LMFDB - Embedded newform 147.6.e.b.79.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.00000 + 8.66025i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-34.0000 - 58.8897i) q^{4} +(-53.0000 + 91.7987i) q^{5} -90.0000 q^{6} +360.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-5.00000 + 8.66025i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-34.0000 - 58.8897i) q^{4} +(-53.0000 + 91.7987i) q^{5} -90.0000 q^{6} +360.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-530.000 - 917.987i) q^{10} +(-46.0000 - 79.6743i) q^{11} +(306.000 - 530.008i) q^{12} -670.000 q^{13} -954.000 q^{15} +(-712.000 + 1233.22i) q^{16} +(-111.000 - 192.258i) q^{17} +(-405.000 - 701.481i) q^{18} +(-454.000 + 786.351i) q^{19} +7208.00 q^{20} +920.000 q^{22} +(588.000 - 1018.45i) q^{23} +(1620.00 + 2805.92i) q^{24} +(-4055.50 - 7024.33i) q^{25} +(3350.00 - 5802.37i) q^{26} -729.000 q^{27} +1118.00 q^{29} +(4770.00 - 8261.88i) q^{30} +(1848.00 + 3200.83i) q^{31} +(-1360.00 - 2355.59i) q^{32} +(414.000 - 717.069i) q^{33} +2220.00 q^{34} +5508.00 q^{36} +(-2091.00 + 3621.72i) q^{37} +(-4540.00 - 7863.51i) q^{38} +(-3015.00 - 5222.13i) q^{39} +(-19080.0 + 33047.5i) q^{40} +6662.00 q^{41} -3700.00 q^{43} +(-3128.00 + 5417.85i) q^{44} +(-4293.00 - 7435.69i) q^{45} +(5880.00 + 10184.5i) q^{46} +(-3528.00 + 6110.68i) q^{47} -12816.0 q^{48} +81110.0 q^{50} +(999.000 - 1730.32i) q^{51} +(22780.0 + 39456.1i) q^{52} +(18789.0 + 32543.5i) q^{53} +(3645.00 - 6313.33i) q^{54} +9752.00 q^{55} -8172.00 q^{57} +(-5590.00 + 9682.16i) q^{58} +(16350.0 + 28319.0i) q^{59} +(32436.0 + 56180.8i) q^{60} +(-5401.00 + 9354.81i) q^{61} -36960.0 q^{62} -18368.0 q^{64} +(35510.0 - 61505.1i) q^{65} +(4140.00 + 7170.69i) q^{66} +(-32498.0 - 56288.2i) q^{67} +(-7548.00 + 13073.5i) q^{68} +10584.0 q^{69} -61320.0 q^{71} +(-14580.0 + 25253.3i) q^{72} +(19461.0 + 33707.4i) q^{73} +(-20910.0 - 36217.2i) q^{74} +(36499.5 - 63219.0i) q^{75} +61744.0 q^{76} +60300.0 q^{78} +(44048.0 - 76293.4i) q^{79} +(-75472.0 - 130721. i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-33310.0 + 57694.6i) q^{82} -71892.0 q^{83} +23532.0 q^{85} +(18500.0 - 32042.9i) q^{86} +(5031.00 + 8713.95i) q^{87} +(-16560.0 - 28682.8i) q^{88} +(55909.0 - 96837.2i) q^{89} +85860.0 q^{90} -79968.0 q^{92} +(-16632.0 + 28807.5i) q^{93} +(-35280.0 - 61106.8i) q^{94} +(-48124.0 - 83353.2i) q^{95} +(12240.0 - 21200.3i) q^{96} +150846. q^{97} +7452.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 10 q^{2} + 9 q^{3} - 68 q^{4} - 106 q^{5} - 180 q^{6} + 720 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q - 10 * q^2 + 9 * q^3 - 68 * q^4 - 106 * q^5 - 180 * q^6 + 720 * q^8 - 81 * q^9	\( 2 q - 10 q^{2} + 9 q^{3} - 68 q^{4} - 106 q^{5} - 180 q^{6} + 720 q^{8} - 81 q^{9} - 1060 q^{10} - 92 q^{11} + 612 q^{12} - 1340 q^{13} - 1908 q^{15} - 1424 q^{16} - 222 q^{17} - 810 q^{18} - 908 q^{19} + 14416 q^{20} + 1840 q^{22} + 1176 q^{23} + 3240 q^{24} - 8111 q^{25} + 6700 q^{26} - 1458 q^{27} + 2236 q^{29} + 9540 q^{30} + 3696 q^{31} - 2720 q^{32} + 828 q^{33} + 4440 q^{34} + 11016 q^{36} - 4182 q^{37} - 9080 q^{38} - 6030 q^{39} - 38160 q^{40} + 13324 q^{41} - 7400 q^{43} - 6256 q^{44} - 8586 q^{45} + 11760 q^{46} - 7056 q^{47} - 25632 q^{48} + 162220 q^{50} + 1998 q^{51} + 45560 q^{52} + 37578 q^{53} + 7290 q^{54} + 19504 q^{55} - 16344 q^{57} - 11180 q^{58} + 32700 q^{59} + 64872 q^{60} - 10802 q^{61} - 73920 q^{62} - 36736 q^{64} + 71020 q^{65} + 8280 q^{66} - 64996 q^{67} - 15096 q^{68} + 21168 q^{69} - 122640 q^{71} - 29160 q^{72} + 38922 q^{73} - 41820 q^{74} + 72999 q^{75} + 123488 q^{76} + 120600 q^{78} + 88096 q^{79} - 150944 q^{80} - 6561 q^{81} - 66620 q^{82} - 143784 q^{83} + 47064 q^{85} + 37000 q^{86} + 10062 q^{87} - 33120 q^{88} + 111818 q^{89} + 171720 q^{90} - 159936 q^{92} - 33264 q^{93} - 70560 q^{94} - 96248 q^{95} + 24480 q^{96} + 301692 q^{97} + 14904 q^{99}+O(q^{100}) \) 2 * q - 10 * q^2 + 9 * q^3 - 68 * q^4 - 106 * q^5 - 180 * q^6 + 720 * q^8 - 81 * q^9 - 1060 * q^10 - 92 * q^11 + 612 * q^12 - 1340 * q^13 - 1908 * q^15 - 1424 * q^16 - 222 * q^17 - 810 * q^18 - 908 * q^19 + 14416 * q^20 + 1840 * q^22 + 1176 * q^23 + 3240 * q^24 - 8111 * q^25 + 6700 * q^26 - 1458 * q^27 + 2236 * q^29 + 9540 * q^30 + 3696 * q^31 - 2720 * q^32 + 828 * q^33 + 4440 * q^34 + 11016 * q^36 - 4182 * q^37 - 9080 * q^38 - 6030 * q^39 - 38160 * q^40 + 13324 * q^41 - 7400 * q^43 - 6256 * q^44 - 8586 * q^45 + 11760 * q^46 - 7056 * q^47 - 25632 * q^48 + 162220 * q^50 + 1998 * q^51 + 45560 * q^52 + 37578 * q^53 + 7290 * q^54 + 19504 * q^55 - 16344 * q^57 - 11180 * q^58 + 32700 * q^59 + 64872 * q^60 - 10802 * q^61 - 73920 * q^62 - 36736 * q^64 + 71020 * q^65 + 8280 * q^66 - 64996 * q^67 - 15096 * q^68 + 21168 * q^69 - 122640 * q^71 - 29160 * q^72 + 38922 * q^73 - 41820 * q^74 + 72999 * q^75 + 123488 * q^76 + 120600 * q^78 + 88096 * q^79 - 150944 * q^80 - 6561 * q^81 - 66620 * q^82 - 143784 * q^83 + 47064 * q^85 + 37000 * q^86 + 10062 * q^87 - 33120 * q^88 + 111818 * q^89 + 171720 * q^90 - 159936 * q^92 - 33264 * q^93 - 70560 * q^94 - 96248 * q^95 + 24480 * q^96 + 301692 * q^97 + 14904 * 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 $

$2$	−5.00000	+	8.66025i	−0.883883	+	1.53093i	−0.0368954	+	0.999319i	$0.511747\pi$
$2$	−5.00000	+	8.66025i	−0.883883	+	1.53093i	−0.846988	+	0.531612i	$0.821586\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−34.0000	−	58.8897i	−1.06250	−	1.84030i
$5$	−53.0000	+	91.7987i	−0.948093	+	1.64214i	−0.198656	+	0.980069i	$0.563658\pi$
$5$	−53.0000	+	91.7987i	−0.948093	+	1.64214i	−0.749437	+	0.662076i	$0.769676\pi$
$6$	−90.0000			−1.02062
$7$		0			0
$7$		0			0
$8$	360.000			1.98874
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−530.000	−	917.987i	−1.67601	−	2.90293i
$11$	−46.0000	−	79.6743i	−0.114624	−	0.198535i	0.803005	−	0.595972i	$-0.203233\pi$
$11$	−46.0000	−	79.6743i	−0.114624	−	0.198535i	−0.917629	+	0.397437i	$0.869900\pi$
$12$	306.000	−	530.008i	0.613435	−	1.06250i
$13$	−670.000			−1.09955			−0.549777	−	0.835312i	$-0.685287\pi$
$13$	−670.000			−1.09955			−0.549777	+	0.835312i	$0.685287\pi$
$14$		0			0
$15$	−954.000			−1.09476
$16$	−712.000	+	1233.22i	−0.695312	+	1.20432i
$17$	−111.000	−	192.258i	−0.0931538	−	0.161347i	0.815683	−	0.578499i	$-0.196362\pi$
$17$	−111.000	−	192.258i	−0.0931538	−	0.161347i	−0.908837	+	0.417152i	$0.863028\pi$
$18$	−405.000	−	701.481i	−0.294628	−	0.510310i
$19$	−454.000	+	786.351i	−0.288517	+	0.499727i	−0.973456	−	0.228874i	$-0.926496\pi$
$19$	−454.000	+	786.351i	−0.288517	+	0.499727i	0.684939	+	0.728601i	$0.259829\pi$
$20$	7208.00			4.02939
$21$		0			0
$22$	920.000			0.405258
$23$	588.000	−	1018.45i	0.231770	−	0.401438i	−0.726559	−	0.687104i	$-0.758882\pi$
$23$	588.000	−	1018.45i	0.231770	−	0.401438i	0.958329	+	0.285666i	$0.0922149\pi$
$24$	1620.00	+	2805.92i	0.574099	+	0.994369i
$25$	−4055.50	−	7024.33i	−1.29776	−	2.24779i
$26$	3350.00	−	5802.37i	0.971877	−	1.68334i
$27$	−729.000			−0.192450
$28$		0			0
$29$	1118.00			0.246858			0.123429	−	0.992353i	$-0.460611\pi$
$29$	1118.00			0.246858			0.123429	+	0.992353i	$0.460611\pi$
$30$	4770.00	−	8261.88i	0.967643	−	1.67601i
$31$	1848.00	+	3200.83i	0.345380	+	0.598216i	0.985423	−	0.170123i	$-0.0544166\pi$
$31$	1848.00	+	3200.83i	0.345380	+	0.598216i	−0.640042	+	0.768340i	$0.721083\pi$
$32$	−1360.00	−	2355.59i	−0.234782	−	0.406654i
$33$	414.000	−	717.069i	0.0661783	−	0.114624i
$34$	2220.00			0.329348
$35$		0			0
$36$	5508.00			0.708333
$37$	−2091.00	+	3621.72i	−0.251102	+	0.434921i	−0.963829	−	0.266520i	$-0.914126\pi$
$37$	−2091.00	+	3621.72i	−0.251102	+	0.434921i	0.712728	+	0.701441i	$0.247460\pi$
$38$	−4540.00	−	7863.51i	−0.510031	−	0.883400i
$39$	−3015.00	−	5222.13i	−0.317414	−	0.549777i
$40$	−19080.0	+	33047.5i	−1.88551	+	3.26580i
$41$	6662.00			0.618935			0.309467	−	0.950910i	$-0.399849\pi$
$41$	6662.00			0.618935			0.309467	+	0.950910i	$0.399849\pi$
$42$		0			0
$43$	−3700.00			−0.305162			−0.152581	−	0.988291i	$-0.548759\pi$
$43$	−3700.00			−0.305162			−0.152581	+	0.988291i	$0.548759\pi$
$44$	−3128.00	+	5417.85i	−0.243576	+	0.421887i
$45$	−4293.00	−	7435.69i	−0.316031	−	0.547382i
$46$	5880.00	+	10184.5i	0.409716	+	0.709649i
$47$	−3528.00	+	6110.68i	−0.232961	+	0.403501i	−0.958678	−	0.284493i	$-0.908175\pi$
$47$	−3528.00	+	6110.68i	−0.232961	+	0.403501i	0.725717	+	0.687993i	$0.241508\pi$
$48$	−12816.0			−0.802878
$49$		0			0
$50$	81110.0			4.58827
$51$	999.000	−	1730.32i	0.0537824	−	0.0931538i
$52$	22780.0	+	39456.1i	1.16828	+	2.02351i
$53$	18789.0	+	32543.5i	0.918785	+	1.59138i	0.801263	+	0.598312i	$0.204162\pi$
