LMFDB - Embedded newform 48.9.l.a.43.23

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			43.23
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.64455 - 12.7665i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-69.9655 - 246.254i) q^{4} +(-171.868 - 171.868i) q^{5} +(741.090 - 103.236i) q^{6} -1880.59 q^{7} +(-3818.57 - 1481.79i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(9.64455 - 12.7665i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-69.9655 - 246.254i) q^{4} +(-171.868 - 171.868i) q^{5} +(741.090 - 103.236i) q^{6} -1880.59 q^{7} +(-3818.57 - 1481.79i) q^{8} +2187.00i q^{9} +(-3851.75 + 536.560i) q^{10} +(-2204.79 + 2204.79i) q^{11} +(5829.52 - 10456.8i) q^{12} +(-7714.68 + 7714.68i) q^{13} +(-18137.4 + 24008.5i) q^{14} -11366.7i q^{15} +(-55745.7 + 34458.5i) q^{16} -89640.5 q^{17} +(27920.3 + 21092.6i) q^{18} +(-43093.9 - 43093.9i) q^{19} +(-30298.4 + 54348.1i) q^{20} +(-62187.6 - 62187.6i) q^{21} +(6883.18 + 49411.6i) q^{22} -135375. q^{23} +(-77273.0 - 175273. i) q^{24} -331548. i q^{25} +(24084.6 + 172894. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(131576. + 463102. i) q^{28} +(-267966. + 267966. i) q^{29} +(-145113. - 109627. i) q^{30} +1.04582e6i q^{31} +(-97728.3 + 1.04401e6i) q^{32} -145816. q^{33} +(-864542. + 1.14439e6i) q^{34} +(323214. + 323214. i) q^{35} +(538557. - 153014. i) q^{36} +(535814. + 535814. i) q^{37} +(-965778. + 134536. i) q^{38} -510220. q^{39} +(401619. + 910965. i) q^{40} -3.57497e6i q^{41} +(-1.39369e6 + 194145. i) q^{42} +(159395. - 159395. i) q^{43} +(697196. + 388678. i) q^{44} +(375876. - 375876. i) q^{45} +(-1.30563e6 + 1.72826e6i) q^{46} -3.34488e6i q^{47} +(-2.98288e6 - 703927. i) q^{48} -2.22818e6 q^{49} +(-4.23269e6 - 3.19763e6i) q^{50} +(-2.96424e6 - 2.96424e6i) q^{51} +(2.43953e6 + 1.36001e6i) q^{52} +(-2.33859e6 - 2.33859e6i) q^{53} +(225777. + 1.62076e6i) q^{54} +757867. q^{55} +(7.18118e6 + 2.78665e6i) q^{56} -2.85007e6i q^{57} +(836570. + 6.00540e6i) q^{58} +(1.64841e7 - 1.64841e7i) q^{59} +(-2.79910e6 + 795278. i) q^{60} +(4.05528e6 - 4.05528e6i) q^{61} +(1.33514e7 + 1.00865e7i) q^{62} -4.11285e6i q^{63} +(1.23858e7 + 1.13167e7i) q^{64} +2.65182e6 q^{65} +(-1.40633e6 + 1.86156e6i) q^{66} +(-1.31489e7 - 1.31489e7i) q^{67} +(6.27174e6 + 2.20743e7i) q^{68} +(-4.47660e6 - 4.47660e6i) q^{69} +(7.24356e6 - 1.00905e6i) q^{70} +2.65909e7 q^{71} +(3.24068e6 - 8.35122e6i) q^{72} -1.89912e7i q^{73} +(1.20081e7 - 1.67277e6i) q^{74} +(1.09636e7 - 1.09636e7i) q^{75} +(-7.59694e6 + 1.36271e7i) q^{76} +(4.14631e6 - 4.14631e6i) q^{77} +(-4.92084e6 + 6.51370e6i) q^{78} -3.22326e7i q^{79} +(1.55032e7 + 3.65859e6i) q^{80} -4.78297e6 q^{81} +(-4.56397e7 - 3.44789e7i) q^{82} +(-8.65538e6 - 8.65538e6i) q^{83} +(-1.09629e7 + 1.96649e7i) q^{84} +(1.54064e7 + 1.54064e7i) q^{85} +(-497620. - 3.57221e6i) q^{86} -1.77223e7 q^{87} +(1.16862e7 - 5.15211e6i) q^{88} +7.39979e7i q^{89} +(-1.17346e6 - 8.42377e6i) q^{90} +(1.45082e7 - 1.45082e7i) q^{91} +(9.47157e6 + 3.33366e7i) q^{92} +(-3.45833e7 + 3.45833e7i) q^{93} +(-4.27024e7 - 3.22599e7i) q^{94} +1.48130e7i q^{95} +(-3.77552e7 + 3.12918e7i) q^{96} -1.58830e8 q^{97} +(-2.14898e7 + 2.84460e7i) q^{98} +(-4.82187e6 - 4.82187e6i) 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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

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

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 $

$2$	9.64455	−	12.7665i	0.602784	−	0.797904i
$2$	9.64455	−	12.7665i	0.602784	−	0.797904i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$	−69.9655	−	246.254i	−0.273303	−	0.961928i
$5$	−171.868	−	171.868i	−0.274989	−	0.274989i	0.556116	−	0.831105i	$-0.312291\pi$
$5$	−171.868	−	171.868i	−0.274989	−	0.274989i	−0.831105	+	0.556116i	$0.812291\pi$
$6$	741.090	−	103.236i	0.571829	−	0.0796575i
$7$	−1880.59			−0.783253			−0.391627	−	0.920124i	$-0.628088\pi$
$7$	−1880.59			−0.783253			−0.391627	+	0.920124i	$0.628088\pi$
$8$	−3818.57	−	1481.79i	−0.932269	−	0.361766i
$9$			2187.00i			0.333333i
$10$	−3851.75	+	536.560i	−0.385175	+	0.0536560i
$11$	−2204.79	+	2204.79i	−0.150590	+	0.150590i	−0.778382	−	0.627791i	$-0.783959\pi$
$11$	−2204.79	+	2204.79i	−0.150590	+	0.150590i	0.627791	+	0.778382i	$0.283959\pi$
$12$	5829.52	−	10456.8i	0.281130	−	0.504281i
$13$	−7714.68	+	7714.68i	−0.270112	+	0.270112i	−0.829145	−	0.559033i	$-0.811172\pi$
$13$	−7714.68	+	7714.68i	−0.270112	+	0.270112i	0.559033	+	0.829145i	$0.311172\pi$
$14$	−18137.4	+	24008.5i	−0.472133	+	0.624961i
$15$		−	11366.7i		−	0.224528i
$16$	−55745.7	+	34458.5i	−0.850611	+	0.525795i
$17$	−89640.5			−1.07327			−0.536634	−	0.843815i	$-0.680305\pi$
$17$	−89640.5			−1.07327			−0.536634	+	0.843815i	$0.680305\pi$
$18$	27920.3	+	21092.6i	0.265968	+	0.200928i
$19$	−43093.9	−	43093.9i	−0.330675	−	0.330675i	0.522168	−	0.852843i	$-0.325123\pi$
$19$	−43093.9	−	43093.9i	−0.330675	−	0.330675i	−0.852843	+	0.522168i	$0.825123\pi$
$20$	−30298.4	+	54348.1i	−0.189365	+	0.339675i
$21$	−62187.6	−	62187.6i	−0.319762	−	0.319762i
$22$	6883.18	+	49411.6i	0.0293832	+	0.210930i
$23$	−135375.			−0.483757			−0.241878	−	0.970307i	$-0.577764\pi$
$23$	−135375.			−0.483757			−0.241878	+	0.970307i	$0.577764\pi$
$24$	−77273.0	−	175273.i	−0.232907	−	0.528287i
$25$		−	331548.i		−	0.848762i
$26$	24084.6	+	172894.i	0.0527044	+	0.378343i
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	131576.	+	463102.i	0.214065	+	0.753433i
$29$	−267966.	+	267966.i	−0.378868	+	0.378868i	−0.870694	−	0.491826i	$-0.836330\pi$
$29$	−267966.	+	267966.i	−0.378868	+	0.378868i	0.491826	+	0.870694i	$0.336330\pi$
$30$	−145113.	−	109627.i	−0.179152	−	0.135342i
$31$			1.04582e6i			1.13243i	0.824259	+	0.566213i	$0.191592\pi$
$31$			1.04582e6i			1.13243i	−0.824259	+	0.566213i	$0.808408\pi$
$32$	−97728.3	+	1.04401e6i	−0.0932010	+	0.995647i
$33$	−145816.			−0.122956
$34$	−864542.	+	1.14439e6i	−0.646949	+	0.856366i
$35$	323214.	+	323214.i	0.215386	+	0.215386i
$36$	538557.	−	153014.i	0.320643	−	0.0911009i
$37$	535814.	+	535814.i	0.285895	+	0.285895i	0.835455	−	0.549559i	$-0.185204\pi$
$37$	535814.	+	535814.i	0.285895	+	0.285895i	−0.549559	+	0.835455i	$0.685204\pi$
$38$	−965778.	+	134536.i	−0.463173	+	0.0645214i
$39$	−510220.			−0.220546
$40$	401619.	+	910965.i	0.156882	+	0.355846i
$41$		−	3.57497e6i		−	1.26513i	−0.774505	−	0.632567i	$-0.782001\pi$
$41$		−	3.57497e6i		−	1.26513i	0.774505	−	0.632567i	$-0.217999\pi$
$42$	−1.39369e6	+	194145.i	−0.447887	+	0.0623920i
$43$	159395.	−	159395.i	0.0466231	−	0.0466231i	−0.683411	−	0.730034i	$-0.739504\pi$
$43$	159395.	−	159395.i	0.0466231	−	0.0466231i	0.730034	+	0.683411i	$0.239504\pi$
$44$	697196.	+	388678.i	0.186013	+	0.103700i
$45$	375876.	−	375876.i	0.0916631	−	0.0916631i
$46$	−1.30563e6	+	1.72826e6i	−0.291601	+	0.385992i
$47$		−	3.34488e6i		−	0.685472i	−0.939432	−	0.342736i	$-0.888646\pi$
$47$		−	3.34488e6i		−	0.685472i	0.939432	−	0.342736i	$-0.111354\pi$
$48$	−2.98288e6	−	703927.i	−0.561916	−	0.132606i
$49$	−2.22818e6			−0.386514
$50$	−4.23269e6	−	3.19763e6i	−0.677231	−	0.511620i
$51$	−2.96424e6	−	2.96424e6i	−0.438160	−	0.438160i
$52$	2.43953e6	+	1.36001e6i	0.333651	+	0.186006i
$53$	−2.33859e6	−	2.33859e6i	−0.296381	−	0.296381i	0.543213	−	0.839595i	$-0.317208\pi$
$53$	−2.33859e6	−	2.33859e6i	−0.296381	−	0.296381i	−0.839595	+	0.543213i	$0.817208\pi$
$54$	225777.	+	1.62076e6i	0.0265525	+	0.190610i
$55$	757867.			0.0828214
$56$	7.18118e6	+	2.78665e6i	0.730203	+	0.283354i
$57$		−	2.85007e6i		−	0.269995i
$58$	836570.	+	6.00540e6i	0.0739249	+	0.530676i
$59$	1.64841e7	−	1.64841e7i	1.36037	−	1.36037i	0.486933	−	0.873439i	$-0.338116\pi$
$59$	1.64841e7	−	1.64841e7i	1.36037	−	1.36037i	0.873439	−	0.486933i	$-0.161884\pi$
$60$	−2.79910e6	+	795278.i	−0.215980	+	0.0613641i
$61$	4.05528e6	−	4.05528e6i	0.292888	−	0.292888i	−0.545332	−	0.838220i	$-0.683596\pi$
$61$	4.05528e6	−	4.05528e6i	0.292888	−	0.292888i	0.838220	+	0.545332i	$0.183596\pi$
$62$	1.33514e7	+	1.00865e7i	0.903568	+	0.682608i
$63$		−	4.11285e6i		−	0.261084i
$64$	1.23858e7	+	1.13167e7i	0.738251	+	0.674526i
$65$	2.65182e6			0.148556
$66$	−1.40633e6	+	1.86156e6i	−0.0741161	+	0.0981073i
$67$	−1.31489e7	−	1.31489e7i	−0.652513	−	0.652513i	0.301085	−	0.953597i	$-0.402651\pi$
$67$	−1.31489e7	−	1.31489e7i	−0.652513	−	0.652513i	−0.953597	+	0.301085i	$0.902651\pi$
$68$	6.27174e6	+	2.20743e7i	0.293327	+	1.03241i
$69$	−4.47660e6	−	4.47660e6i	−0.197493	−	0.197493i
$70$	7.24356e6	−	1.00905e6i	0.301689	−	0.0420262i
$71$	2.65909e7			1.04640			0.523201	−	0.852209i	$-0.324738\pi$
$71$	2.65909e7			1.04640			0.523201	+	0.852209i	$0.324738\pi$
$72$	3.24068e6	−	8.35122e6i	0.120589	−	0.310756i
$73$		−	1.89912e7i		−	0.668747i	−0.942441	−	0.334374i	$-0.891475\pi$
$73$		−	1.89912e7i		−	0.668747i	0.942441	−	0.334374i	$-0.108525\pi$
$74$	1.20081e7	−	1.67277e6i	0.400451	−	0.0557840i
$75$	1.09636e7	−	1.09636e7i	0.346505	−	0.346505i
$76$	−7.59694e6	+	1.36271e7i	−0.227711	+	0.408460i
$77$	4.14631e6	−	4.14631e6i	0.117950	−	0.117950i
$78$	−4.92084e6	+	6.51370e6i	−0.132942	+	0.175974i
$79$		−	3.22326e7i		−	0.827537i	−0.910382	−	0.413768i	$-0.864212\pi$
$79$		−	3.22326e7i		−	0.827537i	0.910382	−	0.413768i	$-0.135788\pi$
