LMFDB - Embedded newform 147.6.e.q.79.2

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			79.2
Root			$1.87676 + 3.25065i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.q.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.10431 + 7.10888i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-17.6908 - 30.6414i) q^{4} +(14.6130 - 25.3104i) q^{5} -73.8777 q^{6} +27.7583 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-4.10431 + 7.10888i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-17.6908 - 30.6414i) q^{4} +(14.6130 - 25.3104i) q^{5} -73.8777 q^{6} +27.7583 q^{8} +(-40.5000 + 70.1481i) q^{9} +(119.952 + 207.764i) q^{10} +(-188.669 - 326.784i) q^{11} +(159.217 - 275.772i) q^{12} -509.772 q^{13} +263.033 q^{15} +(452.177 - 783.193i) q^{16} +(802.990 + 1390.82i) q^{17} +(-332.450 - 575.819i) q^{18} +(1078.37 - 1867.79i) q^{19} -1034.06 q^{20} +3097.43 q^{22} +(2217.19 - 3840.29i) q^{23} +(124.912 + 216.355i) q^{24} +(1135.42 + 1966.61i) q^{25} +(2092.27 - 3623.91i) q^{26} -729.000 q^{27} +4772.55 q^{29} +(-1079.57 + 1869.87i) q^{30} +(-3577.96 - 6197.21i) q^{31} +(4155.88 + 7198.20i) q^{32} +(1698.02 - 2941.06i) q^{33} -13182.9 q^{34} +2865.91 q^{36} +(-2787.16 + 4827.50i) q^{37} +(8851.95 + 15332.0i) q^{38} +(-2293.97 - 3973.28i) q^{39} +(405.631 - 702.574i) q^{40} +9911.64 q^{41} -4886.16 q^{43} +(-6675.41 + 11562.2i) q^{44} +(1183.65 + 2050.14i) q^{45} +(18200.1 + 31523.5i) q^{46} +(4633.04 - 8024.67i) q^{47} +8139.18 q^{48} -18640.5 q^{50} +(-7226.91 + 12517.4i) q^{51} +(9018.28 + 15620.1i) q^{52} +(4623.06 + 8007.37i) q^{53} +(2992.05 - 5182.37i) q^{54} -11028.1 q^{55} +19410.7 q^{57} +(-19588.1 + 33927.5i) q^{58} +(-7060.37 - 12228.9i) q^{59} +(-4653.27 - 8059.70i) q^{60} +(-9015.47 + 15615.2i) q^{61} +58740.4 q^{62} -39288.9 q^{64} +(-7449.28 + 12902.5i) q^{65} +(13938.4 + 24142.1i) q^{66} +(23257.0 + 40282.4i) q^{67} +(28411.1 - 49209.5i) q^{68} +39909.4 q^{69} +64269.9 q^{71} +(-1124.21 + 1947.19i) q^{72} +(-30460.5 - 52759.1i) q^{73} +(-22878.7 - 39627.2i) q^{74} +(-10218.8 + 17699.5i) q^{75} -76309.0 q^{76} +37660.8 q^{78} +(35732.3 - 61890.2i) q^{79} +(-13215.3 - 22889.5i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-40680.5 + 70460.7i) q^{82} -11597.5 q^{83} +46936.3 q^{85} +(20054.3 - 34735.1i) q^{86} +(21476.5 + 37198.4i) q^{87} +(-5237.14 - 9070.98i) q^{88} +(39119.5 - 67756.9i) q^{89} -19432.3 q^{90} -156896. q^{92} +(32201.7 - 55774.9i) q^{93} +(38030.9 + 65871.5i) q^{94} +(-31516.4 - 54588.0i) q^{95} +(-37403.0 + 64783.8i) q^{96} -151480. q^{97} +30564.4 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 $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

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

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 $

$2$	−4.10431	+	7.10888i	−0.725547	+	1.25668i	0.233201	+	0.972429i	$0.425080\pi$
$2$	−4.10431	+	7.10888i	−0.725547	+	1.25668i	−0.958748	+	0.284256i	$0.908253\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−17.6908	−	30.6414i	−0.552838	−	0.957543i
$5$	14.6130	−	25.3104i	0.261405	−	0.452766i	−0.705211	−	0.708998i	$-0.749148\pi$
$5$	14.6130	−	25.3104i	0.261405	−	0.452766i	0.966615	+	0.256232i	$0.0824810\pi$
$6$	−73.8777			−0.837790
$7$		0			0
$7$		0			0
$8$	27.7583			0.153344
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	119.952	+	207.764i	0.379323	+	0.657006i
$11$	−188.669	−	326.784i	−0.470131	−	0.814291i	0.529286	−	0.848444i	$-0.322460\pi$
$11$	−188.669	−	326.784i	−0.470131	−	0.814291i	−0.999417	+	0.0341529i	$0.989127\pi$
$12$	159.217	−	275.772i	0.319181	−	0.552838i
$13$	−509.772			−0.836600			−0.418300	−	0.908309i	$-0.637374\pi$
$13$	−509.772			−0.836600			−0.418300	+	0.908309i	$0.637374\pi$
$14$		0			0
$15$	263.033			0.301844
$16$	452.177	−	783.193i	0.441579	−	0.764837i
$17$	802.990	+	1390.82i	0.673889	+	1.16721i	0.976792	+	0.214188i	$0.0687106\pi$
$17$	802.990	+	1390.82i	0.673889	+	1.16721i	−0.302904	+	0.953021i	$0.597956\pi$
$18$	−332.450	−	575.819i	−0.241849	−	0.418895i
$19$	1078.37	−	1867.79i	0.685306	−	1.18698i	−0.288035	−	0.957620i	$-0.593002\pi$
$19$	1078.37	−	1867.79i	0.685306	−	1.18698i	0.973341	−	0.229364i	$-0.0736647\pi$
$20$	−1034.06			−0.578057
$21$		0			0
$22$	3097.43			1.36441
$23$	2217.19	−	3840.29i	0.873944	−	1.51371i	0.0160599	−	0.999871i	$-0.494888\pi$
$23$	2217.19	−	3840.29i	0.873944	−	1.51371i	0.857884	−	0.513844i	$-0.171779\pi$
$24$	124.912	+	216.355i	0.0442667	+	0.0766722i
$25$	1135.42	+	1966.61i	0.363335	+	0.629315i
$26$	2092.27	−	3623.91i	0.606993	−	1.05134i
$27$	−729.000			−0.192450
$28$		0			0
$29$	4772.55			1.05379			0.526897	−	0.849929i	$-0.323355\pi$
$29$	4772.55			1.05379			0.526897	+	0.849929i	$0.323355\pi$
$30$	−1079.57	+	1869.87i	−0.219002	+	0.379323i
$31$	−3577.96	−	6197.21i	−0.668701	−	1.15822i	−0.978268	−	0.207346i	$-0.933518\pi$
$31$	−3577.96	−	6197.21i	−0.668701	−	1.15822i	0.309567	−	0.950878i	$-0.399816\pi$
$32$	4155.88	+	7198.20i	0.717445	+	1.24265i
$33$	1698.02	−	2941.06i	0.271430	−	0.470131i
$34$	−13182.9			−1.95575
$35$		0			0
$36$	2865.91			0.368558
$37$	−2787.16	+	4827.50i	−0.334701	+	0.579720i	−0.983427	−	0.181302i	$-0.941969\pi$
$37$	−2787.16	+	4827.50i	−0.334701	+	0.579720i	0.648726	+	0.761022i	$0.275302\pi$
$38$	8851.95	+	15332.0i	0.994443	+	1.72243i
$39$	−2293.97	−	3973.28i	−0.241506	−	0.418300i
$40$	405.631	−	702.574i	0.0400850	−	0.0694292i
$41$	9911.64			0.920844			0.460422	−	0.887700i	$-0.347698\pi$
$41$	9911.64			0.920844			0.460422	+	0.887700i	$0.347698\pi$
$42$		0			0
$43$	−4886.16			−0.402992			−0.201496	−	0.979489i	$-0.564580\pi$
$43$	−4886.16			−0.402992			−0.201496	+	0.979489i	$0.564580\pi$
$44$	−6675.41	+	11562.2i	−0.519812	+	0.900341i
$45$	1183.65	+	2050.14i	0.0871349	+	0.150922i
$46$	18200.1	+	31523.5i	1.26817	+	2.19654i
$47$	4633.04	−	8024.67i	0.305930	−	0.529886i	−0.671538	−	0.740970i	$-0.734366\pi$
$47$	4633.04	−	8024.67i	0.305930	−	0.529886i	0.977468	+	0.211084i	$0.0676994\pi$
$48$	8139.18			0.509891
$49$		0			0
$50$	−18640.5			−1.05447
$51$	−7226.91	+	12517.4i	−0.389070	+	0.673889i
$52$	9018.28	+	15620.1i	0.462504	+	0.801080i
$53$	4623.06	+	8007.37i	0.226068	+	0.391562i	0.956639	−	0.291275i	$-0.0940794\pi$
$53$	4623.06	+	8007.37i	0.226068	+	0.391562i	−0.730571	+	0.682837i	$0.760746\pi$
$54$	2992.05	−	5182.37i	0.139632	−	0.241849i
$55$	−11028.1			−0.491578
$56$		0			0
$57$	19410.7			0.791323
$58$	−19588.1	+	33927.5i	−0.764577	+	1.32429i
$59$	−7060.37	−	12228.9i	−0.264057	−	0.457360i	0.703259	−	0.710933i	$-0.251727\pi$
$59$	−7060.37	−	12228.9i	−0.264057	−	0.457360i	−0.967316	+	0.253574i	$0.918394\pi$
$60$	−4653.27	−	8059.70i	−0.166871	−	0.289029i
$61$	−9015.47	+	15615.2i	−0.310216	+	0.537309i	−0.978409	−	0.206679i	$-0.933735\pi$
$61$	−9015.47	+	15615.2i	−0.310216	+	0.537309i	0.668193	+	0.743988i	$0.267068\pi$
$62$	58740.4			1.94070
$63$		0			0
$64$	−39288.9			−1.19900
$65$	−7449.28	+	12902.5i	−0.218691	+	0.378784i
$66$	13938.4	+	24142.1i	0.393871	+	0.682205i
$67$	23257.0	+	40282.4i	0.632947	+	1.09630i	0.986946	+	0.161050i	$0.0514882\pi$
$67$	23257.0	+	40282.4i	0.632947	+	1.09630i	−0.353999	+	0.935246i	$0.615178\pi$
$68$	28411.1	−	49209.5i	0.745102	−	1.29055i
$69$	39909.4			1.00914
$70$		0			0
$71$	64269.9			1.51308			0.756540	−	0.653948i	$-0.226888\pi$
$71$	64269.9			1.51308			0.756540	+	0.653948i	$0.226888\pi$
$72$	−1124.21	+	1947.19i	−0.0255574	+	0.0442667i
$73$	−30460.5	−	52759.1i	−0.669005	−	1.15875i	−0.978183	−	0.207747i	$-0.933387\pi$
$73$	−30460.5	−	52759.1i	−0.669005	−	1.15875i	0.309177	−	0.951004i	$-0.399946\pi$
$74$	−22878.7	−	39627.2i	−0.485683	−	0.841228i
$75$	−10218.8	+	17699.5i	−0.209772	+	0.363335i
$76$	−76309.0			−1.51545
$77$		0			0
$78$	37660.8			0.700895
$79$	35732.3	−	61890.2i	0.644160	−	1.11572i	−0.340335	−	0.940304i	$-0.610540\pi$
$79$	35732.3	−	61890.2i	0.644160	−	1.11572i	0.984495	−	0.175414i	$-0.0561263\pi$
