LMFDB - Embedded newform 63.6.e.e.46.2

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			46.2
Root			$0.895402 + 1.55088i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.e.37.2

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.395402	−	0.684857i	−0.0698979	−	0.121067i	0.828958	−	0.559310i	$-0.188934\pi$
$2$	−0.395402	−	0.684857i	−0.0698979	−	0.121067i	−0.898856	+	0.438244i	$0.855601\pi$
$3$		0			0
$3$		0			0
$4$	15.6873	−	27.1712i	0.490229	−	0.849101i
$5$	−52.0958	−	90.2327i	−0.931919	−	1.61413i	−0.780038	−	0.625732i	$-0.784800\pi$
$5$	−52.0958	−	90.2327i	−0.931919	−	1.61413i	−0.151881	−	0.988399i	$-0.548533\pi$
$6$		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	0.369436	+	0.929256i	$0.379551\pi$
$11$	−248.830	+	430.986i	−0.620041	+	1.07394i	−0.989477	+	0.144687i	$0.953782\pi$
$12$		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	−0.852470	−	0.522776i	$-0.824896\pi$
$17$	31.5793	−	54.6969i	0.0265021	−	0.0459030i	0.878972	+	0.476873i	$0.158230\pi$
$18$		0			0
$19$	−661.977	−	1146.58i	−0.420687	−	0.728651i	0.575320	−	0.817929i	$-0.304878\pi$
$19$	−661.977	−	1146.58i	−0.420687	−	0.728651i	−0.996007	+	0.0892772i	$0.971544\pi$
$20$	−3268.98			−1.82741
$21$		0			0
$22$	393.552			0.173358
$23$	−97.2187	−	168.388i	−0.0383204	−	0.0663729i	0.846229	−	0.532819i	$-0.178867\pi$
$23$	−97.2187	−	168.388i	−0.0383204	−	0.0663729i	−0.884550	+	0.466446i	$0.845534\pi$
$24$		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	−0.264112	−	0.964492i	$-0.585079\pi$
$31$	3762.66	−	6517.11i	0.703219	−	1.21801i	0.967331	−	0.253518i	$-0.0815879\pi$
$32$	−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	−0.989152	−	0.146892i	$-0.953073\pi$
$37$	−5177.82	−	8968.25i	−0.621789	−	1.07697i	0.367364	−	0.930077i	$-0.380260\pi$
$38$	−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	0.784416	−	0.620236i	$-0.212963\pi$
$47$	−2194.87	−	3801.62i	−0.144932	−	0.251029i	−0.929348	+	0.369206i	$0.879630\pi$
$48$		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	−0.562443	−	0.826836i	$-0.690138\pi$
$53$	8892.39	−	15402.1i	0.434839	−	0.753164i	0.997283	+	0.0736720i	$0.0234718\pi$
$54$		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	−0.831439	−	0.555616i	$-0.812482\pi$
$59$	1750.23	−	3031.49i	0.0654585	−	0.113377i	0.896897	+	0.442239i	$0.145816\pi$
$60$		0			0
$61$	5316.23	+	9207.98i	0.182928	+	0.316840i	0.942876	−	0.333143i	$-0.108109\pi$
$61$	5316.23	+	9207.98i	0.182928	+	0.316840i	−0.759949	+	0.649983i	$0.774776\pi$
$62$	−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	−0.761460	−	0.648212i	$-0.775517\pi$
$67$	6637.37	−	11496.3i	0.180638	−	0.312874i	0.942098	+	0.335338i	$0.108850\pi$
$68$	−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	−0.985272	−	0.170992i	$-0.945303\pi$
$73$	−15687.8	+	27172.1i	−0.344552	+	0.596782i	0.640720	+	0.767775i	$0.278636\pi$
$74$	−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	0.631319	−	0.775523i	$-0.282514\pi$
$79$	−19745.7	−	34200.6i	−0.355964	−	0.616547i	−0.987282	+	0.158976i	$0.949181\pi$
$80$	−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	−0.945428	−	0.325831i	$-0.894356\pi$
$89$	−56410.5	−	97705.8i	−0.754892	−	1.30751i	0.190536	−	0.981680i	$-0.438977\pi$
$90$		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	−0.478843	−	0.877900i	$-0.658944\pi$
$101$	53398.2	−	92488.4i	0.520862	−	0.902160i	0.999706	−	0.0242599i	$-0.00772291\pi$
$102$		0			0
$103$	−78767.8	−	136430.i	−0.731570	−	1.26712i	−0.956212	−	0.292674i	$-0.905455\pi$