$53$	18789.0	+	32543.5i	0.918785	+	1.59138i	0.117522	+	0.993070i	$0.462505\pi$
$54$	3645.00	−	6313.33i	0.170103	−	0.294628i
$55$	9752.00			0.434697
$56$		0			0
$57$	−8172.00			−0.333151
$58$	−5590.00	+	9682.16i	−0.218194	+	0.377922i
$59$	16350.0	+	28319.0i	0.611488	+	1.05913i	0.990990	+	0.133937i	$0.0427620\pi$
$59$	16350.0	+	28319.0i	0.611488	+	1.05913i	−0.379502	+	0.925191i	$0.623905\pi$
$60$	32436.0	+	56180.8i	1.16319	+	2.01470i
$61$	−5401.00	+	9354.81i	−0.185844	+	0.321892i	−0.943861	−	0.330344i	$-0.892835\pi$
$61$	−5401.00	+	9354.81i	−0.185844	+	0.321892i	0.758016	+	0.652236i	$0.226169\pi$
$62$	−36960.0			−1.22110
$63$		0			0
$64$	−18368.0			−0.560547
$65$	35510.0	−	61505.1i	1.04248	−	1.80563i
$66$	4140.00	+	7170.69i	0.116988	+	0.202629i
$67$	−32498.0	−	56288.2i	−0.884443	−	1.53190i	−0.846351	−	0.532625i	$-0.821206\pi$
$67$	−32498.0	−	56288.2i	−0.884443	−	1.53190i	−0.0380913	−	0.999274i	$-0.512128\pi$
$68$	−7548.00	+	13073.5i	−0.197952	+	0.342863i
$69$	10584.0			0.267625
$70$		0			0
$71$	−61320.0			−1.44363			−0.721816	−	0.692085i	$-0.756692\pi$
$71$	−61320.0			−1.44363			−0.721816	+	0.692085i	$0.756692\pi$
$72$	−14580.0	+	25253.3i	−0.331456	+	0.574099i
$73$	19461.0	+	33707.4i	0.427423	+	0.740319i	0.996643	−	0.0818666i	$-0.0260881\pi$
$73$	19461.0	+	33707.4i	0.427423	+	0.740319i	−0.569220	+	0.822185i	$0.692755\pi$
$74$	−20910.0	−	36217.2i	−0.443889	−	0.768839i
$75$	36499.5	−	63219.0i	0.749262	−	1.29776i
$76$	61744.0			1.22620
$77$		0			0
$78$	60300.0			1.12223
$79$	44048.0	−	76293.4i	0.794069	−	1.37537i	−0.129359	−	0.991598i	$-0.541292\pi$
$79$	44048.0	−	76293.4i	0.794069	−	1.37537i	0.923428	−	0.383771i	$-0.125375\pi$
$80$	−75472.0	−	130721.i	−1.31844	−	2.28361i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−33310.0	+	57694.6i	−0.547066	+	0.947547i
$83$	−71892.0			−1.14547			−0.572737	−	0.819739i	$-0.694118\pi$
$83$	−71892.0			−1.14547			−0.572737	+	0.819739i	$0.694118\pi$
$84$		0			0
$85$	23532.0			0.353274
$86$	18500.0	−	32042.9i	0.269728	−	0.467182i
$87$	5031.00	+	8713.95i	0.0712617	+	0.123429i
$88$	−16560.0	−	28682.8i	−0.227957	−	0.394834i
$89$	55909.0	−	96837.2i	0.748181	−	1.29589i	−0.200513	−	0.979691i	$-0.564261\pi$
$89$	55909.0	−	96837.2i	0.748181	−	1.29589i	0.948694	−	0.316196i	$-0.102406\pi$
$90$	85860.0			1.11734
$91$		0			0
$92$	−79968.0			−0.985024
$93$	−16632.0	+	28807.5i	−0.199405	+	0.345380i
$94$	−35280.0	−	61106.8i	−0.411821	−	0.713296i
$95$	−48124.0	−	83353.2i	−0.547082	−	0.947574i
$96$	12240.0	−	21200.3i	0.135551	−	0.234782i
$97$	150846.			1.62781			0.813906	−	0.580996i	$-0.197337\pi$
$97$	150846.			1.62781			0.813906	+	0.580996i	$0.197337\pi$
$98$		0			0
$99$	7452.00			0.0764161
$100$	−275774.	+	477655.i	−2.75774	+	4.77655i
$101$	−68677.0	−	118952.i	−0.669897	−	1.16030i	−0.977933	−	0.208920i	$-0.933005\pi$
$101$	−68677.0	−	118952.i	−0.669897	−	1.16030i	0.308036	−	0.951375i	$-0.400328\pi$
$102$	9990.00	+	17303.2i	0.0950747	+	0.164674i
$103$	14380.0	−	24906.9i	0.133557	−	0.231327i	−0.791488	−	0.611184i	$-0.790693\pi$
$103$	14380.0	−	24906.9i	0.133557	−	0.231327i	0.925045	+	0.379857i	$0.124027\pi$
$104$	−241200.			−2.18672
$105$		0			0
$106$	−375780.			−3.24840
$107$	−11278.0	+	19534.1i	−0.0952298	+	0.164943i	−0.909704	−	0.415256i	$-0.863692\pi$
$107$	−11278.0	+	19534.1i	−0.0952298	+	0.164943i	0.814475	+	0.580199i	$0.197025\pi$
$108$	24786.0	+	42930.6i	0.204478	+	0.354167i
$109$	−9999.00	−	17318.8i	−0.0806103	−	0.139621i	0.822902	−	0.568183i	$-0.192354\pi$
$109$	−9999.00	−	17318.8i	−0.0806103	−	0.139621i	−0.903512	+	0.428562i	$0.859020\pi$
$110$	−48760.0	+	84454.8i	−0.384222	+	0.665492i
$111$	−37638.0			−0.289947
$112$		0			0
$113$	17906.0			0.131918			0.0659588	−	0.997822i	$-0.478989\pi$
$113$	17906.0			0.131918			0.0659588	+	0.997822i	$0.478989\pi$
$114$	40860.0	−	70771.6i	0.294467	−	0.510031i
$115$	62328.0	+	107955.i	0.439479	+	0.761201i
$116$	−38012.0	−	65838.7i	−0.262286	−	0.454293i
$117$	27135.0	−	46999.2i	0.183259	−	0.317414i
$118$	−327000.			−2.16194
$119$		0			0
$120$	−343440.			−2.17720
$121$	76293.5	−	132144.i	0.473723	−	0.820512i
$122$	−54010.0	−	93548.1i	−0.328530	−	0.569030i
$123$	29979.0	+	51925.2i	0.178671	+	0.309467i
$124$	125664.	−	217656.i	0.733933	−	1.27121i
$125$	528516.			3.02540
$126$		0			0
$127$	66864.0			0.367860			0.183930	−	0.982939i	$-0.441118\pi$
$127$	66864.0			0.367860			0.183930	+	0.982939i	$0.441118\pi$
$128$	135360.	−	234450.i	0.730240	−	1.26481i
$129$	−16650.0	−	28838.6i	−0.0880927	−	0.152581i
$130$	355100.	+	615051.i	1.84286	+	3.19193i
$131$	76882.0	−	133164.i	0.391423	−	0.677965i	−0.601214	−	0.799088i	$-0.705316\pi$
$131$	76882.0	−	133164.i	0.391423	−	0.677965i	0.992637	+	0.121123i	$0.0386496\pi$
$132$	−56304.0			−0.281258
$133$		0			0
$134$	649960.			3.12698
$135$	38637.0	−	66921.2i	0.182461	−	0.316031i
$136$	−39960.0	−	69212.8i	−0.185259	−	0.320877i
$137$	−127989.	−	221683.i	−0.582601	−	1.00909i	−0.995170	−	0.0981681i	$-0.968702\pi$
$137$	−127989.	−	221683.i	−0.582601	−	1.00909i	0.412569	−	0.910926i	$-0.364632\pi$
$138$	−52920.0	+	91660.1i	−0.236550	+	0.409716i
$139$	−282924.			−1.24203			−0.621016	−	0.783798i	$-0.713280\pi$
$139$	−282924.			−1.24203			−0.621016	+	0.783798i	$0.713280\pi$
$140$		0			0
$141$	−63504.0			−0.269001
$142$	306600.	−	531047.i	1.27600	−	2.21010i
$143$	30820.0	+	53381.8i	0.126035	+	0.218300i
$144$	−57672.0	−	99890.8i	−0.231771	−	0.401439i
$145$	−59254.0	+	102631.i	−0.234044	+	0.405376i
$146$	−389220.			−1.51117
$147$		0			0
$148$	284376.			1.06718
$149$	−204027.	+	353385.i	−0.752873	+	1.30402i	0.193551	+	0.981090i	$0.437999\pi$
$149$	−204027.	+	353385.i	−0.752873	+	1.30402i	−0.946425	+	0.322925i	$0.895334\pi$
$150$	364995.	+	632190.i	1.32452	+	2.29414i
$151$	−181252.	−	313938.i	−0.646905	−	1.12047i	−0.983858	−	0.178951i	$-0.942730\pi$
$151$	−181252.	−	313938.i	−0.646905	−	1.12047i	0.336953	−	0.941521i	$-0.390604\pi$
$152$	−163440.	+	283086.i	−0.573785	+	0.993825i
$153$	17982.0			0.0621025
$154$		0			0
$155$	−391776.			−1.30981
$156$	−205020.	+	355105.i	−0.674504	+	1.16828i
$157$	−76393.0	−	132317.i	−0.247346	−	0.428415i	0.715443	−	0.698671i	$-0.246225\pi$
$157$	−76393.0	−	132317.i	−0.247346	−	0.428415i	−0.962789	+	0.270256i	$0.912892\pi$
$158$	440480.	+	762934.i	1.40373	+	2.43133i
$159$	−169101.	+	292892.i	−0.530461	+	0.918785i
$160$	288320.			0.890379
$161$		0			0
$162$	65610.0			0.196419
$163$	75214.0	−	130274.i	0.221733	−	0.384052i	−0.733602	−	0.679580i	$-0.762162\pi$
$163$	75214.0	−	130274.i	0.221733	−	0.384052i	0.955334	+	0.295528i	$0.0954954\pi$
$164$	−226508.	−	392323.i	−0.657618	−	1.13903i
$165$	43884.0	+	76009.3i	0.125486	+	0.217349i
$166$	359460.	−	622603.i	1.01247	−	1.75364i
$167$	7288.00			0.0202217			0.0101108	−	0.999949i	$-0.496782\pi$
$167$	7288.00			0.0202217			0.0101108	+	0.999949i	$0.496782\pi$
$168$		0			0
$169$	77607.0			0.209018
$170$	−117660.	+	203793.i	−0.312253	+	0.540838i
$171$	−36774.0	−	63694.4i	−0.0961724	−	0.166576i
$172$	125800.	+	217892.i	0.324235	+	0.561591i
$173$	−144577.	+	250415.i	−0.367269	+	0.636128i	−0.989137	−	0.146993i	$-0.953040\pi$
$173$	−144577.	+	250415.i	−0.367269	+	0.636128i	0.621869	+	0.783121i	$0.286374\pi$
$174$	−100620.			−0.251948
$175$		0			0
$176$	131008.			0.318798
$177$	−147150.	+	254871.i	−0.353043	+	0.611488i
$178$	559090.	+	968372.i	1.32261	+	2.29083i
$179$	−99746.0	−	172765.i	−0.232682	−	0.403017i	0.725914	−	0.687785i	$-0.241417\pi$
$179$	−99746.0	−	172765.i	−0.232682	−	0.403017i	−0.958597	+	0.284768i	$0.908083\pi$
$180$	−291924.	+	505627.i	−0.671566	+	1.16319i
$181$	−240550.			−0.545769			−0.272885	−	0.962047i	$-0.587978\pi$
$181$	−240550.			−0.545769			−0.272885	+	0.962047i	$0.587978\pi$
$182$		0			0
$183$	−97218.0			−0.214595
$184$	211680.	−	366641.i	0.460930	−	0.798355i
$185$	−221646.	−	383902.i	−0.476136	−	0.824691i
$186$	−166320.	−	288075.i	−0.352502	−	0.610552i
$187$	−10212.0	+	17687.7i	−0.0213554	+	0.0369886i
$188$	479808.			0.990086
$189$		0			0
$190$	962480.			1.93423
$191$	−145192.	+	251480.i	−0.287978	+	0.498792i	−0.973327	−	0.229422i	$-0.926316\pi$
$191$	−145192.	+	251480.i	−0.287978	+	0.498792i	0.685349	+	0.728215i	$0.259650\pi$
$192$	−82656.0	−	143164.i	−0.161816	−	0.280273i
$193$	85727.0	+	148484.i	0.165663	+	0.286936i	0.936890	−	0.349623i	$-0.113690\pi$
$193$	85727.0	+	148484.i	0.165663	+	0.286936i	−0.771228	+	0.636559i	$0.780357\pi$
$194$	−754230.	+	1.30636e6i	−1.43880	+	2.49207i
$195$	639180.			1.20375
$196$		0			0
$197$	401990.			0.737989			0.368994	−	0.929432i	$-0.379702\pi$
$197$	401990.			0.737989			0.368994	+	0.929432i	$0.379702\pi$
