LMFDB - Embedded newform 289.10.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-44.7383 q^{2} -202.519 q^{3} +1489.51 q^{4} -1685.49 q^{5} +9060.35 q^{6} +4589.24 q^{7} -43732.3 q^{8} +21330.9 q^{9} +O(q^{10})$	\(q-44.7383 q^{2} -202.519 q^{3} +1489.51 q^{4} -1685.49 q^{5} +9060.35 q^{6} +4589.24 q^{7} -43732.3 q^{8} +21330.9 q^{9} +75405.9 q^{10} -29147.4 q^{11} -301655. q^{12} +59631.0 q^{13} -205315. q^{14} +341343. q^{15} +1.19388e6 q^{16} -954309. q^{18} +393350. q^{19} -2.51056e6 q^{20} -929408. q^{21} +1.30401e6 q^{22} +581014. q^{23} +8.85662e6 q^{24} +887748. q^{25} -2.66779e6 q^{26} -333735. q^{27} +6.83573e6 q^{28} -5.69646e6 q^{29} -1.52711e7 q^{30} -557796. q^{31} -3.10211e7 q^{32} +5.90291e6 q^{33} -7.73511e6 q^{35} +3.17727e7 q^{36} +2.31924e6 q^{37} -1.75978e7 q^{38} -1.20764e7 q^{39} +7.37103e7 q^{40} -2.59418e7 q^{41} +4.15801e7 q^{42} +1.10106e7 q^{43} -4.34155e7 q^{44} -3.59530e7 q^{45} -2.59936e7 q^{46} -1.90477e7 q^{47} -2.41783e8 q^{48} -1.92925e7 q^{49} -3.97163e7 q^{50} +8.88212e7 q^{52} -8.95430e7 q^{53} +1.49307e7 q^{54} +4.91277e7 q^{55} -2.00698e8 q^{56} -7.96608e7 q^{57} +2.54850e8 q^{58} +1.61408e8 q^{59} +5.08436e8 q^{60} -8.62127e7 q^{61} +2.49548e7 q^{62} +9.78927e7 q^{63} +7.76564e8 q^{64} -1.00507e8 q^{65} -2.64086e8 q^{66} -7.28639e7 q^{67} -1.17666e8 q^{69} +3.46056e8 q^{70} +2.46821e8 q^{71} -9.32850e8 q^{72} +3.69817e7 q^{73} -1.03759e8 q^{74} -1.79786e8 q^{75} +5.85900e8 q^{76} -1.33765e8 q^{77} +5.40277e8 q^{78} -5.32700e8 q^{79} -2.01227e9 q^{80} -3.52269e8 q^{81} +1.16059e9 q^{82} +3.39461e8 q^{83} -1.38437e9 q^{84} -4.92595e8 q^{86} +1.15364e9 q^{87} +1.27468e9 q^{88} +4.69306e8 q^{89} +1.60848e9 q^{90} +2.73661e8 q^{91} +8.65429e8 q^{92} +1.12964e8 q^{93} +8.52161e8 q^{94} -6.62987e8 q^{95} +6.28235e9 q^{96} +6.49455e6 q^{97} +8.63113e8 q^{98} -6.21742e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) $ 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9} - 60000 q^{10} - 76902 q^{11} - 373248 q^{12} + 54216 q^{13} - 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} - 6439479 q^{20} - 138102 q^{21} - 267324 q^{22} - 4041462 q^{23} - 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} - 13281612 q^{27} - 18614784 q^{28} - 4005936 q^{29} + 22471686 q^{30} - 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} - 22076682 q^{37} - 27401376 q^{38} - 62736162 q^{39} + 12231630 q^{40} - 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} + 49578936 q^{44} - 129308238 q^{45} - 140524827 q^{46} - 118557912 q^{47} - 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} - 209848575 q^{54} - 365439924 q^{55} - 203095059 q^{56} + 4614108 q^{57} + 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} - 175597116 q^{61} - 720602571 q^{62} - 587415936 q^{63} + 853082511 q^{64} - 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} - 1308709542 q^{71} - 275337849 q^{72} - 494841342 q^{73} - 1545361890 q^{74} - 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} - 2270624538 q^{78} - 1980107868 q^{79} - 2897000199 q^{80} + 1598298840 q^{81} - 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} + 2705904618 q^{88} + 148394658 q^{89} - 117916215 q^{90} - 636340896 q^{91} + 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} - 4878626298 q^{95} + 8390096634 q^{96} + 891786822 q^{97} + 4285627647 q^{98} + 1476187998 q^{99}+O(q^{100}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9 - 60000 * q^10 - 76902 * q^11 - 373248 * q^12 + 54216 * q^13 - 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 - 6439479 * q^20 - 138102 * q^21 - 267324 * q^22 - 4041462 * q^23 - 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 - 13281612 * q^27 - 18614784 * q^28 - 4005936 * q^29 + 22471686 * q^30 - 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 - 22076682 * q^37 - 27401376 * q^38 - 62736162 * q^39 + 12231630 * q^40 - 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 + 49578936 * q^44 - 129308238 * q^45 - 140524827 * q^46 - 118557912 * q^47 - 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 - 209848575 * q^54 - 365439924 * q^55 - 203095059 * q^56 + 4614108 * q^57 + 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 - 175597116 * q^61 - 720602571 * q^62 - 587415936 * q^63 + 853082511 * q^64 - 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 - 1308709542 * q^71 - 275337849 * q^72 - 494841342 * q^73 - 1545361890 * q^74 - 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 - 2270624538 * q^78 - 1980107868 * q^79 - 2897000199 * q^80 + 1598298840 * q^81 - 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 + 2705904618 * q^88 + 148394658 * q^89 - 117916215 * q^90 - 636340896 * q^91 + 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 - 4878626298 * q^95 + 8390096634 * q^96 + 891786822 * q^97 + 4285627647 * q^98 + 1476187998 * 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 $

$2$	−44.7383	−1.97717	−0.988586	−	0.150660i	$-0.951860\pi$
$2$	−44.7383	−1.97717	−0.988586	+	0.150660i	$0.951860\pi$
$3$	−202.519	−1.44351	−0.721755	−	0.692148i	$-0.756664\pi$
$3$	−202.519	−1.44351	−0.721755	+	0.692148i	$0.756664\pi$
$4$	1489.51	2.90921
$5$	−1685.49	−1.20604	−0.603019	−	0.797727i	$-0.706036\pi$
$5$	−1685.49	−1.20604	−0.603019	+	0.797727i	$0.706036\pi$
$6$	9060.35	2.85407
$7$	4589.24	0.722436	0.361218	−	0.932481i	$-0.382361\pi$
$7$	4589.24	0.722436	0.361218	+	0.932481i	$0.382361\pi$
$8$	−43732.3	−3.77483
$9$	21330.9	1.08372
$10$	75405.9	2.38454
$11$	−29147.4	−0.600251	−0.300126	−	0.953900i	$-0.597029\pi$
$11$	−29147.4	−0.600251	−0.300126	+	0.953900i	$0.597029\pi$
$12$	−301655.	−4.19947
$13$	59631.0	0.579064	0.289532	−	0.957168i	$-0.406500\pi$
$13$	59631.0	0.579064	0.289532	+	0.957168i	$0.406500\pi$
$14$	−205315.	−1.42838
$15$	341343.	1.74093
$16$	1.19388e6	4.55428
$17$	0	0
$17$	0	0
$18$	−954309.	−2.14271
$19$	393350.	0.692449	0.346224	−	0.938152i	$-0.387464\pi$
$19$	393350.	0.692449	0.346224	+	0.938152i	$0.387464\pi$
$20$	−2.51056e6	−3.50861
$21$	−929408.	−1.04284
$22$	1.30401e6	1.18680
$23$	581014.	0.432924	0.216462	−	0.976291i	$-0.430548\pi$
$23$	581014.	0.432924	0.216462	+	0.976291i	$0.430548\pi$
$24$	8.85662e6	5.44901
$25$	887748.	0.454527
$26$	−2.66779e6	−1.14491
$27$	−333735.	−0.120855
$28$	6.83573e6	2.10172
$29$	−5.69646e6	−1.49559	−0.747797	−	0.663927i	$-0.768888\pi$
$29$	−5.69646e6	−1.49559	−0.747797	+	0.663927i	$0.768888\pi$
$30$	−1.52711e7	−3.44211
$31$	−557796.	−0.108480	−0.0542398	−	0.998528i	$-0.517274\pi$
