LMFDB - Embedded newform 289.10.a.c.1.4

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 122690 x^{10} + 5157152560 x^{8} - 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 $ x^12 - 122690x^10 + 5157152560x^8 - 87983684680032x^6 + 612743619071665152x^4 - 1335826553351738886144*x^2 + 203949399568932198678528
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-225.146$ of defining polynomial
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)

$f(q)$	$=$	$q-25.8215 q^{2} +225.146 q^{3} +154.751 q^{4} +96.4328 q^{5} -5813.61 q^{6} -1385.77 q^{7} +9224.72 q^{8} +31007.8 q^{9} +O(q^{10})$	\(q-25.8215 q^{2} +225.146 q^{3} +154.751 q^{4} +96.4328 q^{5} -5813.61 q^{6} -1385.77 q^{7} +9224.72 q^{8} +31007.8 q^{9} -2490.04 q^{10} -33833.7 q^{11} +34841.5 q^{12} +138558. q^{13} +35782.8 q^{14} +21711.5 q^{15} -317429. q^{16} -800668. q^{18} -429726. q^{19} +14923.1 q^{20} -312001. q^{21} +873638. q^{22} +352831. q^{23} +2.07691e6 q^{24} -1.94383e6 q^{25} -3.57778e6 q^{26} +2.54973e6 q^{27} -214449. q^{28} -508224. q^{29} -560623. q^{30} -8.73026e6 q^{31} +3.47343e6 q^{32} -7.61753e6 q^{33} -133634. q^{35} +4.79848e6 q^{36} +1.62218e7 q^{37} +1.10962e7 q^{38} +3.11958e7 q^{39} +889565. q^{40} +1.12435e7 q^{41} +8.05635e6 q^{42} +2.43795e7 q^{43} -5.23579e6 q^{44} +2.99017e6 q^{45} -9.11064e6 q^{46} -1.11673e7 q^{47} -7.14678e7 q^{48} -3.84332e7 q^{49} +5.01925e7 q^{50} +2.14420e7 q^{52} -3.54297e7 q^{53} -6.58378e7 q^{54} -3.26268e6 q^{55} -1.27834e7 q^{56} -9.67510e7 q^{57} +1.31231e7 q^{58} -5.03437e7 q^{59} +3.35987e6 q^{60} -1.53033e8 q^{61} +2.25429e8 q^{62} -4.29697e7 q^{63} +7.28341e7 q^{64} +1.33615e7 q^{65} +1.96696e8 q^{66} -2.44023e8 q^{67} +7.94386e7 q^{69} +3.45063e6 q^{70} -3.78713e8 q^{71} +2.86038e8 q^{72} +1.38738e7 q^{73} -4.18871e8 q^{74} -4.37645e8 q^{75} -6.65004e7 q^{76} +4.68858e7 q^{77} -8.05523e8 q^{78} +5.65164e8 q^{79} -3.06105e7 q^{80} -3.62648e7 q^{81} -2.90325e8 q^{82} +5.68408e8 q^{83} -4.82825e7 q^{84} -6.29517e8 q^{86} -1.14425e8 q^{87} -3.12106e8 q^{88} +2.61194e8 q^{89} -7.72106e7 q^{90} -1.92010e8 q^{91} +5.46009e7 q^{92} -1.96558e9 q^{93} +2.88357e8 q^{94} -4.14396e7 q^{95} +7.82030e8 q^{96} -1.04492e9 q^{97} +9.92405e8 q^{98} -1.04911e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9}+O(q^{10}) $ 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9	$ 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9} - 63204 q^{13} + 243480 q^{15} + 38978 q^{16} + 547706 q^{18} - 1110672 q^{19} - 172580 q^{21} + 4441796 q^{25} - 1336332 q^{26} - 500496 q^{30} + 1934850 q^{32} - 6557404 q^{33} + 3519864 q^{35} - 30244102 q^{36} + 28748136 q^{38} + 11901296 q^{42} - 10004616 q^{43} - 112552440 q^{47} - 121354720 q^{49} - 164889018 q^{50} - 59093180 q^{52} - 76804272 q^{53} + 300732568 q^{55} - 11618904 q^{59} - 101609232 q^{60} - 260062974 q^{64} - 18429632 q^{66} - 304208752 q^{67} - 211308236 q^{69} - 460311456 q^{70} + 493218954 q^{72} - 416024248 q^{76} - 138357828 q^{77} - 363335792 q^{81} + 845042136 q^{83} + 958037984 q^{84} + 127952904 q^{86} - 610860648 q^{87} - 938223804 q^{89} - 1635779524 q^{93} + 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) $ 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9 - 63204 * q^13 + 243480 * q^15 + 38978 * q^16 + 547706 * q^18 - 1110672 * q^19 - 172580 * q^21 + 4441796 * q^25 - 1336332 * q^26 - 500496 * q^30 + 1934850 * q^32 - 6557404 * q^33 + 3519864 * q^35 - 30244102 * q^36 + 28748136 * q^38 + 11901296 * q^42 - 10004616 * q^43 - 112552440 * q^47 - 121354720 * q^49 - 164889018 * q^50 - 59093180 * q^52 - 76804272 * q^53 + 300732568 * q^55 - 11618904 * q^59 - 101609232 * q^60 - 260062974 * q^64 - 18429632 * q^66 - 304208752 * q^67 - 211308236 * q^69 - 460311456 * q^70 + 493218954 * q^72 - 416024248 * q^76 - 138357828 * q^77 - 363335792 * q^81 + 845042136 * q^83 + 958037984 * q^84 + 127952904 * q^86 - 610860648 * q^87 - 938223804 * q^89 - 1635779524 * q^93 + 238629952 * q^94 - 152046078 * 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 $

