LMFDB - Embedded newform 336.6.q.l.193.2

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} + 564x^{8} + 117814x^{6} + 11067780x^{4} + 427918225x^{2} + 3489248448 $ x^10 + 564x^8 + 117814x^6 + 11067780x^4 + 427918225x^2 + 3489248448
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.2
Root			$10.7938i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.6.q.l.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 + 7.79423i) q^{3} +(-19.4585 - 33.7032i) q^{5} +(-106.179 - 74.3848i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(-4.50000 + 7.79423i) q^{3} +(-19.4585 - 33.7032i) q^{5} +(-106.179 - 74.3848i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(47.5857 - 82.4208i) q^{11} +869.093 q^{13} +350.253 q^{15} +(311.362 - 539.294i) q^{17} +(-447.750 - 775.526i) q^{19} +(1057.58 - 492.849i) q^{21} +(811.512 + 1405.58i) q^{23} +(805.232 - 1394.70i) q^{25} +729.000 q^{27} -2922.10 q^{29} +(-4041.01 + 6999.24i) q^{31} +(428.271 + 741.787i) q^{33} +(-440.925 + 5025.97i) q^{35} +(-2726.37 - 4722.20i) q^{37} +(-3910.92 + 6773.91i) q^{39} -2354.46 q^{41} -2406.59 q^{43} +(-1576.14 + 2729.96i) q^{45} +(-1134.86 - 1965.63i) q^{47} +(5740.79 + 15796.2i) q^{49} +(2802.26 + 4853.65i) q^{51} +(12408.0 - 21491.3i) q^{53} -3703.79 q^{55} +8059.50 q^{57} +(-12198.3 + 21128.0i) q^{59} +(-20021.2 - 34677.7i) q^{61} +(-917.719 + 10460.8i) q^{63} +(-16911.3 - 29291.2i) q^{65} +(-23788.4 + 41202.6i) q^{67} -14607.2 q^{69} -46019.2 q^{71} +(-3683.53 + 6380.06i) q^{73} +(7247.09 + 12552.3i) q^{75} +(-11183.4 + 5211.67i) q^{77} +(-33548.8 - 58108.2i) q^{79} +(-3280.50 + 5681.99i) q^{81} -6886.03 q^{83} -24234.6 q^{85} +(13149.5 - 22775.5i) q^{87} +(6434.67 + 11145.2i) q^{89} +(-92279.1 - 64647.4i) q^{91} +(-36369.1 - 62993.1i) q^{93} +(-17425.1 + 30181.2i) q^{95} +19891.7 q^{97} -7708.88 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9}+O(q^{10}) $ 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9	$ 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9} - 424 q^{11} + 374 q^{13} + 108 q^{15} - 952 q^{17} - 139 q^{19} - 1044 q^{21} - 4288 q^{23} - 5605 q^{25} + 7290 q^{27} - 4216 q^{29} - 8131 q^{31} - 3816 q^{33} - 20106 q^{35} - 5425 q^{37} - 1683 q^{39} + 29364 q^{41} + 46862 q^{43} - 486 q^{45} + 17190 q^{47} + 23255 q^{49} - 8568 q^{51} + 15064 q^{53} + 1176 q^{55} + 2502 q^{57} + 83242 q^{59} + 14954 q^{61} + 1539 q^{63} - 23250 q^{65} - 39501 q^{67} + 77184 q^{69} + 56020 q^{71} - 90395 q^{73} - 50445 q^{75} + 63448 q^{77} + 43067 q^{79} - 32805 q^{81} + 75672 q^{83} - 75272 q^{85} + 18972 q^{87} - 72608 q^{89} - 288287 q^{91} - 73179 q^{93} - 190138 q^{95} + 183000 q^{97} + 68688 q^{99}+O(q^{100}) $ 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9 - 424 * q^11 + 374 * q^13 + 108 * q^15 - 952 * q^17 - 139 * q^19 - 1044 * q^21 - 4288 * q^23 - 5605 * q^25 + 7290 * q^27 - 4216 * q^29 - 8131 * q^31 - 3816 * q^33 - 20106 * q^35 - 5425 * q^37 - 1683 * q^39 + 29364 * q^41 + 46862 * q^43 - 486 * q^45 + 17190 * q^47 + 23255 * q^49 - 8568 * q^51 + 15064 * q^53 + 1176 * q^55 + 2502 * q^57 + 83242 * q^59 + 14954 * q^61 + 1539 * q^63 - 23250 * q^65 - 39501 * q^67 + 77184 * q^69 + 56020 * q^71 - 90395 * q^73 - 50445 * q^75 + 63448 * q^77 + 43067 * q^79 - 32805 * q^81 + 75672 * q^83 - 75272 * q^85 + 18972 * q^87 - 72608 * q^89 - 288287 * q^91 - 73179 * q^93 - 190138 * q^95 + 183000 * q^97 + 68688 * 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
$5$	−19.4585	−	33.7032i	−0.348085	−	0.602900i	0.637825	−	0.770182i	$-0.279834\pi$
$5$	−19.4585	−	33.7032i	−0.348085	−	0.602900i	−0.985909	+	0.167281i	$0.946501\pi$
$6$		0			0
$7$	−106.179	−	74.3848i	−0.819015	−	0.573772i
$7$	−106.179	−	74.3848i	−0.819015	−	0.573772i
$8$		0			0
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$		0			0
$11$	47.5857	−	82.4208i	0.118575	−	0.205379i	−0.800628	−	0.599162i	$-0.795501\pi$
$11$	47.5857	−	82.4208i	0.118575	−	0.205379i	0.919203	+	0.393783i	$0.128834\pi$
$12$		0			0
$13$	869.093			1.42629			0.713145	−	0.701016i	$-0.247270\pi$
$13$	869.093			1.42629			0.713145	+	0.701016i	$0.247270\pi$
$14$		0			0
$15$	350.253			0.401934
$16$		0			0
$17$	311.362	−	539.294i	0.261302	−	0.452589i	−0.705286	−	0.708923i	$-0.749181\pi$
$17$	311.362	−	539.294i	0.261302	−	0.452589i	0.966588	+	0.256334i	$0.0825148\pi$
$18$		0			0
$19$	−447.750	−	775.526i	−0.284546	−	0.492847i	0.687953	−	0.725755i	$-0.258509\pi$
$19$	−447.750	−	775.526i	−0.284546	−	0.492847i	−0.972499	+	0.232908i	$0.925176\pi$
$20$		0			0
$21$	1057.58	−	492.849i	0.523315	−	0.243874i
$22$		0			0
$23$	811.512	+	1405.58i	0.319871	+	0.554034i	0.980461	−	0.196714i	$-0.0630269\pi$
$23$	811.512	+	1405.58i	0.319871	+	0.554034i	−0.660590	+	0.750747i	$0.729694\pi$
$24$		0			0
$25$	805.232	−	1394.70i	0.257674	−	0.446305i
$26$		0			0
$27$	729.000			0.192450
$28$		0			0
$29$	−2922.10			−0.645209			−0.322604	−	0.946534i	$-0.604558\pi$
$29$	−2922.10			−0.645209			−0.322604	+	0.946534i	$0.604558\pi$
$30$		0			0
$31$	−4041.01	+	6999.24i	−0.755241	+	1.30812i	0.190013	+	0.981782i	$0.439147\pi$
$31$	−4041.01	+	6999.24i	−0.755241	+	1.30812i	−0.945254	+	0.326335i	$0.894186\pi$
$32$		0			0
$33$	428.271	+	741.787i	0.0684595	+	0.118575i
$34$		0			0
$35$	−440.925	+	5025.97i	−0.0608407	+	0.693506i
$36$		0			0
$37$	−2726.37	−	4722.20i	−0.327401	−	0.567075i	0.654594	−	0.755980i	$-0.272839\pi$
$37$	−2726.37	−	4722.20i	−0.327401	−	0.567075i	−0.981995	+	0.188905i	$0.939506\pi$
$38$		0			0
$39$	−3910.92	+	6773.91i	−0.411735	+	0.713145i
$40$		0			0
$41$	−2354.46			−0.218742			−0.109371	−	0.994001i	$-0.534884\pi$
$41$	−2354.46			−0.218742			−0.109371	+	0.994001i	$0.534884\pi$
$42$		0			0
$43$	−2406.59			−0.198486			−0.0992432	−	0.995063i	$-0.531642\pi$
$43$	−2406.59			−0.198486			−0.0992432	+	0.995063i	$0.531642\pi$
$44$		0			0
$45$	−1576.14	+	2729.96i	−0.116028	+	0.200967i
$46$		0			0
$47$	−1134.86	−	1965.63i	−0.0749371	−	0.129795i	0.826122	−	0.563492i	$-0.190542\pi$
$47$	−1134.86	−	1965.63i	−0.0749371	−	0.129795i	−0.901059	+	0.433697i	$0.857209\pi$
$48$		0			0
$49$	5740.79	+	15796.2i	0.341571	+	0.939856i
$50$		0			0
$51$	2802.26	+	4853.65i	0.150863	+	0.261302i
$52$		0			0
$53$	12408.0	−	21491.3i	0.606754	−	1.05093i	−0.385017	−	0.922909i	$-0.625805\pi$
$53$	12408.0	−	21491.3i	0.606754	−	1.05093i	0.991772	−	0.128020i	$-0.0408621\pi$
$54$		0			0
$55$	−3703.79			−0.165097
$56$		0			0
$57$	8059.50			0.328565
$58$		0			0
$59$	−12198.3	+	21128.0i	−0.456214	+	0.790186i	−0.998757	−	0.0498420i	$-0.984128\pi$
$59$	−12198.3	+	21128.0i	−0.456214	+	0.790186i	0.542543	+	0.840028i	$0.317462\pi$
$60$		0			0
$61$	−20021.2	−	34677.7i	−0.688915	−	1.19324i	−0.972189	−	0.234197i	$-0.924754\pi$
$61$	−20021.2	−	34677.7i	−0.688915	−	1.19324i	0.283274	−	0.959039i	$-0.408579\pi$
$62$		0			0
$63$	−917.719	+	10460.8i	−0.0291312	+	0.332058i
$64$		0			0
