LMFDB - Embedded newform 147.6.e.c.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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50000 + 4.33013i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-47.0000 + 81.4064i) q^{5} +45.0000 q^{6} -195.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.50000 + 4.33013i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-47.0000 + 81.4064i) q^{5} +45.0000 q^{6} -195.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-235.000 - 407.032i) q^{10} +(-26.0000 - 45.0333i) q^{11} +(31.5000 - 54.5596i) q^{12} -770.000 q^{13} +846.000 q^{15} +(375.500 - 650.385i) q^{16} +(1011.00 + 1751.10i) q^{17} +(-202.500 - 350.740i) q^{18} +(-866.000 + 1499.96i) q^{19} -658.000 q^{20} +260.000 q^{22} +(288.000 - 498.831i) q^{23} +(877.500 + 1519.87i) q^{24} +(-2855.50 - 4945.87i) q^{25} +(1925.00 - 3334.20i) q^{26} +729.000 q^{27} +5518.00 q^{29} +(-2115.00 + 3663.29i) q^{30} +(-3168.00 - 5487.14i) q^{31} +(-1242.50 - 2152.07i) q^{32} +(-234.000 + 405.300i) q^{33} -10110.0 q^{34} -567.000 q^{36} +(3669.00 - 6354.89i) q^{37} +(-4330.00 - 7499.78i) q^{38} +(3465.00 + 6001.56i) q^{39} +(9165.00 - 15874.2i) q^{40} -3262.00 q^{41} +5420.00 q^{43} +(182.000 - 315.233i) q^{44} +(-3807.00 - 6593.92i) q^{45} +(1440.00 + 2494.15i) q^{46} +(-432.000 + 748.246i) q^{47} -6759.00 q^{48} +28555.0 q^{50} +(9099.00 - 15759.9i) q^{51} +(-2695.00 - 4667.88i) q^{52} +(-2091.00 - 3621.72i) q^{53} +(-1822.50 + 3156.66i) q^{54} +4888.00 q^{55} +15588.0 q^{57} +(-13795.0 + 23893.6i) q^{58} +(5610.00 + 9716.81i) q^{59} +(2961.00 + 5128.60i) q^{60} +(22801.0 - 39492.5i) q^{61} +31680.0 q^{62} +36457.0 q^{64} +(36190.0 - 62682.9i) q^{65} +(-1170.00 - 2026.50i) q^{66} +(-698.000 - 1208.97i) q^{67} +(-7077.00 + 12257.7i) q^{68} -5184.00 q^{69} +18720.0 q^{71} +(7897.50 - 13678.9i) q^{72} +(-23181.0 - 40150.7i) q^{73} +(18345.0 + 31774.5i) q^{74} +(-25699.5 + 44512.8i) q^{75} -12124.0 q^{76} -34650.0 q^{78} +(-48712.0 + 84371.7i) q^{79} +(35297.0 + 61136.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(8155.00 - 14124.9i) q^{82} -81228.0 q^{83} -190068. q^{85} +(-13550.0 + 23469.3i) q^{86} +(-24831.0 - 43008.6i) q^{87} +(5070.00 + 8781.50i) q^{88} +(1591.00 - 2755.69i) q^{89} +38070.0 q^{90} +4032.00 q^{92} +(-28512.0 + 49384.2i) q^{93} +(-2160.00 - 3741.23i) q^{94} +(-81404.0 - 140996. i) q^{95} +(-11182.5 + 19368.7i) q^{96} +4914.00 q^{97} +4212.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 5 q^{2} - 9 q^{3} + 7 q^{4} - 94 q^{5} + 90 q^{6} - 390 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q - 5 * q^2 - 9 * q^3 + 7 * q^4 - 94 * q^5 + 90 * q^6 - 390 * q^8 - 81 * q^9	\( 2 q - 5 q^{2} - 9 q^{3} + 7 q^{4} - 94 q^{5} + 90 q^{6} - 390 q^{8} - 81 q^{9} - 470 q^{10} - 52 q^{11} + 63 q^{12} - 1540 q^{13} + 1692 q^{15} + 751 q^{16} + 2022 q^{17} - 405 q^{18} - 1732 q^{19} - 1316 q^{20} + 520 q^{22} + 576 q^{23} + 1755 q^{24} - 5711 q^{25} + 3850 q^{26} + 1458 q^{27} + 11036 q^{29} - 4230 q^{30} - 6336 q^{31} - 2485 q^{32} - 468 q^{33} - 20220 q^{34} - 1134 q^{36} + 7338 q^{37} - 8660 q^{38} + 6930 q^{39} + 18330 q^{40} - 6524 q^{41} + 10840 q^{43} + 364 q^{44} - 7614 q^{45} + 2880 q^{46} - 864 q^{47} - 13518 q^{48} + 57110 q^{50} + 18198 q^{51} - 5390 q^{52} - 4182 q^{53} - 3645 q^{54} + 9776 q^{55} + 31176 q^{57} - 27590 q^{58} + 11220 q^{59} + 5922 q^{60} + 45602 q^{61} + 63360 q^{62} + 72914 q^{64} + 72380 q^{65} - 2340 q^{66} - 1396 q^{67} - 14154 q^{68} - 10368 q^{69} + 37440 q^{71} + 15795 q^{72} - 46362 q^{73} + 36690 q^{74} - 51399 q^{75} - 24248 q^{76} - 69300 q^{78} - 97424 q^{79} + 70594 q^{80} - 6561 q^{81} + 16310 q^{82} - 162456 q^{83} - 380136 q^{85} - 27100 q^{86} - 49662 q^{87} + 10140 q^{88} + 3182 q^{89} + 76140 q^{90} + 8064 q^{92} - 57024 q^{93} - 4320 q^{94} - 162808 q^{95} - 22365 q^{96} + 9828 q^{97} + 8424 q^{99}+O(q^{100}) \) 2 * q - 5 * q^2 - 9 * q^3 + 7 * q^4 - 94 * q^5 + 90 * q^6 - 390 * q^8 - 81 * q^9 - 470 * q^10 - 52 * q^11 + 63 * q^12 - 1540 * q^13 + 1692 * q^15 + 751 * q^16 + 2022 * q^17 - 405 * q^18 - 1732 * q^19 - 1316 * q^20 + 520 * q^22 + 576 * q^23 + 1755 * q^24 - 5711 * q^25 + 3850 * q^26 + 1458 * q^27 + 11036 * q^29 - 4230 * q^30 - 6336 * q^31 - 2485 * q^32 - 468 * q^33 - 20220 * q^34 - 1134 * q^36 + 7338 * q^37 - 8660 * q^38 + 6930 * q^39 + 18330 * q^40 - 6524 * q^41 + 10840 * q^43 + 364 * q^44 - 7614 * q^45 + 2880 * q^46 - 864 * q^47 - 13518 * q^48 + 57110 * q^50 + 18198 * q^51 - 5390 * q^52 - 4182 * q^53 - 3645 * q^54 + 9776 * q^55 + 31176 * q^57 - 27590 * q^58 + 11220 * q^59 + 5922 * q^60 + 45602 * q^61 + 63360 * q^62 + 72914 * q^64 + 72380 * q^65 - 2340 * q^66 - 1396 * q^67 - 14154 * q^68 - 10368 * q^69 + 37440 * q^71 + 15795 * q^72 - 46362 * q^73 + 36690 * q^74 - 51399 * q^75 - 24248 * q^76 - 69300 * q^78 - 97424 * q^79 + 70594 * q^80 - 6561 * q^81 + 16310 * q^82 - 162456 * q^83 - 380136 * q^85 - 27100 * q^86 - 49662 * q^87 + 10140 * q^88 + 3182 * q^89 + 76140 * q^90 + 8064 * q^92 - 57024 * q^93 - 4320 * q^94 - 162808 * q^95 - 22365 * q^96 + 9828 * q^97 + 8424 * 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 $

$2$	−2.50000	+	4.33013i	−0.441942	+	0.765466i	−0.997834	−	0.0657891i	$-0.979044\pi$
$2$	−2.50000	+	4.33013i	−0.441942	+	0.765466i	0.555892	+	0.831255i	$0.312377\pi$
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	3.50000	+	6.06218i	0.109375	+	0.189443i
$5$	−47.0000	+	81.4064i	−0.840762	+	1.45624i	0.0484902	+	0.998824i	$0.484559\pi$
$5$	−47.0000	+	81.4064i	−0.840762	+	1.45624i	−0.889252	+	0.457418i	$0.848774\pi$
$6$	45.0000			0.510310
$7$		0			0
$7$		0			0
$8$	−195.000			−1.07723
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−235.000	−	407.032i	−0.743135	−	1.28715i
$11$	−26.0000	−	45.0333i	−0.0647876	−	0.112215i	0.831812	−	0.555057i	$-0.187304\pi$
$11$	−26.0000	−	45.0333i	−0.0647876	−	0.112215i	−0.896600	+	0.442842i	$0.853970\pi$
$12$	31.5000	−	54.5596i	0.0631477	−	0.109375i
$13$	−770.000			−1.26367			−0.631833	−	0.775104i	$-0.717697\pi$
$13$	−770.000			−1.26367			−0.631833	+	0.775104i	$0.717697\pi$
$14$		0			0
$15$	846.000			0.970828
$16$	375.500	−	650.385i	0.366699	−	0.635142i
$17$	1011.00	+	1751.10i	0.848455	+	1.46957i	0.882587	+	0.470150i	$0.155800\pi$
$17$	1011.00	+	1751.10i	0.848455	+	1.46957i	−0.0341315	+	0.999417i	$0.510866\pi$
$18$	−202.500	−	350.740i	−0.147314	−	0.255155i
$19$	−866.000	+	1499.96i	−0.550344	+	0.953223i	0.447906	+	0.894081i	$0.352170\pi$
$19$	−866.000	+	1499.96i	−0.550344	+	0.953223i	−0.998250	+	0.0591424i	$0.981163\pi$
$20$	−658.000			−0.367833
$21$		0			0
$22$	260.000			0.114529
$23$	288.000	−	498.831i	0.113520	−	0.196623i	−0.803667	−	0.595079i	$-0.797121\pi$
$23$	288.000	−	498.831i	0.113520	−	0.196623i	0.917187	+	0.398457i	$0.130454\pi$
$24$	877.500	+	1519.87i	0.310970	+	0.538616i
$25$	−2855.50	−	4945.87i	−0.913760	−	1.58268i
$26$	1925.00	−	3334.20i	0.558467	−	0.967293i
$27$	729.000			0.192450
$28$		0			0
$29$	5518.00			1.21839			0.609196	−	0.793020i	$-0.291492\pi$
$29$	5518.00			1.21839			0.609196	+	0.793020i	$0.291492\pi$
$30$	−2115.00	+	3663.29i	−0.429049	+	0.743135i
$31$	−3168.00	−	5487.14i	−0.592081	−	1.02551i	−0.993952	−	0.109818i	$-0.964973\pi$
$31$	−3168.00	−	5487.14i	−0.592081	−	1.02551i	0.401871	−	0.915696i	$-0.368360\pi$
$32$	−1242.50	−	2152.07i	−0.214497	−	0.371520i
$33$	−234.000	+	405.300i	−0.0374051	+	0.0647876i
$34$	−10110.0			−1.49987
$35$		0			0
$36$	−567.000			−0.0729167
$37$	3669.00	−	6354.89i	0.440599	−	0.763140i	−0.557135	−	0.830422i	$-0.688099\pi$
$37$	3669.00	−	6354.89i	0.440599	−	0.763140i	0.997734	+	0.0672822i	$0.0214328\pi$
$38$	−4330.00	−	7499.78i	−0.486440	−	0.842538i
$39$	3465.00	+	6001.56i	0.364789	+	0.631833i
$40$	9165.00	−	15874.2i	0.905696	−	1.56871i
$41$	−3262.00			−0.303057			−0.151528	−	0.988453i	$-0.548420\pi$
$41$	−3262.00			−0.303057			−0.151528	+	0.988453i	$0.548420\pi$
$42$		0			0
$43$	5420.00			0.447021			0.223511	−	0.974701i	$-0.428248\pi$
$43$	5420.00			0.447021			0.223511	+	0.974701i	$0.428248\pi$
$44$	182.000	−	315.233i	0.0141723	−	0.0245471i
$45$	−3807.00	−	6593.92i	−0.280254	−	0.485414i
$46$	1440.00	+	2494.15i	0.100339	+	0.173792i
$47$	−432.000	+	748.246i	−0.0285259	+	0.0494083i	−0.879936	−	0.475092i	$-0.842415\pi$
$47$	−432.000	+	748.246i	−0.0285259	+	0.0494083i	0.851410	+	0.524501i	$0.175748\pi$
$48$	−6759.00			−0.423428
$49$		0			0
$50$	28555.0			1.61531
$51$	9099.00	−	15759.9i	0.489856	−	0.848455i
$52$	−2695.00	−	4667.88i	−0.138213	−	0.239393i
$53$	−2091.00	−	3621.72i	−0.102250	−	0.177103i	0.810361	−	0.585931i	$-0.199271\pi$