$80$	−13215.3	−	22889.5i	−0.230861	−	0.399864i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−40680.5	+	70460.7i	−0.668116	+	1.15721i
$83$	−11597.5			−0.184785			−0.0923926	−	0.995723i	$-0.529451\pi$
$83$	−11597.5			−0.184785			−0.0923926	+	0.995723i	$0.529451\pi$
$84$		0			0
$85$	46936.3			0.704630
$86$	20054.3	−	34735.1i	0.292390	−	0.506434i
$87$	21476.5	+	37198.4i	0.304204	+	0.526897i
$88$	−5237.14	−	9070.98i	−0.0720920	−	0.124867i
$89$	39119.5	−	67756.9i	0.523502	−	0.906731i	−0.476124	−	0.879378i	$-0.657959\pi$
$89$	39119.5	−	67756.9i	0.523502	−	0.906731i	0.999626	−	0.0273533i	$-0.00870790\pi$
$90$	−19432.3			−0.252882
$91$		0			0
$92$	−156896.			−1.93260
$93$	32201.7	−	55774.9i	0.386074	−	0.668701i
$94$	38030.9	+	65871.5i	0.443933	+	0.768914i
$95$	−31516.4	−	54588.0i	−0.358284	−	0.620566i
$96$	−37403.0	+	64783.8i	−0.414217	+	0.717445i
$97$	−151480.			−1.63466			−0.817330	−	0.576170i	$-0.804546\pi$
$97$	−151480.			−1.63466			−0.817330	+	0.576170i	$0.804546\pi$
$98$		0			0
$99$	30564.4			0.313421
$100$	40173.1	−	69581.8i	0.401731	−	0.695818i
$101$	−45703.6	−	79161.0i	−0.445807	−	0.772161i	0.552301	−	0.833645i	$-0.313750\pi$
$101$	−45703.6	−	79161.0i	−0.445807	−	0.772161i	−0.998108	+	0.0614841i	$0.980417\pi$
$102$	−59323.1	−	102751.i	−0.564577	−	0.977876i
$103$	−28465.4	+	49303.5i	−0.264377	+	0.457915i	−0.967400	−	0.253252i	$-0.918500\pi$
$103$	−28465.4	+	49303.5i	−0.264377	+	0.457915i	0.703023	+	0.711167i	$0.251833\pi$
$104$	−14150.4			−0.128288
$105$		0			0
$106$	−75897.9			−0.656093
$107$	98104.6	−	169922.i	0.828380	−	1.43480i	−0.0709277	−	0.997481i	$-0.522596\pi$
$107$	98104.6	−	169922.i	0.828380	−	1.43480i	0.899308	−	0.437316i	$-0.144071\pi$
$108$	12896.6	+	22337.6i	0.106394	+	0.184279i
$109$	−52926.4	−	91671.2i	−0.426684	−	0.739038i	0.569892	−	0.821719i	$-0.306985\pi$
$109$	−52926.4	−	91671.2i	−0.426684	−	0.739038i	−0.996576	+	0.0826815i	$0.973652\pi$
$110$	45262.6	−	78397.1i	0.356663	−	0.617758i
$111$	−50168.8			−0.386480
$112$		0			0
$113$	−67589.3			−0.497945			−0.248973	−	0.968511i	$-0.580093\pi$
$113$	−67589.3			−0.497945			−0.248973	+	0.968511i	$0.580093\pi$
$114$	−79667.6	+	137988.i	−0.574142	+	0.994443i
$115$	−64799.4	−	112236.i	−0.456906	−	0.791384i
$116$	−84430.3	−	146238.i	−0.582577	−	1.00905i
$117$	20645.8	−	35759.5i	0.139433	−	0.241506i
$118$	115912.			0.766343
$119$		0			0
$120$	7301.36			0.0462861
$121$	9333.49	−	16166.1i	0.0579536	−	0.100379i
$122$	−74004.6	−	128180.i	−0.450152	−	0.779686i
$123$	44602.4	+	77253.6i	0.265825	+	0.460422i
$124$	−126594.	+	219267.i	−0.739365	+	1.28062i
$125$	157699.			0.902719
$126$		0			0
$127$	281805.			1.55039			0.775193	−	0.631724i	$-0.217653\pi$
$127$	281805.			1.55039			0.775193	+	0.631724i	$0.217653\pi$
$128$	28265.8	−	48957.8i	0.152488	−	0.264117i
$129$	−21987.7	−	38083.9i	−0.116334	−	0.201496i
$130$	−61148.4	−	105912.i	−0.317341	−	0.549651i
$131$	−44288.4	+	76709.7i	−0.225482	+	0.390546i	−0.956464	−	0.291851i	$-0.905729\pi$
$131$	−44288.4	+	76709.7i	−0.225482	+	0.390546i	0.730982	+	0.682397i	$0.239062\pi$
$132$	−120157.			−0.600227
$133$		0			0
$134$	−381817.			−1.83693
$135$	−10652.8	+	18451.3i	−0.0503073	+	0.0871349i
$136$	22289.7	+	38606.8i	0.103337	+	0.178985i
$137$	143415.	+	248402.i	0.652820	+	1.13072i	0.982436	+	0.186602i	$0.0597475\pi$
$137$	143415.	+	248402.i	0.652820	+	1.13072i	−0.329616	+	0.944115i	$0.606919\pi$
$138$	−163801.	+	283711.i	−0.732181	+	1.26817i
$139$	345909.			1.51853			0.759267	−	0.650779i	$-0.225558\pi$
$139$	345909.			1.51853			0.759267	+	0.650779i	$0.225558\pi$
$140$		0			0
$141$	83394.8			0.353257
$142$	−263784.	+	456887.i	−1.09781	+	1.90146i
$143$	96178.2	+	166586.i	0.393311	+	0.681235i
$144$	36626.3	+	63438.6i	0.147193	+	0.254946i
$145$	69741.1	−	120795.i	0.275467	−	0.477122i
$146$	500078.			1.94158
$147$		0			0
$148$	197228.			0.740142
$149$	152379.	−	263928.i	0.562288	−	0.973911i	−0.435009	−	0.900426i	$-0.643255\pi$
$149$	152379.	−	263928.i	0.562288	−	0.973911i	0.997296	−	0.0734844i	$-0.0234119\pi$
$150$	−83882.4	−	145289.i	−0.304399	−	0.527234i
$151$	−174157.	−	301648.i	−0.621581	−	1.07661i	−0.989191	−	0.146630i	$-0.953157\pi$
$151$	−174157.	−	301648.i	−0.621581	−	1.07661i	0.367610	−	0.929980i	$-0.380176\pi$
$152$	29933.8	−	51846.8i	0.105088	−	0.182017i
$153$	−130084.			−0.449259
$154$		0			0
$155$	−209139.			−0.699206
$156$	−81164.5	+	140581.i	−0.267027	+	0.462504i
$157$	94280.4	+	163298.i	0.305262	+	0.528729i	0.977320	−	0.211770i	$-0.0679227\pi$
$157$	94280.4	+	163298.i	0.305262	+	0.528729i	−0.672058	+	0.740499i	$0.734589\pi$
$158$	293314.	+	508034.i	0.934737	+	1.61901i
$159$	−41607.5	+	72066.3i	−0.130521	+	0.226068i
$160$	242919.			0.750174
$161$		0			0
$162$	53856.8			0.161233
$163$	−135624.	+	234908.i	−0.399823	+	0.692513i	−0.993704	−	0.112040i	$-0.964262\pi$
$163$	−135624.	+	234908.i	−0.399823	+	0.692513i	0.593881	+	0.804553i	$0.297595\pi$
$164$	−175345.	−	303706.i	−0.509077	−	0.881747i
$165$	−49626.2	−	85955.2i	−0.141906	−	0.245789i
$166$	47599.6	−	82444.9i	0.134070	−	0.232217i
$167$	−422260.			−1.17163			−0.585813	−	0.810446i	$-0.699225\pi$
$167$	−422260.			−1.17163			−0.585813	+	0.810446i	$0.699225\pi$
$168$		0			0
$169$	−111425.			−0.300101
$170$	−192641.	+	333664.i	−0.511243	+	0.885498i
$171$	87348.1	+	151291.i	0.228435	+	0.395661i
$172$	86440.1	+	149719.i	0.222789	+	0.385882i
$173$	150644.	−	260923.i	0.382681	−	0.662822i	−0.608764	−	0.793351i	$-0.708334\pi$
$173$	150644.	−	260923.i	0.382681	−	0.662822i	0.991444	+	0.130529i	$0.0416676\pi$
$174$	−352585.			−0.882858
$175$		0			0
$176$	−341247.			−0.830400
$177$	63543.3	−	110060.i	0.152453	−	0.264057i
$178$	321117.	+	556191.i	0.759650	+	1.31575i
$179$	142778.	+	247299.i	0.333065	+	0.576886i	0.983111	−	0.183009i	$-0.0585836\pi$
$179$	142778.	+	247299.i	0.333065	+	0.576886i	−0.650046	+	0.759895i	$0.725250\pi$
$180$	41879.4	−	72537.3i	0.0963428	−	0.166871i
$181$	−536753.			−1.21781			−0.608903	−	0.793244i	$-0.708390\pi$
$181$	−536753.			−1.21781			−0.608903	+	0.793244i	$0.708390\pi$
$182$		0			0
$183$	−162278.			−0.358206
$184$	61545.5	−	106600.i	0.134014	−	0.232120i
$185$	81457.3	+	141088.i	0.174985	+	0.303083i
$186$	264332.	+	457836.i	0.560230	+	0.970348i
$187$	302999.	−	524809.i	0.633632	−	1.09748i
$188$	−327849.			−0.676518
$189$		0			0
$190$	517413.			1.03981
$191$	178342.	−	308897.i	0.353729	−	0.612676i	−0.633171	−	0.774012i	$-0.718247\pi$
$191$	178342.	−	308897.i	0.353729	−	0.612676i	0.986900	+	0.161336i	$0.0515803\pi$
$192$	−176800.	−	306227.i	−0.346122	−	0.599501i
$193$	−375426.	−	650257.i	−0.725490	−	1.25659i	−0.958772	−	0.284176i	$-0.908280\pi$
$193$	−375426.	−	650257.i	−0.725490	−	1.25659i	0.233282	−	0.972409i	$-0.425053\pi$
$194$	621723.	−	1.07686e6i	1.18602	−	2.05425i
$195$	−134087.			−0.252523
$196$		0			0
$197$	296470.			0.544272			0.272136	−	0.962259i	$-0.412270\pi$
$197$	296470.			0.544272			0.272136	+	0.962259i	$0.412270\pi$
$198$	−125446.	+	217279.i	−0.227402	+	0.393871i
$199$	242286.	+	419651.i	0.433706	+	0.751200i	0.997189	−	0.0749270i	$-0.0238724\pi$
$199$	242286.	+	419651.i	0.433706	+	0.751200i	−0.563483	+	0.826127i	$0.690539\pi$
$200$	31517.4	+	54589.8i	0.0557155	+	0.0965020i
$201$	−209313.	+	362541.i	−0.365432	+	0.632947i
$202$	750328.			1.29382
$203$		0			0
$204$	511400.			0.860369
$205$	144838.	−	250868.i	0.240713	−	0.416927i
$206$	−233662.	−	404714.i	−0.383636	−	0.664477i
$207$	179592.	+	311063.i	0.291315	+	0.504572i
$208$	−230507.	+	399250.i	−0.369425	+	0.639862i
$209$	−813821.			−1.28873
$210$		0			0
$211$	849306.			1.31328			0.656641	−	0.754203i	$-0.271977\pi$
$211$	849306.			1.31328			0.656641	+	0.754203i	$0.271977\pi$
$212$	163571.	−	283313.i	0.249958	−	0.432940i
$213$	289215.	+	500934.i	0.436789	+	0.756540i
$214$	805304.	+	1.39483e6i	1.20206	+	2.08203i
$215$	−71401.3	+	123671.i	−0.105344	+	0.182461i
$216$	−20235.8			−0.0295112
$217$		0			0
$218$	868906.			1.23832
$219$	274144.	−	474832.i	0.386250	−	0.669005i
$220$	195095.	+	337915.i	0.271763	+	0.470707i