$65$	−16911.3	−	29291.2i	−0.496470	−	0.859911i
$66$		0			0
$67$	−23788.4	+	41202.6i	−0.647407	+	1.12134i	0.336333	+	0.941743i	$0.390813\pi$
$67$	−23788.4	+	41202.6i	−0.647407	+	1.12134i	−0.983740	+	0.179599i	$0.942520\pi$
$68$		0			0
$69$	−14607.2			−0.369356
$70$		0			0
$71$	−46019.2			−1.08341			−0.541705	−	0.840568i	$-0.682221\pi$
$71$	−46019.2			−1.08341			−0.541705	+	0.840568i	$0.682221\pi$
$72$		0			0
$73$	−3683.53	+	6380.06i	−0.0809016	+	0.140126i	−0.903637	−	0.428298i	$-0.859113\pi$
$73$	−3683.53	+	6380.06i	−0.0809016	+	0.140126i	0.822736	+	0.568424i	$0.192447\pi$
$74$		0			0
$75$	7247.09	+	12552.3i	0.148768	+	0.257674i
$76$		0			0
$77$	−11183.4	+	5211.67i	−0.214955	+	0.100173i
$78$		0			0
$79$	−33548.8	−	58108.2i	−0.604796	−	1.04754i	−0.992084	−	0.125579i	$-0.959921\pi$
$79$	−33548.8	−	58108.2i	−0.604796	−	1.04754i	0.387288	−	0.921959i	$-0.373412\pi$
$80$		0			0
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−6886.03			−0.109717			−0.0548585	−	0.998494i	$-0.517471\pi$
$83$	−6886.03			−0.109717			−0.0548585	+	0.998494i	$0.517471\pi$
$84$		0			0
$85$	−24234.6			−0.363821
$86$		0			0
$87$	13149.5	−	22775.5i	0.186256	−	0.322604i
$88$		0			0
$89$	6434.67	+	11145.2i	0.0861095	+	0.149146i	0.905863	−	0.423570i	$-0.139223\pi$
$89$	6434.67	+	11145.2i	0.0861095	+	0.149146i	−0.819754	+	0.572716i	$0.805890\pi$
$90$		0			0
$91$	−92279.1	−	64647.4i	−1.16815	−	0.818365i
$92$		0			0
$93$	−36369.1	−	62993.1i	−0.436039	−	0.755241i
$94$		0			0
$95$	−17425.1	+	30181.2i	−0.198092	+	0.343105i
$96$		0			0
$97$	19891.7			0.214655			0.107328	−	0.994224i	$-0.465771\pi$
$97$	19891.7			0.214655			0.107328	+	0.994224i	$0.465771\pi$
$98$		0			0
$99$	−7708.88			−0.0790502
$100$		0			0
$101$	−87550.0	+	151641.i	−0.853990	+	1.47915i	0.0235893	+	0.999722i	$0.492491\pi$
$101$	−87550.0	+	151641.i	−0.853990	+	1.47915i	−0.877579	+	0.479432i	$0.840843\pi$
$102$		0			0
$103$	−84663.1	−	146641.i	−0.786323	−	1.36195i	−0.928205	−	0.372068i	$-0.878649\pi$
$103$	−84663.1	−	146641.i	−0.786323	−	1.36195i	0.141882	−	0.989884i	$-0.454685\pi$
$104$		0			0
$105$	−37189.4	−	26053.5i	−0.329190	−	0.230618i
$106$		0			0
$107$	82318.3	+	142579.i	0.695083	+	1.20392i	0.970153	+	0.242495i	$0.0779658\pi$
$107$	82318.3	+	142579.i	0.695083	+	1.20392i	−0.275070	+	0.961424i	$0.588701\pi$
$108$		0			0
$109$	−62651.8	+	108516.i	−0.505088	+	0.874838i	0.494894	+	0.868953i	$0.335207\pi$
$109$	−62651.8	+	108516.i	−0.505088	+	0.874838i	−0.999983	+	0.00588537i	$0.998127\pi$
$110$		0			0
$111$	49074.6			0.378050
$112$		0			0
$113$	−194080.			−1.42983			−0.714916	−	0.699211i	$-0.753535\pi$
$113$	−194080.			−1.42983			−0.714916	+	0.699211i	$0.753535\pi$
$114$		0			0
$115$	31581.7	−	54701.0i	0.222685	−	0.385701i
$116$		0			0
$117$	−35198.3	−	60965.2i	−0.237715	−	0.411735i
$118$		0			0
$119$	−73175.3	+	34100.9i	−0.473693	+	0.220749i
$120$		0			0
$121$	75996.7	+	131630.i	0.471880	+	0.817320i
$122$		0			0
$123$	10595.1	−	18351.2i	0.0631453	−	0.109371i
$124$		0			0
$125$	−184290.			−1.05494
$126$		0			0
$127$	26494.6			0.145763			0.0728817	−	0.997341i	$-0.476780\pi$
$127$	26494.6			0.145763			0.0728817	+	0.997341i	$0.476780\pi$
$128$		0			0
$129$	10829.6	−	18757.5i	0.0572981	−	0.0992432i
$130$		0			0
$131$	−47402.8	−	82104.1i	−0.241338	−	0.418010i	0.719758	−	0.694225i	$-0.244253\pi$
$131$	−47402.8	−	82104.1i	−0.241338	−	0.418010i	−0.961096	+	0.276216i	$0.910920\pi$
$132$		0			0
$133$	−10145.9	+	115650.i	−0.0497349	+	0.566914i
$134$		0			0
$135$	−14185.3	−	24569.6i	−0.0669889	−	0.116028i
$136$		0			0
$137$	−8214.72	+	14228.3i	−0.0373931	+	0.0647667i	−0.884116	−	0.467267i	$-0.845239\pi$
$137$	−8214.72	+	14228.3i	−0.0373931	+	0.0647667i	0.846723	+	0.532034i	$0.178572\pi$
$138$		0			0
$139$	−97027.7			−0.425950			−0.212975	−	0.977058i	$-0.568315\pi$
$139$	−97027.7			−0.425950			−0.212975	+	0.977058i	$0.568315\pi$
$140$		0			0
$141$	20427.5			0.0865300
$142$		0			0
$143$	41356.4	−	71631.3i	0.169123	−	0.292929i
$144$		0			0
$145$	56859.8	+	98484.0i	0.224587	+	0.388997i
$146$		0			0
$147$	−148952.	−	26337.7i	−0.568531	−	0.100527i
$148$		0			0
$149$	221433.	+	383533.i	0.817101	+	1.41526i	0.907809	+	0.419383i	$0.137754\pi$
$149$	221433.	+	383533.i	0.817101	+	1.41526i	−0.0907080	+	0.995878i	$0.528913\pi$
$150$		0			0
$151$	35031.9	−	60677.1i	0.125032	−	0.216562i	−0.796713	−	0.604357i	$-0.793430\pi$
$151$	35031.9	−	60677.1i	0.125032	−	0.216562i	0.921746	+	0.387795i	$0.126763\pi$
$152$		0			0
$153$	−50440.6			−0.174201
$154$		0			0
$155$	314528.			1.05155
$156$		0			0
$157$	−179099.	+	310209.i	−0.579888	+	1.00440i	0.415604	+	0.909546i	$0.363570\pi$
$157$	−179099.	+	310209.i	−0.579888	+	1.00440i	−0.995492	+	0.0948493i	$0.969763\pi$
$158$		0			0
$159$	111672.	+	193422.i	0.350310	+	0.606754i
$160$		0			0
$161$	18388.6	−	209607.i	0.0559094	−	0.637295i
$162$		0			0
$163$	−141137.	−	244457.i	−0.416075	−	0.720664i	0.579465	−	0.814997i	$-0.303261\pi$
$163$	−141137.	−	244457.i	−0.416075	−	0.720664i	−0.995541	+	0.0943332i	$0.969928\pi$
$164$		0			0
$165$	16667.0	−	28868.2i	0.0476594	−	0.0825485i
$166$		0			0
$167$	−259891.			−0.721107			−0.360554	−	0.932738i	$-0.617412\pi$
$167$	−259891.			−0.721107			−0.360554	+	0.932738i	$0.617412\pi$
$168$		0			0
$169$	384030.			1.03430
$170$		0			0
$171$	−36267.8	+	62817.6i	−0.0948485	+	0.164282i
$172$		0			0
$173$	−353815.	−	612825.i	−0.898796	−	1.55676i	−0.829036	−	0.559196i	$-0.811110\pi$
$173$	−353815.	−	612825.i	−0.898796	−	1.55676i	−0.0697600	−	0.997564i	$-0.522223\pi$
$174$		0			0
$175$	−189243.	+	88190.5i	−0.467116	+	0.217684i
$176$		0			0
$177$	−109785.	−	190152.i	−0.263395	−	0.456214i
$178$		0			0
$179$	−306990.	+	531722.i	−0.716130	+	1.24037i	0.246392	+	0.969170i	$0.420755\pi$
$179$	−306990.	+	531722.i	−0.716130	+	1.24037i	−0.962522	+	0.271203i	$0.912578\pi$
$180$		0			0
$181$	453472.			1.02885			0.514427	−	0.857534i	$-0.328005\pi$
$181$	453472.			1.02885			0.514427	+	0.857534i	$0.328005\pi$
$182$		0			0
$183$	360382.			0.795490
$184$		0			0
$185$	−106102.	+	183774.i	−0.227926	+	0.394780i
$186$		0			0
$187$	−29632.7	−	51325.4i	−0.0619680	−	0.107332i
$188$		0			0
$189$	−77404.2	−	54226.5i	−0.157620	−	0.110422i
$190$		0			0
$191$	45614.3	+	79006.3i	0.0904727	+	0.156703i	0.907710	−	0.419598i	$-0.137829\pi$
$191$	45614.3	+	79006.3i	0.0904727	+	0.156703i	−0.817237	+	0.576301i	$0.804496\pi$
$192$		0			0
$193$	42513.0	−	73634.7i	0.0821540	−	0.142295i	−0.822021	−	0.569457i	$-0.807153\pi$
$193$	42513.0	−	73634.7i	0.0821540	−	0.142295i	0.904175	+	0.427162i	$0.140487\pi$
$194$		0			0
$195$	304403.			0.573274
$196$		0			0
$197$	−57205.2			−0.105020			−0.0525098	−	0.998620i	$-0.516722\pi$
$197$	−57205.2			−0.105020			−0.0525098	+	0.998620i	$0.516722\pi$
$198$		0			0
$199$	286547.	−	496314.i	0.512936	−	0.888432i	−0.486951	−	0.873429i	$-0.661891\pi$
