LMFDB - Embedded newform 9.6.c.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,6,Mod(4,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("9.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	9.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.44345437832$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 40x^{6} + 568x^{4} + 3363x^{2} + 7056 $ x^8 + 40x^6 + 568x^4 + 3363*x^2 + 7056
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.3
Root			$-3.84183i$ of defining polynomial
Character	$\chi$	$=$	9.4
Dual form			9.6.c.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78978 + 3.09998i) q^{2} +(1.34189 + 15.5306i) q^{3} +(9.59340 - 16.6162i) q^{4} +(4.05388 - 7.02152i) q^{5} +(-45.7429 + 31.9561i) q^{6} +(-87.7139 - 151.925i) q^{7} +183.226 q^{8} +(-239.399 + 41.6808i) q^{9} +O(q^{10})$	\(q+(1.78978 + 3.09998i) q^{2} +(1.34189 + 15.5306i) q^{3} +(9.59340 - 16.6162i) q^{4} +(4.05388 - 7.02152i) q^{5} +(-45.7429 + 31.9561i) q^{6} +(-87.7139 - 151.925i) q^{7} +183.226 q^{8} +(-239.399 + 41.6808i) q^{9} +29.0221 q^{10} +(206.795 + 358.179i) q^{11} +(270.934 + 126.694i) q^{12} +(-61.8514 + 107.130i) q^{13} +(313.977 - 543.824i) q^{14} +(114.488 + 53.5370i) q^{15} +(20.9448 + 36.2775i) q^{16} -2223.70 q^{17} +(-557.680 - 667.533i) q^{18} +891.313 q^{19} +(-77.7809 - 134.720i) q^{20} +(2241.78 - 1566.12i) q^{21} +(-740.234 + 1282.12i) q^{22} +(293.902 - 509.053i) q^{23} +(245.869 + 2845.61i) q^{24} +(1529.63 + 2649.40i) q^{25} -442.801 q^{26} +(-968.574 - 3662.07i) q^{27} -3365.90 q^{28} +(2467.97 + 4274.65i) q^{29} +(38.9446 + 450.731i) q^{30} +(2832.69 - 4906.37i) q^{31} +(2856.64 - 4947.85i) q^{32} +(-5285.24 + 3692.29i) q^{33} +(-3979.93 - 6893.45i) q^{34} -1422.33 q^{35} +(-1604.07 + 4377.77i) q^{36} +1204.25 q^{37} +(1595.25 + 2763.06i) q^{38} +(-1746.79 - 816.832i) q^{39} +(742.775 - 1286.52i) q^{40} +(-1194.48 + 2068.90i) q^{41} +(8867.23 + 4146.49i) q^{42} +(2885.71 + 4998.19i) q^{43} +7935.46 q^{44} +(-677.830 + 1849.91i) q^{45} +2104.08 q^{46} +(-3532.81 - 6119.00i) q^{47} +(-535.306 + 373.966i) q^{48} +(-6983.97 + 12096.6i) q^{49} +(-5475.40 + 9483.67i) q^{50} +(-2983.97 - 34535.4i) q^{51} +(1186.73 + 2055.48i) q^{52} -11521.6 q^{53} +(9618.83 - 9556.86i) q^{54} +3353.28 q^{55} +(-16071.5 - 27836.6i) q^{56} +(1196.05 + 13842.6i) q^{57} +(-8834.24 + 15301.4i) q^{58} +(-4876.49 + 8446.33i) q^{59} +(1987.91 - 1388.76i) q^{60} +(932.881 + 1615.80i) q^{61} +20279.5 q^{62} +(27330.9 + 32714.6i) q^{63} +21791.5 q^{64} +(501.476 + 868.582i) q^{65} +(-20905.4 - 9775.80i) q^{66} +(19671.5 - 34072.0i) q^{67} +(-21332.9 + 36949.6i) q^{68} +(8300.28 + 3881.38i) q^{69} +(-2545.65 - 4409.19i) q^{70} +43602.4 q^{71} +(-43864.0 + 7637.00i) q^{72} -52142.6 q^{73} +(2155.33 + 3733.15i) q^{74} +(-39094.2 + 27311.3i) q^{75} +(8550.72 - 14810.3i) q^{76} +(36277.6 - 62834.6i) q^{77} +(-594.191 - 6876.96i) q^{78} +(-25384.2 - 43966.8i) q^{79} +339.631 q^{80} +(55574.4 - 19956.6i) q^{81} -8551.41 q^{82} +(27810.6 + 48169.3i) q^{83} +(-4516.67 - 52274.4i) q^{84} +(-9014.62 + 15613.8i) q^{85} +(-10329.5 + 17891.3i) q^{86} +(-63076.2 + 44065.2i) q^{87} +(37890.2 + 65627.7i) q^{88} -46554.3 q^{89} +(-6947.86 + 1209.67i) q^{90} +21700.9 q^{91} +(-5639.04 - 9767.10i) q^{92} +(79999.9 + 37409.6i) q^{93} +(12645.9 - 21903.3i) q^{94} +(3613.27 - 6258.38i) q^{95} +(80676.3 + 37725.9i) q^{96} +(21616.0 + 37440.1i) q^{97} -49999.0 q^{98} +(-64435.6 - 77128.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 12 * q^3 - 49 * q^4 + 78 * q^5 + 171 * q^6 + 28 * q^7 - 750 * q^8 - 414 * q^9	\( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9} + 60 q^{10} + 444 q^{11} + 2724 q^{12} - 182 q^{13} + 1392 q^{14} - 2052 q^{15} - 289 q^{16} - 4356 q^{17} - 8100 q^{18} + 952 q^{19} + 6684 q^{20} + 8670 q^{21} + 1011 q^{22} + 8844 q^{23} + 549 q^{24} - 1654 q^{25} - 24888 q^{26} - 10152 q^{27} - 1604 q^{28} + 12018 q^{29} + 22104 q^{30} + 1132 q^{31} + 8703 q^{32} - 8820 q^{33} + 10125 q^{34} - 16224 q^{35} - 14589 q^{36} - 15176 q^{37} - 11145 q^{38} + 8220 q^{39} - 8736 q^{40} + 1248 q^{41} + 10098 q^{42} - 6092 q^{43} + 49530 q^{44} + 43038 q^{45} + 45960 q^{46} - 60 q^{47} - 57405 q^{48} + 9090 q^{49} - 57057 q^{50} - 9396 q^{51} - 32510 q^{52} + 20952 q^{53} + 8181 q^{54} - 36120 q^{55} - 61170 q^{56} - 104298 q^{57} + 8328 q^{58} + 2076 q^{59} + 88308 q^{60} + 48142 q^{61} + 241764 q^{62} + 133524 q^{63} - 20926 q^{64} - 13146 q^{65} - 100998 q^{66} - 7148 q^{67} - 123129 q^{68} - 125982 q^{69} - 654 q^{70} - 71856 q^{71} + 35451 q^{72} + 122452 q^{73} - 160320 q^{74} - 18732 q^{75} - 49571 q^{76} + 39534 q^{77} + 181422 q^{78} - 59516 q^{79} + 124512 q^{80} + 194562 q^{81} - 233598 q^{82} + 117696 q^{83} + 108354 q^{84} + 28836 q^{85} - 15915 q^{86} - 142956 q^{87} + 104523 q^{88} - 451728 q^{89} - 539892 q^{90} + 111392 q^{91} + 134034 q^{92} + 113898 q^{93} + 169464 q^{94} + 294888 q^{95} + 42768 q^{96} + 33976 q^{97} + 57654 q^{98} + 33696 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 12 * q^3 - 49 * q^4 + 78 * q^5 + 171 * q^6 + 28 * q^7 - 750 * q^8 - 414 * q^9 + 60 * q^10 + 444 * q^11 + 2724 * q^12 - 182 * q^13 + 1392 * q^14 - 2052 * q^15 - 289 * q^16 - 4356 * q^17 - 8100 * q^18 + 952 * q^19 + 6684 * q^20 + 8670 * q^21 + 1011 * q^22 + 8844 * q^23 + 549 * q^24 - 1654 * q^25 - 24888 * q^26 - 10152 * q^27 - 1604 * q^28 + 12018 * q^29 + 22104 * q^30 + 1132 * q^31 + 8703 * q^32 - 8820 * q^33 + 10125 * q^34 - 16224 * q^35 - 14589 * q^36 - 15176 * q^37 - 11145 * q^38 + 8220 * q^39 - 8736 * q^40 + 1248 * q^41 + 10098 * q^42 - 6092 * q^43 + 49530 * q^44 + 43038 * q^45 + 45960 * q^46 - 60 * q^47 - 57405 * q^48 + 9090 * q^49 - 57057 * q^50 - 9396 * q^51 - 32510 * q^52 + 20952 * q^53 + 8181 * q^54 - 36120 * q^55 - 61170 * q^56 - 104298 * q^57 + 8328 * q^58 + 2076 * q^59 + 88308 * q^60 + 48142 * q^61 + 241764 * q^62 + 133524 * q^63 - 20926 * q^64 - 13146 * q^65 - 100998 * q^66 - 7148 * q^67 - 123129 * q^68 - 125982 * q^69 - 654 * q^70 - 71856 * q^71 + 35451 * q^72 + 122452 * q^73 - 160320 * q^74 - 18732 * q^75 - 49571 * q^76 + 39534 * q^77 + 181422 * q^78 - 59516 * q^79 + 124512 * q^80 + 194562 * q^81 - 233598 * q^82 + 117696 * q^83 + 108354 * q^84 + 28836 * q^85 - 15915 * q^86 - 142956 * q^87 + 104523 * q^88 - 451728 * q^89 - 539892 * q^90 + 111392 * q^91 + 134034 * q^92 + 113898 * q^93 + 169464 * q^94 + 294888 * q^95 + 42768 * q^96 + 33976 * q^97 + 57654 * q^98 + 33696 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.78978	+	3.09998i	0.316391	+	0.548005i	0.979732	−	0.200312i	$-0.0641956\pi$
$2$	1.78978	+	3.09998i	0.316391	+	0.548005i	−0.663341	+	0.748317i	$0.730862\pi$
$3$	1.34189	+	15.5306i	0.0860825	+	0.996288i
$3$	1.34189	+	15.5306i	0.0860825	+	0.996288i
$4$	9.59340	−	16.6162i	0.299794	−	0.519258i
$5$	4.05388	−	7.02152i	0.0725179	−	0.125605i	−0.827486	−	0.561486i	$-0.810230\pi$
$5$	4.05388	−	7.02152i	0.0725179	−	0.125605i	0.900004	+	0.435881i	$0.143563\pi$
$6$	−45.7429	+	31.9561i	−0.518735	+	0.362390i
$7$	−87.7139	−	151.925i	−0.676587	−	1.17188i	−0.976002	−	0.217760i	$-0.930125\pi$
$7$	−87.7139	−	151.925i	−0.676587	−	1.17188i	0.299416	−	0.954123i	$-0.403208\pi$
$8$	183.226			1.01219
$9$	−239.399	+	41.6808i	−0.985180	+	0.171526i
$10$	29.0221			0.0917761
$11$	206.795	+	358.179i	0.515298	+	0.892522i	0.999842	+	0.0177554i	$0.00565200\pi$
$11$	206.795	+	358.179i	0.515298	+	0.892522i	−0.484545	+	0.874767i	$0.661015\pi$
$12$	270.934	+	126.694i	0.543137	+	0.253982i
$13$	−61.8514	+	107.130i	−0.101506	+	0.175813i	−0.912305	−	0.409511i	$-0.865699\pi$
$13$	−61.8514	+	107.130i	−0.101506	+	0.175813i	0.810799	+	0.585324i	$0.199033\pi$
$14$	313.977	−	543.824i	0.428132	−	0.741546i
$15$	114.488	+	53.5370i	0.131381	+	0.0614364i
$16$	20.9448	+	36.2775i	0.0204539	+	0.0354273i
$17$	−2223.70			−1.86618			−0.933092	−	0.359638i	$-0.882900\pi$
$17$	−2223.70			−1.86618			−0.933092	+	0.359638i	$0.882900\pi$
$18$	−557.680	−	667.533i	−0.405699	−	0.485614i
$19$	891.313			0.566430			0.283215	−	0.959056i	$-0.408599\pi$
$19$	891.313			0.566430			0.283215	+	0.959056i	$0.408599\pi$
$20$	−77.7809	−	134.720i	−0.0434808	−	0.0753110i
$21$	2241.78	−	1566.12i	1.10929	−	0.774954i
$22$	−740.234	+	1282.12i	−0.326071	+	0.564772i
$23$	293.902	−	509.053i	0.115846	−	0.200652i	−0.802271	−	0.596960i	$-0.796375\pi$
$23$	293.902	−	509.053i	0.115846	−	0.200652i	0.918118	+	0.396308i	$0.129709\pi$
$24$	245.869	+	2845.61i	0.0871318	+	1.00843i
$25$	1529.63	+	2649.40i	0.489482	+	0.847808i
$26$	−442.801			−0.128462
$27$	−968.574	−	3662.07i	−0.255696	−	0.966757i
$28$	−3365.90			−0.811346
$29$	2467.97	+	4274.65i	0.544936	+	0.943856i	0.998611	+	0.0526894i	$0.0167793\pi$
$29$	2467.97	+	4274.65i	0.544936	+	0.943856i	−0.453675	+	0.891167i	$0.649887\pi$
$30$	38.9446	+	450.731i	0.00790031	+	0.0914354i
$31$	2832.69	−	4906.37i	0.529414	−	0.916971i	−0.469998	−	0.882668i	$-0.655745\pi$
$31$	2832.69	−	4906.37i	0.529414	−	0.916971i	0.999411	−	0.0343037i	$-0.0109213\pi$
$32$	2856.64	−	4947.85i	0.493152	−	0.854164i
$33$	−5285.24	+	3692.29i	−0.844851	+	0.590215i
$34$	−3979.93	−	6893.45i	−0.590444	−	1.02268i
$35$	−1422.33			−0.196259
$36$	−1604.07	+	4377.77i	−0.206284	+	0.562985i
$37$	1204.25			0.144614			0.0723071	−	0.997382i	$-0.476964\pi$
$37$	1204.25			0.144614			0.0723071	+	0.997382i	$0.476964\pi$
$38$	1595.25	+	2763.06i	0.179213	+	0.310407i
$39$	−1746.79	−	816.832i	−0.183899	−	0.0859947i
$40$	742.775	−	1286.52i	0.0734019	−	0.127136i
$41$	−1194.48	+	2068.90i	−0.110973	+	0.192212i	−0.916163	−	0.400806i	$-0.868730\pi$
$41$	−1194.48	+	2068.90i	−0.110973	+	0.192212i	0.805190	+	0.593018i	$0.202064\pi$
$42$	8867.23	+	4146.49i	0.775648	+	0.362708i
