LMFDB - Embedded newform 147.6.e.o.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.e (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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 $ x^8 - x^7 + 98x^6 + 83x^5 + 9122x^4 - 91x^3 + 28567x^2 + 2058x + 86436
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$-4.61193 + 7.98809i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.o.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.11193 + 8.85412i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(11.8764 - 20.5705i) q^{5} -92.0147 q^{6} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-5.11193 + 8.85412i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(11.8764 - 20.5705i) q^{5} -92.0147 q^{6} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +(121.423 + 210.310i) q^{10} +(-232.763 - 403.157i) q^{11} +(326.372 - 565.293i) q^{12} +1019.30 q^{13} +213.775 q^{15} +(-957.660 + 1658.72i) q^{16} +(280.878 + 486.496i) q^{17} +(-414.066 - 717.183i) q^{18} +(-693.789 + 1201.68i) q^{19} -1722.72 q^{20} +4759.47 q^{22} +(-2056.81 + 3562.50i) q^{23} +(1864.55 + 3229.49i) q^{24} +(1280.40 + 2217.72i) q^{25} +(-5210.59 + 9025.00i) q^{26} -729.000 q^{27} -2381.37 q^{29} +(-1092.80 + 1892.79i) q^{30} +(1475.33 + 2555.34i) q^{31} +(-3161.47 - 5475.84i) q^{32} +(2094.87 - 3628.42i) q^{33} -5743.32 q^{34} +5874.70 q^{36} +(4954.48 - 8581.40i) q^{37} +(-7093.20 - 12285.8i) q^{38} +(4586.85 + 7944.66i) q^{39} +(4920.92 - 8523.28i) q^{40} +4477.13 q^{41} +5181.48 q^{43} +(-16881.6 + 29239.9i) q^{44} +(961.989 + 1666.21i) q^{45} +(-21028.5 - 36422.5i) q^{46} +(-1560.80 + 2703.38i) q^{47} -17237.9 q^{48} -26181.3 q^{50} +(-2527.91 + 4378.46i) q^{51} +(-36963.5 - 64022.6i) q^{52} +(-570.499 - 988.133i) q^{53} +(3726.59 - 6454.65i) q^{54} -11057.6 q^{55} -12488.2 q^{57} +(12173.4 - 21085.0i) q^{58} +(13748.5 + 23813.2i) q^{59} +(-7752.26 - 13427.3i) q^{60} +(-10551.8 + 18276.2i) q^{61} -30167.1 q^{62} +3354.67 q^{64} +(12105.6 - 20967.6i) q^{65} +(21417.6 + 37096.4i) q^{66} +(27794.2 + 48141.0i) q^{67} +(20371.3 - 35284.2i) q^{68} -37022.6 q^{69} -6076.90 q^{71} +(-16780.9 + 29065.4i) q^{72} +(-8389.82 - 14531.6i) q^{73} +(50653.8 + 87735.0i) q^{74} +(-11523.6 + 19959.5i) q^{75} +100637. q^{76} -93790.5 q^{78} +(2422.63 - 4196.12i) q^{79} +(22747.1 + 39399.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-22886.7 + 39641.0i) q^{82} -60145.4 q^{83} +13343.3 q^{85} +(-26487.4 + 45877.5i) q^{86} +(-10716.2 - 18561.0i) q^{87} +(-96443.9 - 167046. i) q^{88} +(-31248.7 + 54124.4i) q^{89} -19670.5 q^{90} +298349. q^{92} +(-13277.9 + 22998.1i) q^{93} +(-15957.4 - 27639.0i) q^{94} +(16479.4 + 28543.2i) q^{95} +(28453.3 - 49282.5i) q^{96} +63653.8 q^{97} +37707.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9 + 283 * q^10 - 402 * q^11 + 621 * q^12 - 924 * q^13 - 3273 * q^16 + 276 * q^17 - 243 * q^18 + 510 * q^19 - 9438 * q^20 + 2750 * q^22 - 6900 * q^23 + 1107 * q^24 - 2814 * q^25 - 15138 * q^26 - 5832 * q^27 + 1080 * q^29 - 2547 * q^30 - 6410 * q^31 - 15519 * q^32 + 3618 * q^33 - 42288 * q^34 + 11178 * q^36 - 15250 * q^37 - 41250 * q^38 - 4158 * q^39 - 8547 * q^40 - 8616 * q^41 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 58914 * q^48 - 14604 * q^50 - 2484 * q^51 - 47476 * q^52 - 13692 * q^53 + 2187 * q^54 - 146248 * q^55 + 9180 * q^57 - 52309 * q^58 + 34830 * q^59 - 42471 * q^60 - 5364 * q^61 - 32058 * q^62 - 146974 * q^64 - 66864 * q^65 + 12375 * q^66 + 5994 * q^67 - 58272 * q^68 - 124200 * q^69 + 178536 * q^71 - 9963 * q^72 + 59638 * q^73 + 185442 * q^74 + 25326 * q^75 - 42616 * q^76 - 272484 * q^78 + 44062 * q^79 - 33381 * q^80 - 26244 * q^81 + 57596 * q^82 + 416892 * q^83 + 72648 * q^85 + 136968 * q^86 + 4860 * q^87 - 87597 * q^88 - 77520 * q^89 - 45846 * q^90 + 316512 * q^92 + 57690 * q^93 - 73722 * q^94 + 221376 * q^95 + 139671 * q^96 + 377260 * q^97 + 65124 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−5.11193	+	8.85412i	−0.903669	+	1.56520i	−0.0809760	+	0.996716i	$0.525804\pi$
$2$	−5.11193	+	8.85412i	−0.903669	+	1.56520i	−0.822693	+	0.568485i	$0.807530\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−36.2636	−	62.8104i	−1.13324	−	1.96282i
$5$	11.8764	−	20.5705i	0.212452	−	0.367977i	−0.740030	−	0.672574i	$-0.765189\pi$
$5$	11.8764	−	20.5705i	0.212452	−	0.367977i	0.952481	+	0.304597i	$0.0985219\pi$
$6$	−92.0147			−1.04347
$7$		0			0
$7$		0			0
$8$	414.344			2.28895
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	121.423	+	210.310i	0.383972	+	0.665059i
$11$	−232.763	−	403.157i	−0.580006	−	1.00460i	−0.995478	−	0.0949934i	$-0.969717\pi$
$11$	−232.763	−	403.157i	−0.580006	−	1.00460i	0.415472	−	0.909606i	$-0.363616\pi$
$12$	326.372	−	565.293i	0.654275	−	1.13324i
$13$	1019.30			1.67280			0.836399	−	0.548121i	$-0.184657\pi$
$13$	1019.30			1.67280			0.836399	+	0.548121i	$0.184657\pi$
$14$		0			0
$15$	213.775			0.245318
$16$	−957.660	+	1658.72i	−0.935215	+	1.61984i
$17$	280.878	+	486.496i	0.235720	+	0.408279i	0.959482	−	0.281771i	$-0.0909219\pi$
$17$	280.878	+	486.496i	0.235720	+	0.408279i	−0.723762	+	0.690050i	$0.757589\pi$
$18$	−414.066	−	717.183i	−0.301223	−	0.521734i
$19$	−693.789	+	1201.68i	−0.440903	+	0.763667i	−0.997757	−	0.0669438i	$-0.978675\pi$
$19$	−693.789	+	1201.68i	−0.440903	+	0.763667i	0.556853	+	0.830611i	$0.312009\pi$
$20$	−1722.72			−0.963032
$21$		0			0
$22$	4759.47			2.09653
$23$	−2056.81	+	3562.50i	−0.810727	+	1.40422i	0.101630	+	0.994822i	$0.467594\pi$
$23$	−2056.81	+	3562.50i	−0.810727	+	1.40422i	−0.912356	+	0.409397i	$0.865739\pi$
$24$	1864.55	+	3229.49i	0.660762	+	1.14447i
$25$	1280.40	+	2217.72i	0.409729	+	0.709671i
$26$	−5210.59	+	9025.00i	−1.51166	+	2.61827i
$27$	−729.000			−0.192450
$28$		0			0
$29$	−2381.37			−0.525814			−0.262907	−	0.964821i	$-0.584681\pi$
$29$	−2381.37			−0.525814			−0.262907	+	0.964821i	$0.584681\pi$
$30$	−1092.80	+	1892.79i	−0.221686	+	0.383972i
$31$	1475.33	+	2555.34i	0.275730	+	0.477579i	0.970319	−	0.241828i	$-0.0777471\pi$
$31$	1475.33	+	2555.34i	0.275730	+	0.477579i	−0.694589	+	0.719407i	$0.744414\pi$
$32$	−3161.47	−	5475.84i	−0.545776	−	0.945313i
$33$	2094.87	−	3628.42i	0.334866	−	0.580006i
$34$	−5743.32			−0.852051
$35$		0			0
$36$	5874.70			0.755491
$37$	4954.48	−	8581.40i	0.594968	−	1.03051i	−0.398584	−	0.917132i	$-0.630498\pi$
$37$	4954.48	−	8581.40i	0.594968	−	1.03051i	0.993551	−	0.113382i	$-0.0361685\pi$
$38$	−7093.20	−	12285.8i	−0.796862	−	1.38021i
$39$	4586.85	+	7944.66i	0.482895	+	0.836399i
