LMFDB - Embedded newform 63.6.i.a.38.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(5,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("63.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.i (of order $6$, 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:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.19
Character	$\chi$	$=$	63.38
Dual form			63.6.i.a.5.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0365780i q^{2} +(-2.02604 + 15.4562i) q^{3} +31.9987 q^{4} +(31.2888 - 54.1937i) q^{5} +(-0.565358 - 0.0741087i) q^{6} +(39.4223 - 123.503i) q^{7} +2.34094i q^{8} +(-234.790 - 62.6300i) q^{9} +O(q^{10})$	\(q+0.0365780i q^{2} +(-2.02604 + 15.4562i) q^{3} +31.9987 q^{4} +(31.2888 - 54.1937i) q^{5} +(-0.565358 - 0.0741087i) q^{6} +(39.4223 - 123.503i) q^{7} +2.34094i q^{8} +(-234.790 - 62.6300i) q^{9} +(1.98230 + 1.14448i) q^{10} +(180.861 - 104.420i) q^{11} +(-64.8307 + 494.579i) q^{12} +(447.217 - 258.201i) q^{13} +(4.51748 + 1.44199i) q^{14} +(774.239 + 593.406i) q^{15} +1023.87 q^{16} +(-558.291 + 966.988i) q^{17} +(2.29088 - 8.58816i) q^{18} +(819.372 - 473.065i) q^{19} +(1001.20 - 1734.13i) q^{20} +(1829.01 + 859.543i) q^{21} +(3.81948 + 6.61553i) q^{22} +(885.200 + 511.070i) q^{23} +(-36.1822 - 4.74286i) q^{24} +(-395.475 - 684.983i) q^{25} +(9.44447 + 16.3583i) q^{26} +(1443.72 - 3502.08i) q^{27} +(1261.46 - 3951.92i) q^{28} +(-4524.33 - 2612.13i) q^{29} +(-21.7056 + 28.3201i) q^{30} +9267.49i q^{31} +112.361i q^{32} +(1247.51 + 3006.99i) q^{33} +(-35.3705 - 20.4212i) q^{34} +(-5459.59 - 6000.69i) q^{35} +(-7512.97 - 2004.08i) q^{36} +(1499.33 + 2596.91i) q^{37} +(17.3038 + 29.9710i) q^{38} +(3084.73 + 7435.42i) q^{39} +(126.865 + 73.2453i) q^{40} +(6210.55 + 10757.0i) q^{41} +(-31.4404 + 66.9016i) q^{42} +(6478.23 - 11220.6i) q^{43} +(5787.31 - 3341.30i) q^{44} +(-10740.5 + 10764.5i) q^{45} +(-18.6939 + 32.3788i) q^{46} -19958.5 q^{47} +(-2074.41 + 15825.2i) q^{48} +(-13698.8 - 9737.52i) q^{49} +(25.0553 - 14.4657i) q^{50} +(-13814.9 - 10588.2i) q^{51} +(14310.3 - 8262.08i) q^{52} +(-21892.1 - 12639.4i) q^{53} +(128.099 + 52.8084i) q^{54} -13068.7i q^{55} +(289.112 + 92.2855i) q^{56} +(5651.72 + 13622.9i) q^{57} +(95.5463 - 165.491i) q^{58} -33306.7 q^{59} +(24774.6 + 18988.2i) q^{60} -12080.5i q^{61} -338.986 q^{62} +(-16991.0 + 26528.2i) q^{63} +32759.8 q^{64} -32315.2i q^{65} +(-109.990 + 45.6314i) q^{66} +23717.0 q^{67} +(-17864.6 + 30942.3i) q^{68} +(-9692.68 + 12646.4i) q^{69} +(219.493 - 199.701i) q^{70} -53406.7i q^{71} +(146.613 - 549.631i) q^{72} +(67780.6 + 39133.2i) q^{73} +(-94.9898 + 54.8424i) q^{74} +(11388.5 - 4724.75i) q^{75} +(26218.8 - 15137.4i) q^{76} +(-5766.19 - 26453.3i) q^{77} +(-271.973 + 112.833i) q^{78} -49330.7 q^{79} +(32035.7 - 55487.4i) q^{80} +(51204.0 + 29409.9i) q^{81} +(-393.469 + 227.170i) q^{82} +(-28362.0 + 49124.5i) q^{83} +(58526.0 + 27504.2i) q^{84} +(34936.5 + 60511.8i) q^{85} +(410.428 + 236.961i) q^{86} +(49540.1 - 64636.9i) q^{87} +(244.442 + 423.385i) q^{88} +(57629.5 + 99817.2i) q^{89} +(-393.746 - 392.865i) q^{90} +(-14258.1 - 65411.3i) q^{91} +(28325.2 + 16353.6i) q^{92} +(-143240. - 18776.3i) q^{93} -730.042i q^{94} -59206.5i q^{95} +(-1736.68 - 227.649i) q^{96} +(-17070.5 - 9855.67i) q^{97} +(356.179 - 501.073i) q^{98} +(-49004.2 + 13189.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9}+O(q^{10}) $ 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9	\( 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9} - 6 q^{10} + 567 q^{11} - 1542 q^{12} + 543 q^{13} - 1638 q^{14} + 234 q^{15} + 16446 q^{16} - 801 q^{17} - 2022 q^{18} - 6 q^{19} + 96 q^{20} - 4119 q^{21} + 62 q^{22} + 7806 q^{23} - 2346 q^{24} - 18749 q^{25} + 10128 q^{26} - 1539 q^{27} + 860 q^{28} + 17904 q^{29} + 11457 q^{30} - 3 q^{33} + 96 q^{34} + 3960 q^{35} - 57846 q^{36} + 2577 q^{37} + 14967 q^{38} - 16269 q^{39} + 9564 q^{40} + 28230 q^{41} + 15606 q^{42} - 9246 q^{43} - 69885 q^{44} - 23649 q^{45} - 9418 q^{46} - 56562 q^{47} + 48615 q^{48} + 7948 q^{49} - 67509 q^{50} - 103722 q^{51} - 40899 q^{52} + 25296 q^{53} + 176211 q^{54} + 104754 q^{56} + 33399 q^{57} - 4951 q^{58} - 59076 q^{59} + 33729 q^{60} + 79536 q^{62} - 95871 q^{63} - 198600 q^{64} + 114900 q^{66} + 1244 q^{67} + 191496 q^{68} + 3702 q^{69} - 127197 q^{70} + 183582 q^{72} - 6 q^{73} - 45681 q^{74} - 240486 q^{75} - 2880 q^{76} + 13854 q^{77} + 184431 q^{78} + 59984 q^{79} + 243225 q^{80} + 177117 q^{81} + 90 q^{82} - 246930 q^{83} + 56085 q^{84} + 11973 q^{85} + 291801 q^{86} + 205125 q^{87} - 34751 q^{88} - 6345 q^{89} - 269187 q^{90} - 120111 q^{91} - 463488 q^{92} + 200946 q^{93} - 382521 q^{96} - 104037 q^{97} - 646797 q^{98} - 144540 q^{99}+O(q^{100}) \) 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9 - 6 * q^10 + 567 * q^11 - 1542 * q^12 + 543 * q^13 - 1638 * q^14 + 234 * q^15 + 16446 * q^16 - 801 * q^17 - 2022 * q^18 - 6 * q^19 + 96 * q^20 - 4119 * q^21 + 62 * q^22 + 7806 * q^23 - 2346 * q^24 - 18749 * q^25 + 10128 * q^26 - 1539 * q^27 + 860 * q^28 + 17904 * q^29 + 11457 * q^30 - 3 * q^33 + 96 * q^34 + 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 14967 * q^38 - 16269 * q^39 + 9564 * q^40 + 28230 * q^41 + 15606 * q^42 - 9246 * q^43 - 69885 * q^44 - 23649 * q^45 - 9418 * q^46 - 56562 * q^47 + 48615 * q^48 + 7948 * q^49 - 67509 * q^50 - 103722 * q^51 - 40899 * q^52 + 25296 * q^53 + 176211 * q^54 + 104754 * q^56 + 33399 * q^57 - 4951 * q^58 - 59076 * q^59 + 33729 * q^60 + 79536 * q^62 - 95871 * q^63 - 198600 * q^64 + 114900 * q^66 + 1244 * q^67 + 191496 * q^68 + 3702 * q^69 - 127197 * q^70 + 183582 * q^72 - 6 * q^73 - 45681 * q^74 - 240486 * q^75 - 2880 * q^76 + 13854 * q^77 + 184431 * q^78 + 59984 * q^79 + 243225 * q^80 + 177117 * q^81 + 90 * q^82 - 246930 * q^83 + 56085 * q^84 + 11973 * q^85 + 291801 * q^86 + 205125 * q^87 - 34751 * q^88 - 6345 * q^89 - 269187 * q^90 - 120111 * q^91 - 463488 * q^92 + 200946 * q^93 - 382521 * q^96 - 104037 * q^97 - 646797 * q^98 - 144540 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			0.0365780i			0.00646614i	0.999995	+	0.00323307i	$0.00102912\pi$
$2$			0.0365780i			0.00646614i	−0.999995	+	0.00323307i	$0.998971\pi$
$3$	−2.02604	+	15.4562i	−0.129971	+	0.991518i
$3$	−2.02604	+	15.4562i	−0.129971	+	0.991518i
$4$	31.9987			0.999958
$5$	31.2888	−	54.1937i	0.559711	−	0.969447i	−0.437810	−	0.899068i	$-0.644246\pi$
$5$	31.2888	−	54.1937i	0.559711	−	0.969447i	0.997520	−	0.0703796i	$-0.0224211\pi$
$6$	−0.565358	−	0.0741087i	−0.00641129	−	0.000840410i
$7$	39.4223	−	123.503i	0.304087	−	0.952644i
$7$	39.4223	−	123.503i	0.304087	−	0.952644i
$8$			2.34094i			0.0129320i
$9$	−234.790	−	62.6300i	−0.966215	−	0.257737i
$10$	1.98230	+	1.14448i	0.00626858	+	0.00361917i
$11$	180.861	−	104.420i	0.450674	−	0.260197i	−0.257441	−	0.966294i	$-0.582879\pi$
$11$	180.861	−	104.420i	0.450674	−	0.260197i	0.708115	+	0.706097i	$0.249546\pi$
$12$	−64.8307	+	494.579i	−0.129965	+	0.991476i
$13$	447.217	−	258.201i	0.733939	−	0.423740i	−0.0859226	−	0.996302i	$-0.527384\pi$
$13$	447.217	−	258.201i	0.733939	−	0.423740i	0.819861	+	0.572562i	$0.194050\pi$
$14$	4.51748	+	1.44199i	0.00615993	+	0.00196627i
$15$	774.239	+	593.406i	0.888478	+	0.680963i
$16$	1023.87			0.999875
$17$	−558.291	+	966.988i	−0.468531	+	0.811519i	−0.999353	−	0.0359638i	$-0.988550\pi$
$17$	−558.291	+	966.988i	−0.468531	+	0.811519i	0.530822	+	0.847483i	$0.321883\pi$
$18$	2.29088	−	8.58816i	0.00166656	−	0.00624768i
$19$	819.372	−	473.065i	0.520712	−	0.300633i	−0.216514	−	0.976279i	$-0.569469\pi$
$19$	819.372	−	473.065i	0.520712	−	0.300633i	0.737226	+	0.675646i	$0.236135\pi$
$20$	1001.20	−	1734.13i	0.559687	−	0.969407i
$21$	1829.01	+	859.543i	0.905041	+	0.425323i
$22$	3.81948	+	6.61553i	0.00168247	+	0.00291412i
$23$	885.200	+	511.070i	0.348917	+	0.201447i	0.664208	−	0.747548i	$-0.268769\pi$
$23$	885.200	+	511.070i	0.348917	+	0.201447i	−0.315291	+	0.948995i	$0.602102\pi$
$24$	−36.1822	−	4.74286i	−0.0128223	−	0.00168078i
$25$	−395.475	−	684.983i	−0.126552	−	0.219195i
$26$	9.44447	+	16.3583i	0.00273996	+	0.00474575i
$27$	1443.72	−	3502.08i	0.381130	−	0.924521i
$28$	1261.46	−	3951.92i	0.304074	−	0.952605i
$29$	−4524.33	−	2612.13i	−0.998987	−	0.576765i	−0.0910383	−	0.995847i	$-0.529019\pi$
$29$	−4524.33	−	2612.13i	−0.998987	−	0.576765i	−0.907948	+	0.419082i	$0.862352\pi$
$30$	−21.7056	+	28.3201i	−0.00440320	+	0.00574502i
$31$			9267.49i			1.73204i	0.500010	+	0.866020i	$0.333330\pi$
$31$			9267.49i			1.73204i	−0.500010	+	0.866020i	$0.666670\pi$
$32$			112.361i			0.0193973i
$33$	1247.51	+	3006.99i	0.199415	+	0.480670i
$34$	−35.3705	−	20.4212i	−0.00524740	−	0.00302959i
$35$	−5459.59	−	6000.69i	−0.753338	−	0.828001i
$36$	−7512.97	−	2004.08i	−0.966175	−	0.257726i
$37$	1499.33	+	2596.91i	0.180050	+	0.311855i	0.941897	−	0.335901i	$-0.109041\pi$
$37$	1499.33	+	2596.91i	0.180050	+	0.311855i	−0.761848	+	0.647756i	$0.775708\pi$
$38$	17.3038	+	29.9710i	0.00194394	+	0.00336699i
$39$	3084.73	+	7435.42i	0.324755	+	0.782787i
$40$	126.865	+	73.2453i	0.0125369	+	0.00723818i
$41$	6210.55	+	10757.0i	0.576993	+	0.999381i	0.995822	+	0.0913162i	$0.0291074\pi$
$41$	6210.55	+	10757.0i	0.576993	+	0.999381i	−0.418829	+	0.908065i	$0.637559\pi$
$42$	−31.4404	+	66.9016i	−0.00275020	+	0.00585212i
$43$	6478.23	−	11220.6i	0.534300	−	0.925434i	−0.464897	−	0.885365i	$-0.653909\pi$
$43$	6478.23	−	11220.6i	0.534300	−	0.925434i	0.999197	−	0.0400696i	$-0.0127580\pi$
$44$	5787.31	−	3341.30i	0.450656	−	0.260186i
$45$	−10740.5	+	10764.5i	−0.790663	+	0.792437i
$46$	−18.6939	+	32.3788i	−0.00130259	+	0.00225614i
$47$	−19958.5			−1.31790			−0.658951	−	0.752186i	$-0.729000\pi$
$47$	−19958.5			−1.31790			−0.658951	+	0.752186i	$0.729000\pi$
$48$	−2074.41	+	15825.2i	−0.129955	+	0.991393i
$49$	−13698.8	−	9737.52i	−0.815063	−	0.579373i