$103$	−78767.8	−	136430.i	−0.731570	−	1.26712i	0.224643	−	0.974441i	$-0.427879\pi$
$104$	10351.7			0.0938490
$105$		0			0
$106$	−14064.3			−0.121578
$107$	−44662.2	−	77357.1i	−0.377121	−	0.653192i	0.613521	−	0.789678i	$-0.289752\pi$
$107$	−44662.2	−	77357.1i	−0.377121	−	0.653192i	−0.990642	+	0.136486i	$0.956419\pi$
$108$		0			0
$109$	−83802.3	+	145150.i	−0.675600	+	1.17017i	0.300693	+	0.953721i	$0.402782\pi$
$109$	−83802.3	+	145150.i	−0.675600	+	1.17017i	−0.976293	+	0.216452i	$0.930551\pi$
$110$	−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	0.910827	−	0.412788i	$-0.135445\pi$
$131$	19234.8	+	33315.6i	0.0979285	+	0.169617i	−0.812899	+	0.582405i	$0.802112\pi$
$132$		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	0.448108	+	0.893979i	$0.352098\pi$
$137$	−120861.	+	209337.i	−0.550155	+	0.952896i	−0.998263	+	0.0589167i	$0.981235\pi$
$138$		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	0.960176	−	0.279396i	$-0.0901342\pi$
$149$	64531.0	+	111771.i	0.238124	+	0.412443i	−0.722052	+	0.691839i	$0.756801\pi$
$150$		0			0
$151$	−76603.2	+	132681.i	−0.273404	+	0.473549i	−0.969731	−	0.244175i	$-0.921483\pi$
$151$	−76603.2	+	132681.i	−0.273404	+	0.473549i	0.696327	+	0.717724i	$0.254816\pi$
$152$	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	−0.717305	−	0.696759i	$-0.754625\pi$
$157$	75593.9	−	130932.i	0.244758	−	0.423934i	0.962064	+	0.272825i	$0.0879581\pi$
$158$	−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	0.889265	−	0.457392i	$-0.151216\pi$
$163$	16458.3	+	28506.7i	0.0485196	+	0.0840384i	−0.840746	+	0.541430i	$0.817883\pi$
$164$	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	−0.999161	−	0.0409458i	$-0.986963\pi$
$173$	−210621.	−	364807.i	−0.535041	−	0.926718i	0.464121	−	0.885772i	$-0.346370\pi$
$174$		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	−0.863981	−	0.503525i	$-0.832036\pi$
$179$	1747.03	−	3025.94i	0.00407538	−	0.00705876i	0.868056	+	0.496466i	$0.165369\pi$
$180$		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	0.904357	+	0.426777i	$0.140351\pi$
$191$	414322.	+	717627.i	0.821778	+	1.42336i	−0.0825782	+	0.996585i	$0.526315\pi$
$192$		0			0
$193$	−109869.	+	190299.i	−0.212316	+	0.367743i	−0.952439	−	0.304729i	$-0.901434\pi$
$193$	−109869.	+	190299.i	−0.212316	+	0.367743i	0.740123	+	0.672472i	$0.234767\pi$
$194$	−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	0.435669	+	0.900107i	$0.356512\pi$
$199$	−313778.	+	543479.i	−0.561681	+	0.972859i	−0.997350	+	0.0727525i	$0.976822\pi$
$200$	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	−0.230204	−	0.973142i	$-0.573939\pi$
$227$	564931.	−	978490.i	0.727664	−	1.26035i	0.957868	−	0.287209i	$-0.0927274\pi$
$228$		0			0
$229$	−402322.	−	696842.i	−0.506973	−	0.878103i	−0.999967	−	0.00807048i	$-0.997431\pi$
$229$	−402322.	−	696842.i	−0.506973	−	0.878103i	0.492994	−	0.870032i	$-0.335902\pi$
$230$	16020.7			0.0199693
$231$		0			0
$232$	216663.			0.264280
$233$	584636.	+	1.01262e6i	0.705498	+	1.22196i	0.966511	+	0.256624i	$0.0826101\pi$
$233$	584636.	+	1.01262e6i	0.705498	+	1.22196i	−0.261013	+	0.965335i	$0.584057\pi$
$234$		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	0.472018	+	0.881589i	$0.343526\pi$
$241$	−475598.	+	823760.i	−0.527470	+	0.913604i	−0.999487	+	0.0320153i	$0.989807\pi$
$242$	−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	0.997582	+	0.0694955i	$0.0221389\pi$
$257$	591869.	+	1.02515e6i	0.558976	+	0.968175i	−0.438606	+	0.898679i	$0.644528\pi$
