LMFDB - Embedded newform 63.6.e.e.37.2

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			37.2
Root			$0.895402 - 1.55088i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.6.e.e.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.395402 + 0.684857i) q^{2} +(15.6873 + 27.1712i) q^{4} +(-52.0958 + 90.2327i) q^{5} +(-7.12980 - 129.446i) q^{7} -50.1170 q^{8} +O(q^{10})$	\(q+(-0.395402 + 0.684857i) q^{2} +(15.6873 + 27.1712i) q^{4} +(-52.0958 + 90.2327i) q^{5} +(-7.12980 - 129.446i) q^{7} -50.1170 q^{8} +(-41.1977 - 71.3564i) q^{10} +(-248.830 - 430.986i) q^{11} -206.551 q^{13} +(91.4709 + 46.3002i) q^{14} +(-482.178 + 835.156i) q^{16} +(31.5793 + 54.6969i) q^{17} +(-661.977 + 1146.58i) q^{19} -3268.98 q^{20} +393.552 q^{22} +(-97.2187 + 168.388i) q^{23} +(-3865.45 - 6695.16i) q^{25} +(81.6709 - 141.458i) q^{26} +(3405.35 - 2224.38i) q^{28} -4323.14 q^{29} +(3762.66 + 6517.11i) q^{31} +(-1183.18 - 2049.33i) q^{32} -49.9461 q^{34} +(12051.7 + 6100.24i) q^{35} +(-5177.82 + 8968.25i) q^{37} +(-523.495 - 906.720i) q^{38} +(2610.89 - 4522.19i) q^{40} +4180.92 q^{41} +5960.87 q^{43} +(7806.94 - 13522.0i) q^{44} +(-76.8810 - 133.162i) q^{46} +(-2194.87 + 3801.62i) q^{47} +(-16705.3 + 1845.84i) q^{49} +6113.64 q^{50} +(-3240.24 - 5612.25i) q^{52} +(8892.39 + 15402.1i) q^{53} +51852.0 q^{55} +(357.324 + 6487.42i) q^{56} +(1709.38 - 2960.73i) q^{58} +(1750.23 + 3031.49i) q^{59} +(5316.23 - 9207.98i) q^{61} -5951.06 q^{62} -28988.0 q^{64} +(10760.5 - 18637.7i) q^{65} +(6637.37 + 11496.3i) q^{67} +(-990.789 + 1716.10i) q^{68} +(-8943.05 + 5841.61i) q^{70} -38811.1 q^{71} +(-15687.8 - 27172.1i) q^{73} +(-4094.65 - 7092.14i) q^{74} -41538.6 q^{76} +(-54015.1 + 35282.8i) q^{77} +(-19745.7 + 34200.6i) q^{79} +(-50238.9 - 87016.3i) q^{80} +(-1653.14 + 2863.33i) q^{82} +102372. q^{83} -6580.60 q^{85} +(-2356.94 + 4082.34i) q^{86} +(12470.6 + 21599.7i) q^{88} +(-56410.5 + 97705.8i) q^{89} +(1472.67 + 26737.2i) q^{91} -6100.40 q^{92} +(-1735.71 - 3006.34i) q^{94} +(-68972.6 - 119464. i) q^{95} +30334.3 q^{97} +(5341.19 - 12170.6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.395402	+	0.684857i	−0.0698979	+	0.121067i	−0.898856	−	0.438244i	$-0.855601\pi$
$2$	−0.395402	+	0.684857i	−0.0698979	+	0.121067i	0.828958	+	0.559310i	$0.188934\pi$
$3$		0			0
$3$		0			0
$4$	15.6873	+	27.1712i	0.490229	+	0.849101i
$5$	−52.0958	+	90.2327i	−0.931919	+	1.61413i	−0.151881	+	0.988399i	$0.548533\pi$
$5$	−52.0958	+	90.2327i	−0.931919	+	1.61413i	−0.780038	+	0.625732i	$0.784800\pi$
$6$		0			0
$7$	−7.12980	−	129.446i	−0.0549961	−	0.998487i
$7$	−7.12980	−	129.446i	−0.0549961	−	0.998487i
$8$	−50.1170			−0.276860
$9$		0			0
$10$	−41.1977	−	71.3564i	−0.130278	−	0.225649i
$11$	−248.830	−	430.986i	−0.620041	−	1.07394i	−0.989477	−	0.144687i	$-0.953782\pi$
$11$	−248.830	−	430.986i	−0.620041	−	1.07394i	0.369436	−	0.929256i	$-0.379551\pi$
$12$		0			0
$13$	−206.551			−0.338977			−0.169488	−	0.985532i	$-0.554211\pi$
$13$	−206.551			−0.338977			−0.169488	+	0.985532i	$0.554211\pi$
$14$	91.4709	+	46.3002i	0.124728	+	0.0631340i
$15$		0			0
$16$	−482.178	+	835.156i	−0.470877	+	0.815582i
$17$	31.5793	+	54.6969i	0.0265021	+	0.0459030i	0.878972	−	0.476873i	$-0.158230\pi$
$17$	31.5793	+	54.6969i	0.0265021	+	0.0459030i	−0.852470	+	0.522776i	$0.824896\pi$
$18$		0			0
$19$	−661.977	+	1146.58i	−0.420687	+	0.728651i	−0.996007	−	0.0892772i	$-0.971544\pi$
$19$	−661.977	+	1146.58i	−0.420687	+	0.728651i	0.575320	+	0.817929i	$0.304878\pi$
$20$	−3268.98			−1.82741
$21$		0			0
$22$	393.552			0.173358
$23$	−97.2187	+	168.388i	−0.0383204	+	0.0663729i	−0.884550	−	0.466446i	$-0.845534\pi$
$23$	−97.2187	+	168.388i	−0.0383204	+	0.0663729i	0.846229	+	0.532819i	$0.178867\pi$
$24$		0			0
$25$	−3865.45	−	6695.16i	−1.23695	−	2.14245i
$26$	81.6709	−	141.458i	0.0236938	−	0.0410388i
$27$		0			0
$28$	3405.35	−	2224.38i	0.820855	−	0.536184i
$29$	−4323.14			−0.954562			−0.477281	−	0.878751i	$-0.658378\pi$
$29$	−4323.14			−0.954562			−0.477281	+	0.878751i	$0.658378\pi$
$30$		0			0
$31$	3762.66	+	6517.11i	0.703219	+	1.21801i	0.967331	+	0.253518i	$0.0815879\pi$
$31$	3762.66	+	6517.11i	0.703219	+	1.21801i	−0.264112	+	0.964492i	$0.585079\pi$
$32$	−1183.18	−	2049.33i	−0.204256	−	0.353783i
$33$		0			0
$34$	−49.9461			−0.00740977
$35$	12051.7	+	6100.24i	1.66294	+	0.841738i
$36$		0			0
$37$	−5177.82	+	8968.25i	−0.621789	+	1.07697i	0.367364	+	0.930077i	$0.380260\pi$
$37$	−5177.82	+	8968.25i	−0.621789	+	1.07697i	−0.989152	+	0.146892i	$0.953073\pi$
$38$	−523.495	−	906.720i	−0.0588103	−	0.101862i
$39$		0			0
$40$	2610.89	−	4522.19i	0.258011	−	0.446888i
$41$	4180.92			0.388429			0.194215	−	0.980959i	$-0.437784\pi$
$41$	4180.92			0.388429			0.194215	+	0.980959i	$0.437784\pi$
$42$		0			0
$43$	5960.87			0.491630			0.245815	−	0.969317i	$-0.420944\pi$
$43$	5960.87			0.491630			0.245815	+	0.969317i	$0.420944\pi$
$44$	7806.94	−	13522.0i	0.607924	−	1.05296i
$45$		0			0
$46$	−76.8810	−	133.162i	−0.00535703	−	0.00927866i
$47$	−2194.87	+	3801.62i	−0.144932	+	0.251029i	−0.929348	−	0.369206i	$-0.879630\pi$
$47$	−2194.87	+	3801.62i	−0.144932	+	0.251029i	0.784416	+	0.620236i	$0.212963\pi$
$48$		0			0
$49$	−16705.3	+	1845.84i	−0.993951	+	0.109826i
$50$	6113.64			0.345840
$51$		0			0
$52$	−3240.24	−	5612.25i	−0.166176	−	0.287825i
$53$	8892.39	+	15402.1i	0.434839	+	0.753164i	0.997283	−	0.0736720i	$-0.0234718\pi$
$53$	8892.39	+	15402.1i	0.434839	+	0.753164i	−0.562443	+	0.826836i	$0.690138\pi$
$54$		0			0
$55$	51852.0			2.31131
$56$	357.324	+	6487.42i	0.0152262	+	0.276441i
$57$		0			0
$58$	1709.38	−	2960.73i	0.0667219	−	0.115566i
$59$	1750.23	+	3031.49i	0.0654585	+	0.113377i	0.896897	−	0.442239i	$-0.145816\pi$
$59$	1750.23	+	3031.49i	0.0654585	+	0.113377i	−0.831439	+	0.555616i	$0.812482\pi$
$60$		0			0
$61$	5316.23	−	9207.98i	0.182928	−	0.316840i	−0.759949	−	0.649983i	$-0.774776\pi$
$61$	5316.23	−	9207.98i	0.182928	−	0.316840i	0.942876	+	0.333143i	$0.108109\pi$
$62$	−5951.06			−0.196614
$63$		0			0
$64$	−28988.0			−0.884645
$65$	10760.5	−	18637.7i	0.315899	−	0.547153i
$66$		0			0
$67$	6637.37	+	11496.3i	0.180638	+	0.312874i	0.942098	−	0.335338i	$-0.108850\pi$
$67$	6637.37	+	11496.3i	0.180638	+	0.312874i	−0.761460	+	0.648212i	$0.775517\pi$
$68$	−990.789	+	1716.10i	−0.0259842	+	0.0450059i
$69$		0			0
$70$	−8943.05	+	5841.61i	−0.218143	+	0.142491i
$71$	−38811.1			−0.913713			−0.456857	−	0.889540i	$-0.651025\pi$
$71$	−38811.1			−0.913713			−0.456857	+	0.889540i	$0.651025\pi$
$72$		0			0
$73$	−15687.8	−	27172.1i	−0.344552	−	0.596782i	0.640720	−	0.767775i	$-0.278636\pi$
$73$	−15687.8	−	27172.1i	−0.344552	−	0.596782i	−0.985272	+	0.170992i	$0.945303\pi$
$74$	−4094.65	−	7092.14i	−0.0869235	−	0.150556i
$75$		0			0
$76$	−41538.6			−0.824931
$77$	−54015.1	+	35282.8i	−1.03822	+	0.678166i
$78$		0			0
$79$	−19745.7	+	34200.6i	−0.355964	+	0.616547i	−0.987282	−	0.158976i	$-0.949181\pi$
$79$	−19745.7	+	34200.6i	−0.355964	+	0.616547i	0.631319	+	0.775523i	$0.282514\pi$
$80$	−50238.9	−	87016.3i	−0.877638	−	1.52011i
$81$		0			0
$82$	−1653.14	+	2863.33i	−0.0271504	+	0.0470259i
$83$	102372.			1.63112			0.815559	−	0.578675i	$-0.196430\pi$
$83$	102372.			1.63112			0.815559	+	0.578675i	$0.196430\pi$
$84$		0			0
$85$	−6580.60			−0.0987912
