LMFDB - Embedded newform 230.6.b.a.139.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("230.139");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.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:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.9
Character	$\chi$	$=$	230.139
Dual form			230.6.b.a.139.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} +11.0852i q^{3} -16.0000 q^{4} +(-42.4833 - 36.3342i) q^{5} +44.3407 q^{6} +240.887i q^{7} +64.0000i q^{8} +120.119 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} +11.0852i q^{3} -16.0000 q^{4} +(-42.4833 - 36.3342i) q^{5} +44.3407 q^{6} +240.887i q^{7} +64.0000i q^{8} +120.119 q^{9} +(-145.337 + 169.933i) q^{10} +467.455 q^{11} -177.363i q^{12} -75.0691i q^{13} +963.547 q^{14} +(402.771 - 470.935i) q^{15} +256.000 q^{16} -1168.59i q^{17} -480.475i q^{18} -2646.80 q^{19} +(679.732 + 581.347i) q^{20} -2670.27 q^{21} -1869.82i q^{22} -529.000i q^{23} -709.451 q^{24} +(484.656 + 3087.19i) q^{25} -300.277 q^{26} +4025.24i q^{27} -3854.19i q^{28} +4647.98 q^{29} +(-1883.74 - 1611.08i) q^{30} -4030.10 q^{31} -1024.00i q^{32} +5181.83i q^{33} -4674.37 q^{34} +(8752.42 - 10233.7i) q^{35} -1921.90 q^{36} +7197.11i q^{37} +10587.2i q^{38} +832.155 q^{39} +(2325.39 - 2718.93i) q^{40} -16876.8 q^{41} +10681.1i q^{42} +21405.8i q^{43} -7479.29 q^{44} +(-5103.04 - 4364.42i) q^{45} -2116.00 q^{46} -7461.45i q^{47} +2837.81i q^{48} -41219.5 q^{49} +(12348.8 - 1938.63i) q^{50} +12954.1 q^{51} +1201.11i q^{52} +2674.52i q^{53} +16100.9 q^{54} +(-19859.0 - 16984.6i) q^{55} -15416.8 q^{56} -29340.2i q^{57} -18591.9i q^{58} +16834.5 q^{59} +(-6444.33 + 7534.95i) q^{60} -54644.2 q^{61} +16120.4i q^{62} +28935.1i q^{63} -4096.00 q^{64} +(-2727.57 + 3189.18i) q^{65} +20727.3 q^{66} -41448.4i q^{67} +18697.5i q^{68} +5864.06 q^{69} +(-40934.6 - 35009.7i) q^{70} -51983.0 q^{71} +7687.61i q^{72} -10162.3i q^{73} +28788.4 q^{74} +(-34222.0 + 5372.50i) q^{75} +42348.8 q^{76} +112604. i q^{77} -3328.62i q^{78} +38861.4 q^{79} +(-10875.7 - 9301.55i) q^{80} -15431.6 q^{81} +67507.2i q^{82} -24056.5i q^{83} +42724.4 q^{84} +(-42459.9 + 49645.7i) q^{85} +85623.1 q^{86} +51523.7i q^{87} +29917.2i q^{88} -19092.2 q^{89} +(-17457.7 + 20412.2i) q^{90} +18083.2 q^{91} +8464.00i q^{92} -44674.3i q^{93} -29845.8 q^{94} +(112445. + 96169.3i) q^{95} +11351.2 q^{96} +174479. i q^{97} +164878. i q^{98} +56150.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$			11.0852i			0.711114i	0.934655	+	0.355557i	$0.115709\pi$
$3$			11.0852i			0.711114i	−0.934655	+	0.355557i	$0.884291\pi$
$4$	−16.0000			−0.500000
$5$	−42.4833	−	36.3342i	−0.759964	−	0.649965i
$5$	−42.4833	−	36.3342i	−0.759964	−	0.649965i
$6$	44.3407			0.502834
$7$			240.887i			1.85810i	0.369960	+	0.929048i	$0.379371\pi$
$7$			240.887i			1.85810i	−0.369960	+	0.929048i	$0.620629\pi$
$8$			64.0000i			0.353553i
$9$	120.119			0.494316
$10$	−145.337	+	169.933i	−0.459595	+	0.537376i
$11$	467.455			1.16482			0.582410	−	0.812895i	$-0.302110\pi$
$11$	467.455			1.16482			0.582410	+	0.812895i	$0.302110\pi$
$12$		−	177.363i		−	0.355557i
$13$		−	75.0691i		−	0.123198i	−0.998101	−	0.0615989i	$-0.980380\pi$
$13$		−	75.0691i		−	0.123198i	0.998101	−	0.0615989i	$-0.0196200\pi$
$14$	963.547			1.31387
$15$	402.771	−	470.935i	0.462200	−	0.540421i
$16$	256.000			0.250000
$17$		−	1168.59i		−	0.980711i	−0.871522	−	0.490356i	$-0.836867\pi$
$17$		−	1168.59i		−	0.980711i	0.871522	−	0.490356i	$-0.163133\pi$
$18$		−	480.475i		−	0.349534i
$19$	−2646.80			−1.68204			−0.841022	−	0.541001i	$-0.818045\pi$
$19$	−2646.80			−1.68204			−0.841022	+	0.541001i	$0.818045\pi$
$20$	679.732	+	581.347i	0.379982	+	0.324983i
$21$	−2670.27			−1.32132
$22$		−	1869.82i		−	0.823652i
$23$		−	529.000i		−	0.208514i
$23$		−	529.000i		−	0.208514i
$24$	−709.451			−0.251417
$25$	484.656	+	3087.19i	0.155090	+	0.987900i
$26$	−300.277			−0.0871140
$27$			4025.24i			1.06263i
$28$		−	3854.19i		−	0.929048i
$29$	4647.98			1.02629			0.513144	−	0.858302i	$-0.328481\pi$
$29$	4647.98			1.02629			0.513144	+	0.858302i	$0.328481\pi$
$30$	−1883.74	−	1611.08i	−0.382136	−	0.326825i
$31$	−4030.10			−0.753201			−0.376601	−	0.926376i	$-0.622907\pi$
$31$	−4030.10			−0.753201			−0.376601	+	0.926376i	$0.622907\pi$
$32$		−	1024.00i		−	0.176777i
$33$			5181.83i			0.828320i
$34$	−4674.37			−0.693467
$35$	8752.42	−	10233.7i	1.20770	−	1.41209i
$36$	−1921.90			−0.247158
$37$			7197.11i			0.864279i	0.901807	+	0.432139i	$0.142241\pi$
$37$			7197.11i			0.864279i	−0.901807	+	0.432139i	$0.857759\pi$
$38$			10587.2i			1.18938i
$39$	832.155			0.0876077
$40$	2325.39	−	2718.93i	0.229797	−	0.268688i
$41$	−16876.8			−1.56794			−0.783972	−	0.620796i	$-0.786809\pi$
$41$	−16876.8			−1.56794			−0.783972	+	0.620796i	$0.786809\pi$
$42$			10681.1i			0.934313i
$43$			21405.8i			1.76547i	0.469873	+	0.882734i	$0.344300\pi$
$43$			21405.8i			1.76547i	−0.469873	+	0.882734i	$0.655700\pi$
$44$	−7479.29			−0.582410
$45$	−5103.04	−	4364.42i	−0.375662	−	0.321288i
$46$	−2116.00			−0.147442
$47$		−	7461.45i		−	0.492695i	−0.969182	−	0.246348i	$-0.920769\pi$
$47$		−	7461.45i		−	0.492695i	0.969182	−	0.246348i	$-0.0792305\pi$
$48$			2837.81i			0.177779i
$49$	−41219.5			−2.45252
$50$	12348.8	−	1938.63i	0.698551	−	0.109665i
$51$	12954.1			0.697398
$52$			1201.11i			0.0615989i
$53$			2674.52i			0.130785i	0.997860	+	0.0653923i	$0.0208299\pi$
$53$			2674.52i			0.130785i	−0.997860	+	0.0653923i	$0.979170\pi$
$54$	16100.9			0.751393
$55$	−19859.0	−	16984.6i	−0.885220	−	0.757092i
$56$	−15416.8			−0.656936
$57$		−	29340.2i		−	1.19613i
$58$		−	18591.9i		−	0.725696i
$59$	16834.5			0.629608			0.314804	−	0.949157i	$-0.398061\pi$
$59$	16834.5			0.629608			0.314804	+	0.949157i	$0.398061\pi$
$60$	−6444.33	+	7534.95i	−0.231100	+	0.270211i
$61$	−54644.2			−1.88027			−0.940133	−	0.340808i	$-0.889299\pi$
$61$	−54644.2			−1.88027			−0.940133	+	0.340808i	$0.889299\pi$
$62$			16120.4i			0.532594i
$63$			28935.1i			0.918487i
$64$	−4096.00			−0.125000
$65$	−2727.57	+	3189.18i	−0.0800743	+	0.0936259i
$66$	20727.3			0.585711
$67$		−	41448.4i		−	1.12803i	−0.825765	−	0.564015i	$-0.809256\pi$
$67$		−	41448.4i		−	1.12803i	0.825765	−	0.564015i	$-0.190744\pi$
$68$			18697.5i			0.490356i
$69$	5864.06			0.148278
$70$	−40934.6	−	35009.7i	−0.998495	−	0.853971i
$71$	−51983.0			−1.22381			−0.611907	−	0.790930i	$-0.709597\pi$
$71$	−51983.0			−1.22381			−0.611907	+	0.790930i	$0.709597\pi$
$72$			7687.61i			0.174767i
$73$		−	10162.3i		−	0.223196i	−0.993753	−	0.111598i	$-0.964403\pi$
$73$		−	10162.3i		−	0.223196i	0.993753	−	0.111598i	$-0.0355968\pi$
$74$	28788.4			0.611137
$75$	−34222.0	+	5372.50i	−0.702510	+	0.110287i
$76$	42348.8			0.841022
$77$			112604.i			2.16435i
$78$		−	3328.62i		−	0.0619480i
$79$	38861.4			0.700569			0.350284	−	0.936643i	$-0.386085\pi$
$79$	38861.4			0.700569			0.350284	+	0.936643i	$0.386085\pi$
$80$	−10875.7	−	9301.55i	−0.189991	−	0.162491i
$81$	−15431.6			−0.261335
