LMFDB - Embedded newform 147.6.e.p.67.4

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 63 x^{10} - 126 x^{9} + 2784 x^{8} - 5290 x^{7} + 62015 x^{6} - 99530 x^{5} + \cdots + 5466244 $ x^12 - 2x^11 + 63x^10 - 126x^9 + 2784x^8 - 5290x^7 + 62015x^6 - 99530x^5 + 973971x^4 - 1176024x^3 + 5644794x^2 + 4339328*x + 5466244
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.4
Root			$2.13607 - 3.69977i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.6.e.p.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.54581 + 2.67743i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(11.2209 - 19.4352i) q^{4} +(-6.89630 - 11.9448i) q^{5} -27.8246 q^{6} +168.314 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(1.54581 + 2.67743i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(11.2209 - 19.4352i) q^{4} +(-6.89630 - 11.9448i) q^{5} -27.8246 q^{6} +168.314 q^{8} +(-40.5000 - 70.1481i) q^{9} +(21.3208 - 36.9287i) q^{10} +(1.83329 - 3.17536i) q^{11} +(100.988 + 174.917i) q^{12} -780.229 q^{13} +124.133 q^{15} +(-98.8879 - 171.279i) q^{16} +(-25.0416 + 43.3733i) q^{17} +(125.211 - 216.872i) q^{18} +(-531.692 - 920.918i) q^{19} -309.532 q^{20} +11.3357 q^{22} +(-2051.23 - 3552.83i) q^{23} +(-757.412 + 1311.88i) q^{24} +(1467.38 - 2541.58i) q^{25} +(-1206.09 - 2089.01i) q^{26} +729.000 q^{27} -1487.11 q^{29} +(191.887 + 332.358i) q^{30} +(-2759.98 + 4780.43i) q^{31} +(2998.75 - 5193.98i) q^{32} +(16.4997 + 28.5782i) q^{33} -154.838 q^{34} -1817.79 q^{36} +(-3071.63 - 5320.23i) q^{37} +(1643.79 - 2847.13i) q^{38} +(3511.03 - 6081.28i) q^{39} +(-1160.74 - 2010.47i) q^{40} +10757.9 q^{41} +17696.7 q^{43} +(-41.1425 - 71.2609i) q^{44} +(-558.601 + 967.525i) q^{45} +(6341.63 - 10984.0i) q^{46} +(-14734.2 - 25520.4i) q^{47} +1779.98 q^{48} +9073.19 q^{50} +(-225.374 - 390.360i) q^{51} +(-8754.89 + 15163.9i) q^{52} +(9627.95 - 16676.1i) q^{53} +(1126.90 + 1951.84i) q^{54} -50.5718 q^{55} +9570.46 q^{57} +(-2298.79 - 3981.62i) q^{58} +(-3309.59 + 5732.38i) q^{59} +(1392.89 - 2412.56i) q^{60} +(-18375.1 - 31826.7i) q^{61} -17065.7 q^{62} +12213.2 q^{64} +(5380.70 + 9319.64i) q^{65} +(-51.0107 + 88.3532i) q^{66} +(-23454.6 + 40624.5i) q^{67} +(561.979 + 973.377i) q^{68} +36922.1 q^{69} -41693.7 q^{71} +(-6816.71 - 11806.9i) q^{72} +(-14725.6 + 25505.4i) q^{73} +(9496.35 - 16448.2i) q^{74} +(13206.4 + 22874.2i) q^{75} -23864.3 q^{76} +21709.6 q^{78} +(-11062.2 - 19160.3i) q^{79} +(-1363.92 + 2362.38i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(16629.7 + 28803.6i) q^{82} -3896.35 q^{83} +690.778 q^{85} +(27355.8 + 47381.6i) q^{86} +(6691.98 - 11590.9i) q^{87} +(308.569 - 534.457i) q^{88} +(-10265.4 - 17780.2i) q^{89} -3453.97 q^{90} -92066.6 q^{92} +(-24839.9 - 43023.9i) q^{93} +(45552.7 - 78899.6i) q^{94} +(-7333.42 + 12701.9i) q^{95} +(26988.7 + 46745.8i) q^{96} +17742.9 q^{97} -296.994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.54581	+	2.67743i	0.273264	+	0.473307i	0.969696	−	0.244316i	$-0.0785635\pi$
$2$	1.54581	+	2.67743i	0.273264	+	0.473307i	−0.696432	+	0.717623i	$0.745230\pi$
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$	11.2209	−	19.4352i	0.350654	−	0.607350i
$5$	−6.89630	−	11.9448i	−0.123365	−	0.213674i	0.797728	−	0.603018i	$-0.206035\pi$
$5$	−6.89630	−	11.9448i	−0.123365	−	0.213674i	−0.921093	+	0.389344i	$0.872702\pi$
$6$	−27.8246			−0.315538
$7$		0			0
$7$		0			0
$8$	168.314			0.929811
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	21.3208	−	36.9287i	0.0674223	−	0.116779i
$11$	1.83329	−	3.17536i	0.00456826	−	0.00791245i	−0.863732	−	0.503951i	$-0.831879\pi$
$11$	1.83329	−	3.17536i	0.00456826	−	0.00791245i	0.868300	+	0.496039i	$0.165213\pi$
$12$	100.988	+	174.917i	0.202450	+	0.350654i
$13$	−780.229			−1.28045			−0.640226	−	0.768186i	$-0.721159\pi$
$13$	−780.229			−1.28045			−0.640226	+	0.768186i	$0.721159\pi$
$14$		0			0
$15$	124.133			0.142449
$16$	−98.8879	−	171.279i	−0.0965702	−	0.167264i
$17$	−25.0416	+	43.3733i	−0.0210155	+	0.0363999i	−0.876342	−	0.481690i	$-0.840023\pi$
$17$	−25.0416	+	43.3733i	−0.0210155	+	0.0363999i	0.855326	+	0.518090i	$0.173357\pi$
$18$	125.211	−	216.872i	0.0910879	−	0.157769i
$19$	−531.692	−	920.918i	−0.337891	−	0.585244i	0.646145	−	0.763215i	$-0.276380\pi$
$19$	−531.692	−	920.918i	−0.337891	−	0.585244i	−0.984036	+	0.177971i	$0.943047\pi$
$20$	−309.532			−0.173033
$21$		0			0
$22$	11.3357			0.00499336
$23$	−2051.23	−	3552.83i	−0.808526	−	1.40041i	−0.913885	−	0.405974i	$-0.866932\pi$
$23$	−2051.23	−	3552.83i	−0.808526	−	1.40041i	0.105358	−	0.994434i	$-0.466401\pi$
$24$	−757.412	+	1311.88i	−0.268413	+	0.464906i
$25$	1467.38	−	2541.58i	0.469562	−	0.813306i
$26$	−1206.09	−	2089.01i	−0.349901	−	0.606047i
$27$	729.000			0.192450
$28$		0			0
$29$	−1487.11			−0.328358			−0.164179	−	0.986431i	$-0.552497\pi$
$29$	−1487.11			−0.328358			−0.164179	+	0.986431i	$0.552497\pi$
$30$	191.887	+	332.358i	0.0389263	+	0.0674223i
$31$	−2759.98	+	4780.43i	−0.515825	+	0.893435i	0.484006	+	0.875065i	$0.339181\pi$
$31$	−2759.98	+	4780.43i	−0.515825	+	0.893435i	−0.999831	+	0.0183707i	$0.994152\pi$
$32$	2998.75	−	5193.98i	0.517684	−	0.896655i
$33$	16.4997	+	28.5782i	0.00263748	+	0.00456826i
$34$	−154.838			−0.0229711
$35$		0			0
$36$	−1817.79			−0.233769
$37$	−3071.63	−	5320.23i	−0.368863	−	0.638890i	0.620525	−	0.784187i	$-0.286920\pi$
$37$	−3071.63	−	5320.23i	−0.368863	−	0.638890i	−0.989388	+	0.145297i	$0.953586\pi$
$38$	1643.79	−	2847.13i	0.184667	−	0.319852i
$39$	3511.03	−	6081.28i	0.369635	−	0.640226i
$40$	−1160.74	−	2010.47i	−0.114706	−	0.198677i
$41$	10757.9			0.999468			0.499734	−	0.866179i	$-0.333431\pi$
$41$	10757.9			0.999468			0.499734	+	0.866179i	$0.333431\pi$
$42$		0			0
$43$	17696.7			1.45956			0.729779	−	0.683683i	$-0.239623\pi$
$43$	17696.7			1.45956			0.729779	+	0.683683i	$0.239623\pi$
$44$	−41.1425	−	71.2609i	−0.00320375	−	0.00554906i
$45$	−558.601	+	967.525i	−0.0411216	+	0.0712247i
$46$	6341.63	−	10984.0i	0.441882	−	0.765362i
$47$	−14734.2	−	25520.4i	−0.972933	−	1.68517i	−0.686595	−	0.727040i	$-0.740896\pi$
$47$	−14734.2	−	25520.4i	−0.972933	−	1.68517i	−0.286337	−	0.958129i	$-0.592438\pi$
$48$	1779.98			0.111510
$49$		0			0
$50$	9073.19			0.513257
$51$	−225.374	−	390.360i	−0.0121333	−	0.0210155i
$52$	−8754.89	+	15163.9i	−0.448996	+	0.777683i
$53$	9627.95	−	16676.1i	0.470808	−	0.815464i	−0.528634	−	0.848850i	$-0.677296\pi$
$53$	9627.95	−	16676.1i	0.470808	−	0.815464i	0.999443	+	0.0333860i	$0.0106291\pi$
$54$	1126.90	+	1951.84i	0.0525896	+	0.0910879i
$55$	−50.5718			−0.00225425
$56$		0			0
$57$	9570.46			0.390163
$58$	−2298.79	−	3981.62i	−0.0897283	−	0.155414i
$59$	−3309.59	+	5732.38i	−0.123778	+	0.214390i	−0.921255	−	0.388960i	$-0.872834\pi$
$59$	−3309.59	+	5732.38i	−0.123778	+	0.214390i	0.797476	+	0.603350i	$0.206168\pi$
$60$	1392.89	−	2412.56i	0.0499505	−	0.0865167i
$61$	−18375.1	−	31826.7i	−0.632275	−	1.09513i	−0.987086	−	0.160194i	$-0.948788\pi$
$61$	−18375.1	−	31826.7i	−0.632275	−	1.09513i	0.354810	−	0.934938i	$-0.384545\pi$
$62$	−17065.7			−0.563825
$63$		0			0
$64$	12213.2			0.372717
$65$	5380.70	+	9319.64i	0.157963	+	0.273600i
$66$	−51.0107	+	88.3532i	−0.00144146	+	0.00249668i
$67$	−23454.6	+	40624.5i	−0.638323	+	1.10561i	0.347477	+	0.937688i	$0.387038\pi$
$67$	−23454.6	+	40624.5i	−0.638323	+	1.10561i	−0.985801	+	0.167920i	$0.946295\pi$
$68$	561.979	+	973.377i	0.0147383	+	0.0255275i
$69$	36922.1			0.933606
$70$		0			0
$71$	−41693.7			−0.981577			−0.490789	−	0.871279i	$-0.663291\pi$
$71$	−41693.7			−0.981577			−0.490789	+	0.871279i	$0.663291\pi$
$72$	−6816.71	−	11806.9i	−0.154969	−	0.268413i
$73$	−14725.6	+	25505.4i	−0.323418	+	0.560177i	−0.981191	−	0.193039i	$-0.938165\pi$
$73$	−14725.6	+	25505.4i	−0.323418	+	0.560177i	0.657773	+	0.753217i	$0.271499\pi$
$74$	9496.35	−	16448.2i	0.201594	−	0.349171i
$75$	13206.4	+	22874.2i	0.271102	+	0.469562i
$76$	−23864.3			−0.473931
$77$		0			0
$78$	21709.6			0.404031
$79$	−11062.2	−	19160.3i	−0.199422	−	0.345409i	0.748919	−	0.662661i	$-0.230573\pi$
