	−0.898133	−	0.439724i	$-0.855076\pi$
$233$	−56561.4	+	97967.3i	−0.0682544	+	0.118220i	0.829879	+	0.557944i	$0.188410\pi$
$234$		0			0
$235$	104738.	+	181411.i	0.123718	+	0.214286i
$236$		0			0
$237$	315004.			0.364288
$238$		0			0
$239$	895100.			1.01362			0.506812	−	0.862057i	$-0.330824\pi$
$239$	895100.			1.01362			0.506812	+	0.862057i	$0.330824\pi$
$240$		0			0
$241$	−263857.	−	457014.i	−0.292635	−	0.506859i	0.681797	−	0.731542i	$-0.261199\pi$
$241$	−263857.	−	457014.i	−0.292635	−	0.506859i	−0.974432	+	0.224683i	$0.927865\pi$
$242$		0			0
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	305102.	+	223201.i	0.324735	+	0.237564i
$246$		0			0
$247$	−373751.	+	647355.i	−0.389798	+	0.675150i
$248$		0			0
$249$	387868.	+	671808.i	0.396448	+	0.686668i
$250$		0			0
$251$	1.19293e6			1.19517			0.597584	−	0.801806i	$-0.296127\pi$
$251$	1.19293e6			1.19517			0.597584	+	0.801806i	$0.296127\pi$
$252$		0			0
$253$	484147.			0.475528
$254$		0			0
$255$	−81969.1	−	141975.i	−0.0789405	−	0.136729i
$256$		0			0
$257$	597462.	−	1.03483e6i	0.564257	−	0.977322i	−0.432861	−	0.901461i	$-0.642496\pi$
$257$	597462.	−	1.03483e6i	0.564257	−	0.977322i	0.997118	−	0.0758617i	$-0.0241707\pi$
$258$		0			0
$259$	342140.	+	1.62272e6i	0.316923	+	1.50312i
$260$		0			0
$261$	−211330.	+	366035.i	−0.192026	+	0.332599i
$262$		0			0
$263$	−1.06115e6	−	1.83797e6i	−0.945993	−	1.63851i	−0.753750	−	0.657161i	$-0.771757\pi$
$263$	−1.06115e6	−	1.83797e6i	−0.945993	−	1.63851i	−0.192244	−	0.981347i	$-0.561576\pi$
$264$		0			0
$265$	801690.			0.701280
$266$		0			0
$267$	701933.			0.602584
$268$		0			0
$269$	−77488.3	−	134214.i	−0.0652913	−	0.113088i	0.831532	−	0.555477i	$-0.187464\pi$
$269$	−77488.3	−	134214.i	−0.0652913	−	0.113088i	−0.896823	+	0.442389i	$0.854131\pi$
$270$		0			0
$271$	979439.	−	1.69644e6i	0.810129	−	1.40318i	−0.102645	−	0.994718i	$-0.532730\pi$
$271$	979439.	−	1.69644e6i	0.810129	−	1.40318i	0.912773	−	0.408466i	$-0.133936\pi$
$272$		0			0
$273$	807870.	+	263957.i	0.656047	+	0.214352i
$274$		0			0
$275$	−445851.	+	772236.i	−0.355515	+	0.615770i
$276$		0			0
$277$	874763.	+	1.51513e6i	0.685001	+	1.18646i	0.973437	+	0.228957i	$0.0735315\pi$
$277$	874763.	+	1.51513e6i	0.685001	+	1.18646i	−0.288436	+	0.957499i	$0.593135\pi$
$278$		0			0
$279$	570057.			0.438438
$280$		0			0
$281$	1.40665e6			1.06272			0.531361	−	0.847145i	$-0.321681\pi$
$281$	1.40665e6			1.06272			0.531361	+	0.847145i	$0.321681\pi$
$282$		0			0
$283$	978536.	+	1.69487e6i	0.726291	+	1.25797i	0.958441	+	0.285292i	$0.0920907\pi$
$283$	978536.	+	1.69487e6i	0.726291	+	1.25797i	−0.232150	+	0.972680i	$0.574576\pi$
$284$		0			0
$285$	103868.	−	179904.i	0.0757474	−	0.131198i
$286$		0			0
$287$	113225.	−	101613.i	0.0811407	−	0.0728189i
$288$		0			0
$289$	382002.	−	661648.i	0.269043	−	0.465996i
$290$		0			0
$291$	727944.	+	1.26084e6i	0.503925	+	0.872823i
$292$		0			0
$293$	−1.26998e6			−0.864229			−0.432114	−	0.901819i	$-0.642232\pi$
$293$	−1.26998e6			−0.864229			−0.432114	+	0.901819i	$0.642232\pi$
$294$		0			0
$295$	683232.			0.457102
$296$		0			0
$297$	124098.	+	214945.i	0.0816347	+	0.141395i
$298$		0			0
$299$	−517915.	+	897055.i	−0.335027	+	0.580285i
$300$		0			0
$301$	−353536.	+	317277.i	−0.224914	+	0.201847i
$302$		0			0
$303$	296345.	−	513284.i	0.185435	−	0.321182i
$304$		0			0
$305$	−361972.	−	626954.i	−0.222805	−	0.385910i
$306$		0			0
$307$	41854.4			0.0253451			0.0126726	−	0.999920i	$-0.495966\pi$
$307$	41854.4			0.0253451			0.0126726	+	0.999920i	$0.495966\pi$
$308$		0			0
$309$	−1.17178e6			−0.698154
$310$		0			0
$311$	−1.14595e6	−	1.98484e6i	−0.671837	−	1.16366i	−0.977383	−	0.211478i	$-0.932172\pi$
$311$	−1.14595e6	−	1.98484e6i	−0.671837	−	1.16366i	0.305546	−	0.952177i	$-0.401161\pi$
$312$		0			0
$313$	−1.13575e6	+	1.96717e6i	−0.655271	+	1.13496i	0.326555	+	0.945178i	$0.394112\pi$
$313$	−1.13575e6	+	1.96717e6i	−0.655271	+	1.13496i	−0.981826	+	0.189785i	$0.939221\pi$
$314$		0			0
$315$	−224512.	−	73355.4i	−0.127486	−	0.0416539i
$316$		0			0
$317$	992372.	−	1.71884e6i	0.554659	−	0.960698i	−0.443271	−	0.896388i	$-0.646182\pi$
$317$	992372.	−	1.71884e6i	0.554659	−	0.960698i	0.997930	−	0.0643100i	$-0.0204847\pi$
$318$		0			0
$319$	888270.	+	1.53853e6i	0.488729	+	0.846504i
$320$		0			0
$321$	−23318.6			−0.0126310
$322$		0			0
$323$	−831066.			−0.443230
$324$		0			0
$325$	−953895.	−	1.65219e6i	−0.500947	−	0.867666i
$326$		0			0
$327$	−497942.	+	862460.i	−0.257519	+	0.446036i
$328$		0			0
$329$	−249092.	−	1.18141e6i	−0.126873	−	0.601740i
$330$		0			0
$331$	319230.	−	552923.i	0.160153	−	0.277393i	−0.774771	−	0.632242i	$-0.782135\pi$
$331$	319230.	−	552923.i	0.160153	−	0.277393i	0.934923	+	0.354850i	$0.115468\pi$
$332$		0			0
$333$	−518080.	−	897342.i	−0.256027	−	0.443453i
$334$		0			0
$335$	−480236.			−0.233799
$336$		0			0
$337$	2.72026e6			1.30478			0.652388	−	0.757886i	$-0.273767\pi$
$337$	2.72026e6			1.30478			0.652388	+	0.757886i	$0.273767\pi$
$338$		0			0