$199$	286547.	−	496314.i	0.512936	−	0.888432i	0.999887	−	0.0150025i	$-0.00477563\pi$
$200$		0			0
$201$	−214095.	−	370824.i	−0.373781	−	0.647407i
$202$		0			0
$203$	310265.	+	217360.i	0.528436	+	0.370203i
$204$		0			0
$205$	45814.3	+	79352.7i	0.0761407	+	0.131880i
$206$		0			0
$207$	65732.5	−	113852.i	0.106624	−	0.184678i
$208$		0			0
$209$	−85225.9			−0.134960
$210$		0			0
$211$	−680041.			−1.05155			−0.525774	−	0.850625i	$-0.676224\pi$
$211$	−680041.			−1.05155			−0.525774	+	0.850625i	$0.676224\pi$
$212$		0			0
$213$	207086.	−	358684.i	0.312754	−	0.541705i
$214$		0			0
$215$	46828.7	+	81109.6i	0.0690901	+	0.119667i
$216$		0			0
$217$	949706.	−	442579.i	1.36911	−	0.638031i
$218$		0			0
$219$	−33151.8	−	57420.5i	−0.0467086	−	0.0809016i
$220$		0			0
$221$	270602.	−	468697.i	0.372693	−	0.645523i
$222$		0			0
$223$	1.36571e6			1.83907			0.919533	−	0.393013i	$-0.128567\pi$
$223$	1.36571e6			1.83907			0.919533	+	0.393013i	$0.128567\pi$
$224$		0			0
$225$	−130448.			−0.171783
$226$		0			0
$227$	−644483.	+	1.11628e6i	−0.830132	+	1.43783i	0.0678011	+	0.997699i	$0.478402\pi$
$227$	−644483.	+	1.11628e6i	−0.830132	+	1.43783i	−0.897933	+	0.440132i	$0.854932\pi$
$228$		0			0
$229$	−385093.	−	667001.i	−0.485263	−	0.840500i	0.514594	−	0.857434i	$-0.327943\pi$
$229$	−385093.	−	667001.i	−0.485263	−	0.840500i	−0.999857	+	0.0169340i	$0.994609\pi$
$230$		0			0
$231$	9704.50	−	110619.i	0.0119658	−	0.136395i
$232$		0			0
$233$	367551.	+	636617.i	0.443535	+	0.768225i	0.997949	−	0.0640160i	$-0.0203909\pi$
$233$	367551.	+	636617.i	0.443535	+	0.768225i	−0.554414	+	0.832241i	$0.687058\pi$
$234$		0			0
$235$	−44165.4	+	76496.6i	−0.0521689	+	0.0903593i
$236$		0			0
$237$	603878.			0.698358
$238$		0			0
$239$	499045.			0.565125			0.282563	−	0.959249i	$-0.408816\pi$
$239$	499045.			0.565125			0.282563	+	0.959249i	$0.408816\pi$
$240$		0			0
$241$	492263.	−	852624.i	0.545952	−	0.945616i	−0.452595	−	0.891716i	$-0.649502\pi$
$241$	492263.	−	852624.i	0.545952	−	0.945616i	0.998546	−	0.0538997i	$-0.0171651\pi$
$242$		0			0
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	420673.	−	500853.i	0.447744	−	0.533083i
$246$		0			0
$247$	−389137.	−	674004.i	−0.405845	−	0.702943i
$248$		0			0
$249$	30987.1	−	53671.3i	0.0316726	−	0.0548585i
$250$		0			0
$251$	792472.			0.793962			0.396981	−	0.917827i	$-0.370058\pi$
$251$	792472.			0.793962			0.396981	+	0.917827i	$0.370058\pi$
$252$		0			0
$253$	154465.			0.151715
$254$		0			0
$255$	109056.	−	188890.i	0.105026	−	0.181911i
$256$		0			0
$257$	728493.	+	1.26179e6i	0.688006	+	1.19166i	0.972482	+	0.232978i	$0.0748472\pi$
$257$	728493.	+	1.26179e6i	0.688006	+	1.19166i	−0.284476	+	0.958683i	$0.591820\pi$
$258$		0			0
$259$	−61778.7	+	704197.i	−0.0572255	+	0.652296i
$260$		0			0
$261$	118345.	+	204980.i	0.107535	+	0.186256i
$262$		0			0
$263$	−723420.	+	1.25300e6i	−0.644913	+	1.11702i	0.339409	+	0.940639i	$0.389773\pi$
$263$	−723420.	+	1.25300e6i	−0.644913	+	1.11702i	−0.984322	+	0.176383i	$0.943560\pi$
$264$		0			0
$265$	−965767.			−0.844807
$266$		0			0
$267$	−115824.			−0.0994307
$268$		0			0
$269$	−560940.	+	971576.i	−0.472646	+	0.818646i	−0.999510	−	0.0313033i	$-0.990034\pi$
$269$	−560940.	+	971576.i	−0.472646	+	0.818646i	0.526864	+	0.849949i	$0.323368\pi$
$270$		0			0
$271$	−499299.	−	864811.i	−0.412988	−	0.715316i	0.582227	−	0.813026i	$-0.302182\pi$
$271$	−499299.	−	864811.i	−0.412988	−	0.715316i	−0.995215	+	0.0977102i	$0.968848\pi$
$272$		0			0
$273$	919132.	−	428331.i	0.746400	−	0.347835i
$274$		0			0
$275$	−76635.0	−	132736.i	−0.0611076	−	0.105841i
$276$		0			0
$277$	478643.	−	829034.i	0.374811	−	0.649192i	−0.615488	−	0.788147i	$-0.711041\pi$
$277$	478643.	−	829034.i	0.374811	−	0.649192i	0.990299	+	0.138955i	$0.0443742\pi$
$278$		0			0
$279$	654644.			0.503494
$280$		0			0
$281$	10669.7			0.00806093			0.00403047	−	0.999992i	$-0.498717\pi$
$281$	10669.7			0.00806093			0.00403047	+	0.999992i	$0.498717\pi$
$282$		0			0
$283$	218626.	−	378672.i	0.162269	−	0.281059i	−0.773413	−	0.633903i	$-0.781452\pi$
$283$	218626.	−	378672.i	0.162269	−	0.281059i	0.935682	+	0.352844i	$0.114785\pi$
$284$		0			0
$285$	−156826.	−	271631.i	−0.114368	−	0.198092i
$286$		0			0
$287$	249993.	+	175136.i	0.179153	+	0.125508i
$288$		0			0
$289$	516036.	+	893801.i	0.363442	+	0.629501i
$290$		0			0
$291$	−89512.5	+	155040.i	−0.0619657	+	0.107328i
$292$		0			0
$293$	−419569.			−0.285518			−0.142759	−	0.989757i	$-0.545597\pi$
$293$	−419569.			−0.285518			−0.142759	+	0.989757i	$0.545597\pi$
$294$		0			0
$295$	949442.			0.635205
$296$		0			0
$297$	34689.9	−	60084.7i	0.0228198	−	0.0395251i
$298$		0			0
$299$	705280.	+	1.22158e6i	0.456230	+	0.790213i
$300$		0			0
$301$	255528.	+	179014.i	0.162563	+	0.113886i
$302$		0			0
$303$	−787950.	−	1.36477e6i	−0.493051	−	0.853990i
$304$		0			0
$305$	−779166.	+	1.34956e6i	−0.479601	+	0.830694i
$306$		0			0
$307$	2.53530e6			1.53527			0.767633	−	0.640890i	$-0.221434\pi$
$307$	2.53530e6			1.53527			0.767633	+	0.640890i	$0.221434\pi$
$308$		0			0
$309$	1.52394e6			0.907968
$310$		0			0
$311$	1.22243e6	−	2.11731e6i	0.716677	−	1.24132i	−0.245632	−	0.969363i	$-0.578996\pi$
$311$	1.22243e6	−	2.11731e6i	0.716677	−	1.24132i	0.962309	−	0.271958i	$-0.0876710\pi$
$312$		0			0
$313$	−563612.	−	976204.i	−0.325177	−	0.563222i	0.656372	−	0.754438i	$-0.272090\pi$
$313$	−563612.	−	976204.i	−0.325177	−	0.563222i	−0.981548	+	0.191216i	$0.938757\pi$
$314$		0			0
$315$	370420.	−	172622.i	0.210338	−	0.0980211i
$316$		0			0
$317$	1.55967e6	+	2.70143e6i	0.871736	+	1.50989i	0.860200	+	0.509957i	$0.170339\pi$
$317$	1.55967e6	+	2.70143e6i	0.871736	+	1.50989i	0.0115356	+	0.999933i	$0.496328\pi$
$318$		0			0
$319$	−139050.	+	240842.i	−0.0765059	+	0.132512i
$320$		0			0
$321$	−1.48173e6			−0.802613
$322$		0			0
$323$	−557649.			−0.297409
$324$		0			0
$325$	699821.	−	1.21213e6i	0.367518	−	0.636560i
$326$		0			0
$327$	−563866.	−	976645.i	−0.291613	−	0.505088i
$328$		0			0
$329$	−25715.6	+	293124.i	−0.0130980	+	0.149301i
$330$		0			0
$331$	−75327.3	−	130471.i	−0.0377905	−	0.0654550i	0.846512	−	0.532370i	$-0.178699\pi$
$331$	−75327.3	−	130471.i	−0.0377905	−	0.0654550i	−0.884302	+	0.466915i	$0.845365\pi$
$332$		0			0
$333$	−220836.	+	382499.i	−0.109134	+	0.189025i
$334$		0			0
$335$	1.85154e6			0.901410
$336$		0			0
$337$	−1.55730e6			−0.746962			−0.373481	−	0.927638i	$-0.621836\pi$
$337$	−1.55730e6			−0.746962			−0.373481	+	0.927638i	$0.621836\pi$
$338$		0			0
$339$	873360.	−	1.51270e6i	0.412757	−	0.714916i
$340$		0			0
$341$	384588.	+	666126.i	0.179106	+	0.310221i
$342$		0			0
$343$	565445.	−	2.10424e6i	0.259511	−	0.965740i
$344$		0			0
$345$	284235.	+	492309.i	0.128567	+	0.222685i
$346$		0			0
$347$	−1.83186e6	+	3.17287e6i	−0.816710	+	1.41458i	0.0913837	+	0.995816i	$0.470871\pi$
$347$	−1.83186e6	+	3.17287e6i	−0.816710	+	1.41458i	−0.908094	+	0.418767i	$0.862462\pi$
