LMFDB - Embedded newform 147.6.e.o.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			79.3
Root			$0.895402 - 1.55088i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.o.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.395402 - 0.684857i) q^{2} +(4.50000 + 7.79423i) q^{3} +(15.6873 + 27.1712i) q^{4} +(-52.0958 + 90.2327i) q^{5} +7.11724 q^{6} +50.1170 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(0.395402 - 0.684857i) q^{2} +(4.50000 + 7.79423i) q^{3} +(15.6873 + 27.1712i) q^{4} +(-52.0958 + 90.2327i) q^{5} +7.11724 q^{6} +50.1170 q^{8} +(-40.5000 + 70.1481i) q^{9} +(41.1977 + 71.3564i) q^{10} +(248.830 + 430.986i) q^{11} +(-141.186 + 244.541i) q^{12} +206.551 q^{13} -937.725 q^{15} +(-482.178 + 835.156i) q^{16} +(31.5793 + 54.6969i) q^{17} +(32.0276 + 55.4734i) q^{18} +(661.977 - 1146.58i) q^{19} -3268.98 q^{20} +393.552 q^{22} +(97.2187 - 168.388i) q^{23} +(225.526 + 390.623i) q^{24} +(-3865.45 - 6695.16i) q^{25} +(81.6709 - 141.458i) q^{26} -729.000 q^{27} +4323.14 q^{29} +(-370.779 + 642.208i) q^{30} +(-3762.66 - 6517.11i) q^{31} +(1183.18 + 2049.33i) q^{32} +(-2239.47 + 3878.87i) q^{33} +49.9461 q^{34} -2541.34 q^{36} +(-5177.82 + 8968.25i) q^{37} +(-523.495 - 906.720i) q^{38} +(929.481 + 1609.91i) q^{39} +(-2610.89 + 4522.19i) q^{40} +4180.92 q^{41} +5960.87 q^{43} +(-7806.94 + 13522.0i) q^{44} +(-4219.76 - 7308.85i) q^{45} +(-76.8810 - 133.162i) q^{46} +(-2194.87 + 3801.62i) q^{47} -8679.20 q^{48} -6113.64 q^{50} +(-284.214 + 492.273i) q^{51} +(3240.24 + 5612.25i) q^{52} +(-8892.39 - 15402.1i) q^{53} +(-288.248 + 499.261i) q^{54} -51852.0 q^{55} +11915.6 q^{57} +(1709.38 - 2960.73i) q^{58} +(1750.23 + 3031.49i) q^{59} +(-14710.4 - 25479.1i) q^{60} +(-5316.23 + 9207.98i) q^{61} -5951.06 q^{62} -28988.0 q^{64} +(-10760.5 + 18637.7i) q^{65} +(1770.98 + 3067.43i) q^{66} +(6637.37 + 11496.3i) q^{67} +(-990.789 + 1716.10i) q^{68} +1749.94 q^{69} +38811.1 q^{71} +(-2029.74 + 3515.61i) q^{72} +(15687.8 + 27172.1i) q^{73} +(4094.65 + 7092.14i) q^{74} +(34789.1 - 60256.5i) q^{75} +41538.6 q^{76} +1470.08 q^{78} +(-19745.7 + 34200.6i) q^{79} +(-50238.9 - 87016.3i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(1653.14 - 2863.33i) q^{82} +102372. q^{83} -6580.60 q^{85} +(2356.94 - 4082.34i) q^{86} +(19454.1 + 33695.5i) q^{87} +(12470.6 + 21599.7i) q^{88} +(-56410.5 + 97705.8i) q^{89} -6674.02 q^{90} +6100.40 q^{92} +(33863.9 - 58654.0i) q^{93} +(1735.71 + 3006.34i) q^{94} +(68972.6 + 119464. i) q^{95} +(-10648.6 + 18444.0i) q^{96} -30334.3 q^{97} -40310.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9 + 283 * q^10 - 402 * q^11 + 621 * q^12 - 924 * q^13 - 3273 * q^16 + 276 * q^17 - 243 * q^18 + 510 * q^19 - 9438 * q^20 + 2750 * q^22 - 6900 * q^23 + 1107 * q^24 - 2814 * q^25 - 15138 * q^26 - 5832 * q^27 + 1080 * q^29 - 2547 * q^30 - 6410 * q^31 - 15519 * q^32 + 3618 * q^33 - 42288 * q^34 + 11178 * q^36 - 15250 * q^37 - 41250 * q^38 - 4158 * q^39 - 8547 * q^40 - 8616 * q^41 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 58914 * q^48 - 14604 * q^50 - 2484 * q^51 - 47476 * q^52 - 13692 * q^53 + 2187 * q^54 - 146248 * q^55 + 9180 * q^57 - 52309 * q^58 + 34830 * q^59 - 42471 * q^60 - 5364 * q^61 - 32058 * q^62 - 146974 * q^64 - 66864 * q^65 + 12375 * q^66 + 5994 * q^67 - 58272 * q^68 - 124200 * q^69 + 178536 * q^71 - 9963 * q^72 + 59638 * q^73 + 185442 * q^74 + 25326 * q^75 - 42616 * q^76 - 272484 * q^78 + 44062 * q^79 - 33381 * q^80 - 26244 * q^81 + 57596 * q^82 + 416892 * q^83 + 72648 * q^85 + 136968 * q^86 + 4860 * q^87 - 87597 * q^88 - 77520 * q^89 - 45846 * q^90 + 316512 * q^92 + 57690 * q^93 - 73722 * q^94 + 221376 * q^95 + 139671 * q^96 + 377260 * q^97 + 65124 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.395402	−	0.684857i	0.0698979	−	0.121067i	−0.828958	−	0.559310i	$-0.811066\pi$
$2$	0.395402	−	0.684857i	0.0698979	−	0.121067i	0.898856	+	0.438244i	$0.144399\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	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	$0.784800\pi$
$6$	7.11724			0.0807112
$7$		0			0
$7$		0			0
$8$	50.1170			0.276860
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	41.1977	+	71.3564i	0.130278	+	0.225649i
$11$	248.830	+	430.986i	0.620041	+	1.07394i	0.989477	+	0.144687i	$0.0462176\pi$
$11$	248.830	+	430.986i	0.620041	+	1.07394i	−0.369436	+	0.929256i	$0.620449\pi$
$12$	−141.186	+	244.541i	−0.283034	+	0.490229i
$13$	206.551			0.338977			0.169488	−	0.985532i	$-0.445789\pi$
$13$	206.551			0.338977			0.169488	+	0.985532i	$0.445789\pi$
$14$		0			0
$15$	−937.725			−1.07609
$16$	−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	$0.824896\pi$
$18$	32.0276	+	55.4734i	0.0232993	+	0.0403556i
$19$	661.977	−	1146.58i	0.420687	−	0.728651i	−0.575320	−	0.817929i	$-0.695122\pi$
$19$	661.977	−	1146.58i	0.420687	−	0.728651i	0.996007	+	0.0892772i	$0.0284557\pi$
$20$	−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	$-0.821133\pi$
$23$	97.2187	−	168.388i	0.0383204	−	0.0663729i	0.884550	+	0.466446i	$0.154466\pi$
$24$	225.526	+	390.623i	0.0799225	+	0.138430i