$86$	−2356.94	+	4082.34i	−0.0343639	+	0.0595201i
$87$		0			0
$88$	12470.6	+	21599.7i	0.171665	+	0.297332i
$89$	−56410.5	+	97705.8i	−0.754892	+	1.30751i	0.190536	+	0.981680i	$0.438977\pi$
$89$	−56410.5	+	97705.8i	−0.754892	+	1.30751i	−0.945428	+	0.325831i	$0.894356\pi$
$90$		0			0
$91$	1472.67	+	26737.2i	0.0186424	+	0.338464i
$92$	−6100.40			−0.0751430
$93$		0			0
$94$	−1735.71	−	3006.34i	−0.0202609	−	0.0350929i
$95$	−68972.6	−	119464.i	−0.784092	−	1.35809i
$96$		0			0
$97$	30334.3			0.327345			0.163672	−	0.986515i	$-0.447666\pi$
$97$	30334.3			0.327345			0.163672	+	0.986515i	$0.447666\pi$
$98$	5341.19	−	12170.6i	0.0561789	−	0.128011i
$99$		0			0
$100$	121277.	−	210058.i	1.21277	−	2.10058i
$101$	53398.2	+	92488.4i	0.520862	+	0.902160i	0.999706	+	0.0242599i	$0.00772291\pi$
$101$	53398.2	+	92488.4i	0.520862	+	0.902160i	−0.478843	+	0.877900i	$0.658944\pi$
$102$		0			0
$103$	−78767.8	+	136430.i	−0.731570	+	1.26712i	0.224643	+	0.974441i	$0.427879\pi$
$103$	−78767.8	+	136430.i	−0.731570	+	1.26712i	−0.956212	+	0.292674i	$0.905455\pi$
$104$	10351.7			0.0938490
$105$		0			0
$106$	−14064.3			−0.121578
$107$	−44662.2	+	77357.1i	−0.377121	+	0.653192i	−0.990642	−	0.136486i	$-0.956419\pi$
$107$	−44662.2	+	77357.1i	−0.377121	+	0.653192i	0.613521	+	0.789678i	$0.289752\pi$
$108$		0			0
$109$	−83802.3	−	145150.i	−0.675600	−	1.17017i	−0.976293	−	0.216452i	$-0.930551\pi$
$109$	−83802.3	−	145150.i	−0.675600	−	1.17017i	0.300693	−	0.953721i	$-0.402782\pi$
$110$	−20502.4	+	35511.2i	−0.161556	+	0.279823i
$111$		0			0
$112$	111545.	+	56461.3i	0.840244	+	0.425310i
$113$	115794.			0.853079			0.426539	−	0.904469i	$-0.359733\pi$
$113$	115794.			0.853079			0.426539	+	0.904469i	$0.359733\pi$
$114$		0			0
$115$	−10129.4	−	17544.6i	−0.0714230	−	0.123708i
$116$	−67818.4	−	117465.i	−0.467954	−	0.810519i
$117$		0			0
$118$	−2768.19			−0.0183017
$119$	6855.13	−	4477.78i	0.0443760	−	0.0289865i
$120$		0			0
$121$	−43307.1	+	75010.0i	−0.268903	+	0.465753i
$122$	4204.10	+	7281.72i	0.0255725	+	0.0442929i
$123$		0			0
$124$	−118052.	+	204472.i	−0.689476	+	1.19421i
$125$	479898.			2.74709
$126$		0			0
$127$	201513.			1.10865			0.554325	−	0.832300i	$-0.312977\pi$
$127$	201513.			1.10865			0.554325	+	0.832300i	$0.312977\pi$
$128$	49323.7	−	85431.2i	0.266091	−	0.460884i
$129$		0			0
$130$	8509.43	+	14738.8i	0.0441613	+	0.0764897i
$131$	19234.8	−	33315.6i	0.0979285	−	0.169617i	−0.812899	−	0.582405i	$-0.802112\pi$
$131$	19234.8	−	33315.6i	0.0979285	−	0.169617i	0.910827	+	0.412788i	$0.135445\pi$
$132$		0			0
$133$	153139.	+	77515.2i	0.750685	+	0.379977i
$134$	−10497.7			−0.0505049
$135$		0			0
$136$	−1582.66	−	2741.25i	−0.00733736	−	0.0127087i
$137$	−120861.	−	209337.i	−0.550155	−	0.952896i	−0.998263	−	0.0589167i	$-0.981235\pi$
$137$	−120861.	−	209337.i	−0.550155	−	0.952896i	0.448108	−	0.893979i	$-0.352098\pi$
$138$		0			0
$139$	−53112.2			−0.233162			−0.116581	−	0.993181i	$-0.537193\pi$
$139$	−53112.2			−0.233162			−0.116581	+	0.993181i	$0.537193\pi$
$140$	23307.1	+	423155.i	0.100501	+	1.82465i
$141$		0			0
$142$	15346.0	−	26580.1i	0.0638667	−	0.110620i
$143$	51396.1	+	89020.7i	0.210180	+	0.364042i
$144$		0			0
$145$	225218.	−	390088.i	0.889574	−	1.54079i
$146$	24812.0			0.0963340
$147$		0			0
$148$	−324905.			−1.21927
$149$	64531.0	−	111771.i	0.238124	−	0.412443i	−0.722052	−	0.691839i	$-0.756801\pi$
$149$	64531.0	−	111771.i	0.238124	−	0.412443i	0.960176	+	0.279396i	$0.0901342\pi$
$150$		0			0
$151$	−76603.2	−	132681.i	−0.273404	−	0.473549i	0.696327	−	0.717724i	$-0.254816\pi$
$151$	−76603.2	−	132681.i	−0.273404	−	0.473549i	−0.969731	+	0.244175i	$0.921483\pi$
$152$	33176.3	−	57463.0i	0.116471	−	0.201734i
$153$		0			0
$154$	−2805.94	−	50943.5i	−0.00953405	−	0.173096i
$155$	−784075.			−2.62137
$156$		0			0
$157$	75593.9	+	130932.i	0.244758	+	0.423934i	0.962064	−	0.272825i	$-0.0879581\pi$
$157$	75593.9	+	130932.i	0.244758	+	0.423934i	−0.717305	+	0.696759i	$0.754625\pi$
$158$	−15615.0	−	27046.0i	−0.0497622	−	0.0861907i
$159$		0			0
$160$	246555.			0.761402
$161$	22490.2	+	11384.0i	0.0683799	+	0.0346122i
$162$		0			0
$163$	16458.3	−	28506.7i	0.0485196	−	0.0840384i	−0.840746	−	0.541430i	$-0.817883\pi$
$163$	16458.3	−	28506.7i	0.0485196	−	0.0840384i	0.889265	+	0.457392i	$0.151216\pi$
$164$	65587.3	+	113601.i	0.190419	+	0.329816i
$165$		0			0
$166$	−40478.1	+	70110.1i	−0.114012	+	0.197474i
$167$	−217586.			−0.603725			−0.301862	−	0.953352i	$-0.597608\pi$
$167$	−217586.			−0.603725			−0.301862	+	0.953352i	$0.597608\pi$
$168$		0			0
$169$	−328630.			−0.885095
$170$	2601.99	−	4506.77i	0.00690530	−	0.0119603i
$171$		0			0
$172$	93510.0	+	161964.i	0.241011	+	0.417443i
$173$	−210621.	+	364807.i	−0.535041	+	0.926718i	0.464121	+	0.885772i	$0.346370\pi$
$173$	−210621.	+	364807.i	−0.535041	+	0.926718i	−0.999161	+	0.0409458i	$0.986963\pi$
$174$		0			0
$175$	−839100.	+	548101.i	−2.07118	+	1.35290i
$176$	479921.			1.16785
$177$		0			0
$178$	−44609.7	−	77266.3i	−0.105531	−	0.182785i
$179$	1747.03	+	3025.94i	0.00407538	+	0.00705876i	0.868056	−	0.496466i	$-0.165369\pi$
$179$	1747.03	+	3025.94i	0.00407538	+	0.00705876i	−0.863981	+	0.503525i	$0.832036\pi$
$180$		0			0
$181$	594611.			1.34908			0.674538	−	0.738240i	$-0.264343\pi$
$181$	594611.			1.34908			0.674538	+	0.738240i	$0.264343\pi$
$182$	−18893.4	−	9563.37i	−0.0422798	−	0.0214009i
$183$		0			0
$184$	4872.30	−	8439.08i	0.0106094	−	0.0183760i
$185$	−539486.	−	934418.i	−1.15891	−	2.00730i
$186$		0			0
$187$	15715.7	−	27220.5i	0.0328648	−	0.0569235i
$188$	−137726.			−0.284199
$189$		0			0
$190$	109088.			0.219226
$191$	414322.	−	717627.i	0.821778	−	1.42336i	−0.0825782	−	0.996585i	$-0.526315\pi$
$191$	414322.	−	717627.i	0.821778	−	1.42336i	0.904357	−	0.426777i	$-0.140351\pi$
$192$		0			0
$193$	−109869.	−	190299.i	−0.212316	−	0.367743i	0.740123	−	0.672472i	$-0.234767\pi$
$193$	−109869.	−	190299.i	−0.212316	−	0.367743i	−0.952439	+	0.304729i	$0.901434\pi$
$194$	−11994.3	+	20774.7i	−0.0228807	+	0.0396306i
$195$		0			0
$196$	−312216.	−	424948.i	−0.580516	−	0.790125i
$197$	−475612.			−0.873146			−0.436573	−	0.899669i	$-0.643808\pi$
$197$	−475612.			−0.873146			−0.436573	+	0.899669i	$0.643808\pi$
$198$		0			0
$199$	−313778.	−	543479.i	−0.561681	−	0.972859i	−0.997350	−	0.0727525i	$-0.976822\pi$
$199$	−313778.	−	543479.i	−0.561681	−	0.972859i	0.435669	−	0.900107i	$-0.356512\pi$
$200$	193725.	+	335541.i	0.342460	+	0.593159i
$201$		0			0
$202$	−84455.1			−0.145629
$203$	30823.1	+	559611.i	0.0524972	+	0.953117i
$204$		0			0
$205$	−217808.	+	377255.i	−0.361984	+	0.626975i
$206$	−62290.0	−	107889.i	−0.102270	−	0.177138i
$207$		0			0
$208$	99594.5	−	172503.i	0.159616	−	0.276463i
$209$	658879.			1.04337
$210$		0			0
$211$	570989.			0.882920			0.441460	−	0.897281i	$-0.354461\pi$
$211$	570989.			0.882920			0.441460	+	0.897281i	$0.354461\pi$
$212$	−278995.	+	483234.i	−0.426341	+	0.738445i
$213$		0			0
$214$	−35319.1	−	61174.4i	−0.0527199	−	0.0913136i
$215$	−310536.	+	537865.i	−0.458159	+	0.793555i
$216$		0			0
$217$	816785.	−	533525.i	1.17749	−	0.769140i
$218$	132543.			0.188892
$219$		0			0
$220$	813419.	+	1.40888e6i	1.13307	+	1.96254i
$221$	−6522.75	−	11297.7i	−0.00898359	−	0.0155600i
$222$		0			0
$223$	4233.11			0.00570029			0.00285015	−	0.999996i	$-0.499093\pi$
