LMFDB - Embedded newform 48.9.l.a.43.25

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			43.25
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.25

$q$-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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	0.890011	−	0.455938i	$-0.150696\pi$
$5$	271.296	+	271.296i	0.434073	+	0.434073i	−0.455938	+	0.890011i	$0.650696\pi$
$6$	−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	−0.0761304	−	0.997098i	$-0.524257\pi$
$11$	13483.9	−	13483.9i	0.920967	−	0.920967i	0.997098	+	0.0761304i	$0.0242565\pi$
$12$	−10719.4	+	5331.14i	−0.516948	+	0.257096i
$13$	53.7468	−	53.7468i	0.00188183	−	0.00188183i	−0.706165	−	0.708047i	$-0.749576\pi$
$13$	53.7468	−	53.7468i	0.00188183	−	0.00188183i	0.708047	+	0.706165i	$0.249576\pi$
$14$	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	0.324201	−	0.945988i	$-0.394905\pi$
$19$	−81031.9	−	81031.9i	−0.621787	−	0.621787i	−0.945988	+	0.324201i	$0.894905\pi$
$20$	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	−0.577259	−	0.816561i	$-0.695878\pi$
$29$	169253.	−	169253.i	0.239301	−	0.239301i	0.816561	+	0.577259i	$0.195878\pi$
$30$	−167610.	−	233070.i	−0.206926	−	0.287741i
$31$			928078.i			1.00493i	0.864596	+	0.502467i	$0.167574\pi$
$31$			928078.i			1.00493i	−0.864596	+	0.502467i	$0.832426\pi$
$32$	−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	0.881425	−	0.472325i	$-0.156585\pi$
$37$	766720.	+	766720.i	0.409100	+	0.409100i	−0.472325	+	0.881425i	$0.656585\pi$
$38$	−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	$-0.651138\pi$
$41$		−	5.02634e6i		−	1.77876i	0.457172	−	0.889378i	$-0.348862\pi$
$42$	−2.31876e6	−	378823.i	−0.745175	−	0.121742i
$43$	2.95586e6	−	2.95586e6i	0.864590	−	0.864590i	−0.127277	−	0.991867i	$-0.540624\pi$
$43$	2.95586e6	−	2.95586e6i	0.864590	−	0.864590i	0.991867	+	0.127277i	$0.0406239\pi$
$44$	−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	$0.133294\pi$
$47$			3.96840e6i			0.813249i	−0.913595	+	0.406624i	$0.866706\pi$
$48$	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	0.993488	+	0.113941i	$0.0363474\pi$
$53$	8.73814e6	+	8.73814e6i	1.10743	+	1.10743i	0.113941	+	0.993488i	$0.463653\pi$
$54$	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	−0.983830	−	0.179107i	$-0.942679\pi$
$59$	−9.75112e6	+	9.75112e6i	−0.804723	+	0.804723i	0.179107	+	0.983830i	$0.442679\pi$
$60$	−4.35445e6	−	1.46182e6i	−0.335992	−	0.112795i
$61$	−4.29071e6	+	4.29071e6i	−0.309892	+	0.309892i	−0.844867	−	0.534976i	$-0.820321\pi$
$61$	−4.29071e6	+	4.29071e6i	−0.309892	+	0.309892i	0.534976	+	0.844867i	$0.320321\pi$
$62$	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	0.853465	−	0.521151i	$-0.174497\pi$
$67$	6.69650e6	+	6.69650e6i	0.332314	+	0.332314i	−0.521151	+	0.853465i	$0.674497\pi$
$68$	−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	$0.249915\pi$
$73$			4.01505e7i			1.41384i	−0.707295	+	0.706918i	$0.750085\pi$
$74$	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	$0.357525\pi$
$79$			7.02261e7i			1.80298i	−0.432803	+	0.901489i	$0.642475\pi$
$80$	−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	0.782165	−	0.623072i	$-0.214116\pi$
$83$	7.55026e6	+	7.55026e6i	0.159093	+	0.159093i	−0.623072	+	0.782165i	$0.714116\pi$
$84$	−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	$-0.702129\pi$
