LMFDB - Embedded newform 18.6.c.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,6,Mod(7,18)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, degree $2$, 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:	$2.88690875663$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.6.c.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-14.6969 + 5.19615i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-28.1969 + 48.8385i) q^{5} +(-47.3939 - 40.5194i) q^{6} +(11.1515 + 19.3150i) q^{7} -64.0000 q^{8} +(189.000 - 152.735i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-14.6969 + 5.19615i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-28.1969 + 48.8385i) q^{5} +(-47.3939 - 40.5194i) q^{6} +(11.1515 + 19.3150i) q^{7} -64.0000 q^{8} +(189.000 - 152.735i) q^{9} -225.576 q^{10} +(296.484 + 513.526i) q^{11} +(45.5755 - 245.216i) q^{12} +(129.531 - 224.354i) q^{13} +(-44.6061 + 77.2601i) q^{14} +(160.636 - 864.292i) q^{15} +(-128.000 - 221.703i) q^{16} +1627.51 q^{17} +(907.090 + 349.245i) q^{18} -2642.42 q^{19} +(-451.151 - 781.416i) q^{20} +(-264.257 - 225.927i) q^{21} +(-1185.94 + 2054.10i) q^{22} +(-1568.21 + 2716.22i) q^{23} +(940.604 - 332.554i) q^{24} +(-27.6347 - 47.8647i) q^{25} +1036.24 q^{26} +(-1984.09 + 3226.81i) q^{27} -356.849 q^{28} +(-62.2898 - 107.889i) q^{29} +(3315.27 - 1172.12i) q^{30} +(4376.08 - 7579.60i) q^{31} +(512.000 - 886.810i) q^{32} +(-7025.77 - 6006.68i) q^{33} +(3255.02 + 5637.87i) q^{34} -1257.76 q^{35} +(604.359 + 3840.74i) q^{36} +9741.67 q^{37} +(-5284.84 - 9153.61i) q^{38} +(-737.928 + 3970.37i) q^{39} +(1804.60 - 3125.67i) q^{40} +(3735.62 - 6470.29i) q^{41} +(254.118 - 1367.27i) q^{42} +(6252.46 + 10829.6i) q^{43} -9487.49 q^{44} +(2130.13 + 13537.1i) q^{45} -12545.7 q^{46} +(4408.73 + 7636.15i) q^{47} +(3033.21 + 2593.24i) q^{48} +(8154.79 - 14124.5i) q^{49} +(110.539 - 191.459i) q^{50} +(-23919.4 + 8456.80i) q^{51} +(2072.49 + 3589.66i) q^{52} -10782.1 q^{53} +(-15146.2 - 419.457i) q^{54} -33439.8 q^{55} +(-713.698 - 1236.16i) q^{56} +(38835.5 - 13730.4i) q^{57} +(249.159 - 431.557i) q^{58} +(7776.87 - 13469.9i) q^{59} +(10690.9 + 9140.18i) q^{60} +(5965.22 + 10332.1i) q^{61} +35008.7 q^{62} +(5057.72 + 1947.31i) q^{63} +4096.00 q^{64} +(7304.73 + 12652.2i) q^{65} +(6756.21 - 36351.3i) q^{66} +(-3089.79 + 5351.68i) q^{67} +(-13020.1 + 22551.5i) q^{68} +(8934.01 - 48068.8i) q^{69} +(-2515.51 - 4356.99i) q^{70} -10498.9 q^{71} +(-12096.0 + 9775.04i) q^{72} -38380.3 q^{73} +(19483.3 + 33746.1i) q^{74} +(654.857 + 559.870i) q^{75} +(21139.4 - 36614.5i) q^{76} +(-6612.50 + 11453.2i) q^{77} +(-15229.6 + 5384.49i) q^{78} +(-8926.87 - 15461.8i) q^{79} +14436.8 q^{80} +(12393.0 - 57733.9i) q^{81} +29885.0 q^{82} +(21610.3 + 37430.1i) q^{83} +(5244.59 - 1854.24i) q^{84} +(-45890.9 + 79485.3i) q^{85} +(-25009.8 + 43318.3i) q^{86} +(1476.08 + 1261.97i) q^{87} +(-18975.0 - 32865.6i) q^{88} -94095.6 q^{89} +(-42633.8 + 34453.3i) q^{90} +5777.86 q^{91} +(-25091.4 - 43459.6i) q^{92} +(-24930.3 + 134136. i) q^{93} +(-17634.9 + 30544.6i) q^{94} +(74508.2 - 129052. i) q^{95} +(-2916.83 + 15693.8i) q^{96} +(40743.3 + 70569.5i) q^{97} +65238.3 q^{98} +(134469. + 51772.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 32 q^{4} - 54 q^{5} - 72 q^{6} + 74 q^{7} - 256 q^{8} + 756 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 - 32 * q^4 - 54 * q^5 - 72 * q^6 + 74 * q^7 - 256 * q^8 + 756 * q^9	\( 4 q + 8 q^{2} - 32 q^{4} - 54 q^{5} - 72 q^{6} + 74 q^{7} - 256 q^{8} + 756 q^{9} - 432 q^{10} - 78 q^{11} - 288 q^{12} + 1106 q^{13} - 296 q^{14} + 378 q^{15} - 512 q^{16} + 984 q^{17} + 1512 q^{18} - 3280 q^{19} - 864 q^{20} - 234 q^{21} + 312 q^{22} - 5538 q^{23} + 3064 q^{25} + 8848 q^{26} - 2368 q^{28} - 3894 q^{29} + 6912 q^{30} + 4718 q^{31} + 2048 q^{32} - 17874 q^{33} + 1968 q^{34} - 2268 q^{35} - 6048 q^{36} - 9592 q^{37} - 6560 q^{38} + 18594 q^{39} + 3456 q^{40} + 15354 q^{41} - 4392 q^{42} + 32858 q^{43} + 2496 q^{44} + 5346 q^{45} - 44304 q^{46} + 24954 q^{47} + 4608 q^{48} + 30444 q^{49} - 12256 q^{50} - 81216 q^{51} + 17696 q^{52} - 32664 q^{53} - 44712 q^{54} - 70092 q^{55} - 4736 q^{56} + 107136 q^{57} + 15576 q^{58} + 21966 q^{59} + 21600 q^{60} + 3050 q^{61} + 37744 q^{62} + 6210 q^{63} + 16384 q^{64} + 12582 q^{65} + 77112 q^{66} + 36758 q^{67} - 7872 q^{68} - 39042 q^{69} - 4536 q^{70} - 147696 q^{71} - 48384 q^{72} - 102376 q^{73} - 19184 q^{74} + 19080 q^{75} + 26240 q^{76} + 21462 q^{77} + 69120 q^{78} - 14926 q^{79} + 27648 q^{80} + 49572 q^{81} + 122832 q^{82} + 90762 q^{83} - 13824 q^{84} - 94500 q^{85} - 131432 q^{86} - 18522 q^{87} + 4992 q^{88} - 18600 q^{89} - 81648 q^{90} + 99124 q^{91} - 88608 q^{92} - 145458 q^{93} - 99816 q^{94} + 151416 q^{95} + 18432 q^{96} - 30262 q^{97} + 243552 q^{98} + 319626 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 32 * q^4 - 54 * q^5 - 72 * q^6 + 74 * q^7 - 256 * q^8 + 756 * q^9 - 432 * q^10 - 78 * q^11 - 288 * q^12 + 1106 * q^13 - 296 * q^14 + 378 * q^15 - 512 * q^16 + 984 * q^17 + 1512 * q^18 - 3280 * q^19 - 864 * q^20 - 234 * q^21 + 312 * q^22 - 5538 * q^23 + 3064 * q^25 + 8848 * q^26 - 2368 * q^28 - 3894 * q^29 + 6912 * q^30 + 4718 * q^31 + 2048 * q^32 - 17874 * q^33 + 1968 * q^34 - 2268 * q^35 - 6048 * q^36 - 9592 * q^37 - 6560 * q^38 + 18594 * q^39 + 3456 * q^40 + 15354 * q^41 - 4392 * q^42 + 32858 * q^43 + 2496 * q^44 + 5346 * q^45 - 44304 * q^46 + 24954 * q^47 + 4608 * q^48 + 30444 * q^49 - 12256 * q^50 - 81216 * q^51 + 17696 * q^52 - 32664 * q^53 - 44712 * q^54 - 70092 * q^55 - 4736 * q^56 + 107136 * q^57 + 15576 * q^58 + 21966 * q^59 + 21600 * q^60 + 3050 * q^61 + 37744 * q^62 + 6210 * q^63 + 16384 * q^64 + 12582 * q^65 + 77112 * q^66 + 36758 * q^67 - 7872 * q^68 - 39042 * q^69 - 4536 * q^70 - 147696 * q^71 - 48384 * q^72 - 102376 * q^73 - 19184 * q^74 + 19080 * q^75 + 26240 * q^76 + 21462 * q^77 + 69120 * q^78 - 14926 * q^79 + 27648 * q^80 + 49572 * q^81 + 122832 * q^82 + 90762 * q^83 - 13824 * q^84 - 94500 * q^85 - 131432 * q^86 - 18522 * q^87 + 4992 * q^88 - 18600 * q^89 - 81648 * q^90 + 99124 * q^91 - 88608 * q^92 - 145458 * q^93 - 99816 * q^94 + 151416 * q^95 + 18432 * q^96 - 30262 * q^97 + 243552 * q^98 + 319626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$3$	−14.6969	+	5.19615i	−0.942809	+	0.333333i
$3$	−14.6969	+	5.19615i	−0.942809	+	0.333333i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−28.1969	+	48.8385i	−0.504402	+	0.873650i	0.495585	+	0.868560i	$0.334954\pi$
$5$	−28.1969	+	48.8385i	−0.504402	+	0.873650i	−0.999987	+	0.00509067i	$0.998380\pi$
$6$	−47.3939	−	40.5194i	−0.537457	−	0.459499i
$7$	11.1515	+	19.3150i	0.0860180	+	0.148988i	0.905825	−	0.423653i	$-0.139252\pi$
$7$	11.1515	+	19.3150i	0.0860180	+	0.148988i	−0.819807	+	0.572641i	$0.805919\pi$
$8$	−64.0000			−0.353553
$9$	189.000	−	152.735i	0.777778	−	0.628539i
$10$	−225.576			−0.713332
$11$	296.484	+	513.526i	0.738788	+	1.27962i	0.953041	+	0.302840i	$0.0979348\pi$
$11$	296.484	+	513.526i	0.738788	+	1.27962i	−0.214253	+	0.976778i	$0.568732\pi$
$12$	45.5755	−	245.216i	0.0913647	−	0.491582i
$13$	129.531	−	224.354i	0.212576	−	0.368192i	−0.739944	−	0.672668i	$-0.765148\pi$
$13$	129.531	−	224.354i	0.212576	−	0.368192i	0.952520	+	0.304476i	$0.0984814\pi$
$14$	−44.6061	+	77.2601i	−0.0608239	+	0.105350i
$15$	160.636	−	864.292i	0.184338	−	0.991819i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	1627.51			1.36585			0.682923	−	0.730490i	$-0.260708\pi$
$17$	1627.51			1.36585			0.682923	+	0.730490i	$0.260708\pi$
$18$	907.090	+	349.245i	0.659886	+	0.254067i
$19$	−2642.42			−1.67926			−0.839630	−	0.543159i	$-0.817228\pi$
$19$	−2642.42			−1.67926			−0.839630	+	0.543159i	$0.817228\pi$
$20$	−451.151	−	781.416i	−0.252201	−	0.436825i
$21$	−264.257	−	225.927i	−0.130761	−	0.111794i
$22$	−1185.94	+	2054.10i	−0.522402	+	0.904827i
$23$	−1568.21	+	2716.22i	−0.618138	+	1.07065i	0.371688	+	0.928358i	$0.378779\pi$
$23$	−1568.21	+	2716.22i	−0.618138	+	1.07065i	−0.989825	+	0.142288i	$0.954554\pi$
$24$	940.604	−	332.554i	0.333333	−	0.117851i
$25$	−27.6347	−	47.8647i	−0.00884310	−	0.0153167i
$26$	1036.24			0.300628
$27$	−1984.09	+	3226.81i	−0.523783	+	0.851852i
$28$	−356.849			−0.0860180
$29$	−62.2898	−	107.889i	−0.0137538	−	0.0238222i	0.859067	−	0.511864i	$-0.171045\pi$
$29$	−62.2898	−	107.889i	−0.0137538	−	0.0238222i	−0.872820	+	0.488042i	$0.837711\pi$
$30$	3315.27	−	1172.12i	0.672536	−	0.237777i
$31$	4376.08	−	7579.60i	0.817865	−	1.41658i	−0.0893879	−	0.995997i	$-0.528491\pi$
$31$	4376.08	−	7579.60i	0.817865	−	1.41658i	0.907253	−	0.420586i	$-0.138176\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−7025.77	−	6006.68i	−1.12308	−	0.960173i
$34$	3255.02	+	5637.87i	0.482900	+	0.836407i
$35$	−1257.76			−0.173551
$36$	604.359	+	3840.74i	0.0777211	+	0.493922i
$37$	9741.67			1.16985			0.584924	−	0.811088i	$-0.301124\pi$
$37$	9741.67			1.16985			0.584924	+	0.811088i	$0.301124\pi$
$38$	−5284.84	−	9153.61i	−0.593708	−	1.02833i
$39$	−737.928	+	3970.37i	−0.0776877	+	0.417994i
$40$	1804.60	−	3125.67i	0.178333	−	0.308882i
$41$	3735.62	−	6470.29i	0.347059	−	0.601124i	−0.638667	−	0.769484i	$-0.720514\pi$
$41$	3735.62	−	6470.29i	0.347059	−	0.601124i	0.985726	+	0.168360i	$0.0538471\pi$
$42$	254.118	−	1367.27i	0.0222286	−	0.119600i
$43$	6252.46	+	10829.6i	0.515679	+	0.893183i	0.999834	+	0.0182005i	$0.00579373\pi$
$43$	6252.46	+	10829.6i	0.515679	+	0.893183i	−0.484155	+	0.874982i	$0.660873\pi$
$44$	−9487.49			−0.738788
$45$	2130.13	+	13537.1i	0.156811	+	0.996542i
$46$	−12545.7			−0.874178
$47$	4408.73	+	7636.15i	0.291118	+	0.504231i	0.974074	−	0.226228i	$-0.0726395\pi$