$339$	872597.	+	1.51138e6i	0.412396	+	0.714291i
$340$		0			0
$341$	1.19804e6	−	2.07507e6i	0.557938	−	0.966377i
$342$		0			0
$343$	−1.27204e6	−	1.76903e6i	−0.583800	−	0.811897i
$344$		0			0
$345$	143932.	−	249297.i	0.0651041	−	0.112764i
$346$		0			0
$347$	1.31038e6	+	2.26965e6i	0.584217	+	1.01189i	0.994973	+	0.100148i	$0.0319317\pi$
$347$	1.31038e6	+	2.26965e6i	0.584217	+	1.01189i	−0.410755	+	0.911746i	$0.634735\pi$
$348$		0			0
$349$	575592.			0.252960			0.126480	−	0.991969i	$-0.459632\pi$
$349$	575592.			0.252960			0.126480	+	0.991969i	$0.459632\pi$
$350$		0			0
$351$	−531015.			−0.230059
$352$		0			0
$353$	1.29486e6	+	2.24276e6i	0.553077	+	0.957957i	0.998050	+	0.0624135i	$0.0198797\pi$
$353$	1.29486e6	+	2.24276e6i	0.553077	+	0.957957i	−0.444974	+	0.895544i	$0.646787\pi$
$354$		0			0
$355$	687746.	−	1.19121e6i	0.289639	−	0.501669i
$356$		0			0
$357$	194943.	+	924582.i	0.0809537	+	0.383950i
$358$		0			0
$359$	1.43389e6	−	2.48358e6i	0.587193	−	1.01705i	−0.407405	−	0.913248i	$-0.633566\pi$
$359$	1.43389e6	−	2.48358e6i	0.587193	−	1.01705i	0.994598	−	0.103801i	$-0.0331005\pi$
$360$		0			0
$361$	711505.	+	1.23236e6i	0.287349	+	0.497703i
$362$		0			0
$363$	−406231.			−0.161811
$364$		0			0
$365$	928210.			0.364682
$366$		0			0
$367$	−977255.	−	1.69265e6i	−0.378741	−	0.655999i	0.612138	−	0.790751i	$-0.290310\pi$
$367$	−977255.	−	1.69265e6i	−0.378741	−	0.655999i	−0.990879	+	0.134752i	$0.956976\pi$
$368$		0			0
$369$	−47527.0	+	82319.1i	−0.0181708	+	0.0314728i
$370$		0			0
$371$	−4.39229e6	−	1.43510e6i	−1.65675	−	0.541314i
$372$		0			0
$373$	−1.10555e6	+	1.91486e6i	−0.411439	+	0.712633i	−0.995047	−	0.0994020i	$-0.968307\pi$
$373$	−1.10555e6	+	1.91486e6i	−0.411439	+	0.712633i	0.583608	+	0.812035i	$0.301640\pi$
$374$		0			0
$375$	581392.	+	1.00700e6i	0.213496	+	0.369787i
$376$		0			0
$377$	−3.80090e6			−1.37731
$378$		0			0
$379$	−3.81232e6			−1.36330			−0.681649	−	0.731679i	$-0.738737\pi$
$379$	−3.81232e6			−1.36330			−0.681649	+	0.731679i	$0.738737\pi$
$380$		0			0
$381$	123432.	+	213790.i	0.0435626	+	0.0754526i
$382$		0			0
$383$	1.90303e6	−	3.29614e6i	0.662901	−	1.14818i	−0.316949	−	0.948442i	$-0.602658\pi$
$383$	1.90303e6	−	3.29614e6i	0.662901	−	1.14818i	0.979850	−	0.199735i	$-0.0640082\pi$
$384$		0			0
$385$	−738859.	+	663082.i	−0.254044	+	0.227990i
$386$		0			0
$387$	148399.	−	257034.i	0.0503678	−	0.0872395i
$388$		0			0
$389$	−1.53762e6	−	2.66324e6i	−0.515200	−	0.892352i	−0.999844	−	0.0176410i	$-0.994384\pi$
$389$	−1.53762e6	−	2.66324e6i	−0.515200	−	0.892352i	0.484645	−	0.874711i	$-0.338949\pi$
$390$		0			0
$391$	−1.15163e6			−0.380952
$392$		0			0
$393$	−1.35338e6			−0.442017
$394$		0			0
$395$	−393621.	−	681772.i	−0.126936	−	0.219860i
$396$		0			0
$397$	−1.09566e6	+	1.89774e6i	−0.348900	+	0.604312i	−0.986054	−	0.166424i	$-0.946778\pi$
$397$	−1.09566e6	+	1.89774e6i	−0.348900	+	0.604312i	0.637154	+	0.770736i	$0.280111\pi$
$398$		0			0
$399$	−891115.	+	799722.i	−0.280221	+	0.251482i
$400$		0			0
$401$	−888340.	+	1.53865e6i	−0.275879	+	0.477836i	−0.970356	−	0.241678i	$-0.922302\pi$
$401$	−888340.	+	1.53865e6i	−0.275879	+	0.477836i	0.694478	+	0.719514i	$0.255635\pi$
$402$		0			0
$403$	2.56320e6	+	4.43960e6i	0.786177	+	1.36170i
$404$		0			0
$405$	147572.			0.0447061
$406$		0			0
$407$	−4.35522e6			−1.30324
$408$		0			0
$409$	−1.18059e6	−	2.04484e6i	−0.348973	−	0.604438i	0.637095	−	0.770786i	$-0.280136\pi$
$409$	−1.18059e6	−	2.04484e6i	−0.348973	−	0.604438i	−0.986067	+	0.166347i	$0.946803\pi$
$410$		0			0
$411$	−432459.	+	749041.i	−0.126282	+	0.218726i
$412$		0			0
$413$	−3.74328e6	−	1.22305e6i	−1.07989	−	0.352834i
$414$		0			0
$415$	969341.	−	1.67895e6i	0.276284	−	0.478539i
$416$		0			0
$417$	453845.	+	786082.i	0.127811	+	0.221375i
$418$		0			0
$419$	3.23493e6			0.900181			0.450090	−	0.892983i	$-0.351392\pi$
$419$	3.23493e6			0.900181			0.450090	+	0.892983i	$0.351392\pi$
$420$		0			0
$421$	−2.85759e6			−0.785769			−0.392884	−	0.919588i	$-0.628523\pi$
$421$	−2.85759e6			−0.785769			−0.392884	+	0.919588i	$0.628523\pi$
$422$		0			0
$423$	377184.	+	653302.i	0.102495	+	0.177527i
$424$		0			0
$425$	1.06053e6	−	1.83690e6i	0.284808	−	0.493301i
$426$		0			0
$427$	860859.	+	4.08292e6i	0.228487	+	1.08368i
$428$		0			0
$429$	−1.11599e6	+	1.93295e6i	−0.292764	+	0.507081i
$430$		0			0
$431$	−44193.1	−	76544.7i	−0.0114594	−	0.0198482i	0.860239	−	0.509891i	$-0.170314\pi$
$431$	−44193.1	−	76544.7i	−0.0114594	−	0.0198482i	−0.871698	+	0.490043i	$0.836981\pi$
$432$		0			0
$433$	−3.09418e6			−0.793097			−0.396549	−	0.918014i	$-0.629792\pi$
$433$	−3.09418e6			−0.793097			−0.396549	+	0.918014i	$0.629792\pi$
$434$		0			0
$435$	1.05629e6			0.267646
$436$		0			0
$437$	−729645.	−	1.26378e6i	−0.182771	−	0.316569i
$438$		0			0
$439$	242589.	−	420177.i	0.0600773	−	0.104057i	−0.834422	−	0.551125i	$-0.814199\pi$
$439$	242589.	−	420177.i	0.0600773	−	0.104057i	0.894500	+	0.447068i	$0.147532\pi$
$440$		0			0
$441$	1.09874e6	+	803797.i	0.269029	+	0.196811i
$442$		0			0
