LMFDB - Embedded newform 76.6.f.a.27.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(27,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("76.27");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.f (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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.19
Character	$\chi$	$=$	76.27
Dual form			76.6.f.a.31.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43312 - 5.10685i) q^{2} +(-12.1499 + 21.0442i) q^{3} +(-20.1598 + 24.8512i) q^{4} +(-36.1399 + 62.5962i) q^{5} +(137.032 + 10.8444i) q^{6} +149.741i q^{7} +(175.963 + 42.4871i) q^{8} +(-173.739 - 300.925i) q^{9} +O(q^{10})$	\(q+(-2.43312 - 5.10685i) q^{2} +(-12.1499 + 21.0442i) q^{3} +(-20.1598 + 24.8512i) q^{4} +(-36.1399 + 62.5962i) q^{5} +(137.032 + 10.8444i) q^{6} +149.741i q^{7} +(175.963 + 42.4871i) q^{8} +(-173.739 - 300.925i) q^{9} +(407.602 + 32.2569i) q^{10} +151.331i q^{11} +(-278.034 - 726.186i) q^{12} +(-587.871 + 339.408i) q^{13} +(764.705 - 364.339i) q^{14} +(-878.192 - 1521.07i) q^{15} +(-211.163 - 1001.99i) q^{16} +(95.4017 - 165.241i) q^{17} +(-1114.05 + 1619.45i) q^{18} +(838.096 + 1331.80i) q^{19} +(-827.016 - 2160.05i) q^{20} +(-3151.18 - 1819.34i) q^{21} +(772.824 - 368.207i) q^{22} +(2500.37 - 1443.59i) q^{23} +(-3032.03 + 3186.78i) q^{24} +(-1049.69 - 1818.12i) q^{25} +(3163.67 + 2176.35i) q^{26} +2538.79 q^{27} +(-3721.25 - 3018.75i) q^{28} +(-6202.55 + 3581.04i) q^{29} +(-5631.14 + 8185.75i) q^{30} +3755.43 q^{31} +(-4603.23 + 3516.35i) q^{32} +(-3184.64 - 1838.65i) q^{33} +(-1075.98 - 85.1513i) q^{34} +(-9373.23 - 5411.64i) q^{35} +(10980.9 + 1748.97i) q^{36} -4030.64i q^{37} +(4762.12 - 7520.47i) q^{38} -16495.0i q^{39} +(-9018.81 + 9479.11i) q^{40} +(9654.16 + 5573.83i) q^{41} +(-1623.86 + 20519.3i) q^{42} +(2672.34 + 1542.87i) q^{43} +(-3760.75 - 3050.80i) q^{44} +25115.7 q^{45} +(-13455.9 - 9256.58i) q^{46} +(23244.7 - 13420.4i) q^{47} +(23651.7 + 7730.30i) q^{48} -5615.41 q^{49} +(-6730.83 + 9784.33i) q^{50} +(2318.24 + 4015.30i) q^{51} +(3416.69 - 21451.7i) q^{52} +(20244.8 - 11688.3i) q^{53} +(-6177.19 - 12965.2i) q^{54} +(-9472.74 - 5469.09i) q^{55} +(-6362.07 + 26348.8i) q^{56} +(-38209.5 + 1455.83i) q^{57} +(33379.4 + 22962.4i) q^{58} +(-14616.0 + 25315.6i) q^{59} +(55504.7 + 8840.44i) q^{60} +(-23477.9 - 40664.9i) q^{61} +(-9137.41 - 19178.4i) q^{62} +(45060.8 - 26015.9i) q^{63} +(29157.7 + 14952.3i) q^{64} -49064.7i q^{65} +(-1641.10 + 20737.1i) q^{66} +(-154.049 - 266.821i) q^{67} +(2183.14 + 5702.06i) q^{68} +70157.7i q^{69} +(-4830.19 + 61034.9i) q^{70} +(-31345.9 + 54292.7i) q^{71} +(-17786.1 - 60333.2i) q^{72} +(-31655.8 + 54829.4i) q^{73} +(-20583.9 + 9807.05i) q^{74} +51014.5 q^{75} +(-49992.7 - 6021.20i) q^{76} -22660.5 q^{77} +(-84237.7 + 40134.5i) q^{78} +(-31332.0 + 54268.6i) q^{79} +(70352.3 + 22993.9i) q^{80} +(11372.6 - 19697.9i) q^{81} +(4974.95 - 62864.2i) q^{82} +78706.9i q^{83} +(108740. - 41633.2i) q^{84} +(6895.62 + 11943.6i) q^{85} +(1377.10 - 17401.2i) q^{86} -174037. i q^{87} +(-6429.62 + 26628.6i) q^{88} +(86683.7 - 50046.9i) q^{89} +(-61109.5 - 128262. i) q^{90} +(-50823.3 - 88028.5i) q^{91} +(-14532.1 + 91239.7i) q^{92} +(-45628.0 + 79029.9i) q^{93} +(-125093. - 86054.0i) q^{94} +(-113654. + 4330.39i) q^{95} +(-18070.1 - 139595. i) q^{96} +(-87915.1 - 50757.8i) q^{97} +(13663.0 + 28677.0i) q^{98} +(45539.2 - 26292.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9}+O(q^{10}) $ 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9	$ 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9} + 648 q^{10} - 354 q^{13} + 2154 q^{14} - 611 q^{16} - 1006 q^{17} + 10524 q^{20} + 7824 q^{21} + 93 q^{22} - 5311 q^{24} - 25002 q^{25} - 13428 q^{26} + 1556 q^{28} - 6 q^{29} - 12656 q^{30} - 30453 q^{32} + 8586 q^{33} + 30102 q^{34} - 2306 q^{36} + 29846 q^{38} - 1392 q^{40} + 29064 q^{41} + 18616 q^{42} + 9155 q^{44} + 13464 q^{45} + 38217 q^{48} - 116224 q^{49} + 36858 q^{52} + 26262 q^{53} - 26355 q^{54} + 53974 q^{57} - 112740 q^{58} - 108810 q^{60} - 77370 q^{61} - 106848 q^{62} + 337966 q^{64} + 166855 q^{66} + 175796 q^{68} + 148122 q^{70} - 259842 q^{72} - 52040 q^{73} + 103690 q^{74} - 194709 q^{76} + 197584 q^{77} + 253206 q^{78} - 171934 q^{80} - 313100 q^{81} + 63919 q^{82} - 161762 q^{85} - 38442 q^{86} + 10482 q^{89} - 372450 q^{90} + 64544 q^{92} + 94012 q^{93} + 537614 q^{96} + 177180 q^{97} - 509397 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9 + 648 * q^10 - 354 * q^13 + 2154 * q^14 - 611 * q^16 - 1006 * q^17 + 10524 * q^20 + 7824 * q^21 + 93 * q^22 - 5311 * q^24 - 25002 * q^25 - 13428 * q^26 + 1556 * q^28 - 6 * q^29 - 12656 * q^30 - 30453 * q^32 + 8586 * q^33 + 30102 * q^34 - 2306 * q^36 + 29846 * q^38 - 1392 * q^40 + 29064 * q^41 + 18616 * q^42 + 9155 * q^44 + 13464 * q^45 + 38217 * q^48 - 116224 * q^49 + 36858 * q^52 + 26262 * q^53 - 26355 * q^54 + 53974 * q^57 - 112740 * q^58 - 108810 * q^60 - 77370 * q^61 - 106848 * q^62 + 337966 * q^64 + 166855 * q^66 + 175796 * q^68 + 148122 * q^70 - 259842 * q^72 - 52040 * q^73 + 103690 * q^74 - 194709 * q^76 + 197584 * q^77 + 253206 * q^78 - 171934 * q^80 - 313100 * q^81 + 63919 * q^82 - 161762 * q^85 - 38442 * q^86 + 10482 * q^89 - 372450 * q^90 + 64544 * q^92 + 94012 * q^93 + 537614 * q^96 + 177180 * q^97 - 509397 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.43312	−	5.10685i	−0.430120	−	0.902772i
$2$	−2.43312	−	5.10685i	−0.430120	−	0.902772i
$3$	−12.1499	+	21.0442i	−0.779415	+	1.34999i	0.152864	+	0.988247i	$0.451150\pi$
$3$	−12.1499	+	21.0442i	−0.779415	+	1.34999i	−0.932279	+	0.361739i	$0.882183\pi$
$4$	−20.1598	+	24.8512i	−0.629994	+	0.776600i
$5$	−36.1399	+	62.5962i	−0.646491	+	1.11976i	0.337464	+	0.941338i	$0.390431\pi$
$5$	−36.1399	+	62.5962i	−0.646491	+	1.11976i	−0.983955	+	0.178417i	$0.942902\pi$
$6$	137.032	+	10.8444i	1.55397	+	0.122978i
$7$			149.741i			1.15504i	0.816377	+	0.577519i	$0.195979\pi$
$7$			149.741i			1.15504i	−0.816377	+	0.577519i	$0.804021\pi$
$8$	175.963	+	42.4871i	0.972065	+	0.234710i
$9$	−173.739	−	300.925i	−0.714975	−	1.23837i
$10$	407.602	+	32.2569i	1.28895	+	0.102005i
$11$			151.331i			0.377091i	0.982064	+	0.188545i	$0.0603773\pi$
$11$			151.331i			0.377091i	−0.982064	+	0.188545i	$0.939623\pi$
$12$	−278.034	−	726.186i	−0.557372	−	1.45578i
$13$	−587.871	+	339.408i	−0.964770	+	0.557010i	−0.897638	−	0.440734i	$-0.854718\pi$
$13$	−587.871	+	339.408i	−0.964770	+	0.557010i	−0.0671322	+	0.997744i	$0.521385\pi$
$14$	764.705	−	364.339i	1.04274	−	0.496804i
$15$	−878.192	−	1521.07i	−1.00777	−	1.74551i
$16$	−211.163	−	1001.99i	−0.206214	−	0.978507i
$17$	95.4017	−	165.241i	0.0800633	−	0.138674i	−0.823214	−	0.567732i	$-0.807821\pi$
$17$	95.4017	−	165.241i	0.0800633	−	0.138674i	0.903277	+	0.429058i	$0.141154\pi$
$18$	−1114.05	+	1619.45i	−0.810444	+	1.17811i
$19$	838.096	+	1331.80i	0.532610	+	0.846361i
$19$	838.096	+	1331.80i	0.532610	+	0.846361i
$20$	−827.016	−	2160.05i	−0.462316	−	1.20750i
$21$	−3151.18	−	1819.34i	−1.55928	−	0.900253i
$22$	772.824	−	368.207i	0.340427	−	0.162194i
$23$	2500.37	−	1443.59i	0.985563	−	0.569015i	0.0816183	−	0.996664i	$-0.473991\pi$
$23$	2500.37	−	1443.59i	0.985563	−	0.569015i	0.903945	+	0.427648i	$0.140658\pi$
$24$	−3032.03	+	3186.78i	−1.07450	+	1.12934i
$25$	−1049.69	−	1818.12i	−0.335901	−	0.581798i
$26$	3163.67	+	2176.35i	0.917820	+	0.631386i
$27$	2538.79			0.670220
$28$	−3721.25	−	3018.75i	−0.897002	−	0.727667i
$29$	−6202.55	+	3581.04i	−1.36954	+	0.790705i	−0.990869	−	0.134826i	$-0.956952\pi$
$29$	−6202.55	+	3581.04i	−1.36954	+	0.790705i	−0.378672	+	0.925531i	$0.623619\pi$
$30$	−5631.14	+	8185.75i	−1.14233	+	1.66056i
$31$	3755.43			0.701867			0.350934	−	0.936400i	$-0.385864\pi$
$31$	3755.43			0.701867			0.350934	+	0.936400i	$0.385864\pi$
$32$	−4603.23	+	3516.35i	−0.794672	+	0.607039i
$33$	−3184.64	−	1838.65i	−0.509067	−	0.293910i
$34$	−1075.98	−	85.1513i	−0.159628	−	0.0126326i
$35$	−9373.23	−	5411.64i	−1.29336	−	0.746721i
$36$	10980.9	+	1748.97i	1.41215	+	0.224919i
$37$		−	4030.64i		−	0.484027i	−0.970273	−	0.242014i	$-0.922192\pi$
$37$		−	4030.64i		−	0.484027i	0.970273	−	0.242014i	$-0.0778079\pi$
$38$	4762.12	−	7520.47i	0.534985	−	0.844862i
$39$		−	16495.0i		−	1.73657i
$40$	−9018.81	+	9479.11i	−0.891250	+	0.936737i
$41$	9654.16	+	5573.83i	0.896922	+	0.517838i	0.876200	−	0.481947i	$-0.160070\pi$
$41$	9654.16	+	5573.83i	0.896922	+	0.517838i	0.0207220	+	0.999785i	$0.493404\pi$
$42$	−1623.86	+	20519.3i	−0.142045	+	1.79489i
$43$	2672.34	+	1542.87i	0.220404	+	0.127250i	0.606137	−	0.795360i	$-0.292718\pi$
$43$	2672.34	+	1542.87i	0.220404	+	0.127250i	−0.385733	+	0.922610i	$0.626051\pi$
$44$	−3760.75	−	3050.80i	−0.292849	−	0.237565i
$45$	25115.7			1.84890
$46$	−13455.9	−	9256.58i	−0.937601	−	0.644994i
$47$	23244.7	−	13420.4i	1.53490	−	0.886175i	0.535774	−	0.844361i	$-0.320020\pi$
$47$	23244.7	−	13420.4i	1.53490	−	0.886175i	0.999125	−	0.0418133i	$-0.0133135\pi$
$48$	23651.7	+	7730.30i	1.48170	+	0.484276i
$49$	−5615.41			−0.334111
$50$	−6730.83	+	9784.33i	−0.380753	+	0.553485i
$51$	2318.24	+	4015.30i	0.124805	+	0.216169i
$52$	3416.69	−	21451.7i	0.175226	−	1.10015i
$53$	20244.8	−	11688.3i	0.989974	−	0.571562i	0.0847077	−	0.996406i	$-0.473004\pi$
$53$	20244.8	−	11688.3i	0.989974	−	0.571562i	0.905267	+	0.424844i	$0.139671\pi$
$54$	−6177.19	−	12965.2i	−0.288275	−	0.605056i
$55$	−9472.74	−	5469.09i	−0.422249	−	0.243786i
$56$	−6362.07	+	26348.8i	−0.271099	+	1.12277i
$57$	−38209.5	+	1455.83i	−1.55770	+	0.0593505i
$58$	33379.4	+	22962.4i	1.30289	+	0.896286i
$59$	−14616.0	+	25315.6i	−0.546636	+	0.946801i	0.451866	+	0.892086i	$0.350759\pi$