$40$	4920.92	−	8523.28i	0.486291	−	0.842280i
$41$	4477.13			0.415949			0.207974	−	0.978134i	$-0.433313\pi$
$41$	4477.13			0.415949			0.207974	+	0.978134i	$0.433313\pi$
$42$		0			0
$43$	5181.48			0.427349			0.213675	−	0.976905i	$-0.431457\pi$
$43$	5181.48			0.427349			0.213675	+	0.976905i	$0.431457\pi$
$44$	−16881.6	+	29239.9i	−1.31457	+	2.27690i
$45$	961.989	+	1666.21i	0.0708172	+	0.122659i
$46$	−21028.5	−	36422.5i	−1.46526	−	2.53790i
$47$	−1560.80	+	2703.38i	−0.103063	+	0.178510i	−0.912945	−	0.408082i	$-0.866198\pi$
$47$	−1560.80	+	2703.38i	−0.103063	+	0.178510i	0.809882	+	0.586592i	$0.199531\pi$
$48$	−17237.9			−1.07989
$49$		0			0
$50$	−26181.3			−1.48104
$51$	−2527.91	+	4378.46i	−0.136093	+	0.235720i
$52$	−36963.5	−	64022.6i	−1.89568	−	3.28341i
$53$	−570.499	−	988.133i	−0.0278975	−	0.0483198i	0.851740	−	0.523965i	$-0.175548\pi$
$53$	−570.499	−	988.133i	−0.0278975	−	0.0483198i	−0.879637	+	0.475645i	$0.842215\pi$
$54$	3726.59	−	6454.65i	0.173911	−	0.301223i
$55$	−11057.6			−0.492893
$56$		0			0
$57$	−12488.2			−0.509111
$58$	12173.4	−	21085.0i	0.475162	−	0.823005i
$59$	13748.5	+	23813.2i	0.514194	+	0.890610i	0.999864	+	0.0164678i	$0.00524209\pi$
$59$	13748.5	+	23813.2i	0.514194	+	0.890610i	−0.485671	+	0.874142i	$0.661425\pi$
$60$	−7752.26	−	13427.3i	−0.278003	−	0.481516i
$61$	−10551.8	+	18276.2i	−0.363078	+	0.628870i	−0.988466	−	0.151444i	$-0.951608\pi$
$61$	−10551.8	+	18276.2i	−0.363078	+	0.628870i	0.625387	+	0.780314i	$0.284941\pi$
$62$	−30167.1			−0.996676
$63$		0			0
$64$	3354.67			0.102376
$65$	12105.6	−	20967.6i	0.355389	−	0.615551i
$66$	21417.6	+	37096.4i	0.605217	+	1.04827i
$67$	27794.2	+	48141.0i	0.756428	+	1.31017i	0.944661	+	0.328047i	$0.106390\pi$
$67$	27794.2	+	48141.0i	0.756428	+	1.31017i	−0.188234	+	0.982124i	$0.560276\pi$
$68$	20371.3	−	35284.2i	0.534253	−	0.925353i
$69$	−37022.6			−0.936146
$70$		0			0
$71$	−6076.90			−0.143066			−0.0715330	−	0.997438i	$-0.522789\pi$
$71$	−6076.90			−0.143066			−0.0715330	+	0.997438i	$0.522789\pi$
$72$	−16780.9	+	29065.4i	−0.381491	+	0.660762i
$73$	−8389.82	−	14531.6i	−0.184266	−	0.319158i	0.759063	−	0.651017i	$-0.225657\pi$
$73$	−8389.82	−	14531.6i	−0.184266	−	0.319158i	−0.943329	+	0.331859i	$0.892324\pi$
$74$	50653.8	+	87735.0i	1.07531	+	1.86249i
$75$	−11523.6	+	19959.5i	−0.236557	+	0.409729i
$76$	100637.			1.99859
$77$		0			0
$78$	−93790.5			−1.74551
$79$	2422.63	−	4196.12i	0.0436737	−	0.0756450i	−0.843362	−	0.537345i	$-0.819427\pi$
$79$	2422.63	−	4196.12i	0.0436737	−	0.0756450i	0.887036	+	0.461700i	$0.152760\pi$
$80$	22747.1	+	39399.2i	0.397376	+	0.688275i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−22886.7	+	39641.0i	−0.375880	+	0.651043i
$83$	−60145.4			−0.958313			−0.479156	−	0.877730i	$-0.659057\pi$
$83$	−60145.4			−0.958313			−0.479156	+	0.877730i	$0.659057\pi$
$84$		0			0
$85$	13343.3			0.200316
$86$	−26487.4	+	45877.5i	−0.386183	+	0.668888i
$87$	−10716.2	−	18561.0i	−0.151790	−	0.262907i
$88$	−96443.9	−	167046.i	−1.32760	−	2.29947i
$89$	−31248.7	+	54124.4i	−0.418174	+	0.724299i	−0.995756	−	0.0920340i	$-0.970663\pi$
$89$	−31248.7	+	54124.4i	−0.418174	+	0.724299i	0.577582	+	0.816333i	$0.303996\pi$
$90$	−19670.5			−0.255981
$91$		0			0
$92$	298349.			3.67498
$93$	−13277.9	+	22998.1i	−0.159193	+	0.275730i
$94$	−15957.4	−	27639.0i	−0.186269	−	0.322628i
$95$	16479.4	+	28543.2i	0.187341	+	0.324485i
$96$	28453.3	−	49282.5i	0.315104	−	0.545776i
$97$	63653.8			0.686903			0.343451	−	0.939170i	$-0.388404\pi$
$97$	63653.8			0.686903			0.343451	+	0.939170i	$0.388404\pi$
$98$		0			0
$99$	37707.6			0.386670
$100$	92863.9	−	160845.i	0.928639	−	1.60845i
$101$	92311.4	+	159888.i	0.900434	+	1.55960i	0.826932	+	0.562302i	$0.190084\pi$
$101$	92311.4	+	159888.i	0.900434	+	1.55960i	0.0735022	+	0.997295i	$0.476582\pi$
$102$	−25844.9	−	44764.7i	−0.245966	−	0.426026i
$103$	26021.9	−	45071.2i	0.241683	−	0.418607i	−0.719511	−	0.694481i	$-0.755634\pi$
$103$	26021.9	−	45071.2i	0.241683	−	0.418607i	0.961194	+	0.275874i	$0.0889674\pi$
$104$	422341.			3.82895
$105$		0			0
$106$	11665.4			0.100840
$107$	−24088.9	+	41723.2i	−0.203403	+	0.352304i	−0.949623	−	0.313395i	$-0.898534\pi$
$107$	−24088.9	+	41723.2i	−0.203403	+	0.352304i	0.746220	+	0.665700i	$0.231867\pi$
$108$	26436.2	+	45788.8i	0.218092	+	0.377746i
$109$	18217.8	+	31554.1i	0.146869	+	0.254384i	0.930069	−	0.367386i	$-0.119747\pi$
$109$	18217.8	+	31554.1i	0.146869	+	0.254384i	−0.783200	+	0.621770i	$0.786414\pi$
$110$	56525.4	−	97904.9i	0.445412	−	0.771476i
$111$	89180.6			0.687010
$112$		0			0
$113$	−96711.1			−0.712492			−0.356246	−	0.934392i	$-0.615944\pi$
$113$	−96711.1			−0.712492			−0.356246	+	0.934392i	$0.615944\pi$
$114$	63838.8	−	110572.i	0.460068	−	0.796862i
$115$	48855.0	+	84619.4i	0.344480	+	0.596658i
$116$	86357.1	+	149575.i	0.595872	+	1.03208i
$117$	−41281.6	+	71501.9i	−0.278800	+	0.482895i
$118$	−281126.			−1.85864
$119$		0			0
$120$	88576.5			0.561520
$121$	−27831.7	+	48206.0i	−0.172813	+	0.299321i
$122$	−107880.	−	186853.i	−0.656206	−	1.13658i
$123$	20147.1	+	34895.7i	0.120074	+	0.207974i
$124$	107001.	−	185332.i	0.624935	−	1.08242i
$125$	135054.			0.773093
$126$		0			0
$127$	23322.9			0.128314			0.0641568	−	0.997940i	$-0.479564\pi$
$127$	23322.9			0.128314			0.0641568	+	0.997940i	$0.479564\pi$
$128$	84018.4	−	145524.i	0.453262	−	0.785073i
$129$	23316.7	+	40385.7i	0.123365	+	0.213675i
$130$	123766.	+	214369.i	0.642308	+	1.11251i
$131$	−169379.	+	293373.i	−0.862345	+	1.49363i	0.00731374	+	0.999973i	$0.497672\pi$
$131$	−169379.	+	293373.i	−0.862345	+	1.49363i	−0.869659	+	0.493653i	$0.835661\pi$
$132$	−303870.			−1.51793
$133$		0			0
$134$	−568328.			−2.73424
$135$	−8657.90	+	14995.9i	−0.0408863	+	0.0708172i
$136$	116380.	+	201576.i	0.539550	+	0.934528i
$137$	31438.4	+	54452.9i	0.143106	+	0.247867i	0.928665	−	0.370920i	$-0.120958\pi$
$137$	31438.4	+	54452.9i	0.143106	+	0.247867i	−0.785559	+	0.618787i	$0.787624\pi$
$138$	189257.	−	327802.i	0.845967	−	1.46526i
$139$	−211927.			−0.930356			−0.465178	−	0.885217i	$-0.654010\pi$
$139$	−211927.			−0.930356			−0.465178	+	0.885217i	$0.654010\pi$
$140$		0			0
$141$	−28094.3			−0.119007
$142$	31064.7	−	53805.6i	0.129284	−	0.223927i
$143$	−237255.	−	410938.i	−0.970233	−	1.68049i
$144$	−77570.5	−	134356.i	−0.311738	−	0.539947i
$145$	−28282.2	+	48986.1i	−0.111710	+	0.193488i
$146$	171553.			0.666062
$147$		0			0
$148$	−718668.			−2.69696
$149$	−70136.4	+	121480.i	−0.258808	+	0.448269i	−0.965923	−	0.258830i	$-0.916663\pi$
$149$	−70136.4	+	121480.i	−0.258808	+	0.448269i	0.707115	+	0.707099i	$0.249996\pi$