$25$	−3865.45	−	6695.16i	−1.23695	−	2.14245i
$26$	81.6709	−	141.458i	0.0236938	−	0.0410388i
$27$	−729.000			−0.192450
$28$		0			0
$29$	4323.14			0.954562			0.477281	−	0.878751i	$-0.341622\pi$
$29$	4323.14			0.954562			0.477281	+	0.878751i	$0.341622\pi$
$30$	−370.779	+	642.208i	−0.0752163	+	0.130278i
$31$	−3762.66	−	6517.11i	−0.703219	−	1.21801i	−0.967331	−	0.253518i	$-0.918412\pi$
$31$	−3762.66	−	6517.11i	−0.703219	−	1.21801i	0.264112	−	0.964492i	$-0.414921\pi$
$32$	1183.18	+	2049.33i	0.204256	+	0.353783i
$33$	−2239.47	+	3878.87i	−0.357981	+	0.620041i
$34$	49.9461			0.00740977
$35$		0			0
$36$	−2541.34			−0.326819
$37$	−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
$39$	929.481	+	1609.91i	0.0978541	+	0.169488i
$40$	−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
$45$	−4219.76	−	7308.85i	−0.310640	−	0.538044i
$46$	−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	$0.212963\pi$
$48$	−8679.20			−0.543721
$49$		0			0
$50$	−6113.64			−0.345840
$51$	−284.214	+	492.273i	−0.0153010	+	0.0265021i
$52$	3240.24	+	5612.25i	0.166176	+	0.287825i
$53$	−8892.39	−	15402.1i	−0.434839	−	0.753164i	0.562443	−	0.826836i	$-0.309862\pi$
$53$	−8892.39	−	15402.1i	−0.434839	−	0.753164i	−0.997283	+	0.0736720i	$0.976528\pi$
$54$	−288.248	+	499.261i	−0.0134519	+	0.0232993i
$55$	−51852.0			−2.31131
$56$		0			0
$57$	11915.6			0.485768
$58$	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	$0.812482\pi$
$60$	−14710.4	−	25479.1i	−0.527529	−	0.913706i
$61$	−5316.23	+	9207.98i	−0.182928	+	0.316840i	−0.942876	−	0.333143i	$-0.891891\pi$
$61$	−5316.23	+	9207.98i	−0.182928	+	0.316840i	0.759949	+	0.649983i	$0.225224\pi$
$62$	−5951.06			−0.196614
$63$		0			0
$64$	−28988.0			−0.884645
$65$	−10760.5	+	18637.7i	−0.315899	+	0.547153i
$66$	1770.98	+	3067.43i	0.0500443	+	0.0866792i
$67$	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
$69$	1749.94			0.0442486
$70$		0			0
$71$	38811.1			0.913713			0.456857	−	0.889540i	$-0.348975\pi$
$71$	38811.1			0.913713			0.456857	+	0.889540i	$0.348975\pi$
$72$	−2029.74	+	3515.61i	−0.0461433	+	0.0799225i
$73$	15687.8	+	27172.1i	0.344552	+	0.596782i	0.985272	−	0.170992i	$-0.0546974\pi$
$73$	15687.8	+	27172.1i	0.344552	+	0.596782i	−0.640720	+	0.767775i	$0.721364\pi$
$74$	4094.65	+	7092.14i	0.0869235	+	0.150556i
$75$	34789.1	−	60256.5i	0.714151	−	1.23695i
$76$	41538.6			0.824931
$77$		0			0
$78$	1470.08			0.0273592
$79$	−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
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	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
$87$	19454.1	+	33695.5i	0.275558	+	0.477281i
$88$	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	$0.894356\pi$
$90$	−6674.02			−0.0868523
$91$		0			0
$92$	6100.40			0.0751430
$93$	33863.9	−	58654.0i	0.406004	−	0.703219i
$94$	1735.71	+	3006.34i	0.0202609	+	0.0350929i
$95$	68972.6	+	119464.i	0.784092	+	1.35809i
$96$	−10648.6	+	18444.0i	−0.117928	+	0.204256i
$97$	−30334.3			−0.327345			−0.163672	−	0.986515i	$-0.552334\pi$
$97$	−30334.3			−0.327345			−0.163672	+	0.986515i	$0.552334\pi$
$98$		0			0
$99$	−40310.4			−0.413361
$100$	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	$0.658944\pi$
$102$	224.758	+	389.292i	0.00213902	+	0.00370488i
$103$	78767.8	−	136430.i	0.731570	−	1.26712i	−0.224643	−	0.974441i	$-0.572121\pi$
$103$	78767.8	−	136430.i	0.731570	−	1.26712i	0.956212	−	0.292674i	$-0.0945452\pi$
$104$	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	$-0.710248\pi$
$107$	44662.2	−	77357.1i	0.377121	−	0.653192i	0.990642	+	0.136486i	$0.0435809\pi$
$108$	−11436.1	−	19807.8i	−0.0943445	−	0.163410i
$109$	−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
$111$	−93200.8			−0.717980
$112$		0			0
$113$	−115794.			−0.853079			−0.426539	−	0.904469i	$-0.640267\pi$
$113$	−115794.			−0.853079			−0.426539	+	0.904469i	$0.640267\pi$
$114$	4711.46	−	8160.48i	0.0339542	−	0.0588103i
$115$	10129.4	+	17544.6i	0.0714230	+	0.123708i
$116$	67818.4	+	117465.i	0.467954	+	0.810519i
$117$	−8365.33	+	14489.2i	−0.0564961	+	0.0978541i
$118$	2768.19			0.0183017
$119$		0			0
$120$	−46995.9			−0.297925
$121$	−43307.1	+	75010.0i	−0.268903	+	0.465753i
$122$	4204.10	+	7281.72i	0.0255725	+	0.0442929i
$123$	18814.1	+	32587.0i	0.112130	+	0.194215i
$124$	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
$129$	26823.9	+	46460.4i	0.141921	+	0.245815i
$130$	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	$0.135445\pi$
$132$	−140525.			−0.701970
$133$		0			0
$134$	10497.7			0.0505049
$135$	37977.9	−	65779.6i	0.179348	−	0.310640i
$136$	1582.66	+	2741.25i	0.00733736	+	0.0127087i
$137$	120861.	+	209337.i	0.550155	+	0.952896i	0.998263	+	0.0589167i	$0.0187646\pi$
$137$	120861.	+	209337.i	0.550155	+	0.952896i	−0.448108	+	0.893979i	$0.647902\pi$
$138$	691.929	−	1198.46i	0.00309289	−	0.00535703i
$139$	53112.2			0.233162			0.116581	−	0.993181i	$-0.462807\pi$
$139$	53112.2			0.233162			0.116581	+	0.993181i	$0.462807\pi$
$140$		0			0
$141$	−39507.6			−0.167353
$142$	15346.0	−	26580.1i	0.0638667	−	0.110620i
$143$	51396.1	+	89020.7i	0.210180	+	0.364042i