$43$	2885.71	+	4998.19i	0.238002	+	0.412232i	0.960141	−	0.279516i	$-0.0901741\pi$
$43$	2885.71	+	4998.19i	0.238002	+	0.412232i	−0.722139	+	0.691748i	$0.756841\pi$
$44$	7935.46			0.617932
$45$	−677.830	+	1849.91i	−0.0498987	+	0.136182i
$46$	2104.08			0.146611
$47$	−3532.81	−	6119.00i	−0.233279	−	0.404051i	0.725492	−	0.688230i	$-0.241612\pi$
$47$	−3532.81	−	6119.00i	−0.233279	−	0.404051i	−0.958771	+	0.284180i	$0.908279\pi$
$48$	−535.306	+	373.966i	−0.0335350	+	0.0234277i
$49$	−6983.97	+	12096.6i	−0.415539	+	0.719735i
$50$	−5475.40	+	9483.67i	−0.309735	+	0.536478i
$51$	−2983.97	−	34535.4i	−0.160646	−	1.85926i
$52$	1186.73	+	2055.48i	0.0608616	+	0.105415i
$53$	−11521.6			−0.563406			−0.281703	−	0.959502i	$-0.590899\pi$
$53$	−11521.6			−0.563406			−0.281703	+	0.959502i	$0.590899\pi$
$54$	9618.83	−	9556.86i	0.448888	−	0.445996i
$55$	3353.28			0.149473
$56$	−16071.5	−	27836.6i	−0.684834	−	1.18617i
$57$	1196.05	+	13842.6i	0.0487597	+	0.564328i
$58$	−8834.24	+	15301.4i	−0.344825	+	0.597255i
$59$	−4876.49	+	8446.33i	−0.182380	+	0.315892i	−0.942691	−	0.333668i	$-0.891713\pi$
$59$	−4876.49	+	8446.33i	−0.182380	+	0.315892i	0.760310	+	0.649560i	$0.225047\pi$
$60$	1987.91	−	1388.76i	0.0712885	−	0.0498024i
$61$	932.881	+	1615.80i	0.0320997	+	0.0555984i	0.881629	−	0.471943i	$-0.156447\pi$
$61$	932.881	+	1615.80i	0.0320997	+	0.0555984i	−0.849529	+	0.527542i	$0.823114\pi$
$62$	20279.5			0.670006
$63$	27330.9	+	32714.6i	0.867568	+	1.03846i
$64$	21791.5			0.665023
$65$	501.476	+	868.582i	0.0147220	+	0.0254992i
$66$	−20905.4	−	9775.80i	−0.590744	−	0.276244i
$67$	19671.5	−	34072.0i	0.535366	−	0.927281i	−0.463780	−	0.885950i	$-0.653507\pi$
$67$	19671.5	−	34072.0i	0.535366	−	0.927281i	0.999146	−	0.0413301i	$-0.0131595\pi$
$68$	−21332.9	+	36949.6i	−0.559470	+	0.969031i
$69$	8300.28	+	3881.38i	0.209880	+	0.0981439i
$70$	−2545.65	−	4409.19i	−0.0620945	−	0.107551i
$71$	43602.4			1.02651			0.513257	−	0.858235i	$-0.328439\pi$
$71$	43602.4			1.02651			0.513257	+	0.858235i	$0.328439\pi$
$72$	−43864.0	+	7637.00i	−0.997189	+	0.173617i
$73$	−52142.6			−1.14521			−0.572605	−	0.819831i	$-0.694067\pi$
$73$	−52142.6			−1.14521			−0.572605	+	0.819831i	$0.694067\pi$
$74$	2155.33	+	3733.15i	0.0457546	+	0.0792494i
$75$	−39094.2	+	27311.3i	−0.802525	+	0.560647i
$76$	8550.72	−	14810.3i	0.169812	−	0.294123i
$77$	36277.6	−	62834.6i	0.697287	−	1.20774i
$78$	−594.191	−	6876.96i	−0.0110583	−	0.127985i
$79$	−25384.2	−	43966.8i	−0.457611	−	0.792605i	0.541223	−	0.840879i	$-0.317961\pi$
$79$	−25384.2	−	43966.8i	−0.457611	−	0.792605i	−0.998834	+	0.0482737i	$0.984628\pi$
$80$	339.631			0.00593311
$81$	55574.4	−	19956.6i	0.941158	−	0.337968i
$82$	−8551.41			−0.140444
$83$	27810.6	+	48169.3i	0.443113	+	0.767494i	0.997919	−	0.0644858i	$-0.0205407\pi$
$83$	27810.6	+	48169.3i	0.443113	+	0.767494i	−0.554806	+	0.831980i	$0.687207\pi$
$84$	−4516.67	−	52274.4i	−0.0698426	−	0.808334i
$85$	−9014.62	+	15613.8i	−0.135332	+	0.234402i
$86$	−10329.5	+	17891.3i	−0.150604	+	0.260853i
$87$	−63076.2	+	44065.2i	−0.893443	+	0.624162i
$88$	37890.2	+	65627.7i	0.521579	+	0.903401i
$89$	−46554.3			−0.622996			−0.311498	−	0.950247i	$-0.600831\pi$
$89$	−46554.3			−0.622996			−0.311498	+	0.950247i	$0.600831\pi$
$90$	−6947.86	+	1209.67i	−0.0904159	+	0.0157420i
$91$	21700.9			0.274710
$92$	−5639.04	−	9767.10i	−0.0694601	−	0.120308i
$93$	79999.9	+	37409.6i	0.959141	+	0.448513i
$94$	12645.9	−	21903.3i	0.147615	−	0.255676i
$95$	3613.27	−	6258.38i	0.0410764	−	0.0711463i
$96$	80676.3	+	37725.9i	0.893445	+	0.417793i
$97$	21616.0	+	37440.1i	0.233264	+	0.404024i	0.958767	−	0.284195i	$-0.0917262\pi$
$97$	21616.0	+	37440.1i	0.233264	+	0.404024i	−0.725503	+	0.688219i	$0.758393\pi$
$98$	−49999.0			−0.525891
$99$	−64435.6	−	77128.3i	−0.660751	−	0.790908i
$100$	58697.5			0.586975
$101$	−37727.5	−	65345.9i	−0.368005	−	0.637404i	0.621248	−	0.783614i	$-0.286626\pi$
$101$	−37727.5	−	65345.9i	−0.368005	−	0.637404i	−0.989254	+	0.146210i	$0.953293\pi$
$102$	101719.	−	71061.0i	0.968055	−	0.676287i
$103$	−50758.5	+	87916.3i	−0.471428	+	0.816538i	−0.999466	−	0.0326834i	$-0.989595\pi$
$103$	−50758.5	+	87916.3i	−0.471428	+	0.816538i	0.528038	+	0.849221i	$0.322928\pi$
$104$	−11332.8	+	19629.0i	−0.102743	+	0.177956i
$105$	−1908.61	−	22089.6i	−0.0168944	−	0.195530i
$106$	−20621.0	−	35716.7i	−0.178257	−	0.308750i
$107$	−178800.			−1.50976			−0.754882	−	0.655860i	$-0.772306\pi$
$107$	−178800.			−1.50976			−0.754882	+	0.655860i	$0.772306\pi$
$108$	−70141.8	−	19037.6i	−0.578652	−	0.157056i
$109$	−37985.3			−0.306231			−0.153116	−	0.988208i	$-0.548931\pi$
$109$	−37985.3			−0.306231			−0.153116	+	0.988208i	$0.548931\pi$
$110$	6001.63	+	10395.1i	0.0472920	+	0.0819121i
$111$	1615.97	+	18702.7i	0.0124488	+	0.144077i
$112$	3674.31	−	6364.09i	0.0276777	−	0.0479392i
$113$	100834.	−	174650.i	0.742867	−	1.28668i	−0.208318	−	0.978061i	$-0.566799\pi$
$113$	100834.	−	174650.i	0.742867	−	1.28668i	0.951185	−	0.308622i	$-0.0998677\pi$
$114$	−40771.3	+	28482.9i	−0.293827	+	0.205269i
$115$	−2382.88	−	4127.28i	−0.0168019	−	0.0291017i
$116$	94705.0			0.653473
$117$	10341.9	−	28224.7i	0.0698450	−	0.190619i
$118$	−34911.3			−0.230814
$119$	195050.	+	337836.i	1.26264	+	2.18695i
$120$	20977.2	+	9809.36i	0.132983	+	0.0621853i
$121$	−5002.82	+	8665.14i	−0.0310636	+	0.0538037i
$122$	−3339.30	+	5783.83i	−0.0203121	+	0.0351816i
$123$	−33734.1	−	15774.7i	−0.201051	−	0.0940155i
$124$	−54350.3	−	94137.4i	−0.317430	−	0.549804i
$125$	50140.5			0.287021
$126$	−52498.6	+	143277.i	−0.294592	+	0.803992i
$127$	255248.			1.40428			0.702138	−	0.712041i	$-0.252229\pi$
$127$	255248.			1.40428			0.702138	+	0.712041i	$0.252229\pi$
$128$	−52410.6	−	90777.9i	−0.282745	−	0.489728i
$129$	−73752.6	+	51523.8i	−0.390214	+	0.272605i
$130$	−1795.06	+	3109.14i	−0.00931581	+	0.0161355i
$131$	−16914.0	+	29295.9i	−0.0861129	+	0.149152i	−0.905865	−	0.423567i	$-0.860778\pi$
$131$	−16914.0	+	29295.9i	−0.0861129	+	0.149152i	0.819752	+	0.572719i	$0.194111\pi$
$132$	10648.5	+	123242.i	0.0531931	+	0.615638i
$133$	−78180.6	−	135413.i	−0.383239	−	0.663790i
$134$	140830.			0.677539
$135$	−29639.8	−	8044.72i	−0.139972	−	0.0379906i
$136$	−407440.			−1.88893
$137$	−93918.5	−	162672.i	−0.427514	−	0.740475i	0.569138	−	0.822242i	$-0.307277\pi$
$137$	−93918.5	−	162672.i	−0.427514	−	0.740475i	−0.996651	+	0.0817669i	$0.973944\pi$
$138$	2823.44	+	32677.5i	0.0126206	+	0.146067i
$139$	169712.	−	293951.i	0.745035	−	1.29044i	−0.205144	−	0.978732i	$-0.565766\pi$
$139$	169712.	−	293951.i	0.745035	−	1.29044i	0.950178	−	0.311706i	$-0.100901\pi$
$140$	−13644.9	+	23633.7i	−0.0588371	+	0.101909i
$141$	90291.0	−	63077.6i	0.382470	−	0.267194i
$142$	78038.6	+	135167.i	0.324780	+	0.562535i
$143$	−51162.2			−0.209223
$144$	−6526.24	−	7811.79i	−0.0262275	−	0.0313938i
$145$	40019.4			0.158070
$146$	−93323.6	−	161641.i	−0.362334	−	0.627581i
$147$	−197239.	−	92232.8i	−0.752834	−	0.352040i
$148$	11552.8	−	20010.1i	0.0433544	−	0.0750921i
$149$	−193953.	+	335937.i	−0.715700	+	1.23963i	0.246988	+	0.969018i	$0.420559\pi$
$149$	−193953.	+	335937.i	−0.715700	+	1.23963i	−0.962689	+	0.270611i	$0.912774\pi$
$150$	−154634.	−	72310.2i	−0.561149	−	0.262404i
$151$	138084.	+	239168.i	0.492833	+	0.853611i	0.999966	−	0.00825649i	$-0.00262815\pi$
$151$	138084.	+	239168.i	0.492833	+	0.853611i	−0.507133	+	0.861868i	$0.669295\pi$
$152$	163312.			0.573335
$153$	532351.	−	92685.7i	1.83853	−	0.320099i
$154$	259715.			0.882461
$155$	−22966.8	−	39779.6i	−0.0767840	−	0.132994i
$156$	−30330.3	+	21188.9i	−0.0997850	+	0.0697101i
$157$	−256623.	+	444485.i	−0.830897	+	1.43916i	0.0664312	+	0.997791i	$0.478839\pi$
$157$	−256623.	+	444485.i	−0.830897	+	1.43916i	−0.897328	+	0.441364i	$0.854495\pi$
$158$	90864.2	−	157381.i	0.289568	−	0.501546i
$159$	−15460.7	−	178937.i	−0.0484994	−	0.561315i
$160$	−23160.9	−	40115.9i	−0.0715247	−	0.123884i
$161$	−103117.			−0.313521
$162$	161331.	+	136562.i	0.482982	+	0.408829i
$163$	−236294.			−0.696601			−0.348300	−	0.937383i	$-0.613241\pi$
$163$	−236294.			−0.696601			−0.348300	+	0.937383i	$0.613241\pi$
$164$	22918.2	+	39695.5i	0.0665383	+	0.115248i
$165$	4499.75	+	52078.5i	0.0128670	+	0.148918i
$166$	−99549.4	+	172425.i	−0.280394	+	0.485656i
$167$	−125015.	+	216533.i	−0.346875	+	0.600805i	−0.985693	−	0.168553i	$-0.946090\pi$
$167$	−125015.	+	216533.i	−0.346875	+	0.600805i	0.638818	+	0.769358i	$0.279424\pi$
$168$	410753.	−	286953.i	1.12281	−	0.784400i
$169$	177995.	+	308297.i	0.479393	+	0.830333i
$170$	−64536.6			−0.171271
$171$	−213379.	+	37150.6i	−0.558036	+	0.0971574i
$172$	110735.			0.285406
$173$	−255819.	−	443091.i	−0.649856	−	1.12558i	−0.983157	−	0.182763i	$-0.941496\pi$
$173$	−255819.	−	443091.i	−0.649856	−	1.12558i	0.333301	−	0.942820i	$-0.391837\pi$
$174$	−249494.	−	116668.i	−0.624722	−	0.292132i
$175$	268340.	−	464779.i	0.662354	−	1.14723i
$176$	−8662.58	+	15004.0i	−0.0210797	+	0.0365112i
$177$	−137720.	−	64400.7i	−0.330419	−	0.154510i
$178$	−83321.9	−	144318.i	−0.197110	−	0.341405i
$179$	254552.			0.593806			0.296903	−	0.954908i	$-0.404046\pi$
$179$	254552.			0.593806			0.296903	+	0.954908i	$0.404046\pi$
$180$	24235.9	+	29009.9i	0.0557542	+	0.0667368i
$181$	−42413.6			−0.0962296			−0.0481148	−	0.998842i	$-0.515321\pi$
$181$	−42413.6			−0.0962296			−0.0481148	+	0.998842i	$0.515321\pi$
$182$	38839.8	+	67272.5i	0.0869158	+	0.150543i
$183$	−23842.5	+	16656.4i	−0.0526288	+	0.0367666i
$184$	53850.4	−	93271.7i	0.117259	−	0.203098i
$185$	4881.87	−	8455.64i	0.0104871	−	0.0181642i
$186$	27213.0	+	314953.i	0.0576758	+	0.667519i
$187$	−459851.	−	796485.i	−0.961640	−	1.66561i
$188$	−135566.			−0.279742
$189$	−471403.	+	468365.i	−0.959926	+	0.953741i
$190$	25867.8			0.0519847
$191$	133628.	+	231451.i	0.265042	+	0.459067i	0.967575	−	0.252585i	$-0.0812808\pi$
