LMFDB - Embedded newform 40.6.k.a.27.28

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			27.28
Character	$\chi$	$=$	40.27
Dual form			40.6.k.a.3.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.63098 - 0.540478i) q^{2} +(-8.83424 + 8.83424i) q^{3} +(31.4158 - 6.08684i) q^{4} +(16.1587 + 53.5154i) q^{5} +(-44.9707 + 54.5201i) q^{6} +(-48.2986 + 48.2986i) q^{7} +(173.612 - 51.2543i) q^{8} +86.9124i q^{9} +O(q^{10})$	\(q+(5.63098 - 0.540478i) 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} +(173.612 - 51.2543i) q^{8} +86.9124i q^{9} +(119.913 + 292.610i) q^{10} +132.916 q^{11} +(-223.762 + 331.307i) 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} +(46.9742 + 489.401i) q^{18} -2785.43i q^{19} +(833.377 + 1582.87i) q^{20} -853.364i q^{21} +(748.445 - 71.8379i) 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} +(-1223.35 + 1811.32i) q^{28} +2091.69 q^{29} +(-3644.33 - 1525.65i) q^{30} -4580.17i q^{31} +(5142.17 - 2666.94i) 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} +(-1505.46 - 15684.7i) q^{38} -8623.80 q^{39} +(5548.23 + 8462.69i) q^{40} +6331.41 q^{41} +(-461.224 - 4805.27i) 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} +(-5013.04 + 11770.3i) q^{48} +12141.5i q^{49} +(-13721.5 + 11145.4i) q^{50} +14182.7 q^{51} +(18304.6 + 12362.8i) 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} +(11778.3 - 1130.51i) q^{58} -35835.0i q^{59} +(-21345.7 - 6621.22i) q^{60} -13145.0i q^{61} +(-2475.48 - 25790.8i) 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} +(-30103.8 - 20331.9i) q^{68} -12579.6 q^{69} +(-19924.3 - 8341.05i) q^{70} -38199.3i q^{71} +(4454.64 + 15089.0i) 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} +(-48560.4 + 4660.97i) q^{78} -60171.0 q^{79} +(35815.9 + 44654.5i) q^{80} +30375.5 q^{81} +(35652.0 - 3421.98i) 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} +(23075.7 - 6812.50i) q^{88} -102464. i q^{89} +(-25431.5 + 10421.9i) q^{90} -47148.1 q^{91} +(26701.1 + 18033.7i) 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} +(6562.20 + 68368.4i) 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 $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

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

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 $

$2$	5.63098	−	0.540478i	0.995425	−	0.0955439i
$2$	5.63098	−	0.540478i	0.995425	−	0.0955439i
$3$	−8.83424	+	8.83424i	−0.566717	+	0.566717i	−0.931207	−	0.364490i	$-0.881243\pi$
$3$	−8.83424	+	8.83424i	−0.566717	+	0.566717i	0.364490	+	0.931207i	$0.381243\pi$
$4$	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	$-0.834856\pi$
$7$	−48.2986	+	48.2986i	−0.372554	+	0.372554i	0.495852	+	0.868407i	$0.334856\pi$
$8$	173.612	−	51.2543i	0.959078	−	0.283143i
$9$			86.9124i			0.357664i
$10$	119.913	+	292.610i	0.379198	+	0.925315i
$11$	132.916			0.331203			0.165602	−	0.986193i	$-0.447043\pi$
$11$	132.916			0.331203			0.165602	+	0.986193i	$0.447043\pi$
$12$	−223.762	+	331.307i	−0.448573	+	0.664167i
$13$	488.089	+	488.089i	0.801015	+	0.801015i	0.983254	−	0.182239i	$-0.0583344\pi$
$13$	488.089	+	488.089i	0.801015	+	0.801015i	−0.182239	+	0.983254i	$0.558334\pi$
$14$	−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	0.284901	−	0.958557i	$-0.408039\pi$
$17$	−802.713	−	802.713i	−0.673656	−	0.673656i	−0.958557	+	0.284901i	$0.908039\pi$
$18$	46.9742	+	489.401i	0.0341726	+	0.356028i
$19$		−	2785.43i		−	1.77014i	−0.465456	−	0.885071i	$-0.654110\pi$
$19$		−	2785.43i		−	1.77014i	0.465456	−	0.885071i	$-0.345890\pi$
$20$	833.377	+	1582.87i	0.465872	+	0.884852i
$21$		−	853.364i		−	0.422266i
$22$	748.445	−	71.8379i	0.329688	−	0.0316444i
$23$	711.980	+	711.980i	0.280639	+	0.280639i	0.833364	−	0.552725i	$-0.186412\pi$
$23$	711.980	+	711.980i	0.280639	+	0.280639i	−0.552725	+	0.833364i	$0.686412\pi$
$24$	−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
$28$	−1223.35	+	1811.32i	−0.294888	+	0.436618i
$29$	2091.69			0.461852			0.230926	−	0.972971i	$-0.425824\pi$
$29$	2091.69			0.461852			0.230926	+	0.972971i	$0.425824\pi$
$30$	−3644.33	−	1525.65i	−0.739290	−	0.309494i
$31$		−	4580.17i		−	0.856007i	−0.903777	−	0.428004i	$-0.859217\pi$
$31$		−	4580.17i		−	0.856007i	0.903777	−	0.428004i	$-0.140783\pi$
$32$	5142.17	−	2666.94i	0.887710	−	0.460403i
$33$	−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	$-0.581347\pi$
$37$	5951.81	−	5951.81i	0.714734	−	0.714734i	0.967522	+	0.252787i	$0.0813473\pi$
$38$	−1505.46	−	15684.7i	−0.169126	−	1.76204i
$39$	−8623.80			−0.907898
$40$	5548.23	+	8462.69i	0.548283	+	0.836293i
$41$	6331.41			0.588221			0.294110	−	0.955771i	$-0.404977\pi$
$41$	6331.41			0.588221			0.294110	+	0.955771i	$0.404977\pi$
$42$	−461.224	−	4805.27i	−0.0403449	−	0.420334i
$43$	1114.08	−	1114.08i	0.0918853	−	0.0918853i	−0.659670	−	0.751555i	$-0.729304\pi$
$43$	1114.08	−	1114.08i	0.0918853	−	0.0918853i	0.751555	+	0.659670i	$0.229304\pi$
$44$	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	$-0.944458\pi$
$47$	−12285.1	+	12285.1i	−0.811209	+	0.811209i	0.173607	+	0.984815i	$0.444458\pi$
$48$	−5013.04	+	11770.3i	−0.314050	+	0.737366i
$49$			12141.5i			0.722406i
$50$	−13721.5	+	11145.4i	−0.776207	+	0.630479i
$51$	14182.7			0.763544
$52$	18304.6	+	12362.8i	0.938755	+	0.634027i
$53$	26052.7	+	26052.7i	1.27398	+	1.27398i	0.943980	+	0.330003i	$0.107050\pi$
$53$	26052.7	+	26052.7i	1.27398	+	1.27398i	0.330003	+	0.943980i	$0.392950\pi$
$54$	−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
$58$	11778.3	−	1130.51i	0.459739	−	0.0441271i
$59$		−	35835.0i		−	1.34022i	−0.742261	−	0.670111i	$-0.766246\pi$
$59$		−	35835.0i		−	1.34022i	0.742261	−	0.670111i	$-0.233754\pi$
$60$	−21345.7	−	6621.22i	−0.765478	−	0.237443i
$61$		−	13145.0i		−	0.452309i	−0.974091	−	0.226155i	$-0.927385\pi$
$61$		−	13145.0i		−	0.452309i	0.974091	−	0.226155i	$-0.0726155\pi$
$62$	−2475.48	−	25790.8i	−0.0817863	−	0.852091i
$63$	−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	0.995158	−	0.0982928i	$-0.0313382\pi$
$67$	32954.4	+	32954.4i	0.896865	+	0.896865i	−0.0982928	+	0.995158i	$0.531338\pi$
$68$	−30103.8	−	20331.9i	−0.789495	−	0.533218i
$69$	−12579.6			−0.318086
$70$	−19924.3	−	8341.05i	−0.486002	−	0.203458i
$71$		−	38199.3i		−	0.899311i	−0.893202	−	0.449656i	$-0.851547\pi$
$71$		−	38199.3i		−	0.899311i	0.893202	−	0.449656i	$-0.148453\pi$
$72$	4454.64	+	15089.0i	0.101270	+	0.343028i
$73$	−27258.7	+	27258.7i	−0.598685	+	0.598685i	−0.939962	−	0.341278i	$-0.889140\pi$
$73$	−27258.7	+	27258.7i	−0.598685	+	0.598685i	0.341278	+	0.939962i	$0.389140\pi$