$79$	−11062.2	−	19160.3i	−0.199422	−	0.345409i	−0.948341	+	0.317252i	$0.897240\pi$
$80$	−1363.92	+	2362.38i	−0.0238267	+	0.0412691i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	16629.7	+	28803.6i	0.273118	+	0.473055i
$83$	−3896.35			−0.0620816			−0.0310408	−	0.999518i	$-0.509882\pi$
$83$	−3896.35			−0.0620816			−0.0310408	+	0.999518i	$0.509882\pi$
$84$		0			0
$85$	690.778			0.0103703
$86$	27355.8	+	47381.6i	0.398844	+	0.690819i
$87$	6691.98	−	11590.9i	0.0947887	−	0.164179i
$88$	308.569	−	534.457i	0.00424762	−	0.00735709i
$89$	−10265.4	−	17780.2i	−0.137373	−	0.237937i	0.789129	−	0.614228i	$-0.210533\pi$
$89$	−10265.4	−	17780.2i	−0.137373	−	0.237937i	−0.926501	+	0.376291i	$0.877199\pi$
$90$	−3453.97			−0.0449482
$91$		0			0
$92$	−92066.6			−1.13405
$93$	−24839.9	−	43023.9i	−0.297812	−	0.515825i
$94$	45552.7	−	78899.6i	0.531734	−	0.920991i
$95$	−7333.42	+	12701.9i	−0.0833677	+	0.144397i
$96$	26988.7	+	46745.8i	0.298885	+	0.517684i
$97$	17742.9			0.191468			0.0957338	−	0.995407i	$-0.469480\pi$
$97$	17742.9			0.191468			0.0957338	+	0.995407i	$0.469480\pi$
$98$		0			0
$99$	−296.994			−0.00304550
$100$	−32930.8	−	57037.8i	−0.329308	−	0.570378i
$101$	71042.6	−	123049.i	0.692971	−	1.20026i	−0.277888	−	0.960613i	$-0.589635\pi$
$101$	71042.6	−	123049.i	0.692971	−	1.20026i	0.970860	−	0.239648i	$-0.0770321\pi$
$102$	696.773	−	1206.85i	0.00663118	−	0.0114855i
$103$	105269.	+	182331.i	0.977702	+	1.69343i	0.670713	+	0.741717i	$0.265988\pi$
$103$	105269.	+	182331.i	0.977702	+	1.69343i	0.306990	+	0.951713i	$0.400678\pi$
$104$	−131323.			−1.19058
$105$		0			0
$106$	59532.0			0.514619
$107$	101335.	+	175518.i	0.855660	+	1.48205i	0.876031	+	0.482254i	$0.160182\pi$
$107$	101335.	+	175518.i	0.855660	+	1.48205i	−0.0203712	+	0.999792i	$0.506485\pi$
$108$	8180.05	−	14168.3i	0.0674834	−	0.116885i
$109$	−69768.9	+	120843.i	−0.562466	+	0.974219i	0.434815	+	0.900520i	$0.356814\pi$
$109$	−69768.9	+	120843.i	−0.562466	+	0.974219i	−0.997281	+	0.0736991i	$0.976520\pi$
$110$	−78.1746	−	135.402i	−0.000616005	−	0.00106695i
$111$	55289.4			0.425926
$112$		0			0
$113$	−206316.			−1.51998			−0.759989	−	0.649936i	$-0.774796\pi$
$113$	−206316.			−1.51998			−0.759989	+	0.649936i	$0.774796\pi$
$114$	14794.1	+	25624.2i	0.106617	+	0.184667i
$115$	−28291.8	+	49002.8i	−0.199487	+	0.345522i
$116$	−16686.7	+	28902.2i	−0.115140	+	0.199428i
$117$	31599.3	+	54731.5i	0.213409	+	0.369635i
$118$	−20464.0			−0.135296
$119$		0			0
$120$	20893.4			0.132451
$121$	80518.8	+	139463.i	0.499958	+	0.865953i
$122$	56809.1	−	98396.2i	0.345556	−	0.598520i
$123$	−48410.7	+	83849.8i	−0.288522	+	0.499734i
$124$	61939.2	+	107282.i	0.361752	+	0.626573i
$125$	−83580.0			−0.478440
$126$		0			0
$127$	89874.2			0.494454			0.247227	−	0.968958i	$-0.420481\pi$
$127$	89874.2			0.494454			0.247227	+	0.968958i	$0.420481\pi$
$128$	−77080.6	−	133507.i	−0.415834	−	0.720246i
$129$	−79635.2	+	137932.i	−0.421338	+	0.729779i
$130$	−16635.1	+	28812.8i	−0.0863310	+	0.149530i
$131$	−160058.	−	277228.i	−0.814889	−	1.41143i	−0.909408	−	0.415906i	$-0.863465\pi$
$131$	−160058.	−	277228.i	−0.814889	−	1.41143i	0.0945188	−	0.995523i	$-0.469869\pi$
$132$	740.565			0.00369938
$133$		0			0
$134$	−145026.			−0.697722
$135$	−5027.41	−	8707.72i	−0.0237416	−	0.0411216i
$136$	−4214.85	+	7300.33i	−0.0195404	+	0.0338450i
$137$	−129486.	+	224276.i	−0.589414	+	1.02089i	0.404895	+	0.914363i	$0.367308\pi$
$137$	−129486.	+	224276.i	−0.589414	+	1.02089i	−0.994309	+	0.106532i	$0.966025\pi$
$138$	57074.6	+	98856.2i	0.255121	+	0.441882i
$139$	282366.			1.23958			0.619791	−	0.784767i	$-0.287217\pi$
$139$	282366.			1.23958			0.619791	+	0.784767i	$0.287217\pi$
$140$		0			0
$141$	265216.			1.12345
$142$	−64450.7	−	111632.i	−0.268229	−	0.464587i
$143$	−1430.39	+	2477.51i	−0.00584944	+	0.0101315i
$144$	−8009.92	+	13873.6i	−0.0321901	+	0.0557548i
$145$	10255.5	+	17763.1i	0.0405078	+	0.0701616i
$146$	−91051.9			−0.353514
$147$		0			0
$148$	−137866.			−0.517373
$149$	159834.	+	276841.i	0.589800	+	1.02156i	0.994258	+	0.107007i	$0.0341268\pi$
$149$	159834.	+	276841.i	0.589800	+	1.02156i	−0.404458	+	0.914556i	$0.632540\pi$
$150$	−40829.4	+	70718.5i	−0.148165	+	0.256629i
$151$	42023.2	−	72786.3i	0.149985	−	0.259781i	−0.781237	−	0.624235i	$-0.785411\pi$
$151$	42023.2	−	72786.3i	0.149985	−	0.259781i	0.931221	+	0.364454i	$0.118744\pi$
$152$	−89491.1	−	155003.i	−0.314175	−	0.544166i
$153$	4056.74			0.0140103
$154$		0			0
$155$	76134.8			0.254539
$156$	−78794.0	−	136475.i	−0.259228	−	0.448996i
$157$	−63097.6	+	109288.i	−0.204298	+	0.353854i	−0.949909	−	0.312527i	$-0.898824\pi$
$157$	−63097.6	+	109288.i	−0.204298	+	0.353854i	0.745611	+	0.666382i	$0.232158\pi$
$158$	34200.1	−	59236.4i	0.108990	−	0.188775i
$159$	86651.5	+	150085.i	0.271821	+	0.470808i
$160$	−82721.1			−0.255456
$161$		0			0
$162$	−20284.2			−0.0607253
$163$	117895.	+	204200.i	0.347557	+	0.601986i	0.985815	−	0.167836i	$-0.0536780\pi$
$163$	117895.	+	204200.i	0.347557	+	0.601986i	−0.638258	+	0.769823i	$0.720345\pi$
$164$	120714.	−	209083.i	0.350467	−	0.607027i
$165$	227.573	−	394.168i	0.000650746	−	0.00112712i
$166$	−6023.04	−	10432.2i	−0.0169647	−	0.0293837i
$167$	149843.			0.415761			0.207881	−	0.978154i	$-0.433343\pi$
$167$	149843.			0.415761			0.207881	+	0.978154i	$0.433343\pi$
$168$		0			0
$169$	237464.			0.639559
$170$	1067.81	+	1849.51i	0.00283382	+	0.00490833i
$171$	−43067.1	+	74594.3i	−0.112630	+	0.195081i
$172$	198573.	−	343939.i	0.511800	−	0.886463i
$173$	−352230.	−	610080.i	−0.894769	−	1.54979i	−0.834090	−	0.551628i	$-0.814007\pi$
$173$	−352230.	−	610080.i	−0.894769	−	1.54979i	−0.0606783	−	0.998157i	$-0.519326\pi$
$174$	41378.2			0.103609
$175$		0			0
$176$	−725.162			−0.00176463
$177$	−29786.3	−	51591.4i	−0.0714634	−	0.123778i
$178$	31736.8	−	54969.7i	0.0750780	−	0.130039i
$179$	278786.	−	482872.i	0.650337	−	1.12642i	−0.332704	−	0.943031i	$-0.607961\pi$
$179$	278786.	−	482872.i	0.650337	−	1.12642i	0.983041	−	0.183386i	$-0.0587058\pi$
$180$	12536.0	+	21713.0i	0.0288389	+	0.0499505i
$181$	443092.			1.00530			0.502652	−	0.864489i	$-0.332358\pi$
$181$	443092.			1.00530			0.502652	+	0.864489i	$0.332358\pi$
$182$		0			0
$183$	330752.			0.730088
$184$	−345250.	−	597990.i	−0.751777	−	1.30212i
$185$	−42365.9	+	73379.8i	−0.0910095	+	0.157633i
$186$	76795.6	−	133014.i	0.162762	−	0.281913i
$187$	91.8172	+	159.032i	0.000192008	+	0.000332568i
$188$	−661327.			−1.36465
$189$		0			0
$190$	−45344.4			−0.0911254
$191$	−78740.7	−	136383.i	−0.156177	−	0.270506i	0.777310	−	0.629117i	$-0.216584\pi$
$191$	−78740.7	−	136383.i	−0.156177	−	0.270506i	−0.933487	+	0.358612i	$0.883250\pi$
$192$	−54959.3	+	95192.3i	−0.107594	+	0.186358i
$193$	389020.	−	673803.i	0.751759	−	1.30209i	−0.195210	−	0.980761i	$-0.562539\pi$
$193$	389020.	−	673803.i	0.751759	−	1.30209i	0.946969	−	0.321324i	$-0.104128\pi$
$194$	27427.2	+	47505.3i	0.0523211	+	0.0906228i
$195$	−96852.5			−0.182400
$196$		0			0
$197$	−340283.			−0.624704			−0.312352	−	0.949966i	$-0.601117\pi$
$197$	−340283.			−0.624704			−0.312352	+	0.949966i	$0.601117\pi$
$198$	−459.097	−	795.179i	−0.000832226	−	0.00144146i
$199$	−148254.	+	256784.i	−0.265384	+	0.459659i	−0.967664	−	0.252242i	$-0.918832\pi$
$199$	−148254.	+	256784.i	−0.265384	+	0.459659i	0.702280	+	0.711901i	$0.252165\pi$
$200$	246981.	−	427783.i	0.436604	−	0.756221i
$201$	−211091.	−	365621.i	−0.368536	−	0.638323i
$202$	439274.			0.757456
$203$		0			0
$204$	−10115.6			−0.0170184
$205$	−74190.0	−	128501.i	−0.123299	−	0.213561i
$206$	−325452.	+	563699.i	−0.534341	+	0.925506i
$207$	−166149.	+	287779.i	−0.269509	+	0.466803i
$208$	77155.2	+	133637.i	0.123654	+	0.214174i
$209$	−3898.99			−0.00617429
$210$		0			0
$211$	506728.			0.783554			0.391777	−	0.920060i	$-0.371860\pi$
$211$	506728.			0.783554			0.391777	+	0.920060i	$0.371860\pi$
$212$	−216069.	−	374242.i	−0.330181	−	0.571891i
$213$	187622.	−	324970.i	0.283357	−	0.490789i
$214$	−313291.	+	542636.i	−0.467642	+	0.809979i
