LMFDB - Embedded newform 76.6.f.a.31.19

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			31.19
Character	$\chi$	$=$	76.31
Dual form			76.6.f.a.27.19

$q$-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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	−0.932279	−	0.361739i	$-0.882183\pi$
$3$	−12.1499	−	21.0442i	−0.779415	−	1.34999i	0.152864	−	0.988247i	$-0.451150\pi$
$4$	−20.1598	−	24.8512i	−0.629994	−	0.776600i
$5$	−36.1399	−	62.5962i	−0.646491	−	1.11976i	−0.983955	−	0.178417i	$-0.942902\pi$
$5$	−36.1399	−	62.5962i	−0.646491	−	1.11976i	0.337464	−	0.941338i	$-0.390431\pi$
$6$	137.032	−	10.8444i	1.55397	−	0.122978i
$7$		−	149.741i		−	1.15504i	−0.816377	−	0.577519i	$-0.804021\pi$
$7$		−	149.741i		−	1.15504i	0.816377	−	0.577519i	$-0.195979\pi$
$8$	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	$-0.939623\pi$
$11$		−	151.331i		−	0.377091i	0.982064	−	0.188545i	$-0.0603773\pi$
$12$	−278.034	+	726.186i	−0.557372	+	1.45578i
$13$	−587.871	−	339.408i	−0.964770	−	0.557010i	−0.0671322	−	0.997744i	$-0.521385\pi$
$13$	−587.871	−	339.408i	−0.964770	−	0.557010i	−0.897638	+	0.440734i	$0.854718\pi$
$14$	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	0.903277	−	0.429058i	$-0.141154\pi$
$17$	95.4017	+	165.241i	0.0800633	+	0.138674i	−0.823214	+	0.567732i	$0.807821\pi$
$18$	−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	0.903945	−	0.427648i	$-0.140658\pi$
$23$	2500.37	+	1443.59i	0.985563	+	0.569015i	0.0816183	+	0.996664i	$0.473991\pi$
$24$	−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	−0.378672	−	0.925531i	$-0.623619\pi$
$29$	−6202.55	−	3581.04i	−1.36954	−	0.790705i	−0.990869	+	0.134826i	$0.956952\pi$
$30$	−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	$0.0778079\pi$
$37$			4030.64i			0.484027i	−0.970273	+	0.242014i	$0.922192\pi$
$38$	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	0.0207220	−	0.999785i	$-0.493404\pi$
$41$	9654.16	−	5573.83i	0.896922	−	0.517838i	0.876200	+	0.481947i	$0.160070\pi$
$42$	−1623.86	−	20519.3i	−0.142045	−	1.79489i
$43$	2672.34	−	1542.87i	0.220404	−	0.127250i	−0.385733	−	0.922610i	$-0.626051\pi$
$43$	2672.34	−	1542.87i	0.220404	−	0.127250i	0.606137	+	0.795360i	$0.292718\pi$
$44$	−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	0.999125	+	0.0418133i	$0.0133135\pi$
$47$	23244.7	+	13420.4i	1.53490	+	0.886175i	0.535774	+	0.844361i	$0.320020\pi$
$48$	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	0.905267	−	0.424844i	$-0.139671\pi$
$53$	20244.8	+	11688.3i	0.989974	+	0.571562i	0.0847077	+	0.996406i	$0.473004\pi$
$54$	−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	−0.998502	−	0.0547155i	$-0.982575\pi$
$59$	−14616.0	−	25315.6i	−0.546636	−	0.946801i	0.451866	−	0.892086i	$-0.350759\pi$
$60$	55504.7	−	8840.44i	1.99045	−	0.317027i
$61$	−23477.9	+	40664.9i	−0.807857	+	1.39925i	0.106488	+	0.994314i	$0.466039\pi$
$61$	−23477.9	+	40664.9i	−0.807857	+	1.39925i	−0.914345	+	0.404935i	$0.867294\pi$
$62$	−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	−0.868114	−	0.496365i	$-0.834668\pi$
$67$	−154.049	+	266.821i	−0.00419250	+	0.00726162i	0.863922	+	0.503626i	$0.168001\pi$
$68$	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	−0.953411	−	0.301675i	$-0.902454\pi$
