LMFDB - Embedded newform 17.12.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,12,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	17.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:	$13.0618340695$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 13381 x^{6} - 182353 x^{5} + 49101741 x^{4} + 1188560917 x^{3} - 22633823135 x^{2} + \cdots + 2663203205942 $ x^8 - x^7 - 13381x^6 - 182353x^5 + 49101741x^4 + 1188560917x^3 - 22633823135x^2 - 272713840835x + 2663203205942
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$92.3600$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-85.3600 q^{2} +403.021 q^{3} +5238.33 q^{4} +11654.5 q^{5} -34401.9 q^{6} +59759.3 q^{7} -272327. q^{8} -14721.1 q^{9} +O(q^{10})$	\(q-85.3600 q^{2} +403.021 q^{3} +5238.33 q^{4} +11654.5 q^{5} -34401.9 q^{6} +59759.3 q^{7} -272327. q^{8} -14721.1 q^{9} -994831. q^{10} +443448. q^{11} +2.11116e6 q^{12} +499279. q^{13} -5.10105e6 q^{14} +4.69702e6 q^{15} +1.25177e7 q^{16} -1.41986e6 q^{17} +1.25660e6 q^{18} -5.08650e6 q^{19} +6.10503e7 q^{20} +2.40842e7 q^{21} -3.78528e7 q^{22} -3.87621e7 q^{23} -1.09753e8 q^{24} +8.70000e7 q^{25} -4.26185e7 q^{26} -7.73269e7 q^{27} +3.13039e8 q^{28} -6.81974e7 q^{29} -4.00938e8 q^{30} +2.23045e8 q^{31} -5.10785e8 q^{32} +1.78719e8 q^{33} +1.21199e8 q^{34} +6.96466e8 q^{35} -7.71142e7 q^{36} +4.95840e8 q^{37} +4.34184e8 q^{38} +2.01220e8 q^{39} -3.17384e9 q^{40} -2.61035e8 q^{41} -2.05583e9 q^{42} -9.38480e8 q^{43} +2.32293e9 q^{44} -1.71568e8 q^{45} +3.30874e9 q^{46} -2.37154e8 q^{47} +5.04489e9 q^{48} +1.59384e9 q^{49} -7.42632e9 q^{50} -5.72232e8 q^{51} +2.61539e9 q^{52} +1.24123e9 q^{53} +6.60062e9 q^{54} +5.16819e9 q^{55} -1.62740e10 q^{56} -2.04997e9 q^{57} +5.82133e9 q^{58} +3.15362e8 q^{59} +2.46045e10 q^{60} -9.32797e9 q^{61} -1.90391e10 q^{62} -8.79724e8 q^{63} +1.79644e10 q^{64} +5.81887e9 q^{65} -1.52555e10 q^{66} +1.78594e10 q^{67} -7.43768e9 q^{68} -1.56220e10 q^{69} -5.94504e10 q^{70} -2.10037e10 q^{71} +4.00896e9 q^{72} +1.15444e10 q^{73} -4.23249e10 q^{74} +3.50628e10 q^{75} -2.66448e10 q^{76} +2.65002e10 q^{77} -1.71761e10 q^{78} +2.34155e10 q^{79} +1.45888e11 q^{80} -2.85565e10 q^{81} +2.22819e10 q^{82} -3.94839e10 q^{83} +1.26161e11 q^{84} -1.65478e10 q^{85} +8.01087e10 q^{86} -2.74850e10 q^{87} -1.20763e11 q^{88} +6.84718e9 q^{89} +1.46450e10 q^{90} +2.98366e10 q^{91} -2.03049e11 q^{92} +8.98917e10 q^{93} +2.02435e10 q^{94} -5.92808e10 q^{95} -2.05857e11 q^{96} +1.02936e11 q^{97} -1.36050e11 q^{98} -6.52807e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 55 q^{2} + 496 q^{3} + 10757 q^{4} + 8592 q^{5} + 17194 q^{6} + 95288 q^{7} - 247863 q^{8} + 500648 q^{9}+O(q^{10}) $ 8 * q + 55 * q^2 + 496 * q^3 + 10757 * q^4 + 8592 * q^5 + 17194 * q^6 + 95288 * q^7 - 247863 * q^8 + 500648 * q^9	\( 8 q + 55 q^{2} + 496 q^{3} + 10757 q^{4} + 8592 q^{5} + 17194 q^{6} + 95288 q^{7} - 247863 q^{8} + 500648 q^{9} + 2824 q^{10} + 435256 q^{11} + 4295182 q^{12} + 4193784 q^{13} + 4377132 q^{14} + 10362648 q^{15} + 20722897 q^{16} - 11358856 q^{17} + 28881887 q^{18} + 15158192 q^{19} + 91612472 q^{20} + 98415768 q^{21} + 81767186 q^{22} + 22374432 q^{23} - 41056218 q^{24} + 133926472 q^{25} - 70553178 q^{26} + 68932744 q^{27} + 108010892 q^{28} - 424656432 q^{29} - 561465200 q^{30} - 172323152 q^{31} - 540258159 q^{32} - 764794592 q^{33} - 78092135 q^{34} - 117251352 q^{35} - 1812061939 q^{36} - 262792640 q^{37} - 674758596 q^{38} - 302706728 q^{39} - 3575120264 q^{40} - 1283308512 q^{41} - 1036128840 q^{42} + 2219398472 q^{43} + 4256110614 q^{44} + 3982117536 q^{45} + 6081288184 q^{46} + 260684408 q^{47} + 6860204310 q^{48} + 12060045320 q^{49} - 1911832923 q^{50} - 704249072 q^{51} + 3548505010 q^{52} + 9402026896 q^{53} - 848951924 q^{54} + 4430702936 q^{55} - 11881582644 q^{56} + 1366983408 q^{57} + 814919720 q^{58} + 14325543480 q^{59} + 4281784208 q^{60} - 9811064576 q^{61} - 41469249572 q^{62} + 14666072688 q^{63} - 27038375199 q^{64} + 29701570288 q^{65} - 43330462276 q^{66} + 52928023248 q^{67} - 15273401749 q^{68} - 13481294472 q^{69} - 128492187744 q^{70} - 34868356504 q^{71} - 52662987279 q^{72} + 1248764080 q^{73} - 135359144436 q^{74} + 59235735072 q^{75} - 49428813052 q^{76} + 112631449800 q^{77} - 87670698684 q^{78} + 18209008736 q^{79} + 96412241400 q^{80} + 67350111224 q^{81} + 41461375370 q^{82} + 169643760088 q^{83} + 117131104968 q^{84} - 12199411344 q^{85} + 88510231200 q^{86} + 35491052136 q^{87} - 51404280146 q^{88} + 201694397904 q^{89} - 4670596888 q^{90} + 36284010568 q^{91} - 3754023808 q^{92} + 106318637912 q^{93} + 253870878768 q^{94} - 383491632 q^{95} - 102115750890 q^{96} + 163430440672 q^{97} - 110963034673 q^{98} - 716459488 q^{99}+O(q^{100}) \) 8 * q + 55 * q^2 + 496 * q^3 + 10757 * q^4 + 8592 * q^5 + 17194 * q^6 + 95288 * q^7 - 247863 * q^8 + 500648 * q^9 + 2824 * q^10 + 435256 * q^11 + 4295182 * q^12 + 4193784 * q^13 + 4377132 * q^14 + 10362648 * q^15 + 20722897 * q^16 - 11358856 * q^17 + 28881887 * q^18 + 15158192 * q^19 + 91612472 * q^20 + 98415768 * q^21 + 81767186 * q^22 + 22374432 * q^23 - 41056218 * q^24 + 133926472 * q^25 - 70553178 * q^26 + 68932744 * q^27 + 108010892 * q^28 - 424656432 * q^29 - 561465200 * q^30 - 172323152 * q^31 - 540258159 * q^32 - 764794592 * q^33 - 78092135 * q^34 - 117251352 * q^35 - 1812061939 * q^36 - 262792640 * q^37 - 674758596 * q^38 - 302706728 * q^39 - 3575120264 * q^40 - 1283308512 * q^41 - 1036128840 * q^42 + 2219398472 * q^43 + 4256110614 * q^44 + 3982117536 * q^45 + 6081288184 * q^46 + 260684408 * q^47 + 6860204310 * q^48 + 12060045320 * q^49 - 1911832923 * q^50 - 704249072 * q^51 + 3548505010 * q^52 + 9402026896 * q^53 - 848951924 * q^54 + 4430702936 * q^55 - 11881582644 * q^56 + 1366983408 * q^57 + 814919720 * q^58 + 14325543480 * q^59 + 4281784208 * q^60 - 9811064576 * q^61 - 41469249572 * q^62 + 14666072688 * q^63 - 27038375199 * q^64 + 29701570288 * q^65 - 43330462276 * q^66 + 52928023248 * q^67 - 15273401749 * q^68 - 13481294472 * q^69 - 128492187744 * q^70 - 34868356504 * q^71 - 52662987279 * q^72 + 1248764080 * q^73 - 135359144436 * q^74 + 59235735072 * q^75 - 49428813052 * q^76 + 112631449800 * q^77 - 87670698684 * q^78 + 18209008736 * q^79 + 96412241400 * q^80 + 67350111224 * q^81 + 41461375370 * q^82 + 169643760088 * q^83 + 117131104968 * q^84 - 12199411344 * q^85 + 88510231200 * q^86 + 35491052136 * q^87 - 51404280146 * q^88 + 201694397904 * q^89 - 4670596888 * q^90 + 36284010568 * q^91 - 3754023808 * q^92 + 106318637912 * q^93 + 253870878768 * q^94 - 383491632 * q^95 - 102115750890 * q^96 + 163430440672 * q^97 - 110963034673 * q^98 - 716459488 * 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 $

$2$	−85.3600	−1.88621	−0.943104	−	0.332499i	$-0.892108\pi$
$2$	−85.3600	−1.88621	−0.943104	+	0.332499i	$0.892108\pi$
$3$	403.021	0.957548	0.478774	−	0.877938i	$-0.341081\pi$
$3$	403.021	0.957548	0.478774	+	0.877938i	$0.341081\pi$
$4$	5238.33	2.55778
$5$	11654.5	1.66786	0.833931	−	0.551869i	$-0.186085\pi$
