LMFDB - Embedded newform 147.10.a.n.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,10,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	147.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:	$75.7102679161$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 3802 x^{8} + 19928 x^{7} + 4922742 x^{6} - 34016432 x^{5} - 2500007760 x^{4} + \cdots + 19340135623186 $ x^10 - 4x^9 - 3802x^8 + 19928x^7 + 4922742x^6 - 34016432x^5 - 2500007760x^4 + 24085389800x^3 + 391621066913x^2 - 5838350189836*x + 19340135623186
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2}\cdot 7^{10} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$13.8435$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.1866 q^{2} +81.0000 q^{3} -386.860 q^{4} -1768.41 q^{5} +906.115 q^{6} -10055.2 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+11.1866 q^{2} +81.0000 q^{3} -386.860 q^{4} -1768.41 q^{5} +906.115 q^{6} -10055.2 q^{8} +6561.00 q^{9} -19782.5 q^{10} -38206.7 q^{11} -31335.6 q^{12} -49330.3 q^{13} -143241. q^{15} +85588.8 q^{16} +197211. q^{17} +73395.3 q^{18} -895731. q^{19} +684128. q^{20} -427403. q^{22} -291324. q^{23} -814470. q^{24} +1.17416e6 q^{25} -551839. q^{26} +531441. q^{27} -5.89320e6 q^{29} -1.60238e6 q^{30} -329766. q^{31} +6.10571e6 q^{32} -3.09474e6 q^{33} +2.20612e6 q^{34} -2.53819e6 q^{36} +1.18461e7 q^{37} -1.00202e7 q^{38} -3.99576e6 q^{39} +1.77817e7 q^{40} +9.34523e6 q^{41} +3.61239e7 q^{43} +1.47806e7 q^{44} -1.16025e7 q^{45} -3.25893e6 q^{46} +1.00553e7 q^{47} +6.93269e6 q^{48} +1.31348e7 q^{50} +1.59741e7 q^{51} +1.90839e7 q^{52} +2.73666e7 q^{53} +5.94502e6 q^{54} +6.75652e7 q^{55} -7.25542e7 q^{57} -6.59249e7 q^{58} +1.33007e8 q^{59} +5.54143e7 q^{60} +1.39082e8 q^{61} -3.68896e6 q^{62} +2.44807e7 q^{64} +8.72363e7 q^{65} -3.46197e7 q^{66} -1.81486e8 q^{67} -7.62931e7 q^{68} -2.35972e7 q^{69} -3.53993e8 q^{71} -6.59721e7 q^{72} +3.98157e8 q^{73} +1.32517e8 q^{74} +9.51066e7 q^{75} +3.46522e8 q^{76} -4.46989e7 q^{78} -4.66650e8 q^{79} -1.51356e8 q^{80} +4.30467e7 q^{81} +1.04541e8 q^{82} -3.85723e8 q^{83} -3.48751e8 q^{85} +4.04104e8 q^{86} -4.77349e8 q^{87} +3.84176e8 q^{88} +6.55688e8 q^{89} -1.29793e8 q^{90} +1.12702e8 q^{92} -2.67110e7 q^{93} +1.12485e8 q^{94} +1.58402e9 q^{95} +4.94562e8 q^{96} -1.01619e9 q^{97} -2.50674e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 34 q^{2} + 810 q^{3} + 2902 q^{4} + 2500 q^{5} + 2754 q^{6} + 33966 q^{8} + 65610 q^{9}+O(q^{10}) $ 10 * q + 34 * q^2 + 810 * q^3 + 2902 * q^4 + 2500 * q^5 + 2754 * q^6 + 33966 * q^8 + 65610 * q^9	\( 10 q + 34 q^{2} + 810 q^{3} + 2902 q^{4} + 2500 q^{5} + 2754 q^{6} + 33966 q^{8} + 65610 q^{9} + 16896 q^{10} - 65860 q^{11} + 235062 q^{12} + 228488 q^{13} + 202500 q^{15} + 370722 q^{16} + 934948 q^{17} + 223074 q^{18} + 865920 q^{19} + 1636388 q^{20} + 953900 q^{22} + 1842236 q^{23} + 2751246 q^{24} + 10100266 q^{25} - 1058820 q^{26} + 5314410 q^{27} + 5490136 q^{29} + 1368576 q^{30} + 14852632 q^{31} + 35422866 q^{32} - 5334660 q^{33} + 10917584 q^{34} + 19040022 q^{36} - 1086664 q^{37} + 50821960 q^{38} + 18507528 q^{39} + 85184440 q^{40} + 37333348 q^{41} + 33064992 q^{43} - 85976716 q^{44} + 16402500 q^{45} + 82555644 q^{46} + 16899936 q^{47} + 30028482 q^{48} + 163420178 q^{50} + 75730788 q^{51} - 207979520 q^{52} + 26637644 q^{53} + 18068994 q^{54} - 153534056 q^{55} + 70139520 q^{57} - 257784480 q^{58} + 54375736 q^{59} + 132547428 q^{60} + 313427536 q^{61} + 85959664 q^{62} + 84075878 q^{64} - 704088228 q^{65} + 77265900 q^{66} + 11289312 q^{67} + 1029044740 q^{68} + 149221116 q^{69} - 460380868 q^{71} + 222850926 q^{72} + 717630728 q^{73} - 1827958120 q^{74} + 818121546 q^{75} + 1523608144 q^{76} - 85764420 q^{78} + 1162327376 q^{79} + 3697302420 q^{80} + 430467210 q^{81} + 2664169496 q^{82} + 292067992 q^{83} + 30841228 q^{85} - 2279150960 q^{86} + 444701016 q^{87} - 943587804 q^{88} + 3469605580 q^{89} + 110854656 q^{90} - 2881942700 q^{92} + 1203063192 q^{93} + 4828323784 q^{94} + 530405560 q^{95} + 2869252146 q^{96} + 1533503432 q^{97} - 432107460 q^{99}+O(q^{100}) \) 10 * q + 34 * q^2 + 810 * q^3 + 2902 * q^4 + 2500 * q^5 + 2754 * q^6 + 33966 * q^8 + 65610 * q^9 + 16896 * q^10 - 65860 * q^11 + 235062 * q^12 + 228488 * q^13 + 202500 * q^15 + 370722 * q^16 + 934948 * q^17 + 223074 * q^18 + 865920 * q^19 + 1636388 * q^20 + 953900 * q^22 + 1842236 * q^23 + 2751246 * q^24 + 10100266 * q^25 - 1058820 * q^26 + 5314410 * q^27 + 5490136 * q^29 + 1368576 * q^30 + 14852632 * q^31 + 35422866 * q^32 - 5334660 * q^33 + 10917584 * q^34 + 19040022 * q^36 - 1086664 * q^37 + 50821960 * q^38 + 18507528 * q^39 + 85184440 * q^40 + 37333348 * q^41 + 33064992 * q^43 - 85976716 * q^44 + 16402500 * q^45 + 82555644 * q^46 + 16899936 * q^47 + 30028482 * q^48 + 163420178 * q^50 + 75730788 * q^51 - 207979520 * q^52 + 26637644 * q^53 + 18068994 * q^54 - 153534056 * q^55 + 70139520 * q^57 - 257784480 * q^58 + 54375736 * q^59 + 132547428 * q^60 + 313427536 * q^61 + 85959664 * q^62 + 84075878 * q^64 - 704088228 * q^65 + 77265900 * q^66 + 11289312 * q^67 + 1029044740 * q^68 + 149221116 * q^69 - 460380868 * q^71 + 222850926 * q^72 + 717630728 * q^73 - 1827958120 * q^74 + 818121546 * q^75 + 1523608144 * q^76 - 85764420 * q^78 + 1162327376 * q^79 + 3697302420 * q^80 + 430467210 * q^81 + 2664169496 * q^82 + 292067992 * q^83 + 30841228 * q^85 - 2279150960 * q^86 + 444701016 * q^87 - 943587804 * q^88 + 3469605580 * q^89 + 110854656 * q^90 - 2881942700 * q^92 + 1203063192 * q^93 + 4828323784 * q^94 + 530405560 * q^95 + 2869252146 * q^96 + 1533503432 * q^97 - 432107460 * 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 $

$2$	11.1866	0.494383	0.247191	−	0.968967i	$-0.420492\pi$
$2$	11.1866	0.494383	0.247191	+	0.968967i	$0.420492\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−386.860	−0.755586
$5$	−1768.41	−1.26537	−0.632686	−	0.774408i	$-0.718048\pi$
$5$	−1768.41	−1.26537	−0.632686	+	0.774408i	$0.718048\pi$
$6$	906.115	0.285432
$7$	0	0
$7$	0	0
$8$	−10055.2	−0.867931
$9$	6561.00	0.333333
$10$	−19782.5	−0.625578
$11$	−38206.7	−0.786815	−0.393408	−	0.919364i	$-0.628704\pi$
$11$	−38206.7	−0.786815	−0.393408	+	0.919364i	$0.628704\pi$
$12$	−31335.6	−0.436238
$13$	−49330.3	−0.479037	−0.239518	−	0.970892i	$-0.576990\pi$
$13$	−49330.3	−0.479037	−0.239518	+	0.970892i	$0.576990\pi$
$14$	0	0
$15$	−143241.	−0.730563
$16$	85588.8	0.326495
$17$	197211.	0.572679	0.286340	−	0.958128i	$-0.407561\pi$
