LMFDB - Embedded newform 152.6.b.b.75.83

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,6,Mod(75,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("152.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	152.b (of order $2$, degree $1$, 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:	$24.3783406116$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.83
Character	$\chi$	$=$	152.75
Dual form			152.6.b.b.75.84

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.05036 - 2.54831i) q^{2} +27.1983i q^{3} +(19.0122 - 25.7398i) q^{4} -36.9812i q^{5} +(69.3098 + 137.361i) q^{6} -150.607i q^{7} +(30.4253 - 178.444i) q^{8} -496.748 q^{9} +O(q^{10})$	\(q+(5.05036 - 2.54831i) q^{2} +27.1983i q^{3} +(19.0122 - 25.7398i) q^{4} -36.9812i q^{5} +(69.3098 + 137.361i) q^{6} -150.607i q^{7} +(30.4253 - 178.444i) q^{8} -496.748 q^{9} +(-94.2398 - 186.768i) q^{10} -603.531 q^{11} +(700.078 + 517.099i) q^{12} -566.677 q^{13} +(-383.795 - 760.620i) q^{14} +1005.83 q^{15} +(-301.073 - 978.739i) q^{16} -1989.92 q^{17} +(-2508.75 + 1265.87i) q^{18} +(1308.75 + 873.651i) q^{19} +(-951.889 - 703.094i) q^{20} +4096.26 q^{21} +(-3048.04 + 1537.99i) q^{22} -1465.34i q^{23} +(4853.38 + 827.515i) q^{24} +1757.39 q^{25} +(-2861.92 + 1444.07i) q^{26} -6901.50i q^{27} +(-3876.60 - 2863.37i) q^{28} -4744.43 q^{29} +(5079.78 - 2563.16i) q^{30} -1904.96 q^{31} +(-4014.66 - 4175.75i) q^{32} -16415.0i q^{33} +(-10049.8 + 5070.95i) q^{34} -5569.64 q^{35} +(-9444.26 + 12786.2i) q^{36} +9126.91 q^{37} +(8836.00 + 1077.14i) q^{38} -15412.6i q^{39} +(-6599.08 - 1125.16i) q^{40} +2640.62i q^{41} +(20687.6 - 10438.6i) q^{42} +10081.0 q^{43} +(-11474.4 + 15534.7i) q^{44} +18370.3i q^{45} +(-3734.16 - 7400.51i) q^{46} -20444.0i q^{47} +(26620.0 - 8188.68i) q^{48} -5875.55 q^{49} +(8875.44 - 4478.38i) q^{50} -54122.5i q^{51} +(-10773.8 + 14586.1i) q^{52} +30065.0 q^{53} +(-17587.2 - 34855.0i) q^{54} +22319.3i q^{55} +(-26875.0 - 4582.26i) q^{56} +(-23761.8 + 35595.8i) q^{57} +(-23961.1 + 12090.3i) q^{58} +15138.2i q^{59} +(19123.0 - 25889.8i) q^{60} +38264.3i q^{61} +(-9620.72 + 4854.43i) q^{62} +74813.8i q^{63} +(-30916.6 - 10858.4i) q^{64} +20956.4i q^{65} +(-41830.6 - 82901.6i) q^{66} -45900.3i q^{67} +(-37832.8 + 51220.2i) q^{68} +39854.9 q^{69} +(-28128.7 + 14193.2i) q^{70} -59869.1 q^{71} +(-15113.7 + 88641.7i) q^{72} +21567.5 q^{73} +(46094.1 - 23258.2i) q^{74} +47798.0i q^{75} +(47369.8 - 17077.0i) q^{76} +90896.1i q^{77} +(-39276.2 - 77839.3i) q^{78} -72787.8 q^{79} +(-36195.0 + 11134.1i) q^{80} +66999.5 q^{81} +(6729.12 + 13336.1i) q^{82} +14628.7 q^{83} +(77878.9 - 105437. i) q^{84} +73589.7i q^{85} +(50912.6 - 25689.5i) q^{86} -129041. i q^{87} +(-18362.6 + 107696. i) q^{88} -18633.0i q^{89} +(46813.4 + 92776.7i) q^{90} +85345.6i q^{91} +(-37717.7 - 27859.4i) q^{92} -51811.7i q^{93} +(-52097.7 - 103249. i) q^{94} +(32308.7 - 48399.3i) q^{95} +(113573. - 109192. i) q^{96} +20961.5i q^{97} +(-29673.6 + 14972.7i) q^{98} +299802. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	5.05036	−	2.54831i	0.892785	−	0.450483i
$2$	5.05036	−	2.54831i	0.892785	−	0.450483i
$3$			27.1983i			1.74477i	0.488818	+	0.872386i	$0.337428\pi$
$3$			27.1983i			1.74477i	−0.488818	+	0.872386i	$0.662572\pi$
$4$	19.0122	−	25.7398i	0.594131	−	0.804368i
$5$		−	36.9812i		−	0.661540i	−0.943711	−	0.330770i	$-0.892692\pi$
$5$		−	36.9812i		−	0.661540i	0.943711	−	0.330770i	$-0.107308\pi$
$6$	69.3098	+	137.361i	0.785989	+	1.55771i
$7$		−	150.607i		−	1.16172i	−0.814004	−	0.580859i	$-0.802717\pi$
$7$		−	150.607i		−	1.16172i	0.814004	−	0.580859i	$-0.197283\pi$
$8$	30.4253	−	178.444i	0.168077	−	0.985774i
$9$	−496.748			−2.04423
$10$	−94.2398	−	186.768i	−0.298012	−	0.590613i
$11$	−603.531			−1.50390			−0.751948	−	0.659223i	$-0.770885\pi$
$11$	−603.531			−1.50390			−0.751948	+	0.659223i	$0.770885\pi$
$12$	700.078	+	517.099i	1.40344	+	1.03662i
$13$	−566.677			−0.929987			−0.464993	−	0.885314i	$-0.653943\pi$
$13$	−566.677			−0.929987			−0.464993	+	0.885314i	$0.653943\pi$
$14$	−383.795	−	760.620i	−0.523334	−	1.03716i
$15$	1005.83			1.15424
$16$	−301.073	−	978.739i	−0.294017	−	0.955800i
$17$	−1989.92			−1.66999			−0.834995	−	0.550258i	$-0.814529\pi$
$17$	−1989.92			−1.66999			−0.834995	+	0.550258i	$0.814529\pi$
$18$	−2508.75	+	1265.87i	−1.82506	+	0.920889i
$19$	1308.75	+	873.651i	0.831713	+	0.555206i
$19$	1308.75	+	873.651i	0.831713	+	0.555206i
$20$	−951.889	−	703.094i	−0.532122	−	0.393041i
$21$	4096.26			2.02693
$22$	−3048.04	+	1537.99i	−1.34266	+	0.677479i
$23$		−	1465.34i		−	0.577591i	−0.957391	−	0.288795i	$-0.906745\pi$
$23$		−	1465.34i		−	0.577591i	0.957391	−	0.288795i	$-0.0932547\pi$
$24$	4853.38	+	827.515i	1.71995	+	0.293257i
$25$	1757.39			0.562365
$26$	−2861.92	+	1444.07i	−0.830279	+	0.418943i
$27$		−	6901.50i		−	1.82194i
$28$	−3876.60	−	2863.37i	−0.934449	−	0.690213i
$29$	−4744.43			−1.04759			−0.523793	−	0.851846i	$-0.675483\pi$
$29$	−4744.43			−1.04759			−0.523793	+	0.851846i	$0.675483\pi$
$30$	5079.78	−	2563.16i	1.03049	−	0.519964i
$31$	−1904.96			−0.356026			−0.178013	−	0.984028i	$-0.556967\pi$
$31$	−1904.96			−0.356026			−0.178013	+	0.984028i	$0.556967\pi$
$32$	−4014.66	−	4175.75i	−0.693065	−	0.720875i
$33$		−	16415.0i		−	2.62395i
$34$	−10049.8	+	5070.95i	−1.49094	+	0.752301i
$35$	−5569.64			−0.768523
$36$	−9444.26	+	12786.2i	−1.21454	+	1.64431i
$37$	9126.91			1.09602			0.548011	−	0.836471i	$-0.315385\pi$
$37$	9126.91			1.09602			0.548011	+	0.836471i	$0.315385\pi$
$38$	8836.00	+	1077.14i	0.992652	+	0.121007i
$39$		−	15412.6i		−	1.62261i
$40$	−6599.08	−	1125.16i	−0.652129	−	0.111190i
$41$			2640.62i			0.245327i	0.992448	+	0.122664i	$0.0391436\pi$
$41$			2640.62i			0.245327i	−0.992448	+	0.122664i	$0.960856\pi$
$42$	20687.6	−	10438.6i	1.80962	−	0.913098i
$43$	10081.0			0.831443			0.415721	−	0.909492i	$-0.363529\pi$
$43$	10081.0			0.831443			0.415721	+	0.909492i	$0.363529\pi$
$44$	−11474.4	+	15534.7i	−0.893511	+	1.20969i
$45$			18370.3i			1.35234i
$46$	−3734.16	−	7400.51i	−0.260195	−	0.515664i
$47$		−	20444.0i		−	1.34996i	−0.737836	−	0.674980i	$-0.764152\pi$
$47$		−	20444.0i		−	1.34996i	0.737836	−	0.674980i	$-0.235848\pi$
$48$	26620.0	−	8188.68i	1.66765	−	0.512992i
$49$	−5875.55			−0.349589
$50$	8875.44	−	4478.38i	0.502071	−	0.253335i
$51$		−	54122.5i		−	2.91375i
$52$	−10773.8	+	14586.1i	−0.552534	+	0.748052i
$53$	30065.0			1.47018			0.735092	−	0.677967i	$-0.237139\pi$
$53$	30065.0			1.47018			0.735092	+	0.677967i	$0.237139\pi$
$54$	−17587.2	−	34855.0i	−0.820752	−	1.62660i
$55$			22319.3i			0.994887i
$56$	−26875.0	−	4582.26i	−1.14519	−	0.195259i
$57$	−23761.8	+	35595.8i	−0.968707	+	1.45115i
$58$	−23961.1	+	12090.3i	−0.935269	+	0.471919i
$59$			15138.2i			0.566167i	0.959095	+	0.283084i	$0.0913574\pi$
$59$			15138.2i			0.566167i	−0.959095	+	0.283084i	$0.908643\pi$
$60$	19123.0	−	25889.8i	0.685768	−	0.928431i
$61$			38264.3i			1.31665i	0.752735	+	0.658323i	$0.228734\pi$
$61$			38264.3i			1.31665i	−0.752735	+	0.658323i	$0.771266\pi$
$62$	−9620.72	+	4854.43i	−0.317855	+	0.160383i
$63$			74813.8i			2.37482i
$64$	−30916.6	−	10858.4i	−0.943500	−	0.331373i
$65$			20956.4i			0.615224i
$66$	−41830.6	−	82901.6i	−1.18205	−	2.34263i
$67$		−	45900.3i		−	1.24919i	−0.780949	−	0.624595i	$-0.785264\pi$
$67$		−	45900.3i		−	1.24919i	0.780949	−	0.624595i	$-0.214736\pi$
$68$	−37832.8	+	51220.2i	−0.992192	+	1.34329i
$69$	39854.9			1.00776
$70$	−28128.7	+	14193.2i	−0.686126	+	0.346206i
$71$	−59869.1			−1.40947			−0.704737	−	0.709468i	$-0.748935\pi$
$71$	−59869.1			−1.40947			−0.704737	+	0.709468i	$0.748935\pi$
$72$	−15113.7	+	88641.7i	−0.343589	+	2.01515i
$73$	21567.5			0.473688			0.236844	−	0.971548i	$-0.423887\pi$
$73$	21567.5			0.473688			0.236844	+	0.971548i	$0.423887\pi$
$74$	46094.1	−	23258.2i	0.978513	−	0.493739i
$75$			47798.0i			0.981198i
$76$	47369.8	−	17077.0i	0.940736	−	0.339139i
$77$			90896.1i			1.74710i
$78$	−39276.2	−	77839.3i	−0.730960	−	1.44865i
$79$	−72787.8			−1.31217			−0.656087	−	0.754686i	$-0.727789\pi$