$258$		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	−0.748642	−	0.662975i	$-0.769294\pi$
$263$	224158.	−	388253.i	0.199832	−	0.346119i	0.948474	+	0.316856i	$0.102627\pi$
$264$		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	−0.664509	−	0.747280i	$-0.731359\pi$
$269$	373737.	−	647332.i	0.314909	−	0.545439i	0.979418	+	0.201841i	$0.0646925\pi$
$270$		0			0
$271$	116319.	+	201470.i	0.0962114	+	0.166643i	0.910114	−	0.414359i	$-0.135994\pi$
$271$	116319.	+	201470.i	0.0962114	+	0.166643i	−0.813902	+	0.581002i	$0.802661\pi$
$272$	−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	0.208157	−	0.978095i	$-0.433253\pi$
$277$	1.21462e6	−	2.10379e6i	0.951134	−	1.64741i	0.742977	−	0.669317i	$-0.233413\pi$
$278$	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	−0.910382	−	0.413768i	$-0.864213\pi$
$283$	−130497.	+	226028.i	−0.0968579	+	0.167763i	0.813525	+	0.581530i	$0.197546\pi$
$284$	−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	0.368445	+	0.929650i	$0.379890\pi$
$311$	−1.05903e6	+	1.83429e6i	−0.620878	+	1.07539i	−0.989323	+	0.145742i	$0.953443\pi$
$312$		0			0
$313$	93756.8	+	162392.i	0.0540931	+	0.0936920i	0.891804	−	0.452422i	$-0.149440\pi$
$313$	93756.8	+	162392.i	0.0540931	+	0.0936920i	−0.837711	+	0.546114i	$0.816107\pi$
$314$	−119560.			−0.0684324
$315$		0			0
$316$	−1.23903e6			−0.698014
$317$	−502705.	−	870711.i	−0.280974	−	0.486661i	0.690651	−	0.723188i	$-0.257324\pi$
$317$	−502705.	−	870711.i	−0.280974	−	0.486661i	−0.971625	+	0.236527i	$0.923991\pi$
$318$		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	0.574700	−	0.818364i	$-0.305119\pi$
$331$	−839920.	−	1.45478e6i	−0.421374	−	0.729841i	−0.996074	+	0.0885229i	$0.971785\pi$
$332$	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	0.0824546	−	0.996595i	$-0.473724\pi$
$347$	2.02833e6	−	3.51317e6i	0.904304	−	1.56630i	0.821849	−	0.569705i	$-0.192943\pi$
$348$		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	−0.763305	−	0.646039i	$-0.776424\pi$
$353$	416343.	−	721126.i	0.177834	−	0.308017i	0.941138	+	0.338022i	$0.109758\pi$
$354$		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	−0.998106	−	0.0615157i	$-0.980407\pi$
$359$	−1.34875e6	−	2.33611e6i	−0.552327	−	0.956659i	0.445779	−	0.895143i	$-0.352927\pi$
$360$		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	−0.971856	−	0.235576i	$-0.924302\pi$
$367$	−727411.	+	1.25991e6i	−0.281913	+	0.488287i	0.689943	+	0.723864i	$0.257636\pi$
$368$	−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	0.991189	−	0.132457i	$-0.0422868\pi$
$373$	1.02344e6	+	1.77265e6i	0.380883	+	0.659708i	−0.610306	+	0.792166i	$0.708953\pi$
$374$	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	−0.976432	−	0.215827i	$-0.930755\pi$
$383$	−1.93813e6	−	3.35694e6i	−0.675127	−	1.16935i	0.301305	−	0.953528i	$-0.402578\pi$
$384$		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	−0.524147	−	0.851628i	$-0.675616\pi$
$389$	1.41901e6	−	2.45780e6i	0.475458	−	0.823517i	0.999605	+	0.0281111i	$0.00894921\pi$
$390$		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	−0.971369	−	0.237577i	$-0.923647\pi$
$397$	−2.17133e6	−	3.76085e6i	−0.691432	−	1.19760i	0.279937	−	0.960018i	$-0.409686\pi$
$398$	496274.			0.157041
$399$		0			0
$400$	7.45534e6			2.32979
$401$	1.70152e6	+	2.94712e6i	0.528417	+	0.915244i	0.999451	+	0.0331296i	$0.0105474\pi$
$401$	1.70152e6	+	2.94712e6i	0.528417	+	0.915244i	−0.471034	+	0.882115i	$0.656119\pi$
$402$		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	−0.148018	−	0.988985i	$-0.547289\pi$
