LMFDB - Embedded newform 15.12.a.b.1.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1609}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 402 $ x^2 - x - 402
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$20.5562$ 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)

$f(q)$	$=$	$q-51.1123 q^{2} +243.000 q^{3} +564.472 q^{4} -3125.00 q^{5} -12420.3 q^{6} +45751.3 q^{7} +75826.6 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-51.1123 q^{2} +243.000 q^{3} +564.472 q^{4} -3125.00 q^{5} -12420.3 q^{6} +45751.3 q^{7} +75826.6 q^{8} +59049.0 q^{9} +159726. q^{10} -597423. q^{11} +137167. q^{12} -990011. q^{13} -2.33846e6 q^{14} -759375. q^{15} -5.03171e6 q^{16} -6.61148e6 q^{17} -3.01813e6 q^{18} +576856. q^{19} -1.76397e6 q^{20} +1.11176e7 q^{21} +3.05357e7 q^{22} -4.64840e7 q^{23} +1.84259e7 q^{24} +9.76562e6 q^{25} +5.06018e7 q^{26} +1.43489e7 q^{27} +2.58253e7 q^{28} -1.59099e8 q^{29} +3.88134e7 q^{30} +1.04664e8 q^{31} +1.01890e8 q^{32} -1.45174e8 q^{33} +3.37928e8 q^{34} -1.42973e8 q^{35} +3.33315e7 q^{36} +4.80096e8 q^{37} -2.94845e7 q^{38} -2.40573e8 q^{39} -2.36958e8 q^{40} +6.63154e8 q^{41} -5.68245e8 q^{42} -1.76838e9 q^{43} -3.37228e8 q^{44} -1.84528e8 q^{45} +2.37591e9 q^{46} -1.39342e9 q^{47} -1.22271e9 q^{48} +1.15859e8 q^{49} -4.99144e8 q^{50} -1.60659e9 q^{51} -5.58833e8 q^{52} -2.28338e9 q^{53} -7.33406e8 q^{54} +1.86695e9 q^{55} +3.46917e9 q^{56} +1.40176e8 q^{57} +8.13193e9 q^{58} +3.12820e9 q^{59} -4.28646e8 q^{60} +6.71630e9 q^{61} -5.34962e9 q^{62} +2.70157e9 q^{63} +5.09713e9 q^{64} +3.09378e9 q^{65} +7.42017e9 q^{66} -5.93071e9 q^{67} -3.73199e9 q^{68} -1.12956e10 q^{69} +7.30768e9 q^{70} -1.13022e10 q^{71} +4.47749e9 q^{72} -9.39160e9 q^{73} -2.45388e10 q^{74} +2.37305e9 q^{75} +3.25619e8 q^{76} -2.73329e10 q^{77} +1.22962e10 q^{78} -3.59922e10 q^{79} +1.57241e10 q^{80} +3.48678e9 q^{81} -3.38953e10 q^{82} +6.01074e10 q^{83} +6.27556e9 q^{84} +2.06609e10 q^{85} +9.03863e10 q^{86} -3.86611e10 q^{87} -4.53005e10 q^{88} -1.46902e9 q^{89} +9.43166e9 q^{90} -4.52943e10 q^{91} -2.62389e10 q^{92} +2.54333e10 q^{93} +7.12210e10 q^{94} -1.80268e9 q^{95} +2.47592e10 q^{96} -7.50721e10 q^{97} -5.92183e9 q^{98} -3.52772e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 22 q^{2} + 486 q^{3} - 636 q^{4} - 6250 q^{5} - 5346 q^{6} - 10864 q^{7} - 18744 q^{8} + 118098 q^{9}+O(q^{10}) $ 2 * q - 22 * q^2 + 486 * q^3 - 636 * q^4 - 6250 * q^5 - 5346 * q^6 - 10864 * q^7 - 18744 * q^8 + 118098 * q^9	\( 2 q - 22 q^{2} + 486 q^{3} - 636 q^{4} - 6250 q^{5} - 5346 q^{6} - 10864 q^{7} - 18744 q^{8} + 118098 q^{9} + 68750 q^{10} - 361792 q^{11} - 154548 q^{12} - 2133732 q^{13} - 3986664 q^{14} - 1518750 q^{15} - 5326320 q^{16} - 7804588 q^{17} - 1299078 q^{18} - 15562224 q^{19} + 1987500 q^{20} - 2639952 q^{21} + 37395424 q^{22} - 37450248 q^{23} - 4554792 q^{24} + 19531250 q^{25} + 17305364 q^{26} + 28697814 q^{27} + 93790448 q^{28} - 70320668 q^{29} + 16706250 q^{30} + 298584872 q^{31} + 286993696 q^{32} - 87915456 q^{33} + 303194188 q^{34} + 33950000 q^{35} - 37555164 q^{36} + 236000956 q^{37} - 499330888 q^{38} - 518496876 q^{39} + 58575000 q^{40} - 464942588 q^{41} - 968759352 q^{42} - 242208600 q^{43} - 620095808 q^{44} - 369056250 q^{45} + 2638898832 q^{46} - 4375796920 q^{47} - 1294295760 q^{48} + 1343830130 q^{49} - 214843750 q^{50} - 1896514884 q^{51} + 814171912 q^{52} - 2189541388 q^{53} - 315675954 q^{54} + 1130600000 q^{55} + 8823318240 q^{56} - 3781620432 q^{57} + 10716478004 q^{58} - 5480385856 q^{59} + 482962500 q^{60} + 14557903980 q^{61} + 295874592 q^{62} - 641508336 q^{63} + 11089288256 q^{64} + 6667912500 q^{65} + 9087088032 q^{66} - 15918388888 q^{67} - 2299702856 q^{68} - 9100410264 q^{69} + 12458325000 q^{70} + 1120561024 q^{71} - 1106814456 q^{72} - 24521574348 q^{73} - 31645012364 q^{74} + 4746093750 q^{75} + 19700124976 q^{76} - 40673194368 q^{77} + 4205203452 q^{78} - 79243055560 q^{79} + 16644750000 q^{80} + 6973568802 q^{81} - 66736852348 q^{82} + 9245226696 q^{83} + 22791078864 q^{84} + 24389337500 q^{85} + 134816793608 q^{86} - 17087922324 q^{87} - 67584257664 q^{88} + 22117321236 q^{89} + 4059618750 q^{90} + 19457850112 q^{91} - 37083635424 q^{92} + 72556123896 q^{93} - 15603010256 q^{94} + 48631950000 q^{95} + 69739468128 q^{96} - 160363673468 q^{97} + 29827277722 q^{98} - 21363455808 q^{99}+O(q^{100}) \) 2 * q - 22 * q^2 + 486 * q^3 - 636 * q^4 - 6250 * q^5 - 5346 * q^6 - 10864 * q^7 - 18744 * q^8 + 118098 * q^9 + 68750 * q^10 - 361792 * q^11 - 154548 * q^12 - 2133732 * q^13 - 3986664 * q^14 - 1518750 * q^15 - 5326320 * q^16 - 7804588 * q^17 - 1299078 * q^18 - 15562224 * q^19 + 1987500 * q^20 - 2639952 * q^21 + 37395424 * q^22 - 37450248 * q^23 - 4554792 * q^24 + 19531250 * q^25 + 17305364 * q^26 + 28697814 * q^27 + 93790448 * q^28 - 70320668 * q^29 + 16706250 * q^30 + 298584872 * q^31 + 286993696 * q^32 - 87915456 * q^33 + 303194188 * q^34 + 33950000 * q^35 - 37555164 * q^36 + 236000956 * q^37 - 499330888 * q^38 - 518496876 * q^39 + 58575000 * q^40 - 464942588 * q^41 - 968759352 * q^42 - 242208600 * q^43 - 620095808 * q^44 - 369056250 * q^45 + 2638898832 * q^46 - 4375796920 * q^47 - 1294295760 * q^48 + 1343830130 * q^49 - 214843750 * q^50 - 1896514884 * q^51 + 814171912 * q^52 - 2189541388 * q^53 - 315675954 * q^54 + 1130600000 * q^55 + 8823318240 * q^56 - 3781620432 * q^57 + 10716478004 * q^58 - 5480385856 * q^59 + 482962500 * q^60 + 14557903980 * q^61 + 295874592 * q^62 - 641508336 * q^63 + 11089288256 * q^64 + 6667912500 * q^65 + 9087088032 * q^66 - 15918388888 * q^67 - 2299702856 * q^68 - 9100410264 * q^69 + 12458325000 * q^70 + 1120561024 * q^71 - 1106814456 * q^72 - 24521574348 * q^73 - 31645012364 * q^74 + 4746093750 * q^75 + 19700124976 * q^76 - 40673194368 * q^77 + 4205203452 * q^78 - 79243055560 * q^79 + 16644750000 * q^80 + 6973568802 * q^81 - 66736852348 * q^82 + 9245226696 * q^83 + 22791078864 * q^84 + 24389337500 * q^85 + 134816793608 * q^86 - 17087922324 * q^87 - 67584257664 * q^88 + 22117321236 * q^89 + 4059618750 * q^90 + 19457850112 * q^91 - 37083635424 * q^92 + 72556123896 * q^93 - 15603010256 * q^94 + 48631950000 * q^95 + 69739468128 * q^96 - 160363673468 * q^97 + 29827277722 * q^98 - 21363455808 * 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 $

$2$	−51.1123	−1.12943	−0.564717	−	0.825285i	$-0.691015\pi$
$2$	−51.1123	−1.12943	−0.564717	+	0.825285i	$0.691015\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	564.472	0.275621
$5$	−3125.00	−0.447214
$5$	−3125.00	−0.447214
$6$	−12420.3	−0.652079
$7$	45751.3	1.02888	0.514440	−	0.857526i	$-0.328000\pi$
$7$	45751.3	1.02888	0.514440	+	0.857526i	$0.328000\pi$
$8$	75826.6	0.818138
$9$	59049.0	0.333333
$10$	159726.	0.505098
$11$	−597423.	−1.11846	−0.559232	−	0.829011i	$-0.688904\pi$
$11$	−597423.	−1.11846	−0.559232	+	0.829011i	$0.688904\pi$
$12$	137167.	0.159130
$13$	−990011.	−0.739523	−0.369761	−	0.929127i	$-0.620561\pi$
$13$	−990011.	−0.739523	−0.369761	+	0.929127i	$0.620561\pi$
$14$	−2.33846e6	−1.16205
$15$	−759375.	−0.258199
$16$	−5.03171e6	−1.19965
