LMFDB - Embedded newform 147.10.a.n.1.8

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			1.8
Root			$23.0552$ 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)

$f(q)$	$=$	$q+31.7120 q^{2} +81.0000 q^{3} +493.652 q^{4} -2528.82 q^{5} +2568.67 q^{6} -581.840 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+31.7120 q^{2} +81.0000 q^{3} +493.652 q^{4} -2528.82 q^{5} +2568.67 q^{6} -581.840 q^{8} +6561.00 q^{9} -80193.9 q^{10} -53154.2 q^{11} +39985.8 q^{12} +165725. q^{13} -204834. q^{15} -271201. q^{16} +176761. q^{17} +208063. q^{18} +948141. q^{19} -1.24836e6 q^{20} -1.68563e6 q^{22} +1.54147e6 q^{23} -47129.0 q^{24} +4.44179e6 q^{25} +5.25548e6 q^{26} +531441. q^{27} -1.17608e6 q^{29} -6.49571e6 q^{30} +94436.5 q^{31} -8.30244e6 q^{32} -4.30549e6 q^{33} +5.60544e6 q^{34} +3.23885e6 q^{36} -325923. q^{37} +3.00675e7 q^{38} +1.34237e7 q^{39} +1.47137e6 q^{40} +1.92437e7 q^{41} +1.17743e7 q^{43} -2.62397e7 q^{44} -1.65916e7 q^{45} +4.88831e7 q^{46} +1.43801e7 q^{47} -2.19673e7 q^{48} +1.40858e8 q^{50} +1.43176e7 q^{51} +8.18107e7 q^{52} +8.55810e6 q^{53} +1.68531e7 q^{54} +1.34417e8 q^{55} +7.67994e7 q^{57} -3.72958e7 q^{58} -1.61765e8 q^{59} -1.01117e8 q^{60} +1.72246e8 q^{61} +2.99477e6 q^{62} -1.24432e8 q^{64} -4.19089e8 q^{65} -1.36536e8 q^{66} -1.40279e8 q^{67} +8.72583e7 q^{68} +1.24859e8 q^{69} -1.76753e8 q^{71} -3.81745e6 q^{72} +2.14991e8 q^{73} -1.03357e7 q^{74} +3.59785e8 q^{75} +4.68052e8 q^{76} +4.25694e8 q^{78} +2.45523e8 q^{79} +6.85818e8 q^{80} +4.30467e7 q^{81} +6.10256e8 q^{82} -3.51175e8 q^{83} -4.46995e8 q^{85} +3.73385e8 q^{86} -9.52622e7 q^{87} +3.09272e7 q^{88} -6.67770e8 q^{89} -5.26152e8 q^{90} +7.60949e8 q^{92} +7.64936e6 q^{93} +4.56022e8 q^{94} -2.39767e9 q^{95} -6.72498e8 q^{96} +1.47599e9 q^{97} -3.48745e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	31.7120	1.40149	0.700743	−	0.713413i	$-0.252852\pi$
$2$	31.7120	1.40149	0.700743	+	0.713413i	$0.252852\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	493.652	0.964165
$5$	−2528.82	−1.80947	−0.904737	−	0.425971i	$-0.859933\pi$
$5$	−2528.82	−1.80947	−0.904737	+	0.425971i	$0.859933\pi$
$6$	2568.67	0.809149
$7$	0	0
$7$	0	0
$8$	−581.840	−0.0502225
$9$	6561.00	0.333333
$10$	−80193.9	−2.53595
$11$	−53154.2	−1.09464	−0.547319	−	0.836924i	$-0.684351\pi$
$11$	−53154.2	−1.09464	−0.547319	+	0.836924i	$0.684351\pi$
$12$	39985.8	0.556661
$13$	165725.	1.60932	0.804662	−	0.593733i	$-0.202346\pi$
$13$	165725.	1.60932	0.804662	+	0.593733i	$0.202346\pi$
$14$	0	0
$15$	−204834.	−1.04470
$16$	−271201.	−1.03455
$17$	176761.	0.513293	0.256646	−	0.966505i	$-0.417382\pi$
$17$	176761.	0.513293	0.256646	+	0.966505i	$0.417382\pi$
$18$	208063.	0.467162
$19$	948141.	1.66910	0.834549	−	0.550934i	$-0.185729\pi$
$19$	948141.	1.66910	0.834549	+	0.550934i	$0.185729\pi$
$20$	−1.24836e6	−1.74463
$21$	0	0
$22$	−1.68563e6	−1.53412
$23$	1.54147e6	1.14857	0.574287	−	0.818654i	$-0.305279\pi$
$23$	1.54147e6	1.14857	0.574287	+	0.818654i	$0.305279\pi$
$24$	−47129.0	−0.0289960
$25$	4.44179e6	2.27420
$26$	5.25548e6	2.25545
$27$	531441.	0.192450
$28$	0	0
$29$	−1.17608e6	−0.308777	−0.154388	−	0.988010i	$-0.549341\pi$
$29$	−1.17608e6	−0.308777	−0.154388	+	0.988010i	$0.549341\pi$
$30$	−6.49571e6	−1.46413
$31$	94436.5	0.0183659	0.00918295	−	0.999958i	$-0.497077\pi$
$31$	94436.5	0.0183659	0.00918295	+	0.999958i	$0.497077\pi$
$32$	−8.30244e6	−1.39969
$33$	−4.30549e6	−0.631989
$34$	5.60544e6	0.719373
$35$	0	0
$36$	3.23885e6	0.321388
$37$	−325923.	−0.0285895	−0.0142948	−	0.999898i	$-0.504550\pi$
$37$	−325923.	−0.0285895	−0.0142948	+	0.999898i	$0.504550\pi$
$38$	3.00675e7	2.33922
$39$	1.34237e7	0.929144
$40$	1.47137e6	0.0908763
$41$	1.92437e7	1.06356	0.531779	−	0.846883i	$-0.321524\pi$
$41$	1.92437e7	1.06356	0.531779	+	0.846883i	$0.321524\pi$
$42$	0	0
$43$	1.17743e7	0.525201	0.262600	−	0.964905i	$-0.415420\pi$
$43$	1.17743e7	0.525201	0.262600	+	0.964905i	$0.415420\pi$
$44$	−2.62397e7	−1.05541
$45$	−1.65916e7	−0.603158
$46$	4.88831e7	1.60971
$47$	1.43801e7	0.429854	0.214927	−	0.976630i	$-0.431049\pi$
$47$	1.43801e7	0.429854	0.214927	+	0.976630i	$0.431049\pi$
$48$	−2.19673e7	−0.597298
$49$	0	0
$50$	1.40858e8	3.18726
$51$	1.43176e7	0.296350
$52$	8.18107e7	1.55165
$53$	8.55810e6	0.148983	0.0744914	−	0.997222i	$-0.476267\pi$
$53$	8.55810e6	0.148983	0.0744914	+	0.997222i	$0.476267\pi$
$54$	1.68531e7	0.269716
$55$	1.34417e8	1.98072
$56$	0	0
$57$	7.67994e7	0.963654
$58$	−3.72958e7	−0.432746
$59$	−1.61765e8	−1.73800	−0.869001	−	0.494810i	$-0.835238\pi$
$59$	−1.61765e8	−1.73800	−0.869001	+	0.494810i	$0.835238\pi$
$60$	−1.01117e8	−1.00726
$61$	1.72246e8	1.59282	0.796408	−	0.604760i	$-0.206731\pi$
$61$	1.72246e8	1.59282	0.796408	+	0.604760i	$0.206731\pi$
$62$	2.99477e6	0.0257396
$63$	0	0
$64$	−1.24432e8	−0.927092
$65$	−4.19089e8	−2.91203
$66$	−1.36536e8	−0.885725
$67$	−1.40279e8	−0.850463	−0.425232	−	0.905085i	$-0.639807\pi$
$67$	−1.40279e8	−0.850463	−0.425232	+	0.905085i	$0.639807\pi$
$68$	8.72583e7	0.494899
$69$	1.24859e8	0.663130
$70$	0	0
$71$	−1.76753e8	−0.825476	−0.412738	−	0.910850i	$-0.635427\pi$
$71$	−1.76753e8	−0.825476	−0.412738	+	0.910850i	$0.635427\pi$
$72$	−3.81745e6	−0.0167408
$73$	2.14991e8	0.886068	0.443034	−	0.896505i	$-0.353902\pi$
$73$	2.14991e8	0.886068	0.443034	+	0.896505i	$0.353902\pi$
$74$	−1.03357e7	−0.0400678
$75$	3.59785e8	1.31301
$76$	4.68052e8	1.60928
$77$	0	0
$78$	4.25694e8	1.30218
$79$	2.45523e8	0.709201	0.354601	−	0.935018i	$-0.384617\pi$
$79$	2.45523e8	0.709201	0.354601	+	0.935018i	$0.384617\pi$
$80$	6.85818e8	1.87199
$81$	4.30467e7	0.111111
$82$	6.10256e8	1.49056
