LMFDB - Embedded newform 147.10.a.h.1.2

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:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1058x^{2} - 2280x + 92160 $ x^4 - x^3 - 1058x^2 - 2280x + 92160
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-11.3372$ 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)

$f(q)$	$=$	$q-3.33717 q^{2} +81.0000 q^{3} -500.863 q^{4} -2645.54 q^{5} -270.311 q^{6} +3380.10 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-3.33717 q^{2} +81.0000 q^{3} -500.863 q^{4} -2645.54 q^{5} -270.311 q^{6} +3380.10 q^{8} +6561.00 q^{9} +8828.63 q^{10} +79031.2 q^{11} -40569.9 q^{12} -99002.2 q^{13} -214289. q^{15} +245162. q^{16} -325991. q^{17} -21895.2 q^{18} +765559. q^{19} +1.32505e6 q^{20} -263741. q^{22} +1.98912e6 q^{23} +273788. q^{24} +5.04577e6 q^{25} +330387. q^{26} +531441. q^{27} -4.67101e6 q^{29} +715119. q^{30} -1.20392e6 q^{31} -2.54876e6 q^{32} +6.40153e6 q^{33} +1.08789e6 q^{34} -3.28616e6 q^{36} -1.05846e7 q^{37} -2.55480e6 q^{38} -8.01918e6 q^{39} -8.94219e6 q^{40} +4.28895e6 q^{41} +1.01835e7 q^{43} -3.95838e7 q^{44} -1.73574e7 q^{45} -6.63802e6 q^{46} +3.04475e7 q^{47} +1.98581e7 q^{48} -1.68386e7 q^{50} -2.64053e7 q^{51} +4.95866e7 q^{52} -4.58569e7 q^{53} -1.77351e6 q^{54} -2.09080e8 q^{55} +6.20102e7 q^{57} +1.55880e7 q^{58} -2.54054e7 q^{59} +1.07329e8 q^{60} -1.76073e8 q^{61} +4.01769e6 q^{62} -1.17017e8 q^{64} +2.61915e8 q^{65} -2.13630e7 q^{66} +3.48566e7 q^{67} +1.63277e8 q^{68} +1.61118e8 q^{69} +1.82411e6 q^{71} +2.21768e7 q^{72} -9.69754e7 q^{73} +3.53225e7 q^{74} +4.08707e8 q^{75} -3.83440e8 q^{76} +2.67614e7 q^{78} +2.60192e8 q^{79} -6.48587e8 q^{80} +4.30467e7 q^{81} -1.43130e7 q^{82} +5.33308e7 q^{83} +8.62424e8 q^{85} -3.39840e7 q^{86} -3.78352e8 q^{87} +2.67133e8 q^{88} +4.66299e8 q^{89} +5.79246e7 q^{90} -9.96275e8 q^{92} -9.75175e7 q^{93} -1.01608e8 q^{94} -2.02532e9 q^{95} -2.06449e8 q^{96} -1.14667e9 q^{97} +5.18524e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 33 q^{2} + 324 q^{3} + 341 q^{4} - 2478 q^{5} + 2673 q^{6} + 29271 q^{8} + 26244 q^{9}+O(q^{10}) $ 4 * q + 33 * q^2 + 324 * q^3 + 341 * q^4 - 2478 * q^5 + 2673 * q^6 + 29271 * q^8 + 26244 * q^9	\( 4 q + 33 q^{2} + 324 q^{3} + 341 q^{4} - 2478 q^{5} + 2673 q^{6} + 29271 q^{8} + 26244 q^{9} - 83028 q^{10} - 26790 q^{11} + 27621 q^{12} - 140448 q^{13} - 200718 q^{15} + 414353 q^{16} - 543558 q^{17} + 216513 q^{18} - 209220 q^{19} - 743028 q^{20} - 3635972 q^{22} - 66690 q^{23} + 2370951 q^{24} + 4122832 q^{25} - 2196084 q^{26} + 2125764 q^{27} - 6216804 q^{29} - 6725268 q^{30} + 6910908 q^{31} + 6750975 q^{32} - 2169990 q^{33} + 60288 q^{34} + 2237301 q^{36} + 2536116 q^{37} - 50706276 q^{38} - 11376288 q^{39} - 37854684 q^{40} - 21866058 q^{41} - 57993648 q^{43} - 115415604 q^{44} - 16258158 q^{45} + 53397632 q^{46} + 23771568 q^{47} + 33562593 q^{48} - 21791253 q^{50} - 44028198 q^{51} - 138084468 q^{52} - 55156332 q^{53} + 17537553 q^{54} - 106082940 q^{55} - 16946820 q^{57} + 93059714 q^{58} - 99247488 q^{59} - 60185268 q^{60} - 159659844 q^{61} + 225718296 q^{62} + 156246145 q^{64} + 474661656 q^{65} - 294513732 q^{66} - 161367812 q^{67} - 113241984 q^{68} - 5401890 q^{69} + 404129562 q^{71} + 192047031 q^{72} - 833772468 q^{73} + 490105914 q^{74} + 333949392 q^{75} - 1485481620 q^{76} - 177882804 q^{78} + 169919972 q^{79} - 1774645764 q^{80} + 172186884 q^{81} + 310238208 q^{82} - 1291623648 q^{83} + 975882636 q^{85} - 525437916 q^{86} - 503561124 q^{87} - 1287251772 q^{88} + 1604461830 q^{89} - 544746708 q^{90} - 54018048 q^{92} + 559783548 q^{93} - 1481116920 q^{94} - 164309616 q^{95} + 546828975 q^{96} - 2179753836 q^{97} - 175769190 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 + 324 * q^3 + 341 * q^4 - 2478 * q^5 + 2673 * q^6 + 29271 * q^8 + 26244 * q^9 - 83028 * q^10 - 26790 * q^11 + 27621 * q^12 - 140448 * q^13 - 200718 * q^15 + 414353 * q^16 - 543558 * q^17 + 216513 * q^18 - 209220 * q^19 - 743028 * q^20 - 3635972 * q^22 - 66690 * q^23 + 2370951 * q^24 + 4122832 * q^25 - 2196084 * q^26 + 2125764 * q^27 - 6216804 * q^29 - 6725268 * q^30 + 6910908 * q^31 + 6750975 * q^32 - 2169990 * q^33 + 60288 * q^34 + 2237301 * q^36 + 2536116 * q^37 - 50706276 * q^38 - 11376288 * q^39 - 37854684 * q^40 - 21866058 * q^41 - 57993648 * q^43 - 115415604 * q^44 - 16258158 * q^45 + 53397632 * q^46 + 23771568 * q^47 + 33562593 * q^48 - 21791253 * q^50 - 44028198 * q^51 - 138084468 * q^52 - 55156332 * q^53 + 17537553 * q^54 - 106082940 * q^55 - 16946820 * q^57 + 93059714 * q^58 - 99247488 * q^59 - 60185268 * q^60 - 159659844 * q^61 + 225718296 * q^62 + 156246145 * q^64 + 474661656 * q^65 - 294513732 * q^66 - 161367812 * q^67 - 113241984 * q^68 - 5401890 * q^69 + 404129562 * q^71 + 192047031 * q^72 - 833772468 * q^73 + 490105914 * q^74 + 333949392 * q^75 - 1485481620 * q^76 - 177882804 * q^78 + 169919972 * q^79 - 1774645764 * q^80 + 172186884 * q^81 + 310238208 * q^82 - 1291623648 * q^83 + 975882636 * q^85 - 525437916 * q^86 - 503561124 * q^87 - 1287251772 * q^88 + 1604461830 * q^89 - 544746708 * q^90 - 54018048 * q^92 + 559783548 * q^93 - 1481116920 * q^94 - 164309616 * q^95 + 546828975 * q^96 - 2179753836 * q^97 - 175769190 * 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 $

$2$	−3.33717	−0.147484	−0.0737418	−	0.997277i	$-0.523494\pi$
$2$	−3.33717	−0.147484	−0.0737418	+	0.997277i	$0.523494\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−500.863	−0.978249
$5$	−2645.54	−1.89300	−0.946498	−	0.322710i	$-0.895406\pi$
$5$	−2645.54	−1.89300	−0.946498	+	0.322710i	$0.895406\pi$
$6$	−270.311	−0.0851496
$7$	0	0
$7$	0	0
$8$	3380.10	0.291759
$9$	6561.00	0.333333
$10$	8828.63	0.279186
$11$	79031.2	1.62754	0.813770	−	0.581188i	$-0.197412\pi$
$11$	79031.2	1.62754	0.813770	+	0.581188i	$0.197412\pi$
$12$	−40569.9	−0.564792
$13$	−99002.2	−0.961391	−0.480695	−	0.876888i	$-0.659616\pi$
$13$	−99002.2	−0.961391	−0.480695	+	0.876888i	$0.659616\pi$
$14$	0	0
$15$	−214289.	−1.09292
$16$	245162.	0.935219
$17$	−325991.	−0.946643	−0.473321	−	0.880890i	$-0.656945\pi$
$17$	−325991.	−0.946643	−0.473321	+	0.880890i	$0.656945\pi$
$18$	−21895.2	−0.0491612
$19$	765559.	1.34768	0.673841	−	0.738877i	$-0.264643\pi$
$19$	765559.	1.34768	0.673841	+	0.738877i	$0.264643\pi$
$20$	1.32505e6	1.85182
$21$	0	0
$22$	−263741.	−0.240035
$23$	1.98912e6	1.48213	0.741063	−	0.671436i	$-0.234322\pi$
$23$	1.98912e6	1.48213	0.741063	+	0.671436i	$0.234322\pi$