$144$	−39056.4	−	67647.7i	−0.156959	−	0.271861i
$145$	−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	$-0.909866\pi$
$149$	−64531.0	+	111771.i	−0.238124	+	0.412443i	0.722052	+	0.691839i	$0.243199\pi$
$150$	−27511.4	−	47651.1i	−0.0998353	−	0.172920i
$151$	−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
$153$	−5115.85			−0.0176681
$154$		0			0
$155$	784075.			2.62137
$156$	−29162.1	+	50510.3i	−0.0959418	+	0.166176i
$157$	−75593.9	−	130932.i	−0.244758	−	0.423934i	0.717305	−	0.696759i	$-0.245375\pi$
$157$	−75593.9	−	130932.i	−0.244758	−	0.423934i	−0.962064	+	0.272825i	$0.912042\pi$
$158$	15615.0	+	27046.0i	0.0497622	+	0.0861907i
$159$	80031.5	−	138619.i	0.251055	−	0.434839i
$160$	−246555.			−0.761402
$161$		0			0
$162$	−5188.47			−0.0155329
$163$	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
$165$	−233334.	−	404146.i	−0.667219	−	1.15566i
$166$	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
$171$	53620.2	+	92872.9i	0.140229	+	0.242884i
$172$	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	$0.986963\pi$
$174$	30768.8			0.0770438
$175$		0			0
$176$	−479921.			−1.16785
$177$	−15752.1	+	27283.4i	−0.0377925	+	0.0654585i
$178$	44609.7	+	77266.3i	0.105531	+	0.182785i
$179$	−1747.03	−	3025.94i	−0.00407538	−	0.00705876i	0.863981	−	0.503525i	$-0.167964\pi$
$179$	−1747.03	−	3025.94i	−0.00407538	−	0.00705876i	−0.868056	+	0.496466i	$0.834631\pi$
$180$	132394.	−	229312.i	0.304569	−	0.527529i
$181$	−594611.			−1.34908			−0.674538	−	0.738240i	$-0.735657\pi$
$181$	−594611.			−1.34908			−0.674538	+	0.738240i	$0.735657\pi$
$182$		0			0
$183$	−95692.2			−0.211227
$184$	4872.30	−	8439.08i	0.0106094	−	0.0183760i
$185$	−539486.	−	934418.i	−1.15891	−	2.00730i
$186$	−26779.8	−	46383.9i	−0.0567576	−	0.0983071i
$187$	−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	$0.473685\pi$
$191$	−414322.	+	717627.i	−0.821778	+	1.42336i	−0.904357	+	0.426777i	$0.859649\pi$
$192$	−130446.	−	225939.i	−0.255375	−	0.442322i
$193$	−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
$195$	−193688.			−0.364768
$196$		0			0
$197$	475612.			0.873146			0.436573	−	0.899669i	$-0.356192\pi$
$197$	475612.			0.873146			0.436573	+	0.899669i	$0.356192\pi$
$198$	−15938.8	+	27606.9i	−0.0288931	+	0.0500443i
$199$	313778.	+	543479.i	0.561681	+	0.972859i	0.997350	+	0.0727525i	$0.0231783\pi$
$199$	313778.	+	543479.i	0.561681	+	0.972859i	−0.435669	+	0.900107i	$0.643488\pi$
$200$	−193725.	−	335541.i	−0.342460	−	0.593159i
$201$	−59736.4	+	103466.i	−0.104291	+	0.180638i
$202$	84455.1			0.145629
$203$		0			0
$204$	−17834.2			−0.0300039
$205$	−217808.	+	377255.i	−0.361984	+	0.626975i
$206$	−62290.0	−	107889.i	−0.102270	−	0.177138i
$207$	7874.71	+	13639.4i	0.0127735	+	0.0221243i
$208$	−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
$213$	174650.	+	302502.i	0.263766	+	0.456857i
$214$	−35319.1	−	61174.4i	−0.0527199	−	0.0913136i
$215$	−310536.	+	537865.i	−0.458159	+	0.793555i
$216$	−36535.3			−0.0532817
$217$		0			0
$218$	−132543.			−0.188892
$219$	−141190.	+	244549.i	−0.198927	+	0.344552i
$220$	−813419.	−	1.40888e6i	−1.13307	−	1.96254i
$221$	6522.75	+	11297.7i	0.00898359	+	0.0155600i
$222$	−36851.8	+	63829.3i	−0.0501853	+	0.0869235i
$223$	−4233.11			−0.00570029			−0.00285015	−	0.999996i	$-0.500907\pi$
$223$	−4233.11			−0.00570029			−0.00285015	+	0.999996i	$0.500907\pi$
$224$		0			0
$225$	626204.			0.824630
$226$	−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	$0.573939\pi$
$228$	186924.	+	323761.i	0.238137	+	0.412466i
$229$	402322.	−	696842.i	0.506973	−	0.878103i	−0.492994	−	0.870032i	$-0.664098\pi$
$229$	402322.	−	696842.i	0.506973	−	0.878103i	0.999967	−	0.00807048i	$-0.00256894\pi$
$230$	16020.7			0.0199693
$231$		0			0
$232$	216663.			0.264280
$233$	−584636.	+	1.01262e6i	−0.705498	+	1.22196i	0.261013	+	0.965335i	$0.415943\pi$
$233$	−584636.	+	1.01262e6i	−0.705498	+	1.22196i	−0.966511	+	0.256624i	$0.917390\pi$
$234$	6615.34	+	11458.1i	0.00789792	+	0.0136796i
$235$	−228687.	−	396098.i	−0.270130	−	0.467878i
$236$	−54912.9	+	95112.0i	−0.0641792	+	0.111162i
$237$	−355423.			−0.411031
$238$		0			0
$239$	−1.70554e6			−1.93138			−0.965689	−	0.259700i	$-0.916376\pi$
$239$	−1.70554e6			−1.93138			−0.965689	+	0.259700i	$0.916376\pi$
$240$	452150.	−	783147.i	0.506704	−	0.877638i
$241$	475598.	+	823760.i	0.527470	+	0.913604i	0.999487	+	0.0320153i	$0.0101925\pi$
$241$	475598.	+	823760.i	0.527470	+	0.913604i	−0.472018	+	0.881589i	$0.656474\pi$
$242$	34247.4	+	59318.3i	0.0375915	+	0.0651104i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	−333590.			−0.358705
$245$		0			0
$246$	29756.6			0.0313506
$247$	136732.	−	236827.i	0.142603	−	0.246996i
$248$	−188573.	−	326618.i	−0.194693	−	0.337218i
$249$	460673.	+	797909.i	0.470863	+	0.815559i
$250$	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
$255$	−29612.7	−	51290.7i	−0.0285186	−	0.0493956i
$256$	−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	$-0.0221389\pi$
$258$	42425.0			0.0396800
$259$		0			0
$260$	−675211.			−0.619450
$261$	−175087.	+	303260.i	−0.159094	+	0.275558i
