LMFDB - Embedded newform 17.12.a.b.1.7

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			1.7
Root			$-65.9081$ 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)

$f(q)$	$=$	$q+72.9081 q^{2} +470.639 q^{3} +3267.59 q^{4} -7122.79 q^{5} +34313.4 q^{6} +82392.3 q^{7} +88918.0 q^{8} +44353.7 q^{9} +O(q^{10})$	\(q+72.9081 q^{2} +470.639 q^{3} +3267.59 q^{4} -7122.79 q^{5} +34313.4 q^{6} +82392.3 q^{7} +88918.0 q^{8} +44353.7 q^{9} -519309. q^{10} +711523. q^{11} +1.53785e6 q^{12} -1.98720e6 q^{13} +6.00706e6 q^{14} -3.35226e6 q^{15} -209185. q^{16} -1.41986e6 q^{17} +3.23374e6 q^{18} -5.71679e6 q^{19} -2.32744e7 q^{20} +3.87770e7 q^{21} +5.18758e7 q^{22} +1.31325e7 q^{23} +4.18482e7 q^{24} +1.90602e6 q^{25} -1.44883e8 q^{26} -6.24977e7 q^{27} +2.69224e8 q^{28} +9.21605e7 q^{29} -2.44407e8 q^{30} -9.38118e7 q^{31} -1.97355e8 q^{32} +3.34870e8 q^{33} -1.03519e8 q^{34} -5.86863e8 q^{35} +1.44930e8 q^{36} -3.81431e8 q^{37} -4.16801e8 q^{38} -9.35251e8 q^{39} -6.33344e8 q^{40} -9.73419e8 q^{41} +2.82716e9 q^{42} +1.11217e9 q^{43} +2.32496e9 q^{44} -3.15922e8 q^{45} +9.57468e8 q^{46} -2.73352e8 q^{47} -9.84504e7 q^{48} +4.81116e9 q^{49} +1.38964e8 q^{50} -6.68239e8 q^{51} -6.49334e9 q^{52} +1.84820e9 q^{53} -4.55659e9 q^{54} -5.06803e9 q^{55} +7.32615e9 q^{56} -2.69054e9 q^{57} +6.71924e9 q^{58} -3.74250e8 q^{59} -1.09538e10 q^{60} +7.70468e9 q^{61} -6.83964e9 q^{62} +3.65440e9 q^{63} -1.39604e10 q^{64} +1.41544e10 q^{65} +2.44147e10 q^{66} +7.09959e9 q^{67} -4.63951e9 q^{68} +6.18068e9 q^{69} -4.27871e10 q^{70} -3.17112e9 q^{71} +3.94384e9 q^{72} +3.91263e9 q^{73} -2.78094e10 q^{74} +8.97047e8 q^{75} -1.86801e10 q^{76} +5.86240e10 q^{77} -6.81874e10 q^{78} +1.69739e10 q^{79} +1.48998e9 q^{80} -3.72709e10 q^{81} -7.09701e10 q^{82} +2.52619e10 q^{83} +1.26707e11 q^{84} +1.01133e10 q^{85} +8.10865e10 q^{86} +4.33743e10 q^{87} +6.32671e10 q^{88} -5.11116e10 q^{89} -2.30333e10 q^{90} -1.63730e11 q^{91} +4.29117e10 q^{92} -4.41515e10 q^{93} -1.99296e10 q^{94} +4.07195e10 q^{95} -9.28830e10 q^{96} +1.43004e11 q^{97} +3.50772e11 q^{98} +3.15586e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	72.9081	1.61106	0.805528	−	0.592557i	$-0.201882\pi$
$2$	72.9081	1.61106	0.805528	+	0.592557i	$0.201882\pi$
$3$	470.639	1.11820	0.559101	−	0.829099i	$-0.311146\pi$
$3$	470.639	1.11820	0.559101	+	0.829099i	$0.311146\pi$
$4$	3267.59	1.59550
$5$	−7122.79	−1.01933	−0.509665	−	0.860373i	$-0.670231\pi$
$5$	−7122.79	−1.01933	−0.509665	+	0.860373i	$0.670231\pi$
$6$	34313.4	1.80149
$7$	82392.3	1.85288	0.926440	−	0.376443i	$-0.122853\pi$
$7$	82392.3	1.85288	0.926440	+	0.376443i	$0.122853\pi$
$8$	88918.0	0.959389
$9$	44353.7	0.250378
$10$	−519309.	−1.64220
$11$	711523.	1.33208	0.666038	−	0.745918i	$-0.267989\pi$
$11$	711523.	1.33208	0.666038	+	0.745918i	$0.267989\pi$
$12$	1.53785e6	1.78410
$13$	−1.98720e6	−1.48440	−0.742202	−	0.670176i	$-0.766219\pi$
$13$	−1.98720e6	−1.48440	−0.742202	+	0.670176i	$0.766219\pi$
$14$	6.00706e6	2.98509
$15$	−3.35226e6	−1.13982
$16$	−209185.	−0.0498735
$17$	−1.41986e6	−0.242536
$17$	−1.41986e6	−0.242536
$18$	3.23374e6	0.403373
$19$	−5.71679e6	−0.529673	−0.264836	−	0.964293i	$-0.585318\pi$
$19$	−5.71679e6	−0.529673	−0.264836	+	0.964293i	$0.585318\pi$
$20$	−2.32744e7	−1.62635
$21$	3.87770e7	2.07190
$22$	5.18758e7	2.14605
$23$	1.31325e7	0.425447	0.212723	−	0.977112i	$-0.431767\pi$
$23$	1.31325e7	0.425447	0.212723	+	0.977112i	$0.431767\pi$
$24$	4.18482e7	1.07279
$25$	1.90602e6	0.0390353
$26$	−1.44883e8	−2.39146
$27$	−6.24977e7	−0.838230
$28$	2.69224e8	2.95627
$29$	9.21605e7	0.834364	0.417182	−	0.908823i	$-0.363018\pi$
$29$	9.21605e7	0.834364	0.417182	+	0.908823i	$0.363018\pi$
$30$	−2.44407e8	−1.83631
$31$	−9.38118e7	−0.588529	−0.294265	−	0.955724i	$-0.595075\pi$
$31$	−9.38118e7	−0.588529	−0.294265	+	0.955724i	$0.595075\pi$
$32$	−1.97355e8	−1.03974
$33$	3.34870e8	1.48953
$34$	−1.03519e8	−0.390739
$35$	−5.86863e8	−1.88870
$36$	1.44930e8	0.399479
$37$	−3.81431e8	−0.904288	−0.452144	−	0.891945i	$-0.649341\pi$
$37$	−3.81431e8	−0.904288	−0.452144	+	0.891945i	$0.649341\pi$
$38$	−4.16801e8	−0.853333
$39$	−9.35251e8	−1.65987
$40$	−6.33344e8	−0.977934
$41$	−9.73419e8	−1.31217	−0.656083	−	0.754689i	$-0.727788\pi$
$41$	−9.73419e8	−1.31217	−0.656083	+	0.754689i	$0.727788\pi$
$42$	2.82716e9	3.33794
$43$	1.11217e9	1.15371	0.576855	−	0.816847i	$-0.304280\pi$
$43$	1.11217e9	1.15371	0.576855	+	0.816847i	$0.304280\pi$
$44$	2.32496e9	2.12533
$45$	−3.15922e8	−0.255218
$46$	9.57468e8	0.685419
$47$	−2.73352e8	−0.173854	−0.0869268	−	0.996215i	$-0.527705\pi$
$47$	−2.73352e8	−0.173854	−0.0869268	+	0.996215i	$0.527705\pi$
$48$	−9.84504e7	−0.0557687
$49$	4.81116e9	2.43316
$50$	1.38964e8	0.0628881
$51$	−6.68239e8	−0.271204
$52$	−6.49334e9	−2.36837
$53$	1.84820e9	0.607060	0.303530	−	0.952822i	$-0.401835\pi$
$53$	1.84820e9	0.607060	0.303530	+	0.952822i	$0.401835\pi$
$54$	−4.55659e9	−1.35044
$55$	−5.06803e9	−1.35783
$56$	7.32615e9	1.77763
$57$	−2.69054e9	−0.592282
$58$	6.71924e9	1.34421
$59$	−3.74250e8	−0.0681515	−0.0340758	−	0.999419i	$-0.510849\pi$
$59$	−3.74250e8	−0.0681515	−0.0340758	+	0.999419i	$0.510849\pi$
$60$	−1.09538e10	−1.81858
$61$	7.70468e9	1.16799	0.583997	−	0.811756i	$-0.301488\pi$
$61$	7.70468e9	1.16799	0.583997	+	0.811756i	$0.301488\pi$
$62$	−6.83964e9	−0.948154
$63$	3.65440e9	0.463920
$64$	−1.39604e10	−1.62520
$65$	1.41544e10	1.51310
$66$	2.44147e10	2.39972
$67$	7.09959e9	0.642424	0.321212	−	0.947007i	$-0.395910\pi$
$67$	7.09959e9	0.642424	0.321212	+	0.947007i	$0.395910\pi$
$68$	−4.63951e9	−0.386966
$69$	6.18068e9	0.475736
$70$	−4.27871e10	−3.04280
$71$	−3.17112e9	−0.208589	−0.104295	−	0.994546i	$-0.533258\pi$
$71$	−3.17112e9	−0.208589	−0.104295	+	0.994546i	$0.533258\pi$
$72$	3.94384e9	0.240210
$73$	3.91263e9	0.220899	0.110449	−	0.993882i	$-0.464771\pi$
$73$	3.91263e9	0.220899	0.110449	+	0.993882i	$0.464771\pi$
$74$	−2.78094e10	−1.45686
$75$	8.97047e8	0.0436494
$76$	−1.86801e10	−0.845095
$77$	5.86240e10	2.46818
$78$	−6.81874e10	−2.67414
