LMFDB - Embedded newform 63.6.e.e.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, 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:	$10.1041806482$
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:	$\Z[a_1, \ldots, a_{7}]$
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			46.4
Root			$-4.61193 - 7.98809i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.e.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.11193 + 8.85412i) q^{2} +(-36.2636 + 62.8104i) q^{4} +(11.8764 + 20.5705i) q^{5} +(30.6840 + 125.958i) q^{7} -414.344 q^{8} +O(q^{10})$	\(q+(5.11193 + 8.85412i) q^{2} +(-36.2636 + 62.8104i) q^{4} +(11.8764 + 20.5705i) q^{5} +(30.6840 + 125.958i) q^{7} -414.344 q^{8} +(-121.423 + 210.310i) q^{10} +(232.763 - 403.157i) q^{11} -1019.30 q^{13} +(-958.395 + 915.570i) q^{14} +(-957.660 - 1658.72i) q^{16} +(280.878 - 486.496i) q^{17} +(693.789 + 1201.68i) q^{19} -1722.72 q^{20} +4759.47 q^{22} +(2056.81 + 3562.50i) q^{23} +(1280.40 - 2217.72i) q^{25} +(-5210.59 - 9025.00i) q^{26} +(-9024.20 - 2640.42i) q^{28} +2381.37 q^{29} +(-1475.33 + 2555.34i) q^{31} +(3161.47 - 5475.84i) q^{32} +5743.32 q^{34} +(-2226.61 + 2127.12i) q^{35} +(4954.48 + 8581.40i) q^{37} +(-7093.20 + 12285.8i) q^{38} +(-4920.92 - 8523.28i) q^{40} +4477.13 q^{41} +5181.48 q^{43} +(16881.6 + 29239.9i) q^{44} +(-21028.5 + 36422.5i) q^{46} +(-1560.80 - 2703.38i) q^{47} +(-14924.0 + 7729.82i) q^{49} +26181.3 q^{50} +(36963.5 - 64022.6i) q^{52} +(570.499 - 988.133i) q^{53} +11057.6 q^{55} +(-12713.7 - 52190.0i) q^{56} +(12173.4 + 21085.0i) q^{58} +(13748.5 - 23813.2i) q^{59} +(10551.8 + 18276.2i) q^{61} -30167.1 q^{62} +3354.67 q^{64} +(-12105.6 - 20967.6i) q^{65} +(27794.2 - 48141.0i) q^{67} +(20371.3 + 35284.2i) q^{68} +(-30216.0 - 8841.02i) q^{70} +6076.90 q^{71} +(8389.82 - 14531.6i) q^{73} +(-50653.8 + 87735.0i) q^{74} -100637. q^{76} +(57923.1 + 16947.9i) q^{77} +(2422.63 + 4196.12i) q^{79} +(22747.1 - 39399.2i) q^{80} +(22886.7 + 39641.0i) q^{82} -60145.4 q^{83} +13343.3 q^{85} +(26487.4 + 45877.5i) q^{86} +(-96443.9 + 167046. i) q^{88} +(-31248.7 - 54124.4i) q^{89} +(-31276.2 - 128389. i) q^{91} -298349. q^{92} +(15957.4 - 27639.0i) q^{94} +(-16479.4 + 28543.2i) q^{95} -63653.8 q^{97} +(-144731. - 92624.4i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8}+O(q^{10}) $ 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8	$ 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8} - 283 q^{10} + 402 q^{11} + 924 q^{13} - 1926 q^{14} - 3273 q^{16} + 276 q^{17} - 510 q^{19} - 9438 q^{20} + 2750 q^{22} + 6900 q^{23} - 2814 q^{25} - 15138 q^{26} - 26221 q^{28} - 1080 q^{29} + 6410 q^{31} + 15519 q^{32} + 42288 q^{34} + 33108 q^{35} - 15250 q^{37} - 41250 q^{38} + 8547 q^{40} - 8616 q^{41} + 58396 q^{43} + 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 64252 q^{49} + 14604 q^{50} + 47476 q^{52} + 13692 q^{53} + 146248 q^{55} + 15921 q^{56} - 52309 q^{58} + 34830 q^{59} + 5364 q^{61} - 32058 q^{62} - 146974 q^{64} + 66864 q^{65} + 5994 q^{67} - 58272 q^{68} - 4307 q^{70} - 178536 q^{71} - 59638 q^{73} - 185442 q^{74} + 42616 q^{76} + 75660 q^{77} + 44062 q^{79} - 33381 q^{80} - 57596 q^{82} + 416892 q^{83} + 72648 q^{85} - 136968 q^{86} - 87597 q^{88} - 77520 q^{89} + 104722 q^{91} - 316512 q^{92} + 73722 q^{94} - 221376 q^{95} - 377260 q^{97} - 382479 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8 - 283 * q^10 + 402 * q^11 + 924 * q^13 - 1926 * q^14 - 3273 * q^16 + 276 * q^17 - 510 * q^19 - 9438 * q^20 + 2750 * q^22 + 6900 * q^23 - 2814 * q^25 - 15138 * q^26 - 26221 * q^28 - 1080 * q^29 + 6410 * q^31 + 15519 * q^32 + 42288 * q^34 + 33108 * q^35 - 15250 * q^37 - 41250 * q^38 + 8547 * q^40 - 8616 * q^41 + 58396 * q^43 + 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 64252 * q^49 + 14604 * q^50 + 47476 * q^52 + 13692 * q^53 + 146248 * q^55 + 15921 * q^56 - 52309 * q^58 + 34830 * q^59 + 5364 * q^61 - 32058 * q^62 - 146974 * q^64 + 66864 * q^65 + 5994 * q^67 - 58272 * q^68 - 4307 * q^70 - 178536 * q^71 - 59638 * q^73 - 185442 * q^74 + 42616 * q^76 + 75660 * q^77 + 44062 * q^79 - 33381 * q^80 - 57596 * q^82 + 416892 * q^83 + 72648 * q^85 - 136968 * q^86 - 87597 * q^88 - 77520 * q^89 + 104722 * q^91 - 316512 * q^92 + 73722 * q^94 - 221376 * q^95 - 377260 * q^97 - 382479 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.822693	+	0.568485i	$0.192470\pi$
$2$	5.11193	+	8.85412i	0.903669	+	1.56520i	0.0809760	+	0.996716i	$0.474196\pi$
$3$		0			0
$3$		0			0
$4$	−36.2636	+	62.8104i	−1.13324	+	1.96282i
$5$	11.8764	+	20.5705i	0.212452	+	0.367977i	0.952481	−	0.304597i	$-0.0985219\pi$
$5$	11.8764	+	20.5705i	0.212452	+	0.367977i	−0.740030	+	0.672574i	$0.765189\pi$
$6$		0			0
$7$	30.6840	+	125.958i	0.236683	+	0.971587i
$7$	30.6840	+	125.958i	0.236683	+	0.971587i
$8$	−414.344			−2.28895
$9$		0			0
$10$	−121.423	+	210.310i	−0.383972	+	0.665059i
$11$	232.763	−	403.157i	0.580006	−	1.00460i	−0.415472	−	0.909606i	$-0.636384\pi$
$11$	232.763	−	403.157i	0.580006	−	1.00460i	0.995478	−	0.0949934i	$-0.0302830\pi$
$12$		0			0
$13$	−1019.30			−1.67280			−0.836399	−	0.548121i	$-0.815343\pi$
$13$	−1019.30			−1.67280			−0.836399	+	0.548121i	$0.815343\pi$
$14$	−958.395	+	915.570i	−1.30685	+	1.24845i
$15$		0			0
$16$	−957.660	−	1658.72i	−0.935215	−	1.61984i
$17$	280.878	−	486.496i	0.235720	−	0.408279i	−0.723762	−	0.690050i	$-0.757589\pi$
$17$	280.878	−	486.496i	0.235720	−	0.408279i	0.959482	+	0.281771i	$0.0909219\pi$
$18$		0			0
$19$	693.789	+	1201.68i	0.440903	+	0.763667i	0.997757	−	0.0669438i	$-0.0213248\pi$
$19$	693.789	+	1201.68i	0.440903	+	0.763667i	−0.556853	+	0.830611i	$0.687991\pi$