$262$	−15211.0	−	26346.2i	−0.0136900	−	0.0237118i
$263$	−224158.	−	388253.i	−0.199832	−	0.346119i	0.748642	−	0.662975i	$-0.230706\pi$
$263$	−224158.	−	388253.i	−0.199832	−	0.346119i	−0.948474	+	0.316856i	$0.897373\pi$
$264$	−112235.	+	194397.i	−0.0991106	+	0.171665i
$265$	1.85303e6			1.62094
$266$		0			0
$267$	−1.01539e6			−0.871674
$268$	−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	$0.731359\pi$
$270$	−30033.1	−	52018.8i	−0.0250721	−	0.0434261i
$271$	−116319.	+	201470.i	−0.0962114	+	0.166643i	−0.910114	−	0.414359i	$-0.864006\pi$
$271$	−116319.	+	201470.i	−0.0962114	+	0.166643i	0.813902	+	0.581002i	$0.197339\pi$
$272$	−60907.3			−0.0499169
$273$		0			0
$274$	191155.			0.153819
$275$	1.92368e6	−	3.33191e6i	1.53391	−	2.65682i
$276$	27451.8	+	47547.9i	0.0216919	+	0.0375715i
$277$	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
$279$	609550.			0.468812
$280$		0			0
$281$	2.51704e6			1.90163			0.950813	−	0.309766i	$-0.100251\pi$
$281$	2.51704e6			1.90163			0.950813	+	0.309766i	$0.100251\pi$
$282$	−15621.4	+	27057.1i	−0.0116976	+	0.0202609i
$283$	130497.	+	226028.i	0.0968579	+	0.167763i	0.910382	−	0.413768i	$-0.135787\pi$
$283$	130497.	+	226028.i	0.0968579	+	0.167763i	−0.813525	+	0.581530i	$0.802454\pi$
$284$	608842.	+	1.05454e6i	0.447928	+	0.775835i
$285$	−620753.	+	1.07518e6i	−0.452696	+	0.784092i
$286$	81288.6			0.0587645
$287$		0			0
$288$	−191675.			−0.136171
$289$	707934.	−	1.22618e6i	0.498595	−	0.863592i
$290$	178103.	+	308484.i	0.124359	+	0.215396i
$291$	−136505.	−	236433.i	−0.0944963	−	0.163672i
$292$	−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
$297$	−181397.	−	314189.i	−0.119327	−	0.206680i
$298$	51031.5	+	88389.1i	0.0332887	+	0.0576578i
$299$	20080.6	−	34780.7i	0.0129897	−	0.0224989i
$300$	2.18299e6			1.40039
$301$		0			0
$302$	−121156.			−0.0764414
$303$	−480584.	+	832395.i	−0.300720	+	0.520862i
$304$	638381.	+	1.10571e6i	0.396183	+	0.686210i
$305$	−553907.	−	959395.i	−0.340947	−	0.590538i
$306$	−2022.82	+	3503.62i	−0.00123496	+	0.00213902i
$307$	2.35599e6			1.42668			0.713342	−	0.700816i	$-0.247181\pi$
$307$	2.35599e6			1.42668			0.713342	+	0.700816i	$0.247181\pi$
$308$		0			0
$309$	1.41782e6			0.844744
$310$	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	$-0.379890\pi$
$312$	46582.8	+	80683.7i	0.0270919	+	0.0469245i
$313$	−93756.8	+	162392.i	−0.0540931	+	0.0936920i	−0.891804	−	0.452422i	$-0.850560\pi$
$313$	−93756.8	+	162392.i	−0.0540931	+	0.0936920i	0.837711	+	0.546114i	$0.183893\pi$
$314$	−119560.			−0.0684324
$315$		0			0
$316$	−1.23903e6			−0.698014
$317$	502705.	−	870711.i	0.280974	−	0.486661i	−0.690651	−	0.723188i	$-0.742676\pi$
$317$	502705.	−	870711.i	0.280974	−	0.486661i	0.971625	+	0.236527i	$0.0760093\pi$
$318$	−63289.3	−	109620.i	−0.0350964	−	0.0607888i
$319$	1.07573e6	+	1.86321e6i	0.591868	+	1.02515i
$320$	1.51016e6	−	2.61567e6i	0.824417	−	1.42793i
$321$	803919.			0.435461
$322$		0			0
$323$	83619.1			0.0445964
$324$	102924.	−	178270.i	0.0544698	−	0.0943445i
$325$	−798415.	−	1.38290e6i	−0.419296	−	0.726241i
$326$	−13015.3	−	22543.2i	−0.00678284	−	0.0117482i
$327$	754220.	−	1.30635e6i	0.390058	−	0.675600i
$328$	209535.			0.107540
$329$		0			0
$330$	−369043.			−0.186549
$331$	−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
$333$	−419404.	−	726429.i	−0.207263	−	0.358990i
$334$	−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
$339$	−521072.	−	902523.i	−0.246263	−	0.426539i
$340$	−103232.	−	178803.i	−0.0484303	−	0.0838837i
$341$	1.87252e6	−	3.24330e6i	0.872049	−	1.51043i
$342$	84806.2			0.0392069
$343$		0			0
$344$	298741.			0.136113
$345$	−91164.4	+	157901.i	−0.0412361	+	0.0714230i
$346$	166560.	+	288491.i	0.0747965	+	0.129551i
$347$	−2.02833e6	−	3.51317e6i	−0.904304	−	1.56630i	−0.821849	−	0.569705i	$-0.807057\pi$
$347$	−2.02833e6	−	3.51317e6i	−0.904304	−	1.56630i	−0.0824546	−	0.996595i	$-0.526276\pi$
$348$	−610366.	+	1.05718e6i	−0.270173	+	0.467954i
$349$	−2.86202e6			−1.25779			−0.628897	−	0.777488i	$-0.716493\pi$
$349$	−2.86202e6			−1.25779			−0.628897	+	0.777488i	$0.716493\pi$
$350$		0			0
$351$	−150576.			−0.0652361
$352$	−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	$0.776424\pi$
$354$	12456.8	+	21575.9i	0.00528323	+	0.00915083i
$355$	−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	$-0.647073\pi$
$359$	1.34875e6	−	2.33611e6i	0.552327	−	0.956659i	0.998106	−	0.0615157i	$-0.0195934\pi$
$360$	−211482.	−	366297.i	−0.0860036	−	0.148963i
$361$	361621.	+	626346.i	0.146045	+	0.252957i
$362$	−235110.	+	407223.i	−0.0942976	+	0.163328i
$363$	−779527.			−0.310502
$364$		0			0
$365$	−3.26908e6			−1.28438
$366$	−37836.9	+	65535.5i	−0.0147643	+	0.0255725i
$367$	727411.	+	1.25991e6i	0.281913	+	0.488287i	0.971856	−	0.235576i	$-0.0756978\pi$
$367$	727411.	+	1.25991e6i	0.281913	+	0.488287i	−0.689943	+	0.723864i	$0.742364\pi$
$368$	93753.3	+	162386.i	0.0360884	+	0.0625069i
$369$	−169327.	+	293283.i	−0.0647382	+	0.112130i
$370$	−853257.			−0.324023
$371$		0			0
$372$	2.12494e6			0.796138
$373$	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
$375$	2.15954e6	+	3.74043e6i	0.793018	+	1.37355i
