LMFDB - Embedded newform 15.18.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,18,Mod(1,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("15.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	15.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$27.4833131017$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 37234x - 350700 $ x^3 - 37234*x - 350700
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-188.067$ of defining polynomial
Character	$\chi$	$=$	15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-670.613 q^{2} -6561.00 q^{3} +318650. q^{4} -390625. q^{5} +4.39989e6 q^{6} -2.70804e7 q^{7} -1.25792e8 q^{8} +4.30467e7 q^{9} +2.61958e8 q^{10} +1.01644e9 q^{11} -2.09066e9 q^{12} -1.04834e9 q^{13} +1.81605e10 q^{14} +2.56289e9 q^{15} +4.25918e10 q^{16} +2.00099e10 q^{17} -2.88677e10 q^{18} +1.64417e10 q^{19} -1.24473e11 q^{20} +1.77675e11 q^{21} -6.81636e11 q^{22} +5.92721e11 q^{23} +8.25322e11 q^{24} +1.52588e11 q^{25} +7.03032e11 q^{26} -2.82430e11 q^{27} -8.62917e12 q^{28} +4.83212e11 q^{29} -1.71871e12 q^{30} -5.20802e12 q^{31} -1.20748e13 q^{32} -6.66885e12 q^{33} -1.34189e13 q^{34} +1.05783e13 q^{35} +1.37168e13 q^{36} +3.82367e13 q^{37} -1.10260e13 q^{38} +6.87817e12 q^{39} +4.91375e13 q^{40} -6.56402e13 q^{41} -1.19151e14 q^{42} -5.83804e13 q^{43} +3.23888e14 q^{44} -1.68151e13 q^{45} -3.97486e14 q^{46} +7.43658e12 q^{47} -2.79445e14 q^{48} +5.00719e14 q^{49} -1.02327e14 q^{50} -1.31285e14 q^{51} -3.34054e14 q^{52} -3.01466e14 q^{53} +1.89401e14 q^{54} -3.97046e14 q^{55} +3.40650e15 q^{56} -1.07874e14 q^{57} -3.24048e14 q^{58} -3.44389e14 q^{59} +8.16665e14 q^{60} -2.43237e15 q^{61} +3.49257e15 q^{62} -1.16572e15 q^{63} +2.51491e15 q^{64} +4.09508e14 q^{65} +4.47222e15 q^{66} +1.19632e15 q^{67} +6.37614e15 q^{68} -3.88884e15 q^{69} -7.09394e15 q^{70} +5.42254e15 q^{71} -5.41494e15 q^{72} -5.84732e15 q^{73} -2.56420e16 q^{74} -1.00113e15 q^{75} +5.23914e15 q^{76} -2.75256e16 q^{77} -4.61259e15 q^{78} +2.03455e15 q^{79} -1.66374e16 q^{80} +1.85302e15 q^{81} +4.40192e16 q^{82} -1.18343e16 q^{83} +5.66160e16 q^{84} -7.81636e15 q^{85} +3.91507e16 q^{86} -3.17035e15 q^{87} -1.27860e17 q^{88} -2.43170e16 q^{89} +1.12764e16 q^{90} +2.83895e16 q^{91} +1.88870e17 q^{92} +3.41698e16 q^{93} -4.98707e15 q^{94} -6.42253e15 q^{95} +7.92225e16 q^{96} -1.06105e17 q^{97} -3.35788e17 q^{98} +4.37543e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 442 q^{2} - 19683 q^{3} + 298148 q^{4} - 1171875 q^{5} + 2899962 q^{6} + 4962644 q^{7} - 108831912 q^{8} + 129140163 q^{9} + 172656250 q^{10} + 1049849720 q^{11} - 1956149028 q^{12} - 3091742090 q^{13}+ \cdots + 45\!\cdots\!20 q^{99}+O(q^{100}) $ 3 * q - 442 * q^2 - 19683 * q^3 + 298148 * q^4 - 1171875 * q^5 + 2899962 * q^6 + 4962644 * q^7 - 108831912 * q^8 + 129140163 * q^9 + 172656250 * q^10 + 1049849720 * q^11 - 1956149028 * q^12 - 3091742090 * q^13 + 27586028328 * q^14 + 7688671875 * q^15 + 22392797456 * q^16 - 15119940094 * q^17 - 19026650682 * q^18 - 111896117996 * q^19 - 116464062500 * q^20 - 32559907284 * q^21 - 693818341648 * q^22 + 784535528472 * q^23 + 714046174632 * q^24 + 457763671875 * q^25 - 1092511841044 * q^26 - 847288609443 * q^27 - 7640185610512 * q^28 + 1395352153678 * q^29 - 1132797656250 * q^30 - 12458197616536 * q^31 - 24074446195616 * q^32 - 6888064012920 * q^33 - 41046727271164 * q^34 - 1938532812500 * q^35 + 12834293772708 * q^36 + 32093748310134 * q^37 - 68757678664024 * q^38 + 20284919852490 * q^39 + 42512465625000 * q^40 - 102276917392466 * q^41 - 180991931860008 * q^42 - 141347515908644 * q^43 + 319886980653472 * q^44 - 50445376171875 * q^45 - 299722933931856 * q^46 - 54182226541768 * q^47 - 146919144108816 * q^48 + 702936204707227 * q^49 - 67443847656250 * q^50 + 99201926956734 * q^51 - 670193699134584 * q^52 + 345545322785582 * q^53 + 124833855124602 * q^54 - 410097546875000 * q^55 + 3014407093472160 * q^56 + 734150430171756 * q^57 + 2198630240496412 * q^58 + 2075534176494536 * q^59 + 764120714062500 * q^60 - 1591128188427998 * q^61 + 1555165628278608 * q^62 + 213625551690324 * q^63 + 4014461944704576 * q^64 + 1207711753906250 * q^65 + 4552142139552528 * q^66 - 2417737431711844 * q^67 + 1338181134241816 * q^68 - 5147337602304792 * q^69 - 10775792315625000 * q^70 + 5019485593673056 * q^71 - 4684856951760552 * q^72 - 10804161755859578 * q^73 - 12140475721796372 * q^74 - 3003387451171875 * q^75 - 3289783191661584 * q^76 - 27418121851422432 * q^77 + 7167970189089684 * q^78 - 40642131657181960 * q^79 - 8747186506250000 * q^80 + 5559060566555523 * q^81 + 15262994262855388 * q^82 - 21823256926416996 * q^83 + 50127257790569232 * q^84 + 5906226599218750 * q^85 + 8867591636371640 * q^86 - 9154905480281358 * q^87 - 125733265675831872 * q^88 - 2700230040372426 * q^89 + 7432285422656250 * q^90 - 46116457499478296 * q^91 + 204241599793288224 * q^92 + 81738234562092696 * q^93 - 72231791695517200 * q^94 + 43709421092187500 * q^95 + 157952441489436576 * q^96 - 79760576372788314 * q^97 - 128015343617626250 * q^98 + 45192587988768120 * q^99

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 $

$2$	−670.613	−1.85232	−0.926162	−	0.377126i	$-0.876912\pi$
$2$	−670.613	−1.85232	−0.926162	+	0.377126i	$0.876912\pi$
$3$	−6561.00	−0.577350
$3$	−6561.00	−0.577350
$4$	318650.	2.43110
$5$	−390625.	−0.447214
$5$	−390625.	−0.447214
$6$	4.39989e6	1.06944
$7$	−2.70804e7	−1.77551	−0.887753	−	0.460320i	$-0.847735\pi$
$7$	−2.70804e7	−1.77551	−0.887753	+	0.460320i	$0.847735\pi$
$8$	−1.25792e8	−2.65087
$9$	4.30467e7	0.333333
$10$	2.61958e8	0.828385
$11$	1.01644e9	1.42969	0.714847	−	0.699281i	$-0.246496\pi$
$11$	1.01644e9	1.42969	0.714847	+	0.699281i	$0.246496\pi$
$12$	−2.09066e9	−1.40360
$13$	−1.04834e9	−0.356438	−0.178219	−	0.983991i	$-0.557034\pi$
$13$	−1.04834e9	−0.356438	−0.178219	+	0.983991i	$0.557034\pi$
$14$	1.81605e10	3.28881
$15$	2.56289e9	0.258199
$16$	4.25918e10	2.47917
$17$	2.00099e10	0.695711	0.347855	−	0.937548i	$-0.386910\pi$
$17$	2.00099e10	0.695711	0.347855	+	0.937548i	$0.386910\pi$
$18$	−2.88677e10	−0.617441
$19$	1.64417e10	0.222096	0.111048	−	0.993815i	$-0.464579\pi$
$19$	1.64417e10	0.222096	0.111048	+	0.993815i	$0.464579\pi$
$20$	−1.24473e11	−1.08722
$21$	1.77675e11	1.02509
$22$	−6.81636e11	−2.64826
$23$	5.92721e11	1.57821	0.789103	−	0.614261i	$-0.210546\pi$
$23$	5.92721e11	1.57821	0.789103	+	0.614261i	$0.210546\pi$
$24$	8.25322e11	1.53048
$25$	1.52588e11	0.200000
$26$	7.03032e11	0.660239
$27$	−2.82430e11	−0.192450
$28$	−8.62917e12	−4.31644
$29$	4.83212e11	0.179372	0.0896860	−	0.995970i	$-0.471414\pi$
$29$	4.83212e11	0.179372	0.0896860	+	0.995970i	$0.471414\pi$
$30$	−1.71871e12	−0.478268
$31$	−5.20802e12	−1.09673	−0.548363	−	0.836240i	$-0.684749\pi$