$20$	−1722.72			−0.963032
$21$		0			0
$22$	4759.47			2.09653
$23$	2056.81	+	3562.50i	0.810727	+	1.40422i	0.912356	+	0.409397i	$0.134261\pi$
$23$	2056.81	+	3562.50i	0.810727	+	1.40422i	−0.101630	+	0.994822i	$0.532406\pi$
$24$		0			0
$25$	1280.40	−	2217.72i	0.409729	−	0.709671i
$26$	−5210.59	−	9025.00i	−1.51166	−	2.61827i
$27$		0			0
$28$	−9024.20	−	2640.42i	−2.17527	−	0.636471i
$29$	2381.37			0.525814			0.262907	−	0.964821i	$-0.415319\pi$
$29$	2381.37			0.525814			0.262907	+	0.964821i	$0.415319\pi$
$30$		0			0
$31$	−1475.33	+	2555.34i	−0.275730	+	0.477579i	−0.970319	−	0.241828i	$-0.922253\pi$
$31$	−1475.33	+	2555.34i	−0.275730	+	0.477579i	0.694589	+	0.719407i	$0.255586\pi$
$32$	3161.47	−	5475.84i	0.545776	−	0.945313i
$33$		0			0
$34$	5743.32			0.852051
$35$	−2226.61	+	2127.12i	−0.307238	+	0.293509i
$36$		0			0
$37$	4954.48	+	8581.40i	0.594968	+	1.03051i	0.993551	+	0.113382i	$0.0361685\pi$
$37$	4954.48	+	8581.40i	0.594968	+	1.03051i	−0.398584	+	0.917132i	$0.630498\pi$
$38$	−7093.20	+	12285.8i	−0.796862	+	1.38021i
$39$		0			0
$40$	−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
$45$		0			0
$46$	−21028.5	+	36422.5i	−1.46526	+	2.53790i
$47$	−1560.80	−	2703.38i	−0.103063	−	0.178510i	0.809882	−	0.586592i	$-0.199531\pi$
$47$	−1560.80	−	2703.38i	−0.103063	−	0.178510i	−0.912945	+	0.408082i	$0.866198\pi$
$48$		0			0
$49$	−14924.0	+	7729.82i	−0.887962	+	0.459917i
$50$	26181.3			1.48104
$51$		0			0
$52$	36963.5	−	64022.6i	1.89568	−	3.28341i
$53$	570.499	−	988.133i	0.0278975	−	0.0483198i	−0.851740	−	0.523965i	$-0.824452\pi$
$53$	570.499	−	988.133i	0.0278975	−	0.0483198i	0.879637	+	0.475645i	$0.157785\pi$
$54$		0			0
$55$	11057.6			0.492893
$56$	−12713.7	−	52190.0i	−0.541755	−	2.22391i
$57$		0			0
$58$	12173.4	+	21085.0i	0.475162	+	0.823005i
$59$	13748.5	−	23813.2i	0.514194	−	0.890610i	−0.485671	−	0.874142i	$-0.661425\pi$
$59$	13748.5	−	23813.2i	0.514194	−	0.890610i	0.999864	−	0.0164678i	$-0.00524209\pi$
$60$		0			0
$61$	10551.8	+	18276.2i	0.363078	+	0.628870i	0.988466	−	0.151444i	$-0.0483924\pi$
$61$	10551.8	+	18276.2i	0.363078	+	0.628870i	−0.625387	+	0.780314i	$0.715059\pi$
$62$	−30167.1			−0.996676
$63$		0			0
$64$	3354.67			0.102376
$65$	−12105.6	−	20967.6i	−0.355389	−	0.615551i
$66$		0			0
$67$	27794.2	−	48141.0i	0.756428	−	1.31017i	−0.188234	−	0.982124i	$-0.560276\pi$
$67$	27794.2	−	48141.0i	0.756428	−	1.31017i	0.944661	−	0.328047i	$-0.106390\pi$
$68$	20371.3	+	35284.2i	0.534253	+	0.925353i
$69$		0			0
$70$	−30216.0	−	8841.02i	−0.737043	−	0.215654i
$71$	6076.90			0.143066			0.0715330	−	0.997438i	$-0.477211\pi$
$71$	6076.90			0.143066			0.0715330	+	0.997438i	$0.477211\pi$
$72$		0			0
$73$	8389.82	−	14531.6i	0.184266	−	0.319158i	−0.759063	−	0.651017i	$-0.774343\pi$
$73$	8389.82	−	14531.6i	0.184266	−	0.319158i	0.943329	+	0.331859i	$0.107676\pi$
$74$	−50653.8	+	87735.0i	−1.07531	+	1.86249i
$75$		0			0
$76$	−100637.			−1.99859
$77$	57923.1	+	16947.9i	1.11333	+	0.325754i
$78$		0			0
$79$	2422.63	+	4196.12i	0.0436737	+	0.0756450i	0.887036	−	0.461700i	$-0.152760\pi$
$79$	2422.63	+	4196.12i	0.0436737	+	0.0756450i	−0.843362	+	0.537345i	$0.819427\pi$
$80$	22747.1	−	39399.2i	0.397376	−	0.688275i
$81$		0			0
$82$	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
$87$		0			0
$88$	−96443.9	+	167046.i	−1.32760	+	2.29947i
$89$	−31248.7	−	54124.4i	−0.418174	−	0.724299i	0.577582	−	0.816333i	$-0.303996\pi$
$89$	−31248.7	−	54124.4i	−0.418174	−	0.724299i	−0.995756	+	0.0920340i	$0.970663\pi$
$90$		0			0
$91$	−31276.2	−	128389.i	−0.395923	−	1.62527i
$92$	−298349.			−3.67498
$93$		0			0
$94$	15957.4	−	27639.0i	0.186269	−	0.322628i
$95$	−16479.4	+	28543.2i	−0.187341	+	0.324485i
$96$		0			0
$97$	−63653.8			−0.686903			−0.343451	−	0.939170i	$-0.611596\pi$
$97$	−63653.8			−0.686903			−0.343451	+	0.939170i	$0.611596\pi$
$98$	−144731.	−	92624.4i	−1.52229	−	0.974227i
$99$		0			0
$100$	92863.9	+	160845.i	0.928639	+	1.60845i
$101$	92311.4	−	159888.i	0.900434	−	1.55960i	0.0735022	−	0.997295i	$-0.476582\pi$
$101$	92311.4	−	159888.i	0.900434	−	1.55960i	0.826932	−	0.562302i	$-0.190084\pi$
$102$		0			0
$103$	−26021.9	−	45071.2i	−0.241683	−	0.418607i	0.719511	−	0.694481i	$-0.244366\pi$
$103$	−26021.9	−	45071.2i	−0.241683	−	0.418607i	−0.961194	+	0.275874i	$0.911033\pi$
$104$	422341.			3.82895
$105$		0			0
$106$	11665.4			0.100840
$107$	24088.9	+	41723.2i	0.203403	+	0.352304i	0.949623	−	0.313395i	$-0.101466\pi$
$107$	24088.9	+	41723.2i	0.203403	+	0.352304i	−0.746220	+	0.665700i	$0.768133\pi$
$108$		0			0
$109$	18217.8	−	31554.1i	0.146869	−	0.254384i	−0.783200	−	0.621770i	$-0.786414\pi$
$109$	18217.8	−	31554.1i	0.146869	−	0.254384i	0.930069	+	0.367386i	$0.119747\pi$
$110$	56525.4	+	97904.9i	0.445412	+	0.771476i
$111$		0			0
$112$	179544.	−	171521.i	1.35247	−	1.29203i
$113$	96711.1			0.712492			0.356246	−	0.934392i	$-0.384056\pi$
$113$	96711.1			0.712492			0.356246	+	0.934392i	$0.384056\pi$
$114$		0			0
$115$	−48855.0	+	84619.4i	−0.344480	+	0.596658i
$116$	−86357.1	+	149575.i	−0.595872	+	1.03208i
$117$		0			0
$118$	281126.			1.85864
$119$	69896.6	+	20451.3i	0.452469	+	0.132390i
$120$		0			0
$121$	−27831.7	−	48206.0i	−0.172813	−	0.299321i
$122$	−107880.	+	186853.i	−0.656206	+	1.13658i
$123$		0			0
$124$	−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
$129$		0			0
$130$	123766.	−	214369.i	0.642308	−	1.11251i
$131$	−169379.	−	293373.i	−0.862345	−	1.49363i	−0.869659	−	0.493653i	$-0.835661\pi$
$131$	−169379.	−	293373.i	−0.862345	−	1.49363i	0.00731374	−	0.999973i	$-0.497672\pi$
$132$		0			0
$133$	−130073.	+	124261.i	−0.637614	+	0.609123i