$59$	−14616.0	+	25315.6i	−0.546636	+	0.946801i	−0.998502	+	0.0547155i	$0.982575\pi$
$60$	55504.7	+	8840.44i	1.99045	+	0.317027i
$61$	−23477.9	−	40664.9i	−0.807857	−	1.39925i	−0.914345	−	0.404935i	$-0.867294\pi$
$61$	−23477.9	−	40664.9i	−0.807857	−	1.39925i	0.106488	−	0.994314i	$-0.466039\pi$
$62$	−9137.41	−	19178.4i	−0.301887	−	0.633626i
$63$	45060.8	−	26015.9i	1.43037	−	0.825823i
$64$	29157.7	+	14952.3i	0.889822	+	0.456308i
$65$		−	49064.7i		−	1.44041i
$66$	−1641.10	+	20737.1i	−0.0463740	+	0.585988i
$67$	−154.049	−	266.821i	−0.00419250	−	0.00726162i	0.863922	−	0.503626i	$-0.168001\pi$
$67$	−154.049	−	266.821i	−0.00419250	−	0.00726162i	−0.868114	+	0.496365i	$0.834668\pi$
$68$	2183.14	+	5702.06i	0.0572546	+	0.149541i
$69$			70157.7i			1.77400i
$70$	−4830.19	+	61034.9i	−0.117820	+	1.48879i
$71$	−31345.9	+	54292.7i	−0.737963	+	1.27819i	0.215448	+	0.976515i	$0.430879\pi$
$71$	−31345.9	+	54292.7i	−0.737963	+	1.27819i	−0.953411	+	0.301675i	$0.902454\pi$
$72$	−17786.1	−	60333.2i	−0.404343	−	1.37159i
$73$	−31655.8	+	54829.4i	−0.695257	+	1.20422i	0.274836	+	0.961491i	$0.411376\pi$
$73$	−31655.8	+	54829.4i	−0.695257	+	1.20422i	−0.970094	+	0.242730i	$0.921957\pi$
$74$	−20583.9	+	9807.05i	−0.436966	+	0.208190i
$75$	51014.5			1.04723
$76$	−49992.7	−	6021.20i	−0.992825	−	0.119577i
$77$	−22660.5			−0.435554
$78$	−84237.7	+	40134.5i	−1.56773	+	0.746932i
$79$	−31332.0	+	54268.6i	−0.564834	+	0.978321i	0.432231	+	0.901763i	$0.357726\pi$
$79$	−31332.0	+	54268.6i	−0.564834	+	0.978321i	−0.997065	+	0.0765579i	$0.975607\pi$
$80$	70352.3	+	22993.9i	1.22900	+	0.401686i
$81$	11372.6	−	19697.9i	0.192596	−	0.333586i
$82$	4974.95	−	62864.2i	0.0817061	−	1.03245i
$83$			78706.9i			1.25406i	0.778996	+	0.627029i	$0.215729\pi$
$83$			78706.9i			1.25406i	−0.778996	+	0.627029i	$0.784271\pi$
$84$	108740.	−	41633.2i	1.68148	−	0.643785i
$85$	6895.62	+	11943.6i	0.103520	+	0.179303i
$86$	1377.10	−	17401.2i	0.0200780	−	0.253708i
$87$		−	174037.i		−	2.46515i
$88$	−6429.62	+	26628.6i	−0.0885072	+	0.366557i
$89$	86683.7	−	50046.9i	1.16001	−	0.669733i	0.208705	−	0.977979i	$-0.433075\pi$
$89$	86683.7	−	50046.9i	1.16001	−	0.669733i	0.951307	+	0.308245i	$0.0997418\pi$
$90$	−61109.5	−	128262.i	−0.795248	−	1.66914i
$91$	−50823.3	−	88028.5i	−0.643368	−	1.11435i
$92$	−14532.1	+	91239.7i	−0.179002	+	1.12386i
$93$	−45628.0	+	79029.9i	−0.547046	+	0.947511i
$94$	−125093.	−	86054.0i	−1.46020	−	1.00450i
$95$	−113654.	+	4330.39i	−1.29204	+	0.0492287i
$96$	−18070.1	−	139595.i	−0.200116	−	1.54593i
$97$	−87915.1	−	50757.8i	−0.948711	−	0.547739i	−0.0560307	−	0.998429i	$-0.517844\pi$
$97$	−87915.1	−	50757.8i	−0.948711	−	0.547739i	−0.892680	+	0.450690i	$0.851178\pi$
$98$	13663.0	+	28677.0i	0.143708	+	0.301626i
$99$	45539.2	−	26292.1i	0.466979	−	0.269611i
$100$	66344.0	+	10566.9i	0.663440	+	0.105669i
$101$	94647.9	+	163935.i	0.923225	+	1.59907i	0.794391	+	0.607407i	$0.207790\pi$
$101$	94647.9	+	163935.i	0.923225	+	1.59907i	0.128835	+	0.991666i	$0.458876\pi$
$102$	14865.0	−	21608.6i	0.141470	−	0.205649i
$103$	−51833.0			−0.481408			−0.240704	−	0.970599i	$-0.577378\pi$
$103$	−51833.0			−0.481408			−0.240704	+	0.970599i	$0.577378\pi$
$104$	−117864.	+	34746.1i	−1.06856	+	0.315009i
$105$	227767.	−	131501.i	2.01613	−	1.16401i
$106$	−108949.	−	74948.0i	−0.941797	−	0.647881i
$107$	65120.2			0.549866			0.274933	−	0.961463i	$-0.411344\pi$
$107$	65120.2			0.549866			0.274933	+	0.961463i	$0.411344\pi$
$108$	−51181.5	+	63091.9i	−0.422235	+	0.520493i
$109$	−189934.	−	109658.i	−1.53122	−	0.884048i	−0.999306	−	0.0372476i	$-0.988141\pi$
$109$	−189934.	−	109658.i	−1.53122	−	0.884048i	−0.531910	−	0.846801i	$-0.678526\pi$
$110$	−4881.47	+	61682.8i	−0.0384653	+	0.486052i
$111$	84821.6	+	48971.8i	0.653430	+	0.377258i
$112$	150039.	−	31619.9i	1.13021	−	0.238185i
$113$		−	16019.6i		−	0.118020i	−0.998257	−	0.0590099i	$-0.981206\pi$
$113$		−	16019.6i		−	0.118020i	0.998257	−	0.0590099i	$-0.0187944\pi$
$114$	100403.	+	191588.i	0.723577	+	1.38072i
$115$			208685.i			1.47145i
$116$	36049.1	−	226334.i	0.248742	−	1.56172i
$117$	204272.	+	117937.i	1.37957	+	0.796497i
$118$	164846.	+	13045.6i	1.08986	+	0.0862499i
$119$	24743.3	+	14285.6i	0.160173	+	0.0924761i
$120$	−89902.9	−	304964.i	−0.569929	−	1.93328i
$121$	138150.			0.857803
$122$	−150545.	+	218841.i	−0.915728	+	1.33116i
$123$	−234594.	+	135443.i	−1.39815	+	0.807222i
$124$	−75708.7	+	93326.8i	−0.442172	+	0.545070i
$125$	−74131.5			−0.424353
$126$	−242498.	−	166819.i	−1.36076	−	0.936093i
$127$	−28481.1	−	49330.8i	−0.156692	−	0.271399i	0.776982	−	0.629523i	$-0.216750\pi$
$127$	−28481.1	−	49330.8i	−0.156692	−	0.271399i	−0.933674	+	0.358124i	$0.883416\pi$
$128$	5414.85	−	185285.i	0.0292120	−	0.999573i
$129$	−64937.1	+	37491.4i	−0.343573	+	0.198362i
$130$	−250566.	+	119380.i	−1.30036	+	0.619548i
$131$	174749.	+	100892.i	0.889687	+	0.513661i	0.873840	−	0.486214i	$-0.161622\pi$
$131$	174749.	+	100892.i	0.889687	+	0.513661i	0.0158467	+	0.999874i	$0.494956\pi$
$132$	109894.	−	42075.2i	0.548960	−	0.210180i
$133$	−199425.	+	125497.i	−0.977578	+	0.615185i
$134$	−987.795	+	1435.92i	−0.00475231	+	0.00690824i
$135$	−91751.7	+	158919.i	−0.433291	+	0.750482i
$136$	23807.7	−	25022.8i	0.110375	−	0.116008i
$137$	−88399.8	−	153113.i	−0.402392	−	0.696964i	0.591622	−	0.806216i	$-0.298488\pi$
$137$	−88399.8	−	153113.i	−0.402392	−	0.696964i	−0.994014	+	0.109252i	$0.965155\pi$
$138$	358285.	−	170702.i	1.60151	−	0.763030i
$139$	16563.1	−	9562.73i	0.0727119	−	0.0419802i	−0.463203	−	0.886252i	$-0.653300\pi$
$139$	16563.1	−	9562.73i	0.0727119	−	0.0419802i	0.535915	+	0.844272i	$0.319967\pi$
$140$	323448.	−	123838.i	1.39471	−	0.533992i
$141$			652223.i			2.76279i
$142$	353533.	+	27977.9i	1.47133	+	0.116438i
$143$	−51362.9	−	88963.1i	−0.210043	−	0.363806i
$144$	−264837.	+	237629.i	−1.06432	+	0.954979i
$145$		−	517675.i		−	2.04473i
$146$	357028.	+	28254.5i	1.38618	+	0.109700i
$147$	68226.5	−	118172.i	0.260411	−	0.451046i
$148$	100166.	+	81257.0i	0.375895	+	0.304934i
$149$	−102457.	+	177461.i	−0.378073	+	0.654842i	−0.990782	−	0.135467i	$-0.956747\pi$
$149$	−102457.	+	177461.i	−0.378073	+	0.654842i	0.612709	+	0.790309i	$0.290080\pi$
$150$	−124125.	−	260523.i	−0.450432	−	0.945406i
$151$	−354197.			−1.26416			−0.632080	−	0.774903i	$-0.717799\pi$
$151$	−354197.			−1.26416			−0.632080	+	0.774903i	$0.717799\pi$
$152$	90889.1	+	269956.i	0.319082	+	0.947727i
$153$	−66300.0			−0.228973
$154$	55135.7	+	115724.i	0.187340	+	0.393206i
$155$	−135721.	+	235075.i	−0.453751	+	0.785919i
$156$	409921.	+	332537.i	1.34862	+	1.09403i
$157$	169716.	−	293956.i	0.549506	−	0.951773i	−0.448802	−	0.893631i	$-0.648149\pi$
$157$	169716.	−	293956.i	0.549506	−	0.951773i	0.998308	−	0.0581418i	$-0.0185176\pi$
$158$	353376.	+	27965.6i	1.12615	+	0.0891211i
$159$			568048.i			1.78194i
$160$	−53749.6	−	415225.i	−0.165987	−	1.28228i
$161$	216165.	+	374408.i	0.657234	+	1.13836i
$162$	−128265.	−	10150.7i	−0.383991	−	0.0303884i
$163$		−	394607.i		−	1.16331i	−0.813435	−	0.581656i	$-0.802405\pi$
$163$		−	394607.i		−	1.16331i	0.813435	−	0.581656i	$-0.197595\pi$
$164$	−333143.	+	127550.i	−0.967209	+	0.370314i
$165$	230185.	−	132898.i	0.658215	−	0.380021i
$166$	401944.	−	191504.i	1.13213	−	0.539395i
$167$	−104881.	−	181660.i	−0.291009	−	0.504043i	0.683039	−	0.730382i	$-0.260658\pi$
$167$	−104881.	−	181660.i	−0.291009	−	0.504043i	−0.974049	+	0.226339i	$0.927324\pi$
$168$	−477192.	−	454020.i	−1.30443	−	1.24109i
$169$	44748.5	−	77506.8i	0.120521	−	0.208748i
$170$	44216.1	−	64275.1i	0.117343	−	0.170577i
$171$	255162.	−	483590.i	0.667307	−	1.26470i
$172$	−92216.0	+	35306.7i	−0.237676	+	0.0909988i
$173$	−5457.85	−	3151.09i	−0.0138646	−	0.00800471i	0.493052	−	0.870000i	$-0.335881\pi$
$173$	−5457.85	−	3151.09i	−0.0138646	−	0.00800471i	−0.506916	+	0.861995i	$0.669215\pi$
$174$	−888780.	+	423453.i	−2.22547	+	1.06031i
$175$	272247.	−	157182.i	0.671999	−	0.387979i
$176$	151632.	−	31955.6i	0.368986	−	0.0777615i
$177$	−355165.	−	615164.i	−0.852113	−	1.47590i
$178$	−466494.	−	320910.i	−1.10356	−	0.759161i
$179$	−103562.			−0.241583			−0.120791	−	0.992678i	$-0.538543\pi$
$179$	−103562.			−0.241583			−0.120791	+	0.992678i	$0.538543\pi$
$180$	−506327.	+	624154.i	−1.16480	+	1.43586i
$181$	648414.	−	374362.i	1.47115	−	0.849367i	0.471671	−	0.881774i	$-0.343651\pi$
$181$	648414.	−	374362.i	1.47115	−	0.849367i	0.999475	+	0.0324079i	$0.0103176\pi$
$182$	−325889.	+	473731.i	−0.729275	+	1.06012i
$183$	1.14101e6			2.51862
$184$	501306.	−	147784.i	1.09159	−	0.321798i
$185$	252303.	+	145667.i	0.541992	+	0.312919i
$186$	514612.	+	40725.5i	1.09068	+	0.0863145i
$187$	25006.0	+	14437.2i	0.0522926	+	0.0301911i
$188$	−135098.	+	848211.i	−0.278775	+	1.75029i
$189$			380161.i			0.774129i
$190$	298650.	+	569880.i	0.600176	+	1.14525i
$191$		−	548060.i		−	1.08704i	−0.839397	−	0.543519i	$-0.817092\pi$
$191$		−	548060.i		−	1.08704i	0.839397	−	0.543519i	$-0.182908\pi$
$192$	−668921.	+	431932.i	−1.30955	+	0.845594i
$193$	−98358.0	−	56787.0i	−0.190071	−	0.109738i	0.401945	−	0.915664i	$-0.368334\pi$
$193$	−98358.0	−	56787.0i	−0.190071	−	0.109738i	−0.592016	+	0.805926i	$0.701668\pi$
$194$	−45304.1	+	572469.i	−0.0864238	+	1.09206i
$195$	1.03253e6	+	596130.i	1.94453	+	1.12268i
$196$	113206.	−	139550.i	0.210488	−	0.259471i
$197$	−374119.			−0.686823			−0.343411	−	0.939185i	$-0.611582\pi$
$197$	−374119.			−0.686823			−0.343411	+	0.939185i	$0.611582\pi$
$198$	−245072.	−	168590.i	−0.444254	−	0.305611i
$199$	−162271.	+	93687.2i	−0.290475	+	0.167706i	−0.638156	−	0.769907i	$-0.720302\pi$