$31$	−5.20802e12	−1.09673	−0.548363	+	0.836240i	$0.684749\pi$
$32$	−1.20748e13	−1.94135
$33$	−6.66885e12	−0.825434
$34$	−1.34189e13	−1.28868
$35$	1.05783e13	0.794030
$36$	1.37168e13	0.810368
$37$	3.82367e13	1.78964	0.894820	−	0.446427i	$-0.147304\pi$
$37$	3.82367e13	1.78964	0.894820	+	0.446427i	$0.147304\pi$
$38$	−1.10260e13	−0.411393
$39$	6.87817e12	0.205790
$40$	4.91375e13	1.18551
$41$	−6.56402e13	−1.28383	−0.641915	−	0.766776i	$-0.721860\pi$
$41$	−6.56402e13	−1.28383	−0.641915	+	0.766776i	$0.721860\pi$
$42$	−1.19151e14	−1.89880
$43$	−5.83804e13	−0.761703	−0.380851	−	0.924636i	$-0.624369\pi$
$43$	−5.83804e13	−0.761703	−0.380851	+	0.924636i	$0.624369\pi$
$44$	3.23888e14	3.47573
$45$	−1.68151e13	−0.149071
$46$	−3.97486e14	−2.92335
$47$	7.43658e12	0.0455556	0.0227778	−	0.999741i	$-0.492749\pi$
$47$	7.43658e12	0.0455556	0.0227778	+	0.999741i	$0.492749\pi$
$48$	−2.79445e14	−1.43135
$49$	5.00719e14	2.15242
$50$	−1.02327e14	−0.370465
$51$	−1.31285e14	−0.401669
$52$	−3.34054e14	−0.866539
$53$	−3.01466e14	−0.665109	−0.332555	−	0.943084i	$-0.607911\pi$
$53$	−3.01466e14	−0.665109	−0.332555	+	0.943084i	$0.607911\pi$
$54$	1.89401e14	0.356480
$55$	−3.97046e14	−0.639378
$56$	3.40650e15	4.70664
$57$	−1.07874e14	−0.128227
$58$	−3.24048e14	−0.332255
$59$	−3.44389e14	−0.305357	−0.152678	−	0.988276i	$-0.548790\pi$
$59$	−3.44389e14	−0.305357	−0.152678	+	0.988276i	$0.548790\pi$
$60$	8.16665e14	0.627709
$61$	−2.43237e15	−1.62452	−0.812261	−	0.583294i	$-0.801763\pi$
$61$	−2.43237e15	−1.62452	−0.812261	+	0.583294i	$0.801763\pi$
$62$	3.49257e15	2.03149
$63$	−1.16572e15	−0.591835
$64$	2.51491e15	1.11684
$65$	4.09508e14	0.159404
$66$	4.47222e15	1.52897
$67$	1.19632e15	0.359924	0.179962	−	0.983674i	$-0.442403\pi$
$67$	1.19632e15	0.359924	0.179962	+	0.983674i	$0.442403\pi$
$68$	6.37614e15	1.69135
$69$	−3.88884e15	−0.911177
$70$	−7.09394e15	−1.47080
$71$	5.42254e15	0.996567	0.498283	−	0.867014i	$-0.333964\pi$
$71$	5.42254e15	0.996567	0.498283	+	0.867014i	$0.333964\pi$
$72$	−5.41494e15	−0.883623
$73$	−5.84732e15	−0.848619	−0.424309	−	0.905517i	$-0.639483\pi$
$73$	−5.84732e15	−0.848619	−0.424309	+	0.905517i	$0.639483\pi$
$74$	−2.56420e16	−3.31499
$75$	−1.00113e15	−0.115470
$76$	5.23914e15	0.539938
$77$	−2.75256e16	−2.53843
$78$	−4.61259e15	−0.381189
$79$	2.03455e15	0.150882	0.0754411	−	0.997150i	$-0.475964\pi$
$79$	2.03455e15	0.150882	0.0754411	+	0.997150i	$0.475964\pi$
$80$	−1.66374e16	−1.10872
$81$	1.85302e15	0.111111
$82$	4.40192e16	2.37807
$83$	−1.18343e16	−0.576740	−0.288370	−	0.957519i	$-0.593113\pi$
$83$	−1.18343e16	−0.576740	−0.288370	+	0.957519i	$0.593113\pi$
$84$	5.66160e16	2.49210
$85$	−7.81636e15	−0.311131
$86$	3.91507e16	1.41092
$87$	−3.17035e15	−0.103560
$88$	−1.27860e17	−3.78993
$89$	−2.43170e16	−0.654780	−0.327390	−	0.944889i	$-0.606169\pi$
$89$	−2.43170e16	−0.654780	−0.327390	+	0.944889i	$0.606169\pi$
$90$	1.12764e16	0.276128
$91$	2.83895e16	0.632858
$92$	1.88870e17	3.83678
$93$	3.41698e16	0.633195
$94$	−4.98707e15	−0.0843837
$95$	−6.42253e15	−0.0993243
$96$	7.92225e16	1.12084
$97$	−1.06105e17	−1.37459	−0.687296	−	0.726377i	$-0.741203\pi$
$97$	−1.06105e17	−1.37459	−0.687296	+	0.726377i	$0.741203\pi$
$98$	−3.35788e17	−3.98698
$99$	4.37543e16	0.476564
$100$	4.86221e16	0.486221
$101$	6.36534e16	0.584911	0.292455	−	0.956279i	$-0.405528\pi$
$101$	6.36534e16	0.584911	0.292455	+	0.956279i	$0.405528\pi$
$102$	8.80413e16	0.744021
$103$	−3.76414e16	−0.292785	−0.146393	−	0.989227i	$-0.546766\pi$
$103$	−3.76414e16	−0.292785	−0.146393	+	0.989227i	$0.546766\pi$
$104$	1.31873e17	0.944872
$105$	−6.94042e16	−0.458434
$106$	2.02167e17	1.23200
$107$	1.97603e17	1.11181	0.555906	−	0.831245i	$-0.312371\pi$
$107$	1.97603e17	1.11181	0.555906	+	0.831245i	$0.312371\pi$
$108$	−8.99961e16	−0.467866
$109$	2.14472e17	1.03097	0.515484	−	0.856899i	$-0.327612\pi$
$109$	2.14472e17	1.03097	0.515484	+	0.856899i	$0.327612\pi$
$110$	2.66264e17	1.18434
$111$	−2.50871e17	−1.03325
$112$	−1.15340e18	−4.40177
$113$	3.29313e17	1.16531	0.582656	−	0.812719i	$-0.302014\pi$
$113$	3.29313e17	1.16531	0.582656	+	0.812719i	$0.302014\pi$
$114$	7.23416e16	0.237518
$115$	−2.31532e17	−0.705795
$116$	1.53975e17	0.436072
$117$	−4.51277e16	−0.118813
$118$	2.30952e17	0.565620
$119$	−5.41876e17	−1.23524
$120$	−3.22391e17	−0.684452
$121$	5.27698e17	1.04402
$122$	1.63118e18	3.00914
$123$	4.30666e17	0.741219
$124$	−1.65953e18	−2.66626
$125$	−5.96046e16	−0.0894427
$126$	7.81749e17	1.09627
$127$	4.24273e17	0.556306	0.278153	−	0.960537i	$-0.410278\pi$
$127$	4.24273e17	0.556306	0.278153	+	0.960537i	$0.410278\pi$
$128$	−1.03865e17	−0.127405
$129$	3.83034e17	0.439769
$130$	−2.74622e17	−0.295268
$131$	−1.01448e18	−1.02197	−0.510985	−	0.859590i	$-0.670719\pi$
$131$	−1.01448e18	−1.02197	−0.510985	+	0.859590i	$0.670719\pi$
$132$	−2.12503e18	−2.00672
$133$	−4.45247e17	−0.394332
$134$	−8.02266e17	−0.666696
$135$	1.10324e17	0.0860663
$136$	−2.51708e18	−1.84424
$137$	−1.60921e18	−1.10787	−0.553934	−	0.832560i	$-0.686874\pi$
$137$	−1.60921e18	−1.10787	−0.553934	+	0.832560i	$0.686874\pi$
$138$	2.60791e18	1.68780
$139$	−1.37382e18	−0.836188	−0.418094	−	0.908404i	$-0.637302\pi$
$139$	−1.37382e18	−0.836188	−0.418094	+	0.908404i	$0.637302\pi$
$140$	3.37077e18	1.93037
$141$	−4.87914e16	−0.0263015
$142$	−3.63642e18	−1.84596
$143$	−1.06557e18	−0.509597
$144$	1.83344e18	0.826389
$145$	−1.88755e17	−0.0802176
$146$	3.92129e18	1.57192
$147$	−3.28521e18	−1.24270
$148$	1.21841e19	4.35080
$149$	−3.59822e18	−1.21340	−0.606701	−	0.794930i	$-0.707507\pi$
$149$	−3.59822e18	−1.21340	−0.606701	+	0.794930i	$0.707507\pi$
$150$	6.71370e17	0.213888
$151$	1.83062e18	0.551182	0.275591	−	0.961275i	$-0.411127\pi$
$151$	1.83062e18	0.551182	0.275591	+	0.961275i	$0.411127\pi$
$152$	−2.06823e18	−0.588747
$153$	8.61360e17	0.231904
$154$	1.84590e19	4.70199
$155$	2.03438e18	0.490471
$156$	2.19173e18	0.500296
$157$	2.03936e18	0.440907	0.220453	−	0.975398i	$-0.429246\pi$
$157$	2.03936e18	0.440907	0.220453	+	0.975398i	$0.429246\pi$
$158$	−1.36440e18	−0.279483
$159$	1.97792e18	0.384001
$160$	4.71670e18	0.868198
$161$	−1.60511e19	−2.80211
$162$	−1.24266e18	−0.205814
$163$	−1.26018e19	−1.98078	−0.990390	−	0.138302i	$-0.955835\pi$
$163$	−1.26018e19	−1.98078	−0.990390	+	0.138302i	$0.955835\pi$
$164$	−2.09162e19	−3.12112
$165$	2.60502e18	0.369145
$166$	7.93626e18	1.06831
$167$	9.46306e18	1.21044	0.605218	−	0.796060i	$-0.293086\pi$
$167$	9.46306e18	1.21044	0.605218	+	0.796060i	$0.293086\pi$
$168$	−2.23501e19	−2.71738
$169$	−7.55140e18	−0.872952
$170$	5.24175e18	0.576316
$171$	7.07760e17	0.0740319
$172$	−1.86029e19	−1.85178
$173$	−5.05953e18	−0.479422	−0.239711	−	0.970844i	$-0.577053\pi$