$409$	2.64716e6	−	4.58501e6i	0.782477	−	1.35529i	0.930495	−	0.366305i	$-0.119377\pi$
$410$	−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	−0.979411	−	0.201876i	$-0.935296\pi$
$431$	−1.21432e6	+	2.10326e6i	−0.314876	+	0.545380i	0.664535	+	0.747257i	$0.268629\pi$
$432$		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	0.654794	−	0.755808i	$-0.272756\pi$
$439$	−1.32102e6	−	2.28808e6i	−0.327152	−	0.566644i	−0.981946	+	0.189164i	$0.939422\pi$
$440$	−2.59867e6			−0.639910
$441$		0			0
$442$	10316.4			0.00251174
$443$	−1.71983e6	−	2.97883e6i	−0.416366	−	0.721168i	0.579205	−	0.815182i	$-0.303363\pi$
$443$	−1.71983e6	−	2.97883e6i	−0.416366	−	0.721168i	−0.995571	+	0.0940147i	$0.970030\pi$
$444$		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	0.964104	−	0.265524i	$-0.0855451\pi$
$457$	1.12555e6	+	1.94951e6i	0.252101	+	0.436652i	−0.712003	+	0.702176i	$0.752212\pi$
$458$	−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	0.803843	−	0.594841i	$-0.202785\pi$
$467$	−533627.	−	924270.i	−0.113226	−	0.196113i	−0.917069	+	0.398728i	$0.869452\pi$
$468$		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	0.430577	+	0.902554i	$0.358310\pi$
$479$	−2.84394e6	+	4.92585e6i	−0.566346	+	0.980939i	−0.996923	+	0.0783858i	$0.975023\pi$
$480$		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	−0.328277	−	0.944582i	$-0.606468\pi$
$487$	3.42239e6	−	5.92775e6i	0.653893	−	1.13258i	0.982170	−	0.187995i	$-0.0601987\pi$
$488$	−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	0.951690	−	0.307061i	$-0.0993455\pi$
$499$	1.16764e6	+	2.02242e6i	0.209923	+	0.363596i	−0.741767	+	0.670657i	$0.766012\pi$
$500$	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	0.969346	−	0.245700i	$-0.0790178\pi$
$509$	1.58924e6	+	2.75264e6i	0.271890	+	0.470928i	−0.697455	+	0.716628i	$0.745684\pi$
$510$		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	0.486761	+	0.873535i	$0.338178\pi$
$521$	−3.17918e6	+	5.50651e6i	−0.513123	+	0.888755i	−0.999884	+	0.0152197i	$0.995155\pi$
$522$		0			0
$523$	3.61094e6	+	6.25433e6i	0.577252	+	0.999830i	0.995793	+	0.0916321i	$0.0292084\pi$
$523$	3.61094e6	+	6.25433e6i	0.577252	+	0.999830i	−0.418541	+	0.908198i	$0.637458\pi$
$524$	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	0.970940	+	0.239325i	$0.0769260\pi$
$541$	4.71583e6	+	8.16805e6i	0.692731	+	1.19985i	−0.278209	+	0.960521i	$0.589741\pi$
$542$	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	−0.322258	−	0.946652i	$-0.604442\pi$
$557$	4.82306e6	−	8.35379e6i	0.658696	−	1.14089i	0.980953	−	0.194243i	$-0.0622249\pi$
$558$		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	−0.744613	−	0.667496i	$-0.767366\pi$
$563$	1.54752e6	−	2.68038e6i	0.205762	−	0.356390i	0.950375	+	0.311106i	$0.100699\pi$
$564$		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	−0.921218	−	0.389046i	$-0.872805\pi$
$569$	−6.15927e6	−	1.06682e7i	−0.797533	−	1.38137i	0.123685	−	0.992322i	$-0.460529\pi$
$570$		0			0
$571$	1.61755e6	−	2.80168e6i	0.207619	−	0.359607i	−0.743345	−	0.668908i	$-0.766762\pi$
$571$	1.61755e6	−	2.80168e6i	0.207619	−	0.359607i	0.950964	+	0.309302i	$0.100095\pi$
$572$	−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	−0.431118	−	0.902296i	$-0.641881\pi$
$577$	4.52525e6	−	7.83796e6i	0.565852	−	0.980084i	0.996970	−	0.0777887i	$-0.0247859\pi$
$578$	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	0.571918	−	0.820311i	$-0.306200\pi$
$593$	−3.63467e6	−	6.29543e6i	−0.424451	−	0.735171i	−0.996369	+	0.0851397i	$0.972866\pi$
