LMFDB - Embedded newform 289.10.a.f.1.11

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:	$24$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-9.57683 q^{2} -3.76279 q^{3} -420.284 q^{4} +1873.25 q^{5} +36.0355 q^{6} -1553.61 q^{7} +8928.33 q^{8} -19668.8 q^{9} +O(q^{10})$	\(q-9.57683 q^{2} -3.76279 q^{3} -420.284 q^{4} +1873.25 q^{5} +36.0355 q^{6} -1553.61 q^{7} +8928.33 q^{8} -19668.8 q^{9} -17939.8 q^{10} +68833.5 q^{11} +1581.44 q^{12} -53127.1 q^{13} +14878.6 q^{14} -7048.63 q^{15} +129681. q^{16} +188365. q^{18} +64384.8 q^{19} -787297. q^{20} +5845.89 q^{21} -659207. q^{22} -2.42958e6 q^{23} -33595.4 q^{24} +1.55593e6 q^{25} +508789. q^{26} +148073. q^{27} +652956. q^{28} +4.67341e6 q^{29} +67503.5 q^{30} +4.15669e6 q^{31} -5.81323e6 q^{32} -259006. q^{33} -2.91029e6 q^{35} +8.26651e6 q^{36} -9.76209e6 q^{37} -616602. q^{38} +199906. q^{39} +1.67250e7 q^{40} -3.09207e7 q^{41} -55985.1 q^{42} +2.81845e7 q^{43} -2.89296e7 q^{44} -3.68446e7 q^{45} +2.32677e7 q^{46} -1.87813e7 q^{47} -487960. q^{48} -3.79399e7 q^{49} -1.49009e7 q^{50} +2.23285e7 q^{52} +4.47911e6 q^{53} -1.41807e6 q^{54} +1.28942e8 q^{55} -1.38711e7 q^{56} -242266. q^{57} -4.47565e7 q^{58} +1.26323e8 q^{59} +2.96243e6 q^{60} +3.41770e7 q^{61} -3.98079e7 q^{62} +3.05576e7 q^{63} -1.07241e7 q^{64} -9.95201e7 q^{65} +2.48045e6 q^{66} +1.37527e8 q^{67} +9.14198e6 q^{69} +2.78713e7 q^{70} -4.06649e7 q^{71} -1.75610e8 q^{72} -2.45684e8 q^{73} +9.34898e7 q^{74} -5.85463e6 q^{75} -2.70599e7 q^{76} -1.06940e8 q^{77} -1.91446e6 q^{78} +3.94690e8 q^{79} +2.42924e8 q^{80} +3.86585e8 q^{81} +2.96122e8 q^{82} +3.15697e8 q^{83} -2.45693e6 q^{84} -2.69918e8 q^{86} -1.75850e7 q^{87} +6.14568e8 q^{88} -4.99389e8 q^{89} +3.52854e8 q^{90} +8.25385e7 q^{91} +1.02111e9 q^{92} -1.56407e7 q^{93} +1.79865e8 q^{94} +1.20609e8 q^{95} +2.18739e7 q^{96} -7.84102e8 q^{97} +3.63344e8 q^{98} -1.35388e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) $ 24 * q + 5124 * q^4 + 108368 * q^9	$ 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) $ 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

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 $

$2$	−9.57683	−0.423240	−0.211620	−	0.977352i	$-0.567874\pi$
$2$	−9.57683	−0.423240	−0.211620	+	0.977352i	$0.567874\pi$
$3$	−3.76279	−0.0268203	−0.0134102	−	0.999910i	$-0.504269\pi$
$3$	−3.76279	−0.0268203	−0.0134102	+	0.999910i	$0.504269\pi$
$4$	−420.284	−0.820868
$5$	1873.25	1.34039	0.670193	−	0.742187i	$-0.266211\pi$
$5$	1873.25	1.34039	0.670193	+	0.742187i	$0.266211\pi$
$6$	36.0355	0.0113514
$7$	−1553.61	−0.244568	−0.122284	−	0.992495i	$-0.539022\pi$
$7$	−1553.61	−0.244568	−0.122284	+	0.992495i	$0.539022\pi$
$8$	8928.33	0.770664
$9$	−19668.8	−0.999281
$10$	−17939.8	−0.567305
$11$	68833.5	1.41753	0.708766	−	0.705444i	$-0.249252\pi$
$11$	68833.5	1.41753	0.708766	+	0.705444i	$0.249252\pi$
$12$	1581.44	0.0220159
$13$	−53127.1	−0.515906	−0.257953	−	0.966157i	$-0.583048\pi$
$13$	−53127.1	−0.515906	−0.257953	+	0.966157i	$0.583048\pi$
$14$	14878.6	0.103511
$15$	−7048.63	−0.0359496
$16$	129681.	0.494692
$17$	0	0
$17$	0	0
$18$	188365.	0.422936
$19$	64384.8	0.113342	0.0566712	−	0.998393i	$-0.481951\pi$
$19$	64384.8	0.113342	0.0566712	+	0.998393i	$0.481951\pi$
$20$	−787297.	−1.10028
$21$	5845.89	0.00655939
$22$	−659207.	−0.599956
$23$	−2.42958e6	−1.81032	−0.905161	−	0.425070i	$-0.860250\pi$
$23$	−2.42958e6	−1.81032	−0.905161	+	0.425070i	$0.860250\pi$
$24$	−33595.4	−0.0206695
$25$	1.55593e6	0.796636
$26$	508789.	0.218352
$27$	148073.	0.0536213
$28$	652956.	0.200758
$29$	4.67341e6	1.22700	0.613498	−	0.789696i	$-0.289762\pi$
$29$	4.67341e6	1.22700	0.613498	+	0.789696i	$0.289762\pi$
$30$	67503.5	0.0152153
$31$	4.15669e6	0.808389	0.404194	−	0.914673i	$-0.367552\pi$
$31$	4.15669e6	0.808389	0.404194	+	0.914673i	$0.367552\pi$
$32$	−5.81323e6	−0.980038
$33$	−259006.	−0.0380186
$34$	0	0
$35$	−2.91029e6	−0.327816
$36$	8.26651e6	0.820277
$37$	−9.76209e6	−0.856318	−0.428159	−	0.903704i	$-0.640838\pi$
$37$	−9.76209e6	−0.856318	−0.428159	+	0.903704i	$0.640838\pi$
$38$	−616602.	−0.0479710
$39$	199906.	0.0138368
$40$	1.67250e7	1.03299
$41$	−3.09207e7	−1.70892	−0.854459	−	0.519518i	$-0.826111\pi$
$41$	−3.09207e7	−1.70892	−0.854459	+	0.519518i	$0.826111\pi$
$42$	−55985.1	−0.00277620
$43$	2.81845e7	1.25719	0.628597	−	0.777731i	$-0.283630\pi$
$43$	2.81845e7	1.25719	0.628597	+	0.777731i	$0.283630\pi$
$44$	−2.89296e7	−1.16361
$45$	−3.68446e7	−1.33942
$46$	2.32677e7	0.766200
$47$	−1.87813e7	−0.561417	−0.280708	−	0.959793i	$-0.590569\pi$
$47$	−1.87813e7	−0.561417	−0.280708	+	0.959793i	$0.590569\pi$
$48$	−487960.	−0.0132678
$49$	−3.79399e7	−0.940186
$50$	−1.49009e7	−0.337168
$51$	0	0
$52$	2.23285e7	0.423491
$53$	4.47911e6	0.0779741	0.0389871	−	0.999240i	$-0.487587\pi$
$53$	4.47911e6	0.0779741	0.0389871	+	0.999240i	$0.487587\pi$
$54$	−1.41807e6	−0.0226947
$55$	1.28942e8	1.90004
$56$	−1.38711e7	−0.188480
$57$	−242266.	−0.00303988
$58$	−4.47565e7	−0.519314
$59$	1.26323e8	1.35722	0.678609	−	0.734499i	$-0.262583\pi$
$59$	1.26323e8	1.35722	0.678609	+	0.734499i	$0.262583\pi$
$60$	2.96243e6	0.0295099
$61$	3.41770e7	0.316045	0.158023	−	0.987436i	$-0.449488\pi$
$61$	3.41770e7	0.316045	0.158023	+	0.987436i	$0.449488\pi$
$62$	−3.98079e7	−0.342143
$63$	3.05576e7	0.244392
$64$	−1.07241e7	−0.0799009
$65$	−9.95201e7	−0.691514
$66$	2.48045e6	0.0160910
$67$	1.37527e8	0.833781	0.416890	−	0.908957i	$-0.363120\pi$
$67$	1.37527e8	0.833781	0.416890	+	0.908957i	$0.363120\pi$
$68$	0	0
$69$	9.14198e6	0.0485534
$70$	2.78713e7	0.138745
$71$	−4.06649e7	−0.189914	−0.0949570	−	0.995481i	$-0.530271\pi$
$71$	−4.06649e7	−0.189914	−0.0949570	+	0.995481i	$0.530271\pi$
$72$	−1.75610e8	−0.770110
$73$	−2.45684e8	−1.01257	−0.506285	−	0.862366i	$-0.668982\pi$
$73$	−2.45684e8	−1.01257	−0.506285	+	0.862366i	$0.668982\pi$
$74$	9.34898e7	0.362428
$75$	−5.85463e6	−0.0213660
$76$	−2.70599e7	−0.0930391