$134$	568328.			2.73424
$135$		0			0
$136$	−116380.	+	201576.i	−0.539550	+	0.934528i
$137$	−31438.4	+	54452.9i	−0.143106	+	0.247867i	−0.928665	−	0.370920i	$-0.879042\pi$
$137$	−31438.4	+	54452.9i	−0.143106	+	0.247867i	0.785559	+	0.618787i	$0.212376\pi$
$138$		0			0
$139$	211927.			0.930356			0.465178	−	0.885217i	$-0.345990\pi$
$139$	211927.			0.930356			0.465178	+	0.885217i	$0.345990\pi$
$140$	−52860.2	−	216991.i	−0.227934	−	0.935669i
$141$		0			0
$142$	31064.7	+	53805.6i	0.129284	+	0.223927i
$143$	−237255.	+	410938.i	−0.970233	+	1.68049i
$144$		0			0
$145$	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	$-0.0833369\pi$
$149$	70136.4	+	121480.i	0.258808	+	0.448269i	−0.707115	+	0.707099i	$0.750004\pi$
$150$		0			0
$151$	81995.7	−	142021.i	0.292650	−	0.506885i	−0.681785	−	0.731552i	$-0.738796\pi$
$151$	81995.7	−	142021.i	0.292650	−	0.506885i	0.974436	+	0.224667i	$0.0721296\pi$
$152$	−287467.	−	497908.i	−1.00920	−	1.74799i
$153$		0			0
$154$	146040.	+	599495.i	0.496214	+	2.03696i
$155$	−70086.4			−0.234317
$156$		0			0
$157$	−278272.	+	481981.i	−0.900990	+	1.56056i	−0.0747781	+	0.997200i	$0.523825\pi$
$157$	−278272.	+	481981.i	−0.900990	+	1.56056i	−0.826212	+	0.563360i	$0.809508\pi$
$158$	−24768.6	+	42900.5i	−0.0789331	+	0.136716i
$159$		0			0
$160$	150188.			0.463804
$161$	−385615.	+	368384.i	−1.17244	+	1.12005i
$162$		0			0
$163$	9863.32	+	17083.8i	0.0290773	+	0.0503634i	0.880198	−	0.474607i	$-0.157410\pi$
$163$	9863.32	+	17083.8i	0.0290773	+	0.0503634i	−0.851121	+	0.524970i	$0.824076\pi$
$164$	−162357.	+	281210.i	−0.471368	+	0.816434i
$165$		0			0
$166$	−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
$171$		0			0
$172$	−187899.	+	325451.i	−0.484288	+	0.838812i
$173$	169420.	+	293445.i	0.430379	+	0.745437i	0.996906	−	0.0786055i	$-0.0250468\pi$
$173$	169420.	+	293445.i	0.430379	+	0.745437i	−0.566527	+	0.824043i	$0.691713\pi$
$174$		0			0
$175$	318628.	+	93228.6i	0.786483	+	0.230120i
$176$	−891631.			−2.16972
$177$		0			0
$178$	319482.	−	553360.i	0.755782	−	1.30905i
$179$	388096.	−	672203.i	0.905330	−	1.56808i	0.0848573	−	0.996393i	$-0.472957\pi$
$179$	388096.	−	672203.i	0.905330	−	1.56808i	0.820473	−	0.571685i	$-0.193710\pi$
$180$		0			0
$181$	−132697.			−0.301067			−0.150534	−	0.988605i	$-0.548099\pi$
$181$	−132697.			−0.301067			−0.150534	+	0.988605i	$0.548099\pi$
$182$	976892.	−	933240.i	2.18609	−	2.08841i
$183$		0			0
$184$	−852226.	−	1.47610e6i	−1.85571	−	3.21418i
$185$	−117683.	+	203833.i	−0.252804	+	0.437869i
$186$		0			0
$187$	−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	$-0.164571\pi$
$191$	3318.71	+	5748.17i	0.00658242	+	0.0114011i	−0.862715	+	0.505690i	$0.831238\pi$
$192$		0			0
$193$	−226295.	+	391954.i	−0.437302	+	0.757430i	−0.997480	−	0.0709425i	$-0.977399\pi$
$193$	−226295.	+	391954.i	−0.437302	+	0.757430i	0.560178	+	0.828372i	$0.310733\pi$
$194$	−325394.	−	563598.i	−0.620733	−	1.07514i
$195$		0			0
$196$	55684.1	−	1.21769e6i	0.103536	−	2.26411i
$197$	−816952.			−1.49979			−0.749896	−	0.661556i	$-0.769896\pi$
$197$	−816952.			−1.49979			−0.749896	+	0.661556i	$0.769896\pi$
$198$		0			0
$199$	−403208.	+	698378.i	−0.721767	+	1.25014i	0.238524	+	0.971137i	$0.423336\pi$
$199$	−403208.	+	698378.i	−0.721767	+	1.25014i	−0.960291	+	0.279000i	$0.909997\pi$
$200$	−530526.	+	918899.i	−0.937847	+	1.62440i
$201$		0			0
$202$	1.88756e6			3.25478
$203$	73070.2	+	299954.i	0.124451	+	0.510874i
$204$		0			0
$205$	53172.2	+	92096.9i	0.0883690	+	0.153060i
$206$	266044.	−	460801.i	0.436802	−	0.756564i
$207$		0			0
$208$	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
$213$		0			0
$214$	−246281.	+	426572.i	−0.367618	+	0.636734i
$215$	61537.4	+	106586.i	0.0907911	+	0.157255i
$216$		0			0
$217$	−367136.	−	107421.i	−0.529270	−	0.154861i
$218$	372512.			0.530883
$219$		0			0
$220$	−400987.	+	694529.i	−0.558564	+	0.967461i
$221$	−286299.	+	495885.i	−0.394312	+	0.682968i
$222$		0			0
$223$	−620227.			−0.835196			−0.417598	−	0.908632i	$-0.637128\pi$
$223$	−620227.			−0.835196			−0.417598	+	0.908632i	$0.637128\pi$
$224$	786734.	+	230193.i	1.04763	+	0.306530i
$225$		0			0
$226$	494380.	+	856291.i	0.643857	+	1.11519i
$227$	501116.	−	867959.i	0.645467	−	1.11798i	−0.338727	−	0.940885i	$-0.609996\pi$
$227$	501116.	−	867959.i	0.645467	−	1.11798i	0.984193	−	0.177096i	$-0.0566705\pi$
$228$		0			0
$229$	−442931.	−	767178.i	−0.558145	−	0.966735i	−0.997651	−	0.0684960i	$-0.978180\pi$
$229$	−442931.	−	767178.i	−0.558145	−	0.966735i	0.439506	−	0.898239i	$-0.355153\pi$
$230$	−998973.			−1.24519
$231$		0			0
$232$	−986707.			−1.20356
$233$	298082.	+	516293.i	0.359704	+	0.623026i	0.987911	−	0.155020i	$-0.0495443\pi$
$233$	298082.	+	516293.i	0.359704	+	0.623026i	−0.628207	+	0.778046i	$0.716211\pi$
$234$		0			0
$235$	37073.3	−	64212.9i	0.0437917	−	0.0758495i
$236$	997143.	+	1.72710e6i	1.16541	+	2.01854i
$237$		0			0
$238$	176228.	+	723419.i	0.201666	+	0.827842i
$239$	−743111.			−0.841509			−0.420754	−	0.907175i	$-0.638235\pi$
$239$	−743111.			−0.841509			−0.420754	+	0.907175i	$0.638235\pi$
$240$		0			0
$241$	587419.	−	1.01744e6i	0.651487	−	1.12841i	−0.331276	−	0.943534i	$-0.607479\pi$
$241$	587419.	−	1.01744e6i	0.651487	−	1.12841i	0.982762	−	0.184874i	$-0.0591877\pi$
$242$	284548.	−	492851.i	0.312332	−	0.540975i
$243$		0			0
$244$	−1.53058e6			−1.64582
$245$	−336250.	−	215192.i	−0.357888	−	0.229040i
$246$		0			0
$247$	−707179.	−	1.22487e6i	−0.737542	−	1.27746i
$248$	611293.	−	1.05879e6i	0.631132	−	1.09315i
$249$		0			0
$250$	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
$255$		0			0
$256$	912666.	−	1.58078e6i	0.870386	−	1.50755i