$83$	−3.51175e8	−0.812217	−0.406109	−	0.913825i	$-0.633115\pi$
$83$	−3.51175e8	−0.812217	−0.406109	+	0.913825i	$0.633115\pi$
$84$	0	0
$85$	−4.46995e8	−0.928790
$86$	3.73385e8	0.736062
$87$	−9.52622e7	−0.178272
$88$	3.09272e7	0.0549754
$89$	−6.67770e8	−1.12816	−0.564082	−	0.825719i	$-0.690770\pi$
$89$	−6.67770e8	−1.12816	−0.564082	+	0.825719i	$0.690770\pi$
$90$	−5.26152e8	−0.845318
$91$	0	0
$92$	7.60949e8	1.10742
$93$	7.64936e6	0.0106036
$94$	4.56022e8	0.602435
$95$	−2.39767e9	−3.02019
$96$	−6.72498e8	−0.808110
$97$	1.47599e9	1.69282	0.846410	−	0.532532i	$-0.178760\pi$
$97$	1.47599e9	1.69282	0.846410	+	0.532532i	$0.178760\pi$
$98$	0	0
$99$	−3.48745e8	−0.364879
$100$	2.19270e9	2.19270
$101$	8.72266e8	0.834070	0.417035	−	0.908890i	$-0.363069\pi$
$101$	8.72266e8	0.834070	0.417035	+	0.908890i	$0.363069\pi$
$102$	4.54040e8	0.415330
$103$	−9.96375e8	−0.872279	−0.436139	−	0.899879i	$-0.643655\pi$
$103$	−9.96375e8	−0.872279	−0.436139	+	0.899879i	$0.643655\pi$
$104$	−9.64255e7	−0.0808243
$105$	0	0
$106$	2.71395e8	0.208797
$107$	1.84837e9	1.36321	0.681603	−	0.731722i	$-0.261283\pi$
$107$	1.84837e9	1.36321	0.681603	+	0.731722i	$0.261283\pi$
$108$	2.62347e8	0.185554
$109$	−1.60354e9	−1.08808	−0.544041	−	0.839058i	$-0.683107\pi$
$109$	−1.60354e9	−1.08808	−0.544041	+	0.839058i	$0.683107\pi$
$110$	4.26264e9	2.77595
$111$	−2.63997e7	−0.0165062
$112$	0	0
$113$	1.23632e9	0.713310	0.356655	−	0.934236i	$-0.383917\pi$
$113$	1.23632e9	0.713310	0.356655	+	0.934236i	$0.383917\pi$
$114$	2.43546e9	1.35055
$115$	−3.89809e9	−2.07832
$116$	−5.80573e8	−0.297712
$117$	1.08732e9	0.536442
$118$	−5.12989e9	−2.43579
$119$	0	0
$120$	1.19181e8	0.0524675
$121$	4.67420e8	0.198232
$122$	5.46228e9	2.23231
$123$	1.55874e9	0.614045
$124$	4.66188e7	0.0177078
$125$	−6.29338e9	−2.30562
$126$	0	0
$127$	1.87320e9	0.638950	0.319475	−	0.947595i	$-0.396493\pi$
$127$	1.87320e9	0.638950	0.319475	+	0.947595i	$0.396493\pi$
$128$	3.04856e8	0.100380
$129$	9.53715e8	0.303225
$130$	−1.32902e10	−4.08117
$131$	4.90024e8	0.145377	0.0726887	−	0.997355i	$-0.476842\pi$
$131$	4.90024e8	0.145377	0.0726887	+	0.997355i	$0.476842\pi$
$132$	−2.12542e9	−0.609342
$133$	0	0
$134$	−4.44853e9	−1.19191
$135$	−1.34392e9	−0.348233
$136$	−1.02846e8	−0.0257789
$137$	3.15917e9	0.766179	0.383090	−	0.923711i	$-0.374860\pi$
$137$	3.15917e9	0.766179	0.383090	+	0.923711i	$0.374860\pi$
$138$	3.95953e9	0.929368
$139$	7.14518e9	1.62348	0.811739	−	0.584020i	$-0.198521\pi$
$139$	7.14518e9	1.62348	0.811739	+	0.584020i	$0.198521\pi$
$140$	0	0
$141$	1.16479e9	0.248176
$142$	−5.60520e9	−1.15689
$143$	−8.80899e9	−1.76163
$144$	−1.77935e9	−0.344850
$145$	2.97408e9	0.558723
$146$	6.81779e9	1.24181
$147$	0	0
$148$	−1.60893e8	−0.0275650
$149$	9.56538e9	1.58988	0.794939	−	0.606689i	$-0.207503\pi$
$149$	9.56538e9	1.58988	0.794939	+	0.606689i	$0.207503\pi$
$150$	1.14095e10	1.84016
$151$	−7.68461e9	−1.20289	−0.601444	−	0.798915i	$-0.705408\pi$
$151$	−7.68461e9	−1.20289	−0.601444	+	0.798915i	$0.705408\pi$
$152$	−5.51666e8	−0.0838262
$153$	1.15973e9	0.171098
$154$	0	0
$155$	−2.38813e8	−0.0332326
$156$	6.62667e9	0.895848
$157$	3.95065e9	0.518944	0.259472	−	0.965751i	$-0.416451\pi$
$157$	3.95065e9	0.518944	0.259472	+	0.965751i	$0.416451\pi$
$158$	7.78602e9	0.993936
$159$	6.93206e8	0.0860152
$160$	2.09954e10	2.53270
$161$	0	0
$162$	1.36510e9	0.155721
$163$	−1.80182e9	−0.199925	−0.0999625	−	0.994991i	$-0.531872\pi$
$163$	−1.80182e9	−0.199925	−0.0999625	+	0.994991i	$0.531872\pi$
$164$	9.49969e9	1.02544
$165$	1.08878e10	1.14357
$166$	−1.11365e10	−1.13831
$167$	−1.58107e9	−0.157300	−0.0786499	−	0.996902i	$-0.525061\pi$
$167$	−1.58107e9	−0.157300	−0.0786499	+	0.996902i	$0.525061\pi$
$168$	0	0
$169$	1.68604e10	1.58993
$170$	−1.41751e10	−1.30169
$171$	6.22075e9	0.556366
$172$	5.81239e9	0.506380
$173$	1.74023e10	1.47706	0.738532	−	0.674219i	$-0.235519\pi$
$173$	1.74023e10	1.47706	0.738532	+	0.674219i	$0.235519\pi$
$174$	−3.02096e9	−0.249846
$175$	0	0
$176$	1.44155e10	1.13246
$177$	−1.31030e10	−1.00344
$178$	−2.11763e10	−1.58111
$179$	1.14350e10	0.832528	0.416264	−	0.909244i	$-0.363339\pi$
$179$	1.14350e10	0.832528	0.416264	+	0.909244i	$0.363339\pi$
$180$	−8.19047e9	−0.581544
$181$	1.70931e10	1.18377	0.591884	−	0.806023i	$-0.298384\pi$
$181$	1.70931e10	1.18377	0.591884	+	0.806023i	$0.298384\pi$
$182$	0	0
$183$	1.39519e10	0.919612
$184$	−8.96887e8	−0.0576843
$185$	8.24199e8	0.0517320
$186$	2.42577e8	0.0148607
$187$	−9.39557e9	−0.561870
$188$	7.09877e9	0.414450
$189$	0	0
$190$	−7.60351e10	−4.23275
$191$	−1.18406e10	−0.643759	−0.321879	−	0.946781i	$-0.604315\pi$
$191$	−1.18406e10	−0.643759	−0.321879	+	0.946781i	$0.604315\pi$
$192$	−1.00790e10	−0.535257
$193$	−2.16314e10	−1.12222	−0.561110	−	0.827742i	$-0.689625\pi$
$193$	−2.16314e10	−1.12222	−0.561110	+	0.827742i	$0.689625\pi$
$194$	4.68066e10	2.37246
$195$	−3.39462e10	−1.68126
$196$	0	0
$197$	2.42928e10	1.14916	0.574578	−	0.818450i	$-0.305166\pi$
$197$	2.42928e10	1.14916	0.574578	+	0.818450i	$0.305166\pi$
$198$	−1.10594e10	−0.511373
$199$	−5.69701e9	−0.257518	−0.128759	−	0.991676i	$-0.541099\pi$
$199$	−5.69701e9	−0.257518	−0.128759	+	0.991676i	$0.541099\pi$
$200$	−2.58441e9	−0.114216
$201$	−1.13626e10	−0.491015
$202$	2.76613e10	1.16894
$203$	0	0
$204$	7.06792e9	0.285730
$205$	−4.86638e10	−1.92448
$206$	−3.15971e10	−1.22249
$207$	1.01136e10	0.382858
$208$	−4.49449e10	−1.66493
$209$	−5.03976e10	−1.82706
$210$	0	0
$211$	1.20709e10	0.419246	0.209623	−	0.977782i	$-0.432776\pi$
$211$	1.20709e10	0.419246	0.209623	+	0.977782i	$0.432776\pi$
$212$	4.22473e9	0.143644
$213$	−1.43170e10	−0.476589
$214$	5.86155e10	1.91051