$376$	−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
$381$	906810.	+	1.57064e6i	0.320040	+	0.554325i
$382$	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	$0.930755\pi$
$384$	−887827.			−0.307256
$385$		0			0
$386$	−173771.			−0.0593619
$387$	−241415.	+	418143.i	−0.0819383	+	0.141921i
$388$	−475864.	−	824221.i	−0.160474	−	0.277949i
$389$	−1.41901e6	−	2.45780e6i	−0.475458	−	0.823517i	0.524147	−	0.851628i	$-0.324384\pi$
$389$	−1.41901e6	−	2.45780e6i	−0.475458	−	0.823517i	−0.999605	+	0.0281111i	$0.991051\pi$
$390$	−76584.9	+	132649.i	−0.0254966	+	0.0441613i
$391$	12280.4			0.00406228
$392$		0			0
$393$	346226.			0.113078
$394$	188058.	−	325726.i	0.0610311	−	0.105709i
$395$	−2.05734e6	−	3.56342e6i	−0.663458	−	1.14914i
$396$	−632362.	−	1.09528e6i	−0.202641	−	0.350985i
$397$	2.17133e6	−	3.76085e6i	0.691432	−	1.19760i	−0.279937	−	0.960018i	$-0.590314\pi$
$397$	2.17133e6	−	3.76085e6i	0.691432	−	1.19760i	0.971369	−	0.237577i	$-0.0763532\pi$
$398$	496274.			0.157041
$399$		0			0
$400$	7.45534e6			2.32979
$401$	−1.70152e6	+	2.94712e6i	−0.528417	+	0.915244i	0.471034	+	0.882115i	$0.343881\pi$
$401$	−1.70152e6	+	2.94712e6i	−0.528417	+	0.915244i	−0.999451	+	0.0331296i	$0.989453\pi$
$402$	47239.8	+	81821.8i	0.0145795	+	0.0252525i
$403$	−777182.	−	1.34612e6i	−0.238375	−	0.412877i
$404$	−1.67535e6	+	2.90179e6i	−0.510683	+	0.884529i
$405$	683602.			0.207093
$406$		0			0
$407$	−5.15359e6			−1.54214
$408$	−14243.9	+	24671.2i	−0.00423623	+	0.00733736i
$409$	−2.64716e6	−	4.58501e6i	−0.782477	−	1.35529i	−0.930495	−	0.366305i	$-0.880623\pi$
$409$	−2.64716e6	−	4.58501e6i	−0.782477	−	1.35529i	0.148018	−	0.988985i	$-0.452711\pi$
$410$	172244.	+	298335.i	0.0506039	+	0.0876486i
$411$	−1.08775e6	+	1.88404e6i	−0.317632	+	0.550155i
$412$	4.94262e6			1.43455
$413$		0			0
$414$	12454.7			0.00357136
$415$	−5.33315e6	+	9.23728e6i	−1.52007	+	2.63284i
$416$	244387.	+	423291.i	0.0692382	+	0.119924i
$417$	239005.	+	413969.i	0.0673080	+	0.116581i
$418$	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
$423$	−177784.	−	307932.i	−0.0483106	−	0.0836765i
$424$	−445660.	−	771905.i	−0.120390	−	0.208521i
$425$	244137.	−	422857.i	0.0655633	−	0.113559i
$426$	276228.			0.0737469
$427$		0			0
$428$	2.80252e6			0.739501
$429$	−462565.	+	801187.i	−0.121347	+	0.210180i
$430$	245574.	+	425346.i	0.0640488	+	0.110936i
$431$	1.21432e6	+	2.10326e6i	0.314876	+	0.545380i	0.979411	−	0.201876i	$-0.0647039\pi$
$431$	1.21432e6	+	2.10326e6i	0.314876	+	0.545380i	−0.664535	+	0.747257i	$0.731371\pi$
$432$	351508.	−	608829.i	0.0906202	−	0.156959i
$433$	−956219.			−0.245097			−0.122548	−	0.992463i	$-0.539107\pi$
$433$	−956219.			−0.245097			−0.122548	+	0.992463i	$0.539107\pi$
$434$		0			0
$435$	−4.05392e6			−1.02719
$436$	2.62927e6	−	4.55402e6i	0.662397	−	1.14730i
$437$	−128713.	−	222938.i	−0.0322418	−	0.0558444i
$438$	111654.	+	193390.i	0.0278092	+	0.0481670i
$439$	1.32102e6	−	2.28808e6i	0.327152	−	0.566644i	−0.654794	−	0.755808i	$-0.727244\pi$
$439$	1.32102e6	−	2.28808e6i	0.327152	−	0.566644i	0.981946	+	0.189164i	$0.0605778\pi$
$440$	−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	$-0.696637\pi$
$443$	1.71983e6	−	2.97883e6i	0.416366	−	0.721168i	0.995571	+	0.0940147i	$0.0299701\pi$
$444$	−1.46207e6	−	2.53238e6i	−0.351974	−	0.609637i
$445$	−5.87750e6	−	1.01801e7i	−1.40700	−	2.43699i
$446$	−1673.78	+	2899.07i	−0.000398439	+	0.000690116i
$447$	−1.16156e6			−0.274962
$448$		0			0
$449$	4.39903e6			1.02977			0.514886	−	0.857259i	$-0.327834\pi$
$449$	4.39903e6			1.02977			0.514886	+	0.857259i	$0.327834\pi$
$450$	247602.	−	428860.i	0.0576400	−	0.0998353i
$451$	1.04034e6	+	1.80192e6i	0.240842	+	0.417151i
$452$	−1.81649e6	−	3.14626e6i	−0.418204	−	0.724350i
$453$	689429.	−	1.19413e6i	0.157850	−	0.273404i
$454$	893501.			0.203449
$455$		0			0
$456$	597173.			0.134490
$457$	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
$459$	−23021.3	−	39874.1i	−0.00510033	−	0.00883403i
$460$	−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
$465$	3.52834e6	+	6.11126e6i	0.756725	+	1.31069i
$466$	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	$0.202785\pi$
$468$	−524918.			−0.110784
$469$		0			0
$470$	−361694.			−0.0755260
$471$	680345.	−	1.17839e6i	0.141311	−	0.244758i
$472$	87716.4	+	151929.i	0.0181228	+	0.0313896i
$473$	1.48324e6	+	2.56905e6i	0.304831	+	0.527983i
$474$	−140535.	+	243414.i	−0.0287302	+	0.0497622i
$475$	−1.02354e7			−2.08147
$476$		0			0
$477$	1.44057e6			0.289893
$478$	−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	$-0.358310\pi$
$480$	−1.10950e6	−	1.92171e6i	−0.219798	−	0.380701i
$481$	−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
$486$	−23348.1	−	40440.1i	−0.00448396	−	0.00776644i
$487$	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
$489$	296250.			0.0560256
$490$		0			0
$491$	5.60132e6			1.04854			0.524272	−	0.851551i	$-0.324338\pi$
$491$	5.60132e6			1.04854			0.524272	+	0.851551i	$0.324338\pi$
$492$	−590286.	+	1.02241e6i	−0.109939	+	0.190419i
$493$	136522.	+	236462.i	0.0252979	+	0.0438172i
$494$	−108129.	−	187284.i	−0.0199353	−	0.0345290i
