LMFDB - Embedded newform 48.9.l.a.19.25

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			19.25
Character	$\chi$	$=$	48.19
Dual form			48.9.l.a.43.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.9899 + 9.34150i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(81.4726 + 242.690i) q^{4} +(271.296 - 271.296i) q^{5} +(-738.456 + 120.644i) q^{6} +3140.01 q^{7} +(-1208.77 + 3913.58i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(12.9899 + 9.34150i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(81.4726 + 242.690i) q^{4} +(271.296 - 271.296i) q^{5} +(-738.456 + 120.644i) q^{6} +3140.01 q^{7} +(-1208.77 + 3913.58i) q^{8} -2187.00i q^{9} +(6058.40 - 989.782i) q^{10} +(13483.9 + 13483.9i) q^{11} +(-10719.4 - 5331.14i) q^{12} +(53.7468 + 53.7468i) q^{13} +(40788.2 + 29332.4i) q^{14} +17942.5i q^{15} +(-52260.4 + 39545.1i) q^{16} -49733.7 q^{17} +(20429.9 - 28408.8i) q^{18} +(-81031.9 + 81031.9i) q^{19} +(87943.8 + 43737.4i) q^{20} +(-103834. + 103834. i) q^{21} +(49194.0 + 301113. i) q^{22} +18878.1 q^{23} +(-89443.0 - 169386. i) q^{24} +243422. i q^{25} +(196.087 + 1200.24i) q^{26} +(72320.0 + 72320.0i) q^{27} +(255825. + 762047. i) q^{28} +(169253. + 169253. i) q^{29} +(-167610. + 233070. i) q^{30} -928078. i q^{31} +(-1.04827e6 + 25494.5i) q^{32} -891773. q^{33} +(-646034. - 464588. i) q^{34} +(851871. - 851871. i) q^{35} +(530762. - 178181. i) q^{36} +(766720. - 766720. i) q^{37} +(-1.80955e6 + 295633. i) q^{38} -3554.61 q^{39} +(733804. + 1.38967e6i) q^{40} +5.02634e6i q^{41} +(-2.31876e6 + 378823. i) q^{42} +(2.95586e6 + 2.95586e6i) q^{43} +(-2.17383e6 + 4.37097e6i) q^{44} +(-593324. - 593324. i) q^{45} +(245224. + 176350. i) q^{46} -3.96840e6i q^{47} +(420471. - 3.03584e6i) q^{48} +4.09485e6 q^{49} +(-2.27393e6 + 3.16202e6i) q^{50} +(1.64460e6 - 1.64460e6i) q^{51} +(-8664.89 + 17422.7i) q^{52} +(8.73814e6 - 8.73814e6i) q^{53} +(263849. + 1.61500e6i) q^{54} +7.31624e6 q^{55} +(-3.79554e6 + 1.22887e7i) q^{56} -5.35915e6i q^{57} +(617495. + 3.77965e6i) q^{58} +(-9.75112e6 - 9.75112e6i) q^{59} +(-4.35445e6 + 1.46182e6i) q^{60} +(-4.29071e6 - 4.29071e6i) q^{61} +(8.66964e6 - 1.20556e7i) q^{62} -6.86720e6i q^{63} +(-1.38550e7 - 9.46121e6i) q^{64} +29162.6 q^{65} +(-1.15840e7 - 8.33050e6i) q^{66} +(6.69650e6 - 6.69650e6i) q^{67} +(-4.05194e6 - 1.20699e7i) q^{68} +(-624263. + 624263. i) q^{69} +(1.90234e7 - 3.10792e6i) q^{70} +2.38140e7 q^{71} +(8.55900e6 + 2.64357e6i) q^{72} -4.01505e7i q^{73} +(1.71219e7 - 2.79726e6i) q^{74} +(-8.04952e6 - 8.04952e6i) q^{75} +(-2.62675e7 - 1.30637e7i) q^{76} +(4.23395e7 + 4.23395e7i) q^{77} +(-46173.9 - 33205.4i) q^{78} -7.02261e7i q^{79} +(-3.44961e6 + 2.49064e7i) q^{80} -4.78297e6 q^{81} +(-4.69536e7 + 6.52914e7i) q^{82} +(7.55026e6 - 7.55026e6i) q^{83} +(-3.36591e7 - 1.67398e7i) q^{84} +(-1.34926e7 + 1.34926e7i) q^{85} +(1.07840e7 + 6.60084e7i) q^{86} -1.11938e7 q^{87} +(-6.90691e7 + 3.64714e7i) q^{88} +1.01023e8i q^{89} +(-2.16465e6 - 1.32497e7i) q^{90} +(168765. + 168765. i) q^{91} +(1.53805e6 + 4.58152e6i) q^{92} +(3.06898e7 + 3.06898e7i) q^{93} +(3.70708e7 - 5.15489e7i) q^{94} +4.39672e7i q^{95} +(3.38211e7 - 3.55072e7i) q^{96} +2.10782e7 q^{97} +(5.31915e7 + 3.82520e7i) q^{98} +(2.94893e7 - 2.94893e7i) 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 $

$2$	12.9899	+	9.34150i	0.811866	+	0.583844i
$2$	12.9899	+	9.34150i	0.811866	+	0.583844i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$4$	81.4726	+	242.690i	0.318253	+	0.948006i
$5$	271.296	−	271.296i	0.434073	−	0.434073i	−0.455938	−	0.890011i	$-0.650696\pi$
$5$	271.296	−	271.296i	0.434073	−	0.434073i	0.890011	+	0.455938i	$0.150696\pi$
$6$	−738.456	+	120.644i	−0.569796	+	0.0930896i
$7$	3140.01			1.30779			0.653896	−	0.756585i	$-0.273133\pi$
$7$	3140.01			1.30779			0.653896	+	0.756585i	$0.273133\pi$
$8$	−1208.77	+	3913.58i	−0.295109	+	0.955464i
$9$		−	2187.00i		−	0.333333i
$10$	6058.40	−	989.782i	0.605840	−	0.0989782i
$11$	13483.9	+	13483.9i	0.920967	+	0.920967i	0.997098	−	0.0761304i	$-0.0242565\pi$
$11$	13483.9	+	13483.9i	0.920967	+	0.920967i	−0.0761304	+	0.997098i	$0.524257\pi$
$12$	−10719.4	−	5331.14i	−0.516948	−	0.257096i
$13$	53.7468	+	53.7468i	0.00188183	+	0.00188183i	0.708047	−	0.706165i	$-0.249576\pi$
$13$	53.7468	+	53.7468i	0.00188183	+	0.00188183i	−0.706165	+	0.708047i	$0.749576\pi$
$14$	40788.2	+	29332.4i	1.06175	+	0.763546i
$15$			17942.5i			0.354419i
$16$	−52260.4	+	39545.1i	−0.797431	+	0.603411i
$17$	−49733.7			−0.595464			−0.297732	−	0.954649i	$-0.596230\pi$
$17$	−49733.7			−0.595464			−0.297732	+	0.954649i	$0.596230\pi$
$18$	20429.9	−	28408.8i	0.194615	−	0.270622i
$19$	−81031.9	+	81031.9i	−0.621787	+	0.621787i	−0.945988	−	0.324201i	$-0.894905\pi$
$19$	−81031.9	+	81031.9i	−0.621787	+	0.621787i	0.324201	+	0.945988i	$0.394905\pi$
$20$	87943.8	+	43737.4i	0.549649	+	0.273359i
$21$	−103834.	+	103834.i	−0.533904	+	0.533904i
$22$	49194.0	+	301113.i	0.210001	+	1.28540i
$23$	18878.1			0.0674601			0.0337301	−	0.999431i	$-0.489261\pi$
$23$	18878.1			0.0674601			0.0337301	+	0.999431i	$0.489261\pi$
$24$	−89443.0	−	169386.i	−0.269589	−	0.510544i
$25$			243422.i			0.623161i
$26$	196.087	+	1200.24i	0.000429098	+	0.00262648i
$27$	72320.0	+	72320.0i	0.136083	+	0.136083i
$28$	255825.	+	762047.i	0.416208	+	1.23979i
$29$	169253.	+	169253.i	0.239301	+	0.239301i	0.816561	−	0.577259i	$-0.195878\pi$
$29$	169253.	+	169253.i	0.239301	+	0.239301i	−0.577259	+	0.816561i	$0.695878\pi$
$30$	−167610.	+	233070.i	−0.206926	+	0.287741i
$31$		−	928078.i		−	1.00493i	−0.864596	−	0.502467i	$-0.832426\pi$
$31$		−	928078.i		−	1.00493i	0.864596	−	0.502467i	$-0.167574\pi$
$32$	−1.04827e6	+	25494.5i	−0.999704	+	0.0243135i
$33$	−891773.			−0.751967
$34$	−646034.	−	464588.i	−0.483437	−	0.347658i
$35$	851871.	−	851871.i	0.567677	−	0.567677i
$36$	530762.	−	178181.i	0.316002	−	0.106084i
$37$	766720.	−	766720.i	0.409100	−	0.409100i	−0.472325	−	0.881425i	$-0.656585\pi$
$37$	766720.	−	766720.i	0.409100	−	0.409100i	0.881425	+	0.472325i	$0.156585\pi$
$38$	−1.80955e6	+	295633.i	−0.867835	+	0.141781i
$39$	−3554.61			−0.00153650
$40$	733804.	+	1.38967e6i	0.286642	+	0.542840i
$41$			5.02634e6i			1.77876i	0.457172	+	0.889378i	$0.348862\pi$
$41$			5.02634e6i			1.77876i	−0.457172	+	0.889378i	$0.651138\pi$
$42$	−2.31876e6	+	378823.i	−0.745175	+	0.121742i
$43$	2.95586e6	+	2.95586e6i	0.864590	+	0.864590i	0.991867	−	0.127277i	$-0.0406239\pi$
$43$	2.95586e6	+	2.95586e6i	0.864590	+	0.864590i	−0.127277	+	0.991867i	$0.540624\pi$
$44$	−2.17383e6	+	4.37097e6i	−0.579982	+	1.16618i
$45$	−593324.	−	593324.i	−0.144691	−	0.144691i
$46$	245224.	+	176350.i	0.0547686	+	0.0393862i
$47$		−	3.96840e6i		−	0.813249i	−0.913595	−	0.406624i	$-0.866706\pi$
$47$		−	3.96840e6i		−	0.813249i	0.913595	−	0.406624i	$-0.133294\pi$
$48$	420471.	−	3.03584e6i	0.0792084	−	0.571891i
$49$	4.09485e6			0.710319
$50$	−2.27393e6	+	3.16202e6i	−0.363829	+	0.505923i
$51$	1.64460e6	−	1.64460e6i	0.243097	−	0.243097i
$52$	−8664.89	+	17422.7i	−0.00118509	+	0.00238288i
$53$	8.73814e6	−	8.73814e6i	1.10743	−	1.10743i	0.113941	−	0.993488i	$-0.463653\pi$
$53$	8.73814e6	−	8.73814e6i	1.10743	−	1.10743i	0.993488	−	0.113941i	$-0.0363474\pi$
$54$	263849.	+	1.61500e6i	0.0310299	+	0.189932i
$55$	7.31624e6			0.799534
$56$	−3.79554e6	+	1.22887e7i	−0.385941	+	1.24955i
$57$		−	5.35915e6i		−	0.507687i
$58$	617495.	+	3.77965e6i	0.0545660	+	0.333995i
$59$	−9.75112e6	−	9.75112e6i	−0.804723	−	0.804723i	0.179107	−	0.983830i	$-0.442679\pi$
$59$	−9.75112e6	−	9.75112e6i	−0.804723	−	0.804723i	−0.983830	+	0.179107i	$0.942679\pi$
$60$	−4.35445e6	+	1.46182e6i	−0.335992	+	0.112795i
$61$	−4.29071e6	−	4.29071e6i	−0.309892	−	0.309892i	0.534976	−	0.844867i	$-0.320321\pi$
$61$	−4.29071e6	−	4.29071e6i	−0.309892	−	0.309892i	−0.844867	+	0.534976i	$0.820321\pi$
$62$	8.66964e6	−	1.20556e7i	0.586725	−	0.815872i
$63$		−	6.86720e6i		−	0.435931i
$64$	−1.38550e7	−	9.46121e6i	−0.825821	−	0.563932i
$65$	29162.6			0.00163370
$66$	−1.15840e7	−	8.33050e6i	−0.610496	−	0.439031i
$67$	6.69650e6	−	6.69650e6i	0.332314	−	0.332314i	−0.521151	−	0.853465i	$-0.674497\pi$
$67$	6.69650e6	−	6.69650e6i	0.332314	−	0.332314i	0.853465	+	0.521151i	$0.174497\pi$
$68$	−4.05194e6	−	1.20699e7i	−0.189508	−	0.564503i
$69$	−624263.	+	624263.i	−0.0275405	+	0.0275405i
$70$	1.90234e7	−	3.10792e6i	0.792313	−	0.129443i
$71$	2.38140e7			0.937127			0.468563	−	0.883430i	$-0.344772\pi$
$71$	2.38140e7			0.937127			0.468563	+	0.883430i	$0.344772\pi$
$72$	8.55900e6	+	2.64357e6i	0.318488	+	0.0983697i
$73$		−	4.01505e7i		−	1.41384i	−0.707295	−	0.706918i	$-0.750085\pi$
$73$		−	4.01505e7i		−	1.41384i	0.707295	−	0.706918i	$-0.249915\pi$
$74$	1.71219e7	−	2.79726e6i	0.570985	−	0.0932838i
$75$	−8.04952e6	−	8.04952e6i	−0.254404	−	0.254404i
$76$	−2.62675e7	−	1.30637e7i	−0.787343	−	0.391573i
$77$	4.23395e7	+	4.23395e7i	1.20443	+	1.20443i
$78$	−46173.9	−	33205.4i	−0.00124744	−	0.000897079i
$79$		−	7.02261e7i		−	1.80298i	−0.432803	−	0.901489i	$-0.642475\pi$
$79$		−	7.02261e7i		−	1.80298i	0.432803	−	0.901489i	$-0.357525\pi$
$80$	−3.44961e6	+	2.49064e7i	−0.0842189	+	0.608068i
$81$	−4.78297e6			−0.111111
$82$	−4.69536e7	+	6.52914e7i	−1.03852	+	1.44411i