$74$	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
$78$	−48560.4	+	4660.97i	−0.903745	+	0.0867441i
$79$	−60171.0			−1.08473			−0.542363	−	0.840145i	$-0.682470\pi$
$79$	−60171.0			−1.08473			−0.542363	+	0.840145i	$0.682470\pi$
$80$	35815.9	+	44654.5i	0.625677	+	0.780082i
$81$	30375.5			0.514412
$82$	35652.0	−	3421.98i	0.585530	−	0.0562009i
$83$	−42310.9	+	42310.9i	−0.674151	+	0.674151i	−0.958670	−	0.284520i	$-0.908166\pi$
$83$	−42310.9	+	42310.9i	−0.674151	+	0.674151i	0.284520	+	0.958670i	$0.408166\pi$
$84$	−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
$88$	23075.7	−	6812.50i	0.317649	−	0.0937778i
$89$		−	102464.i		−	1.37118i	−0.727987	−	0.685591i	$-0.759544\pi$
$89$		−	102464.i		−	1.37118i	0.727987	−	0.685591i	$-0.240456\pi$
$90$	−25431.5	+	10421.9i	−0.330952	+	0.135626i
$91$	−47148.1			−0.596844
$92$	26701.1	+	18033.7i	0.328897	+	0.222134i
$93$	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	−0.999804	−	0.0197845i	$-0.993702\pi$
$97$	−94483.2	−	94483.2i	−1.01959	−	1.01959i	−0.0197845	−	0.999804i	$-0.506298\pi$
$98$	6562.20	+	68368.4i	0.0690215	+	0.719101i
$99$			11552.0i			0.118459i
$100$	−71241.7	+	70175.6i	−0.712417	+	0.701756i
$101$		−	4960.44i		−	0.0483856i	−0.999707	−	0.0241928i	$-0.992298\pi$
$101$		−	4960.44i		−	0.0483856i	0.999707	−	0.0241928i	$-0.00770157\pi$
$102$	79862.5	−	7665.45i	0.760051	−	0.0729520i
$103$	49417.3	+	49417.3i	0.458972	+	0.458972i	0.898318	−	0.439346i	$-0.144790\pi$
$103$	49417.3	+	49417.3i	0.458972	+	0.458972i	−0.439346	+	0.898318i	$0.644790\pi$
$104$	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	0.582814	−	0.812606i	$-0.301952\pi$
$107$	−27214.1	−	27214.1i	−0.229792	−	0.229792i	−0.812606	+	0.582814i	$0.801952\pi$
$108$	−109302.	−	73821.8i	−0.901716	−	0.609011i
$109$	−230822.			−1.86085			−0.930424	−	0.366485i	$-0.880561\pi$
$109$	−230822.			−1.86085			−0.930424	+	0.366485i	$0.880561\pi$
$110$	15938.3	+	38892.5i	0.125592	+	0.306467i
$111$			105159.i			0.810104i
$112$	−27407.3	+	64350.5i	−0.206453	+	0.484738i
$113$	142708.	−	142708.i	1.05136	−	1.05136i	0.0527536	−	0.998608i	$-0.483200\pi$
$113$	142708.	−	142708.i	1.05136	−	1.05136i	0.998608	−	0.0527536i	$-0.0167998\pi$
$114$	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
$118$	−19368.0	−	201786.i	−0.128050	−	1.33409i
$119$	77539.9			0.501947
$120$	−123776.	−	25747.0i	−0.784662	−	0.163220i
$121$	−143384.			−0.890305
$122$	−7104.57	−	74019.1i	−0.0432154	−	0.450240i
$123$	−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	$-0.778058\pi$
$127$	−22629.2	+	22629.2i	−0.124497	+	0.124497i	0.642113	+	0.766610i	$0.278058\pi$
$128$	145312.	−	115083.i	0.783928	−	0.620852i
$129$			19684.1i			0.104146i
$130$	−84291.7	+	201348.i	−0.437448	+	1.04494i
$131$	158250.			0.805683			0.402842	−	0.915270i	$-0.368023\pi$
$131$	158250.			0.805683			0.402842	+	0.915270i	$0.368023\pi$
$132$	−29741.5	+	44035.9i	−0.148569	+	0.219974i
$133$	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	0.626536	−	0.779392i	$-0.284472\pi$
$137$	−33580.3	−	33580.3i	−0.152856	−	0.152856i	−0.779392	+	0.626536i	$0.784472\pi$
$138$	−70835.4	+	6798.99i	−0.316630	+	0.0303911i
$139$			382434.i			1.67888i	0.543453	+	0.839440i	$0.317117\pi$
$139$			382434.i			1.67888i	−0.543453	+	0.839440i	$0.682883\pi$
$140$	−116702.	−	36199.6i	−0.503218	−	0.156093i
$141$		−	217058.i		−	0.919451i
$142$	−20645.9	−	215100.i	−0.0859237	−	0.895197i
$143$	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
$148$	150753.	−	223208.i	0.565733	−	0.837638i
$149$	325846.			1.20239			0.601197	−	0.799100i	$-0.294691\pi$
$149$	325846.			1.20239			0.601197	+	0.799100i	$0.294691\pi$
$150$	22758.1	−	219680.i	0.0825864	−	0.797192i
$151$		−	93886.3i		−	0.335089i	−0.985865	−	0.167544i	$-0.946416\pi$
$151$		−	93886.3i		−	0.335089i	0.985865	−	0.167544i	$-0.0535838\pi$
$152$	−142765.	−	483583.i	−0.501203	−	1.69770i
$153$	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	−0.103899	+	0.994588i	$0.533132\pi$
$157$	−339269.	+	339269.i	−1.09849	+	1.09849i	−0.994588	+	0.103899i	$0.966868\pi$
$158$	−338822.	+	32521.1i	−1.07976	+	0.103639i
$159$	−460312.			−1.44397
$160$	225813.	+	232091.i	0.697347	+	0.716734i
$161$	−68775.3			−0.209107
$162$	171044.	−	16417.3i	0.512059	−	0.0491490i
$163$	−50145.9	+	50145.9i	−0.147831	+	0.147831i	−0.777149	−	0.629317i	$-0.783335\pi$
$163$	−50145.9	+	50145.9i	−0.147831	+	0.147831i	0.629317	+	0.777149i	$0.283335\pi$
$164$	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	$-0.736717\pi$
$167$	21262.4	−	21262.4i	0.0589958	−	0.0589958i	0.735989	+	0.676993i	$0.236717\pi$
$168$	−43738.6	−	148154.i	−0.119562	−	0.404986i
$169$			105169.i			0.283252i
$170$	138626.	−	331138.i	0.367895	−	0.878793i
$171$	242088.			0.633116
$172$	28218.5	−	41781.0i	0.0727299	−	0.107686i
$173$	144580.	+	144580.i	0.367276	+	0.367276i	0.866483	−	0.499207i	$-0.166375\pi$
$173$	144580.	+	144580.i	0.367276	+	0.367276i	−0.499207	+	0.866483i	$0.666375\pi$
$174$	−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
$178$	−55379.3	−	576970.i	−0.131008	−	1.36491i
$179$		−	26195.9i		−	0.0611083i	−0.999533	−	0.0305542i	$-0.990273\pi$
$179$		−	26195.9i		−	0.0611083i	0.999533	−	0.0305542i	$-0.00972721\pi$
$180$	−137571.	+	72430.8i	−0.316480	+	0.166626i
$181$		−	500862.i		−	1.13637i	−0.822899	−	0.568187i	$-0.807645\pi$
$181$		−	500862.i		−	1.13637i	0.822899	−	0.568187i	$-0.192355\pi$
$182$	−265490.	+	25482.5i	−0.594113	+	0.0570248i
$183$	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
$188$	−311167.	+	460722.i	−0.642095	+	0.950701i
$189$	281535.			0.573295
$190$	815046.	−	334009.i	1.63794	−	0.671235i
$191$			804916.i			1.59649i	0.602330	+	0.798247i	$0.294239\pi$
$191$			804916.i			1.59649i	−0.602330	+	0.798247i	$0.705761\pi$
$192$	−85844.8	+	400286.i	−0.168059	+	0.783640i
$193$	−267880.	+	267880.i	−0.517663	+	0.517663i	−0.916864	−	0.399201i	$-0.869288\pi$
$193$	−267880.	+	267880.i	−0.517663	+	0.517663i	0.399201	+	0.916864i	$0.369288\pi$
$194$	−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	$-0.827533\pi$
$197$	−185787.	+	185787.i	−0.341075	+	0.341075i	0.515696	+	0.856771i	$0.327533\pi$
$198$	6243.61	+	65049.1i	0.0113181	+	0.117917i
$199$	−90919.1			−0.162750			−0.0813752	−	0.996684i	$-0.525931\pi$
$199$	−90919.1			−0.162750			−0.0813752	+	0.996684i	$0.525931\pi$
$200$	−363232.	+	433662.i	−0.642109	+	0.766613i
$201$	−582255.			−1.01654
$202$	−2681.01	−	27932.1i	−0.00462295	−	0.0481643i
$203$	−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
$208$	650304.	+	276969.i	1.04222	+	0.443887i
