LMFDB - Embedded newform 63.6.e.e.37.4

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			37.4
Root			$-4.61193 + 7.98809i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.6.e.e.46.4

$q$-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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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	0.0809760	−	0.996716i	$-0.474196\pi$
$2$	5.11193	−	8.85412i	0.903669	−	1.56520i	0.822693	−	0.568485i	$-0.192470\pi$
$3$		0			0
$3$		0			0
$4$	−36.2636	−	62.8104i	−1.13324	−	1.96282i
$5$	11.8764	−	20.5705i	0.212452	−	0.367977i	−0.740030	−	0.672574i	$-0.765189\pi$
$5$	11.8764	−	20.5705i	0.212452	−	0.367977i	0.952481	+	0.304597i	$0.0985219\pi$
$6$		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	0.995478	+	0.0949934i	$0.0302830\pi$
$11$	232.763	+	403.157i	0.580006	+	1.00460i	−0.415472	+	0.909606i	$0.636384\pi$
$12$		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	0.959482	−	0.281771i	$-0.0909219\pi$
$17$	280.878	+	486.496i	0.235720	+	0.408279i	−0.723762	+	0.690050i	$0.757589\pi$
$18$		0			0
$19$	693.789	−	1201.68i	0.440903	−	0.763667i	−0.556853	−	0.830611i	$-0.687991\pi$
$19$	693.789	−	1201.68i	0.440903	−	0.763667i	0.997757	+	0.0669438i	$0.0213248\pi$
$20$	−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	$-0.532406\pi$
$23$	2056.81	−	3562.50i	0.810727	−	1.40422i	0.912356	−	0.409397i	$-0.134261\pi$
$24$		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	0.694589	−	0.719407i	$-0.255586\pi$
$31$	−1475.33	−	2555.34i	−0.275730	−	0.477579i	−0.970319	+	0.241828i	$0.922253\pi$
$32$	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	−0.398584	−	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
$39$		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	−0.912945	−	0.408082i	$-0.866198\pi$
$47$	−1560.80	+	2703.38i	−0.103063	+	0.178510i	0.809882	+	0.586592i	$0.199531\pi$
$48$		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	0.879637	−	0.475645i	$-0.157785\pi$
$53$	570.499	+	988.133i	0.0278975	+	0.0483198i	−0.851740	+	0.523965i	$0.824452\pi$
$54$		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	0.999864	+	0.0164678i	$0.00524209\pi$
$59$	13748.5	+	23813.2i	0.514194	+	0.890610i	−0.485671	+	0.874142i	$0.661425\pi$
$60$		0			0
$61$	10551.8	−	18276.2i	0.363078	−	0.628870i	−0.625387	−	0.780314i	$-0.715059\pi$
$61$	10551.8	−	18276.2i	0.363078	−	0.628870i	0.988466	+	0.151444i	$0.0483924\pi$
$62$	−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	0.944661	+	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
$69$		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	0.943329	−	0.331859i	$-0.107676\pi$
$73$	8389.82	+	14531.6i	0.184266	+	0.319158i	−0.759063	+	0.651017i	$0.774343\pi$
$74$	−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	−0.843362	−	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
$81$		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	−0.995756	−	0.0920340i	$-0.970663\pi$
$89$	−31248.7	+	54124.4i	−0.418174	+	0.724299i	0.577582	+	0.816333i	$0.303996\pi$
$90$		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	0.826932	+	0.562302i	$0.190084\pi$
$101$	92311.4	+	159888.i	0.900434	+	1.55960i	0.0735022	+	0.997295i	$0.476582\pi$
$102$		0			0
$103$	−26021.9	+	45071.2i	−0.241683	+	0.418607i	−0.961194	−	0.275874i	$-0.911033\pi$
$103$	−26021.9	+	45071.2i	−0.241683	+	0.418607i	0.719511	+	0.694481i	$0.244366\pi$
$104$	422341.			3.82895
$105$		0			0
$106$	11665.4			0.100840
$107$	24088.9	−	41723.2i	0.203403	−	0.352304i	−0.746220	−	0.665700i	$-0.768133\pi$