$443$	637598.	−	1.10435e6i	0.154361	−	0.267361i	−0.778465	−	0.627688i	$-0.784001\pi$
$443$	637598.	−	1.10435e6i	0.154361	−	0.267361i	0.932826	+	0.360327i	$0.117335\pi$
$444$		0			0
$445$	−877118.	−	1.51921e6i	−0.209970	−	0.363679i
$446$		0			0
$447$	−3.24850e6			−0.768978
$448$		0			0
$449$	−3.79144e6			−0.887541			−0.443770	−	0.896141i	$-0.646359\pi$
$449$	−3.79144e6			−0.887541			−0.443770	+	0.896141i	$0.646359\pi$
$450$		0			0
$451$	199767.	+	346006.i	0.0462468	+	0.0801019i
$452$		0			0
$453$	−1.95325e6	+	3.38313e6i	−0.447211	+	0.774592i
$454$		0			0
$455$	−438203.	−	2.07833e6i	−0.0992310	−	0.470637i
$456$		0			0
$457$	−851404.	+	1.47467e6i	−0.190698	+	0.330298i	−0.945482	−	0.325675i	$-0.894408\pi$
$457$	−851404.	+	1.47467e6i	−0.190698	+	0.330298i	0.754784	+	0.655973i	$0.227742\pi$
$458$		0			0
$459$	−295189.	−	511283.i	−0.0653986	−	0.113274i
$460$		0			0
$461$	4.55537e6			0.998323			0.499161	−	0.866509i	$-0.333642\pi$
$461$	4.55537e6			0.998323			0.499161	+	0.866509i	$0.333642\pi$
$462$		0			0
$463$	−5.82647e6			−1.26314			−0.631572	−	0.775317i	$-0.717590\pi$
$463$	−5.82647e6			−1.26314			−0.631572	+	0.775317i	$0.717590\pi$
$464$		0			0
$465$	−712329.	−	1.23379e6i	−0.152774	−	0.264612i
$466$		0			0
$467$	−1.77131e6	+	3.06799e6i	−0.375839	+	0.650972i	−0.990452	−	0.137857i	$-0.955979\pi$
$467$	−1.77131e6	+	3.06799e6i	−0.375839	+	0.650972i	0.614614	+	0.788828i	$0.289312\pi$
$468$		0			0
$469$	2.63111e6	+	859670.i	0.552341	+	0.180468i
$470$		0			0
$471$	2.30218e6	−	3.98750e6i	0.478176	−	0.828225i
$472$		0			0
$473$	−623754.	−	1.08037e6i	−0.128192	−	0.222035i
$474$		0			0
$475$	2.68772e6			0.546575
$476$		0			0
$477$	2.88707e6			0.580979
$478$		0			0
$479$	−2.11771e6	−	3.66798e6i	−0.421723	−	0.730446i	0.574385	−	0.818585i	$-0.305241\pi$
$479$	−2.11771e6	−	3.66798e6i	−0.421723	−	0.730446i	−0.996108	+	0.0881390i	$0.971908\pi$
$480$		0			0
$481$	4.65899e6	−	8.06960e6i	0.918182	−	1.59034i
$482$		0			0
$483$	−1.23484e6	+	1.10819e6i	−0.240847	+	0.216146i
$484$		0			0
$485$	1.81924e6	−	3.15102e6i	0.351185	−	0.608270i
$486$		0			0
$487$	−2.82740e6	−	4.89719e6i	−0.540212	−	0.935675i	−0.998891	−	0.0470729i	$-0.985011\pi$
$487$	−2.82740e6	−	4.89719e6i	−0.540212	−	0.935675i	0.458679	−	0.888602i	$-0.348323\pi$
$488$		0			0
$489$	2.26142e6			0.427671
$490$		0			0
$491$	−8.33183e6			−1.55968			−0.779842	−	0.625976i	$-0.784701\pi$
$491$	−8.33183e6			−1.55968			−0.779842	+	0.625976i	$0.784701\pi$
$492$		0			0
$493$	−2.11290e6	−	3.65966e6i	−0.391528	−	0.678146i
$494$		0			0
$495$	310140.	−	537179.i	0.0568912	−	0.0985384i
$496$		0			0
$497$	−5.90040e6	+	5.29526e6i	−1.07150	+	0.961604i
$498$		0			0
$499$	−3.61884e6	+	6.26802e6i	−0.650607	+	1.12688i	0.332369	+	0.943149i	$0.392152\pi$
$499$	−3.61884e6	+	6.26802e6i	−0.650607	+	1.12688i	−0.982976	+	0.183734i	$0.941181\pi$
$500$		0			0
$501$	1.88674e6	+	3.26794e6i	0.335829	+	0.581674i
$502$		0			0
$503$	6.16761e6			1.08692			0.543459	−	0.839436i	$-0.317114\pi$
$503$	6.16761e6			1.08692			0.543459	+	0.839436i	$0.317114\pi$
$504$		0			0
$505$	−1.48122e6			−0.258459
$506$		0			0
$507$	−716835.	−	1.24159e6i	−0.123851	−	0.214516i
$508$		0			0
$509$	−917439.	+	1.58905e6i	−0.156958	+	0.271859i	−0.933770	−	0.357873i	$-0.883502\pi$
$509$	−917439.	+	1.58905e6i	−0.156958	+	0.271859i	0.776812	+	0.629732i	$0.216835\pi$
$510$		0			0
$511$	−5.08547e6	−	1.66159e6i	−0.861546	−	0.281495i
$512$		0			0
$513$	374050.	−	647874.i	0.0627533	−	0.108692i
$514$		0			0
$515$	1.46423e6	+	2.53612e6i	0.243272	+	0.421359i
$516$		0			0
$517$	3.17079e6			0.521724
$518$		0			0
$519$	−4.15239e6			−0.676674
$520$		0			0
$521$	−2.65520e6	−	4.59894e6i	−0.428551	−	0.742273i	0.568193	−	0.822895i	$-0.307643\pi$
$521$	−2.65520e6	−	4.59894e6i	−0.428551	−	0.742273i	−0.996745	+	0.0806224i	$0.974309\pi$
$522$		0			0
$523$	−1.49418e6	+	2.58799e6i	−0.238862	+	0.413722i	−0.960388	−	0.278666i	$-0.910108\pi$
$523$	−1.49418e6	+	2.58799e6i	−0.238862	+	0.413722i	0.721526	+	0.692388i	$0.243441\pi$
$524$		0			0
$525$	−630457.	−	2.99016e6i	−0.0998291	−	0.473473i
$526$		0			0
$527$	−2.84975e6	+	4.93591e6i	−0.446972	+	0.774178i
$528$		0			0
$529$	2.20709e6	+	3.82279e6i	0.342910	+	0.593937i
$530$		0			0
$531$	2.46047e6			0.378688
$532$		0			0
$533$	−854800.			−0.130331
$534$		0			0
$535$	29138.3	+	50469.0i	0.00440128	+	0.00762325i
$536$		0			0
$537$	3.33768e6	−	5.78102e6i	0.499469	−	0.865105i
$538$		0			0
$539$	5.23504e6	−	2.31026e6i	0.776154	−	0.342522i
$540$		0			0
$541$	−1.08416e6	+	1.87782e6i	−0.159258	+	0.275843i	−0.934601	−	0.355697i	$-0.884243\pi$
$541$	−1.08416e6	+	1.87782e6i	−0.159258	+	0.275843i	0.775343	+	0.631540i	$0.217577\pi$
$542$		0			0
$543$	−1.35617e6	−	2.34895e6i	−0.197385	−	0.341881i
$544$		0			0
$545$	2.48886e6			0.358930
$546$		0			0
$547$	9.13272e6			1.30506			0.652532	−	0.757761i	$-0.273707\pi$
$547$	9.13272e6			1.30506			0.652532	+	0.757761i	$0.273707\pi$
$548$		0			0
$549$	−1.30354e6	−	2.25780e6i	−0.184584	−	0.319709i
$550$		0			0