$191$	133628.	+	231451.i	0.265042	+	0.459067i	−0.702532	+	0.711652i	$0.747947\pi$
$192$	29241.8	+	338435.i	0.0572468	+	0.662554i
$193$	−127808.	+	221370.i	−0.246982	+	0.427786i	−0.962687	−	0.270617i	$-0.912772\pi$
$193$	−127808.	+	221370.i	−0.246982	+	0.427786i	0.715705	+	0.698403i	$0.246106\pi$
$194$	−77375.8	+	134019.i	−0.147605	+	0.255659i
$195$	−12816.7	+	8953.76i	−0.0241373	+	0.0168624i
$196$	134000.	+	232095.i	0.249152	+	0.431544i
$197$	650944.			1.19503			0.597514	−	0.801859i	$-0.296155\pi$
$197$	650944.			1.19503			0.597514	+	0.801859i	$0.296155\pi$
$198$	123771.	−	337792.i	0.224366	−	0.612331i
$199$	395656.			0.708248			0.354124	−	0.935199i	$-0.384779\pi$
$199$	395656.			0.708248			0.354124	+	0.935199i	$0.384779\pi$
$200$	280268.	+	485439.i	0.495449	+	0.858143i
$201$	555556.	+	259789.i	0.969924	+	0.453556i
$202$	135047.	−	233909.i	0.232867	−	0.403338i
$203$	432951.	−	749893.i	0.737393	−	1.27720i
$204$	−602476.	−	281730.i	−1.01359	−	0.473977i
$205$	9684.54	+	16774.1i	0.0160951	+	0.0278776i
$206$	−363386.			−0.596622
$207$	−49142.0	+	134117.i	−0.0797126	+	0.217549i
$208$	−5181.87			−0.00830478
$209$	184319.	+	319250.i	0.291880	+	0.505551i
$210$	65061.3	−	45452.0i	0.101806	−	0.0711222i
$211$	−309289.	+	535705.i	−0.478254	+	0.828361i	−0.999689	−	0.0249304i	$-0.992064\pi$
$211$	−309289.	+	535705.i	−0.478254	+	0.828361i	0.521435	+	0.853291i	$0.325397\pi$
$212$	−110531.	+	191445.i	−0.168906	+	0.292553i
$213$	58509.8	+	677172.i	0.0883648	+	1.02270i
$214$	−320013.	−	554279.i	−0.477676	−	0.827359i
$215$	46793.2			0.0690378
$216$	−177468.	−	670986.i	−0.258813	−	0.978542i
$217$	−993866.			−1.43278
$218$	−67985.2	−	117754.i	−0.0968888	−	0.167816i
$219$	−69969.8	−	809805.i	−0.0985826	−	1.14096i
$220$	32169.4	−	55719.0i	0.0448112	−	0.0776152i
$221$	137539.	−	238225.i	0.189429	−	0.328100i
$222$	−55085.8	+	38483.1i	−0.0750165	+	0.0524068i
$223$	438618.	+	759708.i	0.590642	+	1.02302i	0.994146	+	0.108044i	$0.0344586\pi$
$223$	438618.	+	759708.i	0.590642	+	1.02302i	−0.403504	+	0.914978i	$0.632208\pi$
$224$	−1.00227e6			−1.33464
$225$	−476621.	−	570507.i	−0.627649	−	0.751285i
$226$	721881.			0.940145
$227$	−265882.	−	460521.i	−0.342471	−	0.593177i	0.642420	−	0.766353i	$-0.277931\pi$
$227$	−265882.	−	460521.i	−0.342471	−	0.593177i	−0.984891	+	0.173176i	$0.944597\pi$
$228$	241487.	+	112924.i	0.307649	+	0.143863i
$229$	571507.	−	989880.i	0.720167	−	1.24737i	−0.240766	−	0.970583i	$-0.577399\pi$
$229$	571507.	−	989880.i	0.720167	−	1.24737i	0.960933	−	0.276782i	$-0.0892681\pi$
$230$	8529.66	−	14773.8i	0.0106319	−	0.0184151i
$231$	1.02454e6	+	479095.i	1.26328	+	0.590734i
$232$	452196.	+	783227.i	0.551578	+	0.955362i
$233$	−818670.			−0.987913			−0.493957	−	0.869487i	$-0.664450\pi$
$233$	−818670.			−0.987913			−0.493957	+	0.869487i	$0.664450\pi$
$234$	106006.	−	18456.3i	0.126558	−	0.0220346i
$235$	−57286.2			−0.0676676
$236$	93564.2	+	162058.i	0.109353	+	0.189405i
$237$	648767.	−	453231.i	0.750271	−	0.524142i
$238$	−698191.	+	1.20930e6i	−0.798973	+	1.38386i
$239$	−94237.4	+	163224.i	−0.106716	+	0.184837i	−0.914438	−	0.404726i	$-0.867367\pi$
$239$	−94237.4	+	163224.i	−0.106716	+	0.184837i	0.807722	+	0.589563i	$0.200700\pi$
$240$	455.749	+	5274.67i	0.000510737	+	0.00591109i
$241$	−22511.4	−	38990.8i	−0.0249666	−	0.0432434i	0.853272	−	0.521466i	$-0.174615\pi$
$241$	−22511.4	−	38990.8i	−0.0249666	−	0.0432434i	−0.878239	+	0.478222i	$0.841281\pi$
$242$	−35815.7			−0.0393129
$243$	384513.	+	836324.i	0.417730	+	0.908571i
$244$	35798.0			0.0384932
$245$	56624.3	+	98076.1i	0.0602681	+	0.104387i
$246$	−11475.1	−	132808.i	−0.0120898	−	0.139923i
$247$	−55129.0	+	95486.2i	−0.0574960	+	0.0995860i
$248$	519022.	−	898973.i	0.535867	−	0.928149i
$249$	−710779.	+	496552.i	−0.726501	+	0.507536i
$250$	89740.3	+	155435.i	0.0908108	+	0.157289i
$251$	−556667.			−0.557713			−0.278857	−	0.960333i	$-0.589955\pi$
$251$	−556667.			−0.557713			−0.278857	+	0.960333i	$0.589955\pi$
$252$	805791.	−	140293.i	0.799321	−	0.139167i
$253$	243110.			0.238782
$254$	456837.	+	791264.i	0.444300	+	0.769551i
$255$	−254588.	−	119050.i	−0.245181	−	0.114652i
$256$	536270.	−	928847.i	0.511427	−	0.885818i
$257$	−290077.	+	502428.i	−0.273956	+	0.474505i	−0.969871	−	0.243618i	$-0.921666\pi$
$257$	−290077.	+	502428.i	−0.273956	+	0.474505i	0.695915	+	0.718124i	$0.254999\pi$
$258$	−291724.	−	136416.i	−0.272849	−	0.127590i
$259$	−105629.	−	182955.i	−0.0978441	−	0.169471i
$260$	19243.4			0.0176542
$261$	−769000.	−	920479.i	−0.698755	−	0.836398i
$262$	−121089.			−0.108981
$263$	−30271.7	−	52432.1i	−0.0269865	−	0.0467420i	0.852217	−	0.523189i	$-0.175258\pi$
$263$	−30271.7	−	52432.1i	−0.0269865	−	0.0467420i	−0.879203	+	0.476447i	$0.841924\pi$
$264$	−968393.	+	676523.i	−0.855149	+	0.597410i
$265$	−46707.0	+	80898.9i	−0.0408571	+	0.0707665i
$266$	279852.	−	484717.i	0.242507	−	0.420034i
$267$	−62470.9	−	723017.i	−0.0536290	−	0.620683i
$268$	−377433.	−	653733.i	−0.320998	−	0.555986i
$269$	2.17306e6			1.83101			0.915507	−	0.402301i	$-0.131789\pi$
$269$	2.17306e6			1.83101			0.915507	+	0.402301i	$0.131789\pi$
$270$	−28110.1	−	106281.i	−0.0234668	−	0.0887252i
$271$	−1.72652e6			−1.42806			−0.714032	−	0.700113i	$-0.753133\pi$
$271$	−1.72652e6			−1.42806			−0.714032	+	0.700113i	$0.753133\pi$
$272$	−46575.1	−	80670.4i	−0.0381708	−	0.0661138i
$273$	29120.3	+	337028.i	0.0236477	+	0.273690i
$274$	336186.	−	582292.i	0.270523	−	0.468559i
$275$	−632640.	+	1.09577e6i	−0.504458	+	0.873747i
$276$	144122.	−	100684.i	0.113883	−	0.0795587i
$277$	−523243.	−	906283.i	−0.409736	−	0.709683i	0.585124	−	0.810944i	$-0.301046\pi$
$277$	−523243.	−	906283.i	−0.409736	−	0.709683i	−0.994860	+	0.101260i	$0.967712\pi$
$278$	1.21499e6			0.942889
$279$	−473641.	+	1.29265e6i	−0.364283	+	0.994189i
$280$	−260607.			−0.198651
$281$	−673149.	−	1.16593e6i	−0.508564	−	0.880858i	−0.999951	−	0.00991669i	$-0.996843\pi$
$281$	−673149.	−	1.16593e6i	−0.508564	−	0.880858i	0.491387	−	0.870941i	$-0.336490\pi$
$282$	357140.	+	167006.i	0.267434	+	0.125057i
$283$	−284960.	+	493565.i	−0.211503	+	0.366335i	−0.952185	−	0.305521i	$-0.901169\pi$
$283$	−284960.	+	493565.i	−0.211503	+	0.366335i	0.740682	+	0.671856i	$0.234503\pi$
$284$	418295.	−	724509.i	0.307742	−	0.533025i
$285$	102045.	+	47718.2i	0.0744182	+	0.0347994i
$286$	−91569.0	−	158602.i	−0.0661963	−	0.114655i
$287$	419090.			0.300333
$288$	−477646.	+	1.30358e6i	−0.339332	+	0.926093i
$289$	3.52500e6			2.48264
$290$	71625.8	+	124060.i	0.0500121	+	0.0866234i
$291$	−552460.	+	385951.i	−0.382445	+	0.267177i
$292$	−500225.	+	866414.i	−0.343327	+	0.594660i
$293$	−1.22915e6	+	2.12896e6i	−0.836444	+	1.44876i	0.0564045	+	0.998408i	$0.482036\pi$
$293$	−1.22915e6	+	2.12896e6i	−0.836444	+	1.44876i	−0.892849	+	0.450356i	$0.851297\pi$
$294$	−67093.3	−	776514.i	−0.0452700	−	0.523939i
$295$	39537.4	+	68480.8i	0.0264517	+	0.0458156i
$296$	220649.			0.146377
$297$	1.11138e6	−	1.10422e6i	0.731093	−	0.726382i
$298$	−1.38853e6			−0.905764
$299$	36356.5	+	62971.3i	0.0235182	+	0.0407347i
$300$	78765.7	+	911606.i	0.0505282	+	0.584796i
$301$	506234.	−	876822.i	0.322058	−	0.557822i
$302$	−494277.	+	856114.i	−0.311855	+	0.540150i
$303$	964234.	−	673617.i	0.603359	−	0.421509i
$304$	18668.4	+	32334.6i	0.0115857	+	0.0200671i
$305$	15127.1			0.00931123
$306$	1.24011e6	+	1.48439e6i	0.757109	+	0.906245i
$307$	1.25805e6			0.761819			0.380910	−	0.924612i	$-0.375611\pi$
$307$	1.25805e6			0.761819			0.380910	+	0.924612i	$0.375611\pi$
$308$	−696051.	−	1.20560e6i	−0.418085	−	0.724144i
$309$	−1.43350e6	−	670335.i	−0.854088	−	0.399389i
$310$	82210.8	−	142393.i	0.0485875	−	0.0841560i
$311$	1.02249e6	−	1.77101e6i	0.599457	−	1.03829i	−0.393444	−	0.919349i	$-0.628716\pi$
$311$	1.02249e6	−	1.77101e6i	0.599457	−	1.03829i	0.992901	−	0.118942i	$-0.0379503\pi$
$312$	−320057.	−	149665.i	−0.186140	−	0.0870429i
$313$	473219.	+	819640.i	0.273025	+	0.472892i	0.969635	−	0.244557i	$-0.0786426\pi$
$313$	473219.	+	819640.i	0.273025	+	0.472892i	−0.696610	+	0.717450i	$0.745309\pi$
$314$	−1.83719e6			−1.05155
$315$	340503.	−	59283.6i	0.193350	−	0.0336634i
$316$	−974084.			−0.548755
$317$	−197117.	−	341417.i	−0.110173	−	0.190826i	0.805667	−	0.592369i	$-0.201807\pi$
$317$	−197117.	−	341417.i	−0.110173	−	0.190826i	−0.915840	+	0.401543i	$0.868474\pi$
$318$	527030.	−	368185.i	0.292259	−	0.204173i
$319$	−1.02073e6	+	1.76795e6i	−0.561608	+	0.972734i
$320$	88339.9	−	153009.i	0.0482261	−	0.0835301i
$321$	−239931.	−	2.77688e6i	−0.129964	−	1.50416i
$322$	−184557.	−	319662.i	−0.0991951	−	0.171811i
$323$	−1.98202e6			−1.05706
$324$	201543.	−	1.11489e6i	0.106661	−	0.590024i
$325$	−378440.			−0.198741
$326$	−422914.	−	732508.i	−0.220398	−	0.381741i
$327$	−50972.2	−	589934.i	−0.0263611	−	0.305095i
$328$	−218860.	+	379076.i	−0.112326	+	0.194555i
$329$	−619752.	+	1.07344e6i	−0.315667	+	0.546750i
$330$	−153389.	+	107158.i	−0.0775371	+	0.0541677i
$331$	1.36828e6	+	2.36992e6i	0.686442	+	1.18895i	0.972981	+	0.230884i	$0.0741617\pi$
$331$	1.36828e6	+	2.36992e6i	0.686442	+	1.18895i	−0.286539	+	0.958068i	$0.592505\pi$
$332$	1.06719e6			0.531370
$333$	−288295.	+	50193.9i	−0.142471	+	0.0248051i
$334$	−894999.			−0.438992
$335$	−159492.	−	276248.i	−0.0776472	−	0.134489i
$336$	103769.	+	48524.3i	0.0501439	+	0.0234483i
$337$	13015.1	−	22542.8i	0.00624269	−	0.0108127i	−0.862887	−	0.505397i	$-0.831346\pi$
$337$	13015.1	−	22542.8i	0.00624269	−	0.0108127i	0.869130	+	0.494584i	$0.164680\pi$
$338$	−637144.	+	1.10357e6i	−0.303351	+	0.525420i
$339$	2.84772e6	+	1.33165e6i	1.34585	+	0.629348i
$340$	172962.	+	299578.i	0.0811432	+	0.140544i
$341$	2.34315e6			1.09122
$342$	−497068.	−	594981.i	−0.229800	−	0.275067i
$343$	−498052.			−0.228580
$344$	528736.	+	915798.i	0.240904	+	0.417257i
