LMFDB - Embedded newform 40.6.k.a.3.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.14
Character	$\chi$	$=$	40.3
Dual form			40.6.k.a.27.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540478 - 5.63098i) q^{2} +(-8.83424 - 8.83424i) q^{3} +(-31.4158 + 6.08684i) q^{4} +(-16.1587 + 53.5154i) q^{5} +(-44.9707 + 54.5201i) q^{6} +(48.2986 + 48.2986i) q^{7} +(51.2543 + 173.612i) q^{8} -86.9124i q^{9} +O(q^{10})$	\(q+(-0.540478 - 5.63098i) q^{2} +(-8.83424 - 8.83424i) q^{3} +(-31.4158 + 6.08684i) q^{4} +(-16.1587 + 53.5154i) q^{5} +(-44.9707 + 54.5201i) q^{6} +(48.2986 + 48.2986i) q^{7} +(51.2543 + 173.612i) q^{8} -86.9124i q^{9} +(310.077 + 62.0653i) q^{10} +132.916 q^{11} +(331.307 + 223.762i) q^{12} +(-488.089 + 488.089i) q^{13} +(245.864 - 298.073i) q^{14} +(615.518 - 330.018i) q^{15} +(949.901 - 382.445i) q^{16} +(-802.713 + 802.713i) q^{17} +(-489.401 + 46.9742i) q^{18} +2785.43i q^{19} +(181.898 - 1779.58i) q^{20} -853.364i q^{21} +(-71.8379 - 748.445i) q^{22} +(-711.980 + 711.980i) q^{23} +(1080.93 - 1986.52i) q^{24} +(-2602.79 - 1729.48i) q^{25} +(3012.22 + 2484.62i) q^{26} +(-2914.53 + 2914.53i) q^{27} +(-1811.32 - 1223.35i) q^{28} -2091.69 q^{29} +(-2191.00 - 3287.60i) q^{30} -4580.17i q^{31} +(-2666.94 - 5142.17i) q^{32} +(-1174.21 - 1174.21i) q^{33} +(4953.91 + 4086.21i) q^{34} +(-3365.16 + 1804.28i) q^{35} +(529.021 + 2730.42i) q^{36} +(-5951.81 - 5951.81i) q^{37} +(15684.7 - 1505.46i) q^{38} +8623.80 q^{39} +(-10119.1 - 62.4397i) q^{40} +6331.41 q^{41} +(-4805.27 + 461.224i) q^{42} +(1114.08 + 1114.08i) q^{43} +(-4175.65 + 809.035i) q^{44} +(4651.15 + 1404.39i) q^{45} +(4393.95 + 3624.33i) q^{46} +(12285.1 + 12285.1i) q^{47} +(-11770.3 - 5013.04i) q^{48} -12141.5i q^{49} +(-8331.89 + 15591.0i) q^{50} +14182.7 q^{51} +(12362.8 - 18304.6i) q^{52} +(-26052.7 + 26052.7i) q^{53} +(17986.9 + 14836.4i) q^{54} +(-2147.74 + 7113.03i) q^{55} +(-5909.69 + 10860.7i) q^{56} +(24607.2 - 24607.2i) q^{57} +(1130.51 + 11778.3i) q^{58} +35835.0i q^{59} +(-17328.2 + 14114.3i) q^{60} -13145.0i q^{61} +(-25790.8 + 2475.48i) q^{62} +(4197.75 - 4197.75i) q^{63} +(-27514.0 + 17796.7i) q^{64} +(-18233.4 - 34007.2i) q^{65} +(-5977.31 + 7246.57i) q^{66} +(32954.4 - 32954.4i) q^{67} +(20331.9 - 30103.8i) q^{68} +12579.6 q^{69} +(11978.6 + 17974.0i) q^{70} -38199.3i q^{71} +(15089.0 - 4454.64i) q^{72} +(-27258.7 - 27258.7i) q^{73} +(-30297.7 + 36731.3i) q^{74} +(7715.09 + 38272.3i) q^{75} +(-16954.4 - 87506.4i) q^{76} +(6419.64 + 6419.64i) q^{77} +(-4660.97 - 48560.4i) q^{78} +60171.0 q^{79} +(5117.55 + 57014.1i) q^{80} +30375.5 q^{81} +(-3421.98 - 35652.0i) q^{82} +(-42310.9 - 42310.9i) q^{83} +(5194.28 + 26809.1i) q^{84} +(-29986.7 - 55928.3i) q^{85} +(5671.23 - 6875.50i) q^{86} +(18478.5 + 18478.5i) q^{87} +(6812.50 + 23075.7i) q^{88} +102464. i q^{89} +(5394.24 - 26949.5i) q^{90} -47148.1 q^{91} +(18033.7 - 26701.1i) q^{92} +(-40462.3 + 40462.3i) q^{93} +(62537.1 - 75816.7i) q^{94} +(-149063. - 45008.9i) q^{95} +(-21866.7 + 68987.5i) q^{96} +(-94483.2 + 94483.2i) q^{97} +(-68368.4 + 6562.20i) q^{98} -11552.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	−0.540478	−	5.63098i	−0.0955439	−	0.995425i
$2$	−0.540478	−	5.63098i	−0.0955439	−	0.995425i
$3$	−8.83424	−	8.83424i	−0.566717	−	0.566717i	0.364490	−	0.931207i	$-0.381243\pi$
$3$	−8.83424	−	8.83424i	−0.566717	−	0.566717i	−0.931207	+	0.364490i	$0.881243\pi$
$4$	−31.4158	+	6.08684i	−0.981743	+	0.190214i
$5$	−16.1587	+	53.5154i	−0.289055	+	0.957312i
$5$	−16.1587	+	53.5154i	−0.289055	+	0.957312i
$6$	−44.9707	+	54.5201i	−0.509978	+	0.618271i
$7$	48.2986	+	48.2986i	0.372554	+	0.372554i	0.868407	−	0.495852i	$-0.165144\pi$
$7$	48.2986	+	48.2986i	0.372554	+	0.372554i	−0.495852	+	0.868407i	$0.665144\pi$
$8$	51.2543	+	173.612i	0.283143	+	0.959078i
$9$		−	86.9124i		−	0.357664i
$10$	310.077	+	62.0653i	0.980550	+	0.196268i
$11$	132.916			0.331203			0.165602	−	0.986193i	$-0.447043\pi$
$11$	132.916			0.331203			0.165602	+	0.986193i	$0.447043\pi$
$12$	331.307	+	223.762i	0.664167	+	0.448573i
$13$	−488.089	+	488.089i	−0.801015	+	0.801015i	−0.983254	−	0.182239i	$-0.941666\pi$
$13$	−488.089	+	488.089i	−0.801015	+	0.801015i	0.182239	+	0.983254i	$0.441666\pi$
$14$	245.864	−	298.073i	0.335255	−	0.406445i
$15$	615.518	−	330.018i	0.706338	−	0.378712i
$16$	949.901	−	382.445i	0.927638	−	0.373482i
$17$	−802.713	+	802.713i	−0.673656	+	0.673656i	−0.958557	−	0.284901i	$-0.908039\pi$
$17$	−802.713	+	802.713i	−0.673656	+	0.673656i	0.284901	+	0.958557i	$0.408039\pi$
$18$	−489.401	+	46.9742i	−0.356028	+	0.0341726i
$19$			2785.43i			1.77014i	0.465456	+	0.885071i	$0.345890\pi$
$19$			2785.43i			1.77014i	−0.465456	+	0.885071i	$0.654110\pi$
$20$	181.898	−	1779.58i	0.101684	−	0.994817i
$21$		−	853.364i		−	0.422266i
$22$	−71.8379	−	748.445i	−0.0316444	−	0.329688i
$23$	−711.980	+	711.980i	−0.280639	+	0.280639i	−0.833364	−	0.552725i	$-0.813588\pi$
$23$	−711.980	+	711.980i	−0.280639	+	0.280639i	0.552725	+	0.833364i	$0.313588\pi$
$24$	1080.93	−	1986.52i	0.383064	−	0.703987i
$25$	−2602.79	−	1729.48i	−0.832894	−	0.553433i
$26$	3012.22	+	2484.62i	0.873883	+	0.720819i
$27$	−2914.53	+	2914.53i	−0.769411	+	0.769411i
$28$	−1811.32	−	1223.35i	−0.436618	−	0.294888i
$29$	−2091.69			−0.461852			−0.230926	−	0.972971i	$-0.574176\pi$
$29$	−2091.69			−0.461852			−0.230926	+	0.972971i	$0.574176\pi$
$30$	−2191.00	−	3287.60i	−0.444466	−	0.666923i
$31$		−	4580.17i		−	0.856007i	−0.903777	−	0.428004i	$-0.859217\pi$
$31$		−	4580.17i		−	0.856007i	0.903777	−	0.428004i	$-0.140783\pi$
$32$	−2666.94	−	5142.17i	−0.460403	−	0.887710i
$33$	−1174.21	−	1174.21i	−0.187698	−	0.187698i
$34$	4953.91	+	4086.21i	0.734937	+	0.606210i
$35$	−3365.16	+	1804.28i	−0.464340	+	0.248962i
$36$	529.021	+	2730.42i	0.0680326	+	0.351134i
$37$	−5951.81	−	5951.81i	−0.714734	−	0.714734i	0.252787	−	0.967522i	$-0.418653\pi$
$37$	−5951.81	−	5951.81i	−0.714734	−	0.714734i	−0.967522	+	0.252787i	$0.918653\pi$
$38$	15684.7	−	1505.46i	1.76204	−	0.169126i
$39$	8623.80			0.907898
$40$	−10119.1	−	62.4397i	−0.999981	−	0.00617037i
$41$	6331.41			0.588221			0.294110	−	0.955771i	$-0.404977\pi$
$41$	6331.41			0.588221			0.294110	+	0.955771i	$0.404977\pi$
$42$	−4805.27	+	461.224i	−0.420334	+	0.0403449i
$43$	1114.08	+	1114.08i	0.0918853	+	0.0918853i	0.751555	−	0.659670i	$-0.229304\pi$
$43$	1114.08	+	1114.08i	0.0918853	+	0.0918853i	−0.659670	+	0.751555i	$0.729304\pi$
$44$	−4175.65	+	809.035i	−0.325156	+	0.0629993i
$45$	4651.15	+	1404.39i	0.342396	+	0.103385i
$46$	4393.95	+	3624.33i	0.306168	+	0.252542i
$47$	12285.1	+	12285.1i	0.811209	+	0.811209i	0.984815	−	0.173607i	$-0.0555421\pi$
$47$	12285.1	+	12285.1i	0.811209	+	0.811209i	−0.173607	+	0.984815i	$0.555542\pi$
$48$	−11770.3	−	5013.04i	−0.737366	−	0.314050i
$49$		−	12141.5i		−	0.722406i
$50$	−8331.89	+	15591.0i	−0.471323	+	0.881961i
$51$	14182.7			0.763544
$52$	12362.8	−	18304.6i	0.634027	−	0.938755i
$53$	−26052.7	+	26052.7i	−1.27398	+	1.27398i	−0.330003	+	0.943980i	$0.607050\pi$
$53$	−26052.7	+	26052.7i	−1.27398	+	1.27398i	−0.943980	+	0.330003i	$0.892950\pi$
$54$	17986.9	+	14836.4i	0.839404	+	0.692379i
$55$	−2147.74	+	7113.03i	−0.0957360	+	0.317065i
$56$	−5909.69	+	10860.7i	−0.251823	+	0.462795i
$57$	24607.2	−	24607.2i	1.00317	−	1.00317i
$58$	1130.51	+	11778.3i	0.0441271	+	0.459739i
$59$			35835.0i			1.34022i	0.742261	+	0.670111i	$0.233754\pi$
$59$			35835.0i			1.34022i	−0.742261	+	0.670111i	$0.766246\pi$
$60$	−17328.2	+	14114.3i	−0.621406	+	0.506153i
$61$		−	13145.0i		−	0.452309i	−0.974091	−	0.226155i	$-0.927385\pi$
$61$		−	13145.0i		−	0.452309i	0.974091	−	0.226155i	$-0.0726155\pi$
$62$	−25790.8	+	2475.48i	−0.852091	+	0.0817863i
$63$	4197.75	−	4197.75i	0.133249	−	0.133249i
$64$	−27514.0	+	17796.7i	−0.839660	+	0.543112i
$65$	−18233.4	−	34007.2i	−0.535284	−	0.998360i
$66$	−5977.31	+	7246.57i	−0.168906	+	0.204773i
$67$	32954.4	−	32954.4i	0.896865	−	0.896865i	−0.0982928	−	0.995158i	$-0.531338\pi$
$67$	32954.4	−	32954.4i	0.896865	−	0.896865i	0.995158	+	0.0982928i	$0.0313382\pi$
$68$	20331.9	−	30103.8i	0.533218	−	0.789495i
$69$	12579.6			0.318086
$70$	11978.6	+	17974.0i	0.292188	+	0.438429i
$71$		−	38199.3i		−	0.899311i	−0.893202	−	0.449656i	$-0.851547\pi$
$71$		−	38199.3i		−	0.899311i	0.893202	−	0.449656i	$-0.148453\pi$
$72$	15089.0	−	4454.64i	0.343028	−	0.101270i
$73$	−27258.7	−	27258.7i	−0.598685	−	0.598685i	0.341278	−	0.939962i	$-0.389140\pi$
$73$	−27258.7	−	27258.7i	−0.598685	−	0.598685i	−0.939962	+	0.341278i	$0.889140\pi$
$74$	−30297.7	+	36731.3i	−0.643176	+	0.779753i
$75$	7715.09	+	38272.3i	0.158375	+	0.785655i
$76$	−16954.4	−	87506.4i	−0.336705	−	1.73782i
$77$	6419.64	+	6419.64i	0.123391	+	0.123391i
$78$	−4660.97	−	48560.4i	−0.0867441	−	0.903745i
$79$	60171.0			1.08473			0.542363	−	0.840145i	$-0.317530\pi$
$79$	60171.0			1.08473			0.542363	+	0.840145i	$0.317530\pi$
$80$	5117.55	+	57014.1i	0.0893999	+	0.995996i
$81$	30375.5			0.514412
$82$	−3421.98	−	35652.0i	−0.0562009	−	0.585530i