$83$	7.55026e6	−	7.55026e6i	0.159093	−	0.159093i	−0.623072	−	0.782165i	$-0.714116\pi$
$83$	7.55026e6	−	7.55026e6i	0.159093	−	0.159093i	0.782165	+	0.623072i	$0.214116\pi$
$84$	−3.36591e7	−	1.67398e7i	−0.676060	−	0.336228i
$85$	−1.34926e7	+	1.34926e7i	−0.258475	+	0.258475i
$86$	1.07840e7	+	6.60084e7i	0.197145	+	1.20672i
$87$	−1.11938e7			−0.195389
$88$	−6.90691e7	+	3.64714e7i	−1.15174	+	0.608165i
$89$			1.01023e8i			1.61013i	0.593184	+	0.805067i	$0.297871\pi$
$89$			1.01023e8i			1.61013i	−0.593184	+	0.805067i	$0.702129\pi$
$90$	−2.16465e6	−	1.32497e7i	−0.0329927	−	0.201947i
$91$	168765.	+	168765.i	0.00246104	+	0.00246104i
$92$	1.53805e6	+	4.58152e6i	0.0214694	+	0.0639526i
$93$	3.06898e7	+	3.06898e7i	0.410263	+	0.410263i
$94$	3.70708e7	−	5.15489e7i	0.474810	−	0.660249i
$95$			4.39672e7i			0.539802i
$96$	3.38211e7	−	3.55072e7i	0.398202	−	0.418054i
$97$	2.10782e7			0.238093			0.119047	−	0.992889i	$-0.462016\pi$
$97$	2.10782e7			0.238093			0.119047	+	0.992889i	$0.462016\pi$
$98$	5.31915e7	+	3.82520e7i	0.576684	+	0.414716i
$99$	2.94893e7	−	2.94893e7i	0.306989	−	0.306989i
$100$	−5.90760e7	+	1.98323e7i	−0.590760	+	0.198323i
$101$	−2.83838e6	+	2.83838e6i	−0.0272763	+	0.0272763i	−0.720613	−	0.693337i	$-0.756140\pi$
$101$	−2.83838e6	+	2.83838e6i	−0.0272763	+	0.0272763i	0.693337	+	0.720613i	$0.256140\pi$
$102$	3.67262e7	−	6.00008e6i	0.339293	−	0.0554315i
$103$	−1.80583e8			−1.60445			−0.802226	−	0.597020i	$-0.796351\pi$
$103$	−1.80583e8			−1.60445			−0.802226	+	0.597020i	$0.796351\pi$
$104$	−275310.	+	145375.i	−0.00235336	+	0.00124267i
$105$			5.63395e7i			0.463507i
$106$	1.95135e8	−	3.18798e7i	1.54565	−	0.252518i
$107$	1.10577e8	+	1.10577e8i	0.843584	+	0.843584i	0.989323	−	0.145739i	$-0.0465561\pi$
$107$	1.10577e8	+	1.10577e8i	0.843584	+	0.843584i	−0.145739	+	0.989323i	$0.546556\pi$
$108$	−1.16592e7	+	2.34434e7i	−0.0856986	+	0.172316i
$109$	2.48326e7	+	2.48326e7i	0.175920	+	0.175920i	0.789575	−	0.613655i	$-0.210301\pi$
$109$	2.48326e7	+	2.48326e7i	0.175920	+	0.175920i	−0.613655	+	0.789575i	$0.710301\pi$
$110$	9.50369e7	+	6.83447e7i	0.649115	+	0.466803i
$111$			5.07079e7i			0.334029i
$112$	−1.64098e8	+	1.24172e8i	−1.04287	+	0.789135i
$113$	−2.38114e8			−1.46040			−0.730199	−	0.683235i	$-0.760573\pi$
$113$	−2.38114e8			−1.46040			−0.730199	+	0.683235i	$0.760573\pi$
$114$	5.00625e7	−	6.96145e7i	0.296410	−	0.412174i
$115$	5.12155e6	−	5.12155e6i	0.0292826	−	0.0292826i
$116$	−2.72865e7	+	5.48655e7i	−0.150701	+	0.303017i
$117$	117544.	−	117544.i	0.000627275	−	0.000627275i
$118$	−3.55755e7	−	2.17756e8i	−0.183494	−	1.12316i
$119$	−1.56164e8			−0.778743
$120$	−7.02193e7	−	2.16883e7i	−0.338635	−	0.104592i
$121$			1.49271e8i			0.696362i
$122$	−1.56540e7	−	9.58174e7i	−0.0706621	−	0.432519i
$123$	−1.66212e8	−	1.66212e8i	−0.726174	−	0.726174i
$124$	2.25235e8	−	7.56130e7i	0.952684	−	0.319823i
$125$	1.72014e8	+	1.72014e8i	0.704571	+	0.704571i
$126$	6.41499e7	−	8.92039e7i	0.254515	−	0.353917i
$127$		−	4.29074e8i		−	1.64937i	−0.565595	−	0.824683i	$-0.691354\pi$
$127$		−	4.29074e8i		−	1.64937i	0.565595	−	0.824683i	$-0.308646\pi$
$128$	−9.15923e7	−	2.52326e8i	−0.341208	−	0.939988i
$129$	−1.95489e8			−0.705935
$130$	378817.	+	272422.i	0.00132635	+	0.000953826i
$131$	2.20360e8	−	2.20360e8i	0.748250	−	0.748250i	−0.225900	−	0.974150i	$-0.572532\pi$
$131$	2.20360e8	−	2.20360e8i	0.748250	−	0.748250i	0.974150	+	0.225900i	$0.0725324\pi$
$132$	−7.26551e7	−	2.16424e8i	−0.239315	−	0.712869i
$133$	−2.54441e8	+	2.54441e8i	−0.813168	+	0.813168i
$134$	1.49542e8	−	2.44312e7i	0.463814	−	0.0757750i
$135$	3.92402e7			0.118140
$136$	6.01165e7	−	1.94637e8i	0.175727	−	0.568944i
$137$			2.66288e8i			0.755910i	0.925824	+	0.377955i	$0.123373\pi$
$137$			2.66288e8i			0.755910i	−0.925824	+	0.377955i	$0.876627\pi$
$138$	−1.39406e7	+	2.27753e6i	−0.0384385	+	0.00627983i
$139$	−4.27337e8	−	4.27337e8i	−1.14475	−	1.14475i	−0.987570	−	0.157181i	$-0.949759\pi$
$139$	−4.27337e8	−	4.27337e8i	−1.14475	−	1.14475i	−0.157181	−	0.987570i	$-0.550241\pi$
$140$	2.76144e8	+	1.37336e8i	0.718826	+	0.357497i
$141$	1.31227e8	+	1.31227e8i	0.332007	+	0.332007i
$142$	3.09340e8	+	2.22458e8i	0.760821	+	0.547136i
$143$			1.44943e6i			0.00346620i
$144$	8.64852e7	+	1.14294e8i	0.201137	+	0.265810i
$145$	9.18354e7			0.207748
$146$	3.75066e8	−	5.21549e8i	0.825460	−	1.14785i
$147$	−1.35409e8	+	1.35409e8i	−0.289987	+	0.289987i
$148$	2.48542e8	+	1.23608e8i	0.518027	+	0.257632i
$149$	−3.09770e8	+	3.09770e8i	−0.628485	+	0.628485i	−0.947687	−	0.319202i	$-0.896585\pi$
$149$	−3.09770e8	+	3.09770e8i	−0.628485	+	0.628485i	0.319202	+	0.947687i	$0.396585\pi$
$150$	−2.93675e7	−	1.79757e8i	−0.0580098	−	0.355075i
$151$	7.12363e8			1.37023			0.685115	−	0.728435i	$-0.259752\pi$
$151$	7.12363e8			1.37023			0.685115	+	0.728435i	$0.259752\pi$
$152$	−2.19176e8	−	4.15074e8i	−0.410600	−	0.777590i
$153$			1.08768e8i			0.198488i
$154$	1.54469e8	+	9.45499e8i	0.274637	+	1.68104i
$155$	−2.51784e8	−	2.51784e8i	−0.436215	−	0.436215i
$156$	−289604.	−	862667.i	−0.000488996	−	0.00145662i
$157$	2.02672e8	+	2.02672e8i	0.333577	+	0.333577i	0.853943	−	0.520366i	$-0.174205\pi$
$157$	2.02672e8	+	2.02672e8i	0.333577	+	0.333577i	−0.520366	+	0.853943i	$0.674205\pi$
$158$	6.56017e8	−	9.12227e8i	1.05266	−	1.46378i
$159$			5.77908e8i			0.904211i
$160$	−2.77474e8	+	2.91307e8i	−0.423391	+	0.444499i
$161$	5.92774e7			0.0882238
$162$	−6.21301e7	−	4.46801e7i	−0.0902073	−	0.0648715i
$163$	9.79943e8	−	9.79943e8i	1.38820	−	1.38820i	0.559085	−	0.829110i	$-0.311152\pi$
$163$	9.79943e8	−	9.79943e8i	1.38820	−	1.38820i	0.829110	−	0.559085i	$-0.188848\pi$
$164$	−1.21984e9	+	4.09509e8i	−1.68627	+	0.566094i
$165$	−2.41934e8	+	2.41934e8i	−0.326409	+	0.326409i
$166$	1.68608e8	−	2.75460e7i	0.222047	−	0.0362766i
$167$	−7.98570e8			−1.02671			−0.513354	−	0.858177i	$-0.671597\pi$
$167$	−7.98570e8			−1.02671			−0.513354	+	0.858177i	$0.671597\pi$
$168$	−2.80852e8	−	5.31874e8i	−0.352566	−	0.667685i
$169$		−	8.15725e8i		−	0.999993i
$170$	−3.01307e8	+	4.92256e7i	−0.360756	+	0.0589380i
$171$	1.77217e8	+	1.77217e8i	0.207262	+	0.207262i
$172$	−4.76535e8	+	9.58178e8i	−0.544478	+	1.09479i
$173$	4.12260e7	+	4.12260e7i	0.0460243	+	0.0460243i	0.729744	−	0.683720i	$-0.239639\pi$
$173$	4.12260e7	+	4.12260e7i	0.0460243	+	0.0460243i	−0.683720	+	0.729744i	$0.739639\pi$
$174$	−1.45405e8	−	1.04567e8i	−0.158629	−	0.114076i
$175$			7.64348e8i			0.814965i
$176$	−1.23790e9	−	1.71452e8i	−1.29013	−	0.178686i
$177$	6.44902e8			0.657053
$178$	−9.43710e8	+	1.31228e9i	−0.940067	+	1.30721i
$179$	2.80091e7	−	2.80091e7i	0.0272827	−	0.0272827i	−0.693334	−	0.720617i	$-0.743859\pi$
$179$	2.80091e7	−	2.80091e7i	0.0272827	−	0.0272827i	0.720617	+	0.693334i	$0.243859\pi$
$180$	9.56538e7	−	1.92333e8i	0.0911197	−	0.183216i
$181$	8.25608e8	−	8.25608e8i	0.769236	−	0.769236i	−0.208736	−	0.977972i	$-0.566935\pi$
$181$	8.25608e8	−	8.25608e8i	0.769236	−	0.769236i	0.977972	+	0.208736i	$0.0669350\pi$
$182$	615716.	+	3.76876e6i	0.000561170	+	0.00343489i
$183$	2.83771e8			0.253025
$184$	−2.28192e7	+	7.38810e7i	−0.0199081	+	0.0644557i
$185$		−	4.16015e8i		−	0.355159i
$186$	1.11967e8	+	6.85345e8i	0.0935489	+	0.572608i
$187$	−6.70604e8	−	6.70604e8i	−0.548403	−	0.548403i
$188$	9.63088e8	−	3.23316e8i	0.770965	−	0.258819i
$189$	2.27085e8	+	2.27085e8i	0.177968	+	0.177968i
$190$	−4.10720e8	+	5.71128e8i	−0.315160	+	0.438247i
$191$			1.01764e9i			0.764644i	0.924029	+	0.382322i	$0.124875\pi$
$191$			1.01764e9i			0.764644i	−0.924029	+	0.382322i	$0.875125\pi$
$192$	7.71022e8	−	1.45294e8i	0.567364	−	0.106916i
$193$	−6.23062e8			−0.449057			−0.224529	−	0.974467i	$-0.572084\pi$
$193$	−6.23062e8			−0.449057			−0.224529	+	0.974467i	$0.572084\pi$
$194$	2.73803e8	+	1.96902e8i	0.193300	+	0.139009i
$195$	−964351.	+	964351.i	−0.000666955	+	0.000666955i
$196$	3.33618e8	+	9.93777e8i	0.226061	+	0.673387i
$197$	9.82885e8	−	9.82885e8i	0.652586	−	0.652586i	−0.301029	−	0.953615i	$-0.597330\pi$
$197$	9.82885e8	−	9.82885e8i	0.652586	−	0.652586i	0.953615	+	0.301029i	$0.0973301\pi$
$198$	6.58535e8	−	1.07587e8i	0.428468	−	0.0700003i
$199$	−1.94440e9			−1.23986			−0.619931	−	0.784656i	$-0.712840\pi$
$199$	−1.94440e9			−1.23986			−0.619931	+	0.784656i	$0.712840\pi$
$200$	−9.52652e8	−	2.94241e8i	−0.595408	−	0.183901i
$201$			4.42882e8i			0.271333i
$202$	−6.33850e7	+	1.03554e7i	−0.0380698	+	0.00621960i
$203$	5.31457e8	+	5.31457e8i	0.312956	+	0.312956i
$204$	5.33117e8	+	2.65137e8i	0.307824	+	0.153091i
$205$	1.36362e9	+	1.36362e9i	0.772110	+	0.772110i
$206$	−2.34574e9	−	1.68691e9i	−1.30260	−	0.936750i
$207$		−	4.12864e7i		−	0.0224867i
$208$	−4.93426e6	−	683407.i	−0.00263614	−	0.000365112i
$209$	−2.18525e9			−1.14529
$210$	−5.26296e8	+	7.31842e8i	−0.270615	+	0.376305i
$211$	1.17826e9	−	1.17826e9i	0.594443	−	0.594443i	−0.344385	−	0.938828i	$-0.611913\pi$
$211$	1.17826e9	−	1.17826e9i	0.594443	−	0.594443i	0.938828	+	0.344385i	$0.111913\pi$
$212$	2.83258e9	+	1.40874e9i	1.40229	+	0.697407i
$213$	−7.87483e8	+	7.87483e8i	−0.382580	+	0.382580i
$214$	4.03422e8	+	2.46933e9i	0.192356	+	1.17740i
$215$	1.60382e9			0.750590
$216$	−3.70448e8	+	1.95612e8i	−0.170181	+	0.0898629i
$217$		−	2.91417e9i		−	1.31424i
$218$	9.05979e7	+	5.54545e8i	0.0401136	+	0.245533i
