LMFDB - Embedded newform 48.9.l.a.19.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.17
Character	$\chi$	$=$	48.19
Dual form			48.9.l.a.43.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16854 - 15.9573i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(-253.269 - 37.2934i) q^{4} +(-679.500 + 679.500i) q^{5} +(489.036 + 566.318i) q^{6} +4528.78 q^{7} +(-891.055 + 3997.90i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(1.16854 - 15.9573i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(-253.269 - 37.2934i) q^{4} +(-679.500 + 679.500i) q^{5} +(489.036 + 566.318i) q^{6} +4528.78 q^{7} +(-891.055 + 3997.90i) q^{8} -2187.00i q^{9} +(10048.9 + 11637.0i) q^{10} +(-6530.06 - 6530.06i) q^{11} +(9608.35 - 7141.91i) q^{12} +(-13982.9 - 13982.9i) q^{13} +(5292.05 - 72267.0i) q^{14} -44939.6i q^{15} +(62754.4 + 18890.5i) q^{16} -134692. q^{17} +(-34898.6 - 2555.59i) q^{18} +(35978.2 - 35978.2i) q^{19} +(197437. - 146756. i) q^{20} +(-149758. + 149758. i) q^{21} +(-111833. + 96571.3i) q^{22} +399859. q^{23} +(-102738. - 161669. i) q^{24} -532816. i q^{25} +(-239469. + 206790. i) q^{26} +(72320.0 + 72320.0i) q^{27} +(-1.14700e6 - 168893. i) q^{28} +(-131743. - 131743. i) q^{29} +(-717113. - 52513.6i) q^{30} -1.67872e6i q^{31} +(374772. - 979315. i) q^{32} +431874. q^{33} +(-157393. + 2.14931e6i) q^{34} +(-3.07731e6 + 3.07731e6i) q^{35} +(-81560.6 + 553899. i) q^{36} +(593864. - 593864. i) q^{37} +(-532072. - 616156. i) q^{38} +924778. q^{39} +(-2.11110e6 - 3.32205e6i) q^{40} -2.25170e6i q^{41} +(2.21473e6 + 2.56473e6i) q^{42} +(-3.00751e6 - 3.00751e6i) q^{43} +(1.41033e6 + 1.89739e6i) q^{44} +(1.48607e6 + 1.48607e6i) q^{45} +(467250. - 6.38066e6i) q^{46} -3.59403e6i q^{47} +(-2.69984e6 + 1.45050e6i) q^{48} +1.47450e7 q^{49} +(-8.50229e6 - 622615. i) q^{50} +(4.45400e6 - 4.45400e6i) q^{51} +(3.01997e6 + 4.06291e6i) q^{52} +(2.22191e6 - 2.22191e6i) q^{53} +(1.23854e6 - 1.06952e6i) q^{54} +8.87436e6 q^{55} +(-4.03539e6 + 1.81056e7i) q^{56} +2.37946e6i q^{57} +(-2.25621e6 + 1.94831e6i) q^{58} +(7.26513e6 + 7.26513e6i) q^{59} +(-1.67595e6 + 1.13818e7i) q^{60} +(125460. + 125460. i) q^{61} +(-2.67878e7 - 1.96165e6i) q^{62} -9.90444e6i q^{63} +(-1.51893e7 - 7.12470e6i) q^{64} +1.90028e7 q^{65} +(504661. - 6.89152e6i) q^{66} +(-1.15834e7 + 1.15834e7i) q^{67} +(3.41133e7 + 5.02311e6i) q^{68} +(-1.32226e7 + 1.32226e7i) q^{69} +(4.55095e7 + 5.27014e7i) q^{70} -1.29646e7 q^{71} +(8.74342e6 + 1.94874e6i) q^{72} -1.57187e7i q^{73} +(-8.78250e6 - 1.01704e7i) q^{74} +(1.76192e7 + 1.76192e7i) q^{75} +(-1.04539e7 + 7.77042e6i) q^{76} +(-2.95732e7 - 2.95732e7i) q^{77} +(1.08064e6 - 1.47569e7i) q^{78} +4.27261e7i q^{79} +(-5.54777e7 + 2.98055e7i) q^{80} -4.78297e6 q^{81} +(-3.59310e7 - 2.63120e6i) q^{82} +(3.27225e7 - 3.27225e7i) q^{83} +(4.35141e7 - 3.23441e7i) q^{84} +(9.15231e7 - 9.15231e7i) q^{85} +(-5.15061e7 + 4.44773e7i) q^{86} +8.71299e6 q^{87} +(3.19252e7 - 2.02879e7i) q^{88} -2.14578e7i q^{89} +(2.54501e7 - 2.19770e7i) q^{90} +(-6.33256e7 - 6.33256e7i) q^{91} +(-1.01272e8 - 1.49121e7i) q^{92} +(5.55122e7 + 5.55122e7i) q^{93} +(-5.73509e7 - 4.19976e6i) q^{94} +4.88944e7i q^{95} +(1.99911e7 + 4.47771e7i) q^{96} +1.40855e7 q^{97} +(1.72301e7 - 2.35291e8i) q^{98} +(-1.42812e7 + 1.42812e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.16854	−	15.9573i	0.0730336	−	0.997329i
$2$	1.16854	−	15.9573i	0.0730336	−	0.997329i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$4$	−253.269	−	37.2934i	−0.989332	−	0.145677i
$5$	−679.500	+	679.500i	−1.08720	+	1.08720i	−0.0913845	+	0.995816i	$0.529129\pi$
$5$	−679.500	+	679.500i	−1.08720	+	1.08720i	−0.995816	+	0.0913845i	$0.970871\pi$
$6$	489.036	+	566.318i	0.377342	+	0.436974i
$7$	4528.78			1.88621			0.943103	−	0.332501i	$-0.107892\pi$
$7$	4528.78			1.88621			0.943103	+	0.332501i	$0.107892\pi$
$8$	−891.055	+	3997.90i	−0.217543	+	0.976051i
$9$		−	2187.00i		−	0.333333i
$10$	10048.9	+	11637.0i	1.00489	+	1.16370i
$11$	−6530.06	−	6530.06i	−0.446012	−	0.446012i	0.448014	−	0.894026i	$-0.352131\pi$
$11$	−6530.06	−	6530.06i	−0.446012	−	0.446012i	−0.894026	+	0.448014i	$0.852131\pi$
$12$	9608.35	−	7141.91i	0.463366	−	0.344421i
$13$	−13982.9	−	13982.9i	−0.489581	−	0.489581i	0.418593	−	0.908174i	$-0.362523\pi$
$13$	−13982.9	−	13982.9i	−0.489581	−	0.489581i	−0.908174	+	0.418593i	$0.862523\pi$
$14$	5292.05	−	72267.0i	0.137756	−	1.88117i
$15$		−	44939.6i		−	0.887695i
$16$	62754.4	+	18890.5i	0.957556	+	0.288246i
$17$	−134692.			−1.61267			−0.806335	−	0.591459i	$-0.798552\pi$
$17$	−134692.			−1.61267			−0.806335	+	0.591459i	$0.798552\pi$
$18$	−34898.6	−	2555.59i	−0.332443	−	0.0243445i
$19$	35978.2	−	35978.2i	0.276074	−	0.276074i	−0.555466	−	0.831539i	$-0.687460\pi$
$19$	35978.2	−	35978.2i	0.276074	−	0.276074i	0.831539	+	0.555466i	$0.187460\pi$
$20$	197437.	−	146756.i	1.23398	−	0.917222i
$21$	−149758.	+	149758.i	−0.770040	+	0.770040i
$22$	−111833.	+	96571.3i	−0.477395	+	0.412247i
$23$	399859.			1.42888			0.714440	−	0.699697i	$-0.246682\pi$
$23$	399859.			1.42888			0.714440	+	0.699697i	$0.246682\pi$
$24$	−102738.	−	161669.i	−0.309660	−	0.487282i
$25$		−	532816.i		−	1.36401i
$26$	−239469.	+	206790.i	−0.524029	+	0.452518i
$27$	72320.0	+	72320.0i	0.136083	+	0.136083i
$28$	−1.14700e6	−	168893.i	−1.86608	−	0.274777i
$29$	−131743.	−	131743.i	−0.186267	−	0.186267i	0.607813	−	0.794080i	$-0.292047\pi$
$29$	−131743.	−	131743.i	−0.186267	−	0.186267i	−0.794080	+	0.607813i	$0.792047\pi$
$30$	−717113.	−	52513.6i	−0.885325	−	0.0648316i
$31$		−	1.67872e6i		−	1.81774i	−0.417077	−	0.908871i	$-0.636945\pi$
$31$		−	1.67872e6i		−	1.81774i	0.417077	−	0.908871i	$-0.363055\pi$
$32$	374772.	−	979315.i	0.357410	−	0.933948i
$33$	431874.			0.364167
$34$	−157393.	+	2.14931e6i	−0.117779	+	1.60836i
$35$	−3.07731e6	+	3.07731e6i	−2.05068	+	2.05068i
$36$	−81560.6	+	553899.i	−0.0485591	+	0.329777i
$37$	593864.	−	593864.i	0.316869	−	0.316869i	−0.530694	−	0.847563i	$-0.678069\pi$
$37$	593864.	−	593864.i	0.316869	−	0.316869i	0.847563	+	0.530694i	$0.178069\pi$
$38$	−532072.	−	616156.i	−0.255174	−	0.295499i
$39$	924778.			0.399741
$40$	−2.11110e6	−	3.32205e6i	−0.824650	−	1.29767i
$41$		−	2.25170e6i		−	0.796847i	−0.917201	−	0.398424i	$-0.869557\pi$
$41$		−	2.25170e6i		−	0.796847i	0.917201	−	0.398424i	$-0.130443\pi$
$42$	2.21473e6	+	2.56473e6i	0.711745	+	0.824223i
$43$	−3.00751e6	−	3.00751e6i	−0.879698	−	0.879698i	0.113805	−	0.993503i	$-0.463696\pi$
$43$	−3.00751e6	−	3.00751e6i	−0.879698	−	0.879698i	−0.993503	+	0.113805i	$0.963696\pi$
$44$	1.41033e6	+	1.89739e6i	0.376280	+	0.506228i
$45$	1.48607e6	+	1.48607e6i	0.362400	+	0.362400i
$46$	467250.	−	6.38066e6i	0.104356	−	1.42506i
$47$		−	3.59403e6i		−	0.736529i	−0.929721	−	0.368265i	$-0.879952\pi$
$47$		−	3.59403e6i		−	0.736529i	0.929721	−	0.368265i	$-0.120048\pi$
$48$	−2.69984e6	+	1.45050e6i	−0.508597	+	0.273245i
$49$	1.47450e7			2.55777
$50$	−8.50229e6	−	622615.i	−1.36037	−	0.0996185i
$51$	4.45400e6	−	4.45400e6i	0.658370	−	0.658370i
$52$	3.01997e6	+	4.06291e6i	0.413037	+	0.555679i
$53$	2.22191e6	−	2.22191e6i	0.281593	−	0.281593i	−0.552151	−	0.833744i	$-0.686193\pi$
$53$	2.22191e6	−	2.22191e6i	0.281593	−	0.281593i	0.833744	+	0.552151i	$0.186193\pi$
$54$	1.23854e6	−	1.06952e6i	0.145658	−	0.125781i
$55$	8.87436e6			0.969809
$56$	−4.03539e6	+	1.81056e7i	−0.410330	+	1.84103i
$57$			2.37946e6i			0.225413i
$58$	−2.25621e6	+	1.94831e6i	−0.199373	+	0.172166i
$59$	7.26513e6	+	7.26513e6i	0.599563	+	0.599563i	0.940196	−	0.340633i	$-0.110641\pi$
$59$	7.26513e6	+	7.26513e6i	0.599563	+	0.599563i	−0.340633	+	0.940196i	$0.610641\pi$
$60$	−1.67595e6	+	1.13818e7i	−0.129317	+	0.878225i
$61$	125460.	+	125460.i	0.00906121	+	0.00906121i	0.711623	−	0.702562i	$-0.247960\pi$
$61$	125460.	+	125460.i	0.00906121	+	0.00906121i	−0.702562	+	0.711623i	$0.747960\pi$
$62$	−2.67878e7	−	1.96165e6i	−1.81289	−	0.132756i
$63$		−	9.90444e6i		−	0.628735i
$64$	−1.51893e7	−	7.12470e6i	−0.905350	−	0.424665i
$65$	1.90028e7			1.06455
$66$	504661.	−	6.89152e6i	0.0265965	−	0.363195i
$67$	−1.15834e7	+	1.15834e7i	−0.574828	+	0.574828i	−0.933474	−	0.358646i	$-0.883239\pi$
$67$	−1.15834e7	+	1.15834e7i	−0.574828	+	0.574828i	0.358646	+	0.933474i	$0.383239\pi$
$68$	3.41133e7	+	5.02311e6i	1.59547	+	0.234929i
$69$	−1.32226e7	+	1.32226e7i	−0.583338	+	0.583338i
$70$	4.55095e7	+	5.27014e7i	1.89544	+	2.19498i
$71$	−1.29646e7			−0.510184			−0.255092	−	0.966917i	$-0.582106\pi$
$71$	−1.29646e7			−0.510184			−0.255092	+	0.966917i	$0.582106\pi$
$72$	8.74342e6	+	1.94874e6i	0.325350	+	0.0725142i
$73$		−	1.57187e7i		−	0.553508i	−0.960941	−	0.276754i	$-0.910741\pi$
$73$		−	1.57187e7i		−	0.553508i	0.960941	−	0.276754i	$-0.0892587\pi$
$74$	−8.78250e6	−	1.01704e7i	−0.292881	−	0.339165i
$75$	1.76192e7	+	1.76192e7i	0.556854	+	0.556854i
$76$	−1.04539e7	+	7.77042e6i	−0.313346	+	0.232911i
$77$	−2.95732e7	−	2.95732e7i	−0.841270	−	0.841270i
$78$	1.08064e6	−	1.47569e7i	0.0291945	−	0.398674i
$79$			4.27261e7i			1.09694i	0.836169	+	0.548472i	$0.184790\pi$
$79$			4.27261e7i			1.09694i	−0.836169	+	0.548472i	$0.815210\pi$
$80$	−5.54777e7	+	2.98055e7i	−1.35444	+	0.727674i
$81$	−4.78297e6			−0.111111