$107$	24088.9	−	41723.2i	0.203403	−	0.352304i	0.949623	+	0.313395i	$0.101466\pi$
$108$		0			0
$109$	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
$111$		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	0.00731374	+	0.999973i	$0.497672\pi$
$131$	−169379.	+	293373.i	−0.862345	+	1.49363i	−0.869659	+	0.493653i	$0.835661\pi$
$132$		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	0.785559	−	0.618787i	$-0.212376\pi$
$137$	−31438.4	−	54452.9i	−0.143106	−	0.247867i	−0.928665	+	0.370920i	$0.879042\pi$
$138$		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	−0.707115	−	0.707099i	$-0.750004\pi$
$149$	70136.4	−	121480.i	0.258808	−	0.448269i	0.965923	+	0.258830i	$0.0833369\pi$
$150$		0			0
$151$	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
$153$		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	−0.826212	−	0.563360i	$-0.809508\pi$
$157$	−278272.	−	481981.i	−0.900990	−	1.56056i	−0.0747781	−	0.997200i	$-0.523825\pi$
$158$	−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	−0.851121	−	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
$165$		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	−0.566527	−	0.824043i	$-0.691713\pi$
$173$	169420.	−	293445.i	0.430379	−	0.745437i	0.996906	+	0.0786055i	$0.0250468\pi$
$174$		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	0.820473	+	0.571685i	$0.193710\pi$
$179$	388096.	+	672203.i	0.905330	+	1.56808i	0.0848573	+	0.996393i	$0.472957\pi$
$180$		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	−0.862715	−	0.505690i	$-0.831238\pi$
$191$	3318.71	−	5748.17i	0.00658242	−	0.0114011i	0.869298	+	0.494289i	$0.164571\pi$
$192$		0			0
$193$	−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
$195$		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	−0.960291	−	0.279000i	$-0.909997\pi$
$199$	−403208.	−	698378.i	−0.721767	−	1.25014i	0.238524	−	0.971137i	$-0.423336\pi$
$200$	−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	0.984193	+	0.177096i	$0.0566705\pi$
$227$	501116.	+	867959.i	0.645467	+	1.11798i	−0.338727	+	0.940885i	$0.609996\pi$
$228$		0			0
$229$	−442931.	+	767178.i	−0.558145	+	0.966735i	0.439506	+	0.898239i	$0.355153\pi$
$229$	−442931.	+	767178.i	−0.558145	+	0.966735i	−0.997651	+	0.0684960i	$0.978180\pi$
$230$	−998973.			−1.24519
$231$		0			0
$232$	−986707.			−1.20356
$233$	298082.	−	516293.i	0.359704	−	0.623026i	−0.628207	−	0.778046i	$-0.716211\pi$
$233$	298082.	−	516293.i	0.359704	−	0.623026i	0.987911	+	0.155020i	$0.0495443\pi$
$234$		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	0.982762	+	0.184874i	$0.0591877\pi$
$241$	587419.	+	1.01744e6i	0.651487	+	1.12841i	−0.331276	+	0.943534i	$0.607479\pi$
$242$	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	−0.863652	−	0.504089i	$-0.831828\pi$
$257$	5006.34	−	8671.23i	0.00472811	−	0.00818932i	0.868380	+	0.495900i	$0.165162\pi$
$258$		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	0.947993	+	0.318290i	$0.103109\pi$
$263$	840900.	+	1.45648e6i	0.749644	+	1.29842i	−0.198349	+	0.980131i	$0.563558\pi$
$264$		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	−0.914452	−	0.404694i	$-0.867378\pi$
$269$	−958587.	−	1.66032e6i	−0.807702	−	1.39898i	0.106750	−	0.994286i	$-0.465955\pi$
$270$		0			0
$271$	−1.14500e6	+	1.98320e6i	−0.947069	+	1.64037i	−0.195515	+	0.980701i	$0.562638\pi$
$271$	−1.14500e6	+	1.98320e6i	−0.947069	+	1.64037i	−0.751554	+	0.659672i	$0.770695\pi$
$272$	−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	0.932906	−	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