$79$	1.69739e10	0.620629	0.310315	−	0.950634i	$-0.399566\pi$
$79$	1.69739e10	0.620629	0.310315	+	0.950634i	$0.399566\pi$
$80$	1.48998e9	0.0508376
$81$	−3.72709e10	−1.18769
$82$	−7.09701e10	−2.11397
$83$	2.52619e10	0.703940	0.351970	−	0.936011i	$-0.385512\pi$
$83$	2.52619e10	0.703940	0.351970	+	0.936011i	$0.385512\pi$
$84$	1.26707e11	3.30572
$85$	1.01133e10	0.247224
$86$	8.10865e10	1.85869
$87$	4.33743e10	0.932989
$88$	6.32671e10	1.27798
$89$	−5.11116e10	−0.970229	−0.485114	−	0.874451i	$-0.661222\pi$
$89$	−5.11116e10	−0.970229	−0.485114	+	0.874451i	$0.661222\pi$
$90$	−2.30333e10	−0.411170
$91$	−1.63730e11	−2.75042
$92$	4.29117e10	0.678802
$93$	−4.41515e10	−0.658095
$94$	−1.99296e10	−0.280088
$95$	4.07195e10	0.539912
$96$	−9.28830e10	−1.16264
$97$	1.43004e11	1.69085	0.845423	−	0.534097i	$-0.179348\pi$
$97$	1.43004e11	1.69085	0.845423	+	0.534097i	$0.179348\pi$
$98$	3.50772e11	3.91996
$99$	3.15586e10	0.333522
$100$	6.22809e9	0.0622809
$101$	−8.01072e10	−0.758410	−0.379205	−	0.925313i	$-0.623802\pi$
$101$	−8.01072e10	−0.758410	−0.379205	+	0.925313i	$0.623802\pi$
$102$	−4.87201e10	−0.436925
$103$	1.46374e11	1.24411	0.622054	−	0.782974i	$-0.286298\pi$
$103$	1.46374e11	1.24411	0.622054	+	0.782974i	$0.286298\pi$
$104$	−1.76697e11	−1.42412
$105$	−2.76200e11	−2.11195
$106$	1.34749e11	0.978008
$107$	−1.66093e11	−1.14483	−0.572415	−	0.819964i	$-0.693994\pi$
$107$	−1.66093e11	−1.14483	−0.572415	+	0.819964i	$0.693994\pi$
$108$	−2.04217e11	−1.33740
$109$	2.93323e11	1.82600	0.912999	−	0.407963i	$-0.133761\pi$
$109$	2.93323e11	1.82600	0.912999	+	0.407963i	$0.133761\pi$
$110$	−3.69500e11	−2.18753
$111$	−1.79516e11	−1.01118
$112$	−1.72352e10	−0.0924096
$113$	1.24655e11	0.636471	0.318236	−	0.948012i	$-0.396910\pi$
$113$	1.24655e11	0.636471	0.318236	+	0.948012i	$0.396910\pi$
$114$	−1.96162e11	−0.954199
$115$	−9.35403e10	−0.433671
$116$	3.01143e11	1.33123
$117$	−8.81394e10	−0.371662
$118$	−2.72859e10	−0.109796
$119$	−1.16985e11	−0.449389
$120$	−2.98076e11	−1.09353
$121$	2.20953e11	0.774426
$122$	5.61734e11	1.88170
$123$	−4.58129e11	−1.46727
$124$	−3.06539e11	−0.939000
$125$	3.34216e11	0.979541
$126$	2.66435e11	0.747401
$127$	3.24305e11	0.871029	0.435515	−	0.900182i	$-0.356566\pi$
$127$	3.24305e11	0.871029	0.435515	+	0.900182i	$0.356566\pi$
$128$	−6.13641e11	−1.57856
$129$	5.23432e11	1.29008
$130$	1.03197e12	2.43769
$131$	−5.39817e11	−1.22252	−0.611258	−	0.791432i	$-0.709336\pi$
$131$	−5.39817e11	−1.22252	−0.611258	+	0.791432i	$0.709336\pi$
$132$	1.09422e12	2.37655
$133$	−4.71020e11	−0.981420
$134$	5.17617e11	1.03498
$135$	4.45158e11	0.854433
$136$	−1.26251e11	−0.232686
$137$	−1.36861e11	−0.242279	−0.121140	−	0.992635i	$-0.538655\pi$
$137$	−1.36861e11	−0.242279	−0.121140	+	0.992635i	$0.538655\pi$
$138$	4.50621e11	0.766438
$139$	7.18681e11	1.17478	0.587388	−	0.809305i	$-0.300156\pi$
$139$	7.18681e11	1.17478	0.587388	+	0.809305i	$0.300156\pi$
$140$	−1.91763e12	−3.01342
$141$	−1.28650e11	−0.194404
$142$	−2.31200e11	−0.336049
$143$	−1.41393e12	−1.97734
$144$	−9.27811e9	−0.0124872
$145$	−6.56440e11	−0.850493
$146$	2.85262e11	0.355880
$147$	2.26432e12	2.72077
$148$	−1.24636e12	−1.44279
$149$	−6.73048e11	−0.750795	−0.375398	−	0.926864i	$-0.622494\pi$
$149$	−6.73048e11	−0.750795	−0.375398	+	0.926864i	$0.622494\pi$
$150$	6.54020e10	0.0703216
$151$	−2.55261e11	−0.264613	−0.132306	−	0.991209i	$-0.542238\pi$
$151$	−2.55261e11	−0.264613	−0.132306	+	0.991209i	$0.542238\pi$
$152$	−5.08326e11	−0.508162
$153$	−6.29759e10	−0.0607255
$154$	4.27416e12	3.97637
$155$	6.68202e11	0.599906
$156$	−3.05602e12	−2.64832
$157$	−2.13281e12	−1.78445	−0.892225	−	0.451591i	$-0.850856\pi$
$157$	−2.13281e12	−1.78445	−0.892225	+	0.451591i	$0.850856\pi$
$158$	1.23753e12	0.999869
$159$	8.69834e11	0.678816
$160$	1.40572e12	1.05984
$161$	1.08202e12	0.788302
$162$	−2.71735e12	−1.91343
$163$	−2.33417e12	−1.58892	−0.794459	−	0.607318i	$-0.792245\pi$
$163$	−2.33417e12	−1.58892	−0.794459	+	0.607318i	$0.792245\pi$
$164$	−3.18073e12	−2.09356
$165$	−2.38521e12	−1.51832
$166$	1.84179e12	1.13409
$167$	2.81668e11	0.167802	0.0839011	−	0.996474i	$-0.473262\pi$
$167$	2.81668e11	0.167802	0.0839011	+	0.996474i	$0.473262\pi$
$168$	3.44797e12	1.98775
$169$	2.15679e12	1.20346
$170$	7.37345e11	0.398292
$171$	−2.53561e11	−0.132618
$172$	3.63413e12	1.84075
$173$	−2.40591e12	−1.18039	−0.590194	−	0.807261i	$-0.700949\pi$
$173$	−2.40591e12	−1.18039	−0.590194	+	0.807261i	$0.700949\pi$
$174$	3.16234e12	1.50310
$175$	1.57041e11	0.0723277
$176$	−1.48840e11	−0.0664353
$177$	−1.76136e11	−0.0762073
$178$	−3.72645e12	−1.56309
$179$	−1.72651e12	−0.702229	−0.351114	−	0.936333i	$-0.614197\pi$
$179$	−1.72651e12	−0.702229	−0.351114	+	0.936333i	$0.614197\pi$
$180$	−1.03230e12	−0.407201
$181$	4.11462e12	1.57433	0.787167	−	0.616739i	$-0.211547\pi$
$181$	4.11462e12	1.57433	0.787167	+	0.616739i	$0.211547\pi$
$182$	−1.19372e13	−4.43109
$183$	3.62612e12	1.30605
$184$	1.16772e12	0.408169
$185$	2.71686e12	0.921769
$186$	−3.21900e12	−1.06023
$187$	−1.01026e12	−0.323076
$188$	−8.93201e11	−0.277384
$189$	−5.14932e12	−1.55314
$190$	2.96878e12	0.869829
$191$	−6.43067e9	−0.00183051	−0.000915257	−	1.00000i	$-0.500291\pi$
$191$	−6.43067e9	−0.00183051	−0.000915257		1.00000i	$0.500291\pi$
$192$	−6.57030e12	−1.81731
$193$	−8.54060e11	−0.229574	−0.114787	−	0.993390i	$-0.536619\pi$
$193$	−8.54060e11	−0.229574	−0.114787	+	0.993390i	$0.536619\pi$
$194$	1.04262e13	2.72405
$195$	6.66160e12	1.69195
$196$	1.57209e13	3.88212
$197$	−6.85449e12	−1.64593	−0.822964	−	0.568093i	$-0.807681\pi$
$197$	−6.85449e12	−1.64593	−0.822964	+	0.568093i	$0.807681\pi$
$198$	2.30088e12	0.537323
$199$	3.55475e12	0.807453	0.403726	−	0.914880i	$-0.367715\pi$
$199$	3.55475e12	0.807453	0.403726	+	0.914880i	$0.367715\pi$
$200$	1.69479e11	0.0374500
$201$	3.34134e12	0.718360
$202$	−5.84046e12	−1.22184
$203$	7.59331e12	1.54598
$204$	−2.18353e12	−0.432707
$205$	6.93346e12	1.33753
$206$	1.06718e13	2.00433
$207$	5.82476e11	0.106522
$208$	4.15691e11	0.0740324
$209$	−4.06763e12	−0.705564
$210$	−2.01372e13	−3.40247