$215$	−122042.	−	211383.i	−0.180058	−	0.311870i
$216$	122701.			0.178942
$217$		0			0
$218$	−431399.			−0.614806
$219$	−132530.	−	229549.i	−0.186726	−	0.323418i
$220$	−567.463	+	982.874i	−0.000790461	+	0.00136912i
$221$	19538.2	−	33841.1i	0.0269093	−	0.0466083i
$222$	85467.1	+	148033.i	0.116390	+	0.201594i
$223$	−462362.			−0.622615			−0.311308	−	0.950309i	$-0.600767\pi$
$223$	−462362.			−0.622615			−0.311308	+	0.950309i	$0.600767\pi$
$224$		0			0
$225$	−237716.			−0.313041
$226$	−318926.	−	552396.i	−0.415355	−	0.719415i
$227$	49113.3	−	85066.7i	0.0632607	−	0.109571i	−0.832660	−	0.553784i	$-0.813183\pi$
$227$	49113.3	−	85066.7i	0.0632607	−	0.109571i	0.895921	+	0.444213i	$0.146517\pi$
$228$	107389.	−	186004.i	0.136812	−	0.236965i
$229$	−250702.	−	434228.i	−0.315914	−	0.547178i	0.663718	−	0.747983i	$-0.268978\pi$
$229$	−250702.	−	434228.i	−0.315914	−	0.547178i	−0.979631	+	0.200805i	$0.935644\pi$
$230$	−174935.			−0.218051
$231$		0			0
$232$	−250301.			−0.305311
$233$	306958.	+	531667.i	0.370415	+	0.641578i	0.989629	−	0.143644i	$-0.0458820\pi$
$233$	306958.	+	531667.i	0.370415	+	0.641578i	−0.619214	+	0.785222i	$0.712549\pi$
$234$	−97693.1	+	169209.i	−0.116634	+	0.202016i
$235$	−203223.	+	351993.i	−0.240051	+	0.415781i
$236$	74273.4	+	128645.i	0.0868067	+	0.150354i
$237$	199119.			0.230273
$238$		0			0
$239$	1.10020e6			1.24588			0.622940	−	0.782269i	$-0.285938\pi$
$239$	1.10020e6			1.24588			0.622940	+	0.782269i	$0.285938\pi$
$240$	−12275.3	−	21261.4i	−0.0137564	−	0.0238267i
$241$	−44941.8	+	77841.4i	−0.0498434	+	0.0863313i	−0.889871	−	0.456213i	$-0.849206\pi$
$241$	−44941.8	+	77841.4i	−0.0498434	+	0.0863313i	0.840027	+	0.542544i	$0.182539\pi$
$242$	−248934.	+	431166.i	−0.273241	+	0.473267i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	−824744.			−0.886839
$245$		0			0
$246$	−299335.			−0.315370
$247$	414841.	+	718527.i	0.432653	+	0.749377i
$248$	−464544.	+	804613.i	−0.479620	+	0.830726i
$249$	17533.6	−	30369.1i	0.0179214	−	0.0310408i
$250$	−129199.	−	223779.i	−0.130740	−	0.226449i
$251$	1.01050e6			1.01240			0.506202	−	0.862415i	$-0.331049\pi$
$251$	1.01050e6			1.01240			0.506202	+	0.862415i	$0.331049\pi$
$252$		0			0
$253$	−15042.0			−0.0147742
$254$	138929.	+	240632.i	0.135116	+	0.234028i
$255$	−3108.50	+	5384.08i	−0.00299365	+	0.00518515i
$256$	433715.	−	751217.i	0.413623	−	0.716416i
$257$	606163.	+	1.04991e6i	0.572475	+	0.991556i	0.996311	+	0.0858173i	$0.0273501\pi$
$257$	606163.	+	1.04991e6i	0.572475	+	0.991556i	−0.423835	+	0.905739i	$0.639317\pi$
$258$	−492405.			−0.460546
$259$		0			0
$260$	241505.			0.221561
$261$	60227.8	+	104318.i	0.0547263	+	0.0947887i
$262$	494839.	−	857086.i	0.445359	−	0.771385i
$263$	−192451.	+	333334.i	−0.171566	+	0.297160i	−0.938967	−	0.344006i	$-0.888216\pi$
$263$	−192451.	+	333334.i	−0.171566	+	0.297160i	0.767402	+	0.641167i	$0.221549\pi$
$264$	2777.12	+	4810.11i	0.00245236	+	0.00424762i
$265$	−265589.			−0.232325
$266$		0			0
$267$	184777.			0.158625
$268$	526364.	+	911689.i	0.447661	+	0.775372i
$269$	787275.	−	1.36360e6i	0.663355	−	1.14896i	−0.316374	−	0.948634i	$-0.602465\pi$
$269$	787275.	−	1.36360e6i	0.663355	−	1.14896i	0.979729	−	0.200329i	$-0.0642012\pi$
$270$	15542.9	−	26921.0i	0.0129754	−	0.0224741i
$271$	−166135.	−	287754.i	−0.137416	−	0.238012i	0.789102	−	0.614263i	$-0.210546\pi$
$271$	−166135.	−	287754.i	−0.137416	−	0.238012i	−0.926518	+	0.376251i	$0.877213\pi$
$272$	9905.24			0.00811788
$273$		0			0
$274$	−800643.			−0.644262
$275$	−5380.29	−	9318.93i	−0.00429016	−	0.00743078i
$276$	414300.	−	717588.i	0.327372	−	0.567026i
$277$	−1.11772e6	+	1.93594e6i	−0.875251	+	1.51598i	−0.0187556	+	0.999824i	$0.505970\pi$
$277$	−1.11772e6	+	1.93594e6i	−0.875251	+	1.51598i	−0.856495	+	0.516155i	$0.827363\pi$
$278$	436485.	+	756014.i	0.338733	+	0.586702i
$279$	447118.			0.343883
$280$		0			0
$281$	69723.6			0.0526761			0.0263381	−	0.999653i	$-0.491615\pi$
$281$	69723.6			0.0526761			0.0263381	+	0.999653i	$0.491615\pi$
$282$	409975.	+	710097.i	0.306997	+	0.531734i
$283$	238226.	−	412620.i	0.176817	−	0.306256i	−0.763972	−	0.645250i	$-0.776753\pi$
$283$	238226.	−	412620.i	0.176817	−	0.306256i	0.940788	+	0.338994i	$0.110087\pi$
$284$	−467842.	+	810326.i	−0.344194	+	0.596161i
$285$	−66000.8	−	114317.i	−0.0481323	−	0.0833677i
$286$	−8844.46			−0.00639376
$287$		0			0
$288$	−485797.			−0.345123
$289$	708674.	+	1.22746e6i	0.499117	+	0.864495i
$290$	−31706.3	+	54916.9i	−0.0221386	+	0.0383452i
$291$	−79843.0	+	138292.i	−0.0552719	+	0.0957338i
$292$	330469.	+	572389.i	0.226816	+	0.392857i
$293$	2.27589e6			1.54875			0.774377	−	0.632724i	$-0.218063\pi$
$293$	2.27589e6			1.54875			0.774377	+	0.632724i	$0.218063\pi$
$294$		0			0
$295$	91295.8			0.0610796
$296$	−516999.	−	895468.i	−0.342973	−	0.594047i
$297$	1336.47	−	2314.84i	0.000879161	−	0.00152275i
$298$	−494148.	+	855890.i	−0.322342	+	0.558313i
$299$	1.60043e6	+	2.77202e6i	1.03528	+	1.79316i
$300$	592754.			0.380252
$301$		0			0
$302$	259840.			0.163941
$303$	639383.	+	1.10744e6i	0.400087	+	0.692971i
$304$	−105156.	+	182135.i	−0.0652603	+	0.113034i
$305$	−253441.	+	438973.i	−0.156001	+	0.270202i
$306$	6270.96	+	10861.6i	0.00382851	+	0.00663118i
$307$	−1.61790e6			−0.979731			−0.489866	−	0.871798i	$-0.662954\pi$
$307$	−1.61790e6			−0.979731			−0.489866	+	0.871798i	$0.662954\pi$
$308$		0			0
$309$	−1.89484e6			−1.12895
$310$	117690.	+	203845.i	0.0695562	+	0.120475i
$311$	513337.	−	889125.i	0.300955	−	0.521269i	−0.675398	−	0.737454i	$-0.736028\pi$
$311$	513337.	−	889125.i	0.300955	−	0.521269i	0.976352	+	0.216185i	$0.0693613\pi$
$312$	590955.	−	1.02356e6i	0.343691	−	0.595290i
$313$	−158607.	−	274715.i	−0.0915085	−	0.158497i	0.816638	−	0.577151i	$-0.195836\pi$
$313$	−158607.	−	274715.i	−0.0915085	−	0.158497i	−0.908146	+	0.418653i	$0.862502\pi$
$314$	−390149.			−0.223309
$315$		0			0
$316$	−496512.			−0.279712
$317$	−785629.	−	1.36075e6i	−0.439106	−	0.760554i	0.558515	−	0.829495i	$-0.311371\pi$
$317$	−785629.	−	1.36075e6i	−0.439106	−	0.760554i	−0.997621	+	0.0689406i	$0.978038\pi$
$318$	−267894.	+	464006.i	−0.148558	+	0.257310i
$319$	−2726.31	+	4722.10i	−0.00150002	+	0.00259812i
$320$	−84225.8	−	145883.i	−0.0459801	−	0.0796399i
$321$	−1.82404e6			−0.988031
$322$		0			0
$323$	53257.7			0.0284038
$324$	73620.5	+	127514.i	0.0389615	+	0.0674834i
$325$	−1.14489e6	+	1.98301e6i	−0.601252	+	1.04140i
$326$	−364487.	+	631310.i	−0.189949	+	0.329002i
$327$	−627921.	−	1.08759e6i	−0.324740	−	0.562466i
$328$	1.81071e6			0.929317
$329$		0			0
$330$	1407.14			0.000711301
$331$	−769161.	−	1.33223e6i	−0.385875	−	0.668356i	0.606015	−	0.795453i	$-0.292767\pi$
$331$	−769161.	−	1.33223e6i	−0.385875	−	0.668356i	−0.991890	+	0.127098i	$0.959434\pi$
$332$	−43720.7	+	75726.5i	−0.0217692	+	0.0377053i
$333$	−248802.	+	430938.i	−0.122954	+	0.212963i
$334$	231629.	+	401193.i	0.113612	+	0.196783i
$335$	647000.			0.314987
$336$		0			0
$337$	−2.86811e6			−1.37569			−0.687846	−	0.725857i	$-0.741444\pi$
$337$	−2.86811e6			−1.37569			−0.687846	+	0.725857i	$0.741444\pi$
$338$	367075.	+	635792.i	0.174768	+	0.302708i
$339$	928423.	−	1.60808e6i	0.438780	−	0.759989i
$340$	7751.16	−	13425.4i	0.00363638	−	0.00629840i
$341$	10119.7	+	17527.9i	0.00471284	+	0.00816288i
$342$	−266295.			−0.123111
$343$		0			0
$344$	2.97860e6			1.35711
$345$	−254626.	−	441025.i	−0.115174	−	0.199487i
$346$	1.08896e6	−	1.88614e6i	0.489016	−	0.847000i
$347$	55982.9	−	96965.2i	0.0249593	−	0.0432307i	−0.853276	−	0.521460i	$-0.825388\pi$
$347$	55982.9	−	96965.2i	0.0249593	−	0.0432307i	0.878235	+	0.478229i	$0.158721\pi$
$348$	−150180.	−	260120.i	−0.0664761	−	0.115140i
$349$	−3.75314e6			−1.64942			−0.824711	−	0.565555i	$-0.808662\pi$
$349$	−3.75314e6			−1.64942			−0.824711	+	0.565555i	$0.808662\pi$
$350$		0			0
$351$	−568787.			−0.246423
$352$	−10995.2	−	19044.2i	−0.00472983	−	0.00819230i
$353$	−1.61461e6	+	2.79659e6i	−0.689655	+	1.19452i	0.282295	+	0.959328i	$0.408904\pi$
$353$	−1.61461e6	+	2.79659e6i	−0.689655	+	1.19452i	−0.971950	+	0.235189i	$0.924429\pi$