$82$	−3.59310e7	−	2.63120e6i	−0.794719	−	0.0581967i
$83$	3.27225e7	−	3.27225e7i	0.689499	−	0.689499i	−0.272622	−	0.962121i	$-0.587891\pi$
$83$	3.27225e7	−	3.27225e7i	0.689499	−	0.689499i	0.962121	+	0.272622i	$0.0878909\pi$
$84$	4.35141e7	−	3.23441e7i	0.874003	−	0.649648i
$85$	9.15231e7	−	9.15231e7i	1.75330	−	1.75330i
$86$	−5.15061e7	+	4.44773e7i	−0.941597	+	0.813102i
$87$	8.71299e6			0.152086
$88$	3.19252e7	−	2.02879e7i	0.532357	−	0.338304i
$89$		−	2.14578e7i		−	0.342000i	−0.985271	−	0.171000i	$-0.945300\pi$
$89$		−	2.14578e7i		−	0.342000i	0.985271	−	0.171000i	$-0.0546998\pi$
$90$	2.54501e7	−	2.19770e7i	0.387900	−	0.334965i
$91$	−6.33256e7	−	6.33256e7i	−0.923451	−	0.923451i
$92$	−1.01272e8	−	1.49121e7i	−1.41364	−	0.208155i
$93$	5.55122e7	+	5.55122e7i	0.742090	+	0.742090i
$94$	−5.73509e7	−	4.19976e6i	−0.734562	−	0.0537914i
$95$			4.88944e7i			0.600295i
$96$	1.99911e7	+	4.47771e7i	0.235370	+	0.527195i
$97$	1.40855e7			0.159106			0.0795528	−	0.996831i	$-0.474651\pi$
$97$	1.40855e7			0.159106			0.0795528	+	0.996831i	$0.474651\pi$
$98$	1.72301e7	−	2.35291e8i	0.186803	−	2.55094i
$99$	−1.42812e7	+	1.42812e7i	−0.148671	+	0.148671i
$100$	−1.98705e7	+	1.34946e8i	−0.198705	+	1.34946i
$101$	−9.76625e7	+	9.76625e7i	−0.938517	+	0.938517i	−0.998216	−	0.0596994i	$-0.980986\pi$
$101$	−9.76625e7	+	9.76625e7i	−0.938517	+	0.938517i	0.0596994	+	0.998216i	$0.480986\pi$
$102$	−6.58691e7	−	7.62784e7i	−0.608529	−	0.704695i
$103$	7.82061e7			0.694851			0.347426	−	0.937708i	$-0.387056\pi$
$103$	7.82061e7			0.694851			0.347426	+	0.937708i	$0.387056\pi$
$104$	6.83619e7	−	4.34428e7i	0.584361	−	0.371351i
$105$		−	2.03521e8i		−	1.67438i
$106$	−3.28592e7	−	3.80520e7i	−0.260276	−	0.301407i
$107$	−8.55663e7	−	8.55663e7i	−0.652781	−	0.652781i	0.300881	−	0.953662i	$-0.402719\pi$
$107$	−8.55663e7	−	8.55663e7i	−0.652781	−	0.652781i	−0.953662	+	0.300881i	$0.902719\pi$
$108$	−1.56194e7	−	2.10135e7i	−0.114807	−	0.154455i
$109$	8.90855e7	+	8.90855e7i	0.631104	+	0.631104i	0.948345	−	0.317241i	$-0.102756\pi$
$109$	8.90855e7	+	8.90855e7i	0.631104	+	0.631104i	−0.317241	+	0.948345i	$0.602756\pi$
$110$	1.03700e7	−	1.41611e8i	0.0708286	−	0.967219i
$111$			3.92759e7i			0.258723i
$112$	2.84201e8	+	8.55509e7i	1.80615	+	0.543692i
$113$	−2.63941e7			−0.161880			−0.0809401	−	0.996719i	$-0.525792\pi$
$113$	−2.63941e7			−0.161880			−0.0809401	+	0.996719i	$0.525792\pi$
$114$	3.79697e7	+	2.78049e6i	0.224811	+	0.0164627i
$115$	−2.71704e8	+	2.71704e8i	−1.55348	+	1.55348i
$116$	2.84533e7	+	3.82796e7i	0.157145	+	0.211415i
$117$	−3.05807e7	+	3.05807e7i	−0.163194	+	0.163194i
$118$	1.24421e8	−	1.07442e8i	0.641751	−	0.554174i
$119$	−6.09990e8			−3.04183
$120$	1.79664e8	+	4.00436e7i	0.866436	+	0.193112i
$121$		−	1.29075e8i		−	0.602147i
$122$	2.14860e6	−	1.85540e6i	0.00969878	−	0.00837524i
$123$	7.44595e7	+	7.44595e7i	0.325312	+	0.325312i
$124$	−6.26052e7	+	4.25169e8i	−0.264804	+	1.79835i
$125$	9.66186e7	+	9.66186e7i	0.395750	+	0.395750i
$126$	−1.58048e8	−	1.15737e7i	−0.627056	−	0.0459188i
$127$		−	7.73414e7i		−	0.297301i	−0.988890	−	0.148651i	$-0.952507\pi$
$127$		−	7.73414e7i		−	0.297301i	0.988890	−	0.148651i	$-0.0474930\pi$
$128$	−1.31440e8	+	2.34054e8i	−0.489652	+	0.871918i
$129$	1.98906e8			0.718271
$130$	2.22055e7	−	3.03233e8i	0.0777476	−	1.06170i
$131$	−1.57521e8	+	1.57521e8i	−0.534875	+	0.534875i	−0.922019	−	0.387144i	$-0.873462\pi$
$131$	−1.57521e8	+	1.57521e8i	−0.534875	+	0.534875i	0.387144	+	0.922019i	$0.373462\pi$
$132$	−1.09380e8	−	1.61060e7i	−0.360282	−	0.0530509i
$133$	1.62937e8	−	1.62937e8i	0.520732	−	0.520732i
$134$	1.71304e8	+	1.98376e8i	0.531311	+	0.615275i
$135$	−9.82828e7			−0.295898
$136$	1.20018e8	−	5.38485e8i	0.350825	−	1.57405i
$137$			2.81803e8i			0.799950i	0.916526	+	0.399975i	$0.130981\pi$
$137$			2.81803e8i			0.799950i	−0.916526	+	0.399975i	$0.869019\pi$
$138$	1.95545e8	+	2.26447e8i	0.539177	+	0.624383i
$139$	−1.50795e8	−	1.50795e8i	−0.403949	−	0.403949i	0.475673	−	0.879622i	$-0.342205\pi$
$139$	−1.50795e8	−	1.50795e8i	−0.403949	−	0.403949i	−0.879622	+	0.475673i	$0.842205\pi$
$140$	8.94150e8	−	6.64623e8i	2.32754	−	1.73007i
$141$	1.18848e8	+	1.18848e8i	0.300687	+	0.300687i
$142$	−1.51497e7	+	2.06880e8i	−0.0372606	+	0.508822i
$143$			1.82619e8i			0.436718i
$144$	4.13135e7	−	1.37244e8i	0.0960821	−	0.319185i
$145$	1.79039e8			0.405019
$146$	−2.50827e8	−	1.83678e7i	−0.552030	−	0.0404247i
$147$	−4.87591e8	+	4.87591e8i	−1.04421	+	1.04421i
$148$	−1.72555e8	+	1.28260e8i	−0.359650	+	0.267328i
$149$	1.04666e8	−	1.04666e8i	0.212354	−	0.212354i	−0.592913	−	0.805267i	$-0.702022\pi$
$149$	1.04666e8	−	1.04666e8i	0.212354	−	0.212354i	0.805267	+	0.592913i	$0.202022\pi$
$150$	3.01743e8	−	2.60566e8i	0.596036	−	0.514698i
$151$	2.37054e8			0.455973			0.227986	−	0.973664i	$-0.426786\pi$
$151$	2.37054e8			0.455973			0.227986	+	0.973664i	$0.426786\pi$
$152$	1.11779e8	+	1.75896e8i	0.209404	+	0.329520i
$153$			2.94571e8i			0.537557i
$154$	−5.06465e8	+	4.37350e8i	−0.900465	+	0.777583i
$155$	1.14069e9	+	1.14069e9i	1.97625	+	1.97625i
$156$	−2.34218e8	−	3.44881e7i	−0.395477	−	0.0582332i
$157$	−8.49005e8	−	8.49005e8i	−1.39737	−	1.39737i	−0.807490	−	0.589881i	$-0.799175\pi$
$157$	−8.49005e8	−	8.49005e8i	−1.39737	−	1.39737i	−0.589881	−	0.807490i	$-0.700825\pi$
$158$	6.81792e8	+	4.99271e7i	1.09402	+	0.0801138i
$159$			1.46949e8i			0.229920i
$160$	4.10787e8	+	9.20102e8i	0.626811	+	1.40396i
$161$	1.81087e9			2.69516
$162$	−5.58908e6	+	7.63231e7i	−0.00811485	+	0.110814i
$163$	4.68634e8	−	4.68634e8i	0.663870	−	0.663870i	−0.292420	−	0.956290i	$-0.594460\pi$
$163$	4.68634e8	−	4.68634e8i	0.663870	−	0.663870i	0.956290	+	0.292420i	$0.0944604\pi$
$164$	−8.39735e7	+	5.70286e8i	−0.116082	+	0.788347i
$165$	−2.93458e8	+	2.93458e8i	−0.395923	+	0.395923i
$166$	−4.83924e8	−	5.60399e8i	−0.637301	−	0.738014i
$167$	−1.03968e9			−1.33670			−0.668348	−	0.743849i	$-0.732998\pi$
$167$	−1.03968e9			−1.33670			−0.668348	+	0.743849i	$0.732998\pi$
$168$	−4.65276e8	−	7.32162e8i	−0.584082	−	0.919115i
$169$		−	4.24686e8i		−	0.520621i
$170$	−1.35351e9	−	1.56741e9i	−1.62056	−	1.87666i
$171$	−7.86843e7	−	7.86843e7i	−0.0920246	−	0.0920246i
$172$	6.49550e8	+	8.73870e8i	0.742162	+	0.998466i
$173$	−1.16331e9	−	1.16331e9i	−1.29871	−	1.29871i	−0.929244	−	0.369467i	$-0.879540\pi$
$173$	−1.16331e9	−	1.16331e9i	−1.29871	−	1.29871i	−0.369467	−	0.929244i	$-0.620460\pi$
$174$	1.01815e7	−	1.39036e8i	0.0111074	−	0.151680i
$175$		−	2.41301e9i		−	2.57280i
$176$	−2.86434e8	−	5.33146e8i	−0.298520	−	0.555643i
$177$	−4.80488e8			−0.489542
$178$	−3.42409e8	−	2.50743e7i	−0.341087	−	0.0249775i
$179$	4.19316e8	−	4.19316e8i	0.408441	−	0.408441i	−0.472754	−	0.881195i	$-0.656740\pi$
$179$	4.19316e8	−	4.19316e8i	0.408441	−	0.408441i	0.881195	+	0.472754i	$0.156740\pi$
$180$	−3.20954e8	−	4.31795e8i	−0.305741	−	0.411327i
$181$	−7.93363e8	+	7.93363e8i	−0.739192	+	0.739192i	−0.972422	−	0.233229i	$-0.925071\pi$
$181$	−7.93363e8	+	7.93363e8i	−0.739192	+	0.739192i	0.233229	+	0.972422i	$0.425071\pi$
$182$	−1.08450e9	+	9.36505e8i	−0.988427	+	0.853542i
$183$	−8.29745e6			−0.00739844
$184$	−3.56296e8	+	1.59860e9i	−0.310842	+	1.39466i
$185$			8.07061e8i			0.689001i
$186$	9.50692e8	−	8.20955e8i	0.794306	−	0.685911i
$187$	8.79546e8	+	8.79546e8i	0.719270	+	0.719270i
$188$	−1.34033e8	+	9.10256e8i	−0.107295	+	0.728672i
$189$	3.27521e8	+	3.27521e8i	0.256680	+	0.256680i
$190$	7.80221e8	+	5.71349e7i	0.598692	+	0.0438417i
$191$		−	1.91391e8i		−	0.143810i	−0.997411	−	0.0719049i	$-0.977092\pi$
$191$		−	1.91391e8i		−	0.143810i	0.997411	−	0.0719049i	$-0.0229078\pi$
$192$	7.37881e8	−	2.66680e8i	0.542977	−	0.196239i
$193$	1.11633e9			0.804572			0.402286	−	0.915514i	$-0.368216\pi$
$193$	1.11633e9			0.804572			0.402286	+	0.915514i	$0.368216\pi$
$194$	1.64595e7	−	2.24766e8i	0.0116201	−	0.158681i
$195$	−6.28387e8	+	6.28387e8i	−0.434599	+	0.434599i
$196$	−3.73446e9	−	5.49892e8i	−2.53049	−	0.372609i
$197$	6.68856e8	−	6.68856e8i	0.444087	−	0.444087i	−0.449296	−	0.893383i	$-0.648325\pi$
$197$	6.68856e8	−	6.68856e8i	0.444087	−	0.444087i	0.893383	+	0.449296i	$0.148325\pi$
$198$	2.11202e8	+	2.44578e8i	0.137416	+	0.159132i
$199$	−1.96657e9			−1.25400			−0.627000	−	0.779020i	$-0.715717\pi$
$199$	−1.96657e9			−1.25400			−0.627000	+	0.779020i	$0.715717\pi$
$200$	2.13015e9	+	4.74768e8i	1.33134	+	0.296730i
$201$		−	7.66084e8i		−	0.469345i
$202$	1.44430e9	+	1.67255e9i	0.867467	+	1.00455i
$203$	−5.96635e8	−	5.96635e8i	−0.351338	−	0.351338i
$204$	−1.29417e9	+	9.61957e8i	−0.747256	+	0.555437i
$205$	1.53003e9	+	1.53003e9i	0.866333	+	0.866333i
$206$	9.13868e7	−	1.24796e9i	0.0507475	−	0.692995i
$207$		−	8.74492e8i		−	0.476293i
$208$	−6.13346e8	−	1.14163e9i	−0.327682	−	0.609921i
$209$	−4.69880e8			−0.246264
$210$	−3.24765e9	−	2.37822e8i	−1.66990	−	0.122286i
$211$	−1.09422e8	+	1.09422e8i	−0.0552047	+	0.0552047i	−0.734170	−	0.678965i	$-0.762429\pi$
$211$	−1.09422e8	+	1.09422e8i	−0.0552047	+	0.0552047i	0.678965	+	0.734170i	$0.262429\pi$
$212$	−6.45603e8	+	4.79878e8i	−0.319611	+	0.237568i
$213$	4.28716e8	−	4.28716e8i	0.208282	−	0.208282i
$214$	−1.46539e9	+	1.26542e9i	−0.698713	+	0.603363i
$215$	4.08721e9			1.91282
$216$	−3.53569e8	+	2.24687e8i	−0.162427	+	0.103220i