$47$	4408.73	+	7636.15i	0.291118	+	0.504231i	−0.682956	+	0.730459i	$0.739306\pi$
$48$	3033.21	+	2593.24i	0.190020	+	0.162457i
$49$	8154.79	−	14124.5i	0.485202	−	0.840394i
$50$	110.539	−	191.459i	0.00625301	−	0.0108305i
$51$	−23919.4	+	8456.80i	−1.28773	+	0.455282i
$52$	2072.49	+	3589.66i	0.106288	+	0.184096i
$53$	−10782.1			−0.527244			−0.263622	−	0.964626i	$-0.584917\pi$
$53$	−10782.1			−0.527244			−0.263622	+	0.964626i	$0.584917\pi$
$54$	−15146.2	−	419.457i	−0.706836	−	0.0195750i
$55$	−33439.8			−1.49058
$56$	−713.698	−	1236.16i	−0.0304120	−	0.0526751i
$57$	38835.5	−	13730.4i	1.58322	−	0.559753i
$58$	249.159	−	431.557i	0.00972539	−	0.0168449i
$59$	7776.87	−	13469.9i	0.290854	−	0.503774i	−0.683158	−	0.730271i	$-0.739394\pi$
$59$	7776.87	−	13469.9i	0.290854	−	0.503774i	0.974012	+	0.226497i	$0.0727273\pi$
$60$	10690.9	+	9140.18i	0.383386	+	0.327776i
$61$	5965.22	+	10332.1i	0.205259	+	0.355519i	0.950215	−	0.311595i	$-0.100863\pi$
$61$	5965.22	+	10332.1i	0.205259	+	0.355519i	−0.744956	+	0.667113i	$0.767530\pi$
$62$	35008.7			1.15664
$63$	5057.72	+	1947.31i	0.160547	+	0.0618135i
$64$	4096.00			0.125000
$65$	7304.73	+	12652.2i	0.214448	+	0.371434i
$66$	6756.21	−	36351.3i	0.190916	−	1.02721i
$67$	−3089.79	+	5351.68i	−0.0840896	+	0.145647i	−0.905003	−	0.425405i	$-0.860132\pi$
$67$	−3089.79	+	5351.68i	−0.0840896	+	0.145647i	0.820913	+	0.571053i	$0.193465\pi$
$68$	−13020.1	+	22551.5i	−0.341462	+	0.591429i
$69$	8934.01	−	48068.8i	0.225904	−	1.21546i
$70$	−2515.51	−	4356.99i	−0.0613594	−	0.106278i
$71$	−10498.9			−0.247171			−0.123586	−	0.992334i	$-0.539439\pi$
$71$	−10498.9			−0.247171			−0.123586	+	0.992334i	$0.539439\pi$
$72$	−12096.0	+	9775.04i	−0.274986	+	0.222222i
$73$	−38380.3			−0.842950			−0.421475	−	0.906840i	$-0.638487\pi$
$73$	−38380.3			−0.842950			−0.421475	+	0.906840i	$0.638487\pi$
$74$	19483.3	+	33746.1i	0.413603	+	0.716382i
$75$	654.857	+	559.870i	0.0134429	+	0.0114930i
$76$	21139.4	−	36614.5i	0.419815	−	0.727141i
$77$	−6612.50	+	11453.2i	−0.127098	+	0.220140i
$78$	−15229.6	+	5384.49i	−0.283435	+	0.100209i
$79$	−8926.87	−	15461.8i	−0.160928	−	0.278735i	0.774274	−	0.632851i	$-0.218115\pi$
$79$	−8926.87	−	15461.8i	−0.160928	−	0.278735i	−0.935202	+	0.354115i	$0.884782\pi$
$80$	14436.8			0.252201
$81$	12393.0	−	57733.9i	0.209877	−	0.977728i
$82$	29885.0			0.490815
$83$	21610.3	+	37430.1i	0.344322	+	0.596384i	0.985230	−	0.171234i	$-0.0547754\pi$
$83$	21610.3	+	37430.1i	0.344322	+	0.596384i	−0.640908	+	0.767618i	$0.721442\pi$
$84$	5244.59	−	1854.24i	0.0810986	−	0.0286727i
$85$	−45890.9	+	79485.3i	−0.688936	+	1.19327i
$86$	−25009.8	+	43318.3i	−0.364640	+	0.631576i
$87$	1476.08	+	1261.97i	0.0209079	+	0.0178752i
$88$	−18975.0	−	32865.6i	−0.261201	−	0.452413i
$89$	−94095.6			−1.25920			−0.629599	−	0.776920i	$-0.716781\pi$
$89$	−94095.6			−1.25920			−0.629599	+	0.776920i	$0.716781\pi$
$90$	−42633.8	+	34453.3i	−0.554814	+	0.448357i
$91$	5777.86			0.0731414
$92$	−25091.4	−	43459.6i	−0.309069	−	0.535323i
$93$	−24930.3	+	134136.i	−0.298896	+	1.60819i
$94$	−17634.9	+	30544.6i	−0.205851	+	0.356545i
$95$	74508.2	−	129052.i	0.847022	−	1.46709i
$96$	−2916.83	+	15693.8i	−0.0323023	+	0.173800i
$97$	40743.3	+	70569.5i	0.439670	+	0.761532i	0.997664	−	0.0683138i	$-0.0217619\pi$
$97$	40743.3	+	70569.5i	0.439670	+	0.761532i	−0.557993	+	0.829845i	$0.688429\pi$
$98$	65238.3			0.686179
$99$	134469.	+	51772.8i	1.37890	+	0.530901i
$100$	884.310			0.00884310
$101$	−66434.0	−	115067.i	−0.648017	−	1.12240i	−0.983596	−	0.180387i	$-0.942265\pi$
$101$	−66434.0	−	115067.i	−0.648017	−	1.12240i	0.335578	−	0.942012i	$-0.391068\pi$
$102$	−77134.1	−	65945.8i	−0.734085	−	0.627605i
$103$	62055.5	−	107483.i	0.576352	−	0.998270i	−0.419542	−	0.907736i	$-0.637809\pi$
$103$	62055.5	−	107483.i	0.576352	−	0.998270i	0.995893	−	0.0905343i	$-0.0288575\pi$
$104$	−8289.96	+	14358.6i	−0.0751569	+	0.130176i
$105$	18485.2	−	6535.49i	0.163625	−	0.0578502i
$106$	−21564.1	−	37350.1i	−0.186409	−	0.322870i
$107$	102868.			0.868605			0.434303	−	0.900767i	$-0.356995\pi$
$107$	102868.			0.868605			0.434303	+	0.900767i	$0.356995\pi$
$108$	−28839.3	−	53306.8i	−0.237917	−	0.439768i
$109$	229354.			1.84901			0.924506	−	0.381167i	$-0.124478\pi$
$109$	229354.			1.84901			0.924506	+	0.381167i	$0.124478\pi$
$110$	−66879.6	−	115839.i	−0.527001	−	0.912793i
$111$	−143173.	+	50619.2i	−1.10294	+	0.389949i
$112$	2854.79	−	4944.64i	0.0215045	−	0.0372469i
$113$	−37466.9	+	64894.5i	−0.276027	+	0.478092i	−0.970394	−	0.241529i	$-0.922351\pi$
$113$	−37466.9	+	64894.5i	−0.276027	+	0.478092i	0.694367	+	0.719621i	$0.255685\pi$
$114$	125235.	+	107069.i	0.902531	+	0.771618i
$115$	−88437.5	−	153178.i	−0.623580	−	1.08007i
$116$	1993.27			0.0137538
$117$	−9785.38	−	62186.7i	−0.0660865	−	0.419984i
$118$	62215.0			0.411330
$119$	18149.3	+	31435.4i	0.117487	+	0.203494i
$120$	−10280.7	+	55314.7i	−0.0651734	+	0.350661i
$121$	−95280.2	+	165030.i	−0.591615	+	1.02471i
$122$	−23860.9	+	41328.2i	−0.145140	+	0.251390i
$123$	−21281.6	+	114504.i	−0.126836	+	0.682431i
$124$	70017.3	+	121274.i	0.408932	+	0.708292i
$125$	−173114.			−0.990962
$126$	3369.76	+	21415.1i	0.0189092	+	0.120169i
$127$	34578.3			0.190237			0.0951184	−	0.995466i	$-0.469677\pi$
$127$	34578.3			0.190237			0.0951184	+	0.995466i	$0.469677\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	−148164.	−	126673.i	−0.783915	−	0.670208i
$130$	−29218.9	+	50608.7i	−0.151637	+	0.262643i
$131$	−39811.8	+	68956.1i	−0.202691	+	0.351071i	−0.949395	−	0.314086i	$-0.898302\pi$
$131$	−39811.8	+	68956.1i	−0.202691	+	0.351071i	0.746704	+	0.665157i	$0.231635\pi$
$132$	139437.	−	49298.5i	0.696536	−	0.246263i
$133$	−29467.0	−	51038.4i	−0.144447	−	0.250189i
$134$	−24718.3			−0.118921
$135$	−101648.	−	187886.i	−0.480023	−	0.887279i
$136$	−104161.			−0.482900
$137$	135520.	+	234728.i	0.616883	+	1.06847i	0.990051	+	0.140709i	$0.0449383\pi$
$137$	135520.	+	234728.i	0.616883	+	1.06847i	−0.373168	+	0.927764i	$0.621728\pi$
$138$	184383.	−	65189.3i	0.824183	−	0.291393i
$139$	−16584.4	+	28725.0i	−0.0728053	+	0.126102i	−0.900130	−	0.435622i	$-0.856528\pi$
$139$	−16584.4	+	28725.0i	−0.0728053	+	0.126102i	0.827324	+	0.561724i	$0.189862\pi$
$140$	10062.0	−	17428.0i	0.0433877	−	0.0751496i
$141$	−104473.	−	89319.5i	−0.442546	−	0.378354i
$142$	−20997.8	−	36369.3i	−0.0873883	−	0.151361i
$143$	153615.			0.628194
$144$	−58053.7	−	22351.7i	−0.233305	−	0.0898264i
$145$	7025.53			0.0277497
$146$	−76760.7	−	132953.i	−0.298028	−	0.516199i
$147$	−46457.3	+	249960.i	−0.177321	+	0.954065i
$148$	−77933.4	+	134985.i	−0.292462	+	0.506559i
$149$	18317.4	−	31726.7i	0.0675925	−	0.117074i	−0.830249	−	0.557393i	$-0.811802\pi$
$149$	18317.4	−	31726.7i	0.0675925	−	0.117074i	0.897841	+	0.440320i	$0.145135\pi$
$150$	−629.732	+	3388.23i	−0.00228522	+	0.0122955i
$151$	−247485.	−	428657.i	−0.883297	−	1.52992i	−0.847653	−	0.530552i	$-0.821985\pi$
$151$	−247485.	−	428657.i	−0.883297	−	1.52992i	−0.0356448	−	0.999365i	$-0.511349\pi$
$152$	169115.			0.593708
$153$	307600.	−	248578.i	1.06233	−	0.858488i
$154$	−52900.0			−0.179744
$155$	246784.	+	427443.i	0.825065	+	1.42906i
$156$	−49111.7	−	41988.0i	−0.161575	−	0.138138i
$157$	28915.9	−	50083.7i	0.0936239	−	0.162161i	−0.815410	−	0.578885i	$-0.803488\pi$
$157$	28915.9	−	50083.7i	0.0936239	−	0.162161i	0.909033	+	0.416723i	$0.136822\pi$
$158$	35707.5	−	61847.2i	0.113793	−	0.197096i
$159$	158463.	−	56025.2i	0.497091	−	0.175748i
$160$	28873.7	+	50010.7i	0.0891665	+	0.154441i
$161$	−69951.8			−0.212684
$162$	224782.	−	72537.1i	0.672936	−	0.217156i
$163$	−135023.			−0.398050			−0.199025	−	0.979994i	$-0.563777\pi$
$163$	−135023.			−0.398050			−0.199025	+	0.979994i	$0.563777\pi$
$164$	59769.9	+	103525.i	0.173529	+	0.300562i
$165$	491462.	−	173758.i	1.40534	−	0.496862i
$166$	−86441.1	+	149720.i	−0.243473	+	0.421707i
$167$	203014.	−	351631.i	0.563294	−	0.975655i	−0.433912	−	0.900955i	$-0.642867\pi$
$167$	203014.	−	351631.i	0.563294	−	0.975655i	0.997206	−	0.0746992i	$-0.0237997\pi$
$168$	16912.5	+	14459.3i	0.0462310	+	0.0395252i
$169$	152090.	+	263428.i	0.409623	+	0.709488i
$170$	−367127.			−0.974303
$171$	−499417.	+	403590.i	−1.30609	+	1.05548i
$172$	−200079.			−0.515679
$173$	−114121.	−	197663.i	−0.289901	−	0.502123i	0.683885	−	0.729590i	$-0.260289\pi$
$173$	−114121.	−	197663.i	−0.289901	−	0.502123i	−0.973786	+	0.227467i	$0.926956\pi$
$174$	−1419.44	+	7637.23i	−0.00355423	+	0.0191233i
$175$	616.338	−	1067.53i	0.00152133	−	0.00263502i
$176$	75899.9	−	131463.i	0.184697	−	0.319905i
$177$	−44304.4	+	238377.i	−0.106295	+	0.571914i
$178$	−188191.	−	325957.i	−0.445194	−	0.771098i
$179$	−19370.0			−0.0451853			−0.0225927	−	0.999745i	$-0.507192\pi$
$179$	−19370.0			−0.0451853			−0.0225927	+	0.999745i	$0.507192\pi$
$180$	−204617.	−	78781.1i	−0.470718	−	0.181235i
$181$	−137790.			−0.312623			−0.156311	−	0.987708i	$-0.549960\pi$
$181$	−137790.			−0.312623			−0.156311	+	0.987708i	$0.549960\pi$
$182$	11555.7	+	20015.1i	0.0258594	+	0.0447898i
$183$	−141357.	−	120853.i	−0.312026	−	0.266767i
$184$	100366.	−	173838.i	0.218545	−	0.378530i
$185$	−274685.	+	475769.i	−0.590073	+	1.02204i
$186$	−514520.	+	181910.i	−1.09049	+	0.385545i
$187$	482532.	+	835769.i	1.00907	+	1.74776i
$188$	−141079.			−0.291118
$189$	−84451.5	−	2338.79i	−0.171970	−	0.00476252i
$190$	596065.			1.19787
$191$	−168262.	−	291438.i	−0.333735	−	0.578046i	0.649506	−	0.760356i	$-0.274976\pi$
$191$	−168262.	−	291438.i	−0.333735	−	0.578046i	−0.983241	+	0.182311i	$0.941642\pi$
$192$	−60198.7	+	21283.4i	−0.117851	+	0.0416667i
$193$	370436.	−	641615.i	0.715847	−	1.23988i	−0.246785	−	0.969070i	$-0.579374\pi$
$193$	370436.	−	641615.i	0.715847	−	1.23988i	0.962632	−	0.270813i	$-0.0872926\pi$