$79$	−72787.8			−1.31217			−0.656087	+	0.754686i	$0.727789\pi$
$80$	−36195.0	+	11134.1i	−0.632300	+	0.194504i
$81$	66999.5			1.13464
$82$	6729.12	+	13336.1i	0.110516	+	0.219025i
$83$	14628.7			0.233083			0.116541	−	0.993186i	$-0.462819\pi$
$83$	14628.7			0.233083			0.116541	+	0.993186i	$0.462819\pi$
$84$	77878.9	−	105437.i	1.20426	−	1.63040i
$85$			73589.7i			1.10476i
$86$	50912.6	−	25689.5i	0.742300	−	0.374550i
$87$		−	129041.i		−	1.82780i
$88$	−18362.6	+	107696.i	−0.252771	+	1.48250i
$89$		−	18633.0i		−	0.249349i	−0.992198	−	0.124675i	$-0.960211\pi$
$89$		−	18633.0i		−	0.249349i	0.992198	−	0.124675i	$-0.0397887\pi$
$90$	46813.4	+	92776.7i	0.609205	+	1.20735i
$91$			85345.6i			1.08038i
$92$	−37717.7	−	27859.4i	−0.464596	−	0.343164i
$93$		−	51811.7i		−	0.621184i
$94$	−52097.7	−	103249.i	−0.608134	−	1.20523i
$95$	32308.7	−	48399.3i	0.367291	−	0.550212i
$96$	113573.	−	109192.i	1.25776	−	1.20924i
$97$			20961.5i			0.226200i	0.993584	+	0.113100i	$0.0360780\pi$
$97$			20961.5i			0.226200i	−0.993584	+	0.113100i	$0.963922\pi$
$98$	−29673.6	+	14972.7i	−0.312108	+	0.157484i
$99$	299802.			3.07431
$100$	33411.8	−	45234.8i	0.334118	−	0.452348i
$101$		−	83763.7i		−	0.817057i	−0.912745	−	0.408529i	$-0.866042\pi$
$101$		−	83763.7i		−	0.817057i	0.912745	−	0.408529i	$-0.133958\pi$
$102$	−137921.	−	273338.i	−1.31259	−	2.60135i
$103$	171162.			1.58970			0.794848	−	0.606809i	$-0.207551\pi$
$103$	171162.			1.58970			0.794848	+	0.606809i	$0.207551\pi$
$104$	−17241.3	+	101120.i	−0.156310	+	0.916757i
$105$		−	151485.i		−	1.34090i
$106$	151839.	−	76615.1i	1.31256	−	0.662292i
$107$		−	106661.i		−	0.900628i	−0.892870	−	0.450314i	$-0.851312\pi$
$107$		−	106661.i		−	0.900628i	0.892870	−	0.450314i	$-0.148688\pi$
$108$	−177643.	−	131213.i	−1.46551	−	1.08247i
$109$	−74162.6			−0.597886			−0.298943	−	0.954271i	$-0.596634\pi$
$109$	−74162.6			−0.597886			−0.298943	+	0.954271i	$0.596634\pi$
$110$	56876.6	+	112720.i	0.448179	+	0.888221i
$111$			248236.i			1.91231i
$112$	−147405.	+	45343.8i	−1.11037	+	0.341565i
$113$		−	57356.7i		−	0.422560i	−0.977426	−	0.211280i	$-0.932237\pi$
$113$		−	57356.7i		−	0.422560i	0.977426	−	0.211280i	$-0.0677632\pi$
$114$	−29296.3	+	240324.i	−0.211130	+	1.73195i
$115$	−54190.2			−0.382099
$116$	−90202.1	+	122121.i	−0.622403	+	0.842645i
$117$	281495.			1.90111
$118$	38576.9	+	76453.4i	0.255048	+	0.505466i
$119$			299697.i			1.94006i
$120$	30602.5	−	179484.i	0.194001	−	1.13782i
$121$	203198.			1.26170
$122$	97509.5	+	193248.i	0.593126	+	1.17548i
$123$	−71820.3			−0.428040
$124$	−36217.4	+	49033.2i	−0.211526	+	0.286376i
$125$		−	180557.i		−	1.03357i
$126$	190649.	+	377836.i	1.06981	+	2.12020i
$127$	−263384.			−1.44904			−0.724518	−	0.689256i	$-0.757938\pi$
$127$	−263384.			−1.44904			−0.724518	+	0.689256i	$0.757938\pi$
$128$	−183811.	+	23946.4i	−0.991620	+	0.129186i
$129$			274186.i			1.45068i
$130$	53403.5	+	105837.i	0.277148	+	0.549263i
$131$	30274.3			0.154133			0.0770665	−	0.997026i	$-0.475445\pi$
$131$	30274.3			0.154133			0.0770665	+	0.997026i	$0.475445\pi$
$132$	−422519.	−	312085.i	−2.11063	−	1.55897i
$133$	131578.	−	197108.i	0.644993	−	0.966216i
$134$	−116968.	−	231813.i	−0.562738	−	1.11526i
$135$	−255226.			−1.20529
$136$	−60543.9	+	355090.i	−0.280687	+	1.64623i
$137$	−249038.			−1.13361			−0.566807	−	0.823851i	$-0.691821\pi$
$137$	−249038.			−1.13361			−0.566807	+	0.823851i	$0.691821\pi$
$138$	201281.	−	101563.i	0.899717	−	0.453980i
$139$	−423617.			−1.85967			−0.929837	−	0.367972i	$-0.880052\pi$
$139$	−423617.			−1.85967			−0.929837	+	0.367972i	$0.880052\pi$
$140$	−105891.	+	143361.i	−0.456603	+	0.618176i
$141$	556042.			2.35537
$142$	−302360.	+	152565.i	−1.25836	+	0.634944i
$143$	342007.			1.39860
$144$	149557.	+	486186.i	0.601038	+	1.95387i
$145$			175455.i			0.693020i
$146$	108924.	−	54960.7i	0.422902	−	0.213388i
$147$		−	159805.i		−	0.609953i
$148$	173523.	−	234925.i	0.651181	−	0.881606i
$149$			14258.2i			0.0526136i	0.999654	+	0.0263068i	$0.00837469\pi$
$149$			14258.2i			0.0526136i	−0.999654	+	0.0263068i	$0.991625\pi$
$150$	121804.	+	241397.i	0.442013	+	0.875999i
$151$	257437.			0.918814			0.459407	−	0.888226i	$-0.348062\pi$
$151$	257437.			0.918814			0.459407	+	0.888226i	$0.348062\pi$
$152$	195717.	−	206958.i	0.687099	−	0.726563i
$153$	988489.			3.41384
$154$	231632.	+	459058.i	0.787039	+	1.55979i
$155$			70447.7i			0.235525i
$156$	−396718.	−	293028.i	−1.30518	−	0.964046i
$157$		−	588545.i		−	1.90560i	−0.303605	−	0.952798i	$-0.598190\pi$
$157$		−	588545.i		−	1.90560i	0.303605	−	0.952798i	$-0.401810\pi$
$158$	−367605.	+	185486.i	−1.17149	+	0.591111i
$159$			817717.i			2.56514i
$160$	−154424.	+	148467.i	−0.476888	+	0.458491i
$161$	−220692.			−0.670998
$162$	338371.	−	170736.i	1.01299	−	0.511136i
$163$	−410287.			−1.20953			−0.604767	−	0.796402i	$-0.706734\pi$
$163$	−410287.			−1.20953			−0.604767	+	0.796402i	$0.706734\pi$
$164$	67968.9	+	50203.9i	0.197333	+	0.145757i
$165$	−607047.			−1.73585
$166$	73880.1	−	37278.5i	0.208093	−	0.105000i
$167$	130499.			0.362089			0.181045	−	0.983475i	$-0.442052\pi$
$167$	130499.			0.362089			0.181045	+	0.983475i	$0.442052\pi$
$168$	124630.	−	730954.i	0.340682	−	1.99810i
$169$	−50170.7			−0.135124
$170$	187530.	+	371654.i	0.497677	+	0.986318i
$171$	−650120.	−	433984.i	−1.70021	−	1.13497i
$172$	191662.	−	259483.i	0.493986	−	0.668786i
$173$	−60471.8			−0.153616			−0.0768082	−	0.997046i	$-0.524473\pi$
$173$	−60471.8			−0.153616			−0.0768082	+	0.997046i	$0.524473\pi$
$174$	−328836.	−	651701.i	−0.823391	−	1.63183i
$175$		−	264676.i		−	0.653309i
$176$	181707.	+	590699.i	0.442171	+	1.43742i
$177$	−411734.			−0.987832
$178$	−47482.8	−	94103.4i	−0.112328	−	0.222616i
$179$		−	202401.i		−	0.472150i	−0.971735	−	0.236075i	$-0.924139\pi$
$179$		−	202401.i		−	0.472150i	0.971735	−	0.236075i	$-0.0758611\pi$
$180$	472848.	+	349260.i	1.08778	+	0.803467i
$181$	260264.			0.590498			0.295249	−	0.955420i	$-0.404597\pi$
$181$	260264.			0.590498			0.295249	+	0.955420i	$0.404597\pi$
$182$	217487.	+	431026.i	0.486694	+	0.964550i
$183$	−1.04072e6			−2.29725
$184$	−261482.	−	44583.5i	−0.569374	−	0.0970799i
$185$		−	337524.i		−	0.725063i
$186$	−132032.	−	261667.i	−0.279832	−	0.554584i
$187$	1.20098e6			2.51149
$188$	−526224.	−	388685.i	−1.08587	−	0.802053i
$189$	−1.03942e6			−2.11658
$190$	39833.8	−	326766.i	0.0800512	−	0.656679i
$191$		−	33320.5i		−	0.0660888i	−0.999454	−	0.0330444i	$-0.989480\pi$
$191$		−	33320.5i		−	0.0660888i	0.999454	−	0.0330444i	$-0.0105203\pi$
$192$	295330.	−	840879.i	0.578169	−	1.64619i
$193$			689608.i			1.33263i	0.745671	+	0.666314i	$0.232129\pi$
$193$			689608.i			1.33263i	−0.745671	+	0.666314i	$0.767871\pi$
$194$	53416.4	+	105863.i	0.101899	+	0.201948i
$195$	−569978.			−1.07342
$196$	−111707.	+	151235.i	−0.207702	+	0.281199i
$197$			636722.i			1.16892i	0.811423	+	0.584460i	$0.198694\pi$
$197$			636722.i			1.16892i	−0.811423	+	0.584460i	$0.801306\pi$
$198$	1.51411e6	−	763991.i	2.74469	−	1.38492i
$199$		−	379147.i		−	0.678695i	−0.940661	−	0.339348i	$-0.889794\pi$
$199$		−	379147.i		−	0.678695i	0.940661	−	0.339348i	$-0.110206\pi$
$200$	53469.0	−	313596.i	0.0945208	−	0.554364i
$201$	1.24841e6			2.17955
$202$	−213456.	−	423037.i	−0.368070	−	0.729457i
$203$			714546.i			1.21700i
$204$	−1.39310e6	−	1.02899e6i	−2.34373	−	1.73115i
$205$	97653.3			0.162294
$206$	864428.	−	436174.i	1.41926	−	0.716130i
$207$			727906.i			1.18073i
$208$	170611.	+	554629.i	0.273432	+	0.888882i
$209$	−789872.	−	527275.i	−1.25081	−	0.834971i
$210$	−386031.	−	765052.i	−0.604051	−	1.19713i
$211$		−	1.10273e6i		−	1.70515i	−0.522608	−	0.852573i	$-0.675041\pi$
$211$		−	1.10273e6i		−	1.70515i	0.522608	−	0.852573i	$-0.324959\pi$
$212$	571602.	−	773867.i	0.873482	−	1.18257i
$213$		−	1.62834e6i		−	2.45921i
$214$	−271805.	−	538675.i	−0.405717	−	0.804067i
$215$		−	372808.i		−	0.550033i
$216$	−1.23153e6	−	209980.i	−1.79602	−	0.306227i
$217$			286901.i			0.413602i
$218$	−374547.	+	188989.i	−0.533784	+	0.269337i
