LMFDB - Embedded newform 289.10.a.h.1.5

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:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-35.4923 q^{2} -64.4314 q^{3} +747.701 q^{4} -1779.33 q^{5} +2286.82 q^{6} +1603.15 q^{7} -8365.56 q^{8} -15531.6 q^{9} +O(q^{10})$	\(q-35.4923 q^{2} -64.4314 q^{3} +747.701 q^{4} -1779.33 q^{5} +2286.82 q^{6} +1603.15 q^{7} -8365.56 q^{8} -15531.6 q^{9} +63152.6 q^{10} +38189.5 q^{11} -48175.4 q^{12} -116430. q^{13} -56899.3 q^{14} +114645. q^{15} -85910.2 q^{16} +551251. q^{18} +850642. q^{19} -1.33041e6 q^{20} -103293. q^{21} -1.35543e6 q^{22} -1.05393e6 q^{23} +539005. q^{24} +1.21290e6 q^{25} +4.13238e6 q^{26} +2.26893e6 q^{27} +1.19867e6 q^{28} +1.44727e6 q^{29} -4.06901e6 q^{30} -5.24487e6 q^{31} +7.33231e6 q^{32} -2.46061e6 q^{33} -2.85253e6 q^{35} -1.16130e7 q^{36} +5.51006e6 q^{37} -3.01912e7 q^{38} +7.50177e6 q^{39} +1.48851e7 q^{40} -2.30276e7 q^{41} +3.66611e6 q^{42} +1.73443e7 q^{43} +2.85543e7 q^{44} +2.76359e7 q^{45} +3.74062e7 q^{46} +5.62789e7 q^{47} +5.53532e6 q^{48} -3.77835e7 q^{49} -4.30487e7 q^{50} -8.70551e7 q^{52} -7.72272e7 q^{53} -8.05293e7 q^{54} -6.79519e7 q^{55} -1.34112e7 q^{56} -5.48081e7 q^{57} -5.13670e7 q^{58} +9.35882e7 q^{59} +8.57202e7 q^{60} +1.85319e8 q^{61} +1.86152e8 q^{62} -2.48994e7 q^{63} -2.16254e8 q^{64} +2.07168e8 q^{65} +8.73325e7 q^{66} -2.00683e8 q^{67} +6.79060e7 q^{69} +1.01243e8 q^{70} +7.05304e7 q^{71} +1.29930e8 q^{72} -2.21792e8 q^{73} -1.95564e8 q^{74} -7.81491e7 q^{75} +6.36026e8 q^{76} +6.12234e7 q^{77} -2.66255e8 q^{78} -6.34329e8 q^{79} +1.52863e8 q^{80} +1.59518e8 q^{81} +8.17300e8 q^{82} -5.88521e7 q^{83} -7.72323e7 q^{84} -6.15590e8 q^{86} -9.32498e7 q^{87} -3.19477e8 q^{88} -7.76608e8 q^{89} -9.80860e8 q^{90} -1.86655e8 q^{91} -7.88022e8 q^{92} +3.37935e8 q^{93} -1.99747e9 q^{94} -1.51358e9 q^{95} -4.72431e8 q^{96} -6.87791e8 q^{97} +1.34102e9 q^{98} -5.93144e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−35.4923	−1.56855	−0.784276	−	0.620413i	$-0.786965\pi$
$2$	−35.4923	−1.56855	−0.784276	+	0.620413i	$0.786965\pi$
$3$	−64.4314	−0.459253	−0.229627	−	0.973279i	$-0.573750\pi$
$3$	−64.4314	−0.459253	−0.229627	+	0.973279i	$0.573750\pi$
$4$	747.701	1.46035
$5$	−1779.33	−1.27319	−0.636594	−	0.771199i	$-0.719657\pi$
$5$	−1779.33	−1.27319	−0.636594	+	0.771199i	$0.719657\pi$
$6$	2286.82	0.720362
$7$	1603.15	0.252367	0.126183	−	0.992007i	$-0.459727\pi$
$7$	1603.15	0.252367	0.126183	+	0.992007i	$0.459727\pi$
$8$	−8365.56	−0.722088
$9$	−15531.6	−0.789087
$10$	63152.6	1.99706
$11$	38189.5	0.786461	0.393230	−	0.919440i	$-0.371357\pi$
$11$	38189.5	0.786461	0.393230	+	0.919440i	$0.371357\pi$
$12$	−48175.4	−0.670672
$13$	−116430.	−1.13063	−0.565316	−	0.824875i	$-0.691246\pi$
$13$	−116430.	−1.13063	−0.565316	+	0.824875i	$0.691246\pi$
$14$	−56899.3	−0.395850
$15$	114645.	0.584715
$16$	−85910.2	−0.327722
$17$	0	0
$17$	0	0
$18$	551251.	1.23772
$19$	850642.	1.49746	0.748731	−	0.662874i	$-0.230664\pi$
$19$	850642.	1.49746	0.748731	+	0.662874i	$0.230664\pi$
$20$	−1.33041e6	−1.85930
$21$	−103293.	−0.115900
$22$	−1.35543e6	−1.23360
$23$	−1.05393e6	−0.785299	−0.392649	−	0.919688i	$-0.628441\pi$
$23$	−1.05393e6	−0.785299	−0.392649	+	0.919688i	$0.628441\pi$
$24$	539005.	0.331621
$25$	1.21290e6	0.621006
$26$	4.13238e6	1.77345
$27$	2.26893e6	0.821644
$28$	1.19867e6	0.368545
$29$	1.44727e6	0.379979	0.189989	−	0.981786i	$-0.439155\pi$
$29$	1.44727e6	0.379979	0.189989	+	0.981786i	$0.439155\pi$
$30$	−4.06901e6	−0.917156
$31$	−5.24487e6	−1.02002	−0.510008	−	0.860170i	$-0.670358\pi$
$31$	−5.24487e6	−1.02002	−0.510008	+	0.860170i	$0.670358\pi$
$32$	7.33231e6	1.23614
$33$	−2.46061e6	−0.361185
$34$	0	0
$35$	−2.85253e6	−0.321310
$36$	−1.16130e7	−1.15235
$37$	5.51006e6	0.483335	0.241667	−	0.970359i	$-0.422306\pi$
$37$	5.51006e6	0.483335	0.241667	+	0.970359i	$0.422306\pi$
$38$	−3.01912e7	−2.34885
$39$	7.50177e6	0.519246
$40$	1.48851e7	0.919353
$41$	−2.30276e7	−1.27268	−0.636342	−	0.771407i	$-0.719553\pi$
$41$	−2.30276e7	−1.27268	−0.636342	+	0.771407i	$0.719553\pi$
$42$	3.66611e6	0.181796
$43$	1.73443e7	0.773659	0.386830	−	0.922151i	$-0.373570\pi$
$43$	1.73443e7	0.773659	0.386830	+	0.922151i	$0.373570\pi$
$44$	2.85543e7	1.14851
$45$	2.76359e7	1.00466
$46$	3.74062e7	1.23178
$47$	5.62789e7	1.68231	0.841154	−	0.540796i	$-0.181877\pi$
$47$	5.62789e7	1.68231	0.841154	+	0.540796i	$0.181877\pi$
$48$	5.53532e6	0.150507
$49$	−3.77835e7	−0.936311
$50$	−4.30487e7	−0.974080
$51$	0	0
$52$	−8.70551e7	−1.65112
$53$	−7.72272e7	−1.34440	−0.672201	−	0.740369i	$-0.734651\pi$
$53$	−7.72272e7	−1.34440	−0.672201	+	0.740369i	$0.734651\pi$
$54$	−8.05293e7	−1.28879
$55$	−6.79519e7	−1.00131
$56$	−1.34112e7	−0.182231
$57$	−5.48081e7	−0.687714
$58$	−5.13670e7	−0.596016
$59$	9.35882e7	1.00551	0.502756	−	0.864428i	$-0.332319\pi$
$59$	9.35882e7	1.00551	0.502756	+	0.864428i	$0.332319\pi$
$60$	8.57202e7	0.853891
$61$	1.85319e8	1.71371	0.856853	−	0.515560i	$-0.172416\pi$
$61$	1.85319e8	1.71371	0.856853	+	0.515560i	$0.172416\pi$
$62$	1.86152e8	1.59995
$63$	−2.48994e7	−0.199139
$64$	−2.16254e8	−1.61122
$65$	2.07168e8	1.43951
$66$	8.73325e7	0.566537
$67$	−2.00683e8	−1.21667	−0.608337	−	0.793679i	$-0.708163\pi$
$67$	−2.00683e8	−1.21667	−0.608337	+	0.793679i	$0.708163\pi$
$68$	0	0
$69$	6.79060e7	0.360651
$70$	1.01243e8	0.503992
$71$	7.05304e7	0.329392	0.164696	−	0.986344i	$-0.447336\pi$
$71$	7.05304e7	0.329392	0.164696	+	0.986344i	$0.447336\pi$
$72$	1.29930e8	0.569790
$73$	−2.21792e8	−0.914099	−0.457049	−	0.889441i	$-0.651094\pi$
$73$	−2.21792e8	−0.914099	−0.457049	+	0.889441i	$0.651094\pi$
$74$	−1.95564e8	−0.758136
$75$	−7.81491e7	−0.285199
$76$	6.36026e8	2.18682
$77$	6.12234e7	0.198477
$78$	−2.66255e8	−0.814464
$79$	−6.34329e8	−1.83228	−0.916141	−	0.400856i	$-0.868713\pi$