$215$	−2.97749e10	−0.950337
$216$	−3.09213e8	−0.00966532
$217$	0	0
$218$	−5.08516e10	−1.52493
$219$	1.74143e10	0.511572
$220$	6.63554e10	1.90974
$221$	2.92937e10	0.826055
$222$	−8.37189e8	−0.0231332
$223$	−2.89814e10	−0.784780	−0.392390	−	0.919799i	$-0.628352\pi$
$223$	−2.89814e10	−0.784780	−0.392390	+	0.919799i	$0.628352\pi$
$224$	0	0
$225$	2.91426e10	0.758065
$226$	3.92062e10	0.999694
$227$	−4.86878e10	−1.21704	−0.608519	−	0.793539i	$-0.708236\pi$
$227$	−4.86878e10	−1.21704	−0.608519	+	0.793539i	$0.708236\pi$
$228$	3.79122e10	0.929121
$229$	2.66472e10	0.640313	0.320156	−	0.947365i	$-0.396265\pi$
$229$	2.66472e10	0.640313	0.320156	+	0.947365i	$0.396265\pi$
$230$	−1.23616e11	−2.91273
$231$	0	0
$232$	6.84288e8	0.0155075
$233$	−5.06681e10	−1.12624	−0.563122	−	0.826373i	$-0.690400\pi$
$233$	−5.06681e10	−1.12624	−0.563122	+	0.826373i	$0.690400\pi$
$234$	3.44812e10	0.751816
$235$	−3.63646e10	−0.777810
$236$	−7.98557e10	−1.67572
$237$	1.98873e10	0.409458
$238$	0	0
$239$	−2.92424e10	−0.579726	−0.289863	−	0.957068i	$-0.593610\pi$
$239$	−2.92424e10	−0.579726	−0.289863	+	0.957068i	$0.593610\pi$
$240$	5.55513e10	1.08080
$241$	−9.21790e10	−1.76017	−0.880086	−	0.474814i	$-0.842515\pi$
$241$	−9.21790e10	−1.76017	−0.880086	+	0.474814i	$0.842515\pi$
$242$	1.48228e10	0.277819
$243$	3.48678e9	0.0641500
$244$	8.50298e10	1.53574
$245$	0	0
$246$	4.94308e10	0.860576
$247$	1.57131e11	2.68612
$248$	−5.49469e7	−0.000922381 0
$249$	−2.84452e10	−0.468934
$250$	−1.99576e11	−3.23130
$251$	6.50404e10	1.03431	0.517156	−	0.855891i	$-0.326991\pi$
$251$	6.50404e10	1.03431	0.517156	+	0.855891i	$0.326991\pi$
$252$	0	0
$253$	−8.19355e10	−1.25727
$254$	5.94029e10	0.895480
$255$	−3.62066e10	−0.536237
$256$	7.33768e10	1.06777
$257$	−7.42090e10	−1.06110	−0.530552	−	0.847653i	$-0.678015\pi$
$257$	−7.42090e10	−1.06110	−0.530552	+	0.847653i	$0.678015\pi$
$258$	3.02442e10	0.424966
$259$	0	0
$260$	−2.06884e11	−2.80768
$261$	−7.71624e9	−0.102926
$262$	1.55397e10	0.203744
$263$	6.04163e10	0.778669	0.389335	−	0.921096i	$-0.372705\pi$
$263$	6.04163e10	0.778669	0.389335	+	0.921096i	$0.372705\pi$
$264$	2.50510e9	0.0317401
$265$	−2.16419e10	−0.269580
$266$	0	0
$267$	−5.40894e10	−0.651346
$268$	−6.92490e10	−0.819987
$269$	5.45361e10	0.635037	0.317518	−	0.948252i	$-0.397150\pi$
$269$	5.45361e10	0.635037	0.317518	+	0.948252i	$0.397150\pi$
$270$	−4.26183e10	−0.488044
$271$	7.59033e10	0.854867	0.427434	−	0.904047i	$-0.359418\pi$
$271$	7.59033e10	0.854867	0.427434	+	0.904047i	$0.359418\pi$
$272$	−4.79377e10	−0.531028
$273$	0	0
$274$	1.00184e11	1.07379
$275$	−2.36100e11	−2.48942
$276$	6.16369e10	0.639366
$277$	−1.66901e11	−1.70334	−0.851669	−	0.524080i	$-0.824409\pi$
$277$	−1.66901e11	−1.70334	−0.851669	+	0.524080i	$0.824409\pi$
$278$	2.26588e11	2.27528
$279$	6.19598e8	0.00612197
$280$	0	0
$281$	3.79259e10	0.362876	0.181438	−	0.983402i	$-0.441925\pi$
$281$	3.79259e10	0.362876	0.181438	+	0.983402i	$0.441925\pi$
$282$	3.69378e10	0.347816
$283$	−8.93540e10	−0.828085	−0.414043	−	0.910257i	$-0.635884\pi$
$283$	−8.93540e10	−0.828085	−0.414043	+	0.910257i	$0.635884\pi$
$284$	−8.72546e10	−0.795895
$285$	−1.94212e11	−1.74371
$286$	−2.79351e11	−2.46890
$287$	0	0
$288$	−5.44723e10	−0.466562
$289$	−8.73436e10	−0.736530
$290$	9.43141e10	0.783043
$291$	1.19555e11	0.977350
$292$	1.06131e11	0.854315
$293$	−1.97403e10	−0.156476	−0.0782382	−	0.996935i	$-0.524929\pi$
$293$	−1.97403e10	−0.156476	−0.0782382	+	0.996935i	$0.524929\pi$
$294$	0	0
$295$	4.09074e11	3.14487
$296$	1.89635e8	0.00143584
$297$	−2.82483e10	−0.210663
$298$	3.03337e11	2.22819
$299$	2.55460e11	1.84843
$300$	1.77609e11	1.26596
$301$	0	0
$302$	−2.43694e11	−1.68583
$303$	7.06535e10	0.481551
$304$	−2.57137e11	−1.72677
$305$	−4.35579e11	−2.88216
$306$	3.67773e10	0.239791
$307$	1.62811e11	1.04607	0.523034	−	0.852312i	$-0.324800\pi$
$307$	1.62811e11	1.04607	0.523034	+	0.852312i	$0.324800\pi$
$308$	0	0
$309$	−8.07064e10	−0.503610
$310$	−7.57323e9	−0.0465751
$311$	−1.71433e11	−1.03914	−0.519569	−	0.854428i	$-0.673908\pi$
$311$	−1.71433e11	−1.03914	−0.519569	+	0.854428i	$0.673908\pi$
$312$	−7.81047e9	−0.0466639
$313$	−4.05136e10	−0.238589	−0.119295	−	0.992859i	$-0.538063\pi$
$313$	−4.05136e10	−0.238589	−0.119295	+	0.992859i	$0.538063\pi$
$314$	1.25283e11	0.727293
$315$	0	0
$316$	1.21203e11	0.683787
$317$	−2.66783e11	−1.48385	−0.741927	−	0.670481i	$-0.766088\pi$
$317$	−2.66783e11	−1.48385	−0.741927	+	0.670481i	$0.766088\pi$
$318$	2.19830e10	0.120549
$319$	6.25134e10	0.337999
$320$	3.14666e11	1.67755
$321$	1.49718e11	0.787047
$322$	0	0
$323$	1.67594e11	0.856736
$324$	2.12501e10	0.107129
$325$	7.36117e11	3.65992
$326$	−5.71394e10	−0.280192
$327$	−1.29887e11	−0.628205
$328$	−1.11967e10	−0.0534145
$329$	0	0
$330$	3.45274e11	1.60270
$331$	−7.62242e10	−0.349033	−0.174517	−	0.984654i	$-0.555836\pi$
$331$	−7.62242e10	−0.349033	−0.174517	+	0.984654i	$0.555836\pi$
$332$	−1.73358e11	−0.783111
$333$	−2.13838e9	−0.00952984
$334$	−5.01391e10	−0.220454
$335$	3.54740e11	1.53889
$336$	0	0
$337$	3.04725e11	1.28698	0.643492	−	0.765453i	$-0.277485\pi$
$337$	3.04725e11	1.28698	0.643492	+	0.765453i	$0.277485\pi$
$338$	5.34677e11	2.22826
$339$	1.00142e11	0.411830
$340$	−2.20660e11	−0.895507
$341$	−5.01969e9	−0.0201040
$342$	1.97273e11	0.779739
$343$	0	0
$344$	−6.85073e9	−0.0263769
$345$	−3.15745e11	−1.19992
$346$	5.51862e11	2.07008
$347$	5.21711e11	1.93173	0.965867	−	0.259040i	$-0.0834061\pi$
$347$	5.21711e11	1.93173	0.965867	+	0.259040i	$0.0834061\pi$
$348$	−4.70264e10	−0.171884
$349$	−2.68192e11	−0.967680	−0.483840	−	0.875157i	$-0.660758\pi$
$349$	−2.68192e11	−0.967680	−0.483840	+	0.875157i	$0.660758\pi$