$80$	1.55032e7	+	3.65859e6i	0.378497	+	0.0893211i
$81$	−4.78297e6			−0.111111
$82$	−4.56397e7	−	3.44789e7i	−1.00946	−	0.762603i
$83$	−8.65538e6	−	8.65538e6i	−0.182379	−	0.182379i	0.610013	−	0.792392i	$-0.291164\pi$
$83$	−8.65538e6	−	8.65538e6i	−0.182379	−	0.182379i	−0.792392	+	0.610013i	$0.791164\pi$
$84$	−1.09629e7	+	1.96649e7i	−0.220196	+	0.394980i
$85$	1.54064e7	+	1.54064e7i	0.295138	+	0.295138i
$86$	−497620.	−	3.57221e6i	−0.00909711	−	0.0653045i
$87$	−1.77223e7			−0.309345
$88$	1.16862e7	−	5.15211e6i	0.194869	−	0.0859121i
$89$			7.39979e7i			1.17940i	0.807624	+	0.589698i	$0.200753\pi$
$89$			7.39979e7i			1.17940i	−0.807624	+	0.589698i	$0.799247\pi$
$90$	−1.17346e6	−	8.42377e6i	−0.0178853	−	0.128392i
$91$	1.45082e7	−	1.45082e7i	0.211566	−	0.211566i
$92$	9.47157e6	+	3.33366e7i	0.132212	+	0.465339i
$93$	−3.45833e7	+	3.45833e7i	−0.462311	+	0.462311i
$94$	−4.27024e7	−	3.22599e7i	−0.546941	−	0.413192i
$95$			1.48130e7i			0.181864i
$96$	−3.77552e7	+	3.12918e7i	−0.444520	+	0.368422i
$97$	−1.58830e8			−1.79409			−0.897046	−	0.441937i	$-0.854291\pi$
$97$	−1.58830e8			−1.79409			−0.897046	+	0.441937i	$0.854291\pi$
$98$	−2.14898e7	+	2.84460e7i	−0.232985	+	0.308401i
$99$	−4.82187e6	−	4.82187e6i	−0.0501967	−	0.0501967i
$100$	−8.16448e7	+	2.31969e7i	−0.816448	+	0.231969i
$101$	5.50541e7	+	5.50541e7i	0.529059	+	0.529059i	0.920292	−	0.391233i	$-0.127951\pi$
$101$	5.50541e7	+	5.50541e7i	0.529059	+	0.529059i	−0.391233	+	0.920292i	$0.627951\pi$
$102$	−6.64317e7	+	9.25413e6i	−0.613726	+	0.0854939i
$103$	−5.75009e7			−0.510888			−0.255444	−	0.966824i	$-0.582222\pi$
$103$	−5.75009e7			−0.510888			−0.255444	+	0.966824i	$0.582222\pi$
$104$	4.08906e7	−	1.80275e7i	0.349535	−	0.154100i
$105$			2.13762e7i			0.175862i
$106$	−5.24102e7	+	7.30091e6i	−0.415138	+	0.0578300i
$107$	1.20764e8	−	1.20764e8i	0.921306	−	0.921306i	−0.0758157	−	0.997122i	$-0.524156\pi$
$107$	1.20764e8	−	1.20764e8i	0.921306	−	0.921306i	0.997122	+	0.0758157i	$0.0241561\pi$
$108$	2.28689e7	+	1.27492e7i	0.168094	+	0.0937101i
$109$	−1.85495e8	+	1.85495e8i	−1.31409	+	1.31409i	−0.395726	+	0.918368i	$0.629507\pi$
$109$	−1.85495e8	+	1.85495e8i	−1.31409	+	1.31409i	−0.918368	+	0.395726i	$0.870493\pi$
$110$	7.30928e6	−	9.67529e6i	0.0499234	−	0.0660835i
$111$			3.54367e7i			0.233433i
$112$	1.04835e8	−	6.48023e7i	0.666244	−	0.411831i
$113$	7.98431e7			0.489692			0.244846	−	0.969562i	$-0.421263\pi$
$113$	7.98431e7			0.489692			0.244846	+	0.969562i	$0.421263\pi$
$114$	−3.63853e7	−	2.74876e7i	−0.215430	−	0.162749i
$115$	2.32667e7	+	2.32667e7i	0.133028	+	0.133028i
$116$	8.47361e7	+	4.72393e7i	0.467990	+	0.260898i
$117$	−1.68720e7	−	1.68720e7i	−0.0900375	−	0.0900375i
$118$	−5.14622e7	−	3.69426e8i	−0.265436	−	1.90546i
$119$	1.68577e8			0.840641
$120$	−1.68431e7	+	4.34047e7i	−0.0812265	+	0.209320i
$121$			2.04637e8i			0.954645i
$122$	−1.26603e7	−	9.08829e7i	−0.0571483	−	0.410245i
$123$	1.18217e8	−	1.18217e8i	0.516489	−	0.516489i
$124$	2.57537e8	−	7.31712e7i	1.08931	−	0.309495i
$125$	−1.24119e8	+	1.24119e8i	−0.508390	+	0.508390i
$126$	−5.25066e7	−	3.96666e7i	−0.208320	−	0.157378i
$127$			1.07500e8i			0.413232i	0.978422	+	0.206616i	$0.0662451\pi$
$127$			1.07500e8i			0.413232i	−0.978422	+	0.206616i	$0.933755\pi$
$128$	2.63929e8	−	4.89788e7i	0.983213	−	0.182460i
$129$	1.05418e7			0.0380676
$130$	2.55756e7	−	3.38544e7i	0.0895473	−	0.118534i
$131$	4.30194e7	+	4.30194e7i	0.146076	+	0.146076i	0.776363	−	0.630287i	$-0.217063\pi$
$131$	4.30194e7	+	4.30194e7i	0.146076	+	0.146076i	−0.630287	+	0.776363i	$0.717063\pi$
$132$	1.02021e7	+	3.59078e7i	0.0336043	+	0.118275i
$133$	8.10420e7	+	8.10420e7i	0.259002	+	0.259002i
$134$	−2.94679e8	+	4.10497e7i	−0.913967	+	0.127318i
$135$	2.48590e7			0.0748426
$136$	3.42299e8	+	1.32829e8i	1.00058	+	0.388272i
$137$			1.00603e8i			0.285580i	0.989753	+	0.142790i	$0.0456073\pi$
$137$			1.00603e8i			0.285580i	−0.989753	+	0.142790i	$0.954393\pi$
$138$	−1.00325e8	+	1.39756e7i	−0.276626	+	0.0385348i
$139$	−1.08586e8	+	1.08586e8i	−0.290881	+	0.290881i	−0.837428	−	0.546547i	$-0.815942\pi$
$139$	−1.08586e8	+	1.08586e8i	−0.290881	+	0.290881i	0.546547	+	0.837428i	$0.315942\pi$
$140$	5.69788e7	−	1.02206e8i	0.148321	−	0.266052i
$141$	1.10609e8	−	1.10609e8i	0.279843	−	0.279843i
$142$	2.56457e8	−	3.39471e8i	0.630755	−	0.834929i
$143$		−	3.40185e7i		−	0.0813525i
$144$	−7.53607e7	−	1.21916e8i	−0.175265	−	0.283537i
$145$	9.21099e7			0.208370
$146$	−2.42451e8	−	1.83162e8i	−0.533596	−	0.403110i
$147$	−7.36817e7	−	7.36817e7i	−0.157794	−	0.157794i
$148$	9.44577e7	−	1.69435e8i	0.196875	−	0.353147i
$149$	−3.77150e8	−	3.77150e8i	−0.765189	−	0.765189i	0.212067	−	0.977255i	$-0.431981\pi$
$149$	−3.77150e8	−	3.77150e8i	−0.765189	−	0.765189i	−0.977255	+	0.212067i	$0.931981\pi$
$150$	−3.42277e7	−	2.45707e8i	−0.0676102	−	0.485346i
$151$	4.60167e8			0.885131			0.442566	−	0.896736i	$-0.354068\pi$
$151$	4.60167e8			0.885131			0.442566	+	0.896736i	$0.354068\pi$
$152$	1.00701e8	+	2.28413e8i	0.188651	+	0.427905i
$153$		−	1.96044e8i		−	0.357756i
$154$	−1.29444e7	−	9.29229e7i	−0.0230145	−	0.165211i
$155$	1.79743e8	−	1.79743e8i	0.311405	−	0.311405i
$156$	3.56978e7	+	1.25643e8i	0.0602757	+	0.212149i
$157$	−6.32592e8	+	6.32592e8i	−1.04118	+	1.04118i	−0.0420629	+	0.999115i	$0.513393\pi$
$157$	−6.32592e8	+	6.32592e8i	−1.04118	+	1.04118i	−0.999115	+	0.0420629i	$0.986607\pi$
$158$	−4.11497e8	−	3.10869e8i	−0.660295	−	0.498826i
$159$		−	1.54666e8i		−	0.241994i
$160$	1.96229e8	−	1.62636e8i	0.299422	−	0.248163i
$161$	2.54585e8			0.378904
$162$	−4.61296e7	+	6.10616e7i	−0.0669760	+	0.0886560i
$163$	−2.97921e8	−	2.97921e8i	−0.422037	−	0.422037i	0.463868	−	0.885905i	$-0.346461\pi$
$163$	−2.97921e8	−	2.97921e8i	−0.422037	−	0.422037i	−0.885905	+	0.463868i	$0.846461\pi$
$164$	−8.80349e8	+	2.50124e8i	−1.21697	+	0.345765i
$165$	2.50612e7	+	2.50612e7i	0.0338117	+	0.0338117i
$166$	−1.93976e8	+	2.70214e7i	−0.255456	+	0.0355858i
$167$	9.65343e8			1.24113			0.620563	−	0.784156i	$-0.286904\pi$
$167$	9.65343e8			1.24113			0.620563	+	0.784156i	$0.286904\pi$
$168$	1.45319e8	+	3.29617e8i	0.182425	+	0.413783i
$169$			6.96698e8i			0.854079i
$170$	3.45272e8	−	4.80975e7i	0.413396	−	0.0575873i
$171$	9.42464e7	−	9.42464e7i	0.110225	−	0.110225i
$172$	−5.04038e7	−	2.80995e7i	−0.0575903	−	0.0321059i
$173$	−7.22332e8	+	7.22332e8i	−0.806403	+	0.806403i	−0.984088	−	0.177684i	$-0.943139\pi$
$173$	−7.22332e8	+	7.22332e8i	−0.806403	+	0.806403i	0.177684	+	0.984088i	$0.443139\pi$
$174$	−1.70923e8	+	2.26251e8i	−0.186468	+	0.246827i
$175$			6.23505e8i			0.664795i
$176$	4.69337e7	−	1.98881e8i	0.0489141	−	0.207273i
$177$	1.09020e9			1.11074
$178$	9.44692e8	+	7.13676e8i	0.941044	+	0.710921i
$179$	−1.01305e9	−	1.01305e9i	−0.986777	−	0.986777i	0.0131370	−	0.999914i	$-0.495818\pi$
$179$	−1.01305e9	−	1.01305e9i	−0.986777	−	0.986777i	−0.999914	+	0.0131370i	$0.995818\pi$
$180$	−1.18859e8	−	6.62625e7i	−0.113225	−	0.0631216i
$181$	−3.38424e8	−	3.38424e8i	−0.315317	−	0.315317i	0.531648	−	0.846965i	$-0.321573\pi$
$181$	−3.38424e8	−	3.38424e8i	−0.315317	−	0.315317i	−0.846965	+	0.531648i	$0.821573\pi$
$182$	−4.52933e7	−	3.25143e8i	−0.0412809	−	0.296339i
$183$	2.68201e8			0.239142
$184$	5.16939e8	+	2.00598e8i	0.450991	+	0.175007i
$185$		−	1.84179e8i		−	0.157236i
$186$	1.07966e8	+	7.75046e8i	0.0902062	+	0.647554i
$187$	1.97638e8	−	1.97638e8i	0.161624	−	0.161624i
$188$	−8.23690e8	+	2.34026e8i	−0.659375	+	0.187341i
$189$	1.36004e8	−	1.36004e8i	0.106587	−	0.106587i
$190$	1.89109e8	+	1.42864e8i	0.145110	+	0.109625i
$191$		−	6.91207e8i		−	0.519367i	−0.965694	−	0.259684i	$-0.916382\pi$
$191$		−	6.91207e8i		−	0.519367i	0.965694	−	0.259684i	$-0.0836183\pi$
$192$	3.53542e7	+	7.83796e8i	0.0260158	+	0.576764i
$193$	8.47126e8			0.610547			0.305273	−	0.952265i	$-0.401252\pi$
$193$	8.47126e8			0.610547			0.305273	+	0.952265i	$0.401252\pi$
$194$	−1.53184e9	+	2.02769e9i	−1.08145	+	1.43151i
$195$	8.76907e7	+	8.76907e7i	0.0606478	+	0.0606478i
$196$	1.55896e8	+	5.48697e8i	0.105635	+	0.371799i
$197$	−1.35753e9	−	1.35753e9i	−0.901331	−	0.901331i	0.0942208	−	0.995551i	$-0.469964\pi$
$197$	−1.35753e9	−	1.35753e9i	−0.901331	−	0.901331i	−0.995551	+	0.0942208i	$0.969964\pi$
$198$	−1.08063e8	+	1.50535e7i	−0.0703099	+	0.00979439i
$199$	−2.36509e9			−1.50812			−0.754060	−	0.656806i	$-0.771907\pi$
$199$	−2.36509e9			−1.50812			−0.754060	+	0.656806i	$0.771907\pi$
$200$	−4.91284e8	+	1.26604e9i	−0.307053	+	0.791274i
$201$		−	8.69616e8i		−	0.532774i
$202$	1.23382e9	−	1.71875e8i	0.741047	−	0.103230i
$203$	5.03935e8	−	5.03935e8i	0.296750	−	0.296750i
$204$	−5.22561e8	+	9.37350e8i	−0.301728	+	0.541229i
$205$	−6.14424e8	+	6.14424e8i	−0.347899	+	0.347899i
$206$	−5.54570e8	+	7.34084e8i	−0.307955	+	0.407640i
$207$		−	2.96065e8i		−	0.161252i
$208$	1.64224e8	−	6.95896e8i	0.0877369	−	0.371784i
$209$	1.90026e8			0.0995927
$210$	2.72898e8	+	2.06163e8i	0.140321	+	0.106007i
$211$	−1.68621e9	−	1.68621e9i	−0.850708	−	0.850708i	0.139512	−	0.990220i	$-0.455447\pi$
$211$	−1.68621e9	−	1.68621e9i	−0.850708	−	0.850708i	−0.990220	+	0.139512i	$0.955447\pi$
$212$	−4.12266e8	+	7.39508e8i	−0.204096	+	0.366100i
$213$	8.79309e8	+	8.79309e8i	0.427192	+	0.427192i
$214$	−3.77017e8	−	2.70645e9i	−0.179765	−	1.29046i