$217$		−	7.60257e9i		−	3.42864i
$218$	1.52566e9	−	1.31746e9i	0.675511	−	0.583327i
$219$	5.19786e8	+	5.19786e8i	0.225969	+	0.225969i
$220$	−2.24760e9	−	3.30954e8i	−0.959463	−	0.141279i
$221$	1.88339e9	+	1.88339e9i	0.789533	+	0.789533i
$222$	6.26737e8	+	4.58954e7i	0.258032	+	0.0188955i
$223$			1.81189e8i			0.0732678i	0.999329	+	0.0366339i	$0.0116635\pi$
$223$			1.81189e8i			0.0732678i	−0.999329	+	0.0366339i	$0.988336\pi$
$224$	1.69726e9	−	4.43510e9i	0.674149	−	1.76162i
$225$	−1.16527e9			−0.454669
$226$	−3.08425e7	+	4.21178e8i	−0.0118227	+	0.161448i
$227$	1.88422e9	−	1.88422e9i	0.709626	−	0.709626i	−0.256831	−	0.966456i	$-0.582678\pi$
$227$	1.88422e9	−	1.88422e9i	0.709626	−	0.709626i	0.966456	+	0.256831i	$0.0826783\pi$
$228$	8.87381e7	−	6.02644e8i	0.0328376	−	0.223009i
$229$	−1.01805e9	+	1.01805e9i	−0.370194	+	0.370194i	−0.867548	−	0.497354i	$-0.834305\pi$
$229$	−1.01805e9	+	1.01805e9i	−0.370194	+	0.370194i	0.497354	+	0.867548i	$0.334305\pi$
$230$	4.01816e9	+	4.65316e9i	1.43587	+	1.66279i
$231$	1.95586e9			0.686894
$232$	6.44086e8	−	4.09306e8i	0.222327	−	0.141285i
$233$			4.09434e9i			1.38919i	0.719403	+	0.694593i	$0.244416\pi$
$233$			4.09434e9i			1.38919i	−0.719403	+	0.694593i	$0.755584\pi$
$234$	4.52249e8	+	5.23718e8i	0.150839	+	0.174676i
$235$	2.44214e9	+	2.44214e9i	0.800755	+	0.800755i
$236$	−1.56909e9	−	2.11097e9i	−0.505825	−	0.680510i
$237$	−1.41287e9	−	1.41287e9i	−0.447826	−	0.447826i
$238$	−7.12796e8	+	9.73377e9i	−0.222156	+	3.03370i
$239$		−	6.32400e9i		−	1.93821i	−0.246651	−	0.969104i	$-0.579330\pi$
$239$		−	6.32400e9i		−	1.93821i	0.246651	−	0.969104i	$-0.420670\pi$
$240$	8.48931e8	−	2.82016e9i	0.255875	−	0.850018i
$241$	2.18720e9			0.648366			0.324183	−	0.945994i	$-0.394911\pi$
$241$	2.18720e9			0.648366			0.324183	+	0.945994i	$0.394911\pi$
$242$	−2.05969e9	−	1.50830e8i	−0.600539	−	0.0439769i
$243$	1.58164e8	−	1.58164e8i	0.0453609	−	0.0453609i
$244$	−2.70963e7	−	3.64540e7i	−0.00764453	−	0.0102846i
$245$	−1.00193e10	+	1.00193e10i	−2.78081	+	2.78081i
$246$	1.27518e9	−	1.10116e9i	0.348202	−	0.300684i
$247$	−1.00616e9			−0.270321
$248$	6.71138e9	+	1.49583e9i	1.77421	+	0.395436i
$249$			2.16414e9i			0.562974i
$250$	1.65467e9	−	1.42887e9i	0.423596	−	0.365790i
$251$	2.31977e9	+	2.31977e9i	0.584453	+	0.584453i	0.936124	−	0.351671i	$-0.114386\pi$
$251$	2.31977e9	+	2.31977e9i	0.584453	+	0.584453i	−0.351671	+	0.936124i	$0.614386\pi$
$252$	−3.69370e8	+	2.50849e9i	−0.0915924	+	0.622028i
$253$	−2.61110e9	−	2.61110e9i	−0.637297	−	0.637297i
$254$	−1.23416e9	−	9.03763e7i	−0.296507	−	0.0217130i
$255$			6.05299e9i			1.43156i
$256$	3.58127e9	+	2.37092e9i	0.833828	+	0.552024i
$257$	−3.33907e9			−0.765408			−0.382704	−	0.923871i	$-0.625007\pi$
$257$	−3.33907e9			−0.765408			−0.382704	+	0.923871i	$0.625007\pi$
$258$	2.32429e8	−	3.17399e9i	0.0524579	−	0.716353i
$259$	2.68948e9	−	2.68948e9i	0.597681	−	0.597681i
$260$	−4.81282e9	−	7.08678e8i	−1.05319	−	0.155080i
$261$	−2.88122e8	+	2.88122e8i	−0.0620890	+	0.0620890i
$262$	2.32953e9	+	2.69767e9i	0.494383	+	0.572510i
$263$	−5.41361e8			−0.113152			−0.0565762	−	0.998398i	$-0.518018\pi$
$263$	−5.41361e8			−0.113152			−0.0565762	+	0.998398i	$0.518018\pi$
$264$	−3.84823e8	+	1.72659e9i	−0.0792219	+	0.355446i
$265$			3.01957e9i			0.612297i
$266$	−2.40964e9	−	2.79043e9i	−0.481310	−	0.557372i
$267$	7.09571e8	+	7.09571e8i	0.139621	+	0.139621i
$268$	3.36571e9	−	2.50174e9i	0.652435	−	0.484957i
$269$	1.13278e9	+	1.13278e9i	0.216340	+	0.216340i	0.806954	−	0.590614i	$-0.201115\pi$
$269$	1.13278e9	+	1.13278e9i	0.216340	+	0.216340i	−0.590614	+	0.806954i	$0.701115\pi$
$270$	−1.14847e8	+	1.56833e9i	−0.0216105	+	0.295108i
$271$		−	2.84915e9i		−	0.528248i	−0.964489	−	0.264124i	$-0.914917\pi$
$271$		−	2.84915e9i		−	0.528248i	0.964489	−	0.264124i	$-0.0850827\pi$
$272$	−8.45251e9	−	2.54440e9i	−1.54422	−	0.464846i
$273$	4.18812e9			0.753994
$274$	4.49680e9	+	3.29297e8i	0.797814	+	0.0584233i
$275$	−3.47932e9	+	3.47932e9i	−0.608364	+	0.608364i
$276$	3.84199e9	−	2.85576e9i	0.662094	−	0.492136i
$277$	−1.96988e9	+	1.96988e9i	−0.334596	+	0.334596i	−0.854329	−	0.519733i	$-0.826031\pi$
$277$	−1.96988e9	+	1.96988e9i	−0.334596	+	0.334596i	0.519733	+	0.854329i	$0.326031\pi$
$278$	−2.58248e9	+	2.23006e9i	−0.432372	+	0.373368i
$279$	−3.67137e9			−0.605914
$280$	−9.56073e9	−	1.50448e10i	−1.55546	−	2.44768i
$281$		−	3.45382e9i		−	0.553955i	−0.960876	−	0.276978i	$-0.910667\pi$
$281$		−	3.45382e9i		−	0.553955i	0.960876	−	0.276978i	$-0.0893328\pi$
$282$	2.03536e9	−	1.75761e9i	0.321844	−	0.277924i
$283$	2.97629e9	+	2.97629e9i	0.464013	+	0.464013i	0.899968	−	0.435955i	$-0.143589\pi$
$283$	2.97629e9	+	2.97629e9i	0.464013	+	0.464013i	−0.435955	+	0.899968i	$0.643589\pi$
$284$	3.28354e9	+	4.83495e8i	0.504741	+	0.0743221i
$285$	−1.61684e9	−	1.61684e9i	−0.245069	−	0.245069i
$286$	2.91410e9	+	2.13397e8i	0.435552	+	0.0318951i
$287$		−	1.01975e10i		−	1.50302i
$288$	−2.14176e9	−	8.19626e8i	−0.311316	−	0.119137i
$289$	1.11661e10			1.60071
$290$	2.09214e8	−	2.85697e9i	0.0295800	−	0.403937i
$291$	−4.65781e8	+	4.65781e8i	−0.0649546	+	0.0649546i
$292$	−5.86201e8	+	3.98105e9i	−0.0806335	+	0.547603i
$293$	−3.80962e9	+	3.80962e9i	−0.516905	+	0.516905i	−0.916634	−	0.399729i	$-0.869104\pi$
$293$	−3.80962e9	+	3.80962e9i	−0.516905	+	0.516905i	0.399729	+	0.916634i	$0.369104\pi$
$294$	7.21085e9	+	8.35039e9i	0.965155	+	1.11768i
$295$	−9.87331e9			−1.30369
$296$	1.84505e9	+	2.90338e9i	0.240348	+	0.378213i
$297$		−	9.44508e8i		−	0.121389i
$298$	−1.54787e9	−	1.79249e9i	−0.196278	−	0.227295i
$299$	−5.59120e9	−	5.59120e9i	−0.699552	−	0.699552i
$300$	−3.80532e9	−	5.11948e9i	−0.469793	−	0.632035i
$301$	−1.36204e10	−	1.36204e10i	−1.65929	−	1.65929i
$302$	2.77006e8	−	3.78273e9i	0.0333013	−	0.454755i
$303$		−	6.45903e9i		−	0.766296i
$304$	2.93744e9	−	1.57814e9i	0.343933	−	0.184779i
$305$	−1.70500e8			−0.0197027
$306$	4.70055e9	+	3.44217e8i	0.536121	+	0.0392597i
$307$	−7.99570e9	+	7.99570e9i	−0.900125	+	0.900125i	−0.995447	−	0.0953214i	$-0.969612\pi$
$307$	−7.99570e9	+	7.99570e9i	−0.900125	+	0.900125i	0.0953214	+	0.995447i	$0.469612\pi$
$308$	6.38710e9	+	8.59286e9i	0.709742	+	0.954850i
$309$	−2.58613e9	+	2.58613e9i	−0.283672	+	0.283672i
$310$	1.95353e10	−	1.68694e10i	2.11530	−	1.82664i
$311$	3.23854e9			0.346184			0.173092	−	0.984906i	$-0.444624\pi$
$311$	3.23854e9			0.346184			0.173092	+	0.984906i	$0.444624\pi$
$312$	−8.24027e8	+	3.69717e9i	−0.0869608	+	0.390168i
$313$			9.69251e9i			1.00985i	0.863162	+	0.504927i	$0.168481\pi$
$313$			9.69251e9i			1.00985i	−0.863162	+	0.504927i	$0.831519\pi$
$314$	−1.45399e10	+	1.25557e10i	−1.49569	+	1.29158i
$315$	6.73007e9	+	6.73007e9i	0.683561	+	0.683561i
$316$	1.59340e9	−	1.08212e10i	0.159800	−	1.08524i
$317$	1.75318e9	+	1.75318e9i	0.173616	+	0.173616i	0.788566	−	0.614950i	$-0.210824\pi$
$317$	1.75318e9	+	1.75318e9i	0.173616	+	0.173616i	−0.614950	+	0.788566i	$0.710824\pi$
$318$	2.34490e9	+	1.71715e8i	0.229306	+	0.0167919i
$319$			1.72058e9i			0.166155i
$320$	1.51623e10	−	5.47987e9i	1.44599	−	0.522601i
$321$	5.65903e9			0.532993
$322$	2.11607e9	−	2.88966e10i	0.196837	−	2.68796i
$323$	−4.84597e9	+	4.84597e9i	−0.445216	+	0.445216i
$324$	1.21138e9	+	1.78373e8i	0.109926	+	0.0161864i
$325$	−7.45032e9	+	7.45032e9i	−0.667793	+	0.667793i
$326$	−6.93050e9	−	8.02573e9i	−0.613613	−	0.710582i
$327$	−5.89178e9			−0.515295
$328$	9.00208e9	+	2.00639e9i	0.777764	+	0.173348i
$329$		−	1.62766e10i		−	1.38925i
$330$	4.33987e9	+	5.02571e9i	0.365950	+	0.423781i
$331$	1.39679e9	+	1.39679e9i	0.116364	+	0.116364i	0.762891	−	0.646527i	$-0.223779\pi$
$331$	1.39679e9	+	1.39679e9i	0.116364	+	0.116364i	−0.646527	+	0.762891i	$0.723779\pi$
$332$	−9.50792e9	+	7.06726e9i	−0.782588	+	0.581699i
$333$	−1.29878e9	−	1.29878e9i	−0.105623	−	0.105623i
$334$	−1.21490e9	+	1.65904e10i	−0.0976237	+	1.33313i
$335$		−	1.57419e10i		−	1.24991i
$336$	−1.22270e10	+	6.56898e9i	−0.959318	+	0.515396i
$337$	−1.69439e10			−1.31369			−0.656846	−	0.754025i	$-0.728110\pi$
$337$	−1.69439e10			−1.31369			−0.656846	+	0.754025i	$0.728110\pi$
$338$	−6.77684e9	−	4.96262e8i	−0.519231	−	0.0380228i
$339$	8.72804e8	−	8.72804e8i	0.0660873	−	0.0660873i
$340$	−2.65932e10	+	1.97668e10i	−1.99001	+	1.47918i
$341$	−1.09622e10	+	1.09622e10i	−0.810735	+	0.810735i
$342$	−1.34753e9	+	1.16364e9i	−0.0984997	+	0.0850579i
$343$	4.06696e10			2.93828
$344$	1.47036e10	−	9.34389e9i	1.05000	−	0.667259i
$345$		−	1.79695e10i		−	1.26841i
$346$	−1.99227e10	+	1.72039e10i	−1.39009	+	1.20039i
$347$	1.36709e10	+	1.36709e10i	0.942927	+	0.942927i	0.998457	−	0.0555300i	$-0.0176849\pi$
$347$	1.36709e10	+	1.36709e10i	0.942927	+	0.942927i	−0.0555300	+	0.998457i	$0.517685\pi$
$348$	−2.20673e9	−	3.24937e8i	−0.150464	−	0.0221555i
$349$	1.59935e10	+	1.59935e10i	1.07806	+	1.07806i	0.996683	+	0.0813758i	$0.0259314\pi$
$349$	1.59935e10	+	1.59935e10i	1.07806	+	1.07806i	0.0813758	+	0.996683i	$0.474069\pi$
$350$	−3.85050e10	−	2.81969e9i	−2.56593	−	0.187901i
$351$		−	2.02249e9i		−	0.133247i
$352$	−8.84227e9	+	3.94770e9i	−0.575961	+	0.257143i
$353$	4.92936e9			0.317462			0.158731	−	0.987322i	$-0.449260\pi$
$353$	4.92936e9			0.317462			0.158731	+	0.987322i	$0.449260\pi$
$354$	−5.61468e8	+	7.66728e9i	−0.0357530	+	0.488234i