$257$	5006.34	+	8671.23i	0.00472811	+	0.00818932i	0.868380	−	0.495900i	$-0.165162\pi$
$257$	5006.34	+	8671.23i	0.00472811	+	0.00818932i	−0.863652	+	0.504089i	$0.831828\pi$
$258$		0			0
$259$	−928875.	+	887369.i	−0.860415	+	0.821968i
$260$	1.75597e6			1.61096
$261$		0			0
$262$	1.73171e6	−	2.99940e6i	1.55855	−	2.69949i
$263$	840900.	−	1.45648e6i	0.749644	−	1.29842i	−0.198349	−	0.980131i	$-0.563558\pi$
$263$	840900.	−	1.45648e6i	0.749644	−	1.29842i	0.947993	−	0.318290i	$-0.103109\pi$
$264$		0			0
$265$	27101.9			0.0237075
$266$	−1.76514e6	−	516469.i	−1.52959	−	0.447549i
$267$		0			0
$268$	2.01584e6	+	3.49153e6i	1.71442	+	2.96947i
$269$	−958587.	+	1.66032e6i	−0.807702	+	1.39898i	0.106750	+	0.994286i	$0.465955\pi$
$269$	−958587.	+	1.66032e6i	−0.807702	+	1.39898i	−0.914452	+	0.404694i	$0.867378\pi$
$270$		0			0
$271$	−1.14500e6	−	1.98320e6i	−0.947069	−	1.64037i	−0.751554	−	0.659672i	$-0.770695\pi$
$271$	−1.14500e6	−	1.98320e6i	−0.947069	−	1.64037i	−0.195515	−	0.980701i	$-0.562638\pi$
$272$	−1.07594e6			−0.881795
$273$		0			0
$274$	−642843.			−0.517283
$275$	−596060.	−	1.03241e6i	−0.475290	−	0.823226i
$276$		0			0
$277$	197401.	−	341908.i	0.154579	−	0.267738i	−0.778327	−	0.627859i	$-0.783931\pi$
$277$	197401.	−	341908.i	0.154579	−	0.267738i	0.932906	+	0.360121i	$0.117265\pi$
$278$	1.08335e6	+	1.87642e6i	0.840734	+	1.45619i
$279$		0			0
$280$	922584.	−	881359.i	0.703251	−	0.671827i
$281$	1.77699e6			1.34252			0.671259	−	0.741223i	$-0.265754\pi$
$281$	1.77699e6			1.34252			0.671259	+	0.741223i	$0.265754\pi$
$282$		0			0
$283$	−607622.	+	1.05243e6i	−0.450991	+	0.781139i	−0.998448	−	0.0556949i	$-0.982263\pi$
$283$	−607622.	+	1.05243e6i	−0.450991	+	0.781139i	0.547457	+	0.836834i	$0.315596\pi$
$284$	−220370.	+	381693.i	−0.162128	+	0.280813i
$285$		0			0
$286$	−4.85133e6			−3.50708
$287$	137376.	+	563931.i	0.0984481	+	0.404130i
$288$		0			0
$289$	552143.	+	956340.i	0.388872	+	0.673547i
$290$	−289153.	+	500827.i	−0.201898	+	0.349698i
$291$		0			0
$292$	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
$297$		0			0
$298$	−717065.	+	1.24199e6i	−0.467754	+	0.810174i
$299$	−2.09651e6	−	3.63125e6i	−1.35618	−	2.34898i
$300$		0			0
$301$	158989.	+	652651.i	0.101146	+	0.415207i
$302$	1.67662e6			1.05784
$303$		0			0
$304$	1.32883e6	−	2.30160e6i	0.824679	−	1.42839i
$305$	−250634.	+	434111.i	−0.154273	+	0.267209i
$306$		0			0
$307$	2.03109e6			1.22994			0.614968	−	0.788552i	$-0.289169\pi$
$307$	2.03109e6			1.22994			0.614968	+	0.788552i	$0.289169\pi$
$308$	−3.16501e6	+	3.02358e6i	−1.90107	+	1.81612i
$309$		0			0
$310$	−358276.	−	620553.i	−0.211745	−	0.366754i
$311$	144892.	−	250961.i	0.0849463	−	0.147131i	−0.820422	−	0.571758i	$-0.806261\pi$
$311$	144892.	−	250961.i	0.0849463	−	0.147131i	0.905368	+	0.424627i	$0.139595\pi$
$312$		0			0
$313$	−109105.	−	188976.i	−0.0629484	−	0.109030i	0.832834	−	0.553523i	$-0.186717\pi$
$313$	−109105.	−	188976.i	−0.0629484	−	0.109030i	−0.895782	+	0.444493i	$0.853384\pi$
$314$	−5.69002e6			−3.25679
$315$		0			0
$316$	−351413.			−0.197970
$317$	645315.	+	1.11772e6i	0.360681	+	0.624718i	0.988073	−	0.153985i	$-0.0492109\pi$
$317$	645315.	+	1.11772e6i	0.360681	+	0.624718i	−0.627392	+	0.778704i	$0.715878\pi$
$318$		0			0
$319$	554296.	−	960068.i	0.304975	−	0.528233i
$320$	39841.4	+	69007.3i	0.0217500	+	0.0376721i
$321$		0			0
$322$	−5.23295e6	−	1.53113e6i	−2.81259	−	0.822947i
$323$	779481.			0.415719
$324$		0			0
$325$	−1.30511e6	+	2.26052e6i	−0.685393	+	1.18714i
$326$	−100841.	+	174662.i	−0.0525526	+	0.0910237i
$327$		0			0
$328$	−1.85507e6			−0.952084
$329$	292621.	−	279546.i	0.149045	−	0.142385i
$330$		0			0
$331$	1.74280e6	+	3.01862e6i	0.874336	+	1.51439i	0.857469	+	0.514536i	$0.172036\pi$
$331$	1.74280e6	+	3.01862e6i	0.874336	+	1.51439i	0.0168673	+	0.999858i	$0.494631\pi$
$332$	2.18109e6	−	3.77776e6i	1.08600	−	1.88100i
$333$		0			0
$334$	−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
$339$		0			0
$340$	−483876.	+	838098.i	−0.227006	+	0.393186i
$341$	686803.	+	1.18958e6i	0.319850	+	0.553997i
$342$		0			0
$343$	−1.43156e6	−	1.64262e6i	−0.657015	−	0.753878i
$344$	−2.14692e6			−0.978180
$345$		0			0
$346$	−1.73213e6	+	3.00014e6i	−0.777840	+	1.34726i
$347$	−753007.	+	1.30425e6i	−0.335719	+	0.581482i	−0.983623	−	0.180240i	$-0.942312\pi$
$347$	−753007.	+	1.30425e6i	−0.335719	+	0.581482i	0.647904	+	0.761722i	$0.275646\pi$
$348$		0			0
$349$	1.54370e6			0.678423			0.339212	−	0.940710i	$-0.389840\pi$
$349$	1.54370e6			0.678423			0.339212	+	0.940710i	$0.389840\pi$
$350$	803348.	+	3.29775e6i	0.350537	+	1.43896i
$351$		0			0
$352$	−1.47175e6	−	2.54914e6i	−0.633107	−	1.09657i
$353$	−838978.	+	1.45315e6i	−0.358355	+	0.620689i	−0.987686	−	0.156448i	$-0.949996\pi$
$353$	−838978.	+	1.45315e6i	−0.358355	+	0.620689i	0.629331	+	0.777137i	$0.283329\pi$
$354$		0			0
$355$	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	−0.999906	−	0.0137165i	$-0.995634\pi$
$359$	−1.24987e6	−	2.16483e6i	−0.511832	−	0.886519i	0.488074	−	0.872802i	$-0.337700\pi$
$360$		0			0
$361$	275363.	−	476943.i	0.111208	−	0.192619i
$362$	−678335.	−	1.17491e6i	−0.272065	−	0.471231i
$363$		0			0
$364$	9.19836e6	+	2.69138e6i	3.63879	+	1.06469i
$365$	398564.			0.156591
$366$		0			0
$367$	1.05371e6	−	1.82507e6i	0.408370	−	0.707318i	−0.586337	−	0.810067i	$-0.699431\pi$
$367$	1.05371e6	−	1.82507e6i	0.408370	−	0.707318i	0.994707	+	0.102749i	$0.0327639\pi$
$368$	3.93945e6	−	6.82332e6i	1.51641	−	2.62649i
$369$		0			0
$370$	−2.40634e6			−0.913804
$371$	141969.	+	41539.1i	0.0535498	+	0.0156683i
$372$		0			0
$373$	−1.36612e6	−	2.36619e6i	−0.508414	−	0.880599i	−0.999953	−	0.00974333i	$-0.996899\pi$