$79$	−6.34329e8	−1.83228	−0.916141	+	0.400856i	$0.868713\pi$
$80$	1.52863e8	0.417251
$81$	1.59518e8	0.411744
$82$	8.17300e8	1.99627
$83$	−5.88521e7	−0.136116	−0.0680582	−	0.997681i	$-0.521680\pi$
$83$	−5.88521e7	−0.136116	−0.0680582	+	0.997681i	$0.521680\pi$
$84$	−7.72323e7	−0.169255
$85$	0	0
$86$	−6.15590e8	−1.21352
$87$	−9.32498e7	−0.174506
$88$	−3.19477e8	−0.567894
$89$	−7.76608e8	−1.31204	−0.656020	−	0.754743i	$-0.727761\pi$
$89$	−7.76608e8	−1.31204	−0.656020	+	0.754743i	$0.727761\pi$
$90$	−9.80860e8	−1.57585
$91$	−1.86655e8	−0.285334
$92$	−7.88022e8	−1.14681
$93$	3.37935e8	0.468446
$94$	−1.99747e9	−2.63879
$95$	−1.51358e9	−1.90655
$96$	−4.72431e8	−0.567699
$97$	−6.87791e8	−0.788831	−0.394415	−	0.918932i	$-0.629053\pi$
$97$	−6.87791e8	−0.788831	−0.394415	+	0.918932i	$0.629053\pi$
$98$	1.34102e9	1.46865
$99$	−5.93144e8	−0.620586
$100$	9.06889e8	0.906889
$101$	−1.32312e9	−1.26518	−0.632590	−	0.774487i	$-0.718008\pi$
$101$	−1.32312e9	−1.26518	−0.632590	+	0.774487i	$0.718008\pi$
$102$	0	0
$103$	−1.63204e9	−1.42877	−0.714387	−	0.699751i	$-0.753294\pi$
$103$	−1.63204e9	−1.42877	−0.714387	+	0.699751i	$0.753294\pi$
$104$	9.74005e8	0.816415
$105$	1.83793e8	0.147563
$106$	2.74097e9	2.10876
$107$	−9.81220e8	−0.723668	−0.361834	−	0.932243i	$-0.617849\pi$
$107$	−9.81220e8	−0.723668	−0.361834	+	0.932243i	$0.617849\pi$
$108$	1.69648e9	1.19989
$109$	9.30599e8	0.631456	0.315728	−	0.948850i	$-0.397751\pi$
$109$	9.30599e8	0.631456	0.315728	+	0.948850i	$0.397751\pi$
$110$	2.41177e9	1.57061
$111$	−3.55021e8	−0.221973
$112$	−1.37727e8	−0.0827061
$113$	−2.85541e9	−1.64746	−0.823732	−	0.566979i	$-0.808112\pi$
$113$	−2.85541e9	−1.64746	−0.823732	+	0.566979i	$0.808112\pi$
$114$	1.94526e9	1.07871
$115$	1.87529e9	0.999833
$116$	1.08213e9	0.554903
$117$	1.80835e9	0.892166
$118$	−3.32166e9	−1.57720
$119$	0	0
$120$	−9.59069e8	−0.422216
$121$	−8.99508e8	−0.381479
$122$	−6.57740e9	−2.68804
$123$	1.48370e9	0.584484
$124$	−3.92159e9	−1.48958
$125$	1.31710e9	0.482530
$126$	8.83737e8	0.312360
$127$	−6.04257e8	−0.206113	−0.103056	−	0.994676i	$-0.532862\pi$
$127$	−6.04257e8	−0.206113	−0.103056	+	0.994676i	$0.532862\pi$
$128$	3.92121e9	1.29115
$129$	−1.11752e9	−0.355305
$130$	−7.35288e9	−2.25794
$131$	2.35573e9	0.698885	0.349442	−	0.936958i	$-0.386371\pi$
$131$	2.35573e9	0.698885	0.349442	+	0.936958i	$0.386371\pi$
$132$	−1.83980e9	−0.527457
$133$	1.36371e9	0.377910
$134$	7.12270e9	1.90841
$135$	−4.03718e9	−1.04611
$136$	0	0
$137$	−3.70241e9	−0.897928	−0.448964	−	0.893550i	$-0.648207\pi$
$137$	−3.70241e9	−0.897928	−0.448964	+	0.893550i	$0.648207\pi$
$138$	−2.41014e9	−0.565699
$139$	−2.24358e9	−0.509772	−0.254886	−	0.966971i	$-0.582038\pi$
$139$	−2.24358e9	−0.509772	−0.254886	+	0.966971i	$0.582038\pi$
$140$	−2.13284e9	−0.469227
$141$	−3.62613e9	−0.772605
$142$	−2.50328e9	−0.516669
$143$	−4.44642e9	−0.889197
$144$	1.33432e9	0.258601
$145$	−2.57518e9	−0.483784
$146$	7.87190e9	1.43381
$147$	2.43445e9	0.430004
$148$	4.11987e9	0.705840
$149$	2.50473e9	0.416316	0.208158	−	0.978095i	$-0.433253\pi$
$149$	2.50473e9	0.416316	0.208158	+	0.978095i	$0.433253\pi$
$150$	2.77369e9	0.447349
$151$	−6.86721e9	−1.07494	−0.537470	−	0.843283i	$-0.680620\pi$
$151$	−6.86721e9	−1.07494	−0.537470	+	0.843283i	$0.680620\pi$
$152$	−7.11610e9	−1.08130
$153$	0	0
$154$	−2.17296e9	−0.311321
$155$	9.33237e9	1.29867
$156$	5.60908e9	0.758283
$157$	−1.19135e10	−1.56492	−0.782461	−	0.622700i	$-0.786036\pi$
$157$	−1.19135e10	−1.56492	−0.782461	+	0.622700i	$0.786036\pi$
$158$	2.25138e10	2.87403
$159$	4.97586e9	0.617420
$160$	−1.30466e10	−1.57383
$161$	−1.68960e9	−0.198183
$162$	−5.66166e9	−0.645842
$163$	3.24459e9	0.360011	0.180005	−	0.983666i	$-0.442388\pi$
$163$	3.24459e9	0.360011	0.180005	+	0.983666i	$0.442388\pi$
$164$	−1.72177e10	−1.85857
$165$	4.37824e9	0.459856
$166$	2.08879e9	0.213506
$167$	8.72685e9	0.868227	0.434114	−	0.900858i	$-0.357062\pi$
$167$	8.72685e9	0.868227	0.434114	+	0.900858i	$0.357062\pi$
$168$	8.64104e8	0.0836902
$169$	2.95152e9	0.278327
$170$	0	0
$171$	−1.32118e10	−1.18163
$172$	1.29684e10	1.12982
$173$	−5.55058e9	−0.471119	−0.235559	−	0.971860i	$-0.575692\pi$
$173$	−5.55058e9	−0.471119	−0.235559	+	0.971860i	$0.575692\pi$
$174$	3.30965e9	0.273722
$175$	1.94446e9	0.156721
$176$	−3.28087e9	−0.257740
$177$	−6.03002e9	−0.461784
$178$	2.75636e10	2.05800
$179$	1.54065e10	1.12167	0.560834	−	0.827928i	$-0.310480\pi$
$179$	1.54065e10	1.12167	0.560834	+	0.827928i	$0.310480\pi$
$180$	2.06634e10	1.46715
$181$	2.46062e10	1.70409	0.852043	−	0.523472i	$-0.175363\pi$
$181$	2.46062e10	1.70409	0.852043	+	0.523472i	$0.175363\pi$
$182$	6.62481e9	0.447561
$183$	−1.19404e10	−0.787025
$184$	8.81668e9	0.567055
$185$	−9.80423e9	−0.615376
$186$	−1.19941e10	−0.734781
$187$	0	0
$188$	4.20798e10	2.45676
$189$	3.63742e9	0.207356
$190$	5.37202e10	2.99052
$191$	1.53953e10	0.837025	0.418513	−	0.908211i	$-0.362552\pi$
$191$	1.53953e10	0.837025	0.418513	+	0.908211i	$0.362552\pi$
$192$	1.39336e10	0.739958
$193$	3.75476e10	1.94793	0.973967	−	0.226689i	$-0.0727901\pi$
$193$	3.75476e10	1.94793	0.973967	+	0.226689i	$0.0727901\pi$
$194$	2.44113e10	1.23732
$195$	−1.33482e10	−0.661097
$196$	−2.82508e10	−1.36734
$197$	1.69699e10	0.802752	0.401376	−	0.915913i	$-0.368532\pi$
$197$	1.69699e10	0.802752	0.401376	+	0.915913i	$0.368532\pi$
$198$	2.10520e10	0.973421
$199$	−3.68433e10	−1.66541	−0.832703	−	0.553720i	$-0.813208\pi$
$199$	−3.68433e10	−1.66541	−0.832703	+	0.553720i	$0.813208\pi$
$200$	−1.01466e10	−0.448421
$201$	1.29303e10	0.558761
$202$	4.69605e10	1.98450
$203$	2.32019e9	0.0958941
$204$	0	0
$205$	4.09737e10	1.62037
$206$	5.79248e10	2.24111
$207$	1.63692e10	0.619669
$208$	1.00026e10	0.370532
$209$	3.24856e10	1.17770
$210$	−6.52322e9	−0.231460
$211$	−2.86188e9	−0.0993988	−0.0496994	−	0.998764i	$-0.515826\pi$
$211$	−2.86188e9	−0.0993988	−0.0496994	+	0.998764i	$0.515826\pi$