$89$		−	1.01023e8i		−	1.61013i	0.593184	−	0.805067i	$-0.297871\pi$
$90$	−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	0.693337	−	0.720613i	$-0.256140\pi$
$101$	−2.83838e6	−	2.83838e6i	−0.0272763	−	0.0272763i	−0.720613	+	0.693337i	$0.756140\pi$
$102$	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	−0.145739	−	0.989323i	$-0.546556\pi$
$107$	1.10577e8	−	1.10577e8i	0.843584	−	0.843584i	0.989323	+	0.145739i	$0.0465561\pi$
$108$	−1.16592e7	−	2.34434e7i	−0.0856986	−	0.172316i
$109$	2.48326e7	−	2.48326e7i	0.175920	−	0.175920i	−0.613655	−	0.789575i	$-0.710301\pi$
$109$	2.48326e7	−	2.48326e7i	0.175920	−	0.175920i	0.789575	+	0.613655i	$0.210301\pi$
$110$	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	$0.308646\pi$
$127$			4.29074e8i			1.64937i	−0.565595	+	0.824683i	$0.691354\pi$
$128$	−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	0.974150	−	0.225900i	$-0.0725324\pi$
$131$	2.20360e8	+	2.20360e8i	0.748250	+	0.748250i	−0.225900	+	0.974150i	$0.572532\pi$
$132$	−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	$-0.876627\pi$
$137$		−	2.66288e8i		−	0.755910i	0.925824	−	0.377955i	$-0.123373\pi$
$138$	−1.39406e7	−	2.27753e6i	−0.0384385	−	0.00627983i
$139$	−4.27337e8	+	4.27337e8i	−1.14475	+	1.14475i	−0.157181	+	0.987570i	$0.550241\pi$
$139$	−4.27337e8	+	4.27337e8i	−1.14475	+	1.14475i	−0.987570	+	0.157181i	$0.949759\pi$
$140$	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	0.319202	−	0.947687i	$-0.396585\pi$
$149$	−3.09770e8	−	3.09770e8i	−0.628485	−	0.628485i	−0.947687	+	0.319202i	$0.896585\pi$
$150$	−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	−0.520366	−	0.853943i	$-0.674205\pi$
$157$	2.02672e8	−	2.02672e8i	0.333577	−	0.333577i	0.853943	+	0.520366i	$0.174205\pi$
$158$	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	0.829110	+	0.559085i	$0.188848\pi$
$163$	9.79943e8	+	9.79943e8i	1.38820	+	1.38820i	0.559085	+	0.829110i	$0.311152\pi$
$164$	−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	−0.683720	−	0.729744i	$-0.739639\pi$
$173$	4.12260e7	−	4.12260e7i	0.0460243	−	0.0460243i	0.729744	+	0.683720i	$0.239639\pi$
$174$	−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	0.720617	−	0.693334i	$-0.243859\pi$
$179$	2.80091e7	+	2.80091e7i	0.0272827	+	0.0272827i	−0.693334	+	0.720617i	$0.743859\pi$
$180$	9.56538e7	+	1.92333e8i	0.0911197	+	0.183216i
$181$	8.25608e8	+	8.25608e8i	0.769236	+	0.769236i	0.977972	−	0.208736i	$-0.0669350\pi$
$181$	8.25608e8	+	8.25608e8i	0.769236	+	0.769236i	−0.208736	+	0.977972i	$0.566935\pi$
$182$	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	$-0.875125\pi$
$191$		−	1.01764e9i		−	0.764644i	0.924029	−	0.382322i	$-0.124875\pi$
$192$	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	0.953615	−	0.301029i	$-0.0973301\pi$
$197$	9.82885e8	+	9.82885e8i	0.652586	+	0.652586i	−0.301029	+	0.953615i	$0.597330\pi$
$198$	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	0.938828	−	0.344385i	$-0.111913\pi$
$211$	1.17826e9	+	1.17826e9i	0.594443	+	0.594443i	−0.344385	+	0.938828i	$0.611913\pi$
$212$	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	$-0.906003\pi$
$223$		−	1.43941e9i		−	0.582056i	0.956715	−	0.291028i	$-0.0939972\pi$
$224$	−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	0.997779	−	0.0666116i	$-0.0212188\pi$
$227$	2.47247e9	+	2.47247e9i	0.931167	+	0.931167i	−0.0666116	+	0.997779i	$0.521219\pi$