$223$	4233.11			0.00570029			0.00285015	+	0.999996i	$0.499093\pi$
$224$	−256841.	+	167769.i	−0.342014	+	0.223404i
$225$		0			0
$226$	−45785.2	+	79302.2i	−0.0596285	+	0.103280i
$227$	564931.	+	978490.i	0.727664	+	1.26035i	0.957868	+	0.287209i	$0.0927274\pi$
$227$	564931.	+	978490.i	0.727664	+	1.26035i	−0.230204	+	0.973142i	$0.573939\pi$
$228$		0			0
$229$	−402322.	+	696842.i	−0.506973	+	0.878103i	0.492994	+	0.870032i	$0.335902\pi$
$229$	−402322.	+	696842.i	−0.506973	+	0.878103i	−0.999967	+	0.00807048i	$0.997431\pi$
$230$	16020.7			0.0199693
$231$		0			0
$232$	216663.			0.264280
$233$	584636.	−	1.01262e6i	0.705498	−	1.22196i	−0.261013	−	0.965335i	$-0.584057\pi$
$233$	584636.	−	1.01262e6i	0.705498	−	1.22196i	0.966511	−	0.256624i	$-0.0826101\pi$
$234$		0			0
$235$	−228687.	−	396098.i	−0.270130	−	0.467878i
$236$	−54912.9	+	95112.0i	−0.0641792	+	0.111162i
$237$		0			0
$238$	356.106	+	6465.31i	0.000407508	+	0.00739855i
$239$	1.70554e6			1.93138			0.965689	−	0.259700i	$-0.0836238\pi$
$239$	1.70554e6			1.93138			0.965689	+	0.259700i	$0.0836238\pi$
$240$		0			0
$241$	−475598.	−	823760.i	−0.527470	−	0.913604i	−0.999487	−	0.0320153i	$-0.989807\pi$
$241$	−475598.	−	823760.i	−0.527470	−	0.913604i	0.472018	−	0.881589i	$-0.343526\pi$
$242$	−34247.4	−	59318.3i	−0.0375915	−	0.0651104i
$243$		0			0
$244$	333590.			0.358705
$245$	703723.	−	1.60353e6i	0.749008	−	1.70672i
$246$		0			0
$247$	136732.	−	236827.i	0.142603	−	0.246996i
$248$	−188573.	−	326618.i	−0.194693	−	0.337218i
$249$		0			0
$250$	−189753.	+	328661.i	−0.192016	+	0.332582i
$251$	−1.14498e6			−1.14713			−0.573566	−	0.819159i	$-0.694440\pi$
$251$	−1.14498e6			−1.14713			−0.573566	+	0.819159i	$0.694440\pi$
$252$		0			0
$253$	96763.6			0.0950409
$254$	−79678.8	+	138008.i	−0.0774923	+	0.134221i
$255$		0			0
$256$	−424803.	−	735781.i	−0.405124	−	0.701695i
$257$	591869.	−	1.02515e6i	0.558976	−	0.968175i	−0.438606	−	0.898679i	$-0.644528\pi$
$257$	591869.	−	1.02515e6i	0.558976	−	0.968175i	0.997582	−	0.0694955i	$-0.0221389\pi$
$258$		0			0
$259$	1.19782e6	+	606305.i	1.10954	+	0.561619i
$260$	675211.			0.619450
$261$		0			0
$262$	15211.0	+	26346.2i	0.0136900	+	0.0237118i
$263$	224158.	+	388253.i	0.199832	+	0.346119i	0.948474	−	0.316856i	$-0.102627\pi$
$263$	224158.	+	388253.i	0.199832	+	0.346119i	−0.748642	+	0.662975i	$0.769294\pi$
$264$		0			0
$265$	−1.85303e6			−1.62094
$266$	−113639.	+	74228.9i	−0.0984740	+	0.0643234i
$267$		0			0
$268$	−208245.	+	360691.i	−0.177108	+	0.306760i
$269$	373737.	+	647332.i	0.314909	+	0.545439i	0.979418	−	0.201841i	$-0.0646925\pi$
$269$	373737.	+	647332.i	0.314909	+	0.545439i	−0.664509	+	0.747280i	$0.731359\pi$
$270$		0			0
$271$	116319.	−	201470.i	0.0962114	−	0.166643i	−0.813902	−	0.581002i	$-0.802661\pi$
$271$	116319.	−	201470.i	0.0962114	−	0.166643i	0.910114	+	0.414359i	$0.135994\pi$
$272$	−60907.3			−0.0499169
$273$		0			0
$274$	191155.			0.153819
$275$	−1.92368e6	+	3.33191e6i	−1.53391	+	2.65682i
$276$		0			0
$277$	1.21462e6	+	2.10379e6i	0.951134	+	1.64741i	0.742977	+	0.669317i	$0.233413\pi$
$277$	1.21462e6	+	2.10379e6i	0.951134	+	1.64741i	0.208157	+	0.978095i	$0.433253\pi$
$278$	21000.7	−	36374.3i	0.0162975	−	0.0282282i
$279$		0			0
$280$	−603992.	−	305725.i	−0.460401	−	0.233043i
$281$	−2.51704e6			−1.90163			−0.950813	−	0.309766i	$-0.899749\pi$
$281$	−2.51704e6			−1.90163			−0.950813	+	0.309766i	$0.899749\pi$
$282$		0			0
$283$	−130497.	−	226028.i	−0.0968579	−	0.167763i	0.813525	−	0.581530i	$-0.197546\pi$
$283$	−130497.	−	226028.i	−0.0968579	−	0.167763i	−0.910382	+	0.413768i	$0.864213\pi$
$284$	−608842.	−	1.05454e6i	−0.447928	−	0.775835i
$285$		0			0
$286$	−81288.6			−0.0587645
$287$	−29809.1	−	541201.i	−0.0213621	−	0.387841i
$288$		0			0
$289$	707934.	−	1.22618e6i	0.498595	−	0.863592i
$290$	178103.	+	308484.i	0.124359	+	0.215396i
$291$		0			0
$292$	492199.	−	852514.i	0.337819	−	0.585119i
$293$	−65011.7			−0.0442408			−0.0221204	−	0.999755i	$-0.507042\pi$
$293$	−65011.7			−0.0442408			−0.0221204	+	0.999755i	$0.507042\pi$
$294$		0			0
$295$	−364720.			−0.244008
$296$	259497.	−	449462.i	0.172148	−	0.298170i
$297$		0			0
$298$	51031.5	+	88389.1i	0.0332887	+	0.0576578i
$299$	20080.6	−	34780.7i	0.0129897	−	0.0224989i
$300$		0			0
$301$	−42499.8	−	771608.i	−0.0270377	−	0.490886i
$302$	121156.			0.0764414
$303$		0			0
$304$	−638381.	−	1.10571e6i	−0.396183	−	0.686210i
$305$	553907.	+	959395.i	0.340947	+	0.590538i
$306$		0			0
$307$	−2.35599e6			−1.42668			−0.713342	−	0.700816i	$-0.752819\pi$
$307$	−2.35599e6			−1.42668			−0.713342	+	0.700816i	$0.752819\pi$
$308$	−1.80603e6	−	914165.i	−1.08480	−	0.549096i
$309$		0			0
$310$	310025.	−	536980.i	0.183228	−	0.317361i
$311$	−1.05903e6	−	1.83429e6i	−0.620878	−	1.07539i	−0.989323	−	0.145742i	$-0.953443\pi$
$311$	−1.05903e6	−	1.83429e6i	−0.620878	−	1.07539i	0.368445	−	0.929650i	$-0.379890\pi$
$312$		0			0
$313$	93756.8	−	162392.i	0.0540931	−	0.0936920i	−0.837711	−	0.546114i	$-0.816107\pi$
$313$	93756.8	−	162392.i	0.0540931	−	0.0936920i	0.891804	+	0.452422i	$0.149440\pi$
$314$	−119560.			−0.0684324
$315$		0			0
$316$	−1.23903e6			−0.698014
$317$	−502705.	+	870711.i	−0.280974	+	0.486661i	−0.971625	−	0.236527i	$-0.923991\pi$
$317$	−502705.	+	870711.i	−0.280974	+	0.486661i	0.690651	+	0.723188i	$0.257324\pi$
$318$		0			0
$319$	1.07573e6	+	1.86321e6i	0.591868	+	1.02515i
$320$	1.51016e6	−	2.61567e6i	0.824417	−	1.42793i
$321$		0			0
$322$	−16689.1	+	10901.3i	−0.00897000	+	0.00585922i
$323$	−83619.1			−0.0445964
$324$		0			0
$325$	798415.	+	1.38290e6i	0.419296	+	0.726241i
$326$	13015.3	+	22543.2i	0.00678284	+	0.0117482i
$327$		0			0
$328$	−209535.			−0.107540
$329$	507753.	+	257011.i	0.258620	+	0.130907i
$330$		0			0
$331$	−839920.	+	1.45478e6i	−0.421374	+	0.729841i	−0.996074	−	0.0885229i	$-0.971785\pi$
$331$	−839920.	+	1.45478e6i	−0.421374	+	0.729841i	0.574700	+	0.818364i	$0.305119\pi$
$332$	1.60594e6	+	2.78157e6i	0.799620	+	1.38498i
$333$		0			0
$334$	86033.9	−	149015.i	0.0421991	−	0.0730910i
$335$	−1.38312e6			−0.673360
$336$		0			0
$337$	−995036.			−0.477270			−0.238635	−	0.971109i	$-0.576700\pi$
$337$	−995036.			−0.477270			−0.238635	+	0.971109i	$0.576700\pi$
$338$	129941.	−	225064.i	0.0618663	−	0.107156i
$339$		0			0
$340$	−103232.	−	178803.i	−0.0484303	−	0.0838837i
$341$	1.87252e6	−	3.24330e6i	0.872049	−	1.51043i
$342$		0			0
$343$	358042.	+	2.14927e6i	0.164323	+	0.986407i
$344$	−298741.			−0.136113
$345$		0			0
$346$	−166560.	−	288491.i	−0.0747965	−	0.129551i
$347$	2.02833e6	+	3.51317e6i	0.904304	+	1.56630i	0.821849	+	0.569705i	$0.192943\pi$
$347$	2.02833e6	+	3.51317e6i	0.904304	+	1.56630i	0.0824546	+	0.996595i	$0.473724\pi$
$348$		0			0
$349$	2.86202e6			1.25779			0.628897	−	0.777488i	$-0.283507\pi$
$349$	2.86202e6			1.25779			0.628897	+	0.777488i	$0.283507\pi$
$350$	−43589.0	−	791384.i	−0.0190198	−	0.345316i
$351$		0			0
$352$	−588821.	+	1.01987e6i	−0.253295	+	0.438720i
$353$	416343.	+	721126.i	0.177834	+	0.308017i	0.941138	−	0.338022i	$-0.109758\pi$
$353$	416343.	+	721126.i	0.177834	+	0.308017i	−0.763305	+	0.646039i	$0.776424\pi$
$354$		0			0
$355$	2.02190e6	−	3.50203e6i	0.851507	−	1.47485i
$356$	−3.53972e6			−1.48028
$357$		0			0
$358$	−2763.12			−0.00113944