$221$	−409342.	−	709001.i	−0.563775	−	0.976487i
$222$	205909.	−	356644.i	0.280409	−	0.485683i
$223$	−1.06822e6			−1.43847			−0.719233	−	0.694769i	$-0.755506\pi$
$223$	−1.06822e6			−1.43847			−0.719233	+	0.694769i	$0.755506\pi$
$224$		0			0
$225$	−183938.			−0.242224
$226$	277408.	−	480484.i	0.361283	−	0.625760i
$227$	16175.4	+	28016.6i	0.0208349	+	0.0360871i	0.876255	−	0.481848i	$-0.160034\pi$
$227$	16175.4	+	28016.6i	0.0208349	+	0.0360871i	−0.855420	+	0.517935i	$0.826701\pi$
$228$	−343391.	−	594770.i	−0.437473	−	0.757725i
$229$	591436.	−	1.02440e6i	0.745280	−	1.29086i	−0.204784	−	0.978807i	$-0.565649\pi$
$229$	591436.	−	1.02440e6i	0.745280	−	1.29086i	0.950064	−	0.312055i	$-0.101017\pi$
$230$	1.06383e6			1.32603
$231$		0			0
$232$	132478.			0.161593
$233$	−164875.	+	285572.i	−0.198960	+	0.344608i	−0.948191	−	0.317700i	$-0.897090\pi$
$233$	−164875.	+	285572.i	−0.198960	+	0.344608i	0.749232	+	0.662308i	$0.230423\pi$
$234$	169473.	+	293537.i	0.202331	+	0.350447i
$235$	−135405.	−	234528.i	−0.159943	−	0.277029i
$236$	−249807.	+	432679.i	−0.291961	+	0.505691i
$237$	643182.			0.743812
$238$		0			0
$239$	−459379.			−0.520207			−0.260104	−	0.965581i	$-0.583757\pi$
$239$	−459379.			−0.520207			−0.260104	+	0.965581i	$0.583757\pi$
$240$	118938.	−	206006.i	0.133288	−	0.230861i
$241$	−729893.	−	1.26421e6i	−0.809499	−	1.40209i	−0.913211	−	0.407486i	$-0.866405\pi$
$241$	−729893.	−	1.26421e6i	−0.809499	−	1.40209i	0.103712	−	0.994607i	$-0.466928\pi$
$242$	76615.1	+	132701.i	0.0840961	+	0.145659i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	637963.			0.685995
$245$		0			0
$246$	−732249.			−0.771474
$247$	−549724.	+	952149.i	−0.573326	+	0.993031i
$248$	−99318.2	−	172024.i	−0.102542	−	0.177607i
$249$	−52188.5	−	90393.2i	−0.0533429	−	0.0923926i
$250$	−647245.	+	1.12106e6i	−0.654965	+	1.13443i
$251$	−523090.			−0.524074			−0.262037	−	0.965058i	$-0.584394\pi$
$251$	−523090.			−0.524074			−0.262037	+	0.965058i	$0.584394\pi$
$252$		0			0
$253$	−1.67326e6			−1.64347
$254$	−1.15662e6	+	2.00332e6i	−1.12488	+	1.94835i
$255$	211213.	+	365832.i	0.203409	+	0.352315i
$256$	−396599.	−	686930.i	−0.378227	−	0.655108i
$257$	232724.	−	403090.i	0.219790	−	0.380688i	−0.734954	−	0.678117i	$-0.762796\pi$
$257$	232724.	−	403090.i	0.219790	−	0.380688i	0.954744	+	0.297430i	$0.0961294\pi$
$258$	360978.			0.337623
$259$		0			0
$260$	527135.			0.483602
$261$	−193288.	+	334785.i	−0.175632	+	0.304204i
$262$	−363547.	−	629682.i	−0.327195	−	0.566719i
$263$	−64810.7	−	112255.i	−0.0577773	−	0.100073i	0.835690	−	0.549201i	$-0.185068\pi$
$263$	−64810.7	−	112255.i	−0.0577773	−	0.100073i	−0.893467	+	0.449128i	$0.851735\pi$
$264$	47134.2	−	81638.9i	0.0416223	−	0.0720920i
$265$	270226.			0.236381
$266$		0			0
$267$	704150.			0.604488
$268$	822871.	−	1.42525e6i	0.699834	−	1.21215i
$269$	702179.	+	1.21621e6i	0.591653	+	1.02477i	0.994010	+	0.109290i	$0.0348578\pi$
$269$	702179.	+	1.21621e6i	0.591653	+	1.02477i	−0.402357	+	0.915483i	$0.631809\pi$
$270$	−87445.3	−	151460.i	−0.0730007	−	0.126441i
$271$	−442543.	+	766506.i	−0.366043	+	0.634005i	−0.988943	−	0.148297i	$-0.952621\pi$
$271$	−442543.	+	766506.i	−0.366043	+	0.634005i	0.622900	+	0.782301i	$0.285954\pi$
$272$	1.45237e6			1.19030
$273$		0			0
$274$	−2.35448e6			−1.89461
$275$	428438.	−	742077.i	0.341630	−	0.591721i
$276$	−706030.	−	1.22288e6i	−0.557892	−	0.966298i
$277$	668568.	+	1.15799e6i	0.523535	+	0.906790i	0.999625	+	0.0273929i	$0.00872054\pi$
$277$	668568.	+	1.15799e6i	0.523535	+	0.906790i	−0.476089	+	0.879397i	$0.657946\pi$
$278$	−1.41972e6	+	2.45902e6i	−1.10177	+	1.90832i
$279$	579630.			0.445800
$280$		0			0
$281$	−1.80115e6			−1.36077			−0.680383	−	0.732857i	$-0.738187\pi$
$281$	−1.80115e6			−1.36077			−0.680383	+	0.732857i	$0.738187\pi$
$282$	−342278.	+	592844.i	−0.256305	+	0.443933i
$283$	−485944.	−	841679.i	−0.360678	−	0.624713i	0.627394	−	0.778702i	$-0.284121\pi$
$283$	−485944.	−	841679.i	−0.360678	−	0.624713i	−0.988073	+	0.153989i	$0.950788\pi$
$284$	−1.13699e6	−	1.96932e6i	−0.836487	−	1.44884i
$285$	283648.	−	491292.i	0.206855	−	0.358284i
$286$	−1.57898e6			−1.14146
$287$		0			0
$288$	−673253.			−0.478297
$289$	−579659.	+	1.00400e6i	−0.408252	+	0.707113i
$290$	572479.	+	991563.i	0.399728	+	0.692349i
$291$	−681662.	−	1.18067e6i	−0.471886	−	0.817330i
$292$	−1.07774e6	+	1.86670e6i	−0.739703	+	1.28120i
$293$	675064.			0.459384			0.229692	−	0.973263i	$-0.426228\pi$
$293$	675064.			0.459384			0.229692	+	0.973263i	$0.426228\pi$
$294$		0			0
$295$	−412692.			−0.276103
$296$	−77366.8	+	134003.i	−0.0513246	+	0.0888968i
$297$	137540.	+	238226.i	0.0904768	+	0.156710i
$298$	1.25082e6	+	2.16648e6i	0.815932	+	1.41324i
$299$	−1.13026e6	+	1.95767e6i	−0.731141	+	1.26637i
$300$	723115.			0.463879
$301$		0			0
$302$	2.85918e6			1.80395
$303$	411333.	−	712449.i	0.257387	−	0.445807i
$304$	−975229.	−	1.68915e6i	−0.605233	−	1.04829i
$305$	263485.	+	456370.i	0.162184	+	0.280910i
$306$	533908.	−	924755.i	0.325959	−	0.564577i
$307$	−894063.			−0.541405			−0.270702	−	0.962663i	$-0.587256\pi$
$307$	−894063.			−0.541405			−0.270702	+	0.962663i	$0.587256\pi$
$308$		0			0
$309$	−512377.			−0.305276
$310$	858370.	−	1.48674e6i	0.507307	−	0.878681i
$311$	−487006.	−	843519.i	−0.285518	−	0.494531i	0.687217	−	0.726452i	$-0.258832\pi$
$311$	−487006.	−	843519.i	−0.285518	−	0.494531i	−0.972735	+	0.231921i	$0.925499\pi$
$312$	−63676.9	−	110292.i	−0.0370335	−	0.0641440i
$313$	352628.	−	610770.i	0.203449	−	0.352385i	−0.746188	−	0.665735i	$-0.768118\pi$
$313$	352628.	−	610770.i	0.203449	−	0.352385i	0.949638	+	0.313350i	$0.101451\pi$
$314$	−1.54783e6			−0.885927
$315$		0			0
$316$	−2.52854e6			−1.42446
$317$	942457.	−	1.63238e6i	0.526761	−	0.912377i	−0.472753	−	0.881195i	$-0.656740\pi$
$317$	942457.	−	1.63238e6i	0.526761	−	0.912377i	0.999514	−	0.0311815i	$-0.00992699\pi$
$318$	−341541.	−	591566.i	−0.189398	−	0.328046i
$319$	−900433.	−	1.55960e6i	−0.495421	−	0.858095i
$320$	−574128.	+	994418.i	−0.313425	+	0.542868i
$321$	1.76588e6			0.956531
$322$		0			0
$323$	3.46369e6			1.84728
$324$	−116069.	+	201038.i	−0.0614264	+	0.106394i
$325$	−578807.	−	1.00252e6i	−0.303966	−	0.526485i
$326$	−1.11329e6	−	1.92827e6i	−0.580180	−	1.00490i
$327$	476338.	−	825041.i	0.246346	−	0.426684i
$328$	275131.			0.141206
$329$		0			0
$330$	814727.			0.411839
$331$	−302667.	+	524234.i	−0.151843	+	0.263000i	−0.931905	−	0.362702i	$-0.881854\pi$
$331$	−302667.	+	524234.i	−0.151843	+	0.263000i	0.780062	+	0.625702i	$0.215187\pi$
$332$	205168.	+	355362.i	0.102156	+	0.176940i
$333$	−225760.	−	391027.i	−0.111567	−	0.193240i
$334$	1.73309e6	−	3.00180e6i	0.850070	−	1.47236i
$335$	1.35942e6			0.661821
$336$		0			0
$337$	3.50499e6			1.68117			0.840586	−	0.541677i	$-0.182211\pi$
$337$	3.50499e6			1.68117			0.840586	+	0.541677i	$0.182211\pi$
$338$	457325.	−	792110.i	0.217737	−	0.377132i
$339$	−304152.	−	526806.i	−0.143744	−	0.248973i
$340$	−830340.	−	1.43819e6i	−0.389546	−	0.674714i
$341$	−1.35010e6	+	2.33844e6i	−0.628754	+	1.08903i
$342$	−1.43402e6			−0.662962
$343$		0			0
$344$	−135632.			−0.0617966
$345$	583195.	−	1.01012e6i	0.263795	−	0.456906i
$346$	1.23658e6	+	2.14182e6i	0.555306	+	0.961818i
$347$	1.33169e6	+	2.30656e6i	0.593717	+	1.02835i	0.993727	+	0.111837i	$0.0356736\pi$
$347$	1.33169e6	+	2.30656e6i	0.593717	+	1.02835i	−0.400009	+	0.916511i	$0.630993\pi$
$348$	759872.	−	1.31614e6i	0.336351	−	0.582577i
$349$	−2.02690e6			−0.890778			−0.445389	−	0.895337i	$-0.646935\pi$
$349$	−2.02690e6			−0.890778			−0.445389	+	0.895337i	$0.646935\pi$
$350$		0			0
$351$	371624.			0.161004
$352$	1.56817e6	−	2.71616e6i	0.674586	−	1.16842i
$353$	752813.	+	1.30391e6i	0.321551	+	0.556943i	0.980808	−	0.194974i	$-0.0624624\pi$
$353$	752813.	+	1.30391e6i	0.321551	+	0.556943i	−0.659257	+	0.751918i	$0.729129\pi$
$354$	521604.	+	903444.i	0.221224	+	0.383171i
$355$	939174.	−	1.62670e6i	0.395526	−	0.685071i
$356$	−2.76822e6			−1.15765
$357$		0			0
