LMFDB - Embedded newform 147.6.e.f.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:	$0$
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:	$\Z[a_1, a_2]$
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.f.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(4.50000 + 7.79423i) q^{3} +(15.5000 + 26.8468i) q^{4} +(17.0000 - 29.4449i) q^{5} -9.00000 q^{6} -63.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(4.50000 + 7.79423i) q^{3} +(15.5000 + 26.8468i) q^{4} +(17.0000 - 29.4449i) q^{5} -9.00000 q^{6} -63.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(17.0000 + 29.4449i) q^{10} +(170.000 + 294.449i) q^{11} +(-139.500 + 241.621i) q^{12} +454.000 q^{13} +306.000 q^{15} +(-464.500 + 804.538i) q^{16} +(399.000 + 691.088i) q^{17} +(-40.5000 - 70.1481i) q^{18} +(-446.000 + 772.495i) q^{19} +1054.00 q^{20} -340.000 q^{22} +(1596.00 - 2764.35i) q^{23} +(-283.500 - 491.036i) q^{24} +(984.500 + 1705.20i) q^{25} +(-227.000 + 393.176i) q^{26} -729.000 q^{27} -8242.00 q^{29} +(-153.000 + 265.004i) q^{30} +(1248.00 + 2161.60i) q^{31} +(-1472.50 - 2550.44i) q^{32} +(-1530.00 + 2650.04i) q^{33} -798.000 q^{34} -2511.00 q^{36} +(-4899.00 + 8485.32i) q^{37} +(-446.000 - 772.495i) q^{38} +(2043.00 + 3538.58i) q^{39} +(-1071.00 + 1855.03i) q^{40} +19834.0 q^{41} -17236.0 q^{43} +(-5270.00 + 9127.91i) q^{44} +(1377.00 + 2385.03i) q^{45} +(1596.00 + 2764.35i) q^{46} +(-4464.00 + 7731.87i) q^{47} -8361.00 q^{48} -1969.00 q^{50} +(-3591.00 + 6219.79i) q^{51} +(7037.00 + 12188.4i) q^{52} +(-75.0000 - 129.904i) q^{53} +(364.500 - 631.333i) q^{54} +11560.0 q^{55} -8028.00 q^{57} +(4121.00 - 7137.78i) q^{58} +(21198.0 + 36716.0i) q^{59} +(4743.00 + 8215.12i) q^{60} +(-7379.00 + 12780.8i) q^{61} -2496.00 q^{62} -26783.0 q^{64} +(7718.00 - 13368.0i) q^{65} +(-1530.00 - 2650.04i) q^{66} +(838.000 + 1451.46i) q^{67} +(-12369.0 + 21423.7i) q^{68} +28728.0 q^{69} +14568.0 q^{71} +(2551.50 - 4419.33i) q^{72} +(-39189.0 - 67877.3i) q^{73} +(-4899.00 - 8485.32i) q^{74} +(-8860.50 + 15346.8i) q^{75} -27652.0 q^{76} -4086.00 q^{78} +(1136.00 - 1967.61i) q^{79} +(15793.0 + 27354.3i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-9917.00 + 17176.7i) q^{82} -37764.0 q^{83} +27132.0 q^{85} +(8618.00 - 14926.8i) q^{86} +(-37089.0 - 64240.0i) q^{87} +(-10710.0 - 18550.3i) q^{88} +(58643.0 - 101573. i) q^{89} -2754.00 q^{90} +98952.0 q^{92} +(-11232.0 + 19454.4i) q^{93} +(-4464.00 - 7731.87i) q^{94} +(15164.0 + 26264.8i) q^{95} +(13252.5 - 22954.0i) q^{96} +10002.0 q^{97} -27540.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 9 q^{3} + 31 q^{4} + 34 q^{5} - 18 q^{6} - 126 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q - q^2 + 9 * q^3 + 31 * q^4 + 34 * q^5 - 18 * q^6 - 126 * q^8 - 81 * q^9	\( 2 q - q^{2} + 9 q^{3} + 31 q^{4} + 34 q^{5} - 18 q^{6} - 126 q^{8} - 81 q^{9} + 34 q^{10} + 340 q^{11} - 279 q^{12} + 908 q^{13} + 612 q^{15} - 929 q^{16} + 798 q^{17} - 81 q^{18} - 892 q^{19} + 2108 q^{20} - 680 q^{22} + 3192 q^{23} - 567 q^{24} + 1969 q^{25} - 454 q^{26} - 1458 q^{27} - 16484 q^{29} - 306 q^{30} + 2496 q^{31} - 2945 q^{32} - 3060 q^{33} - 1596 q^{34} - 5022 q^{36} - 9798 q^{37} - 892 q^{38} + 4086 q^{39} - 2142 q^{40} + 39668 q^{41} - 34472 q^{43} - 10540 q^{44} + 2754 q^{45} + 3192 q^{46} - 8928 q^{47} - 16722 q^{48} - 3938 q^{50} - 7182 q^{51} + 14074 q^{52} - 150 q^{53} + 729 q^{54} + 23120 q^{55} - 16056 q^{57} + 8242 q^{58} + 42396 q^{59} + 9486 q^{60} - 14758 q^{61} - 4992 q^{62} - 53566 q^{64} + 15436 q^{65} - 3060 q^{66} + 1676 q^{67} - 24738 q^{68} + 57456 q^{69} + 29136 q^{71} + 5103 q^{72} - 78378 q^{73} - 9798 q^{74} - 17721 q^{75} - 55304 q^{76} - 8172 q^{78} + 2272 q^{79} + 31586 q^{80} - 6561 q^{81} - 19834 q^{82} - 75528 q^{83} + 54264 q^{85} + 17236 q^{86} - 74178 q^{87} - 21420 q^{88} + 117286 q^{89} - 5508 q^{90} + 197904 q^{92} - 22464 q^{93} - 8928 q^{94} + 30328 q^{95} + 26505 q^{96} + 20004 q^{97} - 55080 q^{99}+O(q^{100}) \) 2 * q - q^2 + 9 * q^3 + 31 * q^4 + 34 * q^5 - 18 * q^6 - 126 * q^8 - 81 * q^9 + 34 * q^10 + 340 * q^11 - 279 * q^12 + 908 * q^13 + 612 * q^15 - 929 * q^16 + 798 * q^17 - 81 * q^18 - 892 * q^19 + 2108 * q^20 - 680 * q^22 + 3192 * q^23 - 567 * q^24 + 1969 * q^25 - 454 * q^26 - 1458 * q^27 - 16484 * q^29 - 306 * q^30 + 2496 * q^31 - 2945 * q^32 - 3060 * q^33 - 1596 * q^34 - 5022 * q^36 - 9798 * q^37 - 892 * q^38 + 4086 * q^39 - 2142 * q^40 + 39668 * q^41 - 34472 * q^43 - 10540 * q^44 + 2754 * q^45 + 3192 * q^46 - 8928 * q^47 - 16722 * q^48 - 3938 * q^50 - 7182 * q^51 + 14074 * q^52 - 150 * q^53 + 729 * q^54 + 23120 * q^55 - 16056 * q^57 + 8242 * q^58 + 42396 * q^59 + 9486 * q^60 - 14758 * q^61 - 4992 * q^62 - 53566 * q^64 + 15436 * q^65 - 3060 * q^66 + 1676 * q^67 - 24738 * q^68 + 57456 * q^69 + 29136 * q^71 + 5103 * q^72 - 78378 * q^73 - 9798 * q^74 - 17721 * q^75 - 55304 * q^76 - 8172 * q^78 + 2272 * q^79 + 31586 * q^80 - 6561 * q^81 - 19834 * q^82 - 75528 * q^83 + 54264 * q^85 + 17236 * q^86 - 74178 * q^87 - 21420 * q^88 + 117286 * q^89 - 5508 * q^90 + 197904 * q^92 - 22464 * q^93 - 8928 * q^94 + 30328 * q^95 + 26505 * q^96 + 20004 * q^97 - 55080 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i	−0.906830	−	0.421496i	$-0.861505\pi$
$2$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i	0.818442	+	0.574590i	$0.194838\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	15.5000	+	26.8468i	0.484375	+	0.838962i
$5$	17.0000	−	29.4449i	0.304105	−	0.526726i	−0.672956	−	0.739682i	$-0.734976\pi$
$5$	17.0000	−	29.4449i	0.304105	−	0.526726i	0.977062	+	0.212956i	$0.0683092\pi$
$6$	−9.00000			−0.102062
$7$		0			0
$7$		0			0
$8$	−63.0000			−0.348029
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	17.0000	+	29.4449i	0.0537587	+	0.0931128i
$11$	170.000	+	294.449i	0.423611	+	0.733716i	0.996290	−	0.0860642i	$-0.0274290\pi$
$11$	170.000	+	294.449i	0.423611	+	0.733716i	−0.572679	+	0.819780i	$0.694096\pi$
$12$	−139.500	+	241.621i	−0.279654	+	0.484375i
$13$	454.000			0.745071			0.372535	−	0.928018i	$-0.378489\pi$
$13$	454.000			0.745071			0.372535	+	0.928018i	$0.378489\pi$
$14$		0			0
$15$	306.000			0.351150
$16$	−464.500	+	804.538i	−0.453613	+	0.785681i
$17$	399.000	+	691.088i	0.334850	+	0.579978i	0.983456	−	0.181147i	$-0.0579809\pi$
$17$	399.000	+	691.088i	0.334850	+	0.579978i	−0.648606	+	0.761124i	$0.724648\pi$
$18$	−40.5000	−	70.1481i	−0.0294628	−	0.0510310i
$19$	−446.000	+	772.495i	−0.283433	+	0.490921i	−0.972228	−	0.234036i	$-0.924807\pi$
$19$	−446.000	+	772.495i	−0.283433	+	0.490921i	0.688795	+	0.724956i	$0.258140\pi$
$20$	1054.00			0.589204
$21$		0			0
$22$	−340.000			−0.149769
$23$	1596.00	−	2764.35i	0.629091	−	1.08962i	−0.358644	−	0.933475i	$-0.616761\pi$
$23$	1596.00	−	2764.35i	0.629091	−	1.08962i	0.987735	−	0.156143i	$-0.0499060\pi$
$24$	−283.500	−	491.036i	−0.100467	−	0.174015i
