LMFDB - Embedded newform 147.6.e.e.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.e.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	−0.977062	−	0.212956i	$-0.931691\pi$
$5$	−17.0000	+	29.4449i	−0.304105	+	0.526726i	0.672956	+	0.739682i	$0.265024\pi$
$6$	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	$-0.621511\pi$
$13$	−454.000			−0.745071			−0.372535	+	0.928018i	$0.621511\pi$
$14$		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	0.648606	−	0.761124i	$-0.275352\pi$
$17$	−399.000	−	691.088i	−0.334850	−	0.579978i	−0.983456	+	0.181147i	$0.942019\pi$
$18$	−40.5000	−	70.1481i	−0.0294628	−	0.0510310i
$19$	446.000	−	772.495i	0.283433	−	0.490921i	−0.688795	−	0.724956i	$-0.741860\pi$
$19$	446.000	−	772.495i	0.283433	−	0.490921i	0.972228	+	0.234036i	$0.0751932\pi$
$20$	−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	0.725517	−	0.688204i	$-0.241601\pi$
$31$	−1248.00	−	2161.60i	−0.233244	−	0.403990i	−0.958761	+	0.284214i	$0.908267\pi$
$32$	−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	$-0.872906\pi$
$41$	−19834.0			−1.84268			−0.921342	+	0.388754i	$0.872906\pi$
$42$		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	−0.680163	−	0.733061i	$-0.738091\pi$
$47$	4464.00	−	7731.87i	0.294767	−	0.510552i	0.974931	+	0.222508i	$0.0714245\pi$
$48$	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	$-0.875288\pi$
$59$	−21198.0	−	36716.0i	−0.792802	−	1.37317i	0.131423	−	0.991326i	$-0.458045\pi$
$60$	4743.00	+	8215.12i	0.170089	+	0.294602i
$61$	7379.00	−	12780.8i	0.253906	−	0.439778i	−0.710692	−	0.703503i	$-0.751618\pi$
$61$	7379.00	−	12780.8i	0.253906	−	0.439778i	0.964598	+	0.263725i	$0.0849513\pi$
$62$	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	$0.163314\pi$
$73$	39189.0	+	67877.3i	0.860710	+	1.49079i	−0.0105340	+	0.999945i	$0.503353\pi$
$74$	−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	$-0.402729\pi$
$83$	37764.0			0.601704			0.300852	+	0.953671i	$0.402729\pi$
$84$		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	$0.453884\pi$
$89$	−58643.0	+	101573.i	−0.784768	+	1.35926i	−0.929138	+	0.369734i	$0.879449\pi$
$90$	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	$-0.517187\pi$
$97$	−10002.0			−0.107934			−0.0539669	+	0.998543i	$0.517187\pi$
$98$		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	$-0.988675\pi$
$101$	−54385.0	−	94197.6i	−0.530488	−	0.918832i	0.468879	−	0.883262i	$-0.344658\pi$
$102$	−3591.00	−	6219.79i	−0.0341755	−	0.0591937i
$103$	−99596.0	+	172505.i	−0.925015	+	1.60217i	−0.133478	+	0.991052i	$0.542615\pi$
$103$	−99596.0	+	172505.i	−0.925015	+	1.60217i	−0.791537	+	0.611121i	$0.790719\pi$
$104$	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	−0.947348	−	0.320205i	$-0.896248\pi$
$131$	−38570.0	+	66805.2i	−0.196368	+	0.340120i	0.750980	+	0.660325i	$0.229581\pi$
$132$	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	$-0.293215\pi$
$139$	275580.			1.20979			0.604896	+	0.796304i	$0.293215\pi$
$140$		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	0.973560	−	0.228432i	$-0.0733600\pi$
$157$	89243.0	+	154573.i	0.288952	+	0.500479i	−0.684608	+	0.728911i	$0.740027\pi$
$158$	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	$-0.749001\pi$
$167$	−508088.			−1.40977			−0.704884	+	0.709322i	$0.749001\pi$
$168$		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	−0.971819	−	0.235729i	$-0.924252\pi$
$173$	−110917.	+	192114.i	−0.281762	+	0.488027i	0.690057	+	0.723755i	$0.257586\pi$
$174$	−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	$-0.771033\pi$
$181$	−663118.			−1.50451			−0.752254	+	0.658873i	$0.771033\pi$
$182$		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	0.968137	−	0.250420i	$-0.0805687\pi$
$199$	149268.	+	258540.i	0.267199	+	0.462801i	−0.700939	+	0.713221i	$0.747235\pi$
$200$	−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	$-0.586660\pi$
$223$	−399376.			−0.537799			−0.268899	+	0.963168i	$0.586660\pi$