$359$	−1.34875e6	+	2.33611e6i	−0.552327	+	0.956659i	0.445779	+	0.895143i	$0.352927\pi$
$359$	−1.34875e6	+	2.33611e6i	−0.552327	+	0.956659i	−0.998106	+	0.0615157i	$0.980407\pi$
$360$		0			0
$361$	361621.	+	626346.i	0.146045	+	0.252957i
$362$	−235110.	+	407223.i	−0.0942976	+	0.163328i
$363$		0			0
$364$	−703379.	+	459449.i	−0.278251	+	0.181754i
$365$	3.26908e6			1.28438
$366$		0			0
$367$	−727411.	−	1.25991e6i	−0.281913	−	0.488287i	0.689943	−	0.723864i	$-0.257636\pi$
$367$	−727411.	−	1.25991e6i	−0.281913	−	0.488287i	−0.971856	+	0.235576i	$0.924302\pi$
$368$	−93753.3	−	162386.i	−0.0360884	−	0.0625069i
$369$		0			0
$370$	853257.			0.324023
$371$	1.93033e6	−	1.26089e6i	0.728110	−	0.475602i
$372$		0			0
$373$	1.02344e6	−	1.77265e6i	0.380883	−	0.659708i	−0.610306	−	0.792166i	$-0.708953\pi$
$373$	1.02344e6	−	1.77265e6i	0.380883	−	0.659708i	0.991189	+	0.132457i	$0.0422868\pi$
$374$	12428.1	+	21526.1i	0.00459436	+	0.00795767i
$375$		0			0
$376$	110000.	−	190526.i	0.0401258	−	0.0694999i
$377$	892950.			0.323574
$378$		0			0
$379$	−416898.			−0.149084			−0.0745421	−	0.997218i	$-0.523750\pi$
$379$	−416898.			−0.149084			−0.0745421	+	0.997218i	$0.523750\pi$
$380$	2.16399e6	−	3.74814e6i	0.768769	−	1.33155i
$381$		0			0
$382$	327648.	+	567503.i	0.114881	+	0.198980i
$383$	−1.93813e6	+	3.35694e6i	−0.675127	+	1.16935i	0.301305	+	0.953528i	$0.402578\pi$
$383$	−1.93813e6	+	3.35694e6i	−0.675127	+	1.16935i	−0.976432	+	0.215827i	$0.930755\pi$
$384$		0			0
$385$	−369694.	−	6.71201e6i	−0.127113	−	2.30782i
$386$	173771.			0.0593619
$387$		0			0
$388$	475864.	+	824221.i	0.160474	+	0.277949i
$389$	1.41901e6	+	2.45780e6i	0.475458	+	0.823517i	0.999605	−	0.0281111i	$-0.00894921\pi$
$389$	1.41901e6	+	2.45780e6i	0.475458	+	0.823517i	−0.524147	+	0.851628i	$0.675616\pi$
$390$		0			0
$391$	−12280.4			−0.00406228
$392$	837221.	−	92508.0i	0.275185	−	0.0304063i
$393$		0			0
$394$	188058.	−	325726.i	0.0610311	−	0.105709i
$395$	−2.05734e6	−	3.56342e6i	−0.663458	−	1.14914i
$396$		0			0
$397$	−2.17133e6	+	3.76085e6i	−0.691432	+	1.19760i	0.279937	+	0.960018i	$0.409686\pi$
$397$	−2.17133e6	+	3.76085e6i	−0.691432	+	1.19760i	−0.971369	+	0.237577i	$0.923647\pi$
$398$	496274.			0.157041
$399$		0			0
$400$	7.45534e6			2.32979
$401$	1.70152e6	−	2.94712e6i	0.528417	−	0.915244i	−0.471034	−	0.882115i	$-0.656119\pi$
$401$	1.70152e6	−	2.94712e6i	0.528417	−	0.915244i	0.999451	−	0.0331296i	$-0.0105474\pi$
$402$		0			0
$403$	−777182.	−	1.34612e6i	−0.238375	−	0.412877i
$404$	−1.67535e6	+	2.90179e6i	−0.510683	+	0.884529i
$405$		0			0
$406$	−395441.	−	200162.i	−0.119060	−	0.0602653i
$407$	5.15359e6			1.54214
$408$		0			0
$409$	2.64716e6	+	4.58501e6i	0.782477	+	1.35529i	0.930495	+	0.366305i	$0.119377\pi$
$409$	2.64716e6	+	4.58501e6i	0.782477	+	1.35529i	−0.148018	+	0.988985i	$0.547289\pi$
$410$	−172244.	−	298335.i	−0.0506039	−	0.0876486i
$411$		0			0
$412$	−4.94262e6			−1.43455
$413$	379935.	−	248174.i	0.109606	−	0.0715947i
$414$		0			0
$415$	−5.33315e6	+	9.23728e6i	−1.52007	+	2.63284i
$416$	244387.	+	423291.i	0.0692382	+	0.119924i
$417$		0			0
$418$	−260522.	+	451238.i	−0.0729297	+	0.126318i
$419$	−2.87267e6			−0.799376			−0.399688	−	0.916651i	$-0.630881\pi$
$419$	−2.87267e6			−0.799376			−0.399688	+	0.916651i	$0.630881\pi$
$420$		0			0
$421$	2.08688e6			0.573843			0.286921	−	0.957954i	$-0.407368\pi$
$421$	2.08688e6			0.573843			0.286921	+	0.957954i	$0.407368\pi$
$422$	−225770.	+	391046.i	−0.0617143	+	0.106892i
$423$		0			0
$424$	−445660.	−	771905.i	−0.120390	−	0.208521i
$425$	244137.	−	422857.i	0.0655633	−	0.113559i
$426$		0			0
$427$	−1.22984e6	−	622512.i	−0.326421	−	0.165226i
$428$	−2.80252e6			−0.739501
$429$		0			0
$430$	−245574.	−	425346.i	−0.0640488	−	0.110936i
$431$	−1.21432e6	−	2.10326e6i	−0.314876	−	0.545380i	0.664535	−	0.747257i	$-0.268629\pi$
$431$	−1.21432e6	−	2.10326e6i	−0.314876	−	0.545380i	−0.979411	+	0.201876i	$0.935296\pi$
$432$		0			0
$433$	956219.			0.245097			0.122548	−	0.992463i	$-0.460893\pi$
$433$	956219.			0.245097			0.122548	+	0.992463i	$0.460893\pi$
$434$	42429.8	+	770338.i	0.0108130	+	0.196317i
$435$		0			0
$436$	2.62927e6	−	4.55402e6i	0.662397	−	1.14730i
$437$	−128713.	−	222938.i	−0.0322418	−	0.0558444i
$438$		0			0
$439$	−1.32102e6	+	2.28808e6i	−0.327152	+	0.566644i	−0.981946	−	0.189164i	$-0.939422\pi$
$439$	−1.32102e6	+	2.28808e6i	−0.327152	+	0.566644i	0.654794	+	0.755808i	$0.272756\pi$
$440$	−2.59867e6			−0.639910
$441$		0			0
$442$	10316.4			0.00251174
$443$	−1.71983e6	+	2.97883e6i	−0.416366	+	0.721168i	−0.995571	−	0.0940147i	$-0.970030\pi$
$443$	−1.71983e6	+	2.97883e6i	−0.416366	+	0.721168i	0.579205	+	0.815182i	$0.303363\pi$
$444$		0			0
$445$	−5.87750e6	−	1.01801e7i	−1.40700	−	2.43699i
$446$	−1673.78	+	2899.07i	−0.000398439	+	0.000690116i
$447$		0			0
$448$	206679.	+	3.75237e6i	0.0486520	+	0.883306i
$449$	−4.39903e6			−1.02977			−0.514886	−	0.857259i	$-0.672166\pi$
$449$	−4.39903e6			−1.02977			−0.514886	+	0.857259i	$0.672166\pi$
$450$		0			0
$451$	−1.04034e6	−	1.80192e6i	−0.240842	−	0.417151i
$452$	1.81649e6	+	3.14626e6i	0.418204	+	0.724350i
$453$		0			0
$454$	−893501.			−0.203449
$455$	−2.48929e6	−	1.26001e6i	−0.563698	−	0.285329i
$456$		0			0
$457$	1.12555e6	−	1.94951e6i	0.252101	−	0.436652i	−0.712003	−	0.702176i	$-0.752212\pi$
$457$	1.12555e6	−	1.94951e6i	0.252101	−	0.436652i	0.964104	+	0.265524i	$0.0855451\pi$
$458$	−318158.	−	551066.i	−0.0708727	−	0.122755i
$459$		0			0
$460$	317805.	−	550455.i	0.0700272	−	0.121291i
$461$	−1.85307e6			−0.406107			−0.203053	−	0.979168i	$-0.565087\pi$
$461$	−1.85307e6			−0.406107			−0.203053	+	0.979168i	$0.565087\pi$
$462$		0			0
$463$	−3.01089e6			−0.652744			−0.326372	−	0.945241i	$-0.605826\pi$
$463$	−3.01089e6			−0.652744			−0.326372	+	0.945241i	$0.605826\pi$
$464$	2.08452e6	−	3.61050e6i	0.449481	−	0.778524i
$465$		0			0
$466$	462333.	+	800785.i	0.0986258	+	0.170825i
$467$	−533627.	+	924270.i	−0.113226	+	0.196113i	−0.917069	−	0.398728i	$-0.869452\pi$
$467$	−533627.	+	924270.i	−0.113226	+	0.196113i	0.803843	+	0.594841i	$0.202785\pi$
$468$		0			0
$469$	1.44082e6	−	941145.i	0.302466	−	0.197572i
$470$	361694.			0.0755260
$471$		0			0
$472$	−87716.4	−	151929.i	−0.0181228	−	0.0313896i
$473$	−1.48324e6	−	2.56905e6i	−0.304831	−	0.527983i
$474$		0			0
$475$	1.02354e7			2.08147
$476$	229205.	+	116018.i	0.0463668	+	0.0234697i
$477$		0			0
$478$	−674375.	+	1.16805e6i	−0.134999	+	0.233826i
$479$	−2.84394e6	−	4.92585e6i	−0.566346	−	0.980939i	−0.996923	−	0.0783858i	$-0.975023\pi$
$479$	−2.84394e6	−	4.92585e6i	−0.566346	−	0.980939i	0.430577	−	0.902554i	$-0.358310\pi$
$480$		0			0
$481$	1.06949e6	−	1.85240e6i	0.210772	−	0.365068i
$482$	752211.			0.147476
$483$		0			0
$484$	−2.71749e6			−0.527295
$485$	−1.58029e6	+	2.73715e6i	−0.305059	+	0.528377i
$486$		0			0
$487$	3.42239e6	+	5.92775e6i	0.653893	+	1.13258i	0.982170	+	0.187995i	$0.0601987\pi$
$487$	3.42239e6	+	5.92775e6i	0.653893	+	1.13258i	−0.328277	+	0.944582i	$0.606468\pi$
$488$	−266433.	+	461476.i	−0.0506453	+	0.0877202i
$489$		0			0
$490$	819933.	+	1.11599e6i	0.154272	+	0.209976i
$491$	−5.60132e6			−1.04854			−0.524272	−	0.851551i	$-0.675662\pi$
$491$	−5.60132e6			−1.04854			−0.524272	+	0.851551i	$0.675662\pi$
$492$		0			0