$50$	25.0553	−	14.4657i	0.00141734	−	0.000818303i
$51$	−13814.9	−	10588.2i	−0.743741	−	0.570031i
$52$	14310.3	−	8262.08i	0.733908	−	0.423722i
$53$	−21892.1	−	12639.4i	−1.07053	−	0.618069i	−0.142202	−	0.989838i	$-0.545418\pi$
$53$	−21892.1	−	12639.4i	−1.07053	−	0.618069i	−0.928326	+	0.371768i	$0.878752\pi$
$54$	128.099	+	52.8084i	0.00597808	+	0.00246444i
$55$		−	13068.7i		−	0.582540i
$56$	289.112	+	92.2855i	0.0123196	+	0.00393245i
$57$	5651.72	+	13622.9i	0.230406	+	0.555368i
$58$	95.5463	−	165.491i	0.00372944	−	0.00645959i
$59$	−33306.7			−1.24567			−0.622833	−	0.782355i	$-0.714018\pi$
$59$	−33306.7			−1.24567			−0.622833	+	0.782355i	$0.714018\pi$
$60$	24774.6	+	18988.2i	0.888441	+	0.680934i
$61$		−	12080.5i		−	0.415682i	−0.978163	−	0.207841i	$-0.933356\pi$
$61$		−	12080.5i		−	0.415682i	0.978163	−	0.207841i	$-0.0666437\pi$
$62$	−338.986			−0.0111996
$63$	−16991.0	+	26528.2i	−0.539345	+	0.842085i
$64$	32759.8			0.999749
$65$		−	32315.2i		−	0.948687i
$66$	−109.990	+	45.6314i	−0.00310808	+	0.00128945i
$67$	23717.0			0.645464			0.322732	−	0.946490i	$-0.395399\pi$
$67$	23717.0			0.645464			0.322732	+	0.946490i	$0.395399\pi$
$68$	−17864.6	+	30942.3i	−0.468511	+	0.811485i
$69$	−9692.68	+	12646.4i	−0.245087	+	0.319775i
$70$	219.493	−	199.701i	0.00535397	−	0.00487119i
$71$		−	53406.7i		−	1.25733i	−0.777675	−	0.628666i	$-0.783601\pi$
$71$		−	53406.7i		−	1.25733i	0.777675	−	0.628666i	$-0.216399\pi$
$72$	146.613	−	549.631i	0.00333305	−	0.0124951i
$73$	67780.6	+	39133.2i	1.48867	+	0.859484i	0.999916	−	0.0129379i	$-0.00411838\pi$
$73$	67780.6	+	39133.2i	1.48867	+	0.859484i	0.488754	+	0.872422i	$0.337452\pi$
$74$	−94.9898	+	54.8424i	−0.00201650	+	0.00116423i
$75$	11388.5	−	4724.75i	0.233783	−	0.0969897i
$76$	26218.8	−	15137.4i	0.520690	−	0.300620i
$77$	−5766.19	−	26453.3i	−0.110831	−	0.508455i
$78$	−271.973	+	112.833i	−0.00506161	+	0.00209991i
$79$	−49330.7			−0.889303			−0.444651	−	0.895704i	$-0.646672\pi$
$79$	−49330.7			−0.889303			−0.444651	+	0.895704i	$0.646672\pi$
$80$	32035.7	−	55487.4i	0.559640	−	0.969326i
$81$	51204.0	+	29409.9i	0.867143	+	0.498058i
$82$	−393.469	+	227.170i	−0.00646214	+	0.00373092i
$83$	−28362.0	+	49124.5i	−0.451899	+	0.782713i	−0.998504	−	0.0546780i	$-0.982587\pi$
$83$	−28362.0	+	49124.5i	−0.451899	+	0.782713i	0.546605	+	0.837391i	$0.315920\pi$
$84$	58526.0	+	27504.2i	0.905004	+	0.425306i
$85$	34936.5	+	60511.8i	0.524484	+	0.908432i
$86$	410.428	+	236.961i	0.00598399	+	0.00345486i
$87$	49540.1	−	64636.9i	0.701712	−	0.915550i
$88$	244.442	+	423.385i	0.00336487	+	0.00582813i
$89$	57629.5	+	99817.2i	0.771205	+	1.33577i	0.936903	+	0.349589i	$0.113679\pi$
$89$	57629.5	+	99817.2i	0.771205	+	1.33577i	−0.165698	+	0.986177i	$0.552988\pi$
$90$	−393.746	−	392.865i	−0.00512401	−	0.00511254i
$91$	−14258.1	−	65411.3i	−0.180492	−	0.828036i
$92$	28325.2	+	16353.6i	0.348902	+	0.201439i
$93$	−143240.	−	18776.3i	−1.71735	−	0.225115i
$94$		−	730.042i		−	0.00852174i
$95$		−	59206.5i		−	0.673070i
$96$	−1736.68	−	227.649i	−0.0192328	−	0.00252109i
$97$	−17070.5	−	9855.67i	−0.184212	−	0.106355i	0.405058	−	0.914291i	$-0.367251\pi$
$97$	−17070.5	−	9855.67i	−0.184212	−	0.106355i	−0.589270	+	0.807936i	$0.700585\pi$
$98$	356.179	−	501.073i	0.00374631	−	0.00527031i
$99$	−49004.2	+	13189.5i	−0.502511	+	0.135251i
$100$	−12654.7	−	21918.5i	−0.126547	−	0.219185i
$101$	45209.5	+	78305.2i	0.440988	+	0.763813i	0.997763	−	0.0668501i	$-0.0212949\pi$
$101$	45209.5	+	78305.2i	0.440988	+	0.763813i	−0.556775	+	0.830663i	$0.687962\pi$
$102$	387.297	−	505.321i	0.00368590	−	0.00480913i
$103$	−118542.	−	68440.0i	−1.10098	−	0.635649i	−0.164499	−	0.986377i	$-0.552601\pi$
$103$	−118542.	−	68440.0i	−1.10098	−	0.635649i	−0.936477	+	0.350728i	$0.885934\pi$
$104$	604.434	+	1046.91i	0.00547981	+	0.00949130i
$105$	103809.	−	72227.0i	0.918890	−	0.639332i
$106$	462.325	−	800.770i	0.00399652	−	0.00692218i
$107$	42006.7	−	24252.6i	0.354698	−	0.204785i	−0.312055	−	0.950064i	$-0.601017\pi$
$107$	42006.7	−	24252.6i	0.354698	−	0.204785i	0.666752	+	0.745279i	$0.267684\pi$
$108$	46197.1	−	112062.i	0.381115	−	0.924483i
$109$	−62765.7	+	108713.i	−0.506007	+	0.876429i	0.493969	+	0.869479i	$0.335546\pi$
$109$	−62765.7	+	108713.i	−0.506007	+	0.876429i	−0.999976	+	0.00695000i	$0.997788\pi$
$110$	478.027			0.00376679
$111$	−43176.2	+	17912.5i	−0.332611	+	0.137990i
$112$	40363.4	−	126451.i	0.304048	−	0.952525i
$113$	−31167.2	+	17994.4i	−0.229616	+	0.132569i	−0.610395	−	0.792097i	$-0.708989\pi$
$113$	−31167.2	+	17994.4i	−0.229616	+	0.132569i	0.380779	+	0.924666i	$0.375656\pi$
$114$	−498.297	+	206.729i	−0.00359109	+	0.00148984i
$115$	55393.6	−	31981.5i	0.390585	−	0.225504i
$116$	−144773.	−	83584.5i	−0.998945	−	0.576741i
$117$	−121173.	+	32613.8i	−0.818356	+	0.220261i
$118$		−	1218.29i		−	0.00805465i
$119$	97416.4	+	107071.i	0.630615	+	0.693116i
$120$	−1389.13	+	1812.45i	−0.00880622	+	0.0114898i
$121$	−58718.4	+	101703.i	−0.364595	+	0.631497i
$122$	441.882			0.00268786
$123$	−178845.	+	74197.6i	−1.06590	+	0.442208i
$124$			296547.i			1.73197i
$125$	146059.			0.836091
$126$	−970.348	−	621.495i	−0.00544504	−	0.00348748i
$127$	−155648.			−0.856315			−0.428157	−	0.903704i	$-0.640837\pi$
$127$	−155648.			−0.856315			−0.428157	+	0.903704i	$0.640837\pi$
$128$			4793.85i			0.0258619i
$129$	160303.	+	122862.i	0.848141	+	0.650047i
$130$	1182.02			0.00613434
$131$	−119695.	+	207319.i	−0.609395	+	1.05550i	0.381945	+	0.924185i	$0.375254\pi$
$131$	−119695.	+	207319.i	−0.609395	+	1.05550i	−0.991340	+	0.131319i	$0.958079\pi$
$132$	39918.6	+	96219.6i	0.199407	+	0.480650i
$133$	−26123.1	−	119844.i	−0.128055	−	0.587472i
$134$			867.519i			0.00417366i
$135$	−144619.	−	187816.i	−0.682952	−	0.886950i
$136$	−2263.66	−	1306.93i	−0.0104946	−	0.00605905i
$137$	41030.9	−	23689.2i	0.186771	−	0.107832i	−0.403699	−	0.914892i	$-0.632276\pi$
$137$	41030.9	−	23689.2i	0.186771	−	0.107832i	0.590470	+	0.807060i	$0.298942\pi$
$138$	−462.580	−	354.539i	−0.00206771	−	0.00158477i
$139$	−40845.5	+	23582.1i	−0.179311	+	0.103525i	−0.586969	−	0.809609i	$-0.699679\pi$
$139$	−40845.5	+	23582.1i	−0.179311	+	0.103525i	0.407658	+	0.913135i	$0.366346\pi$
$140$	−174700.	−	192014.i	−0.753306	−	0.827967i
$141$	40436.8	−	308483.i	0.171289	−	1.30672i
$142$	1953.51			0.00813009
$143$	53922.7	−	93396.9i	0.220512	−	0.381937i
$144$	−240395.	−	64125.1i	−0.966094	−	0.257704i
$145$	−283122.	+	163460.i	−1.11829	+	0.645643i
$146$	−1431.41	+	2479.28i	−0.00555754	+	0.00962595i
$147$	178260.	−	192003.i	0.680393	−	0.732848i
$148$	47976.5	+	83097.7i	0.180042	+	0.311842i
$149$	−333625.	−	192619.i	−1.23110	−	0.710776i	−0.263841	−	0.964566i	$-0.584989\pi$
$149$	−333625.	−	192619.i	−1.23110	−	0.710776i	−0.967259	+	0.253790i	$0.918323\pi$
$150$	172.822	+	416.569i	0.000627149	+	0.00151168i
$151$	57562.5	+	99701.2i	0.205446	+	0.355843i	0.950275	−	0.311413i	$-0.100802\pi$
$151$	57562.5	+	99701.2i	0.205446	+	0.355843i	−0.744829	+	0.667256i	$0.767469\pi$
$152$	1107.42	+	1918.10i	0.00388779	+	0.00673385i
$153$	191644.	−	192074.i	0.661860	−	0.663345i
$154$	967.608	−	210.916i	0.00328774	−	0.000716650i
$155$	502240.	+	289968.i	1.67912	+	0.969441i
$156$	98707.2	+	237923.i	0.324741	+	0.782755i
$157$			26531.4i			0.0859035i	0.999077	+	0.0429518i	$0.0136762\pi$
$157$			26531.4i			0.0859035i	−0.999077	+	0.0429518i	$0.986324\pi$
$158$		−	1804.42i		−	0.00575036i
$159$	239712.	−	312762.i	0.751964	−	0.981116i
$160$	6089.28	+	3515.65i	0.0188047	+	0.0108569i
$161$	98015.1	−	89176.8i	0.298008	−	0.271136i
$162$	−1075.75	+	1872.94i	−0.00322052	+	0.00560707i
$163$	−224228.	−	388374.i	−0.661030	−	1.14494i	−0.980345	−	0.197289i	$-0.936786\pi$
$163$	−224228.	−	388374.i	−0.661030	−	1.14494i	0.319316	−	0.947648i	$-0.396547\pi$
$164$	198729.	+	344209.i	0.576969	+	0.999340i
$165$	201993.	+	26477.8i	0.577599	+	0.0757132i
$166$	−1796.87	−	1037.43i	−0.00506113	−	0.00292205i
$167$	222908.	+	386089.i	0.618494	+	1.07126i	0.989761	+	0.142737i	$0.0455902\pi$
$167$	222908.	+	386089.i	0.618494	+	1.07126i	−0.371267	+	0.928526i	$0.621077\pi$
$168$	−2012.14	+	4281.62i	−0.00550028	+	0.0117040i
$169$	−52311.2	+	90605.6i	−0.140889	+	0.244027i
$170$	−2213.40	+	1277.91i	−0.00587405	+	0.00339138i
$171$	−222009.	+	59753.7i	−0.580604	+	0.156270i
$172$	207295.	−	359045.i	0.534277	−	0.925396i
$173$	378926.			0.962585			0.481292	−	0.876560i	$-0.340168\pi$
$173$	378926.			0.962585			0.481292	+	0.876560i	$0.340168\pi$
$174$	2364.29	+	1812.08i	0.00592008	+	0.00453737i
$175$	−100188.	+	21838.5i	−0.247297	+	0.0539049i
$176$	185178.	−	106913.i	0.450618	−	0.260164i
$177$	67480.9	−	514796.i	0.161900	−	1.23510i
$178$	−3651.11	+	2107.97i	−0.00863725	+	0.00498672i
$179$	571478.	+	329943.i	1.33311	+	0.769673i	0.985775	−	0.168068i	$-0.0537528\pi$
$179$	571478.	+	329943.i	1.33311	+	0.769673i	0.347337	+	0.937740i	$0.387086\pi$
$180$	−343680.	+	344451.i	−0.790630	+	0.792403i
$181$			551804.i			1.25195i	0.779842	+	0.625977i	$0.215299\pi$
$181$			551804.i			1.25195i	−0.779842	+	0.625977i	$0.784701\pi$
$182$	2392.62	−	521.534i	0.00535420	−	0.00116709i
$183$	186719.	+	24475.7i	0.412156	+	0.0540265i
$184$	−1196.39	+	2072.20i	−0.00260512	+	0.00451219i
$185$	187648.			0.403103
$186$	686.801	−	5239.45i	0.00145562	−	0.0111046i
$187$			233187.i			0.487641i
$188$	−638645.			−1.31785
$189$	−375601.	−	316363.i	−0.764843	−	0.644216i
$190$	2165.66			0.00435216
$191$		−	41151.2i		−	0.0816204i	−0.999167	−	0.0408102i	$-0.987006\pi$
$191$		−	41151.2i		−	0.0816204i	0.999167	−	0.0408102i	$-0.0129939\pi$
$192$	−66372.8	+	506343.i	−0.129938	+	0.991269i
$193$	324000.			0.626111			0.313056	−	0.949735i	$-0.398647\pi$
$193$	324000.			0.626111			0.313056	+	0.949735i	$0.398647\pi$
$194$	360.501	−	624.406i	0.000687705	−	0.00119114i
$195$	499470.	+	65471.9i	0.940640	+	0.123302i
$196$	−438342.	−	311588.i	−0.815029	−	0.579349i