$348$		0			0
$349$	−2.02482e6			−0.889863			−0.444931	−	0.895565i	$-0.646772\pi$
$349$	−2.02482e6			−0.889863			−0.444931	+	0.895565i	$0.646772\pi$
$350$		0			0
$351$	633569.			0.274490
$352$		0			0
$353$	−993558.	+	1.72089e6i	−0.424381	+	0.735050i	−0.996362	−	0.0852167i	$-0.972842\pi$
$353$	−993558.	+	1.72089e6i	−0.424381	+	0.735050i	0.571981	+	0.820267i	$0.306175\pi$
$354$		0			0
$355$	895465.	+	1.55099e6i	0.377119	+	0.653189i
$356$		0			0
$357$	63498.3	−	723799.i	0.0263689	−	0.300571i
$358$		0			0
$359$	−2.32816e6	−	4.03250e6i	−0.953405	−	1.65135i	−0.737977	−	0.674826i	$-0.764219\pi$
$359$	−2.32816e6	−	4.03250e6i	−0.953405	−	1.65135i	−0.215428	−	0.976520i	$-0.569115\pi$
$360$		0			0
$361$	837089.	−	1.44988e6i	0.338068	−	0.585550i
$362$		0			0
$363$	−1.36794e6			−0.544880
$364$		0			0
$365$	286704.			0.112642
$366$		0			0
$367$	1.02143e6	−	1.76917e6i	0.395862	−	0.685653i	−0.597349	−	0.801982i	$-0.703779\pi$
$367$	1.02143e6	−	1.76917e6i	0.395862	−	0.685653i	0.993211	+	0.116328i	$0.0371125\pi$
$368$		0			0
$369$	95355.7	+	165161.i	0.0364570	+	0.0631453i
$370$		0			0
$371$	−2.91609e6	+	1.35895e6i	−1.09993	+	0.512588i
$372$		0			0
$373$	1.19137e6	+	2.06352e6i	0.443380	+	0.767956i	0.997938	−	0.0641888i	$-0.0204460\pi$
$373$	1.19137e6	+	2.06352e6i	0.443380	+	0.767956i	−0.554558	+	0.832145i	$0.687113\pi$
$374$		0			0
$375$	829306.	−	1.43640e6i	0.304535	−	0.527469i
$376$		0			0
$377$	−2.53958e6			−0.920255
$378$		0			0
$379$	1.18232e6			0.422803			0.211402	−	0.977399i	$-0.432197\pi$
$379$	1.18232e6			0.422803			0.211402	+	0.977399i	$0.432197\pi$
$380$		0			0
$381$	−119226.	+	206505.i	−0.0420783	+	0.0728817i
$382$		0			0
$383$	−692612.	−	1.19964e6i	−0.241264	−	0.417882i	0.719810	−	0.694171i	$-0.244229\pi$
$383$	−692612.	−	1.19964e6i	−0.241264	−	0.417882i	−0.961075	+	0.276289i	$0.910895\pi$
$384$		0			0
$385$	393263.	+	275506.i	0.135217	+	0.0947280i
$386$		0			0
$387$	97466.8	+	168817.i	0.0330811	+	0.0572981i
$388$		0			0
$389$	−2.56354e6	+	4.44019e6i	−0.858948	+	1.48774i	0.0139854	+	0.999902i	$0.495548\pi$
$389$	−2.56354e6	+	4.44019e6i	−0.858948	+	1.48774i	−0.872933	+	0.487839i	$0.837785\pi$
$390$		0			0
$391$	1.01070e6			0.334332
$392$		0			0
$393$	853250.			0.278673
$394$		0			0
$395$	−1.30562e6	+	2.26140e6i	−0.421041	+	0.729264i
$396$		0			0
$397$	−1.75060e6	−	3.03212e6i	−0.557455	−	0.965540i	−0.997708	−	0.0676661i	$-0.978445\pi$
$397$	−1.75060e6	−	3.03212e6i	−0.557455	−	0.965540i	0.440253	−	0.897874i	$-0.354889\pi$
$398$		0			0
$399$	−855747.	−	599505.i	−0.269100	−	0.188521i
$400$		0			0
$401$	−1.18949e6	−	2.06026e6i	−0.369403	−	0.639824i	0.620070	−	0.784547i	$-0.287104\pi$
$401$	−1.18949e6	−	2.06026e6i	−0.369403	−	0.639824i	−0.989472	+	0.144723i	$0.953771\pi$
$402$		0			0
$403$	−3.51201e6	+	6.08299e6i	−1.07719	+	1.86575i
$404$		0			0
$405$	255335.			0.0773521
$406$		0			0
$407$	−518944.			−0.155287
$408$		0			0
$409$	645028.	−	1.11722e6i	0.190665	−	0.330241i	−0.754806	−	0.655948i	$-0.772269\pi$
$409$	645028.	−	1.11722e6i	0.190665	−	0.330241i	0.945471	+	0.325707i	$0.105602\pi$
$410$		0			0
$411$	−73932.5	−	128055.i	−0.0215889	−	0.0373931i
$412$		0			0
$413$	2.86680e6	−	1.33598e6i	0.827033	−	0.385411i
$414$		0			0
$415$	133992.	+	232081.i	0.0381908	+	0.0661484i
$416$		0			0
$417$	436625.	−	756256.i	0.122961	−	0.212975i
$418$		0			0
$419$	−4.18879e6			−1.16561			−0.582805	−	0.812612i	$-0.698045\pi$
$419$	−4.18879e6			−1.16561			−0.582805	+	0.812612i	$0.698045\pi$
$420$		0			0
$421$	−4.94226e6			−1.35900			−0.679501	−	0.733674i	$-0.737804\pi$
$421$	−4.94226e6			−1.35900			−0.679501	+	0.733674i	$0.737804\pi$
$422$		0			0
$423$	−91923.6	+	159216.i	−0.0249790	+	0.0432650i
$424$		0			0
$425$	−501437.	−	868514.i	−0.134662	−	0.233241i
$426$		0			0
$427$	−453675.	+	5.17131e6i	−0.120413	+	1.37256i
$428$		0			0
$429$	372207.	+	644682.i	0.0976431	+	0.169123i
$430$		0			0
$431$	−1.09861e6	+	1.90285e6i	−0.284872	+	0.493413i	−0.972578	−	0.232576i	$-0.925284\pi$
$431$	−1.09861e6	+	1.90285e6i	−0.284872	+	0.493413i	0.687706	+	0.725989i	$0.258618\pi$
$432$		0			0
$433$	−6.03003e6			−1.54561			−0.772805	−	0.634644i	$-0.781147\pi$
$433$	−6.03003e6			−1.54561			−0.772805	+	0.634644i	$0.781147\pi$
$434$		0			0
$435$	−1.02348e6			−0.259331
$436$		0			0
$437$	726709.	−	1.25870e6i	0.182036	−	0.315296i
$438$		0			0
$439$	−453322.	−	785176.i	−0.112265	−	0.194449i	0.804418	−	0.594064i	$-0.202477\pi$
$439$	−453322.	−	785176.i	−0.112265	−	0.194449i	−0.916683	+	0.399615i	$0.869144\pi$
$440$		0			0
$441$	875568.	−	1.04245e6i	0.214384	−	0.255246i
$442$		0			0
$443$	−3.04222e6	−	5.26928e6i	−0.736514	−	1.27568i	−0.954056	−	0.299629i	$-0.903137\pi$
$443$	−3.04222e6	−	5.26928e6i	−0.736514	−	1.27568i	0.217542	−	0.976051i	$-0.430196\pi$
$444$		0			0
$445$	250418.	−	433737.i	0.0599468	−	0.103831i
$446$		0			0
$447$	−3.98579e6			−0.943507
$448$		0			0
$449$	714942.			0.167361			0.0836806	−	0.996493i	$-0.473332\pi$
$449$	714942.			0.167361			0.0836806	+	0.996493i	$0.473332\pi$
$450$		0			0
$451$	−112039.	+	194056.i	−0.0259374	+	0.0449249i
$452$		0			0
$453$	315287.	+	546094.i	0.0721874	+	0.125032i
$454$		0			0
$455$	−383205.	+	4.36804e6i	−0.0867765	+	0.989140i
$456$		0			0
$457$	−1.01168e6	−	1.75228e6i	−0.226596	−	0.392476i	0.730201	−	0.683233i	$-0.239426\pi$
$457$	−1.01168e6	−	1.75228e6i	−0.226596	−	0.392476i	−0.956797	+	0.290756i	$0.906093\pi$
$458$		0			0
$459$	226983.	−	393146.i	0.0502876	−	0.0871007i
$460$		0			0
$461$	−3.55201e6			−0.778433			−0.389217	−	0.921146i	$-0.627254\pi$
$461$	−3.55201e6			−0.778433			−0.389217	+	0.921146i	$0.627254\pi$
$462$		0			0
$463$	−1.12514e6			−0.243923			−0.121961	−	0.992535i	$-0.538918\pi$
$463$	−1.12514e6			−0.243923			−0.121961	+	0.992535i	$0.538918\pi$
$464$		0			0
$465$	−1.41538e6	+	2.45151e6i	−0.303557	+	0.525776i
$466$		0			0
$467$	1.59857e6	+	2.76881e6i	0.339188	+	0.587491i	0.984280	−	0.176614i	$-0.0565144\pi$
$467$	1.59857e6	+	2.76881e6i	0.339188	+	0.587491i	−0.645092	+	0.764105i	$0.723181\pi$
$468$		0			0
$469$	5.59067e6	−	2.60535e6i	1.17363	−	0.546932i
$470$		0			0
$471$	−1.61189e6	−	2.79188e6i	−0.334798	−	0.579888i
$472$		0			0
$473$	−114519.	+	198353.i	−0.0235356	+	0.0407648i
$474$		0			0
$475$	−1.44217e6			−0.293280
$476$		0			0
$477$	−2.01010e6			−0.404503
$478$		0			0
$479$	2.45002e6	−	4.24356e6i	0.487900	−	0.845068i	−0.512003	−	0.858984i	$-0.671096\pi$
$479$	2.45002e6	−	4.24356e6i	0.487900	−	0.845068i	0.999903	+	0.0139156i	$0.00442960\pi$
$480$		0			0
$481$	−2.36947e6	−	4.10404e6i	−0.466969	−	0.808814i
$482$		0			0
$483$	1.55097e6	+	1.08656e6i	0.302508	+	0.211926i
$484$		0			0
$485$	−387062.	−	670412.i	−0.0747182	−	0.129416i
$486$		0			0
$487$	−1.04449e6	+	1.80911e6i	−0.199563	+	0.345654i	−0.948387	−	0.317115i	$-0.897286\pi$
$487$	−1.04449e6	+	1.80911e6i	−0.199563	+	0.345654i	0.748824	+	0.662769i	$0.230619\pi$