$17$	−6.61148e6	−1.12935	−0.564677	−	0.825312i	$-0.690999\pi$
$17$	−6.61148e6	−1.12935	−0.564677	+	0.825312i	$0.690999\pi$
$18$	−3.01813e6	−0.376478
$19$	576856.	0.0534469	0.0267235	−	0.999643i	$-0.491493\pi$
$19$	576856.	0.0534469	0.0267235	+	0.999643i	$0.491493\pi$
$20$	−1.76397e6	−0.123261
$21$	1.11176e7	0.594024
$22$	3.05357e7	1.26323
$23$	−4.64840e7	−1.50591	−0.752957	−	0.658069i	$-0.771373\pi$
$23$	−4.64840e7	−1.50591	−0.752957	+	0.658069i	$0.771373\pi$
$24$	1.84259e7	0.472352
$25$	9.76562e6	0.200000
$26$	5.06018e7	0.835242
$27$	1.43489e7	0.192450
$28$	2.58253e7	0.283581
$29$	−1.59099e8	−1.44039	−0.720193	−	0.693774i	$-0.755947\pi$
$29$	−1.59099e8	−1.44039	−0.720193	+	0.693774i	$0.755947\pi$
$30$	3.88134e7	0.291619
$31$	1.04664e8	0.656610	0.328305	−	0.944572i	$-0.393523\pi$
$31$	1.04664e8	0.656610	0.328305	+	0.944572i	$0.393523\pi$
$32$	1.01890e8	0.536792
$33$	−1.45174e8	−0.645745
$34$	3.37928e8	1.27553
$35$	−1.42973e8	−0.460129
$36$	3.33315e7	0.0918736
$37$	4.80096e8	1.13820	0.569100	−	0.822268i	$-0.307292\pi$
$37$	4.80096e8	1.13820	0.569100	+	0.822268i	$0.307292\pi$
$38$	−2.94845e7	−0.0603648
$39$	−2.40573e8	−0.426964
$40$	−2.36958e8	−0.365883
$41$	6.63154e8	0.893929	0.446964	−	0.894552i	$-0.352505\pi$
$41$	6.63154e8	0.893929	0.446964	+	0.894552i	$0.352505\pi$
$42$	−5.68245e8	−0.670911
$43$	−1.76838e9	−1.83443	−0.917213	−	0.398398i	$-0.869566\pi$
$43$	−1.76838e9	−1.83443	−0.917213	+	0.398398i	$0.869566\pi$
$44$	−3.37228e8	−0.308272
$45$	−1.84528e8	−0.149071
$46$	2.37591e9	1.70083
$47$	−1.39342e9	−0.886225	−0.443112	−	0.896466i	$-0.646126\pi$
$47$	−1.39342e9	−0.886225	−0.443112	+	0.896466i	$0.646126\pi$
$48$	−1.22271e9	−0.692621
$49$	1.15859e8	0.0585938
$50$	−4.99144e8	−0.225887
$51$	−1.60659e9	−0.652032
$52$	−5.58833e8	−0.203828
$53$	−2.28338e9	−0.749998	−0.374999	−	0.927025i	$-0.622357\pi$
$53$	−2.28338e9	−0.749998	−0.374999	+	0.927025i	$0.622357\pi$
$54$	−7.33406e8	−0.217360
$55$	1.86695e9	0.500192
$56$	3.46917e9	0.841766
$57$	1.40176e8	0.0308576
$58$	8.13193e9	1.62682
$59$	3.12820e9	0.569650	0.284825	−	0.958580i	$-0.408064\pi$
$59$	3.12820e9	0.569650	0.284825	+	0.958580i	$0.408064\pi$
$60$	−4.28646e8	−0.0711650
$61$	6.71630e9	1.01816	0.509080	−	0.860719i	$-0.329986\pi$
$61$	6.71630e9	1.01816	0.509080	+	0.860719i	$0.329986\pi$
$62$	−5.34962e9	−0.741598
$63$	2.70157e9	0.342960
$64$	5.09713e9	0.593383
$65$	3.09378e9	0.330725
$66$	7.42017e9	0.729327
$67$	−5.93071e9	−0.536655	−0.268328	−	0.963328i	$-0.586471\pi$
$67$	−5.93071e9	−0.536655	−0.268328	+	0.963328i	$0.586471\pi$
$68$	−3.73199e9	−0.311273
$69$	−1.12956e10	−0.869440
$70$	7.30768e9	0.519685
$71$	−1.13022e10	−0.743430	−0.371715	−	0.928347i	$-0.621230\pi$
$71$	−1.13022e10	−0.743430	−0.371715	+	0.928347i	$0.621230\pi$
$72$	4.47749e9	0.272713
$73$	−9.39160e9	−0.530229	−0.265115	−	0.964217i	$-0.585410\pi$
$73$	−9.39160e9	−0.530229	−0.265115	+	0.964217i	$0.585410\pi$
$74$	−2.45388e10	−1.28552
$75$	2.37305e9	0.115470
$76$	3.25619e8	0.0147311
$77$	−2.73329e10	−1.15076
$78$	1.22962e10	0.482227
$79$	−3.59922e10	−1.31601	−0.658006	−	0.753013i	$-0.728600\pi$
$79$	−3.59922e10	−1.31601	−0.658006	+	0.753013i	$0.728600\pi$
$80$	1.57241e10	0.536502
$81$	3.48678e9	0.111111
$82$	−3.38953e10	−1.00963
$83$	6.01074e10	1.67494	0.837468	−	0.546486i	$-0.184035\pi$
$83$	6.01074e10	1.67494	0.837468	+	0.546486i	$0.184035\pi$
$84$	6.27556e9	0.163725
$85$	2.06609e10	0.505062
$86$	9.03863e10	2.07186
$87$	−3.86611e10	−0.831607
$88$	−4.53005e10	−0.915058
$89$	−1.46902e9	−0.0278858	−0.0139429	−	0.999903i	$-0.504438\pi$
$89$	−1.46902e9	−0.0278858	−0.0139429	+	0.999903i	$0.504438\pi$
$90$	9.43166e9	0.168366
$91$	−4.52943e10	−0.760880
$92$	−2.62389e10	−0.415061
$93$	2.54333e10	0.379094
$94$	7.12210e10	1.00093
$95$	−1.80268e9	−0.0239022
$96$	2.47592e10	0.309917
$97$	−7.50721e10	−0.887634	−0.443817	−	0.896117i	$-0.646376\pi$
$97$	−7.50721e10	−0.887634	−0.443817	+	0.896117i	$0.646376\pi$
$98$	−5.92183e9	−0.0661779
$99$	−3.52772e10	−0.372821
$100$	5.51242e9	0.0551242
$101$	1.66482e11	1.57615	0.788077	−	0.615577i	$-0.211077\pi$
$101$	1.66482e11	1.57615	0.788077	+	0.615577i	$0.211077\pi$
$102$	8.21166e10	0.736427
$103$	−1.56404e11	−1.32937	−0.664683	−	0.747126i	$-0.731433\pi$
$103$	−1.56404e11	−1.32937	−0.664683	+	0.747126i	$0.731433\pi$
$104$	−7.50692e10	−0.605032
$105$	−3.47424e10	−0.265656
$106$	1.16709e11	0.847073
$107$	1.72482e11	1.18887	0.594435	−	0.804144i	$-0.297376\pi$
$107$	1.72482e11	1.18887	0.594435	+	0.804144i	$0.297376\pi$
$108$	8.09955e9	0.0530433
$109$	1.98239e11	1.23408	0.617041	−	0.786931i	$-0.288331\pi$
$109$	1.98239e11	1.23408	0.617041	+	0.786931i	$0.288331\pi$
$110$	−9.54240e10	−0.564934
$111$	1.16663e11	0.657140
$112$	−2.30208e11	−1.23430
$113$	−6.00761e10	−0.306740	−0.153370	−	0.988169i	$-0.549013\pi$
$113$	−6.00761e10	−0.306740	−0.153370	+	0.988169i	$0.549013\pi$
$114$	−7.16473e9	−0.0348516
$115$	1.45262e11	0.673465
$116$	−8.98069e10	−0.397000
$117$	−5.84591e10	−0.246508
$118$	−1.59890e11	−0.643382
$119$	−3.02484e11	−1.16197
$120$	−5.75808e10	−0.211242
$121$	7.16020e10	0.250961
$122$	−3.43286e11	−1.14994
$123$	1.61146e11	0.516110
$124$	5.90798e10	0.180976
$125$	−3.05176e10	−0.0894427
$126$	−1.38084e11	−0.387351
$127$	6.55120e11	1.75954	0.879772	−	0.475395i	$-0.157695\pi$
$127$	6.55120e11	1.75954	0.879772	+	0.475395i	$0.157695\pi$
$128$	−4.69196e11	−1.20698
$129$	−4.29717e11	−1.05911
$130$	−1.58131e11	−0.373532
$131$	−2.51548e11	−0.569677	−0.284839	−	0.958575i	$-0.591940\pi$
$131$	−2.51548e11	−0.569677	−0.284839	+	0.958575i	$0.591940\pi$
$132$	−8.19464e10	−0.177981
$133$	2.63919e10	0.0549905
$134$	3.03132e11	0.606116
$135$	−4.48403e10	−0.0860663
$136$	−5.01326e11	−0.923967
$137$	9.65207e11	1.70867	0.854334	−	0.519725i	$-0.173966\pi$
$137$	9.65207e11	1.70867	0.854334	+	0.519725i	$0.173966\pi$
$138$	5.77345e11	0.981975
$139$	9.65084e11	1.57755	0.788776	−	0.614681i	$-0.210715\pi$
$139$	9.65084e11	1.57755	0.788776	+	0.614681i	$0.210715\pi$
$140$	−8.07042e10	−0.126821
$141$	−3.38601e11	−0.511662
$142$	5.77679e11	0.839655
$143$	5.91455e11	0.827129
$144$	−2.97118e11	−0.399885
$145$	4.97185e11	0.644160
$146$	4.80027e11	0.598859
$147$	2.81538e10	0.0338292
$148$	2.71001e11	0.313712
$149$	−2.87526e11	−0.320740	−0.160370	−	0.987057i	$-0.551269\pi$
$149$	−2.87526e11	−0.320740	−0.160370	+	0.987057i	$0.551269\pi$
$150$	−1.21292e11	−0.130416
$151$	−1.58923e12	−1.64745	−0.823725	−	0.566989i	$-0.808108\pi$
$151$	−1.58923e12	−1.64745	−0.823725	+	0.566989i	$0.808108\pi$
$152$	4.37410e10	0.0437270
$153$	−3.90401e11	−0.376451
$154$	1.39705e12	1.29971
$155$	−3.27075e11	−0.293645
$156$	−1.35796e11	−0.117680
$157$	−9.15249e11	−0.765757	−0.382879	−	0.923799i	$-0.625067\pi$
$157$	−9.15249e11	−0.765757	−0.382879	+	0.923799i	$0.625067\pi$
$158$	1.83965e12	1.48635
$159$	−5.54861e11	−0.433012
$160$	−3.18405e11	−0.240060
$161$	−2.12671e12	−1.54941
$162$	−1.78218e11	−0.125493
$163$	5.95458e11	0.405340	0.202670	−	0.979247i	$-0.435038\pi$
$163$	5.95458e11	0.405340	0.202670	+	0.979247i	$0.435038\pi$
$164$	3.74331e11	0.246385
$165$	4.53668e11	0.288786