$197$		−	898843.i		−	1.65013i	−0.565038	−	0.825065i	$-0.691138\pi$
$197$		−	898843.i		−	1.65013i	0.565038	−	0.825065i	$-0.308862\pi$
$198$	−482.445	−	1792.48i	−0.000874551	−	0.00324930i
$199$	−185743.	−	107239.i	−0.332491	−	0.191964i	0.324455	−	0.945901i	$-0.394819\pi$
$199$	−185743.	−	107239.i	−0.332491	−	0.191964i	−0.656947	+	0.753937i	$0.728152\pi$
$200$	1603.51	−	925.785i	0.00283463	−	0.00163657i
$201$	−48051.6	+	366575.i	−0.0838915	+	0.639989i
$202$	−2864.25	+	1653.67i	−0.00493892	+	0.00285149i
$203$	−500964.	+	455791.i	−0.853231	+	0.776292i
$204$	−442057.	−	338809.i	−0.743709	−	0.570007i
$205$	777282.			1.29180
$206$	2503.40	−	4336.02i	0.00411019	−	0.00711906i
$207$	−175828.	−	175434.i	−0.285208	−	0.284570i
$208$	457893.	−	264364.i	0.733847	−	0.423687i
$209$	98794.9	−	171118.i	0.156448	−	0.270975i
$210$	2641.92	+	3797.14i	0.00413401	+	0.00594167i
$211$	77523.0	+	134274.i	0.119874	+	0.207628i	0.919718	−	0.392581i	$-0.128418\pi$
$211$	77523.0	+	134274.i	0.119874	+	0.207628i	−0.799844	+	0.600208i	$0.795084\pi$
$212$	−700518.	−	404444.i	−1.07048	−	0.618044i
$213$	825467.	+	108204.i	1.24667	+	0.163417i
$214$	887.110	+	1536.52i	0.00132417	+	0.00229353i
$215$	−405392.	−	702159.i	−0.598107	−	1.03595i
$216$	8198.18	+	3379.67i	0.0119559	+	0.00492878i
$217$	1.14456e6	+	365346.i	1.65002	+	0.526690i
$218$	−3976.52	−	2295.85i	−0.00566712	−	0.00327191i
$219$	−742178.	+	968348.i	−1.04568	+	1.36433i
$220$		−	418181.i		−	0.582516i
$221$			576605.i			0.794141i
$222$	−655.203	−	1579.30i	−0.000892264	−	0.00215071i
$223$	−906052.	−	523109.i	−1.22009	−	0.704418i	−0.255151	−	0.966901i	$-0.582125\pi$
$223$	−906052.	−	523109.i	−1.22009	−	0.704418i	−0.964937	+	0.262483i	$0.915459\pi$
$224$	13876.9	+	4429.55i	0.0184788	+	0.00589847i
$225$	49953.2	+	185596.i	0.0657820	+	0.244406i
$226$	−658.200	−	1140.04i	−0.000857209	−	0.00148473i
$227$	−451687.	−	782345.i	−0.581799	−	1.00771i	−0.995266	−	0.0971863i	$-0.969016\pi$
$227$	−451687.	−	782345.i	−0.581799	−	1.00771i	0.413467	−	0.910519i	$-0.364318\pi$
$228$	180847.	+	435913.i	0.230396	+	0.555345i
$229$	−523363.	−	302164.i	−0.659499	−	0.380762i	0.132587	−	0.991171i	$-0.457672\pi$
$229$	−523363.	−	302164.i	−0.659499	−	0.380762i	−0.792086	+	0.610409i	$0.791005\pi$
$230$	1169.82	+	2026.19i	0.00145814	+	0.00252557i
$231$	420550.	−	35528.0i	0.518547	−	0.0438067i
$232$	6114.84	−	10591.2i	0.00745873	−	0.0129189i
$233$	−238586.	+	137747.i	−0.287908	+	0.166224i	−0.636998	−	0.770865i	$-0.719824\pi$
$233$	−238586.	+	137747.i	−0.287908	+	0.166224i	0.349090	+	0.937089i	$0.386491\pi$
$234$	−1192.95	−	4432.28i	−0.00142424	−	0.00529160i
$235$	−624477.	+	1.08163e6i	−0.737644	+	1.27764i
$236$	−1.06577e6			−1.24561
$237$	99946.2	−	762467.i	0.115583	−	0.881760i
$238$	−3916.45	+	3563.30i	−0.00448178	+	0.00407765i
$239$	−916492.	+	529137.i	−1.03785	+	0.599202i	−0.919223	−	0.393737i	$-0.871182\pi$
$239$	−916492.	+	529137.i	−1.03785	+	0.599202i	−0.118625	+	0.992939i	$0.537849\pi$
$240$	792721.	+	607571.i	0.888367	+	0.680878i
$241$	429127.	−	247757.i	0.475930	−	0.274778i	−0.242789	−	0.970079i	$-0.578062\pi$
$241$	429127.	−	247757.i	0.475930	−	0.274778i	0.718719	+	0.695301i	$0.244729\pi$
$242$	−3720.10	−	2147.80i	−0.00408335	−	0.00235752i
$243$	−558307.	+	731835.i	−0.606537	+	0.795055i
$244$		−	386561.i		−	0.415665i
$245$	−956330.	+	437712.i	−1.01787	+	0.465879i
$246$	−2714.00	−	6541.81i	−0.00285938	−	0.00689224i
$247$	244291.	−	423125.i	0.254780	−	0.441293i
$248$	−21694.7			−0.0223987
$249$	−701816.	−	537898.i	−0.717340	−	0.549796i
$250$			5342.55i			0.00540628i
$251$	773459.			0.774913			0.387456	−	0.921888i	$-0.373354\pi$
$251$	773459.			0.774913			0.387456	+	0.921888i	$0.373354\pi$
$252$	−543688.	+	848866.i	−0.539322	+	0.842050i
$253$	213464.			0.209664
$254$		−	5693.28i		−	0.00553705i
$255$	−1.00607e6	+	417387.i	−0.968894	+	0.401965i
$256$	1.04814e6			0.999582
$257$	545691.	−	945164.i	0.515364	−	0.892636i	−0.484477	−	0.874804i	$-0.660990\pi$
$257$	545691.	−	945164.i	0.515364	−	0.892636i	0.999841	−	0.0178322i	$-0.00567645\pi$
$258$	−4494.06	+	5863.58i	−0.00420330	+	0.00548420i
$259$	379832.	−	82794.4i	0.351838	−	0.0766923i
$260$		−	1.03404e6i		−	0.948647i
$261$	898672.	+	896661.i	0.816582	+	0.814755i
$262$	−7583.30	−	4378.22i	−0.00682503	−	0.00394044i
$263$	−315104.	+	181925.i	−0.280908	+	0.162183i	−0.633835	−	0.773469i	$-0.718520\pi$
$263$	−315104.	+	181925.i	−0.280908	+	0.162183i	0.352926	+	0.935651i	$0.385187\pi$
$264$	−7039.19	+	2920.35i	−0.00621603	+	0.00257884i
$265$	−1.36995e6	+	790944.i	−1.19837	+	0.691880i
$266$	4383.65	−	955.532i	0.00379867	−	0.000828021i
$267$	−1.65956e6	+	688501.i	−1.42467	+	0.591053i
$268$	758911.			0.645437
$269$	189727.	−	328617.i	0.159863	−	0.276891i	−0.774956	−	0.632015i	$-0.782228\pi$
$269$	189727.	−	328617.i	0.159863	−	0.276891i	0.934819	+	0.355124i	$0.115561\pi$
$270$	6869.95	−	5289.86i	0.00573514	−	0.00441606i
$271$	1.70719e6	−	985645.i	1.41208	−	0.815262i	0.416492	−	0.909139i	$-0.363259\pi$
$271$	1.70719e6	−	985645.i	1.41208	−	0.815262i	0.995584	+	0.0938771i	$0.0299261\pi$
$272$	−571618.	+	990072.i	−0.468472	+	0.811418i
$273$	1.03990e6	−	87850.6i	0.844471	−	0.0713408i
$274$	866.504	+	1500.83i	0.000697259	+	0.00120769i
$275$	−143052.	−	82591.1i	−0.114068	−	0.0658569i
$276$	−310153.	+	404668.i	−0.245077	+	0.319761i
$277$	−1.00005e6	−	1.73214e6i	−0.783109	−	1.35638i	−0.930122	−	0.367250i	$-0.880299\pi$
$277$	−1.00005e6	−	1.73214e6i	−0.783109	−	1.35638i	0.147013	−	0.989135i	$-0.453034\pi$
$278$	−862.588	−	1494.05i	−0.000669408	−	0.00115945i
$279$	580423.	−	2.17592e6i	0.446410	−	1.67352i
$280$	14047.3	−	12780.6i	0.0107077	−	0.00974217i
$281$	2.15849e6	+	1.24620e6i	1.63074	+	0.941506i	0.983866	+	0.178906i	$0.0572558\pi$
$281$	2.15849e6	+	1.24620e6i	1.63074	+	0.941506i	0.646870	+	0.762600i	$0.276078\pi$
$282$	11283.7	+	1479.10i	0.00844946	+	0.00110758i
$283$			418981.i			0.310977i	0.987838	+	0.155489i	$0.0496952\pi$
$283$			418981.i			0.310977i	−0.987838	+	0.155489i	$0.950305\pi$
$284$		−	1.70894e6i		−	1.25728i
$285$	915109.	+	119955.i	0.667361	+	0.0874795i
$286$	3416.27	+	1972.38i	0.00246966	+	0.00142586i
$287$	1.57335e6	−	342953.i	1.12751	−	0.245771i
$288$	7037.20	−	26381.4i	0.00499941	−	0.0187420i
$289$	86550.9	+	149911.i	0.0609575	+	0.105581i
$290$	−5979.06	−	10356.0i	−0.00417482	−	0.00723100i
$291$	186917.	−	243878.i	0.129395	−	0.168826i
$292$	2.16889e6	+	1.25221e6i	1.48861	+	0.859448i
$293$	1.04949e6	+	1.81777e6i	0.714182	+	1.23700i	0.963274	+	0.268520i	$0.0865344\pi$
$293$	1.04949e6	+	1.81777e6i	0.714182	+	1.23700i	−0.249092	+	0.968480i	$0.580132\pi$
$294$	7023.07	+	6520.38i	0.00473869	+	0.00439952i
$295$	−1.04213e6	+	1.80502e6i	−0.697213	+	1.20761i
$296$	−6079.22	+	3509.84i	−0.00403291	+	0.00232840i
$297$	−104575.	−	784143.i	−0.0687919	−	0.515827i
$298$	7045.61	−	12203.4i	0.00459598	−	0.00796047i
$299$	527835.			0.341445
$300$	364417.	−	151186.i	0.233774	−	0.0969856i
$301$	−1.13039e6	−	1.24242e6i	−0.719136	−	0.790410i
$302$	−3646.87	+	2105.52i	−0.00230093	+	0.00132844i
$303$	−1.30190e6	+	540119.i	−0.814650	+	0.337974i
$304$	838932.	−	484358.i	0.520646	−	0.300595i
$305$	−654689.	−	377985.i	−0.402982	−	0.232662i
$306$	7025.67	+	7009.95i	0.00428928	+	0.00427968i
$307$		−	1.64040e6i		−	0.993356i	−0.867935	−	0.496678i	$-0.834553\pi$
$307$		−	1.64040e6i		−	0.993356i	0.867935	−	0.496678i	$-0.165447\pi$
$308$	−184510.	−	846469.i	−0.110827	−	0.508434i
$309$	1.29800e6	−	1.69354e6i	0.773352	−	1.00902i
$310$	−10606.5	+	18370.9i	−0.00626854	+	0.0108574i
$311$	−2.85866e6			−1.67595			−0.837977	−	0.545706i	$-0.816262\pi$
$311$	−2.85866e6			−1.67595			−0.837977	+	0.545706i	$0.816262\pi$
$312$	−17405.9	+	7221.18i	−0.0101230	+	0.00419973i
$313$			419020.i			0.241754i	0.992667	+	0.120877i	$0.0385707\pi$
$313$			419020.i			0.241754i	−0.992667	+	0.120877i	$0.961429\pi$
$314$	−970.465			−0.000555464
$315$	906035.	+	1.75084e6i	0.514480	+	0.994190i
$316$	−1.57852e6			−0.889266
$317$		−	464505.i		−	0.259622i	−0.991539	−	0.129811i	$-0.958563\pi$
$317$		−	464505.i		−	0.259622i	0.991539	−	0.129811i	$-0.0414371\pi$
$318$	11440.2	+	8768.19i	0.00634404	+	0.00486231i
$319$	−1.09103e6			−0.600290
$320$	1.02501e6	−	1.77538e6i	0.559570	−	0.969204i
$321$	289746.	+	698401.i	0.156948	+	0.378305i
$322$	3261.91	+	3585.20i	0.00175320	+	0.00192696i
$323$			1.05643e6i			0.563424i
$324$	1.63846e6	+	941076.i	0.867107	+	0.498038i
$325$	−353726.	−	204224.i	−0.185763	−	0.107250i
$326$	14206.0	−	8201.82i	0.00740332	−	0.00427431i
$327$	−1.55313e6	−	1.19038e6i	−0.803229	−	0.615625i
$328$	−25181.5	+	14538.6i	−0.0129240	+	0.00746168i
$329$	−786811.	+	2.46493e6i	−0.400756	+	1.25549i
$330$	−968.505	+	7388.50i	−0.000489572	+	0.00373484i
$331$	3.42502e6			1.71828			0.859138	−	0.511743i	$-0.171000\pi$
$331$	3.42502e6			1.71828			0.859138	+	0.511743i	$0.171000\pi$
$332$	−907547.	+	1.57192e6i	−0.451881	+	0.782680i
$333$	−189383.	−	703632.i	−0.0935901	−	0.347724i
$334$	−14122.4	+	8153.55i	−0.00692693	+	0.00399927i
$335$	742075.	−	1.28531e6i	0.361273	−	0.625743i
$336$	1.87267e6	+	880061.i	0.904928	+	0.425270i
$337$	1.98556e6	+	3.43909e6i	0.952376	+	1.64956i	0.740262	+	0.672318i	$0.234701\pi$
$337$	1.98556e6	+	3.43909e6i	0.952376	+	1.64956i	0.212114	+	0.977245i	$0.431965\pi$
$338$	−3314.17	−	1913.44i	−0.00157791	−	0.000911009i
$339$	−214980.	−	518186.i	−0.101601	−	0.244898i
$340$	1.11792e6	+	1.93630e6i	0.524462	+	0.908394i
$341$	967712.	+	1.67613e6i	0.450671	+	0.780586i
$342$	−2185.67	−	8120.64i	−0.00101046	−	0.00375426i
$343$	−1.74265e6	+	1.30796e6i	−0.799786	+	0.600285i
$344$	26266.8	+	15165.2i	0.0119677	+	0.00690957i
$345$	382084.	+	920973.i	0.172827	+	0.416581i
$346$			13860.4i			0.00622421i
$347$		−	3.14735e6i		−	1.40321i	−0.712568	−	0.701603i	$-0.752468\pi$
$347$		−	3.14735e6i		−	1.40321i	0.712568	−	0.701603i	$-0.247532\pi$