$53$	−2091.00	−	3621.72i	−0.102250	−	0.177103i	−0.912611	+	0.408828i	$0.865938\pi$
$54$	−1822.50	+	3156.66i	−0.0850517	+	0.147314i
$55$	4888.00			0.217884
$56$		0			0
$57$	15588.0			0.635482
$58$	−13795.0	+	23893.6i	−0.538458	+	0.932636i
$59$	5610.00	+	9716.81i	0.209813	+	0.363407i	0.951656	−	0.307167i	$-0.0993811\pi$
$59$	5610.00	+	9716.81i	0.209813	+	0.363407i	−0.741842	+	0.670574i	$0.766048\pi$
$60$	2961.00	+	5128.60i	0.106184	+	0.183917i
$61$	22801.0	−	39492.5i	0.784566	−	1.35891i	−0.144693	−	0.989477i	$-0.546219\pi$
$61$	22801.0	−	39492.5i	0.784566	−	1.35891i	0.929258	−	0.369431i	$-0.120447\pi$
$62$	31680.0			1.04666
$63$		0			0
$64$	36457.0			1.11258
$65$	36190.0	−	62682.9i	1.06244	−	1.84020i
$66$	−1170.00	−	2026.50i	−0.0330618	−	0.0572647i
$67$	−698.000	−	1208.97i	−0.0189963	−	0.0329025i	0.856371	−	0.516361i	$-0.172714\pi$
$67$	−698.000	−	1208.97i	−0.0189963	−	0.0329025i	−0.875367	+	0.483459i	$0.839380\pi$
$68$	−7077.00	+	12257.7i	−0.185600	+	0.321468i
$69$	−5184.00			−0.131082
$70$		0			0
$71$	18720.0			0.440717			0.220359	−	0.975419i	$-0.429277\pi$
$71$	18720.0			0.440717			0.220359	+	0.975419i	$0.429277\pi$
$72$	7897.50	−	13678.9i	0.179539	−	0.310970i
$73$	−23181.0	−	40150.7i	−0.509126	−	0.881832i	−0.999944	−	0.0105697i	$-0.996635\pi$
$73$	−23181.0	−	40150.7i	−0.509126	−	0.881832i	0.490818	−	0.871262i	$-0.336698\pi$
$74$	18345.0	+	31774.5i	0.389438	+	0.674527i
$75$	−25699.5	+	44512.8i	−0.527560	+	0.913760i
$76$	−12124.0			−0.240775
$77$		0			0
$78$	−34650.0			−0.644862
$79$	−48712.0	+	84371.7i	−0.878149	+	1.52100i	−0.0247791	+	0.999693i	$0.507888\pi$
$79$	−48712.0	+	84371.7i	−0.878149	+	1.52100i	−0.853370	+	0.521306i	$0.825445\pi$
$80$	35297.0	+	61136.2i	0.616613	+	1.06801i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	8155.00	−	14124.9i	0.133934	−	0.231980i
$83$	−81228.0			−1.29423			−0.647114	−	0.762394i	$-0.724024\pi$
$83$	−81228.0			−1.29423			−0.647114	+	0.762394i	$0.724024\pi$
$84$		0			0
$85$	−190068.			−2.85339
$86$	−13550.0	+	23469.3i	−0.197557	+	0.342179i
$87$	−24831.0	−	43008.6i	−0.351719	−	0.609196i
$88$	5070.00	+	8781.50i	0.0697913	+	0.120882i
$89$	1591.00	−	2755.69i	0.0212910	−	0.0368770i	−0.855184	−	0.518325i	$-0.826556\pi$
$89$	1591.00	−	2755.69i	0.0212910	−	0.0368770i	0.876475	+	0.481448i	$0.159889\pi$
$90$	38070.0			0.495424
$91$		0			0
$92$	4032.00			0.0496651
$93$	−28512.0	+	49384.2i	−0.341838	+	0.592081i
$94$	−2160.00	−	3741.23i	−0.0252136	−	0.0436712i
$95$	−81404.0	−	140996.i	−0.925415	−	1.60287i
$96$	−11182.5	+	19368.7i	−0.123840	+	0.214497i
$97$	4914.00			0.0530281			0.0265140	−	0.999648i	$-0.491559\pi$
$97$	4914.00			0.0530281			0.0265140	+	0.999648i	$0.491559\pi$
$98$		0			0
$99$	4212.00			0.0431917
$100$	19988.5	−	34621.1i	0.199885	−	0.346211i
$101$	83177.0	+	144067.i	0.811334	+	1.40527i	0.911930	+	0.410345i	$0.134592\pi$
$101$	83177.0	+	144067.i	0.811334	+	1.40527i	−0.100596	+	0.994927i	$0.532075\pi$
$102$	45495.0	+	78799.7i	0.432975	+	0.749935i
$103$	−78580.0	+	136105.i	−0.729825	+	1.26409i	0.227131	+	0.973864i	$0.427065\pi$
$103$	−78580.0	+	136105.i	−0.729825	+	1.26409i	−0.956957	+	0.290231i	$0.906268\pi$
$104$	150150.			1.36126
$105$		0			0
$106$	20910.0			0.180755
$107$	3382.00	−	5857.80i	0.0285571	−	0.0494624i	−0.851394	−	0.524527i	$-0.824242\pi$
$107$	3382.00	−	5857.80i	0.0285571	−	0.0494624i	0.879951	+	0.475065i	$0.157575\pi$
$108$	2551.50	+	4419.33i	0.0210492	+	0.0364583i
$109$	−89199.0	−	154497.i	−0.719107	−	1.24553i	−0.961354	−	0.275316i	$-0.911218\pi$
$109$	−89199.0	−	154497.i	−0.719107	−	1.24553i	0.242246	−	0.970215i	$-0.422116\pi$
$110$	−12220.0	+	21165.7i	−0.0962918	+	0.166782i
$111$	−66042.0			−0.508760
$112$		0			0
$113$	−45134.0			−0.332512			−0.166256	−	0.986083i	$-0.553168\pi$
$113$	−45134.0			−0.332512			−0.166256	+	0.986083i	$0.553168\pi$
$114$	−38970.0	+	67498.0i	−0.280846	+	0.486440i
$115$	27072.0	+	46890.1i	0.190887	+	0.330626i
$116$	19313.0	+	33451.1i	0.133262	+	0.230816i
$117$	31185.0	−	54014.0i	0.210611	−	0.364789i
$118$	−56100.0			−0.370901
$119$		0			0
$120$	−164970.			−1.04581
$121$	79173.5	−	137133.i	0.491605	−	0.851485i
$122$	114005.	+	197462.i	0.693465	+	1.20112i
$123$	14679.0	+	25424.8i	0.0874850	+	0.151528i
$124$	22176.0	−	38410.0i	0.129518	−	0.224331i
$125$	243084.			1.39149
$126$		0			0
$127$	−205056.			−1.12814			−0.564070	−	0.825727i	$-0.690765\pi$
$127$	−205056.			−1.12814			−0.564070	+	0.825727i	$0.690765\pi$
$128$	−51382.5	+	88997.1i	−0.277198	+	0.480121i
$129$	−24390.0	−	42244.7i	−0.129044	−	0.223511i
$130$	180950.	+	313415.i	0.939075	+	1.62653i
$131$	−36482.0	+	63188.7i	−0.185738	+	0.321707i	−0.943825	−	0.330446i	$-0.892801\pi$
$131$	−36482.0	+	63188.7i	−0.185738	+	0.321707i	0.758087	+	0.652153i	$0.226134\pi$
$132$	−3276.00			−0.0163647
$133$		0			0
$134$	6980.00			0.0335810
$135$	−34263.0	+	59345.3i	−0.161805	+	0.280254i
$136$	−197145.	−	341465.i	−0.913984	−	1.58307i
$137$	47091.0	+	81564.0i	0.214356	+	0.371276i	0.953073	−	0.302740i	$-0.0979013\pi$
$137$	47091.0	+	81564.0i	0.214356	+	0.371276i	−0.738717	+	0.674016i	$0.764568\pi$
$138$	12960.0	−	22447.4i	0.0579305	−	0.100339i
$139$	−47796.0			−0.209824			−0.104912	−	0.994482i	$-0.533456\pi$
$139$	−47796.0			−0.209824			−0.104912	+	0.994482i	$0.533456\pi$
$140$		0			0
$141$	7776.00			0.0329389
$142$	−46800.0	+	81060.0i	−0.194771	+	0.337354i
$143$	20020.0	+	34675.7i	0.0818698	+	0.141803i
$144$	30415.5	+	52681.2i	0.122233	+	0.211714i
$145$	−259346.	+	449200.i	−1.02438	+	1.77427i
$146$	231810.			0.900016
$147$		0			0
$148$	51366.0			0.192762
$149$	62133.0	−	107618.i	0.229275	−	0.397116i	−0.728318	−	0.685239i	$-0.759698\pi$
$149$	62133.0	−	107618.i	0.229275	−	0.397116i	0.957593	+	0.288123i	$0.0930312\pi$
$150$	−128498.	−	222564.i	−0.466301	−	0.807657i
$151$	223148.	+	386504.i	0.796436	+	1.37947i	0.921924	+	0.387372i	$0.126617\pi$
$151$	223148.	+	386504.i	0.796436	+	1.37947i	−0.125488	+	0.992095i	$0.540050\pi$
$152$	168870.	−	292491.i	0.592848	−	1.02684i
$153$	−163782.			−0.565637
$154$		0			0
$155$	595584.			1.99119
$156$	−24255.0	+	42010.9i	−0.0797976	+	0.138213i
$157$	79873.0	+	138344.i	0.258613	+	0.447931i	0.965871	−	0.259025i	$-0.0834011\pi$
$157$	79873.0	+	138344.i	0.258613	+	0.447931i	−0.707257	+	0.706956i	$0.750068\pi$
$158$	−243560.	−	421858.i	−0.776181	−	1.34439i
$159$	−18819.0	+	32595.5i	−0.0590342	+	0.102250i
$160$	233590.			0.721364
$161$		0			0
$162$	32805.0			0.0982093
$163$	−123626.	+	214127.i	−0.364452	+	0.631250i	−0.988688	−	0.149986i	$-0.952077\pi$
$163$	−123626.	+	214127.i	−0.364452	+	0.631250i	0.624236	+	0.781236i	$0.285410\pi$
$164$	−11417.0	−	19774.8i	−0.0331469	−	0.0574120i
$165$	−21996.0	−	38098.2i	−0.0628976	−	0.108942i
$166$	203070.	−	351728.i	0.571973	−	0.990686i
$167$	−684488.			−1.89922			−0.949609	−	0.313438i	$-0.898519\pi$
$167$	−684488.			−1.89922			−0.949609	+	0.313438i	$0.898519\pi$
$168$		0			0
$169$	221607.			0.596852
$170$	475170.	−	823019.i	1.26103	−	2.18417i
$171$	−70146.0	−	121496.i	−0.183448	−	0.317741i
$172$	18970.0	+	32857.0i	0.0488929	+	0.0846851i
$173$	305237.	−	528686.i	0.775393	−	1.34302i	−0.159180	−	0.987250i	$-0.550885\pi$
$173$	305237.	−	528686.i	0.775393	−	1.34302i	0.934573	−	0.355771i	$-0.115782\pi$
$174$	248310.			0.621758
$175$		0			0
$176$	−39052.0			−0.0950302
$177$	50490.0	−	87451.2i	0.121136	−	0.209813i
$178$	7955.00	+	13778.5i	0.0188187	+	0.0325950i
$179$	−331126.	−	573527.i	−0.772433	−	1.33789i	−0.936226	−	0.351398i	$-0.885706\pi$
$179$	−331126.	−	573527.i	−0.772433	−	1.33789i	0.163793	−	0.986495i	$-0.447627\pi$
$180$	26649.0	−	46157.4i	0.0613055	−	0.106184i
$181$	154630.			0.350830			0.175415	−	0.984495i	$-0.443873\pi$
$181$	154630.			0.350830			0.175415	+	0.984495i	$0.443873\pi$
$182$		0			0
$183$	−410418.			−0.905938
$184$	−56160.0	+	97272.0i	−0.122288	+	0.211808i
$185$	344886.	+	597360.i	0.740877	+	1.28324i
$186$	−142560.	−	246921.i	−0.302145	−	0.523330i
$187$	52572.0	−	91057.4i	0.109939	−	0.190419i
$188$	−6048.00			−0.0124801
$189$		0			0
$190$	814040.			1.63592
$191$	−243452.	+	421671.i	−0.482870	+	0.836355i	−0.999807	−	0.0196687i	$-0.993739\pi$
$191$	−243452.	+	421671.i	−0.482870	+	0.836355i	0.516937	+	0.856024i	$0.327072\pi$
$192$	−164056.	−	284154.i	−0.321174	−	0.556290i
$193$	−310273.	−	537409.i	−0.599585	−	1.03851i	−0.992882	−	0.119100i	$-0.961999\pi$
$193$	−310273.	−	537409.i	−0.599585	−	1.03851i	0.393297	−	0.919411i	$-0.371334\pi$
$194$	−12285.0	+	21278.2i	−0.0234353	+	0.0405912i
$195$	−651420.			−1.22680
$196$		0			0
$197$	−236570.			−0.434304			−0.217152	−	0.976138i	$-0.569677\pi$
$197$	−236570.			−0.434304			−0.217152	+	0.976138i	$0.569677\pi$