$488$		0			0
$489$	2.54047e6			0.480442
$490$		0			0
$491$	3.63571e6			0.680589			0.340295	−	0.940319i	$-0.389473\pi$
$491$	3.63571e6			0.680589			0.340295	+	0.940319i	$0.389473\pi$
$492$		0			0
$493$	−909831.	+	1.57587e6i	−0.168594	+	0.292014i
$494$		0			0
$495$	150003.	+	259813.i	0.0275162	+	0.0476594i
$496$		0			0
$497$	4.88625e6	+	3.42313e6i	0.887330	+	0.621631i
$498$		0			0
$499$	914883.	+	1.58462e6i	0.164480	+	0.284888i	0.936471	−	0.350746i	$-0.114072\pi$
$499$	914883.	+	1.58462e6i	0.164480	+	0.284888i	−0.771990	+	0.635634i	$0.780739\pi$
$500$		0			0
$501$	1.16951e6	−	2.02565e6i	0.208166	−	0.360554i
$502$		0			0
$503$	82169.1			0.0144807			0.00724033	−	0.999974i	$-0.497695\pi$
$503$	82169.1			0.0144807			0.00724033	+	0.999974i	$0.497695\pi$
$504$		0			0
$505$	6.81437e6			1.18904
$506$		0			0
$507$	−1.72813e6	+	2.99322e6i	−0.298578	+	0.517152i
$508$		0			0
$509$	−5.44896e6	−	9.43787e6i	−0.932221	−	1.61465i	−0.779516	−	0.626383i	$-0.784535\pi$
$509$	−5.44896e6	−	9.43787e6i	−0.932221	−	1.61465i	−0.152705	−	0.988272i	$-0.548799\pi$
$510$		0			0
$511$	865692.	−	403427.i	0.146660	−	0.0683460i
$512$		0			0
$513$	−326410.	−	565358.i	−0.0547608	−	0.0948485i
$514$		0			0
$515$	−3.29484e6	+	5.70683e6i	−0.547414	+	0.948149i
$516$		0			0
$517$	−216012.			−0.0355428
$518$		0			0
$519$	6.36867e6			1.03784
$520$		0			0
$521$	−2.41997e6	+	4.19151e6i	−0.390585	+	0.676512i	−0.992527	−	0.122027i	$-0.961060\pi$
$521$	−2.41997e6	+	4.19151e6i	−0.390585	+	0.676512i	0.601942	+	0.798540i	$0.294394\pi$
$522$		0			0
$523$	−3.39749e6	−	5.88463e6i	−0.543130	−	0.940729i	−0.998722	−	0.0505405i	$-0.983906\pi$
$523$	−3.39749e6	−	5.88463e6i	−0.543130	−	0.940729i	0.455592	−	0.890189i	$-0.349428\pi$
$524$		0			0
$525$	164217.	−	1.87186e6i	0.0260028	−	0.296398i
$526$		0			0
$527$	2.51643e6	+	4.35859e6i	0.394692	+	0.683627i
$528$		0			0
$529$	1.90107e6	−	3.29275e6i	0.295365	−	0.511586i
$530$		0			0
$531$	1.97612e6			0.304143
$532$		0			0
$533$	−2.04625e6			−0.311989
$534$		0			0
$535$	3.20358e6	−	5.54877e6i	0.483896	−	0.838132i
$536$		0			0
$537$	−2.76291e6	−	4.78550e6i	−0.413458	−	0.716130i
$538$		0			0
$539$	1.57511e6	+	278510.i	0.233528	+	0.0412923i
$540$		0			0
$541$	−1.50474e6	−	2.60629e6i	−0.221039	−	0.382851i	0.734085	−	0.679058i	$-0.237612\pi$
$541$	−1.50474e6	−	2.60629e6i	−0.221039	−	0.382851i	−0.955124	+	0.296207i	$0.904278\pi$
$542$		0			0
$543$	−2.04062e6	+	3.53446e6i	−0.297005	+	0.514427i
$544$		0			0
$545$	4.87645e6			0.703254
$546$		0			0
$547$	−4.87387e6			−0.696476			−0.348238	−	0.937406i	$-0.613220\pi$
$547$	−4.87387e6			−0.696476			−0.348238	+	0.937406i	$0.613220\pi$
$548$		0			0
$549$	−1.62172e6	+	2.80890e6i	−0.229638	+	0.397745i
$550$		0			0
$551$	1.30837e6	+	2.26617e6i	0.183591	+	0.317989i
$552$		0			0
$553$	−760206.	+	8.66537e6i	−0.105711	+	1.20496i
$554$		0			0
$555$	−954919.	−	1.65397e6i	−0.131593	−	0.227926i
$556$		0			0
$557$	−3.11238e6	+	5.39080e6i	−0.425064	+	0.736233i	−0.996426	−	0.0844653i	$-0.973082\pi$
$557$	−3.11238e6	+	5.39080e6i	−0.425064	+	0.736233i	0.571362	+	0.820698i	$0.306415\pi$
$558$		0			0
$559$	−2.09155e6			−0.283099
$560$		0			0
$561$	533389.			0.0715545
$562$		0			0
$563$	−3.15666e6	+	5.46749e6i	−0.419717	+	0.726971i	−0.995911	−	0.0903421i	$-0.971204\pi$
$563$	−3.15666e6	+	5.46749e6i	−0.419717	+	0.726971i	0.576194	+	0.817313i	$0.304537\pi$
$564$		0			0
$565$	3.77651e6	+	6.54111e6i	0.497702	+	0.862046i
$566$		0			0
$567$	770973.	−	359287.i	0.100712	−	0.0469335i
$568$		0			0
$569$	4.14273e6	+	7.17543e6i	0.536422	+	0.929110i	0.999093	+	0.0425798i	$0.0135577\pi$
$569$	4.14273e6	+	7.17543e6i	0.536422	+	0.929110i	−0.462671	+	0.886530i	$0.653109\pi$
$570$		0			0
$571$	−1.93234e6	+	3.34691e6i	−0.248023	+	0.429589i	−0.962977	−	0.269582i	$-0.913114\pi$
$571$	−1.93234e6	+	3.34691e6i	−0.248023	+	0.429589i	0.714954	+	0.699172i	$0.246448\pi$
$572$		0			0
$573$	−821057.			−0.104469
$574$		0			0
$575$	2.61382e6			0.329690
$576$		0			0
$577$	−1.71943e6	+	2.97815e6i	−0.215004	+	0.372398i	−0.953274	−	0.302108i	$-0.902310\pi$
$577$	−1.71943e6	+	2.97815e6i	−0.215004	+	0.372398i	0.738270	+	0.674505i	$0.235643\pi$
$578$		0			0
$579$	382617.	+	662712.i	0.0474316	+	0.0821540i
$580$		0			0
$581$	731149.	+	512216.i	0.0898599	+	0.0629525i
$582$		0			0
$583$	−1.18089e6	−	2.04536e6i	−0.143892	−	0.249229i
$584$		0			0
$585$	−1.36981e6	+	2.37259e6i	−0.165490	+	0.286637i
$586$		0			0
$587$	−4.00304e6			−0.479507			−0.239754	−	0.970834i	$-0.577067\pi$
$587$	−4.00304e6			−0.479507			−0.239754	+	0.970834i	$0.577067\pi$
$588$		0			0
$589$	7.23745e6			0.859602
$590$		0			0
$591$	257423.	−	445871.i	0.0303165	−	0.0525098i
$592$		0			0
$593$	1.33665e6	+	2.31515e6i	0.156092	+	0.270360i	0.933456	−	0.358691i	$-0.116777\pi$
$593$	1.33665e6	+	2.31515e6i	0.156092	+	0.270360i	−0.777364	+	0.629051i	$0.783444\pi$
$594$		0			0
$595$	2.57319e6	+	1.80268e6i	0.297975	+	0.208750i
$596$		0			0
$597$	2.57892e6	+	4.46683e6i	0.296144	+	0.512936i
$598$		0			0
$599$	7.59516e6	−	1.31552e7i	0.864908	−	1.49806i	−0.00223070	−	0.999998i	$-0.500710\pi$
$599$	7.59516e6	−	1.31552e7i	0.864908	−	1.49806i	0.867139	−	0.498067i	$-0.165957\pi$
$600$		0			0
$601$	−1.16215e7			−1.31242			−0.656212	−	0.754576i	$-0.727842\pi$
$601$	−1.16215e7			−1.31242			−0.656212	+	0.754576i	$0.727842\pi$
$602$		0			0
$603$	3.85371e6			0.431605
$604$		0			0
$605$	2.95757e6	−	5.12266e6i	0.328508	−	0.568993i
$606$		0			0
$607$	−7.96035e6	−	1.37877e7i	−0.876921	−	1.51887i	−0.854702	−	0.519119i	$-0.826260\pi$
$607$	−7.96035e6	−	1.37877e7i	−0.876921	−	1.51887i	−0.0222192	−	0.999753i	$-0.507073\pi$
$608$		0			0
$609$	−3.09035e6	+	1.44015e6i	−0.337648	+	0.157350i
$610$		0			0
$611$	−986298.	−	1.70832e6i	−0.106882	−	0.185125i
$612$		0			0
$613$	−2.82505e6	+	4.89313e6i	−0.303651	+	0.525939i	−0.976960	−	0.213422i	$-0.931539\pi$
$613$	−2.82505e6	+	4.89313e6i	−0.303651	+	0.525939i	0.673309	+	0.739361i	$0.264872\pi$
$614$		0			0
$615$	−824658.			−0.0879197
$616$		0			0
$617$	1.22146e7			1.29172			0.645858	−	0.763457i	$-0.276500\pi$
$617$	1.22146e7			1.29172			0.645858	+	0.763457i	$0.276500\pi$
$618$		0			0
$619$	2.89912e6	−	5.02143e6i	0.304116	−	0.526745i	−0.672948	−	0.739690i	$-0.734972\pi$
$619$	2.89912e6	−	5.02143e6i	0.304116	−	0.526745i	0.977064	+	0.212945i	$0.0683055\pi$
$620$		0			0
$621$	591592.	+	1.02467e6i	0.0615593	+	0.106624i
$622$		0			0
$623$	145808.	−	1.66202e6i	0.0150508	−	0.171560i
$624$		0			0
$625$	1.06967e6	+	1.85272e6i	0.109534	+	0.189718i
$626$		0			0
$627$	383517.	−	664270.i	0.0389597	−	0.0674802i
$628$		0			0
$629$	−3.39554e6			−0.342202
$630$		0			0
$631$	1.60470e7			1.60443			0.802213	−	0.597039i	$-0.203656\pi$
$631$	1.60470e7			1.60443			0.802213	+	0.597039i	$0.203656\pi$
$632$		0			0
$633$	3.06018e6	−	5.30039e6i	0.303556	−	0.525774i
$634$		0			0