$24$	273788.	0.168447
$25$	5.04577e6	2.58343
$26$	330387.	0.141789
$27$	531441.	0.192450
$28$	0	0
$29$	−4.67101e6	−1.22636	−0.613182	−	0.789941i	$-0.710111\pi$
$29$	−4.67101e6	−1.22636	−0.613182	+	0.789941i	$0.710111\pi$
$30$	715119.	0.161188
$31$	−1.20392e6	−0.234137	−0.117068	−	0.993124i	$-0.537350\pi$
$31$	−1.20392e6	−0.234137	−0.117068	+	0.993124i	$0.537350\pi$
$32$	−2.54876e6	−0.429688
$33$	6.40153e6	0.939660
$34$	1.08789e6	0.139614
$35$	0	0
$36$	−3.28616e6	−0.326083
$37$	−1.05846e7	−0.928465	−0.464232	−	0.885713i	$-0.653670\pi$
$37$	−1.05846e7	−0.928465	−0.464232	+	0.885713i	$0.653670\pi$
$38$	−2.55480e6	−0.198761
$39$	−8.01918e6	−0.555059
$40$	−8.94219e6	−0.552299
$41$	4.28895e6	0.237041	0.118520	−	0.992952i	$-0.462185\pi$
$41$	4.28895e6	0.237041	0.118520	+	0.992952i	$0.462185\pi$
$42$	0	0
$43$	1.01835e7	0.454242	0.227121	−	0.973866i	$-0.427069\pi$
$43$	1.01835e7	0.454242	0.227121	+	0.973866i	$0.427069\pi$
$44$	−3.95838e7	−1.59214
$45$	−1.73574e7	−0.630999
$46$	−6.63802e6	−0.218589
$47$	3.04475e7	0.910145	0.455072	−	0.890454i	$-0.349613\pi$
$47$	3.04475e7	0.910145	0.455072	+	0.890454i	$0.349613\pi$
$48$	1.98581e7	0.539949
$49$	0	0
$50$	−1.68386e7	−0.381014
$51$	−2.64053e7	−0.546544
$52$	4.95866e7	0.940479
$53$	−4.58569e7	−0.798295	−0.399147	−	0.916887i	$-0.630694\pi$
$53$	−4.58569e7	−0.798295	−0.399147	+	0.916887i	$0.630694\pi$
$54$	−1.77351e6	−0.0283832
$55$	−2.09080e8	−3.08092
$56$	0	0
$57$	6.20102e7	0.778084
$58$	1.55880e7	0.180869
$59$	−2.54054e7	−0.272955	−0.136478	−	0.990643i	$-0.543578\pi$
$59$	−2.54054e7	−0.272955	−0.136478	+	0.990643i	$0.543578\pi$
$60$	1.07329e8	1.06915
$61$	−1.76073e8	−1.62821	−0.814103	−	0.580721i	$-0.802771\pi$
$61$	−1.76073e8	−1.62821	−0.814103	+	0.580721i	$0.802771\pi$
$62$	4.01769e6	0.0345313
$63$	0	0
$64$	−1.17017e8	−0.871847
$65$	2.61915e8	1.81991
$66$	−2.13630e7	−0.138584
$67$	3.48566e7	0.211324	0.105662	−	0.994402i	$-0.466304\pi$
$67$	3.48566e7	0.211324	0.105662	+	0.994402i	$0.466304\pi$
$68$	1.63277e8	0.926052
$69$	1.61118e8	0.855705
$70$	0	0
$71$	1.82411e6	0.00851901	0.00425950	−	0.999991i	$-0.498644\pi$
$71$	1.82411e6	0.00851901	0.00425950	+	0.999991i	$0.498644\pi$
$72$	2.21768e7	0.0972530
$73$	−9.69754e7	−0.399677	−0.199838	−	0.979829i	$-0.564042\pi$
$73$	−9.69754e7	−0.399677	−0.199838	+	0.979829i	$0.564042\pi$
$74$	3.53225e7	0.136933
$75$	4.08707e8	1.49155
$76$	−3.83440e8	−1.31837
$77$	0	0
$78$	2.67614e7	0.0818621
$79$	2.60192e8	0.751573	0.375787	−	0.926706i	$-0.377373\pi$
$79$	2.60192e8	0.751573	0.375787	+	0.926706i	$0.377373\pi$
$80$	−6.48587e8	−1.77037
$81$	4.30467e7	0.111111
$82$	−1.43130e7	−0.0349596
$83$	5.33308e7	0.123347	0.0616733	−	0.998096i	$-0.480356\pi$
$83$	5.33308e7	0.123347	0.0616733	+	0.998096i	$0.480356\pi$
$84$	0	0
$85$	8.62424e8	1.79199
$86$	−3.39840e7	−0.0669933
$87$	−3.78352e8	−0.708042
$88$	2.67133e8	0.474849
$89$	4.66299e8	0.787789	0.393894	−	0.919156i	$-0.371128\pi$
$89$	4.66299e8	0.787789	0.393894	+	0.919156i	$0.371128\pi$
$90$	5.79246e7	0.0930619
$91$	0	0
$92$	−9.96275e8	−1.44989
$93$	−9.75175e7	−0.135179
$94$	−1.01608e8	−0.134231
$95$	−2.02532e9	−2.55116
$96$	−2.06449e8	−0.248081
$97$	−1.14667e9	−1.31512	−0.657560	−	0.753402i	$-0.728411\pi$
$97$	−1.14667e9	−1.31512	−0.657560	+	0.753402i	$0.728411\pi$
$98$	0	0
$99$	5.18524e8	0.542513
$100$	−2.52724e9	−2.52724
$101$	−1.16109e9	−1.11025	−0.555123	−	0.831768i	$-0.687329\pi$
$101$	−1.16109e9	−1.11025	−0.555123	+	0.831768i	$0.687329\pi$
$102$	8.81190e7	0.0806063
$103$	8.35563e8	0.731496	0.365748	−	0.930714i	$-0.380813\pi$
$103$	8.35563e8	0.731496	0.365748	+	0.930714i	$0.380813\pi$
$104$	−3.34637e8	−0.280494
$105$	0	0
$106$	1.53032e8	0.117735
$107$	1.83645e8	0.135441	0.0677207	−	0.997704i	$-0.478427\pi$
$107$	1.83645e8	0.135441	0.0677207	+	0.997704i	$0.478427\pi$
$108$	−2.66179e8	−0.188264
$109$	9.46917e8	0.642529	0.321264	−	0.946990i	$-0.395892\pi$
$109$	9.46917e8	0.642529	0.321264	+	0.946990i	$0.395892\pi$
$110$	6.97737e8	0.454386
$111$	−8.57350e8	−0.536049
$112$	0	0
$113$	1.67020e8	0.0963640	0.0481820	−	0.998839i	$-0.484657\pi$
$113$	1.67020e8	0.0963640	0.0481820	+	0.998839i	$0.484657\pi$
$114$	−2.06939e8	−0.114755
$115$	−5.26229e9	−2.80566
$116$	2.33954e9	1.19969
$117$	−6.49554e8	−0.320464
$118$	8.47821e7	0.0402564
$119$	0	0
$120$	−7.24317e8	−0.318870
$121$	3.88798e9	1.64888
$122$	5.87587e8	0.240134
$123$	3.47405e8	0.136856
$124$	6.02999e8	0.229044
$125$	−8.18172e9	−2.99743
$126$	0	0
$127$	−5.42175e9	−1.84936	−0.924682	−	0.380740i	$-0.875669\pi$
$127$	−5.42175e9	−1.84936	−0.924682	+	0.380740i	$0.875669\pi$
$128$	1.69547e9	0.558271
$129$	8.24861e8	0.262257
$130$	−8.74054e8	−0.268407
$131$	−3.13818e9	−0.931016	−0.465508	−	0.885044i	$-0.654128\pi$
$131$	−3.13818e9	−0.931016	−0.465508	+	0.885044i	$0.654128\pi$
$132$	−3.20629e9	−0.919221
$133$	0	0
$134$	−1.16322e8	−0.0311668
$135$	−1.40595e9	−0.364307
$136$	−1.10188e9	−0.276192
$137$	2.42220e9	0.587446	0.293723	−	0.955891i	$-0.405106\pi$
$137$	2.42220e9	0.587446	0.293723	+	0.955891i	$0.405106\pi$
$138$	−5.37680e8	−0.126202
$139$	2.82906e9	0.642799	0.321400	−	0.946944i	$-0.395847\pi$
$139$	2.82906e9	0.642799	0.321400	+	0.946944i	$0.395847\pi$
$140$	0	0
$141$	2.46624e9	0.525472
$142$	−6.08737e6	−0.00125641
$143$	−7.82426e9	−1.56470
$144$	1.60851e9	0.311740
$145$	1.23574e10	2.32150
$146$	3.23624e8	0.0589457
$147$	0	0
$148$	5.30142e9	0.908269
$149$	−1.41142e9	−0.234595	−0.117298	−	0.993097i	$-0.537423\pi$
$149$	−1.41142e9	−0.234595	−0.117298	+	0.993097i	$0.537423\pi$
$150$	−1.36393e9	−0.219978
$151$	−4.23324e9	−0.662639	−0.331319	−	0.943519i	$-0.607494\pi$
$151$	−4.23324e9	−0.662639	−0.331319	+	0.943519i	$0.607494\pi$
$152$	2.58766e9	0.393198
$153$	−2.13883e9	−0.315548
$154$	0	0
$155$	3.18502e9	0.443220
$156$	4.01651e9	0.542986
$157$	−3.40481e9	−0.447245	−0.223622	−	0.974676i	$-0.571788\pi$
$157$	−3.40481e9	−0.447245	−0.223622	+	0.974676i	$0.571788\pi$
$158$	−8.68304e8	−0.110845
$159$	−3.71441e9	−0.460896
$160$	6.74285e9	0.813398
$161$	0	0
$162$	−1.43654e8	−0.0163871
$163$	−1.17068e10	−1.29895	−0.649475	−	0.760383i	$-0.725011\pi$
$163$	−1.17068e10	−1.29895	−0.649475	+	0.760383i	$0.725011\pi$
$164$	−2.14818e9	−0.231885
$165$	−1.69355e10	−1.77877
$166$	−1.77974e8	−0.0181916
$167$	8.31261e9	0.827015	0.413508	−	0.910501i	$-0.364304\pi$
$167$	8.31261e9	0.827015	0.413508	+	0.910501i	$0.364304\pi$
$168$	0	0
$169$	−8.03056e8	−0.0757278
$170$	−2.87806e9	−0.264289