$77$	−1.06940e8	−0.346683
$78$	−1.91446e6	−0.00585627
$79$	3.94690e8	1.14008	0.570039	−	0.821618i	$-0.306928\pi$
$79$	3.94690e8	1.14008	0.570039	+	0.821618i	$0.306928\pi$
$80$	2.42924e8	0.663079
$81$	3.86585e8	0.997843
$82$	2.96122e8	0.723283
$83$	3.15697e8	0.730162	0.365081	−	0.930976i	$-0.381041\pi$
$83$	3.15697e8	0.730162	0.365081	+	0.930976i	$0.381041\pi$
$84$	−2.45693e6	−0.00538439
$85$	0	0
$86$	−2.69918e8	−0.532095
$87$	−1.75850e7	−0.0329084
$88$	6.14568e8	1.09244
$89$	−4.99389e8	−0.843693	−0.421846	−	0.906667i	$-0.638618\pi$
$89$	−4.99389e8	−0.843693	−0.421846	+	0.906667i	$0.638618\pi$
$90$	3.52854e8	0.566897
$91$	8.25385e7	0.126174
$92$	1.02111e9	1.48603
$93$	−1.56407e7	−0.0216812
$94$	1.79865e8	0.237614
$95$	1.20609e8	0.151923
$96$	2.18739e7	0.0262849
$97$	−7.84102e8	−0.899290	−0.449645	−	0.893207i	$-0.648450\pi$
$97$	−7.84102e8	−0.899290	−0.449645	+	0.893207i	$0.648450\pi$
$98$	3.63344e8	0.397925
$99$	−1.35388e9	−1.41651
$100$	−6.53933e8	−0.653933
$101$	6.53522e8	0.624905	0.312452	−	0.949933i	$-0.398850\pi$
$101$	6.53522e8	0.624905	0.312452	+	0.949933i	$0.398850\pi$
$102$	0	0
$103$	1.02870e7	0.00900581	0.00450291	−	0.999990i	$-0.498567\pi$
$103$	1.02870e7	0.00900581	0.00450291	+	0.999990i	$0.498567\pi$
$104$	−4.74336e8	−0.397590
$105$	1.09508e7	0.00879212
$106$	−4.28957e7	−0.0330018
$107$	2.80325e8	0.206745	0.103373	−	0.994643i	$-0.467037\pi$
$107$	2.80325e8	0.206745	0.103373	+	0.994643i	$0.467037\pi$
$108$	−6.22326e7	−0.0440160
$109$	3.40166e8	0.230819	0.115410	−	0.993318i	$-0.463182\pi$
$109$	3.40166e8	0.230819	0.115410	+	0.993318i	$0.463182\pi$
$110$	−1.23486e9	−0.804173
$111$	3.67326e7	0.0229667
$112$	−2.01473e8	−0.120986
$113$	1.00444e9	0.579523	0.289761	−	0.957099i	$-0.406424\pi$
$113$	1.00444e9	0.579523	0.289761	+	0.957099i	$0.406424\pi$
$114$	2.32014e6	0.00128660
$115$	−4.55120e9	−2.42653
$116$	−1.96416e9	−1.00720
$117$	1.04495e9	0.515535
$118$	−1.20978e9	−0.574429
$119$	0	0
$120$	−6.29325e7	−0.0277051
$121$	2.38010e9	1.00940
$122$	−3.27307e8	−0.133763
$123$	1.16348e8	0.0458337
$124$	−1.74699e9	−0.663581
$125$	−7.44044e8	−0.272586
$126$	−2.92645e8	−0.103437
$127$	2.89317e9	0.986865	0.493432	−	0.869784i	$-0.335742\pi$
$127$	2.89317e9	0.986865	0.493432	+	0.869784i	$0.335742\pi$
$128$	3.07908e9	1.01385
$129$	−1.06052e8	−0.0337183
$130$	9.53087e8	0.292676
$131$	−2.70866e8	−0.0803587	−0.0401794	−	0.999192i	$-0.512793\pi$
$131$	−2.70866e8	−0.0803587	−0.0401794	+	0.999192i	$0.512793\pi$
$132$	1.08856e8	0.0312083
$133$	−1.00029e8	−0.0277199
$134$	−1.31707e9	−0.352889
$135$	2.77376e8	0.0718733
$136$	0	0
$137$	−7.83519e9	−1.90023	−0.950117	−	0.311894i	$-0.899036\pi$
$137$	−7.83519e9	−1.90023	−0.950117	+	0.311894i	$0.899036\pi$
$138$	−8.75512e7	−0.0205497
$139$	−2.42960e9	−0.552038	−0.276019	−	0.961152i	$-0.589015\pi$
$139$	−2.42960e9	−0.552038	−0.276019	+	0.961152i	$0.589015\pi$
$140$	1.22315e9	0.269093
$141$	7.06700e7	0.0150574
$142$	3.89441e8	0.0803792
$143$	−3.65692e9	−0.731313
$144$	−2.55067e9	−0.494336
$145$	8.75445e9	1.64465
$146$	2.35288e9	0.428560
$147$	1.42760e8	0.0252161
$148$	4.10285e9	0.702924
$149$	2.56491e9	0.426319	0.213159	−	0.977017i	$-0.431625\pi$
$149$	2.56491e9	0.426319	0.213159	+	0.977017i	$0.431625\pi$
$150$	5.60688e7	0.00904296
$151$	−1.16618e10	−1.82544	−0.912722	−	0.408581i	$-0.866024\pi$
$151$	−1.16618e10	−1.82544	−0.912722	+	0.408581i	$0.866024\pi$
$152$	5.74849e8	0.0873489
$153$	0	0
$154$	1.02415e9	0.146730
$155$	7.78651e9	1.08355
$156$	−8.40173e7	−0.0113582
$157$	−6.12170e9	−0.804125	−0.402063	−	0.915612i	$-0.631707\pi$
$157$	−6.12170e9	−0.804125	−0.402063	+	0.915612i	$0.631707\pi$
$158$	−3.77988e9	−0.482527
$159$	−1.68539e7	−0.00209129
$160$	−1.08896e10	−1.31363
$161$	3.77461e9	0.442747
$162$	−3.70225e9	−0.422327
$163$	−7.45677e9	−0.827382	−0.413691	−	0.910417i	$-0.635761\pi$
$163$	−7.45677e9	−0.827382	−0.413691	+	0.910417i	$0.635761\pi$
$164$	1.29955e10	1.40280
$165$	−4.85182e8	−0.0509597
$166$	−3.02338e9	−0.309034
$167$	−9.08731e9	−0.904089	−0.452044	−	0.891995i	$-0.649305\pi$
$167$	−9.08731e9	−0.904089	−0.452044	+	0.891995i	$0.649305\pi$
$168$	5.21940e7	0.00505509
$169$	−7.78201e9	−0.733841
$170$	0	0
$171$	−1.26637e9	−0.113261
$172$	−1.18455e10	−1.03199
$173$	2.09520e10	1.77835	0.889175	−	0.457566i	$-0.151279\pi$
$173$	2.09520e10	1.77835	0.889175	+	0.457566i	$0.151279\pi$
$174$	1.68409e8	0.0139282
$175$	−2.41730e9	−0.194832
$176$	8.92636e9	0.701241
$177$	−4.75328e8	−0.0364010
$178$	4.78257e9	0.357084
$179$	−1.81997e10	−1.32503	−0.662516	−	0.749048i	$-0.730511\pi$
$179$	−1.81997e10	−1.32503	−0.662516	+	0.749048i	$0.730511\pi$
$180$	1.54852e10	1.09949
$181$	−4.25507e9	−0.294682	−0.147341	−	0.989086i	$-0.547071\pi$
$181$	−4.25507e9	−0.294682	−0.147341	+	0.989086i	$0.547071\pi$
$182$	−7.90457e8	−0.0534020
$183$	−1.28601e8	−0.00847643
$184$	−2.16921e10	−1.39515
$185$	−1.82868e10	−1.14780
$186$	1.49789e8	0.00917637
$187$	0	0
$188$	7.89349e9	0.460849
$189$	−2.30046e8	−0.0131141
$190$	−1.15505e9	−0.0642997
$191$	−1.04248e10	−0.566784	−0.283392	−	0.959004i	$-0.591460\pi$
$191$	−1.04248e10	−0.566784	−0.283392	+	0.959004i	$0.591460\pi$
$192$	4.03526e7	0.00214297
$193$	2.64500e9	0.137220	0.0686099	−	0.997644i	$-0.478144\pi$
$193$	2.64500e9	0.137220	0.0686099	+	0.997644i	$0.478144\pi$
$194$	7.50921e9	0.380616
$195$	3.74473e8	0.0185466
$196$	1.59456e10	0.771769
$197$	3.57231e10	1.68986	0.844930	−	0.534876i	$-0.179642\pi$
$197$	3.57231e10	1.68986	0.844930	+	0.534876i	$0.179642\pi$
$198$	1.29658e10	0.599524
$199$	−2.74427e10	−1.24047	−0.620237	−	0.784415i	$-0.712964\pi$
$199$	−2.74427e10	−1.24047	−0.620237	+	0.784415i	$0.712964\pi$
$200$	1.38919e10	0.613939
$201$	−5.17485e8	−0.0223623
$202$	−6.25866e9	−0.264485
$203$	−7.26064e9	−0.300084
$204$	0	0
$205$	−5.79220e10	−2.29061
$206$	−9.85172e7	−0.00381162
$207$	4.77870e10	1.80902
$208$	−6.88955e9	−0.255215
$209$	4.43183e9	0.160666
$210$	−1.04874e8	−0.00372118