$373$	−1.36612e6	−	2.36619e6i	−0.508414	−	0.880599i	0.491538	−	0.870856i	$-0.336435\pi$
$374$	1.33683e6	−	2.31546e6i	0.494194	−	0.855970i
$375$		0			0
$376$	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
$381$		0			0
$382$	−33930.0	+	58768.4i	−0.0118967	+	0.0206056i
$383$	754497.	+	1.30683e6i	0.262821	+	0.455220i	0.966991	−	0.254812i	$-0.0820137\pi$
$383$	754497.	+	1.30683e6i	0.262821	+	0.455220i	−0.704169	+	0.710032i	$0.748680\pi$
$384$		0			0
$385$	339290.	+	1.39279e6i	0.116659	+	0.478888i
$386$	−4.62721e6			−1.58071
$387$		0			0
$388$	2.30832e6	−	3.99812e6i	0.778423	−	1.34827i
$389$	2.25033e6	−	3.89768e6i	0.754000	−	1.30597i	−0.191870	−	0.981420i	$-0.561455\pi$
$389$	2.25033e6	−	3.89768e6i	0.754000	−	1.30597i	0.945870	−	0.324546i	$-0.105212\pi$
$390$		0			0
$391$	2.31085e6			0.764417
$392$	6.18366e6	−	3.20280e6i	2.03250	−	1.05273i
$393$		0			0
$394$	−4.17620e6	−	7.23339e6i	−1.35532	−	2.34748i
$395$	−57544.3	+	99669.7i	−0.0185571	+	0.0321418i
$396$		0			0
$397$	1.76068e6	+	3.04958e6i	0.560665	+	0.971101i	0.997439	+	0.0715292i	$0.0227879\pi$
$397$	1.76068e6	+	3.04958e6i	0.560665	+	0.971101i	−0.436773	+	0.899572i	$0.643879\pi$
$398$	−8.24469e6			−2.60895
$399$		0			0
$400$	−4.90476e6			−1.53274
$401$	−453554.	−	785578.i	−0.140853	−	0.243965i	0.786965	−	0.616998i	$-0.211651\pi$
$401$	−453554.	−	785578.i	−0.140853	−	0.243965i	−0.927818	+	0.373033i	$0.878318\pi$
$402$		0			0
$403$	1.50380e6	−	2.60466e6i	0.461241	−	0.798893i
$404$	6.69508e6	+	1.15962e7i	2.04081	+	3.53479i
$405$		0			0
$406$	−2.28230e6	+	2.18031e6i	−0.687158	+	0.656453i
$407$	4.61287e6			1.38034
$408$		0			0
$409$	−2.15927e6	+	3.73996e6i	−0.638260	+	1.10550i	0.347554	+	0.937660i	$0.387012\pi$
$409$	−2.15927e6	+	3.73996e6i	−0.638260	+	1.10550i	−0.985814	+	0.167839i	$0.946321\pi$
$410$	−543624.	+	941585.i	−0.159713	+	0.276630i
$411$		0			0
$412$	3.77458e6			1.09553
$413$	3.42133e6	+	1.00106e6i	0.987006	+	0.288791i
$414$		0			0
$415$	−714311.	−	1.23722e6i	−0.203595	−	0.352637i
$416$	−3.22249e6	+	5.58152e6i	−0.912974	+	1.58132i
$417$		0			0
$418$	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
$423$		0			0
$424$	−236383.	+	409427.i	−0.0638559	+	0.110602i
$425$	−719274.	−	1.24582e6i	−0.193162	−	0.334567i
$426$		0			0
$427$	−1.97827e6	+	1.88987e6i	−0.525068	+	0.501605i
$428$	−3.49420e6			−0.922016
$429$		0			0
$430$	−629150.	+	1.08972e6i	−0.164090	+	0.284213i
$431$	−3.42393e6	+	5.93041e6i	−0.887833	+	1.53777i	−0.0454009	+	0.998969i	$0.514457\pi$
$431$	−3.42393e6	+	5.93041e6i	−0.887833	+	1.53777i	−0.842432	+	0.538803i	$0.818877\pi$
$432$		0			0
$433$	−3.99328e6			−1.02355			−0.511777	−	0.859119i	$-0.671012\pi$
$433$	−3.99328e6			−1.02355			−0.511777	+	0.859119i	$0.671012\pi$
$434$	−925648.	−	3.79979e6i	−0.235896	−	0.968357i
$435$		0			0
$436$	1.32128e6	+	2.28853e6i	0.332874	+	0.576555i
$437$	−2.85398e6	+	4.94324e6i	−0.714904	+	1.23825i
$438$		0			0
$439$	−742783.	−	1.28654e6i	−0.183950	−	0.318611i	0.759272	−	0.650773i	$-0.225555\pi$
$439$	−742783.	−	1.28654e6i	−0.183950	−	0.318611i	−0.943222	+	0.332162i	$0.892222\pi$
$440$	−4.58163e6			−1.12821
$441$		0			0
$442$	−5.85416e6			−1.42531
$443$	−2.81097e6	−	4.86874e6i	−0.680528	−	1.17871i	−0.974820	−	0.222994i	$-0.928417\pi$
$443$	−2.81097e6	−	4.86874e6i	−0.680528	−	1.17871i	0.294291	−	0.955716i	$-0.404916\pi$
$444$		0			0
$445$	742245.	−	1.28561e6i	0.177684	−	0.307757i
$446$	−3.17055e6	−	5.49156e6i	−0.754741	−	1.30725i
$447$		0			0
$448$	102935.	+	422548.i	0.0242308	+	0.0994675i
$449$	−1.94883e6			−0.456202			−0.228101	−	0.973637i	$-0.573252\pi$
$449$	−1.94883e6			−0.456202			−0.228101	+	0.973637i	$0.573252\pi$
$450$		0			0
$451$	1.04211e6	−	1.80499e6i	0.241253	−	0.417862i
$452$	−3.50709e6	+	6.07446e6i	−0.807422	+	1.39850i
$453$		0			0
$454$	1.02467e7			2.33315
$455$	2.26959e6	−	2.16817e6i	0.513947	−	0.490982i
$456$		0			0
$457$	1.33656e6	+	2.31499e6i	0.299363	+	0.518511i	0.975990	−	0.217814i	$-0.0698926\pi$
$457$	1.33656e6	+	2.31499e6i	0.299363	+	0.518511i	−0.676628	+	0.736325i	$0.736559\pi$
$458$	4.52846e6	−	7.84352e6i	1.00876	−	1.74722i
$459$		0			0
$460$	−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
$465$		0			0
$466$	−3.04754e6	+	5.27850e6i	−0.650107	+	1.12602i
$467$	−2.52990e6	−	4.38192e6i	−0.536799	−	0.929763i	−0.999074	−	0.0430263i	$-0.986300\pi$
$467$	−2.52990e6	−	4.38192e6i	−0.536799	−	0.929763i	0.462275	−	0.886737i	$-0.347033\pi$
$468$		0			0
$469$	6.91660e6	+	2.02375e6i	1.45198	+	0.424840i
$470$	758064.			0.158293
$471$		0			0
$472$	−5.69662e6	+	9.86684e6i	−1.17696	+	2.03856i
$473$	1.20606e6	−	2.08895e6i	0.247865	−	0.429315i
$474$		0			0
$475$	3.55331e6			0.722603
$476$	−3.81926e6	+	3.64860e6i	−0.772612	+	0.738088i
$477$		0			0
$478$	−3.79873e6	−	6.57959e6i	−0.760446	−	1.31713i
$479$	−2.77543e6	+	4.80718e6i	−0.552702	+	0.957308i	0.445377	+	0.895343i	$0.353070\pi$
$479$	−2.77543e6	+	4.80718e6i	−0.552702	+	0.957308i	−0.998078	+	0.0619642i	$0.980264\pi$
$480$		0			0
$481$	−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
$486$		0			0
$487$	3.43905e6	−	5.95661e6i	0.657077	−	1.13809i	−0.324292	−	0.945957i	$-0.605126\pi$
$487$	3.43905e6	−	5.95661e6i	0.657077	−	1.13809i	0.981369	−	0.192133i	$-0.0615405\pi$
$488$	−4.37206e6	−	7.57262e6i	−0.831067	−	1.43945i
$489$		0			0
$490$	186449.	−	4.07724e6i	0.0350809	−	0.767143i
$491$	−7.44459e6			−1.39360			−0.696798	−	0.717267i	$-0.745393\pi$
$491$	−7.44459e6			−1.39360			−0.696798	+	0.717267i	$0.745393\pi$
$492$		0			0
$493$	668876.	−	1.15853e6i	0.123945	−	0.214679i
$494$	7.23009e6	−	1.25229e7i	1.33299	−	2.30880i
$495$		0			0
$496$	5.65145e6			1.03147