$173$	−5.05953e18	−0.479422	−0.239711	+	0.970844i	$0.577053\pi$
$174$	2.12608e18	0.191828
$175$	−4.13214e18	−0.355101
$176$	4.32919e19	3.54445
$177$	2.25954e18	0.176298
$178$	1.63073e19	1.21287
$179$	1.38935e18	0.0985284	0.0492642	−	0.998786i	$-0.484312\pi$
$179$	1.38935e18	0.0985284	0.0492642	+	0.998786i	$0.484312\pi$
$180$	−5.35814e18	−0.362408
$181$	6.56442e18	0.423573	0.211787	−	0.977316i	$-0.432072\pi$
$181$	6.56442e18	0.423573	0.211787	+	0.977316i	$0.432072\pi$
$182$	−1.90384e19	−1.17226
$183$	1.59588e19	0.937918
$184$	−7.45596e19	−4.18362
$185$	−1.49362e19	−0.800351
$186$	−2.29147e19	−1.17288
$187$	2.03388e19	0.994653
$188$	2.36966e18	0.110750
$189$	7.64831e18	0.341696
$190$	4.30703e18	0.183981
$191$	1.88960e19	0.771943	0.385972	−	0.922511i	$-0.373866\pi$
$191$	1.88960e19	0.771943	0.385972	+	0.922511i	$0.373866\pi$
$192$	−1.65003e19	−0.644809
$193$	−2.57702e18	−0.0963563	−0.0481781	−	0.998839i	$-0.515342\pi$
$193$	−2.57702e18	−0.0963563	−0.0481781	+	0.998839i	$0.515342\pi$
$194$	7.11551e19	2.54619
$195$	−2.68679e18	−0.0920320
$196$	1.59554e20	5.23276
$197$	−2.58028e19	−0.810410	−0.405205	−	0.914226i	$-0.632800\pi$
$197$	−2.58028e19	−0.810410	−0.405205	+	0.914226i	$0.632800\pi$
$198$	−2.93422e19	−0.882752
$199$	5.04896e18	0.145529	0.0727647	−	0.997349i	$-0.476818\pi$
$199$	5.04896e18	0.145529	0.0727647	+	0.997349i	$0.476818\pi$
$200$	−1.91944e19	−0.530174
$201$	−7.84904e18	−0.207802
$202$	−4.26868e19	−1.08344
$203$	−1.30856e19	−0.318476
$204$	−4.18339e19	−0.976499
$205$	2.56407e19	0.574146
$206$	2.52428e19	0.542333
$207$	2.55147e19	0.526069
$208$	−4.46507e19	−0.883670
$209$	1.67119e19	0.317529
$210$	4.65433e19	0.849168
$211$	4.88902e19	0.856685	0.428342	−	0.903616i	$-0.359098\pi$
$211$	4.88902e19	0.856685	0.428342	+	0.903616i	$0.359098\pi$
$212$	−9.60620e19	−1.61695
$213$	−3.55773e19	−0.575368
$214$	−1.32515e20	−2.05944
$215$	2.28049e19	0.340644
$216$	3.55274e19	0.510160
$217$	1.41035e20	1.94724
$218$	−1.43828e20	−1.90969
$219$	3.83643e19	0.489950
$220$	−1.26519e20	−1.55440
$221$	−2.09772e19	−0.247978
$222$	1.68237e20	1.91391
$223$	6.03668e18	0.0661008	0.0330504	−	0.999454i	$-0.489478\pi$
$223$	6.03668e18	0.0661008	0.0330504	+	0.999454i	$0.489478\pi$
$224$	3.26990e20	3.44688
$225$	6.56841e18	0.0666667
$226$	−2.20842e20	−2.15854
$227$	−1.85243e20	−1.74390	−0.871952	−	0.489591i	$-0.837146\pi$
$227$	−1.85243e20	−1.74390	−0.871952	+	0.489591i	$0.837146\pi$
$228$	−3.43740e19	−0.311733
$229$	1.07933e20	0.943092	0.471546	−	0.881841i	$-0.343696\pi$
$229$	1.07933e20	0.943092	0.471546	+	0.881841i	$0.343696\pi$
$230$	1.55268e20	1.30736
$231$	1.80595e20	1.46556
$232$	−6.07842e19	−0.475492
$233$	−1.20686e20	−0.910190	−0.455095	−	0.890443i	$-0.650395\pi$
$233$	−1.20686e20	−0.910190	−0.455095	+	0.890443i	$0.650395\pi$
$234$	3.02632e19	0.220080
$235$	−2.90491e18	−0.0203731
$236$	−1.09740e20	−0.742355
$237$	−1.33487e19	−0.0871119
$238$	3.63389e20	2.28806
$239$	1.11522e20	0.677607	0.338804	−	0.940857i	$-0.389978\pi$
$239$	1.11522e20	0.677607	0.338804	+	0.940857i	$0.389978\pi$
$240$	1.09158e20	0.640118
$241$	−1.89825e20	−1.07451	−0.537253	−	0.843421i	$-0.680538\pi$
$241$	−1.89825e20	−1.07451	−0.537253	+	0.843421i	$0.680538\pi$
$242$	−3.53881e20	−1.93387
$243$	−1.21577e19	−0.0641500
$244$	−7.75073e20	−3.94938
$245$	−1.95593e20	−0.962592
$246$	−2.88810e20	−1.37298
$247$	−1.72365e19	−0.0791634
$248$	6.55128e20	2.90728
$249$	7.76451e19	0.332981
$250$	3.99716e19	0.165677
$251$	−1.47560e20	−0.591210	−0.295605	−	0.955310i	$-0.595521\pi$
$251$	−1.47560e20	−0.591210	−0.295605	+	0.955310i	$0.595521\pi$
$252$	−3.71457e20	−1.43881
$253$	6.02464e20	2.25635
$254$	−2.84523e20	−1.03046
$255$	5.12831e19	0.179632
$256$	−2.59980e20	−0.880848
$257$	5.88705e20	1.92959	0.964797	−	0.262994i	$-0.0847101\pi$
$257$	5.88705e20	1.92959	0.964797	+	0.262994i	$0.0847101\pi$
$258$	−2.56868e20	−0.814595
$259$	−1.03547e21	−3.17752
$260$	1.30490e20	0.387528
$261$	2.08007e19	0.0597906
$262$	6.80324e20	1.89302
$263$	−2.53714e20	−0.683472	−0.341736	−	0.939796i	$-0.611015\pi$
$263$	−2.53714e20	−0.683472	−0.341736	+	0.939796i	$0.611015\pi$
$264$	8.38888e20	2.18812
$265$	1.17760e20	0.297446
$266$	2.98589e20	0.730431
$267$	1.59544e20	0.378038
$268$	3.81206e20	0.875013
$269$	−3.54749e20	−0.788909	−0.394455	−	0.918915i	$-0.629067\pi$
$269$	−3.54749e20	−0.788909	−0.394455	+	0.918915i	$0.629067\pi$
$270$	−7.39847e19	−0.159423
$271$	6.20629e20	1.29596	0.647982	−	0.761656i	$-0.275613\pi$
$271$	6.20629e20	1.29596	0.647982	+	0.761656i	$0.275613\pi$
$272$	8.52256e20	1.72478
$273$	−1.86264e20	−0.365381
$274$	1.07916e21	2.05213
$275$	1.55096e20	0.285939
$276$	−1.23918e21	−2.21517
$277$	−5.37902e20	−0.932449	−0.466225	−	0.884666i	$-0.654386\pi$
$277$	−5.37902e20	−0.932449	−0.466225	+	0.884666i	$0.654386\pi$
$278$	9.21301e20	1.54889
$279$	−2.24188e20	−0.365575
$280$	−1.33067e21	−2.10487
$281$	−8.40846e20	−1.29037	−0.645183	−	0.764028i	$-0.723219\pi$
$281$	−8.40846e20	−1.29037	−0.645183	+	0.764028i	$0.723219\pi$
$282$	3.27201e19	0.0487189
$283$	−4.49542e20	−0.649510	−0.324755	−	0.945798i	$-0.605282\pi$
$283$	−4.49542e20	−0.649510	−0.324755	+	0.945798i	$0.605282\pi$
$284$	1.72789e21	2.42276
$285$	4.21382e19	0.0573449
$286$	7.14588e20	0.943940
$287$	1.77756e21	2.27945
$288$	−5.19779e20	−0.647117
$289$	−4.26845e20	−0.515987
$290$	1.26581e20	0.148589
$291$	6.96152e20	0.793622
$292$	−1.86325e21	−2.06308
$293$	−8.24381e20	−0.886652	−0.443326	−	0.896360i	$-0.646202\pi$
$293$	−8.24381e20	−0.886652	−0.443326	+	0.896360i	$0.646202\pi$
$294$	2.20311e21	2.30188
$295$	1.34527e20	0.136560
$296$	−4.80987e21	−4.74410
$297$	−2.87072e20	−0.275145
$298$	2.41301e21	2.24761
$299$	−6.21374e20	−0.562533
$300$	−3.19010e20	−0.280720
$301$	1.58097e21	1.35241
$302$	−1.22764e21	−1.02097
$303$	−4.17630e20	−0.337698
$304$	7.00280e20	0.550612
$305$	9.50144e20	0.726508
$306$	−5.77639e20	−0.429560
$307$	2.06003e20	0.149004	0.0745021	−	0.997221i	$-0.476263\pi$
$307$	2.06003e20	0.149004	0.0745021	+	0.997221i	$0.476263\pi$
$308$	−8.77101e21	−6.17119
$309$	2.46965e20	0.169040
$310$	−1.36428e21	−0.908511
$311$	9.73195e20	0.630575	0.315287	−	0.948996i	$-0.397899\pi$
$311$	9.73195e20	0.630575	0.315287	+	0.948996i	$0.397899\pi$
$312$	−8.65219e20	−0.545522
$313$	−1.65984e21	−1.01845	−0.509226	−	0.860633i	$-0.670068\pi$
$313$	−1.65984e21	−1.01845	−0.509226	+	0.860633i	$0.670068\pi$
$314$	−1.36762e21	−0.816702
$315$	4.55361e20	0.264677
$316$	6.48309e20	0.366811
$317$	3.08017e21	1.69657	0.848283	−	0.529543i	$-0.177636\pi$
$317$	3.08017e21	1.69657	0.848283	+	0.529543i	$0.177636\pi$
$318$	−1.32642e21	−0.711294
$319$	4.91155e20	0.256447
$320$	−9.82385e20	−0.499467
$321$	−1.29647e21	−0.641905
$322$	1.07641e22	5.19042
$323$	3.28996e20	0.154514