$358$	−2.34403e6			−0.966619
$359$	−1.04134e6	+	1.80365e6i	−0.426438	+	0.738613i	−0.996554	−	0.0829520i	$-0.973565\pi$
$359$	−1.04134e6	+	1.80365e6i	−0.426438	+	0.738613i	0.570115	+	0.821565i	$0.306899\pi$
$360$	32856.1	+	56908.5i	0.0133617	+	0.0231431i
$361$	−1.08772e6	−	1.88399e6i	−0.439288	−	0.760868i
$362$	2.20300e6	−	3.81572e6i	0.883576	−	1.53040i
$363$	168003.			0.0669191
$364$		0			0
$365$	−1.78047e6			−0.699524
$366$	666042.	−	1.15362e6i	0.259895	−	0.450152i
$367$	−1.46715e6	−	2.54118e6i	−0.568603	−	0.984850i	−0.996704	−	0.0811191i	$-0.974151\pi$
$367$	−1.46715e6	−	2.54118e6i	−0.568603	−	0.984850i	0.428101	−	0.903731i	$-0.359183\pi$
$368$	−2.00512e6	−	3.47298e6i	−0.771830	−	1.33685i
$369$	−401422.	+	695283.i	−0.153474	+	0.265825i
$370$	−1.33731e6			−0.507839
$371$		0			0
$372$	−2.27869e6			−0.853746
$373$	203885.	−	353139.i	0.0758774	−	0.131424i	−0.825590	−	0.564270i	$-0.809158\pi$
$373$	203885.	−	353139.i	0.0758774	−	0.131424i	0.901467	+	0.432847i	$0.142491\pi$
$374$	2.48721e6	+	4.30797e6i	0.919460	+	1.59255i
$375$	709644.	+	1.22914e6i	0.260593	+	0.451360i
$376$	128605.	−	222751.i	0.0469126	−	0.0812551i
$377$	−2.43291e6			−0.881604
$378$		0			0
$379$	326165.			0.116638			0.0583188	−	0.998298i	$-0.481426\pi$
$379$	326165.			0.116638			0.0583188	+	0.998298i	$0.481426\pi$
$380$	−1.11510e6	+	1.93141e6i	−0.396146	+	0.686145i
$381$	1.26812e6	+	2.19646e6i	0.447558	+	0.775193i
$382$	1.46394e6	+	2.53562e6i	0.513293	+	0.889050i
$383$	881091.	−	1.52609e6i	0.306919	−	0.531599i	−0.670768	−	0.741667i	$-0.734035\pi$
$383$	881091.	−	1.52609e6i	0.306919	−	0.531599i	0.977687	+	0.210068i	$0.0673686\pi$
$384$	508785.			0.176078
$385$		0			0
$386$	6.16347e6			2.10551
$387$	197890.	−	342755.i	0.0671654	−	0.116334i
$388$	2.67981e6	+	4.64157e6i	0.903701	+	1.56526i
$389$	1.77975e6	+	3.08262e6i	0.596328	+	1.03287i	0.993358	+	0.115065i	$0.0367075\pi$
$389$	1.77975e6	+	3.08262e6i	0.596328	+	1.03287i	−0.397030	+	0.917806i	$0.629959\pi$
$390$	550335.	−	953209.i	0.183217	−	0.317341i
$391$	7.12153e6			2.35576
$392$		0			0
$393$	−797191.			−0.260364
$394$	−1.21681e6	+	2.10757e6i	−0.394895	+	0.683978i
$395$	−1.04431e6	−	1.80880e6i	−0.336773	−	0.583308i
$396$	−540708.	−	936535.i	−0.173271	−	0.300114i
$397$	−317689.	+	550254.i	−0.101164	+	0.175221i	−0.912165	−	0.409824i	$-0.865590\pi$
$397$	−317689.	+	550254.i	−0.101164	+	0.175221i	0.811000	+	0.585046i	$0.198923\pi$
$398$	−3.97767e6			−1.25870
$399$		0			0
$400$	2.05365e6			0.641765
$401$	−989734.	+	1.71427e6i	−0.307367	+	0.532376i	−0.977786	−	0.209608i	$-0.932781\pi$
$401$	−989734.	+	1.71427e6i	−0.307367	+	0.532376i	0.670418	+	0.741983i	$0.266115\pi$
$402$	−1.71818e6	−	2.97597e6i	−0.530276	−	0.918466i
$403$	1.82395e6	+	3.15917e6i	0.559435	+	0.968969i
$404$	−1.61707e6	+	2.80084e6i	−0.492918	+	0.853759i
$405$	−191751.			−0.0580899
$406$		0			0
$407$	2.10340e6			0.629414
$408$	−200607.	+	347462.i	−0.0596617	+	0.103337i
$409$	2.64144e6	+	4.57510e6i	0.780785	+	1.35236i	0.931485	+	0.363780i	$0.118514\pi$
$409$	2.64144e6	+	4.57510e6i	0.780785	+	1.35236i	−0.150699	+	0.988580i	$0.548153\pi$
$410$	1.18893e6	+	2.05928e6i	0.349297	+	0.605000i
$411$	−1.29074e6	+	2.23562e6i	−0.376906	+	0.652820i
$412$	2.01430e6			0.584630
$413$		0			0
$414$	−2.94842e6			−0.845450
$415$	−169473.	+	293536.i	−0.0483037	+	0.0836645i
$416$	−2.11855e6	−	3.66944e6i	−0.600214	−	1.03960i
$417$	1.55659e6	+	2.69609e6i	0.438363	+	0.759267i
$418$	3.34018e6	−	5.78536e6i	0.935037	−	1.61953i
$419$	318626.			0.0886639			0.0443319	−	0.999017i	$-0.485884\pi$
$419$	318626.			0.0886639			0.0443319	+	0.999017i	$0.485884\pi$
$420$		0			0
$421$	−46024.4			−0.0126556			−0.00632780	−	0.999980i	$-0.502014\pi$
$421$	−46024.4			−0.0126556			−0.00632780	+	0.999980i	$0.502014\pi$
$422$	−3.48582e6	+	6.03761e6i	−0.952848	+	1.65038i
$423$	375276.	+	649998.i	0.101977	+	0.176629i
$424$	128328.	+	222271.i	0.0346663	+	0.0600438i
$425$	−1.82347e6	+	3.15834e6i	−0.489695	+	0.848177i
$426$	−4.74811e6			−1.26764
$427$		0			0
$428$	−6.94219e6			−1.83184
$429$	−865604.	+	1.49927e6i	−0.227078	+	0.393311i
$430$	−586107.	−	1.01517e6i	−0.152864	−	0.264768i
$431$	2.27822e6	+	3.94600e6i	0.590749	+	1.02321i	0.994132	+	0.108176i	$0.0345011\pi$
$431$	2.27822e6	+	3.94600e6i	0.590749	+	1.02321i	−0.403382	+	0.915031i	$0.632166\pi$
$432$	−329637.	+	570948.i	−0.0849819	+	0.147193i
$433$	6.98232e6			1.78970			0.894850	−	0.446368i	$-0.147283\pi$
$433$	6.98232e6			1.78970			0.894850	+	0.446368i	$0.147283\pi$
$434$		0			0
$435$	1.25534e6			0.318081
$436$	−1.87262e6	+	3.24347e6i	−0.471774	+	0.817136i
$437$	−4.78191e6	−	8.28251e6i	−1.19784	−	2.07471i
$438$	2.25035e6	+	3.89772e6i	0.560486	+	0.970790i
$439$	−834519.	+	1.44543e6i	−0.206669	+	0.357961i	−0.950663	−	0.310225i	$-0.899596\pi$
$439$	−834519.	+	1.44543e6i	−0.206669	+	0.357961i	0.743994	+	0.668186i	$0.232929\pi$
$440$	−306120.			−0.0753807
$441$		0			0
$442$	6.72028e6			1.63618
$443$	280705.	−	486195.i	0.0679580	−	0.117707i	−0.830044	−	0.557697i	$-0.811685\pi$
$443$	280705.	−	486195.i	0.0679580	−	0.117707i	0.898002	+	0.439991i	$0.145018\pi$
$444$	887527.	+	1.53724e6i	0.213660	+	0.370071i
$445$	−1.14330e6	−	1.98026e6i	−0.273691	−	0.474047i
$446$	4.38432e6	−	7.59386e6i	1.04367	−	1.80770i
$447$	2.74282e6			0.649274
$448$		0			0
$449$	−3.64485e6			−0.853225			−0.426613	−	0.904434i	$-0.640293\pi$
$449$	−3.64485e6			−0.853225			−0.426613	+	0.904434i	$0.640293\pi$
$450$	754941.	−	1.30760e6i	0.175745	−	0.304399i
$451$	−1.87002e6	−	3.23897e6i	−0.432917	−	0.749835i
$452$	1.19571e6	+	2.07103e6i	0.275283	+	0.476804i
$453$	1.56741e6	−	2.71483e6i	0.358870	−	0.621581i
$454$	−265556.			−0.0604667
$455$		0			0
$456$	538808.			0.121345
$457$	−1.40974e6	+	2.44173e6i	−0.315753	+	0.546900i	−0.979597	−	0.200971i	$-0.935590\pi$
$457$	−1.40974e6	+	2.44173e6i	−0.315753	+	0.546900i	0.663844	+	0.747871i	$0.268924\pi$
$458$	4.85488e6	+	8.40890e6i	1.08147	+	1.87316i
$459$	−585380.	−	1.01391e6i	−0.129690	−	0.224630i
$460$	−2.29271e6	+	3.97109e6i	−0.505189	+	0.875014i
$461$	−803065.			−0.175994			−0.0879971	−	0.996121i	$-0.528047\pi$
$461$	−803065.			−0.175994			−0.0879971	+	0.996121i	$0.528047\pi$
$462$		0			0
$463$	−114276.			−0.0247745			−0.0123872	−	0.999923i	$-0.503943\pi$
$463$	−114276.			−0.0247745			−0.0123872	+	0.999923i	$0.503943\pi$
$464$	2.15804e6	−	3.73783e6i	0.465333	−	0.805981i
$465$	−941124.	−	1.63007e6i	−0.201843	−	0.349603i
$466$	−1.35340e6	−	2.34415e6i	−0.288709	−	0.500059i
$467$	−3.08931e6	+	5.35085e6i	−0.655496	+	1.13535i	0.326274	+	0.945275i	$0.394207\pi$
$467$	−3.08931e6	+	5.35085e6i	−0.655496	+	1.13535i	−0.981769	+	0.190076i	$0.939126\pi$
$468$	−1.46096e6			−0.308336
$469$		0			0
$470$	2.22298e6			0.464184
$471$	−848524.	+	1.46969e6i	−0.176243	+	0.305262i
$472$	−195984.	−	339454.i	−0.0404917	−	0.0701336i
$473$	921867.	+	1.59672e6i	0.189459	+	0.328153i
$474$	−2.63982e6	+	4.57231e6i	−0.539671	+	0.934737i
$475$	4.89763e6			0.995983
$476$		0			0
$477$	−748935.			−0.150712
$478$	1.88544e6	−	3.26567e6i	0.377435	−	0.653736i
$479$	692906.	+	1.20015e6i	0.137986	+	0.238999i	0.926734	−	0.375718i	$-0.122604\pi$
$479$	692906.	+	1.20015e6i	0.137986	+	0.238999i	−0.788748	+	0.614717i	$0.789270\pi$
$480$	1.09314e6	+	1.89337e6i	0.216556	+	0.375087i
$481$	1.42082e6	−	2.46092e6i	0.280011	−	0.484993i
$482$	1.19828e7			2.34932
$483$		0			0
$484$	−660467.			−0.128156
$485$	−2.21358e6	+	3.83403e6i	−0.427307	+	0.740118i
$486$	242356.	+	419772.i	0.0465439	+	0.0806164i
$487$	−109396.	−	189480.i	−0.0209017	−	0.0362027i	0.855385	−	0.517992i	$-0.173320\pi$
$487$	−109396.	−	189480.i	−0.0209017	−	0.0362027i	−0.876287	+	0.481789i	$0.839987\pi$
$488$	−250254.	+	433453.i	−0.0475699	+	0.0823934i
$489$	−2.44123e6			−0.461675
$490$		0			0
$491$	−8.85181e6			−1.65702			−0.828511	−	0.559973i	$-0.810812\pi$
$491$	−8.85181e6			−1.65702			−0.828511	+	0.559973i	$0.810812\pi$
$492$	1.57810e6	−	2.73336e6i	0.293916	−	0.509077i