$150$	−117816.	−	204063.i	−0.427538	−	0.740518i
$151$	81995.7	+	142021.i	0.292650	+	0.506885i	0.974436	−	0.224667i	$-0.0721296\pi$
$151$	81995.7	+	142021.i	0.292650	+	0.506885i	−0.681785	+	0.731552i	$0.738796\pi$
$152$	−287467.	+	497908.i	−1.00920	+	1.74799i
$153$	−45502.3			−0.157147
$154$		0			0
$155$	70086.4			0.234317
$156$	332671.	−	576203.i	1.09447	−	1.89568i
$157$	278272.	+	481981.i	0.900990	+	1.56056i	0.826212	+	0.563360i	$0.190492\pi$
$157$	278272.	+	481981.i	0.900990	+	1.56056i	0.0747781	+	0.997200i	$0.476175\pi$
$158$	24768.6	+	42900.5i	0.0789331	+	0.136716i
$159$	5134.49	−	8893.19i	0.0161066	−	0.0278975i
$160$	−150188.			−0.463804
$161$		0			0
$162$	67078.7			0.200815
$163$	9863.32	−	17083.8i	0.0290773	−	0.0503634i	−0.851121	−	0.524970i	$-0.824076\pi$
$163$	9863.32	−	17083.8i	0.0290773	−	0.0503634i	0.880198	+	0.474607i	$0.157410\pi$
$164$	−162357.	−	281210.i	−0.471368	−	0.816434i
$165$	−49759.0	−	86185.1i	−0.142286	−	0.246446i
$166$	307459.	−	532534.i	0.865998	−	1.49995i
$167$	−94776.2			−0.262971			−0.131486	−	0.991318i	$-0.541975\pi$
$167$	−94776.2			−0.262971			−0.131486	+	0.991318i	$0.541975\pi$
$168$		0			0
$169$	667679.			1.79825
$170$	−68210.0	+	118143.i	−0.181020	+	0.313535i
$171$	−56196.9	−	97335.9i	−0.146968	−	0.254556i
$172$	−187899.	−	325451.i	−0.484288	−	0.838812i
$173$	169420.	−	293445.i	0.430379	−	0.745437i	−0.566527	−	0.824043i	$-0.691713\pi$
$173$	169420.	−	293445.i	0.430379	−	0.745437i	0.996906	+	0.0786055i	$0.0250468\pi$
$174$	219121.			0.548670
$175$		0			0
$176$	891631.			2.16972
$177$	−123737.	+	214319.i	−0.296870	+	0.514194i
$178$	−319482.	−	553360.i	−0.755782	−	1.30905i
$179$	−388096.	−	672203.i	−0.905330	−	1.56808i	−0.820473	−	0.571685i	$-0.806290\pi$
$179$	−388096.	−	672203.i	−0.905330	−	1.56808i	−0.0848573	−	0.996393i	$-0.527043\pi$
$180$	69770.3	−	120846.i	0.160505	−	0.278003i
$181$	132697.			0.301067			0.150534	−	0.988605i	$-0.451901\pi$
$181$	132697.			0.301067			0.150534	+	0.988605i	$0.451901\pi$
$182$		0			0
$183$	−189932.			−0.419247
$184$	−852226.	+	1.47610e6i	−1.85571	+	3.21418i
$185$	−117683.	−	203833.i	−0.252804	−	0.437869i
$186$	−135752.	−	235129.i	−0.287715	−	0.498338i
$187$	130756.	−	226476.i	0.273438	−	0.473608i
$188$	226400.			0.467178
$189$		0			0
$190$	−336967.			−0.677178
$191$	−3318.71	+	5748.17i	−0.00658242	+	0.0114011i	−0.869298	−	0.494289i	$-0.835429\pi$
$191$	−3318.71	+	5748.17i	−0.00658242	+	0.0114011i	0.862715	+	0.505690i	$0.168762\pi$
$192$	15096.0	+	26147.0i	0.0295535	+	0.0511882i
$193$	−226295.	−	391954.i	−0.437302	−	0.757430i	0.560178	−	0.828372i	$-0.310733\pi$
$193$	−226295.	−	391954.i	−0.437302	−	0.757430i	−0.997480	+	0.0709425i	$0.977399\pi$
$194$	−325394.	+	563598.i	−0.620733	+	1.07514i
$195$	217901.			0.410368
$196$		0			0
$197$	816952.			1.49979			0.749896	−	0.661556i	$-0.230104\pi$
$197$	816952.			1.49979			0.749896	+	0.661556i	$0.230104\pi$
$198$	−192759.	+	333868.i	−0.349422	+	0.605217i
$199$	403208.	+	698378.i	0.721767	+	1.25014i	0.960291	+	0.279000i	$0.0900031\pi$
$199$	403208.	+	698378.i	0.721767	+	1.25014i	−0.238524	+	0.971137i	$0.576664\pi$
$200$	530526.	+	918899.i	0.937847	+	1.62440i
$201$	−250148.	+	433269.i	−0.436724	+	0.756428i
$202$	−1.88756e6			−3.25478
$203$		0			0
$204$	366684.			0.616902
$205$	53172.2	−	92096.9i	0.0883690	−	0.153060i
$206$	266044.	+	460801.i	0.436802	+	0.756564i
$207$	−166602.	−	288562.i	−0.270242	−	0.468073i
$208$	−976143.	+	1.69073e6i	−1.56443	+	2.70966i
$209$	645954.			1.02291
$210$		0			0
$211$	68773.9			0.106345			0.0531726	−	0.998585i	$-0.483067\pi$
$211$	68773.9			0.106345			0.0531726	+	0.998585i	$0.483067\pi$
$212$	−41376.6	+	71666.5i	−0.0632289	+	0.109516i
$213$	−27346.1	−	47364.8i	−0.0412996	−	0.0715330i
$214$	−246281.	−	426572.i	−0.367618	−	0.636734i
$215$	61537.4	−	106586.i	0.0907911	−	0.157255i
$216$	−302057.			−0.440508
$217$		0			0
$218$	−372512.			−0.530883
$219$	75508.4	−	130784.i	0.106386	−	0.184266i
$220$	400987.	+	694529.i	0.558564	+	0.967461i
$221$	286299.	+	495885.i	0.394312	+	0.682968i
$222$	−455884.	+	789615.i	−0.620829	+	1.07531i
$223$	620227.			0.835196			0.417598	−	0.908632i	$-0.362872\pi$
$223$	620227.			0.835196			0.417598	+	0.908632i	$0.362872\pi$
$224$		0			0
$225$	−207425.			−0.273152
$226$	494380.	−	856291.i	0.643857	−	1.11519i
$227$	501116.	+	867959.i	0.645467	+	1.11798i	0.984193	+	0.177096i	$0.0566705\pi$
$227$	501116.	+	867959.i	0.645467	+	1.11798i	−0.338727	+	0.940885i	$0.609996\pi$
$228$	452867.	+	784388.i	0.576944	+	0.999296i
$229$	442931.	−	767178.i	0.558145	−	0.966735i	−0.439506	−	0.898239i	$-0.644847\pi$
$229$	442931.	−	767178.i	0.558145	−	0.966735i	0.997651	−	0.0684960i	$-0.0218200\pi$
$230$	−998973.			−1.24519
$231$		0			0
$232$	−986707.			−1.20356
$233$	−298082.	+	516293.i	−0.359704	+	0.623026i	−0.987911	−	0.155020i	$-0.950456\pi$
$233$	−298082.	+	516293.i	−0.359704	+	0.623026i	0.628207	+	0.778046i	$0.283789\pi$
$234$	−422057.	−	731025.i	−0.503886	−	0.872755i
$235$	37073.3	+	64212.9i	0.0437917	+	0.0758495i
$236$	997143.	−	1.72710e6i	1.16541	−	2.01854i
$237$	43607.4			0.0504300
$238$		0			0
$239$	743111.			0.841509			0.420754	−	0.907175i	$-0.361765\pi$
$239$	743111.			0.841509			0.420754	+	0.907175i	$0.361765\pi$
$240$	−204724.	+	354593.i	−0.229425	+	0.397376i
$241$	−587419.	−	1.01744e6i	−0.651487	−	1.12841i	−0.982762	−	0.184874i	$-0.940812\pi$
$241$	−587419.	−	1.01744e6i	−0.651487	−	1.12841i	0.331276	−	0.943534i	$-0.392521\pi$
$242$	−284548.	−	492851.i	−0.312332	−	0.540975i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	1.53058e6			1.64582
$245$		0			0
$246$	−411961.			−0.434029
$247$	−707179.	+	1.22487e6i	−0.737542	+	1.27746i
$248$	611293.	+	1.05879e6i	0.631132	+	1.09315i
$249$	−270654.	−	468787.i	−0.276641	−	0.479156i
$250$	−690385.	+	1.19578e6i	−0.698621	+	1.21005i
$251$	−352992.			−0.353655			−0.176828	−	0.984242i	$-0.556584\pi$
$251$	−352992.			−0.353655			−0.176828	+	0.984242i	$0.556584\pi$
$252$		0			0
$253$	1.91500e6			1.88090
$254$	−119225.	+	206504.i	−0.115953	+	0.200837i
$255$	60044.9	+	104001.i	0.0578263	+	0.100158i
$256$	912666.	+	1.58078e6i	0.870386	+	1.50755i
$257$	5006.34	−	8671.23i	0.00472811	−	0.00818932i	−0.863652	−	0.504089i	$-0.831828\pi$
$257$	5006.34	−	8671.23i	0.00472811	−	0.00818932i	0.868380	+	0.495900i	$0.165162\pi$
$258$	−476773.			−0.445925
$259$		0			0
$260$	−1.75597e6			−1.61096
$261$	96445.6	−	167049.i	0.0876357	−	0.151790i
$262$	−1.73171e6	−	2.99940e6i	−1.55855	−	2.69949i