$224$		0			0
$225$	−159489.			−0.210027
$226$	−131353.	+	227510.i	−0.171068	+	0.296299i
$227$	353958.	+	613073.i	0.455918	+	0.789674i	0.998740	−	0.0501739i	$-0.0159776\pi$
$227$	353958.	+	613073.i	0.455918	+	0.789674i	−0.542822	+	0.839848i	$0.682644\pi$
$228$	−124434.	−	215526.i	−0.158527	−	0.274576i
$229$	−367889.	+	637202.i	−0.463584	+	0.802950i	−0.999136	−	0.0415514i	$-0.986770\pi$
$229$	−367889.	+	637202.i	−0.463584	+	0.802950i	0.535553	+	0.844502i	$0.320103\pi$
$230$	−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	0.691252	−	0.722614i	$-0.257059\pi$
$241$	−252623.	−	437556.i	−0.280176	−	0.485278i	−0.971428	+	0.237335i	$0.923726\pi$
$242$	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	$-0.550779\pi$
$251$	−317108.			−0.317704			−0.158852	+	0.987302i	$0.550779\pi$
$252$		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	$0.405265\pi$
$257$	−721423.	+	1.24954e6i	−0.681329	+	1.18010i	−0.974575	+	0.224060i	$0.928069\pi$
$258$	−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	0.987687	−	0.156441i	$-0.0500021\pi$
$269$	425307.	+	736653.i	0.358362	+	0.620701i	−0.629325	+	0.777142i	$0.716669\pi$
$270$	−12393.0	−	21465.3i	−0.0103459	−	0.0179196i
$271$	−270064.	+	467765.i	−0.223380	+	0.386905i	−0.955832	−	0.293913i	$-0.905042\pi$
$271$	−270064.	+	467765.i	−0.223380	+	0.386905i	0.732452	+	0.680818i	$0.238376\pi$
$272$	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	0.914317	−	0.405000i	$-0.132728\pi$
$283$	143378.	+	248338.i	0.106418	+	0.184322i	−0.807898	+	0.589322i	$0.799395\pi$
$284$	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	$-0.302700\pi$
$293$	1.70727e6			1.16180			0.580901	+	0.813974i	$0.302700\pi$
$294$		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	$-0.447058\pi$
$307$	546788.			0.331111			0.165555	+	0.986201i	$0.447058\pi$
$308$		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	$0.230310\pi$
$311$	1.61713e6	+	2.80095e6i	0.948079	+	1.64212i	0.198613	+	0.980078i	$0.436356\pi$
$312$	−128709.	−	222931.i	−0.0748553	−	0.129653i
$313$	906565.	−	1.57022e6i	0.523044	−	0.905939i	−0.476597	−	0.879122i	$-0.658130\pi$
$313$	906565.	−	1.57022e6i	0.523044	−	0.905939i	0.999640	−	0.0268164i	$-0.00853694\pi$
$314$	−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	$-0.589767\pi$
$349$	−1.26645e6			−0.556578			−0.278289	+	0.960497i	$0.589767\pi$
$350$		0			0
$351$	−330966.			−0.143389
$352$	500650.	−	867151.i	0.215366	−	0.373025i
$353$	286609.	+	496421.i	0.122420	+	0.212038i	0.920722	−	0.390220i	$-0.127601\pi$
$353$	286609.	+	496421.i	0.122420	+	0.212038i	−0.798301	+	0.602258i	$0.794268\pi$
$354$	−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	$-0.828481\pi$
$367$	−2.25398e6	−	3.90401e6i	−0.873546	−	1.51303i	−0.0152419	−	0.999884i	$-0.504852\pi$
$368$	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	−0.788303	−	0.615288i	$-0.789040\pi$
$383$	398184.	−	689675.i	0.138703	−	0.240241i	0.927006	+	0.375046i	$0.122373\pi$
$384$	−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	−0.767028	−	0.641614i	$-0.778265\pi$
$397$	540579.	−	936310.i	0.172140	−	0.298156i	0.939168	+	0.343458i	$0.111598\pi$
$398$	−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	0.986128	−	0.165987i	$-0.0530811\pi$
$409$	1.18175e6	+	2.04685e6i	0.349315	+	0.605031i	−0.636813	+	0.771018i	$0.719748\pi$
$410$	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	$-0.363588\pi$
$419$	2.98669e6			0.831104			0.415552	+	0.909569i	$0.363588\pi$
$420$		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	$-0.351555\pi$
$433$	3.50838e6			0.899264			0.449632	+	0.893214i	$0.351555\pi$
$434$		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	−0.558269	−	0.829660i	$-0.688534\pi$
$439$	1.77416e6	−	3.07294e6i	0.439372	−	0.761015i	0.997641	+	0.0686452i	$0.0218676\pi$
$440$	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	$-0.574584\pi$
$461$	−2.11884e6			−0.464350			−0.232175	+	0.972674i	$0.574584\pi$