$5$	11654.5	1.66786	0.833931	+	0.551869i	$0.186085\pi$
$6$	−34401.9	−1.80613
$7$	59759.3	1.34390	0.671948	−	0.740598i	$-0.265458\pi$
$7$	59759.3	1.34390	0.671948	+	0.740598i	$0.265458\pi$
$8$	−272327.	−2.93829
$9$	−14721.1	−0.0831013
$10$	−994831.	−3.14593
$11$	443448.	0.830201	0.415101	−	0.909775i	$-0.363746\pi$
$11$	443448.	0.830201	0.415101	+	0.909775i	$0.363746\pi$
$12$	2.11116e6	2.44920
$13$	499279.	0.372954	0.186477	−	0.982459i	$-0.440293\pi$
$13$	499279.	0.372954	0.186477	+	0.982459i	$0.440293\pi$
$14$	−5.10105e6	−2.53487
$15$	4.69702e6	1.59706
$16$	1.25177e7	2.98445
$17$	−1.41986e6	−0.242536
$17$	−1.41986e6	−0.242536
$18$	1.25660e6	0.156746
$19$	−5.08650e6	−0.471275	−0.235638	−	0.971841i	$-0.575718\pi$
$19$	−5.08650e6	−0.471275	−0.235638	+	0.971841i	$0.575718\pi$
$20$	6.10503e7	4.26602
$21$	2.40842e7	1.28685
$22$	−3.78528e7	−1.56593
$23$	−3.87621e7	−1.25575	−0.627877	−	0.778312i	$-0.716076\pi$
$23$	−3.87621e7	−1.25575	−0.627877	+	0.778312i	$0.716076\pi$
$24$	−1.09753e8	−2.81356
$25$	8.70000e7	1.78176
$26$	−4.26185e7	−0.703468
$27$	−7.73269e7	−1.03712
$28$	3.13039e8	3.43739
$29$	−6.81974e7	−0.617417	−0.308709	−	0.951157i	$-0.599897\pi$
$29$	−6.81974e7	−0.617417	−0.308709	+	0.951157i	$0.599897\pi$
$30$	−4.00938e8	−3.01238
$31$	2.23045e8	1.39927	0.699637	−	0.714499i	$-0.253345\pi$
$31$	2.23045e8	1.39927	0.699637	+	0.714499i	$0.253345\pi$
$32$	−5.10785e8	−2.69100
$33$	1.78719e8	0.794958
$34$	1.21199e8	0.457472
$35$	6.96466e8	2.24143
$36$	−7.71142e7	−0.212555
$37$	4.95840e8	1.17553	0.587763	−	0.809033i	$-0.300009\pi$
$37$	4.95840e8	1.17553	0.587763	+	0.809033i	$0.300009\pi$
$38$	4.34184e8	0.888923
$39$	2.01220e8	0.357121
$40$	−3.17384e9	−4.90066
$41$	−2.61035e8	−0.351874	−0.175937	−	0.984401i	$-0.556295\pi$
$41$	−2.61035e8	−0.351874	−0.175937	+	0.984401i	$0.556295\pi$
$42$	−2.05583e9	−2.42726
$43$	−9.38480e8	−0.973528	−0.486764	−	0.873533i	$-0.661823\pi$
$43$	−9.38480e8	−0.973528	−0.486764	+	0.873533i	$0.661823\pi$
$44$	2.32293e9	2.12347
$45$	−1.71568e8	−0.138601
$46$	3.30874e9	2.36861
$47$	−2.37154e8	−0.150832	−0.0754158	−	0.997152i	$-0.524028\pi$
$47$	−2.37154e8	−0.150832	−0.0754158	+	0.997152i	$0.524028\pi$
$48$	5.04489e9	2.85776
$49$	1.59384e9	0.806059
$50$	−7.42632e9	−3.36077
$51$	−5.72232e8	−0.232240
$52$	2.61539e9	0.953933
$53$	1.24123e9	0.407694	0.203847	−	0.979003i	$-0.434655\pi$
$53$	1.24123e9	0.407694	0.203847	+	0.979003i	$0.434655\pi$
$54$	6.60062e9	1.95623
$55$	5.16819e9	1.38466
$56$	−1.62740e10	−3.94876
$57$	−2.04997e9	−0.451269
$58$	5.82133e9	1.16458
$59$	3.15362e8	0.0574280	0.0287140	−	0.999588i	$-0.490859\pi$
$59$	3.15362e8	0.0574280	0.0287140	+	0.999588i	$0.490859\pi$
$60$	2.46045e10	4.08492
$61$	−9.32797e9	−1.41408	−0.707039	−	0.707175i	$-0.749969\pi$
$61$	−9.32797e9	−1.41408	−0.707039	+	0.707175i	$0.749969\pi$
$62$	−1.90391e10	−2.63932
$63$	−8.79724e8	−0.111680
$64$	1.79644e10	2.09133
$65$	5.81887e9	0.622035
$66$	−1.52555e10	−1.49946
$67$	1.78594e10	1.61605	0.808026	−	0.589147i	$-0.200536\pi$
$67$	1.78594e10	1.61605	0.808026	+	0.589147i	$0.200536\pi$
$68$	−7.43768e9	−0.620352
$69$	−1.56220e10	−1.20245
$70$	−5.94504e10	−4.22781
$71$	−2.10037e10	−1.38158	−0.690788	−	0.723058i	$-0.742736\pi$
$71$	−2.10037e10	−1.38158	−0.690788	+	0.723058i	$0.742736\pi$
$72$	4.00896e9	0.244176
$73$	1.15444e10	0.651774	0.325887	−	0.945409i	$-0.394337\pi$
$73$	1.15444e10	0.651774	0.325887	+	0.945409i	$0.394337\pi$
$74$	−4.23249e10	−2.21728
$75$	3.50628e10	1.70612
$76$	−2.66448e10	−1.20542
$77$	2.65002e10	1.11570
$78$	−1.71761e10	−0.673605
$79$	2.34155e10	0.856160	0.428080	−	0.903741i	$-0.359190\pi$
$79$	2.34155e10	0.856160	0.428080	+	0.903741i	$0.359190\pi$
$80$	1.45888e11	4.97765
$81$	−2.85565e10	−0.909993
$82$	2.22819e10	0.663707
$83$	−3.94839e10	−1.10025	−0.550123	−	0.835083i	$-0.685419\pi$
$83$	−3.94839e10	−1.10025	−0.550123	+	0.835083i	$0.685419\pi$
$84$	1.26161e11	3.29147
$85$	−1.65478e10	−0.404516
$86$	8.01087e10	1.83628
$87$	−2.74850e10	−0.591207
$88$	−1.20763e11	−2.43937
$89$	6.84718e9	0.129977	0.0649885	−	0.997886i	$-0.479299\pi$
$89$	6.84718e9	0.129977	0.0649885	+	0.997886i	$0.479299\pi$
$90$	1.46450e10	0.261431
$91$	2.98366e10	0.501212
$92$	−2.03049e11	−3.21194
$93$	8.98917e10	1.33987
$94$	2.02435e10	0.284500
$95$	−5.92808e10	−0.786022
$96$	−2.05857e11	−2.57676
$97$	1.02936e11	1.21710	0.608548	−	0.793517i	$-0.291752\pi$
$97$	1.02936e11	1.21710	0.608548	+	0.793517i	$0.291752\pi$
$98$	−1.36050e11	−1.52039
$99$	−6.52807e9	−0.0689908
$100$	4.55735e11	4.55735
$101$	−5.36357e10	−0.507793	−0.253896	−	0.967231i	$-0.581712\pi$
$101$	−5.36357e10	−0.507793	−0.253896	+	0.967231i	$0.581712\pi$
$102$	4.88457e10	0.438052
$103$	−8.38540e10	−0.712720	−0.356360	−	0.934349i	$-0.615982\pi$
$103$	−8.38540e10	−0.712720	−0.356360	+	0.934349i	$0.615982\pi$
$104$	−1.35967e11	−1.09585
$105$	2.80690e11	2.14628
$106$	−1.05951e11	−0.768996
$107$	7.85853e10	0.541665	0.270832	−	0.962627i	$-0.412701\pi$
$107$	7.85853e10	0.541665	0.270832	+	0.962627i	$0.412701\pi$
$108$	−4.05064e11	−2.65273
$109$	6.02729e10	0.375212	0.187606	−	0.982244i	$-0.439927\pi$
$109$	6.02729e10	0.375212	0.187606	+	0.982244i	$0.439927\pi$
$110$	−4.41156e11	−2.61176
$111$	1.99834e11	1.12562
$112$	7.48048e11	4.01079
$113$	1.38843e11	0.708914	0.354457	−	0.935072i	$-0.384666\pi$
$113$	1.38843e11	0.708914	0.354457	+	0.935072i	$0.384666\pi$
$114$	1.74985e11	0.851187
$115$	−4.51755e11	−2.09442
$116$	−3.57240e11	−1.57922
$117$	−7.34996e9	−0.0309929
$118$	−2.69193e10	−0.108321
$119$	−8.48496e10	−0.325943
$120$	−1.27912e12	−4.69262
$121$	−8.86651e10	−0.310766
$122$	7.96236e11	2.66724
$123$	−1.05202e11	−0.336936
$124$	1.16838e12	3.57903
$125$	4.44876e11	1.30387
$126$	7.50933e10	0.210651
$127$	−1.34022e10	−0.0359962	−0.0179981	−	0.999838i	$-0.505729\pi$
$127$	−1.34022e10	−0.0359962	−0.0179981	+	0.999838i	$0.505729\pi$
$128$	−4.87354e11	−1.25369
$129$	−3.78227e11	−0.932200
$130$	−4.96699e11	−1.17329
$131$	−1.93010e11	−0.437106	−0.218553	−	0.975825i	$-0.570134\pi$
$131$	−1.93010e11	−0.437106	−0.218553	+	0.975825i	$0.570134\pi$
$132$	9.36189e11	2.03333
$133$	−3.03966e11	−0.633345
$134$	−1.52448e12	−3.04821
$135$	−9.01209e11	−1.72978
$136$	3.86665e11	0.712641
$137$	3.54419e10	0.0627414	0.0313707	−	0.999508i	$-0.490013\pi$
$137$	3.54419e10	0.0627414	0.0313707	+	0.999508i	$0.490013\pi$
$138$	1.33349e12	2.26806
$139$	−7.52112e11	−1.22942	−0.614711	−	0.788752i	$-0.710727\pi$
$139$	−7.52112e11	−1.22942	−0.614711	+	0.788752i	$0.710727\pi$
$140$	3.64832e12	5.73309
$141$	−9.55781e10	−0.144429
$142$	1.79287e12	2.60594
$143$	2.21405e11	0.309627
$144$	−1.84275e11	−0.248012
$145$	−7.94808e11	−1.02977
$146$	−9.85433e11	−1.22938
$147$	6.42352e11	0.771840
$148$	2.59737e12	3.00673
$149$	−6.32368e11	−0.705416	−0.352708	−	0.935733i	$-0.614739\pi$
$149$	−6.32368e11	−0.705416	−0.352708	+	0.935733i	$0.614739\pi$
$150$	−2.99296e12	−3.21810
$151$	−1.02480e12	−1.06235	−0.531175	−	0.847262i	$-0.678249\pi$
$151$	−1.02480e12	−1.06235	−0.531175	+	0.847262i	$0.678249\pi$
$152$	1.38519e12	1.38474
$153$	2.09019e10	0.0201550
$154$	−2.26205e12	−2.10445