$348$	1.58522e6	−	2.06829e6i	0.701683	−	0.915512i
$349$	−2.32028e6	−	1.33961e6i	−1.01971	−	0.588730i	−0.105690	−	0.994399i	$-0.533705\pi$
$349$	−2.32028e6	−	1.33961e6i	−1.01971	−	0.588730i	−0.914020	+	0.405669i	$0.867038\pi$
$350$	−798.810	−	3664.67i	−0.000348557	−	0.00159906i
$351$	−258584.	−	1.93896e6i	−0.112030	−	0.840042i
$352$	11732.8	+	20321.8i	0.00504713	+	0.00874188i
$353$	−637458.	−	1.10411e6i	−0.272280	−	0.471602i	0.697166	−	0.716910i	$-0.254444\pi$
$353$	−637458.	−	1.10411e6i	−0.272280	−	0.471602i	−0.969445	+	0.245308i	$0.921111\pi$
$354$	18830.2	+	2468.32i	0.00798633	+	0.00104687i
$355$	−2.89431e6	−	1.67103e6i	−1.21892	−	0.703743i
$356$	1.84407e6	+	3.19402e6i	0.771173	+	1.33571i
$357$	−1.85229e6	+	1.28876e6i	−0.769198	+	0.535182i
$358$	−12068.6	+	20903.5i	−0.00497681	+	0.00862009i
$359$	−1.66089e6	+	958913.i	−0.680148	+	0.392684i	−0.799911	−	0.600119i	$-0.795120\pi$
$359$	−1.66089e6	+	958913.i	−0.680148	+	0.392684i	0.119763	+	0.992803i	$0.461787\pi$
$360$	−25199.2	−	25142.8i	−0.0102478	−	0.0102249i
$361$	−790469.	+	1.36913e6i	−0.319240	+	0.552939i
$362$	−20183.9			−0.00809530
$363$	−1.45298e6	−	1.11362e6i	−0.578754	−	0.443579i
$364$	−456241.	−	2.09307e6i	−0.180485	−	0.828002i
$365$	4.24155e6	−	2.44886e6i	1.66645	−	0.962125i
$366$	−895.272	+	6829.82i	−0.000349343	+	0.00266506i
$367$	−2.12996e6	+	1.22973e6i	−0.825478	+	0.476590i	−0.852302	−	0.523050i	$-0.824794\pi$
$367$	−2.12996e6	+	1.22973e6i	−0.825478	+	0.476590i	0.0268238	+	0.999640i	$0.491461\pi$
$368$	906331.	+	523270.i	0.348873	+	0.201422i
$369$	−784466.	−	2.91460e6i	−0.299922	−	1.11433i
$370$			6863.81i			0.00260652i
$371$	−2.42404e6	+	2.20546e6i	−0.914334	+	0.831886i
$372$	−4.58350e6	−	600818.i	−1.71728	−	0.225105i
$373$	1.33024e6	−	2.30405e6i	0.495061	−	0.857471i	−0.504922	−	0.863165i	$-0.668479\pi$
$373$	1.33024e6	−	2.30405e6i	0.495061	−	0.857471i	0.999984	+	0.00569329i	$0.00181224\pi$
$374$	−8529.52			−0.00315316
$375$	−295922.	+	2.25752e6i	−0.108667	+	0.828999i
$376$		−	46721.7i		−	0.0170431i
$377$	−2.69781e6			−0.977593
$378$	11571.9	−	13738.7i	0.00416559	−	0.00494558i
$379$	−1.62518e6			−0.581172			−0.290586	−	0.956849i	$-0.593850\pi$
$379$	−1.62518e6			−0.581172			−0.290586	+	0.956849i	$0.593850\pi$
$380$		−	1.89453e6i		−	0.673042i
$381$	315349.	−	2.40573e6i	0.111296	−	0.849052i
$382$	1505.23			0.000527769
$383$	828772.	−	1.43547e6i	0.288694	−	0.500033i	−0.684804	−	0.728727i	$-0.740112\pi$
$383$	828772.	−	1.43547e6i	0.288694	−	0.500033i	0.973498	+	0.228694i	$0.0734456\pi$
$384$	−74094.9	−	9712.56i	−0.0256425	−	0.00336129i
$385$	−1.61402e6	−	515199.i	−0.554954	−	0.177143i
$386$			11851.3i			0.00404852i
$387$	−2.22377e6	+	2.22876e6i	−0.754767	+	0.756460i
$388$	−546234.	−	315368.i	−0.184204	−	0.106350i
$389$	2.74474e6	−	1.58468e6i	0.919661	−	0.530966i	0.0361339	−	0.999347i	$-0.488496\pi$
$389$	2.74474e6	−	1.58468e6i	0.919661	−	0.530966i	0.883527	+	0.468381i	$0.155162\pi$
$390$	−2394.83	+	18269.6i	−0.000797285	+	0.00608231i
$391$	−988398.	+	570652.i	−0.326956	+	0.188768i
$392$	22795.0	−	32068.0i	0.00749245	−	0.0105404i
$393$	−2.96185e6	−	2.27008e6i	−0.967347	−	0.741411i
$394$	32877.9			0.0106700
$395$	−1.54350e6	+	2.67342e6i	−0.497752	+	0.862132i
$396$	−1.56807e6	+	422046.i	−0.502490	+	0.135245i
$397$	−2.14283e6	+	1.23716e6i	−0.682357	+	0.393959i	−0.800742	−	0.599009i	$-0.795561\pi$
$397$	−2.14283e6	+	1.23716e6i	−0.682357	+	0.393959i	0.118386	+	0.992968i	$0.462228\pi$
$398$	3922.59	−	6794.12i	0.00124127	−	0.00214994i
$399$	1.90526e6	−	160956.i	0.599132	−	0.0506146i
$400$	−404916.	−	701334.i	−0.126536	−	0.219167i
$401$	5.06903e6	+	2.92661e6i	1.57422	+	0.908874i	0.995643	+	0.0932423i	$0.0297231\pi$
$401$	5.06903e6	+	2.92661e6i	1.57422	+	0.908874i	0.578572	+	0.815631i	$0.303610\pi$
$402$	−13408.6	−	1757.63i	−0.00413826	−	0.000542454i
$403$	2.39287e6	+	4.14458e6i	0.733934	+	1.27121i
$404$	1.44664e6	+	2.50566e6i	0.440969	+	0.763781i
$405$	3.19594e6	−	1.85474e6i	0.968191	−	0.561881i
$406$	−16671.9	−	18324.3i	−0.00501962	−	0.00551711i
$407$	542339.	+	313120.i	0.162287	+	0.0936967i
$408$	24786.5	−	32339.8i	0.00737164	−	0.00961806i
$409$		−	1.34746e6i		−	0.398298i	−0.979969	−	0.199149i	$-0.936182\pi$
$409$		−	1.34746e6i		−	0.398298i	0.979969	−	0.199149i	$-0.0638178\pi$
$410$			28431.4i			0.00835294i
$411$	283015.	+	682178.i	0.0826429	+	0.199202i
$412$	−3.79317e6	−	2.18999e6i	−1.10093	−	0.635622i
$413$	−1.31303e6	+	4.11346e6i	−0.378790	+	1.18668i
$414$	6417.04	−	6431.44i	0.00184007	−	0.00184420i
$415$	1.77483e6	+	3.07409e6i	0.505866	+	0.876185i
$416$	29011.8	+	50249.9i	0.00821942	+	0.0142365i
$417$	−281736.	−	679095.i	−0.0793419	−	0.191245i
$418$	6259.15	+	3613.72i	0.00175216	+	0.00101161i
$419$	1.81560e6	+	3.14471e6i	0.505225	+	0.875076i	0.999982	+	0.00604403i	$0.00192389\pi$
$419$	1.81560e6	+	3.14471e6i	0.505225	+	0.875076i	−0.494757	+	0.869032i	$0.664743\pi$
$420$	3.32176e6	−	2.31117e6i	0.918851	−	0.639305i
$421$	−2.21059e6	+	3.82885e6i	−0.607858	+	1.05284i	0.383735	+	0.923443i	$0.374638\pi$
$421$	−2.21059e6	+	3.82885e6i	−0.607858	+	1.05284i	−0.991593	+	0.129397i	$0.958696\pi$
$422$	−4911.47	+	2835.64i	−0.00134255	+	0.000775121i
$423$	4.68606e6	+	1.25000e6i	1.27338	+	0.339672i
$424$	29588.2	−	51248.2i	0.00799288	−	0.0138441i
$425$	883160.			0.237174
$426$	−3957.90	+	30193.9i	−0.00105667	+	0.00806113i
$427$	−1.49198e6	−	476243.i	−0.395997	−	0.126403i
$428$	1.34416e6	−	776049.i	0.354683	−	0.204776i
$429$	1.33431e6	+	1.02267e6i	0.350038	+	0.268282i
$430$	25683.6	−	14828.4i	0.00669860	−	0.00386744i
$431$	−911427.	−	526213.i	−0.236335	−	0.136448i	0.377156	−	0.926150i	$-0.376902\pi$
$431$	−911427.	−	526213.i	−0.236335	−	0.136448i	−0.613491	+	0.789701i	$0.710235\pi$
$432$	1.47818e6	−	3.58568e6i	0.381083	−	0.924405i
$433$		−	3.23100e6i		−	0.828166i	−0.910239	−	0.414083i	$-0.864102\pi$
$433$		−	3.23100e6i		−	0.828166i	0.910239	−	0.414083i	$-0.135898\pi$
$434$	−13363.6	+	41865.7i	−0.00340565	+	0.0106692i
$435$	−1.95286e6	−	4.70717e6i	−0.494822	−	1.19272i
$436$	−2.00842e6	+	3.47868e6i	−0.505986	+	0.876393i
$437$	967078.			0.242247
$438$	−35420.2	−	27147.4i	−0.00882198	−	0.00676150i
$439$		−	391212.i		−	0.0968837i	−0.998826	−	0.0484419i	$-0.984574\pi$
$439$		−	391212.i		−	0.0968837i	0.998826	−	0.0484419i	$-0.0154256\pi$
$440$	30593.1			0.00753341
$441$	2.60647e6	+	3.14423e6i	0.638200	+	0.769870i
$442$	−21091.1			−0.00513503
$443$		−	6.71317e6i		−	1.62524i	−0.582792	−	0.812621i	$-0.698040\pi$
$443$		−	6.71317e6i		−	1.62524i	0.582792	−	0.812621i	$-0.301960\pi$
$444$	−1.38158e6	+	573176.i	−0.332597	+	0.137985i
$445$	7.21262e6			1.72661
$446$	19134.3	−	33141.6i	0.00455486	−	0.00788926i
$447$	3.65310e6	−	4.76634e6i	0.864754	−	1.12828i
$448$	1.29147e6	−	4.04592e6i	0.304010	−	0.952405i
$449$		−	2.96589e6i		−	0.694288i	−0.937812	−	0.347144i	$-0.887152\pi$
$449$		−	2.96589e6i		−	0.694288i	0.937812	−	0.347144i	$-0.112848\pi$
$450$	−6788.73	+	1827.19i	−0.00158036	+	0.000425355i
$451$	2.24649e6	+	1.29701e6i	0.520072	+	0.300264i
$452$	−997310.	+	575797.i	−0.229606	+	0.132563i
$453$	−1.65763e6	+	687700.i	−0.379526	+	0.157454i
$454$	28616.6	−	16521.8i	0.00651596	−	0.00376199i
$455$	−3.99100e6	−	1.27394e6i	−0.903761	−	0.288483i
$456$	−31890.4	+	13230.3i	−0.00718203	+	0.00297961i
$457$	1.71053e6			0.383124			0.191562	−	0.981480i	$-0.438645\pi$
$457$	1.71053e6			0.383124			0.191562	+	0.981480i	$0.438645\pi$
$458$	11052.5	−	19143.6i	0.00246206	−	0.00426441i
$459$	2.58046e6	+	3.35124e6i	0.571696	+	0.742462i
$460$	1.77252e6	−	1.02337e6i	0.390568	−	0.225495i
$461$	−242995.	+	420880.i	−0.0532532	+	0.0922372i	−0.891423	−	0.453172i	$-0.850292\pi$
$461$	−242995.	+	420880.i	−0.0532532	+	0.0922372i	0.838170	+	0.545409i	$0.183626\pi$
$462$	1299.54	+	15382.9i	0.000283261	+	0.00335300i
$463$	1.37552e6	+	2.38247e6i	0.298205	+	0.516507i	0.975725	−	0.218998i	$-0.0702787\pi$
$463$	1.37552e6	+	2.38247e6i	0.298205	+	0.516507i	−0.677520	+	0.735504i	$0.736945\pi$
$464$	−4.63234e6	−	2.67448e6i	−0.998861	−	0.576693i
$465$	−5.49938e6	+	7.17525e6i	−1.17945	+	1.53888i
$466$	−5038.53	−	8726.99i	−0.00107483	−	0.00186166i
$467$	−653915.	−	1.13261e6i	−0.138749	−	0.240320i	0.788274	−	0.615324i	$-0.210975\pi$
$467$	−653915.	−	1.13261e6i	−0.138749	−	0.240320i	−0.927023	+	0.375004i	$0.877641\pi$
$468$	−3.87738e6	+	1.04360e6i	−0.818322	+	0.220252i
$469$	934978.	−	2.92910e6i	0.196277	−	0.614898i
$470$	−39563.7	−	22842.1i	−0.00826138	−	0.00476971i
$471$	−410075.	−	53753.8i	−0.0851749	−	0.0111650i
$472$		−	77969.1i		−	0.0161090i
$473$		−	2.70583e6i		−	0.556093i
$474$	27889.5	+	3655.83i	0.00570158	+	0.000747379i
$475$	−648083.	−	374171.i	−0.131794	−	0.0760914i
$476$	3.11719e6	+	3.42614e6i	0.630589	+	0.693087i
$477$	4.34845e6	+	4.33872e6i	0.875061	+	0.873103i
$478$	−19354.8	−	33523.5i	−0.00387452	−	0.00671087i
$479$	−1.91736e6	−	3.32096e6i	−0.381825	−	0.661341i	0.609498	−	0.792788i	$-0.291371\pi$
$479$	−1.91736e6	−	3.32096e6i	−0.381825	−	0.661341i	−0.991323	+	0.131447i	$0.958038\pi$
$480$	−66675.9	+	86994.5i	−0.0132089	+	0.0172341i
$481$	1.34105e6	+	774255.i	0.264291	+	0.152588i
$482$	9062.44	+	15696.6i	0.00177676	+	0.00307743i
$483$	1.17975e6	+	1.69562e6i	0.230104	+	0.330720i
$484$	−1.87891e6	+	3.25437e6i	−0.364580	+	0.631471i
$485$	−1.06823e6	+	616744.i	−0.206211	+	0.119056i
$486$	−26769.1	−	20421.8i	−0.00514094	−	0.00392195i
$487$	4.09145e6	−	7.08661e6i	0.781727	−	1.35399i	−0.149207	−	0.988806i	$-0.547672\pi$
$487$	4.09145e6	−	7.08661e6i	0.781727	−	1.35399i	0.930935	−	0.365186i	$-0.118994\pi$
$488$	28279.8			0.00537560
$489$	6.45710e6	−	2.67886e6i	1.22114	−	0.506614i
$490$	−16010.6	−	34980.6i	−0.00301244	−	0.00658169i
$491$	4.69323e6	−	2.70964e6i	0.878554	−	0.507233i	0.00837272	−	0.999965i	$-0.497335\pi$
$491$	4.69323e6	−	2.70964e6i	0.878554	−	0.507233i	0.870181	+	0.492731i	$0.164002\pi$