$493$	3.83231e6	+	6.63776e6i	0.710140	+	1.23000i
$494$	−4.51248e6	−	7.81584e6i	−0.831951	−	1.44098i
$495$	446636.	−	773597.i	0.0819296	−	0.141906i
$496$	−6.47149e6			−1.18114
$497$		0			0
$498$	856793.			0.154811
$499$	−1.83379e6	+	3.17621e6i	−0.329684	+	0.571029i	−0.982449	−	0.186531i	$-0.940275\pi$
$499$	−1.83379e6	+	3.17621e6i	−0.329684	+	0.571029i	0.652765	+	0.757560i	$0.273609\pi$
$500$	−2.78981e6	−	4.83210e6i	−0.499057	−	0.864392i
$501$	−1.90017e6	−	3.29119e6i	−0.338219	−	0.585813i
$502$	2.14693e6	−	3.71859e6i	0.380240	−	0.658595i
$503$	−8.87701e6			−1.56440			−0.782198	−	0.623029i	$-0.785902\pi$
$503$	−8.87701e6			−1.56440			−0.782198	+	0.623029i	$0.785902\pi$
$504$		0			0
$505$	−2.67146e6			−0.466144
$506$	6.86759e6	−	1.18950e7i	1.19242	−	2.06533i
$507$	−501414.	−	868475.i	−0.0866317	−	0.150051i
$508$	−4.98536e6	−	8.63490e6i	−0.857112	−	1.48456i
$509$	2.64528e6	−	4.58176e6i	0.452561	−	0.783858i	−0.545984	−	0.837796i	$-0.683844\pi$
$509$	2.64528e6	−	4.58176e6i	0.452561	−	0.783858i	0.998544	+	0.0539377i	$0.0171772\pi$
$510$	−3.46754e6			−0.590332
$511$		0			0
$512$	8.32008e6			1.40266
$513$	−786133.	+	1.36162e6i	−0.131887	+	0.228435i
$514$	1.91035e6	+	3.30881e6i	0.318936	+	0.552414i
$515$	831927.	+	1.44094e6i	0.138219	+	0.239402i
$516$	−777961.	+	1.34747e6i	−0.128627	+	0.222789i
$517$	−3.49645e6			−0.575308
$518$		0			0
$519$	2.71159e6			0.441882
$520$	−206779.	+	358153.i	−0.0335351	+	0.0580844i
$521$	4.39837e6	+	7.61821e6i	0.709901	+	1.22958i	0.964893	+	0.262642i	$0.0845937\pi$
$521$	4.39837e6	+	7.61821e6i	0.709901	+	1.22958i	−0.254992	+	0.966943i	$0.582073\pi$
$522$	−1.58663e6	−	2.74813e6i	−0.254859	−	0.441429i
$523$	−1.51683e6	+	2.62722e6i	−0.242483	+	0.419993i	−0.961421	−	0.275081i	$-0.911295\pi$
$523$	−1.51683e6	+	2.62722e6i	−0.242483	+	0.419993i	0.718938	+	0.695074i	$0.244629\pi$
$524$	3.13399e6			0.498619
$525$		0			0
$526$	1.06401e6			0.167681
$527$	5.74614e6	−	9.95261e6i	0.901259	−	1.56103i
$528$	−1.53561e6	−	2.65976e6i	−0.239716	−	0.415200i
$529$	−6.61370e6	−	1.14553e7i	−1.02756	−	1.77978i
$530$	−1.10909e6	+	1.92101e6i	−0.171506	+	0.297056i
$531$	1.14378e6			0.176038
$532$		0			0
$533$	−5.05268e6			−0.770378
$534$	−2.89006e6	+	5.00572e6i	−0.438584	+	0.759650i
$535$	−2.86720e6	−	4.96613e6i	−0.433085	−	0.750125i
$536$	645576.	+	1.11817e6i	0.0970589	+	0.168111i
$537$	−1.28500e6	+	2.22569e6i	−0.192295	+	0.333065i
$538$	−1.15279e7			−1.71709
$539$		0			0
$540$	753830.			0.111247
$541$	718631.	−	1.24471e6i	0.105563	−	0.182841i	−0.808405	−	0.588627i	$-0.799669\pi$
$541$	718631.	−	1.24471e6i	0.105563	−	0.182841i	0.913968	+	0.405786i	$0.133002\pi$
$542$	−3.63267e6	−	6.29197e6i	−0.531163	−	0.920001i
$543$	−2.41539e6	−	4.18358e6i	−0.351551	−	0.608903i
$544$	−6.67427e6	+	1.15602e7i	−0.966956	+	1.67482i
$545$	−3.09365e6			−0.446148
$546$		0			0
$547$	5.93548e6			0.848179			0.424089	−	0.905620i	$-0.360594\pi$
$547$	5.93548e6			0.848179			0.424089	+	0.905620i	$0.360594\pi$
$548$	5.07426e6	−	8.78887e6i	0.721807	−	1.25021i
$549$	−730253.	−	1.26484e6i	−0.103405	−	0.179103i
$550$	3.51689e6	+	6.09143e6i	0.495738	+	0.858643i
$551$	5.14658e6	−	8.91414e6i	0.722171	−	1.25084i
$552$	1.10782e6			0.154747
$553$		0			0
$554$	−1.09761e7			−1.51940
$555$	−733115.	+	1.26979e6i	−0.101028	+	0.174985i
$556$	−6.11940e6	−	1.05991e7i	−0.839503	−	1.45406i
$557$	−2.19761e6	−	3.80638e6i	−0.300133	−	0.519845i	0.676033	−	0.736871i	$-0.263698\pi$
$557$	−2.19761e6	−	3.80638e6i	−0.300133	−	0.519845i	−0.976166	+	0.217026i	$0.930364\pi$
$558$	−2.37898e6	+	4.12052e6i	−0.323449	+	0.560230i
$559$	2.49083e6			0.337143
$560$		0			0
$561$	5.45398e6			0.731655
$562$	7.39248e6	−	1.28041e7i	0.987300	−	1.71005i
$563$	−3.23207e6	−	5.59811e6i	−0.429744	−	0.744338i	0.567107	−	0.823644i	$-0.308063\pi$
$563$	−3.23207e6	−	5.59811e6i	−0.429744	−	0.744338i	−0.996850	+	0.0793065i	$0.974729\pi$
$564$	−1.47532e6	−	2.55533e6i	−0.195294	−	0.338259i
$565$	−987679.	+	1.71071e6i	−0.130165	+	0.225453i
$566$	7.97786e6			1.04676
$567$		0			0
$568$	1.78402e6			0.232022
$569$	−3.65112e6	+	6.32393e6i	−0.472766	+	0.818854i	−0.999514	−	0.0311672i	$-0.990078\pi$
$569$	−3.65112e6	+	6.32393e6i	−0.472766	+	0.818854i	0.526749	+	0.850021i	$0.323411\pi$
$570$	2.32836e6	+	4.03283e6i	0.300167	+	0.519904i
$571$	4.57948e6	+	7.93189e6i	0.587795	+	1.01809i	0.994521	+	0.104541i	$0.0333372\pi$
$571$	4.57948e6	+	7.93189e6i	0.587795	+	1.01809i	−0.406726	+	0.913550i	$0.633329\pi$
$572$	3.40294e6	−	5.89406e6i	0.434875	−	0.753225i
$573$	3.21015e6			0.408451
$574$		0			0
$575$	1.00698e7			1.27014
$576$	1.59120e6	−	2.75604e6i	0.199834	−	0.346122i
$577$	3.07369e6	+	5.32380e6i	0.384345	+	0.665705i	0.991678	−	0.128742i	$-0.0410940\pi$
$577$	3.07369e6	+	5.32380e6i	0.384345	+	0.665705i	−0.607333	+	0.794447i	$0.707761\pi$
$578$	−4.75821e6	−	8.24145e6i	−0.592412	−	1.02609i
$579$	3.37884e6	−	5.85232e6i	0.418862	−	0.725490i
$580$	−4.93510e6			−0.609153
$581$		0			0
$582$	1.11910e7			1.36950
$583$	1.74445e6	−	3.02148e6i	0.212563	−	0.368171i
$584$	−845532.	−	1.46450e6i	−0.102588	−	0.177688i
$585$	−603392.	−	1.04511e6i	−0.0728970	−	0.126261i
$586$	−2.77067e6	+	4.79895e6i	−0.333305	+	0.577301i
$587$	8.30740e6			0.995107			0.497554	−	0.867433i	$-0.334232\pi$
$587$	8.30740e6			0.995107			0.497554	+	0.867433i	$0.334232\pi$
$588$		0			0
$589$	−1.54335e7			−1.83306
$590$	1.69382e6	−	2.93378e6i	0.200326	−	0.346974i
$591$	1.33412e6	+	2.31076e6i	0.157118	+	0.272136i
$592$	2.52058e6	+	4.36577e6i	0.295594	+	0.511984i
$593$	−6.83344e6	+	1.18359e7i	−0.797999	+	1.38218i	0.122918	+	0.992417i	$0.460775\pi$
$593$	−6.83344e6	+	1.18359e7i	−0.797999	+	1.38218i	−0.920917	+	0.389758i	$0.872559\pi$
$594$	−2.25803e6			−0.262581
$595$		0			0
$596$	−1.07828e7			−1.24341
$597$	−2.18057e6	+	3.77686e6i	−0.250400	+	0.433706i
$598$	−9.27790e6	−	1.60698e7i	−1.06095	−	1.83763i
$599$	1.50792e6	+	2.61180e6i	0.171717	+	0.297422i	0.939020	−	0.343862i	$-0.111735\pi$
$599$	1.50792e6	+	2.61180e6i	0.171717	+	0.297422i	−0.767303	+	0.641284i	$0.778402\pi$
$600$	−283657.	+	491308.i	−0.0321673	+	0.0557155i
$601$	−1.31661e7			−1.48686			−0.743429	−	0.668815i	$-0.766802\pi$
$601$	−1.31661e7			−1.48686			−0.743429	+	0.668815i	$0.766802\pi$
$602$		0			0
$603$	−3.76764e6			−0.421965
$604$	−6.16194e6	+	1.06728e7i	−0.687267	+	1.19038i
$605$	−272780.	−	472468.i	−0.0302987	−	0.0524788i
$606$	3.37648e6	+	5.84823e6i	0.373493	+	0.646908i
$607$	−6.32750e6	+	1.09595e7i	−0.697044	+	1.20732i	0.272443	+	0.962172i	$0.412168\pi$
$607$	−6.32750e6	+	1.09595e7i	−0.697044	+	1.20732i	−0.969487	+	0.245144i	$0.921165\pi$
$608$	1.79263e7			1.96668
$609$		0			0
$610$	−4.32571e6			−0.470687
$611$	−2.36180e6	+	4.09075e6i	−0.255941	+	0.443302i
$612$	2.30130e6	+	3.98597e6i	0.248367	+	0.430185i
$613$	2.01735e6	+	3.49415e6i	0.216835	+	0.375570i	0.953839	−	0.300319i	$-0.0970932\pi$
$613$	2.01735e6	+	3.49415e6i	0.216835	+	0.375570i	−0.737003	+	0.675889i	$0.763760\pi$
$614$	3.66952e6	−	6.35579e6i	0.392815	−	0.680375i
$615$	2.60709e6			0.277951
$616$		0			0
$617$	−1.52192e7			−1.60946			−0.804728	−	0.593644i	$-0.797689\pi$
$617$	−1.52192e7			−1.60946			−0.804728	+	0.593644i	$0.797689\pi$
$618$	2.10296e6	−	3.64243e6i	0.221492	−	0.383636i
$619$	5.23209e6	+	9.06224e6i	0.548843	+	0.950624i	0.998354	+	0.0573495i	$0.0182649\pi$
$619$	5.23209e6	+	9.06224e6i	0.548843	+	0.950624i	−0.449511	+	0.893275i	$0.648402\pi$
$620$	3.69983e6	+	6.40829e6i	0.386547	+	0.669519i
$621$	−1.61633e6	+	2.79957e6i	−0.168191	+	0.291315i
$622$	7.99530e6			0.828626
$623$		0			0
$624$	−4.14913e6			−0.426575
$625$	−1.24375e6	+	2.15424e6i	−0.127360	+	0.220595i
$626$	2.89459e6	+	5.01358e6i	0.295224	+	0.511343i
$627$	−3.66219e6	−	6.34311e6i	−0.372025	−	0.644367i
$628$	3.33579e6	−	5.77776e6i	0.337520	−	0.584602i
$629$	−8.95225e6			−0.902205
$630$		0			0
$631$	5.41229e6			0.541138			0.270569	−	0.962701i	$-0.412788\pi$
$631$	5.41229e6			0.541138			0.270569	+	0.962701i	$0.412788\pi$
$632$	991870.	−	1.71797e6i	0.0987784	−	0.171089i