$355$	8.80947e9	−	8.80947e9i	0.554672	−	0.554672i
$356$	−8.00235e8	+	5.43461e9i	−0.0498216	+	0.338352i
$357$	2.01712e10	−	2.01712e10i	1.24182	−	1.24182i
$358$	−6.20115e9	−	7.18113e9i	−0.377520	−	0.437180i
$359$	−1.05396e10			−0.634522			−0.317261	−	0.948338i	$-0.602763\pi$
$359$	−1.05396e10			−0.634522			−0.317261	+	0.948338i	$0.602763\pi$
$360$	−7.26532e9	+	4.61699e9i	−0.432558	+	0.274883i
$361$			1.43947e10i			0.847567i
$362$	1.17328e10	+	1.35870e10i	0.683232	+	0.791204i
$363$	4.26828e9	+	4.26828e9i	0.245825	+	0.245825i
$364$	1.36768e10	+	1.84000e10i	0.779074	+	1.04813i
$365$	1.06808e10	+	1.06808e10i	0.601774	+	0.601774i
$366$	−9.69589e6	+	1.32405e8i	−0.000540335	+	0.00737869i
$367$			3.44978e10i			1.90163i	0.309752	+	0.950817i	$0.399754\pi$
$367$			3.44978e10i			1.90163i	−0.309752	+	0.950817i	$0.600246\pi$
$368$	2.50929e10	+	7.55354e9i	1.36823	+	0.411869i
$369$	−4.92447e9			−0.265616
$370$	1.28785e10	+	9.43082e8i	0.687161	+	0.0503202i
$371$	1.00625e10	−	1.00625e10i	0.531143	−	0.531143i
$372$	−1.19893e10	−	1.61298e10i	−0.626068	−	0.842279i
$373$	1.88457e10	−	1.88457e10i	0.973593	−	0.973593i	−0.0260668	−	0.999660i	$-0.508298\pi$
$373$	1.88457e10	−	1.88457e10i	0.973593	−	0.973593i	0.999660	+	0.0260668i	$0.00829825\pi$
$374$	1.50629e10	−	1.30074e10i	0.769880	−	0.664819i
$375$	−6.38999e9			−0.323128
$376$	1.43686e10	+	3.20247e9i	0.718890	+	0.160226i
$377$			3.68431e9i			0.182386i
$378$	5.60907e9	−	4.84362e9i	0.274741	−	0.237248i
$379$	−3.59198e9	−	3.59198e9i	−0.174091	−	0.174091i	0.614683	−	0.788774i	$-0.289284\pi$
$379$	−3.59198e9	−	3.59198e9i	−0.174091	−	0.174091i	−0.788774	+	0.614683i	$0.789284\pi$
$380$	1.82344e9	−	1.23834e10i	0.0874492	−	0.593891i
$381$	2.55753e9	+	2.55753e9i	0.121373	+	0.121373i
$382$	−3.05408e9	−	2.23648e8i	−0.143426	−	0.0105029i
$383$		−	5.50805e9i		−	0.255978i	−0.991776	−	0.127989i	$-0.959148\pi$
$383$		−	5.50805e9i		−	0.255978i	0.991776	−	0.127989i	$-0.0408522\pi$
$384$	−3.39324e9	−	1.20862e10i	−0.156059	−	0.555859i
$385$	4.01900e10			1.82926
$386$	1.30448e9	−	1.78136e10i	0.0587608	−	0.802423i
$387$	−6.57743e9	+	6.57743e9i	−0.293233	+	0.293233i
$388$	−3.56742e9	−	5.25296e8i	−0.157408	−	0.0231781i
$389$	2.55695e10	−	2.55695e10i	1.11667	−	1.11667i	0.124442	−	0.992227i	$-0.460286\pi$
$389$	2.55695e10	−	2.55695e10i	1.11667	−	1.11667i	0.992227	−	0.124442i	$-0.0397142\pi$
$390$	9.29304e9	+	1.07616e10i	0.401698	+	0.465178i
$391$	−5.38578e10			−2.30431
$392$	−1.31386e10	+	5.89493e10i	−0.556425	+	2.49652i
$393$		−	1.04178e10i		−	0.436724i
$394$	−9.89154e9	−	1.14547e10i	−0.410468	−	0.475334i
$395$	−2.90324e10	−	2.90324e10i	−1.19260	−	1.19260i
$396$	4.14959e9	−	3.08440e9i	0.168743	−	0.125427i
$397$	−2.52825e10	−	2.52825e10i	−1.01779	−	1.01779i	−0.999839	−	0.0179511i	$-0.994286\pi$
$397$	−2.52825e10	−	2.52825e10i	−1.01779	−	1.01779i	−0.0179511	−	0.999839i	$-0.505714\pi$
$398$	−2.29801e9	+	3.13811e10i	−0.0915841	+	1.25065i
$399$			1.07761e10i			0.425176i
$400$	1.00652e10	−	3.34365e10i	0.393170	−	1.30611i
$401$	−2.32288e9			−0.0898357			−0.0449178	−	0.998991i	$-0.514303\pi$
$401$	−2.32288e9			−0.0898357			−0.0449178	+	0.998991i	$0.514303\pi$
$402$	−1.22246e10	−	8.95199e8i	−0.468092	−	0.0342780i
$403$	−2.34735e10	+	2.34735e10i	−0.889932	+	0.889932i
$404$	2.83770e10	−	2.10927e10i	1.06523	−	0.791785i
$405$	3.25003e9	−	3.25003e9i	0.120800	−	0.120800i
$406$	−1.02179e10	+	8.82348e9i	−0.376059	+	0.324740i
$407$	−7.75594e9			−0.282655
$408$	1.38379e10	+	2.17754e10i	0.499379	+	0.785826i
$409$		−	2.24234e10i		−	0.801325i	−0.916226	−	0.400662i	$-0.868780\pi$
$409$		−	2.24234e10i		−	0.801325i	0.916226	−	0.400662i	$-0.131220\pi$
$410$	2.62030e10	−	2.26272e10i	0.927291	−	0.800748i
$411$	−9.31868e9	−	9.31868e9i	−0.326578	−	0.326578i
$412$	−1.98072e10	−	2.91657e9i	−0.687438	−	0.101224i
$413$	3.29022e10	+	3.29022e10i	1.13090	+	1.13090i
$414$	−1.39545e10	−	1.02188e9i	−0.475021	−	0.0347854i
$415$			4.44698e10i			1.49925i
$416$	−1.89341e10	+	8.45328e9i	−0.632224	+	0.282262i
$417$	9.97298e9			0.329823
$418$	−5.49072e8	+	7.49800e9i	−0.0179856	+	0.245607i
$419$	4.22200e10	−	4.22200e10i	1.36981	−	1.36981i	0.509118	−	0.860697i	$-0.329972\pi$
$419$	4.22200e10	−	4.22200e10i	1.36981	−	1.36981i	0.860697	−	0.509118i	$-0.170028\pi$
$420$	−7.59000e9	+	5.15457e10i	−0.243918	+	1.65651i
$421$	3.19372e10	−	3.19372e10i	1.01664	−	1.01664i	0.0167832	−	0.999859i	$-0.494657\pi$
$421$	3.19372e10	−	3.19372e10i	1.01664	−	1.01664i	0.999859	−	0.0167832i	$-0.00534252\pi$
$422$	1.61822e9	+	1.87395e9i	0.0510255	+	0.0590891i
$423$	−7.86014e9			−0.245510
$424$	6.90313e9	+	1.08628e10i	0.213591	+	0.336108i
$425$			7.17659e10i			2.19970i
$426$	−6.34017e9	−	7.34211e9i	−0.192514	−	0.222937i
$427$	5.68181e8	+	5.68181e8i	0.0170913	+	0.0170913i
$428$	1.84802e10	+	2.48623e10i	0.550722	+	0.740912i
$429$	−6.03886e9	−	6.03886e9i	−0.178289	−	0.178289i
$430$	4.77606e9	−	6.52208e10i	0.139700	−	1.90771i
$431$		−	3.79508e10i		−	1.09980i	−0.835232	−	0.549898i	$-0.814667\pi$
$431$		−	3.79508e10i		−	1.09980i	0.835232	−	0.549898i	$-0.185333\pi$
$432$	3.17224e9	+	5.90456e9i	0.0910816	+	0.169532i
$433$	−1.04555e10			−0.297435			−0.148718	−	0.988880i	$-0.547515\pi$
$433$	−1.04555e10			−0.297435			−0.148718	+	0.988880i	$0.547515\pi$
$434$	−1.21316e11	−	8.88389e9i	−3.41948	−	0.250406i
$435$	−5.92048e9	+	5.92048e9i	−0.165348	+	0.165348i
$436$	−1.92403e10	−	2.58849e10i	−0.532434	−	0.716309i
$437$	1.43862e10	−	1.43862e10i	0.394476	−	0.394476i
$438$	8.90176e9	−	7.68698e9i	0.241869	−	0.208862i
$439$	−6.47565e10			−1.74351			−0.871756	−	0.489940i	$-0.837019\pi$
$439$	−6.47565e10			−1.74351			−0.871756	+	0.489940i	$0.837019\pi$
$440$	−7.90754e9	+	3.54788e10i	−0.210975	+	0.946583i
$441$		−	3.22474e10i		−	0.852591i
$442$	3.22545e10	−	2.78529e10i	0.845087	−	0.729762i
$443$	−8.20950e9	−	8.20950e9i	−0.213158	−	0.213158i	0.592449	−	0.805608i	$-0.298161\pi$
$443$	−8.20950e9	−	8.20950e9i	−0.213158	−	0.213158i	−0.805608	+	0.592449i	$0.798161\pi$
$444$	1.46473e9	−	9.94738e9i	0.0376900	−	0.255963i
$445$	1.45806e10	+	1.45806e10i	0.371822	+	0.371822i
$446$	2.89129e9	+	2.11726e8i	0.0730721	+	0.00535101i
$447$			6.92220e9i			0.173386i
$448$	−6.87888e10	−	3.22662e10i	−1.70768	−	0.801006i
$449$	−4.96997e9			−0.122284			−0.0611418	−	0.998129i	$-0.519474\pi$
$449$	−4.96997e9			−0.122284			−0.0611418	+	0.998129i	$0.519474\pi$
$450$	−1.36166e9	+	1.85945e10i	−0.0332062	+	0.453455i
$451$	−1.47037e10	+	1.47037e10i	−0.355404	+	0.355404i
$452$	6.68482e9	+	9.84326e8i	0.160153	+	0.0235822i
$453$	−7.83892e9	+	7.83892e9i	−0.186150	+	0.186150i
$454$	−2.78653e10	−	3.22689e10i	−0.655904	−	0.759557i
$455$	8.60595e10			2.00795
$456$	−9.51286e9	−	2.12023e9i	−0.220015	−	0.0490370i
$457$			5.55054e8i			0.0127254i	0.999980	+	0.00636268i	$0.00202532\pi$
$457$			5.55054e8i			0.0127254i	−0.999980	+	0.00636268i	$0.997975\pi$
$458$	1.50557e10	+	1.74350e10i	0.342169	+	0.396242i
$459$	−9.74091e9	−	9.74091e9i	−0.219457	−	0.219457i
$460$	7.89470e10	−	5.86815e10i	1.76321	−	1.31060i
$461$	−5.53113e10	−	5.53113e10i	−1.22465	−	1.22465i	−0.965962	−	0.258684i	$-0.916711\pi$
$461$	−5.53113e10	−	5.53113e10i	−1.22465	−	1.22465i	−0.258684	−	0.965962i	$-0.583289\pi$
$462$	2.28550e9	−	3.12102e10i	0.0501664	−	0.685060i
$463$			6.27724e10i			1.36598i	0.730427	+	0.682990i	$0.239321\pi$
$463$			6.27724e10i			1.36598i	−0.730427	+	0.682990i	$0.760679\pi$
$464$	−5.77877e9	−	1.07562e10i	−0.124670	−	0.232052i
$465$	−7.54411e10			−1.61360
$466$	6.53346e10	+	4.78440e9i	1.38548	+	0.101457i
$467$	−6.37319e8	+	6.37319e8i	−0.0133995	+	0.0133995i	−0.713775	−	0.700375i	$-0.753016\pi$
$467$	−6.37319e8	+	6.37319e8i	−0.0133995	+	0.0133995i	0.700375	+	0.713775i	$0.253016\pi$
$468$	8.88559e9	−	6.60468e9i	0.185226	−	0.137679i
$469$	−5.24588e10	+	5.24588e10i	−1.08424	+	1.08424i
$470$	4.18237e10	−	3.61162e10i	0.857098	−	0.740134i
$471$	5.61500e10			1.14095
$472$	−3.55189e10	+	2.25717e10i	−0.715635	+	0.454774i
$473$			3.92785e10i			0.784712i
$474$	−2.41966e10	+	2.08946e10i	−0.479336	+	0.413924i
$475$	−1.91698e10	−	1.91698e10i	−0.376567	−	0.376567i
$476$	1.54492e11	+	2.27486e10i	3.00938	+	0.443125i
$477$	−4.85931e9	−	4.85931e9i	−0.0938645	−	0.0938645i
$478$	−1.00914e11	−	7.38984e9i	−1.93303	−	0.141554i
$479$			1.29246e9i			0.0245513i	0.999925	+	0.0122756i	$0.00390755\pi$
$479$			1.29246e9i			0.0245513i	−0.999925	+	0.0122756i	$0.996092\pi$
$480$	−4.40100e10	−	1.68421e10i	−0.829061	−	0.317271i
$481$	−1.66079e10			−0.310266
$482$	2.55583e9	−	3.49017e10i	0.0473525	−	0.646635i
$483$	−5.98822e10	+	5.98822e10i	−1.10029	+	1.10029i
$484$	−4.81366e9	+	3.26908e10i	−0.0877190	+	0.595723i
$485$	−9.57111e9	+	9.57111e9i	−0.172980	+	0.172980i
$486$	−2.33904e9	−	2.70868e9i	−0.0419269	−	0.0485527i
$487$	6.02411e10			1.07097			0.535485	−	0.844545i	$-0.320129\pi$
$487$	6.02411e10			1.07097			0.535485	+	0.844545i	$0.320129\pi$
$488$	−6.13369e8	+	3.89785e8i	−0.0108154	+	0.00687300i
$489$			3.09937e10i			0.542048i
$490$	1.48172e11	+	1.71588e11i	2.57029	+	2.97648i
$491$	9.92717e9	+	9.92717e9i	0.170805	+	0.170805i	0.787333	−	0.616528i	$-0.211461\pi$
$491$	9.92717e9	+	9.92717e9i	0.170805	+	0.170805i	−0.616528	+	0.787333i	$0.711461\pi$