$198$	−37260.0	+	64536.2i	−0.0675429	+	0.116988i
$199$	−129588.	−	224453.i	−0.231970	−	0.401784i	0.726418	−	0.687253i	$-0.241184\pi$
$199$	−129588.	−	224453.i	−0.231970	−	0.401784i	−0.958388	+	0.285469i	$0.907851\pi$
$200$	−1.45998e6	−	2.52876e6i	−2.58090	−	4.47026i
$201$	292482.	−	506594.i	0.510633	−	0.884443i
$202$	1.37354e6			2.36844
$203$		0			0
$204$	−135864.			−0.228575
$205$	−353086.	+	611563.i	−0.586808	+	1.01638i
$206$	143800.	+	249069.i	0.236097	+	0.408932i
$207$	47628.0	+	82494.1i	0.0772568	+	0.133813i
$208$	477040.	−	826258.i	0.764533	−	1.32421i
$209$	83536.0			0.132284
$210$		0			0
$211$	−1.19179e6			−1.84286			−0.921431	−	0.388542i	$-0.872979\pi$
$211$	−1.19179e6			−1.84286			−0.921431	+	0.388542i	$0.872979\pi$
$212$	1.27765e6	−	2.21296e6i	1.95242	−	3.38169i
$213$	−275940.	−	477942.i	−0.416740	−	0.721816i
$214$	−112780.	−	195341.i	−0.168344	−	0.291580i
$215$	196100.	−	339655.i	0.289322	−	0.501120i
$216$	−262440.			−0.382733
$217$		0			0
$218$	199980.			0.285000
$219$	−175149.	+	303367.i	−0.246773	+	0.427423i
$220$	−331568.	−	574293.i	−0.461866	−	0.799975i
$221$	74370.0	+	128813.i	0.102428	+	0.177410i
$222$	188190.	−	325955.i	0.256280	−	0.443889i
$223$	218384.			0.294075			0.147038	−	0.989131i	$-0.453026\pi$
$223$	218384.			0.294075			0.147038	+	0.989131i	$0.453026\pi$
$224$		0			0
$225$	656991.			0.865173
$226$	−89530.0	+	155071.i	−0.116600	+	0.201957i
$227$	291426.	+	504765.i	0.375374	+	0.650166i	0.990383	−	0.138354i	$-0.0441811\pi$
$227$	291426.	+	504765.i	0.375374	+	0.650166i	−0.615009	+	0.788520i	$0.710848\pi$
$228$	277848.	+	481247.i	0.353973	+	0.613099i
$229$	480523.	−	832290.i	0.605516	−	1.04878i	−0.386454	−	0.922309i	$-0.626300\pi$
$229$	480523.	−	832290.i	0.605516	−	1.04878i	0.991970	−	0.126475i	$-0.0403665\pi$
$230$	−1.24656e6			−1.55379
$231$		0			0
$232$	402480.			0.490935
$233$	−302997.	+	524806.i	−0.365636	+	0.633300i	−0.988878	−	0.148729i	$-0.952482\pi$
$233$	−302997.	+	524806.i	−0.365636	+	0.633300i	0.623242	+	0.782029i	$0.285815\pi$
$234$	271350.	+	469992.i	0.323959	+	0.561114i
$235$	−373968.	−	647732.i	−0.441738	−	0.765113i
$236$	1.11180e6	−	1.92569e6i	1.29941	−	2.25065i
$237$	792864.			0.916912
$238$		0			0
$239$	1.17014e6			1.32509			0.662544	−	0.749023i	$-0.269477\pi$
$239$	1.17014e6			1.32509			0.662544	+	0.749023i	$0.269477\pi$
$240$	679248.	−	1.17649e6i	0.761203	−	1.31844i
$241$	−618455.	−	1.07120e6i	−0.685907	−	1.18803i	−0.973151	−	0.230169i	$-0.926072\pi$
$241$	−618455.	−	1.07120e6i	−0.685907	−	1.18803i	0.287243	−	0.957858i	$-0.407261\pi$
$242$	762935.	+	1.32144e6i	0.837431	+	1.45047i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	734536.			0.789839
$245$		0			0
$246$	−599580.			−0.631698
$247$	304180.	−	526855.i	0.317240	−	0.549476i
$248$	665280.	+	1.15230e6i	0.686871	+	1.18970i
$249$	−323514.	−	560343.i	−0.330670	−	0.572737i
$250$	−2.64258e6	+	4.57708e6i	−2.67410	+	4.63168i
$251$	−959708.			−0.961512			−0.480756	−	0.876854i	$-0.659638\pi$
$251$	−959708.			−0.961512			−0.480756	+	0.876854i	$0.659638\pi$
$252$		0			0
$253$	−108192.			−0.106266
$254$	−334320.	+	579059.i	−0.325146	+	0.563169i
$255$	105894.	+	183414.i	0.101981	+	0.176637i
$256$	1.05971e6	+	1.83548e6i	1.01062	+	1.75045i
$257$	−606295.	+	1.05013e6i	−0.572600	+	0.991772i	0.423698	+	0.905803i	$0.360732\pi$
$257$	−606295.	+	1.05013e6i	−0.572600	+	0.991772i	−0.996298	+	0.0859684i	$0.972602\pi$
$258$	333000.			0.311455
$259$		0			0
$260$	−4.82936e6			−4.43054
$261$	−45279.0	+	78425.5i	−0.0411430	+	0.0712617i
$262$	768820.	+	1.33164e6i	0.691945	+	1.19848i
$263$	626372.	+	1.08491e6i	0.558397	+	0.967172i	0.997631	+	0.0687989i	$0.0219167\pi$
$263$	626372.	+	1.08491e6i	0.558397	+	0.967172i	−0.439234	+	0.898373i	$0.644750\pi$
$264$	149040.	−	258145.i	0.131611	−	0.227957i
$265$	−3.98327e6			−3.48437
$266$		0			0
$267$	1.00636e6			0.863925
$268$	−2.20986e6	+	3.82760e6i	−1.87944	+	3.25529i
$269$	−68433.0	−	118529.i	−0.0576614	−	0.0998724i	0.835754	−	0.549104i	$-0.185031\pi$
$269$	−68433.0	−	118529.i	−0.0576614	−	0.0998724i	−0.893415	+	0.449232i	$0.851698\pi$
$270$	386370.	+	669212.i	0.322548	+	0.558669i
$271$	−480448.	+	832160.i	−0.397396	+	0.688310i	−0.993404	−	0.114669i	$-0.963419\pi$
$271$	−480448.	+	832160.i	−0.397396	+	0.688310i	0.596008	+	0.802978i	$0.296753\pi$
$272$	316128.			0.259084
$273$		0			0
$274$	2.55978e6			2.05981
$275$	−373106.	+	646239.i	−0.297509	+	0.515301i
$276$	−359856.	−	623289.i	−0.284352	−	0.492512i
$277$	−452915.	−	784472.i	−0.354664	−	0.614296i	0.632396	−	0.774645i	$-0.282071\pi$
$277$	−452915.	−	784472.i	−0.354664	−	0.614296i	−0.987060	+	0.160349i	$0.948738\pi$
$278$	1.41462e6	−	2.45019e6i	1.09781	−	1.90147i
$279$	−299376.			−0.230254
$280$		0			0
$281$	−33062.0			−0.0249783			−0.0124892	−	0.999922i	$-0.503976\pi$
$281$	−33062.0			−0.0249783			−0.0124892	+	0.999922i	$0.503976\pi$
$282$	317520.	−	549961.i	0.237765	−	0.411821i
$283$	−431794.	−	747889.i	−0.320487	−	0.555100i	0.660102	−	0.751176i	$-0.270513\pi$
$283$	−431794.	−	747889.i	−0.320487	−	0.555100i	−0.980589	+	0.196076i	$0.937180\pi$
$284$	2.08488e6	+	3.61112e6i	1.53386	+	2.65672i
$285$	433116.	−	750179.i	0.315858	−	0.547082i
$286$	−616400.			−0.445602
$287$		0			0
$288$	220320.			0.156521
$289$	685286.	−	1.18695e6i	0.482645	−	0.835965i
$290$	−592540.	−	1.02631e6i	−0.413735	−	0.716611i
$291$	678807.	+	1.17573e6i	0.469909	+	0.813906i
$292$	1.32335e6	−	2.29211e6i	0.908274	−	1.57318i
$293$	1.33755e6			0.910206			0.455103	−	0.890439i	$-0.349602\pi$
$293$	1.33755e6			0.910206			0.455103	+	0.890439i	$0.349602\pi$
$294$		0			0
$295$	−3.46620e6			−2.31899
$296$	−752760.	+	1.30382e6i	−0.499376	+	0.864944i
$297$	33534.0	+	58082.6i	0.0220594	+	0.0382080i
$298$	−2.04027e6	−	3.53385e6i	−1.33090	−	2.30519i
$299$	−393960.	+	682359.i	−0.254844	+	0.441402i
$300$	−4.96393e6			−3.18436
$301$		0			0
$302$	3.62504e6			2.28715
$303$	618093.	−	1.07057e6i	0.386765	−	0.669897i
$304$	−646496.	−	1.11976e6i	−0.401219	−	0.694932i
$305$	−572506.	−	991609.i	−0.352396	−	0.610367i
$306$	−89910.0	+	155729.i	−0.0548914	+	0.0950747i
$307$	1.32820e6			0.804301			0.402151	−	0.915573i	$-0.368263\pi$
$307$	1.32820e6			0.804301			0.402151	+	0.915573i	$0.368263\pi$
$308$		0			0
$309$	258840.			0.154218
$310$	1.95888e6	−	3.39288e6i	1.15772	−	2.00523i
$311$	−332916.	−	576627.i	−0.195179	−	0.338060i	0.751780	−	0.659414i	$-0.229196\pi$
$311$	−332916.	−	576627.i	−0.195179	−	0.338060i	−0.946959	+	0.321354i	$0.895862\pi$
$312$	−1.08540e6	−	1.87997e6i	−0.631253	−	1.09336i
$313$	−1.54511e6	+	2.67620e6i	−0.891451	+	1.54404i	−0.0533157	+	0.998578i	$0.516979\pi$
$313$	−1.54511e6	+	2.67620e6i	−0.891451	+	1.54404i	−0.838136	+	0.545462i	$0.816354\pi$
$314$	1.52786e6			0.874499
$315$		0			0
$316$	−5.99053e6			−3.37479
$317$	487089.	−	843663.i	0.272245	−	0.471542i	−0.697191	−	0.716885i	$-0.745567\pi$
$317$	487089.	−	843663.i	0.272245	−	0.471542i	0.969436	+	0.245343i	$0.0789005\pi$
$318$	−1.69101e6	−	2.92892e6i	−0.937731	−	1.62420i
$319$	−51428.0	−	89075.9i	−0.0282959	−	0.0490099i
$320$	973504.	−	1.68616e6i	0.531450	−	0.920499i
$321$	−203004.			−0.109962
$322$		0			0
$323$	201576.			0.107506
$324$	−223074.	+	386376.i	−0.118056	+	0.204478i
$325$	2.71718e6	+	4.70630e6i	1.42696	+	2.47156i
$326$	752140.	+	1.30274e6i	0.391972	+	0.678915i
$327$	89991.0	−	155869.i	0.0465404	−	0.0806103i
$328$	2.39832e6			1.23090
$329$		0			0
$330$	−877680.			−0.443661
$331$	−390886.	+	677034.i	−0.196101	+	0.339657i	−0.947261	−	0.320463i	$-0.896161\pi$
$331$	−390886.	+	677034.i	−0.196101	+	0.339657i	0.751160	+	0.660120i	$0.229495\pi$
$332$	2.44433e6	+	4.23370e6i	1.21707	+	2.10802i
$333$	−169371.	−	293359.i	−0.0837006	−	0.144974i
$334$	−36440.0	+	63115.9i	−0.0178736	+	0.0309580i
$335$	6.88958e6			3.35413
$336$		0			0
$337$	348754.			0.167280			0.0836401	−	0.996496i	$-0.473345\pi$
$337$	348754.			0.167280			0.0836401	+	0.996496i	$0.473345\pi$
$338$	−388035.	+	672096.i	−0.184748	+	0.319992i
$339$	80577.0	+	139563.i	0.0380813	+	0.0659588i
$340$	−800088.	−	1.38579e6i	−0.375353	−	0.650131i
$341$	170016.	−	294476.i	0.0791779	−	0.137140i
$342$	735480.			0.340021
$343$		0			0
$344$	−1.33200e6			−0.606887
$345$	−560952.	+	971597.i	−0.253734	+	0.439479i
$346$	−1.44577e6	−	2.50415e6i	−0.649246	−	1.12453i
$347$	−1.25313e6	−	2.17048e6i	−0.558690	−	0.967680i	−0.997606	−	0.0691517i	$-0.977971\pi$
$347$	−1.25313e6	−	2.17048e6i	−0.558690	−	0.967680i	0.438916	−	0.898528i	$-0.355363\pi$
$348$	342108.	−	592548.i	0.151431	−	0.262286i
$349$	−3.05861e6			−1.34419			−0.672094	−	0.740466i	$-0.734605\pi$
$349$	−3.05861e6			−1.34419			−0.672094	+	0.740466i	$0.734605\pi$