$493$	−136522.	−	236462.i	−0.0252979	−	0.0438172i
$494$	108129.	+	187284.i	0.0199353	+	0.0345290i
$495$		0			0
$496$	−7.25708e6			−1.32452
$497$	276715.	+	5.02392e6i	0.0502507	+	0.912330i
$498$		0			0
$499$	1.16764e6	−	2.02242e6i	0.209923	−	0.363596i	−0.741767	−	0.670657i	$-0.766012\pi$
$499$	1.16764e6	−	2.02242e6i	0.209923	−	0.363596i	0.951690	+	0.307061i	$0.0993455\pi$
$500$	7.52830e6	+	1.30394e7i	1.34670	+	2.33256i
$501$		0			0
$502$	452728.	−	784147.i	0.0801822	−	0.138880i
$503$	1.08278e7			1.90819			0.954093	−	0.299510i	$-0.0968233\pi$
$503$	1.08278e7			1.90819			0.954093	+	0.299510i	$0.0968233\pi$
$504$		0			0
$505$	−1.11273e7			−1.94161
$506$	−38260.6	+	66269.3i	−0.00664317	+	0.0115063i
$507$		0			0
$508$	3.16120e6	+	5.47536e6i	0.543492	+	0.941355i
$509$	1.58924e6	−	2.75264e6i	0.271890	−	0.470928i	−0.697455	−	0.716628i	$-0.745684\pi$
$509$	1.58924e6	−	2.75264e6i	0.271890	−	0.470928i	0.969346	+	0.245700i	$0.0790178\pi$
$510$		0			0
$511$	−3.40546e6	+	2.22445e6i	−0.576930	+	0.376852i
$512$	3.82859e6			0.645452
$513$		0			0
$514$	468053.	+	810692.i	0.0781425	+	0.135347i
$515$	−8.20695e6	−	1.42149e7i	−1.36353	−	2.36170i
$516$		0			0
$517$	2.18460e6			0.359455
$518$	−888852.	+	580600.i	−0.145548	+	0.0950720i
$519$		0			0
$520$	−539282.	+	934064.i	−0.0874596	+	0.151485i
$521$	−3.17918e6	−	5.50651e6i	−0.513123	−	0.888755i	−0.999884	−	0.0152197i	$-0.995155\pi$
$521$	−3.17918e6	−	5.50651e6i	−0.513123	−	0.888755i	0.486761	−	0.873535i	$-0.338178\pi$
$522$		0			0
$523$	3.61094e6	−	6.25433e6i	0.577252	−	0.999830i	−0.418541	−	0.908198i	$-0.637458\pi$
$523$	3.61094e6	−	6.25433e6i	0.577252	−	0.999830i	0.995793	−	0.0916321i	$-0.0292084\pi$
$524$	1.20697e6			0.192029
$525$		0			0
$526$	−354531.			−0.0558714
$527$	−237644.	+	411612.i	−0.0372735	+	0.0645597i
$528$		0			0
$529$	3.19927e6	+	5.54130e6i	0.497063	+	0.860939i
$530$	732691.	−	1.26906e6i	0.113300	−	0.196242i
$531$		0			0
$532$	296162.	+	5.37699e6i	0.0453680	+	0.823683i
$533$	−863574.			−0.131668
$534$		0			0
$535$	−4.65343e6	−	8.05997e6i	−0.702892	−	1.21744i
$536$	−332645.	−	576158.i	−0.0500114	−	0.0866223i
$537$		0			0
$538$	−591106.			−0.0880461
$539$	4.95232e6	+	6.74046e6i	0.734237	+	0.999350i
$540$		0			0
$541$	4.71583e6	−	8.16805e6i	0.692731	−	1.19985i	−0.278209	−	0.960521i	$-0.589741\pi$
$541$	4.71583e6	−	8.16805e6i	0.692731	−	1.19985i	0.970940	−	0.239325i	$-0.0769260\pi$
$542$	91985.4	+	159323.i	0.0134500	+	0.0232960i
$543$		0			0
$544$	74728.0	−	129433.i	0.0108264	−	0.0187520i
$545$	1.74630e7			2.51842
$546$		0			0
$547$	9.91568e6			1.41695			0.708474	−	0.705737i	$-0.249384\pi$
$547$	9.91568e6			1.41695			0.708474	+	0.705737i	$0.249384\pi$
$548$	3.79197e6	−	6.56788e6i	0.539403	−	0.934274i
$549$		0			0
$550$	−1.52126e6	−	2.63489e6i	−0.214435	−	0.371412i
$551$	2.86182e6	−	4.95682e6i	0.401572	−	0.695543i
$552$		0			0
$553$	4.56790e6	+	2.31216e6i	0.635191	+	0.321517i
$554$	−1.92106e6			−0.265929
$555$		0			0
$556$	−833188.	−	1.44312e6i	−0.114303	−	0.197978i
$557$	4.82306e6	+	8.35379e6i	0.658696	+	1.14089i	0.980953	+	0.194243i	$0.0622249\pi$
$557$	4.82306e6	+	8.35379e6i	0.658696	+	1.14089i	−0.322258	+	0.946652i	$0.604442\pi$
$558$		0			0
$559$	−1.23123e6			−0.166651
$560$	−1.09057e7	+	7.12362e6i	−1.46955	+	0.959910i
$561$		0			0
$562$	995245.	−	1.72382e6i	0.132920	−	0.230224i
$563$	1.54752e6	+	2.68038e6i	0.205762	+	0.356390i	0.950375	−	0.311106i	$-0.100699\pi$
$563$	1.54752e6	+	2.68038e6i	0.205762	+	0.356390i	−0.744613	+	0.667496i	$0.767366\pi$
$564$		0			0
$565$	−6.03238e6	+	1.04484e7i	−0.795000	+	1.37698i
$566$	206396.			0.0270807
$567$		0			0
$568$	1.94509e6			0.252970
$569$	−6.15927e6	+	1.06682e7i	−0.797533	+	1.38137i	0.123685	+	0.992322i	$0.460529\pi$
$569$	−6.15927e6	+	1.06682e7i	−0.797533	+	1.38137i	−0.921218	+	0.389046i	$0.872805\pi$
$570$		0			0
$571$	1.61755e6	+	2.80168e6i	0.207619	+	0.359607i	0.950964	−	0.309302i	$-0.100095\pi$
$571$	1.61755e6	+	2.80168e6i	0.207619	+	0.359607i	−0.743345	+	0.668908i	$0.766762\pi$
$572$	−1.61253e6	+	2.79299e6i	−0.206072	+	0.356927i
$573$		0			0
$574$	382432.	+	193577.i	0.0484479	+	0.0245231i
$575$	1.50318e6			0.189601
$576$		0			0
$577$	4.52525e6	+	7.83796e6i	0.565852	+	0.980084i	0.996970	+	0.0777887i	$0.0247859\pi$
$577$	4.52525e6	+	7.83796e6i	0.565852	+	0.980084i	−0.431118	+	0.902296i	$0.641881\pi$
$578$	559838.	+	969667.i	0.0697016	+	0.120727i
$579$		0			0
$580$	1.41322e7			1.74438
$581$	−729890.	−	1.32516e7i	−0.0897051	−	1.62865i
$582$		0			0
$583$	4.42538e6	−	7.66499e6i	0.539237	−	0.933986i
$584$	786226.	+	1.36178e6i	0.0953927	+	0.165225i
$585$		0			0
$586$	25705.8	−	44523.8i	0.00309234	−	0.00535609i
$587$	2.13170e6			0.255347			0.127673	−	0.991816i	$-0.459249\pi$
$587$	2.13170e6			0.255347			0.127673	+	0.991816i	$0.459249\pi$
$588$		0			0
$589$	−9.96318e6			−1.18334
$590$	144211.	−	249781.i	0.0170557	−	0.0295413i
$591$		0			0
$592$	−4.99326e6	−	8.64858e6i	−0.585572	−	1.01424i
$593$	−3.63467e6	+	6.29543e6i	−0.424451	+	0.735171i	−0.996369	−	0.0851397i	$-0.972866\pi$
$593$	−3.63467e6	+	6.29543e6i	−0.424451	+	0.735171i	0.571918	+	0.820311i	$0.306200\pi$
$594$		0			0
$595$	46918.4	+	851830.i	0.00543313	+	0.0986417i
$596$	4.04927e6			0.466941
$597$		0			0
$598$	15879.9	+	27504.8i	0.00181591	+	0.00314525i
$599$	−1.10282e6	−	1.91015e6i	−0.125585	−	0.217520i	0.796376	−	0.604802i	$-0.206748\pi$
$599$	−1.10282e6	−	1.91015e6i	−0.125585	−	0.217520i	−0.921962	+	0.387281i	$0.873414\pi$
$600$		0			0
$601$	−1.00121e7			−1.13067			−0.565336	−	0.824860i	$-0.691254\pi$
$601$	−1.00121e7			−1.13067			−0.565336	+	0.824860i	$0.691254\pi$
$602$	545246.	+	275990.i	0.0613199	+	0.0310385i
$603$		0			0
$604$	2.40340e6	−	4.16280e6i	0.268061	−	0.464295i
$605$	−4.51224e6	−	7.81542e6i	−0.501191	−	0.868088i
$606$		0			0
$607$	−3.16069e6	+	5.47448e6i	−0.348185	+	0.603075i	−0.985927	−	0.167175i	$-0.946535\pi$
$607$	−3.16069e6	+	5.47448e6i	−0.348185	+	0.603075i	0.637742	+	0.770250i	$0.279869\pi$
$608$	3.13295e6			0.343712
$609$		0			0
$610$	−876065.			−0.0953261
$611$	453353.	−	785231.i	0.0491285	−	0.0850931i
$612$		0			0
$613$	−7.15392e6	−	1.23910e7i	−0.768941	−	1.33185i	−0.938138	−	0.346263i	$-0.887451\pi$
$613$	−7.15392e6	−	1.23910e7i	−0.768941	−	1.33185i	0.169196	−	0.985582i	$-0.445883\pi$
$614$	931565.	−	1.61352e6i	0.0997223	−	0.172724i
$615$		0			0
$616$	2.70707e6	−	1.76827e6i	0.287441	−	0.187757i
$617$	−1.73991e7			−1.83999			−0.919993	−	0.391936i	$-0.871806\pi$
$617$	−1.73991e7			−1.83999			−0.919993	+	0.391936i	$0.871806\pi$
$618$		0			0
$619$	−4.13368e6	−	7.15975e6i	−0.433621	−	0.751054i	0.563561	−	0.826074i	$-0.309431\pi$
$619$	−4.13368e6	−	7.15975e6i	−0.433621	−	0.751054i	−0.997182	+	0.0750208i	$0.976098\pi$
$620$	−1.23000e7	−	2.13043e7i	−1.28507	−	2.22581i
$621$		0			0
$622$	1.67497e6			0.173592
$623$	1.30498e7	+	6.60547e6i	1.34705	+	0.681841i
$624$		0			0
$625$	−1.29211e7	+	2.23800e7i	−1.32312	+	2.29172i
$626$	74143.4	+	128420.i	0.00756200	+	0.0130978i
$627$		0			0
$628$	−2.37173e6	+	4.10796e6i	−0.239975	+	0.415649i
$629$	−654048.			−0.0659148
$630$		0			0
$631$	2.83238e6			0.283190			0.141595	−	0.989925i	$-0.454777\pi$
$631$	2.83238e6			0.283190			0.141595	+	0.989925i	$0.454777\pi$
$632$	989596.	−	1.71403e6i	0.0985520	−	0.170697i
$633$		0			0