$551$	2.67738e6	−	4.63735e6i	0.375691	−	0.650715i
$552$		0			0
$553$	936128.	+	4.43991e6i	0.130173	+	0.617392i
$554$		0			0
$555$	−1.29476e6	+	2.24259e6i	−0.178426	+	0.309042i
$556$		0			0
$557$	4.61014e6	+	7.98500e6i	0.629617	+	1.09053i	0.987629	+	0.156811i	$0.0501214\pi$
$557$	4.61014e6	+	7.98500e6i	0.629617	+	1.09053i	−0.358012	+	0.933717i	$0.616545\pi$
$558$		0			0
$559$	2.66904e6			0.361264
$560$		0			0
$561$	−2.48150e6			−0.332894
$562$		0			0
$563$	4.24638e6	+	7.35495e6i	0.564610	+	0.977933i	0.997086	+	0.0762872i	$0.0243066\pi$
$563$	4.24638e6	+	7.35495e6i	0.564610	+	0.977933i	−0.432476	+	0.901645i	$0.642360\pi$
$564$		0			0
$565$	2.18075e6	−	3.77717e6i	0.287399	−	0.497789i
$566$		0			0
$567$	−808518.	−	264169.i	−0.105617	−	0.0345084i
$568$		0			0
$569$	2.35456e6	−	4.07822e6i	0.304880	−	0.528068i	−0.672355	−	0.740229i	$-0.734717\pi$
$569$	2.35456e6	−	4.07822e6i	0.304880	−	0.528068i	0.977235	+	0.212162i	$0.0680503\pi$
$570$		0			0
$571$	−864035.	−	1.49655e6i	−0.110902	−	0.192089i	0.805232	−	0.592960i	$-0.202041\pi$
$571$	−864035.	−	1.49655e6i	−0.110902	−	0.192089i	−0.916134	+	0.400871i	$0.868707\pi$
$572$		0			0
$573$	−2.36864e6			−0.301379
$574$		0			0
$575$	3.72443e6			0.469776
$576$		0			0
$577$	−1.19249e6	−	2.06546e6i	−0.149113	−	0.258272i	0.781787	−	0.623546i	$-0.214309\pi$
$577$	−1.19249e6	−	2.06546e6i	−0.149113	−	0.258272i	−0.930900	+	0.365274i	$0.880975\pi$
$578$		0			0
$579$	3.74007e6	−	6.47799e6i	0.463643	−	0.803053i
$580$		0			0
$581$	−8.31630e6	+	7.46339e6i	−1.02209	+	0.917267i
$582$		0			0
$583$	6.06750e6	−	1.05092e7i	0.739330	−	1.28056i
$584$		0			0
$585$	663543.	+	1.14929e6i	0.0801640	+	0.138848i
$586$		0			0
$587$	3.44904e6			0.413145			0.206573	−	0.978431i	$-0.433769\pi$
$587$	3.44904e6			0.413145			0.206573	+	0.978431i	$0.433769\pi$
$588$		0			0
$589$	−7.22214e6			−0.857784
$590$		0			0
$591$	4.74395e6	+	8.21676e6i	0.558691	+	0.967681i
$592$		0			0
$593$	−567341.	+	982664.i	−0.0662533	+	0.114754i	−0.897249	−	0.441524i	$-0.854438\pi$
$593$	−567341.	+	982664.i	−0.0662533	+	0.114754i	0.830996	+	0.556278i	$0.187771\pi$
$594$		0			0
$595$	1.75750e6	−	1.57725e6i	0.203518	−	0.182646i
$596$		0			0
$597$	3.14355e6	−	5.44480e6i	0.360982	−	0.625239i
$598$		0			0
$599$	3.80933e6	+	6.59795e6i	0.433792	+	0.751349i	0.997196	−	0.0748320i	$-0.0238420\pi$
$599$	3.80933e6	+	6.59795e6i	0.433792	+	0.751349i	−0.563404	+	0.826181i	$0.690509\pi$
$600$		0			0
$601$	9.78414e6			1.10493			0.552467	−	0.833535i	$-0.313686\pi$
$601$	9.78414e6			1.10493			0.552467	+	0.833535i	$0.313686\pi$
$602$		0			0
$603$	−1.72944e6			−0.193692
$604$		0			0
$605$	507616.	+	879217.i	0.0563829	+	0.0976580i
$606$		0			0
$607$	926673.	−	1.60504e6i	0.102083	−	0.176813i	−0.810460	−	0.585795i	$-0.800783\pi$
$607$	926673.	−	1.60504e6i	0.102083	−	0.176813i	0.912543	+	0.408981i	$0.134116\pi$
$608$		0			0
$609$	−5.78720e6	−	1.89087e6i	−0.632304	−	0.206594i
$610$		0			0
$611$	−3.39194e6	+	5.87501e6i	−0.367574	+	0.636657i
$612$		0			0
$613$	3.56048e6	+	6.16694e6i	0.382699	+	0.662855i	0.991447	−	0.130509i	$-0.0416612\pi$
$613$	3.56048e6	+	6.16694e6i	0.382699	+	0.662855i	−0.608748	+	0.793364i	$0.708328\pi$
$614$		0			0
$615$	237554.			0.0253265
$616$		0			0
$617$	−2.75212e6			−0.291041			−0.145521	−	0.989355i	$-0.546486\pi$
$617$	−2.75212e6			−0.291041			−0.145521	+	0.989355i	$0.546486\pi$
$618$		0			0
$619$	−6.51660e6	−	1.12871e7i	−0.683588	−	1.18401i	−0.973878	−	0.227070i	$-0.927085\pi$
$619$	−6.51660e6	−	1.12871e7i	−0.683588	−	1.18401i	0.290291	−	0.956939i	$-0.406248\pi$
$620$		0			0
$621$	518330.	−	897774.i	0.0539358	−	0.0934196i
$622$		0			0
$623$	2.08600e6	+	9.89358e6i	0.215325	+	1.02125i
$624$		0			0
$625$	−2.63935e6	+	4.57149e6i	−0.270269	+	0.468120i
$626$		0			0
$627$	−1.57222e6	−	2.72317e6i	−0.159715	−	0.276634i
$628$		0			0
$629$	1.03597e7			1.04404
$630$		0			0
$631$	4.40820e6			0.440745			0.220373	−	0.975416i	$-0.429273\pi$
$631$	4.40820e6			0.440745			0.220373	+	0.975416i	$0.429273\pi$
$632$		0			0
$633$	−448621.	−	777035.i	−0.0445011	−	0.0770781i
$634$		0			0
$635$	308474.	−	534293.i	0.0303588	−	0.0525829i
$636$		0			0
$637$	−1.31959e6	+	1.21712e7i	−0.128852	+	1.18846i
$638$		0			0
$639$	2.47673e6	−	4.28982e6i	0.239953	−	0.415611i
$640$		0			0
$641$	3.99195e6	+	6.91426e6i	0.383742	+	0.664661i	0.991594	−	0.129389i	$-0.0413017\pi$
$641$	3.99195e6	+	6.91426e6i	0.383742	+	0.664661i	−0.607851	+	0.794051i	$0.707968\pi$
$642$		0			0
$643$	−1.52102e6			−0.145080			−0.0725398	−	0.997366i	$-0.523110\pi$
$643$	−1.52102e6			−0.145080			−0.0725398	+	0.997366i	$0.523110\pi$
$644$		0			0
$645$	−741741.			−0.0702026
$646$		0			0
$647$	−6.26247e6	−	1.08469e7i	−0.588146	−	1.01870i	−0.994475	−	0.104972i	$-0.966525\pi$
$647$	−6.26247e6	−	1.08469e7i	−0.588146	−	1.01870i	0.406329	−	0.913727i	$-0.366809\pi$
$648$		0			0
$649$	5.17096e6	−	8.95637e6i	0.481903	−	0.834681i
$650$		0			0
$651$	1.69409e6	+	8.03482e6i	0.156670	+	0.743060i
$652$		0			0
