LMFDB - Embedded newform 15.12.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,12,Mod(1,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("15.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	15.a (trivial)

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:	yes
Analytic conductor:	$11.5251477084$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5450x - 7248 $ x^3 - x^2 - 5450*x - 7248
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-72.6470$ of defining polynomial
Character	$\chi$	$=$	15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+72.6470 q^{2} +243.000 q^{3} +3229.58 q^{4} +3125.00 q^{5} +17653.2 q^{6} +8974.61 q^{7} +85838.4 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+72.6470 q^{2} +243.000 q^{3} +3229.58 q^{4} +3125.00 q^{5} +17653.2 q^{6} +8974.61 q^{7} +85838.4 q^{8} +59049.0 q^{9} +227022. q^{10} +421205. q^{11} +784789. q^{12} -1.24336e6 q^{13} +651979. q^{14} +759375. q^{15} -378284. q^{16} -5.93114e6 q^{17} +4.28973e6 q^{18} +1.88682e7 q^{19} +1.00924e7 q^{20} +2.18083e6 q^{21} +3.05993e7 q^{22} -2.72256e7 q^{23} +2.08587e7 q^{24} +9.76562e6 q^{25} -9.03263e7 q^{26} +1.43489e7 q^{27} +2.89843e7 q^{28} -1.15466e8 q^{29} +5.51663e7 q^{30} -2.73479e8 q^{31} -2.03278e8 q^{32} +1.02353e8 q^{33} -4.30879e8 q^{34} +2.80457e7 q^{35} +1.90704e8 q^{36} -2.86342e8 q^{37} +1.37071e9 q^{38} -3.02136e8 q^{39} +2.68245e8 q^{40} +4.51798e8 q^{41} +1.58431e8 q^{42} +1.30494e9 q^{43} +1.36032e9 q^{44} +1.84528e8 q^{45} -1.97786e9 q^{46} -9.11661e8 q^{47} -9.19231e7 q^{48} -1.89678e9 q^{49} +7.09443e8 q^{50} -1.44127e9 q^{51} -4.01553e9 q^{52} +3.44031e9 q^{53} +1.04240e9 q^{54} +1.31627e9 q^{55} +7.70367e8 q^{56} +4.58496e9 q^{57} -8.38824e9 q^{58} +1.06320e10 q^{59} +2.45246e9 q^{60} +6.85337e9 q^{61} -1.98674e10 q^{62} +5.29942e8 q^{63} -1.39928e10 q^{64} -3.88550e9 q^{65} +7.43563e9 q^{66} +5.26360e9 q^{67} -1.91551e10 q^{68} -6.61583e9 q^{69} +2.03743e9 q^{70} +1.72726e10 q^{71} +5.06867e9 q^{72} +5.86468e9 q^{73} -2.08019e10 q^{74} +2.37305e9 q^{75} +6.09363e10 q^{76} +3.78015e9 q^{77} -2.19493e10 q^{78} -2.16383e10 q^{79} -1.18214e9 q^{80} +3.48678e9 q^{81} +3.28217e10 q^{82} -6.48232e9 q^{83} +7.04317e9 q^{84} -1.85348e10 q^{85} +9.48001e10 q^{86} -2.80582e10 q^{87} +3.61556e10 q^{88} +7.32562e10 q^{89} +1.34054e10 q^{90} -1.11587e10 q^{91} -8.79275e10 q^{92} -6.64553e10 q^{93} -6.62294e10 q^{94} +5.89630e10 q^{95} -4.93966e10 q^{96} -1.45891e11 q^{97} -1.37796e11 q^{98} +2.48718e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 729 q^{3} + 4757 q^{4} + 9375 q^{5} - 243 q^{6} - 14608 q^{7} - 33999 q^{8} + 177147 q^{9}+O(q^{10}) $ 3 * q - q^2 + 729 * q^3 + 4757 * q^4 + 9375 * q^5 - 243 * q^6 - 14608 * q^7 - 33999 * q^8 + 177147 * q^9	\( 3 q - q^{2} + 729 q^{3} + 4757 q^{4} + 9375 q^{5} - 243 q^{6} - 14608 q^{7} - 33999 q^{8} + 177147 q^{9} - 3125 q^{10} + 540620 q^{11} + 1155951 q^{12} + 840970 q^{13} + 5432712 q^{14} + 2278125 q^{15} + 5062961 q^{16} + 15165038 q^{17} - 59049 q^{18} + 17743756 q^{19} + 14865625 q^{20} - 3549744 q^{21} + 11176076 q^{22} - 28140816 q^{23} - 8261757 q^{24} + 29296875 q^{25} - 52021894 q^{26} + 43046721 q^{27} - 277157944 q^{28} - 67382798 q^{29} - 759375 q^{30} - 206919496 q^{31} - 46592663 q^{32} + 131370660 q^{33} - 1230469666 q^{34} - 45650000 q^{35} + 280896093 q^{36} - 318337278 q^{37} + 653190692 q^{38} + 204355710 q^{39} - 106246875 q^{40} + 2110085854 q^{41} + 1320149016 q^{42} + 418259692 q^{43} + 2558131108 q^{44} + 553584375 q^{45} - 137169096 q^{46} - 1599668584 q^{47} + 1230299523 q^{48} - 316107077 q^{49} - 9765625 q^{50} + 3685104234 q^{51} - 10897289202 q^{52} + 4489142234 q^{53} - 14348907 q^{54} + 1689437500 q^{55} + 7768845960 q^{56} + 4311732708 q^{57} - 24168830726 q^{58} + 11102167484 q^{59} + 3612346875 q^{60} - 3568120958 q^{61} - 35509109136 q^{62} - 862587792 q^{63} - 35608208271 q^{64} + 2628031250 q^{65} + 2715786468 q^{66} + 2229942788 q^{67} - 1367872838 q^{68} - 6838218288 q^{69} + 16977225000 q^{70} + 49842766696 q^{71} - 2007606951 q^{72} + 40752219934 q^{73} - 37519971278 q^{74} + 7119140625 q^{75} + 115970329116 q^{76} - 17819224896 q^{77} - 12641320242 q^{78} + 113159960 q^{79} + 15821753125 q^{80} + 10460353203 q^{81} - 30171431066 q^{82} + 6259660308 q^{83} - 67349380392 q^{84} + 47390743750 q^{85} + 114296127740 q^{86} - 16374019914 q^{87} + 7548672276 q^{88} - 59972401554 q^{89} - 184528125 q^{90} + 118873361824 q^{91} - 221705928648 q^{92} - 50281437528 q^{93} + 92816682800 q^{94} + 55449237500 q^{95} - 11322017109 q^{96} - 207831285882 q^{97} - 288264739625 q^{98} + 31923070380 q^{99}+O(q^{100}) \) 3 * q - q^2 + 729 * q^3 + 4757 * q^4 + 9375 * q^5 - 243 * q^6 - 14608 * q^7 - 33999 * q^8 + 177147 * q^9 - 3125 * q^10 + 540620 * q^11 + 1155951 * q^12 + 840970 * q^13 + 5432712 * q^14 + 2278125 * q^15 + 5062961 * q^16 + 15165038 * q^17 - 59049 * q^18 + 17743756 * q^19 + 14865625 * q^20 - 3549744 * q^21 + 11176076 * q^22 - 28140816 * q^23 - 8261757 * q^24 + 29296875 * q^25 - 52021894 * q^26 + 43046721 * q^27 - 277157944 * q^28 - 67382798 * q^29 - 759375 * q^30 - 206919496 * q^31 - 46592663 * q^32 + 131370660 * q^33 - 1230469666 * q^34 - 45650000 * q^35 + 280896093 * q^36 - 318337278 * q^37 + 653190692 * q^38 + 204355710 * q^39 - 106246875 * q^40 + 2110085854 * q^41 + 1320149016 * q^42 + 418259692 * q^43 + 2558131108 * q^44 + 553584375 * q^45 - 137169096 * q^46 - 1599668584 * q^47 + 1230299523 * q^48 - 316107077 * q^49 - 9765625 * q^50 + 3685104234 * q^51 - 10897289202 * q^52 + 4489142234 * q^53 - 14348907 * q^54 + 1689437500 * q^55 + 7768845960 * q^56 + 4311732708 * q^57 - 24168830726 * q^58 + 11102167484 * q^59 + 3612346875 * q^60 - 3568120958 * q^61 - 35509109136 * q^62 - 862587792 * q^63 - 35608208271 * q^64 + 2628031250 * q^65 + 2715786468 * q^66 + 2229942788 * q^67 - 1367872838 * q^68 - 6838218288 * q^69 + 16977225000 * q^70 + 49842766696 * q^71 - 2007606951 * q^72 + 40752219934 * q^73 - 37519971278 * q^74 + 7119140625 * q^75 + 115970329116 * q^76 - 17819224896 * q^77 - 12641320242 * q^78 + 113159960 * q^79 + 15821753125 * q^80 + 10460353203 * q^81 - 30171431066 * q^82 + 6259660308 * q^83 - 67349380392 * q^84 + 47390743750 * q^85 + 114296127740 * q^86 - 16374019914 * q^87 + 7548672276 * q^88 - 59972401554 * q^89 - 184528125 * q^90 + 118873361824 * q^91 - 221705928648 * q^92 - 50281437528 * q^93 + 92816682800 * q^94 + 55449237500 * q^95 - 11322017109 * q^96 - 207831285882 * q^97 - 288264739625 * q^98 + 31923070380 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	72.6470	1.60529	0.802643	−	0.596459i	$-0.203426\pi$
$2$	72.6470	1.60529	0.802643	+	0.596459i	$0.203426\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	3229.58	1.57694
$5$	3125.00	0.447214
$5$	3125.00	0.447214
$6$	17653.2	0.926813
$7$	8974.61	0.201826	0.100913	−	0.994895i	$-0.467824\pi$
$7$	8974.61	0.201826	0.100913	+	0.994895i	$0.467824\pi$
$8$	85838.4	0.926162
$9$	59049.0	0.333333
$10$	227022.	0.717906
$11$	421205.	0.788559	0.394279	−	0.918991i	$-0.370994\pi$
$11$	421205.	0.788559	0.394279	+	0.918991i	$0.370994\pi$