$219$			586599.i			0.826478i
$220$	574494.	+	424339.i	0.800256	+	0.591093i
$221$	1.12764e6			1.55307
$222$	632584.	+	1.25368e6i	0.861462	+	1.70728i
$223$	−12624.3			−0.0169998			−0.00849991	−	0.999964i	$-0.502706\pi$
$223$	−12624.3			−0.0169998			−0.00849991	+	0.999964i	$0.502706\pi$
$224$	−628899.	+	604637.i	−0.837453	+	0.805147i
$225$	−872979.			−1.14960
$226$	−146163.	−	289672.i	−0.190356	−	0.377255i
$227$			581264.i			0.748701i	0.927287	+	0.374351i	$0.122134\pi$
$227$			581264.i			0.748701i	−0.927287	+	0.374351i	$0.877866\pi$
$228$	464465.	+	1.28838e6i	0.591720	+	1.64137i
$229$			1.01092e6i			1.27388i	0.770915	+	0.636938i	$0.219799\pi$
$229$			1.01092e6i			1.27388i	−0.770915	+	0.636938i	$0.780201\pi$
$230$	−273680.	+	138094.i	−0.341133	+	0.172129i
$231$	−2.47222e6			−3.04830
$232$	−144351.	+	846616.i	−0.176075	+	1.03268i
$233$	−722717.			−0.872124			−0.436062	−	0.899917i	$-0.643627\pi$
$233$	−722717.			−0.872124			−0.436062	+	0.899917i	$0.643627\pi$
$234$	1.42165e6	−	717338.i	1.69728	−	0.856415i
$235$	−756044.			−0.893053
$236$	389654.	+	287811.i	0.455407	+	0.336377i
$237$		−	1.97971e6i		−	2.28944i
$238$	763721.	+	1.51357e6i	0.873962	+	1.73205i
$239$		−	586425.i		−	0.664076i	−0.943266	−	0.332038i	$-0.892264\pi$
$239$		−	586425.i		−	0.664076i	0.943266	−	0.332038i	$-0.107736\pi$
$240$	−302827.	−	984442.i	−0.339365	−	1.10322i
$241$			636052.i			0.705424i	0.935732	+	0.352712i	$0.114740\pi$
$241$			636052.i			0.705424i	−0.935732	+	0.352712i	$0.885260\pi$
$242$	1.02622e6	−	517813.i	1.12643	−	0.568374i
$243$			145207.i			0.157751i
$244$	984915.	+	727488.i	1.05907	+	0.782261i
$245$			217285.i			0.231267i
$246$	−362718.	+	183021.i	−0.382148	+	0.192825i
$247$	−741639.	−	495077.i	−0.773482	−	0.516334i
$248$	−57958.9	+	339929.i	−0.0598399	+	0.350961i
$249$			397875.i			0.406676i
$250$	−460115.	−	911876.i	−0.465604	−	0.922753i
$251$	395054.			0.395797			0.197898	−	0.980223i	$-0.436588\pi$
$251$	395054.			0.395797			0.197898	+	0.980223i	$0.436588\pi$
$252$	1.92569e6	+	1.42237e6i	1.91023	+	1.41095i
$253$			884380.i			0.868636i
$254$	−1.33018e6	+	671184.i	−1.29368	+	0.652766i
$255$	−2.00152e6			−1.92756
$256$	−867286.	+	589345.i	−0.827108	+	0.562043i
$257$			1.32766e6i			1.25388i	0.779069	+	0.626939i	$0.215692\pi$
$257$			1.32766e6i			1.25388i	−0.779069	+	0.626939i	$0.784308\pi$
$258$	698712.	+	1.38474e6i	0.653505	+	1.29514i
$259$		−	1.37458e6i		−	1.27327i
$260$	539413.	+	398427.i	0.494866	+	0.365523i
$261$	2.35679e6			2.14150
$262$	152896.	−	77148.4i	0.137608	−	0.0694342i
$263$			689459.i			0.614638i	0.951607	+	0.307319i	$0.0994318\pi$
$263$			689459.i			0.614638i	−0.951607	+	0.307319i	$0.900568\pi$
$264$	−2.92916e6	−	499431.i	−2.58663	−	0.441027i
$265$		−	1.11184e6i		−	0.972586i
$266$	162224.	−	1.33077e6i	0.140576	−	1.15318i
$267$	506787.			0.435058
$268$	−1.18146e6	−	872665.i	−1.00481	−	0.742182i
$269$	977952.			0.824018			0.412009	−	0.911180i	$-0.364827\pi$
$269$	977952.			0.824018			0.412009	+	0.911180i	$0.364827\pi$
$270$	−1.28898e6	+	650396.i	−1.07606	+	0.542961i
$271$		−	1.49359e6i		−	1.23540i	−0.786413	−	0.617701i	$-0.788064\pi$
$271$		−	1.49359e6i		−	1.23540i	0.786413	−	0.617701i	$-0.211936\pi$
$272$	599112.	+	1.94761e6i	0.491005	+	1.59618i
$273$	−2.32126e6			−1.88502
$274$	−1.25773e6	+	634628.i	−1.01207	+	0.510673i
$275$	−1.06064e6			−0.845737
$276$	757729.	−	1.02586e6i	0.598744	−	0.810613i
$277$		−	1.32182e6i		−	1.03507i	−0.855661	−	0.517537i	$-0.826849\pi$
$277$		−	1.32182e6i		−	1.03507i	0.855661	−	0.517537i	$-0.173151\pi$
$278$	−2.13942e6	+	1.07951e6i	−1.66029	+	0.837751i
$279$	946284.			0.727798
$280$	−169458.	+	993870.i	−0.129171	+	0.757590i
$281$		−	2.25632e6i		−	1.70465i	−0.523016	−	0.852323i	$-0.675193\pi$
$281$		−	2.25632e6i		−	1.70465i	0.523016	−	0.852323i	$-0.324807\pi$
$282$	2.80821e6	−	1.41697e6i	2.10284	−	1.06105i
$283$	849766.			0.630715			0.315358	−	0.948973i	$-0.397876\pi$
$283$	849766.			0.630715			0.315358	+	0.948973i	$0.397876\pi$
$284$	−1.13824e6	+	1.54102e6i	−0.837412	+	1.13374i
$285$	1.31638e6	+	878741.i	0.959994	+	0.640839i
$286$	1.72726e6	−	871540.i	1.24865	−	0.630046i
$287$	397696.			0.285001
$288$	1.99427e6	+	2.07430e6i	1.41678	+	1.47363i
$289$	2.53993e6			1.78886
$290$	447114.	+	886110.i	0.312193	+	0.618718i
$291$	−570116.			−0.394667
$292$	410045.	−	555143.i	0.281433	−	0.381020i
$293$	1.23388e6			0.839659			0.419830	−	0.907603i	$-0.362090\pi$
$293$	1.23388e6			0.839659			0.419830	+	0.907603i	$0.362090\pi$
$294$	−407233.	−	807072.i	−0.274773	−	0.544557i
$295$	559830.			0.374542
$296$	277689.	−	1.62864e6i	0.184217	−	1.08043i
$297$			4.16527e6i			2.74001i
$298$	36334.3	+	72008.9i	0.0237015	+	0.0469727i
$299$			830376.i			0.537152i
$300$	1.23031e6	+	908745.i	0.789244	+	0.582960i
$301$		−	1.51827e6i		−	0.965902i
$302$	1.30015e6	−	656029.i	0.820304	−	0.413910i
$303$	2.27823e6			1.42558
$304$	461046.	−	1.54396e6i	0.286128	−	0.958191i
$305$	1.41506e6			0.871015
$306$	4.99222e6	−	2.51898e6i	3.04783	−	1.53788i
$307$		−	19289.4i		−	0.0116808i	−0.999983	−	0.00584041i	$-0.998141\pi$
$307$		−	19289.4i		−	0.0116808i	0.999983	−	0.00584041i	$-0.00185907\pi$
$308$	2.33965e6	+	1.72813e6i	1.40531	+	1.03801i
$309$			4.65531e6i			2.77366i
$310$	179523.	+	355786.i	0.106100	+	0.210274i
$311$		−	696484.i		−	0.408329i	−0.978937	−	0.204165i	$-0.934552\pi$
$311$		−	696484.i		−	0.408329i	0.978937	−	0.204165i	$-0.0654478\pi$
$312$	−2.75029e6	−	468933.i	−1.59953	−	0.272725i
$313$	−1.56308e6			−0.901819			−0.450909	−	0.892570i	$-0.648900\pi$
$313$	−1.56308e6			−0.901819			−0.450909	+	0.892570i	$0.648900\pi$
$314$	−1.49980e6	−	2.97236e6i	−0.858438	−	1.70129i
$315$	2.76671e6			1.57104
$316$	−1.38386e6	+	1.87354e6i	−0.779603	+	1.05547i
$317$	−1.55098e6			−0.866880			−0.433440	−	0.901183i	$-0.642700\pi$
$317$	−1.55098e6			−0.866880			−0.433440	+	0.901183i	$0.642700\pi$
$318$	2.08380e6	+	4.12976e6i	1.15555	+	2.29011i
$319$	2.86341e6			1.57546
$320$	−401557.	+	1.14333e6i	−0.219216	+	0.624163i
$321$	2.90099e6			1.57139
$322$	−1.11457e6	+	562391.i	−0.599057	+	0.302273i
$323$	−2.60431e6	−	1.73850e6i	−1.38895	−	0.927188i
$324$	1.27381e6	−	1.72455e6i	0.674126	−	0.912670i
$325$	−995871.			−0.522992
$326$	−2.07209e6	+	1.04554e6i	−1.07985	+	0.544874i
$327$		−	2.01710e6i		−	1.04317i
$328$	471203.	+	80341.5i	0.241837	+	0.0412340i
$329$	−3.07901e6			−1.56827
$330$	−3.06580e6	+	1.54695e6i	−1.54974	+	0.781971i
$331$		−	515679.i		−	0.258708i	−0.991598	−	0.129354i	$-0.958710\pi$
$331$		−	515679.i		−	0.258708i	0.991598	−	0.129354i	$-0.0412903\pi$
$332$	278123.	−	376539.i	0.138482	−	0.187484i
$333$	−4.53377e6			−2.24052
$334$	659066.	−	332552.i	0.323268	−	0.163115i
$335$	−1.69745e6			−0.826389
$336$	−1.23328e6	−	4.00917e6i	−0.595953	−	1.93734i
$337$		−	180334.i		−	0.0864972i	−0.999064	−	0.0432486i	$-0.986229\pi$
$337$		−	180334.i		−	0.0864972i	0.999064	−	0.0432486i	$-0.0137708\pi$
$338$	−253380.	+	127851.i	−0.120637	+	0.0608712i
$339$	1.56001e6			0.737271
$340$	1.89418e6	+	1.39910e6i	0.888638	+	0.656375i
$341$	1.14970e6			0.535425
$342$	−4.38926e6	−	535065.i	−2.02921	−	0.247367i
$343$		−	1.64636e6i		−	0.755594i
$344$	306717.	−	1.79889e6i	0.139747	−	0.819614i
$345$		−	1.47388e6i		−	0.666676i
$346$	−305404.	+	154101.i	−0.137146	+	0.0692015i
$347$	2.02177e6			0.901379			0.450690	−	0.892681i	$-0.351178\pi$
$347$	2.02177e6			0.901379			0.450690	+	0.892681i	$0.351178\pi$
$348$	−3.32148e6	−	2.45334e6i	−1.47022	−	1.08595i
$349$			3.23137e6i			1.42011i	0.704144	+	0.710057i	$0.251331\pi$
$349$			3.23137e6i			1.42011i	−0.704144	+	0.710057i	$0.748669\pi$
$350$	−674477.	−	1.33671e6i	−0.294304	−	0.583265i
$351$			3.91092e6i			1.69438i
$352$	2.42297e6	+	2.52019e6i	1.04230	+	1.08412i
$353$	368290.			0.157309			0.0786545	−	0.996902i	$-0.474938\pi$
$353$	368290.			0.157309			0.0786545	+	0.996902i	$0.474938\pi$
$354$	−2.07940e6	+	1.04923e6i	−0.881922	+	0.445001i
$355$			2.21403e6i			0.932424i
$356$	−479610.	−	354255.i	−0.200569	−	0.148146i
$357$	−8.15124e6			−3.38496