$83$	−42310.9	−	42310.9i	−0.674151	−	0.674151i	0.284520	−	0.958670i	$-0.408166\pi$
$83$	−42310.9	−	42310.9i	−0.674151	−	0.674151i	−0.958670	+	0.284520i	$0.908166\pi$
$84$	5194.28	+	26809.1i	0.0803207	+	0.414556i
$85$	−29986.7	−	55928.3i	−0.450175	−	0.839623i
$86$	5671.23	−	6875.50i	0.0826859	−	0.100244i
$87$	18478.5	+	18478.5i	0.261739	+	0.261739i
$88$	6812.50	+	23075.7i	0.0937778	+	0.317649i
$89$			102464.i			1.37118i	0.727987	+	0.685591i	$0.240456\pi$
$89$			102464.i			1.37118i	−0.727987	+	0.685591i	$0.759544\pi$
$90$	5394.24	−	26949.5i	0.0701979	−	0.350708i
$91$	−47148.1			−0.596844
$92$	18033.7	−	26701.1i	0.222134	−	0.328897i
$93$	−40462.3	+	40462.3i	−0.485114	+	0.485114i
$94$	62537.1	−	75816.7i	0.729991	−	0.885004i
$95$	−149063.	−	45008.9i	−1.69458	−	0.511669i
$96$	−21866.7	+	68987.5i	−0.242162	+	0.763998i
$97$	−94483.2	+	94483.2i	−1.01959	+	1.01959i	−0.0197845	+	0.999804i	$0.506298\pi$
$97$	−94483.2	+	94483.2i	−1.01959	+	1.01959i	−0.999804	+	0.0197845i	$0.993702\pi$
$98$	−68368.4	+	6562.20i	−0.719101	+	0.0690215i
$99$		−	11552.0i		−	0.118459i
$100$	92295.8	+	38490.1i	0.922958	+	0.384901i
$101$		−	4960.44i		−	0.0483856i	−0.999707	−	0.0241928i	$-0.992298\pi$
$101$		−	4960.44i		−	0.0483856i	0.999707	−	0.0241928i	$-0.00770157\pi$
$102$	−7665.45	−	79862.5i	−0.0729520	−	0.760051i
$103$	−49417.3	+	49417.3i	−0.458972	+	0.458972i	−0.898318	−	0.439346i	$-0.855210\pi$
$103$	−49417.3	+	49417.3i	−0.458972	+	0.458972i	0.439346	+	0.898318i	$0.355210\pi$
$104$	−109755.	−	59721.3i	−0.995038	−	0.541434i
$105$	45668.1	+	13789.2i	0.404240	+	0.122058i
$106$	160783.	+	132621.i	1.38988	+	1.14643i
$107$	−27214.1	+	27214.1i	−0.229792	+	0.229792i	−0.812606	−	0.582814i	$-0.801952\pi$
$107$	−27214.1	+	27214.1i	−0.229792	+	0.229792i	0.582814	+	0.812606i	$0.301952\pi$
$108$	73821.8	−	109302.i	0.609011	−	0.901716i
$109$	230822.			1.86085			0.930424	−	0.366485i	$-0.119439\pi$
$109$	230822.			1.86085			0.930424	+	0.366485i	$0.119439\pi$
$110$	41214.1	+	8249.45i	0.324761	+	0.0650045i
$111$			105159.i			0.810104i
$112$	64350.5	+	27407.3i	0.484738	+	0.206453i
$113$	142708.	+	142708.i	1.05136	+	1.05136i	0.998608	+	0.0527536i	$0.0167998\pi$
$113$	142708.	+	142708.i	1.05136	+	1.05136i	0.0527536	+	0.998608i	$0.483200\pi$
$114$	−151862.	−	125263.i	−1.09443	−	0.902733i
$115$	−26597.2	−	49606.5i	−0.187539	−	0.349779i
$116$	65712.1	−	12731.8i	0.453420	−	0.0878505i
$117$	42421.0	+	42421.0i	0.286494	+	0.286494i
$118$	201786.	−	19368.0i	1.33409	−	0.128050i
$119$	−77539.9			−0.501947
$120$	88842.9	+	89946.1i	0.563209	+	0.570203i
$121$	−143384.			−0.890305
$122$	−74019.1	+	7104.57i	−0.450240	+	0.0432154i
$123$	−55933.2	−	55933.2i	−0.333355	−	0.333355i
$124$	27878.7	+	143890.i	0.162824	+	0.840379i
$125$	134611.	−	111343.i	0.770560	−	0.637367i
$126$	−25906.2	−	21368.6i	−0.145371	−	0.119909i
$127$	22629.2	+	22629.2i	0.124497	+	0.124497i	0.766610	−	0.642113i	$-0.221942\pi$
$127$	22629.2	+	22629.2i	0.124497	+	0.124497i	−0.642113	+	0.766610i	$0.721942\pi$
$128$	115083.	+	145312.i	0.620852	+	0.783928i
$129$		−	19684.1i		−	0.104146i
$130$	−181639.	+	121052.i	−0.942649	+	0.628223i
$131$	158250.			0.805683			0.402842	−	0.915270i	$-0.368023\pi$
$131$	158250.			0.805683			0.402842	+	0.915270i	$0.368023\pi$
$132$	44035.9	+	29741.5i	0.219974	+	0.148569i
$133$	−134532.	+	134532.i	−0.659474	+	0.659474i
$134$	−203377.	−	167755.i	−0.978452	−	0.807072i
$135$	−108877.	−	203067.i	−0.514164	−	0.958969i
$136$	−180503.	−	98217.8i	−0.836829	−	0.455347i
$137$	−33580.3	+	33580.3i	−0.152856	+	0.152856i	−0.779392	−	0.626536i	$-0.784472\pi$
$137$	−33580.3	+	33580.3i	−0.152856	+	0.152856i	0.626536	+	0.779392i	$0.284472\pi$
$138$	−6798.99	−	70835.4i	−0.0303911	−	0.316630i
$139$		−	382434.i		−	1.67888i	−0.543453	−	0.839440i	$-0.682883\pi$
$139$		−	382434.i		−	1.67888i	0.543453	−	0.839440i	$-0.317117\pi$
$140$	94736.8	−	77166.0i	0.408506	−	0.332741i
$141$		−	217058.i		−	0.919451i
$142$	−215100.	+	20645.9i	−0.895197	+	0.0859237i
$143$	−64874.7	+	64874.7i	−0.265299	+	0.265299i
$144$	−33239.2	−	82558.1i	−0.133581	−	0.331783i
$145$	33799.0	−	111938.i	0.133501	−	0.442137i
$146$	−138760.	+	168226.i	−0.538745	+	0.653147i
$147$	−107261.	+	107261.i	−0.409400	+	0.409400i
$148$	223208.	+	150753.i	0.837638	+	0.565733i
$149$	−325846.			−1.20239			−0.601197	−	0.799100i	$-0.705309\pi$
$149$	−325846.			−1.20239			−0.601197	+	0.799100i	$0.705309\pi$
$150$	211341.	−	64128.8i	0.766929	−	0.232715i
$151$		−	93886.3i		−	0.335089i	−0.985865	−	0.167544i	$-0.946416\pi$
$151$		−	93886.3i		−	0.335089i	0.985865	−	0.167544i	$-0.0535838\pi$
$152$	−483583.	+	142765.i	−1.69770	+	0.501203i
$153$	69765.7	+	69765.7i	0.240942	+	0.240942i
$154$	32679.2	−	39618.5i	0.111037	−	0.134616i
$155$	245110.	+	74009.5i	0.819466	+	0.247434i
$156$	−270923.	+	52491.6i	−0.891322	+	0.172695i
$157$	339269.	+	339269.i	1.09849	+	1.09849i	0.994588	+	0.103899i	$0.0331318\pi$
$157$	339269.	+	339269.i	1.09849	+	1.09849i	0.103899	+	0.994588i	$0.466868\pi$
$158$	−32521.1	−	338822.i	−0.103639	−	1.07976i
$159$	460312.			1.44397
$160$	318279.	−	59631.7i	0.982898	−	0.184152i
$161$	−68775.3			−0.209107
$162$	−16417.3	−	171044.i	−0.0491490	−	0.512059i
$163$	−50145.9	−	50145.9i	−0.147831	−	0.147831i	0.629317	−	0.777149i	$-0.283335\pi$
$163$	−50145.9	−	50145.9i	−0.147831	−	0.147831i	−0.777149	+	0.629317i	$0.783335\pi$
$164$	−198906.	+	38538.2i	−0.577482	+	0.111888i
$165$	81811.9	−	43864.6i	0.233941	−	0.125431i
$166$	−215384.	+	261120.i	−0.606656	+	0.735478i
$167$	−21262.4	−	21262.4i	−0.0589958	−	0.0589958i	0.676993	−	0.735989i	$-0.263283\pi$
$167$	−21262.4	−	21262.4i	−0.0589958	−	0.0589958i	−0.735989	+	0.676993i	$0.763283\pi$
$168$	148154.	−	43738.6i	0.404986	−	0.119562i
$169$		−	105169.i		−	0.283252i
$170$	−298724.	+	199082.i	−0.792770	+	0.528336i
$171$	242088.			0.633116
$172$	−41781.0	−	28218.5i	−0.107686	−	0.0727299i
$173$	−144580.	+	144580.i	−0.367276	+	0.367276i	−0.866483	−	0.499207i	$-0.833625\pi$
$173$	−144580.	+	144580.i	−0.367276	+	0.367276i	0.499207	+	0.866483i	$0.333625\pi$
$174$	94064.8	−	114039.i	0.235534	−	0.285549i
$175$	−42180.0	−	209243.i	−0.104115	−	0.516482i
$176$	126257.	−	50832.9i	0.307236	−	0.123698i
$177$	316575.	−	316575.i	0.759527	−	0.759527i
$178$	576970.	−	55379.3i	1.36491	−	0.131008i
$179$			26195.9i			0.0611083i	0.999533	+	0.0305542i	$0.00972721\pi$
$179$			26195.9i			0.0611083i	−0.999533	+	0.0305542i	$0.990273\pi$
$180$	−154668.	−	15809.2i	−0.355810	−	0.0363688i
$181$		−	500862.i		−	1.13637i	−0.822899	−	0.568187i	$-0.807645\pi$
$181$		−	500862.i		−	1.13637i	0.822899	−	0.568187i	$-0.192355\pi$
$182$	25482.5	+	265490.i	0.0570248	+	0.594113i
$183$	−116126.	+	116126.i	−0.256331	+	0.256331i
$184$	−160100.	−	87115.9i	−0.348615	−	0.189694i
$185$	414687.	−	222340.i	0.890822	−	0.477626i
$186$	249711.	+	205973.i	0.529244	+	0.436545i
$187$	−106693.	+	106693.i	−0.223117	+	0.223117i
$188$	−460722.	−	311167.i	−0.950701	−	0.642095i
$189$	−281535.			−0.573295
$190$	−172878.	+	863698.i	−0.347422	+	1.73571i
$191$			804916.i			1.59649i	0.602330	+	0.798247i	$0.294239\pi$
$191$			804916.i			1.59649i	−0.602330	+	0.798247i	$0.705761\pi$
$192$	400286.	+	85844.8i	0.783640	+	0.168059i
$193$	−267880.	−	267880.i	−0.517663	−	0.517663i	0.399201	−	0.916864i	$-0.369288\pi$
$193$	−267880.	−	267880.i	−0.517663	−	0.517663i	−0.916864	+	0.399201i	$0.869288\pi$
$194$	583098.	+	480966.i	1.11234	+	0.917509i
$195$	−139349.	+	461506.i	−0.262433	+	0.869142i
$196$	73903.2	+	381434.i	0.137412	+	0.709217i
$197$	185787.	+	185787.i	0.341075	+	0.341075i	0.856771	−	0.515696i	$-0.172467\pi$
$197$	185787.	+	185787.i	0.341075	+	0.341075i	−0.515696	+	0.856771i	$0.672467\pi$
$198$	−65049.1	+	6243.61i	−0.117917	+	0.0113181i
$199$	90919.1			0.162750			0.0813752	−	0.996684i	$-0.474069\pi$
$199$	90919.1			0.162750			0.0813752	+	0.996684i	$0.474069\pi$
$200$	166853.	−	540518.i	0.294957	−	0.955511i
$201$	−582255.			−1.01654
$202$	−27932.1	+	2681.01i	−0.0481643	+	0.00462295i
$203$	−101026.	−	101026.i	−0.172065	−	0.172065i
$204$	−445561.	+	86327.9i	−0.749604	+	0.145236i
$205$	−102307.	+	338828.i	−0.170028	+	0.563111i
$206$	304977.	+	251559.i	0.500724	+	0.413020i
$207$	61879.8	+	61879.8i	0.100374	+	0.100374i
$208$	−276969.	+	650304.i	−0.443887	+	1.04222i
$209$			370227.i			0.586276i
$210$	52964.3	−	264609.i	0.0828771	−	0.414053i
$211$	163692.			0.253117			0.126559	−	0.991959i	$-0.459607\pi$
$211$	163692.			0.253117			0.126559	+	0.991959i	$0.459607\pi$
$212$	659888.	−	977045.i	1.00839	−	1.49305i
$213$	−337462.	+	337462.i	−0.509655	+	0.509655i
$214$	167951.	+	138533.i	0.250696	+	0.206785i
$215$	−77622.6	+	41618.4i	−0.114523	+	0.0614030i
$216$	−655378.	−	356613.i	−0.955778	−	0.520072i
$217$	221216.	−	221216.i	0.318909	−	0.318909i
$218$	−124754.	−	1.29975e6i	−0.177793	−	1.85233i
$219$			481620.i			0.678569i
$220$	24177.1	−	236534.i	0.0336781	−	0.329486i
$221$		−	783591.i		−	1.07922i
$222$	592150.	−	56836.4i	0.806398	−	0.0774005i