$279$		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	0.547457	−	0.836834i	$-0.315596\pi$
$283$	−607622.	−	1.05243e6i	−0.450991	−	0.781139i	−0.998448	+	0.0556949i	$0.982263\pi$
$284$	−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	0.905368	−	0.424627i	$-0.139595\pi$
$311$	144892.	+	250961.i	0.0849463	+	0.147131i	−0.820422	+	0.571758i	$0.806261\pi$
$312$		0			0
$313$	−109105.	+	188976.i	−0.0629484	+	0.109030i	−0.895782	−	0.444493i	$-0.853384\pi$
$313$	−109105.	+	188976.i	−0.0629484	+	0.109030i	0.832834	+	0.553523i	$0.186717\pi$
$314$	−5.69002e6			−3.25679
$315$		0			0
$316$	−351413.			−0.197970
$317$	645315.	−	1.11772e6i	0.360681	−	0.624718i	−0.627392	−	0.778704i	$-0.715878\pi$
$317$	645315.	−	1.11772e6i	0.360681	−	0.624718i	0.988073	+	0.153985i	$0.0492109\pi$
$318$		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	0.0168673	−	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
$333$		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	0.647904	−	0.761722i	$-0.275646\pi$
$347$	−753007.	−	1.30425e6i	−0.335719	−	0.581482i	−0.983623	+	0.180240i	$0.942312\pi$
$348$		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	0.629331	−	0.777137i	$-0.283329\pi$
$353$	−838978.	−	1.45315e6i	−0.358355	−	0.620689i	−0.987686	+	0.156448i	$0.949996\pi$
$354$		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	0.488074	+	0.872802i	$0.337700\pi$
$359$	−1.24987e6	+	2.16483e6i	−0.511832	+	0.886519i	−0.999906	+	0.0137165i	$0.995634\pi$
$360$		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	0.994707	−	0.102749i	$-0.0327639\pi$
$367$	1.05371e6	+	1.82507e6i	0.408370	+	0.707318i	−0.586337	+	0.810067i	$0.699431\pi$
$368$	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	0.491538	+	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
$375$		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	−0.704169	−	0.710032i	$-0.748680\pi$
$383$	754497.	−	1.30683e6i	0.262821	−	0.455220i	0.966991	+	0.254812i	$0.0820137\pi$
$384$		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	0.945870	+	0.324546i	$0.105212\pi$
$389$	2.25033e6	+	3.89768e6i	0.754000	+	1.30597i	−0.191870	+	0.981420i	$0.561455\pi$
$390$		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	−0.436773	−	0.899572i	$-0.643879\pi$
$397$	1.76068e6	−	3.04958e6i	0.560665	−	0.971101i	0.997439	−	0.0715292i	$-0.0227879\pi$
$398$	−8.24469e6			−2.60895
$399$		0			0
$400$	−4.90476e6			−1.53274
$401$	−453554.	+	785578.i	−0.140853	+	0.243965i	−0.927818	−	0.373033i	$-0.878318\pi$
$401$	−453554.	+	785578.i	−0.140853	+	0.243965i	0.786965	+	0.616998i	$0.211651\pi$
$402$		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	−0.985814	−	0.167839i	$-0.946321\pi$
$409$	−2.15927e6	−	3.73996e6i	−0.638260	−	1.10550i	0.347554	−	0.937660i	$-0.387012\pi$
$410$	−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	−0.842432	−	0.538803i	$-0.818877\pi$
$431$	−3.42393e6	−	5.93041e6i	−0.887833	−	1.53777i	−0.0454009	−	0.998969i	$-0.514457\pi$
$432$		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	−0.943222	−	0.332162i	$-0.892222\pi$
$439$	−742783.	+	1.28654e6i	−0.183950	+	0.318611i	0.759272	+	0.650773i	$0.225555\pi$
$440$	−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	$0.404916\pi$
$443$	−2.81097e6	+	4.86874e6i	−0.680528	+	1.17871i	−0.974820	+	0.222994i	$0.928417\pi$
$444$		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	−0.676628	−	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