$345$	60901.5	−	42546.0i	0.0275474	−	0.0192447i
$346$	915717.	−	1.58607e6i	0.411217	−	0.712249i
$347$	935583.	−	1.62048e6i	0.417118	−	0.722469i	−0.578531	−	0.815661i	$-0.696374\pi$
$347$	935583.	−	1.62048e6i	0.417118	−	0.722469i	0.995648	+	0.0931918i	$0.0297070\pi$
$348$	127084.	+	1.47082e6i	0.0562526	+	0.651047i
$349$	−644297.	−	1.11595e6i	−0.283154	−	0.490437i	0.689006	−	0.724756i	$-0.258047\pi$
$349$	−644297.	−	1.11595e6i	−0.283154	−	0.490437i	−0.972160	+	0.234319i	$0.924714\pi$
$350$	1.92108e6			0.838252
$351$	452225.	+	122741.i	0.195923	+	0.0531768i
$352$	2.36296e6			1.01648
$353$	697250.	+	1.20767e6i	0.297818	+	0.515837i	0.975637	−	0.219393i	$-0.0704077\pi$
$353$	697250.	+	1.20767e6i	0.297818	+	0.515837i	−0.677818	+	0.735230i	$0.737074\pi$
$354$	−46847.3	−	542194.i	−0.0198690	−	0.229957i
$355$	176759.	−	306155.i	0.0744407	−	0.128935i
$356$	−446614.	+	773559.i	−0.186770	+	0.323495i
$357$	−4.98506e6	+	3.48258e6i	−2.07014	+	1.44621i
$358$	455592.	+	789108.i	0.187875	+	0.325408i
$359$	−3.14929e6			−1.28967			−0.644833	−	0.764324i	$-0.723073\pi$
$359$	−3.14929e6			−1.28967			−0.644833	+	0.764324i	$0.723073\pi$
$360$	−124196.	+	338952.i	−0.0505070	+	0.137842i
$361$	−1.68166e6			−0.679157
$362$	−75910.9	−	131482.i	−0.0304462	−	0.0527343i
$363$	−141288.	−	66069.1i	−0.0562780	−	0.0263167i
$364$	208186.	−	360588.i	0.0823563	−	0.142645i
$365$	−211380.	+	366120.i	−0.0830483	+	0.143844i
$366$	−94307.3	−	44100.0i	−0.0367996	−	0.0172082i
$367$	−1.79452e6	−	3.10820e6i	−0.695478	−	1.20460i	−0.970019	−	0.243028i	$-0.921859\pi$
$367$	−1.79452e6	−	3.10820e6i	−0.695478	−	1.20460i	0.274541	−	0.961575i	$-0.411474\pi$
$368$	24622.9			0.00947807
$369$	199723.	−	545078.i	0.0763595	−	0.208398i
$370$	34949.8			0.0132721
$371$	1.01060e6	+	1.75041e6i	0.381193	+	0.660246i
$372$	1.38908e6	−	970414.i	0.520438	−	0.363580i
$373$	1.68552e6	−	2.91941e6i	0.627280	−	1.08648i	−0.360815	−	0.932638i	$-0.617501\pi$
$373$	1.68552e6	−	2.91941e6i	0.627280	−	1.08648i	0.988095	−	0.153844i	$-0.0491654\pi$
$374$	1.64606e6	−	2.85106e6i	0.608509	−	1.05397i
$375$	67283.1	+	778711.i	0.0247075	+	0.285955i
$376$	−647301.	−	1.12116e6i	−0.236122	−	0.408976i
$377$	−610590.			−0.221257
$378$	−2.29563e6	−	623072.i	−0.826366	−	0.224289i
$379$	−1.82703e6			−0.653352			−0.326676	−	0.945136i	$-0.605929\pi$
$379$	−1.82703e6			−0.653352			−0.326676	+	0.945136i	$0.605929\pi$
$380$	−69327.1	−	120078.i	−0.0246289	−	0.0426584i
$381$	342515.	+	3.96415e6i	0.120884	+	1.39906i
$382$	−478330.	+	828492.i	−0.167714	+	0.290489i
$383$	2.84772e6	−	4.93239e6i	0.991973	−	1.71815i	0.386480	−	0.922298i	$-0.373691\pi$
$383$	2.84772e6	−	4.93239e6i	0.991973	−	1.71815i	0.605494	−	0.795850i	$-0.292976\pi$
$384$	1.33950e6	−	935782.i	0.463571	−	0.323852i
$385$	−294130.	−	509448.i	−0.101132	−	0.175165i
$386$	−914993.			−0.312572
$387$	−899163.	−	1.07628e6i	−0.305184	−	0.365299i
$388$	829485.			0.279724
$389$	1.43125e6	+	2.47899e6i	0.479557	+	0.830617i	0.999725	−	0.0234470i	$-0.00746411\pi$
$389$	1.43125e6	+	2.47899e6i	0.479557	+	0.830617i	−0.520168	+	0.854064i	$0.674131\pi$
$390$	−50695.5	−	23706.2i	−0.0168775	−	0.00789225i
$391$	−653551.	+	1.13198e6i	−0.216191	+	0.374454i
$392$	−1.27964e6	+	2.21641e6i	−0.420604	+	0.728508i
$393$	−477680.	−	223373.i	−0.156011	−	0.0729539i
$394$	1.16504e6	+	2.01792e6i	0.378096	+	0.654881i
$395$	−411618.			−0.132740
$396$	−1.89974e6	+	330756.i	−0.608774	+	0.105991i
$397$	−373432.			−0.118915			−0.0594574	−	0.998231i	$-0.518937\pi$
$397$	−373432.			−0.118915			−0.0594574	+	0.998231i	$0.518937\pi$
$398$	708136.	+	1.22653e6i	0.224083	+	0.388123i
$399$	1.99813e6	−	1.39590e6i	0.628336	−	0.438957i
$400$	−64075.8	+	110983.i	−0.0200237	+	0.0346820i
$401$	−1.18967e6	+	2.06056e6i	−0.369457	+	0.639918i	−0.989481	−	0.144665i	$-0.953790\pi$
$401$	−1.18967e6	+	2.06056e6i	−0.369457	+	0.639918i	0.620024	+	0.784583i	$0.287123\pi$
$402$	188979.	+	2.18718e6i	0.0583242	+	0.675024i
$403$	350412.	+	606931.i	0.107477	+	0.186156i
$404$	−1.44774e6			−0.441303
$405$	85165.9	−	471119.i	0.0258005	−	0.142723i
$406$	3.09954e6			0.933217
$407$	249032.	+	431336.i	0.0745194	+	0.129071i
$408$	−546741.	−	6.32778e6i	−0.162604	−	1.88192i
$409$	−2.02677e6	+	3.51046e6i	−0.599094	+	1.03766i	0.393861	+	0.919170i	$0.371139\pi$
$409$	−2.02677e6	+	3.51046e6i	−0.599094	+	1.03766i	−0.992955	+	0.118492i	$0.962194\pi$
$410$	−34666.3	+	60043.9i	−0.0101847	+	0.0176404i
$411$	2.40036e6	−	1.67690e6i	0.700925	−	0.489669i
$412$	973893.	+	1.68683e6i	0.282662	+	0.489586i
$413$	1.71094e6			0.493584
$414$	−503713.	+	87699.5i	−0.144438	+	0.0251476i
$415$	450962.			0.128535
$416$	353375.	+	612063.i	0.100116	+	0.173405i
$417$	4.79296e6	+	2.24128e6i	1.34978	+	0.631185i
$418$	−659780.	+	1.14277e6i	−0.184697	+	0.319904i
$419$	2.01845e6	−	3.49605e6i	0.561671	−	0.972843i	−0.435680	−	0.900102i	$-0.643492\pi$
$419$	2.01845e6	−	3.49605e6i	0.561671	−	0.972843i	0.997351	−	0.0727412i	$-0.0231747\pi$
$420$	−385356.	−	180200.i	−0.106595	−	0.0498461i
$421$	295419.	+	511680.i	0.0812330	+	0.140700i	0.903780	−	0.427998i	$-0.140781\pi$
$421$	295419.	+	511680.i	0.0812330	+	0.140700i	−0.822547	+	0.568697i	$0.807448\pi$
$422$	−2.21424e6			−0.605261
$423$	1.10079e6	+	1.31763e6i	0.299127	+	0.358049i
$424$	−2.11105e6			−0.570274
$425$	−3.40145e6	−	5.89148e6i	−0.913464	−	1.58217i
$426$	−1.99450e6	+	1.39337e6i	−0.532489	+	0.371998i
$427$	163653.	−	283456.i	0.0434365	−	0.0752343i
$428$	−1.71530e6	+	2.97099e6i	−0.452618	+	0.783957i
$429$	−68654.2	−	794580.i	−0.0180104	−	0.208446i
$430$	83749.4	+	145058.i	0.0218429	+	0.0378330i
$431$	−5.06059e6			−1.31222			−0.656112	−	0.754663i	$-0.727800\pi$
$431$	−5.06059e6			−1.31222			−0.656112	+	0.754663i	$0.727800\pi$
$432$	112564.	−	111839.i	0.0290196	−	0.0288326i
$433$	3.37592e6			0.865312			0.432656	−	0.901559i	$-0.357576\pi$
$433$	3.37592e6			0.865312			0.432656	+	0.901559i	$0.357576\pi$
$434$	−1.77880e6	−	3.08097e6i	−0.453317	−	0.785169i
$435$	53701.8	+	621525.i	0.0136071	+	0.157484i
$436$	−364408.	+	631173.i	−0.0918062	+	0.159013i
$437$	261959.	−	453726.i	0.0656190	−	0.113655i
$438$	2.38515e6	−	1.66628e6i	0.594061	−	0.415013i
$439$	−1.69856e6	−	2.94199e6i	−0.420648	−	0.728584i	0.575355	−	0.817904i	$-0.304864\pi$
$439$	−1.69856e6	−	2.94199e6i	−0.420648	−	0.728584i	−0.996003	+	0.0893200i	$0.971531\pi$
$440$	614409.			0.151295
$441$	1.16776e6	−	3.18700e6i	0.285928	−	0.780344i
$442$	984658.			0.239734
$443$	2.12190e6	+	3.67523e6i	0.513706	+	0.889765i	0.999874	+	0.0158995i	$0.00506120\pi$
$443$	2.12190e6	+	3.67523e6i	0.513706	+	0.889765i	−0.486167	+	0.873866i	$0.661605\pi$
$444$	326271.	+	152571.i	0.0785454	+	0.0367294i
$445$	−188726.	+	326882.i	−0.0451784	+	0.0782512i
$446$	−1.57006e6	+	2.71942e6i	−0.373747	+	0.647349i
$447$	−5.47756e6	−	2.56142e6i	−1.29664	−	0.606333i
$448$	−1.91142e6	−	3.31067e6i	−0.449946	−	0.779329i
$449$	519362.			0.121578			0.0607889	−	0.998151i	$-0.480638\pi$
$449$	519362.			0.121578			0.0607889	+	0.998151i	$0.480638\pi$
$450$	915517.	−	2.49860e6i	0.213125	−	0.581654i
$451$	−988049.			−0.228737
$452$	−1.93468e6	−	3.35097e6i	−0.445413	−	0.771479i
$453$	−3.52912e6	+	2.46546e6i	−0.808018	+	0.564484i
$454$	951738.	−	1.64846e6i	0.216709	−	0.375352i
$455$	87972.8	−	152373.i	0.0199214	−	0.0345049i
$456$	219147.	+	2.53633e6i	0.0493541	+	0.571207i
$457$	4.02545e6	+	6.97228e6i	0.901621	+	1.56165i	0.825390	+	0.564563i	$0.190955\pi$
$457$	4.02545e6	+	6.97228e6i	0.901621	+	1.56165i	0.0762309	+	0.997090i	$0.475711\pi$
$458$	4.09148e6			0.911417
$459$	2.15382e6	+	8.14336e6i	0.477175	+	1.80415i
$460$	−91439.8			−0.0201484
$461$	1.76486e6	+	3.05683e6i	0.386775	+	0.669914i	0.992014	−	0.126130i	$-0.0402556\pi$
$461$	1.76486e6	+	3.05683e6i	0.386775	+	0.669914i	−0.605239	+	0.796044i	$0.706922\pi$
$462$	348510.	+	4.03353e6i	0.0759644	+	0.879186i
$463$	3.80617e6	−	6.59248e6i	0.825156	−	1.42921i	−0.0766442	−	0.997059i	$-0.524421\pi$
$463$	3.80617e6	−	6.59248e6i	0.825156	−	1.42921i	0.901800	−	0.432153i	$-0.142246\pi$
$464$	−103383.	+	179064.i	−0.0222922	+	0.0386112i
$465$	586982.	−	410067.i	0.125890	−	0.0879474i
$466$	−1.46524e6	−	2.53786e6i	−0.312567	−	0.541382i
$467$	7.10090e6			1.50668			0.753340	−	0.657631i	$-0.228441\pi$
$467$	7.10090e6			1.50668			0.753340	+	0.657631i	$0.228441\pi$
$468$	−369775.	−	442615.i	−0.0780411	−	0.0934138i
$469$	−6.90186e6			−1.44889
$470$	−102530.	−	177586.i	−0.0214094	−	0.0370822i
$471$	−7.24747e6	−	3.38906e6i	−1.50534	−	0.703926i
$472$	−893499.	+	1.54759e6i	−0.184603	+	0.319742i
$473$	−1.19350e6	+	2.06720e6i	−0.245284	+	0.424845i
$474$	2.56616e6	+	1.19999e6i	0.524611	+	0.245319i
$475$	1.36338e6	+	2.36145e6i	0.277258	+	0.480224i
$476$	7.48476e6			1.51412
$477$	2.75825e6	−	480228.i	0.555056	−	0.0966387i
$478$	−674656.			−0.135056
$479$	564151.	+	977138.i	0.112346	+	0.194589i	0.916716	−	0.399540i	$-0.130830\pi$
$479$	564151.	+	977138.i	0.112346	+	0.194589i	−0.804370	+	0.594129i	$0.797497\pi$
$480$	591945.	−	413534.i	0.117268	−	0.0819235i
$481$	−74484.4	+	129011.i	−0.0146792	+	0.0254251i
$482$	80580.6	−	139570.i	0.0157984	−	0.0273636i
$483$	−138372.	−	1.60147e6i	−0.0269886	−	0.312357i
$484$	95988.1	+	166256.i	0.0186253	+	0.0322600i
$485$	350515.			0.0676632
$486$	−1.90440e6	+	2.68882e6i	−0.365736	+	0.516382i
$487$	2.19304e6			0.419009			0.209505	−	0.977808i	$-0.432815\pi$
$487$	2.19304e6			0.419009			0.209505	+	0.977808i	$0.432815\pi$
$488$	170928.	+	296056.i	0.0324910	+	0.0562761i
$489$	−317081.	−	3.66979e6i	−0.0599651	−	0.694015i
$490$	−202690.	+	351069.i	−0.0381365	+	0.0660544i
$491$	−2.08709e6	+	3.61494e6i	−0.390694	+	0.676701i	−0.992541	−	0.121910i	$-0.961098\pi$
$491$	−2.08709e6	+	3.61494e6i	−0.390694	+	0.676701i	0.601847	+	0.798611i	$0.294432\pi$
