LMFDB - Embedded newform 98.14.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,14,Mod(1,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("98.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	98.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:	$105.086310373$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 692090x^{2} - 221993874x - 1534236795 $ x^4 - 2x^3 - 692090x^2 - 221993874*x - 1534236795
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-435.873$ of defining polynomial
Character	$\chi$	$=$	98.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+64.0000 q^{2} +2284.71 q^{3} +4096.00 q^{4} -36512.9 q^{5} +146221. q^{6} +262144. q^{8} +3.62557e6 q^{9} +O(q^{10})$	\(q+64.0000 q^{2} +2284.71 q^{3} +4096.00 q^{4} -36512.9 q^{5} +146221. q^{6} +262144. q^{8} +3.62557e6 q^{9} -2.33683e6 q^{10} -3.83854e6 q^{11} +9.35817e6 q^{12} -1.67406e7 q^{13} -8.34214e7 q^{15} +1.67772e7 q^{16} -1.61306e8 q^{17} +2.32037e8 q^{18} -2.58886e8 q^{19} -1.49557e8 q^{20} -2.45667e8 q^{22} -8.79407e8 q^{23} +5.98923e8 q^{24} +1.12489e8 q^{25} -1.07140e9 q^{26} +4.64082e9 q^{27} +6.01309e8 q^{29} -5.33897e9 q^{30} +3.33631e9 q^{31} +1.07374e9 q^{32} -8.76995e9 q^{33} -1.03236e10 q^{34} +1.48503e10 q^{36} +5.89294e9 q^{37} -1.65687e10 q^{38} -3.82475e10 q^{39} -9.57164e9 q^{40} +4.54312e10 q^{41} -2.12865e10 q^{43} -1.57227e10 q^{44} -1.32380e11 q^{45} -5.62821e10 q^{46} -7.03488e10 q^{47} +3.83311e10 q^{48} +7.19929e9 q^{50} -3.68537e11 q^{51} -6.85696e10 q^{52} -3.14204e10 q^{53} +2.97012e11 q^{54} +1.40156e11 q^{55} -5.91480e11 q^{57} +3.84838e10 q^{58} +2.04979e11 q^{59} -3.41694e11 q^{60} -4.90234e11 q^{61} +2.13524e11 q^{62} +6.87195e10 q^{64} +6.11249e11 q^{65} -5.61277e11 q^{66} +1.94113e10 q^{67} -6.60708e11 q^{68} -2.00919e12 q^{69} +1.11249e12 q^{71} +9.50422e11 q^{72} -2.98705e11 q^{73} +3.77148e11 q^{74} +2.57005e11 q^{75} -1.06040e12 q^{76} -2.44784e12 q^{78} +3.20750e12 q^{79} -6.12585e11 q^{80} +4.82258e12 q^{81} +2.90760e12 q^{82} +2.08048e12 q^{83} +5.88974e12 q^{85} -1.36234e12 q^{86} +1.37382e12 q^{87} -1.00625e12 q^{88} -3.87093e12 q^{89} -8.47233e12 q^{90} -3.60205e12 q^{92} +7.62251e12 q^{93} -4.50232e12 q^{94} +9.45268e12 q^{95} +2.45319e12 q^{96} -1.42174e13 q^{97} -1.39169e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 256 q^{2} - 182 q^{3} + 16384 q^{4} - 64400 q^{5} - 11648 q^{6} + 1048576 q^{8} + 3983752 q^{9}+O(q^{10}) $ 4 * q + 256 * q^2 - 182 * q^3 + 16384 * q^4 - 64400 * q^5 - 11648 * q^6 + 1048576 * q^8 + 3983752 * q^9	\( 4 q + 256 q^{2} - 182 q^{3} + 16384 q^{4} - 64400 q^{5} - 11648 q^{6} + 1048576 q^{8} + 3983752 q^{9} - 4121600 q^{10} + 1008790 q^{11} - 745472 q^{12} - 26903632 q^{13} - 44444458 q^{15} + 67108864 q^{16} - 165333028 q^{17} + 254960128 q^{18} - 423405794 q^{19} - 263782400 q^{20} + 64562560 q^{22} - 286233866 q^{23} - 47710208 q^{24} + 472017432 q^{25} - 1721832448 q^{26} + 5202970822 q^{27} + 9100337408 q^{29} - 2844445312 q^{30} + 1507094246 q^{31} + 4294967296 q^{32} - 16888935028 q^{33} - 10581313792 q^{34} + 16317448192 q^{36} + 18959705336 q^{37} - 27097970816 q^{38} - 35759388756 q^{39} - 16882073600 q^{40} - 56825955312 q^{41} - 45778809712 q^{43} + 4132003840 q^{44} - 119804452768 q^{45} - 18318967424 q^{46} - 81351201078 q^{47} - 3053453312 q^{48} + 30209115648 q^{50} - 14996824142 q^{51} - 110197276672 q^{52} - 87497947440 q^{53} + 332990132608 q^{54} - 350818705174 q^{55} - 903663464132 q^{57} + 582421594112 q^{58} - 194140265102 q^{59} - 182044499968 q^{60} + 175816313120 q^{61} + 96454031744 q^{62} + 274877906944 q^{64} + 1689866774568 q^{65} - 1080891841792 q^{66} + 243815218758 q^{67} - 677204082688 q^{68} - 3022078976392 q^{69} - 1637697339536 q^{71} + 1044316684288 q^{72} - 3492491920596 q^{73} + 1213421141504 q^{74} - 2370218127424 q^{75} - 1734270132224 q^{76} - 2288600880384 q^{78} + 1016380081246 q^{79} - 1080452710400 q^{80} - 17492694092 q^{81} - 3636861139968 q^{82} - 3513747871648 q^{83} + 284557420264 q^{85} - 2929843821568 q^{86} - 9706955821052 q^{87} + 264448245760 q^{88} - 8034124428036 q^{89} - 7667484977152 q^{90} - 1172413915136 q^{92} + 3388371390552 q^{93} - 5206476868992 q^{94} - 1429435505438 q^{95} - 195421011968 q^{96} - 27175565862816 q^{97} - 12918917288164 q^{99}+O(q^{100}) \) 4 * q + 256 * q^2 - 182 * q^3 + 16384 * q^4 - 64400 * q^5 - 11648 * q^6 + 1048576 * q^8 + 3983752 * q^9 - 4121600 * q^10 + 1008790 * q^11 - 745472 * q^12 - 26903632 * q^13 - 44444458 * q^15 + 67108864 * q^16 - 165333028 * q^17 + 254960128 * q^18 - 423405794 * q^19 - 263782400 * q^20 + 64562560 * q^22 - 286233866 * q^23 - 47710208 * q^24 + 472017432 * q^25 - 1721832448 * q^26 + 5202970822 * q^27 + 9100337408 * q^29 - 2844445312 * q^30 + 1507094246 * q^31 + 4294967296 * q^32 - 16888935028 * q^33 - 10581313792 * q^34 + 16317448192 * q^36 + 18959705336 * q^37 - 27097970816 * q^38 - 35759388756 * q^39 - 16882073600 * q^40 - 56825955312 * q^41 - 45778809712 * q^43 + 4132003840 * q^44 - 119804452768 * q^45 - 18318967424 * q^46 - 81351201078 * q^47 - 3053453312 * q^48 + 30209115648 * q^50 - 14996824142 * q^51 - 110197276672 * q^52 - 87497947440 * q^53 + 332990132608 * q^54 - 350818705174 * q^55 - 903663464132 * q^57 + 582421594112 * q^58 - 194140265102 * q^59 - 182044499968 * q^60 + 175816313120 * q^61 + 96454031744 * q^62 + 274877906944 * q^64 + 1689866774568 * q^65 - 1080891841792 * q^66 + 243815218758 * q^67 - 677204082688 * q^68 - 3022078976392 * q^69 - 1637697339536 * q^71 + 1044316684288 * q^72 - 3492491920596 * q^73 + 1213421141504 * q^74 - 2370218127424 * q^75 - 1734270132224 * q^76 - 2288600880384 * q^78 + 1016380081246 * q^79 - 1080452710400 * q^80 - 17492694092 * q^81 - 3636861139968 * q^82 - 3513747871648 * q^83 + 284557420264 * q^85 - 2929843821568 * q^86 - 9706955821052 * q^87 + 264448245760 * q^88 - 8034124428036 * q^89 - 7667484977152 * q^90 - 1172413915136 * q^92 + 3388371390552 * q^93 - 5206476868992 * q^94 - 1429435505438 * q^95 - 195421011968 * q^96 - 27175565862816 * q^97 - 12918917288164 * 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 $

$2$	64.0000	0.707107
$2$	64.0000	0.707107
$3$	2284.71	1.80943	0.904717	−	0.426013i	$-0.140082\pi$
$3$	2284.71	1.80943	0.904717	+	0.426013i	$0.140082\pi$
$4$	4096.00	0.500000
$5$	−36512.9	−1.04506	−0.522530	−	0.852621i	$-0.675012\pi$
$5$	−36512.9	−1.04506	−0.522530	+	0.852621i	$0.675012\pi$
$6$	146221.	1.27946
$7$	0	0
$7$	0	0
$8$	262144.	0.353553
$9$	3.62557e6	2.27405
$10$	−2.33683e6	−0.738969
$11$	−3.83854e6	−0.653301	−0.326651	−	0.945145i	$-0.605920\pi$
$11$	−3.83854e6	−0.653301	−0.326651	+	0.945145i	$0.605920\pi$
$12$	9.35817e6	0.904717