$31$	−557796.	−0.108480	−0.0542398	+	0.998528i	$0.517274\pi$
$32$	−3.10211e7	−5.22976
$33$	5.90291e6	0.866469
$34$	0	0
$35$	−7.73511e6	−0.871285
$36$	3.17727e7	3.15277
$37$	2.31924e6	0.203441	0.101720	−	0.994813i	$-0.467565\pi$
$37$	2.31924e6	0.203441	0.101720	+	0.994813i	$0.467565\pi$
$38$	−1.75978e7	−1.36909
$39$	−1.20764e7	−0.835885
$40$	7.37103e7	4.55259
$41$	−2.59418e7	−1.43375	−0.716873	−	0.697204i	$-0.754427\pi$
$41$	−2.59418e7	−1.43375	−0.716873	+	0.697204i	$0.754427\pi$
$42$	4.15801e7	2.06188
$43$	1.10106e7	0.491137	0.245569	−	0.969379i	$-0.421025\pi$
$43$	1.10106e7	0.491137	0.245569	+	0.969379i	$0.421025\pi$
$44$	−4.34155e7	−1.74626
$45$	−3.59530e7	−1.30701
$46$	−2.59936e7	−0.855965
$47$	−1.90477e7	−0.569380	−0.284690	−	0.958620i	$-0.591891\pi$
$47$	−1.90477e7	−0.569380	−0.284690	+	0.958620i	$0.591891\pi$
$48$	−2.41783e8	−6.57415
$49$	−1.92925e7	−0.478086
$50$	−3.97163e7	−0.898678
$51$	0	0
$52$	8.88212e7	1.68462
$53$	−8.95430e7	−1.55880	−0.779400	−	0.626527i	$-0.784476\pi$
$53$	−8.95430e7	−1.55880	−0.779400	+	0.626527i	$0.784476\pi$
$54$	1.49307e7	0.238951
$55$	4.91277e7	0.723926
$56$	−2.00698e8	−2.72707
$57$	−7.96608e7	−0.999557
$58$	2.54850e8	2.95705
$59$	1.61408e8	1.73417	0.867086	−	0.498158i	$-0.165990\pi$
$59$	1.61408e8	1.73417	0.867086	+	0.498158i	$0.165990\pi$
$60$	5.08436e8	5.06472
$61$	−8.62127e7	−0.797237	−0.398618	−	0.917117i	$-0.630510\pi$
$61$	−8.62127e7	−0.797237	−0.398618	+	0.917117i	$0.630510\pi$
$62$	2.49548e7	0.214483
$63$	9.78927e7	0.782921
$64$	7.76564e8	5.78585
$65$	−1.00507e8	−0.698373
$66$	−2.64086e8	−1.71316
$67$	−7.28639e7	−0.441749	−0.220875	−	0.975302i	$-0.570891\pi$
$67$	−7.28639e7	−0.441749	−0.220875	+	0.975302i	$0.570891\pi$
$68$	0	0
$69$	−1.17666e8	−0.624930
$70$	3.46056e8	1.72268
$71$	2.46821e8	1.15271	0.576355	−	0.817200i	$-0.304475\pi$
$71$	2.46821e8	1.15271	0.576355	+	0.817200i	$0.304475\pi$
$72$	−9.32850e8	−4.09087
$73$	3.69817e7	0.152417	0.0762085	−	0.997092i	$-0.475719\pi$
$73$	3.69817e7	0.152417	0.0762085	+	0.997092i	$0.475719\pi$
$74$	−1.03759e8	−0.402237
$75$	−1.79786e8	−0.656115
$76$	5.85900e8	2.01448
$77$	−1.33765e8	−0.433643
$78$	5.40277e8	1.65269
$79$	−5.32700e8	−1.53872	−0.769362	−	0.638812i	$-0.779426\pi$
$79$	−5.32700e8	−1.53872	−0.769362	+	0.638812i	$0.779426\pi$
$80$	−2.01227e9	−5.49263
$81$	−3.52269e8	−0.909267
$82$	1.16059e9	2.83476
$83$	3.39461e8	0.785125	0.392562	−	0.919725i	$-0.371589\pi$
$83$	3.39461e8	0.785125	0.392562	+	0.919725i	$0.371589\pi$
$84$	−1.38437e9	−3.03385
$85$	0	0
$86$	−4.92595e8	−0.971063
$87$	1.15364e9	2.15891
$88$	1.27468e9	2.26585
$89$	4.69306e8	0.792868	0.396434	−	0.918063i	$-0.370248\pi$
$89$	4.69306e8	0.792868	0.396434	+	0.918063i	$0.370248\pi$
$90$	1.60848e9	2.58418
$91$	2.73661e8	0.418337
$92$	8.65429e8	1.25946
$93$	1.12964e8	0.156591
$94$	8.52161e8	1.12576
$95$	−6.62987e8	−0.835120
$96$	6.28235e9	7.54921
$97$	6.49455e6	0.00744863	0.00372432	−	0.999993i	$-0.498815\pi$
$97$	6.49455e6	0.00744863	0.00372432	+	0.999993i	$0.498815\pi$
$98$	8.63113e8	0.945258
$99$	−6.21742e8	−0.650506
$100$	1.32231e9	1.32231
$101$	2.04216e9	1.95273	0.976366	−	0.216123i	$-0.0693411\pi$
$101$	2.04216e9	1.95273	0.976366	+	0.216123i	$0.0693411\pi$
$102$	0	0
$103$	6.58293e8	0.576304	0.288152	−	0.957585i	$-0.406959\pi$
$103$	6.58293e8	0.576304	0.288152	+	0.957585i	$0.406959\pi$
$104$	−2.60780e9	−2.18587
$105$	1.56651e9	1.25771
$106$	4.00600e9	3.08202
$107$	2.13709e9	1.57614	0.788071	−	0.615584i	$-0.211080\pi$
$107$	2.13709e9	1.57614	0.788071	+	0.615584i	$0.211080\pi$
$108$	−4.97103e8	−0.351592
$109$	−2.24135e8	−0.152087	−0.0760434	−	0.997105i	$-0.524229\pi$
$109$	−2.24135e8	−0.152087	−0.0760434	+	0.997105i	$0.524229\pi$
$110$	−2.19789e9	−1.43133
$111$	−4.69690e8	−0.293669
$112$	5.47898e9	3.29017
$113$	6.81116e8	0.392978	0.196489	−	0.980506i	$-0.437046\pi$
$113$	6.81116e8	0.392978	0.196489	+	0.980506i	$0.437046\pi$
$114$	3.56389e9	1.97630
$115$	−9.79293e8	−0.522123
$116$	−8.48495e9	−4.35099
$117$	1.27198e9	0.627545
$118$	−7.22114e9	−3.42876
$119$	0	0
$120$	−1.49277e10	−6.57171
$121$	−1.50837e9	−0.639698
$122$	3.85701e9	1.57627
$123$	5.25370e9	2.06963
$124$	−8.30845e8	−0.315589
$125$	1.79568e9	0.657861
$126$	−4.37955e9	−1.54797
$127$	2.46598e9	0.841148	0.420574	−	0.907258i	$-0.361829\pi$
$127$	2.46598e9	0.841148	0.420574	+	0.907258i	$0.361829\pi$
$128$	−1.88594e10	−6.20986
$129$	−2.22986e9	−0.708962
$130$	4.49653e9	1.38080
$131$	−2.56271e9	−0.760289	−0.380145	−	0.924927i	$-0.624126\pi$
$131$	−2.56271e9	−0.760289	−0.380145	+	0.924927i	$0.624126\pi$
$132$	8.79246e9	2.52074
$133$	1.80518e9	0.500250
$134$	3.25981e9	0.873414
$135$	5.62507e8	0.145756
$136$	0	0
$137$	7.21417e9	1.74962	0.874810	−	0.484466i	$-0.160986\pi$
$137$	7.21417e9	1.74962	0.874810	+	0.484466i	$0.160986\pi$
$138$	5.26419e9	1.23559
$139$	−5.33039e8	−0.121114	−0.0605568	−	0.998165i	$-0.519288\pi$
$139$	−5.33039e8	−0.121114	−0.0605568	+	0.998165i	$0.519288\pi$
$140$	−1.15216e10	−2.53475
$141$	3.85752e9	0.821905
$142$	−1.10424e10	−2.27910
$143$	−1.73809e9	−0.347584
$144$	2.54665e10	4.93558
$145$	9.60131e9	1.80374
$146$	−1.65450e9	−0.301355
$147$	3.90710e9	0.690122
$148$	3.45454e9	0.591851
$149$	−7.39170e9	−1.22859	−0.614294	−	0.789078i	$-0.710559\pi$
$149$	−7.39170e9	−1.22859	−0.614294	+	0.789078i	$0.710559\pi$
$150$	8.04331e9	1.29725
$151$	−3.19788e9	−0.500572	−0.250286	−	0.968172i	$-0.580525\pi$
$151$	−3.19788e9	−0.500572	−0.250286	+	0.968172i	$0.580525\pi$
$152$	−1.72021e10	−2.61388
$153$	0	0
$154$	5.98440e9	0.857387
$155$	9.40159e8	0.130830
$156$	−1.79880e10	−2.43176
$157$	4.26085e9	0.559691	0.279845	−	0.960045i	$-0.409717\pi$
$157$	4.26085e9	0.559691	0.279845	+	0.960045i	$0.409717\pi$
$158$	2.38321e10	3.04232
$159$	1.81342e10	2.25014
$160$	5.22856e10	6.30729
$161$	2.66641e9	0.312760
$162$	1.57599e10	1.79778
$163$	−2.55595e9	−0.283601	−0.141800	−	0.989895i	$-0.545289\pi$
$163$	−2.55595e9	−0.283601	−0.141800	+	0.989895i	$0.545289\pi$
$164$	−3.86406e10	−4.17106
$165$	−9.94929e9	−1.04499
$166$	−1.51869e10	−1.55233
$167$	−1.08794e10	−1.08238	−0.541191	−	0.840900i	$-0.682026\pi$
$167$	−1.08794e10	−1.08238	−0.541191	+	0.840900i	$0.682026\pi$
$168$	4.06451e10	3.93656
$169$	−7.04865e9	−0.664685
$170$	0	0
$171$	8.39051e9	0.750423
$172$	1.64004e10	1.42882
$173$	−1.34690e10	−1.14322	−0.571608	−	0.820527i	$-0.693680\pi$
$173$	−1.34690e10	−1.14322	−0.571608	+	0.820527i	$0.693680\pi$
$174$	−5.16119e10	−4.26853
$175$	4.07409e9	0.328367
$176$	−3.47984e10	−2.73371
$177$	−3.26883e10	−2.50330
$178$	−2.09959e10	−1.56764