$350$	0	0
$351$	8.80732e10	0.309715
$352$	4.41310e11	1.53215
$353$	−2.89886e10	−0.0993668	−0.0496834	−	0.998765i	$-0.515821\pi$
$353$	−2.89886e10	−0.0993668	−0.0496834	+	0.998765i	$0.515821\pi$
$354$	−4.15521e11	−1.40630
$355$	4.46976e11	1.49368
$356$	−3.29646e11	−1.08774
$357$	0	0
$358$	3.62628e11	1.16678
$359$	8.84144e9	0.0280930	0.0140465	−	0.999901i	$-0.495529\pi$
$359$	8.84144e9	0.0280930	0.0140465	+	0.999901i	$0.495529\pi$
$360$	9.65363e9	0.0302921
$361$	5.76283e11	1.78589
$362$	5.42056e11	1.65903
$363$	3.78610e10	0.114449
$364$	0	0
$365$	−5.43672e11	−1.60332
$366$	4.42444e11	1.28882
$367$	1.09317e11	0.314551	0.157276	−	0.987555i	$-0.449729\pi$
$367$	1.09317e11	0.314551	0.157276	+	0.987555i	$0.449729\pi$
$368$	−4.18048e11	−1.18826
$369$	1.26258e11	0.354519
$370$	2.61370e10	0.0725017
$371$	0	0
$372$	3.77612e9	0.0102236
$373$	1.25959e11	0.336929	0.168465	−	0.985708i	$-0.446119\pi$
$373$	1.25959e11	0.336929	0.168465	+	0.985708i	$0.446119\pi$
$374$	−2.97952e11	−0.787453
$375$	−5.09763e11	−1.33115
$376$	−8.36690e9	−0.0215884
$377$	−1.94906e11	−0.496922
$378$	0	0
$379$	−2.25305e11	−0.560913	−0.280456	−	0.959867i	$-0.590486\pi$
$379$	−2.25305e11	−0.560913	−0.280456	+	0.959867i	$0.590486\pi$
$380$	−1.18362e12	−2.91196
$381$	1.51729e11	0.368898
$382$	−3.75489e11	−0.902219
$383$	−3.16295e10	−0.0751101	−0.0375551	−	0.999295i	$-0.511957\pi$
$383$	−3.16295e10	−0.0751101	−0.0375551	+	0.999295i	$0.511957\pi$
$384$	2.46933e10	0.0579547
$385$	0	0
$386$	−6.85977e11	−1.57278
$387$	7.72509e10	0.175067
$388$	7.28626e11	1.63216
$389$	−3.09015e11	−0.684238	−0.342119	−	0.939657i	$-0.611145\pi$
$389$	−3.09015e11	−0.684238	−0.342119	+	0.939657i	$0.611145\pi$
$390$	−1.07650e12	−2.35627
$391$	2.72471e11	0.589555
$392$	0	0
$393$	3.96920e10	0.0839336
$394$	7.70373e11	1.61053
$395$	−6.20882e11	−1.28328
$396$	−1.72159e11	−0.351804
$397$	3.94336e11	0.796725	0.398363	−	0.917228i	$-0.369579\pi$
$397$	3.94336e11	0.796725	0.398363	+	0.917228i	$0.369579\pi$
$398$	−1.80664e11	−0.360908
$399$	0	0
$400$	−1.20462e12	−2.35277
$401$	4.61343e11	0.890993	0.445497	−	0.895284i	$-0.353027\pi$
$401$	4.61343e11	0.890993	0.445497	+	0.895284i	$0.353027\pi$
$402$	−3.60331e11	−0.688151
$403$	1.56505e10	0.0295567
$404$	4.30596e11	0.804181
$405$	−1.08857e11	−0.201053
$406$	0	0
$407$	1.73242e10	0.0312952
$408$	−8.33055e9	−0.0148834
$409$	−3.34020e10	−0.0590225	−0.0295113	−	0.999564i	$-0.509395\pi$
$409$	−3.34020e10	−0.0590225	−0.0295113	+	0.999564i	$0.509395\pi$
$410$	−1.54323e12	−2.69713
$411$	2.55893e11	0.442354
$412$	−4.91863e11	−0.841021
$413$	0	0
$414$	3.20722e11	0.536571
$415$	8.88057e11	1.46969
$416$	−1.37592e12	−2.25255
$417$	5.78760e11	0.937316
$418$	−1.59821e12	−2.56060
$419$	−7.12374e11	−1.12913	−0.564566	−	0.825388i	$-0.690956\pi$
$419$	−7.12374e11	−1.12913	−0.564566	+	0.825388i	$0.690956\pi$
$420$	0	0
$421$	4.14907e11	0.643697	0.321848	−	0.946791i	$-0.395696\pi$
$421$	4.14907e11	0.643697	0.321848	+	0.946791i	$0.395696\pi$
$422$	3.82793e11	0.587567
$423$	9.43478e10	0.143285
$424$	−4.97944e9	−0.00748229
$425$	7.85133e11	1.16733
$426$	−4.54021e11	−0.667933
$427$	0	0
$428$	9.12451e11	1.31435
$429$	−7.13528e11	−1.01708
$430$	−9.44223e11	−1.33188
$431$	7.03297e11	0.981727	0.490864	−	0.871236i	$-0.336681\pi$
$431$	7.03297e11	0.981727	0.490864	+	0.871236i	$0.336681\pi$
$432$	−1.44128e11	−0.199099
$433$	2.54987e11	0.348596	0.174298	−	0.984693i	$-0.444234\pi$
$433$	2.54987e11	0.348596	0.174298	+	0.984693i	$0.444234\pi$
$434$	0	0
$435$	2.40901e11	0.322579
$436$	−7.91594e11	−1.04909
$437$	1.46153e12	1.91708
$438$	5.52241e11	0.716961
$439$	−6.19737e10	−0.0796373	−0.0398187	−	0.999207i	$-0.512678\pi$
$439$	−6.19737e10	−0.0796373	−0.0398187	+	0.999207i	$0.512678\pi$
$440$	−7.82092e10	−0.0994766
$441$	0	0
$442$	9.28963e11	1.15771
$443$	5.28252e11	0.651665	0.325832	−	0.945428i	$-0.394355\pi$
$443$	5.28252e11	0.651665	0.325832	+	0.945428i	$0.394355\pi$
$444$	−1.30323e10	−0.0159147
$445$	1.68867e12	2.04138
$446$	−9.19059e11	−1.09986
$447$	7.74796e11	0.917917
$448$	0	0
$449$	−1.00803e12	−1.17048	−0.585242	−	0.810859i	$-0.699000\pi$
$449$	−1.00803e12	−1.17048	−0.585242	+	0.810859i	$0.699000\pi$
$450$	9.24170e11	1.06242
$451$	−1.02288e12	−1.16421
$452$	6.10313e11	0.687748
$453$	−6.22453e11	−0.694488
$454$	−1.54399e12	−1.70566
$455$	0	0
$456$	−4.46849e10	−0.0483971
$457$	−1.13812e12	−1.22058	−0.610290	−	0.792178i	$-0.708947\pi$
$457$	−1.13812e12	−1.22058	−0.610290	+	0.792178i	$0.708947\pi$
$458$	8.45037e11	0.897390
$459$	9.39378e10	0.0987833
$460$	−1.92430e12	−2.00384
$461$	8.62164e11	0.889070	0.444535	−	0.895761i	$-0.353369\pi$
$461$	8.62164e11	0.889070	0.444535	+	0.895761i	$0.353369\pi$
$462$	0	0
$463$	5.32609e11	0.538634	0.269317	−	0.963052i	$-0.413202\pi$
$463$	5.32609e11	0.538634	0.269317	+	0.963052i	$0.413202\pi$
$464$	3.18953e11	0.319445
$465$	−1.93438e10	−0.0191869
$466$	−1.60679e12	−1.57842
$467$	−2.98897e11	−0.290801	−0.145400	−	0.989373i	$-0.546447\pi$
$467$	−2.98897e11	−0.290801	−0.145400	+	0.989373i	$0.546447\pi$
$468$	5.36760e11	0.517218
$469$	0	0
$470$	−1.15320e12	−1.09009
$471$	3.20003e11	0.299612
$472$	9.41213e10	0.0872868
$473$	−6.25851e11	−0.574905
$474$	6.30667e11	0.573849
$475$	4.21144e12	3.79585
$476$	0	0
$477$	5.61497e10	0.0496609
$478$	−9.27336e11	−0.812478
$479$	1.99260e12	1.72946	0.864728	−	0.502241i	$-0.167491\pi$
$479$	1.99260e12	1.72946	0.864728	+	0.502241i	$0.167491\pi$
$480$	1.70062e12	1.46225
$481$	−5.40137e10	−0.0460098
$482$	−2.92318e12	−2.46686
$483$	0	0
$484$	2.30743e11	0.191128
$485$	−3.73251e12	−3.06311
$486$	1.10573e11	0.0899054