$350$		0			0
$351$	488430.			0.211609
$352$	−125120.	+	216714.i	−0.0538233	+	0.0932246i
$353$	−1.74646e6	−	3.02495e6i	−0.745969	−	1.29206i	−0.949741	−	0.313037i	$-0.898653\pi$
$353$	−1.74646e6	−	3.02495e6i	−0.745969	−	1.29206i	0.203772	−	0.979018i	$-0.434680\pi$
$354$	−1.47150e6	−	2.54871e6i	−0.624097	−	1.08097i
$355$	3.24996e6	−	5.62910e6i	1.36870	−	2.37065i
$356$	−7.60362e6			−3.17977
$357$		0			0
$358$	1.99492e6			0.822655
$359$	−1.06017e6	+	1.83627e6i	−0.434150	+	0.751971i	−0.997226	−	0.0744349i	$-0.976285\pi$
$359$	−1.06017e6	+	1.83627e6i	−0.434150	+	0.751971i	0.563075	+	0.826405i	$0.309618\pi$
$360$	−1.54548e6	−	2.67685e6i	−0.628503	−	1.08860i
$361$	825817.	+	1.43036e6i	0.333516	+	0.577666i
$362$	1.20275e6	−	2.08322e6i	0.482396	−	0.835535i
$363$	1.37328e6			0.547008
$364$		0			0
$365$	−4.12573e6			−1.62095
$366$	486090.	−	841933.i	0.189677	−	0.328530i
$367$	373296.	+	646568.i	0.144673	+	0.250581i	0.929251	−	0.369449i	$-0.120454\pi$
$367$	373296.	+	646568.i	0.144673	+	0.250581i	−0.784578	+	0.620030i	$0.787120\pi$
$368$	837312.	+	1.45027e6i	0.322306	+	0.558250i
$369$	−269811.	+	467326.i	−0.103156	+	0.178671i
$370$	4.43292e6			1.68339
$371$		0			0
$372$	2.26195e6			0.847473
$373$	469517.	−	813227.i	0.174735	−	0.302649i	−0.765335	−	0.643632i	$-0.777427\pi$
$373$	469517.	−	813227.i	0.174735	−	0.302649i	0.940069	+	0.340983i	$0.110760\pi$
$374$	−102120.	−	176877.i	−0.0377513	−	0.0653872i
$375$	2.37832e6	+	4.11937e6i	0.873358	+	1.51270i
$376$	−1.27008e6	+	2.19984e6i	−0.463299	+	0.802458i
$377$	−749060.			−0.271433
$378$		0			0
$379$	5.16534e6			1.84714			0.923572	−	0.383424i	$-0.125255\pi$
$379$	5.16534e6			1.84714			0.923572	+	0.383424i	$0.125255\pi$
$380$	−3.27243e6	+	5.66802e6i	−1.16255	+	2.01360i
$381$	300888.	+	521153.i	0.106192	+	0.183930i
$382$	−1.45192e6	−	2.51480e6i	−0.509078	−	0.881749i
$383$	200256.	−	346854.i	0.0697571	−	0.120823i	−0.829037	−	0.559193i	$-0.811111\pi$
$383$	200256.	−	346854.i	0.0697571	−	0.120823i	0.898794	+	0.438371i	$0.144444\pi$
$384$	2.43648e6			0.843208
$385$		0			0
$386$	−1.71454e6			−0.585706
$387$	149850.	−	259548.i	0.0508603	−	0.0880927i
$388$	−5.12876e6	−	8.88328e6i	−1.72955	−	2.99567i
$389$	−153411.	−	265716.i	−0.0514023	−	0.0890314i	0.839179	−	0.543855i	$-0.183036\pi$
$389$	−153411.	−	265716.i	−0.0514023	−	0.0890314i	−0.890582	+	0.454823i	$0.849702\pi$
$390$	−3.19590e6	+	5.53546e6i	−1.06398	+	1.84286i
$391$	−261072.			−0.0863611
$392$		0			0
$393$	1.38388e6			0.451976
$394$	−2.00995e6	+	3.48134e6i	−0.652296	+	1.12981i
$395$	4.66909e6	+	8.08710e6i	1.50570	+	2.60795i
$396$	−253368.	−	438846.i	−0.0811921	−	0.140629i
$397$	−1.91710e6	+	3.32052e6i	−0.610477	+	1.05738i	0.380683	+	0.924706i	$0.375689\pi$
$397$	−1.91710e6	+	3.32052e6i	−0.610477	+	1.05738i	−0.991160	+	0.132672i	$0.957644\pi$
$398$	2.59176e6			0.820138
$399$		0			0
$400$	1.15501e7			3.60940
$401$	1.64678e6	−	2.85230e6i	0.511415	−	0.885797i	−0.488498	−	0.872565i	$-0.662455\pi$
$401$	1.64678e6	−	2.85230e6i	0.511415	−	0.885797i	0.999912	−	0.0132313i	$-0.00421177\pi$
$402$	2.92482e6	+	5.06594e6i	0.902680	+	1.56349i
$403$	−1.23816e6	−	2.14456e6i	−0.379764	−	0.657771i
$404$	−4.67004e6	+	8.08874e6i	−1.42353	+	2.46563i
$405$	695466.			0.210687
$406$		0			0
$407$	384744.			0.115129
$408$	359640.	−	622915.i	0.106959	−	0.185259i
$409$	−677363.	−	1.17323e6i	−0.200223	−	0.346796i	0.748377	−	0.663273i	$-0.230833\pi$
$409$	−677363.	−	1.17323e6i	−0.200223	−	0.346796i	−0.948600	+	0.316477i	$0.897500\pi$
$410$	−3.53086e6	−	6.11563e6i	−1.03734	−	1.79672i
$411$	1.15190e6	−	1.99515e6i	0.336365	−	0.582601i
$412$	−1.95568e6			−0.567616
$413$		0			0
$414$	−952560.			−0.273144
$415$	3.81028e6	−	6.59959e6i	1.08602	−	1.88103i
$416$	911200.	+	1.57824e6i	0.258155	+	0.447137i
$417$	−1.27316e6	−	2.20517e6i	−0.358544	−	0.621016i
$418$	−417680.	+	723443.i	−0.116924	+	0.202518i
$419$	−5.08199e6			−1.41416			−0.707080	−	0.707134i	$-0.749988\pi$
$419$	−5.08199e6			−1.41416			−0.707080	+	0.707134i	$0.749988\pi$
$420$		0			0
$421$	628022.			0.172691			0.0863455	−	0.996265i	$-0.472481\pi$
$421$	628022.			0.172691			0.0863455	+	0.996265i	$0.472481\pi$
$422$	5.95894e6	−	1.03212e7i	1.62888	−	2.82130i
$423$	−285768.	−	494965.i	−0.0776538	−	0.134500i
$424$	6.76404e6	+	1.17157e7i	1.82722	+	3.16484i
$425$	−900321.	+	1.55940e6i	−0.241783	+	0.418780i
$426$	5.51880e6			1.47340
$427$		0			0
$428$	1.53381e6			0.404726
$429$	−277380.	+	480436.i	−0.0727666	+	0.126035i
$430$	1.96100e6	+	3.39655e6i	0.511454	+	0.885864i
$431$	1.50043e6	+	2.59882e6i	0.389066	+	0.673882i	0.992324	−	0.123664i	$-0.0394645\pi$
$431$	1.50043e6	+	2.59882e6i	0.389066	+	0.673882i	−0.603258	+	0.797546i	$0.706131\pi$
$432$	519048.	−	899018.i	0.133813	−	0.231771i
$433$	−1.21496e6			−0.311417			−0.155709	−	0.987803i	$-0.549766\pi$
$433$	−1.21496e6			−0.311417			−0.155709	+	0.987803i	$0.549766\pi$
$434$		0			0
$435$	−1.06657e6			−0.270251
$436$	−679932.	+	1.17768e6i	−0.171297	+	0.296695i
$437$	533904.	+	924749.i	0.133739	+	0.231644i
$438$	−1.75149e6	−	3.03367e6i	−0.436237	−	0.755584i
$439$	2.00327e6	−	3.46976e6i	0.496110	−	0.859287i	−0.503880	−	0.863774i	$-0.668095\pi$
$439$	2.00327e6	−	3.46976e6i	0.496110	−	0.859287i	0.999990	+	0.00448628i	$0.00142803\pi$
$440$	3.51072e6			0.864499
$441$		0			0
$442$	−1.48740e6			−0.362136
$443$	2.72375e6	−	4.71768e6i	0.659415	−	1.14214i	−0.321353	−	0.946960i	$-0.604138\pi$
$443$	2.72375e6	−	4.71768e6i	0.659415	−	1.14214i	0.980767	−	0.195180i	$-0.0625291\pi$
$444$	1.27969e6	+	2.21649e6i	0.308069	+	0.533591i
$445$	5.92635e6	+	1.02647e7i	1.41869	+	2.45724i
$446$	−1.09192e6	+	1.89126e6i	−0.259928	+	0.450209i
$447$	−3.67249e6			−0.869343
$448$		0			0
$449$	−1.81577e6			−0.425056			−0.212528	−	0.977155i	$-0.568170\pi$
$449$	−1.81577e6			−0.425056			−0.212528	+	0.977155i	$0.568170\pi$
$450$	−3.28496e6	+	5.68971e6i	−0.764712	+	1.32452i
$451$	−306452.	−	530790.i	−0.0709449	−	0.122880i
$452$	−608804.	−	1.05448e6i	−0.140162	−	0.242768i
$453$	1.63127e6	−	2.82544e6i	0.373491	−	0.646905i
$454$	−5.82852e6			−1.32715
$455$		0			0
$456$	−2.94192e6			−0.662550
$457$	2.65041e6	−	4.59065e6i	0.593639	−	1.02821i	−0.400098	−	0.916472i	$-0.631024\pi$
$457$	2.65041e6	−	4.59065e6i	0.593639	−	1.02821i	0.993737	−	0.111741i	$-0.0356428\pi$
$458$	4.80523e6	+	8.32290e6i	1.07041	+	1.85401i
$459$	80919.0	+	140156.i	0.0179275	+	0.0310513i
$460$	4.23830e6	−	7.34096e6i	0.933894	−	1.61755i
$461$	−3.20381e6			−0.702124			−0.351062	−	0.936352i	$-0.614179\pi$
$461$	−3.20381e6			−0.702124			−0.351062	+	0.936352i	$0.614179\pi$
$462$		0			0
$463$	−1.11853e6			−0.242490			−0.121245	−	0.992623i	$-0.538689\pi$
$463$	−1.11853e6			−0.242490			−0.121245	+	0.992623i	$0.538689\pi$
$464$	−796016.	+	1.37874e6i	−0.171643	+	0.297295i
$465$	−1.76299e6	−	3.05359e6i	−0.378110	−	0.654905i
$466$	−3.02997e6	−	5.24806e6i	−0.646359	−	1.11953i
$467$	−1.92567e6	+	3.33536e6i	−0.408592	+	0.707702i	−0.994732	−	0.102508i	$-0.967313\pi$
$467$	−1.92567e6	+	3.33536e6i	−0.408592	+	0.707702i	0.586140	+	0.810210i	$0.300647\pi$
$468$	−3.69036e6			−0.778850
$469$		0			0
$470$	7.47936e6			1.56178
$471$	687537.	−	1.19085e6i	0.142805	−	0.247346i
$472$	5.88600e6	+	1.01949e7i	1.21609	+	2.10633i
$473$	170200.	+	294795.i	0.0349789	+	0.0605853i
$474$	−3.96432e6	+	6.86640e6i	−0.810444	+	1.40373i
$475$	7.36479e6			1.49770
$476$		0			0
$477$	−3.04382e6			−0.612523
$478$	−5.85072e6	+	1.01337e7i	−1.17122	+	2.02862i
$479$	717680.	+	1.24306e6i	0.142920	+	0.247544i	0.928595	−	0.371095i	$-0.121018\pi$
$479$	717680.	+	1.24306e6i	0.142920	+	0.247544i	−0.785675	+	0.618639i	$0.787684\pi$
$480$	1.29744e6	+	2.24723e6i	0.257030	+	0.445189i
$481$	1.40097e6	−	2.42655e6i	0.276100	−	0.478219i
$482$	1.23691e7			2.42505
$483$		0			0
$484$	−1.03759e7			−2.01332
$485$	−7.99484e6	+	1.38475e7i	−1.54332	+	2.67310i
$486$	295245.	+	511379.i	0.0567012	+	0.0982093i
$487$	−2.30548e6	−	3.99322e6i	−0.440494	−	0.762957i	0.557232	−	0.830357i	$-0.311863\pi$
$487$	−2.30548e6	−	3.99322e6i	−0.440494	−	0.762957i	−0.997726	+	0.0673991i	$0.978530\pi$
$488$	−1.94436e6	+	3.36773e6i	−0.369596	+	0.640159i
$489$	1.35385e6			0.256035
$490$		0			0
$491$	7.40518e6			1.38622			0.693110	−	0.720832i	$-0.256240\pi$
$491$	7.40518e6			1.38622			0.693110	+	0.720832i	$0.256240\pi$
$492$	2.03857e6	−	3.53091e6i	0.379676	−	0.657618i
$493$	−124098.	−	214944.i	−0.0229957	−	0.0398298i
$494$	3.04180e6	+	5.26855e6i	0.560807	+	0.971346i
$495$	−394956.	+	684084.i	−0.0724496	+	0.125486i
$496$	−5.26310e6			−0.960589
$497$		0			0
$498$	6.47028e6			1.16909
$499$	−1.96716e6	+	3.40722e6i	−0.353662	+	0.612561i	−0.986888	−	0.161406i	$-0.948397\pi$