$13$	−1.67406e7	−0.961923	−0.480961	−	0.876742i	$-0.659712\pi$
$13$	−1.67406e7	−0.961923	−0.480961	+	0.876742i	$0.659712\pi$
$14$	0	0
$15$	−8.34214e7	−1.89097
$16$	1.67772e7	0.250000
$17$	−1.61306e8	−1.62081	−0.810404	−	0.585871i	$-0.800752\pi$
$17$	−1.61306e8	−1.62081	−0.810404	+	0.585871i	$0.800752\pi$
$18$	2.32037e8	1.60800
$19$	−2.58886e8	−1.26244	−0.631220	−	0.775604i	$-0.717445\pi$
$19$	−2.58886e8	−1.26244	−0.631220	+	0.775604i	$0.717445\pi$
$20$	−1.49557e8	−0.522530
$21$	0	0
$22$	−2.45667e8	−0.461954
$23$	−8.79407e8	−1.23868	−0.619340	−	0.785123i	$-0.712600\pi$
$23$	−8.79407e8	−1.23868	−0.619340	+	0.785123i	$0.712600\pi$
$24$	5.98923e8	0.639732
$25$	1.12489e8	0.0921509
$26$	−1.07140e9	−0.680182
$27$	4.64082e9	2.30531
$28$	0	0
$29$	6.01309e8	0.187720	0.0938600	−	0.995585i	$-0.470079\pi$
$29$	6.01309e8	0.187720	0.0938600	+	0.995585i	$0.470079\pi$
$30$	−5.33897e9	−1.33712
$31$	3.33631e9	0.675174	0.337587	−	0.941294i	$-0.390389\pi$
$31$	3.33631e9	0.675174	0.337587	+	0.941294i	$0.390389\pi$
$32$	1.07374e9	0.176777
$33$	−8.76995e9	−1.18211
$34$	−1.03236e10	−1.14608
$35$	0	0
$36$	1.48503e10	1.13703
$37$	5.89294e9	0.377590	0.188795	−	0.982017i	$-0.439542\pi$
$37$	5.89294e9	0.377590	0.188795	+	0.982017i	$0.439542\pi$
$38$	−1.65687e10	−0.892679
$39$	−3.82475e10	−1.74054
$40$	−9.57164e9	−0.369485
$41$	4.54312e10	1.49369	0.746843	−	0.665000i	$-0.231568\pi$
$41$	4.54312e10	1.49369	0.746843	+	0.665000i	$0.231568\pi$
$42$	0	0
$43$	−2.12865e10	−0.513523	−0.256762	−	0.966475i	$-0.582656\pi$
$43$	−2.12865e10	−0.513523	−0.256762	+	0.966475i	$0.582656\pi$
$44$	−1.57227e10	−0.326651
$45$	−1.32380e11	−2.37652
$46$	−5.62821e10	−0.875879
$47$	−7.03488e10	−0.951964	−0.475982	−	0.879455i	$-0.657907\pi$
$47$	−7.03488e10	−0.951964	−0.475982	+	0.879455i	$0.657907\pi$
$48$	3.83311e10	0.452359
$49$	0	0
$50$	7.19929e9	0.0651606
$51$	−3.68537e11	−2.93275
$52$	−6.85696e10	−0.480961
$53$	−3.14204e10	−0.194723	−0.0973617	−	0.995249i	$-0.531040\pi$
$53$	−3.14204e10	−0.194723	−0.0973617	+	0.995249i	$0.531040\pi$
$54$	2.97012e11	1.63010
$55$	1.40156e11	0.682739
$56$	0	0
$57$	−5.91480e11	−2.28430
$58$	3.84838e10	0.132738
$59$	2.04979e11	0.632660	0.316330	−	0.948649i	$-0.397549\pi$
$59$	2.04979e11	0.632660	0.316330	+	0.948649i	$0.397549\pi$
$60$	−3.41694e11	−0.945484
$61$	−4.90234e11	−1.21831	−0.609157	−	0.793050i	$-0.708492\pi$
$61$	−4.90234e11	−1.21831	−0.609157	+	0.793050i	$0.708492\pi$
$62$	2.13524e11	0.477420
$63$	0	0
$64$	6.87195e10	0.125000
$65$	6.11249e11	1.00527
$66$	−5.61277e11	−0.835875
$67$	1.94113e10	0.0262162	0.0131081	−	0.999914i	$-0.495827\pi$
$67$	1.94113e10	0.0262162	0.0131081	+	0.999914i	$0.495827\pi$
$68$	−6.60708e11	−0.810404
$69$	−2.00919e12	−2.24131
$70$	0	0
$71$	1.11249e12	1.03067	0.515334	−	0.856989i	$-0.327668\pi$
$71$	1.11249e12	1.03067	0.515334	+	0.856989i	$0.327668\pi$
$72$	9.50422e11	0.803999
$73$	−2.98705e11	−0.231017	−0.115508	−	0.993307i	$-0.536850\pi$
$73$	−2.98705e11	−0.231017	−0.115508	+	0.993307i	$0.536850\pi$
$74$	3.77148e11	0.266997
$75$	2.57005e11	0.166741
$76$	−1.06040e12	−0.631220
$77$	0	0
$78$	−2.44784e12	−1.23074
$79$	3.20750e12	1.48453	0.742267	−	0.670105i	$-0.233751\pi$
$79$	3.20750e12	1.48453	0.742267	+	0.670105i	$0.233751\pi$
$80$	−6.12585e11	−0.261265
$81$	4.82258e12	1.89726
$82$	2.90760e12	1.05620
$83$	2.08048e12	0.698483	0.349241	−	0.937033i	$-0.386439\pi$
$83$	2.08048e12	0.698483	0.349241	+	0.937033i	$0.386439\pi$
$84$	0	0
$85$	5.88974e12	1.69384
$86$	−1.36234e12	−0.363116
$87$	1.37382e12	0.339667
$88$	−1.00625e12	−0.230977
$89$	−3.87093e12	−0.825619	−0.412810	−	0.910817i	$-0.635453\pi$
$89$	−3.87093e12	−0.825619	−0.412810	+	0.910817i	$0.635453\pi$
$90$	−8.47233e12	−1.68045
$91$	0	0
$92$	−3.60205e12	−0.619340
$93$	7.62251e12	1.22168
$94$	−4.50232e12	−0.673140
$95$	9.45268e12	1.31932
$96$	2.45319e12	0.319866
$97$	−1.42174e13	−1.73302	−0.866509	−	0.499162i	$-0.833641\pi$
$97$	−1.42174e13	−1.73302	−0.866509	+	0.499162i	$0.833641\pi$
$98$	0	0
$99$	−1.39169e13	−1.48564
$100$	4.60755e11	0.0460755
$101$	−1.04990e13	−0.984145	−0.492072	−	0.870554i	$-0.663760\pi$
$101$	−1.04990e13	−0.984145	−0.492072	+	0.870554i	$0.663760\pi$
$102$	−2.35863e13	−2.07376
$103$	−1.11974e13	−0.924009	−0.462005	−	0.886878i	$-0.652870\pi$
$103$	−1.11974e13	−0.924009	−0.462005	+	0.886878i	$0.652870\pi$
$104$	−4.38846e12	−0.340091
$105$	0	0
$106$	−2.01090e12	−0.137690
$107$	−2.32117e13	−1.49524	−0.747622	−	0.664124i	$-0.768805\pi$
$107$	−2.32117e13	−1.49524	−0.747622	+	0.664124i	$0.768805\pi$
$108$	1.90088e13	1.15266
$109$	8.54021e12	0.487749	0.243874	−	0.969807i	$-0.421582\pi$
$109$	8.54021e12	0.487749	0.243874	+	0.969807i	$0.421582\pi$
$110$	8.97000e12	0.482770
$111$	1.34636e13	0.683224
$112$	0	0
$113$	1.63979e13	0.740934	0.370467	−	0.928846i	$-0.379198\pi$
$113$	1.63979e13	0.740934	0.370467	+	0.928846i	$0.379198\pi$
$114$	−3.78547e13	−1.61524
$115$	3.21097e13	1.29449
$116$	2.46296e12	0.0938600
$117$	−6.06944e13	−2.18746
$118$	1.31186e13	0.447358
$119$	0	0
$120$	−2.18684e13	−0.668558
$121$	−1.97883e13	−0.573197
$122$	−3.13750e13	−0.861478
$123$	1.03797e14	2.70273
$124$	1.36655e13	0.337587
$125$	4.04641e13	0.948757
$126$	0	0
$127$	3.77685e13	0.798741	0.399371	−	0.916790i	$-0.369229\pi$
$127$	3.77685e13	0.798741	0.399371	+	0.916790i	$0.369229\pi$
$128$	4.39805e12	0.0883883
$129$	−4.86336e13	−0.929186
$130$	3.91199e13	0.710831
$131$	4.44497e13	0.768431	0.384216	−	0.923243i	$-0.374472\pi$
$131$	4.44497e13	0.768431	0.384216	+	0.923243i	$0.374472\pi$
$132$	−3.59217e13	−0.591053
$133$	0	0
$134$	1.24232e12	0.0185376
$135$	−1.69450e14	−2.40919
$136$	−4.22853e13	−0.573042
$137$	−1.10807e14	−1.43181	−0.715904	−	0.698199i	$-0.753985\pi$
$137$	−1.10807e14	−1.43181	−0.715904	+	0.698199i	$0.753985\pi$
$138$	−1.28588e14	−1.58485
$139$	−8.82502e13	−1.03781	−0.518907	−	0.854831i	$-0.673661\pi$
$139$	−8.82502e13	−1.03781	−0.518907	+	0.854831i	$0.673661\pi$
$140$	0	0
$141$	−1.60726e14	−1.72252
$142$	7.11997e13	0.728792
$143$	6.42596e13	0.628425
$144$	6.08270e13	0.568513
$145$	−2.19555e13	−0.196179
$146$	−1.91171e13	−0.163353
$147$	0	0
$148$	2.41375e13	0.188795
$149$	1.27387e14	0.953704	0.476852	−	0.878984i	$-0.341778\pi$
$149$	1.27387e14	0.953704	0.476852	+	0.878984i	$0.341778\pi$
$150$	1.64483e13	0.117904
$151$	9.58883e13	0.658287	0.329144	−	0.944280i	$-0.393240\pi$
$151$	9.58883e13	0.658287	0.329144	+	0.944280i	$0.393240\pi$
$152$	−6.78655e13	−0.446340
$153$	−5.84825e14	−3.68580
$154$	0	0
$155$	−1.21819e14	−0.705598
$156$	−1.56662e14	−0.870268
$157$	2.94681e14	1.57038	0.785189	−	0.619257i	$-0.212566\pi$
$157$	2.94681e14	1.57038	0.785189	+	0.619257i	$0.212566\pi$
$158$	2.05280e14	1.04972