$179$	6.61516e9	0.481617	0.240809	−	0.970573i	$-0.422587\pi$
$179$	6.61516e9	0.481617	0.240809	+	0.970573i	$0.422587\pi$
$180$	−5.35525e10	−3.80237
$181$	−4.23515e9	−0.293302	−0.146651	−	0.989188i	$-0.546849\pi$
$181$	−4.23515e9	−0.293302	−0.146651	+	0.989188i	$0.546849\pi$
$182$	−1.22431e10	−0.827124
$183$	1.74597e10	1.15082
$184$	−2.54091e10	−1.63421
$185$	−3.90905e9	−0.245357
$186$	−5.05383e9	−0.309608
$187$	0	0
$188$	−2.83718e10	−1.65644
$189$	−1.53159e9	−0.0873101
$190$	2.96609e10	1.65117
$191$	2.04632e10	1.11256	0.556279	−	0.830996i	$-0.312229\pi$
$191$	2.04632e10	1.11256	0.556279	+	0.830996i	$0.312229\pi$
$192$	−1.57269e11	−8.35194
$193$	2.03719e10	1.05688	0.528438	−	0.848972i	$-0.322778\pi$
$193$	2.03719e10	1.05688	0.528438	+	0.848972i	$0.322778\pi$
$194$	−2.90555e8	−0.0147272
$195$	2.03546e10	1.00811
$196$	−2.87364e10	−1.39085
$197$	3.14257e9	0.148658	0.0743289	−	0.997234i	$-0.476319\pi$
$197$	3.14257e9	0.148658	0.0743289	+	0.997234i	$0.476319\pi$
$198$	2.78156e10	1.28616
$199$	2.17856e10	0.984761	0.492381	−	0.870380i	$-0.336127\pi$
$199$	2.17856e10	0.984761	0.492381	+	0.870380i	$0.336127\pi$
$200$	−3.88233e10	−1.71576
$201$	1.47563e10	0.637670
$202$	−9.13626e10	−3.86089
$203$	−2.61424e10	−1.08047
$204$	0	0
$205$	4.37245e10	1.72915
$206$	−2.94509e10	−1.13945
$207$	1.23936e10	0.469170
$208$	7.11920e10	2.63722
$209$	−1.14651e10	−0.415643
$210$	−7.00828e10	−2.48671
$211$	1.80701e10	0.627608	0.313804	−	0.949488i	$-0.398396\pi$
$211$	1.80701e10	0.627608	0.313804	+	0.949488i	$0.398396\pi$
$212$	−1.33376e11	−4.53487
$213$	−4.99860e10	−1.66395
$214$	−9.56097e10	−3.11630
$215$	−1.85583e10	−0.592330
$216$	1.45950e10	0.456207
$217$	−2.55986e9	−0.0783695
$218$	1.00274e10	0.300702
$219$	−7.48949e9	−0.220016
$220$	7.31764e10	2.10605
$221$	0	0
$222$	2.10131e10	0.580633
$223$	−2.54770e10	−0.689883	−0.344942	−	0.938624i	$-0.612101\pi$
$223$	−2.54770e10	−0.689883	−0.344942	+	0.938624i	$0.612101\pi$
$224$	−1.42363e11	−3.77817
$225$	1.89365e10	0.492582
$226$	−3.04720e10	−0.776985
$227$	5.83836e10	1.45940	0.729700	−	0.683767i	$-0.239660\pi$
$227$	5.83836e10	1.45940	0.729700	+	0.683767i	$0.239660\pi$
$228$	−1.18656e11	−2.90792
$229$	9.30702e9	0.223641	0.111820	−	0.993728i	$-0.464332\pi$
$229$	9.30702e9	0.223641	0.111820	+	0.993728i	$0.464332\pi$
$230$	4.38119e10	1.03233
$231$	2.70899e10	0.625969
$232$	2.49119e11	5.64561
$233$	1.79447e10	0.398873	0.199436	−	0.979911i	$-0.436089\pi$
$233$	1.79447e10	0.398873	0.199436	+	0.979911i	$0.436089\pi$
$234$	−5.69064e10	−1.24076
$235$	3.21047e10	0.686693
$236$	2.40420e11	5.04507
$237$	1.07882e11	2.22117
$238$	0	0
$239$	−7.54713e10	−1.49621	−0.748103	−	0.663582i	$-0.769035\pi$
$239$	−7.54713e10	−1.49621	−0.748103	+	0.663582i	$0.769035\pi$
$240$	4.07522e11	7.92867
$241$	−8.81448e10	−1.68314	−0.841570	−	0.540148i	$-0.818368\pi$
$241$	−8.81448e10	−1.68314	−0.841570	+	0.540148i	$0.818368\pi$
$242$	6.74821e10	1.26479
$243$	7.79100e10	1.43339
$244$	−1.28415e11	−2.31933
$245$	3.25173e10	0.576590
$246$	−2.35041e11	−4.09201
$247$	2.34558e10	0.400972
$248$	2.43937e10	0.409492
$249$	−6.87473e10	−1.13334
$250$	−8.03357e10	−1.30070
$251$	5.70117e10	0.906635	0.453317	−	0.891349i	$-0.350240\pi$
$251$	5.70117e10	0.906635	0.453317	+	0.891349i	$0.350240\pi$
$252$	1.45813e11	2.27768
$253$	−1.69351e10	−0.259863
$254$	−1.10324e11	−1.66309
$255$	0	0
$256$	4.46134e11	6.49211
$257$	8.70477e10	1.24468	0.622341	−	0.782747i	$-0.286182\pi$
$257$	8.70477e10	1.24468	0.622341	+	0.782747i	$0.286182\pi$
$258$	9.97599e10	1.40174
$259$	1.06435e10	0.146973
$260$	−1.49707e11	−2.03171
$261$	−1.21511e11	−1.62081
$262$	1.14651e11	1.50322
$263$	1.02557e11	1.32180	0.660900	−	0.750474i	$-0.270175\pi$
$263$	1.02557e11	1.32180	0.660900	+	0.750474i	$0.270175\pi$
$264$	−2.58148e11	−3.27077
$265$	1.50924e11	1.87997
$266$	−8.07605e10	−0.989080
$267$	−9.50433e10	−1.14451
$268$	−1.08532e11	−1.28514
$269$	6.29115e10	0.732563	0.366281	−	0.930504i	$-0.380631\pi$
$269$	6.29115e10	0.732563	0.366281	+	0.930504i	$0.380631\pi$
$270$	−2.51656e10	−0.288184
$271$	7.40442e10	0.833929	0.416965	−	0.908923i	$-0.363094\pi$
$271$	7.40442e10	0.833929	0.416965	+	0.908923i	$0.363094\pi$
$272$	0	0
$273$	−5.54215e10	−0.603874
$274$	−3.22750e11	−3.45930
$275$	−2.58756e10	−0.272831
$276$	−1.75266e11	−1.81805
$277$	−4.14432e10	−0.422955	−0.211477	−	0.977383i	$-0.567827\pi$
$277$	−4.14432e10	−0.422955	−0.211477	+	0.977383i	$0.567827\pi$
$278$	2.38473e10	0.239462
$279$	−1.18983e10	−0.117562
$280$	3.38274e11	3.28895
$281$	−5.09100e10	−0.487107	−0.243554	−	0.969887i	$-0.578313\pi$
$281$	−5.09100e10	−0.487107	−0.243554	+	0.969887i	$0.578313\pi$
$282$	−1.72579e11	−1.62505
$283$	6.84392e9	0.0634258	0.0317129	−	0.999497i	$-0.489904\pi$
$283$	6.84392e9	0.0634258	0.0317129	+	0.999497i	$0.489904\pi$
$284$	3.67644e11	3.35347
$285$	1.34267e11	1.20550
$286$	7.77591e10	0.687233
$287$	−1.19053e11	−1.03579
$288$	−6.61708e11	−5.66761
$289$	0	0
$290$	−4.29546e11	−3.56631
$291$	−1.31527e9	−0.0107522
$292$	5.50847e10	0.443413
$293$	2.94258e10	0.233251	0.116626	−	0.993176i	$-0.462792\pi$
$293$	2.94258e10	0.233251	0.116626	+	0.993176i	$0.462792\pi$
$294$	−1.74797e11	−1.36449
$295$	−2.72052e11	−2.09148
$296$	−1.01426e11	−0.767954
$297$	9.72752e9	0.0725434
$298$	3.30692e11	2.42913
$299$	3.46464e10	0.250691
$300$	−2.67794e11	−1.90877
$301$	5.05303e10	0.354815
$302$	1.43068e11	0.989716
$303$	−4.13575e11	−2.81879
$304$	4.69611e11	3.15360
$305$	1.45311e11	0.961497
$306$	0	0
$307$	2.13656e10	0.137275	0.0686377	−	0.997642i	$-0.478135\pi$
$307$	2.13656e10	0.137275	0.0686377	+	0.997642i	$0.478135\pi$
$308$	−1.99244e11	−1.26156
$309$	−1.33317e11	−0.831901
$310$	−4.20611e10	−0.258674
$311$	−1.54702e11	−0.937721	−0.468861	−	0.883272i	$-0.655335\pi$
$311$	−1.54702e11	−0.937721	−0.468861	+	0.883272i	$0.655335\pi$
$312$	5.28129e11	3.15532
$313$	2.42927e11	1.43063	0.715314	−	0.698803i	$-0.246284\pi$
$313$	2.42927e11	1.43063	0.715314	+	0.698803i	$0.246284\pi$
$314$	−1.90623e11	−1.10660
$315$	−1.64997e11	−0.944232
$316$	−7.93464e11	−4.47647
$317$	−1.16285e11	−0.646781	−0.323390	−	0.946266i	$-0.604823\pi$
$317$	−1.16285e11	−0.646781	−0.323390	+	0.946266i	$0.604823\pi$
$318$	−8.11291e11	−4.44892
$319$	1.66037e11	0.897732
$320$	−1.30889e12	−6.97795
$321$	−4.32801e11	−2.27518
$322$	−1.19291e11	−0.618380
$323$	0	0
$324$	−5.24709e11	−2.64525
$325$	5.29373e10	0.263200
$326$	1.14349e11	0.560727
$327$	4.53917e10	0.219539
$328$	1.13449e12	5.41214
$329$	−8.74144e10	−0.411340
$330$	4.45114e11	2.06613