$219$	1.32770e9	+	1.32770e9i	0.577196	+	0.577196i
$220$	5.96073e8	+	1.77557e9i	0.254454	+	0.757963i
$221$	−2.67303e6	−	2.67303e6i	−0.00112056	−	0.00112056i
$222$	−4.73688e8	+	6.58689e8i	−0.195021	+	0.271187i
$223$			1.43941e9i			0.582056i	0.956715	+	0.291028i	$0.0939972\pi$
$223$			1.43941e9i			0.582056i	−0.956715	+	0.291028i	$0.906003\pi$
$224$	−3.29156e9	+	8.00529e7i	−1.30741	+	0.0317969i
$225$	5.32365e8			0.207720
$226$	−3.09307e9	−	2.22434e9i	−1.18565	−	0.852645i
$227$	2.47247e9	−	2.47247e9i	0.931167	−	0.931167i	−0.0666116	−	0.997779i	$-0.521219\pi$
$227$	2.47247e9	−	2.47247e9i	0.931167	−	0.931167i	0.997779	+	0.0666116i	$0.0212188\pi$
$228$	1.30061e9	−	4.36624e8i	0.481291	−	0.161573i
$229$	2.82439e9	−	2.82439e9i	1.02703	−	1.02703i	0.0274030	−	0.999624i	$-0.491276\pi$
$229$	2.82439e9	−	2.82439e9i	1.02703	−	1.02703i	0.999624	−	0.0274030i	$-0.00872373\pi$
$230$	1.14371e8	−	1.86852e7i	0.0408700	−	0.00667708i
$231$	−2.80017e9			−0.983416
$232$	−8.66974e8	+	4.57798e8i	−0.299264	+	0.158024i
$233$		−	4.00466e9i		−	1.35876i	−0.733788	−	0.679379i	$-0.762249\pi$
$233$		−	4.00466e9i		−	1.35876i	0.733788	−	0.679379i	$-0.237751\pi$
$234$	2.62492e6	−	428843.i	0.000875494	−	0.000143033i
$235$	−1.07661e9	−	1.07661e9i	−0.353009	−	0.353009i
$236$	1.57204e9	−	3.16094e9i	0.506777	−	1.01899i
$237$	2.32224e9	+	2.32224e9i	0.736062	+	0.736062i
$238$	−2.02855e9	−	1.45881e9i	−0.632235	−	0.454664i
$239$			4.00603e9i			1.22779i	0.789389	+	0.613893i	$0.210397\pi$
$239$			4.00603e9i			1.22779i	−0.789389	+	0.613893i	$0.789603\pi$
$240$	−7.09537e8	−	9.37681e8i	−0.213860	−	0.282625i
$241$	−3.87088e9			−1.14747			−0.573736	−	0.819040i	$-0.694506\pi$
$241$	−3.87088e9			−1.14747			−0.573736	+	0.819040i	$0.694506\pi$
$242$	−1.39442e9	+	1.93901e9i	−0.406567	+	0.565353i
$243$	1.58164e8	−	1.58164e8i	0.0453609	−	0.0453609i
$244$	6.91735e8	−	1.39089e9i	0.195155	−	0.392403i
$245$	1.11091e9	−	1.11091e9i	0.308330	−	0.308330i
$246$	−6.06398e8	−	3.71173e9i	−0.165584	−	1.01353i
$247$	−8.71042e6			−0.00234019
$248$	3.63211e9	+	1.12183e9i	0.960178	+	0.296565i
$249$			4.99346e8i			0.129898i
$250$	6.27569e8	+	3.84131e9i	0.160658	+	0.983376i
$251$	4.32665e9	+	4.32665e9i	1.09008	+	1.09008i	0.995520	+	0.0945555i	$0.0301430\pi$
$251$	4.32665e9	+	4.32665e9i	1.09008	+	1.09008i	0.0945555	+	0.995520i	$0.469857\pi$
$252$	1.66660e9	−	5.59489e8i	0.413265	−	0.138736i
$253$	2.54550e8	+	2.54550e8i	0.0621286	+	0.0621286i
$254$	4.00819e9	−	5.57360e9i	0.962972	−	1.33906i
$255$		−	8.92346e8i		−	0.211044i
$256$	1.16733e9	−	4.13329e9i	0.271791	−	0.962356i
$257$	−6.30105e9			−1.44438			−0.722188	−	0.691697i	$-0.756863\pi$
$257$	−6.30105e9			−1.44438			−0.722188	+	0.691697i	$0.756863\pi$
$258$	−2.53938e9	−	1.82617e9i	−0.573124	−	0.412156i
$259$	2.40751e9	−	2.40751e9i	0.535018	−	0.535018i
$260$	2.37595e6	+	7.07745e6i	0.000519929	+	0.00154876i
$261$	3.70157e8	−	3.70157e8i	0.0797671	−	0.0797671i
$262$	4.92093e9	−	8.03949e8i	1.04434	−	0.170617i
$263$	−1.92249e9			−0.401828			−0.200914	−	0.979609i	$-0.564391\pi$
$263$	−1.92249e9			−0.401828			−0.200914	+	0.979609i	$0.564391\pi$
$264$	1.07795e9	−	3.49002e9i	0.221912	−	0.718477i
$265$		−	4.74124e9i		−	0.961410i
$266$	−5.68201e9	+	9.28290e8i	−1.13495	+	0.185420i
$267$	−3.34065e9	−	3.34065e9i	−0.657334	−	0.657334i
$268$	2.17075e9	+	1.07959e9i	0.420796	+	0.209276i
$269$	−1.23805e9	−	1.23805e9i	−0.236444	−	0.236444i	0.578932	−	0.815376i	$-0.303470\pi$
$269$	−1.23805e9	−	1.23805e9i	−0.236444	−	0.236444i	−0.815376	+	0.578932i	$0.803470\pi$
$270$	5.09724e8	+	3.66562e8i	0.0959136	+	0.0689752i
$271$			3.07221e9i			0.569604i	0.958586	+	0.284802i	$0.0919279\pi$
$271$			3.07221e9i			0.569604i	−0.958586	+	0.284802i	$0.908072\pi$
$272$	2.59911e9	−	1.96673e9i	0.474841	−	0.359309i
$273$	−1.11615e7			−0.00200943
$274$	−2.48753e9	+	3.45905e9i	−0.441333	+	0.613697i
$275$	−3.28228e9	+	3.28228e9i	−0.573911	+	0.573911i
$276$	−2.02363e8	−	1.00642e8i	−0.0348734	−	0.0173437i
$277$	−2.14710e8	+	2.14710e8i	−0.0364697	+	0.0364697i	−0.725106	−	0.688637i	$-0.758209\pi$
$277$	−2.14710e8	+	2.14710e8i	−0.0364697	+	0.0364697i	0.688637	+	0.725106i	$0.258209\pi$
$278$	−1.55907e9	−	9.54301e9i	−0.261028	−	1.59774i
$279$	−2.02971e9			−0.334978
$280$	2.30415e9	+	4.36358e9i	0.374868	+	0.709922i
$281$		−	2.59845e9i		−	0.416763i	−0.978048	−	0.208381i	$-0.933180\pi$
$281$		−	2.59845e9i		−	0.416763i	0.978048	−	0.208381i	$-0.0668196\pi$
$282$	4.78763e8	+	2.93048e9i	0.0757050	+	0.463386i
$283$	1.05105e9	+	1.05105e9i	0.163862	+	0.163862i	0.784275	−	0.620413i	$-0.213035\pi$
$283$	1.05105e9	+	1.05105e9i	0.163862	+	0.163862i	−0.620413	+	0.784275i	$0.713035\pi$
$284$	1.94019e9	+	5.77940e9i	0.298243	+	0.888402i
$285$	−1.45391e9	−	1.45391e9i	−0.220373	−	0.220373i
$286$	−1.35399e7	+	1.88279e7i	−0.00202372	+	0.00281409i
$287$			1.57828e10i			2.32624i
$288$	5.57565e7	+	2.29256e9i	0.00810448	+	0.333235i
$289$	−4.50231e9			−0.645423
$290$	1.19293e9	+	8.57880e8i	0.168664	+	0.121293i
$291$	−6.97017e8	+	6.97017e8i	−0.0972011	+	0.0972011i
$292$	9.74410e9	−	3.27117e9i	1.34033	−	0.449957i
$293$	−7.05749e9	+	7.05749e9i	−0.957591	+	0.957591i	−0.999137	−	0.0415456i	$-0.986772\pi$
$293$	−7.05749e9	+	7.05749e9i	−0.957591	+	0.957591i	0.0415456	+	0.999137i	$0.486772\pi$
$294$	−3.02386e9	+	4.94019e8i	−0.404737	+	0.0661233i
$295$	−5.29087e9			−0.698617
$296$	2.07383e9	+	3.92740e9i	0.270151	+	0.511610i
$297$			1.95031e9i			0.250656i
$298$	−6.91759e9	+	1.13015e9i	−0.877182	+	0.143308i
$299$	1.01464e6	+	1.01464e6i	0.000126948	+	0.000126948i
$300$	1.29772e9	−	2.60935e9i	0.160212	−	0.322142i
$301$	9.28142e9	+	9.28142e9i	1.13070	+	1.13070i
$302$	9.25349e9	+	6.65454e9i	1.11244	+	0.800001i
$303$		−	1.87720e8i		−	0.0222710i
$304$	1.03035e9	−	7.43918e9i	0.120639	−	0.871025i
$305$	−2.32810e9			−0.269031
$306$	−1.01605e9	+	1.41288e9i	−0.115886	+	0.161146i
$307$	−8.00453e9	+	8.00453e9i	−0.901119	+	0.901119i	−0.995533	−	0.0944136i	$-0.969902\pi$
$307$	−8.00453e9	+	8.00453e9i	−0.901119	+	0.901119i	0.0944136	+	0.995533i	$0.469902\pi$
$308$	−6.82584e9	+	1.37249e10i	−0.758496	+	1.52512i
$309$	5.97152e9	−	5.97152e9i	0.655015	−	0.655015i
$310$	−9.18595e8	−	5.62267e9i	−0.0994666	−	0.608830i
$311$	3.34398e9			0.357456			0.178728	−	0.983899i	$-0.442802\pi$
$311$	3.34398e9			0.357456			0.178728	+	0.983899i	$0.442802\pi$
$312$	4.29670e6	−	1.39113e7i	0.000453436	−	0.00146807i
$313$			8.74516e9i			0.911151i	0.890197	+	0.455575i	$0.150566\pi$
$313$			8.74516e9i			0.911151i	−0.890197	+	0.455575i	$0.849434\pi$
$314$	7.39420e8	+	4.52595e9i	0.0760629	+	0.465577i
$315$	−1.86304e9	−	1.86304e9i	−0.189226	−	0.189226i
$316$	1.70431e10	−	5.72151e9i	1.70923	−	0.573802i
$317$	4.28630e9	+	4.28630e9i	0.424468	+	0.424468i	0.886739	−	0.462271i	$-0.152965\pi$
$317$	4.28630e9	+	4.28630e9i	0.424468	+	0.424468i	−0.462271	+	0.886739i	$0.652965\pi$
$318$	−5.39853e9	+	7.50694e9i	−0.527918	+	0.734098i
$319$			4.56438e9i			0.440777i
$320$	−6.32558e9	+	1.19201e9i	−0.603255	+	0.113679i
$321$	−7.31312e9			−0.688783
$322$	7.70005e8	+	5.53740e8i	0.0716259	+	0.0515089i
$323$	4.03002e9	−	4.03002e9i	0.370252	−	0.370252i
$324$	−3.89681e8	−	1.16078e9i	−0.0353614	−	0.105334i
$325$	−1.30832e7	+	1.30832e7i	−0.00117268	+	0.00117268i
$326$	2.18835e10	−	3.57518e9i	1.93752	−	0.316539i
$327$	−1.64233e9			−0.143638
$328$	−1.96710e10	−	6.07568e9i	−1.69954	−	0.524927i
$329$		−	1.24608e10i		−	1.06356i
$330$	−5.40272e9	+	8.82661e8i	−0.455572	+	0.0744283i
$331$	−4.73680e9	−	4.73680e9i	−0.394615	−	0.394615i	0.481714	−	0.876329i	$-0.340014\pi$
$331$	−4.73680e9	−	4.73680e9i	−0.394615	−	0.394615i	−0.876329	+	0.481714i	$0.840014\pi$
$332$	2.44751e9	+	1.21723e9i	0.201452	+	0.100189i
$333$	−1.67682e9	−	1.67682e9i	−0.136367	−	0.136367i
$334$	−1.03733e10	−	7.45984e9i	−0.833549	−	0.599437i
$335$		−	3.63347e9i		−	0.288497i
$336$	1.32028e9	−	9.53255e9i	0.103588	−	0.747914i
$337$	7.25132e9			0.562209			0.281104	−	0.959677i	$-0.409299\pi$
$337$	7.25132e9			0.562209			0.281104	+	0.959677i	$0.409299\pi$
$338$	7.62010e9	−	1.05961e10i	0.583840	−	0.811860i
$339$	7.87398e9	−	7.87398e9i	0.596205	−	0.596205i
$340$	−4.37377e9	−	2.17523e9i	−0.327296	−	0.162775i
$341$	1.25141e10	−	1.25141e10i	0.925512	−	0.925512i
$342$	6.46549e8	+	3.95749e9i	0.0472604	+	0.289278i
$343$	−5.24366e9			−0.378842
$344$	−1.51409e10	+	7.99504e9i	−1.08123	+	0.570936i
$345$			3.38720e8i			0.0239092i
$346$	1.50407e8	+	9.20634e8i	0.0104946	+	0.0642366i
$347$	9.09788e9	+	9.09788e9i	0.627512	+	0.627512i	0.947441	−	0.319929i	$-0.103659\pi$
$347$	9.09788e9	+	9.09788e9i	0.627512	+	0.627512i	−0.319929	+	0.947441i	$0.603659\pi$
$348$	−9.11986e8	−	2.71661e9i	−0.0621829	−	0.185230i
$349$	−3.60901e9	−	3.60901e9i	−0.243269	−	0.243269i	0.574932	−	0.818201i	$-0.305028\pi$
$349$	−3.60901e9	−	3.60901e9i	−0.243269	−	0.243269i	−0.818201	+	0.574932i	$0.805028\pi$
$350$	−7.14016e9	+	9.92877e9i	−0.475812	+	0.661642i
$351$			7.77394e6i			0.000512168i
$352$	−1.44785e10	−	1.37909e10i	−0.943087	−	0.898303i
$353$	−6.40769e9			−0.412670			−0.206335	−	0.978481i	$-0.566154\pi$
$353$	−6.40769e9			−0.412670			−0.206335	+	0.978481i	$0.566154\pi$
$354$	8.37718e9	+	6.02435e9i	0.533439	+	0.383617i
$355$	6.46063e9	−	6.46063e9i	0.406781	−	0.406781i