$82$			67507.2i			1.10870i
$83$		−	24056.5i		−	0.383298i	−0.981463	−	0.191649i	$-0.938616\pi$
$83$		−	24056.5i		−	0.383298i	0.981463	−	0.191649i	$-0.0613836\pi$
$84$	42724.4			0.660659
$85$	−42459.9	+	49645.7i	−0.637428	+	0.745305i
$86$	85623.1			1.24837
$87$			51523.7i			0.729809i
$88$			29917.2i			0.411826i
$89$	−19092.2			−0.255494			−0.127747	−	0.991807i	$-0.540775\pi$
$89$	−19092.2			−0.255494			−0.127747	+	0.991807i	$0.540775\pi$
$90$	−17457.7	+	20412.2i	−0.227185	+	0.265633i
$91$	18083.2			0.228913
$92$			8464.00i			0.104257i
$93$		−	44674.3i		−	0.535612i
$94$	−29845.8			−0.348388
$95$	112445.	+	96169.3i	1.27829	+	1.09327i
$96$	11351.2			0.125708
$97$			174479.i			1.88285i	0.337227	+	0.941423i	$0.390511\pi$
$97$			174479.i			1.88285i	−0.337227	+	0.941423i	$0.609489\pi$
$98$			164878.i			1.73419i
$99$	56150.2			0.575789
$100$	−7754.50	−	49395.0i	−0.0775450	−	0.493950i
$101$	−181569.			−1.77108			−0.885541	−	0.464561i	$-0.846212\pi$
$101$	−181569.			−1.77108			−0.885541	+	0.464561i	$0.846212\pi$
$102$		−	51816.3i		−	0.493135i
$103$		−	117292.i		−	1.08937i	−0.838642	−	0.544683i	$-0.816650\pi$
$103$		−	117292.i		−	1.08937i	0.838642	−	0.544683i	$-0.183350\pi$
$104$	4804.42			0.0435570
$105$	113442.	+	97022.2i	1.00415	+	0.858811i
$106$	10698.1			0.0924786
$107$		−	47463.4i		−	0.400774i	−0.979717	−	0.200387i	$-0.935780\pi$
$107$		−	47463.4i		−	0.400774i	0.979717	−	0.200387i	$-0.0642199\pi$
$108$		−	64403.8i		−	0.531315i
$109$	−163475.			−1.31791			−0.658956	−	0.752182i	$-0.729002\pi$
$109$	−163475.			−1.31791			−0.658956	+	0.752182i	$0.729002\pi$
$110$	−67938.4	+	79436.1i	−0.535345	+	0.625945i
$111$	−79781.2			−0.614601
$112$			61667.0i			0.464524i
$113$		−	6183.70i		−	0.0455567i	−0.999741	−	0.0227784i	$-0.992749\pi$
$113$		−	6183.70i		−	0.0455567i	0.999741	−	0.0227784i	$-0.00725120\pi$
$114$	−117361.			−0.845788
$115$	−19220.8	+	22473.6i	−0.135527	+	0.158463i
$116$	−74367.7			−0.513144
$117$		−	9017.22i		−	0.0608987i
$118$		−	67338.0i		−	0.445200i
$119$	281499.			1.82225
$120$	30139.8	+	25777.3i	0.191068	+	0.163412i
$121$	57463.6			0.356804
$122$			218577.i			1.32955i
$123$		−	187082.i		−	1.11499i
$124$	64481.5			0.376601
$125$	91580.6	−	148763.i	0.524238	−	0.851572i
$126$	115740.			0.649468
$127$		−	239198.i		−	1.31598i	−0.753027	−	0.657989i	$-0.771407\pi$
$127$		−	239198.i		−	1.31598i	0.753027	−	0.657989i	$-0.228593\pi$
$128$			16384.0i			0.0883883i
$129$	−237287.			−1.25545
$130$	12756.7	+	10910.3i	0.0662035	+	0.0566211i
$131$	−231915.			−1.18073			−0.590366	−	0.807136i	$-0.701016\pi$
$131$	−231915.			−1.18073			−0.590366	+	0.807136i	$0.701016\pi$
$132$		−	82909.2i		−	0.414160i
$133$		−	637579.i		−	3.12540i
$134$	−165794.			−0.797637
$135$	146254.	−	171005.i	0.690673	−	0.807560i
$136$	74790.0			0.346734
$137$			151431.i			0.689310i	0.938729	+	0.344655i	$0.112004\pi$
$137$			151431.i			0.689310i	−0.938729	+	0.344655i	$0.887996\pi$
$138$		−	23456.2i		−	0.104848i
$139$	45050.3			0.197770			0.0988851	−	0.995099i	$-0.468472\pi$
$139$	45050.3			0.197770			0.0988851	+	0.995099i	$0.468472\pi$
$140$	−140039.	+	163739.i	−0.603849	+	0.706043i
$141$	82711.5			0.350363
$142$			207932.i			0.865367i
$143$		−	35091.5i		−	0.143503i
$144$	30750.4			0.123579
$145$	−197462.	−	168881.i	−0.779942	−	0.667052i
$146$	−40649.3			−0.157823
$147$		−	456925.i		−	1.74402i
$148$		−	115154.i		−	0.432139i
$149$	70780.4			0.261185			0.130592	−	0.991436i	$-0.458312\pi$
$149$	70780.4			0.261185			0.130592	+	0.991436i	$0.458312\pi$
$150$	21490.0	+	136888.i	0.0779845	+	0.496750i
$151$	129250.			0.461306			0.230653	−	0.973036i	$-0.425914\pi$
$151$	129250.			0.461306			0.230653	+	0.973036i	$0.425914\pi$
$152$		−	169395.i		−	0.594692i
$153$		−	140370.i		−	0.484781i
$154$	450416.			1.53042
$155$	171212.	+	146430.i	0.572406	+	0.489555i
$156$	−13314.5			−0.0438039
$157$			571274.i			1.84968i	0.380362	+	0.924838i	$0.375799\pi$
$157$			571274.i			1.84968i	−0.380362	+	0.924838i	$0.624201\pi$
$158$		−	155446.i		−	0.495377i
$159$	−29647.5			−0.0930028
$160$	−37206.2	+	43502.9i	−0.114899	+	0.134344i
$161$	127429.			0.387440
$162$			61726.3i			0.184792i
$163$			69100.1i			0.203709i	0.994799	+	0.101854i	$0.0324776\pi$
$163$			69100.1i			0.203709i	−0.994799	+	0.101854i	$0.967522\pi$
$164$	270029.			0.783972
$165$	188277.	−	220141.i	0.538379	−	0.629493i
$166$	−96226.0			−0.271033
$167$			379286.i			1.05239i	0.850365	+	0.526193i	$0.176381\pi$
$167$			379286.i			1.05239i	−0.850365	+	0.526193i	$0.823619\pi$
$168$		−	170898.i		−	0.467157i
$169$	365658.			0.984822
$170$	198583.	+	169839.i	0.527010	+	0.450730i
$171$	−317931.			−0.831461
$172$		−	342492.i		−	0.882734i
$173$		−	471489.i		−	1.19772i	−0.800853	−	0.598861i	$-0.795620\pi$
$173$		−	471489.i		−	1.19772i	0.800853	−	0.598861i	$-0.204380\pi$
$174$	206095.			0.516053
$175$	−743663.	+	116747.i	−1.83561	+	0.288172i
$176$	119669.			0.291205
$177$			186613.i			0.447723i
$178$			76368.8i			0.180662i
$179$	65589.8			0.153004			0.0765022	−	0.997069i	$-0.475625\pi$
$179$	65589.8			0.153004			0.0765022	+	0.997069i	$0.475625\pi$
$180$	81648.7	+	69830.7i	0.187831	+	0.160644i
$181$	−567192.			−1.28687			−0.643434	−	0.765502i	$-0.722491\pi$
$181$	−567192.			−1.28687			−0.643434	+	0.765502i	$0.722491\pi$
$182$		−	72332.7i		−	0.161866i
$183$		−	605740.i		−	1.33708i
$184$	33856.0			0.0737210
$185$	261501.	−	305757.i	0.561751	−	0.656821i
$186$	−178697.			−0.378735
$187$		−	546265.i		−	1.14235i
$188$			119383.i			0.246348i
$189$	−969627.			−1.97447
$190$	384677.	−	449779.i	0.773059	−	0.903889i
$191$	375259.			0.744299			0.372150	−	0.928173i	$-0.378621\pi$
$191$	375259.			0.744299			0.372150	+	0.928173i	$0.378621\pi$
$192$		−	45404.9i		−	0.0888893i
$193$			713752.i			1.37929i	0.724150	+	0.689643i	$0.242232\pi$
$193$			713752.i			1.37929i	−0.724150	+	0.689643i	$0.757768\pi$
$194$	697918.			1.33137
$195$	−35352.6	−	30235.6i	−0.0665787	−	0.0569420i
$196$	659512.			1.22626
$197$		−	617969.i		−	1.13449i	−0.823549	−	0.567245i	$-0.808009\pi$
$197$		−	617969.i		−	1.13449i	0.823549	−	0.567245i	$-0.191991\pi$
$198$		−	224601.i		−	0.407144i
$199$	−326418.			−0.584307			−0.292154	−	0.956371i	$-0.594372\pi$
$199$	−326418.			−0.584307			−0.292154	+	0.956371i	$0.594372\pi$
$200$	−197580.	+	31018.0i	−0.349276	+	0.0548326i
$201$	459463.			0.802158
$202$			726277.i			1.25234i
$203$			1.11964e6i			1.90694i
$204$	−207265.			−0.348699
$205$	716982.	+	613205.i	1.19158	+	1.01911i
$206$	−469167.			−0.770299
$207$		−	63542.9i		−	0.103072i
$208$		−	19217.7i		−	0.0307995i
$209$	−1.23726e6			−1.95928
$210$	388089.	−	453768.i	0.607271	−	0.710044i
$211$	470647.			0.727761			0.363881	−	0.931446i	$-0.381452\pi$
$211$	470647.			0.727761			0.363881	+	0.931446i	$0.381452\pi$
$212$		−	42792.3i		−	0.0653923i
$213$		−	576240.i		−	0.870271i
$214$	−189854.			−0.283390
$215$	777761.	−	909387.i	1.14749	−	1.34169i
$216$	−257615.			−0.375696
$217$		−	970797.i		−	1.39952i
$218$			653902.i			0.931904i