$155$	2.59948e12	2.33379
$156$	1.05406e12	0.913437
$157$	−2.20389e12	−1.84392	−0.921961	−	0.387283i	$-0.873414\pi$
$157$	−2.20389e12	−1.84392	−0.921961	+	0.387283i	$0.873414\pi$
$158$	−1.99875e12	−1.61489
$159$	5.00241e11	0.390387
$160$	−5.95297e12	−4.48821
$161$	−2.31640e12	−1.68760
$162$	2.43759e12	1.71644
$163$	2.75172e12	1.87315	0.936576	−	0.350465i	$-0.113976\pi$
$163$	2.75172e12	1.87315	0.936576	+	0.350465i	$0.113976\pi$
$164$	−1.36739e12	−0.900015
$165$	2.08289e12	1.32588
$166$	3.37034e12	2.07529
$167$	−2.79541e11	−0.166535	−0.0832674	−	0.996527i	$-0.526536\pi$
$167$	−2.79541e11	−0.166535	−0.0832674	+	0.996527i	$0.526536\pi$
$168$	−6.55877e12	−3.78113
$169$	−1.54288e12	−0.860905
$170$	1.41252e12	0.763001
$171$	7.48791e10	0.0391636
$172$	−4.91607e12	−2.49007
$173$	2.86396e11	0.140512	0.0702561	−	0.997529i	$-0.477618\pi$
$173$	2.86396e11	0.140512	0.0702561	+	0.997529i	$0.477618\pi$
$174$	2.34612e12	1.11514
$175$	5.19906e12	2.39450
$176$	5.55095e12	2.47769
$177$	1.27098e11	0.0549901
$178$	−5.84475e11	−0.245164
$179$	3.60049e12	1.46443	0.732217	−	0.681071i	$-0.238486\pi$
$179$	3.60049e12	1.46443	0.732217	+	0.681071i	$0.238486\pi$
$180$	−8.98730e11	−0.354512
$181$	−4.09942e12	−1.56852	−0.784261	−	0.620431i	$-0.786958\pi$
$181$	−4.09942e12	−1.56852	−0.784261	+	0.620431i	$0.786958\pi$
$182$	−2.54685e12	−0.945389
$183$	−3.75937e12	−1.35405
$184$	1.05560e13	3.68977
$185$	5.77878e12	1.96061
$186$	−7.67315e12	−2.52728
$187$	−6.29633e11	−0.201353
$188$	−1.24229e12	−0.385794
$189$	−4.62100e12	−1.39378
$190$	5.06021e12	1.48260
$191$	1.74292e12	0.496129	0.248064	−	0.968744i	$-0.420206\pi$
$191$	1.74292e12	0.496129	0.248064	+	0.968744i	$0.420206\pi$
$192$	7.24003e12	2.00255
$193$	4.87795e12	1.31121	0.655605	−	0.755104i	$-0.272414\pi$
$193$	4.87795e12	1.31121	0.655605	+	0.755104i	$0.272414\pi$
$194$	−8.78665e12	−2.29569
$195$	2.34513e12	0.595629
$196$	8.34907e12	2.06172
$197$	1.11620e11	0.0268027	0.0134013	−	0.999910i	$-0.495734\pi$
$197$	1.11620e11	0.0268027	0.0134013	+	0.999910i	$0.495734\pi$
$198$	5.57236e11	0.130131
$199$	1.55670e12	0.353600	0.176800	−	0.984247i	$-0.443425\pi$
$199$	1.55670e12	0.353600	0.176800	+	0.984247i	$0.443425\pi$
$200$	−2.36924e13	−5.23533
$201$	7.19771e12	1.54745
$202$	4.57835e12	0.957803
$203$	−4.07542e12	−0.829745
$204$	−2.99754e12	−0.594017
$205$	−3.04224e12	−0.586877
$206$	7.15778e12	1.34434
$207$	5.70623e11	0.104355
$208$	6.24983e12	1.11306
$209$	−2.25560e12	−0.391253
$210$	−2.39597e13	−4.04833
$211$	2.66260e12	0.438281	0.219140	−	0.975693i	$-0.429675\pi$
$211$	2.66260e12	0.438281	0.219140	+	0.975693i	$0.429675\pi$
$212$	6.50197e12	1.04279
$213$	−8.46492e12	−1.32293
$214$	−6.70804e12	−1.02169
$215$	−1.09375e13	−1.62371
$216$	2.10582e13	3.04737
$217$	1.33290e13	1.88048
$218$	−5.14490e12	−0.707728
$219$	4.65265e12	0.624105
$220$	2.70727e13	3.54165
$221$	−7.08905e11	−0.0904546
$222$	−1.70578e13	−2.12316
$223$	−1.44033e13	−1.74898	−0.874489	−	0.485046i	$-0.838803\pi$
$223$	−1.44033e13	−1.74898	−0.874489	+	0.485046i	$0.838803\pi$
$224$	−3.05242e13	−3.61643
$225$	−1.28074e12	−0.148067
$226$	−1.18517e13	−1.33716
$227$	7.67360e12	0.845000	0.422500	−	0.906363i	$-0.361153\pi$
$227$	7.67360e12	0.845000	0.422500	+	0.906363i	$0.361153\pi$
$228$	−1.07384e13	−1.15425
$229$	−4.20550e12	−0.441288	−0.220644	−	0.975354i	$-0.570816\pi$
$229$	−4.20550e12	−0.441288	−0.220644	+	0.975354i	$0.570816\pi$
$230$	3.85618e13	3.95052
$231$	1.06801e13	1.06834
$232$	1.85720e13	1.81415
$233$	−1.40420e13	−1.33959	−0.669794	−	0.742547i	$-0.733617\pi$
$233$	−1.40420e13	−1.33959	−0.669794	+	0.742547i	$0.733617\pi$
$234$	6.27393e11	0.0584591
$235$	−2.76392e12	−0.251566
$236$	1.65197e12	0.146888
$237$	9.43694e12	0.819814
$238$	7.24276e12	0.614796
$239$	5.42713e12	0.450176	0.225088	−	0.974338i	$-0.427733\pi$
$239$	5.42713e12	0.450176	0.225088	+	0.974338i	$0.427733\pi$
$240$	5.87959e13	4.76634
$241$	−2.42234e13	−1.91929	−0.959646	−	0.281212i	$-0.909263\pi$
$241$	−2.42234e13	−1.91929	−0.959646	+	0.281212i	$0.909263\pi$
$242$	7.56845e12	0.586169
$243$	2.18934e12	0.165760
$244$	−4.88630e13	−3.61690
$245$	1.85755e13	1.34439
$246$	8.98008e12	0.635532
$247$	−2.53959e12	−0.175764
$248$	−6.07410e13	−4.11147
$249$	−1.59128e13	−1.05354
$250$	−3.79746e13	−2.45937
$251$	9.18068e12	0.581660	0.290830	−	0.956775i	$-0.406069\pi$
$251$	9.18068e12	0.581660	0.290830	+	0.956775i	$0.406069\pi$
$252$	−4.60829e12	−0.285651
$253$	−1.71890e13	−1.04253
$254$	1.14401e12	0.0678963
$255$	−6.66910e12	−0.387343
$256$	4.80939e12	0.273382
$257$	−1.85531e13	−1.03225	−0.516126	−	0.856513i	$-0.672626\pi$
$257$	−1.85531e13	−1.03225	−0.516126	+	0.856513i	$0.672626\pi$
$258$	3.22855e13	1.75832
$259$	2.96310e13	1.57978
$260$	3.04812e13	1.59103
$261$	1.00394e12	0.0513081
$262$	1.64753e13	0.824473
$263$	5.36351e12	0.262841	0.131420	−	0.991327i	$-0.458046\pi$
$263$	5.36351e12	0.262841	0.131420	+	0.991327i	$0.458046\pi$
$264$	−4.86699e13	−2.33582
$265$	1.44659e13	0.679978
$266$	2.59465e13	1.19462
$267$	2.75956e12	0.124459
$268$	9.35533e13	4.13350
$269$	3.78277e13	1.63747	0.818733	−	0.574174i	$-0.194677\pi$
$269$	3.78277e13	1.63747	0.818733	+	0.574174i	$0.194677\pi$
$270$	7.69272e13	3.26271
$271$	−1.89879e13	−0.789126	−0.394563	−	0.918869i	$-0.629104\pi$
$271$	−1.89879e13	−0.789126	−0.394563	+	0.918869i	$0.629104\pi$
$272$	−1.77733e13	−0.723836
$273$	1.20248e13	0.479934
$274$	−3.02532e12	−0.118343
$275$	3.85800e13	1.47922
$276$	−8.18329e13	−3.07559
$277$	2.64877e13	0.975900	0.487950	−	0.872872i	$-0.337745\pi$
$277$	2.64877e13	0.975900	0.487950	+	0.872872i	$0.337745\pi$
$278$	6.42003e13	2.31895
$279$	−3.28347e12	−0.116281
$280$	−1.89666e14	−6.58599
$281$	−5.49501e13	−1.87104	−0.935522	−	0.353268i	$-0.885070\pi$
$281$	−5.49501e13	−1.87104	−0.935522	+	0.353268i	$0.885070\pi$
$282$	8.15855e12	0.272422
$283$	−6.28055e12	−0.205671	−0.102835	−	0.994698i	$-0.532791\pi$
$283$	−6.28055e12	−0.205671	−0.102835	+	0.994698i	$0.532791\pi$
$284$	−1.10024e14	−3.53376
$285$	−2.38914e13	−0.752654
$286$	−1.88991e13	−0.584020
$287$	−1.55992e13	−0.472882
$288$	7.51934e12	0.223625
$289$	2.01599e12	0.0588235
$290$	6.78449e13	1.94235
$291$	4.14855e13	1.16543
$292$	6.04736e13	1.66709
$293$	−8.66465e12	−0.234412	−0.117206	−	0.993108i	$-0.537394\pi$
$293$	−8.66465e12	−0.234412	−0.117206	+	0.993108i	$0.537394\pi$
$294$	−5.48311e13	−1.45585
$295$	3.67540e12	0.0957819
$296$	−1.35030e14	−3.45404
$297$	−3.42905e13	−0.861020
$298$	5.39789e13	1.33056
$299$	−1.93531e13	−0.468339
$300$	1.83671e14	4.36388
$301$	−5.60829e13	−1.30832
$302$	8.74772e13	2.00381
$303$	−2.16163e13	−0.486236
$304$	−6.36713e13	−1.40650
$305$	−1.08713e14	−2.35849
$306$	−1.78419e12	−0.0380165
$307$	4.46552e13	0.934568	0.467284	−	0.884107i	$-0.345233\pi$
$307$	4.46552e13	0.934568	0.467284	+	0.884107i	$0.345233\pi$
$308$	1.38817e14	2.85373
$309$	−3.37949e13	−0.682464
$310$	−2.21892e14	−4.40202
$311$	−4.45754e12	−0.0868786	−0.0434393	−	0.999056i	$-0.513832\pi$
$311$	−4.45754e12	−0.0868786	−0.0434393	+	0.999056i	$0.513832\pi$
$312$	−5.47976e13	−1.04933
$313$	3.02029e12	0.0568270	0.0284135	−	0.999596i	$-0.490954\pi$