$356$	−2.45173e10	+	8.23064e9i	−1.52642	+	0.512429i
$357$	5.16406e9	−	5.16406e9i	0.317920	−	0.317920i
$358$	6.25482e8	−	1.02187e8i	0.0380788	−	0.00622106i
$359$	1.09610e10			0.659891			0.329946	−	0.944000i	$-0.392970\pi$
$359$	1.09610e10			0.659891			0.329946	+	0.944000i	$0.392970\pi$
$360$	3.03921e9	−	1.60483e9i	0.180947	−	0.0955474i
$361$			3.85121e9i			0.226761i
$362$	1.84369e10	−	3.01211e9i	1.07363	−	0.175403i
$363$	−4.93612e9	−	4.93612e9i	−0.284289	−	0.284289i
$364$	−2.72078e7	+	5.47074e7i	−0.00154985	+	0.00311631i
$365$	−1.08926e10	−	1.08926e10i	−0.613708	−	0.613708i
$366$	3.68615e9	+	2.65085e9i	0.205423	+	0.147727i
$367$		−	3.06694e10i		−	1.69060i	−0.534291	−	0.845300i	$-0.679421\pi$
$367$		−	3.06694e10i		−	1.69060i	0.534291	−	0.845300i	$-0.320579\pi$
$368$	−9.86578e8	+	7.46537e8i	−0.0537948	+	0.0407062i
$369$	1.09926e10			0.592919
$370$	3.88621e9	−	5.40398e9i	0.207357	−	0.288341i
$371$	2.74378e10	−	2.74378e10i	1.44829	−	1.44829i
$372$	−4.94771e9	+	9.94847e9i	−0.258364	+	0.519499i
$373$	−1.99773e10	+	1.99773e10i	−1.03205	+	1.03205i	−0.0325850	+	0.999469i	$0.510374\pi$
$373$	−1.99773e10	+	1.99773e10i	−1.03205	+	1.03205i	−0.999469	+	0.0325850i	$0.989626\pi$
$374$	−2.44660e9	−	1.49755e10i	−0.125048	−	0.765411i
$375$	−1.13764e10			−0.575279
$376$	1.55306e10	+	4.79687e9i	0.777030	+	0.239997i
$377$			1.81936e7i			0.000900646i
$378$	8.28487e8	+	5.07112e9i	0.0405806	+	0.248392i
$379$	−7.49423e8	−	7.49423e8i	−0.0363220	−	0.0363220i	0.688713	−	0.725035i	$-0.258176\pi$
$379$	−7.49423e8	−	7.49423e8i	−0.0363220	−	0.0363220i	−0.725035	+	0.688713i	$0.758176\pi$
$380$	−1.06704e10	+	3.58213e9i	−0.511736	+	0.171793i
$381$	1.41887e10	+	1.41887e10i	0.673351	+	0.673351i
$382$	−9.50625e9	+	1.32190e10i	−0.446433	+	0.620788i
$383$			5.73000e9i			0.266293i	0.991096	+	0.133146i	$0.0425080\pi$
$383$			5.73000e9i			0.266293i	−0.991096	+	0.133146i	$0.957492\pi$
$384$	1.13727e10	+	5.31516e9i	0.523046	+	0.244451i
$385$	2.29731e10			1.04562
$386$	−8.09348e9	−	5.82033e9i	−0.364574	−	0.262179i
$387$	6.46447e9	−	6.46447e9i	0.288197	−	0.288197i
$388$	1.71730e9	+	5.11546e9i	0.0757737	+	0.225714i
$389$	−4.07315e9	+	4.07315e9i	−0.177882	+	0.177882i	−0.790432	−	0.612550i	$-0.790144\pi$
$389$	−4.07315e9	+	4.07315e9i	−0.177882	+	0.177882i	0.612550	+	0.790432i	$0.290144\pi$
$390$	−2.15353e7	+	3.51829e6i	−0.000930876	+	0.000152080i
$391$	−9.38879e8			−0.0401701
$392$	−4.94972e9	+	1.60255e10i	−0.209622	+	0.678684i
$393$			1.45738e10i			0.610944i
$394$	2.19492e10	−	3.58591e9i	0.910821	−	0.148804i
$395$	−1.90520e10	−	1.90520e10i	−0.782624	−	0.782624i
$396$	9.55930e9	+	4.75417e9i	0.388728	+	0.193327i
$397$	3.21221e10	+	3.21221e10i	1.29313	+	1.29313i	0.932842	+	0.360287i	$0.117321\pi$
$397$	3.21221e10	+	3.21221e10i	1.29313	+	1.29313i	0.360287	+	0.932842i	$0.382679\pi$
$398$	−2.52575e10	−	1.81636e10i	−1.00660	−	0.723886i
$399$		−	1.68278e10i		−	0.663949i
$400$	−9.62616e9	−	1.27214e10i	−0.376022	−	0.496928i
$401$	−3.00084e9			−0.116055			−0.0580277	−	0.998315i	$-0.518481\pi$
$401$	−3.00084e9			−0.116055			−0.0580277	+	0.998315i	$0.518481\pi$
$402$	−4.13718e9	+	5.75297e9i	−0.158416	+	0.220286i
$403$	4.98812e7	−	4.98812e7i	0.00189111	−	0.00189111i
$404$	−9.20097e8	−	4.57596e8i	−0.0345389	−	0.0171774i
$405$	−1.29760e9	+	1.29760e9i	−0.0482303	+	0.0482303i
$406$	1.93894e9	+	1.18681e10i	0.0713609	+	0.436796i
$407$	2.06767e10			0.753536
$408$	4.44834e9	+	8.42422e9i	0.160530	+	0.304011i
$409$			1.45503e10i			0.519970i	0.965613	+	0.259985i	$0.0837177\pi$
$409$			1.45503e10i			0.519970i	−0.965613	+	0.259985i	$0.916282\pi$
$410$	4.97498e9	+	3.04516e10i	0.176058	+	1.07764i
$411$	−8.80565e9	−	8.80565e9i	−0.308599	−	0.308599i
$412$	−1.47125e10	−	4.38255e10i	−0.510621	−	1.52103i
$413$	−3.06186e10	−	3.06186e10i	−1.05241	−	1.05241i
$414$	3.85677e8	−	5.36305e8i	0.0131287	−	0.0182562i
$415$		−	4.09671e9i		−	0.138116i
$416$	−5.77112e7	−	5.49707e7i	−0.00192702	−	0.00183552i
$417$	2.82624e10			0.934685
$418$	−2.83861e10	−	2.04135e10i	−0.929823	−	0.668672i
$419$	−6.20388e9	+	6.20388e9i	−0.201283	+	0.201283i	−0.800550	−	0.599267i	$-0.795459\pi$
$419$	−6.20388e9	+	6.20388e9i	−0.201283	+	0.201283i	0.599267	+	0.800550i	$0.295459\pi$
$420$	−1.36730e10	+	4.59013e9i	−0.439407	+	0.147512i
$421$	−3.11957e10	+	3.11957e10i	−0.993040	+	0.993040i	−0.999976	−	0.00693560i	$-0.997792\pi$
$421$	−3.11957e10	+	3.11957e10i	−0.993040	+	0.993040i	0.00693560	+	0.999976i	$0.497792\pi$
$422$	2.63121e10	−	4.29870e9i	0.829670	−	0.135546i
$423$	−8.67888e9			−0.271083
$424$	2.36350e10	+	4.47598e10i	0.731295	+	1.38492i
$425$		−	1.21063e10i		−	0.371070i
$426$	−1.75856e10	+	2.87301e9i	−0.533971	+	0.0872367i
$427$	−1.34729e10	−	1.34729e10i	−0.405274	−	0.405274i
$428$	−1.78268e10	+	3.58448e10i	−0.531250	+	1.06819i
$429$	−4.79300e7	−	4.79300e7i	−0.00141507	−	0.00141507i
$430$	2.08334e10	+	1.49821e10i	0.609379	+	0.438228i
$431$		−	1.45305e10i		−	0.421087i	−0.977584	−	0.210544i	$-0.932477\pi$
$431$		−	1.45305e10i		−	0.421087i	0.977584	−	0.210544i	$-0.0675234\pi$
$432$	−6.63937e9	−	9.19570e8i	−0.190630	−	0.0264028i
$433$	9.84633e9			0.280106			0.140053	−	0.990144i	$-0.455273\pi$
$433$	9.84633e9			0.280106			0.140053	+	0.990144i	$0.455273\pi$
$434$	2.72227e10	−	3.78547e10i	0.767314	−	1.06699i
$435$	−3.03682e9	+	3.03682e9i	−0.0848130	+	0.0848130i
$436$	−4.00343e9	+	8.04977e9i	−0.110786	+	0.222760i
$437$	−1.52973e9	+	1.52973e9i	−0.0419458	+	0.0419458i
$438$	4.84392e9	+	2.96493e10i	0.131613	+	0.805599i
$439$	5.46119e10			1.47038			0.735189	−	0.677862i	$-0.237093\pi$
$439$	5.46119e10			1.47038			0.735189	+	0.677862i	$0.237093\pi$
$440$	−8.84363e9	+	2.86327e10i	−0.235950	+	0.763926i
$441$		−	8.95543e9i		−	0.236773i
$442$	−9.75216e6	−	5.96924e7i	−0.000255512	−	0.00156398i
$443$	2.33132e10	+	2.33132e10i	0.605323	+	0.605323i	0.941720	−	0.336397i	$-0.109208\pi$
$443$	2.33132e10	+	2.33132e10i	0.605323	+	0.605323i	−0.336397	+	0.941720i	$0.609208\pi$
$444$	−1.23063e10	+	4.13131e9i	−0.316661	+	0.106306i
$445$	2.74072e10	+	2.74072e10i	0.698916	+	0.698916i
$446$	−1.34462e10	+	1.86977e10i	−0.339830	+	0.472551i
$447$		−	2.04870e10i		−	0.513156i
$448$	−4.35047e10	−	2.97083e10i	−1.08000	−	0.737506i
$449$	−4.03382e10			−0.992502			−0.496251	−	0.868179i	$-0.665290\pi$
$449$	−4.03382e10			−0.992502			−0.496251	+	0.868179i	$0.665290\pi$
$450$	6.91534e9	+	4.97308e9i	0.168641	+	0.121276i
$451$	−6.77746e10	+	6.77746e10i	−1.63818	+	1.63818i
$452$	−1.93998e10	−	5.77878e10i	−0.464775	−	1.38447i
$453$	−2.35565e10	+	2.35565e10i	−0.559394	+	0.559394i
$454$	5.52136e10	−	9.02044e9i	1.29964	−	0.212327i
$455$	9.15707e7			0.00213654
$456$	2.09734e10	+	6.47796e9i	0.485077	+	0.149823i
$457$			1.77877e10i			0.407808i	0.978991	+	0.203904i	$0.0653630\pi$
$457$			1.77877e10i			0.407808i	−0.978991	+	0.203904i	$0.934637\pi$
$458$	6.30724e10	−	1.03044e10i	1.43343	−	0.234185i
$459$	−3.59674e9	−	3.59674e9i	−0.0810324	−	0.0810324i
$460$	1.66021e9	+	8.25680e8i	0.0370794	+	0.0184408i
$461$	−5.65754e10	−	5.65754e10i	−1.25263	−	1.25263i	−0.954535	−	0.298099i	$-0.903647\pi$
$461$	−5.65754e10	−	5.65754e10i	−1.25263	−	1.25263i	−0.298099	−	0.954535i	$-0.596353\pi$
$462$	−3.63739e10	−	2.61578e10i	−0.798402	−	0.574161i
$463$			6.34281e10i			1.38025i	0.723690	+	0.690125i	$0.242445\pi$
$463$			6.34281e10i			1.38025i	−0.723690	+	0.690125i	$0.757555\pi$
$464$	−1.55384e10	−	2.15211e9i	−0.335223	−	0.0464292i
$465$	1.66520e10			0.356168
$466$	3.74095e10	−	5.20199e10i	0.793302	−	1.10313i
$467$	−2.52894e10	+	2.52894e10i	−0.531706	+	0.531706i	−0.921080	−	0.389374i	$-0.872691\pi$
$467$	−2.52894e10	+	2.52894e10i	−0.531706	+	0.531706i	0.389374	+	0.921080i	$0.372691\pi$
$468$	3.81034e7	+	1.89501e7i	0.000794292	+	0.000395029i
$469$	2.10271e10	−	2.10271e10i	0.434598	−	0.434598i
$470$	−3.92785e9	−	2.40421e10i	−0.0804939	−	0.492699i
$471$	−1.34040e10			−0.272364
$472$	4.99486e10	−	2.63749e10i	1.00636	−	0.531402i
$473$			7.97130e10i			1.59252i
$474$	8.47237e9	+	5.18589e10i	0.167838	+	1.02733i
$475$	−1.97250e10	−	1.97250e10i	−0.387474	−	0.387474i
$476$	−1.27231e10	−	3.78995e10i	−0.247837	−	0.738253i
$477$	−1.91103e10	−	1.91103e10i	−0.369143	−	0.369143i
$478$	−3.74223e10	+	5.20377e10i	−0.716835	+	0.996797i
$479$		−	8.00871e10i		−	1.52132i	−0.649151	−	0.760660i	$-0.724876\pi$
$479$		−	8.00871e10i		−	1.52132i	0.649151	−	0.760660i	$-0.275124\pi$
$480$	−4.57434e8	−	1.88085e10i	−0.00861716	−	0.354314i
$481$	8.24175e7			0.00153971
$482$	−5.02822e10	−	3.61599e10i	−0.931593	−	0.669944i
$483$	−1.96019e9	+	1.96019e9i	−0.0360172	+	0.0360172i
$484$	−3.62266e10	+	1.21615e10i	−0.660156	+	0.221619i
$485$	5.71843e9	−	5.71843e9i	0.103350	−	0.103350i
$486$	3.53201e9	−	5.77037e8i	0.0633107	−	0.0103433i
$487$	−2.29804e9			−0.0408546			−0.0204273	−	0.999791i	$-0.506503\pi$
$487$	−2.29804e9			−0.0408546			−0.0204273	+	0.999791i	$0.506503\pi$
$488$	2.19785e10	−	1.16056e10i	0.387542	−	0.204638i
$489$			6.48098e10i			1.13346i
$490$	2.48082e10	−	4.05301e9i	0.430340	−	0.0703061i
$491$	6.62220e10	+	6.62220e10i	1.13940	+	1.13940i	0.988558	+	0.150842i	$0.0481986\pi$
$491$	6.62220e10	+	6.62220e10i	1.13940	+	1.13940i	0.150842	+	0.988558i	$0.451801\pi$
$492$	2.67961e10	−	5.38795e10i	0.457311	−	0.919524i
$493$	−8.41760e9	−	8.41760e9i	−0.142495	−	0.142495i