$497$	186464.	+	765436.i	0.0338613	+	0.139001i
$498$		0			0
$499$	−1.07665e6	−	1.86481e6i	−0.193563	−	0.335261i	0.752866	−	0.658174i	$-0.228671\pi$
$499$	−1.07665e6	−	1.86481e6i	−0.193563	−	0.335261i	−0.946428	+	0.322914i	$0.895338\pi$
$500$	−4.89754e6	+	8.48278e6i	−0.876098	+	1.51745i
$501$		0			0
$502$	−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
$507$		0			0
$508$	−845771.	+	1.46492e6i	−0.145410	+	0.251857i
$509$	1.67100e6	+	2.89426e6i	0.285879	+	0.495157i	0.972822	−	0.231554i	$-0.0743810\pi$
$509$	1.67100e6	+	2.89426e6i	0.285879	+	0.495157i	−0.686943	+	0.726712i	$0.741048\pi$
$510$		0			0
$511$	2.08781e6	+	610879.i	0.353703	+	0.103491i
$512$	1.32848e7			2.23964
$513$		0			0
$514$	−51184.1	+	88653.4i	−0.00854529	+	0.0148009i
$515$	618093.	−	1.07057e6i	0.102692	−	0.177867i
$516$		0			0
$517$	−1.45318e6			−0.239108
$518$	−1.26052e7	−	3.68820e6i	−2.06408	−	0.603936i
$519$		0			0
$520$	5.01589e6	+	8.68777e6i	0.813466	+	1.40896i
$521$	−1.34152e6	+	2.32359e6i	−0.216523	+	0.375029i	−0.953743	−	0.300624i	$-0.902805\pi$
$521$	−1.34152e6	+	2.32359e6i	−0.216523	+	0.375029i	0.737220	+	0.675653i	$0.236138\pi$
$522$		0			0
$523$	2.71178e6	+	4.69694e6i	0.433511	+	0.750863i	0.997173	−	0.0751429i	$-0.0239413\pi$
$523$	2.71178e6	+	4.69694e6i	0.433511	+	0.750863i	−0.563662	+	0.826005i	$0.690608\pi$
$524$	2.45692e7			3.90897
$525$		0			0
$526$	1.71945e7			2.70972
$527$	828775.	+	1.43548e6i	0.129990	+	0.225149i
$528$		0			0
$529$	−5.24276e6	+	9.08072e6i	−0.814555	+	1.41085i
$530$	138543.	+	239963.i	0.0214237	+	0.0371070i
$531$		0			0
$532$	−3.08795e6	−	1.26761e7i	−0.473033	−	1.94181i
$533$	−4.56353e6			−0.695798
$534$		0			0
$535$	−572179.	+	991044.i	−0.0864266	+	0.149695i
$536$	−1.15164e7	+	1.99469e7i	−1.73142	+	2.99891i
$537$		0			0
$538$	−1.96009e7			−2.91958
$539$	−357417.	+	7.81593e6i	−0.0529911	+	1.15880i
$540$		0			0
$541$	−1.09228e6	−	1.89188e6i	−0.160450	−	0.277908i	0.774580	−	0.632476i	$-0.217961\pi$
$541$	−1.09228e6	−	1.89188e6i	−0.160450	−	0.277908i	−0.935030	+	0.354568i	$0.884628\pi$
$542$	1.17063e7	−	2.02759e7i	1.71168	−	2.96471i
$543$		0			0
$544$	−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
$549$		0			0
$550$	6.09403e6	−	1.05552e7i	0.859010	−	1.48785i
$551$	1.65217e6	+	2.86164e6i	0.231833	+	0.401547i
$552$		0			0
$553$	−454200.	+	433904.i	−0.0631589	+	0.0603367i
$554$	4.03639e6			0.558752
$555$		0			0
$556$	−7.68523e6	+	1.33112e7i	−1.05431	+	1.82612i
$557$	2.73828e6	−	4.74284e6i	0.373973	−	0.647740i	−0.616200	−	0.787590i	$-0.711329\pi$
$557$	2.73828e6	−	4.74284e6i	0.373973	−	0.647740i	0.990173	+	0.139850i	$0.0446620\pi$
$558$		0			0
$559$	−5.28149e6			−0.714869
$560$	5.66063e6	+	1.65626e6i	0.762771	+	0.223182i
$561$		0			0
$562$	9.08386e6	+	1.57337e7i	1.21319	+	2.10131i
$563$	199488.	−	345523.i	0.0265244	−	0.0459416i	−0.852459	−	0.522795i	$-0.824889\pi$
$563$	199488.	−	345523.i	0.0265244	−	0.0459416i	0.878983	+	0.476853i	$0.158223\pi$
$564$		0			0
$565$	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	$-0.254992\pi$
$569$	−2.11556e6	−	3.66426e6i	−0.273934	−	0.474467i	−0.969866	+	0.243641i	$0.921658\pi$
$570$		0			0
$571$	−4.37551e6	+	7.57861e6i	−0.561615	+	0.972746i	0.435741	+	0.900072i	$0.356486\pi$
$571$	−4.37551e6	+	7.57861e6i	−0.561615	+	0.972746i	−0.997356	+	0.0726734i	$0.976847\pi$
$572$	−1.72075e7	−	2.98042e7i	−2.19901	−	3.80879i
$573$		0			0
$574$	−4.29085e6	+	4.09912e6i	−0.543581	+	0.519291i
$575$	1.05342e7			1.32871
$576$		0			0
$577$	883558.	−	1.53037e6i	0.110483	−	0.191362i	−0.805482	−	0.592620i	$-0.798094\pi$
$577$	883558.	−	1.53037e6i	0.110483	−	0.191362i	0.915965	+	0.401258i	$0.131427\pi$
$578$	−5.64503e6	+	9.77748e6i	−0.702824	+	1.21733i
$579$		0			0
$580$	−4.10245e6			−0.506376
$581$	−1.84550e6	−	7.57581e6i	−0.226817	−	0.931084i
$582$		0			0
$583$	−265582.	−	460001.i	−0.0323614	−	0.0560516i
$584$	−3.47627e6	+	6.02107e6i	−0.421775	+	0.730536i
$585$		0			0
$586$	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
$591$		0			0
$592$	9.48941e6	−	1.64361e7i	1.11285	−	1.92750i
$593$	7.72568e6	+	1.33813e7i	0.902194	+	1.56265i	0.824640	+	0.565659i	$0.191378\pi$
$593$	7.72568e6	+	1.33813e7i	0.902194	+	1.56265i	0.0775549	+	0.996988i	$0.475289\pi$
$594$		0			0
$595$	409427.	+	1.68070e6i	0.0474115	+	0.194625i
$596$	−1.01736e7			−1.17316
$597$		0			0
$598$	2.14344e7	−	3.71254e7i	2.45108	−	4.24540i
$599$	−1.92400e6	+	3.33247e6i	−0.219098	+	0.379489i	−0.954533	−	0.298107i	$-0.903645\pi$
$599$	−1.92400e6	+	3.33247e6i	−0.219098	+	0.379489i	0.735434	+	0.677596i	$0.236978\pi$
$600$		0			0
$601$	1.27578e7			1.44075			0.720376	−	0.693583i	$-0.243969\pi$
$601$	1.27578e7			1.44075			0.720376	+	0.693583i	$0.243969\pi$
$602$	−4.96591e6	+	4.74401e6i	−0.558480	+	0.533524i
$603$		0			0
$604$	5.94691e6	+	1.03004e7i	0.663284	+	1.14884i
$605$	661082.	−	1.14503e6i	0.0734289	−	0.127183i
$606$		0			0
$607$	6.81033e6	+	1.17958e7i	0.750233	+	1.29944i	0.947709	+	0.319135i	$0.103392\pi$
$607$	6.81033e6	+	1.17958e7i	0.750233	+	1.29944i	−0.197476	+	0.980308i	$0.563274\pi$
$608$	8.77359e6			0.962539
$609$		0			0
$610$	−5.12489e6			−0.557648
$611$	1.59092e6	+	2.75555e6i	0.172403	+	0.298611i
$612$		0			0
$613$	−7.67372e6	+	1.32913e7i	−0.824812	+	1.42862i	0.0772508	+	0.997012i	$0.475386\pi$
$613$	−7.67372e6	+	1.32913e7i	−0.824812	+	1.42862i	−0.902063	+	0.431605i	$0.857948\pi$
$614$	1.03828e7	+	1.79835e7i	1.11145	+	1.92510i
$615$		0			0
$616$	−2.40001e7	−	7.02227e6i	−2.54836	−	0.745634i
$617$	−1.18485e7			−1.25300			−0.626500	−	0.779421i	$-0.715513\pi$
$617$	−1.18485e7			−1.25300			−0.626500	+	0.779421i	$0.715513\pi$
$618$		0			0