$209$		−	370227.i		−	0.586276i
$210$	249703.	−	102329.i	0.390729	−	0.160123i
$211$	163692.			0.253117			0.126559	−	0.991959i	$-0.459607\pi$
$211$	163692.			0.253117			0.126559	+	0.991959i	$0.459607\pi$
$212$	977045.	+	659888.i	1.49305	+	1.00839i
$213$	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
$218$	−1.29975e6	+	124754.i	−1.85233	+	0.177793i
$219$		−	481620.i		−	0.678569i
$220$	110769.	+	210388.i	0.154298	+	0.293066i
$221$		−	783591.i		−	1.07922i
$222$	56836.4	+	592150.i	0.0774005	+	0.806398i
$223$	−933470.	−	933470.i	−1.25701	−	1.25701i	−0.952514	−	0.304495i	$-0.901512\pi$
$223$	−933470.	−	933470.i	−1.25701	−	1.25701i	−0.304495	−	0.952514i	$-0.598488\pi$
$224$	−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	−0.995960	−	0.0897951i	$-0.971379\pi$
$227$	−842940.	−	842940.i	−1.08576	−	1.08576i	−0.0897951	−	0.995960i	$-0.528621\pi$
$228$	922832.	+	623273.i	1.17567	+	0.794038i
$229$	798268.			1.00591			0.502956	−	0.864312i	$-0.332246\pi$
$229$	798268.			1.00591			0.502956	+	0.864312i	$0.332246\pi$
$230$	−122957.	+	293708.i	−0.153262	+	0.366097i
$231$		−	113425.i		−	0.139856i
$232$	363142.	−	107208.i	0.442952	−	0.130770i
$233$	118131.	−	118131.i	0.142553	−	0.142553i	−0.632229	−	0.774782i	$-0.717860\pi$
$233$	118131.	−	118131.i	0.142553	−	0.142553i	0.774782	+	0.632229i	$0.217860\pi$
$234$	−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
$238$	436625.	−	41908.6i	0.499651	−	0.0479580i
$239$	−921010.			−1.04296			−0.521482	−	0.853262i	$-0.674621\pi$
$239$	−921010.			−1.04296			−0.521482	+	0.853262i	$0.674621\pi$
$240$	−710895.	−	78082.7i	−0.796667	−	0.0875038i
$241$	−1.17647e6			−1.30478			−0.652391	−	0.757882i	$-0.726234\pi$
$241$	−1.17647e6			−1.30478			−0.652391	+	0.757882i	$0.726234\pi$
$242$	−807394.	+	77496.1i	−0.886232	+	0.0850632i
$243$	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
$248$	−234754.	−	795171.i	−0.242372	−	0.820977i
$249$		−	747569.i		−	0.764105i
$250$	−818172.	−	554218.i	−0.827932	−	0.560829i
$251$	922201.			0.923935			0.461968	−	0.886897i	$-0.347144\pi$
$251$	922201.			0.923935			0.461968	+	0.886897i	$0.347144\pi$
$252$	−157426.	−	106324.i	−0.156162	−	0.105471i
$253$	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	0.940037	−	0.341072i	$-0.110790\pi$
$257$	634212.	+	634212.i	0.598965	+	0.598965i	−0.341072	+	0.940037i	$0.610790\pi$
$258$	10638.8	+	110841.i	0.00995050	+	0.103669i
$259$			574929.i			0.532555i
$260$	−365820.	+	1.17935e6i	−0.335610	+	1.08195i
$261$			181794.i			0.165188i
$262$	891100.	−	85530.4i	0.801998	−	0.0769781i
$263$	−744074.	−	744074.i	−0.663326	−	0.663326i	0.292837	−	0.956163i	$-0.405401\pi$
$263$	−744074.	−	744074.i	−0.663326	−	0.663326i	−0.956163	+	0.292837i	$0.905401\pi$
$264$	−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
$268$	1.23588e6	+	834701.i	1.05109	+	0.709895i
$269$	268211.			0.225993			0.112997	−	0.993595i	$-0.463955\pi$
$269$	268211.			0.225993			0.112997	+	0.993595i	$0.463955\pi$
$270$	503331.	−	1.20231e6i	0.420188	−	1.00371i
$271$			2.36545e6i			1.95654i	0.207325	+	0.978272i	$0.433524\pi$
$271$			2.36545e6i			1.95654i	−0.207325	+	0.978272i	$0.566476\pi$
$272$	−1.06949e6	−	455504.i	−0.876506	−	0.373310i
$273$	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	$-0.826661\pi$
$277$	−430756.	+	430756.i	−0.337312	+	0.337312i	0.518043	+	0.855355i	$0.326661\pi$
$278$	206697.	+	2.15348e6i	0.160407	+	1.67120i
$279$	398073.			0.306163
$280$	−676708.	−	140764.i	−0.515830	−	0.107299i
$281$	1.37421e6			1.03821			0.519106	−	0.854710i	$-0.326265\pi$
$281$	1.37421e6			1.03821			0.519106	+	0.854710i	$0.326265\pi$
$282$	−117315.	−	1.22225e6i	−0.0878479	−	0.915245i
$283$	−889337.	+	889337.i	−0.660085	+	0.660085i	−0.955400	−	0.295315i	$-0.904575\pi$
$283$	−889337.	+	889337.i	−0.660085	+	0.660085i	0.295315	+	0.955400i	$0.404575\pi$
$284$	−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
$288$	231790.	+	446918.i	0.164670	+	0.317502i
$289$		−	131161.i		−	0.0923762i
$290$	250821.	+	612051.i	0.175134	+	0.427359i
$291$	1.66937e6			1.15564
$292$	−690434.	+	1.02227e6i	−0.473876	+	0.701632i
$293$	−1.32774e6	−	1.32774e6i	−0.903535	−	0.903535i	0.0922047	−	0.995740i	$-0.470609\pi$
$293$	−1.32774e6	−	1.32774e6i	−0.903535	−	0.903535i	−0.995740	+	0.0922047i	$0.970609\pi$
$294$	−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
$298$	1.83483e6	−	176113.i	1.19689	−	0.114881i
$299$			695019.i			0.449592i
$300$	9418.10	−	1.24931e6i	0.00604172	−	0.801436i
$301$			107617.i			0.0684646i
$302$	−50743.5	−	528672.i	−0.0320157	−	0.333556i
$303$	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	0.964643	−	0.263558i	$-0.0848962\pi$
$307$	1.15775e6	+	1.15775e6i	0.701085	+	0.701085i	−0.263558	+	0.964643i	$0.584896\pi$
$308$	−162603.	+	240753.i	−0.0976677	+	0.144609i
$309$	−873129.			−0.520214
$310$	1.34021e6	−	549222.i	0.792077	−	0.324597i
$311$			1.15192e6i			0.675337i	0.941265	+	0.337668i	$0.109638\pi$
$311$			1.15192e6i			0.675337i	−0.941265	+	0.337668i	$0.890362\pi$
$312$	−1.49719e6	+	442007.i	−0.870745	+	0.257065i
$313$	2.03938e6	−	2.03938e6i	1.17662	−	1.17662i	0.196023	−	0.980599i	$-0.437197\pi$
$313$	2.03938e6	−	2.03938e6i	1.17662	−	1.17662i	0.980599	−	0.196023i	$-0.0628026\pi$
$314$	−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	$-0.616315\pi$
$317$	1.03170e6	−	1.03170e6i	0.576640	−	0.576640i	0.933976	+	0.357336i	$0.116315\pi$
$318$	−2.59201e6	+	248789.i	−1.43737	+	0.137963i
$319$	278019.			0.152967
$320$	1.39699e6	+	1.18485e6i	0.762636	+	0.646828i
$321$	480832.			0.260454
$322$	−387272.	+	37171.5i	−0.208150	+	0.0199789i
$323$	−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
$328$	1.09921e6	−	324512.i	0.564150	−	0.166551i
$329$		−	1.18670e6i		−	0.604439i
$330$	−484389.	−	202783.i	−0.244855	−	0.102505i
$331$	−1.08093e6			−0.542286			−0.271143	−	0.962539i	$-0.587402\pi$
$331$	−1.08093e6			−0.542286			−0.271143	+	0.962539i	$0.587402\pi$
$332$	−1.07169e6	+	1.58677e6i	−0.533610	+	0.790075i
$333$	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	0.481138	−	0.876645i	$-0.340224\pi$
$337$	−824573.	−	824573.i	−0.395507	−	0.395507i	−0.876645	+	0.481138i	$0.840224\pi$
$338$	56841.7	+	592206.i	0.0270630	+	0.281956i
$339$			2.52143e6i			1.19165i
$340$	601629.	−	1.93955e6i	0.282248	−	0.909923i
$341$		−	608776.i		−	0.283512i
$342$	1.36319e6	−	130843.i	0.630220	−	0.0604904i
$343$	−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	0.285732	−	0.958310i	$-0.407763\pi$
$347$	−1.50857e6	−	1.50857e6i	−0.672577	−	0.672577i	−0.958310	+	0.285732i	$0.907763\pi$