$354$	92088.2	−	159501.i	0.0390567	−	0.0676482i
$355$	287532.	+	498021.i	0.121092	+	0.209738i
$356$	−460749.			−0.192681
$357$		0			0
$358$	1.72381e6			0.710855
$359$	−918294.	−	1.59053e6i	−0.376050	−	0.651338i	0.614433	−	0.788969i	$-0.289385\pi$
$359$	−918294.	−	1.59053e6i	−0.376050	−	0.651338i	−0.990484	+	0.137631i	$0.956051\pi$
$360$	−94020.2	+	162848.i	−0.0382353	+	0.0662256i
$361$	672656.	−	1.16508e6i	0.271660	−	0.470528i
$362$	684938.	+	1.18635e6i	0.274713	+	0.475817i
$363$	−1.44934e6			−0.577302
$364$		0			0
$365$	406208.			0.159594
$366$	511281.	+	885566.i	0.199507	+	0.345556i
$367$	169513.	−	293605.i	0.0656957	−	0.113788i	−0.831307	−	0.555814i	$-0.812407\pi$
$367$	169513.	−	293605.i	0.0656957	−	0.113788i	0.897002	+	0.442026i	$0.145740\pi$
$368$	−405683.	+	702663.i	−0.156159	+	0.270475i
$369$	−435696.	−	754648.i	−0.166578	−	0.288522i
$370$	−261959.			−0.0994784
$371$		0			0
$372$	−1.11490e6			−0.417715
$373$	353311.	+	611952.i	0.131488	+	0.227743i	0.924250	−	0.381787i	$-0.124691\pi$
$373$	353311.	+	611952.i	0.131488	+	0.227743i	−0.792763	+	0.609531i	$0.791358\pi$
$374$	−283.864	+	491.668i	−0.000104938	+	0.000181758i
$375$	376110.	−	651441.i	0.138114	−	0.239220i
$376$	−2.47997e6	−	4.29544e6i	−0.904644	−	1.56689i
$377$	1.16028e6			0.420447
$378$		0			0
$379$	648296.			0.231833			0.115917	−	0.993259i	$-0.463019\pi$
$379$	648296.			0.231833			0.115917	+	0.993259i	$0.463019\pi$
$380$	164576.	+	285053.i	0.0584664	+	0.101267i
$381$	−404434.	+	700500.i	−0.142737	+	0.247227i
$382$	243437.	−	421645.i	0.0853547	−	0.147839i
$383$	1.53511e6	+	2.65889e6i	0.534741	+	0.926198i	0.999176	+	0.0405910i	$0.0129241\pi$
$383$	1.53511e6	+	2.65889e6i	0.534741	+	0.926198i	−0.464435	+	0.885607i	$0.653743\pi$
$384$	1.38745e6			0.480164
$385$		0			0
$386$	2.40541e6			0.821714
$387$	−716717.	−	1.24139e6i	−0.243260	−	0.421338i
$388$	199092.	−	344837.i	0.0671388	−	0.116288i
$389$	2.29999e6	−	3.98370e6i	0.770641	−	1.33479i	−0.166572	−	0.986029i	$-0.553270\pi$
$389$	2.29999e6	−	3.98370e6i	0.770641	−	1.33479i	0.937212	−	0.348759i	$-0.113397\pi$
$390$	−149716.	−	259315.i	−0.0498432	−	0.0863310i
$391$	205464.			0.0679663
$392$		0			0
$393$	2.88104e6			0.940953
$394$	−526013.	−	911082.i	−0.170709	−	0.295677i
$395$	−152576.	+	264270.i	−0.0492033	+	0.0852227i
$396$	−3332.54	+	5772.14i	−0.00106792	+	0.00184969i
$397$	−1.32080e6	−	2.28768e6i	−0.420590	−	0.728484i	0.575407	−	0.817867i	$-0.304844\pi$
$397$	−1.32080e6	−	2.28768e6i	−0.420590	−	0.728484i	−0.995997	+	0.0893835i	$0.971510\pi$
$398$	−916694.			−0.290079
$399$		0			0
$400$	−580425.			−0.181383
$401$	−2.44839e6	−	4.24073e6i	−0.760359	−	1.31698i	−0.942665	−	0.333739i	$-0.891689\pi$
$401$	−2.44839e6	−	4.24073e6i	−0.760359	−	1.31698i	0.182306	−	0.983242i	$-0.441644\pi$
$402$	652615.	−	1.13036e6i	0.201415	−	0.348861i
$403$	2.15342e6	−	3.72983e6i	0.660490	−	1.14400i
$404$	−1.59433e6	−	2.76146e6i	−0.485986	−	0.841753i
$405$	90493.3			0.0274144
$406$		0			0
$407$	−22524.8			−0.00674025
$408$	−37933.6	−	65702.9i	−0.0112817	−	0.0195404i
$409$	−48168.1	+	83429.6i	−0.0142381	+	0.0246611i	−0.873057	−	0.487619i	$-0.837866\pi$
$409$	−48168.1	+	83429.6i	−0.0142381	+	0.0246611i	0.858819	+	0.512280i	$0.171199\pi$
$410$	229368.	−	397276.i	0.0673864	−	0.116717i
$411$	−1.16537e6	−	2.01848e6i	−0.340298	−	0.589414i
$412$	4.72485e6			1.37134
$413$		0			0
$414$	−1.02734e6			−0.294588
$415$	26870.4	+	46541.0i	0.00765869	+	0.0132652i
$416$	−2.33971e6	+	4.05249e6i	−0.662870	+	1.14812i
$417$	−1.27065e6	+	2.20082e6i	−0.357836	+	0.619791i
$418$	−6027.11	−	10439.3i	−0.00168721	−	0.00292233i
$419$	1.09657e6			0.305142			0.152571	−	0.988292i	$-0.451245\pi$
$419$	1.09657e6			0.305142			0.152571	+	0.988292i	$0.451245\pi$
$420$		0			0
$421$	−1.93660e6			−0.532517			−0.266259	−	0.963902i	$-0.585788\pi$
$421$	−1.93660e6			−0.532517			−0.266259	+	0.963902i	$0.585788\pi$
$422$	783307.	+	1.35673e6i	0.214117	+	0.370861i
$423$	−1.19347e6	+	2.06716e6i	−0.324311	+	0.561723i
$424$	1.62052e6	−	2.80682e6i	0.437763	−	0.758227i
$425$	73491.1	+	127290.i	0.0197362	+	0.0341840i
$426$	1.16011e6			0.309725
$427$		0			0
$428$	4.54830e6			1.20016
$429$	−12873.5	−	22297.6i	−0.00337717	−	0.00584944i
$430$	377308.	−	653517.i	0.0984067	−	0.170445i
$431$	1.53665e6	−	2.66155e6i	0.398457	−	0.690148i	−0.595079	−	0.803667i	$-0.702879\pi$
$431$	1.53665e6	−	2.66155e6i	0.398457	−	0.690148i	0.993536	+	0.113519i	$0.0362124\pi$
$432$	−72089.3	−	124862.i	−0.0185849	−	0.0321901i
$433$	3.80919e6			0.976366			0.488183	−	0.872741i	$-0.337660\pi$
$433$	3.80919e6			0.976366			0.488183	+	0.872741i	$0.337660\pi$
$434$		0			0
$435$	−184600.			−0.0467744
$436$	1.56574e6	+	2.71195e6i	0.394461	+	0.683227i
$437$	−2.18124e6	+	3.77802e6i	−0.546387	+	0.946370i
$438$	409733.	−	709679.i	0.102051	−	0.176757i
$439$	−266509.	−	461608.i	−0.0660011	−	0.114317i	0.831137	−	0.556068i	$-0.187691\pi$
$439$	−266509.	−	461608.i	−0.0660011	−	0.114317i	−0.897138	+	0.441751i	$0.854357\pi$
$440$	−8511.94			−0.00209603
$441$		0			0
$442$	120809.			0.0294134
$443$	2.33373e6	+	4.04213e6i	0.564990	+	0.978592i	0.997051	+	0.0767469i	$0.0244533\pi$
$443$	2.33373e6	+	4.04213e6i	0.564990	+	0.978592i	−0.432061	+	0.901845i	$0.642213\pi$
$444$	620398.	−	1.07456e6i	0.149353	−	0.258687i
$445$	−141587.	+	245235.i	−0.0338940	+	0.0587061i
$446$	−714725.	−	1.23794e6i	−0.170138	−	0.294688i
$447$	−2.87702e6			−0.681042
$448$		0			0
$449$	−6.10134e6			−1.42827			−0.714133	−	0.700010i	$-0.753179\pi$
$449$	−6.10134e6			−1.42827			−0.714133	+	0.700010i	$0.753179\pi$
$450$	−367464.	−	636467.i	−0.0855429	−	0.148165i
$451$	19722.5	−	34160.3i	0.00456583	−	0.00790825i
$452$	−2.31506e6	+	4.00980e6i	−0.532986	+	0.923159i
$453$	378208.	+	655076.i	0.0865936	+	0.149985i
$454$	303680.			0.0691475
$455$		0			0
$456$	1.61084e6			0.362778
$457$	−2.97249e6	−	5.14851e6i	−0.665779	−	1.15316i	−0.979073	−	0.203507i	$-0.934766\pi$
$457$	−2.97249e6	−	5.14851e6i	−0.665779	−	1.15316i	0.313295	−	0.949656i	$-0.398567\pi$
$458$	775076.	−	1.34247e6i	0.172655	−	0.299048i
$459$	−18255.3	+	31619.1i	−0.00404443	+	0.00700516i
$460$	634920.	+	1.09971e6i	0.139902	+	0.242318i
$461$	2.09415e6			0.458940			0.229470	−	0.973316i	$-0.426301\pi$
$461$	2.09415e6			0.458940			0.229470	+	0.973316i	$0.426301\pi$
$462$		0			0
$463$	2.41123e6			0.522741			0.261371	−	0.965239i	$-0.415826\pi$
$463$	2.41123e6			0.522741			0.261371	+	0.965239i	$0.415826\pi$
$464$	147057.	+	254710.i	0.0317096	+	0.0549226i
$465$	−342607.	+	593412.i	−0.0734790	+	0.127269i
$466$	−948999.	+	1.64371e6i	−0.202442	+	0.350640i
$467$	−2.25916e6	−	3.91298e6i	−0.479353	−	0.830264i	0.520367	−	0.853943i	$-0.325795\pi$
$467$	−2.25916e6	−	3.91298e6i	−0.479353	−	0.830264i	−0.999720	+	0.0236794i	$0.992462\pi$
$468$	1.41829e6			0.299330
$469$		0			0
$470$	−1.25658e6			−0.262389
$471$	−567879.	−	983595.i	−0.117951	−	0.204298i
$472$	−557050.	+	964839.i	−0.115090	+	0.199342i
$473$	32443.3	−	56193.4i	0.00666764	−	0.0115487i
$474$	307801.	+	533127.i	0.0629252	+	0.108990i
$475$	−3.12078e6			−0.634643
$476$		0			0
$477$	−1.55973e6			−0.313872
$478$	1.70070e6	+	2.94570e6i	0.340454	+	0.589683i
$479$	4.17964e6	−	7.23935e6i	0.832339	−	1.44165i	−0.0638394	−	0.997960i	$-0.520335\pi$
$479$	4.17964e6	−	7.23935e6i	0.832339	−	1.44165i	0.896179	−	0.443694i	$-0.146332\pi$
$480$	372245.	−	644747.i	0.0737438	−	0.127728i
$481$	2.39658e6	+	4.15099e6i	0.472312	+	0.818068i
$482$	−277886.			−0.0544815
$483$		0			0
$484$	3.61398e6			0.701249
$485$	−122360.	−	211934.i	−0.0236204	−	0.0409117i
$486$	91278.7	−	158099.i	0.0175299	−	0.0303626i
$487$	−299152.	+	518147.i	−0.0571570	+	0.0989989i	−0.893188	−	0.449683i	$-0.851537\pi$
$487$	−299152.	+	518147.i	−0.0571570	+	0.0989989i	0.836031	+	0.548682i	$0.184870\pi$
$488$	−3.09279e6	−	5.35687e6i	−0.587897	−	1.01827i
$489$	−2.12211e6			−0.401324
$490$		0			0
$491$	2.76760e6			0.518084			0.259042	−	0.965866i	$-0.416593\pi$
$491$	2.76760e6			0.518084			0.259042	+	0.965866i	$0.416593\pi$