$495$	2.10001e6	−	3.63732e6i	0.385219	−	0.667219i
$496$	7.25708e6			1.32452
$497$		0			0
$498$	728605.			0.131649
$499$	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
$501$	−979135.	−	1.69591e6i	−0.174280	−	0.301862i
$502$	−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
$507$	−1.47883e6	−	2.56141e6i	−0.255505	−	0.442547i
$508$	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	$0.0790178\pi$
$510$	−46835.7			−0.00797356
$511$		0			0
$512$	−3.82859e6			−0.645452
$513$	−482582.	+	835856.i	−0.0809613	+	0.140229i
$514$	−468053.	−	810692.i	−0.0781425	−	0.135347i
$515$	8.20695e6	+	1.42149e7i	1.36353	+	2.36170i
$516$	−841590.	+	1.45768e6i	−0.139148	+	0.241011i
$517$	−2.18460e6			−0.359455
$518$		0			0
$519$	−3.79118e6			−0.617812
$520$	−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	$-0.338178\pi$
$522$	138460.	+	239819.i	0.0222406	+	0.0385219i
$523$	−3.61094e6	+	6.25433e6i	−0.577252	+	0.999830i	0.418541	+	0.908198i	$0.362542\pi$
$523$	−3.61094e6	+	6.25433e6i	−0.577252	+	0.999830i	−0.995793	+	0.0916321i	$0.970792\pi$
$524$	1.20697e6			0.192029
$525$		0			0
$526$	−354531.			−0.0558714
$527$	237644.	−	411612.i	0.0372735	−	0.0645597i
$528$	−2.15964e6	−	3.74061e6i	−0.337130	−	0.583926i
$529$	3.19927e6	+	5.54130e6i	0.497063	+	0.860939i
$530$	732691.	−	1.26906e6i	0.113300	−	0.196242i
$531$	−283538.			−0.0436390
$532$		0			0
$533$	863574.			0.131668
$534$	−401487.	+	695396.i	−0.0609282	+	0.105531i
$535$	4.65343e6	+	8.05997e6i	0.702892	+	1.21744i
$536$	332645.	+	576158.i	0.0500114	+	0.0866223i
$537$	15723.3	−	27233.5i	0.00235292	−	0.00407538i
$538$	591106.			0.0880461
$539$		0			0
$540$	2.38308e6			0.351686
$541$	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
$543$	−2.67575e6	−	4.63453e6i	−0.389444	−	0.674538i
$544$	−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
$549$	−430615.	−	745847.i	−0.0609759	−	0.105613i
$550$	−1.52126e6	−	2.63489e6i	−0.214435	−	0.371412i
$551$	2.86182e6	−	4.95682e6i	0.401572	−	0.695543i
$552$	87701.5			0.0122507
$553$		0			0
$554$	1.92106e6			0.265929
$555$	4.85538e6	−	8.40976e6i	0.669099	−	1.15891i
$556$	833188.	+	1.44312e6i	0.114303	+	0.197978i
$557$	−4.82306e6	−	8.35379e6i	−0.658696	−	1.14089i	−0.980953	−	0.194243i	$-0.937775\pi$
$557$	−4.82306e6	−	8.35379e6i	−0.658696	−	1.14089i	0.322258	−	0.946652i	$-0.395558\pi$
$558$	241018.	−	417455.i	0.0327690	−	0.0567576i
$559$	1.23123e6			0.166651
$560$		0			0
$561$	−282883.			−0.0379490
$562$	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	$0.767366\pi$
$564$	−619769.	−	1.07347e6i	−0.0820412	−	0.142100i
$565$	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	$-0.539471\pi$
$569$	6.15927e6	−	1.06682e7i	0.797533	−	1.38137i	0.921218	−	0.389046i	$-0.127195\pi$
$570$	490895.	+	850254.i	0.0632850	+	0.109613i
$571$	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
$573$	−7.45780e6			−0.948908
$574$		0			0
$575$	−1.50318e6			−0.189601
$576$	1.17402e6	−	2.03345e6i	0.147441	−	0.255375i
$577$	−4.52525e6	−	7.83796e6i	−0.565852	−	0.980084i	−0.996970	−	0.0777887i	$-0.975214\pi$
$577$	−4.52525e6	−	7.83796e6i	−0.565852	−	0.980084i	0.431118	−	0.902296i	$-0.358119\pi$
$578$	−559838.	−	969667.i	−0.0697016	−	0.120727i
$579$	988825.	−	1.71269e6i	0.122581	−	0.212316i
$580$	−1.41322e7			−1.74438
$581$		0			0
$582$	−215897.			−0.0264204
$583$	4.42538e6	−	7.66499e6i	0.539237	−	0.933986i
$584$	786226.	+	1.36178e6i	0.0953927	+	0.165225i
$585$	−871598.	−	1.50965e6i	−0.105300	−	0.182384i
$586$	−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
$591$	2.14025e6	+	3.70703e6i	0.252056	+	0.436573i
$592$	−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	$0.306200\pi$
$594$	−286899.			−0.0333629
$595$		0			0
$596$	−4.04927e6			−0.466941
$597$	−2.82400e6	+	4.89131e6i	−0.324286	+	0.561681i
$598$	−15879.9	−	27504.8i	−0.00181591	−	0.00314525i
$599$	1.10282e6	+	1.91015e6i	0.125585	+	0.217520i	0.921962	−	0.387281i	$-0.126586\pi$
$599$	1.10282e6	+	1.91015e6i	0.125585	+	0.217520i	−0.796376	+	0.604802i	$0.793252\pi$
$600$	1.74352e6	−	3.01987e6i	0.197720	−	0.342460i
$601$	1.00121e7			1.13067			0.565336	−	0.824860i	$-0.308746\pi$
$601$	1.00121e7			1.13067			0.565336	+	0.824860i	$0.308746\pi$
$602$		0			0
$603$	−1.07525e6			−0.120425
$604$	2.40340e6	−	4.16280e6i	0.268061	−	0.464295i
$605$	−4.51224e6	−	7.81542e6i	−0.501191	−	0.868088i
$606$	380048.	+	658262.i	0.0420394	+	0.0728144i
$607$	3.16069e6	−	5.47448e6i	0.348185	−	0.603075i	−0.637742	−	0.770250i	$-0.720131\pi$
$607$	3.16069e6	−	5.47448e6i	0.348185	−	0.603075i	0.985927	+	0.167175i	$0.0534646\pi$
$608$	3.13295e6			0.343712
$609$		0			0
$610$	−876065.			−0.0953261
$611$	−453353.	+	785231.i	−0.0491285	+	0.0850931i
$612$	−80253.9	−	139004.i	−0.00866139	−	0.0150020i
$613$	−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
$615$	−3.92055e6			−0.417984
$616$		0			0
$617$	1.73991e7			1.83999			0.919993	−	0.391936i	$-0.128194\pi$
$617$	1.73991e7			1.83999			0.919993	+	0.391936i	$0.128194\pi$
$618$	560610.	−	971004.i	0.0590459	−	0.102270i