$487$	−6.63500e11	−0.534516	−0.267258	−	0.963625i	$-0.586118\pi$
$487$	−6.63500e11	−0.534516	−0.267258	+	0.963625i	$0.586118\pi$
$488$	−1.00220e11	−0.0799952
$489$	−1.45947e11	−0.115427
$490$	0	0
$491$	−1.97913e12	−1.53676	−0.768382	−	0.639992i	$-0.778938\pi$
$491$	−1.97913e12	−1.53676	−0.768382	+	0.639992i	$0.778938\pi$
$492$	7.69475e11	0.592041
$493$	−2.07884e11	−0.158493
$494$	4.98294e12	3.76456
$495$	8.81911e11	0.660239
$496$	−2.56113e10	−0.0190005
$497$	0	0
$498$	−9.02054e11	−0.657205
$499$	−1.12082e12	−0.809249	−0.404624	−	0.914483i	$-0.632598\pi$
$499$	−1.12082e12	−0.809249	−0.404624	+	0.914483i	$0.632598\pi$
$500$	−3.10674e12	−2.22300
$501$	−1.28067e11	−0.0908171
$502$	2.06256e12	1.44957
$503$	5.55636e11	0.387021	0.193510	−	0.981098i	$-0.438013\pi$
$503$	5.55636e11	0.387021	0.193510	+	0.981098i	$0.438013\pi$
$504$	0	0
$505$	−2.20580e12	−1.50923
$506$	−2.59834e12	−1.76205
$507$	1.36569e12	0.917945
$508$	9.24709e11	0.616053
$509$	1.08334e12	0.715374	0.357687	−	0.933841i	$-0.383565\pi$
$509$	1.08334e12	0.715374	0.357687	+	0.933841i	$0.383565\pi$
$510$	−1.14818e12	−0.751529
$511$	0	0
$512$	2.17084e12	1.39609
$513$	5.03881e11	0.321218
$514$	−2.35332e12	−1.48712
$515$	2.51965e12	1.57837
$516$	4.70804e11	0.292359
$517$	−7.64362e11	−0.470535
$518$	0	0
$519$	1.40959e12	0.852783
$520$	2.43843e11	0.146249
$521$	5.67213e11	0.337269	0.168635	−	0.985679i	$-0.446064\pi$
$521$	5.67213e11	0.337269	0.168635	+	0.985679i	$0.446064\pi$
$522$	−2.44697e11	−0.144249
$523$	5.35980e10	0.0313250	0.0156625	−	0.999877i	$-0.495014\pi$
$523$	5.35980e10	0.0313250	0.0156625	+	0.999877i	$0.495014\pi$
$524$	2.41902e11	0.140168
$525$	0	0
$526$	1.91592e12	1.09129
$527$	1.66926e10	0.00942709
$528$	1.16765e12	0.653825
$529$	5.74970e11	0.319223
$530$	−6.86308e11	−0.377813
$531$	−1.06134e12	−0.579334
$532$	0	0
$533$	3.18917e12	1.71161
$534$	−1.71528e12	−0.912852
$535$	−4.67418e12	−2.46668
$536$	8.16198e10	0.0427124
$537$	9.26238e11	0.480661
$538$	1.72945e12	0.889996
$539$	0	0
$540$	−6.63428e11	−0.335754
$541$	−3.64222e11	−0.182801	−0.0914006	−	0.995814i	$-0.529134\pi$
$541$	−3.64222e11	−0.182801	−0.0914006	+	0.995814i	$0.529134\pi$
$542$	2.40705e12	1.19808
$543$	1.38454e12	0.683449
$544$	−1.46754e12	−0.718449
$545$	4.05507e12	1.96886
$546$	0	0
$547$	−2.46516e12	−1.17734	−0.588670	−	0.808373i	$-0.700348\pi$
$547$	−2.46516e12	−1.17734	−0.588670	+	0.808373i	$0.700348\pi$
$548$	1.55953e12	0.738723
$549$	1.13011e12	0.530938
$550$	−7.48720e12	−3.48889
$551$	−1.11509e12	−0.515378
$552$	−7.26478e10	−0.0333040
$553$	0	0
$554$	−5.29278e12	−2.38721
$555$	6.67601e10	0.0298675
$556$	3.52724e12	1.56530
$557$	−3.07680e12	−1.35441	−0.677207	−	0.735793i	$-0.736810\pi$
$557$	−3.07680e12	−1.35441	−0.677207	+	0.735793i	$0.736810\pi$
$558$	1.96487e10	0.00857985
$559$	1.95129e12	0.845219
$560$	0	0
$561$	−7.61041e11	−0.324396
$562$	1.20271e12	0.508565
$563$	−2.36518e11	−0.0992148	−0.0496074	−	0.998769i	$-0.515797\pi$
$563$	−2.36518e11	−0.0992148	−0.0496074	+	0.998769i	$0.515797\pi$
$564$	5.75000e11	0.239283
$565$	−3.12643e12	−1.29072
$566$	−2.83360e12	−1.16055
$567$	0	0
$568$	1.02842e11	0.0414575
$569$	1.92907e10	0.00771511	0.00385755	−	0.999993i	$-0.498772\pi$
$569$	1.92907e10	0.00771511	0.00385755	+	0.999993i	$0.498772\pi$
$570$	−6.15884e12	−2.44378
$571$	4.60961e12	1.81469	0.907344	−	0.420388i	$-0.138106\pi$
$571$	4.60961e12	1.81469	0.907344	+	0.420388i	$0.138106\pi$
$572$	−4.34858e12	−1.69850
$573$	−9.59087e11	−0.371674
$574$	0	0
$575$	6.84687e12	2.61208
$576$	−8.16399e11	−0.309031
$577$	−3.86253e12	−1.45071	−0.725355	−	0.688375i	$-0.758324\pi$
$577$	−3.86253e12	−1.45071	−0.725355	+	0.688375i	$0.758324\pi$
$578$	−2.76984e12	−1.03224
$579$	−1.75215e12	−0.647914
$580$	1.46816e12	0.538701
$581$	0	0
$582$	3.79134e12	1.36974
$583$	−4.54899e11	−0.163082
$584$	−1.25090e11	−0.0445005
$585$	−2.74964e12	−0.970677
$586$	−6.26004e11	−0.219299
$587$	−2.26815e11	−0.0788496	−0.0394248	−	0.999223i	$-0.512553\pi$
$587$	−2.26815e11	−0.0788496	−0.0394248	+	0.999223i	$0.512553\pi$
$588$	0	0
$589$	8.95391e10	0.0306545
$590$	1.29726e13	4.40749
$591$	1.96771e12	0.663466
$592$	8.83907e10	0.0295773
$593$	3.69003e12	1.22542	0.612708	−	0.790310i	$-0.290080\pi$
$593$	3.69003e12	1.22542	0.612708	+	0.790310i	$0.290080\pi$
$594$	−8.95811e11	−0.295242
$595$	0	0
$596$	4.72197e12	1.53290
$597$	−4.61458e11	−0.148678
$598$	8.10116e12	2.59055
$599$	−4.36657e12	−1.38586	−0.692931	−	0.721004i	$-0.743681\pi$
$599$	−4.36657e12	−1.38586	−0.692931	+	0.721004i	$0.743681\pi$
$600$	−2.09337e11	−0.0659425
$601$	1.48003e12	0.462738	0.231369	−	0.972866i	$-0.425680\pi$
$601$	1.48003e12	0.462738	0.231369	+	0.972866i	$0.425680\pi$
$602$	0	0
$603$	−9.20370e11	−0.283488
$604$	−3.79353e12	−1.15978
$605$	−1.18202e12	−0.358695
$606$	2.24057e12	0.674887
$607$	2.56582e12	0.767144	0.383572	−	0.923511i	$-0.374694\pi$
$607$	2.56582e12	0.767144	0.383572	+	0.923511i	$0.374694\pi$
$608$	−7.87188e12	−2.33621
$609$	0	0
$610$	−1.38131e13	−4.03931
$611$	2.38314e12	0.691775
$612$	5.72502e11	0.164966
$613$	−8.24420e11	−0.235818	−0.117909	−	0.993024i	$-0.537619\pi$
$613$	−8.24420e11	−0.235818	−0.117909	+	0.993024i	$0.537619\pi$
$614$	5.16306e12	1.46605
$615$	−3.94177e12	−1.11110
$616$	0	0
$617$	6.62228e11	0.183960	0.0919802	−	0.995761i	$-0.470680\pi$
$617$	6.62228e11	0.183960	0.0919802	+	0.995761i	$0.470680\pi$
$618$	−2.55936e12	−0.705803
$619$	7.04893e12	1.92981	0.964907	−	0.262591i	$-0.0845769\pi$
$619$	7.04893e12	1.92981	0.964907	+	0.262591i	$0.0845769\pi$
$620$	−1.17890e11	−0.0320417
$621$	8.19199e11	0.221043
$622$	−5.43650e12	−1.45634
$623$	0	0
$624$	−3.64054e12	−0.961247