$25$	984.500	+	1705.20i	0.315040	+	0.545665i
$26$	−227.000	+	393.176i	−0.0658556	+	0.114065i
$27$	−729.000			−0.192450
$28$		0			0
$29$	−8242.00			−1.81986			−0.909929	−	0.414764i	$-0.863864\pi$
$29$	−8242.00			−1.81986			−0.909929	+	0.414764i	$0.863864\pi$
$30$	−153.000	+	265.004i	−0.0310376	+	0.0537587i
$31$	1248.00	+	2161.60i	0.233244	+	0.403990i	0.958761	−	0.284214i	$-0.0917326\pi$
$31$	1248.00	+	2161.60i	0.233244	+	0.403990i	−0.725517	+	0.688204i	$0.758399\pi$
$32$	−1472.50	−	2550.44i	−0.254203	−	0.440292i
$33$	−1530.00	+	2650.04i	−0.244572	+	0.423611i
$34$	−798.000			−0.118387
$35$		0			0
$36$	−2511.00			−0.322917
$37$	−4899.00	+	8485.32i	−0.588306	+	1.01898i	0.406149	+	0.913807i	$0.366872\pi$
$37$	−4899.00	+	8485.32i	−0.588306	+	1.01898i	−0.994454	+	0.105168i	$0.966462\pi$
$38$	−446.000	−	772.495i	−0.0501044	−	0.0867834i
$39$	2043.00	+	3538.58i	0.215083	+	0.372535i
$40$	−1071.00	+	1855.03i	−0.105837	+	0.183316i
$41$	19834.0			1.84268			0.921342	−	0.388754i	$-0.127094\pi$
$41$	19834.0			1.84268			0.921342	+	0.388754i	$0.127094\pi$
$42$		0			0
$43$	−17236.0			−1.42156			−0.710780	−	0.703414i	$-0.751658\pi$
$43$	−17236.0			−1.42156			−0.710780	+	0.703414i	$0.751658\pi$
$44$	−5270.00	+	9127.91i	−0.410373	+	0.710787i
$45$	1377.00	+	2385.03i	0.101368	+	0.175575i
$46$	1596.00	+	2764.35i	0.111209	+	0.192619i
$47$	−4464.00	+	7731.87i	−0.294767	+	0.510552i	−0.974931	−	0.222508i	$-0.928576\pi$
$47$	−4464.00	+	7731.87i	−0.294767	+	0.510552i	0.680163	+	0.733061i	$0.261909\pi$
$48$	−8361.00			−0.523788
$49$		0			0
$50$	−1969.00			−0.111383
$51$	−3591.00	+	6219.79i	−0.193326	+	0.334850i
$52$	7037.00	+	12188.4i	0.360894	+	0.625086i
$53$	−75.0000	−	129.904i	−0.00366751	−	0.00635232i	0.864186	−	0.503173i	$-0.167834\pi$
$53$	−75.0000	−	129.904i	−0.00366751	−	0.00635232i	−0.867853	+	0.496820i	$0.834501\pi$
$54$	364.500	−	631.333i	0.0170103	−	0.0294628i
$55$	11560.0			0.515289
$56$		0			0
$57$	−8028.00			−0.327281
$58$	4121.00	−	7137.78i	0.160854	−	0.278608i
$59$	21198.0	+	36716.0i	0.792802	+	1.37317i	0.924225	+	0.381847i	$0.124712\pi$
$59$	21198.0	+	36716.0i	0.792802	+	1.37317i	−0.131423	+	0.991326i	$0.541955\pi$
$60$	4743.00	+	8215.12i	0.170089	+	0.294602i
$61$	−7379.00	+	12780.8i	−0.253906	+	0.439778i	−0.964598	−	0.263725i	$-0.915049\pi$
$61$	−7379.00	+	12780.8i	−0.253906	+	0.439778i	0.710692	+	0.703503i	$0.248382\pi$
$62$	−2496.00			−0.0824642
$63$		0			0
$64$	−26783.0			−0.817352
$65$	7718.00	−	13368.0i	0.226580	−	0.392448i
$66$	−1530.00	−	2650.04i	−0.0432346	−	0.0748845i
$67$	838.000	+	1451.46i	0.0228064	+	0.0395019i	0.877203	−	0.480119i	$-0.159407\pi$
$67$	838.000	+	1451.46i	0.0228064	+	0.0395019i	−0.854397	+	0.519621i	$0.826073\pi$
$68$	−12369.0	+	21423.7i	−0.324386	+	0.561853i
$69$	28728.0			0.726411
$70$		0			0
$71$	14568.0			0.342968			0.171484	−	0.985187i	$-0.445144\pi$
$71$	14568.0			0.342968			0.171484	+	0.985187i	$0.445144\pi$
$72$	2551.50	−	4419.33i	0.0580049	−	0.100467i
$73$	−39189.0	−	67877.3i	−0.860710	−	1.49079i	−0.871244	−	0.490850i	$-0.836686\pi$
$73$	−39189.0	−	67877.3i	−0.860710	−	1.49079i	0.0105340	−	0.999945i	$-0.496647\pi$
$74$	−4899.00	−	8485.32i	−0.103999	−	0.180131i
$75$	−8860.50	+	15346.8i	−0.181888	+	0.315040i
$76$	−27652.0			−0.549152
$77$		0			0
$78$	−4086.00			−0.0760435
$79$	1136.00	−	1967.61i	0.0204791	−	0.0354708i	−0.855604	−	0.517631i	$-0.826814\pi$
$79$	1136.00	−	1967.61i	0.0204791	−	0.0354708i	0.876083	+	0.482160i	$0.160148\pi$
$80$	15793.0	+	27354.3i	0.275892	+	0.477860i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−9917.00	+	17176.7i	−0.162872	+	0.282102i
$83$	−37764.0			−0.601704			−0.300852	−	0.953671i	$-0.597271\pi$
$83$	−37764.0			−0.601704			−0.300852	+	0.953671i	$0.597271\pi$
$84$		0			0
$85$	27132.0			0.407319
$86$	8618.00	−	14926.8i	0.125649	−	0.217631i
$87$	−37089.0	−	64240.0i	−0.525348	−	0.909929i
$88$	−10710.0	−	18550.3i	−0.147429	−	0.255354i
$89$	58643.0	−	101573.i	0.784768	−	1.35926i	−0.144370	−	0.989524i	$-0.546116\pi$
$89$	58643.0	−	101573.i	0.784768	−	1.35926i	0.929138	−	0.369734i	$-0.120551\pi$
$90$	−2754.00			−0.0358391
$91$		0			0
$92$	98952.0			1.21886
$93$	−11232.0	+	19454.4i	−0.134663	+	0.233244i
$94$	−4464.00	−	7731.87i	−0.0521080	−	0.0902537i
$95$	15164.0	+	26264.8i	0.172387	+	0.298583i
$96$	13252.5	−	22954.0i	0.146764	−	0.254203i
$97$	10002.0			0.107934			0.0539669	−	0.998543i	$-0.482813\pi$
$97$	10002.0			0.107934			0.0539669	+	0.998543i	$0.482813\pi$
$98$		0			0
$99$	−27540.0			−0.282407
$100$	−30519.5	+	52861.3i	−0.305195	+	0.528613i
$101$	54385.0	+	94197.6i	0.530488	+	0.918832i	0.999367	+	0.0355701i	$0.0113247\pi$
$101$	54385.0	+	94197.6i	0.530488	+	0.918832i	−0.468879	+	0.883262i	$0.655342\pi$
$102$	−3591.00	−	6219.79i	−0.0341755	−	0.0591937i
$103$	99596.0	−	172505.i	0.925015	−	1.60217i	0.133478	−	0.991052i	$-0.457385\pi$
$103$	99596.0	−	172505.i	0.925015	−	1.60217i	0.791537	−	0.611121i	$-0.209281\pi$
$104$	−28602.0			−0.259306
$105$		0			0
$106$	150.000			0.00129666
$107$	39986.0	−	69257.8i	0.337636	−	0.584802i	−0.646352	−	0.763040i	$-0.723706\pi$
$107$	39986.0	−	69257.8i	0.337636	−	0.584802i	0.983988	+	0.178237i	$0.0570394\pi$
$108$	−11299.5	−	19571.3i	−0.0932180	−	0.161458i
$109$	23049.0	+	39922.0i	0.185817	+	0.321845i	0.943852	−	0.330370i	$-0.107173\pi$
$109$	23049.0	+	39922.0i	0.185817	+	0.321845i	−0.758034	+	0.652215i	$0.773840\pi$
$110$	−5780.00	+	10011.3i	−0.0455456	+	0.0788872i
$111$	−88182.0			−0.679317
$112$		0			0
$113$	262706.			1.93541			0.967707	−	0.252078i	$-0.0811138\pi$
$113$	262706.			1.93541			0.967707	+	0.252078i	$0.0811138\pi$
$114$	4014.00	−	6952.45i	0.0289278	−	0.0501044i
$115$	−54264.0	−	93988.0i	−0.382620	−	0.662717i
$116$	−127751.	−	221271.i	−0.881494	−	1.52679i
$117$	−18387.0	+	31847.2i	−0.124178	+	0.215083i
$118$	−42396.0			−0.280298
$119$		0			0
$120$	−19278.0			−0.122211
$121$	22725.5	−	39361.7i	0.141107	−	0.244405i
$122$	−7379.00	−	12780.8i	−0.0448847	−	0.0777425i
$123$	89253.0	+	154591.i	0.531937	+	0.921342i
$124$	−38688.0	+	67009.6i	−0.225955	+	0.391366i
$125$	173196.			0.991432
$126$		0			0
$127$	196608.			1.08166			0.540831	−	0.841131i	$-0.318110\pi$
$127$	196608.			1.08166			0.540831	+	0.841131i	$0.318110\pi$
$128$	60511.5	−	104809.i	0.326447	−	0.565423i
$129$	−77562.0	−	134341.i	−0.410369	−	0.710780i
$130$	7718.00	+	13368.0i	0.0400540	+	0.0693756i
$131$	38570.0	−	66805.2i	0.196368	−	0.340120i	−0.750980	−	0.660325i	$-0.770419\pi$
$131$	38570.0	−	66805.2i	0.196368	−	0.340120i	0.947348	+	0.320205i	$0.103752\pi$
$132$	−94860.0			−0.473858
$133$		0			0
$134$	−1676.00			−0.00806329
$135$	−12393.0	+	21465.3i	−0.0585251	+	0.101368i
$136$	−25137.0	−	43538.6i	−0.116538	−	0.201849i
$137$	−104085.	−	180281.i	−0.473791	−	0.820630i	0.525759	−	0.850634i	$-0.323781\pi$
$137$	−104085.	−	180281.i	−0.473791	−	0.820630i	−0.999550	+	0.0300037i	$0.990448\pi$