$215$	−5.47900e7			−0.0256417
$216$	3.83322e8	−	1.68996e8i	0.176096	−	0.0776357i
$217$		−	1.96676e9i		−	0.886976i
$218$	5.79102e8	+	4.15714e9i	0.256406	+	1.84064i
$219$	6.28005e8	−	6.28005e8i	0.273015	−	0.273015i
$220$	−5.30245e7	−	1.86628e8i	−0.0226353	−	0.0796682i
$221$	6.91548e8	−	6.91548e8i	0.289903	−	0.289903i
$222$	4.52402e8	+	3.41771e8i	0.186257	+	0.140710i
$223$			4.08144e9i			1.65042i	0.564827	+	0.825209i	$0.308943\pi$
$223$			4.08144e9i			1.65042i	−0.564827	+	0.825209i	$0.691057\pi$
$224$	1.83787e8	−	1.96336e9i	0.0730000	−	0.779844i
$225$	7.25094e8			0.282921
$226$	7.70050e8	−	1.01931e9i	0.295179	−	0.390728i
$227$	4.12927e7	+	4.12927e7i	0.0155514	+	0.0155514i	0.714840	−	0.699288i	$-0.246500\pi$
$227$	4.12927e7	+	4.12927e7i	0.0155514	+	0.0155514i	−0.699288	+	0.714840i	$0.746500\pi$
$228$	−7.01839e8	+	1.99406e8i	−0.259716	+	0.0737903i
$229$	−1.94536e9	−	1.94536e9i	−0.707388	−	0.707388i	0.258597	−	0.965985i	$-0.416740\pi$
$229$	−1.94536e9	−	1.94536e9i	−0.707388	−	0.707388i	−0.965985	+	0.258597i	$0.916740\pi$
$230$	5.21430e8	−	7.26368e7i	0.186331	−	0.0259565i
$231$	2.74221e8			0.0963059
$232$	1.42032e9	−	6.26179e8i	0.490269	−	0.216146i
$233$		−	3.42381e9i		−	1.16168i	−0.814019	−	0.580838i	$-0.802725\pi$
$233$		−	3.42381e9i		−	1.16168i	0.814019	−	0.580838i	$-0.197275\pi$
$234$	−3.78119e8	+	5.26731e7i	−0.126114	+	0.0175681i
$235$	−5.74880e8	+	5.74880e8i	−0.188498	+	0.188498i
$236$	−5.21259e9	−	2.90595e9i	−1.68037	−	0.936787i
$237$	1.06587e9	−	1.06587e9i	0.337840	−	0.337840i
$238$	1.62585e9	−	2.15213e9i	0.506725	−	0.670751i
$239$			5.04156e9i			1.54516i	0.634917	+	0.772580i	$0.281034\pi$
$239$			5.04156e9i			1.54516i	−0.634917	+	0.772580i	$0.718966\pi$
$240$	3.91680e8	+	6.33646e8i	0.118056	+	0.190986i
$241$	5.49639e9			1.62933			0.814666	−	0.579931i	$-0.196921\pi$
$241$	5.49639e9			1.62933			0.814666	+	0.579931i	$0.196921\pi$
$242$	2.61249e9	+	1.97363e9i	0.761716	+	0.575445i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	−1.28236e9	−	7.14898e8i	−0.361784	−	0.201690i
$245$	3.82953e8	+	3.82953e8i	0.106287	+	0.106287i
$246$	−3.69066e8	−	2.64937e9i	−0.100777	−	0.723440i
$247$	6.64911e8			0.178639
$248$	1.54969e9	−	3.99354e9i	0.409673	−	1.05573i
$249$		−	5.72434e8i		−	0.148912i
$250$	3.87489e8	+	2.78162e9i	0.0991971	+	0.712096i
$251$	2.53152e9	−	2.53152e9i	0.637802	−	0.637802i	−0.312211	−	0.950013i	$-0.601070\pi$
$251$	2.53152e9	−	2.53152e9i	0.637802	−	0.637802i	0.950013	+	0.312211i	$0.101070\pi$
$252$	−1.01280e9	+	2.87758e8i	−0.251144	+	0.0713550i
$253$	2.98473e8	−	2.98473e8i	0.0728490	−	0.0728490i
$254$	1.37240e9	+	1.03679e9i	0.329720	+	0.249090i
$255$			1.01892e9i			0.240979i
$256$	1.92019e9	−	3.84182e9i	0.447079	−	0.894494i
$257$	4.15128e9			0.951588			0.475794	−	0.879557i	$-0.342161\pi$
$257$	4.15128e9			0.951588			0.475794	+	0.879557i	$0.342161\pi$
$258$	1.01671e8	−	1.34582e8i	0.0229466	−	0.0303743i
$259$	−1.00765e9	−	1.00765e9i	−0.223929	−	0.223929i
$260$	−1.85536e8	−	6.53020e8i	−0.0406008	−	0.142900i
$261$	−5.86042e8	−	5.86042e8i	−0.126289	−	0.126289i
$262$	9.64108e8	−	1.34303e8i	0.204607	−	0.0285024i
$263$	1.52176e9			0.318070			0.159035	−	0.987273i	$-0.449162\pi$
$263$	1.52176e9			0.318070			0.159035	+	0.987273i	$0.449162\pi$
$264$	5.56811e8	+	2.16070e8i	0.114628	+	0.0444814i
$265$			8.03860e8i			0.163004i
$266$	1.81623e9	−	2.53007e8i	0.362781	−	0.0505366i
$267$	−2.44697e9	+	2.44697e9i	−0.481486	+	0.481486i
$268$	−2.31799e9	+	4.15792e9i	−0.449337	+	0.806004i
$269$	−3.44683e9	+	3.44683e9i	−0.658281	+	0.658281i	−0.954973	−	0.296692i	$-0.904116\pi$
$269$	−3.44683e9	+	3.44683e9i	−0.658281	+	0.658281i	0.296692	+	0.954973i	$0.404116\pi$
$270$	2.39754e8	−	3.17362e8i	0.0451140	−	0.0597173i
$271$			1.04180e10i			1.93156i	0.259359	+	0.965781i	$0.416489\pi$
$271$			1.04180e10i			1.93156i	−0.259359	+	0.965781i	$0.583511\pi$
$272$	4.99707e9	−	3.08888e9i	0.912935	−	0.564319i
$273$	9.59515e8			0.172743
$274$	1.28434e9	+	9.70268e8i	0.227865	+	0.172143i
$275$	7.30992e8	+	7.30992e8i	0.127815	+	0.127815i
$276$	−7.89171e8	+	1.41558e9i	−0.135999	+	0.243949i
$277$	1.38788e9	+	1.38788e9i	0.235739	+	0.235739i	0.815083	−	0.579344i	$-0.196691\pi$
$277$	1.38788e9	+	1.38788e9i	0.235739	+	0.235739i	−0.579344	+	0.815083i	$0.696691\pi$
$278$	3.38998e8	+	2.43353e9i	0.0567567	+	0.407434i
$279$	−2.28721e9			−0.377475
$280$	−7.55281e8	−	1.71315e9i	−0.122879	−	0.278717i
$281$		−	2.56772e9i		−	0.411834i	−0.978569	−	0.205917i	$-0.933982\pi$
$281$		−	2.56772e9i		−	0.411834i	0.978569	−	0.205917i	$-0.0660177\pi$
$282$	−3.45313e8	−	2.47886e9i	−0.0546030	−	0.391972i
$283$	−4.71183e9	+	4.71183e9i	−0.734588	+	0.734588i	−0.971525	−	0.236937i	$-0.923857\pi$
$283$	−4.71183e9	+	4.71183e9i	−0.734588	+	0.734588i	0.236937	+	0.971525i	$0.423857\pi$
$284$	−1.86044e9	−	6.54809e9i	−0.285985	−	1.00656i
$285$	−4.89837e8	+	4.89837e8i	−0.0742458	+	0.0742458i
$286$	−4.34296e8	−	3.28093e8i	−0.0649115	−	0.0490380i
$287$			6.72305e9i			0.990921i
$288$	−2.28325e9	−	2.13732e8i	−0.331882	−	0.0310670i
$289$	1.05966e9			0.151906
$290$	8.88358e8	−	1.17592e9i	0.125602	−	0.166259i
$291$	−5.25220e9	−	5.25220e9i	−0.732435	−	0.732435i
$292$	−4.67666e9	+	1.32873e9i	−0.643287	+	0.182770i
$293$	−1.76455e9	−	1.76455e9i	−0.239421	−	0.239421i	0.577189	−	0.816610i	$-0.304150\pi$
$293$	−1.76455e9	−	1.76455e9i	−0.239421	−	0.239421i	−0.816610	+	0.577189i	$0.804150\pi$
$294$	−1.65128e9	+	2.30028e8i	−0.221020	+	0.0307888i
$295$	−5.66620e9			−0.748176
$296$	−1.25208e9	−	2.84001e9i	−0.163104	−	0.369959i
$297$		−	3.18901e8i		−	0.0409854i
$298$	−8.45230e9	+	1.17743e9i	−1.07179	+	0.149304i
$299$	1.04437e9	−	1.04437e9i	0.130669	−	0.130669i
$300$	−3.46692e9	−	1.93276e9i	−0.428014	−	0.238613i
$301$	−2.99757e8	+	2.99757e8i	−0.0365177	+	0.0365177i
$302$	4.43810e9	−	5.87471e9i	0.533543	−	0.706250i
$303$			3.64107e9i			0.431975i
$304$	3.88725e9	+	9.17347e8i	0.455143	+	0.107409i
$305$	−1.39395e9			−0.161082
$306$	−2.50279e9	−	1.89075e9i	−0.285455	−	0.215650i
$307$	−8.12538e9	−	8.12538e9i	−0.914724	−	0.914724i	0.0819153	−	0.996639i	$-0.473896\pi$
$307$	−8.12538e9	−	8.12538e9i	−0.914724	−	0.914724i	−0.996639	+	0.0819153i	$0.973896\pi$
$308$	−1.31114e9	−	7.30945e8i	−0.145696	−	0.0812235i
$309$	−1.90145e9	−	1.90145e9i	−0.208569	−	0.208569i
$310$	−5.61145e8	−	4.02823e9i	−0.0607614	−	0.436182i
$311$	9.49491e9			1.01496			0.507480	−	0.861663i	$-0.330577\pi$
$311$	9.49491e9			1.01496			0.507480	+	0.861663i	$0.330577\pi$
$312$	1.94831e9	+	7.56040e8i	0.205608	+	0.0797859i
$313$			1.62139e9i			0.168931i	0.996426	+	0.0844655i	$0.0269183\pi$
$313$			1.62139e9i			0.168931i	−0.996426	+	0.0844655i	$0.973082\pi$
$314$	1.97490e9	+	1.41770e10i	0.203155	+	1.45837i
$315$	−7.06869e8	+	7.06869e8i	−0.0717955	+	0.0717955i
$316$	−7.93740e9	+	2.25517e9i	−0.796031	+	0.226168i
$317$	−1.27482e10	+	1.27482e10i	−1.26244	+	1.26244i	−0.312532	+	0.949907i	$0.601177\pi$
$317$	−1.27482e10	+	1.27482e10i	−1.26244	+	1.26244i	−0.949907	+	0.312532i	$0.898823\pi$
$318$	−1.97453e9	−	1.49168e9i	−0.193088	−	0.145870i
$319$		−	1.18162e9i		−	0.114108i
$320$	−1.83750e8	−	4.07370e9i	−0.0175238	−	0.388499i
$321$	7.98690e9			0.752243
$322$	2.45536e9	−	3.25015e9i	0.228397	−	0.302329i
$323$	3.86296e9	+	3.86296e9i	0.354903	+	0.354903i
$324$	3.34643e8	+	1.17782e9i	0.0303670	+	0.106881i
$325$	2.55778e9	+	2.55778e9i	0.229261	+	0.229261i
$326$	−6.67671e9	+	9.30086e8i	−0.591142	+	0.0823479i
$327$	−1.22680e10			−1.07295
$328$	−5.29736e9	+	1.36513e10i	−0.457682	+	1.17945i
$329$			6.29036e9i			0.536898i
$330$	5.61648e8	−	7.82392e7i	0.0473596	−	0.00659734i
$331$	3.13629e9	−	3.13629e9i	0.261278	−	0.261278i	−0.564295	−	0.825573i	$-0.690852\pi$
$331$	3.13629e9	−	3.13629e9i	0.261278	−	0.261278i	0.825573	+	0.564295i	$0.190852\pi$
$332$	−1.52584e9	+	2.73700e9i	−0.125591	+	0.225280i
$333$	−1.17183e9	+	1.17183e9i	−0.0952985	+	0.0952985i
$334$	9.31030e9	−	1.23240e10i	0.748131	−	0.990300i
$335$			4.51975e9i			0.358868i
$336$	5.60958e9	+	1.32380e9i	0.440122	+	0.103864i
$337$	1.00940e10			0.782609			0.391305	−	0.920261i	$-0.372024\pi$
$337$	1.00940e10			0.782609			0.391305	+	0.920261i	$0.372024\pi$
$338$	8.89438e9	+	6.71934e9i	0.681473	+	0.514825i
$339$	2.64026e9	+	2.64026e9i	0.199916	+	0.199916i
$340$	2.71596e9	−	4.87179e9i	0.203239	−	0.364563i
$341$	−2.30581e9	−	2.30581e9i	−0.170532	−	0.170532i
$342$	−2.94230e8	−	2.11216e9i	−0.0215071	−	0.154391i
$343$	1.50315e10			1.08599
$344$	−8.44853e8	+	3.72472e8i	−0.0603319	+	0.0265987i
$345$			1.53877e9i			0.108617i
$346$	2.25506e9	+	1.61882e10i	0.157346	+	1.12952i
$347$	1.97537e10	−	1.97537e10i	1.36248	−	1.36248i	0.491739	−	0.870743i	$-0.336361\pi$
$347$	1.97537e10	−	1.97537e10i	1.36248	−	1.36248i	0.870743	−	0.491739i	$-0.163639\pi$
$348$	1.23995e9	+	4.36418e9i	0.0845447	+	0.297567i
$349$	6.08836e9	−	6.08836e9i	0.410392	−	0.410392i	−0.471483	−	0.881875i	$-0.656281\pi$
$349$	6.08836e9	−	6.08836e9i	0.410392	−	0.410392i	0.881875	+	0.471483i	$0.156281\pi$
$350$	7.95996e9	+	6.01343e9i	0.530443	+	0.400728i
$351$		−	1.11585e9i		−	0.0735153i
$352$	−2.08636e9	−	2.51730e9i	−0.135899	−	0.163970i
$353$	−1.19706e10			−0.770934			−0.385467	−	0.922722i	$-0.625960\pi$
$353$	−1.19706e10			−0.770934			−0.385467	+	0.922722i	$0.625960\pi$