$348$	−468041.	+	692992.i	−0.207174	+	0.306747i
$349$	1.98154e6			0.870844			0.435422	−	0.900226i	$-0.356599\pi$
$349$	1.98154e6			0.870844			0.435422	+	0.900226i	$0.356599\pi$
$350$	124423.	−	1.20104e6i	0.0542915	−	0.524067i
$351$		−	2.84510e6i		−	1.23262i
$352$	683474.	−	354478.i	0.294012	−	0.152487i
$353$	3162.85	−	3162.85i	0.00135096	−	0.00135096i	−0.706431	−	0.707782i	$-0.749696\pi$
$353$	3162.85	−	3162.85i	0.00135096	−	0.00135096i	0.707782	+	0.706431i	$0.249696\pi$
$354$	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
$358$	−14158.3	−	147508.i	−0.00583853	−	0.0608288i
$359$	4.01967e6			1.64609			0.823047	−	0.567973i	$-0.192272\pi$
$359$	4.01967e6			1.64609			0.823047	+	0.567973i	$0.192272\pi$
$360$	−735512.	+	482210.i	−0.299112	+	0.196101i
$361$	−5.28252e6			−2.13340
$362$	−270705.	−	2.82034e6i	−0.108574	−	1.13118i
$363$	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	−0.305723	+	0.952121i	$0.598898\pi$
$367$	−3.24558e6	+	3.24558e6i	−1.25784	+	1.25784i	−0.952121	+	0.305723i	$0.901102\pi$
$368$	948603.	+	404017.i	0.365145	+	0.155518i
$369$			550277.i			0.210385i
$370$	2.45526e6	+	1.02786e6i	0.932381	+	0.390329i
$371$	−2.51662e6			−0.949256
$372$	1.51744e6	+	1.02487e6i	0.568532	+	0.383982i
$373$	−107814.	−	107814.i	−0.0401237	−	0.0401237i	0.686760	−	0.726884i	$-0.259032\pi$
$373$	−107814.	−	107814.i	−0.0401237	−	0.0401237i	−0.726884	+	0.686760i	$0.759032\pi$
$374$	−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
$378$	1.58532e6	−	152164.i	0.570672	−	0.0547748i
$379$		−	1.79110e6i		−	0.640504i	−0.947332	−	0.320252i	$-0.896232\pi$
$379$		−	1.79110e6i		−	0.640504i	0.947332	−	0.320252i	$-0.103768\pi$
$380$	4.40898e6	−	2.32131e6i	1.56631	−	0.824659i
$381$		−	399823.i		−	0.141109i
$382$	435039.	+	4.53246e6i	0.152535	+	1.58919i
$383$	−102633.	−	102633.i	−0.0357511	−	0.0357511i	0.689005	−	0.724756i	$-0.258048\pi$
$383$	−102633.	−	102633.i	−0.0357511	−	0.0357511i	−0.724756	+	0.689005i	$0.758048\pi$
$384$	−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
$388$	−3.54336e6	−	2.39316e6i	−1.19491	−	0.807034i
$389$	2.45331e6			0.822013			0.411007	−	0.911632i	$-0.365177\pi$
$389$	2.45331e6			0.822013			0.411007	+	0.911632i	$0.365177\pi$
$390$	−1.03411e6	−	2.52341e6i	−0.344273	−	0.840092i
$391$		−	1.14303e6i		−	0.378108i
$392$	622304.	+	2.10790e6i	0.204544	+	0.692844i
$393$	−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	$-0.769147\pi$
$397$	−266983.	+	266983.i	−0.0850172	+	0.0850172i	0.663319	+	0.748337i	$0.269147\pi$
$398$	−511963.	+	49139.7i	−0.162006	+	0.0155498i
$399$	−2.37698e6			−0.747470
$400$	−1.81097e6	+	2.63826e6i	−0.565927	+	0.824456i
$401$	3.29213e6			1.02239			0.511195	−	0.859465i	$-0.329203\pi$
$401$	3.29213e6			1.02239			0.511195	+	0.859465i	$0.329203\pi$
$402$	−3.27866e6	+	314696.i	−1.01189	+	0.0971239i
$403$	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
$408$	2.46228e6	−	726926.i	0.732298	−	0.216192i
$409$			1.56045e6i			0.461255i	0.973042	+	0.230628i	$0.0740780\pi$
$409$			1.56045e6i			0.461255i	−0.973042	+	0.230628i	$0.925922\pi$
$410$	759218.	+	1.85264e6i	0.223052	+	0.544290i
$411$	593314.			0.173253
$412$	1.85328e6	+	1.25169e6i	0.537895	+	0.363290i
$413$	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
$418$	−200100.	−	2.08474e6i	−0.0560151	−	0.583594i
$419$		−	2.32937e6i		−	0.648191i	−0.946024	−	0.324095i	$-0.894940\pi$
$419$		−	2.32937e6i		−	0.648191i	0.946024	−	0.324095i	$-0.105060\pi$
$420$	1.35077e6	−	711174.i	0.373643	−	0.196722i
$421$			2.41688e6i			0.664585i	0.943176	+	0.332292i	$0.107822\pi$
$421$			2.41688e6i			0.664585i	−0.943176	+	0.332292i	$0.892178\pi$
$422$	921746.	−	88472.0i	0.251959	−	0.0241838i
$423$	−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
$428$	−1.02060e6	−	689305.i	−0.269306	−	0.181887i
$429$	−1.14624e6			−0.300699
$430$	459585.	+	192399.i	0.119866	+	0.0501801i
$431$			6.38964e6i			1.65685i	0.560100	+	0.828425i	$0.310763\pi$
$431$			6.38964e6i			1.65685i	−0.560100	+	0.828425i	$0.689237\pi$
$432$	−3.88316e6	−	1.65386e6i	−1.00110	−	0.426374i
$433$	156498.	−	156498.i	0.0401134	−	0.0401134i	−0.686766	−	0.726879i	$-0.740970\pi$
$433$	156498.	−	156498.i	0.0401134	−	0.0401134i	0.726879	+	0.686766i	$0.240970\pi$
$434$	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
$438$	−260305.	−	2.71199e6i	−0.0648332	−	0.675465i
$439$	4542.17			0.00112487			0.000562434	−	1.00000i	$-0.499821\pi$
$439$	4542.17			0.00112487			0.000562434		1.00000i	$0.499821\pi$
$440$	737447.	+	1.12482e6i	0.181593	+	0.276983i
$441$	−1.05524e6			−0.258379
$442$	−423514.	−	4.41238e6i	−0.103113	−	1.07428i
$443$	−854779.	+	854779.i	−0.206940	+	0.206940i	−0.802966	−	0.596025i	$-0.796746\pi$
$443$	−854779.	+	854779.i	−0.206940	+	0.206940i	0.596025	+	0.802966i	$0.296746\pi$
$444$	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
$448$	−469332.	+	2.18844e6i	−0.110480	+	0.515158i
$449$			6.16439e6i			1.44303i	0.692400	+	0.721514i	$0.256553\pi$
$449$			6.16439e6i			1.44303i	−0.692400	+	0.721514i	$0.743447\pi$
$450$	−968672.	−	1.19257e6i	−0.225500	−	0.277621i
$451$	841543.			0.194821
$452$	3.61464e6	−	5.35192e6i	0.832183	−	1.23215i
$453$	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	0.944826	−	0.327572i	$-0.106230\pi$
$457$	2.75584e6	+	2.75584e6i	0.617254	+	0.617254i	−0.327572	+	0.944826i	$0.606230\pi$
$458$	4.49503e6	−	431446.i	1.00131	−	0.0961087i
$459$			4.67905e6i			1.03664i
$460$	−533625.	+	1.72032e6i	−0.117582	+	0.379066i
$461$		−	1.99091e6i		−	0.436315i	−0.975914	−	0.218157i	$-0.929995\pi$
$461$		−	1.99091e6i		−	0.436315i	0.975914	−	0.218157i	$-0.0700046\pi$
$462$	−61303.9	−	638695.i	−0.0133624	−	0.139216i
$463$	1.20628e6	+	1.20628e6i	0.261514	+	0.261514i	0.825669	−	0.564155i	$-0.190798\pi$
$463$	1.20628e6	+	1.20628e6i	0.261514	+	0.261514i	−0.564155	+	0.825669i	$0.690798\pi$
$464$	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	0.367271	−	0.930114i	$-0.380292\pi$
$467$	−2.65264e6	−	2.65264e6i	−0.562842	−	0.562842i	−0.930114	+	0.367271i	$0.880292\pi$
$468$	−1.07448e6	+	1.59090e6i	−0.226769	+	0.335759i
$469$	−3.18331e6			−0.668262
$470$	−5.06787e6	−	2.12160e6i	−1.05823	−	0.443015i
$471$		−	5.99436e6i		−	1.24506i
$472$	−1.83670e6	−	6.22137e6i	−0.379475	−	1.28538i
$473$	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
$478$	−5.18619e6	+	497786.i	−1.03819	+	0.0996489i
$479$	−5.94725e6			−1.18434			−0.592171	−	0.805812i	$-0.701729\pi$
$479$	−5.94725e6			−1.18434			−0.592171	+	0.805812i	$0.701729\pi$
$480$	−4.04523e6	−	55459.1i	−0.801383	−	0.0109868i
$481$	5.81003e6			1.14503