$17$	197211.	0.572679	0.286340	+	0.958128i	$0.407561\pi$
$18$	73395.3	0.164794
$19$	−895731.	−1.57684	−0.788418	−	0.615140i	$-0.789099\pi$
$19$	−895731.	−1.57684	−0.788418	+	0.615140i	$0.789099\pi$
$20$	684128.	0.956097
$21$	0	0
$22$	−427403.	−0.388988
$23$	−291324.	−0.217070	−0.108535	−	0.994093i	$-0.534616\pi$
$23$	−291324.	−0.217070	−0.108535	+	0.994093i	$0.534616\pi$
$24$	−814470.	−0.501100
$25$	1.17416e6	0.601167
$26$	−551839.	−0.236827
$27$	531441.	0.192450
$28$	0	0
$29$	−5.89320e6	−1.54725	−0.773624	−	0.633645i	$-0.781558\pi$
$29$	−5.89320e6	−1.54725	−0.773624	+	0.633645i	$0.781558\pi$
$30$	−1.60238e6	−0.361178
$31$	−329766.	−0.0641324	−0.0320662	−	0.999486i	$-0.510209\pi$
$31$	−329766.	−0.0641324	−0.0320662	+	0.999486i	$0.510209\pi$
$32$	6.10571e6	1.02935
$33$	−3.09474e6	−0.454268
$34$	2.20612e6	0.283123
$35$	0	0
$36$	−2.53819e6	−0.251862
$37$	1.18461e7	1.03912	0.519561	−	0.854433i	$-0.326096\pi$
$37$	1.18461e7	1.03912	0.519561	+	0.854433i	$0.326096\pi$
$38$	−1.00202e7	−0.779560
$39$	−3.99576e6	−0.276572
$40$	1.77817e7	1.09826
$41$	9.34523e6	0.516491	0.258245	−	0.966079i	$-0.416856\pi$
$41$	9.34523e6	0.516491	0.258245	+	0.966079i	$0.416856\pi$
$42$	0	0
$43$	3.61239e7	1.61134	0.805669	−	0.592366i	$-0.201806\pi$
$43$	3.61239e7	1.61134	0.805669	+	0.592366i	$0.201806\pi$
$44$	1.47806e7	0.594506
$45$	−1.16025e7	−0.421791
$46$	−3.25893e6	−0.107316
$47$	1.00553e7	0.300576	0.150288	−	0.988642i	$-0.451980\pi$
$47$	1.00553e7	0.300576	0.150288	+	0.988642i	$0.451980\pi$
$48$	6.93269e6	0.188502
$49$	0	0
$50$	1.31348e7	0.297207
$51$	1.59741e7	0.330637
$52$	1.90839e7	0.361953
$53$	2.73666e7	0.476409	0.238205	−	0.971215i	$-0.423441\pi$
$53$	2.73666e7	0.476409	0.238205	+	0.971215i	$0.423441\pi$
$54$	5.94502e6	0.0951440
$55$	6.75652e7	0.995614
$56$	0	0
$57$	−7.25542e7	−0.910387
$58$	−6.59249e7	−0.764933
$59$	1.33007e8	1.42903	0.714515	−	0.699620i	$-0.246647\pi$
$59$	1.33007e8	1.42903	0.714515	+	0.699620i	$0.246647\pi$
$60$	5.54143e7	0.552003
$61$	1.39082e8	1.28614	0.643069	−	0.765809i	$-0.277661\pi$
$61$	1.39082e8	1.28614	0.643069	+	0.765809i	$0.277661\pi$
$62$	−3.68896e6	−0.0317060
$63$	0	0
$64$	2.44807e7	0.182395
$65$	8.72363e7	0.606160
$66$	−3.46197e7	−0.224582
$67$	−1.81486e8	−1.10029	−0.550143	−	0.835071i	$-0.685427\pi$
$67$	−1.81486e8	−1.10029	−0.550143	+	0.835071i	$0.685427\pi$
$68$	−7.62931e7	−0.432708
$69$	−2.35972e7	−0.125326
$70$	0	0
$71$	−3.53993e8	−1.65323	−0.826613	−	0.562770i	$-0.809736\pi$
$71$	−3.53993e8	−1.65323	−0.826613	+	0.562770i	$0.809736\pi$
$72$	−6.59721e7	−0.289310
$73$	3.98157e8	1.64097	0.820487	−	0.571665i	$-0.193702\pi$
$73$	3.98157e8	1.64097	0.820487	+	0.571665i	$0.193702\pi$
$74$	1.32517e8	0.513724
$75$	9.51066e7	0.347084
$76$	3.46522e8	1.19143
$77$	0	0
$78$	−4.46989e7	−0.136732
$79$	−4.66650e8	−1.34794	−0.673968	−	0.738761i	$-0.735411\pi$
$79$	−4.66650e8	−1.34794	−0.673968	+	0.738761i	$0.735411\pi$
$80$	−1.51356e8	−0.413138
$81$	4.30467e7	0.111111
$82$	1.04541e8	0.255344
$83$	−3.85723e8	−0.892123	−0.446061	−	0.895002i	$-0.647174\pi$
$83$	−3.85723e8	−0.892123	−0.446061	+	0.895002i	$0.647174\pi$
$84$	0	0
$85$	−3.48751e8	−0.724653
$86$	4.04104e8	0.796617
$87$	−4.77349e8	−0.893304
$88$	3.84176e8	0.682901
$89$	6.55688e8	1.10775	0.553876	−	0.832599i	$-0.313148\pi$
$89$	6.55688e8	1.10775	0.553876	+	0.832599i	$0.313148\pi$
$90$	−1.29793e8	−0.208526
$91$	0	0
$92$	1.12702e8	0.164015
$93$	−2.67110e7	−0.0370269
$94$	1.12485e8	0.148600
$95$	1.58402e9	1.99528
$96$	4.94562e8	0.594293
$97$	−1.01619e9	−1.16548	−0.582739	−	0.812659i	$-0.698019\pi$
$97$	−1.01619e9	−1.16548	−0.582739	+	0.812659i	$0.698019\pi$
$98$	0	0
$99$	−2.50674e8	−0.262272
$100$	−4.54233e8	−0.454233
$101$	1.52612e9	1.45929	0.729645	−	0.683827i	$-0.239685\pi$
$101$	1.52612e9	1.45929	0.729645	+	0.683827i	$0.239685\pi$
$102$	1.78696e8	0.163461
$103$	1.48706e9	1.30185	0.650923	−	0.759144i	$-0.274382\pi$
$103$	1.48706e9	1.30185	0.650923	+	0.759144i	$0.274382\pi$
$104$	4.96026e8	0.415771
$105$	0	0
$106$	3.06140e8	0.235529
$107$	−1.70753e9	−1.25933	−0.629667	−	0.776865i	$-0.716809\pi$
$107$	−1.70753e9	−1.25933	−0.629667	+	0.776865i	$0.716809\pi$
$108$	−2.05593e8	−0.145413
$109$	1.65036e9	1.11985	0.559925	−	0.828543i	$-0.310830\pi$
$109$	1.65036e9	1.11985	0.559925	+	0.828543i	$0.310830\pi$
$110$	7.55825e8	0.492214
$111$	9.59531e8	0.599937
$112$	0	0
$113$	4.37169e8	0.252230	0.126115	−	0.992016i	$-0.459749\pi$
$113$	4.37169e8	0.252230	0.126115	+	0.992016i	$0.459749\pi$
$114$	−8.11635e8	−0.450079
$115$	5.15181e8	0.274675
$116$	2.27984e9	1.16908
$117$	−3.23656e8	−0.159679
$118$	1.48790e9	0.706488
$119$	0	0
$120$	1.44032e9	0.634079
$121$	−8.98194e8	−0.380922
$122$	1.55586e9	0.635844
$123$	7.56964e8	0.298196
$124$	1.27573e8	0.0484575
$125$	1.37754e9	0.504672
$126$	0	0
$127$	−3.24576e9	−1.10713	−0.553566	−	0.832805i	$-0.686733\pi$
$127$	−3.24576e9	−1.10713	−0.553566	+	0.832805i	$0.686733\pi$
$128$	−2.85227e9	−0.939172
$129$	2.92604e9	0.930306
$130$	9.75878e8	0.299675
$131$	−2.85720e9	−0.847656	−0.423828	−	0.905743i	$-0.639314\pi$
$131$	−2.85720e9	−0.847656	−0.423828	+	0.905743i	$0.639314\pi$
$132$	1.19723e9	0.343238
$133$	0	0
$134$	−2.03021e9	−0.543962
$135$	−9.39806e8	−0.243521
$136$	−1.98300e9	−0.497046
$137$	1.36625e9	0.331351	0.165676	−	0.986180i	$-0.447020\pi$
$137$	1.36625e9	0.331351	0.165676	+	0.986180i	$0.447020\pi$
$138$	−2.63973e8	−0.0619589
$139$	−5.68909e9	−1.29264	−0.646318	−	0.763068i	$-0.723692\pi$
$139$	−5.68909e9	−1.29264	−0.646318	+	0.763068i	$0.723692\pi$
$140$	0	0
$141$	8.14478e8	0.173538
$142$	−3.95998e9	−0.817327
$143$	1.88475e9	0.376913
$144$	5.61548e8	0.108832
$145$	1.04216e10	1.95785
$146$	4.45403e9	0.811269
$147$	0	0
$148$	−4.58277e9	−0.785145
$149$	1.01988e8	0.0169517	0.00847583	−	0.999964i	$-0.497302\pi$
$149$	1.01988e8	0.0169517	0.00847583	+	0.999964i	$0.497302\pi$
$150$	1.06392e9	0.171592
$151$	8.28965e9	1.29760	0.648798	−	0.760960i	$-0.275272\pi$
$151$	8.28965e9	1.29760	0.648798	+	0.760960i	$0.275272\pi$
$152$	9.00675e9	1.36859
$153$	1.29390e9	0.190893
$154$	0	0
$155$	5.83161e8	0.0811514
$156$	1.54580e9	0.208974
$157$	4.18830e9	0.550161	0.275080	−	0.961421i	$-0.411296\pi$
$157$	4.18830e9	0.550161	0.275080	+	0.961421i	$0.411296\pi$
$158$	−5.22023e9	−0.666396
$159$	2.21670e9	0.275055
$160$	−1.07974e10	−1.30250
$161$	0	0
$162$	4.81547e8	0.0549314
$163$	1.45984e10	1.61980	0.809901	−	0.586567i	$-0.199521\pi$
$163$	1.45984e10	1.61980	0.809901	+	0.586567i	$0.199521\pi$
$164$	−3.61529e9	−0.390253