$159$	−7.17864e13	−0.352339
$160$	−3.92054e13	−0.184742
$161$	0	0
$162$	3.08645e14	1.34157
$163$	−3.54177e13	−0.147911	−0.0739556	−	0.997262i	$-0.523562\pi$
$163$	−3.54177e13	−0.147911	−0.0739556	+	0.997262i	$0.523562\pi$
$164$	1.86086e14	0.746843
$165$	3.20216e14	1.23537
$166$	1.33151e14	0.493902
$167$	−1.84001e14	−0.656390	−0.328195	−	0.944610i	$-0.606440\pi$
$167$	−1.84001e14	−0.656390	−0.328195	+	0.944610i	$0.606440\pi$
$168$	0	0
$169$	−2.26262e13	−0.0747049
$170$	3.76943e14	1.19773
$171$	−9.38611e14	−2.87085
$172$	−8.71897e13	−0.256762
$173$	−6.50091e13	−0.184363	−0.0921817	−	0.995742i	$-0.529384\pi$
$173$	−6.50091e13	−0.184363	−0.0921817	+	0.995742i	$0.529384\pi$
$174$	8.79242e13	0.240181
$175$	0	0
$176$	−6.44000e13	−0.163325
$177$	4.68317e14	1.14476
$178$	−2.47739e14	−0.583801
$179$	2.62490e14	0.596442	0.298221	−	0.954497i	$-0.403607\pi$
$179$	2.62490e14	0.596442	0.298221	+	0.954497i	$0.403607\pi$
$180$	−5.42229e14	−1.18826
$181$	−4.09833e14	−0.866355	−0.433178	−	0.901309i	$-0.642608\pi$
$181$	−4.09833e14	−0.866355	−0.433178	+	0.901309i	$0.642608\pi$
$182$	0	0
$183$	−1.12004e15	−2.20446
$184$	−2.30531e14	−0.437939
$185$	−2.15168e14	−0.394604
$186$	4.87841e14	0.863861
$187$	6.19178e14	1.05888
$188$	−2.88149e14	−0.475982
$189$	0	0
$190$	6.04972e14	0.932904
$191$	6.50994e13	0.0970197	0.0485099	−	0.998823i	$-0.484553\pi$
$191$	6.50994e13	0.0970197	0.0485099	+	0.998823i	$0.484553\pi$
$192$	1.57004e14	0.226179
$193$	−3.24597e14	−0.452088	−0.226044	−	0.974117i	$-0.572579\pi$
$193$	−3.24597e14	−0.452088	−0.226044	+	0.974117i	$0.572579\pi$
$194$	−9.09912e14	−1.22543
$195$	1.39653e15	1.81896
$196$	0	0
$197$	8.88338e14	1.08280	0.541399	−	0.840766i	$-0.317895\pi$
$197$	8.88338e14	1.08280	0.541399	+	0.840766i	$0.317895\pi$
$198$	−8.90682e14	−1.05051
$199$	1.56895e14	0.179087	0.0895433	−	0.995983i	$-0.471459\pi$
$199$	1.56895e14	0.179087	0.0895433	+	0.995983i	$0.471459\pi$
$200$	2.94883e13	0.0325803
$201$	4.43492e13	0.0474364
$202$	−6.71936e14	−0.695895
$203$	0	0
$204$	−1.50953e15	−1.46637
$205$	−1.65883e15	−1.56099
$206$	−7.16635e14	−0.653373
$207$	−3.18835e15	−2.81682
$208$	−2.80861e14	−0.240481
$209$	9.93745e14	0.824753
$210$	0	0
$211$	−3.37886e14	−0.263593	−0.131797	−	0.991277i	$-0.542075\pi$
$211$	−3.37886e14	−0.263593	−0.131797	+	0.991277i	$0.542075\pi$
$212$	−1.28698e14	−0.0973617
$213$	2.54173e15	1.86493
$214$	−1.48555e15	−1.05730
$215$	7.77233e14	0.536663
$216$	1.21656e15	0.815051
$217$	0	0
$218$	5.46573e14	0.344890
$219$	−6.82453e14	−0.418010
$220$	5.74080e14	0.341370
$221$	2.70036e15	1.55909
$222$	8.61674e14	0.483113
$223$	−2.69510e15	−1.46755	−0.733775	−	0.679392i	$-0.762244\pi$
$223$	−2.69510e15	−1.46755	−0.733775	+	0.679392i	$0.762244\pi$
$224$	0	0
$225$	4.07837e14	0.209556
$226$	1.04947e15	0.523920
$227$	−3.10157e15	−1.50458	−0.752288	−	0.658835i	$-0.771050\pi$
$227$	−3.10157e15	−1.50458	−0.752288	+	0.658835i	$0.771050\pi$
$228$	−2.42270e15	−1.14215
$229$	−6.50416e14	−0.298030	−0.149015	−	0.988835i	$-0.547610\pi$
$229$	−6.50416e14	−0.298030	−0.149015	+	0.988835i	$0.547610\pi$
$230$	2.05502e15	0.915346
$231$	0	0
$232$	1.57630e14	0.0663691
$233$	3.63527e15	1.48841	0.744206	−	0.667950i	$-0.232828\pi$
$233$	3.63527e15	1.48841	0.744206	+	0.667950i	$0.232828\pi$
$234$	−3.88444e15	−1.54677
$235$	2.56864e15	0.994860
$236$	8.39593e14	0.316330
$237$	7.32819e15	2.68617
$238$	0	0
$239$	1.13012e15	0.392228	0.196114	−	0.980581i	$-0.437168\pi$
$239$	1.13012e15	0.392228	0.196114	+	0.980581i	$0.437168\pi$
$240$	−1.39958e15	−0.472742
$241$	4.17463e15	1.37248	0.686242	−	0.727374i	$-0.259259\pi$
$241$	4.17463e15	1.37248	0.686242	+	0.727374i	$0.259259\pi$
$242$	−1.26645e15	−0.405312
$243$	3.61924e15	1.12765
$244$	−2.00800e15	−0.609157
$245$	0	0
$246$	6.64302e15	1.91112
$247$	4.33392e15	1.21437
$248$	8.74595e14	0.238710
$249$	4.75329e15	1.26386
$250$	2.58970e15	0.670872
$251$	1.57148e15	0.396669	0.198335	−	0.980134i	$-0.436447\pi$
$251$	1.57148e15	0.396669	0.198335	+	0.980134i	$0.436447\pi$
$252$	0	0
$253$	3.37564e15	0.809231
$254$	2.41719e15	0.564795
$255$	1.34563e16	3.06490
$256$	2.81475e14	0.0625000
$257$	4.28839e15	0.928386	0.464193	−	0.885734i	$-0.346344\pi$
$257$	4.28839e15	0.928386	0.464193	+	0.885734i	$0.346344\pi$
$258$	−3.11255e15	−0.657034
$259$	0	0
$260$	2.50368e15	0.502634
$261$	2.18009e15	0.426885
$262$	2.84478e15	0.543363
$263$	−1.10180e15	−0.205300	−0.102650	−	0.994718i	$-0.532732\pi$
$263$	−1.10180e15	−0.205300	−0.102650	+	0.994718i	$0.532732\pi$
$264$	−2.29899e15	−0.417938
$265$	1.14725e15	0.203498
$266$	0	0
$267$	−8.84394e15	−1.49390
$268$	7.95088e13	0.0131081
$269$	5.64351e15	0.908155	0.454077	−	0.890962i	$-0.349969\pi$
$269$	5.64351e15	0.908155	0.454077	+	0.890962i	$0.349969\pi$
$270$	−1.08448e16	−1.70356
$271$	−3.48896e15	−0.535051	−0.267526	−	0.963551i	$-0.586206\pi$
$271$	−3.48896e15	−0.535051	−0.267526	+	0.963551i	$0.586206\pi$
$272$	−2.70626e15	−0.405202
$273$	0	0
$274$	−7.09167e15	−1.01244
$275$	−4.31793e14	−0.0602023
$276$	−8.22964e15	−1.12065
$277$	−1.79177e15	−0.238321	−0.119161	−	0.992875i	$-0.538020\pi$
$277$	−1.79177e15	−0.238321	−0.119161	+	0.992875i	$0.538020\pi$
$278$	−5.64802e15	−0.733846
$279$	1.20961e16	1.53538
$280$	0	0
$281$	2.57574e15	0.312112	0.156056	−	0.987748i	$-0.450122\pi$
$281$	2.57574e15	0.312112	0.156056	+	0.987748i	$0.450122\pi$
$282$	−1.02865e16	−1.21800
$283$	−1.44167e16	−1.66822	−0.834112	−	0.551595i	$-0.814019\pi$
$283$	−1.44167e16	−1.66822	−0.834112	+	0.551595i	$0.814019\pi$
$284$	4.55678e15	0.515334
$285$	2.15966e16	2.38723
$286$	4.11261e15	0.444364
$287$	0	0
$288$	3.89293e15	0.401999
$289$	1.61149e16	1.62702
$290$	−1.40515e15	−0.138719
$291$	−3.24826e16	−3.13578
$292$	−1.22349e15	−0.115508
$293$	−5.01501e15	−0.463055	−0.231527	−	0.972828i	$-0.574372\pi$
$293$	−5.01501e15	−0.463055	−0.231527	+	0.972828i	$0.574372\pi$
$294$	0	0
$295$	−7.48437e15	−0.661168
$296$	1.54480e15	0.133498
$297$	−1.78140e16	−1.50606
$298$	8.15275e15	0.674370
$299$	1.47218e16	1.19151
$300$	1.05269e15	0.0833705
$301$	0	0
$302$	6.13685e15	0.465479
$303$	−2.39872e16	−1.78075
$304$	−4.34339e15	−0.315610
$305$	1.78999e16	1.27321
$306$	−3.74288e16	−2.60626
$307$	1.74053e16	1.18654	0.593271	−	0.805003i	$-0.297836\pi$
$307$	1.74053e16	1.18654	0.593271	+	0.805003i	$0.297836\pi$
$308$	0	0
$309$	−2.55829e16	−1.67193
$310$	−7.79639e15	−0.498933
$311$	2.42505e15	0.151977	0.0759886	−	0.997109i	$-0.475789\pi$
$311$	2.42505e15	0.151977	0.0759886	+	0.997109i	$0.475789\pi$
$312$	−1.00263e16	−0.615372
$313$	−1.83199e16	−1.10125	−0.550625	−	0.834753i	$-0.685611\pi$
$313$	−1.83199e16	−1.10125	−0.550625	+	0.834753i	$0.685611\pi$
$314$	1.88596e16	1.11042
$315$	0	0