$354$	1.05145e10	−	1.39180e10i	0.669536	−	0.886264i
$355$	−4.57013e9	−	4.57013e9i	−0.287750	−	0.287750i
$356$	1.82222e10	−	5.17730e9i	1.13449	−	0.322332i
$357$	5.57453e9	+	5.57453e9i	0.343190	+	0.343190i
$358$	−2.27035e10	+	3.16267e9i	−1.38217	+	0.192540i
$359$	9.69453e9			0.583645			0.291823	−	0.956472i	$-0.405738\pi$
$359$	9.69453e9			0.583645			0.291823	+	0.956472i	$0.405738\pi$
$360$	−1.99228e9	+	8.78341e8i	−0.118615	+	0.0522941i
$361$		−	1.32694e10i		−	0.781308i
$362$	−7.58444e9	+	1.05654e9i	−0.441661	+	0.0615247i
$363$	−6.76695e9	+	6.76695e9i	−0.389732	+	0.389732i
$364$	−4.58776e9	−	2.55762e9i	−0.261333	−	0.145690i
$365$	−3.26399e9	+	3.26399e9i	−0.183898	+	0.183898i
$366$	2.58668e9	−	3.42398e9i	0.144151	−	0.190812i
$367$		−	3.60750e10i		−	1.98858i	−0.106725	−	0.994289i	$-0.534036\pi$
$367$		−	3.60750e10i		−	1.98858i	0.106725	−	0.994289i	$-0.465964\pi$
$368$	7.54657e9	−	4.66482e9i	0.411489	−	0.254357i
$369$	7.81846e9			0.421712
$370$	−2.35132e9	−	1.77632e9i	−0.125460	−	0.0947797i
$371$	4.39794e9	+	4.39794e9i	0.232142	+	0.232142i
$372$	1.09359e10	+	6.09662e9i	0.571061	+	0.318359i
$373$	−6.45993e9	−	6.45993e9i	−0.333728	−	0.333728i	0.520272	−	0.854000i	$-0.325830\pi$
$373$	−6.45993e9	−	6.45993e9i	−0.333728	−	0.333728i	−0.854000	+	0.520272i	$0.825830\pi$
$374$	−6.17012e8	−	4.42928e9i	−0.0315360	−	0.226384i
$375$	−8.20874e9			−0.415099
$376$	−4.95642e9	+	1.27727e10i	−0.247980	+	0.639044i
$377$		−	4.13455e9i		−	0.204674i
$378$	−4.24595e8	−	3.04799e9i	−0.0207973	−	0.149296i
$379$	1.25889e10	−	1.25889e10i	0.610144	−	0.610144i	−0.332840	−	0.942983i	$-0.608007\pi$
$379$	1.25889e10	−	1.25889e10i	0.610144	−	0.610144i	0.942983	+	0.332840i	$0.108007\pi$
$380$	3.64774e9	−	1.03640e9i	0.174940	−	0.0497040i
$381$	−3.55483e9	+	3.55483e9i	−0.168701	+	0.168701i
$382$	−8.82427e9	−	6.66637e9i	−0.414405	−	0.313066i
$383$		−	2.60103e10i		−	1.20879i	−0.796686	−	0.604394i	$-0.793415\pi$
$383$		−	2.60103e10i		−	1.20879i	0.796686	−	0.604394i	$-0.206585\pi$
$384$	1.03473e10	+	7.10801e9i	0.475884	+	0.326906i
$385$	−1.42524e9			−0.0648701
$386$	8.17015e9	−	1.08148e10i	0.368028	−	0.487158i
$387$	3.48597e8	+	3.48597e8i	0.0155410	+	0.0155410i
$388$	1.11126e10	+	3.91124e10i	0.490330	+	1.72579i
$389$	−2.45800e10	−	2.45800e10i	−1.07346	−	1.07346i	−0.997079	−	0.0763764i	$-0.975665\pi$
$389$	−2.45800e10	−	2.45800e10i	−1.07346	−	1.07346i	−0.0763764	−	0.997079i	$-0.524335\pi$
$390$	1.96524e9	−	2.73763e8i	0.0849486	−	0.0118336i
$391$	1.21351e10			0.519201
$392$	8.50846e9	+	3.30170e9i	0.360335	+	0.139828i
$393$			2.84514e9i			0.119271i
$394$	−3.04236e10	+	4.23810e9i	−1.26248	+	0.175868i
$395$	−5.53977e9	+	5.53977e9i	−0.227564	+	0.227564i
$396$	−8.50039e8	+	1.52477e9i	−0.0345667	+	0.0620045i
$397$	2.76011e10	−	2.76011e10i	1.11113	−	1.11113i	0.118131	−	0.992998i	$-0.462310\pi$
$397$	2.76011e10	−	2.76011e10i	1.11113	−	1.11113i	0.992998	−	0.118131i	$-0.0376903\pi$
$398$	−2.28102e10	+	3.01939e10i	−0.909071	+	1.20334i
$399$			5.35981e9i			0.211474i
$400$	1.14246e10	+	1.84823e10i	0.446275	+	0.721966i
$401$	−2.26861e10			−0.877368			−0.438684	−	0.898641i	$-0.644555\pi$
$401$	−2.26861e10			−0.877368			−0.438684	+	0.898641i	$0.644555\pi$
$402$	−1.11019e10	−	8.38705e9i	−0.425103	−	0.321148i
$403$	−8.06816e9	−	8.06816e9i	−0.305882	−	0.305882i
$404$	9.70538e9	−	1.74092e10i	0.364324	−	0.653510i
$405$	8.22041e8	+	8.22041e8i	0.0305544	+	0.0305544i
$406$	−1.57325e9	−	1.12937e10i	−0.0579019	−	0.415654i
$407$	−2.36271e9			−0.0861060
$408$	6.92679e9	+	1.57116e10i	0.249972	+	0.566994i
$409$			1.83763e10i			0.656697i	0.944557	+	0.328349i	$0.106492\pi$
$409$			1.83763e10i			0.656697i	−0.944557	+	0.328349i	$0.893508\pi$
$410$	1.91818e9	+	1.37699e10i	0.0678821	+	0.487298i
$411$	−3.32674e9	+	3.32674e9i	−0.116587	+	0.116587i
$412$	4.02308e9	+	1.41598e10i	0.139627	+	0.491438i
$413$	−3.09999e10	+	3.09999e10i	−1.06552	+	1.06552i
$414$	−3.77971e9	−	2.85541e9i	−0.128664	−	0.0972003i
$415$			2.97517e9i			0.100304i
$416$	−7.30027e9	−	8.80816e9i	−0.243762	−	0.294111i
$417$	−7.18148e9			−0.237503
$418$	1.83271e9	−	2.42596e9i	0.0600329	−	0.0794655i
$419$	8.56104e9	+	8.56104e9i	0.277760	+	0.277760i	0.832214	−	0.554454i	$-0.187073\pi$
$419$	8.56104e9	+	8.56104e9i	0.277760	+	0.277760i	−0.554454	+	0.832214i	$0.687073\pi$
$420$	5.26396e9	−	1.49559e9i	0.169167	−	0.0480636i
$421$	9.93211e9	+	9.93211e9i	0.316165	+	0.316165i	0.847292	−	0.531127i	$-0.178231\pi$
$421$	9.93211e9	+	9.93211e9i	0.316165	+	0.316165i	−0.531127	+	0.847292i	$0.678231\pi$
$422$	−3.77896e10	+	5.26420e9i	−1.19158	+	0.165990i
$423$	7.31526e9			0.228491
$424$	5.46478e9	+	1.23954e10i	0.169087	+	0.383528i
$425$			2.97201e10i			0.910949i
$426$	1.97062e10	−	2.74514e9i	0.598363	−	0.0833538i
$427$	−7.62632e9	+	7.62632e9i	−0.229405	+	0.229405i
$428$	−3.81880e10	−	2.12893e10i	−1.13803	−	0.634435i
$429$	1.12493e9	−	1.12493e9i	0.0332120	−	0.0332120i
$430$	−5.28425e8	+	6.99475e8i	−0.0154564	+	0.0204597i
$431$		−	3.60496e10i		−	1.04470i	−0.852732	−	0.522349i	$-0.825056\pi$
$431$		−	3.60496e10i		−	1.04470i	0.852732	−	0.522349i	$-0.174944\pi$
$432$	1.53949e9	−	6.52356e9i	0.0442019	−	0.187305i
$433$	−5.19397e9			−0.147757			−0.0738785	−	0.997267i	$-0.523538\pi$
$433$	−5.19397e9			−0.147757			−0.0738785	+	0.997267i	$0.523538\pi$
$434$	−2.51086e10	−	1.89685e10i	−0.707722	−	0.534655i
$435$	3.04590e9	+	3.04590e9i	0.0850665	+	0.0850665i
$436$	5.86571e10	+	3.27006e10i	1.62321	+	0.904919i
$437$	5.83384e9	+	5.83384e9i	0.159966	+	0.159966i
$438$	−1.96058e9	−	1.40742e10i	−0.0532707	−	0.382409i
$439$	2.43023e10			0.654318			0.327159	−	0.944969i	$-0.393909\pi$
$439$	2.43023e10			0.654318			0.327159	+	0.944969i	$0.393909\pi$
$440$	−2.89397e9	−	1.12300e9i	−0.0772118	−	0.0299619i
$441$		−	4.87303e9i		−	0.128838i
$442$	−2.15896e9	−	1.54983e10i	−0.0565660	−	0.406064i
$443$	−4.82825e9	+	4.82825e9i	−0.125365	+	0.125365i	−0.767005	−	0.641641i	$-0.778254\pi$
$443$	−4.82825e9	+	4.82825e9i	−0.125365	+	0.125365i	0.641641	+	0.767005i	$0.278254\pi$
$444$	8.72642e9	−	2.47935e9i	0.224545	−	0.0637978i
$445$	1.27179e10	−	1.27179e10i	0.324321	−	0.324321i
$446$	5.21056e10	+	3.93637e10i	1.31688	+	0.994846i
$447$		−	2.49432e10i		−	0.624774i
$448$	−2.32926e10	−	2.12820e10i	−0.578238	−	0.528325i
$449$	−6.82155e10			−1.67841			−0.839205	−	0.543816i	$-0.816979\pi$
$449$	−6.82155e10			−1.67841			−0.839205	+	0.543816i	$0.816979\pi$
$450$	6.99321e9	−	9.25690e9i	0.170540	−	0.225744i
$451$	7.88205e9	+	7.88205e9i	0.190517	+	0.190517i
$452$	−5.58626e9	−	1.96616e10i	−0.133834	−	0.471049i
$453$	1.52169e10	+	1.52169e10i	0.361353	+	0.361353i
$454$	9.25411e8	−	1.28913e8i	0.0217827	−	0.00303439i
$455$	−4.98699e9			−0.116357
$456$	−4.22321e9	+	1.08832e10i	−0.0976749	+	0.251708i
$457$			5.79130e10i			1.32774i	0.747850	+	0.663868i	$0.231086\pi$
$457$			5.79130e10i			1.32774i	−0.747850	+	0.663868i	$0.768914\pi$
$458$	−4.35974e10	+	6.07326e9i	−0.990830	+	0.138026i
$459$	6.48280e9	−	6.48280e9i	0.146053	−	0.146053i
$460$	4.10164e9	−	7.35737e9i	0.0916065	−	0.164320i
$461$	−1.23734e10	+	1.23734e10i	−0.273958	+	0.273958i	−0.830691	−	0.556733i	$-0.812055\pi$
$461$	−1.23734e10	+	1.23734e10i	−0.273958	+	0.273958i	0.556733	+	0.830691i	$0.312055\pi$
$462$	2.64474e9	−	3.50083e9i	0.0580517	−	0.0768429i
$463$			1.65359e10i			0.359835i	0.983682	+	0.179917i	$0.0575831\pi$
$463$			1.65359e10i			0.359835i	−0.983682	+	0.179917i	$0.942417\pi$
$464$	5.70425e9	−	2.41717e10i	0.123063	−	0.521477i
$465$	1.18875e10			0.254261
$466$	−4.37099e10	−	3.30210e10i	−0.926907	−	0.700240i
$467$	4.08731e10	+	4.08731e10i	0.859350	+	0.859350i	0.991262	−	0.131911i	$-0.0421114\pi$
$467$	4.08731e10	+	4.08731e10i	0.859350	+	0.859350i	−0.131911	+	0.991262i	$0.542111\pi$
$468$	−2.97433e9	+	5.33525e9i	−0.0620021	+	0.111217i
$469$	2.47276e10	+	2.47276e10i	0.511083	+	0.511083i
$470$	1.79473e9	+	1.28836e10i	0.0367797	+	0.264026i
$471$	−4.18372e10			−0.850118
$472$	−8.73719e10	+	3.85198e10i	−1.76037	+	0.776097i
$473$			7.02866e8i			0.0140420i
$474$	−3.32757e9	−	2.38873e10i	−0.0659195	−	0.473209i
$475$	−1.42877e10	+	1.42877e10i	−0.280664	+	0.280664i
$476$	−1.17946e10	−	4.15127e10i	−0.229749	−	0.808636i
$477$	5.11450e9	−	5.11450e9i	0.0987938	−	0.0987938i
$478$	6.43630e10	+	4.86236e10i	1.23289	+	0.931398i
$479$			2.12005e10i			0.402721i	0.979517	+	0.201360i	$0.0645362\pi$
$479$			2.12005e10i			0.402721i	−0.979517	+	0.201360i	$0.935464\pi$
$480$	1.18670e10	+	1.11085e9i	0.223551	+	0.0209262i
$481$	−8.26727e9			−0.154448
$482$	5.30102e10	−	7.01695e10i	0.982135	−	1.30005i
$483$	8.41864e9	+	8.41864e9i	0.154687	+	0.154687i
$484$	5.03925e10	−	1.43175e10i	0.918300	−	0.260907i
$485$	2.72978e10	+	2.72978e10i	0.493356	+	0.493356i
$486$	−3.54461e9	+	4.93775e8i	−0.0635365	+	0.00885083i
$487$	−4.29880e10			−0.764243			−0.382121	−	0.924112i	$-0.624806\pi$
$487$	−4.29880e10			−0.764243			−0.382121	+	0.924112i	$0.624806\pi$
$488$	−2.14945e10	+	9.47630e9i	−0.379007	+	0.167094i
$489$		−	1.97034e10i		−	0.344592i
$490$	8.58238e9	−	1.19555e9i	0.148875	−	0.0207388i
$491$	3.19789e9	−	3.19789e9i	0.0550221	−	0.0550221i	−0.679060	−	0.734082i	$-0.737613\pi$
$491$	3.19789e9	−	3.19789e9i	0.0550221	−	0.0550221i	0.734082	+	0.679060i	$0.237613\pi$