$492$	−1.60814e10	−	2.16351e10i	−0.274451	−	0.369232i
$493$	1.77447e10	+	1.77447e10i	0.300387	+	0.300387i
$494$	−1.17574e9	+	1.60556e10i	−0.0197425	+	0.269599i
$495$		−	1.94082e10i		−	0.323270i
$496$	3.17119e10	−	1.05347e11i	0.523957	−	1.74059i
$497$	−5.87140e10			−0.962312
$498$	3.45338e10	+	2.52888e9i	0.561470	+	0.0411160i
$499$	2.53004e10	−	2.53004e10i	0.408061	−	0.408061i	−0.473001	−	0.881062i	$-0.656829\pi$
$499$	2.53004e10	−	2.53004e10i	0.408061	−	0.408061i	0.881062	+	0.473001i	$0.156829\pi$
$500$	−2.08673e10	−	2.80737e10i	−0.333876	−	0.449180i
$501$	3.43802e10	−	3.43802e10i	0.545704	−	0.545704i
$502$	3.97279e10	−	3.43064e10i	0.625577	−	0.540207i
$503$	−5.25968e10			−0.821652			−0.410826	−	0.911714i	$-0.634760\pi$
$503$	−5.25968e10			−0.821652			−0.410826	+	0.911714i	$0.634760\pi$
$504$	3.95970e10	+	8.82540e9i	0.613678	+	0.136777i
$505$		−	1.32723e11i		−	2.04071i
$506$	−4.47173e10	+	3.86149e10i	−0.682140	+	0.589051i
$507$	1.40436e10	+	1.40436e10i	0.212543	+	0.212543i
$508$	−2.88432e9	+	1.95882e10i	−0.0433100	+	0.294130i
$509$	1.49549e10	+	1.49549e10i	0.222798	+	0.222798i	0.809676	−	0.586878i	$-0.199643\pi$
$509$	1.49549e10	+	1.49549e10i	0.222798	+	0.222798i	−0.586878	+	0.809676i	$0.699643\pi$
$510$	9.65893e10	+	7.07315e9i	1.42774	+	0.104552i
$511$		−	7.11863e10i		−	1.04403i
$512$	4.20183e10	−	5.43767e10i	0.611447	−	0.791285i
$513$	5.20388e9			0.0751377
$514$	−3.90183e9	+	5.32825e10i	−0.0559005	+	0.763364i
$515$	−5.31410e10	+	5.31410e10i	−0.755442	+	0.755442i
$516$	−5.03766e10	−	7.41786e9i	−0.710608	−	0.104636i
$517$	−2.34692e10	+	2.34692e10i	−0.328501	+	0.328501i
$518$	−3.97740e10	−	4.60595e10i	−0.552434	−	0.639735i
$519$	7.69372e10			1.06039
$520$	−1.69325e10	+	7.59714e10i	−0.231584	+	1.03905i
$521$			3.73582e10i			0.507032i	0.967331	+	0.253516i	$0.0815870\pi$
$521$			3.73582e10i			0.507032i	−0.967331	+	0.253516i	$0.918413\pi$
$522$	4.26096e9	+	4.93432e9i	0.0573886	+	0.0664578i
$523$	−3.83671e10	−	3.83671e10i	−0.512805	−	0.512805i	0.402580	−	0.915385i	$-0.368113\pi$
$523$	−3.83671e10	−	3.83671e10i	−0.512805	−	0.512805i	−0.915385	+	0.402580i	$0.868113\pi$
$524$	4.57696e10	−	3.40206e10i	0.607088	−	0.451250i
$525$	7.97935e10	+	7.97935e10i	1.05034	+	1.05034i
$526$	−6.32601e8	+	8.63865e9i	−0.00826393	+	0.112850i
$527$			2.26110e11i			2.93142i
$528$	2.71020e10	+	8.15831e9i	0.348711	+	0.104970i
$529$	8.15763e10			1.04170
$530$	4.81841e10	+	3.52849e9i	0.610662	+	0.0447183i
$531$	1.58888e10	−	1.58888e10i	0.199854	−	0.199854i
$532$	−4.73435e10	+	3.51905e10i	−0.591036	+	0.439318i
$533$	−3.14854e10	+	3.14854e10i	−0.390121	+	0.390121i
$534$	1.21520e10	−	1.04936e10i	0.149445	−	0.129051i
$535$	1.16285e11			1.41941
$536$	−3.59880e10	−	5.66309e10i	−0.436012	−	0.686111i
$537$			2.77320e10i			0.333491i
$538$	1.93998e10	−	1.67524e10i	0.231562	−	0.199962i
$539$	−9.62861e10	−	9.62861e10i	−1.14080	−	1.14080i
$540$	2.48920e10	+	3.66530e9i	0.292742	+	0.0431056i
$541$	−4.08204e10	−	4.08204e10i	−0.476528	−	0.476528i	0.427492	−	0.904019i	$-0.359397\pi$
$541$	−4.08204e10	−	4.08204e10i	−0.476528	−	0.476528i	−0.904019	+	0.427492i	$0.859397\pi$
$542$	−4.54646e10	−	3.32933e9i	−0.526837	−	0.0385798i
$543$		−	5.24700e10i		−	0.603548i
$544$	−5.04787e10	+	1.31906e11i	−0.576385	+	1.50615i
$545$	−1.21067e11			−1.37227
$546$	4.89397e9	−	6.68309e10i	0.0550669	−	0.751981i
$547$	3.56939e10	−	3.56939e10i	0.398699	−	0.398699i	−0.479075	−	0.877774i	$-0.659028\pi$
$547$	3.56939e10	−	3.56939e10i	0.398699	−	0.398699i	0.877774	+	0.479075i	$0.159028\pi$
$548$	1.05094e10	−	7.13719e10i	0.116534	−	0.791416i
$549$	2.74381e8	−	2.74381e8i	0.00302040	−	0.00302040i
$550$	5.14547e10	+	5.95862e10i	0.562308	+	0.651170i
$551$	−9.47976e9			−0.102847
$552$	−4.10806e10	−	6.46447e10i	−0.442466	−	0.696268i
$553$			1.93497e11i			2.06906i
$554$	2.91320e10	+	3.37358e10i	0.309266	+	0.358139i
$555$	−2.66880e10	−	2.66880e10i	−0.281283	−	0.281283i
$556$	3.25680e10	+	4.38152e10i	0.340794	+	0.458486i
$557$	2.99923e10	+	2.99923e10i	0.311594	+	0.311594i	0.845527	−	0.533933i	$-0.179286\pi$
$557$	2.99923e10	+	2.99923e10i	0.311594	+	0.311594i	−0.533933	+	0.845527i	$0.679286\pi$
$558$	−4.29013e9	+	5.85850e10i	−0.0442521	+	0.604296i
$559$			8.41077e10i			0.861367i
$560$	−2.51246e11	+	1.34983e11i	−2.55475	+	1.37254i
$561$	−5.81699e10			−0.587282
$562$	−5.51136e10	−	4.03592e9i	−0.552476	−	0.0404574i
$563$	1.04358e11	−	1.04358e11i	1.03870	−	1.03870i	0.0394803	−	0.999220i	$-0.487430\pi$
$563$	1.04358e11	−	1.04358e11i	1.03870	−	1.03870i	0.999220	−	0.0394803i	$-0.0125702\pi$
$564$	−2.56682e10	−	3.45327e10i	−0.253676	−	0.341282i
$565$	1.79348e10	−	1.79348e10i	0.175996	−	0.175996i
$566$	5.09714e10	−	4.40156e10i	0.496662	−	0.428885i
$567$	−2.16610e10			−0.209578
$568$	1.15522e10	−	5.18314e10i	0.110987	−	0.497965i
$569$			3.65227e10i			0.348429i	0.984708	+	0.174214i	$0.0557386\pi$
$569$			3.65227e10i			0.348429i	−0.984708	+	0.174214i	$0.944261\pi$
$570$	−2.76898e10	+	2.39111e10i	−0.262313	+	0.226517i
$571$	−3.14798e10	−	3.14798e10i	−0.296134	−	0.296134i	0.543364	−	0.839497i	$-0.317150\pi$
$571$	−3.14798e10	−	3.14798e10i	−0.296134	−	0.296134i	−0.839497	+	0.543364i	$0.817150\pi$
$572$	6.81046e9	−	4.62517e10i	0.0636198	−	0.432059i
$573$	6.32894e9	+	6.32894e9i	0.0587101	+	0.0587101i
$574$	−1.62724e11	−	1.19161e10i	−1.49900	−	0.109771i
$575$		−	2.13051e11i		−	1.94900i
$576$	−1.55817e10	+	3.32189e10i	−0.141555	+	0.301783i
$577$	−1.20311e11			−1.08543			−0.542715	−	0.839917i	$-0.682603\pi$
$577$	−1.20311e11			−1.08543			−0.542715	+	0.839917i	$0.682603\pi$
$578$	1.30481e10	−	1.78181e11i	0.116905	−	1.59643i
$579$	−3.69150e10	+	3.69150e10i	−0.328465	+	0.328465i
$580$	−4.53450e10	−	6.67696e9i	−0.400698	−	0.0590020i
$581$	1.48193e11	−	1.48193e11i	1.30054	−	1.30054i
$582$	6.88832e9	+	7.97688e9i	0.0600373	+	0.0695250i
$583$	−2.90184e10			−0.251188
$584$	6.28417e10	+	1.40062e10i	0.540252	+	0.120412i
$585$		−	4.15591e10i		−	0.354848i
$586$	5.63394e10	+	6.52428e10i	0.477773	+	0.553276i
$587$	7.13597e10	+	7.13597e10i	0.601036	+	0.601036i	0.940588	−	0.339551i	$-0.110275\pi$
$587$	7.13597e10	+	7.13597e10i	0.601036	+	0.601036i	−0.339551	+	0.940588i	$0.610275\pi$
$588$	1.41676e11	−	1.05308e11i	1.18518	−	0.880950i
$589$	−6.03975e10	−	6.03975e10i	−0.501831	−	0.501831i
$590$	−1.15373e10	+	1.57551e11i	−0.0952133	+	1.30021i
$591$			4.42356e10i			0.362595i
$592$	4.84860e10	−	2.60492e10i	0.394757	−	0.212084i
$593$	−1.19391e11			−0.965503			−0.482751	−	0.875757i	$-0.660363\pi$
$593$	−1.19391e11			−0.965503			−0.482751	+	0.875757i	$0.660363\pi$
$594$	−1.50718e10	−	1.10369e9i	−0.121065	−	0.00886548i
$595$	4.14488e11	−	4.14488e11i	3.30708	−	3.30708i
$596$	−3.04119e10	+	2.26053e10i	−0.241023	+	0.179153i
$597$	6.50308e10	−	6.50308e10i	0.511943	−	0.511943i
$598$	−9.57538e10	+	8.26868e10i	−0.748775	+	0.646593i
$599$	6.50734e9			0.0505471			0.0252735	−	0.999681i	$-0.491954\pi$
$599$	6.50734e9			0.0505471			0.0252735	+	0.999681i	$0.491954\pi$
$600$	−8.61396e10	+	5.47402e10i	−0.664657	+	0.422378i
$601$			1.01230e11i			0.775914i	0.921678	+	0.387957i	$0.126819\pi$
$601$			1.01230e11i			0.775914i	−0.921678	+	0.387957i	$0.873181\pi$
$602$	−2.33260e11	+	2.01428e11i	−1.77605	+	1.53368i
$603$	2.53330e10	+	2.53330e10i	0.191609	+	0.191609i
$604$	−6.00383e10	−	8.84052e9i	−0.451108	−	0.0664248i
$605$	8.77068e10	+	8.77068e10i	0.654654	+	0.654654i
$606$	−1.03068e11	−	7.54762e9i	−0.764250	−	0.0559654i
$607$			2.46248e11i			1.81392i	0.421218	+	0.906960i	$0.361603\pi$
$607$			2.46248e11i			1.81392i	−0.421218	+	0.906960i	$0.638397\pi$
$608$	−2.17504e10	−	4.87176e10i	−0.159167	−	0.356510i
$609$	3.94592e10			0.286866
$610$	−1.99236e8	+	2.72072e9i	−0.00143896	+	0.0196501i
$611$	−5.02550e10	+	5.02550e10i	−0.360591	+	0.360591i
$612$	1.09855e10	−	7.46057e10i	0.0783097	−	0.531822i
$613$	4.75120e10	−	4.75120e10i	0.336482	−	0.336482i	−0.518560	−	0.855041i	$-0.673532\pi$
$613$	4.75120e10	−	4.75120e10i	0.336482	−	0.336482i	0.855041	+	0.518560i	$0.173532\pi$
$614$	1.18246e11	+	1.36933e11i	0.831982	+	0.963461i
$615$	−1.01190e11			−0.707358
$616$	1.44582e11	−	9.18795e10i	1.00413	−	0.638111i
$617$		−	2.52324e11i		−	1.74107i	−0.492103	−	0.870537i	$-0.663772\pi$
$617$		−	2.52324e11i		−	1.74107i	0.492103	−	0.870537i	$-0.336228\pi$
$618$	3.82456e10	+	4.42895e10i	0.262197	+	0.303632i
$619$	−1.23794e11	−	1.23794e11i	−0.843215	−	0.843215i	0.146061	−	0.989276i	$-0.453341\pi$
$619$	−1.23794e11	−	1.23794e11i	−0.843215	−	0.843215i	−0.989276	+	0.146061i	$0.953341\pi$
$620$	−2.46362e11	−	3.31442e11i	−1.66727	−	2.24306i
$621$	2.89178e10	+	2.89178e10i	0.194446	+	0.194446i
$622$	3.78436e9	−	5.16782e10i	0.0252831	−	0.345260i
$623$		−	9.71779e10i		−	0.645082i
$624$	5.80339e10	+	1.74695e10i	0.382775	+	0.115224i
$625$	7.68264e10			0.503490
$626$	1.54666e11	+	1.13261e10i	1.00716	+	0.0737533i
$627$	1.55380e10	−	1.55380e10i	0.100537	−	0.100537i
$628$	1.83365e11	+	2.46689e11i	1.17890	+	1.58603i
$629$	−7.99886e10	+	7.99886e10i	−0.511006	+	0.511006i
$630$	1.15258e11	−	9.95292e10i	0.731659	−	0.631813i
$631$	2.87490e10			0.181345			0.0906724	−	0.995881i	$-0.471098\pi$
$631$	2.87490e10			0.181345			0.0906724	+	0.995881i	$0.471098\pi$