$211$	−4.93385e10	−1.71362	−0.856811	−	0.515631i	$-0.827558\pi$
$211$	−4.93385e10	−1.71362	−0.856811	+	0.515631i	$0.827558\pi$
$212$	−1.88250e9	−0.0640064
$213$	1.53013e8	0.00509355
$214$	−2.68463e9	−0.0875028
$215$	5.27965e10	1.68513
$216$	1.32204e9	0.0413240
$217$	−6.45786e9	−0.197706
$218$	−3.25771e9	−0.0976920
$219$	9.24458e8	0.0271574
$220$	−5.41924e10	−1.55968
$221$	0	0
$222$	−3.51782e8	−0.00972043
$223$	3.12685e10	0.846710	0.423355	−	0.905964i	$-0.360852\pi$
$223$	3.12685e10	0.846710	0.423355	+	0.905964i	$0.360852\pi$
$224$	9.03147e9	0.239686
$225$	−3.06033e10	−0.796063
$226$	−9.61934e9	−0.245277
$227$	−3.74858e9	−0.0937023	−0.0468512	−	0.998902i	$-0.514919\pi$
$227$	−3.74858e9	−0.0937023	−0.0468512	+	0.998902i	$0.514919\pi$
$228$	1.01821e8	0.00249534
$229$	−4.94370e10	−1.18793	−0.593967	−	0.804489i	$-0.702439\pi$
$229$	−4.94370e10	−1.18793	−0.593967	+	0.804489i	$0.702439\pi$
$230$	4.35861e10	1.02700
$231$	4.02393e8	0.00929814
$232$	4.17257e10	0.945601
$233$	−5.15582e10	−1.14603	−0.573015	−	0.819545i	$-0.694226\pi$
$233$	−5.15582e10	−1.14603	−0.573015	+	0.819545i	$0.694226\pi$
$234$	−1.00073e10	−0.218195
$235$	−3.51820e10	−0.752516
$236$	−5.30918e10	−1.11410
$237$	−1.48513e9	−0.0305772
$238$	0	0
$239$	−6.14267e10	−1.21777	−0.608887	−	0.793257i	$-0.708384\pi$
$239$	−6.14267e10	−1.21777	−0.608887	+	0.793257i	$0.708384\pi$
$240$	−9.14070e8	−0.0177840
$241$	−8.25422e10	−1.57616	−0.788078	−	0.615575i	$-0.788924\pi$
$241$	−8.25422e10	−1.57616	−0.788078	+	0.615575i	$0.788924\pi$
$242$	−2.27938e10	−0.427217
$243$	−4.36915e9	−0.0803838
$244$	−1.43640e10	−0.259431
$245$	−7.10708e10	−1.26021
$246$	−1.11424e9	−0.0193987
$247$	−3.42058e9	−0.0584740
$248$	3.71123e10	0.622996
$249$	−1.18790e9	−0.0195832
$250$	7.12558e9	0.115369
$251$	−9.98436e10	−1.58777	−0.793887	−	0.608066i	$-0.791946\pi$
$251$	−9.98436e10	−1.58777	−0.793887	+	0.608066i	$0.791946\pi$
$252$	−1.28429e10	−0.200614
$253$	−1.67236e11	−2.56619
$254$	−2.77074e10	−0.417681
$255$	0	0
$256$	−2.39970e10	−0.349203
$257$	−4.07145e10	−0.582171	−0.291085	−	0.956697i	$-0.594016\pi$
$257$	−4.07145e10	−0.582171	−0.291085	+	0.956697i	$0.594016\pi$
$258$	1.01564e9	0.0142709
$259$	1.51664e10	0.209428
$260$	4.18268e10	0.567641
$261$	−9.19206e10	−1.22611
$262$	2.59403e9	0.0340110
$263$	3.57313e10	0.460520	0.230260	−	0.973129i	$-0.426042\pi$
$263$	3.57313e10	0.460520	0.230260	+	0.973129i	$0.426042\pi$
$264$	−2.31249e9	−0.0292996
$265$	8.39048e9	0.104515
$266$	9.57957e8	0.0117322
$267$	1.87909e9	0.0226281
$268$	−5.78005e10	−0.684424
$269$	−1.32773e11	−1.54606	−0.773028	−	0.634372i	$-0.781259\pi$
$269$	−1.32773e11	−1.54606	−0.773028	+	0.634372i	$0.781259\pi$
$270$	−2.65639e9	−0.0304197
$271$	−1.31223e11	−1.47791	−0.738956	−	0.673754i	$-0.764681\pi$
$271$	−1.31223e11	−1.47791	−0.738956	+	0.673754i	$0.764681\pi$
$272$	0	0
$273$	−3.10575e8	−0.00338403
$274$	7.50363e10	0.804255
$275$	1.07100e11	1.12926
$276$	−3.84223e9	−0.0398559
$277$	−3.70561e10	−0.378182	−0.189091	−	0.981960i	$-0.560554\pi$
$277$	−3.70561e10	−0.378182	−0.189091	+	0.981960i	$0.560554\pi$
$278$	2.32679e10	0.233645
$279$	−8.17573e10	−0.807807
$280$	−2.59840e10	−0.252636
$281$	1.01765e11	0.973685	0.486843	−	0.873490i	$-0.338149\pi$
$281$	1.01765e11	0.973685	0.486843	+	0.873490i	$0.338149\pi$
$282$	−6.76795e8	−0.00637288
$283$	9.33903e10	0.865491	0.432746	−	0.901516i	$-0.357545\pi$
$283$	9.33903e10	0.865491	0.432746	+	0.901516i	$0.357545\pi$
$284$	1.70908e10	0.155894
$285$	−4.53825e8	−0.00407461
$286$	3.50217e10	0.309521
$287$	4.80385e10	0.417947
$288$	1.14340e11	0.979333
$289$	0	0
$290$	−8.38399e10	−0.696081
$291$	2.95041e9	0.0241192
$292$	1.03257e11	0.831186
$293$	−3.94765e10	−0.312921	−0.156460	−	0.987684i	$-0.550008\pi$
$293$	−3.94765e10	−0.312921	−0.156460	+	0.987684i	$0.550008\pi$
$294$	−1.36719e9	−0.0106725
$295$	2.36635e11	1.81920
$296$	−8.71591e10	−0.659933
$297$	1.01923e10	0.0760099
$298$	−2.45637e10	−0.180435
$299$	1.29076e11	0.933956
$300$	2.46061e9	0.0175387
$301$	−4.37876e10	−0.307469
$302$	1.11683e11	0.772601
$303$	−2.45906e9	−0.0167601
$304$	8.34946e9	0.0560696
$305$	6.40219e10	0.423623
$306$	0	0
$307$	3.10911e10	0.199762	0.0998812	−	0.994999i	$-0.468154\pi$
$307$	3.10911e10	0.199762	0.0998812	+	0.994999i	$0.468154\pi$
$308$	4.49453e10	0.284581
$309$	−3.87079e7	−0.000241539 0
$310$	−7.45701e10	−0.458603
$311$	−1.33143e10	−0.0807046	−0.0403523	−	0.999186i	$-0.512848\pi$
$311$	−1.33143e10	−0.0807046	−0.0403523	+	0.999186i	$0.512848\pi$
$312$	1.78482e9	0.0106635
$313$	2.01278e11	1.18535	0.592674	−	0.805442i	$-0.298072\pi$
$313$	2.01278e11	1.18535	0.592674	+	0.805442i	$0.298072\pi$
$314$	5.86265e10	0.340338
$315$	5.72420e10	0.327580
$316$	−1.65882e11	−0.935853
$317$	3.61827e10	0.201249	0.100625	−	0.994924i	$-0.467916\pi$
$317$	3.61827e10	0.201249	0.100625	+	0.994924i	$0.467916\pi$
$318$	1.61407e8	0.000885117 0
$319$	3.21687e11	1.73930
$320$	−2.00889e10	−0.107098
$321$	−1.05480e9	−0.00554497
$322$	−3.61488e10	−0.187388
$323$	0	0
$324$	−1.62475e11	−0.819097
$325$	−8.26620e10	−0.410990
$326$	7.14122e10	0.350181
$327$	−1.27997e9	−0.00619064
$328$	−2.76070e11	−1.31700
$329$	2.91788e10	0.137305
$330$	4.64650e9	0.0215682
$331$	2.52419e11	1.15583	0.577917	−	0.816096i	$-0.303866\pi$
$331$	2.52419e11	1.15583	0.577917	+	0.816096i	$0.303866\pi$
$332$	−1.32682e11	−0.599366
$333$	1.92009e11	0.855702
$334$	8.70276e10	0.382646
$335$	2.57622e11	1.11759
$336$	7.58098e8	0.00324488
$337$	−1.75954e11	−0.743129	−0.371564	−	0.928407i	$-0.621179\pi$
$337$	−1.75954e11	−0.743129	−0.371564	+	0.928407i	$0.621179\pi$
$338$	7.45270e10	0.310591
$339$	−3.77949e9	−0.0155430
$340$	0	0
$341$	2.86120e11	1.14592
$342$	1.21279e10	0.0479365
$343$	1.21637e11	0.474508
$344$	2.51640e11	0.968874
$345$	1.71252e10	0.0650803
$346$	−2.00653e11	−0.752669
$347$	1.25482e11	0.464620	0.232310	−	0.972642i	$-0.425372\pi$
$347$	1.25482e11	0.464620	0.232310	+	0.972642i	$0.425372\pi$