$228$	1.30061e9	+	4.36624e8i	0.481291	+	0.161573i
$229$	2.82439e9	+	2.82439e9i	1.02703	+	1.02703i	0.999624	+	0.0274030i	$0.00872373\pi$
$229$	2.82439e9	+	2.82439e9i	1.02703	+	1.02703i	0.0274030	+	0.999624i	$0.491276\pi$
$230$	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	$0.237751\pi$
$233$			4.00466e9i			1.35876i	−0.733788	+	0.679379i	$0.762249\pi$
$234$	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	$-0.789603\pi$
$239$		−	4.00603e9i		−	1.22779i	0.789389	−	0.613893i	$-0.210397\pi$
$240$	−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	0.0945555	−	0.995520i	$-0.469857\pi$
$251$	4.32665e9	−	4.32665e9i	1.09008	−	1.09008i	0.995520	−	0.0945555i	$-0.0301430\pi$
$252$	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	−0.815376	−	0.578932i	$-0.803470\pi$
$269$	−1.23805e9	+	1.23805e9i	−0.236444	+	0.236444i	0.578932	+	0.815376i	$0.303470\pi$
$270$	5.09724e8	−	3.66562e8i	0.0959136	−	0.0689752i
$271$		−	3.07221e9i		−	0.569604i	−0.958586	−	0.284802i	$-0.908072\pi$
$271$		−	3.07221e9i		−	0.569604i	0.958586	−	0.284802i	$-0.0919279\pi$
$272$	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	0.688637	−	0.725106i	$-0.258209\pi$
$277$	−2.14710e8	−	2.14710e8i	−0.0364697	−	0.0364697i	−0.725106	+	0.688637i	$0.758209\pi$
$278$	−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	$0.0668196\pi$
$281$			2.59845e9i			0.416763i	−0.978048	+	0.208381i	$0.933180\pi$
$282$	4.78763e8	−	2.93048e9i	0.0757050	−	0.463386i
$283$	1.05105e9	−	1.05105e9i	0.163862	−	0.163862i	−0.620413	−	0.784275i	$-0.713035\pi$
$283$	1.05105e9	−	1.05105e9i	0.163862	−	0.163862i	0.784275	+	0.620413i	$0.213035\pi$
$284$	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	0.0415456	−	0.999137i	$-0.486772\pi$
$293$	−7.05749e9	−	7.05749e9i	−0.957591	−	0.957591i	−0.999137	+	0.0415456i	$0.986772\pi$
$294$	−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	0.0944136	−	0.995533i	$-0.469902\pi$
$307$	−8.00453e9	−	8.00453e9i	−0.901119	−	0.901119i	−0.995533	+	0.0944136i	$0.969902\pi$
$308$	−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	$-0.849434\pi$
$313$		−	8.74516e9i		−	0.911151i	0.890197	−	0.455575i	$-0.150566\pi$
$314$	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	−0.462271	−	0.886739i	$-0.652965\pi$
$317$	4.28630e9	−	4.28630e9i	0.424468	−	0.424468i	0.886739	+	0.462271i	$0.152965\pi$
$318$	−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	−0.876329	−	0.481714i	$-0.840014\pi$
$331$	−4.73680e9	+	4.73680e9i	−0.394615	+	0.394615i	0.481714	+	0.876329i	$0.340014\pi$
$332$	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	−0.319929	−	0.947441i	$-0.603659\pi$
$347$	9.09788e9	−	9.09788e9i	0.627512	−	0.627512i	0.947441	+	0.319929i	$0.103659\pi$
$348$	−9.11986e8	+	2.71661e9i	−0.0621829	+	0.185230i
$349$	−3.60901e9	+	3.60901e9i	−0.243269	+	0.243269i	−0.818201	−	0.574932i	$-0.805028\pi$
$349$	−3.60901e9	+	3.60901e9i	−0.243269	+	0.243269i	0.574932	+	0.818201i	$0.305028\pi$
$350$	−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	$0.320579\pi$
$367$			3.06694e10i			1.69060i	−0.534291	+	0.845300i	$0.679421\pi$
$368$	−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	−0.999469	−	0.0325850i	$-0.989626\pi$
$373$	−1.99773e10	−	1.99773e10i	−1.03205	−	1.03205i	−0.0325850	−	0.999469i	$-0.510374\pi$