$492$	−3.73826e10	−	2.08403e10i	−0.637983	−	0.355668i
$493$	2.40206e10	−	2.40206e10i	0.406627	−	0.406627i
$494$	6.41277e9	−	8.48857e9i	0.107681	−	0.142537i
$495$			1.65746e9i			0.0276071i
$496$	−3.60374e10	−	5.82999e10i	−0.595424	−	0.963255i
$497$	−5.00065e10			−0.819598
$498$	−7.30797e9	−	5.52087e9i	−0.118817	−	0.0897615i
$499$	1.47768e10	+	1.47768e10i	0.238329	+	0.238329i	0.816158	−	0.577829i	$-0.196100\pi$
$499$	1.47768e10	+	1.47768e10i	0.238329	+	0.238329i	−0.577829	+	0.816158i	$0.696100\pi$
$500$	3.92487e10	+	2.18806e10i	0.627979	+	0.350090i
$501$	3.19221e10	+	3.19221e10i	0.506688	+	0.506688i
$502$	−7.90320e9	−	5.67338e10i	−0.124448	−	0.893362i
$503$	2.96936e10			0.463864			0.231932	−	0.972732i	$-0.425495\pi$
$503$	2.96936e10			0.463864			0.231932	+	0.972732i	$0.425495\pi$
$504$	−6.09439e9	+	1.57052e10i	−0.0944514	+	0.243401i
$505$		−	1.89241e10i		−	0.290971i
$506$	−9.31811e8	−	6.68909e9i	−0.0142143	−	0.102039i
$507$	−2.30385e10	+	2.30385e10i	−0.348676	+	0.348676i
$508$	2.64723e10	−	7.52130e9i	0.397500	−	0.112937i
$509$	3.14827e10	−	3.14827e10i	0.469030	−	0.469030i	−0.432570	−	0.901600i	$-0.642393\pi$
$509$	3.14827e10	−	3.14827e10i	0.469030	−	0.469030i	0.901600	+	0.432570i	$0.142393\pi$
$510$	1.30080e10	+	9.82701e9i	0.192278	+	0.145258i
$511$			3.57148e10i			0.523798i
$512$	−3.05271e10	−	6.15667e10i	−0.444228	−	0.895914i
$513$	6.23310e9			0.0899983
$514$	4.00372e10	−	5.29971e10i	0.573602	−	0.759276i
$515$	9.88259e9	+	9.88259e9i	0.140489	+	0.140489i
$516$	−7.37562e8	−	2.59596e9i	−0.0104040	−	0.0366183i
$517$	7.37476e9	+	7.37476e9i	0.103225	+	0.103225i
$518$	−2.25824e10	+	3.14580e9i	−0.313654	+	0.0436930i
$519$	−4.77723e10			−0.658425
$520$	−1.01262e10	−	3.92944e9i	−0.138494	−	0.0537425i
$521$		−	4.89916e10i		−	0.664922i	−0.943117	−	0.332461i	$-0.892121\pi$
$521$		−	4.89916e10i		−	0.664922i	0.943117	−	0.332461i	$-0.107879\pi$
$522$	−1.31338e10	+	1.82958e9i	−0.176892	+	0.0246416i
$523$	−1.88506e10	+	1.88506e10i	−0.251953	+	0.251953i	−0.821771	−	0.569818i	$-0.807014\pi$
$523$	−1.88506e10	+	1.88506e10i	−0.251953	+	0.251953i	0.569818	+	0.821771i	$0.307014\pi$
$524$	7.58381e9	−	1.36036e10i	0.100592	−	0.180438i
$525$	−2.06181e10	+	2.06181e10i	−0.271402	+	0.271402i
$526$	1.46767e10	−	1.94275e10i	0.191728	−	0.253789i
$527$		−	9.37477e10i		−	1.21540i
$528$	8.12863e9	−	5.02461e9i	0.104588	−	0.0646498i
$529$	−5.99846e10			−0.765979
$530$	1.02625e10	+	7.75287e9i	0.130061	+	0.0982560i
$531$	3.60508e10	+	3.60508e10i	0.453457	+	0.453457i
$532$	1.42867e10	−	2.56270e10i	0.178356	−	0.319928i
$533$	2.75797e10	+	2.75797e10i	0.341729	+	0.341729i
$534$	7.63925e9	+	5.48391e10i	0.0939477	+	0.674412i
$535$	−4.15112e10			−0.506699
$536$	3.07260e10	+	6.96938e10i	0.372261	+	0.844374i
$537$		−	6.69993e10i		−	0.805700i
$538$	1.07608e10	+	7.72470e10i	0.128444	+	0.922046i
$539$	4.91266e9	−	4.91266e9i	0.0582052	−	0.0582052i
$540$	−1.73927e9	−	6.12163e9i	−0.0204547	−	0.0719932i
$541$	9.92653e10	−	9.92653e10i	1.15880	−	1.15880i	0.174065	−	0.984734i	$-0.444310\pi$
$541$	9.92653e10	−	9.92653e10i	1.15880	−	1.15880i	0.984734	−	0.174065i	$-0.0556903\pi$
$542$	1.33002e11	+	1.00477e11i	1.54120	+	1.16431i
$543$		−	2.23821e10i		−	0.257455i
$544$	8.76041e9	−	9.35857e10i	0.100030	−	1.06860i
$545$	6.37615e10			0.722724
$546$	9.25408e9	−	1.22496e10i	0.104127	−	0.137833i
$547$	−7.64437e10	−	7.64437e10i	−0.853872	−	0.853872i	0.136736	−	0.990608i	$-0.456339\pi$
$547$	−7.64437e10	−	7.64437e10i	−0.853872	−	0.853872i	−0.990608	+	0.136736i	$0.956339\pi$
$548$	2.47738e10	−	7.03872e9i	0.274707	−	0.0780497i
$549$	8.86889e9	+	8.86889e9i	0.0976293	+	0.0976293i
$550$	1.63823e10	−	2.28210e9i	0.179029	−	0.0249393i
$551$	2.30954e10			0.250565
$552$	1.04608e10	+	2.37276e10i	0.112670	+	0.255563i
$553$			6.06164e10i			0.648171i
$554$	3.11037e10	−	4.33284e9i	0.330197	−	0.0459974i
$555$	6.09045e9	−	6.09045e9i	0.0641915	−	0.0641915i
$556$	3.43370e10	+	1.91425e10i	0.359305	+	0.200308i
$557$	8.37689e10	−	8.37689e10i	0.870286	−	0.870286i	−0.122217	−	0.992503i	$-0.539000\pi$
$557$	8.37689e10	−	8.37689e10i	0.870286	−	0.870286i	0.992503	+	0.122217i	$0.0390004\pi$
$558$	−2.20591e10	+	2.91996e10i	−0.227536	+	0.301189i
$559$			2.45937e9i			0.0251870i
$560$	−2.91553e10	−	6.88032e9i	−0.296459	−	0.0699610i
$561$	1.30711e10			0.131965
$562$	−3.27807e10	−	2.47645e10i	−0.328604	−	0.248247i
$563$	1.17620e11	+	1.17620e11i	1.17071	+	1.17071i	0.982041	+	0.188666i	$0.0604162\pi$
$563$	1.17620e11	+	1.17620e11i	1.17071	+	1.17071i	0.188666	+	0.982041i	$0.439584\pi$
$564$	−3.49767e10	−	1.94991e10i	−0.345670	−	0.192707i
$565$	−1.37225e10	−	1.37225e10i	−0.134660	−	0.134660i
$566$	1.47100e10	+	1.05597e11i	0.143333	+	1.02893i
$567$	8.99481e9			0.0870281
$568$	−1.01539e11	−	3.94021e10i	−0.975529	−	0.378553i
$569$		−	2.21478e10i		−	0.211291i	−0.994404	−	0.105645i	$-0.966309\pi$
$569$		−	2.21478e10i		−	0.211291i	0.994404	−	0.105645i	$-0.0336909\pi$
$570$	1.52923e9	+	1.09777e10i	0.0144869	+	0.103995i
$571$	−9.86907e10	+	9.86907e10i	−0.928392	+	0.928392i	−0.997602	−	0.0692097i	$-0.977952\pi$
$571$	−9.86907e10	+	9.86907e10i	−0.928392	+	0.928392i	0.0692097	+	0.997602i	$0.477952\pi$
$572$	−8.37717e9	+	2.38012e9i	−0.0782552	+	0.0222338i
$573$	2.28569e10	−	2.28569e10i	0.212031	−	0.212031i
$574$	8.58296e10	+	6.48408e10i	0.790660	+	0.597311i
$575$			4.48832e10i			0.410594i
$576$	−2.47495e10	+	2.70877e10i	−0.224842	+	0.246084i
$577$	−1.84370e11			−1.66336			−0.831680	−	0.555255i	$-0.812621\pi$
$577$	−1.84370e11			−1.66336			−0.831680	+	0.555255i	$0.812621\pi$
$578$	1.02199e10	−	1.35281e10i	0.0915664	−	0.121206i
$579$	2.80129e10	+	2.80129e10i	0.249255	+	0.249255i
$580$	−6.44451e9	−	2.26824e10i	−0.0569479	−	0.200437i
$581$	1.62772e10	+	1.62772e10i	0.142849	+	0.142849i
$582$	−1.17707e11	+	1.63970e10i	−1.02591	+	0.142913i
$583$	1.03122e10			0.0892642
$584$	−2.81411e10	+	7.25195e10i	−0.241930	+	0.623452i
$585$			5.79953e9i			0.0495187i
$586$	−3.95453e10	+	5.50878e9i	−0.335355	+	0.0467159i
$587$	−6.63391e10	+	6.63391e10i	−0.558750	+	0.558750i	−0.928951	−	0.370202i	$-0.879289\pi$
$587$	−6.63391e10	+	6.63391e10i	−0.558750	+	0.558750i	0.370202	+	0.928951i	$0.379289\pi$
$588$	−1.29892e10	+	2.32995e10i	−0.108661	+	0.194912i
$589$	4.50684e10	−	4.50684e10i	0.374465	−	0.374465i
$590$	−5.46479e10	+	7.23374e10i	−0.450989	+	0.596973i
$591$		−	8.97818e10i		−	0.735933i
$592$	−4.83327e10	−	1.14060e10i	−0.393508	−	0.0928636i
$593$	8.41974e10			0.680895			0.340447	−	0.940264i	$-0.389421\pi$
$593$	8.41974e10			0.680895			0.340447	+	0.940264i	$0.389421\pi$
$594$	−4.07123e9	−	3.07565e9i	−0.0327024	−	0.0247054i
$595$	−2.89731e10	−	2.89731e10i	−0.231167	−	0.231167i
$596$	−6.64870e10	+	1.19262e11i	−0.526928	+	0.945185i
$597$	−7.82091e10	−	7.82091e10i	−0.615687	−	0.615687i
$598$	−3.26046e9	−	2.34055e10i	−0.0254961	−	0.183026i
$599$	−1.53411e11			−1.19165			−0.595824	−	0.803115i	$-0.703175\pi$
$599$	−1.53411e11			−1.19165			−0.595824	+	0.803115i	$0.703175\pi$
$600$	−5.81114e10	+	2.56197e10i	−0.448390	+	0.197683i
$601$			1.09337e11i			0.838047i	0.907975	+	0.419023i	$0.137627\pi$
$601$			1.09337e11i			0.838047i	−0.907975	+	0.419023i	$0.862373\pi$
$602$	9.35819e8	+	6.71786e9i	0.00712534	+	0.0511499i
$603$	2.87566e10	−	2.87566e10i	0.217504	−	0.217504i
$604$	−3.21958e10	−	1.13318e11i	−0.241909	−	0.851432i
$605$	3.51706e10	−	3.51706e10i	0.262517	−	0.262517i
$606$	4.64836e10	+	3.51165e10i	0.344675	+	0.260388i
$607$			7.82324e10i			0.576278i	0.957589	+	0.288139i	$0.0930365\pi$
$607$			7.82324e10i			0.576278i	−0.957589	+	0.288139i	$0.906963\pi$
$608$	4.92020e10	−	4.07790e10i	0.360055	−	0.298416i
$609$	3.33284e10			0.242295
$610$	−1.34440e10	+	1.77958e10i	−0.0970978	+	0.128528i
$611$	2.58047e10	+	2.58047e10i	0.185154	+	0.185154i
$612$	−4.82765e10	+	1.37163e10i	−0.344136	+	0.0977757i
$613$	−1.32138e11	−	1.32138e11i	−0.935809	−	0.935809i	0.0622513	−	0.998061i	$-0.480172\pi$
$613$	−1.32138e11	−	1.32138e11i	−0.935809	−	0.935809i	−0.998061	+	0.0622513i	$0.980172\pi$
$614$	−1.82098e11	+	2.53668e10i	−1.28124	+	0.178481i
$615$	−4.06357e10			−0.284058
$616$	−2.19769e10	+	9.68901e9i	−0.152632	+	0.0672910i
$617$		−	1.89061e11i		−	1.30455i	−0.757983	−	0.652274i	$-0.773815\pi$
$617$		−	1.89061e11i		−	1.30455i	0.757983	−	0.652274i	$-0.226185\pi$
$618$	−4.26134e10	+	5.93617e9i	−0.292141	+	0.0406961i
$619$	−1.25860e11	+	1.25860e11i	−0.857287	+	0.857287i	−0.991018	−	0.133731i	$-0.957304\pi$
$619$	−1.25860e11	+	1.25860e11i	−0.857287	+	0.857287i	0.133731	+	0.991018i	$0.457304\pi$
$620$	−5.68383e10	−	3.16866e10i	−0.384657	−	0.214442i
$621$	9.79031e9	−	9.79031e9i	0.0658310	−	0.0658310i
$622$	9.15741e10	−	1.21216e11i	0.611802	−	0.809841i
$623$		−	1.39160e11i		−	0.923765i
$624$	2.84425e10	−	1.75814e10i	0.187599	−	0.115962i
$625$	−8.68466e10			−0.569158
$626$	2.06994e10	+	1.56375e10i	0.134791	+	0.101829i
$627$	6.28380e9	+	6.28380e9i	0.0406586	+	0.0406586i
$628$	2.00038e11	+	1.11518e11i	1.28609	+	0.716982i
$629$	−4.80306e10	−	4.80306e10i	−0.306843	−	0.306843i
$630$	2.20679e9	+	1.58417e10i	0.0140087	+	0.100563i
$631$	1.81663e11			1.14591			0.572953	−	0.819588i	$-0.305798\pi$
$631$	1.81663e11			1.14591			0.572953	+	0.819588i	$0.305798\pi$
$632$	−4.77620e10	+	1.23083e11i	−0.299374	+	0.771487i