$219$	112651.			0.158718
$220$	317745.	+	271754.i	0.442610	+	0.378546i
$221$	−87725.3			−0.120821
$222$			319125.i			0.434589i
$223$			761226.i			1.02507i	0.858668	+	0.512533i	$0.171293\pi$
$223$			761226.i			1.02507i	−0.858668	+	0.512533i	$0.828707\pi$
$224$	246668.			0.328468
$225$	58216.4	+	370830.i	0.0766635	+	0.488335i
$226$	−24734.8			−0.0322135
$227$			516579.i			0.665383i	0.943036	+	0.332692i	$0.107957\pi$
$227$			516579.i			0.665383i	−0.943036	+	0.332692i	$0.892043\pi$
$228$			469444.i			0.598063i
$229$	1.20041e6			1.51265			0.756327	−	0.654194i	$-0.226992\pi$
$229$	1.20041e6			1.51265			0.756327	+	0.654194i	$0.226992\pi$
$230$	89894.6	+	76883.1i	0.112051	+	0.0958322i
$231$	−1.24823e6			−1.53910
$232$			297471.i			0.362848i
$233$		−	399621.i		−	0.482235i	−0.970496	−	0.241118i	$-0.922486\pi$
$233$		−	399621.i		−	0.482235i	0.970496	−	0.241118i	$-0.0775139\pi$
$234$	−36068.9			−0.0430619
$235$	−271106.	+	316987.i	−0.320235	+	0.374431i
$236$	−269352.			−0.314804
$237$			430785.i			0.498184i
$238$		−	1.12600e6i		−	1.28853i
$239$	1.59947e6			1.81127			0.905633	−	0.424062i	$-0.139396\pi$
$239$	1.59947e6			1.81127			0.905633	+	0.424062i	$0.139396\pi$
$240$	103109.	−	120559.i	0.115550	−	0.135105i
$241$	1.14639e6			1.27143			0.635714	−	0.771925i	$-0.280706\pi$
$241$	1.14639e6			1.27143			0.635714	+	0.771925i	$0.280706\pi$
$242$		−	229854.i		−	0.252298i
$243$			807071.i			0.876791i
$244$	874307.			0.940133
$245$	1.75114e6	+	1.49768e6i	1.86383	+	1.59405i
$246$	−748329.			−0.788415
$247$			198693.i			0.207224i
$248$		−	257926.i		−	0.266297i
$249$	266671.			0.272569
$250$	−595054.	−	366323.i	−0.602152	−	0.370692i
$251$	11639.9			0.0116618			0.00583091	−	0.999983i	$-0.498144\pi$
$251$	11639.9			0.0116618			0.00583091	+	0.999983i	$0.498144\pi$
$252$		−	462961.i		−	0.459243i
$253$		−	247284.i		−	0.242882i
$254$	−956793.			−0.930537
$255$	−550331.	−	470675.i	−0.529997	−	0.453284i
$256$	65536.0			0.0625000
$257$		−	178759.i		−	0.168824i	−0.996431	−	0.0844122i	$-0.973099\pi$
$257$		−	178759.i		−	0.168824i	0.996431	−	0.0844122i	$-0.0269012\pi$
$258$			949147.i			0.887737i
$259$	−1.73369e6			−1.60591
$260$	43641.2	−	51026.9i	0.0400372	−	0.0468129i
$261$	558310.			0.507311
$262$			927661.i			0.834903i
$263$		−	409538.i		−	0.365094i	−0.983197	−	0.182547i	$-0.941566\pi$
$263$		−	409538.i		−	0.365094i	0.983197	−	0.182547i	$-0.0584342\pi$
$264$	−331637.			−0.292855
$265$	97176.5	−	113622.i	0.0850054	−	0.0993915i
$266$	−2.55032e6			−2.20999
$267$		−	211641.i		−	0.181686i
$268$			663174.i			0.564015i
$269$	−366312.			−0.308653			−0.154326	−	0.988020i	$-0.549321\pi$
$269$	−366312.			−0.308653			−0.154326	+	0.988020i	$0.549321\pi$
$270$	−684021.	−	585015.i	−0.571031	−	0.488379i
$271$	−498282.			−0.412147			−0.206073	−	0.978537i	$-0.566069\pi$
$271$	−498282.			−0.412147			−0.206073	+	0.978537i	$0.566069\pi$
$272$		−	299160.i		−	0.245178i
$273$			200455.i			0.162784i
$274$	605726.			0.487416
$275$	226555.	+	1.44312e6i	0.180652	+	1.15073i
$276$	−93824.9			−0.0741388
$277$			918935.i			0.719590i	0.933031	+	0.359795i	$0.117153\pi$
$277$			918935.i			0.719590i	−0.933031	+	0.359795i	$0.882847\pi$
$278$		−	180201.i		−	0.139845i
$279$	−484091.			−0.372320
$280$	654954.	+	560155.i	0.499248	+	0.426986i
$281$	−1.16495e6			−0.880120			−0.440060	−	0.897968i	$-0.645043\pi$
$281$	−1.16495e6			−0.880120			−0.440060	+	0.897968i	$0.645043\pi$
$282$		−	330846.i		−	0.247744i
$283$		−	1.07010e6i		−	0.794250i	−0.917764	−	0.397125i	$-0.870008\pi$
$283$		−	1.07010e6i		−	0.794250i	0.917764	−	0.397125i	$-0.129992\pi$
$284$	831727.			0.611907
$285$	−1.06605e6	+	1.24647e6i	−0.777440	+	0.909012i
$286$	−140366.			−0.101472
$287$		−	4.06540e6i		−	2.91339i
$288$		−	123002.i		−	0.0873836i
$289$	54246.8			0.0382058
$290$	−675522.	+	789846.i	−0.471677	+	0.551503i
$291$	−1.93414e6			−1.33892
$292$			162597.i			0.111598i
$293$			924569.i			0.629173i	0.949229	+	0.314587i	$0.101866\pi$
$293$			924569.i			0.629173i	−0.949229	+	0.314587i	$0.898134\pi$
$294$	−1.82770e6			−1.23321
$295$	−715185.	−	611668.i	−0.478479	−	0.409223i
$296$	−460615.			−0.305569
$297$			1.88162e6i			1.23777i
$298$		−	283122.i		−	0.184685i
$299$	−39711.6			−0.0256885
$300$	547553.	−	85960.0i	0.351255	−	0.0551434i
$301$	−5.15637e6			−3.28041
$302$		−	517001.i		−	0.326192i
$303$		−	2.01273e6i		−	1.25944i
$304$	−677581.			−0.420511
$305$	2.32146e6	+	1.98545e6i	1.42893	+	1.22211i
$306$	−561480.			−0.342792
$307$			1.23705e6i			0.749104i	0.927206	+	0.374552i	$0.122204\pi$
$307$			1.23705e6i			0.749104i	−0.927206	+	0.374552i	$0.877796\pi$
$308$		−	1.80166e6i		−	1.08217i
$309$	1.30020e6			0.774664
$310$	585721.	−	684847.i	0.346168	−	0.404752i
$311$	497167.			0.291475			0.145737	−	0.989323i	$-0.453445\pi$
$311$	497167.			0.291475			0.145737	+	0.989323i	$0.453445\pi$
$312$			53257.9i			0.0309740i
$313$			2.95569e6i			1.70529i	0.522490	+	0.852646i	$0.325003\pi$
$313$			2.95569e6i			1.70529i	−0.522490	+	0.852646i	$0.674997\pi$
$314$	2.28510e6			1.30792
$315$	1.05133e6	−	1.22926e6i	0.596985	−	0.698017i
$316$	−621782.			−0.350284
$317$		−	1.17823e6i		−	0.658537i	−0.944236	−	0.329269i	$-0.893198\pi$
$317$		−	1.17823e6i		−	0.658537i	0.944236	−	0.329269i	$-0.106802\pi$
$318$			118590.i			0.0657629i
$319$	2.17273e6			1.19544
$320$	174011.	+	148825.i	0.0949955	+	0.0812457i
$321$	526140.			0.284996
$322$		−	509717.i		−	0.273961i
$323$			3.09303e6i			1.64960i
$324$	246905.			0.130668
$325$	231753.	−	36382.7i	0.121707	−	0.0191068i
$326$	276400.			0.144044
$327$		−	1.81215e6i		−	0.937186i
$328$		−	1.08012e6i		−	0.554352i
$329$	1.79737e6			0.915475
$330$	−880564.	−	753109.i	−0.445119	−	0.380692i
$331$	−2.45769e6			−1.23299			−0.616493	−	0.787361i	$-0.711447\pi$
$331$	−2.45769e6			−1.23299			−0.616493	+	0.787361i	$0.711447\pi$
$332$			384904.i			0.191649i
$333$			864509.i			0.427227i
$334$	1.51714e6			0.744150
$335$	−1.50599e6	+	1.76086e6i	−0.733180	+	0.857262i
$336$	−683590.			−0.330330
$337$		−	839672.i		−	0.402749i	−0.979514	−	0.201375i	$-0.935459\pi$
$337$		−	839672.i		−	0.402749i	0.979514	−	0.201375i	$-0.0645409\pi$
$338$		−	1.46263e6i		−	0.696375i
$339$	68547.4			0.0323960
$340$	679358.	−	794331.i	0.318714	−	0.372652i
$341$	−1.88389e6			−0.877344
$342$			1.27172e6i			0.587932i
$343$		−	5.88065e6i		−	2.69892i
$344$	−1.36997e6			−0.624187
$345$	−249124.	−	213066.i	−0.112686	−	0.0963753i
$346$	−1.88596e6			−0.846918
$347$			393343.i			0.175367i	0.996148	+	0.0876835i	$0.0279464\pi$
$347$			393343.i			0.175367i	−0.996148	+	0.0876835i	$0.972054\pi$
$348$		−	824380.i		−	0.364904i
$349$	−1.14079e6			−0.501351			−0.250676	−	0.968071i	$-0.580653\pi$
$349$	−1.14079e6			−0.501351			−0.250676	+	0.968071i	$0.580653\pi$
$350$	466989.	+	2.97465e6i	0.203768	+	1.29797i
$351$	302171.			0.130914
$352$		−	478674.i		−	0.205913i
$353$			2.66729e6i			1.13929i	0.821892	+	0.569644i	$0.192919\pi$
$353$			2.66729e6i			1.13929i	−0.821892	+	0.569644i	$0.807081\pi$