$632$	−1.70815e11	−	3.80713e10i	−1.07067	−	0.238632i
$633$		−	7.23678e9i		−	0.0450745i
$634$	3.00247e10	−	2.59274e10i	0.185832	−	0.160473i
$635$	5.25535e10	+	5.25535e10i	0.323226	+	0.323226i
$636$	5.48021e9	−	3.72175e10i	0.0334941	−	0.227467i
$637$	−2.06179e11	−	2.06179e11i	−1.25224	−	1.25224i
$638$	2.74558e10	+	2.01056e9i	0.165711	+	0.0121349i
$639$			2.83537e10i			0.170061i
$640$	−6.97260e10	−	2.48353e11i	−0.415599	−	1.48030i
$641$	2.14308e10			0.126942			0.0634711	−	0.997984i	$-0.479783\pi$
$641$	2.14308e10			0.126942			0.0634711	+	0.997984i	$0.479783\pi$
$642$	6.61279e9	−	9.03027e10i	0.0389264	−	0.531570i
$643$	−7.00844e9	+	7.00844e9i	−0.0409994	+	0.0409994i	−0.727309	−	0.686310i	$-0.759229\pi$
$643$	−7.00844e9	+	7.00844e9i	−0.0409994	+	0.0409994i	0.686310	+	0.727309i	$0.259229\pi$
$644$	−4.58638e11	−	6.75336e10i	−2.66641	−	0.392623i
$645$	−1.35156e11	+	1.35156e11i	−0.780904	+	0.780904i
$646$	7.16658e10	+	8.29912e10i	0.411511	+	0.476543i
$647$	1.53705e11			0.877141			0.438571	−	0.898697i	$-0.355485\pi$
$647$	1.53705e11			0.877141			0.438571	+	0.898697i	$0.355485\pi$
$648$	4.26189e9	−	1.91219e10i	0.0241714	−	0.108450i
$649$		−	9.48835e10i		−	0.534825i
$650$	1.10181e11	+	1.27593e11i	0.617238	+	0.714781i
$651$	2.51403e11	+	2.51403e11i	1.39974	+	1.39974i
$652$	−1.36167e11	+	1.01214e11i	−0.753499	+	0.560078i
$653$	5.95825e10	+	5.95825e10i	0.327692	+	0.327692i	0.851708	−	0.524016i	$-0.175567\pi$
$653$	5.95825e10	+	5.95825e10i	0.327692	+	0.327692i	−0.524016	+	0.851708i	$0.675567\pi$
$654$	−6.88477e9	+	9.40167e10i	−0.0376338	+	0.513918i
$655$		−	2.14071e11i		−	1.16303i
$656$	4.25358e10	−	1.41304e11i	0.229688	−	0.763026i
$657$	−3.43767e10			−0.184503
$658$	−2.59729e11	−	1.90198e10i	−1.38554	−	0.101462i
$659$	−1.96772e11	+	1.96772e11i	−1.04333	+	1.04333i	−0.0443126	+	0.999018i	$0.514110\pi$
$659$	−1.96772e11	+	1.96772e11i	−1.04333	+	1.04333i	−0.999018	+	0.0443126i	$0.985890\pi$
$660$	8.52679e10	−	6.33798e10i	0.449376	−	0.334022i
$661$	1.46830e11	−	1.46830e11i	0.769144	−	0.769144i	−0.208812	−	0.977956i	$-0.566960\pi$
$661$	1.46830e11	−	1.46830e11i	0.769144	−	0.769144i	0.977956	+	0.208812i	$0.0669597\pi$
$662$	2.39211e10	−	2.06567e10i	0.124552	−	0.107555i
$663$	−1.24560e11			−0.644651
$664$	1.01664e11	+	1.59979e11i	0.522991	+	0.822982i
$665$			2.21432e11i			1.13228i
$666$	−2.22427e10	+	1.92073e10i	−0.113055	+	0.0976270i
$667$	−5.26787e10	−	5.26787e10i	−0.266153	−	0.266153i
$668$	2.63318e11	+	3.87731e10i	1.32244	+	0.194726i
$669$	−5.99159e9	−	5.99159e9i	−0.0299114	−	0.0299114i
$670$	−2.51198e11	−	1.83950e10i	−1.24657	−	0.0912852i
$671$		−	1.63852e9i		−	0.00808281i
$672$	9.05353e10	+	2.02786e11i	0.443957	+	0.994397i
$673$	2.81771e11			1.37352			0.686761	−	0.726883i	$-0.259032\pi$
$673$	2.81771e11			1.37352			0.686761	+	0.726883i	$0.259032\pi$
$674$	−1.97996e10	+	2.70378e11i	−0.0959437	+	1.31018i
$675$	3.85332e10	−	3.85332e10i	0.185618	−	0.185618i
$676$	−1.58380e10	+	1.07560e11i	−0.0758426	+	0.515067i
$677$	−3.89977e10	+	3.89977e10i	−0.185645	+	0.185645i	−0.793811	−	0.608165i	$-0.791906\pi$
$677$	−3.89977e10	+	3.89977e10i	−0.185645	+	0.185645i	0.608165	+	0.793811i	$0.291906\pi$
$678$	−1.29077e10	−	1.49475e10i	−0.0610842	−	0.0707374i
$679$	6.37902e10			0.300106
$680$	2.84349e11	+	4.47453e11i	1.32989	+	2.09272i
$681$			1.24616e11i			0.579407i
$682$	1.62117e11	+	1.87736e11i	0.749359	+	0.867781i
$683$	8.13630e10	+	8.13630e10i	0.373890	+	0.373890i	0.868892	−	0.495002i	$-0.164833\pi$
$683$	8.13630e10	+	8.13630e10i	0.373890	+	0.373890i	−0.495002	+	0.868892i	$0.664833\pi$
$684$	1.69939e10	+	2.28627e10i	0.0776370	+	0.104449i
$685$	−1.91485e11	−	1.91485e11i	−0.869706	−	0.869706i
$686$	4.75239e10	−	6.48975e11i	0.214593	−	2.93043i
$687$		−	6.73303e10i		−	0.302262i
$688$	−1.31921e11	−	2.45548e11i	−0.588791	−	1.09593i
$689$	−6.21375e10			−0.275726
$690$	−2.86744e11	−	2.09980e10i	−1.26502	−	0.0926365i
$691$	−1.93523e11	+	1.93523e11i	−0.848831	+	0.848831i	−0.989987	−	0.141156i	$-0.954918\pi$
$691$	−1.93523e11	+	1.93523e11i	−0.848831	+	0.848831i	0.141156	+	0.989987i	$0.454918\pi$
$692$	2.51247e11	+	3.38015e11i	1.09566	+	1.47405i
$693$	−6.46766e10	+	6.46766e10i	−0.280423	+	0.280423i
$694$	2.34125e11	−	2.02175e11i	1.00927	−	0.871544i
$695$	2.04930e11			0.878347
$696$	−7.76375e9	+	3.48337e10i	−0.0330853	+	0.148444i
$697$			3.03286e11i			1.28505i
$698$	2.73902e11	−	2.36524e11i	1.15391	−	0.996446i
$699$	−1.35392e11	−	1.35392e11i	−0.567133	−	0.567133i
$700$	−8.99891e10	+	6.11140e11i	−0.374798	+	2.54535i
$701$	2.40775e11	+	2.40775e11i	0.997100	+	0.997100i	0.999996	−	0.00289586i	$-0.000921781\pi$
$701$	2.40775e11	+	2.40775e11i	0.997100	+	0.997100i	−0.00289586	+	0.999996i	$0.500922\pi$
$702$	−3.22734e10	−	2.36335e9i	−0.132891	−	0.00973152i
$703$		−	4.27323e10i		−	0.174959i
$704$	5.26621e10	+	1.45712e11i	0.214391	+	0.593203i
$705$	−1.61514e11			−0.653813
$706$	5.76014e9	−	7.86591e10i	0.0231854	−	0.316614i
$707$	−4.42292e11	+	4.42292e11i	−1.77024	+	1.77024i
$708$	1.21693e11	+	1.79190e10i	0.484319	+	0.0713150i
$709$	−2.43465e11	+	2.43465e11i	−0.963498	+	0.963498i	−0.999357	−	0.0358590i	$-0.988583\pi$
$709$	−2.43465e11	+	2.43465e11i	−0.963498	+	0.963498i	0.0358590	+	0.999357i	$0.488583\pi$
$710$	−1.30281e11	−	1.50869e11i	−0.512681	−	0.593701i
$711$	9.34420e10			0.365648
$712$	8.57864e10	+	1.91201e10i	0.333809	+	0.0743996i
$713$		−	6.71253e11i		−	2.59734i
$714$	−2.98307e11	−	3.45448e11i	−1.14781	−	1.32920i
$715$	−1.24089e11	−	1.24089e11i	−0.474800	−	0.474800i
$716$	−1.21837e11	+	9.05621e10i	−0.463584	+	0.344583i
$717$	2.09123e11	+	2.09123e11i	0.791270	+	0.791270i
$718$	−1.23159e10	+	1.68183e11i	−0.0463414	+	0.632827i
$719$			5.72949e10i			0.214388i	0.994238	+	0.107194i	$0.0341866\pi$
$719$			5.72949e10i			0.214388i	−0.994238	+	0.107194i	$0.965813\pi$
$720$	6.51847e10	+	1.21330e11i	0.242558	+	0.451479i
$721$	3.54178e11			1.31063
$722$	2.29700e11	+	1.68208e10i	0.845303	+	0.0619009i
$723$	−7.23266e10	+	7.23266e10i	−0.264694	+	0.264694i
$724$	2.30521e11	−	1.71347e11i	0.838990	−	0.623623i
$725$	−7.01948e10	+	7.01948e10i	−0.254070	+	0.254070i
$726$	7.30978e10	−	6.31225e10i	0.263122	−	0.227215i
$727$	−4.46091e11			−1.59693			−0.798464	−	0.602042i	$-0.794354\pi$
$727$	−4.46091e11			−1.59693			−0.798464	+	0.602042i	$0.794354\pi$
$728$	3.09596e11	−	1.96743e11i	1.10222	−	0.700445i
$729$			1.04604e10i			0.0370370i
$730$	1.82918e11	−	1.57956e11i	0.644117	−	0.556217i
$731$	4.05088e11	+	4.05088e11i	1.41866	+	1.41866i
$732$	2.10149e9	+	3.09440e8i	0.00731952	+	0.00107778i
$733$	−3.86360e9	−	3.86360e9i	−0.0133837	−	0.0133837i	0.700383	−	0.713767i	$-0.253012\pi$
$733$	−3.86360e9	−	3.86360e9i	−0.0133837	−	0.0133837i	−0.713767	+	0.700383i	$0.753012\pi$
$734$	5.50491e11	+	4.03120e10i	1.89656	+	0.138883i
$735$		−	6.62636e11i		−	2.27052i
$736$	1.49856e11	−	3.91588e11i	0.510696	−	1.33450i
$737$	1.51281e11			0.512760
$738$	−5.75443e9	+	7.85811e10i	−0.0193989	+	0.264906i
$739$	3.88066e10	−	3.88066e10i	0.130115	−	0.130115i	−0.639050	−	0.769165i	$-0.720672\pi$
$739$	3.88066e10	−	3.88066e10i	0.130115	−	0.130115i	0.769165	+	0.639050i	$0.220672\pi$
$740$	3.00980e10	−	2.04404e11i	0.100372	−	0.681651i
$741$	3.32718e10	−	3.32718e10i	0.110358	−	0.110358i
$742$	−1.48812e11	−	1.72329e11i	−0.490933	−	0.568516i
$743$	−4.38384e11			−1.43846			−0.719232	−	0.694770i	$-0.755506\pi$
$743$	−4.38384e11			−1.43846			−0.719232	+	0.694770i	$0.755506\pi$
$744$	−2.71397e11	+	1.72468e11i	−0.885754	+	0.562882i
$745$			1.42241e11i			0.461742i
$746$	−2.78704e11	−	3.22748e11i	−0.899888	−	1.04210i
$747$	−7.15640e10	−	7.15640e10i	−0.229833	−	0.229833i
$748$	−1.89961e11	−	2.55563e11i	−0.606816	−	0.816379i
$749$	−3.87511e11	−	3.87511e11i	−1.23128	−	1.23128i
$750$	−7.46695e9	+	1.01967e11i	−0.0235992	+	0.322266i
$751$			4.54182e11i			1.42781i	0.700243	+	0.713905i	$0.253075\pi$
$751$			4.54182e11i			1.42781i	−0.700243	+	0.713905i	$0.746925\pi$
$752$	6.78930e10	−	2.25541e11i	0.212302	−	0.705268i
$753$	−1.53421e11			−0.477204
$754$	5.87915e10	+	4.30525e9i	0.181898	+	0.0133203i
$755$	−1.61078e11	+	1.61078e11i	−0.495734	+	0.495734i
$756$	−7.07366e10	−	9.51653e10i	−0.216549	−	0.291334i
$757$	4.92663e10	−	4.92663e10i	0.150026	−	0.150026i	−0.628104	−	0.778130i	$-0.716169\pi$
$757$	4.92663e10	−	4.92663e10i	0.150026	−	0.150026i	0.778130	+	0.628104i	$0.216169\pi$
$758$	−6.15155e10	+	5.31208e10i	−0.186341	+	0.160912i
$759$	1.72689e11			0.520351
$760$	−1.95475e11	−	4.35676e10i	−0.585918	−	0.130590i
$761$		−	4.10936e11i		−	1.22528i	−0.790361	−	0.612641i	$-0.790107\pi$
$761$		−	4.10936e11i		−	1.22528i	0.790361	−	0.612641i	$-0.209893\pi$
$762$	4.37998e10	−	3.78227e10i	0.129913	−	0.112184i
$763$	4.03449e11	+	4.03449e11i	1.19039	+	1.19039i
$764$	−7.13762e9	+	4.84734e10i	−0.0209498	+	0.142276i
$765$	−2.00161e11	−	2.00161e11i	−0.584432	−	0.584432i
$766$	−8.78934e10	−	6.43636e9i	−0.255294	−	0.0186950i
$767$		−	2.03175e11i		−	0.587070i
$768$	−1.96828e11	+	4.00237e10i	−0.565772	+	0.115046i
$769$	5.73892e11			1.64106			0.820530	−	0.571603i	$-0.193678\pi$
$769$	5.73892e11			1.64106			0.820530	+	0.571603i	$0.193678\pi$
$770$	4.69635e10	−	6.41323e11i	0.133597	−	1.82437i