$653$	8.53702e6	−	1.47865e7i	0.783471	−	1.35701i	−0.146436	−	0.989220i	$-0.546780\pi$
$653$	8.53702e6	−	1.47865e7i	0.783471	−	1.35701i	0.929908	−	0.367792i	$-0.119886\pi$
$654$		0			0
$655$	1.69115e6	+	2.92916e6i	0.154021	+	0.266772i
$656$		0			0
$657$	3.34269e6			0.302122
$658$		0			0
$659$	2.12585e6			0.190686			0.0953432	−	0.995444i	$-0.469605\pi$
$659$	2.12585e6			0.190686			0.0953432	+	0.995444i	$0.469605\pi$
$660$		0			0
$661$	1.30005e6	+	2.25176e6i	0.115733	+	0.200456i	0.918073	−	0.396412i	$-0.129745\pi$
$661$	1.30005e6	+	2.25176e6i	0.115733	+	0.200456i	−0.802339	+	0.596868i	$0.796412\pi$
$662$		0			0
$663$	2.65457e6	−	4.59786e6i	0.234537	−	0.406230i
$664$		0			0
$665$	2.84438e6	+	929350.i	0.249421	+	0.0814940i
$666$		0			0
$667$	3.71010e6	−	6.42608e6i	0.322902	−	0.559283i
$668$		0			0
$669$	2.36787e6	+	4.10128e6i	0.204547	+	0.354286i
$670$		0			0
$671$	−1.09582e7			−0.939577
$672$		0			0
$673$	−1.44746e7			−1.23188			−0.615942	−	0.787792i	$-0.711224\pi$
$673$	−1.44746e7			−1.23188			−0.615942	+	0.787792i	$0.711224\pi$
$674$		0			0
$675$	954660.	+	1.65352e6i	0.0806472	+	0.139685i
$676$		0			0
$677$	1.64423e6	−	2.84788e6i	0.137876	−	0.238809i	−0.788816	−	0.614629i	$-0.789306\pi$
$677$	1.64423e6	−	2.84788e6i	0.137876	−	0.238809i	0.926693	+	0.375820i	$0.122639\pi$
$678$		0			0
$679$	−1.56079e7	+	1.40071e7i	−1.29918	+	1.16594i
$680$		0			0
$681$	−4.41722e6	+	7.65085e6i	−0.364990	+	0.632182i
$682$		0			0
$683$	4.40943e6	+	7.63736e6i	0.361685	+	0.626458i	0.988238	−	0.152921i	$-0.0488681\pi$
$683$	4.40943e6	+	7.63736e6i	0.361685	+	0.626458i	−0.626553	+	0.779379i	$0.715535\pi$
$684$		0			0
$685$	2.16156e6			0.176011
$686$		0			0
$687$	−765729.			−0.0618989
$688$		0			0
$689$	1.29814e7	+	2.24844e7i	1.04177	+	1.80440i
$690$		0			0
$691$	−4.29808e6	+	7.44450e6i	−0.342436	+	0.593117i	−0.984885	−	0.173212i	$-0.944585\pi$
$691$	−4.29808e6	+	7.44450e6i	−0.342436	+	0.593117i	0.642448	+	0.766329i	$0.277919\pi$
$692$		0			0
$693$	−2.66080e6	+	2.38791e6i	−0.210464	+	0.188879i
$694$		0			0
$695$	1.13423e6	−	1.96454e6i	0.0890713	−	0.154276i
$696$		0			0
$697$	−475180.	−	823035.i	−0.0370490	−	0.0641707i
$698$		0			0
$699$	1.01811e6			0.0788134
$700$		0			0
$701$	2.06437e7			1.58669			0.793347	−	0.608770i	$-0.208337\pi$
$701$	2.06437e7			1.58669			0.793347	+	0.608770i	$0.208337\pi$
$702$		0			0
$703$	6.56364e6	+	1.13686e7i	0.500906	+	0.867595i
$704$		0			0
$705$	942640.	−	1.63270e6i	0.0714288	−	0.123718i
$706$		0			0
$707$	8.11530e6	+	2.65153e6i	0.610599	+	0.199503i
$708$		0			0
$709$	213441.	−	369691.i	0.0159464	−	0.0276200i	−0.857942	−	0.513746i	$-0.828257\pi$
$709$	213441.	−	369691.i	0.0159464	−	0.0276200i	0.873888	+	0.486126i	$0.161591\pi$
$710$		0			0
$711$	−1.41752e6	−	2.45521e6i	−0.105161	−	0.182144i
$712$		0			0
$713$	−1.00079e7			−0.737257
$714$		0			0
$715$	5.57805e6			0.408054
$716$		0			0
$717$	−4.02795e6	−	6.97662e6i	−0.292608	−	0.506812i
$718$		0			0
$719$	1.90362e6	−	3.29716e6i	0.137328	−	0.237858i	−0.789157	−	0.614192i	$-0.789482\pi$
$719$	1.90362e6	−	3.29716e6i	0.137328	−	0.237858i	0.926484	+	0.376334i	$0.122815\pi$
$720$		0			0
$721$	−3.48230e6	−	1.65160e7i	−0.249476	−	1.18322i
$722$		0			0
$723$	−2.37472e6	+	4.11313e6i	−0.168953	+	0.292635i
$724$		0			0
$725$	6.83326e6	+	1.18356e7i	0.482817	+	0.836264i
$726$		0			0
$727$	2.22044e7			1.55813			0.779065	−	0.626943i	$-0.215694\pi$
$727$	2.22044e7			1.55813			0.779065	+	0.626943i	$0.215694\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	1.48371e6	+	2.56986e6i	0.102696	+	0.177875i
$732$		0			0
$733$	1.45286e7	−	2.51643e7i	0.998766	−	1.72991i	0.456365	−	0.889793i	$-0.349151\pi$
$733$	1.45286e7	−	2.51643e7i	0.998766	−	1.72991i	0.542401	−	0.840120i	$-0.317515\pi$
$734$		0			0
$735$	366723.	−	3.38244e6i	0.0250391	−	0.230947i
$736$		0			0
$737$	−3.63461e6	+	6.29533e6i	−0.246484	+	0.426923i
$738$		0			0
$739$	1.06761e7	+	1.84916e7i	0.719122	+	1.24556i	0.961348	+	0.275337i	$0.0887893\pi$
$739$	1.06761e7	+	1.84916e7i	0.719122	+	1.24556i	−0.242226	+	0.970220i	$0.577877\pi$
$740$		0			0
$741$	6.72751e6			0.450100
$742$		0			0
$743$	−3.91874e6			−0.260420			−0.130210	−	0.991486i	$-0.541565\pi$
$743$	−3.91874e6			−0.260420			−0.130210	+	0.991486i	$0.541565\pi$
$744$		0			0
$745$	4.05924e6	+	7.03081e6i	0.267950	+	0.464103i
$746$		0			0
$747$	3.49081e6	−	6.04627e6i	0.228889	−	0.396448i
$748$		0			0
$749$	−69298.0	−	328669.i	−0.00451353	−	0.0214069i
$750$		0			0
$751$	2.83456e6	−	4.90960e6i	0.183394	−	0.317648i	−0.759640	−	0.650344i	$-0.774625\pi$
$751$	2.83456e6	−	4.90960e6i	0.183394	−	0.317648i	0.943034	+	0.332696i	$0.107958\pi$
$752$		0			0
$753$	−5.36817e6	−	9.29794e6i	−0.345015	−	0.597584i
$754$		0			0
$755$	9.76293e6			0.623323
$756$		0			0
$757$	−1.91706e7			−1.21590			−0.607949	−	0.793976i	$-0.708007\pi$
$757$	−1.91706e7			−1.21590			−0.607949	+	0.793976i	$0.708007\pi$
$758$		0			0
$759$	−2.17866e6	−	3.77355e6i	−0.137273	−	0.237764i
$760$		0			0
$761$	−7.31680e6	+	1.26731e7i	−0.457993	+	0.793268i	−0.998855	−	0.0478438i	$-0.984765\pi$