$313$	3.02029e12	0.0568270	0.0284135	+	0.999596i	$0.490954\pi$
$314$	1.88124e14	3.47802
$315$	−1.02528e13	−0.186266
$316$	1.22658e14	2.18987
$317$	7.89798e13	1.38577	0.692883	−	0.721050i	$-0.256340\pi$
$317$	7.89798e13	1.38577	0.692883	+	0.721050i	$0.256340\pi$
$318$	−4.27006e13	−0.736351
$319$	−3.02420e13	−0.512580
$320$	2.09367e14	3.48805
$321$	3.16715e13	0.518670
$322$	1.97728e14	3.18317
$323$	7.22211e12	0.114301
$324$	−1.49589e14	−2.32756
$325$	4.34373e13	0.664515
$326$	−2.34887e14	−3.53315
$327$	2.42913e13	0.359284
$328$	7.10867e13	1.03391
$329$	−1.41722e13	−0.202702
$330$	−1.77795e14	−2.50088
$331$	−3.69213e13	−0.510767	−0.255384	−	0.966840i	$-0.582202\pi$
$331$	−3.69213e13	−0.510767	−0.255384	+	0.966840i	$0.582202\pi$
$332$	−2.06829e14	−2.81419
$333$	−7.29933e12	−0.0976876
$334$	2.38616e13	0.314119
$335$	2.08143e14	2.69535
$336$	3.01479e14	3.84053
$337$	−7.83754e13	−0.982235	−0.491117	−	0.871093i	$-0.663411\pi$
$337$	−7.83754e13	−0.982235	−0.491117	+	0.871093i	$0.663411\pi$
$338$	1.31700e14	1.62385
$339$	5.59567e13	0.678819
$340$	−8.66827e13	−1.03466
$341$	9.89088e13	1.16168
$342$	−6.39168e12	−0.0738706
$343$	−2.29168e13	−0.260637
$344$	2.55573e14	2.86051
$345$	−1.82067e14	−2.00551
$346$	−2.44468e13	−0.265035
$347$	1.09876e14	1.17244	0.586220	−	0.810152i	$-0.300616\pi$
$347$	1.09876e14	1.17244	0.586220	+	0.810152i	$0.300616\pi$
$348$	−1.43975e14	−1.51218
$349$	1.04679e14	1.08223	0.541115	−	0.840948i	$-0.318002\pi$
$349$	1.04679e14	1.08223	0.541115	+	0.840948i	$0.318002\pi$
$350$	−4.43791e14	−4.51653
$351$	−3.86077e13	−0.386799
$352$	−2.26507e14	−2.23407
$353$	1.65947e12	0.0161142	0.00805709	−	0.999968i	$-0.497435\pi$
$353$	1.65947e12	0.0161142	0.00805709	+	0.999968i	$0.497435\pi$
$354$	−1.08491e13	−0.103723
$355$	−2.44788e14	−2.30428
$356$	3.58678e13	0.332452
$357$	−3.41962e13	−0.312106
$358$	−3.07338e14	−2.76223
$359$	−1.52216e13	−0.134723	−0.0673613	−	0.997729i	$-0.521458\pi$
$359$	−1.52216e13	−0.134723	−0.0673613	+	0.997729i	$0.521458\pi$
$360$	4.67225e13	0.407251
$361$	−9.06177e13	−0.777900
$362$	3.49927e14	2.95856
$363$	−3.57339e13	−0.297573
$364$	1.56294e14	1.28199
$365$	1.34545e14	1.08707
$366$	3.20900e14	2.55401
$367$	1.24395e14	0.975299	0.487650	−	0.873039i	$-0.337854\pi$
$367$	1.24395e14	0.975299	0.487650	+	0.873039i	$0.337854\pi$
$368$	−4.85213e14	−3.74774
$369$	3.84273e12	0.0292412
$370$	−4.93277e14	−3.69812
$371$	7.41749e13	0.547899
$372$	4.70882e14	3.42709
$373$	−3.44884e13	−0.247329	−0.123664	−	0.992324i	$-0.539465\pi$
$373$	−3.44884e13	−0.247329	−0.123664	+	0.992324i	$0.539465\pi$
$374$	5.37455e13	0.379794
$375$	1.79294e14	1.24852
$376$	6.45834e13	0.443188
$377$	−3.40495e13	−0.230268
$378$	3.94448e14	2.62897
$379$	3.75169e13	0.246440	0.123220	−	0.992379i	$-0.460678\pi$
$379$	3.75169e13	0.246440	0.123220	+	0.992379i	$0.460678\pi$
$380$	−3.10533e14	−2.01047
$381$	−5.40138e12	−0.0344681
$382$	−1.48776e14	−0.935802
$383$	2.49334e14	1.54592	0.772962	−	0.634452i	$-0.218774\pi$
$383$	2.49334e14	1.54592	0.772962	+	0.634452i	$0.218774\pi$
$384$	−1.96414e14	−1.20047
$385$	3.08847e14	1.86084
$386$	−4.16382e14	−2.47321
$387$	1.38155e13	0.0809014
$388$	5.39215e14	3.11306
$389$	−1.07394e14	−0.611304	−0.305652	−	0.952143i	$-0.598874\pi$
$389$	−1.07394e14	−0.611304	−0.305652	+	0.952143i	$0.598874\pi$
$390$	−2.00180e14	−1.12348
$391$	5.50367e13	0.304565
$392$	−4.34045e14	−2.36844
$393$	−7.77870e13	−0.418550
$394$	−9.52789e12	−0.0505554
$395$	2.72897e14	1.42796
$396$	−3.41962e13	−0.176463
$397$	−2.01327e14	−1.02460	−0.512301	−	0.858806i	$-0.671207\pi$
$397$	−2.01327e14	−1.02460	−0.512301	+	0.858806i	$0.671207\pi$
$398$	−1.32880e14	−0.666963
$399$	−1.22505e14	−0.606459
$400$	1.08904e15	5.31758
$401$	−1.24718e14	−0.600667	−0.300333	−	0.953834i	$-0.597098\pi$
$401$	−1.24718e14	−0.600667	−0.300333	+	0.953834i	$0.597098\pi$
$402$	−6.14396e14	−2.91881
$403$	1.11362e14	0.521865
$404$	−2.80962e14	−1.29882
$405$	−3.32813e14	−1.51774
$406$	3.47878e14	1.56507
$407$	2.19879e14	0.975923
$408$	1.55834e14	0.682388
$409$	2.05212e14	0.886595	0.443298	−	0.896375i	$-0.353809\pi$
$409$	2.05212e14	0.886595	0.443298	+	0.896375i	$0.353809\pi$
$410$	2.59685e14	1.10697
$411$	1.42838e13	0.0600779
$412$	−4.39255e14	−1.82298
$413$	1.88458e13	0.0771773
$414$	−4.87084e13	−0.196835
$415$	−4.60166e14	−1.83506
$416$	−2.55025e14	−1.00362
$417$	−3.03117e14	−1.17723
$418$	1.92538e14	0.737985
$419$	1.94808e14	0.736936	0.368468	−	0.929640i	$-0.379882\pi$
$419$	1.94808e14	0.736936	0.368468	+	0.929640i	$0.379882\pi$
$420$	1.47035e15	5.48971
$421$	8.95392e13	0.329960	0.164980	−	0.986297i	$-0.447244\pi$
$421$	8.95392e13	0.329960	0.164980	+	0.986297i	$0.447244\pi$
$422$	−2.27280e14	−0.826688
$423$	3.49118e12	0.0125343
$424$	−3.38020e14	−1.19793
$425$	−1.23528e14	−0.432140
$426$	7.22566e14	2.49531
$427$	−5.57433e14	−1.90037
$428$	4.11656e14	1.38546
$429$	8.92307e13	0.296483
$430$	9.33629e14	3.06265
$431$	3.69057e13	0.119528	0.0597638	−	0.998213i	$-0.480965\pi$
$431$	3.69057e13	0.119528	0.0597638	+	0.998213i	$0.480965\pi$
$432$	−9.67954e14	−3.09524
$433$	2.84753e14	0.899051	0.449525	−	0.893268i	$-0.351593\pi$
$433$	2.84753e14	0.899051	0.449525	+	0.893268i	$0.351593\pi$
$434$	−1.13776e15	−3.54697
$435$	−3.20324e14	−0.986051
$436$	3.15730e14	0.959709
$437$	1.97164e14	0.591806
$438$	−3.97150e14	−1.17719
$439$	1.15404e14	0.337805	0.168903	−	0.985633i	$-0.445978\pi$
$439$	1.15404e14	0.337805	0.168903	+	0.985633i	$0.445978\pi$
$440$	−1.40743e15	−4.06854
$441$	−2.34632e13	−0.0669845
$442$	6.05122e13	0.170616
$443$	−6.03059e14	−1.67934	−0.839672	−	0.543094i	$-0.817253\pi$
$443$	−6.03059e14	−1.67934	−0.839672	+	0.543094i	$0.817253\pi$
$444$	1.04680e15	2.87909
$445$	7.98006e13	0.216784
$446$	1.22946e15	3.29893
$447$	−2.54857e14	−0.675470
$448$	1.07354e15	2.81054
$449$	−6.62152e14	−1.71239	−0.856195	−	0.516652i	$-0.827178\pi$
$449$	−6.62152e14	−1.71239	−0.856195	+	0.516652i	$0.827178\pi$
$450$	1.09324e14	0.279284
$451$	−1.15755e14	−0.292126
$452$	7.27307e14	1.81324
$453$	−4.13017e14	−1.01725
$454$	−6.55018e14	−1.59385
$455$	3.47731e14	0.835951
$456$	5.58261e14	1.32596
$457$	−2.70494e14	−0.634774	−0.317387	−	0.948296i	$-0.602805\pi$
$457$	−2.70494e14	−0.634774	−0.317387	+	0.948296i	$0.602805\pi$
$458$	3.58981e14	0.832361
$459$	1.09793e14	0.251539
$460$	−2.36644e15	−5.35707
$461$	−6.13233e14	−1.37174	−0.685868	−	0.727726i	$-0.740577\pi$
$461$	−6.13233e14	−1.37174	−0.685868	+	0.727726i	$0.740577\pi$
$462$	−9.11655e14	−2.01511
$463$	6.09449e14	1.33120	0.665598	−	0.746311i	$-0.268177\pi$
$463$	6.09449e14	1.33120	0.665598	+	0.746311i	$0.268177\pi$
$464$	−8.53674e14	−1.84265
$465$	1.04765e15	2.23472
$466$	1.19862e15	2.52674
$467$	3.75378e14	0.782034	0.391017	−	0.920383i	$-0.372123\pi$
$467$	3.75378e14	0.782034	0.391017	+	0.920383i	$0.372123\pi$
$468$	−3.85015e13	−0.0792731
$469$	1.06726e15	2.17181
$470$	2.35928e14	0.474506
$471$	−8.88215e14	−1.76564
$472$	−8.58815e13	−0.168740
$473$	−4.16168e14	−0.808224
$474$	−8.05538e14	−1.54634
$475$	−4.42526e14	−0.839700
$476$	−4.44470e14	−0.833690