$354$	746454.			0.316588
$355$	2.20841e6	+	1.88876e6i	0.930054	+	0.795436i
$356$	305475.			0.127747
$357$			3.12046e6i			1.29583i
$358$		−	262359.i		−	0.108190i
$359$	−4.35952e6			−1.78526			−0.892631	−	0.450787i	$-0.851143\pi$
$359$	−4.35952e6			−1.78526			−0.892631	+	0.450787i	$0.851143\pi$
$360$	279323.	−	326595.i	0.113593	−	0.132817i
$361$	4.52945e6			1.82927
$362$			2.26877e6i			0.909952i
$363$			636994.i			0.253728i
$364$	−289331.			−0.114457
$365$	−369240.	+	431729.i	−0.145069	+	0.169621i
$366$	−2.42296e6			−0.945461
$367$			1.93173e6i			0.748656i	0.927296	+	0.374328i	$0.122127\pi$
$367$			1.93173e6i			0.748656i	−0.927296	+	0.374328i	$0.877873\pi$
$368$		−	135424.i		−	0.0521286i
$369$	−2.02722e6			−0.775060
$370$	−1.22303e6	−	1.04600e6i	−0.464442	−	0.397218i
$371$	−644257.			−0.243010
$372$			714789.i			0.267806i
$373$		−	1.36926e6i		−	0.509580i	−0.966996	−	0.254790i	$-0.917994\pi$
$373$		−	1.36926e6i		−	0.509580i	0.966996	−	0.254790i	$-0.0820063\pi$
$374$	−2.18506e6			−0.807764
$375$	1.64907e6	+	1.01519e6i	0.605565	+	0.372793i
$376$	477533.			0.174194
$377$		−	348920.i		−	0.126437i
$378$			3.87851e6i			1.39616i
$379$	337322.			0.120628			0.0603138	−	0.998179i	$-0.480790\pi$
$379$	337322.			0.120628			0.0603138	+	0.998179i	$0.480790\pi$
$380$	−1.79912e6	−	1.53871e6i	−0.639146	−	0.546635i
$381$	2.65156e6			0.935811
$382$		−	1.50104e6i		−	0.526299i
$383$			4.57274e6i			1.59287i	0.604726	+	0.796434i	$0.293283\pi$
$383$			4.57274e6i			1.59287i	−0.604726	+	0.796434i	$0.706717\pi$
$384$	−181620.			−0.0628542
$385$	4.09137e6	−	4.78378e6i	1.40675	−	1.64482i
$386$	2.85501e6			0.975302
$387$			2.57124e6i			0.872699i
$388$		−	2.79167e6i		−	0.941423i
$389$	−3.22013e6			−1.07894			−0.539472	−	0.842003i	$-0.681376\pi$
$389$	−3.22013e6			−1.07894			−0.539472	+	0.842003i	$0.681376\pi$
$390$	−120943.	+	141411.i	−0.0402641	+	0.0470783i
$391$	−618186.			−0.204492
$392$		−	2.63805e6i		−	0.867096i
$393$		−	2.57082e6i		−	0.839635i
$394$	−2.47188e6			−0.802206
$395$	−1.65096e6	−	1.41200e6i	−0.532407	−	0.455345i
$396$	−898403.			−0.287895
$397$		−	3.83322e6i		−	1.22064i	−0.792155	−	0.610320i	$-0.791041\pi$
$397$		−	3.83322e6i		−	1.22064i	0.792155	−	0.610320i	$-0.208959\pi$
$398$			1.30567e6i			0.413167i
$399$	7.06768e6			2.22251
$400$	124072.	+	790320.i	0.0387725	+	0.246975i
$401$	526941.			0.163644			0.0818222	−	0.996647i	$-0.473926\pi$
$401$	526941.			0.163644			0.0818222	+	0.996647i	$0.473926\pi$
$402$		−	1.83785e6i		−	0.567212i
$403$			302536.i			0.0927928i
$404$	2.90511e6			0.885541
$405$	655584.	+	560694.i	0.198605	+	0.169859i
$406$	4.47855e6			1.34841
$407$			3.36433e6i			1.00673i
$408$			829060.i			0.246567i
$409$	3.55539e6			1.05094			0.525471	−	0.850812i	$-0.323889\pi$
$409$	3.55539e6			1.05094			0.525471	+	0.850812i	$0.323889\pi$
$410$	2.45282e6	−	2.86793e6i	0.720619	−	0.842575i
$411$	−1.67864e6			−0.490178
$412$			1.87667e6i			0.544683i
$413$			4.05521e6i			1.16987i
$414$	−254171.			−0.0728830
$415$	−874073.	+	1.02200e6i	−0.249131	+	0.291293i
$416$	−76870.8			−0.0217785
$417$			499391.i			0.140637i
$418$			4.94905e6i			1.38542i
$419$	4.90833e6			1.36584			0.682918	−	0.730495i	$-0.260711\pi$
$419$	4.90833e6			1.36584			0.682918	+	0.730495i	$0.260711\pi$
$420$	−1.81507e6	−	1.55235e6i	−0.502077	−	0.429406i
$421$	−390256.			−0.107311			−0.0536555	−	0.998560i	$-0.517087\pi$
$421$	−390256.			−0.107311			−0.0536555	+	0.998560i	$0.517087\pi$
$422$		−	1.88259e6i		−	0.514605i
$423$		−	896261.i		−	0.243547i
$424$	−171169.			−0.0462393
$425$	3.60767e6	−	566366.i	0.968845	−	0.152098i
$426$	−2.30496e6			−0.615375
$427$		−	1.31631e7i		−	3.49371i
$428$			759415.i			0.200387i
$429$	388995.			0.102047
$430$	−3.63755e6	−	3.11104e6i	−0.948719	−	0.811400i
$431$	1.73752e6			0.450542			0.225271	−	0.974296i	$-0.427673\pi$
$431$	1.73752e6			0.450542			0.225271	+	0.974296i	$0.427673\pi$
$432$			1.03046e6i			0.265657i
$433$			2.02888e6i			0.520040i	0.965603	+	0.260020i	$0.0837292\pi$
$433$			2.02888e6i			0.520040i	−0.965603	+	0.260020i	$0.916271\pi$
$434$	−3.88319e6			−0.989610
$435$	1.87207e6	−	2.18890e6i	0.474350	−	0.554628i
$436$	2.61561e6			0.658956
$437$			1.40016e6i			0.350730i
$438$		−	450605.i		−	0.112230i
$439$	3.02179e6			0.748346			0.374173	−	0.927359i	$-0.377927\pi$
$439$	3.02179e6			0.748346			0.374173	+	0.927359i	$0.377927\pi$
$440$	1.08701e6	−	1.27098e6i	0.267673	−	0.312973i
$441$	−4.95124e6			−1.21232
$442$			350901.i			0.0854337i
$443$			4.48368e6i			1.08549i	0.839898	+	0.542745i	$0.182615\pi$
$443$			4.48368e6i			1.08549i	−0.839898	+	0.542745i	$0.817385\pi$
$444$	1.27650e6			0.307301
$445$	811099.	+	693700.i	0.194166	+	0.166062i
$446$	3.04490e6			0.724831
$447$			784614.i			0.185732i
$448$		−	986673.i		−	0.232262i
$449$	906332.			0.212164			0.106082	−	0.994357i	$-0.466169\pi$
$449$	906332.			0.212164			0.106082	+	0.994357i	$0.466169\pi$
$450$	1.48332e6	−	232865.i	0.345305	−	0.0542093i
$451$	−7.88915e6			−1.82637
$452$			98939.2i			0.0227784i
$453$			1.43276e6i			0.328041i
$454$	2.06631e6			0.470497
$455$	−768232.	−	657037.i	−0.173966	−	0.148786i
$456$	1.87778e6			0.422894
$457$			4.45659e6i			0.998189i	0.866548	+	0.499094i	$0.166334\pi$
$457$			4.45659e6i			0.998189i	−0.866548	+	0.499094i	$0.833666\pi$
$458$		−	4.80163e6i		−	1.06961i
$459$	4.70386e6			1.04213
$460$	307532.	−	359578.i	0.0677636	−	0.0792317i
$461$	185845.			0.0407284			0.0203642	−	0.999793i	$-0.493517\pi$
$461$	185845.			0.0407284			0.0203642	+	0.999793i	$0.493517\pi$
$462$			4.99294e6i			1.08831i
$463$		−	2.02317e6i		−	0.438611i	−0.975656	−	0.219305i	$-0.929621\pi$
$463$		−	2.02317e6i		−	0.438611i	0.975656	−	0.219305i	$-0.0703791\pi$
$464$	1.18988e6			0.256572
$465$	−1.62320e6	+	1.89791e6i	−0.348130	+	0.407046i
$466$	−1.59849e6			−0.340992
$467$		−	7.25814e6i		−	1.54004i	−0.638018	−	0.770022i	$-0.720245\pi$
$467$		−	7.25814e6i		−	1.54004i	0.638018	−	0.770022i	$-0.279755\pi$
$468$			144275.i			0.0304493i
$469$	9.98437e6			2.09599
$470$	1.26795e6	+	1.08442e6i	0.264762	+	0.226440i
$471$	−6.33268e6			−1.31533
$472$			1.07741e6i			0.222600i
$473$			1.00062e7i			2.05645i
$474$	1.72314e6			0.352270
$475$	−1.28279e6	−	8.17117e6i	−0.260868	−	1.66169i
$476$	−4.50398e6			−0.911127
$477$			321260.i			0.0646489i
$478$		−	6.39789e6i		−	1.28076i
$479$	3.25941e6			0.649082			0.324541	−	0.945872i	$-0.394790\pi$
$479$	3.25941e6			0.649082			0.324541	+	0.945872i	$0.394790\pi$
$480$	−482237.	−	412437.i	−0.0955339	−	0.0817061i
$481$	540281.			0.106477
$482$		−	4.58558e6i		−	0.899035i
$483$			1.41257e6i			0.275514i
$484$	−919418.			−0.178402
$485$	6.33957e6	−	7.41246e6i	1.22379	−	1.43090i
$486$	3.22828e6			0.619985
$487$			4.70745e6i			0.899421i	0.893174	+	0.449711i	$0.148473\pi$
$487$			4.70745e6i			0.899421i	−0.893174	+	0.449711i	$0.851527\pi$
$488$		−	3.49723e6i		−	0.664774i
$489$	−765987.			−0.144860
$490$	5.99070e6	−	7.00455e6i	1.12717	−	1.31792i
$491$	−7.84649e6			−1.46883			−0.734415	−	0.678701i	$-0.762543\pi$