$316$	1.31379e16	0.742267
$317$	−4.78872e15	−0.265054	−0.132527	−	0.991179i	$-0.542309\pi$
$317$	−4.78872e15	−0.265054	−0.132527	+	0.991179i	$0.542309\pi$
$318$	−4.59433e15	−0.249141
$319$	−2.30815e15	−0.122638
$320$	−2.50915e15	−0.130633
$321$	−5.30320e16	−2.70555
$322$	0	0
$323$	4.17598e16	2.04617
$324$	1.97533e16	0.948630
$325$	−1.88314e15	−0.0886421
$326$	−2.26673e15	−0.104589
$327$	1.95119e16	0.882549
$328$	1.19095e16	0.528098
$329$	0	0
$330$	2.04938e16	0.873540
$331$	−1.40126e16	−0.585650	−0.292825	−	0.956166i	$-0.594595\pi$
$331$	−1.40126e16	−0.585650	−0.292825	+	0.956166i	$0.594595\pi$
$332$	8.52164e15	0.349241
$333$	2.13653e16	0.858660
$334$	−1.17760e16	−0.464138
$335$	−7.08764e14	−0.0273975
$336$	0	0
$337$	−5.03253e16	−1.87151	−0.935755	−	0.352650i	$-0.885281\pi$
$337$	−5.03253e16	−1.87151	−0.935755	+	0.352650i	$0.885281\pi$
$338$	−1.44808e15	−0.0528243
$339$	3.74645e16	1.34067
$340$	2.41244e16	0.846921
$341$	−1.28066e16	−0.441092
$342$	−6.00711e16	−2.03000
$343$	0	0
$344$	−5.58014e15	−0.181558
$345$	7.33613e16	2.34230
$346$	−4.16058e15	−0.130365
$347$	1.06124e16	0.326341	0.163171	−	0.986598i	$-0.447828\pi$
$347$	1.06124e16	0.326341	0.163171	+	0.986598i	$0.447828\pi$
$348$	5.62715e15	0.169834
$349$	−1.98547e16	−0.588163	−0.294082	−	0.955780i	$-0.595014\pi$
$349$	−1.98547e16	−0.588163	−0.294082	+	0.955780i	$0.595014\pi$
$350$	0	0
$351$	−7.76902e16	−2.21753
$352$	−4.12160e15	−0.115488
$353$	2.15311e15	0.0592286	0.0296143	−	0.999561i	$-0.490572\pi$
$353$	2.15311e15	0.0592286	0.0296143	+	0.999561i	$0.490572\pi$
$354$	2.99723e16	0.809466
$355$	−4.06204e16	−1.07711
$356$	−1.58553e16	−0.412810
$357$	0	0
$358$	1.67994e16	0.421748
$359$	−4.01753e16	−0.990479	−0.495240	−	0.868756i	$-0.664920\pi$
$359$	−4.01753e16	−0.990479	−0.495240	+	0.868756i	$0.664920\pi$
$360$	−3.47027e16	−0.840227
$361$	2.49691e16	0.593752
$362$	−2.62293e16	−0.612606
$363$	−4.52106e16	−1.03716
$364$	0	0
$365$	1.09066e16	0.241426
$366$	−7.16826e16	−1.55879
$367$	1.86915e16	0.399315	0.199657	−	0.979866i	$-0.436017\pi$
$367$	1.86915e16	0.399315	0.199657	+	0.979866i	$0.436017\pi$
$368$	−1.47540e16	−0.309670
$369$	1.64714e17	3.39672
$370$	−1.37708e16	−0.279027
$371$	0	0
$372$	3.12218e16	0.610842
$373$	2.78085e16	0.534650	0.267325	−	0.963606i	$-0.413860\pi$
$373$	2.78085e16	0.534650	0.267325	+	0.963606i	$0.413860\pi$
$374$	3.96274e16	0.748738
$375$	9.24487e16	1.71671
$376$	−1.84415e16	−0.336570
$377$	−1.00663e16	−0.180572
$378$	0	0
$379$	5.13829e15	0.0890562	0.0445281	−	0.999008i	$-0.485822\pi$
$379$	5.13829e15	0.0890562	0.0445281	+	0.999008i	$0.485822\pi$
$380$	3.87182e16	0.659662
$381$	8.62902e16	1.44527
$382$	4.16636e15	0.0686033
$383$	−7.09034e16	−1.14782	−0.573911	−	0.818917i	$-0.694575\pi$
$383$	−7.09034e16	−1.14782	−0.573911	+	0.818917i	$0.694575\pi$
$384$	1.00483e16	0.159933
$385$	0	0
$386$	−2.07742e16	−0.319674
$387$	−7.71759e16	−1.16778
$388$	−5.82343e16	−0.866509
$389$	8.14888e16	1.19241	0.596205	−	0.802833i	$-0.296675\pi$
$389$	8.14888e16	1.19241	0.596205	+	0.802833i	$0.296675\pi$
$390$	8.93777e16	1.28620
$391$	1.41853e17	2.00766
$392$	0	0
$393$	1.01555e17	1.39043
$394$	5.68536e16	0.765654
$395$	−1.17115e17	−1.55143
$396$	−5.70036e16	−0.742821
$397$	−1.25907e17	−1.61403	−0.807014	−	0.590532i	$-0.798918\pi$
$397$	−1.25907e17	−1.61403	−0.807014	+	0.590532i	$0.798918\pi$
$398$	1.00413e16	0.126633
$399$	0	0
$400$	1.88725e15	0.0230377
$401$	−6.89032e16	−0.827563	−0.413781	−	0.910376i	$-0.635792\pi$
$401$	−6.89032e16	−0.827563	−0.413781	+	0.910376i	$0.635792\pi$
$402$	2.83835e15	0.0335426
$403$	−5.58520e16	−0.649466
$404$	−4.30039e16	−0.492072
$405$	−1.76086e17	−1.98275
$406$	0	0
$407$	−2.26203e16	−0.246680
$408$	−9.66096e16	−1.03688
$409$	9.40470e16	0.993444	0.496722	−	0.867910i	$-0.334537\pi$
$409$	9.40470e16	0.993444	0.496722	+	0.867910i	$0.334537\pi$
$410$	−1.06165e17	−1.10379
$411$	−2.53163e17	−2.59076
$412$	−4.58647e16	−0.462005
$413$	0	0
$414$	−2.04055e17	−1.99179
$415$	−7.59643e16	−0.729957
$416$	−1.79751e16	−0.170046
$417$	−2.01626e17	−1.87786
$418$	6.35997e16	0.583189
$419$	7.38113e16	0.666395	0.333198	−	0.942857i	$-0.391872\pi$
$419$	7.38113e16	0.666395	0.333198	+	0.942857i	$0.391872\pi$
$420$	0	0
$421$	1.83025e17	1.60205	0.801026	−	0.598630i	$-0.204288\pi$
$421$	1.83025e17	1.60205	0.801026	+	0.598630i	$0.204288\pi$
$422$	−2.16247e16	−0.186388
$423$	−2.55055e17	−2.16482
$424$	−8.23666e15	−0.0688451
$425$	−1.81451e16	−0.149359
$426$	1.62671e17	1.31870
$427$	0	0
$428$	−9.50751e16	−0.747622
$429$	1.46814e17	1.13709
$430$	4.97429e16	0.379478
$431$	2.58099e17	1.93948	0.969739	−	0.244144i	$-0.0785070\pi$
$431$	2.58099e17	1.93948	0.969739	+	0.244144i	$0.0785070\pi$
$432$	7.78600e16	0.576328
$433$	6.73189e16	0.490869	0.245435	−	0.969413i	$-0.421069\pi$
$433$	6.73189e16	0.490869	0.245435	+	0.969413i	$0.421069\pi$
$434$	0	0
$435$	−5.01620e16	−0.354973
$436$	3.49807e16	0.243874
$437$	2.27666e17	1.56376
$438$	−4.36770e16	−0.295577
$439$	2.60230e17	1.73515	0.867577	−	0.497304i	$-0.165676\pi$
$439$	2.60230e17	1.73515	0.867577	+	0.497304i	$0.165676\pi$
$440$	3.67411e16	0.241385
$441$	0	0
$442$	1.72823e17	1.10244
$443$	−1.81094e17	−1.13836	−0.569179	−	0.822213i	$-0.692739\pi$
$443$	−1.81094e17	−1.13836	−0.569179	+	0.822213i	$0.692739\pi$
$444$	5.51471e16	0.341612
$445$	1.41339e17	0.862822
$446$	−1.72486e17	−1.03772
$447$	2.91042e17	1.72566
$448$	0	0
$449$	−1.16257e17	−0.669603	−0.334801	−	0.942289i	$-0.608669\pi$
$449$	−1.16257e17	−0.669603	−0.334801	+	0.942289i	$0.608669\pi$
$450$	2.61016e16	0.148178
$451$	−1.74390e17	−0.975828
$452$	6.71660e16	0.370467
$453$	2.19077e17	1.19113
$454$	−1.98501e17	−1.06390
$455$	0	0
$456$	−1.55053e17	−0.807622
$457$	1.64335e17	0.843869	0.421935	−	0.906626i	$-0.361351\pi$
$457$	1.64335e17	0.843869	0.421935	+	0.906626i	$0.361351\pi$
$458$	−4.16266e16	−0.210739
$459$	−7.48590e17	−3.73647
$460$	1.31521e17	0.647247
$461$	−1.27102e17	−0.616732	−0.308366	−	0.951268i	$-0.599782\pi$
$461$	−1.27102e17	−0.616732	−0.308366	+	0.951268i	$0.599782\pi$
$462$	0	0
$463$	1.15615e17	0.545427	0.272714	−	0.962095i	$-0.412079\pi$
$463$	1.15615e17	0.545427	0.272714	+	0.962095i	$0.412079\pi$
$464$	1.00883e16	0.0469300
$465$	−2.78320e17	−1.27673
$466$	2.32657e17	1.05247
$467$	−1.01395e17	−0.452333	−0.226166	−	0.974089i	$-0.572619\pi$
$467$	−1.01395e17	−0.452333	−0.226166	+	0.974089i	$0.572619\pi$
$468$	−2.48604e17	−1.09373
$469$	0	0
$470$	1.64393e17	0.703472
$471$	6.73260e17	2.84149
$472$	5.37339e16	0.223679
$473$	8.17092e16	0.335485
$474$	4.69004e17	1.89941
$475$	−2.91218e16	−0.116335
$476$	0	0
$477$	−1.13917e17	−0.442811
$478$	7.23278e16	0.277347
$479$	2.74106e17	1.03690	0.518451	−	0.855107i	$-0.326509\pi$