$199$	−162271.	+	93687.2i	−0.290475	+	0.167706i	0.347681	+	0.937613i	$0.386969\pi$
$200$	−107460.	−	364519.i	−0.189964	−	0.644385i
$201$	7486.72			0.0130708
$202$	606901.	−	882227.i	1.04650	−	1.52125i
$203$	−536229.	−	928776.i	−0.913294	−	1.58187i
$204$	−146520.	−	23336.9i	−0.246503	−	0.0392615i
$205$	−697802.	+	402876.i	−1.15970	+	0.669556i
$206$	126116.	+	264703.i	0.207063	+	0.434601i
$207$	−868823.	−	501615.i	−1.40931	−	0.813664i
$208$	464220.	+	517371.i	0.743988	+	0.829171i
$209$	−201543.	+	126830.i	−0.319155	+	0.200842i
$210$	−1.22574e6	−	843213.i	−1.91801	−	1.31944i
$211$	55352.7	−	95873.7i	0.0855919	−	0.148249i	−0.820051	−	0.572290i	$-0.806055\pi$
$211$	55352.7	−	95873.7i	0.0855919	−	0.148249i	0.905643	+	0.424040i	$0.139389\pi$
$212$	−117662.	+	738742.i	−0.179803	+	1.12889i
$213$	−761697.	−	1.31930e6i	−1.15036	−	1.99248i
$214$	−158446.	−	332559.i	−0.236508	−	0.496403i
$215$	−193156.	+	111519.i	−0.284979	+	0.164532i
$216$	446732.	+	107866.i	0.651497	+	0.157308i
$217$			562342.i			0.810683i
$218$	−97876.3	+	1.23678e6i	−0.139488	+	1.76259i
$219$	−769227.	−	1.33234e6i	−1.08379	−	1.87718i
$220$	326882.	−	125153.i	0.455339	−	0.174335i
$221$			129520.i			0.178384i
$222$	43710.0	−	552326.i	0.0595249	−	0.752164i
$223$	136667.	−	236714.i	0.184035	−	0.318759i	−0.759216	−	0.650839i	$-0.774417\pi$
$223$	136667.	−	236714.i	0.184035	−	0.318759i	0.943251	+	0.332081i	$0.107751\pi$
$224$	−526542.	−	689293.i	−0.701153	−	0.917876i
$225$	−364745.	+	631756.i	−0.480322	+	0.831943i
$226$	−81809.6	+	38977.6i	−0.106545	+	0.0507626i
$227$	580973.			0.748327			0.374163	−	0.927363i	$-0.377930\pi$
$227$	580973.			0.748327			0.374163	+	0.927363i	$0.377930\pi$
$228$	734117.	−	978900.i	0.935250	−	1.24710i
$229$	−256666.			−0.323429			−0.161715	−	0.986838i	$-0.551702\pi$
$229$	−256666.			−0.323429			−0.161715	+	0.986838i	$0.551702\pi$
$230$	1.06572e6	−	507756.i	1.32839	−	0.632901i
$231$	275322.	−	476871.i	0.339477	−	0.587992i
$232$	−1.24356e6	+	366601.i	−1.51687	+	0.447171i
$233$	76951.3	−	133284.i	0.0928595	−	0.160837i	−0.815854	−	0.578258i	$-0.803733\pi$
$233$	76951.3	−	133284.i	0.0928595	−	0.160837i	0.908713	+	0.417421i	$0.137066\pi$
$234$	105265.	−	1.33014e6i	0.125674	−	1.58803i
$235$			1.94004e6i			2.29162i
$236$	−334468.	−	873584.i	−0.390908	−	1.02100i
$237$	−761360.	−	1.31871e6i	−0.880480	−	1.52504i
$238$	12750.7	−	161119.i	0.0145912	−	0.184376i
$239$			1.48017e6i			1.67616i	0.545546	+	0.838081i	$0.316322\pi$
$239$			1.48017e6i			1.67616i	−0.545546	+	0.838081i	$0.683678\pi$
$240$	−1.33866e6	+	1.20114e6i	−1.50018	+	1.34606i
$241$	−483902.	+	279381.i	−0.536679	+	0.309852i	−0.743732	−	0.668478i	$-0.766946\pi$
$241$	−483902.	+	279381.i	−0.536679	+	0.309852i	0.207053	+	0.978330i	$0.433613\pi$
$242$	−336136.	−	705511.i	−0.368958	−	0.774400i
$243$	584814.	+	1.01293e6i	0.635334	+	1.10043i
$244$	1.48388e6	+	236343.i	1.59560	+	0.254138i
$245$	202941.	−	351503.i	0.216000	−	0.374123i
$246$	1.26248e6	+	868486.i	1.33011	+	0.915008i
$247$	−944716.	−	498472.i	−0.985278	−	0.519874i
$248$	660814.	+	159557.i	0.682261	+	0.164736i
$249$	−1.65632e6	−	956279.i	−1.69296	−	0.977431i
$250$	180371.	+	378578.i	0.182523	+	0.383094i
$251$	1.22736e6	−	708615.i	1.22967	−	0.709947i	0.262705	−	0.964876i	$-0.415385\pi$
$251$	1.22736e6	−	708615.i	1.22967	−	0.709947i	0.966960	+	0.254929i	$0.0820520\pi$
$252$	−261892.	+	1.64429e6i	−0.259789	+	1.63109i
$253$	218460.	+	378383.i	0.214570	+	0.371647i
$254$	−182627.	+	265477.i	−0.177615	+	0.258192i
$255$	−335124.			−0.322742
$256$	−959396.	+	423168.i	−0.914951	+	0.403564i
$257$	−26297.0	+	15182.6i	−0.0248355	+	0.0143388i	−0.512366	−	0.858767i	$-0.671231\pi$
$257$	−26297.0	+	15182.6i	−0.0248355	+	0.0143388i	0.487531	+	0.873106i	$0.337898\pi$
$258$	349463.	+	240403.i	0.326853	+	0.224848i
$259$	603553.			0.559069
$260$	1.21932e6	+	989135.i	1.11862	+	0.907449i
$261$	2.15525e6	+	1.24433e6i	1.95838	+	1.13067i
$262$	90051.3	−	1.13790e6i	0.0810469	−	1.02412i
$263$	−704790.	−	406911.i	−0.628305	−	0.362752i	0.151791	−	0.988413i	$-0.451496\pi$
$263$	−704790.	−	406911.i	−0.628305	−	0.362752i	−0.780095	+	0.625661i	$0.784829\pi$
$264$	−482258.	−	458840.i	−0.425863	−	0.405183i
$265$			1.68966e6i			1.47804i
$266$	1.12612e6	+	713085.i	0.975847	+	0.617927i
$267$			2.43225e6i			2.08800i
$268$	9736.44	+	1550.76i	0.00828062	+	0.00131889i
$269$	490470.	+	283173.i	0.413268	+	0.238600i	0.692193	−	0.721713i	$-0.256645\pi$
$269$	490470.	+	283173.i	0.413268	+	0.238600i	−0.278925	+	0.960313i	$0.589978\pi$
$270$	1.03482e6	+	81893.5i	0.863881	+	0.0683660i
$271$	145102.	+	83774.7i	0.120019	+	0.0692930i	0.558808	−	0.829297i	$-0.311259\pi$
$271$	145102.	+	83774.7i	0.120019	+	0.0692930i	−0.438789	+	0.898590i	$0.644592\pi$
$272$	−185715.	−	60698.9i	−0.152203	−	0.0497460i
$273$	2.46999e6			2.00580
$274$	−566837.	+	823987.i	−0.456123	+	0.663046i
$275$	275138.	−	158851.i	0.219391	−	0.126665i
$276$	−1.74350e6	−	1.41437e6i	−1.37769	−	1.11761i
$277$	1.37831e6			1.07931			0.539657	−	0.841885i	$-0.318554\pi$
$277$	1.37831e6			1.07931			0.539657	+	0.841885i	$0.318554\pi$
$278$	−89135.6	−	61318.1i	−0.0691734	−	0.0475857i
$279$	−652464.	−	1.13010e6i	−0.501818	−	0.869174i
$280$	−1.41941e6	−	1.35049e6i	−1.08197	−	1.02943i
$281$	−659503.	+	380764.i	−0.498254	+	0.287667i	−0.727992	−	0.685585i	$-0.759546\pi$
$281$	−659503.	+	380764.i	−0.498254	+	0.287667i	0.229738	+	0.973252i	$0.426213\pi$
$282$	3.33080e6	−	1.58694e6i	2.49417	−	1.18833i
$283$	81487.5	+	47046.9i	0.0604819	+	0.0349192i	0.529936	−	0.848038i	$-0.322216\pi$
$283$	81487.5	+	47046.9i	0.0604819	+	0.0349192i	−0.469454	+	0.882957i	$0.655549\pi$
$284$	−717310.	−	1.87351e6i	−0.527729	−	1.37835i
$285$	1.28976e6	−	2.44438e6i	0.940581	−	1.78261i
$286$	−329349.	+	478761.i	−0.238090	+	0.346101i
$287$	−834632.	+	1.44563e6i	−0.598123	+	1.03598i
$288$	1.85792e6	+	774299.i	1.31991	+	0.550082i
$289$	691726.	+	1.19810e6i	0.487180	+	0.843820i
$290$	−2.64369e6	+	1.25957e6i	−1.84593	+	0.879480i
$291$	2.13631e6	−	1.23340e6i	1.47888	−	0.853831i
$292$	−724401.	−	1.89203e6i	−0.497190	−	1.29859i
$293$		−	1.59978e6i		−	1.08866i	−0.838872	−	0.544329i	$-0.816784\pi$
$293$		−	1.59978e6i		−	1.08866i	0.838872	−	0.544329i	$-0.183216\pi$
$294$	−769489.	−	60896.0i	−0.519199	−	0.0410885i
$295$	−1.05644e6	−	1.82981e6i	−0.706791	−	1.22420i
$296$	171250.	−	709242.i	0.113606	−	0.470506i
$297$			384197.i			0.252734i
$298$	1.15555e6	+	91448.5i	0.753789	+	0.0596535i
$299$	−979930.	+	1.69729e6i	−0.633895	+	1.09794i
$300$	−1.02844e6	+	1.26777e6i	−0.659746	+	0.813275i
$301$	−231032.	+	400159.i	−0.146979	+	0.254575i
$302$	861805.	+	1.80883e6i	0.543740	+	1.14125i
$303$	−4.59984e6			−2.87830
$304$	1.15748e6	−	1.12099e6i	0.718338	−	0.695694i
$305$	3.39396e6			2.08909
$306$	161316.	+	338584.i	0.0984859	+	0.206711i
$307$	−299730.	+	519147.i	−0.181503	+	0.314373i	−0.942393	−	0.334509i	$-0.891430\pi$
$307$	−299730.	+	519147.i	−0.181503	+	0.314373i	0.760889	+	0.648881i	$0.224763\pi$
$308$	456831.	−	563139.i	0.274397	−	0.338251i
$309$	629764.	−	1.09078e6i	0.375216	−	0.649894i
$310$	1.53072e6	+	121138.i	0.904673	+	0.0715942i
$311$		−	1.05415e6i		−	0.618020i	−0.951059	−	0.309010i	$-0.900002\pi$
$311$		−	1.05415e6i		−	0.618020i	0.951059	−	0.309010i	$-0.0999976\pi$
$312$	700827.	−	2.90251e6i	0.407591	−	1.68806i
$313$	45964.5	+	79612.9i	0.0265193	+	0.0459327i	0.878980	−	0.476858i	$-0.158224\pi$
$313$	45964.5	+	79612.9i	0.0265193	+	0.0459327i	−0.852461	+	0.522791i	$0.824891\pi$
$314$	−1.91413e6	−	151481.i	−1.09559	−	0.0867028i
$315$			3.76085e6i			2.13555i
$316$	−716993.	−	1.87268e6i	−0.403922	−	1.05499i
$317$	−2.62948e6	+	1.51813e6i	−1.46968	+	0.848518i	−0.999421	−	0.0340118i	$-0.989172\pi$
$317$	−2.62948e6	+	1.51813e6i	−1.46968	+	0.848518i	−0.470256	+	0.882530i	$0.655838\pi$
$318$	2.90093e6	−	1.38213e6i	1.60868	−	0.766445i
$319$	−541922.	−	938637.i	−0.298168	−	0.516441i
$320$	−1.98971e6	+	1.28479e6i	−1.08622	+	0.701384i
$321$	−791203.	+	1.37040e6i	−0.428573	+	0.742311i
$322$	1.38609e6	−	2.01490e6i	0.744993	−	1.08296i
$323$	300023.	−	11431.3i	0.160011	−	0.00609662i
$324$	260247.	+	679729.i	0.137728	+	0.359727i
$325$	1.23417e6	+	712547.i	0.648135	+	0.374201i
$326$	−2.01520e6	+	960128.i	−1.05020	+	0.500363i
$327$	4.61535e6	−	2.66467e6i	2.38691	−	1.37808i
$328$	1.46196e6	+	1.39096e6i	0.750325	+	0.713890i
$329$	2.00958e6	+	3.48069e6i	1.02356	+	1.77287i
$330$	−1.23876e6	−	852166.i	−0.626183	−	0.430764i
$331$	−2.10350e6			−1.05529			−0.527645	−	0.849465i	$-0.676925\pi$
$331$	−2.10350e6			−1.05529			−0.527645	+	0.849465i	$0.676925\pi$
$332$	−1.95596e6	−	1.58672e6i	−0.973900	−	0.790049i
$333$	−1.21292e6	+	700279.i	−0.599406	+	0.346067i
$334$	−672520.	+	977614.i	−0.329867	+	0.479514i
$335$	22269.3			0.0108417
$336$	−1.15754e6	+	3.54163e6i	−0.559357	+	1.71142i
$337$	−558874.	−	322666.i	−0.268064	−	0.154767i	0.359943	−	0.932974i	$-0.382796\pi$
$337$	−558874.	−	322666.i	−0.268064	−	0.154767i	−0.628008	+	0.778207i	$0.716129\pi$
$338$	−504694.	−	39940.6i	−0.240290	−	0.0190161i
$339$	337119.	+	194636.i	0.159325	+	0.0919864i
$340$	−435826.	−	69415.7i	−0.204464	−	0.0325657i
$341$			568312.i			0.264668i
$342$	−3.09046e6	−	126441.i	−1.42876	−	0.0584553i
$343$			1.67584e6i			0.769126i
$344$	404679.	+	385028.i	0.184380	+	0.175427i
$345$	−4.39161e6	−	2.53550e6i	−1.98644	−	1.14687i
$346$	−2812.52	+	35539.4i	−0.00126301	+	0.0159595i
$347$	2.88360e6	+	1.66485e6i	1.28562	+	0.742251i	0.977869	−	0.209217i	$-0.0670914\pi$
$347$	2.88360e6	+	1.66485e6i	1.28562	+	0.742251i	0.307748	+	0.951468i	$0.400425\pi$
$348$	4.32502e6	+	3.50855e6i	1.91443	+	1.55303i
$349$	−1.55545e6			−0.683584			−0.341792	−	0.939776i	$-0.611034\pi$