$211$	−6.62963e12	−1.09128	−0.545640	−	0.838020i	$-0.683713\pi$
$211$	−6.62963e12	−1.09128	−0.545640	+	0.838020i	$0.683713\pi$
$212$	6.03916e12	0.968566
$213$	−1.49245e12	−0.233245
$214$	−1.21095e13	−1.84439
$215$	−7.92179e12	−1.17601
$216$	−5.55716e12	−0.804188
$217$	−7.72937e12	−1.09047
$218$	2.13856e13	2.94178
$219$	1.84143e12	0.247010
$220$	−1.65602e13	−2.16641
$221$	2.82153e12	0.360021
$222$	−1.30882e13	−1.62906
$223$	4.64635e12	0.564203	0.282102	−	0.959385i	$-0.408968\pi$
$223$	4.64635e12	0.564203	0.282102	+	0.959385i	$0.408968\pi$
$224$	−1.62605e13	−1.92651
$225$	8.45390e10	0.00977358
$226$	9.08837e12	1.02539
$227$	−6.67365e12	−0.734888	−0.367444	−	0.930046i	$-0.619767\pi$
$227$	−6.67365e12	−0.734888	−0.367444	+	0.930046i	$0.619767\pi$
$228$	−8.79159e12	−0.944987
$229$	−2.39558e12	−0.251371	−0.125686	−	0.992070i	$-0.540113\pi$
$229$	−2.39558e12	−0.251371	−0.125686	+	0.992070i	$0.540113\pi$
$230$	−6.81984e12	−0.698669
$231$	2.75907e13	2.75992
$232$	8.19472e12	0.800480
$233$	1.37196e13	1.30883	0.654414	−	0.756137i	$-0.272916\pi$
$233$	1.37196e13	1.30883	0.654414	+	0.756137i	$0.272916\pi$
$234$	−6.42608e12	−0.598768
$235$	1.94703e12	0.177214
$236$	−1.22290e12	−0.108736
$237$	7.98856e12	0.693989
$238$	−8.52917e12	−0.723992
$239$	1.74026e13	1.44353	0.721765	−	0.692138i	$-0.243331\pi$
$239$	1.74026e13	1.44353	0.721765	+	0.692138i	$0.243331\pi$
$240$	7.01241e11	0.0568468
$241$	−1.25576e13	−0.994974	−0.497487	−	0.867472i	$-0.665744\pi$
$241$	−1.25576e13	−0.994974	−0.497487	+	0.867472i	$0.665744\pi$
$242$	1.61092e13	1.24764
$243$	−6.46987e12	−0.489847
$244$	2.51757e13	1.86354
$245$	−3.42689e13	−2.48020
$246$	−3.34013e13	−2.36385
$247$	1.13604e13	0.786249
$248$	−8.34156e12	−0.564628
$249$	1.18892e13	0.787148
$250$	2.43671e13	1.57810
$251$	1.03372e13	0.654935	0.327467	−	0.944862i	$-0.393805\pi$
$251$	1.03372e13	0.654935	0.327467	+	0.944862i	$0.393805\pi$
$252$	1.19411e13	0.740186
$253$	9.34409e12	0.566728
$254$	2.36444e13	1.40328
$255$	4.75973e12	0.276447
$256$	−1.61486e13	−0.917939
$257$	−2.35510e13	−1.31032	−0.655160	−	0.755491i	$-0.727399\pi$
$257$	−2.35510e13	−1.31032	−0.655160	+	0.755491i	$0.727399\pi$
$258$	3.81625e13	2.07839
$259$	−3.14270e13	−1.67554
$260$	4.62507e13	2.41415
$261$	4.08766e12	0.208906
$262$	−3.93570e13	−1.96954
$263$	5.98544e12	0.293319	0.146659	−	0.989187i	$-0.453148\pi$
$263$	5.98544e12	0.293319	0.146659	+	0.989187i	$0.453148\pi$
$264$	2.97760e13	1.42904
$265$	−1.31643e13	−0.618795
$266$	−3.43411e13	−1.58112
$267$	−2.40551e13	−1.08491
$268$	2.31985e13	1.02499
$269$	−3.18817e12	−0.138008	−0.0690039	−	0.997616i	$-0.521982\pi$
$269$	−3.18817e12	−0.138008	−0.0690039	+	0.997616i	$0.521982\pi$
$270$	3.24556e13	1.37654
$271$	1.29592e12	0.0538578	0.0269289	−	0.999637i	$-0.491427\pi$
$271$	1.29592e12	0.0538578	0.0269289	+	0.999637i	$0.491427\pi$
$272$	2.97012e11	0.0120961
$273$	−7.70574e13	−3.07553
$274$	−9.97828e12	−0.390326
$275$	1.35618e12	0.0519980
$276$	2.01959e13	0.759038
$277$	−2.75073e12	−0.101347	−0.0506733	−	0.998715i	$-0.516137\pi$
$277$	−2.75073e12	−0.101347	−0.0506733	+	0.998715i	$0.516137\pi$
$278$	5.23977e13	1.89263
$279$	−4.16090e12	−0.147355
$280$	−5.21827e13	−1.81200
$281$	3.32134e13	1.13091	0.565456	−	0.824778i	$-0.308700\pi$
$281$	3.32134e13	1.13091	0.565456	+	0.824778i	$0.308700\pi$
$282$	−9.37962e12	−0.313195
$283$	4.43186e12	0.145131	0.0725655	−	0.997364i	$-0.476881\pi$
$283$	4.43186e12	0.145131	0.0725655	+	0.997364i	$0.476881\pi$
$284$	−1.03619e13	−0.332804
$285$	1.91642e13	0.603731
$286$	−1.03087e14	−3.18560
$287$	−8.02022e13	−2.43129
$288$	−8.75343e12	−0.260327
$289$	2.01599e12	0.0588235
$290$	−4.78598e13	−1.37019
$291$	6.73033e13	1.89071
$292$	1.27849e13	0.352444
$293$	2.91358e13	0.788234	0.394117	−	0.919060i	$-0.371050\pi$
$293$	2.91358e13	0.788234	0.394117	+	0.919060i	$0.371050\pi$
$294$	1.65087e14	4.38332
$295$	2.66570e12	0.0694690
$296$	−3.39161e13	−0.867564
$297$	−4.44685e13	−1.11659
$298$	−4.90706e13	−1.20957
$299$	−2.60969e13	−0.631535
$300$	2.93118e12	0.0696427
$301$	9.16346e13	2.13769
$302$	−1.86106e13	−0.426306
$303$	−3.77015e13	−0.848056
$304$	1.19587e12	0.0264166
$305$	−5.48788e13	−1.19057
$306$	−4.59145e12	−0.0978323
$307$	8.51889e11	0.0178288	0.00891439	−	0.999960i	$-0.497162\pi$
$307$	8.51889e11	0.0178288	0.00891439	+	0.999960i	$0.497162\pi$
$308$	1.91559e14	3.93798
$309$	6.88891e13	1.39117
$310$	4.87173e13	0.966483
$311$	−3.92240e12	−0.0764487	−0.0382243	−	0.999269i	$-0.512170\pi$
$311$	−3.92240e12	−0.0764487	−0.0382243	+	0.999269i	$0.512170\pi$
$312$	−8.31606e13	−1.59246
$313$	−2.39255e13	−0.450160	−0.225080	−	0.974340i	$-0.572264\pi$
$313$	−2.39255e13	−0.450160	−0.225080	+	0.974340i	$0.572264\pi$
$314$	−1.55499e14	−2.87485
$315$	−2.60295e13	−0.472888
$316$	5.54637e13	0.990216
$317$	−1.64522e13	−0.288668	−0.144334	−	0.989529i	$-0.546104\pi$
$317$	−1.64522e13	−0.288668	−0.144334	+	0.989529i	$0.546104\pi$
$318$	6.34179e13	1.09361
$319$	6.55743e13	1.11144
$320$	9.94369e13	1.65662
$321$	−7.81699e13	−1.28015
$322$	7.88880e13	1.27000
$323$	8.11703e12	0.128465
$324$	−1.21786e14	−1.89496
$325$	−3.78764e12	−0.0579442
$326$	−1.70180e14	−2.55984
$327$	1.38049e14	2.04184
$328$	−8.65544e13	−1.25888
$329$	−2.25221e13	−0.322130
$330$	−1.73901e14	−2.44611
$331$	−7.21217e12	−0.0997727	−0.0498864	−	0.998755i	$-0.515886\pi$
$331$	−7.21217e12	−0.0997727	−0.0498864	+	0.998755i	$0.515886\pi$
$332$	8.25454e13	1.12314
$333$	−1.69179e13	−0.226414
$334$	2.05359e13	0.270339
$335$	−5.05689e13	−0.654842
$336$	−8.11155e12	−0.103333
$337$	1.04181e14	1.30565	0.652824	−	0.757510i	$-0.273584\pi$
$337$	1.04181e14	1.30565	0.652824	+	0.757510i	$0.273584\pi$
$338$	1.57247e14	1.93884
$339$	5.86675e13	0.711704
$340$	3.30463e13	0.394447
$341$	−6.67492e13	−0.783966
$342$	−1.84866e13	−0.213656
$343$	2.33486e14	2.65548
$344$	9.88923e13	1.10686
$345$	−4.40237e13	−0.484932
$346$	−1.75410e14	−1.90167
$347$	1.42362e14	1.51909	0.759543	−	0.650457i	$-0.225422\pi$
$347$	1.42362e14	1.51909	0.759543	+	0.650457i	$0.225422\pi$
$348$	1.41729e14	1.48859