$619$	437230.	−	757304.i	0.0458652	−	0.0794408i	−0.842181	−	0.539194i	$-0.818729\pi$
$619$	437230.	−	757304.i	0.0458652	−	0.0794408i	0.888047	+	0.459753i	$0.152062\pi$
$620$	2.54158e6	−	4.40215e6i	0.265537	−	0.459924i
$621$		0			0
$622$	2.96272e6			0.307054
$623$	5.85858e6	−	5.59679e6i	0.604744	−	0.577722i
$624$		0			0
$625$	−2.39730e6	−	4.15225e6i	−0.245484	−	0.425190i
$626$	1.11548e6	−	1.93206e6i	0.113769	−	0.197054i
$627$		0			0
$628$	−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
$633$		0			0
$634$	−6.59761e6	+	1.14274e7i	−0.651873	+	1.12908i
$635$	276992.	+	479764.i	0.0272605	+	0.0472165i
$636$		0			0
$637$	1.52120e7	−	7.87900e6i	1.48538	−	0.769348i
$638$	1.13341e7			1.10239
$639$		0			0
$640$	1.99567e6	−	3.45661e6i	0.192593	−	0.333580i
$641$	406276.	−	703690.i	0.0390549	−	0.0676451i	−0.845837	−	0.533441i	$-0.820899\pi$
$641$	406276.	−	703690.i	0.0390549	−	0.0676451i	0.884892	+	0.465796i	$0.154232\pi$
$642$		0			0
$643$	−1.17941e7			−1.12496			−0.562481	−	0.826810i	$-0.690153\pi$
$643$	−1.17941e7			−1.12496			−0.562481	+	0.826810i	$0.690153\pi$
$644$	−9.15456e6	−	3.75795e7i	−0.869806	−	3.57056i
$645$		0			0
$646$	3.98465e6	+	6.90162e6i	0.375672	+	0.650683i
$647$	−1.21690e6	+	2.10773e6i	−0.114286	+	0.197950i	−0.917494	−	0.397749i	$-0.869791\pi$
$647$	−1.21690e6	+	2.10773e6i	−0.114286	+	0.197950i	0.803208	+	0.595699i	$0.203125\pi$
$648$		0			0
$649$	−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	$-0.309704\pi$
$653$	−4.73332e6	−	8.19835e6i	−0.434393	−	0.752391i	−0.997246	+	0.0741664i	$0.976370\pi$
$654$		0			0
$655$	4.02323e6	−	6.96843e6i	0.366413	−	0.634647i
$656$	−4.28756e6	−	7.42628e6i	−0.389001	−	0.673770i
$657$		0			0
$658$	3.97099e6	+	1.16189e6i	0.357548	+	0.104616i
$659$	−1.40662e7			−1.26172			−0.630860	−	0.775896i	$-0.717298\pi$
$659$	−1.40662e7			−1.26172			−0.630860	+	0.775896i	$0.717298\pi$
$660$		0			0
$661$	8.58029e6	−	1.48615e7i	0.763832	−	1.32300i	−0.177029	−	0.984206i	$-0.556649\pi$
$661$	8.58029e6	−	1.48615e7i	0.763832	−	1.32300i	0.940862	−	0.338791i	$-0.110018\pi$
$662$	−1.78182e7	+	3.08620e7i	−1.58022	+	2.73702i
$663$		0			0
$664$	2.49209e7			2.19353
$665$	−4.10091e6	−	1.19990e6i	−0.359606	−	0.105218i
$666$		0			0
$667$	4.89803e6	+	8.48364e6i	0.426292	+	0.738359i
$668$	3.43692e6	−	5.95293e6i	0.298009	−	0.516166i
$669$		0			0
$670$	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
$675$		0			0
$676$	−2.42124e7	+	4.19372e7i	−2.03785	+	3.52966i
$677$	6.96368e6	+	1.20614e7i	0.583938	+	1.01141i	0.995007	+	0.0998062i	$0.0318223\pi$
$677$	6.96368e6	+	1.20614e7i	0.583938	+	1.01141i	−0.411069	+	0.911604i	$0.634844\pi$
$678$		0			0
$679$	−1.95316e6	−	8.01773e6i	−0.162578	−	0.667386i
$680$	−5.52872e6			−0.458513
$681$		0			0
$682$	−7.02178e6	+	1.21621e7i	−0.578077	+	1.00126i
$683$	9.15503e6	−	1.58570e7i	0.750945	−	1.30067i	−0.196421	−	0.980520i	$-0.562932\pi$
$683$	9.15503e6	−	1.58570e7i	0.750945	−	1.30067i	0.947365	−	0.320155i	$-0.103735\pi$
$684$		0			0
$685$	−1.49350e6			−0.121613
$686$	7.22587e6	−	2.10722e7i	0.586246	−	1.70962i
$687$		0			0
$688$	−4.96210e6	−	8.59461e6i	−0.399663	−	0.692237i
$689$	−581509.	+	1.00720e6i	−0.0466669	+	0.0808294i
$690$		0			0
$691$	8.83583e6	+	1.53041e7i	0.703967	+	1.21931i	0.967063	+	0.254537i	$0.0819230\pi$
$691$	8.83583e6	+	1.53041e7i	0.703967	+	1.21931i	−0.263096	+	0.964770i	$0.584744\pi$
$692$	−2.45752e7			−1.95088
$693$		0			0
$694$	−1.53973e7			−1.21351
$695$	2.51693e6	+	4.35945e6i	0.197656	+	0.342350i
$696$		0			0
$697$	1.25753e6	−	2.17810e6i	0.0980473	−	0.169823i
$698$	7.89131e6	+	1.36681e7i	0.613070	+	1.06187i
$699$		0			0
$700$	−1.74103e7	+	1.66324e7i	−1.34296	+	1.28295i
$701$	−8.22993e6			−0.632559			−0.316279	−	0.948666i	$-0.602434\pi$
$701$	−8.22993e6			−0.632559			−0.316279	+	0.948666i	$0.602434\pi$
$702$		0			0
$703$	−6.87472e6	+	1.19074e7i	−0.524646	+	0.908714i
$704$	780843.	−	1.35246e6i	0.0593789	−	0.102847i
$705$		0			0
$706$	−1.71552e7			−1.29534
$707$	2.29717e7	+	6.72137e6i	1.72840	+	0.505719i
$708$		0			0
$709$	−1.23183e7	−	2.13360e7i	−0.920314	−	1.59403i	−0.798929	−	0.601426i	$-0.794600\pi$
$709$	−1.23183e7	−	2.13360e7i	−0.920314	−	1.59403i	−0.121386	−	0.992605i	$-0.538734\pi$
$710$	−737874.	+	1.27803e6i	−0.0549334	+	0.0951474i
$711$		0			0
$712$	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
$717$		0			0
$718$	1.27784e7	−	2.21329e7i	0.925053	−	1.60224i
$719$	−9.41269e6	−	1.63033e7i	−0.679034	−	1.17612i	−0.975272	−	0.221007i	$-0.929066\pi$
$719$	−9.41269e6	−	1.63033e7i	−0.679034	−	1.17612i	0.296238	−	0.955114i	$-0.404268\pi$
$720$		0			0
$721$	4.87863e6	−	4.66064e6i	0.349510	−	0.333893i
$722$	5.63055e6			0.401983
$723$		0			0
$724$	4.81205e6	−	8.33472e6i	0.341180	−	0.590942i
$725$	3.04911e6	−	5.28122e6i	0.215441	−	0.373155i
$726$		0			0
$727$	6.77607e6			0.475491			0.237745	−	0.971328i	$-0.423592\pi$
$727$	6.77607e6			0.475491			0.237745	+	0.971328i	$0.423592\pi$
$728$	1.29591e7	+	5.31973e7i	0.906248	+	3.72015i
$729$		0			0
$730$	2.03743e6	+	3.52893e6i	0.141506	+	0.245096i
$731$	1.45537e6	−	2.52077e6i	0.100735	−	0.174478i
$732$		0			0
$733$	8.61136e6	+	1.49153e7i	0.591986	+	1.02535i	0.993965	+	0.109701i	$0.0349894\pi$
$733$	8.61136e6	+	1.49153e7i	0.591986	+	1.02535i	−0.401978	+	0.915649i	$0.631677\pi$
$734$	2.15459e7			1.47613
$735$		0			0
$736$	2.60102e7			1.76990
$737$	−1.29389e7	−	2.24109e7i	−0.877465	−	1.51981i
$738$		0			0
$739$	8.82669e6	−	1.52883e7i	0.594548	−	1.02979i	−0.399062	−	0.916924i	$-0.630664\pi$
$739$	8.82669e6	−	1.52883e7i	0.594548	−	1.02979i	0.993610	−	0.112864i	$-0.0360023\pi$
$740$	−8.53520e6	−	1.47834e7i	−0.572973	−	0.992418i