$358$	−515781.	−	1.02220e6i	−0.212695	−	0.421529i
$359$			61762.2i			0.0252922i	0.999920	+	0.0126461i	$0.00402549\pi$
$359$			61762.2i			0.0252922i	−0.999920	+	0.0126461i	$0.995975\pi$
$360$	3.27808e6	+	558922.i	1.33310	+	0.227298i
$361$	949567.	+	2.28679e6i	0.383493	+	0.923544i
$362$	1.31443e6	−	663236.i	0.527188	−	0.266009i
$363$			5.52665e6i			2.20138i
$364$	2.19678e6	+	1.62261e6i	0.869026	+	0.641889i
$365$		−	797592.i		−	0.313364i
$366$	−5.25603e6	+	2.65209e6i	−2.05095	+	1.03487i
$367$			529501.i			0.205211i	0.994722	+	0.102606i	$0.0327180\pi$
$367$			529501.i			0.205211i	−0.994722	+	0.102606i	$0.967282\pi$
$368$	−1.43419e6	+	441176.i	−0.552061	+	0.169821i
$369$		−	1.31172e6i		−	0.501505i
$370$	−860118.	−	1.70462e6i	−0.326628	−	0.647325i
$371$		−	4.52801e6i		−	1.70794i
$372$	−1.33362e6	−	985053.i	−0.499661	−	0.369064i
$373$	4.19693e6			1.56192			0.780961	−	0.624580i	$-0.214730\pi$
$373$	4.19693e6			1.56192			0.780961	+	0.624580i	$0.214730\pi$
$374$	6.06537e6	−	3.06047e6i	2.24222	−	1.13138i
$375$	4.91084e6			1.80334
$376$	−3.64811e6	−	622014.i	−1.33076	−	0.226898i
$377$	2.68856e6			0.974241
$378$	−5.24942e6	+	2.64876e6i	−1.88965	+	0.953483i
$379$			870364.i			0.311245i	0.987817	+	0.155623i	$0.0497384\pi$
$379$			870364.i			0.311245i	−0.987817	+	0.155623i	$0.950262\pi$
$380$	−631528.	−	1.75179e6i	−0.224354	−	0.622335i
$381$		−	7.16358e6i		−	2.52824i
$382$	−84911.0	−	168280.i	−0.0297718	−	0.0590031i
$383$	−3.88095e6			−1.35189			−0.675945	−	0.736952i	$-0.736264\pi$
$383$	−3.88095e6			−1.35189			−0.675945	+	0.736952i	$0.736264\pi$
$384$	−651300.	−	4.99933e6i	−0.225400	−	1.73015i
$385$	3.36145e6			1.15578
$386$	1.75734e6	+	3.48276e6i	0.600325	+	1.18975i
$387$	−5.00771e6			−1.69966
$388$	539543.	+	398523.i	0.181948	+	0.134392i
$389$		−	55797.8i		−	0.0186958i	−0.999956	−	0.00934788i	$-0.997024\pi$
$389$		−	55797.8i		−	0.0186958i	0.999956	−	0.00934788i	$-0.00297557\pi$
$390$	−2.87859e6	+	1.45248e6i	−0.958338	+	0.483559i
$391$			2.91592e6i			0.964570i
$392$	−178765.	+	1.04846e6i	−0.0587580	+	0.344616i
$393$			823409.i			0.268927i
$394$	1.62257e6	+	3.21568e6i	0.526578	+	1.04359i
$395$			2.69178e6i			0.868055i
$396$	5.69990e6	−	7.71685e6i	1.82654	−	2.47287i
$397$			2.63936e6i			0.840470i	0.907415	+	0.420235i	$0.138052\pi$
$397$			2.63936e6i			0.840470i	−0.907415	+	0.420235i	$0.861948\pi$
$398$	−966185.	−	1.91483e6i	−0.305740	−	0.605929i
$399$	5.36099e6	+	3.57870e6i	1.68583	+	1.12536i
$400$	−529103.	−	1.72003e6i	−0.165345	−	0.537508i
$401$		−	4.73912e6i		−	1.47176i	−0.677112	−	0.735880i	$-0.736769\pi$
$401$		−	4.73912e6i		−	1.47176i	0.677112	−	0.735880i	$-0.263231\pi$
$402$	6.30491e6	−	3.18134e6i	1.94587	−	0.981849i
$403$	1.07950e6			0.331099
$404$	−2.15606e6	−	1.59253e6i	−0.657215	−	0.485439i
$405$		−	2.47772e6i		−	0.750611i
$406$	1.82089e6	+	3.60871e6i	0.548237	+	1.08652i
$407$	−5.50837e6			−1.64830
$408$	−9.65784e6	−	1.64669e6i	−2.87230	−	0.489735i
$409$			1.03043e6i			0.304585i	0.988335	+	0.152293i	$0.0486656\pi$
$409$			1.03043e6i			0.304585i	−0.988335	+	0.152293i	$0.951334\pi$
$410$	493184.	−	248851.i	0.144894	−	0.0731106i
$411$		−	6.77342e6i		−	1.97790i
$412$	3.25416e6	−	4.40567e6i	0.944487	−	1.27870i
$413$	2.27992e6			0.657727
$414$	1.85493e6	+	3.67619e6i	0.531897	+	1.05414i
$415$		−	540987.i		−	0.154194i
$416$	2.27502e6	+	2.36630e6i	0.644542	+	0.670404i
$417$		−	1.15217e7i		−	3.24471i
$418$	−5.33280e6	−	650084.i	−1.49284	−	0.181982i
$419$	792428.			0.220508			0.110254	−	0.993903i	$-0.464834\pi$
$419$	792428.			0.220508			0.110254	+	0.993903i	$0.464834\pi$
$420$	−3.89919e6	−	2.88006e6i	−1.07858	−	0.796669i
$421$	408226.			0.112252			0.0561262	−	0.998424i	$-0.482125\pi$
$421$	408226.			0.112252			0.0561262	+	0.998424i	$0.482125\pi$
$422$	−2.81009e6	−	5.56916e6i	−0.768139	−	1.52233i
$423$			1.01555e7i			2.75963i
$424$	914736.	−	5.36492e6i	0.247105	−	1.44927i
$425$	−3.49707e6			−0.939143
$426$	−4.14952e6	−	8.22369e6i	−1.10783	−	2.19555i
$427$	5.76288e6			1.52957
$428$	−2.74543e6	−	2.02786e6i	−0.724437	−	0.535091i
$429$			9.30200e6i			2.44024i
$430$	−950031.	−	1.88281e6i	−0.247780	−	0.491061i
$431$	−1.00984e6			−0.261854			−0.130927	−	0.991392i	$-0.541795\pi$
$431$	−1.00984e6			−0.261854			−0.130927	+	0.991392i	$0.541795\pi$
$432$	−6.75477e6	+	2.07786e6i	−1.74141	+	0.535681i
$433$			1.59950e6i			0.409982i	0.978764	+	0.204991i	$0.0657165\pi$
$433$			1.59950e6i			0.409982i	−0.978764	+	0.204991i	$0.934283\pi$
$434$	731113.	+	1.44895e6i	0.186320	+	0.369257i
$435$	−4.77208e6			−1.20916
$436$	−1.40999e6	+	1.90893e6i	−0.355223	+	0.480921i
$437$	1.28020e6	−	1.91777e6i	0.320682	−	0.480390i
$438$	1.49484e6	+	2.96253e6i	0.372314	+	0.737867i
$439$	6.61321e6			1.63776			0.818882	−	0.573962i	$-0.194594\pi$
$439$	6.61321e6			1.63776			0.818882	+	0.573962i	$0.194594\pi$
$440$	3.98275e6	+	679070.i	0.980734	+	0.167218i
$441$	2.91866e6			0.714640
$442$	5.69499e6	−	2.87359e6i	1.38656	−	0.699630i
$443$	2.90633e6			0.703617			0.351808	−	0.936072i	$-0.385567\pi$
$443$	2.90633e6			0.703617			0.351808	+	0.936072i	$0.385567\pi$
$444$	6.38955e6	+	4.71952e6i	1.53820	+	1.13616i
$445$	−689072.			−0.164955
$446$	−63757.1	+	32170.6i	−0.0151772	+	0.00765812i
$447$	−387798.			−0.0917988
$448$	−1.63536e6	+	4.65627e6i	−0.384962	+	1.09608i
$449$		−	1.22462e6i		−	0.286671i	−0.989674	−	0.143336i	$-0.954217\pi$
$449$		−	1.22462e6i		−	0.286671i	0.989674	−	0.143336i	$-0.0457828\pi$
$450$	−4.40885e6	+	2.22462e6i	−1.02635	+	0.517876i
$451$		−	1.59369e6i		−	0.368947i
$452$	−1.47635e6	−	1.09048e6i	−0.339894	−	0.251056i
$453$			7.00184e6i			1.60312i
$454$	1.48124e6	+	2.93559e6i	0.337277	+	0.668429i
$455$	3.15618e6			0.714717
$456$	5.62891e6	+	5.32317e6i	1.26769	+	1.19883i
$457$	−3.30328e6			−0.739869			−0.369935	−	0.929058i	$-0.620620\pi$
$457$	−3.30328e6			−0.739869			−0.369935	+	0.929058i	$0.620620\pi$
$458$	2.57614e6	+	5.10549e6i	0.573859	+	1.13730i
$459$			1.37334e7i			3.04262i
$460$	−1.03027e6	+	1.39484e6i	−0.227017	+	0.307349i
$461$		−	7.00106e6i		−	1.53430i	−0.641465	−	0.767152i	$-0.721673\pi$
$461$		−	7.00106e6i		−	1.53430i	0.641465	−	0.767152i	$-0.278327\pi$
$462$	−1.24856e7	+	6.29999e6i	−2.72147	+	1.37320i
$463$		−	3.15394e6i		−	0.683755i	−0.939745	−	0.341878i	$-0.888937\pi$
$463$		−	3.15394e6i		−	0.683755i	0.939745	−	0.341878i	$-0.111063\pi$
$464$	1.42842e6	+	4.64357e6i	0.308008	+	1.00128i
$465$	−1.91606e6			−0.410938
$466$	−3.64998e6	+	1.84171e6i	−0.778620	+	0.392877i
$467$	2.07779e6			0.440869			0.220435	−	0.975402i	$-0.429252\pi$
$467$	2.07779e6			0.440869			0.220435	+	0.975402i	$0.429252\pi$
$468$	5.35184e6	−	7.24563e6i	1.12951	−	1.52919i
$469$	−6.91291e6			−1.45121
$470$	−3.81829e6	+	1.92664e6i	−0.797305	+	0.402305i
$471$	1.60074e7			3.32483
$472$	2.70132e6	+	460584.i	0.558113	+	0.0951599i
$473$	−6.08419e6			−1.25040
$474$	−5.04491e6	−	9.99822e6i	−1.03135	−	2.04398i
$475$	2.29999e6	+	1.53534e6i	0.467726	+	0.312228i
$476$	7.71413e6	+	5.69789e6i	1.56052	+	1.15265i
$477$	−1.49347e7			−3.00539
$478$	−1.49440e6	−	2.96166e6i	−0.299155	−	0.592877i
$479$		−	8.24274e6i		−	1.64147i	−0.571310	−	0.820734i	$-0.693565\pi$
$479$		−	8.24274e6i		−	1.64147i	0.571310	−	0.820734i	$-0.306435\pi$
$480$	−4.03805e6	−	4.20008e6i	−0.799961	−	0.832060i
$481$	−5.17201e6			−1.01929
$482$	1.62086e6	+	3.21229e6i	0.317781	+	0.629792i
$483$		−	6.00243e6i		−	1.17074i
$484$	3.86324e6	−	5.23028e6i	0.749616	−	1.01487i
$485$	775180.			0.149640
$486$	370032.	+	733345.i	0.0710639	+	0.140837i
$487$	2.01001e6			0.384039			0.192020	−	0.981391i	$-0.438496\pi$
$487$	2.01001e6			0.384039			0.192020	+	0.981391i	$0.438496\pi$
$488$	6.82804e6	+	1.16420e6i	1.29792	+	0.221299i
$489$		−	1.11591e7i		−	2.11036i
$490$	553710.	+	1.09737e6i	0.104182	+	0.206472i
$491$	−6.35888e6			−1.19036			−0.595178	−	0.803594i	$-0.702918\pi$
$491$	−6.35888e6			−1.19036			−0.595178	+	0.803594i	$0.702918\pi$
$492$	−1.36546e6	+	1.84864e6i	−0.254312	+	0.344302i
$493$	9.44105e6			1.74946
$494$	−5.00716e6	−	610388.i	−0.923153	−	0.112535i