$492$	−5.72282e6	+	2.37422e6i	−1.06585	+	0.442190i
$493$	5.05179e6	−	2.91665e6i	0.936112	−	0.540465i
$494$	15477.1	+	8935.70i	0.00285346	+	0.00164745i
$495$	−818494.	+	3.06841e6i	−0.150142	+	0.562859i
$496$			9.48872e6i			1.73182i
$497$	−6.59587e6	−	2.10542e6i	−1.19779	−	0.382338i
$498$	19675.2	−	25671.0i	0.00355506	−	0.00463842i
$499$	3.20453e6	−	5.55041e6i	0.576120	−	0.997869i	−0.419799	−	0.907617i	$-0.637899\pi$
$499$	3.20453e6	−	5.55041e6i	0.576120	−	0.997869i	0.995919	−	0.0902519i	$-0.0287672\pi$
$500$	4.67370e6			0.836056
$501$	−6.41910e6	+	2.66309e6i	−1.14256	+	0.474015i
$502$			28291.6i			0.00501069i
$503$	350628.			0.0617912			0.0308956	−	0.999523i	$-0.490164\pi$
$503$	350628.			0.0617912			0.0308956	+	0.999523i	$0.490164\pi$
$504$	−62101.0	−	39774.9i	−0.0108899	−	0.00697481i
$505$	5.65820e6			0.987302
$506$			7808.09i			0.00135571i
$507$	−1.29444e6	−	992105.i	−0.223646	−	0.171411i
$508$	−4.98052e6			−0.856279
$509$	−3.04265e6	+	5.27003e6i	−0.520545	+	0.901610i	0.479170	+	0.877722i	$0.340938\pi$
$509$	−3.04265e6	+	5.27003e6i	−0.520545	+	0.901610i	−0.999715	+	0.0238878i	$0.992396\pi$
$510$	−15267.2	−	36799.9i	−0.00259916	−	0.00626500i
$511$	7.50512e6	−	6.82836e6i	1.27147	−	1.15682i
$512$			191742.i			0.0323253i
$513$	−473767.	−	3.55248e6i	−0.0794826	−	0.595989i
$514$	34572.2	+	19960.3i	0.00577191	+	0.00333241i
$515$	−7.41805e6	+	4.28281e6i	−1.23246	+	0.711559i
$516$	5.12949e6	+	3.93143e6i	0.848106	+	0.650020i
$517$	−3.60971e6	+	2.08407e6i	−0.593945	+	0.342914i
$518$	3028.45	+	13893.5i	0.000495903	+	0.00227503i
$519$	−767721.	+	5.85677e6i	−0.125108	+	0.954420i
$520$	75647.9			0.0122684
$521$	4.61410e6	−	7.99185e6i	0.744719	−	1.28989i	−0.205607	−	0.978635i	$-0.565917\pi$
$521$	4.61410e6	−	7.99185e6i	0.744719	−	1.28989i	0.950326	−	0.311256i	$-0.100750\pi$
$522$	−32798.1	+	32871.6i	−0.00526832	+	0.00528014i
$523$	−6.25767e6	+	3.61287e6i	−1.00037	+	0.577561i	−0.908356	−	0.418197i	$-0.862662\pi$
$523$	−6.25767e6	+	3.61287e6i	−1.00037	+	0.577561i	−0.0920089	+	0.995758i	$0.529329\pi$
$524$	−3.83009e6	+	6.63391e6i	−0.609370	+	1.05546i
$525$	−134557.	−	1.59277e6i	−0.0213063	−	0.252206i
$526$	−6654.47	−	11525.9i	−0.00104869	−	0.00181639i
$527$	−8.96155e6	−	5.17395e6i	−1.40558	−	0.811514i
$528$	1.27729e6	+	3.07877e6i	0.199390	+	0.480609i
$529$	−2.69579e6	−	4.66924e6i	−0.418838	−	0.725449i
$530$	−28931.1	−	50110.2i	−0.00447379	−	0.00774884i
$531$	7.82009e6	+	2.08600e6i	1.20358	+	0.321054i
$532$	−835905.	−	3.83484e6i	−0.128050	−	0.587447i
$533$	5.55493e6	+	3.20714e6i	0.846955	+	0.488990i
$534$	−25184.0	−	60703.3i	−0.00382183	−	0.00921211i
$535$		−	3.03533e6i		−	0.458481i
$536$			55520.1i			0.00834715i
$537$	−6.25751e6	+	8.16441e6i	−0.936410	+	1.22177i
$538$	12020.1	+	6939.83i	0.00179042	+	0.00103370i
$539$	−3.49436e6	−	330711.i	−0.518079	−	0.0490317i
$540$	−4.62761e6	−	6.00988e6i	−0.682923	−	0.886913i
$541$	−649951.	−	1.12575e6i	−0.0954746	−	0.165367i	0.814332	−	0.580399i	$-0.197104\pi$
$541$	−649951.	−	1.12575e6i	−0.0954746	−	0.165367i	−0.909807	+	0.415033i	$0.863770\pi$
$542$	36052.9	+	62445.5i	0.00527160	+	0.00913068i
$543$	−8.52881e6	−	1.11798e6i	−1.24133	−	0.162717i
$544$	−108652.	−	62730.3i	−0.0157413	−	0.00908825i
$545$	3.92773e6	+	6.80302e6i	0.566435	+	0.981094i
$546$	3213.40	+	38037.5i	0.000461300	+	0.00546047i
$547$	1.06154e6	−	1.83864e6i	0.151694	−	0.262742i	−0.780156	−	0.625585i	$-0.784861\pi$
$547$	1.06154e6	−	1.83864e6i	0.151694	−	0.262742i	0.931850	+	0.362843i	$0.118194\pi$
$548$	1.31293e6	−	758023.i	0.186763	−	0.107828i
$549$	−756604.	+	2.83639e6i	−0.107137	+	0.401638i
$550$	3021.02	−	5232.55i	0.000425840	−	0.000737576i
$551$	−4.94282e6			−0.693579
$552$	−29604.5	−	22690.0i	−0.00413533	−	0.00316947i
$553$	−1.94473e6	+	6.09247e6i	−0.270425	+	0.847189i
$554$	63358.1	−	36579.8i	0.00877057	−	0.00506369i
$555$	−380184.	+	2.90034e6i	−0.0523916	+	0.399683i
$556$	−1.30700e6	+	754597.i	−0.179303	+	0.103521i
$557$	−616805.	−	356112.i	−0.0842383	−	0.0486350i	0.457289	−	0.889318i	$-0.348820\pi$
$557$	−616805.	−	356112.i	−0.0842383	−	0.0486350i	−0.541527	+	0.840683i	$0.682154\pi$
$558$	79590.7	+	21230.7i	0.0108212	+	0.00288655i
$559$		−	6.69073e6i		−	0.905616i
$560$	−5.58992e6	−	6.14393e6i	−0.753243	−	0.827897i
$561$	−3.60419e6	−	472448.i	−0.483505	−	0.0633792i
$562$	−45583.6	+	78953.2i	−0.00608791	+	0.0105446i
$563$	−3.07890e6			−0.409378			−0.204689	−	0.978827i	$-0.565618\pi$
$563$	−3.07890e6			−0.409378			−0.204689	+	0.978827i	$0.565618\pi$
$564$	1.29392e6	−	9.87105e6i	0.171282	−	1.30667i
$565$			2.25209e6i			0.296801i
$566$	−15325.5			−0.00201082
$567$	5.65077e6	−	5.16441e6i	0.738159	−	0.674626i
$568$	125022.			0.0162598
$569$		−	297074.i		−	0.0384667i	−0.999815	−	0.0192333i	$-0.993877\pi$
$569$		−	297074.i		−	0.0384667i	0.999815	−	0.0192333i	$-0.00612254\pi$
$570$	−4387.71	+	33472.9i	−0.000565655	+	0.00431525i
$571$	−96219.0			−0.0123501			−0.00617505	−	0.999981i	$-0.501966\pi$
$571$	−96219.0			−0.0123501			−0.00617505	+	0.999981i	$0.501966\pi$
$572$	1.72545e6	−	2.98857e6i	0.220502	−	0.381921i
$573$	636042.	+	83374.1i	0.0809281	+	0.0106083i
$574$	12544.5	+	57550.0i	0.00158919	+	0.00729064i
$575$		−	808462.i		−	0.101974i
$576$	−7.69168e6	−	2.05175e6i	−0.965973	−	0.257672i
$577$	695339.	+	401454.i	0.0869475	+	0.0501991i	0.542843	−	0.839834i	$-0.317348\pi$
$577$	695339.	+	401454.i	0.0869475	+	0.0501991i	−0.455896	+	0.890033i	$0.650681\pi$
$578$	−5483.43	+	3165.86i	−0.000682705	+	0.000394160i
$579$	−656438.	+	5.00782e6i	−0.0813762	+	0.620801i
$580$	−9.05952e6	+	5.23051e6i	−1.11824	+	0.645616i
$581$	4.94890e6	+	5.43938e6i	0.608230	+	0.668512i
$582$	8920.57	+	6837.06i	0.00109165	+	0.000836685i
$583$	−5.27923e6			−0.643279
$584$	−91608.5	+	158671.i	−0.0111149	+	0.0192515i
$585$	−2.02390e6	+	7.58728e6i	−0.244511	+	0.916635i
$586$	−66490.4	+	38388.2i	−0.00799861	+	0.00461800i
$587$	3.17488e6	−	5.49905e6i	0.380305	−	0.658707i	−0.610801	−	0.791784i	$-0.709152\pi$
$587$	3.17488e6	−	5.49905e6i	0.380305	−	0.658707i	0.991106	+	0.133077i	$0.0424857\pi$
$588$	5.70407e6	−	6.14382e6i	0.680364	−	0.732817i
$589$	4.38412e6	+	7.59352e6i	0.520708	+	0.901893i
$590$	−66023.9	−	38118.9i	−0.00780856	−	0.00450827i
$591$	1.38927e7	+	1.82110e6i	1.63613	+	0.214469i
$592$	1.53512e6	+	2.65890e6i	0.180027	+	0.311816i
$593$	−6.03938e6	−	1.04605e7i	−0.705271	−	1.22156i	−0.966594	−	0.256313i	$-0.917492\pi$
$593$	−6.03938e6	−	1.04605e7i	−0.705271	−	1.22156i	0.261323	−	0.965251i	$-0.415841\pi$
$594$	28682.4	−	3825.15i	0.00333541	−	0.000444818i
$595$	8.85063e6	−	1.92923e6i	1.02490	−	0.223404i
$596$	−1.06756e7	−	6.16354e6i	−1.23105	−	0.710746i
$597$	2.03383e6	−	2.65362e6i	0.233550	−	0.304721i
$598$			19307.2i			0.00220783i
$599$		−	1.91644e6i		−	0.218237i	−0.994029	−	0.109119i	$-0.965197\pi$
$599$		−	1.91644e6i		−	0.218237i	0.994029	−	0.109119i	$-0.0348028\pi$
$600$	11060.4	+	26659.8i	0.00125427	+	0.00302329i
$601$	198299.	+	114488.i	0.0223941	+	0.0129292i	0.511155	−	0.859488i	$-0.329218\pi$
$601$	198299.	+	114488.i	0.0223941	+	0.0129292i	−0.488761	+	0.872418i	$0.662551\pi$
$602$	45445.3	−	41347.3i	0.00511090	−	0.00465004i
$603$	−5.56851e6	−	1.48539e6i	−0.623657	−	0.166360i
$604$	1.84192e6	+	3.19030e6i	0.205437	+	0.355828i
$605$	3.67445e6	+	6.36434e6i	0.408135	+	0.706911i
$606$	−19756.5	−	47620.9i	−0.00218538	−	0.00526764i
$607$	8.13797e6	+	4.69846e6i	0.896488	+	0.517588i	0.876059	−	0.482204i	$-0.160163\pi$
$607$	8.13797e6	+	4.69846e6i	0.896488	+	0.517588i	0.0204291	+	0.999791i	$0.493497\pi$
$608$	53154.2	+	92065.8i	0.00583148	+	0.0101004i
$609$	−6.02983e6	−	8.66647e6i	−0.658813	−	0.946889i
$610$	13825.9	−	23947.2i	0.00150442	−	0.00260574i
$611$	−8.92578e6	+	5.15330e6i	−0.967260	+	0.558448i
$612$	6.13235e6	−	6.14610e6i	0.661832	−	0.663317i
$613$	−2.24094e6	+	3.88142e6i	−0.240868	+	0.417195i	−0.960962	−	0.276681i	$-0.910765\pi$
$613$	−2.24094e6	+	3.88142e6i	−0.240868	+	0.417195i	0.720094	+	0.693877i	$0.244099\pi$
$614$	60002.7			0.00642318
$615$	−1.57481e6	+	1.20139e7i	−0.167896	+	1.28084i
$616$	61925.6	−	13498.3i	0.00657534	−	0.00143327i
$617$	2.69919e6	−	1.55838e6i	0.285444	−	0.164801i	−0.350441	−	0.936585i	$-0.613968\pi$
$617$	2.69919e6	−	1.55838e6i	0.285444	−	0.164801i	0.635885	+	0.771783i	$0.280635\pi$
$618$	61946.5	+	47478.1i	0.00652447	+	0.00500060i
$619$	6.99093e6	−	4.03621e6i	0.733344	−	0.423397i	−0.0863000	−	0.996269i	$-0.527504\pi$
$619$	6.99093e6	−	4.03621e6i	0.733344	−	0.423397i	0.819644	+	0.572873i	$0.194171\pi$
$620$	1.60710e7	+	9.27860e6i	1.67905	+	0.969400i
$621$	3.06779e6	−	2.36220e6i	0.319225	−	0.245803i
$622$		−	104564.i		−	0.0108369i
$623$	1.45996e7	−	3.18236e6i	1.50702	−	0.328495i
$624$	3.15837e6	+	7.61291e6i	0.324714	+	0.782689i
$625$	5.80587e6	−	1.00561e7i	0.594521	−	1.02974i
$626$	−15326.9			−0.00156322
$627$	2.44467e6	+	1.87369e6i	0.248343	+	0.190339i
$628$			848969.i			0.0858999i
$629$	−3.34824e6			−0.337435
$630$	−64042.2	+	33141.0i	−0.00642857	+	0.00332670i
$631$	−2.90946e6			−0.290897			−0.145448	−	0.989366i	$-0.546463\pi$
$631$	−2.90946e6			−0.290897			−0.145448	+	0.989366i	$0.546463\pi$
$632$		−	115480.i		−	0.0115005i
$633$	−2.23243e6	+	926169.i	−0.221447	+	0.0918715i
$634$	16990.6			0.00167875
$635$	−4.87003e6	+	8.43513e6i	−0.479289	+	0.830152i
$636$	7.67047e6	−	1.00080e7i	0.751933	−	0.981075i
$637$	−8.64055e6	−	817753.i	−0.843709	−	0.0798497i
$638$		−	39907.8i		−	0.00388156i
$639$	−3.34487e6	+	1.25394e7i	−0.324061	+	1.21485i
$640$	259797.	+	149994.i	0.0250717	+	0.0144752i
$641$	3.71463e6	−	2.14464e6i	0.357084	−	0.206162i	−0.310717	−	0.950502i	$-0.600569\pi$
$641$	3.71463e6	−	2.14464e6i	0.357084	−	0.206162i	0.667801	+	0.744340i	$0.267236\pi$
$642$	−25546.1	+	10598.3i	−0.00244618	+	0.00101484i
$643$	7.44581e6	−	4.29884e6i	0.710206	−	0.410038i	−0.100931	−	0.994893i	$-0.532182\pi$