$349$	6.95810e13	0.719367	0.359684	−	0.933074i	$-0.382885\pi$
$349$	6.95810e13	0.719367	0.359684	+	0.933074i	$0.382885\pi$
$350$	1.14496e13	0.116524
$351$	1.24195e14	1.24427
$352$	−1.40423e14	−1.38501
$353$	−1.53250e14	−1.48812	−0.744061	−	0.668112i	$-0.767103\pi$
$353$	−1.53250e14	−1.48812	−0.744061	+	0.668112i	$0.767103\pi$
$354$	−1.28418e13	−0.122774
$355$	2.25872e13	0.212621
$356$	−1.67012e14	−1.54800
$357$	−5.50578e13	−0.502509
$358$	−1.25877e14	−1.13133
$359$	−4.53791e13	−0.401640	−0.200820	−	0.979628i	$-0.564361\pi$
$359$	−4.53791e13	−0.401640	−0.200820	+	0.979628i	$0.564361\pi$
$360$	−2.80911e13	−0.244853
$361$	−8.38085e13	−0.719447
$362$	2.99989e14	2.53634
$363$	1.03989e14	0.865965
$364$	−5.35001e14	−4.38831
$365$	−2.78688e13	−0.225169
$366$	2.64374e14	2.10413
$367$	−1.52325e14	−1.19429	−0.597144	−	0.802134i	$-0.703698\pi$
$367$	−1.52325e14	−1.19429	−0.597144	+	0.802134i	$0.703698\pi$
$368$	−2.74712e12	−0.0212185
$369$	−4.31747e13	−0.328537
$370$	1.98081e14	1.48502
$371$	1.52277e14	1.12481
$372$	−1.44269e14	−1.04999
$373$	−9.07937e13	−0.651114	−0.325557	−	0.945522i	$-0.605552\pi$
$373$	−9.07937e13	−0.651114	−0.325557	+	0.945522i	$0.605552\pi$
$374$	−7.36561e13	−0.520493
$375$	1.57295e14	1.09533
$376$	−2.43059e13	−0.166793
$377$	−1.83141e14	−1.23853
$378$	−3.75427e14	−2.50219
$379$	−1.21559e14	−0.798494	−0.399247	−	0.916843i	$-0.630728\pi$
$379$	−1.21559e14	−0.798494	−0.399247	+	0.916843i	$0.630728\pi$
$380$	1.33055e14	0.861431
$381$	1.52630e14	0.973987
$382$	−4.68848e11	−0.00294906
$383$	6.47365e13	0.401380	0.200690	−	0.979655i	$-0.435682\pi$
$383$	6.47365e13	0.401380	0.200690	+	0.979655i	$0.435682\pi$
$384$	−2.88803e14	−1.76515
$385$	−4.17566e14	−2.51589
$386$	−6.22679e13	−0.369857
$387$	4.93291e13	0.288863
$388$	4.67279e14	2.69775
$389$	7.64249e13	0.435023	0.217511	−	0.976058i	$-0.430206\pi$
$389$	7.64249e13	0.435023	0.217511	+	0.976058i	$0.430206\pi$
$390$	4.85684e14	2.72583
$391$	−1.86463e13	−0.103186
$392$	4.27799e14	2.33435
$393$	−2.54059e14	−1.36702
$394$	−4.99748e14	−2.65168
$395$	−1.20901e14	−0.632626
$396$	1.03121e14	0.532136
$397$	−1.53406e13	−0.0780719	−0.0390360	−	0.999238i	$-0.512429\pi$
$397$	−1.53406e13	−0.0780719	−0.0390360	+	0.999238i	$0.512429\pi$
$398$	2.59170e14	1.30085
$399$	−2.21680e14	−1.09743
$400$	−3.98710e11	−0.00194683
$401$	1.01060e14	0.486729	0.243364	−	0.969935i	$-0.421749\pi$
$401$	1.01060e14	0.486729	0.243364	+	0.969935i	$0.421749\pi$
$402$	2.43611e14	1.15732
$403$	1.86422e14	0.873616
$404$	−2.61757e14	−1.21004
$405$	2.65473e14	1.21065
$406$	5.53614e14	2.49066
$407$	−2.71397e14	−1.20458
$408$	−5.94185e13	−0.260190
$409$	2.77374e14	1.19836	0.599180	−	0.800615i	$-0.295494\pi$
$409$	2.77374e14	1.19836	0.599180	+	0.800615i	$0.295494\pi$
$410$	5.05505e14	2.15484
$411$	−6.44121e13	−0.270918
$412$	4.78289e14	1.98498
$413$	−3.08353e13	−0.126277
$414$	4.24672e13	0.171614
$415$	−1.79935e14	−0.717548
$416$	3.92183e14	1.54339
$417$	3.38239e14	1.31364
$418$	−2.96563e14	−1.13670
$419$	5.54407e13	0.209725	0.104863	−	0.994487i	$-0.466560\pi$
$419$	5.54407e13	0.209725	0.104863	+	0.994487i	$0.466560\pi$
$420$	−9.02509e14	−3.36962
$421$	2.07061e14	0.763038	0.381519	−	0.924361i	$-0.375401\pi$
$421$	2.07061e14	0.763038	0.381519	+	0.924361i	$0.375401\pi$
$422$	−4.83354e14	−1.75811
$423$	−1.21242e13	−0.0435291
$424$	1.64338e14	0.582406
$425$	−2.70628e12	−0.00946745
$426$	−1.08812e14	−0.375771
$427$	6.34806e14	2.16415
$428$	−5.42725e14	−1.82658
$429$	−6.65452e14	−2.21107
$430$	−5.77563e14	−1.89462
$431$	8.62005e12	0.0279180	0.0139590	−	0.999903i	$-0.495557\pi$
$431$	8.62005e12	0.0279180	0.0139590	+	0.999903i	$0.495557\pi$
$432$	1.30736e13	0.0418055
$433$	1.81675e14	0.573602	0.286801	−	0.957990i	$-0.407408\pi$
$433$	1.81675e14	0.573602	0.286801	+	0.957990i	$0.407408\pi$
$434$	−5.63533e14	−1.75682
$435$	−3.08946e14	−0.951024
$436$	9.58459e14	2.91338
$437$	−7.50760e13	−0.225348
$438$	1.34255e14	0.397946
$439$	1.06795e14	0.312604	0.156302	−	0.987709i	$-0.450043\pi$
$439$	1.06795e14	0.312604	0.156302	+	0.987709i	$0.450043\pi$
$440$	−4.50639e14	−1.30268
$441$	2.13393e14	0.609210
$442$	2.05713e14	0.580014
$443$	−1.00635e14	−0.280238	−0.140119	−	0.990135i	$-0.544749\pi$
$443$	−1.00635e14	−0.280238	−0.140119	+	0.990135i	$0.544749\pi$
$444$	−5.86586e14	−1.61334
$445$	3.64057e14	0.988984
$446$	3.38757e14	0.908963
$447$	−3.16762e14	−0.839541
$448$	−1.15023e15	−3.01131
$449$	−1.54038e14	−0.398358	−0.199179	−	0.979963i	$-0.563828\pi$
$449$	−1.54038e14	−0.398358	−0.199179	+	0.979963i	$0.563828\pi$
$450$	6.16358e12	0.0157458
$451$	−6.92610e14	−1.74790
$452$	4.07322e14	1.01549
$453$	−1.20135e14	−0.295891
$454$	−4.86563e14	−1.18395
$455$	1.16621e15	2.80359
$456$	−2.39238e14	−0.568228
$457$	1.39161e14	0.326571	0.163286	−	0.986579i	$-0.447791\pi$
$457$	1.39161e14	0.326571	0.163286	+	0.986579i	$0.447791\pi$
$458$	−1.74657e14	−0.404973
$459$	8.87377e13	0.203301
$460$	−3.05651e14	−0.691924
$461$	−1.35110e13	−0.0302225	−0.0151113	−	0.999886i	$-0.504810\pi$
$461$	−1.35110e13	−0.0302225	−0.0151113	+	0.999886i	$0.504810\pi$
$462$	2.01159e15	4.44639
$463$	−3.46428e14	−0.756690	−0.378345	−	0.925665i	$-0.623507\pi$
$463$	−3.46428e14	−0.756690	−0.378345	+	0.925665i	$0.623507\pi$
$464$	−1.92786e13	−0.0416127
$465$	3.14482e14	0.670817
$466$	1.00027e15	2.10859
$467$	−8.88204e14	−1.85042	−0.925209	−	0.379457i	$-0.876111\pi$
$467$	−8.88204e14	−1.85042	−0.925209	+	0.379457i	$0.876111\pi$
$468$	−2.88004e14	−0.592988
$469$	5.84951e14	1.19033
$470$	1.41954e14	0.285502
$471$	−1.00378e15	−1.99538
$472$	−3.32775e13	−0.0653838
$473$	7.91338e14	1.53683
$474$	5.82431e14	1.11806
$475$	−1.08963e13	−0.0206759
$476$	−3.82260e14	−0.717002
$477$	8.19744e13	0.151994
$478$	1.26879e15	2.32561
$479$	−8.93473e14	−1.61896	−0.809480	−	0.587148i	$-0.800251\pi$
$479$	−8.93473e14	−1.61896	−0.809480	+	0.587148i	$0.800251\pi$
$480$	6.61586e14	1.18511
$481$	7.57979e14	1.34233
$482$	−9.15548e14	−1.60296
$483$	5.09240e14	0.881482
$484$	7.21983e14	1.23560
$485$	−1.01859e15	−1.72353