$212$	−5.77428e10	−1.96330
$213$	−4.54437e9	−0.151274
$214$	3.48257e10	1.13511
$215$	−3.08614e10	−0.985013
$216$	−1.89808e10	−0.593299
$217$	−8.40830e9	−0.257418
$218$	−3.30290e10	−0.990471
$219$	1.42904e10	0.419803
$220$	−5.08077e10	−1.46227
$221$	0	0
$222$	1.26005e10	0.348176
$223$	−8.66212e9	−0.234559	−0.117279	−	0.993099i	$-0.537417\pi$
$223$	−8.66212e9	−0.234559	−0.117279	+	0.993099i	$0.537417\pi$
$224$	1.17548e10	0.311960
$225$	−1.88383e10	−0.490028
$226$	1.01345e11	2.58413
$227$	3.39293e10	0.848122	0.424061	−	0.905634i	$-0.360604\pi$
$227$	3.39293e10	0.848122	0.424061	+	0.905634i	$0.360604\pi$
$228$	−4.09801e10	−1.00431
$229$	−4.32441e10	−1.03912	−0.519561	−	0.854433i	$-0.673905\pi$
$229$	−4.32441e10	−1.03912	−0.519561	+	0.854433i	$0.673905\pi$
$230$	−6.65582e10	−1.56829
$231$	−3.94471e9	−0.0911510
$232$	−1.21072e10	−0.274378
$233$	2.83037e10	0.629131	0.314566	−	0.949236i	$-0.398141\pi$
$233$	2.83037e10	0.629131	0.314566	+	0.949236i	$0.398141\pi$
$234$	−6.41824e10	−1.39941
$235$	−1.00139e11	−2.14189
$236$	6.99760e10	1.46840
$237$	4.08707e10	0.841481
$238$	0	0
$239$	−4.13610e10	−0.819976	−0.409988	−	0.912091i	$-0.634467\pi$
$239$	−4.13610e10	−0.819976	−0.409988	+	0.912091i	$0.634467\pi$
$240$	−9.84918e9	−0.191624
$241$	4.75351e10	0.907691	0.453846	−	0.891080i	$-0.350052\pi$
$241$	4.75351e10	0.907691	0.453846	+	0.891080i	$0.350052\pi$
$242$	3.19256e10	0.598370
$243$	−5.49373e10	−1.01074
$244$	1.38563e11	2.50262
$245$	6.72295e10	1.19210
$246$	−5.26598e10	−0.916793
$247$	−9.90406e10	−1.69308
$248$	4.38763e10	0.736541
$249$	3.79192e9	0.0625119
$250$	−4.67469e10	−0.756873
$251$	−1.97131e10	−0.313490	−0.156745	−	0.987639i	$-0.550100\pi$
$251$	−1.97131e10	−0.313490	−0.156745	+	0.987639i	$0.550100\pi$
$252$	−1.86173e10	−0.290814
$253$	−4.02489e10	−0.617607
$254$	2.14465e10	0.323299
$255$	0	0
$256$	−2.84505e10	−0.414009
$257$	1.37584e9	0.0196729	0.00983643	−	0.999952i	$-0.496869\pi$
$257$	1.37584e9	0.0196729	0.00983643	+	0.999952i	$0.496869\pi$
$258$	3.96633e10	0.557315
$259$	8.83343e9	0.121978
$260$	1.54900e11	2.10219
$261$	−2.24784e10	−0.299836
$262$	−8.36104e10	−1.09624
$263$	−6.61395e10	−0.852432	−0.426216	−	0.904621i	$-0.640154\pi$
$263$	−6.61395e10	−0.852432	−0.426216	+	0.904621i	$0.640154\pi$
$264$	2.05843e10	0.260807
$265$	1.37413e11	1.71167
$266$	−4.84010e10	−0.592771
$267$	5.00380e10	0.602558
$268$	−1.50051e11	−1.77677
$269$	1.71759e10	0.200002	0.100001	−	0.994987i	$-0.468115\pi$
$269$	1.71759e10	0.200002	0.100001	+	0.994987i	$0.468115\pi$
$270$	1.43289e11	1.64087
$271$	−3.72624e10	−0.419671	−0.209835	−	0.977737i	$-0.567293\pi$
$271$	−3.72624e10	−0.419671	−0.209835	+	0.977737i	$0.567293\pi$
$272$	0	0
$273$	1.20264e10	0.131040
$274$	1.31407e11	1.40845
$275$	4.63202e10	0.488397
$276$	5.07734e10	0.526678
$277$	−3.67272e10	−0.374825	−0.187413	−	0.982281i	$-0.560010\pi$
$277$	−3.67272e10	−0.374825	−0.187413	+	0.982281i	$0.560010\pi$
$278$	7.96299e10	0.799603
$279$	8.14612e10	0.804881
$280$	2.38630e10	0.232014
$281$	1.47776e11	1.41392	0.706962	−	0.707252i	$-0.250065\pi$
$281$	1.47776e11	1.41392	0.706962	+	0.707252i	$0.250065\pi$
$282$	1.28700e11	1.21187
$283$	−1.11330e11	−1.03175	−0.515873	−	0.856665i	$-0.672532\pi$
$283$	−1.11330e11	−1.03175	−0.515873	+	0.856665i	$0.672532\pi$
$284$	5.27356e10	0.481029
$285$	9.75219e10	0.875589
$286$	1.57813e11	1.39475
$287$	−3.69166e10	−0.321183
$288$	−1.13883e11	−0.975418
$289$	0	0
$290$	9.13990e10	0.758840
$291$	4.43154e10	0.362273
$292$	−1.65834e11	−1.33491
$293$	1.00582e11	0.797290	0.398645	−	0.917105i	$-0.369480\pi$
$293$	1.00582e11	0.797290	0.398645	+	0.917105i	$0.369480\pi$
$294$	−8.64040e10	−0.674483
$295$	−1.66525e11	−1.28021
$296$	−4.60947e10	−0.349010
$297$	8.66492e10	0.646191
$298$	−8.88987e10	−0.653013
$299$	1.22709e11	0.887884
$300$	−5.84321e10	−0.416491
$301$	2.78055e10	0.195246
$302$	2.43733e11	1.68610
$303$	8.52504e10	0.581038
$304$	−7.30789e10	−0.490751
$305$	−3.29745e11	−2.18187
$306$	0	0
$307$	−1.00813e11	−0.647733	−0.323866	−	0.946103i	$-0.604983\pi$
$307$	−1.00813e11	−0.647733	−0.323866	+	0.946103i	$0.604983\pi$
$308$	4.57768e10	0.289846
$309$	1.05155e11	0.656169
$310$	−3.31227e11	−2.03703
$311$	6.42046e10	0.389175	0.194587	−	0.980885i	$-0.437663\pi$
$311$	6.42046e10	0.389175	0.194587	+	0.980885i	$0.437663\pi$
$312$	−6.27565e10	−0.374941
$313$	−1.95618e11	−1.15202	−0.576008	−	0.817444i	$-0.695390\pi$
$313$	−1.95618e11	−1.15202	−0.576008	+	0.817444i	$0.695390\pi$
$314$	4.22839e11	2.45466
$315$	4.43044e10	0.253542
$316$	−4.74288e11	−2.67578
$317$	2.98622e11	1.66095	0.830473	−	0.557059i	$-0.188070\pi$
$317$	2.98622e11	1.66095	0.830473	+	0.557059i	$0.188070\pi$
$318$	−1.76605e11	−0.968456
$319$	5.52707e10	0.298838
$320$	3.84789e11	2.05139
$321$	6.32214e10	0.332347
$322$	5.99677e10	0.310861
$323$	0	0
$324$	1.19272e11	0.601292
$325$	−1.41219e11	−0.702129
$326$	−1.15158e11	−0.564695
$327$	−5.99598e10	−0.289998
$328$	1.92638e11	0.918990
$329$	9.02234e10	0.424559
$330$	−1.55394e11	−0.721307
$331$	2.80470e11	1.28428	0.642140	−	0.766587i	$-0.278047\pi$
$331$	2.80470e11	1.28428	0.642140	+	0.766587i	$0.278047\pi$
$332$	−4.40037e10	−0.198778
$333$	−8.55799e10	−0.381393
$334$	−3.09736e11	−1.36186
$335$	3.57082e11	1.54905
$336$	8.87393e9	0.0379830
$337$	−1.33080e11	−0.562053	−0.281027	−	0.959700i	$-0.590675\pi$
$337$	−1.33080e11	−0.562053	−0.281027	+	0.959700i	$0.590675\pi$
$338$	−1.04756e11	−0.436571
$339$	1.83978e11	0.756603
$340$	0	0
$341$	−2.00299e11	−0.802203
$342$	4.68918e11	1.85344
$343$	−1.25265e11	−0.488661
$344$	−1.45095e11	−0.558650
$345$	−1.20827e11	−0.459176
$346$	1.97002e11	0.738974
$347$	−1.27576e10	−0.0472373	−0.0236187	−	0.999721i	$-0.507519\pi$
$347$	−1.27576e10	−0.0472373	−0.0236187	+	0.999721i	$0.507519\pi$
$348$	−6.97230e10	−0.254841