$491$	−7.84649e6			−1.46883			−0.734415	+	0.678701i	$0.762543\pi$
$492$			2.99332e6i			0.557494i
$493$		−	5.43160e6i		−	1.00649i
$494$	794772.			0.146530
$495$	−2.38544e6	−	2.04017e6i	−0.437579	−	0.374243i
$496$	−1.03170e6			−0.188300
$497$		−	1.25220e7i		−	2.27396i
$498$		−	1.06668e6i		−	0.192735i
$499$	1.24426e6			0.223697			0.111848	−	0.993725i	$-0.464323\pi$
$499$	1.24426e6			0.223697			0.111848	+	0.993725i	$0.464323\pi$
$500$	−1.46529e6	+	2.38022e6i	−0.262119	+	0.425786i
$501$	−4.20445e6			−0.748367
$502$		−	46559.8i		−	0.00824616i
$503$			4.59595e6i			0.809944i	0.914329	+	0.404972i	$0.132719\pi$
$503$			4.59595e6i			0.809944i	−0.914329	+	0.404972i	$0.867281\pi$
$504$	−1.85184e6			−0.324734
$505$	7.71365e6	+	6.59717e6i	1.34596	+	1.15114i
$506$	−989136.			−0.171743
$507$			4.05338e6i			0.700321i
$508$			3.82717e6i			0.657989i
$509$	−9.70582e6			−1.66050			−0.830248	−	0.557395i	$-0.811801\pi$
$509$	−9.70582e6			−1.66050			−0.830248	+	0.557395i	$0.811801\pi$
$510$	−1.88270e6	+	2.20132e6i	−0.320520	+	0.374765i
$511$	2.44797e6			0.414719
$512$		−	262144.i		−	0.0441942i
$513$		−	1.06540e7i		−	1.78739i
$514$	−715036.			−0.119377
$515$	−4.26170e6	+	4.98293e6i	−0.708051	+	0.827879i
$516$	3.79659e6			0.627725
$517$		−	3.48790e6i		−	0.573901i
$518$			6.93476e6i			1.13555i
$519$	5.22654e6			0.851718
$520$	−204108.	−	174565.i	−0.0331017	−	0.0283105i
$521$	2.58019e6			0.416445			0.208222	−	0.978082i	$-0.433232\pi$
$521$	2.58019e6			0.416445			0.208222	+	0.978082i	$0.433232\pi$
$522$		−	2.23324e6i		−	0.358723i
$523$		−	8.38725e6i		−	1.34080i	−0.741998	−	0.670402i	$-0.766122\pi$
$523$		−	8.38725e6i		−	1.34080i	0.741998	−	0.670402i	$-0.233878\pi$
$524$	3.71064e6			0.590366
$525$	−1.29416e6	−	8.24364e6i	−0.204923	−	1.30533i
$526$	−1.63815e6			−0.258161
$527$			4.70954e6i			0.738673i
$528$			1.32655e6i			0.207080i
$529$	−279841.			−0.0434783
$530$	−454490.	−	388706.i	−0.0702804	−	0.0601079i
$531$	2.02214e6			0.311226
$532$			1.02013e7i			1.56270i
$533$			1.26693e6i			0.193167i
$534$	−846562.			−0.128471
$535$	−1.72454e6	+	2.01640e6i	−0.260489	+	0.304574i
$536$	2.65270e6			0.398819
$537$			727075.i			0.108804i
$538$			1.46525e6i			0.218250i
$539$	−1.92683e7			−2.85674
$540$	−2.34006e6	+	2.73608e6i	−0.345336	+	0.403780i
$541$	−5.32944e6			−0.782868			−0.391434	−	0.920206i	$-0.628021\pi$
$541$	−5.32944e6			−0.782868			−0.391434	+	0.920206i	$0.628021\pi$
$542$			1.99313e6i			0.291432i
$543$		−	6.28742e6i		−	0.915110i
$544$	−1.19664e6			−0.173367
$545$	6.94497e6	+	5.93974e6i	1.00156	+	0.856597i
$546$	801820.			0.115105
$547$		−	5.58230e6i		−	0.797710i	−0.917014	−	0.398855i	$-0.869408\pi$
$547$		−	5.58230e6i		−	0.797710i	0.917014	−	0.398855i	$-0.130592\pi$
$548$		−	2.42290e6i		−	0.344655i
$549$	−6.56379e6			−0.929446
$550$	5.77249e6	−	906221.i	0.813686	−	0.127740i
$551$	−1.23023e7			−1.72626
$552$			375300.i			0.0524241i
$553$			9.36120e6i			1.30172i
$554$	3.67574e6			0.508827
$555$	3.38937e6	+	2.89879e6i	0.467075	+	0.399469i
$556$	−720805.			−0.0988851
$557$		−	187335.i		−	0.0255848i	−0.999918	−	0.0127924i	$-0.995928\pi$
$557$		−	187335.i		−	0.0255848i	0.999918	−	0.0127924i	$-0.00407206\pi$
$558$			1.93636e6i			0.263270i
$559$	1.60691e6			0.217502
$560$	2.24062e6	−	2.61982e6i	0.301924	−	0.353021i
$561$	6.05545e6			0.812342
$562$			4.65981e6i			0.622339i
$563$			5.69297e6i			0.756951i	0.925611	+	0.378476i	$0.123552\pi$
$563$			5.69297e6i			0.756951i	−0.925611	+	0.378476i	$0.876448\pi$
$564$	−1.32338e6			−0.175181
$565$	−224680.	+	262704.i	−0.0296103	+	0.0346215i
$566$	−4.28039e6			−0.561620
$567$		−	3.71727e6i		−	0.485586i
$568$		−	3.32691e6i		−	0.432683i
$569$	9.50428e6			1.23066			0.615330	−	0.788269i	$-0.289023\pi$
$569$	9.50428e6			1.23066			0.615330	+	0.788269i	$0.289023\pi$
$570$	4.98588e6	+	4.26421e6i	0.642768	+	0.549733i
$571$	7.18798e6			0.922607			0.461303	−	0.887243i	$-0.347382\pi$
$571$	7.18798e6			0.922607			0.461303	+	0.887243i	$0.347382\pi$
$572$			561464.i			0.0717516i
$573$			4.15981e6i			0.529282i
$574$	−1.62616e7			−2.06008
$575$	1.63312e6	−	256383.i	0.205991	−	0.0323385i
$576$	−492007.			−0.0617895
$577$		−	1.33248e6i		−	0.166617i	−0.996524	−	0.0833087i	$-0.973451\pi$
$577$		−	1.33248e6i		−	0.166617i	0.996524	−	0.0833087i	$-0.0265488\pi$
$578$		−	216987.i		−	0.0270156i
$579$	−7.91207e6			−0.980830
$580$	3.15938e6	+	2.70209e6i	0.389971	+	0.333526i
$581$	5.79489e6			0.712205
$582$			7.73654e6i			0.946759i
$583$			1.25022e6i			0.152340i
$584$	650389.			0.0789116
$585$	−327633.	+	383081.i	−0.0395820	+	0.0462808i
$586$	3.69828e6			0.444893
$587$			2.07178e6i			0.248169i	0.992272	+	0.124085i	$0.0395994\pi$
$587$			2.07178e6i			0.248169i	−0.992272	+	0.124085i	$0.960401\pi$
$588$			7.31080e6i			0.872011i
$589$	1.06669e7			1.26692
$590$	−2.44667e6	+	2.86074e6i	−0.289365	+	0.338336i
$591$	6.85029e6			0.806753
$592$			1.84246e6i			0.216070i
$593$		−	1.19320e7i		−	1.39340i	−0.717361	−	0.696702i	$-0.754650\pi$
$593$		−	1.19320e7i		−	1.39340i	0.717361	−	0.696702i	$-0.245350\pi$
$594$	7.52648e6			0.875237
$595$	−1.19590e7	−	1.02280e7i	−1.38485	−	1.18440i
$596$	−1.13249e6			−0.130592
$597$		−	3.61840e6i		−	0.415509i
$598$			158846.i			0.0181645i
$599$	−1.23047e7			−1.40121			−0.700604	−	0.713551i	$-0.747086\pi$
$599$	−1.23047e7			−1.40121			−0.700604	+	0.713551i	$0.747086\pi$
$600$	−343840.	−	2.19021e6i	−0.0389923	−	0.248375i
$601$	3.96504e6			0.447777			0.223889	−	0.974615i	$-0.428125\pi$
$601$	3.96504e6			0.447777			0.223889	+	0.974615i	$0.428125\pi$
$602$			2.06255e7i			2.31960i
$603$		−	4.97873e6i		−	0.557603i
$604$	−2.06800e6			−0.230653
$605$	−2.44124e6	−	2.08789e6i	−0.271158	−	0.231910i
$606$	−8.05091e6			−0.890560
$607$		−	1.15817e7i		−	1.27585i	−0.770097	−	0.637926i	$-0.779792\pi$
$607$		−	1.15817e7i		−	1.27585i	0.770097	−	0.637926i	$-0.220208\pi$
$608$			2.71032e6i			0.297346i
$609$	−1.24114e7			−1.35605
$610$	7.94180e6	−	9.28585e6i	0.864161	−	1.01041i
$611$	−560124.			−0.0606990
$612$			2.24592e6i			0.242391i
$613$			8.88158e6i			0.954639i	0.878730	+	0.477320i	$0.158392\pi$
$613$			8.88158e6i			0.954639i	−0.878730	+	0.477320i	$0.841608\pi$
$614$	4.94821e6			0.529697
$615$	−6.79748e6	+	7.94787e6i	−0.724703	+	0.847350i
$616$	−7.20665e6			−0.765212
$617$			3.21626e6i			0.340125i	0.985433	+	0.170062i	$0.0543969\pi$
$617$			3.21626e6i			0.340125i	−0.985433	+	0.170062i	$0.945603\pi$
$618$		−	5.20080e6i		−	0.547771i
$619$	9.25873e6			0.971236			0.485618	−	0.874171i	$-0.338595\pi$
$619$	9.25873e6			0.971236			0.485618	+	0.874171i	$0.338595\pi$
$620$	−2.73939e6	−	2.34288e6i	−0.286203	−	0.244777i
$621$	2.12935e6			0.221574
$622$		−	1.98867e6i		−	0.206104i
$623$		−	4.59906e6i		−	0.474733i
$624$	213032.			0.0219019
$625$	−9.29584e6	+	2.99245e6i	−0.951894	+	0.306427i
$626$	1.18228e7			1.20582
$627$		−	1.37153e7i		−	1.39327i
$628$		−	9.14039e6i		−	0.924838i
$629$	8.41050e6			0.847608
$630$	−4.91702e6	−	4.20532e6i	−0.493572	−	0.422132i