$486$	−4.71706e14	−0.789172
$487$	−2.97643e13	−0.0492363	−0.0246182	−	0.999697i	$-0.507837\pi$
$487$	−2.97643e13	−0.0492363	−0.0246182	+	0.999697i	$0.507837\pi$
$488$	6.85085e14	1.12056
$489$	−1.09855e15	−1.77673
$490$	−2.49848e15	−3.99574
$491$	−1.18250e15	−1.87004	−0.935022	−	0.354591i	$-0.884620\pi$
$491$	−1.18250e15	−1.87004	−0.935022	+	0.354591i	$0.884620\pi$
$492$	−1.49698e15	−2.34103
$493$	−1.30855e14	−0.202363
$494$	8.28264e14	1.26669
$495$	−2.24786e14	−0.339969
$496$	1.96240e13	0.0293520
$497$	−2.61276e14	−0.386491
$498$	8.66819e14	1.26814
$499$	7.42191e14	1.07390	0.536949	−	0.843615i	$-0.319577\pi$
$499$	7.42191e14	1.07390	0.536949	+	0.843615i	$0.319577\pi$
$500$	1.09208e15	1.56286
$501$	1.32564e14	0.187637
$502$	7.53666e14	1.05514
$503$	8.70029e14	1.20479	0.602393	−	0.798200i	$-0.294214\pi$
$503$	8.70029e14	1.20479	0.602393	+	0.798200i	$0.294214\pi$
$504$	3.24942e14	0.445080
$505$	5.70587e14	0.773070
$506$	6.81260e14	0.913030
$507$	1.01507e15	1.34571
$508$	1.05969e15	1.38973
$509$	7.62815e14	0.989626	0.494813	−	0.868999i	$-0.335237\pi$
$509$	7.62815e14	0.989626	0.494813	+	0.868999i	$0.335237\pi$
$510$	3.47023e14	0.445371
$511$	3.22370e14	0.409299
$512$	7.93771e13	0.0997035
$513$	3.57286e14	0.443988
$514$	−1.71706e15	−2.11100
$515$	−1.04259e15	−1.26816
$516$	1.71036e15	2.05833
$517$	−1.94496e14	−0.231586
$518$	−2.29128e15	−2.69939
$519$	−1.13231e15	−1.31991
$520$	1.25858e15	1.45165
$521$	−1.12547e15	−1.28447	−0.642236	−	0.766507i	$-0.721993\pi$
$521$	−1.12547e15	−1.28447	−0.642236	+	0.766507i	$0.721993\pi$
$522$	2.98023e14	0.336560
$523$	−1.28275e15	−1.43345	−0.716723	−	0.697358i	$-0.754359\pi$
$523$	−1.28275e15	−1.43345	−0.716723	+	0.697358i	$0.754359\pi$
$524$	−1.76390e15	−1.95053
$525$	7.39097e13	0.0808771
$526$	4.36387e14	0.472553
$527$	1.33199e14	0.142739
$528$	−7.00497e13	−0.0742881
$529$	−7.80346e14	−0.818995
$530$	−9.59787e14	−0.996913
$531$	−1.65994e13	−0.0170636
$532$	−1.53910e15	−1.56586
$533$	1.93437e15	1.94778
$534$	−1.75381e15	−1.74786
$535$	1.18305e15	1.16696
$536$	6.31281e14	0.616334
$537$	−8.12564e14	−0.785234
$538$	−2.32443e14	−0.222339
$539$	3.42325e15	3.24116
$540$	1.45459e15	1.36325
$541$	4.93628e14	0.457946	0.228973	−	0.973433i	$-0.426463\pi$
$541$	4.93628e14	0.457946	0.228973	+	0.973433i	$0.426463\pi$
$542$	9.44834e13	0.0867680
$543$	1.93650e15	1.76043
$544$	2.80216e14	0.252173
$545$	−2.08928e15	−1.86130
$546$	−5.61811e15	−4.95485
$547$	3.41397e14	0.298078	0.149039	−	0.988831i	$-0.452382\pi$
$547$	3.41397e14	0.298078	0.149039	+	0.988831i	$0.452382\pi$
$548$	−4.47206e14	−0.386558
$549$	3.41731e14	0.292440
$550$	9.88763e13	0.0837717
$551$	−5.26862e14	−0.441940
$552$	5.49573e14	0.456416
$553$	1.39852e15	1.14995
$554$	−2.00550e14	−0.163275
$555$	1.27866e15	1.03072
$556$	2.34836e15	1.87436
$557$	1.59595e15	1.26129	0.630645	−	0.776071i	$-0.282790\pi$
$557$	1.59595e15	1.26129	0.630645	+	0.776071i	$0.282790\pi$
$558$	−3.03363e14	−0.237397
$559$	−2.21011e15	−1.71257
$560$	1.22763e14	0.0941960
$561$	−4.75467e14	−0.361264
$562$	2.42153e15	1.82196
$563$	−4.63827e14	−0.345589	−0.172795	−	0.984958i	$-0.555280\pi$
$563$	−4.63827e14	−0.345589	−0.172795	+	0.984958i	$0.555280\pi$
$564$	−4.20375e14	−0.310171
$565$	−8.87893e14	−0.648775
$566$	3.23118e14	0.233814
$567$	−3.07084e15	−2.20064
$568$	−2.81969e14	−0.200118
$569$	2.48647e15	1.74769	0.873846	−	0.486202i	$-0.161618\pi$
$569$	2.48647e15	1.74769	0.873846	+	0.486202i	$0.161618\pi$
$570$	1.39722e15	0.972645
$571$	−2.46577e15	−1.70002	−0.850010	−	0.526766i	$-0.823404\pi$
$571$	−2.46577e15	−1.70002	−0.850010	+	0.526766i	$0.823404\pi$
$572$	−4.62016e15	−3.15485
$573$	−3.02652e12	−0.00204689
$574$	−5.84739e15	−3.91694
$575$	2.50309e13	0.0166075
$576$	−6.19194e14	−0.406915
$577$	3.91006e14	0.254517	0.127259	−	0.991870i	$-0.459382\pi$
$577$	3.91006e14	0.254517	0.127259	+	0.991870i	$0.459382\pi$
$578$	1.46982e14	0.0947680
$579$	−4.01953e14	−0.256711
$580$	−2.14498e15	−1.35696
$581$	2.08138e15	1.30432
$582$	4.90695e15	3.04604
$583$	1.31504e15	0.808650
$584$	3.47903e14	0.211928
$585$	6.27799e14	0.378846
$586$	2.12424e15	1.26989
$587$	−6.20306e14	−0.367364	−0.183682	−	0.982986i	$-0.558802\pi$
$587$	−6.20306e14	−0.367364	−0.183682	+	0.982986i	$0.558802\pi$
$588$	7.39886e15	4.34100
$589$	5.36303e14	0.311728
$590$	1.94351e14	0.111918
$591$	−3.22599e15	−1.84048
$592$	7.97896e13	0.0451000
$593$	1.74580e15	0.977674	0.488837	−	0.872375i	$-0.337421\pi$
$593$	1.74580e15	0.977674	0.488837	+	0.872375i	$0.337421\pi$
$594$	−3.24211e15	−1.79888
$595$	8.33261e14	0.458076
$596$	−2.19924e15	−1.19790
$597$	1.67300e15	0.902896
$598$	−1.90268e15	−1.01744
$599$	1.21440e15	0.643450	0.321725	−	0.946833i	$-0.395737\pi$
$599$	1.21440e15	0.643450	0.321725	+	0.946833i	$0.395737\pi$
$600$	7.97636e13	0.0418767
$601$	−1.73804e14	−0.0904172	−0.0452086	−	0.998978i	$-0.514395\pi$
$601$	−1.73804e14	−0.0904172	−0.0452086	+	0.998978i	$0.514395\pi$
$602$	6.68090e15	3.44393
$603$	3.14893e14	0.160849
$604$	−8.34087e14	−0.422190
$605$	−1.57380e15	−0.789396
$606$	−2.74875e15	−1.36627
$607$	2.52172e15	1.24211	0.621053	−	0.783769i	$-0.286705\pi$
$607$	2.52172e15	1.24211	0.621053	+	0.783769i	$0.286705\pi$
$608$	1.12824e15	0.550721
$609$	3.57371e15	1.72872
$610$	−4.00111e15	−1.91808
$611$	5.43203e14	0.258069
$612$	−2.05779e14	−0.0968878
$613$	2.23727e15	1.04396	0.521982	−	0.852956i	$-0.325193\pi$
$613$	2.23727e15	1.04396	0.521982	+	0.852956i	$0.325193\pi$
$614$	6.21096e13	0.0287232
$615$	3.26315e15	1.49563
$616$	5.21272e15	2.36794
$617$	−2.56802e15	−1.15619	−0.578095	−	0.815969i	$-0.696204\pi$
$617$	−2.56802e15	−1.15619	−0.578095	+	0.815969i	$0.696204\pi$
$618$	5.02257e15	2.24125
$619$	−3.64586e15	−1.61250	−0.806252	−	0.591572i	$-0.798508\pi$
$619$	−3.64586e15	−1.61250	−0.806252	+	0.591572i	$0.798508\pi$
$620$	2.18341e15	0.957152
$621$	−8.20753e14	−0.356622
$622$	−2.85975e14	−0.123163
$623$	−4.21120e15	−1.79772
$624$	1.95640e14	0.0827833
$625$	−2.47362e15	−1.03751
$626$	−1.74436e15	−0.725234
$627$	−1.91438e15	−0.788964
$628$	−6.96915e15	−2.84709