$619$	4.13368e6	+	7.15975e6i	0.433621	+	0.751054i	0.997182	−	0.0750208i	$-0.0239023\pi$
$619$	4.13368e6	+	7.15975e6i	0.433621	+	0.751054i	−0.563561	+	0.826074i	$0.690569\pi$
$620$	1.23000e7	+	2.13043e7i	1.28507	+	2.22581i
$621$	−70872.4	+	122755.i	−0.00737476	+	0.0127735i
$622$	−1.67497e6			−0.173592
$623$		0			0
$624$	−1.79270e6			−0.184309
$625$	−1.29211e7	+	2.23800e7i	−1.32312	+	2.29172i
$626$	74143.4	+	128420.i	0.00756200	+	0.0130978i
$627$	2.96495e6	+	5.13545e6i	0.301196	+	0.521687i
$628$	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
$633$	2.56945e6	+	4.45041e6i	0.254877	+	0.441460i
$634$	−397542.	−	688563.i	−0.0392790	−	0.0680331i
$635$	−1.04980e7	+	1.81831e7i	−1.03317	+	1.78951i
$636$	5.02192e6			0.492297
$637$		0			0
$638$	1.70138e6			0.165481
$639$	−1.57185e6	+	2.72252e6i	−0.152286	+	0.263766i
$640$	−5.13912e6	−	8.90122e6i	−0.495951	−	0.859012i
$641$	1.78588e6	+	3.09324e6i	0.171675	+	0.297350i	0.939006	−	0.343902i	$-0.111749\pi$
$641$	1.78588e6	+	3.09324e6i	0.171675	+	0.297350i	−0.767330	+	0.641252i	$0.778415\pi$
$642$	317872.	−	550570.i	0.0304379	−	0.0527199i
$643$	5.96911e6			0.569354			0.284677	−	0.958624i	$-0.408114\pi$
$643$	5.96911e6			0.569354			0.284677	+	0.958624i	$0.408114\pi$
$644$		0			0
$645$	−5.58966e6			−0.529037
$646$	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	$0.858512\pi$
$648$	−164409.	−	284764.i	−0.0153811	−	0.0266408i
$649$	−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	$0.452199\pi$
$653$	−8.51526e6	+	1.47489e7i	−0.781475	+	1.35355i	−0.931082	+	0.364809i	$0.881134\pi$
$654$	−596441.	−	1.03307e6i	−0.0545285	−	0.0944461i
$655$	2.00411e6	+	3.47121e6i	0.182523	+	0.316139i
$656$	−2.01594e6	+	3.49172e6i	−0.182902	+	0.316796i
$657$	−2.54143e6			−0.229702
$658$		0			0
$659$	−1.99303e7			−1.78772			−0.893862	−	0.448342i	$-0.852015\pi$
$659$	−1.99303e7			−1.78772			−0.893862	+	0.448342i	$0.852015\pi$
$660$	7.32077e6	−	1.26799e7i	0.654179	−	1.13307i
$661$	4.77867e6	+	8.27691e6i	0.425406	+	0.736825i	0.996458	−	0.0840888i	$-0.0267979\pi$
$661$	4.77867e6	+	8.27691e6i	0.425406	+	0.736825i	−0.571052	+	0.820914i	$0.693465\pi$
$662$	664213.	+	1.15045e6i	0.0589064	+	0.102029i
$663$	−58704.7	+	101680.i	−0.00518668	+	0.00898359i
$664$	5.13056e6			0.451591
$665$		0			0
$666$	−663333.			−0.0579490
$667$	420290.	−	727963.i	0.0365792	−	0.0633570i
$668$	−3.41333e6	−	5.91207e6i	−0.295963	−	0.512623i
$669$	−19049.0	−	32993.8i	−0.00164553	−	0.00285015i
$670$	−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
$675$	2.81792e6	+	4.88077e6i	0.238050	+	0.412315i
$676$	−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	$0.959095\pi$
$678$	−824133.			−0.0688530
$679$		0			0
$680$	−329800.			−0.0273513
$681$	−5.08438e6	+	8.80641e6i	−0.420117	+	0.727664i
$682$	−1.48080e6	−	2.56482e6i	−0.121909	−	0.211152i
$683$	−1.34392e6	−	2.32774e6i	−0.110236	−	0.190934i	0.805629	−	0.592420i	$-0.201827\pi$
$683$	−1.34392e6	−	2.32774e6i	−0.110236	−	0.190934i	−0.915865	+	0.401486i	$0.868494\pi$
$684$	−1.68231e6	+	2.91385e6i	−0.137489	+	0.238137i
$685$	−2.51854e7			−2.05080
$686$		0			0
$687$	7.24179e6			0.585402
$688$	−2.87420e6	+	4.97826e6i	−0.231497	+	0.400965i
$689$	−1.83674e6	−	3.18132e6i	−0.147400	−	0.255305i
$690$	72093.3	+	124869.i	0.00576464	+	0.00998464i
$691$	2.33814e6	−	4.04977e6i	0.186284	−	0.322653i	−0.757725	−	0.652574i	$-0.773689\pi$
$691$	2.33814e6	−	4.04977e6i	0.186284	−	0.322653i	0.944008	+	0.329922i	$0.107022\pi$
$692$	−1.32163e7			−1.04917
$693$		0			0
$694$	−3.20802e6			−0.252836
$695$	−2.76693e6	+	4.79246e6i	−0.217288	+	0.376354i
$696$	974982.	+	1.68872e6i	0.0762910	+	0.132140i
$697$	132030.	+	228683.i	0.0102942	+	0.0178301i
$698$	−1.13165e6	+	1.96008e6i	−0.0879172	+	0.152277i
$699$	−1.05235e7			−0.814639
$700$		0			0
$701$	6.34801e6			0.487913			0.243957	−	0.969786i	$-0.421555\pi$
$701$	6.34801e6			0.487913			0.243957	+	0.969786i	$0.421555\pi$
$702$	−59538.1	+	103123.i	−0.00455987	+	0.00789792i
$703$	6.85520e6	+	1.18736e7i	0.523157	+	0.906135i
$704$	−7.21309e6	−	1.24934e7i	−0.548516	−	0.950058i
$705$	2.05818e6	−	3.56488e6i	0.155959	−	0.270130i
$706$	658492.			0.0497208
$707$		0			0
$708$	−988433.			−0.0741078
$709$	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
$711$	−1.59940e6	−	2.77025e6i	−0.118655	−	0.205516i
$712$	−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
$717$	−7.67493e6	−	1.32934e7i	−0.557541	−	0.965689i
$718$	−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	$0.0813155\pi$
$720$	8.13870e6			0.585092
$721$		0			0
$722$	571944.			0.0408329
$723$	−4.28038e6	+	7.41384e6i	−0.304535	+	0.527470i
$724$	−9.32784e6	−	1.61563e7i	−0.661355	−	1.14550i
$725$	−1.67109e7	−	2.89441e7i	−1.18074	−	2.04510i
$726$	−308227.	+	533865.i	−0.0217035	+	0.0375915i
$727$	−1.57839e7			−1.10759			−0.553793	−	0.832655i	$-0.686820\pi$
$727$	−1.57839e7			−1.10759			−0.553793	+	0.832655i	$0.686820\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−1.29260e6	+	2.23885e6i	−0.0897755	+	0.155496i
$731$	188240.	+	326041.i	0.0130292	+	0.0225673i
$732$	−1.50115e6	−	2.60007e6i	−0.103549	−	0.179353i