$633$	3.82188e6	+	6.61968e6i	0.379112	+	0.656641i
$634$	7.73628e6	+	1.33996e7i	0.764380	+	1.32394i
$635$	4.11801e6	−	7.13260e6i	0.405278	−	0.701962i
$636$	2.94428e6			0.288627
$637$		0			0
$638$	1.47826e7			1.43781
$639$	−2.60293e6	+	4.50841e6i	−0.252180	+	0.436789i
$640$	−826094.	−	1.43084e6i	−0.0797223	−	0.138083i
$641$	−4.91404e6	−	8.51137e6i	−0.472382	−	0.818190i	0.527118	−	0.849792i	$-0.323273\pi$
$641$	−4.91404e6	−	8.51137e6i	−0.472382	−	0.818190i	−0.999501	+	0.0316016i	$0.989939\pi$
$642$	−7.24774e6	+	1.25534e7i	−0.694009	+	1.20206i
$643$	−8.06067e6			−0.768854			−0.384427	−	0.923155i	$-0.625601\pi$
$643$	−8.06067e6			−0.768854			−0.384427	+	0.923155i	$0.625601\pi$
$644$		0			0
$645$	−1.28522e6			−0.121641
$646$	−1.42161e7	+	2.46229e7i	−1.34029	+	2.32145i
$647$	−8.51795e6	−	1.47535e7i	−0.799971	−	1.38559i	−0.919634	−	0.392776i	$-0.871515\pi$
$647$	−8.51795e6	−	1.47535e7i	−0.799971	−	1.38559i	0.119663	−	0.992815i	$-0.461819\pi$
$648$	−91061.2	−	157723.i	−0.00851914	−	0.0147556i
$649$	−2.66415e6	+	4.61444e6i	−0.248283	+	0.430038i
$650$	9.50242e6			0.882167
$651$		0			0
$652$	9.59718e6			0.884148
$653$	−7.72236e6	+	1.33755e7i	−0.708707	+	1.22752i	0.256630	+	0.966510i	$0.417388\pi$
$653$	−7.72236e6	+	1.33755e7i	−0.708707	+	1.22752i	−0.965337	+	0.261007i	$0.915945\pi$
$654$	3.91008e6	+	6.77246e6i	0.357471	+	0.619158i
$655$	1.29437e6	+	2.24191e6i	0.117884	+	0.204181i
$656$	4.48182e6	−	7.76273e6i	0.406625	−	0.704296i
$657$	4.93460e6			0.446004
$658$		0			0
$659$	−1.28485e7			−1.15250			−0.576248	−	0.817275i	$-0.695484\pi$
$659$	−1.28485e7			−1.15250			−0.576248	+	0.817275i	$0.695484\pi$
$660$	−1.75586e6	+	3.04123e6i	−0.156902	+	0.271763i
$661$	9.43967e6	+	1.63500e7i	0.840337	+	1.45551i	0.889610	+	0.456721i	$0.150976\pi$
$661$	9.43967e6	+	1.63500e7i	0.840337	+	1.45551i	−0.0492734	+	0.998785i	$0.515691\pi$
$662$	−2.48448e6	−	4.30324e6i	−0.220338	−	0.381637i
$663$	3.68408e6	−	6.38101e6i	0.325496	−	0.563775i
$664$	−321926.			−0.0283358
$665$		0			0
$666$	3.70636e6			0.323789
$667$	1.05817e7	−	1.83280e7i	0.920956	−	1.59514i
$668$	7.47012e6	+	1.29386e7i	0.647719	+	1.12188i
$669$	−4.80700e6	−	8.32597e6i	−0.415249	−	0.719233i
$670$	−5.57947e6	+	9.66393e6i	−0.480182	+	0.831700i
$671$	6.80376e6			0.583368
$672$		0			0
$673$	1.42483e6			0.121262			0.0606311	−	0.998160i	$-0.480689\pi$
$673$	1.42483e6			0.121262			0.0606311	+	0.998160i	$0.480689\pi$
$674$	−1.43856e7	+	2.49166e7i	−1.21977	+	2.11270i
$675$	−827723.	−	1.43366e6i	−0.0699239	−	0.121112i
$676$	1.97120e6	+	3.41423e6i	0.165907	+	0.287360i
$677$	9.19906e6	−	1.59332e7i	0.771386	−	1.33608i	−0.165418	−	0.986224i	$-0.552897\pi$
$677$	9.19906e6	−	1.59332e7i	0.771386	−	1.33608i	0.936803	−	0.349856i	$-0.113769\pi$
$678$	4.99334e6			0.417173
$679$		0			0
$680$	1.30287e6			0.108051
$681$	−145579.	+	252150.i	−0.0120290	+	0.0208349i
$682$	−1.10825e7	−	1.91954e7i	−0.912381	−	1.58029i
$683$	1.84569e6	+	3.19682e6i	0.151393	+	0.262220i	0.931740	−	0.363127i	$-0.118291\pi$
$683$	1.84569e6	+	3.19682e6i	0.151393	+	0.262220i	−0.780347	+	0.625347i	$0.784957\pi$
$684$	3.09051e6	−	5.35293e6i	0.252575	−	0.437473i
$685$	8.38288e6			0.682600
$686$		0			0
$687$	1.06459e7			0.860575
$688$	−2.20941e6	+	3.82681e6i	−0.177953	+	0.308223i
$689$	−2.35670e6	−	4.08193e6i	−0.189129	−	0.327580i
$690$	4.78723e6	+	8.29173e6i	0.382791	+	0.663013i
$691$	7.13555e6	−	1.23591e7i	0.568502	−	0.984675i	−0.428212	−	0.903678i	$-0.640856\pi$
$691$	7.13555e6	−	1.23591e7i	0.568502	−	0.984675i	0.996714	−	0.0809966i	$-0.0258103\pi$
$692$	−1.06600e7			−0.846241
$693$		0			0
$694$	−2.18627e7			−1.72308
$695$	5.05475e6	−	8.75509e6i	0.396952	−	0.687541i
$696$	596151.	+	1.03256e6i	0.0466480	+	0.0807967i
$697$	7.95896e6	+	1.37853e7i	0.620546	+	1.07482i
$698$	8.31905e6	−	1.44090e7i	0.646302	−	1.11943i
$699$	−2.96775e6			−0.229739
$700$		0			0
$701$	1.09094e7			0.838507			0.419254	−	0.907869i	$-0.362292\pi$
$701$	1.09094e7			0.838507			0.419254	+	0.907869i	$0.362292\pi$
$702$	−1.52526e6	+	2.64183e6i	−0.116816	+	0.202331i
$703$	6.01118e6	+	1.04117e7i	0.458745	+	0.794570i
$704$	7.41260e6	+	1.28390e7i	0.563688	+	0.976337i
$705$	1.21864e6	−	2.11075e6i	0.0923431	−	0.159943i
$706$	−1.23591e7			−0.933203
$707$		0			0
$708$	−4.49653e6			−0.337128
$709$	1.31343e6	−	2.27493e6i	0.0981277	−	0.169962i	−0.812782	−	0.582568i	$-0.802048\pi$
$709$	1.31343e6	−	2.27493e6i	0.0981277	−	0.169962i	0.910910	+	0.412606i	$0.135381\pi$
$710$	7.70933e6	+	1.33530e7i	0.573946	+	0.994103i
$711$	2.89432e6	+	5.01311e6i	0.214720	+	0.371906i
$712$	1.08589e6	−	1.88082e6i	0.0802761	−	0.139042i
$713$	−3.17321e7			−2.33763
$714$		0			0
$715$	5.62179e6			0.411254
$716$	5.05173e6	−	8.74984e6i	0.368262	−	0.637849i
$717$	−2.06720e6	−	3.58050e6i	−0.150171	−	0.260104i
$718$	−8.54797e6	−	1.48055e7i	−0.618802	−	1.07180i
$719$	−1.19389e7	+	2.06787e7i	−0.861272	+	1.49177i	0.00942947	+	0.999956i	$0.496998\pi$
$719$	−1.19389e7	+	2.06787e7i	−0.861272	+	1.49177i	−0.870702	+	0.491812i	$0.836335\pi$
$720$	2.14088e6			0.153908
$721$		0			0
$722$	1.78574e7			1.27490
$723$	6.56903e6	−	1.13779e7i	0.467365	−	0.809499i
$724$	9.49560e6	+	1.64469e7i	0.673249	+	1.16610i
$725$	5.41886e6	+	9.38575e6i	0.382880	+	0.663168i
$726$	−689536.	+	1.19431e6i	−0.0485529	+	0.0840961i
$727$	2.62895e7			1.84479			0.922393	−	0.386253i	$-0.126231\pi$
$727$	2.62895e7			1.84479			0.922393	+	0.386253i	$0.126231\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	7.30761e6	−	1.26572e7i	0.507538	−	0.879081i
$731$	−3.92354e6	−	6.79577e6i	−0.271572	−	0.470376i
$732$	2.87084e6	+	4.97243e6i	0.198030	+	0.342998i
$733$	5.67352e6	−	9.82683e6i	0.390025	−	0.675544i	−0.602427	−	0.798174i	$-0.705800\pi$
$733$	5.67352e6	−	9.82683e6i	0.390025	−	0.675544i	0.992452	+	0.122630i	$0.0391329\pi$
$734$	2.40866e7			1.65019
$735$		0			0
$736$	3.68576e7			2.50803
$737$	8.77576e6	−	1.52001e7i	0.595136	−	1.03081i
$738$	−3.29512e6	−	5.70732e6i	−0.222705	−	0.385737i
$739$	2.44834e6	+	4.24065e6i	0.164915	+	0.285641i	0.936625	−	0.350333i	$-0.113932\pi$
$739$	2.44834e6	+	4.24065e6i	0.164915	+	0.285641i	−0.771710	+	0.635975i	$0.780598\pi$
$740$	2.88209e6	−	4.99192e6i	0.193476	−	0.335111i
$741$	−9.89502e6			−0.662020
$742$		0			0
$743$	1.56896e7			1.04265			0.521326	−	0.853357i	$-0.325437\pi$
$743$	1.56896e7			1.04265			0.521326	+	0.853357i	$0.325437\pi$
$744$	893864.	−	1.54822e6i	0.0592024	−	0.102542i
$745$	−4.45341e6	−	7.71353e6i	−0.293969	−	0.509169i
$746$	1.67361e6	+	2.89878e6i	0.110105	+	0.190708i
$747$	469697.	−	813539.i	0.0307975	−	0.0533429i
$748$	−2.14412e7			−1.40118
$749$		0			0
$750$	−1.16504e7			−0.756289
$751$	6.80599e6	−	1.17883e7i	0.440344	−	0.762698i	−0.557371	−	0.830263i	$-0.688190\pi$
$751$	6.80599e6	−	1.17883e7i	0.440344	−	0.762698i	0.997715	+	0.0675659i	$0.0215233\pi$
$752$	−4.18991e6	−	7.25713e6i	−0.270184	−	0.467973i
$753$	−2.35391e6	−	4.07708e6i	−0.151287	−	0.262037i
$754$	9.98544e6	−	1.72953e7i	0.639645	−	1.10790i
$755$	−1.01798e7			−0.649937
$756$		0			0
$757$	5.65571e6			0.358713			0.179357	−	0.983784i	$-0.442598\pi$
$757$	5.65571e6			0.358713			0.179357	+	0.983784i	$0.442598\pi$
$758$	−1.33868e6	+	2.31867e6i	−0.0846261	+	0.146577i
$759$	−7.52967e6	−	1.30418e7i	−0.474430	−	0.821736i
$760$	−874842.	−	1.51527e6i	−0.0549409	−	0.0951604i
$761$	8.73590e6	−	1.51310e7i	0.546822	−	0.947124i	−0.451668	−	0.892186i	$-0.649171\pi$
$761$	8.73590e6	−	1.51310e7i	0.546822	−	0.947124i	0.998490	−	0.0549374i	$-0.0174959\pi$
$762$	−2.08191e7			−1.29890
$763$		0			0
$764$	−1.26200e7			−0.782218
$765$	−1.90092e6	+	3.29249e6i	−0.117438	+	0.203409i
$766$	7.23255e6	+	1.25271e7i	0.445368	+	0.771401i
$767$	3.59918e6	+	6.23396e6i	0.220910	+	0.382627i
$768$	3.56939e6	−	6.18237e6i	0.218369	−	0.378227i
$769$	−1.34195e7			−0.818316			−0.409158	−	0.912464i	$-0.634177\pi$
$769$	−1.34195e7			−0.818316			−0.409158	+	0.912464i	$0.634177\pi$
$770$		0			0
$771$	4.18903e6			0.253792
$772$	−1.32832e7	+	2.30071e7i	−0.802156	+	1.38938i