$494$	−1.13147e8	−	8.13684e7i	−0.00189992	−	0.00136631i
$495$		−	1.60006e10i		−	0.266511i
$496$	3.67009e10	+	4.85017e10i	0.606388	+	0.801365i
$497$	7.47760e10			1.22557
$498$	−4.66464e9	+	6.48643e9i	−0.0758405	+	0.105460i
$499$	−5.75501e9	+	5.75501e9i	−0.0928205	+	0.0928205i	−0.751992	−	0.659172i	$-0.770907\pi$
$499$	−5.75501e9	+	5.75501e9i	−0.0928205	+	0.0928205i	0.659172	+	0.751992i	$0.270907\pi$
$500$	−2.77316e10	+	5.57605e10i	−0.443706	+	0.892168i
$501$	2.64072e10	−	2.64072e10i	0.419152	−	0.419152i
$502$	1.57851e10	+	9.66199e10i	0.248561	+	1.52143i
$503$	−5.76352e10			−0.900359			−0.450180	−	0.892938i	$-0.648640\pi$
$503$	−5.76352e10			−0.900359			−0.450180	+	0.892938i	$0.648640\pi$
$504$	2.68753e10	+	8.30084e9i	0.416516	+	0.128647i
$505$			1.54008e9i			0.0236798i
$506$	9.28689e8	+	5.68445e9i	0.0141667	+	0.0867135i
$507$	2.69745e10	+	2.69745e10i	0.408245	+	0.408245i
$508$	1.04132e11	−	3.49578e10i	1.56361	−	0.524915i
$509$	−2.41241e10	−	2.41241e10i	−0.359401	−	0.359401i	0.504191	−	0.863592i	$-0.331791\pi$
$509$	−2.41241e10	−	2.41241e10i	−0.359401	−	0.359401i	−0.863592	+	0.504191i	$0.831791\pi$
$510$	8.33586e9	−	1.15915e10i	0.123217	−	0.171339i
$511$		−	1.26073e11i		−	1.84900i
$512$	5.37746e10	−	4.27862e10i	0.782524	−	0.622621i
$513$	−1.17205e10			−0.169229
$514$	−8.18497e10	−	5.88612e10i	−1.17264	−	0.843290i
$515$	−4.89913e10	+	4.89913e10i	−0.696450	+	0.696450i
$516$	−1.59270e10	−	4.74432e10i	−0.224665	−	0.669230i
$517$	5.35094e10	−	5.35094e10i	0.748976	−	0.748976i
$518$	5.37629e10	−	8.78343e9i	0.746730	−	0.121996i
$519$	−2.72654e9			−0.0375787
$520$	−3.52507e7	+	1.14130e8i	−0.000482120	+	0.00156094i
$521$			2.14533e10i			0.291168i	0.989346	+	0.145584i	$0.0465061\pi$
$521$			2.14533e10i			0.291168i	−0.989346	+	0.145584i	$0.953494\pi$
$522$	8.26610e9	−	1.35046e9i	0.111332	−	0.0181887i
$523$	−1.31508e10	−	1.31508e10i	−0.175770	−	0.175770i	0.613739	−	0.789509i	$-0.289665\pi$
$523$	−1.31508e10	−	1.31508e10i	−0.175770	−	0.175770i	−0.789509	+	0.613739i	$0.789665\pi$
$524$	7.14322e10	+	3.55257e10i	0.947478	+	0.471213i
$525$	−2.52755e10	−	2.52755e10i	−0.332708	−	0.332708i
$526$	−2.49728e10	−	1.79589e10i	−0.326231	−	0.234605i
$527$			4.61568e10i			0.598402i
$528$	4.66044e10	−	3.52653e10i	0.599641	−	0.453745i
$529$	−7.79546e10			−0.995449
$530$	4.42903e10	−	6.15880e10i	0.561313	−	0.780536i
$531$	−2.13257e10	+	2.13257e10i	−0.268241	+	0.268241i
$532$	−8.24801e10	−	4.10202e10i	−1.02968	−	0.512096i
$533$	−2.70150e8	+	2.70150e8i	−0.00334731	+	0.00334731i
$534$	−1.21879e10	−	7.46013e10i	−0.149887	−	0.917448i
$535$	5.99979e10			0.732354
$536$	1.81128e10	+	3.43018e10i	0.219445	+	0.415583i
$537$			1.85242e9i			0.0222762i
$538$	−4.51683e9	−	2.76473e10i	−0.0539144	−	0.330007i
$539$	5.52145e10	+	5.52145e10i	0.654181	+	0.654181i
$540$	3.19700e9	+	9.52318e9i	0.0375983	+	0.111997i
$541$	−1.06324e11	−	1.06324e11i	−1.24121	−	1.24121i	−0.959501	−	0.281704i	$-0.909100\pi$
$541$	−1.06324e11	−	1.06324e11i	−1.24121	−	1.24121i	−0.281704	−	0.959501i	$-0.590900\pi$
$542$	−2.86990e10	+	3.99075e10i	−0.332560	+	0.462442i
$543$			5.46026e10i			0.628078i
$544$	5.21342e10	−	1.26794e9i	0.595288	−	0.0144778i
$545$	1.34739e10			0.152724
$546$	−1.44986e8	−	1.04265e8i	−0.00163139	−	0.00117319i
$547$	−7.97862e10	+	7.97862e10i	−0.891207	+	0.891207i	−0.994637	−	0.103430i	$-0.967018\pi$
$547$	−7.97862e10	+	7.97862e10i	−0.891207	+	0.891207i	0.103430	+	0.994637i	$0.467018\pi$
$548$	−6.46254e10	+	2.16952e10i	−0.716607	+	0.240570i
$549$	−9.38378e9	+	9.38378e9i	−0.103297	+	0.103297i
$550$	−7.32977e10	+	1.19749e10i	−0.801013	+	0.130864i
$551$	−2.74298e10			−0.297589
$552$	−1.68851e9	−	3.19769e9i	−0.0181865	−	0.0344414i
$553$		−	2.20511e11i		−	2.35792i
$554$	−4.79476e9	+	7.83337e8i	−0.0509012	+	0.00831590i
$555$	1.37568e10	+	1.37568e10i	0.144993	+	0.144993i
$556$	6.88939e10	−	1.38526e11i	0.720911	−	1.44955i
$557$	−4.43348e8	−	4.43348e8i	−0.00460600	−	0.00460600i	0.704800	−	0.709406i	$-0.251037\pi$
$557$	−4.43348e8	−	4.43348e8i	−0.00460600	−	0.00460600i	−0.709406	+	0.704800i	$0.751037\pi$
$558$	−2.63656e10	−	1.89605e10i	−0.271957	−	0.195575i
$559$			3.17736e8i			0.00325401i
$560$	−1.08318e10	+	7.82064e10i	−0.110141	+	0.795226i
$561$	4.43512e10			0.447769
$562$	2.42734e10	−	3.37535e10i	0.243325	−	0.338356i
$563$	1.99839e9	−	1.99839e9i	0.0198906	−	0.0198906i	−0.697092	−	0.716982i	$-0.745523\pi$
$563$	1.99839e9	−	1.99839e9i	0.0198906	−	0.0198906i	0.716982	+	0.697092i	$0.245523\pi$
$564$	−2.11561e10	+	4.25389e10i	−0.209083	+	0.420407i
$565$	−6.45993e10	+	6.45993e10i	−0.633920	+	0.633920i
$566$	3.83460e9	+	2.34714e10i	0.0373641	+	0.228703i
$567$	−1.50186e10			−0.145310
$568$	−2.87855e10	+	9.31978e10i	−0.276555	+	0.895390i
$569$		−	8.53338e10i		−	0.814089i	−0.913408	−	0.407044i	$-0.866559\pi$
$569$		−	8.53338e10i		−	0.814089i	0.913408	−	0.407044i	$-0.133441\pi$
$570$	−5.30439e9	−	3.24679e10i	−0.0502500	−	0.307577i
$571$	−6.51521e10	−	6.51521e10i	−0.612892	−	0.612892i	0.330807	−	0.943698i	$-0.392679\pi$
$571$	−6.51521e10	−	6.51521e10i	−0.612892	−	0.612892i	−0.943698	+	0.330807i	$0.892679\pi$
$572$	−3.51762e8	+	1.18089e8i	−0.00328598	+	0.00110313i
$573$	−3.36513e10	−	3.36513e10i	−0.312165	−	0.312165i
$574$	−1.47435e11	+	2.05016e11i	−1.35816	+	1.88860i
$575$			4.59535e9i			0.0420385i
$576$	−2.06917e10	+	3.03008e10i	−0.187977	+	0.275274i
$577$	1.10409e11			0.996099			0.498050	−	0.867148i	$-0.334050\pi$
$577$	1.10409e11			0.996099			0.498050	+	0.867148i	$0.334050\pi$
$578$	−5.84844e10	−	4.20584e10i	−0.523997	−	0.376826i
$579$	2.06035e10	−	2.06035e10i	0.183327	−	0.183327i
$580$	7.48207e9	+	2.22875e10i	0.0661165	+	0.196947i
$581$	2.37079e10	−	2.37079e10i	0.208060	−	0.208060i
$582$	−1.55653e10	+	2.54296e9i	−0.135665	+	0.0221640i
$583$	2.35648e11			2.03981
$584$	1.57132e11	+	4.85326e10i	1.35087	+	0.417236i
$585$		−	6.37785e7i		−	0.000544567i
$586$	−1.57603e11	+	2.57482e10i	−1.33652	+	0.218352i
$587$	9.02561e10	+	9.02561e10i	0.760193	+	0.760193i	0.976357	−	0.216164i	$-0.0693546\pi$
$587$	9.02561e10	+	9.02561e10i	0.760193	+	0.760193i	−0.216164	+	0.976357i	$0.569355\pi$
$588$	−4.38944e10	−	2.18302e10i	−0.367198	−	0.182620i
$589$	7.52040e10	+	7.52040e10i	0.624855	+	0.624855i
$590$	−6.87277e10	−	4.94247e10i	−0.567183	−	0.407883i
$591$			6.50043e10i			0.532834i
$592$	−9.74907e9	+	7.03891e10i	−0.0793736	+	0.573084i
$593$	1.75238e11			1.41713			0.708566	−	0.705644i	$-0.249342\pi$
$593$	1.75238e11			1.41713			0.708566	+	0.705644i	$0.249342\pi$
$594$	−1.82188e10	+	2.53342e10i	−0.146344	+	0.203499i
$595$	−4.23667e10	+	4.23667e10i	−0.338031	+	0.338031i
$596$	−1.00416e11	−	4.99402e10i	−0.795824	−	0.395790i
$597$	6.42977e10	−	6.42977e10i	0.506172	−	0.506172i
$598$	3.70176e6	+	2.26582e7i	2.89470e−5	+	0.000177183i
$599$	1.74002e11			1.35160			0.675799	−	0.737086i	$-0.263799\pi$
$599$	1.74002e11			1.35160			0.675799	+	0.737086i	$0.263799\pi$
$600$	4.12324e10	−	2.17724e10i	0.318151	−	0.167997i
$601$		−	7.22356e10i		−	0.553673i	−0.960917	−	0.276837i	$-0.910714\pi$
$601$		−	7.22356e10i		−	0.553673i	0.960917	−	0.276837i	$-0.0892861\pi$
$602$	3.38619e10	+	2.07267e11i	0.257825	+	1.57813i
$603$	−1.46453e10	−	1.46453e10i	−0.110771	−	0.110771i
$604$	5.80381e10	+	1.72883e11i	0.436079	+	1.29899i
$605$	4.04967e10	+	4.04967e10i	0.302272	+	0.302272i
$606$	1.75359e9	−	2.43846e9i	0.0130028	−	0.0180811i
$607$		−	1.60214e11i		−	1.18017i	−0.807341	−	0.590086i	$-0.799094\pi$
$607$		−	1.60214e11i		−	1.18017i	0.807341	−	0.590086i	$-0.200906\pi$
$608$	8.28772e10	−	8.70089e10i	0.606486	−	0.636721i
$609$	−3.51485e10			−0.255528
$610$	−3.02417e10	−	2.17480e10i	−0.218417	−	0.157072i
$611$	2.13289e8	−	2.13289e8i	0.00153039	−	0.00153039i
$612$	−2.63968e10	+	8.86159e9i	−0.188168	+	0.0631693i
$613$	−7.01772e10	+	7.01772e10i	−0.496997	+	0.496997i	−0.910502	−	0.413505i	$-0.864305\pi$
$613$	−7.01772e10	+	7.01772e10i	−0.496997	+	0.496997i	0.413505	+	0.910502i	$0.364305\pi$
$614$	−1.78752e11	+	2.92033e10i	−1.25770	+	0.205475i
$615$	−9.01850e10			−0.630426
$616$	−2.16878e11	+	1.14520e11i	−1.50623	+	0.795353i
$617$			2.04847e11i			1.41348i	0.707476	+	0.706738i	$0.249834\pi$
$617$			2.04847e11i			1.41348i	−0.707476	+	0.706738i	$0.750166\pi$
$618$	1.33352e11	−	2.17862e10i	0.914211	−	0.149358i
$619$	3.37307e10	+	3.37307e10i	0.229754	+	0.229754i	0.812590	−	0.582836i	$-0.198057\pi$
$619$	3.37307e10	+	3.37307e10i	0.229754	+	0.229754i	−0.582836	+	0.812590i	$0.698057\pi$
$620$	4.05918e10	−	8.16187e10i	0.274708	−	0.552361i
$621$	1.36526e9	+	1.36526e9i	0.00918016	+	0.00918016i
$622$	4.34379e10	+	3.12378e10i	0.290206	+	0.208699i
$623$			3.17214e11i			2.10572i
$624$	1.85765e8	−	1.40568e8i	0.00122526	−	0.000927143i
$625$	−1.75335e9			−0.0114908
$626$	−8.16929e10	+	1.13598e11i	−0.531970	+	0.739732i
$627$	7.22621e10	−	7.22621e10i	0.467563	−	0.467563i
$628$	−3.26742e10	+	6.56987e10i	−0.210071	+	0.422395i
$629$	−3.81318e10	+	3.81318e10i	−0.243604	+	0.243604i
$630$	−6.79703e9	−	4.16042e10i	−0.0431476	−	0.264104i
$631$	−4.86240e10			−0.306714			−0.153357	−	0.988171i	$-0.549008\pi$
$631$	−4.86240e10			−0.306714			−0.153357	+	0.988171i	$0.549008\pi$
$632$	2.74835e11	+	8.48870e10i	1.72268	+	0.532075i