$165$	5.47278e9	0.574818
$166$	−4.31494e9	−0.441050
$167$	4.62590e9	0.460227	0.230114	−	0.973164i	$-0.426090\pi$
$167$	4.62590e9	0.460227	0.230114	+	0.973164i	$0.426090\pi$
$168$	0	0
$169$	−8.17102e9	−0.770524
$170$	−3.90134e9	−0.358256
$171$	−5.87689e9	−0.525612
$172$	−1.39749e10	−1.21750
$173$	−1.94013e9	−0.164673	−0.0823365	−	0.996605i	$-0.526238\pi$
$173$	−1.94013e9	−0.164673	−0.0823365	+	0.996605i	$0.526238\pi$
$174$	−5.33992e9	−0.441634
$175$	0	0
$176$	−3.27007e9	−0.256891
$177$	1.07736e10	0.825051
$178$	7.33493e9	0.547653
$179$	3.16862e9	0.230692	0.115346	−	0.993325i	$-0.463202\pi$
$179$	3.16862e9	0.230692	0.115346	+	0.993325i	$0.463202\pi$
$180$	4.48856e9	0.318699
$181$	5.20941e9	0.360774	0.180387	−	0.983596i	$-0.442265\pi$
$181$	5.20941e9	0.360774	0.180387	+	0.983596i	$0.442265\pi$
$182$	0	0
$183$	1.12657e10	0.742552
$184$	2.92932e9	0.188402
$185$	−2.09487e10	−1.31488
$186$	−2.98806e8	−0.0183054
$187$	−7.53479e9	−0.450593
$188$	−3.88999e9	−0.227111
$189$	0	0
$190$	1.77198e10	0.986434
$191$	−5.60524e8	−0.0304750	−0.0152375	−	0.999884i	$-0.504850\pi$
$191$	−5.60524e8	−0.0304750	−0.0152375	+	0.999884i	$0.504850\pi$
$192$	1.98293e9	0.105306
$193$	−2.67701e10	−1.38881	−0.694404	−	0.719585i	$-0.744332\pi$
$193$	−2.67701e10	−1.38881	−0.694404	+	0.719585i	$0.744332\pi$
$194$	−1.13678e10	−0.576192
$195$	7.06614e9	0.349967
$196$	0	0
$197$	−2.11955e10	−1.00264	−0.501322	−	0.865261i	$-0.667153\pi$
$197$	−2.11955e10	−1.00264	−0.501322	+	0.865261i	$0.667153\pi$
$198$	−2.80419e9	−0.129663
$199$	2.31766e10	1.04764	0.523819	−	0.851829i	$-0.324507\pi$
$199$	2.31766e10	1.04764	0.523819	+	0.851829i	$0.324507\pi$
$200$	−1.18064e10	−0.521772
$201$	−1.47003e10	−0.635250
$202$	1.70721e10	0.721447
$203$	0	0
$204$	−6.17974e9	−0.249824
$205$	−1.65262e10	−0.653553
$206$	1.66351e10	0.643610
$207$	−1.91138e9	−0.0723568
$208$	−4.22212e9	−0.156403
$209$	3.42229e10	1.24068
$210$	0	0
$211$	2.53265e10	0.879637	0.439818	−	0.898087i	$-0.355043\pi$
$211$	2.53265e10	0.879637	0.439818	+	0.898087i	$0.355043\pi$
$212$	−1.05871e10	−0.359968
$213$	−2.86734e10	−0.954491
$214$	−1.91014e10	−0.622593
$215$	−6.38819e10	−2.03894
$216$	−5.34374e9	−0.167033
$217$	0	0
$218$	1.84619e10	0.553635
$219$	3.22507e10	0.947417
$220$	−2.61383e10	−0.752272
$221$	−9.72849e9	−0.274334
$222$	1.07339e10	0.296599
$223$	−2.93709e10	−0.795327	−0.397664	−	0.917531i	$-0.630179\pi$
$223$	−2.93709e10	−0.795327	−0.397664	+	0.917531i	$0.630179\pi$
$224$	0	0
$225$	7.70363e9	0.200389
$226$	4.89043e9	0.124698
$227$	−2.41760e10	−0.604323	−0.302161	−	0.953257i	$-0.597708\pi$
$227$	−2.41760e10	−0.604323	−0.302161	+	0.953257i	$0.597708\pi$
$228$	2.80683e10	0.687875
$229$	1.36309e10	0.327540	0.163770	−	0.986499i	$-0.447634\pi$
$229$	1.36309e10	0.327540	0.163770	+	0.986499i	$0.447634\pi$
$230$	5.76312e9	0.135795
$231$	0	0
$232$	5.92572e10	1.34291
$233$	5.75893e10	1.28009	0.640045	−	0.768338i	$-0.278916\pi$
$233$	5.75893e10	1.28009	0.640045	+	0.768338i	$0.278916\pi$
$234$	−3.62061e9	−0.0789425
$235$	−1.77819e10	−0.380340
$236$	−5.14552e10	−1.07976
$237$	−3.77986e10	−0.778231
$238$	0	0
$239$	−7.53598e9	−0.149399	−0.0746997	−	0.997206i	$-0.523800\pi$
$239$	−7.53598e9	−0.149399	−0.0746997	+	0.997206i	$0.523800\pi$
$240$	−1.22599e10	−0.238525
$241$	−7.05833e10	−1.34780	−0.673900	−	0.738823i	$-0.735382\pi$
$241$	−7.05833e10	−1.34780	−0.673900	+	0.738823i	$0.735382\pi$
$242$	−1.00477e10	−0.188321
$243$	3.48678e9	0.0641500
$244$	−5.38053e10	−0.971787
$245$	0	0
$246$	8.46785e9	0.147423
$247$	4.41867e10	0.755362
$248$	3.31586e9	0.0556625
$249$	−3.12436e10	−0.515067
$250$	1.54100e10	0.249501
$251$	−7.44191e10	−1.18346	−0.591729	−	0.806137i	$-0.701554\pi$
$251$	−7.44191e10	−1.18346	−0.591729	+	0.806137i	$0.701554\pi$
$252$	0	0
$253$	1.11305e10	0.170794
$254$	−3.63090e10	−0.547347
$255$	−2.82488e10	−0.418378
$256$	−4.44413e10	−0.646706
$257$	−1.08750e11	−1.55499	−0.777497	−	0.628887i	$-0.783511\pi$
$257$	−1.08750e11	−1.55499	−0.777497	+	0.628887i	$0.783511\pi$
$258$	3.27324e10	0.459927
$259$	0	0
$260$	−3.37482e10	−0.458006
$261$	−3.86653e10	−0.515749
$262$	−3.19624e10	−0.419067
$263$	−9.51494e10	−1.22632	−0.613162	−	0.789957i	$-0.710103\pi$
$263$	−9.51494e10	−1.22632	−0.613162	+	0.789957i	$0.710103\pi$
$264$	3.11182e10	0.394273
$265$	−4.83955e10	−0.602835
$266$	0	0
$267$	5.31108e10	0.639561
$268$	7.02095e10	0.831360
$269$	8.22853e10	0.958158	0.479079	−	0.877772i	$-0.340971\pi$
$269$	8.22853e10	0.958158	0.479079	+	0.877772i	$0.340971\pi$
$270$	−1.05132e10	−0.120393
$271$	5.11581e10	0.576172	0.288086	−	0.957605i	$-0.406981\pi$
$271$	5.11581e10	0.576172	0.288086	+	0.957605i	$0.406981\pi$
$272$	1.68791e10	0.186977
$273$	0	0
$274$	1.52837e10	0.163814
$275$	−4.48606e10	−0.473008
$276$	9.12882e9	0.0946943
$277$	9.46611e10	0.966079	0.483040	−	0.875599i	$-0.339533\pi$
$277$	9.46611e10	0.966079	0.483040	+	0.875599i	$0.339533\pi$
$278$	−6.36416e10	−0.639057
$279$	−2.16359e9	−0.0213775
$280$	0	0
$281$	−1.71675e11	−1.64259	−0.821293	−	0.570506i	$-0.806747\pi$
$281$	−1.71675e11	−1.64259	−0.821293	+	0.570506i	$0.806747\pi$
$282$	9.11125e9	0.0857940
$283$	4.90697e8	0.00454752	0.00227376	−	0.999997i	$-0.499276\pi$
$283$	4.90697e8	0.00454752	0.00227376	+	0.999997i	$0.499276\pi$
$284$	1.36946e11	1.24915
$285$	1.28306e11	1.15198
$286$	2.10839e10	0.186339
$287$	0	0
$288$	4.00595e10	0.343115
$289$	−7.96956e10	−0.672038
$290$	1.16582e11	0.967925
$291$	−8.23117e10	−0.672889
$292$	−1.54031e11	−1.23990
$293$	1.91462e11	1.51768	0.758838	−	0.651279i	$-0.225767\pi$
$293$	1.91462e11	1.51768	0.758838	+	0.651279i	$0.225767\pi$
$294$	0	0
$295$	−2.35212e11	−1.80826
$296$	−1.19114e11	−0.901886
$297$	−2.03046e10	−0.151423
$298$	1.14090e9	0.00838061
$299$	1.43711e10	0.103985
$300$	−3.67929e10	−0.262252
$301$	0	0
$302$	9.27330e10	0.641509
$303$	1.23615e11	0.842521
$304$	−7.66646e10	−0.514830
$305$	−2.45955e11	−1.62744
$306$	1.44744e10	0.0943743
$307$	1.03496e11	0.664970	0.332485	−	0.943109i	$-0.392113\pi$
$307$	1.03496e11	0.664970	0.332485	+	0.943109i	$0.392113\pi$
$308$	0	0
$309$	1.20452e11	0.751621
$310$	6.52359e9	0.0401199
$311$	2.20229e11	1.33491	0.667455	−	0.744650i	$-0.267383\pi$
$311$	2.20229e11	1.33491	0.667455	+	0.744650i	$0.267383\pi$
$312$	4.01781e10	0.240045
$313$	2.82859e11	1.66579	0.832894	−	0.553432i	$-0.186682\pi$
$313$	2.82859e11	1.66579	0.832894	+	0.553432i	$0.186682\pi$
$314$	4.68529e10	0.271990
$315$	0	0
$316$	1.80528e11	1.01848
$317$	−9.82458e10	−0.546446	−0.273223	−	0.961951i	$-0.588090\pi$