$198$	−10530.0	+	18238.5i	−0.0190882	+	0.0330618i
$199$	−41052.0	−	71104.1i	−0.0734855	−	0.127281i	0.826941	−	0.562288i	$-0.190079\pi$
$199$	−41052.0	−	71104.1i	−0.0734855	−	0.127281i	−0.900427	+	0.435008i	$0.856746\pi$
$200$	556822.	+	964445.i	0.984332	+	1.70491i
$201$	−6282.00	+	10880.7i	−0.0109675	+	0.0189963i
$202$	−831770.			−1.43425
$203$		0			0
$204$	127386.			0.214312
$205$	153314.	−	265548.i	0.254799	−	0.441324i
$206$	−392900.	−	680523.i	−0.645081	−	1.11731i
$207$	23328.0	+	40405.3i	0.0378400	+	0.0655409i
$208$	−289135.	+	500797.i	−0.463385	+	0.802607i
$209$	90064.0			0.142622
$210$		0			0
$211$	99892.0			0.154463			0.0772315	−	0.997013i	$-0.475392\pi$
$211$	99892.0			0.154463			0.0772315	+	0.997013i	$0.475392\pi$
$212$	14637.0	−	25352.0i	0.0223672	−	0.0387412i
$213$	−84240.0	−	145908.i	−0.127224	−	0.220359i
$214$	16910.0	+	29289.0i	0.0252412	+	0.0437190i
$215$	−254740.	+	441223.i	−0.375838	+	0.650971i
$216$	−142155.			−0.207314
$217$		0			0
$218$	891990.			1.27121
$219$	−208629.	+	361356.i	−0.293944	+	0.509126i
$220$	17108.0	+	29631.9i	0.0238310	+	0.0412765i
$221$	−778470.	−	1.34835e6i	−1.07216	−	1.85704i
$222$	165105.	−	285970.i	0.224842	−	0.389438i
$223$	−186704.			−0.251415			−0.125708	−	0.992067i	$-0.540120\pi$
$223$	−186704.			−0.251415			−0.125708	+	0.992067i	$0.540120\pi$
$224$		0			0
$225$	462591.			0.609173
$226$	112835.	−	195436.i	0.146951	−	0.254527i
$227$	−168186.	−	291307.i	−0.216633	−	0.375220i	0.737143	−	0.675736i	$-0.236174\pi$
$227$	−168186.	−	291307.i	−0.216633	−	0.375220i	−0.953777	+	0.300517i	$0.902841\pi$
$228$	54558.0	+	94497.2i	0.0695058	+	0.120388i
$229$	463157.	−	802211.i	0.583633	−	1.01088i	−0.411412	−	0.911450i	$-0.634964\pi$
$229$	463157.	−	802211.i	0.583633	−	1.01088i	0.995044	−	0.0994317i	$-0.0317025\pi$
$230$	−270720.			−0.337443
$231$		0			0
$232$	−1.07601e6			−1.31249
$233$	−628557.	+	1.08869e6i	−0.758499	+	1.31376i	0.185117	+	0.982716i	$0.440733\pi$
$233$	−628557.	+	1.08869e6i	−0.758499	+	1.31376i	−0.943616	+	0.331042i	$0.892600\pi$
$234$	155925.	+	270070.i	0.186156	+	0.322431i
$235$	−40608.0	−	70335.1i	−0.0479669	−	0.0830812i
$236$	−39270.0	+	68017.6i	−0.0458966	+	0.0794953i
$237$	876816.			1.01400
$238$		0			0
$239$	−347016.			−0.392966			−0.196483	−	0.980507i	$-0.562952\pi$
$239$	−347016.			−0.392966			−0.196483	+	0.980507i	$0.562952\pi$
$240$	317673.	−	550226.i	0.356002	−	0.616613i
$241$	−49585.0	−	85883.7i	−0.0549930	−	0.0952507i	0.837218	−	0.546869i	$-0.184180\pi$
$241$	−49585.0	−	85883.7i	−0.0549930	−	0.0952507i	−0.892211	+	0.451618i	$0.850847\pi$
$242$	395868.	+	685663.i	0.434522	+	0.752614i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	319214.			0.343247
$245$		0			0
$246$	−146790.			−0.154653
$247$	666820.	−	1.15497e6i	0.695451	−	1.20456i
$248$	617760.	+	1.06999e6i	0.637809	+	1.10472i
$249$	365526.	+	633110.i	0.373611	+	0.647114i
$250$	−607710.	+	1.05258e6i	−0.614959	+	1.06514i
$251$	344428.			0.345076			0.172538	−	0.985003i	$-0.444803\pi$
$251$	344428.			0.345076			0.172538	+	0.985003i	$0.444803\pi$
$252$		0			0
$253$	−29952.0			−0.0294188
$254$	512640.	−	887919.i	0.498572	−	0.863553i
$255$	855306.	+	1.48143e6i	0.823704	+	1.42670i
$256$	326400.	+	565341.i	0.311279	+	0.539151i
$257$	−147565.	+	255590.i	−0.139364	+	0.241386i	−0.927256	−	0.374428i	$-0.877839\pi$
$257$	−147565.	+	255590.i	−0.139364	+	0.241386i	0.787892	+	0.615813i	$0.211172\pi$
$258$	243900.			0.228120
$259$		0			0
$260$	506660.			0.464818
$261$	−223479.	+	387077.i	−0.203065	+	0.351719i
$262$	−182410.	−	315943.i	−0.164171	−	0.284352i
$263$	636232.	+	1.10199e6i	0.567187	+	0.982396i	0.996843	+	0.0794036i	$0.0253016\pi$
$263$	636232.	+	1.10199e6i	0.567187	+	0.982396i	−0.429656	+	0.902993i	$0.641365\pi$
$264$	45630.0	−	79033.5i	0.0402940	−	0.0697913i
$265$	393108.			0.343872
$266$		0			0
$267$	−28638.0			−0.0245847
$268$	4886.00	−	8462.80i	0.00415543	−	0.00719742i
$269$	−138387.	−	239693.i	−0.116604	−	0.201965i	0.801816	−	0.597572i	$-0.203868\pi$
$269$	−138387.	−	239693.i	−0.116604	−	0.201965i	−0.918420	+	0.395607i	$0.870534\pi$
$270$	−171315.	−	296726.i	−0.143016	−	0.247712i
$271$	644968.	−	1.11712e6i	0.533476	−	0.924008i	−0.465759	−	0.884911i	$-0.654219\pi$
$271$	644968.	−	1.11712e6i	0.533476	−	0.924008i	0.999235	−	0.0390962i	$-0.0124479\pi$
$272$	1.51852e6			1.24451
$273$		0			0
$274$	−470910.			−0.378932
$275$	−148486.	+	257185.i	−0.118401	+	0.205076i
$276$	−18144.0	−	31426.3i	−0.0143371	−	0.0248325i
$277$	−858275.	−	1.48658e6i	−0.672089	−	1.16409i	−0.977311	−	0.211811i	$-0.932064\pi$
$277$	−858275.	−	1.48658e6i	−0.672089	−	1.16409i	0.305221	−	0.952281i	$-0.401270\pi$
$278$	119490.	−	206963.i	0.0927299	−	0.160613i
$279$	513216.			0.394720
$280$		0			0
$281$	−1.47218e6			−1.11223			−0.556116	−	0.831104i	$-0.687709\pi$
$281$	−1.47218e6			−1.11223			−0.556116	+	0.831104i	$0.687709\pi$
$282$	−19440.0	+	33671.1i	−0.0145571	+	0.0252136i
$283$	−514406.	−	890977.i	−0.381804	−	0.661303i	0.609517	−	0.792773i	$-0.291364\pi$
$283$	−514406.	−	890977.i	−0.381804	−	0.661303i	−0.991320	+	0.131470i	$0.958030\pi$
$284$	65520.0	+	113484.i	0.0482034	+	0.0834908i
$285$	−732636.	+	1.26896e6i	−0.534289	+	0.925415i
$286$	−200200.			−0.144727
$287$		0			0
$288$	201285.			0.142998
$289$	−1.33431e6	+	2.31110e6i	−0.939752	+	1.62770i
$290$	−1.29673e6	−	2.24600e6i	−0.905429	−	1.56825i
$291$	−22113.0	−	38300.8i	−0.0153079	−	0.0265140i
$292$	162267.	−	281055.i	0.111371	−	0.192901i
$293$	−1.18607e6			−0.807123			−0.403562	−	0.914952i	$-0.632228\pi$
$293$	−1.18607e6			−0.807123			−0.403562	+	0.914952i	$0.632228\pi$
$294$		0			0
$295$	−1.05468e6			−0.705612
$296$	−715455.	+	1.23920e6i	−0.474628	+	0.822079i
$297$	−18954.0	−	32829.3i	−0.0124684	−	0.0215959i
$298$	310665.	+	538088.i	0.202652	+	0.351004i
$299$	−221760.	+	384100.i	−0.143452	+	0.248465i
$300$	−359793.			−0.230807
$301$		0			0
$302$	−2.23148e6			−1.40791
$303$	748593.	−	1.29660e6i	0.468424	−	0.811334i
$304$	650366.	+	1.12647e6i	0.403621	+	0.699092i
$305$	2.14329e6	+	3.71229e6i	1.31927	+	2.28503i
$306$	409455.	−	709197.i	0.249978	−	0.432975i
$307$	1.51892e6			0.919788			0.459894	−	0.887974i	$-0.347887\pi$
$307$	1.51892e6			0.919788			0.459894	+	0.887974i	$0.347887\pi$
$308$		0			0
$309$	1.41444e6			0.842730
$310$	−1.48896e6	+	2.57895e6i	−0.879992	+	1.52419i
$311$	−106404.	−	184297.i	−0.0623817	−	0.108048i	0.833148	−	0.553050i	$-0.186536\pi$
$311$	−106404.	−	184297.i	−0.0623817	−	0.108048i	−0.895530	+	0.445002i	$0.853203\pi$
$312$	−675675.	−	1.17030e6i	−0.392963	−	0.680631i
$313$	947.000	−	1640.25i	0.000546373	−	0.000946346i	−0.865752	−	0.500473i	$-0.833159\pi$
$313$	947.000	−	1640.25i	0.000546373	−	0.000946346i	0.866298	+	0.499527i	$0.166493\pi$
$314$	−798730.			−0.457168
$315$		0			0
$316$	−681968.			−0.384190
$317$	789489.	−	1.36744e6i	0.441263	−	0.764291i	−0.556520	−	0.830834i	$-0.687864\pi$
$317$	789489.	−	1.36744e6i	0.441263	−	0.764291i	0.997784	+	0.0665435i	$0.0211971\pi$
$318$	−94095.0	−	162977.i	−0.0521794	−	0.0903773i
$319$	−143468.	−	248494.i	−0.0789366	−	0.136722i
$320$	−1.71348e6	+	2.96783e6i	−0.935414	+	1.62018i
$321$	−60876.0			−0.0329749
$322$		0			0
$323$	−3.50210e6			−1.86777
$324$	22963.5	−	39773.9i	0.0121528	−	0.0210492i
$325$	2.19874e6	+	3.80832e6i	1.15469	+	1.99998i
$326$	−618130.	−	1.07063e6i	−0.322133	−	0.557951i
$327$	−802791.	+	1.39047e6i	−0.415177	+	0.719107i
$328$	636090.			0.326463
$329$		0			0
$330$	219960.			0.111188
$331$	1.69735e6	−	2.93990e6i	0.851535	−	1.47490i	−0.0282879	−	0.999600i	$-0.509006\pi$
$331$	1.69735e6	−	2.93990e6i	0.851535	−	1.47490i	0.879823	−	0.475302i	$-0.157661\pi$
$332$	−284298.	−	492419.i	−0.141556	−	0.245182i
$333$	297189.	+	514746.i	0.146866	+	0.254380i
$334$	1.71122e6	−	2.96392e6i	0.839343	−	1.45379i
$335$	131224.			0.0638853
$336$		0			0
$337$	2.02731e6			0.972403			0.486201	−	0.873847i	$-0.338382\pi$
$337$	2.02731e6			0.972403			0.486201	+	0.873847i	$0.338382\pi$
$338$	−554018.	+	959586.i	−0.263774	+	0.456870i
$339$	203103.	+	351785.i	0.0959880	+	0.166256i
$340$	−665238.	−	1.15223e6i	−0.312090	−	0.540556i
$341$	−164736.	+	285331.i	−0.0767189	+	0.132881i
$342$	701460.			0.324293
$343$		0			0
$344$	−1.05690e6			−0.481546
$345$	243648.	−	422011.i	0.110209	−	0.190887i
$346$	1.52618e6	+	2.64343e6i	0.685357	+	1.18707i
$347$	−1.74443e6	−	3.02143e6i	−0.777730	−	1.34707i	−0.933247	−	0.359235i	$-0.883038\pi$
$347$	−1.74443e6	−	3.02143e6i	−0.777730	−	1.34707i	0.155517	−	0.987833i	$-0.450296\pi$
$348$	173817.	−	301060.i	0.0769386	−	0.133262i
$349$	965566.			0.424344			0.212172	−	0.977232i	$-0.431946\pi$