$374$	−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	−0.725035	−	0.688713i	$-0.758176\pi$
$379$	−7.49423e8	+	7.49423e8i	−0.0363220	+	0.0363220i	0.688713	+	0.725035i	$0.258176\pi$
$380$	−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	$-0.957492\pi$
$383$		−	5.73000e9i		−	0.266293i	0.991096	−	0.133146i	$-0.0425080\pi$
$384$	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	0.612550	−	0.790432i	$-0.290144\pi$
$389$	−4.07315e9	−	4.07315e9i	−0.177882	−	0.177882i	−0.790432	+	0.612550i	$0.790144\pi$
$390$	−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	0.360287	−	0.932842i	$-0.382679\pi$
$397$	3.21221e10	−	3.21221e10i	1.29313	−	1.29313i	0.932842	−	0.360287i	$-0.117321\pi$
$398$	−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	$-0.916282\pi$
$409$		−	1.45503e10i		−	0.519970i	0.965613	−	0.259985i	$-0.0837177\pi$
$410$	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	0.599267	−	0.800550i	$-0.295459\pi$
$419$	−6.20388e9	−	6.20388e9i	−0.201283	−	0.201283i	−0.800550	+	0.599267i	$0.795459\pi$
$420$	−1.36730e10	−	4.59013e9i	−0.439407	−	0.147512i
$421$	−3.11957e10	−	3.11957e10i	−0.993040	−	0.993040i	0.00693560	−	0.999976i	$-0.497792\pi$
$421$	−3.11957e10	−	3.11957e10i	−0.993040	−	0.993040i	−0.999976	+	0.00693560i	$0.997792\pi$
$422$	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	$0.0675234\pi$
$431$			1.45305e10i			0.421087i	−0.977584	+	0.210544i	$0.932477\pi$
$432$	−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	−0.336397	−	0.941720i	$-0.609208\pi$
$443$	2.33132e10	−	2.33132e10i	0.605323	−	0.605323i	0.941720	+	0.336397i	$0.109208\pi$
$444$	−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	$-0.934637\pi$
$457$		−	1.77877e10i		−	0.407808i	0.978991	−	0.203904i	$-0.0653630\pi$
$458$	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	−0.298099	+	0.954535i	$0.596353\pi$
$461$	−5.65754e10	+	5.65754e10i	−1.25263	+	1.25263i	−0.954535	+	0.298099i	$0.903647\pi$
$462$	−3.63739e10	+	2.61578e10i	−0.798402	+	0.574161i
$463$		−	6.34281e10i		−	1.38025i	−0.723690	−	0.690125i	$-0.757555\pi$
$463$		−	6.34281e10i		−	1.38025i	0.723690	−	0.690125i	$-0.242445\pi$
$464$	−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	0.389374	−	0.921080i	$-0.372691\pi$
$467$	−2.52894e10	−	2.52894e10i	−0.531706	−	0.531706i	−0.921080	+	0.389374i	$0.872691\pi$
$468$	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	$0.275124\pi$
$479$			8.00871e10i			1.52132i	−0.649151	+	0.760660i	$0.724876\pi$
$480$	−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	0.150842	−	0.988558i	$-0.451801\pi$
$491$	6.62220e10	−	6.62220e10i	1.13940	−	1.13940i	0.988558	−	0.150842i	$-0.0481986\pi$
$492$	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	0.659172	−	0.751992i	$-0.270907\pi$
$499$	−5.75501e9	−	5.75501e9i	−0.0928205	−	0.0928205i	−0.751992	+	0.659172i	$0.770907\pi$
$500$	−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	−0.863592	−	0.504191i	$-0.831791\pi$
$509$	−2.41241e10	+	2.41241e10i	−0.359401	+	0.359401i	0.504191	+	0.863592i	$0.331791\pi$
$510$	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	$-0.953494\pi$
$521$		−	2.14533e10i		−	0.291168i	0.989346	−	0.145584i	$-0.0465061\pi$
$522$	8.26610e9	+	1.35046e9i	0.111332	+	0.0181887i
$523$	−1.31508e10	+	1.31508e10i	−0.175770	+	0.175770i	−0.789509	−	0.613739i	$-0.789665\pi$
$523$	−1.31508e10	+	1.31508e10i	−0.175770	+	0.175770i	0.613739	+	0.789509i	$0.289665\pi$