$331$	4.77798e10	0.218786	0.109393	−	0.993999i	$-0.465109\pi$
$331$	4.77798e10	0.218786	0.109393	+	0.993999i	$0.465109\pi$
$332$	5.05632e11	2.28409
$333$	4.94715e10	0.220473
$334$	4.86725e11	2.14005
$335$	1.22811e11	0.532766
$336$	−1.10960e12	−4.74940
$337$	2.52033e11	1.06444	0.532222	−	0.846605i	$-0.321357\pi$
$337$	2.52033e11	1.06444	0.532222	+	0.846605i	$0.321357\pi$
$338$	3.15344e11	1.31420
$339$	−1.37939e11	−0.567268
$340$	0	0
$341$	1.62583e10	0.0651150
$342$	−3.75377e11	−1.48371
$343$	−2.73730e11	−1.06782
$344$	−4.81519e11	−1.85396
$345$	1.98325e11	0.753689
$346$	6.02581e11	2.26033
$347$	−1.56803e11	−0.580591	−0.290296	−	0.956937i	$-0.593754\pi$
$347$	−1.56803e11	−0.580591	−0.290296	+	0.956937i	$0.593754\pi$
$348$	1.71836e12	6.28070
$349$	−3.68186e11	−1.32847	−0.664237	−	0.747522i	$-0.731243\pi$
$349$	−3.68186e11	−1.32847	−0.664237	+	0.747522i	$0.731243\pi$
$350$	−1.82268e11	−0.649238
$351$	−1.99009e10	−0.0699829
$352$	9.04184e11	3.13917
$353$	3.45826e11	1.18542	0.592708	−	0.805417i	$-0.298059\pi$
$353$	3.45826e11	1.18542	0.592708	+	0.805417i	$0.298059\pi$
$354$	1.46242e12	4.94945
$355$	−4.16014e11	−1.39021
$356$	6.99038e11	2.30662
$357$	0	0
$358$	−2.95951e11	−0.952240
$359$	8.59874e10	0.273218	0.136609	−	0.990625i	$-0.456380\pi$
$359$	8.59874e10	0.273218	0.136609	+	0.990625i	$0.456380\pi$
$360$	1.57231e12	4.93374
$361$	−1.67964e11	−0.520515
$362$	1.89474e11	0.579909
$363$	3.05474e11	0.923411
$364$	4.07621e11	1.21703
$365$	−6.23322e10	−0.183821
$366$	−7.81118e11	−2.27537
$367$	8.64170e10	0.248658	0.124329	−	0.992241i	$-0.460322\pi$
$367$	8.64170e10	0.248658	0.124329	+	0.992241i	$0.460322\pi$
$368$	6.93659e11	1.97166
$369$	−5.53361e11	−1.55378
$370$	1.74884e11	0.485113
$371$	−4.10934e11	−1.12613
$372$	1.68262e11	0.455557
$373$	−4.74953e11	−1.27046	−0.635230	−	0.772323i	$-0.719095\pi$
$373$	−4.74953e11	−1.27046	−0.635230	+	0.772323i	$0.719095\pi$
$374$	0	0
$375$	−3.63659e11	−0.949629
$376$	8.32999e11	2.14931
$377$	−3.39685e11	−0.866045
$378$	6.85207e10	0.172627
$379$	2.21680e11	0.551887	0.275943	−	0.961174i	$-0.411010\pi$
$379$	2.21680e11	0.551887	0.275943	+	0.961174i	$0.411010\pi$
$380$	−9.87528e11	−2.42954
$381$	−4.99407e11	−1.21421
$382$	−9.15487e11	−2.19972
$383$	−3.14470e10	−0.0746766	−0.0373383	−	0.999303i	$-0.511888\pi$
$383$	−3.14470e10	−0.0746766	−0.0373383	+	0.999303i	$0.511888\pi$
$384$	3.81938e12	8.96400
$385$	2.25459e11	0.522990
$386$	−9.11404e11	−2.08962
$387$	2.34866e11	0.532257
$388$	9.67373e9	0.0216696
$389$	−9.75546e10	−0.216010	−0.108005	−	0.994150i	$-0.534446\pi$
$389$	−9.75546e10	−0.216010	−0.108005	+	0.994150i	$0.534446\pi$
$390$	−9.10632e11	−1.99321
$391$	0	0
$392$	8.43705e11	1.80469
$393$	5.18998e11	1.09749
$394$	−1.40593e11	−0.293922
$395$	8.97860e11	1.85576
$396$	−9.26093e11	−1.89246
$397$	5.98808e10	0.120985	0.0604923	−	0.998169i	$-0.480733\pi$
$397$	5.98808e10	0.120985	0.0604923	+	0.998169i	$0.480733\pi$
$398$	−9.74651e11	−1.94704
$399$	−3.65582e11	−0.722116
$400$	1.05986e12	2.07004
$401$	−3.95262e11	−0.763370	−0.381685	−	0.924292i	$-0.624656\pi$
$401$	−3.95262e11	−0.763370	−0.381685	+	0.924292i	$0.624656\pi$
$402$	−6.60173e11	−1.26078
$403$	−3.32619e10	−0.0628166
$404$	3.04182e12	5.68090
$405$	5.93745e11	1.09661
$406$	1.16957e12	2.13628
$407$	−6.75998e10	−0.122116
$408$	0	0
$409$	−4.42152e11	−0.781299	−0.390649	−	0.920540i	$-0.627749\pi$
$409$	−4.42152e11	−0.781299	−0.390649	+	0.920540i	$0.627749\pi$
$410$	−1.95616e12	−3.41883
$411$	−1.46101e12	−2.52560
$412$	9.80536e11	1.67659
$413$	7.40742e11	1.25283
$414$	−5.54467e11	−0.927629
$415$	−5.72158e11	−0.946890
$416$	−1.84982e12	−3.02837
$417$	1.07951e11	0.174829
$418$	5.12931e11	0.821798
$419$	5.57958e10	0.0884380	0.0442190	−	0.999022i	$-0.485920\pi$
$419$	5.57958e10	0.0884380	0.0442190	+	0.999022i	$0.485920\pi$
$420$	2.33333e12	3.65894
$421$	−6.67629e11	−1.03578	−0.517888	−	0.855449i	$-0.673281\pi$
$421$	−6.67629e11	−1.03578	−0.517888	+	0.855449i	$0.673281\pi$
$422$	−8.08424e11	−1.24089
$423$	−4.06305e11	−0.617050
$424$	3.91592e12	5.88420
$425$	0	0
$426$	2.23629e12	3.28991
$427$	−3.95651e11	−0.575953
$428$	3.18322e12	4.58532
$429$	3.51996e11	0.501741
$430$	8.30264e11	1.17114
$431$	−1.16472e12	−1.62583	−0.812916	−	0.582381i	$-0.802121\pi$
$431$	−1.16472e12	−1.62583	−0.812916	+	0.582381i	$0.802121\pi$
$432$	−3.98438e11	−0.550408
$433$	8.51716e11	1.16439	0.582196	−	0.813048i	$-0.302193\pi$
$433$	8.51716e11	1.16439	0.582196	+	0.813048i	$0.302193\pi$
$434$	1.14524e11	0.154950
$435$	−1.94445e12	−2.60372
$436$	−3.33853e11	−0.442452
$437$	2.28542e11	0.299778
$438$	3.35067e11	0.435009
$439$	−3.21133e10	−0.0412662	−0.0206331	−	0.999787i	$-0.506568\pi$
$439$	−3.21133e10	−0.0412662	−0.0206331	+	0.999787i	$0.506568\pi$
$440$	−2.14847e12	−2.73270
$441$	−4.11527e11	−0.518113
$442$	0	0
$443$	1.46852e12	1.81160	0.905799	−	0.423707i	$-0.139271\pi$
$443$	1.46852e12	1.81160	0.905799	+	0.423707i	$0.139271\pi$
$444$	−6.99609e11	−0.854343
$445$	−7.91010e11	−0.956229
$446$	1.13980e12	1.36402
$447$	1.49696e12	1.77348
$448$	3.56384e12	4.17991
$449$	2.98654e11	0.346784	0.173392	−	0.984853i	$-0.444527\pi$
$449$	2.98654e11	0.346784	0.173392	+	0.984853i	$0.444527\pi$
$450$	−8.47186e11	−0.973918
$451$	7.56136e11	0.860608
$452$	1.01453e12	1.14325
$453$	6.47632e11	0.722580
$454$	−2.61198e12	−2.88548
$455$	−4.61252e11	−0.504530
$456$	3.48375e12	3.77316
$457$	−3.16156e11	−0.339061	−0.169531	−	0.985525i	$-0.554225\pi$
$457$	−3.16156e11	−0.339061	−0.169531	+	0.985525i	$0.554225\pi$
$458$	−4.16380e11	−0.442176
$459$	0	0
$460$	−1.45867e12	−1.51896
$461$	7.38260e11	0.761298	0.380649	−	0.924720i	$-0.375701\pi$
$461$	7.38260e11	0.761298	0.380649	+	0.924720i	$0.375701\pi$
$462$	−1.21195e12	−1.23765
$463$	1.74516e12	1.76490	0.882452	−	0.470402i	$-0.155891\pi$
$463$	1.74516e12	1.76490	0.882452	+	0.470402i	$0.155891\pi$
$464$	−6.80086e12	−6.81135
$465$	−1.90400e11	−0.188855
$466$	−8.02815e11	−0.788640
$467$	4.90423e11	0.477139	0.238569	−	0.971125i	$-0.423322\pi$
$467$	4.90423e11	0.477139	0.238569	+	0.971125i	$0.423322\pi$
$468$	1.89464e12	1.82566
$469$	−3.34390e11	−0.319136
$470$	−1.43631e12	−1.35771
$471$	−8.62904e11	−0.807920
$472$	−7.05876e12	−6.54620
$473$	−3.20931e11	−0.294806
$474$	−4.82645e12	−4.39163
$475$	3.49196e11	0.314737
$476$	0	0
$477$	−1.91004e12	−1.68931
$478$	3.37646e12	2.95826
$479$	−3.66099e11	−0.317752	−0.158876	−	0.987299i	$-0.550787\pi$
$479$	−3.66099e11	−0.317752	−0.158876	+	0.987299i	$0.550787\pi$
$480$	−1.05888e13	−9.10463
$481$	1.38298e11	0.117805
$482$	3.94345e12	3.32786