$482$	−6.62467e6	+	635856.i	−1.29881	+	0.124664i
$483$	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	$-0.600288\pi$
$487$	3.35438e6	−	3.35438e6i	0.640900	−	0.640900i	0.950777	+	0.309877i	$0.100288\pi$
$488$	−673738.	−	2.28212e6i	−0.128068	−	0.433800i
$489$		−	886003.i		−	0.167557i
$490$	−3.55272e6	+	1.45592e6i	−0.668454	+	0.273935i
$491$	−1.32658e6			−0.248330			−0.124165	−	0.992262i	$-0.539625\pi$
$491$	−1.32658e6			−0.248330			−0.124165	+	0.992262i	$0.539625\pi$
$492$	−1.41673e6	+	2.09764e6i	−0.263860	+	0.390677i
$493$	−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
$498$	−404045.	−	4.20954e6i	−0.0730056	−	0.760610i
$499$		−	8.63773e6i		−	1.55292i	−0.630168	−	0.776459i	$-0.717014\pi$
$499$		−	8.63773e6i		−	1.55292i	0.630168	−	0.776459i	$-0.282986\pi$
$500$	−4.90665e6	−	2.67858e6i	−0.877728	−	0.479159i
$501$			375674.i			0.0668678i
$502$	5.19289e6	−	498429.i	0.919708	−	0.0882764i
$503$	7.03064e6	+	7.03064e6i	1.23901	+	1.23901i	0.960406	+	0.278604i	$0.0898718\pi$
$503$	7.03064e6	+	7.03064e6i	1.23901	+	1.23901i	0.278604	+	0.960406i	$0.410128\pi$
$504$	−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
$508$	−573173.	+	848653.i	−0.0985431	+	0.145905i
$509$	−5.41942e6			−0.927168			−0.463584	−	0.886053i	$-0.653437\pi$
$509$	−5.41942e6			−0.927168			−0.463584	+	0.886053i	$0.653437\pi$
$510$	1.70069e6	+	4.15001e6i	0.289535	+	0.706519i
$511$		−	2.63312e6i		−	0.446085i
$512$	3.86459e6	−	4.49993e6i	0.651521	−	0.758631i
$513$	−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
$518$	310736.	+	3.23741e6i	0.0508824	+	0.530119i
$519$	−2.55450e6			−0.416283
$520$	−1.42252e6	+	6.83858e6i	−0.230701	+	1.10907i
$521$	568375.			0.0917362			0.0458681	−	0.998948i	$-0.485395\pi$
$521$	568375.			0.0917362			0.0458681	+	0.998948i	$0.485395\pi$
$522$	98255.6	+	1.02368e6i	0.0157827	+	0.164432i
$523$	5.95145e6	−	5.95145e6i	0.951413	−	0.951413i	−0.0474606	−	0.998873i	$-0.515113\pi$
$523$	5.95145e6	−	5.95145e6i	0.951413	−	0.951413i	0.998873	+	0.0474606i	$0.0151128\pi$
$524$	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
$528$	−666311.	+	1.56445e6i	−0.104014	+	0.244218i
$529$		−	5.42251e6i		−	0.842484i
$530$	−4.49924e6	+	1.07474e7i	−0.695744	+	1.66193i
$531$	3.11450e6			0.479349
$532$	5.04532e6	+	3.40756e6i	0.772875	+	0.521993i
$533$	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
$538$	1.51029e6	−	144962.i	0.224960	−	0.0215923i
$539$			1.61379e6i			0.239263i
$540$	2.18442e6	−	7.04222e6i	0.322368	−	1.03926i
$541$			8.15230e6i			1.19753i	0.800924	+	0.598766i	$0.204342\pi$
$541$			8.15230e6i			1.19753i	−0.800924	+	0.598766i	$0.795658\pi$
$542$	1.27847e6	+	1.33198e7i	0.186936	+	1.94759i
$543$	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	0.879896	−	0.475167i	$-0.157612\pi$
$547$	2.83225e6	+	2.83225e6i	0.404729	+	0.404729i	−0.475167	+	0.879896i	$0.657612\pi$
$548$	−1.25935e6	−	850554.i	−0.179141	−	0.120990i
$549$	1.14246e6			0.161775
$550$	−1.82380e6	+	1.48140e6i	−0.257082	+	0.208816i
$551$		−	5.82626e6i		−	0.817543i
$552$	−2.18396e6	+	644759.i	−0.305069	+	0.0900637i
$553$	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	$-0.728524\pi$
$557$	698101.	−	698101.i	0.0953411	−	0.0953411i	0.753169	+	0.657827i	$0.228524\pi$
$558$	2.24154e6	−	215150.i	0.304762	−	0.0292520i
$559$	1.08754e6			0.147203
$560$	−3.88661e6	−	426894.i	−0.523722	−	0.0575242i
$561$	1.88510e6			0.252888
$562$	7.73812e6	−	742728.i	1.03346	−	0.0991949i
$563$	−5.64471e6	+	5.64471e6i	−0.750535	+	0.750535i	−0.974579	−	0.224044i	$-0.928074\pi$
$563$	−5.64471e6	+	5.64471e6i	−0.750535	+	0.750535i	0.224044	+	0.974579i	$0.428074\pi$
$564$	−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
$568$	−1.95788e6	−	6.63185e6i	−0.254634	−	0.862509i
$569$		−	5.48350e6i		−	0.710031i	−0.934860	−	0.355015i	$-0.884476\pi$
$569$		−	5.48350e6i		−	0.710031i	0.934860	−	0.355015i	$-0.115524\pi$
$570$	−4.24959e6	+	1.01510e7i	−0.547848	+	1.30865i
$571$	−2.18796e6			−0.280833			−0.140417	−	0.990093i	$-0.544844\pi$
$571$	−2.18796e6			−0.280833			−0.140417	+	0.990093i	$0.544844\pi$
$572$	2.43297e6	+	1.64321e6i	0.310919	+	0.209992i
$573$	−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	0.512261	−	0.858830i	$-0.328808\pi$
$577$	−2.77158e6	−	2.77158e6i	−0.346568	−	0.346568i	−0.858830	+	0.512261i	$0.828808\pi$
$578$	−70889.6	−	738564.i	−0.00882598	−	0.0919536i
$579$		−	4.73303e6i		−	0.586737i
$580$	1.74317e6	+	3.31088e6i	0.215164	+	0.408671i
$581$		−	4.08712e6i		−	0.502316i
$582$	9.40020e6	−	902260.i	1.15035	−	0.110414i
$583$	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	0.903075	−	0.429483i	$-0.141304\pi$
$587$	3.95366e6	+	3.95366e6i	0.473592	+	0.473592i	−0.429483	+	0.903075i	$0.641304\pi$
$588$	−4.02256e6	−	2.71680e6i	−0.479799	−	0.324052i
$589$	−1.27577e7			−1.51525
$590$	1.04857e7	−	4.29708e6i	1.24013	−	0.508210i
$591$		−	3.28258e6i		−	0.386586i
$592$	3.37739e6	−	7.92987e6i	0.396074	−	0.929955i
$593$	−485319.	+	485319.i	−0.0566749	+	0.0566749i	−0.734876	−	0.678201i	$-0.762760\pi$
$593$	−485319.	+	485319.i	−0.0566749	+	0.0566749i	0.678201	+	0.734876i	$0.262760\pi$
$594$	−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
$598$	375642.	+	3.91364e6i	0.0429558	+	0.447535i
$599$	1.01773e7			1.15895			0.579476	−	0.814989i	$-0.303257\pi$
$599$	1.01773e7			1.15895			0.579476	+	0.814989i	$0.303257\pi$
$600$	−622194.	−	7.03995e6i	−0.0705582	−	0.798347i
$601$	−4.47941e6			−0.505865			−0.252932	−	0.967484i	$-0.581395\pi$
$601$	−4.47941e6			−0.505865			−0.252932	+	0.967484i	$0.581395\pi$
$602$	58164.8	+	605990.i	0.00654137	+	0.0681513i
$603$	−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	$-0.641422\pi$
$607$	4.29459e6	−	4.29459e6i	0.473097	−	0.473097i	0.902915	+	0.429818i	$0.141422\pi$
$608$	−7.42857e6	−	1.43231e7i	−0.814979	−	1.57137i
$609$		−	1.78497e6i		−	0.195024i
$610$	3.84636e6	−	1.57626e6i	0.418529	−	0.171515i
$611$	−1.19924e7			−1.29958
$612$	1.76709e6	−	2.61639e6i	0.190713	−	0.282374i
$613$	−796329.	−	796329.i	−0.0855936	−	0.0855936i	0.663014	−	0.748607i	$-0.269277\pi$
$613$	−796329.	−	796329.i	−0.0855936	−	0.0855936i	−0.748607	+	0.663014i	$0.769277\pi$
$614$	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	0.600250	−	0.799812i	$-0.295068\pi$
$617$	−1.88708e6	−	1.88708e6i	−0.199562	−	0.199562i	−0.799812	+	0.600250i	$0.795068\pi$
$618$	−4.91657e6	+	471907.i	−0.517835	+	0.0497033i
$619$		−	5.43191e6i		−	0.569805i	−0.958556	−	0.284903i	$-0.908039\pi$
$619$		−	5.43191e6i		−	0.569805i	0.958556	−	0.284903i	$-0.0919612\pi$
$620$	7.24982e6	−	3.81701e6i	0.757440	−	0.398790i