$349$	−1.55545e6			−0.683584			−0.341792	+	0.939776i	$0.611034\pi$
$350$	−1.46512e6	−	1.00788e6i	−0.639296	−	0.439784i
$351$	−1.49248e6	+	861684.i	−0.646608	+	0.373319i
$352$	−532132.	−	696611.i	−0.228909	−	0.299663i
$353$	−2.34138e6			−1.00008			−0.500040	−	0.866003i	$-0.666681\pi$
$353$	−2.34138e6			−1.00008			−0.500040	+	0.866003i	$0.666681\pi$
$354$	−2.27739e6	+	3.31054e6i	−0.965893	+	1.40408i
$355$	−2.26568e6	−	3.92427e6i	−0.954173	−	1.65268i
$356$	−503804.	+	3.16313e6i	−0.210686	+	1.32279i
$357$	−601256.	+	347135.i	−0.249683	+	0.144155i
$358$	251978.	+	528873.i	0.103909	+	0.218094i
$359$	3.04857e6	+	1.76009e6i	1.24842	+	0.720774i	0.970794	−	0.239916i	$-0.0771200\pi$
$359$	3.04857e6	+	1.76009e6i	1.24842	+	0.720774i	0.277623	+	0.960690i	$0.410453\pi$
$360$	4.41942e6	+	1.06709e6i	1.79725	+	0.433956i
$361$	−1.07129e6	+	2.23235e6i	−0.432653	+	0.901561i
$362$	−3.48948e6	−	2.40048e6i	−1.39955	−	0.962780i
$363$	−1.67850e6	+	2.90726e6i	−0.668584	+	1.15802i
$364$	3.21220e6	+	511620.i	1.27072	+	0.202392i
$365$	−2.28808e6	−	3.96306e6i	−0.898955	−	1.55704i
$366$	−2.77623e6	−	5.82699e6i	−1.08331	−	2.27374i
$367$	−708529.	+	409070.i	−0.274595	+	0.158538i	−0.630974	−	0.775804i	$-0.717345\pi$
$367$	−708529.	+	409070.i	−0.274595	+	0.158538i	0.356379	+	0.934342i	$0.384011\pi$
$368$	−1.97445e6	−	2.20051e6i	−0.760023	−	0.847042i
$369$		−	3.87357e6i		−	1.48097i
$370$	130016.	−	1.64290e6i	0.0493733	−	0.623888i
$371$	1.75023e6	+	3.03148e6i	0.660175	+	1.14346i
$372$	−1.04414e6	−	2.72714e6i	−0.391201	−	1.02176i
$373$		−	2.04495e6i		−	0.761047i	−0.924771	−	0.380523i	$-0.875744\pi$
$373$		−	2.04495e6i		−	0.761047i	0.924771	−	0.380523i	$-0.124256\pi$
$374$	12886.0	−	162829.i	0.00476365	−	0.0601941i
$375$	900688.	−	1.56004e6i	0.330747	−	0.572871i
$376$	4.66040e6	−	1.37388e6i	1.70002	−	0.501163i
$377$	2.43087e6	−	4.21038e6i	0.880861	−	1.52570i
$378$	1.94143e6	−	924979.i	0.698862	−	0.332968i
$379$	1.43613e6			0.513564			0.256782	−	0.966469i	$-0.417338\pi$
$379$	1.43613e6			0.513564			0.256782	+	0.966469i	$0.417338\pi$
$380$	2.18364e6	−	2.91175e6i	0.775750	−	1.03442i
$381$	1.38417e6			0.488514
$382$	−2.79886e6	+	1.33350e6i	−0.981348	+	0.467556i
$383$	1.06609e6	−	1.84652e6i	0.371361	−	0.643216i	−0.618414	−	0.785852i	$-0.712225\pi$
$383$	1.06609e6	−	1.84652e6i	0.371361	−	0.643216i	0.989775	+	0.142636i	$0.0455579\pi$
$384$	3.83338e6	+	2.36514e6i	1.32664	+	0.818518i
$385$	818948.	−	1.41846e6i	0.281582	−	0.487714i
$386$	−50685.6	+	640469.i	−0.0173147	+	0.218791i
$387$		−	1.07223e6i		−	0.363924i
$388$	3.03374e6	−	1.16153e6i	1.02306	−	0.391697i
$389$	280455.	+	485763.i	0.0939700	+	0.162761i	0.909178	−	0.416407i	$-0.136711\pi$
$389$	280455.	+	485763.i	0.0939700	+	0.162761i	−0.815208	+	0.579168i	$0.803378\pi$
$390$	532079.	−	6.72342e6i	0.177139	−	2.23835i
$391$		−	550883.i		−	0.182229i
$392$	−988102.	−	238583.i	−0.324778	−	0.0784194i
$393$	−4.24636e6	+	2.45164e6i	−1.38687	+	0.800710i
$394$	910279.	+	1.91057e6i	0.295416	+	0.620044i
$395$	−2.26467e6	−	3.92253e6i	−0.730320	−	1.26495i
$396$	−264673.	+	1.66175e6i	−0.0848148	+	0.532509i
$397$	−1.69307e6	+	2.93248e6i	−0.539136	+	0.933812i	0.459814	+	0.888015i	$0.347916\pi$
$397$	−1.69307e6	+	2.93248e6i	−0.539136	+	0.933812i	−0.998951	+	0.0457967i	$0.985417\pi$
$398$	873272.	+	600741.i	0.276339	+	0.190099i
$399$	−217998.	−	5.72153e6i	−0.0685520	−	1.79920i
$400$	−1.60008e6	+	1.43570e6i	−0.500026	+	0.448657i
$401$	4.50495e6	+	2.60094e6i	1.39904	+	0.807734i	0.994292	−	0.106695i	$-0.0340268\pi$
$401$	4.50495e6	+	2.60094e6i	1.39904	+	0.807734i	0.404745	+	0.914429i	$0.367360\pi$
$402$	−18216.1	−	38233.6i	−0.00562200	−	0.0117999i
$403$	−2.20771e6	+	1.27462e6i	−0.677140	+	0.390947i
$404$	−5.98207e6	−	952787.i	−1.82347	−	0.290431i
$405$	822010.	+	1.42376e6i	0.249023	+	0.431321i
$406$	−3.43841e6	+	4.99827e6i	−1.03524	+	1.50489i
$407$	609960.			0.182522
$408$	237324.	+	805039.i	0.0705817	+	0.239423i
$409$	−130898.	+	75574.2i	−0.0386924	+	0.0223391i	−0.519221	−	0.854640i	$-0.673778\pi$
$409$	−130898.	+	75574.2i	−0.0386924	+	0.0223391i	0.480529	+	0.876979i	$0.340445\pi$
$410$	3.75527e6	+	2.58332e6i	1.10327	+	0.758960i
$411$	4.29618e6			1.25452
$412$	1.04494e6	−	1.28811e6i	0.303284	−	0.373861i
$413$	−3.79079e6	−	2.18862e6i	−1.09359	−	0.631385i
$414$	−447720.	+	5.65744e6i	−0.128382	+	1.62226i
$415$	−4.92675e6	−	2.84446e6i	−1.40424	−	0.810737i
$416$	1.51263e6	−	3.62953e6i	0.428548	−	1.02829i
$417$			464744.i			0.130880i
$418$	1.13808e6	+	720656.i	0.318590	+	0.201738i
$419$			1.51552e6i			0.421724i	0.977516	+	0.210862i	$0.0676270\pi$
$419$			1.51552e6i			0.421724i	−0.977516	+	0.210862i	$0.932373\pi$
$420$	−1.32378e6	+	8.31133e6i	−0.366178	+	2.29904i
$421$	−841090.	−	485604.i	−0.231280	−	0.133529i	0.379883	−	0.925035i	$-0.375964\pi$
$421$	−841090.	−	485604.i	−0.231280	−	0.133529i	−0.611162	+	0.791505i	$0.709298\pi$
$422$	−624292.	−	49405.3i	−0.170650	−	0.0135049i
$423$	−8.07703e6	−	4.66328e6i	−2.19483	−	1.26719i
$424$	4.05893e6	−	1.19657e6i	1.09647	−	0.323238i
$425$	−400569.			−0.107574
$426$	−4.88416e6	+	7.09989e6i	−1.30396	+	1.89552i
$427$	6.08921e6	−	3.51561e6i	1.61619	−	0.933105i
$428$	−1.31281e6	+	1.61832e6i	−0.346412	+	0.427025i
$429$	2.49621e6			0.654844
$430$	1.03948e6	+	715080.i	0.271110	+	0.186502i
$431$	120766.	+	209172.i	0.0313148	+	0.0542389i	0.881258	−	0.472635i	$-0.156697\pi$
$431$	120766.	+	209172.i	0.0313148	+	0.0542389i	−0.849943	+	0.526874i	$0.823364\pi$
$432$	−536099.	−	2.54384e6i	−0.138209	−	0.655815i
$433$	4.10485e6	−	2.36994e6i	1.05215	−	0.607459i	0.128899	−	0.991658i	$-0.458856\pi$
$433$	4.10485e6	−	2.36994e6i	1.05215	−	0.607459i	0.923250	+	0.384199i	$0.125522\pi$
$434$	2.87179e6	−	1.36825e6i	0.731862	−	0.348691i
$435$	1.08941e7	+	6.28968e6i	2.76036	+	1.59370i
$436$	6.55418e6	−	2.50939e6i	1.65121	−	0.632197i
$437$	4.01812e6	+	2.12013e6i	1.00651	+	0.531079i
$438$	−4.93244e6	+	7.17008e6i	−1.22850	+	1.78582i
$439$	−2.94614e6	+	5.10286e6i	−0.729612	+	1.26373i	0.227435	+	0.973793i	$0.426966\pi$
$439$	−2.94614e6	+	5.10286e6i	−0.729612	+	1.26373i	−0.957047	+	0.289932i	$0.906367\pi$
$440$	−1.43448e6	−	1.36483e6i	−0.353235	−	0.336082i
$441$	975615.	+	1.68982e6i	0.238881	+	0.413755i
$442$	661440.	−	315139.i	0.161040	−	0.0767266i
$443$	2.78533e6	−	1.60811e6i	0.674323	−	0.389321i	−0.123390	−	0.992358i	$-0.539377\pi$
$443$	2.78533e6	−	1.60811e6i	0.674323	−	0.389321i	0.797713	+	0.603038i	$0.206043\pi$
$444$	−2.92700e6	+	1.12066e6i	−0.704636	+	0.269783i
$445$			7.23476e6i			1.73191i
$446$	−1.54139e6	−	121983.i	−0.366924	−	0.0290377i
$447$	−2.48968e6	−	4.31225e6i	−0.589351	−	1.02079i
$448$	−2.23897e6	+	4.36611e6i	−0.527053	+	1.02778i
$449$		−	40741.7i		−	0.00953724i	−0.999989	−	0.00476862i	$-0.998482\pi$
$449$		−	40741.7i		−	0.00953724i	0.999989	−	0.00476862i	$-0.00151791\pi$
$450$	4.11375e6	+	325555.i	0.957650	+	0.0757867i
$451$	−843493.	+	1.46097e6i	−0.195272	+	0.338221i
$452$	398106.	+	322952.i	0.0916542	+	0.0743518i
$453$	4.30345e6	−	7.45379e6i	0.985306	−	1.70660i
$454$	−1.41358e6	−	2.96694e6i	−0.321870	−	0.675568i
$455$	7.34700e6			1.66373
$456$	−6.78529e6	−	1.36724e6i	−1.52812	−	0.307916i
$457$	−2.64962e6			−0.593461			−0.296731	−	0.954961i	$-0.595896\pi$
$457$	−2.64962e6			−0.593461			−0.296731	+	0.954961i	$0.595896\pi$
$458$	624500.	+	1.31075e6i	0.139113	+	0.291983i
$459$	242205.	−	419511.i	0.0536600	−	0.0929419i
$460$	−5.18607e6	−	4.20705e6i	−1.14273	−	0.927007i
$461$	−520499.	+	901530.i	−0.114069	+	0.197573i	−0.917407	−	0.397950i	$-0.869722\pi$
$461$	−520499.	+	901530.i	−0.114069	+	0.197573i	0.803338	+	0.595523i	$0.203055\pi$
$462$	−3.10520e6	−	245740.i	−0.676838	−	0.0535637i
$463$			3.68379e6i			0.798624i	0.916815	+	0.399312i	$0.130751\pi$
$463$			3.68379e6i			0.798624i	−0.916815	+	0.399312i	$0.869249\pi$
$464$	4.89792e6	+	5.45871e6i	1.05613	+	1.17705i
$465$	−3.29798e6	−	5.71228e6i	−0.707320	−	1.22511i
$466$	−867891.	−	68683.3i	−0.185140	−	0.0146516i
$467$		−	3.73655e6i		−	0.792827i	−0.918072	−	0.396414i	$-0.870255\pi$
$467$		−	3.73655e6i		−	0.792827i	0.918072	−	0.396414i	$-0.129745\pi$
$468$	−7.04896e6	+	2.69883e6i	−1.48768	+	0.569588i
$469$	39954.1	−	23067.5i	0.00838744	−	0.00484249i
$470$	9.90751e6	−	4.72037e6i	2.06881	−	0.985669i
$471$	4.12405e6	+	7.14306e6i	0.856587	+	1.48365i
$472$	−3.64746e6	+	3.83361e6i	−0.753590	+	0.792052i
$473$	−233484.	+	404407.i	−0.0479850	+	0.0831124i
$474$	−4.88199e6	+	7.09675e6i	−0.998048	+	1.45082i
$475$	1.54163e6	−	2.92174e6i	0.313507	−	0.594165i
$476$	−853834.	+	326906.i	−0.172725	+	0.0661312i
$477$	−7.03462e6	−	4.06144e6i	−1.41561	−	0.817305i
$478$	7.55899e6	−	3.60143e6i	1.51319	−	0.720950i
$479$	4.52631e6	−	2.61327e6i	0.901375	−	0.520409i	0.0237292	−	0.999718i	$-0.492446\pi$
$479$	4.52631e6	−	2.61327e6i	0.901375	−	0.520409i	0.877646	+	0.479309i	$0.159113\pi$
$480$	9.39114e6	+	3.91382e6i	1.86044	+	0.775350i
$481$	1.36803e6	+	2.36950e6i	0.269608	+	0.466975i
$482$	2.60415e6	+	1.79145e6i	0.510562	+	0.351225i
$483$	−1.05055e7			−2.04903
$484$	−2.78508e6	+	3.43319e6i	−0.540411	+	0.666169i
$485$	6.35449e6	−	3.66877e6i	1.22667	−	0.708216i
$486$	3.74995e6	−	5.45114e6i	0.720169	−	1.04688i
$487$	−7.66997e6			−1.46545			−0.732726	−	0.680524i	$-0.761752\pi$
$487$	−7.66997e6			−1.46545			−0.732726	+	0.680524i	$0.761752\pi$
$488$	−2.40350e6	−	8.15301e6i	−0.456871	−	1.54977i
$489$	8.30419e6	+	4.79443e6i	1.57045	+	0.906702i
$490$	−2.28885e6	−	181136.i	−0.430653	−	0.0340811i
$491$	−1.56962e6	−	906223.i	−0.293827	−	0.169641i	0.345839	−	0.938294i	$-0.387594\pi$
$491$	−1.56962e6	−	906223.i	−0.293827	−	0.169641i	−0.639666	+	0.768653i	$0.720928\pi$