$171$	5.02283e9	0.449227
$172$	−5.10053e9	−0.444362
$173$	4.45141e9	0.377825	0.188912	−	0.981994i	$-0.439504\pi$
$173$	4.45141e9	0.377825	0.188912	+	0.981994i	$0.439504\pi$
$174$	1.26262e9	0.104425
$175$	0	0
$176$	1.93754e10	1.52211
$177$	−2.05784e9	−0.157591
$178$	−1.55612e9	−0.116186
$179$	1.41244e10	1.02833	0.514165	−	0.857691i	$-0.328102\pi$
$179$	1.41244e10	1.02833	0.514165	+	0.857691i	$0.328102\pi$
$180$	8.69369e9	0.617274
$181$	−1.76205e10	−1.22029	−0.610146	−	0.792289i	$-0.708889\pi$
$181$	−1.76205e10	−1.22029	−0.610146	+	0.792289i	$0.708889\pi$
$182$	0	0
$183$	−1.42619e10	−0.940045
$184$	6.72341e9	0.432423
$185$	2.80019e10	1.75758
$186$	3.25433e8	0.0199367
$187$	−2.57635e10	−1.54070
$188$	−1.52500e10	−0.890348
$189$	0	0
$190$	6.75883e9	0.376253
$191$	2.45726e10	1.33598	0.667992	−	0.744169i	$-0.267154\pi$
$191$	2.45726e10	1.33598	0.667992	+	0.744169i	$0.267154\pi$
$192$	−9.47840e9	−0.503361
$193$	8.79194e9	0.456118	0.228059	−	0.973647i	$-0.426762\pi$
$193$	8.79194e9	0.456118	0.228059	+	0.973647i	$0.426762\pi$
$194$	3.82663e9	0.193959
$195$	2.12151e10	1.05072
$196$	0	0
$197$	−3.49920e10	−1.65528	−0.827638	−	0.561263i	$-0.810316\pi$
$197$	−3.49920e10	−1.65528	−0.827638	+	0.561263i	$0.810316\pi$
$198$	−1.73040e9	−0.0800117
$199$	2.25288e10	1.01836	0.509179	−	0.860661i	$-0.329949\pi$
$199$	2.25288e10	1.01836	0.509179	+	0.860661i	$0.329949\pi$
$200$	1.70552e10	0.753740
$201$	2.82339e9	0.122008
$202$	3.87475e9	0.163743
$203$	0	0
$204$	1.32255e10	0.534656
$205$	−1.13466e10	−0.448718
$206$	−2.78842e9	−0.107884
$207$	1.30506e10	0.494042
$208$	−2.42716e10	−0.899111
$209$	6.05030e10	2.19340
$210$	0	0
$211$	−3.94443e10	−1.36998	−0.684988	−	0.728554i	$-0.740193\pi$
$211$	−3.94443e10	−1.36998	−0.684988	+	0.728554i	$0.740193\pi$
$212$	2.29680e10	0.780931
$213$	1.47753e8	0.00491845
$214$	−6.12854e8	−0.0199754
$215$	−2.69408e10	−0.859879
$216$	1.79632e9	0.0561491
$217$	0	0
$218$	−3.16002e9	−0.0947624
$219$	−7.85501e9	−0.230753
$220$	1.04721e11	3.01391
$221$	3.22739e10	0.910094
$222$	2.86112e9	0.0790584
$223$	−4.83501e10	−1.30926	−0.654629	−	0.755950i	$-0.727175\pi$
$223$	−4.83501e10	−1.30926	−0.654629	+	0.755950i	$0.727175\pi$
$224$	0	0
$225$	3.31053e10	0.861144
$226$	−5.57373e8	−0.0142121
$227$	1.35086e10	0.337672	0.168836	−	0.985644i	$-0.445999\pi$
$227$	1.35086e10	0.337672	0.168836	+	0.985644i	$0.445999\pi$
$228$	−3.10587e10	−0.761160
$229$	−4.42325e10	−1.06288	−0.531438	−	0.847097i	$-0.678348\pi$
$229$	−4.42325e10	−1.06288	−0.531438	+	0.847097i	$0.678348\pi$
$230$	1.75612e10	0.413788
$231$	0	0
$232$	−1.57885e10	−0.357803
$233$	−2.06551e10	−0.459120	−0.229560	−	0.973295i	$-0.573729\pi$
$233$	−2.06551e10	−0.459120	−0.229560	+	0.973295i	$0.573729\pi$
$234$	2.16767e9	0.0472631
$235$	−8.05500e10	−1.72290
$236$	1.27246e10	0.267018
$237$	2.10755e10	0.433921
$238$	0	0
$239$	1.80030e10	0.356906	0.178453	−	0.983948i	$-0.442891\pi$
$239$	1.80030e10	0.356906	0.178453	+	0.983948i	$0.442891\pi$
$240$	−5.25355e10	−1.02212
$241$	−6.02661e10	−1.15079	−0.575395	−	0.817876i	$-0.695152\pi$
$241$	−6.02661e10	−1.15079	−0.575395	+	0.817876i	$0.695152\pi$
$242$	−1.29749e10	−0.243183
$243$	3.48678e9	0.0641500
$244$	8.81887e10	1.59279
$245$	0	0
$246$	−1.15935e9	−0.0201840
$247$	−7.57920e10	−1.29565
$248$	−4.06937e9	−0.0683116
$249$	4.31980e9	0.0712142
$250$	2.73038e10	0.442072
$251$	7.14624e10	1.13644	0.568219	−	0.822877i	$-0.307633\pi$
$251$	7.14624e10	1.13644	0.568219	+	0.822877i	$0.307633\pi$
$252$	0	0
$253$	1.57202e11	2.41222
$254$	1.80933e10	0.272751
$255$	6.98564e10	1.03461
$256$	5.42548e10	0.789511
$257$	−1.40190e10	−0.200456	−0.100228	−	0.994965i	$-0.531957\pi$
$257$	−1.40190e10	−0.200456	−0.100228	+	0.994965i	$0.531957\pi$
$258$	−2.75270e9	−0.0386786
$259$	0	0
$260$	−1.31183e11	−1.78032
$261$	−3.06465e10	−0.408788
$262$	1.04726e10	0.137310
$263$	−6.10227e10	−0.786485	−0.393242	−	0.919435i	$-0.628647\pi$
$263$	−6.10227e10	−0.786485	−0.393242	+	0.919435i	$0.628647\pi$
$264$	2.16378e10	0.274154
$265$	1.21316e11	1.51117
$266$	0	0
$267$	3.77702e10	0.454830
$268$	−1.74584e10	−0.206727
$269$	1.28797e11	1.49975	0.749877	−	0.661577i	$-0.230113\pi$
$269$	1.28797e11	1.49975	0.749877	+	0.661577i	$0.230113\pi$
$270$	4.69189e9	0.0537293
$271$	6.02716e10	0.678814	0.339407	−	0.940640i	$-0.389774\pi$
$271$	6.02716e10	0.678814	0.339407	+	0.940640i	$0.389774\pi$
$272$	−7.99207e10	−0.885318
$273$	0	0
$274$	−8.08330e9	−0.0866385
$275$	3.98773e11	4.20464
$276$	−8.06983e10	−0.837093
$277$	7.30796e10	0.745825	0.372913	−	0.927866i	$-0.378359\pi$
$277$	7.30796e10	0.745825	0.372913	+	0.927866i	$0.378359\pi$
$278$	−9.44105e9	−0.0948023
$279$	−7.89892e9	−0.0780457
$280$	0	0
$281$	−5.34370e10	−0.511286	−0.255643	−	0.966771i	$-0.582287\pi$
$281$	−5.34370e10	−0.511286	−0.255643	+	0.966771i	$0.582287\pi$
$282$	−8.23028e9	−0.0774985
$283$	−1.02299e11	−0.948054	−0.474027	−	0.880510i	$-0.657200\pi$
$283$	−1.02299e11	−0.948054	−0.474027	+	0.880510i	$0.657200\pi$
$284$	−9.13631e8	−0.00833371
$285$	−1.64051e11	−1.47291
$286$	2.61109e10	0.230768
$287$	0	0
$288$	−1.67224e10	−0.143229
$289$	−1.23174e10	−0.103867
$290$	−4.12386e10	−0.342383
$291$	−9.28802e10	−0.759285
$292$	4.85714e10	0.390983
$293$	−1.87842e11	−1.48897	−0.744487	−	0.667637i	$-0.767306\pi$
$293$	−1.87842e11	−1.48897	−0.744487	+	0.667637i	$0.767306\pi$
$294$	0	0
$295$	6.72110e10	0.516703
$296$	−3.57769e10	−0.270888
$297$	4.20004e10	0.313220
$298$	4.71016e9	0.0345989
$299$	−1.96927e11	−1.42490
$300$	−2.04706e11	−1.45910
$301$	0	0
$302$	1.41271e10	0.0977283
$303$	−9.40482e10	−0.641001
$304$	1.87686e11	1.26038
$305$	4.65809e11	3.08219
$306$	7.13764e9	0.0465381
$307$	−7.08123e10	−0.454973	−0.227487	−	0.973781i	$-0.573051\pi$
$307$	−7.08123e10	−0.454973	−0.227487	+	0.973781i	$0.573051\pi$
$308$	0	0
$309$	6.76806e10	0.422329
$310$	−1.06290e10	−0.0653677
$311$	−1.05151e11	−0.637367	−0.318684	−	0.947861i	$-0.603241\pi$
$311$	−1.05151e11	−0.637367	−0.318684	+	0.947861i	$0.603241\pi$
$312$	−2.71056e10	−0.161944
$313$	1.74653e11	1.02855	0.514277	−	0.857624i	$-0.328060\pi$
$313$	1.74653e11	1.02855	0.514277	+	0.857624i	$0.328060\pi$
$314$	1.13624e10	0.0659612
$315$	0	0
$316$	−1.30320e11	−0.735226
$317$	8.57687e10	0.477048	0.238524	−	0.971137i	$-0.423336\pi$
$317$	8.57687e10	0.477048	0.238524	+	0.971137i	$0.423336\pi$
$318$	1.23956e10	0.0679745
$319$	−3.69155e11	−1.99596
$320$	3.09574e11	1.65040
$321$	1.48752e10	0.0781972
$322$	0	0
$323$	−2.49566e11	−1.27577