$317$	−9.82458e10	−0.546446	−0.273223	+	0.961951i	$0.588090\pi$
$318$	2.47973e10	0.135982
$319$	2.25160e11	1.21740
$320$	−4.32919e10	−0.230798
$321$	−1.38310e11	−0.727077
$322$	0	0
$323$	−1.76648e11	−0.903021
$324$	−1.66530e10	−0.0839540
$325$	−5.79214e10	−0.287981
$326$	1.63307e11	0.800802
$327$	1.33679e11	0.646546
$328$	−9.39681e10	−0.448279
$329$	0	0
$330$	6.12218e10	0.284180
$331$	3.31300e11	1.51704	0.758518	−	0.651652i	$-0.225924\pi$
$331$	3.31300e11	1.51704	0.758518	+	0.651652i	$0.225924\pi$
$332$	1.49221e11	0.674075
$333$	7.77220e10	0.346374
$334$	5.17481e10	0.227528
$335$	3.20941e11	1.39227
$336$	0	0
$337$	1.93058e11	0.815369	0.407684	−	0.913123i	$-0.366336\pi$
$337$	1.93058e11	0.815369	0.407684	+	0.913123i	$0.366336\pi$
$338$	−9.14060e10	−0.380934
$339$	3.54107e10	0.145625
$340$	1.34918e11	0.547537
$341$	1.25993e10	0.0504604
$342$	−6.57425e10	−0.259853
$343$	0	0
$344$	−3.63233e11	−1.39853
$345$	4.17296e10	0.158584
$346$	−2.17034e10	−0.0814115
$347$	3.02277e11	1.11924	0.559619	−	0.828750i	$-0.310948\pi$
$347$	3.02277e11	1.11924	0.559619	+	0.828750i	$0.310948\pi$
$348$	1.84667e11	0.674968
$349$	3.81619e11	1.37694	0.688471	−	0.725264i	$-0.258282\pi$
$349$	3.81619e11	1.37694	0.688471	+	0.725264i	$0.258282\pi$
$350$	0	0
$351$	−2.62162e10	−0.0921907
$352$	−2.33279e11	−0.809904
$353$	−3.28328e11	−1.12544	−0.562719	−	0.826648i	$-0.690245\pi$
$353$	−3.28328e11	−1.12544	−0.562719	+	0.826648i	$0.690245\pi$
$354$	1.20520e11	0.407891
$355$	6.26006e11	2.09195
$356$	−2.53660e11	−0.837001
$357$	0	0
$358$	3.54461e10	0.114050
$359$	−9.97959e10	−0.317094	−0.158547	−	0.987351i	$-0.550681\pi$
$359$	−9.97959e10	−0.317094	−0.158547	+	0.987351i	$0.550681\pi$
$360$	1.16666e11	0.366085
$361$	4.79646e11	1.48641
$362$	5.82757e10	0.178360
$363$	−7.27538e10	−0.219925
$364$	0	0
$365$	−7.04106e11	−2.07644
$366$	1.26024e11	0.367105
$367$	1.54229e11	0.443781	0.221890	−	0.975072i	$-0.428777\pi$
$367$	1.54229e11	0.443781	0.221890	+	0.975072i	$0.428777\pi$
$368$	−2.49341e10	−0.0708725
$369$	6.13141e10	0.172164
$370$	−2.34345e11	−0.650052
$371$	0	0
$372$	1.03334e10	0.0279770
$373$	1.92910e10	0.0516019	0.0258009	−	0.999667i	$-0.491786\pi$
$373$	1.92910e10	0.0516019	0.0258009	+	0.999667i	$0.491786\pi$
$374$	−8.42888e10	−0.222765
$375$	1.11581e11	0.291372
$376$	−1.01108e11	−0.260879
$377$	2.90713e11	0.741189
$378$	0	0
$379$	5.21666e11	1.29872	0.649361	−	0.760480i	$-0.275036\pi$
$379$	5.21666e11	1.29872	0.649361	+	0.760480i	$0.275036\pi$
$380$	−6.12794e11	−1.50761
$381$	−2.62907e11	−0.639203
$382$	−6.27036e9	−0.0150663
$383$	−6.46468e11	−1.53516	−0.767578	−	0.640956i	$-0.778538\pi$
$383$	−6.46468e11	−1.53516	−0.767578	+	0.640956i	$0.778538\pi$
$384$	−2.31034e11	−0.542231
$385$	0	0
$386$	−2.99467e11	−0.686603
$387$	2.37009e11	0.537112
$388$	3.93125e11	0.880618
$389$	−5.41589e11	−1.19921	−0.599607	−	0.800295i	$-0.704676\pi$
$389$	−5.41589e11	−1.19921	−0.599607	+	0.800295i	$0.704676\pi$
$390$	7.90461e10	0.173017
$391$	−5.74523e10	−0.124312
$392$	0	0
$393$	−2.31433e11	−0.489395
$394$	−2.37106e11	−0.495690
$395$	8.25229e11	1.70564
$396$	9.69758e10	0.198169
$397$	2.28028e10	0.0460713	0.0230356	−	0.999735i	$-0.492667\pi$
$397$	2.28028e10	0.0460713	0.0230356	+	0.999735i	$0.492667\pi$
$398$	2.59268e11	0.517934
$399$	0	0
$400$	1.00495e11	0.196278
$401$	−9.85512e11	−1.90332	−0.951661	−	0.307151i	$-0.900624\pi$
$401$	−9.85512e11	−1.90332	−0.951661	+	0.307151i	$0.900624\pi$
$402$	−1.64447e11	−0.314057
$403$	1.62674e10	0.0307218
$404$	−5.90393e11	−1.10262
$405$	−7.61243e10	−0.140597
$406$	0	0
$407$	−4.52599e11	−0.817597
$408$	−1.60623e11	−0.286970
$409$	3.82025e11	0.675052	0.337526	−	0.941316i	$-0.390410\pi$
$409$	3.82025e11	0.675052	0.337526	+	0.941316i	$0.390410\pi$
$410$	−1.84872e11	−0.323106
$411$	1.10667e11	0.191306
$412$	−5.75282e11	−0.983656
$413$	0	0
$414$	−2.13818e10	−0.0357720
$415$	6.82118e11	1.12887
$416$	−3.01196e11	−0.493094
$417$	−4.60816e11	−0.746304
$418$	3.82839e11	0.613370
$419$	−6.52071e10	−0.103355	−0.0516775	−	0.998664i	$-0.516457\pi$
$419$	−6.52071e10	−0.103355	−0.0516775	+	0.998664i	$0.516457\pi$
$420$	0	0
$421$	6.82267e11	1.05849	0.529243	−	0.848470i	$-0.322476\pi$
$421$	6.82267e11	1.05849	0.529243	+	0.848470i	$0.322476\pi$
$422$	2.83317e11	0.434877
$423$	6.59727e10	0.100192
$424$	−2.75177e11	−0.413491
$425$	2.31557e11	0.344276
$426$	−3.20759e11	−0.471884
$427$	0	0
$428$	6.60574e11	0.951535
$429$	1.52665e11	0.217611
$430$	−7.14622e11	−1.00802
$431$	8.27921e11	1.15569	0.577845	−	0.816147i	$-0.303894\pi$
$431$	8.27921e11	1.15569	0.577845	+	0.816147i	$0.303894\pi$
$432$	4.54854e10	0.0628341
$433$	6.41155e11	0.876531	0.438266	−	0.898846i	$-0.355593\pi$
$433$	6.41155e11	0.876531	0.438266	+	0.898846i	$0.355593\pi$
$434$	0	0
$435$	8.44150e11	1.13036
$436$	−6.38459e11	−0.846143
$437$	2.60948e11	0.342285
$438$	3.60776e11	0.468386
$439$	−2.97012e11	−0.381666	−0.190833	−	0.981622i	$-0.561119\pi$
$439$	−2.97012e11	−0.381666	−0.190833	+	0.981622i	$0.561119\pi$
$440$	−6.79381e11	−0.864125
$441$	0	0
$442$	−1.08829e11	−0.135626
$443$	1.14393e12	1.41118	0.705588	−	0.708622i	$-0.250683\pi$
$443$	1.14393e12	1.41118	0.705588	+	0.708622i	$0.250683\pi$
$444$	−3.71204e11	−0.453304
$445$	−1.15953e12	−1.40172
$446$	−3.28561e11	−0.393196
$447$	8.26105e9	0.00978704
$448$	0	0
$449$	−1.33814e11	−0.155379	−0.0776896	−	0.996978i	$-0.524754\pi$
$449$	−1.33814e11	−0.155379	−0.0776896	+	0.996978i	$0.524754\pi$
$450$	8.61775e10	0.0990689
$451$	−3.57051e11	−0.406383
$452$	−1.69123e11	−0.190581
$453$	6.71461e11	0.749168
$454$	−2.70448e11	−0.298767
$455$	0	0
$456$	7.29546e11	0.790153
$457$	4.48919e11	0.481443	0.240721	−	0.970594i	$-0.422616\pi$
$457$	4.48919e11	0.481443	0.240721	+	0.970594i	$0.422616\pi$
$458$	1.52484e11	0.161930
$459$	1.04806e11	0.110212
$460$	−1.99303e11	−0.207541
$461$	1.30327e12	1.34394	0.671969	−	0.740579i	$-0.265449\pi$
$461$	1.30327e12	1.34394	0.671969	+	0.740579i	$0.265449\pi$
$462$	0	0
$463$	−5.44956e11	−0.551121	−0.275561	−	0.961284i	$-0.588863\pi$
$463$	−5.44956e11	−0.551121	−0.275561	+	0.961284i	$0.588863\pi$
$464$	−5.04392e11	−0.505169
$465$	4.72361e10	0.0468528
$466$	6.44229e11	0.632854
$467$	−6.26701e11	−0.609726	−0.304863	−	0.952396i	$-0.598611\pi$
$467$	−6.26701e11	−0.609726	−0.304863	+	0.952396i	$0.598611\pi$
$468$	1.25210e11	0.120651
$469$	0	0
$470$	−1.98919e11	−0.188034
$471$	3.39253e11	0.317635
$472$	−1.33741e12	−1.24030
$473$	−1.38018e12	−1.26782
$474$	−4.22838e11	−0.384744
$475$	−1.05173e12	−0.947942