$348$	7.39072e9	0.0270135
$349$	−2.12956e11	−0.768380	−0.384190	−	0.923254i	$-0.625519\pi$
$349$	−2.12956e11	−0.768380	−0.384190	+	0.923254i	$0.625519\pi$
$350$	2.31501e10	0.0824606
$351$	−7.86666e9	−0.0276636
$352$	−4.00145e11	−1.38923
$353$	−4.20619e11	−1.44179	−0.720896	−	0.693043i	$-0.756270\pi$
$353$	−4.20619e11	−1.44179	−0.720896	+	0.693043i	$0.756270\pi$
$354$	4.55213e9	0.0154064
$355$	−7.61754e10	−0.254558
$356$	2.09886e11	0.692560
$357$	0	0
$358$	1.74296e11	0.560807
$359$	6.56670e9	0.0208652	0.0104326	−	0.999946i	$-0.496679\pi$
$359$	6.56670e9	0.0208652	0.0104326	+	0.999946i	$0.496679\pi$
$360$	−3.28961e11	−1.03224
$361$	−3.18542e11	−0.987154
$362$	4.07501e10	0.124721
$363$	−8.95581e9	−0.0270723
$364$	−3.46897e10	−0.103572
$365$	−4.60228e11	−1.35723
$366$	1.23159e9	0.00358756
$367$	−5.62708e11	−1.61914	−0.809572	−	0.587021i	$-0.800301\pi$
$367$	−5.62708e11	−1.61914	−0.809572	+	0.587021i	$0.800301\pi$
$368$	−3.15069e11	−0.895551
$369$	6.08174e11	1.70769
$370$	1.75130e11	0.485793
$371$	−6.95877e9	−0.0190700
$372$	6.57356e9	0.0177974
$373$	3.47635e11	0.929896	0.464948	−	0.885338i	$-0.346073\pi$
$373$	3.47635e11	0.929896	0.464948	+	0.885338i	$0.346073\pi$
$374$	0	0
$375$	2.79968e9	0.00731084
$376$	−1.67686e11	−0.432664
$377$	−2.48285e11	−0.633015
$378$	2.20312e9	0.00555040
$379$	2.78766e11	0.694005	0.347003	−	0.937864i	$-0.387199\pi$
$379$	2.78766e11	0.694005	0.347003	+	0.937864i	$0.387199\pi$
$380$	−5.06899e10	−0.124708
$381$	−1.08864e10	−0.0264680
$382$	9.98365e10	0.239886
$383$	5.20359e11	1.23569	0.617844	−	0.786301i	$-0.288006\pi$
$383$	5.20359e11	1.23569	0.617844	+	0.786301i	$0.288006\pi$
$384$	−1.15859e10	−0.0271919
$385$	−2.00325e11	−0.464689
$386$	−2.53307e10	−0.0580769
$387$	−5.54356e11	−1.25629
$388$	3.29546e11	0.738199
$389$	5.11901e11	1.13348	0.566738	−	0.823898i	$-0.308205\pi$
$389$	5.11901e11	1.13348	0.566738	+	0.823898i	$0.308205\pi$
$390$	−3.58626e9	−0.00784967
$391$	0	0
$392$	−3.38740e11	−0.724568
$393$	1.01921e9	0.00215525
$394$	−3.42114e11	−0.715217
$395$	7.39352e11	1.52815
$396$	5.69013e11	1.16277
$397$	2.70464e11	0.546452	0.273226	−	0.961950i	$-0.411909\pi$
$397$	2.70464e11	0.546452	0.273226	+	0.961950i	$0.411909\pi$
$398$	2.62814e11	0.525018
$399$	3.76386e8	0.000743457 0
$400$	2.01774e11	0.394090
$401$	−1.00714e11	−0.194510	−0.0972548	−	0.995260i	$-0.531006\pi$
$401$	−1.00714e11	−0.194510	−0.0972548	+	0.995260i	$0.531006\pi$
$402$	4.95587e9	0.00946460
$403$	−2.20833e11	−0.417053
$404$	−2.74665e11	−0.512964
$405$	7.24169e11	1.33749
$406$	6.95339e10	0.127008
$407$	−6.71958e11	−1.21386
$408$	0	0
$409$	4.06059e11	0.717521	0.358760	−	0.933430i	$-0.383199\pi$
$409$	4.06059e11	0.717521	0.358760	+	0.933430i	$0.383199\pi$
$410$	5.54709e11	0.969479
$411$	2.94821e10	0.0509649
$412$	−4.32348e9	−0.00739258
$413$	−1.96257e11	−0.331932
$414$	−4.57648e11	−0.765649
$415$	5.91378e11	0.978699
$416$	3.08840e11	0.505607
$417$	9.14208e9	0.0148058
$418$	−4.24429e10	−0.0680004
$419$	−9.21834e11	−1.46113	−0.730566	−	0.682842i	$-0.760744\pi$
$419$	−9.21834e11	−1.46113	−0.730566	+	0.682842i	$0.760744\pi$
$420$	−4.60245e9	−0.00721717
$421$	9.29663e11	1.44230	0.721150	−	0.692778i	$-0.243614\pi$
$421$	9.29663e11	1.44230	0.721150	+	0.692778i	$0.243614\pi$
$422$	4.72506e11	0.725273
$423$	3.69407e11	0.561013
$424$	3.99910e10	0.0600918
$425$	0	0
$426$	−1.46538e9	−0.00215580
$427$	−5.30975e10	−0.0772946
$428$	−1.17816e11	−0.169710
$429$	1.37602e10	0.0196140
$430$	−5.05623e11	−0.713213
$431$	−2.38808e11	−0.333351	−0.166675	−	0.986012i	$-0.553303\pi$
$431$	−2.38808e11	−0.333351	−0.166675	+	0.986012i	$0.553303\pi$
$432$	1.92021e10	0.0265260
$433$	−9.66720e11	−1.32162	−0.660808	−	0.750555i	$-0.729786\pi$
$433$	−9.66720e11	−1.32162	−0.660808	+	0.750555i	$0.729786\pi$
$434$	6.18459e10	0.0836771
$435$	−3.29411e10	−0.0441100
$436$	−1.42967e11	−0.189472
$437$	−1.56428e11	−0.205186
$438$	−8.85337e9	−0.0114941
$439$	−3.49759e11	−0.449447	−0.224724	−	0.974423i	$-0.572148\pi$
$439$	−3.49759e11	−0.449447	−0.224724	+	0.974423i	$0.572148\pi$
$440$	1.15124e12	1.46429
$441$	7.46234e11	0.939510
$442$	0	0
$443$	6.21165e11	0.766285	0.383142	−	0.923689i	$-0.374842\pi$
$443$	6.21165e11	0.766285	0.383142	+	0.923689i	$0.374842\pi$
$444$	−1.54382e10	−0.0188526
$445$	−9.35480e11	−1.13087
$446$	−2.99453e11	−0.358362
$447$	−9.65121e9	−0.0114340
$448$	1.66611e10	0.0195412
$449$	2.15975e11	0.250781	0.125390	−	0.992107i	$-0.459982\pi$
$449$	2.15975e11	0.250781	0.125390	+	0.992107i	$0.459982\pi$
$450$	2.93083e11	0.336926
$451$	−2.12838e12	−2.42245
$452$	−4.22150e11	−0.475712
$453$	4.38808e10	0.0489590
$454$	3.58995e10	0.0396586
$455$	1.54615e11	0.169122
$456$	−2.16303e9	−0.00234272
$457$	−4.26877e11	−0.457804	−0.228902	−	0.973449i	$-0.573514\pi$
$457$	−4.26877e11	−0.457804	−0.228902	+	0.973449i	$0.573514\pi$
$458$	4.73450e11	0.502781
$459$	0	0
$460$	1.91280e12	1.99186
$461$	−1.33434e12	−1.37598	−0.687992	−	0.725718i	$-0.741508\pi$
$461$	−1.33434e12	−1.37598	−0.687992	+	0.725718i	$0.741508\pi$
$462$	−3.85365e9	−0.00393535
$463$	9.52978e11	0.963759	0.481880	−	0.876237i	$-0.339954\pi$
$463$	9.52978e11	0.963759	0.481880	+	0.876237i	$0.339954\pi$
$464$	6.06050e11	0.606985
$465$	−2.92990e10	−0.0290612
$466$	4.93764e11	0.485046
$467$	1.15911e12	1.12772	0.563859	−	0.825871i	$-0.309316\pi$
$467$	1.15911e12	1.12772	0.563859	+	0.825871i	$0.309316\pi$
$468$	−4.39175e11	−0.423186
$469$	−2.13663e11	−0.203916
$470$	3.36932e11	0.318495
$471$	2.30346e10	0.0215669
$472$	1.12786e12	1.04596
$473$	1.94004e12	1.78211
$474$	1.42229e10	0.0129415
$475$	1.00178e11	0.0902926
$476$	0	0
$477$	−8.80989e10	−0.0779180
$478$	5.88273e11	0.515411
$479$	9.36778e11	0.813068	0.406534	−	0.913636i	$-0.366737\pi$
$479$	9.36778e11	0.813068	0.406534	+	0.913636i	$0.366737\pi$
$480$	4.09753e10	0.0352319
$481$	5.18631e11	0.441780
$482$	7.90493e11	0.667093
$483$	−1.42030e10	−0.0118746
$484$	−1.00032e12	−0.828580