$324$	−2.15605e10	−0.108694
$325$	−4.99542e11	−2.48369
$326$	3.90675e10	0.191574
$327$	7.67003e10	0.370964
$328$	1.44971e10	0.0691588
$329$	0	0
$330$	5.65167e10	0.262340
$331$	−2.64576e11	−1.21150	−0.605751	−	0.795655i	$-0.707127\pi$
$331$	−2.64576e11	−1.21150	−0.605751	+	0.795655i	$0.707127\pi$
$332$	−2.67115e10	−0.120664
$333$	−6.94453e10	−0.309488
$334$	−2.77406e10	−0.121971
$335$	−9.22146e10	−0.400035
$336$	0	0
$337$	2.20252e11	0.930218	0.465109	−	0.885253i	$-0.346015\pi$
$337$	2.20252e11	0.930218	0.465109	+	0.885253i	$0.346015\pi$
$338$	2.67993e9	0.0111686
$339$	1.35286e10	0.0556358
$340$	−4.31957e11	−1.75301
$341$	−9.51472e10	−0.381067
$342$	−1.67620e10	−0.0662536
$343$	0	0
$344$	3.44211e10	0.132529
$345$	−4.26246e11	−1.61985
$346$	−1.48551e10	−0.0557229
$347$	1.50766e11	0.558239	0.279120	−	0.960256i	$-0.409957\pi$
$347$	1.50766e11	0.558239	0.279120	+	0.960256i	$0.409957\pi$
$348$	1.89502e11	0.692641
$349$	−4.14159e11	−1.49435	−0.747175	−	0.664627i	$-0.768590\pi$
$349$	−4.14159e11	−1.49435	−0.747175	+	0.664627i	$0.768590\pi$
$350$	0	0
$351$	−5.26139e10	−0.185020
$352$	−2.01431e11	−0.699335
$353$	−4.85781e11	−1.66515	−0.832576	−	0.553911i	$-0.813135\pi$
$353$	−4.85781e11	−1.66515	−0.832576	+	0.553911i	$0.813135\pi$
$354$	6.86735e9	0.0232420
$355$	−4.82577e9	−0.0161264
$356$	−2.33552e11	−0.770653
$357$	0	0
$358$	−4.71357e10	−0.151662
$359$	1.89715e10	0.0602806	0.0301403	−	0.999546i	$-0.490405\pi$
$359$	1.89715e10	0.0602806	0.0301403	+	0.999546i	$0.490405\pi$
$360$	−5.86697e10	−0.184100
$361$	2.63392e11	0.816245
$362$	5.88025e10	0.179973
$363$	3.14926e11	0.951983
$364$	0	0
$365$	2.56553e11	0.756586
$366$	4.75945e10	0.138641
$367$	−1.85003e11	−0.532330	−0.266165	−	0.963927i	$-0.585757\pi$
$367$	−1.85003e11	−0.532330	−0.266165	+	0.963927i	$0.585757\pi$
$368$	4.87656e11	1.38611
$369$	2.81398e10	0.0790137
$370$	−9.34472e10	−0.259214
$371$	0	0
$372$	4.88429e10	0.132239
$373$	1.62744e11	0.435326	0.217663	−	0.976024i	$-0.430157\pi$
$373$	1.62744e11	0.435326	0.217663	+	0.976024i	$0.430157\pi$
$374$	8.59772e10	0.227228
$375$	−6.62719e11	−1.73057
$376$	1.02915e11	0.265543
$377$	4.62440e11	1.17902
$378$	0	0
$379$	−6.31454e11	−1.57205	−0.786023	−	0.618197i	$-0.787863\pi$
$379$	−6.31454e11	−1.57205	−0.786023	+	0.618197i	$0.787863\pi$
$380$	1.01441e12	2.49566
$381$	−4.39161e11	−1.06773
$382$	−8.20030e10	−0.197036
$383$	6.64362e11	1.57765	0.788824	−	0.614619i	$-0.210690\pi$
$383$	6.64362e11	1.57765	0.788824	+	0.614619i	$0.210690\pi$
$384$	1.37333e11	0.322318
$385$	0	0
$386$	−2.93402e10	−0.0672698
$387$	6.68137e10	0.151414
$388$	5.74325e11	1.28651
$389$	8.52403e11	1.88743	0.943717	−	0.330755i	$-0.107303\pi$
$389$	8.52403e11	1.88743	0.943717	+	0.330755i	$0.107303\pi$
$390$	−7.07984e10	−0.154965
$391$	−6.48435e11	−1.40304
$392$	0	0
$393$	−2.54193e11	−0.537522
$394$	1.16774e11	0.244126
$395$	−6.88348e11	−1.42273
$396$	−2.59709e11	−0.530713
$397$	−7.56347e11	−1.52814	−0.764072	−	0.645131i	$-0.776803\pi$
$397$	−7.56347e11	−1.52814	−0.764072	+	0.645131i	$0.776803\pi$
$398$	−7.51826e10	−0.150191
$399$	0	0
$400$	1.23703e12	2.41608
$401$	4.04861e11	0.781910	0.390955	−	0.920410i	$-0.372145\pi$
$401$	4.04861e11	0.781910	0.390955	+	0.920410i	$0.372145\pi$
$402$	−9.42212e9	−0.0179942
$403$	1.19191e11	0.225097
$404$	5.81547e11	1.08610
$405$	−1.13882e11	−0.210333
$406$	0	0
$407$	−8.36511e11	−1.51111
$408$	−8.92525e10	−0.159459
$409$	−2.34147e11	−0.413746	−0.206873	−	0.978368i	$-0.566329\pi$
$409$	−2.34147e11	−0.413746	−0.206873	+	0.978368i	$0.566329\pi$
$410$	3.78655e10	0.0661784
$411$	1.96198e11	0.339162
$412$	−4.18503e11	−0.715585
$413$	0	0
$414$	−4.35521e10	−0.0728630
$415$	−1.41089e11	−0.233495
$416$	2.52333e11	0.413098
$417$	2.29154e11	0.371120
$418$	−2.01909e11	−0.323491
$419$	1.47195e11	0.233308	0.116654	−	0.993173i	$-0.462783\pi$
$419$	1.47195e11	0.233308	0.116654	+	0.993173i	$0.462783\pi$
$420$	0	0
$421$	3.78623e11	0.587405	0.293703	−	0.955897i	$-0.405112\pi$
$421$	3.78623e11	0.587405	0.293703	+	0.955897i	$0.405112\pi$
$422$	1.31632e11	0.202049
$423$	1.99766e11	0.303382
$424$	−1.55001e11	−0.232910
$425$	−1.64488e12	−2.44559
$426$	−4.93077e8	−0.000725390 0
$427$	0	0
$428$	−9.19809e10	−0.132495
$429$	−6.33765e11	−0.903381
$430$	8.99060e10	0.126818
$431$	−5.59181e11	−0.780557	−0.390279	−	0.920697i	$-0.627621\pi$
$431$	−5.59181e11	−0.780557	−0.390279	+	0.920697i	$0.627621\pi$
$432$	1.30289e11	0.179983
$433$	6.23977e11	0.853047	0.426524	−	0.904476i	$-0.359738\pi$
$433$	6.23977e11	0.853047	0.426524	+	0.904476i	$0.359738\pi$
$434$	0	0
$435$	1.00095e12	1.34032
$436$	−4.74276e11	−0.628553
$437$	1.52279e12	1.99743
$438$	2.62135e10	0.0340323
$439$	−1.20029e12	−1.54240	−0.771198	−	0.636595i	$-0.780342\pi$
$439$	−1.20029e12	−1.54240	−0.771198	+	0.636595i	$0.780342\pi$
$440$	−7.06712e11	−0.898888
$441$	0	0
$442$	−1.07703e11	−0.134224
$443$	2.81076e11	0.346742	0.173371	−	0.984857i	$-0.444534\pi$
$443$	2.81076e11	0.346742	0.173371	+	0.984857i	$0.444534\pi$
$444$	4.29415e11	0.524389
$445$	−1.23361e12	−1.49128
$446$	1.61352e11	0.193094
$447$	−1.14325e11	−0.135444
$448$	0	0
$449$	2.35237e11	0.273147	0.136574	−	0.990630i	$-0.456391\pi$
$449$	2.35237e11	0.273147	0.136574	+	0.990630i	$0.456391\pi$
$450$	−1.10478e11	−0.127005
$451$	3.38961e11	0.385793
$452$	−8.36540e10	−0.0942679
$453$	−3.42893e11	−0.382575
$454$	−4.50807e10	−0.0498011
$455$	0	0
$456$	2.09601e11	0.227013
$457$	−1.23596e12	−1.32550	−0.662751	−	0.748840i	$-0.730611\pi$
$457$	−1.23596e12	−1.32550	−0.662751	+	0.748840i	$0.730611\pi$
$458$	1.47612e11	0.156757
$459$	−1.73245e11	−0.182181
$460$	2.63569e12	2.74463
$461$	1.46983e12	1.51570	0.757851	−	0.652428i	$-0.226249\pi$
$461$	1.46983e12	1.51570	0.757851	+	0.652428i	$0.226249\pi$
$462$	0	0
$463$	−7.53498e11	−0.762022	−0.381011	−	0.924571i	$-0.624424\pi$
$463$	−7.53498e11	−0.762022	−0.381011	+	0.924571i	$0.624424\pi$
$464$	−1.14515e12	−1.14692
$465$	2.57987e11	0.255893
$466$	6.89296e10	0.0677126
$467$	−9.58758e11	−0.932788	−0.466394	−	0.884577i	$-0.654447\pi$
$467$	−9.58758e11	−0.932788	−0.466394	+	0.884577i	$0.654447\pi$
$468$	3.25338e11	0.313493
$469$	0	0
$470$	2.68809e11	0.254099
$471$	−2.75790e11	−0.258217
$472$	−8.58727e10	−0.0796372
$473$	8.04812e11	0.739297
$474$	−7.03326e10	−0.0639962
$475$	3.86283e12	3.48164
$476$	0	0
$477$	−3.00867e11	−0.266098
$478$	−6.00790e10	−0.0526377
$479$	−1.43624e12	−1.24657	−0.623287	−	0.781993i	$-0.714203\pi$