$349$	965566.			0.424344			0.212172	+	0.977232i	$0.431946\pi$
$350$		0			0
$351$	−561330.			−0.243193
$352$	−64610.0	+	111908.i	−0.0277935	+	0.0481397i
$353$	−576965.	−	999333.i	−0.246441	−	0.426848i	0.716095	−	0.698003i	$-0.245928\pi$
$353$	−576965.	−	999333.i	−0.246441	−	0.426848i	−0.962536	+	0.271155i	$0.912594\pi$
$354$	252450.	+	437256.i	0.107070	+	0.185450i
$355$	−879840.	+	1.52393e6i	−0.370538	+	0.641791i
$356$	22274.0			0.00931479
$357$		0			0
$358$	3.31126e6			1.36548
$359$	−805552.	+	1.39526e6i	−0.329881	+	0.571371i	−0.982488	−	0.186326i	$-0.940342\pi$
$359$	−805552.	+	1.39526e6i	−0.329881	+	0.571371i	0.652607	+	0.757697i	$0.273675\pi$
$360$	742365.	+	1.28581e6i	0.301899	+	0.522904i
$361$	−261862.	−	453559.i	−0.105756	−	0.183175i
$362$	−386575.	+	669568.i	−0.155047	+	0.268549i
$363$	−1.42512e6			−0.567657
$364$		0			0
$365$	4.35803e6			1.71221
$366$	1.02605e6	−	1.77716e6i	0.400372	−	0.693465i
$367$	−1.83874e6	−	3.18478e6i	−0.712614	−	1.23428i	−0.963873	−	0.266363i	$-0.914178\pi$
$367$	−1.83874e6	−	3.18478e6i	−0.712614	−	1.23428i	0.251259	−	0.967920i	$-0.419155\pi$
$368$	−216288.	−	374622.i	−0.0832555	−	0.144203i
$369$	132111.	−	228823.i	0.0505095	−	0.0874850i
$370$	−3.44886e6			−1.30970
$371$		0			0
$372$	−399168.			−0.149554
$373$	−324883.	+	562714.i	−0.120908	+	0.209419i	−0.920126	−	0.391622i	$-0.871914\pi$
$373$	−324883.	+	562714.i	−0.120908	+	0.209419i	0.799218	+	0.601041i	$0.205247\pi$
$374$	262860.	+	455287.i	0.0971730	+	0.168309i
$375$	−1.09388e6	−	1.89465e6i	−0.401690	−	0.695747i
$376$	84240.0	−	145908.i	0.0307290	−	0.0532242i
$377$	−4.24886e6			−1.53964
$378$		0			0
$379$	320700.			0.114683			0.0573417	−	0.998355i	$-0.481738\pi$
$379$	320700.			0.114683			0.0573417	+	0.998355i	$0.481738\pi$
$380$	569828.	−	986971.i	0.202435	−	0.350627i
$381$	922752.	+	1.59825e6i	0.325666	+	0.564070i
$382$	−1.21726e6	−	2.10836e6i	−0.426801	−	0.739240i
$383$	1.18094e6	−	2.04546e6i	0.411370	−	0.712513i	−0.583670	−	0.811991i	$-0.698384\pi$
$383$	1.18094e6	−	2.04546e6i	0.411370	−	0.712513i	0.995040	+	0.0994776i	$0.0317172\pi$
$384$	924885.			0.320081
$385$		0			0
$386$	3.10273e6			1.05993
$387$	−219510.	+	380202.i	−0.0745035	+	0.129044i
$388$	17199.0	+	29789.5i	0.00579995	+	0.0100458i
$389$	1.76695e6	+	3.06045e6i	0.592039	+	1.02544i	0.993957	+	0.109766i	$0.0350100\pi$
$389$	1.76695e6	+	3.06045e6i	0.592039	+	1.02544i	−0.401919	+	0.915675i	$0.631657\pi$
$390$	1.62855e6	−	2.82073e6i	0.542175	−	0.939075i
$391$	1.16467e6			0.385267
$392$		0			0
$393$	656676.			0.214472
$394$	591425.	−	1.02438e6i	0.191937	−	0.332445i
$395$	−4.57893e6	−	7.93094e6i	−1.47663	−	2.55759i
$396$	14742.0	+	25533.9i	0.00472409	+	0.00818237i
$397$	−2.02405e6	+	3.50577e6i	−0.644534	+	1.11637i	0.339875	+	0.940471i	$0.389615\pi$
$397$	−2.02405e6	+	3.50577e6i	−0.644534	+	1.11637i	−0.984409	+	0.175895i	$0.943718\pi$
$398$	410520.			0.129905
$399$		0			0
$400$	−4.28896e6			−1.34030
$401$	−1.03822e6	+	1.79826e6i	−0.322426	+	0.558459i	−0.980988	−	0.194068i	$-0.937832\pi$
$401$	−1.03822e6	+	1.79826e6i	−0.322426	+	0.558459i	0.658562	+	0.752527i	$0.271165\pi$
$402$	−31410.0	−	54403.7i	−0.00969400	−	0.0167905i
$403$	2.43936e6	+	4.22510e6i	0.748192	+	1.29591i
$404$	−582239.	+	1.00847e6i	−0.177479	+	0.307403i
$405$	616734.			0.186836
$406$		0			0
$407$	−381576.			−0.114181
$408$	−1.77431e6	+	3.07319e6i	−0.527689	+	0.913984i
$409$	−1.28716e6	−	2.22942e6i	−0.380472	−	0.658998i	0.610657	−	0.791895i	$-0.290905\pi$
$409$	−1.28716e6	−	2.22942e6i	−0.380472	−	0.658998i	−0.991130	+	0.132897i	$0.957572\pi$
$410$	766570.	+	1.32774e6i	0.225212	+	0.390079i
$411$	423819.	−	734076.i	0.123759	−	0.214356i
$412$	−1.10012e6			−0.319299
$413$		0			0
$414$	−233280.			−0.0668924
$415$	3.81772e6	−	6.61248e6i	1.08814	−	1.88471i
$416$	956725.	+	1.65710e6i	0.271053	+	0.469477i
$417$	215082.	+	372533.i	0.0605709	+	0.104912i
$418$	−225160.	+	389989.i	−0.0630305	+	0.109172i
$419$	848148.			0.236013			0.118007	−	0.993013i	$-0.462350\pi$
$419$	848148.			0.236013			0.118007	+	0.993013i	$0.462350\pi$
$420$		0			0
$421$	1.43682e6			0.395092			0.197546	−	0.980294i	$-0.436703\pi$
$421$	1.43682e6			0.395092			0.197546	+	0.980294i	$0.436703\pi$
$422$	−249730.	+	432545.i	−0.0682637	+	0.118236i
$423$	−34992.0	−	60607.9i	−0.00950863	−	0.0164694i
$424$	407745.	+	706235.i	0.110147	+	0.190781i
$425$	5.77382e6	−	1.00006e7i	1.55057	−	2.68566i
$426$	842400.			0.224903
$427$		0			0
$428$	47348.0			0.0124937
$429$	180180.	−	312081.i	0.0472676	−	0.0818698i
$430$	−1.27370e6	−	2.20611e6i	−0.332197	−	0.575382i
$431$	−1.17719e6	−	2.03895e6i	−0.305248	−	0.528705i	0.672069	−	0.740489i	$-0.265406\pi$
$431$	−1.17719e6	−	2.03895e6i	−0.305248	−	0.528705i	−0.977316	+	0.211784i	$0.932073\pi$
$432$	273740.	−	474131.i	0.0705713	−	0.122233i
$433$	−3.78808e6			−0.970955			−0.485478	−	0.874249i	$-0.661354\pi$
$433$	−3.78808e6			−0.970955			−0.485478	+	0.874249i	$0.661354\pi$
$434$		0			0
$435$	4.66823e6			1.18285
$436$	624393.	−	1.08148e6i	0.157305	−	0.272460i
$437$	498816.	+	863975.i	0.124950	+	0.216420i
$438$	−1.04314e6	−	1.80678e6i	−0.259812	−	0.450008i
$439$	1.82161e6	−	3.15512e6i	0.451123	−	0.781367i	−0.547333	−	0.836915i	$-0.684357\pi$
$439$	1.82161e6	−	3.15512e6i	0.451123	−	0.781367i	0.998456	+	0.0555474i	$0.0176904\pi$
$440$	−953160.			−0.234711
$441$		0			0
$442$	7.78470e6			1.89534
$443$	−1.24195e6	+	2.15111e6i	−0.300672	+	0.520780i	−0.976288	−	0.216474i	$-0.930544\pi$
$443$	−1.24195e6	+	2.15111e6i	−0.300672	+	0.520780i	0.675616	+	0.737254i	$0.263878\pi$
$444$	−231147.	−	400358.i	−0.0556456	−	0.0963810i
$445$	149554.	+	259035.i	0.0358012	+	0.0620096i
$446$	466760.	−	808452.i	0.111111	−	0.192450i
$447$	−1.11839e6			−0.264744
$448$		0			0
$449$	−2.63177e6			−0.616074			−0.308037	−	0.951374i	$-0.599672\pi$
$449$	−2.63177e6			−0.616074			−0.308037	+	0.951374i	$0.599672\pi$
$450$	−1.15648e6	+	2.00308e6i	−0.269219	+	0.466301i
$451$	84812.0	+	146899.i	0.0196343	+	0.0340076i
$452$	−157969.	−	273610.i	−0.0363685	−	0.0629921i
$453$	2.00833e6	−	3.47853e6i	0.459822	−	0.796436i
$454$	1.68186e6			0.382957
$455$		0			0
$456$	−3.03966e6			−0.684562
$457$	580651.	−	1.00572e6i	0.130054	−	0.225261i	−0.793643	−	0.608384i	$-0.791818\pi$
$457$	580651.	−	1.00572e6i	0.130054	−	0.225261i	0.923697	+	0.383123i	$0.125152\pi$
$458$	2.31578e6	+	4.01106e6i	0.515863	+	0.893501i
$459$	737019.	+	1.27655e6i	0.163285	+	0.282818i
$460$	−189504.	+	328231.i	−0.0417565	+	0.0723243i
$461$	2.81385e6			0.616663			0.308332	−	0.951279i	$-0.400229\pi$
$461$	2.81385e6			0.616663			0.308332	+	0.951279i	$0.400229\pi$
$462$		0			0
$463$	6.84299e6			1.48352			0.741760	−	0.670665i	$-0.233991\pi$
$463$	6.84299e6			1.48352			0.741760	+	0.670665i	$0.233991\pi$
$464$	2.07201e6	−	3.58882e6i	0.446783	−	0.773851i
$465$	−2.68013e6	−	4.64212e6i	−0.574808	−	0.995597i
$466$	−3.14279e6	−	5.44346e6i	−0.670425	−	1.16121i
$467$	−1.67157e6	+	2.89524e6i	−0.354676	+	0.614318i	−0.987063	−	0.160336i	$-0.948742\pi$
$467$	−1.67157e6	+	2.89524e6i	−0.354676	+	0.614318i	0.632386	+	0.774653i	$0.282076\pi$
$468$	436590.			0.0921423
$469$		0			0
$470$	406080.			0.0847944
$471$	718857.	−	1.24510e6i	0.149310	−	0.258613i
$472$	−1.09395e6	−	1.89478e6i	−0.226018	−	0.391474i
$473$	−140920.	−	244081.i	−0.0289614	−	0.0501626i
$474$	−2.19204e6	+	3.79672e6i	−0.448129	+	0.776181i
$475$	9.89145e6			2.01153
$476$		0			0
$477$	338742.			0.0681668
$478$	867540.	−	1.50262e6i	0.173668	−	0.300802i
$479$	2.14124e6	+	3.70874e6i	0.426409	+	0.738562i	0.996551	−	0.0829840i	$-0.0264450\pi$
$479$	2.14124e6	+	3.70874e6i	0.426409	+	0.738562i	−0.570142	+	0.821546i	$0.693112\pi$
$480$	−1.05116e6	−	1.82065e6i	−0.208240	−	0.360682i
$481$	−2.82513e6	+	4.89327e6i	−0.556770	+	0.964354i
$482$	495850.			0.0972149
$483$		0			0
$484$	1.10843e6			0.215077
$485$	−230958.	+	400031.i	−0.0445840	+	0.0772217i
$486$	−147622.	−	255690.i	−0.0283506	−	0.0491046i
$487$	4.46588e6	+	7.73512e6i	0.853266	+	1.47790i	0.878245	+	0.478211i	$0.158715\pi$
$487$	4.46588e6	+	7.73512e6i	0.853266	+	1.47790i	−0.0249791	+	0.999688i	$0.507952\pi$
$488$	−4.44620e6	+	7.70104e6i	−0.845160	+	1.46386i
$489$	2.22527e6			0.420833
$490$		0			0
$491$	2.75306e6			0.515361			0.257681	−	0.966230i	$-0.417042\pi$
$491$	2.75306e6			0.515361			0.257681	+	0.966230i	$0.417042\pi$
$492$	−102753.	+	177973.i	−0.0191373	+	0.0331469i
$493$	5.57870e6	+	9.66259e6i	1.03375	+	1.79051i
$494$	3.33410e6	+	5.77483e6i	0.614697	+	1.06469i
$495$	−197964.	+	342884.i	−0.0363139	+	0.0628976i
$496$	−4.75834e6			−0.868462
$497$		0			0
$498$	−3.65526e6			−0.660458