$524$	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	−0.281704	+	0.959501i	$0.590900\pi$
$541$	−1.06324e11	+	1.06324e11i	−1.24121	+	1.24121i	−0.959501	+	0.281704i	$0.909100\pi$
$542$	−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	0.103430	−	0.994637i	$-0.467018\pi$
$547$	−7.97862e10	−	7.97862e10i	−0.891207	−	0.891207i	−0.994637	+	0.103430i	$0.967018\pi$
$548$	−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	−0.709406	−	0.704800i	$-0.751037\pi$
$557$	−4.43348e8	+	4.43348e8i	−0.00460600	+	0.00460600i	0.704800	+	0.709406i	$0.251037\pi$
$558$	−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	0.716982	−	0.697092i	$-0.245523\pi$
$563$	1.99839e9	+	1.99839e9i	0.0198906	+	0.0198906i	−0.697092	+	0.716982i	$0.745523\pi$
$564$	−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	$0.133441\pi$
$569$			8.53338e10i			0.814089i	−0.913408	+	0.407044i	$0.866559\pi$
$570$	−5.30439e9	+	3.24679e10i	−0.0502500	+	0.307577i
$571$	−6.51521e10	+	6.51521e10i	−0.612892	+	0.612892i	−0.943698	−	0.330807i	$-0.892679\pi$
$571$	−6.51521e10	+	6.51521e10i	−0.612892	+	0.612892i	0.330807	+	0.943698i	$0.392679\pi$
$572$	−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	−0.216164	−	0.976357i	$-0.569355\pi$
$587$	9.02561e10	−	9.02561e10i	0.760193	−	0.760193i	0.976357	+	0.216164i	$0.0693546\pi$
$588$	−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	$0.0892861\pi$
$601$			7.22356e10i			0.553673i	−0.960917	+	0.276837i	$0.910714\pi$
$602$	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	$0.200906\pi$
$607$			1.60214e11i			1.18017i	−0.807341	+	0.590086i	$0.799094\pi$
$608$	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	0.413505	−	0.910502i	$-0.364305\pi$
$613$	−7.01772e10	−	7.01772e10i	−0.496997	−	0.496997i	−0.910502	+	0.413505i	$0.864305\pi$
$614$	−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	$-0.750166\pi$
$617$		−	2.04847e11i		−	1.41348i	0.707476	−	0.706738i	$-0.249834\pi$
$618$	1.33352e11	+	2.17862e10i	0.914211	+	0.149358i
$619$	3.37307e10	−	3.37307e10i	0.229754	−	0.229754i	−0.582836	−	0.812590i	$-0.698057\pi$
$619$	3.37307e10	−	3.37307e10i	0.229754	−	0.229754i	0.812590	+	0.582836i	$0.198057\pi$
$620$	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	0.886067	−	0.463558i	$-0.153427\pi$
$643$	7.22237e10	+	7.22237e10i	0.422509	+	0.422509i	−0.463558	+	0.886067i	$0.653427\pi$
$644$	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	−0.453255	+	0.891381i	$0.649737\pi$
$653$	−2.44488e11	+	2.44488e11i	−1.34464	+	1.34464i	−0.891381	+	0.453255i	$0.850263\pi$
$654$	−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	0.961452	−	0.274973i	$-0.0886691\pi$
$659$	1.29470e11	+	1.29470e11i	0.686478	+	0.686478i	−0.274973	+	0.961452i	$0.588669\pi$
$660$	−7.84259e10	+	3.90039e10i	−0.413318	+	0.205557i
$661$	7.86836e10	+	7.86836e10i	0.412172	+	0.412172i	0.882495	−	0.470322i	$-0.155862\pi$
$661$	7.86836e10	+	7.86836e10i	0.412172	+	0.412172i	−0.470322	+	0.882495i	$0.655862\pi$
$662$	−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	0.979408	−	0.201891i	$-0.0647087\pi$
$677$	1.63329e11	+	1.63329e11i	0.777517	+	0.777517i	−0.201891	+	0.979408i	$0.564709\pi$
$678$	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	−0.146539	+	0.989205i	$0.546813\pi$
$683$	−2.47151e11	+	2.47151e11i	−1.13574	+	1.13574i	−0.989205	+	0.146539i	$0.953187\pi$