$12$	784789.	0.910449
$13$	−1.24336e6	−0.928770	−0.464385	−	0.885633i	$-0.653725\pi$
$13$	−1.24336e6	−0.928770	−0.464385	+	0.885633i	$0.653725\pi$
$14$	651979.	0.323988
$15$	759375.	0.258199
$16$	−378284.	−0.0901900
$17$	−5.93114e6	−1.01314	−0.506569	−	0.862199i	$-0.669087\pi$
$17$	−5.93114e6	−1.01314	−0.506569	+	0.862199i	$0.669087\pi$
$18$	4.28973e6	0.535096
$19$	1.88682e7	1.74817	0.874087	−	0.485769i	$-0.161460\pi$
$19$	1.88682e7	1.74817	0.874087	+	0.485769i	$0.161460\pi$
$20$	1.00924e7	0.705231
$21$	2.18083e6	0.116524
$22$	3.05993e7	1.26586
$23$	−2.72256e7	−0.882013	−0.441007	−	0.897504i	$-0.645378\pi$
$23$	−2.72256e7	−0.882013	−0.441007	+	0.897504i	$0.645378\pi$
$24$	2.08587e7	0.534720
$25$	9.76562e6	0.200000
$26$	−9.03263e7	−1.49094
$27$	1.43489e7	0.192450
$28$	2.89843e7	0.318268
$29$	−1.15466e8	−1.04536	−0.522678	−	0.852530i	$-0.675067\pi$
$29$	−1.15466e8	−1.04536	−0.522678	+	0.852530i	$0.675067\pi$
$30$	5.51663e7	0.414483
$31$	−2.73479e8	−1.71567	−0.857836	−	0.513924i	$-0.828191\pi$
$31$	−2.73479e8	−1.71567	−0.857836	+	0.513924i	$0.828191\pi$
$32$	−2.03278e8	−1.07094
$33$	1.02353e8	0.455275
$34$	−4.30879e8	−1.62638
$35$	2.80457e7	0.0902592
$36$	1.90704e8	0.525648
$37$	−2.86342e8	−0.678852	−0.339426	−	0.940633i	$-0.610233\pi$
$37$	−2.86342e8	−0.678852	−0.339426	+	0.940633i	$0.610233\pi$
$38$	1.37071e9	2.80632
$39$	−3.02136e8	−0.536226
$40$	2.68245e8	0.414192
$41$	4.51798e8	0.609022	0.304511	−	0.952509i	$-0.401507\pi$
$41$	4.51798e8	0.609022	0.304511	+	0.952509i	$0.401507\pi$
$42$	1.58431e8	0.187055
$43$	1.30494e9	1.35368	0.676838	−	0.736132i	$-0.263350\pi$
$43$	1.30494e9	1.35368	0.676838	+	0.736132i	$0.263350\pi$
$44$	1.36032e9	1.24351
$45$	1.84528e8	0.149071
$46$	−1.97786e9	−1.41588
$47$	−9.11661e8	−0.579823	−0.289911	−	0.957053i	$-0.593626\pi$
$47$	−9.11661e8	−0.579823	−0.289911	+	0.957053i	$0.593626\pi$
$48$	−9.19231e7	−0.0520712
$49$	−1.89678e9	−0.959266
$50$	7.09443e8	0.321057
$51$	−1.44127e9	−0.584936
$52$	−4.01553e9	−1.46462
$53$	3.44031e9	1.13001	0.565003	−	0.825089i	$-0.308875\pi$
$53$	3.44031e9	1.13001	0.565003	+	0.825089i	$0.308875\pi$
$54$	1.04240e9	0.308938
$55$	1.31627e9	0.352654
$56$	7.70367e8	0.186923
$57$	4.58496e9	1.00931
$58$	−8.38824e9	−1.67810
$59$	1.06320e10	1.93610	0.968049	−	0.250762i	$-0.0806812\pi$
$59$	1.06320e10	1.93610	0.968049	+	0.250762i	$0.0806812\pi$
$60$	2.45246e9	0.407165
$61$	6.85337e9	1.03894	0.519469	−	0.854489i	$-0.326130\pi$
$61$	6.85337e9	1.03894	0.519469	+	0.854489i	$0.326130\pi$
$62$	−1.98674e10	−2.75414
$63$	5.29942e8	0.0672752
$64$	−1.39928e10	−1.62898
$65$	−3.88550e9	−0.415359
$66$	7.43563e9	0.730846
$67$	5.26360e9	0.476290	0.238145	−	0.971230i	$-0.423461\pi$
$67$	5.26360e9	0.476290	0.238145	+	0.971230i	$0.423461\pi$
$68$	−1.91551e10	−1.59766
$69$	−6.61583e9	−0.509231
$70$	2.03743e9	0.144892
$71$	1.72726e10	1.13615	0.568076	−	0.822976i	$-0.307688\pi$
$71$	1.72726e10	1.13615	0.568076	+	0.822976i	$0.307688\pi$
$72$	5.06867e9	0.308721
$73$	5.86468e9	0.331107	0.165554	−	0.986201i	$-0.447059\pi$
$73$	5.86468e9	0.331107	0.165554	+	0.986201i	$0.447059\pi$
$74$	−2.08019e10	−1.08975
$75$	2.37305e9	0.115470
$76$	6.09363e10	2.75677
$77$	3.78015e9	0.159151
$78$	−2.19493e10	−0.860796
$79$	−2.16383e10	−0.791178	−0.395589	−	0.918428i	$-0.629459\pi$
$79$	−2.16383e10	−0.791178	−0.395589	+	0.918428i	$0.629459\pi$
$80$	−1.18214e9	−0.0403342
$81$	3.48678e9	0.111111
$82$	3.28217e10	0.977655
$83$	−6.48232e9	−0.180635	−0.0903173	−	0.995913i	$-0.528788\pi$
$83$	−6.48232e9	−0.180635	−0.0903173	+	0.995913i	$0.528788\pi$
$84$	7.04317e9	0.183752
$85$	−1.85348e10	−0.453089
$86$	9.48001e10	2.17304
$87$	−2.80582e10	−0.603537
$88$	3.61556e10	0.730333
$89$	7.32562e10	1.39059	0.695296	−	0.718724i	$-0.255273\pi$
$89$	7.32562e10	1.39059	0.695296	+	0.718724i	$0.255273\pi$
$90$	1.34054e10	0.239302
$91$	−1.11587e10	−0.187450
$92$	−8.79275e10	−1.39089
$93$	−6.64553e10	−0.990543
$94$	−6.62294e10	−0.930782
$95$	5.89630e10	0.781807
$96$	−4.93966e10	−0.618309
$97$	−1.45891e11	−1.72498	−0.862489	−	0.506076i	$-0.831096\pi$
$97$	−1.45891e11	−1.72498	−0.862489	+	0.506076i	$0.831096\pi$
$98$	−1.37796e11	−1.53990
$99$	2.48718e10	0.262853
$100$	3.15389e10	0.315389
$101$	−9.19701e10	−0.870721	−0.435360	−	0.900256i	$-0.643379\pi$
$101$	−9.19701e10	−0.870721	−0.435360	+	0.900256i	$0.643379\pi$
$102$	−1.04704e11	−0.938990
$103$	1.18655e11	1.00851	0.504257	−	0.863553i	$-0.331766\pi$
$103$	1.18655e11	1.00851	0.504257	+	0.863553i	$0.331766\pi$
$104$	−1.06728e11	−0.860191
$105$	6.81510e9	0.0521112
$106$	2.49928e11	1.81398
$107$	2.63515e10	0.181633	0.0908164	−	0.995868i	$-0.471052\pi$
$107$	2.63515e10	0.181633	0.0908164	+	0.995868i	$0.471052\pi$
$108$	4.63410e10	0.303483
$109$	1.24011e9	0.00771994	0.00385997	−	0.999993i	$-0.498771\pi$
$109$	1.24011e9	0.00771994	0.00385997	+	0.999993i	$0.498771\pi$
$110$	9.56228e10	0.566111
$111$	−6.95810e10	−0.391935
$112$	−3.39495e9	−0.0182027
$113$	1.82045e11	0.929498	0.464749	−	0.885443i	$-0.346145\pi$
$113$	1.82045e11	0.929498	0.464749	+	0.885443i	$0.346145\pi$
$114$	3.33084e11	1.62023
$115$	−8.50802e10	−0.394448
$116$	−3.72906e11	−1.64847
$117$	−7.34191e10	−0.309590
$118$	7.72380e11	3.10799
$119$	−5.32297e10	−0.204477
$120$	6.51836e10	0.239134
$121$	−1.07898e11	−0.378175
$122$	4.97876e11	1.66779
$123$	1.09787e11	0.351619
$124$	−8.83222e11	−2.70552
$125$	3.05176e10	0.0894427
$126$	3.84987e10	0.107996
$127$	−3.53295e11	−0.948892	−0.474446	−	0.880285i	$-0.657351\pi$
$127$	−3.53295e11	−0.948892	−0.474446	+	0.880285i	$0.657351\pi$
$128$	−6.00223e11	−1.54404
$129$	3.17101e11	0.781545
$130$	−2.82270e11	−0.666770
$131$	2.61604e11	0.592451	0.296225	−	0.955118i	$-0.404272\pi$
$131$	2.61604e11	0.592451	0.296225	+	0.955118i	$0.404272\pi$
$132$	3.30557e11	0.717943
$133$	1.69334e11	0.352827
$134$	3.82384e11	0.764582
$135$	4.48403e10	0.0860663
$136$	−5.09119e11	−0.938330
$137$	−1.30283e11	−0.230634	−0.115317	−	0.993329i	$-0.536788\pi$
$137$	−1.30283e11	−0.230634	−0.115317	+	0.993329i	$0.536788\pi$
$138$	−4.80620e11	−0.817461
$139$	−5.52082e11	−0.902447	−0.451224	−	0.892411i	$-0.649012\pi$
$139$	−5.52082e11	−0.902447	−0.451224	+	0.892411i	$0.649012\pi$
$140$	9.05758e10	0.142334
$141$	−2.21534e11	−0.334761
$142$	1.25480e12	1.82385
$143$	−5.23710e11	−0.732390
$144$	−2.23373e10	−0.0300633
$145$	−3.60831e11	−0.467498
$146$	4.26051e11	0.531522
$147$	−4.60918e11	−0.553833
$148$	−9.24764e11	−1.07051
$149$	1.76536e12	1.96929	0.984646	−	0.174564i	$-0.0558517\pi$
$149$	1.76536e12	1.96929	0.984646	+	0.174564i	$0.0558517\pi$
$150$	1.72395e11	0.185363
$151$	−3.08570e11	−0.319875	−0.159937	−	0.987127i	$-0.551129\pi$
$151$	−3.08570e11	−0.319875	−0.159937	+	0.987127i	$0.551129\pi$
$152$	1.61961e12	1.61909
$153$	−3.50228e11	−0.337713
$154$	2.74617e11	0.255484
$155$	−8.54621e11	−0.767271
$156$	−9.75774e11	−0.845598
$157$	−3.92737e11	−0.328590	−0.164295	−	0.986411i	$-0.552535\pi$
$157$	−3.92737e11	−0.328590	−0.164295	+	0.986411i	$0.552535\pi$
$158$	−1.57196e12	−1.27007
$159$	8.35996e11	0.652409
$160$	−6.35245e11	−0.478940
$161$	−2.44340e11	−0.178013
$162$	2.53304e11	0.178365