$495$		−	1.10871e7i		−	2.03378i
$496$	573532.	+	1.86446e6i	0.104678	+	0.340290i
$497$			9.01673e6i			1.63741i
$498$	1.01391e6	+	2.00941e6i	0.183201	+	0.363074i
$499$	−1.82256e6			−0.327665			−0.163833	−	0.986488i	$-0.552386\pi$
$499$	−1.82256e6			−0.327665			−0.163833	+	0.986488i	$0.552386\pi$
$500$	−4.64749e6	−	3.43278e6i	−0.831369	−	0.614074i
$501$			3.54935e6i			0.631763i
$502$	1.99516e6	−	1.00672e6i	0.353361	−	0.178299i
$503$		−	5.97846e6i		−	1.05358i	−0.849994	−	0.526792i	$-0.823395\pi$
$503$		−	5.97846e6i		−	1.05358i	0.849994	−	0.526792i	$-0.176605\pi$
$504$	1.33501e7	+	2.27623e6i	2.34103	+	0.399153i
$505$	−3.09769e6			−0.540516
$506$	2.25368e6	+	4.46644e6i	0.391305	+	0.775505i
$507$		−	1.36456e6i		−	0.235761i
$508$	−5.00750e6	+	6.77944e6i	−0.860917	+	1.16556i
$509$	−4.68133e6			−0.800894			−0.400447	−	0.916320i	$-0.631145\pi$
$509$	−4.68133e6			−0.800894			−0.400447	+	0.916320i	$0.631145\pi$
$510$	−1.01084e7	+	5.10049e6i	−1.72090	+	0.868333i
$511$		−	3.24822e6i		−	0.550292i
$512$	−2.87827e6	+	5.18652e6i	−0.485239	+	0.874381i
$513$	6.02950e6	−	9.03236e6i	1.01155	−	1.51533i
$514$	3.38330e6	+	6.70517e6i	0.564850	+	1.11944i
$515$		−	6.32977e6i		−	1.05165i
$516$	7.05749e6	+	5.21288e6i	1.16688	+	0.861893i
$517$			1.23386e7i			2.03020i
$518$	−3.50286e6	−	6.94211e6i	−0.573586	−	1.13676i
$519$		−	1.64473e6i		−	0.268026i
$520$	3.73954e6	+	637604.i	0.606471	+	0.103405i
$521$		−	2.59329e6i		−	0.418559i	−0.977856	−	0.209280i	$-0.932888\pi$
$521$		−	2.59329e6i		−	0.418559i	0.977856	−	0.209280i	$-0.0671119\pi$
$522$	1.19026e7	−	6.00583e6i	1.91190	−	0.964710i
$523$			1.21768e7i			1.94661i	0.229511	+	0.973306i	$0.426287\pi$
$523$			1.21768e7i			1.94661i	−0.229511	+	0.973306i	$0.573713\pi$
$524$	575580.	−	779253.i	0.0915751	−	0.123980i
$525$	7.19873e6			1.13988
$526$	1.75696e6	+	3.48201e6i	0.276884	+	0.548739i
$527$	3.79072e6			0.594559
$528$	−1.60660e7	+	4.94212e6i	−2.50798	+	0.771487i
$529$	4.28911e6			0.666389
$530$	−2.83332e6	−	5.61519e6i	−0.438133	−	0.868310i
$531$		−	7.51987e6i		−	1.15737i
$532$	−2.57192e6	−	7.13424e6i	−0.393984	−	1.09287i
$533$		−	1.49638e6i		−	0.228151i
$534$	2.55945e6	−	1.29145e6i	0.388413	−	0.195986i
$535$	−3.94445e6			−0.595802
$536$	−8.19063e6	−	1.39653e6i	−1.23142	−	0.209960i
$537$	5.50496e6			0.823794
$538$	4.93900e6	−	2.49213e6i	0.735671	−	0.371206i
$539$	3.54607e6			0.525746
$540$	−4.85240e6	+	6.56946e6i	−0.716098	+	0.969495i
$541$			2.89110e6i			0.424688i	0.977195	+	0.212344i	$0.0681097\pi$
$541$			2.89110e6i			0.424688i	−0.977195	+	0.212344i	$0.931890\pi$
$542$	−3.80614e6	−	7.54316e6i	−0.556527	−	1.10295i
$543$			7.07875e6i			1.03028i
$544$	7.98886e6	+	8.30942e6i	1.15741	+	1.20385i
$545$			2.74262e6i			0.395526i
$546$	−1.17232e7	+	5.91529e6i	−1.68292	+	0.849169i
$547$			5.14595e6i			0.735355i	0.929953	+	0.367678i	$0.119847\pi$
$547$			5.14595e6i			0.735355i	−0.929953	+	0.367678i	$0.880153\pi$
$548$	−4.73477e6	+	6.41020e6i	−0.673515	+	0.911843i
$549$		−	1.90077e7i		−	2.69153i
$550$	−5.35660e6	+	2.70284e6i	−0.755062	+	0.380990i
$551$	−6.20929e6	−	4.14498e6i	−0.871290	−	0.581625i
$552$	1.21259e6	−	7.11187e6i	0.169382	−	0.993427i
$553$			1.09624e7i			1.52438i
$554$	−3.36840e6	−	6.67564e6i	−0.466283	−	0.924100i
$555$	9.18009e6			1.26507
$556$	−8.05389e6	+	1.09038e7i	−1.10489	+	1.49586i
$557$			1.15665e7i			1.57967i	0.613323	+	0.789833i	$0.289833\pi$
$557$			1.15665e7i			1.57967i	−0.613323	+	0.789833i	$0.710167\pi$
$558$	4.77907e6	−	2.41143e6i	0.649767	−	0.327860i
$559$	−5.71266e6			−0.773231
$560$	1.67687e6	+	5.45123e6i	0.225959	+	0.734555i
$561$			3.26646e7i			4.38197i
$562$	−5.74980e6	−	1.13952e7i	−0.767913	−	1.52188i
$563$		−	1.26700e7i		−	1.68463i	−0.538986	−	0.842315i	$-0.681193\pi$
$563$		−	1.26700e7i		−	1.68463i	0.538986	−	0.842315i	$-0.318807\pi$
$564$	1.05716e7	−	1.43124e7i	1.39940	−	1.89459i
$565$	−2.12112e6			−0.279540
$566$	4.29162e6	−	2.16547e6i	0.563093	−	0.284126i
$567$		−	1.00906e7i		−	1.31813i
$568$	−1.82153e6	+	1.06833e7i	−0.236901	+	1.38942i
$569$			6.08549e6i			0.787980i	0.919115	+	0.393990i	$0.128906\pi$
$569$			6.08549e6i			0.787980i	−0.919115	+	0.393990i	$0.871094\pi$
$570$	8.88748e6	+	1.08341e6i	1.14575	+	0.139671i
$571$	9.25086e6			1.18739			0.593693	−	0.804692i	$-0.297669\pi$
$571$	9.25086e6			1.18739			0.593693	+	0.804692i	$0.297669\pi$
$572$	6.50229e6	−	8.80318e6i	0.830953	−	1.12499i
$573$	906260.			0.115310
$574$	2.00851e6	−	1.01345e6i	0.254445	−	0.128388i
$575$		−	2.57518e6i		−	0.324817i
$576$	1.53577e7	+	5.39389e6i	1.92873	+	0.677401i
$577$	−3.88697e6			−0.486040			−0.243020	−	0.970021i	$-0.578138\pi$
$577$	−3.88697e6			−0.486040			−0.243020	+	0.970021i	$0.578138\pi$
$578$	1.28276e7	−	6.47254e6i	1.59707	−	0.805852i
$579$	−1.87562e7			−2.32513
$580$	4.51617e6	+	3.33578e6i	0.557443	+	0.411745i
$581$		−	2.20319e6i		−	0.270776i
$582$	−2.87929e6	+	1.45283e6i	−0.352353	+	0.177791i
$583$	−1.81452e7			−2.21100
$584$	656196.	−	3.84859e6i	0.0796163	−	0.466949i
$585$		−	1.04100e7i		−	1.25766i
$586$	6.23152e6	−	3.14431e6i	0.749635	−	0.378252i
$587$	2.42989e6			0.291066			0.145533	−	0.989353i	$-0.453510\pi$
$587$	2.42989e6			0.291066			0.145533	+	0.989353i	$0.453510\pi$
$588$	−4.11334e6	−	3.03824e6i	−0.490627	−	0.362392i
$589$	−2.49312e6	−	1.66427e6i	−0.296111	−	0.197668i
$590$	2.82734e6	−	1.42662e6i	0.334386	−	0.168725i
$591$	−1.73178e7			−2.03950
$592$	−2.74787e6	−	8.93287e6i	−0.322249	−	1.04758i
$593$	−1.21632e7			−1.42040			−0.710199	−	0.704001i	$-0.751395\pi$
$593$	−1.21632e7			−1.42040			−0.710199	+	0.704001i	$0.751395\pi$
$594$	1.06144e7	+	2.10361e7i	1.23433	+	2.44624i
$595$	1.10831e7			1.28343
$596$	367002.	+	271079.i	0.0423207	+	0.0312594i
$597$	1.03121e7			1.18417
$598$	2.11606e6	+	4.19370e6i	0.241977	+	0.479561i
$599$	−7.66883e6			−0.873297			−0.436649	−	0.899632i	$-0.643835\pi$
$599$	−7.66883e6			−0.873297			−0.436649	+	0.899632i	$0.643835\pi$
$600$	8.52927e6	+	1.45427e6i	0.967239	+	0.164917i
$601$		−	925541.i		−	0.104522i	−0.998633	−	0.0522612i	$-0.983357\pi$
$601$		−	925541.i		−	0.104522i	0.998633	−	0.0522612i	$-0.0166429\pi$
$602$	−3.86903e6	−	7.66781e6i	−0.435122	−	0.862343i
$603$			2.28008e7i			2.55363i
$604$	4.89443e6	−	6.62636e6i	0.545896	−	0.739065i
$605$		−	7.51452e6i		−	0.834666i
$606$	1.15059e7	−	5.80565e6i	1.27274	−	0.642198i
$607$	3.05032e6			0.336027			0.168013	−	0.985785i	$-0.446265\pi$
$607$	3.05032e6			0.336027			0.168013	+	0.985785i	$0.446265\pi$
$608$	−1.60605e6	−	8.97244e6i	−0.176198	−	0.984355i
$609$	−1.94344e7			−2.12339
$610$	7.14656e6	−	3.60602e6i	0.777629	−	0.392377i
$611$			1.15851e7i			1.25545i
$612$	1.87933e7	−	2.54435e7i	2.02827	−	2.74598i
$613$			9.58896e6i			1.03067i	0.856988	+	0.515336i	$0.172333\pi$
$613$			9.58896e6i			1.03067i	−0.856988	+	0.515336i	$0.827667\pi$
$614$	−49155.5	−	97418.4i	−0.00526200	−	0.0104285i
$615$			2.65600e6i			0.283166i
$616$	1.62199e7	+	2.76554e6i	1.72225	+	0.293648i
$617$	1.60113e7			1.69323			0.846613	−	0.532209i	$-0.178638\pi$
$617$	1.60113e7			1.69323			0.846613	+	0.532209i	$0.178638\pi$
$618$	1.18632e7	+	2.35110e7i	1.24948	+	2.47628i
$619$	−1.43260e7			−1.50279			−0.751394	−	0.659854i	$-0.770618\pi$
$619$	−1.43260e7			−1.50279			−0.751394	+	0.659854i	$0.770618\pi$
$620$	1.81331e6	+	1.33937e6i	0.189449	+	0.139933i
$621$	−1.01131e7			−1.05234
$622$	−1.77486e6	−	3.51749e6i	−0.183945	−	0.364550i
$623$	−2.80627e6			−0.289674
$624$	−1.50850e7	+	4.64033e6i	−1.55090	+	0.477076i
$625$	−1.18537e6			−0.121382
$626$	−7.89409e6	+	3.98321e6i	−0.805131	+	0.406254i
$627$	1.43410e7	−	2.14832e7i	1.45683	−	2.18238i
$628$	−1.51490e7	−	1.11895e7i	−1.53280	−	1.13217i
$629$	−1.81618e7			−1.83035
$630$	1.39728e7	−	7.05043e6i	1.40260	−	0.707725i
$631$			1.53824e6i			0.153798i	0.997039	+	0.0768990i	$0.0245019\pi$
$631$			1.53824e6i			0.153798i	−0.997039	+	0.0768990i	$0.975498\pi$
$632$	−2.21459e6	+	1.29886e7i	−0.220547	+	1.29351i
$633$	2.99923e7			2.97509
$634$	−7.83301e6	+	3.95239e6i	−0.773937	+	0.390514i
$635$			9.74025e6i			0.958596i