$459$		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	0.462275	+	0.886737i	$0.347033\pi$
$467$	−2.52990e6	+	4.38192e6i	−0.536799	+	0.929763i	−0.999074	+	0.0430263i	$0.986300\pi$
$468$		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	−0.998078	−	0.0619642i	$-0.980264\pi$
$479$	−2.77543e6	−	4.80718e6i	−0.552702	−	0.957308i	0.445377	−	0.895343i	$-0.353070\pi$
$480$		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	0.981369	+	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
$489$		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	−0.946428	−	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
$501$		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	−0.686943	−	0.726712i	$-0.741048\pi$
$509$	1.67100e6	−	2.89426e6i	0.285879	−	0.495157i	0.972822	+	0.231554i	$0.0743810\pi$
$510$		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	0.737220	−	0.675653i	$-0.236138\pi$
$521$	−1.34152e6	−	2.32359e6i	−0.216523	−	0.375029i	−0.953743	+	0.300624i	$0.902805\pi$
$522$		0			0
$523$	2.71178e6	−	4.69694e6i	0.433511	−	0.750863i	−0.563662	−	0.826005i	$-0.690608\pi$
$523$	2.71178e6	−	4.69694e6i	0.433511	−	0.750863i	0.997173	+	0.0751429i	$0.0239413\pi$
$524$	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	−0.935030	−	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
$543$		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	0.990173	−	0.139850i	$-0.0446620\pi$
$557$	2.73828e6	+	4.74284e6i	0.373973	+	0.647740i	−0.616200	+	0.787590i	$0.711329\pi$
$558$		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	0.878983	−	0.476853i	$-0.158223\pi$
$563$	199488.	+	345523.i	0.0265244	+	0.0459416i	−0.852459	+	0.522795i	$0.824889\pi$
$564$		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	−0.969866	−	0.243641i	$-0.921658\pi$
$569$	−2.11556e6	+	3.66426e6i	−0.273934	+	0.474467i	0.695932	+	0.718108i	$0.254992\pi$
$570$		0			0
$571$	−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
$573$		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	0.915965	−	0.401258i	$-0.131427\pi$
$577$	883558.	+	1.53037e6i	0.110483	+	0.191362i	−0.805482	+	0.592620i	$0.798094\pi$
$578$	−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	0.0775549	−	0.996988i	$-0.475289\pi$
$593$	7.72568e6	−	1.33813e7i	0.902194	−	1.56265i	0.824640	−	0.565659i	$-0.191378\pi$
$594$		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	0.735434	−	0.677596i	$-0.236978\pi$
$599$	−1.92400e6	−	3.33247e6i	−0.219098	−	0.379489i	−0.954533	+	0.298107i	$0.903645\pi$
$600$		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	−0.197476	−	0.980308i	$-0.563274\pi$
$607$	6.81033e6	−	1.17958e7i	0.750233	−	1.29944i	0.947709	−	0.319135i	$-0.103392\pi$
$608$	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	−0.902063	−	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
$615$		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	0.888047	−	0.459753i	$-0.152062\pi$
$619$	437230.	+	757304.i	0.0458652	+	0.0794408i	−0.842181	+	0.539194i	$0.818729\pi$
$620$	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	0.884892	−	0.465796i	$-0.154232\pi$
$641$	406276.	+	703690.i	0.0390549	+	0.0676451i	−0.845837	+	0.533441i	$0.820899\pi$
$642$		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	0.803208	−	0.595699i	$-0.203125\pi$
$647$	−1.21690e6	−	2.10773e6i	−0.114286	−	0.197950i	−0.917494	+	0.397749i	$0.869791\pi$
$648$		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	−0.997246	−	0.0741664i	$-0.976370\pi$
$653$	−4.73332e6	+	8.19835e6i	−0.434393	+	0.752391i	0.562853	+	0.826557i	$0.309704\pi$