$733$	6.76835e6	−	1.17231e7i	0.465289	−	0.805905i	−0.533925	−	0.845532i	$-0.679284\pi$
$733$	6.76835e6	−	1.17231e7i	0.465289	−	0.805905i	0.999215	+	0.0396269i	$0.0126170\pi$
$734$	1.15048e6			0.0788205
$735$		0			0
$736$	460109.			0.0313088
$737$	−3.30315e6	+	5.72123e6i	−0.224006	+	0.387990i
$738$	133905.	+	231930.i	0.00905013	+	0.0156753i
$739$	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
$741$	2.46118e6			0.164664
$742$		0			0
$743$	1.20844e7			0.803068			0.401534	−	0.915844i	$-0.368477\pi$
$743$	1.20844e7			0.803068			0.401534	+	0.915844i	$0.368477\pi$
$744$	1.69716e6	−	2.93956e6i	0.112406	−	0.194693i
$745$	−6.72360e6	−	1.16456e7i	−0.443824	−	0.768726i
$746$	−809343.	−	1.40182e6i	−0.0532459	−	0.0922245i
$747$	−4.14606e6	+	7.18118e6i	−0.271853	+	0.470863i
$748$	−986151.			−0.0644450
$749$		0			0
$750$	3.41555e6			0.221721
$751$	−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
$753$	−5.15241e6	−	8.92423e6i	−0.331148	−	0.573566i
$754$	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
$759$	435436.	+	754198.i	0.0274360	+	0.0475205i
$760$	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	$0.0111394\pi$
$762$	1.43422e6			0.0894804
$763$		0			0
$764$	−2.59984e7			−1.61144
$765$	266514.	−	461616.i	0.0164652	−	0.0285186i
$766$	1.53268e6	+	2.65468e6i	0.0943800	+	0.163471i
$767$	361513.	+	626159.i	0.0221889	+	0.0384323i
$768$	3.82323e6	−	6.62203e6i	0.233898	−	0.405124i
$769$	1.85606e7			1.13181			0.565907	−	0.824469i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.395402 - 0.684857i) q^{2} +(4.50000 + 7.79423i) q^{3} +(15.6873 + 27.1712i) q^{4} +(-52.0958 + 90.2327i) q^{5} +7.11724 q^{6} +50.1170 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(0.395402 - 0.684857i) q^{2} +(4.50000 + 7.79423i) q^{3} +(15.6873 + 27.1712i) q^{4} +(-52.0958 + 90.2327i) q^{5} +7.11724 q^{6} +50.1170 q^{8} +(-40.5000 + 70.1481i) q^{9} +(41.1977 + 71.3564i) q^{10} +(248.830 + 430.986i) q^{11} +(-141.186 + 244.541i) q^{12} +206.551 q^{13} -937.725 q^{15} +(-482.178 + 835.156i) q^{16} +(31.5793 + 54.6969i) q^{17} +(32.0276 + 55.4734i) q^{18} +(661.977 - 1146.58i) q^{19} -3268.98 q^{20} +393.552 q^{22} +(97.2187 - 168.388i) q^{23} +(225.526 + 390.623i) q^{24} +(-3865.45 - 6695.16i) q^{25} +(81.6709 - 141.458i) q^{26} -729.000 q^{27} +4323.14 q^{29} +(-370.779 + 642.208i) q^{30} +(-3762.66 - 6517.11i) q^{31} +(1183.18 + 2049.33i) q^{32} +(-2239.47 + 3878.87i) q^{33} +49.9461 q^{34} -2541.34 q^{36} +(-5177.82 + 8968.25i) q^{37} +(-523.495 - 906.720i) q^{38} +(929.481 + 1609.91i) q^{39} +(-2610.89 + 4522.19i) q^{40} +4180.92 q^{41} +5960.87 q^{43} +(-7806.94 + 13522.0i) q^{44} +(-4219.76 - 7308.85i) q^{45} +(-76.8810 - 133.162i) q^{46} +(-2194.87 + 3801.62i) q^{47} -8679.20 q^{48} -6113.64 q^{50} +(-284.214 + 492.273i) q^{51} +(3240.24 + 5612.25i) q^{52} +(-8892.39 - 15402.1i) q^{53} +(-288.248 + 499.261i) q^{54} -51852.0 q^{55} +11915.6 q^{57} +(1709.38 - 2960.73i) q^{58} +(1750.23 + 3031.49i) q^{59} +(-14710.4 - 25479.1i) q^{60} +(-5316.23 + 9207.98i) q^{61} -5951.06 q^{62} -28988.0 q^{64} +(-10760.5 + 18637.7i) q^{65} +(1770.98 + 3067.43i) q^{66} +(6637.37 + 11496.3i) q^{67} +(-990.789 + 1716.10i) q^{68} +1749.94 q^{69} +38811.1 q^{71} +(-2029.74 + 3515.61i) q^{72} +(15687.8 + 27172.1i) q^{73} +(4094.65 + 7092.14i) q^{74} +(34789.1 - 60256.5i) q^{75} +41538.6 q^{76} +1470.08 q^{78} +(-19745.7 + 34200.6i) q^{79} +(-50238.9 - 87016.3i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(1653.14 - 2863.33i) q^{82} +102372. q^{83} -6580.60 q^{85} +(2356.94 - 4082.34i) q^{86} +(19454.1 + 33695.5i) q^{87} +(12470.6 + 21599.7i) q^{88} +(-56410.5 + 97705.8i) q^{89} -6674.02 q^{90} +6100.40 q^{92} +(33863.9 - 58654.0i) q^{93} +(1735.71 + 3006.34i) q^{94} +(68972.6 + 119464. i) q^{95} +(-10648.6 + 18444.0i) q^{96} -30334.3 q^{97} -40310.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + 36 * q^3 - 69 * q^4 - 54 * q^6 + 246 * q^8 - 324 * q^9 + 283 * q^10 - 402 * q^11 + 621 * q^12 - 924 * q^13 - 3273 * q^16 + 276 * q^17 - 243 * q^18 + 510 * q^19 - 9438 * q^20 + 2750 * q^22 - 6900 * q^23 + 1107 * q^24 - 2814 * q^25 - 15138 * q^26 - 5832 * q^27 + 1080 * q^29 - 2547 * q^30 - 6410 * q^31 - 15519 * q^32 + 3618 * q^33 - 42288 * q^34 + 11178 * q^36 - 15250 * q^37 - 41250 * q^38 - 4158 * q^39 - 8547 * q^40 - 8616 * q^41 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 58914 * q^48 - 14604 * q^50 - 2484 * q^51 - 47476 * q^52 - 13692 * q^53 + 2187 * q^54 - 146248 * q^55 + 9180 * q^57 - 52309 * q^58 + 34830 * q^59 - 42471 * q^60 - 5364 * q^61 - 32058 * q^62 - 146974 * q^64 - 66864 * q^65 + 12375 * q^66 + 5994 * q^67 - 58272 * q^68 - 124200 * q^69 + 178536 * q^71 - 9963 * q^72 + 59638 * q^73 + 185442 * q^74 + 25326 * q^75 - 42616 * q^76 - 272484 * q^78 + 44062 * q^79 - 33381 * q^80 - 26244 * q^81 + 57596 * q^82 + 416892 * q^83 + 72648 * q^85 + 136968 * q^86 + 4860 * q^87 - 87597 * q^88 - 77520 * q^89 - 45846 * q^90 + 316512 * q^92 + 57690 * q^93 - 73722 * q^94 + 221376 * q^95 + 139671 * q^96 + 377260 * q^97 + 65124 * q^99

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