$263$	−840900.	−	1.45648e6i	−0.749644	−	1.29842i	−0.947993	−	0.318290i	$-0.896891\pi$
$263$	−840900.	−	1.45648e6i	−0.749644	−	1.29842i	0.198349	−	0.980131i	$-0.436442\pi$
$264$	867995.	−	1.50341e6i	0.766492	−	1.32760i
$265$	−27101.9			−0.0237075
$266$		0			0
$267$	−562477.			−0.482866
$268$	2.01584e6	−	3.49153e6i	1.71442	−	2.96947i
$269$	−958587.	−	1.66032e6i	−0.807702	−	1.39898i	−0.914452	−	0.404694i	$-0.867378\pi$
$269$	−958587.	−	1.66032e6i	−0.807702	−	1.39898i	0.106750	−	0.994286i	$-0.465955\pi$
$270$	−88517.1	−	153316.i	−0.0738955	−	0.127991i
$271$	1.14500e6	−	1.98320e6i	0.947069	−	1.64037i	0.195515	−	0.980701i	$-0.437362\pi$
$271$	1.14500e6	−	1.98320e6i	0.947069	−	1.64037i	0.751554	−	0.659672i	$-0.229305\pi$
$272$	−1.07594e6			−0.881795
$273$		0			0
$274$	−642843.			−0.517283
$275$	596060.	−	1.03241e6i	0.475290	−	0.823226i
$276$	1.34257e6	+	2.32540e6i	1.06088	+	1.83749i
$277$	197401.	+	341908.i	0.154579	+	0.267738i	0.932906	−	0.360121i	$-0.117265\pi$
$277$	197401.	+	341908.i	0.154579	+	0.267738i	−0.778327	+	0.627859i	$0.783931\pi$
$278$	1.08335e6	−	1.87642e6i	0.840734	−	1.45619i
$279$	−239003.			−0.183820
$280$		0			0
$281$	−1.77699e6			−1.34252			−0.671259	−	0.741223i	$-0.734246\pi$
$281$	−1.77699e6			−1.34252			−0.671259	+	0.741223i	$0.734246\pi$
$282$	143616.	−	248751.i	0.107543	−	0.186269i
$283$	607622.	+	1.05243e6i	0.450991	+	0.781139i	0.998448	−	0.0556949i	$-0.0177374\pi$
$283$	607622.	+	1.05243e6i	0.450991	+	0.781139i	−0.547457	+	0.836834i	$0.684404\pi$
$284$	220370.	+	381693.i	0.162128	+	0.280813i
$285$	−148315.	+	256889.i	−0.108162	+	0.187341i
$286$	4.85133e6			3.50708
$287$		0			0
$288$	512159.			0.363851
$289$	552143.	−	956340.i	0.388872	−	0.673547i
$290$	−289153.	−	500827.i	−0.201898	−	0.349698i
$291$	286442.	+	496132.i	0.198292	+	0.343451i
$292$	−608490.	+	1.05393e6i	−0.417634	+	0.723364i
$293$	1.48897e6			1.01325			0.506627	−	0.862165i	$-0.330892\pi$
$293$	1.48897e6			1.01325			0.506627	+	0.862165i	$0.330892\pi$
$294$		0			0
$295$	653133.			0.436965
$296$	2.05286e6	−	3.55565e6i	1.36185	−	2.35879i
$297$	169684.	+	293902.i	0.111622	+	0.193335i
$298$	−717065.	−	1.24199e6i	−0.467754	−	0.810174i
$299$	−2.09651e6	+	3.63125e6i	−1.35618	+	2.34898i
$300$	1.67155e6			1.07230
$301$		0			0
$302$	−1.67662e6			−1.05784
$303$	−830803.	+	1.43899e6i	−0.519866	+	0.900434i
$304$	−1.32883e6	−	2.30160e6i	−0.824679	−	1.42839i
$305$	250634.	+	434111.i	0.154273	+	0.267209i
$306$	232604.	−	402883.i	0.142009	−	0.245966i
$307$	−2.03109e6			−1.22994			−0.614968	−	0.788552i	$-0.710831\pi$
$307$	−2.03109e6			−1.22994			−0.614968	+	0.788552i	$0.710831\pi$
$308$		0			0
$309$	468394.			0.279071
$310$	−358276.	+	620553.i	−0.211745	+	0.366754i
$311$	144892.	+	250961.i	0.0849463	+	0.147131i	0.905368	−	0.424627i	$-0.139595\pi$
$311$	144892.	+	250961.i	0.0849463	+	0.147131i	−0.820422	+	0.571758i	$0.806261\pi$
$312$	1.90053e6	+	3.29182e6i	1.10532	+	1.91447i
$313$	109105.	−	188976.i	0.0629484	−	0.109030i	−0.832834	−	0.553523i	$-0.813283\pi$
$313$	109105.	−	188976.i	0.0629484	−	0.109030i	0.895782	+	0.444493i	$0.146616\pi$
$314$	−5.69002e6			−3.25679
$315$		0			0
$316$	−351413.			−0.197970
$317$	−645315.	+	1.11772e6i	−0.360681	+	0.624718i	−0.988073	−	0.153985i	$-0.950789\pi$
$317$	−645315.	+	1.11772e6i	−0.360681	+	0.624718i	0.627392	+	0.778704i	$0.284122\pi$
$318$	52494.2	+	90922.7i	0.0291101	+	0.0504202i
$319$	554296.	+	960068.i	0.304975	+	0.528233i
$320$	39841.4	−	69007.3i	0.0217500	−	0.0376721i
$321$	−433600.			−0.234870
$322$		0			0
$323$	−779481.			−0.415719
$324$	−237925.	+	412099.i	−0.125915	+	0.218092i
$325$	1.30511e6	+	2.26052e6i	0.685393	+	1.18714i
$326$	100841.	+	174662.i	0.0525526	+	0.0910237i
$327$	−163960.	+	283987.i	−0.0847947	+	0.146869i
$328$	1.85507e6			0.952084
$329$		0			0
$330$	1.01746e6			0.514318
$331$	1.74280e6	−	3.01862e6i	0.874336	−	1.51439i	0.0168673	−	0.999858i	$-0.494631\pi$
$331$	1.74280e6	−	3.01862e6i	0.874336	−	1.51439i	0.857469	−	0.514536i	$-0.172036\pi$
$332$	2.18109e6	+	3.77776e6i	1.08600	+	1.88100i
$333$	401313.	+	695094.i	0.198323	+	0.343505i
$334$	484489.	−	839160.i	0.237639	−	0.411603i
$335$	1.32038e6			0.642817
$336$		0			0
$337$	249198.			0.119528			0.0597641	−	0.998213i	$-0.480965\pi$
$337$	249198.			0.119528			0.0597641	+	0.998213i	$0.480965\pi$
$338$	−3.41313e6	+	5.91171e6i	−1.62503	+	2.81463i
$339$	−435200.	−	753788.i	−0.205679	−	0.356246i
$340$	−483876.	−	838098.i	−0.227006	−	0.393186i
$341$	686803.	−	1.18958e6i	0.319850	−	0.553997i
$342$	1.14910e6			0.531241
$343$		0			0
$344$	2.14692e6			0.978180
$345$	−439695.	+	761574.i	−0.198886	+	0.344480i
$346$	1.73213e6	+	3.00014e6i	0.777840	+	1.34726i
$347$	753007.	+	1.30425e6i	0.335719	+	0.581482i	0.983623	−	0.180240i	$-0.0576875\pi$
$347$	753007.	+	1.30425e6i	0.335719	+	0.581482i	−0.647904	+	0.761722i	$0.724354\pi$
$348$	−777214.	+	1.34617e6i	−0.344027	+	0.595872i
$349$	−1.54370e6			−0.678423			−0.339212	−	0.940710i	$-0.610160\pi$
$349$	−1.54370e6			−0.678423			−0.339212	+	0.940710i	$0.610160\pi$
$350$		0			0
$351$	−743070.			−0.321930
$352$	−1.47175e6	+	2.54914e6i	−0.633107	+	1.09657i
$353$	−838978.	−	1.45315e6i	−0.358355	−	0.620689i	0.629331	−	0.777137i	$-0.283329\pi$
$353$	−838978.	−	1.45315e6i	−0.358355	−	0.620689i	−0.987686	+	0.156448i	$0.949996\pi$
$354$	−1.26507e6	−	2.19116e6i	−0.536544	−	0.929322i
$355$	−72171.8	+	125005.i	−0.0303946	+	0.0526450i
$356$	4.53276e6			1.89556
$357$		0			0
$358$	7.93568e6			3.27248
$359$	1.24987e6	−	2.16483e6i	0.511832	−	0.886519i	−0.488074	−	0.872802i	$-0.662300\pi$
$359$	1.24987e6	−	2.16483e6i	0.511832	−	0.886519i	0.999906	−	0.0137165i	$-0.00436623\pi$
$360$	398594.	+	690385.i	0.162097	+	0.280760i
$361$	275363.	+	476943.i	0.111208	+	0.192619i
$362$	−678335.	+	1.17491e6i	−0.272065	+	0.471231i
$363$	−500971.			−0.199547
$364$		0			0
$365$	−398564.			−0.156591
$366$	970917.	−	1.68168e6i	0.378861	−	0.656206i
$367$	−1.05371e6	−	1.82507e6i	−0.408370	−	0.707318i	0.586337	−	0.810067i	$-0.300569\pi$
$367$	−1.05371e6	−	1.82507e6i	−0.408370	−	0.707318i	−0.994707	+	0.102749i	$0.967236\pi$
$368$	−3.93945e6	−	6.82332e6i	−1.51641	−	2.62649i
$369$	−181324.	+	314062.i	−0.0693248	+	0.120074i
$370$	2.40634e6			0.913804
$371$		0			0
$372$	1.92602e6			0.721613
$373$	−1.36612e6	+	2.36619e6i	−0.508414	+	0.880599i	0.491538	+	0.870856i	$0.336435\pi$
$373$	−1.36612e6	+	2.36619e6i	−0.508414	+	0.880599i	−0.999953	+	0.00974333i	$0.996899\pi$
$374$	1.33683e6	+	2.31546e6i	0.494194	+	0.855970i
$375$	607742.	+	1.05264e6i	0.223173	+	0.386547i
$376$	−646706.	+	1.12013e6i	−0.235905	+	0.408600i