$163$	3.08103e11	0.209732	0.104866	−	0.994486i	$-0.466559\pi$
$163$	3.08103e11	0.209732	0.104866	+	0.994486i	$0.466559\pi$
$164$	1.45912e12	0.960394
$165$	3.19853e11	0.203605
$166$	−4.70921e11	−0.289970
$167$	−2.05731e12	−1.22563	−0.612814	−	0.790227i	$-0.709962\pi$
$167$	−2.05731e12	−1.22563	−0.612814	+	0.790227i	$0.709962\pi$
$168$	1.87199e11	0.107920
$169$	−2.46218e11	−0.137386
$170$	−1.34650e12	−0.727338
$171$	1.11415e12	0.582725
$172$	4.21442e12	2.13467
$173$	1.53807e12	0.754610	0.377305	−	0.926089i	$-0.376851\pi$
$173$	1.53807e12	0.754610	0.377305	+	0.926089i	$0.376851\pi$
$174$	−2.03834e12	−0.968849
$175$	8.76427e10	0.0403651
$176$	−1.59335e11	−0.0711201
$177$	2.58357e12	1.11781
$178$	5.32184e12	2.23230
$179$	7.80906e11	0.317619	0.158810	−	0.987309i	$-0.449234\pi$
$179$	7.80906e11	0.317619	0.158810	+	0.987309i	$0.449234\pi$
$180$	5.95949e11	0.235077
$181$	3.43484e12	1.31424	0.657119	−	0.753787i	$-0.271775\pi$
$181$	3.43484e12	1.31424	0.657119	+	0.753787i	$0.271775\pi$
$182$	−8.10644e11	−0.300911
$183$	1.66537e12	0.599831
$184$	−2.33701e12	−0.816887
$185$	−8.94818e11	−0.303592
$186$	−4.82778e12	−1.59011
$187$	−2.49823e12	−0.798919
$188$	−2.94429e12	−0.914348
$189$	1.28776e11	0.0388414
$190$	4.28348e12	1.25502
$191$	−1.22458e12	−0.348580	−0.174290	−	0.984694i	$-0.555763\pi$
$191$	−1.22458e12	−0.348580	−0.174290	+	0.984694i	$0.555763\pi$
$192$	−3.40026e12	−0.940492
$193$	−4.63699e11	−0.124644	−0.0623220	−	0.998056i	$-0.519851\pi$
$193$	−4.63699e11	−0.124644	−0.0623220	+	0.998056i	$0.519851\pi$
$194$	−1.05985e13	−2.76908
$195$	−9.44176e11	−0.239807
$196$	−6.12582e12	−1.51271
$197$	−3.26993e12	−0.785188	−0.392594	−	0.919712i	$-0.628422\pi$
$197$	−3.26993e12	−0.785188	−0.392594	+	0.919712i	$0.628422\pi$
$198$	1.80686e12	0.421954
$199$	8.62553e12	1.95927	0.979634	−	0.200792i	$-0.0643514\pi$
$199$	8.62553e12	1.95927	0.979634	+	0.200792i	$0.0643514\pi$
$200$	8.38266e11	0.185232
$201$	1.27905e12	0.274986
$202$	−6.68135e12	−1.39776
$203$	−1.03626e12	−0.210980
$204$	−4.65469e12	−0.922412
$205$	1.41187e12	0.272363
$206$	8.61994e12	1.61895
$207$	−1.60765e12	−0.294004
$208$	4.70343e11	0.0837658
$209$	7.94737e12	1.37854
$210$	4.95096e11	0.0836534
$211$	−1.20136e13	−1.97752	−0.988761	−	0.149506i	$-0.952232\pi$
$211$	−1.20136e13	−1.97752	−0.988761	+	0.149506i	$0.952232\pi$
$212$	1.11108e13	1.78196
$213$	4.19724e12	0.655958
$214$	1.91436e12	0.291573
$215$	4.07794e12	0.605382
$216$	1.23169e12	0.178240
$217$	−2.45436e12	−0.346267
$218$	9.00901e10	0.0123927
$219$	1.42512e12	0.191165
$220$	4.25099e12	0.556116
$221$	7.37454e12	0.940973
$222$	−5.05485e12	−0.629169
$223$	−1.23299e13	−1.49722	−0.748608	−	0.663013i	$-0.769277\pi$
$223$	−1.23299e13	−1.49722	−0.748608	+	0.663013i	$0.769277\pi$
$224$	−1.82434e12	−0.216144
$225$	5.76650e11	0.0666667
$226$	1.32250e13	1.49211
$227$	8.62723e12	0.950012	0.475006	−	0.879983i	$-0.342446\pi$
$227$	8.62723e12	0.950012	0.475006	+	0.879983i	$0.342446\pi$
$228$	1.48075e13	1.59162
$229$	6.94039e11	0.0728264	0.0364132	−	0.999337i	$-0.488407\pi$
$229$	6.94039e11	0.0728264	0.0364132	+	0.999337i	$0.488407\pi$
$230$	−6.18082e12	−0.633203
$231$	9.18578e11	0.0918861
$232$	−9.91140e12	−0.968169
$233$	−1.07799e13	−1.02839	−0.514196	−	0.857673i	$-0.671910\pi$
$233$	−1.07799e13	−1.02839	−0.514196	+	0.857673i	$0.671910\pi$
$234$	−5.33368e12	−0.496981
$235$	−2.84894e12	−0.259305
$236$	3.43368e13	3.05312
$237$	−5.25811e12	−0.456787
$238$	−3.86697e12	−0.328245
$239$	−2.37538e13	−1.97036	−0.985178	−	0.171534i	$-0.945128\pi$
$239$	−2.37538e13	−1.97036	−0.985178	+	0.171534i	$0.945128\pi$
$240$	−2.87260e11	−0.0232870
$241$	2.23146e12	0.176805	0.0884026	−	0.996085i	$-0.471824\pi$
$241$	2.23146e12	0.176805	0.0884026	+	0.996085i	$0.471824\pi$
$242$	−7.83845e12	−0.607079
$243$	8.47289e11	0.0641500
$244$	2.21335e13	1.63835
$245$	−5.92745e12	−0.428997
$246$	7.97568e12	0.564449
$247$	−2.34599e13	−1.62365
$248$	−2.34750e13	−1.58899
$249$	−1.57520e12	−0.104289
$250$	2.21701e12	0.143581
$251$	4.42422e12	0.280305	0.140153	−	0.990130i	$-0.455241\pi$
$251$	4.42422e12	0.280305	0.140153	+	0.990130i	$0.455241\pi$
$252$	1.71149e12	0.106089
$253$	−1.14676e13	−0.695519
$254$	−2.56658e13	−1.52324
$255$	−4.50396e12	−0.261591
$256$	−1.49470e13	−0.849641
$257$	1.74889e13	0.973039	0.486520	−	0.873670i	$-0.338266\pi$
$257$	1.74889e13	0.973039	0.486520	+	0.873670i	$0.338266\pi$
$258$	2.30364e13	1.25460
$259$	−2.56981e12	−0.137010
$260$	−1.25485e13	−0.654998
$261$	−6.81814e12	−0.348452
$262$	1.90047e13	0.951053
$263$	−9.99599e12	−0.489857	−0.244929	−	0.969541i	$-0.578765\pi$
$263$	−9.99599e12	−0.489857	−0.244929	+	0.969541i	$0.578765\pi$
$264$	8.78581e12	0.421658
$265$	1.07510e13	0.505354
$266$	1.23016e13	0.566388
$267$	1.78013e13	0.802858
$268$	1.69992e13	0.751083
$269$	3.47374e13	1.50370	0.751848	−	0.659336i	$-0.229163\pi$
$269$	3.47374e13	1.50370	0.751848	+	0.659336i	$0.229163\pi$
$270$	3.25751e12	0.138161
$271$	−5.11553e12	−0.212598	−0.106299	−	0.994334i	$-0.533900\pi$
$271$	−5.11553e12	−0.212598	−0.106299	+	0.994334i	$0.533900\pi$
$272$	2.24366e12	0.0913750
$273$	−2.71156e12	−0.108224
$274$	−9.46464e12	−0.370234
$275$	4.11333e12	0.157712
$276$	−2.13664e13	−0.803029
$277$	1.12045e13	0.412812	0.206406	−	0.978466i	$-0.433823\pi$
$277$	1.12045e13	0.412812	0.206406	+	0.978466i	$0.433823\pi$
$278$	−4.01071e13	−1.44869
$279$	−1.61486e13	−0.571890
$280$	2.40740e12	0.0835946
$281$	−1.18779e13	−0.404441	−0.202220	−	0.979340i	$-0.564816\pi$
$281$	−1.18779e13	−0.404441	−0.202220	+	0.979340i	$0.564816\pi$
$282$	−1.60938e13	−0.537387
$283$	−1.81554e13	−0.594540	−0.297270	−	0.954793i	$-0.596076\pi$
$283$	−1.81554e13	−0.594540	−0.297270	+	0.954793i	$0.596076\pi$
$284$	5.57832e13	1.79165
$285$	1.43280e13	0.451377
$286$	−3.80459e13	−1.17570
$287$	4.05471e12	0.122916
$288$	−1.20034e13	−0.356981
$289$	9.06488e11	0.0264499
$290$	−2.62133e13	−0.750467
$291$	−3.54515e13	−0.995917
$292$	1.89405e13	0.522138
$293$	6.34023e13	1.71527	0.857637	−	0.514256i	$-0.171932\pi$
$293$	6.34023e13	1.71527	0.857637	+	0.514256i	$0.171932\pi$
$294$	−3.34843e13	−0.889060
$295$	3.32249e13	0.865849
$296$	−2.45791e13	−0.628727
$297$	6.04384e12	0.151758
$298$	1.28248e14	3.16128
$299$	3.38513e13	0.819188
$300$	7.66395e12	0.182090
$301$	1.17113e13	0.273207
$302$	−2.24167e13	−0.513491
$303$	−2.23487e13	−0.502711
$304$	−7.13753e12	−0.157668
$305$	2.14168e13	0.464627
$306$	−2.54430e13	−0.542126
$307$	5.09373e13	1.06604	0.533021	−	0.846102i	$-0.321057\pi$
$307$	5.09373e13	1.06604	0.533021	+	0.846102i	$0.321057\pi$
$308$	1.22083e13	0.250973
$309$	2.88332e13	0.582266
$310$	−6.20856e13	−1.23169
$311$	−2.18208e13	−0.425292	−0.212646	−	0.977129i	$-0.568208\pi$
$311$	−2.18208e13	−0.425292	−0.212646	+	0.977129i	$0.568208\pi$
$312$	−2.59349e13	−0.496632
$313$	4.34705e13	0.817901	0.408950	−	0.912557i	$-0.365895\pi$
$313$	4.34705e13	0.817901	0.408950	+	0.912557i	$0.365895\pi$
$314$	−2.85312e13	−0.527481
$315$	1.65607e12	0.0300864
$316$	−6.98827e13	−1.24764
$317$	6.91742e12	0.121372	0.0606860	−	0.998157i	$-0.480671\pi$
$317$	6.91742e12	0.121372	0.0606860	+	0.998157i	$0.480671\pi$