$166$	−3.07223e12	−1.89173
$167$	−2.27609e11	−0.135597	−0.0677983	−	0.997699i	$-0.521597\pi$
$167$	−2.27609e11	−0.135597	−0.0677983	+	0.997699i	$0.521597\pi$
$168$	8.43008e11	0.485994
$169$	−8.12039e11	−0.453106
$170$	−1.05603e12	−0.570434
$171$	3.40628e10	0.0178156
$172$	−9.98202e11	−0.505606
$173$	−3.94129e12	−1.93368	−0.966841	−	0.255380i	$-0.917800\pi$
$173$	−3.94129e12	−1.93368	−0.966841	+	0.255380i	$0.917800\pi$
$174$	1.97606e12	0.939245
$175$	4.46791e11	0.205776
$176$	3.00606e12	1.34177
$177$	7.60152e11	0.328888
$178$	7.50850e10	0.0314951
$179$	−6.63949e11	−0.270049	−0.135025	−	0.990842i	$-0.543111\pi$
$179$	−6.63949e11	−0.270049	−0.135025	+	0.990842i	$0.543111\pi$
$180$	−1.04161e11	−0.0410871
$181$	2.97961e12	1.14006	0.570029	−	0.821625i	$-0.306932\pi$
$181$	2.97961e12	1.14006	0.570029	+	0.821625i	$0.306932\pi$
$182$	2.31510e12	0.859364
$183$	1.63206e12	0.587835
$184$	−3.52472e12	−1.23205
$185$	−1.50030e12	−0.509019
$186$	−1.29996e12	−0.428162
$187$	3.94985e12	1.26314
$188$	−7.86546e11	−0.244262
$189$	6.56482e11	0.198008
$190$	9.21390e10	0.0269959
$191$	2.39137e12	0.680713	0.340356	−	0.940296i	$-0.389452\pi$
$191$	2.39137e12	0.680713	0.340356	+	0.940296i	$0.389452\pi$
$192$	1.23860e12	0.342590
$193$	−3.54987e12	−0.954217	−0.477108	−	0.878845i	$-0.658315\pi$
$193$	−3.54987e12	−0.954217	−0.477108	+	0.878845i	$0.658315\pi$
$194$	3.83711e12	1.00252
$195$	7.51789e11	0.190944
$196$	6.53992e10	0.0161497
$197$	2.10097e12	0.504493	0.252246	−	0.967663i	$-0.418831\pi$
$197$	2.10097e12	0.504493	0.252246	+	0.967663i	$0.418831\pi$
$198$	1.80310e12	0.421077
$199$	1.38114e12	0.313722	0.156861	−	0.987621i	$-0.449863\pi$
$199$	1.38114e12	0.313722	0.156861	+	0.987621i	$0.449863\pi$
$200$	7.40494e11	0.163628
$201$	−1.44116e12	−0.309838
$202$	−8.50926e12	−1.78016
$203$	−7.27900e12	−1.48198
$204$	−9.06874e11	−0.179714
$205$	−2.07235e12	−0.399777
$206$	7.99420e12	1.50143
$207$	−2.74483e12	−0.501971
$208$	4.98145e12	0.887171
$209$	−3.44627e11	−0.0597784
$210$	1.77577e12	0.300040
$211$	5.03751e12	0.829205	0.414603	−	0.910003i	$-0.363921\pi$
$211$	5.03751e12	0.829205	0.414603	+	0.910003i	$0.363921\pi$
$212$	−1.28890e12	−0.206715
$213$	−2.74642e12	−0.429220
$214$	−8.81598e12	−1.34275
$215$	5.52620e12	0.820380
$216$	1.08803e12	0.157451
$217$	4.78852e12	0.675573
$218$	−1.01325e13	−1.39381
$219$	−2.28216e12	−0.306128
$220$	1.05384e12	0.137863
$221$	6.54544e12	0.835182
$222$	−5.96294e12	−0.742196
$223$	1.54066e13	1.87081	0.935403	−	0.353583i	$-0.115037\pi$
$223$	1.54066e13	1.87081	0.935403	+	0.353583i	$0.115037\pi$
$224$	4.66159e12	0.552294
$225$	5.76650e11	0.0666667
$226$	3.07063e12	0.346442
$227$	−3.09266e12	−0.340557	−0.170279	−	0.985396i	$-0.554467\pi$
$227$	−3.09266e12	−0.340557	−0.170279	+	0.985396i	$0.554467\pi$
$228$	7.91254e10	0.00850500
$229$	−1.18942e13	−1.24808	−0.624039	−	0.781393i	$-0.714509\pi$
$229$	−1.18942e13	−1.24808	−0.624039	+	0.781393i	$0.714509\pi$
$230$	−7.42470e12	−0.760635
$231$	−6.64189e12	−0.664394
$232$	−1.20639e13	−1.17843
$233$	−1.95406e13	−1.86415	−0.932075	−	0.362267i	$-0.882003\pi$
$233$	−1.95406e13	−1.86415	−0.932075	+	0.362267i	$0.882003\pi$
$234$	2.98798e12	0.278414
$235$	4.35444e12	0.396332
$236$	1.76578e12	0.157007
$237$	−8.74611e12	−0.759800
$238$	1.54607e13	1.31237
$239$	4.39049e12	0.364187	0.182093	−	0.983281i	$-0.441713\pi$
$239$	4.39049e12	0.364187	0.182093	+	0.983281i	$0.441713\pi$
$240$	3.82096e12	0.309749
$241$	−9.72399e12	−0.770461	−0.385231	−	0.922820i	$-0.625878\pi$
$241$	−9.72399e12	−0.770461	−0.385231	+	0.922820i	$0.625878\pi$
$242$	−3.65975e12	−0.283444
$243$	8.47289e11	0.0641500
$244$	3.79116e12	0.280626
$245$	−3.62060e11	−0.0262040
$246$	−8.23657e12	−0.582912
$247$	−5.71094e11	−0.0395252
$248$	7.93631e12	0.537198
$249$	1.46061e13	0.967025
$250$	1.55982e12	0.101020
$251$	1.53165e13	0.970405	0.485203	−	0.874402i	$-0.338746\pi$
$251$	1.53165e13	0.970405	0.485203	+	0.874402i	$0.338746\pi$
$252$	1.52496e12	0.0945269
$253$	2.77706e13	1.68431
$254$	−3.34847e13	−1.98729
$255$	5.02059e12	0.291598
$256$	1.35428e13	0.769819
$257$	−1.18634e13	−0.660050	−0.330025	−	0.943972i	$-0.607057\pi$
$257$	−1.18634e13	−0.660050	−0.330025	+	0.943972i	$0.607057\pi$
$258$	2.19639e13	1.19619
$259$	2.19650e13	1.17107
$260$	1.74635e12	0.0911546
$261$	−9.39464e12	−0.480129
$262$	1.28572e13	0.643413
$263$	5.17670e11	0.0253686	0.0126843	−	0.999920i	$-0.495962\pi$
$263$	5.17670e11	0.0253686	0.0126843	+	0.999920i	$0.495962\pi$
$264$	−1.10080e13	−0.528309
$265$	7.13555e12	0.335409
$266$	−1.34895e12	−0.0621081
$267$	−3.56972e11	−0.0160999
$268$	−3.34772e12	−0.147913
$269$	3.74208e13	1.61985	0.809927	−	0.586531i	$-0.199507\pi$
$269$	3.74208e13	1.61985	0.809927	+	0.586531i	$0.199507\pi$
$270$	2.29189e12	0.0972062
$271$	−4.10753e12	−0.170706	−0.0853532	−	0.996351i	$-0.527202\pi$
$271$	−4.10753e12	−0.170706	−0.0853532	+	0.996351i	$0.527202\pi$
$272$	3.32671e13	1.35483
$273$	−1.10065e13	−0.439294
$274$	−4.93340e13	−1.92983
$275$	−5.83420e12	−0.223693
$276$	−6.37605e12	−0.239636
$277$	−2.08709e13	−0.768959	−0.384479	−	0.923134i	$-0.625619\pi$
$277$	−2.08709e13	−0.768959	−0.384479	+	0.923134i	$0.625619\pi$
$278$	−4.93277e13	−1.78174
$279$	6.18030e12	0.218870
$280$	−1.08412e13	−0.376449
$281$	−1.03477e12	−0.0352337	−0.0176168	−	0.999845i	$-0.505608\pi$
$281$	−1.03477e12	−0.0352337	−0.0176168	+	0.999845i	$0.505608\pi$
$282$	1.73067e13	0.577888
$283$	−4.80808e13	−1.57451	−0.787257	−	0.616625i	$-0.788500\pi$
$283$	−4.80808e13	−1.57451	−0.787257	+	0.616625i	$0.788500\pi$
$284$	−6.37974e12	−0.204905
$285$	−4.38050e11	−0.0137999
$286$	−3.02306e13	−0.934188
$287$	3.03402e13	0.919745
$288$	6.01649e12	0.178931
$289$	9.43979e12	0.275438
$290$	−2.54123e13	−0.727536
$291$	−1.82425e13	−0.512476
$292$	−5.30129e12	−0.146142
$293$	−1.96764e13	−0.532322	−0.266161	−	0.963929i	$-0.585755\pi$
$293$	−1.96764e13	−0.532322	−0.266161	+	0.963929i	$0.585755\pi$
$294$	−1.43901e12	−0.0382078
$295$	−9.77562e12	−0.254755
$296$	3.64041e13	0.931205
$297$	−8.57236e12	−0.215248
$298$	1.46961e13	0.362254
$299$	4.60196e13	1.11366
$300$	1.33952e12	0.0318260
$301$	−8.09060e13	−1.88740
$302$	8.12290e13	1.86069
$303$	4.04550e13	0.909993
$304$	−2.90257e12	−0.0641178
$305$	−2.09884e13	−0.455335
$306$	1.99543e13	0.425177
$307$	2.21562e13	0.463696	0.231848	−	0.972752i	$-0.425523\pi$
$307$	2.21562e13	0.463696	0.231848	+	0.972752i	$0.425523\pi$
$308$	−1.54286e13	−0.317175
$309$	−3.80063e13	−0.767509
$310$	1.67176e13	0.331653
$311$	4.75136e13	0.926053	0.463026	−	0.886345i	$-0.346764\pi$
$311$	4.75136e13	0.926053	0.463026	+	0.886345i	$0.346764\pi$
$312$	−1.82418e13	−0.349315
$313$	−2.39850e13	−0.451280	−0.225640	−	0.974211i	$-0.572447\pi$
$313$	−2.39850e13	−0.451280	−0.225640	+	0.974211i	$0.572447\pi$
$314$	4.67805e13	0.864872
$315$	−8.44241e12	−0.153376
$316$	−2.03166e13	−0.362720
$317$	−8.02864e13	−1.40869	−0.704346	−	0.709857i	$-0.748759\pi$
$317$	−8.02864e13	−1.40869	−0.704346	+	0.709857i	$0.748759\pi$
$318$	2.83602e13	0.489058
$319$	9.50494e13	1.61102
$320$	−1.59285e13	−0.265369
$321$	4.19132e13	0.686394
$322$	1.08701e14	1.74995