$643$	7.44581e6	−	4.29884e6i	0.710206	−	0.410038i	0.811137	+	0.584856i	$0.198849\pi$
$644$	3.13635e6	−	2.85354e6i	0.297996	−	0.271125i
$645$	1.16741e7	−	4.84322e6i	1.10490	−	0.458390i
$646$	−38642.2			−0.00364318
$647$	2.55765e6	−	4.42997e6i	0.240204	−	0.416045i	−0.720568	−	0.693384i	$-0.756119\pi$
$647$	2.55765e6	−	4.42997e6i	0.240204	−	0.416045i	0.960772	+	0.277339i	$0.0894524\pi$
$648$	−68846.8	+	119866.i	−0.00644090	+	0.0112139i
$649$	−6.02388e6	+	3.47789e6i	−0.561390	+	0.324119i
$650$	7470.11	−	12938.6i	0.000693495	−	0.00120117i
$651$	−7.96580e6	+	1.69504e7i	−0.736677	+	1.56757i
$652$	−7.17500e6	−	1.24275e7i	−0.661002	−	1.14489i
$653$	−1.43413e7	−	8.27996e6i	−1.31615	−	0.759880i	−0.333044	−	0.942911i	$-0.608076\pi$
$653$	−1.43413e7	−	8.27996e6i	−1.31615	−	0.759880i	−0.983107	+	0.183031i	$0.941409\pi$
$654$	43541.7	−	56810.5i	0.00398072	−	0.00519379i
$655$	7.49024e6	+	1.29735e7i	0.682170	+	1.18155i
$656$	6.35881e6	+	1.10138e7i	0.576921	+	0.999256i
$657$	−1.34633e7	−	1.34332e7i	−1.21685	−	1.21413i
$658$	−90162.1	−	28780.0i	−0.00811819	−	0.00259135i
$659$	1.63291e7	+	9.42759e6i	1.46470	+	0.845644i	0.999223	−	0.0394175i	$-0.0125502\pi$
$659$	1.63291e7	+	9.42759e6i	1.46470	+	0.845644i	0.465475	+	0.885061i	$0.345884\pi$
$660$	6.46350e6	+	847254.i	0.577575	+	0.0757101i
$661$		−	5.32265e6i		−	0.473832i	−0.971530	−	0.236916i	$-0.923863\pi$
$661$		−	5.32265e6i		−	0.473832i	0.971530	−	0.236916i	$-0.0761366\pi$
$662$			125280.i			0.0111106i
$663$	−8.91214e6	−	1.16823e6i	−0.787405	−	0.103215i
$664$	−114998.	−	66393.9i	−0.0101220	−	0.00584397i
$665$	−7.31215e6	−	2.33406e6i	−0.641196	−	0.204672i
$666$	25737.5	−	6927.25i	0.00224843	−	0.000605167i
$667$	−2.66996e6	−	4.62451e6i	−0.232375	−	0.402486i
$668$	7.13277e6	+	1.23543e7i	0.618468	+	1.07122i
$669$	9.92100e6	−	1.29443e7i	0.857019	−	1.11818i
$670$	47014.1	+	27143.6i	0.00404614	+	0.00233604i
$671$	−1.26145e6	−	2.18489e6i	−0.108159	−	0.187337i
$672$	−96579.4	+	205510.i	−0.00825014	+	0.0175554i
$673$	−3.88232e6	+	6.72437e6i	−0.330410	+	0.572287i	−0.982592	−	0.185775i	$-0.940520\pi$
$673$	−3.88232e6	+	6.72437e6i	−0.330410	+	0.572287i	0.652182	+	0.758062i	$0.273854\pi$
$674$	−125795.	+	72627.8i	−0.0106663	+	0.00615819i
$675$	−2.96982e6	+	396062.i	−0.250883	+	0.0334583i
$676$	−1.67389e6	+	2.89926e6i	−0.140883	+	0.244017i
$677$	1.47421e7			1.23620			0.618100	−	0.786100i	$-0.287903\pi$
$677$	1.47421e7			1.23620			0.618100	+	0.786100i	$0.287903\pi$
$678$	18954.2	−	7863.53i	0.00158355	−	0.000656966i
$679$	−1.89016e6	+	1.71972e6i	−0.157335	+	0.143147i
$680$	−141655.	+	81784.3i	−0.0117479	+	0.00678263i
$681$	1.30072e7	−	5.39631e6i	1.07477	−	0.445892i
$682$	−61309.3	+	35397.0i	−0.00504738	+	0.00291410i
$683$	−3.30879e6	−	1.91033e6i	−0.271404	−	0.156695i	0.358121	−	0.933675i	$-0.383417\pi$
$683$	−3.30879e6	−	1.91033e6i	−0.271404	−	0.156695i	−0.629526	+	0.776980i	$0.716751\pi$
$684$	−7.10398e6	+	1.91204e6i	−0.580579	+	0.156263i
$685$		−	2.96482e6i		−	0.241420i
$686$	−47842.4	−	63742.5i	−0.00388153	−	0.00517153i
$687$	5.73067e6	−	7.47702e6i	0.463248	−	0.604417i
$688$	6.63287e6	−	1.14885e7i	0.534233	−	0.925318i
$689$	−1.30540e7			−1.04760
$690$	−33687.4	+	13975.9i	−0.00269367	+	0.00111752i
$691$		−	4.28800e6i		−	0.341633i	−0.985303	−	0.170817i	$-0.945359\pi$
$691$		−	4.28800e6i		−	0.341633i	0.985303	−	0.170817i	$-0.0546406\pi$
$692$	1.21251e7			0.962545
$693$	−302925.	+	6.57211e6i	−0.0239608	+	0.519842i
$694$	115124.			0.00907333
$695$			2.95142e6i			0.231777i
$696$	151311.	+	115971.i	0.0118399	+	0.00907455i
$697$	−1.38692e7			−1.08136
$698$	49000.4	−	84871.2i	0.00380681	−	0.00659359i
$699$	−1.64567e6	−	3.96672e6i	−0.127394	−	0.307071i
$700$	−3.20587e6	+	698804.i	−0.247287	+	0.0539027i
$701$			3.30925e6i			0.254351i	0.991880	+	0.127176i	$0.0405912\pi$
$701$			3.30925e6i			0.254351i	−0.991880	+	0.127176i	$0.959409\pi$
$702$	70923.3	−	9458.50i	0.00543183	−	0.000724402i
$703$	2.45701e6	+	1.41856e6i	0.187508	+	0.108258i
$704$	5.92496e6	−	3.42078e6i	0.450561	−	0.260132i
$705$	−1.54526e7	−	1.18435e7i	−1.17093	−	0.897443i
$706$	40386.2	−	23317.0i	0.00304945	−	0.00176060i
$707$	1.14532e7	−	2.49652e6i	0.861741	−	0.187839i
$708$	2.15930e6	−	1.64728e7i	0.161894	−	1.23505i
$709$	−2.11776e7			−1.58220			−0.791099	−	0.611688i	$-0.790491\pi$
$709$	−2.11776e7			−1.58220			−0.791099	+	0.611688i	$0.790491\pi$
$710$	61123.0	−	105868.i	0.00455050	−	0.00788169i
$711$	1.15824e7	+	3.08958e6i	0.859258	+	0.229206i
$712$	−233666.	+	134907.i	−0.0172741	+	0.00997323i
$713$	−4.73634e6	+	8.20358e6i	−0.348914	+	0.604337i
$714$	−47140.2	−	67753.0i	−0.00346056	−	0.00497374i
$715$	−3.37435e6	−	5.84455e6i	−0.246845	−	0.427549i
$716$	1.82865e7	+	1.05577e7i	1.33306	+	0.769640i
$717$	−6.32161e6	−	1.52376e7i	−0.459230	−	1.10692i
$718$	−35075.1	−	60751.9i	−0.00253915	−	0.00439793i
$719$	−1.36318e7	−	2.36110e7i	−0.983401	−	1.70330i	−0.648837	−	0.760927i	$-0.724744\pi$
$719$	−1.36318e7	−	2.36110e7i	−0.983401	−	1.70330i	−0.334564	−	0.942373i	$-0.608589\pi$
$720$	−1.09968e7	+	1.10215e7i	−0.790564	+	0.792337i
$721$	−1.31257e7	+	1.19421e7i	−0.940339	+	0.855546i
$722$	−50080.1	−	28913.8i	−0.00357538	−	0.00206425i
$723$	2.95995e6	+	7.13465e6i	0.210591	+	0.507606i
$724$			1.76570e7i			1.25190i
$725$			4.13212e6i			0.291963i
$726$	40734.0	−	53147.2i	0.00286824	−	0.00374230i
$727$	9.28331e6	+	5.35972e6i	0.651429	+	0.376103i	0.789003	−	0.614389i	$-0.210597\pi$
$727$	9.28331e6	+	5.35972e6i	0.651429	+	0.376103i	−0.137575	+	0.990491i	$0.543931\pi$
$728$	153124.	−	33377.5i	0.0107082	−	0.00233413i
$729$	−1.01803e7	−	1.01121e7i	−0.709479	−	0.704726i
$730$	89574.3	+	155147.i	0.00622123	+	0.0107755i
$731$	7.23347e6	+	1.25287e7i	0.500672	+	0.867189i
$732$	5.97477e6	+	783189.i	0.412139	+	0.0540243i
$733$	1.17596e7	+	6.78944e6i	0.808415	+	0.466739i	0.846405	−	0.532539i	$-0.178762\pi$
$733$	1.17596e7	+	6.78944e6i	0.808415	+	0.466739i	−0.0379900	+	0.999278i	$0.512096\pi$
$734$	−44981.1	−	77909.6i	−0.00308170	−	0.00533766i
$735$	−4.82781e6	−	1.56681e7i	−0.329634	−	1.06979i
$736$	−57424.6	+	99462.3i	−0.00390754	+	0.00676805i
$737$	4.28947e6	−	2.47653e6i	0.290894	−	0.167948i
$738$	106610.	−	28694.2i	0.00720541	−	0.00193934i
$739$	−3.64402e6	+	6.31163e6i	−0.245454	+	0.425139i	−0.962259	−	0.272135i	$-0.912270\pi$
$739$	−3.64402e6	+	6.31163e6i	−0.245454	+	0.425139i	0.716805	+	0.697274i	$0.245604\pi$
$740$	6.00450e6			0.403086
$741$	6.04498e6	+	4.63310e6i	0.404435	+	0.309974i
$742$	−80671.2	−	88666.5i	−0.00537909	−	0.00591221i
$743$	−1.67522e7	+	9.67187e6i	−1.11327	+	0.642744i	−0.939673	−	0.342073i	$-0.888871\pi$
$743$	−1.67522e7	+	9.67187e6i	−1.11327	+	0.642744i	−0.173593	+	0.984818i	$0.555538\pi$
$744$	43954.4	−	335318.i	0.00291118	−	0.0222088i
$745$	−2.08775e7	+	1.20536e7i	−1.37812	+	0.795658i
$746$	84277.5	+	48657.7i	0.00554453	+	0.00320114i
$747$	9.73579e6	−	9.75763e6i	0.638366	−	0.639798i
$748$			7.46168e6i			0.487621i
$749$	−1.33925e6	−	6.14402e6i	−0.0872283	−	0.400173i
$750$	−82575.7	−	10824.3i	−0.00536043	−	0.000702659i
$751$	−7.59290e6	+	1.31513e7i	−0.491256	+	0.850880i	−0.999949	−	0.0100676i	$-0.996795\pi$
$751$	−7.59290e6	+	1.31513e7i	−0.491256	+	0.850880i	0.508693	+	0.860948i	$0.330129\pi$
$752$	−2.04349e7			−1.31774
$753$	−1.56706e6	+	1.19548e7i	−0.100716	+	0.768340i
$754$		−	98680.6i		−	0.00632126i
$755$	7.20424e6			0.459961
$756$	−1.20187e7	−	1.01232e7i	−0.764811	−	0.644189i
$757$	−1.74980e7			−1.10981			−0.554906	−	0.831913i	$-0.687246\pi$
$757$	−1.74980e7			−1.10981			−0.554906	+	0.831913i	$0.687246\pi$
$758$		−	59446.0i		−	0.00375794i
$759$	−432488.	+	3.29935e6i	−0.0272502	+	0.207885i
$760$	138599.			0.00870415
$761$	−5.38915e6	+	9.33428e6i	−0.337333	+	0.584278i	−0.983930	−	0.178554i	$-0.942858\pi$
$761$	−5.38915e6	+	9.33428e6i	−0.337333	+	0.584278i	0.646597	+	0.762832i	$0.276191\pi$
$762$	87996.7	+	11534.8i	0.00549009	+	0.000719655i
$763$	1.09520e7	+	1.20375e7i	0.681056	+	0.748555i
$764$		−	1.31678e6i		−	0.0816170i
$765$	−4.41289e6	−	1.63956e7i	−0.272628	−	1.01292i
$766$	52506.8	+	30314.8i	0.00323328	+	0.00186674i
$767$	−1.48953e7	+	8.59982e6i	−0.914243	+	0.527838i
$768$	−2.12357e6	+	1.62003e7i	−0.129917	+	0.991103i
$769$	−8.07648e6	+	4.66296e6i	−0.492500	+	0.284345i	−0.725611	−	0.688105i	$-0.758443\pi$
$769$	−8.07648e6	+	4.66296e6i	−0.492500	+	0.284345i	0.233111	+	0.972450i	$0.425109\pi$
$770$	18845.0	−	59037.6i	0.00114543	−	0.00358841i
$771$	1.35031e7	+	1.03493e7i	0.818082	+	0.627009i
$772$	1.03676e7			0.626085
$773$	5.87761e6	−	1.01803e7i	0.353795	−	0.612792i	−0.633116	−	0.774057i	$-0.718224\pi$
$773$	5.87761e6	−	1.01803e7i	0.353795	−	0.612792i	0.986911	+	0.161266i	$0.0515576\pi$
$774$	−81523.6	−	81341.2i	−0.00489138	−	0.00488043i
$775$	6.34807e6	−	3.66506e6i	0.379654	−	0.219193i
$776$	23071.6	−	39961.1i	0.00137538	−	0.00238223i
$777$	510133.	+	6.03852e6i	0.0303131	+	0.358821i
$778$	57964.4	+	100397.i	0.00343330	+	0.00594665i
$779$	1.01775e7	+	5.87599e6i	0.600894	+	0.346926i
$780$	1.59824e7	+	2.09501e6i	0.940600	+	0.123296i
$781$	−5.57674e6	−	9.65919e6i	−0.327154	−	0.566648i
$782$	−20873.3	−	36153.6i	−0.00122060	−	0.00211415i
$783$	−1.56798e7	+	1.20734e7i	−0.913976	+	0.703762i
$784$	−1.40258e7	−	9.96997e6i	−0.814960	−	0.579300i
$785$	1.43784e6	+	830135.i	0.0832789	+	0.0480811i
$786$	83034.9	−	108339.i	0.00479407	−	0.00625500i
$787$		−	9.06024e6i		−	0.521438i	−0.965415	−	0.260719i	$-0.916040\pi$
$787$		−	9.06024e6i		−	0.521438i	0.965415	−	0.260719i	$-0.0839596\pi$
$788$		−	2.87618e7i		−	1.65006i
$789$	−2.17347e6	−	5.23891e6i	−0.124297	−	0.299605i
$790$	−97788.2	−	56458.1i	−0.00557467	−	0.00321854i
$791$	993670.	+	4.55861e6i	0.0564678	+	0.259055i
$792$	−30875.9	−	114716.i	−0.00174907	−	0.00649847i
$793$	−3.11920e6	−	5.40262e6i	−0.176141	−	0.305085i
$794$	−45253.0	−	78380.5i	−0.00254739	−	0.00441221i
$795$	−9.44942e6	−	2.27768e7i	−0.530258	−	1.27813i