$318$	6.07326e13	1.04730
$319$	−4.86348e13	−0.824325
$320$	−4.37276e13	−0.728502
$321$	6.40341e12	0.104866
$322$	−1.77505e13	−0.285762
$323$	−1.11910e14	−1.77114
$324$	1.12609e13	0.175216
$325$	−1.21422e13	−0.185754
$326$	2.23828e13	0.336679
$327$	3.01346e11	0.00445711
$328$	3.87816e13	0.564053
$329$	−8.18181e12	−0.117023
$330$	2.32363e13	0.326844
$331$	−3.99718e13	−0.552967	−0.276484	−	0.961019i	$-0.589169\pi$
$331$	−3.99718e13	−0.552967	−0.276484	+	0.961019i	$0.589169\pi$
$332$	−2.09352e13	−0.284851
$333$	−1.69082e13	−0.226284
$334$	−1.49457e14	−1.96748
$335$	1.64487e13	0.213003
$336$	−8.24974e11	−0.0105093
$337$	6.16325e13	0.772405	0.386202	−	0.922414i	$-0.373787\pi$
$337$	6.16325e13	0.772405	0.386202	+	0.922414i	$0.373787\pi$
$338$	−1.78870e13	−0.220544
$339$	4.42370e13	0.536646
$340$	−5.98597e13	−0.714497
$341$	−1.15191e14	−1.35291
$342$	8.09393e13	0.935440
$343$	−3.47686e13	−0.395430
$344$	1.12014e14	1.25372
$345$	−2.06745e13	−0.227735
$346$	1.11736e14	1.21137
$347$	−1.69421e13	−0.180782	−0.0903912	−	0.995906i	$-0.528812\pi$
$347$	−1.69421e13	−0.180782	−0.0903912	+	0.995906i	$0.528812\pi$
$348$	−9.06162e13	−0.951744
$349$	8.63767e13	0.893011	0.446506	−	0.894781i	$-0.352668\pi$
$349$	8.63767e13	0.893011	0.446506	+	0.894781i	$0.352668\pi$
$350$	6.36698e12	0.0647976
$351$	−1.78408e13	−0.178742
$352$	−8.56219e13	−0.844501
$353$	−1.74597e14	−1.69541	−0.847706	−	0.530467i	$-0.822017\pi$
$353$	−1.74597e14	−1.69541	−0.847706	+	0.530467i	$0.822017\pi$
$354$	1.87688e14	1.79440
$355$	5.39768e13	0.508103
$356$	2.36587e14	2.19289
$357$	−1.29348e13	−0.118055
$358$	5.67304e13	0.509870
$359$	4.82814e13	0.427327	0.213664	−	0.976907i	$-0.431460\pi$
$359$	4.82814e13	0.427327	0.213664	+	0.976907i	$0.431460\pi$
$360$	1.58396e13	0.138064
$361$	2.39517e14	2.05611
$362$	2.49530e14	2.10973
$363$	−2.62192e13	−0.218339
$364$	−3.60379e13	−0.295598
$365$	1.83271e13	0.148076
$366$	1.20984e14	0.962901
$367$	−8.66249e13	−0.679171	−0.339586	−	0.940575i	$-0.610287\pi$
$367$	−8.66249e13	−0.679171	−0.339586	+	0.940575i	$0.610287\pi$
$368$	1.02990e13	0.0795488
$369$	2.66782e13	0.203007
$370$	−6.50058e13	−0.487352
$371$	3.08755e13	0.228064
$372$	−2.14623e14	−1.56203
$373$	−6.19068e13	−0.443956	−0.221978	−	0.975052i	$-0.571251\pi$
$373$	−6.19068e13	−0.443956	−0.221978	+	0.975052i	$0.571251\pi$
$374$	−1.81489e14	−1.28249
$375$	7.41577e12	0.0516398
$376$	−7.82556e13	−0.537010
$377$	1.43565e14	0.970896
$378$	9.35518e12	0.0623515
$379$	−1.30905e14	−0.859883	−0.429942	−	0.902857i	$-0.641466\pi$
$379$	−1.30905e14	−0.859883	−0.429942	+	0.902857i	$0.641466\pi$
$380$	1.90426e14	1.23287
$381$	−8.58506e13	−0.547843
$382$	−8.89617e13	−0.559570
$383$	−1.24954e14	−0.774741	−0.387371	−	0.921924i	$-0.626617\pi$
$383$	−1.24954e14	−0.774741	−0.387371	+	0.921924i	$0.626617\pi$
$384$	−1.45854e14	−0.891450
$385$	1.18130e13	0.0711747
$386$	−3.36863e13	−0.200089
$387$	7.70555e13	0.451225
$388$	−4.71167e14	−2.72020
$389$	1.96127e13	0.111639	0.0558193	−	0.998441i	$-0.482223\pi$
$389$	1.96127e13	0.111639	0.0558193	+	0.998441i	$0.482223\pi$
$390$	−6.85915e13	−0.384960
$391$	1.61479e14	0.893602
$392$	−1.62817e14	−0.888436
$393$	6.35698e13	0.342052
$394$	−2.37550e14	−1.26045
$395$	−6.76197e13	−0.353825
$396$	8.03254e13	0.414505
$397$	−3.05579e14	−1.55516	−0.777580	−	0.628784i	$-0.783553\pi$
$397$	−3.05579e14	−1.55516	−0.777580	+	0.628784i	$0.783553\pi$
$398$	6.26619e14	3.14519
$399$	4.11483e13	0.203704
$400$	−3.69418e12	−0.0180380
$401$	−2.19942e14	−1.05929	−0.529645	−	0.848220i	$-0.677675\pi$
$401$	−2.19942e14	−1.05929	−0.529645	+	0.848220i	$0.677675\pi$
$402$	9.29194e13	0.441431
$403$	3.40032e14	1.59346
$404$	−2.97025e14	−1.37308
$405$	1.08962e13	0.0496904
$406$	−7.52812e13	−0.338683
$407$	−1.20609e14	−0.535315
$408$	−1.23716e14	−0.541745
$409$	2.96496e14	1.28098	0.640488	−	0.767968i	$-0.278732\pi$
$409$	2.96496e14	1.28098	0.640488	+	0.767968i	$0.278732\pi$
$410$	1.02568e14	0.437220
$411$	−3.16587e13	−0.133157
$412$	3.83207e14	1.59037
$413$	9.54177e13	0.390754
$414$	−1.16791e14	−0.471961
$415$	−2.02573e13	−0.0807823
$416$	2.52748e14	0.994659
$417$	−1.34156e14	−0.521028
$418$	5.77352e14	2.21295
$419$	6.30261e13	0.238420	0.119210	−	0.992869i	$-0.461964\pi$
$419$	6.30261e13	0.238420	0.119210	+	0.992869i	$0.461964\pi$
$420$	2.20099e13	0.0821765
$421$	2.35891e13	0.0869282	0.0434641	−	0.999055i	$-0.486161\pi$
$421$	2.35891e13	0.0869282	0.0434641	+	0.999055i	$0.486161\pi$
$422$	−8.72755e14	−3.17449
$423$	−5.38327e13	−0.193274
$424$	2.95311e14	1.04657
$425$	−5.79213e13	−0.202628
$426$	3.04917e14	1.05300
$427$	6.15063e13	0.209685
$428$	8.51043e13	0.286425
$429$	−1.27261e14	−0.422845
$430$	2.96250e14	0.971812
$431$	−2.46226e14	−0.797461	−0.398731	−	0.917068i	$-0.630549\pi$
$431$	−2.46226e14	−0.797461	−0.398731	+	0.917068i	$0.630549\pi$
$432$	−5.42796e12	−0.0173571
$433$	−5.82563e14	−1.83933	−0.919665	−	0.392704i	$-0.871540\pi$
$433$	−5.82563e14	−1.83933	−0.919665	+	0.392704i	$0.871540\pi$
$434$	−1.78302e14	−0.555857
$435$	−8.76818e13	−0.269910
$436$	4.00503e12	0.0121739
$437$	−5.13698e14	−1.54191
$438$	1.03530e14	0.306874
$439$	3.32296e14	0.972681	0.486340	−	0.873769i	$-0.338331\pi$
$439$	3.32296e14	0.972681	0.486340	+	0.873769i	$0.338331\pi$
$440$	1.12986e14	0.326615
$441$	−1.12003e14	−0.319755
$442$	5.35738e14	1.51053
$443$	5.20556e14	1.44960	0.724798	−	0.688961i	$-0.241933\pi$
$443$	5.20556e14	1.44960	0.724798	+	0.688961i	$0.241933\pi$
$444$	−2.24718e14	−0.618060
$445$	2.28926e14	0.621891
$446$	−8.95733e14	−2.40346
$447$	4.28984e14	1.13697
$448$	−1.25580e14	−0.328770
$449$	1.80442e14	0.466642	0.233321	−	0.972400i	$-0.425041\pi$
$449$	1.80442e14	0.466642	0.233321	+	0.972400i	$0.425041\pi$
$450$	4.18919e13	0.107019
$451$	1.90300e14	0.480250
$452$	5.87931e14	1.46577
$453$	−7.49825e13	−0.184680
$454$	6.26742e14	1.52504
$455$	−3.48708e13	−0.0838301
$456$	3.93566e14	0.934783
$457$	−8.24111e14	−1.93396	−0.966978	−	0.254861i	$-0.917970\pi$
$457$	−8.24111e14	−1.93396	−0.966978	+	0.254861i	$0.917970\pi$
$458$	5.04198e13	0.116907
$459$	−8.51053e13	−0.194979
$460$	−2.74773e14	−0.622023
$461$	2.21805e14	0.496153	0.248076	−	0.968740i	$-0.420202\pi$
$461$	2.21805e14	0.496153	0.248076	+	0.968740i	$0.420202\pi$
$462$	6.67319e13	0.147504
$463$	−7.96390e14	−1.73952	−0.869761	−	0.493473i	$-0.835727\pi$
$463$	−7.96390e14	−1.73952	−0.869761	+	0.493473i	$0.835727\pi$
$464$	4.36789e13	0.0942807
$465$	−2.07673e14	−0.442984
$466$	−7.83130e14	−1.65086
$467$	3.19815e14	0.666280	0.333140	−	0.942877i	$-0.391892\pi$
$467$	3.19815e14	0.666280	0.333140	+	0.942877i	$0.391892\pi$
$468$	−2.37113e14	−0.488206
$469$	4.72388e13	0.0961275
$470$	−2.06967e14	−0.416258
$471$	−9.54352e13	−0.189711
$472$	9.12631e14	1.79314
$473$	5.49648e14	1.06745
$474$	−3.81985e14	−0.733273
$475$	1.84259e14	0.349635
$476$	−1.71910e14	−0.322450
$477$	2.03147e14	0.376669
$478$	−1.72564e15	−3.16299
$479$	9.20568e14	1.66806	0.834028	−	0.551722i	$-0.186029\pi$
$479$	9.20568e14	1.66806	0.834028	+	0.551722i	$0.186029\pi$
$480$	−1.54364e14	−0.276516
$481$	3.56026e14	0.630497
$482$	1.62109e14	0.283823