$477$	−1.82723e13	−0.0338799
$478$	−4.63260e14	−0.849125
$479$	−1.75239e14	−0.317530	−0.158765	−	0.987316i	$-0.550751\pi$
$479$	−1.75239e14	−0.317530	−0.158765	+	0.987316i	$0.550751\pi$
$480$	−2.39917e15	−4.29768
$481$	2.47563e14	0.438417
$482$	2.06771e15	3.62018
$483$	−9.33556e14	−1.61596
$484$	−4.64457e14	−0.794870
$485$	1.19968e15	2.02995
$486$	−1.86882e14	−0.312657
$487$	3.93553e14	0.651019	0.325509	−	0.945539i	$-0.394464\pi$
$487$	3.93553e14	0.651019	0.325509	+	0.945539i	$0.394464\pi$
$488$	2.54025e15	4.15497
$489$	1.10900e15	1.79363
$490$	−1.58560e15	−2.53581
$491$	1.38307e14	0.218725	0.109362	−	0.994002i	$-0.465119\pi$
$491$	1.38307e14	0.218725	0.109362	+	0.994002i	$0.465119\pi$
$492$	−5.51085e14	−0.861808
$493$	9.68305e13	0.149746
$494$	2.16779e14	0.331527
$495$	−7.60816e13	−0.115067
$496$	2.79200e15	4.17606
$497$	−1.25516e15	−1.85669
$498$	1.35832e15	1.98719
$499$	−7.63400e14	−1.10458	−0.552292	−	0.833650i	$-0.686247\pi$
$499$	−7.63400e14	−1.10458	−0.552292	+	0.833650i	$0.686247\pi$
$500$	2.33041e15	3.33501
$501$	−1.12661e14	−0.159465
$502$	−7.83663e14	−1.09713
$503$	8.66070e14	1.19930	0.599652	−	0.800261i	$-0.295306\pi$
$503$	8.66070e14	1.19930	0.599652	+	0.800261i	$0.295306\pi$
$504$	2.39572e14	0.328147
$505$	−6.25099e14	−0.846928
$506$	1.46725e15	1.96643
$507$	−6.21813e14	−0.824358
$508$	−7.02053e13	−0.0920703
$509$	−2.96407e14	−0.384540	−0.192270	−	0.981342i	$-0.561585\pi$
$509$	−2.96407e14	−0.384540	−0.192270	+	0.981342i	$0.561585\pi$
$510$	5.69274e14	0.730610
$511$	6.89887e14	0.875917
$512$	5.87571e14	0.738032
$513$	3.93324e14	0.488770
$514$	1.58370e15	1.94704
$515$	−9.77280e14	−1.18872
$516$	−1.98128e15	−2.38436
$517$	−1.05166e14	−0.125221
$518$	−2.52930e15	−2.97980
$519$	1.15424e14	0.134547
$520$	−1.58463e15	−1.82772
$521$	1.35441e14	0.154577	0.0772883	−	0.997009i	$-0.475374\pi$
$521$	1.35441e14	0.154577	0.0772883	+	0.997009i	$0.475374\pi$
$522$	−8.56966e13	−0.0967778
$523$	1.42233e14	0.158943	0.0794714	−	0.996837i	$-0.474677\pi$
$523$	1.42233e14	0.158943	0.0794714	+	0.996837i	$0.474677\pi$
$524$	−1.01105e15	−1.11802
$525$	2.09533e15	2.29285
$526$	−4.57829e14	−0.495772
$527$	−3.16692e14	−0.339374
$528$	2.23715e15	2.37251
$529$	5.49694e14	0.576919
$530$	−1.23481e15	−1.28258
$531$	−4.64249e12	−0.00477234
$532$	−1.59227e15	−1.61996
$533$	−1.30329e14	−0.131233
$534$	−2.35556e14	−0.234756
$535$	9.15875e14	0.903422
$536$	−4.86358e15	−4.74843
$537$	1.45107e15	1.40227
$538$	−3.22897e15	−3.08860
$539$	7.06787e14	0.669191
$540$	−4.72083e15	−4.42438
$541$	1.65339e15	1.53387	0.766937	−	0.641723i	$-0.221780\pi$
$541$	1.65339e15	1.53387	0.766937	+	0.641723i	$0.221780\pi$
$542$	1.62081e15	1.48845
$543$	−1.65215e15	−1.50194
$544$	7.25242e14	0.652663
$545$	7.02453e14	0.625801
$546$	−1.02643e15	−0.905256
$547$	1.74477e13	0.0152338	0.00761691	−	0.999971i	$-0.497575\pi$
$547$	1.74477e13	0.0152338	0.00761691	+	0.999971i	$0.497575\pi$
$548$	1.85656e14	0.160479
$549$	1.37318e14	0.117512
$550$	−3.29319e15	−2.79012
$551$	3.46886e14	0.290973
$552$	4.25427e15	3.53314
$553$	1.39929e15	1.15059
$554$	−2.26099e15	−1.84075
$555$	2.32897e15	1.87738
$556$	−3.93981e15	−3.14459
$557$	−1.02709e15	−0.811716	−0.405858	−	0.913936i	$-0.633027\pi$
$557$	−1.02709e15	−0.811716	−0.405858	+	0.913936i	$0.633027\pi$
$558$	2.80277e14	0.219331
$559$	−4.68564e14	−0.363081
$560$	8.71815e15	6.68945
$561$	−2.53755e14	−0.192806
$562$	4.69054e15	3.52918
$563$	−1.65558e15	−1.23354	−0.616772	−	0.787142i	$-0.711560\pi$
$563$	−1.65558e15	−1.23354	−0.616772	+	0.787142i	$0.711560\pi$
$564$	−5.00670e14	−0.369416
$565$	1.61815e15	1.18237
$566$	5.36108e14	0.387937
$567$	−1.70652e15	−1.22294
$568$	5.71986e15	4.05947
$569$	−1.34001e15	−0.941867	−0.470934	−	0.882169i	$-0.656083\pi$
$569$	−1.34001e15	−0.941867	−0.470934	+	0.882169i	$0.656083\pi$
$570$	2.03937e15	1.41966
$571$	−1.22598e15	−0.845252	−0.422626	−	0.906304i	$-0.638892\pi$
$571$	−1.22598e15	−0.845252	−0.422626	+	0.906304i	$0.638892\pi$
$572$	1.15979e15	0.791957
$573$	7.02434e14	0.475067
$574$	1.33155e15	0.891954
$575$	−3.37231e15	−2.23745
$576$	−2.64457e14	−0.173792
$577$	−2.49027e15	−1.62099	−0.810493	−	0.585748i	$-0.800801\pi$
$577$	−2.49027e15	−1.62099	−0.810493	+	0.585748i	$0.800801\pi$
$578$	−1.72085e14	−0.110953
$579$	1.96592e15	1.25555
$580$	−4.16347e15	−2.63391
$581$	−2.35953e15	−1.47862
$582$	−3.54121e15	−2.19824
$583$	5.50421e14	0.338468
$584$	−3.14386e15	−1.91510
$585$	−8.56604e13	−0.0516919
$586$	7.39615e14	0.442149
$587$	1.61292e15	0.955220	0.477610	−	0.878572i	$-0.341503\pi$
$587$	1.61292e15	0.955220	0.477610	+	0.878572i	$0.341503\pi$
$588$	3.36485e15	1.97420
$589$	−1.13452e15	−0.659443
$590$	−3.13732e14	−0.180665
$591$	4.49852e13	0.0256648
$592$	6.20677e15	3.50830
$593$	−1.56720e15	−0.877652	−0.438826	−	0.898572i	$-0.644606\pi$
$593$	−1.56720e15	−0.877652	−0.438826	+	0.898572i	$0.644606\pi$
$594$	2.92704e15	1.62406
$595$	−9.88882e14	−0.543627
$596$	−3.31255e15	−1.80430
$597$	6.27381e14	0.338589
$598$	1.65198e15	0.883384
$599$	9.11202e14	0.482800	0.241400	−	0.970426i	$-0.422393\pi$
$599$	9.11202e14	0.482800	0.241400	+	0.970426i	$0.422393\pi$
$600$	−9.54854e15	−5.01308
$601$	2.78729e15	1.45001	0.725007	−	0.688742i	$-0.241837\pi$
$601$	2.78729e15	1.45001	0.725007	+	0.688742i	$0.241837\pi$
$602$	4.78723e15	2.46777
$603$	−2.62911e14	−0.134296
$604$	−5.36826e15	−2.71725
$605$	−1.03335e15	−0.518314
$606$	1.84517e15	0.917142
$607$	−1.16441e15	−0.573544	−0.286772	−	0.957999i	$-0.592582\pi$
$607$	−1.16441e15	−0.573544	−0.286772	+	0.957999i	$0.592582\pi$
$608$	2.59811e15	1.26820
$609$	−1.64248e15	−0.794521
$610$	9.27976e15	4.44859
$611$	−1.18406e14	−0.0562533
$612$	1.09491e14	0.0515521
$613$	−3.61903e15	−1.68873	−0.844363	−	0.535771i	$-0.820021\pi$
$613$	−3.61903e15	−1.68873	−0.844363	+	0.535771i	$0.820021\pi$
$614$	−3.81177e15	−1.76279
$615$	−1.22609e15	−0.561963
$616$	−7.21669e15	−3.27827
$617$	2.32653e15	1.04747	0.523734	−	0.851882i	$-0.324539\pi$
$617$	2.32653e15	1.04747	0.523734	+	0.851882i	$0.324539\pi$
$618$	2.88473e15	1.28727
$619$	4.94130e14	0.218546	0.109273	−	0.994012i	$-0.465148\pi$
$619$	4.94130e14	0.218546	0.109273	+	0.994012i	$0.465148\pi$
$620$	1.36169e16	5.96933
$621$	2.99736e15	1.30237
$622$	3.80495e14	0.163871
$623$	4.09182e14	0.174676
$624$	2.51881e15	1.06581
$625$	9.36771e14	0.392910
$626$	−2.57812e14	−0.107188
$627$	−9.09055e14	−0.374644
$628$	−1.15447e16	−4.71634
$629$	−7.04022e14	−0.285107
$630$	8.75177e14	0.351336
$631$	3.17579e15	1.26383	0.631917	−	0.775036i	$-0.282268\pi$
$631$	3.17579e15	1.26383	0.631917	+	0.775036i	$0.282268\pi$
$632$	−6.37667e15	−2.51565
$633$	1.07308e15	0.419675
$634$	−6.74171e15	−2.61384
$635$	−1.56197e14	−0.0600367
$636$	2.62043e15	0.998523
$637$	7.95772e14	0.300623
$638$	2.58146e15	0.966833
$639$	3.09198e14	0.114811
$640$	−5.67988e15	−2.09098
$641$	−2.12912e15	−0.777106	−0.388553	−	0.921426i	$-0.627025\pi$
$641$	−2.12912e15	−0.777106	−0.388553	+	0.921426i	$0.627025\pi$
$642$	−2.70348e15	−0.978320
$643$	−2.22852e15	−0.799568	−0.399784	−	0.916609i	$-0.630915\pi$