$594$		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	−0.921962	−	0.387281i	$-0.873414\pi$
$599$	−1.10282e6	+	1.91015e6i	−0.125585	+	0.217520i	0.796376	+	0.604802i	$0.206748\pi$
$600$		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	0.637742	−	0.770250i	$-0.279869\pi$
$607$	−3.16069e6	−	5.47448e6i	−0.348185	−	0.603075i	−0.985927	+	0.167175i	$0.946535\pi$
$608$	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	0.169196	+	0.985582i	$0.445883\pi$
$613$	−7.15392e6	+	1.23910e7i	−0.768941	+	1.33185i	−0.938138	+	0.346263i	$0.887451\pi$
$614$	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	−0.997182	−	0.0750208i	$-0.976098\pi$
$619$	−4.13368e6	+	7.15975e6i	−0.433621	+	0.751054i	0.563561	+	0.826074i	$0.309431\pi$
$620$	−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	−0.939006	−	0.343902i	$-0.888251\pi$
$641$	−1.78588e6	+	3.09324e6i	−0.171675	+	0.297350i	0.767330	+	0.641252i	$0.221585\pi$
$642$		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	−0.902827	−	0.430004i	$-0.858512\pi$
$647$	−841379.	+	1.45731e6i	−0.0790189	+	0.136865i	0.823808	+	0.566869i	$0.191845\pi$
$648$		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	0.931082	+	0.364809i	$0.118866\pi$
$653$	8.51526e6	+	1.47489e7i	0.781475	+	1.35355i	−0.149608	+	0.988745i	$0.547801\pi$
$654$		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	−0.996458	−	0.0840888i	$-0.973202\pi$
$661$	−4.77867e6	+	8.27691e6i	−0.425406	+	0.736825i	0.571052	+	0.820914i	$0.306535\pi$
$662$	−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	−0.991754	−	0.128153i	$-0.959095\pi$
$677$	−7.23704e6	−	1.25349e7i	−0.606861	−	1.05111i	0.384894	−	0.922961i	$-0.374238\pi$
$678$		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	−0.805629	−	0.592420i	$-0.798173\pi$
$683$	1.34392e6	−	2.32774e6i	0.110236	−	0.190934i	0.915865	+	0.401486i	$0.131506\pi$
$684$		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	0.757725	−	0.652574i	$-0.226311\pi$
$691$	−2.33814e6	−	4.04977e6i	−0.186284	−	0.322653i	−0.944008	+	0.329922i	$0.892978\pi$
$692$	−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	0.960562	−	0.278067i	$-0.0896936\pi$
$709$	3.20526e6	+	5.55168e6i	0.239468	+	0.414771i	−0.721094	+	0.692838i	$0.756360\pi$
$710$	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	0.967547	−	0.252691i	$-0.0813155\pi$
$719$	3.67253e6	+	6.36100e6i	0.264937	+	0.458885i	−0.702610	+	0.711575i	$0.747982\pi$
$720$		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	0.533925	−	0.845532i	$-0.320716\pi$
$733$	−6.76835e6	−	1.17231e7i	−0.465289	−	0.805905i	−0.999215	+	0.0396269i	$0.987383\pi$
$734$	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	−0.715617	−	0.698492i	$-0.753855\pi$
$739$	3.66851e6	−	6.35405e6i	0.247103	−	0.427996i	0.962721	+	0.270497i	$0.0871879\pi$
$740$	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	0.688300	−	0.725426i	$-0.258357\pi$
$751$	−4.39088e6	−	7.60523e6i	−0.284087	−	0.492054i	−0.972387	+	0.233372i	$0.925024\pi$
$752$	−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	0.999388	−	0.0349882i	$-0.0111394\pi$
$761$	7.49891e6	+	1.29885e7i	0.469393	+	0.813013i	−0.529995	+	0.848001i	$0.677806\pi$
$762$		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	−0.620013	−	0.784592i	$-0.712872\pi$
$773$	6.13802e6	−	1.06314e7i	0.369470	−	0.639941i	0.989483	+	0.144651i	$0.0462058\pi$
$774$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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