$633$			7.79255e10i			0.485361i
$634$	1.56379e10	+	9.57188e10i	0.0967881	+	0.592434i
$635$	−1.16406e11	−	1.16406e11i	−0.715945	−	0.715945i
$636$	−1.40252e11	+	4.70837e10i	−0.857198	+	0.287768i
$637$	2.20085e8	+	2.20085e8i	0.00133670	+	0.00133670i
$638$	−4.26382e10	+	5.92907e10i	−0.257345	+	0.357852i
$639$		−	5.20811e10i		−	0.312376i
$640$	−9.33036e10	−	4.36064e10i	−0.556133	−	0.259914i
$641$	−1.56196e11			−0.925206			−0.462603	−	0.886566i	$-0.653084\pi$
$641$	−1.56196e11			−0.925206			−0.462603	+	0.886566i	$0.653084\pi$
$642$	−9.49964e10	−	6.83155e10i	−0.559200	−	0.402142i
$643$	7.22237e10	−	7.22237e10i	0.422509	−	0.422509i	−0.463558	−	0.886067i	$-0.653427\pi$
$643$	7.22237e10	−	7.22237e10i	0.422509	−	0.422509i	0.886067	+	0.463558i	$0.153427\pi$
$644$	4.82949e9	+	1.43860e10i	0.0280774	+	0.0836367i
$645$	−5.30354e10	+	5.30354e10i	−0.306427	+	0.306427i
$646$	8.99959e10	−	1.47029e10i	0.516764	−	0.0844256i
$647$	−1.71618e11			−0.979370			−0.489685	−	0.871899i	$-0.662888\pi$
$647$	−1.71618e11			−0.979370			−0.489685	+	0.871899i	$0.662888\pi$
$648$	5.78150e9	−	1.87185e10i	0.0327899	−	0.106163i
$649$		−	2.62966e11i		−	1.48225i
$650$	−2.92165e8	+	4.77320e7i	−0.00163672	+	0.000267397i
$651$	9.63662e10	+	9.63662e10i	0.536538	+	0.536538i
$652$	3.17661e11	+	1.57983e11i	1.75781	+	0.874221i
$653$	−2.44488e11	−	2.44488e11i	−1.34464	−	1.34464i	−0.891381	−	0.453255i	$-0.850263\pi$
$653$	−2.44488e11	−	2.44488e11i	−1.34464	−	1.34464i	−0.453255	−	0.891381i	$-0.649737\pi$
$654$	−2.13336e10	−	1.53418e10i	−0.116615	−	0.0838623i
$655$		−	1.19565e11i		−	0.649590i
$656$	−1.98767e11	−	2.62679e11i	−1.07332	−	1.41844i
$657$	−8.78091e10			−0.471279
$658$	1.16403e11	−	1.61864e11i	0.620953	−	0.863468i
$659$	1.29470e11	−	1.29470e11i	0.686478	−	0.686478i	−0.274973	−	0.961452i	$-0.588669\pi$
$659$	1.29470e11	−	1.29470e11i	0.686478	−	0.686478i	0.961452	+	0.274973i	$0.0886691\pi$
$660$	−7.84259e10	−	3.90039e10i	−0.413318	−	0.205557i
$661$	7.86836e10	−	7.86836e10i	0.412172	−	0.412172i	−0.470322	−	0.882495i	$-0.655862\pi$
$661$	7.86836e10	−	7.86836e10i	0.412172	−	0.412172i	0.882495	+	0.470322i	$0.155862\pi$
$662$	−1.72815e10	−	1.05779e11i	−0.0899808	−	0.550767i
$663$	1.76784e8			0.000914933
$664$	2.04220e10	+	3.86751e10i	0.105057	+	0.198957i
$665$			1.38057e11i			0.705949i
$666$	−6.11761e9	−	3.74456e10i	−0.0310946	−	0.190328i
$667$	3.19518e9	+	3.19518e9i	0.0161433	+	0.0161433i
$668$	−6.50616e10	−	1.93804e11i	−0.326752	−	0.973325i
$669$	−4.75985e10	−	4.75985e10i	−0.237623	−	0.237623i
$670$	3.39420e10	−	4.71982e10i	0.168437	−	0.234221i
$671$		−	1.15711e11i		−	0.570800i
$672$	1.06199e11	−	1.11493e11i	0.520765	−	0.546727i
$673$	2.87102e11			1.39951			0.699754	−	0.714384i	$-0.253293\pi$
$673$	2.87102e11			1.39951			0.699754	+	0.714384i	$0.253293\pi$
$674$	9.41936e10	+	6.77382e10i	0.456438	+	0.328242i
$675$	−1.76043e10	+	1.76043e10i	−0.0848015	+	0.0848015i
$676$	1.97968e11	−	6.64593e10i	0.947999	−	0.318250i
$677$	1.63329e11	−	1.63329e11i	0.777517	−	0.777517i	−0.201891	−	0.979408i	$-0.564709\pi$
$677$	1.63329e11	−	1.63329e11i	0.777517	−	0.777517i	0.979408	+	0.201891i	$0.0647087\pi$
$678$	1.75837e11	−	2.87271e10i	0.832129	−	0.135948i
$679$	6.61857e10			0.311376
$680$	−3.64948e10	−	6.91135e10i	−0.170685	−	0.323242i
$681$			1.63520e11i			0.760295i
$682$	2.79457e11	−	4.56558e10i	1.29175	−	0.211037i
$683$	−2.47151e11	−	2.47151e11i	−1.13574	−	1.13574i	−0.989205	−	0.146539i	$-0.953187\pi$
$683$	−2.47151e11	−	2.47151e11i	−1.13574	−	1.13574i	−0.146539	−	0.989205i	$-0.546813\pi$
$684$	−2.85703e10	+	5.74470e10i	−0.130524	+	0.262448i
$685$	7.22429e10	+	7.22429e10i	0.328120	+	0.328120i
$686$	−6.81144e10	−	4.89837e10i	−0.307569	−	0.221185i
$687$			1.86794e11i			0.838564i
$688$	−2.71364e11	−	3.75846e10i	−1.21115	−	0.167748i
$689$	9.39295e8			0.00416797
$690$	−3.16415e9	+	4.39992e9i	−0.0139592	+	0.0194110i
$691$	−8.24396e10	+	8.24396e10i	−0.361596	+	0.361596i	−0.864400	−	0.502804i	$-0.832302\pi$
$691$	−8.24396e10	+	8.24396e10i	−0.361596	+	0.361596i	0.502804	+	0.864400i	$0.332302\pi$
$692$	−6.64633e9	+	1.33639e10i	−0.0289840	+	0.0582787i
$693$	9.25965e10	−	9.25965e10i	0.401478	−	0.401478i
$694$	3.31923e10	+	2.03168e11i	0.143087	+	0.875825i
$695$	−2.31869e11			−0.993811
$696$	1.35307e10	−	4.38077e10i	0.0576610	−	0.186687i
$697$		−	2.49979e11i		−	1.05919i
$698$	−1.31669e10	−	8.05941e10i	−0.0554706	−	0.339533i
$699$	1.32426e11	+	1.32426e11i	0.554710	+	0.554710i
$700$	−1.85499e11	+	6.22734e10i	−0.772592	+	0.259365i
$701$	2.95574e11	+	2.95574e11i	1.22404	+	1.22404i	0.966184	+	0.257853i	$0.0830152\pi$
$701$	2.95574e11	+	2.95574e11i	1.22404	+	1.22404i	0.257853	+	0.966184i	$0.416985\pi$
$702$	−7.26202e7	+	1.00982e8i	−0.000299026	+	0.000415812i
$703$			1.24258e11i			0.508747i
$704$	−5.92451e10	−	3.14393e11i	−0.241191	−	1.27992i
$705$	7.12028e10			0.288231
$706$	−8.32350e10	−	5.98575e10i	−0.335033	−	0.240935i
$707$	−8.91255e9	+	8.91255e9i	−0.0356717	+	0.0356717i
$708$	5.25419e10	+	1.56511e11i	0.209109	+	0.622891i
$709$	−9.26548e10	+	9.26548e10i	−0.366676	+	0.366676i	−0.866264	−	0.499587i	$-0.833485\pi$
$709$	−9.26548e10	+	9.26548e10i	−0.366676	+	0.366676i	0.499587	+	0.866264i	$0.333485\pi$
$710$	1.44275e11	−	2.35706e10i	0.567749	−	0.0927551i
$711$	−1.53585e11			−0.600992
$712$	−3.95363e11	−	1.22114e11i	−1.53842	−	0.475165i
$713$		−	1.75204e10i		−	0.0677930i
$714$	1.15320e11	−	1.88403e10i	0.443725	−	0.0724929i
$715$	3.93225e8	+	3.93225e8i	0.00150458	+	0.00150458i
$716$	9.07950e9	+	4.51555e9i	0.0345470	+	0.0171814i
$717$	−1.32472e11	−	1.32472e11i	−0.501241	−	0.501241i
$718$	1.42382e11	+	1.02392e11i	0.535743	+	0.385273i
$719$		−	2.75614e11i		−	1.03130i	−0.856799	−	0.515651i	$-0.827550\pi$
$719$		−	2.75614e11i		−	1.03130i	0.856799	−	0.515651i	$-0.172450\pi$
$720$	5.44704e10	+	7.54429e9i	0.202689	+	0.0280730i
$721$	−5.67031e11			−2.09829
$722$	−3.59761e10	+	5.00267e10i	−0.132393	+	0.184100i
$723$	1.28003e11	−	1.28003e11i	0.468453	−	0.468453i
$724$	2.67631e11	+	1.33102e11i	0.974051	+	0.484429i
$725$	−4.12000e10	+	4.12000e10i	−0.149123	+	0.149123i
$726$	−1.80087e10	−	1.10230e11i	−0.0648241	−	0.396784i
$727$	2.56071e11			0.916689			0.458345	−	0.888775i	$-0.348443\pi$
$727$	2.56071e11			0.916689			0.458345	+	0.888775i	$0.348443\pi$
$728$	−8.64475e8	+	4.56479e8i	−0.00307770	+	0.00162516i
$729$			1.04604e10i			0.0370370i
$730$	−3.97402e10	−	2.43248e11i	−0.139939	−	0.856559i
$731$	−1.47006e11	−	1.47006e11i	−0.514832	−	0.514832i
$732$	2.31196e10	+	6.88683e10i	0.0805260	+	0.239870i
$733$	1.70023e11	+	1.70023e11i	0.588967	+	0.588967i	0.937352	−	0.348385i	$-0.113270\pi$
$733$	1.70023e11	+	1.70023e11i	0.588967	+	0.588967i	−0.348385	+	0.937352i	$0.613270\pi$
$734$	2.86498e11	−	3.98391e11i	0.987047	−	1.37254i
$735$			7.34717e10i			0.251751i
$736$	−1.97893e10	+	4.81288e8i	−0.0674402	+	0.00164019i
$737$	1.80590e11			0.612101
$738$	1.42792e11	+	1.02687e11i	0.481371	+	0.346172i
$739$	−3.69241e11	+	3.69241e11i	−1.23803	+	1.23803i	−0.277228	+	0.960804i	$0.589416\pi$
$739$	−3.69241e11	+	3.69241e11i	−1.23803	+	1.23803i	−0.960804	+	0.277228i	$0.910584\pi$
$740$	1.00963e11	−	3.38939e10i	0.336693	−	0.113030i
$741$	2.88037e8	−	2.88037e8i	0.000955379	−	0.000955379i
$742$	6.12724e11	−	1.00103e11i	2.02139	−	0.330241i
$743$	−1.74679e11			−0.573173			−0.286587	−	0.958054i	$-0.592521\pi$
$743$	−1.74679e11			−0.573173			−0.286587	+	0.958054i	$0.592521\pi$
$744$	−1.57204e11	+	8.30101e10i	−0.513063	+	0.270919i
$745$			1.68079e11i			0.545617i
$746$	−4.46121e11	+	7.28844e10i	−1.44045	+	0.235331i
$747$	−1.65124e10	−	1.65124e10i	−0.0530308	−	0.0530308i
$748$	1.08113e11	−	2.17384e11i	0.345359	−	0.694420i
$749$	3.47211e11	+	3.47211e11i	1.10323	+	1.10323i
$750$	−1.47777e11	−	1.06272e11i	−0.467050	−	0.335873i
$751$			2.76638e11i			0.869665i	0.900511	+	0.434833i	$0.143193\pi$
$751$			2.76638e11i			0.869665i	−0.900511	+	0.434833i	$0.856807\pi$
$752$	1.56931e11	+	2.07390e11i	0.490723	+	0.648510i
$753$	−2.86148e11			−0.890043
$754$	−1.69956e8	+	2.36333e8i	−0.000525837	+	0.000731204i
$755$	1.93261e11	−	1.93261e11i	0.594780	−	0.594780i
$756$	−3.66100e10	+	7.36124e10i	−0.112076	+	0.225353i
$757$	−4.35648e11	+	4.35648e11i	−1.32664	+	1.32664i	−0.418355	+	0.908283i	$0.637393\pi$
$757$	−4.35648e11	+	4.35648e11i	−1.32664	+	1.32664i	−0.908283	+	0.418355i	$0.862607\pi$
$758$	−2.73416e9	−	1.67356e10i	−0.00828222	−	0.0506950i
$759$	−1.68350e10			−0.0507278
$760$	−1.72069e11	−	5.31461e10i	−0.515761	−	0.159301i
$761$			4.59202e11i			1.36920i	0.728921	+	0.684598i	$0.240022\pi$
$761$			4.59202e11i			1.36920i	−0.728921	+	0.684598i	$0.759978\pi$
$762$	5.17652e10	+	3.16852e11i	0.153539	+	0.939802i
$763$	7.79744e10	+	7.79744e10i	0.230067	+	0.230067i
$764$	−2.46970e11	+	8.29095e10i	−0.724887	+	0.243350i
$765$	2.95082e10	+	2.95082e10i	0.0861583	+	0.0861583i
$766$	−5.35268e10	+	7.44318e10i	−0.155473	+	0.216194i
$767$		−	1.04818e9i		−	0.00302870i
$768$	9.80785e10	+	1.75282e11i	0.281922	+	0.503839i
$769$	−5.72952e11			−1.63837			−0.819187	−	0.573526i	$-0.805575\pi$
$769$	−5.72952e11			−1.63837			−0.819187	+	0.573526i	$0.805575\pi$
$770$	2.98417e11	+	2.14603e11i	0.848907	+	0.610482i
$771$	2.08364e11	−	2.08364e11i	0.589664	−	0.589664i