$323$	−3.81387e12	−0.0603604
$324$	1.96819e12	0.0306245
$325$	−9.66807e12	−0.147905
$326$	−3.04352e13	−0.457804
$327$	4.81722e13	0.712498
$328$	5.02847e13	0.731357
$329$	−6.37508e13	−0.911819
$330$	−2.31880e13	−0.326165
$331$	−7.35975e13	−1.01814	−0.509072	−	0.860724i	$-0.670011\pi$
$331$	−7.35975e13	−1.01814	−0.509072	+	0.860724i	$0.670011\pi$
$332$	3.39289e13	0.461647
$333$	2.83492e13	0.379400
$334$	1.16336e13	0.153147
$335$	1.85335e13	0.239999
$336$	−5.59405e13	−0.712623
$337$	−1.11762e14	−1.40065	−0.700323	−	0.713826i	$-0.746961\pi$
$337$	−1.11762e14	−1.40065	−0.700323	+	0.713826i	$0.746961\pi$
$338$	4.15052e13	0.511754
$339$	−1.45985e13	−0.177096
$340$	1.16625e13	0.139206
$341$	−6.25286e13	−0.734395
$342$	−1.74103e12	−0.0201216
$343$	−8.51647e13	−0.968594
$344$	−1.34091e14	−1.50081
$345$	3.52988e13	0.388825
$346$	2.01449e14	2.18397
$347$	−2.31381e12	−0.0246896	−0.0123448	−	0.999924i	$-0.503930\pi$
$347$	−2.31381e12	−0.0246896	−0.0123448	+	0.999924i	$0.503930\pi$
$348$	−2.18231e13	−0.229208
$349$	1.79579e14	1.85659	0.928294	−	0.371848i	$-0.121276\pi$
$349$	1.79579e14	1.85659	0.928294	+	0.371848i	$0.121276\pi$
$350$	−2.28365e13	−0.232410
$351$	−1.42056e13	−0.142321
$352$	−6.08712e13	−0.600382
$353$	−1.62870e13	−0.158154	−0.0790768	−	0.996869i	$-0.525197\pi$
$353$	−1.62870e13	−0.158154	−0.0790768	+	0.996869i	$0.525197\pi$
$354$	−3.88532e13	−0.371457
$355$	3.53192e13	0.332472
$356$	−8.29220e11	−0.00768590
$357$	−7.35037e13	−0.670863
$358$	3.39360e13	0.305003
$359$	1.48987e13	0.131865	0.0659325	−	0.997824i	$-0.478998\pi$
$359$	1.48987e13	0.131865	0.0659325	+	0.997824i	$0.478998\pi$
$360$	−1.39921e13	−0.121961
$361$	−1.16157e14	−0.997143
$362$	−1.52295e14	−1.28762
$363$	1.73993e13	0.144892
$364$	−2.55674e13	−0.209714
$365$	2.93487e13	0.237126
$366$	−8.34184e13	−0.663921
$367$	9.81686e13	0.769679	0.384839	−	0.922984i	$-0.374257\pi$
$367$	9.81686e13	0.769679	0.384839	+	0.922984i	$0.374257\pi$
$368$	2.33894e14	1.80658
$369$	3.91586e13	0.297976
$370$	7.66839e13	0.574903
$371$	−1.04468e14	−0.771658
$372$	1.43564e13	0.104486
$373$	4.21169e12	0.0302036	0.0151018	−	0.999886i	$-0.495193\pi$
$373$	4.21169e12	0.0302036	0.0151018	+	0.999886i	$0.495193\pi$
$374$	−2.01886e14	−1.42663
$375$	−7.41577e12	−0.0516398
$376$	−1.05658e14	−0.725054
$377$	1.57510e14	1.06520
$378$	−3.35543e13	−0.223637
$379$	−8.03941e13	−0.528090	−0.264045	−	0.964510i	$-0.585057\pi$
$379$	−8.03941e13	−0.528090	−0.264045	+	0.964510i	$0.585057\pi$
$380$	−1.01756e12	−0.00658794
$381$	1.59194e14	1.01587
$382$	−1.22229e14	−0.768820
$383$	−4.60952e13	−0.285800	−0.142900	−	0.989737i	$-0.545643\pi$
$383$	−4.60952e13	−0.285800	−0.142900	+	0.989737i	$0.545643\pi$
$384$	−1.14015e14	−0.696850
$385$	8.54153e13	0.514638
$386$	1.81442e14	1.07772
$387$	−1.04421e14	−0.611475
$388$	−4.23761e13	−0.244651
$389$	1.07321e14	0.610891	0.305445	−	0.952210i	$-0.401195\pi$
$389$	1.07321e14	0.610891	0.305445	+	0.952210i	$0.401195\pi$
$390$	−3.84257e13	−0.215659
$391$	3.07328e14	1.70071
$392$	8.78521e12	0.0479379
$393$	−6.11262e13	−0.328903
$394$	−1.07385e14	−0.569791
$395$	1.12476e14	0.588539
$396$	−1.99130e13	−0.102757
$397$	−5.20270e13	−0.264778	−0.132389	−	0.991198i	$-0.542265\pi$
$397$	−5.20270e13	−0.264778	−0.132389	+	0.991198i	$0.542265\pi$
$398$	−7.05932e13	−0.354328
$399$	6.41324e12	0.0317488
$400$	−4.91378e13	−0.239931
$401$	2.47673e14	1.19284	0.596422	−	0.802671i	$-0.296588\pi$
$401$	2.47673e14	1.19284	0.596422	+	0.802671i	$0.296588\pi$
$402$	7.36612e13	0.349942
$403$	−1.03618e14	−0.485578
$404$	9.39741e13	0.434421
$405$	−1.08962e13	−0.0496904
$406$	3.72047e14	1.67380
$407$	−2.86820e14	−1.27304
$408$	−1.21822e14	−0.533453
$409$	7.24362e13	0.312952	0.156476	−	0.987682i	$-0.449987\pi$
$409$	7.24362e13	0.312952	0.156476	+	0.987682i	$0.449987\pi$
$410$	1.05923e14	0.451522
$411$	2.34545e14	0.986499
$412$	−8.82858e13	−0.366401
$413$	1.43119e14	0.586102
$414$	1.40295e14	0.566944
$415$	−1.87836e14	−0.749054
$416$	−1.00872e14	−0.396969
$417$	2.34515e14	0.910800
$418$	1.76147e13	0.0675158
$419$	1.89636e14	0.717369	0.358684	−	0.933459i	$-0.383225\pi$
$419$	1.89636e14	0.717369	0.358684	+	0.933459i	$0.383225\pi$
$420$	−1.96111e13	−0.0732202
$421$	−1.11470e14	−0.410776	−0.205388	−	0.978681i	$-0.565846\pi$
$421$	−1.11470e14	−0.410776	−0.205388	+	0.978681i	$0.565846\pi$
$422$	−2.57479e14	−0.936533
$423$	−8.22801e13	−0.295408
$424$	−1.73141e14	−0.613602
$425$	−6.45652e13	−0.225871
$426$	1.40376e14	0.484775
$427$	3.07280e14	1.04756
$428$	9.73614e13	0.327677
$429$	1.43724e14	0.477543
$430$	−2.82457e14	−0.926565
$431$	−1.11843e14	−0.362230	−0.181115	−	0.983462i	$-0.557971\pi$
$431$	−1.11843e14	−0.362230	−0.181115	+	0.983462i	$0.557971\pi$
$432$	−7.21996e13	−0.230874
$433$	−4.22999e14	−1.33554	−0.667768	−	0.744369i	$-0.732750\pi$
$433$	−4.22999e14	−1.33554	−0.667768	+	0.744369i	$0.732750\pi$
$434$	−2.44752e14	−0.763015
$435$	1.20816e14	0.371906
$436$	1.11900e14	0.340139
$437$	−2.68146e13	−0.0804865
$438$	1.16646e14	0.345751
$439$	−5.11444e14	−1.49707	−0.748537	−	0.663093i	$-0.769243\pi$
$439$	−5.11444e14	−1.49707	−0.748537	+	0.663093i	$0.769243\pi$
$440$	1.41564e14	0.409226
$441$	6.84137e12	0.0195313
$442$	−3.34553e14	−0.943283
$443$	−5.35642e14	−1.49161	−0.745803	−	0.666167i	$-0.767934\pi$
$443$	−5.35642e14	−1.49161	−0.745803	+	0.666167i	$0.767934\pi$
$444$	6.58531e13	0.181122
$445$	4.59069e12	0.0124709
$446$	−7.87465e14	−2.11295
$447$	−6.98688e13	−0.185179
$448$	2.33200e14	0.610520
$449$	1.75234e14	0.453173	0.226587	−	0.973991i	$-0.427243\pi$
$449$	1.75234e14	0.453173	0.226587	+	0.973991i	$0.427243\pi$
$450$	−2.94740e13	−0.0752956
$451$	−3.96183e14	−0.999827
$452$	−3.39112e13	−0.0845439
$453$	−3.86182e14	−0.951156
$454$	1.58073e14	0.384637
$455$	1.41545e14	0.340276
$456$	1.06291e13	0.0252458
$457$	2.72581e14	0.639671	0.319836	−	0.947473i	$-0.396372\pi$
$457$	2.72581e14	0.639671	0.319836	+	0.947473i	$0.396372\pi$
$458$	6.07942e14	1.40962
$459$	−9.48675e13	−0.217344
$460$	8.19965e13	0.185621
$461$	−2.76659e13	−0.0618856	−0.0309428	−	0.999521i	$-0.509851\pi$
$461$	−2.76659e13	−0.0618856	−0.0309428	+	0.999521i	$0.509851\pi$
$462$	3.39483e14	0.750389
$463$	7.26472e13	0.158680	0.0793402	−	0.996848i	$-0.474719\pi$
$463$	7.26472e13	0.158680	0.0793402	+	0.996848i	$0.474719\pi$
$464$	8.00541e14	1.72796
$465$	−7.94792e13	−0.169536
$466$	9.98767e14	2.10543
$467$	2.28552e14	0.476148	0.238074	−	0.971247i	$-0.423484\pi$
$467$	2.28552e14	0.476148	0.238074	+	0.971247i	$0.423484\pi$
$468$	−3.29985e13	−0.0679426
$469$	−2.71338e14	−0.552154
$470$	−2.22566e14	−0.447630
$471$	−2.22406e14	−0.442110
$472$	2.37201e14	0.466053
$473$	1.05647e15	2.05174
$474$	4.47034e14	0.858144
$475$	5.63336e12	0.0106894
$476$	−1.70744e14	−0.320263
$477$	−1.34831e14	−0.249999
$478$	−2.24408e14	−0.411325
$479$	−6.47644e14	−1.17352	−0.586761	−	0.809760i	$-0.699597\pi$
$479$	−6.47644e14	−1.17352	−0.586761	+	0.809760i	$0.699597\pi$
$480$	−7.73725e13	−0.138599
$481$	−4.75300e14	−0.841725
$482$	4.97016e14	0.870185
$483$	−5.16789e14	−0.894549
$484$	4.04173e13	0.0691700
$485$	2.34600e14	0.396962
$486$	−4.33069e13	−0.0724532