$629$	5.41578e14	0.219322
$630$	−1.89776e15	−0.761849
$631$	3.59282e15	1.42979	0.714897	−	0.699229i	$-0.246473\pi$
$631$	3.59282e15	1.42979	0.714897	+	0.699229i	$0.246473\pi$
$632$	1.50928e15	0.595425
$633$	−3.12016e15	−1.22027
$634$	−1.19950e15	−0.465060
$635$	−2.30995e15	−0.887867
$636$	2.84226e15	1.08305
$637$	−9.56071e15	−3.61180
$638$	4.78089e15	1.79059
$639$	−1.40651e14	−0.0522261
$640$	4.37084e15	1.60907
$641$	−5.75644e11	−0.000210104 0	−0.000105052	−	1.00000i	$-0.500033\pi$
$641$	−5.75644e11	−0.000210104 0	−0.000105052		1.00000i	$0.500033\pi$
$642$	−5.69922e15	−2.06240
$643$	−3.15086e15	−1.13049	−0.565247	−	0.824922i	$-0.691219\pi$
$643$	−3.15086e15	−1.13049	−0.565247	+	0.824922i	$0.691219\pi$
$644$	3.53560e15	1.25774
$645$	−3.72830e15	−1.31502
$646$	5.91797e14	0.206964
$647$	−2.94474e15	−1.02111	−0.510556	−	0.859844i	$-0.670561\pi$
$647$	−2.94474e15	−1.02111	−0.510556	+	0.859844i	$0.670561\pi$
$648$	−3.31406e15	−1.13946
$649$	−2.66287e14	−0.0907830
$650$	−2.76149e14	−0.0933513
$651$	−3.63774e15	−1.21937
$652$	−7.62712e15	−2.53512
$653$	5.59989e15	1.84568	0.922841	−	0.385181i	$-0.125861\pi$
$653$	5.59989e15	1.84568	0.922841	+	0.385181i	$0.125861\pi$
$654$	1.00649e16	3.28951
$655$	3.84500e15	1.24615
$656$	2.03624e14	0.0654423
$657$	1.73540e14	0.0553081
$658$	−1.64204e15	−0.518969
$659$	1.56369e15	0.490095	0.245047	−	0.969511i	$-0.421196\pi$
$659$	1.56369e15	0.490095	0.245047	+	0.969511i	$0.421196\pi$
$660$	−7.79388e15	−2.42249
$661$	−1.30441e15	−0.402074	−0.201037	−	0.979584i	$-0.564431\pi$
$661$	−1.30441e15	−0.402074	−0.201037	+	0.979584i	$0.564431\pi$
$662$	−5.25825e14	−0.160739
$663$	1.32792e15	0.402576
$664$	2.24623e15	0.675352
$665$	3.35497e15	1.00039
$666$	−1.23345e15	−0.364765
$667$	1.21030e15	0.354978
$668$	9.20377e14	0.267729
$669$	2.18675e15	0.630894
$670$	−3.68688e15	−1.05499
$671$	5.48205e15	1.55586
$672$	−7.65284e15	−2.15423
$673$	1.39009e14	0.0388114	0.0194057	−	0.999812i	$-0.493823\pi$
$673$	1.39009e14	0.0388114	0.0194057	+	0.999812i	$0.493823\pi$
$674$	7.59567e15	2.10347
$675$	−1.19122e14	−0.0327206
$676$	7.04749e15	1.92012
$677$	−1.43498e15	−0.387801	−0.193900	−	0.981021i	$-0.562114\pi$
$677$	−1.43498e15	−0.387801	−0.193900	+	0.981021i	$0.562114\pi$
$678$	4.27734e15	1.14660
$679$	1.17824e16	3.13294
$680$	8.99258e14	0.237184
$681$	−3.14088e15	−0.821754
$682$	−4.86656e15	−1.26301
$683$	−4.88209e15	−1.25687	−0.628437	−	0.777861i	$-0.716305\pi$
$683$	−4.88209e15	−1.25687	−0.628437	+	0.777861i	$0.716305\pi$
$684$	−8.28533e14	−0.211593
$685$	9.74832e14	0.246963
$686$	1.70230e16	4.27813
$687$	−1.12745e15	−0.281084
$688$	−2.32650e14	−0.0575396
$689$	−3.67273e15	−0.901122
$690$	−3.20968e15	−0.781254
$691$	−7.29259e15	−1.76097	−0.880486	−	0.474073i	$-0.842783\pi$
$691$	−7.29259e15	−1.76097	−0.880486	+	0.474073i	$0.842783\pi$
$692$	−7.86151e15	−1.88331
$693$	2.60019e15	0.617977
$694$	1.03794e16	2.44733
$695$	−5.11902e15	−1.19749
$696$	3.85675e15	0.895099
$697$	1.38212e15	0.318247
$698$	5.07301e15	1.15894
$699$	6.45695e15	1.46353
$700$	5.13147e14	0.115399
$701$	−3.65477e15	−0.815476	−0.407738	−	0.913099i	$-0.633682\pi$
$701$	−3.65477e15	−0.815476	−0.407738	+	0.913099i	$0.633682\pi$
$702$	9.05483e15	2.00459
$703$	2.18056e15	0.478977
$704$	−9.93313e15	−2.16489
$705$	9.16346e14	0.198162
$706$	−1.11731e16	−2.39745
$707$	−6.60021e15	−1.40524
$708$	−5.75542e14	−0.121589
$709$	−9.11406e15	−1.91055	−0.955273	−	0.295724i	$-0.904439\pi$
$709$	−9.11406e15	−1.91055	−0.955273	+	0.295724i	$0.904439\pi$
$710$	1.64679e15	0.342545
$711$	7.52854e14	0.155392
$712$	−4.54474e15	−0.930826
$713$	−1.23199e15	−0.250388
$714$	−4.01416e15	−0.809570
$715$	1.00712e16	2.01556
$716$	−5.64154e15	−1.12041
$717$	8.19034e15	1.61416
$718$	−3.30851e15	−0.647064
$719$	−6.85648e14	−0.133074	−0.0665368	−	0.997784i	$-0.521195\pi$
$719$	−6.85648e14	−0.133074	−0.0665368	+	0.997784i	$0.521195\pi$
$720$	6.60860e13	0.0127286
$721$	1.20601e16	2.30518
$722$	−6.11032e15	−1.15907
$723$	−5.91007e15	−1.11258
$724$	1.34449e16	2.51186
$725$	1.75660e14	0.0325697
$726$	7.58163e15	1.39512
$727$	3.23647e15	0.591060	0.295530	−	0.955333i	$-0.404504\pi$
$727$	3.23647e15	0.591060	0.295530	+	0.955333i	$0.404504\pi$
$728$	−1.45585e16	−2.63872
$729$	3.55747e15	0.639940
$730$	−2.03186e15	−0.362760
$731$	−1.57913e15	−0.279816
$732$	1.18487e16	2.08381
$733$	−6.81981e15	−1.19042	−0.595210	−	0.803570i	$-0.702931\pi$
$733$	−6.81981e15	−1.19042	−0.595210	+	0.803570i	$0.702931\pi$
$734$	−1.11058e16	−1.92407
$735$	−1.61283e16	−2.77337
$736$	−2.59177e15	−0.442353
$737$	5.05151e15	0.855757
$738$	−3.14779e15	−0.529292
$739$	−7.00346e14	−0.116888	−0.0584438	−	0.998291i	$-0.518614\pi$
$739$	−7.00346e14	−0.116888	−0.0584438	+	0.998291i	$0.518614\pi$
$740$	8.87757e15	1.47069
$741$	5.34664e15	0.879186
$742$	1.11022e16	1.81213
$743$	1.65758e15	0.268557	0.134278	−	0.990944i	$-0.457128\pi$
$743$	1.65758e15	0.268557	0.134278	+	0.990944i	$0.457128\pi$
$744$	−3.92586e15	−0.631369
$745$	4.79398e15	0.765309
$746$	−6.61959e15	−1.04898
$747$	1.12046e15	0.176251
$748$	−3.30112e15	−0.515468
$749$	−1.36848e16	−2.12123
$750$	1.14681e16	1.76463
$751$	1.68651e15	0.257614	0.128807	−	0.991670i	$-0.458885\pi$
$751$	1.68651e15	0.257614	0.128807	+	0.991670i	$0.458885\pi$
$752$	5.71810e13	0.00867069
$753$	4.86509e15	0.732350
$754$	−1.33525e16	−1.99535
$755$	1.81817e15	0.269728
$756$	−1.68259e16	−2.47804
$757$	3.26481e14	0.0477344	0.0238672	−	0.999715i	$-0.492402\pi$
$757$	3.26481e14	0.0477344	0.0238672	+	0.999715i	$0.492402\pi$
$758$	−8.86264e15	−1.28642
$759$	4.39769e15	0.633716
$760$	3.62070e15	0.517985
$761$	9.04784e15	1.28508	0.642539	−	0.766253i	$-0.277881\pi$
$761$	9.04784e15	1.28508	0.642539	+	0.766253i	$0.277881\pi$
$762$	1.11280e16	1.56915
$763$	2.41675e16	3.38335
$764$	−2.10128e13	−0.00292059
$765$	4.48564e14	0.0618994
$766$	4.71981e15	0.646646
$767$	7.43708e14	0.101164
$768$	−7.60014e15	−1.02644
$769$	2.68699e15	0.360305	0.180153	−	0.983639i	$-0.442341\pi$
$769$	2.68699e15	0.360305	0.180153	+	0.983639i	$0.442341\pi$