$138$	−14364.0	+	24879.2i	−0.0642063	+	0.111209i
$139$	−275580.			−1.20979			−0.604896	−	0.796304i	$-0.706785\pi$
$139$	−275580.			−1.20979			−0.604896	+	0.796304i	$0.706785\pi$
$140$		0			0
$141$	−80352.0			−0.340368
$142$	−7284.00	+	12616.3i	−0.0303144	+	0.0525061i
$143$	77180.0	+	133680.i	0.315620	+	0.546670i
$144$	−37624.5	−	65167.5i	−0.151204	−	0.261894i
$145$	−140114.	+	242685.i	−0.553429	+	0.958566i
$146$	78378.0			0.304307
$147$		0			0
$148$	−303738.			−1.13984
$149$	148053.	−	256435.i	0.546326	−	0.946264i	−0.452197	−	0.891918i	$-0.649359\pi$
$149$	148053.	−	256435.i	0.546326	−	0.946264i	0.998522	−	0.0543454i	$-0.0173072\pi$
$150$	−8860.50	−	15346.8i	−0.0321536	−	0.0556917i
$151$	213236.	+	369336.i	0.761059	+	1.31819i	0.942305	+	0.334755i	$0.108653\pi$
$151$	213236.	+	369336.i	0.761059	+	1.31819i	−0.181247	+	0.983438i	$0.558013\pi$
$152$	28098.0	−	48667.2i	0.0986430	−	0.170855i
$153$	−64638.0			−0.223233
$154$		0			0
$155$	84864.0			0.283723
$156$	−63333.0	+	109696.i	−0.208362	+	0.360894i
$157$	−89243.0	−	154573.i	−0.288952	−	0.500479i	0.684608	−	0.728911i	$-0.259973\pi$
$157$	−89243.0	−	154573.i	−0.288952	−	0.500479i	−0.973560	+	0.228432i	$0.926640\pi$
$158$	1136.00	+	1967.61i	0.00362023	+	0.00627041i
$159$	675.000	−	1169.13i	0.00211744	−	0.00366751i
$160$	−100130.			−0.309218
$161$		0			0
$162$	6561.00			0.0196419
$163$	−126386.	+	218907.i	−0.372589	+	0.645343i	−0.989963	−	0.141327i	$-0.954863\pi$
$163$	−126386.	+	218907.i	−0.372589	+	0.645343i	0.617374	+	0.786670i	$0.288197\pi$
$164$	307427.	+	532479.i	0.892550	+	1.54594i
$165$	52020.0	+	90101.3i	0.148751	+	0.257645i
$166$	18882.0	−	32704.6i	0.0531836	−	0.0921167i
$167$	508088.			1.40977			0.704884	−	0.709322i	$-0.250999\pi$
$167$	508088.			1.40977			0.704884	+	0.709322i	$0.250999\pi$
$168$		0			0
$169$	−165177.			−0.444870
$170$	−13566.0	+	23497.0i	−0.0360022	+	0.0623577i
$171$	−36126.0	−	62572.1i	−0.0944778	−	0.163640i
$172$	−267158.	−	462731.i	−0.688568	−	1.19264i
$173$	110917.	−	192114.i	0.281762	−	0.488027i	−0.690057	−	0.723755i	$-0.742414\pi$
$173$	110917.	−	192114.i	0.281762	−	0.488027i	0.971819	+	0.235729i	$0.0757477\pi$
$174$	74178.0			0.185739
$175$		0			0
$176$	−315860.			−0.768622
$177$	−190782.	+	330444.i	−0.457725	+	0.792802i
$178$	58643.0	+	101573.i	0.138729	+	0.240285i
$179$	56782.0	+	98349.3i	0.132458	+	0.229424i	0.924624	−	0.380882i	$-0.124380\pi$
$179$	56782.0	+	98349.3i	0.132458	+	0.229424i	−0.792166	+	0.610306i	$0.791046\pi$
$180$	−42687.0	+	73936.1i	−0.0982007	+	0.170089i
$181$	663118.			1.50451			0.752254	−	0.658873i	$-0.228967\pi$
$181$	663118.			1.50451			0.752254	+	0.658873i	$0.228967\pi$
$182$		0			0
$183$	−132822.			−0.293185
$184$	−100548.	+	174154.i	−0.218942	+	0.379218i
$185$	166566.	+	288501.i	0.357814	+	0.619752i
$186$	−11232.0	−	19454.4i	−0.0238054	−	0.0412321i
$187$	−135660.	+	234970.i	−0.283692	+	0.491370i
$188$	−276768.			−0.571112
$189$		0			0
$190$	−30328.0			−0.0609480
$191$	−252832.	+	437918.i	−0.501474	+	0.868579i	0.498524	+	0.866876i	$0.333875\pi$
$191$	−252832.	+	437918.i	−0.501474	+	0.868579i	−0.999999	+	0.00170313i	$0.999458\pi$
$192$	−120524.	−	208753.i	−0.235949	−	0.408676i
$193$	216191.	+	374454.i	0.417777	+	0.723611i	0.995716	−	0.0924695i	$-0.0294761\pi$
$193$	216191.	+	374454.i	0.417777	+	0.723611i	−0.577939	+	0.816080i	$0.696143\pi$
$194$	−5001.00	+	8661.99i	−0.00954009	+	0.0165239i
$195$	138924.			0.261632
$196$		0			0
$197$	−131962.			−0.242261			−0.121130	−	0.992637i	$-0.538652\pi$
$197$	−131962.			−0.242261			−0.121130	+	0.992637i	$0.538652\pi$
$198$	13770.0	−	23850.3i	0.0249615	−	0.0432346i
$199$	−149268.	−	258540.i	−0.267199	−	0.462801i	0.700939	−	0.713221i	$-0.252765\pi$
$199$	−149268.	−	258540.i	−0.267199	−	0.462801i	−0.968137	+	0.250420i	$0.919431\pi$
$200$	−62023.5	−	107428.i	−0.109643	−	0.189907i
$201$	−7542.00	+	13063.1i	−0.0131673	+	0.0228064i
$202$	−108770.			−0.187556
$203$		0			0
$204$	−222642.			−0.374569
$205$	337178.	−	584009.i	0.560370	−	0.970589i
$206$	99596.0	+	172505.i	0.163521	+	0.283227i
$207$	129276.	+	223913.i	0.209697	+	0.363206i
$208$	−210883.	+	365260.i	−0.337974	+	0.585388i
$209$	−303280.			−0.480262
$210$		0			0
$211$	−1.17062e6			−1.81013			−0.905065	−	0.425273i	$-0.860178\pi$
$211$	−1.17062e6			−1.81013			−0.905065	+	0.425273i	$0.860178\pi$
$212$	2325.00	−	4027.02i	0.00355290	−	0.00615381i
$213$	65556.0	+	113546.i	0.0990064	+	0.171484i
$214$	39986.0	+	69257.8i	0.0596861	+	0.103379i
$215$	−293012.	+	507512.i	−0.432304	+	0.748772i
$216$	45927.0			0.0669782
$217$		0			0
$218$	−46098.0			−0.0656963
$219$	352701.	−	610896.i	0.496931	−	0.860710i
$220$	179180.	+	310349.i	0.249593	+	0.432308i
$221$	181146.	+	313754.i	0.249487	+	0.432124i
$222$	44091.0	−	76367.9i	0.0600437	−	0.103999i
$223$	399376.			0.537799			0.268899	−	0.963168i	$-0.413340\pi$
$223$	399376.			0.537799			0.268899	+	0.963168i	$0.413340\pi$
$224$		0			0
$225$	−159489.			−0.210027
$226$	−131353.	+	227510.i	−0.171068	+	0.296299i
$227$	−353958.	−	613073.i	−0.455918	−	0.789674i	0.542822	−	0.839848i	$-0.317356\pi$
$227$	−353958.	−	613073.i	−0.455918	−	0.789674i	−0.998740	+	0.0501739i	$0.984022\pi$
$228$	−124434.	−	215526.i	−0.158527	−	0.274576i
$229$	367889.	−	637202.i	0.463584	−	0.802950i	−0.535553	−	0.844502i	$-0.679897\pi$
$229$	367889.	−	637202.i	0.463584	−	0.802950i	0.999136	+	0.0415514i	$0.0132300\pi$
$230$	108528.			0.135276
$231$		0			0
$232$	519246.			0.633364
$233$	104379.	−	180790.i	0.125957	−	0.218164i	−0.796149	−	0.605100i	$-0.793133\pi$
$233$	104379.	−	180790.i	0.125957	−	0.218164i	0.922107	+	0.386936i	$0.126466\pi$
$234$	−18387.0	−	31847.2i	−0.0219519	−	0.0380217i
$235$	151776.	+	262884.i	0.179281	+	0.310523i
$236$	−657138.	+	1.13820e6i	−0.768027	+	1.33026i
$237$	20448.0			0.0236472
$238$		0			0
$239$	713376.			0.807837			0.403919	−	0.914795i	$-0.367648\pi$
$239$	713376.			0.807837			0.403919	+	0.914795i	$0.367648\pi$
$240$	−142137.	+	246189.i	−0.159287	+	0.275892i
$241$	252623.	+	437556.i	0.280176	+	0.485278i	0.971428	−	0.237335i	$-0.0762740\pi$
$241$	252623.	+	437556.i	0.280176	+	0.485278i	−0.691252	+	0.722614i	$0.742941\pi$
$242$	22725.5	+	39361.7i	0.0249445	+	0.0432052i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	−457498.			−0.491943
$245$		0			0
$246$	−178506.			−0.188068
$247$	−202484.	+	350713.i	−0.211178	+	0.365771i
$248$	−78624.0	−	136181.i	−0.0811757	−	0.140600i
$249$	−169938.	−	294341.i	−0.173697	−	0.300852i
$250$	−86598.0	+	149992.i	−0.0876310	+	0.151781i
$251$	317108.			0.317704			0.158852	−	0.987302i	$-0.449221\pi$
$251$	317108.			0.317704			0.158852	+	0.987302i	$0.449221\pi$
$252$		0			0
$253$	1.08528e6			1.06596
$254$	−98304.0	+	170268.i	−0.0956064	+	0.165595i
$255$	122094.	+	211473.i	0.117583	+	0.203659i
$256$	−368016.	−	637423.i	−0.350968	−	0.607894i
$257$	721423.	−	1.24954e6i	0.681329	−	1.18010i	−0.293246	−	0.956037i	$-0.594735\pi$