$377$	−2.42733e6			−0.879581
$378$		0			0
$379$	−2.04295e6			−0.730567			−0.365283	−	0.930896i	$-0.619028\pi$
$379$	−2.04295e6			−0.730567			−0.365283	+	0.930896i	$0.619028\pi$
$380$	1.19521e6	−	2.07016e6i	0.424604	−	0.735436i
$381$	104953.	+	181784.i	0.0370410	+	0.0641568i
$382$	−33930.0	−	58768.4i	−0.0118967	−	0.0206056i
$383$	754497.	−	1.30683e6i	0.262821	−	0.455220i	−0.704169	−	0.710032i	$-0.748680\pi$
$383$	754497.	−	1.30683e6i	0.262821	−	0.455220i	0.966991	+	0.254812i	$0.0820137\pi$
$384$	1.51233e6			0.523382
$385$		0			0
$386$	4.62721e6			1.58071
$387$	−209850.	+	363471.i	−0.0712249	+	0.123365i
$388$	−2.30832e6	−	3.99812e6i	−0.778423	−	1.34827i
$389$	−2.25033e6	−	3.89768e6i	−0.754000	−	1.30597i	−0.945870	−	0.324546i	$-0.894788\pi$
$389$	−2.25033e6	−	3.89768e6i	−0.754000	−	1.30597i	0.191870	−	0.981420i	$-0.438545\pi$
$390$	−1.11389e6	+	1.92932e6i	−0.370837	+	0.642308i
$391$	−2.31085e6			−0.764417
$392$		0			0
$393$	−3.04882e6			−0.995751
$394$	−4.17620e6	+	7.23339e6i	−1.35532	+	2.34748i
$395$	−57544.3	−	99669.7i	−0.0185571	−	0.0321418i
$396$	−1.36741e6	−	2.36843e6i	−0.438189	−	0.758966i
$397$	−1.76068e6	+	3.04958e6i	−0.560665	+	0.971101i	0.436773	+	0.899572i	$0.356121\pi$
$397$	−1.76068e6	+	3.04958e6i	−0.560665	+	0.971101i	−0.997439	+	0.0715292i	$0.977212\pi$
$398$	−8.24469e6			−2.60895
$399$		0			0
$400$	−4.90476e6			−1.53274
$401$	453554.	−	785578.i	0.140853	−	0.243965i	−0.786965	−	0.616998i	$-0.788349\pi$
$401$	453554.	−	785578.i	0.140853	−	0.243965i	0.927818	+	0.373033i	$0.121682\pi$
$402$	−2.55748e6	−	4.42968e6i	−0.789308	−	1.36712i
$403$	1.50380e6	+	2.60466e6i	0.461241	+	0.798893i
$404$	6.69508e6	−	1.15962e7i	2.04081	−	3.53479i
$405$	−155842.			−0.0472115
$406$		0			0
$407$	−4.61287e6			−1.38034
$408$	−1.04742e6	+	1.81419e6i	−0.311509	+	0.539550i
$409$	2.15927e6	+	3.73996e6i	0.638260	+	1.10550i	0.985814	+	0.167839i	$0.0536790\pi$
$409$	2.15927e6	+	3.73996e6i	0.638260	+	1.10550i	−0.347554	+	0.937660i	$0.612988\pi$
$410$	543624.	+	941585.i	0.159713	+	0.276630i
$411$	−282945.	+	490076.i	−0.0826224	+	0.143106i
$412$	−3.77458e6			−1.09553
$413$		0			0
$414$	3.40662e6			0.976838
$415$	−714311.	+	1.23722e6i	−0.203595	+	0.352637i
$416$	−3.22249e6	−	5.58152e6i	−0.912974	−	1.58132i
$417$	−953671.	−	1.65181e6i	−0.268571	−	0.465178i
$418$	−3.30207e6	+	5.71935e6i	−0.924369	+	1.60105i
$419$	1.52041e6			0.423083			0.211541	−	0.977369i	$-0.432152\pi$
$419$	1.52041e6			0.423083			0.211541	+	0.977369i	$0.432152\pi$
$420$		0			0
$421$	−4.42050e6			−1.21553			−0.607766	−	0.794116i	$-0.707934\pi$
$421$	−4.42050e6			−1.21553			−0.607766	+	0.794116i	$0.707934\pi$
$422$	−351567.	+	608932.i	−0.0961008	+	0.166452i
$423$	−126425.	−	218974.i	−0.0343542	−	0.0595033i
$424$	−236383.	−	409427.i	−0.0638559	−	0.110602i
$425$	−719274.	+	1.24582e6i	−0.193162	+	0.334567i
$426$	559164.			0.149285
$427$		0			0
$428$	3.49420e6			0.922016
$429$	2.13530e6	−	3.69844e6i	0.560164	−	0.970233i
$430$	629150.	+	1.08972e6i	0.164090	+	0.284213i
$431$	3.42393e6	+	5.93041e6i	0.887833	+	1.53777i	0.842432	+	0.538803i	$0.181123\pi$
$431$	3.42393e6	+	5.93041e6i	0.887833	+	1.53777i	0.0454009	+	0.998969i	$0.485543\pi$
$432$	698134.	−	1.20920e6i	0.179982	−	0.311738i
$433$	3.99328e6			1.02355			0.511777	−	0.859119i	$-0.328988\pi$
$433$	3.99328e6			1.02355			0.511777	+	0.859119i	$0.328988\pi$
$434$		0			0
$435$	−509079.			−0.128992
$436$	1.32128e6	−	2.28853e6i	0.332874	−	0.576555i
$437$	−2.85398e6	−	4.94324e6i	−0.714904	−	1.23825i
$438$	771986.	+	1.33712e6i	0.192276	+	0.333031i
$439$	742783.	−	1.28654e6i	0.183950	−	0.318611i	−0.759272	−	0.650773i	$-0.774445\pi$
$439$	742783.	−	1.28654e6i	0.183950	−	0.318611i	0.943222	+	0.332162i	$0.107778\pi$
$440$	−4.58163e6			−1.12821
$441$		0			0
$442$	−5.85416e6			−1.42531
$443$	2.81097e6	−	4.86874e6i	0.680528	−	1.17871i	−0.294291	−	0.955716i	$-0.595084\pi$
$443$	2.81097e6	−	4.86874e6i	0.680528	−	1.17871i	0.974820	−	0.222994i	$-0.0715831\pi$
$444$	−3.23401e6	−	5.60146e6i	−0.778545	−	1.34848i
$445$	742245.	+	1.28561e6i	0.177684	+	0.307757i
$446$	−3.17055e6	+	5.49156e6i	−0.754741	+	1.30725i
$447$	−1.26246e6			−0.298846
$448$		0			0
$449$	1.94883e6			0.456202			0.228101	−	0.973637i	$-0.426748\pi$
$449$	1.94883e6			0.456202			0.228101	+	0.973637i	$0.426748\pi$
$450$	1.06034e6	−	1.83657e6i	0.246839	−	0.427538i
$451$	−1.04211e6	−	1.80499e6i	−0.241253	−	0.417862i
$452$	3.50709e6	+	6.07446e6i	0.807422	+	1.39850i
$453$	−737961.	+	1.27819e6i	−0.168962	+	0.292650i
$454$	−1.02467e7			−2.33315
$455$		0			0
$456$	−5.17441e6			−1.16533
$457$	1.33656e6	−	2.31499e6i	0.299363	−	0.518511i	−0.676628	−	0.736325i	$-0.736559\pi$
$457$	1.33656e6	−	2.31499e6i	0.299363	−	0.518511i	0.975990	+	0.217814i	$0.0698926\pi$
$458$	4.52846e6	+	7.84352e6i	1.00876	+	1.74722i
$459$	−204760.	−	354655.i	−0.0453643	−	0.0785733i
$460$	3.54332e6	−	6.13720e6i	0.780756	−	1.35231i
$461$	4.65262e6			1.01964			0.509819	−	0.860282i	$-0.329713\pi$
$461$	4.65262e6			1.01964			0.509819	+	0.860282i	$0.329713\pi$
$462$		0			0
$463$	−5.18586e6			−1.12426			−0.562132	−	0.827047i	$-0.690019\pi$
$463$	−5.18586e6			−1.12426			−0.562132	+	0.827047i	$0.690019\pi$
$464$	2.28055e6	−	3.95002e6i	0.491749	−	0.851735i
$465$	315389.	+	546269.i	0.0676416	+	0.117159i
$466$	−3.04754e6	−	5.27850e6i	−0.650107	−	1.12602i
$467$	−2.52990e6	+	4.38192e6i	−0.536799	+	0.929763i	0.462275	+	0.886737i	$0.347033\pi$
$467$	−2.52990e6	+	4.38192e6i	−0.536799	+	0.929763i	−0.999074	+	0.0430263i	$0.986300\pi$
$468$	5.98808e6			1.26378
$469$		0			0
$470$	−758064.			−0.158293
$471$	−2.50444e6	+	4.33783e6i	−0.520187	+	0.900990i
$472$	5.69662e6	+	9.86684e6i	1.17696	+	2.03856i
$473$	−1.20606e6	−	2.08895e6i	−0.247865	−	0.429315i
$474$	−222918.	+	386105.i	−0.0455720	+	0.0789331i
$475$	−3.55331e6			−0.722603
$476$		0			0
$477$	92420.8			0.0185983
$478$	−3.79873e6	+	6.57959e6i	−0.760446	+	1.31713i
$479$	−2.77543e6	−	4.80718e6i	−0.552702	−	0.957308i	−0.998078	−	0.0619642i	$-0.980264\pi$
$479$	−2.77543e6	−	4.80718e6i	−0.552702	−	0.957308i	0.445377	−	0.895343i	$-0.353070\pi$
$480$	−675845.	−	1.17060e6i	−0.133889	−	0.231902i
$481$	5.05010e6	−	8.74702e6i	0.995261	−	1.72384i
$482$	1.20114e7			2.35491
$483$		0			0
$484$	4.03711e6			0.783353
$485$	755979.	−	1.30939e6i	0.145934	−	0.252764i
$486$	301854.	+	522827.i	0.0579704	+	0.100408i
$487$	3.43905e6	+	5.95661e6i	0.657077	+	1.13809i	0.981369	+	0.192133i	$0.0615405\pi$
$487$	3.43905e6	+	5.95661e6i	0.657077	+	1.13809i	−0.324292	+	0.945957i	$0.605126\pi$