$483$	−5.93745e13	−0.102776
$484$	−3.48465e14	−0.596361
$485$	−4.55909e14	−0.771434
$486$	6.15530e13	0.102979
$487$	6.15748e13	0.101858	0.0509288	−	0.998702i	$-0.483782\pi$
$487$	6.15748e13	0.101858	0.0509288	+	0.998702i	$0.483782\pi$
$488$	5.88282e14	0.962225
$489$	7.48690e13	0.121089
$490$	−4.30611e14	−0.688663
$491$	5.24202e14	0.828992	0.414496	−	0.910051i	$-0.363958\pi$
$491$	5.24202e14	0.828992	0.414496	+	0.910051i	$0.363958\pi$
$492$	3.54566e14	0.554484
$493$	6.84843e14	1.05909
$494$	−1.70429e15	−2.60643
$495$	7.77242e13	0.117551
$496$	1.03453e14	0.154736
$497$	1.55015e14	0.229305
$498$	−1.14434e14	−0.167414
$499$	−5.82465e14	−0.842784	−0.421392	−	0.906878i	$-0.638458\pi$
$499$	−5.82465e14	−0.842784	−0.421392	+	0.906878i	$0.638458\pi$
$500$	9.85590e13	0.141046
$501$	−4.99926e14	−0.707616
$502$	3.21406e14	0.449970
$503$	2.94219e14	0.407424	0.203712	−	0.979031i	$-0.434699\pi$
$503$	2.94219e14	0.407424	0.203712	+	0.979031i	$0.434699\pi$
$504$	4.54894e13	0.0623078
$505$	−2.87407e14	−0.389398
$506$	−8.33086e14	−1.11651
$507$	−5.98309e13	−0.0793198
$508$	−1.14099e15	−1.49635
$509$	1.77642e13	0.0230462	0.0115231	−	0.999934i	$-0.496332\pi$
$509$	1.77642e13	0.0230462	0.0115231	+	0.999934i	$0.496332\pi$
$510$	−3.27199e14	−0.419929
$511$	5.26332e13	0.0668259
$512$	1.43398e14	0.180119
$513$	2.70737e14	0.336436
$514$	1.27052e15	1.56201
$515$	3.70798e14	0.451021
$516$	1.02410e15	1.23245
$517$	−3.83997e14	−0.457224
$518$	−1.86689e14	−0.219940
$519$	3.73751e14	0.435674
$520$	−3.33525e14	−0.384689
$521$	−1.74393e14	−0.199031	−0.0995154	−	0.995036i	$-0.531729\pi$
$521$	−1.74393e14	−0.199031	−0.0995154	+	0.995036i	$0.531729\pi$
$522$	−4.95317e14	−0.559365
$523$	3.37057e14	0.376656	0.188328	−	0.982106i	$-0.439693\pi$
$523$	3.37057e14	0.376656	0.188328	+	0.982106i	$0.439693\pi$
$524$	8.44872e14	0.934262
$525$	2.12972e13	0.0233048
$526$	−7.26179e14	−0.786361
$527$	1.62204e15	1.73821
$528$	−3.87185e13	−0.0410612
$529$	−2.11574e14	−0.222052
$530$	7.81026e14	0.811238
$531$	6.27807e14	0.645366
$532$	5.46880e14	0.556388
$533$	−5.61747e14	−0.565641
$534$	1.29321e15	1.28882
$535$	8.23484e13	0.0812287
$536$	4.51819e14	0.441121
$537$	1.89760e14	0.183378
$538$	2.52357e15	2.41386
$539$	−7.98935e14	−0.756438
$540$	1.44816e14	0.135722
$541$	4.06015e14	0.376667	0.188333	−	0.982105i	$-0.439691\pi$
$541$	4.06015e14	0.376667	0.188333	+	0.982105i	$0.439691\pi$
$542$	−3.71628e14	−0.341281
$543$	8.34665e14	0.758775
$544$	1.20567e15	1.08501
$545$	3.87534e12	0.00345246
$546$	−1.96986e14	−0.173731
$547$	−1.88321e15	−1.64425	−0.822125	−	0.569307i	$-0.807212\pi$
$547$	−1.88321e15	−1.64425	−0.822125	+	0.569307i	$0.807212\pi$
$548$	−4.20759e14	−0.363697
$549$	4.04684e14	0.346313
$550$	2.98821e14	0.253173
$551$	−2.17863e15	−1.82746
$552$	−5.67893e14	−0.471630
$553$	−1.94195e14	−0.159680
$554$	8.13970e14	0.662681
$555$	−2.17441e14	−0.175279
$556$	−1.78299e15	−1.42311
$557$	−1.68243e15	−1.32964	−0.664818	−	0.747005i	$-0.731491\pi$
$557$	−1.68243e15	−1.32964	−0.664818	+	0.747005i	$0.731491\pi$
$558$	−1.17315e15	−0.918048
$559$	−1.62251e15	−1.25725
$560$	−1.06092e13	−0.00814048
$561$	−6.07069e14	−0.461256
$562$	−8.62894e14	−0.649243
$563$	−2.54683e14	−0.189760	−0.0948798	−	0.995489i	$-0.530247\pi$
$563$	−2.54683e14	−0.189760	−0.0948798	+	0.995489i	$0.530247\pi$
$564$	−7.15461e14	−0.527899
$565$	5.68892e14	0.415684
$566$	−1.31894e15	−0.954407
$567$	3.12925e13	0.0224251
$568$	1.48265e15	1.05226
$569$	−1.14053e15	−0.801656	−0.400828	−	0.916153i	$-0.631277\pi$
$569$	−1.14053e15	−0.801656	−0.400828	+	0.916153i	$0.631277\pi$
$570$	1.04089e15	0.724589
$571$	5.33268e14	0.367660	0.183830	−	0.982958i	$-0.441150\pi$
$571$	5.33268e14	0.367660	0.183830	+	0.982958i	$0.441150\pi$
$572$	−1.69136e15	−1.15494
$573$	−2.97572e14	−0.201253
$574$	2.94562e14	0.197316
$575$	−2.65875e14	−0.176403
$576$	−8.26262e14	−0.542993
$577$	1.94156e15	1.26382	0.631909	−	0.775043i	$-0.282272\pi$
$577$	1.94156e15	1.26382	0.631909	+	0.775043i	$0.282272\pi$
$578$	6.58536e13	0.0424597
$579$	−1.12679e14	−0.0719632
$580$	−1.16533e15	−0.737218
$581$	−5.81763e13	−0.0364567
$582$	−2.57544e15	−1.59873
$583$	1.44908e15	0.891076
$584$	5.03415e14	0.306659
$585$	−2.29435e14	−0.138453
$586$	4.60599e15	2.75350
$587$	1.35103e15	0.800123	0.400062	−	0.916488i	$-0.368989\pi$
$587$	1.35103e15	0.800123	0.400062	+	0.916488i	$0.368989\pi$
$588$	−1.48857e15	−0.873364
$589$	−5.16004e15	−2.99929
$590$	2.41369e15	1.38994
$591$	−7.94592e14	−0.453329
$592$	1.08319e14	0.0612256
$593$	1.05549e15	0.591089	0.295544	−	0.955329i	$-0.404499\pi$
$593$	1.05549e15	0.591089	0.295544	+	0.955329i	$0.404499\pi$
$594$	4.39066e14	0.243615
$595$	−1.66343e14	−0.0914451
$596$	5.70139e15	3.10546
$597$	2.09600e15	1.13118
$598$	2.45919e15	1.31503
$599$	−8.49546e14	−0.450132	−0.225066	−	0.974344i	$-0.572260\pi$
$599$	−8.49546e14	−0.450132	−0.225066	+	0.974344i	$0.572260\pi$
$600$	2.03699e14	0.106944
$601$	1.43534e15	0.746696	0.373348	−	0.927691i	$-0.378210\pi$
$601$	1.43534e15	0.746696	0.373348	+	0.927691i	$0.378210\pi$
$602$	8.50794e14	0.438575
$603$	3.10810e14	0.158763
$604$	−9.96552e14	−0.504425
$605$	−3.37181e14	−0.169125
$606$	−1.62357e15	−0.806995
$607$	−8.76288e14	−0.431627	−0.215814	−	0.976435i	$-0.569240\pi$
$607$	−8.76288e14	−0.431627	−0.215814	+	0.976435i	$0.569240\pi$
$608$	−3.83549e15	−1.87219
$609$	−2.51811e14	−0.121809
$610$	1.55586e15	0.745860
$611$	1.13352e15	0.538522
$612$	−1.13109e15	−0.532555
$613$	3.29080e14	0.153557	0.0767784	−	0.997048i	$-0.475537\pi$
$613$	3.29080e14	0.153557	0.0767784	+	0.997048i	$0.475537\pi$
$614$	3.70044e15	1.71130
$615$	3.43084e14	0.157249
$616$	3.24483e14	0.147400
$617$	−1.42160e15	−0.640041	−0.320021	−	0.947411i	$-0.603690\pi$
$617$	−1.42160e15	−0.640041	−0.320021	+	0.947411i	$0.603690\pi$
$618$	2.09465e15	0.934704
$619$	−2.67970e15	−1.18519	−0.592595	−	0.805501i	$-0.701896\pi$
$619$	−2.67970e15	−1.18519	−0.592595	+	0.805501i	$0.701896\pi$
$620$	−2.76007e15	−1.20994
$621$	−3.90658e14	−0.169744
$622$	−1.58521e15	−0.682716
$623$	6.57446e14	0.280657
$624$	1.14293e14	0.0483622
$625$	9.53674e13	0.0400000
$626$	3.15800e15	1.31296
$627$	1.93121e15	0.795899
$628$	−1.26838e15	−0.518168
$629$	1.69833e15	0.687771
$630$	1.20308e14	0.0482973
$631$	3.85938e15	1.53588	0.767939	−	0.640523i	$-0.221283\pi$
$631$	3.85938e15	1.53588	0.767939	+	0.640523i	$0.221283\pi$
$632$	−1.85740e15	−0.732758
$633$	−2.91932e15	−1.14172
$634$	5.02530e14	0.194837
$635$	−1.10405e15	−0.424357
$636$	2.69992e15	1.02881
$637$	2.35838e15	0.890938
$638$	−3.53317e15	−1.32328
$639$	1.01993e15	0.378717
$640$	−1.87570e15	−0.690514
$641$	−9.95208e14	−0.363241	−0.181620	−	0.983369i	$-0.558134\pi$
$641$	−9.95208e14	−0.363241	−0.181620	+	0.983369i	$0.558134\pi$
$642$	4.65188e14	0.168340
$643$	−4.37182e15	−1.56856	−0.784282	−	0.620404i	$-0.786968\pi$
$643$	−4.37182e15	−1.56856	−0.784282	+	0.620404i	$0.786968\pi$
$644$	−7.89115e14	−0.280717
$645$	9.90940e14	0.349518
$646$	−8.12990e15	−2.84319
$647$	1.50021e14	0.0520208	0.0260104	−	0.999662i	$-0.491720\pi$
$647$	1.50021e14	0.0520208	0.0260104	+	0.999662i	$0.491720\pi$