$476$	0	0
$477$	1.79553e11	0.158803
$478$	−8.43020e10	−0.0738605
$479$	−5.26164e10	−0.0456679	−0.0228339	−	0.999739i	$-0.507269\pi$
$479$	−5.26164e10	−0.0456679	−0.0228339	+	0.999739i	$0.507269\pi$
$480$	−8.74590e11	−0.752001
$481$	−5.84370e11	−0.497777
$482$	−7.89588e11	−0.666329
$483$	0	0
$484$	3.47475e11	0.287819
$485$	1.79705e12	1.47476
$486$	3.90053e10	0.0317147
$487$	−1.64610e12	−1.32610	−0.663050	−	0.748575i	$-0.730739\pi$
$487$	−1.64610e12	−1.32610	−0.663050	+	0.748575i	$0.730739\pi$
$488$	−1.39850e12	−1.11628
$489$	1.18247e12	0.935193
$490$	0	0
$491$	9.67445e11	0.751207	0.375603	−	0.926780i	$-0.377435\pi$
$491$	9.67445e11	0.751207	0.375603	+	0.926780i	$0.377435\pi$
$492$	−2.92839e11	−0.225313
$493$	−1.16220e12	−0.886077
$494$	4.94299e11	0.373438
$495$	4.43295e11	0.331871
$496$	−2.82242e10	−0.0209389
$497$	0	0
$498$	−3.49510e11	−0.254640
$499$	2.13350e12	1.54042	0.770212	−	0.637788i	$-0.220150\pi$
$499$	2.13350e12	1.54042	0.770212	+	0.637788i	$0.220150\pi$
$500$	−5.32915e11	−0.381323
$501$	3.74698e11	0.265712
$502$	−8.32497e11	−0.585081
$503$	1.51675e12	1.05647	0.528235	−	0.849098i	$-0.322854\pi$
$503$	1.51675e12	1.05647	0.528235	+	0.849098i	$0.322854\pi$
$504$	0	0
$505$	−2.69880e12	−1.84654
$506$	1.24513e11	0.0844378
$507$	−6.61853e11	−0.444862
$508$	1.25565e12	0.836534
$509$	−2.25185e12	−1.48699	−0.743497	−	0.668739i	$-0.766834\pi$
$509$	−2.25185e12	−1.48699	−0.743497	+	0.668739i	$0.766834\pi$
$510$	−3.16008e11	−0.206839
$511$	0	0
$512$	9.63213e11	0.619452
$513$	−4.76028e11	−0.303462
$514$	−1.21654e12	−0.768762
$515$	−2.62973e12	−1.64732
$516$	−1.13197e12	−0.702926
$517$	−3.84180e11	−0.236498
$518$	0	0
$519$	−1.57150e11	−0.0950740
$520$	−8.77178e11	−0.526105
$521$	6.39005e11	0.379957	0.189979	−	0.981788i	$-0.439158\pi$
$521$	6.39005e11	0.379957	0.189979	+	0.981788i	$0.439158\pi$
$522$	−4.32533e11	−0.254978
$523$	5.72048e11	0.334330	0.167165	−	0.985929i	$-0.446539\pi$
$523$	5.72048e11	0.334330	0.167165	+	0.985929i	$0.446539\pi$
$524$	1.10534e12	0.640477
$525$	0	0
$526$	−1.06440e12	−0.606273
$527$	−6.50335e10	−0.0367273
$528$	−2.64875e11	−0.148316
$529$	−1.71628e12	−0.952880
$530$	−5.41381e11	−0.298031
$531$	8.72661e11	0.476344
$532$	0	0
$533$	−4.61003e11	−0.247418
$534$	5.94129e11	0.316188
$535$	3.01961e12	1.59353
$536$	1.82487e12	0.954973
$537$	2.56658e11	0.133190
$538$	9.20493e11	0.473697
$539$	0	0
$540$	3.63573e11	0.184001
$541$	2.01591e12	1.01178	0.505888	−	0.862599i	$-0.331165\pi$
$541$	2.01591e12	1.01178	0.505888	+	0.862599i	$0.331165\pi$
$542$	5.72285e11	0.284850
$543$	4.21963e11	0.208293
$544$	1.20411e12	0.589485
$545$	−2.91852e12	−1.41703
$546$	0	0
$547$	2.11109e12	1.00824	0.504120	−	0.863633i	$-0.331817\pi$
$547$	2.11109e12	1.00824	0.504120	+	0.863633i	$0.331817\pi$
$548$	−5.28549e11	−0.250364
$549$	9.12518e11	0.428712
$550$	−5.01838e11	−0.233847
$551$	5.27872e12	2.43976
$552$	2.37275e11	0.108774
$553$	0	0
$554$	1.05894e12	0.477613
$555$	−1.69685e12	−0.759144
$556$	2.20088e12	0.976697
$557$	6.22557e11	0.274051	0.137025	−	0.990568i	$-0.456246\pi$
$557$	6.22557e11	0.274051	0.137025	+	0.990568i	$0.456246\pi$
$558$	−2.42032e10	−0.0105687
$559$	−1.78200e12	−0.771890
$560$	0	0
$561$	−6.10318e11	−0.260150
$562$	−1.92046e12	−0.812066
$563$	−1.89141e12	−0.793411	−0.396706	−	0.917946i	$-0.629847\pi$
$563$	−1.89141e12	−0.793411	−0.396706	+	0.917946i	$0.629847\pi$
$564$	−3.15089e11	−0.131123
$565$	−7.73094e11	−0.319164
$566$	5.48924e9	0.00224822
$567$	0	0
$568$	3.55947e12	1.43489
$569$	1.65272e12	0.660989	0.330495	−	0.943808i	$-0.392784\pi$
$569$	1.65272e12	0.660989	0.330495	+	0.943808i	$0.392784\pi$
$570$	1.43531e12	0.569518
$571$	−2.86468e12	−1.12775	−0.563875	−	0.825860i	$-0.690690\pi$
$571$	−2.86468e12	−1.12775	−0.563875	+	0.825860i	$0.690690\pi$
$572$	−7.29134e11	−0.284790
$573$	−4.54024e10	−0.0175948
$574$	0	0
$575$	−3.42059e11	−0.130496
$576$	1.60618e11	0.0607984
$577$	3.93957e11	0.147965	0.0739823	−	0.997260i	$-0.476429\pi$
$577$	3.93957e11	0.147965	0.0739823	+	0.997260i	$0.476429\pi$
$578$	−8.91523e11	−0.332244
$579$	−2.16838e12	−0.801829
$580$	−4.03170e12	−1.47932
$581$	0	0
$582$	−9.20789e11	−0.332665
$583$	−1.04559e12	−0.374846
$584$	−4.00355e12	−1.42425
$585$	5.72357e11	0.202053
$586$	2.14181e12	0.750313
$587$	1.38604e12	0.481843	0.240921	−	0.970545i	$-0.422550\pi$
$587$	1.38604e12	0.481843	0.240921	+	0.970545i	$0.422550\pi$
$588$	0	0
$589$	2.95381e11	0.101126
$590$	−2.63122e12	−0.893971
$591$	−1.71684e12	−0.578877
$592$	1.01389e12	0.339268
$593$	4.94779e12	1.64310	0.821552	−	0.570134i	$-0.193109\pi$
$593$	4.94779e12	1.64310	0.821552	+	0.570134i	$0.193109\pi$
$594$	−2.27140e11	−0.0748607
$595$	0	0
$596$	−3.94552e10	−0.0128084
$597$	1.87731e12	0.604854
$598$	1.60764e11	0.0514083
$599$	3.93218e12	1.24800	0.623998	−	0.781426i	$-0.285507\pi$
$599$	3.93218e12	1.24800	0.623998	+	0.781426i	$0.285507\pi$
$600$	−9.56315e11	−0.301245
$601$	5.26981e12	1.64763	0.823816	−	0.566858i	$-0.191841\pi$
$601$	5.26981e12	1.64763	0.823816	+	0.566858i	$0.191841\pi$
$602$	0	0
$603$	−1.19073e12	−0.366762
$604$	−3.20693e12	−0.980445
$605$	1.58838e12	0.482008
$606$	1.38284e12	0.416528
$607$	−1.96412e12	−0.587246	−0.293623	−	0.955921i	$-0.594861\pi$
$607$	−1.96412e12	−0.587246	−0.293623	+	0.955921i	$0.594861\pi$
$608$	−5.46907e12	−1.62311
$609$	0	0
$610$	−2.75140e12	−0.804579
$611$	−4.96030e11	−0.143987
$612$	−5.00559e11	−0.144236
$613$	5.16920e12	1.47860	0.739301	−	0.673375i	$-0.235156\pi$
$613$	5.16920e12	1.47860	0.739301	+	0.673375i	$0.235156\pi$
$614$	1.15777e12	0.328750
$615$	−1.33862e12	−0.377329
$616$	0	0
$617$	1.18724e12	0.329803	0.164902	−	0.986310i	$-0.447269\pi$
$617$	1.18724e12	0.329803	0.164902	+	0.986310i	$0.447269\pi$
$618$	1.34744e12	0.371589
$619$	1.39880e12	0.382955	0.191478	−	0.981497i	$-0.438672\pi$
$619$	1.39880e12	0.382955	0.191478	+	0.981497i	$0.438672\pi$
$620$	−2.25602e11	−0.0613168
$621$	−1.54821e11	−0.0417752
$622$	2.46361e12	0.659957
$623$	0	0
$624$	−3.41992e11	−0.0902995
$625$	−4.72933e12	−1.23977
$626$	3.16423e12	0.823537
$627$	2.77206e12	0.716306
$628$	−1.62029e12	−0.415694
$629$	2.33618e12	0.595083
$630$	0	0
$631$	−4.62783e12	−1.16211	−0.581053	−	0.813866i	$-0.697359\pi$
$631$	−4.62783e12	−1.16211	−0.581053	+	0.813866i	$0.697359\pi$
$632$	4.69225e12	1.16992
$633$	2.05144e12	0.507858
$634$	−1.09904e12	−0.270154
$635$	5.73984e12	1.40094
$636$	−8.57552e11	−0.207828
$637$	0	0
$638$	2.51877e12	0.601861
$639$	−2.32255e12	−0.551075
$640$	5.04398e12	1.18840