$684$	−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	0.502804	−	0.864400i	$-0.332302\pi$
$691$	−8.24396e10	−	8.24396e10i	−0.361596	−	0.361596i	−0.864400	+	0.502804i	$0.832302\pi$
$692$	−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	0.257853	−	0.966184i	$-0.416985\pi$
$701$	2.95574e11	−	2.95574e11i	1.22404	−	1.22404i	0.966184	−	0.257853i	$-0.0830152\pi$
$702$	−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	0.499587	−	0.866264i	$-0.333485\pi$
$709$	−9.26548e10	−	9.26548e10i	−0.366676	−	0.366676i	−0.866264	+	0.499587i	$0.833485\pi$
$710$	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	$0.172450\pi$
$719$			2.75614e11i			1.03130i	−0.856799	+	0.515651i	$0.827550\pi$
$720$	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	−0.348385	−	0.937352i	$-0.613270\pi$
$733$	1.70023e11	−	1.70023e11i	0.588967	−	0.588967i	0.937352	+	0.348385i	$0.113270\pi$
$734$	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	−0.960804	−	0.277228i	$-0.910584\pi$
$739$	−3.69241e11	−	3.69241e11i	−1.23803	−	1.23803i	−0.277228	−	0.960804i	$-0.589416\pi$
$740$	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	$-0.856807\pi$
$751$		−	2.76638e11i		−	0.869665i	0.900511	−	0.434833i	$-0.143193\pi$
$752$	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	−0.908283	−	0.418355i	$-0.862607\pi$
$757$	−4.35648e11	−	4.35648e11i	−1.32664	−	1.32664i	−0.418355	−	0.908283i	$-0.637393\pi$
$758$	−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	$-0.759978\pi$
$761$		−	4.59202e11i		−	1.36920i	0.728921	−	0.684598i	$-0.240022\pi$
$762$	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	0.558639	−	0.829411i	$-0.311324\pi$
$773$	−9.66765e10	−	9.66765e10i	−0.270771	−	0.270771i	−0.829411	+	0.558639i	$0.811324\pi$
$774$	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	0.999397	−	0.0347224i	$-0.0110547\pi$
$787$	3.70067e11	+	3.70067e11i	0.964675	+	0.964675i	−0.0347224	+	0.999397i	$0.511055\pi$
$788$	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	−0.449782	−	0.893139i	$-0.648498\pi$
$797$	1.78890e11	−	1.78890e11i	0.443357	−	0.443357i	0.893139	+	0.449782i	$0.148498\pi$
$798$	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	$0.100079\pi$
$809$			2.64934e11i			0.618506i	−0.950980	+	0.309253i	$0.899921\pi$
$810$	−2.89771e10	−	4.73410e9i	−0.0673156	−	0.0109976i
$811$	−5.54367e11	+	5.54367e11i	−1.28149	+	1.28149i	−0.341665	+	0.939822i	$0.610991\pi$
$811$	−5.54367e11	+	5.54367e11i	−1.28149	+	1.28149i	−0.939822	+	0.341665i	$0.889009\pi$
$812$	−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	0.174742	−	0.984614i	$-0.444091\pi$
$821$	−3.67950e11	−	3.67950e11i	−0.809872	−	0.809872i	−0.984614	+	0.174742i	$0.944091\pi$
$822$	−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	0.0223220	−	0.999751i	$-0.492894\pi$
$827$	4.78084e11	−	4.78084e11i	1.02207	−	1.02207i	0.999751	−	0.0223220i	$-0.00710591\pi$
$828$	1.00198e10	+	3.36371e9i	0.0213175	+	0.00715645i
$829$	5.05866e11	−	5.05866e11i	1.07107	−	1.07107i	0.0737948	−	0.997273i	$-0.476489\pi$
$829$	5.05866e11	−	5.05866e11i	1.07107	−	1.07107i	0.997273	−	0.0737948i	$-0.0235110\pi$
$830$	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	0.996660	−	0.0816625i	$-0.0260230\pi$
$853$	4.84413e11	+	4.84413e11i	0.914998	+	0.914998i	−0.0816625	+	0.996660i	$0.526023\pi$