$324$	5.90465e20	0.270123
$325$	−1.59964e20	−0.0712877
$326$	8.45090e21	3.66905
$327$	−1.40715e21	−0.595229
$328$	8.25702e21	3.40327
$329$	−2.01386e20	−0.0808841
$330$	−1.74696e21	−0.683777
$331$	−3.68783e21	−1.40680	−0.703401	−	0.710794i	$-0.748336\pi$
$331$	−3.68783e21	−1.40680	−0.703401	+	0.710794i	$0.748336\pi$
$332$	−3.77101e21	−1.40212
$333$	1.64596e21	0.596547
$334$	−6.34605e21	−2.24212
$335$	−4.67312e20	−0.160963
$336$	7.56747e21	2.54137
$337$	2.06121e20	0.0674946	0.0337473	−	0.999430i	$-0.489256\pi$
$337$	2.06121e20	0.0674946	0.0337473	+	0.999430i	$0.489256\pi$
$338$	5.06406e21	1.61699
$339$	−2.16062e21	−0.672793
$340$	−2.49068e21	−0.756393
$341$	−5.29363e21	−1.56798
$342$	−4.74633e20	−0.137131
$343$	−7.25994e21	−2.04613
$344$	7.34380e21	2.01918
$345$	1.51908e21	0.407491
$346$	3.39299e21	0.888045
$347$	1.45695e21	0.372087	0.186044	−	0.982541i	$-0.440433\pi$
$347$	1.45695e21	0.372087	0.186044	+	0.982541i	$0.440433\pi$
$348$	−1.01023e21	−0.251766
$349$	−6.15182e21	−1.49619	−0.748096	−	0.663590i	$-0.769032\pi$
$349$	−6.15182e21	−1.49619	−0.748096	+	0.663590i	$0.769032\pi$
$350$	2.77107e21	0.657762
$351$	2.96083e20	0.0685966
$352$	−1.22732e22	−2.77553
$353$	4.05523e21	0.895222	0.447611	−	0.894228i	$-0.352275\pi$
$353$	4.05523e21	0.895222	0.447611	+	0.894228i	$0.352275\pi$
$354$	−1.51528e21	−0.326561
$355$	−2.11818e21	−0.445678
$356$	−7.74862e21	−1.59184
$357$	3.55525e21	0.713165
$358$	−9.31717e20	−0.182507
$359$	2.30064e21	0.440094	0.220047	−	0.975489i	$-0.429379\pi$
$359$	2.30064e21	0.440094	0.220047	+	0.975489i	$0.429379\pi$
$360$	2.11521e21	0.395168
$361$	−5.21006e21	−0.950673
$362$	−4.40219e21	−0.784595
$363$	−3.46223e21	−0.602767
$364$	9.04632e21	1.53854
$365$	2.28411e21	0.379514
$366$	−1.07022e22	−1.73733
$367$	3.92558e21	0.622648	0.311324	−	0.950304i	$-0.399228\pi$
$367$	3.92558e21	0.622648	0.311324	+	0.950304i	$0.399228\pi$
$368$	2.52450e22	3.91263
$369$	−2.82560e21	−0.427943
$370$	1.00164e22	1.48251
$371$	8.16382e21	1.18091
$372$	1.08882e22	1.53936
$373$	1.72627e20	0.0238553	0.0119276	−	0.999929i	$-0.496203\pi$
$373$	1.72627e20	0.0238553	0.0119276	+	0.999929i	$0.496203\pi$
$374$	−1.36395e22	−1.84242
$375$	3.91066e20	0.0516398
$376$	−9.35463e20	−0.120762
$377$	−5.06571e20	−0.0639350
$378$	−5.12906e21	−0.632932
$379$	−2.57296e21	−0.310455	−0.155228	−	0.987879i	$-0.549611\pi$
$379$	−2.57296e21	−0.310455	−0.155228	+	0.987879i	$0.549611\pi$
$380$	−2.04654e21	−0.241468
$381$	−2.78365e21	−0.321183
$382$	−1.26719e22	−1.42989
$383$	1.66889e21	0.184178	0.0920890	−	0.995751i	$-0.470646\pi$
$383$	1.66889e21	0.184178	0.0920890	+	0.995751i	$0.470646\pi$
$384$	6.81460e20	0.0735572
$385$	1.07522e22	1.13522
$386$	1.72818e21	0.178483
$387$	−2.51309e21	−0.253901
$388$	−3.38102e22	−3.34178
$389$	5.43023e21	0.525106	0.262553	−	0.964918i	$-0.415436\pi$
$389$	5.43023e21	0.525106	0.262553	+	0.964918i	$0.415436\pi$
$390$	1.80179e21	0.170473
$391$	1.18603e22	1.09797
$392$	−6.29865e22	−5.70579
$393$	6.65601e21	0.590034
$394$	1.73037e22	1.50114
$395$	−7.94746e20	−0.0674766
$396$	1.39423e22	1.15858
$397$	−1.04340e22	−0.848659	−0.424330	−	0.905508i	$-0.639490\pi$
$397$	−1.04340e22	−0.848659	−0.424330	+	0.905508i	$0.639490\pi$
$398$	−3.38590e21	−0.269568
$399$	2.92127e21	0.227668
$400$	6.49899e21	0.495833
$401$	−1.07284e22	−0.801326	−0.400663	−	0.916225i	$-0.631220\pi$
$401$	−1.07284e22	−0.801326	−0.400663	+	0.916225i	$0.631220\pi$
$402$	5.26367e21	0.384917
$403$	5.45979e21	0.390915
$404$	2.02831e22	1.42198
$405$	−7.23836e20	−0.0496904
$406$	8.77536e21	0.589921
$407$	3.88652e22	2.55864
$408$	1.65146e22	1.06477
$409$	−3.09142e22	−1.95213	−0.976066	−	0.217474i	$-0.930218\pi$
$409$	−3.09142e22	−1.95213	−0.976066	+	0.217474i	$0.930218\pi$
$410$	−1.71950e22	−1.06350
$411$	1.05580e22	0.639628
$412$	−1.19944e22	−0.711791
$413$	9.32621e21	0.542163
$414$	−1.71105e22	−0.974450
$415$	4.62279e21	0.257926
$416$	1.26585e22	0.691971
$417$	9.01363e21	0.482773
$418$	−1.12072e22	−0.588166
$419$	−1.50465e22	−0.773780	−0.386890	−	0.922126i	$-0.626451\pi$
$419$	−1.50465e22	−0.773780	−0.386890	+	0.922126i	$0.626451\pi$
$420$	−2.21156e22	−1.11450
$421$	−2.30163e22	−1.13668	−0.568339	−	0.822795i	$-0.692414\pi$
$421$	−2.30163e22	−1.13668	−0.568339	+	0.822795i	$0.692414\pi$
$422$	−3.27864e22	−1.58686
$423$	3.20120e20	0.0151852
$424$	3.79220e22	1.76312
$425$	3.05326e21	0.139142
$426$	2.38586e22	1.06577
$427$	6.58695e22	2.88435
$428$	6.29662e22	2.70293
$429$	6.99123e21	0.294216
$430$	−1.52932e22	−0.630983
$431$	1.28296e22	0.518985	0.259493	−	0.965745i	$-0.416445\pi$
$431$	1.28296e22	0.518985	0.259493	+	0.965745i	$0.416445\pi$
$432$	−1.20292e22	−0.477116
$433$	7.37153e21	0.286689	0.143344	−	0.989673i	$-0.454214\pi$
$433$	7.37153e21	0.286689	0.143344	+	0.989673i	$0.454214\pi$
$434$	−9.45802e22	−3.60693
$435$	1.23842e21	0.0463136
$436$	6.83414e22	2.50639
$437$	9.74532e21	0.350513
$438$	−2.57276e22	−0.907547
$439$	3.49450e22	1.20903	0.604514	−	0.796595i	$-0.293367\pi$
$439$	3.49450e22	1.20903	0.604514	+	0.796595i	$0.293367\pi$
$440$	4.99452e22	1.69491
$441$	2.15543e22	0.717473
$442$	1.40676e22	0.459335
$443$	−3.18362e22	−1.01974	−0.509870	−	0.860251i	$-0.670307\pi$
$443$	−3.18362e22	−1.01974	−0.509870	+	0.860251i	$0.670307\pi$
$444$	−7.99400e22	−2.51194
$445$	9.49885e21	0.292827
$446$	−4.04828e21	−0.122440
$447$	2.36079e22	0.700558
$448$	−6.81047e22	−1.98296
$449$	−1.60496e22	−0.458532	−0.229266	−	0.973364i	$-0.573633\pi$
$449$	−1.60496e22	−0.458532	−0.229266	+	0.973364i	$0.573633\pi$
$450$	−4.40486e21	−0.123488
$451$	−6.67192e22	−1.83548
$452$	1.04936e23	2.83300
$453$	−1.20107e22	−0.318225
$454$	1.24227e23	3.23028
$455$	−1.10897e22	−0.283023
$456$	1.35697e22	0.339913
$457$	−6.60625e22	−1.62430	−0.812152	−	0.583446i	$-0.801704\pi$
$457$	−6.60625e22	−1.62430	−0.812152	+	0.583446i	$0.801704\pi$
$458$	−7.23815e22	−1.74691
$459$	−5.65138e21	−0.133890
$460$	−7.37775e22	−1.71586
$461$	2.90192e22	0.662563	0.331282	−	0.943532i	$-0.392519\pi$
$461$	2.90192e22	0.662563	0.331282	+	0.943532i	$0.392519\pi$
$462$	−1.21109e23	−2.71470
$463$	−8.02536e22	−1.76614	−0.883072	−	0.469237i	$-0.844529\pi$
$463$	−8.02536e22	−1.76614	−0.883072	+	0.469237i	$0.844529\pi$
$464$	2.05808e22	0.444693
$465$	−1.33476e22	−0.283174
$466$	8.09337e22	1.68597
$467$	−3.77237e22	−0.771651	−0.385826	−	0.922572i	$-0.626083\pi$
$467$	−3.77237e22	−0.771651	−0.385826	+	0.922572i	$0.626083\pi$
$468$	−1.43799e22	−0.288846
$469$	−3.23968e22	−0.639047
$470$	1.94807e21	0.0377375
$471$	−1.33802e22	−0.254558
$472$	4.33215e22	0.809462
$473$	−5.93401e22	−1.08900
$474$	8.95180e21	0.161359
$475$	2.50880e21	0.0444192
$476$	−1.72669e23	−3.00299
$477$	−1.29771e22	−0.221703
$478$	−7.47881e22	−1.25515