$641$	5.70621e12	1.33502	0.667508	−	0.744603i	$-0.267361\pi$
$641$	5.70621e12	1.33502	0.667508	+	0.744603i	$0.267361\pi$
$642$	−1.54722e12	−0.359454
$643$	3.59325e12	0.828968	0.414484	−	0.910057i	$-0.363962\pi$
$643$	3.59325e12	0.828968	0.414484	+	0.910057i	$0.363962\pi$
$644$	0	0
$645$	−5.17443e12	−1.17718
$646$	−1.97609e12	−0.446438
$647$	−7.71001e12	−1.72976	−0.864880	−	0.501979i	$-0.832605\pi$
$647$	−7.71001e12	−1.72976	−0.864880	+	0.501979i	$0.832605\pi$
$648$	−4.32843e11	−0.0964368
$649$	−5.08177e12	−1.12438
$650$	−6.47944e11	−0.142373
$651$	0	0
$652$	−5.64754e12	−1.22390
$653$	−7.97713e12	−1.71687	−0.858435	−	0.512923i	$-0.828563\pi$
$653$	−7.97713e12	−1.71687	−0.858435	+	0.512923i	$0.828563\pi$
$654$	1.49542e12	0.319641
$655$	5.05271e12	1.07260
$656$	7.99847e11	0.168632
$657$	2.61231e12	0.546991
$658$	0	0
$659$	−1.13324e12	−0.234065	−0.117033	−	0.993128i	$-0.537338\pi$
$659$	−1.13324e12	−0.234065	−0.117033	+	0.993128i	$0.537338\pi$
$660$	−2.11720e12	−0.434324
$661$	4.54329e12	0.925687	0.462843	−	0.886440i	$-0.346829\pi$
$661$	4.54329e12	0.925687	0.462843	+	0.886440i	$0.346829\pi$
$662$	3.70613e12	0.749996
$663$	−7.88008e11	−0.158387
$664$	3.87852e12	0.774301
$665$	0	0
$666$	8.69446e11	0.171241
$667$	1.71683e12	0.335862
$668$	−1.78958e12	−0.347741
$669$	−2.37905e12	−0.459182
$670$	3.59024e12	0.688315
$671$	−5.31387e12	−1.01195
$672$	0	0
$673$	2.47316e12	0.464712	0.232356	−	0.972631i	$-0.425357\pi$
$673$	2.47316e12	0.464712	0.232356	+	0.972631i	$0.425357\pi$
$674$	2.15967e12	0.403104
$675$	6.23994e11	0.115695
$676$	3.16104e12	0.582197
$677$	4.44483e12	0.813216	0.406608	−	0.913603i	$-0.366711\pi$
$677$	4.44483e12	0.813216	0.406608	+	0.913603i	$0.366711\pi$
$678$	3.96125e11	0.0719944
$679$	0	0
$680$	3.50675e12	0.628949
$681$	−1.95826e12	−0.348906
$682$	1.40943e11	0.0249467
$683$	−2.65317e12	−0.466521	−0.233261	−	0.972414i	$-0.574940\pi$
$683$	−2.65317e12	−0.466521	−0.233261	+	0.972414i	$0.574940\pi$
$684$	2.27353e12	0.397145
$685$	−2.41610e12	−0.419283
$686$	0	0
$687$	1.10410e12	0.189106
$688$	3.09180e12	0.526094
$689$	−1.35001e12	−0.228218
$690$	4.66813e11	0.0784010
$691$	4.73134e12	0.789466	0.394733	−	0.918796i	$-0.370837\pi$
$691$	4.73134e12	0.789466	0.394733	+	0.918796i	$0.370837\pi$
$692$	7.50557e11	0.124425
$693$	0	0
$694$	3.38145e12	0.553332
$695$	1.00607e13	1.63567
$696$	4.79984e12	0.775327
$697$	1.84298e12	0.295784
$698$	4.26902e12	0.680737
$699$	4.66473e12	0.739060
$700$	0	0
$701$	3.63922e12	0.569216	0.284608	−	0.958644i	$-0.408137\pi$
$701$	3.63922e12	0.569216	0.284608	+	0.958644i	$0.408137\pi$
$702$	−2.93270e11	−0.0455775
$703$	−1.06109e13	−1.63852
$704$	−9.35325e11	−0.143511
$705$	−1.44033e12	−0.219590
$706$	−3.67287e12	−0.556397
$707$	0	0
$708$	−4.16787e12	−0.623397
$709$	4.35507e12	0.647272	0.323636	−	0.946182i	$-0.395095\pi$
$709$	4.35507e12	0.647272	0.323636	+	0.946182i	$0.395095\pi$
$710$	7.00288e12	1.03422
$711$	−3.06169e12	−0.449312
$712$	−6.59307e12	−0.961453
$713$	9.60686e10	0.0139213
$714$	0	0
$715$	−3.33301e12	−0.476936
$716$	−1.22581e12	−0.174307
$717$	−6.10414e11	−0.0862558
$718$	−1.11638e12	−0.156766
$719$	8.53408e12	1.19090	0.595452	−	0.803391i	$-0.296973\pi$
$719$	8.53408e12	1.19090	0.595452	+	0.803391i	$0.296973\pi$
$720$	−9.93048e11	−0.137713
$721$	0	0
$722$	5.36562e12	0.734856
$723$	−5.71725e12	−0.778153
$724$	−2.01531e12	−0.272596
$725$	−6.91953e12	−0.930155
$726$	−8.13867e11	−0.108727
$727$	7.95847e12	1.05663	0.528317	−	0.849047i	$-0.322823\pi$
$727$	7.95847e12	1.05663	0.528317	+	0.849047i	$0.322823\pi$
$728$	0	0
$729$	2.82430e11	0.0370370
$730$	−7.87655e12	−1.02656
$731$	7.12404e12	0.922779
$732$	−4.35823e12	−0.561061
$733$	−3.15180e12	−0.403265	−0.201633	−	0.979461i	$-0.564625\pi$
$733$	−3.15180e12	−0.403265	−0.201633	+	0.979461i	$0.564625\pi$
$734$	1.72530e12	0.219397
$735$	0	0
$736$	−1.77874e12	−0.223440
$737$	6.93397e12	0.865721
$738$	6.85896e11	0.0851147
$739$	2.92924e12	0.361289	0.180645	−	0.983548i	$-0.442182\pi$
$739$	2.92924e12	0.361289	0.180645	+	0.983548i	$0.442182\pi$
$740$	8.10422e12	0.993501
$741$	3.57912e12	0.436109
$742$	0	0
$743$	8.69347e12	1.04651	0.523255	−	0.852176i	$-0.324717\pi$
$743$	8.69347e12	1.04651	0.523255	+	0.852176i	$0.324717\pi$
$744$	2.68584e11	0.0321368
$745$	−1.80357e11	−0.0214502
$746$	2.15801e11	0.0255111
$747$	−2.53073e12	−0.297374
$748$	2.91491e12	0.340461
$749$	0	0
$750$	1.24821e12	0.144049
$751$	3.47441e12	0.398567	0.199283	−	0.979942i	$-0.436139\pi$
$751$	3.47441e12	0.398567	0.199283	+	0.979942i	$0.436139\pi$
$752$	8.60620e11	0.0981366
$753$	−6.02795e12	−0.683270
$754$	3.25210e12	0.366431
$755$	−1.46595e13	−1.64194
$756$	0	0
$757$	−7.08202e12	−0.783837	−0.391919	−	0.920000i	$-0.628189\pi$
$757$	−7.08202e12	−0.783837	−0.391919	+	0.920000i	$0.628189\pi$
$758$	5.83568e12	0.642066
$759$	9.01573e11	0.0986081
$760$	−1.59276e13	−1.73177
$761$	−8.78493e12	−0.949527	−0.474764	−	0.880113i	$-0.657466\pi$
$761$	−8.78493e12	−0.949527	−0.474764	+	0.880113i	$0.657466\pi$
$762$	−2.94103e12	−0.316011
$763$	0	0
$764$	2.16844e11	0.0230265
$765$	−2.28815e12	−0.241551
$766$	−7.23178e12	−0.758955
$767$	−6.56129e12	−0.684558
$768$	−3.59974e12	−0.373376
$769$	−1.27252e13	−1.31218	−0.656092	−	0.754681i	$-0.727792\pi$
$769$	−1.27252e13	−1.31218	−0.656092	+	0.754681i	$0.727792\pi$
$770$	0	0
$771$	−8.80872e12	−0.897776
$772$	1.03563e13	1.04936
$773$	3.95150e12	0.398065	0.199033	−	0.979993i	$-0.436220\pi$
$773$	3.95150e12	0.398065	0.199033	+	0.979993i	$0.436220\pi$
$774$	2.65132e12	0.265539
$775$	−3.87196e11	−0.0385543
$776$	1.02180e13	1.01155
$777$	0	0
$778$	−6.05854e12	−0.592871
$779$	−8.37081e12	−0.814421
$780$	−2.73361e12	−0.264430
$781$	1.35249e13	1.30078
$782$	−6.42697e11	−0.0614576
$783$	−3.13189e12	−0.297768
$784$	0	0
$785$	−7.40664e12	−0.696158
$786$	−2.58895e12	−0.241948
$787$	−2.58264e12	−0.239982	−0.119991	−	0.992775i	$-0.538287\pi$
$787$	−2.58264e12	−0.239982	−0.119991	+	0.992775i	$0.538287\pi$
$788$	8.19971e12	0.757583
$789$	−7.70710e12	−0.708018
$790$	9.23151e12	0.843239
$791$	0	0
$792$	2.52058e12	0.227634
$793$	−6.86097e12	−0.616107
$794$	2.55086e11	0.0227769
$795$	−3.92004e12	−0.348047
$796$	−8.96611e12	−0.791581
$797$	−1.80367e13	−1.58341	−0.791707	−	0.610901i	$-0.790807\pi$
$797$	−1.80367e13	−1.58341	−0.791707	+	0.610901i	$0.790807\pi$
$798$	0	0
$799$	1.98302e12	0.172134
$800$	7.16905e12	0.618809
$801$	4.30197e12	0.369251
$802$	−1.10245e13	−0.940969
$803$	−1.52123e13	−1.29114
$804$	5.68697e12	0.479986