$631$	5.84125e6			0.584026			0.292013	−	0.956414i	$-0.405675\pi$
$631$	5.84125e6			0.584026			0.292013	+	0.956414i	$0.405675\pi$
$632$			2.48713e6i			0.247688i
$633$			5.21720e6i			0.517521i
$634$	−4.71290e6			−0.465656
$635$	−8.69107e6	+	1.01619e7i	−0.855340	+	1.00010i
$636$	474361.			0.0465014
$637$			3.09431e6i			0.302145i
$638$		−	8.69090e6i		−	0.845304i
$639$	−6.24413e6			−0.604951
$640$	595299.	−	696046.i	0.0574494	−	0.0671719i
$641$	−8.45939e6			−0.813194			−0.406597	−	0.913608i	$-0.633285\pi$
$641$	−8.45939e6			−0.813194			−0.406597	+	0.913608i	$0.633285\pi$
$642$		−	2.10456e6i		−	0.201523i
$643$		−	5.60107e6i		−	0.534249i	−0.963662	−	0.267124i	$-0.913927\pi$
$643$		−	5.60107e6i		−	0.534249i	0.963662	−	0.267124i	$-0.0860735\pi$
$644$	−2.03887e6			−0.193720
$645$	1.00807e7	+	8.62162e6i	0.954096	+	0.815999i
$646$	1.23721e7			1.16644
$647$		−	3.41934e6i		−	0.321131i	−0.987025	−	0.160565i	$-0.948668\pi$
$647$		−	3.41934e6i		−	0.321131i	0.987025	−	0.160565i	$-0.0513317\pi$
$648$		−	987621.i		−	0.0923959i
$649$	7.86938e6			0.733380
$650$	−145531.	−	927010.i	−0.0135105	−	0.0860600i
$651$	1.07615e7			0.995219
$652$		−	1.10560e6i		−	0.101854i
$653$		−	1.51391e7i		−	1.38937i	−0.719314	−	0.694685i	$-0.755544\pi$
$653$		−	1.51391e7i		−	1.38937i	0.719314	−	0.694685i	$-0.244456\pi$
$654$	−7.24862e6			−0.662690
$655$	9.85252e6	+	8.42645e6i	0.897313	+	0.767435i
$656$	−4.32046e6			−0.391986
$657$		−	1.22069e6i		−	0.110329i
$658$		−	7.18946e6i		−	0.647339i
$659$	1.57325e6			0.141119			0.0705593	−	0.997508i	$-0.477522\pi$
$659$	1.57325e6			0.141119			0.0705593	+	0.997508i	$0.477522\pi$
$660$	−3.01244e6	+	3.52225e6i	−0.269190	+	0.314747i
$661$	−4.39858e6			−0.391569			−0.195785	−	0.980647i	$-0.562725\pi$
$661$	−4.39858e6			−0.391569			−0.195785	+	0.980647i	$0.562725\pi$
$662$			9.83078e6i			0.871852i
$663$		−	972450.i		−	0.0859179i
$664$	1.53962e6			0.135516
$665$	−2.31659e7	+	2.70865e7i	−2.03140	+	2.37519i
$666$	3.45803e6			0.302095
$667$		−	2.45878e6i		−	0.213996i
$668$		−	6.06857e6i		−	0.526193i
$669$	−8.43833e6			−0.728939
$670$	7.04345e6	+	6.02397e6i	0.606176	+	0.518437i
$671$	−2.55437e7			−2.19017
$672$			2.73436e6i			0.233578i
$673$		−	300627.i		−	0.0255853i	−0.999918	−	0.0127927i	$-0.995928\pi$
$673$		−	300627.i		−	0.0255853i	0.999918	−	0.0127927i	$-0.00407214\pi$
$674$	−3.35869e6			−0.284787
$675$	−1.24267e7	+	1.95086e6i	−1.04977	+	0.164803i
$676$	−5.85052e6			−0.492411
$677$			1.00774e7i			0.845036i	0.906355	+	0.422518i	$0.138854\pi$
$677$			1.00774e7i			0.845036i	−0.906355	+	0.422518i	$0.861146\pi$
$678$		−	274190.i		−	0.0229075i
$679$	−4.20298e7			−3.49851
$680$	−3.17732e6	−	2.71743e6i	−0.263505	−	0.225365i
$681$	−5.72637e6			−0.473164
$682$			7.53556e6i			0.620376i
$683$			8.51086e6i			0.698107i	0.937103	+	0.349053i	$0.113497\pi$
$683$			8.51086e6i			0.698107i	−0.937103	+	0.349053i	$0.886503\pi$
$684$	5.08689e6			0.415731
$685$	5.50214e6	−	6.43330e6i	0.448028	−	0.523851i
$686$	−2.35226e7			−1.90842
$687$			1.33067e7i			1.07567i
$688$			5.47988e6i			0.441367i
$689$	200774.			0.0161124
$690$	−852263.	+	996498.i	−0.0681476	+	0.0796808i
$691$	2.21320e7			1.76330			0.881649	−	0.471906i	$-0.156434\pi$
$691$	2.21320e7			1.76330			0.881649	+	0.471906i	$0.156434\pi$
$692$			7.54382e6i			0.598861i
$693$			1.35258e7i			1.06987i
$694$	1.57337e6			0.124003
$695$	−1.91389e6	−	1.63687e6i	−0.150298	−	0.128544i
$696$	−3.29752e6			−0.258026
$697$			1.97221e7i			1.53770i
$698$			4.56316e6i			0.354509i
$699$	4.42987e6			0.342924
$700$	1.18986e7	−	1.86796e6i	0.917807	−	0.144086i
$701$	−3.59062e6			−0.275978			−0.137989	−	0.990434i	$-0.544064\pi$
$701$	−3.59062e6			−0.275978			−0.137989	+	0.990434i	$0.544064\pi$
$702$		−	1.20868e6i		−	0.0925699i
$703$		−	1.90493e7i		−	1.45375i
$704$	−1.91470e6			−0.145602
$705$	−3.51385e6	−	3.00525e6i	−0.266263	−	0.227724i
$706$	1.06692e7			0.805598
$707$		−	4.37376e7i		−	3.29084i
$708$		−	2.98582e6i		−	0.223862i
$709$	−3.53834e6			−0.264353			−0.132176	−	0.991226i	$-0.542196\pi$
$709$	−3.53834e6			−0.264353			−0.132176	+	0.991226i	$0.542196\pi$
$710$	7.55503e6	−	8.83362e6i	0.562458	−	0.657647i
$711$	4.66799e6			0.346302
$712$		−	1.22190e6i		−	0.0903309i
$713$			2.13192e6i			0.157053i
$714$	1.24819e7			0.916291
$715$	−1.27502e6	+	1.49080e6i	−0.0932721	+	0.109057i
$716$	−1.04944e6			−0.0765022
$717$			1.77304e7i			1.28802i
$718$			1.74381e7i			1.26237i
$719$	−2.83904e6			−0.204809			−0.102405	−	0.994743i	$-0.532654\pi$
$719$	−2.83904e6			−0.204809			−0.102405	+	0.994743i	$0.532654\pi$
$720$	−1.30638e6	−	1.11729e6i	−0.0939156	−	0.0803221i
$721$	2.82540e7			2.02415
$722$		−	1.81178e7i		−	1.29349i
$723$			1.27080e7i			0.904131i
$724$	9.07507e6			0.643434
$725$	2.25267e6	+	1.43492e7i	0.159167	+	1.01387i
$726$	2.54798e6			0.179413
$727$			1.38839e7i			0.974262i	0.873329	+	0.487131i	$0.161957\pi$
$727$			1.38839e7i			0.974262i	−0.873329	+	0.487131i	$0.838043\pi$
$728$			1.15732e6i			0.0809331i
$729$	−1.26964e7			−0.884834
$730$	1.72691e6	+	1.47696e6i	0.119940	+	0.102580i
$731$	2.50146e7			1.73141
$732$			9.69184e6i			0.668542i
$733$			2.16742e7i			1.48999i	0.667070	+	0.744995i	$0.267548\pi$
$733$			2.16742e7i			1.48999i	−0.667070	+	0.744995i	$0.732452\pi$
$734$	7.72694e6			0.529380
$735$	−1.66020e7	+	1.94117e7i	−1.13355	+	1.32539i
$736$	−541696.			−0.0368605
$737$		−	1.93753e7i		−	1.31395i
$738$			8.10889e6i			0.548050i
$739$	1.71089e7			1.15242			0.576209	−	0.817303i	$-0.304532\pi$
$739$	1.71089e7			1.15242			0.576209	+	0.817303i	$0.304532\pi$
$740$	−4.18402e6	+	4.89211e6i	−0.280876	+	0.328410i
$741$	−2.20255e6			−0.147360
$742$			2.57703e6i			0.171834i
$743$		−	1.57138e7i		−	1.04426i	−0.852866	−	0.522130i	$-0.825138\pi$
$743$		−	1.57138e7i		−	1.04426i	0.852866	−	0.522130i	$-0.174862\pi$
$744$	2.85916e6			0.189368
$745$	−3.00698e6	−	2.57175e6i	−0.198491	−	0.169761i
$746$	−5.47702e6			−0.360327
$747$		−	2.88964e6i		−	0.189471i
$748$			8.74025e6i			0.571176i
$749$	1.14333e7			0.744676
$750$	4.06075e6	−	6.59628e6i	0.263605	−	0.428199i
$751$	−1.09890e7			−0.710983			−0.355492	−	0.934679i	$-0.615687\pi$
$751$	−1.09890e7			−0.710983			−0.355492	+	0.934679i	$0.615687\pi$
$752$		−	1.91013e6i		−	0.123174i
$753$			129031.i			0.00829289i
$754$	−1.39568e6			−0.0894041
$755$	−5.49097e6	−	4.69620e6i	−0.350576	−	0.299833i
$756$	1.55140e7			0.987234
$757$			1.69387e7i			1.07434i	0.843475	+	0.537168i	$0.180506\pi$
$757$			1.69387e7i			1.07434i	−0.843475	+	0.537168i	$0.819494\pi$
$758$		−	1.34929e6i		−	0.0852966i
$759$	2.74119e6			0.172717
$760$	−6.15483e6	+	7.19646e6i	−0.386529	+	0.451944i
$761$	2.72518e7			1.70582			0.852911	−	0.522056i	$-0.174835\pi$
$761$	2.72518e7			1.70582			0.852911	+	0.522056i	$0.174835\pi$
$762$		−	1.06062e7i		−	0.661718i
$763$		−	3.93791e7i		−	2.44881i
$764$	−6.00414e6			−0.372150
$765$	−5.10023e6	+	5.96338e6i	−0.315091	+	0.368416i
$766$	1.82910e7			1.12633
$767$		−	1.26375e6i		−	0.0775663i