$648$	2.99300e14	0.102907
$649$	4.47824e15	1.52673
$650$	−8.82093e14	−0.298188
$651$	−5.96411e14	−0.199917
$652$	9.95044e14	0.330735
$653$	−3.11485e15	−1.02663	−0.513315	−	0.858200i	$-0.671583\pi$
$653$	−3.11485e15	−1.02663	−0.513315	+	0.858200i	$0.671583\pi$
$654$	2.18919e13	0.00715493
$655$	8.17513e14	0.264952
$656$	−1.70908e14	−0.0549277
$657$	3.46303e14	0.110369
$658$	−5.94384e14	−0.187856
$659$	1.93056e15	0.605079	0.302540	−	0.953137i	$-0.402166\pi$
$659$	1.93056e15	0.605079	0.302540	+	0.953137i	$0.402166\pi$
$660$	1.03299e15	0.321074
$661$	2.24334e15	0.691491	0.345745	−	0.938328i	$-0.387626\pi$
$661$	2.24334e15	0.691491	0.345745	+	0.938328i	$0.387626\pi$
$662$	−2.90383e15	−0.887671
$663$	1.79201e15	0.543271
$664$	−5.56432e14	−0.167297
$665$	5.29170e14	0.157789
$666$	−1.22833e15	−0.363251
$667$	3.14363e15	0.922018
$668$	−6.64424e15	−1.93275
$669$	−2.99618e15	−0.864418
$670$	1.19495e15	0.341931
$671$	2.88667e15	0.819264
$672$	−4.43316e14	−0.124791
$673$	6.77758e15	1.89231	0.946154	−	0.323716i	$-0.104932\pi$
$673$	6.77758e15	1.89231	0.946154	+	0.323716i	$0.104932\pi$
$674$	4.47741e15	1.23993
$675$	1.40126e14	0.0384900
$676$	−7.95180e14	−0.216650
$677$	3.35870e15	0.907682	0.453841	−	0.891083i	$-0.350053\pi$
$677$	3.35870e15	0.907682	0.453841	+	0.891083i	$0.350053\pi$
$678$	3.21369e15	0.861470
$679$	−1.30931e15	−0.348145
$680$	−1.59100e15	−0.419634
$681$	2.09642e15	0.548490
$682$	−8.36825e15	−2.17180
$683$	8.39057e14	0.216012	0.108006	−	0.994150i	$-0.465553\pi$
$683$	8.39057e14	0.216012	0.108006	+	0.994150i	$0.465553\pi$
$684$	3.59823e15	0.918925
$685$	−4.07133e14	−0.103143
$686$	−2.52584e15	−0.634779
$687$	1.68651e14	0.0420463
$688$	−4.93639e14	−0.122088
$689$	−4.27755e15	−1.04952
$690$	−1.50194e15	−0.365580
$691$	−7.05750e15	−1.70421	−0.852103	−	0.523375i	$-0.824673\pi$
$691$	−7.05750e15	−1.70421	−0.852103	+	0.523375i	$0.824673\pi$
$692$	4.96732e15	1.18998
$693$	2.23214e14	0.0530505
$694$	−1.23080e15	−0.290208
$695$	−1.72525e15	−0.403587
$696$	−2.40847e15	−0.558973
$697$	−2.67967e15	−0.617024
$698$	6.27501e15	1.43354
$699$	−2.61953e15	−0.593743
$700$	2.83049e14	0.0636536
$701$	4.30034e15	0.959519	0.479760	−	0.877400i	$-0.340724\pi$
$701$	4.30034e15	0.959519	0.479760	+	0.877400i	$0.340724\pi$
$702$	−1.29608e15	−0.286932
$703$	−5.40274e15	−1.18675
$704$	−5.89385e15	−1.28455
$705$	−6.92293e14	−0.149710
$706$	−1.26839e16	−2.72162
$707$	−8.25396e14	−0.175734
$708$	8.34384e15	1.76272
$709$	2.30816e15	0.483850	0.241925	−	0.970295i	$-0.422221\pi$
$709$	2.30816e15	0.483850	0.241925	+	0.970295i	$0.422221\pi$
$710$	3.92125e15	0.815650
$711$	−1.27772e15	−0.263726
$712$	6.28820e15	1.28791
$713$	7.44563e15	1.51324
$714$	−9.39675e14	−0.189512
$715$	−1.63659e15	−0.327535
$716$	2.52200e15	0.500868
$717$	−5.77218e15	−1.13759
$718$	3.50750e15	0.685983
$719$	2.20705e14	0.0428354	0.0214177	−	0.999771i	$-0.493182\pi$
$719$	2.20705e14	0.0428354	0.0214177	+	0.999771i	$0.493182\pi$
$720$	−6.98041e13	−0.0134447
$721$	1.06488e15	0.203544
$722$	1.74002e16	3.30065
$723$	5.42244e14	0.102079
$724$	1.10931e16	2.07248
$725$	−1.12760e15	−0.209071
$726$	−1.90474e15	−0.350497
$727$	−2.09923e15	−0.383373	−0.191686	−	0.981456i	$-0.561396\pi$
$727$	−2.09923e15	−0.383373	−0.191686	+	0.981456i	$0.561396\pi$
$728$	−9.57843e14	−0.173609
$729$	2.05891e14	0.0370370
$730$	1.33141e15	0.237704
$731$	−7.73979e15	−1.37146
$732$	5.37844e15	0.945901
$733$	6.86229e15	1.19784	0.598918	−	0.800810i	$-0.295597\pi$
$733$	6.86229e15	1.19784	0.598918	+	0.800810i	$0.295597\pi$
$734$	−6.29304e15	−1.09026
$735$	−1.44037e15	−0.247682
$736$	5.53438e15	0.944585
$737$	2.21706e15	0.375582
$738$	1.93809e15	0.325885
$739$	4.84418e14	0.0808493	0.0404246	−	0.999183i	$-0.487129\pi$
$739$	4.84418e14	0.0808493	0.0404246	+	0.999183i	$0.487129\pi$
$740$	−2.88989e15	−0.478748
$741$	−5.70076e15	−0.937416
$742$	2.24301e15	0.366109
$743$	5.18709e15	0.840398	0.420199	−	0.907432i	$-0.361960\pi$
$743$	5.18709e15	0.840398	0.420199	+	0.907432i	$0.361960\pi$
$744$	−5.70442e15	−0.917403
$745$	5.51677e15	0.880694
$746$	−4.49734e15	−0.712677
$747$	−3.82775e14	−0.0602115
$748$	−8.06823e15	−1.25985
$749$	2.36494e14	0.0366582
$750$	5.38733e14	0.0828966
$751$	−5.82780e15	−0.890195	−0.445098	−	0.895482i	$-0.646831\pi$
$751$	−5.82780e15	−0.890195	−0.445098	+	0.895482i	$0.646831\pi$
$752$	3.44867e14	0.0522942
$753$	1.07508e15	0.161834
$754$	1.04296e16	1.55857
$755$	−9.64281e14	−0.143052
$756$	4.15892e14	0.0612507
$757$	−5.62401e14	−0.0822277	−0.0411139	−	0.999154i	$-0.513091\pi$
$757$	−5.62401e14	−0.0822277	−0.0411139	+	0.999154i	$0.513091\pi$
$758$	−9.50983e15	−1.38036
$759$	−2.78662e15	−0.401558
$760$	5.06129e15	0.724080
$761$	5.86147e15	0.832512	0.416256	−	0.909247i	$-0.363342\pi$
$761$	5.86147e15	0.832512	0.416256	+	0.909247i	$0.363342\pi$
$762$	−6.23679e15	−0.879445
$763$	1.11295e13	0.00155808
$764$	−3.95487e15	−0.549691
$765$	−1.09446e15	−0.151030
$766$	−9.07752e15	−1.24368
$767$	−1.32193e16	−1.79819
$768$	−3.63213e15	−0.490541
$769$	5.18352e15	0.695072	0.347536	−	0.937667i	$-0.387018\pi$
$769$	5.18352e15	0.695072	0.347536	+	0.937667i	$0.387018\pi$
$770$	8.58178e14	0.114256
$771$	4.24980e15	0.561785
$772$	−1.49756e15	−0.196557
$773$	−1.29318e16	−1.68528	−0.842640	−	0.538478i	$-0.819000\pi$
$773$	−1.29318e16	−1.68528	−0.842640	+	0.538478i	$0.819000\pi$
$774$	5.59785e15	0.724346
$775$	−2.67069e15	−0.343134
$776$	−1.25230e16	−1.59761
$777$	−6.24463e14	−0.0791026
$778$	1.42480e15	0.179212
$779$	8.52459e15	1.06468
$780$	−3.04929e15	−0.378163
$781$	7.27530e15	0.895923
$782$	1.17310e16	1.43449
$783$	−1.65681e15	−0.201179
$784$	7.17523e14	0.0865162
$785$	−1.22730e15	−0.146950
$786$	4.61815e15	0.549091
$787$	−2.08385e15	−0.246040	−0.123020	−	0.992404i	$-0.539258\pi$
$787$	−2.08385e15	−0.246040	−0.123020	+	0.992404i	$0.539258\pi$
$788$	−1.05605e16	−1.23820
$789$	−2.42903e15	−0.282819
$790$	−4.91236e15	−0.567991
$791$	1.63379e15	0.187597
$792$	2.13495e15	0.243444
$793$	−8.52120e15	−0.964935
$794$	−2.21994e16	−2.49648
$795$	2.61249e15	0.291766
$796$	2.78569e16	3.08966
$797$	−1.37867e16	−1.51859	−0.759293	−	0.650749i	$-0.774455\pi$
$797$	−1.37867e16	−1.51859	−0.759293	+	0.650749i	$0.774455\pi$
$798$	2.98930e15	0.327004
$799$	5.40719e15	0.587441
$800$	−1.98514e15	−0.214188
$801$	4.32571e15	0.463530
$802$	−1.59781e16	−1.70046
$803$	2.47023e15	0.261097
$804$	4.13081e15	0.433638
$805$	−7.63562e14	−0.0796098
$806$	2.47023e16	2.55797
$807$	8.44119e15	0.868159
$808$	−7.89457e15	−0.806428
$809$	1.04031e16	1.05547	0.527737	−	0.849408i	$-0.323041\pi$
$809$	1.04031e16	1.05547	0.527737	+	0.849408i	$0.323041\pi$
$810$	7.91576e14	0.0797673
$811$	−1.01334e16	−1.01424	−0.507118	−	0.861877i	$-0.669289\pi$
$811$	−1.01334e16	−1.01424	−0.507118	+	0.861877i	$0.669289\pi$
$812$	−3.34669e15	−0.332703
$813$	−1.24307e15	−0.122744
$814$	−8.76185e15	−0.859333
$815$	9.62822e14	0.0937949
$816$	5.45208e14	0.0527554
$817$	2.46218e16	2.36646
$818$	2.15396e16	2.05634
$819$	−6.58908e14	−0.0624832
$820$	4.55975e15	0.429501
$821$	−2.71594e15	−0.254116	−0.127058	−	0.991895i	$-0.540553\pi$