$499$	−1.96716e6	+	3.40722e6i	−0.353662	+	0.612561i	0.633226	+	0.773967i	$0.281730\pi$
$500$	−1.79695e7	−	3.11242e7i	−3.21449	−	5.56766i
$501$	32796.0	+	56804.3i	0.00583750	+	0.0101108i
$502$	4.79854e6	−	8.31132e6i	0.849865	−	1.47201i
$503$	−3.40975e6			−0.600901			−0.300450	−	0.953797i	$-0.597137\pi$
$503$	−3.40975e6			−0.600901			−0.300450	+	0.953797i	$0.597137\pi$
$504$		0			0
$505$	1.45595e7			2.54050
$506$	540960.	−	936970.i	0.0939267	−	0.162686i
$507$	349231.	+	604887.i	0.0603384	+	0.104509i
$508$	−2.27338e6	−	3.93760e6i	−0.390852	−	0.676975i
$509$	−3.86191e6	+	6.68903e6i	−0.660706	+	1.14438i	0.319725	+	0.947510i	$0.396410\pi$
$509$	−3.86191e6	+	6.68903e6i	−0.660706	+	1.14438i	−0.980431	+	0.196865i	$0.936924\pi$
$510$	−2.11788e6			−0.360559
$511$		0			0
$512$	−1.25312e7			−2.11260
$513$	330966.	−	573250.i	0.0555252	−	0.0961724i
$514$	−6.06295e6	−	1.05013e7i	−1.01222	−	1.75322i
$515$	1.52428e6	+	2.64013e6i	0.253248	+	0.438639i
$516$	−1.13220e6	+	1.96103e6i	−0.187197	+	0.324235i
$517$	649152.			0.106812
$518$		0			0
$519$	−2.60239e6			−0.424085
$520$	1.27836e7	−	2.21418e7i	2.07322	−	3.59092i
$521$	−2.38829e6	−	4.13664e6i	−0.385472	−	0.667657i	0.606362	−	0.795188i	$-0.292628\pi$
$521$	−2.38829e6	−	4.13664e6i	−0.385472	−	0.667657i	−0.991835	+	0.127531i	$0.959295\pi$
$522$	−452790.	−	784255.i	−0.0727312	−	0.125974i
$523$	−4.64377e6	+	8.04325e6i	−0.742363	+	1.28581i	0.209053	+	0.977904i	$0.432962\pi$
$523$	−4.64377e6	+	8.04325e6i	−0.742363	+	1.28581i	−0.951417	+	0.307907i	$0.900372\pi$
$524$	−1.04560e7			−1.66355
$525$		0			0
$526$	−1.25274e7			−1.97423
$527$	410256.	−	710584.i	0.0643470	−	0.111452i
$528$	589536.	+	1.02111e6i	0.0920292	+	0.159399i
$529$	2.52668e6	+	4.37634e6i	0.392565	+	0.679943i
$530$	1.99163e7	−	3.44961e7i	3.07978	−	5.33434i
$531$	−2.64870e6			−0.407658
$532$		0			0
$533$	−4.46354e6			−0.680552
$534$	−5.03181e6	+	8.71535e6i	−0.763609	+	1.32261i
$535$	−1.19547e6	−	2.07061e6i	−0.180573	−	0.312762i
$536$	−1.16993e7	−	2.02637e7i	−1.75892	−	3.04655i
$537$	897714.	−	1.55489e6i	0.134339	−	0.232682i
$538$	1.36866e6			0.203864
$539$		0			0
$540$	−5.25463e6			−0.775457
$541$	−3.86458e6	+	6.69365e6i	−0.567688	+	0.983264i	0.429106	+	0.903254i	$0.358829\pi$
$541$	−3.86458e6	+	6.69365e6i	−0.567688	+	0.983264i	−0.996794	+	0.0800100i	$0.974505\pi$
$542$	−4.80448e6	−	8.32160e6i	−0.702503	−	1.21677i
$543$	−1.08248e6	−	1.87490e6i	−0.157550	−	0.272885i
$544$	−301920.	+	522941.i	−0.0437416	+	0.0757627i
$545$	2.11979e6			0.305704
$546$		0			0
$547$	−8.60361e6			−1.22945			−0.614727	−	0.788740i	$-0.710734\pi$
$547$	−8.60361e6			−1.22945			−0.614727	+	0.788740i	$0.710734\pi$
$548$	−8.70325e6	+	1.50745e7i	−1.23803	+	2.14433i
$549$	−437481.	−	757739.i	−0.0619481	−	0.107297i
$550$	−3.73106e6	−	6.46239e6i	−0.525927	−	0.910932i
$551$	−507572.	+	879140.i	−0.0712227	+	0.123361i
$552$	3.81024e6			0.532236
$553$		0			0
$554$	9.05830e6			1.25393
$555$	1.99481e6	−	3.45512e6i	0.274897	−	0.476136i
$556$	9.61942e6	+	1.66613e7i	1.31966	+	2.28572i
$557$	888617.	+	1.53913e6i	0.121360	+	0.210202i	0.920304	−	0.391203i	$-0.127941\pi$
$557$	888617.	+	1.53913e6i	0.121360	+	0.210202i	−0.798944	+	0.601405i	$0.794608\pi$
$558$	1.49688e6	−	2.59267e6i	0.203517	−	0.352502i
$559$	2.47900e6			0.335542
$560$		0			0
$561$	−183816.			−0.0246590
$562$	165310.	−	286325.i	0.0220779	−	0.0382401i
$563$	1.34430e6	+	2.32839e6i	0.178741	+	0.309589i	0.941450	−	0.337154i	$-0.109464\pi$
$563$	1.34430e6	+	2.32839e6i	0.178741	+	0.309589i	−0.762708	+	0.646742i	$0.776131\pi$
$564$	2.15914e6	+	3.73973e6i	0.285813	+	0.495043i
$565$	−949018.	+	1.64375e6i	−0.125070	+	0.216628i
$566$	8.63588e6			1.13309
$567$		0			0
$568$	−2.20752e7			−2.87100
$569$	−2.66315e6	+	4.61271e6i	−0.344838	+	0.597276i	−0.985324	−	0.170693i	$-0.945399\pi$
$569$	−2.66315e6	+	4.61271e6i	−0.344838	+	0.597276i	0.640487	+	0.767969i	$0.278733\pi$
$570$	4.33116e6	+	7.50179e6i	0.558364	+	0.967114i
$571$	−6.69960e6	−	1.16040e7i	−0.859921	−	1.48943i	−0.872004	−	0.489500i	$-0.837179\pi$
$571$	−6.69960e6	−	1.16040e7i	−0.859921	−	1.48943i	0.0120827	−	0.999927i	$-0.496154\pi$
$572$	2.09576e6	−	3.62996e6i	0.267825	−	0.463887i
$573$	−2.61346e6			−0.332528
$574$		0			0
$575$	−9.53854e6			−1.20313
$576$	743904.	−	1.28848e6i	0.0934245	−	0.161816i
$577$	−552511.	−	956977.i	−0.0690878	−	0.119664i	0.829412	−	0.558637i	$-0.188676\pi$
$577$	−552511.	−	956977.i	−0.0690878	−	0.119664i	−0.898500	+	0.438973i	$0.855342\pi$
$578$	6.85286e6	+	1.18695e7i	0.853203	+	1.47779i
$579$	−771543.	+	1.33635e6i	−0.0956453	+	0.165663i
$580$	8.05854e6			0.994687
$581$		0			0
$582$	−1.35761e7			−1.66138
$583$	1.72859e6	−	2.99400e6i	0.210630	−	0.364822i
$584$	7.00596e6	+	1.21347e7i	0.850033	+	1.47230i
$585$	2.87631e6	+	4.98192e6i	0.347493	+	0.601875i
$586$	−6.68773e6	+	1.15835e7i	−0.804516	+	1.39346i
$587$	−5.97288e6			−0.715465			−0.357732	−	0.933824i	$-0.616450\pi$
$587$	−5.97288e6			−0.715465			−0.357732	+	0.933824i	$0.616450\pi$
$588$		0			0
$589$	−3.35597e6			−0.398593
$590$	1.73310e7	−	3.00182e7i	2.04972	−	3.55021i
$591$	1.80896e6	+	3.13320e6i	0.213039	+	0.368994i
$592$	−2.97758e6	−	5.15733e6i	−0.349188	−	0.604812i
$593$	−5.59725e6	+	9.69472e6i	−0.653639	+	1.13214i	0.328595	+	0.944471i	$0.393425\pi$
$593$	−5.59725e6	+	9.69472e6i	−0.653639	+	1.13214i	−0.982233	+	0.187664i	$0.939908\pi$
$594$	−670680.			−0.0779919
$595$		0			0
$596$	2.77477e7			3.19971
$597$	1.16629e6	−	2.02008e6i	0.133928	−	0.231970i
$598$	−3.93960e6	−	6.82359e6i	−0.450505	−	0.780297i
$599$	−5.45274e6	−	9.44442e6i	−0.620937	−	1.07549i	−0.989312	−	0.145817i	$-0.953419\pi$
$599$	−5.45274e6	−	9.44442e6i	−0.620937	−	1.07549i	0.368374	−	0.929678i	$-0.379915\pi$
$600$	1.31398e7	−	2.27588e7i	1.49009	−	2.58090i
$601$	−7.39737e6			−0.835394			−0.417697	−	0.908586i	$-0.637163\pi$
$601$	−7.39737e6			−0.835394			−0.417697	+	0.908586i	$0.637163\pi$
$602$		0			0
$603$	5.26468e6			0.589628
$604$	−1.23251e7	+	2.13478e7i	−1.37467	+	2.38100i
$605$	8.08711e6	+	1.40073e7i	0.898266	+	1.55584i
$606$	6.18093e6	+	1.07057e7i	0.683711	+	1.18422i
$607$	3.56678e6	−	6.17784e6i	0.392920	−	0.680557i	−0.599913	−	0.800065i	$-0.704798\pi$
$607$	3.56678e6	−	6.17784e6i	0.392920	−	0.680557i	0.992833	+	0.119508i	$0.0381316\pi$
$608$	2.46976e6			0.270954
$609$		0			0
$610$	1.14501e7			1.24591
$611$	2.36376e6	−	4.09415e6i	0.256154	−	0.443671i
$612$	−611388.	−	1.05896e6i	−0.0659840	−	0.114288i
$613$	8.56319e6	+	1.48319e7i	0.920416	+	1.59421i	0.798772	+	0.601634i	$0.205484\pi$
$613$	8.56319e6	+	1.48319e7i	0.920416	+	1.59421i	0.121645	+	0.992574i	$0.461183\pi$
$614$	−6.64102e6	+	1.15026e7i	−0.710909	+	1.23133i
$615$	−6.35555e6			−0.677587
$616$		0			0
$617$	2.29924e6			0.243149			0.121574	−	0.992582i	$-0.461206\pi$
$617$	2.29924e6			0.243149			0.121574	+	0.992582i	$0.461206\pi$
$618$	−1.29420e6	+	2.24162e6i	−0.136311	+	0.236097i
$619$	−925882.	−	1.60367e6i	−0.0971245	−	0.168225i	0.813369	−	0.581748i	$-0.197631\pi$
$619$	−925882.	−	1.60367e6i	−0.0971245	−	0.168225i	−0.910493	+	0.413524i	$0.864298\pi$
$620$	1.33204e7	+	2.30716e7i	1.39167	+	2.41045i
$621$	−428652.	+	742447.i	−0.0446042	+	0.0772568i
$622$	6.65832e6			0.690063
$623$		0			0
$624$	8.58672e6			0.882807
$625$	−1.53379e7	+	2.65660e7i	−1.57060	+	2.72036i
$626$	−1.54511e7	−	2.67620e7i	−1.57588	−	2.72950i
$627$	375912.	+	651099.i	0.0381872	+	0.0661421i
$628$	−5.19472e6	+	8.99753e6i	−0.525610	+	0.910383i
$629$	928404.			0.0935643
$630$		0			0
$631$	9.25978e6			0.925822			0.462911	−	0.886405i	$-0.346805\pi$
$631$	9.25978e6			0.925822			0.462911	+	0.886405i	$0.346805\pi$
$632$	1.58573e7	−	2.74656e7i	1.57920	−	2.73525i
$633$	−5.36305e6	−	9.28907e6i	−0.531989	−	0.921431i
$634$	4.87089e6	+	8.43663e6i	0.481266	+	0.833577i
$635$	−3.54379e6	+	6.13803e6i	−0.348766	+	0.604080i
$636$	2.29977e7			2.25446
$637$		0			0
$638$	1.02856e6			0.100041
$639$	2.48346e6	−	4.30148e6i	0.240605	−	0.416740i
$640$	1.43482e7	+	2.48517e7i	1.38467	+	2.39832i
$641$	−8.97094e6	−	1.55381e7i	−0.862369	−	1.49367i	−0.869636	−	0.493693i	$-0.835647\pi$
$641$	−8.97094e6	−	1.55381e7i	−0.862369	−	1.49367i	0.00726713	−	0.999974i	$-0.497687\pi$
$642$	1.01502e6	−	1.75807e6i	0.0971935	−	0.168344i
$643$	−6.70020e6			−0.639087			−0.319544	−	0.947572i	$-0.603530\pi$
$643$	−6.70020e6			−0.639087			−0.319544	+	0.947572i	$0.603530\pi$
$644$		0			0
$645$	3.52980e6			0.334080
$646$	−1.00788e6	+	1.74570e6i	−0.0950227	+	0.164584i
$647$	−5.62745e6	−	9.74703e6i	−0.528507	−	0.915402i	−0.999448	−	0.0332365i	$-0.989419\pi$
$647$	−5.62745e6	−	9.74703e6i	−0.528507	−	0.915402i	0.470940	−	0.882165i	$-0.343915\pi$