$194$	−162973.	+	282278.i	−0.310894	+	0.538484i
$195$	−173100.	−	147992.i	−0.325994	−	0.278709i
$196$	130477.	+	225992.i	0.242601	+	0.420197i
$197$	219128.			0.402284			0.201142	−	0.979562i	$-0.435535\pi$
$197$	219128.			0.402284			0.201142	+	0.979562i	$0.435535\pi$
$198$	89591.5	+	569360.i	0.162407	+	1.03210i
$199$	−215378.			−0.385540			−0.192770	−	0.981244i	$-0.561747\pi$
$199$	−215378.			−0.385540			−0.192770	+	0.981244i	$0.561747\pi$
$200$	1768.62	+	3063.34i	0.00312651	+	0.00541527i
$201$	17602.4	−	94708.3i	0.0307313	−	0.165348i
$202$	265736.	−	460268.i	0.458218	−	0.793656i
$203$	1389.25	−	2406.26i	0.00236615	−	0.00409828i
$204$	74174.7	−	399092.i	0.124790	−	0.671425i
$205$	210666.	+	364885.i	0.350115	+	0.606416i
$206$	496444.			0.815084
$207$	118470.	+	752887.i	0.192169	+	1.22125i
$208$	−66319.7			−0.106288
$209$	−783436.	−	1.35695e6i	−1.24062	−	2.14881i
$210$	59609.9	+	50963.5i	0.0932761	+	0.0797464i
$211$	−2285.57	+	3958.73i	−0.00353419	+	0.00612139i	−0.867787	−	0.496936i	$-0.834458\pi$
$211$	−2285.57	+	3958.73i	−0.00353419	+	0.00612139i	0.864253	+	0.503058i	$0.167792\pi$
$212$	86256.4	−	149401.i	0.131811	−	0.228303i
$213$	154302.	−	54553.9i	0.233035	−	0.0823904i
$214$	205737.	+	356347.i	0.307098	+	0.531910i
$215$	−705201.			−1.04044
$216$	126982.	−	206516.i	0.185185	−	0.301175i
$217$	195200.			0.281404
$218$	458708.	+	794505.i	0.653725	+	1.13228i
$219$	564073.	−	199430.i	0.794741	−	0.280983i
$220$	267518.	−	463355.i	0.372646	−	0.645442i
$221$	210813.	−	365138.i	0.290346	−	0.502894i
$222$	−461696.	−	394727.i	−0.628743	−	0.537544i
$223$	−472764.	−	818852.i	−0.636623	−	1.10266i	−0.986169	−	0.165744i	$-0.946997\pi$
$223$	−472764.	−	818852.i	−0.636623	−	1.10266i	0.349546	−	0.936919i	$-0.386336\pi$
$224$	22838.3			0.0304120
$225$	−12533.6	−	4825.64i	−0.0165051	−	0.00635475i
$226$	−299735.			−0.390361
$227$	−91944.9	−	159253.i	−0.118430	−	0.205127i	0.800715	−	0.599045i	$-0.204453\pi$
$227$	−91944.9	−	159253.i	−0.118430	−	0.205127i	−0.919146	+	0.393917i	$0.871120\pi$
$228$	−120430.	+	647964.i	−0.153425	+	0.825493i
$229$	−279217.	+	483618.i	−0.351846	+	0.609416i	−0.986573	−	0.163321i	$-0.947779\pi$
$229$	−279217.	+	483618.i	−0.351846	+	0.609416i	0.634727	+	0.772737i	$0.281113\pi$
$230$	353750.	−	612713.i	0.440938	−	0.763726i
$231$	37671.0	−	202686.i	0.0464491	−	0.249916i
$232$	3986.55	+	6904.90i	0.00486270	+	0.00842244i
$233$	1.04850e6			1.26526			0.632630	−	0.774454i	$-0.281975\pi$
$233$	1.04850e6			1.26526			0.632630	+	0.774454i	$0.281975\pi$
$234$	195850.	−	158271.i	0.233822	−	0.188956i
$235$	−497251.			−0.587362
$236$	124430.	+	215519.i	0.145427	+	0.251887i
$237$	211539.	+	180856.i	0.244636	+	0.209152i
$238$	−72597.0	+	125742.i	−0.0830761	+	0.143892i
$239$	−356902.	+	618172.i	−0.404160	+	0.700026i	−0.994223	−	0.107331i	$-0.965770\pi$
$239$	−356902.	+	618172.i	−0.404160	+	0.700026i	0.590063	+	0.807357i	$0.299103\pi$
$240$	−212177.	+	75016.0i	−0.237777	+	0.0840670i
$241$	385469.	+	667651.i	0.427510	+	0.740469i	0.996651	−	0.0817707i	$-0.0260575\pi$
$241$	385469.	+	667651.i	0.427510	+	0.740469i	−0.569141	+	0.822240i	$0.692724\pi$
$242$	−762242.			−0.836670
$243$	117855.	+	912907.i	0.128036	+	0.991770i
$244$	−190887.			−0.205259
$245$	459880.	+	796536.i	0.489474	+	0.847793i
$246$	−439218.	+	155287.i	−0.462745	+	0.163605i
$247$	−342274.	+	592837.i	−0.356970	+	0.618291i
$248$	−280069.	+	485094.i	−0.289159	+	0.500838i
$249$	−512097.	−	437818.i	−0.523425	−	0.447502i
$250$	−346228.	−	599685.i	−0.350358	−	0.606838i
$251$	450848.			0.451696			0.225848	−	0.974163i	$-0.427485\pi$
$251$	450848.			0.451696			0.225848	+	0.974163i	$0.427485\pi$
$252$	−67444.5	+	54503.4i	−0.0669029	+	0.0540657i
$253$	−1.85980e6			−1.82669
$254$	69156.6	+	119783.i	0.0672589	+	0.116496i
$255$	261437.	−	1.40665e6i	0.251778	−	1.35467i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−442803.	+	766958.i	−0.418194	+	0.724334i	−0.995758	−	0.0920119i	$-0.970670\pi$
$257$	−442803.	+	766958.i	−0.418194	+	0.724334i	0.577564	+	0.816346i	$0.304004\pi$
$258$	142479.	−	766601.i	0.133261	−	0.717002i
$259$	108635.	+	188161.i	0.100628	+	0.174293i
$260$	−233751.			−0.214448
$261$	−28251.2	−	10877.2i	−0.0256706	−	0.00988362i
$262$	−318495.			−0.286648
$263$	143984.	+	249388.i	0.128359	+	0.222324i	0.923041	−	0.384702i	$-0.125696\pi$
$263$	143984.	+	249388.i	0.128359	+	0.222324i	−0.794682	+	0.607026i	$0.792362\pi$
$264$	449649.	+	384427.i	0.397067	+	0.339472i
$265$	304021.	−	526580.i	0.265943	−	0.460627i
$266$	117868.	−	204154.i	0.102139	−	0.176910i
$267$	1.38292e6	−	488935.i	1.18718	−	0.419733i
$268$	−49436.7	−	85626.8i	−0.0420448	−	0.0728237i
$269$	898860.			0.757376			0.378688	−	0.925524i	$-0.376375\pi$
$269$	898860.			0.757376			0.378688	+	0.925524i	$0.376375\pi$
$270$	447561.	−	727889.i	0.373631	−	0.607654i
$271$	1.89319e6			1.56592			0.782962	−	0.622069i	$-0.213708\pi$
$271$	1.89319e6			1.56592			0.782962	+	0.622069i	$0.213708\pi$
$272$	−208322.	−	360824.i	−0.170731	−	0.295714i
$273$	−84916.8	+	30022.6i	−0.0689584	+	0.0243805i
$274$	−542081.	+	938913.i	−0.436202	+	0.755525i
$275$	16386.5	−	28382.2i	0.0130663	−	0.0226316i
$276$	594589.	+	508344.i	0.469834	+	0.401684i
$277$	−866062.	−	1.50006e6i	−0.678187	−	1.17465i	−0.975526	−	0.219882i	$-0.929433\pi$
$277$	−866062.	−	1.50006e6i	−0.678187	−	1.17465i	0.297340	−	0.954772i	$-0.403901\pi$
$278$	−132675.			−0.102962
$279$	−330591.	−	2.10093e6i	−0.254261	−	1.61585i
$280$	80496.4			0.0613594
$281$	146629.	+	253968.i	0.110778	+	0.191873i	0.916084	−	0.400986i	$-0.131332\pi$
$281$	146629.	+	253968.i	0.110778	+	0.191873i	−0.805306	+	0.592859i	$0.797999\pi$
$282$	100465.	−	540546.i	0.0752302	−	0.404771i
$283$	399082.	−	691230.i	0.296208	−	0.513046i	−0.679058	−	0.734085i	$-0.737611\pi$
$283$	399082.	−	691230.i	0.296208	−	0.513046i	0.975265	+	0.221039i	$0.0709447\pi$
$284$	83991.2	−	145477.i	0.0617928	−	0.107028i
$285$	−424468.	+	2.28382e6i	−0.309552	+	1.66552i
$286$	307230.	+	532138.i	0.222100	+	0.384689i
$287$	166632.			0.119413
$288$	−38679.0	−	245807.i	−0.0274786	−	0.174628i
$289$	1.22894e6			0.865537
$290$	14051.1	+	24337.1i	0.00981102	+	0.0169932i
$291$	−965492.	−	825447.i	−0.668369	−	0.571422i
$292$	307043.	−	531814.i	0.210737	−	0.365008i
$293$	−695365.	+	1.20441e6i	−0.473199	+	0.819605i	−0.999529	−	0.0306753i	$-0.990234\pi$
$293$	−695365.	+	1.20441e6i	−0.473199	+	0.819605i	0.526330	+	0.850280i	$0.323568\pi$
$294$	−958803.	+	338988.i	−0.646936	+	0.228726i
$295$	438568.	+	759622.i	0.293415	+	0.508209i
$296$	−623467.			−0.413603
$297$	−2.24530e6	−	62181.1i	−1.47701	−	0.0409042i
$298$	146539.			0.0955902
$299$	406263.	+	703668.i	0.262802	+	0.455187i
$300$	−12996.6	+	4595.01i	−0.00833735	+	0.00294770i
$301$	−139449.	+	241533.i	−0.0887154	+	0.153660i
$302$	989941.	−	1.71463e6i	0.624586	−	1.08181i
$303$	1.57428e6	+	1.34593e6i	0.985090	+	0.842202i
$304$	338230.	+	585831.i	0.209907	+	0.363570i
$305$	−672803.			−0.414132
$306$	1.47630e6	+	568401.i	0.901303	+	0.347017i
$307$	598019.			0.362134			0.181067	−	0.983471i	$-0.442045\pi$
$307$	598019.			0.362134			0.181067	+	0.983471i	$0.442045\pi$
$308$	−105800.	−	183251.i	−0.0635491	−	0.110070i
$309$	−353527.	+	1.90213e6i	−0.210633	+	1.13330i
$310$	−987137.	+	1.70977e6i	−0.583409	+	1.01049i
$311$	1.48902e6	−	2.57905e6i	0.872968	−	1.51203i	0.0140565	−	0.999901i	$-0.495526\pi$
$311$	1.48902e6	−	2.57905e6i	0.872968	−	1.51203i	0.858912	−	0.512124i	$-0.171141\pi$
$312$	47227.4	−	254104.i	0.0274668	−	0.147783i
$313$	−1.25187e6	−	2.16830e6i	−0.722266	−	1.25100i	−0.960089	−	0.279694i	$-0.909767\pi$
$313$	−1.25187e6	−	2.16830e6i	−0.722266	−	1.25100i	0.237823	−	0.971309i	$-0.423566\pi$
$314$	231327.			0.132404
$315$	−237716.	+	192103.i	−0.134984	+	0.109083i
$316$	285660.			0.160928
$317$	−1.04317e6	−	1.80683e6i	−0.583053	−	1.00988i	−0.995115	−	0.0987220i	$-0.968525\pi$
$317$	−1.04317e6	−	1.80683e6i	−0.583053	−	1.00988i	0.412062	−	0.911156i	$-0.364809\pi$
$318$	511003.	+	436882.i	0.283371	+	0.242268i
$319$	36935.9	−	63974.8i	0.0203223	−	0.0351992i
$320$	−115495.	+	200043.i	−0.0630503	+	0.109206i
$321$	−1.51185e6	+	534520.i	−0.818929	+	0.289535i
$322$	−139904.	−	242320.i	−0.0751951	−	0.130242i
$323$	−4.30057e6			−2.29361
$324$	700840.	+	633593.i	0.370899	+	0.335311i
$325$	−14318.1			−0.00751932
$326$	−270045.	−	467732.i	−0.140732	−	0.243755i
$327$	−3.37080e6	+	1.19176e6i	−1.74327	+	0.616338i
$328$	−239080.	+	414098.i	−0.122704	+	0.212529i
$329$	−98328.2	+	170309.i	−0.0500828	+	0.0867459i
$330$	1.58484e6	+	1.35496e6i	0.801126	+	0.684923i
$331$	947564.	+	1.64123e6i	0.475378	+	0.823378i	0.999602	−	0.0282018i	$-0.00897810\pi$
$331$	947564.	+	1.64123e6i	0.475378	+	0.823378i	−0.524225	+	0.851580i	$0.675645\pi$
$332$	−691529.			−0.344322
$333$	1.84118e6	−	1.48789e6i	0.909881	−	0.735295i
$334$	1.62411e6			0.796619
$335$	−174245.	−	301802.i	−0.0848299	−	0.146930i
$336$	−16263.6	+	87505.1i	−0.00785901	+	0.0422849i
$337$	−666562.	+	1.15452e6i	−0.319717	+	0.553766i	−0.980429	−	0.196874i	$-0.936921\pi$
$337$	−666562.	+	1.15452e6i	−0.319717	+	0.553766i	0.660712	+	0.750639i	$0.270254\pi$
$338$	−608361.	+	1.05371e6i	−0.289647	+	0.501684i
$339$	213446.	−	1.14843e6i	0.100876	−	0.542759i
$340$	−734254.	−	1.27176e6i	−0.344468	−	0.596636i
$341$	5.18976e6			2.41691
$342$	−2.39691e6	−	922852.i	−1.10812	−	0.426645i
$343$	738601.			0.338980
$344$	−400157.	−	693093.i	−0.182320	−	0.315788i
$345$	2.09570e6	+	1.79172e6i	0.947941	+	0.810442i
$346$	456483.	−	790652.i	0.204991	−	0.355055i
$347$	−184376.	+	319349.i	−0.0822018	+	0.142378i	−0.904195	−	0.427119i	$-0.859529\pi$
$347$	−184376.	+	319349.i	−0.0822018	+	0.142378i	0.821994	+	0.569497i	$0.192862\pi$
$348$	−29295.0	+	10357.4i	−0.0129672	+	0.00458459i