$771$	1.10417e11	−	1.10417e11i	0.312477	−	0.312477i
$772$	−2.82733e11	−	4.16318e10i	−0.795989	−	0.117208i
$773$	3.36619e11	−	3.36619e11i	0.942802	−	0.942802i	−0.0556488	−	0.998450i	$-0.517723\pi$
$773$	3.36619e11	−	3.36619e11i	0.942802	−	0.942802i	0.998450	+	0.0556488i	$0.0177227\pi$
$774$	9.72719e10	+	1.12644e11i	0.271034	+	0.313866i
$775$	−8.94450e11			−2.47942
$776$	−1.25510e10	+	5.63125e10i	−0.0346123	+	0.155295i
$777$			1.77872e11i			0.488004i
$778$	−3.78141e11	−	4.37899e11i	−1.03213	−	1.19524i
$779$	−8.10121e10	−	8.10121e10i	−0.219989	−	0.219989i
$780$	1.82585e11	−	1.35716e11i	0.493274	−	0.366651i
$781$	8.46599e10	+	8.46599e10i	0.227548	+	0.227548i
$782$	−6.29348e10	+	8.59423e11i	−0.168292	+	2.29816i
$783$		−	1.90553e10i		−	0.0506954i
$784$	9.25317e11	+	2.78541e11i	2.44921	+	0.737268i
$785$	1.15380e12			3.03844
$786$	−1.66240e11	−	1.21736e10i	−0.435557	−	0.0318955i
$787$	3.91030e10	−	3.91030e10i	0.101932	−	0.101932i	−0.654302	−	0.756234i	$-0.727037\pi$
$787$	3.91030e10	−	3.91030e10i	0.101932	−	0.101932i	0.756234	+	0.654302i	$0.227037\pi$
$788$	−1.94344e11	+	1.44457e11i	−0.504043	+	0.374656i
$789$	1.79018e10	−	1.79018e10i	0.0461943	−	0.0461943i
$790$	−4.97203e11	+	4.29352e11i	−1.27651	+	1.10231i
$791$	−1.19533e11			−0.305339
$792$	−4.43697e10	−	6.98204e10i	−0.112768	−	0.177452i
$793$		−	3.50860e9i		−	0.00887239i
$794$	−4.32983e11	+	3.73896e11i	−1.08940	+	0.940739i
$795$	−9.98516e10	−	9.98516e10i	−0.249969	−	0.249969i
$796$	4.98071e11	+	7.33400e10i	1.24062	+	0.182679i
$797$	2.51294e10	+	2.51294e10i	0.0622800	+	0.0622800i	0.737561	−	0.675281i	$-0.235978\pi$
$797$	2.51294e10	+	2.51294e10i	0.0622800	+	0.0622800i	−0.675281	+	0.737561i	$0.735978\pi$
$798$	1.71957e11	+	1.25922e10i	0.424040	+	0.0310521i
$799$			4.84086e11i			1.18778i
$800$	−5.21794e11	−	1.99684e11i	−1.27391	−	0.487511i
$801$	−4.69283e10			−0.114000
$802$	−2.71437e9	+	3.70668e10i	−0.00656103	+	0.0895958i
$803$	−1.02644e11	+	1.02644e11i	−0.246871	+	0.246871i
$804$	−2.85699e10	+	1.94025e11i	−0.0683729	+	0.464338i
$805$	−1.23049e12	+	1.23049e12i	−2.93018	+	2.93018i
$806$	3.47143e11	+	4.02002e11i	0.822561	+	0.952551i
$807$	−7.49177e10			−0.176641
$808$	−3.03423e11	−	4.77468e11i	−0.711873	−	1.12021i
$809$		−	5.08105e11i		−	1.18620i	−0.805128	−	0.593102i	$-0.797903\pi$
$809$		−	5.08105e11i		−	1.18620i	0.805128	−	0.593102i	$-0.202097\pi$
$810$	−4.80638e10	−	5.56594e10i	−0.111655	−	0.129300i
$811$	−4.30096e11	−	4.30096e11i	−0.994220	−	0.994220i	0.00576373	−	0.999983i	$-0.498165\pi$
$811$	−4.30096e11	−	4.30096e11i	−0.994220	−	0.994220i	−0.999983	+	0.00576373i	$0.998165\pi$
$812$	1.28859e11	+	1.73360e11i	0.296408	+	0.398772i
$813$	9.42159e10	+	9.42159e10i	0.215656	+	0.215656i
$814$	−9.06311e9	+	1.23764e11i	−0.0206433	+	0.281900i
$815$			6.36874e11i			1.44352i
$816$	3.63647e11	−	1.95370e11i	0.820199	−	0.440654i
$817$	−2.16410e11			−0.485723
$818$	−3.57817e11	−	2.62026e10i	−0.799185	−	0.0585237i
$819$	−1.38493e11	+	1.38493e11i	−0.307817	+	0.307817i
$820$	−3.30449e11	−	4.44569e11i	−0.730886	−	0.983296i
$821$	4.77746e11	−	4.77746e11i	1.05154	−	1.05154i	0.0529384	−	0.998598i	$-0.483141\pi$
$821$	4.77746e11	−	4.77746e11i	1.05154	−	1.05154i	0.998598	−	0.0529384i	$-0.0168587\pi$
$822$	−1.59590e11	+	1.37812e11i	−0.349557	+	0.301855i
$823$	1.36158e11			0.296786			0.148393	−	0.988928i	$-0.452590\pi$
$823$	1.36158e11			0.296786			0.148393	+	0.988928i	$0.452590\pi$
$824$	−6.96859e10	+	3.12660e11i	−0.151160	+	0.678210i
$825$		−	2.30109e11i		−	0.496727i
$826$	5.63476e11	−	4.86581e11i	1.21047	−	1.04529i
$827$	−1.92351e11	−	1.92351e11i	−0.411218	−	0.411218i	0.470945	−	0.882163i	$-0.343913\pi$
$827$	−1.92351e11	−	1.92351e11i	−0.411218	−	0.411218i	−0.882163	+	0.470945i	$0.843913\pi$
$828$	−3.26127e10	+	2.21482e11i	−0.0693850	+	0.471212i
$829$	−4.44879e11	−	4.44879e11i	−0.941940	−	0.941940i	0.0564643	−	0.998405i	$-0.482017\pi$
$829$	−4.44879e11	−	4.44879e11i	−0.941940	−	0.941940i	−0.998405	+	0.0564643i	$0.982017\pi$
$830$	7.09617e11	+	5.19647e10i	1.49524	+	0.109495i
$831$		−	1.30280e11i		−	0.273197i
$832$	1.12766e11	+	3.12014e11i	0.235334	+	0.651150i
$833$	−1.98604e12			−4.12484
$834$	1.16538e10	−	1.59142e11i	0.0240882	−	0.328942i
$835$	7.06461e11	−	7.06461e11i	1.45326	−	1.45326i
$836$	1.19006e11	+	1.75234e10i	0.243637	+	0.0358751i
$837$	1.21405e11	−	1.21405e11i	0.247363	−	0.247363i
$838$	−6.24380e11	−	7.23051e11i	−1.26611	−	1.46620i
$839$	1.04856e11			0.211614			0.105807	−	0.994387i	$-0.466257\pi$
$839$	1.04856e11			0.211614			0.105807	+	0.994387i	$0.466257\pi$
$840$	8.13659e11	+	1.81349e11i	1.63428	+	0.364248i
$841$		−	4.65534e11i		−	0.930609i
$842$	−4.72310e11	−	5.46950e11i	−0.939678	−	1.08818i
$843$	1.14211e11	+	1.14211e11i	0.226151	+	0.226151i
$844$	3.17940e10	−	2.36326e10i	0.0626579	−	0.0465737i
$845$	2.88574e11	+	2.88574e11i	0.566019	+	0.566019i
$846$	−9.18487e9	+	1.25426e11i	−0.0179305	+	0.244854i
$847$		−	5.84554e11i		−	1.13577i
$848$	1.81407e11	−	9.74616e10i	0.350810	−	0.188473i
$849$	−1.96841e11			−0.378865
$850$	1.14519e12	+	8.38612e10i	2.19382	+	0.160652i
$851$	2.37462e11	−	2.37462e11i	0.452768	−	0.452768i
$852$	−1.24569e11	+	9.25922e10i	−0.236402	+	0.175718i
$853$	−2.87610e10	+	2.87610e10i	−0.0543259	+	0.0543259i	−0.733748	−	0.679422i	$-0.762231\pi$
$853$	−2.87610e10	+	2.87610e10i	−0.0543259	+	0.0543259i	0.679422	+	0.733748i	$0.262231\pi$
$854$	9.73056e9	−	8.40268e9i	0.0182939	−	0.0157974i
$855$	1.06932e11			0.200098
$856$	4.18330e11	−	2.65841e11i	0.779155	−	0.495140i
$857$			9.22142e11i			1.70952i	0.519022	+	0.854761i	$0.326296\pi$
$857$			9.22142e11i			1.70952i	−0.519022	+	0.854761i	$0.673704\pi$
$858$	−1.03420e11	+	8.93070e10i	−0.190834	+	0.164792i
$859$	4.37815e11	+	4.37815e11i	0.804115	+	0.804115i	0.983736	−	0.179621i	$-0.0574872\pi$
$859$	4.37815e11	+	4.37815e11i	0.804115	+	0.804115i	−0.179621	+	0.983736i	$0.557487\pi$
$860$	−1.03516e12	−	1.52426e11i	−1.89241	−	0.278654i
$861$	3.37211e11	+	3.37211e11i	0.613605	+	0.613605i
$862$	−6.05591e11	−	4.43469e10i	−1.09686	−	0.0803220i
$863$		−	8.52968e11i		−	1.53776i	−0.639391	−	0.768882i	$-0.720813\pi$
$863$		−	8.52968e11i		−	1.53776i	0.639391	−	0.768882i	$-0.279187\pi$
$864$	9.79275e10	−	4.37205e10i	0.175732	−	0.0784568i
$865$	1.58094e12			2.82392
$866$	−1.22176e10	+	1.66841e11i	−0.0217228	+	0.296641i
$867$	−3.69243e11	+	3.69243e11i	−0.653485	+	0.653485i
$868$	−2.83525e11	+	1.92550e12i	−0.499474	+	3.39206i
$869$	2.79004e11	−	2.79004e11i	0.489251	−	0.489251i
$870$	8.75564e10	+	1.01393e11i	0.152831	+	0.176983i
$871$	3.23940e11			0.562850
$872$	−4.35535e11	+	2.76775e11i	−0.753282	+	0.478698i
$873$		−	3.08050e10i		−	0.0530352i
$874$	−2.12754e11	−	2.46376e11i	−0.364613	−	0.422233i
$875$	4.37565e11	+	4.37565e11i	0.746466	+	0.746466i
$876$	−1.12261e11	−	1.51030e11i	−0.190640	−	0.256477i
$877$	8.01532e11	+	8.01532e11i	1.35495	+	1.35495i	0.880030	+	0.474918i	$0.157522\pi$
$877$	8.01532e11	+	8.01532e11i	1.35495	+	1.35495i	0.474918	+	0.880030i	$0.342478\pi$
$878$	−7.56704e10	+	1.03334e12i	−0.127335	+	1.73886i
$879$		−	2.51954e11i		−	0.422051i
$880$	5.56905e11	+	1.67641e11i	0.928646	+	0.279544i
$881$	1.20086e12			1.99337			0.996685	−	0.0813537i	$-0.0259243\pi$
$881$	1.20086e12			1.99337			0.996685	+	0.0813537i	$0.0259243\pi$
$882$	−5.14581e11	−	3.76823e10i	−0.850314	−	0.0622678i
$883$	−2.62745e11	+	2.62745e11i	−0.432206	+	0.432206i	−0.889378	−	0.457172i	$-0.848862\pi$
$883$	−2.62745e11	+	2.62745e11i	−0.432206	+	0.432206i	0.457172	+	0.889378i	$0.348862\pi$
$884$	−4.06766e11	−	5.47241e11i	−0.666093	−	0.896127i
$885$	3.26492e11	−	3.26492e11i	0.532230	−	0.532230i
$886$	−1.40594e11	+	1.21408e11i	−0.228157	+	0.197021i
$887$	1.93518e11			0.312628			0.156314	−	0.987707i	$-0.450039\pi$
$887$	1.93518e11			0.312628			0.156314	+	0.987707i	$0.450039\pi$
$888$	−1.57021e11	−	3.49970e10i	−0.252527	−	0.0562832i
$889$		−	3.50262e11i		−	0.560772i
$890$	2.49705e11	−	2.15629e11i	0.397985	−	0.343674i
$891$	3.12331e10	+	3.12331e10i	0.0495569	+	0.0495569i
$892$	6.75715e9	−	4.58896e10i	0.0106734	−	0.0724862i
$893$	−1.29307e11	−	1.29307e11i	−0.203336	−	0.203336i
$894$	1.10459e11	+	8.08885e9i	0.172923	+	0.0126630i
$895$			5.69851e11i			0.888114i
$896$	−5.95263e11	+	1.05998e12i	−0.923585	+	1.64462i
$897$	3.69781e11			0.571182
$898$	−5.80760e9	+	7.93072e10i	−0.00893082	+	0.121957i
$899$	−2.21160e11	+	2.21160e11i	−0.338585	+	0.338585i
$900$	2.95126e11	+	4.34567e10i	0.449819	+	0.0662349i
$901$	−2.99273e11	+	2.99273e11i	−0.454117	+	0.454117i
$902$	2.17450e11	+	2.51814e11i	0.328498	+	0.380411i
$903$	9.00800e11			1.35481
$904$	2.35186e10	−	1.05521e11i	0.0352158	−	0.158003i
$905$		−	1.07818e12i		−	1.60730i
$906$	1.15928e11	+	1.34248e11i	0.172058	+	0.199248i
$907$	3.07970e11	+	3.07970e11i	0.455071	+	0.455071i	0.897034	−	0.441963i	$-0.145718\pi$
$907$	3.07970e11	+	3.07970e11i	0.455071	+	0.455071i	−0.441963	+	0.897034i	$0.645718\pi$
$908$	−5.47485e11	+	4.06947e11i	−0.805432	+	0.598679i
$909$	2.13588e11	+	2.13588e11i	0.312839	+	0.312839i
$910$	1.00564e11	−	1.37327e12i	0.146648	−	2.00259i
$911$		−	1.16048e12i		−	1.68486i	−0.538802	−	0.842432i	$-0.681123\pi$
$911$		−	1.16048e12i		−	1.68486i	0.538802	−	0.842432i	$-0.318877\pi$