$821$	−2.71594e15	−0.254116	−0.127058	+	0.991895i	$0.540553\pi$
$822$	−2.29991e15	−0.213755
$823$	−2.37956e15	−0.219683	−0.109842	−	0.993949i	$-0.535034\pi$
$823$	−2.37956e15	−0.219683	−0.109842	+	0.993949i	$0.535034\pi$
$824$	1.01852e16	0.934047
$825$	9.99540e14	0.0910549
$826$	6.93181e15	0.627273
$827$	−1.53241e16	−1.37751	−0.688757	−	0.724992i	$-0.741843\pi$
$827$	−1.53241e16	−1.37751	−0.688757	+	0.724992i	$0.741843\pi$
$828$	−5.19203e15	−0.463629
$829$	6.12649e15	0.543453	0.271727	−	0.962375i	$-0.412405\pi$
$829$	6.12649e15	0.543453	0.271727	+	0.962375i	$0.412405\pi$
$830$	−1.47163e15	−0.129679
$831$	2.72268e15	0.238337
$832$	1.73981e16	1.51295
$833$	1.12501e16	0.971870
$834$	−9.74601e15	−0.836399
$835$	−6.42908e15	−0.548117
$836$	2.56667e16	2.17388
$837$	−3.92412e15	−0.330181
$838$	4.57866e15	0.382733
$839$	9.29081e15	0.771547	0.385774	−	0.922593i	$-0.373935\pi$
$839$	9.29081e15	0.771547	0.385774	+	0.922593i	$0.373935\pi$
$840$	5.84997e14	0.0482634
$841$	1.13184e15	0.0927697
$842$	1.71368e15	0.139545
$843$	−2.88633e15	−0.233504
$844$	−3.87991e16	−3.11844
$845$	−7.69430e14	−0.0614409
$846$	−3.91078e15	−0.310261
$847$	−9.68341e14	−0.0763255
$848$	−1.30142e15	−0.101915
$849$	−4.41177e15	−0.343258
$850$	−4.20780e15	−0.325276
$851$	7.79584e15	0.598756
$852$	1.35553e16	1.03441
$853$	−4.51480e15	−0.342310	−0.171155	−	0.985244i	$-0.554750\pi$
$853$	−4.51480e15	−0.342310	−0.171155	+	0.985244i	$0.554750\pi$
$854$	4.46825e15	0.336604
$855$	3.48171e15	0.260602
$856$	2.26197e15	0.168221
$857$	−1.35507e16	−1.00131	−0.500653	−	0.865648i	$-0.666907\pi$
$857$	−1.35507e16	−1.00131	−0.500653	+	0.865648i	$0.666907\pi$
$858$	−9.24516e15	−0.678788
$859$	−4.51231e15	−0.329182	−0.164591	−	0.986362i	$-0.552630\pi$
$859$	−4.51231e15	−0.329182	−0.164591	+	0.986362i	$0.552630\pi$
$860$	1.31701e16	0.954654
$861$	9.85295e14	0.0709658
$862$	−1.78876e16	−1.28015
$863$	1.85534e15	0.131937	0.0659683	−	0.997822i	$-0.478986\pi$
$863$	1.85534e15	0.131937	0.0659683	+	0.997822i	$0.478986\pi$
$864$	−2.91682e15	−0.206103
$865$	4.80647e15	0.337472
$866$	−4.23214e16	−2.95265
$867$	2.20277e14	0.0152709
$868$	−7.92657e15	−0.546043
$869$	−9.11417e15	−0.623890
$870$	−6.36982e15	−0.433283
$871$	−6.54454e15	−0.442364
$872$	1.06449e14	0.00714991
$873$	−8.61471e15	−0.574993
$874$	−3.73186e16	−2.47521
$875$	2.73883e14	0.0180518
$876$	4.60253e15	0.301456
$877$	−1.67204e16	−1.08830	−0.544150	−	0.838988i	$-0.683148\pi$
$877$	−1.67204e16	−1.08830	−0.544150	+	0.838988i	$0.683148\pi$
$878$	2.41403e16	1.56143
$879$	1.54068e16	0.990313
$880$	−4.97923e14	−0.0318059
$881$	−2.06898e16	−1.31337	−0.656687	−	0.754163i	$-0.728043\pi$
$881$	−2.06898e16	−1.31337	−0.656687	+	0.754163i	$0.728043\pi$
$882$	−8.13669e15	−0.513299
$883$	1.78687e16	1.12024	0.560118	−	0.828413i	$-0.310756\pi$
$883$	1.78687e16	1.12024	0.560118	+	0.828413i	$0.310756\pi$
$884$	2.38167e16	1.48386
$885$	8.07364e15	0.499898
$886$	3.78168e16	2.32702
$887$	−1.14519e16	−0.700323	−0.350161	−	0.936689i	$-0.613873\pi$
$887$	−1.14519e16	−0.700323	−0.350161	+	0.936689i	$0.613873\pi$
$888$	−5.97273e15	−0.362995
$889$	−3.17068e15	−0.191511
$890$	1.66308e16	0.998314
$891$	1.46865e15	0.0876176
$892$	−3.98206e16	−2.36103
$893$	−1.72014e16	−1.01363
$894$	3.11644e16	1.82516
$895$	2.44033e15	0.142044
$896$	−5.38677e15	−0.311626
$897$	8.22586e15	0.472958
$898$	1.31086e16	0.749094
$899$	3.15774e16	1.79349
$900$	1.86234e15	0.105130
$901$	−2.04050e16	−1.14485
$902$	1.38247e16	0.770938
$903$	2.84586e15	0.157736
$904$	1.56265e16	0.860865
$905$	1.07339e16	0.587745
$906$	−5.44725e15	−0.296464
$907$	2.79226e16	1.51048	0.755242	−	0.655447i	$-0.227520\pi$
$907$	2.79226e16	1.51048	0.755242	+	0.655447i	$0.227520\pi$
$908$	2.78623e16	1.49812
$909$	−5.43074e15	−0.290240
$910$	−2.53326e15	−0.134571
$911$	6.98498e15	0.368820	0.184410	−	0.982849i	$-0.440963\pi$
$911$	6.98498e15	0.368820	0.184410	+	0.982849i	$0.440963\pi$
$912$	−1.73442e15	−0.0910295
$913$	−2.73039e15	−0.142441
$914$	−5.98691e16	−3.10455
$915$	5.20428e15	0.268253
$916$	2.24146e15	0.114843
$917$	2.34780e15	0.119572
$918$	−6.18264e15	−0.312997
$919$	−7.45215e15	−0.375013	−0.187506	−	0.982263i	$-0.560041\pi$
$919$	−7.45215e15	−0.375013	−0.187506	+	0.982263i	$0.560041\pi$
$920$	−7.30315e15	−0.365323
$921$	1.23778e16	0.615480
$922$	1.61134e16	0.796467
$923$	−2.14760e16	−1.05522
$924$	2.96662e15	0.144899
$925$	−2.79631e15	−0.135770
$926$	−5.78553e16	−2.79243
$927$	7.00647e15	0.336172
$928$	2.34717e16	1.11952
$929$	6.90338e15	0.327322	0.163661	−	0.986517i	$-0.447670\pi$
$929$	6.90338e15	0.327322	0.163661	+	0.986517i	$0.447670\pi$
$930$	−1.50868e16	−0.711117
$931$	−3.57888e16	−1.67696
$932$	−3.48147e16	−1.62172
$933$	−5.30244e15	−0.245543
$934$	2.32336e16	1.06957
$935$	−7.80696e15	−0.357288
$936$	−6.30218e15	−0.286730
$937$	3.61273e16	1.63406	0.817030	−	0.576596i	$-0.195619\pi$
$937$	3.61273e16	1.63406	0.817030	+	0.576596i	$0.195619\pi$
$938$	3.43175e15	0.154312
$939$	1.05633e16	0.472215
$940$	−9.20089e15	−0.408909
$941$	2.07857e16	0.918380	0.459190	−	0.888338i	$-0.348140\pi$
$941$	2.07857e16	0.918380	0.459190	+	0.888338i	$0.348140\pi$
$942$	−6.93308e15	−0.304541
$943$	−1.23005e16	−0.537165
$944$	−4.02190e15	−0.174617
$945$	4.02425e14	0.0173704
$946$	3.99303e16	1.71357
$947$	3.77508e16	1.61065	0.805326	−	0.592833i	$-0.201990\pi$
$947$	3.77508e16	1.61065	0.805326	+	0.592833i	$0.201990\pi$
$948$	−1.69815e16	−0.720327
$949$	−7.29190e15	−0.307522
$950$	1.33859e16	0.561264
$951$	1.68093e15	0.0700741
$952$	−4.56915e15	−0.189379
$953$	2.01734e16	0.831319	0.415659	−	0.909520i	$-0.363551\pi$
$953$	2.01734e16	0.831319	0.415659	+	0.909520i	$0.363551\pi$
$954$	1.47580e16	0.604661
$955$	−3.82680e15	−0.155890
$956$	−7.67149e16	−3.10714
$957$	−1.18183e16	−0.475924
$958$	6.68765e16	2.67771
$959$	−1.16924e15	−0.0465479
$960$	−1.06258e16	−0.420601
$961$	4.93821e16	1.94353
$962$	2.58642e16	1.01213
$963$	1.55603e15	0.0605443
$964$	7.20668e15	0.278812
$965$	−1.44906e15	−0.0557425
$966$	−4.31338e15	−0.164985
$967$	−2.86737e15	−0.109053	−0.0545266	−	0.998512i	$-0.517365\pi$
$967$	−2.86737e15	−0.109053	−0.0545266	+	0.998512i	$0.517365\pi$
$968$	−9.26177e15	−0.350251
$969$	−2.71940e16	−1.02257
$970$	−3.31204e16	−1.23837
$971$	4.06331e16	1.51069	0.755344	−	0.655329i	$-0.227470\pi$
$971$	4.06331e16	1.51069	0.755344	+	0.655329i	$0.227470\pi$
$972$	2.73639e15	0.101161
$973$	−4.95472e15	−0.182137
$974$	4.47322e15	0.163511
$975$	−2.95055e15	−0.107245
$976$	−2.59252e15	−0.0937018
$977$	−4.73358e16	−1.70126	−0.850628	−	0.525768i	$-0.823778\pi$
$977$	−4.73358e16	−1.70126	−0.850628	+	0.525768i	$0.823778\pi$
$978$	5.43901e15	0.194382
$979$	3.08559e16	1.09656
$980$	−1.91432e16	−0.676505
$981$	7.32271e13	0.00257331
$982$	3.80817e16	1.33077
$983$	3.36593e16	1.16966	0.584831	−	0.811155i	$-0.301161\pi$
$983$	3.36593e16	1.16966	0.584831	+	0.811155i	$0.301161\pi$
$984$	9.42393e15	0.325656
$985$	−1.02185e16	−0.351147
$986$	4.97518e16	1.70014
$987$	−1.98818e15	−0.0675633
$988$	−7.57657e16	−2.56041
$989$	−3.55279e16	−1.19396
$990$	5.64643e15	0.188704
$991$	−4.96944e16	−1.65159	−0.825795	−	0.563970i	$-0.809273\pi$