$349$	−1.36770e6	−	2.36892e6i	−0.601071	−	1.04109i	−0.992659	−	0.120945i	$-0.961407\pi$
$349$	−1.36770e6	−	2.36892e6i	−0.601071	−	1.04109i	0.391588	−	0.920141i	$-0.371926\pi$
$350$	4930.70			0.00215149
$351$	466947.	+	863108.i	0.202302	+	0.373936i
$352$	607200.			0.261201
$353$	1.64512e6	+	2.84944e6i	0.702687	+	1.21709i	0.967520	+	0.252795i	$0.0813500\pi$
$353$	1.64512e6	+	2.84944e6i	0.702687	+	1.21709i	−0.264833	+	0.964294i	$0.585317\pi$
$354$	−914370.	+	323279.i	−0.387805	+	0.137110i
$355$	296037.	−	512751.i	0.124674	−	0.215941i
$356$	752765.	−	1.30383e6i	0.314800	−	0.545249i
$357$	−430082.	−	367698.i	−0.178600	−	0.152694i
$358$	−38740.0	−	67099.7i	−0.0159754	−	0.0276702i
$359$	−1.85769e6			−0.760740			−0.380370	−	0.924834i	$-0.624203\pi$
$359$	−1.85769e6			−0.760740			−0.380370	+	0.924834i	$0.624203\pi$
$360$	−136329.	−	866377.i	−0.0554410	−	0.352331i
$361$	4.50629e6			1.81991
$362$	−275580.	−	477318.i	−0.110529	−	0.191442i
$363$	542806.	−	2.92053e6i	0.216211	−	1.16331i
$364$	−46222.9	+	80060.4i	−0.0182854	+	0.0316712i
$365$	1.08221e6	−	1.87444e6i	0.425186	−	0.736443i
$366$	135934.	−	731383.i	0.0530426	−	0.285392i
$367$	1.13820e6	+	1.97141e6i	0.441115	+	0.764034i	0.997773	−	0.0667081i	$-0.0212496\pi$
$367$	1.13820e6	+	1.97141e6i	0.441115	+	0.764034i	−0.556657	+	0.830742i	$0.687916\pi$
$368$	802924.			0.309069
$369$	−282207.	−	1.79344e6i	−0.107895	−	0.685681i
$370$	−2.19748e6			−0.834490
$371$	−120236.	−	208256.i	−0.0453525	−	0.0785528i
$372$	−1.65920e6	−	1.41853e6i	−0.621642	−	0.531473i
$373$	−264482.	+	458096.i	−0.0984292	+	0.170484i	−0.911035	−	0.412330i	$-0.864715\pi$
$373$	−264482.	+	458096.i	−0.0984292	+	0.170484i	0.812605	+	0.582814i	$0.198048\pi$
$374$	−1.93013e6	+	3.34308e6i	−0.713521	+	1.23585i
$375$	2.54425e6	−	899527.i	0.934288	−	0.330321i
$376$	−282159.	−	488713.i	−0.102926	−	0.178273i
$377$	−32273.8			−0.0116949
$378$	−160801.	−	297226.i	−0.0578842	−	0.106994i
$379$	−3.23027e6			−1.15516			−0.577578	−	0.816336i	$-0.696002\pi$
$379$	−3.23027e6			−1.15516			−0.577578	+	0.816336i	$0.696002\pi$
$380$	1.19213e6	+	2.06483e6i	0.423511	+	0.733543i
$381$	−508195.	+	179674.i	−0.179357	+	0.0634123i
$382$	673046.	−	1.16575e6i	0.235986	−	0.408740i
$383$	−1.96451e6	+	3.40264e6i	−0.684319	+	1.18527i	0.289332	+	0.957229i	$0.406567\pi$
$383$	−1.96451e6	+	3.40264e6i	−0.684319	+	1.18527i	−0.973650	+	0.228046i	$0.926766\pi$
$384$	−194125.	−	165967.i	−0.0671822	−	0.0574374i
$385$	−372905.	−	645890.i	−0.128217	−	0.222079i
$386$	2.96349e6			1.01236
$387$	2.83577e6	+	1.09182e6i	0.962484	+	0.370573i
$388$	−1.30379e6			−0.439670
$389$	−2.34603e6	−	4.06344e6i	−0.786066	−	1.36151i	−0.928360	−	0.371682i	$-0.878781\pi$
$389$	−2.34603e6	−	4.06344e6i	−0.786066	−	1.36151i	0.142294	−	0.989825i	$-0.454552\pi$
$390$	166458.	−	895619.i	0.0554172	−	0.298168i
$391$	−2.55228e6	+	4.42069e6i	−0.844281	+	1.46234i
$392$	−521906.	+	903968.i	−0.171545	+	0.297124i
$393$	226806.	−	1.22031e6i	0.0740751	−	0.398556i
$394$	438257.	+	759083.i	0.142229	+	0.246348i
$395$	1.00684e6			0.324690
$396$	−1.79314e6	+	1.44907e6i	−0.574613	+	0.464357i
$397$	−4.97999e6			−1.58581			−0.792907	−	0.609343i	$-0.791433\pi$
$397$	−4.97999e6			−1.58581			−0.792907	+	0.609343i	$0.791433\pi$
$398$	−430757.	−	746092.i	−0.136309	−	0.236094i
$399$	698278.	+	596993.i	0.219582	+	0.187731i
$400$	−7074.48	+	12253.4i	−0.00221077	+	0.00382917i
$401$	−1.74213e6	+	3.01746e6i	−0.541027	+	0.937087i	0.457818	+	0.889046i	$0.348631\pi$
$401$	−1.74213e6	+	3.01746e6i	−0.541027	+	0.937087i	−0.998845	+	0.0480411i	$0.984702\pi$
$402$	363284.	−	128440.i	0.112119	−	0.0396402i
$403$	−1.13367e6	−	1.96358e6i	−0.347717	−	0.602263i
$404$	2.12589e6			0.648017
$405$	2.47019e6	+	2.23317e6i	0.748330	+	0.676527i
$406$	11114.0			0.00334623
$407$	2.88825e6	+	5.00260e6i	0.864269	+	1.49696i
$408$	1.53084e6	−	541235.i	0.455282	−	0.160967i
$409$	647421.	−	1.12137e6i	0.191372	−	0.331466i	−0.754333	−	0.656492i	$-0.772040\pi$
$409$	647421.	−	1.12137e6i	0.191372	−	0.331466i	0.945705	+	0.325026i	$0.105373\pi$
$410$	−842665.	+	1.45954e6i	−0.247568	+	0.428801i
$411$	−3.21142e6	−	2.74560e6i	−0.937761	−	0.801739i
$412$	992889.	+	1.71973e6i	0.288176	+	0.499135i
$413$	346896.			0.100075
$414$	−2.37114e6	+	1.91617e6i	−0.679917	+	0.549456i
$415$	−2.43737e6			−0.694708
$416$	−132639.	−	229738.i	−0.0375785	−	0.0650878i
$417$	94480.3	−	508345.i	0.0266073	−	0.143159i
$418$	3.13374e6	−	5.42780e6i	0.877249	−	1.51944i
$419$	3.18739e6	−	5.52073e6i	0.886953	−	1.53625i	0.0434947	−	0.999054i	$-0.486151\pi$
$419$	3.18739e6	−	5.52073e6i	0.886953	−	1.53625i	0.843459	−	0.537194i	$-0.180516\pi$
$420$	−57322.9	+	308422.i	−0.0158564	+	0.0853143i
$421$	2.20802e6	+	3.82440e6i	0.607152	+	1.05162i	0.991707	+	0.128516i	$0.0410214\pi$
$421$	2.20802e6	+	3.82440e6i	0.607152	+	1.05162i	−0.384555	+	0.923102i	$0.625645\pi$
$422$	−18284.6			−0.00499809
$423$	1.99956e6	+	769864.i	0.543354	+	0.209201i
$424$	690052.			0.186409
$425$	−44975.8	−	77900.3i	−0.0120783	−	0.0209203i
$426$	497584.	+	425409.i	0.132844	+	0.113575i
$427$	−133043.	+	230437.i	−0.0353119	+	0.0611620i
$428$	−822947.	+	1.42539e6i	−0.217151	+	0.376117i
$429$	−2.25767e6	+	798208.i	−0.592267	+	0.209398i
$430$	−1.41040e6	−	2.44289e6i	−0.367851	−	0.637136i
$431$	−6.65197e6			−1.72487			−0.862436	−	0.506166i	$-0.831062\pi$
$431$	−6.65197e6			−1.72487			−0.862436	+	0.506166i	$0.831062\pi$
$432$	969355.	+	26845.2i	0.249904	+	0.00692082i
$433$	−3.41878e6			−0.876297			−0.438149	−	0.898903i	$-0.644366\pi$
$433$	−3.41878e6			−0.876297			−0.438149	+	0.898903i	$0.644366\pi$
$434$	390400.	+	676193.i	0.0994915	+	0.172324i
$435$	−103254.	+	36505.7i	−0.0261627	+	0.00924991i
$436$	−1.83483e6	+	3.17802e6i	−0.462253	+	0.800646i
$437$	4.14387e6	−	7.17740e6i	1.03801	−	1.79789i
$438$	1.81899e6	+	1.55515e6i	0.453050	+	0.387335i
$439$	−1982.34	−	3433.51i	−0.000490927	−	0.000850310i	0.865780	−	0.500425i	$-0.166823\pi$
$439$	−1982.34	−	3433.51i	−0.000490927	−	0.000850310i	−0.866271	+	0.499575i	$0.833490\pi$
$440$	2.14015e6			0.527001
$441$	−616052.	−	3.91505e6i	−0.150842	−	0.958608i
$442$	1.68650e6			0.410611
$443$	−1.91417e6	−	3.31544e6i	−0.463417	−	0.802661i	0.535712	−	0.844401i	$-0.320043\pi$
$443$	−1.91417e6	−	3.31544e6i	−0.463417	−	0.802661i	−0.999129	+	0.0417398i	$0.986710\pi$
$444$	443982.	−	2.38881e6i	0.106883	−	0.575075i
$445$	2.65321e6	−	4.59549e6i	0.635142	−	1.10010i
$446$	1.89106e6	−	3.27541e6i	0.450160	−	0.779701i
$447$	−104353.	+	561465.i	−0.0247023	+	0.132909i
$448$	45676.7	+	79114.3i	0.0107523	+	0.0186234i
$449$	1.62273e6			0.379866			0.189933	−	0.981797i	$-0.439173\pi$
$449$	1.62273e6			0.379866			0.189933	+	0.981797i	$0.439173\pi$
$450$	−8350.63	−	53068.8i	−0.00194396	−	0.0123540i
$451$	4.43021e6			1.02561
$452$	−599470.	−	1.03831e6i	−0.138013	−	0.239046i
$453$	5.86464e6	+	5.01398e6i	1.34275	+	1.14799i
$454$	367780.	−	637013.i	0.0837429	−	0.145047i
$455$	−162918.	+	282182.i	−0.0368927	+	0.0639000i
$456$	−2.48547e6	+	878747.i	−0.559753	+	0.197903i
$457$	3.76377e6	+	6.51904e6i	0.843010	+	1.46014i	0.887338	+	0.461119i	$0.152552\pi$
$457$	3.76377e6	+	6.51904e6i	0.843010	+	1.46014i	−0.0443285	+	0.999017i	$0.514115\pi$
$458$	−2.23374e6			−0.497586
$459$	−3.22913e6	+	5.25167e6i	−0.715407	+	1.16350i
$460$	2.83000e6			0.623580
$461$	−360297.	−	624052.i	−0.0789602	−	0.136763i	0.823841	−	0.566820i	$-0.191827\pi$
$461$	−360297.	−	624052.i	−0.0789602	−	0.136763i	−0.902802	+	0.430057i	$0.858493\pi$
$462$	777469.	−	274877.i	0.169464	−	0.0599146i
$463$	2.72788e6	−	4.72483e6i	0.591389	−	1.02432i	−0.402656	−	0.915351i	$-0.631913\pi$
$463$	2.72788e6	−	4.72483e6i	0.591389	−	1.02432i	0.994046	−	0.108965i	$-0.0347536\pi$
$464$	−15946.2	+	27619.6i	−0.00343844	+	0.00595556i
$465$	−5.84803e6	−	4.99977e6i	−1.25423	−	1.07230i
$466$	2.09701e6	+	3.63212e6i	0.447337	+	0.774810i
$467$	−3.70082e6			−0.785245			−0.392623	−	0.919700i	$-0.628432\pi$
$467$	−3.70082e6			−0.785245			−0.392623	+	0.919700i	$0.628432\pi$
$468$	939967.	+	361903.i	0.198380	+	0.0763797i
$469$	−137824.			−0.0289329
$470$	−994502.	−	1.72253e6i	−0.207664	−	0.359684i
$471$	−164732.	+	886329.i	−0.0342157	+	0.184095i
$472$	−497720.	+	862076.i	−0.102832	+	0.178111i
$473$	−3.70751e6	+	6.42160e6i	−0.761955	+	1.31975i
$474$	−203423.	+	1.09451e6i	−0.0415867	+	0.223755i
$475$	73022.4	+	126479.i	0.0148499	+	0.0257207i
$476$	−580776.			−0.117487
$477$	−2.03781e6	+	1.64680e6i	−0.410079	+	0.331394i
$478$	−2.85521e6			−0.571569
$479$	3.00801e6	+	5.21003e6i	0.599020	+	1.03753i	0.992966	+	0.118399i	$0.0377762\pi$
$479$	3.00801e6	+	5.21003e6i	0.599020	+	1.03753i	−0.393946	+	0.919133i	$0.628890\pi$
$480$	−684217.	−	584972.i	−0.135547	−	0.115886i
$481$	1.26184e6	−	2.18558e6i	0.248681	−	0.430729i
$482$	−1.54187e6	+	2.67060e6i	−0.302295	+	0.523591i
$483$	1.02808e6	−	363480.i	0.200520	−	0.0708946i
$484$	−1.52448e6	−	2.64048e6i	−0.295808	−	0.512354i
$485$	−4.59535e6			−0.887083
$486$	−2.92669e6	+	2.23407e6i	−0.562065	+	0.429049i
$487$	1.27159e6			0.242954			0.121477	−	0.992594i	$-0.461237\pi$
$487$	1.27159e6			0.242954			0.121477	+	0.992594i	$0.461237\pi$
$488$	−381774.	−	661252.i	−0.0725699	−	0.125695i
$489$	1.98442e6	−	701598.i	0.375285	−	0.132683i
$490$	−1.83952e6	+	3.18614e6i	−0.346110	+	0.599480i
$491$	1.96015e6	−	3.39507e6i	0.366931	−	0.635544i	−0.622153	−	0.782896i	$-0.713742\pi$
$491$	1.96015e6	−	3.39507e6i	0.366931	−	0.635544i	0.989084	+	0.147352i	$0.0470751\pi$
$492$	−1.41636e6	−	1.21092e6i	−0.263792	−	0.225529i
$493$	−101377.	−	175591.i	−0.0187856	−	0.0325375i
$494$	−2.73819e6			−0.504832
$495$	−6.32012e6	+	5.10743e6i	−1.15934	+	0.936891i
$496$	−2.24056e6			−0.408932