$621$		−	4.15016e6i		−	0.431853i
$622$	622586.	+	6.48642e6i	0.0645243	+	0.672247i
$623$	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
$628$	−8.59332e6	+	1.27235e7i	−0.869484	+	1.28738i
$629$	−9.55519e6			−0.962970
$630$	724940.	−	1.73167e6i	0.0727697	−	0.173826i
$631$		−	7.61895e6i		−	0.761767i	−0.924623	−	0.380883i	$-0.875620\pi$
$631$		−	7.61895e6i		−	0.761767i	0.924623	−	0.380883i	$-0.124380\pi$
$632$	−1.04464e7	+	3.08403e6i	−1.04034	+	0.307132i
$633$	−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
$638$	1.56552e6	−	150263.i	0.152267	−	0.0146150i
$639$	3.31999e6			0.321651
$640$	8.50679e6	+	5.91682e6i	0.820948	+	0.571003i
$641$	1.19901e7			1.15260			0.576299	−	0.817239i	$-0.304496\pi$
$641$	1.19901e7			1.15260			0.576299	+	0.817239i	$0.304496\pi$
$642$	2.70755e6	−	259879.i	0.259262	−	0.0248848i
$643$	−578939.	+	578939.i	−0.0552211	+	0.0552211i	−0.734178	−	0.678957i	$-0.762432\pi$
$643$	−578939.	+	578939.i	−0.0552211	+	0.0552211i	0.678957	+	0.734178i	$0.262432\pi$
$644$	−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	$-0.755966\pi$
$647$	−282199.	+	282199.i	−0.0265030	+	0.0265030i	0.693731	+	0.720234i	$0.255966\pi$
$648$	5.27355e6	−	1.55688e6i	0.493362	−	0.145652i
$649$		−	4.76303e6i		−	0.443886i
$650$	−1.21373e7	−	1.25738e6i	−1.12678	−	0.116730i
$651$	−3.90855e6			−0.361463
$652$	−1.27014e6	+	1.88060e6i	−0.117013	+	0.173252i
$653$	−874624.	−	874624.i	−0.0802673	−	0.0802673i	0.665833	−	0.746101i	$-0.268076\pi$
$653$	−874624.	−	874624.i	−0.0802673	−	0.0802673i	−0.746101	+	0.665833i	$0.768076\pi$
$654$	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
$658$	−641387.	−	6.68230e6i	−0.0577504	−	0.601674i
$659$			1.09283e7i			0.980255i	0.871651	+	0.490127i	$0.163050\pi$
$659$			1.09283e7i			0.980255i	−0.871651	+	0.490127i	$0.836950\pi$
$660$	−2.83718e6	−	880063.i	−0.253529	−	0.0786419i
$661$		−	643996.i		−	0.0573297i	−0.999589	−	0.0286648i	$-0.990874\pi$
$661$		−	643996.i		−	0.0573297i	0.999589	−	0.0286648i	$-0.00912555\pi$
$662$	−6.08670e6	+	584219.i	−0.539805	+	0.0518121i
$663$	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
$668$	538554.	−	797395.i	0.0466969	−	0.0691405i
$669$	1.64930e7			1.42474
$670$	−5.69114e6	+	1.35945e7i	−0.489793	+	1.16997i
$671$		−	1.74717e6i		−	0.149806i
$672$	−2.27587e6	−	4.38814e6i	−0.194413	−	0.374850i
$673$	−2.17855e6	+	2.17855e6i	−0.185409	+	0.185409i	−0.793708	−	0.608299i	$-0.791852\pi$
$673$	−2.17855e6	+	2.17855e6i	−0.185409	+	0.185409i	0.608299	+	0.793708i	$0.291852\pi$
$674$	−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	$-0.686744\pi$
$677$	3.32948e6	−	3.32948e6i	0.279193	−	0.279193i	0.832787	+	0.553594i	$0.186744\pi$
$678$	1.36278e6	+	1.41981e7i	0.113855	+	1.18620i
$679$	9.12682e6			0.759705
$680$	2.33947e6	−	1.12467e7i	0.194020	−	0.932727i
$681$	1.48935e7			1.23063
$682$	−329030.	−	3.42800e6i	−0.0270879	−	0.282215i
$683$	5.82341e6	−	5.82341e6i	0.477667	−	0.477667i	−0.426718	−	0.904385i	$-0.640330\pi$
$683$	5.82341e6	−	5.82341e6i	0.477667	−	0.477667i	0.904385	+	0.426718i	$0.140330\pi$
$684$	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
$688$	632192.	−	1.48434e6i	0.0509188	−	0.119554i
$689$			2.54321e7i			2.04096i
$690$	−1.50846e6	−	3.68092e6i	−0.120618	−	0.294330i
$691$	6.20240e6			0.494157			0.247078	−	0.968995i	$-0.420529\pi$
$691$	6.20240e6			0.494157			0.247078	+	0.968995i	$0.420529\pi$
$692$	5.42212e6	+	3.66205e6i	0.430431	+	0.290709i
$693$	−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
$698$	1.11580e7	−	1.07098e6i	0.866860	−	0.0832038i
$699$			2.08720e6i			0.161574i
$700$	51490.7	−	6.83027e6i	0.00397177	−	0.526857i
$701$			2.06771e7i			1.58926i	0.607097	+	0.794628i	$0.292334\pi$
$701$			2.06771e7i			1.58926i	−0.607097	+	0.794628i	$0.707666\pi$
$702$	−1.53771e6	−	1.60207e7i	−0.117769	−	1.22698i
$703$	−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
$708$	1.18724e7	+	8.01850e6i	0.890132	+	0.601188i
$709$	−3.44323e6			−0.257247			−0.128624	−	0.991693i	$-0.541056\pi$
$709$	−3.44323e6			−0.257247			−0.128624	+	0.991693i	$0.541056\pi$
$710$	1.11775e7	−	4.58060e6i	0.832146	−	0.341017i
$711$		−	5.22960e6i		−	0.387967i
$712$	−5.25171e6	−	1.77889e7i	−0.388240	−	1.31507i
$713$	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
$718$	2.26347e7	−	2.17255e6i	1.63856	−	0.157274i
$719$	−1.23455e6			−0.0890610			−0.0445305	−	0.999008i	$-0.514179\pi$
$719$	−1.23455e6			−0.0890610			−0.0445305	+	0.999008i	$0.514179\pi$
$720$	−3.88103e6	+	3.11284e6i	−0.279007	+	0.223782i
$721$	−4.77358e6			−0.341984
$722$	−2.97457e7	+	2.85508e6i	−2.12364	+	0.203834i
$723$	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	−0.109274	+	0.994012i	$0.534853\pi$
$727$	−1.57226e7	+	1.57226e7i	−1.10329	+	1.10329i	−0.994012	+	0.109274i	$0.965147\pi$
$728$	−8.18546e6	+	2.41655e6i	−0.572420	+	0.168992i
$729$			1.51534e7i			1.05606i
$730$	−1.12449e7	−	4.70751e6i	−0.780993	−	0.326952i
$731$	−1.78858e6			−0.123798
$732$	4.35503e6	+	2.94135e6i	0.300409	+	0.202894i
$733$	7.49288e6	+	7.49288e6i	0.515097	+	0.515097i	0.916084	−	0.400987i	$-0.131333\pi$
$733$	7.49288e6	+	7.49288e6i	0.515097	+	0.515097i	−0.400987	+	0.916084i	$0.631333\pi$
$734$	−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
$738$	297413.	+	3.09860e6i	0.0201010	+	0.209423i
$739$		−	468516.i		−	0.0315583i	−0.999876	−	0.0157791i	$-0.994977\pi$
$739$		−	468516.i		−	0.0315583i	0.999876	−	0.0157791i	$-0.00502287\pi$
$740$	1.43811e7	+	4.46085e6i	0.965409	+	0.299460i
$741$			2.40210e7i			1.60711i
$742$	−1.41710e7	+	1.36018e6i	−0.944913	+	0.0906956i
$743$	−9.11716e6	−	9.11716e6i	−0.605881	−	0.605881i	0.335986	−	0.941867i	$-0.390931\pi$
$743$	−9.11716e6	−	9.11716e6i	−0.605881	−	0.605881i	−0.941867	+	0.335986i	$0.890931\pi$
$744$	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
$748$	−4.00127e6	−	2.70242e6i	−0.261483	−	0.176603i
$749$	2.62881e6			0.171220
$750$	1.21240e7	−	2.33184e6i	0.787034	−	0.151372i
$751$			5.22559e6i			0.338093i	0.985608	+	0.169046i	$0.0540687\pi$
$751$			5.22559e6i			0.338093i	−0.985608	+	0.169046i	$0.945931\pi$
$752$	−6.97123e6	+	1.63679e7i	−0.449536	+	1.05548i
$753$	−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	0.156242	−	0.987719i	$-0.450062\pi$
$757$	1.80364e7	−	1.80364e7i	1.14396	−	1.14396i	0.987719	−	0.156242i	$-0.0499381\pi$
$758$	−968050.	−	1.00856e7i	−0.0611962	−	0.637574i
$759$	−1.67203e6			−0.105351
$760$	2.35722e7	−	1.54542e7i	1.48036	−	0.970538i
$761$	−1.48328e7			−0.928455			−0.464227	−	0.885716i	$-0.653668\pi$
$761$	−1.48328e7			−0.928455			−0.464227	+	0.885716i	$0.653668\pi$