$492$	−585741.	+	409201.i	−0.109092	+	0.0762121i
$493$	−5.48804e6	−	9.50556e6i	−1.01695	−	1.76141i
$494$	−394674.			−0.0727649
$495$	−802772.	+	139768.i	−0.147258	+	0.0256385i
$496$	237321.			0.0433144
$497$	−3.82454e6	−	6.62430e6i	−0.694526	−	1.20295i
$498$	−2.81144e6	−	1.31469e6i	−0.507991	−	0.237547i
$499$	−2.01487e6	+	3.48985e6i	−0.362239	+	0.627416i	−0.988329	−	0.152335i	$-0.951321\pi$
$499$	−2.01487e6	+	3.48985e6i	−0.362239	+	0.627416i	0.626090	+	0.779751i	$0.284654\pi$
$500$	481018.	−	833147.i	0.0860470	−	0.149038i
$501$	−3.53065e6	−	1.65100e6i	−0.628434	−	0.293868i
$502$	−996309.	−	1.72566e6i	−0.176455	−	0.305630i
$503$	−3.13647e6			−0.552740			−0.276370	−	0.961051i	$-0.589132\pi$
$503$	−3.13647e6			−0.552740			−0.276370	+	0.961051i	$0.589132\pi$
$504$	5.00774e6	+	5.99417e6i	0.878143	+	1.05112i
$505$	−611770.			−0.106748
$506$	435112.	+	753637.i	0.0755484	+	0.130854i
$507$	−4.54918e6	+	3.17807e6i	−0.785984	+	0.549091i
$508$	2.44869e6	−	4.24126e6i	0.420993	−	0.729181i
$509$	2.68135e6	−	4.64424e6i	0.458733	−	0.794548i	−0.540161	−	0.841561i	$-0.681637\pi$
$509$	2.68135e6	−	4.64424e6i	0.458733	−	0.794548i	0.998894	+	0.0470129i	$0.0149702\pi$
$510$	−86601.2	−	1.00229e6i	−0.0147434	−	0.170635i
$511$	4.57363e6	+	7.92176e6i	0.774834	+	1.34205i
$512$	484936.			0.0817542
$513$	−863303.	−	3.26405e6i	−0.144834	−	0.547601i
$514$	−2.07669e6			−0.346708
$515$	411537.	+	712803.i	0.0683740	+	0.118427i
$516$	148594.	+	1.71978e6i	0.0245685	+	0.284347i
$517$	1.46113e6	−	2.53076e6i	0.240416	−	0.416413i
$518$	378106.	−	654898.i	0.0619140	−	0.107238i
$519$	6.53818e6	−	4.56760e6i	1.06546	−	0.744337i
$520$	91883.4	+	159147.i	0.0149015	+	0.0258101i
$521$	−7.05392e6			−1.13851			−0.569254	−	0.822162i	$-0.692768\pi$
$521$	−7.05392e6			−1.13851			−0.569254	+	0.822162i	$0.692768\pi$
$522$	1.47713e6	−	4.03134e6i	0.237270	−	0.647550i
$523$	5.48751e6			0.877246			0.438623	−	0.898671i	$-0.355466\pi$
$523$	5.48751e6			0.877246			0.438623	+	0.898671i	$0.355466\pi$
$524$	324526.	+	562095.i	0.0516322	+	0.0894296i
$525$	7.57837e6	+	3.54380e6i	1.19999	+	0.561139i
$526$	108359.	−	187683.i	0.0170766	−	0.0295775i
$527$	−6.29906e6	+	1.09103e7i	−0.987983	+	1.71124i
$528$	−244646.	−	114401.i	−0.0381903	−	0.0178585i
$529$	3.04541e6	+	5.27481e6i	0.473159	+	0.819536i
$530$	−334380.			−0.0517072
$531$	815376.	−	2.22530e6i	0.125494	−	0.342493i
$532$	−3.00007e6			−0.459571
$533$	−147760.	−	255929.i	−0.0225289	−	0.0390212i
$534$	2.12953e6	−	1.48770e6i	0.323170	−	0.225768i
$535$	−724835.	+	1.25545e6i	−0.109485	+	0.189634i
$536$	3.60433e6	−	6.24288e6i	0.541892	−	0.938584i
$537$	341582.	+	3.95335e6i	0.0511162	+	0.591601i
$538$	3.88930e6	+	6.73647e6i	0.579316	+	1.00341i
$539$	−5.77700e6			−0.856506
$540$	−418019.	+	415326.i	−0.0616896	+	0.0612921i
$541$	9.61784e6			1.41281			0.706406	−	0.707807i	$-0.250315\pi$
$541$	9.61784e6			1.41281			0.706406	+	0.707807i	$0.250315\pi$
$542$	−3.09008e6	−	5.35218e6i	−0.451827	−	0.782587i
$543$	−56914.5	−	658708.i	−0.00828368	−	0.0958724i
$544$	−6.35232e6	+	1.10025e7i	−0.920312	+	1.59403i
$545$	−153988.	+	266715.i	−0.0222073	+	0.0384641i
$546$	−992663.	+	693478.i	−0.142502	+	0.0995522i
$547$	−3.52168e6	−	6.09973e6i	−0.503247	−	0.871650i	−0.999993	−	0.00375395i	$-0.998805\pi$
$547$	−3.52168e6	−	6.09973e6i	−0.503247	−	0.871650i	0.496745	−	0.867896i	$-0.334528\pi$
$548$	−3.60399e6			−0.512663
$549$	−290678.	−	347936.i	−0.0411606	−	0.0492685i
$550$	−4.52914e6			−0.638424
$551$	2.19974e6	+	3.81006e6i	0.308668	+	0.534629i
$552$	1.52083e6	+	711169.i	0.212438	+	0.0993402i
$553$	−4.45310e6	+	7.71300e6i	−0.619227	+	1.07253i
$554$	1.87298e6	−	3.24409e6i	0.259273	−	0.449075i
$555$	137872.	+	64471.7i	0.0189996	+	0.00888458i
$556$	−3.25624e6	−	5.63997e6i	−0.446713	−	0.773730i
$557$	1.13517e7			1.55032			0.775162	−	0.631762i	$-0.217668\pi$
$557$	1.13517e7			1.55032			0.775162	+	0.631762i	$0.217668\pi$
$558$	−4.85490e6	+	845267.i	−0.660077	+	0.114923i
$559$	−713941.			−0.0966346
$560$	−29790.4	−	51598.5i	−0.00401426	−	0.00695291i
$561$	1.17528e7	−	8.21055e6i	1.57665	−	1.10145i
$562$	2.40957e6	−	4.17350e6i	0.321810	−	0.557391i
$563$	−1.47052e6	+	2.54702e6i	−0.195524	+	0.338658i	−0.947072	−	0.321020i	$-0.895974\pi$
$563$	−1.47052e6	+	2.54702e6i	−0.195524	+	0.338658i	0.751548	+	0.659678i	$0.229308\pi$
$564$	−181916.	−	2.10543e6i	−0.0240809	−	0.278703i
$565$	−817537.	−	1.41602e6i	−0.107742	−	0.186615i
$566$	−2.04006e6			−0.267671
$567$	−7.90656e6	−	6.69267e6i	−1.03283	−	0.874262i
$568$	7.98909e6			1.03903
$569$	−2.60302e6	−	4.50857e6i	−0.337052	−	0.583792i	0.646825	−	0.762639i	$-0.276097\pi$
$569$	−2.60302e6	−	4.50857e6i	−0.337052	−	0.583792i	−0.983877	+	0.178847i	$0.942763\pi$
$570$	34711.8	+	401743.i	0.00447497	+	0.0517918i
$571$	3.43649e6	−	5.95217e6i	0.441087	−	0.763986i	−0.556683	−	0.830725i	$-0.687926\pi$
$571$	3.43649e6	−	5.95217e6i	0.441087	−	0.763986i	0.997770	+	0.0667391i	$0.0212595\pi$
$572$	−490820.	+	850125.i	−0.0627237	+	0.108641i
$573$	−3.41526e6	+	2.38591e6i	−0.434547	+	0.303576i
$574$	750078.	+	1.29917e6i	0.0950225	+	0.164584i
$575$	1.79825e6			0.226819
$576$	−5.21685e6	+	908286.i	−0.655167	+	0.114069i
$577$	−6.61342e6			−0.826964			−0.413482	−	0.910512i	$-0.635688\pi$
$577$	−6.61342e6			−0.826964			−0.413482	+	0.910512i	$0.635688\pi$
$578$	6.30896e6	+	1.09274e7i	0.785485	+	1.36050i
$579$	−3.60952e6	−	1.68788e6i	−0.447459	−	0.209241i
$580$	383922.	−	664973.i	0.0473885	−	0.0820793i
$581$	4.87875e6	−	8.45024e6i	0.599609	−	1.03855i
$582$	−2.18522e6	−	1.02185e6i	−0.267416	−	0.125049i
$583$	−2.38260e6	−	4.12679e6i	−0.290322	−	0.502853i
$584$	−9.55387e6			−1.15917
$585$	−156256.	−	187035.i	−0.0188776	−	0.0225961i
$586$	−8.79964e6			−1.05857
$587$	3.31969e6	+	5.74987e6i	0.397651	+	0.688751i	0.993436	−	0.114393i	$-0.0364922\pi$
$587$	3.31969e6	+	5.74987e6i	0.397651	+	0.688751i	−0.595785	+	0.803144i	$0.703159\pi$
$588$	−3.42475e6	+	2.39254e6i	−0.408494	+	0.285375i
$589$	2.52482e6	−	4.37311e6i	0.299876	−	0.519400i
$590$	−141526.	+	245131.i	−0.0167381	+	0.0289913i
$591$	873497.	+	1.01095e7i	0.102871	+	1.19059i
$592$	25222.8	+	43687.1i	0.00295793	+	0.00512329i
$593$	−2.49082e6			−0.290875			−0.145437	−	0.989367i	$-0.546459\pi$
$593$	−2.49082e6			−0.290875			−0.145437	+	0.989367i	$0.546459\pi$
$594$	5.41220e6	+	1.46896e6i	0.629372	+	0.170822i
$595$	3.16283e6			0.366255
$596$	3.72134e6	+	6.44555e6i	0.429125	+	0.743266i
$597$	530928.	+	6.14477e6i	0.0609677	+	0.705619i
$598$	−130140.	+	225409.i	−0.0148819	+	0.0257762i
$599$	6.54109e6	−	1.13295e7i	0.744875	−	1.29016i	−0.205378	−	0.978683i	$-0.565842\pi$
$599$	6.54109e6	−	1.13295e7i	0.744875	−	1.29016i	0.950253	−	0.311478i	$-0.100824\pi$
$600$	−7.16306e6	+	5.00414e6i	−0.812308	+	0.567481i
$601$	−1.50119e6	−	2.60013e6i	−0.169531	−	0.293636i	0.768724	−	0.639580i	$-0.220892\pi$
$601$	−1.50119e6	−	2.60013e6i	−0.169531	−	0.293636i	−0.938255	+	0.345944i	$0.887559\pi$
$602$	3.62418e6			0.407585
$603$	−3.28918e6	+	8.97672e6i	−0.368379	+	1.00537i
$604$	5.29876e6			0.590992
$605$	40561.6	+	70254.8i	0.00450533	+	0.00780347i
$606$	3.81397e6	+	1.78349e6i	0.421886	+	0.197282i
$607$	757606.	−	1.31221e6i	0.0834587	−	0.144555i	−0.821275	−	0.570533i	$-0.806737\pi$
$607$	757606.	−	1.31221e6i	0.0834587	−	0.144555i	0.904733	+	0.425978i	$0.140070\pi$
$608$	2.54616e6	−	4.41008e6i	0.279336	−	0.483824i
$609$	1.22273e7	+	5.71771e6i	1.33594	+	0.624711i
$610$	27074.2	+	46893.9i	0.00294599	+	0.00510260i
$611$	874036.			0.0947166
$612$	3.56697e6	−	9.73485e6i	0.384965	−	1.05063i
$613$	−6.71159e6			−0.721397			−0.360698	−	0.932683i	$-0.617462\pi$
$613$	−6.71159e6			−0.721397			−0.360698	+	0.932683i	$0.617462\pi$
$614$	2.25163e6	+	3.89994e6i	0.241033	+	0.417481i
$615$	−247516.	+	172916.i	−0.0263886	+	0.0184352i
$616$	6.64700e6	−	1.15129e7i	0.705787	−	1.22246i
$617$	−3.98994e6	+	6.91077e6i	−0.421942	+	0.730826i	−0.996129	−	0.0878986i	$-0.971985\pi$
$617$	−3.98994e6	+	6.91077e6i	−0.421942	+	0.730826i	0.574187	+	0.818724i	$0.305318\pi$
$618$	−487624.	−	5.64359e6i	−0.0513587	−	0.594408i
$619$	335377.	+	580890.i	0.0351809	+	0.0609351i	0.883080	−	0.469223i	$-0.155466\pi$
$619$	335377.	+	580890.i	0.0351809	+	0.0609351i	−0.847899	+	0.530158i	$0.822133\pi$
$620$	−881317.			−0.0920774
$621$	−2.14885e6	−	583234.i	−0.223603	−	0.0606896i
$622$	7.32012e6			0.758652
$623$	4.08346e6	+	7.07277e6i	0.421511	+	0.730078i
$624$	−6953.52	−	80477.5i	−0.000714896	−	0.00827396i
$625$	−4.57684e6	+	7.92731e6i	−0.468668	+	0.811757i
$626$	−1.69391e6	+	2.93395e6i	−0.172765	+	0.299238i
$627$	−4.71081e6	+	3.29099e6i	−0.478549	+	0.334316i
$628$	4.92378e6	+	8.52824e6i	0.498195	+	0.862899i
$629$	−2.67789e6			−0.269877
$630$	793203.	+	949449.i	0.0796219	+	0.0953060i
$631$	−4.37169e6			−0.437095			−0.218548	−	0.975826i	$-0.570132\pi$
$631$	−4.37169e6			−0.437095			−0.218548	+	0.975826i	$0.570132\pi$
$632$	−4.65105e6	−	8.05585e6i	−0.463189	−	0.802267i
$633$	−8.73485e6	−	4.08459e6i	−0.866455	−	0.405172i
$634$	705591.	−	1.22212e6i	0.0697156	−	0.120751i
$635$	1.03474e6	−	1.79223e6i	0.101835	−	0.176384i
$636$	−3.12158e6	−	1.45971e6i	−0.306007	−	0.143095i
$637$	−863936.	−	1.49638e6i	−0.0843593	−	0.146115i
$638$	−7.30751e6			−0.710751
$639$	−1.04384e7	+	1.81738e6i	−1.01130	+	0.176074i
$640$	−849865.			−0.0820163
$641$	−6.89117e6	−	1.19359e7i	−0.662442	−	1.14738i	−0.979972	−	0.199135i	$-0.936187\pi$
$641$	−6.89117e6	−	1.19359e7i	−0.662442	−	1.14738i	0.317530	−	0.948248i	$-0.397147\pi$
$642$	8.17886e6	−	5.71377e6i	0.783168	−	0.547124i
$643$	746906.	−	1.29368e6i	0.0712424	−	0.123395i	−0.828204	−	0.560427i	$-0.810637\pi$
$643$	746906.	−	1.29368e6i	0.0712424	−	0.123395i	0.899446	+	0.437032i	$0.143970\pi$
$644$	−989244.	+	1.71342e6i	−0.0939915	+	0.162798i