$634$	−397542.	−	688563.i	−0.0392790	−	0.0680331i
$635$	−1.04980e7	+	1.81831e7i	−1.03317	+	1.78951i
$636$		0			0
$637$	3.45051e6	−	381261.i	0.336926	−	0.0372284i
$638$	−1.70138e6			−0.165481
$639$		0			0
$640$	5.13912e6	+	8.90122e6i	0.495951	+	0.859012i
$641$	−1.78588e6	−	3.09324e6i	−0.171675	−	0.297350i	0.767330	−	0.641252i	$-0.221585\pi$
$641$	−1.78588e6	−	3.09324e6i	−0.171675	−	0.297350i	−0.939006	+	0.343902i	$0.888251\pi$
$642$		0			0
$643$	−5.96911e6			−0.569354			−0.284677	−	0.958624i	$-0.591886\pi$
$643$	−5.96911e6			−0.569354			−0.284677	+	0.958624i	$0.591886\pi$
$644$	43494.6	+	789670.i	0.00413258	+	0.0750293i
$645$		0			0
$646$	33063.2	−	57267.2i	0.00311719	−	0.00539914i
$647$	−841379.	−	1.45731e6i	−0.0790189	−	0.136865i	0.823808	−	0.566869i	$-0.191845\pi$
$647$	−841379.	−	1.45731e6i	−0.0790189	−	0.136865i	−0.902827	+	0.430004i	$0.858512\pi$
$648$		0			0
$649$	871021.	−	1.50865e6i	0.0811739	−	0.140597i
$650$	−1.26278e6			−0.117232
$651$		0			0
$652$	1.03275e6			0.0951427
$653$	8.51526e6	−	1.47489e7i	0.781475	−	1.35355i	−0.149608	−	0.988745i	$-0.547801\pi$
$653$	8.51526e6	−	1.47489e7i	0.781475	−	1.35355i	0.931082	−	0.364809i	$-0.118866\pi$
$654$		0			0
$655$	2.00411e6	+	3.47121e6i	0.182523	+	0.316139i
$656$	−2.01594e6	+	3.49172e6i	−0.182902	+	0.316796i
$657$		0			0
$658$	−376783.	+	246115.i	−0.0339255	+	0.0221602i
$659$	1.99303e7			1.78772			0.893862	−	0.448342i	$-0.147985\pi$
$659$	1.99303e7			1.78772			0.893862	+	0.448342i	$0.147985\pi$
$660$		0			0
$661$	−4.77867e6	−	8.27691e6i	−0.425406	−	0.736825i	0.571052	−	0.820914i	$-0.306535\pi$
$661$	−4.77867e6	−	8.27691e6i	−0.425406	−	0.736825i	−0.996458	+	0.0840888i	$0.973202\pi$
$662$	−664213.	−	1.15045e6i	−0.0589064	−	0.102029i
$663$		0			0
$664$	−5.13056e6			−0.451591
$665$	−1.49723e7	+	9.77995e6i	−1.31291	+	0.857595i
$666$		0			0
$667$	420290.	−	727963.i	0.0365792	−	0.0633570i
$668$	−3.41333e6	−	5.91207e6i	−0.295963	−	0.512623i
$669$		0			0
$670$	546889.	−	947239.i	0.0470665	−	0.0815216i
$671$	−5.29135e6			−0.453691
$672$		0			0
$673$	1.80397e7			1.53530			0.767648	−	0.640872i	$-0.221427\pi$
$673$	1.80397e7			1.53530			0.767648	+	0.640872i	$0.221427\pi$
$674$	393440.	−	681457.i	0.0333602	−	0.0577815i
$675$		0			0
$676$	−5.15531e6	−	8.92927e6i	−0.433899	−	0.751535i
$677$	−7.23704e6	+	1.25349e7i	−0.606861	+	1.05111i	0.384894	+	0.922961i	$0.374238\pi$
$677$	−7.23704e6	+	1.25349e7i	−0.606861	+	1.05111i	−0.991754	+	0.128153i	$0.959095\pi$
$678$		0			0
$679$	−216278.	−	3.92665e6i	−0.0180027	−	0.326849i
$680$	329800.			0.0273513
$681$		0			0
$682$	1.48080e6	+	2.56482e6i	0.121909	+	0.211152i
$683$	1.34392e6	+	2.32774e6i	0.110236	+	0.190934i	0.915865	−	0.401486i	$-0.131506\pi$
$683$	1.34392e6	+	2.32774e6i	0.110236	+	0.190934i	−0.805629	+	0.592420i	$0.798173\pi$
$684$		0			0
$685$	2.51854e7			2.05080
$686$	−1.61351e6	−	604620.i	−0.130907	−	0.0490537i
$687$		0			0
$688$	−2.87420e6	+	4.97826e6i	−0.231497	+	0.400965i
$689$	−1.83674e6	−	3.18132e6i	−0.147400	−	0.255305i
$690$		0			0
$691$	−2.33814e6	+	4.04977e6i	−0.186284	+	0.322653i	−0.944008	−	0.329922i	$-0.892978\pi$
$691$	−2.33814e6	+	4.04977e6i	−0.186284	+	0.322653i	0.757725	+	0.652574i	$0.226311\pi$
$692$	−1.32163e7			−1.04917
$693$		0			0
$694$	−3.20802e6			−0.252836
$695$	2.76693e6	−	4.79246e6i	0.217288	−	0.376354i
$696$		0			0
$697$	132030.	+	228683.i	0.0102942	+	0.0178301i
$698$	−1.13165e6	+	1.96008e6i	−0.0879172	+	0.152277i
$699$		0			0
$700$	−2.80558e7	−	1.42011e7i	−2.16410	−	1.09541i
$701$	−6.34801e6			−0.487913			−0.243957	−	0.969786i	$-0.578445\pi$
$701$	−6.34801e6			−0.487913			−0.243957	+	0.969786i	$0.578445\pi$
$702$		0			0
$703$	−6.85520e6	−	1.18736e7i	−0.523157	−	0.906135i
$704$	7.21309e6	+	1.24934e7i	0.548516	+	0.950058i
$705$		0			0
$706$	−658492.			−0.0497208
$707$	1.15915e7	−	7.57158e6i	0.872150	−	0.569690i
$708$		0			0
$709$	3.20526e6	−	5.55168e6i	0.239468	−	0.414771i	−0.721094	−	0.692838i	$-0.756360\pi$
$709$	3.20526e6	−	5.55168e6i	0.239468	−	0.414771i	0.960562	+	0.278067i	$0.0896936\pi$
$710$	1.59893e6	+	2.76942e6i	0.119037	+	0.206178i
$711$		0			0
$712$	2.82712e6	−	4.89672e6i	0.208999	−	0.361997i
$713$	−1.46320e6			−0.107790
$714$		0			0
$715$	−1.07101e7			−0.783481
$716$	−54812.4	+	94937.9i	−0.00399573	+	0.00692081i
$717$		0			0
$718$	−1.06660e6	−	1.84741e6i	−0.0772131	−	0.133737i
$719$	3.67253e6	−	6.36100e6i	0.264937	−	0.458885i	−0.702610	−	0.711575i	$-0.747982\pi$
$719$	3.67253e6	−	6.36100e6i	0.264937	−	0.458885i	0.967547	+	0.252691i	$0.0813155\pi$
$720$		0			0
$721$	1.82218e7	+	9.22343e6i	1.30543	+	0.660776i
$722$	−571944.			−0.0408329
$723$		0			0
$724$	9.32784e6	+	1.61563e7i	0.661355	+	1.14550i
$725$	1.67109e7	+	2.89441e7i	1.18074	+	2.04510i
$726$		0			0
$727$	1.57839e7			1.10759			0.553793	−	0.832655i	$-0.313180\pi$
$727$	1.57839e7			1.10759			0.553793	+	0.832655i	$0.313180\pi$
$728$	−73805.7	−	1.33999e6i	−0.00516133	−	0.0937069i
$729$		0			0
$730$	−1.29260e6	+	2.23885e6i	−0.0897755	+	0.155496i
$731$	188240.	+	326041.i	0.0130292	+	0.0225673i
$732$		0			0
$733$	−6.76835e6	+	1.17231e7i	−0.465289	+	0.805905i	−0.999215	−	0.0396269i	$-0.987383\pi$
$733$	−6.76835e6	+	1.17231e7i	−0.465289	+	0.805905i	0.533925	+	0.845532i	$0.320716\pi$
$734$	1.15048e6			0.0788205
$735$		0			0
$736$	460109.			0.0313088
$737$	3.30315e6	−	5.72123e6i	0.224006	−	0.387990i
$738$		0			0
$739$	3.66851e6	+	6.35405e6i	0.247103	+	0.427996i	0.962721	−	0.270497i	$-0.0871879\pi$
$739$	3.66851e6	+	6.35405e6i	0.247103	+	0.427996i	−0.715617	+	0.698492i	$0.753855\pi$
$740$	1.69262e7	−	2.93170e7i	1.13626	−	1.96807i
$741$		0			0
$742$	100276.	+	1.82056e6i	0.00668629	+	0.121394i
$743$	−1.20844e7			−0.803068			−0.401534	−	0.915844i	$-0.631523\pi$
$743$	−1.20844e7			−0.803068			−0.401534	+	0.915844i	$0.631523\pi$
$744$		0			0
$745$	6.72360e6	+	1.16456e7i	0.443824	+	0.768726i
$746$	809343.	+	1.40182e6i	0.0532459	+	0.0922245i
$747$		0			0
$748$	986151.			0.0644450
$749$	1.03320e7	+	5.22978e6i	0.672944	+	0.340627i
$750$		0			0
$751$	−4.39088e6	+	7.60523e6i	−0.284087	+	0.492054i	−0.972387	−	0.233372i	$-0.925024\pi$
$751$	−4.39088e6	+	7.60523e6i	−0.284087	+	0.492054i	0.688300	+	0.725426i	$0.258357\pi$
$752$	−2.11663e6	−	3.66612e6i	−0.136490	−	0.236408i
$753$		0			0
$754$	−353075.	+	611543.i	−0.0226172	+	0.0391741i
$755$	1.59628e7			1.01916
$756$		0			0
$757$	465874.			0.0295480			0.0147740	−	0.999891i	$-0.495297\pi$
$757$	465874.			0.0295480			0.0147740	+	0.999891i	$0.495297\pi$
$758$	164842.	−	285516.i	0.0104207	−	0.0180491i
$759$		0			0
$760$	3.45670e6	+	5.98717e6i	0.217084	+	0.376000i
$761$	7.49891e6	−	1.29885e7i	0.469393	−	0.813013i	−0.529995	−	0.848001i	$-0.677806\pi$
$761$	7.49891e6	−	1.29885e7i	0.469393	−	0.813013i	0.999388	+	0.0349882i	$0.0111394\pi$
$762$		0			0
$763$	−1.81915e7	+	1.18827e7i	−1.13125	+	0.738932i
$764$	2.59984e7			1.61144
$765$		0			0
$766$	−1.53268e6	−	2.65468e6i	−0.0943800	−	0.163471i
$767$	−361513.	−	626159.i	−0.0221889	−	0.0384323i
$768$		0			0
$769$	−1.85606e7			−1.13181			−0.565907	−	0.824469i	$-0.691474\pi$
$769$	−1.85606e7			−1.13181			−0.565907	+	0.824469i	$0.691474\pi$
$770$	4.74295e6	+	2.40076e6i	0.288285	+	0.145922i
$771$		0			0
$772$	3.44711e6	−	5.97057e6i	0.208167	−	0.360556i