$483$	−5.39999e11	−0.451472
$484$	−2.24675e12	−1.86101
$485$	−1.09465e10	−0.00898333
$486$	−3.48556e12	−2.83406
$487$	−1.83184e12	−1.47573	−0.737866	−	0.674948i	$-0.764166\pi$
$487$	−1.83184e12	−1.47573	−0.737866	+	0.674948i	$0.764166\pi$
$488$	3.77028e12	3.00943
$489$	5.17628e11	0.409381
$490$	−1.45477e12	−1.14002
$491$	6.41422e11	0.498055	0.249027	−	0.968496i	$-0.419889\pi$
$491$	6.41422e11	0.498055	0.249027	+	0.968496i	$0.419889\pi$
$492$	7.82545e12	6.02097
$493$	0	0
$494$	−1.04937e12	−0.792791
$495$	1.04794e12	0.784535
$496$	−6.65939e11	−0.494046
$497$	1.13272e12	0.832759
$498$	3.07564e12	2.24080
$499$	8.16394e10	0.0589451	0.0294725	−	0.999566i	$-0.490617\pi$
$499$	8.16394e10	0.0589451	0.0294725	+	0.999566i	$0.490617\pi$
$500$	2.67469e12	1.91385
$501$	2.20328e12	1.56243
$502$	−2.55061e12	−1.79257
$503$	−2.05382e12	−1.43056	−0.715281	−	0.698837i	$-0.753701\pi$
$503$	−2.05382e12	−1.43056	−0.715281	+	0.698837i	$0.753701\pi$
$504$	−4.28107e12	−2.95539
$505$	−3.44203e12	−2.35507
$506$	7.57646e11	0.513794
$507$	1.42748e12	0.959479
$508$	3.67311e12	2.44707
$509$	−1.53618e11	−0.101441	−0.0507203	−	0.998713i	$-0.516152\pi$
$509$	−1.53618e11	−0.101441	−0.0507203	+	0.998713i	$0.516152\pi$
$510$	0	0
$511$	1.69718e11	0.110112
$512$	−1.03033e13	−6.62615
$513$	−1.31275e11	−0.0836860
$514$	−3.89436e12	−2.46095
$515$	−1.10954e12	−0.695044
$516$	−3.32140e12	−2.06252
$517$	5.55191e11	0.341771
$518$	−4.76174e11	−0.290591
$519$	2.72773e12	1.65024
$520$	4.39542e12	2.63624
$521$	−9.45774e11	−0.562364	−0.281182	−	0.959654i	$-0.590727\pi$
$521$	−9.45774e11	−0.562364	−0.281182	+	0.959654i	$0.590727\pi$
$522$	5.43618e12	3.20462
$523$	1.60345e12	0.937123	0.468561	−	0.883431i	$-0.344772\pi$
$523$	1.60345e12	0.937123	0.468561	+	0.883431i	$0.344772\pi$
$524$	−3.81719e12	−2.21184
$525$	−8.25080e11	−0.474001
$526$	−4.58824e12	−2.61342
$527$	0	0
$528$	7.04734e12	3.94614
$529$	−1.46358e12	−0.812577
$530$	−6.75207e12	−3.71703
$531$	3.44299e12	1.87936
$532$	2.68883e12	1.45533
$533$	−1.54693e12	−0.830231
$534$	4.25207e12	2.26290
$535$	−3.60204e12	−1.90089
$536$	3.18651e12	1.66753
$537$	−1.33970e12	−0.695219
$538$	−2.81455e12	−1.44840
$539$	5.62327e11	0.286972
$540$	8.37862e11	0.424034
$541$	1.70973e12	0.858102	0.429051	−	0.903280i	$-0.358848\pi$
$541$	1.70973e12	0.858102	0.429051	+	0.903280i	$0.358848\pi$
$542$	−3.31261e12	−1.64882
$543$	8.57699e11	0.423385
$544$	0	0
$545$	3.77778e11	0.183422
$546$	2.47946e12	1.19396
$547$	2.56587e12	1.22544	0.612720	−	0.790300i	$-0.290075\pi$
$547$	2.56587e12	1.22544	0.612720	+	0.790300i	$0.290075\pi$
$548$	1.07456e13	5.09001
$549$	−1.83900e12	−0.863984
$550$	1.15763e12	0.539433
$551$	−2.24070e12	−1.03562
$552$	5.14582e12	2.35900
$553$	−2.44469e12	−1.11163
$554$	1.85410e12	0.836254
$555$	7.91657e11	0.354176
$556$	−7.93970e11	−0.352344
$557$	2.29359e12	1.00964	0.504820	−	0.863225i	$-0.331559\pi$
$557$	2.29359e12	1.00964	0.504820	+	0.863225i	$0.331559\pi$
$558$	5.32310e11	0.232440
$559$	6.56573e11	0.284400
$560$	−9.23477e12	−3.96808
$561$	0	0
$562$	2.27763e12	0.963094
$563$	−2.87194e12	−1.20472	−0.602362	−	0.798223i	$-0.705774\pi$
$563$	−2.87194e12	−1.20472	−0.602362	+	0.798223i	$0.705774\pi$
$564$	5.74583e12	2.39109
$565$	−1.14801e12	−0.473946
$566$	−3.06185e11	−0.125404
$567$	−1.61665e12	−0.656888
$568$	−1.07941e13	−4.35128
$569$	3.45359e12	1.38123	0.690615	−	0.723222i	$-0.257340\pi$
$569$	3.45359e12	1.38123	0.690615	+	0.723222i	$0.257340\pi$
$570$	−6.00689e12	−2.38349
$571$	−1.13524e12	−0.446916	−0.223458	−	0.974714i	$-0.571735\pi$
$571$	−1.13524e12	−0.446916	−0.223458	+	0.974714i	$0.571735\pi$
$572$	−2.58891e12	−1.01119
$573$	−4.14418e12	−1.60599
$574$	5.32622e12	2.04793
$575$	5.15794e11	0.196776
$576$	1.65648e13	6.27026
$577$	1.00514e11	0.0377516	0.0188758	−	0.999822i	$-0.493991\pi$
$577$	1.00514e11	0.0377516	0.0188758	+	0.999822i	$0.493991\pi$
$578$	0	0
$579$	−4.12570e12	−1.52561
$580$	1.43013e13	5.24746
$581$	1.55787e12	0.567202
$582$	5.88429e10	0.0212589
$583$	2.60995e12	0.935672
$584$	−1.61729e12	−0.575348
$585$	−2.14391e12	−0.756843
$586$	−1.31646e12	−0.461178
$587$	−1.73536e12	−0.603279	−0.301640	−	0.953422i	$-0.597534\pi$
$587$	−1.73536e12	−0.603279	−0.301640	+	0.953422i	$0.597534\pi$
$588$	5.81967e12	2.00771
$589$	−2.19409e11	−0.0751165
$590$	1.21711e13	4.13521
$591$	−6.36431e11	−0.214589
$592$	2.76888e12	0.926525
$593$	−5.34487e12	−1.77497	−0.887485	−	0.460836i	$-0.847550\pi$
$593$	−5.34487e12	−1.77497	−0.887485	+	0.460836i	$0.847550\pi$
$594$	−4.35193e11	−0.143431
$595$	0	0
$596$	−1.10100e13	−3.57421
$597$	−4.41200e12	−1.42151
$598$	−1.55002e12	−0.495659
$599$	−3.97236e12	−1.26075	−0.630374	−	0.776292i	$-0.717098\pi$
$599$	−3.97236e12	−1.26075	−0.630374	+	0.776292i	$0.717098\pi$
$600$	7.86245e12	2.47672
$601$	−2.57946e12	−0.806480	−0.403240	−	0.915094i	$-0.632116\pi$
$601$	−2.57946e12	−0.806480	−0.403240	+	0.915094i	$0.632116\pi$
$602$	−2.26064e12	−0.701531
$603$	−1.55425e12	−0.478734
$604$	−4.76329e12	−1.45627
$605$	2.54235e12	0.771500
$606$	1.85026e13	5.57323
$607$	−4.42720e12	−1.32367	−0.661836	−	0.749649i	$-0.730222\pi$
$607$	−4.42720e12	−1.32367	−0.661836	+	0.749649i	$0.730222\pi$
$608$	−1.22021e13	−3.62134
$609$	5.29433e12	1.55967
$610$	−6.50095e12	−1.90105
$611$	−1.13583e12	−0.329707
$612$	0	0
$613$	−2.14087e12	−0.612376	−0.306188	−	0.951971i	$-0.599054\pi$
$613$	−2.14087e12	−0.612376	−0.306188	+	0.951971i	$0.599054\pi$
$614$	−9.55861e11	−0.271417
$615$	−8.85505e12	−2.49605
$616$	5.84983e12	1.63693
$617$	−6.79042e11	−0.188631	−0.0943155	−	0.995542i	$-0.530066\pi$
$617$	−6.79042e11	−0.188631	−0.0943155	+	0.995542i	$0.530066\pi$
$618$	5.96436e12	1.64481
$619$	6.49200e12	1.77734	0.888671	−	0.458546i	$-0.151630\pi$
$619$	6.49200e12	1.77734	0.888671	+	0.458546i	$0.151630\pi$
$620$	1.40038e12	0.380613
$621$	−1.93905e11	−0.0523210
$622$	6.92110e12	1.85404
$623$	2.15376e12	0.572797
$624$	−1.44177e13	−3.80685
$625$	−4.76048e12	−1.24793
$626$	−1.08682e13	−2.82860
$627$	2.32191e12	0.599986
$628$	6.34660e12	1.62826
$629$	0	0
$630$	7.38168e12	1.86691
$631$	−3.66553e12	−0.920459	−0.460230	−	0.887800i	$-0.652233\pi$
$631$	−3.66553e12	−0.920459	−0.460230	+	0.887800i	$0.652233\pi$
$632$	2.32962e13	5.80842
$633$	−3.65953e12	−0.905960
$634$	5.20239e12	1.27880
$635$	−4.15638e12	−1.01446
$636$	2.70111e13	6.54614
$637$	−1.15043e12	−0.276843
$638$	−7.42821e12	−1.77497
$639$	5.26492e12	1.24922
$640$	3.17872e13	7.48933
$641$	−1.67471e12	−0.391813	−0.195907	−	0.980623i	$-0.562765\pi$
$641$	−1.67471e12	−0.391813	−0.195907	+	0.980623i	$0.562765\pi$