$349$	9.97908e10	0.360061	0.180030	−	0.983661i	$-0.442380\pi$
$349$	9.97908e10	0.360061	0.180030	+	0.983661i	$0.442380\pi$
$350$	−6.90134e10	−0.245826
$351$	−2.64172e11	−0.928976
$352$	2.80018e11	0.972173
$353$	2.18588e11	0.749272	0.374636	−	0.927172i	$-0.377768\pi$
$353$	2.18588e11	0.749272	0.374636	+	0.927172i	$0.377768\pi$
$354$	2.14019e11	0.724333
$355$	−1.25497e11	−0.419378
$356$	−5.80671e11	−1.91604
$357$	0	0
$358$	−5.46811e11	−1.75940
$359$	−2.37311e11	−0.754038	−0.377019	−	0.926205i	$-0.623051\pi$
$359$	−2.37311e11	−0.754038	−0.377019	+	0.926205i	$0.623051\pi$
$360$	−2.31190e11	−0.725449
$361$	4.00904e11	1.24239
$362$	−8.73331e11	−2.67295
$363$	5.79566e10	0.175196
$364$	−1.39562e11	−0.416688
$365$	3.94642e11	1.16382
$366$	4.23792e11	1.23449
$367$	−7.38520e10	−0.212503	−0.106251	−	0.994339i	$-0.533885\pi$
$367$	−7.38520e10	−0.212503	−0.106251	+	0.994339i	$0.533885\pi$
$368$	9.05431e10	0.257359
$369$	3.57655e11	1.00426
$370$	3.47974e11	0.965249
$371$	−1.23807e11	−0.339282
$372$	2.52674e11	0.684096
$373$	1.63830e11	0.438232	0.219116	−	0.975699i	$-0.429683\pi$
$373$	1.63830e11	0.438232	0.219116	+	0.975699i	$0.429683\pi$
$374$	0	0
$375$	−8.48628e10	−0.221603
$376$	−4.70805e11	−1.21477
$377$	−1.68506e11	−0.429616
$378$	−1.29100e11	−0.325248
$379$	−5.52844e11	−1.37634	−0.688171	−	0.725548i	$-0.741586\pi$
$379$	−5.52844e11	−1.37634	−0.688171	+	0.725548i	$0.741586\pi$
$380$	−1.13170e12	−2.78424
$381$	3.89332e10	0.0946580
$382$	−5.46415e11	−1.31292
$383$	−4.45678e11	−1.05834	−0.529172	−	0.848515i	$-0.677497\pi$
$383$	−4.45678e11	−1.05834	−0.529172	+	0.848515i	$0.677497\pi$
$384$	−2.52649e11	−0.592963
$385$	−1.08937e11	−0.252698
$386$	−1.33265e12	−3.05543
$387$	−2.69385e11	−0.610484
$388$	−5.14262e11	−1.15197
$389$	1.27952e11	0.283317	0.141659	−	0.989916i	$-0.454756\pi$
$389$	1.27952e11	0.283317	0.141659	+	0.989916i	$0.454756\pi$
$390$	4.73756e11	1.03697
$391$	0	0
$392$	3.16080e11	0.676099
$393$	−1.51783e11	−0.320965
$394$	−6.02300e11	−1.25916
$395$	1.12868e12	2.33284
$396$	−4.43494e11	−0.906274
$397$	3.31658e11	0.670091	0.335045	−	0.942202i	$-0.391248\pi$
$397$	3.31658e11	0.670091	0.335045	+	0.942202i	$0.391248\pi$
$398$	1.30765e12	2.61227
$399$	−8.78655e10	−0.173556
$400$	−1.04201e11	−0.203517
$401$	6.03112e11	1.16479	0.582396	−	0.812905i	$-0.302115\pi$
$401$	6.03112e11	1.16479	0.582396	+	0.812905i	$0.302115\pi$
$402$	−4.58925e11	−0.876445
$403$	6.10662e11	1.15326
$404$	−9.89297e11	−1.84761
$405$	−2.83836e11	−0.524228
$406$	−8.23489e10	−0.150415
$407$	2.10426e11	0.380124
$408$	0	0
$409$	−4.86595e11	−0.859830	−0.429915	−	0.902869i	$-0.641456\pi$
$409$	−4.86595e11	−0.859830	−0.429915	+	0.902869i	$0.641456\pi$
$410$	−1.45425e12	−2.54163
$411$	2.38551e11	0.412376
$412$	−1.22028e12	−2.08651
$413$	1.50036e11	0.253758
$414$	−5.80978e11	−0.971982
$415$	1.04717e11	0.173302
$416$	−8.53704e11	−1.39761
$417$	1.44557e11	0.234114
$418$	−1.15299e12	−1.84728
$419$	5.39425e11	0.855003	0.427502	−	0.904015i	$-0.359394\pi$
$419$	5.39425e11	0.855003	0.427502	+	0.904015i	$0.359394\pi$
$420$	1.37422e11	0.215494
$421$	9.96515e11	1.54602	0.773008	−	0.634396i	$-0.218751\pi$
$421$	9.96515e11	1.54602	0.773008	+	0.634396i	$0.218751\pi$
$422$	1.01575e11	0.155912
$423$	−8.74101e11	−1.32749
$424$	6.46049e11	0.970776
$425$	0	0
$426$	1.61290e11	0.237282
$427$	2.97094e11	0.432483
$428$	−7.33659e11	−1.05681
$429$	2.86489e11	0.408367
$430$	1.09534e12	1.54504
$431$	1.04616e12	1.46033	0.730167	−	0.683268i	$-0.239442\pi$
$431$	1.04616e12	1.46033	0.730167	+	0.683268i	$0.239442\pi$
$432$	−1.94924e11	−0.269270
$433$	−4.38391e11	−0.599330	−0.299665	−	0.954044i	$-0.596875\pi$
$433$	−4.38391e11	−0.599330	−0.299665	+	0.954044i	$0.596875\pi$
$434$	2.98430e11	0.403774
$435$	1.65923e11	0.222179
$436$	6.95809e11	0.922149
$437$	−8.96514e11	−1.17595
$438$	−5.07198e11	−0.658482
$439$	−1.24765e12	−1.60325	−0.801626	−	0.597825i	$-0.796032\pi$
$439$	−1.24765e12	−1.60325	−0.801626	+	0.597825i	$0.796032\pi$
$440$	5.68456e11	0.723035
$441$	5.86838e11	0.738830
$442$	0	0
$443$	−4.55140e11	−0.561472	−0.280736	−	0.959785i	$-0.590578\pi$
$443$	−4.55140e11	−0.561472	−0.280736	+	0.959785i	$0.590578\pi$
$444$	−2.65449e11	−0.324159
$445$	1.38185e12	1.67047
$446$	3.07438e11	0.367918
$447$	−1.61384e11	−0.191195
$448$	−3.46688e11	−0.406619
$449$	4.52274e11	0.525161	0.262581	−	0.964910i	$-0.415426\pi$
$449$	4.52274e11	0.525161	0.262581	+	0.964910i	$0.415426\pi$
$450$	6.68614e11	0.768634
$451$	−8.79412e11	−1.00092
$452$	−2.13500e12	−2.40588
$453$	4.42464e11	0.493669
$454$	−1.20423e12	−1.33032
$455$	3.32122e11	0.363284
$456$	4.58500e11	0.496590
$457$	−7.54079e11	−0.808712	−0.404356	−	0.914602i	$-0.632504\pi$
$457$	−7.54079e11	−0.808712	−0.404356	+	0.914602i	$0.632504\pi$
$458$	1.53483e12	1.62992
$459$	0	0
$460$	1.40215e12	1.46011
$461$	−8.30299e11	−0.856210	−0.428105	−	0.903729i	$-0.640819\pi$
$461$	−8.30299e11	−0.856210	−0.428105	+	0.903729i	$0.640819\pi$
$462$	1.40007e11	0.142975
$463$	−1.63965e12	−1.65820	−0.829098	−	0.559104i	$-0.811145\pi$
$463$	−1.63965e12	−1.65820	−0.829098	+	0.559104i	$0.811145\pi$
$464$	−1.24336e11	−0.124527
$465$	−6.01298e11	−0.596419
$466$	−1.00456e12	−0.986824
$467$	5.39940e10	0.0525314	0.0262657	−	0.999655i	$-0.491638\pi$
$467$	5.39940e10	0.0525314	0.0262657	+	0.999655i	$0.491638\pi$
$468$	1.35210e12	1.30288
$469$	−3.21725e11	−0.307048
$470$	3.55416e12	3.35967
$471$	7.67607e11	0.718695
$472$	−7.82918e11	−0.726068
$473$	6.62372e11	0.608453
$474$	−1.45059e12	−1.31991
$475$	1.03175e12	0.929933
$476$	0	0
$477$	1.19946e12	1.06085
$478$	1.46800e12	1.28617
$479$	1.51563e12	1.31548	0.657740	−	0.753245i	$-0.271513\pi$
$479$	1.51563e12	1.31548	0.657740	+	0.753245i	$0.271513\pi$
$480$	8.40613e11	0.722788
$481$	−6.41538e11	−0.546474
$482$	−1.68713e12	−1.42376
$483$	1.08863e11	0.0910163