$643$	−2.22852e15	−0.799568	−0.399784	+	0.916609i	$0.630915\pi$
$644$	−1.21340e16	−4.31652
$645$	−4.40806e15	−1.55478
$646$	−6.16479e14	−0.215595
$647$	4.11099e15	1.42552	0.712760	−	0.701408i	$-0.247445\pi$
$647$	4.11099e15	1.42552	0.712760	+	0.701408i	$0.247445\pi$
$648$	7.77670e15	2.67383
$649$	1.39847e14	0.0476768
$650$	−3.70781e15	−1.25341
$651$	5.37186e15	1.80065
$652$	1.44144e16	4.79111
$653$	4.07842e15	1.34422	0.672108	−	0.740453i	$-0.265389\pi$
$653$	4.07842e15	1.34422	0.672108	+	0.740453i	$0.265389\pi$
$654$	−2.07350e15	−0.677683
$655$	−2.24944e15	−0.729033
$656$	−3.26755e15	−1.05015
$657$	−1.69947e14	−0.0541632
$658$	1.20974e15	0.382338
$659$	1.39711e15	0.437886	0.218943	−	0.975738i	$-0.429739\pi$
$659$	1.39711e15	0.437886	0.218943	+	0.975738i	$0.429739\pi$
$660$	1.09108e16	3.39130
$661$	4.81673e15	1.48472	0.742359	−	0.670002i	$-0.233707\pi$
$661$	4.81673e15	1.48472	0.742359	+	0.670002i	$0.233707\pi$
$662$	3.15160e15	0.963413
$663$	−2.85704e14	−0.0866147
$664$	1.07525e16	3.23285
$665$	−3.54258e15	−1.05633
$666$	6.23071e14	0.184259
$667$	2.64348e15	0.775324
$668$	−1.46433e15	−0.425959
$669$	−5.80482e15	−1.67473
$670$	−1.77671e16	−5.08399
$671$	−4.13648e15	−1.17397
$672$	−1.23019e16	−3.46290
$673$	5.19052e15	1.44920	0.724599	−	0.689171i	$-0.242025\pi$
$673$	5.19052e15	1.44920	0.724599	+	0.689171i	$0.242025\pi$
$674$	6.69013e15	1.85270
$675$	−6.72744e15	−1.84790
$676$	−8.08212e15	−2.20200
$677$	−5.20042e15	−1.40540	−0.702701	−	0.711485i	$-0.748023\pi$
$677$	−5.20042e15	−1.40540	−0.702701	+	0.711485i	$0.748023\pi$
$678$	−4.77647e15	−1.28039
$679$	6.15140e15	1.63565
$680$	4.50640e15	1.18859
$681$	3.09262e15	0.809129
$682$	−8.44286e15	−2.19117
$683$	2.32574e14	0.0598751	0.0299376	−	0.999552i	$-0.490469\pi$
$683$	2.32574e14	0.0598751	0.0299376	+	0.999552i	$0.490469\pi$
$684$	3.92242e14	0.100172
$685$	4.13059e14	0.104644
$686$	1.95618e15	0.491615
$687$	−1.69490e15	−0.422555
$688$	−1.17476e16	−2.90545
$689$	6.19720e14	0.152051
$690$	1.55412e16	3.78281
$691$	7.34741e15	1.77421	0.887105	−	0.461568i	$-0.152713\pi$
$691$	7.34741e15	1.77421	0.887105	+	0.461568i	$0.152713\pi$
$692$	1.50024e15	0.359399
$693$	−3.90112e14	−0.0927165
$694$	−9.37901e15	−2.21146
$695$	−8.76551e15	−2.05051
$696$	7.48488e15	1.73714
$697$	3.70632e14	0.0853420
$698$	−8.93540e15	−2.04131
$699$	−5.65922e15	−1.28272
$700$	2.72344e16	6.12461
$701$	8.42417e15	1.87966	0.939828	−	0.341649i	$-0.110985\pi$
$701$	8.42417e15	1.87966	0.939828	+	0.341649i	$0.110985\pi$
$702$	3.29555e15	0.729582
$703$	−2.52209e15	−0.553996
$704$	7.96629e15	1.73623
$705$	−1.11392e15	−0.240887
$706$	−1.41652e14	−0.0303947
$707$	−3.20523e15	−0.682421
$708$	6.65779e14	0.140652
$709$	2.38085e15	0.499088	0.249544	−	0.968363i	$-0.419719\pi$
$709$	2.38085e15	0.499088	0.249544	+	0.968363i	$0.419719\pi$
$710$	2.08951e16	4.34634
$711$	−3.44703e14	−0.0711480
$712$	−1.86467e15	−0.381910
$713$	−8.64569e15	−1.75714
$714$	2.91898e15	0.588697
$715$	2.58037e15	0.516415
$716$	1.88605e16	3.74570
$717$	2.18725e15	0.431065
$718$	1.29932e15	0.254115
$719$	−3.22573e14	−0.0626064	−0.0313032	−	0.999510i	$-0.509966\pi$
$719$	−3.22573e14	−0.0626064	−0.0313032	+	0.999510i	$0.509966\pi$
$720$	−2.14764e15	−0.413649
$721$	−5.01105e15	−0.957823
$722$	7.73513e15	1.46728
$723$	−9.76253e15	−1.83781
$724$	−2.14741e16	−4.01193
$725$	−5.93317e15	−1.10009
$726$	3.05025e15	0.561285
$727$	−6.75758e15	−1.23411	−0.617053	−	0.786922i	$-0.711673\pi$
$727$	−6.75758e15	−1.23411	−0.617053	+	0.786922i	$0.711673\pi$
$728$	−8.12529e15	−1.47271
$729$	5.94106e15	1.06872
$730$	−1.14848e16	−2.05044
$731$	1.33251e15	0.236115
$732$	−1.96928e16	−3.46335
$733$	5.83859e15	1.01914	0.509572	−	0.860428i	$-0.329804\pi$
$733$	5.83859e15	1.01914	0.509572	+	0.860428i	$0.329804\pi$
$734$	−1.06183e16	−1.83962
$735$	7.48631e15	1.28732
$736$	1.97991e16	3.37923
$737$	7.91972e15	1.34165
$738$	−3.28015e14	−0.0551549
$739$	1.15467e16	1.92714	0.963572	−	0.267450i	$-0.0861809\pi$
$739$	1.15467e16	1.92714	0.963572	+	0.267450i	$0.0861809\pi$
$740$	3.02712e16	5.01481
$741$	−1.02351e15	−0.168303
$742$	−6.33157e15	−1.03345
$743$	−3.18837e15	−0.516571	−0.258285	−	0.966069i	$-0.583158\pi$
$743$	−3.18837e15	−0.516571	−0.258285	+	0.966069i	$0.583158\pi$
$744$	−2.44799e16	−3.93694
$745$	−7.36995e15	−1.17654
$746$	2.94393e15	0.466514
$747$	5.81247e14	0.0914319
$748$	−3.29823e15	−0.515017
$749$	4.69620e15	0.727942
$750$	−1.53046e16	−2.35496
$751$	−2.67279e15	−0.408269	−0.204134	−	0.978943i	$-0.565438\pi$
$751$	−2.67279e15	−0.408269	−0.204134	+	0.978943i	$0.565438\pi$
$752$	−2.96862e15	−0.450150
$753$	3.70001e15	0.556968
$754$	2.90647e15	0.434333
$755$	−1.19436e16	−1.77185
$756$	−2.42063e16	−3.56499
$757$	−4.44676e15	−0.650154	−0.325077	−	0.945688i	$-0.605390\pi$
$757$	−4.44676e15	−0.650154	−0.325077	+	0.945688i	$0.605390\pi$
$758$	−3.20244e15	−0.464837
$759$	−6.92753e15	−0.998272
$760$	1.61437e16	2.30956
$761$	1.13274e16	1.60884	0.804421	−	0.594059i	$-0.202476\pi$
$761$	1.13274e16	1.60884	0.804421	+	0.594059i	$0.202476\pi$
$762$	4.61062e14	0.0650140
$763$	3.60187e15	0.504246
$764$	9.13000e15	1.26899
$765$	2.43602e14	0.0336158
$766$	−2.12831e16	−2.91593
$767$	1.57454e14	0.0214180
$768$	1.93829e15	0.261777
$769$	6.52841e15	0.875412	0.437706	−	0.899118i	$-0.355791\pi$
$769$	6.52841e15	0.875412	0.437706	+	0.899118i	$0.355791\pi$
$770$	−2.63632e16	−3.50993
$771$	−7.47731e15	−0.988431
$772$	2.55523e16	3.35378
$773$	−5.01781e14	−0.0653923	−0.0326962	−	0.999465i	$-0.510409\pi$
$773$	−5.01781e14	−0.0653923	−0.0326962	+	0.999465i	$0.510409\pi$
$774$	−1.17929e15	−0.152597
$775$	1.94049e16	2.49317
$776$	−2.80323e16	−3.57618
$777$	1.19419e16	1.51272
$778$	9.16715e15	1.15305
$779$	1.32775e15	0.165829
$780$	1.22845e16	1.52349
$781$	−9.31405e15	−1.14699
$782$	−4.69793e15	−0.574473
$783$	5.27349e15	0.640337
$784$	1.99512e16	2.40564
$785$	−2.56853e16	−3.07541
$786$	6.63989e15	0.789473
$787$	1.03097e16	1.21727	0.608635	−	0.793451i	$-0.291718\pi$
$787$	1.03097e16	1.21727	0.608635	+	0.793451i	$0.291718\pi$
$788$	5.84703e14	0.0685553
$789$	2.16161e15	0.251683
$790$	−2.32945e16	−2.69342
$791$	8.29717e15	0.952707
$792$	1.77777e15	0.202715
$793$	−4.65727e15	−0.527386
$794$	1.71853e16	1.93261
$795$	5.83008e15	0.651111
$796$	8.15449e15	0.904430
$797$	−4.54724e15	−0.500873	−0.250436	−	0.968133i	$-0.580574\pi$
$797$	−4.54724e15	−0.500873	−0.250436	+	0.968133i	$0.580574\pi$
$798$	1.04570e16	1.14391
$799$	3.36725e14	0.0365821
$800$	−4.44384e16	−4.79472
$801$	−1.00798e14	−0.0108013
$802$	1.06459e16	1.13298
$803$	5.11936e15	0.541104
$804$	3.77040e16	3.95803
$805$	−2.69965e16	−2.81469
$806$	−9.50583e15	−0.984345
$807$	1.52454e16	1.56795
$808$	1.46064e16	1.49204
$809$	1.64156e16	1.66549	0.832743	−	0.553660i	$-0.186769\pi$
$809$	1.64156e16	1.66549	0.832743	+	0.553660i	$0.186769\pi$
$810$	2.84089e16	2.86278
$811$	6.26175e15	0.626731	0.313366	−	0.949633i	$-0.398544\pi$
$811$	6.26175e15	0.626731	0.313366	+	0.949633i	$0.398544\pi$
$812$	−2.13484e16	−2.12230
$813$	−7.65253e15	−0.755626
$814$	−1.87689e16	−1.84079
$815$	3.20701e16	3.12416
$816$	−7.16302e15	−0.693107