$492$	1.08643e6	+	1.88174e6i	0.202342	+	0.350467i
$493$	37239.5	−	64500.8i	0.00690060	−	0.0119522i
$494$	−1.28253e6	+	2.22142e6i	−0.236457	+	0.409555i
$495$	2048.16	+	3547.52i	0.000375708	+	0.000650746i
$496$	1.09172e6			0.199253
$497$		0			0
$498$	108415.			0.0195891
$499$	−1.51960e6	−	2.63203e6i	−0.273199	−	0.473195i	0.696480	−	0.717576i	$-0.254748\pi$
$499$	−1.51960e6	−	2.63203e6i	−0.273199	−	0.473195i	−0.969679	+	0.244381i	$0.921415\pi$
$500$	−937844.	+	1.62439e6i	−0.167767	+	0.290580i
$501$	−674292.	+	1.16791e6i	−0.120020	+	0.207881i
$502$	1.56205e6	+	2.70555e6i	0.276653	+	0.479178i
$503$	−9.37896e6			−1.65286			−0.826428	−	0.563043i	$-0.809631\pi$
$503$	−9.37896e6			−1.65286			−0.826428	+	0.563043i	$0.809631\pi$
$504$		0			0
$505$	−1.95973e6			−0.341953
$506$	−23252.1	−	40273.9i	−0.00403726	−	0.00699274i
$507$	−1.06859e6	+	1.85085e6i	−0.184625	+	0.319780i
$508$	1.00847e6	−	1.74672e6i	0.173382	−	0.300307i
$509$	2.95069e6	+	5.11075e6i	0.504812	+	0.874360i	0.999985	+	0.00556552i	$0.00177157\pi$
$509$	2.95069e6	+	5.11075e6i	0.504812	+	0.874360i	−0.495172	+	0.868795i	$0.664895\pi$
$510$	−19220.6			−0.00327222
$511$		0			0
$512$	−2.25139e6			−0.379555
$513$	−387604.	−	671349.i	−0.0650271	−	0.112630i
$514$	−1.87403e6	+	3.24592e6i	−0.312874	+	0.541913i
$515$	1.45193e6	−	2.51482e6i	0.241228	−	0.417820i
$516$	1.78716e6	+	3.09545e6i	0.295488	+	0.511800i
$517$	−108049.			−0.0177784
$518$		0			0
$519$	6.34014e6			1.03319
$520$	905645.	+	1.56862e6i	0.146876	+	0.254396i
$521$	4.68713e6	−	8.11834e6i	0.756506	−	1.31031i	−0.188116	−	0.982147i	$-0.560238\pi$
$521$	4.68713e6	−	8.11834e6i	0.756506	−	1.31031i	0.944622	−	0.328160i	$-0.106429\pi$
$522$	−186202.	+	322511.i	−0.0299094	+	0.0518046i
$523$	3.23415e6	+	5.60171e6i	0.517018	+	0.895501i	0.999805	+	0.0197635i	$0.00629132\pi$
$523$	3.23415e6	+	5.60171e6i	0.517018	+	0.895501i	−0.482787	+	0.875738i	$0.660375\pi$
$524$	−7.18398e6			−1.14298
$525$		0			0
$526$	−1.18997e6			−0.187531
$527$	−138229.	−	239419.i	−0.0216806	−	0.0375520i
$528$	3263.23	−	5652.08i	0.000509405	−	0.000882315i
$529$	−5.19689e6	+	9.00128e6i	−0.807429	+	1.39851i
$530$	−410551.	−	711095.i	−0.0634859	−	0.109961i
$531$	536154.			0.0825188
$532$		0			0
$533$	−8.39364e6			−1.27977
$534$	285631.	+	494728.i	0.0433463	+	0.0750780i
$535$	1.39768e6	−	2.42085e6i	0.211117	−	0.365665i
$536$	−3.94773e6	+	6.83767e6i	−0.593520	+	1.02801i
$537$	2.50908e6	+	4.34585e6i	0.375473	+	0.650337i
$538$	4.86792e6			0.725083
$539$		0			0
$540$	−225649.			−0.0333003
$541$	1.23044e6	+	2.13119e6i	0.180746	+	0.313061i	0.942135	−	0.335234i	$-0.108815\pi$
$541$	1.23044e6	+	2.13119e6i	0.180746	+	0.313061i	−0.761389	+	0.648296i	$0.775482\pi$
$542$	513627.	−	889628.i	0.0751017	−	0.130080i
$543$	−1.99392e6	+	3.45356e6i	−0.290207	+	0.502652i
$544$	150187.	+	260131.i	0.0217588	+	0.0376873i
$545$	1.92459e6			0.277554
$546$		0			0
$547$	503726.			0.0719824			0.0359912	−	0.999352i	$-0.488541\pi$
$547$	503726.			0.0719824			0.0359912	+	0.999352i	$0.488541\pi$
$548$	2.90590e6	+	5.03316e6i	0.413361	+	0.715961i
$549$	−1.48839e6	+	2.57796e6i	−0.210758	+	0.365044i
$550$	16633.8	−	28810.6i	0.00234469	−	0.00406112i
$551$	790683.	+	1.36950e6i	0.110949	+	0.192169i
$552$	6.21450e6			0.868077
$553$		0			0
$554$	−6.91113e6			−0.956697
$555$	−381293.	−	660418.i	−0.0525444	−	0.0910095i
$556$	3.16841e6	−	5.48784e6i	0.434664	−	0.752860i
$557$	−316324.	+	547890.i	−0.0432011	+	0.0748264i	−0.886817	−	0.462120i	$-0.847089\pi$
$557$	−316324.	+	547890.i	−0.0432011	+	0.0748264i	0.843616	+	0.536946i	$0.180422\pi$
$558$	691160.	+	1.19712e6i	0.0939709	+	0.162762i
$559$	−1.38075e7			−1.86890
$560$		0			0
$561$	−1652.71			−0.000221712
$562$	107780.	+	186680.i	0.0143945	+	0.0249320i
$563$	5.03898e6	−	8.72777e6i	0.669995	−	1.16047i	−0.307910	−	0.951415i	$-0.599630\pi$
$563$	5.03898e6	−	8.72777e6i	0.669995	−	1.16047i	0.977905	−	0.209050i	$-0.0670371\pi$
$564$	2.97597e6	−	5.15453e6i	0.393941	−	0.682325i
$565$	1.42282e6	+	2.46439e6i	0.187512	+	0.324780i
$566$	1.47301e6			0.193270
$567$		0			0
$568$	−7.01763e6			−0.912682
$569$	−1.00842e6	−	1.74664e6i	−0.130576	−	0.226164i	0.793323	−	0.608801i	$-0.208349\pi$
$569$	−1.00842e6	−	1.74664e6i	−0.130576	−	0.226164i	−0.923899	+	0.382637i	$0.875016\pi$
$570$	204050.	−	353425.i	0.0263056	−	0.0455627i
$571$	−2.04864e6	+	3.54834e6i	−0.262951	+	0.455444i	−0.967025	−	0.254682i	$-0.918029\pi$
$571$	−2.04864e6	+	3.54834e6i	−0.262951	+	0.455444i	0.704074	+	0.710127i	$0.251362\pi$
$572$	32100.6	+	55599.8i	0.00410226	+	0.00710532i
$573$	1.41733e6			0.180337
$574$		0			0
$575$	−1.20397e7			−1.51861
$576$	−494634.	−	856731.i	−0.0621194	−	0.107594i
$577$	−4.07161e6	+	7.05224e6i	−0.509128	+	0.881835i	0.490816	+	0.871263i	$0.336699\pi$
$577$	−4.07161e6	+	7.05224e6i	−0.509128	+	0.881835i	−0.999944	+	0.0105723i	$0.996635\pi$
$578$	−2.19096e6	+	3.79485e6i	−0.272781	+	0.472470i
$579$	3.50118e6	+	6.06423e6i	0.434029	+	0.751759i
$580$	460307.			0.0568169
$581$		0			0
$582$	−493689.			−0.0604152
$583$	−35301.7	−	61144.4i	−0.00430155	−	0.00745050i
$584$	−2.47852e6	+	4.29292e6i	−0.300718	+	0.520859i
$585$	435836.	−	754891.i	0.0526543	−	0.0911999i
$586$	3.51810e6	+	6.09354e6i	0.423219	+	0.733036i
$587$	8.81465e6			1.05587			0.527934	−	0.849285i	$-0.322967\pi$
$587$	8.81465e6			1.05587			0.527934	+	0.849285i	$0.322967\pi$
$588$		0			0
$589$	5.86985e6			0.697170
$590$	141126.	+	244438.i	0.0166908	+	0.0289094i
$591$	1.53127e6	−	2.65224e6i	0.180336	−	0.312352i
$592$	−607495.	+	1.05221e6i	−0.0712424	+	0.123395i
$593$	−5.78695e6	−	1.00233e7i	−0.675792	−	1.17051i	−0.976237	−	0.216706i	$-0.930469\pi$
$593$	−5.78695e6	−	1.00233e7i	−0.675792	−	1.17051i	0.300445	−	0.953799i	$-0.402865\pi$
$594$	8263.74			0.000960972
$595$		0			0
$596$	7.17396e6			0.827263
$597$	−1.33429e6	−	2.31106e6i	−0.153220	−	0.265384i
$598$	−4.94792e6	+	8.57005e6i	−0.565809	+	0.980009i
$599$	6.17753e6	−	1.06998e7i	0.703474	−	1.21845i	−0.263766	−	0.964587i	$-0.584965\pi$
$599$	6.17753e6	−	1.06998e7i	0.703474	−	1.21845i	0.967240	−	0.253865i	$-0.0817020\pi$
$600$	2.22283e6	+	3.85005e6i	0.252074	+	0.436604i
$601$	8.33752e6			0.941566			0.470783	−	0.882249i	$-0.343971\pi$
$601$	8.33752e6			0.941566			0.470783	+	0.882249i	$0.343971\pi$
$602$		0			0
$603$	3.79964e6			0.425549
$604$	−943078.	−	1.63346e6i	−0.105185	−	0.182186i
$605$	1.11056e6	−	1.92355e6i	0.123355	−	0.213656i
$606$	−1.97673e6	+	3.42380e6i	−0.218659	+	0.378728i
$607$	−4.33595e6	−	7.51008e6i	−0.477653	−	0.827319i	0.522019	−	0.852934i	$-0.325179\pi$
$607$	−4.33595e6	−	7.51008e6i	−0.477653	−	0.827319i	−0.999672	+	0.0256151i	$0.991846\pi$
$608$	−6.37764e6			−0.699682
$609$		0			0
$610$	−1.56709e6			−0.170518
$611$	1.14961e7	+	1.99118e7i	1.24579	+	2.15778i
$612$	45520.3	−	78843.5i	0.00491278	−	0.00850918i
$613$	−2.62016e6	+	4.53825e6i	−0.281628	+	0.487794i	−0.971786	−	0.235865i	$-0.924208\pi$
$613$	−2.62016e6	+	4.53825e6i	−0.281628	+	0.487794i	0.690158	+	0.723659i	$0.257541\pi$
$614$	−2.50098e6	−	4.33182e6i	−0.267725	−	0.463713i
$615$	1.33542e6			0.142374
$616$		0			0
$617$	−6.95644e6			−0.735655			−0.367828	−	0.929894i	$-0.619898\pi$
$617$	−6.95644e6			−0.735655			−0.367828	+	0.929894i	$0.619898\pi$
$618$	−2.92907e6	−	5.07329e6i	−0.308502	−	0.534341i
$619$	9.13814e6	−	1.58277e7i	0.958586	−	1.66032i	0.232647	−	0.972561i	$-0.425261\pi$
$619$	9.13814e6	−	1.58277e7i	0.958586	−	1.66032i	0.725939	−	0.687759i	$-0.241406\pi$
$620$	854303.	−	1.47970e6i	0.0892550	−	0.154594i
$621$	−1.49534e6	−	2.59001e6i	−0.155601	−	0.269509i
$622$	3.17409e6			0.328960
$623$		0			0
$624$	−1.38879e6			−0.142783
$625$	−4.00918e6	−	6.94410e6i	−0.410540	−	0.711075i
$626$	490354.	−	849317.i	0.0500119	−	0.0866232i
$627$	17545.5	−	30389.6i	0.00178236	−	0.00308714i
$628$	1.41603e6	+	2.45263e6i	0.143276	+	0.248161i
$629$	307674.			0.0310074
$630$		0			0
$631$	1.90708e7			1.90676			0.953379	−	0.301777i	$-0.0975798\pi$
$631$	1.90708e7			1.90676			0.953379	+	0.301777i	$0.0975798\pi$