$805$	0	0
$806$	1.81977e11	0.0151883
$807$	6.66511e12	0.553193
$808$	−1.53454e13	−1.26656
$809$	−8.13781e12	−0.667943	−0.333971	−	0.942583i	$-0.608389\pi$
$809$	−8.13781e12	−0.667943	−0.333971	+	0.942583i	$0.608389\pi$
$810$	−8.51573e11	−0.0695087
$811$	1.14798e13	0.931836	0.465918	−	0.884828i	$-0.345724\pi$
$811$	1.14798e13	0.931836	0.465918	+	0.884828i	$0.345724\pi$
$812$	0	0
$813$	4.14380e12	0.332653
$814$	−5.06305e12	−0.404206
$815$	−2.58160e13	−2.04965
$816$	1.36720e12	0.107951
$817$	−3.23573e13	−2.54081
$818$	4.27356e12	0.333734
$819$	0	0
$820$	6.39333e12	0.493816
$821$	1.93120e13	1.48349	0.741744	−	0.670683i	$-0.233999\pi$
$821$	1.93120e13	1.48349	0.741744	+	0.670683i	$0.233999\pi$
$822$	1.23798e12	0.0945783
$823$	−1.34161e13	−1.01936	−0.509678	−	0.860365i	$-0.670235\pi$
$823$	−1.34161e13	−1.01936	−0.509678	+	0.860365i	$0.670235\pi$
$824$	−1.49526e13	−1.12991
$825$	−3.63371e12	−0.273091
$826$	0	0
$827$	1.15564e13	0.859110	0.429555	−	0.903041i	$-0.358670\pi$
$827$	1.15564e13	0.859110	0.429555	+	0.903041i	$0.358670\pi$
$828$	7.39435e11	0.0546718
$829$	1.66641e13	1.22543	0.612713	−	0.790305i	$-0.290078\pi$
$829$	1.66641e13	1.22543	0.612713	+	0.790305i	$0.290078\pi$
$830$	7.63058e12	0.558093
$831$	7.66755e12	0.557766
$832$	−1.20764e12	−0.0873739
$833$	0	0
$834$	−5.15497e12	−0.368960
$835$	−8.18050e12	−0.582359
$836$	−1.32395e13	−0.937439
$837$	−1.75251e11	−0.0123423
$838$	−7.29446e11	−0.0510969
$839$	−2.10892e13	−1.46937	−0.734687	−	0.678406i	$-0.762671\pi$
$839$	−2.10892e13	−1.46937	−0.734687	+	0.678406i	$0.762671\pi$
$840$	0	0
$841$	2.02226e13	1.39398
$842$	7.63225e12	0.523297
$843$	−1.39057e13	−0.948348
$844$	−9.79779e12	−0.664641
$845$	1.44497e13	0.975000
$846$	7.38011e11	0.0495332
$847$	0	0
$848$	2.34228e12	0.155545
$849$	3.97465e10	0.00262551
$850$	2.59033e12	0.170204
$851$	−3.45104e12	−0.225563
$852$	1.10926e13	0.721200
$853$	−9.39039e12	−0.607314	−0.303657	−	0.952781i	$-0.598208\pi$
$853$	−9.39039e12	−0.607314	−0.303657	+	0.952781i	$0.598208\pi$
$854$	0	0
$855$	1.03928e13	0.665095
$856$	1.71695e13	1.09302
$857$	−7.67820e11	−0.0486234	−0.0243117	−	0.999704i	$-0.507739\pi$
$857$	−7.67820e11	−0.0486234	−0.0243117	+	0.999704i	$0.507739\pi$
$858$	1.70780e12	0.107583
$859$	1.13337e13	0.710234	0.355117	−	0.934822i	$-0.384441\pi$
$859$	1.13337e13	0.710234	0.355117	+	0.934822i	$0.384441\pi$
$860$	2.47133e13	1.54060
$861$	0	0
$862$	9.26163e12	0.571353
$863$	−3.01579e13	−1.85077	−0.925384	−	0.379031i	$-0.876257\pi$
$863$	−3.01579e13	−1.85077	−0.925384	+	0.379031i	$0.876257\pi$
$864$	3.24482e12	0.198098
$865$	3.43094e12	0.208373
$866$	7.17234e12	0.433342
$867$	−6.45534e12	−0.388002
$868$	0	0
$869$	1.78292e13	1.06058
$870$	9.44317e12	0.558832
$871$	8.95274e12	0.527077
$872$	−1.65947e13	−0.971953
$873$	−6.66725e12	−0.388493
$874$	2.91912e12	0.169220
$875$	0	0
$876$	−1.24765e13	−0.715854
$877$	−1.07917e13	−0.616017	−0.308008	−	0.951384i	$-0.599662\pi$
$877$	−1.07917e13	−0.616017	−0.308008	+	0.951384i	$0.599662\pi$
$878$	−3.32256e12	−0.188689
$879$	1.55085e13	0.876231
$880$	5.78283e12	0.325063
$881$	1.64443e12	0.0919653	0.0459826	−	0.998942i	$-0.485358\pi$
$881$	1.64443e12	0.0919653	0.0459826	+	0.998942i	$0.485358\pi$
$882$	0	0
$883$	9.67496e12	0.535582	0.267791	−	0.963477i	$-0.413706\pi$
$883$	9.67496e12	0.535582	0.267791	+	0.963477i	$0.413706\pi$
$884$	3.76356e12	0.207283
$885$	−1.90522e13	−1.04400
$886$	1.27967e13	0.697662
$887$	−1.50083e13	−0.814093	−0.407046	−	0.913407i	$-0.633441\pi$
$887$	−1.50083e13	−0.814093	−0.407046	+	0.913407i	$0.633441\pi$
$888$	−9.64827e12	−0.520704
$889$	0	0
$890$	−1.29712e13	−0.692986
$891$	−1.64467e12	−0.0874239
$892$	1.13624e13	0.600938
$893$	−9.00683e12	−0.473959
$894$	9.24131e10	0.00483855
$895$	−5.60343e12	−0.291911
$896$	0	0
$897$	1.16406e12	0.0600356
$898$	−1.49692e12	−0.0768168
$899$	1.94337e12	0.0992288
$900$	−2.98023e12	−0.151411
$901$	5.39701e12	0.272830
$902$	−3.99418e12	−0.200909
$903$	0	0
$904$	−4.39581e12	−0.218918
$905$	−9.21239e12	−0.456514
$906$	7.51137e12	0.370376
$907$	1.59099e13	0.780609	0.390305	−	0.920686i	$-0.372370\pi$
$907$	1.59099e13	0.780609	0.390305	+	0.920686i	$0.372370\pi$
$908$	9.35274e12	0.456618
$909$	1.00128e13	0.486430
$910$	0	0
$911$	−6.50349e12	−0.312834	−0.156417	−	0.987691i	$-0.549994\pi$
$911$	−6.50349e12	−0.312834	−0.156417	+	0.987691i	$0.549994\pi$
$912$	−6.20983e12	−0.297237
$913$	1.47372e13	0.701935
$914$	5.02187e12	0.238017
$915$	−1.99223e13	−0.939604
$916$	−5.27325e12	−0.247485
$917$	0	0
$918$	1.17242e12	0.0544870
$919$	1.68373e13	0.778669	0.389335	−	0.921096i	$-0.372705\pi$
$919$	1.68373e13	0.778669	0.389335	+	0.921096i	$0.372705\pi$
$920$	−5.18024e12	−0.238399
$921$	8.38319e12	0.383920
$922$	1.45791e13	0.664420
$923$	1.74626e13	0.791956
$924$	0	0
$925$	1.39091e13	0.624686
$926$	−6.09621e12	−0.272465
$927$	9.75657e12	0.433949
$928$	−3.59821e13	−1.59265
$929$	−1.72314e13	−0.759015	−0.379508	−	0.925189i	$-0.623907\pi$
$929$	−1.72314e13	−0.759015	−0.379508	+	0.925189i	$0.623907\pi$
$930$	5.28411e11	0.0231632
$931$	0	0
$932$	−2.22790e13	−0.967217
$933$	1.78385e13	0.770711
$934$	−7.01066e12	−0.301438
$935$	1.33246e13	0.570168
$936$	3.25442e12	0.138590
$937$	−9.51914e12	−0.403431	−0.201716	−	0.979444i	$-0.564652\pi$
$937$	−9.51914e12	−0.403431	−0.201716	+	0.979444i	$0.564652\pi$
$938$	0	0
$939$	2.29115e13	0.961743
$940$	6.87910e12	0.287380
$941$	2.67319e13	1.11142	0.555708	−	0.831378i	$-0.312447\pi$
$941$	2.67319e13	1.11142	0.555708	+	0.831378i	$0.312447\pi$
$942$	3.79508e12	0.157034
$943$	−2.72249e12	−0.112115
$944$	1.13839e13	0.466572
$945$	0	0
$946$	−1.54395e13	−0.626791
$947$	−2.85733e13	−1.15448	−0.577239	−	0.816575i	$-0.695870\pi$
$947$	−2.85733e13	−1.15448	−0.577239	+	0.816575i	$0.695870\pi$
$948$	1.46228e13	0.588020
$949$	−1.96412e13	−0.786087
$950$	−1.17653e13	−0.468646
$951$	−7.95791e12	−0.315491
$952$	0	0
$953$	−4.39474e13	−1.72590	−0.862948	−	0.505292i	$-0.831385\pi$
$953$	−4.39474e13	−1.72590	−0.862948	+	0.505292i	$0.831385\pi$
$954$	2.00858e12	0.0785095
$955$	9.91237e11	0.0385623
$956$	2.91537e12	0.112884
$957$	1.82379e13	0.702865
$958$	−5.88598e11	−0.0225774
$959$	0	0
$960$	−3.50664e12	−0.133251
$961$	−2.63309e13	−0.995887
$962$	−6.53712e12	−0.246093
$963$	−1.12031e13	−0.419778
$964$	2.73059e13	1.01838
$965$	4.73406e13	1.75736
$966$	0	0
$967$	−3.90275e13	−1.43533	−0.717665	−	0.696388i	$-0.754789\pi$
$967$	−3.90275e13	−1.43533	−0.717665	+	0.696388i	$0.754789\pi$
$968$	9.03152e12	0.330614