$257$	721423.	−	1.24954e6i	0.681329	−	1.18010i	0.974575	−	0.224060i	$-0.0719312\pi$
$258$	155124.			0.145087
$259$		0			0
$260$	478516.			0.438999
$261$	333801.	−	578160.i	0.303310	−	0.525348i
$262$	38570.0	+	66805.2i	0.0347133	+	0.0601253i
$263$	−135748.	−	235122.i	−0.121016	−	0.209606i	0.799152	−	0.601128i	$-0.205282\pi$
$263$	−135748.	−	235122.i	−0.121016	−	0.209606i	−0.920169	+	0.391522i	$0.871949\pi$
$264$	96390.0	−	166952.i	0.0851181	−	0.147429i
$265$	−5100.00			−0.00446124
$266$		0			0
$267$	1.05557e6			0.906172
$268$	−25978.0	+	44995.2i	−0.0220937	+	0.0382674i
$269$	−425307.	−	736653.i	−0.358362	−	0.620701i	0.629325	−	0.777142i	$-0.283331\pi$
$269$	−425307.	−	736653.i	−0.358362	−	0.620701i	−0.987687	+	0.156441i	$0.949998\pi$
$270$	−12393.0	−	21465.3i	−0.0103459	−	0.0179196i
$271$	270064.	−	467765.i	0.223380	−	0.386905i	−0.732452	−	0.680818i	$-0.761624\pi$
$271$	270064.	−	467765.i	0.223380	−	0.386905i	0.955832	+	0.293913i	$0.0949577\pi$
$272$	−741342.			−0.607570
$273$		0			0
$274$	208170.			0.167510
$275$	−334730.	+	579769.i	−0.266909	+	0.462300i
$276$	445284.	+	771255.i	0.351856	+	0.609432i
$277$	−256787.	−	444768.i	−0.201082	−	0.348285i	0.747795	−	0.663929i	$-0.231112\pi$
$277$	−256787.	−	444768.i	−0.201082	−	0.348285i	−0.948877	+	0.315645i	$0.897779\pi$
$278$	137790.	−	238659.i	0.106932	−	0.185211i
$279$	−202176.			−0.155496
$280$		0			0
$281$	−1.35642e6			−1.02478			−0.512388	−	0.858754i	$-0.671239\pi$
$281$	−1.35642e6			−1.02478			−0.512388	+	0.858754i	$0.671239\pi$
$282$	40176.0	−	69586.9i	0.0300846	−	0.0521080i
$283$	−143378.	−	248338.i	−0.106418	−	0.184322i	0.807898	−	0.589322i	$-0.200605\pi$
$283$	−143378.	−	248338.i	−0.106418	−	0.184322i	−0.914317	+	0.405000i	$0.867272\pi$
$284$	225804.	+	391104.i	0.166125	+	0.287737i
$285$	−136476.	+	236383.i	−0.0995277	+	0.172387i
$286$	−154360.			−0.111589
$287$		0			0
$288$	238545.			0.169469
$289$	391526.	−	678144.i	0.275751	−	0.477614i
$290$	−140114.	−	242685.i	−0.0978333	−	0.169452i
$291$	45009.0	+	77957.9i	0.0311578	+	0.0539669i
$292$	1.21486e6	−	2.10420e6i	0.833813	−	1.44421i
$293$	−1.70727e6			−1.16180			−0.580901	−	0.813974i	$-0.697300\pi$
$293$	−1.70727e6			−1.16180			−0.580901	+	0.813974i	$0.697300\pi$
$294$		0			0
$295$	1.44146e6			0.964381
$296$	308637.	−	534575.i	0.204748	−	0.354633i
$297$	−123930.	−	214653.i	−0.0815240	−	0.141204i
$298$	148053.	+	256435.i	0.0965776	+	0.167277i
$299$	724584.	−	1.25502e6i	0.468717	−	0.811842i
$300$	−549351.			−0.352409
$301$		0			0
$302$	−426472.			−0.269075
$303$	−489465.	+	847778.i	−0.306277	+	0.530488i
$304$	−414334.	−	717648.i	−0.257138	−	0.445376i
$305$	250886.	+	434547.i	0.154428	+	0.267478i
$306$	32319.0	−	55978.2i	0.0197312	−	0.0341755i
$307$	−546788.			−0.331111			−0.165555	−	0.986201i	$-0.552942\pi$
$307$	−546788.			−0.331111			−0.165555	+	0.986201i	$0.552942\pi$
$308$		0			0
$309$	1.79273e6			1.06812
$310$	−42432.0	+	73494.4i	−0.0250778	+	0.0434360i
$311$	−1.61713e6	−	2.80095e6i	−0.948079	−	1.64212i	−0.749466	−	0.662043i	$-0.769690\pi$
$311$	−1.61713e6	−	2.80095e6i	−0.948079	−	1.64212i	−0.198613	−	0.980078i	$-0.563644\pi$
$312$	−128709.	−	222931.i	−0.0748553	−	0.129653i
$313$	−906565.	+	1.57022e6i	−0.523044	+	0.905939i	0.476597	+	0.879122i	$0.341870\pi$
$313$	−906565.	+	1.57022e6i	−0.523044	+	0.905939i	−0.999640	+	0.0268164i	$0.991463\pi$
$314$	178486.			0.102160
$315$		0			0
$316$	70432.0			0.0396782
$317$	638289.	−	1.10555e6i	0.356754	−	0.617917i	−0.630662	−	0.776057i	$-0.717217\pi$
$317$	638289.	−	1.10555e6i	0.356754	−	0.617917i	0.987417	+	0.158141i	$0.0505500\pi$
$318$	675.000	+	1169.13i	0.000374314	+	0.000648331i
$319$	−1.40114e6	−	2.42685e6i	−0.770912	−	1.33526i
$320$	−455311.	+	788622.i	−0.248561	+	0.430520i
$321$	719748.			0.389868
$322$		0			0
$323$	−711816.			−0.379631
$324$	101696.	−	176142.i	0.0538194	−	0.0932180i
$325$	446963.	+	774163.i	0.234727	+	0.406559i
$326$	−126386.	−	218907.i	−0.0658650	−	0.114082i
$327$	−207441.	+	359298.i	−0.107282	+	0.185817i
$328$	−1.24954e6			−0.641307
$329$		0			0
$330$	−104040.			−0.0525915
$331$	868106.	−	1.50360e6i	0.435515	−	0.754334i	−0.561823	−	0.827258i	$-0.689900\pi$
$331$	868106.	−	1.50360e6i	0.435515	−	0.754334i	0.997337	+	0.0729241i	$0.0232331\pi$
$332$	−585342.	−	1.01384e6i	−0.291450	−	0.504807i
$333$	−396819.	−	687311.i	−0.196102	−	0.339659i
$334$	−254044.	+	440017.i	−0.124607	+	0.215826i
$335$	56984.0			0.0277422
$336$		0			0
$337$	2.07215e6			0.993907			0.496953	−	0.867777i	$-0.334452\pi$
$337$	2.07215e6			0.993907			0.496953	+	0.867777i	$0.334452\pi$
$338$	82588.5	−	143047.i	0.0393213	−	0.0681065i
$339$	1.18218e6	+	2.04759e6i	0.558706	+	0.967707i
$340$	420546.	+	728407.i	0.197295	+	0.341725i
$341$	−424320.	+	734944.i	−0.197609	+	0.342269i
$342$	72252.0			0.0334029
$343$		0			0
$344$	1.08587e6			0.494744
$345$	488376.	−	845892.i	0.220906	−	0.382620i
$346$	110917.	+	192114.i	0.0498090	+	0.0862717i
$347$	825730.	+	1.43021e6i	0.368141	+	0.637639i	0.989275	−	0.146065i	$-0.0466610\pi$
$347$	825730.	+	1.43021e6i	0.368141	+	0.637639i	−0.621134	+	0.783705i	$0.713328\pi$
$348$	1.14976e6	−	1.99144e6i	0.508931	−	0.881494i
$349$	1.26645e6			0.556578			0.278289	−	0.960497i	$-0.410233\pi$
$349$	1.26645e6			0.556578			0.278289	+	0.960497i	$0.410233\pi$
$350$		0			0
$351$	−330966.			−0.143389
$352$	500650.	−	867151.i	0.215366	−	0.373025i
$353$	−286609.	−	496421.i	−0.122420	−	0.212038i	0.798301	−	0.602258i	$-0.205732\pi$
$353$	−286609.	−	496421.i	−0.122420	−	0.212038i	−0.920722	+	0.390220i	$0.872399\pi$
$354$	−190782.	−	330444.i	−0.0809150	−	0.140149i
$355$	247656.	−	428953.i	0.104298	−	0.180650i
$356$	3.63587e6			1.52049
$357$		0			0
$358$	−113564.			−0.0468310
$359$	−2.23161e6	+	3.86527e6i	−0.913866	+	1.58286i	−0.105313	+	0.994439i	$0.533584\pi$
$359$	−2.23161e6	+	3.86527e6i	−0.913866	+	1.58286i	−0.808553	+	0.588423i	$0.799749\pi$
$360$	−86751.0	−	150257.i	−0.0352792	−	0.0611053i
$361$	840218.	+	1.45530e6i	0.339331	+	0.587739i
$362$	−331559.	+	574277.i	−0.132981	+	0.230330i
$363$	409059.			0.162937
$364$		0			0
$365$	−2.66485e6			−1.04699
$366$	66411.0	−	115027.i	0.0259142	−	0.0448847i
$367$	2.25398e6	+	3.90401e6i	0.873546	+	1.51303i	0.858304	+	0.513142i	$0.171519\pi$
$367$	2.25398e6	+	3.90401e6i	0.873546	+	1.51303i	0.0152419	+	0.999884i	$0.495148\pi$
$368$	1.48268e6	+	2.56808e6i	0.570728	+	0.988530i
$369$	−803277.	+	1.39132e6i	−0.307114	+	0.531937i
$370$	−333132.			−0.126506
$371$		0			0
$372$	−696384.			−0.260910
$373$	−832675.	+	1.44224e6i	−0.309887	+	0.536740i	−0.978337	−	0.207017i	$-0.933625\pi$
$373$	−832675.	+	1.44224e6i	−0.309887	+	0.536740i	0.668450	+	0.743757i	$0.266958\pi$
$374$	−135660.	−	234970.i	−0.0501502	−	0.0868627i
$375$	779382.	+	1.34993e6i	0.286202	+	0.495716i
$376$	281232.	−	487108.i	0.102588	−	0.177687i
$377$	−3.74187e6			−1.35592
$378$		0			0