$485$	−1.46882e12	−1.20540
$486$	4.18426e10	0.0340216
$487$	−2.11074e12	−1.70041	−0.850207	−	0.526448i	$-0.823523\pi$
$487$	−2.11074e12	−1.70041	−0.850207	+	0.526448i	$0.823523\pi$
$488$	3.05143e11	0.243565
$489$	2.80582e10	0.0221907
$490$	6.80633e11	0.533373
$491$	2.40038e12	1.86386	0.931929	−	0.362641i	$-0.118125\pi$
$491$	2.40038e12	1.86386	0.931929	+	0.362641i	$0.118125\pi$
$492$	−4.88992e10	−0.0376234
$493$	0	0
$494$	3.27583e10	0.0247485
$495$	−2.53614e12	−1.89867
$496$	5.39042e11	0.399904
$497$	6.31772e10	0.0464469
$498$	1.13763e10	0.00828838
$499$	−4.49766e11	−0.324739	−0.162370	−	0.986730i	$-0.551914\pi$
$499$	−4.49766e11	−0.324739	−0.162370	+	0.986730i	$0.551914\pi$
$500$	3.12710e11	0.223757
$501$	3.41936e10	0.0242479
$502$	9.56185e11	0.672009
$503$	1.01494e12	0.706943	0.353471	−	0.935445i	$-0.385001\pi$
$503$	1.01494e12	0.706943	0.353471	+	0.935445i	$0.385001\pi$
$504$	2.72829e11	0.188344
$505$	1.22421e12	0.837614
$506$	1.60159e12	1.08611
$507$	2.92821e10	0.0196818
$508$	−1.21596e12	−0.810085
$509$	5.53282e11	0.365356	0.182678	−	0.983173i	$-0.441523\pi$
$509$	5.53282e11	0.365356	0.182678	+	0.983173i	$0.441523\pi$
$510$	0	0
$511$	3.81697e11	0.247642
$512$	−1.34667e12	−0.866058
$513$	9.53362e9	0.00607757
$514$	3.89916e11	0.246398
$515$	1.92702e10	0.0120713
$516$	4.45721e10	0.0276783
$517$	−1.29278e12	−0.795826
$518$	−1.45246e11	−0.0886383
$519$	−7.88378e10	−0.0476959
$520$	−8.88548e11	−0.532925
$521$	−2.14089e12	−1.27299	−0.636493	−	0.771282i	$-0.719616\pi$
$521$	−2.14089e12	−1.27299	−0.636493	+	0.771282i	$0.719616\pi$
$522$	8.80308e11	0.518940
$523$	3.97935e11	0.232570	0.116285	−	0.993216i	$-0.462901\pi$
$523$	3.97935e11	0.232570	0.116285	+	0.993216i	$0.462901\pi$
$524$	1.13841e11	0.0659639
$525$	9.09579e9	0.00522545
$526$	−3.42193e11	−0.194910
$527$	0	0
$528$	−3.35880e10	−0.0188075
$529$	4.10170e12	2.27726
$530$	−8.03542e10	−0.0442351
$531$	−2.48463e12	−1.35624
$532$	4.20405e10	0.0227544
$533$	1.64272e12	0.881642
$534$	−1.79958e10	−0.00957712
$535$	5.25119e11	0.277118
$536$	1.22789e12	0.642565
$537$	6.84817e10	0.0355378
$538$	1.27155e12	0.654353
$539$	−2.61154e12	−1.33274
$540$	−1.16577e11	−0.0589985
$541$	8.78322e11	0.440825	0.220412	−	0.975407i	$-0.429260\pi$
$541$	8.78322e11	0.440825	0.220412	+	0.975407i	$0.429260\pi$
$542$	1.25670e12	0.625511
$543$	1.60109e10	0.00790345
$544$	0	0
$545$	6.37216e11	0.309387
$546$	2.97432e9	0.00143226
$547$	−2.51249e12	−1.19995	−0.599973	−	0.800021i	$-0.704822\pi$
$547$	−2.51249e12	−1.19995	−0.599973	+	0.800021i	$0.704822\pi$
$548$	3.29301e12	1.55984
$549$	−6.72221e11	−0.315818
$550$	−1.02568e12	−0.477947
$551$	3.00897e11	0.139071
$552$	8.16226e10	0.0374183
$553$	−6.13193e11	−0.278827
$554$	3.54880e11	0.160062
$555$	6.88093e10	0.0307843
$556$	1.02112e12	0.453150
$557$	−3.99416e12	−1.75823	−0.879117	−	0.476606i	$-0.841867\pi$
$557$	−3.99416e12	−1.75823	−0.879117	+	0.476606i	$0.841867\pi$
$558$	7.82976e11	0.341896
$559$	−1.49736e12	−0.648594
$560$	−3.77408e11	−0.162168
$561$	0	0
$562$	−9.74583e11	−0.412103
$563$	3.88071e12	1.62789	0.813943	−	0.580945i	$-0.197317\pi$
$563$	3.88071e12	1.62789	0.813943	+	0.580945i	$0.197317\pi$
$564$	−2.97015e10	−0.0123601
$565$	1.88156e12	0.776785
$566$	−8.94383e11	−0.366311
$567$	−6.00600e11	−0.244040
$568$	−3.63070e11	−0.146360
$569$	1.04083e12	0.416270	0.208135	−	0.978100i	$-0.433261\pi$
$569$	1.04083e12	0.416270	0.208135	+	0.978100i	$0.433261\pi$
$570$	4.34620e9	0.00172454
$571$	−3.42931e12	−1.35003	−0.675017	−	0.737802i	$-0.735864\pi$
$571$	−3.42931e12	−1.35003	−0.675017	+	0.737802i	$0.735864\pi$
$572$	1.53695e12	0.600312
$573$	3.92263e10	0.0152013
$574$	−4.60057e11	−0.176892
$575$	−3.78025e12	−1.44217
$576$	2.10931e11	0.0798434
$577$	−2.26487e12	−0.850652	−0.425326	−	0.905040i	$-0.639841\pi$
$577$	−2.26487e12	−0.850652	−0.425326	+	0.905040i	$0.639841\pi$
$578$	0	0
$579$	−9.95255e9	−0.00368028
$580$	−3.67936e12	−1.35004
$581$	−4.90469e11	−0.178574
$582$	−2.82556e10	−0.0102082
$583$	3.08313e11	0.110531
$584$	−2.19355e12	−0.780351
$585$	1.95745e12	0.691016
$586$	3.78060e11	0.132441
$587$	2.23470e12	0.776870	0.388435	−	0.921476i	$-0.373016\pi$
$587$	2.23470e12	0.776870	0.388435	+	0.921476i	$0.373016\pi$
$588$	−5.99997e10	−0.0206991
$589$	2.67628e11	0.0916247
$590$	−2.26621e12	−0.769957
$591$	−1.34418e11	−0.0453226
$592$	−1.26595e12	−0.423613
$593$	−3.12521e12	−1.03785	−0.518923	−	0.854821i	$-0.673667\pi$
$593$	−3.12521e12	−1.03785	−0.518923	+	0.854821i	$0.673667\pi$
$594$	−9.76104e10	−0.0321704
$595$	0	0
$596$	−1.07799e12	−0.349951
$597$	1.03261e11	0.0332699
$598$	−1.23614e12	−0.395287
$599$	−4.98049e12	−1.58071	−0.790353	−	0.612652i	$-0.790103\pi$
$599$	−4.98049e12	−1.58071	−0.790353	+	0.612652i	$0.790103\pi$
$600$	−5.22721e10	−0.0164660
$601$	−1.92193e12	−0.600901	−0.300451	−	0.953797i	$-0.597137\pi$
$601$	−1.92193e12	−0.600901	−0.300451	+	0.953797i	$0.597137\pi$
$602$	4.19346e11	0.130133
$603$	−2.70500e12	−0.833181
$604$	4.90126e12	1.49845
$605$	4.45852e12	1.35298
$606$	2.35500e10	0.00709356
$607$	1.10595e12	0.330662	0.165331	−	0.986238i	$-0.447131\pi$
$607$	1.10595e12	0.330662	0.165331	+	0.986238i	$0.447131\pi$
$608$	−3.74284e11	−0.111080
$609$	2.73202e10	0.00804835
$610$	−6.13127e11	−0.179294
$611$	9.97796e11	0.289638
$612$	0	0
$613$	−3.38242e12	−0.967511	−0.483755	−	0.875203i	$-0.660728\pi$
$613$	−3.38242e12	−0.967511	−0.483755	+	0.875203i	$0.660728\pi$
$614$	−2.97754e11	−0.0845474
$615$	2.17948e11	0.0614349
$616$	−9.54797e11	−0.267176
$617$	1.73474e12	0.481893	0.240947	−	0.970538i	$-0.422542\pi$
$617$	1.73474e12	0.481893	0.240947	+	0.970538i	$0.422542\pi$
$618$	3.70699e8	0.000102229 0
$619$	−4.13205e12	−1.13125	−0.565624	−	0.824663i	$-0.691365\pi$
$619$	−4.13205e12	−1.13125	−0.565624	+	0.824663i	$0.691365\pi$
$620$	−3.27255e12	−0.889454
$621$	−3.59754e11	−0.0970718
$622$	1.27509e11	0.0341574
$623$	7.75854e11	0.206340