$625$	7.23942e12	1.89777
$626$	−1.28477e12	−0.334380
$627$	−4.08221e12	−1.05485
$628$	1.95025e12	0.500347
$629$	−5.76103e10	−0.0146748
$630$	0	0
$631$	2.09975e12	0.527272	0.263636	−	0.964622i	$-0.415078\pi$
$631$	2.09975e12	0.527272	0.263636	+	0.964622i	$0.415078\pi$
$632$	−1.42855e11	−0.0356179
$633$	9.77743e11	0.242052
$634$	−8.46022e12	−2.07960
$635$	−4.73698e12	−1.15616
$636$	3.42203e11	0.0829329
$637$	0	0
$638$	1.98243e12	0.473700
$639$	−1.15968e12	−0.275159
$640$	−7.70924e11	−0.181636
$641$	8.12292e12	1.90043	0.950213	−	0.311600i	$-0.100865\pi$
$641$	8.12292e12	1.90043	0.950213	+	0.311600i	$0.100865\pi$
$642$	4.74785e12	1.10304
$643$	−6.16186e12	−1.42155	−0.710776	−	0.703418i	$-0.751656\pi$
$643$	−6.16186e12	−1.42155	−0.710776	+	0.703418i	$0.751656\pi$
$644$	0	0
$645$	−2.41177e12	−0.548677
$646$	5.31474e12	1.20070
$647$	2.34493e12	0.526090	0.263045	−	0.964784i	$-0.415273\pi$
$647$	2.34493e12	0.526090	0.263045	+	0.964784i	$0.415273\pi$
$648$	−2.50463e10	−0.00558028
$649$	8.59848e12	1.90248
$650$	2.33438e13	5.12933
$651$	0	0
$652$	−8.89473e11	−0.192761
$653$	−3.16575e12	−0.681346	−0.340673	−	0.940182i	$-0.610655\pi$
$653$	−3.16575e12	−0.681346	−0.340673	+	0.940182i	$0.610655\pi$
$654$	−4.11898e12	−0.880421
$655$	−1.23918e12	−0.263056
$656$	−5.21891e12	−1.10030
$657$	1.41055e12	0.295356
$658$	0	0
$659$	−1.30944e12	−0.270458	−0.135229	−	0.990814i	$-0.543177\pi$
$659$	−1.30944e12	−0.270458	−0.135229	+	0.990814i	$0.543177\pi$
$660$	5.37479e12	1.10259
$661$	−3.33103e12	−0.678690	−0.339345	−	0.940662i	$-0.610205\pi$
$661$	−3.33103e12	−0.678690	−0.339345	+	0.940662i	$0.610205\pi$
$662$	−2.41722e12	−0.489165
$663$	2.37279e12	0.476923
$664$	2.04328e11	0.0407916
$665$	0	0
$666$	−6.78123e10	−0.0133559
$667$	−1.81288e12	−0.354653
$668$	−7.80501e11	−0.151663
$669$	−2.34749e12	−0.453093
$670$	1.12495e13	2.15674
$671$	−9.15561e12	−1.74356
$672$	0	0
$673$	1.09048e12	0.204904	0.102452	−	0.994738i	$-0.467331\pi$
$673$	1.09048e12	0.204904	0.102452	+	0.994738i	$0.467331\pi$
$674$	9.66344e12	1.80369
$675$	2.36055e12	0.437669
$676$	8.32317e12	1.53295
$677$	8.43297e11	0.154288	0.0771439	−	0.997020i	$-0.475420\pi$
$677$	8.43297e11	0.154288	0.0771439	+	0.997020i	$0.475420\pi$
$678$	3.17570e12	0.577174
$679$	0	0
$680$	2.60079e11	0.0466462
$681$	−3.94371e12	−0.702657
$682$	−1.59185e11	−0.0281755
$683$	−5.86080e12	−1.03054	−0.515269	−	0.857029i	$-0.672308\pi$
$683$	−5.86080e12	−1.03054	−0.515269	+	0.857029i	$0.672308\pi$
$684$	3.07089e12	0.536428
$685$	−7.98896e12	−1.38638
$686$	0	0
$687$	2.15842e12	0.369685
$688$	−3.19319e12	−0.543347
$689$	1.41829e12	0.239762
$690$	−1.00129e13	−1.68167
$691$	−2.79832e12	−0.466925	−0.233462	−	0.972366i	$-0.575006\pi$
$691$	−2.79832e12	−0.466925	−0.233462	+	0.972366i	$0.575006\pi$
$692$	8.59069e12	1.42413
$693$	0	0
$694$	1.65445e13	2.70730
$695$	−1.80689e13	−2.93764
$696$	5.54273e10	0.00895328
$697$	3.40153e12	0.545917
$698$	−8.50491e12	−1.35619
$699$	−4.10412e12	−0.650238
$700$	0	0
$701$	1.11193e12	0.173919	0.0869596	−	0.996212i	$-0.472285\pi$
$701$	1.11193e12	0.173919	0.0869596	+	0.996212i	$0.472285\pi$
$702$	2.79298e12	0.434061
$703$	−3.09021e11	−0.0477187
$704$	6.61409e12	1.01483
$705$	−2.94553e12	−0.449069
$706$	−9.19288e11	−0.139261
$707$	0	0
$708$	−6.46831e12	−0.967478
$709$	3.25439e12	0.483683	0.241842	−	0.970316i	$-0.422249\pi$
$709$	3.25439e12	0.483683	0.241842	+	0.970316i	$0.422249\pi$
$710$	1.41745e13	2.09337
$711$	1.61087e12	0.236400
$712$	3.88535e11	0.0566592
$713$	1.45571e11	0.0210946
$714$	0	0
$715$	2.22763e13	3.18762
$716$	5.64494e12	0.802695
$717$	−2.36864e12	−0.334705
$718$	2.80380e11	0.0393720
$719$	−8.38180e12	−1.16965	−0.584827	−	0.811158i	$-0.698838\pi$
$719$	−8.38180e12	−1.16965	−0.584827	+	0.811158i	$0.698838\pi$
$720$	4.49966e12	0.623998
$721$	0	0
$722$	1.82751e13	2.50289
$723$	−7.46650e12	−1.01624
$724$	8.43804e12	1.14135
$725$	−5.22388e12	−0.702219
$726$	1.20065e12	0.160399
$727$	9.03956e12	1.20017	0.600085	−	0.799937i	$-0.295134\pi$
$727$	9.03956e12	1.20017	0.600085	+	0.799937i	$0.295134\pi$
$728$	0	0
$729$	2.82430e11	0.0370370
$730$	−1.72409e13	−2.24703
$731$	2.08122e12	0.269582
$732$	6.88741e12	0.886658
$733$	9.57982e12	1.22572	0.612858	−	0.790193i	$-0.290020\pi$
$733$	9.57982e12	1.22572	0.612858	+	0.790193i	$0.290020\pi$
$734$	3.46667e12	0.440840
$735$	0	0
$736$	−1.27979e13	−1.60764
$737$	7.45641e12	0.930949
$738$	4.00389e12	0.496854
$739$	4.05566e12	0.500220	0.250110	−	0.968217i	$-0.419533\pi$
$739$	4.05566e12	0.500220	0.250110	+	0.968217i	$0.419533\pi$
$740$	4.06868e11	0.0498782
$741$	1.27276e13	1.55083
$742$	0	0
$743$	−5.72132e12	−0.688726	−0.344363	−	0.938837i	$-0.611905\pi$
$743$	−5.72132e12	−0.688726	−0.344363	+	0.938837i	$0.611905\pi$
$744$	−4.45070e9	−0.000532537 0
$745$	−2.41891e13	−2.87684
$746$	3.99441e12	0.472202
$747$	−2.30406e12	−0.270739
$748$	−4.63814e12	−0.541735
$749$	0	0
$750$	−1.61656e13	−1.86559
$751$	−1.05758e13	−1.21321	−0.606603	−	0.795005i	$-0.707468\pi$
$751$	−1.05758e13	−1.21321	−0.606603	+	0.795005i	$0.707468\pi$
$752$	−3.89990e12	−0.444706
$753$	5.26827e12	0.597160
$754$	−6.18085e12	−0.696430
$755$	1.94330e13	2.17660
$756$	0	0
$757$	4.92447e11	0.0545040	0.0272520	−	0.999629i	$-0.491324\pi$
$757$	4.92447e11	0.0545040	0.0272520	+	0.999629i	$0.491324\pi$
$758$	−7.14489e12	−0.786112
$759$	−6.63677e12	−0.725887
$760$	1.39506e12	0.151681
$761$	−7.08628e12	−0.765927	−0.382963	−	0.923764i	$-0.625096\pi$
$761$	−7.08628e12	−0.765927	−0.382963	+	0.923764i	$0.625096\pi$
$762$	4.81164e12	0.517006
$763$	0	0
$764$	−5.84513e12	−0.620689
$765$	−2.93274e12	−0.309597
$766$	−1.00304e12	−0.105266