$654$		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	0.940862	+	0.338791i	$0.110018\pi$
$661$	8.58029e6	+	1.48615e7i	0.763832	+	1.32300i	−0.177029	+	0.984206i	$0.556649\pi$
$662$	−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	−0.411069	−	0.911604i	$-0.634844\pi$
$677$	6.96368e6	−	1.20614e7i	0.583938	−	1.01141i	0.995007	−	0.0998062i	$-0.0318223\pi$
$678$		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	0.947365	+	0.320155i	$0.103735\pi$
$683$	9.15503e6	+	1.58570e7i	0.750945	+	1.30067i	−0.196421	+	0.980520i	$0.562932\pi$
$684$		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	−0.263096	−	0.964770i	$-0.584744\pi$
$691$	8.83583e6	−	1.53041e7i	0.703967	−	1.21931i	0.967063	−	0.254537i	$-0.0819230\pi$
$692$	−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	−0.121386	+	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
$711$		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	0.296238	+	0.955114i	$0.404268\pi$
$719$	−9.41269e6	+	1.63033e7i	−0.679034	+	1.17612i	−0.975272	+	0.221007i	$0.929066\pi$
$720$		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	−0.401978	−	0.915649i	$-0.631677\pi$
$733$	8.61136e6	−	1.49153e7i	0.591986	−	1.02535i	0.993965	−	0.109701i	$-0.0349894\pi$
$734$	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	0.993610	+	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
$741$		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	−0.990408	−	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
$753$		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	−0.190977	+	0.981595i	$0.561166\pi$
$761$	−1.51063e7	+	2.61648e7i	−0.945574	+	1.63778i	−0.754597	+	0.656188i	$0.772168\pi$
$762$		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	0.938267	+	0.345911i	$0.112430\pi$
$773$	1.27705e7	+	2.21191e7i	0.768701	+	1.33143i	−0.169566	+	0.985519i	$0.554237\pi$
$774$		0			0
$775$	3.77802e6	−	6.54373e6i	0.225949	−	0.391355i
$776$	2.63746e7			1.57228
$777$		0			0
$778$	4.60140e7			2.72547
$779$	3.10618e6	−	5.38006e6i	0.183393	−	0.317646i
$780$		0			0
$781$	1.41448e6	+	2.44995e6i	0.0829791	+	0.143724i
$782$	1.18129e7	−	2.04606e7i	0.690780	−	1.19647i
$783$		0			0
$784$	2.71137e7	−	1.73521e7i	1.57543	−	1.00824i
$785$	−1.32195e7			−0.765667
$786$		0			0
$787$	4.40589e6	+	7.63123e6i	0.253570	+	0.439195i	0.964506	−	0.264061i	$-0.0850620\pi$
$787$	4.40589e6	+	7.63123e6i	0.253570	+	0.439195i	−0.710936	+	0.703256i	$0.751729\pi$
$788$	2.96256e7	+	5.13130e7i	1.69962	+	2.94383i
$789$		0			0
$790$	−1.17665e6			−0.0670779
$791$	2.96749e6	−	1.21816e7i	0.168635	−	0.692248i
$792$		0			0
$793$	−1.07554e7	+	1.86289e7i	−0.607357	+	1.05197i
$794$	−1.80009e7	−	3.11785e7i	−1.01331	−	1.75511i
$795$		0			0
$796$	−2.92436e7	+	5.06513e7i	−1.63587	+	2.83340i
$797$	2.07624e7			1.15780			0.578899	−	0.815399i	$-0.303483\pi$
$797$	2.07624e7			1.15780			0.578899	+	0.815399i	$0.303483\pi$
$798$		0			0
$799$	−1.75358e6			−0.0971757
$800$	−8.09592e6	+	1.40225e7i	−0.447240	+	0.774643i
$801$		0			0
$802$	4.63706e6	+	8.03163e6i	0.254570	+	0.440928i
$803$	−3.90568e6	+	6.76483e6i	−0.213751	+	0.370227i
$804$		0			0
$805$	−1.21576e7	+	3.55723e6i	−0.661237	+	0.193474i
$806$	3.07493e7			1.66724
$807$		0			0
$808$	−3.82486e7	−	6.62486e7i	−2.06105	−	3.56984i
$809$	6.85107e6	+	1.18664e7i	0.368034	+	0.637453i	0.989258	−	0.146180i	$-0.0466978\pi$
$809$	6.85107e6	+	1.18664e7i	0.368034	+	0.637453i	−0.621224	+	0.783633i	$0.713364\pi$
$810$		0			0
$811$	3.30799e7			1.76609			0.883043	−	0.469292i	$-0.155491\pi$