$796$	−5.94354e6	−	3.43150e6i	−0.332478	−	0.191956i
$797$	−588634.	−	1.01954e6i	−0.0328246	−	0.0568538i	0.849146	−	0.528157i	$-0.177117\pi$
$797$	−588634.	−	1.01954e6i	−0.0328246	−	0.0568538i	−0.881971	+	0.471304i	$0.843784\pi$
$798$	5887.46	+	69690.7i	0.000327281	+	0.00387407i
$799$	1.11426e7	−	1.92996e7i	0.617478	−	1.06950i
$800$	76965.6	−	44436.1i	0.00425179	−	0.00245477i
$801$	−7.27929e6	−	2.70454e7i	−0.400874	−	1.48941i
$802$	−107049.	+	185415.i	−0.00587690	+	0.0101791i
$803$	1.63452e7			0.894541
$804$	−1.53759e6	+	1.17299e7i	−0.0838880	+	0.639962i
$805$	−1.76605e6	−	8.10204e6i	−0.0960537	−	0.440661i
$806$	−151600.	+	87526.5i	−0.00821983	+	0.00474572i
$807$	4.69478e6	+	3.59826e6i	0.253765	+	0.194495i
$808$	−183308.	+	105833.i	−0.00987764	+	0.00570286i
$809$	−2.15920e6	−	1.24662e6i	−0.115990	−	0.0669671i	0.440882	−	0.897565i	$-0.354666\pi$
$809$	−2.15920e6	−	1.24662e6i	−0.115990	−	0.0669671i	−0.556873	+	0.830598i	$0.687999\pi$
$810$	67842.5	+	116901.i	0.00363320	+	0.00626046i
$811$		−	2.14197e7i		−	1.14357i	−0.820405	−	0.571783i	$-0.806252\pi$
$811$		−	2.14197e7i		−	1.14357i	0.820405	−	0.571783i	$-0.193748\pi$
$812$	−1.60302e7	+	1.45847e7i	−0.853195	+	0.776260i
$813$	1.17755e7	+	2.83836e7i	0.624818	+	1.50606i
$814$	−11453.3	+	19837.7i	−0.000605856	+	0.00104937i
$815$	−2.80633e7			−1.47994
$816$	−1.41447e7	−	1.08410e7i	−0.743647	−	0.569959i
$817$		−	1.22585e7i		−	0.642513i
$818$	49287.5			0.00257545
$819$	−749045.	+	1.62509e7i	−0.0390210	+	0.846581i
$820$	2.48720e7			1.29174
$821$			1.29698e7i			0.671547i	0.941943	+	0.335774i	$0.108998\pi$
$821$			1.29698e7i			0.671547i	−0.941943	+	0.335774i	$0.891002\pi$
$822$	−24952.7	+	10352.1i	−0.00128807	+	0.000534380i
$823$	−6.14936e6			−0.316468			−0.158234	−	0.987402i	$-0.550580\pi$
$823$	−6.14936e6			−0.316468			−0.158234	+	0.987402i	$0.550580\pi$
$824$	160214.	−	277499.i	0.00822022	−	0.0142378i
$825$	1.56638e6	−	2.04371e6i	0.0801237	−	0.104540i
$826$	−150462.	−	48028.0i	−0.00767322	−	0.00244931i
$827$			8.96370e6i			0.455747i	0.973691	+	0.227873i	$0.0731772\pi$
$827$			8.96370e6i			0.455747i	−0.973691	+	0.227873i	$0.926823\pi$
$828$	−5.62626e6	−	5.61367e6i	−0.285196	−	0.284558i
$829$	9.22718e6	+	5.32732e6i	0.466319	+	0.269229i	0.714697	−	0.699434i	$-0.246564\pi$
$829$	9.22718e6	+	5.32732e6i	0.466319	+	0.269229i	−0.248379	+	0.968663i	$0.579898\pi$
$830$	−112444.	+	64919.6i	−0.00566554	+	0.00327100i
$831$	2.87985e7	−	1.19476e7i	1.44666	−	0.600176i
$832$	1.46507e7	−	8.45860e6i	0.733755	−	0.423633i
$833$	1.70640e7	−	7.81017e6i	0.852054	−	0.389985i
$834$	24840.0	−	10305.4i	0.00123662	−	0.000513036i
$835$	2.78981e7			1.38471
$836$	3.16131e6	−	5.47554e6i	0.156441	−	0.270964i
$837$	3.24555e7	+	1.33797e7i	1.60131	+	0.660133i
$838$	−115027.	+	66411.0i	−0.00565836	+	0.00326686i
$839$	1.54509e7	−	2.67618e7i	0.757791	−	1.31253i	−0.186184	−	0.982515i	$-0.559612\pi$
$839$	1.54509e7	−	2.67618e7i	0.757791	−	1.31253i	0.943975	−	0.330017i	$-0.107054\pi$
$840$	169079.	+	243012.i	0.00826785	+	0.0118831i
$841$	3.39083e6	+	5.87308e6i	0.165316	+	0.286336i
$842$	−140052.	−	80858.8i	−0.00680781	−	0.00393049i
$843$	−2.36348e7	+	3.08372e7i	−1.14547	+	1.49454i
$844$	2.48063e6	+	4.29658e6i	0.119869	+	0.207619i
$845$	3.27351e6	+	5.66988e6i	0.157714	+	0.273169i
$846$	−45722.6	+	171407.i	−0.00219637	+	0.00823383i
$847$	1.02458e7	+	1.12613e7i	0.490724	+	0.539359i
$848$	−2.24147e7	−	1.29411e7i	−1.07039	−	0.617992i
$849$	−6.47587e6	−	848875.i	−0.308339	−	0.0404180i
$850$			32304.3i			0.00153360i
$851$			3.06505e6i			0.145082i
$852$	2.64138e7	+	3.46240e6i	1.24662	+	0.163410i
$853$	1.38828e7	+	8.01527e6i	0.653290	+	0.377177i	0.789716	−	0.613473i	$-0.210228\pi$
$853$	1.38828e7	+	8.01527e6i	0.653290	+	0.377177i	−0.136426	+	0.990650i	$0.543561\pi$
$854$	17420.0	−	54573.5i	0.000817342	−	0.00256057i
$855$	−3.70810e6	+	1.39011e7i	−0.173475	+	0.650330i
$856$	56773.9	+	98335.2i	0.00264828	+	0.00458696i
$857$	9.99190e6	+	1.73065e7i	0.464725	+	0.804928i	0.999189	−	0.0402637i	$-0.0128198\pi$
$857$	9.99190e6	+	1.73065e7i	0.464725	+	0.804928i	−0.534464	+	0.845191i	$0.679486\pi$
$858$	−37407.2	+	48806.5i	−0.00173475	+	0.00226339i
$859$	−1.43053e7	−	8.25919e6i	−0.661477	−	0.381904i	0.131362	−	0.991334i	$-0.458065\pi$
$859$	−1.43053e7	−	8.25919e6i	−0.661477	−	0.381904i	−0.792840	+	0.609430i	$0.791398\pi$
$860$	−1.29720e7	−	2.24681e7i	−0.598082	−	1.03591i
$861$	2.11309e6	+	2.50129e7i	0.0971425	+	1.14989i
$862$	19247.8	−	33338.2i	0.000882294	−	0.00152818i
$863$	2.59300e7	−	1.49707e7i	1.18516	−	0.684251i	0.227956	−	0.973672i	$-0.426796\pi$
$863$	2.59300e7	−	1.49707e7i	1.18516	−	0.684251i	0.957202	+	0.289420i	$0.0934625\pi$
$864$	393499.	+	162218.i	0.0179333	+	0.00739292i
$865$	1.18561e7	−	2.05354e7i	0.538769	−	0.933175i
$866$	118184.			0.00535504
$867$	−2.49241e6	+	1.03403e6i	−0.112609	+	0.0467179i
$868$	3.66243e7	+	1.16906e7i	1.64995	+	0.526668i
$869$	−8.92200e6	+	5.15112e6i	−0.400786	+	0.231394i
$870$	172179.	−	71431.9i	0.00771227	−	0.00319959i
$871$	1.06066e7	−	6.12374e6i	0.473731	−	0.273509i
$872$	−254492.	−	146931.i	−0.0113340	−	0.00654368i
$873$	3.39073e6	+	3.38314e6i	0.150577	+	0.150240i
$874$			35373.8i			0.00156640i
$875$	5.75799e6	−	1.80387e7i	0.254244	−	0.796498i
$876$	−2.37487e7	+	3.09858e7i	−1.04563	+	1.36428i
$877$	−2.11657e7	+	3.66600e7i	−0.929252	+	1.60951i	−0.144675	+	0.989479i	$0.546214\pi$
$877$	−2.11657e7	+	3.66600e7i	−0.929252	+	1.60951i	−0.784577	+	0.620032i	$0.787120\pi$
$878$	14309.8			0.000626464
$879$	−3.02222e7	+	1.25383e7i	−1.31933	+	0.547350i
$880$		−	1.33807e7i		−	0.582467i
$881$	−3.17552e7			−1.37840			−0.689201	−	0.724571i	$-0.742038\pi$
$881$	−3.17552e7			−1.37840			−0.689201	+	0.724571i	$0.742038\pi$
$882$	−115010.	+	95339.6i	−0.00497809	+	0.00412669i
$883$	1.71883e7			0.741874			0.370937	−	0.928658i	$-0.379037\pi$
$883$	1.71883e7			0.741874			0.370937	+	0.928658i	$0.379037\pi$
$884$			1.84506e7i			0.794108i
$885$	−2.57873e7	−	1.97644e7i	−1.10675	−	0.848253i
$886$	245554.			0.0105090
$887$	−1.18430e7	+	2.05126e7i	−0.505419	+	0.875411i	0.494562	+	0.869142i	$0.335329\pi$
$887$	−1.18430e7	+	2.05126e7i	−0.505419	+	0.875411i	−0.999980	+	0.00626809i	$0.998005\pi$
$888$	−41932.1	−	101073.i	−0.00178449	−	0.00430133i
$889$	−6.13600e6	+	1.92229e7i	−0.260394	+	0.815764i
$890$			263823.i			0.0111645i
$891$	1.23318e7	−	27629.1i	0.520393	−	0.00116593i
$892$	−2.89925e7	−	1.67388e7i	−1.22004	−	0.704388i
$893$	−1.63534e7	+	9.44166e6i	−0.686247	+	0.396205i
$894$	174343.	+	133623.i	0.00729560	+	0.00559162i
$895$	3.57617e7	−	2.06470e7i	1.49231	−	0.861588i
$896$	592053.	+	188985.i	0.0246371	+	0.00786424i
$897$	−1.06942e6	+	8.15834e6i	−0.0443778	+	0.338548i
$898$	108486.			0.00448936
$899$	2.42078e7	−	4.19292e7i	0.998980	−	1.73028i
$900$	1.59844e6	+	5.93882e6i	0.0657792	+	0.244396i
$901$	2.44443e7	−	1.41129e7i	1.00315	−	0.579169i
$902$	−47442.1	+	82172.2i	−0.00194155	+	0.00336286i
$903$	2.14934e7	−	1.49543e7i	0.877172	−	0.610306i
$904$	−42123.9	−	72960.7i	−0.00171438	−	0.00296940i
$905$	2.99043e7	+	1.72653e7i	1.21370	+	0.700732i
$906$	−25154.7	−	60632.8i	−0.00101812	−	0.00245407i
$907$	−2.45733e7	−	4.25622e7i	−0.991849	−	1.71793i	−0.606274	−	0.795256i	$-0.707336\pi$
$907$	−2.45733e7	−	4.25622e7i	−0.991849	−	1.71793i	−0.385575	−	0.922676i	$-0.625997\pi$
$908$	−1.44534e7	−	2.50340e7i	−0.581775	−	1.00766i
$909$	−5.71050e6	−	2.12168e7i	−0.229226	−	0.851666i
$910$	46598.1	−	145983.i	0.00186537	−	0.00584384i
$911$	−3.73255e7	−	2.15499e7i	−1.49008	−	0.860298i	−0.490145	−	0.871641i	$-0.663056\pi$
$911$	−3.73255e7	−	2.15499e7i	−1.49008	−	0.860298i	−0.999936	+	0.0113430i	$0.996389\pi$
$912$	5.78663e6	+	1.39481e7i	0.230377	+	0.555299i
$913$			1.18463e7i			0.470332i
$914$			62567.7i			0.00247733i
$915$	7.16865e6	−	9.35321e6i	0.283064	−	0.369324i
$916$	−1.67469e7	−	9.66883e6i	−0.659472	−	0.380746i
$917$	2.08857e7	+	2.29557e7i	0.820211	+	0.901502i
$918$	−122582.	+	94388.0i	−0.00480086	+	0.00369666i
$919$	1.93863e7	+	3.35781e7i	0.757193	+	1.31150i	0.944277	+	0.329152i	$0.106763\pi$
$919$	1.93863e7	+	3.35781e7i	0.757193	+	1.31150i	−0.187084	+	0.982344i	$0.559904\pi$
$920$	74866.9	+	129673.i	0.00291622	+	0.00505104i
$921$	2.53545e7	+	3.32353e6i	0.984931	+	0.129107i
$922$	−15395.0	−	8888.29i	−0.000596419	−	0.000344343i
$923$	−1.37897e7	−	2.38844e7i	−0.532782	−	0.922805i
$924$	1.34570e7	−	1.13685e6i	0.518525	−	0.0438049i
$925$	1.18589e6	−	2.05403e6i	0.0455713	−	0.0789317i
$926$	−87146.2	+	50313.9i	−0.00333980	+	0.00192824i
$927$	2.35460e7	+	2.34933e7i	0.899950	+	0.897936i
$928$	293502.	−	508360.i	0.0111877	−	0.0193777i
$929$	137633.			0.00523219			0.00261610	−	0.999997i	$-0.499167\pi$
$929$	137633.			0.00523219			0.00261610	+	0.999997i	$0.499167\pi$
$930$	−262456.	−	201156.i	−0.00995061	−	0.00762652i
$931$	−1.58309e7	−	1.49825e6i	−0.598591	−	0.0566514i
$932$	−7.63442e6	+	4.40773e6i	−0.287896	+	0.166217i
$933$	5.79178e6	−	4.41842e7i	0.217825	−	1.66174i
$934$	41428.8	−	23918.9i	0.00155394	−	0.000897169i
$935$	1.26373e7	+	7.29614e6i	0.472743	+	0.272938i
$936$	−76347.1	−	283660.i	−0.00284841	−	0.0105830i
$937$			3.30702e7i			1.23052i	0.788325	+	0.615259i	$0.210948\pi$
$937$			3.30702e7i			1.23052i	−0.788325	+	0.615259i	$0.789052\pi$
$938$	107141.	+	34199.6i	0.00397601	+	0.00126915i
$939$	−6.47647e6	−	848954.i	−0.239704	−	0.0314210i
$940$	−1.99824e7	+	3.46106e7i	−0.737613	+	1.27758i
$941$	6.75074e6			0.248529			0.124265	−	0.992249i	$-0.460343\pi$
$941$	6.75074e6			0.248529			0.124265	+	0.992249i	$0.460343\pi$
$942$	1966.21	−	14999.7i	7.21941e−5	−	0.000550753i
$943$			1.26961e7i			0.464934i
$944$	−3.41018e7			−1.24551
$945$	−2.88970e7	+	1.04566e7i	−1.05262	+	0.380901i
$946$	98973.8			0.00359577
$947$			213554.i			0.00773808i	0.999993	+	0.00386904i	$0.00123156\pi$
$947$			213554.i			0.00773808i	−0.999993	+	0.00386904i	$0.998768\pi$