$991$	−4.96944e16	−1.65159	−0.825795	+	0.563970i	$0.809273\pi$
$992$	5.55923e16	1.83738
$993$	−9.71314e15	−0.319256
$994$	1.12614e16	0.368100
$995$	2.69548e16	0.876211
$996$	−5.08725e15	−0.164459
$997$	6.41698e15	0.206304	0.103152	−	0.994666i	$-0.467107\pi$
$997$	6.41698e15	0.206304	0.103152	+	0.994666i	$0.467107\pi$
$998$	−4.23143e16	−1.35291
$999$	−4.10869e15	−0.130645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.12.a.d.1.3	✓	3
3.2	odd	2		45.12.a.f.1.1		3
4.3	odd	2		240.12.a.r.1.2		3
5.2	odd	4		75.12.b.e.49.5		6
5.3	odd	4		75.12.b.e.49.2		6
5.4	even	2		75.12.a.g.1.1		3
15.2	even	4		225.12.b.j.199.2		6
15.8	even	4		225.12.b.j.199.5		6
15.14	odd	2		225.12.a.l.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.12.a.d.1.3	✓	3	1.1	even	1	trivial
45.12.a.f.1.1		3	3.2	odd	2
75.12.a.g.1.1		3	5.4	even	2
75.12.b.e.49.2		6	5.3	odd	4
75.12.b.e.49.5		6	5.2	odd	4
225.12.a.l.1.3		3	15.14	odd	2
225.12.b.j.199.2		6	15.2	even	4
225.12.b.j.199.5		6	15.8	even	4
240.12.a.r.1.2		3	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q+72.6470 q^{2} +243.000 q^{3} +3229.58 q^{4} +3125.00 q^{5} +17653.2 q^{6} +8974.61 q^{7} +85838.4 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+72.6470 q^{2} +243.000 q^{3} +3229.58 q^{4} +3125.00 q^{5} +17653.2 q^{6} +8974.61 q^{7} +85838.4 q^{8} +59049.0 q^{9} +227022. q^{10} +421205. q^{11} +784789. q^{12} -1.24336e6 q^{13} +651979. q^{14} +759375. q^{15} -378284. q^{16} -5.93114e6 q^{17} +4.28973e6 q^{18} +1.88682e7 q^{19} +1.00924e7 q^{20} +2.18083e6 q^{21} +3.05993e7 q^{22} -2.72256e7 q^{23} +2.08587e7 q^{24} +9.76562e6 q^{25} -9.03263e7 q^{26} +1.43489e7 q^{27} +2.89843e7 q^{28} -1.15466e8 q^{29} +5.51663e7 q^{30} -2.73479e8 q^{31} -2.03278e8 q^{32} +1.02353e8 q^{33} -4.30879e8 q^{34} +2.80457e7 q^{35} +1.90704e8 q^{36} -2.86342e8 q^{37} +1.37071e9 q^{38} -3.02136e8 q^{39} +2.68245e8 q^{40} +4.51798e8 q^{41} +1.58431e8 q^{42} +1.30494e9 q^{43} +1.36032e9 q^{44} +1.84528e8 q^{45} -1.97786e9 q^{46} -9.11661e8 q^{47} -9.19231e7 q^{48} -1.89678e9 q^{49} +7.09443e8 q^{50} -1.44127e9 q^{51} -4.01553e9 q^{52} +3.44031e9 q^{53} +1.04240e9 q^{54} +1.31627e9 q^{55} +7.70367e8 q^{56} +4.58496e9 q^{57} -8.38824e9 q^{58} +1.06320e10 q^{59} +2.45246e9 q^{60} +6.85337e9 q^{61} -1.98674e10 q^{62} +5.29942e8 q^{63} -1.39928e10 q^{64} -3.88550e9 q^{65} +7.43563e9 q^{66} +5.26360e9 q^{67} -1.91551e10 q^{68} -6.61583e9 q^{69} +2.03743e9 q^{70} +1.72726e10 q^{71} +5.06867e9 q^{72} +5.86468e9 q^{73} -2.08019e10 q^{74} +2.37305e9 q^{75} +6.09363e10 q^{76} +3.78015e9 q^{77} -2.19493e10 q^{78} -2.16383e10 q^{79} -1.18214e9 q^{80} +3.48678e9 q^{81} +3.28217e10 q^{82} -6.48232e9 q^{83} +7.04317e9 q^{84} -1.85348e10 q^{85} +9.48001e10 q^{86} -2.80582e10 q^{87} +3.61556e10 q^{88} +7.32562e10 q^{89} +1.34054e10 q^{90} -1.11587e10 q^{91} -8.79275e10 q^{92} -6.64553e10 q^{93} -6.62294e10 q^{94} +5.89630e10 q^{95} -4.93966e10 q^{96} -1.45891e11 q^{97} -1.37796e11 q^{98} +2.48718e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 729 q^{3} + 4757 q^{4} + 9375 q^{5} - 243 q^{6} - 14608 q^{7} - 33999 q^{8} + 177147 q^{9}+O(q^{10}) \) 3 * q - q^2 + 729 * q^3 + 4757 * q^4 + 9375 * q^5 - 243 * q^6 - 14608 * q^7 - 33999 * q^8 + 177147 * q^9	\( 3 q - q^{2} + 729 q^{3} + 4757 q^{4} + 9375 q^{5} - 243 q^{6} - 14608 q^{7} - 33999 q^{8} + 177147 q^{9} - 3125 q^{10} + 540620 q^{11} + 1155951 q^{12} + 840970 q^{13} + 5432712 q^{14} + 2278125 q^{15} + 5062961 q^{16} + 15165038 q^{17} - 59049 q^{18} + 17743756 q^{19} + 14865625 q^{20} - 3549744 q^{21} + 11176076 q^{22} - 28140816 q^{23} - 8261757 q^{24} + 29296875 q^{25} - 52021894 q^{26} + 43046721 q^{27} - 277157944 q^{28} - 67382798 q^{29} - 759375 q^{30} - 206919496 q^{31} - 46592663 q^{32} + 131370660 q^{33} - 1230469666 q^{34} - 45650000 q^{35} + 280896093 q^{36} - 318337278 q^{37} + 653190692 q^{38} + 204355710 q^{39} - 106246875 q^{40} + 2110085854 q^{41} + 1320149016 q^{42} + 418259692 q^{43} + 2558131108 q^{44} + 553584375 q^{45} - 137169096 q^{46} - 1599668584 q^{47} + 1230299523 q^{48} - 316107077 q^{49} - 9765625 q^{50} + 3685104234 q^{51} - 10897289202 q^{52} + 4489142234 q^{53} - 14348907 q^{54} + 1689437500 q^{55} + 7768845960 q^{56} + 4311732708 q^{57} - 24168830726 q^{58} + 11102167484 q^{59} + 3612346875 q^{60} - 3568120958 q^{61} - 35509109136 q^{62} - 862587792 q^{63} - 35608208271 q^{64} + 2628031250 q^{65} + 2715786468 q^{66} + 2229942788 q^{67} - 1367872838 q^{68} - 6838218288 q^{69} + 16977225000 q^{70} + 49842766696 q^{71} - 2007606951 q^{72} + 40752219934 q^{73} - 37519971278 q^{74} + 7119140625 q^{75} + 115970329116 q^{76} - 17819224896 q^{77} - 12641320242 q^{78} + 113159960 q^{79} + 15821753125 q^{80} + 10460353203 q^{81} - 30171431066 q^{82} + 6259660308 q^{83} - 67349380392 q^{84} + 47390743750 q^{85} + 114296127740 q^{86} - 16374019914 q^{87} + 7548672276 q^{88} - 59972401554 q^{89} - 184528125 q^{90} + 118873361824 q^{91} - 221705928648 q^{92} - 50281437528 q^{93} + 92816682800 q^{94} + 55449237500 q^{95} - 11322017109 q^{96} - 207831285882 q^{97} - 288264739625 q^{98} + 31923070380 q^{99}+O(q^{100}) \) 3 * q - q^2 + 729 * q^3 + 4757 * q^4 + 9375 * q^5 - 243 * q^6 - 14608 * q^7 - 33999 * q^8 + 177147 * q^9 - 3125 * q^10 + 540620 * q^11 + 1155951 * q^12 + 840970 * q^13 + 5432712 * q^14 + 2278125 * q^15 + 5062961 * q^16 + 15165038 * q^17 - 59049 * q^18 + 17743756 * q^19 + 14865625 * q^20 - 3549744 * q^21 + 11176076 * q^22 - 28140816 * q^23 - 8261757 * q^24 + 29296875 * q^25 - 52021894 * q^26 + 43046721 * q^27 - 277157944 * q^28 - 67382798 * q^29 - 759375 * q^30 - 206919496 * q^31 - 46592663 * q^32 + 131370660 * q^33 - 1230469666 * q^34 - 45650000 * q^35 + 280896093 * q^36 - 318337278 * q^37 + 653190692 * q^38 + 204355710 * q^39 - 106246875 * q^40 + 2110085854 * q^41 + 1320149016 * q^42 + 418259692 * q^43 + 2558131108 * q^44 + 553584375 * q^45 - 137169096 * q^46 - 1599668584 * q^47 + 1230299523 * q^48 - 316107077 * q^49 - 9765625 * q^50 + 3685104234 * q^51 - 10897289202 * q^52 + 4489142234 * q^53 - 14348907 * q^54 + 1689437500 * q^55 + 7768845960 * q^56 + 4311732708 * q^57 - 24168830726 * q^58 + 11102167484 * q^59 + 3612346875 * q^60 - 3568120958 * q^61 - 35509109136 * q^62 - 862587792 * q^63 - 35608208271 * q^64 + 2628031250 * q^65 + 2715786468 * q^66 + 2229942788 * q^67 - 1367872838 * q^68 - 6838218288 * q^69 + 16977225000 * q^70 + 49842766696 * q^71 - 2007606951 * q^72 + 40752219934 * q^73 - 37519971278 * q^74 + 7119140625 * q^75 + 115970329116 * q^76 - 17819224896 * q^77 - 12641320242 * q^78 + 113159960 * q^79 + 15821753125 * q^80 + 10460353203 * q^81 - 30171431066 * q^82 + 6259660308 * q^83 - 67349380392 * q^84 + 47390743750 * q^85 + 114296127740 * q^86 - 16374019914 * q^87 + 7548672276 * q^88 - 59972401554 * q^89 - 184528125 * q^90 + 118873361824 * q^91 - 221705928648 * q^92 - 50281437528 * q^93 + 92816682800 * q^94 + 55449237500 * q^95 - 11322017109 * q^96 - 207831285882 * q^97 - 288264739625 * q^98 + 31923070380 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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