$768$			726478.i			0.0444447i
$769$	9.87616e6			0.602244			0.301122	−	0.953586i	$-0.402639\pi$
$769$	9.87616e6			0.602244			0.301122	+	0.953586i	$0.402639\pi$
$770$	−1.91351e7	−	1.63655e7i	−1.16307	−	0.994722i
$771$	1.98157e6			0.120053
$772$		−	1.14200e7i		−	0.689643i
$773$			8.64858e6i			0.520590i	0.965529	+	0.260295i	$0.0838199\pi$
$773$			8.64858e6i			0.520590i	−0.965529	+	0.260295i	$0.916180\pi$
$774$	1.02849e7			0.617092
$775$	−1.95321e6	−	1.24417e7i	−0.116814	−	0.744088i
$776$	−1.11667e7			−0.665687
$777$		−	1.92183e7i		−	1.14199i
$778$			1.28805e7i			0.762929i
$779$	4.46695e7			2.63735
$780$	565642.	+	483770.i	0.0332894	+	0.0284710i
$781$	−2.42997e7			−1.42552
$782$			2.47274e6i			0.144598i
$783$			1.87092e7i			1.09057i
$784$	−1.05522e7			−0.613130
$785$	2.07568e7	−	2.42696e7i	1.20222	−	1.40569i
$786$	−1.02833e7			−0.593712
$787$		−	3.88477e6i		−	0.223578i	−0.993732	−	0.111789i	$-0.964342\pi$
$787$		−	3.88477e6i		−	0.223578i	0.993732	−	0.111789i	$-0.0356580\pi$
$788$			9.88750e6i			0.567245i
$789$	4.53980e6			0.259624
$790$	−5.64799e6	+	6.60384e6i	−0.321978	+	0.376468i
$791$	1.48957e6			0.0846487
$792$			3.59361e6i			0.203572i
$793$			4.10209e6i			0.231645i
$794$	−1.53329e7			−0.863123
$795$	1.25952e6	+	1.07722e6i	0.0706787	+	0.0604486i
$796$	5.22268e6			0.292154
$797$			5.07215e6i			0.282843i	0.989949	+	0.141422i	$0.0451673\pi$
$797$			5.07215e6i			0.282843i	−0.989949	+	0.141422i	$0.954833\pi$
$798$		−	2.82707e7i		−	1.57156i
$799$	−8.71940e6			−0.483192
$800$	3.16128e6	−	496288.i	0.174638	−	0.0274163i
$801$	−2.29333e6			−0.126295
$802$		−	2.10776e6i		−	0.115714i
$803$		−	4.75043e6i		−	0.259983i
$804$	−7.35140e6			−0.401079
$805$	−5.41361e6	−	4.63003e6i	−0.294440	−	0.251822i
$806$	1.21014e6			0.0656144
$807$		−	4.06063e6i		−	0.219487i
$808$		−	1.16204e7i		−	0.626172i
$809$	−2.20449e7			−1.18423			−0.592117	−	0.805852i	$-0.701708\pi$
$809$	−2.20449e7			−1.18423			−0.592117	+	0.805852i	$0.701708\pi$
$810$	2.24277e6	−	2.62234e6i	0.120108	−	0.140435i
$811$	1.65965e7			0.886065			0.443032	−	0.896506i	$-0.353903\pi$
$811$	1.65965e7			0.886065			0.443032	+	0.896506i	$0.353903\pi$
$812$		−	1.79142e7i		−	0.953471i
$813$		−	5.52355e6i		−	0.293084i
$814$	1.34573e7			0.711865
$815$	2.51069e6	−	2.93560e6i	0.132404	−	0.154811i
$816$	3.31624e6			0.174349
$817$		−	5.66568e7i		−	2.96959i
$818$		−	1.42216e7i		−	0.743128i
$819$	2.17213e6			0.113156
$820$	−1.14717e7	−	9.81127e6i	−0.595790	−	0.509555i
$821$	−9.07512e6			−0.469888			−0.234944	−	0.972009i	$-0.575491\pi$
$821$	−9.07512e6			−0.469888			−0.234944	+	0.972009i	$0.575491\pi$
$822$			6.71458e6i			0.346608i
$823$			1.11786e6i			0.0575293i	0.999586	+	0.0287646i	$0.00915733\pi$
$823$			1.11786e6i			0.0575293i	−0.999586	+	0.0287646i	$0.990843\pi$
$824$	7.50667e6			0.385149
$825$	−1.59973e7	+	2.51140e6i	−0.818297	+	0.128464i
$826$	1.62208e7			0.827224
$827$		−	5.70507e6i		−	0.290066i	−0.989427	−	0.145033i	$-0.953671\pi$
$827$		−	5.70507e6i		−	0.290066i	0.989427	−	0.145033i	$-0.0463289\pi$
$828$			1.01669e6i			0.0515360i
$829$	−1.38004e7			−0.697436			−0.348718	−	0.937228i	$-0.613383\pi$
$829$	−1.38004e7			−0.697436			−0.348718	+	0.937228i	$0.613383\pi$
$830$	4.08799e6	+	3.49629e6i	0.205975	+	0.176162i
$831$	−1.01866e7			−0.511711
$832$			307483.i			0.0153997i
$833$			4.81688e7i			2.40521i
$834$	1.99756e6			0.0994456
$835$	1.37810e7	−	1.61133e7i	0.684015	−	0.799776i
$836$	1.97962e7			0.979638
$837$		−	1.62221e7i		−	0.800374i
$838$		−	1.96333e7i		−	0.965792i
$839$	1.10380e7			0.541359			0.270680	−	0.962670i	$-0.412752\pi$
$839$	1.10380e7			0.541359			0.270680	+	0.962670i	$0.412752\pi$
$840$	−6.20942e6	+	7.26028e6i	−0.303636	+	0.355022i
$841$	1.09260e6			0.0532687
$842$			1.56102e6i			0.0758803i
$843$		−	1.29137e7i		−	0.625866i
$844$	−7.53035e6			−0.363881
$845$	−1.55343e7	−	1.32859e7i	−0.748429	−	0.640100i
$846$	−3.58504e6			−0.172214
$847$			1.38422e7i			0.662976i
$848$			684677.i			0.0326961i
$849$	1.18622e7			0.564803
$850$	−2.26546e6	−	1.44307e7i	−0.107550	−	0.685077i
$851$	3.80727e6			0.180215
$852$			9.21984e6i			0.435136i
$853$		−	2.44866e7i		−	1.15228i	−0.817353	−	0.576138i	$-0.804559\pi$
$853$		−	2.44866e7i		−	1.15228i	0.817353	−	0.576138i	$-0.195441\pi$
$854$	−5.26523e7			−2.47043
$855$	1.35067e7	+	1.15517e7i	0.631881	+	0.540421i
$856$	3.03766e6			0.141695
$857$			9.78483e6i			0.455094i	0.973767	+	0.227547i	$0.0730706\pi$
$857$			9.78483e6i			0.455094i	−0.973767	+	0.227547i	$0.926929\pi$
$858$		−	1.55598e6i		−	0.0721583i
$859$	−1.88811e7			−0.873062			−0.436531	−	0.899689i	$-0.643793\pi$
$859$	−1.88811e7			−0.873062			−0.436531	+	0.899689i	$0.643793\pi$
$860$	−1.24442e7	+	1.45502e7i	−0.573746	+	0.670846i
$861$	4.50657e7			2.07175
$862$		−	6.95007e6i		−	0.318582i
$863$			5.88375e6i			0.268922i	0.990919	+	0.134461i	$0.0429304\pi$
$863$			5.88375e6i			0.268922i	−0.990919	+	0.134461i	$0.957070\pi$
$864$	4.12184e6			0.187848
$865$	−1.71312e7	+	2.00304e7i	−0.778478	+	0.910226i
$866$	8.11552e6			0.367724
$867$			601335.i			0.0271687i
$868$			1.55328e7i			0.699760i
$869$	1.81660e7			0.816036
$870$	−8.75558e6	−	7.48829e6i	−0.392181	−	0.335416i
$871$	−3.11149e6			−0.138971
$872$		−	1.04624e7i		−	0.465952i
$873$			2.09583e7i			0.930722i
$874$	5.60063e6			0.248004
$875$	3.58352e7	+	2.20606e7i	1.58230	+	0.974085i
$876$	−1.80242e6			−0.0793588
$877$		−	2.38869e7i		−	1.04872i	−0.851496	−	0.524361i	$-0.824304\pi$
$877$		−	2.38869e7i		−	1.04872i	0.851496	−	0.524361i	$-0.175696\pi$
$878$		−	1.20871e7i		−	0.529161i
$879$	−1.02490e7			−0.447414
$880$	−5.08391e6	−	4.34806e6i	−0.221305	−	0.189273i
$881$	−1.33669e7			−0.580219			−0.290109	−	0.956994i	$-0.593692\pi$
$881$	−1.33669e7			−0.580219			−0.290109	+	0.956994i	$0.593692\pi$
$882$			1.98049e7i			0.857240i
$883$			1.88690e7i			0.814417i	0.913335	+	0.407208i	$0.133498\pi$
$883$			1.88690e7i			0.814417i	−0.913335	+	0.407208i	$0.866502\pi$
$884$	1.40360e6			0.0604107
$885$	6.78045e6	−	7.92795e6i	0.291005	−	0.340254i
$886$	1.79347e7			0.767557
$887$			8.69715e6i			0.371166i	0.982629	+	0.185583i	$0.0594173\pi$
$887$			8.69715e6i			0.371166i	−0.982629	+	0.185583i	$0.940583\pi$
$888$		−	5.10600e6i		−	0.217294i
$889$	5.76197e7			2.44521
$890$	2.77480e6	−	3.24440e6i	0.117424	−	0.137296i
$891$	−7.21358e6			−0.304408
$892$		−	1.21796e7i		−	0.512533i
$893$			1.97490e7i			0.828735i
$894$	3.13846e6			0.131332
$895$	−2.78647e6	−	2.38315e6i	−0.116278	−	0.0994475i
$896$	−3.94669e6			−0.164234
$897$		−	440210.i		−	0.0182675i
$898$		−	3.62533e6i		−	0.150023i
$899$	−1.87318e7			−0.773002
$900$	−931462.	−	5.93327e6i	−0.0383318	−	0.244168i
$901$	3.12543e6			0.128262
$902$			3.15566e7i			1.29144i
$903$		−	5.71593e7i		−	2.33275i
$904$	395757.			0.0161067
$905$	2.40962e7	+	2.06085e7i	0.977972	+	0.836419i
$906$	5.73105e6			0.231960
$907$			7.87711e6i			0.317942i	0.987283	+	0.158971i	$0.0508177\pi$
$907$			7.87711e6i			0.317942i	−0.987283	+	0.158971i	$0.949182\pi$