$497$	−117079.	−	202787.i	−0.0212612	−	0.0368255i
$498$	492450.	−	2.64959e6i	0.0889792	−	0.478747i
$499$	2.19781e6	−	3.80672e6i	0.395129	−	0.684383i	−0.597989	−	0.801504i	$-0.704033\pi$
$499$	2.19781e6	−	3.80672e6i	0.395129	−	0.684383i	0.993118	+	0.117122i	$0.0373667\pi$
$500$	1.38491e6	−	2.39874e6i	0.247741	−	0.429099i
$501$	−1.15656e6	+	6.22279e6i	−0.205861	+	1.10762i
$502$	901696.	+	1.56178e6i	0.159698	+	0.276606i
$503$	6.81583e6			1.20115			0.600577	−	0.799567i	$-0.294938\pi$
$503$	6.81583e6			1.20115			0.600577	+	0.799567i	$0.294938\pi$
$504$	−323694.	−	124628.i	−0.0567621	−	0.0218544i
$505$	7.49294e6			1.30745
$506$	−3.71960e6	−	6.44254e6i	−0.645833	−	1.11861i
$507$	−3.60407e6	−	3.08130e6i	−0.622692	−	0.532371i
$508$	−276626.	+	479131.i	−0.0475592	+	0.0823749i
$509$	−2.33301e6	+	4.04089e6i	−0.399137	+	0.691325i	−0.993620	−	0.112783i	$-0.964023\pi$
$509$	−2.33301e6	+	4.04089e6i	−0.399137	+	0.691325i	0.594483	+	0.804108i	$0.297357\pi$
$510$	5.39564e6	−	1.90765e6i	0.918581	−	0.324768i
$511$	−428000.	−	741317.i	−0.0725088	−	0.125589i
$512$	−262144.			−0.0441942
$513$	5.24279e6	−	8.52659e6i	0.879567	−	1.43048i
$514$	−3.54243e6			−0.591416
$515$	3.49955e6	+	6.06140e6i	0.581426	+	1.00706i
$516$	2.94054e6	−	1.03964e6i	0.486187	−	0.171893i
$517$	−2.61424e6	+	4.52799e6i	−0.430149	+	0.745040i
$518$	−434538.	+	752642.i	−0.0711547	+	0.123244i
$519$	2.70431e6	+	2.31205e6i	0.440696	+	0.376773i
$520$	−467503.	−	809739.i	−0.0758186	−	0.131322i
$521$	−619313.			−0.0999576			−0.0499788	−	0.998750i	$-0.515915\pi$
$521$	−619313.			−0.0999576			−0.0499788	+	0.998750i	$0.515915\pi$
$522$	−18822.7	−	119620.i	−0.00302347	−	0.0192144i
$523$	−4.63344e6			−0.740713			−0.370356	−	0.928890i	$-0.620764\pi$
$523$	−4.63344e6			−0.740713			−0.370356	+	0.928890i	$0.620764\pi$
$524$	−636989.	−	1.10330e6i	−0.101345	−	0.175535i
$525$	−3511.24	+	18892.0i	−0.000555984	+	0.00299143i
$526$	−575937.	+	997552.i	−0.0907634	+	0.157207i
$527$	7.12213e6	−	1.23359e7i	1.11708	−	1.93484i
$528$	−432397.	+	2.32648e6i	−0.0674991	+	0.363175i
$529$	−1.70040e6	−	2.94519e6i	−0.264188	−	0.457587i
$530$	2.43217e6			0.376100
$531$	−587503.	−	3.73362e6i	−0.0904219	−	0.574637i
$532$	942945.			0.144447
$533$	−967755.	−	1.67620e6i	−0.147553	−	0.255569i
$534$	4.45955e6	+	3.81269e6i	0.676766	+	0.578601i
$535$	−2.90057e6	+	5.02394e6i	−0.438126	+	0.758857i
$536$	197747.	−	342507.i	0.0297302	−	0.0514941i
$537$	284680.	−	100650.i	0.0426011	−	0.0150618i
$538$	1.79772e6	+	3.11374e6i	0.267773	+	0.463796i
$539$	9.67106e6			1.43384
$540$	3.41661e6	+	94619.1i	0.504209	+	0.0139635i
$541$	−9.72857e6			−1.42908			−0.714539	−	0.699596i	$-0.753364\pi$
$541$	−9.72857e6			−1.42908			−0.714539	+	0.699596i	$0.753364\pi$
$542$	3.78638e6	+	6.55820e6i	0.553638	+	0.958929i
$543$	2.02509e6	−	715977.i	0.294744	−	0.104208i
$544$	833286.	−	1.44329e6i	0.120725	−	0.209102i
$545$	−6.46708e6	+	1.12013e7i	−0.932646	+	1.61539i
$546$	−273835.	−	234115.i	−0.0393104	−	0.0336084i
$547$	−4.63898e6	−	8.03494e6i	−0.662909	−	1.14819i	−0.979848	−	0.199746i	$-0.935988\pi$
$547$	−4.63898e6	−	8.03494e6i	−0.662909	−	1.14819i	0.316939	−	0.948446i	$-0.397345\pi$
$548$	−4.33665e6			−0.616883
$549$	2.70549e6	+	1.04166e6i	0.383103	+	0.147501i
$550$	131092.			0.0184786
$551$	164596.	+	285088.i	0.0230962	+	0.0400037i
$552$	−571776.	+	3.07640e6i	−0.0798690	+	0.429730i
$553$	199096.	−	344845.i	0.0276854	−	0.0479525i
$554$	3.46425e6	−	6.00025e6i	0.479551	−	0.830606i
$555$	1.56487e6	−	8.41965e6i	0.215648	−	1.16028i
$556$	−265350.	−	459600.i	−0.0364026	−	0.0630512i
$557$	2.83520e6			0.387209			0.193604	−	0.981080i	$-0.437982\pi$
$557$	2.83520e6			0.387209			0.193604	+	0.981080i	$0.437982\pi$
$558$	6.61664e6	−	5.34705e6i	0.899605	−	0.726991i
$559$	3.23954e6			0.438484
$560$	160993.	+	278848.i	0.0216938	+	0.0375748i
$561$	−1.14345e7	−	9.77594e6i	−1.53395	−	1.31145i
$562$	−586514.	+	1.01587e6i	−0.0783317	+	0.135675i
$563$	−4.85708e6	+	8.41271e6i	−0.645809	+	1.11857i	0.338305	+	0.941037i	$0.390147\pi$
$563$	−4.85708e6	+	8.41271e6i	−0.645809	+	1.11857i	−0.984114	+	0.177538i	$0.943187\pi$
$564$	2.07344e6	−	733070.i	0.274469	−	0.0970393i
$565$	−2.11290e6	−	3.65965e6i	−0.278457	−	0.482302i
$566$	3.19266e6			0.418901
$567$	1.25333e6	−	404450.i	0.163722	−	0.0528332i
$568$	671930.			0.0873883
$569$	901486.	+	1.56142e6i	0.116729	+	0.202180i	0.918470	−	0.395492i	$-0.129426\pi$
$569$	901486.	+	1.56142e6i	0.116729	+	0.202180i	−0.801741	+	0.597672i	$0.796092\pi$
$570$	−8.76034e6	+	3.09725e6i	−1.12936	+	0.399290i
$571$	3.24846e6	−	5.62649e6i	0.416953	−	0.722183i	−0.578679	−	0.815556i	$-0.696431\pi$
$571$	3.24846e6	−	5.62649e6i	0.416953	−	0.722183i	0.995631	+	0.0933726i	$0.0297648\pi$
$572$	−1.22892e6	+	2.12855e6i	−0.157049	+	0.272016i
$573$	3.98728e6	+	3.40893e6i	0.507330	+	0.433742i
$574$	333263.	+	577229.i	0.0422190	+	0.0731254i
$575$	173348.			0.0218650
$576$	774144.	−	625603.i	0.0972222	−	0.0785674i
$577$	3.93067e6			0.491504			0.245752	−	0.969333i	$-0.420965\pi$
$577$	3.93067e6			0.491504			0.245752	+	0.969333i	$0.420965\pi$
$578$	2.45788e6	+	4.25717e6i	0.306014	+	0.530031i
$579$	−2.11035e6	+	1.13546e7i	−0.261613	+	1.40759i
$580$	−56204.2	+	97348.6i	−0.00693744	+	0.0120160i
$581$	−481975.	+	834806.i	−0.0592358	+	0.102599i
$582$	928449.	−	4.99546e6i	0.113619	−	0.611319i
$583$	−3.19671e6	−	5.53686e6i	−0.389522	−	0.674671i
$584$	2.45634e6			0.298028
$585$	3.31302e6	+	1.27557e6i	0.400253	+	0.154104i
$586$	−5.56292e6			−0.669205
$587$	−1.07731e6	−	1.86595e6i	−0.129046	−	0.223514i	0.794261	−	0.607576i	$-0.207858\pi$
$587$	−1.07731e6	−	1.86595e6i	−0.129046	−	0.223514i	−0.923307	+	0.384062i	$0.874525\pi$
$588$	−3.09190e6	−	2.64342e6i	−0.368792	−	0.315299i
$589$	−1.15635e7	+	2.00285e7i	−1.37341	+	2.37881i
$590$	−1.75427e6	+	3.03849e6i	−0.207476	+	0.359358i
$591$	−3.22052e6	+	1.13862e6i	−0.379277	+	0.134095i
$592$	−1.24693e6	−	2.15975e6i	−0.146231	−	0.253279i
$593$	−1.38401e7			−1.61623			−0.808113	−	0.589027i	$-0.799511\pi$
$593$	−1.38401e7			−1.61623			−0.808113	+	0.589027i	$0.799511\pi$
$594$	−4.27520e6	−	7.90231e6i	−0.497153	−	0.918942i
$595$	−2.04701e6			−0.237044
$596$	293079.	+	507627.i	0.0337962	+	0.0585368i
$597$	3.16540e6	−	1.11914e6i	0.363490	−	0.128513i
$598$	−1.62505e6	+	2.81467e6i	−0.185829	+	0.321866i
$599$	83012.3	−	143782.i	0.00945313	−	0.0163733i	−0.861260	−	0.508164i	$-0.830324\pi$
$599$	83012.3	−	143782.i	0.00945313	−	0.0163733i	0.870713	+	0.491791i	$0.163658\pi$
$600$	−41910.9	−	35831.7i	−0.00475279	−	0.00406340i
$601$	7.32908e6	+	1.26943e7i	0.827682	+	1.43359i	0.899852	+	0.436194i	$0.143674\pi$
$601$	7.32908e6	+	1.26943e7i	0.827682	+	1.43359i	−0.0721708	+	0.997392i	$0.522993\pi$
$602$	−1.11559e6			−0.125463
$603$	233418.	+	1.48339e6i	0.0261421	+	0.166135i
$604$	7.91953e6			0.883297
$605$	−5.37322e6	−	9.30669e6i	−0.596824	−	1.03373i
$606$	−1.51388e6	+	8.14533e6i	−0.167460	+	0.901005i
$607$	1.45547e6	−	2.52096e6i	0.160337	−	0.277711i	−0.774653	−	0.632387i	$-0.782075\pi$
$607$	1.45547e6	−	2.52096e6i	0.160337	−	0.277711i	0.934989	+	0.354676i	$0.115409\pi$
$608$	−1.35292e6	+	2.34332e6i	−0.148427	+	0.257083i
$609$	−7914.49	+	42583.4i	−0.000864729	+	0.00465261i
$610$	−1.34561e6	−	2.33066e6i	−0.146418	−	0.253603i
$611$	2.28426e6			0.247539
$612$	983602.	+	6.25085e6i	0.106155	+	0.674622i
$613$	1.46967e7			1.57968			0.789838	−	0.613315i	$-0.210164\pi$
$613$	1.46967e7			1.57968			0.789838	+	0.613315i	$0.210164\pi$
$614$	1.19604e6	+	2.07160e6i	0.128034	+	0.221761i
$615$	−4.99214e6	−	4.26803e6i	−0.532230	−	0.455030i
$616$	423200.	−	733004.i	0.0449360	−	0.0778314i
$617$	1.49092e6	−	2.58235e6i	0.157668	−	0.273088i	−0.776360	−	0.630290i	$-0.782936\pi$
$617$	1.49092e6	−	2.58235e6i	0.157668	−	0.273088i	0.934027	+	0.357202i	$0.116269\pi$
$618$	−7.29621e6	+	2.57960e6i	−0.768469	+	0.271695i
$619$	−879493.	−	1.52333e6i	−0.0922583	−	0.159796i	0.816203	−	0.577766i	$-0.196075\pi$
$619$	−879493.	−	1.52333e6i	−0.0922583	−	0.159796i	−0.908461	+	0.417969i	$0.862742\pi$
$620$	−7.89710e6			−0.825065
$621$	−5.65327e6	−	1.04495e7i	−0.588262	−	1.08735i
$622$	1.19121e7			1.23456
$623$	−1.04931e6	−	1.81746e6i	−0.108314	−	0.187605i
$624$	974696.	−	344607.i	0.100209	−	0.0354293i
$625$	4.96764e6	−	8.60421e6i	0.508687	−	0.881071i
$626$	5.00747e6	−	8.67319e6i	0.510720	−	0.884592i
$627$	1.85650e7	+	1.58722e7i	1.88594	+	1.61238i
$628$	462654.	+	801340.i	0.0468120	+	0.0810807i
$629$	1.58547e7			1.59783
$630$	−1.14090e6	−	439265.i	−0.114524	−	0.0440936i
$631$	4.55795e6			0.455718			0.227859	−	0.973694i	$-0.426827\pi$
$631$	4.55795e6			0.455718			0.227859	+	0.973694i	$0.426827\pi$
$632$	571320.	+	989554.i	0.0568966	+	0.0985478i
$633$	13020.8	−	70057.4i	0.00129160	−	0.00694936i
$634$	4.17269e6	−	7.22732e6i	0.412281	−	0.714092i
$635$	−975003.	+	1.68875e6i	−0.0959558	+	0.166200i
$636$	−491398.	+	2.64393e6i	−0.0481715	+	0.259184i
$637$	−2.11259e6	−	3.65911e6i	−0.206284	−	0.357295i
$638$	295487.			0.0287400
$639$	−1.98429e6	+	1.60355e6i	−0.192244	+	0.155357i
$640$	−923957.			−0.0891665
$641$	−8.62721e6	−	1.49428e7i	−0.829326	−	1.43643i	−0.898568	−	0.438835i	$-0.855391\pi$
$641$	−8.62721e6	−	1.49428e7i	−0.829326	−	1.43643i	0.0692419	−	0.997600i	$-0.477942\pi$
$642$	−4.87533e6	−	4.16816e6i	−0.466838	−	0.399123i
$643$	−6.68107e6	+	1.15719e7i	−0.637263	+	1.10377i	0.348768	+	0.937209i	$0.386600\pi$
$643$	−6.68107e6	+	1.15719e7i	−0.637263	+	1.10377i	−0.986031	+	0.166562i	$0.946733\pi$
$644$	559615.	−	969281.i	0.0531710	−	0.0920948i
$645$	1.03643e7	−	3.66433e6i	0.980935	−	0.346813i
$646$	−8.60114e6	−	1.48976e7i	−0.810914	−	1.40454i
$647$	357748.			0.0335982			0.0167991	−	0.999859i	$-0.494652\pi$
$647$	357748.			0.0335982			0.0167991	+	0.999859i	$0.494652\pi$