$642$	1.93628e13	4.49842
$643$	1.46537e12	0.338064	0.169032	−	0.985611i	$-0.445936\pi$
$643$	1.46537e12	0.338064	0.169032	+	0.985611i	$0.445936\pi$
$644$	3.97166e12	0.909883
$645$	3.75840e12	0.855035
$646$	0	0
$647$	−2.25306e12	−0.505479	−0.252739	−	0.967534i	$-0.581332\pi$
$647$	−2.25306e12	−0.505479	−0.252739	+	0.967534i	$0.581332\pi$
$648$	1.54055e13	3.43233
$649$	−4.70464e12	−1.04094
$650$	−2.36832e12	−0.520392
$651$	5.18420e11	0.113127
$652$	−3.80712e12	−0.825053
$653$	−4.56703e12	−0.982935	−0.491467	−	0.870896i	$-0.663539\pi$
$653$	−4.56703e12	−0.982935	−0.491467	+	0.870896i	$0.663539\pi$
$654$	−2.03075e12	−0.434066
$655$	4.31942e12	0.916938
$656$	−3.09712e13	−6.52967
$657$	7.88853e11	0.165178
$658$	3.91077e12	0.813290
$659$	2.93270e12	0.605735	0.302868	−	0.953033i	$-0.402056\pi$
$659$	2.93270e12	0.605735	0.302868	+	0.953033i	$0.402056\pi$
$660$	−1.48196e13	−3.04011
$661$	1.85770e12	0.378502	0.189251	−	0.981929i	$-0.439394\pi$
$661$	1.85770e12	0.378502	0.189251	+	0.981929i	$0.439394\pi$
$662$	−2.13759e12	−0.432576
$663$	0	0
$664$	−1.48454e13	−2.96371
$665$	−3.04260e12	−0.603321
$666$	−2.21327e12	−0.435913
$667$	−3.30972e12	−0.647478
$668$	−1.62050e13	−3.14887
$669$	5.15957e12	0.995854
$670$	−5.49437e12	−1.05337
$671$	2.51288e12	0.478542
$672$	2.88312e13	5.45382
$673$	−1.36336e12	−0.256178	−0.128089	−	0.991763i	$-0.540884\pi$
$673$	−1.36336e12	−0.256178	−0.128089	+	0.991763i	$0.540884\pi$
$674$	−1.12755e13	−2.10459
$675$	−2.96273e11	−0.0549319
$676$	−1.04991e13	−1.93370
$677$	−2.24931e12	−0.411529	−0.205764	−	0.978602i	$-0.565968\pi$
$677$	−2.24931e12	−0.411529	−0.205764	+	0.978602i	$0.565968\pi$
$678$	6.17115e12	1.12159
$679$	2.98051e10	0.00538116
$680$	0	0
$681$	−1.18238e13	−2.10666
$682$	−7.27369e11	−0.128743
$683$	−6.85651e12	−1.20562	−0.602810	−	0.797885i	$-0.705952\pi$
$683$	−6.85651e12	−1.20562	−0.602810	+	0.797885i	$0.705952\pi$
$684$	1.24978e13	2.18314
$685$	−1.21594e13	−2.11011
$686$	1.22462e13	2.11127
$687$	−1.88485e12	−0.322828
$688$	1.31453e13	2.23678
$689$	−5.33954e12	−0.902645
$690$	−8.87274e12	−1.49017
$691$	4.67266e12	0.779674	0.389837	−	0.920884i	$-0.372531\pi$
$691$	4.67266e12	0.779674	0.389837	+	0.920884i	$0.372531\pi$
$692$	−2.00623e13	−3.32585
$693$	−2.85332e12	−0.469949
$694$	7.01508e12	1.14793
$695$	8.98432e11	0.146068
$696$	−5.04513e13	−8.14950
$697$	0	0
$698$	1.64720e13	2.62662
$699$	−3.63414e12	−0.575777
$700$	6.06841e12	0.955287
$701$	−1.94630e12	−0.304423	−0.152212	−	0.988348i	$-0.548640\pi$
$701$	−1.94630e12	−0.304423	−0.152212	+	0.988348i	$0.548640\pi$
$702$	8.90334e11	0.138368
$703$	9.12272e11	0.140872
$704$	−2.26348e13	−3.47297
$705$	−6.50180e12	−0.991249
$706$	−1.54716e13	−2.34377
$707$	9.37194e12	1.41072
$708$	−4.86896e13	−7.28261
$709$	1.10631e13	1.64425	0.822127	−	0.569304i	$-0.192787\pi$
$709$	1.10631e13	1.64425	0.822127	+	0.569304i	$0.192787\pi$
$710$	1.86118e13	2.74869
$711$	−1.13630e13	−1.66755
$712$	−2.05238e13	−2.99294
$713$	−3.24087e11	−0.0469634
$714$	0	0
$715$	2.92953e12	0.419200
$716$	9.85338e12	1.40112
$717$	1.52844e13	2.15979
$718$	−3.84693e12	−0.540199
$719$	1.25182e13	1.74688	0.873438	−	0.486935i	$-0.161885\pi$
$719$	1.25182e13	1.74688	0.873438	+	0.486935i	$0.161885\pi$
$720$	−4.29235e13	−5.95249
$721$	3.02106e12	0.416343
$722$	7.51440e12	1.02915
$723$	1.78510e13	2.42963
$724$	−6.30832e12	−0.853277
$725$	−5.05702e12	−0.679788
$726$	−1.36664e13	−1.82574
$727$	−5.12484e11	−0.0680417	−0.0340208	−	0.999421i	$-0.510831\pi$
$727$	−5.12484e11	−0.0680417	−0.0340208	+	0.999421i	$0.510831\pi$
$728$	−1.19678e13	−1.57915
$729$	−8.84455e12	−1.15985
$730$	2.78863e12	0.363445
$731$	0	0
$732$	2.60065e13	3.34797
$733$	−8.38135e12	−1.07237	−0.536187	−	0.844099i	$-0.680136\pi$
$733$	−8.38135e12	−1.07237	−0.536187	+	0.844099i	$0.680136\pi$
$734$	−3.86615e12	−0.491639
$735$	−6.58537e12	−0.832314
$736$	−1.80237e13	−2.26409
$737$	2.12380e12	0.265161
$738$	2.47564e13	3.07209
$739$	6.99883e12	0.863228	0.431614	−	0.902058i	$-0.357944\pi$
$739$	6.99883e12	0.863228	0.431614	+	0.902058i	$0.357944\pi$
$740$	−5.82259e12	−0.713794
$741$	−4.75025e12	−0.578808
$742$	1.83845e13	2.22656
$743$	9.88346e12	1.18976	0.594880	−	0.803814i	$-0.297199\pi$
$743$	9.88346e12	1.18976	0.594880	+	0.803814i	$0.297199\pi$
$744$	−4.94019e12	−0.591106
$745$	1.24586e13	1.48172
$746$	2.12486e13	2.51192
$747$	7.24102e12	0.850858
$748$	0	0
$749$	9.80761e12	1.13866
$750$	1.62695e13	1.87758
$751$	1.11071e13	1.27415	0.637077	−	0.770800i	$-0.280143\pi$
$751$	1.11071e13	1.27415	0.637077	+	0.770800i	$0.280143\pi$
$752$	−2.27406e13	−2.59311
$753$	−1.15460e13	−1.30874
$754$	1.51969e13	1.71232
$755$	5.38999e12	0.603708
$756$	−2.28132e12	−0.254003
$757$	6.98226e12	0.772796	0.386398	−	0.922332i	$-0.373719\pi$
$757$	6.98226e12	0.772796	0.386398	+	0.922332i	$0.373719\pi$
$758$	−9.91758e12	−1.09118
$759$	3.42967e12	0.375115
$760$	2.89939e13	3.15243
$761$	−1.11765e12	−0.120802	−0.0604009	−	0.998174i	$-0.519238\pi$
$761$	−1.11765e12	−0.120802	−0.0604009	+	0.998174i	$0.519238\pi$
$762$	2.23426e13	2.40069
$763$	−1.02861e12	−0.109873
$764$	3.04802e13	3.23666
$765$	0	0
$766$	1.40688e12	0.147649
$767$	9.62494e12	1.00420
$768$	−9.03506e13	−9.37143
$769$	1.47341e13	1.51934	0.759671	−	0.650307i	$-0.225360\pi$
$769$	1.47341e13	1.51934	0.759671	+	0.650307i	$0.225360\pi$
$770$	−1.00866e13	−1.03404
$771$	−1.76288e13	−1.79671
$772$	3.03442e13	3.07467
$773$	8.37182e12	0.843358	0.421679	−	0.906745i	$-0.361441\pi$
$773$	8.37182e12	0.843358	0.421679	+	0.906745i	$0.361441\pi$
$774$	−1.05075e13	−1.05236
$775$	−4.95182e11	−0.0493069
$776$	−2.84022e11	−0.0281173
$777$	−2.15552e12	−0.212157
$778$	4.36442e12	0.427089
$779$	−1.02042e13	−0.992795
$780$	3.03185e13	2.93280
$781$	−7.19420e12	−0.691915
$782$	0	0
$783$	1.90111e12	0.180750
$784$	−2.30329e13	−2.17734
$785$	−7.18162e12	−0.675008
$786$	−2.32191e13	−2.16992
$787$	1.86469e13	1.73269	0.866345	−	0.499445i	$-0.166463\pi$
$787$	1.86469e13	1.73269	0.866345	+	0.499445i	$0.166463\pi$
$788$	4.68091e12	0.432476
$789$	−2.07698e13	−1.90803
$790$	−4.01687e13	−3.66916
$791$	3.12580e12	0.283901
$792$	2.71902e13	2.45555
$793$	−5.14095e12	−0.461651
$794$	−2.67896e12	−0.239207
$795$	−3.05649e13	−2.71376
$796$	3.24500e13	2.86487
$797$	7.45382e12	0.654360	0.327180	−	0.944962i	$-0.393902\pi$
$797$	7.45382e12	0.654360	0.327180	+	0.944962i	$0.393902\pi$
$798$	1.63555e13	1.42775
$799$	0	0
$800$	−2.75389e13	−2.37707
$801$	1.00107e13	0.859249
$802$	1.76833e13	1.50931
$803$	−1.07792e12	−0.0914885