$854$	−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	$-0.895583\pi$
$857$		−	3.47582e11i		−	0.644369i	0.946677	−	0.322184i	$-0.104417\pi$
$858$	−1.74865e8	+	1.07034e9i	−0.000322667	+	0.00197503i
$859$	3.27033e9	−	3.27033e9i	0.00600647	−	0.00600647i	−0.704097	−	0.710104i	$-0.748648\pi$
$859$	3.27033e9	−	3.27033e9i	0.00600647	−	0.00600647i	0.710104	+	0.704097i	$0.248648\pi$
$860$	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	$-0.910284\pi$
$863$		−	3.08551e11i		−	0.556268i	0.960542	−	0.278134i	$-0.0897160\pi$
$864$	−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	0.0993605	−	0.995052i	$-0.468320\pi$
$877$	6.47410e11	−	6.47410e11i	1.09441	−	1.09441i	0.995052	−	0.0993605i	$-0.0316797\pi$
$878$	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	0.893495	−	0.449074i	$-0.148246\pi$
$883$	2.70170e11	+	2.70170e11i	0.444421	+	0.444421i	−0.449074	+	0.893495i	$0.648246\pi$
$884$	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	−0.731361	−	0.681991i	$-0.761115\pi$
$907$	−3.34116e10	+	3.34116e10i	−0.0493705	+	0.0493705i	0.681991	+	0.731361i	$0.261115\pi$
$908$	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	$0.00322348\pi$
$911$			1.39499e10i			0.0202534i	−0.999949	+	0.0101267i	$0.996777\pi$
$912$	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	$-0.779826\pi$
$937$		−	9.83338e11i		−	1.27569i	0.770166	−	0.637844i	$-0.220174\pi$
$938$	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	−0.317749	+	0.948175i	$0.602927\pi$
$941$	−9.92581e11	+	9.92581e11i	−1.26592	+	1.26592i	−0.948175	+	0.317749i	$0.897073\pi$
$942$	−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	0.767884	−	0.640588i	$-0.221309\pi$
$947$	1.02380e11	+	1.02380e11i	0.127296	+	0.127296i	−0.640588	+	0.767884i	$0.721309\pi$
$948$	−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	$-0.876451\pi$
$953$		−	6.24354e11i		−	0.756936i	0.925614	−	0.378468i	$-0.123549\pi$
$954$	−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	−0.985287	−	0.170909i	$-0.945329\pi$
$971$	−7.23940e11	+	7.23940e11i	−0.814377	+	0.814377i	0.170909	+	0.985287i	$0.445329\pi$
$972$	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	$-0.925973\pi$
$991$		−	4.44574e11i		−	0.460945i	0.973079	−	0.230473i	$-0.0740272\pi$
$992$	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	0.106129	−	0.994352i	$-0.466155\pi$
$997$	−8.77613e11	−	8.77613e11i	−0.888224	−	0.888224i	−0.994352	+	0.106129i	$0.966155\pi$
$998$	−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.43.25	yes	64
4.3	odd	2		192.9.l.a.79.27		64
16.3	odd	4	inner	48.9.l.a.19.25	✓	64
16.13	even	4		192.9.l.a.175.27		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.25	✓	64	16.3	odd	4	inner
48.9.l.a.43.25	yes	64	1.1	even	1	trivial
192.9.l.a.79.27		64	4.3	odd	2
192.9.l.a.175.27		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)

\(f(q)\)	\(=\)	\(q+(12.9899 - 9.34150i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(81.4726 - 242.690i) q^{4} +(271.296 + 271.296i) q^{5} +(-738.456 - 120.644i) q^{6} +3140.01 q^{7} +(-1208.77 - 3913.58i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(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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Representations

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Database

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