$479$	−1.43624e12	−1.24657	−0.623287	+	0.781993i	$0.714203\pi$
$480$	5.46171e11	0.469616
$481$	1.04790e12	0.892617
$482$	2.01118e11	0.169723
$483$	0	0
$484$	−1.94735e12	−1.61302
$485$	3.03356e12	2.48952
$486$	−1.16360e10	−0.00946107
$487$	−1.99054e11	−0.160358	−0.0801790	−	0.996780i	$-0.525549\pi$
$487$	−1.99054e11	−0.160358	−0.0801790	+	0.996780i	$0.525549\pi$
$488$	−5.95145e11	−0.475044
$489$	−9.48248e11	−0.749949
$490$	0	0
$491$	−1.61605e12	−1.25484	−0.627418	−	0.778683i	$-0.715888\pi$
$491$	−1.61605e12	−1.25484	−0.627418	+	0.778683i	$0.715888\pi$
$492$	−1.74002e11	−0.133879
$493$	1.52271e12	1.16093
$494$	2.52931e11	0.191087
$495$	−1.37178e12	−1.02697
$496$	−2.95155e11	−0.218969
$497$	0	0
$498$	−1.44159e10	−0.0105029
$499$	3.53655e11	0.255345	0.127672	−	0.991816i	$-0.459249\pi$
$499$	3.53655e11	0.255345	0.127672	+	0.991816i	$0.459249\pi$
$500$	4.09792e12	2.93223
$501$	6.73322e11	0.477477
$502$	−2.38482e11	−0.167606
$503$	−8.09793e11	−0.564051	−0.282025	−	0.959407i	$-0.591006\pi$
$503$	−8.09793e11	−0.564051	−0.282025	+	0.959407i	$0.591006\pi$
$504$	0	0
$505$	3.07171e12	2.10169
$506$	−5.24611e11	−0.355762
$507$	−6.50475e10	−0.0437215
$508$	2.71555e12	1.80914
$509$	2.13076e12	1.40703	0.703516	−	0.710679i	$-0.251612\pi$
$509$	2.13076e12	1.40703	0.703516	+	0.710679i	$0.251612\pi$
$510$	−2.33123e11	−0.152587
$511$	0	0
$512$	−1.04914e12	−0.674711
$513$	4.06849e11	0.259361
$514$	4.67839e10	0.0295639
$515$	−2.21052e12	−1.38472
$516$	−4.13143e11	−0.256553
$517$	2.40630e12	1.48130
$518$	0	0
$519$	3.60564e11	0.218137
$520$	8.85297e11	0.530975
$521$	−8.69918e11	−0.517260	−0.258630	−	0.965977i	$-0.583271\pi$
$521$	−8.69918e11	−0.517260	−0.258630	+	0.965977i	$0.583271\pi$
$522$	1.02273e11	0.0602895
$523$	−2.51543e12	−1.47012	−0.735062	−	0.678000i	$-0.762847\pi$
$523$	−2.51543e12	−1.47012	−0.735062	+	0.678000i	$0.762847\pi$
$524$	1.57180e12	0.910765
$525$	0	0
$526$	2.03643e11	0.115994
$527$	3.92468e11	0.221644
$528$	1.56941e12	0.878788
$529$	2.15543e12	1.19670
$530$	−4.04853e11	−0.222872
$531$	−1.66685e11	−0.0909851
$532$	0	0
$533$	−4.24615e11	−0.227889
$534$	−1.26046e11	−0.0670799
$535$	−4.85840e11	−0.256390
$536$	1.17819e11	0.0616556
$537$	1.14408e12	0.593707
$538$	−4.29817e11	−0.221189
$539$	0	0
$540$	7.04189e11	0.356383
$541$	5.21096e11	0.261535	0.130768	−	0.991413i	$-0.458256\pi$
$541$	5.21096e11	0.261535	0.130768	+	0.991413i	$0.458256\pi$
$542$	−2.01136e11	−0.100114
$543$	−1.42726e12	−0.704536
$544$	8.30873e11	0.406761
$545$	−2.50511e12	−1.21630
$546$	0	0
$547$	−8.17443e11	−0.390404	−0.195202	−	0.980763i	$-0.562536\pi$
$547$	−8.17443e11	−0.390404	−0.195202	+	0.980763i	$0.562536\pi$
$548$	−1.21319e12	−0.574668
$549$	−1.15522e12	−0.542735
$550$	−1.33077e12	−0.620115
$551$	−3.57593e12	−1.65275
$552$	5.44596e11	0.249660
$553$	0	0
$554$	−2.43879e11	−0.109997
$555$	2.26816e12	1.01474
$556$	−1.41697e12	−0.628818
$557$	−1.67622e12	−0.737875	−0.368937	−	0.929454i	$-0.620278\pi$
$557$	−1.67622e12	−0.737875	−0.368937	+	0.929454i	$0.620278\pi$
$558$	2.63600e10	0.0115104
$559$	−1.00819e12	−0.436704
$560$	0	0
$561$	−2.08684e12	−0.889522
$562$	1.78328e11	0.0754062
$563$	1.70000e12	0.713117	0.356559	−	0.934273i	$-0.383950\pi$
$563$	1.70000e12	0.713117	0.356559	+	0.934273i	$0.383950\pi$
$564$	−1.23525e12	−0.514043
$565$	−4.41858e11	−0.182417
$566$	3.41390e11	0.139822
$567$	0	0
$568$	6.16568e9	0.00248550
$569$	−4.40477e12	−1.76164	−0.880822	−	0.473447i	$-0.843010\pi$
$569$	−4.40477e12	−1.76164	−0.880822	+	0.473447i	$0.843010\pi$
$570$	5.47465e11	0.217230
$571$	−1.92465e12	−0.757687	−0.378844	−	0.925461i	$-0.623678\pi$
$571$	−1.92465e12	−0.757687	−0.378844	+	0.925461i	$0.623678\pi$
$572$	3.91889e12	1.53067
$573$	1.99038e12	0.771330
$574$	0	0
$575$	1.00366e13	3.82897
$576$	−7.67751e11	−0.290616
$577$	2.89993e12	1.08917	0.544585	−	0.838705i	$-0.316687\pi$
$577$	2.89993e12	1.08917	0.544585	+	0.838705i	$0.316687\pi$
$578$	4.11053e10	0.0153187
$579$	7.12147e11	0.263340
$580$	−6.18934e12	−2.27101
$581$	0	0
$582$	3.09957e11	0.111982
$583$	−3.62412e12	−1.29926
$584$	−3.27786e11	−0.116609
$585$	1.71842e12	0.606636
$586$	6.26859e11	0.219599
$587$	2.57559e12	0.895377	0.447688	−	0.894190i	$-0.352247\pi$
$587$	2.57559e12	0.895377	0.447688	+	0.894190i	$0.352247\pi$
$588$	0	0
$589$	−9.21671e11	−0.315542
$590$	−2.24295e11	−0.0762052
$591$	−2.83435e12	−0.955674
$592$	−2.59493e12	−0.868318
$593$	−3.47502e12	−1.15401	−0.577007	−	0.816739i	$-0.695780\pi$
$593$	−3.47502e12	−1.15401	−0.577007	+	0.816739i	$0.695780\pi$
$594$	−1.40163e11	−0.0461948
$595$	0	0
$596$	7.06930e11	0.229492
$597$	1.82484e12	0.587949
$598$	6.57179e11	0.210149
$599$	7.98246e11	0.253347	0.126674	−	0.991944i	$-0.459570\pi$
$599$	7.98246e11	0.253347	0.126674	+	0.991944i	$0.459570\pi$
$600$	1.38147e12	0.435172
$601$	−5.79019e12	−1.81033	−0.905165	−	0.425061i	$-0.860253\pi$
$601$	−5.79019e12	−1.81033	−0.905165	+	0.425061i	$0.860253\pi$
$602$	0	0
$603$	2.28694e11	0.0704413
$604$	2.12028e12	0.648226
$605$	−1.02858e13	−3.12133
$606$	3.13855e11	0.0945371
$607$	−4.05043e12	−1.21102	−0.605512	−	0.795836i	$-0.707031\pi$
$607$	−4.05043e12	−1.21102	−0.605512	+	0.795836i	$0.707031\pi$
$608$	−1.95122e12	−0.579083
$609$	0	0
$610$	−1.55449e12	−0.454572
$611$	−3.01437e12	−0.875005
$612$	1.07126e12	0.308684
$613$	1.24056e12	0.354852	0.177426	−	0.984134i	$-0.443223\pi$
$613$	1.24056e12	0.354852	0.177426	+	0.984134i	$0.443223\pi$
$614$	2.36313e11	0.0671010
$615$	−9.19074e11	−0.259067
$616$	0	0
$617$	−4.49901e12	−1.24978	−0.624890	−	0.780713i	$-0.714856\pi$
$617$	−4.49901e12	−1.24978	−0.624890	+	0.780713i	$0.714856\pi$
$618$	−2.25862e11	−0.0622866
$619$	−2.62927e12	−0.719824	−0.359912	−	0.932986i	$-0.617193\pi$
$619$	−2.62927e12	−0.719824	−0.359912	+	0.932986i	$0.617193\pi$
$620$	−1.59526e12	−0.433580
$621$	1.05710e12	0.285235
$622$	3.50905e11	0.0940012
$623$	0	0
$624$	−1.96600e12	−0.519102
$625$	1.17901e13	3.09070
$626$	−5.82847e11	−0.151695
$627$	4.90074e12	1.26636
$628$	1.70535e12	0.437516
$629$	3.45048e12	0.878924
$630$	0	0
$631$	−7.36205e12	−1.84870	−0.924351	−	0.381543i	$-0.875393\pi$
$631$	−7.36205e12	−1.84870	−0.924351	+	0.381543i	$0.875393\pi$
$632$	8.79473e11	0.219278
$633$	−3.19499e12	−0.790956
$634$	−2.86225e11	−0.0703567
$635$	1.43435e13	3.50084
$636$	1.86041e12	0.450870
$637$	0	0
$638$	1.23193e12	0.294371
$639$	1.19680e10	0.00283967
$640$	−4.48544e12	−1.05681
$641$	2.66273e12	0.622968	0.311484	−	0.950251i	$-0.399174\pi$
$641$	2.66273e12	0.622968	0.311484	+	0.950251i	$0.399174\pi$