$648$	−1.18098e6	−	2.04552e6i	−0.110485	−	0.191366i
$649$	1.50420e6	−	2.60535e6i	0.140183	−	0.242803i
$650$	−5.43437e7			−5.04505
$651$		0			0
$652$	−1.02291e7			−0.942364
$653$	−6.58521e6	+	1.14059e7i	−0.604347	+	1.04676i	0.387807	+	0.921741i	$0.373233\pi$
$653$	−6.58521e6	+	1.14059e7i	−0.604347	+	1.04676i	−0.992154	+	0.125019i	$0.960101\pi$
$654$	899910.	+	1.55869e6i	0.0822725	+	0.142500i
$655$	8.14949e6	+	1.41153e7i	0.742211	+	1.28555i
$656$	−4.74334e6	+	8.21571e6i	−0.430353	+	0.745394i
$657$	−3.15268e6			−0.284949
$658$		0			0
$659$	−1.43453e7			−1.28676			−0.643380	−	0.765547i	$-0.722468\pi$
$659$	−1.43453e7			−1.28676			−0.643380	+	0.765547i	$0.722468\pi$
$660$	2.98411e6	−	5.16863e6i	0.266658	−	0.461866i
$661$	−7069.00	−	12243.9i	−0.000629295	−	0.00108997i	0.865711	−	0.500545i	$-0.166867\pi$
$661$	−7069.00	−	12243.9i	−0.000629295	−	0.00108997i	−0.866340	+	0.499455i	$0.833534\pi$
$662$	−3.90886e6	−	6.77034e6i	−0.346661	−	0.600435i
$663$	−669330.	+	1.15931e6i	−0.0591366	+	0.102428i
$664$	−2.58811e7			−2.27805
$665$		0			0
$666$	3.38742e6			0.295926
$667$	657384.	−	1.13862e6i	0.0572143	−	0.0990981i
$668$	−247792.	−	429188.i	−0.0214855	−	0.0372140i
$669$	982728.	+	1.70213e6i	0.0848922	+	0.147038i
$670$	−3.44479e7	+	5.96655e7i	−2.96466	+	5.13495i
$671$	993784.			0.0852090
$672$		0			0
$673$	1.37787e7			1.17266			0.586329	−	0.810073i	$-0.300573\pi$
$673$	1.37787e7			1.17266			0.586329	+	0.810073i	$0.300573\pi$
$674$	−1.74377e6	+	3.02030e6i	−0.147856	+	0.256094i
$675$	2.95646e6	+	5.12074e6i	0.249754	+	0.432587i
$676$	−2.63864e6	−	4.57026e6i	−0.222082	−	0.384657i
$677$	6.30776e6	−	1.09254e7i	0.528936	−	0.916144i	−0.470495	−	0.882403i	$-0.655924\pi$
$677$	6.30776e6	−	1.09254e7i	0.528936	−	0.916144i	0.999431	−	0.0337412i	$-0.0107422\pi$
$678$	−1.61154e6			−0.134638
$679$		0			0
$680$	8.47152e6			0.702569
$681$	−2.62283e6	+	4.54288e6i	−0.216722	+	0.375374i
$682$	1.70016e6	+	2.94476e6i	0.139968	+	0.242432i
$683$	543282.	+	940992.i	0.0445629	+	0.0771852i	0.887447	−	0.460911i	$-0.152477\pi$
$683$	543282.	+	940992.i	0.0445629	+	0.0771852i	−0.842884	+	0.538096i	$0.819144\pi$
$684$	−2.50063e6	+	4.33122e6i	−0.204366	+	0.353973i
$685$	2.71337e7			2.20944
$686$		0			0
$687$	8.64941e6			0.699189
$688$	2.63440e6	−	4.56291e6i	0.212183	−	0.367512i
$689$	−1.25886e7	−	2.18041e7i	−1.01025	−	1.74981i
$690$	−5.60952e6	−	9.71597e6i	−0.448542	−	0.776897i
$691$	9.56147e6	−	1.65609e7i	0.761780	−	1.31944i	−0.180153	−	0.983639i	$-0.557659\pi$
$691$	9.56147e6	−	1.65609e7i	0.761780	−	1.31944i	0.941932	−	0.335802i	$-0.109007\pi$
$692$	1.96625e7			1.56089
$693$		0			0
$694$	2.50625e7			1.97527
$695$	1.49950e7	−	2.59721e7i	1.17756	−	2.03960i
$696$	1.81116e6	+	3.13702e6i	0.141721	+	0.245468i
$697$	−739482.	−	1.28082e6i	−0.0576562	−	0.0998634i
$698$	1.52930e7	−	2.64883e7i	1.18811	−	2.05786i
$699$	−5.45395e6			−0.422200
$700$		0			0
$701$	1.15000e7			0.883897			0.441948	−	0.897040i	$-0.354287\pi$
$701$	1.15000e7			0.883897			0.441948	+	0.897040i	$0.354287\pi$
$702$	−2.44215e6	+	4.22993e6i	−0.187038	+	0.323959i
$703$	−1.89863e6	−	3.28852e6i	−0.144894	−	0.250964i
$704$	844928.	+	1.46346e6i	0.0642522	+	0.111288i
$705$	3.36571e6	−	5.82958e6i	0.255038	−	0.441738i
$706$	3.49291e7			2.63740
$707$		0			0
$708$	2.00124e7			1.50043
$709$	−3.48776e6	+	6.04097e6i	−0.260574	+	0.451327i	−0.966394	−	0.257064i	$-0.917245\pi$
$709$	−3.48776e6	+	6.04097e6i	−0.260574	+	0.451327i	0.705821	+	0.708390i	$0.250578\pi$
$710$	3.24996e7	+	5.62910e7i	2.41954	+	4.19076i
$711$	3.56789e6	+	6.17976e6i	0.264690	+	0.458456i
$712$	2.01272e7	−	3.48614e7i	1.48794	−	2.57718i
$713$	4.34650e6			0.320196
$714$		0			0
$715$	−6.53384e6			−0.477973
$716$	−6.78273e6	+	1.17480e7i	−0.494449	+	0.856411i
$717$	5.26565e6	+	9.12037e6i	0.382520	+	0.662544i
$718$	−1.06017e7	−	1.83627e7i	−0.767477	−	1.32931i
$719$	−721320.	+	1.24936e6i	−0.0520362	+	0.0901294i	−0.890870	−	0.454258i	$-0.849904\pi$
$719$	−721320.	+	1.24936e6i	−0.0520362	+	0.0901294i	0.838834	+	0.544387i	$0.183238\pi$
$720$	1.22265e7			0.878961
$721$		0			0
$722$	−1.65164e7			−1.17916
$723$	5.56610e6	−	9.64076e6i	0.396009	−	0.685907i
$724$	8.17870e6	+	1.41659e7i	0.579880	+	1.00438i
$725$	−4.53405e6	−	7.85320e6i	−0.320362	−	0.554884i
$726$	−6.86642e6	+	1.18930e7i	−0.483491	+	0.837431i
$727$	1.90334e7			1.33561			0.667807	−	0.744334i	$-0.267233\pi$
$727$	1.90334e7			1.33561			0.667807	+	0.744334i	$0.267233\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	2.06287e7	−	3.57299e7i	1.43273	−	2.48156i
$731$	410700.	+	711353.i	0.0284270	+	0.0492370i
$732$	3.30541e6	+	5.72514e6i	0.228007	+	0.394919i
$733$	2.72793e6	−	4.72491e6i	0.187531	−	0.324813i	−0.756896	−	0.653536i	$-0.773285\pi$
$733$	2.72793e6	−	4.72491e6i	0.187531	−	0.324813i	0.944426	+	0.328723i	$0.106618\pi$
$734$	−7.46592e6			−0.511497
$735$		0			0
$736$	−3.19872e6			−0.217662
$737$	−2.98982e6	+	5.17851e6i	−0.202757	+	0.351185i
$738$	−2.69811e6	−	4.67326e6i	−0.182355	−	0.315849i
$739$	−3.92599e6	−	6.80001e6i	−0.264446	−	0.458035i	0.702972	−	0.711217i	$-0.251856\pi$
$739$	−3.92599e6	−	6.80001e6i	−0.264446	−	0.458035i	−0.967418	+	0.253183i	$0.918523\pi$
$740$	−1.50719e7	+	2.61053e7i	−1.01179	+	1.75247i
$741$	5.47524e6			0.366317
$742$		0			0
$743$	−1.48695e7			−0.988154			−0.494077	−	0.869418i	$-0.664494\pi$
$743$	−1.48695e7			−0.988154			−0.494077	+	0.869418i	$0.664494\pi$
$744$	−5.98752e6	+	1.03707e7i	−0.396565	+	0.686871i
$745$	−2.16269e7	−	3.74588e7i	−1.42759	−	2.47265i
$746$	4.69517e6	+	8.13227e6i	0.308890	+	0.535014i
$747$	2.91163e6	−	5.04308e6i	0.190912	−	0.330670i
$748$	1.38883e6			0.0907603
$749$		0			0
$750$	−4.75664e7			−3.08779
$751$	1.25655e7	−	2.17640e7i	0.812977	−	1.40812i	−0.0977940	−	0.995207i	$-0.531179\pi$
$751$	1.25655e7	−	2.17640e7i	0.812977	−	1.40812i	0.910771	−	0.412911i	$-0.135488\pi$
$752$	−5.02387e6	−	8.70160e6i	−0.323962	−	0.561119i
$753$	−4.31869e6	−	7.48018e6i	−0.277565	−	0.480756i
$754$	3.74530e6	−	6.48705e6i	0.239915	−	0.415546i
$755$	3.84254e7			2.45330
$756$		0			0
$757$	−1.97874e7			−1.25501			−0.627507	−	0.778611i	$-0.715925\pi$
$757$	−1.97874e7			−1.25501			−0.627507	+	0.778611i	$0.715925\pi$
$758$	−2.58267e7	+	4.47332e7i	−1.63266	+	2.82785i
$759$	−486864.	−	843273.i	−0.0306763	−	0.0531329i
$760$	−1.73246e7	−	3.00072e7i	−1.08800	−	1.88448i
$761$	−7.48208e6	+	1.29593e7i	−0.468339	+	0.811187i	−0.999345	−	0.0361808i	$-0.988481\pi$
$761$	−7.48208e6	+	1.29593e7i	−0.468339	+	0.811187i	0.531006	+	0.847368i	$0.321814\pi$
$762$	−6.01776e6			−0.375446
$763$		0			0
$764$	1.97461e7			1.22391
$765$	−953046.	+	1.65072e6i	−0.0588790	+	0.101981i
$766$	2.00256e6	+	3.46854e6i	0.123314	+	0.213587i
$767$	−1.09545e7	−	1.89738e7i	−0.672364	−	1.16457i
$768$	−9.53741e6	+	1.65193e7i	−0.583482	+	1.01062i
$769$	−5.06419e6			−0.308812			−0.154406	−	0.988007i	$-0.549346\pi$
$769$	−5.06419e6			−0.308812			−0.154406	+	0.988007i	$0.549346\pi$
$770$		0			0
$771$	−1.09133e7			−0.661181
$772$	5.82944e6	−	1.00969e7i	0.352033	−	0.609739i
$773$	1.31512e7	+	2.27786e7i	0.791622	+	1.37113i	0.924962	+	0.380060i	$0.124097\pi$
$773$	1.31512e7	+	2.27786e7i	0.791622	+	1.37113i	−0.133340	+	0.991070i	$0.542570\pi$
$774$	1.49850e6	+	2.59548e6i	0.0899092	+	0.155727i
$775$	1.49891e7	−	2.59619e7i	0.896442	−	1.55268i
$776$	5.43046e7			3.23729
$777$		0			0
$778$	3.06822e6			0.181735
$779$	−3.02455e6	+	5.23867e6i	−0.178573	+	0.309298i
$780$	−2.17321e7	−	3.76411e7i	−1.27899	−	2.21527i
$781$	2.82072e6	+	4.88563e6i	0.165475	+	0.286611i
$782$	1.30536e6	−	2.26095e6i	0.0763332	−	0.132213i
$783$	−815022.			−0.0475078
$784$		0			0
$785$	1.61953e7			0.938027
$786$	−6.91938e6	+	1.19847e7i	−0.399495	+	0.691945i
$787$	5.02625e6	+	8.70572e6i	0.289273	+	0.501035i	0.973636	−	0.228106i	$-0.0732533\pi$
$787$	5.02625e6	+	8.70572e6i	0.289273	+	0.501035i	−0.684364	+	0.729141i	$0.739920\pi$
$788$	−1.36677e7	−	2.36731e7i	−0.784113	−	1.35812i
$789$	−5.63735e6	+	9.76417e6i	−0.322391	+	0.558397i
$790$	−9.33818e7			−5.32346
$791$		0			0
$792$	2.68272e6			0.151972
$793$	3.61867e6	−	6.26772e6i	0.204346	−	0.353938i
$794$	−1.91710e7	−	3.32052e7i	−1.07918	−	1.86920i
$795$	−1.79247e7	−	3.10465e7i	−1.00585	−	1.74219i
$796$	−8.81198e6	+	1.52628e7i	−0.492937	+	0.853791i
$797$	−2.78516e7			−1.55312			−0.776560	−	0.630044i	$-0.783037\pi$
$797$	−2.78516e7			−1.55312			−0.776560	+	0.630044i	$0.783037\pi$
$798$		0			0
$799$	1.56643e6			0.0868050
$800$	−1.10310e7	+	1.91062e7i	−0.609380	+	1.05548i
$801$	4.52863e6	+	7.84382e6i	0.249394	+	0.431963i
$802$	1.64678e7	+	2.85230e7i	0.904062	+	1.56588i
$803$	1.79041e6	−	3.10108e6i	0.0979860	−	0.169717i