$223$	933470.	−	933470.i	1.25701	−	1.25701i	0.304495	−	0.952514i	$-0.401512\pi$
$223$	933470.	−	933470.i	1.25701	−	1.25701i	0.952514	−	0.304495i	$-0.0984877\pi$
$224$	119550.	−	377169.i	0.159195	−	0.502246i
$225$	−150313.	+	226215.i	−0.197943	+	0.297896i
$226$	726454.	−	880715.i	0.946100	−	1.14700i
$227$	−842940.	+	842940.i	−1.08576	+	1.08576i	−0.0897951	+	0.995960i	$0.528621\pi$
$227$	−842940.	+	842940.i	−1.08576	+	1.08576i	−0.995960	+	0.0897951i	$0.971379\pi$
$228$	−623273.	+	922832.i	−0.794038	+	1.17567i
$229$	−798268.			−1.00591			−0.502956	−	0.864312i	$-0.667754\pi$
$229$	−798268.			−1.00591			−0.502956	+	0.864312i	$0.667754\pi$
$230$	−264958.	+	176579.i	−0.330261	+	0.220100i
$231$		−	113425.i		−	0.139856i
$232$	−107208.	−	363142.i	−0.130770	−	0.442952i
$233$	118131.	+	118131.i	0.142553	+	0.142553i	0.774782	−	0.632229i	$-0.217860\pi$
$233$	118131.	+	118131.i	0.142553	+	0.142553i	−0.632229	+	0.774782i	$0.717860\pi$
$234$	215944.	−	261799.i	0.257811	−	0.312557i
$235$	−855950.	+	458929.i	−1.01106	+	0.542096i
$236$	−218122.	−	1.12578e6i	−0.254929	−	1.31575i
$237$	−531565.	−	531565.i	−0.614732	−	0.614732i
$238$	41908.6	+	436625.i	0.0479580	+	0.499651i
$239$	921010.			1.04296			0.521482	−	0.853262i	$-0.325379\pi$
$239$	921010.			1.04296			0.521482	+	0.853262i	$0.325379\pi$
$240$	458467.	−	548886.i	0.513783	−	0.615112i
$241$	−1.17647e6			−1.30478			−0.652391	−	0.757882i	$-0.726234\pi$
$241$	−1.17647e6			−1.30478			−0.652391	+	0.757882i	$0.726234\pi$
$242$	77496.1	+	807394.i	0.0850632	+	0.886232i
$243$	439885.	+	439885.i	0.477885	+	0.477885i
$244$	80011.3	+	412960.i	0.0860354	+	0.444051i
$245$	649756.	+	196190.i	0.691568	+	0.208815i
$246$	−284728.	+	345189.i	−0.299980	+	0.363680i
$247$	−1.35954e6	−	1.35954e6i	−1.41791	−	1.41791i
$248$	795171.	−	234754.i	0.820977	−	0.242372i
$249$			747569.i			0.764105i
$250$	−699727.	−	697815.i	−0.708073	−	0.706139i
$251$	922201.			0.923935			0.461968	−	0.886897i	$-0.347144\pi$
$251$	922201.			0.923935			0.461968	+	0.886897i	$0.347144\pi$
$252$	−106324.	+	157426.i	−0.105471	+	0.156162i
$253$	−94633.2	+	94633.2i	−0.0929485	+	0.0929485i
$254$	115194.	−	139655.i	0.112033	−	0.135822i
$255$	−229174.	+	758994.i	−0.220707	+	0.730950i
$256$	756047.	−	726570.i	0.721023	−	0.692911i
$257$	634212.	−	634212.i	0.598965	−	0.598965i	−0.341072	−	0.940037i	$-0.610790\pi$
$257$	634212.	−	634212.i	0.598965	−	0.598965i	0.940037	+	0.341072i	$0.110790\pi$
$258$	−110841.	+	10638.8i	−0.103669	+	0.00995050i
$259$		−	574929.i		−	0.532555i
$260$	779812.	+	957378.i	0.715413	+	0.878314i
$261$			181794.i			0.165188i
$262$	−85530.4	−	891100.i	−0.0769781	−	0.801998i
$263$	744074.	−	744074.i	0.663326	−	0.663326i	−0.292837	−	0.956163i	$-0.594599\pi$
$263$	744074.	−	744074.i	0.663326	−	0.663326i	0.956163	+	0.292837i	$0.0945992\pi$
$264$	143673.	−	264040.i	0.126872	−	0.233163i
$265$	−973244.	−	1.81520e6i	−0.851348	−	1.58785i
$266$	830261.	+	684837.i	0.719466	+	0.593449i
$267$	905189.	−	905189.i	0.777072	−	0.777072i
$268$	−834701.	+	1.23588e6i	−0.709895	+	1.05109i
$269$	−268211.			−0.225993			−0.112997	−	0.993595i	$-0.536045\pi$
$269$	−268211.			−0.225993			−0.112997	+	0.993595i	$0.536045\pi$
$270$	−1.08462e6	+	722837.i	−0.905457	+	0.603436i
$271$			2.36545e6i			1.95654i	0.207325	+	0.978272i	$0.433524\pi$
$271$			2.36545e6i			1.95654i	−0.207325	+	0.978272i	$0.566476\pi$
$272$	−455504.	+	1.06949e6i	−0.373310	+	0.876506i
$273$	416518.	+	416518.i	0.338241	+	0.338241i
$274$	207239.	+	170941.i	0.166762	+	0.137553i
$275$	−345952.	−	229874.i	−0.275857	−	0.183299i
$276$	−395198.	+	76569.9i	−0.312278	+	0.0605042i
$277$	430756.	+	430756.i	0.337312	+	0.337312i	0.855355	−	0.518043i	$-0.173339\pi$
$277$	430756.	+	430756.i	0.337312	+	0.337312i	−0.518043	+	0.855355i	$0.673339\pi$
$278$	−2.15348e6	+	206697.i	−1.67120	+	0.160407i
$279$	−398073.			−0.306163
$280$	−485723.	−	491754.i	−0.370249	−	0.374846i
$281$	1.37421e6			1.03821			0.519106	−	0.854710i	$-0.326265\pi$
$281$	1.37421e6			1.03821			0.519106	+	0.854710i	$0.326265\pi$
$282$	−1.22225e6	+	117315.i	−0.915245	+	0.0878479i
$283$	−889337.	−	889337.i	−0.660085	−	0.660085i	0.295315	−	0.955400i	$-0.404575\pi$
$283$	−889337.	−	889337.i	−0.660085	−	0.660085i	−0.955400	+	0.295315i	$0.904575\pi$
$284$	232513.	+	1.20006e6i	0.171061	+	0.882892i
$285$	919242.	+	1.71448e6i	0.670375	+	1.25032i
$286$	400371.	+	330244.i	0.289433	+	0.238737i
$287$	305798.	+	305798.i	0.219144	+	0.219144i
$288$	−446918.	+	231790.i	−0.317502	+	0.164670i
$289$			131161.i			0.0923762i
$290$	−648586.	−	129821.i	−0.452869	−	0.0906466i
$291$	1.66937e6			1.15564
$292$	1.02227e6	+	690434.i	0.701632	+	0.473876i
$293$	1.32774e6	−	1.32774e6i	0.903535	−	0.903535i	−0.0922047	−	0.995740i	$-0.529391\pi$
$293$	1.32774e6	−	1.32774e6i	0.903535	−	0.903535i	0.995740	+	0.0922047i	$0.0293914\pi$
$294$	661955.	+	546011.i	0.446643	+	0.368411i
$295$	−1.91772e6	−	579046.i	−1.28301	−	0.387399i
$296$	728247.	−	1.33836e6i	0.483114	−	0.887858i
$297$	−387386.	+	387386.i	−0.254831	+	0.254831i
$298$	176113.	+	1.83483e6i	0.114881	+	1.19689i
$299$		−	695019.i		−	0.449592i
$300$	−475333.	−	1.15539e6i	−0.304926	−	0.741186i
$301$			107617.i			0.0684646i
$302$	−528672.	+	50743.5i	−0.333556	+	0.0320157i
$303$	−43821.7	+	43821.7i	−0.0274210	+	0.0274210i
$304$	1.06527e6	+	2.64588e6i	0.661116	+	1.64205i
$305$	703459.	+	212406.i	0.433001	+	0.130742i
$306$	355142.	−	430556.i	0.216820	−	0.262861i
$307$	1.15775e6	−	1.15775e6i	0.701085	−	0.701085i	−0.263558	−	0.964643i	$-0.584896\pi$
$307$	1.15775e6	−	1.15775e6i	0.701085	−	0.701085i	0.964643	+	0.263558i	$0.0848962\pi$
$308$	−240753.	−	162603.i	−0.144609	−	0.0976677i
$309$	873129.			0.520214
$310$	284270.	−	1.42021e6i	0.168007	−	0.839358i
$311$			1.15192e6i			0.675337i	0.941265	+	0.337668i	$0.109638\pi$
$311$			1.15192e6i			0.675337i	−0.941265	+	0.337668i	$0.890362\pi$
$312$	442007.	+	1.49719e6i	0.257065	+	0.870745i
$313$	2.03938e6	+	2.03938e6i	1.17662	+	1.17662i	0.980599	+	0.196023i	$0.0628026\pi$
$313$	2.03938e6	+	2.03938e6i	1.17662	+	1.17662i	0.196023	+	0.980599i	$0.437197\pi$
$314$	1.72705e6	−	2.09378e6i	0.988508	−	1.19841i
$315$	156814.	+	292474.i	0.0890448	+	0.166078i
$316$	−1.89032e6	+	366251.i	−1.06492	+	0.206329i
$317$	−1.03170e6	−	1.03170e6i	−0.576640	−	0.576640i	0.357336	−	0.933976i	$-0.383685\pi$
$317$	−1.03170e6	−	1.03170e6i	−0.576640	−	0.576640i	−0.933976	+	0.357336i	$0.883685\pi$
$318$	−248789.	−	2.59201e6i	−0.137963	−	1.43737i
$319$	−278019.			−0.152967
$320$	−507807.	−	1.75999e6i	−0.277220	−	0.960807i
$321$	480832.			0.260454
$322$	37171.5	+	387272.i	0.0199789	+	0.208150i
$323$	−2.23590e6	−	2.23590e6i	−1.19247	−	1.19247i
$324$	−954271.	+	184891.i	−0.505021	+	0.0978482i
$325$	2.11453e6	−	426256.i	1.11047	−	0.223853i
$326$	−255268.	+	309473.i	−0.133031	+	0.161280i
$327$	−2.03914e6	−	2.03914e6i	−1.05457	−	1.05457i
$328$	324512.	+	1.09921e6i	0.166551	+	0.564150i
$329$			1.18670e6i			0.604439i
$330$	−291218.	−	436973.i	−0.147209	−	0.220887i
$331$	−1.08093e6			−0.542286			−0.271143	−	0.962539i	$-0.587402\pi$
$331$	−1.08093e6			−0.542286			−0.271143	+	0.962539i	$0.587402\pi$
$332$	1.58677e6	+	1.07169e6i	0.790075	+	0.533610i
$333$	−517286.	+	517286.i	−0.255635	+	0.255635i
$334$	−108236.	+	131220.i	−0.0530892	+	0.0643626i
$335$	1.23107e6	+	2.29607e6i	0.599336	+	1.11782i
$336$	−326365.	−	810611.i	−0.157709	−	0.391710i
$337$	−824573.	+	824573.i	−0.395507	+	0.395507i	−0.876645	−	0.481138i	$-0.840224\pi$
$337$	−824573.	+	824573.i	−0.395507	+	0.395507i	0.481138	+	0.876645i	$0.340224\pi$
$338$	−592206.	+	56841.7i	−0.281956	+	0.0270630i
$339$		−	2.52143e6i		−	1.19165i
$340$	1.28248e6	+	1.57451e6i	0.601664	+	0.738664i
$341$		−	608776.i		−	0.283512i
$342$	−130843.	−	1.36319e6i	−0.0604904	−	0.630220i
$343$	1.39817e6	−	1.39817e6i	0.641690	−	0.641690i
$344$	−136316.	+	250519.i	−0.0621085	+	0.114142i
$345$	−203270.	+	673202.i	−0.0919444	+	0.304507i
$346$	892267.	+	735983.i	0.400686	+	0.330505i
$347$	−1.50857e6	+	1.50857e6i	−0.672577	+	0.672577i	−0.958310	−	0.285732i	$-0.907763\pi$
$347$	−1.50857e6	+	1.50857e6i	−0.672577	+	0.672577i	0.285732	+	0.958310i	$0.407763\pi$
$348$	−692992.	−	468041.i	−0.306747	−	0.207174i
$349$	−1.98154e6			−0.870844			−0.435422	−	0.900226i	$-0.643401\pi$
$349$	−1.98154e6			−0.870844			−0.435422	+	0.900226i	$0.643401\pi$
$350$	−1.15544e6	+	350606.i	−0.504172	+	0.152985i
$351$		−	2.84510e6i		−	1.23262i
$352$	−354478.	−	683474.i	−0.152487	−	0.294012i
$353$	3162.85	+	3162.85i	0.00135096	+	0.00135096i	0.707782	−	0.706431i	$-0.249696\pi$
$353$	3162.85	+	3162.85i	0.00135096	+	0.00135096i	−0.706431	+	0.707782i	$0.749696\pi$
$354$	−1.95373e6	−	1.61152e6i	−0.828620	−	0.683484i
$355$	2.04425e6	+	617251.i	0.860922	+	0.259951i
$356$	−623680.	−	3.21897e6i	−0.260817	−	1.34615i
$357$	685006.	+	685006.i	0.284462	+	0.284462i
$358$	147508.	−	14158.3i	0.0608288	−	0.00583853i
$359$	−4.01967e6			−1.64609			−0.823047	−	0.567973i	$-0.807728\pi$