$645$	62791.5	+	726726.i	0.00594294	+	0.0687815i
$646$	−3.54737e6	−	6.14422e6i	−0.334445	−	0.579276i
$647$	1.27773e7			1.19999			0.599997	−	0.800002i	$-0.295168\pi$
$647$	1.27773e7			1.19999			0.599997	+	0.800002i	$0.295168\pi$
$648$	1.01827e7	−	3.65657e6i	0.952630	−	0.342087i
$649$	−4.03374e6			−0.375920
$650$	−677323.	−	1.17316e6i	−0.0628799	−	0.108911i
$651$	−1.33366e6	−	1.54353e7i	−0.123337	−	1.42746i
$652$	−2.26686e6	+	3.92632e6i	−0.208836	+	0.361715i
$653$	−2.42085e6	+	4.19304e6i	−0.222170	+	0.384810i	−0.955467	−	0.295099i	$-0.904647\pi$
$653$	−2.42085e6	+	4.19304e6i	−0.222170	+	0.384810i	0.733297	+	0.679909i	$0.237981\pi$
$654$	1.73756e6	−	1.21386e6i	0.158853	−	0.110975i
$655$	137135.	+	237524.i	0.0124895	+	0.0216324i
$656$	−100073.			−0.00907938
$657$	1.24829e7	−	2.17334e6i	1.12824	−	0.196433i
$658$	−4.43688e6			−0.399496
$659$	−6.63829e6	−	1.14979e7i	−0.595447	−	1.03134i	−0.993484	−	0.113975i	$-0.963642\pi$
$659$	−6.63829e6	−	1.14979e7i	−0.595447	−	1.03134i	0.398037	−	0.917369i	$-0.369692\pi$
$660$	908517.	+	424841.i	0.0811845	+	0.0379635i
$661$	−8.76351e6	+	1.51788e7i	−0.780143	+	1.35125i	0.151715	+	0.988424i	$0.451520\pi$
$661$	−8.76351e6	+	1.51788e7i	−0.780143	+	1.35125i	−0.931858	+	0.362823i	$0.881813\pi$
$662$	−4.89782e6	+	8.48327e6i	−0.434368	+	0.752347i
$663$	3.88434e6	+	1.81639e6i	0.343189	+	0.160482i
$664$	5.09561e6	+	8.82586e6i	0.448514	+	0.776850i
$665$	−1.26774e6			−0.111167
$666$	−671584.	−	803874.i	−0.0586699	−	0.0702268i
$667$	2.90137e6			0.252516
$668$	2.39865e6	+	4.15458e6i	0.207982	+	0.360235i
$669$	−1.12101e7	+	7.83144e6i	−0.968380	+	0.676513i
$670$	570909.	−	988843.i	0.0491338	−	0.0851022i
$671$	−385830.	+	668277.i	−0.0330819	+	0.0572995i
$672$	−1.34494e6	−	1.55658e7i	−0.114889	−	1.32969i
$673$	9.25108e6	+	1.60233e7i	0.787326	+	1.36369i	0.927599	+	0.373576i	$0.121869\pi$
$673$	9.25108e6	+	1.60233e7i	0.787326	+	1.36369i	−0.140273	+	0.990113i	$0.544798\pi$
$674$	93176.3			0.00790052
$675$	8.22073e6	−	8.16776e6i	0.694466	−	0.689992i
$676$	6.83032e6			0.574876
$677$	−1.97541e6	−	3.42152e6i	−0.165648	−	0.286911i	0.771237	−	0.636548i	$-0.219638\pi$
$677$	−1.97541e6	−	3.42152e6i	−0.165648	−	0.286911i	−0.936885	+	0.349637i	$0.886305\pi$
$678$	968687.	+	1.12112e7i	0.0809300	+	0.936655i
$679$	3.79206e6	−	6.56803e6i	0.315646	−	0.546715i
$680$	−1.65171e6	+	2.86085e6i	−0.136981	+	0.237259i
$681$	6.79537e6	−	4.74727e6i	0.561495	−	0.392262i
$682$	4.19371e6	+	7.26372e6i	0.345253	+	0.597995i
$683$	746853.			0.0612609			0.0306304	−	0.999531i	$-0.490249\pi$
$683$	746853.			0.0612609			0.0306304	+	0.999531i	$0.490249\pi$
$684$	−1.42973e6	+	3.90196e6i	−0.116846	+	0.318891i
$685$	−1.52294e6			−0.124010
$686$	−891401.	−	1.54395e6i	−0.0723208	−	0.125263i
$687$	1.61403e7	+	7.54754e6i	1.30473	+	0.610117i
$688$	−120881.	+	209373.i	−0.00973618	+	0.0168636i
$689$	712625.	−	1.23430e6i	0.0571891	−	0.0990544i
$690$	240892.	+	112646.i	0.0192619	+	0.00900726i
$691$	−4.00126e6	−	6.93039e6i	−0.318788	−	0.552157i	0.661448	−	0.749991i	$-0.269942\pi$
$691$	−4.00126e6	−	6.93039e6i	−0.318788	−	0.552157i	−0.980235	+	0.197835i	$0.936609\pi$
$692$	−9.81668e6			−0.779291
$693$	−6.06581e6	+	1.65546e7i	−0.479795	+	1.30944i
$694$	6.69794e6			0.527889
$695$	−1.37599e6	−	2.38328e6i	−0.108057	−	0.187160i
$696$	−1.15572e7	+	8.07389e6i	−0.904334	+	0.631771i
$697$	2.65617e6	−	4.60062e6i	0.207097	−	0.358702i
$698$	2.30629e6	−	3.99462e6i	0.179175	−	0.310339i
$699$	−1.09857e6	−	1.27144e7i	−0.0850420	−	0.984246i
$700$	−5.14859e6	−	8.91761e6i	−0.397139	−	0.687865i
$701$	1.57926e7			1.21383			0.606914	−	0.794767i	$-0.292407\pi$
$701$	1.57926e7			1.21383			0.606914	+	0.794767i	$0.292407\pi$
$702$	428886.	+	1.62157e6i	0.0328472	+	0.124192i
$703$	1.07336e6			0.0819139
$704$	4.50637e6	+	7.80526e6i	0.342685	+	0.593548i
$705$	−76872.0	−	889689.i	−0.00582499	−	0.0674164i
$706$	−2.49584e6	+	4.32293e6i	−0.188454	+	0.326412i
$707$	−6.61845e6	+	1.14635e7i	−0.497975	+	0.862518i
$708$	−2.39130e6	+	1.67057e6i	−0.179288	+	0.125251i
$709$	−9.54046e6	−	1.65246e7i	−0.712777	−	1.23457i	−0.963811	−	0.266588i	$-0.914104\pi$
$709$	−9.54046e6	−	1.65246e7i	−0.712777	−	1.23457i	0.251033	−	0.967978i	$-0.419230\pi$
$710$	1.26544e6			0.0942094
$711$	7.90952e6	+	9.46755e6i	0.586781	+	0.702366i
$712$	−8.52996e6			−0.630590
$713$	−1.66507e6	−	2.88398e6i	−0.122661	−	0.212456i
$714$	−1.97181e7	−	9.22057e6i	−1.44750	−	0.676881i
$715$	−207405.	+	359237.i	−0.0151724	+	0.0262794i
$716$	2.44202e6	−	4.22970e6i	0.178019	−	0.308338i
$717$	−2.66142e6	−	1.24453e6i	−0.193337	−	0.0904084i
$718$	−5.63653e6	−	9.76276e6i	−0.408038	−	0.706743i
$719$	1.74493e6			0.125880			0.0629399	−	0.998017i	$-0.479952\pi$
$719$	1.74493e6			0.125880			0.0629399	+	0.998017i	$0.479952\pi$
$720$	−81307.2	+	14156.1i	−0.00584518	+	0.00101768i
$721$	1.78089e7			1.27585
$722$	−3.00980e6	−	5.21312e6i	−0.214879	−	0.372181i
$723$	575343.	−	401936.i	0.0409337	−	0.0285964i
$724$	−406890.	+	704755.i	−0.0288490	+	0.0499680i
$725$	−7.55018e6	+	1.30773e7i	−0.533473	+	0.924002i
$726$	−48060.9	−	556240.i	−0.00338415	−	0.0391670i
$727$	−1.04470e6	−	1.80947e6i	−0.0733087	−	0.126974i	0.827041	−	0.562142i	$-0.190022\pi$
$727$	−1.04470e6	−	1.80947e6i	−0.0733087	−	0.126974i	−0.900350	+	0.435167i	$0.856689\pi$
$728$	3.97617e6			0.278059
$729$	−1.24726e7	+	7.09398e6i	−0.869239	+	0.494392i
$730$	−1.51329e6			−0.105103
$731$	−6.41696e6	−	1.11145e7i	−0.444156	−	0.769301i
$732$	48037.0	+	555964.i	0.00331359	+	0.0383503i
$733$	1.00097e7	−	1.73373e7i	0.688114	−	1.19185i	−0.284333	−	0.958726i	$-0.591772\pi$
$733$	1.00097e7	−	1.73373e7i	0.688114	−	1.19185i	0.972447	−	0.233123i	$-0.0748946\pi$
$734$	6.42359e6	−	1.11260e7i	0.440086	−	0.762251i
$735$	−1.44720e6	+	1.01102e6i	−0.0988119	+	0.0690303i
$736$	−1.67914e6	−	2.90836e6i	−0.114260	−	0.197904i
$737$	1.62719e7			1.10349
$738$	2.04720e6	−	356429.i	0.138363	−	0.0240898i
$739$	−1.93522e6			−0.130353			−0.0651763	−	0.997874i	$-0.520761\pi$
$739$	−1.93522e6			−0.130353			−0.0651763	+	0.997874i	$0.520761\pi$
$740$	−93667.4	−	162237.i	−0.00628795	−	0.0108910i
$741$	−1.55693e6	−	728054.i	−0.104166	−	0.0487100i
$742$	−3.61750e6	+	6.26570e6i	−0.241212	+	0.417792i
$743$	4.52092e6	−	7.83046e6i	0.300438	−	0.520373i	−0.675797	−	0.737087i	$-0.736201\pi$
$743$	4.52092e6	−	7.83046e6i	0.300438	−	0.520373i	0.976235	+	0.216714i	$0.0695339\pi$
$744$	1.46581e7	+	6.85440e6i	0.970832	+	0.453980i
$745$	1.57252e6	+	2.72369e6i	0.103802	+	0.179791i
$746$	1.20668e7			0.793863
$747$	−8.66554e6	−	1.03725e7i	−0.568191	−	0.680114i
$748$	−1.76461e7			−1.15317
$749$	1.56833e7	+	2.71643e7i	1.02149	+	1.76927i
$750$	−2.29357e6	+	1.60230e6i	−0.148888	+	0.104014i
$751$	−9.16416e6	+	1.58728e7i	−0.592915	+	1.02696i	0.400922	+	0.916112i	$0.368690\pi$
$751$	−9.16416e6	+	1.58728e7i	−0.592915	+	1.02696i	−0.993837	+	0.110847i	$0.964644\pi$
$752$	147988.	−	256323.i	0.00954294	−	0.0165289i
$753$	−746987.	−	8.64536e6i	−0.0480093	−	0.555643i
$754$	−1.09282e6	−	1.89282e6i	−0.0700036	−	0.121250i
$755$	2.23909e6			0.142957
$756$	3.26012e6	+	1.23262e7i	0.207458	+	0.784374i
$757$	−2.00372e7			−1.27086			−0.635429	−	0.772159i	$-0.719177\pi$
$757$	−2.00372e7			−1.27086			−0.635429	+	0.772159i	$0.719177\pi$
$758$	−3.26997e6	−	5.66376e6i	−0.206715	−	0.358040i
$759$	326227.	+	3.77564e6i	0.0205549	+	0.237895i
$760$	662045.	−	1.14670e6i	0.0415771	−	0.0720136i
$761$	−7.82878e6	+	1.35598e7i	−0.490041	+	0.848776i	−0.999934	−	0.0114616i	$-0.996352\pi$
$761$	−7.82878e6	+	1.35598e7i	−0.490041	+	0.848776i	0.509893	+	0.860238i	$0.329685\pi$
$762$	−1.16758e7	+	8.15673e6i	−0.728448	+	0.508896i
$763$	3.33184e6	+	5.77092e6i	0.207192	+	0.358867i
$764$	5.12780e6			0.317832
$765$	1.50729e6	−	4.11365e6i	0.0931202	−	0.254141i
$766$	2.03871e7			1.25541
$767$	−603236.	−	1.04483e6i	−0.0370253	−	0.0641297i
$768$	1.51452e7	+	7.08218e6i	0.926555	+	0.433275i
$769$	8.33840e6	−	1.44425e7i	0.508472	−	0.880699i	−0.491480	−	0.870889i	$-0.663544\pi$
$769$	8.33840e6	−	1.44425e7i	0.508472	−	0.880699i	0.999952	−	0.00981049i	$-0.00312282\pi$
$770$	1.05285e6	−	1.82360e6i	0.0639943	−	0.110841i
$771$	−8.19226e6	−	3.83086e6i	−0.496327	−	0.232092i
$772$	2.45223e6	+	4.24739e6i	0.148087	+	0.256495i
$773$	−1.89296e7			−1.13944			−0.569721	−	0.821838i	$-0.692949\pi$
$773$	−1.89296e7			−1.13944			−0.569721	+	0.821838i	$0.692949\pi$
$774$	1.72716e6	−	4.71370e6i	0.103629	−	0.282819i
$775$	1.73319e7			1.03655
$776$	3.96062e6	+	6.85999e6i	0.236107	+	0.408949i
$777$	2.69966e6	−	1.88599e6i	0.160419	−	0.112069i
$778$	−5.12322e6	+	8.87368e6i	−0.303455	+	0.525599i
$779$	−1.06466e6	+	1.84404e6i	−0.0628587	+	0.108874i
$780$	25822.6	+	298862.i	0.00151972	+	0.0175887i
$781$	9.01676e6	+	1.56175e7i	0.528960	+	0.916186i
$782$	−4.67884e6			−0.273603
$783$	1.32637e7	−	1.31782e7i	0.773142	−	0.768161i
$784$	−585112.			−0.0339977
$785$	2.08064e6	+	3.60377e6i	0.120510	+	0.208729i
$786$	−162489.	−	1.88059e6i	−0.00938139	−	0.108577i
$787$	1.87371e6	−	3.24536e6i	0.107837	−	0.186778i	−0.807057	−	0.590473i	$-0.798941\pi$
$787$	1.87371e6	−	3.24536e6i	0.107837	−	0.186778i	0.914894	+	0.403695i	$0.132274\pi$
$788$	6.24476e6	−	1.08162e7i	0.358262	−	0.620527i
$789$	773680.	−	540495.i	0.0442455	−	0.0309100i
$790$	−736705.	−	1.27601e6i	−0.0419977	−	0.0727422i
$791$	−3.53782e7			−2.01045
$792$	−1.18063e7	−	1.41319e7i	−0.668806	−	0.800548i
$793$	−230800.			−0.0130333
$794$	−668361.	−	1.15763e6i	−0.0376235	−	0.0651659i
$795$	−1.31908e6	−	616830.i	−0.0740209	−	0.0346137i
$796$	3.79568e6	−	6.57432e6i	0.212328	−	0.367763i
$797$	7.58701e6	−	1.31411e7i	0.423082	−	0.732800i	−0.573157	−	0.819446i	$-0.694281\pi$
$797$	7.58701e6	−	1.31411e7i	0.423082	−	0.732800i	0.996239	+	0.0866454i	$0.0276147\pi$
$798$	7.90348e6	+	3.69582e6i	0.439350	+	0.205449i