$624$	2.59239e10	0.00684494
$625$	−4.43270e12	−1.16201
$626$	−1.92760e12	−0.501687
$627$	−1.66760e10	−0.00430912
$628$	2.57286e12	0.660081
$629$	0	0
$630$	−5.48197e11	−0.138645
$631$	−1.18926e12	−0.298637	−0.149318	−	0.988789i	$-0.547708\pi$
$631$	−1.18926e12	−0.298637	−0.149318	+	0.988789i	$0.547708\pi$
$632$	3.52392e12	0.878617
$633$	1.85650e11	0.0459599
$634$	−3.46516e11	−0.0851768
$635$	5.41963e12	1.32278
$636$	7.08344e9	0.00171667
$637$	2.01564e12	0.485048
$638$	−3.08074e12	−0.736143
$639$	7.99831e11	0.189777
$640$	5.76787e12	1.35896
$641$	1.36967e12	0.320447	0.160224	−	0.987081i	$-0.448779\pi$
$641$	1.36967e12	0.320447	0.160224	+	0.987081i	$0.448779\pi$
$642$	1.01017e10	0.00234685
$643$	−4.23668e12	−0.977409	−0.488705	−	0.872449i	$-0.662530\pi$
$643$	−4.23668e12	−0.977409	−0.488705	+	0.872449i	$0.662530\pi$
$644$	−1.58641e12	−0.363437
$645$	−1.98662e11	−0.0451956
$646$	0	0
$647$	−7.27863e12	−1.63298	−0.816489	−	0.577361i	$-0.804082\pi$
$647$	−7.27863e12	−1.63298	−0.816489	+	0.577361i	$0.804082\pi$
$648$	3.45155e12	0.769001
$649$	8.69528e12	1.92390
$650$	7.91640e11	0.173947
$651$	2.42996e10	0.00530254
$652$	3.13396e12	0.679172
$653$	2.58771e12	0.556937	0.278468	−	0.960445i	$-0.410173\pi$
$653$	2.58771e12	0.556937	0.278468	+	0.960445i	$0.410173\pi$
$654$	1.22581e10	0.00262013
$655$	−5.07398e11	−0.107712
$656$	−4.00981e12	−0.845388
$657$	4.83233e12	1.01184
$658$	−2.79440e11	−0.0581128
$659$	3.62332e12	0.748381	0.374190	−	0.927352i	$-0.377921\pi$
$659$	3.62332e12	0.748381	0.374190	+	0.927352i	$0.377921\pi$
$660$	2.03914e11	0.0418312
$661$	1.90260e11	0.0387651	0.0193826	−	0.999812i	$-0.493830\pi$
$661$	1.90260e11	0.0387651	0.0193826	+	0.999812i	$0.493830\pi$
$662$	−2.41737e12	−0.489195
$663$	0	0
$664$	2.81865e12	0.562709
$665$	−1.87378e11	−0.0371554
$666$	−1.83884e12	−0.362167
$667$	−1.13544e13	−2.22126
$668$	3.81925e12	0.742137
$669$	−1.17657e11	−0.0227090
$670$	−2.46721e12	−0.473008
$671$	2.35252e12	0.448004
$672$	−3.39835e10	−0.00642845
$673$	1.03919e13	1.95266	0.976332	−	0.216278i	$-0.0693919\pi$
$673$	1.03919e13	1.95266	0.976332	+	0.216278i	$0.0693919\pi$
$674$	1.68508e12	0.314522
$675$	2.30391e11	0.0427167
$676$	3.27066e12	0.602386
$677$	−5.50581e12	−1.00733	−0.503666	−	0.863899i	$-0.668016\pi$
$677$	−5.50581e12	−1.00733	−0.503666	+	0.863899i	$0.668016\pi$
$678$	3.61955e10	0.00657841
$679$	1.21819e12	0.219938
$680$	0	0
$681$	1.41051e10	0.00251313
$682$	−2.74012e12	−0.484998
$683$	1.92719e12	0.338869	0.169434	−	0.985541i	$-0.445806\pi$
$683$	1.92719e12	0.338869	0.169434	+	0.985541i	$0.445806\pi$
$684$	5.32237e11	0.0929722
$685$	−1.46772e13	−2.54705
$686$	−1.16490e12	−0.200831
$687$	1.86021e11	0.0318608
$688$	3.65498e12	0.621924
$689$	−2.37962e11	−0.0402273
$690$	−1.64005e11	−0.0275446
$691$	−1.24650e12	−0.207989	−0.103994	−	0.994578i	$-0.533162\pi$
$691$	−1.24650e12	−0.207989	−0.103994	+	0.994578i	$0.533162\pi$
$692$	−8.80579e12	−1.45979
$693$	2.10339e12	0.346434
$694$	−1.20172e12	−0.196646
$695$	−4.55125e12	−0.739944
$696$	−1.57005e11	−0.0253613
$697$	0	0
$698$	2.03944e12	0.325209
$699$	1.94002e11	0.0307369
$700$	1.01595e12	0.159931
$701$	9.42697e12	1.47449	0.737244	−	0.675627i	$-0.236127\pi$
$701$	9.42697e12	1.47449	0.737244	+	0.675627i	$0.236127\pi$
$702$	7.53376e10	0.0117083
$703$	−6.28530e11	−0.0970570
$704$	−7.38178e11	−0.113262
$705$	1.32382e11	0.0201827
$706$	4.02820e12	0.610224
$707$	−1.01532e12	−0.152832
$708$	1.99773e11	0.0298804
$709$	1.44728e12	0.215103	0.107551	−	0.994200i	$-0.465699\pi$
$709$	1.44728e12	0.215103	0.107551	+	0.994200i	$0.465699\pi$
$710$	7.29519e11	0.107739
$711$	−7.76310e12	−1.13926
$712$	−4.45871e12	−0.650204
$713$	−1.00990e13	−1.46344
$714$	0	0
$715$	−6.85032e12	−0.980243
$716$	7.64907e12	1.08768
$717$	2.31136e11	0.0326611
$718$	−6.28882e10	−0.00883098
$719$	−7.25929e12	−1.01301	−0.506506	−	0.862237i	$-0.669063\pi$
$719$	−7.25929e12	−1.01301	−0.506506	+	0.862237i	$0.669063\pi$
$720$	−4.77803e12	−0.662602
$721$	−1.59820e10	−0.00220253
$722$	3.05062e12	0.417803
$723$	3.10589e11	0.0422730
$724$	1.78834e12	0.241895
$725$	7.27150e12	0.977469
$726$	8.57683e10	0.0114581
$727$	−3.08455e12	−0.409531	−0.204765	−	0.978811i	$-0.565643\pi$
$727$	−3.08455e12	−0.409531	−0.204765	+	0.978811i	$0.565643\pi$
$728$	7.36931e11	0.0972379
$729$	−7.59271e12	−0.995687
$730$	4.40752e12	0.574436
$731$	0	0
$732$	5.40488e10	0.00695803
$733$	3.11662e12	0.398764	0.199382	−	0.979922i	$-0.436106\pi$
$733$	3.11662e12	0.398764	0.199382	+	0.979922i	$0.436106\pi$
$734$	5.38895e12	0.685286
$735$	2.67424e11	0.0337993
$736$	1.41237e13	1.77418
$737$	9.46648e12	1.18191
$738$	−5.82437e12	−0.722762
$739$	4.75055e12	0.585927	0.292964	−	0.956124i	$-0.405359\pi$
$739$	4.75055e12	0.585927	0.292964	+	0.956124i	$0.405359\pi$
$740$	7.68566e12	0.942189
$741$	1.28709e10	0.00156829
$742$	6.66430e10	0.00807118
$743$	7.29991e12	0.878755	0.439377	−	0.898303i	$-0.355199\pi$
$743$	7.29991e12	0.878755	0.439377	+	0.898303i	$0.355199\pi$
$744$	−1.39646e11	−0.0167090
$745$	4.80471e12	0.571432
$746$	−3.32925e12	−0.393569
$747$	−6.20939e12	−0.729636
$748$	0	0
$749$	−4.35515e11	−0.0505633
$750$	−2.68120e10	−0.00309424
$751$	−2.03675e12	−0.233646	−0.116823	−	0.993153i	$-0.537271\pi$
$751$	−2.03675e12	−0.233646	−0.116823	+	0.993153i	$0.537271\pi$
$752$	−2.43557e12	−0.277728
$753$	3.75690e11	0.0425846
$754$	2.37778e12	0.267917
$755$	−2.18454e13	−2.44680
$756$	9.66849e10	0.0107649
$757$	−6.50159e12	−0.719595	−0.359798	−	0.933030i	$-0.617154\pi$
$757$	−6.50159e12	−0.719595	−0.359798	+	0.933030i	$0.617154\pi$
$758$	−2.66969e12	−0.293731
$759$	6.29274e11	0.0688259
$760$	1.07683e12	0.117081
$761$	−9.68338e12	−1.04664	−0.523318	−	0.852137i	$-0.675306\pi$
$761$	−9.68338e12	−1.04664	−0.523318	+	0.852137i	$0.675306\pi$
$762$	1.04257e11	0.0112023
$763$	−5.28485e11	−0.0564510
$764$	4.38138e12	0.465255
$765$	0	0
$766$	−4.98339e12	−0.522992
$767$	−6.71119e12	−0.700197
$768$	9.02957e10	0.00936573