$492$	1.36345e6	−	8.56044e6i	0.253938	−	1.59435i
$493$			1.36655e6i			0.253226i
$494$	−247009.	+	6.03736e6i	−0.0455403	+	1.11309i
$495$			3.80078e6i			0.697203i
$496$	−793009.	−	3.76290e6i	−0.144735	−	0.686782i
$497$	−8.12985e6	−	4.69377e6i	−1.47636	−	0.852375i
$498$	−853532.	+	1.07853e7i	−0.154222	+	1.94877i
$499$	418040.	+	241355.i	0.0751565	+	0.0433916i	0.537107	−	0.843514i	$-0.319517\pi$
$499$	418040.	+	241355.i	0.0751565	+	0.0433916i	−0.461951	+	0.886906i	$0.652850\pi$
$500$	1.49448e6	−	1.84226e6i	0.267340	−	0.329553i
$501$	5.09718e6			0.907268
$502$	−6.60510e6	−	4.54378e6i	−1.16982	−	0.804745i
$503$	−278131.	+	160579.i	−0.0490150	+	0.0282988i	−0.524307	−	0.851529i	$-0.675676\pi$
$503$	−278131.	+	160579.i	−0.0490150	+	0.0282988i	0.475292	+	0.879828i	$0.342342\pi$
$504$	9.03436e6	−	2.66332e6i	1.58424	−	0.467032i
$505$	−1.36823e7			−2.38743
$506$	1.40081e6	−	2.03629e6i	0.243221	−	0.353561i
$507$	1.08738e6	+	1.88340e6i	0.187871	+	0.325403i
$508$	1.80010e6	+	286709.i	0.309484	+	0.0492927i
$509$	−1.34789e6	+	778203.i	−0.230600	+	0.133137i	−0.610849	−	0.791747i	$-0.709172\pi$
$509$	−1.34789e6	+	778203.i	−0.230600	+	0.133137i	0.380249	+	0.924884i	$0.375838\pi$
$510$	815398.	+	1.71143e6i	0.138817	+	0.291362i
$511$	−8.21022e6	−	4.74017e6i	−1.39092	−	0.803048i
$512$	4.49538e6	+	3.86987e6i	0.757865	+	0.652412i
$513$	2.12775e6	+	3.38116e6i	0.356966	+	0.567248i
$514$	141519.	+	97353.7i	0.0236269	+	0.0162534i
$515$	1.87324e6	−	3.24455e6i	0.311226	−	0.539059i
$516$	377413.	−	2.36958e6i	0.0624011	−	0.391785i
$517$	2.03091e6	+	3.51765e6i	0.334168	+	0.578796i
$518$	−1.46852e6	−	3.08225e6i	−0.240467	−	0.504712i
$519$	132624.	−	76570.7i	0.0216125	−	0.0124780i
$520$	2.08462e6	−	8.63355e6i	0.338079	−	1.40017i
$521$		−	3.59580e6i		−	0.580365i	−0.956971	−	0.290183i	$-0.906284\pi$
$521$		−	3.59580e6i		−	0.580365i	0.956971	−	0.290183i	$-0.0937160\pi$
$522$	1.11064e6	−	1.40341e7i	0.178400	−	2.25429i
$523$	−127288.	−	220470.i	−0.0203486	−	0.0352448i	0.855672	−	0.517519i	$-0.173144\pi$
$523$	−127288.	−	220470.i	−0.0203486	−	0.0352448i	−0.876020	+	0.482274i	$0.839811\pi$
$524$	−6.03019e6	+	2.30877e6i	−0.959406	+	0.367327i
$525$			7.63897e6i			1.20959i
$526$	−363190.	+	4.58932e6i	−0.0572361	+	0.723242i
$527$	358274.	−	620549.i	0.0561938	−	0.0973306i
$528$	−1.16983e6	+	3.57924e6i	−0.182616	+	0.558734i
$529$	949727.	−	1.64498e6i	0.147557	−	0.255576i
$530$	8.62886e6	−	4.11116e6i	1.33433	−	0.635733i
$531$	1.01575e7			1.56333
$532$	901621.	−	7.48596e6i	0.138116	−	1.14675i
$533$	−7.56720e6			−1.15377
$534$	1.24211e7	−	5.91797e6i	1.88499	−	0.898090i
$535$	−2.35344e6	+	4.07628e6i	−0.355483	+	0.615715i
$536$	−15770.5	−	53495.7i	−0.00237100	−	0.00804279i
$537$	1.25826e6	−	2.17937e6i	0.188293	−	0.326133i
$538$	252747.	−	3.19375e6i	0.0376471	−	0.475713i
$539$		−	849785.i		−	0.125990i
$540$	−2.09962e6	−	5.48391e6i	−0.309853	−	0.809293i
$541$	4.71638e6	+	8.16901e6i	0.692812	+	1.19999i	0.970913	+	0.239434i	$0.0769618\pi$
$541$	4.71638e6	+	8.16901e6i	0.692812	+	1.19999i	−0.278101	+	0.960552i	$0.589705\pi$
$542$	74773.5	−	944848.i	0.0109333	−	0.138154i
$543$			1.81938e7i			2.64804i
$544$	141887.	+	1.09611e6i	0.0205564	+	0.158802i
$545$	1.37284e7	−	7.92610e6i	1.97984	−	1.14306i
$546$	−6.00978e6	−	1.26138e7i	−0.862734	−	1.81078i
$547$	3.76853e6	+	6.52728e6i	0.538522	+	0.932747i	0.998984	+	0.0450677i	$0.0143504\pi$
$547$	3.76853e6	+	6.52728e6i	0.538522	+	0.932747i	−0.460462	+	0.887679i	$0.652316\pi$
$548$	5.58716e6	+	889888.i	0.794767	+	0.126586i
$549$	−8.15805e6	+	1.41302e7i	−1.15520	+	2.00086i
$550$	−1.48067e6	−	1.01858e6i	−0.208714	−	0.143579i
$551$	−9.96756e6	−	5.25930e6i	−1.39865	−	0.737988i
$552$	−2.98080e6	+	1.23451e7i	−0.416375	+	1.72444i
$553$	−8.12625e6	−	4.69169e6i	−1.13000	−	0.652404i
$554$	−3.35360e6	−	7.03883e6i	−0.464234	−	0.974374i
$555$	−6.13090e6	+	3.53968e6i	−0.844873	+	0.487788i
$556$	−96264.5	+	604396.i	−0.0132062	+	0.0829153i
$557$	−5.61221e6	−	9.72064e6i	−0.766472	−	1.32757i	−0.939465	−	0.342645i	$-0.888677\pi$
$557$	−5.61221e6	−	9.72064e6i	−0.766472	−	1.32757i	0.172993	−	0.984923i	$-0.444656\pi$
$558$	−4.18373e6	+	6.08171e6i	−0.568824	+	0.826875i
$559$	−2.09465e6			−0.283519
$560$	−3.44313e6	+	1.05346e7i	−0.463963	+	1.41955i
$561$	−607640.	+	350821.i	−0.0815153	+	0.0470629i
$562$	3.54916e6	+	2.44154e6i	0.474007	+	0.326079i
$563$	−1.02775e7			−1.36652			−0.683260	−	0.730175i	$-0.739439\pi$
$563$	−1.02775e7			−1.36652			−0.683260	+	0.730175i	$0.739439\pi$
$564$	−1.62085e7	−	1.31487e7i	−2.14558	−	1.74054i
$565$	1.00277e6	+	578947.i	0.132153	+	0.0762988i
$566$	41991.9	−	530615.i	0.00550966	−	0.0696208i
$567$	2.94959e6	+	1.70295e6i	0.385304	+	0.222456i
$568$	−7.82245e6	+	8.22168e6i	−1.01735	+	1.06928i
$569$		−	1.08551e7i		−	1.40557i	−0.711401	−	0.702787i	$-0.751939\pi$
$569$		−	1.08551e7i		−	1.40557i	0.711401	−	0.702787i	$-0.248061\pi$
$570$	−1.56212e7	−	639118.i	−2.01385	−	0.0823937i
$571$		−	4.38032e6i		−	0.562232i	−0.959674	−	0.281116i	$-0.909295\pi$
$571$		−	4.38032e6i		−	0.562232i	0.959674	−	0.281116i	$-0.0907046\pi$
$572$	3.24630e6	+	517051.i	0.414858	+	0.0660760i
$573$	1.15335e7	+	6.65886e6i	1.46749	+	0.847254i
$574$	9.41335e6	+	744955.i	1.19252	+	0.0943736i
$575$	−5.24923e6	−	3.03065e6i	−0.662104	−	0.382266i
$576$	−566312.	−	1.13721e7i	−0.0711212	−	1.42818i
$577$	1.11884e7			1.39904			0.699519	−	0.714614i	$-0.253398\pi$
$577$	1.11884e7			1.39904			0.699519	+	0.714614i	$0.253398\pi$
$578$	4.43548e6	−	6.44767e6i	0.552232	−	0.802756i
$579$	2.39008e6	−	1.37991e6i	0.296289	−	0.171062i
$580$	1.28648e7	+	1.04362e7i	1.58794	+	1.28817i
$581$	−1.17857e7			−1.44848
$582$	−1.14967e7	−	7.90882e6i	−1.40691	−	0.967841i
$583$	1.76881e6	+	3.06366e6i	0.215531	+	0.373310i
$584$	−7.89978e6	+	8.30296e6i	−0.958479	+	1.00740i
$585$	−1.47648e7	+	8.52445e6i	−1.78376	+	1.02986i
$586$	−8.16984e6	+	3.89246e6i	−0.982810	+	0.468253i
$587$	1.03468e7	+	5.97374e6i	1.23940	+	0.715568i	0.968972	−	0.247172i	$-0.0795012\pi$
$587$	1.03468e7	+	5.97374e6i	1.23940	+	0.715568i	0.270429	+	0.962740i	$0.412835\pi$
$588$	1.56128e6	+	4.07783e6i	0.186224	+	0.486392i
$589$	3.14741e6	+	5.00148e6i	0.373822	+	0.594033i
$590$	−6.77412e6	+	9.84725e6i	−0.801166	+	1.16462i
$591$	4.54550e6	−	7.87304e6i	0.535320	−	0.927201i
$592$	−4.03867e6	+	851124.i	−0.473624	+	0.0998133i
$593$	−858229.	−	1.48650e6i	−0.100223	−	0.173591i	0.811554	−	0.584278i	$-0.198622\pi$
$593$	−858229.	−	1.48650e6i	−0.100223	−	0.173591i	−0.911776	+	0.410687i	$0.865289\pi$
$594$	1.96204e6	−	934800.i	0.228161	−	0.108706i
$595$	−1.78844e6	+	1.03256e6i	−0.207101	+	0.119570i
$596$	−2.34459e6	−	6.12375e6i	−0.270366	−	0.706158i
$597$		−	4.55315e6i		−	0.522849i
$598$	1.10521e7	+	874642.i	1.26384	+	0.100018i
$599$	−2.84509e6	−	4.92785e6i	−0.323988	−	0.561165i	0.657319	−	0.753613i	$-0.271691\pi$
$599$	−2.84509e6	−	4.92785e6i	−0.323988	−	0.561165i	−0.981307	+	0.192448i	$0.938357\pi$
$600$	8.97664e6	+	2.16746e6i	1.01797	+	0.245795i
$601$			7.34960e6i			0.829999i	0.909822	+	0.414999i	$0.136218\pi$
$601$			7.34960e6i			0.829999i	−0.909822	+	0.414999i	$0.863782\pi$
$602$	2.60568e6	+	206209.i	0.293042	+	0.0231908i
$603$	−53528.8	+	92714.6i	−0.00599507	+	0.0103838i
$604$	7.14054e6	−	8.80221e6i	0.796414	−	0.981747i
$605$	−4.99273e6	+	8.64767e6i	−0.554562	+	0.960529i
$606$	1.11920e7	+	2.34907e7i	1.23801	+	2.59845i
$607$	7.44313e6			0.819944			0.409972	−	0.912098i	$-0.365538\pi$
$607$	7.44313e6			0.819944			0.409972	+	0.912098i	$0.365538\pi$
$608$	−8.54102e6	−	3.18355e6i	−0.937025	−	0.349263i
$609$	2.60605e7			2.84734
$610$	−8.25792e6	−	1.73324e7i	−0.898558	−	1.88597i
$611$	−9.10994e6	+	1.57789e7i	−0.987217	+	1.70991i
$612$	1.33660e6	−	1.64763e6i	0.144252	−	0.177821i
$613$	1.31747e6	−	2.28192e6i	0.141608	−	0.245273i	−0.786494	−	0.617598i	$-0.788106\pi$
$613$	1.31747e6	−	2.28192e6i	0.141608	−	0.245273i	0.928102	+	0.372325i	$0.121439\pi$
$614$	3.38049e6	+	267526.i	0.361875	+	0.0286381i
$615$		−	1.95796e7i		−	2.08745i
$616$	−3.98739e6	−	962778.i	−0.423387	−	0.102229i
$617$	2.58277e6	+	4.47348e6i	0.273132	+	0.473078i	0.969662	−	0.244449i	$-0.0786071\pi$
$617$	2.58277e6	+	4.47348e6i	0.273132	+	0.473078i	−0.696530	+	0.717527i	$0.745274\pi$
$618$	−7.10276e6	−	562099.i	−0.748093	−	0.0592027i
$619$		−	1.03971e7i		−	1.09065i	−0.838226	−	0.545323i	$-0.816407\pi$
$619$		−	1.03971e7i		−	1.09065i	0.838226	−	0.545323i	$-0.183593\pi$
$620$	−3.10580e6	−	8.11190e6i	−0.324484	−	0.847508i
$621$	6.34791e6	−	3.66497e6i	0.660544	−	0.381365i
$622$	−5.38340e6	+	2.56488e6i	−0.557931	+	0.265822i
$623$	7.49407e6	+	1.29801e7i	0.773567	+	1.33986i
$624$	−1.65279e7	+	3.48315e6i	−1.69924	+	0.358105i
$625$	5.95939e6	−	1.03220e7i	0.610242	−	1.05697i
$626$	294734.	−	428442.i	0.0300603	−	0.0436974i
$627$	−220312.	−	5.78227e6i	−0.0223805	−	0.587394i
$628$	3.88372e6	+	1.01437e7i	0.392961	+	1.02636i
$629$	−666025.	−	384530.i	−0.0671219	−	0.0387528i
$630$	1.92061e7	−	9.15061e6i	1.92791	−	0.918541i
$631$	−1.18361e7	+	6.83359e6i	−1.18341	+	0.683243i	−0.956802	−	0.290742i	$-0.906098\pi$
$631$	−1.18361e7	+	6.83359e6i	−1.18341	+	0.683243i	−0.226611	+	0.973985i	$0.572765\pi$
$632$	−7.81898e6	+	8.21804e6i	−0.778677	+	0.818419i
$633$	1.34506e6	+	2.32971e6i	0.133423	+	0.231096i
$634$	1.41507e7	+	9.73456e6i	1.39816	+	0.961819i
$635$	4.11723e6			0.405201
$636$	−1.41167e7	−	1.14517e7i	−1.38385	−	1.12261i
$637$	3.30114e6	−	1.90591e6i	0.322341	−	0.186103i
$638$	−3.47491e6	+	5.05134e6i	−0.337981	+	0.491309i
$639$	2.17840e7			2.11050
$640$	1.14024e7	+	7.03513e6i	1.10039	+	0.678925i
$641$	−5.58199e6	−	3.22277e6i	−0.536592	−	0.309802i	0.207105	−	0.978319i	$-0.433596\pi$