$633$		−	1.11519e11i		−	0.694601i
$634$	3.97988e10	+	2.85699e11i	0.246327	+	1.76828i
$635$	1.84759e10	−	1.84759e10i	0.113634	−	0.113634i
$636$	−3.80870e10	+	1.08213e10i	−0.232781	+	0.0661377i
$637$	1.71897e10	−	1.71897e10i	0.104402	−	0.104402i
$638$	−1.50851e10	−	1.13962e10i	−0.0910469	−	0.0687822i
$639$			5.81542e10i			0.348801i
$640$	−5.37790e10	−	3.69432e10i	−0.320548	−	0.220199i
$641$	2.54049e11			1.50482			0.752412	−	0.658693i	$-0.228890\pi$
$641$	2.54049e11			1.50482			0.752412	+	0.658693i	$0.228890\pi$
$642$	7.70301e10	−	1.01965e11i	0.453440	−	0.600218i
$643$	−6.89942e10	−	6.89942e10i	−0.403616	−	0.403616i	0.475889	−	0.879505i	$-0.342126\pi$
$643$	−6.89942e10	−	6.89942e10i	−0.403616	−	0.403616i	−0.879505	+	0.475889i	$0.842126\pi$
$644$	−1.78122e10	−	6.26925e10i	−0.103555	−	0.364478i
$645$	−1.81180e9	−	1.81180e9i	−0.0104682	−	0.0104682i
$646$	8.65728e10	−	1.20599e10i	0.497109	−	0.0692488i
$647$	−2.32197e11			−1.32507			−0.662535	−	0.749031i	$-0.730519\pi$
$647$	−2.32197e11			−1.32507			−0.662535	+	0.749031i	$0.730519\pi$
$648$	1.82641e10	+	7.08737e9i	0.103585	+	0.0401962i
$649$			7.26880e10i			0.409717i
$650$	5.73225e10	−	7.98520e9i	0.321123	−	0.0447335i
$651$	6.50370e10	−	6.50370e10i	0.362107	−	0.362107i
$652$	−5.25199e10	+	9.42083e10i	−0.290625	+	0.521313i
$653$	1.86104e10	−	1.86104e10i	0.102354	−	0.102354i	−0.654076	−	0.756429i	$-0.726942\pi$
$653$	1.86104e10	−	1.86104e10i	0.102354	−	0.102354i	0.756429	+	0.654076i	$0.226942\pi$
$654$	−1.18319e11	+	1.56618e11i	−0.646760	+	0.856115i
$655$		−	1.47873e10i		−	0.0803388i
$656$	1.23188e11	+	1.99289e11i	0.665201	+	1.07614i
$657$	4.15339e10			0.222916
$658$	8.03057e10	+	6.06677e10i	0.428393	+	0.323634i
$659$	−8.13555e10	−	8.13555e10i	−0.431366	−	0.431366i	0.457727	−	0.889093i	$-0.348664\pi$
$659$	−8.13555e10	−	8.13555e10i	−0.431366	−	0.431366i	−0.889093	+	0.457727i	$0.848664\pi$
$660$	4.41800e9	−	7.92484e9i	0.0232836	−	0.0417652i
$661$	4.80475e10	+	4.80475e10i	0.251689	+	0.251689i	0.821663	−	0.569974i	$-0.193047\pi$
$661$	4.80475e10	+	4.80475e10i	0.251689	+	0.251689i	−0.569974	+	0.821663i	$0.693047\pi$
$662$	−9.79124e9	−	7.02873e10i	−0.0509807	−	0.365970i
$663$	4.57363e10			0.236705
$664$	2.02257e10	+	4.58767e10i	0.104048	+	0.236004i
$665$		−	2.78571e10i		−	0.142446i
$666$	3.65835e9	+	2.62618e10i	0.0185947	+	0.133484i
$667$	3.62759e10	−	3.62759e10i	0.183280	−	0.183280i
$668$	−6.75407e10	−	2.37719e11i	−0.339203	−	1.19387i
$669$	−1.34966e11	+	1.34966e11i	−0.673781	+	0.673781i
$670$	5.77012e10	+	4.35909e10i	0.286343	+	0.216320i
$671$			1.78821e10i			0.0882120i
$672$	7.10021e10	−	5.88471e10i	0.348172	−	0.288568i
$673$	−5.22305e10			−0.254603			−0.127302	−	0.991864i	$-0.540632\pi$
$673$	−5.22305e10			−0.254603			−0.127302	+	0.991864i	$0.540632\pi$
$674$	9.73523e10	−	1.28865e11i	0.471744	−	0.624447i
$675$	2.39775e10	+	2.39775e10i	0.115502	+	0.115502i
$676$	1.71564e11	−	4.87448e10i	0.821562	−	0.233422i
$677$	9.69469e10	+	9.69469e10i	0.461508	+	0.461508i	0.899150	−	0.437641i	$-0.144186\pi$
$677$	9.69469e10	+	9.69469e10i	0.461508	+	0.461508i	−0.437641	+	0.899150i	$0.644186\pi$
$678$	5.91709e10	−	8.24269e9i	0.280020	−	0.0390077i
$679$	2.98694e11			1.40523
$680$	−3.60013e10	−	8.16594e10i	−0.168377	−	0.381918i
$681$			2.73094e9i			0.0126977i
$682$	−5.16756e10	+	7.19856e9i	−0.238862	+	0.0332743i
$683$	1.24581e11	−	1.24581e11i	0.572490	−	0.572490i	−0.360333	−	0.932824i	$-0.617337\pi$
$683$	1.24581e11	−	1.24581e11i	0.572490	−	0.572490i	0.932824	+	0.360333i	$0.117337\pi$
$684$	−2.98025e10	−	1.66145e10i	−0.136153	−	0.0759037i
$685$	1.72904e10	−	1.72904e10i	0.0785314	−	0.0785314i
$686$	1.44972e11	−	1.91900e11i	0.654619	−	0.866518i
$687$		−	1.28659e11i		−	0.577580i
$688$	−3.39307e9	+	1.43781e10i	−0.0151440	+	0.0641724i
$689$	3.60830e10			0.160113
$690$	1.96447e10	+	1.48407e10i	0.0866659	+	0.0654726i
$691$	5.60138e10	+	5.60138e10i	0.245688	+	0.245688i	0.819198	−	0.573511i	$-0.194419\pi$
$691$	5.60138e10	+	5.60138e10i	0.245688	+	0.245688i	−0.573511	+	0.819198i	$0.694419\pi$
$692$	2.28415e11	+	1.27338e11i	0.996094	+	0.555310i
$693$	9.06797e9	+	9.06797e9i	0.0393167	+	0.0393167i
$694$	−6.16695e10	−	4.42701e11i	−0.265848	−	1.90841i
$695$	3.73251e10			0.159978
$696$	6.76738e10	+	2.62607e10i	0.288392	+	0.111910i
$697$			3.20462e11i			1.35783i
$698$	−1.90074e10	−	1.36446e11i	−0.0800758	−	0.574831i
$699$	1.13219e11	−	1.13219e11i	0.474253	−	0.474253i
$700$	1.53540e11	−	4.36238e10i	0.639485	−	0.181690i
$701$	−2.71143e11	+	2.71143e11i	−1.12286	+	1.12286i	−0.131553	+	0.991309i	$0.541996\pi$
$701$	−2.71143e11	+	2.71143e11i	−1.12286	+	1.12286i	−0.991309	+	0.131553i	$0.958004\pi$
$702$	−1.42455e10	−	1.07619e10i	−0.0586582	−	0.0443138i
$703$		−	4.61806e10i		−	0.189077i
$704$	−5.22589e10	+	2.35721e9i	−0.212750	+	0.00959640i
$705$	−3.80204e10			−0.153908
$706$	−1.15451e11	+	1.52822e11i	−0.464707	+	0.615132i
$707$	−1.03534e11	−	1.03534e11i	−0.414387	−	0.414387i
$708$	−7.62762e10	−	2.68465e11i	−0.303568	−	1.06845i
$709$	1.22832e11	+	1.22832e11i	0.486102	+	0.486102i	0.907074	−	0.420972i	$-0.138311\pi$
$709$	1.22832e11	+	1.22832e11i	0.486102	+	0.486102i	−0.420972	+	0.907074i	$0.638311\pi$
$710$	−1.02421e11	+	1.42676e10i	−0.403048	+	0.0561458i
$711$	7.04927e10			0.275846
$712$	1.09649e11	−	2.82566e11i	0.426665	−	1.09951i
$713$		−	1.41578e11i		−	0.547819i
$714$	1.24931e11	−	1.74032e10i	0.480703	−	0.0669634i
$715$	−5.84670e9	+	5.84670e9i	−0.0223711	+	0.0223711i
$716$	−1.78589e11	+	3.20346e11i	−0.679520	+	1.21890i
$717$	−1.66715e11	+	1.66715e11i	−0.630809	+	0.630809i
$718$	9.34993e10	−	1.23765e11i	0.351812	−	0.465693i
$719$			4.91873e10i			0.184051i	0.995757	+	0.0920253i	$0.0293341\pi$
$719$			4.91873e10i			0.184051i	−0.995757	+	0.0920253i	$0.970666\pi$
$720$	−8.00134e9	+	3.39056e10i	−0.0297737	+	0.126166i
$721$	1.08136e11			0.400155
$722$	−1.69403e11	−	1.27977e11i	−0.623409	−	0.470960i
$723$	1.81755e11	+	1.81755e11i	0.665172	+	0.665172i
$724$	−5.96602e10	+	1.07016e11i	−0.217135	+	0.389489i
$725$	8.88436e10	+	8.88436e10i	0.321569	+	0.321569i
$726$	2.11259e10	+	1.51654e11i	0.0760446	+	0.545894i
$727$	2.77304e11			0.992699			0.496350	−	0.868123i	$-0.334673\pi$
$727$	2.77304e11			0.992699			0.496350	+	0.868123i	$0.334673\pi$
$728$	−7.68985e10	+	3.39024e10i	−0.273774	+	0.120699i
$729$		−	1.04604e10i		−	0.0370370i
$730$	1.01899e10	+	7.31494e10i	0.0358823	+	0.257584i
$731$	−1.42883e10	+	1.42883e10i	−0.0500391	+	0.0500391i
$732$	−1.87648e10	−	6.60454e10i	−0.0653581	−	0.230037i
$733$	−9.89266e10	+	9.89266e10i	−0.342687	+	0.342687i	−0.857376	−	0.514690i	$-0.827907\pi$
$733$	−9.89266e10	+	9.89266e10i	−0.342687	+	0.342687i	0.514690	+	0.857376i	$0.327907\pi$
$734$	−4.60551e11	−	3.47927e11i	−1.58669	−	1.19868i
$735$			2.53271e10i			0.0867833i
$736$	1.32300e10	−	1.41333e11i	0.0450866	−	0.481651i
$737$	5.79809e10			0.196524
$738$	7.54054e10	−	9.98141e10i	0.254201	−	0.336485i
$739$	−3.89214e11	−	3.89214e11i	−1.30500	−	1.30500i	−0.924977	−	0.380024i	$-0.875916\pi$
$739$	−3.89214e11	−	3.89214e11i	−1.30500	−	1.30500i	−0.380024	−	0.924977i	$-0.624084\pi$
$740$	−4.53548e10	+	1.28862e10i	−0.151250	+	0.0429731i
$741$	2.19874e10	+	2.19874e10i	0.0729290	+	0.0729290i
$742$	9.85622e10	−	1.37300e10i	0.325158	−	0.0452955i
$743$	−3.16892e11			−1.03981			−0.519907	−	0.854223i	$-0.674033\pi$
$743$	−3.16892e11			−1.03981			−0.519907	+	0.854223i	$0.674033\pi$
$744$	1.83304e11	−	8.08136e10i	0.598247	−	0.263750i
$745$			1.29640e11i			0.420838i
$746$	−1.44774e11	+	2.01674e10i	−0.467449	+	0.0651171i
$747$	1.89293e10	−	1.89293e10i	0.0607929	−	0.0607929i
$748$	−6.24970e10	−	3.48413e10i	−0.199642	−	0.111298i
$749$	−2.27109e11	+	2.27109e11i	−0.721616	+	0.721616i
$750$	−7.91695e10	+	1.04797e11i	−0.250215	+	0.331209i
$751$			6.15544e11i			1.93508i	0.252716	+	0.967541i	$0.418676\pi$
$751$			6.15544e11i			1.93508i	−0.252716	+	0.967541i	$0.581324\pi$
$752$	1.15260e11	+	1.86463e11i	0.360418	+	0.583070i
$753$	1.67425e11			0.520763
$754$	−5.27836e10	−	3.98758e10i	−0.163310	−	0.123374i
$755$	−7.90882e10	−	7.90882e10i	−0.243402	−	0.243402i
$756$	−4.30071e10	−	2.39759e10i	−0.131660	−	0.0733987i
$757$	−3.57241e11	−	3.57241e11i	−1.08787	−	1.08787i	−0.995747	−	0.0921253i	$-0.970634\pi$
$757$	−3.57241e11	−	3.57241e11i	−1.08787	−	1.08787i	−0.0921253	−	0.995747i	$-0.529366\pi$
$758$	−3.93017e10	−	2.82131e11i	−0.119051	−	0.854621i
$759$	1.97399e10			0.0594809
$760$	2.19497e10	−	5.65644e10i	0.0657922	−	0.169546i
$761$			5.15284e11i			1.53641i	0.640202	+	0.768206i	$0.278850\pi$
$761$			5.15284e11i			1.53641i	−0.640202	+	0.768206i	$0.721150\pi$
$762$	1.10979e10	+	7.96673e10i	0.0329170	+	0.236298i
$763$	3.48841e11	−	3.48841e11i	1.02927	−	1.02927i
$764$	−1.70212e11	+	4.83606e10i	−0.499594	+	0.141944i
$765$	−3.36937e10	+	3.36937e10i	−0.0983792	+	0.0983792i
$766$	−3.32059e11	−	2.50857e11i	−0.964497	−	0.728638i
$767$			2.54339e11i			0.734907i
$768$	1.90539e11	−	6.35447e10i	0.547695	−	0.182656i
$769$	−2.24736e11			−0.642638			−0.321319	−	0.946971i	$-0.604126\pi$
$769$	−2.24736e11			−0.642638			−0.321319	+	0.946971i	$0.604126\pi$
$770$	−1.37458e10	+	1.81953e10i	−0.0391027	+	0.0517601i
$771$	1.37275e11	+	1.37275e11i	0.388484	+	0.388484i