$359$	−4.01967e6			−1.64609			−0.823047	+	0.567973i	$0.807728\pi$
$360$	−5426.79	+	879474.i	−0.00220692	+	0.357657i
$361$	−5.28252e6			−2.13340
$362$	−2.82034e6	+	270705.i	−1.13118	+	0.108574i
$363$	1.26669e6	+	1.26669e6i	0.504551	+	0.504551i
$364$	1.48119e6	−	286983.i	0.585947	−	0.113528i
$365$	1.89923e6	−	1.01830e6i	0.746181	−	0.400075i
$366$	716666.	+	591139.i	0.279649	+	0.230668i
$367$	3.24558e6	+	3.24558e6i	1.25784	+	1.25784i	0.952121	+	0.305723i	$0.0988981\pi$
$367$	3.24558e6	+	3.24558e6i	1.25784	+	1.25784i	0.305723	+	0.952121i	$0.401102\pi$
$368$	−404017.	+	948603.i	−0.155518	+	0.365145i
$369$		−	550277.i		−	0.210385i
$370$	−1.47612e6	−	2.21492e6i	−0.560554	−	0.841112i
$371$	−2.51662e6			−0.949256
$372$	1.02487e6	−	1.51744e6i	0.383982	−	0.568532i
$373$	107814.	−	107814.i	0.0401237	−	0.0401237i	−0.686760	−	0.726884i	$-0.740968\pi$
$373$	107814.	−	107814.i	0.0401237	−	0.0401237i	0.726884	+	0.686760i	$0.240968\pi$
$374$	658451.	+	543121.i	0.243414	+	0.200779i
$375$	−2.17282e6	−	205555.i	−0.797896	−	0.0754830i
$376$	−1.50317e6	+	2.76249e6i	−0.548324	+	1.00770i
$377$	1.02093e6	−	1.02093e6i	0.369951	−	0.369951i
$378$	152164.	+	1.58532e6i	0.0547748	+	0.570672i
$379$			1.79110e6i			0.640504i	0.947332	+	0.320252i	$0.103768\pi$
$379$			1.79110e6i			0.640504i	−0.947332	+	0.320252i	$0.896232\pi$
$380$	4.95690e6	+	506665.i	1.76097	+	0.179996i
$381$		−	399823.i		−	0.141109i
$382$	4.53246e6	−	435039.i	1.58919	−	0.152535i
$383$	102633.	−	102633.i	0.0357511	−	0.0357511i	−0.689005	−	0.724756i	$-0.741952\pi$
$383$	102633.	−	102633.i	0.0357511	−	0.0357511i	0.724756	+	0.689005i	$0.241952\pi$
$384$	267045.	−	2.30040e6i	0.0924178	−	0.796112i
$385$	−447283.	+	239817.i	−0.153791	+	0.0824570i
$386$	−1.36364e6	+	1.65321e6i	−0.465835	+	0.564754i
$387$	96827.5	−	96827.5i	0.0328641	−	0.0328641i
$388$	2.39316e6	−	3.54336e6i	0.807034	−	1.19491i
$389$	−2.45331e6			−0.822013			−0.411007	−	0.911632i	$-0.634823\pi$
$389$	−2.45331e6			−0.822013			−0.411007	+	0.911632i	$0.634823\pi$
$390$	2.67404e6	+	535239.i	0.890240	+	0.178191i
$391$		−	1.14303e6i		−	0.378108i
$392$	2.10790e6	−	622304.i	0.692844	−	0.204544i
$393$	−1.39802e6	−	1.39802e6i	−0.456594	−	0.456594i
$394$	945749.	−	1.14658e6i	0.306927	−	0.372102i
$395$	−972285.	+	3.22008e6i	−0.313546	+	1.03842i
$396$	70315.2	+	362915.i	0.0225326	+	0.116297i
$397$	266983.	+	266983.i	0.0850172	+	0.0850172i	0.748337	−	0.663319i	$-0.230853\pi$
$397$	266983.	+	266983.i	0.0850172	+	0.0850172i	−0.663319	+	0.748337i	$0.730853\pi$
$398$	−49139.7	−	511963.i	−0.0155498	−	0.162006i
$399$	2.37698e6			0.747470
$400$	−3.13383e6	−	647406.i	−0.979321	−	0.202314i
$401$	3.29213e6			1.02239			0.511195	−	0.859465i	$-0.329203\pi$
$401$	3.29213e6			1.02239			0.511195	+	0.859465i	$0.329203\pi$
$402$	314696.	+	3.27866e6i	0.0971239	+	1.01189i
$403$	2.23553e6	+	2.23553e6i	0.685675	+	0.685675i
$404$	30193.4	+	155836.i	0.00920361	+	0.0475022i
$405$	−490829.	+	1.62556e6i	−0.148694	+	0.492453i
$406$	−514272.	+	623476.i	−0.154838	+	0.187718i
$407$	−791088.	−	791088.i	−0.236722	−	0.236722i
$408$	726926.	+	2.46228e6i	0.216192	+	0.732298i
$409$		−	1.56045e6i		−	0.461255i	−0.973042	−	0.230628i	$-0.925922\pi$
$409$		−	1.56045e6i		−	0.461255i	0.973042	−	0.230628i	$-0.0740780\pi$
$410$	1.96322e6	+	392961.i	0.576780	+	0.115449i
$411$	593314.			0.173253
$412$	1.25169e6	−	1.85328e6i	0.363290	−	0.537895i
$413$	−1.73078e6	+	1.73078e6i	−0.499306	+	0.499306i
$414$	314999.	−	381888.i	0.0903251	−	0.109505i
$415$	2.94797e6	−	1.58060e6i	0.840240	−	0.450506i
$416$	3.81154e6	+	1.20813e6i	1.07986	+	0.342279i
$417$	−3.37851e6	+	3.37851e6i	−0.951449	+	0.951449i
$418$	2.08474e6	−	200100.i	0.583594	−	0.0560151i
$419$			2.32937e6i			0.648191i	0.946024	+	0.324095i	$0.105060\pi$
$419$			2.32937e6i			0.648191i	−0.946024	+	0.324095i	$0.894940\pi$
$420$	−1.51863e6	−	155225.i	−0.420077	−	0.0429378i
$421$			2.41688e6i			0.664585i	0.943176	+	0.332292i	$0.107822\pi$
$421$			2.41688e6i			0.664585i	−0.943176	+	0.332292i	$0.892178\pi$
$422$	−88472.0	−	921746.i	−0.0241838	−	0.251959i
$423$	1.06772e6	−	1.06772e6i	0.290140	−	0.290140i
$424$	−5.85837e6	−	3.18774e6i	−1.58257	−	0.861129i
$425$	3.47757e6	−	701022.i	0.933907	−	0.188261i
$426$	2.08263e6	+	1.71785e6i	0.556018	+	0.458629i
$427$	634885.	−	634885.i	0.168510	−	0.168510i
$428$	689305.	−	1.02060e6i	0.181887	−	0.269306i
$429$	1.14624e6			0.300699
$430$	276306.	+	414597.i	0.0720640	+	0.108132i
$431$			6.38964e6i			1.65685i	0.560100	+	0.828425i	$0.310763\pi$
$431$			6.38964e6i			1.65685i	−0.560100	+	0.828425i	$0.689237\pi$
$432$	−1.65386e6	+	3.88316e6i	−0.426374	+	1.00110i
$433$	156498.	+	156498.i	0.0401134	+	0.0401134i	0.726879	−	0.686766i	$-0.240970\pi$
$433$	156498.	+	156498.i	0.0401134	+	0.0401134i	−0.686766	+	0.726879i	$0.740970\pi$
$434$	−1.36522e6	−	1.12610e6i	−0.347920	−	0.286981i
$435$	−1.28747e6	+	690296.i	−0.326223	+	0.174909i
$436$	−7.25145e6	+	1.40498e6i	−1.82687	+	0.353959i
$437$	−1.98317e6	−	1.98317e6i	−0.496771	−	0.496771i
$438$	2.71199e6	−	260305.i	0.675465	−	0.0648332i
$439$	−4542.17			−0.00112487			−0.000562434	−	1.00000i	$-0.500179\pi$
$439$	−4542.17			−0.00112487			−0.000562434		1.00000i	$0.500179\pi$
$440$	−1.34499e6	−	8299.22i	−0.331197	−	0.00204364i
$441$	−1.05524e6			−0.258379
$442$	−4.41238e6	+	423514.i	−1.07428	+	0.103113i
$443$	−854779.	−	854779.i	−0.206940	−	0.206940i	0.596025	−	0.802966i	$-0.296746\pi$
$443$	−854779.	−	854779.i	−0.206940	−	0.206940i	−0.802966	+	0.596025i	$0.796746\pi$
$444$	−640088.	−	3.30366e6i	−0.154093	−	0.795314i
$445$	−5.48338e6	−	1.65568e6i	−1.31265	−	0.396347i
$446$	−5.76087e6	−	4.75183e6i	−1.37136	−	1.13116i
$447$	2.87861e6	+	2.87861e6i	0.681417	+	0.681417i
$448$	−2.18844e6	−	469332.i	−0.515158	−	0.110480i
$449$		−	6.16439e6i		−	1.44303i	−0.692400	−	0.721514i	$-0.743447\pi$
$449$		−	6.16439e6i		−	1.44303i	0.692400	−	0.721514i	$-0.256553\pi$
$450$	1.35505e6	+	724144.i	0.315446	+	0.168575i
$451$	841543.			0.194821
$452$	−5.35192e6	−	3.61464e6i	−1.23215	−	0.832183i
$453$	−829414.	+	829414.i	−0.189900	+	0.189900i
$454$	5.20216e6	+	4.29098e6i	1.18453	+	0.977051i
$455$	761851.	−	2.52315e6i	0.172521	−	0.571366i
$456$	5.53331e6	+	3.01086e6i	1.24616	+	0.678077i
$457$	2.75584e6	−	2.75584e6i	0.617254	−	0.617254i	−0.327572	−	0.944826i	$-0.606230\pi$
$457$	2.75584e6	−	2.75584e6i	0.617254	−	0.617254i	0.944826	+	0.327572i	$0.106230\pi$
$458$	431446.	+	4.49503e6i	0.0961087	+	1.00131i
$459$		−	4.67905e6i		−	1.03664i
$460$	1.13752e6	+	1.39653e6i	0.250648	+	0.307721i
$461$		−	1.99091e6i		−	0.436315i	−0.975914	−	0.218157i	$-0.929995\pi$
$461$		−	1.99091e6i		−	0.436315i	0.975914	−	0.218157i	$-0.0700046\pi$
$462$	−638695.	+	61303.9i	−0.139216	+	0.0133624i
$463$	−1.20628e6	+	1.20628e6i	−0.261514	+	0.261514i	−0.825669	−	0.564155i	$-0.809202\pi$
$463$	−1.20628e6	+	1.20628e6i	−0.261514	+	0.261514i	0.564155	+	0.825669i	$0.309202\pi$
$464$	−1.98690e6	+	799958.i	−0.428431	+	0.172493i
$465$	−1.51154e6	−	2.81918e6i	−0.324181	−	0.604630i
$466$	601348.	−	729043.i	0.128281	−	0.155521i
$467$	−2.65264e6	+	2.65264e6i	−0.562842	+	0.562842i	−0.930114	−	0.367271i	$-0.880292\pi$
$467$	−2.65264e6	+	2.65264e6i	−0.562842	+	0.562842i	0.367271	+	0.930114i	$0.380292\pi$
$468$	−1.59090e6	−	1.07448e6i	−0.335759	−	0.226769i
$469$	3.18331e6			0.668262
$470$	3.04684e6	+	4.57179e6i	0.636217	+	0.954645i
$471$		−	5.99436e6i		−	1.24506i
$472$	−6.22137e6	+	1.83670e6i	−1.28538	+	0.379475i
$473$	148079.	+	148079.i	0.0304327	+	0.0304327i
$474$	−2.70593e6	+	3.28053e6i	−0.553186	+	0.670654i
$475$	4.81734e6	−	7.24990e6i	0.979654	−	1.47434i
$476$	2.43597e6	−	471973.i	0.492783	−	0.0954771i
$477$	2.26430e6	+	2.26430e6i	0.455658	+	0.455658i
$478$	−497786.	−	5.18619e6i	−0.0996489	−	1.03819i
$479$	5.94725e6			1.18434			0.592171	−	0.805812i	$-0.298271\pi$
$479$	5.94725e6			1.18434			0.592171	+	0.805812i	$0.298271\pi$
$480$	−3.33856e6	−	2.28495e6i	−0.661387	−	0.452663i
$481$	5.81003e6			1.14503
$482$	635856.	+	6.62467e6i	0.124664	+	1.29881i
$483$	607577.	+	607577.i	0.118504	+	0.118504i
$484$	4.50453e6	−	872757.i	0.874050	−	0.169348i
$485$	−3.52958e6	−	6.58303e6i	−0.681347	−	1.27078i
$486$	2.23923e6	−	2.71473e6i	0.430040	−	0.521358i
$487$	−3.35438e6	−	3.35438e6i	−0.640900	−	0.640900i	0.309877	−	0.950777i	$-0.399712\pi$
$487$	−3.35438e6	−	3.35438e6i	−0.640900	−	0.640900i	−0.950777	+	0.309877i	$0.899712\pi$
$488$	2.28212e6	−	673738.i	0.433800	−	0.128068i
$489$			886003.i			0.167557i
$490$	753565.	−	3.76480e6i	0.141785	−	0.708356i
$491$	−1.32658e6			−0.248330			−0.124165	−	0.992262i	$-0.539625\pi$
$491$	−1.32658e6			−0.248330			−0.124165	+	0.992262i	$0.539625\pi$
$492$	2.09764e6	+	1.41673e6i	0.390677	+	0.263860i
$493$	1.67903e6	−	1.67903e6i	0.311129	−	0.311129i
$494$	−6.92073e6	+	8.39033e6i	−1.27595	+	1.54690i
$495$	618210.	+	186665.i	0.113403	+	0.0342413i
$496$	−1.75166e6	−	4.35071e6i	−0.319703	−	0.794064i
$497$	1.84498e6	−	1.84498e6i	0.335042	−	0.335042i