$632$	−1.86192e6	−	3.22494e6i	−0.185425	−	0.321165i
$633$	−2.28028e6	+	3.94956e6i	−0.226193	+	0.391777i
$634$	2.42887e6	−	4.20693e6i	0.239984	−	0.415664i
$635$	−619800.	−	1.07353e6i	−0.0609983	−	0.105652i
$636$	3.88924e6			0.381261
$637$		0			0
$638$	−16857.4			−0.00163961
$639$	1.68859e6	+	2.92473e6i	0.163596	+	0.283357i
$640$	−1.06314e6	+	1.84142e6i	−0.102599	+	0.177706i
$641$	−1.60312e6	+	2.77668e6i	−0.154106	+	0.266920i	−0.932733	−	0.360567i	$-0.882583\pi$
$641$	−1.60312e6	+	2.77668e6i	−0.154106	+	0.266920i	0.778627	+	0.627487i	$0.215917\pi$
$642$	−2.81962e6	−	4.88372e6i	−0.269993	−	0.467642i
$643$	−4.35153e6			−0.415063			−0.207532	−	0.978228i	$-0.566543\pi$
$643$	−4.35153e6			−0.415063			−0.207532	+	0.978228i	$0.566543\pi$
$644$		0			0
$645$	2.19675e6			0.207913
$646$	82326.4	+	142593.i	0.00776172	+	0.0134437i
$647$	−2.79988e6	+	4.84953e6i	−0.262953	+	0.455448i	−0.967025	−	0.254680i	$-0.918030\pi$
$647$	−2.79988e6	+	4.84953e6i	−0.262953	+	0.455448i	0.704072	+	0.710129i	$0.251363\pi$
$648$	−552154.	+	956358.i	−0.0516562	+	0.0894711i
$649$	12134.9	+	21018.3i	0.00113090	+	0.00195878i
$650$	−7.07917e6			−0.657202
$651$		0			0
$652$	5.29156e6			0.487489
$653$	3.37247e6	+	5.84130e6i	0.309504	+	0.536076i	0.978254	−	0.207411i	$-0.0665038\pi$
$653$	3.37247e6	+	5.84130e6i	0.309504	+	0.536076i	−0.668750	+	0.743487i	$0.733170\pi$
$654$	1.94130e6	−	3.36242e6i	0.177479	−	0.307403i
$655$	−2.20761e6	+	3.82370e6i	−0.201057	+	0.348241i
$656$	−1.06383e6	−	1.84261e6i	−0.0965188	−	0.167176i
$657$	2.38554e6			0.215612
$658$		0			0
$659$	2.09622e6			0.188029			0.0940143	−	0.995571i	$-0.470030\pi$
$659$	2.09622e6			0.188029			0.0940143	+	0.995571i	$0.470030\pi$
$660$	−5107.16	−	8845.87i	−0.000456373	−	0.000790461i
$661$	−9.70925e6	+	1.68169e7i	−0.864335	+	1.49707i	0.00337135	+	0.999994i	$0.498927\pi$
$661$	−9.70925e6	+	1.68169e7i	−0.864335	+	1.49707i	−0.867706	+	0.497077i	$0.834406\pi$
$662$	2.37796e6	−	4.11874e6i	0.210891	−	0.365275i
$663$	175843.	+	304570.i	0.0155361	+	0.0269093i
$664$	−655810.			−0.0577242
$665$		0			0
$666$	−1.53841e6			−0.134396
$667$	3.05039e6	+	5.28344e6i	0.265486	+	0.459835i
$668$	1.68137e6	−	2.91222e6i	0.145788	−	0.252513i
$669$	2.08063e6	−	3.60375e6i	0.179734	−	0.311308i
$670$	1.00014e6	+	1.73229e6i	0.0860744	+	0.149085i
$671$	−134748.			−0.0115536
$672$		0			0
$673$	1.27627e7			1.08619			0.543094	−	0.839672i	$-0.317253\pi$
$673$	1.27627e7			1.08619			0.543094	+	0.839672i	$0.317253\pi$
$674$	−4.43356e6	−	7.67916e6i	−0.375927	−	0.651124i
$675$	1.06972e6	−	1.85281e6i	0.0903673	−	0.156521i
$676$	2.66456e6	−	4.61516e6i	0.224264	−	0.388437i
$677$	−1.93251e6	−	3.34720e6i	−0.162050	−	0.280679i	0.773554	−	0.633731i	$-0.218477\pi$
$677$	−1.93251e6	−	3.34720e6i	−0.162050	−	0.280679i	−0.935604	+	0.353052i	$0.885144\pi$
$678$	5.74067e6			0.479610
$679$		0			0
$680$	116267.			0.00964241
$681$	442020.	+	765600.i	0.0365236	+	0.0632607i
$682$	−31286.4	+	54189.7i	−0.00257570	+	0.00446124i
$683$	1.03209e7	−	1.78764e7i	0.846578	−	1.46632i	−0.0376665	−	0.999290i	$-0.511992\pi$
$683$	1.03209e7	−	1.78764e7i	0.846578	−	1.46632i	0.884244	−	0.467025i	$-0.154674\pi$
$684$	966505.	+	1.67403e6i	0.0789885	+	0.136812i
$685$	3.57189e6			0.290852
$686$		0			0
$687$	4.51263e6			0.364786
$688$	−1.74999e6	−	3.03107e6i	−0.140950	−	0.244132i
$689$	−7.51200e6	+	1.30112e7i	−0.602848	+	1.04416i
$690$	787208.	−	1.36348e6i	0.0629458	−	0.109025i
$691$	−8.11643e6	−	1.40581e7i	−0.646651	−	1.12003i	−0.983918	−	0.178623i	$-0.942836\pi$
$691$	−8.11643e6	−	1.40581e7i	−0.646651	−	1.12003i	0.337267	−	0.941409i	$-0.390498\pi$
$692$	−1.58094e7			−1.25502
$693$		0			0
$694$	346156.			0.0272818
$695$	−1.94728e6	−	3.37279e6i	−0.152921	−	0.264867i
$696$	1.12635e6	−	1.95090e6i	0.0881356	−	0.152655i
$697$	−269396.	+	466607.i	−0.0210043	+	0.0363805i
$698$	−5.80166e6	−	1.00488e7i	−0.450727	−	0.780682i
$699$	−5.52524e6			−0.427719
$700$		0			0
$701$	−8.27590e6			−0.636092			−0.318046	−	0.948075i	$-0.603027\pi$
$701$	−8.27590e6			−0.636092			−0.318046	+	0.948075i	$0.603027\pi$
$702$	−879238.	−	1.52288e6i	−0.0673385	−	0.116634i
$703$	−3.26633e6	+	5.65745e6i	−0.249271	+	0.431750i
$704$	22390.3	−	38781.2i	0.00170267	−	0.00294910i
$705$	−1.82901e6	−	3.16794e6i	−0.138594	−	0.240051i
$706$	−9.98356e6			−0.753830
$707$		0			0
$708$	−1.33692e6			−0.100236
$709$	−1.19487e7	−	2.06957e7i	−0.892696	−	1.54619i	−0.836631	−	0.547767i	$-0.815478\pi$
$709$	−1.19487e7	−	2.06957e7i	−0.892696	−	1.54619i	−0.0560652	−	0.998427i	$-0.517855\pi$
$710$	−888943.	+	1.53969e6i	−0.0661802	+	0.114627i
$711$	−896037.	+	1.55198e6i	−0.0664740	+	0.115136i
$712$	−1.72781e6	−	2.99265e6i	−0.127731	−	0.221236i
$713$	2.26454e7			1.66823
$714$		0			0
$715$	39457.6			0.00288646
$716$	−6.25648e6	−	1.08365e7i	−0.456087	−	0.789965i
$717$	−4.95089e6	+	8.57520e6i	−0.359655	+	0.622940i
$718$	2.83902e6	−	4.91733e6i	0.205522	−	0.355974i
$719$	−392175.	−	679266.i	−0.0282916	−	0.0490025i	0.851533	−	0.524301i	$-0.175673\pi$
$719$	−392175.	−	679266.i	−0.0282916	−	0.0490025i	−0.879825	+	0.475299i	$0.842340\pi$
$720$	220955.			0.0158845
$721$		0			0
$722$	4.15920e6			0.296939
$723$	−404476.	−	700573.i	−0.0287771	−	0.0498434i
$724$	4.97191e6	−	8.61159e6i	0.352514	−	0.610572i
$725$	−2.18215e6	+	3.77960e6i	−0.154184	+	0.267055i
$726$	−2.24041e6	−	3.88050e6i	−0.157756	−	0.273241i
$727$	1.61766e7			1.13514			0.567571	−	0.823324i	$-0.307883\pi$
$727$	1.61766e7			1.13514			0.567571	+	0.823324i	$0.307883\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	627921.	+	1.08759e6i	0.0436112	+	0.0755368i
$731$	−443154.	+	767565.i	−0.0306733	+	0.0531278i
$732$	3.71135e6	−	6.42824e6i	0.256008	−	0.443419i
$733$	−6.84890e6	−	1.18627e7i	−0.470827	−	0.815496i	0.528616	−	0.848861i	$-0.322711\pi$
$733$	−6.84890e6	−	1.18627e7i	−0.470827	−	0.815496i	−0.999443	+	0.0333649i	$0.989378\pi$
$734$	1.04814e6			0.0718090
$735$		0			0
$736$	−2.46044e7			−1.67424
$737$	85998.3	+	148953.i	0.00583205	+	0.0101014i
$738$	1.34701e6	−	2.33309e6i	0.0910395	−	0.157685i
$739$	1.26856e7	−	2.19721e7i	0.854477	−	1.48000i	−0.0226532	−	0.999743i	$-0.507211\pi$
$739$	1.26856e7	−	2.19721e7i	0.854477	−	1.48000i	0.877130	−	0.480253i	$-0.159455\pi$
$740$	950768.	+	1.64678e6i	0.0638257	+	0.110549i
$741$	−7.46715e6			−0.499585
$742$		0			0
$743$	2.45336e7			1.63038			0.815192	−	0.579191i	$-0.196632\pi$
$743$	2.45336e7			1.63038			0.815192	+	0.579191i	$0.196632\pi$
$744$	−4.18089e6	−	7.24152e6i	−0.276909	−	0.479620i
$745$	2.20453e6	−	3.81837e6i	0.145521	−	0.252050i
$746$	−1.09230e6	+	1.89193e6i	−0.0718616	+	0.124468i
$747$	157802.	+	273322.i	0.0103469	+	0.0179214i
$748$	4121.10			0.000269314
$749$		0			0
$750$	2.32558e6			0.150966
$751$	9.24536e6	+	1.60134e7i	0.598169	+	1.03606i	0.993091	+	0.117345i	$0.0374384\pi$
$751$	9.24536e6	+	1.60134e7i	0.598169	+	1.03606i	−0.394922	+	0.918715i	$0.629228\pi$
$752$	−2.91407e6	+	5.04732e6i	−0.187913	+	0.325474i
$753$	−4.54727e6	+	7.87610e6i	−0.292256	+	0.506202i
$754$	1.79358e6	+	3.10657e6i	0.114893	+	0.199000i
$755$	−1.15922e6			−0.0740113
$756$		0			0
$757$	−2.94413e7			−1.86732			−0.933658	−	0.358166i	$-0.883402\pi$
$757$	−2.94413e7			−1.86732			−0.933658	+	0.358166i	$0.883402\pi$
$758$	1.00214e6	+	1.73577e6i	0.0633516	+	0.109728i
$759$	67689.1	−	117241.i	0.00426495	−	0.00738711i
$760$	−1.23432e6	+	2.13790e6i	−0.0775162	+	0.134262i
$761$	9.31179e6	+	1.61285e7i	0.582870	+	1.00956i	0.995137	+	0.0984975i	$0.0314036\pi$
$761$	9.31179e6	+	1.61285e7i	0.582870	+	1.00956i	−0.412267	+	0.911063i	$0.635263\pi$
$762$	−2.50072e6			−0.156019
$763$		0			0
$764$	−3.53417e6			−0.219056
$765$	−27976.5	−	48456.7i	−0.00172838	−	0.00299365i
$766$	−4.74599e6	+	8.22030e6i	−0.292250	+	0.506193i
$767$	2.58224e6	−	4.47257e6i	0.158492	−	0.274517i
$768$	3.90344e6	+	6.76095e6i	0.238805	+	0.413623i
$769$	−1.13326e7			−0.691056			−0.345528	−	0.938408i	$-0.612300\pi$
$769$	−1.13326e7			−0.691056			−0.345528	+	0.938408i	$0.612300\pi$
$770$		0			0
$771$	−1.09109e7			−0.661038