$484$	−6.72563e11	−0.557094
$485$	1.22381e12	1.00433
$486$	1.94985e12	1.58540
$487$	1.37608e12	1.10857	0.554287	−	0.832326i	$-0.312991\pi$
$487$	1.37608e12	1.10857	0.554287	+	0.832326i	$0.312991\pi$
$488$	−1.55030e12	−1.23745
$489$	−2.09053e11	−0.165336
$490$	−2.38613e12	−1.86987
$491$	−1.98919e12	−1.54457	−0.772287	−	0.635273i	$-0.780887\pi$
$491$	−1.98919e12	−1.54457	−0.772287	+	0.635273i	$0.780887\pi$
$492$	1.10936e12	0.853553
$493$	0	0
$494$	3.51517e12	2.65568
$495$	1.05540e12	0.790122
$496$	4.50588e11	0.334281
$497$	1.13071e11	0.0831277
$498$	−1.34584e11	−0.0980531
$499$	−6.52474e11	−0.471098	−0.235549	−	0.971863i	$-0.575689\pi$
$499$	−6.52474e11	−0.471098	−0.235549	+	0.971863i	$0.575689\pi$
$500$	9.84798e11	0.704664
$501$	−5.62283e11	−0.398736
$502$	6.99663e11	0.491725
$503$	1.99625e12	1.39046	0.695229	−	0.718788i	$-0.255303\pi$
$503$	1.99625e12	1.39046	0.695229	+	0.718788i	$0.255303\pi$
$504$	2.08298e11	0.143796
$505$	2.35427e12	1.61081
$506$	1.42853e12	0.968748
$507$	−1.90171e11	−0.127823
$508$	−4.51804e11	−0.300998
$509$	−1.28730e12	−0.850063	−0.425032	−	0.905179i	$-0.639737\pi$
$509$	−1.28730e12	−0.850063	−0.425032	+	0.905179i	$0.639737\pi$
$510$	0	0
$511$	−3.55565e11	−0.230688
$512$	−9.97889e11	−0.641752
$513$	1.93004e12	1.23038
$514$	−4.88315e10	−0.0308579
$515$	2.90395e12	1.81910
$516$	−8.35571e11	−0.518871
$517$	2.14927e12	1.32307
$518$	−3.13519e11	−0.191328
$519$	3.57631e11	0.216363
$520$	−1.73308e12	−1.03945
$521$	−8.54672e11	−0.508194	−0.254097	−	0.967179i	$-0.581778\pi$
$521$	−8.54672e11	−0.508194	−0.254097	+	0.967179i	$0.581778\pi$
$522$	7.97811e11	0.470308
$523$	−4.36274e11	−0.254978	−0.127489	−	0.991840i	$-0.540692\pi$
$523$	−4.36274e11	−0.254978	−0.127489	+	0.991840i	$0.540692\pi$
$524$	1.76138e12	1.02062
$525$	−1.25284e11	−0.0719748
$526$	2.34744e12	1.33708
$527$	0	0
$528$	2.11391e11	0.118368
$529$	−6.90392e11	−0.383306
$530$	−4.87710e12	−2.68485
$531$	−1.45357e12	−0.793436
$532$	1.01964e12	0.551882
$533$	2.68111e12	1.43894
$534$	−1.77596e12	−0.945144
$535$	1.74592e12	0.921365
$536$	1.67883e12	0.878545
$537$	−9.92661e11	−0.515130
$538$	−6.09612e11	−0.313714
$539$	−1.44293e12	−0.736372
$540$	−3.01860e12	−1.52768
$541$	2.18108e12	1.09467	0.547337	−	0.836913i	$-0.315642\pi$
$541$	2.18108e12	1.09467	0.547337	+	0.836913i	$0.315642\pi$
$542$	1.32253e12	0.658275
$543$	−1.58541e12	−0.782607
$544$	0	0
$545$	−1.65585e12	−0.803962
$546$	−4.26846e11	−0.205544
$547$	2.19466e12	1.04815	0.524077	−	0.851671i	$-0.324411\pi$
$547$	2.19466e12	1.04815	0.524077	+	0.851671i	$0.324411\pi$
$548$	−2.76829e12	−1.31129
$549$	−2.87830e12	−1.35226
$550$	−1.64401e12	−0.766076
$551$	1.23111e12	0.569004
$552$	−5.68071e11	−0.260422
$553$	−1.01692e12	−0.462407
$554$	1.30353e12	0.587932
$555$	6.31700e11	0.282613
$556$	−1.67753e12	−0.744447
$557$	2.19414e12	0.965864	0.482932	−	0.875658i	$-0.339572\pi$
$557$	2.19414e12	0.965864	0.482932	+	0.875658i	$0.339572\pi$
$558$	−2.89124e12	−1.26250
$559$	−2.01941e12	−0.874723
$560$	2.45062e11	0.105300
$561$	0	0
$562$	−5.24491e12	−2.21781
$563$	−2.03940e12	−0.855489	−0.427745	−	0.903900i	$-0.640692\pi$
$563$	−2.03940e12	−0.855489	−0.427745	+	0.903900i	$0.640692\pi$
$564$	−2.71126e12	−1.12828
$565$	5.08073e12	2.09753
$566$	3.95135e12	1.61835
$567$	2.55731e11	0.103911
$568$	−5.90026e11	−0.237850
$569$	−3.56626e12	−1.42629	−0.713144	−	0.701017i	$-0.752730\pi$
$569$	−3.56626e12	−1.42629	−0.713144	+	0.701017i	$0.752730\pi$
$570$	−3.46127e12	−1.37341
$571$	−2.49685e12	−0.982945	−0.491473	−	0.870893i	$-0.663541\pi$
$571$	−2.49685e12	−0.982945	−0.491473	+	0.870893i	$0.663541\pi$
$572$	−3.32459e12	−1.29854
$573$	−9.91942e11	−0.384406
$574$	1.31025e12	0.503792
$575$	−1.27831e12	−0.487675
$576$	3.35878e12	1.27139
$577$	3.19650e12	1.20056	0.600279	−	0.799791i	$-0.295056\pi$
$577$	3.19650e12	1.20056	0.600279	+	0.799791i	$0.295056\pi$
$578$	0	0
$579$	−2.41925e12	−0.894595
$580$	−1.92547e12	−0.706496
$581$	−9.43486e10	−0.0343513
$582$	−1.57285e12	−0.568244
$583$	−2.94927e12	−1.05732
$584$	1.85541e12	0.660059
$585$	−3.21765e12	−1.13589
$586$	−3.56989e12	−1.25059
$587$	4.21874e12	1.46660	0.733299	−	0.679906i	$-0.237979\pi$
$587$	4.21874e12	1.46660	0.733299	+	0.679906i	$0.237979\pi$
$588$	1.82024e12	0.627957
$589$	−4.46151e12	−1.52744
$590$	5.91034e12	2.00807
$591$	−1.09340e12	−0.368666
$592$	−4.73370e11	−0.158399
$593$	−1.41657e12	−0.470427	−0.235214	−	0.971944i	$-0.575579\pi$
$593$	−1.41657e12	−0.470427	−0.235214	+	0.971944i	$0.575579\pi$
$594$	−3.07538e12	−1.01358
$595$	0	0
$596$	1.87279e12	0.607969
$597$	2.37387e12	0.764843
$598$	−4.35522e12	−1.39269
$599$	4.20552e12	1.33475	0.667374	−	0.744722i	$-0.267418\pi$
$599$	4.20552e12	1.33475	0.667374	+	0.744722i	$0.267418\pi$
$600$	6.53760e11	0.205939
$601$	4.21313e12	1.31725	0.658627	−	0.752469i	$-0.271137\pi$
$601$	4.21313e12	1.31725	0.658627	+	0.752469i	$0.271137\pi$
$602$	−9.86882e11	−0.306253
$603$	3.11693e12	0.960061
$604$	−5.13462e12	−1.56979
$605$	1.60052e12	0.485695
$606$	−3.02573e12	−0.911388
$607$	5.49794e11	0.164381	0.0821904	−	0.996617i	$-0.473808\pi$
$607$	5.49794e11	0.164381	0.0821904	+	0.996617i	$0.473808\pi$
$608$	6.23718e12	1.85107
$609$	−1.49493e11	−0.0440396
$610$	1.17034e13	3.42238
$611$	−6.55257e12	−1.90207
$612$	0	0
$613$	4.73227e11	0.135362	0.0676810	−	0.997707i	$-0.478440\pi$
$613$	4.73227e11	0.135362	0.0676810	+	0.997707i	$0.478440\pi$
$614$	3.57810e12	1.01600
$615$	−2.63999e12	−0.744158
$616$	−5.12168e11	−0.143318
$617$	−6.13226e12	−1.70348	−0.851740	−	0.523964i	$-0.824453\pi$
$617$	−6.13226e12	−1.70348	−0.851740	+	0.523964i	$0.824453\pi$
$618$	−3.73218e12	−1.02923
$619$	2.20706e12	0.604237	0.302118	−	0.953270i	$-0.402306\pi$
$619$	2.20706e12	0.604237	0.302118	+	0.953270i	$0.402306\pi$
$620$	6.97782e12	1.89652
$621$	−2.39128e12	−0.645236
$622$	−2.27877e12	−0.610440