$479$	2.74106e17	1.03690	0.518451	+	0.855107i	$0.326509\pi$
$480$	−8.95730e16	−0.334279
$481$	−9.86515e16	−0.363212
$482$	2.67176e17	0.970492
$483$	0	0
$484$	−8.10530e16	−0.286599
$485$	5.19117e17	1.81111
$486$	2.31631e17	0.797372
$487$	−3.17916e17	−1.07988	−0.539939	−	0.841704i	$-0.681553\pi$
$487$	−3.17916e17	−1.07988	−0.539939	+	0.841704i	$0.681553\pi$
$488$	−1.28512e17	−0.430739
$489$	−8.09192e16	−0.267636
$490$	0	0
$491$	2.94376e17	0.948140	0.474070	−	0.880487i	$-0.342784\pi$
$491$	2.94376e17	0.948140	0.474070	+	0.880487i	$0.342784\pi$
$492$	4.25153e17	1.35136
$493$	−9.69945e16	−0.304258
$494$	2.77371e17	0.858688
$495$	5.08147e17	1.55258
$496$	5.59741e16	0.168794
$497$	0	0
$498$	3.04211e17	0.893683
$499$	−5.35396e17	−1.55246	−0.776232	−	0.630448i	$-0.782871\pi$
$499$	−5.35396e17	−1.55246	−0.776232	+	0.630448i	$0.782871\pi$
$500$	1.65741e17	0.474378
$501$	−4.20388e17	−1.18769
$502$	1.00574e17	0.280488
$503$	−3.35892e17	−0.924716	−0.462358	−	0.886693i	$-0.652996\pi$
$503$	−3.35892e17	−0.924716	−0.462358	+	0.886693i	$0.652996\pi$
$504$	0	0
$505$	3.83349e17	1.02849
$506$	2.16041e17	0.572213
$507$	−5.16944e16	−0.135174
$508$	1.54700e17	0.399371
$509$	−3.53434e17	−0.900831	−0.450415	−	0.892819i	$-0.648724\pi$
$509$	−3.53434e17	−0.900831	−0.450415	+	0.892819i	$0.648724\pi$
$510$	8.61206e17	2.16721
$511$	0	0
$512$	1.80144e16	0.0441942
$513$	−1.20144e18	−2.91032
$514$	2.74457e17	0.656468
$515$	4.08851e17	0.965645
$516$	−1.99203e17	−0.464593
$517$	2.70037e17	0.621919
$518$	0	0
$519$	−1.48527e17	−0.333593
$520$	1.60235e17	0.355416
$521$	3.06867e17	0.672210	0.336105	−	0.941825i	$-0.390890\pi$
$521$	3.06867e17	0.672210	0.336105	+	0.941825i	$0.390890\pi$
$522$	1.39526e17	0.301853
$523$	−6.85685e17	−1.46509	−0.732544	−	0.680719i	$-0.761667\pi$
$523$	−6.85685e17	−1.46509	−0.732544	+	0.680719i	$0.761667\pi$
$524$	1.82066e17	0.384216
$525$	0	0
$526$	−7.05150e16	−0.145169
$527$	−5.38166e17	−1.09433
$528$	−1.47135e17	−0.295526
$529$	2.69320e17	0.534327
$530$	7.34239e16	0.143895
$531$	7.43165e17	1.43870
$532$	0	0
$533$	−7.60548e17	−1.43681
$534$	−5.66012e17	−1.05635
$535$	8.47526e17	1.56262
$536$	5.08856e15	0.00926881
$537$	5.99713e17	1.07922
$538$	3.61185e17	0.642162
$539$	0	0
$540$	−6.94066e17	−1.20460
$541$	3.29478e17	0.564994	0.282497	−	0.959268i	$-0.408837\pi$
$541$	3.29478e17	0.564994	0.282497	+	0.959268i	$0.408837\pi$
$542$	−2.23293e17	−0.378338
$543$	−9.36349e17	−1.56761
$544$	−1.73201e17	−0.286521
$545$	−3.11828e17	−0.509727
$546$	0	0
$547$	7.07530e17	1.12935	0.564673	−	0.825315i	$-0.309002\pi$
$547$	7.07530e17	1.12935	0.564673	+	0.825315i	$0.309002\pi$
$548$	−4.53867e17	−0.715904
$549$	−1.77738e18	−2.77051
$550$	−2.76348e16	−0.0425695
$551$	−1.55671e17	−0.236985
$552$	−5.26697e17	−0.792423
$553$	0	0
$554$	−1.14673e17	−0.168519
$555$	−4.91597e17	−0.714011
$556$	−3.61473e17	−0.518907
$557$	−8.28103e17	−1.17497	−0.587484	−	0.809236i	$-0.699881\pi$
$557$	−8.28103e17	−1.17497	−0.587484	+	0.809236i	$0.699881\pi$
$558$	7.74147e17	1.08568
$559$	3.56350e17	0.493970
$560$	0	0
$561$	1.41464e18	1.91597
$562$	1.64847e17	0.220697
$563$	−9.92312e17	−1.31324	−0.656620	−	0.754222i	$-0.728014\pi$
$563$	−9.92312e17	−1.31324	−0.656620	+	0.754222i	$0.728014\pi$
$564$	−6.58336e17	−0.861258
$565$	−5.98737e17	−0.774321
$566$	−9.22670e17	−1.17961
$567$	0	0
$568$	2.91634e17	0.364396
$569$	5.17432e17	0.639181	0.319590	−	0.947556i	$-0.396455\pi$
$569$	5.17432e17	0.639181	0.319590	+	0.947556i	$0.396455\pi$
$570$	1.38218e18	1.68803
$571$	−1.90210e17	−0.229667	−0.114834	−	0.993385i	$-0.536633\pi$
$571$	−1.90210e17	−0.229667	−0.114834	+	0.993385i	$0.536633\pi$
$572$	2.63207e17	0.314213
$573$	1.48733e17	0.175551
$574$	0	0
$575$	−9.89236e16	−0.114145
$576$	2.49147e17	0.284256
$577$	−1.26110e17	−0.142267	−0.0711337	−	0.997467i	$-0.522662\pi$
$577$	−1.26110e17	−0.142267	−0.0711337	+	0.997467i	$0.522662\pi$
$578$	1.03136e18	1.15048
$579$	−7.41611e17	−0.818023
$580$	−8.99299e16	−0.0980894
$581$	0	0
$582$	−2.07888e18	−2.21733
$583$	1.20608e17	0.127213
$584$	−7.83036e16	−0.0816767
$585$	2.21613e18	2.28603
$586$	−3.20961e17	−0.327429
$587$	−1.15869e18	−1.16902	−0.584508	−	0.811388i	$-0.698712\pi$
$587$	−1.15869e18	−1.16902	−0.584508	+	0.811388i	$0.698712\pi$
$588$	0	0
$589$	−8.63726e17	−0.852367
$590$	−4.78999e17	−0.467517
$591$	2.02959e18	1.95925
$592$	9.88671e16	0.0943975
$593$	−1.54128e17	−0.145554	−0.0727771	−	0.997348i	$-0.523186\pi$
$593$	−1.54128e17	−0.145554	−0.0727771	+	0.997348i	$0.523186\pi$
$594$	−1.14009e18	−1.06495
$595$	0	0
$596$	5.21776e17	0.476852
$597$	3.58459e17	0.324046
$598$	9.42197e17	0.842528
$599$	1.43365e18	1.26814	0.634071	−	0.773275i	$-0.281383\pi$
$599$	1.43365e18	1.26814	0.634071	+	0.773275i	$0.281383\pi$
$600$	6.73722e16	0.0589519
$601$	1.25241e18	1.08408	0.542040	−	0.840353i	$-0.317652\pi$
$601$	1.25241e18	1.08408	0.542040	+	0.840353i	$0.317652\pi$
$602$	0	0
$603$	7.03772e16	0.0596169
$604$	3.92759e17	0.329144
$605$	7.22529e17	0.599026
$606$	−1.53518e18	−1.25918
$607$	1.18607e18	0.962459	0.481230	−	0.876595i	$-0.340190\pi$
$607$	1.18607e18	0.962459	0.481230	+	0.876595i	$0.340190\pi$
$608$	−2.77977e17	−0.223170
$609$	0	0
$610$	1.14559e18	0.900296
$611$	1.17768e18	0.915716
$612$	−2.39545e18	−1.84290
$613$	1.89871e18	1.44532	0.722661	−	0.691202i	$-0.242919\pi$
$613$	1.89871e18	1.44532	0.722661	+	0.691202i	$0.242919\pi$
$614$	1.11394e18	0.839011
$615$	−3.78994e18	−2.82451
$616$	0	0
$617$	−4.94808e17	−0.361063	−0.180532	−	0.983569i	$-0.557782\pi$
$617$	−4.94808e17	−0.361063	−0.180532	+	0.983569i	$0.557782\pi$
$618$	−1.63730e18	−1.18224
$619$	−1.16747e18	−0.834172	−0.417086	−	0.908867i	$-0.636949\pi$
$619$	−1.16747e18	−0.834172	−0.417086	+	0.908867i	$0.636949\pi$
$620$	−4.98969e17	−0.352799
$621$	−4.08117e18	−2.85554
$622$	1.55203e17	0.107464
$623$	0	0
$624$	−6.41686e17	−0.435134
$625$	−1.61478e18	−1.08366
$626$	−1.17248e18	−0.778702
$627$	2.27042e18	1.49234
$628$	1.20701e18	0.785189
$629$	−9.50564e17	−0.612001
$630$	0	0
$631$	−2.58748e18	−1.63187	−0.815935	−	0.578143i	$-0.803777\pi$
$631$	−2.58748e18	−1.63187	−0.815935	+	0.578143i	$0.803777\pi$
$632$	8.40826e17	0.524862
$633$	−7.71971e17	−0.476954
$634$	−3.06478e17	−0.187422
$635$	−1.37904e18	−0.834733
$636$	−2.94037e17	−0.176170
$637$	0	0
$638$	−1.47722e17	−0.0867180
$639$	4.03343e18	2.34379
$640$	−1.60585e17	−0.0923711
$641$	2.10381e18	1.19792	0.598962	−	0.800777i	$-0.295580\pi$
$641$	2.10381e18	1.19792	0.598962	+	0.800777i	$0.295580\pi$
$642$	−3.39405e18	−1.91311
$643$	−2.34494e18	−1.30846	−0.654230	−	0.756296i	$-0.727007\pi$
$643$	−2.34494e18	−1.30846	−0.654230	+	0.756296i	$0.727007\pi$
$644$	0	0
$645$	1.77575e18	0.971056