$648$	−793152.	+	3.69497e6i	−0.0742026	+	0.345679i
$649$	9.22288e6			0.859518
$650$	−28636.3	−	49599.5i	−0.00265848	−	0.00460462i
$651$	−2.86884e6	+	1.01429e6i	−0.265311	+	0.0938014i
$652$	1.08018e6	−	1.87093e6i	0.0995125	−	0.172361i
$653$	6.12091e6	−	1.06017e7i	0.561737	−	0.972957i	−0.435608	−	0.900137i	$-0.643467\pi$
$653$	6.12091e6	−	1.06017e7i	0.561737	−	0.972957i	0.997345	−	0.0728208i	$-0.0232001\pi$
$654$	−1.08700e7	−	9.29328e6i	−0.993766	−	0.849620i
$655$	−2.24514e6	−	3.88870e6i	−0.204475	−	0.354162i
$656$	−1.91264e6			−0.173529
$657$	−7.25388e6	+	5.86202e6i	−0.655627	+	0.529827i
$658$	−786626.			−0.0708277
$659$	−5.25518e6	−	9.10224e6i	−0.471383	−	0.816460i	0.528081	−	0.849194i	$-0.322912\pi$
$659$	−5.25518e6	−	9.10224e6i	−0.471383	−	0.816460i	−0.999464	+	0.0327344i	$0.989578\pi$
$660$	−1.52404e6	+	8.19997e6i	−0.136187	+	0.732744i
$661$	−1.51211e6	+	2.61905e6i	−0.134611	+	0.233153i	−0.925449	−	0.378873i	$-0.876312\pi$
$661$	−1.51211e6	+	2.61905e6i	−0.134611	+	0.233153i	0.790838	+	0.612026i	$0.209645\pi$
$662$	−3.79026e6	+	6.56492e6i	−0.336143	+	0.582216i
$663$	−1.20099e6	+	6.46183e6i	−0.106110	+	0.570915i
$664$	−1.38306e6	−	2.39553e6i	−0.121736	−	0.210853i
$665$	3.32352e6			0.291437
$666$	8.83657e6	+	3.40223e6i	0.771966	+	0.297220i
$667$	390734.			0.0340069
$668$	3.24823e6	+	5.62610e6i	0.281647	+	0.487827i
$669$	1.12031e7	+	9.57806e6i	0.967769	+	0.827393i
$670$	696981.	−	1.20721e6i	0.0599838	−	0.103895i
$671$	−3.53718e6	+	6.12658e6i	−0.303285	+	0.525306i
$672$	−335654.	+	118671.i	−0.0286727	+	0.0101373i
$673$	6.14813e6	+	1.06489e7i	0.523245	+	0.906287i	0.999634	+	0.0270524i	$0.00861210\pi$
$673$	6.14813e6	+	1.06489e7i	0.523245	+	0.906287i	−0.476389	+	0.879235i	$0.658055\pi$
$674$	−5.33249e6			−0.452148
$675$	209280.	+	5795.77i	0.0176794	+	0.000489612i
$676$	−4.86688e6			−0.409623
$677$	−605609.	−	1.04895e6i	−0.0507833	−	0.0879592i	0.839516	−	0.543334i	$-0.182838\pi$
$677$	−605609.	−	1.04895e6i	−0.0507833	−	0.0879592i	−0.890300	+	0.455375i	$0.849505\pi$
$678$	4.40519e6	−	1.55747e6i	0.368036	−	0.130120i
$679$	−908701.	+	1.57392e6i	−0.0756392	+	0.131011i
$680$	2.93702e6	−	5.08706e6i	0.243576	−	0.421885i
$681$	2.17881e6	+	1.86278e6i	0.180033	+	0.153919i
$682$	1.03795e7	+	1.79779e7i	0.854508	+	1.48005i
$683$	−5.89207e6			−0.483299			−0.241650	−	0.970364i	$-0.577688\pi$
$683$	−5.89207e6			−0.483299			−0.241650	+	0.970364i	$0.577688\pi$
$684$	−1.59697e6	−	1.01489e7i	−0.130514	−	0.829424i
$685$	−1.52850e7			−1.24463
$686$	1.47720e6	+	2.55859e6i	0.119848	+	0.207582i
$687$	1.59068e6	−	8.55856e6i	0.128585	−	0.691845i
$688$	1.60063e6	−	2.77237e6i	0.128920	−	0.223296i
$689$	−1.39661e6	+	2.41899e6i	−0.112079	+	0.194127i
$690$	−2.01529e6	+	1.08431e7i	−0.161144	+	0.867027i
$691$	6.20006e6	+	1.07388e7i	0.493970	+	0.855581i	0.999976	−	0.00694867i	$-0.00221185\pi$
$691$	6.20006e6	+	1.07388e7i	0.493970	+	0.855581i	−0.506006	+	0.862530i	$0.668879\pi$
$692$	3.65187e6			0.289901
$693$	499541.	+	3.17462e6i	0.0395128	+	0.251107i
$694$	−1.47501e6			−0.116251
$695$	−935259.	−	1.61992e6i	−0.0734463	−	0.127213i
$696$	−94469.0	−	80766.2i	−0.00739207	−	0.00631985i
$697$	6.07977e6	−	1.05305e7i	0.474029	−	0.821043i
$698$	5.47079e6	−	9.47568e6i	0.425022	−	0.736159i
$699$	−1.54098e7	+	5.44818e6i	−1.19290	+	0.421753i
$700$	9861.41	+	17080.5i	0.000760666	+	0.00131751i
$701$	−1.29116e7			−0.992396			−0.496198	−	0.868209i	$-0.665271\pi$
$701$	−1.29116e7			−0.992396			−0.496198	+	0.868209i	$0.665271\pi$
$702$	−2.05600e6	+	3.34377e6i	−0.157464	+	0.256090i
$703$	−2.57416e7			−1.96448
$704$	1.21440e6	+	2.10340e6i	0.0923485	+	0.159952i
$705$	7.30807e6	−	2.58379e6i	0.553770	−	0.195787i
$706$	−6.58050e6	+	1.13978e7i	−0.496875	+	0.860612i
$707$	1.48168e6	−	2.56635e6i	0.111482	−	0.193093i
$708$	−2.94861e6	−	2.52091e6i	−0.221072	−	0.189006i
$709$	−9.36762e6	−	1.62252e7i	−0.699864	−	1.21220i	−0.968513	−	0.248962i	$-0.919911\pi$
$709$	−9.36762e6	−	1.62252e7i	−0.699864	−	1.21220i	0.268650	−	0.963238i	$-0.413423\pi$
$710$	2.36830e6			0.176315
$711$	−4.04874e6	−	1.55883e6i	−0.300362	−	0.115645i
$712$	6.02212e6			0.445194
$713$	1.37253e7	+	2.37728e7i	1.01111	+	1.75129i
$714$	413581.	−	2.22524e6i	0.0303609	−	0.163355i
$715$	−4.33148e6	+	7.50234e6i	−0.316862	+	0.548822i
$716$	154960.	−	268399.i	0.0112963	−	0.0195658i
$717$	2.03325e6	−	1.09397e7i	0.147704	−	0.794711i
$718$	−3.71537e6	−	6.43522e6i	−0.268962	−	0.465856i
$719$	−1.08129e7			−0.780044			−0.390022	−	0.920806i	$-0.627533\pi$
$719$	−1.08129e7			−0.780044			−0.390022	+	0.920806i	$0.627533\pi$
$720$	2.72856e6	−	2.20501e6i	0.196156	−	0.158518i
$721$	2.76806e6			0.198306
$722$	9.01257e6	+	1.56102e7i	0.643437	+	1.11446i
$723$	−9.13442e6	−	7.80947e6i	−0.649883	−	0.555618i
$724$	1.10232e6	−	1.90927e6i	0.0781557	−	0.135370i
$725$	−3442.72	+	5962.96i	−0.000243252	+	0.000421325i
$726$	1.12026e7	−	3.96072e6i	0.788820	−	0.278890i
$727$	2.80710e6	+	4.86205e6i	0.196980	+	0.341180i	0.947548	−	0.319614i	$-0.103553\pi$
$727$	2.80710e6	+	4.86205e6i	0.196980	+	0.341180i	−0.750568	+	0.660794i	$0.770220\pi$
$728$	−369783.			−0.0258594
$729$	−6.47571e6	−	1.28045e7i	−0.451303	−	0.892371i
$730$	8.65766e6			0.601303
$731$	1.01760e7	+	1.76253e7i	0.704339	+	1.21995i
$732$	2.80545e6	−	991878.i	0.193520	−	0.0684196i
$733$	8.84117e6	−	1.53133e7i	0.607785	−	1.05271i	−0.383820	−	0.923408i	$-0.625392\pi$
$733$	8.84117e6	−	1.53133e7i	0.607785	−	1.05271i	0.991605	−	0.129306i	$-0.0412749\pi$
$734$	−4.55279e6	+	7.88566e6i	−0.311916	+	0.540254i
$735$	−1.08977e7	−	9.31703e6i	−0.744078	−	0.636149i
$736$	1.60585e6	+	2.78141e6i	0.109272	+	0.189265i
$737$	−3.66430e6			−0.248498
$738$	5.64826e6	−	4.56448e6i	0.381745	−	0.308497i
$739$	9.10643e6			0.613390			0.306695	−	0.951808i	$-0.400777\pi$
$739$	9.10643e6			0.613390			0.306695	+	0.951808i	$0.400777\pi$
$740$	−4.39496e6	−	7.61230e6i	−0.295037	−	0.511019i
$741$	1.94992e6	−	1.04914e7i	0.130458	−	0.701920i
$742$	480946.	−	833022.i	0.0320691	−	0.0555452i
$743$	165517.	−	286683.i	0.0109994	−	0.0190515i	−0.860473	−	0.509496i	$-0.829832\pi$
$743$	165517.	−	286683.i	0.0109994	−	0.0190515i	0.871473	+	0.490444i	$0.163165\pi$
$744$	1.59554e6	−	8.58469e6i	0.105676	−	0.568581i
$745$	1.03299e6	+	1.78919e6i	0.0681876	+	0.118104i
$746$	−2.11585e6			−0.139200
$747$	9.80123e6	+	3.77364e6i	0.642657	+	0.247434i
$748$	−1.54410e7			−1.00907
$749$	1.14714e6	+	1.98690e6i	0.0747157	+	0.129411i
$750$	8.20454e6	+	7.01447e6i	0.532600	+	0.455346i
$751$	1.40412e7	−	2.43202e7i	0.908460	−	1.57350i	0.0922561	−	0.995735i	$-0.470592\pi$
$751$	1.40412e7	−	2.43202e7i	0.908460	−	1.57350i	0.816204	−	0.577764i	$-0.196074\pi$
$752$	1.12864e6	−	1.95485e6i	0.0727795	−	0.126058i
$753$	−6.62608e6	+	2.34267e6i	−0.425863	+	0.150565i
$754$	−64547.5	−	111800.i	−0.00413477	−	0.00716163i
$755$	2.79133e7			1.78215
$756$	708019.	−	1.15148e6i	0.0450548	−	0.0732746i
$757$	−1.85991e7			−1.17965			−0.589824	−	0.807532i	$-0.700803\pi$
$757$	−1.85991e7			−1.17965			−0.589824	+	0.807532i	$0.700803\pi$
$758$	−6.46054e6	−	1.11900e7i	−0.408409	−	0.707385i
$759$	2.73334e7	−	9.66380e6i	1.72222	−	0.608897i
$760$	−4.76852e6	+	8.25932e6i	−0.299468	+	0.518693i
$761$	−5.16614e6	+	8.94802e6i	−0.323374	+	0.560099i	−0.981182	−	0.193086i	$-0.938150\pi$
$761$	−5.16614e6	+	8.94802e6i	−0.323374	+	0.560099i	0.657808	+	0.753185i	$0.271484\pi$
$762$	−1.63880e6	−	1.40109e6i	−0.102244	−	0.0874136i
$763$	2.55765e6	+	4.42997e6i	0.159048	+	0.275480i
$764$	5.38437e6			0.333735
$765$	3.46682e6	+	2.20319e7i	0.214179	+	1.36112i
$766$	−1.57161e7			−0.967773
$767$	−2.01469e6	−	3.48954e6i	−0.123657	−	0.214180i
$768$	186677.	−	1.00440e6i	0.0114206	−	0.0614477i
$769$	−1.00261e7	+	1.73658e7i	−0.611388	+	1.05896i	0.379618	+	0.925143i	$0.376055\pi$
$769$	−1.00261e7	+	1.73658e7i	−0.611388	+	1.05896i	−0.991007	+	0.133813i	$0.957278\pi$
$770$	1.49162e6	−	2.58356e6i	0.0906632	−	0.157033i
$771$	2.52262e6	−	1.35728e7i	0.152833	−	0.822306i
$772$	5.92698e6	+	1.02658e7i	0.357924	+	0.619942i
$773$	2.68448e7			1.61589			0.807943	−	0.589260i	$-0.200581\pi$
$773$	2.68448e7			1.61589			0.807943	+	0.589260i	$0.200581\pi$
$774$	1.88937e6	+	1.20070e7i	0.113361	+	0.720416i
$775$	−483727.			−0.0289298
$776$	−2.60757e6	−	4.51645e6i	−0.155447	−	0.269242i
$777$	−2.57431e6	−	2.20090e6i	−0.152970	−	0.130782i
$778$	9.38411e6	−	1.62538e7i	0.555833	−	0.962731i
$779$	−9.87108e6	+	1.70972e7i	−0.582802	+	1.00944i
$780$	3.43543e6	−	1.21461e6i	0.202183	−	0.0714825i
$781$	−3.11276e6	−	5.39146e6i	−0.182607	−	0.316285i
$782$	−2.04183e7			−1.19399
$783$	471726.	+	13063.9i	0.0274970	+	0.000761500i
$784$	−4.17525e6			−0.242601
$785$	1.63068e6	+	2.82442e6i	0.0944482	+	0.163589i
$786$	4.68090e6	−	1.65495e6i	0.270254	−	0.0955494i
$787$	−3.83561e6	+	6.64347e6i	−0.220748	+	0.382347i	−0.955035	−	0.296492i	$-0.904183\pi$
$787$	−3.83561e6	+	6.64347e6i	−0.220748	+	0.382347i	0.734287	+	0.678839i	$0.237517\pi$
$788$	−1.75303e6	+	3.03633e6i	−0.100571	+	0.174194i
$789$	−3.41199e6	−	2.91708e6i	−0.195126	−	0.166823i
$790$	2.01368e6	+	3.48780e6i	0.114795	+	0.198831i
$791$	−1.67125e6			−0.0949731
$792$	−8.60601e6	−	3.31346e6i	−0.487516	−	0.187702i
$793$	3.09071e6			0.174532
$794$	−9.95998e6	−	1.72512e7i	−0.560670	−	0.971109i
$795$	−1.73199e6	+	9.31885e6i	−0.0971913	+	0.522931i
$796$	1.72303e6	−	2.98437e6i	0.0963850	−	0.166944i
$797$	4.41643e6	−	7.64949e6i	0.246278	−	0.426566i	−0.716212	−	0.697883i	$-0.754126\pi$
$797$	4.41643e6	−	7.64949e6i	0.246278	−	0.426566i	0.962490	+	0.271316i	$0.0874590\pi$
$798$	−671487.	+	3.61289e6i	−0.0373277	+	0.200839i
$799$	7.17526e6	+	1.24279e7i	0.397622	+	0.688702i
$800$	−56595.8			−0.00312651
$801$	−1.77841e7	+	1.43717e7i	−0.979377	+	0.791456i