$623$	−1.24502e12	−0.331115
$624$	−6.44479e11	−0.170168
$625$	−4.71251e12	−1.23536
$626$	6.94292e12	1.80700
$627$	−2.09309e12	−0.540860
$628$	−8.90777e12	−2.28534
$629$	0	0
$630$	−1.57246e12	−0.397693
$631$	5.73681e12	1.44058	0.720291	−	0.693672i	$-0.244008\pi$
$631$	5.73681e12	1.44058	0.720291	+	0.693672i	$0.244008\pi$
$632$	5.30651e12	1.32307
$633$	1.84395e11	0.0456492
$634$	−1.05988e13	−2.60528
$635$	1.07518e12	0.262420
$636$	3.72045e12	0.901652
$637$	4.39915e12	1.05862
$638$	−1.96168e12	−0.468744
$639$	−1.09545e12	−0.259919
$640$	−6.97715e12	−1.64387
$641$	3.02882e12	0.708618	0.354309	−	0.935128i	$-0.384716\pi$
$641$	3.02882e12	0.708618	0.354309	+	0.935128i	$0.384716\pi$
$642$	−2.24387e12	−0.521303
$643$	−3.56039e12	−0.821389	−0.410694	−	0.911773i	$-0.634714\pi$
$643$	−3.56039e12	−0.821389	−0.410694	+	0.911773i	$0.634714\pi$
$644$	−1.26331e12	−0.289418
$645$	1.98844e12	0.452370
$646$	0	0
$647$	−1.12696e12	−0.252835	−0.126418	−	0.991977i	$-0.540348\pi$
$647$	−1.12696e12	−0.252835	−0.126418	+	0.991977i	$0.540348\pi$
$648$	−1.33446e12	−0.297315
$649$	3.57409e12	0.790796
$650$	5.01217e12	1.10133
$651$	5.41759e11	0.118220
$652$	2.42598e12	0.525743
$653$	−5.96043e11	−0.128283	−0.0641413	−	0.997941i	$-0.520431\pi$
$653$	−5.96043e11	−0.128283	−0.0641413	+	0.997941i	$0.520431\pi$
$654$	2.12811e12	0.454877
$655$	−4.19164e12	−0.889811
$656$	1.97830e12	0.417086
$657$	3.44478e12	0.721303
$658$	−3.20223e12	−0.665942
$659$	3.31591e12	0.684887	0.342443	−	0.939538i	$-0.388745\pi$
$659$	3.31591e12	0.684887	0.342443	+	0.939538i	$0.388745\pi$
$660$	3.27361e12	0.671552
$661$	7.15298e12	1.45740	0.728702	−	0.684831i	$-0.240124\pi$
$661$	7.15298e12	1.45740	0.728702	+	0.684831i	$0.240124\pi$
$662$	−9.95450e12	−2.01446
$663$	0	0
$664$	4.92330e11	0.0982880
$665$	−2.42649e12	−0.481150
$666$	3.03743e12	0.598235
$667$	−1.52532e12	−0.298397
$668$	6.52507e12	1.26792
$669$	5.58112e11	0.107722
$670$	−1.26737e13	−2.42977
$671$	7.07726e12	1.34776
$672$	−7.57377e11	−0.143268
$673$	−1.72634e12	−0.324384	−0.162192	−	0.986759i	$-0.551856\pi$
$673$	−1.72634e12	−0.324384	−0.162192	+	0.986759i	$0.551856\pi$
$674$	4.72330e12	0.881609
$675$	2.75199e12	0.510246
$676$	2.20686e12	0.406456
$677$	9.74400e12	1.78274	0.891370	−	0.453276i	$-0.149745\pi$
$677$	9.74400e12	1.78274	0.891370	+	0.453276i	$0.149745\pi$
$678$	−6.52981e12	−1.18677
$679$	−1.10263e12	−0.199075
$680$	0	0
$681$	−2.18611e12	−0.389503
$682$	7.10907e12	1.25830
$683$	−5.73218e12	−1.00792	−0.503961	−	0.863726i	$-0.668124\pi$
$683$	−5.73218e12	−1.00792	−0.503961	+	0.863726i	$0.668124\pi$
$684$	−9.87850e12	−1.72559
$685$	6.58781e12	1.14323
$686$	4.44595e12	0.766489
$687$	2.78628e12	0.477220
$688$	−1.49006e12	−0.253545
$689$	8.99159e12	1.52002
$690$	4.28844e12	0.720241
$691$	−1.94747e12	−0.324952	−0.162476	−	0.986712i	$-0.551948\pi$
$691$	−1.94747e12	−0.324952	−0.162476	+	0.986712i	$0.551948\pi$
$692$	−4.15017e12	−0.688000
$693$	−9.50898e11	−0.156615
$694$	4.52795e11	0.0740942
$695$	3.99208e12	0.649035
$696$	7.80087e11	0.126009
$697$	0	0
$698$	−3.54180e12	−0.564774
$699$	−1.82365e12	−0.288930
$700$	1.45388e12	0.228869
$701$	−4.61502e12	−0.721842	−0.360921	−	0.932596i	$-0.617538\pi$
$701$	−4.61502e12	−0.721842	−0.360921	+	0.932596i	$0.617538\pi$
$702$	9.37606e12	1.45715
$703$	4.68709e12	0.723776
$704$	−8.25865e12	−1.26716
$705$	6.45210e12	0.983671
$706$	−7.75817e12	−1.17527
$707$	−2.12115e12	−0.319290
$708$	−4.50865e12	−0.674368
$709$	−2.50294e12	−0.372000	−0.186000	−	0.982550i	$-0.559552\pi$
$709$	−2.50294e12	−0.372000	−0.186000	+	0.982550i	$0.559552\pi$
$710$	4.45417e12	0.657816
$711$	9.85213e12	1.44583
$712$	6.49676e12	0.947408
$713$	5.52771e12	0.801018
$714$	0	0
$715$	7.91166e12	1.13211
$716$	1.15194e13	1.63803
$717$	2.66495e12	0.376576
$718$	8.42272e12	1.18275
$719$	1.15159e13	1.60701	0.803504	−	0.595300i	$-0.202967\pi$
$719$	1.15159e13	1.60701	0.803504	+	0.595300i	$0.202967\pi$
$720$	−2.37421e12	−0.329247
$721$	−2.61640e12	−0.360575
$722$	−1.42290e13	−1.94875
$723$	−3.06276e12	−0.416860
$724$	1.83981e13	2.48857
$725$	1.75540e12	0.235969
$726$	−2.05701e12	−0.274803
$727$	−4.59761e12	−0.610418	−0.305209	−	0.952285i	$-0.598726\pi$
$727$	−4.59761e12	−0.610418	−0.305209	+	0.952285i	$0.598726\pi$
$728$	1.56147e12	0.206036
$729$	3.99890e11	0.0524405
$730$	−1.40067e13	−1.82551
$731$	0	0
$732$	−8.92784e12	−1.14933
$733$	−5.97894e12	−0.764991	−0.382495	−	0.923957i	$-0.624935\pi$
$733$	−5.97894e12	−0.764991	−0.382495	+	0.923957i	$0.624935\pi$
$734$	2.62118e12	0.333322
$735$	−4.33169e12	−0.547475
$736$	−7.72772e12	−0.970736
$737$	−7.66399e12	−0.956866
$738$	−1.26940e13	−1.57523
$739$	6.24601e12	0.770376	0.385188	−	0.922838i	$-0.374137\pi$
$739$	6.24601e12	0.770376	0.385188	+	0.922838i	$0.374137\pi$
$740$	−7.33063e12	−0.898666
$741$	6.38132e12	0.777551
$742$	4.39418e12	0.532182
$743$	7.10024e12	0.854719	0.427360	−	0.904082i	$-0.359444\pi$
$743$	7.10024e12	0.854719	0.427360	+	0.904082i	$0.359444\pi$
$744$	−2.82701e12	−0.338259
$745$	−4.45676e12	−0.530049
$746$	−5.81470e12	−0.687390
$747$	9.14066e11	0.107408
$748$	0	0
$749$	−1.57304e12	−0.182630
$750$	3.01197e12	0.347596
$751$	1.86664e12	0.214132	0.107066	−	0.994252i	$-0.465854\pi$
$751$	1.86664e12	0.214132	0.107066	+	0.994252i	$0.465854\pi$
$752$	−4.83494e12	−0.551329
$753$	1.27014e12	0.143971
$754$	5.98068e12	0.673875
$755$	1.22191e13	1.36860
$756$	2.71971e12	0.302812
$757$	1.50795e13	1.66900	0.834498	−	0.551012i	$-0.185758\pi$
$757$	1.50795e13	1.66900	0.834498	+	0.551012i	$0.185758\pi$
$758$	1.96217e13	2.15886
$759$	2.59330e12	0.283638
$760$	1.26619e13	1.37670
$761$	−1.49680e13	−1.61782	−0.808912	−	0.587929i	$-0.799943\pi$
$761$	−1.49680e13	−1.61782	−0.808912	+	0.587929i	$0.799943\pi$
$762$	−1.38183e12	−0.148476
$763$	1.49189e12	0.159359
$764$	1.15111e13	1.22235