$641$	−5.58199e6	−	3.22277e6i	−0.536592	−	0.309802i	−0.743697	+	0.668517i	$0.766929\pi$
$642$	8.92354e6	+	706192.i	0.854475	+	0.0676216i
$643$	−3.13969e6	−	1.81270e6i	−0.299474	−	0.172902i	0.342732	−	0.939433i	$-0.388648\pi$
$643$	−3.13969e6	−	1.81270e6i	−0.299474	−	0.172902i	−0.642207	+	0.766531i	$0.721981\pi$
$644$	−1.36623e7	−	2.17605e6i	−1.29811	−	0.206754i
$645$		−	5.41976e6i		−	0.512956i
$646$	−788372.	−	1.50436e6i	−0.0743275	−	0.141831i
$647$		−	1.11845e7i		−	1.05040i	−0.850978	−	0.525201i	$-0.823990\pi$
$647$		−	1.11845e7i		−	1.05040i	0.850978	−	0.525201i	$-0.176010\pi$
$648$	2.83806e6	−	2.98291e6i	0.265512	−	0.279063i
$649$	−3.83104e6	−	2.21185e6i	−0.357030	−	0.206131i
$650$	635987.	−	8.03642e6i	0.0590426	−	0.746069i
$651$	−1.18340e7	−	6.83238e6i	−1.09441	−	0.631858i
$652$	9.80646e6	+	7.95521e6i	0.903427	+	0.732879i
$653$	−6.19319e6			−0.568371			−0.284185	−	0.958769i	$-0.591723\pi$
$653$	−6.19319e6			−0.568371			−0.284185	+	0.958769i	$0.591723\pi$
$654$	−2.48378e7	−	1.70864e7i	−2.27075	−	1.56209i
$655$	−1.26309e7	+	7.29243e6i	−1.15035	+	0.664154i
$656$	3.54632e6	−	1.08504e7i	0.321750	−	0.984430i
$657$	2.19994e7			1.98837
$658$	1.28858e7	−	1.87316e7i	1.16024	−	1.68659i
$659$	8.13481e6	+	1.40899e7i	0.729682	+	1.26385i	0.957018	+	0.290030i	$0.0936653\pi$
$659$	8.13481e6	+	1.40899e7i	0.729682	+	1.26385i	−0.227335	+	0.973817i	$0.573001\pi$
$660$	−1.33783e6	+	8.39957e6i	−0.119548	+	0.750580i
$661$	−1.57130e6	+	907190.i	−0.139880	+	0.0807597i	−0.568307	−	0.822817i	$-0.692401\pi$
$661$	−1.57130e6	+	907190.i	−0.139880	+	0.0807597i	0.428427	+	0.903576i	$0.359068\pi$
$662$	5.11807e6	+	1.07422e7i	0.453901	+	0.952687i
$663$	−2.72565e6	−	1.57365e6i	−0.240816	−	0.139035i
$664$	−3.34403e6	+	1.38495e7i	−0.294340	+	1.21903i
$665$	−648437.	−	1.70187e7i	−0.0568609	−	1.49236i
$666$	6.52740e6	+	4.49033e6i	0.570236	+	0.392277i
$667$	−1.03391e7	+	1.79079e7i	−0.899846	+	1.55858i
$668$	6.62885e6	+	1.05580e6i	0.574774	+	0.0915465i
$669$	3.32097e6	+	5.75209e6i	0.286880	+	0.496890i
$670$	−54184.1	−	113726.i	−0.00466321	−	0.00978754i
$671$	6.15386e6	−	3.55293e6i	0.527644	−	0.304635i
$672$	2.09030e7	−	2.70583e6i	1.78561	−	0.231141i
$673$			1.63923e7i			1.39509i	0.716540	+	0.697546i	$0.245725\pi$
$673$			1.63923e7i			1.39509i	−0.716540	+	0.697546i	$0.754275\pi$
$674$	−287997.	+	3.63917e6i	−0.0244196	+	0.308569i
$675$	−2.66495e6	−	4.61582e6i	−0.225128	−	0.389933i
$676$	1.02401e6	+	2.67458e6i	0.0861864	+	0.225107i
$677$			1.68800e6i			0.141547i	0.997492	+	0.0707735i	$0.0225468\pi$
$677$			1.68800e6i			0.141547i	−0.997492	+	0.0707735i	$0.977453\pi$
$678$	173723.	−	2.19519e6i	0.0145139	−	0.183399i
$679$	7.60053e6	−	1.31645e7i	0.632659	−	1.09580i
$680$	705924.	+	2.39460e6i	0.0585444	+	0.198591i
$681$	−7.05875e6	+	1.22261e7i	−0.583257	+	1.01023i
$682$	2.90228e6	−	1.38277e6i	0.238935	−	0.113839i
$683$	−3.96777e6			−0.325457			−0.162729	−	0.986671i	$-0.552030\pi$
$683$	−3.96777e6			−0.325457			−0.162729	+	0.986671i	$0.552030\pi$
$684$	6.87375e6	+	1.60902e7i	0.561764	+	1.31498i
$685$	1.27791e7			1.04057
$686$	8.55827e6	−	4.07753e6i	0.694346	−	0.330816i
$687$	3.11846e6	−	5.40133e6i	0.252086	−	0.436625i
$688$	981646.	−	3.00345e6i	0.0790649	−	0.241908i
$689$	−7.93423e6	+	1.37425e7i	−0.636732	+	1.10285i
$690$	−2.26307e6	+	2.85965e7i	−0.180957	+	2.28660i
$691$			8.48573e6i			0.676074i	0.941133	+	0.338037i	$0.109763\pi$
$691$			8.48573e6i			0.676074i	−0.941133	+	0.338037i	$0.890237\pi$
$692$	188338.	−	72108.7i	0.0149511	−	0.00572430i
$693$	3.93701e6	+	6.81909e6i	0.311410	+	0.539378i
$694$	1.48597e6	−	1.87769e7i	0.117115	−	1.47988i
$695$			1.38239e6i			0.108559i
$696$	7.39433e6	−	3.06240e7i	0.578596	−	2.39629i
$697$	1.84205e6	−	1.06351e6i	0.143621	−	0.0829198i
$698$	3.78459e6	+	7.94343e6i	0.294023	+	0.617120i
$699$	1.86990e6	+	3.23876e6i	0.144752	+	0.250718i
$700$	−1.58229e6	+	9.93443e6i	−0.122051	+	0.766298i
$701$	−608501.	+	1.05396e6i	−0.0467699	+	0.0810078i	−0.888463	−	0.458949i	$-0.848226\pi$
$701$	−608501.	+	1.05396e6i	−0.0467699	+	0.0810078i	0.841693	+	0.539957i	$0.181559\pi$
$702$	8.03188e6	+	5.52529e6i	0.615141	+	0.423168i
$703$	5.36801e6	−	3.37806e6i	0.409662	−	0.257798i
$704$	−2.26274e6	+	4.41246e6i	−0.172069	+	0.335544i
$705$	−4.08267e7	−	2.35713e7i	−3.09365	−	1.78612i
$706$	5.69686e6	+	1.19571e7i	0.430154	+	0.902843i
$707$	−2.45478e7	+	1.41727e7i	−1.84699	+	1.06636i
$708$	2.24476e7	+	3.57532e6i	1.68301	+	0.268060i
$709$	−8.24017e6	−	1.42724e7i	−0.615631	−	1.06631i	−0.990273	−	0.139135i	$-0.955568\pi$
$709$	−8.24017e6	−	1.42724e7i	−0.615631	−	1.06631i	0.374642	−	0.927170i	$-0.377766\pi$
$710$	−1.45280e7	+	2.11187e7i	−1.08158	+	1.57225i
$711$	2.17744e7			1.61537
$712$	1.73794e7	−	5.12343e6i	1.28480	−	0.378757i
$713$	9.38995e6	−	5.42129e6i	0.691735	−	0.399373i
$714$	3.23570e6	+	2.22590e6i	0.237532	+	0.163403i
$715$	7.42500e6			0.543165
$716$	2.08778e6	−	2.57363e6i	0.152196	−	0.187613i
$717$	−3.11489e7	−	1.79838e7i	−2.26280	−	1.30643i
$718$	1.57098e6	−	1.98511e7i	0.113726	−	1.43705i
$719$	1.21480e7	+	7.01364e6i	0.876359	+	0.505966i	0.869456	−	0.494010i	$-0.164469\pi$
$719$	1.21480e7	+	7.01364e6i	0.876359	+	0.505966i	0.00690298	+	0.999976i	$0.497803\pi$
$720$	−5.30351e6	−	2.51657e7i	−0.381270	−	1.80916i
$721$		−	7.76153e6i		−	0.556044i
$722$	1.40069e7	+	39327.1i	0.999996	+	0.00280769i
$723$		−	1.35778e7i		−	0.966012i
$724$	−3.76857e6	+	2.36609e7i	−0.267196	+	1.67759i
$725$	1.30215e7	+	7.51798e6i	0.920061	+	0.531198i
$726$	1.89309e7	+	1.49816e6i	1.33300	+	0.105491i
$727$	−1.08038e7	−	6.23755e6i	−0.758122	−	0.437702i	0.0704993	−	0.997512i	$-0.477541\pi$
$727$	−1.08038e7	−	6.23755e6i	−0.758122	−	0.437702i	−0.828621	+	0.559810i	$0.810874\pi$
$728$	−5.20292e6	−	1.76491e7i	−0.363847	−	1.23422i
$729$	−2.28946e7			−1.59556
$730$	−1.46716e7	+	2.13275e7i	−1.01899	+	1.48126i
$731$	509891.	−	294385.i	0.0352926	−	0.0203762i
$732$	−2.30026e7	+	2.83556e7i	−1.58672	+	1.95596i
$733$	−2.22451e7			−1.52924			−0.764619	−	0.644483i	$-0.777073\pi$
$733$	−2.22451e7			−1.52924			−0.764619	+	0.644483i	$0.777073\pi$
$734$	3.81300e6	+	2.62304e6i	0.261232	+	0.179707i
$735$	4.93141e6	+	8.54145e6i	0.336707	+	0.583194i
$736$	−6.43362e6	+	1.54373e7i	−0.437785	+	1.05046i
$737$	40378.3	−	23312.4i	0.00273829	−	0.00158095i
$738$	−1.97817e7	+	9.42487e6i	−1.33698	+	0.636993i
$739$	−3.07838e6	−	1.77730e6i	−0.207354	−	0.119716i	0.392727	−	0.919655i	$-0.371532\pi$
$739$	−3.07838e6	−	1.77730e6i	−0.207354	−	0.119716i	−0.600081	+	0.799939i	$0.704865\pi$
$740$	−8.70638e6	+	3.33340e6i	−0.584465	+	0.223774i
$741$	2.19681e7	−	1.38244e7i	1.46976	−	0.924914i
$742$	1.12228e7	−	1.63141e7i	0.748327	−	1.08781i
$743$	1.31507e6	−	2.27777e6i	0.0873931	−	0.151369i	−0.819015	−	0.573772i	$-0.805480\pi$
$743$	1.31507e6	−	2.27777e6i	0.0873931	−	0.151369i	0.906408	+	0.422402i	$0.138813\pi$
$744$	−1.13866e7	+	1.19677e7i	−0.754155	+	0.792645i
$745$	−7.40558e6	−	1.28268e7i	−0.488842	−	0.846699i
$746$	−1.04433e7	+	4.97562e6i	−0.687051	+	0.327341i
$747$	2.36848e7	−	1.36744e7i	1.55299	−	0.896620i
$748$	−862899.	+	330377.i	−0.0563905	+	0.0215902i
$749$			9.75118e6i			0.635115i
$750$	−1.01584e7	−	803914.i	−0.659433	−	0.0521863i
$751$	1.57000e6	+	2.71932e6i	0.101578	+	0.175939i	0.912335	−	0.409445i	$-0.134277\pi$
$751$	1.57000e6	+	2.71932e6i	0.101578	+	0.175939i	−0.810757	+	0.585383i	$0.800944\pi$
$752$	−1.83555e7	−	2.04571e7i	−1.18365	−	1.31917i
$753$			3.44384e7i			2.21337i
$754$	−2.74164e7	−	2.16968e6i	−1.75623	−	0.138985i
$755$	1.28007e7	−	2.21714e7i	0.817269	−	1.41555i
$756$	−9.44746e6	−	7.66398e6i	−0.601188	−	0.487697i
$757$	1.34083e7	−	2.32239e7i	0.850424	−	1.47298i	−0.0304027	−	0.999538i	$-0.509679\pi$
$757$	1.34083e7	−	2.32239e7i	0.850424	−	1.47298i	0.880826	−	0.473439i	$-0.156988\pi$
$758$	−3.49427e6	−	7.33407e6i	−0.220894	−	0.463631i
$759$	−1.06170e7			−0.668958
$760$	−2.01829e7	−	4.06687e6i	−1.26751	−	0.255403i
$761$	−1.08156e7			−0.676999			−0.338499	−	0.940967i	$-0.609919\pi$
$761$	−1.08156e7			−0.676999			−0.338499	+	0.940967i	$0.609919\pi$
$762$	−3.36785e6	−	7.06874e6i	−0.210119	−	0.441016i
$763$	1.64204e7	−	2.84409e7i	1.02111	−	1.76861i
$764$	1.36199e7	+	1.10488e7i	0.844194	+	0.684828i
$765$	2.39608e6	−	4.15013e6i	0.148029	−	0.256394i
$766$	−1.20238e7	−	951543.i	−0.740407	−	0.0585944i
$767$		−	1.98431e7i		−	1.21793i
$768$	2.75132e6	−	2.53312e7i	0.168321	−	1.54972i
$769$	1.15420e7	+	1.99914e7i	0.703827	+	1.21906i	0.967113	+	0.254346i	$0.0818604\pi$
$769$	1.15420e7	+	1.99914e7i	0.703827	+	1.21906i	−0.263286	+	0.964718i	$0.584806\pi$
$770$	−9.23646e6	−	730956.i	−0.561408	−	0.0444288i
$771$		−	737866.i		−	0.0447035i
$772$	3.39411e6	−	1.29950e6i	0.204966	−	0.0784752i
$773$	1.18754e7	−	6.85624e6i	0.714822	−	0.412703i	−0.0980218	−	0.995184i	$-0.531251\pi$
$773$	1.18754e7	−	6.85624e6i	0.714822	−	0.412703i	0.812844	+	0.582481i	$0.197918\pi$
$774$	−5.47571e6	+	2.60887e6i	−0.328540	+	0.156531i
$775$	−3.94204e6	−	6.82781e6i	−0.235758	−	0.408345i
$776$	−1.33132e7	−	1.26667e7i	−0.793649	−	0.755110i
$777$	−7.33309e6	+	1.27013e7i	−0.435747	+	0.754736i
$778$	1.79833e6	−	2.61416e6i	0.106518	−	0.154840i
$779$	667872.	+	1.75288e7i	0.0394321	+	1.03493i
$780$	−3.56301e7	+	1.36417e7i	−2.09691	+	0.802843i
$781$	−8.21616e6	−	4.74360e6i	−0.481994	−	0.278279i
$782$	−2.81328e6	+	1.34037e6i	−0.164511	+	0.0783803i
$783$	−1.57470e7	+	9.09151e6i	−0.917894	+	0.529946i
$784$	1.18577e6	+	5.62659e6i	0.0688985	+	0.326930i
$785$	1.22670e7	+	2.12471e7i	0.710502	+	1.23063i
$786$	2.28521e7	+	1.57204e7i	1.31938	+	0.907626i
$787$	3.14057e7			1.80747			0.903736	−	0.428089i	$-0.140813\pi$