$773$	6.13802e6	+	1.06314e7i	0.369470	+	0.639941i	0.989483	−	0.144651i	$-0.0462058\pi$
$773$	6.13802e6	+	1.06314e7i	0.369470	+	0.639941i	−0.620013	+	0.784592i	$0.712872\pi$
$774$		0			0
$775$	2.90888e7	−	5.03832e7i	1.73969	−	3.01323i
$776$	−1.52027e6			−0.0906286
$777$		0			0
$778$	−2.24432e6			−0.132934
$779$	−2.76767e6	+	4.79375e6i	−0.163407	+	0.283029i
$780$		0			0
$781$	9.65736e6	+	1.67270e7i	0.566540	+	0.981276i
$782$	4855.70	−	8410.31i	0.000283945	−	0.000491808i
$783$		0			0
$784$	6.51337e6	−	1.48416e7i	0.378456	−	0.862363i
$785$	−1.57525e7			−0.912380
$786$		0			0
$787$	−2.63496e6	−	4.56388e6i	−0.151648	−	0.262662i	0.780185	−	0.625548i	$-0.215125\pi$
$787$	−2.63496e6	−	4.56388e6i	−0.151648	−	0.262662i	−0.931833	+	0.362886i	$0.881791\pi$
$788$	−7.46107e6	−	1.29230e7i	−0.428041	−	0.741389i
$789$		0			0
$790$	3.25391e6			0.185497
$791$	−825586.	−	1.49890e7i	−0.0469160	−	0.851788i
$792$		0			0
$793$	−1.09807e6	+	1.90192e6i	−0.0620082	+	0.107401i
$794$	−1.71710e6	−	2.97410e6i	−0.0966593	−	0.167419i
$795$		0			0
$796$	9.84466e6	−	1.70514e7i	0.550704	−	0.953847i
$797$	−1.11889e7			−0.623940			−0.311970	−	0.950092i	$-0.600989\pi$
$797$	−1.11889e7			−0.623940			−0.311970	+	0.950092i	$0.600989\pi$
$798$		0			0
$799$	−277250.			−0.0153640
$800$	−9.14706e6	+	1.58432e7i	−0.505308	+	0.875220i
$801$		0			0
$802$	1.34557e6	+	2.33060e6i	0.0738705	+	0.127947i
$803$	−7.80719e6	+	1.35225e7i	−0.427274	+	0.740059i
$804$		0			0
$805$	−2.19885e6	+	1.43629e6i	−0.119593	+	0.0781184i
$806$	1.22920e6			0.0666476
$807$		0			0
$808$	−2.67616e6	−	4.63524e6i	−0.144206	−	0.249772i
$809$	3.52526e6	+	6.10592e6i	0.189374	+	0.328005i	0.945042	−	0.326950i	$-0.106021\pi$
$809$	3.52526e6	+	6.10592e6i	0.189374	+	0.328005i	−0.755668	+	0.654955i	$0.772688\pi$
$810$		0			0
$811$	−2.54873e7			−1.36073			−0.680364	−	0.732875i	$-0.738178\pi$
$811$	−2.54873e7			−1.36073			−0.680364	+	0.732875i	$0.738178\pi$
$812$	−1.47218e7	+	9.61630e6i	−0.783557	+	0.511821i
$813$		0			0
$814$	−2.03774e6	+	3.52947e6i	−0.107792	+	0.186702i
$815$	1.71482e6	+	2.97016e6i	0.0904326	+	0.156634i
$816$		0			0
$817$	−3.94596e6	+	6.83460e6i	−0.206822	+	0.358227i
$818$	−4.18677e6			−0.218774
$819$		0			0
$820$	−1.36673e7			−0.709820
$821$	−1.17439e7	+	2.03411e7i	−0.608073	+	1.05321i	0.383485	+	0.923547i	$0.374724\pi$
$821$	−1.17439e7	+	2.03411e7i	−0.608073	+	1.05321i	−0.991558	+	0.129666i	$0.958610\pi$
$822$		0			0
$823$	6.04517e6	+	1.04705e7i	0.311107	+	0.538852i	0.978602	−	0.205761i	$-0.0659671\pi$
$823$	6.04517e6	+	1.04705e7i	0.311107	+	0.538852i	−0.667496	+	0.744614i	$0.732634\pi$
$824$	3.94760e6	−	6.83745e6i	0.202542	−	0.350813i
$825$		0			0
$826$	19736.6	+	358330.i	0.00100652	+	0.0182740i
$827$	−3.33335e6			−0.169480			−0.0847398	−	0.996403i	$-0.527006\pi$
$827$	−3.33335e6			−0.169480			−0.0847398	+	0.996403i	$0.527006\pi$
$828$		0			0
$829$	3.85267e6	+	6.67302e6i	0.194704	+	0.337238i	0.946804	−	0.321812i	$-0.104292\pi$
$829$	3.85267e6	+	6.67302e6i	0.194704	+	0.337238i	−0.752099	+	0.659050i	$0.770959\pi$
$830$	−4.21748e6	−	7.30489e6i	−0.212499	−	0.368060i
$831$		0			0
$832$	5.98752e6			0.299874
$833$	−628505.	−	855440.i	−0.0313831	−	0.0427147i
$834$		0			0
$835$	1.13353e7	−	1.96333e7i	0.562622	−	0.974490i
$836$	1.03360e7	+	1.79025e7i	0.511492	+	0.885929i
$837$		0			0
$838$	1.13586e6	−	1.96737e6i	0.0558747	−	0.0967779i
$839$	−2.40843e7			−1.18121			−0.590607	−	0.806959i	$-0.701112\pi$
$839$	−2.40843e7			−1.18121			−0.590607	+	0.806959i	$0.701112\pi$
$840$		0			0
$841$	−1.82163e6			−0.0888116
$842$	−825159.	+	1.42922e6i	−0.0401104	+	0.0694733i
$843$		0			0
$844$	8.95728e6	+	1.55145e7i	0.432832	+	0.749688i
$845$	1.71202e7	−	2.96531e7i	0.824837	−	1.42866i
$846$		0			0
$847$	1.00185e7	+	5.07110e6i	0.479837	+	0.242881i
$848$	−1.71509e7			−0.819023
$849$		0			0
$850$	193064.	+	334398.i	0.00916548	+	0.0158751i
$851$	−1.00676e6	−	1.74376e6i	−0.0476544	−	0.0825398i
$852$		0			0
$853$	−2.82938e7			−1.33143			−0.665716	−	0.746206i	$-0.731874\pi$
$853$	−2.82938e7			−1.33143			−0.665716	+	0.746206i	$0.731874\pi$
$854$	912612.	−	596120.i	0.0428195	−	0.0279698i
$855$		0			0
$856$	2.23833e6	−	3.87690e6i	0.104410	−	0.180843i
$857$	1.08088e7	+	1.87214e7i	0.502719	+	0.870734i	0.999995	+	0.00314220i	$0.00100019\pi$
$857$	1.08088e7	+	1.87214e7i	0.502719	+	0.870734i	−0.497276	+	0.867592i	$0.665666\pi$
$858$		0			0
$859$	−1.62691e7	+	2.81789e7i	−0.752282	+	1.30299i	0.194432	+	0.980916i	$0.437714\pi$
$859$	−1.62691e7	+	2.81789e7i	−0.752282	+	1.30299i	−0.946714	+	0.322075i	$0.895620\pi$
$860$	−1.94859e7			−0.898411
$861$		0			0
$862$	1.92058e6			0.0880366
$863$	4.03192e6	−	6.98349e6i	0.184283	−	0.319187i	−0.759052	−	0.651030i	$-0.774337\pi$
$863$	4.03192e6	−	6.98349e6i	0.184283	−	0.319187i	0.943335	+	0.331843i	$0.107670\pi$
$864$		0			0
$865$	−2.19450e7	−	3.80098e7i	−0.997229	−	1.72725i
$866$	−378091.	+	654874.i	−0.0171318	+	0.0296731i
$867$		0			0
$868$	2.73097e7	+	1.38235e7i	1.23032	+	0.622756i
$869$	1.96533e7			0.882849
$870$		0			0
$871$	−1.37096e6	−	2.37457e6i	−0.0612321	−	0.106057i
$872$	4.19992e6	+	7.27447e6i	0.187046	+	0.323974i
$873$		0			0
$874$	203574.			0.00901454
$875$	−3.42157e6	−	6.21206e7i	−0.151080	−	2.74294i
$876$		0			0
$877$	−8.51559e6	+	1.47494e7i	−0.373866	+	0.647555i	−0.990157	−	0.139964i	$-0.955301\pi$
$877$	−8.51559e6	+	1.47494e7i	−0.373866	+	0.647555i	0.616291	+	0.787519i	$0.288635\pi$
$878$	−1.04467e6	−	1.80943e6i	−0.0457345	−	0.0792145i
$879$		0			0
$880$	−2.50019e7	+	4.33045e7i	−1.08834	+	1.88507i
$881$	−1.24740e7			−0.541459			−0.270729	−	0.962655i	$-0.587265\pi$
$881$	−1.24740e7			−0.541459			−0.270729	+	0.962655i	$0.587265\pi$
$882$		0			0
$883$	7.28955e6			0.314629			0.157315	−	0.987549i	$-0.449716\pi$
$883$	7.28955e6			0.314629			0.157315	+	0.987549i	$0.449716\pi$
$884$	204649.	−	354462.i	0.00880802	−	0.0152559i
$885$		0			0
$886$	−1.36005e6	−	2.35567e6i	−0.0582063	−	0.100816i
$887$	9.38377e6	−	1.62532e7i	0.400469	−	0.693632i	−0.593314	−	0.804971i	$-0.702181\pi$
$887$	9.38377e6	−	1.62532e7i	0.400469	−	0.693632i	0.993782	+	0.111339i	$0.0355140\pi$
$888$		0			0
$889$	−1.43675e6	−	2.60850e7i	−0.0609714	−	1.10697i
$890$	9.29592e6			0.393385
$891$		0			0
$892$	66406.1	+	115019.i	0.00279445	+	0.00484012i
$893$	−2.90591e6	−	5.03318e6i	−0.121942	−	0.211210i
$894$		0			0
$895$	−364052.			−0.0151917
$896$	−1.14104e7	−	5.77563e6i	−0.474820	−	0.240342i
$897$		0			0
$898$	1.73939e6	−	3.01271e6i	0.0719790	−	0.124671i
$899$	−1.62665e7	−	2.81744e7i	−0.671266	−	1.16267i
$900$		0			0
$901$	−561631.	+	972773.i	−0.0230483	+	0.0399208i
$902$	1.64541e6			0.0673375
$903$		0			0
$904$	−5.80323e6			−0.236183
$905$	−3.09767e7	+	5.36533e7i	−1.25723	+	2.17758i
$906$		0			0
$907$	−631833.	−	1.09437e6i	−0.0255026	−	0.0441718i	0.852992	−	0.521923i	$-0.174785\pi$
$907$	−631833.	−	1.09437e6i	−0.0255026	−	0.0441718i	−0.878495	+	0.477751i	$0.841452\pi$
$908$	−1.77245e7	+	3.06998e7i	−0.713444	+	1.23572i
$909$		0			0
$910$	1.84720e6	−	1.20659e6i	0.0739452	−	0.0483011i
$911$	2.47718e7			0.988921			0.494461	−	0.869200i	$-0.335366\pi$
$911$	2.47718e7			0.988921			0.494461	+	0.869200i	$0.335366\pi$
$912$		0			0
$913$	−2.54732e7	−	4.41208e7i	−1.01136	−	1.75173i
$914$	890092.	+	1.54168e6i	0.0352427	+	0.0610422i