$802$	−1.39370e7			−0.765128
$803$	−1.13792e7	−	1.97093e7i	−0.622761	−	1.07865i
$804$	1.17150e6	+	1.00157e6i	0.0639148	+	0.0546439i
$805$	1.97243e6	−	3.41635e6i	0.107278	−	0.185811i
$806$	4.53469e6	−	7.85432e6i	0.245873	−	0.425864i
$807$	−1.32105e7	+	4.67061e6i	−0.714061	+	0.252459i
$808$	4.25177e6	+	7.36429e6i	0.229109	+	0.396828i
$809$	−2.96255e6			−0.159146			−0.0795729	−	0.996829i	$-0.525356\pi$
$809$	−2.96255e6			−0.159146			−0.0795729	+	0.996829i	$0.525356\pi$
$810$	−2.79556e6	+	1.30233e7i	−0.149712	+	0.697445i
$811$	1.86775e7			0.997161			0.498581	−	0.866843i	$-0.333855\pi$
$811$	1.86775e7			0.997161			0.498581	+	0.866843i	$0.333855\pi$
$812$	22228.1	+	38500.1i	0.00118307	+	0.00204914i
$813$	−2.78241e7	+	9.83730e6i	−1.47637	+	0.521975i
$814$	−1.15530e7	+	2.00104e7i	−0.611131	+	1.05851i
$815$	3.80722e6	−	6.59431e6i	0.200777	−	0.347756i
$816$	4.93658e6	+	4.22053e6i	0.259538	+	0.221892i
$817$	−1.65216e7	−	2.86163e7i	−0.865960	−	1.49989i
$818$	5.17937e6			0.270641
$819$	1.09202e6	−	882482.i	0.0568878	−	0.0459723i
$820$	−6.74132e6			−0.350115
$821$	1.36264e7	+	2.36015e7i	0.705540	+	1.22203i	0.966496	+	0.256681i	$0.0826290\pi$
$821$	1.36264e7	+	2.36015e7i	0.705540	+	1.22203i	−0.260956	+	0.965351i	$0.584038\pi$
$822$	3.08820e6	−	1.66159e7i	0.159414	−	0.857716i
$823$	8.78359e6	−	1.52136e7i	0.452035	−	0.782948i	−0.546477	−	0.837474i	$-0.684031\pi$
$823$	8.78359e6	−	1.52136e7i	0.452035	−	0.782948i	0.998512	+	0.0545260i	$0.0173648\pi$
$824$	−3.97156e6	+	6.87894e6i	−0.203771	+	0.352942i
$825$	−93352.8	+	502279.i	−0.00477521	+	0.0256927i
$826$	693792.	+	1.20168e6i	0.0353818	+	0.0612830i
$827$	−1.92954e7			−0.981046			−0.490523	−	0.871428i	$-0.663194\pi$
$827$	−1.92954e7			−0.981046			−0.490523	+	0.871428i	$0.663194\pi$
$828$	−1.13801e7	−	4.38152e6i	−0.576858	−	0.222100i
$829$	4.98059e6			0.251707			0.125853	−	0.992049i	$-0.459833\pi$
$829$	4.98059e6			0.251707			0.125853	+	0.992049i	$0.459833\pi$
$830$	−4.87475e6	−	8.44331e6i	−0.245616	−	0.425420i
$831$	2.05230e7	+	1.75461e7i	1.03095	+	0.881412i
$832$	530557.	−	918952.i	0.0265720	−	0.0460240i
$833$	1.32720e7	−	2.29878e7i	0.662711	−	1.14785i
$834$	1.94992e6	−	689401.i	0.0970737	−	0.0343207i
$835$	1.14488e7	+	1.98298e7i	0.568254	+	0.984245i
$836$	2.50699e7			1.24062
$837$	1.57754e7	+	2.91594e7i	0.778336	+	1.43868i
$838$	2.54992e7			1.25434
$839$	−1.47355e7	−	2.55226e7i	−0.722703	−	1.25176i	−0.959913	−	0.280300i	$-0.909566\pi$
$839$	−1.47355e7	−	2.55226e7i	−0.722703	−	1.25176i	0.237210	−	0.971458i	$-0.423767\pi$
$840$	−1.18305e6	+	418272.i	−0.0578502	+	0.0204531i
$841$	1.02478e7	−	1.77497e7i	0.499622	−	0.865370i
$842$	−8.83207e6	+	1.52976e7i	−0.429321	+	0.743606i
$843$	−3.47465e6	−	2.97065e6i	−0.168400	−	0.143973i
$844$	−36569.2	−	63339.7i	−0.00176709	−	0.00306069i
$845$	−1.71539e7			−0.826459
$846$	1.33223e6	+	8.46640e6i	0.0639960	+	0.406699i
$847$	−4.25008e6			−0.203558
$848$	1.38010e6	+	2.39041e6i	0.0659055	+	0.114152i
$849$	−2.27355e6	+	1.22327e7i	−0.108252	+	0.582441i
$850$	179903.	−	311601.i	0.00854066	−	0.0147929i
$851$	−1.52770e7	+	2.64605e7i	−0.723126	+	1.25249i
$852$	−478493.	+	2.57450e6i	−0.0225827	+	0.121505i
$853$	1.36546e7	+	2.36505e7i	0.642551	+	1.11293i	0.984861	+	0.173344i	$0.0554572\pi$
$853$	1.36546e7	+	2.36505e7i	0.642551	+	1.11293i	−0.342310	+	0.939587i	$0.611209\pi$
$854$	−1.06434e6			−0.0499386
$855$	−5.62871e6	−	3.57708e7i	−0.263326	−	1.67345i
$856$	−6.58358e6			−0.307098
$857$	1.54427e6	+	2.67476e6i	0.0718244	+	0.124404i	0.899701	−	0.436507i	$-0.143785\pi$
$857$	1.54427e6	+	2.67476e6i	0.0718244	+	0.124404i	−0.827876	+	0.560910i	$0.810451\pi$
$858$	−7.28042e6	−	6.22439e6i	−0.337628	−	0.288655i
$859$	1.24557e6	−	2.15740e6i	0.0575952	−	0.0997578i	−0.835790	−	0.549049i	$-0.814990\pi$
$859$	1.24557e6	−	2.15740e6i	0.0575952	−	0.0997578i	0.893385	+	0.449291i	$0.148323\pi$
$860$	5.64161e6	−	9.77155e6i	0.260110	−	0.450523i
$861$	−2.44897e6	+	865843.i	−0.112584	+	0.0398044i
$862$	−1.33039e7	−	2.30431e7i	−0.609834	−	1.05626i
$863$	6.26889e6			0.286526			0.143263	−	0.989685i	$-0.454241\pi$
$863$	6.26889e6			0.286526			0.143263	+	0.989685i	$0.454241\pi$
$864$	1.84572e6	+	3.41164e6i	0.0841164	+	0.155481i
$865$	1.28714e7			0.584907
$866$	−6.83756e6	−	1.18430e7i	−0.309818	−	0.536620i
$867$	−1.80616e7	+	6.38575e6i	−0.816036	+	0.288512i
$868$	−1.56160e6	+	2.70477e6i	−0.0703511	+	0.121852i
$869$	5.29335e6	−	9.16835e6i	0.237783	−	0.411853i
$870$	−332967.	−	284670.i	−0.0149143	−	0.0127510i
$871$	800445.	+	1.38641e6i	0.0357508	+	0.0619223i
$872$	−1.46786e7			−0.653725
$873$	1.84789e7	+	7.11470e6i	0.820618	+	0.315952i
$874$	3.31510e7			1.46797
$875$	−1.93049e6	−	3.34370e6i	−0.0852406	−	0.147641i
$876$	−1.74920e6	+	9.41147e6i	−0.0770158	+	0.414379i
$877$	−1.30800e6	+	2.26553e6i	−0.0574261	+	0.0994650i	−0.893309	−	0.449442i	$-0.851623\pi$
$877$	−1.30800e6	+	2.26553e6i	−0.0574261	+	0.0994650i	0.835883	+	0.548907i	$0.184956\pi$
$878$	7929.36	−	13734.1i	0.000347138	−	0.000601260i
$879$	3.96145e6	−	2.13143e7i	0.172935	−	0.930464i
$880$	4.28029e6	+	7.41368e6i	0.186323	+	0.322721i
$881$	−1.63208e7			−0.708436			−0.354218	−	0.935163i	$-0.615253\pi$
$881$	−1.63208e7			−0.708436			−0.354218	+	0.935163i	$0.615253\pi$
$882$	1.23300e7	−	9.96418e6i	0.533695	−	0.431290i
$883$	−2.80814e6			−0.121204			−0.0606020	−	0.998162i	$-0.519302\pi$
$883$	−2.80814e6			−0.121204			−0.0606020	+	0.998162i	$0.519302\pi$
$884$	3.37300e6	+	5.84221e6i	0.145173	+	0.251447i
$885$	−1.03927e7	−	8.88525e6i	−0.446037	−	0.381339i
$886$	7.65669e6	−	1.32618e7i	0.327685	−	0.567567i
$887$	1.30991e7	−	2.26883e7i	0.559027	−	0.968263i	−0.438551	−	0.898706i	$-0.644508\pi$
$887$	1.30991e7	−	2.26883e7i	0.559027	−	0.968263i	0.997578	−	0.0695566i	$-0.0221584\pi$
$888$	9.16306e6	−	3.23963e6i	0.389949	−	0.137868i
$889$	385601.	+	667881.i	0.0163638	+	0.0283429i
$890$	2.12257e7			0.898227
$891$	3.33221e7	−	1.07531e7i	1.40617	−	0.453772i
$892$	1.51285e7			0.636623
$893$	−1.16497e7	−	2.01779e7i	−0.488863	−	0.846735i
$894$	−2.15368e6	+	761441.i	−0.0901233	+	0.0318634i
$895$	546175.	−	946003.i	0.0227916	−	0.0394762i
$896$	−182707.	+	316457.i	−0.00760299	+	0.0131688i
$897$	−9.62719e6	−	8.23076e6i	−0.399501	−	0.341554i
$898$	3.24546e6	+	5.62131e6i	0.134303	+	0.232620i
$899$	−1.09034e6			−0.0449949
$900$	167135.	−	135065.i	0.00687796	−	0.00555823i
$901$	−1.75479e7			−0.720135
$902$	8.86042e6	+	1.53467e7i	0.362609	+	0.628056i
$903$	794432.	−	4.27439e6i	0.0324218	−	0.174443i
$904$	2.39788e6	−	4.15325e6i	0.0975902	−	0.169031i
$905$	3.88525e6	−	6.72945e6i	0.157688	−	0.273123i
$906$	−5.63963e6	+	3.03437e7i	−0.228260	+	1.22814i
$907$	−1.39621e7	−	2.41831e7i	−0.563550	−	0.976097i	−0.997183	−	0.0750075i	$-0.976102\pi$
$907$	−1.39621e7	−	2.41831e7i	−0.563550	−	0.976097i	0.433633	−	0.901090i	$-0.357231\pi$
$908$	2.94224e6			0.118430
$909$	−3.01308e7	−	1.16009e7i	−1.20949	−	0.465673i
$910$	−1.30334e6			−0.0521741
$911$	2.28045e7	+	3.94986e7i	0.910384	+	1.57683i	0.813522	+	0.581534i	$0.197547\pi$
$911$	2.28045e7	+	3.94986e7i	0.910384	+	1.57683i	0.0968626	+	0.995298i	$0.469119\pi$
$912$	−8.01501e6	−	6.85243e6i	−0.319093	−	0.272808i
$913$	−1.28142e7	+	2.21949e7i	−0.508762	+	0.881202i
$914$	−1.50551e7	+	2.60762e7i	−0.596098	+	1.03247i
$915$	9.88815e6	−	3.49599e6i	0.390447	−	0.138044i
$916$	−4.46747e6	−	7.73789e6i	−0.175923	−	0.304708i
$917$	−1.77585e6			−0.0697402
$918$	−2.46506e7	−	682671.i	−0.965429	−	0.0267365i
$919$	6.63615e6			0.259196			0.129598	−	0.991567i	$-0.458631\pi$
$919$	6.63615e6			0.259196			0.129598	+	0.991567i	$0.458631\pi$
$920$	5.66000e6	+	9.80341e6i	0.220469	+	0.381863i
$921$	−8.78904e6	+	3.10740e6i	−0.341423	+	0.120711i
$922$	1.44119e6	−	2.49621e6i	0.0558333	−	0.0967061i
$923$	−1.35993e6	+	2.35547e6i	−0.0525427	+	0.0910066i
$924$	2.50714e6	+	2.14348e6i	0.0966047	+	0.0825922i
$925$	−269208.	−	466282.i	−0.0103451	−	0.0179182i
$926$	2.18231e7			0.836351
$927$	−4.68798e6	−	2.97924e7i	−0.179179	−	1.13869i
$928$	−127570.			−0.00486270
$929$	1.02667e7	+	1.77825e7i	0.390295	+	0.676011i	0.992488	−	0.122339i	$-0.0390396\pi$
$929$	1.02667e7	+	1.77825e7i	0.390295	+	0.676011i	−0.602193	+	0.798350i	$0.705706\pi$
$930$	5.62366e6	−	3.02577e7i	0.213212	−	1.14717i
$931$	−2.15484e7	+	3.73229e7i	−0.814780	+	1.41124i
$932$	−8.38802e6	+	1.45285e7i	−0.316315	+	0.547874i
$933$	−8.48283e6	+	4.56413e7i	−0.319034	+	1.71654i
$934$	−7.40163e6	−	1.28200e7i	−0.277626	−	0.480863i
$935$	−5.44237e7			−2.03591
$936$	626264.	+	3.97995e6i	0.0233651	+	0.148487i
$937$	−3.95168e7			−1.47039			−0.735196	−	0.677855i	$-0.762910\pi$
$937$	−3.95168e7			−1.47039			−0.735196	+	0.677855i	$0.762910\pi$
$938$	−275647.	−	477435.i	−0.0102293	−	0.0177177i
$939$	2.96654e7	+	2.53624e7i	1.09796	+	0.938701i
$940$	3.97801e6	−	6.89011e6i	0.146841	−	0.254335i
$941$	4.91319e6	−	8.50989e6i	0.180879	−	0.313292i	−0.761301	−	0.648399i	$-0.775439\pi$
$941$	4.91319e6	−	8.50989e6i	0.180879	−	0.313292i	0.942180	+	0.335106i	$0.108772\pi$
$942$	−3.39980e6	+	1.20201e6i	−0.124832	+	0.0441348i
$943$	1.17165e7	+	2.02936e7i	0.429060	+	0.743154i
$944$	−3.98176e6			−0.145427
$945$	2.49550e6	−	4.05854e6i	0.0909029	−	0.147839i
$946$	−2.96601e7			−1.07757
$947$	−9.54088e6	−	1.65253e7i	−0.345711	−	0.598789i	0.639772	−	0.768565i	$-0.279029\pi$
$947$	−9.54088e6	−	1.65253e7i	−0.345711	−	0.598789i	−0.985483	+	0.169776i	$0.945696\pi$
$948$	−4.19832e6	+	1.48433e6i	−0.151724	+	0.0536426i
$949$	−4.97143e6	+	8.61077e6i	−0.179191	+	0.310368i
$950$	−292090.	+	505914.i	−0.0105004	+	0.0181873i
$951$	2.47200e7	+	2.11344e7i	0.886334	+	0.757771i
$952$	−1.16155e6	−	2.01187e6i	−0.0415381	−	0.0719461i
$953$	3.72070e7			1.32707			0.663533	−	0.748147i	$-0.269056\pi$