$636$	2.10479e7	+	1.55466e7i	2.06331	+	1.52403i
$637$	3.32953e6			0.325113
$638$	1.44612e7	−	7.29687e6i	1.40655	−	0.709717i
$639$	2.97398e7			2.88129
$640$	885566.	+	6.79754e6i	0.0854616	+	0.655997i
$641$			4.45367e6i			0.428128i	0.976820	+	0.214064i	$0.0686701\pi$
$641$			4.45367e6i			0.428128i	−0.976820	+	0.214064i	$0.931330\pi$
$642$	1.46510e7	−	7.39264e6i	1.40291	−	0.707884i
$643$	−9.68595e6			−0.923878			−0.461939	−	0.886912i	$-0.652846\pi$
$643$	−9.68595e6			−0.923878			−0.461939	+	0.886912i	$0.652846\pi$
$644$	−4.19583e6	+	5.68055e6i	−0.398660	+	0.539729i
$645$	1.01397e7			0.959682
$646$	−1.75830e7	−	2.14342e6i	−1.65772	−	0.202081i
$647$		−	1.23914e7i		−	1.16375i	−0.813277	−	0.581877i	$-0.802319\pi$
$647$		−	1.23914e7i		−	1.16375i	0.813277	−	0.581877i	$-0.197681\pi$
$648$	2.03848e6	−	1.19557e7i	0.190708	−	1.11850i
$649$		−	9.13637e6i		−	0.851456i
$650$	−5.02950e6	+	2.53779e6i	−0.466919	+	0.235599i
$651$	−7.80321e6			−0.721640
$652$	−7.80045e6	+	1.05607e7i	−0.718622	+	0.972911i
$653$			1.22140e7i			1.12093i	0.828180	+	0.560463i	$0.189377\pi$
$653$			1.22140e7i			1.12093i	−0.828180	+	0.560463i	$0.810623\pi$
$654$	−5.14019e6	−	1.01870e7i	−0.469932	−	0.931331i
$655$		−	1.11958e6i		−	0.101965i
$656$	2.58448e6	−	795019.i	0.234484	−	0.0721304i
$657$	−1.07136e7			−0.968327
$658$	−1.55501e7	+	7.84630e6i	−1.40013	+	0.706480i
$659$			1.71867e7i			1.54162i	0.637064	+	0.770811i	$0.280149\pi$
$659$			1.71867e7i			1.54162i	−0.637064	+	0.770811i	$0.719851\pi$
$660$	−1.15413e7	+	1.56253e7i	−1.03132	+	1.39626i
$661$	1.24496e7			1.10828			0.554141	−	0.832423i	$-0.313047\pi$
$661$	1.24496e7			1.10828			0.554141	+	0.832423i	$0.313047\pi$
$662$	−1.31411e6	−	2.60436e6i	−0.116543	−	0.230970i
$663$			3.06699e7i			2.70975i
$664$	445081.	−	2.61040e6i	0.0391759	−	0.229767i
$665$	−7.28928e6	−	4.86592e6i	−0.639191	−	0.426689i
$666$	−2.28972e7	+	1.15535e7i	−2.00030	+	1.00932i
$667$			6.95223e6i			0.605076i
$668$	2.48107e6	−	3.35901e6i	0.215128	−	0.291253i
$669$		−	343359.i		−	0.0296608i
$670$	−8.57272e6	+	4.32563e6i	−0.737788	+	0.372274i
$671$		−	2.30937e7i		−	1.98010i
$672$	−1.64451e7	−	1.71050e7i	−1.40480	−	1.46117i
$673$			3.43928e6i			0.292705i	0.989232	+	0.146353i	$0.0467534\pi$
$673$			3.43928e6i			0.292705i	−0.989232	+	0.146353i	$0.953247\pi$
$674$	−459547.	−	910749.i	−0.0389655	−	0.0772234i
$675$		−	1.21286e7i		−	1.02459i
$676$	−953856.	+	1.29138e6i	−0.0802816	+	0.108690i
$677$	−9.71121e6			−0.814332			−0.407166	−	0.913354i	$-0.633483\pi$
$677$	−9.71121e6			−0.814332			−0.407166	+	0.913354i	$0.633483\pi$
$678$	7.87859e6	−	3.97539e6i	0.658224	−	0.332128i
$679$	3.15695e6			0.262780
$680$	1.31317e7	+	2.23899e6i	1.08905	+	0.185686i
$681$	−1.58094e7			−1.30631
$682$	5.80640e6	−	2.92980e6i	0.478020	−	0.241200i
$683$		−	5.58761e6i		−	0.458325i	−0.973388	−	0.229163i	$-0.926401\pi$
$683$		−	5.58761e6i		−	0.458325i	0.973388	−	0.229163i	$-0.0735988\pi$
$684$	−2.35309e7	+	8.48295e6i	−1.92308	+	0.693277i
$685$			9.20975e6i			0.749931i
$686$	−4.19543e6	−	8.31468e6i	−0.340382	−	0.674583i
$687$	−2.74952e7			−2.22262
$688$	−3.03512e6	−	9.86667e6i	−0.244458	−	0.794693i
$689$	−1.70371e7			−1.36725
$690$	−3.75591e6	−	7.44363e6i	−0.300326	−	0.595199i
$691$	1.96566e7			1.56608			0.783039	−	0.621973i	$-0.213669\pi$
$691$	1.96566e7			1.56608			0.783039	+	0.621973i	$0.213669\pi$
$692$	−1.14970e6	+	1.55653e6i	−0.0912683	+	0.123564i
$693$		−	4.51524e7i		−	3.57148i
$694$	1.02106e7	−	5.15210e6i	0.804738	−	0.406056i
$695$			1.56659e7i			1.23025i
$696$	−2.30265e7	−	3.92609e6i	−1.80179	−	0.307211i
$697$		−	5.25462e6i		−	0.409694i
$698$	8.23454e6	+	1.63196e7i	0.639736	+	1.26786i
$699$		−	1.96567e7i		−	1.52166i
$700$	−6.81269e6	−	5.03206e6i	−0.525501	−	0.388151i
$701$			7.29308e6i			0.560552i	0.959919	+	0.280276i	$0.0904260\pi$
$701$			7.29308e6i			0.560552i	−0.959919	+	0.280276i	$0.909574\pi$
$702$	9.96625e6	+	1.97515e7i	0.763289	+	1.51272i
$703$	1.19449e7	+	7.97373e6i	0.911576	+	0.608518i
$704$	1.86591e7	+	6.55339e6i	1.41893	+	0.498350i
$705$		−	2.05631e7i		−	1.55817i
$706$	1.86000e6	−	938519.i	0.140443	−	0.0708649i
$707$	−1.26154e7			−0.949190
$708$	−7.82796e6	+	1.05979e7i	−0.586902	+	0.794581i
$709$			8.20141e6i			0.612735i	0.951913	+	0.306368i	$0.0991136\pi$
$709$			8.20141e6i			0.612735i	−0.951913	+	0.306368i	$0.900886\pi$
$710$	5.64205e6	+	1.11817e7i	0.420041	+	0.832454i
$711$	3.61572e7			2.68238
$712$	−3.32495e6	−	566915.i	−0.245802	−	0.0419100i
$713$			2.79142e6i			0.205637i
$714$	−4.11667e7	+	2.07719e7i	−3.02204	+	1.52486i
$715$		−	1.26478e7i		−	0.925232i
$716$	−5.20976e6	−	3.84809e6i	−0.379783	−	0.280519i
$717$	1.59498e7			1.15866
$718$	157389.	+	311921.i	0.0113937	+	0.0225805i
$719$			8.13778e6i			0.587062i	0.955950	+	0.293531i	$0.0948303\pi$
$719$			8.13778e6i			0.587062i	−0.955950	+	0.293531i	$0.905170\pi$
$720$	1.79798e7	−	5.53082e6i	1.29257	−	0.397611i
$721$		−	2.57782e7i		−	1.84678i
$722$	1.06231e7	+	9.12929e6i	0.758417	+	0.651769i
$723$	−1.72995e7			−1.23080
$724$	4.94820e6	−	6.69915e6i	0.350833	−	0.474978i
$725$	−8.33782e6			−0.589125
$726$	1.40836e7	+	2.79115e7i	0.991683	+	1.96536i
$727$		−	3.38258e6i		−	0.237363i	−0.992932	−	0.118681i	$-0.962133\pi$
$727$		−	3.38258e6i		−	0.237363i	0.992932	−	0.118681i	$-0.0378667\pi$
$728$	1.52294e7	+	2.59666e6i	1.06501	+	0.181588i
$729$	1.23315e7			0.859403
$730$	−2.03252e6	−	4.02812e6i	−0.141165	−	0.279767i
$731$	−2.00604e7			−1.38850
$732$	−1.97864e7	+	2.67880e7i	−1.36487	+	1.84783i
$733$		−	2.60792e7i		−	1.79281i	−0.443233	−	0.896407i	$-0.646168\pi$
$733$		−	2.60792e7i		−	1.79281i	0.443233	−	0.896407i	$-0.353832\pi$
$734$	1.34933e6	+	2.67417e6i	0.0924442	+	0.183210i
$735$	−5.90978e6			−0.403509
$736$	−6.11892e6	+	5.88286e6i	−0.416371	+	0.400308i
$737$			2.77022e7i			1.87865i
$738$	−3.34268e6	−	6.62465e6i	−0.225919	−	0.447736i
$739$	9.29414e6			0.626035			0.313017	−	0.949747i	$-0.398660\pi$
$739$	9.29414e6			0.626035			0.313017	+	0.949747i	$0.398660\pi$
$740$	−8.68780e6	−	6.41708e6i	−0.583218	−	0.430782i
$741$	1.34653e7	−	2.01713e7i	0.900885	−	1.34955i
$742$	−1.15388e7	−	2.28681e7i	−0.769397	−	1.52482i
$743$	−7.55420e6			−0.502015			−0.251007	−	0.967985i	$-0.580762\pi$
$743$	−7.55420e6			−0.502015			−0.251007	+	0.967985i	$0.580762\pi$
$744$	−9.24548e6	−	1.57638e6i	−0.612347	−	0.104407i
$745$	527285.			0.0348060
$746$	2.11960e7	−	1.06951e7i	1.39446	−	0.703618i
$747$	−7.26676e6			−0.476474
$748$	2.28332e7	−	3.09129e7i	1.49215	−	2.02016i
$749$	−1.60639e7			−1.04628
$750$	2.48015e7	−	1.25144e7i	1.60999	−	0.812373i
$751$	−4.11726e6			−0.266384			−0.133192	−	0.991090i	$-0.542523\pi$
$751$	−4.11726e6			−0.266384			−0.133192	+	0.991090i	$0.542523\pi$
$752$	−2.00093e7	+	6.15514e6i	−1.29029	+	0.396911i
$753$			1.07448e7i			0.690575i
$754$	1.35782e7	−	6.85129e6i	0.869788	−	0.438878i
$755$		−	9.52032e6i		−	0.607833i
$756$	−1.97616e7	+	2.67544e7i	−1.25753	+	1.70251i
$757$			2.99636e6i			0.190044i	0.995475	+	0.0950219i	$0.0302921\pi$
$757$			2.99636e6i			0.190044i	−0.995475	+	0.0950219i	$0.969708\pi$
$758$	2.21796e6	+	4.39565e6i	0.140211	+	0.277875i
$759$	−2.40536e7			−1.51557
$760$	−7.65356e6	−	7.23785e6i	−0.480651	−	0.454544i
$761$	1.82731e7			1.14380			0.571900	−	0.820323i	$-0.306206\pi$
$761$	1.82731e7			1.14380			0.571900	+	0.820323i	$0.306206\pi$
$762$	−1.82551e7	−	3.61787e7i	−1.13893	−	2.25717i
$763$			1.11694e7i			0.694575i
$764$	−857662.	−	633495.i	−0.0531597	−	0.0392654i
$765$		−	3.65555e7i		−	2.25839i
$766$	−1.96002e7	+	9.88988e6i	−1.20695	+	0.609003i
$767$		−	8.57847e6i		−	0.526528i
$768$	−1.60292e7	−	2.35887e7i	−0.980637	−	1.44311i
$769$	2.24831e7			1.37101			0.685505	−	0.728068i	$-0.259581\pi$
$769$	2.24831e7			1.37101			0.685505	+	0.728068i	$0.259581\pi$
$770$	1.69765e7	−	8.56603e6i	1.03186	−	0.520658i
$771$	−3.61102e7			−2.18773
$772$	1.77504e7	+	1.31110e7i	1.07192	+	0.791755i
$773$	−2.42067e6			−0.145709			−0.0728545	−	0.997343i	$-0.523211\pi$
$773$	−2.42067e6			−0.145709			−0.0728545	+	0.997343i	$0.523211\pi$