$741$		0			0
$742$	357941.	+	1.46935e6i	0.0238672	+	0.0979752i
$743$	1.36977e7			0.910281			0.455141	−	0.890420i	$-0.349589\pi$
$743$	1.36977e7			0.910281			0.455141	+	0.890420i	$0.349589\pi$
$744$		0			0
$745$	−1.66594e6	+	2.88549e6i	−0.109968	+	0.190471i
$746$	1.39670e7	−	2.41916e7i	0.918877	−	1.59154i
$747$		0			0
$748$	1.89668e7			1.23948
$749$	−4.51624e6	+	4.31443e6i	−0.294152	+	0.281008i
$750$		0			0
$751$	−5.80446e6	−	1.00536e7i	−0.375545	−	0.650463i	0.614864	−	0.788633i	$-0.289211\pi$
$751$	−5.80446e6	−	1.00536e7i	−0.375545	−	0.650463i	−0.990408	+	0.138171i	$0.955878\pi$
$752$	−2.98943e6	+	5.17784e6i	−0.192772	+	0.333890i
$753$		0			0
$754$	−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
$759$		0			0
$760$	6.82815e6	−	1.18267e7i	0.428814	−	0.742728i
$761$	−1.51063e7	−	2.61648e7i	−0.945574	−	1.63778i	−0.754597	−	0.656188i	$-0.772168\pi$
$761$	−1.51063e7	−	2.61648e7i	−0.945574	−	1.63778i	−0.190977	−	0.981595i	$-0.561166\pi$
$762$		0			0
$763$	4.53350e6	+	1.32647e6i	0.281918	+	0.0824873i
$764$	−481393.			−0.0298378
$765$		0			0
$766$	−7.71386e6	+	1.33608e7i	−0.475007	+	0.822736i
$767$	−1.40139e7	+	2.42728e7i	−0.860142	+	1.48981i
$768$		0			0
$769$	−2.58756e7			−1.57788			−0.788940	−	0.614470i	$-0.789370\pi$
$769$	−2.58756e7			−1.57788			−0.788940	+	0.614470i	$0.789370\pi$
$770$	−1.05975e7	+	1.01240e7i	−0.644135	+	0.615352i
$771$		0			0
$772$	−1.64125e7	−	2.84273e7i	−0.991134	−	1.71669i
$773$	1.27705e7	−	2.21191e7i	0.768701	−	1.33143i	−0.169566	−	0.985519i	$-0.554237\pi$
$773$	1.27705e7	−	2.21191e7i	0.768701	−	1.33143i	0.938267	−	0.345911i	$-0.112430\pi$
$774$		0			0

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.11193 + 8.85412i) q^{2} +(-36.2636 + 62.8104i) q^{4} +(11.8764 + 20.5705i) q^{5} +(30.6840 + 125.958i) q^{7} -414.344 q^{8} +O(q^{10})\)	\(q+(5.11193 + 8.85412i) q^{2} +(-36.2636 + 62.8104i) q^{4} +(11.8764 + 20.5705i) q^{5} +(30.6840 + 125.958i) q^{7} -414.344 q^{8} +(-121.423 + 210.310i) q^{10} +(232.763 - 403.157i) q^{11} -1019.30 q^{13} +(-958.395 + 915.570i) q^{14} +(-957.660 - 1658.72i) q^{16} +(280.878 - 486.496i) q^{17} +(693.789 + 1201.68i) q^{19} -1722.72 q^{20} +4759.47 q^{22} +(2056.81 + 3562.50i) q^{23} +(1280.40 - 2217.72i) q^{25} +(-5210.59 - 9025.00i) q^{26} +(-9024.20 - 2640.42i) q^{28} +2381.37 q^{29} +(-1475.33 + 2555.34i) q^{31} +(3161.47 - 5475.84i) q^{32} +5743.32 q^{34} +(-2226.61 + 2127.12i) q^{35} +(4954.48 + 8581.40i) q^{37} +(-7093.20 + 12285.8i) q^{38} +(-4920.92 - 8523.28i) q^{40} +4477.13 q^{41} +5181.48 q^{43} +(16881.6 + 29239.9i) q^{44} +(-21028.5 + 36422.5i) q^{46} +(-1560.80 - 2703.38i) q^{47} +(-14924.0 + 7729.82i) q^{49} +26181.3 q^{50} +(36963.5 - 64022.6i) q^{52} +(570.499 - 988.133i) q^{53} +11057.6 q^{55} +(-12713.7 - 52190.0i) q^{56} +(12173.4 + 21085.0i) q^{58} +(13748.5 - 23813.2i) q^{59} +(10551.8 + 18276.2i) q^{61} -30167.1 q^{62} +3354.67 q^{64} +(-12105.6 - 20967.6i) q^{65} +(27794.2 - 48141.0i) q^{67} +(20371.3 + 35284.2i) q^{68} +(-30216.0 - 8841.02i) q^{70} +6076.90 q^{71} +(8389.82 - 14531.6i) q^{73} +(-50653.8 + 87735.0i) q^{74} -100637. q^{76} +(57923.1 + 16947.9i) q^{77} +(2422.63 + 4196.12i) q^{79} +(22747.1 - 39399.2i) q^{80} +(22886.7 + 39641.0i) q^{82} -60145.4 q^{83} +13343.3 q^{85} +(26487.4 + 45877.5i) q^{86} +(-96443.9 + 167046. i) q^{88} +(-31248.7 - 54124.4i) q^{89} +(-31276.2 - 128389. i) q^{91} -298349. q^{92} +(15957.4 - 27639.0i) q^{94} +(-16479.4 + 28543.2i) q^{95} -63653.8 q^{97} +(-144731. - 92624.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8}+O(q^{10}) \) 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8	\( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8} - 283 q^{10} + 402 q^{11} + 924 q^{13} - 1926 q^{14} - 3273 q^{16} + 276 q^{17} - 510 q^{19} - 9438 q^{20} + 2750 q^{22} + 6900 q^{23} - 2814 q^{25} - 15138 q^{26} - 26221 q^{28} - 1080 q^{29} + 6410 q^{31} + 15519 q^{32} + 42288 q^{34} + 33108 q^{35} - 15250 q^{37} - 41250 q^{38} + 8547 q^{40} - 8616 q^{41} + 58396 q^{43} + 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 64252 q^{49} + 14604 q^{50} + 47476 q^{52} + 13692 q^{53} + 146248 q^{55} + 15921 q^{56} - 52309 q^{58} + 34830 q^{59} + 5364 q^{61} - 32058 q^{62} - 146974 q^{64} + 66864 q^{65} + 5994 q^{67} - 58272 q^{68} - 4307 q^{70} - 178536 q^{71} - 59638 q^{73} - 185442 q^{74} + 42616 q^{76} + 75660 q^{77} + 44062 q^{79} - 33381 q^{80} - 57596 q^{82} + 416892 q^{83} + 72648 q^{85} - 136968 q^{86} - 87597 q^{88} - 77520 q^{89} + 104722 q^{91} - 316512 q^{92} + 73722 q^{94} - 221376 q^{95} - 377260 q^{97} - 382479 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8 - 283 * q^10 + 402 * q^11 + 924 * q^13 - 1926 * q^14 - 3273 * q^16 + 276 * q^17 - 510 * q^19 - 9438 * q^20 + 2750 * q^22 + 6900 * q^23 - 2814 * q^25 - 15138 * q^26 - 26221 * q^28 - 1080 * q^29 + 6410 * q^31 + 15519 * q^32 + 42288 * q^34 + 33108 * q^35 - 15250 * q^37 - 41250 * q^38 + 8547 * q^40 - 8616 * q^41 + 58396 * q^43 + 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 64252 * q^49 + 14604 * q^50 + 47476 * q^52 + 13692 * q^53 + 146248 * q^55 + 15921 * q^56 - 52309 * q^58 + 34830 * q^59 + 5364 * q^61 - 32058 * q^62 - 146974 * q^64 + 66864 * q^65 + 5994 * q^67 - 58272 * q^68 - 4307 * q^70 - 178536 * q^71 - 59638 * q^73 - 185442 * q^74 + 42616 * q^76 + 75660 * q^77 + 44062 * q^79 - 33381 * q^80 - 57596 * q^82 + 416892 * q^83 + 72648 * q^85 - 136968 * q^86 - 87597 * q^88 - 77520 * q^89 + 104722 * q^91 - 316512 * q^92 + 73722 * q^94 - 221376 * q^95 - 377260 * q^97 - 382479 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more