$762$	−216096.	−	2.25139e6i	−0.0134821	−	0.140464i
$763$	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
$768$	−260409.	+	1.30978e7i	−0.0159314	+	0.801300i
$769$			1.13642e7i			0.692982i	0.938053	+	0.346491i	$0.112627\pi$
$769$			1.13642e7i			0.692982i	−0.938053	+	0.346491i	$0.887373\pi$
$770$	−2.64825e6	−	1.10866e6i	−0.160965	−	0.0673860i
$771$	−1.12056e7			−0.678887
$772$	−6.78511e6	+	1.00462e7i	−0.409745	+	0.606678i
$773$	−1.28867e7	−	1.28867e7i	−0.775698	−	0.775698i	0.203398	−	0.979096i	$-0.434801\pi$
$773$	−1.28867e7	−	1.28867e7i	−0.775698	−	0.775698i	−0.979096	+	0.203398i	$0.934801\pi$
$774$	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
$778$	1.38145e7	−	1.32596e6i	0.818253	−	0.0785384i
$779$		−	1.76357e7i		−	1.04123i
$780$	−7.18687e6	−	1.36504e7i	−0.422964	−	0.803355i
$781$		−	5.07729e6i		−	0.297855i
$782$	−617783.	−	6.43638e6i	−0.0361259	−	0.376378i
$783$	−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	0.225910	−	0.974148i	$-0.427465\pi$
$787$	−1.30010e7	−	1.30010e7i	−0.748239	−	0.748239i	−0.974148	+	0.225910i	$0.927465\pi$
$788$	−4.70579e6	+	6.96750e6i	−0.269971	+	0.399725i
$789$	1.31467e7			0.751836
$790$	−7.21529e6	−	1.76067e7i	−0.411326	−	1.00371i
$791$			1.37852e7i			0.783379i
$792$	592091.	+	2.00556e6i	0.0335409	+	0.113612i
$793$	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	$-0.623582\pi$
$797$	9.80941e6	−	9.80941e6i	0.547012	−	0.547012i	0.925575	+	0.378563i	$0.123582\pi$
$798$	−1.33847e7	+	1.28471e6i	−0.744051	+	0.0714162i
$799$	1.97227e7			1.09295
$800$	−8.77158e6	+	1.58348e7i	−0.484566	+	0.874755i
$801$	8.90536e6			0.490422
$802$	1.85379e7	−	1.77932e6i	1.01771	−	0.0976831i
$803$	−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
$808$	−254244.	−	861189.i	−0.0137001	−	0.0464056i
$809$		−	8.76581e6i		−	0.470891i	−0.971888	−	0.235446i	$-0.924345\pi$
$809$		−	8.76581e6i		−	0.470891i	0.971888	−	0.235446i	$-0.0756550\pi$
$810$	3.64242e6	+	8.88820e6i	0.195064	+	0.475994i
$811$	−1.75325e7			−0.936036			−0.468018	−	0.883719i	$-0.655032\pi$
$811$	−1.75325e7			−0.936036			−0.468018	+	0.883719i	$0.655032\pi$
$812$	−2.55888e6	+	3.78873e6i	−0.136194	+	0.201653i
$813$	−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
$818$	843389.	+	8.78685e6i	0.0440701	+	0.459145i
$819$		−	4.09775e6i		−	0.213470i
$820$	5.27645e6	+	1.00218e7i	0.274036	+	0.520489i
$821$			7.22018e6i			0.373844i	0.982375	+	0.186922i	$0.0598512\pi$
$821$			7.22018e6i			0.373844i	−0.982375	+	0.186922i	$0.940149\pi$
$822$	3.34093e6	−	320673.i	0.172460	−	0.0165532i
$823$	−2.02345e7	−	2.02345e7i	−1.04134	−	1.04134i	−0.999108	−	0.0422319i	$-0.986553\pi$
$823$	−2.02345e7	−	2.02345e7i	−1.04134	−	1.04134i	−0.0422319	−	0.999108i	$-0.513447\pi$
$824$	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	0.837192	−	0.546909i	$-0.184196\pi$
$827$	5.70933e6	+	5.70933e6i	0.290283	+	0.290283i	−0.546909	+	0.837192i	$0.684196\pi$
$828$	−1.56735e6	+	2.32065e6i	−0.0794493	+	0.117634i
$829$	2.23001e7			1.12699			0.563496	−	0.826119i	$-0.309456\pi$
$829$	2.23001e7			1.12699			0.563496	+	0.826119i	$0.309456\pi$
$830$	−1.74542e7	−	7.30698e6i	−0.879439	−	0.368165i
$831$		−	7.61081e6i		−	0.382321i
$832$	2.21157e7	+	4.74290e6i	1.10762	+	0.237540i
$833$	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
$838$	−1.25897e6	−	1.31166e7i	−0.0619307	−	0.645225i
$839$	−3.22117e7			−1.57982			−0.789912	−	0.613221i	$-0.789874\pi$
$839$	−3.22117e7			−1.57982			−0.789912	+	0.613221i	$0.789874\pi$
$840$	7.22175e6	−	4.73466e6i	0.353138	−	0.231521i
$841$	−1.61360e7			−0.786693
$842$	1.30627e6	+	1.36094e7i	0.0634970	+	0.661544i
$843$	−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
$848$	3.47112e7	+	1.47838e7i	1.65760	+	0.705985i
$849$		−	1.57132e7i		−	0.748163i
$850$	1.99610e7	+	2.06789e6i	0.947621	+	0.0981703i
$851$	8.47513e6			0.401165
$852$	1.26557e7	+	8.54756e6i	0.597293	+	0.403407i
$853$	−2.37704e6	−	2.37704e6i	−0.111857	−	0.111857i	0.648963	−	0.760820i	$-0.275203\pi$
$853$	−2.37704e6	−	2.37704e6i	−0.111857	−	0.111857i	−0.760820	+	0.648963i	$0.775203\pi$
$854$	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	0.951471	−	0.307738i	$-0.0995721\pi$
$857$	1.38407e7	+	1.38407e7i	0.643733	+	0.643733i	−0.307738	+	0.951471i	$0.599572\pi$
$858$	−6.45443e6	+	619516.i	−0.299323	+	0.0287299i
$859$			1.48385e7i			0.686129i	0.939312	+	0.343064i	$0.111465\pi$
$859$			1.48385e7i			0.686129i	−0.939312	+	0.343064i	$0.888535\pi$
$860$	2.69190e6	+	834999.i	0.124112	+	0.0384981i
$861$		−	5.40299e6i		−	0.248386i
$862$	3.45346e6	+	3.59799e7i	0.158302	+	1.64927i
$863$	1.53835e7	+	1.53835e7i	0.703116	+	0.703116i	0.965078	−	0.261962i	$-0.0843696\pi$
$863$	1.53835e7	+	1.53835e7i	0.703116	+	0.703116i	−0.261962	+	0.965078i	$0.584370\pi$
$864$	−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
$868$	8.29618e6	+	5.60316e6i	0.373748	+	0.252426i
$869$	−7.99767e6			−0.359264
$870$	−7.62282e6	−	3.19119e6i	−0.341442	−	0.142940i
$871$			3.21694e7i			1.43681i
$872$	−4.00734e7	+	1.18306e7i	−1.78470	+	0.526886i
$873$	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	$-0.816792\pi$
$877$	−6.70962e6	+	6.70962e6i	−0.294577	+	0.294577i	0.544308	+	0.838885i	$0.316792\pi$
$878$	25576.8	−	2454.94i	0.00111972	−	0.000107474i
$879$	2.34592e7			1.02410
$880$	4.76049e6	+	5.93528e6i	0.207226	+	0.258366i
$881$	4.84600e6			0.210351			0.105175	−	0.994454i	$-0.466460\pi$
$881$	4.84600e6			0.210351			0.105175	+	0.994454i	$0.466460\pi$
$882$	−5.94206e6	+	570336.i	−0.257197	+	0.0246865i
$883$	−2.65671e7	+	2.65671e7i	−1.14668	+	1.14668i	−0.159479	+	0.987201i	$0.550981\pi$
$883$	−2.65671e7	+	2.65671e7i	−1.14668	+	1.14668i	−0.987201	+	0.159479i	$0.949019\pi$
$884$	−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	$-0.638913\pi$
$887$	1.13315e7	−	1.13315e7i	0.483590	−	0.483590i	0.906276	+	0.422686i	$0.138913\pi$
$888$	5.38988e6	+	1.82569e7i	0.229375	+	0.776953i
$889$		−	2.18592e6i		−	0.0927639i
$890$	2.99819e7	−	1.22867e7i	1.26878	−	0.519950i
$891$	4.03738e6			0.170375
$892$	−3.50076e7	−	2.36438e7i	−1.47316	−	0.994959i
$893$	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
$898$	3.33172e6	+	3.47116e7i	0.137872	+	1.43643i
$899$		−	9.58031e6i		−	0.395349i
$900$	−6.09913e6	−	6.19179e6i	−0.250993	−	0.254806i
$901$		−	4.18257e7i		−	1.71645i
$902$	4.73871e6	−	454835.i	0.193929	−	0.0186139i
$903$	−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	0.987584	−	0.157093i	$-0.0502121\pi$
$907$	2.05756e7	+	2.05756e7i	0.830491	+	0.830491i	−0.157093	+	0.987584i	$0.550212\pi$