$761$	−7.31680e6	+	1.26731e7i	−0.457993	+	0.793268i	0.540861	+	0.841112i	$0.318098\pi$
$762$		0			0
$763$	−1.36360e7	−	4.45531e6i	−0.847958	−	0.277056i
$764$		0			0
$765$	−737722.	+	1.27777e6i	−0.0455763	+	0.0789405i
$766$		0			0
$767$	1.10632e7	+	1.91621e7i	0.679038	+	1.17613i
$768$		0			0
$769$	1.57337e7			0.959432			0.479716	−	0.877424i	$-0.340740\pi$
$769$	1.57337e7			0.959432			0.479716	+	0.877424i	$0.340740\pi$
$770$		0			0
$771$	−1.07543e7			−0.651548
$772$		0			0
$773$	−2.02452e6	−	3.50658e6i	−0.121864	−	0.211074i	0.798639	−	0.601810i	$-0.205554\pi$
$773$	−2.02452e6	−	3.50658e6i	−0.121864	−	0.211074i	−0.920503	+	0.390736i	$0.872220\pi$
$774$		0			0
$775$	9.21626e6	−	1.59630e7i	0.551189	−	0.954687i
$776$		0			0
$777$	1.11082e7	−	9.96894e6i	0.660071	−	0.592374i
$778$		0			0
$779$	602126.	−	1.04291e6i	0.0355504	−	0.0615750i
$780$		0			0
$781$	−1.04103e7	−	1.80311e7i	−0.610708	−	1.05778i
$782$		0			0
$783$	3.80395e6			0.221733
$784$		0			0
$785$	−1.15070e7			−0.666481
$786$		0			0
$787$	−1.08056e7	−	1.87158e7i	−0.621886	−	1.07714i	−0.989134	−	0.147015i	$-0.953033\pi$
$787$	−1.08056e7	−	1.87158e7i	−0.621886	−	1.07714i	0.367248	−	0.930123i	$-0.380300\pi$
$788$		0			0
$789$	−9.55037e6	+	1.65417e7i	−0.546170	+	0.945993i
$790$		0			0
$791$	−1.87094e7	+	1.67906e7i	−1.06321	+	0.954166i
$792$		0			0
$793$	1.17225e7	−	2.03039e7i	0.661968	−	1.14656i
$794$		0			0
$795$	−3.60760e6	−	6.24855e6i	−0.202442	−	0.350640i
$796$		0			0
$797$	1.38162e7			0.770445			0.385222	−	0.922824i	$-0.374125\pi$
$797$	1.38162e7			0.770445			0.385222	+	0.922824i	$0.374125\pi$
$798$		0			0
$799$	−7.54226e6			−0.417960
$800$		0			0
$801$	−3.15870e6	−	5.47103e6i	−0.173951	−	0.301292i
$802$		0			0
$803$	7.02505e6	−	1.21678e7i	0.384469	−	0.665919i
$804$		0			0
$805$	3.94152e6	+	1.28782e6i	0.214375	+	0.0700432i
$806$		0			0
$807$	−697395.	+	1.20792e6i	−0.0376960	+	0.0652913i
$808$		0			0
$809$	1.75378e7	+	3.03764e7i	0.942116	+	1.63179i	0.761425	+	0.648253i	$0.224500\pi$
$809$	1.75378e7	+	3.03764e7i	0.942116	+	1.63179i	0.180691	+	0.983540i	$0.442167\pi$
$810$		0			0
$811$	−6.56287e6			−0.350382			−0.175191	−	0.984534i	$-0.556054\pi$
$811$	−6.56287e6			−0.350382			−0.175191	+	0.984534i	$0.556054\pi$
$812$		0			0
$813$	−1.76299e7			−0.935456
$814$		0			0
$815$	−2.82582e6	−	4.89446e6i	−0.149022	−	0.258114i
$816$		0			0
$817$	−1.88009e6	+	3.25640e6i	−0.0985423	+	0.170680i
$818$		0			0
$819$	−1.57807e6	−	7.48453e6i	−0.0822084	−	0.389901i
$820$		0			0
$821$	889470.	−	1.54061e6i	0.0460547	−	0.0797690i	−0.842079	−	0.539354i	$-0.818668\pi$
$821$	889470.	−	1.54061e6i	0.0460547	−	0.0797690i	0.888134	+	0.459585i	$0.152002\pi$
$822$		0			0
$823$	9.47928e6	+	1.64186e7i	0.487838	+	0.844960i	0.999902	−	0.0139869i	$-0.00445232\pi$
$823$	9.47928e6	+	1.64186e7i	0.487838	+	0.844960i	−0.512064	+	0.858947i	$0.671119\pi$
$824$		0			0
$825$	8.02531e6			0.410513
$826$		0			0
$827$	−2.82110e7			−1.43435			−0.717174	−	0.696894i	$-0.754565\pi$
$827$	−2.82110e7			−1.43435			−0.717174	+	0.696894i	$0.754565\pi$
$828$		0			0
$829$	1.12010e7	+	1.94008e7i	0.566072	+	0.980466i	0.996949	+	0.0780553i	$0.0248711\pi$
$829$	1.12010e7	+	1.94008e7i	0.566072	+	0.980466i	−0.430877	+	0.902411i	$0.641796\pi$
$830$		0			0
$831$	7.87287e6	−	1.36362e7i	0.395485	−	0.685001i
$832$		0			0
$833$	−1.24524e7	+	5.49534e6i	−0.621787	+	0.274399i
$834$		0			0
$835$	4.71526e6	−	8.16707e6i	0.234040	−	0.405368i
$836$		0			0
$837$	−2.56526e6	−	4.44316e6i	−0.126566	−	0.219219i
$838$		0			0
$839$	1.50303e7			0.737162			0.368581	−	0.929596i	$-0.379844\pi$
$839$	1.50303e7			0.737162			0.368581	+	0.929596i	$0.379844\pi$
$840$		0			0
$841$	6.71672e6			0.327467
$842$		0			0
$843$	−6.32992e6	−	1.09637e7i	−0.306782	−	0.531361i
$844$		0			0
$845$	−1.79148e6	+	3.10293e6i	−0.0863117	+	0.149496i
$846$		0			0
$847$	−1.20724e6	−	5.72573e6i	−0.0578208	−	0.274235i
$848$		0			0
$849$	8.80682e6	−	1.52539e7i	0.419324	−	0.726291i
$850$		0			0
$851$	9.09539e6	+	1.57537e7i	0.430524	+	0.745689i
$852$		0			0
$853$	−3.18297e7			−1.49782			−0.748911	−	0.662670i	$-0.769423\pi$
$853$	−3.18297e7			−1.49782			−0.748911	+	0.662670i	$0.769423\pi$
$854$		0			0
$855$	−1.86962e6			−0.0874656
$856$		0			0
$857$	−1.08911e7	−	1.88640e7i	−0.506549	−	0.877369i	−0.999971	−	0.00757884i	$-0.997588\pi$
$857$	−1.08911e7	−	1.88640e7i	−0.506549	−	0.877369i	0.493422	−	0.869790i	$-0.335746\pi$
$858$		0			0
$859$	1.86674e7	−	3.23329e7i	0.863181	−	1.49507i	−0.00566184	−	0.999984i	$-0.501802\pi$
$859$	1.86674e7	−	3.23329e7i	0.863181	−	1.49507i	0.868842	−	0.495089i	$-0.164864\pi$
$860$		0			0
$861$	−1.30151e6	−	425245.i	−0.0598328	−	0.0195493i
$862$		0			0
$863$	−7.73066e6	+	1.33899e7i	−0.353338	+	0.611999i	−0.986832	−	0.161749i	$-0.948287\pi$
$863$	−7.73066e6	+	1.33899e7i	−0.353338	+	0.611999i	0.633494	+	0.773747i	$0.281620\pi$
$864$		0			0
$865$	5.18872e6	+	8.98712e6i	0.235787	+	0.408395i
$866$		0			0
$867$	−6.87604e6			−0.310664