$769$	−3.78295e12	−0.390088	−0.195044	−	0.980795i	$-0.562485\pi$
$769$	−3.78295e12	−0.390088	−0.195044	+	0.980795i	$0.562485\pi$
$770$	1.91848e12	0.196675
$771$	1.53200e11	0.0156140
$772$	−1.11165e12	−0.112639
$773$	−1.52760e13	−1.53887	−0.769435	−	0.638726i	$-0.779462\pi$
$773$	−1.52760e13	−1.53887	−0.769435	+	0.638726i	$0.779462\pi$
$774$	5.30898e12	0.531712
$775$	6.46753e12	0.643992
$776$	−7.00072e12	−0.693051
$777$	−5.70681e10	−0.00561692
$778$	−4.90238e12	−0.479732
$779$	−1.99082e12	−0.193693
$780$	−1.57385e11	−0.0152243
$781$	−2.79911e12	−0.269209
$782$	0	0
$783$	6.92004e11	0.0657931
$784$	−4.92007e12	−0.465103
$785$	−1.14675e13	−1.07784
$786$	−9.76079e9	−0.000912186 0
$787$	1.49696e12	0.139099	0.0695497	−	0.997578i	$-0.477844\pi$
$787$	1.49696e12	0.139099	0.0695497	+	0.997578i	$0.477844\pi$
$788$	−1.50139e13	−1.38715
$789$	−1.34449e11	−0.0123513
$790$	−7.08065e12	−0.646772
$791$	−1.56050e12	−0.141733
$792$	−1.20878e13	−1.09165
$793$	−1.81572e12	−0.163050
$794$	−2.59018e12	−0.231280
$795$	−3.15716e10	−0.00280314
$796$	1.15337e13	1.01827
$797$	−9.20364e12	−0.807974	−0.403987	−	0.914765i	$-0.632376\pi$
$797$	−9.20364e12	−0.807974	−0.403987	+	0.914765i	$0.632376\pi$
$798$	−3.60459e9	−0.000314661 0
$799$	0	0
$800$	−9.04498e12	−0.780734
$801$	9.82241e12	0.843086
$802$	9.64523e11	0.0823242
$803$	−1.69113e13	−1.43535
$804$	2.17491e11	0.0183565
$805$	7.07077e12	0.593452
$806$	2.11488e12	0.176513
$807$	4.99597e11	0.0414657
$808$	5.83485e12	0.481592
$809$	1.38525e13	1.13700	0.568498	−	0.822684i	$-0.307525\pi$
$809$	1.38525e13	1.13700	0.568498	+	0.822684i	$0.307525\pi$
$810$	−6.93524e12	−0.566081
$811$	7.80849e12	0.633831	0.316915	−	0.948454i	$-0.397353\pi$
$811$	7.80849e12	0.633831	0.316915	+	0.948454i	$0.397353\pi$
$812$	3.05153e12	0.246329
$813$	4.93764e11	0.0396380
$814$	6.43523e12	0.513753
$815$	−1.39684e13	−1.10901
$816$	0	0
$817$	1.81465e12	0.142493
$818$	−3.88876e12	−0.303684
$819$	−1.62344e12	−0.126083
$820$	2.43437e13	1.88029
$821$	−4.91660e12	−0.377677	−0.188838	−	0.982008i	$-0.560472\pi$
$821$	−4.91660e12	−0.377677	−0.188838	+	0.982008i	$0.560472\pi$
$822$	−2.82345e11	−0.0215704
$823$	1.09549e13	0.832360	0.416180	−	0.909282i	$-0.363369\pi$
$823$	1.09549e13	0.832360	0.416180	+	0.909282i	$0.363369\pi$
$824$	9.18461e10	0.00694046
$825$	−4.02995e11	−0.0302870
$826$	1.87952e12	0.140487
$827$	2.82911e12	0.210317	0.105159	−	0.994455i	$-0.466465\pi$
$827$	2.82911e12	0.210317	0.105159	+	0.994455i	$0.466465\pi$
$828$	−2.00841e13	−1.48497
$829$	−2.90839e12	−0.213873	−0.106937	−	0.994266i	$-0.534104\pi$
$829$	−2.90839e12	−0.213873	−0.106937	+	0.994266i	$0.534104\pi$
$830$	−5.66353e12	−0.414225
$831$	1.39434e11	0.0101430
$832$	5.69741e11	0.0412214
$833$	0	0
$834$	−8.75521e10	−0.00626642
$835$	−1.70228e13	−1.21183
$836$	−1.86263e12	−0.131886
$837$	6.15492e11	0.0433469
$838$	8.82825e12	0.618410
$839$	−2.60868e13	−1.81757	−0.908787	−	0.417259i	$-0.862991\pi$
$839$	−2.60868e13	−1.81757	−0.908787	+	0.417259i	$0.862991\pi$
$840$	9.77723e10	0.00677577
$841$	7.33362e12	0.505518
$842$	−8.90322e12	−0.610439
$843$	−3.82919e11	−0.0261145
$844$	2.07362e13	1.40666
$845$	−1.45776e13	−0.983630
$846$	−3.53774e12	−0.237443
$847$	−3.69774e12	−0.246866
$848$	5.80854e11	0.0385732
$849$	−3.51408e11	−0.0232127
$850$	0	0
$851$	2.37177e13	1.55021
$852$	−6.43091e10	−0.00418114
$853$	4.84767e12	0.313518	0.156759	−	0.987637i	$-0.449895\pi$
$853$	4.84767e12	0.313518	0.156759	+	0.987637i	$0.449895\pi$
$854$	5.08506e11	0.0327141
$855$	−2.37223e12	−0.151813
$856$	2.50284e12	0.159331
$857$	2.06896e13	1.31020	0.655101	−	0.755541i	$-0.272626\pi$
$857$	2.06896e13	1.31020	0.655101	+	0.755541i	$0.272626\pi$
$858$	−1.31779e11	−0.00830145
$859$	−2.50372e13	−1.56898	−0.784488	−	0.620144i	$-0.787074\pi$
$859$	−2.50372e13	−1.56898	−0.784488	+	0.620144i	$0.787074\pi$
$860$	−2.21896e13	−1.38327
$861$	−1.80759e11	−0.0112095
$862$	2.28703e12	0.141087
$863$	1.89430e13	1.16252	0.581260	−	0.813718i	$-0.302560\pi$
$863$	1.89430e13	1.16252	0.581260	+	0.813718i	$0.302560\pi$
$864$	−8.60780e11	−0.0525509
$865$	3.92482e13	2.38368
$866$	9.25811e12	0.559361
$867$	0	0
$868$	2.71414e12	0.162291
$869$	2.71679e13	1.61610
$870$	3.15472e11	0.0186691
$871$	−7.30642e12	−0.430153
$872$	3.03712e12	0.177884
$873$	1.54224e13	0.898643
$874$	1.49808e12	0.0868429
$875$	1.15595e12	0.0666658
$876$	−3.88535e11	−0.0222927
$877$	1.70384e13	0.972591	0.486295	−	0.873794i	$-0.338348\pi$
$877$	1.70384e13	0.972591	0.486295	+	0.873794i	$0.338348\pi$
$878$	3.34958e12	0.190224
$879$	1.48542e11	0.00839263
$880$	1.67213e13	0.939935
$881$	2.66051e13	1.48790	0.743950	−	0.668235i	$-0.232950\pi$
$881$	2.66051e13	1.48790	0.743950	+	0.668235i	$0.232950\pi$
$882$	−7.14656e12	−0.397638
$883$	1.28352e13	0.710525	0.355263	−	0.934767i	$-0.384391\pi$
$883$	1.28352e13	0.710525	0.355263	+	0.934767i	$0.384391\pi$
$884$	0	0
$885$	−8.90407e11	−0.0487914
$886$	−5.94879e12	−0.324322
$887$	−1.18450e12	−0.0642511	−0.0321255	−	0.999484i	$-0.510228\pi$
$887$	−1.18450e12	−0.0642511	−0.0321255	+	0.999484i	$0.510228\pi$
$888$	3.27961e11	0.0176996
$889$	−4.49485e12	−0.241356
$890$	8.95893e12	0.478631
$891$	2.66100e13	1.41447
$892$	−1.31417e13	−0.695037
$893$	−1.20923e12	−0.0636323
$894$	9.24280e10	0.00483933
$895$	−3.40926e13	−1.77606
$896$	−4.78367e12	−0.247957
$897$	−4.85687e11	−0.0250490
$898$	−2.06835e12	−0.106140
$899$	1.94259e13	0.991890
$900$	1.28621e13	0.653463
$901$	0	0
$902$	2.03831e13	1.02528
$903$	1.64763e11	0.00824643
$904$	8.96796e12	0.446617
$905$	−7.97079e12	−0.394987
$906$	−4.20239e11	−0.0207214
$907$	4.15423e12	0.203825	0.101913	−	0.994793i	$-0.467504\pi$
$907$	4.15423e12	0.203825	0.101913	+	0.994793i	$0.467504\pi$
$908$	1.57547e12	0.0769172
$909$	−1.28540e13	−0.624455
$910$	−1.48072e12	−0.0715793
$911$	7.95629e12	0.382717	0.191359	−	0.981520i	$-0.438711\pi$
$911$	7.95629e12	0.382717	0.191359	+	0.981520i	$0.438711\pi$