$635$	−515546.	−	892952.i	−0.0507380	−	0.0878808i
$636$		0			0
$637$	4.98928e6	+	1.37283e7i	0.487180	+	1.34051i
$638$		0			0
$639$	1.86378e6	+	3.22816e6i	0.180568	+	0.312754i
$640$		0			0
$641$	3.76573e6	−	6.52243e6i	0.361996	−	0.626996i	−0.626293	−	0.779588i	$-0.715429\pi$
$641$	3.76573e6	−	6.52243e6i	0.361996	−	0.626996i	0.988289	+	0.152592i	$0.0487620\pi$
$642$		0			0
$643$	1.15518e7			1.10185			0.550926	−	0.834554i	$-0.314275\pi$
$643$	1.15518e7			1.10185			0.550926	+	0.834554i	$0.314275\pi$
$644$		0			0
$645$	−842916.			−0.0797783
$646$		0			0
$647$	1.01253e7	−	1.75375e7i	0.950928	−	1.64706i	0.207504	−	0.978234i	$-0.433466\pi$
$647$	1.01253e7	−	1.75375e7i	0.950928	−	1.64706i	0.743424	−	0.668821i	$-0.233201\pi$
$648$		0			0
$649$	1.16093e6	+	2.01078e6i	0.108191	+	0.187393i
$650$		0			0
$651$	−824113.	+	9.39383e6i	−0.0762140	+	0.868741i
$652$		0			0
$653$	−9.88289e6	−	1.71177e7i	−0.906987	−	1.57095i	−0.818227	−	0.574895i	$-0.805043\pi$
$653$	−9.88289e6	−	1.71177e7i	−0.906987	−	1.57095i	−0.0887596	−	0.996053i	$-0.528290\pi$
$654$		0			0
$655$	−1.84478e6	+	3.19525e6i	−0.168012	+	0.291006i
$656$		0			0
$657$	596732.			0.0539344
$658$		0			0
$659$	1.85458e7			1.66353			0.831766	−	0.555127i	$-0.187330\pi$
$659$	1.85458e7			1.66353			0.831766	+	0.555127i	$0.187330\pi$
$660$		0			0
$661$	3.28000e6	−	5.68113e6i	0.291992	−	0.505744i	−0.682289	−	0.731083i	$-0.739015\pi$
$661$	3.28000e6	−	5.68113e6i	0.291992	−	0.505744i	0.974281	+	0.225338i	$0.0723488\pi$
$662$		0			0
$663$	2.43542e6	+	4.21827e6i	0.215174	+	0.372693i
$664$		0			0
$665$	4.09520e6	−	1.90843e6i	0.359104	−	0.167349i
$666$		0			0
$667$	−2.37132e6	−	4.10725e6i	−0.206384	−	0.357467i
$668$		0			0
$669$	−6.14571e6	+	1.06447e7i	−0.530893	+	0.919533i
$670$		0			0
$671$	−3.81089e6			−0.326753
$672$		0			0
$673$	1.06297e7			0.904657			0.452328	−	0.891851i	$-0.350594\pi$
$673$	1.06297e7			0.904657			0.452328	+	0.891851i	$0.350594\pi$
$674$		0			0
$675$	587014.	−	1.01674e6i	0.0495894	−	0.0858914i
$676$		0			0
$677$	−5.52041e6	−	9.56164e6i	−0.462914	−	0.801790i	0.536191	−	0.844097i	$-0.319863\pi$
$677$	−5.52041e6	−	9.56164e6i	−0.462914	−	0.801790i	−0.999105	+	0.0423067i	$0.986529\pi$
$678$		0			0
$679$	−2.11207e6	−	1.47964e6i	−0.175806	−	0.123163i
$680$		0			0
$681$	−5.80035e6	−	1.00465e7i	−0.479277	−	0.830132i
$682$		0			0
$683$	7.06934e6	−	1.22445e7i	0.579866	−	1.00436i	−0.415629	−	0.909534i	$-0.636438\pi$
$683$	7.06934e6	−	1.22445e7i	0.579866	−	1.00436i	0.995494	−	0.0948222i	$-0.0302282\pi$
$684$		0			0
$685$	639385.			0.0520638
$686$		0			0
$687$	6.93168e6			0.560333
$688$		0			0
$689$	1.07837e7	−	1.86780e7i	0.865408	−	1.49893i
$690$		0			0
$691$	−9.28696e6	−	1.60855e7i	−0.739909	−	1.28156i	−0.952536	−	0.304426i	$-0.901535\pi$
$691$	−9.28696e6	−	1.60855e7i	−0.739909	−	1.28156i	0.212627	−	0.977133i	$-0.431798\pi$
$692$		0			0
$693$	818518.	+	573424.i	0.0647433	+	0.0453568i
$694$		0			0
$695$	1.88802e6	+	3.27014e6i	0.148267	+	0.256805i
$696$		0			0
$697$	−733089.	+	1.26975e6i	−0.0571577	+	0.0990000i
$698$		0			0
$699$	−6.61592e6			−0.512150
$700$		0			0
$701$	2.68113e6			0.206074			0.103037	−	0.994678i	$-0.467144\pi$
$701$	2.68113e6			0.206074			0.103037	+	0.994678i	$0.467144\pi$
$702$		0			0
$703$	−2.44146e6	+	4.22874e6i	−0.186321	+	0.322717i
$704$		0			0
$705$	−397488.	−	688470.i	−0.0301198	−	0.0521689i
$706$		0			0
$707$	2.05757e7	−	9.58864e6i	1.54813	−	0.721454i
$708$		0			0
$709$	8.00549e6	+	1.38659e7i	0.598098	+	1.03594i	0.993102	+	0.117256i	$0.0374100\pi$
$709$	8.00549e6	+	1.38659e7i	0.598098	+	1.03594i	−0.395004	+	0.918680i	$0.629257\pi$
$710$		0			0
$711$	−2.71745e6	+	4.70676e6i	−0.201599	+	0.349179i
$712$		0			0
$713$	−1.31173e7			−0.966321
$714$		0			0
$715$	−3.21894e6			−0.235476
$716$		0			0
$717$	−2.24570e6	+	3.88967e6i	−0.163138	+	0.282563i
$718$		0			0
$719$	−6.79064e6	−	1.17617e7i	−0.489879	−	0.848495i	0.510054	−	0.860143i	$-0.329626\pi$
$719$	−6.79064e6	−	1.17617e7i	−0.489879	−	0.848495i	−0.999932	+	0.0116480i	$0.996292\pi$
$720$		0			0
$721$	−1.91844e6	+	2.18678e7i	−0.137439	+	1.56663i
$722$		0			0
$723$	4.43036e6	+	7.67361e6i	0.315205	+	0.545952i
$724$		0			0
$725$	−2.35297e6	+	4.07546e6i	−0.166254	+	0.287960i
$726$		0			0
$727$	−1.29764e7			−0.910579			−0.455290	−	0.890343i	$-0.650464\pi$
$727$	−1.29764e7			−0.910579			−0.455290	+	0.890343i	$0.650464\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	−749320.	+	1.29786e6i	−0.0518649	+	0.0898327i
$732$		0			0
$733$	6.16417e6	+	1.06767e7i	0.423755	+	0.733965i	0.996303	−	0.0859061i	$-0.0273785\pi$
$733$	6.16417e6	+	1.06767e7i	0.423755	+	0.733965i	−0.572549	+	0.819871i	$0.694045\pi$
$734$		0			0
$735$	2.01073e6	+	5.53266e6i	0.137289	+	0.377760i
$736$		0			0
$737$	2.26397e6	+	3.92131e6i	0.153533	+	0.265927i
$738$		0			0
$739$	−1.13390e7	+	1.96398e7i	−0.763774	+	1.32290i	0.177118	+	0.984190i	$0.443323\pi$
$739$	−1.13390e7	+	1.96398e7i	−0.763774	+	1.32290i	−0.940892	+	0.338706i	$0.890011\pi$
$740$		0			0
$741$	7.00446e6			0.468629
$742$		0			0
$743$	−9.98857e6			−0.663791			−0.331895	−	0.943316i	$-0.607688\pi$
$743$	−9.98857e6			−0.663791			−0.331895	+	0.943316i	$0.607688\pi$
$744$		0			0
$745$	8.61750e6	−	1.49260e7i	0.568841	−	0.985261i
$746$		0			0
$747$	278884.	+	483042.i	0.0182862	+	0.0316726i
$748$		0			0
$749$	1.86531e6	−	2.12621e7i	0.121492	−	1.38485i
$750$		0			0
$751$	7.28408e6	+	1.26164e7i	0.471275	+	0.816273i	0.999460	−	0.0328567i	$-0.0104605\pi$
$751$	7.28408e6	+	1.26164e7i	0.471275	+	0.816273i	−0.528185	+	0.849129i	$0.677127\pi$
$752$		0			0
$753$	−3.56612e6	+	6.17671e6i	−0.229197	+	0.396981i
$754$		0			0
$755$	−2.72668e6			−0.174087
$756$		0			0
$757$	2.35583e7			1.49419			0.747094	−	0.664719i	$-0.231449\pi$
$757$	2.35583e7			1.49419			0.747094	+	0.664719i	$0.231449\pi$
$758$		0			0
$759$	−695094.	+	1.20394e6i	−0.0437965	+	0.0758577i
$760$		0			0
$761$	−5.18008e6	−	8.97217e6i	−0.324246	−	0.561611i	0.657113	−	0.753792i	$-0.271777\pi$
$761$	−5.18008e6	−	8.97217e6i	−0.324246	−	0.561611i	−0.981360	+	0.192181i	$0.938444\pi$
$762$		0			0
$763$	1.47242e7	−	6.86174e6i	0.915633	−	0.426700i
$764$		0			0
$765$	981500.	+	1.70001e6i	0.0606368	+	0.105026i
$766$		0			0
$767$	−1.06014e7	+	1.83622e7i	−0.650694	+	1.12703i
$768$		0			0
$769$	8.30967e6			0.506720			0.253360	−	0.967372i	$-0.418464\pi$
$769$	8.30967e6			0.506720			0.253360	+	0.967372i	$0.418464\pi$
$770$		0			0
$771$	−1.31129e7			−0.794441
$772$		0			0
$773$	943010.	−	1.63334e6i	0.0567633	−	0.0983169i	−0.836247	−	0.548352i	$-0.815255\pi$
$773$	943010.	−	1.63334e6i	0.0567633	−	0.0983169i	0.893011	+	0.450035i	$0.148589\pi$
$774$		0			0
$775$	6.50790e6	+	1.12720e7i	0.389212	+	0.674135i
$776$		0			0
$777$	−5.21067e6	−	3.65041e6i	−0.309629	−	0.216914i
$778$		0			0
$779$	1.05421e6	+	1.82595e6i	0.0622420	+	0.107806i
$780$		0			0
$781$	−2.18985e6	+	3.79294e6i	−0.128466	+	0.222509i