$868$		0			0
$869$	−1.19163e7			−0.535294
$870$		0			0
$871$	−7.77623e6	−	1.34688e7i	−0.347315	−	0.601568i
$872$		0			0
$873$	6.55150e6	−	1.13475e7i	0.290941	−	0.503925i
$874$		0			0
$875$	−1.24656e7	+	1.11872e7i	−0.550421	+	0.493970i
$876$		0			0
$877$	3.40881e6	−	5.90423e6i	0.149659	−	0.259218i	−0.781442	−	0.623978i	$-0.785516\pi$
$877$	3.40881e6	−	5.90423e6i	0.149659	−	0.259218i	0.931102	+	0.364760i	$0.118849\pi$
$878$		0			0
$879$	5.71492e6	+	9.89853e6i	0.249481	+	0.432114i
$880$		0			0
$881$	−1.20903e7			−0.524805			−0.262402	−	0.964959i	$-0.584515\pi$
$881$	−1.20903e7			−0.524805			−0.262402	+	0.964959i	$0.584515\pi$
$882$		0			0
$883$	−1.63966e7			−0.707706			−0.353853	−	0.935301i	$-0.615129\pi$
$883$	−1.63966e7			−0.707706			−0.353853	+	0.935301i	$0.615129\pi$
$884$		0			0
$885$	−3.07454e6	−	5.32526e6i	−0.131954	−	0.228551i
$886$		0			0
$887$	−1.28503e7	+	2.22574e7i	−0.548409	+	0.949872i	0.449975	+	0.893041i	$0.351433\pi$
$887$	−1.28503e7	+	2.22574e7i	−0.548409	+	0.949872i	−0.998384	+	0.0568310i	$0.981900\pi$
$888$		0			0
$889$	−2.64650e6	+	2.37508e6i	−0.112310	+	0.100791i
$890$		0			0
$891$	1.11688e6	−	1.93450e6i	0.0471318	−	0.0816347i
$892$		0			0
$893$	−4.77861e6	−	8.27679e6i	−0.200527	−	0.347323i
$894$		0			0
$895$	−1.66827e7			−0.696160
$896$		0			0
$897$	9.32247e6			0.386856
$898$		0			0
$899$	−1.83616e7	−	3.18032e7i	−0.757724	−	1.31242i
$900$		0			0
$901$	−1.44326e7	+	2.49980e7i	−0.592287	+	1.02587i
$902$		0			0
$903$	4.06384e6	+	1.32779e6i	0.165851	+	0.0541889i
$904$		0			0
$905$	−3.38927e6	+	5.87039e6i	−0.137558	+	0.238257i
$906$		0			0
$907$	−1.17241e7	−	2.03067e7i	−0.473217	−	0.819636i	0.526313	−	0.850291i	$-0.323574\pi$
$907$	−1.17241e7	−	2.03067e7i	−0.473217	−	0.819636i	−0.999530	+	0.0306552i	$0.990241\pi$
$908$		0			0
$909$	−5.33421e6			−0.214121
$910$		0			0
$911$	3.29134e7			1.31395			0.656973	−	0.753914i	$-0.271837\pi$
$911$	3.29134e7			1.31395			0.656973	+	0.753914i	$0.271837\pi$
$912$		0			0
$913$	−1.46727e7	−	2.54139e7i	−0.582550	−	1.00901i
$914$		0			0
$915$	−3.25775e6	+	5.64259e6i	−0.128637	+	0.222805i
$916$		0			0
$917$	−4.02198e6	−	1.90756e7i	−0.157949	−	0.749126i
$918$		0			0
$919$	−1.26132e7	+	2.18467e7i	−0.492647	+	0.853290i	−0.999964	−	0.00846958i	$-0.997304\pi$
$919$	−1.26132e7	+	2.18467e7i	−0.492647	+	0.853290i	0.507317	+	0.861760i	$0.330637\pi$
$920$		0			0
$921$	−188345.	−	326222.i	−0.00731651	−	0.0126726i
$922$		0			0
$923$	4.45454e7			1.72107
$924$		0			0
$925$	−3.35037e7			−1.28748
$926$		0			0
$927$	5.27302e6	+	9.13314e6i	0.201540	+	0.349077i
$928$		0			0
$929$	−1.25582e7	+	2.17514e7i	−0.477406	+	0.826891i	−0.999665	−	0.0258958i	$-0.991756\pi$
$929$	−1.25582e7	+	2.17514e7i	−0.477406	+	0.826891i	0.522259	+	0.852787i	$0.325090\pi$
$930$		0			0
$931$	−1.39201e7	−	1.01834e7i	−0.526342	−	0.385053i
$932$		0			0
$933$	−1.03135e7	+	1.78635e7i	−0.387885	+	0.671837i
$934$		0			0
$935$	3.10082e6	+	5.37077e6i	0.115997	+	0.200913i
$936$		0			0
$937$	8.25845e6			0.307291			0.153645	−	0.988126i	$-0.450899\pi$
$937$	8.25845e6			0.307291			0.153645	+	0.988126i	$0.450899\pi$
$938$		0			0
$939$	2.04435e7			0.756642
$940$		0			0
$941$	−6.35439e6	−	1.10061e7i	−0.233938	−	0.405192i	0.725026	−	0.688722i	$-0.241828\pi$
$941$	−6.35439e6	−	1.10061e7i	−0.233938	−	0.405192i	−0.958963	+	0.283530i	$0.908494\pi$
$942$		0			0
$943$	834380.	−	1.44519e6i	0.0305552	−	0.0529231i
$944$		0			0
$945$	438555.	+	2.08000e6i	0.0159751	+	0.0757675i
$946$		0			0
$947$	5.31391e6	−	9.20397e6i	0.192548	−	0.333503i	−0.753546	−	0.657395i	$-0.771658\pi$
$947$	5.31391e6	−	9.20397e6i	0.192548	−	0.333503i	0.946094	+	0.323892i	$0.104991\pi$
$948$		0			0
$949$	1.50301e7	+	2.60328e7i	0.541745	+	0.938330i
$950$		0			0
$951$	−1.78627e7			−0.640465
$952$		0			0
$953$	749727.			0.0267406			0.0133703	−	0.999911i	$-0.495744\pi$
$953$	749727.			0.0267406			0.0133703	+	0.999911i	$0.495744\pi$
$954$		0			0
$955$	2.95980e6	+	5.12652e6i	0.105016	+	0.181892i
$956$		0			0
$957$	7.99443e6	−	1.38468e7i	0.282168	−	0.488729i
$958$		0			0
$959$	−1.18427e7	−	3.86941e6i	−0.415820	−	0.135862i
$960$		0			0
$961$	−1.04504e7	+	1.81005e7i	−0.365025	+	0.632242i
$962$		0			0
$963$	104934.	+	181750.i	0.00364627	+	0.00631552i
$964$		0			0
$965$	−1.86940e7			−0.646225
$966$		0			0
$967$	−2.97713e7			−1.02384			−0.511920	−	0.859033i	$-0.671066\pi$
$967$	−2.97713e7			−1.02384			−0.511920	+	0.859033i	$0.671066\pi$
$968$		0			0
$969$	3.73980e6	+	6.47752e6i	0.127950	+	0.221615i
$970$		0			0
$971$	−7.56052e6	+	1.30952e7i	−0.257338	+	0.445722i	−0.965528	−	0.260300i	$-0.916179\pi$
$971$	−7.56052e6	+	1.30952e7i	−0.257338	+	0.445722i	0.708190	+	0.706022i	$0.249512\pi$
$972$		0			0
$973$	−9.73091e6	+	8.73291e6i	−0.329512	+	0.295717i
$974$		0			0
$975$	−8.58505e6	+	1.48697e7i	−0.289222	+	0.500947i
$976$		0			0
$977$	−965535.	−	1.67236e6i	−0.0323617	−	0.0560522i	0.849391	−	0.527764i	$-0.176970\pi$
$977$	−965535.	−	1.67236e6i	−0.0323617	−	0.0560522i	−0.881753	+	0.471712i	$0.843636\pi$