$498$	4.20954e6	−	404045.i	0.760610	−	0.0730056i
$499$			8.63773e6i			1.55292i	0.630168	+	0.776459i	$0.282986\pi$
$499$			8.63773e6i			1.55292i	−0.630168	+	0.776459i	$0.717014\pi$
$500$	−3.55119e6	+	4.31730e6i	−0.635256	+	0.772301i
$501$			375674.i			0.0668678i
$502$	−498429.	−	5.19289e6i	−0.0882764	−	0.919708i
$503$	−7.03064e6	+	7.03064e6i	−1.23901	+	1.23901i	−0.278604	+	0.960406i	$0.589872\pi$
$503$	−7.03064e6	+	7.03064e6i	−1.23901	+	1.23901i	−0.960406	+	0.278604i	$0.910128\pi$
$504$	943931.	+	513625.i	0.165525	+	0.0900679i
$505$	265460.	+	80154.2i	0.0463202	+	0.0139861i
$506$	584024.	+	481730.i	0.101404	+	0.0836426i
$507$	−929091.	+	929091.i	−0.160523	+	0.160523i
$508$	−848653.	−	573173.i	−0.145905	−	0.0985431i
$509$	5.41942e6			0.927168			0.463584	−	0.886053i	$-0.346563\pi$
$509$	5.41942e6			0.927168			0.463584	+	0.886053i	$0.346563\pi$
$510$	4.39774e6	+	880255.i	0.748693	+	0.149859i
$511$		−	2.63312e6i		−	0.446085i
$512$	−4.49993e6	−	3.86459e6i	−0.758631	−	0.651521i
$513$	−8.11820e6	−	8.11820e6i	−1.36197	−	1.36197i
$514$	−3.91401e6	−	3.22845e6i	−0.653452	−	0.538997i
$515$	−1.84607e6	−	3.44311e6i	−0.306711	−	0.572048i
$516$	119814.	+	618392.i	0.0198100	+	0.102244i
$517$	1.63288e6	+	1.63288e6i	0.268675	+	0.268675i
$518$	−3.23741e6	+	310736.i	−0.530119	+	0.0508824i
$519$	2.55450e6			0.416283
$520$	4.96950e6	−	4.90855e6i	0.805943	−	0.796058i
$521$	568375.			0.0917362			0.0458681	−	0.998948i	$-0.485395\pi$
$521$	568375.			0.0917362			0.0458681	+	0.998948i	$0.485395\pi$
$522$	1.02368e6	−	98255.6i	0.164432	−	0.0157827i
$523$	5.95145e6	+	5.95145e6i	0.951413	+	0.951413i	0.998873	−	0.0474606i	$-0.0151128\pi$
$523$	5.95145e6	+	5.95145e6i	0.951413	+	0.951413i	−0.0474606	+	0.998873i	$0.515113\pi$
$524$	−4.97153e6	+	963239.i	−0.790974	+	0.153252i
$525$	−1.47587e6	+	2.22113e6i	−0.233696	+	0.351703i
$526$	−4.59202e6	−	3.78771e6i	−0.723668	−	0.596915i
$527$	3.67656e6	+	3.67656e6i	0.576654	+	0.576654i
$528$	−1.56445e6	−	666311.i	−0.244218	−	0.104014i
$529$			5.42251e6i			0.842484i
$530$	−9.69533e6	+	6.46139e6i	−1.49925	+	0.999162i
$531$	3.11450e6			0.479349
$532$	3.40756e6	−	5.04532e6i	0.521993	−	0.772875i
$533$	−3.09029e6	+	3.09029e6i	−0.471174	+	0.471174i
$534$	−5.58633e6	−	4.60786e6i	−0.847761	−	0.699272i
$535$	−1.01663e6	−	1.89612e6i	−0.153560	−	0.286405i
$536$	7.41033e6	+	4.03222e6i	1.11410	+	0.606222i
$537$	231421.	−	231421.i	0.0346311	−	0.0346311i
$538$	144962.	+	1.51029e6i	0.0215923	+	0.224960i
$539$		−	1.61379e6i		−	0.239263i
$540$	4.65649e6	+	5.71678e6i	0.687186	+	0.843660i
$541$			8.15230e6i			1.19753i	0.800924	+	0.598766i	$0.204342\pi$
$541$			8.15230e6i			1.19753i	−0.800924	+	0.598766i	$0.795658\pi$
$542$	1.33198e7	−	1.27847e6i	1.94759	−	0.186936i
$543$	−4.42474e6	+	4.42474e6i	−0.644003	+	0.644003i
$544$	6.26847e6	+	1.98690e6i	0.908164	+	0.287858i
$545$	−3.72978e6	+	1.23525e7i	−0.537888	+	1.78141i
$546$	2.12028e6	−	2.57052e6i	0.304377	−	0.369011i
$547$	2.83225e6	−	2.83225e6i	0.404729	−	0.404729i	−0.475167	−	0.879896i	$-0.657612\pi$
$547$	2.83225e6	−	2.83225e6i	0.404729	−	0.404729i	0.879896	+	0.475167i	$0.157612\pi$
$548$	850554.	−	1.25935e6i	0.120990	−	0.179141i
$549$	−1.14246e6			−0.161775
$550$	−1.10744e6	+	2.07229e6i	−0.156104	+	0.292108i
$551$		−	5.82626e6i		−	0.817543i
$552$	644759.	+	2.18396e6i	0.0900637	+	0.305069i
$553$	2.90618e6	+	2.90618e6i	0.404119	+	0.404119i
$554$	2.19276e6	−	2.65839e6i	0.303541	−	0.367997i
$555$	−5.62765e6	−	1.69924e6i	−0.775523	−	0.234165i
$556$	2.32781e6	+	1.20145e7i	0.319346	+	1.64823i
$557$	−698101.	−	698101.i	−0.0953411	−	0.0953411i	0.657827	−	0.753169i	$-0.271476\pi$
$557$	−698101.	−	698101.i	−0.0953411	−	0.0953411i	−0.753169	+	0.657827i	$0.771476\pi$
$558$	215150.	+	2.24154e6i	0.0292520	+	0.304762i
$559$	−1.08754e6			−0.147203
$560$	−2.50653e6	+	3.00088e6i	−0.337756	+	0.404369i
$561$	1.88510e6			0.252888
$562$	−742728.	−	7.73812e6i	−0.0991949	−	1.03346i
$563$	−5.64471e6	−	5.64471e6i	−0.750535	−	0.750535i	0.224044	−	0.974579i	$-0.428074\pi$
$563$	−5.64471e6	−	5.64471e6i	−0.750535	−	0.750535i	−0.974579	+	0.224044i	$0.928074\pi$
$564$	1.32120e6	+	6.81905e6i	0.174892	+	0.902665i
$565$	−9.94304e6	+	5.33110e6i	−1.31038	+	0.702579i
$566$	−4.52717e6	+	5.48850e6i	−0.593998	+	0.720133i
$567$	1.46710e6	+	1.46710e6i	0.191647	+	0.191647i
$568$	6.63185e6	−	1.95788e6i	0.862509	−	0.254634i
$569$			5.48350e6i			0.710031i	0.934860	+	0.355015i	$0.115524\pi$
$569$			5.48350e6i			0.710031i	−0.934860	+	0.355015i	$0.884476\pi$
$570$	9.15737e6	−	6.10287e6i	1.18055	−	0.786768i
$571$	−2.18796e6			−0.280833			−0.140417	−	0.990093i	$-0.544844\pi$
$571$	−2.18796e6			−0.280833			−0.140417	+	0.990093i	$0.544844\pi$
$572$	1.64321e6	−	2.43297e6i	0.209992	−	0.310919i
$573$	7.11082e6	−	7.11082e6i	0.904760	−	0.904760i
$574$	1.55667e6	−	1.88722e6i	0.197204	−	0.239080i
$575$	3.08449e6	−	621783.i	0.389057	−	0.0784277i
$576$	1.54675e6	+	2.39131e6i	0.194252	+	0.300316i
$577$	−2.77158e6	+	2.77158e6i	−0.346568	+	0.346568i	−0.858830	−	0.512261i	$-0.828808\pi$
$577$	−2.77158e6	+	2.77158e6i	−0.346568	+	0.346568i	0.512261	+	0.858830i	$0.328808\pi$
$578$	738564.	−	70889.6i	0.0919536	−	0.00882598i
$579$			4.73303e6i			0.586737i
$580$	−380475.	+	3.72234e6i	−0.0469630	+	0.459458i
$581$		−	4.08712e6i		−	0.502316i
$582$	−902260.	−	9.40020e6i	−0.110414	−	1.15035i
$583$	−3.46281e6	+	3.46281e6i	−0.421947	+	0.421947i
$584$	3.33530e6	−	6.12956e6i	0.404672	−	0.743699i
$585$	−2.95564e6	+	1.58471e6i	−0.357077	+	0.191452i
$586$	−8.19411e6	−	6.75888e6i	−0.985729	−	0.813075i
$587$	3.95366e6	−	3.95366e6i	0.473592	−	0.473592i	−0.429483	−	0.903075i	$-0.641304\pi$
$587$	3.95366e6	−	3.95366e6i	0.473592	−	0.473592i	0.903075	+	0.429483i	$0.141304\pi$
$588$	2.71680e6	−	4.02256e6i	0.324052	−	0.479799i
$589$	1.27577e7			1.51525
$590$	−2.22411e6	+	1.11116e7i	−0.263042	+	1.31416i
$591$		−	3.28258e6i		−	0.386586i
$592$	−7.92987e6	−	3.37739e6i	−0.929955	−	0.396074i
$593$	−485319.	−	485319.i	−0.0566749	−	0.0566749i	0.678201	−	0.734876i	$-0.262760\pi$
$593$	−485319.	−	485319.i	−0.0566749	−	0.0566749i	−0.734876	+	0.678201i	$0.762760\pi$
$594$	2.39073e6	+	1.97199e6i	0.278013	+	0.229318i
$595$	1.25294e6	−	4.14958e6i	0.145090	−	0.480520i
$596$	1.02367e7	−	1.98337e6i	1.18044	−	0.228712i
$597$	−803201.	−	803201.i	−0.0922334	−	0.0922334i
$598$	−3.91364e6	+	375642.i	−0.447535	+	0.0429558i
$599$	−1.01773e7			−1.15895			−0.579476	−	0.814989i	$-0.696743\pi$
$599$	−1.01773e7			−1.15895			−0.579476	+	0.814989i	$0.696743\pi$
$600$	−6.24909e6	+	3.30105e6i	−0.708661	+	0.374347i
$601$	−4.47941e6			−0.505865			−0.252932	−	0.967484i	$-0.581395\pi$
$601$	−4.47941e6			−0.505865			−0.252932	+	0.967484i	$0.581395\pi$
$602$	605990.	−	58164.8i	0.0681513	−	0.00654137i
$603$	−2.86415e6	−	2.86415e6i	−0.320776	−	0.320776i
$604$	571471.	+	2.94951e6i	0.0637385	+	0.328971i
$605$	2.31690e6	−	7.67327e6i	0.257347	−	0.852300i
$606$	270444.	+	223074.i	0.0299154	+	0.0246756i
$607$	−4.29459e6	−	4.29459e6i	−0.473097	−	0.473097i	0.429818	−	0.902915i	$-0.358578\pi$
$607$	−4.29459e6	−	4.29459e6i	−0.473097	−	0.473097i	−0.902915	+	0.429818i	$0.858578\pi$
$608$	1.43231e7	−	7.42857e6i	1.57137	−	0.814979i
$609$			1.78497e6i			0.195024i
$610$	815847.	−	4.07596e6i	0.0887737	−	0.443512i
$611$	−1.19924e7			−1.29958
$612$	−2.61639e6	−	1.76709e6i	−0.282374	−	0.190713i
$613$	796329.	−	796329.i	0.0855936	−	0.0855936i	−0.663014	−	0.748607i	$-0.730723\pi$
$613$	796329.	−	796329.i	0.0855936	−	0.0855936i	0.748607	+	0.663014i	$0.230723\pi$
$614$	−7.14503e6	−	5.89355e6i	−0.764862	−	0.630893i
$615$	3.89709e6	−	2.08948e6i	0.415483	−	0.222767i
$616$	−785490.	+	1.44356e6i	−0.0834044	+	0.153279i
$617$	−1.88708e6	+	1.88708e6i	−0.199562	+	0.199562i	−0.799812	−	0.600250i	$-0.795068\pi$
$617$	−1.88708e6	+	1.88708e6i	−0.199562	+	0.199562i	0.600250	+	0.799812i	$0.295068\pi$
$618$	−471907.	−	4.91657e6i	−0.0497033	−	0.517835i
$619$			5.43191e6i			0.569805i	0.958556	+	0.284903i	$0.0919612\pi$
$619$			5.43191e6i			0.569805i	−0.958556	+	0.284903i	$0.908039\pi$
$620$	−8.15079e6	−	833125.i	−0.851570	−	0.0870424i
$621$		−	4.15016e6i		−	0.431853i
$622$	6.48642e6	−	622586.i	0.672247	−	0.0645243i
$623$	−4.94886e6	+	4.94886e6i	−0.510840	+	0.510840i
$624$	8.19175e6	−	3.29813e6i	0.842200	−	0.339083i
$625$	3.78344e6	+	9.00294e6i	0.387425	+	0.921901i
$626$	1.03814e7	−	1.25859e7i	1.05882	−	1.28366i
$627$	3.27067e6	−	3.27067e6i	0.332253	−	0.332253i
$628$	−1.27235e7	−	8.59332e6i	−1.28738	−	0.869484i
$629$	9.55519e6			0.962970
$630$	1.56216e6	−	1.04109e6i	0.156810	−	0.104505i
$631$		−	7.61895e6i		−	0.761767i	−0.924623	−	0.380883i	$-0.875620\pi$
$631$		−	7.61895e6i		−	0.761767i	0.924623	−	0.380883i	$-0.124380\pi$
$632$	3.08403e6	+	1.04464e7i	0.307132	+	1.04034i
$633$	−1.44610e6	−	1.44610e6i	−0.143446	−	0.143446i
$634$	−5.25186e6	+	6.36708e6i	−0.518907	+	0.629096i
$635$	−1.57667e6	+	845351.i	−0.155169	+	0.0831961i
$636$	−1.44611e7	+	2.80184e6i	−1.41761	+	0.274664i
$637$	5.92613e6	+	5.92613e6i	0.578659	+	0.578659i