$969$	−1.43085e13	−0.521359
$970$	2.01029e13	0.729098
$971$	−7.45694e12	−0.269200	−0.134600	−	0.990900i	$-0.542975\pi$
$971$	−7.45694e12	−0.269200	−0.134600	+	0.990900i	$0.542975\pi$
$972$	−1.34890e12	−0.0484708
$973$	0	0
$974$	−1.84143e13	−0.655601
$975$	−4.69164e12	−0.166266
$976$	1.19039e13	0.419918
$977$	6.62598e12	0.232662	0.116331	−	0.993211i	$-0.462887\pi$
$977$	6.62598e12	0.232662	0.116331	+	0.993211i	$0.462887\pi$
$978$	1.32279e13	0.462343
$979$	−2.50517e13	−0.871596
$980$	0	0
$981$	1.08280e13	0.373283
$982$	1.08224e13	0.371384
$983$	2.94034e13	1.00440	0.502201	−	0.864751i	$-0.332524\pi$
$983$	2.94034e13	1.00440	0.502201	+	0.864751i	$0.332524\pi$
$984$	−7.61141e12	−0.258814
$985$	3.74825e13	1.26872
$986$	−1.30011e13	−0.438061
$987$	0	0
$988$	−1.70941e13	−0.570741
$989$	−1.05238e13	−0.349774
$990$	4.95897e12	0.164071
$991$	4.61297e13	1.51932	0.759660	−	0.650320i	$-0.225365\pi$
$991$	4.61297e13	1.51932	0.759660	+	0.650320i	$0.225365\pi$
$992$	−2.01345e12	−0.0660144
$993$	2.68353e13	0.875861
$994$	0	0
$995$	−4.09858e13	−1.32565
$996$	1.20869e13	0.389177
$997$	−4.16186e13	−1.33401	−0.667006	−	0.745053i	$-0.732424\pi$
$997$	−4.16186e13	−1.33401	−0.667006	+	0.745053i	$0.732424\pi$
$998$	2.38666e13	0.761559
$999$	6.29549e12	0.199979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.10.a.n.1.6	yes	10
7.6	odd	2		147.10.a.m.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.10.a.m.1.6	✓	10	7.6	odd	2
147.10.a.n.1.6	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q+11.1866 q^{2} +81.0000 q^{3} -386.860 q^{4} -1768.41 q^{5} +906.115 q^{6} -10055.2 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+11.1866 q^{2} +81.0000 q^{3} -386.860 q^{4} -1768.41 q^{5} +906.115 q^{6} -10055.2 q^{8} +6561.00 q^{9} -19782.5 q^{10} -38206.7 q^{11} -31335.6 q^{12} -49330.3 q^{13} -143241. q^{15} +85588.8 q^{16} +197211. q^{17} +73395.3 q^{18} -895731. q^{19} +684128. q^{20} -427403. q^{22} -291324. q^{23} -814470. q^{24} +1.17416e6 q^{25} -551839. q^{26} +531441. q^{27} -5.89320e6 q^{29} -1.60238e6 q^{30} -329766. q^{31} +6.10571e6 q^{32} -3.09474e6 q^{33} +2.20612e6 q^{34} -2.53819e6 q^{36} +1.18461e7 q^{37} -1.00202e7 q^{38} -3.99576e6 q^{39} +1.77817e7 q^{40} +9.34523e6 q^{41} +3.61239e7 q^{43} +1.47806e7 q^{44} -1.16025e7 q^{45} -3.25893e6 q^{46} +1.00553e7 q^{47} +6.93269e6 q^{48} +1.31348e7 q^{50} +1.59741e7 q^{51} +1.90839e7 q^{52} +2.73666e7 q^{53} +5.94502e6 q^{54} +6.75652e7 q^{55} -7.25542e7 q^{57} -6.59249e7 q^{58} +1.33007e8 q^{59} +5.54143e7 q^{60} +1.39082e8 q^{61} -3.68896e6 q^{62} +2.44807e7 q^{64} +8.72363e7 q^{65} -3.46197e7 q^{66} -1.81486e8 q^{67} -7.62931e7 q^{68} -2.35972e7 q^{69} -3.53993e8 q^{71} -6.59721e7 q^{72} +3.98157e8 q^{73} +1.32517e8 q^{74} +9.51066e7 q^{75} +3.46522e8 q^{76} -4.46989e7 q^{78} -4.66650e8 q^{79} -1.51356e8 q^{80} +4.30467e7 q^{81} +1.04541e8 q^{82} -3.85723e8 q^{83} -3.48751e8 q^{85} +4.04104e8 q^{86} -4.77349e8 q^{87} +3.84176e8 q^{88} +6.55688e8 q^{89} -1.29793e8 q^{90} +1.12702e8 q^{92} -2.67110e7 q^{93} +1.12485e8 q^{94} +1.58402e9 q^{95} +4.94562e8 q^{96} -1.01619e9 q^{97} -2.50674e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 34 q^{2} + 810 q^{3} + 2902 q^{4} + 2500 q^{5} + 2754 q^{6} + 33966 q^{8} + 65610 q^{9}+O(q^{10}) \) 10 * q + 34 * q^2 + 810 * q^3 + 2902 * q^4 + 2500 * q^5 + 2754 * q^6 + 33966 * q^8 + 65610 * q^9	\( 10 q + 34 q^{2} + 810 q^{3} + 2902 q^{4} + 2500 q^{5} + 2754 q^{6} + 33966 q^{8} + 65610 q^{9} + 16896 q^{10} - 65860 q^{11} + 235062 q^{12} + 228488 q^{13} + 202500 q^{15} + 370722 q^{16} + 934948 q^{17} + 223074 q^{18} + 865920 q^{19} + 1636388 q^{20} + 953900 q^{22} + 1842236 q^{23} + 2751246 q^{24} + 10100266 q^{25} - 1058820 q^{26} + 5314410 q^{27} + 5490136 q^{29} + 1368576 q^{30} + 14852632 q^{31} + 35422866 q^{32} - 5334660 q^{33} + 10917584 q^{34} + 19040022 q^{36} - 1086664 q^{37} + 50821960 q^{38} + 18507528 q^{39} + 85184440 q^{40} + 37333348 q^{41} + 33064992 q^{43} - 85976716 q^{44} + 16402500 q^{45} + 82555644 q^{46} + 16899936 q^{47} + 30028482 q^{48} + 163420178 q^{50} + 75730788 q^{51} - 207979520 q^{52} + 26637644 q^{53} + 18068994 q^{54} - 153534056 q^{55} + 70139520 q^{57} - 257784480 q^{58} + 54375736 q^{59} + 132547428 q^{60} + 313427536 q^{61} + 85959664 q^{62} + 84075878 q^{64} - 704088228 q^{65} + 77265900 q^{66} + 11289312 q^{67} + 1029044740 q^{68} + 149221116 q^{69} - 460380868 q^{71} + 222850926 q^{72} + 717630728 q^{73} - 1827958120 q^{74} + 818121546 q^{75} + 1523608144 q^{76} - 85764420 q^{78} + 1162327376 q^{79} + 3697302420 q^{80} + 430467210 q^{81} + 2664169496 q^{82} + 292067992 q^{83} + 30841228 q^{85} - 2279150960 q^{86} + 444701016 q^{87} - 943587804 q^{88} + 3469605580 q^{89} + 110854656 q^{90} - 2881942700 q^{92} + 1203063192 q^{93} + 4828323784 q^{94} + 530405560 q^{95} + 2869252146 q^{96} + 1533503432 q^{97} - 432107460 q^{99}+O(q^{100}) \) 10 * q + 34 * q^2 + 810 * q^3 + 2902 * q^4 + 2500 * q^5 + 2754 * q^6 + 33966 * q^8 + 65610 * q^9 + 16896 * q^10 - 65860 * q^11 + 235062 * q^12 + 228488 * q^13 + 202500 * q^15 + 370722 * q^16 + 934948 * q^17 + 223074 * q^18 + 865920 * q^19 + 1636388 * q^20 + 953900 * q^22 + 1842236 * q^23 + 2751246 * q^24 + 10100266 * q^25 - 1058820 * q^26 + 5314410 * q^27 + 5490136 * q^29 + 1368576 * q^30 + 14852632 * q^31 + 35422866 * q^32 - 5334660 * q^33 + 10917584 * q^34 + 19040022 * q^36 - 1086664 * q^37 + 50821960 * q^38 + 18507528 * q^39 + 85184440 * q^40 + 37333348 * q^41 + 33064992 * q^43 - 85976716 * q^44 + 16402500 * q^45 + 82555644 * q^46 + 16899936 * q^47 + 30028482 * q^48 + 163420178 * q^50 + 75730788 * q^51 - 207979520 * q^52 + 26637644 * q^53 + 18068994 * q^54 - 153534056 * q^55 + 70139520 * q^57 - 257784480 * q^58 + 54375736 * q^59 + 132547428 * q^60 + 313427536 * q^61 + 85959664 * q^62 + 84075878 * q^64 - 704088228 * q^65 + 77265900 * q^66 + 11289312 * q^67 + 1029044740 * q^68 + 149221116 * q^69 - 460380868 * q^71 + 222850926 * q^72 + 717630728 * q^73 - 1827958120 * q^74 + 818121546 * q^75 + 1523608144 * q^76 - 85764420 * q^78 + 1162327376 * q^79 + 3697302420 * q^80 + 430467210 * q^81 + 2664169496 * q^82 + 292067992 * q^83 + 30841228 * q^85 - 2279150960 * q^86 + 444701016 * q^87 - 943587804 * q^88 + 3469605580 * q^89 + 110854656 * q^90 - 2881942700 * q^92 + 1203063192 * q^93 + 4828323784 * q^94 + 530405560 * q^95 + 2869252146 * q^96 + 1533503432 * q^97 - 432107460 * q^99

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