$379$	−2.53232e6			−0.905568			−0.452784	−	0.891620i	$-0.649569\pi$
$379$	−2.53232e6			−0.905568			−0.452784	+	0.891620i	$0.649569\pi$
$380$	−470084.	+	814209.i	−0.167000	+	0.289252i
$381$	884736.	+	1.53241e6i	0.312249	+	0.540831i
$382$	−252832.	−	437918.i	−0.0886490	−	0.153544i
$383$	−398184.	+	689675.i	−0.138703	+	0.240241i	−0.927006	−	0.375046i	$-0.877627\pi$
$383$	−398184.	+	689675.i	−0.138703	+	0.240241i	0.788303	+	0.615288i	$0.210960\pi$
$384$	1.08921e6			0.376949
$385$		0			0
$386$	−432382.			−0.147706
$387$	698058.	−	1.20907e6i	0.236927	−	0.410369i
$388$	155031.	+	268522.i	0.0522804	+	0.0905524i
$389$	−973995.	−	1.68701e6i	−0.326349	−	0.565254i	0.655435	−	0.755251i	$-0.272485\pi$
$389$	−973995.	−	1.68701e6i	−0.326349	−	0.565254i	−0.981785	+	0.189998i	$0.939152\pi$
$390$	−69462.0	+	120312.i	−0.0231252	+	0.0400540i
$391$	2.54722e6			0.842605
$392$		0			0
$393$	694260.			0.226747
$394$	65981.0	−	114282.i	0.0214130	−	0.0370885i
$395$	−38624.0	−	66898.7i	−0.0124556	−	0.0215737i
$396$	−426870.	−	739361.i	−0.136791	−	0.236929i
$397$	−540579.	+	936310.i	−0.172140	+	0.298156i	−0.939168	−	0.343458i	$-0.888402\pi$
$397$	−540579.	+	936310.i	−0.172140	+	0.298156i	0.767028	+	0.641614i	$0.221735\pi$
$398$	298536.			0.0944689
$399$		0			0
$400$	−1.82920e6			−0.571625
$401$	−1.38385e6	+	2.39690e6i	−0.429762	+	0.744369i	−0.996852	−	0.0792866i	$-0.974736\pi$
$401$	−1.38385e6	+	2.39690e6i	−0.429762	+	0.744369i	0.567090	+	0.823656i	$0.308069\pi$
$402$	−7542.00	−	13063.1i	−0.00232767	−	0.00403164i
$403$	566592.	+	981366.i	0.173783	+	0.301001i
$404$	−1.68593e6	+	2.92013e6i	−0.513910	+	0.890119i
$405$	−223074.			−0.0675789
$406$		0			0
$407$	−3.33132e6			−0.996851
$408$	226233.	−	391847.i	0.0672830	−	0.116538i
$409$	−1.18175e6	−	2.04685e6i	−0.349315	−	0.605031i	0.636813	−	0.771018i	$-0.280252\pi$
$409$	−1.18175e6	−	2.04685e6i	−0.349315	−	0.605031i	−0.986128	+	0.165987i	$0.946919\pi$
$410$	337178.	+	584009.i	0.0990603	+	0.171577i
$411$	936765.	−	1.62252e6i	0.273543	−	0.473791i
$412$	6.17495e6			1.79222
$413$		0			0
$414$	−258552.			−0.0741391
$415$	−641988.	+	1.11196e6i	−0.182981	+	0.316933i
$416$	−668515.	−	1.15790e6i	−0.189399	−	0.328049i
$417$	−1.24011e6	−	2.14793e6i	−0.349237	−	0.604896i
$418$	151640.	−	262648.i	0.0424495	−	0.0735248i
$419$	−2.98669e6			−0.831104			−0.415552	−	0.909569i	$-0.636412\pi$
$419$	−2.98669e6			−0.831104			−0.415552	+	0.909569i	$0.636412\pi$
$420$		0			0
$421$	−3.46331e6			−0.952326			−0.476163	−	0.879357i	$-0.657973\pi$
$421$	−3.46331e6			−0.952326			−0.476163	+	0.879357i	$0.657973\pi$
$422$	585310.	−	1.01379e6i	0.159994	−	0.277118i
$423$	−361584.	−	626282.i	−0.0982558	−	0.170184i
$424$	4725.00	+	8183.94i	0.00127640	+	0.00221079i
$425$	−785631.	+	1.36075e6i	−0.210982	+	0.365432i
$426$	−131112.			−0.0350041
$427$		0			0
$428$	2.47913e6			0.654169
$429$	−694620.	+	1.20312e6i	−0.182223	+	0.315620i
$430$	−293012.	−	507512.i	−0.0764213	−	0.132366i
$431$	−1.16846e6	−	2.02384e6i	−0.302986	−	0.524787i	0.673825	−	0.738891i	$-0.264650\pi$
$431$	−1.16846e6	−	2.02384e6i	−0.302986	−	0.524787i	−0.976811	+	0.214104i	$0.931317\pi$
$432$	338620.	−	586508.i	0.0872979	−	0.151204i
$433$	−3.50838e6			−0.899264			−0.449632	−	0.893214i	$-0.648445\pi$
$433$	−3.50838e6			−0.899264			−0.449632	+	0.893214i	$0.648445\pi$
$434$		0			0
$435$	−2.52205e6			−0.639044
$436$	−714519.	+	1.23758e6i	−0.180010	+	0.311787i
$437$	1.42363e6	+	2.46580e6i	0.356611	+	0.617668i
$438$	352701.	+	610896.i	0.0878459	+	0.152154i
$439$	−1.77416e6	+	3.07294e6i	−0.439372	+	0.761015i	−0.997641	−	0.0686452i	$-0.978132\pi$
$439$	−1.77416e6	+	3.07294e6i	−0.439372	+	0.761015i	0.558269	+	0.829660i	$0.311466\pi$
$440$	−728280.			−0.179336
$441$		0			0
$442$	−362292.			−0.0882070
$443$	−884166.	+	1.53142e6i	−0.214055	+	0.370753i	−0.952980	−	0.303034i	$-0.902000\pi$
$443$	−884166.	+	1.53142e6i	−0.214055	+	0.370753i	0.738925	+	0.673788i	$0.235334\pi$
$444$	−1.36682e6	−	2.36740e6i	−0.329044	−	0.569921i
$445$	−1.99386e6	−	3.45347e6i	−0.477304	−	0.826715i
$446$	−199688.	+	345870.i	−0.0475351	+	0.0823333i
$447$	2.66495e6			0.630842
$448$		0			0
$449$	−5.52579e6			−1.29354			−0.646768	−	0.762687i	$-0.723880\pi$
$449$	−5.52579e6			−1.29354			−0.646768	+	0.762687i	$0.723880\pi$
$450$	79744.5	−	138122.i	0.0185639	−	0.0321536i
$451$	3.37178e6	+	5.84009e6i	0.780581	+	1.35201i
$452$	4.07194e6	+	7.05281e6i	0.937466	+	1.62374i
$453$	−1.91912e6	+	3.32402e6i	−0.439397	+	0.761059i
$454$	707916.			0.161191
$455$		0			0
$456$	505764.			0.113903
$457$	1.48113e6	−	2.56539e6i	0.331744	−	0.574597i	−0.651110	−	0.758983i	$-0.725696\pi$
$457$	1.48113e6	−	2.56539e6i	0.331744	−	0.574597i	0.982854	+	0.184386i	$0.0590297\pi$
$458$	367889.	+	637202.i	0.0819508	+	0.141943i
$459$	−290871.	−	503803.i	−0.0644420	−	0.111617i
$460$	1.68218e6	−	2.91363e6i	0.370663	−	0.642007i
$461$	2.11884e6			0.464350			0.232175	−	0.972674i	$-0.425416\pi$
$461$	2.11884e6			0.464350			0.232175	+	0.972674i	$0.425416\pi$
$462$		0			0
$463$	3.19226e6			0.692062			0.346031	−	0.938223i	$-0.387529\pi$
$463$	3.19226e6			0.692062			0.346031	+	0.938223i	$0.387529\pi$
$464$	3.82841e6	−	6.63100e6i	0.825512	−	1.42983i
$465$	381888.	+	661449.i	0.0819037	+	0.141861i
$466$	104379.	+	180790.i	0.0222663	+	0.0385664i
$467$	3.71311e6	−	6.43129e6i	0.787853	−	1.36460i	−0.139427	−	0.990232i	$-0.544526\pi$
$467$	3.71311e6	−	6.43129e6i	0.787853	−	1.36460i	0.927280	−	0.374369i	$-0.122141\pi$
$468$	−1.13999e6			−0.240596
$469$		0			0
$470$	−303552.			−0.0633853
$471$	803187.	−	1.39116e6i	0.166826	−	0.288952i
$472$	−1.33547e6	−	2.31311e6i	−0.275918	−	0.477904i
$473$	−2.93012e6	−	5.07512e6i	−0.602189	−	1.04302i
$474$	−10224.0	+	17708.5i	−0.00209014	+	0.00362023i
$475$	−1.75635e6			−0.357171
$476$		0			0
$477$	12150.0			0.00244501
$478$	−356688.	+	617802.i	−0.0714034	+	0.123674i
$479$	1.69842e6	+	2.94176e6i	0.338226	+	0.585825i	0.984099	−	0.177620i	$-0.0568397\pi$
$479$	1.69842e6	+	2.94176e6i	0.338226	+	0.585825i	−0.645873	+	0.763445i	$0.723506\pi$
$480$	−450585.	−	780436.i	−0.0892634	−	0.154609i
$481$	−2.22415e6	+	3.85233e6i	−0.438329	+	0.759209i
$482$	−505246.			−0.0990570
$483$		0			0
$484$	1.40898e6			0.273396
$485$	170034.	−	294508.i	0.0328232	−	0.0568515i
$486$	29524.5	+	51137.9i	0.00567012	+	0.00982093i
$487$	1.85691e6	+	3.21626e6i	0.354787	+	0.614510i	0.987082	−	0.160219i	$-0.0512200\pi$
$487$	1.85691e6	+	3.21626e6i	0.354787	+	0.614510i	−0.632294	+	0.774728i	$0.717887\pi$
$488$	464877.	−	805191.i	0.0883667	−	0.153056i
$489$	−2.27495e6			−0.430229
$490$		0			0
$491$	5.57494e6			1.04361			0.521803	−	0.853066i	$-0.325260\pi$
$491$	5.57494e6			1.04361			0.521803	+	0.853066i	$0.325260\pi$
$492$	−2.76684e6	+	4.79231e6i	−0.515314	+	0.892550i
$493$	−3.28856e6	−	5.69595e6i	−0.609380	−	1.05548i
$494$	−202484.	−	350713.i	−0.0373313	−	0.0646597i
$495$	−468180.	+	810912.i	−0.0858815	+	0.148751i