$773$	8.64454e6	+	1.49728e7i	0.520347	+	0.901268i	0.999720	+	0.0236566i	$0.00753084\pi$
$773$	8.64454e6	+	1.49728e7i	0.520347	+	0.901268i	−0.479373	+	0.877611i	$0.659136\pi$
$774$	1.62440e6	+	2.81355e6i	0.0974633	+	0.168811i
$775$	8.12500e6	−	1.40729e7i	0.485925	−	0.841647i
$776$	−4.20484e6			−0.250666
$777$		0			0
$778$	−2.92186e7			−1.73066
$779$	1.06884e7	−	1.85129e7i	0.631060	−	1.09303i
$780$	2.37211e6	+	4.10861e6i	0.139604	+	0.241801i
$781$	−1.21257e7	−	2.10024e7i	−0.711346	−	1.23209i
$782$	−2.92290e7	+	5.06261e7i	−1.70922	+	2.96045i
$783$	−3.47919e6			−0.202803
$784$		0			0
$785$	5.51086e6			0.319187
$786$	3.27192e6	−	5.66713e6i	0.188906	−	0.327195i
$787$	−7.26236e6	−	1.25788e7i	−0.417966	−	0.723938i	0.577769	−	0.816200i	$-0.303924\pi$
$787$	−7.26236e6	−	1.25788e7i	−0.417966	−	0.723938i	−0.995735	+	0.0922623i	$0.970590\pi$
$788$	−5.24480e6	−	9.08426e6i	−0.300894	−	0.521164i
$789$	583296.	−	1.01030e6i	0.0333577	−	0.0577773i
$790$	1.71447e7			0.977378
$791$		0			0
$792$	848416.			0.0480613
$793$	4.59583e6	−	7.96022e6i	0.259526	−	0.449513i
$794$	−2.60779e6	−	4.51683e6i	−0.146799	−	0.254263i
$795$	1.21602e6	+	2.10620e6i	0.0682373	+	0.118191i
$796$	8.57246e6	−	1.48479e7i	0.479538	−	0.830584i
$797$	−1.33304e7			−0.743354			−0.371677	−	0.928362i	$-0.621217\pi$
$797$	−1.33304e7			−0.743354			−0.371677	+	0.928362i	$0.621217\pi$
$798$		0			0
$799$	1.48812e7			0.824650
$800$	−9.43737e6	+	1.63460e7i	−0.521346	+	0.902998i
$801$	3.16868e6	+	5.48831e6i	0.174501	+	0.302244i
$802$	−8.12436e6	−	1.40718e7i	−0.446019	−	0.772527i
$803$	−1.14939e7	+	1.99080e7i	−0.629040	+	1.08953i
$804$	1.48117e7			0.808098
$805$		0			0
$806$	−2.99442e7			−1.62358
$807$	−6.31961e6	+	1.09459e7i	−0.341591	+	0.591653i
$808$	−1.26866e6	−	2.19738e6i	−0.0683621	−	0.118407i
$809$	−4.14828e6	−	7.18502e6i	−0.222842	−	0.385973i	0.732828	−	0.680414i	$-0.238200\pi$
$809$	−4.14828e6	−	7.18502e6i	−0.222842	−	0.385973i	−0.955670	+	0.294441i	$0.904867\pi$
$810$	787008.	−	1.36314e6i	0.0421470	−	0.0730007i
$811$	4.73910e6			0.253013			0.126507	−	0.991966i	$-0.459623\pi$
$811$	4.73910e6			0.253013			0.126507	+	0.991966i	$0.459623\pi$
$812$		0			0
$813$	−7.96577e6			−0.422670
$814$	−8.63302e6	+	1.49528e7i	−0.456669	+	0.790975i
$815$	3.96373e6	+	6.86539e6i	0.209031	+	0.362052i
$816$	6.53569e6	+	1.13201e7i	0.343610	+	0.595150i
$817$	−5.26910e6	+	9.12634e6i	−0.276173	+	0.478345i
$818$	−4.33651e7			−2.26599
$819$		0			0
$820$	−1.02492e7			−0.532300
$821$	3.86647e6	−	6.69692e6i	0.200197	−	0.346751i	−0.748395	−	0.663253i	$-0.769175\pi$
$821$	3.86647e6	−	6.69692e6i	0.200197	−	0.346751i	0.948592	+	0.316502i	$0.102509\pi$
$822$	−1.05952e7	−	1.83514e7i	−0.546926	−	0.947303i
$823$	−7.61823e6	−	1.31952e7i	−0.392062	−	0.679071i	0.600660	−	0.799505i	$-0.294905\pi$
$823$	−7.61823e6	−	1.31952e7i	−0.392062	−	0.679071i	−0.992721	+	0.120434i	$0.961571\pi$
$824$	−790151.	+	1.36858e6i	−0.0405408	+	0.0702187i
$825$	7.71189e6			0.394481
$826$		0			0
$827$	2.56525e7			1.30427			0.652133	−	0.758105i	$-0.273874\pi$
$827$	2.56525e7			1.30427			0.652133	+	0.758105i	$0.273874\pi$
$828$	6.35427e6	−	1.10059e7i	0.322099	−	0.557892i
$829$	1.13034e7	+	1.95781e7i	0.571248	+	0.989430i	0.996438	+	0.0843264i	$0.0268739\pi$
$829$	1.13034e7	+	1.95781e7i	0.571248	+	0.989430i	−0.425190	+	0.905104i	$0.639793\pi$
$830$	−1.39114e6	−	2.40953e6i	−0.0700933	−	0.121405i
$831$	−6.01711e6	+	1.04219e7i	−0.302263	+	0.523535i
$832$	2.00284e7			1.00309
$833$		0			0
$834$	−2.55549e7			−1.27221
$835$	−6.17047e6	+	1.06876e7i	−0.306268	+	0.530472i
$836$	1.43971e7	+	2.49366e7i	0.712460	+	1.23402i
$837$	2.60834e6	+	4.51777e6i	0.128691	+	0.222900i
$838$	−1.30774e6	+	2.26508e6i	−0.0643298	+	0.111423i
$839$	1.59455e7			0.782049			0.391024	−	0.920380i	$-0.372121\pi$
$839$	1.59455e7			0.782049			0.391024	+	0.920380i	$0.372121\pi$
$840$		0			0
$841$	2.26610e6			0.110481
$842$	188899.	−	327182.i	0.00918224	−	0.0159041i
$843$	−8.10517e6	−	1.40386e7i	−0.392819	−	0.680383i
$844$	−1.50249e7	−	2.60239e7i	−0.726031	−	1.25752i
$845$	−1.62826e6	+	2.82022e6i	−0.0784478	+	0.135876i
$846$	−6.16101e6			−0.295955
$847$		0			0
$848$	8.36175e6			0.399308
$849$	4.37349e6	−	7.57511e6i	0.208238	−	0.360678i
$850$	−1.49682e7	−	2.59256e7i	−0.710594	−	1.23078i
$851$	1.23593e7	+	2.14070e7i	0.585020	+	1.01328i
$852$	1.02329e7	−	1.77239e7i	0.482946	−	0.836487i
$853$	3.44060e7			1.61906			0.809528	−	0.587082i	$-0.199723\pi$
$853$	3.44060e7			1.61906			0.809528	+	0.587082i	$0.199723\pi$
$854$		0			0
$855$	5.10566e6			0.238856
$856$	2.72322e6	−	4.71675e6i	0.127028	−	0.220018i
$857$	−2.76519e6	−	4.78946e6i	−0.128610	−	0.222758i	0.794529	−	0.607227i	$-0.207718\pi$
$857$	−2.76519e6	−	4.78946e6i	−0.128610	−	0.222758i	−0.923138	+	0.384468i	$0.874385\pi$
$858$	−7.10542e6	−	1.23070e7i	−0.329512	−	0.570732i
$859$	−6.97829e6	+	1.20868e7i	−0.322676	+	0.558891i	−0.981039	−	0.193810i	$-0.937916\pi$
$859$	−6.97829e6	+	1.20868e7i	−0.322676	+	0.558891i	0.658364	+	0.752700i	$0.271249\pi$
$860$	5.05258e6			0.232953
$861$		0			0
$862$	−3.74022e7			−1.71447
$863$	−6.92659e6	+	1.19972e7i	−0.316586	+	0.548344i	−0.979773	−	0.200110i	$-0.935870\pi$
$863$	−6.92659e6	+	1.19972e7i	−0.316586	+	0.548344i	0.663187	+	0.748454i	$0.269203\pi$
$864$	−3.02964e6	−	5.24749e6i	−0.138072	−	0.239148i
$865$	−4.40271e6	−	7.62572e6i	−0.200069	−	0.346530i
$866$	−2.86576e7	+	4.96365e7i	−1.29851	+	2.24909i
$867$	−1.04339e7			−0.471408
$868$		0			0
$869$	−2.69663e7			−1.21136
$870$	−5.15231e6	+	8.92406e6i	−0.230783	+	0.399728i
$871$	−1.18558e7	−	2.05348e7i	−0.529523	−	0.917161i
$872$	−1.46915e6	−	2.54464e6i	−0.0654296	−	0.113327i
$873$	6.13496e6	−	1.06261e7i	0.272443	−	0.471886i
$874$	7.85058e7			3.47635
$875$		0			0
$876$	−1.93993e7			−0.854135
$877$	1.21369e7	−	2.10218e7i	0.532856	−	0.922934i	−0.466408	−	0.884570i	$-0.654452\pi$
$877$	1.21369e7	−	2.10218e7i	0.532856	−	0.922934i	0.999264	−	0.0383638i	$-0.0122146\pi$
$878$	−6.85026e6	−	1.18650e7i	−0.299896	−	0.519435i
$879$	3.03779e6	+	5.26160e6i	0.132613	+	0.229692i
$880$	−4.98663e6	+	8.63710e6i	−0.217070	+	0.375977i
$881$	1.86802e7			0.810854			0.405427	−	0.914127i	$-0.367123\pi$
$881$	1.86802e7			0.810854			0.405427	+	0.914127i	$0.367123\pi$
$882$		0			0
$883$	2.91586e7			1.25854			0.629268	−	0.777188i	$-0.283355\pi$
$883$	2.91586e7			1.25854			0.629268	+	0.777188i	$0.283355\pi$
$884$	−1.44832e7	+	2.50856e7i	−0.623352	+	1.07968i
$885$	−1.85711e6	−	3.21661e6i	−0.0797040	−	0.138051i
$886$	2.30420e6	+	3.99100e6i	0.0986135	+	0.170804i
$887$	312551.	−	541354.i	0.0133387	−	0.0231032i	−0.859279	−	0.511507i	$-0.829087\pi$
$887$	312551.	−	541354.i	0.0133387	−	0.0231032i	0.872618	+	0.488404i	$0.162421\pi$
$888$	−1.39260e6			−0.0592645
$889$		0			0
$890$	1.87699e7			0.794304
$891$	−1.23786e6	+	2.14403e6i	−0.0522368	+	0.0904768i
$892$	1.88977e7	+	3.27318e7i	0.795238	+	1.37739i
$893$	−9.99228e6	−	1.73071e7i	−0.419311	−	0.726268i
$894$	−1.12574e7	+	1.94984e7i	−0.471079	+	0.815932i
$895$	8.34566e6			0.348259
$896$		0			0
$897$	−2.03447e7			−0.844249
$898$	1.49596e7	−	2.59108e7i	0.619055	−	1.07223i
$899$	−1.70760e7	−	2.95765e7i	−0.704672	−	1.22053i
$900$	3.25402e6	+	5.63613e6i	0.133910	+	0.231939i
$901$	−7.42454e6	+	1.28597e7i	−0.304690	+	0.527738i
$902$	3.07006e7			1.25641
$903$		0			0
$904$	−1.87616e6			−0.0763572
$905$	−7.84356e6	+	1.35854e7i	−0.318340	+	0.551382i
$906$	1.28663e7	+	2.22851e7i	0.520754	+	0.901973i
$907$	1.90836e6	+	3.30538e6i	0.0770268	+	0.133414i	0.901966	−	0.431807i	$-0.142124\pi$
$907$	1.90836e6	+	3.30538e6i	0.0770268	+	0.133414i	−0.824939	+	0.565222i	$0.808791\pi$
$908$	572312.	−	991274.i	0.0230366	−	0.0399006i
$909$	7.40399e6			0.297205
$910$		0			0
$911$	9.41226e6			0.375749			0.187875	−	0.982193i	$-0.439840\pi$
$911$	9.41226e6			0.375749			0.187875	+	0.982193i	$0.439840\pi$
$912$	8.77706e6	−	1.52023e7i	0.349431	−	0.605233i
$913$	2.18808e6	+	3.78987e6i	0.0868733	+	0.150469i