$479$	6.60372e21	0.108877	0.0544385	−	0.998517i	$-0.482663\pi$
$479$	6.60372e21	0.108877	0.0544385	+	0.998517i	$0.482663\pi$
$480$	−3.09463e22	−0.501254
$481$	−4.00851e22	−0.637896
$482$	1.27299e23	1.99033
$483$	1.05311e23	1.61780
$484$	1.68151e23	2.53813
$485$	4.14471e22	0.614737
$486$	8.15309e21	0.118827
$487$	−5.47261e22	−0.783788	−0.391894	−	0.920010i	$-0.628180\pi$
$487$	−5.47261e22	−0.783788	−0.391894	+	0.920010i	$0.628180\pi$
$488$	3.05973e23	4.30640
$489$	8.26801e22	1.14360
$490$	1.31167e23	1.78303
$491$	8.78896e22	1.17421	0.587103	−	0.809512i	$-0.300268\pi$
$491$	8.78896e22	1.17421	0.587103	+	0.809512i	$0.300268\pi$
$492$	1.37231e23	1.80198
$493$	9.66901e21	0.124791
$494$	1.15590e22	0.146636
$495$	−1.70915e22	−0.213126
$496$	−2.21819e23	−2.71897
$497$	−1.46845e23	−1.76941
$498$	−5.20698e22	−0.616789
$499$	5.68475e22	0.661998	0.330999	−	0.943631i	$-0.392614\pi$
$499$	5.68475e22	0.661998	0.330999	+	0.943631i	$0.392614\pi$
$500$	−1.89930e22	−0.217445
$501$	−6.20871e22	−0.698845
$502$	9.89556e22	1.09511
$503$	−9.35523e22	−1.01795	−0.508975	−	0.860781i	$-0.669976\pi$
$503$	−9.35523e22	−1.01795	−0.508975	+	0.860781i	$0.669976\pi$
$504$	1.46639e23	1.56888
$505$	−2.48646e22	−0.261580
$506$	−4.04020e23	−4.17949
$507$	4.95447e22	0.503999
$508$	1.35194e23	1.35244
$509$	−1.72895e23	−1.70091	−0.850454	−	0.526050i	$-0.823673\pi$
$509$	−1.72895e23	−1.70091	−0.850454	+	0.526050i	$0.823673\pi$
$510$	−3.43911e22	−0.332736
$511$	1.58348e23	1.50673
$512$	1.87960e23	1.75902
$513$	−4.64361e21	−0.0427424
$514$	−3.94793e23	−3.57423
$515$	1.47037e22	0.130937
$516$	1.22054e23	1.06913
$517$	7.55882e21	0.0651305
$518$	6.94397e23	5.88579
$519$	3.31956e22	0.276795
$520$	−5.15129e22	−0.422559
$521$	−1.19149e23	−0.961542	−0.480771	−	0.876846i	$-0.659643\pi$
$521$	−1.19149e23	−0.961542	−0.480771	+	0.876846i	$0.659643\pi$
$522$	−1.39492e22	−0.110752
$523$	1.24654e22	0.0973735	0.0486868	−	0.998814i	$-0.484496\pi$
$523$	1.24654e22	0.0973735	0.0486868	+	0.998814i	$0.484496\pi$
$524$	−3.23264e23	−2.48452
$525$	2.71110e22	0.205018
$526$	1.70144e23	1.26601
$527$	−1.04212e23	−0.763004
$528$	−2.84038e23	−2.04639
$529$	2.10268e23	1.49073
$530$	−7.89714e22	−0.550966
$531$	−1.48248e22	−0.101786
$532$	−1.41878e23	−0.958663
$533$	6.88134e22	0.457606
$534$	−1.06992e23	−0.700248
$535$	−7.71887e22	−0.497218
$536$	−1.50487e23	−0.954112
$537$	−9.11554e21	−0.0568854
$538$	2.37899e23	1.46132
$539$	5.08949e23	3.07730
$540$	3.51547e22	0.209236
$541$	−7.61271e22	−0.446028	−0.223014	−	0.974815i	$-0.571590\pi$
$541$	−7.61271e22	−0.446028	−0.223014	+	0.974815i	$0.571590\pi$
$542$	−4.16202e23	−2.40054
$543$	−4.30692e22	−0.244550
$544$	−2.41614e23	−1.35062
$545$	−8.37780e22	−0.461063
$546$	1.24911e23	0.676804
$547$	−1.74228e23	−0.929447	−0.464723	−	0.885456i	$-0.653846\pi$
$547$	−1.74228e23	−0.929447	−0.464723	+	0.885456i	$0.653846\pi$
$548$	−5.12775e23	−2.69335
$549$	−1.04705e23	−0.541507
$550$	−1.04009e23	−0.529651
$551$	7.94481e21	0.0398378
$552$	4.89186e23	2.41541
$553$	−5.50965e22	−0.267892
$554$	3.60724e23	1.72720
$555$	9.79965e22	0.462083
$556$	−4.37767e23	−2.03286
$557$	4.06323e22	0.185824	0.0929122	−	0.995674i	$-0.470382\pi$
$557$	4.06323e22	0.185824	0.0929122	+	0.995674i	$0.470382\pi$
$558$	1.50344e23	0.677164
$559$	6.12027e22	0.271500
$560$	4.50548e23	1.96853
$561$	−1.33443e23	−0.574263
$562$	5.63882e23	2.39017
$563$	3.27464e23	1.36723	0.683615	−	0.729843i	$-0.260407\pi$
$563$	3.27464e23	1.36723	0.683615	+	0.729843i	$0.260407\pi$
$564$	−1.55474e22	−0.0639417
$565$	−1.28638e23	−0.521143
$566$	3.01469e23	1.20310
$567$	−5.01806e22	−0.197278
$568$	−6.82112e23	−2.64177
$569$	3.74009e23	1.42701	0.713506	−	0.700649i	$-0.247106\pi$
$569$	3.74009e23	1.42701	0.713506	+	0.700649i	$0.247106\pi$
$570$	−2.82584e22	−0.106221
$571$	2.13597e23	0.791021	0.395511	−	0.918461i	$-0.370568\pi$
$571$	2.13597e23	0.791021	0.395511	+	0.918461i	$0.370568\pi$
$572$	−3.39545e23	−1.23888
$573$	−1.23976e23	−0.445682
$574$	−1.19206e24	−4.22227
$575$	9.04420e22	0.315641
$576$	1.08258e23	0.372281
$577$	8.63899e22	0.292731	0.146366	−	0.989231i	$-0.453242\pi$
$577$	8.63899e22	0.292731	0.146366	+	0.989231i	$0.453242\pi$
$578$	2.86248e23	0.955775
$579$	1.69078e22	0.0556313
$580$	−6.01466e22	−0.195017
$581$	3.20479e23	1.02400
$582$	−4.66848e23	−1.47004
$583$	−3.06421e23	−0.950902
$584$	7.35547e23	2.24958
$585$	1.76280e22	0.0531347
$586$	5.52841e23	1.64237
$587$	1.46869e23	0.430037	0.215018	−	0.976610i	$-0.431019\pi$
$587$	1.46869e23	0.430037	0.215018	+	0.976610i	$0.431019\pi$
$588$	−1.04683e24	−3.02114
$589$	−8.56286e22	−0.243578
$590$	−9.02156e22	−0.252953
$591$	1.69292e23	0.467890
$592$	1.62857e24	4.43682
$593$	−6.72164e23	−1.80514	−0.902569	−	0.430545i	$-0.858321\pi$
$593$	−6.72164e23	−1.80514	−0.902569	+	0.430545i	$0.858321\pi$
$594$	1.92514e23	0.509657
$595$	2.11670e23	0.552415
$596$	−1.14657e24	−2.94991
$597$	−3.31262e22	−0.0840214
$598$	4.16701e23	1.04199
$599$	−2.15383e23	−0.530986	−0.265493	−	0.964113i	$-0.585535\pi$
$599$	−2.15383e23	−0.530986	−0.265493	+	0.964113i	$0.585535\pi$
$600$	1.25934e23	0.306096
$601$	−3.86809e23	−0.926964	−0.463482	−	0.886106i	$-0.653400\pi$
$601$	−3.86809e23	−0.926964	−0.463482	+	0.886106i	$0.653400\pi$
$602$	−1.06022e24	−2.50510
$603$	5.14976e22	0.119975
$604$	5.83328e23	1.33998
$605$	−2.06132e23	−0.466901
$606$	2.80068e23	0.625527
$607$	−5.57542e23	−1.22793	−0.613965	−	0.789333i	$-0.710426\pi$
$607$	−5.57542e23	−1.22793	−0.613965	+	0.789333i	$0.710426\pi$
$608$	−1.98529e23	−0.431166
$609$	8.58545e22	0.183872
$610$	−6.37179e23	−1.34573
$611$	−7.79607e21	−0.0162377
$612$	2.74472e23	0.563782
$613$	3.77874e23	0.765478	0.382739	−	0.923857i	$-0.374981\pi$
$613$	3.77874e23	0.765478	0.382739	+	0.923857i	$0.374981\pi$
$614$	−1.38149e23	−0.276004
$615$	−1.68229e23	−0.331483
$616$	3.46250e24	6.72904
$617$	−2.68278e23	−0.514235	−0.257118	−	0.966380i	$-0.582773\pi$
$617$	−2.68278e23	−0.514235	−0.257118	+	0.966380i	$0.582773\pi$
$618$	−1.65618e23	−0.313116
$619$	3.02103e23	0.563358	0.281679	−	0.959509i	$-0.409109\pi$
$619$	3.02103e23	0.563358	0.281679	+	0.959509i	$0.409109\pi$
$620$	6.48256e23	1.19239
$621$	−1.67402e23	−0.303726
$622$	−6.52637e23	−1.16803
$623$	6.58516e23	1.16257
$624$	2.92953e23	0.510187
$625$	2.32831e22	0.0400000
$626$	1.11311e24	1.88650
$627$	−1.09647e23	−0.183325
$628$	6.49842e23	1.07189
$629$	7.65112e23	1.24507
$630$	−3.05371e23	−0.490267
$631$	4.97599e23	0.788189	0.394094	−	0.919070i	$-0.371058\pi$
$631$	4.97599e23	0.788189	0.394094	+	0.919070i	$0.371058\pi$
$632$	−2.55930e23	−0.399969
$633$	−3.20769e23	−0.494607
$634$	−2.06560e24	−3.14259
$635$	−1.65732e23	−0.248787
$636$	6.30263e23	0.933547
$637$	−5.24924e23	−0.767205