$487$	9.59498e14	1.58721	0.793606	−	0.608433i	$-0.208201\pi$
$487$	9.59498e14	1.58721	0.793606	+	0.608433i	$0.208201\pi$
$488$	5.09274e14	0.832995
$489$	1.44696e14	0.234023
$490$	1.85057e13	0.0295956
$491$	−8.15780e14	−1.29010	−0.645052	−	0.764138i	$-0.723164\pi$
$491$	−8.15780e14	−1.29010	−0.645052	+	0.764138i	$0.723164\pi$
$492$	9.09625e13	0.142251
$493$	1.05188e15	1.62670
$494$	2.91899e13	0.0446411
$495$	1.10241e14	0.166731
$496$	−5.26639e14	−0.787705
$497$	−5.17089e14	−0.764900
$498$	−7.46552e14	−1.09219
$499$	−2.28979e14	−0.331316	−0.165658	−	0.986183i	$-0.552975\pi$
$499$	−2.28979e14	−0.331316	−0.165658	+	0.986183i	$0.552975\pi$
$500$	−1.72263e13	−0.0246523
$501$	−5.53090e13	−0.0782867
$502$	−7.82861e14	−1.09601
$503$	5.81915e14	0.805815	0.402908	−	0.915241i	$-0.368000\pi$
$503$	5.81915e14	0.805815	0.402908	+	0.915241i	$0.368000\pi$
$504$	2.04851e14	0.280589
$505$	−5.20255e14	−0.704877
$506$	−1.41942e15	−1.90232
$507$	−1.97326e14	−0.261601
$508$	3.69797e14	0.484967
$509$	−2.09435e14	−0.271707	−0.135854	−	0.990729i	$-0.543378\pi$
$509$	−2.09435e14	−0.271707	−0.135854	+	0.990729i	$0.543378\pi$
$510$	−2.56614e14	−0.329340
$511$	−4.29678e14	−0.545542
$512$	2.68709e14	0.337519
$513$	8.27725e12	0.0102859
$514$	6.06366e14	0.745483
$515$	4.88764e14	0.594510
$516$	−2.42563e14	−0.291912
$517$	8.32461e14	0.991210
$518$	−1.12268e15	−1.32265
$519$	−9.57734e14	−1.11641
$520$	2.34591e14	0.270578
$521$	4.47986e14	0.511278	0.255639	−	0.966772i	$-0.417714\pi$
$521$	4.47986e14	0.511278	0.255639	+	0.966772i	$0.417714\pi$
$522$	4.80182e14	0.542273
$523$	6.17551e14	0.690102	0.345051	−	0.938584i	$-0.387862\pi$
$523$	6.17551e14	0.690102	0.345051	+	0.938584i	$0.387862\pi$
$524$	−1.41992e14	−0.157015
$525$	1.08570e14	0.118805
$526$	−2.64593e13	−0.0286522
$527$	−6.91984e14	−0.741545
$528$	7.30472e14	0.774671
$529$	1.20795e15	1.26778
$530$	−3.64715e14	−0.378823
$531$	1.84717e14	0.189883
$532$	1.48975e13	0.0151565
$533$	−6.56529e14	−0.661081
$534$	1.82457e13	0.0181837
$535$	−5.39008e14	−0.531678
$536$	−4.49706e14	−0.439058
$537$	−1.61340e14	−0.155913
$538$	−1.91267e15	−1.82952
$539$	−6.92169e13	−0.0655351
$540$	−2.53111e13	−0.0237217
$541$	1.60818e15	1.49194	0.745969	−	0.665981i	$-0.231987\pi$
$541$	1.60818e15	1.49194	0.745969	+	0.665981i	$0.231987\pi$
$542$	2.09946e14	0.192802
$543$	7.24045e14	0.658213
$544$	−6.73642e14	−0.606227
$545$	−6.19498e14	−0.551899
$546$	5.62569e14	0.496154
$547$	−2.14344e13	−0.0187146	−0.00935732	−	0.999956i	$-0.502979\pi$
$547$	−2.14344e13	−0.0187146	−0.00935732	+	0.999956i	$0.502979\pi$
$548$	5.44832e14	0.470944
$549$	3.96591e14	0.339387
$550$	2.98200e14	0.252646
$551$	−9.17773e13	−0.0769842
$552$	−8.56508e14	−0.711322
$553$	−1.64669e15	−1.35402
$554$	1.06676e15	0.868488
$555$	−3.64573e14	−0.293882
$556$	5.44762e14	0.434806
$557$	−3.80343e14	−0.300588	−0.150294	−	0.988641i	$-0.548022\pi$
$557$	−3.80343e14	−0.300588	−0.150294	+	0.988641i	$0.548022\pi$
$558$	−3.15890e14	−0.247199
$559$	1.75072e15	1.35660
$560$	7.19399e14	0.551996
$561$	9.59813e14	0.729274
$562$	5.28894e13	0.0397941
$563$	−4.56848e14	−0.340389	−0.170194	−	0.985411i	$-0.554440\pi$
$563$	−4.56848e14	−0.340389	−0.170194	+	0.985411i	$0.554440\pi$
$564$	−1.91131e14	−0.141025
$565$	1.87738e14	0.137178
$566$	2.45752e15	1.77831
$567$	1.59525e14	0.114320
$568$	−8.57004e14	−0.608229
$569$	−1.02008e15	−0.716993	−0.358496	−	0.933531i	$-0.616710\pi$
$569$	−1.02008e15	−0.716993	−0.358496	+	0.933531i	$0.616710\pi$
$570$	2.23898e13	0.0155861
$571$	−1.16801e15	−0.805285	−0.402642	−	0.915357i	$-0.631908\pi$
$571$	−1.16801e15	−0.805285	−0.402642	+	0.915357i	$0.631908\pi$
$572$	3.33859e14	0.227974
$573$	5.81104e14	0.393010
$574$	−1.55076e15	−1.03879
$575$	−4.53945e14	−0.301183
$576$	3.00980e14	0.197794
$577$	−4.17243e14	−0.271595	−0.135798	−	0.990737i	$-0.543360\pi$
$577$	−4.17243e14	−0.271595	−0.135798	+	0.990737i	$0.543360\pi$
$578$	−4.82490e14	−0.311089
$579$	−8.62618e14	−0.550917
$580$	2.80647e14	0.177544
$581$	2.74999e15	1.72331
$582$	9.32418e14	0.578808
$583$	1.36414e15	0.838846
$584$	−7.12133e14	−0.433801
$585$	1.82685e14	0.110242
$586$	1.00571e15	0.601223
$587$	−3.15560e14	−0.186884	−0.0934421	−	0.995625i	$-0.529787\pi$
$587$	−3.15560e14	−0.186884	−0.0934421	+	0.995625i	$0.529787\pi$
$588$	1.58920e13	0.00932402
$589$	6.03760e13	0.0350938
$590$	4.99655e14	0.287729
$591$	5.10535e14	0.291269
$592$	−2.41571e15	−1.36545
$593$	1.66344e15	0.931551	0.465775	−	0.884903i	$-0.345775\pi$
$593$	1.66344e15	0.931551	0.465775	+	0.884903i	$0.345775\pi$
$594$	4.38153e14	0.243109
$595$	9.45263e14	0.519648
$596$	−1.62300e14	−0.0884026
$597$	3.35616e14	0.181128
$598$	−2.35217e15	−1.25780
$599$	6.19005e14	0.327979	0.163990	−	0.986462i	$-0.447564\pi$
$599$	6.19005e14	0.327979	0.163990	+	0.986462i	$0.447564\pi$
$600$	1.79940e14	0.0944705
$601$	−1.90367e15	−0.990333	−0.495167	−	0.868798i	$-0.664893\pi$
$601$	−1.90367e15	−0.990333	−0.495167	+	0.868798i	$0.664893\pi$
$602$	4.13529e15	2.13170
$603$	−3.50202e14	−0.178885
$604$	−8.97072e14	−0.454072
$605$	−2.23756e14	−0.112233
$606$	−2.06775e15	−1.02778
$607$	−1.45859e15	−0.718450	−0.359225	−	0.933251i	$-0.616959\pi$
$607$	−1.45859e15	−0.718450	−0.359225	+	0.933251i	$0.616959\pi$
$608$	5.87757e13	0.0286899
$609$	−1.76880e15	−0.855624
$610$	1.07277e15	0.514271
$611$	1.37950e15	0.655383
$612$	−2.20370e14	−0.103758
$613$	2.48221e14	0.115826	0.0579130	−	0.998322i	$-0.481555\pi$
$613$	2.48221e14	0.115826	0.0579130	+	0.998322i	$0.481555\pi$
$614$	−1.13245e15	−0.523714
$615$	−5.03582e14	−0.230811
$616$	−2.07256e15	−0.941485
$617$	−2.70824e15	−1.21932	−0.609662	−	0.792662i	$-0.708695\pi$
$617$	−2.70824e15	−1.21932	−0.609662	+	0.792662i	$0.708695\pi$
$618$	1.94259e15	0.866851
$619$	−1.22881e14	−0.0543483	−0.0271741	−	0.999631i	$-0.508651\pi$
$619$	−1.22881e14	−0.0543483	−0.0271741	+	0.999631i	$0.508651\pi$
$620$	−1.84624e14	−0.0809347
$621$	−6.66994e14	−0.289813
$622$	−2.42853e15	−1.04592
$623$	−6.72096e13	−0.0286911
$624$	1.21049e15	0.512209
$625$	9.53674e13	0.0400000
$626$	1.22593e15	0.509691
$627$	−8.37443e13	−0.0345131
$628$	−5.16632e14	−0.211059
$629$	−3.17415e15	−1.28543
$630$	4.31511e14	0.173228
$631$	2.44958e15	0.974832	0.487416	−	0.873170i	$-0.337940\pi$
$631$	2.44958e15	0.974832	0.487416	+	0.873170i	$0.337940\pi$
$632$	−2.72917e15	−1.07668
$633$	1.22411e15	0.478742
$634$	4.10362e15	1.59102
$635$	−2.04725e15	−0.786892
$636$	−3.13203e14	−0.119347
$637$	−1.14702e14	−0.0433315
$638$	−4.85820e15	−1.81954
$639$	−6.67381e14	−0.247810
$640$	1.46624e15	0.539777
$641$	2.91178e15	1.06277	0.531386	−	0.847130i	$-0.321671\pi$
$641$	2.91178e15	1.06277	0.531386	+	0.847130i	$0.321671\pi$
$642$	−2.14228e15	−0.775237
$643$	2.55085e15	0.915219	0.457610	−	0.889153i	$-0.348706\pi$
$643$	2.55085e15	0.915219	0.457610	+	0.889153i	$0.348706\pi$
$644$	−1.20046e15	−0.427048
$645$	1.34287e15	0.473647
$646$	1.94936e14	0.0681731
$647$	−2.35946e15	−0.818163	−0.409082	−	0.912498i	$-0.634151\pi$
$647$	−2.35946e15	−0.818163	−0.409082	+	0.912498i	$0.634151\pi$
$648$	2.64391e14	0.0909043
$649$	−1.86886e15	−0.637133