$765$	0	0
$766$	1.58181e13	1.66007
$767$	−1.08965e13	−1.13686
$768$	1.83311e12	0.190135
$769$	4.90137e12	0.505416	0.252708	−	0.967543i	$-0.418679\pi$
$769$	4.90137e12	0.505416	0.252708	+	0.967543i	$0.418679\pi$
$770$	3.86642e12	0.396370
$771$	−8.86470e10	−0.00903482
$772$	2.80744e13	2.84467
$773$	−1.28051e13	−1.28996	−0.644978	−	0.764201i	$-0.723133\pi$
$773$	−1.28051e13	−1.28996	−0.644978	+	0.764201i	$0.723133\pi$
$774$	9.56109e12	0.957576
$775$	−6.36152e12	−0.633437
$776$	5.75376e12	0.569605
$777$	−5.69151e11	−0.0560186
$778$	−4.54130e12	−0.444398
$779$	−1.95882e13	−1.90580
$780$	−9.98043e12	−0.965436
$781$	2.69352e12	0.259054
$782$	0	0
$783$	3.28376e12	0.312207
$784$	3.24599e12	0.306849
$785$	2.11982e13	1.99244
$786$	5.38713e12	0.503450
$787$	7.79210e12	0.724050	0.362025	−	0.932168i	$-0.382086\pi$
$787$	7.79210e12	0.724050	0.362025	+	0.932168i	$0.382086\pi$
$788$	1.26884e13	1.17230
$789$	4.26146e12	0.391482
$790$	−4.00595e13	−3.65918
$791$	−4.57765e12	−0.415766
$792$	4.96198e12	0.448117
$793$	−2.15768e13	−1.93757
$794$	−1.17713e13	−1.05107
$795$	−8.85371e12	−0.786092
$796$	−2.75478e13	−2.43208
$797$	1.20701e13	1.05961	0.529807	−	0.848118i	$-0.322264\pi$
$797$	1.20701e13	1.05961	0.529807	+	0.848118i	$0.322264\pi$
$798$	3.11854e12	0.272232
$799$	0	0
$800$	8.89339e12	0.767648
$801$	1.20620e13	1.03531
$802$	−2.14058e13	−1.82704
$803$	−8.47013e12	−0.718903
$804$	9.66799e12	0.815989
$805$	3.00636e12	0.252325
$806$	−2.16738e13	−1.80895
$807$	−1.10667e12	−0.0918516
$808$	1.10686e13	0.913572
$809$	−1.04899e13	−0.860999	−0.430500	−	0.902591i	$-0.641663\pi$
$809$	−1.04899e13	−0.860999	−0.430500	+	0.902591i	$0.641663\pi$
$810$	1.00740e13	0.822278
$811$	−4.24679e12	−0.344721	−0.172360	−	0.985034i	$-0.555139\pi$
$811$	−4.24679e12	−0.344721	−0.172360	+	0.985034i	$0.555139\pi$
$812$	1.73481e12	0.140039
$813$	2.40087e12	0.192735
$814$	−7.46851e12	−0.596244
$815$	−5.77321e12	−0.458361
$816$	0	0
$817$	1.47538e13	1.15853
$818$	1.72703e13	1.34869
$819$	2.89905e12	0.225153
$820$	3.06361e13	2.36631
$821$	8.29736e12	0.637376	0.318688	−	0.947860i	$-0.396758\pi$
$821$	8.29736e12	0.637376	0.318688	+	0.947860i	$0.396758\pi$
$822$	−8.46673e12	−0.646833
$823$	1.69218e13	1.28572	0.642860	−	0.765984i	$-0.277748\pi$
$823$	1.69218e13	1.28572	0.642860	+	0.765984i	$0.277748\pi$
$824$	1.36529e13	1.03170
$825$	−2.98448e12	−0.224298
$826$	−5.32511e12	−0.398032
$827$	5.01967e12	0.373165	0.186582	−	0.982439i	$-0.440259\pi$
$827$	5.01967e12	0.373165	0.186582	+	0.982439i	$0.440259\pi$
$828$	1.22392e13	0.904935
$829$	8.26746e12	0.607963	0.303981	−	0.952678i	$-0.401684\pi$
$829$	8.26746e12	0.607963	0.303981	+	0.952678i	$0.401684\pi$
$830$	−3.71666e12	−0.271833
$831$	2.36638e12	0.172140
$832$	2.51786e13	1.82170
$833$	0	0
$834$	−5.13067e12	−0.367220
$835$	−1.55280e13	−1.10542
$836$	2.42895e13	1.71985
$837$	−1.19002e13	−0.838090
$838$	−1.91454e13	−1.34112
$839$	1.09618e13	0.763751	0.381875	−	0.924214i	$-0.375278\pi$
$839$	1.09618e13	0.763751	0.381875	+	0.924214i	$0.375278\pi$
$840$	−1.53753e12	−0.106553
$841$	−1.24125e13	−0.855616
$842$	−3.53686e13	−2.42501
$843$	−9.52143e12	−0.649349
$844$	−2.13983e12	−0.145157
$845$	−5.25174e12	−0.354363
$846$	3.10238e13	2.08223
$847$	−1.44204e12	−0.0962727
$848$	6.63461e12	0.440589
$849$	7.17315e12	0.473833
$850$	0	0
$851$	−5.80719e12	−0.379562
$852$	−3.39783e12	−0.220914
$853$	−5.66078e12	−0.366105	−0.183052	−	0.983103i	$-0.558598\pi$
$853$	−5.66078e12	−0.366105	−0.183052	+	0.983103i	$0.558598\pi$
$854$	−1.05446e13	−0.678372
$855$	2.35082e13	1.50443
$856$	8.20845e12	0.522552
$857$	−2.86169e13	−1.81221	−0.906106	−	0.423050i	$-0.860959\pi$
$857$	−2.86169e13	−1.81221	−0.906106	+	0.423050i	$0.860959\pi$
$858$	−1.01681e13	−0.640544
$859$	−2.17190e13	−1.36104	−0.680521	−	0.732729i	$-0.738246\pi$
$859$	−2.17190e13	−1.36104	−0.680521	+	0.732729i	$0.738246\pi$
$860$	−2.30751e13	−1.43847
$861$	2.37859e12	0.147504
$862$	−3.71308e13	−2.29061
$863$	−2.05248e13	−1.25959	−0.629796	−	0.776761i	$-0.716861\pi$
$863$	−2.05248e13	−1.25959	−0.629796	+	0.776761i	$0.716861\pi$
$864$	1.66365e13	1.01566
$865$	9.87632e12	0.599823
$866$	1.55595e13	0.940080
$867$	0	0
$868$	−6.28690e12	−0.375922
$869$	−2.42247e13	−1.44102
$870$	−5.88897e12	−0.348500
$871$	2.33656e13	1.37561
$872$	−7.78498e12	−0.455967
$873$	1.06825e13	0.622456
$874$	3.18193e13	1.84455
$875$	2.11151e12	0.121775
$876$	1.06849e13	0.613060
$877$	−3.10724e13	−1.77369	−0.886843	−	0.462072i	$-0.847106\pi$
$877$	−3.10724e13	−1.77369	−0.886843	+	0.462072i	$0.847106\pi$
$878$	4.42819e13	2.51478
$879$	−6.48065e12	−0.366158
$880$	5.83776e12	0.328152
$881$	−4.35667e12	−0.243648	−0.121824	−	0.992552i	$-0.538874\pi$
$881$	−4.35667e12	−0.243648	−0.121824	+	0.992552i	$0.538874\pi$
$882$	−2.08282e13	−1.15889
$883$	1.30562e13	0.722758	0.361379	−	0.932419i	$-0.382306\pi$
$883$	1.30562e13	0.722758	0.361379	+	0.932419i	$0.382306\pi$
$884$	0	0
$885$	1.07294e13	0.587938
$886$	1.61539e13	0.880697
$887$	−3.11601e13	−1.69022	−0.845108	−	0.534596i	$-0.820464\pi$
$887$	−3.11601e13	−1.69022	−0.845108	+	0.534596i	$0.820464\pi$
$888$	2.96995e12	0.160284
$889$	−9.68714e11	−0.0520161
$890$	−4.90448e13	−2.62022
$891$	6.09192e12	0.323821
$892$	−6.47667e12	−0.342539
$893$	4.78732e13	2.51919
$894$	5.72787e12	0.299898
$895$	−2.74133e13	−1.42809
$896$	6.28628e12	0.325843
$897$	−7.90631e12	−0.407763
$898$	−1.60522e13	−0.823742
$899$	−7.59076e12	−0.387585
$900$	−1.40854e13	−0.715614
$901$	0	0
$902$	3.12123e13	1.56999
$903$	−1.79155e12	−0.0896673
$904$	2.38871e13	1.18961
$905$	−4.37827e13	−2.16962
$906$	−1.57041e13	−0.774346
$907$	−1.75730e13	−0.862208	−0.431104	−	0.902302i	$-0.641876\pi$
$907$	−1.75730e13	−0.862208	−0.431104	+	0.902302i	$0.641876\pi$
$908$	2.53689e13	1.23856
$909$	2.05501e13	0.998337
$910$	−1.17877e13	−0.569829