$638$	−3.29375e23	−0.475023
$639$	2.33422e23	0.332189
$640$	4.05724e22	0.0569772
$641$	2.45883e23	0.340750	0.170375	−	0.985379i	$-0.445502\pi$
$641$	2.45883e23	0.340750	0.170375	+	0.985379i	$0.445502\pi$
$642$	8.69432e23	1.18902
$643$	1.29703e24	1.75048	0.875239	−	0.483691i	$-0.160704\pi$
$643$	1.29703e24	1.75048	0.875239	+	0.483691i	$0.160704\pi$
$644$	−5.11469e24	−6.81223
$645$	−1.49623e23	−0.196671
$646$	−2.20629e23	−0.286211
$647$	6.72178e23	0.860593	0.430297	−	0.902688i	$-0.358409\pi$
$647$	6.72178e23	0.860593	0.430297	+	0.902688i	$0.358409\pi$
$648$	−2.33095e23	−0.294541
$649$	−3.50050e23	−0.436567
$650$	1.07274e23	0.132048
$651$	−9.25333e23	−1.12424
$652$	−4.01555e24	−4.81548
$653$	−9.05901e23	−1.07231	−0.536153	−	0.844121i	$-0.680123\pi$
$653$	−9.05901e23	−1.07231	−0.536153	+	0.844121i	$0.680123\pi$
$654$	9.43653e23	1.10256
$655$	3.96282e23	0.457039
$656$	−2.79573e24	−3.18283
$657$	−2.51708e23	−0.282873
$658$	1.35052e23	0.149824
$659$	9.59082e23	1.05034	0.525170	−	0.850997i	$-0.324002\pi$
$659$	9.59082e23	1.05034	0.525170	+	0.850997i	$0.324002\pi$
$660$	8.30089e23	0.897431
$661$	−9.10262e23	−0.971525	−0.485762	−	0.874091i	$-0.661458\pi$
$661$	−9.10262e23	−0.971525	−0.485762	+	0.874091i	$0.661458\pi$
$662$	2.47311e24	2.60585
$663$	1.37631e23	0.143170
$664$	1.48867e24	1.52886
$665$	1.73925e23	0.176351
$666$	−1.10381e24	−1.10500
$667$	2.86410e23	0.283086
$668$	3.01540e24	2.94270
$669$	−3.96067e22	−0.0381633
$670$	3.13385e23	0.298155
$671$	−2.47235e24	−2.32257
$672$	−2.14538e24	−1.99006
$673$	−8.50468e23	−0.778987	−0.389493	−	0.921029i	$-0.627350\pi$
$673$	−8.50468e23	−0.778987	−0.389493	+	0.921029i	$0.627350\pi$
$674$	−1.38228e23	−0.125022
$675$	−4.30953e22	−0.0384900
$676$	−2.40625e24	−2.12224
$677$	4.30263e23	0.374741	0.187370	−	0.982289i	$-0.440004\pi$
$677$	4.30263e23	0.374741	0.187370	+	0.982289i	$0.440004\pi$
$678$	1.44894e24	1.24623
$679$	2.87335e24	2.44060
$680$	9.83236e23	0.824768
$681$	1.21538e24	1.00684
$682$	3.54998e24	2.90441
$683$	−1.92309e23	−0.155390	−0.0776950	−	0.996977i	$-0.524756\pi$
$683$	−1.92309e23	−0.155390	−0.0776950	+	0.996977i	$0.524756\pi$
$684$	2.25528e23	0.179979
$685$	6.28598e23	0.495454
$686$	4.86861e24	3.79009
$687$	−7.08151e23	−0.544495
$688$	−2.48653e24	−1.88839
$689$	3.16039e23	0.237070
$690$	−1.01871e24	−0.754805
$691$	9.14440e23	0.669255	0.334627	−	0.942350i	$-0.391390\pi$
$691$	9.14440e23	0.669255	0.334627	+	0.942350i	$0.391390\pi$
$692$	−1.61222e24	−1.16553
$693$	−1.18488e24	−0.846143
$694$	−9.77051e23	−0.689226
$695$	5.36648e23	0.373954
$696$	3.98805e23	0.274525
$697$	−1.31345e24	−0.893174
$698$	4.12549e24	2.77143
$699$	7.91822e23	0.525499
$700$	−1.31671e24	−0.863288
$701$	−1.18189e24	−0.765548	−0.382774	−	0.923842i	$-0.625031\pi$
$701$	−1.18189e24	−0.765548	−0.382774	+	0.923842i	$0.625031\pi$
$702$	−1.98557e23	−0.127063
$703$	6.28675e23	0.397472
$704$	2.55624e24	1.59674
$705$	1.90591e22	0.0117624
$706$	−2.71949e24	−1.65824
$707$	−1.72376e24	−1.03851
$708$	7.20002e23	0.428599
$709$	3.06841e23	0.180476	0.0902381	−	0.995920i	$-0.471237\pi$
$709$	3.06841e23	0.180476	0.0902381	+	0.995920i	$0.471237\pi$
$710$	1.42048e24	0.825541
$711$	8.75807e22	0.0502941
$712$	3.05889e24	1.73574
$713$	−3.08690e24	−1.73086
$714$	−2.38420e24	−1.32101
$715$	4.16240e23	0.227899
$716$	4.42717e23	0.239533
$717$	−7.31695e23	−0.391217
$718$	−1.54284e24	−0.815197
$719$	1.71139e24	0.893621	0.446811	−	0.894629i	$-0.352560\pi$
$719$	1.71139e24	0.893621	0.446811	+	0.894629i	$0.352560\pi$
$720$	−7.16186e23	−0.369572
$721$	1.01934e24	0.519841
$722$	3.49393e24	1.76096
$723$	1.24544e24	0.620366
$724$	2.09175e24	1.02975
$725$	7.37323e22	0.0358744
$726$	2.32182e24	1.11652
$727$	1.28685e24	0.611623	0.305812	−	0.952092i	$-0.401072\pi$
$727$	1.28685e24	0.611623	0.305812	+	0.952092i	$0.401072\pi$
$728$	−3.57118e24	−1.67763
$729$	7.97664e22	0.0370370
$730$	−1.53175e24	−0.702983
$731$	−1.16819e24	−0.529925
$732$	5.08526e24	2.28018
$733$	−3.55442e24	−1.57538	−0.787690	−	0.616072i	$-0.788723\pi$
$733$	−3.55442e24	−1.57538	−0.787690	+	0.616072i	$0.788723\pi$
$734$	−2.63255e24	−1.15335
$735$	1.28329e24	0.555753
$736$	−7.15696e24	−3.06385
$737$	1.21598e24	0.514581
$738$	1.89488e24	0.792689
$739$	−3.45741e24	−1.42979	−0.714895	−	0.699231i	$-0.753526\pi$
$739$	−3.45741e24	−1.42979	−0.714895	+	0.699231i	$0.753526\pi$
$740$	−4.75942e24	−1.94574
$741$	1.13089e23	0.0457050
$742$	−5.47476e24	−2.18742
$743$	1.33858e24	0.528737	0.264369	−	0.964422i	$-0.414836\pi$
$743$	1.33858e24	0.528737	0.264369	+	0.964422i	$0.414836\pi$
$744$	−4.29829e24	−1.67852
$745$	1.40556e24	0.542650
$746$	−1.15766e23	−0.0441877
$747$	−5.09429e23	−0.192247
$748$	6.48095e24	2.41810
$749$	−5.35117e24	−1.97403
$750$	−2.62254e23	−0.0956536
$751$	1.02936e24	0.371217	0.185609	−	0.982624i	$-0.440574\pi$
$751$	1.02936e24	0.371217	0.185609	+	0.982624i	$0.440574\pi$
$752$	3.16737e23	0.112940
$753$	9.68141e23	0.341335
$754$	3.39713e23	0.118428
$755$	−7.15087e23	−0.246496
$756$	2.43713e24	0.830699
$757$	2.63626e24	0.888531	0.444265	−	0.895895i	$-0.353465\pi$
$757$	2.63626e24	0.888531	0.444265	+	0.895895i	$0.353465\pi$
$758$	1.72546e24	0.575064
$759$	−3.95276e24	−1.30270
$760$	8.07903e23	0.263296
$761$	−6.77132e23	−0.218225	−0.109112	−	0.994029i	$-0.534801\pi$
$761$	−6.77132e23	−0.218225	−0.109112	+	0.994029i	$0.534801\pi$
$762$	1.86675e24	0.594935
$763$	−5.80799e24	−1.83049
$764$	6.02119e24	1.87667
$765$	−3.36469e23	−0.103710
$766$	−1.11918e24	−0.341157
$767$	3.61038e23	0.108841
$768$	1.70573e24	0.508558
$769$	2.15350e24	0.634996	0.317498	−	0.948259i	$-0.397157\pi$
$769$	2.15350e24	0.634996	0.317498	+	0.948259i	$0.397157\pi$
$770$	−7.21054e24	−2.10279
$771$	−3.86249e24	−1.11405
$772$	−8.21166e23	−0.234252
$773$	−8.52370e23	−0.240493	−0.120246	−	0.992744i	$-0.538368\pi$
$773$	−8.52370e23	−0.240493	−0.120246	+	0.992744i	$0.538368\pi$
$774$	1.68531e24	0.470307
$775$	−7.94681e23	−0.219345
$776$	1.33471e25	3.64387
$777$	6.79369e24	1.83454
$778$	−3.64158e24	−0.972666
$779$	−1.07924e24	−0.285133
$780$	−8.56144e23	−0.223739
$781$	5.51167e24	1.42478
$782$	−7.95365e24	−2.03380
$783$	−1.36473e23	−0.0345201
$784$	2.13265e25	5.33621
$785$	−7.96625e23	−0.197180
$786$	−4.46361e24	−1.09294
$787$	5.38452e24	1.30425	0.652126	−	0.758110i	$-0.273877\pi$
$787$	5.38452e24	1.30425	0.652126	+	0.758110i	$0.273877\pi$
$788$	−8.22207e24	−1.97019
$789$	1.66462e24	0.394603
$790$	5.32967e23	0.124989
$791$	−8.91794e24	−2.06902
$792$	−5.50395e24	−1.26331
$793$	2.54995e24	0.579042
$794$	6.99721e24	1.57199
$795$	−7.72624e23	−0.171730
$796$	1.60885e24	0.353797
$797$	1.12702e24	0.245208	0.122604	−	0.992456i	$-0.460876\pi$
$797$	1.12702e24	0.245208	0.122604	+	0.992456i	$0.460876\pi$