$953$	3.72070e7			1.32707			0.663533	+	0.748147i	$0.269056\pi$
$954$	−9.78029e6	−	3.76558e6i	−0.347921	−	0.133956i
$955$	1.89778e7			0.673346
$956$	−5.71043e6	−	9.89075e6i	−0.202080	−	0.350013i
$957$	−210421.	+	1.13216e6i	−0.00742695	+	0.0399602i
$958$	−1.20321e7	+	2.08401e7i	−0.423571	+	0.733646i
$959$	−3.02252e6	+	5.23516e6i	−0.106126	+	0.183816i
$960$	657966.	−	3.54014e6i	0.0230423	−	0.123977i
$961$	−2.39856e7	−	4.15444e7i	−0.837805	−	1.45112i
$962$	1.00948e7			0.351689
$963$	1.94421e7	−	1.57116e7i	0.675582	−	0.545953i
$964$	−1.23350e7			−0.427510
$965$	2.08903e7	+	3.61831e7i	0.722150	+	1.25080i
$966$	3.31529e6	+	2.83441e6i	0.114309	+	0.0977280i
$967$	−2.69082e7	+	4.66064e7i	−0.925377	+	1.60280i	−0.134423	+	0.990924i	$0.542918\pi$
$967$	−2.69082e7	+	4.66064e7i	−0.925377	+	1.60280i	−0.790954	+	0.611876i	$0.790415\pi$
$968$	6.09793e6	−	1.05619e7i	0.209168	−	0.362289i
$969$	6.32052e7	−	2.23464e7i	2.16244	−	0.764537i
$970$	−9.19070e6	−	1.59188e7i	−0.313631	−	0.543225i
$971$	3.16679e7			1.07788			0.538940	−	0.842344i	$-0.318825\pi$
$971$	3.16679e7			1.07788			0.538940	+	0.842344i	$0.318825\pi$
$972$	−1.35924e7	−	5.67021e6i	−0.461458	−	0.192501i
$973$	−739766.			−0.0250503
$974$	2.54318e6	+	4.40491e6i	0.0858972	+	0.148778i
$975$	210433.	−	74399.3i	0.00708928	−	0.00250644i
$976$	1.52710e6	−	2.64501e6i	0.0513147	−	0.0888796i
$977$	3.03115e6	−	5.25011e6i	0.101595	−	0.175967i	−0.810747	−	0.585397i	$-0.800939\pi$
$977$	3.03115e6	−	5.25011e6i	0.101595	−	0.175967i	0.912342	+	0.409429i	$0.134272\pi$
$978$	6.39924e6	+	5.47103e6i	0.213935	+	0.182904i
$979$	−2.78978e7	−	4.83205e7i	−0.930281	−	1.61129i
$980$	−1.47162e7			−0.489474
$981$	4.33479e7	−	3.50304e7i	1.43812	−	1.16218i
$982$	1.56812e7			0.518919
$983$	−1.13501e7	−	1.96590e7i	−0.374642	−	0.648898i	0.615632	−	0.788034i	$-0.288901\pi$
$983$	−1.13501e7	−	1.96590e7i	−0.374642	−	0.648898i	−0.990273	+	0.139136i	$0.955568\pi$
$984$	1.36202e6	−	7.32827e6i	0.0448432	−	0.241276i
$985$	−6.17875e6	+	1.07019e7i	−0.202913	+	0.351456i
$986$	405510.	−	702363.i	0.0132834	−	0.0230075i
$987$	560170.	−	3.01396e6i	0.0183032	−	0.0984791i
$988$	−5.47639e6	−	9.48538e6i	−0.178485	−	0.309145i
$989$	−3.92207e7			−1.27504
$990$	−3.03329e7	−	1.16787e7i	−0.983616	−	0.378709i
$991$	4.31783e7			1.39663			0.698315	−	0.715790i	$-0.253933\pi$
$991$	4.31783e7			1.39663			0.698315	+	0.715790i	$0.253933\pi$
$992$	−4.48111e6	−	7.76151e6i	−0.144579	−	0.250419i
$993$	−2.24544e7	−	1.91974e7i	−0.722650	−	0.617829i
$994$	468315.	−	811146.i	0.0150339	−	0.0260395i
$995$	6.07301e6	−	1.05188e7i	0.194467	−	0.336827i
$996$	1.01634e7	−	3.59329e6i	0.324630	−	0.114774i
$997$	1.32803e7	+	2.30021e7i	0.423125	+	0.732874i	0.996243	−	0.0865984i	$-0.0275997\pi$
$997$	1.32803e7	+	2.30021e7i	0.423125	+	0.732874i	−0.573118	+	0.819473i	$0.694266\pi$
$998$	1.75825e7			0.558796
$999$	−1.93283e7	+	3.14345e7i	−0.612746	+	0.996537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.6.c.a.13.1	yes	4
3.2	odd	2		54.6.c.a.37.2		4
4.3	odd	2		144.6.i.a.49.2		4
9.2	odd	6		54.6.c.a.19.2		4
9.4	even	3		162.6.a.e.1.2		2
9.5	odd	6		162.6.a.f.1.1		2
9.7	even	3	inner	18.6.c.a.7.1	✓	4
12.11	even	2		432.6.i.a.145.2		4
36.7	odd	6		144.6.i.a.97.2		4
36.11	even	6		432.6.i.a.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.a.7.1	✓	4	9.7	even	3	inner
18.6.c.a.13.1	yes	4	1.1	even	1	trivial
54.6.c.a.19.2		4	9.2	odd	6
54.6.c.a.37.2		4	3.2	odd	2
144.6.i.a.49.2		4	4.3	odd	2
144.6.i.a.97.2		4	36.7	odd	6
162.6.a.e.1.2		2	9.4	even	3
162.6.a.f.1.1		2	9.5	odd	6
432.6.i.a.145.2		4	12.11	even	2
432.6.i.a.289.2		4	36.11	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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-14.6969 + 5.19615i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-28.1969 + 48.8385i) q^{5} +(-47.3939 - 40.5194i) q^{6} +(11.1515 + 19.3150i) q^{7} -64.0000 q^{8} +(189.000 - 152.735i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-14.6969 + 5.19615i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-28.1969 + 48.8385i) q^{5} +(-47.3939 - 40.5194i) q^{6} +(11.1515 + 19.3150i) q^{7} -64.0000 q^{8} +(189.000 - 152.735i) q^{9} -225.576 q^{10} +(296.484 + 513.526i) q^{11} +(45.5755 - 245.216i) q^{12} +(129.531 - 224.354i) q^{13} +(-44.6061 + 77.2601i) q^{14} +(160.636 - 864.292i) q^{15} +(-128.000 - 221.703i) q^{16} +1627.51 q^{17} +(907.090 + 349.245i) q^{18} -2642.42 q^{19} +(-451.151 - 781.416i) q^{20} +(-264.257 - 225.927i) q^{21} +(-1185.94 + 2054.10i) q^{22} +(-1568.21 + 2716.22i) q^{23} +(940.604 - 332.554i) q^{24} +(-27.6347 - 47.8647i) q^{25} +1036.24 q^{26} +(-1984.09 + 3226.81i) q^{27} -356.849 q^{28} +(-62.2898 - 107.889i) q^{29} +(3315.27 - 1172.12i) q^{30} +(4376.08 - 7579.60i) q^{31} +(512.000 - 886.810i) q^{32} +(-7025.77 - 6006.68i) q^{33} +(3255.02 + 5637.87i) q^{34} -1257.76 q^{35} +(604.359 + 3840.74i) q^{36} +9741.67 q^{37} +(-5284.84 - 9153.61i) q^{38} +(-737.928 + 3970.37i) q^{39} +(1804.60 - 3125.67i) q^{40} +(3735.62 - 6470.29i) q^{41} +(254.118 - 1367.27i) q^{42} +(6252.46 + 10829.6i) q^{43} -9487.49 q^{44} +(2130.13 + 13537.1i) q^{45} -12545.7 q^{46} +(4408.73 + 7636.15i) q^{47} +(3033.21 + 2593.24i) q^{48} +(8154.79 - 14124.5i) q^{49} +(110.539 - 191.459i) q^{50} +(-23919.4 + 8456.80i) q^{51} +(2072.49 + 3589.66i) q^{52} -10782.1 q^{53} +(-15146.2 - 419.457i) q^{54} -33439.8 q^{55} +(-713.698 - 1236.16i) q^{56} +(38835.5 - 13730.4i) q^{57} +(249.159 - 431.557i) q^{58} +(7776.87 - 13469.9i) q^{59} +(10690.9 + 9140.18i) q^{60} +(5965.22 + 10332.1i) q^{61} +35008.7 q^{62} +(5057.72 + 1947.31i) q^{63} +4096.00 q^{64} +(7304.73 + 12652.2i) q^{65} +(6756.21 - 36351.3i) q^{66} +(-3089.79 + 5351.68i) q^{67} +(-13020.1 + 22551.5i) q^{68} +(8934.01 - 48068.8i) q^{69} +(-2515.51 - 4356.99i) q^{70} -10498.9 q^{71} +(-12096.0 + 9775.04i) q^{72} -38380.3 q^{73} +(19483.3 + 33746.1i) q^{74} +(654.857 + 559.870i) q^{75} +(21139.4 - 36614.5i) q^{76} +(-6612.50 + 11453.2i) q^{77} +(-15229.6 + 5384.49i) q^{78} +(-8926.87 - 15461.8i) q^{79} +14436.8 q^{80} +(12393.0 - 57733.9i) q^{81} +29885.0 q^{82} +(21610.3 + 37430.1i) q^{83} +(5244.59 - 1854.24i) q^{84} +(-45890.9 + 79485.3i) q^{85} +(-25009.8 + 43318.3i) q^{86} +(1476.08 + 1261.97i) q^{87} +(-18975.0 - 32865.6i) q^{88} -94095.6 q^{89} +(-42633.8 + 34453.3i) q^{90} +5777.86 q^{91} +(-25091.4 - 43459.6i) q^{92} +(-24930.3 + 134136. i) q^{93} +(-17634.9 + 30544.6i) q^{94} +(74508.2 - 129052. i) q^{95} +(-2916.83 + 15693.8i) q^{96} +(40743.3 + 70569.5i) q^{97} +65238.3 q^{98} +(134469. + 51772.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 32 q^{4} - 54 q^{5} - 72 q^{6} + 74 q^{7} - 256 q^{8} + 756 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 - 32 * q^4 - 54 * q^5 - 72 * q^6 + 74 * q^7 - 256 * q^8 + 756 * q^9	\( 4 q + 8 q^{2} - 32 q^{4} - 54 q^{5} - 72 q^{6} + 74 q^{7} - 256 q^{8} + 756 q^{9} - 432 q^{10} - 78 q^{11} - 288 q^{12} + 1106 q^{13} - 296 q^{14} + 378 q^{15} - 512 q^{16} + 984 q^{17} + 1512 q^{18} - 3280 q^{19} - 864 q^{20} - 234 q^{21} + 312 q^{22} - 5538 q^{23} + 3064 q^{25} + 8848 q^{26} - 2368 q^{28} - 3894 q^{29} + 6912 q^{30} + 4718 q^{31} + 2048 q^{32} - 17874 q^{33} + 1968 q^{34} - 2268 q^{35} - 6048 q^{36} - 9592 q^{37} - 6560 q^{38} + 18594 q^{39} + 3456 q^{40} + 15354 q^{41} - 4392 q^{42} + 32858 q^{43} + 2496 q^{44} + 5346 q^{45} - 44304 q^{46} + 24954 q^{47} + 4608 q^{48} + 30444 q^{49} - 12256 q^{50} - 81216 q^{51} + 17696 q^{52} - 32664 q^{53} - 44712 q^{54} - 70092 q^{55} - 4736 q^{56} + 107136 q^{57} + 15576 q^{58} + 21966 q^{59} + 21600 q^{60} + 3050 q^{61} + 37744 q^{62} + 6210 q^{63} + 16384 q^{64} + 12582 q^{65} + 77112 q^{66} + 36758 q^{67} - 7872 q^{68} - 39042 q^{69} - 4536 q^{70} - 147696 q^{71} - 48384 q^{72} - 102376 q^{73} - 19184 q^{74} + 19080 q^{75} + 26240 q^{76} + 21462 q^{77} + 69120 q^{78} - 14926 q^{79} + 27648 q^{80} + 49572 q^{81} + 122832 q^{82} + 90762 q^{83} - 13824 q^{84} - 94500 q^{85} - 131432 q^{86} - 18522 q^{87} + 4992 q^{88} - 18600 q^{89} - 81648 q^{90} + 99124 q^{91} - 88608 q^{92} - 145458 q^{93} - 99816 q^{94} + 151416 q^{95} + 18432 q^{96} - 30262 q^{97} + 243552 q^{98} + 319626 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 32 * q^4 - 54 * q^5 - 72 * q^6 + 74 * q^7 - 256 * q^8 + 756 * q^9 - 432 * q^10 - 78 * q^11 - 288 * q^12 + 1106 * q^13 - 296 * q^14 + 378 * q^15 - 512 * q^16 + 984 * q^17 + 1512 * q^18 - 3280 * q^19 - 864 * q^20 - 234 * q^21 + 312 * q^22 - 5538 * q^23 + 3064 * q^25 + 8848 * q^26 - 2368 * q^28 - 3894 * q^29 + 6912 * q^30 + 4718 * q^31 + 2048 * q^32 - 17874 * q^33 + 1968 * q^34 - 2268 * q^35 - 6048 * q^36 - 9592 * q^37 - 6560 * q^38 + 18594 * q^39 + 3456 * q^40 + 15354 * q^41 - 4392 * q^42 + 32858 * q^43 + 2496 * q^44 + 5346 * q^45 - 44304 * q^46 + 24954 * q^47 + 4608 * q^48 + 30444 * q^49 - 12256 * q^50 - 81216 * q^51 + 17696 * q^52 - 32664 * q^53 - 44712 * q^54 - 70092 * q^55 - 4736 * q^56 + 107136 * q^57 + 15576 * q^58 + 21966 * q^59 + 21600 * q^60 + 3050 * q^61 + 37744 * q^62 + 6210 * q^63 + 16384 * q^64 + 12582 * q^65 + 77112 * q^66 + 36758 * q^67 - 7872 * q^68 - 39042 * q^69 - 4536 * q^70 - 147696 * q^71 - 48384 * q^72 - 102376 * q^73 - 19184 * q^74 + 19080 * q^75 + 26240 * q^76 + 21462 * q^77 + 69120 * q^78 - 14926 * q^79 + 27648 * q^80 + 49572 * q^81 + 122832 * q^82 + 90762 * q^83 - 13824 * q^84 - 94500 * q^85 - 131432 * q^86 - 18522 * q^87 + 4992 * q^88 - 18600 * q^89 - 81648 * q^90 + 99124 * q^91 - 88608 * q^92 - 145458 * q^93 - 99816 * q^94 + 151416 * q^95 + 18432 * q^96 - 30262 * q^97 + 243552 * q^98 + 319626 * q^99

Introduction

L-functions

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