$799$	7.85591e6	+	1.36068e7i	0.435341	+	0.754033i
$800$	1.74784e7			0.965557
$801$	1.11450e7	−	1.94042e6i	0.613763	−	0.106860i
$802$	−8.51694e6			−0.467571
$803$	−1.07828e7	−	1.86764e7i	−0.590125	−	1.02213i
$804$	9.64639e6	−	6.73900e6i	0.526289	−	0.367667i
$805$	−418024.	+	724039.i	−0.0227359	+	0.0393797i
$806$	−1.25432e6	+	2.17254e6i	−0.0680096	+	0.117796i
$807$	2.91602e6	+	3.37490e7i	0.157618	+	1.82422i
$808$	−6.91265e6	−	1.19731e7i	−0.372491	−	0.645174i
$809$	−3.67446e7			−1.97389			−0.986943	−	0.161067i	$-0.948506\pi$
$809$	−3.67446e7			−1.97389			−0.986943	+	0.161067i	$0.948506\pi$
$810$	1.61289e6	−	579184.i	0.0863758	−	0.0310173i
$811$	−3.10069e7			−1.65541			−0.827706	−	0.561162i	$-0.810355\pi$
$811$	−3.10069e7			−1.65541			−0.827706	+	0.561162i	$0.810355\pi$
$812$	−8.30694e6	−	1.43880e7i	−0.442131	−	0.765794i
$813$	−2.31680e6	−	2.68138e7i	−0.122931	−	1.42276i
$814$	−891424.	+	1.54399e6i	−0.0471545	+	0.0816740i
$815$	−957907.	+	1.65914e6i	−0.0505160	+	0.0874963i
$816$	1.19036e6	−	831590.i	0.0625826	−	0.0437204i
$817$	2.57207e6	+	4.45496e6i	0.134812	+	0.233501i
$818$	−1.45098e7			−0.758192
$819$	−5.19517e6	+	904511.i	−0.270639	+	0.0471199i
$820$	371631.			0.0193009
$821$	2.14433e6	+	3.71409e6i	0.111028	+	0.192307i	0.916185	−	0.400755i	$-0.131252\pi$
$821$	2.14433e6	+	3.71409e6i	0.111028	+	0.192307i	−0.805157	+	0.593062i	$0.797919\pi$
$822$	9.49447e6	+	4.43980e6i	0.490107	+	0.229184i
$823$	−6.66686e6	+	1.15473e7i	−0.343101	+	0.594268i	−0.985007	−	0.172515i	$-0.944811\pi$
$823$	−6.66686e6	+	1.15473e7i	−0.343101	+	0.594268i	0.641906	+	0.766783i	$0.278144\pi$
$824$	−9.30027e6	+	1.61085e7i	−0.477175	+	0.826491i
$825$	−1.78668e7	−	8.35488e6i	−0.913929	−	0.427371i
$826$	3.06221e6	+	5.30390e6i	0.156165	+	0.270486i
$827$	6.58421e6			0.334765			0.167382	−	0.985892i	$-0.446469\pi$
$827$	6.58421e6			0.334765			0.167382	+	0.985892i	$0.446469\pi$
$828$	1.75708e6	+	2.10319e6i	0.0890666	+	0.106611i
$829$	3.49408e7			1.76582			0.882909	−	0.469544i	$-0.155582\pi$
$829$	3.49408e7			1.76582			0.882909	+	0.469544i	$0.155582\pi$
$830$	807122.	+	1.39798e6i	0.0406672	+	0.0704376i
$831$	1.33730e7	−	9.34241e6i	0.671778	−	0.469306i
$832$	−1.34783e6	+	2.33452e6i	−0.0675038	+	0.116920i
$833$	1.55303e7	−	2.68992e7i	0.775472	−	1.34316i
$834$	1.63039e6	+	1.88695e7i	0.0811662	+	0.939389i
$835$	1.01359e6	+	1.75560e6i	0.0503093	+	0.0871382i
$836$	7.07299e6			0.350015
$837$	−2.07111e7	−	5.62134e6i	−1.02186	−	0.277349i
$838$	1.44503e7			0.710831
$839$	1.85769e7	+	3.21761e7i	0.911105	+	1.57808i	0.812507	+	0.582952i	$0.198102\pi$
$839$	1.85769e7	+	3.21761e7i	0.911105	+	1.57808i	0.0985980	+	0.995127i	$0.468564\pi$
$840$	−349706.	−	4.04738e6i	−0.0171004	−	0.197914i
$841$	−1.92620e6	+	3.33628e6i	−0.0939100	+	0.162657i
$842$	−1.05747e6	+	1.83159e6i	−0.0514028	+	0.0890322i
$843$	1.72043e7	−	1.20189e7i	0.833810	−	0.582502i
$844$	5.93427e6	+	1.02785e7i	0.286755	+	0.496674i
$845$	2.88628e6			0.139058
$846$	−2.11446e6	+	5.77071e6i	−0.101572	+	0.277206i
$847$	1.75527e6			0.0840688
$848$	−241317.	−	417974.i	−0.0115239	−	0.0199600i
$849$	−8.04774e6	−	3.76328e6i	−0.383181	−	0.179183i
$850$	1.21757e7	−	2.10889e7i	0.578023	−	1.00117i
$851$	353931.	−	613026.i	0.0167531	−	0.0290171i
$852$	1.18134e7	+	5.52416e6i	0.557538	+	0.260716i
$853$	−6.28069e6	−	1.08785e7i	−0.295552	−	0.511912i	0.679561	−	0.733619i	$-0.262170\pi$
$853$	−6.28069e6	−	1.08785e7i	−0.295552	−	0.511912i	−0.975113	+	0.221707i	$0.928837\pi$
$854$	1.17161e6			0.0549717
$855$	−604159.	+	1.64885e6i	−0.0282642	+	0.0771376i
$856$	−3.27609e7			−1.52817
$857$	1.88788e7	+	3.26990e7i	0.878055	+	1.52084i	0.853472	+	0.521138i	$0.174492\pi$
$857$	1.88788e7	+	3.26990e7i	0.878055	+	1.52084i	0.0245827	+	0.999698i	$0.492174\pi$
$858$	2.34031e6	−	1.63495e6i	0.108531	−	0.0758203i
$859$	−4.11422e6	+	7.12604e6i	−0.190241	+	0.329507i	−0.945330	−	0.326115i	$-0.894260\pi$
$859$	−4.11422e6	+	7.12604e6i	−0.190241	+	0.329507i	0.755089	+	0.655622i	$0.227594\pi$
$860$	448906.	−	777528.i	0.0206971	−	0.0358484i
$861$	562374.	+	6.50872e6i	0.0258534	+	0.299218i
$862$	−9.05733e6	−	1.56878e7i	−0.415176	−	0.719105i
$863$	2.85773e7			1.30615			0.653077	−	0.757291i	$-0.273478\pi$
$863$	2.85773e7			1.30615			0.653077	+	0.757291i	$0.273478\pi$
$864$	−2.08862e7	−	5.66887e6i	−0.951866	−	0.258352i
$865$	−4.14823e6			−0.188505
$866$	6.04215e6	+	1.04653e7i	0.273777	+	0.474195i
$867$	4.73017e6	+	5.47453e7i	0.213712	+	2.47343i
$868$	−9.53455e6	+	1.65143e7i	−0.429537	+	0.743980i
$869$	1.04987e7	−	1.81842e7i	0.471612	−	0.816855i
$870$	−1.83060e6	+	1.27887e6i	−0.0819967	+	0.0572832i
$871$	2.43342e6	+	4.21481e6i	0.108686	+	0.188249i
$872$	−6.95989e6			−0.309964
$873$	−6.73538e6	−	8.06213e6i	−0.299107	−	0.358026i
$874$	1.87539e6			0.0830450
$875$	−4.39802e6	−	7.61759e6i	−0.194195	−	0.336355i
$876$	−1.41272e7	−	6.60615e6i	−0.622007	−	0.290863i
$877$	1.58797e7	−	2.75045e7i	0.697180	−	1.20755i	−0.272261	−	0.962223i	$-0.587771\pi$
$877$	1.58797e7	−	2.75045e7i	0.697180	−	1.20755i	0.969440	−	0.245327i	$-0.0788953\pi$
$878$	6.08008e6	−	1.05310e7i	0.266178	−	0.461035i
$879$	−3.47133e7	−	1.62327e7i	−1.51539	−	0.708626i
$880$	70234.0	+	121649.i	0.00305732	+	0.00529543i
$881$	−1.74609e7			−0.757924			−0.378962	−	0.925412i	$-0.623719\pi$
$881$	−1.74609e7			−0.757924			−0.378962	+	0.925412i	$0.623719\pi$
$882$	1.19697e7	−	2.08400e6i	0.518097	−	0.0902039i
$883$	−1.63763e7			−0.706829			−0.353415	−	0.935467i	$-0.614979\pi$
$883$	−1.63763e7			−0.706829			−0.353415	+	0.935467i	$0.614979\pi$
$884$	−2.63894e6	−	4.57077e6i	−0.113579	−	0.196725i
$885$	−1.01049e6	+	705933.i	−0.0433685	+	0.0302974i
$886$	−7.59544e6	+	1.31557e7i	−0.325064	+	0.563027i
$887$	2.53921e6	−	4.39804e6i	0.108365	−	0.187694i	−0.806743	−	0.590903i	$-0.798772\pi$
$887$	2.53921e6	−	4.39804e6i	0.108365	−	0.187694i	0.915108	+	0.403209i	$0.132105\pi$
$888$	296088.	+	3.42681e6i	0.0126005	+	0.145834i
$889$	−2.23888e7	−	3.87785e7i	−0.950115	−	1.64565i
$890$	−1.35111e6			−0.0571761
$891$	1.86406e7	+	1.57787e7i	0.786620	+	0.665850i
$892$	1.68313e7			0.708282
$893$	−3.14884e6	−	5.45395e6i	−0.132136	−	0.228866i
$894$	−1.86326e6	−	2.15647e7i	−0.0779704	−	0.902402i
$895$	1.03192e6	−	1.78734e6i	0.0430616	−	0.0745848i
$896$	−9.19429e6	+	1.59250e7i	−0.382603	+	0.662687i
$897$	−929195.	+	649139.i	−0.0385590	+	0.0269374i
$898$	929542.	+	1.61001e6i	0.0384661	+	0.0666252i
$899$	2.79640e7			1.15399
$900$	−1.40521e7	+	2.44656e6i	−0.578275	+	0.100681i
$901$	2.56205e7			1.05142
$902$	−1.76839e6	−	3.06294e6i	−0.0723704	−	0.125349i
$903$	1.42969e7	+	6.68551e6i	0.583475	+	0.272844i
$904$	1.84754e7	−	3.20003e7i	0.751922	−	1.30237i
$905$	−171939.	+	297808.i	−0.00697837	+	0.0120869i
$906$	−1.39592e7	−	6.52761e6i	−0.564990	−	0.264200i
$907$	923315.	+	1.59923e6i	0.0372676	+	0.0645494i	0.884058	−	0.467378i	$-0.154801\pi$
$907$	923315.	+	1.59923e6i	0.0372676	+	0.0645494i	−0.846790	+	0.531927i	$0.821468\pi$
$908$	−1.02028e7			−0.410682
$909$	1.17556e7	+	1.40712e7i	0.471883	+	0.564835i
$910$	629807.			0.0252118
$911$	−2.19578e7	−	3.80320e7i	−0.876582	−	1.51829i	−0.855067	−	0.518517i	$-0.826484\pi$
$911$	−2.19578e7	−	3.80320e7i	−0.876582	−	1.51829i	−0.0215150	−	0.999769i	$-0.506849\pi$
$912$	−477125.	+	333321.i	−0.0189953	+	0.0132702i
$913$	−1.15022e7	+	1.99223e7i	−0.456670	+	0.790976i
$914$	−1.44093e7	+	2.49577e7i	−0.570529	+	0.988186i
$915$	20299.0	+	234933.i	0.000801534	+	0.00927667i
$916$	−1.09654e7	−	1.89926e7i	−0.431803	−	0.747904i
$917$	5.93438e6			0.233051
$918$	−2.13894e7	+	2.12516e7i	−0.837708	+	0.832310i
$919$	−2.53760e7			−0.991140			−0.495570	−	0.868568i	$-0.665041\pi$
$919$	−2.53760e7			−0.991140			−0.495570	+	0.868568i	$0.665041\pi$
$920$	−436606.	−	756224.i	−0.0170067	−	0.0294565i
$921$	1.68817e6	+	1.95383e7i	0.0655793	+	0.758991i
$922$	−6.31742e6	+	1.09421e7i	−0.244744	+	0.423909i
$923$	−2.69687e6	+	4.67112e6i	−0.104197	+	0.180475i
$924$	1.77896e7	−	1.24279e7i	0.685466	−	0.478869i
$925$	1.84205e6	+	3.19053e6i	0.0707861	+	0.122605i
$926$	2.72488e7			1.04429
$927$	8.48709e6	−	2.31627e7i	0.324384	−	0.885298i
$928$	2.82004e7			1.07494
$929$	2.02111e7	+	3.50067e7i	0.768336	+	1.33080i	0.938465	+	0.345375i	$0.112248\pi$
$929$	2.02111e7	+	3.50067e7i	0.768336	+	1.33080i	−0.170129	+	0.985422i	$0.554418\pi$
$930$	2.32177e6	+	1.08571e6i	0.0880262	+	0.0411628i
$931$	−6.22490e6	+	1.07818e7i	−0.235374	+	0.407680i
$932$	−7.85382e6	+	1.36032e7i	−0.296170	+	0.512982i
$933$	2.88768e7	+	1.35034e7i	1.08604	+	0.507854i
$934$	1.27090e7	+	2.20127e7i	0.476700	+	0.825668i
$935$	−7.45671e6			−0.278945
$936$	1.89490e6	−	5.17150e6i	0.0706964	−	0.192942i
$937$	1.79012e7			0.666089			0.333044	−	0.942911i	$-0.391924\pi$
$937$	1.79012e7			0.666089			0.333044	+	0.942911i	$0.391924\pi$
$938$	−1.23528e7	−	2.13957e7i	−0.458414	−	0.793996i
$939$	−1.20945e7	+	8.44925e6i	−0.447634	+	0.312719i
$940$	−549569.	+	951882.i	−0.0202863	+	0.0351369i
$941$	412928.	−	715212.i	0.0152020	−	0.0263306i	−0.858324	−	0.513108i	$-0.828494\pi$
$941$	412928.	−	715212.i	0.0152020	−	0.0263306i	0.873526	+	0.486777i	$0.161828\pi$
$942$	−2.46532e6	−	2.85327e7i	−0.0905202	−	1.04765i
$943$	702120.	+	1.21611e6i	0.0257118	+	0.0445341i
$944$	−408549.			−0.0149216
$945$	1.37763e6	+	5.20866e6i	0.0501825	+	0.189735i
$946$	−8.54440e6			−0.310423
$947$	−2.71734e7	−	4.70657e7i	−0.984620	−	1.70541i	−0.643614	−	0.765351i	$-0.722566\pi$
$947$	−2.71734e7	−	4.70657e7i	−0.984620	−	1.70541i	−0.341006	−	0.940061i	$-0.610768\pi$
$948$	−1.30712e6	−	1.51281e7i	−0.0472382	−	0.546718i
$949$	3.22509e6	−	5.58602e6i	0.116246	−	0.201343i
$950$	−4.88030e6	+	8.45293e6i	−0.175444	+	0.303877i
$951$	5.03789e6	−	3.51949e6i	0.180633	−	0.126191i
$952$	3.57382e7	+	6.19003e7i	1.27803	+	2.21361i