$787$	3.14057e7			1.80747			0.903736	+	0.428089i	$0.140813\pi$
$788$	7.54218e6	−	9.29731e6i	0.432694	−	0.533386i
$789$	1.71262e7	−	9.88783e6i	0.979420	−	0.565468i
$790$	−1.45215e7	+	2.11094e7i	−0.827837	+	1.20339i
$791$	2.39879e6			0.136317
$792$	9.13028e6	−	2.69159e6i	0.517215	−	0.152474i
$793$	2.76040e7	+	1.59371e7i	1.55879	+	0.899969i
$794$	1.90952e7	+	1.51116e6i	1.07491	+	0.0850666i
$795$	−3.55576e7	−	2.05292e7i	−1.99533	−	1.15201i
$796$	943116.	−	5.92135e6i	0.0527573	−	0.331236i
$797$		−	1.51408e7i		−	0.844310i	−0.906524	−	0.422155i	$-0.861274\pi$
$797$		−	1.51408e7i		−	0.844310i	0.906524	−	0.422155i	$-0.138726\pi$
$798$	−2.86886e7	+	1.50345e7i	−1.59478	+	0.835758i
$799$		−	5.12130e6i		−	0.283800i
$800$	1.12251e7	+	4.67814e6i	0.620106	+	0.258433i
$801$	−3.01207e7	−	1.73902e7i	−1.65876	−	0.957685i
$802$	2.32148e6	−	2.93345e7i	0.127447	−	1.61043i
$803$	−8.29738e6	−	4.79050e6i	−0.454101	−	0.262175i
$804$	−150931.	+	186054.i	−0.00823452	+	0.0101508i
$805$	−3.12487e7			−1.69958
$806$	1.18809e7	+	8.17312e6i	0.644187	+	0.443149i
$807$	−1.19183e7	+	6.88103e6i	−0.644214	+	0.371937i
$808$	9.68937e6	+	3.28678e7i	0.522116	+	1.77109i
$809$	1.40094e7			0.752574			0.376287	−	0.926503i	$-0.377201\pi$
$809$	1.40094e7			0.752574			0.376287	+	0.926503i	$0.377201\pi$
$810$	5.27089e6	−	7.66208e6i	0.282275	−	0.410331i
$811$	−4.96644e6	−	8.60213e6i	−0.265151	−	0.459255i	0.702452	−	0.711731i	$-0.252089\pi$
$811$	−4.96644e6	−	8.60213e6i	−0.265151	−	0.459255i	−0.967603	+	0.252476i	$0.918755\pi$
$812$	3.38915e7	+	5.39803e6i	1.80385	+	0.287306i
$813$	−3.52594e6	+	2.03570e6i	−0.187089	+	0.108016i
$814$	−1.48411e6	−	3.11498e6i	−0.0785064	−	0.164776i
$815$	2.47009e7	+	1.42611e7i	1.30262	+	0.752070i
$816$	3.53377e6	−	3.17074e6i	0.185786	−	0.166700i
$817$	184871.	+	4.85210e6i	0.00968980	+	0.254316i
$818$	704438.	+	484597.i	0.0368095	+	0.0253220i
$819$	−1.76600e7	+	3.05880e7i	−0.919984	+	1.59346i
$820$	4.05561e6	−	2.54631e7i	0.210631	−	1.32244i
$821$	−1.59136e6	−	2.75632e6i	−0.0823969	−	0.142716i	0.821882	−	0.569658i	$-0.192924\pi$
$821$	−1.59136e6	−	2.75632e6i	−0.0823969	−	0.142716i	−0.904279	+	0.426942i	$0.859591\pi$
$822$	−1.04531e7	−	2.19400e7i	−0.539595	−	1.13255i
$823$	8.11005e6	−	4.68234e6i	0.417373	−	0.240970i	−0.276580	−	0.960991i	$-0.589201\pi$
$823$	8.11005e6	−	4.68234e6i	0.417373	−	0.240970i	0.693953	+	0.720021i	$0.255868\pi$
$824$	−9.12066e6	−	2.20223e6i	−0.467960	−	0.112991i
$825$			7.72007e6i			0.394899i
$826$	−1.95346e6	+	2.46842e7i	−0.0996218	+	1.25883i
$827$	−1.53488e7	−	2.65850e7i	−0.780391	−	1.35168i	−0.931714	−	0.363192i	$-0.881687\pi$
$827$	−1.53488e7	−	2.65850e7i	−0.780391	−	1.35168i	0.151324	−	0.988484i	$-0.451646\pi$
$828$	2.99811e7	−	1.14788e7i	1.51975	−	0.581864i
$829$		−	829188.i		−	0.0419051i	−0.999780	−	0.0209525i	$-0.993330\pi$
$829$		−	829188.i		−	0.0419051i	0.999780	−	0.0209525i	$-0.00666989\pi$
$830$	−2.53884e6	+	3.20811e7i	−0.127920	+	1.61642i
$831$	−1.67463e7	+	2.90055e7i	−0.841233	+	1.45706i
$832$	−2.22159e7	+	1.10632e6i	−1.11264	+	0.0554079i
$833$	−535719.	+	927893.i	−0.0267501	+	0.0463325i
$834$	2.37338e6	−	1.13078e6i	0.118155	−	0.0562941i
$835$	1.51616e7			0.752540
$836$	911194.	−	7.56544e6i	0.0450915	−	0.374385i
$837$	9.53423e6			0.470405
$838$	7.73956e6	−	3.68746e6i	0.380720	−	0.181392i
$839$	−9.38993e6	+	1.62638e7i	−0.460530	+	0.797661i	−0.998987	−	0.0449918i	$-0.985674\pi$
$839$	−9.38993e6	+	1.62638e7i	−0.460530	+	0.797661i	0.538458	+	0.842653i	$0.319007\pi$
$840$	4.56656e7	−	1.34622e7i	2.23301	−	0.658289i
$841$	1.53921e7	−	2.66600e7i	0.750428	−	1.29978i
$842$	−433428.	+	5.47685e6i	−0.0210687	+	0.266226i
$843$		−	1.85049e7i		−	0.896848i
$844$	1.26667e6	+	3.30838e6i	0.0612081	+	0.159867i
$845$	3.23442e6	+	5.60218e6i	0.155831	+	0.269908i
$846$	−4.16223e6	+	5.25945e7i	−0.199940	+	2.52647i
$847$			2.06867e7i			0.990794i
$848$	−1.59866e7	−	1.78170e7i	−0.763424	−	0.850832i
$849$	−1.98013e6	+	1.14323e6i	−0.0942809	+	0.0544331i
$850$	974635.	+	2.04565e6i	0.0462695	+	0.0971144i
$851$	−5.81859e6	−	1.00781e7i	−0.275419	−	0.477040i
$852$	4.81418e7	+	7.66773e6i	2.27208	+	0.361883i
$853$	−2.01056e7	+	3.48239e7i	−0.946115	+	1.63872i	−0.192613	+	0.981275i	$0.561696\pi$
$853$	−2.01056e7	+	3.48239e7i	−0.946115	+	1.63872i	−0.753502	+	0.657445i	$0.771637\pi$
$854$	−3.27695e7	−	2.25428e7i	−1.53753	−	1.05770i
$855$	2.10493e7	+	3.34491e7i	0.984743	+	1.56484i
$856$	1.14587e7	+	2.76677e6i	0.534505	+	0.129059i
$857$	2.51495e7	+	1.45201e7i	1.16971	+	0.675332i	0.953612	−	0.301039i	$-0.0973336\pi$
$857$	2.51495e7	+	1.45201e7i	1.16971	+	0.675332i	0.216098	+	0.976372i	$0.430667\pi$
$858$	−6.07359e6	−	1.27478e7i	−0.281661	−	0.591175i
$859$	1.43937e6	−	831021.i	0.0665564	−	0.0384263i	−0.466353	−	0.884599i	$-0.654432\pi$
$859$	1.43937e6	−	831021.i	0.0665564	−	0.0384263i	0.532909	+	0.846173i	$0.321099\pi$
$860$	1.12262e6	−	7.04836e6i	0.0517590	−	0.324969i
$861$	−2.02814e7	−	3.51283e7i	−0.932372	−	1.61491i
$862$	774373.	−	1.12567e6i	0.0354962	−	0.0515994i
$863$	−3.77714e6			−0.172638			−0.0863189	−	0.996268i	$-0.527510\pi$
$863$	−3.77714e6			−0.172638			−0.0863189	+	0.996268i	$0.527510\pi$
$864$	−1.16866e7	+	8.92727e6i	−0.532605	+	0.406850i
$865$	394493.	−	227761.i	0.0179266	−	0.0103499i
$866$	−2.20905e7	−	1.51965e7i	−1.00095	−	0.688571i
$867$	−3.36175e7			−1.51886
$868$	−1.39749e7	−	1.13367e7i	−0.629576	−	0.510726i
$869$	−8.21252e6	−	4.74150e6i	−0.368916	−	0.212994i
$870$	5.61389e6	−	7.09379e7i	0.251458	−	3.17746i
$871$	181122.	+	104571.i	0.00808960	+	0.00467053i
$872$	−2.87622e7	−	2.73655e7i	−1.28095	−	1.21875i
$873$			3.52744e7i			1.56648i
$874$	1.05059e6	−	2.56785e7i	0.0465218	−	1.13708i
$875$		−	1.11005e7i		−	0.490144i
$876$	4.86177e7	+	7.74353e6i	2.14059	+	0.340941i
$877$	−4.72862e6	−	2.73007e6i	−0.207604	−	0.119860i	0.392593	−	0.919712i	$-0.371578\pi$
$877$	−4.72862e6	−	2.73007e6i	−0.207604	−	0.119860i	−0.600197	+	0.799852i	$0.704911\pi$
$878$	3.32279e7	+	2.62959e6i	1.45468	+	0.115120i
$879$	3.36661e7	+	1.94371e7i	1.46967	+	0.848516i
$880$	−3.47968e6	+	1.06465e7i	−0.151472	+	0.463446i
$881$	1.82315e7			0.791376			0.395688	−	0.918385i	$-0.370506\pi$
$881$	1.82315e7			0.791376			0.395688	+	0.918385i	$0.370506\pi$
$882$	6.25584e6	−	9.09385e6i	0.270779	−	0.393619i
$883$	79489.3	−	45893.2i	0.00343089	−	0.00198083i	−0.498284	−	0.867014i	$-0.666036\pi$
$883$	79489.3	−	45893.2i	0.00343089	−	0.00198083i	0.501714	+	0.865033i	$0.332703\pi$
$884$	−3.21873e6	−	2.61110e6i	−0.138533	−	0.112381i
$885$	5.13426e7			2.20353
$886$	−1.49895e7	−	1.03115e7i	−0.641507	−	0.441305i
$887$	1.21302e7	+	2.10102e7i	0.517678	+	0.896644i	0.999789	+	0.0205343i	$0.00653673\pi$
$887$	1.21302e7	+	2.10102e7i	0.517678	+	0.896644i	−0.482111	+	0.876110i	$0.660130\pi$
$888$	1.28448e7	+	1.22210e7i	0.546630	+	0.520086i
$889$	7.38685e6	−	4.26480e6i	0.313476	−	0.180986i
$890$	3.69468e7	−	1.76031e7i	1.56352	−	0.744927i
$891$	2.98090e6	+	1.72103e6i	0.125792	+	0.0726262i
$892$	3.12745e6	+	8.16845e6i	0.131607	+	0.343738i
$893$	3.73546e7	+	1.97098e7i	1.56753	+	0.827093i
$894$	−1.59643e7	+	2.32066e7i	−0.668046	+	0.971110i
$895$	3.74271e6	−	6.48256e6i	0.156181	−	0.270513i
$896$	2.77447e7	+	810826.i	1.15454	+	0.0337410i
$897$	−2.38121e7	−	4.12437e7i	−0.988134	−	1.71150i
$898$	−208062.	+	99129.5i	−0.00860996	+	0.00410215i
$899$	−2.32932e7	+	1.34483e7i	−0.961236	+	0.554970i
$900$	−8.34671e6	−	2.18004e7i	−0.343486	−	0.897137i
$901$		−	4.46035e6i		−	0.183045i
$902$	9.51329e6	+	752864.i	0.389327	+	0.0308106i
$903$	−5.61401e6	−	9.72375e6i	−0.229115	−	0.396839i
$904$	680626.	−	2.81885e6i	0.0277005	−	0.114723i
$905$			5.41177e7i			2.19643i
$906$	−4.85362e7	−	3.84107e6i	−1.96447	−	0.155465i
$907$	5.58073e6	−	9.66610e6i	0.225254	−	0.390151i	−0.731142	−	0.682226i	$-0.761012\pi$
$907$	5.58073e6	−	9.66610e6i	0.225254	−	0.390151i	0.956396	+	0.292074i	$0.0943455\pi$
$908$	−1.17123e7	+	1.44379e7i	−0.471442	+	0.581150i
$909$	3.28881e7	−	5.69638e7i	1.32017	−	2.28660i
$910$	−1.78762e7	−	3.75200e7i	−0.715601	−	1.50196i
$911$	−3.10489e7			−1.23951			−0.619756	−	0.784794i	$-0.712769\pi$
$911$	−3.10489e7			−1.23951			−0.619756	+	0.784794i	$0.712769\pi$
$912$	9.52717e6	+	3.79781e7i	0.379295	+	1.51198i
$913$	−1.19108e7			−0.472893
$914$	6.44684e6	+	1.35312e7i	0.255259	+	0.535760i
$915$	−4.12362e7	+	7.14232e7i	−1.62827	+	2.82024i
$916$	5.17434e6	−	6.37846e6i	0.203759	−	0.251175i
$917$	−1.51076e7	+	2.61672e7i	−0.593297	+	1.02762i
$918$	−2.73169e6	−	216181.i	−0.106986	−	0.00846664i
$919$			4.32636e7i			1.68980i	0.534927	+	0.844898i	$0.320339\pi$
$919$			4.32636e7i			1.68980i	−0.534927	+	0.844898i	$0.679661\pi$
$920$	−8.86642e6	+	3.67207e7i	−0.345365	+	1.43035i
$921$	−7.28336e6	−	1.26152e7i	−0.282932	−	0.490053i
$922$	5.87041e6	+	464574.i	0.227427	+	0.0179981i
$923$		−	4.25561e7i		−	1.64421i
$924$	6.30038e6	+	1.64557e7i	0.242766	+	0.634069i
$925$	−7.32818e6	+	4.23093e6i	−0.281606	+	0.162585i
$926$	1.88125e7	−	8.96311e6i	0.720975	−	0.343504i
$927$	9.00540e6	+	1.55978e7i	0.344194	+	0.596162i
$928$	1.59596e7	−	3.82947e7i	0.608347	−	1.45972i
$929$	−6.93584e6	+	1.20132e7i	−0.263669	+	0.456689i	−0.967214	−	0.253962i	$-0.918266\pi$
$929$	−6.93584e6	+	1.20132e7i	−0.263669	+	0.456689i	0.703545	+	0.710651i	$0.251599\pi$
$930$	−2.11473e7	+	3.07410e7i	−0.801767	+	1.16549i
$931$	−4.70625e6	−	7.47861e6i	−0.177951	−	0.282779i
$932$	1.76093e6	+	4.59930e6i	0.0664053	+	0.173441i
$933$	2.21838e7	+	1.28078e7i	0.834318	+	0.481694i
$934$	−1.90820e7	+	9.09149e6i	−0.715742	+	0.341010i
$935$	−1.80743e6	+	1.04352e6i	−0.0676134	+	0.0390366i
$936$	3.09335e7	+	2.94314e7i	1.15409	+	1.09805i