$978$		0			0
$979$	−2.65535e7			−0.885452
$980$		0			0
$981$	8.96295e6			0.297357
$982$		0			0
$983$	2.11172e7	+	3.65760e7i	0.697030	+	1.20729i	0.969491	+	0.245125i	$0.0788291\pi$
$983$	2.11172e7	+	3.65760e7i	0.697030	+	1.20729i	−0.272461	+	0.962167i	$0.587838\pi$
$984$		0			0
$985$	1.18558e7	−	2.05349e7i	0.389352	−	0.674377i
$986$		0			0
$987$	−8.08723e6	+	7.25781e6i	−0.264245	+	0.237144i
$988$		0			0
$989$	−2.60528e6	+	4.51247e6i	−0.0846961	+	0.146698i
$990$		0			0
$991$	2.91740e6	+	5.05308e6i	0.0943651	+	0.163445i	0.909343	−	0.416046i	$-0.136585\pi$
$991$	2.91740e6	+	5.05308e6i	0.0943651	+	0.163445i	−0.814978	+	0.579491i	$0.803251\pi$
$992$		0			0
$993$	−5.74615e6			−0.184928
$994$		0			0
$995$	−1.57124e7			−0.503136
$996$		0			0
$997$	−6.17303e6	−	1.06920e7i	−0.196680	−	0.340660i	0.750770	−	0.660564i	$-0.229683\pi$
$997$	−6.17303e6	−	1.06920e7i	−0.196680	−	0.340660i	−0.947450	+	0.319904i	$0.896349\pi$
$998$		0			0
$999$	−4.66272e6	+	8.07607e6i	−0.147818	+	0.256027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.f.289.1		4
4.3	odd	2		42.6.e.c.37.1	yes	4
7.4	even	3	inner	336.6.q.f.193.1		4
12.11	even	2		126.6.g.h.37.2		4
28.3	even	6		294.6.e.s.67.2		4
28.11	odd	6		42.6.e.c.25.1	✓	4
28.19	even	6		294.6.a.w.1.1		2
28.23	odd	6		294.6.a.r.1.2		2
28.27	even	2		294.6.e.s.79.2		4
84.11	even	6		126.6.g.h.109.2		4
84.23	even	6		882.6.a.bh.1.1		2
84.47	odd	6		882.6.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.e.c.25.1	✓	4	28.11	odd	6
42.6.e.c.37.1	yes	4	4.3	odd	2
126.6.g.h.37.2		4	12.11	even	2
126.6.g.h.109.2		4	84.11	even	6
294.6.a.r.1.2		2	28.23	odd	6
294.6.a.w.1.1		2	28.19	even	6
294.6.e.s.67.2		4	28.3	even	6
294.6.e.s.79.2		4	28.27	even	2
336.6.q.f.193.1		4	7.4	even	3	inner
336.6.q.f.289.1		4	1.1	even	1	trivial
882.6.a.bb.1.2		2	84.47	odd	6
882.6.a.bh.1.1		2	84.23	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)

\(f(q)\)	\(=\)	\(q+(-4.50000 - 7.79423i) q^{3} +(-11.2462 + 19.4789i) q^{5} +(96.4847 - 86.5893i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-4.50000 - 7.79423i) q^{3} +(-11.2462 + 19.4789i) q^{5} +(96.4847 - 86.5893i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(170.231 + 294.849i) q^{11} -728.416 q^{13} +202.431 q^{15} +(-404.923 - 701.348i) q^{17} +(513.101 - 888.717i) q^{19} +(-1109.08 - 362.372i) q^{21} +(711.015 - 1231.51i) q^{23} +(1309.55 + 2268.20i) q^{25} +729.000 q^{27} +5218.03 q^{29} +(-3518.87 - 6094.87i) q^{31} +(1532.08 - 2653.64i) q^{33} +(601.584 + 2853.22i) q^{35} +(-6396.05 + 11078.3i) q^{37} +(3277.87 + 5677.44i) q^{39} +1173.51 q^{41} -3664.17 q^{43} +(-910.940 - 1577.79i) q^{45} +(4656.60 - 8065.46i) q^{47} +(1811.59 - 16709.1i) q^{49} +(-3644.31 + 6312.13i) q^{51} +(-17821.4 - 30867.6i) q^{53} -7657.78 q^{55} -9235.81 q^{57} +(-15188.1 - 26306.5i) q^{59} +(-16093.1 + 27874.1i) q^{61} +(2166.44 + 10275.1i) q^{63} +(8191.89 - 14188.8i) q^{65} +(10675.5 + 18490.6i) q^{67} -12798.3 q^{69} -61153.7 q^{71} +(-20633.9 - 35739.0i) q^{73} +(11785.9 - 20413.8i) q^{75} +(41955.4 + 13708.2i) q^{77} +(-17500.2 + 30311.3i) q^{79} +(-3280.50 - 5681.99i) q^{81} -86193.0 q^{83} +18215.4 q^{85} +(-23481.1 - 40670.5i) q^{87} +(-38996.3 + 67543.6i) q^{89} +(-70281.0 + 63073.0i) q^{91} +(-31669.9 + 54853.8i) q^{93} +(11540.8 + 19989.3i) q^{95} -161765. q^{97} -27577.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{3} + 53 q^{5} - 6 q^{7} - 162 q^{9}+O(q^{10}) \) 4 * q - 18 * q^3 + 53 * q^5 - 6 * q^7 - 162 * q^9	\( 4 q - 18 q^{3} + 53 q^{5} - 6 q^{7} - 162 q^{9} + 191 q^{11} - 758 q^{13} - 954 q^{15} + 340 q^{17} - 1769 q^{19} - 27 q^{21} + 3236 q^{23} + 45 q^{25} + 2916 q^{27} + 8918 q^{29} + 1994 q^{31} + 1719 q^{33} + 4562 q^{35} - 20587 q^{37} + 3411 q^{39} + 17628 q^{41} - 31706 q^{43} + 4293 q^{45} + 33912 q^{47} + 9598 q^{49} + 3060 q^{51} - 49239 q^{53} - 37882 q^{55} + 31842 q^{57} - 56735 q^{59} - 67508 q^{61} + 729 q^{63} + 42762 q^{65} + 75723 q^{67} - 58248 q^{69} + 17984 q^{71} + 3201 q^{73} + 405 q^{75} + 120299 q^{77} + 26612 q^{79} - 13122 q^{81} + 1898 q^{83} + 210040 q^{85} - 40131 q^{87} - 176562 q^{89} - 210085 q^{91} + 17946 q^{93} + 234098 q^{95} - 258846 q^{97} - 30942 q^{99}+O(q^{100}) \) 4 * q - 18 * q^3 + 53 * q^5 - 6 * q^7 - 162 * q^9 + 191 * q^11 - 758 * q^13 - 954 * q^15 + 340 * q^17 - 1769 * q^19 - 27 * q^21 + 3236 * q^23 + 45 * q^25 + 2916 * q^27 + 8918 * q^29 + 1994 * q^31 + 1719 * q^33 + 4562 * q^35 - 20587 * q^37 + 3411 * q^39 + 17628 * q^41 - 31706 * q^43 + 4293 * q^45 + 33912 * q^47 + 9598 * q^49 + 3060 * q^51 - 49239 * q^53 - 37882 * q^55 + 31842 * q^57 - 56735 * q^59 - 67508 * q^61 + 729 * q^63 + 42762 * q^65 + 75723 * q^67 - 58248 * q^69 + 17984 * q^71 + 3201 * q^73 + 405 * q^75 + 120299 * q^77 + 26612 * q^79 - 13122 * q^81 + 1898 * q^83 + 210040 * q^85 - 40131 * q^87 - 176562 * q^89 - 210085 * q^91 + 17946 * q^93 + 234098 * q^95 - 258846 * q^97 - 30942 * q^99

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