$953$	4.00436e6			0.142824			0.0714119	−	0.997447i	$-0.477250\pi$
$953$	4.00436e6			0.142824			0.0714119	+	0.997447i	$0.477250\pi$
$954$	6.42535e6	+	7.69102e6i	0.228573	+	0.273598i
$955$	2.16685e6			0.0768813
$956$	1.80811e6	+	3.13174e6i	0.0639854	+	0.110826i
$957$	−2.88271e7	−	1.34801e7i	−1.01747	−	0.475788i
$958$	−2.01941e6	+	3.49772e6i	−0.0710903	+	0.123132i
$959$	−1.64759e7	+	2.85371e7i	−0.578500	+	1.00199i
$960$	2.49487e6	+	1.16665e6i	0.0873714	+	0.0408566i
$961$	−1.73371e6	−	3.00287e6i	−0.0605574	−	0.104889i
$962$	−533242.			−0.0185775
$963$	4.28046e7	−	7.45254e6i	1.48739	−	0.258964i
$964$	−863842.			−0.0299393
$965$	1.03624e6	+	1.79482e6i	0.0358213	+	0.0620443i
$966$	4.71688e6	−	3.29523e6i	0.162634	−	0.113617i
$967$	−1.61712e7	+	2.80093e7i	−0.556130	+	0.963245i	0.441685	+	0.897170i	$0.354381\pi$
$967$	−1.61712e7	+	2.80093e7i	−0.556130	+	0.963245i	−0.997815	+	0.0660745i	$0.978952\pi$
$968$	−916646.	+	1.58768e6i	−0.0314422	+	0.0544595i
$969$	−2.65965e6	−	3.07819e7i	−0.0909946	−	1.05314i
$970$	627344.	+	1.08659e6i	0.0214080	+	0.0370798i
$971$	−2.08060e7			−0.708176			−0.354088	−	0.935212i	$-0.615209\pi$
$971$	−2.08060e7			−0.708176			−0.354088	+	0.935212i	$0.615209\pi$
$972$	1.75854e7	+	1.63402e6i	0.597015	+	0.0554742i
$973$	−5.95446e7			−2.01632
$974$	3.92505e6	+	6.79838e6i	0.132571	+	0.229619i
$975$	−507825.	−	5.87739e6i	−0.0171081	−	0.198004i
$976$	−39078.1	+	67685.2i	−0.00131313	+	0.00227441i
$977$	1.24444e7	−	2.15543e7i	0.417097	−	0.722433i	−0.578549	−	0.815647i	$-0.696381\pi$
$977$	1.24444e7	−	2.15543e7i	0.417097	−	0.722433i	0.995646	+	0.0932148i	$0.0297143\pi$
$978$	1.08088e7	−	7.55105e6i	0.361351	−	0.252441i
$979$	−9.62720e6	−	1.66748e7i	−0.321028	−	0.556037i
$980$	2.17288e6			0.0722719
$981$	9.09363e6	−	1.58326e6i	0.301693	−	0.0525266i
$982$	−1.49417e7			−0.494448
$983$	2.11280e6	+	3.65948e6i	0.0697388	+	0.120791i	0.898786	−	0.438387i	$-0.144450\pi$
$983$	2.11280e6	+	3.65948e6i	0.0697388	+	0.120791i	−0.829047	+	0.559178i	$0.811117\pi$
$984$	−6.18096e6	−	2.89034e6i	−0.203502	−	0.0951615i
$985$	2.63885e6	−	4.57062e6i	0.0866610	−	0.150101i
$986$	1.96447e7	−	3.40257e7i	0.643508	−	1.11459i
$987$	−1.75028e7	−	8.18468e6i	−0.571894	−	0.267429i
$988$	1.05775e6	+	1.83207e6i	0.0344739	+	0.0597105i
$989$	3.39246e6			0.110287
$990$	−1.87006e6	−	2.23843e6i	−0.0606412	−	0.0725864i
$991$	3.01661e7			0.975741			0.487871	−	0.872916i	$-0.337774\pi$
$991$	3.01661e7			0.975741			0.487871	+	0.872916i	$0.337774\pi$
$992$	−1.61840e7	−	2.80315e7i	−0.522163	−	0.904412i
$993$	−3.49702e7	+	2.44303e7i	−1.12545	+	0.786242i
$994$	1.36901e7	−	2.37120e7i	0.439483	−	0.761207i
$995$	1.60394e6	−	2.77811e6i	0.0513607	−	0.0889593i
$996$	1.43206e6	+	1.65741e7i	0.0457416	+	0.529397i
$997$	3.97488e6	+	6.88470e6i	0.126645	+	0.219355i	0.922375	−	0.386297i	$-0.126246\pi$
$997$	3.97488e6	+	6.88470e6i	0.126645	+	0.219355i	−0.795730	+	0.605652i	$0.792913\pi$
$998$	−1.44246e7			−0.458436
$999$	−1.16640e6	−	4.41004e6i	−0.0369773	−	0.139807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.6.c.a.4.3	✓	8
3.2	odd	2		27.6.c.a.10.2		8
4.3	odd	2		144.6.i.c.49.2		8
9.2	odd	6		27.6.c.a.19.2		8
9.4	even	3		81.6.a.c.1.2		4
9.5	odd	6		81.6.a.d.1.3		4
9.7	even	3	inner	9.6.c.a.7.3	yes	8
12.11	even	2		432.6.i.c.145.3		8
36.7	odd	6		144.6.i.c.97.2		8
36.11	even	6		432.6.i.c.289.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.6.c.a.4.3	✓	8	1.1	even	1	trivial
9.6.c.a.7.3	yes	8	9.7	even	3	inner
27.6.c.a.10.2		8	3.2	odd	2
27.6.c.a.19.2		8	9.2	odd	6
81.6.a.c.1.2		4	9.4	even	3
81.6.a.d.1.3		4	9.5	odd	6
144.6.i.c.49.2		8	4.3	odd	2
144.6.i.c.97.2		8	36.7	odd	6
432.6.i.c.145.3		8	12.11	even	2
432.6.i.c.289.3		8	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.78978 + 3.09998i) q^{2} +(1.34189 + 15.5306i) q^{3} +(9.59340 - 16.6162i) q^{4} +(4.05388 - 7.02152i) q^{5} +(-45.7429 + 31.9561i) q^{6} +(-87.7139 - 151.925i) q^{7} +183.226 q^{8} +(-239.399 + 41.6808i) q^{9} +O(q^{10})\)	\(q+(1.78978 + 3.09998i) q^{2} +(1.34189 + 15.5306i) q^{3} +(9.59340 - 16.6162i) q^{4} +(4.05388 - 7.02152i) q^{5} +(-45.7429 + 31.9561i) q^{6} +(-87.7139 - 151.925i) q^{7} +183.226 q^{8} +(-239.399 + 41.6808i) q^{9} +29.0221 q^{10} +(206.795 + 358.179i) q^{11} +(270.934 + 126.694i) q^{12} +(-61.8514 + 107.130i) q^{13} +(313.977 - 543.824i) q^{14} +(114.488 + 53.5370i) q^{15} +(20.9448 + 36.2775i) q^{16} -2223.70 q^{17} +(-557.680 - 667.533i) q^{18} +891.313 q^{19} +(-77.7809 - 134.720i) q^{20} +(2241.78 - 1566.12i) q^{21} +(-740.234 + 1282.12i) q^{22} +(293.902 - 509.053i) q^{23} +(245.869 + 2845.61i) q^{24} +(1529.63 + 2649.40i) q^{25} -442.801 q^{26} +(-968.574 - 3662.07i) q^{27} -3365.90 q^{28} +(2467.97 + 4274.65i) q^{29} +(38.9446 + 450.731i) q^{30} +(2832.69 - 4906.37i) q^{31} +(2856.64 - 4947.85i) q^{32} +(-5285.24 + 3692.29i) q^{33} +(-3979.93 - 6893.45i) q^{34} -1422.33 q^{35} +(-1604.07 + 4377.77i) q^{36} +1204.25 q^{37} +(1595.25 + 2763.06i) q^{38} +(-1746.79 - 816.832i) q^{39} +(742.775 - 1286.52i) q^{40} +(-1194.48 + 2068.90i) q^{41} +(8867.23 + 4146.49i) q^{42} +(2885.71 + 4998.19i) q^{43} +7935.46 q^{44} +(-677.830 + 1849.91i) q^{45} +2104.08 q^{46} +(-3532.81 - 6119.00i) q^{47} +(-535.306 + 373.966i) q^{48} +(-6983.97 + 12096.6i) q^{49} +(-5475.40 + 9483.67i) q^{50} +(-2983.97 - 34535.4i) q^{51} +(1186.73 + 2055.48i) q^{52} -11521.6 q^{53} +(9618.83 - 9556.86i) q^{54} +3353.28 q^{55} +(-16071.5 - 27836.6i) q^{56} +(1196.05 + 13842.6i) q^{57} +(-8834.24 + 15301.4i) q^{58} +(-4876.49 + 8446.33i) q^{59} +(1987.91 - 1388.76i) q^{60} +(932.881 + 1615.80i) q^{61} +20279.5 q^{62} +(27330.9 + 32714.6i) q^{63} +21791.5 q^{64} +(501.476 + 868.582i) q^{65} +(-20905.4 - 9775.80i) q^{66} +(19671.5 - 34072.0i) q^{67} +(-21332.9 + 36949.6i) q^{68} +(8300.28 + 3881.38i) q^{69} +(-2545.65 - 4409.19i) q^{70} +43602.4 q^{71} +(-43864.0 + 7637.00i) q^{72} -52142.6 q^{73} +(2155.33 + 3733.15i) q^{74} +(-39094.2 + 27311.3i) q^{75} +(8550.72 - 14810.3i) q^{76} +(36277.6 - 62834.6i) q^{77} +(-594.191 - 6876.96i) q^{78} +(-25384.2 - 43966.8i) q^{79} +339.631 q^{80} +(55574.4 - 19956.6i) q^{81} -8551.41 q^{82} +(27810.6 + 48169.3i) q^{83} +(-4516.67 - 52274.4i) q^{84} +(-9014.62 + 15613.8i) q^{85} +(-10329.5 + 17891.3i) q^{86} +(-63076.2 + 44065.2i) q^{87} +(37890.2 + 65627.7i) q^{88} -46554.3 q^{89} +(-6947.86 + 1209.67i) q^{90} +21700.9 q^{91} +(-5639.04 - 9767.10i) q^{92} +(79999.9 + 37409.6i) q^{93} +(12645.9 - 21903.3i) q^{94} +(3613.27 - 6258.38i) q^{95} +(80676.3 + 37725.9i) q^{96} +(21616.0 + 37440.1i) q^{97} -49999.0 q^{98} +(-64435.6 - 77128.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 12 * q^3 - 49 * q^4 + 78 * q^5 + 171 * q^6 + 28 * q^7 - 750 * q^8 - 414 * q^9	\( 8 q + 3 q^{2} - 12 q^{3} - 49 q^{4} + 78 q^{5} + 171 q^{6} + 28 q^{7} - 750 q^{8} - 414 q^{9} + 60 q^{10} + 444 q^{11} + 2724 q^{12} - 182 q^{13} + 1392 q^{14} - 2052 q^{15} - 289 q^{16} - 4356 q^{17} - 8100 q^{18} + 952 q^{19} + 6684 q^{20} + 8670 q^{21} + 1011 q^{22} + 8844 q^{23} + 549 q^{24} - 1654 q^{25} - 24888 q^{26} - 10152 q^{27} - 1604 q^{28} + 12018 q^{29} + 22104 q^{30} + 1132 q^{31} + 8703 q^{32} - 8820 q^{33} + 10125 q^{34} - 16224 q^{35} - 14589 q^{36} - 15176 q^{37} - 11145 q^{38} + 8220 q^{39} - 8736 q^{40} + 1248 q^{41} + 10098 q^{42} - 6092 q^{43} + 49530 q^{44} + 43038 q^{45} + 45960 q^{46} - 60 q^{47} - 57405 q^{48} + 9090 q^{49} - 57057 q^{50} - 9396 q^{51} - 32510 q^{52} + 20952 q^{53} + 8181 q^{54} - 36120 q^{55} - 61170 q^{56} - 104298 q^{57} + 8328 q^{58} + 2076 q^{59} + 88308 q^{60} + 48142 q^{61} + 241764 q^{62} + 133524 q^{63} - 20926 q^{64} - 13146 q^{65} - 100998 q^{66} - 7148 q^{67} - 123129 q^{68} - 125982 q^{69} - 654 q^{70} - 71856 q^{71} + 35451 q^{72} + 122452 q^{73} - 160320 q^{74} - 18732 q^{75} - 49571 q^{76} + 39534 q^{77} + 181422 q^{78} - 59516 q^{79} + 124512 q^{80} + 194562 q^{81} - 233598 q^{82} + 117696 q^{83} + 108354 q^{84} + 28836 q^{85} - 15915 q^{86} - 142956 q^{87} + 104523 q^{88} - 451728 q^{89} - 539892 q^{90} + 111392 q^{91} + 134034 q^{92} + 113898 q^{93} + 169464 q^{94} + 294888 q^{95} + 42768 q^{96} + 33976 q^{97} + 57654 q^{98} + 33696 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 12 * q^3 - 49 * q^4 + 78 * q^5 + 171 * q^6 + 28 * q^7 - 750 * q^8 - 414 * q^9 + 60 * q^10 + 444 * q^11 + 2724 * q^12 - 182 * q^13 + 1392 * q^14 - 2052 * q^15 - 289 * q^16 - 4356 * q^17 - 8100 * q^18 + 952 * q^19 + 6684 * q^20 + 8670 * q^21 + 1011 * q^22 + 8844 * q^23 + 549 * q^24 - 1654 * q^25 - 24888 * q^26 - 10152 * q^27 - 1604 * q^28 + 12018 * q^29 + 22104 * q^30 + 1132 * q^31 + 8703 * q^32 - 8820 * q^33 + 10125 * q^34 - 16224 * q^35 - 14589 * q^36 - 15176 * q^37 - 11145 * q^38 + 8220 * q^39 - 8736 * q^40 + 1248 * q^41 + 10098 * q^42 - 6092 * q^43 + 49530 * q^44 + 43038 * q^45 + 45960 * q^46 - 60 * q^47 - 57405 * q^48 + 9090 * q^49 - 57057 * q^50 - 9396 * q^51 - 32510 * q^52 + 20952 * q^53 + 8181 * q^54 - 36120 * q^55 - 61170 * q^56 - 104298 * q^57 + 8328 * q^58 + 2076 * q^59 + 88308 * q^60 + 48142 * q^61 + 241764 * q^62 + 133524 * q^63 - 20926 * q^64 - 13146 * q^65 - 100998 * q^66 - 7148 * q^67 - 123129 * q^68 - 125982 * q^69 - 654 * q^70 - 71856 * q^71 + 35451 * q^72 + 122452 * q^73 - 160320 * q^74 - 18732 * q^75 - 49571 * q^76 + 39534 * q^77 + 181422 * q^78 - 59516 * q^79 + 124512 * q^80 + 194562 * q^81 - 233598 * q^82 + 117696 * q^83 + 108354 * q^84 + 28836 * q^85 - 15915 * q^86 - 142956 * q^87 + 104523 * q^88 - 451728 * q^89 - 539892 * q^90 + 111392 * q^91 + 134034 * q^92 + 113898 * q^93 + 169464 * q^94 + 294888 * q^95 + 42768 * q^96 + 33976 * q^97 + 57654 * q^98 + 33696 * q^99

Introduction

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