$650$	4.94158e14	0.167048
$651$	1.16361e15	0.390042
$652$	3.36119e14	0.111720
$653$	3.85495e15	1.27056	0.635282	−	0.772280i	$-0.280884\pi$
$653$	3.85495e15	1.27056	0.635282	+	0.772280i	$0.280884\pi$
$654$	−2.46219e15	−0.804719
$655$	7.86088e14	0.254767
$656$	−3.33680e15	−1.07241
$657$	−5.54565e14	−0.176743
$658$	3.25846e15	1.02984
$659$	2.43185e15	0.762198	0.381099	−	0.924534i	$-0.375546\pi$
$659$	2.43185e15	0.762198	0.381099	+	0.924534i	$0.375546\pi$
$660$	2.56083e14	0.0795955
$661$	−2.91546e15	−0.898668	−0.449334	−	0.893364i	$-0.648339\pi$
$661$	−2.91546e15	−0.898668	−0.449334	+	0.893364i	$0.648339\pi$
$662$	3.76174e15	1.14993
$663$	1.59054e15	0.482193
$664$	4.55774e15	1.37033
$665$	−8.24748e13	−0.0245925
$666$	−1.44899e15	−0.428507
$667$	7.39556e15	2.16910
$668$	−1.28479e14	−0.0373732
$669$	3.74379e15	1.08011
$670$	−9.47289e14	−0.271064
$671$	−4.01247e15	−1.13877
$672$	1.13277e15	0.318867
$673$	−2.73025e14	−0.0762289	−0.0381145	−	0.999273i	$-0.512135\pi$
$673$	−2.73025e14	−0.0762289	−0.0381145	+	0.999273i	$0.512135\pi$
$674$	5.71240e15	1.58194
$675$	1.40126e14	0.0384900
$676$	−4.58373e14	−0.124886
$677$	5.49970e14	0.148628	0.0743142	−	0.997235i	$-0.476323\pi$
$677$	5.49970e14	0.148628	0.0743142	+	0.997235i	$0.476323\pi$
$678$	7.46163e14	0.200019
$679$	−3.43465e15	−0.913269
$680$	1.56664e15	0.413211
$681$	−7.51517e14	−0.196621
$682$	3.19598e15	0.829450
$683$	−5.37455e15	−1.38366	−0.691828	−	0.722062i	$-0.743194\pi$
$683$	−5.37455e15	−1.38366	−0.691828	+	0.722062i	$0.743194\pi$
$684$	1.92275e13	0.00491036
$685$	−3.01627e15	−0.764139
$686$	4.35296e15	1.09396
$687$	−2.89030e15	−0.720578
$688$	8.89800e15	2.20068
$689$	2.26057e15	0.554641
$690$	−1.80420e15	−0.439153
$691$	1.45481e15	0.351298	0.175649	−	0.984453i	$-0.443798\pi$
$691$	1.45481e15	0.351298	0.175649	+	0.984453i	$0.443798\pi$
$692$	−2.22475e15	−0.532963
$693$	−1.61398e15	−0.383588
$694$	1.18264e14	0.0278853
$695$	−3.01589e15	−0.705503
$696$	−2.93154e15	−0.680370
$697$	−4.38443e15	−1.00956
$698$	−9.17870e15	−2.09689
$699$	−4.74837e15	−1.07627
$700$	2.52201e14	0.0567162
$701$	−8.94470e14	−0.199580	−0.0997899	−	0.995009i	$-0.531817\pi$
$701$	−8.94470e14	−0.199580	−0.0997899	+	0.995009i	$0.531817\pi$
$702$	7.26080e14	0.160742
$703$	2.76946e14	0.0608333
$704$	−3.04514e15	−0.663678
$705$	1.05813e15	0.228822
$706$	8.32465e14	0.178624
$707$	7.61676e15	1.62167
$708$	4.29084e14	0.0906483
$709$	−6.98755e15	−1.46477	−0.732387	−	0.680889i	$-0.761594\pi$
$709$	−6.98755e15	−1.46477	−0.732387	+	0.680889i	$0.761594\pi$
$710$	−1.80525e15	−0.375505
$711$	−2.12531e15	−0.438671
$712$	−1.11391e14	−0.0228144
$713$	−4.86520e15	−0.988799
$714$	3.75694e15	0.757695
$715$	−1.84830e15	−0.369903
$716$	−3.74780e14	−0.0744312
$717$	1.06689e15	0.210263
$718$	−7.61508e14	−0.148933
$719$	4.29436e15	0.833469	0.416735	−	0.909028i	$-0.363174\pi$
$719$	4.29436e15	0.833469	0.416735	+	0.909028i	$0.363174\pi$
$720$	9.28493e14	0.178834
$721$	−7.15571e15	−1.36776
$722$	5.93708e15	1.12621
$723$	−2.36293e15	−0.444826
$724$	1.68190e15	0.314224
$725$	−1.55370e15	−0.288077
$726$	−8.89319e14	−0.163646
$727$	−1.43942e15	−0.262874	−0.131437	−	0.991325i	$-0.541959\pi$
$727$	−1.43942e15	−0.262874	−0.131437	+	0.991325i	$0.541959\pi$
$728$	−3.43452e15	−0.622505
$729$	2.05891e14	0.0370370
$730$	−1.50008e15	−0.267818
$731$	1.16916e16	2.07171
$732$	9.21252e14	0.162020
$733$	−5.59957e15	−0.977424	−0.488712	−	0.872445i	$-0.662533\pi$
$733$	−5.59957e15	−0.977424	−0.488712	+	0.872445i	$0.662533\pi$
$734$	−5.01763e15	−0.869301
$735$	−8.79806e13	−0.0151289
$736$	−4.73624e15	−0.808362
$737$	3.54314e15	0.600229
$738$	−2.00149e15	−0.336544
$739$	2.27349e15	0.379446	0.189723	−	0.981838i	$-0.439241\pi$
$739$	2.27349e15	0.379446	0.189723	+	0.981838i	$0.439241\pi$
$740$	−8.46877e14	−0.140296
$741$	−1.38776e14	−0.0228199
$742$	5.33958e15	0.871537
$743$	8.38494e14	0.135851	0.0679253	−	0.997690i	$-0.478362\pi$
$743$	8.38494e14	0.135851	0.0679253	+	0.997690i	$0.478362\pi$
$744$	1.92852e15	0.310151
$745$	8.98519e14	0.143439
$746$	−2.15270e14	−0.0341129
$747$	3.54928e15	0.558312
$748$	2.22958e15	0.348148
$749$	7.89130e15	1.22320
$750$	3.79037e14	0.0583237
$751$	4.57452e15	0.698756	0.349378	−	0.936982i	$-0.386393\pi$
$751$	4.57452e15	0.698756	0.349378	+	0.936982i	$0.386393\pi$
$752$	7.01129e15	1.06316
$753$	3.72190e15	0.560264
$754$	−8.05070e15	−1.20307
$755$	4.96633e15	0.736762
$756$	3.70565e14	0.0545751
$757$	−2.03687e15	−0.297808	−0.148904	−	0.988852i	$-0.547575\pi$
$757$	−2.03687e15	−0.297808	−0.148904	+	0.988852i	$0.547575\pi$
$758$	4.10913e15	0.596443
$759$	6.74825e15	0.972437
$760$	−1.36691e14	−0.0195553
$761$	−1.18948e16	−1.68943	−0.844716	−	0.535215i	$-0.820230\pi$
$761$	−1.18948e16	−1.68943	−0.844716	+	0.535215i	$0.820230\pi$
$762$	−8.13678e15	−1.14736
$763$	9.06972e15	1.26972
$764$	1.34986e15	0.187619
$765$	1.22000e15	0.168354
$766$	2.35603e15	0.322792
$767$	−3.09695e15	−0.421269
$768$	3.29090e15	0.444455
$769$	−1.03701e16	−1.39056	−0.695280	−	0.718739i	$-0.744720\pi$
$769$	−1.03701e16	−1.39056	−0.695280	+	0.718739i	$0.744720\pi$
$770$	−4.36577e15	−0.581249
$771$	−2.88280e15	−0.381080
$772$	−2.00380e15	−0.263002
$773$	5.86680e15	0.764564	0.382282	−	0.924046i	$-0.375138\pi$
$773$	5.86680e15	0.764564	0.382282	+	0.924046i	$0.375138\pi$
$774$	5.33722e15	0.690621
$775$	1.02211e15	0.131322
$776$	−5.69246e15	−0.726208
$777$	5.33750e15	0.676118
$778$	−5.48545e15	−0.689961
$779$	3.82544e14	0.0477777
$780$	4.24364e14	0.0526281
$781$	6.75216e15	0.831500
$782$	−1.57083e16	−1.92084
$783$	−2.28290e15	−0.277202
$784$	−5.82970e14	−0.0702923
$785$	2.86015e15	0.342457
$786$	3.12430e15	0.371475
$787$	4.35191e15	0.513829	0.256915	−	0.966434i	$-0.417294\pi$
$787$	4.35191e15	0.513829	0.256915	+	0.966434i	$0.417294\pi$
$788$	1.18594e15	0.139049
$789$	1.25794e14	0.0146466
$790$	−5.74890e15	−0.664715
$791$	−2.74856e15	−0.315598
$792$	−2.67495e15	−0.305019
$793$	−6.64921e15	−0.752952
$794$	2.65922e15	0.299049
$795$	1.73394e15	0.193649
$796$	7.79613e14	0.0864683
$797$	3.97211e15	0.437522	0.218761	−	0.975778i	$-0.429798\pi$
$797$	3.97211e15	0.437522	0.218761	+	0.975778i	$0.429798\pi$
$798$	−3.27796e14	−0.0358581
$799$	9.21257e15	1.00086
$800$	9.95017e14	0.107358
$801$	−8.67441e13	−0.00929526
$802$	−1.26591e16	−1.34724
$803$	5.61075e15	0.593042
$804$	−8.13495e14	−0.0853978
$805$	6.64595e15	0.692915
$806$	5.29618e15	0.548428
$807$	9.09326e15	0.935223
$808$	1.26237e16	1.28951
$809$	−9.34419e15	−0.948036	−0.474018	−	0.880515i	$-0.657197\pi$
$809$	−9.34419e15	−0.948036	−0.474018	+	0.880515i	$0.657197\pi$
$810$	5.56930e14	0.0561220
$811$	−1.25244e16	−1.25355	−0.626777	−	0.779199i	$-0.715626\pi$
$811$	−1.25244e16	−1.25355	−0.626777	+	0.779199i	$0.715626\pi$
$812$	−4.10879e15	−0.408466
$813$	−9.98130e14	−0.0985574
$814$	1.46601e16	1.43781
$815$	−1.86081e15	−0.181273
$816$	8.08390e15	0.782213
$817$	−1.02010e15	−0.0980444
$818$	−3.70238e15	−0.353458
$819$	−2.67458e15	−0.253627
$820$	−1.16979e15	−0.110187
$821$	1.78922e16	1.67408	0.837042	−	0.547138i	$-0.184283\pi$
$821$	1.78922e16	1.67408	0.837042	+	0.547138i	$0.184283\pi$