$488$	−4.37206e6	+	7.57262e6i	−0.831067	+	1.43945i
$489$	177540.			0.0335756
$490$		0			0
$491$	7.44459e6			1.39360			0.696798	−	0.717267i	$-0.254607\pi$
$491$	7.44459e6			1.39360			0.696798	+	0.717267i	$0.254607\pi$
$492$	1.46121e6	−	2.53089e6i	0.272145	−	0.471368i
$493$	−668876.	−	1.15853e6i	−0.123945	−	0.214679i
$494$	−7.23009e6	−	1.25229e7i	−1.33299	−	2.30880i
$495$	447831.	−	775666.i	0.0821488	−	0.142286i
$496$	−5.65145e6			−1.03147
$497$		0			0
$498$	5.53426e6			0.999968
$499$	−1.07665e6	+	1.86481e6i	−0.193563	+	0.335261i	−0.946428	−	0.322914i	$-0.895338\pi$
$499$	−1.07665e6	+	1.86481e6i	−0.193563	+	0.335261i	0.752866	+	0.658174i	$0.228671\pi$
$500$	−4.89754e6	−	8.48278e6i	−0.876098	−	1.51745i
$501$	−426493.	−	738707.i	−0.0759132	−	0.131486i
$502$	1.80447e6	−	3.12543e6i	0.319588	−	0.553542i
$503$	−8.61012e6			−1.51736			−0.758681	−	0.651463i	$-0.774156\pi$
$503$	−8.61012e6			−1.51736			−0.758681	+	0.651463i	$0.774156\pi$
$504$		0			0
$505$	4.38531e6			0.765195
$506$	−9.78932e6	+	1.69556e7i	−1.69972	+	2.94399i
$507$	3.00456e6	+	5.20404e6i	0.519111	+	0.899127i
$508$	−845771.	−	1.46492e6i	−0.145410	−	0.251857i
$509$	1.67100e6	−	2.89426e6i	0.285879	−	0.495157i	−0.686943	−	0.726712i	$-0.741048\pi$
$509$	1.67100e6	−	2.89426e6i	0.285879	−	0.495157i	0.972822	+	0.231554i	$0.0743810\pi$
$510$	−1.22778e6			−0.209024
$511$		0			0
$512$	−1.32848e7			−2.23964
$513$	505772.	−	876023.i	0.0848519	−	0.146968i
$514$	51184.1	+	88653.4i	0.00854529	+	0.0148009i
$515$	−618093.	−	1.07057e6i	−0.102692	−	0.177867i
$516$	1.69109e6	−	2.92906e6i	0.279604	−	0.484288i
$517$	1.45318e6			0.239108
$518$		0			0
$519$	3.04957e6			0.496958
$520$	5.01589e6	−	8.68777e6i	0.813466	−	1.40896i
$521$	−1.34152e6	−	2.32359e6i	−0.216523	−	0.375029i	0.737220	−	0.675653i	$-0.236138\pi$
$521$	−1.34152e6	−	2.32359e6i	−0.216523	−	0.375029i	−0.953743	+	0.300624i	$0.902805\pi$
$522$	986046.	+	1.70788e6i	0.158387	+	0.274335i
$523$	−2.71178e6	+	4.69694e6i	−0.433511	+	0.750863i	−0.997173	−	0.0751429i	$-0.976059\pi$
$523$	−2.71178e6	+	4.69694e6i	−0.433511	+	0.750863i	0.563662	+	0.826005i	$0.309392\pi$
$524$	2.45692e7			3.90897
$525$		0			0
$526$	1.71945e7			2.70972
$527$	−828775.	+	1.43548e6i	−0.129990	+	0.225149i
$528$	4.01234e6	+	6.94958e6i	0.626344	+	1.08486i
$529$	−5.24276e6	−	9.08072e6i	−0.814555	−	1.41085i
$530$	138543.	−	239963.i	0.0214237	−	0.0371070i
$531$	−2.22726e6			−0.342796
$532$		0			0
$533$	4.56353e6			0.695798
$534$	2.87534e6	−	4.98024e6i	0.436351	−	0.755782i
$535$	572179.	+	991044.i	0.0864266	+	0.149695i
$536$	1.15164e7	+	1.99469e7i	1.73142	+	2.99891i
$537$	3.49287e6	−	6.04983e6i	0.522693	−	0.905330i
$538$	1.96009e7			2.91958
$539$		0			0
$540$	1.25587e6			0.185336
$541$	−1.09228e6	+	1.89188e6i	−0.160450	+	0.277908i	−0.935030	−	0.354568i	$-0.884628\pi$
$541$	−1.09228e6	+	1.89188e6i	−0.160450	+	0.277908i	0.774580	+	0.632476i	$0.217961\pi$
$542$	1.17063e7	+	2.02759e7i	1.71168	+	2.96471i
$543$	597135.	+	1.03427e6i	0.0869106	+	0.150534i
$544$	1.77598e6	−	3.07609e6i	0.257301	−	0.445658i
$545$	865447.			0.124810
$546$		0			0
$547$	−691437.			−0.0988062			−0.0494031	−	0.998779i	$-0.515732\pi$
$547$	−691437.			−0.0988062			−0.0494031	+	0.998779i	$0.515732\pi$
$548$	2.28014e6	−	3.94931e6i	0.324347	−	0.561785i
$549$	−854693.	−	1.48037e6i	−0.121026	−	0.209623i
$550$	6.09403e6	+	1.05552e7i	0.859010	+	1.48785i
$551$	1.65217e6	−	2.86164e6i	0.231833	−	0.401547i
$552$	−1.53401e7			−2.14279
$553$		0			0
$554$	−4.03639e6			−0.558752
$555$	1.05914e6	−	1.83449e6i	0.145956	−	0.252804i
$556$	7.68523e6	+	1.33112e7i	1.05431	+	1.82612i
$557$	−2.73828e6	−	4.74284e6i	−0.373973	−	0.647740i	0.616200	−	0.787590i	$-0.288671\pi$
$557$	−2.73828e6	−	4.74284e6i	−0.373973	−	0.647740i	−0.990173	+	0.139850i	$0.955338\pi$
$558$	1.22177e6	−	2.11616e6i	0.166113	−	0.287715i
$559$	5.28149e6			0.714869
$560$		0			0
$561$	2.35361e6			0.315739
$562$	9.08386e6	−	1.57337e7i	1.21319	−	2.10131i
$563$	199488.	+	345523.i	0.0265244	+	0.0459416i	0.878983	−	0.476853i	$-0.158223\pi$
$563$	199488.	+	345523.i	0.0265244	+	0.0459416i	−0.852459	+	0.522795i	$0.824889\pi$
$564$	1.01880e6	+	1.76462e6i	0.134863	+	0.233589i
$565$	−1.14858e6	+	1.98940e6i	−0.151370	+	0.262181i
$566$	−1.24245e7			−1.63019
$567$		0			0
$568$	−2.51793e6			−0.327471
$569$	2.11556e6	−	3.66426e6i	0.273934	−	0.474467i	−0.695932	−	0.718108i	$-0.745008\pi$
$569$	2.11556e6	−	3.66426e6i	0.273934	−	0.474467i	0.969866	+	0.243641i	$0.0783418\pi$
$570$	−1.51635e6	−	2.62640e6i	−0.195485	−	0.338589i
$571$	−4.37551e6	−	7.57861e6i	−0.561615	−	0.972746i	−0.997356	−	0.0726734i	$-0.976847\pi$
$571$	−4.37551e6	−	7.57861e6i	−0.561615	−	0.972746i	0.435741	−	0.900072i	$-0.356486\pi$
$572$	−1.72075e7	+	2.98042e7i	−2.19901	+	3.80879i
$573$	−59736.7			−0.00760072
$574$		0			0
$575$	−1.05342e7			−1.32871
$576$	−135864.	+	235323.i	−0.0170627	+	0.0295535i
$577$	−883558.	−	1.53037e6i	−0.110483	−	0.191362i	0.805482	−	0.592620i	$-0.201906\pi$
$577$	−883558.	−	1.53037e6i	−0.110483	−	0.191362i	−0.915965	+	0.401258i	$0.868573\pi$
$578$	5.64503e6	+	9.77748e6i	0.702824	+	1.21733i
$579$	2.03665e6	−	3.52759e6i	0.252477	−	0.437302i
$580$	4.10245e6			0.506376
$581$		0			0
$582$	−5.85709e6			−0.716761
$583$	−265582.	+	460001.i	−0.0323614	+	0.0560516i
$584$	−3.47627e6	−	6.02107e6i	−0.421775	−	0.730536i
$585$	980555.	+	1.69837e6i	0.118463	+	0.205184i
$586$	−7.61153e6	+	1.31835e7i	−0.915646	+	1.58595i
$587$	8.65009e6			1.03616			0.518078	−	0.855333i	$-0.326648\pi$
$587$	8.65009e6			1.03616			0.518078	+	0.855333i	$0.326648\pi$
$588$		0			0
$589$	−4.09426e6			−0.486281
$590$	−3.33877e6	+	5.78292e6i	−0.394872	+	0.683939i
$591$	3.67628e6	+	6.36751e6i	0.432953	+	0.749896i
$592$	9.48941e6	+	1.64361e7i	1.11285	+	1.92750i
$593$	7.72568e6	−	1.33813e7i	0.902194	−	1.56265i	0.0775549	−	0.996988i	$-0.475289\pi$
$593$	7.72568e6	−	1.33813e7i	0.902194	−	1.56265i	0.824640	−	0.565659i	$-0.191378\pi$
$594$	−3.46965e6			−0.403478
$595$		0			0
$596$	1.01736e7			1.17316
$597$	−3.62888e6	+	6.28540e6i	−0.416712	+	0.721767i
$598$	−2.14344e7	−	3.71254e7i	−2.45108	−	4.24540i
$599$	1.92400e6	+	3.33247e6i	0.219098	+	0.379489i	0.954533	−	0.298107i	$-0.0963552\pi$
$599$	1.92400e6	+	3.33247e6i	0.219098	+	0.379489i	−0.735434	+	0.677596i	$0.763022\pi$
$600$	−4.77474e6	+	8.27009e6i	−0.541466	+	0.937847i
$601$	−1.27578e7			−1.44075			−0.720376	−	0.693583i	$-0.756031\pi$
$601$	−1.27578e7			−1.44075			−0.720376	+	0.693583i	$0.756031\pi$
$602$		0			0
$603$	−4.50266e6			−0.504285
$604$	5.94691e6	−	1.03004e7i	0.663284	−	1.14884i