$811$	3.30799e7			1.76609			0.883043	+	0.469292i	$0.155491\pi$
$812$	−2.14900e7	+	6.28783e6i	−1.14379	+	0.334665i
$813$		0			0
$814$	2.35807e7	−	4.08429e7i	1.24737	−	2.16051i
$815$	−234282.	−	405788.i	−0.0123550	−	0.0213996i
$816$		0			0
$817$	3.59486e6	−	6.22647e6i	0.188420	−	0.326353i
$818$	−4.41520e7			−2.30711
$819$		0			0
$820$	−7.71285e6			−0.400572
$821$	7.41616e6	−	1.28452e7i	0.383991	−	0.665092i	−0.607638	−	0.794214i	$-0.707883\pi$
$821$	7.41616e6	−	1.28452e7i	0.383991	−	0.665092i	0.991629	+	0.129122i	$0.0412160\pi$
$822$		0			0
$823$	−5.43612e6	−	9.41563e6i	−0.279762	−	0.484563i	0.691563	−	0.722316i	$-0.256922\pi$
$823$	−5.43612e6	−	9.41563e6i	−0.279762	−	0.484563i	−0.971326	+	0.237753i	$0.923589\pi$
$824$	1.07820e7	−	1.86750e7i	0.553199	−	0.958168i
$825$		0			0
$826$	8.62609e6	−	3.54102e7i	0.439910	−	1.80583i
$827$	1.34267e7			0.682662			0.341331	−	0.939943i	$-0.389122\pi$
$827$	1.34267e7			0.682662			0.341331	+	0.939943i	$0.389122\pi$
$828$		0			0
$829$	7.33770e6	+	1.27093e7i	0.370829	+	0.642295i	0.989693	−	0.143203i	$-0.0457402\pi$
$829$	7.33770e6	+	1.27093e7i	0.370829	+	0.642295i	−0.618864	+	0.785498i	$0.712407\pi$
$830$	7.30302e6	+	1.26492e7i	0.367965	+	0.637335i
$831$		0			0
$832$	−3.41941e6			−0.171255
$833$	−431300.	−	9.43159e6i	−0.0215361	−	0.470947i
$834$		0			0
$835$	−1.12560e6	+	1.94960e6i	−0.0558687	+	0.0967674i
$836$	−2.34246e7	−	4.05726e7i	−1.15919	−	2.00778i
$837$		0			0
$838$	7.77222e6	−	1.34619e7i	0.382327	−	0.662210i
$839$	−2.76635e7			−1.35676			−0.678379	−	0.734712i	$-0.737317\pi$
$839$	−2.76635e7			−1.35676			−0.678379	+	0.734712i	$0.737317\pi$
$840$		0			0
$841$	−1.48402e7			−0.723519
$842$	−2.25973e7	+	3.91396e7i	−1.09844	+	1.90255i
$843$		0			0
$844$	−2.49399e6	−	4.31971e6i	−0.120514	−	0.208737i
$845$	7.92963e6	−	1.37345e7i	0.382042	−	0.661716i
$846$		0			0
$847$	5.21795e6	+	4.98479e6i	0.249915	+	0.238747i
$848$	−2.18537e6			−0.104361
$849$		0			0
$850$	7.35376e6	+	1.27371e7i	0.349110	+	0.604676i
$851$	−2.03808e7	−	3.53006e7i	−0.964712	−	1.67093i
$852$		0			0
$853$	3.43515e6			0.161649			0.0808244	−	0.996728i	$-0.474245\pi$
$853$	3.43515e6			0.161649			0.0808244	+	0.996728i	$0.474245\pi$
$854$	−2.68459e7	+	7.85493e6i	−1.25960	+	0.368551i
$855$		0			0
$856$	−9.98108e6	+	1.72877e7i	−0.465579	+	0.806406i
$857$	−3.20313e6	−	5.54799e6i	−0.148978	−	0.258038i	0.781872	−	0.623439i	$-0.214265\pi$
$857$	−3.20313e6	−	5.54799e6i	−0.148978	−	0.258038i	−0.930850	+	0.365401i	$0.880932\pi$
$858$		0			0
$859$	−9.08695e6	+	1.57391e7i	−0.420180	+	0.727773i	−0.995957	−	0.0898340i	$-0.971366\pi$
$859$	−9.08695e6	+	1.57391e7i	−0.420180	+	0.727773i	0.575777	+	0.817607i	$0.304700\pi$
$860$	−8.92627e6			−0.411551
$861$		0			0
$862$	−7.00114e7			−3.20923
$863$	409387.	−	709079.i	0.0187114	−	0.0324091i	−0.856518	−	0.516117i	$-0.827377\pi$
$863$	409387.	−	709079.i	0.0187114	−	0.0324091i	0.875230	+	0.483708i	$0.160710\pi$
$864$		0			0
$865$	−4.02421e6	−	6.97014e6i	−0.182869	−	0.316739i
$866$	−2.04134e7	+	3.53570e7i	−0.924954	+	1.60207i
$867$		0			0
$868$	2.00608e7	+	1.91644e7i	0.903753	+	0.863369i
$869$	2.25560e6			0.101324
$870$		0			0
$871$	−2.83306e7	−	4.90701e7i	−1.26535	−	2.19165i
$872$	−7.54842e6	−	1.30743e7i	−0.336175	−	0.582272i
$873$		0			0
$874$	−5.83574e7			−2.58415
$875$	4.14400e6	−	1.70112e7i	0.182978	−	0.751127i
$876$		0			0
$877$	1.66981e7	−	2.89219e7i	0.733108	−	1.26978i	−0.222441	−	0.974946i	$-0.571402\pi$
$877$	1.66981e7	−	2.89219e7i	0.733108	−	1.26978i	0.955549	−	0.294834i	$-0.0952642\pi$