$937$	1.04866e7	+	1.81633e7i	0.390198	+	0.675842i	0.992475	−	0.122444i	$-0.0390733\pi$
$937$	1.04866e7	+	1.81633e7i	0.390198	+	0.675842i	−0.602278	+	0.798287i	$0.705740\pi$
$938$	−215016.	−	147914.i	−0.00797927	−	0.00548910i
$939$	−2.23385e6			−0.0826781
$940$	−4.82124e7	−	3.91109e7i	−1.77967	−	1.44370i
$941$	−4.55607e7	+	2.63045e7i	−1.67732	+	0.968403i	−0.713966	+	0.700181i	$0.753103\pi$
$941$	−4.55607e7	+	2.63045e7i	−1.67732	+	0.968403i	−0.963357	+	0.268222i	$0.913564\pi$
$942$	2.64442e7	−	3.84408e7i	0.970965	−	1.41145i
$943$	3.21853e7			1.17863
$944$	2.84524e7	+	9.29936e6i	1.03918	+	0.339643i
$945$	−2.37967e7	−	1.37390e7i	−0.866835	−	0.500467i
$946$	2.63334e6	+	208398.i	0.0956708	+	0.00757121i
$947$	9.86687e6	+	5.69664e6i	0.357523	+	0.206416i	0.667994	−	0.744167i	$-0.267153\pi$
$947$	9.86687e6	+	5.69664e6i	0.357523	+	0.206416i	−0.310471	+	0.950583i	$0.600487\pi$
$948$	4.81205e7	+	7.66434e6i	1.73904	+	0.276983i
$949$		−	4.29768e7i		−	1.54906i
$950$	−1.86719e7	−	763930.i	−0.671241	−	0.0274628i
$951$		−	7.37805e7i		−	2.64539i
$952$	3.74695e6	+	3.56500e6i	0.133994	+	0.127487i
$953$	−1.17990e7	−	6.81217e6i	−0.420837	−	0.242970i	0.274598	−	0.961559i	$-0.411455\pi$
$953$	−1.17990e7	−	6.81217e6i	−0.420837	−	0.242970i	−0.695435	+	0.718589i	$0.744788\pi$
$954$	−3.62506e6	+	4.58068e7i	−0.128957	+	1.62952i
$955$	3.43065e7	+	1.98069e7i	1.21722	+	0.702761i
$956$	−3.67839e7	−	2.98399e7i	−1.30171	−	1.05597i
$957$	2.63372e7			0.929585
$958$	−2.43586e7	−	1.67568e7i	−0.857510	−	0.589898i
$959$	2.29273e7	−	1.32371e7i	0.805019	−	0.464778i
$960$	−2.86251e6	−	5.74819e7i	−0.100247	−	2.01304i
$961$	−1.45259e7			−0.507383
$962$	8.77208e6	−	1.27516e7i	0.305608	−	0.444250i
$963$	−1.13139e7	−	1.95963e7i	−0.393140	−	0.680939i
$964$	2.81243e6	−	1.76578e7i	0.0974739	−	0.611990i
$965$	7.10931e6	−	4.10456e6i	0.245759	−	0.141889i
$966$	2.55612e7	+	5.36500e7i	0.881329	+	1.84981i
$967$	6.87983e6	+	3.97207e6i	0.236598	+	0.136600i	0.613612	−	0.789608i	$-0.289716\pi$
$967$	6.87983e6	+	3.97207e6i	0.236598	+	0.136600i	−0.377014	+	0.926208i	$0.623049\pi$
$968$	2.43092e7	+	5.86960e6i	0.833840	+	0.201335i
$969$	−3.40468e6	+	6.45264e6i	−0.116484	+	0.220764i
$970$	−3.41971e7	−	2.35249e7i	−1.16697	−	0.802782i
$971$	−3.80493e6	+	6.59034e6i	−0.129509	+	0.224316i	−0.923486	−	0.383631i	$-0.874673\pi$
$971$	−3.80493e6	+	6.59034e6i	−0.129509	+	0.224316i	0.793978	+	0.607947i	$0.208007\pi$
$972$	−3.69622e7	−	5.88711e6i	−1.25485	−	0.199865i
$973$	1.43193e6	+	2.48018e6i	0.0484887	+	0.0839850i
$974$	1.86620e7	+	3.91694e7i	0.630319	+	1.32297i
$975$	−2.99900e7	+	1.73147e7i	−1.01033	+	0.583316i
$976$	−3.57882e7	+	3.21116e7i	−1.20258	+	1.07904i
$977$			3.48479e7i			1.16799i	0.811756	+	0.583997i	$0.198512\pi$
$977$			3.48479e7i			1.16799i	−0.811756	+	0.583997i	$0.801488\pi$
$978$	4.27929e6	−	5.40737e7i	0.143062	−	1.80775i
$979$	7.57364e6	+	1.31179e7i	0.252550	+	0.437430i
$980$	4.64403e6	+	1.21296e7i	0.154465	+	0.403441i
$981$			7.62078e7i			2.52829i
$982$	−808854.	+	1.02208e7i	−0.0267665	+	0.338225i
$983$	−2.40360e7	+	4.16316e7i	−0.793376	+	1.37417i	0.130489	+	0.991450i	$0.458345\pi$
$983$	−2.40360e7	+	4.16316e7i	−0.793376	+	1.37417i	−0.923865	+	0.382718i	$0.874988\pi$
$984$	−4.70343e7	+	1.38656e7i	−1.54856	+	0.456512i
$985$	1.35207e7	−	2.34185e7i	0.444025	−	0.769073i
$986$	6.97876e6	−	3.32498e6i	0.228605	−	0.108917i
$987$	−9.76645e7			−3.19113
$988$	3.14329e7	−	1.34282e7i	1.02445	−	0.437649i
$989$	8.90910e6			0.289630
$990$	1.94100e7	−	9.24776e6i	0.629416	−	0.299881i
$991$	−7.90852e6	+	1.36980e7i	−0.255806	+	0.443069i	−0.965114	−	0.261829i	$-0.915674\pi$
$991$	−7.90852e6	+	1.36980e7i	−0.255806	+	0.443069i	0.709308	+	0.704899i	$0.249008\pi$
$992$	−1.72871e7	+	1.32054e7i	−0.557754	+	0.426061i
$993$	2.55572e7	−	4.42664e7i	0.822510	−	1.42463i
$994$	−4.18945e6	+	5.29384e7i	−0.134490	+	1.69944i
$995$		−	1.35434e7i		−	0.433681i
$996$	5.71558e7	−	2.18832e7i	1.82563	−	0.698976i
$997$	−2.07922e7	−	3.60131e7i	−0.662464	−	1.14742i	−0.979966	−	0.199163i	$-0.936178\pi$
$997$	−2.07922e7	−	3.60131e7i	−0.662464	−	1.14742i	0.317503	−	0.948257i	$-0.397156\pi$
$998$	215423.	−	2.72211e6i	0.00684646	−	0.0865127i
$999$		−	1.02329e7i		−	0.324405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.f.a.27.19	yes	96
4.3	odd	2	inner	76.6.f.a.27.4	✓	96
19.12	odd	6	inner	76.6.f.a.31.4	yes	96
76.31	even	6	inner	76.6.f.a.31.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.f.a.27.4	✓	96	4.3	odd	2	inner
76.6.f.a.27.19	yes	96	1.1	even	1	trivial
76.6.f.a.31.4	yes	96	19.12	odd	6	inner
76.6.f.a.31.19	yes	96	76.31	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43312 - 5.10685i) q^{2} +(-12.1499 + 21.0442i) q^{3} +(-20.1598 + 24.8512i) q^{4} +(-36.1399 + 62.5962i) q^{5} +(137.032 + 10.8444i) q^{6} +149.741i q^{7} +(175.963 + 42.4871i) q^{8} +(-173.739 - 300.925i) q^{9} +O(q^{10})\)	\(q+(-2.43312 - 5.10685i) q^{2} +(-12.1499 + 21.0442i) q^{3} +(-20.1598 + 24.8512i) q^{4} +(-36.1399 + 62.5962i) q^{5} +(137.032 + 10.8444i) q^{6} +149.741i q^{7} +(175.963 + 42.4871i) q^{8} +(-173.739 - 300.925i) q^{9} +(407.602 + 32.2569i) q^{10} +151.331i q^{11} +(-278.034 - 726.186i) q^{12} +(-587.871 + 339.408i) q^{13} +(764.705 - 364.339i) q^{14} +(-878.192 - 1521.07i) q^{15} +(-211.163 - 1001.99i) q^{16} +(95.4017 - 165.241i) q^{17} +(-1114.05 + 1619.45i) q^{18} +(838.096 + 1331.80i) q^{19} +(-827.016 - 2160.05i) q^{20} +(-3151.18 - 1819.34i) q^{21} +(772.824 - 368.207i) q^{22} +(2500.37 - 1443.59i) q^{23} +(-3032.03 + 3186.78i) q^{24} +(-1049.69 - 1818.12i) q^{25} +(3163.67 + 2176.35i) q^{26} +2538.79 q^{27} +(-3721.25 - 3018.75i) q^{28} +(-6202.55 + 3581.04i) q^{29} +(-5631.14 + 8185.75i) q^{30} +3755.43 q^{31} +(-4603.23 + 3516.35i) q^{32} +(-3184.64 - 1838.65i) q^{33} +(-1075.98 - 85.1513i) q^{34} +(-9373.23 - 5411.64i) q^{35} +(10980.9 + 1748.97i) q^{36} -4030.64i q^{37} +(4762.12 - 7520.47i) q^{38} -16495.0i q^{39} +(-9018.81 + 9479.11i) q^{40} +(9654.16 + 5573.83i) q^{41} +(-1623.86 + 20519.3i) q^{42} +(2672.34 + 1542.87i) q^{43} +(-3760.75 - 3050.80i) q^{44} +25115.7 q^{45} +(-13455.9 - 9256.58i) q^{46} +(23244.7 - 13420.4i) q^{47} +(23651.7 + 7730.30i) q^{48} -5615.41 q^{49} +(-6730.83 + 9784.33i) q^{50} +(2318.24 + 4015.30i) q^{51} +(3416.69 - 21451.7i) q^{52} +(20244.8 - 11688.3i) q^{53} +(-6177.19 - 12965.2i) q^{54} +(-9472.74 - 5469.09i) q^{55} +(-6362.07 + 26348.8i) q^{56} +(-38209.5 + 1455.83i) q^{57} +(33379.4 + 22962.4i) q^{58} +(-14616.0 + 25315.6i) q^{59} +(55504.7 + 8840.44i) q^{60} +(-23477.9 - 40664.9i) q^{61} +(-9137.41 - 19178.4i) q^{62} +(45060.8 - 26015.9i) q^{63} +(29157.7 + 14952.3i) q^{64} -49064.7i q^{65} +(-1641.10 + 20737.1i) q^{66} +(-154.049 - 266.821i) q^{67} +(2183.14 + 5702.06i) q^{68} +70157.7i q^{69} +(-4830.19 + 61034.9i) q^{70} +(-31345.9 + 54292.7i) q^{71} +(-17786.1 - 60333.2i) q^{72} +(-31655.8 + 54829.4i) q^{73} +(-20583.9 + 9807.05i) q^{74} +51014.5 q^{75} +(-49992.7 - 6021.20i) q^{76} -22660.5 q^{77} +(-84237.7 + 40134.5i) q^{78} +(-31332.0 + 54268.6i) q^{79} +(70352.3 + 22993.9i) q^{80} +(11372.6 - 19697.9i) q^{81} +(4974.95 - 62864.2i) q^{82} +78706.9i q^{83} +(108740. - 41633.2i) q^{84} +(6895.62 + 11943.6i) q^{85} +(1377.10 - 17401.2i) q^{86} -174037. i q^{87} +(-6429.62 + 26628.6i) q^{88} +(86683.7 - 50046.9i) q^{89} +(-61109.5 - 128262. i) q^{90} +(-50823.3 - 88028.5i) q^{91} +(-14532.1 + 91239.7i) q^{92} +(-45628.0 + 79029.9i) q^{93} +(-125093. - 86054.0i) q^{94} +(-113654. + 4330.39i) q^{95} +(-18070.1 - 139595. i) q^{96} +(-87915.1 - 50757.8i) q^{97} +(13663.0 + 28677.0i) q^{98} +(45539.2 - 26292.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9}+O(q^{10}) \) 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9	\( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9} + 648 q^{10} - 354 q^{13} + 2154 q^{14} - 611 q^{16} - 1006 q^{17} + 10524 q^{20} + 7824 q^{21} + 93 q^{22} - 5311 q^{24} - 25002 q^{25} - 13428 q^{26} + 1556 q^{28} - 6 q^{29} - 12656 q^{30} - 30453 q^{32} + 8586 q^{33} + 30102 q^{34} - 2306 q^{36} + 29846 q^{38} - 1392 q^{40} + 29064 q^{41} + 18616 q^{42} + 9155 q^{44} + 13464 q^{45} + 38217 q^{48} - 116224 q^{49} + 36858 q^{52} + 26262 q^{53} - 26355 q^{54} + 53974 q^{57} - 112740 q^{58} - 108810 q^{60} - 77370 q^{61} - 106848 q^{62} + 337966 q^{64} + 166855 q^{66} + 175796 q^{68} + 148122 q^{70} - 259842 q^{72} - 52040 q^{73} + 103690 q^{74} - 194709 q^{76} + 197584 q^{77} + 253206 q^{78} - 171934 q^{80} - 313100 q^{81} + 63919 q^{82} - 161762 q^{85} - 38442 q^{86} + 10482 q^{89} - 372450 q^{90} + 64544 q^{92} + 94012 q^{93} + 537614 q^{96} + 177180 q^{97} - 509397 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9 + 648 * q^10 - 354 * q^13 + 2154 * q^14 - 611 * q^16 - 1006 * q^17 + 10524 * q^20 + 7824 * q^21 + 93 * q^22 - 5311 * q^24 - 25002 * q^25 - 13428 * q^26 + 1556 * q^28 - 6 * q^29 - 12656 * q^30 - 30453 * q^32 + 8586 * q^33 + 30102 * q^34 - 2306 * q^36 + 29846 * q^38 - 1392 * q^40 + 29064 * q^41 + 18616 * q^42 + 9155 * q^44 + 13464 * q^45 + 38217 * q^48 - 116224 * q^49 + 36858 * q^52 + 26262 * q^53 - 26355 * q^54 + 53974 * q^57 - 112740 * q^58 - 108810 * q^60 - 77370 * q^61 - 106848 * q^62 + 337966 * q^64 + 166855 * q^66 + 175796 * q^68 + 148122 * q^70 - 259842 * q^72 - 52040 * q^73 + 103690 * q^74 - 194709 * q^76 + 197584 * q^77 + 253206 * q^78 - 171934 * q^80 - 313100 * q^81 + 63919 * q^82 - 161762 * q^85 - 38442 * q^86 + 10482 * q^89 - 372450 * q^90 + 64544 * q^92 + 94012 * q^93 + 537614 * q^96 + 177180 * q^97 - 509397 * q^98

Introduction

L-functions

Modular forms

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