$767$	−2.68085e13	−2.79701
$768$	5.94352e12	0.616479
$769$	−1.68522e13	−1.73775	−0.868874	−	0.495033i	$-0.835156\pi$
$769$	−1.68522e13	−1.73775	−0.868874	+	0.495033i	$0.835156\pi$
$770$	0	0
$771$	−6.01093e12	−0.612628
$772$	−1.06784e13	−1.08200
$773$	−3.11290e12	−0.313586	−0.156793	−	0.987631i	$-0.550116\pi$
$773$	−3.11290e12	−0.313586	−0.156793	+	0.987631i	$0.550116\pi$
$774$	2.44978e12	0.245354
$775$	4.19467e11	0.0417677
$776$	−8.58789e11	−0.0850176
$777$	0	0
$778$	−9.79950e12	−0.958950
$779$	1.82457e13	1.77518
$780$	−1.67576e13	−1.62101
$781$	9.39516e12	0.903597
$782$	8.64060e12	0.826254
$783$	−6.25015e11	−0.0594241
$784$	0	0
$785$	−9.99048e12	−0.939015
$786$	1.25871e12	0.117632
$787$	4.98461e11	0.0463175	0.0231587	−	0.999732i	$-0.492628\pi$
$787$	4.98461e11	0.0463175	0.0231587	+	0.999732i	$0.492628\pi$
$788$	1.19922e13	1.10798
$789$	4.89372e12	0.449565
$790$	−1.96894e13	−1.79850
$791$	0	0
$792$	2.02913e11	0.0183251
$793$	2.85456e13	2.56336
$794$	1.25052e13	1.11660
$795$	−1.75299e12	−0.155642
$796$	−2.81234e12	−0.248290
$797$	−6.05843e12	−0.531861	−0.265930	−	0.963992i	$-0.585679\pi$
$797$	−6.05843e12	−0.531861	−0.265930	+	0.963992i	$0.585679\pi$
$798$	0	0
$799$	2.54183e12	0.220641
$800$	−3.68777e13	−3.18316
$801$	−4.38124e12	−0.376055
$802$	1.46301e13	1.24872
$803$	−1.14277e13	−0.969923
$804$	−5.60917e12	−0.473420
$805$	0	0
$806$	4.96309e11	0.0414233
$807$	4.41743e12	0.366639
$808$	−5.07519e11	−0.0418891
$809$	7.58264e12	0.622375	0.311187	−	0.950349i	$-0.399273\pi$
$809$	7.58264e12	0.622375	0.311187	+	0.950349i	$0.399273\pi$
$810$	−3.45208e12	−0.281773
$811$	9.65159e12	0.783439	0.391720	−	0.920085i	$-0.371880\pi$
$811$	9.65159e12	0.783439	0.391720	+	0.920085i	$0.371880\pi$
$812$	0	0
$813$	6.14816e12	0.493558
$814$	5.49384e11	0.0438598
$815$	4.55647e12	0.361759
$816$	−3.88295e12	−0.306589
$817$	1.11637e13	0.876611
$818$	−1.05925e12	−0.0827193
$819$	0	0
$820$	−2.40230e13	−1.85552
$821$	7.37731e12	0.566701	0.283350	−	0.959016i	$-0.408554\pi$
$821$	7.37731e12	0.566701	0.283350	+	0.959016i	$0.408554\pi$
$822$	8.11488e12	0.619953
$823$	1.61207e13	1.22485	0.612427	−	0.790527i	$-0.290193\pi$
$823$	1.61207e13	1.22485	0.612427	+	0.790527i	$0.290193\pi$
$824$	5.79730e11	0.0438080
$825$	−1.91241e13	−1.43727
$826$	0	0
$827$	−3.51169e12	−0.261060	−0.130530	−	0.991444i	$-0.541668\pi$
$827$	−3.51169e12	−0.261060	−0.130530	+	0.991444i	$0.541668\pi$
$828$	4.99259e12	0.369138
$829$	1.45284e13	1.06837	0.534186	−	0.845367i	$-0.320618\pi$
$829$	1.45284e13	1.06837	0.534186	+	0.845367i	$0.320618\pi$
$830$	2.81621e13	2.05975
$831$	−1.35190e13	−0.983423
$832$	−2.06216e13	−1.49199
$833$	0	0
$834$	1.83536e13	1.31364
$835$	3.99825e12	0.284630
$836$	−2.48789e13	−1.76158
$837$	5.01874e10	0.00353452
$838$	−2.25908e13	−1.58246
$839$	−1.12702e13	−0.785239	−0.392619	−	0.919701i	$-0.628431\pi$
$839$	−1.12702e13	−0.785239	−0.392619	+	0.919701i	$0.628431\pi$
$840$	0	0
$841$	−1.31240e13	−0.904657
$842$	1.31575e13	0.902133
$843$	3.07200e12	0.209506
$844$	5.95883e12	0.404222
$845$	−4.26368e13	−2.87693
$846$	2.99196e12	0.200812
$847$	0	0
$848$	−2.32097e12	−0.154130
$849$	−7.23767e12	−0.478095
$850$	2.48982e13	1.63600
$851$	−5.02400e11	−0.0328372
$852$	−7.06762e12	−0.459510
$853$	1.98459e13	1.28351	0.641756	−	0.766909i	$-0.278206\pi$
$853$	1.98459e13	1.28351	0.641756	+	0.766909i	$0.278206\pi$
$854$	0	0
$855$	−1.57311e13	−1.00673
$856$	−1.07545e12	−0.0684636
$857$	−2.65273e13	−1.67989	−0.839943	−	0.542675i	$-0.817412\pi$
$857$	−2.65273e13	−1.67989	−0.839943	+	0.542675i	$0.817412\pi$
$858$	−2.26274e13	−1.42542
$859$	1.58942e12	0.0996025	0.0498012	−	0.998759i	$-0.484141\pi$
$859$	1.58942e12	0.0996025	0.0498012	+	0.998759i	$0.484141\pi$
$860$	−1.46985e13	−0.916282
$861$	0	0
$862$	2.23030e13	1.37588
$863$	5.57707e12	0.342261	0.171131	−	0.985248i	$-0.445258\pi$
$863$	5.57707e12	0.342261	0.171131	+	0.985248i	$0.445258\pi$
$864$	−4.41226e12	−0.269370
$865$	−4.40072e13	−2.67271
$866$	8.08614e12	0.488552
$867$	−7.07483e12	−0.425236
$868$	0	0
$869$	−1.30506e13	−0.776318
$870$	7.63944e12	0.452090
$871$	−2.32478e13	−1.36867
$872$	9.33006e11	0.0546462
$873$	9.68397e12	0.564273
$874$	4.63480e13	2.68677
$875$	0	0
$876$	8.59659e12	0.493239
$877$	2.88886e13	1.64903	0.824514	−	0.565842i	$-0.191449\pi$
$877$	2.88886e13	1.64903	0.824514	+	0.565842i	$0.191449\pi$
$878$	−1.96531e12	−0.111611
$879$	−1.59896e12	−0.0903417
$880$	−3.64541e13	−2.04915
$881$	−6.88512e12	−0.385052	−0.192526	−	0.981292i	$-0.561668\pi$
$881$	−6.88512e12	−0.385052	−0.192526	+	0.981292i	$0.561668\pi$
$882$	0	0
$883$	−2.60773e13	−1.44358	−0.721788	−	0.692115i	$-0.756679\pi$
$883$	−2.60773e13	−1.44358	−0.721788	+	0.692115i	$0.756679\pi$
$884$	1.44609e13	0.796453
$885$	3.31350e13	1.81569
$886$	1.67519e13	0.913300
$887$	−2.22883e12	−0.120898	−0.0604491	−	0.998171i	$-0.519253\pi$
$887$	−2.22883e12	−0.120898	−0.0604491	+	0.998171i	$0.519253\pi$
$888$	1.53604e10	0.000828981 0
$889$	0	0
$890$	5.35511e13	2.86097
$891$	−2.28811e12	−0.121626
$892$	−1.43067e13	−0.756657
$893$	1.36343e13	0.717469
$894$	2.45703e13	1.28645
$895$	−2.89171e13	−1.50644
$896$	0	0
$897$	2.06923e13	1.06719
$898$	−3.19667e13	−1.64042
$899$	−1.11064e11	−0.00567096
$900$	1.43863e13	0.730900
$901$	1.51274e12	0.0764718
$902$	−3.24377e13	−1.63163
$903$	0	0
$904$	−7.19340e11	−0.0358242
$905$	−4.32252e13	−2.14200
$906$	−1.97393e13	−0.973316
$907$	−2.94641e13	−1.44564	−0.722820	−	0.691037i	$-0.757154\pi$
$907$	−2.94641e13	−1.44564	−0.722820	+	0.691037i	$0.757154\pi$
$908$	−2.40349e13	−1.17343
$909$	5.72294e12	0.278023
$910$	0	0
$911$	3.21138e12	0.154475	0.0772376	−	0.997013i	$-0.475390\pi$