$878$	7.59411e6	+	1.31534e7i	0.332461	+	0.575839i
$879$		0			0
$880$	−1.05894e7	+	1.83413e7i	−0.460961	+	0.798407i
$881$	1.24325e7			0.539658			0.269829	−	0.962908i	$-0.413033\pi$
$881$	1.24325e7			0.539658			0.269829	+	0.962908i	$0.413033\pi$
$882$		0			0
$883$	−2.33298e7			−1.00695			−0.503476	−	0.864009i	$-0.667946\pi$
$883$	−2.33298e7			−1.00695			−0.503476	+	0.864009i	$0.667946\pi$
$884$	−2.07645e7	+	3.59651e7i	−0.893697	+	1.54793i
$885$		0			0
$886$	2.87389e7	+	4.97772e7i	1.22995	+	2.13033i
$887$	−2.37764e6	+	4.11819e6i	−0.101470	+	0.175751i	−0.912290	−	0.409544i	$-0.865688\pi$
$887$	−2.37764e6	+	4.11819e6i	−0.101470	+	0.175751i	0.810821	+	0.585295i	$0.199021\pi$
$888$		0			0
$889$	715640.	−	2.93771e6i	0.0303697	−	0.124668i
$890$	1.51772e7			0.642269
$891$		0			0
$892$	2.24916e7	+	3.89567e7i	0.946475	+	1.63934i
$893$	2.16573e6	+	3.75115e6i	0.0908814	+	0.157411i
$894$		0			0
$895$	1.84368e7			0.769356
$896$	1.57519e7	+	1.50481e7i	0.655487	+	0.626197i
$897$		0			0
$898$	−9.96226e6	+	1.72551e7i	−0.412256	+	0.714048i
$899$	−3.51331e6	−	6.08522e6i	−0.144983	−	0.251118i
$900$		0			0
$901$	−320482.	+	555090.i	−0.0131520	+	0.0227799i
$902$	2.13087e7			0.872050
$903$		0			0
$904$	−4.00716e7			−1.63086
$905$	−1.57596e6	+	2.72964e6i	−0.0639622	+	0.110786i
$906$		0			0
$907$	9.54512e6	+	1.65326e7i	0.385268	+	0.667304i	0.991806	−	0.127750i	$-0.0407755\pi$
$907$	9.54512e6	+	1.65326e7i	0.385268	+	0.667304i	−0.606538	+	0.795054i	$0.707442\pi$
$908$	3.63445e7	−	6.29506e7i	1.46293	−	2.53388i
$909$		0			0
$910$	3.07992e7	−	9.01165e6i	1.23292	−	0.360745i
$911$	1.22591e6			0.0489399			0.0244700	−	0.999701i	$-0.492210\pi$
$911$	1.22591e6			0.0489399			0.0244700	+	0.999701i	$0.492210\pi$
$912$		0			0
$913$	−1.39996e7	−	2.42481e7i	−0.555827	−	0.962720i
$914$	−1.36648e7	−	2.36681e7i	−0.541050	−	0.937126i
$915$		0			0
$916$	6.42490e7			2.53004
$917$	3.17555e7	+	3.03366e7i	1.24708	+	1.19136i
$918$		0			0
$919$	8.46136e6	−	1.46555e7i	0.330485	−	0.572417i	−0.652122	−	0.758114i	$-0.726121\pi$
$919$	8.46136e6	−	1.46555e7i	0.330485	−	0.572417i	0.982607	+	0.185697i	$0.0594544\pi$
$920$	2.02428e7	+	3.50615e7i	0.788497	+	1.36572i
$921$		0			0
$922$	2.37839e7	−	4.11949e7i	0.921415	−	1.59594i
$923$	−6.19419e6			−0.239321
$924$		0			0
$925$	2.53749e7			0.975101
$926$	−2.65098e7	+	4.59162e7i	−1.01596	+	1.75970i
$927$		0			0
$928$	7.52865e6	+	1.30400e7i	0.286977	+	0.497059i
$929$	3.38620e6	−	5.86507e6i	0.128728	−	0.222964i	−0.794456	−	0.607322i	$-0.792244\pi$
$929$	3.38620e6	−	5.86507e6i	0.128728	−	0.222964i	0.923184	+	0.384358i	$0.125577\pi$
$930$		0			0
$931$	−1.96428e7	+	1.25709e7i	−0.742729	+	0.475329i
$932$	−4.32380e7			−1.63052
$933$		0			0
$934$	2.58653e7	+	4.48001e7i	0.970177	+	1.68040i
$935$	3.10583e6	+	5.37945e6i	0.116185	+	0.201238i
$936$		0			0
$937$	−1.41035e7			−0.524779			−0.262389	−	0.964962i	$-0.584511\pi$
$937$	−1.41035e7			−0.524779			−0.262389	+	0.964962i	$0.584511\pi$
$938$	1.74386e7	−	7.15856e7i	0.647149	−	2.65655i
$939$		0			0
$940$	2.68882e6	−	4.65718e6i	0.0992527	−	0.171911i
$941$	−2.81262e6	−	4.87160e6i	−0.103547	−	0.179349i	0.809597	−	0.586987i	$-0.199686\pi$
$941$	−2.81262e6	−	4.87160e6i	−0.103547	−	0.179349i	−0.913144	+	0.407638i	$0.866353\pi$
$942$		0			0
$943$	9.20859e6	−	1.59498e7i	0.337221	−	0.584083i
$944$	−5.26657e7			−1.92353
$945$		0			0
$946$	2.46611e7			0.895952
$947$	1.32063e7	−	2.28739e7i	0.478526	−	0.828831i	−0.521171	−	0.853452i	$-0.674505\pi$
$947$	1.32063e7	−	2.28739e7i	0.478526	−	0.828831i	0.999697	+	0.0246212i	$0.00783796\pi$