$914$	−1.15720e7	−	2.00433e7i	−0.458187	−	0.793603i
$915$	−2.37137e6	+	4.10733e6i	−0.0936367	+	0.162184i
$916$	−4.18519e7			−1.64807
$917$		0			0
$918$	9.61034e6			0.376385
$919$	−3.40546e6	+	5.89843e6i	−0.133011	+	0.230382i	−0.924836	−	0.380366i	$-0.875798\pi$
$919$	−3.40546e6	+	5.89843e6i	−0.133011	+	0.230382i	0.791825	+	0.610748i	$0.209131\pi$
$920$	−1.79872e6	−	3.11548e6i	−0.0700640	−	0.121354i
$921$	−4.02328e6	−	6.96853e6i	−0.156290	−	0.270702i
$922$	3.29603e6	−	5.70890e6i	0.127692	−	0.221169i
$923$	−3.27630e7			−1.26584
$924$		0			0
$925$	−1.26584e7			−0.486435
$926$	469027.	−	812378.i	0.0179750	−	0.0311337i
$927$	−2.30570e6	−	3.99358e6i	−0.0881257	−	0.152638i
$928$	1.98342e7	+	3.43538e7i	0.756039	+	1.30950i
$929$	−3.48956e6	+	6.04410e6i	−0.132658	+	0.229770i	−0.924700	−	0.380696i	$-0.875684\pi$
$929$	−3.48956e6	+	6.04410e6i	−0.132658	+	0.229770i	0.792043	+	0.610466i	$0.209018\pi$
$930$	1.54507e7			0.585787
$931$		0			0
$932$	1.16671e7			0.439969
$933$	4.38305e6	−	7.59167e6i	0.164844	−	0.285518i
$934$	−2.53590e7	−	4.39231e7i	−0.951186	−	1.64750i
$935$	−8.85542e6	−	1.53380e7i	−0.331269	−	0.573774i
$936$	573092.	−	992624.i	0.0213813	−	0.0370335i
$937$	−2.31557e7			−0.861606			−0.430803	−	0.902446i	$-0.641770\pi$
$937$	−2.31557e7			−0.861606			−0.430803	+	0.902446i	$0.641770\pi$
$938$		0			0
$939$	6.34731e6			0.234923
$940$	−4.79084e6	+	8.29799e6i	−0.176845	+	0.306304i
$941$	−9.12446e6	−	1.58040e7i	−0.335918	−	0.581827i	0.647743	−	0.761859i	$-0.275713\pi$
$941$	−9.12446e6	−	1.58040e7i	−0.335918	−	0.581827i	−0.983661	+	0.180032i	$0.942380\pi$
$942$	−6.96522e6	−	1.20641e7i	−0.255745	−	0.442964i
$943$	2.19760e7	−	3.80636e7i	0.804766	−	1.39390i
$944$	−1.27701e7			−0.466408
$945$		0			0
$946$	−1.51345e7			−0.549846
$947$	−7.30508e6	+	1.26528e7i	−0.264698	+	0.458470i	−0.967484	−	0.252931i	$-0.918606\pi$
$947$	−7.30508e6	+	1.26528e7i	−0.264698	+	0.458470i	0.702787	+	0.711401i	$0.251939\pi$
$948$	−1.13784e7	−	1.97080e7i	−0.411207	−	0.712232i
$949$	1.55279e7	+	2.68951e7i	0.559690	+	0.969411i
$950$	−2.01014e7	+	3.48167e7i	−0.722633	+	1.25164i
$951$	1.69642e7			0.608251
$952$		0			0
$953$	1.49338e7			0.532645			0.266322	−	0.963884i	$-0.414191\pi$
$953$	1.49338e7			0.532645			0.266322	+	0.963884i	$0.414191\pi$
$954$	3.07387e6	−	5.32409e6i	0.109349	−	0.189398i
$955$	−5.21221e6	−	9.02781e6i	−0.184933	−	0.320313i
$956$	8.12678e6	+	1.40760e7i	0.287590	+	0.498120i
$957$	8.10389e6	−	1.40364e7i	0.286032	−	0.495421i
$958$	−1.13756e7			−0.400462
$959$		0			0
$960$	−1.03343e7			−0.361912
$961$	−1.12891e7	+	1.95532e7i	−0.394321	+	0.682984i
$962$	1.16629e7	+	2.02008e7i	0.406322	+	0.703771i
$963$	7.94647e6	+	1.37637e7i	0.276127	+	0.478266i
$964$	−2.58248e7	+	4.47298e7i	−0.895043	+	1.55026i
$965$	−2.19444e7			−0.758586
$966$		0			0
$967$	−4.73806e6			−0.162942			−0.0814712	−	0.996676i	$-0.525962\pi$
$967$	−4.73806e6			−0.162942			−0.0814712	+	0.996676i	$0.525962\pi$
$968$	259082.	−	448743.i	0.00888687	−	0.0153925i
$969$	1.55866e7	+	2.69968e7i	0.533263	+	0.923639i
$970$	−1.81704e7	−	3.14721e7i	−0.620063	−	1.07398i
$971$	6.73781e6	−	1.16702e7i	0.229335	−	0.397220i	−0.728276	−	0.685284i	$-0.759678\pi$
$971$	6.73781e6	−	1.16702e7i	0.229335	−	0.397220i	0.957611	+	0.288064i	$0.0930115\pi$
$972$	−2.08925e6			−0.0709291
$973$		0			0
$974$	1.79599e6			0.0606606
$975$	5.20926e6	−	9.02271e6i	0.175495	−	0.303966i
$976$	8.15317e6	+	1.41217e7i	0.273969	+	0.474529i
$977$	−1.16719e7	−	2.02163e7i	−0.391205	−	0.677587i	0.601404	−	0.798945i	$-0.294608\pi$
$977$	−1.16719e7	−	2.02163e7i	−0.391205	−	0.677587i	−0.992609	+	0.121359i	$0.961275\pi$
$978$	1.00196e7	−	1.73544e7i	0.334967	−	0.580180i
$979$	−2.95225e7			−0.984457
$980$		0			0
$981$	8.57408e6			0.284456
$982$	3.63306e7	−	6.29265e7i	1.20225	−	2.08235i
$983$	1.00973e7	+	1.74890e7i	0.333289	+	0.577273i	0.983155	−	0.182776i	$-0.0585082\pi$
$983$	1.00973e7	+	1.74890e7i	0.333289	+	0.577273i	−0.649866	+	0.760049i	$0.725175\pi$
$984$	1.23809e6	+	2.14443e6i	0.0407628	+	0.0706032i
$985$	4.33231e6	−	7.50378e6i	0.142275	−	0.246428i
$986$	−6.29161e7			−2.06096
$987$		0			0
$988$	3.89002e7			1.26783
$989$	−1.08336e7	+	1.87643e7i	−0.352193	+	0.610015i
$990$	3.66627e6	+	6.35017e6i	0.118888	+	0.205919i
$991$	−1.21087e7	−	2.09730e7i	−0.391665	−	0.678384i	0.601004	−	0.799246i	$-0.294768\pi$
$991$	−1.21087e7	−	2.09730e7i	−0.391665	−	0.678384i	−0.992669	+	0.120862i	$0.961434\pi$
$992$	2.97392e7	−	5.15098e7i	0.959511	−	1.66192i
$993$	−5.44800e6			−0.175333
$994$		0			0
$995$	1.41621e7			0.453491
$996$	−1.84651e6	+	3.19826e6i	−0.0589799	+	0.102156i
$997$	2.92135e6	+	5.05992e6i	0.0930776	+	0.161215i	0.908805	−	0.417222i	$-0.136996\pi$
$997$	2.92135e6	+	5.05992e6i	0.0930776	+	0.161215i	−0.815727	+	0.578437i	$0.803663\pi$
$998$	−1.50529e7	−	2.60723e7i	−0.478402	−	0.828617i
$999$	2.03184e6	−	3.51925e6i	0.0644133	−	0.111567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.q.79.2		12
7.2	even	3		147.6.a.n.1.5	✓	6
7.3	odd	6		147.6.e.p.67.2		12
7.4	even	3	inner	147.6.e.q.67.2		12
7.5	odd	6		147.6.a.o.1.5	yes	6
7.6	odd	2		147.6.e.p.79.2		12
21.2	odd	6		441.6.a.bb.1.2		6
21.5	even	6		441.6.a.ba.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.n.1.5	✓	6	7.2	even	3
147.6.a.o.1.5	yes	6	7.5	odd	6
147.6.e.p.67.2		12	7.3	odd	6
147.6.e.p.79.2		12	7.6	odd	2
147.6.e.q.67.2		12	7.4	even	3	inner
147.6.e.q.79.2		12	1.1	even	1	trivial
441.6.a.ba.1.2		6	21.5	even	6
441.6.a.bb.1.2		6	21.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-4.10431 + 7.10888i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-17.6908 - 30.6414i) q^{4} +(14.6130 - 25.3104i) q^{5} -73.8777 q^{6} +27.7583 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-4.10431 + 7.10888i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-17.6908 - 30.6414i) q^{4} +(14.6130 - 25.3104i) q^{5} -73.8777 q^{6} +27.7583 q^{8} +(-40.5000 + 70.1481i) q^{9} +(119.952 + 207.764i) q^{10} +(-188.669 - 326.784i) q^{11} +(159.217 - 275.772i) q^{12} -509.772 q^{13} +263.033 q^{15} +(452.177 - 783.193i) q^{16} +(802.990 + 1390.82i) q^{17} +(-332.450 - 575.819i) q^{18} +(1078.37 - 1867.79i) q^{19} -1034.06 q^{20} +3097.43 q^{22} +(2217.19 - 3840.29i) q^{23} +(124.912 + 216.355i) q^{24} +(1135.42 + 1966.61i) q^{25} +(2092.27 - 3623.91i) q^{26} -729.000 q^{27} +4772.55 q^{29} +(-1079.57 + 1869.87i) q^{30} +(-3577.96 - 6197.21i) q^{31} +(4155.88 + 7198.20i) q^{32} +(1698.02 - 2941.06i) q^{33} -13182.9 q^{34} +2865.91 q^{36} +(-2787.16 + 4827.50i) q^{37} +(8851.95 + 15332.0i) q^{38} +(-2293.97 - 3973.28i) q^{39} +(405.631 - 702.574i) q^{40} +9911.64 q^{41} -4886.16 q^{43} +(-6675.41 + 11562.2i) q^{44} +(1183.65 + 2050.14i) q^{45} +(18200.1 + 31523.5i) q^{46} +(4633.04 - 8024.67i) q^{47} +8139.18 q^{48} -18640.5 q^{50} +(-7226.91 + 12517.4i) q^{51} +(9018.28 + 15620.1i) q^{52} +(4623.06 + 8007.37i) q^{53} +(2992.05 - 5182.37i) q^{54} -11028.1 q^{55} +19410.7 q^{57} +(-19588.1 + 33927.5i) q^{58} +(-7060.37 - 12228.9i) q^{59} +(-4653.27 - 8059.70i) q^{60} +(-9015.47 + 15615.2i) q^{61} +58740.4 q^{62} -39288.9 q^{64} +(-7449.28 + 12902.5i) q^{65} +(13938.4 + 24142.1i) q^{66} +(23257.0 + 40282.4i) q^{67} +(28411.1 - 49209.5i) q^{68} +39909.4 q^{69} +64269.9 q^{71} +(-1124.21 + 1947.19i) q^{72} +(-30460.5 - 52759.1i) q^{73} +(-22878.7 - 39627.2i) q^{74} +(-10218.8 + 17699.5i) q^{75} -76309.0 q^{76} +37660.8 q^{78} +(35732.3 - 61890.2i) q^{79} +(-13215.3 - 22889.5i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-40680.5 + 70460.7i) q^{82} -11597.5 q^{83} +46936.3 q^{85} +(20054.3 - 34735.1i) q^{86} +(21476.5 + 37198.4i) q^{87} +(-5237.14 - 9070.98i) q^{88} +(39119.5 - 67756.9i) q^{89} -19432.3 q^{90} -156896. q^{92} +(32201.7 - 55774.9i) q^{93} +(38030.9 + 65871.5i) q^{94} +(-31516.4 - 54588.0i) q^{95} +(-37403.0 + 64783.8i) q^{96} -151480. q^{97} +30564.4 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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