$911$	3.21138e12	0.154475	0.0772376	+	0.997013i	$0.475390\pi$
$912$	−2.08281e13	−0.996949
$913$	1.86664e13	0.889084
$914$	−3.60922e13	−1.71063
$915$	−3.52819e13	−1.66401
$916$	1.31545e13	0.617367
$917$	0	0
$918$	2.97896e12	0.138443
$919$	3.22326e13	1.49065	0.745326	−	0.666700i	$-0.232294\pi$
$919$	3.22326e13	1.49065	0.745326	+	0.666700i	$0.232294\pi$
$920$	2.26806e12	0.104378
$921$	1.31877e13	0.603948
$922$	2.73410e13	1.24602
$923$	−2.92925e13	−1.32846
$924$	0	0
$925$	−1.44768e12	−0.0650182
$926$	1.68901e13	0.754889
$927$	−6.53722e12	−0.290760
$928$	9.76430e12	0.432191
$929$	4.13247e13	1.82028	0.910141	−	0.414298i	$-0.135973\pi$
$929$	4.13247e13	1.82028	0.910141	+	0.414298i	$0.135973\pi$
$930$	−6.13432e11	−0.0268901
$931$	0	0
$932$	−2.50124e13	−1.08589
$933$	−1.38861e13	−0.599947
$934$	−9.47863e12	−0.407554
$935$	2.37597e13	1.01669
$936$	−6.32648e11	−0.0269414
$937$	5.51722e12	0.233826	0.116913	−	0.993142i	$-0.462700\pi$
$937$	5.51722e12	0.233826	0.116913	+	0.993142i	$0.462700\pi$
$938$	0	0
$939$	−3.28160e12	−0.137750
$940$	−1.79515e13	−0.749937
$941$	−8.77760e12	−0.364941	−0.182470	−	0.983211i	$-0.558409\pi$
$941$	−8.77760e12	−0.364941	−0.182470	+	0.983211i	$0.558409\pi$
$942$	1.01479e13	0.419903
$943$	2.96635e13	1.22158
$944$	4.38709e13	1.79805
$945$	0	0
$946$	−1.98470e13	−0.805721
$947$	2.45390e13	0.991474	0.495737	−	0.868473i	$-0.334898\pi$
$947$	2.45390e13	0.991474	0.495737	+	0.868473i	$0.334898\pi$
$948$	9.81743e12	0.394785
$949$	3.56294e13	1.42597
$950$	1.33553e14	5.31984
$951$	−2.16094e13	−0.856703
$952$	0	0
$953$	−2.64691e13	−1.03949	−0.519745	−	0.854321i	$-0.673973\pi$
$953$	−2.64691e13	−1.03949	−0.519745	+	0.854321i	$0.673973\pi$
$954$	1.78062e12	0.0695991
$955$	2.99427e13	1.16486
$956$	−1.44356e13	−0.558951
$957$	5.06358e12	0.195144
$958$	6.31892e13	2.42381
$959$	0	0
$960$	2.54879e13	0.968533
$961$	−2.64307e13	−0.999663
$962$	−1.71288e12	−0.0644822
$963$	1.21271e13	0.454402
$964$	−4.55044e13	−1.69710
$965$	5.47020e13	2.03063
$966$	0	0
$967$	1.86428e12	0.0685632	0.0342816	−	0.999412i	$-0.489086\pi$
$967$	1.86428e12	0.0685632	0.0342816	+	0.999412i	$0.489086\pi$
$968$	−2.71963e11	−0.00995569
$969$	1.35751e13	0.494637
$970$	−1.18365e14	−4.29291
$971$	5.46496e13	1.97288	0.986440	−	0.164122i	$-0.0524791\pi$
$971$	5.46496e13	1.97288	0.986440	+	0.164122i	$0.0524791\pi$
$972$	1.72126e12	0.0618512
$973$	0	0
$974$	−2.10409e13	−0.749116
$975$	5.96255e13	2.11306
$976$	−4.67134e13	−1.64785
$977$	1.85008e12	0.0649628	0.0324814	−	0.999472i	$-0.489659\pi$
$977$	1.85008e12	0.0649628	0.0324814	+	0.999472i	$0.489659\pi$
$978$	−4.62829e12	−0.161769
$979$	3.54948e13	1.23493
$980$	0	0
$981$	−1.05209e13	−0.362694
$982$	−6.27621e13	−2.15375
$983$	1.73851e13	0.593862	0.296931	−	0.954899i	$-0.404037\pi$
$983$	1.73851e13	0.593862	0.296931	+	0.954899i	$0.404037\pi$
$984$	−9.06936e11	−0.0308389
$985$	−6.14320e13	−2.07937
$986$	−6.59242e12	−0.222126
$987$	0	0
$988$	7.75681e13	2.58986
$989$	1.81496e13	0.603232
$990$	2.79672e13	0.925317
$991$	1.43972e13	0.474183	0.237092	−	0.971487i	$-0.423806\pi$
$991$	1.43972e13	0.474183	0.237092	+	0.971487i	$0.423806\pi$
$992$	−7.84053e11	−0.0257065
$993$	−6.17416e12	−0.201514
$994$	0	0
$995$	1.44067e13	0.465973
$996$	−1.40420e13	−0.452130
$997$	−1.47385e13	−0.472417	−0.236208	−	0.971702i	$-0.575905\pi$
$997$	−1.47385e13	−0.472417	−0.236208	+	0.971702i	$0.575905\pi$
$998$	−3.55434e13	−1.13415
$999$	−1.73209e11	−0.00550206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.10.a.n.1.8	yes	10
7.6	odd	2		147.10.a.m.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.10.a.m.1.8	✓	10	7.6	odd	2
147.10.a.n.1.8	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)

\(f(q)\)	\(=\)	\(q+31.7120 q^{2} +81.0000 q^{3} +493.652 q^{4} -2528.82 q^{5} +2568.67 q^{6} -581.840 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+31.7120 q^{2} +81.0000 q^{3} +493.652 q^{4} -2528.82 q^{5} +2568.67 q^{6} -581.840 q^{8} +6561.00 q^{9} -80193.9 q^{10} -53154.2 q^{11} +39985.8 q^{12} +165725. q^{13} -204834. q^{15} -271201. q^{16} +176761. q^{17} +208063. q^{18} +948141. q^{19} -1.24836e6 q^{20} -1.68563e6 q^{22} +1.54147e6 q^{23} -47129.0 q^{24} +4.44179e6 q^{25} +5.25548e6 q^{26} +531441. q^{27} -1.17608e6 q^{29} -6.49571e6 q^{30} +94436.5 q^{31} -8.30244e6 q^{32} -4.30549e6 q^{33} +5.60544e6 q^{34} +3.23885e6 q^{36} -325923. q^{37} +3.00675e7 q^{38} +1.34237e7 q^{39} +1.47137e6 q^{40} +1.92437e7 q^{41} +1.17743e7 q^{43} -2.62397e7 q^{44} -1.65916e7 q^{45} +4.88831e7 q^{46} +1.43801e7 q^{47} -2.19673e7 q^{48} +1.40858e8 q^{50} +1.43176e7 q^{51} +8.18107e7 q^{52} +8.55810e6 q^{53} +1.68531e7 q^{54} +1.34417e8 q^{55} +7.67994e7 q^{57} -3.72958e7 q^{58} -1.61765e8 q^{59} -1.01117e8 q^{60} +1.72246e8 q^{61} +2.99477e6 q^{62} -1.24432e8 q^{64} -4.19089e8 q^{65} -1.36536e8 q^{66} -1.40279e8 q^{67} +8.72583e7 q^{68} +1.24859e8 q^{69} -1.76753e8 q^{71} -3.81745e6 q^{72} +2.14991e8 q^{73} -1.03357e7 q^{74} +3.59785e8 q^{75} +4.68052e8 q^{76} +4.25694e8 q^{78} +2.45523e8 q^{79} +6.85818e8 q^{80} +4.30467e7 q^{81} +6.10256e8 q^{82} -3.51175e8 q^{83} -4.46995e8 q^{85} +3.73385e8 q^{86} -9.52622e7 q^{87} +3.09272e7 q^{88} -6.67770e8 q^{89} -5.26152e8 q^{90} +7.60949e8 q^{92} +7.64936e6 q^{93} +4.56022e8 q^{94} -2.39767e9 q^{95} -6.72498e8 q^{96} +1.47599e9 q^{97} -3.48745e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 34 q^{2} + 810 q^{3} + 2902 q^{4} + 2500 q^{5} + 2754 q^{6} + 33966 q^{8} + 65610 q^{9}+O(q^{10}) \) 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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