$499$	−2.40204e6	+	4.16046e6i	−0.431846	+	0.747980i	−0.997032	−	0.0769837i	$-0.975471\pi$
$499$	−2.40204e6	+	4.16046e6i	−0.431846	+	0.747980i	0.565186	+	0.824963i	$0.308804\pi$
$500$	850794.	+	1.47362e6i	0.152195	+	0.263609i
$501$	3.08020e6	+	5.33506e6i	0.548257	+	0.949609i
$502$	−861070.	+	1.49142e6i	−0.152503	+	0.264143i
$503$	−6.02465e6			−1.06172			−0.530862	−	0.847458i	$-0.678132\pi$
$503$	−6.02465e6			−1.06172			−0.530862	+	0.847458i	$0.678132\pi$
$504$		0			0
$505$	−1.56373e7			−2.72855
$506$	74880.0	−	129696.i	0.0130014	−	0.0225191i
$507$	−997232.	−	1.72726e6i	−0.172296	−	0.298426i
$508$	−717696.	−	1.24309e6i	−0.123390	−	0.213718i
$509$	4.21493e6	−	7.30048e6i	0.721101	−	1.24898i	−0.239458	−	0.970907i	$-0.576970\pi$
$509$	4.21493e6	−	7.30048e6i	0.721101	−	1.24898i	0.960559	−	0.278077i	$-0.0896971\pi$
$510$	−8.55306e6			−1.45612
$511$		0			0
$512$	−6.55248e6			−1.10466
$513$	−631314.	+	1.09347e6i	−0.105914	+	0.183448i
$514$	−737825.	−	1.27795e6i	−0.123182	−	0.213357i
$515$	−7.38652e6	−	1.27938e7i	−1.22722	−	2.12560i
$516$	170730.	−	295713.i	0.0282284	−	0.0488929i
$517$	44928.0			0.00739249
$518$		0			0
$519$	−5.49427e6			−0.895347
$520$	−7.05705e6	+	1.22232e7i	−1.14450	+	1.98233i
$521$	−4.62529e6	−	8.01124e6i	−0.746525	−	1.29302i	−0.949479	−	0.313831i	$-0.898387\pi$
$521$	−4.62529e6	−	8.01124e6i	−0.746525	−	1.29302i	0.202953	−	0.979188i	$-0.434946\pi$
$522$	−1.11740e6	−	1.93538e6i	−0.179486	−	0.310879i
$523$	−2.92247e6	+	5.06187e6i	−0.467192	+	0.809201i	−0.999297	−	0.0374773i	$-0.988068\pi$
$523$	−2.92247e6	+	5.06187e6i	−0.467192	+	0.809201i	0.532105	+	0.846678i	$0.321401\pi$
$524$	−510748.			−0.0812603
$525$		0			0
$526$	−6.36232e6			−1.00265
$527$	6.40570e6	−	1.10950e7i	1.00471	−	1.74021i
$528$	175734.	+	304380.i	0.0274329	+	0.0475151i
$529$	3.05228e6	+	5.28671e6i	0.474226	+	0.821384i
$530$	−982770.	+	1.70221e6i	−0.151972	+	0.263222i
$531$	−908820.			−0.139875
$532$		0			0
$533$	2.51174e6			0.382963
$534$	71595.0	−	124006.i	0.0108650	−	0.0188187i
$535$	317908.	+	550633.i	0.0480194	+	0.0831721i
$536$	136110.	+	235749.i	0.0204634	+	0.0354437i
$537$	−2.98013e6	+	5.16174e6i	−0.445964	+	0.772433i
$538$	1.38387e6			0.206129
$539$		0			0
$540$	−479682.			−0.0707895
$541$	−4.61266e6	+	7.98937e6i	−0.677577	+	1.17360i	0.298132	+	0.954525i	$0.403637\pi$
$541$	−4.61266e6	+	7.98937e6i	−0.677577	+	1.17360i	−0.975709	+	0.219073i	$0.929697\pi$
$542$	3.22484e6	+	5.58559e6i	0.471531	+	0.816715i
$543$	−695835.	−	1.20522e6i	−0.101276	−	0.175415i
$544$	2.51234e6	−	4.35149e6i	0.363982	−	0.630436i
$545$	1.67694e7			2.41839
$546$		0			0
$547$	−6.44337e6			−0.920757			−0.460378	−	0.887723i	$-0.652286\pi$
$547$	−6.44337e6			−0.920757			−0.460378	+	0.887723i	$0.652286\pi$
$548$	−329637.	+	570948.i	−0.0468905	+	0.0812167i
$549$	1.84688e6	+	3.19889e6i	0.261522	+	0.452969i
$550$	−742430.	−	1.28593e6i	−0.104652	−	0.181263i
$551$	−4.77859e6	+	8.27676e6i	−0.670534	+	1.16140i
$552$	1.01088e6			0.141206
$553$		0			0
$554$	8.58275e6			1.18810
$555$	3.10397e6	−	5.37624e6i	0.427746	−	0.740877i
$556$	−167286.	−	289748.i	−0.0229495	−	0.0397496i
$557$	−1.87106e6	−	3.24078e6i	−0.255535	−	0.442600i	0.709506	−	0.704700i	$-0.248918\pi$
$557$	−1.87106e6	−	3.24078e6i	−0.255535	−	0.442600i	−0.965041	+	0.262100i	$0.915585\pi$
$558$	−1.28304e6	+	2.22229e6i	−0.174443	+	0.302145i
$559$	−4.17340e6			−0.564886
$560$		0			0
$561$	−946296.			−0.126946
$562$	3.68046e6	−	6.37474e6i	0.491542	−	0.851376i
$563$	7.31918e6	+	1.26772e7i	0.973176	+	1.68559i	0.685826	+	0.727765i	$0.259441\pi$
$563$	7.31918e6	+	1.26772e7i	0.973176	+	1.68559i	0.287350	+	0.957826i	$0.407226\pi$
$564$	27216.0	+	47139.5i	0.00360269	+	0.00624004i
$565$	2.12130e6	−	3.67420e6i	0.279564	−	0.484218i
$566$	5.14406e6			0.674940
$567$		0			0
$568$	−3.65040e6			−0.474755
$569$	−7.09023e6	+	1.22806e7i	−0.918078	+	1.59016i	−0.115747	+	0.993279i	$0.536926\pi$
$569$	−7.09023e6	+	1.22806e7i	−0.918078	+	1.59016i	−0.802331	+	0.596879i	$0.796407\pi$
$570$	−3.66318e6	−	6.34481e6i	−0.472249	−	0.817959i
$571$	625802.	+	1.08392e6i	0.0803242	+	0.139126i	0.903389	−	0.428822i	$-0.141071\pi$
$571$	625802.	+	1.08392e6i	0.0803242	+	0.139126i	−0.823065	+	0.567947i	$0.807738\pi$
$572$	−140140.	+	242730.i	−0.0179090	+	0.0310193i
$573$	4.38214e6			0.557570
$574$		0			0
$575$	−3.28954e6			−0.414921
$576$	−1.47651e6	+	2.55739e6i	−0.185430	+	0.321174i
$577$	−2.97189e6	−	5.14746e6i	−0.371615	−	0.643656i	0.618199	−	0.786021i	$-0.287862\pi$
$577$	−2.97189e6	−	5.14746e6i	−0.371615	−	0.643656i	−0.989814	+	0.142366i	$0.954529\pi$
$578$	−6.67157e6	−	1.15555e7i	−0.830631	−	1.43870i
$579$	−2.79246e6	+	4.83668e6i	−0.346171	+	0.599585i
$580$	−3.63084e6			−0.448165
$581$		0			0
$582$	221130.			0.0270608
$583$	−108732.	+	188329.i	−0.0132491	+	0.0229481i
$584$	4.52030e6	+	7.82938e6i	0.548447	+	0.949938i
$585$	2.93139e6	+	5.07732e6i	0.354147	+	0.613401i
$586$	2.96516e6	−	5.13582e6i	0.356701	−	0.617825i
$587$	−6.46192e6			−0.774046			−0.387023	−	0.922070i	$-0.626497\pi$
$587$	−6.46192e6			−0.774046			−0.387023	+	0.922070i	$0.626497\pi$
$588$		0			0
$589$	1.09740e7			1.30339
$590$	2.63670e6	−	4.56690e6i	0.311839	−	0.540121i
$591$	1.06456e6	+	1.84388e6i	0.125373	+	0.217152i
$592$	−2.75542e6	−	4.77253e6i	−0.323135	−	0.559685i
$593$	1.17303e6	−	2.03174e6i	0.136984	−	0.237264i	−0.789369	−	0.613919i	$-0.789592\pi$
$593$	1.17303e6	−	2.03174e6i	0.136984	−	0.237264i	0.926354	+	0.376655i	$0.122926\pi$
$594$	189540.			0.0220412
$595$		0			0
$596$	869862.			0.100308
$597$	−369468.	+	639937.i	−0.0424269	+	0.0734855i
$598$	−1.10880e6	−	1.92050e6i	−0.126794	−	0.219614i
$599$	6.74796e6	+	1.16878e7i	0.768432	+	1.33096i	0.938413	+	0.345516i	$0.112296\pi$
$599$	6.74796e6	+	1.16878e7i	0.768432	+	1.33096i	−0.169981	+	0.985447i	$0.554371\pi$
$600$	5.01140e6	−	8.68000e6i	0.568305	−	0.984332i
$601$	3.87849e6			0.438002			0.219001	−	0.975725i	$-0.429720\pi$
$601$	3.87849e6			0.438002			0.219001	+	0.975725i	$0.429720\pi$
$602$		0			0
$603$	113076.			0.0126642
$604$	−1.56204e6	+	2.70553e6i	−0.174220	+	0.301758i
$605$	7.44231e6	+	1.28905e7i	0.826645	+	1.43179i
$606$	3.74296e6	+	6.48301e6i	0.414032	+	0.717125i
$607$	266744.	−	462014.i	0.0293848	−	0.0508960i	−0.850959	−	0.525232i	$-0.823979\pi$
$607$	266744.	−	462014.i	0.0293848	−	0.0508960i	0.880344	+	0.474336i	$0.157312\pi$
$608$	4.30402e6			0.472188
$609$		0			0
$610$	−2.14329e7			−2.33215
$611$	332640.	−	576149.i	0.0360472	−	0.0624356i
$612$	−573237.	−	992876.i	−0.0618665	−	0.107156i
$613$	−2.57305e6	−	4.45666e6i	−0.276565	−	0.479025i	0.693964	−	0.720010i	$-0.255863\pi$
$613$	−2.57305e6	−	4.45666e6i	−0.276565	−	0.479025i	−0.970529	+	0.240985i	$0.922529\pi$
$614$	−3.79729e6	+	6.57710e6i	−0.406493	+	0.704066i
$615$	−2.75965e6			−0.294216
$616$		0			0
$617$	−2.37860e6			−0.251541			−0.125770	−	0.992059i	$-0.540140\pi$
$617$	−2.37860e6			−0.251541			−0.125770	+	0.992059i	$0.540140\pi$
$618$	−3.53610e6	+	6.12470e6i	−0.372437	+	0.645081i
$619$	−8.00116e6	−	1.38584e7i	−0.839317	−	1.45374i	−0.890466	−	0.455049i	$-0.849622\pi$
$619$	−8.00116e6	−	1.38584e7i	−0.839317	−	1.45374i	0.0511488	−	0.998691i	$-0.483712\pi$
$620$	2.08454e6	+	3.61054e6i	0.217787	+	0.377218i
$621$	209952.	−	363648.i	0.0218470	−	0.0378400i
$622$	1.06404e6			0.110276
$623$		0			0
$624$	5.20443e6			0.535071
$625$	−2.50151e6	+	4.33274e6i	−0.256155	+	0.443673i
$626$	4735.00	+	8201.26i	0.000482930	+	0.000836459i
$627$	−405288.	−	701979.i	−0.0411713	−	0.0713108i
$628$	−559111.	+	968409.i	−0.0565717	+	0.0979850i
$629$	1.48374e7			1.49531
$630$		0			0
$631$	1.23459e7			1.23439			0.617193	−	0.786812i	$-0.288270\pi$
$631$	1.23459e7			1.23439			0.617193	+	0.786812i	$0.288270\pi$
$632$	9.49884e6	−	1.64525e7i	0.945971	−	1.63847i
$633$	−449514.	−	778581.i	−0.0445896	−	0.0772315i
$634$	3.94744e6	+	6.83718e6i	0.390025	+	0.675544i
$635$	9.63763e6	−	1.66929e7i	0.948497	−	1.64285i
$636$	−263466.			−0.0258275
$637$		0			0
$638$	1.43468e6			0.139541
$639$	−758160.	+	1.31317e6i	−0.0734529	+	0.127224i
$640$	−4.82996e6	−	8.36573e6i	−0.466115	−	0.807335i
$641$	1.71878e6	+	2.97701e6i	0.165224	+	0.286177i	0.936735	−	0.350040i	$-0.113832\pi$
$641$	1.71878e6	+	2.97701e6i	0.165224	+	0.286177i	−0.771511	+	0.636216i	$0.780499\pi$
$642$	152190.	−	263601.i	0.0145730	−	0.0252412i
$643$	−1.62191e7			−1.54703			−0.773515	−	0.633778i	$-0.781503\pi$
$643$	−1.62191e7			−1.54703			−0.773515	+	0.633778i	$0.781503\pi$
$644$		0			0
$645$	4.58532e6			0.433981
$646$	8.75526e6	−	1.51646e7i	0.825444	−	1.42971i
$647$	−5.99643e6	−	1.03861e7i	−0.563160	−	0.975422i	−0.997218	−	0.0745371i	$-0.976252\pi$