$638$	150263.	+	1.56552e6i	0.0146150	+	0.152267i
$639$	−3.31999e6			−0.321651
$640$	−9.63602e6	+	3.81069e6i	−0.929924	+	0.367751i
$641$	1.19901e7			1.15260			0.576299	−	0.817239i	$-0.304496\pi$
$641$	1.19901e7			1.15260			0.576299	+	0.817239i	$0.304496\pi$
$642$	−259879.	−	2.70755e6i	−0.0248848	−	0.259262i
$643$	−578939.	−	578939.i	−0.0552211	−	0.0552211i	0.678957	−	0.734178i	$-0.262432\pi$
$643$	−578939.	−	578939.i	−0.0552211	−	0.0552211i	−0.734178	+	0.678957i	$0.762432\pi$
$644$	2.16063e6	−	418624.i	0.205289	−	0.0397749i
$645$	1.05340e6	+	318070.i	0.0997002	+	0.0301039i
$646$	−1.13818e7	+	1.37988e7i	−1.07308	+	1.30094i
$647$	282199.	+	282199.i	0.0265030	+	0.0265030i	0.720234	−	0.693731i	$-0.244034\pi$
$647$	282199.	+	282199.i	0.0265030	+	0.0265030i	−0.693731	+	0.720234i	$0.744034\pi$
$648$	1.55688e6	+	5.27355e6i	0.145652	+	0.493362i
$649$			4.76303e6i			0.443886i
$650$	−3.54310e6	−	1.16765e7i	−0.328927	−	1.08400i
$651$	−3.90855e6			−0.361463
$652$	1.88060e6	+	1.27014e6i	0.173252	+	0.117013i
$653$	874624.	−	874624.i	0.0802673	−	0.0802673i	−0.665833	−	0.746101i	$-0.731924\pi$
$653$	874624.	−	874624.i	0.0802673	−	0.0802673i	0.746101	+	0.665833i	$0.231924\pi$
$654$	−1.03802e7	+	1.25844e7i	−0.948991	+	1.15051i
$655$	−2.55711e6	+	8.46879e6i	−0.232887	+	0.771291i
$656$	6.01421e6	−	2.42142e6i	0.545656	−	0.219690i
$657$	−2.36912e6	+	2.36912e6i	−0.214128	+	0.214128i
$658$	6.68230e6	−	641387.i	0.601674	−	0.0577504i
$659$		−	1.09283e7i		−	0.980255i	−0.871651	−	0.490127i	$-0.836950\pi$
$659$		−	1.09283e7i		−	0.980255i	0.871651	−	0.490127i	$-0.163050\pi$
$660$	−2.30319e6	+	1.87601e6i	−0.205811	+	0.167639i
$661$		−	643996.i		−	0.0573297i	−0.999589	−	0.0286648i	$-0.990874\pi$
$661$		−	643996.i		−	0.0573297i	0.999589	−	0.0286648i	$-0.00912555\pi$
$662$	584219.	+	6.08670e6i	0.0518121	+	0.539805i
$663$	−6.92243e6	+	6.92243e6i	−0.611611	+	0.611611i
$664$	5.17705e6	−	9.51428e6i	0.455682	−	0.837444i
$665$	−5.02569e6	−	9.37342e6i	−0.440698	−	0.821948i
$666$	3.19241e6	+	2.63324e6i	0.278890	+	0.230041i
$667$	1.48924e6	−	1.48924e6i	0.129614	−	0.129614i
$668$	797395.	+	538554.i	0.0691405	+	0.0466969i
$669$	−1.64930e7			−1.42474
$670$	1.22637e7	−	8.17310e6i	1.05545	−	0.703395i
$671$		−	1.74717e6i		−	0.149806i
$672$	−4.38814e6	+	2.27587e6i	−0.374850	+	0.194413i
$673$	−2.17855e6	−	2.17855e6i	−0.185409	−	0.185409i	0.608299	−	0.793708i	$-0.291852\pi$
$673$	−2.17855e6	−	2.17855e6i	−0.185409	−	0.185409i	−0.793708	+	0.608299i	$0.791852\pi$
$674$	5.08882e6	+	4.19749e6i	0.431486	+	0.355910i
$675$	1.26265e7	−	2.54530e6i	1.06666	−	0.215021i
$676$	640148.	+	3.30398e6i	0.0538783	+	0.278080i
$677$	−3.32948e6	−	3.32948e6i	−0.279193	−	0.279193i	0.553594	−	0.832787i	$-0.313256\pi$
$677$	−3.32948e6	−	3.32948e6i	−0.279193	−	0.279193i	−0.832787	+	0.553594i	$0.813256\pi$
$678$	−1.41981e7	+	1.36278e6i	−1.18620	+	0.113855i
$679$	−9.12682e6			−0.759705
$680$	8.17285e6	−	8.07261e6i	0.677800	−	0.669486i
$681$	1.48935e7			1.23063
$682$	−3.42800e6	+	329030.i	−0.282215	+	0.0270879i
$683$	5.82341e6	+	5.82341e6i	0.477667	+	0.477667i	0.904385	−	0.426718i	$-0.140330\pi$
$683$	5.82341e6	+	5.82341e6i	0.477667	+	0.477667i	−0.426718	+	0.904385i	$0.640330\pi$
$684$	−7.60539e6	+	1.47355e6i	−0.621557	+	0.120427i
$685$	−1.25445e6	−	2.33968e6i	−0.102147	−	0.190515i
$686$	−8.62876e6	−	7.11739e6i	−0.700064	−	0.577445i
$687$	7.05209e6	+	7.05209e6i	0.570067	+	0.570067i
$688$	1.48434e6	+	632192.i	0.119554	+	0.0509188i
$689$		−	2.54321e7i		−	2.04096i
$690$	3.90065e6	+	780756.i	0.311899	+	0.0624299i
$691$	6.20240e6			0.494157			0.247078	−	0.968995i	$-0.420529\pi$
$691$	6.20240e6			0.494157			0.247078	+	0.968995i	$0.420529\pi$
$692$	3.66205e6	−	5.42212e6i	0.290709	−	0.430431i
$693$	557946.	−	557946.i	0.0441326	−	0.0441326i
$694$	9.31008e6	+	7.67938e6i	0.733761	+	0.605240i
$695$	2.04661e7	+	6.17963e6i	1.60721	+	0.485289i
$696$	−2.26098e6	+	4.15519e6i	−0.176919	+	0.325138i
$697$	−5.08230e6	+	5.08230e6i	−0.396258	+	0.396258i
$698$	1.07098e6	+	1.11580e7i	0.0832038	+	0.866860i
$699$		−	2.08720e6i		−	0.161574i
$700$	2.59874e6	+	6.31678e6i	0.200456	+	0.487249i
$701$			2.06771e7i			1.58926i	0.607097	+	0.794628i	$0.292334\pi$
$701$			2.06771e7i			1.58926i	−0.607097	+	0.794628i	$0.707666\pi$
$702$	−1.60207e7	+	1.53771e6i	−1.22698	+	0.117769i
$703$	1.65783e7	−	1.65783e7i	1.26518	−	1.26518i
$704$	−3.65704e6	+	2.36546e6i	−0.278098	+	0.179880i
$705$	1.16160e7	+	3.50738e6i	0.880202	+	0.265772i
$706$	16100.5	−	19519.4i	0.00121570	−	0.00147385i
$707$	239582.	−	239582.i	0.0180263	−	0.0180263i
$708$	−8.01850e6	+	1.18724e7i	−0.601188	+	0.890132i
$709$	3.44323e6			0.257247			0.128624	−	0.991693i	$-0.458944\pi$
$709$	3.44323e6			0.257247			0.128624	+	0.991693i	$0.458944\pi$
$710$	2.37085e6	−	1.18447e7i	0.176506	−	0.881820i
$711$		−	5.22960e6i		−	0.387967i
$712$	−1.77889e7	+	5.25171e6i	−1.31507	+	0.388240i
$713$	3.26099e6	+	3.26099e6i	0.240229	+	0.240229i
$714$	3.48702e6	−	4.22748e6i	0.255982	−	0.310339i
$715$	−2.42350e6	−	4.52008e6i	−0.177288	−	0.330660i
$716$	−159450.	−	822964.i	−0.0116236	−	0.0599926i
$717$	−8.13643e6	−	8.13643e6i	−0.591066	−	0.591066i
$718$	2.17255e6	+	2.26347e7i	0.157274	+	1.63856i
$719$	1.23455e6			0.0890610			0.0445305	−	0.999008i	$-0.485821\pi$
$719$	1.23455e6			0.0890610			0.0445305	+	0.999008i	$0.485821\pi$
$720$	4.95523e6	−	444778.i	0.356232	−	0.0319751i
$721$	−4.77358e6			−0.341984
$722$	2.85508e6	+	2.97457e7i	0.203834	+	2.12364i
$723$	1.03932e7	+	1.03932e7i	0.739442	+	0.739442i
$724$	3.04866e6	+	1.57350e7i	0.216154	+	1.11563i
$725$	5.44424e6	+	3.61753e6i	0.384674	+	0.255604i
$726$	6.44810e6	−	7.81734e6i	0.454036	−	0.550449i
$727$	1.57226e7	+	1.57226e7i	1.10329	+	1.10329i	0.994012	+	0.109274i	$0.0348526\pi$
$727$	1.57226e7	+	1.57226e7i	1.10329	+	1.10329i	0.109274	+	0.994012i	$0.465147\pi$
$728$	−2.41655e6	−	8.18546e6i	−0.168992	−	0.572420i
$729$		−	1.51534e7i		−	1.05606i
$730$	−6.76049e6	−	1.01441e7i	−0.469538	−	0.704543i
$731$	−1.78858e6			−0.123798
$732$	2.94135e6	−	4.35503e6i	0.202894	−	0.300409i
$733$	−7.49288e6	+	7.49288e6i	−0.515097	+	0.515097i	−0.916084	−	0.400987i	$-0.868667\pi$
$733$	−7.49288e6	+	7.49288e6i	−0.515097	+	0.515097i	0.400987	+	0.916084i	$0.368667\pi$
$734$	1.65216e7	−	2.00299e7i	1.13191	−	1.37227i
$735$	−4.00691e6	−	7.47330e6i	−0.273584	−	0.510263i
$736$	5.55992e6	+	1.76231e6i	0.378333	+	0.119919i
$737$	4.38016e6	−	4.38016e6i	0.297044	−	0.297044i
$738$	−3.09860e6	+	297413.i	−0.209423	+	0.0201010i
$739$			468516.i			0.0315583i	0.999876	+	0.0157791i	$0.00502287\pi$
$739$			468516.i			0.0315583i	−0.999876	+	0.0157791i	$0.994977\pi$
$740$	−1.16744e7	+	9.50911e6i	−0.783707	+	0.638353i
$741$			2.40210e7i			1.60711i
$742$	1.36018e6	+	1.41710e7i	0.0906956	+	0.944913i
$743$	9.11716e6	−	9.11716e6i	0.605881	−	0.605881i	−0.335986	−	0.941867i	$-0.609069\pi$
$743$	9.11716e6	−	9.11716e6i	0.605881	−	0.605881i	0.941867	+	0.335986i	$0.109069\pi$
$744$	−9.09860e6	−	4.95086e6i	−0.602618	−	0.327905i
$745$	5.26525e6	−	1.74378e7i	0.347559	−	1.15107i
$746$	−665366.	−	548825.i	−0.0437738	−	0.0361066i
$747$	−3.67734e6	+	3.67734e6i	−0.241119	+	0.241119i
$748$	2.70242e6	−	4.00127e6i	0.176603	−	0.261483i
$749$	−2.62881e6			−0.171220
$750$	16890.4	+	1.23462e7i	0.00109644	+	0.801458i
$751$			5.22559e6i			0.338093i	0.985608	+	0.169046i	$0.0540687\pi$
$751$			5.22559e6i			0.338093i	−0.985608	+	0.169046i	$0.945931\pi$
$752$	1.63679e7	+	6.97123e6i	1.05548	+	0.449536i
$753$	−8.14695e6	−	8.14695e6i	−0.523610	−	0.523610i
$754$	−6.30064e6	−	5.19705e6i	−0.403605	−	0.332912i
$755$	5.02436e6	+	1.51708e6i	0.320785	+	0.0968592i
$756$	8.84465e6	−	1.71366e6i	0.562828	−	0.109049i
$757$	−1.80364e7	−	1.80364e7i	−1.14396	−	1.14396i	−0.987719	−	0.156242i	$-0.950062\pi$
$757$	−1.80364e7	−	1.80364e7i	−1.14396	−	1.14396i	−0.156242	−	0.987719i	$-0.549938\pi$
$758$	1.00856e7	−	968050.i	0.637574	−	0.0611962i
$759$	1.67203e6			0.105351
$760$	173921.	−	2.81860e7i	0.0109224	−	1.77011i
$761$	−1.48328e7			−0.928455			−0.464227	−	0.885716i	$-0.653668\pi$
$761$	−1.48328e7			−0.928455			−0.464227	+	0.885716i	$0.653668\pi$
$762$	−2.25139e6	+	216096.i	−0.140464	+	0.0134821i
$763$	1.11484e7	+	1.11484e7i	0.693267	+	0.693267i
$764$	−4.89939e6	−	2.52871e7i	−0.303675	−	1.56735i
$765$	−4.86086e6	+	2.60622e6i	−0.300303	+	0.161011i
$766$	−633393.	−	522451.i	−0.0390033	−	0.0321717i
$767$	−1.74907e7	−	1.74907e7i	−1.07354	−	1.07354i
$768$	−1.30978e7	−	260409.i	−0.801300	−	0.0159314i
$769$		−	1.13642e7i		−	0.692982i	−0.938053	−	0.346491i	$-0.887373\pi$
$769$		−	1.13642e7i		−	0.692982i	0.938053	−	0.346491i	$-0.112627\pi$
$770$	1.59215e6	+	2.38902e6i	0.0967736	+	0.145209i
$771$	−1.12056e7			−0.678887
$772$	1.00462e7	+	6.78511e6i	0.606678	+	0.409745i
$773$	1.28867e7	−	1.28867e7i	0.775698	−	0.775698i	−0.203398	−	0.979096i	$-0.565199\pi$
$773$	1.28867e7	−	1.28867e7i	0.775698	−	0.775698i	0.979096	+	0.203398i	$0.0651986\pi$
$774$	−597566.	−	492900.i	−0.0358537	−	0.0295738i