$71$	−31345.9	−	54292.7i	−0.737963	−	1.27819i	0.215448	−	0.976515i	$-0.430879\pi$
$72$	−17786.1	+	60333.2i	−0.404343	+	1.37159i
$73$	−31655.8	−	54829.4i	−0.695257	−	1.20422i	−0.970094	−	0.242730i	$-0.921957\pi$
$73$	−31655.8	−	54829.4i	−0.695257	−	1.20422i	0.274836	−	0.961491i	$-0.411376\pi$
$74$	−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	−0.997065	−	0.0765579i	$-0.975607\pi$
$79$	−31332.0	−	54268.6i	−0.564834	−	0.978321i	0.432231	−	0.901763i	$-0.357726\pi$
$80$	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	$-0.784271\pi$
$83$		−	78706.9i		−	1.25406i	0.778996	−	0.627029i	$-0.215729\pi$
$84$	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	0.951307	−	0.308245i	$-0.0997418\pi$
$89$	86683.7	+	50046.9i	1.16001	+	0.669733i	0.208705	+	0.977979i	$0.433075\pi$
$90$	−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	−0.892680	−	0.450690i	$-0.851178\pi$
$97$	−87915.1	+	50757.8i	−0.948711	+	0.547739i	−0.0560307	+	0.998429i	$0.517844\pi$
$98$	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	0.128835	−	0.991666i	$-0.458876\pi$
$101$	94647.9	−	163935.i	0.923225	−	1.59907i	0.794391	−	0.607407i	$-0.207790\pi$
$102$	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	−0.531910	+	0.846801i	$0.678526\pi$
$109$	−189934.	+	109658.i	−1.53122	+	0.884048i	−0.999306	+	0.0372476i	$0.988141\pi$
$110$	−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	$0.0187944\pi$
$113$			16019.6i			0.118020i	−0.998257	+	0.0590099i	$0.981206\pi$
$114$	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	−0.933674	−	0.358124i	$-0.883416\pi$
$127$	−28481.1	+	49330.8i	−0.156692	+	0.271399i	0.776982	+	0.629523i	$0.216750\pi$
$128$	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	0.0158467	−	0.999874i	$-0.494956\pi$
$131$	174749.	−	100892.i	0.889687	−	0.513661i	0.873840	+	0.486214i	$0.161622\pi$
$132$	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	−0.994014	−	0.109252i	$-0.965155\pi$
$137$	−88399.8	+	153113.i	−0.402392	+	0.696964i	0.591622	+	0.806216i	$0.298488\pi$
$138$	358285.	+	170702.i	1.60151	+	0.763030i
$139$	16563.1	+	9562.73i	0.0727119	+	0.0419802i	0.535915	−	0.844272i	$-0.319967\pi$
$139$	16563.1	+	9562.73i	0.0727119	+	0.0419802i	−0.463203	+	0.886252i	$0.653300\pi$
$140$	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	0.612709	−	0.790309i	$-0.290080\pi$
$149$	−102457.	−	177461.i	−0.378073	−	0.654842i	−0.990782	+	0.135467i	$0.956747\pi$
$150$	−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	0.998308	+	0.0581418i	$0.0185176\pi$
$157$	169716.	+	293956.i	0.549506	+	0.951773i	−0.448802	+	0.893631i	$0.648149\pi$
$158$	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	$0.197595\pi$
$163$			394607.i			1.16331i	−0.813435	+	0.581656i	$0.802405\pi$
$164$	−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	−0.974049	−	0.226339i	$-0.927324\pi$
$167$	−104881.	+	181660.i	−0.291009	+	0.504043i	0.683039	+	0.730382i	$0.260658\pi$
$168$	−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	−0.506916	−	0.861995i	$-0.669215\pi$
$173$	−5457.85	+	3151.09i	−0.0138646	+	0.00800471i	0.493052	+	0.870000i	$0.335881\pi$
$174$	−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	0.999475	−	0.0324079i	$-0.0103176\pi$
$181$	648414.	+	374362.i	1.47115	+	0.849367i	0.471671	+	0.881774i	$0.343651\pi$