$912$	−3.14172e10	−0.00150380
$913$	2.17305e13	1.03503
$914$	4.08812e12	0.193761
$915$	−2.40901e11	−0.0113617
$916$	2.07776e13	0.975137
$917$	4.20819e11	0.0196532
$918$	0	0
$919$	−1.01245e13	−0.468225	−0.234112	−	0.972210i	$-0.575218\pi$
$919$	−1.01245e13	−0.468225	−0.234112	+	0.972210i	$0.575218\pi$
$920$	−4.06346e13	−1.87004
$921$	−1.16989e11	−0.00535769
$922$	1.27788e13	0.582372
$923$	2.16041e12	0.0979778
$924$	−1.69119e11	−0.00763255
$925$	−1.51891e13	−0.682174
$926$	−9.12651e12	−0.407901
$927$	−2.02334e11	−0.00899934
$928$	−2.71676e13	−1.20250
$929$	−3.17571e13	−1.39885	−0.699424	−	0.714707i	$-0.746560\pi$
$929$	−3.17571e13	−1.39885	−0.699424	+	0.714707i	$0.746560\pi$
$930$	2.80591e11	0.0122999
$931$	−2.44275e12	−0.106563
$932$	2.16691e13	0.940739
$933$	5.00990e10	0.00216452
$934$	−1.11006e13	−0.477295
$935$	0	0
$936$	9.32964e12	0.397304
$937$	1.04267e13	0.441897	0.220948	−	0.975286i	$-0.429085\pi$
$937$	1.04267e13	0.441897	0.220948	+	0.975286i	$0.429085\pi$
$938$	2.04621e12	0.0863055
$939$	−7.57364e11	−0.0317914
$940$	1.47865e13	0.617716
$941$	1.39589e13	0.580359	0.290180	−	0.956972i	$-0.406285\pi$
$941$	1.39589e13	0.580359	0.290180	+	0.956972i	$0.406285\pi$
$942$	−2.20599e11	−0.00912797
$943$	7.51242e13	3.09369
$944$	1.63817e13	0.671405
$945$	−4.30934e11	−0.0175779
$946$	−1.85794e13	−0.754261
$947$	3.37968e13	1.36553	0.682764	−	0.730639i	$-0.260778\pi$
$947$	3.37968e13	1.36553	0.682764	+	0.730639i	$0.260778\pi$
$948$	6.24179e11	0.0250999
$949$	1.30525e13	0.522391
$950$	−9.59390e11	−0.0382155
$951$	−1.36148e11	−0.00539757
$952$	0	0
$953$	3.89333e12	0.152898	0.0764492	−	0.997073i	$-0.475642\pi$
$953$	3.89333e12	0.152898	0.0764492	+	0.997073i	$0.475642\pi$
$954$	8.43708e11	0.0329780
$955$	−1.95282e13	−0.759709
$956$	2.58167e13	0.999632
$957$	−1.21044e12	−0.0466487
$958$	−8.97136e12	−0.344123
$959$	1.21728e13	0.464736
$960$	7.55903e10	0.00287240
$961$	−9.16152e12	−0.346507
$962$	−4.96684e12	−0.186979
$963$	−5.51367e12	−0.206596
$964$	3.46912e13	1.29382
$965$	4.95473e12	0.183928
$966$	1.36020e11	0.00502581
$967$	−2.13333e13	−0.784584	−0.392292	−	0.919841i	$-0.628318\pi$
$967$	−2.13333e13	−0.784584	−0.392292	+	0.919841i	$0.628318\pi$
$968$	2.12503e13	0.777905
$969$	0	0
$970$	1.40666e13	0.510172
$971$	6.06046e12	0.218786	0.109393	−	0.993999i	$-0.465109\pi$
$971$	6.06046e12	0.218786	0.109393	+	0.993999i	$0.465109\pi$
$972$	1.83628e12	0.0659845
$973$	3.77465e12	0.135011
$974$	2.02142e13	0.719683
$975$	3.11039e11	0.0110229
$976$	4.43209e12	0.156345
$977$	−3.07781e13	−1.08073	−0.540363	−	0.841432i	$-0.681713\pi$
$977$	−3.07781e13	−1.08073	−0.540363	+	0.841432i	$0.681713\pi$
$978$	−2.68709e11	−0.00939197
$979$	−3.43747e13	−1.19596
$980$	2.98700e13	1.03447
$981$	−6.69068e12	−0.230653
$982$	−2.29880e13	−0.788859
$983$	1.64085e13	0.560504	0.280252	−	0.959927i	$-0.409582\pi$
$983$	1.64085e13	0.560504	0.280252	+	0.959927i	$0.409582\pi$
$984$	1.03879e12	0.0353224
$985$	6.69182e13	2.26507
$986$	0	0
$987$	−1.09793e11	−0.00368255
$988$	1.43761e12	0.0479994
$989$	−6.84764e13	−2.27592
$990$	2.42882e13	0.803595
$991$	−4.00736e13	−1.31986	−0.659928	−	0.751329i	$-0.729413\pi$
$991$	−4.00736e13	−1.31986	−0.659928	+	0.751329i	$0.729413\pi$
$992$	−2.41638e13	−0.792252
$993$	−9.49797e11	−0.0309998
$994$	−6.05038e11	−0.0196582
$995$	−5.14069e13	−1.66271
$996$	4.99256e11	0.0160752
$997$	−5.15990e13	−1.65391	−0.826957	−	0.562266i	$-0.809930\pi$
$997$	−5.15990e13	−1.65391	−0.826957	+	0.562266i	$0.809930\pi$
$998$	4.30734e12	0.137443
$999$	−1.44550e12	−0.0459169

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.f.1.11		24
17.2	even	8		17.10.c.a.4.6	✓	24
17.9	even	8		17.10.c.a.13.7	yes	24
17.16	even	2	inner	289.10.a.f.1.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.6	✓	24	17.2	even	8
17.10.c.a.13.7	yes	24	17.9	even	8
289.10.a.f.1.11		24	1.1	even	1	trivial
289.10.a.f.1.12		24	17.16	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-9.57683 q^{2} -3.76279 q^{3} -420.284 q^{4} +1873.25 q^{5} +36.0355 q^{6} -1553.61 q^{7} +8928.33 q^{8} -19668.8 q^{9} +O(q^{10})\)	\(q-9.57683 q^{2} -3.76279 q^{3} -420.284 q^{4} +1873.25 q^{5} +36.0355 q^{6} -1553.61 q^{7} +8928.33 q^{8} -19668.8 q^{9} -17939.8 q^{10} +68833.5 q^{11} +1581.44 q^{12} -53127.1 q^{13} +14878.6 q^{14} -7048.63 q^{15} +129681. q^{16} +188365. q^{18} +64384.8 q^{19} -787297. q^{20} +5845.89 q^{21} -659207. q^{22} -2.42958e6 q^{23} -33595.4 q^{24} +1.55593e6 q^{25} +508789. q^{26} +148073. q^{27} +652956. q^{28} +4.67341e6 q^{29} +67503.5 q^{30} +4.15669e6 q^{31} -5.81323e6 q^{32} -259006. q^{33} -2.91029e6 q^{35} +8.26651e6 q^{36} -9.76209e6 q^{37} -616602. q^{38} +199906. q^{39} +1.67250e7 q^{40} -3.09207e7 q^{41} -55985.1 q^{42} +2.81845e7 q^{43} -2.89296e7 q^{44} -3.68446e7 q^{45} +2.32677e7 q^{46} -1.87813e7 q^{47} -487960. q^{48} -3.79399e7 q^{49} -1.49009e7 q^{50} +2.23285e7 q^{52} +4.47911e6 q^{53} -1.41807e6 q^{54} +1.28942e8 q^{55} -1.38711e7 q^{56} -242266. q^{57} -4.47565e7 q^{58} +1.26323e8 q^{59} +2.96243e6 q^{60} +3.41770e7 q^{61} -3.98079e7 q^{62} +3.05576e7 q^{63} -1.07241e7 q^{64} -9.95201e7 q^{65} +2.48045e6 q^{66} +1.37527e8 q^{67} +9.14198e6 q^{69} +2.78713e7 q^{70} -4.06649e7 q^{71} -1.75610e8 q^{72} -2.45684e8 q^{73} +9.34898e7 q^{74} -5.85463e6 q^{75} -2.70599e7 q^{76} -1.06940e8 q^{77} -1.91446e6 q^{78} +3.94690e8 q^{79} +2.42924e8 q^{80} +3.86585e8 q^{81} +2.96122e8 q^{82} +3.15697e8 q^{83} -2.45693e6 q^{84} -2.69918e8 q^{86} -1.75850e7 q^{87} +6.14568e8 q^{88} -4.99389e8 q^{89} +3.52854e8 q^{90} +8.25385e7 q^{91} +1.02111e9 q^{92} -1.56407e7 q^{93} +1.79865e8 q^{94} +1.20609e8 q^{95} +2.18739e7 q^{96} -7.84102e8 q^{97} +3.63344e8 q^{98} -1.35388e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) \) 24 * q + 5124 * q^4 + 108368 * q^9	\( 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) \) 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more