$804$	2.19798e13	1.85511
$805$	−4.49421e12	−0.377200
$806$	1.48808e12	0.124199
$807$	−1.27408e13	−1.05746
$808$	−8.93082e13	−7.37123
$809$	1.42628e13	1.17068	0.585338	−	0.810790i	$-0.300962\pi$
$809$	1.42628e13	1.17068	0.585338	+	0.810790i	$0.300962\pi$
$810$	−2.65631e13	−2.16819
$811$	−1.18731e12	−0.0963766	−0.0481883	−	0.998838i	$-0.515345\pi$
$811$	−1.18731e12	−0.0963766	−0.0481883	+	0.998838i	$0.515345\pi$
$812$	−3.89395e13	−3.14331
$813$	−1.49954e13	−1.20379
$814$	3.02430e12	0.241443
$815$	4.30802e12	0.342033
$816$	0	0
$817$	4.33102e12	0.340088
$818$	1.97811e13	1.54476
$819$	5.83744e12	0.453361
$820$	6.51283e13	5.03046
$821$	−1.56983e13	−1.20589	−0.602947	−	0.797781i	$-0.706007\pi$
$821$	−1.56983e13	−1.20589	−0.602947	+	0.797781i	$0.706007\pi$
$822$	6.53629e13	4.99354
$823$	−1.41366e13	−1.07410	−0.537052	−	0.843549i	$-0.680462\pi$
$823$	−1.41366e13	−1.07410	−0.537052	+	0.843549i	$0.680462\pi$
$824$	−2.87886e13	−2.17545
$825$	5.24030e12	0.393834
$826$	−3.31395e13	−2.47706
$827$	7.28652e12	0.541683	0.270842	−	0.962624i	$-0.412698\pi$
$827$	7.28652e12	0.541683	0.270842	+	0.962624i	$0.412698\pi$
$828$	1.84604e13	1.36491
$829$	−2.46257e13	−1.81089	−0.905447	−	0.424460i	$-0.860464\pi$
$829$	−2.46257e13	−1.81089	−0.905447	+	0.424460i	$0.860464\pi$
$830$	2.55974e13	1.87216
$831$	8.39303e12	0.610540
$832$	4.63072e13	3.35038
$833$	0	0
$834$	−4.82952e12	−0.345666
$835$	1.83371e13	1.30539
$836$	−1.70775e13	−1.20919
$837$	1.86156e11	0.0131103
$838$	−2.49621e12	−0.174857
$839$	5.37332e12	0.374381	0.187191	−	0.982324i	$-0.440062\pi$
$839$	5.37332e12	0.374381	0.187191	+	0.982324i	$0.440062\pi$
$840$	−6.85069e13	−4.74764
$841$	1.79425e13	1.23680
$842$	2.98686e13	2.04790
$843$	1.03102e13	0.703144
$844$	2.69156e13	1.82584
$845$	1.18804e13	0.801635
$846$	1.81774e13	1.22001
$847$	−6.92229e12	−0.462141
$848$	−1.06903e14	−7.09921
$849$	−1.38602e12	−0.0915558
$850$	0	0
$851$	1.34751e12	0.0880743
$852$	−7.44548e13	−4.84077
$853$	1.32534e13	0.857150	0.428575	−	0.903506i	$-0.359016\pi$
$853$	1.32534e13	0.857150	0.428575	+	0.903506i	$0.359016\pi$
$854$	1.77007e13	1.13876
$855$	−1.41421e13	−0.905038
$856$	−9.34598e13	−5.94967
$857$	−2.61157e13	−1.65382	−0.826909	−	0.562335i	$-0.809903\pi$
$857$	−2.61157e13	−1.65382	−0.826909	+	0.562335i	$0.809903\pi$
$858$	−1.57477e13	−0.992029
$859$	1.81576e13	1.13786	0.568929	−	0.822387i	$-0.307358\pi$
$859$	1.81576e13	1.13786	0.568929	+	0.822387i	$0.307358\pi$
$860$	−2.76428e13	−1.72321
$861$	2.41105e13	1.49517
$862$	5.21078e13	3.21455
$863$	−9.67154e12	−0.593536	−0.296768	−	0.954950i	$-0.595909\pi$
$863$	−9.67154e12	−0.593536	−0.296768	+	0.954950i	$0.595909\pi$
$864$	1.03528e13	0.632043
$865$	2.27019e13	1.37876
$866$	−3.81043e13	−2.30220
$867$	0	0
$868$	−3.81295e12	−0.227993
$869$	1.55268e13	0.923622
$870$	8.69912e13	5.14800
$871$	−4.34495e12	−0.255801
$872$	9.80196e12	0.574102
$873$	1.38535e11	0.00807225
$874$	−1.02246e13	−0.592712
$875$	8.24081e12	0.475262
$876$	−1.11557e13	−0.640071
$877$	2.58930e13	1.47803	0.739016	−	0.673688i	$-0.235291\pi$
$877$	2.58930e13	1.47803	0.739016	+	0.673688i	$0.235291\pi$
$878$	1.43669e12	0.0815903
$879$	−5.95929e12	−0.336701
$880$	5.86524e13	3.29696
$881$	−3.09147e12	−0.172891	−0.0864457	−	0.996257i	$-0.527551\pi$
$881$	−3.09147e12	−0.172891	−0.0864457	+	0.996257i	$0.527551\pi$
$882$	1.84110e13	1.02440
$883$	−1.12784e13	−0.624345	−0.312173	−	0.950025i	$-0.601057\pi$
$883$	−1.12784e13	−0.624345	−0.312173	+	0.950025i	$0.601057\pi$
$884$	0	0
$885$	5.50957e13	3.01907
$886$	−6.56989e13	−3.58184
$887$	−2.10294e13	−1.14070	−0.570348	−	0.821403i	$-0.693191\pi$
$887$	−2.10294e13	−1.14070	−0.570348	+	0.821403i	$0.693191\pi$
$888$	2.05406e13	1.10855
$889$	1.13170e13	0.607676
$890$	3.53884e13	1.89063
$891$	1.02677e13	0.545789
$892$	−3.79483e13	−2.00701
$893$	−7.49240e12	−0.394266
$894$	−6.69714e13	−3.50647
$895$	−1.11498e13	−0.580848
$896$	−8.65501e13	−4.48623
$897$	−7.01656e12	−0.361875
$898$	−1.33612e13	−0.685652
$899$	3.17746e12	0.162241
$900$	2.82062e13	1.43302
$901$	0	0
$902$	−3.38282e13	−1.70157
$903$	−1.02333e13	−0.512180
$904$	−2.97868e13	−1.48342
$905$	7.13831e12	0.353734
$906$	−2.89739e13	−1.42867
$907$	−1.65206e13	−0.810576	−0.405288	−	0.914189i	$-0.632829\pi$
$907$	−1.65206e13	−0.810576	−0.405288	+	0.914189i	$0.632829\pi$
$908$	8.69632e13	4.24570
$909$	4.35611e13	2.11622
$910$	2.06356e13	0.997543
$911$	1.94745e13	0.936773	0.468387	−	0.883524i	$-0.344835\pi$
$911$	1.94745e13	0.936773	0.468387	+	0.883524i	$0.344835\pi$
$912$	−9.51051e13	−4.55226
$913$	−9.89442e12	−0.471272
$914$	1.41443e13	0.670382
$915$	−2.94282e13	−1.38793
$916$	1.38629e13	0.650617
$917$	−1.17609e13	−0.549260
$918$	0	0
$919$	7.57232e12	0.350194	0.175097	−	0.984551i	$-0.443976\pi$
$919$	7.57232e12	0.350194	0.175097	+	0.984551i	$0.443976\pi$
$920$	4.28267e13	1.97092
$921$	−4.32694e12	−0.198159
$922$	−3.30285e13	−1.50522
$923$	1.47182e13	0.667493
$924$	4.03507e13	1.82107
$925$	2.05890e12	0.0924693
$926$	−7.80756e13	−3.48952
$927$	1.40420e13	0.624554
$928$	1.76710e14	7.82159
$929$	−2.50574e12	−0.110374	−0.0551868	−	0.998476i	$-0.517575\pi$
$929$	−2.50574e12	−0.110374	−0.0551868	+	0.998476i	$0.517575\pi$
$930$	8.51817e12	0.373399
$931$	−7.58870e12	−0.331050
$932$	2.67289e13	1.16040
$933$	3.13301e13	1.35361
$934$	−2.19407e13	−0.943385
$935$	0	0
$936$	−5.56267e13	−2.36888
$937$	−3.81545e13	−1.61703	−0.808515	−	0.588476i	$-0.799728\pi$
$937$	−3.81545e13	−1.61703	−0.808515	+	0.588476i	$0.799728\pi$
$938$	1.49600e13	0.630986
$939$	−4.91974e13	−2.06513
$940$	4.78203e13	1.99773
$941$	3.98075e13	1.65505	0.827526	−	0.561427i	$-0.189747\pi$
$941$	3.98075e13	1.65505	0.827526	+	0.561427i	$0.189747\pi$
$942$	3.86048e13	1.59740
$943$	−1.50725e13	−0.620702
$944$	1.92702e14	7.89790
$945$	2.58148e12	0.105299
$946$	1.43579e13	0.582882
$947$	3.10230e13	1.25345	0.626727	−	0.779239i	$-0.284394\pi$
$947$	3.10230e13	1.25345	0.626727	+	0.779239i	$0.284394\pi$
$948$	1.60692e14	6.46183
$949$	2.20525e12	0.0882593
$950$	−1.56224e13	−0.622289
$951$	2.35499e13	0.933635
$952$	0	0
$953$	2.23124e13	0.876252	0.438126	−	0.898914i	$-0.355642\pi$
$953$	2.23124e13	0.876252	0.438126	+	0.898914i	$0.355642\pi$
$954$	8.54517e13	3.34005
$955$	−3.44904e13	−1.34179
$956$	−1.12416e14	−4.35277
$957$	−3.36256e13	−1.29589
$958$	1.63786e13	0.628251
$959$	3.31075e13	1.26399
$960$	2.65075e14	10.0728
$961$	−2.61285e13	−0.988232
$962$	−6.18723e12	−0.232921
$963$	4.55861e13	1.70810
$964$	−1.31293e14	−4.89660
$965$	−3.43366e13	−1.27463
$966$	2.41586e13	0.892638