$774$	−2.52907e7	+	1.27612e7i	−1.51743	+	0.765667i
$775$	−3.34775e6			−0.200216
$776$	3.74045e6	+	637758.i	0.222982	+	0.0380191i
$777$	3.73862e7			2.22156
$778$	−142190.	−	281799.i	−0.00842211	−	0.0166913i
$779$	−2.30698e6	+	3.45591e6i	−0.136207	+	0.204042i
$780$	−1.08365e7	+	1.46711e7i	−0.637755	+	0.863429i
$781$	3.61329e7			2.11970
$782$	7.43068e6	+	1.47264e7i	0.434522	+	0.861154i
$783$			3.27437e7i			1.90864i
$784$	1.76897e6	+	5.75063e6i	0.102785	+	0.334137i
$785$	−2.17651e7			−1.26063
$786$	2.09830e6	+	4.15851e6i	0.121147	+	0.240094i
$787$		−	1.59992e7i		−	0.920794i	−0.887713	−	0.460397i	$-0.847707\pi$
$787$		−	1.59992e7i		−	0.920794i	0.887713	−	0.460397i	$-0.152293\pi$
$788$	1.63891e7	+	1.21055e7i	0.940242	+	0.694491i
$789$	−1.87521e7			−1.07240
$790$	6.85951e6	+	1.35945e7i	0.391044	+	0.774987i
$791$	−8.63834e6			−0.490896
$792$	9.12156e6	−	5.34980e7i	0.516721	−	3.03057i
$793$		−	2.16835e7i		−	1.22446i
$794$	6.72591e6	+	1.33297e7i	0.378617	+	0.750359i
$795$	3.02402e7			1.69694
$796$	−9.75916e6	−	7.20841e6i	−0.545921	−	0.403234i
$797$	2.14331e7			1.19519			0.597597	−	0.801797i	$-0.296122\pi$
$797$	2.14331e7			1.19519			0.597597	+	0.801797i	$0.296122\pi$
$798$	3.61946e7	+	4.41223e6i	2.01204	+	0.245274i
$799$			4.06819e7i			2.25442i
$800$	−7.05533e6	−	7.33842e6i	−0.389755	−	0.405394i
$801$			9.25591e6i			0.509727i
$802$	−1.20768e7	−	2.39342e7i	−0.663002	−	1.31397i
$803$	−1.30166e7			−0.712377
$804$	2.37350e7	−	3.21338e7i	1.29494	−	1.75316i
$805$			8.16144e6i			0.443892i
$806$	5.45184e6	−	2.75089e6i	0.295601	−	0.149154i
$807$			2.65986e7i			1.43772i
$808$	−1.49471e7	−	2.54853e6i	−0.805434	−	0.137329i
$809$	−2.78269e6			−0.149484			−0.0747418	−	0.997203i	$-0.523813\pi$
$809$	−2.78269e6			−0.149484			−0.0747418	+	0.997203i	$0.523813\pi$
$810$	−6.31401e6	−	1.25134e7i	−0.338137	−	0.670135i
$811$		−	1.93966e7i		−	1.03555i	−0.855516	−	0.517777i	$-0.826760\pi$
$811$		−	1.93966e7i		−	1.03555i	0.855516	−	0.517777i	$-0.173240\pi$
$812$	1.83923e7	+	1.35851e7i	0.978916	+	0.723057i
$813$	4.06231e7			2.15549
$814$	−2.78192e7	+	1.40371e7i	−1.47158	+	0.742532i
$815$			1.51729e7i			0.800156i
$816$	−5.29718e7	+	1.62948e7i	−2.78496	+	0.856692i
$817$	1.31935e7	+	8.80727e6i	0.691522	+	0.461622i
$818$	2.62585e6	+	5.20402e6i	0.137210	+	0.271929i
$819$		−	4.23952e7i		−	2.20855i
$820$	1.85660e6	−	2.51357e6i	0.0964238	−	0.130544i
$821$			9.94941e6i			0.515157i	0.966257	+	0.257579i	$0.0829246\pi$
$821$			9.94941e6i			0.515157i	−0.966257	+	0.257579i	$0.917075\pi$
$822$	−1.72608e7	−	3.42082e7i	−0.891008	−	1.76584i
$823$		−	3.58026e7i		−	1.84253i	−0.388936	−	0.921265i	$-0.627157\pi$
$823$		−	3.58026e7i		−	1.84253i	0.388936	−	0.921265i	$-0.372843\pi$
$824$	5.20764e6	−	3.05428e7i	0.267192	−	1.56708i
$825$		−	2.88476e7i		−	1.47562i
$826$	1.15144e7	−	5.80996e6i	0.587209	−	0.296294i
$827$			1.95579e7i			0.994394i	0.867638	+	0.497197i	$0.165637\pi$
$827$			1.95579e7i			0.994394i	−0.867638	+	0.497197i	$0.834363\pi$
$828$	1.87362e7	+	1.38391e7i	0.949740	+	0.701507i
$829$	−2.71049e7			−1.36982			−0.684908	−	0.728630i	$-0.740157\pi$
$829$	−2.71049e7			−1.36982			−0.684908	+	0.728630i	$0.740157\pi$
$830$	−1.37860e6	−	2.73218e6i	−0.0694615	−	0.137662i
$831$	3.59512e7			1.80597
$832$	1.75197e7	+	6.15321e6i	0.877443	+	0.308172i
$833$	1.16919e7			0.583810
$834$	−2.93608e7	−	5.81885e7i	−1.46168	−	2.89683i
$835$		−	4.82601e6i		−	0.239537i
$836$	−2.85891e7	+	1.03065e7i	−1.41477	+	0.510029i
$837$			1.31471e7i			0.648658i
$838$	4.00204e6	−	2.01936e6i	0.196867	−	0.0993351i
$839$	−1.30660e7			−0.640820			−0.320410	−	0.947279i	$-0.603821\pi$
$839$	−1.30660e7			−0.640820			−0.320410	+	0.947279i	$0.603821\pi$
$840$	−2.70316e7	−	4.60896e6i	−1.32182	−	0.225375i
$841$	1.99851e6			0.0974353
$842$	2.06169e6	−	1.04029e6i	0.100217	−	0.0505677i
$843$	6.13679e7			2.97422
$844$	−2.83839e7	−	2.09652e7i	−1.37157	−	1.01308i
$845$			1.85538e6i			0.0893902i
$846$	2.58794e7	+	5.12889e7i	1.24316	+	2.46376i
$847$		−	3.06031e7i		−	1.46574i
$848$	−9.05177e6	−	2.94258e7i	−0.432259	−	1.40520i
$849$			2.31122e7i			1.10045i
$850$	−1.76614e7	+	8.91162e6i	−0.838453	+	0.423067i
$851$		−	1.33741e7i		−	0.633052i
$852$	−4.19131e7	−	3.09583e7i	−1.97811	−	1.46109i
$853$			8.29122e6i			0.390163i	0.980787	+	0.195081i	$0.0624971\pi$
$853$			8.29122e6i			0.390163i	−0.980787	+	0.195081i	$0.937503\pi$
$854$	2.91046e7	−	1.46856e7i	1.36558	−	0.689046i
$855$	−1.60493e7	+	2.40422e7i	−0.750827	+	1.12476i
$856$	−1.90330e7	−	3.24518e6i	−0.887815	−	0.151375i
$857$			3.08173e7i			1.43332i	0.697424	+	0.716659i	$0.254329\pi$
$857$			3.08173e7i			1.43332i	−0.697424	+	0.716659i	$0.745671\pi$
$858$	2.37044e7	+	4.69784e7i	1.09929	+	2.17861i
$859$	2.55864e7			1.18311			0.591557	−	0.806263i	$-0.298513\pi$
$859$	2.55864e7			1.18311			0.591557	+	0.806263i	$0.298513\pi$
$860$	−9.59599e6	−	7.08789e6i	−0.442429	−	0.326791i
$861$			1.08167e7i			0.497262i
$862$	−5.10004e6	+	2.57339e6i	−0.233779	+	0.117961i
$863$	−1.18111e7			−0.539836			−0.269918	−	0.962883i	$-0.586997\pi$
$863$	−1.18111e7			−0.539836			−0.269918	+	0.962883i	$0.586997\pi$
$864$	−2.88190e7	+	2.77072e7i	−1.31339	+	1.26272i
$865$			2.23632e6i			0.101623i
$866$	4.07603e6	+	8.07805e6i	0.184690	+	0.366026i
$867$			6.90818e7i			3.12116i
$868$	7.38476e6	+	5.45461e6i	0.332688	+	0.245734i
$869$	4.39297e7			1.97337
$870$	−2.41007e7	+	1.21608e7i	−1.07952	+	0.544706i
$871$			2.60106e7i			1.16173i
$872$	−2.25641e6	+	1.32339e7i	−0.100491	+	0.589380i
$873$		−	1.04126e7i		−	0.462404i
$874$	1.57838e6	−	1.29478e7i	0.0698927	−	0.573346i
$875$	−2.71932e7			−1.20071
$876$	1.50989e7	+	1.11525e7i	0.664792	+	0.491036i
$877$	−2.57059e7			−1.12858			−0.564292	−	0.825575i	$-0.690851\pi$
$877$	−2.57059e7			−1.12858			−0.564292	+	0.825575i	$0.690851\pi$
$878$	3.33991e7	−	1.68525e7i	1.46217	−	0.737784i
$879$			3.35594e7i			1.46501i
$880$	2.18448e7	−	6.71975e6i	0.950913	−	0.292514i
$881$	8.50822e6			0.369317			0.184658	−	0.982803i	$-0.440882\pi$
$881$	8.50822e6			0.369317			0.184658	+	0.982803i	$0.440882\pi$
$882$	1.47403e7	−	7.43767e6i	0.638020	−	0.321933i
$883$	1.68717e7			0.728212			0.364106	−	0.931358i	$-0.381375\pi$
$883$	1.68717e7			0.728212			0.364106	+	0.931358i	$0.381375\pi$
$884$	2.14389e7	−	2.90253e7i	0.922726	−	1.24924i
$885$			1.52264e7i			0.653491i
$886$	1.46780e7	−	7.40625e6i	0.628178	−	0.316967i
$887$	2.00106e6			0.0853986			0.0426993	−	0.999088i	$-0.486404\pi$
$887$	2.00106e6			0.0853986			0.0426993	+	0.999088i	$0.486404\pi$
$888$	4.42963e7	+	7.55266e6i	1.88510	+	0.321416i
$889$			3.96675e7i			1.68337i
$890$	−3.48006e6	+	1.75597e6i	−0.147269	+	0.0743092i
$891$	−4.04362e7			−1.70638
$892$	−240015.	+	324946.i	−0.0101001	+	0.0136741i
$893$	1.78609e7	−	2.67561e7i	0.749506	−	1.12278i
$894$	−1.95852e6	+	988232.i	−0.0819566	+	0.0413538i
$895$	−7.48504e6			−0.312346
$896$	3.60650e6	+	2.76832e7i	0.150077	+	1.15198i
$897$	−2.25848e7			−0.937207
$898$	−3.12070e6	−	6.18474e6i	−0.129140	−	0.255936i
$899$	9.03795e6			0.372967
$900$	−1.65972e7	+	2.24703e7i	−0.683014	+	0.924703i
$901$	−5.98270e7			−2.45519
$902$	−4.06123e6	−	8.04872e6i	−0.166204	−	0.329390i
$903$	4.12944e7			1.68528
$904$	−1.02350e7	−	1.74509e6i	−0.416549	−	0.0710228i
$905$		−	9.62490e6i		−	0.390638i
$906$	1.78429e7	+	3.53618e7i	0.722178	+	1.43124i
$907$			1.33783e7i			0.539985i	0.962862	+	0.269993i	$0.0870213\pi$
$907$			1.33783e7i			0.539985i	−0.962862	+	0.269993i	$0.912979\pi$
$908$	1.49616e7	+	1.10511e7i	0.602231	+	0.444826i
$909$			4.16094e7i			1.67025i
$910$	1.59399e7	−	8.04295e6i	0.638088	−	0.321967i
$911$	1.78700e6			0.0713393			0.0356696	−	0.999364i	$-0.488644\pi$
$911$	1.78700e6			0.0713393			0.0356696	+	0.999364i	$0.488644\pi$
$912$	4.19931e7	+	1.25397e7i	1.67183	+	0.499228i
$913$	−8.82886e6			−0.350532
$914$	−1.66827e7	+	8.41780e6i	−0.660544	+	0.333298i
$915$			3.84873e7i			1.51972i
$916$	2.60208e7	+	1.92198e7i	1.02467	+	0.756849i
$917$		−	4.55953e6i		−	0.179059i
$918$	3.49971e7	+	6.93588e7i	1.37065	+	2.71641i