$908$		−	8.26526e6i		−	0.332692i
$909$	−2.18099e7			−0.875475
$910$	−2.62815e6	+	3.07293e6i	−0.105207	+	0.123012i
$911$	3.92278e6			0.156602			0.0783011	−	0.996930i	$-0.475050\pi$
$911$	3.92278e6			0.156602			0.0783011	+	0.996930i	$0.475050\pi$
$912$		−	7.51110e6i		−	0.299031i
$913$		−	1.12453e7i		−	0.446473i
$914$	1.78264e7			0.705826
$915$	−2.20091e7	+	2.57338e7i	−0.869058	+	1.01614i
$916$	−1.92065e7			−0.756327
$917$		−	5.58653e7i		−	2.19391i
$918$		−	1.88155e7i		−	0.736899i
$919$	−9.68483e6			−0.378271			−0.189136	−	0.981951i	$-0.560569\pi$
$919$	−9.68483e6			−0.378271			−0.189136	+	0.981951i	$0.560569\pi$
$920$	−1.43831e6	−	1.23013e6i	−0.0560253	−	0.0479161i
$921$	−1.37130e7			−0.532699
$922$		−	743379.i		−	0.0287994i
$923$			3.90232e6i			0.150771i
$924$	1.99717e7			0.769549
$925$	−2.22188e7	+	3.48813e6i	−0.853821	+	0.134041i
$926$	−8.09267e6			−0.310145
$927$		−	1.40889e7i		−	0.538492i
$928$		−	4.75954e6i		−	0.181424i
$929$	1.56242e7			0.593961			0.296980	−	0.954884i	$-0.404020\pi$
$929$	1.56242e7			0.593961			0.296980	+	0.954884i	$0.404020\pi$
$930$	7.59165e6	+	6.49282e6i	0.287825	+	0.246165i
$931$	1.09100e8			4.12524
$932$			6.39394e6i			0.241118i
$933$			5.51118e6i			0.207272i
$934$	−2.90326e7			−1.08898
$935$	−1.98481e7	+	2.32071e7i	−0.742489	+	0.868146i
$936$	577102.			0.0215309
$937$			1.64114e7i			0.610655i	0.952247	+	0.305327i	$0.0987659\pi$
$937$			1.64114e7i			0.610655i	−0.952247	+	0.305327i	$0.901234\pi$
$938$		−	3.99375e7i		−	1.48209i
$939$	−3.27644e7			−1.21266
$940$	4.33769e6	−	5.07179e6i	0.160117	−	0.187215i
$941$	1.24284e7			0.457552			0.228776	−	0.973479i	$-0.426528\pi$
$941$	1.24284e7			0.457552			0.228776	+	0.973479i	$0.426528\pi$
$942$			2.53307e7i			0.930079i
$943$			8.92783e6i			0.326939i
$944$	4.30963e6			0.157402
$945$	4.11929e7	+	3.52306e7i	1.50052	+	1.28334i
$946$	4.00250e7			1.45413
$947$		−	1.25920e7i		−	0.456266i	−0.973630	−	0.228133i	$-0.926738\pi$
$947$		−	1.25920e7i		−	0.456266i	0.973630	−	0.228133i	$-0.0732621\pi$
$948$		−	6.89257e6i		−	0.249092i
$949$	−762877.			−0.0274972
$950$	−3.26847e7	+	5.13115e6i	−1.17499	+	0.184462i
$951$	1.30608e7			0.468295
$952$			1.80159e7i			0.644264i
$953$		−	1.61708e7i		−	0.576764i	−0.957515	−	0.288382i	$-0.906883\pi$
$953$		−	1.61708e7i		−	0.576764i	0.957515	−	0.288382i	$-0.0931173\pi$
$954$	1.28504e6			0.0457137
$955$	−1.59422e7	−	1.36347e7i	−0.565640	−	0.483769i
$956$	−2.55916e7			−0.905633
$957$			2.40850e7i			0.850095i
$958$		−	1.30376e7i		−	0.458970i
$959$	−3.64778e7			−1.28080
$960$	−1.64975e6	+	1.92895e6i	−0.0577750	+	0.0675527i
$961$	−1.23875e7			−0.432688
$962$		−	2.16112e6i		−	0.0752908i
$963$		−	5.70125e6i		−	0.198109i
$964$	−1.83423e7			−0.635714
$965$	2.59336e7	−	3.03225e7i	0.896488	−	1.04821i
$966$	5.65030e6			0.194818
$967$			4.48225e7i			1.54145i	0.637167	+	0.770726i	$0.280106\pi$
$967$			4.48225e7i			1.54145i	−0.637167	+	0.770726i	$0.719894\pi$
$968$			3.67767e6i			0.126149i
$969$	−3.42868e7			−1.17305
$970$	−2.96498e7	−	2.53583e7i	−1.01180	−	0.865347i
$971$	2.12406e7			0.722968			0.361484	−	0.932378i	$-0.382270\pi$
$971$	2.12406e7			0.722968			0.361484	+	0.932378i	$0.382270\pi$
$972$		−	1.29131e7i		−	0.438395i
$973$			1.08520e7i			0.367476i
$974$	1.88298e7			0.635987
$975$	403309.	+	2.56902e6i	0.0135871	+	0.0865477i
$976$	−1.39889e7			−0.470066
$977$			3.29908e7i			1.10575i	0.833264	+	0.552875i	$0.186469\pi$
$977$			3.29908e7i			1.10575i	−0.833264	+	0.552875i	$0.813531\pi$
$978$			3.06395e6i			0.102432i
$979$	−8.92476e6			−0.297605
$980$	−2.80182e7	−	2.39628e7i	−0.931913	−	0.797026i
$981$	−1.96365e7			−0.651465
$982$			3.13859e7i			1.03862i
$983$			3.27286e7i			1.08030i	0.841569	+	0.540149i	$0.181632\pi$
$983$			3.27286e7i			1.08030i	−0.841569	+	0.540149i	$0.818368\pi$
$984$	1.19733e7			0.394208
$985$	−2.24534e7	+	2.62533e7i	−0.737380	+	0.862172i
$986$	−2.17264e7			−0.711698
$987$			1.99241e7i			0.651008i
$988$		−	3.17909e6i		−	0.103612i
$989$	1.13237e7			0.368125
$990$	−8.16069e6	+	9.54178e6i	−0.264630	+	0.309415i
$991$	1.81647e7			0.587547			0.293774	−	0.955875i	$-0.405089\pi$
$991$	1.81647e7			0.587547			0.293774	+	0.955875i	$0.405089\pi$
$992$			4.12682e6i			0.133148i
$993$		−	2.72440e7i		−	0.876794i
$994$	−5.00881e7			−1.60793
$995$	1.38673e7	+	1.18601e7i	0.444052	+	0.379779i
$996$	−4.26673e6			−0.136285
$997$		−	4.95919e7i		−	1.58006i	−0.613071	−	0.790028i	$-0.710066\pi$
$997$		−	4.95919e7i		−	1.58006i	0.613071	−	0.790028i	$-0.289934\pi$
$998$		−	4.97703e6i		−	0.158177i
$999$	−2.89701e7			−0.918409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.a.139.9	✓	26
5.4	even	2	inner	230.6.b.a.139.18	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.a.139.9	✓	26	1.1	even	1	trivial
230.6.b.a.139.18	yes	26	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} +11.0852i q^{3} -16.0000 q^{4} +(-42.4833 - 36.3342i) q^{5} +44.3407 q^{6} +240.887i q^{7} +64.0000i q^{8} +120.119 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} +11.0852i q^{3} -16.0000 q^{4} +(-42.4833 - 36.3342i) q^{5} +44.3407 q^{6} +240.887i q^{7} +64.0000i q^{8} +120.119 q^{9} +(-145.337 + 169.933i) q^{10} +467.455 q^{11} -177.363i q^{12} -75.0691i q^{13} +963.547 q^{14} +(402.771 - 470.935i) q^{15} +256.000 q^{16} -1168.59i q^{17} -480.475i q^{18} -2646.80 q^{19} +(679.732 + 581.347i) q^{20} -2670.27 q^{21} -1869.82i q^{22} -529.000i q^{23} -709.451 q^{24} +(484.656 + 3087.19i) q^{25} -300.277 q^{26} +4025.24i q^{27} -3854.19i q^{28} +4647.98 q^{29} +(-1883.74 - 1611.08i) q^{30} -4030.10 q^{31} -1024.00i q^{32} +5181.83i q^{33} -4674.37 q^{34} +(8752.42 - 10233.7i) q^{35} -1921.90 q^{36} +7197.11i q^{37} +10587.2i q^{38} +832.155 q^{39} +(2325.39 - 2718.93i) q^{40} -16876.8 q^{41} +10681.1i q^{42} +21405.8i q^{43} -7479.29 q^{44} +(-5103.04 - 4364.42i) q^{45} -2116.00 q^{46} -7461.45i q^{47} +2837.81i q^{48} -41219.5 q^{49} +(12348.8 - 1938.63i) q^{50} +12954.1 q^{51} +1201.11i q^{52} +2674.52i q^{53} +16100.9 q^{54} +(-19859.0 - 16984.6i) q^{55} -15416.8 q^{56} -29340.2i q^{57} -18591.9i q^{58} +16834.5 q^{59} +(-6444.33 + 7534.95i) q^{60} -54644.2 q^{61} +16120.4i q^{62} +28935.1i q^{63} -4096.00 q^{64} +(-2727.57 + 3189.18i) q^{65} +20727.3 q^{66} -41448.4i q^{67} +18697.5i q^{68} +5864.06 q^{69} +(-40934.6 - 35009.7i) q^{70} -51983.0 q^{71} +7687.61i q^{72} -10162.3i q^{73} +28788.4 q^{74} +(-34222.0 + 5372.50i) q^{75} +42348.8 q^{76} +112604. i q^{77} -3328.62i q^{78} +38861.4 q^{79} +(-10875.7 - 9301.55i) q^{80} -15431.6 q^{81} +67507.2i q^{82} -24056.5i q^{83} +42724.4 q^{84} +(-42459.9 + 49645.7i) q^{85} +85623.1 q^{86} +51523.7i q^{87} +29917.2i q^{88} -19092.2 q^{89} +(-17457.7 + 20412.2i) q^{90} +18083.2 q^{91} +8464.00i q^{92} -44674.3i q^{93} -29845.8 q^{94} +(112445. + 96169.3i) q^{95} +11351.2 q^{96} +174479. i q^{97} +164878. i q^{98} +56150.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

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