$605$	661082.	+	1.14503e6i	0.0734289	+	0.127183i
$606$	−8.49400e6	−	1.47120e7i	−0.939574	−	1.62739i
$607$	−6.81033e6	+	1.17958e7i	−0.750233	+	1.29944i	0.197476	+	0.980308i	$0.436726\pi$
$607$	−6.81033e6	+	1.17958e7i	−0.750233	+	1.29944i	−0.947709	+	0.319135i	$0.896608\pi$
$608$	8.77359e6			0.962539
$609$		0			0
$610$	−5.12489e6			−0.557648
$611$	−1.59092e6	+	2.75555e6i	−0.172403	+	0.298611i
$612$	1.65008e6	+	2.85802e6i	0.178084	+	0.308451i
$613$	−7.67372e6	−	1.32913e7i	−0.824812	−	1.42862i	−0.902063	−	0.431605i	$-0.857948\pi$
$613$	−7.67372e6	−	1.32913e7i	−0.824812	−	1.42862i	0.0772508	−	0.997012i	$-0.475386\pi$
$614$	1.03828e7	−	1.79835e7i	1.11145	−	1.92510i
$615$	957099.			0.102040
$616$		0			0
$617$	1.18485e7			1.25300			0.626500	−	0.779421i	$-0.284487\pi$
$617$	1.18485e7			1.25300			0.626500	+	0.779421i	$0.284487\pi$
$618$	−2.39439e6	+	4.14721e6i	−0.252188	+	0.436802i
$619$	−437230.	−	757304.i	−0.0458652	−	0.0794408i	0.842181	−	0.539194i	$-0.181271\pi$
$619$	−437230.	−	757304.i	−0.0458652	−	0.0794408i	−0.888047	+	0.459753i	$0.847938\pi$
$620$	−2.54158e6	−	4.40215e6i	−0.265537	−	0.459924i
$621$	1.49941e6	−	2.59706e6i	0.156024	−	0.270242i
$622$	−2.96272e6			−0.307054
$623$		0			0
$624$	−1.75706e7			−1.80644
$625$	−2.39730e6	+	4.15225e6i	−0.245484	+	0.425190i
$626$	1.11548e6	+	1.93206e6i	0.113769	+	0.197054i
$627$	2.90679e6	+	5.03471e6i	0.295287	+	0.511453i
$628$	2.01823e7	−	3.49567e7i	2.04207	−	3.53697i
$629$	5.56642e6			0.560983
$630$		0			0
$631$	−4.43859e6			−0.443784			−0.221892	−	0.975071i	$-0.571223\pi$
$631$	−4.43859e6			−0.443784			−0.221892	+	0.975071i	$0.571223\pi$
$632$	1.00380e6	−	1.73864e6i	0.0999667	−	0.173147i
$633$	309483.	+	536040.i	0.0306992	+	0.0531726i
$634$	−6.59761e6	−	1.14274e7i	−0.651873	−	1.12908i
$635$	276992.	−	479764.i	0.0272605	−	0.0472165i
$636$	−744780.			−0.0730104
$637$		0			0
$638$	−1.13341e7			−1.10239
$639$	246115.	−	426283.i	0.0238443	−	0.0412996i
$640$	−1.99567e6	−	3.45661e6i	−0.192593	−	0.333580i
$641$	−406276.	−	703690.i	−0.0390549	−	0.0676451i	0.845837	−	0.533441i	$-0.179101\pi$
$641$	−406276.	−	703690.i	−0.0390549	−	0.0676451i	−0.884892	+	0.465796i	$0.845768\pi$
$642$	2.21653e6	−	3.83915e6i	0.212245	−	0.367618i
$643$	1.17941e7			1.12496			0.562481	−	0.826810i	$-0.309847\pi$
$643$	1.17941e7			1.12496			0.562481	+	0.826810i	$0.309847\pi$
$644$		0			0
$645$	1.10767e6			0.104837
$646$	3.98465e6	−	6.90162e6i	0.375672	−	0.650683i
$647$	−1.21690e6	−	2.10773e6i	−0.114286	−	0.197950i	0.803208	−	0.595699i	$-0.203125\pi$
$647$	−1.21690e6	−	2.10773e6i	−0.114286	−	0.197950i	−0.917494	+	0.397749i	$0.869791\pi$
$648$	−1.35925e6	−	2.35430e6i	−0.127164	−	0.220254i
$649$	6.40031e6	−	1.10857e7i	0.596471	−	1.03312i
$650$	−2.66866e7			−2.47748
$651$		0			0
$652$	−1.43072e6			−0.131806
$653$	4.73332e6	−	8.19835e6i	0.434393	−	0.752391i	−0.562853	−	0.826557i	$-0.690296\pi$
$653$	4.73332e6	−	8.19835e6i	0.434393	−	0.752391i	0.997246	+	0.0741664i	$0.0236296\pi$
$654$	−1.67630e6	−	2.90344e6i	−0.153253	−	0.265442i
$655$	4.02323e6	+	6.96843e6i	0.366413	+	0.634647i
$656$	−4.28756e6	+	7.42628e6i	−0.389001	+	0.673770i
$657$	1.35915e6			0.122844
$658$		0			0
$659$	1.40662e7			1.26172			0.630860	−	0.775896i	$-0.282702\pi$
$659$	1.40662e7			1.26172			0.630860	+	0.775896i	$0.282702\pi$
$660$	−3.60888e6	+	6.25076e6i	−0.322487	+	0.558564i
$661$	−8.58029e6	−	1.48615e7i	−0.763832	−	1.32300i	−0.940862	−	0.338791i	$-0.889982\pi$
$661$	−8.58029e6	−	1.48615e7i	−0.763832	−	1.32300i	0.177029	−	0.984206i	$-0.443351\pi$
$662$	1.78182e7	+	3.08620e7i	1.58022	+	2.73702i
$663$	−2.57669e6	+	4.46296e6i	−0.227656	+	0.394312i
$664$	−2.49209e7			−2.19353
$665$		0			0
$666$	−8.20592e6			−0.716872
$667$	4.89803e6	−	8.48364e6i	0.426292	−	0.738359i
$668$	3.43692e6	+	5.95293e6i	0.298009	+	0.516166i
$669$	2.79102e6	+	4.83419e6i	0.241100	+	0.417598i
$670$	−6.74969e6	+	1.16908e7i	−0.580894	+	1.00614i
$671$	9.82424e6			0.842350
$672$		0			0
$673$	5.87113e6			0.499671			0.249836	−	0.968288i	$-0.419623\pi$
$673$	5.87113e6			0.499671			0.249836	+	0.968288i	$0.419623\pi$
$674$	−1.27388e6	+	2.20643e6i	−0.108014	+	0.187086i
$675$	−933413.	−	1.61672e6i	−0.0788523	−	0.136576i
$676$	−2.42124e7	−	4.19372e7i	−2.03785	−	3.52966i
$677$	6.96368e6	−	1.20614e7i	0.583938	−	1.01141i	−0.411069	−	0.911604i	$-0.634844\pi$
$677$	6.96368e6	−	1.20614e7i	0.583938	−	1.01141i	0.995007	−	0.0998062i	$-0.0318223\pi$
$678$	8.89884e6			0.743462
$679$		0			0
$680$	5.52872e6			0.458513
$681$	−4.51005e6	+	7.81163e6i	−0.372660	+	0.645467i
$682$	7.02178e6	+	1.21621e7i	0.578077	+	1.00126i
$683$	−9.15503e6	−	1.58570e7i	−0.750945	−	1.30067i	−0.947365	−	0.320155i	$-0.896265\pi$
$683$	−9.15503e6	−	1.58570e7i	−0.750945	−	1.30067i	0.196421	−	0.980520i	$-0.437068\pi$
$684$	−4.07580e6	+	7.05950e6i	−0.333099	+	0.576944i
$685$	1.49350e6			0.121613
$686$		0			0
$687$	7.97275e6			0.644490
$688$	−4.96210e6	+	8.59461e6i	−0.399663	+	0.692237i
$689$	−581509.	−	1.00720e6i	−0.0466669	−	0.0808294i
$690$	−4.49538e6	−	7.78622e6i	−0.359454	−	0.622593i
$691$	−8.83583e6	+	1.53041e7i	−0.703967	+	1.21931i	0.263096	+	0.964770i	$0.415256\pi$
$691$	−8.83583e6	+	1.53041e7i	−0.703967	+	1.21931i	−0.967063	+	0.254537i	$0.918077\pi$
$692$	−2.45752e7			−1.95088
$693$		0			0
$694$	−1.53973e7			−1.21351
$695$	−2.51693e6	+	4.35945e6i	−0.197656	+	0.342350i
$696$	−4.44018e6	−	7.69062e6i	−0.347438	−	0.601781i
$697$	1.25753e6	+	2.17810e6i	0.0980473	+	0.169823i
$698$	7.89131e6	−	1.36681e7i	0.613070	−	1.06187i
$699$	−5.36547e6			−0.415351
$700$		0			0
$701$	8.22993e6			0.632559			0.316279	−	0.948666i	$-0.397566\pi$
$701$	8.22993e6			0.632559			0.316279	+	0.948666i	$0.397566\pi$
$702$	3.79852e6	−	6.57922e6i	0.290918	−	0.503886i
$703$	6.87472e6	+	1.19074e7i	0.524646	+	0.908714i
$704$	−780843.	−	1.35246e6i	−0.0593789	−	0.102847i
$705$	−333660.	+	577916.i	−0.0252832	+	0.0437917i
$706$	1.71552e7			1.29534
$707$		0			0
$708$	1.79486e7			1.34570
$709$	−1.23183e7	+	2.13360e7i	−0.920314	+	1.59403i	−0.121386	+	0.992605i	$0.538734\pi$
$709$	−1.23183e7	+	2.13360e7i	−0.920314	+	1.59403i	−0.798929	+	0.601426i	$0.794600\pi$
$710$	−737874.	−	1.27803e6i	−0.0549334	−	0.0951474i
$711$	196233.	+	339886.i	0.0145579	+	0.0252150i
$712$	−1.29477e7	+	2.24261e7i	−0.957179	+	1.65788i
$713$	−1.21379e7			−0.894167
$714$		0			0
$715$	−1.12710e7			−0.824510
$716$	−2.81475e7	+	4.87530e7i	−2.05191	+	3.55401i
$717$	3.34400e6	+	5.79197e6i	0.242923	+	0.420754i
$718$	1.27784e7	+	2.21329e7i	0.925053	+	1.60224i