$775$	−7.92130e6	+	1.19212e7i	−0.473742	+	0.712963i
$776$	−2.12460e7	−	1.15607e7i	−1.26655	−	0.689176i
$777$	−5.07906e6	+	5.07906e6i	−0.301808	+	0.301808i
$778$	1.32596e6	+	1.38145e7i	0.0785384	+	0.818253i
$779$			1.76357e7i			1.04123i
$780$	1.56865e6	−	1.53468e7i	0.0923189	−	0.903192i
$781$		−	5.07729e6i		−	0.297855i
$782$	−6.43638e6	+	617783.i	−0.376378	+	0.0361259i
$783$	6.09629e6	−	6.09629e6i	0.355354	−	0.355354i
$784$	−4.64345e6	−	1.15332e7i	−0.269805	−	0.670131i
$785$	−2.36382e7	+	1.26740e7i	−1.36912	+	0.734071i
$786$	−7.11659e6	+	8.62779e6i	−0.410881	+	0.498130i
$787$	−1.30010e7	+	1.30010e7i	−0.748239	+	0.748239i	−0.974148	−	0.225910i	$-0.927465\pi$
$787$	−1.30010e7	+	1.30010e7i	−0.748239	+	0.748239i	0.225910	+	0.974148i	$0.427465\pi$
$788$	−6.96750e6	−	4.70579e6i	−0.399725	−	0.269971i
$789$	−1.31467e7			−0.751836
$790$	1.86577e7	+	3.73453e6i	1.06363	+	0.212896i
$791$			1.37852e7i			0.783379i
$792$	2.00556e6	−	592091.i	0.113612	−	0.0335409i
$793$	6.41593e6	+	6.41593e6i	0.362307	+	0.362307i
$794$	1.35907e6	−	1.64767e6i	0.0765054	−	0.0927512i
$795$	−7.43804e6	+	2.46338e7i	−0.417389	+	1.38233i
$796$	−2.85629e6	+	553409.i	−0.159779	+	0.0309574i
$797$	−9.80941e6	−	9.80941e6i	−0.547012	−	0.547012i	0.378563	−	0.925575i	$-0.376418\pi$
$797$	−9.80941e6	−	9.80941e6i	−0.547012	−	0.547012i	−0.925575	+	0.378563i	$0.876418\pi$
$798$	−1.28471e6	−	1.33847e7i	−0.0714162	−	0.744051i
$799$	−1.97227e7			−1.09295
$800$	−1.95176e6	+	1.79964e7i	−0.107821	+	0.994170i
$801$	8.90536e6			0.490422
$802$	−1.77932e6	−	1.85379e7i	−0.0976831	−	1.01771i
$803$	−3.62311e6	−	3.62311e6i	−0.198286	−	0.198286i
$804$	1.82920e7	−	3.54409e6i	0.997978	−	0.193359i
$805$	1.11132e6	−	3.68054e6i	0.0604434	−	0.200180i
$806$	1.13800e7	−	1.37965e7i	0.617026	−	0.748050i
$807$	2.36944e6	+	2.36944e6i	0.128074	+	0.128074i
$808$	861189.	−	254244.i	0.0464056	−	0.0137001i
$809$			8.76581e6i			0.470891i	0.971888	+	0.235446i	$0.0756550\pi$
$809$			8.76581e6i			0.470891i	−0.971888	+	0.235446i	$0.924345\pi$
$810$	9.41876e6	+	1.88527e6i	0.504407	+	0.100963i
$811$	−1.75325e7			−0.936036			−0.468018	−	0.883719i	$-0.655032\pi$
$811$	−1.75325e7			−0.936036			−0.468018	+	0.883719i	$0.655032\pi$
$812$	3.78873e6	+	2.55888e6i	0.201653	+	0.136194i
$813$	2.08969e7	−	2.08969e7i	1.10881	−	1.10881i
$814$	−4.02703e6	+	4.88217e6i	−0.213022	+	0.258257i
$815$	3.49387e6	−	1.87329e6i	0.184252	−	0.0987894i
$816$	1.34722e7	−	5.42411e6i	0.708292	−	0.285170i
$817$	−3.10320e6	+	3.10320e6i	−0.162650	+	0.162650i
$818$	−8.78685e6	+	843389.i	−0.459145	+	0.0440701i
$819$			4.09775e6i			0.213470i
$820$	1.15167e6	−	1.12673e7i	0.0598128	−	0.585172i
$821$			7.22018e6i			0.373844i	0.982375	+	0.186922i	$0.0598512\pi$
$821$			7.22018e6i			0.373844i	−0.982375	+	0.186922i	$0.940149\pi$
$822$	−320673.	−	3.34093e6i	−0.0165532	−	0.172460i
$823$	2.02345e7	−	2.02345e7i	1.04134	−	1.04134i	0.0422319	−	0.999108i	$-0.486553\pi$
$823$	2.02345e7	−	2.02345e7i	1.04134	−	1.04134i	0.999108	−	0.0422319i	$-0.0134468\pi$
$824$	−1.11123e7	−	6.04657e6i	−0.570145	−	0.310235i
$825$	1.02546e6	+	5.08699e6i	0.0524544	+	0.260211i
$826$	1.06814e7	+	8.81053e6i	0.544727	+	0.449316i
$827$	5.70933e6	−	5.70933e6i	0.290283	−	0.290283i	−0.546909	−	0.837192i	$-0.684196\pi$
$827$	5.70933e6	−	5.70933e6i	0.290283	−	0.290283i	0.837192	+	0.546909i	$0.184196\pi$
$828$	−2.32065e6	−	1.56735e6i	−0.117634	−	0.0794493i
$829$	−2.23001e7			−1.12699			−0.563496	−	0.826119i	$-0.690544\pi$
$829$	−2.23001e7			−1.12699			−0.563496	+	0.826119i	$0.690544\pi$
$830$	−1.04936e7	−	1.57457e7i	−0.528725	−	0.793353i
$831$		−	7.61081e6i		−	0.382321i
$832$	4.74290e6	−	2.21157e7i	0.237540	−	1.10762i
$833$	9.74613e6	+	9.74613e6i	0.486653	+	0.486653i
$834$	2.08503e7	+	1.71983e7i	1.03800	+	0.856191i
$835$	1.48144e6	−	794293.i	0.0735305	−	0.0394243i
$836$	−2.25351e6	−	1.16310e7i	−0.111518	−	0.575573i
$837$	1.33490e7	+	1.33490e7i	0.658621	+	0.658621i
$838$	1.31166e7	−	1.25897e6i	0.645225	−	0.0619307i
$839$	3.22117e7			1.57982			0.789912	−	0.613221i	$-0.210126\pi$
$839$	3.22117e7			1.57982			0.789912	+	0.613221i	$0.210126\pi$
$840$	−53283.8	+	8.63527e6i	−0.00260554	+	0.422258i
$841$	−1.61360e7			−0.786693
$842$	1.36094e7	−	1.30627e6i	0.661544	−	0.0634970i
$843$	−1.21401e7	−	1.21401e7i	−0.588373	−	0.588373i
$844$	−5.14251e6	+	996367.i	−0.248496	+	0.0481463i
$845$	5.62818e6	+	1.69940e6i	0.271160	+	0.0818754i
$846$	−6.58940e6	−	5.43524e6i	−0.316534	−	0.261092i
$847$	−6.92527e6	−	6.92527e6i	−0.331687	−	0.331687i
$848$	−1.47838e7	+	3.47112e7i	−0.705985	+	1.65760i
$849$			1.57132e7i			0.748163i
$850$	−5.82699e6	−	1.92032e7i	−0.276629	−	0.911647i
$851$	8.47513e6			0.401165
$852$	8.54756e6	−	1.26557e7i	0.403407	−	0.597293i
$853$	2.37704e6	−	2.37704e6i	0.111857	−	0.111857i	−0.648963	−	0.760820i	$-0.724797\pi$
$853$	2.37704e6	−	2.37704e6i	0.111857	−	0.111857i	0.760820	+	0.648963i	$0.224797\pi$
$854$	−3.91816e6	−	3.23188e6i	−0.183839	−	0.151639i
$855$	−3.91183e6	+	1.29554e7i	−0.183006	+	0.606090i
$856$	−6.11953e6	−	3.32984e6i	−0.285452	−	0.155324i
$857$	1.38407e7	−	1.38407e7i	0.643733	−	0.643733i	−0.307738	−	0.951471i	$-0.599572\pi$
$857$	1.38407e7	−	1.38407e7i	0.643733	−	0.643733i	0.951471	+	0.307738i	$0.0995721\pi$
$858$	−619516.	−	6.45443e6i	−0.0287299	−	0.299323i
$859$		−	1.48385e7i		−	0.686129i	−0.939312	−	0.343064i	$-0.888535\pi$
$859$		−	1.48385e7i		−	0.686129i	0.939312	−	0.343064i	$-0.111465\pi$
$860$	2.18525e6	−	1.77995e6i	0.100752	−	0.0820657i
$861$		−	5.40299e6i		−	0.248386i
$862$	3.59799e7	−	3.45346e6i	1.64927	−	0.158302i
$863$	−1.53835e7	+	1.53835e7i	−0.703116	+	0.703116i	−0.965078	−	0.261962i	$-0.915630\pi$
$863$	−1.53835e7	+	1.53835e7i	−0.703116	+	0.703116i	0.261962	+	0.965078i	$0.415630\pi$
$864$	2.27598e7	+	7.21411e6i	1.03725	+	0.328775i
$865$	−5.40102e6	−	1.00735e7i	−0.245435	−	0.457761i
$866$	796653.	−	965821.i	0.0360973	−	0.0437625i
$867$	1.15871e6	−	1.15871e6i	0.0523511	−	0.0523511i
$868$	−5.60316e6	+	8.29618e6i	−0.252426	+	0.373748i
$869$	7.99767e6			0.359264
$870$	4.58289e6	+	6.87664e6i	0.205278	+	0.308019i
$871$			3.21694e7i			1.43681i
$872$	1.18306e7	+	4.00734e7i	0.526886	+	1.78470i
$873$	8.21175e6	+	8.21175e6i	0.364670	+	0.364670i
$874$	−1.00953e7	+	1.22390e7i	−0.447035	+	0.541962i
$875$	1.18793e7	+	1.12381e6i	0.524530	+	0.0496218i
$876$	−2.93154e6	−	1.51305e7i	−0.129073	−	0.666181i
$877$	6.70962e6	+	6.70962e6i	0.294577	+	0.294577i	0.838885	−	0.544308i	$-0.183208\pi$
$877$	6.70962e6	+	6.70962e6i	0.294577	+	0.294577i	−0.544308	+	0.838885i	$0.683208\pi$
$878$	2454.94	+	25576.8i	0.000107474	+	0.00111972i
$879$	−2.34592e7			−1.02410
$880$	680202.	+	7.57807e6i	0.0296095	+	0.329877i
$881$	4.84600e6			0.210351			0.105175	−	0.994454i	$-0.466460\pi$
$881$	4.84600e6			0.210351			0.105175	+	0.994454i	$0.466460\pi$
$882$	570336.	+	5.94206e6i	0.0246865	+	0.257197i
$883$	−2.65671e7	−	2.65671e7i	−1.14668	−	1.14668i	−0.987201	−	0.159479i	$-0.949019\pi$
$883$	−2.65671e7	−	2.65671e7i	−1.14668	−	1.14668i	−0.159479	−	0.987201i	$-0.550981\pi$
$884$	4.76959e6	+	2.46171e7i	0.205282	+	1.05951i
$885$	1.18262e7	+	2.20571e7i	0.507559	+	0.946650i
$886$	−4.35125e6	+	5.27523e6i	−0.186222	+	0.225765i
$887$	−1.13315e7	−	1.13315e7i	−0.483590	−	0.483590i	0.422686	−	0.906276i	$-0.361087\pi$
$887$	−1.13315e7	−	1.13315e7i	−0.483590	−	0.483590i	−0.906276	+	0.422686i	$0.861087\pi$
$888$	−1.82569e7	+	5.38988e6i	−0.776953	+	0.229375i
$889$			2.18592e6i			0.0927639i
$890$	−6.35944e6	+	3.17717e7i	−0.269119	+	1.34451i
$891$	4.03738e6			0.170375
$892$	−2.36438e7	+	3.50076e7i	−0.994959	+	1.47316i
$893$	−3.42192e7	+	3.42192e7i	−1.43595	+	1.43595i
$894$	1.46535e7	−	1.77652e7i	0.613195	−	0.743405i
$895$	−1.40188e6	−	423291.i	−0.0584998	−	0.0176637i
$896$	−1.45999e6	+	1.25767e7i	−0.0607546	+	0.523357i
$897$	−6.13997e6	+	6.13997e6i	−0.254792	+	0.254792i
$898$	−3.47116e7	+	3.33172e6i	−1.43643	+	0.137872i
$899$			9.58031e6i			0.395349i
$900$	3.34526e6	−	8.02164e6i	0.137665	−	0.330109i
$901$		−	4.18257e7i		−	1.71645i
$902$	−454835.	−	4.73871e6i	−0.0186139	−	0.193929i
$903$	950717.	−	950717.i	0.0388000	−	0.0388000i
$904$	−1.74613e7	+	3.20901e7i	−0.710652	+	1.30602i
$905$	2.68038e7	+	8.09327e6i	1.08787	+	0.328475i
$906$	5.11869e6	+	4.22213e6i	0.207176	+	0.170888i
$907$	2.05756e7	−	2.05756e7i	0.830491	−	0.830491i	−0.157093	−	0.987584i	$-0.550212\pi$
$907$	2.05756e7	−	2.05756e7i	0.830491	−	0.830491i	0.987584	+	0.157093i	$0.0502121\pi$
$908$	2.13508e7	−	3.16124e7i	0.859407	−	1.27246i
$909$	−431123.			−0.0173058
$910$	−1.46196e7	−	2.92626e6i	−0.585235	−	0.117141i
$911$		−	1.96863e7i		−	0.785901i	−0.919560	−	0.392951i	$-0.871454\pi$
$911$		−	1.96863e7i		−	0.785901i	0.919560	−	0.392951i	$-0.128546\pi$
$912$	1.39635e7	−	3.27852e7i	0.555912	−	1.30524i
$913$	−5.62378e6	−	5.62378e6i	−0.223281	−	0.223281i
$914$	−1.70076e7	−	1.40286e7i	−0.673405	−	0.555456i
$915$	−4.33808e6	−	8.09097e6i	−0.171295	−	0.319483i
$916$	2.50782e7	−	4.85893e6i	0.987547	−	0.191338i