$822$	−1.19882e16	−1.11419
$823$	1.07441e16	0.991910	0.495955	−	0.868348i	$-0.334818\pi$
$823$	1.07441e16	0.991910	0.495955	+	0.868348i	$0.334818\pi$
$824$	−1.18596e16	−1.08760
$825$	−1.41771e15	−0.129149
$826$	−7.31516e15	−0.661963
$827$	−1.91483e16	−1.72128	−0.860638	−	0.509217i	$-0.829935\pi$
$827$	−1.91483e16	−1.72128	−0.860638	+	0.509217i	$0.829935\pi$
$828$	−1.54938e15	−0.138354
$829$	−1.76350e16	−1.56432	−0.782158	−	0.623080i	$-0.785881\pi$
$829$	−1.76350e16	−1.56432	−0.782158	+	0.623080i	$0.785881\pi$
$830$	9.60071e15	0.846007
$831$	−5.07164e15	−0.443959
$832$	−5.04621e15	−0.438821
$833$	−7.66001e14	−0.0661731
$834$	−1.19866e16	−1.02869
$835$	7.11278e14	0.0606406
$836$	−1.94532e14	−0.0164762
$837$	1.50181e15	0.126365
$838$	−9.69271e15	−0.810221
$839$	9.56616e15	0.794414	0.397207	−	0.917729i	$-0.369979\pi$
$839$	9.56616e15	0.794414	0.397207	+	0.917729i	$0.369979\pi$
$840$	−2.63440e15	−0.217343
$841$	1.31120e16	1.07471
$842$	5.69748e15	0.463945
$843$	−2.51449e14	−0.0203422
$844$	2.84353e15	0.228546
$845$	2.53762e15	0.202635
$846$	4.20553e15	0.333644
$847$	3.27589e15	0.258209
$848$	1.14893e16	0.899738
$849$	−1.16836e16	−0.909046
$850$	3.30008e15	0.255106
$851$	−2.23168e16	−1.71403
$852$	−1.55028e15	−0.118302
$853$	−1.51540e16	−1.14896	−0.574482	−	0.818517i	$-0.694797\pi$
$853$	−1.51540e16	−1.14896	−0.574482	+	0.818517i	$0.694797\pi$
$854$	−1.57058e16	−1.18315
$855$	−1.06446e14	−0.00796740
$856$	1.30788e16	0.972659
$857$	−1.68905e16	−1.24810	−0.624048	−	0.781386i	$-0.714513\pi$
$857$	−1.68905e16	−1.24810	−0.624048	+	0.781386i	$0.714513\pi$
$858$	−7.34605e15	−0.539354
$859$	−3.39202e15	−0.247455	−0.123727	−	0.992316i	$-0.539485\pi$
$859$	−3.39202e15	−0.247455	−0.123727	+	0.992316i	$0.539485\pi$
$860$	3.11938e15	0.226114
$861$	7.37266e15	0.531015
$862$	5.71656e15	0.409115
$863$	−8.29475e15	−0.589853	−0.294927	−	0.955520i	$-0.595295\pi$
$863$	−8.29475e15	−0.589853	−0.294927	+	0.955520i	$0.595295\pi$
$864$	1.46201e15	0.103306
$865$	1.23165e16	0.864769
$866$	2.16205e16	1.50840
$867$	2.29387e15	0.159024
$868$	2.70298e15	0.186202
$869$	2.15026e16	1.47191
$870$	−6.17518e15	−0.420043
$871$	5.87147e15	0.396869
$872$	1.50318e16	1.00965
$873$	−4.43293e15	−0.295878
$874$	1.37056e15	0.0909042
$875$	−1.39622e15	−0.0920258
$876$	−1.28821e15	−0.0843753
$877$	−4.24748e15	−0.276461	−0.138230	−	0.990400i	$-0.544141\pi$
$877$	−4.24748e15	−0.276461	−0.138230	+	0.990400i	$0.544141\pi$
$878$	2.61411e16	1.69085
$879$	−4.78138e15	−0.307336
$880$	−9.39394e15	−0.600057
$881$	−4.11863e15	−0.261448	−0.130724	−	0.991419i	$-0.541730\pi$
$881$	−4.11863e15	−0.261448	−0.130724	+	0.991419i	$0.541730\pi$
$882$	−3.49678e14	−0.0220593
$883$	−1.48075e16	−0.928319	−0.464160	−	0.885752i	$-0.653644\pi$
$883$	−1.48075e16	−0.928319	−0.464160	+	0.885752i	$0.653644\pi$
$884$	3.69471e15	0.230194
$885$	−2.37548e15	−0.147083
$886$	2.73779e16	1.68467
$887$	−8.21370e15	−0.502295	−0.251147	−	0.967949i	$-0.580808\pi$
$887$	−8.21370e15	−0.502295	−0.251147	+	0.967949i	$0.580808\pi$
$888$	8.84619e15	0.537632
$889$	2.99726e16	1.81036
$890$	−2.34641e14	−0.0140851
$891$	−2.08308e15	−0.124274
$892$	8.69656e15	0.515633
$893$	−8.03803e14	−0.0473660
$894$	3.57116e15	0.209148
$895$	2.07484e15	0.120770
$896$	−2.14664e16	−1.24184
$897$	1.11828e16	0.642971
$898$	−8.95664e15	−0.511829
$899$	−1.66519e16	−0.945772
$900$	3.25503e14	0.0183747
$901$	1.50965e16	0.847013
$902$	2.02498e16	1.12924
$903$	−1.96601e16	−1.08969
$904$	−4.55537e15	−0.250956
$905$	−9.31128e15	−0.509849
$906$	1.97387e16	1.07427
$907$	2.79307e16	1.51092	0.755462	−	0.655193i	$-0.227413\pi$
$907$	2.79307e16	1.51092	0.755462	+	0.655193i	$0.227413\pi$
$908$	−1.74572e15	−0.0938647
$909$	9.83057e15	0.525385
$910$	−7.23468e15	−0.384319
$911$	−9.25991e15	−0.488940	−0.244470	−	0.969657i	$-0.578614\pi$
$911$	−9.25991e15	−0.488940	−0.244470	+	0.969657i	$0.578614\pi$
$912$	−7.05326e14	−0.0370184
$913$	−3.59095e16	−1.87335
$914$	−1.39323e16	−0.722466
$915$	−5.10019e15	−0.262888
$916$	−6.71396e15	−0.343996
$917$	−1.15087e16	−0.586129
$918$	4.84890e15	0.245476
$919$	3.66664e16	1.84516	0.922578	−	0.385810i	$-0.126078\pi$
$919$	3.66664e16	1.84516	0.922578	+	0.385810i	$0.126078\pi$
$920$	1.10148e16	0.550988
$921$	5.38395e15	0.267715
$922$	1.41407e15	0.0698956
$923$	1.11893e16	0.549784
$924$	−3.74916e15	−0.183121
$925$	4.68844e15	0.227640
$926$	−3.71317e15	−0.179219
$927$	−9.23553e15	−0.443122
$928$	−1.62106e16	−0.773187
$929$	−2.64404e16	−1.25367	−0.626834	−	0.779153i	$-0.715649\pi$
$929$	−2.64404e16	−1.25367	−0.626834	+	0.779153i	$0.715649\pi$
$930$	4.06237e15	0.191480
$931$	6.68341e13	0.00313166
$932$	−1.10301e16	−0.513798
$933$	1.15458e16	0.534657
$934$	−1.16818e16	−0.537778
$935$	−1.23433e16	−0.564893
$936$	−4.43276e15	−0.201677
$937$	−2.56311e16	−1.15931	−0.579655	−	0.814862i	$-0.696813\pi$
$937$	−2.56311e16	−1.15931	−0.579655	+	0.814862i	$0.696813\pi$
$938$	1.38687e16	0.623621
$939$	−5.82836e15	−0.260547
$940$	2.45796e15	0.109237
$941$	7.37922e15	0.326038	0.163019	−	0.986623i	$-0.447877\pi$
$941$	7.37922e15	0.326038	0.163019	+	0.986623i	$0.447877\pi$
$942$	1.13677e16	0.499334
$943$	−3.08260e16	−1.34618
$944$	−1.57402e16	−0.683383
$945$	−2.05151e15	−0.0885519
$946$	−5.39988e16	−2.31730
$947$	−1.91401e16	−0.816619	−0.408309	−	0.912844i	$-0.633882\pi$
$947$	−1.91401e16	−0.816619	−0.408309	+	0.912844i	$0.633882\pi$
$948$	−4.93693e15	−0.209417
$949$	9.29778e15	0.392117
$950$	−2.87934e14	−0.0120730
$951$	−1.95096e16	−0.813308
$952$	−2.29364e16	−0.950651
$953$	2.15693e16	0.888845	0.444422	−	0.895817i	$-0.353409\pi$
$953$	2.15693e16	0.888845	0.444422	+	0.895817i	$0.353409\pi$
$954$	6.89153e15	0.282358
$955$	−7.47304e15	−0.304424
$956$	2.47831e15	0.100378
$957$	2.30970e16	0.930122
$958$	3.31026e16	1.32542
$959$	4.41595e16	1.75801
$960$	−3.87063e15	−0.153211
$961$	−1.44539e16	−0.568863
$962$	2.42937e16	0.950672
$963$	1.01849e16	0.396290
$964$	−5.48891e15	−0.212355
$965$	1.10933e16	0.426739
$966$	2.64143e16	1.01033
$967$	−2.47540e16	−0.941456	−0.470728	−	0.882278i	$-0.656009\pi$
$967$	−2.47540e16	−0.941456	−0.470728	+	0.882278i	$0.656009\pi$
$968$	5.42934e15	0.205321
$969$	−9.26771e14	−0.0348491
$970$	−1.19910e16	−0.448343
$971$	−4.43638e16	−1.64939	−0.824695	−	0.565578i	$-0.808653\pi$
$971$	−4.43638e16	−1.64939	−0.824695	+	0.565578i	$0.808653\pi$
$972$	4.78270e14	0.0176811
$973$	4.41539e16	1.62311
$974$	−4.90422e16	−1.79265
$975$	−2.34934e15	−0.0853927
$976$	−3.37945e16	−1.22144
$977$	2.48061e16	0.891536	0.445768	−	0.895149i	$-0.352931\pi$
$977$	2.48061e16	0.891536	0.445768	+	0.895149i	$0.352931\pi$
$978$	−7.39576e15	−0.264313
$979$	8.77626e14	0.0311892
$980$	−2.04372e14	−0.00722236
$981$	1.17058e16	0.411361
$982$	4.16964e16	1.45709
$983$	4.74780e16	1.64986	0.824932	−	0.565232i	$-0.191213\pi$
$983$	4.74780e16	1.64986	0.824932	+	0.565232i	$0.191213\pi$
$984$	1.22192e16	0.422249
$985$	−6.56552e15	−0.225616
$986$	−5.37641e16	−1.83725
$987$	−1.54915e16	−0.526439
$988$	−3.22366e14	−0.0108940
$989$	8.22015e16	2.76249
$990$	−5.63469e15	−0.188311
$991$	2.01588e16	0.669976	0.334988	−	0.942222i	$-0.391268\pi$