$817$	4.77358e15	0.458800
$818$	−1.75169e16	−1.67230
$819$	−4.39228e14	−0.0416513
$820$	−1.59362e16	−1.50110
$821$	−3.10612e15	−0.290624	−0.145312	−	0.989386i	$-0.546419\pi$
$821$	−3.10612e15	−0.290624	−0.145312	+	0.989386i	$0.546419\pi$
$822$	−1.21927e15	−0.113319
$823$	−3.52822e15	−0.325729	−0.162864	−	0.986648i	$-0.552073\pi$
$823$	−3.52822e15	−0.325729	−0.162864	+	0.986648i	$0.552073\pi$
$824$	2.28357e16	2.09418
$825$	1.55486e16	1.41642
$826$	−1.60868e15	−0.145572
$827$	4.68143e15	0.420821	0.210411	−	0.977613i	$-0.432520\pi$
$827$	4.68143e15	0.420821	0.210411	+	0.977613i	$0.432520\pi$
$828$	2.98911e15	0.266916
$829$	−1.66819e16	−1.47977	−0.739887	−	0.672731i	$-0.765121\pi$
$829$	−1.66819e16	−1.47977	−0.739887	+	0.672731i	$0.765121\pi$
$830$	3.92798e16	3.46130
$831$	1.06751e16	0.934471
$832$	8.96926e15	0.779971
$833$	−2.26303e15	−0.195498
$834$	2.58741e16	2.22050
$835$	−3.25792e15	−0.277757
$836$	−1.18156e16	−1.00074
$837$	−1.72473e16	−1.45122
$838$	−1.66288e16	−1.39001
$839$	1.75926e16	1.46096	0.730482	−	0.682932i	$-0.239295\pi$
$839$	1.75926e16	1.46096	0.730482	+	0.682932i	$0.239295\pi$
$840$	−7.64395e16	−6.30640
$841$	−7.54963e15	−0.618796
$842$	−7.64307e15	−0.622374
$843$	−2.21461e16	−1.79162
$844$	1.39476e16	1.12102
$845$	−1.79816e16	−1.43587
$846$	−2.98007e14	−0.0236423
$847$	−5.29856e15	−0.417637
$848$	1.55373e16	1.21674
$849$	−2.53119e15	−0.196940
$850$	1.05443e16	0.815106
$851$	−1.92198e16	−1.47617
$852$	−4.43421e16	−3.38375
$853$	8.12950e14	0.0616374	0.0308187	−	0.999525i	$-0.490189\pi$
$853$	8.12950e14	0.0616374	0.0308187	+	0.999525i	$0.490189\pi$
$854$	4.75825e16	3.58450
$855$	8.72682e14	0.0653194
$856$	−2.14009e16	−1.59157
$857$	9.25145e14	0.0683621	0.0341810	−	0.999416i	$-0.489118\pi$
$857$	9.25145e14	0.0683621	0.0341810	+	0.999416i	$0.489118\pi$
$858$	−7.61673e15	−0.559228
$859$	−1.20518e16	−0.879203	−0.439602	−	0.898193i	$-0.644880\pi$
$859$	−1.20518e16	−0.879203	−0.439602	+	0.898193i	$0.644880\pi$
$860$	−5.72945e16	−4.15309
$861$	−6.28682e15	−0.452808
$862$	−3.15027e15	−0.225454
$863$	−9.07830e15	−0.645573	−0.322786	−	0.946472i	$-0.604620\pi$
$863$	−9.07830e15	−0.645573	−0.322786	+	0.946472i	$0.604620\pi$
$864$	3.94974e16	2.79089
$865$	3.33782e15	0.234355
$866$	−2.43065e16	−1.69580
$867$	8.12488e14	0.0563264
$868$	6.98216e16	4.80985
$869$	1.03836e16	0.710785
$870$	2.73429e16	1.85990
$871$	8.91682e15	0.602713
$872$	−1.64139e16	−1.10248
$873$	−1.51534e15	−0.101142
$874$	−1.68299e16	−1.11627
$875$	2.65854e16	1.75226
$876$	2.43721e16	1.59632
$877$	1.44363e16	0.939632	0.469816	−	0.882764i	$-0.344320\pi$
$877$	1.44363e16	0.939632	0.469816	+	0.882764i	$0.344320\pi$
$878$	−9.85089e15	−0.637171
$879$	−3.49204e15	−0.224460
$880$	6.46938e16	4.13245
$881$	−1.18121e16	−0.749822	−0.374911	−	0.927061i	$-0.622327\pi$
$881$	−1.18121e16	−0.749822	−0.374911	+	0.927061i	$0.622327\pi$
$882$	2.00282e15	0.126347
$883$	−1.52353e16	−0.955141	−0.477570	−	0.878593i	$-0.658482\pi$
$883$	−1.52353e16	−0.955141	−0.477570	+	0.878593i	$0.658482\pi$
$884$	−3.71348e15	−0.231363
$885$	1.48126e15	0.0917158
$886$	5.14771e16	3.16759
$887$	2.48210e16	1.51788	0.758942	−	0.651158i	$-0.225717\pi$
$887$	2.48210e16	1.51788	0.758942	+	0.651158i	$0.225717\pi$
$888$	−5.44201e16	−3.30741
$889$	−8.00908e14	−0.0483752
$890$	−6.81178e15	−0.408899
$891$	−1.26634e16	−0.755477
$892$	−7.54490e16	−4.47350
$893$	1.20629e15	0.0710833
$894$	2.17546e16	1.27408
$895$	4.19620e16	2.44247
$896$	−2.91239e16	−1.68483
$897$	−7.79972e15	−0.448457
$898$	5.65213e16	3.22992
$899$	−1.52111e16	−0.863935
$900$	−6.70894e15	−0.378721
$901$	−1.76237e15	−0.0988804
$902$	9.88088e15	0.551010
$903$	−2.26026e16	−1.25278
$904$	−3.78107e16	−2.08300
$905$	−4.77769e16	−2.61608
$906$	3.52551e16	1.91875
$907$	−7.45091e15	−0.403060	−0.201530	−	0.979482i	$-0.564591\pi$
$907$	−7.45091e15	−0.403060	−0.201530	+	0.979482i	$0.564591\pi$
$908$	4.01968e16	2.16132
$909$	7.89579e14	0.0421982
$910$	−2.96823e16	−1.57678
$911$	−7.60996e15	−0.401820	−0.200910	−	0.979610i	$-0.564390\pi$
$911$	−7.60996e15	−0.401820	−0.200910	+	0.979610i	$0.564390\pi$
$912$	−2.56609e16	−1.34679
$913$	−1.75091e16	−0.913426
$914$	2.30894e16	1.19732
$915$	−4.38137e16	−2.25836
$916$	−2.20298e16	−1.12872
$917$	−1.15341e16	−0.587426
$918$	−9.37194e15	−0.474455
$919$	−2.37581e16	−1.19557	−0.597787	−	0.801655i	$-0.703953\pi$
$919$	−2.37581e16	−1.19557	−0.597787	+	0.801655i	$0.703953\pi$
$920$	1.23025e17	6.15403
$921$	1.79970e16	0.894894
$922$	5.23456e16	2.58738
$923$	−1.04867e16	−0.515264
$924$	5.59460e16	2.73258
$925$	4.31381e16	2.09450
$926$	−5.20225e16	−2.51091
$927$	1.23443e15	0.0592280
$928$	3.48342e16	1.66147
$929$	−1.37517e16	−0.652032	−0.326016	−	0.945364i	$-0.605706\pi$
$929$	−1.37517e16	−0.652032	−0.326016	+	0.945364i	$0.605706\pi$
$930$	−8.94270e16	−4.21515
$931$	−8.10708e15	−0.379876
$932$	−7.35566e16	−3.42637
$933$	−1.79648e15	−0.0831905
$934$	−3.20422e16	−1.47508
$935$	−7.33808e15	−0.335829
$936$	2.00159e15	0.0910663
$937$	2.87787e16	1.30168	0.650838	−	0.759216i	$-0.274418\pi$
$937$	2.87787e16	1.30168	0.650838	+	0.759216i	$0.274418\pi$
$938$	−9.11016e16	−4.09648
$939$	1.21724e15	0.0544146
$940$	−1.44783e16	−0.643451
$941$	2.16081e16	0.954714	0.477357	−	0.878710i	$-0.341595\pi$
$941$	2.16081e16	0.954714	0.477357	+	0.878710i	$0.341595\pi$
$942$	7.58180e16	3.33037
$943$	1.01183e16	0.441867
$944$	3.94761e15	0.171391
$945$	−5.38556e16	−2.32464
$946$	3.55241e16	1.52448
$947$	2.32881e16	0.993595	0.496798	−	0.867866i	$-0.334509\pi$
$947$	2.32881e16	0.993595	0.496798	+	0.867866i	$0.334509\pi$
$948$	4.94338e16	2.09690
$949$	5.76390e15	0.243082
$950$	3.77740e16	1.58385
$951$	3.18305e16	1.32694
$952$	2.31068e16	0.957715
$953$	4.46871e16	1.84150	0.920749	−	0.390154i	$-0.127578\pi$
$953$	4.46871e16	1.84150	0.920749	+	0.390154i	$0.127578\pi$
$954$	1.55972e15	0.0639045
$955$	2.03129e16	0.827474
$956$	2.84291e16	1.15145
$957$	−1.21882e16	−0.490821
$958$	1.49584e16	0.598927
$959$	2.11798e15	0.0843179
$960$	8.43792e16	3.33998
$961$	2.43405e16	0.957966
$962$	−2.11320e16	−0.826945
$963$	−1.15687e15	−0.0450130
$964$	−1.26890e17	−4.90912
$965$	5.68502e16	2.18692
$966$	7.96884e16	3.04804
$967$	−3.24154e16	−1.23284	−0.616419	−	0.787418i	$-0.711417\pi$
$967$	−3.24154e16	−1.23284	−0.616419	+	0.787418i	$0.711417\pi$
$968$	2.41459e16	0.913121
$969$	2.91066e15	0.109449
$970$	−1.02404e17	−3.82890
$971$	−3.70409e16	−1.37713	−0.688566	−	0.725174i	$-0.741760\pi$
$971$	−3.70409e16	−1.37713	−0.688566	+	0.725174i	$0.741760\pi$
$972$	1.14685e16	0.423976
$973$	−4.49457e16	−1.65222
$974$	−3.35937e16	−1.22796
$975$	1.75062e16	0.636305
$976$	−1.16765e17	−4.22024
$977$	2.53420e16	0.910796	0.455398	−	0.890288i	$-0.349497\pi$
$977$	2.53420e16	0.910796	0.455398	+	0.890288i	$0.349497\pi$
$978$	−9.46644e16	−3.38316
$979$	3.03637e15	0.107907
$980$	9.73045e16	3.43866
$981$	−8.87286e14	−0.0311806
$982$	−1.18059e16	−0.412560
$983$	3.00353e16	1.04373	0.521865	−	0.853028i	$-0.325237\pi$
$983$	3.00353e16	1.04373	0.521865	+	0.853028i	$0.325237\pi$
$984$	2.86494e16	0.990017