$646$	2.67263e18	1.44686
$647$	−1.39692e18	−0.748674	−0.374337	−	0.927293i	$-0.622130\pi$
$647$	−1.39692e18	−0.748674	−0.374337	+	0.927293i	$0.622130\pi$
$648$	1.26421e18	0.670783
$649$	−7.86819e17	−0.413318
$650$	−1.20521e17	−0.0626794
$651$	0	0
$652$	−1.45071e17	−0.0739556
$653$	−2.06721e18	−1.04339	−0.521697	−	0.853131i	$-0.674701\pi$
$653$	−2.06721e18	−1.04339	−0.521697	+	0.853131i	$0.674701\pi$
$654$	1.24876e18	0.624056
$655$	−1.62299e18	−0.803057
$656$	7.62210e17	0.373422
$657$	−1.08298e18	−0.525344
$658$	0	0
$659$	2.93883e18	1.39772	0.698858	−	0.715261i	$-0.253692\pi$
$659$	2.93883e18	1.39772	0.698858	+	0.715261i	$0.253692\pi$
$660$	1.31161e18	0.617686
$661$	2.53531e18	1.18228	0.591141	−	0.806568i	$-0.298678\pi$
$661$	2.53531e18	1.18228	0.591141	+	0.806568i	$0.298678\pi$
$662$	−8.96809e17	−0.414117
$663$	6.16954e18	2.82107
$664$	5.45385e17	0.246951
$665$	0	0
$666$	1.36738e18	0.607164
$667$	−5.28795e17	−0.232525
$668$	−7.53666e17	−0.328195
$669$	−6.15752e18	−2.65544
$670$	−4.53609e16	−0.0193729
$671$	1.88178e18	0.795926
$672$	0	0
$673$	−3.04015e18	−1.26124	−0.630618	−	0.776093i	$-0.717199\pi$
$673$	−3.04015e18	−1.26124	−0.630618	+	0.776093i	$0.717199\pi$
$674$	−3.22082e18	−1.32336
$675$	5.22040e17	0.212437
$676$	−9.26771e16	−0.0373524
$677$	5.42540e17	0.216574	0.108287	−	0.994120i	$-0.465464\pi$
$677$	5.42540e17	0.216574	0.108287	+	0.994120i	$0.465464\pi$
$678$	2.39773e18	0.947998
$679$	0	0
$680$	1.54396e18	0.598864
$681$	−7.08619e18	−2.72243
$682$	−8.19621e17	−0.311899
$683$	−2.94428e18	−1.10980	−0.554900	−	0.831917i	$-0.687243\pi$
$683$	−2.94428e18	−1.10980	−0.554900	+	0.831917i	$0.687243\pi$
$684$	−3.84455e18	−1.43543
$685$	4.04590e18	1.49633
$686$	0	0
$687$	−1.48601e18	−0.539266
$688$	−3.57129e17	−0.128381
$689$	5.25997e17	0.187309
$690$	4.69513e18	1.65626
$691$	1.59020e18	0.555706	0.277853	−	0.960624i	$-0.410377\pi$
$691$	1.59020e18	0.555706	0.277853	+	0.960624i	$0.410377\pi$
$692$	−2.66277e17	−0.0921817
$693$	0	0
$694$	6.79193e17	0.230758
$695$	3.22227e18	1.08458
$696$	3.60138e17	0.120090
$697$	−7.32832e18	−2.42098
$698$	−1.27070e18	−0.415894
$699$	8.30553e18	2.69318
$700$	0	0
$701$	−3.34716e18	−1.06539	−0.532695	−	0.846307i	$-0.678821\pi$
$701$	−3.34716e18	−1.06539	−0.532695	+	0.846307i	$0.678821\pi$
$702$	−4.97217e18	−1.56803
$703$	−1.52560e18	−0.476685
$704$	−2.63782e17	−0.0816627
$705$	5.86859e18	1.80013
$706$	1.37799e17	0.0418809
$707$	0	0
$708$	1.91823e18	0.572379
$709$	−4.34546e18	−1.28480	−0.642400	−	0.766370i	$-0.722061\pi$
$709$	−4.34546e18	−1.28480	−0.642400	+	0.766370i	$0.722061\pi$
$710$	−2.59971e18	−0.761632
$711$	1.16290e19	3.37591
$712$	−1.01474e18	−0.291901
$713$	−2.93398e18	−0.836325
$714$	0	0
$715$	−2.34630e18	−0.656742
$716$	1.07516e18	0.298221
$717$	2.58200e18	0.709711
$718$	−2.57122e18	−0.700375
$719$	−2.11374e18	−0.570575	−0.285288	−	0.958442i	$-0.592089\pi$
$719$	−2.11374e18	−0.570575	−0.285288	+	0.958442i	$0.592089\pi$
$720$	−2.22097e18	−0.594130
$721$	0	0
$722$	1.59802e18	0.419846
$723$	9.53781e18	2.48342
$724$	−1.67868e18	−0.433178
$725$	6.76406e16	0.0172986
$726$	−2.89348e18	−0.733385
$727$	−1.17297e18	−0.294656	−0.147328	−	0.989088i	$-0.547067\pi$
$727$	−1.17297e18	−0.294656	−0.147328	+	0.989088i	$0.547067\pi$
$728$	0	0
$729$	5.80148e17	0.143156
$730$	6.98021e17	0.170714
$731$	3.43364e18	0.832323
$732$	−4.58769e18	−1.10223
$733$	1.49248e18	0.355413	0.177706	−	0.984084i	$-0.443132\pi$
$733$	1.49248e18	0.355413	0.177706	+	0.984084i	$0.443132\pi$
$734$	1.19626e18	0.282358
$735$	0	0
$736$	−9.44256e17	−0.218970
$737$	−7.45111e16	−0.0171270
$738$	1.05417e19	2.40184
$739$	−4.02747e18	−0.909586	−0.454793	−	0.890597i	$-0.650287\pi$
$739$	−4.02747e18	−0.909586	−0.454793	+	0.890597i	$0.650287\pi$
$740$	−8.81329e17	−0.197302
$741$	9.90174e18	2.19732
$742$	0	0
$743$	−4.29776e18	−0.937163	−0.468582	−	0.883420i	$-0.655235\pi$
$743$	−4.29776e18	−0.937163	−0.468582	+	0.883420i	$0.655235\pi$
$744$	1.99819e18	0.431930
$745$	−4.65126e18	−0.996678
$746$	1.77974e18	0.378055
$747$	7.54293e18	1.58839
$748$	2.53615e18	0.529438
$749$	0	0
$750$	5.91672e18	1.21390
$751$	−5.70323e18	−1.16001	−0.580004	−	0.814614i	$-0.696949\pi$
$751$	−5.70323e18	−1.16001	−0.580004	+	0.814614i	$0.696949\pi$
$752$	−1.18026e18	−0.237991
$753$	3.59037e18	0.717747
$754$	−6.44243e17	−0.127684
$755$	−3.50116e18	−0.687950
$756$	0	0
$757$	9.41377e18	1.81819	0.909097	−	0.416584i	$-0.136773\pi$
$757$	9.41377e18	1.81819	0.909097	+	0.416584i	$0.136773\pi$
$758$	3.28851e17	0.0629722
$759$	7.71235e18	1.46425
$760$	2.47796e18	0.466452
$761$	2.95022e18	0.550624	0.275312	−	0.961355i	$-0.411219\pi$
$761$	2.95022e18	0.550624	0.275312	+	0.961355i	$0.411219\pi$
$762$	5.52257e18	1.02196
$763$	0	0
$764$	2.66647e17	0.0485099
$765$	2.13537e19	3.85188
$766$	−4.53782e18	−0.811633
$767$	−3.43147e18	−0.608570
$768$	6.43088e17	0.113090
$769$	−6.59719e18	−1.15037	−0.575185	−	0.818023i	$-0.695070\pi$
$769$	−6.59719e18	−1.15037	−0.575185	+	0.818023i	$0.695070\pi$
$770$	0	0
$771$	9.79772e18	1.67985
$772$	−1.32955e18	−0.226044
$773$	2.27431e18	0.383427	0.191713	−	0.981451i	$-0.438596\pi$
$773$	2.27431e18	0.383427	0.191713	+	0.981451i	$0.438596\pi$
$774$	−4.93926e18	−0.825744
$775$	3.75298e17	0.0622180
$776$	−3.72700e18	−0.612714
$777$	0	0
$778$	5.21528e18	0.843161
$779$	−1.17615e19	−1.88569
$780$	5.72017e18	0.909482
$781$	−4.27036e18	−0.673337
$782$	9.07861e18	1.41963
$783$	2.79056e18	0.432754
$784$	0	0
$785$	−1.07596e19	−1.64114
$786$	6.49949e18	0.983179
$787$	3.84845e18	0.577364	0.288682	−	0.957425i	$-0.406783\pi$
$787$	3.84845e18	0.577364	0.288682	+	0.957425i	$0.406783\pi$
$788$	3.63863e18	0.541399
$789$	−2.51728e18	−0.371477
$790$	−7.49536e18	−1.09702
$791$	0	0
$792$	−3.64823e18	−0.525253
$793$	8.20682e18	1.17192
$794$	−8.05804e18	−1.14129
$795$	2.62113e18	0.368216
$796$	6.42641e17	0.0895433
$797$	−7.52899e17	−0.104054	−0.0520269	−	0.998646i	$-0.516568\pi$
$797$	−7.52899e17	−0.104054	−0.0520269	+	0.998646i	$0.516568\pi$
$798$	0	0
$799$	1.13477e19	1.54295
$800$	1.20784e17	0.0162901
$801$	−1.40343e19	−1.87750
$802$	−4.40981e18	−0.585175
$803$	1.14659e18	0.150924
$804$	1.81654e17	0.0237182
$805$	0	0
$806$	−3.57453e18	−0.459241
$807$	1.28938e19	1.64325
$808$	−2.75225e18	−0.347948
$809$	4.71288e17	0.0591046	0.0295523	−	0.999563i	$-0.490592\pi$
$809$	4.71288e17	0.0591046	0.0295523	+	0.999563i	$0.490592\pi$
$810$	−1.12695e19	−1.40202
$811$	1.90998e18	0.235719	0.117859	−	0.993030i	$-0.462397\pi$
$811$	1.90998e18	0.235719	0.117859	+	0.993030i	$0.462397\pi$
$812$	0	0
$813$	−7.97125e18	−0.968140
$814$	−1.44770e18	−0.174429
$815$	1.29320e18	0.154576
$816$	−6.18302e18	−0.733186
$817$	5.51079e18	0.648292