$919$		−	3.22979e7i		−	1.26149i	−0.775989	−	0.630747i	$-0.782749\pi$
$919$		−	3.22979e7i		−	1.26149i	0.775989	−	0.630747i	$-0.217251\pi$
$920$	−1.64875e6	+	9.66993e6i	−0.0642223	+	0.376664i
$921$	524639.			0.0203804
$922$	−1.78409e7	−	3.53578e7i	−0.691177	−	1.36980i
$923$	3.39264e7			1.31079
$924$	−4.70023e7	+	6.36344e7i	−1.81109	+	2.45195i
$925$	1.60395e7			0.616364
$926$	−8.03722e6	−	1.59285e7i	−0.308020	−	0.610446i
$927$	−8.50242e7			−3.24970
$928$	1.90473e7	+	1.98116e7i	0.726045	+	0.755178i
$929$	2.14880e7			0.816875			0.408438	−	0.912786i	$-0.366074\pi$
$929$	2.14880e7			0.816875			0.408438	+	0.912786i	$0.366074\pi$
$930$	−9.67678e6	+	4.88272e6i	−0.366879	+	0.185120i
$931$	−7.68964e6	−	5.13318e6i	−0.290758	−	0.194094i
$932$	−1.37404e7	+	1.86026e7i	−0.518156	+	0.701509i
$933$	1.89432e7			0.712441
$934$	1.04936e7	−	5.29486e6i	0.393601	−	0.198604i
$935$		−	4.44137e7i		−	1.66145i
$936$	8.56456e6	−	5.02312e7i	0.319533	−	1.87406i
$937$	−3.69853e7			−1.37619			−0.688097	−	0.725619i	$-0.741554\pi$
$937$	−3.69853e7			−1.37619			−0.688097	+	0.725619i	$0.741554\pi$
$938$	−3.49127e7	+	1.76163e7i	−1.29562	+	0.653743i
$939$		−	4.25130e7i		−	1.57347i
$940$	−1.43741e7	+	1.94604e7i	−0.530591	+	0.718344i
$941$	1.46476e7			0.539252			0.269626	−	0.962965i	$-0.413100\pi$
$941$	1.46476e7			0.539252			0.269626	+	0.962965i	$0.413100\pi$
$942$	8.08432e7	−	4.07920e7i	2.96836	−	1.49778i
$943$	3.86941e6			0.141699
$944$	1.48164e7	−	4.55771e6i	0.541143	−	0.166463i
$945$			3.84389e7i			1.40020i
$946$	−3.07273e7	+	1.55044e7i	−1.11634	+	0.563285i
$947$	1.57533e7			0.570816			0.285408	−	0.958406i	$-0.407871\pi$
$947$	1.57533e7			0.570816			0.285408	+	0.958406i	$0.407871\pi$
$948$	−5.09572e7	−	3.76385e7i	−1.84156	−	1.36023i
$949$	−1.22218e7			−0.440524
$950$	1.55283e7	+	1.89295e6i	0.558232	+	0.0680502i
$951$		−	4.21841e7i		−	1.51251i
$952$	5.34791e7	+	9.11835e6i	1.91246	+	0.326080i
$953$			5.45212e7i			1.94461i	0.233709	+	0.972307i	$0.424914\pi$
$953$			5.45212e7i			1.94461i	−0.233709	+	0.972307i	$0.575086\pi$
$954$	−7.54256e7	+	3.80584e7i	−2.68317	+	1.35388i
$955$	−1.23223e6			−0.0437204
$956$	−1.50945e7	−	1.11492e7i	−0.534162	−	0.394548i
$957$			7.78799e7i			2.74882i
$958$	−2.10051e7	−	4.16287e7i	−0.739453	−	1.46548i
$959$			3.75070e7i			1.31694i
$960$	−3.10967e7	−	1.09217e7i	−1.08902	−	0.382482i
$961$	−2.50003e7			−0.873246
$962$	−2.61205e7	+	1.31799e7i	−0.910004	+	0.459171i
$963$			5.29835e7i			1.84109i
$964$	1.63718e7	+	1.20927e7i	0.567421	+	0.419114i
$965$	2.55025e7			0.881587
$966$	−1.52961e7	−	3.03144e7i	−0.527397	−	1.04522i
$967$			5.94249e6i			0.204363i	0.994766	+	0.102181i	$0.0325822\pi$
$967$			5.94249e6i			0.204363i	−0.994766	+	0.102181i	$0.967418\pi$
$968$	6.18236e6	−	3.62595e7i	0.212063	−	1.24375i
$969$	4.72842e7	−	7.08329e7i	1.61773	−	2.42340i
$970$	3.91494e6	−	1.97540e6i	0.133597	−	0.0674103i
$971$			758200.i			0.0258069i	0.999917	+	0.0129034i	$0.00410741\pi$
$971$			758200.i			0.0258069i	−0.999917	+	0.0129034i	$0.995893\pi$
$972$	3.73759e6	+	2.76070e6i	0.126890	+	0.0937245i
$973$			6.37998e7i			2.16042i
$974$	1.01513e7	−	5.12214e6i	0.342865	−	0.173003i
$975$		−	2.70860e7i		−	0.912501i
$976$	3.74508e7	−	1.15204e7i	1.25845	−	0.387116i
$977$		−	1.14601e7i		−	0.384107i	−0.981384	−	0.192054i	$-0.938485\pi$
$977$		−	1.14601e7i		−	0.384107i	0.981384	−	0.192054i	$-0.0615148\pi$
$978$	−2.84369e7	−	5.63574e7i	−0.950681	−	1.88410i
$979$			1.12456e7i			0.374995i
$980$	5.59287e6	+	4.13106e6i	0.186024	+	0.137403i
$981$	3.68401e7			1.22222
$982$	−3.21146e7	+	1.62044e7i	−1.06273	+	0.536234i
$983$	−4.07508e7			−1.34509			−0.672546	−	0.740055i	$-0.734799\pi$
$983$	−4.07508e7			−1.34509			−0.672546	+	0.740055i	$0.734799\pi$
$984$	−2.18515e6	+	1.28159e7i	−0.0719439	+	0.421951i
$985$	2.35468e7			0.773287
$986$	4.76807e7	−	2.40588e7i	1.56189	−	0.788100i
$987$		−	8.37440e7i		−	2.73628i
$988$	−2.68434e7	+	9.67713e6i	−0.874872	+	0.315395i
$989$		−	1.47721e7i		−	0.480234i
$990$	−2.82533e7	−	5.59936e7i	−0.916181	−	1.81573i
$991$	5.70617e7			1.84570			0.922849	−	0.385161i	$-0.125854\pi$
$991$	5.70617e7			1.84570			0.922849	+	0.385161i	$0.125854\pi$
$992$	7.64777e6	+	7.95464e6i	0.246749	+	0.256650i
$993$	1.40256e7			0.451386
$994$	2.29775e7	+	4.55377e7i	0.737626	+	1.46186i
$995$	−1.40213e7			−0.448984
$996$	1.02412e7	+	7.56448e6i	0.327117	+	0.241619i
$997$		−	3.72819e7i		−	1.18785i	−0.804522	−	0.593923i	$-0.797578\pi$
$997$		−	3.72819e7i		−	1.18785i	0.804522	−	0.593923i	$-0.202422\pi$
$998$	−9.20458e6	+	4.64446e6i	−0.292535	+	0.147608i
$999$		−	6.29894e7i		−	1.99689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.6.b.b.75.83	yes	96
4.3	odd	2		608.6.b.b.303.3		96
8.3	odd	2	inner	152.6.b.b.75.13	✓	96
8.5	even	2		608.6.b.b.303.4		96
19.18	odd	2	inner	152.6.b.b.75.14	yes	96
76.75	even	2		608.6.b.b.303.93		96
152.37	odd	2		608.6.b.b.303.94		96
152.75	even	2	inner	152.6.b.b.75.84	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.6.b.b.75.13	✓	96	8.3	odd	2	inner
152.6.b.b.75.14	yes	96	19.18	odd	2	inner
152.6.b.b.75.83	yes	96	1.1	even	1	trivial
152.6.b.b.75.84	yes	96	152.75	even	2	inner
608.6.b.b.303.3		96	4.3	odd	2
608.6.b.b.303.4		96	8.5	even	2
608.6.b.b.303.93		96	76.75	even	2
608.6.b.b.303.94		96	152.37	odd	2

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	152.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(5.05036 - 2.54831i) q^{2} +27.1983i q^{3} +(19.0122 - 25.7398i) q^{4} -36.9812i q^{5} +(69.3098 + 137.361i) q^{6} -150.607i q^{7} +(30.4253 - 178.444i) q^{8} -496.748 q^{9} +O(q^{10})\)	\(q+(5.05036 - 2.54831i) q^{2} +27.1983i q^{3} +(19.0122 - 25.7398i) q^{4} -36.9812i q^{5} +(69.3098 + 137.361i) q^{6} -150.607i q^{7} +(30.4253 - 178.444i) q^{8} -496.748 q^{9} +(-94.2398 - 186.768i) q^{10} -603.531 q^{11} +(700.078 + 517.099i) q^{12} -566.677 q^{13} +(-383.795 - 760.620i) q^{14} +1005.83 q^{15} +(-301.073 - 978.739i) q^{16} -1989.92 q^{17} +(-2508.75 + 1265.87i) q^{18} +(1308.75 + 873.651i) q^{19} +(-951.889 - 703.094i) q^{20} +4096.26 q^{21} +(-3048.04 + 1537.99i) q^{22} -1465.34i q^{23} +(4853.38 + 827.515i) q^{24} +1757.39 q^{25} +(-2861.92 + 1444.07i) q^{26} -6901.50i q^{27} +(-3876.60 - 2863.37i) q^{28} -4744.43 q^{29} +(5079.78 - 2563.16i) q^{30} -1904.96 q^{31} +(-4014.66 - 4175.75i) q^{32} -16415.0i q^{33} +(-10049.8 + 5070.95i) q^{34} -5569.64 q^{35} +(-9444.26 + 12786.2i) q^{36} +9126.91 q^{37} +(8836.00 + 1077.14i) q^{38} -15412.6i q^{39} +(-6599.08 - 1125.16i) q^{40} +2640.62i q^{41} +(20687.6 - 10438.6i) q^{42} +10081.0 q^{43} +(-11474.4 + 15534.7i) q^{44} +18370.3i q^{45} +(-3734.16 - 7400.51i) q^{46} -20444.0i q^{47} +(26620.0 - 8188.68i) q^{48} -5875.55 q^{49} +(8875.44 - 4478.38i) q^{50} -54122.5i q^{51} +(-10773.8 + 14586.1i) q^{52} +30065.0 q^{53} +(-17587.2 - 34855.0i) q^{54} +22319.3i q^{55} +(-26875.0 - 4582.26i) q^{56} +(-23761.8 + 35595.8i) q^{57} +(-23961.1 + 12090.3i) q^{58} +15138.2i q^{59} +(19123.0 - 25889.8i) q^{60} +38264.3i q^{61} +(-9620.72 + 4854.43i) q^{62} +74813.8i q^{63} +(-30916.6 - 10858.4i) q^{64} +20956.4i q^{65} +(-41830.6 - 82901.6i) q^{66} -45900.3i q^{67} +(-37832.8 + 51220.2i) q^{68} +39854.9 q^{69} +(-28128.7 + 14193.2i) q^{70} -59869.1 q^{71} +(-15113.7 + 88641.7i) q^{72} +21567.5 q^{73} +(46094.1 - 23258.2i) q^{74} +47798.0i q^{75} +(47369.8 - 17077.0i) q^{76} +90896.1i q^{77} +(-39276.2 - 77839.3i) q^{78} -72787.8 q^{79} +(-36195.0 + 11134.1i) q^{80} +66999.5 q^{81} +(6729.12 + 13336.1i) q^{82} +14628.7 q^{83} +(77878.9 - 105437. i) q^{84} +73589.7i q^{85} +(50912.6 - 25689.5i) q^{86} -129041. i q^{87} +(-18362.6 + 107696. i) q^{88} -18633.0i q^{89} +(46813.4 + 92776.7i) q^{90} +85345.6i q^{91} +(-37717.7 - 27859.4i) q^{92} -51811.7i q^{93} +(-52097.7 - 103249. i) q^{94} +(32308.7 - 48399.3i) q^{95} +(113573. - 109192. i) q^{96} +20961.5i q^{97} +(-29673.6 + 14972.7i) q^{98} +299802. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Introduction

L-functions

Modular forms

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