$182$	−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	$0.182908\pi$
$191$			548060.i			1.08704i	−0.839397	+	0.543519i	$0.817092\pi$
$192$	−668921.	−	431932.i	−1.30955	−	0.845594i
$193$	−98358.0	+	56787.0i	−0.190071	+	0.109738i	−0.592016	−	0.805926i	$-0.701668\pi$
$193$	−98358.0	+	56787.0i	−0.190071	+	0.109738i	0.401945	+	0.915664i	$0.368334\pi$
$194$	−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	0.347681	−	0.937613i	$-0.386969\pi$
$199$	−162271.	−	93687.2i	−0.290475	−	0.167706i	−0.638156	+	0.769907i	$0.720302\pi$
$200$	−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	0.905643	−	0.424040i	$-0.139389\pi$
$211$	55352.7	+	95873.7i	0.0855919	+	0.148249i	−0.820051	+	0.572290i	$0.806055\pi$
$212$	−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	0.943251	−	0.332081i	$-0.107751\pi$
$223$	136667.	+	236714.i	0.184035	+	0.318759i	−0.759216	+	0.650839i	$0.774417\pi$
$224$	−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	0.908713	−	0.417421i	$-0.137066\pi$
$233$	76951.3	+	133284.i	0.0928595	+	0.160837i	−0.815854	+	0.578258i	$0.803733\pi$
$234$	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	$-0.683678\pi$
$239$		−	1.48017e6i		−	1.67616i	0.545546	−	0.838081i	$-0.316322\pi$
$240$	−1.33866e6	−	1.20114e6i	−1.50018	−	1.34606i
$241$	−483902.	−	279381.i	−0.536679	−	0.309852i	0.207053	−	0.978330i	$-0.433613\pi$
$241$	−483902.	−	279381.i	−0.536679	−	0.309852i	−0.743732	+	0.668478i	$0.766946\pi$
$242$	−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	0.966960	−	0.254929i	$-0.0820520\pi$
$251$	1.22736e6	+	708615.i	1.22967	+	0.709947i	0.262705	+	0.964876i	$0.415385\pi$
$252$	−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	0.487531	−	0.873106i	$-0.337898\pi$
$257$	−26297.0	−	15182.6i	−0.0248355	−	0.0143388i	−0.512366	+	0.858767i	$0.671231\pi$
$258$	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	−0.780095	−	0.625661i	$-0.784829\pi$
$263$	−704790.	+	406911.i	−0.628305	+	0.362752i	0.151791	+	0.988413i	$0.451496\pi$
$264$	−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	−0.278925	−	0.960313i	$-0.589978\pi$
$269$	490470.	−	283173.i	0.413268	−	0.238600i	0.692193	+	0.721713i	$0.256645\pi$
$270$	1.03482e6	−	81893.5i	0.863881	−	0.0683660i
$271$	145102.	−	83774.7i	0.120019	−	0.0692930i	−0.438789	−	0.898590i	$-0.644592\pi$
$271$	145102.	−	83774.7i	0.120019	−	0.0692930i	0.558808	+	0.829297i	$0.311259\pi$
$272$	−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	0.229738	−	0.973252i	$-0.426213\pi$
$281$	−659503.	−	380764.i	−0.498254	−	0.287667i	−0.727992	+	0.685585i	$0.759546\pi$
$282$	3.33080e6	+	1.58694e6i	2.49417	+	1.18833i
$283$	81487.5	−	47046.9i	0.0604819	−	0.0349192i	−0.469454	−	0.882957i	$-0.655549\pi$
$283$	81487.5	−	47046.9i	0.0604819	−	0.0349192i	0.529936	+	0.848038i	$0.322216\pi$
$284$	−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	$0.183216\pi$
$293$			1.59978e6i			1.08866i	−0.838872	+	0.544329i	$0.816784\pi$
$294$	−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	0.760889	−	0.648881i	$-0.224763\pi$
$307$	−299730.	−	519147.i	−0.181503	−	0.314373i	−0.942393	+	0.334509i	$0.891430\pi$
$308$	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	$0.0999976\pi$