$818$	6.01901e18	0.702471
$819$	0	0
$820$	−6.79455e18	−0.780496
$821$	−1.17979e19	−1.34455	−0.672273	−	0.740303i	$-0.734682\pi$
$821$	−1.17979e19	−1.34455	−0.672273	+	0.740303i	$0.734682\pi$
$822$	−1.62024e19	−1.83195
$823$	−1.94358e18	−0.218024	−0.109012	−	0.994040i	$-0.534769\pi$
$823$	−1.94358e18	−0.218024	−0.109012	+	0.994040i	$0.534769\pi$
$824$	−2.93534e18	−0.326687
$825$	−9.86522e17	−0.108932
$826$	0	0
$827$	−1.46200e19	−1.58914	−0.794570	−	0.607173i	$-0.792304\pi$
$827$	−1.46200e19	−1.58914	−0.794570	+	0.607173i	$0.792304\pi$
$828$	−1.30595e19	−1.40841
$829$	3.01396e18	0.322502	0.161251	−	0.986913i	$-0.448447\pi$
$829$	3.01396e18	0.322502	0.161251	+	0.986913i	$0.448447\pi$
$830$	−4.86172e18	−0.516157
$831$	−4.09367e18	−0.431227
$832$	−1.15041e18	−0.120240
$833$	0	0
$834$	−1.29041e19	−1.32785
$835$	6.71839e18	0.685967
$836$	4.07038e18	0.412377
$837$	1.54832e19	1.55649
$838$	4.72393e18	0.471213
$839$	3.67263e18	0.363517	0.181759	−	0.983343i	$-0.441821\pi$
$839$	3.67263e18	0.363517	0.181759	+	0.983343i	$0.441821\pi$
$840$	0	0
$841$	−9.89906e18	−0.964761
$842$	1.17136e19	1.13282
$843$	5.88482e18	0.564747
$844$	−1.38398e18	−0.131797
$845$	8.26150e17	0.0780711
$846$	−1.63235e19	−1.53076
$847$	0	0
$848$	−5.27146e17	−0.0486809
$849$	−3.29380e19	−3.01854
$850$	−1.16129e18	−0.105613
$851$	−5.18229e18	−0.467713
$852$	1.04109e19	0.932463
$853$	−1.22672e19	−1.09038	−0.545189	−	0.838313i	$-0.683542\pi$
$853$	−1.22672e19	−1.09038	−0.545189	+	0.838313i	$0.683542\pi$
$854$	0	0
$855$	3.42714e19	3.00021
$856$	−6.08481e18	−0.528649
$857$	1.60186e18	0.138117	0.0690587	−	0.997613i	$-0.478000\pi$
$857$	1.60186e18	0.138117	0.0690587	+	0.997613i	$0.478000\pi$
$858$	9.39613e18	0.804047
$859$	−1.22929e19	−1.04400	−0.521998	−	0.852947i	$-0.674813\pi$
$859$	−1.22929e19	−1.04400	−0.521998	+	0.852947i	$0.674813\pi$
$860$	3.18355e18	0.268331
$861$	0	0
$862$	1.65184e19	1.37142
$863$	−3.69849e18	−0.304758	−0.152379	−	0.988322i	$-0.548693\pi$
$863$	−3.69849e18	−0.304758	−0.152379	+	0.988322i	$0.548693\pi$
$864$	4.98304e18	0.407526
$865$	2.37367e18	0.192671
$866$	4.30841e18	0.347097
$867$	3.68179e19	2.94398
$868$	0	0
$869$	−1.23121e19	−0.969848
$870$	−3.21037e18	−0.251004
$871$	−3.24958e17	−0.0252179
$872$	2.23876e18	0.172445
$873$	−5.15461e19	−3.94097
$874$	1.45706e19	1.10574
$875$	0	0
$876$	−2.79533e18	−0.209005
$877$	3.42159e18	0.253940	0.126970	−	0.991907i	$-0.459475\pi$
$877$	3.42159e18	0.253940	0.126970	+	0.991907i	$0.459475\pi$
$878$	1.66547e19	1.22694
$879$	−1.14578e19	−0.837867
$880$	2.35143e18	0.170685
$881$	−1.42953e19	−1.03003	−0.515015	−	0.857181i	$-0.672214\pi$
$881$	−1.42953e19	−1.03003	−0.515015	+	0.857181i	$0.672214\pi$
$882$	0	0
$883$	−2.07001e19	−1.46970	−0.734848	−	0.678232i	$-0.762747\pi$
$883$	−2.07001e19	−1.46970	−0.734848	+	0.678232i	$0.762747\pi$
$884$	1.10607e19	0.779546
$885$	−1.70996e19	−1.19634
$886$	−1.15900e19	−0.804941
$887$	−1.20939e19	−0.833804	−0.416902	−	0.908951i	$-0.636884\pi$
$887$	−1.20939e19	−0.833804	−0.416902	+	0.908951i	$0.636884\pi$
$888$	3.52941e18	0.241556
$889$	0	0
$890$	9.04568e18	0.610107
$891$	−1.85117e19	−1.23948
$892$	−1.10391e19	−0.733775
$893$	1.82123e19	1.20180
$894$	1.86267e19	1.22023
$895$	−9.58427e18	−0.623318
$896$	0	0
$897$	3.36351e19	2.15597
$898$	−7.44044e18	−0.473481
$899$	2.00616e18	0.126744
$900$	1.67050e18	0.104778
$901$	5.06828e18	0.315609
$902$	−1.11609e19	−0.690014
$903$	0	0
$904$	4.29862e18	0.261960
$905$	1.49642e19	0.905394
$906$	1.40209e19	0.842254
$907$	8.75742e18	0.522310	0.261155	−	0.965297i	$-0.415897\pi$
$907$	8.75742e18	0.522310	0.261155	+	0.965297i	$0.415897\pi$
$908$	−1.27040e19	−0.752288
$909$	−3.80649e19	−2.23800
$910$	0	0
$911$	3.20011e18	0.185480	0.0927398	−	0.995690i	$-0.470438\pi$
$911$	3.20011e18	0.185480	0.0927398	+	0.995690i	$0.470438\pi$
$912$	−9.92338e18	−0.571075
$913$	−7.98600e18	−0.456320
$914$	1.05174e19	0.596706
$915$	4.08960e19	2.30379
$916$	−2.66410e18	−0.149015
$917$	0	0
$918$	−4.79098e19	−2.64208
$919$	1.96768e19	1.07747	0.538734	−	0.842476i	$-0.318903\pi$
$919$	1.96768e19	1.07747	0.538734	+	0.842476i	$0.318903\pi$
$920$	8.41737e18	0.457673
$921$	3.97661e19	2.14697
$922$	−8.13453e18	−0.436095
$923$	−1.86239e19	−0.991423
$924$	0	0
$925$	6.62890e17	0.0347953
$926$	7.39935e18	0.385675
$927$	−4.05971e19	−2.10124
$928$	6.45651e17	0.0331845
$929$	2.71520e19	1.38580	0.692899	−	0.721034i	$-0.256333\pi$
$929$	2.71520e19	1.38580	0.692899	+	0.721034i	$0.256333\pi$
$930$	−1.78125e19	−0.902787
$931$	0	0
$932$	1.48901e19	0.744206
$933$	5.54054e18	0.274993
$934$	−6.48930e18	−0.319848
$935$	−2.26080e19	−1.10659
$936$	−1.59107e19	−0.773385
$937$	−5.82871e18	−0.281362	−0.140681	−	0.990055i	$-0.544929\pi$
$937$	−5.82871e18	−0.281362	−0.140681	+	0.990055i	$0.544929\pi$
$938$	0	0
$939$	−4.18558e19	−1.99264
$940$	1.05211e19	0.497430
$941$	1.44508e19	0.678516	0.339258	−	0.940693i	$-0.389824\pi$
$941$	1.44508e19	0.678516	0.339258	+	0.940693i	$0.389824\pi$
$942$	4.30886e19	2.00924
$943$	−3.99526e19	−1.85020
$944$	3.43897e18	0.158165
$945$	0	0
$946$	5.22939e18	0.237224
$947$	−3.02410e19	−1.36245	−0.681226	−	0.732074i	$-0.738553\pi$
$947$	−3.02410e19	−1.36245	−0.681226	+	0.732074i	$0.738553\pi$
$948$	3.00163e19	1.34308
$949$	5.00051e18	0.222220
$950$	−1.86380e18	−0.0822612
$951$	−1.09408e19	−0.479598
$952$	0	0
$953$	8.71317e18	0.376767	0.188383	−	0.982096i	$-0.439675\pi$
$953$	8.71317e18	0.376767	0.188383	+	0.982096i	$0.439675\pi$
$954$	−7.29068e18	−0.313115
$955$	−2.37697e18	−0.101391
$956$	4.62898e18	0.196114
$957$	−5.27345e18	−0.221905
$958$	1.75428e19	0.733200
$959$	0	0
$960$	−5.73267e18	−0.236371
$961$	−1.32866e19	−0.544139
$962$	−6.31370e18	−0.256830
$963$	−8.41557e19	−3.40026
$964$	1.70993e19	0.686242
$965$	1.18520e19	0.472459
$966$	0	0
$967$	4.61552e19	1.81530	0.907650	−	0.419728i	$-0.137874\pi$
$967$	4.61552e19	1.81530	0.907650	+	0.419728i	$0.137874\pi$
$968$	−5.18739e18	−0.202656
$969$	9.54090e19	3.70241
$970$	3.32235e19	1.28065
$971$	3.08990e19	1.18310	0.591548	−	0.806270i	$-0.298517\pi$
$971$	3.08990e19	1.18310	0.591548	+	0.806270i	$0.298517\pi$
$972$	1.48244e19	0.563827
$973$	0	0
$974$	−2.03466e19	−0.763589
$975$	−4.30242e18	−0.160392
$976$	−8.22476e18	−0.304578
$977$	2.36206e19	0.868914	0.434457	−	0.900693i	$-0.356940\pi$
$977$	2.36206e19	0.868914	0.434457	+	0.900693i	$0.356940\pi$
$978$	−5.17883e18	−0.189247
$979$	1.48587e19	0.539378
$980$	0	0
$981$	3.09631e19	1.10917
$982$	1.88400e19	0.670436
$983$	−1.34195e18	−0.0474393	−0.0237196	−	0.999719i	$-0.507551\pi$
$983$	−1.34195e18	−0.0474393	−0.0237196	+	0.999719i	$0.507551\pi$
$984$	2.72098e19	0.955559
$985$	−3.24358e19	−1.13159
$986$	−6.20765e18	−0.215143
$987$	0	0