$642$	−4.96412e10	−0.0115328
$643$	3.54121e12	0.816963	0.408482	−	0.912767i	$-0.366058\pi$
$643$	3.54121e12	0.816963	0.408482	+	0.912767i	$0.366058\pi$
$644$	0	0
$645$	−2.18220e12	−0.496451
$646$	8.32843e11	0.188155
$647$	1.72826e12	0.387740	0.193870	−	0.981027i	$-0.437896\pi$
$647$	1.72826e12	0.387740	0.193870	+	0.981027i	$0.437896\pi$
$648$	1.45502e11	0.0324177
$649$	−2.00782e12	−0.444245
$650$	1.66706e12	0.366303
$651$	0	0
$652$	5.86349e12	1.27070
$653$	−8.59193e12	−1.84919	−0.924595	−	0.380951i	$-0.875597\pi$
$653$	−8.59193e12	−1.84919	−0.924595	+	0.380951i	$0.875597\pi$
$654$	−2.55962e11	−0.0547111
$655$	8.30219e12	1.76241
$656$	1.05149e12	0.221685
$657$	−6.36256e11	−0.133226
$658$	0	0
$659$	3.58554e12	0.740577	0.370289	−	0.928917i	$-0.379259\pi$
$659$	3.58554e12	0.740577	0.370289	+	0.928917i	$0.379259\pi$
$660$	8.48237e12	1.74008
$661$	−3.11814e12	−0.635314	−0.317657	−	0.948206i	$-0.602896\pi$
$661$	−3.11814e12	−0.635314	−0.317657	+	0.948206i	$0.602896\pi$
$662$	8.82934e11	0.178676
$663$	2.61419e12	0.525443
$664$	1.80263e11	0.0359875
$665$	0	0
$666$	2.31751e11	0.0456444
$667$	−9.29118e12	−1.81763
$668$	−4.16348e12	−0.809026
$669$	−3.91636e12	−0.755901
$670$	3.07736e11	0.0589986
$671$	−1.39153e13	−2.64997
$672$	0	0
$673$	−5.88890e12	−1.10654	−0.553269	−	0.833003i	$-0.686620\pi$
$673$	−5.88890e12	−1.10654	−0.553269	+	0.833003i	$0.686620\pi$
$674$	−7.35018e11	−0.137192
$675$	2.68153e12	0.497182
$676$	4.02221e11	0.0740806
$677$	−1.07865e13	−1.97348	−0.986738	−	0.162324i	$-0.948101\pi$
$677$	−1.07865e13	−1.97348	−0.986738	+	0.162324i	$0.948101\pi$
$678$	−4.51472e10	−0.00820536
$679$	0	0
$680$	2.91508e12	0.522830
$681$	1.09420e12	0.194955
$682$	3.17523e11	0.0562011
$683$	−5.09454e12	−0.895802	−0.447901	−	0.894083i	$-0.647828\pi$
$683$	−5.09454e12	−0.895802	−0.447901	+	0.894083i	$0.647828\pi$
$684$	−2.51575e12	−0.439456
$685$	−6.40804e12	−1.11203
$686$	0	0
$687$	−3.58284e12	−0.613651
$688$	2.49660e12	0.424816
$689$	4.53993e12	0.767473
$690$	1.42245e12	0.238901
$691$	9.97523e12	1.66445	0.832227	−	0.554435i	$-0.187066\pi$
$691$	9.97523e12	1.66445	0.832227	+	0.554435i	$0.187066\pi$
$692$	−2.22955e12	−0.369606
$693$	0	0
$694$	−5.03132e11	−0.0823311
$695$	−7.48440e12	−1.21682
$696$	−1.27887e12	−0.206578
$697$	−1.39816e12	−0.224393
$698$	1.38212e12	0.220392
$699$	−1.67306e12	−0.265073
$700$	0	0
$701$	−5.65217e12	−0.884065	−0.442033	−	0.896999i	$-0.645742\pi$
$701$	−5.65217e12	−0.884065	−0.442033	+	0.896999i	$0.645742\pi$
$702$	1.75581e11	0.0272874
$703$	−8.10311e12	−1.25127
$704$	−9.24802e12	−1.41897
$705$	−6.52455e12	−0.994717
$706$	1.62113e12	0.245582
$707$	0	0
$708$	1.03069e12	0.154163
$709$	3.58384e12	0.532649	0.266324	−	0.963883i	$-0.414191\pi$
$709$	3.58384e12	0.532649	0.266324	+	0.963883i	$0.414191\pi$
$710$	1.61044e10	0.00237838
$711$	1.70712e12	0.250524
$712$	1.57614e12	0.229844
$713$	−2.39474e12	−0.347020
$714$	0	0
$715$	2.06994e13	2.96197
$716$	−7.07442e12	−1.00596
$717$	1.45824e12	0.206060
$718$	−6.33112e10	−0.00889039
$719$	−2.92793e12	−0.408584	−0.204292	−	0.978910i	$-0.565489\pi$
$719$	−2.92793e12	−0.408584	−0.204292	+	0.978910i	$0.565489\pi$
$720$	−4.25538e12	−0.590122
$721$	0	0
$722$	−8.78985e11	−0.120383
$723$	−4.88155e12	−0.664409
$724$	8.82544e12	1.19375
$725$	−2.35688e13	−3.16823
$726$	−1.05096e12	−0.140402
$727$	5.01516e12	0.665855	0.332927	−	0.942952i	$-0.391964\pi$
$727$	5.01516e12	0.665855	0.332927	+	0.942952i	$0.391964\pi$
$728$	0	0
$729$	2.82430e11	0.0370370
$730$	−8.56160e11	−0.111584
$731$	−3.31972e12	−0.430005
$732$	7.14328e12	0.919598
$733$	7.65340e12	0.979234	0.489617	−	0.871938i	$-0.337137\pi$
$733$	7.65340e12	0.979234	0.489617	+	0.871938i	$0.337137\pi$
$734$	6.17386e11	0.0785099
$735$	0	0
$736$	−5.06978e12	−0.636852
$737$	2.75476e12	0.343938
$738$	−9.39073e10	−0.0116532
$739$	1.44387e13	1.78085	0.890426	−	0.455129i	$-0.150407\pi$
$739$	1.44387e13	1.78085	0.890426	+	0.455129i	$0.150407\pi$
$740$	−1.40251e13	−1.71935
$741$	−6.13915e12	−0.748043
$742$	0	0
$743$	1.36693e13	1.64549	0.822745	−	0.568411i	$-0.192442\pi$
$743$	1.36693e13	1.64549	0.822745	+	0.568411i	$0.192442\pi$
$744$	−3.29619e11	−0.0394397
$745$	3.73398e12	0.444088
$746$	−5.43104e11	−0.0642034
$747$	3.49904e11	0.0411155
$748$	1.29040e13	1.50719
$749$	0	0
$750$	2.21161e12	0.255230
$751$	1.26119e13	1.44677	0.723385	−	0.690445i	$-0.242585\pi$
$751$	1.26119e13	1.44677	0.723385	+	0.690445i	$0.242585\pi$
$752$	7.46456e12	0.851185
$753$	5.78845e12	0.656123
$754$	−1.54324e12	−0.173885
$755$	1.11992e13	1.25437
$756$	0	0
$757$	−7.92893e12	−0.877573	−0.438786	−	0.898591i	$-0.644592\pi$
$757$	−7.92893e12	−0.877573	−0.438786	+	0.898591i	$0.644592\pi$
$758$	2.10727e12	0.231851
$759$	1.27334e13	1.39269
$760$	−6.84577e12	−0.744323
$761$	1.15722e13	1.25080	0.625398	−	0.780306i	$-0.284937\pi$
$761$	1.15722e13	1.25080	0.625398	+	0.780306i	$0.284937\pi$
$762$	1.46556e12	0.157473
$763$	0	0
$764$	−1.23075e13	−1.30692
$765$	5.65837e12	0.597330
$766$	−2.21709e12	−0.232677
$767$	2.51519e12	0.262417
$768$	4.39464e12	0.455824
$769$	9.49969e12	0.979582	0.489791	−	0.871840i	$-0.337073\pi$
$769$	9.49969e12	0.979582	0.489791	+	0.871840i	$0.337073\pi$
$770$	0	0
$771$	−1.13554e12	−0.115733
$772$	−4.40356e12	−0.446197
$773$	4.79402e12	0.482939	0.241470	−	0.970408i	$-0.422371\pi$
$773$	4.79402e12	0.482939	0.241470	+	0.970408i	$0.422371\pi$
$774$	−2.22969e11	−0.0223311
$775$	−6.07470e12	−0.604877
$776$	−3.87585e12	−0.383698
$777$	0	0
$778$	−2.84461e12	−0.278365
$779$	3.28344e12	0.319456
$780$	−1.06259e13	−1.02787
$781$	1.44162e11	0.0138650
$782$	2.16394e12	0.206926
$783$	−2.48237e12	−0.236014
$784$	0	0
$785$	9.00758e12	0.846632
$786$	8.48285e11	0.0792757
$787$	2.70592e12	0.251437	0.125719	−	0.992066i	$-0.459876\pi$
$787$	2.70592e12	0.251437	0.125719	+	0.992066i	$0.459876\pi$
$788$	1.75262e13	1.61927
$789$	−4.94284e12	−0.454077
$790$	2.29713e12	0.209829
$791$	0	0
$792$	1.75266e12	0.158283
$793$	1.74317e13	1.56534
$794$	2.52406e12	0.225376
$795$	9.82662e12	0.872473
$796$	−1.12839e13	−0.996206
$797$	6.59613e12	0.579065	0.289532	−	0.957168i	$-0.406500\pi$
$797$	6.59613e12	0.579065	0.289532	+	0.957168i	$0.406500\pi$
$798$	0	0
$799$	−9.92561e12	−0.861582
$800$	−1.28604e13	−1.11007
$801$	3.05939e12	0.262596
$802$	−1.35109e12	−0.115319
$803$	−7.66408e12	−0.650490
$804$	−1.41413e12	−0.119354
$805$	0	0
$806$	−3.97760e11	−0.0331981
$807$	1.04325e13	0.865883
$808$	−3.92460e12	−0.323924