$908$	−3.16124e7	−	2.13508e7i	−1.27246	−	0.859407i
$909$	431123.			0.0173058
$910$	−5.65367e6	−	1.37960e7i	−0.226322	−	0.552269i
$911$		−	1.96863e7i		−	0.785901i	−0.919560	−	0.392951i	$-0.871454\pi$
$911$		−	1.96863e7i		−	0.785901i	0.919560	−	0.392951i	$-0.128546\pi$
$912$	3.27852e7	+	1.39635e7i	1.30524	+	0.555912i
$913$	−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
$918$	2.52893e6	+	2.63476e7i	0.0990443	+	1.03189i
$919$	−684770.			−0.0267458			−0.0133729	−	0.999911i	$-0.504257\pi$
$919$	−684770.			−0.0267458			−0.0133729	+	0.999911i	$0.504257\pi$
$920$	−2.07503e6	+	9.97549e6i	−0.0808268	+	0.388566i
$921$	−2.04558e7			−0.794633
$922$	−1.07604e6	−	1.12108e7i	−0.0416872	−	0.434319i
$923$	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
$928$	1.07558e7	−	5.57842e6i	0.409991	−	0.212638i
$929$		−	2.13324e7i		−	0.810963i	−0.914103	−	0.405482i	$-0.867104\pi$
$929$		−	2.13324e7i		−	0.810963i	0.914103	−	0.405482i	$-0.132896\pi$
$930$	−6.98774e6	+	1.66917e7i	−0.264929	+	0.632837i
$931$	3.38192e7			1.27876
$932$	2.99214e6	−	4.43024e6i	0.112835	−	0.167066i
$933$	−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	0.995502	−	0.0947402i	$-0.0302020\pi$
$937$	2.42080e7	+	2.42080e7i	0.900762	+	0.900762i	−0.0947402	+	0.995502i	$0.530202\pi$
$938$	−1.79251e7	+	1.72051e6i	−0.665205	+	0.0638484i
$939$			3.60327e7i			1.33362i
$940$	−2.96838e7	−	9.20759e6i	−1.09572	−	0.339880i
$941$		−	6.58378e6i		−	0.242382i	−0.992629	−	0.121191i	$-0.961329\pi$
$941$		−	6.58378e6i		−	0.242382i	0.992629	−	0.121191i	$-0.0386714\pi$
$942$	−3.23982e6	−	3.37541e7i	−0.118958	−	1.23937i
$943$	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	0.575475	−	0.817820i	$-0.304817\pi$
$947$	−6.68820e6	−	6.68820e6i	−0.242345	−	0.242345i	−0.817820	+	0.575475i	$0.804817\pi$
$948$	1.34640e7	−	1.99351e7i	0.486578	−	0.720439i
$949$	−2.66094e7			−0.959111
$950$	3.10447e7	+	3.82203e7i	1.11604	+	1.37400i
$951$			1.82285e7i			0.653583i
$952$	1.34618e7	−	3.97426e6i	0.481406	−	0.142123i
$953$	−1.60762e7	+	1.60762e7i	−0.573392	+	0.573392i	−0.933075	−	0.359683i	$-0.882885\pi$
$953$	−1.60762e7	+	1.60762e7i	−0.573392	+	0.573392i	0.359683	+	0.933075i	$0.382885\pi$
$954$	−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
$958$	−3.34888e7	+	3.21435e6i	−1.17892	+	0.113157i
$959$	3.24377e6			0.113895
$960$	−2.28086e7	+	1.87407e6i	−0.798767	+	0.0656308i
$961$	7.65119e6			0.267252
$962$	3.27161e7	−	3.14019e6i	1.13979	−	0.109400i
$963$	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	$-0.858164\pi$
$967$	−1.37064e7	+	1.37064e7i	−0.471366	+	0.471366i	0.430990	+	0.902357i	$0.358164\pi$
$968$	−2.48932e7	+	7.34908e6i	−0.853871	+	0.252083i
$969$		−	3.95050e7i		−	1.35158i
$970$	1.63170e7	−	3.89765e7i	0.556815	−	1.33007i
$971$	5.44433e7			1.85309			0.926544	−	0.376186i	$-0.122765\pi$
$971$	5.44433e7			1.85309			0.926544	+	0.376186i	$0.122765\pi$
$972$	1.11418e7	−	1.64968e7i	0.378260	−	0.560060i
$973$	−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	0.548902	−	0.835887i	$-0.315046\pi$
$977$	−8.56239e6	−	8.56239e6i	−0.286985	−	0.286985i	−0.835887	+	0.548902i	$0.815046\pi$
$978$	−478865.	−	4.98906e6i	−0.0160091	−	0.166791i
$979$		−	1.36190e7i		−	0.454139i
$980$	−1.92184e7	+	1.01184e7i	−0.639223	+	0.336549i
$981$		−	2.00613e7i		−	0.665558i
$982$	−7.46992e6	+	716985.i	−0.247193	+	0.0237264i
$983$	4.58761e6	+	4.58761e6i	0.151427	+	0.151427i	0.778755	−	0.627328i	$-0.215852\pi$
$983$	4.58761e6	+	4.58761e6i	0.151427	+	0.151427i	−0.627328	+	0.778755i	$0.715852\pi$
$984$	−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
$988$	3.44356e7	−	5.09862e7i	1.12232	−	1.66173i
$989$	1.58641e6			0.0515732
$990$	−3.38024e6	+	1.38524e6i	−0.109612	+	0.0449196i
$991$		−	2.17107e7i		−	0.702246i	−0.936329	−	0.351123i	$-0.885800\pi$
$991$		−	2.17107e7i		−	0.702246i	0.936329	−	0.351123i	$-0.114200\pi$
$992$	−1.22150e7	−	2.35520e7i	−0.394108	−	0.759886i
$993$	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	$-0.860826\pi$
$997$	−1.51438e7	+	1.51438e7i	−0.482498	+	0.482498i	0.423430	+	0.905929i	$0.360826\pi$
$998$	−4.66850e6	−	4.86389e7i	−0.148372	−	1.54581i
$999$	−3.46934e7			−1.09985

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.14	✓	56	5.3	odd	4	inner
40.6.k.a.3.28	yes	56	40.3	even	4	inner
40.6.k.a.27.14	yes	56	8.3	odd	2	inner
40.6.k.a.27.28	yes	56	1.1	even	1	trivial
160.6.o.a.47.21		56	4.3	odd	2
160.6.o.a.47.22		56	8.5	even	2
160.6.o.a.143.21		56	40.13	odd	4
160.6.o.a.143.22		56	20.3	even	4

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)

\(f(q)\)	\(=\)	\(q+(5.63098 - 0.540478i) q^{2} +(-8.83424 + 8.83424i) q^{3} +(31.4158 - 6.08684i) q^{4} +(16.1587 + 53.5154i) q^{5} +(-44.9707 + 54.5201i) q^{6} +(-48.2986 + 48.2986i) q^{7} +(173.612 - 51.2543i) q^{8} +86.9124i q^{9} +O(q^{10})\)	\(q+(5.63098 - 0.540478i) 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} +(173.612 - 51.2543i) q^{8} +86.9124i q^{9} +(119.913 + 292.610i) q^{10} +132.916 q^{11} +(-223.762 + 331.307i) 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} +(46.9742 + 489.401i) q^{18} -2785.43i q^{19} +(833.377 + 1582.87i) q^{20} -853.364i q^{21} +(748.445 - 71.8379i) 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} +(-1223.35 + 1811.32i) q^{28} +2091.69 q^{29} +(-3644.33 - 1525.65i) q^{30} -4580.17i q^{31} +(5142.17 - 2666.94i) 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} +(-1505.46 - 15684.7i) q^{38} -8623.80 q^{39} +(5548.23 + 8462.69i) q^{40} +6331.41 q^{41} +(-461.224 - 4805.27i) 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} +(-5013.04 + 11770.3i) q^{48} +12141.5i q^{49} +(-13721.5 + 11145.4i) q^{50} +14182.7 q^{51} +(18304.6 + 12362.8i) 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} +(11778.3 - 1130.51i) q^{58} -35835.0i q^{59} +(-21345.7 - 6621.22i) q^{60} -13145.0i q^{61} +(-2475.48 - 25790.8i) 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} +(-30103.8 - 20331.9i) q^{68} -12579.6 q^{69} +(-19924.3 - 8341.05i) q^{70} -38199.3i q^{71} +(4454.64 + 15089.0i) 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} +(-48560.4 + 4660.97i) q^{78} -60171.0 q^{79} +(35815.9 + 44654.5i) q^{80} +30375.5 q^{81} +(35652.0 - 3421.98i) 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} +(23075.7 - 6812.50i) q^{88} -102464. i q^{89} +(-25431.5 + 10421.9i) q^{90} -47148.1 q^{91} +(26701.1 + 18033.7i) 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} +(6562.20 + 68368.4i) 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

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