$770$	−3.04440e16	−4.05324
$771$	−1.10840e16	−1.46520
$772$	−2.79072e15	−0.366286
$773$	7.64504e15	0.996306	0.498153	−	0.867089i	$-0.334012\pi$
$773$	7.64504e15	0.996306	0.498153	+	0.867089i	$0.334012\pi$
$774$	3.59649e15	0.465375
$775$	−1.78807e14	−0.0229734
$776$	1.27156e16	1.62218
$777$	−1.47908e16	−1.87359
$778$	5.57199e15	0.700846
$779$	5.56484e15	0.695019
$780$	2.17674e16	2.69951
$781$	−2.25632e15	−0.277856
$782$	−1.35947e15	−0.166239
$783$	−5.75981e15	−0.699389
$784$	−1.00642e15	−0.121350
$785$	1.51916e16	1.81894
$786$	−1.85229e16	−2.20235
$787$	−2.56606e14	−0.0302975	−0.0151487	−	0.999885i	$-0.504822\pi$
$787$	−2.56606e14	−0.0302975	−0.0151487	+	0.999885i	$0.504822\pi$
$788$	−2.23977e16	−2.62608
$789$	2.81698e15	0.327990
$790$	−8.81469e15	−1.01920
$791$	1.02706e16	1.17930
$792$	2.80613e15	0.319977
$793$	−1.53107e16	−1.73378
$794$	−1.11845e15	−0.125778
$795$	−6.19564e15	−0.691938
$796$	1.16155e16	1.28829
$797$	−1.07336e16	−1.18230	−0.591149	−	0.806563i	$-0.701325\pi$
$797$	−1.07336e16	−1.18230	−0.591149	+	0.806563i	$0.701325\pi$
$798$	−1.61623e16	−1.76802
$799$	3.88120e14	0.0421657
$800$	−3.76163e14	−0.0405865
$801$	−2.26699e15	−0.242924
$802$	7.36812e15	0.784148
$803$	2.78392e15	0.294254
$804$	1.09181e16	1.14615
$805$	−7.70700e15	−0.803541
$806$	1.35917e16	1.40744
$807$	−1.50048e15	−0.154321
$808$	−7.12297e15	−0.727610
$809$	−1.59049e16	−1.61367	−0.806835	−	0.590777i	$-0.798821\pi$
$809$	−1.59049e16	−1.61367	−0.806835	+	0.590777i	$0.798821\pi$
$810$	1.93551e16	1.95042
$811$	6.21666e15	0.622218	0.311109	−	0.950374i	$-0.399300\pi$
$811$	6.21666e15	0.622218	0.311109	+	0.950374i	$0.399300\pi$
$812$	2.48118e16	2.46661
$813$	6.09912e14	0.0602240
$814$	−1.97870e16	−1.94065
$815$	1.66258e16	1.61963
$816$	1.39785e14	0.0135259
$817$	−6.35807e15	−0.611089
$818$	2.02228e16	1.93062
$819$	−7.26201e15	−0.688645
$820$	2.26557e16	2.13403
$821$	2.79977e15	0.261960	0.130980	−	0.991385i	$-0.458188\pi$
$821$	2.79977e15	0.261960	0.130980	+	0.991385i	$0.458188\pi$
$822$	−4.69616e15	−0.436464
$823$	−3.44908e10	−3.18423e−6 0	−1.59212e−6	−	1.00000i	$-0.500001\pi$
$823$	−3.44908e10	−3.18423e−6 0	−1.59212e−6		1.00000i	$0.500001\pi$
$824$	1.30153e16	1.19358
$825$	6.38269e14	0.0581443
$826$	−2.24814e15	−0.203439
$827$	8.95682e15	0.805144	0.402572	−	0.915388i	$-0.368116\pi$
$827$	8.95682e15	0.805144	0.402572	+	0.915388i	$0.368116\pi$
$828$	1.90329e15	0.169957
$829$	−7.20279e15	−0.638927	−0.319463	−	0.947599i	$-0.603503\pi$
$829$	−7.20279e15	−0.638927	−0.319463	+	0.947599i	$0.603503\pi$
$830$	−1.31187e16	−1.15601
$831$	−1.29460e15	−0.113326
$832$	2.77420e16	2.41246
$833$	−6.83116e15	−0.590129
$834$	2.46604e16	2.11634
$835$	−2.00627e15	−0.171046
$836$	−1.32913e16	−1.12573
$837$	5.86302e15	0.493323
$838$	4.04207e15	0.337880
$839$	−1.18485e16	−0.983948	−0.491974	−	0.870610i	$-0.663725\pi$
$839$	−1.18485e16	−0.983948	−0.491974	+	0.870610i	$0.663725\pi$
$840$	−2.45592e16	−2.02618
$841$	−3.70696e15	−0.303836
$842$	1.50964e16	1.22930
$843$	1.56315e16	1.26459
$844$	−2.16629e16	−1.74114
$845$	−1.53623e16	−1.22672
$846$	−8.83949e14	−0.0701278
$847$	1.82048e16	1.43492
$848$	−3.86615e14	−0.0302762
$849$	2.08580e15	0.162286
$850$	−1.97309e14	−0.0152526
$851$	−5.00916e15	−0.384727
$852$	−4.87672e15	−0.372143
$853$	8.21584e15	0.622920	0.311460	−	0.950259i	$-0.399182\pi$
$853$	8.21584e15	0.622920	0.311460	+	0.950259i	$0.399182\pi$
$854$	4.62825e16	3.48657
$855$	1.80606e15	0.135182
$856$	−1.47687e16	−1.09834
$857$	2.65251e15	0.196003	0.0980015	−	0.995186i	$-0.468755\pi$
$857$	2.65251e15	0.196003	0.0980015	+	0.995186i	$0.468755\pi$
$858$	−4.85168e16	−3.56215
$859$	−2.03485e16	−1.48446	−0.742231	−	0.670144i	$-0.766232\pi$
$859$	−2.03485e16	−1.48446	−0.742231	+	0.670144i	$0.766232\pi$
$860$	−2.58852e16	−1.87633
$861$	−3.77463e16	−2.71867
$862$	6.28471e14	0.0449775
$863$	−7.67395e15	−0.545707	−0.272854	−	0.962056i	$-0.587967\pi$
$863$	−7.67395e15	−0.545707	−0.272854	+	0.962056i	$0.587967\pi$
$864$	1.23342e16	0.871539
$865$	1.71368e16	1.20321
$866$	1.32455e16	0.924105
$867$	9.48805e14	0.0657766
$868$	−2.52564e16	−1.73985
$869$	1.20773e16	0.826725
$870$	−2.25247e16	−1.53215
$871$	−1.41083e16	−0.953616
$872$	2.60817e16	1.75184
$873$	6.34276e15	0.423351
$874$	−5.47365e15	−0.363048
$875$	2.75368e16	1.81497
$876$	6.01705e15	0.394104
$877$	−2.09426e16	−1.36312	−0.681559	−	0.731763i	$-0.738698\pi$
$877$	−2.09426e16	−1.36312	−0.681559	+	0.731763i	$0.738698\pi$
$878$	7.78620e15	0.503623
$879$	1.37124e16	0.881406
$880$	1.06015e15	0.0677195
$881$	−1.44937e16	−0.920052	−0.460026	−	0.887905i	$-0.652160\pi$
$881$	−1.44937e16	−0.920052	−0.460026	+	0.887905i	$0.652160\pi$
$882$	1.55580e16	0.981472
$883$	−1.22461e15	−0.0767742	−0.0383871	−	0.999263i	$-0.512222\pi$
$883$	−1.22461e15	−0.0767742	−0.0383871	+	0.999263i	$0.512222\pi$
$884$	9.21961e15	0.574414
$885$	1.25458e15	0.0776804
$886$	−7.33709e15	−0.451480
$887$	−2.35348e16	−1.43923	−0.719617	−	0.694372i	$-0.755682\pi$
$887$	−2.35348e16	−1.43923	−0.719617	+	0.694372i	$0.755682\pi$
$888$	−1.59622e16	−0.970113
$889$	2.67202e16	1.61391
$890$	2.65427e16	1.59331
$891$	−2.65191e16	−1.58209
$892$	1.51824e16	0.900188
$893$	1.56270e15	0.0920855
$894$	−2.30945e16	−1.35255
$895$	1.22976e16	0.715803
$896$	−5.05593e16	−2.92487
$897$	−1.22822e16	−0.706185
$898$	−1.12306e16	−0.641778
$899$	−8.64574e15	−0.491048
$900$	2.76239e14	0.0155938
$901$	−2.62418e15	−0.147234
$902$	−5.04968e16	−2.81597
$903$	4.31268e16	2.39037
$904$	1.10841e16	0.610623
$905$	−2.93075e16	−1.60477
$906$	−8.75885e15	−0.476696
$907$	3.58000e16	1.93662	0.968308	−	0.249760i	$-0.0803519\pi$
$907$	3.58000e16	1.93662	0.968308	+	0.249760i	$0.0803519\pi$
$908$	−2.18068e16	−1.17252
$909$	−3.55305e15	−0.189889
$910$	8.50262e16	4.51674
$911$	2.58060e16	1.36261	0.681303	−	0.732002i	$-0.261414\pi$
$911$	2.58060e16	1.36261	0.681303	+	0.732002i	$0.261414\pi$
$912$	5.62821e14	0.0295392
$913$	1.79744e16	0.937702
$914$	1.01460e16	0.526125
$915$	−2.58281e16	−1.33130
$916$	−7.82777e15	−0.401063
$917$	−4.44767e16	−2.26517