$496$	−2.31878e6			−0.423210
$497$		0			0
$498$	339876.			0.0614111
$499$	−1.96349e6	+	3.40086e6i	−0.353002	+	0.611418i	−0.986774	−	0.162102i	$-0.948172\pi$
$499$	−1.96349e6	+	3.40086e6i	−0.353002	+	0.611418i	0.633772	+	0.773520i	$0.281506\pi$
$500$	2.68454e6	+	4.64976e6i	0.480225	+	0.831774i
$501$	2.28640e6	+	3.96015e6i	0.406965	+	0.704884i
$502$	−158554.	+	274624.i	−0.0280813	+	0.0486383i
$503$	6.42079e6			1.13154			0.565768	−	0.824564i	$-0.308580\pi$
$503$	6.42079e6			1.13154			0.565768	+	0.824564i	$0.308580\pi$
$504$		0			0
$505$	3.69818e6			0.645297
$506$	−542640.	+	939880.i	−0.0942184	+	0.163191i
$507$	−743296.	−	1.28743e6i	−0.128423	−	0.222435i
$508$	3.04742e6	+	5.27829e6i	0.523930	+	0.907474i
$509$	−73139.0	+	126680.i	−0.0125128	+	0.0216728i	−0.872214	−	0.489124i	$-0.837316\pi$
$509$	−73139.0	+	126680.i	−0.0125128	+	0.0216728i	0.859701	+	0.510797i	$0.170650\pi$
$510$	−244188.			−0.0415718
$511$		0			0
$512$	4.60877e6			0.776980
$513$	325134.	−	563149.i	0.0545468	−	0.0944778i
$514$	721423.	+	1.24954e6i	0.120443	+	0.208614i
$515$	−3.38626e6	−	5.86518e6i	−0.562604	−	0.974459i
$516$	2.40442e6	−	4.16458e6i	0.397545	−	0.688568i
$517$	−3.03552e6			−0.499467
$518$		0			0
$519$	1.99651e6			0.325351
$520$	−486234.	+	842182.i	−0.0788564	+	0.136583i
$521$	−3.85468e6	−	6.67651e6i	−0.622149	−	1.07759i	−0.989085	−	0.147348i	$-0.952926\pi$
$521$	−3.85468e6	−	6.67651e6i	−0.622149	−	1.07759i	0.366935	−	0.930246i	$-0.380407\pi$
$522$	333801.	+	578160.i	0.0536181	+	0.0928693i
$523$	284710.	−	493132.i	0.0455144	−	0.0788332i	−0.842371	−	0.538898i	$-0.818841\pi$
$523$	284710.	−	493132.i	0.0455144	−	0.0788332i	0.887885	+	0.460065i	$0.152174\pi$
$524$	2.39134e6			0.380464
$525$		0			0
$526$	271496.			0.0427857
$527$	−995904.	+	1.72496e6i	−0.156204	+	0.270553i
$528$	−1.42137e6	−	2.46189e6i	−0.221882	−	0.384311i
$529$	−1.87626e6	−	3.24978e6i	−0.291510	−	0.504911i
$530$	2550.00	−	4416.73i	0.000394322	−	0.000682985i
$531$	−3.43408e6			−0.528535
$532$		0			0
$533$	9.00464e6			1.37293
$534$	−527787.	+	914154.i	−0.0800950	+	0.138729i
$535$	−1.35952e6	−	2.35476e6i	−0.205354	−	0.355683i
$536$	−52794.0	−	91441.9i	−0.00793730	−	0.0137478i
$537$	−511038.	+	885144.i	−0.0764746	+	0.132458i
$538$	850614.			0.126700
$539$		0			0
$540$	−768366.			−0.113392
$541$	4.72401e6	−	8.18222e6i	0.693933	−	1.20193i	−0.276606	−	0.960983i	$-0.589210\pi$
$541$	4.72401e6	−	8.18222e6i	0.693933	−	1.20193i	0.970539	−	0.240944i	$-0.0774570\pi$
$542$	270064.	+	467765.i	0.0394883	+	0.0683957i
$543$	2.98403e6	+	5.16849e6i	0.434314	+	0.752254i
$544$	1.17506e6	−	2.03525e6i	0.170240	−	0.294864i
$545$	1.56733e6			0.226032
$546$		0			0
$547$	−1.35321e6			−0.193374			−0.0966869	−	0.995315i	$-0.530825\pi$
$547$	−1.35321e6			−0.193374			−0.0966869	+	0.995315i	$0.530825\pi$
$548$	3.22664e6	−	5.58870e6i	0.458985	−	0.794985i
$549$	−597699.	−	1.03525e6i	−0.0846353	−	0.146593i
$550$	−334730.	−	579769.i	−0.0471833	−	0.0817238i
$551$	3.67593e6	−	6.36690e6i	0.515808	−	0.893406i
$552$	−1.80986e6			−0.252812
$553$		0			0
$554$	513574.			0.0710933
$555$	−1.49909e6	+	2.59651e6i	−0.206584	+	0.357814i
$556$	−4.27149e6	−	7.39844e6i	−0.585993	−	1.01497i
$557$	−4.09695e6	−	7.09613e6i	−0.559529	−	0.969133i	−0.997536	−	0.0701612i	$-0.977649\pi$
$557$	−4.09695e6	−	7.09613e6i	−0.559529	−	0.969133i	0.438006	−	0.898972i	$-0.355685\pi$
$558$	101088.	−	175090.i	0.0137440	−	0.0238054i
$559$	−7.82514e6			−1.05916
$560$		0			0
$561$	−2.44188e6			−0.327580
$562$	678211.	−	1.17470e6i	0.0905783	−	0.156886i
$563$	5.28982e6	+	9.16223e6i	0.703347	+	1.21823i	0.967285	+	0.253693i	$0.0816454\pi$
$563$	5.28982e6	+	9.16223e6i	0.703347	+	1.21823i	−0.263938	+	0.964540i	$0.585021\pi$
$564$	−1.24546e6	−	2.15719e6i	−0.164866	−	0.285556i
$565$	4.46600e6	−	7.73534e6i	0.588570	−	1.01943i
$566$	286756.			0.0376246
$567$		0			0
$568$	−917784.			−0.119363
$569$	6.01026e6	−	1.04101e7i	0.778238	−	1.34795i	−0.154718	−	0.987959i	$-0.549447\pi$
$569$	6.01026e6	−	1.04101e7i	0.778238	−	1.34795i	0.932956	−	0.359989i	$-0.117220\pi$
$570$	−136476.	−	236383.i	−0.0175942	−	0.0304740i
$571$	1.24474e6	+	2.15595e6i	0.159767	+	0.276725i	0.934785	−	0.355215i	$-0.115592\pi$
$571$	1.24474e6	+	2.15595e6i	0.159767	+	0.276725i	−0.775017	+	0.631940i	$0.782259\pi$
$572$	−2.39258e6	+	4.14407e6i	−0.305757	+	0.529587i
$573$	−4.55098e6			−0.579053
$574$		0			0
$575$	6.28505e6			0.792755
$576$	1.08471e6	−	1.87878e6i	0.136225	−	0.235949i
$577$	−4.10661e6	−	7.11286e6i	−0.513504	−	0.889415i	−0.999877	−	0.0156639i	$-0.995014\pi$
$577$	−4.10661e6	−	7.11286e6i	−0.513504	−	0.889415i	0.486373	−	0.873751i	$-0.338320\pi$
$578$	391526.	+	678144.i	0.0487463	+	0.0844311i
$579$	−1.94572e6	+	3.37008e6i	−0.241204	+	0.417777i
$580$	−8.68707e6			−1.07227
$581$		0			0
$582$	−90018.0			−0.0110159
$583$	25500.0	−	44167.3i	0.00310720	−	0.00538182i
$584$	2.46891e6	+	4.27627e6i	0.299552	+	0.518840i
$585$	625158.	+	1.08281e6i	0.0755266	+	0.130816i
$586$	853633.	−	1.47854e6i	0.102690	−	0.177864i
$587$	−1.21827e6			−0.145931			−0.0729655	−	0.997334i	$-0.523246\pi$
$587$	−1.21827e6			−0.145931			−0.0729655	+	0.997334i	$0.523246\pi$
$588$		0			0
$589$	−2.22643e6			−0.264436
$590$	−720732.	+	1.24834e6i	−0.0852401	+	0.147640i
$591$	−593829.	−	1.02854e6i	−0.0699347	−	0.121130i
$592$	−4.55117e6	−	7.88286e6i	−0.533727	−	0.924442i
$593$	4.21190e6	−	7.29522e6i	0.491859	−	0.851925i	−0.508097	−	0.861300i	$-0.669651\pi$
$593$	4.21190e6	−	7.29522e6i	0.491859	−	0.851925i	0.999956	+	0.00937481i	$0.00298414\pi$
$594$	247860.			0.0288231
$595$		0			0
$596$	9.17929e6			1.05851
$597$	1.34341e6	−	2.32686e6i	0.154267	−	0.267199i
$598$	724584.	+	1.25502e6i	0.0828583	+	0.143515i
$599$	−4.10627e6	−	7.11226e6i	−0.467606	−	0.809918i	0.531709	−	0.846927i	$-0.321550\pi$
$599$	−4.10627e6	−	7.11226e6i	−0.467606	−	0.809918i	−0.999315	+	0.0370096i	$0.988217\pi$
$600$	558212.	−	966851.i	0.0633025	−	0.109643i
$601$	3.25478e6			0.367566			0.183783	−	0.982967i	$-0.441166\pi$
$601$	3.25478e6			0.367566			0.183783	+	0.982967i	$0.441166\pi$
$602$		0			0
$603$	−135756.			−0.0152043
$604$	−6.61032e6	+	1.14494e7i	−0.737276	+	1.27700i
$605$	−772667.	−	1.33830e6i	−0.0858230	−	0.148650i
$606$	−489465.	−	847778.i	−0.0541427	−	0.0937779i
$607$	−3.91050e6	+	6.77319e6i	−0.430785	+	0.746142i	−0.996941	−	0.0781561i	$-0.975097\pi$
$607$	−3.91050e6	+	6.77319e6i	−0.430785	+	0.746142i	0.566156	+	0.824298i	$0.308430\pi$
$608$	2.62694e6			0.288198
$609$		0			0
$610$	−501772.			−0.0545986
$611$	−2.02666e6	+	3.51027e6i	−0.219623	+	0.380397i
$612$	−1.00189e6	−	1.73532e6i	−0.108129	−	0.187284i
$613$	4.75835e6	+	8.24170e6i	0.511452	+	0.885861i	0.999912	+	0.0132748i	$0.00422563\pi$
$613$	4.75835e6	+	8.24170e6i	0.511452	+	0.885861i	−0.488460	+	0.872586i	$0.662441\pi$
$614$	273394.	−	473532.i	0.0292663	−	0.0506907i
$615$	6.06920e6			0.647059
$616$		0			0
$617$	−7.04895e6			−0.745438			−0.372719	−	0.927944i	$-0.621574\pi$