$991$	2.01588e16	0.669976	0.334988	+	0.942222i	$0.391268\pi$
$992$	1.06642e16	0.352463
$993$	−1.78842e16	−0.587825
$994$	2.64296e16	0.863904
$995$	−4.31606e15	−0.140301
$996$	8.24472e15	0.266532
$997$	3.44516e16	1.10761	0.553805	−	0.832647i	$-0.313175\pi$
$997$	3.44516e16	1.10761	0.553805	+	0.832647i	$0.313175\pi$
$998$	1.17036e16	0.374199
$999$	6.88885e15	0.219047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.12.a.b.1.1	✓	2
3.2	odd	2		45.12.a.e.1.2		2
4.3	odd	2		240.12.a.j.1.1		2
5.2	odd	4		75.12.b.c.49.1		4
5.3	odd	4		75.12.b.c.49.4		4
5.4	even	2		75.12.a.d.1.2		2
15.2	even	4		225.12.b.h.199.4		4
15.8	even	4		225.12.b.h.199.1		4
15.14	odd	2		225.12.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.12.a.b.1.1	✓	2	1.1	even	1	trivial
45.12.a.e.1.2		2	3.2	odd	2
75.12.a.d.1.2		2	5.4	even	2
75.12.b.c.49.1		4	5.2	odd	4
75.12.b.c.49.4		4	5.3	odd	4
225.12.a.g.1.1		2	15.14	odd	2
225.12.b.h.199.1		4	15.8	even	4
225.12.b.h.199.4		4	15.2	even	4
240.12.a.j.1.1		2	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)

\(f(q)\)	\(=\)	\(q-51.1123 q^{2} +243.000 q^{3} +564.472 q^{4} -3125.00 q^{5} -12420.3 q^{6} +45751.3 q^{7} +75826.6 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-51.1123 q^{2} +243.000 q^{3} +564.472 q^{4} -3125.00 q^{5} -12420.3 q^{6} +45751.3 q^{7} +75826.6 q^{8} +59049.0 q^{9} +159726. q^{10} -597423. q^{11} +137167. q^{12} -990011. q^{13} -2.33846e6 q^{14} -759375. q^{15} -5.03171e6 q^{16} -6.61148e6 q^{17} -3.01813e6 q^{18} +576856. q^{19} -1.76397e6 q^{20} +1.11176e7 q^{21} +3.05357e7 q^{22} -4.64840e7 q^{23} +1.84259e7 q^{24} +9.76562e6 q^{25} +5.06018e7 q^{26} +1.43489e7 q^{27} +2.58253e7 q^{28} -1.59099e8 q^{29} +3.88134e7 q^{30} +1.04664e8 q^{31} +1.01890e8 q^{32} -1.45174e8 q^{33} +3.37928e8 q^{34} -1.42973e8 q^{35} +3.33315e7 q^{36} +4.80096e8 q^{37} -2.94845e7 q^{38} -2.40573e8 q^{39} -2.36958e8 q^{40} +6.63154e8 q^{41} -5.68245e8 q^{42} -1.76838e9 q^{43} -3.37228e8 q^{44} -1.84528e8 q^{45} +2.37591e9 q^{46} -1.39342e9 q^{47} -1.22271e9 q^{48} +1.15859e8 q^{49} -4.99144e8 q^{50} -1.60659e9 q^{51} -5.58833e8 q^{52} -2.28338e9 q^{53} -7.33406e8 q^{54} +1.86695e9 q^{55} +3.46917e9 q^{56} +1.40176e8 q^{57} +8.13193e9 q^{58} +3.12820e9 q^{59} -4.28646e8 q^{60} +6.71630e9 q^{61} -5.34962e9 q^{62} +2.70157e9 q^{63} +5.09713e9 q^{64} +3.09378e9 q^{65} +7.42017e9 q^{66} -5.93071e9 q^{67} -3.73199e9 q^{68} -1.12956e10 q^{69} +7.30768e9 q^{70} -1.13022e10 q^{71} +4.47749e9 q^{72} -9.39160e9 q^{73} -2.45388e10 q^{74} +2.37305e9 q^{75} +3.25619e8 q^{76} -2.73329e10 q^{77} +1.22962e10 q^{78} -3.59922e10 q^{79} +1.57241e10 q^{80} +3.48678e9 q^{81} -3.38953e10 q^{82} +6.01074e10 q^{83} +6.27556e9 q^{84} +2.06609e10 q^{85} +9.03863e10 q^{86} -3.86611e10 q^{87} -4.53005e10 q^{88} -1.46902e9 q^{89} +9.43166e9 q^{90} -4.52943e10 q^{91} -2.62389e10 q^{92} +2.54333e10 q^{93} +7.12210e10 q^{94} -1.80268e9 q^{95} +2.47592e10 q^{96} -7.50721e10 q^{97} -5.92183e9 q^{98} -3.52772e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 22 q^{2} + 486 q^{3} - 636 q^{4} - 6250 q^{5} - 5346 q^{6} - 10864 q^{7} - 18744 q^{8} + 118098 q^{9}+O(q^{10}) \) 2 * q - 22 * q^2 + 486 * q^3 - 636 * q^4 - 6250 * q^5 - 5346 * q^6 - 10864 * q^7 - 18744 * q^8 + 118098 * q^9	\( 2 q - 22 q^{2} + 486 q^{3} - 636 q^{4} - 6250 q^{5} - 5346 q^{6} - 10864 q^{7} - 18744 q^{8} + 118098 q^{9} + 68750 q^{10} - 361792 q^{11} - 154548 q^{12} - 2133732 q^{13} - 3986664 q^{14} - 1518750 q^{15} - 5326320 q^{16} - 7804588 q^{17} - 1299078 q^{18} - 15562224 q^{19} + 1987500 q^{20} - 2639952 q^{21} + 37395424 q^{22} - 37450248 q^{23} - 4554792 q^{24} + 19531250 q^{25} + 17305364 q^{26} + 28697814 q^{27} + 93790448 q^{28} - 70320668 q^{29} + 16706250 q^{30} + 298584872 q^{31} + 286993696 q^{32} - 87915456 q^{33} + 303194188 q^{34} + 33950000 q^{35} - 37555164 q^{36} + 236000956 q^{37} - 499330888 q^{38} - 518496876 q^{39} + 58575000 q^{40} - 464942588 q^{41} - 968759352 q^{42} - 242208600 q^{43} - 620095808 q^{44} - 369056250 q^{45} + 2638898832 q^{46} - 4375796920 q^{47} - 1294295760 q^{48} + 1343830130 q^{49} - 214843750 q^{50} - 1896514884 q^{51} + 814171912 q^{52} - 2189541388 q^{53} - 315675954 q^{54} + 1130600000 q^{55} + 8823318240 q^{56} - 3781620432 q^{57} + 10716478004 q^{58} - 5480385856 q^{59} + 482962500 q^{60} + 14557903980 q^{61} + 295874592 q^{62} - 641508336 q^{63} + 11089288256 q^{64} + 6667912500 q^{65} + 9087088032 q^{66} - 15918388888 q^{67} - 2299702856 q^{68} - 9100410264 q^{69} + 12458325000 q^{70} + 1120561024 q^{71} - 1106814456 q^{72} - 24521574348 q^{73} - 31645012364 q^{74} + 4746093750 q^{75} + 19700124976 q^{76} - 40673194368 q^{77} + 4205203452 q^{78} - 79243055560 q^{79} + 16644750000 q^{80} + 6973568802 q^{81} - 66736852348 q^{82} + 9245226696 q^{83} + 22791078864 q^{84} + 24389337500 q^{85} + 134816793608 q^{86} - 17087922324 q^{87} - 67584257664 q^{88} + 22117321236 q^{89} + 4059618750 q^{90} + 19457850112 q^{91} - 37083635424 q^{92} + 72556123896 q^{93} - 15603010256 q^{94} + 48631950000 q^{95} + 69739468128 q^{96} - 160363673468 q^{97} + 29827277722 q^{98} - 21363455808 q^{99}+O(q^{100}) \) 2 * q - 22 * q^2 + 486 * q^3 - 636 * q^4 - 6250 * q^5 - 5346 * q^6 - 10864 * q^7 - 18744 * q^8 + 118098 * q^9 + 68750 * q^10 - 361792 * q^11 - 154548 * q^12 - 2133732 * q^13 - 3986664 * q^14 - 1518750 * q^15 - 5326320 * q^16 - 7804588 * q^17 - 1299078 * q^18 - 15562224 * q^19 + 1987500 * q^20 - 2639952 * q^21 + 37395424 * q^22 - 37450248 * q^23 - 4554792 * q^24 + 19531250 * q^25 + 17305364 * q^26 + 28697814 * q^27 + 93790448 * q^28 - 70320668 * q^29 + 16706250 * q^30 + 298584872 * q^31 + 286993696 * q^32 - 87915456 * q^33 + 303194188 * q^34 + 33950000 * q^35 - 37555164 * q^36 + 236000956 * q^37 - 499330888 * q^38 - 518496876 * q^39 + 58575000 * q^40 - 464942588 * q^41 - 968759352 * q^42 - 242208600 * q^43 - 620095808 * q^44 - 369056250 * q^45 + 2638898832 * q^46 - 4375796920 * q^47 - 1294295760 * q^48 + 1343830130 * q^49 - 214843750 * q^50 - 1896514884 * q^51 + 814171912 * q^52 - 2189541388 * q^53 - 315675954 * q^54 + 1130600000 * q^55 + 8823318240 * q^56 - 3781620432 * q^57 + 10716478004 * q^58 - 5480385856 * q^59 + 482962500 * q^60 + 14557903980 * q^61 + 295874592 * q^62 - 641508336 * q^63 + 11089288256 * q^64 + 6667912500 * q^65 + 9087088032 * q^66 - 15918388888 * q^67 - 2299702856 * q^68 - 9100410264 * q^69 + 12458325000 * q^70 + 1120561024 * q^71 - 1106814456 * q^72 - 24521574348 * q^73 - 31645012364 * q^74 + 4746093750 * q^75 + 19700124976 * q^76 - 40673194368 * q^77 + 4205203452 * q^78 - 79243055560 * q^79 + 16644750000 * q^80 + 6973568802 * q^81 - 66736852348 * q^82 + 9245226696 * q^83 + 22791078864 * q^84 + 24389337500 * q^85 + 134816793608 * q^86 - 17087922324 * q^87 - 67584257664 * q^88 + 22117321236 * q^89 + 4059618750 * q^90 + 19457850112 * q^91 - 37083635424 * q^92 + 72556123896 * q^93 - 15603010256 * q^94 + 48631950000 * q^95 + 69739468128 * q^96 - 160363673468 * q^97 + 29827277722 * q^98 - 21363455808 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more