$798$	−1.95904e24	−0.421715
$799$	1.48805e23	0.0316935
$800$	−1.84246e24	−0.388270
$801$	−1.04677e24	−0.218260
$802$	7.19463e24	1.48432
$803$	−5.94344e24	−1.21326
$804$	−2.50109e24	−0.505189
$805$	6.26997e24	1.25314
$806$	−3.66140e24	−0.724102
$807$	2.32751e24	0.455477
$808$	−8.00709e24	−1.55052
$809$	−1.34479e24	−0.257686	−0.128843	−	0.991665i	$-0.541126\pi$
$809$	−1.34479e24	−0.257686	−0.128843	+	0.991665i	$0.541126\pi$
$810$	4.85414e23	0.0920427
$811$	4.40358e24	0.826283	0.413141	−	0.910667i	$-0.364432\pi$
$811$	4.40358e24	0.826283	0.413141	+	0.910667i	$0.364432\pi$
$812$	−4.16972e24	−0.774248
$813$	−4.07194e24	−0.748225
$814$	−2.60635e25	−4.73942
$815$	4.92256e24	0.885832
$816$	−5.59165e24	−0.995803
$817$	−9.59872e23	−0.169171
$818$	2.07314e25	3.61598
$819$	1.22208e24	0.210953
$820$	8.17041e24	1.39581
$821$	1.72971e24	0.292453	0.146227	−	0.989251i	$-0.453287\pi$
$821$	1.72971e24	0.292453	0.146227	+	0.989251i	$0.453287\pi$
$822$	−7.08036e24	−1.18480
$823$	−1.17051e25	−1.93855	−0.969274	−	0.245986i	$-0.920888\pi$
$823$	−1.17051e25	−1.93855	−0.969274	+	0.245986i	$0.920888\pi$
$824$	4.73499e24	0.776135
$825$	−1.01759e24	−0.165087
$826$	−6.25428e24	−1.00426
$827$	6.19900e24	0.985202	0.492601	−	0.870255i	$-0.336046\pi$
$827$	6.19900e24	0.985202	0.492601	+	0.870255i	$0.336046\pi$
$828$	8.13025e24	1.27893
$829$	5.61442e24	0.874161	0.437081	−	0.899422i	$-0.356012\pi$
$829$	5.61442e24	0.874161	0.437081	+	0.899422i	$0.356012\pi$
$830$	−3.10010e24	−0.477762
$831$	3.52918e24	0.538350
$832$	−2.63648e24	−0.398085
$833$	1.00193e25	1.49746
$834$	−6.04465e24	−0.894252
$835$	−3.69651e24	−0.541323
$836$	5.32525e24	0.771946
$837$	1.47090e24	0.211065
$838$	1.00904e25	1.43329
$839$	8.30559e24	1.16787	0.583934	−	0.811801i	$-0.301513\pi$
$839$	8.30559e24	1.16787	0.583934	+	0.811801i	$0.301513\pi$
$840$	8.73049e24	1.21525
$841$	−7.02365e24	−0.967826
$842$	1.54350e25	2.10550
$843$	5.51679e24	0.744993
$844$	1.55789e25	2.08269
$845$	2.94976e24	0.390396
$846$	−2.14677e23	−0.0281279
$847$	−1.42903e25	−1.85367
$848$	−1.28400e25	−1.64892
$849$	2.94945e24	0.374995
$850$	−2.04756e24	−0.257736
$851$	2.26637e25	2.82442
$852$	−1.13367e25	−1.39878
$853$	9.95169e24	1.21571	0.607855	−	0.794048i	$-0.292030\pi$
$853$	9.95169e24	1.21571	0.607855	+	0.794048i	$0.292030\pi$
$854$	−4.41730e25	−5.34275
$855$	−2.76469e23	−0.0331081
$856$	−2.48569e25	−2.94727
$857$	2.47493e24	0.290553	0.145276	−	0.989391i	$-0.453593\pi$
$857$	2.47493e24	0.290553	0.145276	+	0.989391i	$0.453593\pi$
$858$	−4.68841e24	−0.544984
$859$	3.92176e24	0.451377	0.225689	−	0.974200i	$-0.427537\pi$
$859$	3.92176e24	0.451377	0.225689	+	0.974200i	$0.427537\pi$
$860$	7.26676e24	0.828141
$861$	−1.16626e25	−1.31604
$862$	−8.60367e24	−0.961329
$863$	−1.05637e25	−1.16876	−0.584381	−	0.811480i	$-0.698663\pi$
$863$	−1.05637e25	−1.16876	−0.584381	+	0.811480i	$0.698663\pi$
$864$	3.41027e24	0.373613
$865$	1.97638e24	0.214404
$866$	−4.94344e24	−0.531040
$867$	2.80053e24	0.297905
$868$	4.49409e25	4.73395
$869$	2.06799e24	0.215715
$870$	−8.30500e23	−0.0857879
$871$	−1.25415e24	−0.128291
$872$	−2.69789e25	−2.73296
$873$	−4.56745e24	−0.458198
$874$	−6.53534e24	−0.649263
$875$	1.61412e24	0.158806
$876$	1.22248e25	1.19112
$877$	−8.71589e23	−0.0841037	−0.0420518	−	0.999115i	$-0.513389\pi$
$877$	−8.71589e23	−0.0841037	−0.0420518	+	0.999115i	$0.513389\pi$
$878$	−2.34346e25	−2.23951
$879$	5.40876e24	0.511909
$880$	−1.69109e25	−1.58513
$881$	3.51372e24	0.326191	0.163096	−	0.986610i	$-0.447852\pi$
$881$	3.51372e24	0.326191	0.163096	+	0.986610i	$0.447852\pi$
$882$	−1.44546e25	−1.32899
$883$	1.29043e25	1.17508	0.587540	−	0.809195i	$-0.300096\pi$
$883$	1.29043e25	1.17508	0.587540	+	0.809195i	$0.300096\pi$
$884$	−6.68438e24	−0.602860
$885$	−8.82633e23	−0.0788428
$886$	2.13498e25	1.88889
$887$	−3.42654e24	−0.300265	−0.150133	−	0.988666i	$-0.547970\pi$
$887$	−3.42654e24	−0.300265	−0.150133	+	0.988666i	$0.547970\pi$
$888$	3.15576e25	2.73901
$889$	−1.14895e25	−0.987724
$890$	−6.37005e24	−0.542410
$891$	1.88348e24	0.158855
$892$	1.92359e24	0.160698
$893$	1.22270e23	0.0101177
$894$	−1.58318e25	−1.29766
$895$	−5.42716e23	−0.0440632
$896$	2.81272e24	0.226208
$897$	4.07683e24	0.324779
$898$	1.07630e25	0.849349
$899$	−2.51658e24	−0.196722
$900$	2.09302e24	0.162074
$901$	−6.03229e24	−0.462724
$902$	4.47428e25	3.39991
$903$	−1.03727e25	−0.780813
$904$	−4.14250e25	−3.08909
$905$	−2.56423e24	−0.189428
$906$	8.05454e24	0.589456
$907$	−1.11742e25	−0.810126	−0.405063	−	0.914289i	$-0.632750\pi$
$907$	−1.11742e25	−0.810126	−0.405063	+	0.914289i	$0.632750\pi$
$908$	−5.90277e25	−4.23961
$909$	2.74007e24	0.194970
$910$	7.43687e24	0.524250
$911$	−2.26295e25	−1.58041	−0.790204	−	0.612843i	$-0.790026\pi$
$911$	−2.26295e25	−1.58041	−0.790204	+	0.612843i	$0.790026\pi$
$912$	−4.59453e24	−0.317896
$913$	−1.20289e25	−0.824561
$914$	4.43024e25	3.00874
$915$	−6.23389e24	−0.419450
$916$	3.43930e25	2.29276
$917$	2.74726e25	1.81451
$918$	3.78989e24	0.248007
$919$	−2.06020e25	−1.33576	−0.667879	−	0.744270i	$-0.732798\pi$
$919$	−2.06020e25	−1.33576	−0.667879	+	0.744270i	$0.732798\pi$
$920$	2.91248e25	1.87097
$921$	−1.35159e24	−0.0860276
$922$	−1.94606e25	−1.22728
$923$	−5.68467e24	−0.355215
$924$	5.75466e25	3.56294
$925$	5.83446e24	0.357928
$926$	5.38191e25	3.27147
$927$	−1.62034e24	−0.0975950
$928$	−5.83467e24	−0.348224
$929$	1.38098e25	0.816681	0.408341	−	0.912830i	$-0.366108\pi$
$929$	1.38098e25	0.816681	0.408341	+	0.912830i	$0.366108\pi$
$930$	8.95107e24	0.524529
$931$	8.23265e24	0.478043
$932$	−3.84566e25	−2.21277
$933$	−6.38513e24	−0.364063
$934$	2.52980e25	1.42935
$935$	−7.94484e24	−0.444822
$936$	5.67670e24	0.314957
$937$	−1.59511e25	−0.877011	−0.438506	−	0.898728i	$-0.644492\pi$
$937$	−1.59511e25	−0.877011	−0.438506	+	0.898728i	$0.644492\pi$
$938$	2.17257e25	1.18372
$939$	1.08902e25	0.588003
$940$	−9.25650e23	−0.0495291
$941$	−2.23853e25	−1.18700	−0.593500	−	0.804834i	$-0.702254\pi$
$941$	−2.23853e25	−1.18700	−0.593500	+	0.804834i	$0.702254\pi$
$942$	8.97296e24	0.471523
$943$	−3.89063e25	−2.02615
$944$	−1.46682e25	−0.757031
$945$	−2.98762e24	−0.152811
$946$	3.97942e25	2.01718
$947$	−2.89242e25	−1.45307	−0.726534	−	0.687130i	$-0.758870\pi$
$947$	−2.89242e25	−1.45307	−0.726534	+	0.687130i	$0.758870\pi$
$948$	−4.25356e24	−0.211778
$949$	6.12999e24	0.302480
$950$	−1.68243e24	−0.0822787
$951$	−2.02090e25	−0.979513
$952$	6.81637e25	3.27446
$953$	2.32682e25	1.10783	0.553915	−	0.832573i	$-0.313133\pi$
$953$	2.32682e25	1.10783	0.553915	+	0.832573i	$0.313133\pi$
$954$	8.70262e24	0.410666
$955$	−7.38123e24	−0.345223
$956$	3.55364e25	1.64733
$957$	−3.22246e24	−0.148060
$958$	−4.42854e24	−0.201676
$959$	4.35781e25	1.96703
$960$	6.44543e24	0.288368