$967$	3.20654e13	1.17928	0.589640	−	0.807666i	$-0.299270\pi$
$967$	3.20654e13	1.17928	0.589640	+	0.807666i	$0.299270\pi$
$968$	6.59647e13	2.41475
$969$	0	0
$970$	4.89728e11	0.0177616
$971$	1.32073e13	0.476791	0.238395	−	0.971168i	$-0.423379\pi$
$971$	1.32073e13	0.476791	0.238395	+	0.971168i	$0.423379\pi$
$972$	1.16048e14	4.17003
$973$	−2.44625e12	−0.0874968
$974$	8.19534e13	2.91777
$975$	−1.07208e13	−0.379933
$976$	−1.02927e14	−3.63084
$977$	5.28646e13	1.85626	0.928131	−	0.372254i	$-0.121415\pi$
$977$	5.28646e13	1.85626	0.928131	+	0.372254i	$0.121415\pi$
$978$	−2.31578e13	−0.809416
$979$	−1.36791e13	−0.475920
$980$	4.84350e13	1.67742
$981$	−4.78102e12	−0.164820
$982$	−2.86961e13	−0.984739
$983$	−1.32999e13	−0.454316	−0.227158	−	0.973858i	$-0.572943\pi$
$983$	−1.32999e13	−0.454316	−0.227158	+	0.973858i	$0.572943\pi$
$984$	−2.29756e14	−7.81249
$985$	−5.29677e12	−0.179287
$986$	0	0
$987$	1.77031e13	0.593774
$988$	3.49378e13	1.16651
$989$	6.39732e12	0.212625
$990$	−4.68830e13	−1.55116
$991$	−4.09247e13	−1.34789	−0.673945	−	0.738782i	$-0.735402\pi$
$991$	−4.09247e13	−1.34789	−0.673945	+	0.738782i	$0.735402\pi$
$992$	1.73034e13	0.567322
$993$	−9.67632e12	−0.315819
$994$	−5.06760e13	−1.64651
$995$	−3.67194e13	−1.18766
$996$	−1.02400e14	−3.29711
$997$	−7.60358e12	−0.243719	−0.121860	−	0.992547i	$-0.538886\pi$
$997$	−7.60358e12	−0.243719	−0.121860	+	0.992547i	$0.538886\pi$
$998$	−3.65241e12	−0.116544
$999$	−7.74011e11	−0.0245868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.1	✓	36
17.16	even	2		289.10.a.h.1.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.1	✓	36	1.1	even	1	trivial
289.10.a.h.1.1	yes	36	17.16	even	2

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-44.7383 q^{2} -202.519 q^{3} +1489.51 q^{4} -1685.49 q^{5} +9060.35 q^{6} +4589.24 q^{7} -43732.3 q^{8} +21330.9 q^{9} +O(q^{10})\)	\(q-44.7383 q^{2} -202.519 q^{3} +1489.51 q^{4} -1685.49 q^{5} +9060.35 q^{6} +4589.24 q^{7} -43732.3 q^{8} +21330.9 q^{9} +75405.9 q^{10} -29147.4 q^{11} -301655. q^{12} +59631.0 q^{13} -205315. q^{14} +341343. q^{15} +1.19388e6 q^{16} -954309. q^{18} +393350. q^{19} -2.51056e6 q^{20} -929408. q^{21} +1.30401e6 q^{22} +581014. q^{23} +8.85662e6 q^{24} +887748. q^{25} -2.66779e6 q^{26} -333735. q^{27} +6.83573e6 q^{28} -5.69646e6 q^{29} -1.52711e7 q^{30} -557796. q^{31} -3.10211e7 q^{32} +5.90291e6 q^{33} -7.73511e6 q^{35} +3.17727e7 q^{36} +2.31924e6 q^{37} -1.75978e7 q^{38} -1.20764e7 q^{39} +7.37103e7 q^{40} -2.59418e7 q^{41} +4.15801e7 q^{42} +1.10106e7 q^{43} -4.34155e7 q^{44} -3.59530e7 q^{45} -2.59936e7 q^{46} -1.90477e7 q^{47} -2.41783e8 q^{48} -1.92925e7 q^{49} -3.97163e7 q^{50} +8.88212e7 q^{52} -8.95430e7 q^{53} +1.49307e7 q^{54} +4.91277e7 q^{55} -2.00698e8 q^{56} -7.96608e7 q^{57} +2.54850e8 q^{58} +1.61408e8 q^{59} +5.08436e8 q^{60} -8.62127e7 q^{61} +2.49548e7 q^{62} +9.78927e7 q^{63} +7.76564e8 q^{64} -1.00507e8 q^{65} -2.64086e8 q^{66} -7.28639e7 q^{67} -1.17666e8 q^{69} +3.46056e8 q^{70} +2.46821e8 q^{71} -9.32850e8 q^{72} +3.69817e7 q^{73} -1.03759e8 q^{74} -1.79786e8 q^{75} +5.85900e8 q^{76} -1.33765e8 q^{77} +5.40277e8 q^{78} -5.32700e8 q^{79} -2.01227e9 q^{80} -3.52269e8 q^{81} +1.16059e9 q^{82} +3.39461e8 q^{83} -1.38437e9 q^{84} -4.92595e8 q^{86} +1.15364e9 q^{87} +1.27468e9 q^{88} +4.69306e8 q^{89} +1.60848e9 q^{90} +2.73661e8 q^{91} +8.65429e8 q^{92} +1.12964e8 q^{93} +8.52161e8 q^{94} -6.62987e8 q^{95} +6.28235e9 q^{96} +6.49455e6 q^{97} +8.63113e8 q^{98} -6.21742e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9} - 60000 q^{10} - 76902 q^{11} - 373248 q^{12} + 54216 q^{13} - 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} - 6439479 q^{20} - 138102 q^{21} - 267324 q^{22} - 4041462 q^{23} - 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} - 13281612 q^{27} - 18614784 q^{28} - 4005936 q^{29} + 22471686 q^{30} - 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} - 22076682 q^{37} - 27401376 q^{38} - 62736162 q^{39} + 12231630 q^{40} - 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} + 49578936 q^{44} - 129308238 q^{45} - 140524827 q^{46} - 118557912 q^{47} - 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} - 209848575 q^{54} - 365439924 q^{55} - 203095059 q^{56} + 4614108 q^{57} + 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} - 175597116 q^{61} - 720602571 q^{62} - 587415936 q^{63} + 853082511 q^{64} - 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} - 1308709542 q^{71} - 275337849 q^{72} - 494841342 q^{73} - 1545361890 q^{74} - 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} - 2270624538 q^{78} - 1980107868 q^{79} - 2897000199 q^{80} + 1598298840 q^{81} - 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} + 2705904618 q^{88} + 148394658 q^{89} - 117916215 q^{90} - 636340896 q^{91} + 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} - 4878626298 q^{95} + 8390096634 q^{96} + 891786822 q^{97} + 4285627647 q^{98} + 1476187998 q^{99}+O(q^{100}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9 - 60000 * q^10 - 76902 * q^11 - 373248 * q^12 + 54216 * q^13 - 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 - 6439479 * q^20 - 138102 * q^21 - 267324 * q^22 - 4041462 * q^23 - 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 - 13281612 * q^27 - 18614784 * q^28 - 4005936 * q^29 + 22471686 * q^30 - 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 - 22076682 * q^37 - 27401376 * q^38 - 62736162 * q^39 + 12231630 * q^40 - 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 + 49578936 * q^44 - 129308238 * q^45 - 140524827 * q^46 - 118557912 * q^47 - 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 - 209848575 * q^54 - 365439924 * q^55 - 203095059 * q^56 + 4614108 * q^57 + 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 - 175597116 * q^61 - 720602571 * q^62 - 587415936 * q^63 + 853082511 * q^64 - 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 - 1308709542 * q^71 - 275337849 * q^72 - 494841342 * q^73 - 1545361890 * q^74 - 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 - 2270624538 * q^78 - 1980107868 * q^79 - 2897000199 * q^80 + 1598298840 * q^81 - 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 + 2705904618 * q^88 + 148394658 * q^89 - 117916215 * q^90 - 636340896 * q^91 + 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 - 4878626298 * q^95 + 8390096634 * q^96 + 891786822 * q^97 + 4285627647 * q^98 + 1476187998 * q^99

Introduction

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