$617$	−7.04895e6			−0.745438			−0.372719	+	0.927944i	$0.621574\pi$
$618$	−896364.	+	1.55255e6i	−0.0944090	+	0.163521i
$619$	3.16087e6	+	5.47479e6i	0.331574	+	0.574302i	0.982821	−	0.184563i	$-0.0590871\pi$
$619$	3.16087e6	+	5.47479e6i	0.331574	+	0.574302i	−0.651247	+	0.758866i	$0.725754\pi$
$620$	1.31539e6	+	2.27833e6i	0.137428	+	0.238033i
$621$	−1.16348e6	+	2.01521e6i	−0.121069	+	0.209697i
$622$	3.23426e6			0.335197
$623$		0			0
$624$	−3.79589e6			−0.390259
$625$	−132230.	+	229030.i	−0.0135404	+	0.0234527i
$626$	−906565.	−	1.57022e6i	−0.0924620	−	0.160149i
$627$	−1.36476e6	−	2.36383e6i	−0.138640	−	0.240131i
$628$	2.76653e6	−	4.79178e6i	0.279922	−	0.484839i
$629$	−7.81880e6			−0.787977
$630$		0			0
$631$	8.61236e6			0.861090			0.430545	−	0.902569i	$-0.358321\pi$
$631$	8.61236e6			0.861090			0.430545	+	0.902569i	$0.358321\pi$
$632$	−71568.0	+	123959.i	−0.00712732	+	0.0123449i
$633$	−5.26779e6	−	9.12408e6i	−0.522540	−	0.905065i
$634$	638289.	+	1.10555e6i	0.0630658	+	0.109233i
$635$	3.34234e6	−	5.78910e6i	0.328939	−	0.569740i
$636$	41850.0			0.00410254
$637$		0			0
$638$	2.80228e6			0.272559
$639$	−590004.	+	1.02192e6i	−0.0571614	+	0.0990064i
$640$	−2.05739e6	−	3.56351e6i	−0.198549	−	0.343896i
$641$	2.61414e6	+	4.52783e6i	0.251295	+	0.435256i	0.963883	−	0.266327i	$-0.0858102\pi$
$641$	2.61414e6	+	4.52783e6i	0.251295	+	0.435256i	−0.712587	+	0.701583i	$0.752477\pi$
$642$	−359874.	+	623320.i	−0.0344598	+	0.0596861i
$643$	1.61373e7			1.53923			0.769615	−	0.638508i	$-0.220448\pi$
$643$	1.61373e7			1.53923			0.769615	+	0.638508i	$0.220448\pi$
$644$		0			0
$645$	−5.27422e6			−0.499182
$646$	355908.	−	616451.i	0.0335549	−	0.0581189i
$647$	7.93743e6	+	1.37480e7i	0.745451	+	1.29116i	0.949984	+	0.312299i	$0.101099\pi$
$647$	7.93743e6	+	1.37480e7i	0.745451	+	1.29116i	−0.204533	+	0.978860i	$0.565567\pi$
$648$	206672.	+	357966.i	0.0193350	+	0.0334891i
$649$	−7.20732e6	+	1.24834e7i	−0.671679	+	1.16338i
$650$	−893926.			−0.0829886
$651$		0			0
$652$	−7.83593e6			−0.721891
$653$	2.97056e6	−	5.14516e6i	0.272619	−	0.472189i	−0.696913	−	0.717156i	$-0.745444\pi$
$653$	2.97056e6	−	5.14516e6i	0.272619	−	0.472189i	0.969532	+	0.244966i	$0.0787769\pi$
$654$	−207441.	−	359298.i	−0.0189649	−	0.0328481i
$655$	−1.31138e6	−	2.27138e6i	−0.119433	−	0.206864i
$656$	−9.21289e6	+	1.59572e7i	−0.835866	+	1.44776i
$657$	6.34862e6			0.573807
$658$		0			0
$659$	−7.64430e6			−0.685684			−0.342842	−	0.939393i	$-0.611390\pi$
$659$	−7.64430e6			−0.685684			−0.342842	+	0.939393i	$0.611390\pi$
$660$	−1.61262e6	+	2.79314e6i	−0.144103	+	0.249593i
$661$	3.79344e6	+	6.57043e6i	0.337699	+	0.584912i	0.983999	−	0.178171i	$-0.0570181\pi$
$661$	3.79344e6	+	6.57043e6i	0.337699	+	0.584912i	−0.646301	+	0.763083i	$0.723685\pi$
$662$	868106.	+	1.50360e6i	0.0769888	+	0.133349i
$663$	−1.63031e6	+	2.82379e6i	−0.144041	+	0.249487i
$664$	2.37913e6			0.209410
$665$		0			0
$666$	793638.			0.0693325
$667$	−1.31542e7	+	2.27838e7i	−1.14486	+	1.98295i
$668$	7.87536e6	+	1.36405e7i	0.682857	+	1.18274i
$669$	1.79719e6	+	3.11283e6i	0.155249	+	0.268899i
$670$	−28492.0	+	49349.6i	−0.00245209	+	0.00424714i
$671$	−5.01772e6			−0.430229
$672$		0			0
$673$	−2.06681e7			−1.75899			−0.879494	−	0.475910i	$-0.842119\pi$
$673$	−2.06681e7			−1.75899			−0.879494	+	0.475910i	$0.842119\pi$
$674$	−1.03607e6	+	1.79453e6i	−0.0878498	+	0.152160i
$675$	−717700.	−	1.24309e6i	−0.0606295	−	0.105013i
$676$	−2.56024e6	−	4.43447e6i	−0.215484	−	0.373229i
$677$	−3.94770e6	+	6.83762e6i	−0.331034	+	0.573368i	−0.982715	−	0.185125i	$-0.940731\pi$
$677$	−3.94770e6	+	6.83762e6i	−0.331034	+	0.573368i	0.651681	+	0.758493i	$0.274064\pi$
$678$	−2.36435e6			−0.197532
$679$		0			0
$680$	−1.70932e6			−0.141759
$681$	3.18562e6	−	5.51766e6i	0.263225	−	0.455918i
$682$	−424320.	−	734944.i	−0.0349327	−	0.0605053i
$683$	9.80075e6	+	1.69754e7i	0.803911	+	1.39241i	0.917024	+	0.398832i	$0.130584\pi$
$683$	9.80075e6	+	1.69754e7i	0.803911	+	1.39241i	−0.113114	+	0.993582i	$0.536082\pi$
$684$	1.11991e6	−	1.93973e6i	0.0915253	−	0.158527i
$685$	−7.07778e6			−0.576329
$686$		0			0
$687$	6.62200e6			0.535300
$688$	8.00612e6	−	1.38670e7i	0.644839	−	1.11689i
$689$	−34050.0	−	58976.3i	−0.00273256	−	0.00473293i
$690$	488376.	+	845892.i	0.0390509	+	0.0676382i
$691$	8.63549e6	−	1.49571e7i	0.688005	−	1.19166i	−0.284477	−	0.958683i	$-0.591820\pi$
$691$	8.63549e6	−	1.49571e7i	0.688005	−	1.19166i	0.972482	−	0.232977i	$-0.0748468\pi$
$692$	6.87685e6			0.545914
$693$		0			0
$694$	−1.65146e6			−0.130158
$695$	−4.68486e6	+	8.11442e6i	−0.367904	+	0.637229i
$696$	2.33661e6	+	4.04712e6i	0.182836	+	0.316682i
$697$	7.91377e6	+	1.37070e7i	0.617023	+	1.06871i
$698$	−633227.	+	1.09678e6i	−0.0491950	+	0.0852082i
$699$	1.87882e6			0.145443
$700$		0			0
$701$	−5.36344e6			−0.412238			−0.206119	−	0.978527i	$-0.566083\pi$
$701$	−5.36344e6			−0.412238			−0.206119	+	0.978527i	$0.566083\pi$
$702$	165483.	−	286625.i	0.0126739	−	0.0219519i
$703$	−4.36991e6	−	7.56890e6i	−0.333491	−	0.577623i
$704$	−4.55311e6	−	7.88622e6i	−0.346239	−	0.599704i
$705$	−1.36598e6	+	2.36595e6i	−0.103508	+	0.179281i
$706$	573218.			0.0432821
$707$		0			0
$708$	−1.18285e7			−0.886841
$709$	8.68665e6	−	1.50457e7i	0.648988	−	1.12408i	−0.334377	−	0.942440i	$-0.608526\pi$
$709$	8.68665e6	−	1.50457e7i	0.648988	−	1.12408i	0.983365	−	0.181641i	$-0.0581409\pi$
$710$	247656.	+	428953.i	0.0184375	+	0.0319348i
$711$	92016.0	+	159376.i	0.00682636	+	0.0118236i
$712$	−3.69451e6	+	6.39908e6i	−0.273122	+	0.473061i
$713$	7.96723e6			0.586926
$714$		0			0
$715$	5.24824e6			0.383927
$716$	−1.76024e6	+	3.04883e6i	−0.128319	+	0.222254i
$717$	3.21019e6	+	5.56022e6i	0.233202	+	0.403919i
$718$	−2.23161e6	−	3.86527e6i	−0.161550	−	0.279813i
$719$	−212304.	+	367721.i	−0.0153157	+	0.0265275i	−0.873582	−	0.486678i	$-0.838209\pi$
$719$	−212304.	+	367721.i	−0.0153157	+	0.0265275i	0.858266	+	0.513205i	$0.171542\pi$
$720$	−2.55847e6			−0.183928
$721$		0			0
$722$	−1.68044e6			−0.119972
$723$	−2.27361e6	+	3.93800e6i	−0.161759	+	0.280176i
$724$	1.02783e7	+	1.78026e7i	0.728746	+	1.26222i
$725$	−8.11425e6	−	1.40543e7i	−0.573328	−	0.993034i
$726$	−204530.	+	354255.i	−0.0144017	+	0.0249445i
$727$	2.18290e7			1.53179			0.765893	−	0.642968i	$-0.222297\pi$
$727$	2.18290e7			1.53179			0.765893	+	0.642968i	$0.222297\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	1.33243e6	−	2.30783e6i	0.0925414	−	0.160286i
$731$	−6.87716e6	−	1.19116e7i	−0.476010	−	0.824473i
$732$	−2.05874e6	−	3.56584e6i	−0.142012	−	0.245971i
$733$	−1.08838e7	+	1.88512e7i	−0.748202	+	1.29592i	0.200481	+	0.979698i	$0.435749\pi$
$733$	−1.08838e7	+	1.88512e7i	−0.748202	+	1.29592i	−0.948684	+	0.316227i	$0.897584\pi$
$734$	−4.50797e6			−0.308845
$735$		0			0
$736$	−9.40044e6			−0.639667
$737$	−284920.	+	493496.i	−0.0193221	+	0.0334669i
$738$	−803277.	−	1.39132e6i	−0.0542906	−	0.0940340i