$961$	4.57337e24	0.202809
$962$	2.68816e25	1.18159
$963$	8.50616e24	0.370604
$964$	−6.04877e25	−2.61224
$965$	1.00665e24	0.0430918
$966$	−7.06232e25	−2.99669
$967$	−3.76920e25	−1.58535	−0.792674	−	0.609646i	$-0.791311\pi$
$967$	−3.76920e25	−1.58535	−0.792674	+	0.609646i	$0.791311\pi$
$968$	−6.63803e25	−2.76757
$969$	−2.15854e24	−0.0892089
$970$	−2.77949e25	−1.13869
$971$	−1.07235e25	−0.435484	−0.217742	−	0.976006i	$-0.569869\pi$
$971$	−1.07235e25	−0.435484	−0.217742	+	0.976006i	$0.569869\pi$
$972$	−3.87404e24	−0.155955
$973$	3.72036e25	1.48466
$974$	3.67000e25	1.45183
$975$	1.04953e24	0.0411579
$976$	−1.03599e26	−4.02746
$977$	1.87551e25	0.722795	0.361398	−	0.932412i	$-0.382300\pi$
$977$	1.87551e25	0.722795	0.361398	+	0.932412i	$0.382300\pi$
$978$	−5.54463e25	−2.11833
$979$	−2.47168e25	−0.936135
$980$	−6.23257e25	−2.34016
$981$	9.23231e24	0.343656
$982$	−5.89399e25	−2.17501
$983$	−1.72208e24	−0.0630013	−0.0315006	−	0.999504i	$-0.510029\pi$
$983$	−1.72208e24	−0.0630013	−0.0315006	+	0.999504i	$0.510029\pi$
$984$	−5.41743e25	−1.96488
$985$	1.00792e25	0.362426
$986$	−6.48416e24	−0.231153
$987$	1.32129e24	0.0466985
$988$	−5.49240e24	−0.192455
$989$	−3.46033e25	−1.20212
$990$	1.14618e25	0.394779
$991$	5.69965e25	1.94636	0.973178	−	0.230053i	$-0.0738901\pi$
$991$	5.69965e25	1.94636	0.973178	+	0.230053i	$0.0738901\pi$
$992$	6.28856e25	2.12913
$993$	2.41958e25	0.812217
$994$	9.84759e25	3.27752
$995$	−1.97225e24	−0.0650827
$996$	2.47416e25	0.809512
$997$	1.93741e24	0.0628512	0.0314256	−	0.999506i	$-0.489995\pi$
$997$	1.93741e24	0.0628512	0.0314256	+	0.999506i	$0.489995\pi$
$998$	−3.81227e25	−1.22623
$999$	−1.07992e25	−0.344416

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.18.a.b.1.1	✓	3
3.2	odd	2		45.18.a.e.1.3		3
5.2	odd	4		75.18.b.d.49.1		6
5.3	odd	4		75.18.b.d.49.6		6
5.4	even	2		75.18.a.e.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.18.a.b.1.1	✓	3	1.1	even	1	trivial
45.18.a.e.1.3		3	3.2	odd	2
75.18.a.e.1.3		3	5.4	even	2
75.18.b.d.49.1		6	5.2	odd	4
75.18.b.d.49.6		6	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q-670.613 q^{2} -6561.00 q^{3} +318650. q^{4} -390625. q^{5} +4.39989e6 q^{6} -2.70804e7 q^{7} -1.25792e8 q^{8} +4.30467e7 q^{9} +2.61958e8 q^{10} +1.01644e9 q^{11} -2.09066e9 q^{12} -1.04834e9 q^{13} +1.81605e10 q^{14} +2.56289e9 q^{15} +4.25918e10 q^{16} +2.00099e10 q^{17} -2.88677e10 q^{18} +1.64417e10 q^{19} -1.24473e11 q^{20} +1.77675e11 q^{21} -6.81636e11 q^{22} +5.92721e11 q^{23} +8.25322e11 q^{24} +1.52588e11 q^{25} +7.03032e11 q^{26} -2.82430e11 q^{27} -8.62917e12 q^{28} +4.83212e11 q^{29} -1.71871e12 q^{30} -5.20802e12 q^{31} -1.20748e13 q^{32} -6.66885e12 q^{33} -1.34189e13 q^{34} +1.05783e13 q^{35} +1.37168e13 q^{36} +3.82367e13 q^{37} -1.10260e13 q^{38} +6.87817e12 q^{39} +4.91375e13 q^{40} -6.56402e13 q^{41} -1.19151e14 q^{42} -5.83804e13 q^{43} +3.23888e14 q^{44} -1.68151e13 q^{45} -3.97486e14 q^{46} +7.43658e12 q^{47} -2.79445e14 q^{48} +5.00719e14 q^{49} -1.02327e14 q^{50} -1.31285e14 q^{51} -3.34054e14 q^{52} -3.01466e14 q^{53} +1.89401e14 q^{54} -3.97046e14 q^{55} +3.40650e15 q^{56} -1.07874e14 q^{57} -3.24048e14 q^{58} -3.44389e14 q^{59} +8.16665e14 q^{60} -2.43237e15 q^{61} +3.49257e15 q^{62} -1.16572e15 q^{63} +2.51491e15 q^{64} +4.09508e14 q^{65} +4.47222e15 q^{66} +1.19632e15 q^{67} +6.37614e15 q^{68} -3.88884e15 q^{69} -7.09394e15 q^{70} +5.42254e15 q^{71} -5.41494e15 q^{72} -5.84732e15 q^{73} -2.56420e16 q^{74} -1.00113e15 q^{75} +5.23914e15 q^{76} -2.75256e16 q^{77} -4.61259e15 q^{78} +2.03455e15 q^{79} -1.66374e16 q^{80} +1.85302e15 q^{81} +4.40192e16 q^{82} -1.18343e16 q^{83} +5.66160e16 q^{84} -7.81636e15 q^{85} +3.91507e16 q^{86} -3.17035e15 q^{87} -1.27860e17 q^{88} -2.43170e16 q^{89} +1.12764e16 q^{90} +2.83895e16 q^{91} +1.88870e17 q^{92} +3.41698e16 q^{93} -4.98707e15 q^{94} -6.42253e15 q^{95} +7.92225e16 q^{96} -1.06105e17 q^{97} -3.35788e17 q^{98} +4.37543e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 442 q^{2} - 19683 q^{3} + 298148 q^{4} - 1171875 q^{5} + 2899962 q^{6} + 4962644 q^{7} - 108831912 q^{8} + 129140163 q^{9} + 172656250 q^{10} + 1049849720 q^{11} - 1956149028 q^{12} - 3091742090 q^{13}+ \cdots + 45\!\cdots\!20 q^{99}+O(q^{100}) \) 3 * q - 442 * q^2 - 19683 * q^3 + 298148 * q^4 - 1171875 * q^5 + 2899962 * q^6 + 4962644 * q^7 - 108831912 * q^8 + 129140163 * q^9 + 172656250 * q^10 + 1049849720 * q^11 - 1956149028 * q^12 - 3091742090 * q^13 + 27586028328 * q^14 + 7688671875 * q^15 + 22392797456 * q^16 - 15119940094 * q^17 - 19026650682 * q^18 - 111896117996 * q^19 - 116464062500 * q^20 - 32559907284 * q^21 - 693818341648 * q^22 + 784535528472 * q^23 + 714046174632 * q^24 + 457763671875 * q^25 - 1092511841044 * q^26 - 847288609443 * q^27 - 7640185610512 * q^28 + 1395352153678 * q^29 - 1132797656250 * q^30 - 12458197616536 * q^31 - 24074446195616 * q^32 - 6888064012920 * q^33 - 41046727271164 * q^34 - 1938532812500 * q^35 + 12834293772708 * q^36 + 32093748310134 * q^37 - 68757678664024 * q^38 + 20284919852490 * q^39 + 42512465625000 * q^40 - 102276917392466 * q^41 - 180991931860008 * q^42 - 141347515908644 * q^43 + 319886980653472 * q^44 - 50445376171875 * q^45 - 299722933931856 * q^46 - 54182226541768 * q^47 - 146919144108816 * q^48 + 702936204707227 * q^49 - 67443847656250 * q^50 + 99201926956734 * q^51 - 670193699134584 * q^52 + 345545322785582 * q^53 + 124833855124602 * q^54 - 410097546875000 * q^55 + 3014407093472160 * q^56 + 734150430171756 * q^57 + 2198630240496412 * q^58 + 2075534176494536 * q^59 + 764120714062500 * q^60 - 1591128188427998 * q^61 + 1555165628278608 * q^62 + 213625551690324 * q^63 + 4014461944704576 * q^64 + 1207711753906250 * q^65 + 4552142139552528 * q^66 - 2417737431711844 * q^67 + 1338181134241816 * q^68 - 5147337602304792 * q^69 - 10775792315625000 * q^70 + 5019485593673056 * q^71 - 4684856951760552 * q^72 - 10804161755859578 * q^73 - 12140475721796372 * q^74 - 3003387451171875 * q^75 - 3289783191661584 * q^76 - 27418121851422432 * q^77 + 7167970189089684 * q^78 - 40642131657181960 * q^79 - 8747186506250000 * q^80 + 5559060566555523 * q^81 + 15262994262855388 * q^82 - 21823256926416996 * q^83 + 50127257790569232 * q^84 + 5906226599218750 * q^85 + 8867591636371640 * q^86 - 9154905480281358 * q^87 - 125733265675831872 * q^88 - 2700230040372426 * q^89 + 7432285422656250 * q^90 - 46116457499478296 * q^91 + 204241599793288224 * q^92 + 81738234562092696 * q^93 - 72231791695517200 * q^94 + 43709421092187500 * q^95 + 157952441489436576 * q^96 - 79760576372788314 * q^97 - 128015343617626250 * q^98 + 45192587988768120 * q^99

Introduction

L-functions

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