$782$		0			0
$783$	−2.13021e6			−0.124171
$784$		0			0
$785$	1.39400e7			0.807400
$786$		0			0
$787$	−9.02154e6	+	1.56258e7i	−0.519211	+	0.899300i	0.480540	+	0.876973i	$0.340441\pi$
$787$	−9.02154e6	+	1.56258e7i	−0.519211	+	0.899300i	−0.999751	+	0.0223270i	$0.992893\pi$
$788$		0			0
$789$	−6.51078e6	−	1.12770e7i	−0.372341	−	0.644913i
$790$		0			0
$791$	2.06072e7	+	1.44366e7i	1.17105	+	0.820397i
$792$		0			0
$793$	−1.74003e7	−	3.01382e7i	−0.982593	−	1.70190i
$794$		0			0
$795$	4.34595e6	−	7.52741e6i	0.243875	−	0.422404i
$796$		0			0
$797$	2.30420e7			1.28491			0.642456	−	0.766322i	$-0.277915\pi$
$797$	2.30420e7			1.28491			0.642456	+	0.766322i	$0.277915\pi$
$798$		0			0
$799$	−1.41341e6			−0.0783249
$800$		0			0
$801$	521208.	−	902759.i	0.0287032	−	0.0497153i
$802$		0			0
$803$	350566.	+	607199.i	0.0191859	+	0.0332309i
$804$		0			0
$805$	−7.42222e6	+	3.45888e6i	−0.403687	+	0.188125i
$806$		0			0
$807$	−5.04846e6	−	8.74419e6i	−0.272882	−	0.472646i
$808$		0			0
$809$	−1.30316e7	+	2.25714e7i	−0.700045	+	1.21251i	0.268405	+	0.963306i	$0.413504\pi$
$809$	−1.30316e7	+	2.25714e7i	−0.700045	+	1.21251i	−0.968450	+	0.249208i	$0.919830\pi$
$810$		0			0
$811$	4.08558e6			0.218123			0.109061	−	0.994035i	$-0.465215\pi$
$811$	4.08558e6			0.218123			0.109061	+	0.994035i	$0.465215\pi$
$812$		0			0
$813$	8.98738e6			0.476877
$814$		0			0
$815$	−5.49264e6	+	9.51353e6i	−0.289659	+	0.501704i
$816$		0			0
$817$	1.07755e6	+	1.86637e6i	0.0564784	+	0.0978235i
$818$		0			0
$819$	−797583.	+	9.09142e6i	−0.0415495	+	0.473611i
$820$		0			0
$821$	−6.36823e6	−	1.10301e7i	−0.329732	−	0.571112i	0.652727	−	0.757593i	$-0.273625\pi$
$821$	−6.36823e6	−	1.10301e7i	−0.329732	−	0.571112i	−0.982459	+	0.186481i	$0.940292\pi$
$822$		0			0
$823$	−4.97936e6	+	8.62451e6i	−0.256256	+	0.443848i	−0.965236	−	0.261380i	$-0.915822\pi$
$823$	−4.97936e6	+	8.62451e6i	−0.256256	+	0.443848i	0.708980	+	0.705229i	$0.249156\pi$
$824$		0			0
$825$	1.37943e6			0.0705610
$826$		0			0
$827$	4.51208e6			0.229411			0.114705	−	0.993400i	$-0.463408\pi$
$827$	4.51208e6			0.229411			0.114705	+	0.993400i	$0.463408\pi$
$828$		0			0
$829$	776596.	−	1.34510e6i	0.0392472	−	0.0679782i	−0.845735	−	0.533604i	$-0.820837\pi$
$829$	776596.	−	1.34510e6i	0.0392472	−	0.0679782i	0.884982	+	0.465626i	$0.154171\pi$
$830$		0			0
$831$	4.30779e6	+	7.46131e6i	0.216397	+	0.374811i
$832$		0			0
$833$	1.03062e7	+	1.82234e6i	0.514621	+	0.0909950i
$834$		0			0
$835$	5.05709e6	+	8.75914e6i	0.251006	+	0.434756i
$836$		0			0
$837$	−2.94590e6	+	5.10244e6i	−0.145346	+	0.251747i
$838$		0			0
$839$	−3.34326e7			−1.63970			−0.819852	−	0.572575i	$-0.805945\pi$
$839$	−3.34326e7			−1.63970			−0.819852	+	0.572575i	$0.805945\pi$
$840$		0			0
$841$	−1.19725e7			−0.583705
$842$		0			0
$843$	−48013.5	+	83161.8i	−0.00232699	+	0.00403047i
$844$		0			0
$845$	−7.47265e6	−	1.29430e7i	−0.360025	−	0.623582i
$846$		0			0
$847$	1.72206e6	−	1.96293e7i	0.0824785	−	0.940149i
$848$		0			0
$849$	1.96764e6	+	3.40805e6i	0.0936862	+	0.162269i
$850$		0			0
$851$	4.42496e6	−	7.66425e6i	0.209452	−	0.362782i
$852$		0			0
$853$	−1.15063e7			−0.541455			−0.270727	−	0.962656i	$-0.587264\pi$
$853$	−1.15063e7			−0.541455			−0.270727	+	0.962656i	$0.587264\pi$
$854$		0			0
$855$	2.82287e6			0.132061
$856$		0			0
$857$	3.05718e6	−	5.29518e6i	0.142190	−	0.246280i	−0.786131	−	0.618060i	$-0.787919\pi$
$857$	3.05718e6	−	5.29518e6i	0.142190	−	0.246280i	0.928321	+	0.371780i	$0.121252\pi$
$858$		0			0
$859$	−9.36226e6	−	1.62159e7i	−0.432910	−	0.749822i	0.564212	−	0.825630i	$-0.309180\pi$
$859$	−9.36226e6	−	1.62159e7i	−0.432910	−	0.749822i	−0.997122	+	0.0758073i	$0.975847\pi$
$860$		0			0
$861$	−2.49002e6	+	1.16039e6i	−0.114471	+	0.0533454i
$862$		0			0
$863$	−3.96188e6	−	6.86218e6i	−0.181082	−	0.313643i	0.761167	−	0.648555i	$-0.224627\pi$
$863$	−3.96188e6	−	6.86218e6i	−0.181082	−	0.313643i	−0.942249	+	0.334913i	$0.891293\pi$
$864$		0			0
$865$	−1.37694e7	+	2.38494e7i	−0.625714	+	1.08377i
$866$		0			0
$867$	−9.28865e6			−0.419667
$868$		0			0
$869$	−6.38576e6			−0.286856
$870$		0			0
$871$	−2.06743e7	+	3.58089e7i	−0.923390	+	1.59936i
$872$		0			0
$873$	−805612.	−	1.39536e6i	−0.0357759	−	0.0619657i
$874$		0			0
$875$	1.95677e7	+	1.37084e7i	0.864011	+	0.605294i
$876$		0			0
$877$	−1.32837e7	−	2.30081e7i	−0.583204	−	1.01014i	−0.995097	−	0.0989066i	$-0.968465\pi$
$877$	−1.32837e7	−	2.30081e7i	−0.583204	−	1.01014i	0.411893	−	0.911232i	$-0.364868\pi$
$878$		0			0
$879$	1.88806e6	−	3.27021e6i	0.0824221	−	0.142759i
$880$		0			0
$881$	2.72314e7			1.18203			0.591017	−	0.806659i	$-0.298726\pi$
$881$	2.72314e7			1.18203			0.591017	+	0.806659i	$0.298726\pi$
$882$		0			0
$883$	−8.72713e6			−0.376677			−0.188339	−	0.982104i	$-0.560310\pi$
$883$	−8.72713e6			−0.376677			−0.188339	+	0.982104i	$0.560310\pi$
$884$		0			0
$885$	−4.27249e6	+	7.40017e6i	−0.183368	+	0.317602i
$886$		0			0
$887$	−1.11819e7	−	1.93676e7i	−0.477206	−	0.826545i	0.522453	−	0.852668i	$-0.325017\pi$
$887$	−1.11819e7	−	1.93676e7i	−0.477206	−	0.826545i	−0.999659	+	0.0261236i	$0.991684\pi$
$888$		0			0
$889$	−2.81316e6	−	1.97080e6i	−0.119382	−	0.0836349i
$890$		0			0
$891$	312210.	+	540763.i	0.0131750	+	0.0228198i
$892$		0			0
$893$	−1.01627e6	+	1.76022e6i	−0.0426461	+	0.0738651i
$894$		0			0
$895$	2.38943e7			0.997095
$896$		0			0
$897$	−1.26950e7			−0.526809
$898$		0			0
$899$	1.18082e7	−	2.04525e7i	0.487288	−	0.844008i
$900$		0			0
$901$	−7.72677e6	−	1.33832e7i	−0.317092	−	0.549220i
$902$		0			0
$903$	−2.54515e6	+	1.18608e6i	−0.103871	+	0.0484056i
$904$		0			0
$905$	−8.82389e6	−	1.52834e7i	−0.358128	−	0.620296i
$906$		0			0
$907$	4.98104e6	−	8.62742e6i	0.201049	−	0.348227i	−0.747818	−	0.663904i	$-0.768898\pi$
$907$	4.98104e6	−	8.62742e6i	0.201049	−	0.348227i	0.948867	+	0.315677i	$0.102232\pi$
$908$		0			0
$909$	1.41831e7			0.569327
$910$		0			0
$911$	9.78387e6			0.390584			0.195292	−	0.980745i	$-0.437435\pi$
$911$	9.78387e6			0.390584			0.195292	+	0.980745i	$0.437435\pi$
$912$		0			0
$913$	−327676.	+	567552.i	−0.0130097	+	0.0225335i
$914$		0			0
$915$	−7.01249e6	−	1.21460e7i	−0.276898	−	0.479601i
$916$		0			0
$917$	−1.07413e6	+	1.22437e7i	−0.0421828	+	0.480829i
$918$		0			0
$919$	1.01681e7	+	1.76116e7i	0.397145	+	0.687876i	0.993372	−	0.114940i	$-0.0366675\pi$
$919$	1.01681e7	+	1.76116e7i	0.397145	+	0.687876i	−0.596227	+	0.802816i	$0.703334\pi$
$920$		0			0
$921$	−1.14089e7	+	1.97607e7i	−0.443193	+	0.767633i
$922$		0			0
$923$	−3.99950e7			−1.54526
$924$		0			0
$925$	−8.78143e6			−0.337451
$926$		0			0
$927$	−6.85771e6	+	1.18779e7i	−0.262108	+	0.453984i
$928$		0			0
$929$	1.60168e7	+	2.77418e7i	0.608885	+	1.05462i	0.991425	+	0.130681i	$0.0417163\pi$
$929$	1.60168e7	+	2.77418e7i	0.608885	+	1.05462i	−0.382540	+	0.923939i	$0.624950\pi$
$930$		0			0
$931$	9.67989e6	−	1.15249e7i	0.366013	−	0.435774i