$462$		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	$0.455474\pi$
$467$	−3.71311e6	+	6.43129e6i	−0.787853	+	1.36460i	−0.927280	+	0.374369i	$0.877859\pi$
$468$	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	0.645873	−	0.763445i	$-0.276494\pi$
$479$	−1.69842e6	−	2.94176e6i	−0.338226	−	0.585825i	−0.984099	+	0.177620i	$0.943160\pi$
$480$	−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	$-0.691420\pi$
$503$	−6.42079e6			−1.13154			−0.565768	+	0.824564i	$0.691420\pi$
$504$		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	−0.859701	−	0.510797i	$-0.829350\pi$
$509$	73139.0	−	126680.i	0.0125128	−	0.0216728i	0.872214	+	0.489124i	$0.162684\pi$
$510$	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	$0.0470736\pi$
$521$	3.85468e6	+	6.67651e6i	0.622149	+	1.07759i	−0.366935	+	0.930246i	$0.619593\pi$
$522$	333801.	+	578160.i	0.0536181	+	0.0928693i
$523$	−284710.	+	493132.i	−0.0455144	+	0.0788332i	−0.887885	−	0.460065i	$-0.847826\pi$
$523$	−284710.	+	493132.i	−0.0455144	+	0.0788332i	0.842371	+	0.538898i	$0.181159\pi$
$524$	−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	$-0.918355\pi$
$563$	−5.28982e6	−	9.16223e6i	−0.703347	−	1.21823i	0.263938	−	0.964540i	$-0.414979\pi$
$564$	−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	$0.00498618\pi$
$577$	4.10661e6	+	7.11286e6i	0.513504	+	0.889415i	−0.486373	+	0.873751i	$0.661680\pi$
$578$	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	$-0.476754\pi$
$587$	1.21827e6			0.145931			0.0729655	+	0.997334i	$0.476754\pi$
$588$		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	−0.999956	−	0.00937481i	$-0.997016\pi$
$593$	−4.21190e6	+	7.29522e6i	−0.491859	+	0.851925i	0.508097	+	0.861300i	$0.330349\pi$
$594$	−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	$-0.558834\pi$
$601$	−3.25478e6			−0.367566			−0.183783	+	0.982967i	$0.558834\pi$
$602$		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	−0.566156	−	0.824298i	$-0.691570\pi$
$607$	3.91050e6	−	6.77319e6i	0.430785	−	0.746142i	0.996941	+	0.0781561i	$0.0249032\pi$
$608$	−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	0.651247	−	0.758866i	$-0.274246\pi$
$619$	−3.16087e6	−	5.47479e6i	−0.331574	−	0.574302i	−0.982821	+	0.184563i	$0.940913\pi$
$620$	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	$-0.779552\pi$
$643$	−1.61373e7			−1.53923			−0.769615	+	0.638508i	$0.779552\pi$
$644$		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	$-0.898901\pi$
$647$	−7.93743e6	−	1.37480e7i	−0.745451	−	1.29116i	0.204533	−	0.978860i	$-0.434433\pi$
$648$	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	0.646301	−	0.763083i	$-0.276315\pi$
$661$	−3.79344e6	−	6.57043e6i	−0.337699	−	0.584912i	−0.983999	+	0.178171i	$0.942982\pi$
$662$	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	−0.651681	−	0.758493i	$-0.725936\pi$
$677$	3.94770e6	−	6.83762e6i	0.331034	−	0.573368i	0.982715	+	0.185125i	$0.0592691\pi$
$678$	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	$0.408180\pi$
$691$	−8.63549e6	+	1.49571e7i	−0.688005	+	1.19166i	−0.972482	+	0.232977i	$0.925153\pi$
$692$	−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	−0.858266	−	0.513205i	$-0.828458\pi$
$719$	212304.	−	367721.i	0.0153157	−	0.0265275i	0.873582	+	0.486678i	$0.161791\pi$
$720$	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	$-0.777703\pi$
$727$	−2.18290e7			−1.53179			−0.765893	+	0.642968i	$0.777703\pi$
$728$		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	$-0.564251\pi$
$733$	1.08838e7	−	1.88512e7i	0.748202	−	1.29592i	0.948684	−	0.316227i	$-0.102416\pi$
$734$	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	−0.998147	−	0.0608533i	$-0.980618\pi$
$761$	−7.13115e6	+	1.23515e7i	−0.446373	+	0.773140i	0.551774	+	0.833994i	$0.313951\pi$
$762$	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

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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