$647$	−5.99643e6	−	1.03861e7i	−0.563160	−	0.975422i	0.434058	−	0.900885i	$-0.357081\pi$
$648$	639698.	+	1.10799e6i	0.0598463	+	0.103657i
$649$	291720.	−	505274.i	0.0271866	−	0.0470885i
$650$	−2.19873e7			−2.04122
$651$		0			0
$652$	−1.73076e6			−0.159448
$653$	−790047.	+	1.36840e6i	−0.0725053	+	0.125583i	−0.899999	−	0.435893i	$-0.856433\pi$
$653$	−790047.	+	1.36840e6i	−0.0725053	+	0.125583i	0.827493	+	0.561475i	$0.189766\pi$
$654$	−4.01396e6	−	6.95237e6i	−0.366968	−	0.635607i
$655$	−3.42931e6	−	5.93974e6i	−0.312322	−	0.540958i
$656$	−1.22488e6	+	2.12156e6i	−0.111131	+	0.192484i
$657$	3.75532e6			0.339417
$658$		0			0
$659$	6.98358e6			0.626419			0.313209	−	0.949684i	$-0.398596\pi$
$659$	6.98358e6			0.626419			0.313209	+	0.949684i	$0.398596\pi$
$660$	153972.	−	266687.i	0.0137588	−	0.0238310i
$661$	−1.84801e6	−	3.20085e6i	−0.164513	−	0.284945i	0.771969	−	0.635660i	$-0.219272\pi$
$661$	−1.84801e6	−	3.20085e6i	−0.164513	−	0.284945i	−0.936482	+	0.350715i	$0.885939\pi$
$662$	8.48677e6	+	1.46995e7i	0.752658	+	1.30364i
$663$	−7.00623e6	+	1.21351e7i	−0.619014	+	1.07216i
$664$	1.58395e7			1.39418
$665$		0			0
$666$	−2.97189e6			−0.259625
$667$	1.58918e6	−	2.75255e6i	0.138312	−	0.239563i
$668$	−2.39571e6	−	4.14949e6i	−0.207727	−	0.359794i
$669$	840168.	+	1.45521e6i	0.0725773	+	0.125708i
$670$	−328060.	+	568217.i	−0.0282336	+	0.0489020i
$671$	−2.37130e6			−0.203320
$672$		0			0
$673$	1.84688e6			0.157182			0.0785908	−	0.996907i	$-0.474958\pi$
$673$	1.84688e6			0.157182			0.0785908	+	0.996907i	$0.474958\pi$
$674$	−5.06828e6	+	8.77853e6i	−0.429745	+	0.744341i
$675$	−2.08166e6	−	3.60554e6i	−0.175853	−	0.304587i
$676$	775624.	+	1.34342e6i	0.0652807	+	0.113069i
$677$	3.84250e6	−	6.65541e6i	0.322213	−	0.558089i	−0.658732	−	0.752378i	$-0.728907\pi$
$677$	3.84250e6	−	6.65541e6i	0.322213	−	0.558089i	0.980944	+	0.194289i	$0.0622400\pi$
$678$	−2.03103e6			−0.169684
$679$		0			0
$680$	3.70633e7			3.07377
$681$	−1.51367e6	+	2.62176e6i	−0.125073	+	0.216633i
$682$	−823680.	−	1.42666e6i	−0.0678106	−	0.117451i
$683$	−3.56090e6	−	6.16766e6i	−0.292084	−	0.505904i	0.682218	−	0.731149i	$-0.261015\pi$
$683$	−3.56090e6	−	6.16766e6i	−0.292084	−	0.505904i	−0.974302	+	0.225244i	$0.927682\pi$
$684$	491022.	−	850475.i	0.0401292	−	0.0695058i
$685$	−8.85311e6			−0.720891
$686$		0			0
$687$	−8.33683e6			−0.673921
$688$	2.03521e6	−	3.52509e6i	0.163922	−	0.283922i
$689$	1.61007e6	+	2.78872e6i	0.129210	+	0.223799i
$690$	1.21824e6	+	2.11005e6i	0.0974115	+	0.168722i
$691$	1.61893e6	−	2.80408e6i	0.128983	−	0.223406i	−0.794300	−	0.607526i	$-0.792162\pi$
$691$	1.61893e6	−	2.80408e6i	0.128983	−	0.223406i	0.923283	+	0.384120i	$0.125495\pi$
$692$	4.27332e6			0.339234
$693$		0			0
$694$	1.74443e7			1.37485
$695$	2.24641e6	−	3.89090e6i	0.176412	−	0.305554i
$696$	4.84204e6	+	8.38667e6i	0.378884	+	0.656246i
$697$	−3.29788e6	−	5.71210e6i	−0.257130	−	0.445363i
$698$	−2.41392e6	+	4.18102e6i	−0.187535	+	0.324821i
$699$	1.13140e7			0.875839
$700$		0			0
$701$	−7.39163e6			−0.568127			−0.284063	−	0.958805i	$-0.591683\pi$
$701$	−7.39163e6			−0.568127			−0.284063	+	0.958805i	$0.591683\pi$
$702$	1.40332e6	−	2.43063e6i	0.107477	−	0.186156i
$703$	6.35471e6	+	1.10067e7i	0.484962	+	0.839978i
$704$	−947882.	−	1.64178e6i	−0.0720813	−	0.124848i
$705$	−365472.	+	633016.i	−0.0276937	+	0.0479669i
$706$	5.76965e6			0.435650
$707$		0			0
$708$	706860.			0.0529969
$709$	2.66680e6	−	4.61904e6i	0.199240	−	0.345093i	−0.749042	−	0.662522i	$-0.769486\pi$
$709$	2.66680e6	−	4.61904e6i	0.199240	−	0.345093i	0.948282	+	0.317429i	$0.102819\pi$
$710$	−4.39920e6	−	7.61964e6i	−0.327512	−	0.567268i
$711$	−3.94567e6	−	6.83410e6i	−0.292716	−	0.507000i
$712$	−310245.	+	537360.i	−0.0229353	+	0.0397251i
$713$	−3.64954e6			−0.268852
$714$		0			0
$715$	−3.76376e6			−0.275332
$716$	2.31788e6	−	4.01469e6i	0.168970	−	0.292664i
$717$	1.56157e6	+	2.70472e6i	0.113439	+	0.196483i
$718$	−4.02776e6	−	6.97628e6i	−0.291576	−	0.505025i
$719$	5.72820e6	−	9.92153e6i	0.413234	−	0.715742i	−0.582007	−	0.813184i	$-0.697733\pi$
$719$	5.72820e6	−	9.92153e6i	0.413234	−	0.715742i	0.995241	+	0.0974414i	$0.0310659\pi$
$720$	−5.71811e6			−0.411075
$721$		0			0
$722$	2.61862e6			0.186952
$723$	−446265.	+	772954.i	−0.0317502	+	0.0549930i
$724$	541205.	+	937395.i	0.0383721	+	0.0664624i
$725$	−1.57566e7	−	2.72913e7i	−1.11332	−	1.92832i
$726$	3.56281e6	−	6.17096e6i	0.250871	−	0.434522i
$727$	−2.49540e7			−1.75107			−0.875536	−	0.483153i	$-0.839492\pi$
$727$	−2.49540e7			−1.75107			−0.875536	+	0.483153i	$0.839492\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−1.08951e7	+	1.88708e7i	−0.756699	+	1.31064i
$731$	5.47962e6	+	9.49098e6i	0.379277	+	0.656928i
$732$	−1.43646e6	−	2.48803e6i	−0.0990870	−	0.171624i
$733$	7.16991e6	−	1.24187e7i	0.492894	−	0.853718i	−0.507072	−	0.861904i	$-0.669272\pi$
$733$	7.16991e6	−	1.24187e7i	0.492894	−	0.853718i	0.999966	+	0.00818541i	$0.00260553\pi$
$734$	1.83874e7			1.25974
$735$		0			0
$736$	−1.43136e6			−0.0973990
$737$	−36296.0	+	62866.5i	−0.00246144	+	0.00426335i
$738$	660555.	+	1.14411e6i	0.0446445	+	0.0773266i
$739$	−461466.	−	799283.i	−0.0310834	−	0.0538380i	0.850065	−	0.526677i	$-0.176562\pi$
$739$	−461466.	−	799283.i	−0.0310834	−	0.0538380i	−0.881149	+	0.472839i	$0.843229\pi$
$740$	−2.41420e6	+	4.18152e6i	−0.162067	+	0.280708i
$741$	−1.20028e7			−0.803037
$742$		0			0
$743$	−9.38995e6			−0.624010			−0.312005	−	0.950081i	$-0.601001\pi$
$743$	−9.38995e6			−0.624010			−0.312005	+	0.950081i	$0.601001\pi$
$744$	5.55984e6	−	9.62993e6i	0.368239	−	0.637809i
$745$	5.84050e6	+	1.01160e7i	0.385531	+	0.667760i
$746$	−1.62442e6	−	2.81357e6i	−0.106869	−	0.185102i
$747$	3.28973e6	−	5.69799e6i	0.215705	−	0.373611i
$748$	736008.			0.0480982
$749$		0			0
$750$	1.09388e7			0.710094
$751$	204016.	−	353366.i	0.0131997	−	0.0228626i	−0.859350	−	0.511388i	$-0.829132\pi$
$751$	204016.	−	353366.i	0.0131997	−	0.0228626i	0.872550	+	0.488525i	$0.162465\pi$
$752$	324432.	+	561933.i	0.0209208	+	0.0362360i
$753$	−1.54993e6	−	2.68455e6i	−0.0996147	−	0.172538i
$754$	1.06222e7	−	1.83981e7i	0.680431	−	1.17854i
$755$	−4.19518e7			−2.67845
$756$		0			0
$757$	2.59605e7			1.64654			0.823271	−	0.567649i	$-0.192147\pi$
$757$	2.59605e7			1.64654			0.823271	+	0.567649i	$0.192147\pi$
$758$	−801750.	+	1.38867e6i	−0.0506834	+	0.0877863i
$759$	134784.	+	233453.i	0.00849247	+	0.0147094i
$760$	1.58738e7	+	2.74942e7i	0.996888	+	1.72666i
$761$	−9.17770e6	+	1.58963e7i	−0.574477	+	0.995023i	0.421622	+	0.906772i	$0.361461\pi$
$761$	−9.17770e6	+	1.58963e7i	−0.574477	+	0.995023i	−0.996098	+	0.0882510i	$0.971872\pi$
$762$	−9.22752e6			−0.575702
$763$		0			0
$764$	−3.40833e6			−0.211255
$765$	7.69775e6	−	1.33329e7i	0.475566	−	0.823704i
$766$	5.90472e6	+	1.02273e7i	0.363603	+	0.629779i
$767$	−4.31970e6	−	7.48194e6i	−0.265134	−	0.459225i
$768$	2.93760e6	−	5.08806e6i	0.179717	−	0.311279i
$769$	−747166.			−0.0455618			−0.0227809	−	0.999740i	$-0.507252\pi$
$769$	−747166.			−0.0455618			−0.0227809	+	0.999740i	$0.507252\pi$
$770$		0			0
$771$	2.65617e6			0.160924
$772$	2.17191e6	−	3.76186e6i	0.131159	−	0.227174i
$773$	−1.01346e7	−	1.75536e7i	−0.610038	−	1.05662i	−0.991233	−	0.132123i	$-0.957821\pi$
$773$	−1.01346e7	−	1.75536e7i	−0.610038	−	1.05662i	0.381195	−	0.924495i	$-0.375513\pi$
$774$	−1.09755e6	−	1.90101e6i	−0.0658524	−	0.114060i
$775$	−1.80924e7	+	3.13370e7i	−1.08204	+	1.87415i
$776$	−958230.			−0.0571236
$777$		0			0
$778$	−1.76695e7			−1.04659
$779$	2.82489e6	−	4.89286e6i	0.166785	−	0.288881i
$780$	−2.27997e6	−	3.94902e6i	−0.134181	−	0.232409i
$781$	−486720.	−	843024.i	−0.0285530	−	0.0494552i
$782$	−2.91168e6	+	5.04318e6i	−0.170266	+	0.294909i
$783$	4.02262e6			0.234479
$784$		0			0
$785$	−1.50161e7			−0.869729
$786$	−1.64169e6	+	2.84349e6i	−0.0947839	+	0.164171i
$787$	2.34991e6	+	4.07016e6i	0.135243	+	0.234248i	0.925690	−	0.378282i	$-0.123485\pi$
$787$	2.34991e6	+	4.07016e6i	0.135243	+	0.234248i	−0.790447	+	0.612530i	$0.790152\pi$
$788$	−827995.	−	1.43413e6i	−0.0475020	−	0.0822759i
$789$	5.72609e6	−	9.91788e6i	0.327465	−	0.567187i
$790$	4.57893e7			2.61033
$791$		0			0
$792$	−821340.			−0.0465275
$793$	−1.75568e7	+	3.04092e7i	−0.991429	+	1.71721i
$794$	−1.01203e7	−	1.75288e7i	−0.569693	−	0.986738i
$795$	−1.76899e6	−	3.06397e6i	−0.0992674	−	0.171936i
$796$	287364.	−	497729.i	0.0160750	−	0.0278426i
$797$	584710.			0.0326058			0.0163029	−	0.999867i	$-0.494810\pi$
$797$	584710.			0.0326058			0.0163029	+	0.999867i	$0.494810\pi$
$798$		0			0
$799$	−1.74701e6			−0.0968117
$800$	−7.09592e6	+	1.22905e7i	−0.391998	+	0.678960i
$801$	128871.	+	223211.i	0.00709699	+	0.0122923i