$719$	−9.41269e6	+	1.63033e7i	−0.679034	+	1.17612i	0.296238	+	0.955114i	$0.404268\pi$
$719$	−9.41269e6	+	1.63033e7i	−0.679034	+	1.17612i	−0.975272	+	0.221007i	$0.929066\pi$
$720$	−3.68503e6			−0.264917
$721$		0			0
$722$	−5.63055e6			−0.401983
$723$	5.28677e6	−	9.15696e6i	0.376136	−	0.651487i
$724$	−4.81205e6	−	8.33472e6i	−0.341180	−	0.590942i
$725$	−3.04911e6	−	5.28122e6i	−0.215441	−	0.373155i
$726$	2.56093e6	−	4.43566e6i	0.180325	−	0.312332i
$727$	−6.77607e6			−0.475491			−0.237745	−	0.971328i	$-0.576408\pi$
$727$	−6.77607e6			−0.475491			−0.237745	+	0.971328i	$0.576408\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	2.03743e6	−	3.52893e6i	0.141506	−	0.245096i
$731$	1.45537e6	+	2.52077e6i	0.100735	+	0.174478i
$732$	6.88760e6	+	1.19297e7i	0.475106	+	0.822908i
$733$	−8.61136e6	+	1.49153e7i	−0.591986	+	1.02535i	0.401978	+	0.915649i	$0.368323\pi$
$733$	−8.61136e6	+	1.49153e7i	−0.591986	+	1.02535i	−0.993965	+	0.109701i	$0.965011\pi$
$734$	2.15459e7			1.47613
$735$		0			0
$736$	2.60102e7			1.76990
$737$	1.29389e7	−	2.24109e7i	0.877465	−	1.51981i
$738$	−1.85383e6	−	3.21092e6i	−0.125293	−	0.217014i
$739$	8.82669e6	+	1.52883e7i	0.594548	+	1.02979i	0.993610	+	0.112864i	$0.0360023\pi$
$739$	8.82669e6	+	1.52883e7i	0.594548	+	1.02979i	−0.399062	+	0.916924i	$0.630664\pi$
$740$	−8.53520e6	+	1.47834e7i	−0.572973	+	0.992418i
$741$	−1.27292e7			−0.851641
$742$		0			0
$743$	−1.36977e7			−0.910281			−0.455141	−	0.890420i	$-0.650411\pi$
$743$	−1.36977e7			−0.910281			−0.455141	+	0.890420i	$0.650411\pi$
$744$	−5.50163e6	+	9.52911e6i	−0.364384	+	0.631132i
$745$	1.66594e6	+	2.88549e6i	0.109968	+	0.190471i
$746$	−1.39670e7	−	2.41916e7i	−0.918877	−	1.59154i
$747$	2.43589e6	−	4.21908e6i	0.159719	−	0.276641i
$748$	−1.89668e7			−1.23948
$749$		0			0
$750$	−1.24269e7			−0.806698
$751$	−5.80446e6	+	1.00536e7i	−0.375545	+	0.650463i	−0.990408	−	0.138171i	$-0.955878\pi$
$751$	−5.80446e6	+	1.00536e7i	−0.375545	+	0.650463i	0.614864	+	0.788633i	$0.289211\pi$
$752$	−2.98943e6	−	5.17784e6i	−0.192772	−	0.333890i
$753$	−1.58846e6	−	2.75130e6i	−0.102092	−	0.176828i
$754$	1.24083e7	−	2.14919e7i	0.794851	−	1.37672i
$755$	3.89526e6			0.248696
$756$		0			0
$757$	6.25226e6			0.396550			0.198275	−	0.980146i	$-0.436466\pi$
$757$	6.25226e6			0.396550			0.198275	+	0.980146i	$0.436466\pi$
$758$	1.04434e7	−	1.80885e7i	0.660191	−	1.14348i
$759$	8.61748e6	+	1.49259e7i	0.542970	+	0.940452i
$760$	6.82815e6	+	1.18267e7i	0.428814	+	0.742728i
$761$	−1.51063e7	+	2.61648e7i	−0.945574	+	1.63778i	−0.190977	+	0.981595i	$0.561166\pi$
$761$	−1.51063e7	+	2.61648e7i	−0.945574	+	1.63778i	−0.754597	+	0.656188i	$0.772168\pi$
$762$	−2.14605e6			−0.133891
$763$		0			0
$764$	481393.			0.0298378
$765$	−540404.	+	936007.i	−0.0333860	+	0.0578263i
$766$	7.71386e6	+	1.33608e7i	0.475007	+	0.822736i
$767$	1.40139e7	+	2.42728e7i	0.860142	+	1.48981i
$768$	−8.21400e6	+	1.42271e7i	−0.502518	+	0.870386i
$769$	2.58756e7			1.57788			0.788940	−	0.614470i	\(-0.210630\pi

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.11193 + 8.85412i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(11.8764 - 20.5705i) q^{5} -92.0147 q^{6} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-5.11193 + 8.85412i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(11.8764 - 20.5705i) q^{5} -92.0147 q^{6} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +(121.423 + 210.310i) q^{10} +(-232.763 - 403.157i) q^{11} +(326.372 - 565.293i) q^{12} +1019.30 q^{13} +213.775 q^{15} +(-957.660 + 1658.72i) q^{16} +(280.878 + 486.496i) q^{17} +(-414.066 - 717.183i) q^{18} +(-693.789 + 1201.68i) q^{19} -1722.72 q^{20} +4759.47 q^{22} +(-2056.81 + 3562.50i) q^{23} +(1864.55 + 3229.49i) q^{24} +(1280.40 + 2217.72i) q^{25} +(-5210.59 + 9025.00i) q^{26} -729.000 q^{27} -2381.37 q^{29} +(-1092.80 + 1892.79i) q^{30} +(1475.33 + 2555.34i) q^{31} +(-3161.47 - 5475.84i) q^{32} +(2094.87 - 3628.42i) q^{33} -5743.32 q^{34} +5874.70 q^{36} +(4954.48 - 8581.40i) q^{37} +(-7093.20 - 12285.8i) q^{38} +(4586.85 + 7944.66i) q^{39} +(4920.92 - 8523.28i) q^{40} +4477.13 q^{41} +5181.48 q^{43} +(-16881.6 + 29239.9i) q^{44} +(961.989 + 1666.21i) q^{45} +(-21028.5 - 36422.5i) q^{46} +(-1560.80 + 2703.38i) q^{47} -17237.9 q^{48} -26181.3 q^{50} +(-2527.91 + 4378.46i) q^{51} +(-36963.5 - 64022.6i) q^{52} +(-570.499 - 988.133i) q^{53} +(3726.59 - 6454.65i) q^{54} -11057.6 q^{55} -12488.2 q^{57} +(12173.4 - 21085.0i) q^{58} +(13748.5 + 23813.2i) q^{59} +(-7752.26 - 13427.3i) q^{60} +(-10551.8 + 18276.2i) q^{61} -30167.1 q^{62} +3354.67 q^{64} +(12105.6 - 20967.6i) q^{65} +(21417.6 + 37096.4i) q^{66} +(27794.2 + 48141.0i) q^{67} +(20371.3 - 35284.2i) q^{68} -37022.6 q^{69} -6076.90 q^{71} +(-16780.9 + 29065.4i) q^{72} +(-8389.82 - 14531.6i) q^{73} +(50653.8 + 87735.0i) q^{74} +(-11523.6 + 19959.5i) q^{75} +100637. q^{76} -93790.5 q^{78} +(2422.63 - 4196.12i) q^{79} +(22747.1 + 39399.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-22886.7 + 39641.0i) q^{82} -60145.4 q^{83} +13343.3 q^{85} +(-26487.4 + 45877.5i) q^{86} +(-10716.2 - 18561.0i) q^{87} +(-96443.9 - 167046. i) q^{88} +(-31248.7 + 54124.4i) q^{89} -19670.5 q^{90} +298349. q^{92} +(-13277.9 + 22998.1i) q^{93} +(-15957.4 - 27639.0i) q^{94} +(16479.4 + 28543.2i) q^{95} +(28453.3 - 49282.5i) q^{96} +63653.8 q^{97} +37707.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9 + 283 * q^10 - 402 * q^11 + 621 * q^12 - 924 * q^13 - 3273 * q^16 + 276 * q^17 - 243 * q^18 + 510 * q^19 - 9438 * q^20 + 2750 * q^22 - 6900 * q^23 + 1107 * q^24 - 2814 * q^25 - 15138 * q^26 - 5832 * q^27 + 1080 * q^29 - 2547 * q^30 - 6410 * q^31 - 15519 * q^32 + 3618 * q^33 - 42288 * q^34 + 11178 * q^36 - 15250 * q^37 - 41250 * q^38 - 4158 * q^39 - 8547 * q^40 - 8616 * q^41 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 58914 * q^48 - 14604 * q^50 - 2484 * q^51 - 47476 * q^52 - 13692 * q^53 + 2187 * q^54 - 146248 * q^55 + 9180 * q^57 - 52309 * q^58 + 34830 * q^59 - 42471 * q^60 - 5364 * q^61 - 32058 * q^62 - 146974 * q^64 - 66864 * q^65 + 12375 * q^66 + 5994 * q^67 - 58272 * q^68 - 124200 * q^69 + 178536 * q^71 - 9963 * q^72 + 59638 * q^73 + 185442 * q^74 + 25326 * q^75 - 42616 * q^76 - 272484 * q^78 + 44062 * q^79 - 33381 * q^80 - 26244 * q^81 + 57596 * q^82 + 416892 * q^83 + 72648 * q^85 + 136968 * q^86 + 4860 * q^87 - 87597 * q^88 - 77520 * q^89 - 45846 * q^90 + 316512 * q^92 + 57690 * q^93 - 73722 * q^94 + 221376 * q^95 + 139671 * q^96 + 377260 * q^97 + 65124 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more