$772$	−5.07625e10	−	1.51211e11i	−0.142914	−	0.425709i
$773$	−9.66765e10	+	9.66765e10i	−0.270771	+	0.270771i	−0.829411	−	0.558639i	$-0.811324\pi$
$773$	−9.66765e10	+	9.66765e10i	−0.270771	+	0.270771i	0.558639	+	0.829411i	$0.311324\pi$
$774$	1.44360e11	−	2.35846e10i	0.402239	−	0.0657152i
$775$	2.25915e11			0.626236
$776$	−2.54786e10	+	8.24912e10i	−0.0702635	+	0.227489i
$777$			1.59223e11i			0.436840i
$778$	−9.09589e10	+	1.48603e10i	−0.248271	+	0.0405610i
$779$	−4.07294e11	−	4.07294e11i	−1.10601	−	1.10601i
$780$	−3.12606e8	−	1.55470e8i	−0.000844538	−	0.000420017i
$781$	3.21105e11	+	3.21105e11i	0.863063	+	0.863063i
$782$	−1.21959e10	−	8.77054e9i	−0.0326127	−	0.0234531i
$783$			2.44808e10i			0.0651296i
$784$	−2.13998e11	+	1.61931e11i	−0.566430	+	0.428614i
$785$	1.09968e11			0.289594
$786$	−1.36141e11	+	1.89311e11i	−0.356696	+	0.496004i
$787$	3.70067e11	−	3.70067e11i	0.964675	−	0.964675i	−0.0347224	−	0.999397i	$-0.511055\pi$
$787$	3.70067e11	−	3.70067e11i	0.964675	−	0.964675i	0.999397	+	0.0347224i	$0.0110547\pi$
$788$	3.18614e11	+	1.58458e11i	0.826343	+	0.410968i
$789$	6.35730e10	−	6.35730e10i	0.164046	−	0.164046i
$790$	−6.95085e10	−	4.25458e11i	−0.178455	−	1.09232i
$791$	−7.47680e11			−1.90990
$792$	7.97629e10	+	1.51054e11i	0.202722	+	0.383912i
$793$		−	4.61224e8i		−	0.00116632i
$794$	1.17193e11	+	7.17330e11i	0.294862	+	1.80483i
$795$	1.56784e11	+	1.56784e11i	0.392494	+	0.392494i
$796$	−1.58415e11	−	4.71886e11i	−0.394589	−	1.17540i
$797$	1.78890e11	+	1.78890e11i	0.443357	+	0.443357i	0.893139	−	0.449782i	$-0.148498\pi$
$797$	1.78890e11	+	1.78890e11i	0.443357	+	0.443357i	−0.449782	+	0.893139i	$0.648498\pi$
$798$	1.57197e11	−	2.18590e11i	0.387643	−	0.539038i
$799$			1.97363e11i			0.484260i
$800$	−6.20593e9	−	2.55171e11i	−0.0151512	−	0.622977i
$801$	2.20938e11			0.536711
$802$	−3.89805e10	−	2.80324e10i	−0.0942215	−	0.0677583i
$803$	5.41384e11	−	5.41384e11i	1.30210	−	1.30210i
$804$	−1.07483e11	+	3.60827e10i	−0.257226	+	0.0863526i
$805$	1.60817e10	−	1.60817e10i	0.0382956	−	0.0382956i
$806$	1.11392e9	−	1.81984e8i	0.00263944	−	0.000431215i
$807$	8.18798e10			0.193056
$808$	−7.67730e9	−	1.45392e10i	−0.0180120	−	0.0341110i
$809$		−	2.64934e11i		−	0.618506i	−0.950980	−	0.309253i	$-0.899921\pi$
$809$		−	2.64934e11i		−	0.618506i	0.950980	−	0.309253i	$-0.100079\pi$
$810$	−2.89771e10	+	4.73410e9i	−0.0673156	+	0.0109976i
$811$	−5.54367e11	−	5.54367e11i	−1.28149	−	1.28149i	−0.939822	−	0.341665i	$-0.889009\pi$
$811$	−5.54367e11	−	5.54367e11i	−1.28149	−	1.28149i	−0.341665	−	0.939822i	$-0.610991\pi$
$812$	−8.56798e10	+	1.72278e11i	−0.197085	+	0.396283i
$813$	−1.01592e11	−	1.01592e11i	−0.232540	−	0.232540i
$814$	2.68588e11	+	1.93152e11i	0.611770	+	0.439947i
$815$		−	5.31709e11i		−	1.20516i
$816$	−2.09116e10	+	1.50983e11i	−0.0471657	+	0.340541i
$817$	−4.79038e11			−1.07518
$818$	−1.35922e11	+	1.89006e11i	−0.303581	+	0.422146i
$819$	3.69090e8	−	3.69090e8i	0.000820345	−	0.000820345i
$820$	−2.19839e11	+	4.42036e11i	−0.486239	+	0.977691i
$821$	−3.67950e11	+	3.67950e11i	−0.809872	+	0.809872i	−0.984614	−	0.174742i	$-0.944091\pi$
$821$	−3.67950e11	+	3.67950e11i	−0.809872	+	0.809872i	0.174742	+	0.984614i	$0.444091\pi$
$822$	−3.21261e10	−	1.96642e11i	−0.0703673	−	0.430715i
$823$	3.90849e11			0.851942			0.425971	−	0.904737i	$-0.359933\pi$
$823$	3.90849e11			0.851942			0.425971	+	0.904737i	$0.359933\pi$
$824$	2.18282e11	−	7.06724e11i	0.473489	−	1.53300i
$825$		−	2.17077e11i		−	0.468596i
$826$	−1.11707e11	−	6.83755e11i	−0.239973	−	1.46886i
$827$	4.78084e11	+	4.78084e11i	1.02207	+	1.02207i	0.999751	+	0.0223220i	$0.00710591\pi$
$827$	4.78084e11	+	4.78084e11i	1.02207	+	1.02207i	0.0223220	+	0.999751i	$0.492894\pi$
$828$	1.00198e10	−	3.36371e9i	0.0213175	−	0.00715645i
$829$	5.05866e11	+	5.05866e11i	1.07107	+	1.07107i	0.997273	+	0.0737948i	$0.0235110\pi$
$829$	5.05866e11	+	5.05866e11i	1.07107	+	1.07107i	0.0737948	+	0.997273i	$0.476489\pi$
$830$	3.82694e10	−	5.32156e10i	0.0806379	−	0.112131i
$831$		−	1.42001e10i		−	0.0297774i
$832$	−2.36151e8	−	1.25317e9i	−0.000492830	−	0.00261527i
$833$	−2.03652e11			−0.422969
$834$	3.67125e11	+	2.64014e11i	0.758839	+	0.545710i
$835$	−2.16648e11	+	2.16648e11i	−0.445666	+	0.445666i
$836$	−1.78038e11	−	5.30337e11i	−0.364492	−	1.08574i
$837$	6.71186e10	−	6.71186e10i	0.136754	−	0.136754i
$838$	−1.38541e11	+	2.26339e10i	−0.280933	+	0.0458969i
$839$	−7.72532e11			−1.55908			−0.779541	−	0.626351i	$-0.784548\pi$
$839$	−7.72532e11			−1.55908			−0.779541	+	0.626351i	$0.784548\pi$
$840$	−2.20489e11	−	6.81013e10i	−0.442864	−	0.136785i
$841$		−	4.42953e11i		−	0.885470i
$842$	−6.96643e11	+	1.13813e11i	−1.38600	+	0.226435i
$843$	8.59258e10	+	8.59258e10i	0.170143	+	0.170143i
$844$	3.81947e11	+	1.89955e11i	0.752719	+	0.374353i
$845$	−2.21303e11	−	2.21303e11i	−0.434070	−	0.434070i
$846$	−1.12737e11	−	8.10738e10i	−0.220083	−	0.158270i
$847$			4.68713e11i			0.910697i
$848$	−1.11108e11	+	8.02210e11i	−0.214863	+	1.55133i
$849$	−6.95124e10			−0.133792
$850$	1.13091e11	−	1.57259e11i	0.216647	−	0.301259i
$851$	1.44742e10	−	1.44742e10i	0.0275979	−	0.0275979i
$852$	−2.55272e11	−	1.26956e11i	−0.484446	−	0.240931i
$853$	4.84413e11	−	4.84413e11i	0.914998	−	0.914998i	−0.0816625	−	0.996660i	$-0.526023\pi$
$853$	4.84413e11	−	4.84413e11i	0.914998	−	0.914998i	0.996660	+	0.0816625i	$0.0260230\pi$
$854$	−4.91537e10	−	3.00867e11i	−0.0924113	−	0.565645i
$855$	9.61563e10			0.179934
$856$	−5.66412e11	+	2.99089e11i	−1.05496	+	0.557064i
$857$			3.47582e11i			0.644369i	0.946677	+	0.322184i	$0.104417\pi$
$857$			3.47582e11i			0.644369i	−0.946677	+	0.322184i	$0.895583\pi$
$858$	−1.74865e8	−	1.07034e9i	−0.000322667	−	0.00197503i
$859$	3.27033e9	+	3.27033e9i	0.00600647	+	0.00600647i	0.710104	−	0.704097i	$-0.248648\pi$
$859$	3.27033e9	+	3.27033e9i	0.00600647	+	0.00600647i	−0.704097	+	0.710104i	$0.748648\pi$
$860$	1.30668e11	+	3.89231e11i	0.238877	+	0.711564i
$861$	−5.21906e11	−	5.21906e11i	−0.949685	−	0.949685i
$862$	1.35737e11	−	1.88749e11i	0.245849	−	0.341866i
$863$			3.08551e11i			0.556268i	0.960542	+	0.278134i	$0.0897160\pi$
$863$			3.08551e11i			0.556268i	−0.960542	+	0.278134i	$0.910284\pi$
$864$	−7.76543e10	−	7.39668e10i	−0.139351	−	0.132734i
$865$	2.23689e10			0.0399558
$866$	1.27902e11	+	9.19795e10i	0.227409	+	0.163538i
$867$	1.48883e11	−	1.48883e11i	0.263493	−	0.263493i
$868$	7.07239e11	−	2.37425e11i	1.24591	−	0.418262i
$869$	9.46921e11	−	9.46921e11i	1.66048	−	1.66048i
$870$	−6.78164e10	+	1.10794e10i	−0.118374	+	0.0193392i
$871$	7.19832e8			0.00125071
$872$	−1.27201e11	+	6.71674e10i	−0.220001	+	0.116170i
$873$		−	4.60980e10i		−	0.0793644i
$874$	−3.41609e10	+	5.58099e9i	−0.0585442	+	0.00956458i
$875$	5.40126e11	+	5.40126e11i	0.921432	+	0.921432i
$876$	−2.14048e11	+	4.30390e11i	−0.363491	+	0.730880i
$877$	6.47410e11	+	6.47410e11i	1.09441	+	1.09441i	0.995052	+	0.0993605i	$0.0316797\pi$
$877$	6.47410e11	+	6.47410e11i	1.09441	+	1.09441i	0.0993605	+	0.995052i	$0.468320\pi$
$878$	7.09400e11	+	5.10157e11i	1.19375	+	0.858471i
$879$		−	4.66756e11i		−	0.781870i
$880$	−3.82350e11	+	2.89322e11i	−0.637573	+	0.482448i
$881$	3.52208e10			0.0584650			0.0292325	−	0.999573i	$-0.490694\pi$
$881$	3.52208e10			0.0584650			0.0292325	+	0.999573i	$0.490694\pi$
$882$	8.36572e10	−	1.16330e11i	0.138239	−	0.192228i
$883$	2.70170e11	−	2.70170e11i	0.444421	−	0.444421i	−0.449074	−	0.893495i	$-0.648246\pi$
$883$	2.70170e11	−	2.70170e11i	0.444421	−	0.444421i	0.893495	+	0.449074i	$0.148246\pi$
$884$	4.30938e8	−	8.66495e8i	0.000705676	−	0.00141892i
$885$	1.74959e11	−	1.74959e11i	0.285209	−	0.285209i
$886$	8.50548e10	+	5.20616e11i	0.138027	+	0.844855i
$887$	8.56295e11			1.38334			0.691670	−	0.722214i	$-0.256875\pi$
$887$	8.56295e11			1.38334			0.691670	+	0.722214i	$0.256875\pi$
$888$	−1.98450e11	−	6.12941e10i	−0.319152	−	0.0985750i
$889$		−	1.34729e12i		−	2.15703i
$890$	9.99911e10	+	6.12040e11i	0.159368	+	0.975483i
$891$	−6.44930e10	−	6.44930e10i	−0.102330	−	0.102330i
$892$	−3.49329e11	+	1.17272e11i	−0.551792	+	0.185241i
$893$	3.21567e11	+	3.21567e11i	0.505668	+	0.505668i
$894$	1.91380e11	−	2.66124e11i	0.299603	−	0.416614i
$895$		−	1.51975e10i		−	0.0236854i
$896$	−2.87600e11	−	7.92306e11i	−0.446229	−	1.22931i
$897$	−6.71043e7			−0.000103653
$898$	−5.23988e11	−	3.76820e11i	−0.805779	−	0.579466i
$899$	1.57080e11	−	1.57080e11i	0.240482	−	0.240482i
$900$	4.33731e10	+	1.29199e11i	0.0661075	+	0.196920i
$901$	−4.34581e11	+	4.34581e11i	−0.659434	+	0.659434i
$902$	−1.51350e12	+	2.47266e11i	−2.28642	+	0.373540i
$903$	−6.13838e11			−0.923215
$904$	2.87824e11	−	9.31878e11i	0.430977	−	1.39536i
$905$		−	4.47968e11i		−	0.667809i
$906$	−5.26049e11	+	8.59424e10i	−0.780752	+	0.127554i
$907$	−3.34116e10	−	3.34116e10i	−0.0493705	−	0.0493705i	0.681991	−	0.731361i	$-0.261115\pi$
$907$	−3.34116e10	−	3.34116e10i	−0.0493705	−	0.0493705i	−0.731361	+	0.681991i	$0.761115\pi$
$908$	8.01482e11	+	3.98604e11i	1.17910	+	0.586406i
$909$	6.20755e9	+	6.20755e9i	0.00909211	+	0.00909211i
$910$	1.18949e9	+	8.55408e8i	0.00173458	+	0.00124741i
$911$		−	1.39499e10i		−	0.0202534i	−0.999949	−	0.0101267i	$-0.996777\pi$
$911$		−	1.39499e10i		−	0.0202534i	0.999949	−	0.0101267i	$-0.00322348\pi$
$912$	2.11928e11	+	2.80071e11i	0.306344	+	0.404845i