$809$	−7.41384e12	−0.608520	−0.304260	−	0.952589i	$-0.598409\pi$
$809$	−7.41384e12	−0.608520	−0.304260	+	0.952589i	$0.598409\pi$
$810$	3.80043e11	0.0310206
$811$	−1.27838e12	−0.103768	−0.0518842	−	0.998653i	$-0.516523\pi$
$811$	−1.27838e12	−0.103768	−0.0518842	+	0.998653i	$0.516523\pi$
$812$	0	0
$813$	4.88200e12	0.391913
$814$	2.79158e12	0.222864
$815$	3.09707e13	2.45891
$816$	−6.47358e12	−0.511139
$817$	7.79604e12	0.612174
$818$	7.81389e11	0.0610208
$819$	0	0
$820$	5.68309e12	0.438957
$821$	7.91579e12	0.608065	0.304032	−	0.952662i	$-0.401667\pi$
$821$	7.91579e12	0.608065	0.304032	+	0.952662i	$0.401667\pi$
$822$	−6.54747e11	−0.0500208
$823$	−4.31347e12	−0.327739	−0.163869	−	0.986482i	$-0.552398\pi$
$823$	−4.31347e12	−0.327739	−0.163869	+	0.986482i	$0.552398\pi$
$824$	2.82428e12	0.213420
$825$	3.23006e13	2.42755
$826$	0	0
$827$	−1.47664e13	−1.09774	−0.548872	−	0.835907i	$-0.684942\pi$
$827$	−1.47664e13	−1.09774	−0.548872	+	0.835907i	$0.684942\pi$
$828$	−6.53656e12	−0.483296
$829$	2.59534e13	1.90853	0.954265	−	0.298962i	$-0.0966405\pi$
$829$	2.59534e13	1.90853	0.954265	+	0.298962i	$0.0966405\pi$
$830$	4.70838e11	0.0344366
$831$	5.91945e12	0.430602
$832$	1.15850e13	0.838186
$833$	0	0
$834$	−7.64725e11	−0.0547341
$835$	−2.19914e13	−1.56554
$836$	−3.03037e13	−2.14569
$837$	−6.39812e11	−0.0450597
$838$	−4.91214e11	−0.0344090
$839$	2.41907e13	1.68547	0.842734	−	0.538330i	$-0.180945\pi$
$839$	2.41907e13	1.68547	0.842734	+	0.538330i	$0.180945\pi$
$840$	0	0
$841$	7.31118e12	0.503971
$842$	−1.26353e12	−0.0866326
$843$	−4.32840e12	−0.295191
$844$	1.97562e13	1.34018
$845$	2.12452e12	0.143352
$846$	−6.66652e11	−0.0447438
$847$	0	0
$848$	−1.12424e13	−0.746580
$849$	−8.28623e12	−0.547359
$850$	5.48924e12	0.360684
$851$	−2.10539e13	−1.37610
$852$	−7.40041e10	−0.00481147
$853$	−2.84196e13	−1.83801	−0.919005	−	0.394246i	$-0.871006\pi$
$853$	−2.84196e13	−1.83801	−0.919005	+	0.394246i	$0.871006\pi$
$854$	0	0
$855$	−1.32881e13	−0.850385
$856$	6.20737e11	0.0395163
$857$	6.51983e12	0.412879	0.206440	−	0.978459i	$-0.433812\pi$
$857$	6.51983e12	0.412879	0.206440	+	0.978459i	$0.433812\pi$
$858$	2.11498e12	0.133234
$859$	−1.24485e13	−0.780097	−0.390048	−	0.920794i	$-0.627542\pi$
$859$	−1.24485e13	−0.780097	−0.390048	+	0.920794i	$0.627542\pi$
$860$	1.34937e13	0.841175
$861$	0	0
$862$	1.86608e12	0.115119
$863$	−1.77195e13	−1.08743	−0.543717	−	0.839269i	$-0.682984\pi$
$863$	−1.77195e13	−1.08743	−0.543717	+	0.839269i	$0.682984\pi$
$864$	−1.35451e12	−0.0826936
$865$	−1.17764e13	−0.715220
$866$	−2.08232e12	−0.125810
$867$	−9.97711e11	−0.0599679
$868$	0	0
$869$	2.05633e13	1.22322
$870$	−3.34033e12	−0.197675
$871$	−3.45088e12	−0.203165
$872$	3.20067e12	0.187464
$873$	−7.52330e12	−0.438373
$874$	−5.08179e12	−0.294588
$875$	0	0
$876$	3.93429e12	0.225734
$877$	−3.45274e13	−1.97090	−0.985452	−	0.169951i	$-0.945639\pi$
$877$	−3.45274e13	−1.97090	−0.985452	+	0.169951i	$0.945639\pi$
$878$	4.00557e12	0.227478
$879$	−1.52152e13	−0.859660
$880$	−5.12586e13	−2.88134
$881$	−1.37388e13	−0.768348	−0.384174	−	0.923261i	$-0.625514\pi$
$881$	−1.37388e13	−0.768348	−0.384174	+	0.923261i	$0.625514\pi$
$882$	0	0
$883$	1.57462e13	0.871672	0.435836	−	0.900026i	$-0.356453\pi$
$883$	1.57462e13	0.871672	0.435836	+	0.900026i	$0.356453\pi$
$884$	−1.61648e13	−0.890298
$885$	5.44409e12	0.298319
$886$	−9.37998e11	−0.0511388
$887$	3.13789e12	0.170209	0.0851044	−	0.996372i	$-0.472878\pi$
$887$	3.13789e12	0.170209	0.0851044	+	0.996372i	$0.472878\pi$
$888$	−2.89793e12	−0.156397
$889$	0	0
$890$	4.11678e12	0.219939
$891$	3.40203e12	0.180838
$892$	2.42168e13	1.28078
$893$	2.33093e13	1.22659
$894$	3.81523e11	0.0199757
$895$	−3.73668e13	−1.94663
$896$	0	0
$897$	−1.59511e13	−0.822667
$898$	−7.85026e11	−0.0402847
$899$	5.62352e12	0.287137
$900$	−1.65812e13	−0.842413
$901$	1.49490e13	0.755700
$902$	−1.13117e12	−0.0568982
$903$	0	0
$904$	5.64543e11	0.0281151
$905$	4.66157e13	2.31001
$906$	1.14429e12	0.0564235
$907$	−2.78510e13	−1.36650	−0.683248	−	0.730186i	$-0.739433\pi$
$907$	−2.78510e13	−1.36650	−0.683248	+	0.730186i	$0.739433\pi$
$908$	−6.76599e12	−0.330327
$909$	−7.61791e12	−0.370082
$910$	0	0
$911$	1.08031e13	0.519656	0.259828	−	0.965655i	$-0.416334\pi$
$911$	1.08031e13	0.519656	0.259828	+	0.965655i	$0.416334\pi$
$912$	1.52026e13	0.727679
$913$	4.21480e12	0.200751
$914$	4.12460e12	0.195490
$915$	3.77306e13	1.77950
$916$	2.21545e13	1.03976
$917$	0	0
$918$	5.78149e11	0.0268688
$919$	1.93214e13	0.893549	0.446775	−	0.894646i	$-0.352573\pi$
$919$	1.93214e13	0.893549	0.446775	+	0.894646i	$0.352573\pi$
$920$	−1.77871e13	−0.818576
$921$	−5.73579e12	−0.262679
$922$	−4.90508e12	−0.223541
$923$	−1.80591e11	−0.00819009
$924$	0	0
$925$	−5.34073e13	−2.39863
$926$	2.51455e12	0.112386
$927$	5.48213e12	0.243832
$928$	1.19053e13	0.526955
$929$	1.12994e13	0.497721	0.248860	−	0.968539i	$-0.419944\pi$
$929$	1.12994e13	0.497721	0.248860	+	0.968539i	$0.419944\pi$
$930$	−8.60946e11	−0.0377400
$931$	0	0
$932$	1.03454e13	0.449133
$933$	−8.51719e12	−0.367984
$934$	3.19954e12	0.137571
$935$	6.81584e13	2.91654
$936$	−2.19555e12	−0.0934981
$937$	−1.95390e12	−0.0828082	−0.0414041	−	0.999142i	$-0.513183\pi$
$937$	−1.95390e12	−0.0828082	−0.0414041	+	0.999142i	$0.513183\pi$
$938$	0	0
$939$	1.41469e13	0.593835
$940$	4.03445e13	1.68543
$941$	−1.35013e13	−0.561334	−0.280667	−	0.959805i	$-0.590556\pi$
$941$	−1.35013e13	−0.561334	−0.280667	+	0.959805i	$0.590556\pi$
$942$	9.20358e11	0.0380827
$943$	8.53122e12	0.351324
$944$	−6.22843e12	−0.255273
$945$	0	0
$946$	−2.68579e12	−0.109034
$947$	2.63565e13	1.06491	0.532455	−	0.846458i	$-0.321270\pi$
$947$	2.63565e13	1.06491	0.532455	+	0.846458i	$0.321270\pi$
$948$	−1.05560e13	−0.424483
$949$	9.60079e12	0.384246
$950$	−1.28909e13	−0.513485
$951$	6.94726e12	0.275424
$952$	0	0
$953$	−3.71071e12	−0.145727	−0.0728634	−	0.997342i	$-0.523214\pi$
$953$	−3.71071e12	−0.145727	−0.0728634	+	0.997342i	$0.523214\pi$
$954$	1.00404e12	0.0392451
$955$	−6.50079e13	−2.52901
$956$	−9.01703e12	−0.349143
$957$	−2.99016e13	−1.15237
$958$	4.79298e12	0.183849
$959$	0	0
$960$	2.50755e13	0.952861
$961$	−2.49902e13	−0.945180
$962$	−3.49701e12	−0.131646
$963$	1.20489e12	0.0451472
$964$	3.01851e13	1.12576
$965$	−2.32595e13	−0.863429
$966$	0	0
$967$	1.74492e13	0.641734	0.320867	−	0.947124i	$-0.396026\pi$
$967$	1.74492e13	0.641734	0.320867	+	0.947124i	$0.396026\pi$
$968$	1.31418e13	0.481077
$969$	−2.02148e13	−0.736568