$917$	7.64324e6	+	7.64324e6i	0.300161	+	0.300161i
$918$	−2.63476e7	+	2.52893e6i	−1.03189	+	0.0990443i
$919$	684770.			0.0267458			0.0133729	−	0.999911i	$-0.495743\pi$
$919$	684770.			0.0267458			0.0133729	+	0.999911i	$0.495743\pi$
$920$	7.24904e6	−	7.16013e6i	0.282365	−	0.278902i
$921$	−2.04558e7			−0.794633
$922$	−1.12108e7	+	1.07604e6i	−0.434319	+	0.0416872i
$923$	1.86447e7	+	1.86447e7i	0.720362	+	0.720362i
$924$	690401.	+	3.56334e6i	0.0266025	+	0.137302i
$925$	5.19781e6	+	2.57848e7i	0.199741	+	0.990855i
$926$	7.44449e6	+	6.14056e6i	0.285304	+	0.235332i
$927$	4.29498e6	+	4.29498e6i	0.164158	+	0.164158i
$928$	5.57842e6	+	1.07558e7i	0.212638	+	0.409991i
$929$			2.13324e7i			0.810963i	0.914103	+	0.405482i	$0.132896\pi$
$929$			2.13324e7i			0.810963i	−0.914103	+	0.405482i	$0.867104\pi$
$930$	−1.50578e7	+	1.00351e7i	−0.570891	+	0.380466i
$931$	3.38192e7			1.27876
$932$	−4.43024e6	−	2.99214e6i	−0.167066	−	0.112835i
$933$	1.01763e7	−	1.01763e7i	0.382725	−	0.382725i
$934$	1.63707e7	+	1.35033e7i	0.614044	+	0.506491i
$935$	−3.98570e6	−	7.43374e6i	−0.149099	−	0.278086i
$936$	−5.19052e6	+	9.53904e6i	−0.193652	+	0.355889i
$937$	2.42080e7	−	2.42080e7i	0.900762	−	0.900762i	−0.0947402	−	0.995502i	$-0.530202\pi$
$937$	2.42080e7	−	2.42080e7i	0.900762	−	0.900762i	0.995502	+	0.0947402i	$0.0302020\pi$
$938$	−1.72051e6	−	1.79251e7i	−0.0638484	−	0.665205i
$939$		−	3.60327e7i		−	1.33362i
$940$	2.40969e7	−	1.96276e7i	0.889491	−	0.724517i
$941$		−	6.58378e6i		−	0.242382i	−0.992629	−	0.121191i	$-0.961329\pi$
$941$		−	6.58378e6i		−	0.242382i	0.992629	−	0.121191i	$-0.0386714\pi$
$942$	−3.37541e7	+	3.23982e6i	−1.23937	+	0.118958i
$943$	−4.50783e6	+	4.50783e6i	−0.165078	+	0.165078i
$944$	1.37049e7	+	3.40397e7i	0.500549	+	1.24324i
$945$	4.54924e6	−	1.50665e7i	0.165714	−	0.548822i
$946$	753795.	−	913862.i	0.0273858	−	0.0332011i
$947$	−6.68820e6	+	6.68820e6i	−0.242345	+	0.242345i	−0.817820	−	0.575475i	$-0.804817\pi$
$947$	−6.68820e6	+	6.68820e6i	−0.242345	+	0.242345i	0.575475	+	0.817820i	$0.304817\pi$
$948$	1.99351e7	+	1.34640e7i	0.720439	+	0.486578i
$949$	2.66094e7			0.959111
$950$	−4.34277e7	−	2.32079e7i	−1.56120	−	0.834308i
$951$			1.82285e7i			0.653583i
$952$	−3.97426e6	−	1.34618e7i	−0.142123	−	0.481406i
$953$	−1.60762e7	−	1.60762e7i	−0.573392	−	0.573392i	0.359683	−	0.933075i	$-0.382885\pi$
$953$	−1.60762e7	−	1.60762e7i	−0.573392	−	0.573392i	−0.933075	+	0.359683i	$0.882885\pi$
$954$	1.15264e7	−	1.39740e7i	0.410038	−	0.497109i
$955$	−4.30754e7	−	1.30064e7i	−1.52834	−	0.461475i
$956$	−2.89342e7	+	5.60604e6i	−1.02392	+	0.198386i
$957$	2.45608e6	+	2.45608e6i	0.0866888	+	0.0866888i
$958$	−3.21435e6	−	3.34888e7i	−0.113157	−	1.17892i
$959$	−3.24377e6			−0.113895
$960$	−1.10621e7	+	2.00343e7i	−0.387400	+	0.701610i
$961$	7.65119e6			0.267252
$962$	−3.14019e6	−	3.27161e7i	−0.109400	−	1.13979i
$963$	2.36524e6	+	2.36524e6i	0.0821883	+	0.0821883i
$964$	3.69597e7	−	7.16098e6i	1.28096	−	0.248187i
$965$	1.86643e7	−	1.00071e7i	0.645198	−	0.345932i
$966$	3.09287e6	−	3.74964e6i	0.106640	−	0.129284i
$967$	1.37064e7	+	1.37064e7i	0.471366	+	0.471366i	0.902357	−	0.430990i	$-0.141836\pi$
$967$	1.37064e7	+	1.37064e7i	0.471366	+	0.471366i	−0.430990	+	0.902357i	$0.641836\pi$
$968$	−7.34908e6	−	2.48932e7i	−0.252083	−	0.853871i
$969$			3.95050e7i			1.35158i
$970$	−3.51612e7	+	2.34330e7i	−1.19987	+	0.799646i
$971$	5.44433e7			1.85309			0.926544	−	0.376186i	$-0.122765\pi$
$971$	5.44433e7			1.85309			0.926544	+	0.376186i	$0.122765\pi$
$972$	−1.64968e7	−	1.11418e7i	−0.560060	−	0.378260i
$973$	1.84710e7	−	1.84710e7i	0.625474	−	0.625474i
$974$	−1.70755e7	+	2.07014e7i	−0.576734	+	0.699202i
$975$	−2.24460e7	−	1.49147e7i	−0.756183	−	0.502460i
$976$	−5.02724e6	−	1.24864e7i	−0.168929	−	0.419579i
$977$	−8.56239e6	+	8.56239e6i	−0.286985	+	0.286985i	−0.835887	−	0.548902i	$-0.815046\pi$
$977$	−8.56239e6	+	8.56239e6i	−0.286985	+	0.286985i	0.548902	+	0.835887i	$0.315046\pi$
$978$	4.98906e6	−	478865.i	0.166791	−	0.0160091i
$979$			1.36190e7i			0.454139i
$980$	−2.16068e7	−	2.20851e6i	−0.718662	−	0.0734573i
$981$		−	2.00613e7i		−	0.665558i
$982$	716985.	+	7.46992e6i	0.0237264	+	0.247193i
$983$	−4.58761e6	+	4.58761e6i	−0.151427	+	0.151427i	−0.778755	−	0.627328i	$-0.784148\pi$
$983$	−4.58761e6	+	4.58761e6i	−0.151427	+	0.151427i	0.627328	+	0.778755i	$0.284148\pi$
$984$	6.84383e6	−	1.25775e7i	0.225326	−	0.414100i
$985$	−1.29445e7	+	6.94039e6i	−0.425105	+	0.227926i
$986$	−1.03620e7	−	8.54709e6i	−0.339432	−	0.279979i
$987$	1.04836e7	−	1.04836e7i	0.342546	−	0.342546i
$988$	5.09862e7	+	3.44356e7i	1.66173	+	1.12232i
$989$	−1.58641e6			−0.0515732
$990$	716979.	−	3.58202e6i	0.0232498	−	0.116155i
$991$		−	2.17107e7i		−	0.702246i	−0.936329	−	0.351123i	$-0.885800\pi$
$991$		−	2.17107e7i		−	0.702246i	0.936329	−	0.351123i	$-0.114200\pi$
$992$	−2.35520e7	+	1.22150e7i	−0.759886	+	0.394108i
$993$	9.54921e6	+	9.54921e6i	0.307322	+	0.307322i
$994$	−1.13862e7	−	9.39185e6i	−0.365521	−	0.301498i
$995$	−1.46913e6	+	4.86557e6i	−0.0470439	+	0.155803i
$996$	−4.55033e6	−	2.34855e7i	−0.145343	−	0.750155i
$997$	1.51438e7	+	1.51438e7i	0.482498	+	0.482498i	0.905929	−	0.423430i	$-0.139174\pi$
$997$	1.51438e7	+	1.51438e7i	0.482498	+	0.482498i	−0.423430	+	0.905929i	$0.639174\pi$
$998$	4.86389e7	−	4.66850e6i	1.54581	−	0.148372i
$999$	3.46934e7			1.09985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.3.14	✓	56
4.3	odd	2		160.6.o.a.143.22		56
5.2	odd	4	inner	40.6.k.a.27.28	yes	56
8.3	odd	2	inner	40.6.k.a.3.28	yes	56
8.5	even	2		160.6.o.a.143.21		56
20.7	even	4		160.6.o.a.47.21		56
40.27	even	4	inner	40.6.k.a.27.14	yes	56
40.37	odd	4		160.6.o.a.47.22		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.14	✓	56	1.1	even	1	trivial
40.6.k.a.3.28	yes	56	8.3	odd	2	inner
40.6.k.a.27.14	yes	56	40.27	even	4	inner
40.6.k.a.27.28	yes	56	5.2	odd	4	inner
160.6.o.a.47.21		56	20.7	even	4
160.6.o.a.47.22		56	40.37	odd	4
160.6.o.a.143.21		56	8.5	even	2
160.6.o.a.143.22		56	4.3	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540478 - 5.63098i) q^{2} +(-8.83424 - 8.83424i) q^{3} +(-31.4158 + 6.08684i) q^{4} +(-16.1587 + 53.5154i) q^{5} +(-44.9707 + 54.5201i) q^{6} +(48.2986 + 48.2986i) q^{7} +(51.2543 + 173.612i) q^{8} -86.9124i q^{9} +O(q^{10})\)	\(q+(-0.540478 - 5.63098i) q^{2} +(-8.83424 - 8.83424i) q^{3} +(-31.4158 + 6.08684i) q^{4} +(-16.1587 + 53.5154i) q^{5} +(-44.9707 + 54.5201i) q^{6} +(48.2986 + 48.2986i) q^{7} +(51.2543 + 173.612i) q^{8} -86.9124i q^{9} +(310.077 + 62.0653i) q^{10} +132.916 q^{11} +(331.307 + 223.762i) q^{12} +(-488.089 + 488.089i) q^{13} +(245.864 - 298.073i) q^{14} +(615.518 - 330.018i) q^{15} +(949.901 - 382.445i) q^{16} +(-802.713 + 802.713i) q^{17} +(-489.401 + 46.9742i) q^{18} +2785.43i q^{19} +(181.898 - 1779.58i) q^{20} -853.364i q^{21} +(-71.8379 - 748.445i) q^{22} +(-711.980 + 711.980i) q^{23} +(1080.93 - 1986.52i) q^{24} +(-2602.79 - 1729.48i) q^{25} +(3012.22 + 2484.62i) q^{26} +(-2914.53 + 2914.53i) q^{27} +(-1811.32 - 1223.35i) q^{28} -2091.69 q^{29} +(-2191.00 - 3287.60i) q^{30} -4580.17i q^{31} +(-2666.94 - 5142.17i) q^{32} +(-1174.21 - 1174.21i) q^{33} +(4953.91 + 4086.21i) q^{34} +(-3365.16 + 1804.28i) q^{35} +(529.021 + 2730.42i) q^{36} +(-5951.81 - 5951.81i) q^{37} +(15684.7 - 1505.46i) q^{38} +8623.80 q^{39} +(-10119.1 - 62.4397i) q^{40} +6331.41 q^{41} +(-4805.27 + 461.224i) q^{42} +(1114.08 + 1114.08i) q^{43} +(-4175.65 + 809.035i) q^{44} +(4651.15 + 1404.39i) q^{45} +(4393.95 + 3624.33i) q^{46} +(12285.1 + 12285.1i) q^{47} +(-11770.3 - 5013.04i) q^{48} -12141.5i q^{49} +(-8331.89 + 15591.0i) q^{50} +14182.7 q^{51} +(12362.8 - 18304.6i) q^{52} +(-26052.7 + 26052.7i) q^{53} +(17986.9 + 14836.4i) q^{54} +(-2147.74 + 7113.03i) q^{55} +(-5909.69 + 10860.7i) q^{56} +(24607.2 - 24607.2i) q^{57} +(1130.51 + 11778.3i) q^{58} +35835.0i q^{59} +(-17328.2 + 14114.3i) q^{60} -13145.0i q^{61} +(-25790.8 + 2475.48i) q^{62} +(4197.75 - 4197.75i) q^{63} +(-27514.0 + 17796.7i) q^{64} +(-18233.4 - 34007.2i) q^{65} +(-5977.31 + 7246.57i) q^{66} +(32954.4 - 32954.4i) q^{67} +(20331.9 - 30103.8i) q^{68} +12579.6 q^{69} +(11978.6 + 17974.0i) q^{70} -38199.3i q^{71} +(15089.0 - 4454.64i) q^{72} +(-27258.7 - 27258.7i) q^{73} +(-30297.7 + 36731.3i) q^{74} +(7715.09 + 38272.3i) q^{75} +(-16954.4 - 87506.4i) q^{76} +(6419.64 + 6419.64i) q^{77} +(-4660.97 - 48560.4i) q^{78} +60171.0 q^{79} +(5117.55 + 57014.1i) q^{80} +30375.5 q^{81} +(-3421.98 - 35652.0i) q^{82} +(-42310.9 - 42310.9i) q^{83} +(5194.28 + 26809.1i) q^{84} +(-29986.7 - 55928.3i) q^{85} +(5671.23 - 6875.50i) q^{86} +(18478.5 + 18478.5i) q^{87} +(6812.50 + 23075.7i) q^{88} +102464. i q^{89} +(5394.24 - 26949.5i) q^{90} -47148.1 q^{91} +(18033.7 - 26701.1i) q^{92} +(-40462.3 + 40462.3i) q^{93} +(62537.1 - 75816.7i) q^{94} +(-149063. - 45008.9i) q^{95} +(-21866.7 + 68987.5i) q^{96} +(-94483.2 + 94483.2i) q^{97} +(-68368.4 + 6562.20i) q^{98} -11552.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more