$985$	1.30088e15	0.0447031
$986$	−8.26545e15	−0.282451
$987$	−5.71168e15	−0.194097
$988$	−1.33032e16	−0.449565
$989$	3.63775e16	1.22251
$990$	6.49432e15	0.217040
$991$	5.64066e16	1.87467	0.937334	−	0.348431i	$-0.113286\pi$
$991$	5.64066e16	1.87467	0.937334	+	0.348431i	$0.113286\pi$
$992$	−1.13928e17	−3.76544
$993$	−1.48801e16	−0.489084
$994$	1.07141e17	3.50211
$995$	1.81426e16	0.589755
$996$	−8.33566e16	−2.69472
$997$	−3.94195e16	−1.26732	−0.633662	−	0.773610i	$-0.718449\pi$
$997$	−3.94195e16	−1.26732	−0.633662	+	0.773610i	$0.718449\pi$
$998$	6.51638e16	2.08348
$999$	−3.83418e16	−1.21916

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.a.b.1.1	✓	8
3.2	odd	2		153.12.a.d.1.8		8
4.3	odd	2		272.12.a.h.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.a.b.1.1	✓	8	1.1	even	1	trivial
153.12.a.d.1.8		8	3.2	odd	2
272.12.a.h.1.3		8	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q-85.3600 q^{2} +403.021 q^{3} +5238.33 q^{4} +11654.5 q^{5} -34401.9 q^{6} +59759.3 q^{7} -272327. q^{8} -14721.1 q^{9} +O(q^{10})\)	\(q-85.3600 q^{2} +403.021 q^{3} +5238.33 q^{4} +11654.5 q^{5} -34401.9 q^{6} +59759.3 q^{7} -272327. q^{8} -14721.1 q^{9} -994831. q^{10} +443448. q^{11} +2.11116e6 q^{12} +499279. q^{13} -5.10105e6 q^{14} +4.69702e6 q^{15} +1.25177e7 q^{16} -1.41986e6 q^{17} +1.25660e6 q^{18} -5.08650e6 q^{19} +6.10503e7 q^{20} +2.40842e7 q^{21} -3.78528e7 q^{22} -3.87621e7 q^{23} -1.09753e8 q^{24} +8.70000e7 q^{25} -4.26185e7 q^{26} -7.73269e7 q^{27} +3.13039e8 q^{28} -6.81974e7 q^{29} -4.00938e8 q^{30} +2.23045e8 q^{31} -5.10785e8 q^{32} +1.78719e8 q^{33} +1.21199e8 q^{34} +6.96466e8 q^{35} -7.71142e7 q^{36} +4.95840e8 q^{37} +4.34184e8 q^{38} +2.01220e8 q^{39} -3.17384e9 q^{40} -2.61035e8 q^{41} -2.05583e9 q^{42} -9.38480e8 q^{43} +2.32293e9 q^{44} -1.71568e8 q^{45} +3.30874e9 q^{46} -2.37154e8 q^{47} +5.04489e9 q^{48} +1.59384e9 q^{49} -7.42632e9 q^{50} -5.72232e8 q^{51} +2.61539e9 q^{52} +1.24123e9 q^{53} +6.60062e9 q^{54} +5.16819e9 q^{55} -1.62740e10 q^{56} -2.04997e9 q^{57} +5.82133e9 q^{58} +3.15362e8 q^{59} +2.46045e10 q^{60} -9.32797e9 q^{61} -1.90391e10 q^{62} -8.79724e8 q^{63} +1.79644e10 q^{64} +5.81887e9 q^{65} -1.52555e10 q^{66} +1.78594e10 q^{67} -7.43768e9 q^{68} -1.56220e10 q^{69} -5.94504e10 q^{70} -2.10037e10 q^{71} +4.00896e9 q^{72} +1.15444e10 q^{73} -4.23249e10 q^{74} +3.50628e10 q^{75} -2.66448e10 q^{76} +2.65002e10 q^{77} -1.71761e10 q^{78} +2.34155e10 q^{79} +1.45888e11 q^{80} -2.85565e10 q^{81} +2.22819e10 q^{82} -3.94839e10 q^{83} +1.26161e11 q^{84} -1.65478e10 q^{85} +8.01087e10 q^{86} -2.74850e10 q^{87} -1.20763e11 q^{88} +6.84718e9 q^{89} +1.46450e10 q^{90} +2.98366e10 q^{91} -2.03049e11 q^{92} +8.98917e10 q^{93} +2.02435e10 q^{94} -5.92808e10 q^{95} -2.05857e11 q^{96} +1.02936e11 q^{97} -1.36050e11 q^{98} -6.52807e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 55 q^{2} + 496 q^{3} + 10757 q^{4} + 8592 q^{5} + 17194 q^{6} + 95288 q^{7} - 247863 q^{8} + 500648 q^{9}+O(q^{10}) \) 8 * q + 55 * q^2 + 496 * q^3 + 10757 * q^4 + 8592 * q^5 + 17194 * q^6 + 95288 * q^7 - 247863 * q^8 + 500648 * q^9	\( 8 q + 55 q^{2} + 496 q^{3} + 10757 q^{4} + 8592 q^{5} + 17194 q^{6} + 95288 q^{7} - 247863 q^{8} + 500648 q^{9} + 2824 q^{10} + 435256 q^{11} + 4295182 q^{12} + 4193784 q^{13} + 4377132 q^{14} + 10362648 q^{15} + 20722897 q^{16} - 11358856 q^{17} + 28881887 q^{18} + 15158192 q^{19} + 91612472 q^{20} + 98415768 q^{21} + 81767186 q^{22} + 22374432 q^{23} - 41056218 q^{24} + 133926472 q^{25} - 70553178 q^{26} + 68932744 q^{27} + 108010892 q^{28} - 424656432 q^{29} - 561465200 q^{30} - 172323152 q^{31} - 540258159 q^{32} - 764794592 q^{33} - 78092135 q^{34} - 117251352 q^{35} - 1812061939 q^{36} - 262792640 q^{37} - 674758596 q^{38} - 302706728 q^{39} - 3575120264 q^{40} - 1283308512 q^{41} - 1036128840 q^{42} + 2219398472 q^{43} + 4256110614 q^{44} + 3982117536 q^{45} + 6081288184 q^{46} + 260684408 q^{47} + 6860204310 q^{48} + 12060045320 q^{49} - 1911832923 q^{50} - 704249072 q^{51} + 3548505010 q^{52} + 9402026896 q^{53} - 848951924 q^{54} + 4430702936 q^{55} - 11881582644 q^{56} + 1366983408 q^{57} + 814919720 q^{58} + 14325543480 q^{59} + 4281784208 q^{60} - 9811064576 q^{61} - 41469249572 q^{62} + 14666072688 q^{63} - 27038375199 q^{64} + 29701570288 q^{65} - 43330462276 q^{66} + 52928023248 q^{67} - 15273401749 q^{68} - 13481294472 q^{69} - 128492187744 q^{70} - 34868356504 q^{71} - 52662987279 q^{72} + 1248764080 q^{73} - 135359144436 q^{74} + 59235735072 q^{75} - 49428813052 q^{76} + 112631449800 q^{77} - 87670698684 q^{78} + 18209008736 q^{79} + 96412241400 q^{80} + 67350111224 q^{81} + 41461375370 q^{82} + 169643760088 q^{83} + 117131104968 q^{84} - 12199411344 q^{85} + 88510231200 q^{86} + 35491052136 q^{87} - 51404280146 q^{88} + 201694397904 q^{89} - 4670596888 q^{90} + 36284010568 q^{91} - 3754023808 q^{92} + 106318637912 q^{93} + 253870878768 q^{94} - 383491632 q^{95} - 102115750890 q^{96} + 163430440672 q^{97} - 110963034673 q^{98} - 716459488 q^{99}+O(q^{100}) \) 8 * q + 55 * q^2 + 496 * q^3 + 10757 * q^4 + 8592 * q^5 + 17194 * q^6 + 95288 * q^7 - 247863 * q^8 + 500648 * q^9 + 2824 * q^10 + 435256 * q^11 + 4295182 * q^12 + 4193784 * q^13 + 4377132 * q^14 + 10362648 * q^15 + 20722897 * q^16 - 11358856 * q^17 + 28881887 * q^18 + 15158192 * q^19 + 91612472 * q^20 + 98415768 * q^21 + 81767186 * q^22 + 22374432 * q^23 - 41056218 * q^24 + 133926472 * q^25 - 70553178 * q^26 + 68932744 * q^27 + 108010892 * q^28 - 424656432 * q^29 - 561465200 * q^30 - 172323152 * q^31 - 540258159 * q^32 - 764794592 * q^33 - 78092135 * q^34 - 117251352 * q^35 - 1812061939 * q^36 - 262792640 * q^37 - 674758596 * q^38 - 302706728 * q^39 - 3575120264 * q^40 - 1283308512 * q^41 - 1036128840 * q^42 + 2219398472 * q^43 + 4256110614 * q^44 + 3982117536 * q^45 + 6081288184 * q^46 + 260684408 * q^47 + 6860204310 * q^48 + 12060045320 * q^49 - 1911832923 * q^50 - 704249072 * q^51 + 3548505010 * q^52 + 9402026896 * q^53 - 848951924 * q^54 + 4430702936 * q^55 - 11881582644 * q^56 + 1366983408 * q^57 + 814919720 * q^58 + 14325543480 * q^59 + 4281784208 * q^60 - 9811064576 * q^61 - 41469249572 * q^62 + 14666072688 * q^63 - 27038375199 * q^64 + 29701570288 * q^65 - 43330462276 * q^66 + 52928023248 * q^67 - 15273401749 * q^68 - 13481294472 * q^69 - 128492187744 * q^70 - 34868356504 * q^71 - 52662987279 * q^72 + 1248764080 * q^73 - 135359144436 * q^74 + 59235735072 * q^75 - 49428813052 * q^76 + 112631449800 * q^77 - 87670698684 * q^78 + 18209008736 * q^79 + 96412241400 * q^80 + 67350111224 * q^81 + 41461375370 * q^82 + 169643760088 * q^83 + 117131104968 * q^84 - 12199411344 * q^85 + 88510231200 * q^86 + 35491052136 * q^87 - 51404280146 * q^88 + 201694397904 * q^89 - 4670596888 * q^90 + 36284010568 * q^91 - 3754023808 * q^92 + 106318637912 * q^93 + 253870878768 * q^94 - 383491632 * q^95 - 102115750890 * q^96 + 163430440672 * q^97 - 110963034673 * q^98 - 716459488 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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