$772$	−8.73033e6	−	1.51214e7i	−0.527215	−	0.913163i
$773$	4.11010e6	−	7.11890e6i	0.247402	−	0.428513i	−0.715402	−	0.698713i	$-0.753756\pi$
$773$	4.11010e6	−	7.11890e6i	0.247402	−	0.428513i	0.962804	+	0.270200i	$0.0870898\pi$
$774$	2.21582e6	−	3.83791e6i	0.132948	−	0.230273i
$775$	8.09990e6	+	1.40294e7i	0.484424	+	0.839047i
$776$	2.98637e6			0.178029
$777$		0			0
$778$	1.42214e7			0.842352
$779$	−5.71991e6	−	9.90717e6i	−0.337711	−	0.584933i
$780$	−1.08677e6	+	1.88235e6i	−0.0639592	+	0.110781i
$781$	−76436.8	+	132392.i	−0.00448410	+	0.00776668i
$782$	317609.	+	550114.i	0.0185727	+	0.0321689i
$783$	−1.08410e6			−0.0631925
$784$		0			0
$785$	1.74056e6			0.100813
$786$	4.45355e6	+	7.71377e6i	0.257128	+	0.445359i
$787$	2.71541e6	−	4.70322e6i	0.156278	−	0.270681i	−0.777246	−	0.629197i	$-0.783384\pi$
$787$	2.71541e6	−	4.70322e6i	0.156278	−	0.270681i	0.933524	+	0.358516i	$0.116717\pi$
$788$	−3.81829e6	+	6.61347e6i	−0.219055	+	0.379414i
$789$	−1.73206e6	−	3.00001e6i	−0.0990534	−	0.171566i
$790$	−943418.			−0.0537819
$791$		0			0
$792$	−49988.1			−0.00283174
$793$	1.43368e7	+	2.48321e7i	0.809598	+	1.40227i
$794$	4.08340e6	−	7.07266e6i	0.229864	−	0.398136i
$795$	1.19515e6	−	2.07006e6i	0.0670664	−	0.116162i
$796$	3.32710e6	+	5.76271e6i	0.186116	+	0.322362i
$797$	1.78388e7			0.994765			0.497382	−	0.867531i	$-0.334295\pi$
$797$	1.78388e7			0.994765			0.497382	+	0.867531i	$0.334295\pi$
$798$		0			0
$799$	1.47587e6			0.0817866
$800$	−8.80061e6	−	1.52431e7i	−0.486170	−	0.842071i
$801$	−831498.	+	1.44020e6i	−0.0457910	+	0.0793123i
$802$	7.56949e6	−	1.31107e7i	0.415557	−	0.719766i
$803$	53992.6	+	93517.9i	0.00295492	+	0.00511807i
$804$	−9.47455e6			−0.516914
$805$		0			0
$806$	1.33151e7			0.721951
$807$	7.08547e6	+	1.22724e7i	0.382988	+	0.663355i
$808$	1.19574e7	−	2.07109e7i	0.644333	−	1.11602i
$809$	−5.92153e6	+	1.02564e7i	−0.318099	+	0.550964i	−0.980091	−	0.198546i	$-0.936378\pi$
$809$	−5.92153e6	+	1.02564e7i	−0.318099	+	0.550964i	0.661992	+	0.749511i	$0.269711\pi$
$810$	139886.	+	242289.i	0.00749136	+	0.0129754i
$811$	618053.			0.0329969			0.0164985	−	0.999864i	$-0.494748\pi$
$811$	618053.			0.0329969			0.0164985	+	0.999864i	$0.494748\pi$
$812$		0			0
$813$	2.99043e6			0.158674
$814$	−34819.2	−	60308.6i	−0.00184186	−	0.00319020i
$815$	1.62608e6	−	2.81645e6i	0.0857526	−	0.148528i
$816$	−44573.6	+	77203.7i	−0.00234343	+	0.00405894i
$817$	−9.40920e6	−	1.62972e7i	−0.493171	−	0.854198i
$818$	−297836.			−0.0155630
$819$		0			0
$820$	−3.32992e6			−0.172941
$821$	−2.15628e6	−	3.73479e6i	−0.111647	−	0.193378i	0.804787	−	0.593563i	$-0.202279\pi$
$821$	−2.15628e6	−	3.73479e6i	−0.111647	−	0.193378i	−0.916434	+	0.400185i	$0.868946\pi$
$822$	3.60289e6	−	6.24039e6i	0.185982	−	0.322131i
$823$	−1.43310e7	+	2.48220e7i	−0.737524	+	1.27743i	0.216083	+	0.976375i	$0.430672\pi$
$823$	−1.43310e7	+	2.48220e7i	−0.737524	+	1.27743i	−0.953607	+	0.301054i	$0.902662\pi$
$824$	1.77182e7	+	3.06888e7i	0.909079	+	1.57457i
$825$	96845.2			0.00495385
$826$		0			0
$827$	1.86894e7			0.950235			0.475117	−	0.879922i	$-0.342406\pi$
$827$	1.86894e7			0.950235			0.475117	+	0.879922i	$0.342406\pi$
$828$	3.72870e6	+	6.45830e6i	0.189009	+	0.327372i
$829$	−6.62429e6	+	1.14736e7i	−0.334775	+	0.579847i	−0.983442	−	0.181225i	$-0.941994\pi$
$829$	−6.62429e6	+	1.14736e7i	−0.334775	+	0.579847i	0.648667	+	0.761073i	$0.275327\pi$
$830$	−83073.4	+	143887.i	−0.00418569	+	0.00724982i
$831$	−1.00595e7	−	1.74235e7i	−0.505326	−	0.875251i
$832$	−9.52907e6			−0.477246
$833$		0			0
$834$	−7.85673e6			−0.391135
$835$	−1.03336e6	−	1.78983e6i	−0.0512903	−	0.0888375i
$836$	−43750.3	+	75777.8i	−0.00216504	+	0.00374995i
$837$	−2.01203e6	+	3.48494e6i	−0.0992706	+	0.171942i
$838$	1.69510e6	+	2.93599e6i	0.0833843	+	0.144426i
$839$	−2.52930e7			−1.24049			−0.620247	−	0.784406i	$-0.712968\pi$
$839$	−2.52930e7			−1.24049			−0.620247	+	0.784406i	$0.712968\pi$
$840$		0			0
$841$	−1.82997e7			−0.892181
$842$	−2.99361e6	−	5.18509e6i	−0.145518	−	0.252044i
$843$	−313756.	+	543441.i	−0.0152063	+	0.0263381i
$844$	5.68596e6	−	9.84837e6i	0.274756	−	0.475892i
$845$	−1.63762e6	−	2.83645e6i	−0.0788991	−	0.136657i
$846$	−7.37954e6			−0.354490
$847$		0			0
$848$	−3.80835e6			−0.181864
$849$	2.14404e6	+	3.71358e6i	0.102085	+	0.176817i
$850$	−227207.	+	393534.i	−0.0107864	+	0.0186825i
$851$	−1.26012e7	+	2.18260e7i	−0.596471	+	1.03312i
$852$	−4.21058e6	−	7.29293e6i	−0.198720	−	0.344194i
$853$	4.05806e7			1.90962			0.954808	−	0.297223i	$-0.0960605\pi$
$853$	4.05806e7			1.90962			0.954808	+	0.297223i	$0.0960605\pi$
$854$		0			0
$855$	1.18801e6			0.0555784
$856$	1.70561e7	+	2.95421e7i	0.795602	+	1.37802i
$857$	−9.72346e6	+	1.68415e7i	−0.452240	+	0.783302i	−0.998525	−	0.0542970i	$-0.982708\pi$
$857$	−9.72346e6	+	1.68415e7i	−0.452240	+	0.783302i	0.546285	+	0.837599i	$0.316042\pi$
$858$	39800.1	−	68935.7i	0.00184572	−	0.00319688i
$859$	1.01621e7	+	1.76012e7i	0.469894	+	0.813880i	0.999407	−	0.0344214i	$-0.0109588\pi$
$859$	1.01621e7	+	1.76012e7i	0.469894	+	0.813880i	−0.529513	+	0.848302i	$0.677625\pi$
$860$	−5.47769e6			−0.252552
$861$		0			0
$862$	9.50149e6			0.435536
$863$	1.30601e7	+	2.26208e7i	0.596926	+	1.03391i	0.993272	+	0.115804i	$0.0369446\pi$
$863$	1.30601e7	+	2.26208e7i	0.596926	+	1.03391i	−0.396346	+	0.918101i	$0.629722\pi$
$864$	2.18609e6	−	3.78641e6i	0.0996283	−	0.172561i
$865$	−4.85817e6	+	8.41459e6i	−0.220766	+	0.382378i
$866$	5.88829e6	+	1.01988e7i	0.266805	+	0.462121i
$867$	−1.27561e7			−0.576330
$868$		0			0
$869$	−81120.9			−0.00364404
$870$	−285357.	−	494252.i	−0.0127817	−	0.0221386i
$871$	1.82999e7	−	3.16964e7i	0.817343	−	1.41568i
$872$	−1.17431e7	+	2.03396e7i	−0.522987	+	0.905840i
$873$	−718587.	−	1.24463e6i	−0.0319113	−	0.0552719i
$874$	−1.34872e7			−0.597231
$875$		0			0
$876$	−5.94844e6			−0.261904
$877$	8.14779e6	+	1.41124e7i	0.357718	+	0.619585i	0.987579	−	0.157122i	$-0.0502216\pi$
$877$	8.14779e6	+	1.41124e7i	0.357718	+	0.619585i	−0.629861	+	0.776708i	$0.716888\pi$
$878$	823947.	−	1.42712e6i	0.0360714	−	0.0624775i
$879$	−1.02415e7	+	1.77388e7i	−0.447087	+	0.774377i
$880$	5000.94	+	8661.88i	0.000217693	+	0.000377056i
$881$	2.93722e7			1.27496			0.637479	−	0.770467i	$-0.279977\pi$
$881$	2.93722e7			1.27496			0.637479	+	0.770467i	$0.279977\pi$
$882$		0			0
$883$	1.21821e7			0.525800			0.262900	−	0.964823i	$-0.415321\pi$
$883$	1.21821e7			0.525800			0.262900	+	0.964823i	$0.415321\pi$
$884$	−438473.	−	759457.i	−0.0188717	−	0.0326868i
$885$	−410831.	+	711580.i	−0.0176321	+	0.0305398i
$886$	−7.21501e6	+	1.24968e7i	−0.308783	+	0.534827i
$887$	1.19010e7	+	2.06132e7i	0.507897	+	0.879704i	0.999958	+	0.00914296i	$0.00291033\pi$
$887$	1.19010e7	+	2.06132e7i	0.507897	+	0.879704i	−0.492061	+	0.870561i	$0.663756\pi$
$888$	9.30597e6			0.396031
$889$		0			0
$890$	−875466.			−0.0370480
$891$	12028.2	+	20833.5i	0.000507584	+	0.000879161i
$892$	−5.18813e6	+	8.98610e6i	−0.218323	+	0.378146i
$893$	−1.56681e7	+	2.71380e7i	−0.657490	+	1.13881i
$894$	−4.44734e6	−	7.70301e6i	−0.186104	−	0.322342i
$895$	−7.69038e6			−0.320915
$896$		0			0
$897$	−2.88077e7			−1.19544
$898$	−9.43153e6	−	1.63359e7i	−0.390293	−	0.676008i
$899$	4.10439e6	−	7.10902e6i	0.169375	−	0.293366i
$900$	−2.66739e6	+	4.62006e6i	−0.109769	+	0.190126i
$901$	482198.	+	835192.i	0.0197885	+	0.0342747i
$902$	121949.			0.00499070
$903$		0			0
$904$	−3.47259e7			−1.41329
$905$	−3.05570e6	−	5.29263e6i	−0.124019	−	0.214808i
$906$	−1.16928e6	+	2.02525e6i	−0.0473258	+	0.0819706i
$907$	−1.05435e7	+	1.82619e7i	−0.425566	+	0.737102i	−0.996473	−	0.0839124i	$-0.973258\pi$
$907$	−1.05435e7	+	1.82619e7i	−0.425566	+	0.737102i	0.570907	+	0.821015i	$0.306592\pi$
$908$	−1.10219e6	−	1.90905e6i	−0.0443653	−	0.0768429i
$909$	−1.15089e7			−0.461981
$910$		0			0
$911$	1.71528e7			0.684761			0.342381	−	0.939561i	$-0.388767\pi$
$911$	1.71528e7			0.684761			0.342381	+	0.939561i	$0.388767\pi$
$912$	−946402.	−	1.63922e6i	−0.0376781	−	0.0652603i
$913$	−7143.16	+	12372.3i	−0.000283605	+	0.000491218i