$970$	−1.01235e13	−0.367163
$971$	2.82463e13	1.01971	0.509853	−	0.860261i	$-0.329700\pi$
$971$	2.82463e13	1.01971	0.509853	+	0.860261i	$0.329700\pi$
$972$	−1.74640e12	−0.0627547
$973$	0	0
$974$	6.64277e11	0.0236502
$975$	−4.04629e13	−1.43396
$976$	−4.31665e13	−1.52273
$977$	1.74154e13	0.611517	0.305759	−	0.952109i	$-0.401090\pi$
$977$	1.74154e13	0.611517	0.305759	+	0.952109i	$0.401090\pi$
$978$	3.16447e12	0.110605
$979$	3.68522e13	1.28216
$980$	0	0
$981$	6.21272e12	0.214176
$982$	5.39302e12	0.185068
$983$	1.23853e13	0.423074	0.211537	−	0.977370i	$-0.432153\pi$
$983$	1.23853e13	0.423074	0.211537	+	0.977370i	$0.432153\pi$
$984$	1.17426e12	0.0399289
$985$	9.25727e13	3.13343
$986$	−5.08154e12	−0.171218
$987$	0	0
$988$	3.79614e13	1.26747
$989$	2.02561e13	0.673244
$990$	4.57785e12	0.151462
$991$	−2.23365e13	−0.735672	−0.367836	−	0.929891i	$-0.619901\pi$
$991$	−2.23365e13	−0.735672	−0.367836	+	0.929891i	$0.619901\pi$
$992$	3.06850e12	0.100606
$993$	−2.14306e13	−0.699460
$994$	0	0
$995$	−5.96010e13	−1.92775
$996$	−2.16363e12	−0.0696652
$997$	2.17593e13	0.697455	0.348727	−	0.937224i	$-0.386614\pi$
$997$	2.17593e13	0.697455	0.348727	+	0.937224i	$0.386614\pi$
$998$	−1.18021e12	−0.0376591
$999$	−5.62507e12	−0.178683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.10.a.h.1.2	yes	4
7.6	odd	2		147.10.a.g.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.10.a.g.1.2	✓	4	7.6	odd	2
147.10.a.h.1.2	yes	4	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)

\(f(q)\)	\(=\)	\(q-3.33717 q^{2} +81.0000 q^{3} -500.863 q^{4} -2645.54 q^{5} -270.311 q^{6} +3380.10 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-3.33717 q^{2} +81.0000 q^{3} -500.863 q^{4} -2645.54 q^{5} -270.311 q^{6} +3380.10 q^{8} +6561.00 q^{9} +8828.63 q^{10} +79031.2 q^{11} -40569.9 q^{12} -99002.2 q^{13} -214289. q^{15} +245162. q^{16} -325991. q^{17} -21895.2 q^{18} +765559. q^{19} +1.32505e6 q^{20} -263741. q^{22} +1.98912e6 q^{23} +273788. q^{24} +5.04577e6 q^{25} +330387. q^{26} +531441. q^{27} -4.67101e6 q^{29} +715119. q^{30} -1.20392e6 q^{31} -2.54876e6 q^{32} +6.40153e6 q^{33} +1.08789e6 q^{34} -3.28616e6 q^{36} -1.05846e7 q^{37} -2.55480e6 q^{38} -8.01918e6 q^{39} -8.94219e6 q^{40} +4.28895e6 q^{41} +1.01835e7 q^{43} -3.95838e7 q^{44} -1.73574e7 q^{45} -6.63802e6 q^{46} +3.04475e7 q^{47} +1.98581e7 q^{48} -1.68386e7 q^{50} -2.64053e7 q^{51} +4.95866e7 q^{52} -4.58569e7 q^{53} -1.77351e6 q^{54} -2.09080e8 q^{55} +6.20102e7 q^{57} +1.55880e7 q^{58} -2.54054e7 q^{59} +1.07329e8 q^{60} -1.76073e8 q^{61} +4.01769e6 q^{62} -1.17017e8 q^{64} +2.61915e8 q^{65} -2.13630e7 q^{66} +3.48566e7 q^{67} +1.63277e8 q^{68} +1.61118e8 q^{69} +1.82411e6 q^{71} +2.21768e7 q^{72} -9.69754e7 q^{73} +3.53225e7 q^{74} +4.08707e8 q^{75} -3.83440e8 q^{76} +2.67614e7 q^{78} +2.60192e8 q^{79} -6.48587e8 q^{80} +4.30467e7 q^{81} -1.43130e7 q^{82} +5.33308e7 q^{83} +8.62424e8 q^{85} -3.39840e7 q^{86} -3.78352e8 q^{87} +2.67133e8 q^{88} +4.66299e8 q^{89} +5.79246e7 q^{90} -9.96275e8 q^{92} -9.75175e7 q^{93} -1.01608e8 q^{94} -2.02532e9 q^{95} -2.06449e8 q^{96} -1.14667e9 q^{97} +5.18524e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 33 q^{2} + 324 q^{3} + 341 q^{4} - 2478 q^{5} + 2673 q^{6} + 29271 q^{8} + 26244 q^{9}+O(q^{10}) \) 4 * q + 33 * q^2 + 324 * q^3 + 341 * q^4 - 2478 * q^5 + 2673 * q^6 + 29271 * q^8 + 26244 * q^9	\( 4 q + 33 q^{2} + 324 q^{3} + 341 q^{4} - 2478 q^{5} + 2673 q^{6} + 29271 q^{8} + 26244 q^{9} - 83028 q^{10} - 26790 q^{11} + 27621 q^{12} - 140448 q^{13} - 200718 q^{15} + 414353 q^{16} - 543558 q^{17} + 216513 q^{18} - 209220 q^{19} - 743028 q^{20} - 3635972 q^{22} - 66690 q^{23} + 2370951 q^{24} + 4122832 q^{25} - 2196084 q^{26} + 2125764 q^{27} - 6216804 q^{29} - 6725268 q^{30} + 6910908 q^{31} + 6750975 q^{32} - 2169990 q^{33} + 60288 q^{34} + 2237301 q^{36} + 2536116 q^{37} - 50706276 q^{38} - 11376288 q^{39} - 37854684 q^{40} - 21866058 q^{41} - 57993648 q^{43} - 115415604 q^{44} - 16258158 q^{45} + 53397632 q^{46} + 23771568 q^{47} + 33562593 q^{48} - 21791253 q^{50} - 44028198 q^{51} - 138084468 q^{52} - 55156332 q^{53} + 17537553 q^{54} - 106082940 q^{55} - 16946820 q^{57} + 93059714 q^{58} - 99247488 q^{59} - 60185268 q^{60} - 159659844 q^{61} + 225718296 q^{62} + 156246145 q^{64} + 474661656 q^{65} - 294513732 q^{66} - 161367812 q^{67} - 113241984 q^{68} - 5401890 q^{69} + 404129562 q^{71} + 192047031 q^{72} - 833772468 q^{73} + 490105914 q^{74} + 333949392 q^{75} - 1485481620 q^{76} - 177882804 q^{78} + 169919972 q^{79} - 1774645764 q^{80} + 172186884 q^{81} + 310238208 q^{82} - 1291623648 q^{83} + 975882636 q^{85} - 525437916 q^{86} - 503561124 q^{87} - 1287251772 q^{88} + 1604461830 q^{89} - 544746708 q^{90} - 54018048 q^{92} + 559783548 q^{93} - 1481116920 q^{94} - 164309616 q^{95} + 546828975 q^{96} - 2179753836 q^{97} - 175769190 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 + 324 * q^3 + 341 * q^4 - 2478 * q^5 + 2673 * q^6 + 29271 * q^8 + 26244 * q^9 - 83028 * q^10 - 26790 * q^11 + 27621 * q^12 - 140448 * q^13 - 200718 * q^15 + 414353 * q^16 - 543558 * q^17 + 216513 * q^18 - 209220 * q^19 - 743028 * q^20 - 3635972 * q^22 - 66690 * q^23 + 2370951 * q^24 + 4122832 * q^25 - 2196084 * q^26 + 2125764 * q^27 - 6216804 * q^29 - 6725268 * q^30 + 6910908 * q^31 + 6750975 * q^32 - 2169990 * q^33 + 60288 * q^34 + 2237301 * q^36 + 2536116 * q^37 - 50706276 * q^38 - 11376288 * q^39 - 37854684 * q^40 - 21866058 * q^41 - 57993648 * q^43 - 115415604 * q^44 - 16258158 * q^45 + 53397632 * q^46 + 23771568 * q^47 + 33562593 * q^48 - 21791253 * q^50 - 44028198 * q^51 - 138084468 * q^52 - 55156332 * q^53 + 17537553 * q^54 - 106082940 * q^55 - 16946820 * q^57 + 93059714 * q^58 - 99247488 * q^59 - 60185268 * q^60 - 159659844 * q^61 + 225718296 * q^62 + 156246145 * q^64 + 474661656 * q^65 - 294513732 * q^66 - 161367812 * q^67 - 113241984 * q^68 - 5401890 * q^69 + 404129562 * q^71 + 192047031 * q^72 - 833772468 * q^73 + 490105914 * q^74 + 333949392 * q^75 - 1485481620 * q^76 - 177882804 * q^78 + 169919972 * q^79 - 1774645764 * q^80 + 172186884 * q^81 + 310238208 * q^82 - 1291623648 * q^83 + 975882636 * q^85 - 525437916 * q^86 - 503561124 * q^87 - 1287251772 * q^88 + 1604461830 * q^89 - 544746708 * q^90 - 54018048 * q^92 + 559783548 * q^93 - 1481116920 * q^94 - 164309616 * q^95 + 546828975 * q^96 - 2179753836 * q^97 - 175769190 * q^99

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