$918$	6.46970e15	0.327529
$919$	2.79859e16	1.40833	0.704165	−	0.710036i	$-0.251322\pi$
$919$	2.79859e16	1.40833	0.704165	+	0.710036i	$0.251322\pi$
$920$	−8.31741e15	−0.416059
$921$	4.00932e14	0.0199362
$922$	−9.85058e14	−0.0486902
$923$	6.30163e15	0.309631
$924$	9.01551e16	4.40346
$925$	−7.27016e14	−0.0352992
$926$	−2.52574e16	−1.21907
$927$	6.49221e15	0.311497
$928$	−1.81884e16	−0.867520
$929$	5.05363e15	0.239617	0.119808	−	0.992797i	$-0.461772\pi$
$929$	5.05363e15	0.239617	0.119808	+	0.992797i	$0.461772\pi$
$930$	2.29283e16	1.08072
$931$	−2.75044e16	−1.28878
$932$	4.48299e16	2.08824
$933$	−1.84603e15	−0.0854851
$934$	−6.47573e16	−2.98113
$935$	7.19587e15	0.329321
$936$	−7.83718e15	−0.356568
$937$	1.32963e16	0.601398	0.300699	−	0.953719i	$-0.402780\pi$
$937$	1.32963e16	0.601398	0.300699	+	0.953719i	$0.402780\pi$
$938$	4.26477e16	1.91770
$939$	−1.12603e16	−0.503371
$940$	6.36209e15	0.282746
$941$	1.19817e16	0.529389	0.264694	−	0.964332i	$-0.414729\pi$
$941$	1.19817e16	0.529389	0.264694	+	0.964332i	$0.414729\pi$
$942$	−7.31839e16	−3.21466
$943$	−1.27835e16	−0.558257
$944$	7.82874e13	0.00339896
$945$	3.66776e16	1.58316
$946$	5.76949e16	2.47592
$947$	3.34232e16	1.42601	0.713006	−	0.701158i	$-0.247333\pi$
$947$	3.34232e16	1.42601	0.713006	+	0.701158i	$0.247333\pi$
$948$	2.61033e16	1.10726
$949$	−7.77516e15	−0.327903
$950$	−7.94430e14	−0.0333101
$951$	−7.74304e15	−0.322789
$952$	−1.04021e16	−0.431139
$953$	−1.52862e16	−0.629923	−0.314962	−	0.949104i	$-0.601992\pi$
$953$	−1.52862e16	−0.629923	−0.314962	+	0.949104i	$0.601992\pi$
$954$	5.97660e15	0.244871
$955$	4.58043e13	0.00186590
$956$	5.68646e16	2.30316
$957$	3.08618e16	1.24281
$958$	−6.51414e16	−2.60824
$959$	−1.12763e16	−0.448915
$960$	4.67988e16	1.85244
$961$	−1.66078e16	−0.653633
$962$	5.52628e16	2.16257
$963$	−7.36685e15	−0.286640
$964$	−4.10330e16	−1.58748
$965$	6.08329e15	0.234012
$966$	3.71277e16	1.42012
$967$	−1.30013e16	−0.494473	−0.247236	−	0.968955i	$-0.579522\pi$
$967$	−1.30013e16	−0.494473	−0.247236	+	0.968955i	$0.579522\pi$
$968$	1.96467e16	0.742975
$969$	3.82019e15	0.143649
$970$	−7.42634e16	−2.77671
$971$	−2.89874e16	−1.07771	−0.538856	−	0.842398i	$-0.681143\pi$
$971$	−2.89874e16	−1.07771	−0.538856	+	0.842398i	$0.681143\pi$
$972$	−2.11409e16	−0.781553
$973$	5.92138e16	2.17672
$974$	−2.17006e15	−0.0793225
$975$	−1.78261e15	−0.0647933
$976$	−1.61170e15	−0.0582520
$977$	−2.08764e16	−0.750302	−0.375151	−	0.926964i	$-0.622409\pi$
$977$	−2.08764e16	−0.750302	−0.375151	+	0.926964i	$0.622409\pi$
$978$	−8.00934e16	−2.86242
$979$	−3.63670e16	−1.29242
$980$	−1.11977e17	−3.95716
$981$	1.30099e16	0.457189
$982$	−8.62136e16	−3.01274
$983$	−1.75058e16	−0.608327	−0.304164	−	0.952620i	$-0.598377\pi$
$983$	−1.75058e16	−0.608327	−0.304164	+	0.952620i	$0.598377\pi$
$984$	−4.07359e16	−1.40768
$985$	4.88231e16	1.67775
$986$	−9.54037e15	−0.326018
$987$	−1.05998e16	−0.360206
$988$	3.71211e16	1.25446
$989$	1.46057e16	0.490842
$990$	−1.63887e16	−0.547710
$991$	7.29450e15	0.242432	0.121216	−	0.992626i	$-0.461321\pi$
$991$	7.29450e15	0.242432	0.121216	+	0.992626i	$0.461321\pi$
$992$	1.85143e16	0.611916
$993$	−3.39432e15	−0.111566
$994$	−1.90491e16	−0.622658
$995$	−2.53197e16	−0.823062
$996$	3.88491e16	1.25590
$997$	−2.90069e16	−0.932562	−0.466281	−	0.884637i	$-0.654406\pi$
$997$	−2.90069e16	−0.932562	−0.466281	+	0.884637i	$0.654406\pi$
$998$	5.41117e16	1.73011
$999$	2.38386e16	0.758001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.a.b.1.7	✓	8
3.2	odd	2		153.12.a.d.1.2		8
4.3	odd	2		272.12.a.h.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.a.b.1.7	✓	8	1.1	even	1	trivial
153.12.a.d.1.2		8	3.2	odd	2
272.12.a.h.1.2		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)

\(f(q)\)	\(=\)	\(q+72.9081 q^{2} +470.639 q^{3} +3267.59 q^{4} -7122.79 q^{5} +34313.4 q^{6} +82392.3 q^{7} +88918.0 q^{8} +44353.7 q^{9} +O(q^{10})\)	\(q+72.9081 q^{2} +470.639 q^{3} +3267.59 q^{4} -7122.79 q^{5} +34313.4 q^{6} +82392.3 q^{7} +88918.0 q^{8} +44353.7 q^{9} -519309. q^{10} +711523. q^{11} +1.53785e6 q^{12} -1.98720e6 q^{13} +6.00706e6 q^{14} -3.35226e6 q^{15} -209185. q^{16} -1.41986e6 q^{17} +3.23374e6 q^{18} -5.71679e6 q^{19} -2.32744e7 q^{20} +3.87770e7 q^{21} +5.18758e7 q^{22} +1.31325e7 q^{23} +4.18482e7 q^{24} +1.90602e6 q^{25} -1.44883e8 q^{26} -6.24977e7 q^{27} +2.69224e8 q^{28} +9.21605e7 q^{29} -2.44407e8 q^{30} -9.38118e7 q^{31} -1.97355e8 q^{32} +3.34870e8 q^{33} -1.03519e8 q^{34} -5.86863e8 q^{35} +1.44930e8 q^{36} -3.81431e8 q^{37} -4.16801e8 q^{38} -9.35251e8 q^{39} -6.33344e8 q^{40} -9.73419e8 q^{41} +2.82716e9 q^{42} +1.11217e9 q^{43} +2.32496e9 q^{44} -3.15922e8 q^{45} +9.57468e8 q^{46} -2.73352e8 q^{47} -9.84504e7 q^{48} +4.81116e9 q^{49} +1.38964e8 q^{50} -6.68239e8 q^{51} -6.49334e9 q^{52} +1.84820e9 q^{53} -4.55659e9 q^{54} -5.06803e9 q^{55} +7.32615e9 q^{56} -2.69054e9 q^{57} +6.71924e9 q^{58} -3.74250e8 q^{59} -1.09538e10 q^{60} +7.70468e9 q^{61} -6.83964e9 q^{62} +3.65440e9 q^{63} -1.39604e10 q^{64} +1.41544e10 q^{65} +2.44147e10 q^{66} +7.09959e9 q^{67} -4.63951e9 q^{68} +6.18068e9 q^{69} -4.27871e10 q^{70} -3.17112e9 q^{71} +3.94384e9 q^{72} +3.91263e9 q^{73} -2.78094e10 q^{74} +8.97047e8 q^{75} -1.86801e10 q^{76} +5.86240e10 q^{77} -6.81874e10 q^{78} +1.69739e10 q^{79} +1.48998e9 q^{80} -3.72709e10 q^{81} -7.09701e10 q^{82} +2.52619e10 q^{83} +1.26707e11 q^{84} +1.01133e10 q^{85} +8.10865e10 q^{86} +4.33743e10 q^{87} +6.32671e10 q^{88} -5.11116e10 q^{89} -2.30333e10 q^{90} -1.63730e11 q^{91} +4.29117e10 q^{92} -4.41515e10 q^{93} -1.99296e10 q^{94} +4.07195e10 q^{95} -9.28830e10 q^{96} +1.43004e11 q^{97} +3.50772e11 q^{98} +3.15586e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 55 q^{2} + 496 q^{3} + 10757 q^{4} + 8592 q^{5} + 17194 q^{6} + 95288 q^{7} - 247863 q^{8} + 500648 q^{9}+O(q^{10}) \) 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

Fields

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Database

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