$772$	−5.92696e10	−	2.08608e11i	−0.166864	−	0.587302i
$773$	−1.81076e11	−	1.81076e11i	−0.507158	−	0.507158i	0.406495	−	0.913653i	$-0.366751\pi$
$773$	−1.81076e11	−	1.81076e11i	−0.507158	−	0.507158i	−0.913653	+	0.406495i	$0.866751\pi$
$774$	7.81242e9	−	1.08829e9i	0.0217682	−	0.00303237i
$775$	3.46739e11			0.961160
$776$	6.06503e11	+	2.35353e11i	1.67258	+	0.649041i
$777$		−	6.66420e10i		−	0.182837i
$778$	−5.50863e11	+	7.67370e10i	−1.50358	+	0.209453i
$779$	−1.54059e11	+	1.54059e11i	−0.418348	+	0.418348i
$780$	1.54588e10	−	2.77295e10i	0.0417636	−	0.0749140i
$781$	−5.86272e10	+	5.86272e10i	−0.157578	+	0.157578i
$782$	1.17037e11	−	1.54922e11i	0.312966	−	0.414273i
$783$		−	3.87586e10i		−	0.103115i
$784$	1.24211e11	−	7.67797e10i	0.328774	−	0.203227i
$785$	2.17445e11			0.572626
$786$	3.63224e10	+	2.74401e10i	0.0951665	+	0.0718944i
$787$	−2.56289e11	−	2.56289e11i	−0.668085	−	0.668085i	0.289188	−	0.957272i	$-0.406615\pi$
$787$	−2.56289e11	−	2.56289e11i	−0.668085	−	0.668085i	−0.957272	+	0.289188i	$0.906615\pi$
$788$	−2.39316e11	+	4.29276e11i	−0.620679	+	1.11335i
$789$	5.03217e10	+	5.03217e10i	0.129852	+	0.129852i
$790$	1.72947e10	+	1.24152e11i	0.0444023	+	0.318746i
$791$	−1.50152e11			−0.383553
$792$	1.12677e10	+	2.55577e10i	0.0286374	+	0.0649563i
$793$			6.25704e10i			0.158225i
$794$	−8.61685e10	−	6.18569e11i	−0.216804	−	1.55635i
$795$	−2.65821e10	+	2.65821e10i	−0.0665459	+	0.0665459i
$796$	1.65475e11	+	5.82412e11i	0.412173	+	1.45070i
$797$	−2.11480e11	+	2.11480e11i	−0.524127	+	0.524127i	−0.918815	−	0.394688i	$-0.870853\pi$
$797$	−2.11480e11	+	2.11480e11i	−0.524127	+	0.524127i	0.394688	+	0.918815i	$0.370853\pi$
$798$	6.84259e10	+	5.16929e10i	0.168736	+	0.127473i
$799$			2.99837e11i			0.735695i
$800$	3.46140e11	+	3.24016e10i	0.845067	+	0.0791054i
$801$	−1.61833e11			−0.393132
$802$	−2.18797e11	+	2.89621e11i	−0.528864	+	0.700056i
$803$	4.18717e10	+	4.18717e10i	0.100707	+	0.100707i
$804$	−2.14146e11	+	6.08431e10i	−0.512491	+	0.145609i
$805$	−4.37551e10	−	4.37551e10i	−0.104195	−	0.104195i
$806$	−1.80816e11	+	2.51882e10i	−0.428446	+	0.0596838i
$807$	−2.27961e11			−0.537484
$808$	−1.28649e11	−	2.91807e11i	−0.301830	−	0.684621i
$809$		−	5.34882e11i		−	1.24872i	−0.781138	−	0.624358i	$-0.785361\pi$
$809$		−	5.34882e11i		−	1.24872i	0.781138	−	0.624358i	$-0.214639\pi$
$810$	1.84228e10	−	2.56635e9i	0.0427972	−	0.00596178i
$811$	2.10323e11	−	2.10323e11i	0.486186	−	0.486186i	−0.420914	−	0.907100i	$-0.638291\pi$
$811$	2.10323e11	−	2.10323e11i	0.486186	−	0.486186i	0.907100	+	0.420914i	$0.138291\pi$
$812$	−1.59354e11	−	8.88378e10i	−0.366554	−	0.204349i
$813$	−3.44505e11	+	3.44505e11i	−0.788557	+	0.788557i
$814$	−2.27873e10	+	3.01635e10i	−0.0519034	+	0.0687044i
$815$			1.02406e11i			0.232111i
$816$	2.67387e11	+	6.31003e10i	0.603086	+	0.142322i
$817$	−1.37379e10			−0.0308342
$818$	2.34601e11	+	1.77231e11i	0.523982	+	0.395847i
$819$	3.17293e10	+	3.17293e10i	0.0705221	+	0.0705221i
$820$	1.94293e11	+	1.08316e11i	0.429735	+	0.239572i
$821$	3.56050e11	+	3.56050e11i	0.783678	+	0.783678i	0.980449	−	0.196771i	$-0.0630456\pi$
$821$	3.56050e11	+	3.56050e11i	0.783678	+	0.783678i	−0.196771	+	0.980449i	$0.563046\pi$
$822$	1.03858e10	+	7.45557e10i	0.0227486	+	0.163303i
$823$	4.79936e11			1.04613			0.523063	−	0.852294i	$-0.324789\pi$
$823$	4.79936e11			1.04613			0.523063	+	0.852294i	$0.324789\pi$
$824$	2.19572e11	+	8.52044e10i	0.476285	+	0.184822i
$825$			4.83451e10i			0.104361i
$826$	9.67793e10	+	6.94739e11i	0.207904	+	1.49246i
$827$	−3.24300e10	+	3.24300e10i	−0.0693306	+	0.0693306i	−0.740922	−	0.671591i	$-0.765611\pi$
$827$	−3.24300e10	+	3.24300e10i	−0.0693306	+	0.0693306i	0.671591	+	0.740922i	$0.265611\pi$
$828$	−7.29071e10	+	2.07143e10i	−0.155113	+	0.0440707i
$829$	5.34399e11	−	5.34399e11i	1.13148	−	1.13148i	0.141550	−	0.989931i	$-0.454791\pi$
$829$	5.34399e11	−	5.34399e11i	1.13148	−	1.13148i	0.989931	−	0.141550i	$-0.0452086\pi$
$830$	3.79825e10	+	2.86942e10i	0.0800333	+	0.0604619i
$831$			9.17888e10i			0.192480i
$832$	−1.82857e11	+	8.24802e9i	−0.381609	+	0.0172130i
$833$	1.99735e11			0.414834
$834$	−6.92621e10	+	9.16821e10i	−0.143163	+	0.189505i
$835$	−1.65912e11	−	1.65912e11i	−0.341297	−	0.341297i
$836$	−1.32953e10	−	4.67946e10i	−0.0272190	−	0.0958010i
$837$	−7.56336e10	−	7.56336e10i	−0.154104	−	0.154104i
$838$	1.91862e11	−	2.67269e10i	0.389056	−	0.0541967i
$839$	−1.32395e11			−0.267192			−0.133596	−	0.991036i	$-0.542653\pi$
$839$	−1.32395e11			−0.267192			−0.133596	+	0.991036i	$0.542653\pi$
$840$	3.16750e10	−	8.16265e10i	0.0636209	−	0.163951i
$841$			3.56635e11i			0.712918i
$842$	2.22589e11	−	3.10073e10i	0.442848	−	0.0616901i
$843$	8.49096e10	−	8.49096e10i	0.168130	−	0.168130i
$844$	−2.97258e11	+	5.33210e11i	−0.585820	+	1.05082i
$845$	1.19740e11	−	1.19740e11i	0.234863	−	0.234863i
$846$	7.05524e10	−	9.33901e10i	0.137731	−	0.182314i
$847$		−	3.84838e11i		−	0.747729i
$848$	2.10951e11	+	4.97820e10i	0.407941	+	0.0962696i
$849$	−3.11623e11			−0.599789
$850$	3.79420e11	+	2.86637e11i	0.726850	+	0.549106i
$851$	−7.25358e10	−	7.25358e10i	−0.138304	−	0.138304i
$852$	1.55012e11	−	2.78054e11i	0.294175	−	0.527681i
$853$	−5.33113e11	−	5.33113e11i	−1.00699	−	1.00699i	−0.999975	−	0.00700978i	$-0.997769\pi$
$853$	−5.33113e11	−	5.33113e11i	−1.00699	−	1.00699i	−0.00700978	−	0.999975i	$-0.502231\pi$
$854$	2.38088e10	+	1.70914e11i	0.0447616	+	0.321325i
$855$	−3.23959e10			−0.0606214
$856$	−6.40096e11	+	2.82200e11i	−1.19220	+	0.525608i
$857$		−	6.70457e11i		−	1.24293i	−0.783441	−	0.621466i	$-0.786537\pi$
$857$		−	6.70457e11i		−	1.24293i	0.783441	−	0.621466i	$-0.213463\pi$
$858$	−3.51194e9	−	2.52108e10i	−0.00648033	−	0.0465197i
$859$	6.74984e11	−	6.74984e11i	1.23971	−	1.23971i	0.279595	−	0.960118i	$-0.409800\pi$
$859$	6.74984e11	−	6.74984e11i	1.23971	−	1.23971i	0.960118	−	0.279595i	$-0.0902001\pi$
$860$	3.83341e9	+	1.34922e10i	0.00700795	+	0.0246655i
$861$	−2.22319e11	+	2.22319e11i	−0.404542	+	0.404542i
$862$	−4.60226e11	−	3.47682e11i	−0.833570	−	0.629728i
$863$		−	2.61546e11i		−	0.471525i	−0.971811	−	0.235763i	$-0.924241\pi$
$863$		−	2.61546e11i		−	0.471525i	0.971811	−	0.235763i	$-0.0757588\pi$
$864$	−6.84352e10	−	8.25706e10i	−0.122807	−	0.148173i
$865$	2.48292e11			0.443505
$866$	−5.00935e10	+	6.63087e10i	−0.0890655	+	0.117896i
$867$	3.50409e10	+	3.50409e10i	0.0620153	+	0.0620153i
$868$	−4.84321e11	+	1.37605e11i	−0.853208	+	0.242413i
$869$	7.10661e10	+	7.10661e10i	0.124619	+	0.124619i
$870$	6.82617e10	−	9.50907e9i	0.119152	−	0.0165982i
$871$	2.02879e11			0.352504
$872$	9.83193e11	−	4.33462e11i	1.70048	−	0.749696i
$873$		−	3.47360e11i		−	0.598031i
$874$	1.30742e11	−	1.82128e10i	0.224063	−	0.0312127i
$875$	2.33416e11	−	2.33416e11i	0.398198	−	0.398198i
$876$	−1.98587e11	−	1.10710e11i	−0.337236	−	0.188005i
$877$	5.97741e10	−	5.97741e10i	0.101045	−	0.101045i	−0.654777	−	0.755822i	$-0.727237\pi$
$877$	5.97741e10	−	5.97741e10i	0.101045	−	0.101045i	0.755822	+	0.654777i	$0.227237\pi$
$878$	2.34384e11	−	3.10254e11i	0.394412	−	0.522083i
$879$		−	1.16700e11i		−	0.195487i
$880$	−4.22478e10	+	2.61150e10i	−0.0704488	+	0.0435470i
$881$	6.12411e11			1.01657			0.508287	−	0.861187i	$-0.330279\pi$
$881$	6.12411e11			1.01657			0.508287	+	0.861187i	$0.330279\pi$
$882$	−6.22113e10	−	4.69981e10i	−0.102800	−	0.0776616i
$883$	−4.96732e11	−	4.96732e11i	−0.817108	−	0.817108i	0.168580	−	0.985688i	$-0.446082\pi$
$883$	−4.96732e11	−	4.96732e11i	−0.817108	−	0.817108i	−0.985688	+	0.168580i	$0.946082\pi$
$884$	−2.18681e11	−	1.21912e11i	−0.358097	−	0.199635i
$885$	−1.87371e11	−	1.87371e11i	−0.305442	−	0.305442i
$886$	1.50734e10	+	1.08206e11i	0.0244612	+	0.175597i
$887$	−5.78957e11			−0.935301			−0.467651	−	0.883913i	$-0.654899\pi$
$887$	−5.78957e11			−0.935301			−0.467651	+	0.883913i	$0.654899\pi$
$888$	5.25099e10	−	1.35318e11i	0.0844479	−	0.217622i
$889$		−	2.02164e11i		−	0.323665i
$890$	−3.97043e10	−	2.85021e11i	−0.0632816	−	0.454273i
$891$	1.05454e10	−	1.05454e10i	0.0167322	−	0.0167322i
$892$	1.00507e12	−	2.85560e11i	1.58758	−	0.451064i
$893$	−1.44144e11	+	1.44144e11i	−0.226668	+	0.226668i
$894$	−3.18437e11	−	2.40566e11i	−0.498510	−	0.376604i
$895$			3.48223e11i			0.542706i
$896$	−4.96343e11	+	9.21091e10i	−0.770105	+	0.142913i
$897$	6.90710e10			0.106691
$898$	−6.57908e11	+	8.70872e11i	−1.01172	+	1.33921i
$899$	−2.80244e11	−	2.80244e11i	−0.429040	−	0.429040i
$900$	−5.07316e10	−	1.78557e11i	−0.0773229	−	0.272149i
$901$	2.09633e11	+	2.09633e11i	0.318097	+	0.318097i
$902$	1.76645e11	−	2.46072e10i	0.266855	−	0.0371737i
$903$	−1.98248e10			−0.0298166
$904$	−3.04887e11	−	1.18311e11i	−0.456525	−	0.177154i
$905$			1.16329e11i			0.173418i
$906$	3.41025e11	−	4.75058e10i	0.506143	−	0.0705073i
$907$	−3.14177e11	+	3.14177e11i	−0.464243	+	0.464243i	−0.900043	−	0.435801i	$-0.856465\pi$
$907$	−3.14177e11	+	3.14177e11i	−0.464243	+	0.464243i	0.435801	+	0.900043i	$0.356465\pi$
$908$	7.27941e9	−	1.30575e10i	0.0107091	−	0.0192096i
$909$	−1.20403e11	+	1.20403e11i	−0.176353	+	0.176353i
$910$	−4.80972e10	+	6.36662e10i	−0.0701382	+	0.0928418i
$911$			3.73519e11i			0.542299i	0.962537	+	0.271149i	$0.0874038\pi$
$911$			3.73519e11i			0.542299i	−0.962537	+	0.271149i	$0.912596\pi$
$912$	9.82090e10	+	1.58879e11i	0.141962	+	0.229661i