$932$		0			0
$933$	1.10019e7	+	1.90558e7i	0.413774	+	0.716677i
$934$		0			0
$935$	−1.15322e6	+	1.99743e6i	−0.0431402	+	0.0747210i
$936$		0			0
$937$	−3.13301e7			−1.16577			−0.582886	−	0.812554i	$-0.698077\pi$
$937$	−3.13301e7			−1.16577			−0.582886	+	0.812554i	$0.698077\pi$
$938$		0			0
$939$	1.01450e7			0.375482
$940$		0			0
$941$	1.34552e7	−	2.33051e7i	0.495354	−	0.857978i	−0.504632	−	0.863335i	$-0.668372\pi$
$941$	1.34552e7	−	2.33051e7i	0.495354	−	0.857978i	0.999986	+	0.00535665i	$0.00170508\pi$
$942$		0			0
$943$	−1.91067e6	−	3.30938e6i	−0.0699693	−	0.121190i
$944$		0			0
$945$	−321434.	+	3.66393e6i	−0.0117088	+	0.133465i
$946$		0			0
$947$	−1.93418e7	−	3.35011e7i	−0.700847	−	1.21390i	−0.968170	−	0.250295i	$-0.919472\pi$
$947$	−1.93418e7	−	3.35011e7i	−0.700847	−	1.21390i	0.267323	−	0.963607i	$-0.413861\pi$
$948$		0			0
$949$	−3.20133e6	+	5.54487e6i	−0.115389	+	0.199860i
$950$		0			0
$951$	−2.80741e7			−1.00659
$952$		0			0
$953$	−4.66148e7			−1.66261			−0.831307	−	0.555813i	$-0.812407\pi$
$953$	−4.66148e7			−1.66261			−0.831307	+	0.555813i	$0.812407\pi$
$954$		0			0
$955$	1.77517e6	−	3.07469e6i	0.0629843	−	0.109092i
$956$		0			0
$957$	−1.25145e6	−	2.16758e6i	−0.0441707	−	0.0765059i
$958$		0			0
$959$	1.93060e6	−	899692.i	0.0677868	−	0.0315898i
$960$		0			0
$961$	−1.83450e7	−	3.17744e7i	−0.640779	−	1.10986i
$962$		0			0
$963$	6.66778e6	−	1.15489e7i	0.231694	−	0.401306i
$964$		0			0
$965$	−3.30896e6			−0.114386
$966$		0			0
$967$	−3.82537e7			−1.31555			−0.657774	−	0.753215i	$-0.728502\pi$
$967$	−3.82537e7			−1.31555			−0.657774	+	0.753215i	$0.728502\pi$
$968$		0			0
$969$	2.50942e6	−	4.34644e6i	0.0858547	−	0.148705i
$970$		0			0
$971$	−7.13620e6	−	1.23603e7i	−0.242895	−	0.420707i	0.718643	−	0.695380i	$-0.244764\pi$
$971$	−7.13620e6	−	1.23603e7i	−0.242895	−	0.420707i	−0.961538	+	0.274673i	$0.911430\pi$
$972$		0			0
$973$	1.03023e7	+	7.21739e6i	0.348860	+	0.244398i
$974$		0			0
$975$	6.29839e6	+	1.09091e7i	0.212187	+	0.367518i
$976$		0			0
$977$	−2.92753e7	+	5.07063e7i	−0.981218	+	1.69952i	−0.323549	+	0.946212i	$0.604876\pi$
$977$	−2.92753e7	+	5.07063e7i	−0.981218	+	1.69952i	−0.657669	+	0.753307i	$0.728457\pi$
$978$		0			0
$979$	1.22479e6			0.0408418
$980$		0			0
$981$	1.01496e7			0.336725
$982$		0			0
$983$	1.57290e7	−	2.72435e7i	0.519180	−	0.899246i	−0.480572	−	0.876955i	$-0.659571\pi$
$983$	1.57290e7	−	2.72435e7i	0.519180	−	0.899246i	0.999752	−	0.0222904i	$-0.00709585\pi$
$984$		0			0
$985$	1.11313e6	+	1.92800e6i	0.0365557	+	0.0633163i
$986$		0			0
$987$	−2.16896e6	−	1.51949e6i	−0.0708693	−	0.0496485i
$988$		0			0
$989$	−1.95298e6	−	3.38265e6i	−0.0634901	−	0.109968i
$990$		0			0
$991$	−2.78176e7	+	4.81816e7i	−0.899779	+	1.55846i	−0.0720039	+	0.997404i	$0.522939\pi$
$991$	−2.78176e7	+	4.81816e7i	−0.899779	+	1.55846i	−0.827776	+	0.561059i	$0.810394\pi$
$992$		0			0
$993$	1.35589e6			0.0436367
$994$		0			0
$995$	−2.23031e7			−0.714181
$996$		0			0
$997$	−1.54069e7	+	2.66855e7i	−0.490882	+	0.850233i	−0.999945	−	0.0104966i	$-0.996659\pi$
$997$	−1.54069e7	+	2.66855e7i	−0.490882	+	0.850233i	0.509063	+	0.860729i	$0.329992\pi$
$998$		0			0
$999$	−1.98752e6	−	3.44249e6i	−0.0630083	−	0.109134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.l.193.2		10
4.3	odd	2		168.6.q.c.25.2	✓	10
7.2	even	3	inner	336.6.q.l.289.2		10
12.11	even	2		504.6.s.c.361.4		10
28.23	odd	6		168.6.q.c.121.2	yes	10
84.23	even	6		504.6.s.c.289.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.6.q.c.25.2	✓	10	4.3	odd	2
168.6.q.c.121.2	yes	10	28.23	odd	6
336.6.q.l.193.2		10	1.1	even	1	trivial
336.6.q.l.289.2		10	7.2	even	3	inner
504.6.s.c.289.4		10	84.23	even	6
504.6.s.c.361.4		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)

\(f(q)\)	\(=\)	\(q+(-4.50000 + 7.79423i) q^{3} +(-19.4585 - 33.7032i) q^{5} +(-106.179 - 74.3848i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(-4.50000 + 7.79423i) q^{3} +(-19.4585 - 33.7032i) q^{5} +(-106.179 - 74.3848i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(47.5857 - 82.4208i) q^{11} +869.093 q^{13} +350.253 q^{15} +(311.362 - 539.294i) q^{17} +(-447.750 - 775.526i) q^{19} +(1057.58 - 492.849i) q^{21} +(811.512 + 1405.58i) q^{23} +(805.232 - 1394.70i) q^{25} +729.000 q^{27} -2922.10 q^{29} +(-4041.01 + 6999.24i) q^{31} +(428.271 + 741.787i) q^{33} +(-440.925 + 5025.97i) q^{35} +(-2726.37 - 4722.20i) q^{37} +(-3910.92 + 6773.91i) q^{39} -2354.46 q^{41} -2406.59 q^{43} +(-1576.14 + 2729.96i) q^{45} +(-1134.86 - 1965.63i) q^{47} +(5740.79 + 15796.2i) q^{49} +(2802.26 + 4853.65i) q^{51} +(12408.0 - 21491.3i) q^{53} -3703.79 q^{55} +8059.50 q^{57} +(-12198.3 + 21128.0i) q^{59} +(-20021.2 - 34677.7i) q^{61} +(-917.719 + 10460.8i) q^{63} +(-16911.3 - 29291.2i) q^{65} +(-23788.4 + 41202.6i) q^{67} -14607.2 q^{69} -46019.2 q^{71} +(-3683.53 + 6380.06i) q^{73} +(7247.09 + 12552.3i) q^{75} +(-11183.4 + 5211.67i) q^{77} +(-33548.8 - 58108.2i) q^{79} +(-3280.50 + 5681.99i) q^{81} -6886.03 q^{83} -24234.6 q^{85} +(13149.5 - 22775.5i) q^{87} +(6434.67 + 11145.2i) q^{89} +(-92279.1 - 64647.4i) q^{91} +(-36369.1 - 62993.1i) q^{93} +(-17425.1 + 30181.2i) q^{95} +19891.7 q^{97} -7708.88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9}+O(q^{10}) \) 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9	\( 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9} - 424 q^{11} + 374 q^{13} + 108 q^{15} - 952 q^{17} - 139 q^{19} - 1044 q^{21} - 4288 q^{23} - 5605 q^{25} + 7290 q^{27} - 4216 q^{29} - 8131 q^{31} - 3816 q^{33} - 20106 q^{35} - 5425 q^{37} - 1683 q^{39} + 29364 q^{41} + 46862 q^{43} - 486 q^{45} + 17190 q^{47} + 23255 q^{49} - 8568 q^{51} + 15064 q^{53} + 1176 q^{55} + 2502 q^{57} + 83242 q^{59} + 14954 q^{61} + 1539 q^{63} - 23250 q^{65} - 39501 q^{67} + 77184 q^{69} + 56020 q^{71} - 90395 q^{73} - 50445 q^{75} + 63448 q^{77} + 43067 q^{79} - 32805 q^{81} + 75672 q^{83} - 75272 q^{85} + 18972 q^{87} - 72608 q^{89} - 288287 q^{91} - 73179 q^{93} - 190138 q^{95} + 183000 q^{97} + 68688 q^{99}+O(q^{100}) \) 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9 - 424 * q^11 + 374 * q^13 + 108 * q^15 - 952 * q^17 - 139 * q^19 - 1044 * q^21 - 4288 * q^23 - 5605 * q^25 + 7290 * q^27 - 4216 * q^29 - 8131 * q^31 - 3816 * q^33 - 20106 * q^35 - 5425 * q^37 - 1683 * q^39 + 29364 * q^41 + 46862 * q^43 - 486 * q^45 + 17190 * q^47 + 23255 * q^49 - 8568 * q^51 + 15064 * q^53 + 1176 * q^55 + 2502 * q^57 + 83242 * q^59 + 14954 * q^61 + 1539 * q^63 - 23250 * q^65 - 39501 * q^67 + 77184 * q^69 + 56020 * q^71 - 90395 * q^73 - 50445 * q^75 + 63448 * q^77 + 43067 * q^79 - 32805 * q^81 + 75672 * q^83 - 75272 * q^85 + 18972 * q^87 - 72608 * q^89 - 288287 * q^91 - 73179 * q^93 - 190138 * q^95 + 183000 * q^97 + 68688 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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