$311$			1.05415e6i			0.618020i	−0.951059	+	0.309010i	$0.900002\pi$
$312$	700827.	+	2.90251e6i	0.407591	+	1.68806i
$313$	45964.5	−	79612.9i	0.0265193	−	0.0459327i	−0.852461	−	0.522791i	$-0.824891\pi$
$313$	45964.5	−	79612.9i	0.0265193	−	0.0459327i	0.878980	+	0.476858i	$0.158224\pi$
$314$	−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	−0.470256	−	0.882530i	$-0.655838\pi$
$317$	−2.62948e6	−	1.51813e6i	−1.46968	−	0.848518i	−0.999421	+	0.0340118i	$0.989172\pi$
$318$	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	−0.628008	−	0.778207i	$-0.716129\pi$
$337$	−558874.	+	322666.i	−0.268064	+	0.154767i	0.359943	+	0.932974i	$0.382796\pi$
$338$	−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	0.307748	−	0.951468i	$-0.400425\pi$
$347$	2.88360e6	−	1.66485e6i	1.28562	−	0.742251i	0.977869	+	0.209217i	$0.0670914\pi$
$348$	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	0.277623	−	0.960690i	$-0.410453\pi$
$359$	3.04857e6	−	1.76009e6i	1.24842	−	0.720774i	0.970794	+	0.239916i	$0.0771200\pi$
$360$	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	0.356379	−	0.934342i	$-0.384011\pi$
$367$	−708529.	−	409070.i	−0.274595	−	0.158538i	−0.630974	+	0.775804i	$0.717345\pi$
$368$	−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	$0.124256\pi$
$373$			2.04495e6i			0.761047i	−0.924771	+	0.380523i	$0.875744\pi$
$374$	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	0.989775	−	0.142636i	$-0.0455579\pi$
$383$	1.06609e6	+	1.84652e6i	0.371361	+	0.643216i	−0.618414	+	0.785852i	$0.712225\pi$
$384$	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	−0.815208	−	0.579168i	$-0.803378\pi$
$389$	280455.	−	485763.i	0.0939700	−	0.162761i	0.909178	+	0.416407i	$0.136711\pi$
$390$	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	−0.998951	−	0.0457967i	$-0.985417\pi$
$397$	−1.69307e6	−	2.93248e6i	−0.539136	−	0.933812i	0.459814	−	0.888015i	$-0.347916\pi$
$398$	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	0.404745	−	0.914429i	$-0.367360\pi$
$401$	4.50495e6	−	2.60094e6i	1.39904	−	0.807734i	0.994292	+	0.106695i	$0.0340268\pi$
$402$	−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	0.480529	−	0.876979i	$-0.340445\pi$
$409$	−130898.	−	75574.2i	−0.0386924	−	0.0223391i	−0.519221	+	0.854640i	$0.673778\pi$
$410$	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	$-0.932373\pi$
$419$		−	1.51552e6i		−	0.421724i	0.977516	−	0.210862i	$-0.0676270\pi$
$420$	−1.32378e6	−	8.31133e6i	−0.366178	−	2.29904i
$421$	−841090.	+	485604.i	−0.231280	+	0.133529i	−0.611162	−	0.791505i	$-0.709298\pi$
$421$	−841090.	+	485604.i	−0.231280	+	0.133529i	0.379883	+	0.925035i	$0.375964\pi$
$422$	−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	−0.849943	−	0.526874i	$-0.823364\pi$
$431$	120766.	−	209172.i	0.0313148	−	0.0542389i	0.881258	+	0.472635i	$0.156697\pi$
$432$	−536099.	+	2.54384e6i	−0.138209	+	0.655815i
$433$	4.10485e6	+	2.36994e6i	1.05215	+	0.607459i	0.923250	−	0.384199i	$-0.125522\pi$
$433$	4.10485e6	+	2.36994e6i	1.05215	+	0.607459i	0.128899	+	0.991658i	$0.458856\pi$
$434$	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	−0.957047	−	0.289932i	$-0.906367\pi$
$439$	−2.94614e6	−	5.10286e6i	−0.729612	−	1.26373i	0.227435	−	0.973793i	$-0.426966\pi$