$913$	3.81666e10			0.0549288
$914$	7.39345e11	+	5.58545e11i	1.05941	+	0.800338i
$915$	−4.60952e10	−	4.60952e10i	−0.0657615	−	0.0657615i
$916$	−3.42943e11	+	6.15159e11i	−0.487125	+	0.873787i
$917$	−8.09019e10	−	8.09019e10i	−0.114415	−	0.114415i
$918$	−2.02388e10	−	1.45286e11i	−0.0284980	−	0.204575i
$919$	7.90211e11			1.10785			0.553925	−	0.832566i	$-0.313129\pi$
$919$	7.90211e11			1.10785			0.553925	+	0.832566i	$0.313129\pi$
$920$	−5.43692e10	−	1.23322e11i	−0.0758929	−	0.172143i
$921$		−	5.37382e11i		−	0.746869i
$922$	3.86287e10	+	2.77300e11i	0.0534548	+	0.383730i
$923$	−2.05140e11	+	2.05140e11i	−0.282646	+	0.282646i
$924$	−1.91860e10	−	6.75279e10i	−0.0263207	−	0.0926393i
$925$	1.77648e11	−	1.77648e11i	0.242657	−	0.242657i
$926$	2.11105e11	+	1.59481e11i	0.287114	+	0.216903i
$927$		−	1.25755e11i		−	0.170296i
$928$	−2.53572e11	−	3.05948e11i	−0.341908	−	0.412530i
$929$	1.45462e12			1.95293			0.976466	−	0.215673i	$-0.0691944\pi$
$929$	1.45462e12			1.95293			0.976466	+	0.215673i	$0.0691944\pi$
$930$	1.14650e11	−	1.51762e11i	0.153265	−	0.202876i
$931$	9.60209e10	+	9.60209e10i	0.127811	+	0.127811i
$932$	−8.43124e11	+	2.39548e11i	−1.11745	+	0.317489i
$933$	3.13979e11	+	3.13979e11i	0.414356	+	0.414356i
$934$	9.16008e11	−	1.27603e11i	1.20368	−	0.167677i
$935$	−6.79356e10			−0.0888896
$936$	3.94262e10	+	8.94278e10i	0.0513667	+	0.116512i
$937$		−	4.21955e11i		−	0.547403i	−0.961815	−	0.273702i	$-0.911752\pi$
$937$		−	4.21955e11i		−	0.547403i	0.961815	−	0.273702i	$-0.0882481\pi$
$938$	5.54171e11	−	7.71978e10i	0.715868	−	0.0997226i
$939$	−5.36162e10	+	5.36162e10i	−0.0689658	+	0.0689658i
$940$	1.81788e11	+	1.01344e11i	0.232838	+	0.129804i
$941$	5.94575e11	−	5.94575e11i	0.758313	−	0.758313i	−0.217703	−	0.976015i	$-0.569856\pi$
$941$	5.94575e11	−	5.94575e11i	0.758313	−	0.758313i	0.976015	+	0.217703i	$0.0698563\pi$
$942$	−4.03501e11	+	5.34114e11i	−0.512438	+	0.678313i
$943$			4.83961e11i			0.612017i
$944$	−3.50900e11	+	1.48694e12i	−0.441871	+	1.87242i
$945$	−4.67497e10			−0.0586207
$946$	8.97311e9	+	6.77882e9i	0.0112041	+	0.00846427i
$947$	2.61909e11	+	2.61909e11i	0.325649	+	0.325649i	0.850929	−	0.525280i	$-0.176040\pi$
$947$	2.61909e11	+	2.61909e11i	0.325649	+	0.325649i	−0.525280	+	0.850929i	$0.676040\pi$
$948$	−3.37049e11	−	1.87901e11i	−0.417311	−	0.232646i
$949$	1.46511e11	+	1.46511e11i	0.180637	+	0.180637i
$950$	4.46050e10	+	3.20201e11i	0.0547633	+	0.393123i
$951$	−8.43115e11			−1.03078
$952$	−6.43724e11	−	2.49796e11i	−0.783704	−	0.304115i
$953$			1.53605e11i			0.186224i	0.995656	+	0.0931119i	$0.0296814\pi$
$953$			1.53605e11i			0.186224i	−0.995656	+	0.0931119i	$0.970319\pi$
$954$	−1.59671e10	−	1.14621e11i	−0.0192767	−	0.138379i
$955$	−1.18797e11	+	1.18797e11i	−0.142820	+	0.142820i
$956$	1.24150e12	−	3.52735e11i	1.48633	−	0.422296i
$957$	3.90739e10	−	3.90739e10i	0.0465842	−	0.0465842i
$958$	2.70656e11	+	2.04469e11i	0.321333	+	0.242754i
$959$		−	1.89193e11i		−	0.223681i
$960$	1.28633e11	−	1.40786e11i	0.151450	−	0.165758i
$961$	−2.40847e11			−0.282389
$962$	−7.97341e10	+	1.05544e11i	−0.0930987	+	0.123235i
$963$	2.64112e11	+	2.64112e11i	0.307102	+	0.307102i
$964$	−3.84557e11	−	1.35351e12i	−0.445300	−	1.56730i
$965$	−1.45594e11	−	1.45594e11i	−0.167894	−	0.167894i
$966$	1.88670e11	−	2.62824e10i	0.216668	−	0.0301825i
$967$	−7.52392e11			−0.860475			−0.430237	−	0.902716i	$-0.641570\pi$
$967$	−7.52392e11			−0.860475			−0.430237	+	0.902716i	$0.641570\pi$
$968$	3.03229e11	−	7.81420e11i	0.345358	−	0.889986i
$969$			2.55481e11i			0.289777i
$970$	6.11771e11	−	8.52216e10i	0.691038	−	0.0962638i
$971$	−6.99738e11	+	6.99738e11i	−0.787152	+	0.787152i	−0.981026	−	0.193874i	$-0.937895\pi$
$971$	−6.99738e11	+	6.99738e11i	−0.787152	+	0.787152i	0.193874	+	0.981026i	$0.437895\pi$
$972$	−2.78824e10	+	5.00144e10i	−0.0312367	+	0.0560312i
$973$	2.04206e11	−	2.04206e11i	0.227833	−	0.227833i
$974$	−4.14600e11	+	5.48805e11i	−0.460673	+	0.609793i
$975$			1.69162e11i			0.187191i
$976$	−8.63254e10	+	3.65803e11i	−0.0951348	+	0.403133i
$977$	−8.88879e11			−0.975583			−0.487792	−	0.872960i	$-0.662197\pi$
$977$	−8.88879e11			−0.975583			−0.487792	+	0.872960i	$0.662197\pi$
$978$	−2.51542e11	−	1.90030e11i	−0.274951	−	0.207714i
$979$	−1.63150e11	−	1.63150e11i	−0.177605	−	0.177605i
$980$	6.75101e10	−	1.21097e11i	0.0731922	−	0.131289i
$981$	−4.05678e11	−	4.05678e11i	−0.438032	−	0.438032i
$982$	−9.98357e9	−	7.16680e10i	−0.0107359	−	0.0770689i
$983$	8.99987e11			0.963878			0.481939	−	0.876205i	$-0.339933\pi$
$983$	8.99987e11			0.963878			0.481939	+	0.876205i	$0.339933\pi$
$984$	−6.26596e11	+	2.76248e11i	−0.668355	+	0.294659i
$985$			4.66633e11i			0.495713i
$986$	−7.49906e10	−	5.38327e11i	−0.0793412	−	0.569558i
$987$	−2.08010e11	+	2.08010e11i	−0.219188	+	0.219188i
$988$	−4.65208e10	−	1.63737e11i	−0.0488225	−	0.171838i
$989$	−2.15781e10	+	2.15781e10i	−0.0225543	+	0.0225543i
$990$	2.11599e10	+	1.59854e10i	0.0220278	+	0.0166411i
$991$		−	2.76086e11i		−	0.286253i	−0.989704	−	0.143127i	$-0.954284\pi$
$991$		−	2.76086e11i		−	0.286253i	0.989704	−	0.143127i	$-0.0457156\pi$
$992$	−1.09185e12	−	1.02206e11i	−1.12750	−	0.105543i
$993$	2.07422e11			0.213333
$994$	−4.82290e11	+	6.38407e11i	−0.494041	+	0.653961i
$995$	4.06485e11	+	4.06485e11i	0.414717	+	0.414717i
$996$	−1.40964e11	+	4.00506e10i	−0.143242	+	0.0406979i
$997$	−2.71165e11	−	2.71165e11i	−0.274444	−	0.274444i	0.556443	−	0.830886i	$-0.312166\pi$
$997$	−2.71165e11	−	2.71165e11i	−0.274444	−	0.274444i	−0.830886	+	0.556443i	$0.812166\pi$
$998$	3.31163e11	−	4.61320e10i	0.333825	−	0.0465029i
$999$	−7.75001e10			−0.0778109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.23	yes	64
4.3	odd	2		192.9.l.a.79.7		64
16.3	odd	4	inner	48.9.l.a.19.23	✓	64
16.13	even	4		192.9.l.a.175.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.23	✓	64	16.3	odd	4	inner
48.9.l.a.43.23	yes	64	1.1	even	1	trivial
192.9.l.a.79.7		64	4.3	odd	2
192.9.l.a.175.7		64	16.13	even	4

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)

\(f(q)\)	\(=\)	\(q+(9.64455 - 12.7665i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-69.9655 - 246.254i) q^{4} +(-171.868 - 171.868i) q^{5} +(741.090 - 103.236i) q^{6} -1880.59 q^{7} +(-3818.57 - 1481.79i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(9.64455 - 12.7665i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-69.9655 - 246.254i) q^{4} +(-171.868 - 171.868i) q^{5} +(741.090 - 103.236i) q^{6} -1880.59 q^{7} +(-3818.57 - 1481.79i) q^{8} +2187.00i q^{9} +(-3851.75 + 536.560i) q^{10} +(-2204.79 + 2204.79i) q^{11} +(5829.52 - 10456.8i) q^{12} +(-7714.68 + 7714.68i) q^{13} +(-18137.4 + 24008.5i) q^{14} -11366.7i q^{15} +(-55745.7 + 34458.5i) q^{16} -89640.5 q^{17} +(27920.3 + 21092.6i) q^{18} +(-43093.9 - 43093.9i) q^{19} +(-30298.4 + 54348.1i) q^{20} +(-62187.6 - 62187.6i) q^{21} +(6883.18 + 49411.6i) q^{22} -135375. q^{23} +(-77273.0 - 175273. i) q^{24} -331548. i q^{25} +(24084.6 + 172894. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(131576. + 463102. i) q^{28} +(-267966. + 267966. i) q^{29} +(-145113. - 109627. i) q^{30} +1.04582e6i q^{31} +(-97728.3 + 1.04401e6i) q^{32} -145816. q^{33} +(-864542. + 1.14439e6i) q^{34} +(323214. + 323214. i) q^{35} +(538557. - 153014. i) q^{36} +(535814. + 535814. i) q^{37} +(-965778. + 134536. i) q^{38} -510220. q^{39} +(401619. + 910965. i) q^{40} -3.57497e6i q^{41} +(-1.39369e6 + 194145. i) q^{42} +(159395. - 159395. i) q^{43} +(697196. + 388678. i) q^{44} +(375876. - 375876. i) q^{45} +(-1.30563e6 + 1.72826e6i) q^{46} -3.34488e6i q^{47} +(-2.98288e6 - 703927. i) q^{48} -2.22818e6 q^{49} +(-4.23269e6 - 3.19763e6i) q^{50} +(-2.96424e6 - 2.96424e6i) q^{51} +(2.43953e6 + 1.36001e6i) q^{52} +(-2.33859e6 - 2.33859e6i) q^{53} +(225777. + 1.62076e6i) q^{54} +757867. q^{55} +(7.18118e6 + 2.78665e6i) q^{56} -2.85007e6i q^{57} +(836570. + 6.00540e6i) q^{58} +(1.64841e7 - 1.64841e7i) q^{59} +(-2.79910e6 + 795278. i) q^{60} +(4.05528e6 - 4.05528e6i) q^{61} +(1.33514e7 + 1.00865e7i) q^{62} -4.11285e6i q^{63} +(1.23858e7 + 1.13167e7i) q^{64} +2.65182e6 q^{65} +(-1.40633e6 + 1.86156e6i) q^{66} +(-1.31489e7 - 1.31489e7i) q^{67} +(6.27174e6 + 2.20743e7i) q^{68} +(-4.47660e6 - 4.47660e6i) q^{69} +(7.24356e6 - 1.00905e6i) q^{70} +2.65909e7 q^{71} +(3.24068e6 - 8.35122e6i) q^{72} -1.89912e7i q^{73} +(1.20081e7 - 1.67277e6i) q^{74} +(1.09636e7 - 1.09636e7i) q^{75} +(-7.59694e6 + 1.36271e7i) q^{76} +(4.14631e6 - 4.14631e6i) q^{77} +(-4.92084e6 + 6.51370e6i) q^{78} -3.22326e7i q^{79} +(1.55032e7 + 3.65859e6i) q^{80} -4.78297e6 q^{81} +(-4.56397e7 - 3.44789e7i) q^{82} +(-8.65538e6 - 8.65538e6i) q^{83} +(-1.09629e7 + 1.96649e7i) q^{84} +(1.54064e7 + 1.54064e7i) q^{85} +(-497620. - 3.57221e6i) q^{86} -1.77223e7 q^{87} +(1.16862e7 - 5.15211e6i) q^{88} +7.39979e7i q^{89} +(-1.17346e6 - 8.42377e6i) q^{90} +(1.45082e7 - 1.45082e7i) q^{91} +(9.47157e6 + 3.33366e7i) q^{92} +(-3.45833e7 + 3.45833e7i) q^{93} +(-4.27024e7 - 3.22599e7i) q^{94} +1.48130e7i q^{95} +(-3.77552e7 + 3.12918e7i) q^{96} -1.58830e8 q^{97} +(-2.14898e7 + 2.84460e7i) q^{98} +(-4.82187e6 - 4.82187e6i) 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

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