$988$	1.77517e19	0.607184
$989$	1.87195e19	0.636091
$990$	3.25214e19	1.09784
$991$	−1.41158e19	−0.473399	−0.236699	−	0.971583i	$-0.576066\pi$
$991$	−1.41158e19	−0.473399	−0.236699	+	0.971583i	$0.576066\pi$
$992$	3.58234e18	0.119355
$993$	−3.20148e19	−1.05969
$994$	0	0
$995$	−5.72868e18	−0.187156
$996$	1.94695e19	0.631929
$997$	−3.83239e19	−1.23581	−0.617905	−	0.786253i	$-0.712018\pi$
$997$	−3.83239e19	−1.23581	−0.617905	+	0.786253i	$0.712018\pi$
$998$	−3.42653e19	−1.09776
$999$	2.73480e19	0.870463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.14.a.k.1.4		4
7.2	even	3		98.14.c.n.67.1		8
7.3	odd	6		14.14.c.a.9.4	✓	8
7.4	even	3		98.14.c.n.79.1		8
7.5	odd	6		14.14.c.a.11.4	yes	8
7.6	odd	2		98.14.a.l.1.1		4
21.5	even	6		126.14.g.d.109.3		8
21.17	even	6		126.14.g.d.37.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.a.9.4	✓	8	7.3	odd	6
14.14.c.a.11.4	yes	8	7.5	odd	6
98.14.a.k.1.4		4	1.1	even	1	trivial
98.14.a.l.1.1		4	7.6	odd	2
98.14.c.n.67.1		8	7.2	even	3
98.14.c.n.79.1		8	7.4	even	3
126.14.g.d.37.3		8	21.17	even	6
126.14.g.d.109.3		8	21.5	even	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q+64.0000 q^{2} +2284.71 q^{3} +4096.00 q^{4} -36512.9 q^{5} +146221. q^{6} +262144. q^{8} +3.62557e6 q^{9} +O(q^{10})\)	\(q+64.0000 q^{2} +2284.71 q^{3} +4096.00 q^{4} -36512.9 q^{5} +146221. q^{6} +262144. q^{8} +3.62557e6 q^{9} -2.33683e6 q^{10} -3.83854e6 q^{11} +9.35817e6 q^{12} -1.67406e7 q^{13} -8.34214e7 q^{15} +1.67772e7 q^{16} -1.61306e8 q^{17} +2.32037e8 q^{18} -2.58886e8 q^{19} -1.49557e8 q^{20} -2.45667e8 q^{22} -8.79407e8 q^{23} +5.98923e8 q^{24} +1.12489e8 q^{25} -1.07140e9 q^{26} +4.64082e9 q^{27} +6.01309e8 q^{29} -5.33897e9 q^{30} +3.33631e9 q^{31} +1.07374e9 q^{32} -8.76995e9 q^{33} -1.03236e10 q^{34} +1.48503e10 q^{36} +5.89294e9 q^{37} -1.65687e10 q^{38} -3.82475e10 q^{39} -9.57164e9 q^{40} +4.54312e10 q^{41} -2.12865e10 q^{43} -1.57227e10 q^{44} -1.32380e11 q^{45} -5.62821e10 q^{46} -7.03488e10 q^{47} +3.83311e10 q^{48} +7.19929e9 q^{50} -3.68537e11 q^{51} -6.85696e10 q^{52} -3.14204e10 q^{53} +2.97012e11 q^{54} +1.40156e11 q^{55} -5.91480e11 q^{57} +3.84838e10 q^{58} +2.04979e11 q^{59} -3.41694e11 q^{60} -4.90234e11 q^{61} +2.13524e11 q^{62} +6.87195e10 q^{64} +6.11249e11 q^{65} -5.61277e11 q^{66} +1.94113e10 q^{67} -6.60708e11 q^{68} -2.00919e12 q^{69} +1.11249e12 q^{71} +9.50422e11 q^{72} -2.98705e11 q^{73} +3.77148e11 q^{74} +2.57005e11 q^{75} -1.06040e12 q^{76} -2.44784e12 q^{78} +3.20750e12 q^{79} -6.12585e11 q^{80} +4.82258e12 q^{81} +2.90760e12 q^{82} +2.08048e12 q^{83} +5.88974e12 q^{85} -1.36234e12 q^{86} +1.37382e12 q^{87} -1.00625e12 q^{88} -3.87093e12 q^{89} -8.47233e12 q^{90} -3.60205e12 q^{92} +7.62251e12 q^{93} -4.50232e12 q^{94} +9.45268e12 q^{95} +2.45319e12 q^{96} -1.42174e13 q^{97} -1.39169e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 256 q^{2} - 182 q^{3} + 16384 q^{4} - 64400 q^{5} - 11648 q^{6} + 1048576 q^{8} + 3983752 q^{9}+O(q^{10}) \) 4 * q + 256 * q^2 - 182 * q^3 + 16384 * q^4 - 64400 * q^5 - 11648 * q^6 + 1048576 * q^8 + 3983752 * q^9	\( 4 q + 256 q^{2} - 182 q^{3} + 16384 q^{4} - 64400 q^{5} - 11648 q^{6} + 1048576 q^{8} + 3983752 q^{9} - 4121600 q^{10} + 1008790 q^{11} - 745472 q^{12} - 26903632 q^{13} - 44444458 q^{15} + 67108864 q^{16} - 165333028 q^{17} + 254960128 q^{18} - 423405794 q^{19} - 263782400 q^{20} + 64562560 q^{22} - 286233866 q^{23} - 47710208 q^{24} + 472017432 q^{25} - 1721832448 q^{26} + 5202970822 q^{27} + 9100337408 q^{29} - 2844445312 q^{30} + 1507094246 q^{31} + 4294967296 q^{32} - 16888935028 q^{33} - 10581313792 q^{34} + 16317448192 q^{36} + 18959705336 q^{37} - 27097970816 q^{38} - 35759388756 q^{39} - 16882073600 q^{40} - 56825955312 q^{41} - 45778809712 q^{43} + 4132003840 q^{44} - 119804452768 q^{45} - 18318967424 q^{46} - 81351201078 q^{47} - 3053453312 q^{48} + 30209115648 q^{50} - 14996824142 q^{51} - 110197276672 q^{52} - 87497947440 q^{53} + 332990132608 q^{54} - 350818705174 q^{55} - 903663464132 q^{57} + 582421594112 q^{58} - 194140265102 q^{59} - 182044499968 q^{60} + 175816313120 q^{61} + 96454031744 q^{62} + 274877906944 q^{64} + 1689866774568 q^{65} - 1080891841792 q^{66} + 243815218758 q^{67} - 677204082688 q^{68} - 3022078976392 q^{69} - 1637697339536 q^{71} + 1044316684288 q^{72} - 3492491920596 q^{73} + 1213421141504 q^{74} - 2370218127424 q^{75} - 1734270132224 q^{76} - 2288600880384 q^{78} + 1016380081246 q^{79} - 1080452710400 q^{80} - 17492694092 q^{81} - 3636861139968 q^{82} - 3513747871648 q^{83} + 284557420264 q^{85} - 2929843821568 q^{86} - 9706955821052 q^{87} + 264448245760 q^{88} - 8034124428036 q^{89} - 7667484977152 q^{90} - 1172413915136 q^{92} + 3388371390552 q^{93} - 5206476868992 q^{94} - 1429435505438 q^{95} - 195421011968 q^{96} - 27175565862816 q^{97} - 12918917288164 q^{99}+O(q^{100}) \) 4 * q + 256 * q^2 - 182 * q^3 + 16384 * q^4 - 64400 * q^5 - 11648 * q^6 + 1048576 * q^8 + 3983752 * q^9 - 4121600 * q^10 + 1008790 * q^11 - 745472 * q^12 - 26903632 * q^13 - 44444458 * q^15 + 67108864 * q^16 - 165333028 * q^17 + 254960128 * q^18 - 423405794 * q^19 - 263782400 * q^20 + 64562560 * q^22 - 286233866 * q^23 - 47710208 * q^24 + 472017432 * q^25 - 1721832448 * q^26 + 5202970822 * q^27 + 9100337408 * q^29 - 2844445312 * q^30 + 1507094246 * q^31 + 4294967296 * q^32 - 16888935028 * q^33 - 10581313792 * q^34 + 16317448192 * q^36 + 18959705336 * q^37 - 27097970816 * q^38 - 35759388756 * q^39 - 16882073600 * q^40 - 56825955312 * q^41 - 45778809712 * q^43 + 4132003840 * q^44 - 119804452768 * q^45 - 18318967424 * q^46 - 81351201078 * q^47 - 3053453312 * q^48 + 30209115648 * q^50 - 14996824142 * q^51 - 110197276672 * q^52 - 87497947440 * q^53 + 332990132608 * q^54 - 350818705174 * q^55 - 903663464132 * q^57 + 582421594112 * q^58 - 194140265102 * q^59 - 182044499968 * q^60 + 175816313120 * q^61 + 96454031744 * q^62 + 274877906944 * q^64 + 1689866774568 * q^65 - 1080891841792 * q^66 + 243815218758 * q^67 - 677204082688 * q^68 - 3022078976392 * q^69 - 1637697339536 * q^71 + 1044316684288 * q^72 - 3492491920596 * q^73 + 1213421141504 * q^74 - 2370218127424 * q^75 - 1734270132224 * q^76 - 2288600880384 * q^78 + 1016380081246 * q^79 - 1080452710400 * q^80 - 17492694092 * q^81 - 3636861139968 * q^82 - 3513747871648 * q^83 + 284557420264 * q^85 - 2929843821568 * q^86 - 9706955821052 * q^87 + 264448245760 * q^88 - 8034124428036 * q^89 - 7667484977152 * q^90 - 1172413915136 * q^92 + 3388371390552 * q^93 - 5206476868992 * q^94 - 1429435505438 * q^95 - 195421011968 * q^96 - 27175565862816 * q^97 - 12918917288164 * q^99

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