$440$	−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	0.797713	−	0.603038i	$-0.206043\pi$
$443$	2.78533e6	+	1.60811e6i	0.674323	+	0.389321i	−0.123390	+	0.992358i	$0.539377\pi$
$444$	−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	$0.00151791\pi$
$449$			40741.7i			0.00953724i	−0.999989	+	0.00476862i	$0.998482\pi$
$450$	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	0.803338	−	0.595523i	$-0.203055\pi$
$461$	−520499.	−	901530.i	−0.114069	−	0.197573i	−0.917407	+	0.397950i	$0.869722\pi$
$462$	−3.10520e6	+	245740.i	−0.676838	+	0.0535637i
$463$		−	3.68379e6i		−	0.798624i	−0.916815	−	0.399312i	$-0.869249\pi$
$463$		−	3.68379e6i		−	0.798624i	0.916815	−	0.399312i	$-0.130751\pi$
$464$	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	$0.129745\pi$
$467$			3.73655e6i			0.792827i	−0.918072	+	0.396414i	$0.870255\pi$
$468$	−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	0.877646	−	0.479309i	$-0.159113\pi$
$479$	4.52631e6	+	2.61327e6i	0.901375	+	0.520409i	0.0237292	+	0.999718i	$0.492446\pi$
$480$	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	−0.639666	−	0.768653i	$-0.720928\pi$
$491$	−1.56962e6	+	906223.i	−0.293827	+	0.169641i	0.345839	+	0.938294i	$0.387594\pi$
$492$	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	−0.461951	−	0.886906i	$-0.652850\pi$
$499$	418040.	−	241355.i	0.0751565	−	0.0433916i	0.537107	+	0.843514i	$0.319517\pi$
$500$	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	0.475292	−	0.879828i	$-0.342342\pi$
$503$	−278131.	−	160579.i	−0.0490150	−	0.0282988i	−0.524307	+	0.851529i	$0.675676\pi$
$504$	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	0.380249	−	0.924884i	$-0.375838\pi$
$509$	−1.34789e6	−	778203.i	−0.230600	−	0.133137i	−0.610849	+	0.791747i	$0.709172\pi$
$510$	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	$0.0937160\pi$
$521$			3.59580e6i			0.580365i	−0.956971	+	0.290183i	$0.906284\pi$
$522$	1.11064e6	+	1.40341e7i	0.178400	+	2.25429i
$523$	−127288.	+	220470.i	−0.0203486	+	0.0352448i	−0.876020	−	0.482274i	$-0.839811\pi$
$523$	−127288.	+	220470.i	−0.0203486	+	0.0352448i	0.855672	+	0.517519i	$0.173144\pi$
$524$	−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	−0.278101	−	0.960552i	$-0.589705\pi$
$541$	4.71638e6	−	8.16901e6i	0.692812	−	1.19999i	0.970913	−	0.239434i	$-0.0769618\pi$
$542$	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	−0.460462	−	0.887679i	$-0.652316\pi$
$547$	3.76853e6	−	6.52728e6i	0.538522	−	0.932747i	0.998984	−	0.0450677i	$-0.0143504\pi$
$548$	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	0.172993	+	0.984923i	$0.444656\pi$
$557$	−5.61221e6	+	9.72064e6i	−0.766472	+	1.32757i	−0.939465	+	0.342645i	$0.888677\pi$
$558$	−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	$0.248061\pi$
$569$			1.08551e7i			1.40557i	−0.711401	+	0.702787i	$0.751939\pi$
$570$	−1.56212e7	+	639118.i	−2.01385	+	0.0823937i
$571$			4.38032e6i			0.562232i	0.959674	+	0.281116i	$0.0907046\pi$
$571$			4.38032e6i			0.562232i	−0.959674	+	0.281116i	$0.909295\pi$
$572$	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	0.270429	−	0.962740i	$-0.412835\pi$
$587$	1.03468e7	−	5.97374e6i	1.23940	−	0.715568i	0.968972	+	0.247172i	$0.0795012\pi$
$588$	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	−0.911776	−	0.410687i	$-0.865289\pi$