$948$		0			0
$949$	−8.55174e6	−	1.48120e7i	−0.308240	−	0.533887i
$950$	1.81643e7	−	3.14615e7i	0.652994	−	1.13102i
$951$		0			0
$952$	−2.89612e7	+	8.47387e6i	−1.03568	+	0.303033i
$953$	−4.21824e7			−1.50452			−0.752262	−	0.658864i	$-0.771037\pi$
$953$	−4.21824e7			−1.50452			−0.752262	+	0.658864i	$0.771037\pi$
$954$		0			0
$955$	−78828.6	−	136535.i	−0.00279689	−	0.00484436i
$956$	2.69479e7	+	4.66751e7i	0.953629	+	1.65173i
$957$		0			0
$958$	−5.67511e7			−1.99784
$959$	−7.82344e6	+	2.28909e6i	−0.274695	+	0.0803741i
$960$		0			0
$961$	9.96139e6	−	1.72536e7i	0.347946	−	0.602660i
$962$	5.16314e7	+	8.94283e7i	1.79877	+	3.11557i
$963$		0			0
$964$	4.26038e7	−	7.37920e7i	1.47658	−	2.55751i
$965$	−1.07503e7			−0.371622
$966$		0			0
$967$	4.01501e7			1.38077			0.690384	−	0.723443i	$-0.257441\pi$
$967$	4.01501e7			1.38077			0.690384	+	0.723443i	$0.257441\pi$
$968$	1.15319e7	−	1.99738e7i	0.395560	−	0.685130i
$969$		0			0
$970$	7.72902e6	+	1.33870e7i	0.263751	+	0.456831i
$971$	8.22756e6	−	1.42506e7i	0.280042	−	0.485047i	−0.691353	−	0.722517i	$-0.742985\pi$
$971$	8.22756e6	−	1.42506e7i	0.280042	−	0.485047i	0.971395	+	0.237471i	$0.0763183\pi$
$972$		0			0
$973$	6.50277e6	−	2.66939e7i	0.220200	−	0.903921i
$974$	7.03207e7			2.37512
$975$		0			0
$976$	2.02100e7	+	3.50048e7i	0.679113	+	1.17626i
$977$	8.55881e6	+	1.48243e7i	0.286865	+	0.496864i	0.973060	−	0.230554i	$-0.0740537\pi$
$977$	8.55881e6	+	1.48243e7i	0.286865	+	0.496864i	−0.686195	+	0.727418i	$0.740720\pi$
$978$		0			0
$979$	−2.90942e7			−0.970174
$980$	2.57099e7	+	1.33163e7i	0.855136	+	0.442915i
$981$		0			0
$982$	−3.80562e7	+	6.59153e7i	−1.25935	+	2.18126i
$983$	−1.16901e7	−	2.02479e7i	−0.385865	−	0.668338i	0.606024	−	0.795447i	$-0.292764\pi$
$983$	−1.16901e7	−	2.02479e7i	−0.385865	−	0.668338i	−0.991889	+	0.127108i	$0.959430\pi$
$984$		0			0
$985$	−9.70245e6	+	1.68051e7i	−0.318633	+	0.551889i
$986$	1.36770e7			0.448021
$987$		0			0
$988$	1.02579e8			3.34324
$989$	1.06573e7	−	1.84590e7i	0.346463	−	0.600092i
$990$		0			0
$991$	2.35478e6	+	4.07859e6i	0.0761667	+	0.131925i	0.901593	−	0.432585i	$-0.142399\pi$
$991$	2.35478e6	+	4.07859e6i	0.0761667	+	0.131925i	−0.825426	+	0.564510i	$0.809065\pi$
$992$	9.32842e6	−	1.61573e7i	0.300974	−	0.521302i
$993$		0			0
$994$	−5.82407e6	−	5.56383e6i	−0.186965	−	0.178611i
$995$	−1.91547e7			−0.613362
$996$		0			0
$997$	2.27714e7	+	3.94412e7i	0.725524	+	1.25665i	0.958758	+	0.284224i	$0.0917360\pi$
$997$	2.27714e7	+	3.94412e7i	0.725524	+	1.25665i	−0.233233	+	0.972421i	$0.574931\pi$
$998$	1.10075e7	+	1.90655e7i	0.349834	+	0.605930i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.e.e.37.4		8
3.2	odd	2		21.6.e.c.16.1	yes	8
7.2	even	3		441.6.a.w.1.1		4
7.4	even	3	inner	63.6.e.e.46.4		8
7.5	odd	6		441.6.a.v.1.1		4
12.11	even	2		336.6.q.j.289.2		8
21.2	odd	6		147.6.a.m.1.4		4
21.5	even	6		147.6.a.l.1.4		4
21.11	odd	6		21.6.e.c.4.1	✓	8
21.17	even	6		147.6.e.o.67.1		8
21.20	even	2		147.6.e.o.79.1		8
84.11	even	6		336.6.q.j.193.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.1	✓	8	21.11	odd	6
21.6.e.c.16.1	yes	8	3.2	odd	2
63.6.e.e.37.4		8	1.1	even	1	trivial
63.6.e.e.46.4		8	7.4	even	3	inner
147.6.a.l.1.4		4	21.5	even	6
147.6.a.m.1.4		4	21.2	odd	6
147.6.e.o.67.1		8	21.17	even	6
147.6.e.o.79.1		8	21.20	even	2
336.6.q.j.193.2		8	84.11	even	6
336.6.q.j.289.2		8	12.11	even	2
441.6.a.v.1.1		4	7.5	odd	6
441.6.a.w.1.1		4	7.2	even	3

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

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