$804$	−3.97776e7			−2.17019
$805$		0			0
$806$	2.47632e7			1.34267
$807$	615897.	−	1.06676e6i	0.0332908	−	0.0576614i
$808$	−2.47237e7	−	4.28227e7i	−1.33225	−	2.30752i
$809$	9.84680e6	+	1.70551e7i	0.528961	+	0.916187i	0.999430	+	0.0337705i	$0.0107515\pi$
$809$	9.84680e6	+	1.70551e7i	0.528961	+	0.916187i	−0.470469	+	0.882417i	$0.655915\pi$
$810$	−3.47733e6	+	6.02291e6i	−0.186223	+	0.322548i
$811$	−5.05617e6			−0.269942			−0.134971	−	0.990850i	$-0.543094\pi$
$811$	−5.05617e6			−0.269942			−0.134971	+	0.990850i	$0.543094\pi$
$812$		0			0
$813$	−8.64806e6			−0.458873
$814$	−1.92372e6	+	3.33198e6i	−0.101761	+	0.176255i
$815$	7.97268e6	+	1.38091e7i	0.420446	+	0.728234i
$816$	1.42258e6	+	2.46397e6i	0.0747911	+	0.129542i
$817$	1.67980e6	−	2.90950e6i	0.0880445	−	0.152498i
$818$	1.35473e7			0.707894
$819$		0			0
$820$	4.80197e7			2.49393
$821$	1.41162e6	−	2.44500e6i	0.0730904	−	0.126596i	−0.827164	−	0.561961i	$-0.810047\pi$
$821$	1.41162e6	−	2.44500e6i	0.0730904	−	0.126596i	0.900254	+	0.435365i	$0.143381\pi$
$822$	1.15190e7	+	1.99515e7i	0.594615	+	1.02990i
$823$	−1.27370e7	−	2.20612e7i	−0.655494	−	1.13535i	−0.981770	−	0.190074i	$-0.939127\pi$
$823$	−1.27370e7	−	2.20612e7i	−0.655494	−	1.13535i	0.326276	−	0.945275i	$-0.394206\pi$
$824$	5.17680e6	−	8.96648e6i	0.265609	−	0.460049i
$825$	−6.71591e6			−0.343534
$826$		0			0
$827$	−1.75616e7			−0.892893			−0.446446	−	0.894810i	$-0.647311\pi$
$827$	−1.75616e7			−0.892893			−0.446446	+	0.894810i	$0.647311\pi$
$828$	3.23870e6	−	5.60960e6i	0.164171	−	0.284352i
$829$	4.57364e6	+	7.92178e6i	0.231140	+	0.400347i	0.958144	−	0.286287i	$-0.0924210\pi$
$829$	4.57364e6	+	7.92178e6i	0.231140	+	0.400347i	−0.727004	+	0.686634i	$0.759088\pi$
$830$	3.81028e7	+	6.59959e7i	1.91982	+	3.32523i
$831$	4.07624e6	−	7.06025e6i	0.204765	−	0.354664i
$832$	1.23066e7			0.616351
$833$		0			0
$834$	2.54632e7			1.26764
$835$	−386264.	+	669029.i	−0.0191720	+	0.0332069i
$836$	−2.84022e6	−	4.91941e6i	−0.140552	−	0.243443i
$837$	−1.34719e6	−	2.33340e6i	−0.0664685	−	0.115127i
$838$	2.54099e7	−	4.40113e7i	1.24995	−	2.16498i
$839$	1.09891e7			0.538961			0.269481	−	0.963006i	$-0.413148\pi$
$839$	1.09891e7			0.538961			0.269481	+	0.963006i	$0.413148\pi$
$840$		0			0
$841$	−1.92612e7			−0.939061
$842$	−3.14011e6	+	5.43883e6i	−0.152639	+	0.264378i
$843$	−148779.	−	257693.i	−0.00721062	−	0.0124892i
$844$	4.05208e7	+	7.01841e7i	1.95804	+	3.39143i
$845$	−4.11317e6	+	7.12422e6i	−0.198169	+	0.343238i
$846$	5.71536e6			0.274548
$847$		0			0
$848$	−5.35111e7			−2.55537
$849$	3.88615e6	−	6.73100e6i	0.185033	−	0.320487i
$850$	−9.00321e6	−	1.55940e7i	−0.427415	−	0.740305i
$851$	2.45902e6	+	4.25914e6i	0.116396	+	0.201604i
$852$	−1.87639e7	+	3.25001e7i	−0.885573	+	1.53386i
$853$	1.34854e7			0.634586			0.317293	−	0.948328i	$-0.397226\pi$
$853$	1.34854e7			0.634586			0.317293	+	0.948328i	$0.397226\pi$
$854$		0			0
$855$	7.79609e6			0.364722
$856$	−4.06008e6	+	7.03226e6i	−0.189387	+	0.328028i
$857$	5.35160e6	+	9.26925e6i	0.248904	+	0.431114i	0.963222	−	0.268707i	$-0.0865963\pi$
$857$	5.35160e6	+	9.26925e6i	0.248904	+	0.431114i	−0.714318	+	0.699821i	$0.753263\pi$
$858$	−2.77380e6	−	4.80436e6i	−0.128634	−	0.222801i
$859$	−6.68736e6	+	1.15829e7i	−0.309223	+	0.535590i	−0.978193	−	0.207700i	$-0.933402\pi$
$859$	−6.68736e6	+	1.15829e7i	−0.309223	+	0.535590i	0.668970	+	0.743290i	$0.266736\pi$
$860$	−2.66696e7			−1.22962
$861$		0			0
$862$	−3.00086e7			−1.37556
$863$	−9.98839e6	+	1.73004e7i	−0.456529	+	0.790732i	−0.998775	−	0.0494883i	$-0.984241\pi$
$863$	−9.98839e6	+	1.73004e7i	−0.456529	+	0.790732i	0.542245	+	0.840220i	$0.317574\pi$
$864$	991440.	+	1.71722e6i	0.0451837	+	0.0782605i
$865$	−1.53252e7	−	2.65440e7i	−0.696410	−	1.20622i
$866$	6.07481e6	−	1.05219e7i	0.275257	−	0.476759i
$867$	1.23352e7			0.557310
$868$		0			0
$869$	−8.10483e6			−0.364078
$870$	5.33286e6	−	9.23678e6i	0.238870	−	0.413735i
$871$	2.17737e7	+	3.77131e7i	0.972492	+	1.68441i
$872$	−3.59964e6	−	6.23476e6i	−0.160313	−	0.277670i
$873$	−6.10926e6	+	1.05816e7i	−0.271302	+	0.469909i
$874$	−1.06781e7			−0.472840
$875$		0			0
$876$	2.38203e7			1.04878
$877$	−4.40554e6	+	7.63061e6i	−0.193419	+	0.335012i	−0.946381	−	0.323052i	$-0.895291\pi$
$877$	−4.40554e6	+	7.63061e6i	−0.193419	+	0.335012i	0.752962	+	0.658064i	$0.228624\pi$
$878$	2.00327e7	+	3.46976e7i	0.877006	+	1.51902i
$879$	6.01896e6	+	1.04251e7i	0.262754	+	0.455103i
$880$	−6.94342e6	+	1.20264e7i	−0.302250	+	0.523513i
$881$	−4.01078e7			−1.74096			−0.870481	−	0.492202i	$-0.836192\pi$
$881$	−4.01078e7			−1.74096			−0.870481	+	0.492202i	$0.836192\pi$
$882$		0			0
$883$	1.49664e7			0.645976			0.322988	−	0.946403i	$-0.395313\pi$
$883$	1.49664e7			0.645976			0.322988	+	0.946403i	$0.395313\pi$
$884$	5.05716e6	−	8.75926e6i	0.217659	−	0.376996i
$885$	−1.55979e7	−	2.70164e7i	−0.669434	−	1.15949i
$886$	2.72375e7	+	4.71768e7i	1.16569	+	2.01904i
$887$	−287572.	+	498089.i	−0.0122726	+	0.0212568i	−0.872096	−	0.489334i	$-0.837240\pi$
$887$	−287572.	+	498089.i	−0.0122726	+	0.0212568i	0.859824	+	0.510591i	$0.170573\pi$
$888$	−1.35497e7			−0.576629
$889$		0			0
$890$	−1.18527e8			−5.01583
$891$	−301806.	+	522743.i	−0.0127360	+	0.0220594i
$892$	−7.42506e6	−	1.28606e7i	−0.312455	−	0.541188i
$893$	−3.20342e6	−	5.54849e6i	−0.134427	−	0.232834i
$894$	1.83624e7	−	3.18047e7i	0.768398	−	1.33090i
$895$	2.11462e7			0.882417
$896$		0			0
$897$	−7.09128e6			−0.294268
$898$	9.07887e6	−	1.57251e7i	0.375700	−	0.650731i
$899$	2.06606e6	+	3.57853e6i	0.0852598	+	0.147674i
$900$	−2.23377e7	−	3.86900e7i	−0.919247	−	1.59218i
$901$	4.17116e6	−	7.22466e6i	0.171177	−	0.296487i
$902$	6.12904e6			0.250828
$903$		0			0
$904$	6.44616e6			0.262349
$905$	1.27492e7	−	2.20822e7i	0.517440	−	0.896232i
$906$	1.63127e7	+	2.82544e7i	0.660245	+	1.14358i
$907$	1.66684e7	+	2.88704e7i	0.672783	+	1.16529i	0.977112	+	0.212727i	$0.0682344\pi$
$907$	1.66684e7	+	2.88704e7i	0.672783	+	1.16529i	−0.304329	+	0.952567i	$0.598432\pi$
$908$	1.98170e7	−	3.43240e7i	0.797669	−	1.38160i
$909$	1.11257e7			0.446598
$910$		0			0
$911$	2.17451e7			0.868090			0.434045	−	0.900891i	$-0.357086\pi$
$911$	2.17451e7			0.868090			0.434045	+	0.900891i	$0.357086\pi$
$912$	5.81846e6	−	1.00779e7i	0.231644	−	0.401219i
$913$	3.30703e6	+	5.72795e6i	0.131299	+	0.227417i
$914$	2.65041e7	+	4.59065e7i	1.04942	+	1.81764i
$915$	5.15255e6	−	8.92449e6i	0.203456	−	0.352396i
$916$	−6.53511e7			−2.57344
$917$		0			0
$918$	−1.61838e6			−0.0633831
$919$	2.01993e6	−	3.49862e6i	0.0788947	−	0.136650i	−0.823879	−	0.566766i	$-0.808194\pi$
$919$	2.01993e6	−	3.49862e6i	0.0788947	−	0.136650i	0.902773	+	0.430117i	$0.141528\pi$
$920$	2.24381e7	+	3.88639e7i	0.874009	+	1.51383i
$921$	5.97692e6	+	1.03523e7i	0.232182	+	0.402151i
$922$	1.60190e7	−	2.77458e7i	0.620596	−	1.07490i
$923$	4.10844e7			1.58735
$924$		0			0
$925$	3.39202e7			1.30348
$926$	5.59264e6	−	9.68674e6i	0.214333	−	0.371236i
$927$	1.16478e6	+	2.01746e6i	0.0445189	+	0.0771090i
$928$	−1.52048e6	−	2.63355e6i	−0.0579577	−	0.100386i
$929$	3.84839e6	−	6.66561e6i	0.146299	−	0.253397i	−0.783558	−	0.621319i	$-0.786597\pi$
$929$	3.84839e6	−	6.66561e6i	0.146299	−	0.253397i	0.929857	+	0.367922i	$0.119931\pi$
$930$	3.52598e7			1.33682
$931$		0			0
$932$	4.12076e7			1.55395
$933$	2.99624e6	−	5.18965e6i	0.112687	−	0.195179i
$934$	−1.92567e7	−	3.33536e7i	−0.722295	−	1.25105i
$935$	−1.08247e6	−	1.87490e6i	−0.0404937	−	0.0701372i
$936$	9.76860e6	−	1.69197e7i	0.364454	−	0.631253i
$937$	453558.			0.0168766			0.00843828	−	0.999964i	$-0.497314\pi$
$937$	453558.			0.0168766			0.00843828	+	0.999964i	$0.497314\pi$
$938$		0			0
$939$	−2.78119e7			−1.02936
$940$	−2.54298e7	+	4.40457e7i	−0.938693	+	1.62586i
$941$	−1.21926e7	−	2.11182e7i	−0.448873	−	0.777470i	0.549440	−	0.835533i	$-0.314841\pi$
$941$	−1.21926e7	−	2.11182e7i	−0.448873	−	0.777470i	−0.998313	+	0.0580627i	$0.981508\pi$
$942$	6.87537e6	+	1.19085e7i	0.252446	+	0.437250i
$943$	3.91726e6	−	6.78489e6i	0.143451	−	0.248464i
$944$	−4.65648e7			−1.70070
$945$		0			0
$946$	−3.40400e6			−0.123669
$947$	1.09372e7	−	1.89438e7i	0.396308	−	0.686425i	−0.596960	−	0.802271i	$-0.703625\pi$
$947$	1.09372e7	−	1.89438e7i	0.396308	−	0.686425i	0.993267	+	0.115846i	$0.0369581\pi$
$948$	−2.69574e7	−	4.66915e7i	−0.974219	−	1.68740i
$949$	−1.30389e7	−	2.25840e7i	−0.469975	−	0.814020i
$950$	−3.68239e7	+	6.37809e7i	−1.32380	+	2.29288i
$951$	8.76760e6			0.314362
$952$		0			0
$953$	−3.93319e7			−1.40286			−0.701428	−	0.712741i	$-0.747454\pi$
$953$	−3.93319e7			−1.40286			−0.701428	+	0.712741i	$0.747454\pi$
$954$	1.52191e7	−	2.63602e7i	0.541399	−	0.937731i