$913$	2.03614e11			0.293038
$914$	−1.66164e11	+	2.31060e11i	−0.238096	+	0.331085i
$915$	7.69860e10	−	7.69860e10i	0.109832	−	0.109832i
$916$	9.15559e11	+	4.55339e11i	1.30048	+	0.646774i
$917$	6.91931e11	−	6.91931e11i	0.978555	−	0.978555i
$918$	−1.31222e10	−	8.03201e10i	−0.0184772	−	0.113098i
$919$	1.93733e11			0.271607			0.135804	−	0.990736i	$-0.456638\pi$
$919$	1.93733e11			0.271607			0.135804	+	0.990736i	$0.456638\pi$
$920$	1.38528e10	+	2.62343e10i	0.0193369	+	0.0366201i
$921$		−	5.29389e11i		−	0.735761i
$922$	−2.06407e11	−	1.26341e12i	−0.285628	−	1.74831i
$923$	1.27992e9	+	1.27992e9i	0.00176351	+	0.00176351i
$924$	−2.28138e11	−	6.79573e11i	−0.312975	−	0.932284i
$925$	1.86637e11	+	1.86637e11i	0.254935	+	0.254935i
$926$	−5.92514e11	+	8.23922e11i	−0.805851	+	1.12058i
$927$			3.94934e11i			0.534818i
$928$	−1.81737e11	−	1.73107e11i	−0.245049	−	0.233412i
$929$	3.31956e11			0.445674			0.222837	−	0.974856i	$-0.428468\pi$
$929$	3.31956e11			0.445674			0.222837	+	0.974856i	$0.428468\pi$
$930$	2.16307e11	+	1.55555e11i	0.289161	+	0.207947i
$931$	−3.31814e11	+	3.31814e11i	−0.441667	+	0.441667i
$932$	9.71889e11	−	3.26270e11i	1.28811	−	0.432428i
$933$	−1.10579e11	+	1.10579e11i	−0.145931	+	0.145931i
$934$	−5.64747e11	+	9.22647e10i	−0.742107	+	0.121241i
$935$	−3.63864e11			−0.476094
$936$	3.17935e8	+	6.02102e8i	0.000414224	+	0.000784453i
$937$			9.83338e11i			1.27569i	0.770166	+	0.637844i	$0.220174\pi$
$937$			9.83338e11i			1.27569i	−0.770166	+	0.637844i	$0.779826\pi$
$938$	4.69563e11	−	7.67142e10i	0.606572	−	0.0990979i
$939$	−2.89186e11	−	2.89186e11i	−0.371976	−	0.371976i
$940$	1.73567e11	−	3.48996e11i	0.222309	−	0.447001i
$941$	−9.92581e11	−	9.92581e11i	−1.26592	−	1.26592i	−0.948175	−	0.317749i	$-0.897073\pi$
$941$	−9.92581e11	−	9.92581e11i	−1.26592	−	1.26592i	−0.317749	−	0.948175i	$-0.602927\pi$
$942$	−1.74116e11	−	1.25213e11i	−0.221123	−	0.159018i
$943$			9.48878e10i			0.119995i
$944$	8.95206e11	+	1.23988e11i	1.12729	+	0.156132i
$945$	1.23214e11			0.154502
$946$	−7.44639e11	+	1.03546e12i	−0.929782	+	1.29291i
$947$	1.02380e11	−	1.02380e11i	0.127296	−	0.127296i	−0.640588	−	0.767884i	$-0.721309\pi$
$947$	1.02380e11	−	1.02380e11i	0.127296	−	0.127296i	0.767884	+	0.640588i	$0.221309\pi$
$948$	−3.74385e11	+	7.52784e11i	−0.463538	+	0.932045i
$949$	2.15796e9	−	2.15796e9i	0.00266059	−	0.00266059i
$950$	−7.19637e10	−	4.40486e11i	−0.0883525	−	0.540801i
$951$	−2.83479e11			−0.346577
$952$	1.88766e11	−	6.11162e11i	0.229814	−	0.744060i
$953$			6.24354e11i			0.756936i	0.925614	+	0.378468i	$0.123549\pi$
$953$			6.24354e11i			0.756936i	−0.925614	+	0.378468i	$0.876451\pi$
$954$	−6.97212e10	−	4.26759e11i	−0.0841727	−	0.515216i
$955$	2.76080e11	+	2.76080e11i	0.331911	+	0.331911i
$956$	−9.72222e11	+	3.26382e11i	−1.16395	+	0.390746i
$957$	−1.50936e11	−	1.50936e11i	−0.179947	−	0.179947i
$958$	7.48134e11	−	1.04032e12i	0.888213	−	1.23511i
$959$			8.36148e11i			0.988573i
$960$	1.69758e11	−	2.48593e11i	0.199868	−	0.292687i
$961$	−8.43758e9			−0.00989291
$962$	1.07059e9	+	7.69903e8i	0.00125004	+	0.000898951i
$963$	2.41831e11	−	2.41831e11i	0.281195	−	0.281195i
$964$	−3.15371e11	−	9.39423e11i	−0.365186	−	1.08781i
$965$	−1.69034e11	+	1.69034e11i	−0.194924	+	0.194924i
$966$	−4.37737e10	+	7.15147e9i	−0.0502696	+	0.00821272i
$967$	8.54464e11			0.977209			0.488605	−	0.872505i	$-0.337506\pi$
$967$	8.54464e11			0.977209			0.488605	+	0.872505i	$0.337506\pi$
$968$	−5.84185e11	−	1.80434e11i	−0.665349	−	0.205503i
$969$			2.66530e11i			0.302309i
$970$	1.27700e11	−	2.08628e10i	0.144246	−	0.0235660i
$971$	−7.23940e11	−	7.23940e11i	−0.814377	−	0.814377i	0.170909	−	0.985287i	$-0.445329\pi$
$971$	−7.23940e11	−	7.23940e11i	−0.814377	−	0.814377i	−0.985287	+	0.170909i	$0.945329\pi$
$972$	5.12707e10	+	2.54987e10i	0.0574387	+	0.0285662i
$973$	−1.34184e12	−	1.34184e12i	−1.49710	−	1.49710i
$974$	−2.98512e10	−	2.14671e10i	−0.0331685	−	0.0238527i
$975$		−	8.65272e8i		−	0.000957490i
$976$	3.93911e11	+	5.45577e10i	0.434109	+	0.0601252i
$977$	2.95655e11			0.324494			0.162247	−	0.986750i	$-0.448126\pi$
$977$	2.95655e11			0.324494			0.162247	+	0.986750i	$0.448126\pi$
$978$	−6.05421e11	+	8.41869e11i	−0.661762	+	0.920215i
$979$	−1.36219e12	+	1.36219e12i	−1.48288	+	1.48288i
$980$	3.60117e11	+	1.79098e11i	0.390426	+	0.194172i
$981$	5.43088e10	−	5.43088e10i	0.0586400	−	0.0586400i
$982$	2.41601e11	+	1.47883e12i	0.259808	+	1.59027i
$983$	9.94055e9			0.0106462			0.00532312	−	0.999986i	$-0.498306\pi$
$983$	9.94055e9			0.0106462			0.00532312	+	0.999986i	$0.498306\pi$
$984$	8.51393e11	−	4.49571e11i	0.908134	−	0.479532i
$985$		−	5.33305e11i		−	0.566540i
$986$	−3.07104e10	−	1.87976e11i	−0.0324921	−	0.198882i
$987$	4.12055e11	+	4.12055e11i	0.434197	+	0.434197i
$988$	−7.09661e8	−	2.11393e9i	−0.000744772	−	0.00221851i
$989$	5.58010e10	+	5.58010e10i	0.0583253	+	0.0583253i
$990$	1.49470e11	−	2.07846e11i	0.155601	−	0.216372i
$991$			4.44574e11i			0.460945i	0.973079	+	0.230473i	$0.0740272\pi$
$991$			4.44574e11i			0.460945i	−0.973079	+	0.230473i	$0.925973\pi$
$992$	2.36609e10	+	9.72873e11i	0.0244334	+	1.00464i
$993$	3.13274e11			0.322201
$994$	9.71330e11	+	6.98521e11i	0.994996	+	0.715540i
$995$	−5.27508e11	+	5.27508e11i	−0.538191	+	0.538191i
$996$	−1.21186e11	+	4.06830e10i	−0.123145	+	0.0413405i
$997$	−8.77613e11	+	8.77613e11i	−0.888224	+	0.888224i	−0.994352	−	0.106129i	$-0.966155\pi$
$997$	−8.77613e11	+	8.77613e11i	−0.888224	+	0.888224i	0.106129	+	0.994352i	$0.466155\pi$
$998$	−1.28517e11	+	2.09963e10i	−0.129551	+	0.0211651i
$999$	1.10898e11			0.111343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.19.25	✓	64
4.3	odd	2		192.9.l.a.175.27		64
16.5	even	4		192.9.l.a.79.27		64
16.11	odd	4	inner	48.9.l.a.43.25	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.25	✓	64	1.1	even	1	trivial
48.9.l.a.43.25	yes	64	16.11	odd	4	inner
192.9.l.a.79.27		64	16.5	even	4
192.9.l.a.175.27		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)

\(f(q)\)	\(=\)	\(q+(12.9899 + 9.34150i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(81.4726 + 242.690i) q^{4} +(271.296 - 271.296i) q^{5} +(-738.456 + 120.644i) q^{6} +3140.01 q^{7} +(-1208.77 + 3913.58i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(12.9899 + 9.34150i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(81.4726 + 242.690i) q^{4} +(271.296 - 271.296i) q^{5} +(-738.456 + 120.644i) q^{6} +3140.01 q^{7} +(-1208.77 + 3913.58i) q^{8} -2187.00i q^{9} +(6058.40 - 989.782i) q^{10} +(13483.9 + 13483.9i) q^{11} +(-10719.4 - 5331.14i) q^{12} +(53.7468 + 53.7468i) q^{13} +(40788.2 + 29332.4i) q^{14} +17942.5i q^{15} +(-52260.4 + 39545.1i) q^{16} -49733.7 q^{17} +(20429.9 - 28408.8i) q^{18} +(-81031.9 + 81031.9i) q^{19} +(87943.8 + 43737.4i) q^{20} +(-103834. + 103834. i) q^{21} +(49194.0 + 301113. i) q^{22} +18878.1 q^{23} +(-89443.0 - 169386. i) q^{24} +243422. i q^{25} +(196.087 + 1200.24i) q^{26} +(72320.0 + 72320.0i) q^{27} +(255825. + 762047. i) q^{28} +(169253. + 169253. i) q^{29} +(-167610. + 233070. i) q^{30} -928078. i q^{31} +(-1.04827e6 + 25494.5i) q^{32} -891773. q^{33} +(-646034. - 464588. i) q^{34} +(851871. - 851871. i) q^{35} +(530762. - 178181. i) q^{36} +(766720. - 766720. i) q^{37} +(-1.80955e6 + 295633. i) q^{38} -3554.61 q^{39} +(733804. + 1.38967e6i) q^{40} +5.02634e6i q^{41} +(-2.31876e6 + 378823. i) q^{42} +(2.95586e6 + 2.95586e6i) q^{43} +(-2.17383e6 + 4.37097e6i) q^{44} +(-593324. - 593324. i) q^{45} +(245224. + 176350. i) q^{46} -3.96840e6i q^{47} +(420471. - 3.03584e6i) q^{48} +4.09485e6 q^{49} +(-2.27393e6 + 3.16202e6i) q^{50} +(1.64460e6 - 1.64460e6i) q^{51} +(-8664.89 + 17422.7i) q^{52} +(8.73814e6 - 8.73814e6i) q^{53} +(263849. + 1.61500e6i) q^{54} +7.31624e6 q^{55} +(-3.79554e6 + 1.22887e7i) q^{56} -5.35915e6i q^{57} +(617495. + 3.77965e6i) q^{58} +(-9.75112e6 - 9.75112e6i) q^{59} +(-4.35445e6 + 1.46182e6i) q^{60} +(-4.29071e6 - 4.29071e6i) q^{61} +(8.66964e6 - 1.20556e7i) q^{62} -6.86720e6i q^{63} +(-1.38550e7 - 9.46121e6i) q^{64} +29162.6 q^{65} +(-1.15840e7 - 8.33050e6i) q^{66} +(6.69650e6 - 6.69650e6i) q^{67} +(-4.05194e6 - 1.20699e7i) q^{68} +(-624263. + 624263. i) q^{69} +(1.90234e7 - 3.10792e6i) q^{70} +2.38140e7 q^{71} +(8.55900e6 + 2.64357e6i) q^{72} -4.01505e7i q^{73} +(1.71219e7 - 2.79726e6i) q^{74} +(-8.04952e6 - 8.04952e6i) q^{75} +(-2.62675e7 - 1.30637e7i) q^{76} +(4.23395e7 + 4.23395e7i) q^{77} +(-46173.9 - 33205.4i) q^{78} -7.02261e7i q^{79} +(-3.44961e6 + 2.49064e7i) q^{80} -4.78297e6 q^{81} +(-4.69536e7 + 6.52914e7i) q^{82} +(7.55026e6 - 7.55026e6i) q^{83} +(-3.36591e7 - 1.67398e7i) q^{84} +(-1.34926e7 + 1.34926e7i) q^{85} +(1.07840e7 + 6.60084e7i) q^{86} -1.11938e7 q^{87} +(-6.90691e7 + 3.64714e7i) q^{88} +1.01023e8i q^{89} +(-2.16465e6 - 1.32497e7i) q^{90} +(168765. + 168765. i) q^{91} +(1.53805e6 + 4.58152e6i) q^{92} +(3.06898e7 + 3.06898e7i) q^{93} +(3.70708e7 - 5.15489e7i) q^{94} +4.39672e7i q^{95} +(3.38211e7 - 3.55072e7i) q^{96} +2.10782e7 q^{97} +(5.31915e7 + 3.82520e7i) q^{98} +(2.94893e7 - 2.94893e7i) 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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Groups

Database

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