$802$	−5.19112e6	−	8.99129e6i	−0.284987	−	0.493613i
$803$	−1.20541e6	+	2.08783e6i	−0.0659700	+	0.114263i
$804$	−87948.0			−0.00479828
$805$		0			0
$806$	−2.43936e7			−1.32263
$807$	−1.24548e6	+	2.15724e6i	−0.0673215	+	0.116604i
$808$	−1.62195e7	−	2.80930e7i	−0.873996	−	1.51381i
$809$	8.20063e6	+	1.42039e7i	0.440531	+	0.763022i	0.997729	−	0.0673580i	$-0.0214570\pi$
$809$	8.20063e6	+	1.42039e7i	0.440531	+	0.763022i	−0.557198	+	0.830380i	$0.688124\pi$
$810$	−1.54183e6	+	2.67054e6i	−0.0825706	+	0.143016i
$811$	−304948.			−0.0162807			−0.00814036	−	0.999967i	$-0.502591\pi$
$811$	−304948.			−0.0162807			−0.00814036	+	0.999967i	$0.502591\pi$
$812$		0			0
$813$	−1.16094e7			−0.616005
$814$	953940.	−	1.65227e6i	0.0504615	−	0.0874019i
$815$	−1.16208e7	−	2.01279e7i	−0.612835	−	1.06146i
$816$	−6.83335e6	−	1.18357e7i	−0.359259	−	0.622256i
$817$	−4.69372e6	+	8.12976e6i	−0.246015	+	0.426111i
$818$	1.28716e7			0.672587
$819$		0			0
$820$	2.14640e6			0.111474
$821$	−1.71714e7	+	2.97418e7i	−0.889095	+	1.53996i	−0.0481486	+	0.998840i	$0.515332\pi$
$821$	−1.71714e7	+	2.97418e7i	−0.889095	+	1.53996i	−0.840947	+	0.541118i	$0.818001\pi$
$822$	2.11910e6	+	3.67038e6i	0.109388	+	0.189466i
$823$	−7.83419e6	−	1.35692e7i	−0.403176	−	0.698321i	0.590932	−	0.806722i	$-0.298760\pi$
$823$	−7.83419e6	−	1.35692e7i	−0.403176	−	0.698321i	−0.994107	+	0.108401i	$0.965427\pi$
$824$	1.53231e7	−	2.65404e7i	0.786192	−	1.36172i
$825$	2.67275e6			0.136717
$826$		0			0
$827$	−2.96886e7			−1.50948			−0.754738	−	0.656026i	$-0.772236\pi$
$827$	−2.96886e7			−1.50948			−0.754738	+	0.656026i	$0.772236\pi$
$828$	−163296.	+	282837.i	−0.00827751	+	0.0143371i
$829$	1.15354e7	+	1.99799e7i	0.582970	+	1.00973i	0.995125	+	0.0986203i	$0.0314429\pi$
$829$	1.15354e7	+	1.99799e7i	0.582970	+	1.00973i	−0.412155	+	0.911114i	$0.635224\pi$
$830$	1.90886e7	+	3.30624e7i	0.961786	+	1.66586i
$831$	−7.72448e6	+	1.33792e7i	−0.388031	+	0.672089i
$832$	−2.80719e7			−1.40593
$833$		0			0
$834$	−2.15082e6			−0.107075
$835$	3.21709e7	−	5.57217e7i	1.59679	−	2.76572i
$836$	315224.	+	545984.i	0.0155992	+	0.0270187i
$837$	−2.30947e6	−	4.00012e6i	−0.113946	−	0.197360i
$838$	−2.12037e6	+	3.67259e6i	−0.104304	+	0.180660i
$839$	2.32642e7			1.14100			0.570498	−	0.821299i	$-0.306750\pi$
$839$	2.32642e7			1.14100			0.570498	+	0.821299i	$0.306750\pi$
$840$		0			0
$841$	9.93718e6			0.484477
$842$	−3.59206e6	+	6.22162e6i	−0.174607	+	0.302429i
$843$	6.62482e6	+	1.14745e7i	0.321074	+	0.556116i
$844$	349622.	+	605563.i	0.0168944	+	0.0292619i
$845$	−1.04155e7	+	1.80402e7i	−0.501810	+	0.869161i
$846$	349920.			0.0168090
$847$		0			0
$848$	−3.14068e6			−0.149980
$849$	−4.62965e6	+	8.01880e6i	−0.220434	+	0.381804i
$850$	2.88691e7	+	5.00028e7i	1.37052	+	2.37381i
$851$	−2.11334e6	−	3.66042e6i	−0.100034	−	0.173263i
$852$	589680.	−	1.02136e6i	0.0278303	−	0.0482034i
$853$	1.91515e7			0.901219			0.450610	−	0.892721i	$-0.351207\pi$
$853$	1.91515e7			0.901219			0.450610	+	0.892721i	$0.351207\pi$
$854$		0			0
$855$	1.31874e7			0.616944
$856$	−659490.	+	1.14227e6i	−0.0307627	+	0.0532825i
$857$	2.67342e6	+	4.63049e6i	0.124341	+	0.215365i	0.921475	−	0.388437i	$-0.126985\pi$
$857$	2.67342e6	+	4.63049e6i	0.124341	+	0.215365i	−0.797134	+	0.603802i	$0.793652\pi$
$858$	900900.	+	1.56040e6i	0.0417790	+	0.0723634i
$859$	−1.97929e7	+	3.42823e7i	−0.915223	+	1.58521i	−0.108648	+	0.994080i	$0.534652\pi$
$859$	−1.97929e7	+	3.42823e7i	−0.915223	+	1.58521i	−0.806574	+	0.591132i	$0.798681\pi$
$860$	−3.56636e6			−0.164429
$861$		0			0
$862$	1.17719e7			0.539607
$863$	1.25142e7	−	2.16752e7i	0.571973	−	0.990687i	−0.424390	−	0.905479i	$-0.639511\pi$
$863$	1.25142e7	−	2.16752e7i	0.571973	−	0.990687i	0.996363	−	0.0852072i	$-0.0271552\pi$
$864$	−905782.	−	1.56886e6i	−0.0412800	−	0.0714990i
$865$	2.86923e7	+	4.96965e7i	1.30384	+	2.25832i
$866$	9.47020e6	−	1.64029e7i	0.429106	−	0.743233i
$867$	2.40176e7			1.08513
$868$		0			0
$869$	5.06605e6			0.227573
$870$	−1.16706e7	+	2.02140e7i	−0.522750	+	0.905429i
$871$	537460.	+	930908.i	0.0240049	+	0.0415778i
$872$	1.73938e7	+	3.01270e7i	0.774646	+	1.34173i
$873$	−199017.	+	344708.i	−0.00883801	+	0.0153079i
$874$	−4.98816e6			−0.220883
$875$		0			0
$876$	−2.92081e6			−0.128600
$877$	2.51294e6	−	4.35255e6i	0.110328	−	0.191093i	−0.805575	−	0.592494i	$-0.798143\pi$
$877$	2.51294e6	−	4.35255e6i	0.110328	−	0.191093i	0.915902	+	0.401401i	$0.131477\pi$
$878$	9.10806e6	+	1.57756e7i	0.398740	+	0.690638i
$879$	5.33730e6	+	9.24447e6i	0.232996	+	0.403562i
$880$	1.83544e6	−	3.17908e6i	0.0798977	−	0.138387i
$881$	−2.60490e7			−1.13071			−0.565356	−	0.824847i	$-0.691261\pi$
$881$	−2.60490e7			−1.13071			−0.565356	+	0.824847i	$0.691261\pi$
$882$		0			0
$883$	−6.82462e6			−0.294562			−0.147281	−	0.989095i	$-0.547052\pi$
$883$	−6.82462e6			−0.294562			−0.147281	+	0.989095i	$0.547052\pi$
$884$	5.44929e6	−	9.43845e6i	0.234536	−	0.406228i
$885$	4.74606e6	+	8.22042e6i	0.203693	+	0.352806i
$886$	−6.20973e6	−	1.07556e7i	−0.265759	−	0.460309i
$887$	−1.16917e7	+	2.02507e7i	−0.498965	+	0.864233i	−0.999999	−	0.00119429i	$-0.999620\pi$
$887$	−1.16917e7	+	2.02507e7i	−0.498965	+	0.864233i	0.501034	+	0.865428i	$0.332953\pi$
$888$	1.28782e7			0.548053
$889$		0			0
$890$	−1.49554e6			−0.0632882
$891$	−170586.	+	295464.i	−0.00719862	+	0.0124684i
$892$	−653464.	−	1.13183e6i	−0.0274985	−	0.0476289i
$893$	−748224.	−	1.29596e6i	−0.0313981	−	0.0543831i
$894$	2.79598e6	−	4.84279e6i	0.117001	−	0.202652i
$895$	6.22517e7			2.59773
$896$		0			0
$897$	3.99168e6			0.165644
$898$	6.57944e6	−	1.13959e7i	0.272269	−	0.471583i
$899$	−1.74810e7	−	3.02780e7i	−0.721386	−	1.24948i
$900$	1.61907e6	+	2.80431e6i	0.0666283	+	0.115404i
$901$	4.22800e6	−	7.32311e6i	0.173509	−	0.300527i
$902$	−848120.			−0.0347089
$903$		0			0
$904$	8.80113e6			0.358193
$905$	−7.26761e6	+	1.25879e7i	−0.294965	+	0.510894i
$906$	1.00417e7	+	1.73927e7i	0.406429	+	0.703956i
$907$	−1.97980e7	−	3.42911e7i	−0.799102	−	1.38409i	−0.920202	−	0.391445i	$-0.871975\pi$
$907$	−1.97980e7	−	3.42911e7i	−0.799102	−	1.38409i	0.121100	−	0.992640i	$-0.461358\pi$
$908$	1.17730e6	−	2.03915e6i	0.0473885	−	0.0820793i
$909$	−1.34747e7			−0.540890
$910$		0			0
$911$	−4.67570e6			−0.186660			−0.0933300	−	0.995635i	$-0.529751\pi$
$911$	−4.67570e6			−0.186660			−0.0933300	+	0.995635i	$0.529751\pi$
$912$	5.85329e6	−	1.01382e7i	0.233031	−	0.403621i
$913$	2.11193e6	+	3.65797e6i	0.0838498	+	0.145232i
$914$	2.90326e6	+	5.02859e6i	0.114953	+	0.199104i
$915$	1.92896e7	−	3.34106e7i	0.761678	−	1.31927i
$916$	6.48420e6			0.255339
$917$		0			0
$918$	−7.37019e6			−0.288650
$919$	2.46297e6	−	4.26599e6i	0.0961990	−	0.166622i	−0.813909	−	0.580992i	$-0.802665\pi$
$919$	2.46297e6	−	4.26599e6i	0.0961990	−	0.166622i	0.910108	+	0.414370i	$0.135998\pi$
$920$	−5.27904e6	−	9.14357e6i	−0.205629	−	0.356161i
$921$	−6.83512e6	−	1.18388e7i	−0.265520	−	0.459894i
$922$	−7.03462e6	+	1.21843e7i	−0.272529	+	0.472034i
$923$	−1.44144e7			−0.556919
$924$		0			0
$925$	−4.19073e7			−1.61041
$926$	−1.71075e7	+	2.96310e7i	−0.655630	+	1.13558i
$927$	−6.36498e6	−	1.10245e7i	−0.243275	−	0.421365i
$928$	−6.85612e6	−	1.18751e7i	−0.261341	−	0.452657i
$929$	1.61844e7	−	2.80322e7i	0.615258	−	1.06566i	−0.375082	−	0.926992i	$-0.622385\pi$
$929$	1.61844e7	−	2.80322e7i	0.615258	−	1.06566i	0.990339	−	0.138666i	$-0.0442813\pi$
$930$	2.68013e7			1.01613
$931$		0			0
$932$	−8.79980e6			−0.331843
$933$	−957636.	+	1.65867e6i	−0.0360161	+	0.0623817i
$934$	−8.35785e6	−	1.44762e7i	−0.313493	−	0.542985i
$935$	4.94177e6	+	8.55939e6i	0.184864	+	0.320195i
$936$	−6.08108e6	+	1.05327e7i	−0.226877	+	0.392963i
$937$	−3.32337e7			−1.23660			−0.618301	−	0.785941i	$-0.712179\pi$
$937$	−3.32337e7			−1.23660			−0.618301	+	0.785941i	$0.712179\pi$
$938$		0			0
$939$	−17046.0			−0.000630897
$940$	284256.	−	492346.i	0.0104928	−	0.0181740i
$941$	1.33213e7	+	2.30732e7i	0.490426	+	0.849443i	0.999939	−	0.0110202i	$-0.00350791\pi$
$941$	1.33213e7	+	2.30732e7i	0.490426	+	0.849443i	−0.509513	+	0.860463i	$0.670175\pi$
$942$	3.59428e6	+	6.22548e6i	0.131973	+	0.228584i
$943$	−939456.	+	1.62719e6i	−0.0344031	+	0.0595879i
$944$	8.42622e6			0.307753
$945$		0			0
$946$	1.40920e6			0.0511970
$947$	−1.57332e7	+	2.72506e7i	−0.570086	+	0.987419i	0.426470	+	0.904502i	$0.359757\pi$
$947$	−1.57332e7	+	2.72506e7i	−0.570086	+	0.987419i	−0.996556	+	0.0829170i	$0.973576\pi$
$948$	3.06886e6	+	5.31541e6i	0.110906	+	0.192095i
$949$	1.78494e7	+	3.09160e7i	0.643365	+	1.11434i
$950$	−2.47286e7	+	4.28312e7i	−0.888978	+	1.53976i
$951$	−1.42108e7			−0.509527
$952$		0			0
$953$	−1.34516e7			−0.479779			−0.239890	−	0.970800i	$-0.577111\pi$