$955$	−1.53904e7	−	2.66569e7i	−0.546060	−	0.945803i
$956$	−3.97849e7	−	6.89095e7i	−1.40791	−	2.43856i
$957$	462852.	−	801683.i	0.0163366	−	0.0282959i
$958$	−1.43536e7			−0.505297
$959$		0			0
$960$	1.75231e7			0.613666
$961$	7.48437e6	−	1.29633e7i	0.261425	−	0.452801i
$962$	1.40097e7	+	2.42655e7i	0.488080	+	0.845380i
$963$	−913518.	−	1.58226e6i	−0.0317433	−	0.0549809i
$964$	−4.20549e7	+	7.28413e7i	−1.45755	+	2.52456i
$965$	−1.81741e7			−0.628254
$966$		0			0
$967$	3.85234e7			1.32483			0.662413	−	0.749139i	$-0.269532\pi$
$967$	3.85234e7			1.32483			0.662413	+	0.749139i	$0.269532\pi$
$968$	2.74657e7	−	4.75719e7i	0.942110	−	1.63178i
$969$	907092.	+	1.57113e6i	0.0310343	+	0.0537530i
$970$	−7.99484e7	−	1.38475e8i	−2.72823	−	4.72543i
$971$	1.21771e7	−	2.10914e7i	0.414473	−	0.717889i	−0.580900	−	0.813975i	$-0.697299\pi$
$971$	1.21771e7	−	2.10914e7i	0.414473	−	0.717889i	0.995373	+	0.0960862i	$0.0306324\pi$
$972$	−4.01533e6			−0.136319
$973$		0			0
$974$	4.61097e7			1.55738
$975$	−2.44547e7	+	4.23567e7i	−0.823854	+	1.42696i
$976$	−7.69102e6	−	1.33212e7i	−0.258440	−	0.447631i
$977$	−8.12670e6	−	1.40759e7i	−0.272382	−	0.471779i	0.697090	−	0.716984i	$-0.254478\pi$
$977$	−8.12670e6	−	1.40759e7i	−0.272382	−	0.471779i	−0.969471	+	0.245205i	$0.921145\pi$
$978$	−6.76926e6	+	1.17247e7i	−0.226305	+	0.391972i
$979$	−1.02873e7			−0.343038
$980$		0			0
$981$	1.61984e6			0.0537402
$982$	−3.70259e7	+	6.41307e7i	−1.22526	+	2.12221i
$983$	−126228.	−	218633.i	−0.00416650	−	0.00721660i	0.863935	−	0.503604i	$-0.167993\pi$
$983$	−126228.	−	218633.i	−0.00416650	−	0.00721660i	−0.868101	+	0.496387i	$0.834660\pi$
$984$	1.07924e7	+	1.86931e7i	0.355330	+	0.615450i
$985$	−2.13055e7	+	3.69022e7i	−0.699682	+	1.21188i
$986$	2.48196e6			0.0813022
$987$		0			0
$988$	−4.13685e7			−1.34827
$989$	−2.17560e6	+	3.76825e6i	−0.0707275	+	0.122504i
$990$	−3.94956e6	−	6.84084e6i	−0.128074	−	0.221831i
$991$	1.24864e7	+	2.16271e7i	0.403880	+	0.699541i	0.994190	−	0.107635i	$-0.0343278\pi$
$991$	1.24864e7	+	2.16271e7i	0.403880	+	0.699541i	−0.590310	+	0.807177i	$0.700995\pi$
$992$	5.02656e6	−	8.70626e6i	0.162178	−	0.280900i
$993$	−7.03595e6			−0.226438
$994$		0			0
$995$	2.74727e7			0.879717
$996$	−2.19990e7	+	3.81033e7i	−0.702674	+	1.21707i
$997$	−1.80491e7	−	3.12620e7i	−0.575067	−	0.996046i	−0.996034	−	0.0889698i	$-0.971643\pi$
$997$	−1.80491e7	−	3.12620e7i	−0.575067	−	0.996046i	0.420967	−	0.907076i	$-0.361691\pi$
$998$	−1.96716e7	−	3.40722e7i	−0.625193	−	1.08287i
$999$	1.52434e6	−	2.64023e6i	0.0483246	−	0.0837006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.b.79.1		2
7.2	even	3		147.6.a.g.1.1		1
7.3	odd	6		147.6.e.a.67.1		2
7.4	even	3	inner	147.6.e.b.67.1		2
7.5	odd	6		21.6.a.d.1.1	✓	1
7.6	odd	2		147.6.e.a.79.1		2
21.2	odd	6		441.6.a.b.1.1		1
21.5	even	6		63.6.a.a.1.1		1
28.19	even	6		336.6.a.a.1.1		1
35.12	even	12		525.6.d.a.274.2		2
35.19	odd	6		525.6.a.a.1.1		1
35.33	even	12		525.6.d.a.274.1		2
84.47	odd	6		1008.6.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.a.d.1.1	✓	1	7.5	odd	6
63.6.a.a.1.1		1	21.5	even	6
147.6.a.g.1.1		1	7.2	even	3
147.6.e.a.67.1		2	7.3	odd	6
147.6.e.a.79.1		2	7.6	odd	2
147.6.e.b.67.1		2	7.4	even	3	inner
147.6.e.b.79.1		2	1.1	even	1	trivial
336.6.a.a.1.1		1	28.19	even	6
441.6.a.b.1.1		1	21.2	odd	6
525.6.a.a.1.1		1	35.19	odd	6
525.6.d.a.274.1		2	35.33	even	12
525.6.d.a.274.2		2	35.12	even	12
1008.6.a.bc.1.1		1	84.47	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)

\(f(q)\)	\(=\)	\(q+(-5.00000 + 8.66025i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-34.0000 - 58.8897i) q^{4} +(-53.0000 + 91.7987i) q^{5} -90.0000 q^{6} +360.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-5.00000 + 8.66025i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-34.0000 - 58.8897i) q^{4} +(-53.0000 + 91.7987i) q^{5} -90.0000 q^{6} +360.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-530.000 - 917.987i) q^{10} +(-46.0000 - 79.6743i) q^{11} +(306.000 - 530.008i) q^{12} -670.000 q^{13} -954.000 q^{15} +(-712.000 + 1233.22i) q^{16} +(-111.000 - 192.258i) q^{17} +(-405.000 - 701.481i) q^{18} +(-454.000 + 786.351i) q^{19} +7208.00 q^{20} +920.000 q^{22} +(588.000 - 1018.45i) q^{23} +(1620.00 + 2805.92i) q^{24} +(-4055.50 - 7024.33i) q^{25} +(3350.00 - 5802.37i) q^{26} -729.000 q^{27} +1118.00 q^{29} +(4770.00 - 8261.88i) q^{30} +(1848.00 + 3200.83i) q^{31} +(-1360.00 - 2355.59i) q^{32} +(414.000 - 717.069i) q^{33} +2220.00 q^{34} +5508.00 q^{36} +(-2091.00 + 3621.72i) q^{37} +(-4540.00 - 7863.51i) q^{38} +(-3015.00 - 5222.13i) q^{39} +(-19080.0 + 33047.5i) q^{40} +6662.00 q^{41} -3700.00 q^{43} +(-3128.00 + 5417.85i) q^{44} +(-4293.00 - 7435.69i) q^{45} +(5880.00 + 10184.5i) q^{46} +(-3528.00 + 6110.68i) q^{47} -12816.0 q^{48} +81110.0 q^{50} +(999.000 - 1730.32i) q^{51} +(22780.0 + 39456.1i) q^{52} +(18789.0 + 32543.5i) q^{53} +(3645.00 - 6313.33i) q^{54} +9752.00 q^{55} -8172.00 q^{57} +(-5590.00 + 9682.16i) q^{58} +(16350.0 + 28319.0i) q^{59} +(32436.0 + 56180.8i) q^{60} +(-5401.00 + 9354.81i) q^{61} -36960.0 q^{62} -18368.0 q^{64} +(35510.0 - 61505.1i) q^{65} +(4140.00 + 7170.69i) q^{66} +(-32498.0 - 56288.2i) q^{67} +(-7548.00 + 13073.5i) q^{68} +10584.0 q^{69} -61320.0 q^{71} +(-14580.0 + 25253.3i) q^{72} +(19461.0 + 33707.4i) q^{73} +(-20910.0 - 36217.2i) q^{74} +(36499.5 - 63219.0i) q^{75} +61744.0 q^{76} +60300.0 q^{78} +(44048.0 - 76293.4i) q^{79} +(-75472.0 - 130721. i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-33310.0 + 57694.6i) q^{82} -71892.0 q^{83} +23532.0 q^{85} +(18500.0 - 32042.9i) q^{86} +(5031.00 + 8713.95i) q^{87} +(-16560.0 - 28682.8i) q^{88} +(55909.0 - 96837.2i) q^{89} +85860.0 q^{90} -79968.0 q^{92} +(-16632.0 + 28807.5i) q^{93} +(-35280.0 - 61106.8i) q^{94} +(-48124.0 - 83353.2i) q^{95} +(12240.0 - 21200.3i) q^{96} +150846. q^{97} +7452.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 10 q^{2} + 9 q^{3} - 68 q^{4} - 106 q^{5} - 180 q^{6} + 720 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q - 10 * q^2 + 9 * q^3 - 68 * q^4 - 106 * q^5 - 180 * q^6 + 720 * q^8 - 81 * q^9	\( 2 q - 10 q^{2} + 9 q^{3} - 68 q^{4} - 106 q^{5} - 180 q^{6} + 720 q^{8} - 81 q^{9} - 1060 q^{10} - 92 q^{11} + 612 q^{12} - 1340 q^{13} - 1908 q^{15} - 1424 q^{16} - 222 q^{17} - 810 q^{18} - 908 q^{19} + 14416 q^{20} + 1840 q^{22} + 1176 q^{23} + 3240 q^{24} - 8111 q^{25} + 6700 q^{26} - 1458 q^{27} + 2236 q^{29} + 9540 q^{30} + 3696 q^{31} - 2720 q^{32} + 828 q^{33} + 4440 q^{34} + 11016 q^{36} - 4182 q^{37} - 9080 q^{38} - 6030 q^{39} - 38160 q^{40} + 13324 q^{41} - 7400 q^{43} - 6256 q^{44} - 8586 q^{45} + 11760 q^{46} - 7056 q^{47} - 25632 q^{48} + 162220 q^{50} + 1998 q^{51} + 45560 q^{52} + 37578 q^{53} + 7290 q^{54} + 19504 q^{55} - 16344 q^{57} - 11180 q^{58} + 32700 q^{59} + 64872 q^{60} - 10802 q^{61} - 73920 q^{62} - 36736 q^{64} + 71020 q^{65} + 8280 q^{66} - 64996 q^{67} - 15096 q^{68} + 21168 q^{69} - 122640 q^{71} - 29160 q^{72} + 38922 q^{73} - 41820 q^{74} + 72999 q^{75} + 123488 q^{76} + 120600 q^{78} + 88096 q^{79} - 150944 q^{80} - 6561 q^{81} - 66620 q^{82} - 143784 q^{83} + 47064 q^{85} + 37000 q^{86} + 10062 q^{87} - 33120 q^{88} + 111818 q^{89} + 171720 q^{90} - 159936 q^{92} - 33264 q^{93} - 70560 q^{94} - 96248 q^{95} + 24480 q^{96} + 301692 q^{97} + 14904 q^{99}+O(q^{100}) \) 2 * q - 10 * q^2 + 9 * q^3 - 68 * q^4 - 106 * q^5 - 180 * q^6 + 720 * q^8 - 81 * q^9 - 1060 * q^10 - 92 * q^11 + 612 * q^12 - 1340 * q^13 - 1908 * q^15 - 1424 * q^16 - 222 * q^17 - 810 * q^18 - 908 * q^19 + 14416 * q^20 + 1840 * q^22 + 1176 * q^23 + 3240 * q^24 - 8111 * q^25 + 6700 * q^26 - 1458 * q^27 + 2236 * q^29 + 9540 * q^30 + 3696 * q^31 - 2720 * q^32 + 828 * q^33 + 4440 * q^34 + 11016 * q^36 - 4182 * q^37 - 9080 * q^38 - 6030 * q^39 - 38160 * q^40 + 13324 * q^41 - 7400 * q^43 - 6256 * q^44 - 8586 * q^45 + 11760 * q^46 - 7056 * q^47 - 25632 * q^48 + 162220 * q^50 + 1998 * q^51 + 45560 * q^52 + 37578 * q^53 + 7290 * q^54 + 19504 * q^55 - 16344 * q^57 - 11180 * q^58 + 32700 * q^59 + 64872 * q^60 - 10802 * q^61 - 73920 * q^62 - 36736 * q^64 + 71020 * q^65 + 8280 * q^66 - 64996 * q^67 - 15096 * q^68 + 21168 * q^69 - 122640 * q^71 - 29160 * q^72 + 38922 * q^73 - 41820 * q^74 + 72999 * q^75 + 123488 * q^76 + 120600 * q^78 + 88096 * q^79 - 150944 * q^80 - 6561 * q^81 - 66620 * q^82 - 143784 * q^83 + 47064 * q^85 + 37000 * q^86 + 10062 * q^87 - 33120 * q^88 + 111818 * q^89 + 171720 * q^90 - 159936 * q^92 - 33264 * q^93 - 70560 * q^94 - 96248 * q^95 + 24480 * q^96 + 301692 * q^97 + 14904 * q^99

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