$593$	−858229.	+	1.48650e6i	−0.100223	+	0.173591i	0.811554	+	0.584278i	$0.198622\pi$
$594$	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	−0.981307	−	0.192448i	$-0.938357\pi$
$599$	−2.84509e6	+	4.92785e6i	−0.323988	+	0.561165i	0.657319	+	0.753613i	$0.271691\pi$
$600$	8.97664e6	−	2.16746e6i	1.01797	−	0.245795i
$601$		−	7.34960e6i		−	0.829999i	−0.909822	−	0.414999i	$-0.863782\pi$
$601$		−	7.34960e6i		−	0.829999i	0.909822	−	0.414999i	$-0.136218\pi$
$602$	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	0.928102	−	0.372325i	$-0.121439\pi$
$613$	1.31747e6	+	2.28192e6i	0.141608	+	0.245273i	−0.786494	+	0.617598i	$0.788106\pi$
$614$	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	−0.696530	−	0.717527i	$-0.745274\pi$
$617$	2.58277e6	−	4.47348e6i	0.273132	−	0.473078i	0.969662	+	0.244449i	$0.0786071\pi$
$618$	−7.10276e6	+	562099.i	−0.748093	+	0.0592027i
$619$			1.03971e7i			1.09065i	0.838226	+	0.545323i	$0.183593\pi$
$619$			1.03971e7i			1.09065i	−0.838226	+	0.545323i	$0.816407\pi$
$620$	−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	−0.226611	−	0.973985i	$-0.572765\pi$
$631$	−1.18361e7	−	6.83359e6i	−1.18341	−	0.683243i	−0.956802	+	0.290742i	$0.906098\pi$
$632$	−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	−0.743697	−	0.668517i	$-0.766929\pi$
$641$	−5.58199e6	+	3.22277e6i	−0.536592	+	0.309802i	0.207105	+	0.978319i	$0.433596\pi$
$642$	8.92354e6	−	706192.i	0.854475	−	0.0676216i
$643$	−3.13969e6	+	1.81270e6i	−0.299474	+	0.172902i	−0.642207	−	0.766531i	$-0.721981\pi$
$643$	−3.13969e6	+	1.81270e6i	−0.299474	+	0.172902i	0.342732	+	0.939433i	$0.388648\pi$
$644$	−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	$0.176010\pi$
$647$			1.11845e7i			1.05040i	−0.850978	+	0.525201i	$0.823990\pi$
$648$	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	−0.227335	−	0.973817i	$-0.573001\pi$
$659$	8.13481e6	−	1.40899e7i	0.729682	−	1.26385i	0.957018	−	0.290030i	$-0.0936653\pi$
$660$	−1.33783e6	−	8.39957e6i	−0.119548	−	0.750580i
$661$	−1.57130e6	−	907190.i	−0.139880	−	0.0807597i	0.428427	−	0.903576i	$-0.359068\pi$
$661$	−1.57130e6	−	907190.i	−0.139880	−	0.0807597i	−0.568307	+	0.822817i	$0.692401\pi$
$662$	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	$-0.754275\pi$
$673$		−	1.63923e7i		−	1.39509i	0.716540	−	0.697546i	$-0.245725\pi$
$674$	−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	$-0.977453\pi$
$677$		−	1.68800e6i		−	0.141547i	0.997492	−	0.0707735i	$-0.0225468\pi$
$678$	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	$-0.890237\pi$
$691$		−	8.48573e6i		−	0.676074i	0.941133	−	0.338037i	$-0.109763\pi$
$692$	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	0.841693	−	0.539957i	$-0.181559\pi$
$701$	−608501.	−	1.05396e6i	−0.0467699	−	0.0810078i	−0.888463	+	0.458949i	$0.848226\pi$
$702$	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	0.374642	+	0.927170i	$0.377766\pi$
$709$	−8.24017e6	+	1.42724e7i	−0.615631	+	1.06631i	−0.990273	+	0.139135i	$0.955568\pi$
$710$	−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	0.00690298	−	0.999976i	$-0.497803\pi$
$719$	1.21480e7	−	7.01364e6i	0.876359	−	0.505966i	0.869456	+	0.494010i	$0.164469\pi$