$912$	−4.49492e10	+	1.49322e11i	−0.0649745	+	0.215846i
$913$	−4.27359e11			−0.615050
$914$	8.85715e9	+	6.48602e8i	0.0126914	+	0.000929380i
$915$	5.63812e9	−	5.63812e9i	0.00804359	−	0.00804359i
$916$	2.95808e11	−	2.19875e11i	0.420173	−	0.312316i
$917$	−7.13376e11	+	7.13376e11i	−1.00888	+	1.00888i
$918$	−1.66821e11	+	1.44056e11i	−0.234898	+	0.202843i
$919$	1.19992e12			1.68225			0.841127	−	0.540837i	$-0.181893\pi$
$919$	1.19992e12			1.68225			0.841127	+	0.540837i	$0.181893\pi$
$920$	−8.44144e11	−	1.32835e12i	−1.17833	−	1.85422i
$921$		−	5.28805e11i		−	0.734949i
$922$	−9.47252e11	+	8.17985e11i	−1.31082	+	1.13194i
$923$	1.81283e11	+	1.81283e11i	0.249776	+	0.249776i
$924$	−4.95359e11	−	7.29406e10i	−0.679567	−	0.100065i
$925$	−3.16420e11	−	3.16420e11i	−0.432212	−	0.432212i
$926$	1.00168e12	+	7.33519e10i	1.36233	+	0.0997625i
$927$		−	1.71037e11i		−	0.231617i
$928$	−1.78392e11	+	7.96444e10i	−0.240537	+	0.107390i
$929$	6.17944e11			0.829634			0.414817	−	0.909905i	$-0.363846\pi$
$929$	6.17944e11			0.829634			0.414817	+	0.909905i	$0.363846\pi$
$930$	−8.81558e10	+	1.20383e12i	−0.117847	+	1.60929i
$931$	5.30500e11	−	5.30500e11i	0.706134	−	0.706134i
$932$	1.52692e11	−	1.03697e12i	0.202373	−	1.37437i
$933$	−1.07092e11	+	1.07092e11i	−0.141329	+	0.141329i
$934$	9.42515e9	+	1.09146e10i	0.0123851	+	0.0143424i
$935$	−1.19530e12			−1.56398
$936$	−9.50095e10	−	1.49508e11i	−0.123784	−	0.194787i
$937$			1.01454e12i			1.31617i	0.752943	+	0.658085i	$0.228633\pi$
$937$			1.01454e12i			1.31617i	−0.752943	+	0.658085i	$0.771367\pi$
$938$	7.75799e11	+	8.98400e11i	1.00216	+	1.16053i
$939$	−3.20513e11	−	3.20513e11i	−0.412271	−	0.412271i
$940$	−5.27443e11	−	7.09595e11i	−0.675561	−	0.908864i
$941$	−7.30530e11	−	7.30530e11i	−0.931707	−	0.931707i	0.0661055	−	0.997813i	$-0.478943\pi$
$941$	−7.30530e11	−	7.30530e11i	−0.931707	−	0.931707i	−0.997813	+	0.0661055i	$0.978943\pi$
$942$	6.56134e10	−	8.96001e11i	0.0833276	−	1.13790i
$943$		−	9.00363e11i		−	1.13860i
$944$	3.18677e11	+	5.93161e11i	0.401294	+	0.746938i
$945$	−4.45101e11			−0.558125
$946$	6.26778e11	+	4.58984e10i	0.782617	+	0.0573104i
$947$	−2.84681e11	+	2.84681e11i	−0.353964	+	0.353964i	−0.861582	−	0.507618i	$-0.830526\pi$
$947$	−2.84681e11	+	2.84681e11i	−0.353964	+	0.353964i	0.507618	+	0.861582i	$0.330526\pi$
$948$	3.05146e11	+	4.10527e11i	0.377811	+	0.508287i
$949$	−2.19793e11	+	2.19793e11i	−0.270987	+	0.270987i
$950$	−3.28298e11	+	2.83496e11i	−0.403063	+	0.348059i
$951$	−1.15949e11			−0.141757
$952$	5.43534e11	−	2.43868e12i	0.661727	−	2.96898i
$953$			1.20488e12i			1.46074i	0.683054	+	0.730368i	$0.260651\pi$
$953$			1.20488e12i			1.46074i	−0.683054	+	0.730368i	$0.739349\pi$
$954$	−8.32197e10	+	7.18631e10i	−0.100469	+	0.0867586i
$955$	1.30050e11	+	1.30050e11i	0.156350	+	0.156350i
$956$	−2.35843e11	+	1.60167e12i	−0.282353	+	1.91753i
$957$	−5.68964e10	−	5.68964e10i	−0.0678323	−	0.0678323i
$958$	2.06241e10	+	1.51028e9i	0.0244857	+	0.00179307i
$959$			1.27622e12i			1.50887i
$960$	−3.20181e11	+	6.82599e11i	−0.376973	+	0.803675i
$961$	−1.96522e12			−2.30419
$962$	−1.94070e10	+	2.65017e11i	−0.0226599	+	0.309438i
$963$	−1.87133e11	+	1.87133e11i	−0.217594	+	0.217594i
$964$	−5.53950e11	−	8.15680e10i	−0.641449	−	0.0944521i
$965$	−7.58549e11	+	7.58549e11i	−0.874730	+	0.874730i
$966$	8.85582e11	+	1.02553e12i	1.01700	+	1.17772i
$967$	−8.11464e11			−0.928033			−0.464017	−	0.885826i	$-0.653592\pi$
$967$	−8.11464e11			−0.928033			−0.464017	+	0.885826i	$0.653592\pi$
$968$	5.16031e11	+	1.15013e11i	0.587726	+	0.130993i
$969$		−	3.20494e11i		−	0.363517i
$970$	1.41545e11	+	1.63913e11i	0.159884	+	0.185151i
$971$	1.35287e11	+	1.35287e11i	0.152188	+	0.152188i	0.779094	−	0.626907i	$-0.215679\pi$
$971$	1.35287e11	+	1.35287e11i	0.152188	+	0.152188i	−0.626907	+	0.779094i	$0.715679\pi$
$972$	−4.59564e10	+	3.41595e10i	−0.0514851	+	0.0382690i
$973$	−6.82915e11	−	6.82915e11i	−0.761931	−	0.761931i
$974$	7.03941e10	−	9.61284e11i	0.0782168	−	1.06811i
$975$		−	4.92736e11i		−	0.545250i
$976$	5.50317e9	+	1.02432e10i	0.00606476	+	0.0112885i
$977$	−1.23065e12			−1.35069			−0.675346	−	0.737501i	$-0.736006\pi$
$977$	−1.23065e12			−1.35069			−0.675346	+	0.737501i	$0.736006\pi$
$978$	4.94574e11	+	3.62173e10i	0.540600	+	0.0395877i
$979$	−1.40121e11	+	1.40121e11i	−0.152536	+	0.152536i
$980$	2.91122e12	−	2.16392e12i	3.15625	−	2.34604i
$981$	1.94830e11	−	1.94830e11i	0.210368	−	0.210368i
$982$	1.70011e11	−	1.46810e11i	0.182823	−	0.157874i
$983$	8.02594e11			0.859571			0.429786	−	0.902931i	$-0.358589\pi$
$983$	8.02594e11			0.859571			0.429786	+	0.902931i	$0.358589\pi$
$984$	−3.64029e11	+	2.31334e11i	−0.388290	+	0.246752i
$985$			9.08976e11i			0.965622i
$986$	3.03893e11	−	2.62422e11i	0.321523	−	0.277647i
$987$	5.38235e11	+	5.38235e11i	0.567157	+	0.567157i
$988$	2.54829e11	+	3.75231e10i	0.267437	+	0.0393796i
$989$	−1.20258e12	−	1.20258e12i	−1.25698	−	1.25698i
$990$	−3.09702e11	−	2.26792e10i	−0.322406	−	0.0236095i
$991$			7.66270e11i			0.794488i	0.917713	+	0.397244i	$0.130033\pi$
$991$			7.66270e11i			0.794488i	−0.917713	+	0.397244i	$0.869967\pi$
$992$	−1.64400e12	−	6.29138e11i	−1.69768	−	0.649680i
$993$	−9.23781e10			−0.0950106
$994$	−6.86095e10	+	9.36915e11i	−0.0702811	+	0.959742i
$995$	1.33628e12	−	1.33628e12i	1.36335	−	1.36335i
$996$	8.07080e10	−	5.48110e11i	0.0820124	−	0.556968i
$997$	5.38100e11	−	5.38100e11i	0.544606	−	0.544606i	−0.380270	−	0.924876i	$-0.624169\pi$
$997$	5.38100e11	−	5.38100e11i	0.544606	−	0.544606i	0.924876	+	0.380270i	$0.124169\pi$
$998$	−3.74161e11	−	4.33290e11i	−0.377169	−	0.436773i
$999$	8.58965e10			0.0862409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.19.17	✓	64
4.3	odd	2		192.9.l.a.175.18		64
16.5	even	4		192.9.l.a.79.18		64
16.11	odd	4	inner	48.9.l.a.43.17	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.17	✓	64	1.1	even	1	trivial
48.9.l.a.43.17	yes	64	16.11	odd	4	inner
192.9.l.a.79.18		64	16.5	even	4
192.9.l.a.175.18		64	4.3	odd	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16854 - 15.9573i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(-253.269 - 37.2934i) q^{4} +(-679.500 + 679.500i) q^{5} +(489.036 + 566.318i) q^{6} +4528.78 q^{7} +(-891.055 + 3997.90i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(1.16854 - 15.9573i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(-253.269 - 37.2934i) q^{4} +(-679.500 + 679.500i) q^{5} +(489.036 + 566.318i) q^{6} +4528.78 q^{7} +(-891.055 + 3997.90i) q^{8} -2187.00i q^{9} +(10048.9 + 11637.0i) q^{10} +(-6530.06 - 6530.06i) q^{11} +(9608.35 - 7141.91i) q^{12} +(-13982.9 - 13982.9i) q^{13} +(5292.05 - 72267.0i) q^{14} -44939.6i q^{15} +(62754.4 + 18890.5i) q^{16} -134692. q^{17} +(-34898.6 - 2555.59i) q^{18} +(35978.2 - 35978.2i) q^{19} +(197437. - 146756. i) q^{20} +(-149758. + 149758. i) q^{21} +(-111833. + 96571.3i) q^{22} +399859. q^{23} +(-102738. - 161669. i) q^{24} -532816. i q^{25} +(-239469. + 206790. i) q^{26} +(72320.0 + 72320.0i) q^{27} +(-1.14700e6 - 168893. i) q^{28} +(-131743. - 131743. i) q^{29} +(-717113. - 52513.6i) q^{30} -1.67872e6i q^{31} +(374772. - 979315. i) q^{32} +431874. q^{33} +(-157393. + 2.14931e6i) q^{34} +(-3.07731e6 + 3.07731e6i) q^{35} +(-81560.6 + 553899. i) q^{36} +(593864. - 593864. i) q^{37} +(-532072. - 616156. i) q^{38} +924778. q^{39} +(-2.11110e6 - 3.32205e6i) q^{40} -2.25170e6i q^{41} +(2.21473e6 + 2.56473e6i) q^{42} +(-3.00751e6 - 3.00751e6i) q^{43} +(1.41033e6 + 1.89739e6i) q^{44} +(1.48607e6 + 1.48607e6i) q^{45} +(467250. - 6.38066e6i) q^{46} -3.59403e6i q^{47} +(-2.69984e6 + 1.45050e6i) q^{48} +1.47450e7 q^{49} +(-8.50229e6 - 622615. i) q^{50} +(4.45400e6 - 4.45400e6i) q^{51} +(3.01997e6 + 4.06291e6i) q^{52} +(2.22191e6 - 2.22191e6i) q^{53} +(1.23854e6 - 1.06952e6i) q^{54} +8.87436e6 q^{55} +(-4.03539e6 + 1.81056e7i) q^{56} +2.37946e6i q^{57} +(-2.25621e6 + 1.94831e6i) q^{58} +(7.26513e6 + 7.26513e6i) q^{59} +(-1.67595e6 + 1.13818e7i) q^{60} +(125460. + 125460. i) q^{61} +(-2.67878e7 - 1.96165e6i) q^{62} -9.90444e6i q^{63} +(-1.51893e7 - 7.12470e6i) q^{64} +1.90028e7 q^{65} +(504661. - 6.89152e6i) q^{66} +(-1.15834e7 + 1.15834e7i) q^{67} +(3.41133e7 + 5.02311e6i) q^{68} +(-1.32226e7 + 1.32226e7i) q^{69} +(4.55095e7 + 5.27014e7i) q^{70} -1.29646e7 q^{71} +(8.74342e6 + 1.94874e6i) q^{72} -1.57187e7i q^{73} +(-8.78250e6 - 1.01704e7i) q^{74} +(1.76192e7 + 1.76192e7i) q^{75} +(-1.04539e7 + 7.77042e6i) q^{76} +(-2.95732e7 - 2.95732e7i) q^{77} +(1.08064e6 - 1.47569e7i) q^{78} +4.27261e7i q^{79} +(-5.54777e7 + 2.98055e7i) q^{80} -4.78297e6 q^{81} +(-3.59310e7 - 2.63120e6i) q^{82} +(3.27225e7 - 3.27225e7i) q^{83} +(4.35141e7 - 3.23441e7i) q^{84} +(9.15231e7 - 9.15231e7i) q^{85} +(-5.15061e7 + 4.44773e7i) q^{86} +8.71299e6 q^{87} +(3.19252e7 - 2.02879e7i) q^{88} -2.14578e7i q^{89} +(2.54501e7 - 2.19770e7i) q^{90} +(-6.33256e7 - 6.33256e7i) q^{91} +(-1.01272e8 - 1.49121e7i) q^{92} +(5.55122e7 + 5.55122e7i) q^{93} +(-5.73509e7 - 4.19976e6i) q^{94} +4.88944e7i q^{95} +(1.99911e7 + 4.47771e7i) q^{96} +1.40855e7 q^{97} +(1.72301e7 - 2.35291e8i) q^{98} +(-1.42812e7 + 1.42812e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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