$911$	3.26951e12	0.157272	0.0786358	−	0.996903i	$-0.474944\pi$
$911$	3.26951e12	0.157272	0.0786358	+	0.996903i	$0.474944\pi$
$912$	4.70858e12	0.225379
$913$	−2.24753e12	−0.107050
$914$	2.67640e13	1.26851
$915$	2.12459e13	1.00203
$916$	−3.23336e13	−1.51749
$917$	3.77659e12	0.176375
$918$	0	0
$919$	−1.28770e13	−0.595517	−0.297759	−	0.954641i	$-0.596239\pi$
$919$	−1.28770e13	−0.595517	−0.297759	+	0.954641i	$0.596239\pi$
$920$	−1.56878e13	−0.721967
$921$	6.49556e12	0.297473
$922$	2.94692e13	1.34301
$923$	−8.21187e12	−0.372421
$924$	−2.94947e12	−0.133113
$925$	6.68316e12	0.300154
$926$	5.81947e13	2.60096
$927$	2.53482e13	1.12743
$928$	1.06119e13	0.469705
$929$	8.08221e12	0.356008	0.178004	−	0.984030i	$-0.443036\pi$
$929$	8.08221e12	0.356008	0.178004	+	0.984030i	$0.443036\pi$
$930$	2.13414e13	0.935514
$931$	−3.21403e13	−1.40209
$932$	2.11627e13	0.918754
$933$	−4.13679e12	−0.178730
$934$	−1.91637e12	−0.0823983
$935$	0	0
$936$	−1.51278e13	−0.644222
$937$	6.49112e12	0.275101	0.137550	−	0.990495i	$-0.456077\pi$
$937$	6.49112e12	0.275101	0.137550	+	0.990495i	$0.456077\pi$
$938$	1.14187e13	0.481621
$939$	1.26039e13	0.529067
$940$	−7.48740e13	−3.12792
$941$	1.21565e11	0.00505423	0.00252711	−	0.999997i	$-0.499196\pi$
$941$	1.21565e11	0.00505423	0.00252711	+	0.999997i	$0.499196\pi$
$942$	−2.72441e13	−1.12731
$943$	2.42694e13	0.999437
$944$	−8.04019e12	−0.329528
$945$	−6.47219e12	−0.264003
$946$	−2.35091e13	−0.954389
$947$	−4.00324e12	−0.161747	−0.0808735	−	0.996724i	$-0.525771\pi$
$947$	−4.00324e12	−0.161747	−0.0808735	+	0.996724i	$0.525771\pi$
$948$	3.05591e13	1.22886
$949$	2.58233e13	1.03351
$950$	−3.66190e13	−1.45865
$951$	−1.92407e13	−0.762795
$952$	0	0
$953$	−3.60121e13	−1.41426	−0.707131	−	0.707082i	$-0.750011\pi$
$953$	−3.60121e13	−1.41426	−0.707131	+	0.707082i	$0.750011\pi$
$954$	−4.25716e13	−1.66400
$955$	−2.73934e13	−1.06569
$956$	−3.09257e13	−1.19745
$957$	−3.56117e12	−0.137242
$958$	−5.37932e13	−2.06340
$959$	−5.93550e12	−0.226607
$960$	−2.47925e13	−0.942105
$961$	1.06905e12	0.0404336
$962$	2.27696e13	0.857172
$963$	1.52399e13	0.571037
$964$	3.55421e13	1.32555
$965$	−6.68097e13	−2.48009
$966$	−3.86380e12	−0.142764
$967$	4.03493e13	1.48394	0.741972	−	0.670431i	$-0.233891\pi$
$967$	4.03493e13	1.48394	0.741972	+	0.670431i	$0.233891\pi$
$968$	7.52489e12	0.275461
$969$	0	0
$970$	−4.34358e13	−1.57534
$971$	1.94578e13	0.702435	0.351218	−	0.936294i	$-0.385768\pi$
$971$	1.94578e13	0.702435	0.351218	+	0.936294i	$0.385768\pi$
$972$	−4.10766e13	−1.47604
$973$	−3.59680e12	−0.128649
$974$	−4.88404e13	−1.73886
$975$	9.09892e12	0.322455
$976$	−1.59208e13	−0.561619
$977$	4.00163e13	1.40511	0.702557	−	0.711627i	$-0.252042\pi$
$977$	4.00163e13	1.40511	0.702557	+	0.711627i	$0.252042\pi$
$978$	7.41978e12	0.259338
$979$	−2.96583e13	−1.03187
$980$	5.02676e13	1.74089
$981$	−1.44537e13	−0.498273
$982$	7.06007e13	2.42274
$983$	−1.03796e13	−0.354559	−0.177280	−	0.984161i	$-0.556730\pi$
$983$	−1.03796e13	−0.354559	−0.177280	+	0.984161i	$0.556730\pi$
$984$	−1.24120e13	−0.422049
$985$	−3.01951e13	−1.02205
$986$	0	0
$987$	−5.81322e12	−0.194980
$988$	−7.40527e13	−2.47249
$989$	−1.82797e13	−0.607554
$990$	−3.74586e13	−1.23935
$991$	1.11004e13	0.365601	0.182800	−	0.983150i	$-0.441484\pi$
$991$	1.11004e13	0.365601	0.182800	+	0.983150i	$0.441484\pi$
$992$	−3.84570e13	−1.26088
$993$	−1.80711e13	−0.589810
$994$	−4.01313e12	−0.130390
$995$	6.55566e13	2.12037
$996$	2.83522e12	0.0912894
$997$	−5.51871e12	−0.176892	−0.0884462	−	0.996081i	$-0.528190\pi$
$997$	−5.51871e12	−0.176892	−0.0884462	+	0.996081i	$0.528190\pi$
$998$	2.31578e13	0.738941
$999$	1.25019e13	0.397129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.5	yes	36
17.16	even	2		289.10.a.g.1.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.5	✓	36	17.16	even	2
289.10.a.h.1.5	yes	36	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-35.4923 q^{2} -64.4314 q^{3} +747.701 q^{4} -1779.33 q^{5} +2286.82 q^{6} +1603.15 q^{7} -8365.56 q^{8} -15531.6 q^{9} +O(q^{10})\)	\(q-35.4923 q^{2} -64.4314 q^{3} +747.701 q^{4} -1779.33 q^{5} +2286.82 q^{6} +1603.15 q^{7} -8365.56 q^{8} -15531.6 q^{9} +63152.6 q^{10} +38189.5 q^{11} -48175.4 q^{12} -116430. q^{13} -56899.3 q^{14} +114645. q^{15} -85910.2 q^{16} +551251. q^{18} +850642. q^{19} -1.33041e6 q^{20} -103293. q^{21} -1.35543e6 q^{22} -1.05393e6 q^{23} +539005. q^{24} +1.21290e6 q^{25} +4.13238e6 q^{26} +2.26893e6 q^{27} +1.19867e6 q^{28} +1.44727e6 q^{29} -4.06901e6 q^{30} -5.24487e6 q^{31} +7.33231e6 q^{32} -2.46061e6 q^{33} -2.85253e6 q^{35} -1.16130e7 q^{36} +5.51006e6 q^{37} -3.01912e7 q^{38} +7.50177e6 q^{39} +1.48851e7 q^{40} -2.30276e7 q^{41} +3.66611e6 q^{42} +1.73443e7 q^{43} +2.85543e7 q^{44} +2.76359e7 q^{45} +3.74062e7 q^{46} +5.62789e7 q^{47} +5.53532e6 q^{48} -3.77835e7 q^{49} -4.30487e7 q^{50} -8.70551e7 q^{52} -7.72272e7 q^{53} -8.05293e7 q^{54} -6.79519e7 q^{55} -1.34112e7 q^{56} -5.48081e7 q^{57} -5.13670e7 q^{58} +9.35882e7 q^{59} +8.57202e7 q^{60} +1.85319e8 q^{61} +1.86152e8 q^{62} -2.48994e7 q^{63} -2.16254e8 q^{64} +2.07168e8 q^{65} +8.73325e7 q^{66} -2.00683e8 q^{67} +6.79060e7 q^{69} +1.01243e8 q^{70} +7.05304e7 q^{71} +1.29930e8 q^{72} -2.21792e8 q^{73} -1.95564e8 q^{74} -7.81491e7 q^{75} +6.36026e8 q^{76} +6.12234e7 q^{77} -2.66255e8 q^{78} -6.34329e8 q^{79} +1.52863e8 q^{80} +1.59518e8 q^{81} +8.17300e8 q^{82} -5.88521e7 q^{83} -7.72323e7 q^{84} -6.15590e8 q^{86} -9.32498e7 q^{87} -3.19477e8 q^{88} -7.76608e8 q^{89} -9.80860e8 q^{90} -1.86655e8 q^{91} -7.88022e8 q^{92} +3.37935e8 q^{93} -1.99747e9 q^{94} -1.51358e9 q^{95} -4.72431e8 q^{96} -6.87791e8 q^{97} +1.34102e9 q^{98} -5.93144e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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

L-functions

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