$720$	−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	−0.828621	−	0.559810i	$-0.810874\pi$
$727$	−1.08038e7	+	6.23755e6i	−0.758122	+	0.437702i	0.0704993	+	0.997512i	$0.477541\pi$
$728$	−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	−0.600081	−	0.799939i	$-0.704865\pi$
$739$	−3.07838e6	+	1.77730e6i	−0.207354	+	0.119716i	0.392727	+	0.919655i	$0.371532\pi$
$740$	−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	0.906408	−	0.422402i	$-0.138813\pi$
$743$	1.31507e6	+	2.27777e6i	0.0873931	+	0.151369i	−0.819015	+	0.573772i	$0.805480\pi$
$744$	−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	−0.810757	−	0.585383i	$-0.800944\pi$
$751$	1.57000e6	−	2.71932e6i	0.101578	−	0.175939i	0.912335	+	0.409445i	$0.134277\pi$
$752$	−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	0.880826	+	0.473439i	$0.156988\pi$
$757$	1.34083e7	+	2.32239e7i	0.850424	+	1.47298i	−0.0304027	+	0.999538i	$0.509679\pi$
$758$	−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	−0.263286	−	0.964718i	$-0.584806\pi$
$769$	1.15420e7	−	1.99914e7i	0.703827	−	1.21906i	0.967113	−	0.254346i	$-0.0818604\pi$
$770$	−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	0.812844	−	0.582481i	$-0.197918\pi$
$773$	1.18754e7	+	6.85624e6i	0.714822	+	0.412703i	−0.0980218	+	0.995184i	$0.531251\pi$
$774$	−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	$0.138726\pi$
$797$			1.51408e7i			0.844310i	−0.906524	+	0.422155i	$0.861274\pi$
$798$	−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	−0.967603	−	0.252476i	$-0.918755\pi$
$811$	−4.96644e6	+	8.60213e6i	−0.265151	+	0.459255i	0.702452	+	0.711731i	$0.252089\pi$
$812$	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	−0.904279	−	0.426942i	$-0.859591\pi$
$821$	−1.59136e6	+	2.75632e6i	−0.0823969	+	0.142716i	0.821882	+	0.569658i	$0.192924\pi$
$822$	−1.04531e7	+	2.19400e7i	−0.539595	+	1.13255i
$823$	8.11005e6	+	4.68234e6i	0.417373	+	0.240970i	0.693953	−	0.720021i	$-0.255868\pi$
$823$	8.11005e6	+	4.68234e6i	0.417373	+	0.240970i	−0.276580	+	0.960991i	$0.589201\pi$
$824$	−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	0.151324	+	0.988484i	$0.451646\pi$
$827$	−1.53488e7	+	2.65850e7i	−0.780391	+	1.35168i	−0.931714	+	0.363192i	$0.881687\pi$
$828$	2.99811e7	+	1.14788e7i	1.51975	+	0.581864i
$829$			829188.i			0.0419051i	0.999780	+	0.0209525i	$0.00666989\pi$
$829$			829188.i			0.0419051i	−0.999780	+	0.0209525i	$0.993330\pi$
$830$	−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	0.538458	−	0.842653i	$-0.319007\pi$
$839$	−9.38993e6	−	1.62638e7i	−0.460530	−	0.797661i	−0.998987	+	0.0449918i	$0.985674\pi$
$840$	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	−0.753502	−	0.657445i	$-0.771637\pi$
$853$	−2.01056e7	−	3.48239e7i	−0.946115	−	1.63872i	−0.192613	−	0.981275i	$-0.561696\pi$
$854$	−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	0.216098	−	0.976372i	$-0.430667\pi$
$857$	2.51495e7	−	1.45201e7i	1.16971	−	0.675332i	0.953612	+	0.301039i	$0.0973336\pi$
$858$	−6.07359e6	+	1.27478e7i	−0.281661	+	0.591175i
$859$	1.43937e6	+	831021.i	0.0665564	+	0.0384263i	0.532909	−	0.846173i	$-0.321099\pi$
$859$	1.43937e6	+	831021.i	0.0665564	+	0.0384263i	−0.466353	+	0.884599i	$0.654432\pi$
$860$	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	−0.600197	−	0.799852i	$-0.704911\pi$