$914$	9.18983e6	−	1.59173e7i	0.363866	−	0.630235i
$915$	−2.28097e6	−	3.95076e6i	−0.0900672	−	0.156001i
$916$	−1.12524e7			−0.443105
$917$		0			0
$918$	−112877.			−0.00442079
$919$	−3.67771e6	−	6.36997e6i	−0.143644	−	0.248799i	0.785222	−	0.619214i	$-0.212549\pi$
$919$	−3.67771e6	−	6.36997e6i	−0.143644	−	0.248799i	−0.928866	+	0.370415i	$0.879215\pi$
$920$	−4.76190e6	+	8.24785e6i	−0.185486	+	0.321271i
$921$	7.28057e6	−	1.26103e7i	0.282824	−	0.489866i
$922$	3.23717e6	+	5.60694e6i	0.125412	+	0.217219i
$923$	3.25306e7			1.25686
$924$		0			0
$925$	−1.80290e7			−0.692817
$926$	3.72732e6	+	6.45590e6i	0.142846	+	0.247417i
$927$	8.52677e6	−	1.47688e7i	0.325901	−	0.564477i
$928$	−4.45946e6	+	7.72401e6i	−0.169986	+	0.294424i
$929$	1.67099e7	+	2.89424e7i	0.635236	+	1.10026i	0.986465	+	0.163972i	$0.0524306\pi$
$929$	1.67099e7	+	2.89424e7i	0.635236	+	1.10026i	−0.351229	+	0.936290i	$0.614236\pi$
$930$	−2.11842e6			−0.0803166
$931$		0			0
$932$	1.37774e7			0.519550
$933$	4.62003e6	+	8.00213e6i	0.173756	+	0.300955i
$934$	6.98449e6	−	1.20975e7i	0.261979	−	0.453762i
$935$	1266.40	−	2193.47i	4.73742e−5	−	8.20544e-5i
$936$	5.31859e6	+	9.21207e6i	0.198430	+	0.343691i
$937$	−2.87696e7			−1.07049			−0.535247	−	0.844696i	$-0.679781\pi$
$937$	−2.87696e7			−1.07049			−0.535247	+	0.844696i	$0.679781\pi$
$938$		0			0
$939$	2.85493e6			0.105665
$940$	4.56071e6	+	7.89938e6i	0.168350	+	0.291591i
$941$	−1.08189e7	+	1.87390e7i	−0.398300	+	0.689876i	−0.993516	−	0.113689i	$-0.963733\pi$
$941$	−1.08189e7	+	1.87390e7i	−0.398300	+	0.689876i	0.595216	+	0.803566i	$0.297066\pi$
$942$	1.75567e6	−	3.04091e6i	0.0644637	−	0.111654i
$943$	−2.20670e7	−	3.82211e7i	−0.808096	−	1.39966i
$944$	1.30911e6			0.0478132
$945$		0			0
$946$	200605.			0.00728809
$947$	3.15627e6	+	5.46682e6i	0.114367	+	0.198089i	0.917526	−	0.397675i	$-0.130183\pi$
$947$	3.15627e6	+	5.46682e6i	0.114367	+	0.198089i	−0.803160	+	0.595764i	$0.796849\pi$
$948$	2.23430e6	−	3.86992e6i	0.0807460	−	0.139856i
$949$	1.14893e7	−	1.99001e7i	0.414122	−	0.717280i
$950$	−4.82415e6	−	8.35566e6i	−0.173425	−	0.300381i
$951$	1.41413e7			0.507036
$952$		0			0
$953$	−5.59599e6			−0.199593			−0.0997963	−	0.995008i	$-0.531819\pi$
$953$	−5.59599e6			−0.199593			−0.0997963	+	0.995008i	$0.531819\pi$
$954$	−2.41105e6	−	4.17606e6i	−0.0857699	−	0.148558i
$955$	−1.08604e6	+	1.88108e6i	−0.0385334	+	0.0667418i
$956$	1.23452e7	−	2.13826e7i	0.436873	−	0.756686i
$957$	−24536.8	−	42498.9i	−0.000866039	−	0.00150002i
$958$	2.58438e7			0.909792
$959$		0			0
$960$	1.51606e6			0.0530933
$961$	−920457.	−	1.59428e6i	−0.0321510	−	0.0556872i
$962$	−7.40932e6	+	1.28333e7i	−0.258131	+	0.447097i
$963$	8.20816e6	−	1.42169e7i	0.285220	−	0.494016i
$964$	1.00858e6	+	1.74691e6i	0.0349555	+	0.0605448i
$965$	−1.07312e7			−0.370963
$966$		0			0
$967$	1.33277e7			0.458340			0.229170	−	0.973386i	$-0.426399\pi$
$967$	1.33277e7			0.458340			0.229170	+	0.973386i	$0.426399\pi$
$968$	1.35524e7	+	2.34735e7i	0.464867	+	0.805173i
$969$	−239659.	+	415102.i	−0.00819946	+	0.0142019i
$970$	378293.	−	655222.i	0.0129092	−	0.0223593i
$971$	1.81628e7	+	3.14590e7i	0.618210	+	1.07077i	0.989812	+	0.142379i	$0.0454751\pi$
$971$	1.81628e7	+	3.14590e7i	0.618210	+	1.07077i	−0.371603	+	0.928392i	$0.621192\pi$
$972$	−1.32517e6			−0.0449889
$973$		0			0
$974$	−1.84973e6			−0.0624758
$975$	−1.03040e7	−	1.78471e7i	−0.347133	−	0.601252i
$976$	−3.63416e6	+	6.29454e6i	−0.122118	+	0.211514i
$977$	4.51869e6	−	7.82661e6i	0.151453	−	0.262323i	−0.780309	−	0.625394i	$-0.784938\pi$
$977$	4.51869e6	−	7.82661e6i	0.151453	−	0.262323i	0.931762	+	0.363071i	$0.118272\pi$
$978$	−3.28038e6	−	5.68179e6i	−0.109667	−	0.189949i
$979$	−75278.0			−0.00251022
$980$		0			0
$981$	1.13026e7			0.374977
$982$	4.27819e6	+	7.41005e6i	0.141573	+	0.245212i
$983$	−9.92693e6	+	1.71939e7i	−0.327666	+	0.567534i	−0.982048	−	0.188630i	$-0.939595\pi$
$983$	−9.92693e6	+	1.71939e7i	−0.327666	+	0.567534i	0.654382	+	0.756164i	$0.272929\pi$
$984$	−8.14819e6	+	1.41131e7i	−0.268271	+	0.464658i
$985$	2.34669e6	+	4.06459e6i	0.0770665	+	0.133483i
$986$	230261.			0.00754273
$987$		0			0
$988$	1.86196e7			0.606846
$989$	−3.63000e7	−	6.28734e7i	−1.18009	−	2.04398i
$990$	−6332.14	+	10967.6i	−0.000205335	+	0.000355650i
$991$	2.27779e7	−	3.94524e7i	0.736764	−	1.27611i	−0.217181	−	0.976131i	$-0.569686\pi$
$991$	2.27779e7	−	3.94524e7i	0.736764	−	1.27611i	0.953945	−	0.299982i	$-0.0969806\pi$
$992$	1.65530e7	+	2.86706e7i	0.534069	+	0.925034i
$993$	1.38449e7			0.445570
$994$		0			0
$995$	4.08963e6			0.130956
$996$	−393486.	−	681538.i	−0.0125684	−	0.0217692i
$997$	2.25832e7	−	3.91153e7i	0.719529	−	1.24626i	−0.241658	−	0.970362i	$-0.577691\pi$
$997$	2.25832e7	−	3.91153e7i	0.719529	−	1.24626i	0.961187	−	0.275899i	$-0.0889756\pi$
$998$	4.69805e6	−	8.13726e6i	0.149311	−	0.258614i
$999$	−2.23922e6	−	3.87845e6i	−0.0709877	−	0.122954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.p.67.4		12
7.2	even	3	inner	147.6.e.p.79.4		12
7.3	odd	6		147.6.a.n.1.3	✓	6
7.4	even	3		147.6.a.o.1.3	yes	6
7.5	odd	6		147.6.e.q.79.4		12
7.6	odd	2		147.6.e.q.67.4		12
21.11	odd	6		441.6.a.ba.1.4		6
21.17	even	6		441.6.a.bb.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.n.1.3	✓	6	7.3	odd	6
147.6.a.o.1.3	yes	6	7.4	even	3
147.6.e.p.67.4		12	1.1	even	1	trivial
147.6.e.p.79.4		12	7.2	even	3	inner
147.6.e.q.67.4		12	7.6	odd	2
147.6.e.q.79.4		12	7.5	odd	6
441.6.a.ba.1.4		6	21.11	odd	6
441.6.a.bb.1.4		6	21.17	even	6

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)

\(f(q)\)	\(=\)	\(q+(1.54581 + 2.67743i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(11.2209 - 19.4352i) q^{4} +(-6.89630 - 11.9448i) q^{5} -27.8246 q^{6} +168.314 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(1.54581 + 2.67743i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(11.2209 - 19.4352i) q^{4} +(-6.89630 - 11.9448i) q^{5} -27.8246 q^{6} +168.314 q^{8} +(-40.5000 - 70.1481i) q^{9} +(21.3208 - 36.9287i) q^{10} +(1.83329 - 3.17536i) q^{11} +(100.988 + 174.917i) q^{12} -780.229 q^{13} +124.133 q^{15} +(-98.8879 - 171.279i) q^{16} +(-25.0416 + 43.3733i) q^{17} +(125.211 - 216.872i) q^{18} +(-531.692 - 920.918i) q^{19} -309.532 q^{20} +11.3357 q^{22} +(-2051.23 - 3552.83i) q^{23} +(-757.412 + 1311.88i) q^{24} +(1467.38 - 2541.58i) q^{25} +(-1206.09 - 2089.01i) q^{26} +729.000 q^{27} -1487.11 q^{29} +(191.887 + 332.358i) q^{30} +(-2759.98 + 4780.43i) q^{31} +(2998.75 - 5193.98i) q^{32} +(16.4997 + 28.5782i) q^{33} -154.838 q^{34} -1817.79 q^{36} +(-3071.63 - 5320.23i) q^{37} +(1643.79 - 2847.13i) q^{38} +(3511.03 - 6081.28i) q^{39} +(-1160.74 - 2010.47i) q^{40} +10757.9 q^{41} +17696.7 q^{43} +(-41.1425 - 71.2609i) q^{44} +(-558.601 + 967.525i) q^{45} +(6341.63 - 10984.0i) q^{46} +(-14734.2 - 25520.4i) q^{47} +1779.98 q^{48} +9073.19 q^{50} +(-225.374 - 390.360i) q^{51} +(-8754.89 + 15163.9i) q^{52} +(9627.95 - 16676.1i) q^{53} +(1126.90 + 1951.84i) q^{54} -50.5718 q^{55} +9570.46 q^{57} +(-2298.79 - 3981.62i) q^{58} +(-3309.59 + 5732.38i) q^{59} +(1392.89 - 2412.56i) q^{60} +(-18375.1 - 31826.7i) q^{61} -17065.7 q^{62} +12213.2 q^{64} +(5380.70 + 9319.64i) q^{65} +(-51.0107 + 88.3532i) q^{66} +(-23454.6 + 40624.5i) q^{67} +(561.979 + 973.377i) q^{68} +36922.1 q^{69} -41693.7 q^{71} +(-6816.71 - 11806.9i) q^{72} +(-14725.6 + 25505.4i) q^{73} +(9496.35 - 16448.2i) q^{74} +(13206.4 + 22874.2i) q^{75} -23864.3 q^{76} +21709.6 q^{78} +(-11062.2 - 19160.3i) q^{79} +(-1363.92 + 2362.38i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(16629.7 + 28803.6i) q^{82} -3896.35 q^{83} +690.778 q^{85} +(27355.8 + 47381.6i) q^{86} +(6691.98 - 11590.9i) q^{87} +(308.569 - 534.457i) q^{88} +(-10265.4 - 17780.2i) q^{89} -3453.97 q^{90} -92066.6 q^{92} +(-24839.9 - 43023.9i) q^{93} +(45552.7 - 78899.6i) q^{94} +(-7333.42 + 12701.9i) q^{95} +(26988.7 + 46745.8i) q^{96} +17742.9 q^{97} -296.994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

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