$739$	−3.10893e6	−	5.38482e6i	−0.209411	−	0.362711i	0.742118	−	0.670269i	$-0.233821\pi$
$739$	−3.10893e6	−	5.38482e6i	−0.209411	−	0.362711i	−0.951529	+	0.307558i	$0.900488\pi$
$740$	−5.16355e6	+	8.94352e6i	−0.346632	+	0.600384i
$741$	−3.64471e6			−0.243847
$742$		0			0
$743$	3.77647e6			0.250966			0.125483	−	0.992096i	$-0.459952\pi$
$743$	3.77647e6			0.250966			0.125483	+	0.992096i	$0.459952\pi$
$744$	707616.	−	1.22563e6i	0.0468668	−	0.0811757i
$745$	−5.03380e6	−	8.71880e6i	−0.332281	−	0.575527i
$746$	−832675.	−	1.44224e6i	−0.0547808	−	0.0948831i
$747$	1.52944e6	−	2.64907e6i	0.100284	−	0.173697i
$748$	−8.41092e6			−0.549654
$749$		0			0
$750$	−1.55876e6			−0.101188
$751$	1.44398e6	−	2.50104e6i	0.0934244	−	0.161816i	−0.815526	−	0.578721i	$-0.803552\pi$
$751$	1.44398e6	−	2.50104e6i	0.0934244	−	0.161816i	0.908950	+	0.416905i	$0.136885\pi$
$752$	−4.14706e6	−	7.18291e6i	−0.267421	−	0.463187i
$753$	1.42699e6	+	2.47161e6i	0.0917133	+	0.158852i
$754$	1.87093e6	−	3.24055e6i	0.119848	−	0.207582i
$755$	1.45000e7			0.925768
$756$		0			0
$757$	1.25519e6			0.0796104			0.0398052	−	0.999207i	$-0.487326\pi$
$757$	1.25519e6			0.0796104			0.0398052	+	0.999207i	$0.487326\pi$
$758$	1.26616e6	−	2.19306e6i	0.0800417	−	0.138636i
$759$	4.88376e6	+	8.45892e6i	0.307716	+	0.532979i
$760$	−955332.	−	1.65468e6i	−0.0599957	−	0.103916i
$761$	7.13115e6	−	1.23515e7i	0.446373	−	0.773140i	−0.551774	−	0.833994i	$-0.686049\pi$
$761$	7.13115e6	−	1.23515e7i	0.446373	−	0.773140i	0.998147	+	0.0608533i	$0.0193822\pi$
$762$	−1.76947e6			−0.110397
$763$		0			0
$764$	−1.56756e7			−0.971606
$765$	−1.09885e6	+	1.90326e6i	−0.0678865	+	0.117583i
$766$	−398184.	−	689675.i	−0.0245195	−	0.0424690i
$767$	9.62389e6	+	1.66691e7i	0.590694	+	1.02311i
$768$	3.31215e6	−	5.73681e6i	0.202631	−	0.350968i
$769$	−2.02261e7			−1.23338			−0.616689	−	0.787207i	$-0.711526\pi$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(4.50000 + 7.79423i) q^{3} +(15.5000 + 26.8468i) q^{4} +(17.0000 - 29.4449i) q^{5} -9.00000 q^{6} -63.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(4.50000 + 7.79423i) q^{3} +(15.5000 + 26.8468i) q^{4} +(17.0000 - 29.4449i) q^{5} -9.00000 q^{6} -63.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(17.0000 + 29.4449i) q^{10} +(170.000 + 294.449i) q^{11} +(-139.500 + 241.621i) q^{12} +454.000 q^{13} +306.000 q^{15} +(-464.500 + 804.538i) q^{16} +(399.000 + 691.088i) q^{17} +(-40.5000 - 70.1481i) q^{18} +(-446.000 + 772.495i) q^{19} +1054.00 q^{20} -340.000 q^{22} +(1596.00 - 2764.35i) q^{23} +(-283.500 - 491.036i) q^{24} +(984.500 + 1705.20i) q^{25} +(-227.000 + 393.176i) q^{26} -729.000 q^{27} -8242.00 q^{29} +(-153.000 + 265.004i) q^{30} +(1248.00 + 2161.60i) q^{31} +(-1472.50 - 2550.44i) q^{32} +(-1530.00 + 2650.04i) q^{33} -798.000 q^{34} -2511.00 q^{36} +(-4899.00 + 8485.32i) q^{37} +(-446.000 - 772.495i) q^{38} +(2043.00 + 3538.58i) q^{39} +(-1071.00 + 1855.03i) q^{40} +19834.0 q^{41} -17236.0 q^{43} +(-5270.00 + 9127.91i) q^{44} +(1377.00 + 2385.03i) q^{45} +(1596.00 + 2764.35i) q^{46} +(-4464.00 + 7731.87i) q^{47} -8361.00 q^{48} -1969.00 q^{50} +(-3591.00 + 6219.79i) q^{51} +(7037.00 + 12188.4i) q^{52} +(-75.0000 - 129.904i) q^{53} +(364.500 - 631.333i) q^{54} +11560.0 q^{55} -8028.00 q^{57} +(4121.00 - 7137.78i) q^{58} +(21198.0 + 36716.0i) q^{59} +(4743.00 + 8215.12i) q^{60} +(-7379.00 + 12780.8i) q^{61} -2496.00 q^{62} -26783.0 q^{64} +(7718.00 - 13368.0i) q^{65} +(-1530.00 - 2650.04i) q^{66} +(838.000 + 1451.46i) q^{67} +(-12369.0 + 21423.7i) q^{68} +28728.0 q^{69} +14568.0 q^{71} +(2551.50 - 4419.33i) q^{72} +(-39189.0 - 67877.3i) q^{73} +(-4899.00 - 8485.32i) q^{74} +(-8860.50 + 15346.8i) q^{75} -27652.0 q^{76} -4086.00 q^{78} +(1136.00 - 1967.61i) q^{79} +(15793.0 + 27354.3i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-9917.00 + 17176.7i) q^{82} -37764.0 q^{83} +27132.0 q^{85} +(8618.00 - 14926.8i) q^{86} +(-37089.0 - 64240.0i) q^{87} +(-10710.0 - 18550.3i) q^{88} +(58643.0 - 101573. i) q^{89} -2754.00 q^{90} +98952.0 q^{92} +(-11232.0 + 19454.4i) q^{93} +(-4464.00 - 7731.87i) q^{94} +(15164.0 + 26264.8i) q^{95} +(13252.5 - 22954.0i) q^{96} +10002.0 q^{97} -27540.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 9 q^{3} + 31 q^{4} + 34 q^{5} - 18 q^{6} - 126 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q - q^2 + 9 * q^3 + 31 * q^4 + 34 * q^5 - 18 * q^6 - 126 * q^8 - 81 * q^9	\( 2 q - q^{2} + 9 q^{3} + 31 q^{4} + 34 q^{5} - 18 q^{6} - 126 q^{8} - 81 q^{9} + 34 q^{10} + 340 q^{11} - 279 q^{12} + 908 q^{13} + 612 q^{15} - 929 q^{16} + 798 q^{17} - 81 q^{18} - 892 q^{19} + 2108 q^{20} - 680 q^{22} + 3192 q^{23} - 567 q^{24} + 1969 q^{25} - 454 q^{26} - 1458 q^{27} - 16484 q^{29} - 306 q^{30} + 2496 q^{31} - 2945 q^{32} - 3060 q^{33} - 1596 q^{34} - 5022 q^{36} - 9798 q^{37} - 892 q^{38} + 4086 q^{39} - 2142 q^{40} + 39668 q^{41} - 34472 q^{43} - 10540 q^{44} + 2754 q^{45} + 3192 q^{46} - 8928 q^{47} - 16722 q^{48} - 3938 q^{50} - 7182 q^{51} + 14074 q^{52} - 150 q^{53} + 729 q^{54} + 23120 q^{55} - 16056 q^{57} + 8242 q^{58} + 42396 q^{59} + 9486 q^{60} - 14758 q^{61} - 4992 q^{62} - 53566 q^{64} + 15436 q^{65} - 3060 q^{66} + 1676 q^{67} - 24738 q^{68} + 57456 q^{69} + 29136 q^{71} + 5103 q^{72} - 78378 q^{73} - 9798 q^{74} - 17721 q^{75} - 55304 q^{76} - 8172 q^{78} + 2272 q^{79} + 31586 q^{80} - 6561 q^{81} - 19834 q^{82} - 75528 q^{83} + 54264 q^{85} + 17236 q^{86} - 74178 q^{87} - 21420 q^{88} + 117286 q^{89} - 5508 q^{90} + 197904 q^{92} - 22464 q^{93} - 8928 q^{94} + 30328 q^{95} + 26505 q^{96} + 20004 q^{97} - 55080 q^{99}+O(q^{100}) \) 2 * q - q^2 + 9 * q^3 + 31 * q^4 + 34 * q^5 - 18 * q^6 - 126 * q^8 - 81 * q^9 + 34 * q^10 + 340 * q^11 - 279 * q^12 + 908 * q^13 + 612 * q^15 - 929 * q^16 + 798 * q^17 - 81 * q^18 - 892 * q^19 + 2108 * q^20 - 680 * q^22 + 3192 * q^23 - 567 * q^24 + 1969 * q^25 - 454 * q^26 - 1458 * q^27 - 16484 * q^29 - 306 * q^30 + 2496 * q^31 - 2945 * q^32 - 3060 * q^33 - 1596 * q^34 - 5022 * q^36 - 9798 * q^37 - 892 * q^38 + 4086 * q^39 - 2142 * q^40 + 39668 * q^41 - 34472 * q^43 - 10540 * q^44 + 2754 * q^45 + 3192 * q^46 - 8928 * q^47 - 16722 * q^48 - 3938 * q^50 - 7182 * q^51 + 14074 * q^52 - 150 * q^53 + 729 * q^54 + 23120 * q^55 - 16056 * q^57 + 8242 * q^58 + 42396 * q^59 + 9486 * q^60 - 14758 * q^61 - 4992 * q^62 - 53566 * q^64 + 15436 * q^65 - 3060 * q^66 + 1676 * q^67 - 24738 * q^68 + 57456 * q^69 + 29136 * q^71 + 5103 * q^72 - 78378 * q^73 - 9798 * q^74 - 17721 * q^75 - 55304 * q^76 - 8172 * q^78 + 2272 * q^79 + 31586 * q^80 - 6561 * q^81 - 19834 * q^82 - 75528 * q^83 + 54264 * q^85 + 17236 * q^86 - 74178 * q^87 - 21420 * q^88 + 117286 * q^89 - 5508 * q^90 + 197904 * q^92 - 22464 * q^93 - 8928 * q^94 + 30328 * q^95 + 26505 * q^96 + 20004 * q^97 - 55080 * q^99

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