$877$	−4.72862e6	+	2.73007e6i	−0.207604	+	0.119860i	0.392593	+	0.919712i	$0.371578\pi$
$878$	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	0.501714	−	0.865033i	$-0.332703\pi$
$883$	79489.3	+	45893.2i	0.00343089	+	0.00198083i	−0.498284	+	0.867014i	$0.666036\pi$
$884$	−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	−0.482111	−	0.876110i	$-0.660130\pi$
$887$	1.21302e7	−	2.10102e7i	0.517678	−	0.896644i	0.999789	−	0.0205343i	$-0.00653673\pi$
$888$	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	0.956396	−	0.292074i	$-0.0943455\pi$
$907$	5.58073e6	+	9.66610e6i	0.225254	+	0.390151i	−0.731142	+	0.682226i	$0.761012\pi$
$908$	−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	$-0.679661\pi$
$919$		−	4.32636e7i		−	1.68980i	0.534927	−	0.844898i	$-0.320339\pi$
$920$	−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	0.703545	−	0.710651i	$-0.251599\pi$
$929$	−6.93584e6	−	1.20132e7i	−0.263669	−	0.456689i	−0.967214	+	0.253962i	$0.918266\pi$
$930$	−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	−0.602278	−	0.798287i	$-0.705740\pi$
$937$	1.04866e7	−	1.81633e7i	0.390198	−	0.675842i	0.992475	+	0.122444i	$0.0390733\pi$
$938$	−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	−0.963357	−	0.268222i	$-0.913564\pi$
$941$	−4.55607e7	−	2.63045e7i	−1.67732	−	0.968403i	−0.713966	−	0.700181i	$-0.753103\pi$
$942$	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	−0.310471	−	0.950583i	$-0.600487\pi$
$947$	9.86687e6	−	5.69664e6i	0.357523	−	0.206416i	0.667994	+	0.744167i	$0.267153\pi$
$948$	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	−0.695435	−	0.718589i	$-0.744788\pi$
$953$	−1.17990e7	+	6.81217e6i	−0.420837	+	0.242970i	0.274598	+	0.961559i	$0.411455\pi$
$954$	−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	−0.377014	−	0.926208i	$-0.623049\pi$
$967$	6.87983e6	−	3.97207e6i	0.236598	−	0.136600i	0.613612	+	0.789608i	$0.289716\pi$
$968$	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	0.793978	−	0.607947i	$-0.208007\pi$
$971$	−3.80493e6	−	6.59034e6i	−0.129509	−	0.224316i	−0.923486	+	0.383631i	$0.874673\pi$
$972$	−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	$-0.801488\pi$
$977$		−	3.48479e7i		−	1.16799i	0.811756	−	0.583997i	$-0.198512\pi$
$978$	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	−0.923865	−	0.382718i	$-0.874988\pi$
$983$	−2.40360e7	−	4.16316e7i	−0.793376	−	1.37417i	0.130489	−	0.991450i	$-0.458345\pi$
$984$	−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	0.709308	−	0.704899i	$-0.249008\pi$
$991$	−7.90852e6	−	1.36980e7i	−0.255806	−	0.443069i	−0.965114	+	0.261829i	$0.915674\pi$
$992$	−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	0.317503	+	0.948257i	$0.397156\pi$
$997$	−2.07922e7	+	3.60131e7i	−0.662464	+	1.14742i	−0.979966	+	0.199163i	$0.936178\pi$
$998$	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.31.19	yes	96
4.3	odd	2	inner	76.6.f.a.31.4	yes	96
19.8	odd	6	inner	76.6.f.a.27.4	✓	96
76.27	even	6	inner	76.6.f.a.27.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.f.a.27.4	✓	96	19.8	odd	6	inner
76.6.f.a.27.19	yes	96	76.27	even	6	inner
76.6.f.a.31.4	yes	96	4.3	odd	2	inner
76.6.f.a.31.19	yes	96	1.1	even	1	trivial

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more