$948$	3.19815e6	−	2.43979e7i	0.115579	−	0.881723i
$949$	4.04169e7			1.45679
$950$	13686.4	−	23705.6i	0.000492018	−	0.000852200i
$951$	7.17949e6	+	941107.i	0.257420	+	0.0337433i
$952$	−250648.	+	228046.i	−0.00896338	+	0.00815512i
$953$		−	5.03164e6i		−	0.179464i	−0.995966	−	0.0897320i	$-0.971399\pi$
$953$		−	5.03164e6i		−	0.179464i	0.995966	−	0.0897320i	$-0.0286011\pi$
$954$	−158702.	+	159058.i	−0.00564560	+	0.00565827i
$955$	−2.23014e6	−	1.28757e6i	−0.0791267	−	0.0456838i
$956$	−2.93265e7	+	1.69317e7i	−1.03781	+	0.599177i
$957$	2.21048e6	−	1.68633e7i	0.0780202	−	0.595199i
$958$	121474.	−	70133.2i	0.00427632	−	0.00246894i
$959$	−1.30814e6	−	6.00130e6i	−0.0459313	−	0.210717i
$960$	2.53639e7	+	1.94398e7i	0.888255	+	0.680792i
$961$	−5.72572e7			−1.99996
$962$	−28320.7	+	49052.9i	−0.000986657	+	0.00170894i
$963$	−1.13817e7	+	3.06338e6i	−0.395495	+	0.106448i
$964$	1.37315e7	−	7.92788e6i	0.475910	−	0.274767i
$965$	1.01376e7	−	1.75588e7i	0.350441	−	0.606982i
$966$	−62022.4	+	43153.1i	−0.00213848	+	0.00148788i
$967$	−1.93524e7	−	3.35193e7i	−0.665531	−	1.15273i	−0.979141	−	0.203182i	$-0.934872\pi$
$967$	−1.93524e7	−	3.35193e7i	−0.665531	−	1.15273i	0.313610	−	0.949552i	$-0.398462\pi$
$968$	−238082.	−	137456.i	−0.00816653	−	0.00471495i
$969$	−1.63284e7	−	2.14038e6i	−0.558644	−	0.0732286i
$970$	−22559.3	−	39073.8i	−0.000769831	−	0.00133339i
$971$	2.76587e6	+	4.79062e6i	0.0941419	+	0.163059i	0.909250	−	0.416250i	$-0.136656\pi$
$971$	2.76587e6	+	4.79062e6i	0.0941419	+	0.163059i	−0.815108	+	0.579309i	$0.803323\pi$
$972$	−1.78651e7	+	2.34177e7i	−0.606512	+	0.795022i
$973$	1.30223e6	+	5.97418e6i	0.0440967	+	0.202300i
$974$	259214.	+	149657.i	0.00875510	+	0.00505476i
$975$	3.87320e6	−	5.05351e6i	0.130484	−	0.170248i
$976$		−	1.23689e7i		−	0.415630i
$977$			4.14158e7i			1.38813i	0.719913	+	0.694064i	$0.244181\pi$
$977$			4.14158e7i			1.38813i	−0.719913	+	0.694064i	$0.755819\pi$
$978$	97987.3	+	236188.i	0.00327584	+	0.00789606i
$979$	2.08458e7	+	1.20354e7i	0.695125	+	0.401330i
$980$	−3.06013e7	+	1.40062e7i	−1.01783	+	0.465860i
$981$	2.15455e7	−	2.15938e7i	0.714800	−	0.716403i
$982$	99113.2	+	171669.i	0.00327984	+	0.00568085i
$983$	−3.57567e6	−	6.19324e6i	−0.118025	−	0.204425i	0.800960	−	0.598718i	$-0.204323\pi$
$983$	−3.57567e6	−	6.19324e6i	−0.118025	−	0.204425i	−0.918985	+	0.394293i	$0.870990\pi$
$984$	−173692.	−	418667.i	−0.00571864	−	0.0137842i
$985$	−4.87117e7	−	2.81237e7i	−1.59971	−	0.923595i
$986$	106685.	+	184784.i	0.00349472	+	0.00605303i
$987$	−3.65043e7	−	1.71552e7i	−1.19276	−	0.560535i
$988$	7.81700e6	−	1.35394e7i	0.254770	−	0.441274i
$989$	1.14690e7	−	6.62166e6i	0.372852	−	0.215266i
$990$	−112236.	−	29938.9i	−0.00363953	−	0.000970839i
$991$	6.45962e6	−	1.11884e7i	0.208941	−	0.361896i	−0.742440	−	0.669912i	$-0.766332\pi$
$991$	6.45962e6	−	1.11884e7i	0.208941	−	0.361896i	0.951381	+	0.308016i	$0.0996651\pi$
$992$	−1.04131e6			−0.0335970
$993$	−6.93924e6	+	5.29379e7i	−0.223326	+	1.70370i
$994$	77012.0	−	241264.i	0.00247225	−	0.00774508i
$995$	−1.16234e7	+	6.71075e6i	−0.372198	+	0.214889i
$996$	−2.24572e7	−	1.72120e7i	−0.717310	−	0.549773i
$997$	6.23677e6	−	3.60080e6i	0.198711	−	0.114726i	−0.397343	−	0.917670i	$-0.630068\pi$
$997$	6.23677e6	−	3.60080e6i	0.198711	−	0.114726i	0.596054	+	0.802944i	$0.296734\pi$
$998$	203023.	+	117215.i	0.00645236	+	0.00372527i
$999$	1.12592e7	−	1.50155e6i	0.356939	−	0.0476022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.i.a.38.19	yes	76
3.2	odd	2		189.6.i.a.143.20		76
7.5	odd	6		63.6.s.a.47.19	yes	76
9.4	even	3		189.6.s.a.17.20		76
9.5	odd	6		63.6.s.a.59.19	yes	76
21.5	even	6		189.6.s.a.89.20		76
63.5	even	6	inner	63.6.i.a.5.20	✓	76
63.40	odd	6		189.6.i.a.152.19		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.i.a.5.20	✓	76	63.5	even	6	inner
63.6.i.a.38.19	yes	76	1.1	even	1	trivial
63.6.s.a.47.19	yes	76	7.5	odd	6
63.6.s.a.59.19	yes	76	9.5	odd	6
189.6.i.a.143.20		76	3.2	odd	2
189.6.i.a.152.19		76	63.40	odd	6
189.6.s.a.17.20		76	9.4	even	3
189.6.s.a.89.20		76	21.5	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.0365780i q^{2} +(-2.02604 + 15.4562i) q^{3} +31.9987 q^{4} +(31.2888 - 54.1937i) q^{5} +(-0.565358 - 0.0741087i) q^{6} +(39.4223 - 123.503i) q^{7} +2.34094i q^{8} +(-234.790 - 62.6300i) q^{9} +O(q^{10})\)	\(q+0.0365780i q^{2} +(-2.02604 + 15.4562i) q^{3} +31.9987 q^{4} +(31.2888 - 54.1937i) q^{5} +(-0.565358 - 0.0741087i) q^{6} +(39.4223 - 123.503i) q^{7} +2.34094i q^{8} +(-234.790 - 62.6300i) q^{9} +(1.98230 + 1.14448i) q^{10} +(180.861 - 104.420i) q^{11} +(-64.8307 + 494.579i) q^{12} +(447.217 - 258.201i) q^{13} +(4.51748 + 1.44199i) q^{14} +(774.239 + 593.406i) q^{15} +1023.87 q^{16} +(-558.291 + 966.988i) q^{17} +(2.29088 - 8.58816i) q^{18} +(819.372 - 473.065i) q^{19} +(1001.20 - 1734.13i) q^{20} +(1829.01 + 859.543i) q^{21} +(3.81948 + 6.61553i) q^{22} +(885.200 + 511.070i) q^{23} +(-36.1822 - 4.74286i) q^{24} +(-395.475 - 684.983i) q^{25} +(9.44447 + 16.3583i) q^{26} +(1443.72 - 3502.08i) q^{27} +(1261.46 - 3951.92i) q^{28} +(-4524.33 - 2612.13i) q^{29} +(-21.7056 + 28.3201i) q^{30} +9267.49i q^{31} +112.361i q^{32} +(1247.51 + 3006.99i) q^{33} +(-35.3705 - 20.4212i) q^{34} +(-5459.59 - 6000.69i) q^{35} +(-7512.97 - 2004.08i) q^{36} +(1499.33 + 2596.91i) q^{37} +(17.3038 + 29.9710i) q^{38} +(3084.73 + 7435.42i) q^{39} +(126.865 + 73.2453i) q^{40} +(6210.55 + 10757.0i) q^{41} +(-31.4404 + 66.9016i) q^{42} +(6478.23 - 11220.6i) q^{43} +(5787.31 - 3341.30i) q^{44} +(-10740.5 + 10764.5i) q^{45} +(-18.6939 + 32.3788i) q^{46} -19958.5 q^{47} +(-2074.41 + 15825.2i) q^{48} +(-13698.8 - 9737.52i) q^{49} +(25.0553 - 14.4657i) q^{50} +(-13814.9 - 10588.2i) q^{51} +(14310.3 - 8262.08i) q^{52} +(-21892.1 - 12639.4i) q^{53} +(128.099 + 52.8084i) q^{54} -13068.7i q^{55} +(289.112 + 92.2855i) q^{56} +(5651.72 + 13622.9i) q^{57} +(95.5463 - 165.491i) q^{58} -33306.7 q^{59} +(24774.6 + 18988.2i) q^{60} -12080.5i q^{61} -338.986 q^{62} +(-16991.0 + 26528.2i) q^{63} +32759.8 q^{64} -32315.2i q^{65} +(-109.990 + 45.6314i) q^{66} +23717.0 q^{67} +(-17864.6 + 30942.3i) q^{68} +(-9692.68 + 12646.4i) q^{69} +(219.493 - 199.701i) q^{70} -53406.7i q^{71} +(146.613 - 549.631i) q^{72} +(67780.6 + 39133.2i) q^{73} +(-94.9898 + 54.8424i) q^{74} +(11388.5 - 4724.75i) q^{75} +(26218.8 - 15137.4i) q^{76} +(-5766.19 - 26453.3i) q^{77} +(-271.973 + 112.833i) q^{78} -49330.7 q^{79} +(32035.7 - 55487.4i) q^{80} +(51204.0 + 29409.9i) q^{81} +(-393.469 + 227.170i) q^{82} +(-28362.0 + 49124.5i) q^{83} +(58526.0 + 27504.2i) q^{84} +(34936.5 + 60511.8i) q^{85} +(410.428 + 236.961i) q^{86} +(49540.1 - 64636.9i) q^{87} +(244.442 + 423.385i) q^{88} +(57629.5 + 99817.2i) q^{89} +(-393.746 - 392.865i) q^{90} +(-14258.1 - 65411.3i) q^{91} +(28325.2 + 16353.6i) q^{92} +(-143240. - 18776.3i) q^{93} -730.042i q^{94} -59206.5i q^{95} +(-1736.68 - 227.649i) q^{96} +(-17070.5 - 9855.67i) q^{97} +(356.179 - 501.073i) q^{98} +(-49004.2 + 13189.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9}+O(q^{10}) \) 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9	\( 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9} - 6 q^{10} + 567 q^{11} - 1542 q^{12} + 543 q^{13} - 1638 q^{14} + 234 q^{15} + 16446 q^{16} - 801 q^{17} - 2022 q^{18} - 6 q^{19} + 96 q^{20} - 4119 q^{21} + 62 q^{22} + 7806 q^{23} - 2346 q^{24} - 18749 q^{25} + 10128 q^{26} - 1539 q^{27} + 860 q^{28} + 17904 q^{29} + 11457 q^{30} - 3 q^{33} + 96 q^{34} + 3960 q^{35} - 57846 q^{36} + 2577 q^{37} + 14967 q^{38} - 16269 q^{39} + 9564 q^{40} + 28230 q^{41} + 15606 q^{42} - 9246 q^{43} - 69885 q^{44} - 23649 q^{45} - 9418 q^{46} - 56562 q^{47} + 48615 q^{48} + 7948 q^{49} - 67509 q^{50} - 103722 q^{51} - 40899 q^{52} + 25296 q^{53} + 176211 q^{54} + 104754 q^{56} + 33399 q^{57} - 4951 q^{58} - 59076 q^{59} + 33729 q^{60} + 79536 q^{62} - 95871 q^{63} - 198600 q^{64} + 114900 q^{66} + 1244 q^{67} + 191496 q^{68} + 3702 q^{69} - 127197 q^{70} + 183582 q^{72} - 6 q^{73} - 45681 q^{74} - 240486 q^{75} - 2880 q^{76} + 13854 q^{77} + 184431 q^{78} + 59984 q^{79} + 243225 q^{80} + 177117 q^{81} + 90 q^{82} - 246930 q^{83} + 56085 q^{84} + 11973 q^{85} + 291801 q^{86} + 205125 q^{87} - 34751 q^{88} - 6345 q^{89} - 269187 q^{90} - 120111 q^{91} - 463488 q^{92} + 200946 q^{93} - 382521 q^{96} - 104037 q^{97} - 646797 q^{98} - 144540 q^{99}+O(q^{100}) \) 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9 - 6 * q^10 + 567 * q^11 - 1542 * q^12 + 543 * q^13 - 1638 * q^14 + 234 * q^15 + 16446 * q^16 - 801 * q^17 - 2022 * q^18 - 6 * q^19 + 96 * q^20 - 4119 * q^21 + 62 * q^22 + 7806 * q^23 - 2346 * q^24 - 18749 * q^25 + 10128 * q^26 - 1539 * q^27 + 860 * q^28 + 17904 * q^29 + 11457 * q^30 - 3 * q^33 + 96 * q^34 + 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 14967 * q^38 - 16269 * q^39 + 9564 * q^40 + 28230 * q^41 + 15606 * q^42 - 9246 * q^43 - 69885 * q^44 - 23649 * q^45 - 9418 * q^46 - 56562 * q^47 + 48615 * q^48 + 7948 * q^49 - 67509 * q^50 - 103722 * q^51 - 40899 * q^52 + 25296 * q^53 + 176211 * q^54 + 104754 * q^56 + 33399 * q^57 - 4951 * q^58 - 59076 * q^59 + 33729 * q^60 + 79536 * q^62 - 95871 * q^63 - 198600 * q^64 + 114900 * q^66 + 1244 * q^67 + 191496 * q^68 + 3702 * q^69 - 127197 * q^70 + 183582 * q^72 - 6 * q^73 - 45681 * q^74 - 240486 * q^75 - 2880 * q^76 + 13854 * q^77 + 184431 * q^78 + 59984 * q^79 + 243225 * q^80 + 177117 * q^81 + 90 * q^82 - 246930 * q^83 + 56085 * q^84 + 11973 * q^85 + 291801 * q^86 + 205125 * q^87 - 34751 * q^88 - 6345 * q^89 - 269187 * q^90 - 120111 * q^91 - 463488 * q^92 + 200946 * q^93 - 382521 * q^96 - 104037 * q^97 - 646797 * q^98 - 144540 * q^99

Introduction

L-functions

Modular forms

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Database

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