$953$	−1.34516e7			−0.479779			−0.239890	+	0.970800i	$0.577111\pi$
$954$	−846855.	+	1.46680e6i	−0.0301258	+	0.0521794i
$955$	−2.28845e7	−	3.96371e7i	−0.811957	−	1.40635i
$956$	−1.21456e6	−	2.10367e6i	−0.0429806	−	0.0744446i
$957$	−1.29121e6	+	2.23644e6i	−0.0455741	+	0.0789366i
$958$	−2.14124e7			−0.753792
$959$		0			0
$960$	3.08426e7			1.08012
$961$	−5.75787e6	+	9.97293e6i	−0.201119	+	0.348349i
$962$	−1.41256e7	−	2.44663e7i	−0.492120	−	0.852376i
$963$	273942.	+	474481.i	0.00951903	+	0.0164875i
$964$	347095.	−	601186.i	0.0120297	−	0.0208361i
$965$	5.83313e7			2.01643
$966$		0			0
$967$	−2.84963e7			−0.979992			−0.489996	−	0.871725i	$-0.663002\pi$
$967$	−2.84963e7			−0.979992			−0.489996	+	0.871725i	$0.663002\pi$
$968$	−1.54388e7	+	2.67408e7i	−0.529573	+	0.917248i
$969$	1.57595e7	+	2.72962e7i	0.539178	+	0.933884i
$970$	−1.15479e6	−	2.00015e6i	−0.0394070	−	0.0682550i
$971$	−9.09289e6	+	1.57493e7i	−0.309495	+	0.536061i	−0.978252	−	0.207420i	$-0.933493\pi$
$971$	−9.09289e6	+	1.57493e7i	−0.309495	+	0.536061i	0.668757	+	0.743481i	$0.266827\pi$
$972$	−413343.			−0.0140328
$973$		0			0
$974$	−4.46588e7			−1.50837
$975$	1.97886e7	−	3.42749e7i	0.666659	−	1.15469i
$976$	−1.71236e7	−	2.96589e7i	−0.575399	−	0.996621i
$977$	−1.60471e7	−	2.77943e7i	−0.537847	−	0.931579i	−0.999020	−	0.0442683i	$-0.985904\pi$
$977$	−1.60471e7	−	2.77943e7i	−0.537847	−	0.931579i	0.461172	−	0.887311i	$-0.347429\pi$
$978$	−5.56317e6	+	9.63569e6i	−0.185984	+	0.322133i
$979$	−165464.			−0.00551756
$980$		0			0
$981$	1.44502e7			0.479405
$982$	−6.88265e6	+	1.19211e7i	−0.227760	+	0.394491i
$983$	−7.80769e6	−	1.35233e7i	−0.257715	−	0.446375i	0.707915	−	0.706298i	$-0.249636\pi$
$983$	−7.80769e6	−	1.35233e7i	−0.257715	−	0.446375i	−0.965629	+	0.259923i	$0.916303\pi$
$984$	−2.86240e6	−	4.95783e6i	−0.0942417	−	0.163231i
$985$	1.11188e7	−	1.92583e7i	0.365146	−	0.632452i
$986$	−5.57870e7			−1.82743
$987$		0			0
$988$	9.33548e6			0.304260
$989$	1.56096e6	−	2.70366e6i	0.0507459	−	0.0878945i
$990$	−989820.	−	1.71442e6i	−0.0320973	−	0.0555941i
$991$	−2.42250e7	−	4.19589e7i	−0.783572	−	1.35719i	−0.929848	−	0.367943i	$-0.880062\pi$
$991$	−2.42250e7	−	4.19589e7i	−0.783572	−	1.35719i	0.146276	−	0.989244i	$-0.453271\pi$
$992$	−7.87248e6	+	1.36355e7i	−0.253999	+	0.439940i
$993$	−3.05524e7			−0.983268
$994$		0			0
$995$	7.71778e6			0.247135
$996$	−2.55868e6	+	4.43177e6i	−0.0817275	+	0.141556i
$997$	2.27168e7	+	3.93466e7i	0.723784	+	1.25363i	0.959473	+	0.281802i	$0.0909321\pi$
$997$	2.27168e7	+	3.93466e7i	0.723784	+	1.25363i	−0.235689	+	0.971829i	$0.575735\pi$
$998$	−1.20102e7	−	2.08023e7i	−0.381702	−	0.661127i
$999$	2.67470e6	−	4.63272e6i	0.0847933	−	0.146866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.c.79.1		2
7.2	even	3		21.6.a.c.1.1	✓	1
7.3	odd	6		147.6.e.d.67.1		2
7.4	even	3	inner	147.6.e.c.67.1		2
7.5	odd	6		147.6.a.f.1.1		1
7.6	odd	2		147.6.e.d.79.1		2
21.2	odd	6		63.6.a.b.1.1		1
21.5	even	6		441.6.a.c.1.1		1
28.23	odd	6		336.6.a.i.1.1		1
35.2	odd	12		525.6.d.c.274.2		2
35.9	even	6		525.6.a.b.1.1		1
35.23	odd	12		525.6.d.c.274.1		2
84.23	even	6		1008.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.a.c.1.1	✓	1	7.2	even	3
63.6.a.b.1.1		1	21.2	odd	6
147.6.a.f.1.1		1	7.5	odd	6
147.6.e.c.67.1		2	7.4	even	3	inner
147.6.e.c.79.1		2	1.1	even	1	trivial
147.6.e.d.67.1		2	7.3	odd	6
147.6.e.d.79.1		2	7.6	odd	2
336.6.a.i.1.1		1	28.23	odd	6
441.6.a.c.1.1		1	21.5	even	6
525.6.a.b.1.1		1	35.9	even	6
525.6.d.c.274.1		2	35.23	odd	12
525.6.d.c.274.2		2	35.2	odd	12
1008.6.a.a.1.1		1	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.50000 + 4.33013i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-47.0000 + 81.4064i) q^{5} +45.0000 q^{6} -195.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.50000 + 4.33013i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-47.0000 + 81.4064i) q^{5} +45.0000 q^{6} -195.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-235.000 - 407.032i) q^{10} +(-26.0000 - 45.0333i) q^{11} +(31.5000 - 54.5596i) q^{12} -770.000 q^{13} +846.000 q^{15} +(375.500 - 650.385i) q^{16} +(1011.00 + 1751.10i) q^{17} +(-202.500 - 350.740i) q^{18} +(-866.000 + 1499.96i) q^{19} -658.000 q^{20} +260.000 q^{22} +(288.000 - 498.831i) q^{23} +(877.500 + 1519.87i) q^{24} +(-2855.50 - 4945.87i) q^{25} +(1925.00 - 3334.20i) q^{26} +729.000 q^{27} +5518.00 q^{29} +(-2115.00 + 3663.29i) q^{30} +(-3168.00 - 5487.14i) q^{31} +(-1242.50 - 2152.07i) q^{32} +(-234.000 + 405.300i) q^{33} -10110.0 q^{34} -567.000 q^{36} +(3669.00 - 6354.89i) q^{37} +(-4330.00 - 7499.78i) q^{38} +(3465.00 + 6001.56i) q^{39} +(9165.00 - 15874.2i) q^{40} -3262.00 q^{41} +5420.00 q^{43} +(182.000 - 315.233i) q^{44} +(-3807.00 - 6593.92i) q^{45} +(1440.00 + 2494.15i) q^{46} +(-432.000 + 748.246i) q^{47} -6759.00 q^{48} +28555.0 q^{50} +(9099.00 - 15759.9i) q^{51} +(-2695.00 - 4667.88i) q^{52} +(-2091.00 - 3621.72i) q^{53} +(-1822.50 + 3156.66i) q^{54} +4888.00 q^{55} +15588.0 q^{57} +(-13795.0 + 23893.6i) q^{58} +(5610.00 + 9716.81i) q^{59} +(2961.00 + 5128.60i) q^{60} +(22801.0 - 39492.5i) q^{61} +31680.0 q^{62} +36457.0 q^{64} +(36190.0 - 62682.9i) q^{65} +(-1170.00 - 2026.50i) q^{66} +(-698.000 - 1208.97i) q^{67} +(-7077.00 + 12257.7i) q^{68} -5184.00 q^{69} +18720.0 q^{71} +(7897.50 - 13678.9i) q^{72} +(-23181.0 - 40150.7i) q^{73} +(18345.0 + 31774.5i) q^{74} +(-25699.5 + 44512.8i) q^{75} -12124.0 q^{76} -34650.0 q^{78} +(-48712.0 + 84371.7i) q^{79} +(35297.0 + 61136.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(8155.00 - 14124.9i) q^{82} -81228.0 q^{83} -190068. q^{85} +(-13550.0 + 23469.3i) q^{86} +(-24831.0 - 43008.6i) q^{87} +(5070.00 + 8781.50i) q^{88} +(1591.00 - 2755.69i) q^{89} +38070.0 q^{90} +4032.00 q^{92} +(-28512.0 + 49384.2i) q^{93} +(-2160.00 - 3741.23i) q^{94} +(-81404.0 - 140996. i) q^{95} +(-11182.5 + 19368.7i) q^{96} +4914.00 q^{97} +4212.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 5 q^{2} - 9 q^{3} + 7 q^{4} - 94 q^{5} + 90 q^{6} - 390 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q - 5 * q^2 - 9 * q^3 + 7 * q^4 - 94 * q^5 + 90 * q^6 - 390 * q^8 - 81 * q^9	\( 2 q - 5 q^{2} - 9 q^{3} + 7 q^{4} - 94 q^{5} + 90 q^{6} - 390 q^{8} - 81 q^{9} - 470 q^{10} - 52 q^{11} + 63 q^{12} - 1540 q^{13} + 1692 q^{15} + 751 q^{16} + 2022 q^{17} - 405 q^{18} - 1732 q^{19} - 1316 q^{20} + 520 q^{22} + 576 q^{23} + 1755 q^{24} - 5711 q^{25} + 3850 q^{26} + 1458 q^{27} + 11036 q^{29} - 4230 q^{30} - 6336 q^{31} - 2485 q^{32} - 468 q^{33} - 20220 q^{34} - 1134 q^{36} + 7338 q^{37} - 8660 q^{38} + 6930 q^{39} + 18330 q^{40} - 6524 q^{41} + 10840 q^{43} + 364 q^{44} - 7614 q^{45} + 2880 q^{46} - 864 q^{47} - 13518 q^{48} + 57110 q^{50} + 18198 q^{51} - 5390 q^{52} - 4182 q^{53} - 3645 q^{54} + 9776 q^{55} + 31176 q^{57} - 27590 q^{58} + 11220 q^{59} + 5922 q^{60} + 45602 q^{61} + 63360 q^{62} + 72914 q^{64} + 72380 q^{65} - 2340 q^{66} - 1396 q^{67} - 14154 q^{68} - 10368 q^{69} + 37440 q^{71} + 15795 q^{72} - 46362 q^{73} + 36690 q^{74} - 51399 q^{75} - 24248 q^{76} - 69300 q^{78} - 97424 q^{79} + 70594 q^{80} - 6561 q^{81} + 16310 q^{82} - 162456 q^{83} - 380136 q^{85} - 27100 q^{86} - 49662 q^{87} + 10140 q^{88} + 3182 q^{89} + 76140 q^{90} + 8064 q^{92} - 57024 q^{93} - 4320 q^{94} - 162808 q^{95} - 22365 q^{96} + 9828 q^{97} + 8424 q^{99}+O(q^{100}) \) 2 * q - 5 * q^2 - 9 * q^3 + 7 * q^4 - 94 * q^5 + 90 * q^6 - 390 * q^8 - 81 * q^9 - 470 * q^10 - 52 * q^11 + 63 * q^12 - 1540 * q^13 + 1692 * q^15 + 751 * q^16 + 2022 * q^17 - 405 * q^18 - 1732 * q^19 - 1316 * q^20 + 520 * q^22 + 576 * q^23 + 1755 * q^24 - 5711 * q^25 + 3850 * q^26 + 1458 * q^27 + 11036 * q^29 - 4230 * q^30 - 6336 * q^31 - 2485 * q^32 - 468 * q^33 - 20220 * q^34 - 1134 * q^36 + 7338 * q^37 - 8660 * q^38 + 6930 * q^39 + 18330 * q^40 - 6524 * q^41 + 10840 * q^43 + 364 * q^44 - 7614 * q^45 + 2880 * q^46 - 864 * q^47 - 13518 * q^48 + 57110 * q^50 + 18198 * q^51 - 5390 * q^52 - 4182 * q^53 - 3645 * q^54 + 9776 * q^55 + 31176 * q^57 - 27590 * q^58 + 11220 * q^59 + 5922 * q^60 + 45602 * q^61 + 63360 * q^62 + 72914 * q^64 + 72380 * q^65 - 2340 * q^66 - 1396 * q^67 - 14154 * q^68 - 10368 * q^69 + 37440 * q^71 + 15795 * q^72 - 46362 * q^73 + 36690 * q^74 - 51399 * q^75 - 24248 * q^76 - 69300 * q^78 - 97424 * q^79 + 70594 * q^80 - 6561 * q^81 + 16310 * q^82 - 162456 * q^83 - 380136 * q^85 - 27100 * q^86 - 49662 * q^87 + 10140 * q^88 + 3182 * q^89 + 76140 * q^90 + 8064 * q^92 - 57024 * q^93 - 4320 * q^94 - 162808 * q^95 - 22365 * q^96 + 9828 * q^97 + 8424 * q^99

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