$915$		0			0
$916$	−2.52454e7			−0.994130
$917$	−4.44970e6	−	2.25233e6i	−0.174746	−	0.0884520i
$918$		0			0
$919$	4.68338e6	−	8.11185e6i	0.182924	−	0.316834i	−0.759951	−	0.649980i	$-0.774777\pi$
$919$	4.68338e6	−	8.11185e6i	0.182924	−	0.316834i	0.942875	+	0.333147i	$0.108110\pi$
$920$	507654.	+	879282.i	0.0197742	+	0.0342498i
$921$		0			0
$922$	732710.	−	1.26909e6i	0.0283860	−	0.0491661i
$923$	8.01648e6			0.309727
$924$		0			0
$925$	8.00586e7			3.07648
$926$	1.19051e6	−	2.06203e6i	0.0456255	−	0.0790256i
$927$		0			0
$928$	5.11505e6	+	8.85953e6i	0.194975	+	0.337707i
$929$	−3.43675e6	+	5.95263e6i	−0.130650	+	0.226292i	−0.923927	−	0.382568i	$-0.875040\pi$
$929$	−3.43675e6	+	5.95263e6i	−0.130650	+	0.226292i	0.793277	+	0.608860i	$0.208373\pi$
$930$		0			0
$931$	8.94215e6	−	2.03759e7i	0.338118	−	0.770446i
$932$	3.66855e7			1.38342
$933$		0			0
$934$	−421995.	−	730917.i	−0.0158285	−	0.0274158i
$935$	1.63745e6	+	2.83615e6i	0.0612546	+	0.106096i
$936$		0			0
$937$	−4.26197e7			−1.58585			−0.792923	−	0.609322i	$-0.791442\pi$
$937$	−4.26197e7			−1.58585			−0.792923	+	0.609322i	$0.791442\pi$
$938$	74846.7	+	1.35889e6i	0.00277758	+	0.0504285i
$939$		0			0
$940$	7.17497e6	−	1.24274e7i	0.264850	−	0.458734i
$941$	2.25113e6	+	3.89907e6i	0.0828755	+	0.143545i	0.904484	−	0.426508i	$-0.140256\pi$
$941$	2.25113e6	+	3.89907e6i	0.0828755	+	0.143545i	−0.821608	+	0.570052i	$0.806923\pi$
$942$		0			0
$943$	−406463.	+	704015.i	−0.0148848	+	0.0257812i
$944$	−3.37569e6			−0.123291
$945$		0			0
$946$	2.34591e6			0.0852282
$947$	1.68863e7	−	2.92479e7i	0.611870	−	1.05979i	−0.379055	−	0.925374i	$-0.623751\pi$
$947$	1.68863e7	−	2.92479e7i	0.611870	−	1.05979i	0.990925	−	0.134415i	$-0.0429156\pi$
$948$		0			0
$949$	3.24034e6	+	5.61243e6i	0.116795	+	0.202295i
$950$	−4.04709e6	+	7.00977e6i	−0.145490	+	0.251997i
$951$		0			0
$952$	−343558.	+	224413.i	−0.0122859	+	0.00802519i
$953$	−4.81813e7			−1.71849			−0.859244	−	0.511566i	$-0.829066\pi$
$953$	−4.81813e7			−1.71849			−0.859244	+	0.511566i	$0.829066\pi$
$954$		0			0
$955$	4.31689e7	+	7.47708e7i	1.53166	+	2.65292i
$956$	2.67554e7	+	4.63416e7i	0.946817	+	1.63993i
$957$		0			0
$958$	4.49800e6			0.158346
$959$	−2.62361e7	+	1.71375e7i	−0.921198	+	0.601728i
$960$		0			0
$961$	−1.40006e7	+	2.42498e7i	−0.489033	+	0.847030i
$962$	845755.	+	1.46489e6i	0.0294650	+	0.0510349i
$963$		0			0
$964$	1.49217e7	−	2.58452e7i	0.517161	−	0.895750i
$965$	2.28950e7			0.791446
$966$		0			0
$967$	−3.54640e7			−1.21961			−0.609805	−	0.792551i	$-0.708752\pi$
$967$	−3.54640e7			−1.21961			−0.609805	+	0.792551i	$0.708752\pi$
$968$	2.17042e6	−	3.75927e6i	0.0744483	−	0.128948i
$969$		0			0
$970$	−1.24970e6	−	2.16455e6i	−0.0426459	−	0.0738649i
$971$	−3.92148e6	+	6.79221e6i	−0.133476	+	0.231187i	−0.925014	−	0.379933i	$-0.875947\pi$
$971$	−3.92148e6	+	6.79221e6i	−0.133476	+	0.231187i	0.791538	+	0.611119i	$0.209280\pi$
$972$		0			0
$973$	378679.	+	6.87514e6i	0.0128230	+	0.232809i
$974$	−5.41288e6			−0.182823
$975$		0			0
$976$	5.12674e6	+	8.87977e6i	0.172273	+	0.298385i
$977$	−1.23767e7	−	2.14371e7i	−0.414829	−	0.718505i	0.580582	−	0.814202i	$-0.302825\pi$
$977$	−1.23767e7	−	2.14371e7i	−0.414829	−	0.718505i	−0.995410	+	0.0956975i	$0.969492\pi$
$978$		0			0
$979$	5.61464e7			1.87226
$980$	5.46093e7	−	6.03401e6i	1.81636	−	0.200697i
$981$		0			0
$982$	2.21477e6	−	3.83610e6i	0.0732910	−	0.126944i
$983$	2.26564e7	+	3.92421e7i	0.747838	+	1.29529i	0.948857	+	0.315707i	$0.102242\pi$
$983$	2.26564e7	+	3.92421e7i	0.747838	+	1.29529i	−0.201018	+	0.979587i	$0.564425\pi$
$984$		0			0
$985$	2.47774e7	−	4.29157e7i	0.813701	−	1.40937i
$986$	215924.			0.00707308
$987$		0			0
$988$	8.57985e6			0.279632
$989$	−579508.	+	1.00374e6i	−0.0188395	+	0.0326309i
$990$		0			0
$991$	1.87071e7	+	3.24017e7i	0.605095	+	1.04805i	0.992037	+	0.125951i	$0.0401981\pi$
$991$	1.87071e7	+	3.24017e7i	0.605095	+	1.04805i	−0.386942	+	0.922104i	$0.626469\pi$
$992$	8.90380e6	−	1.54218e7i	0.287274	−	0.497573i
$993$		0			0
$994$	−3.55008e6	−	1.79696e6i	−0.113965	−	0.0576863i
$995$	6.53861e7			2.09376
$996$		0			0
$997$	−2.32639e7	−	4.02943e7i	−0.741216	−	1.28382i	−0.951942	−	0.306279i	$-0.900916\pi$
$997$	−2.32639e7	−	4.02943e7i	−0.741216	−	1.28382i	0.210726	−	0.977545i	$-0.432417\pi$
$998$	923379.	+	1.59934e6i	0.0293463	+	0.0508293i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.e.e.37.2		8
3.2	odd	2		21.6.e.c.16.3	yes	8
7.2	even	3		441.6.a.w.1.3		4
7.4	even	3	inner	63.6.e.e.46.2		8
7.5	odd	6		441.6.a.v.1.3		4
12.11	even	2		336.6.q.j.289.4		8
21.2	odd	6		147.6.a.m.1.2		4
21.5	even	6		147.6.a.l.1.2		4
21.11	odd	6		21.6.e.c.4.3	✓	8
21.17	even	6		147.6.e.o.67.3		8
21.20	even	2		147.6.e.o.79.3		8
84.11	even	6		336.6.q.j.193.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.3	✓	8	21.11	odd	6
21.6.e.c.16.3	yes	8	3.2	odd	2
63.6.e.e.37.2		8	1.1	even	1	trivial
63.6.e.e.46.2		8	7.4	even	3	inner
147.6.a.l.1.2		4	21.5	even	6
147.6.a.m.1.2		4	21.2	odd	6
147.6.e.o.67.3		8	21.17	even	6
147.6.e.o.79.3		8	21.20	even	2
336.6.q.j.193.4		8	84.11	even	6
336.6.q.j.289.4		8	12.11	even	2
441.6.a.v.1.3		4	7.5	odd	6
441.6.a.w.1.3		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)

\(f(q)\)	\(=\)	\(q+(-0.395402 + 0.684857i) q^{2} +(15.6873 + 27.1712i) q^{4} +(-52.0958 + 90.2327i) q^{5} +(-7.12980 - 129.446i) q^{7} -50.1170 q^{8} +O(q^{10})\)	\(q+(-0.395402 + 0.684857i) q^{2} +(15.6873 + 27.1712i) q^{4} +(-52.0958 + 90.2327i) q^{5} +(-7.12980 - 129.446i) q^{7} -50.1170 q^{8} +(-41.1977 - 71.3564i) q^{10} +(-248.830 - 430.986i) q^{11} -206.551 q^{13} +(91.4709 + 46.3002i) q^{14} +(-482.178 + 835.156i) q^{16} +(31.5793 + 54.6969i) q^{17} +(-661.977 + 1146.58i) q^{19} -3268.98 q^{20} +393.552 q^{22} +(-97.2187 + 168.388i) q^{23} +(-3865.45 - 6695.16i) q^{25} +(81.6709 - 141.458i) q^{26} +(3405.35 - 2224.38i) q^{28} -4323.14 q^{29} +(3762.66 + 6517.11i) q^{31} +(-1183.18 - 2049.33i) q^{32} -49.9461 q^{34} +(12051.7 + 6100.24i) q^{35} +(-5177.82 + 8968.25i) q^{37} +(-523.495 - 906.720i) q^{38} +(2610.89 - 4522.19i) q^{40} +4180.92 q^{41} +5960.87 q^{43} +(7806.94 - 13522.0i) q^{44} +(-76.8810 - 133.162i) q^{46} +(-2194.87 + 3801.62i) q^{47} +(-16705.3 + 1845.84i) q^{49} +6113.64 q^{50} +(-3240.24 - 5612.25i) q^{52} +(8892.39 + 15402.1i) q^{53} +51852.0 q^{55} +(357.324 + 6487.42i) q^{56} +(1709.38 - 2960.73i) q^{58} +(1750.23 + 3031.49i) q^{59} +(5316.23 - 9207.98i) q^{61} -5951.06 q^{62} -28988.0 q^{64} +(10760.5 - 18637.7i) q^{65} +(6637.37 + 11496.3i) q^{67} +(-990.789 + 1716.10i) q^{68} +(-8943.05 + 5841.61i) q^{70} -38811.1 q^{71} +(-15687.8 - 27172.1i) q^{73} +(-4094.65 - 7092.14i) q^{74} -41538.6 q^{76} +(-54015.1 + 35282.8i) q^{77} +(-19745.7 + 34200.6i) q^{79} +(-50238.9 - 87016.3i) q^{80} +(-1653.14 + 2863.33i) q^{82} +102372. q^{83} -6580.60 q^{85} +(-2356.94 + 4082.34i) q^{86} +(12470.6 + 21599.7i) q^{88} +(-56410.5 + 97705.8i) q^{89} +(1472.67 + 26737.2i) q^{91} -6100.40 q^{92} +(-1735.71 - 3006.34i) q^{94} +(-68972.6 - 119464. i) q^{95} +30334.3 q^{97} +(5341.19 - 12170.6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8}+O(q^{10}) \) 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

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