$2$	−25.8215	−1.14116	−0.570580	−	0.821242i	$-0.693282\pi$
$2$	−25.8215	−1.14116	−0.570580	+	0.821242i	$0.693282\pi$
$3$	225.146	1.60479	0.802396	−	0.596792i	$-0.203558\pi$
$3$	225.146	1.60479	0.802396	+	0.596792i	$0.203558\pi$
$4$	154.751	0.302248
$5$	96.4328	0.0690017	0.0345009	−	0.999405i	$-0.489016\pi$
$5$	96.4328	0.0690017	0.0345009	+	0.999405i	$0.489016\pi$
$6$	−5813.61	−1.83133
$7$	−1385.77	−0.218148	−0.109074	−	0.994034i	$-0.534789\pi$
$7$	−1385.77	−0.218148	−0.109074	+	0.994034i	$0.534789\pi$
$8$	9224.72	0.796248
$9$	31007.8	1.57536
$10$	−2490.04	−0.0787420
$11$	−33833.7	−0.696759	−0.348379	−	0.937354i	$-0.613268\pi$
$11$	−33833.7	−0.696759	−0.348379	+	0.937354i	$0.613268\pi$
$12$	34841.5	0.485045
$13$	138558.	1.34551	0.672755	−	0.739866i	$-0.265111\pi$
$13$	138558.	1.34551	0.672755	+	0.739866i	$0.265111\pi$
$14$	35782.8	0.248942
$15$	21711.5	0.110733
$16$	−317429.	−1.21089
$17$	0	0
$17$	0	0
$18$	−800668.	−1.79774
$19$	−429726.	−0.756484	−0.378242	−	0.925707i	$-0.623471\pi$
$19$	−429726.	−0.756484	−0.378242	+	0.925707i	$0.623471\pi$
$20$	14923.1	0.0208556
$21$	−312001.	−0.350082
$22$	873638.	0.795114
$23$	352831.	0.262901	0.131450	−	0.991323i	$-0.458037\pi$
$23$	352831.	0.262901	0.131450	+	0.991323i	$0.458037\pi$
$24$	2.07691e6	1.27781
$25$	−1.94383e6	−0.995239
$26$	−3.57778e6	−1.53544
$27$	2.54973e6	0.923330
$28$	−214449.	−0.0659347
$29$	−508224.	−0.133433	−0.0667166	−	0.997772i	$-0.521252\pi$
$29$	−508224.	−0.133433	−0.0667166	+	0.997772i	$0.521252\pi$
$30$	−560623.	−0.126365
$31$	−8.73026e6	−1.69785	−0.848925	−	0.528513i	$-0.822750\pi$
$31$	−8.73026e6	−1.69785	−0.848925	+	0.528513i	$0.822750\pi$
$32$	3.47343e6	0.585577
$33$	−7.61753e6	−1.11815
$34$	0	0
$35$	−133634.	−0.0150526
$36$	4.79848e6	0.476148
$37$	1.62218e7	1.42295	0.711476	−	0.702710i	$-0.248027\pi$
$37$	1.62218e7	1.42295	0.711476	+	0.702710i	$0.248027\pi$
$38$	1.10962e7	0.863270
$39$	3.11958e7	2.15926
$40$	889565.	0.0549424
$41$	1.12435e7	0.621406	0.310703	−	0.950507i	$-0.399436\pi$
$41$	1.12435e7	0.621406	0.310703	+	0.950507i	$0.399436\pi$
$42$	8.05635e6	0.399500
$43$	2.43795e7	1.08747	0.543735	−	0.839257i	$-0.317010\pi$
$43$	2.43795e7	1.08747	0.543735	+	0.839257i	$0.317010\pi$
$44$	−5.23579e6	−0.210594
$45$	2.99017e6	0.108702
$46$	−9.11064e6	−0.300012
$47$	−1.11673e7	−0.333817	−0.166909	−	0.985972i	$-0.553379\pi$
$47$	−1.11673e7	−0.333817	−0.166909	+	0.985972i	$0.553379\pi$
$48$	−7.14678e7	−1.94323
$49$	−3.84332e7	−0.952412
$50$	5.01925e7	1.13573
$51$	0	0
$52$	2.14420e7	0.406677
$53$	−3.54297e7	−0.616774	−0.308387	−	0.951261i	$-0.599789\pi$
$53$	−3.54297e7	−0.616774	−0.308387	+	0.951261i	$0.599789\pi$
$54$	−6.58378e7	−1.05367
$55$	−3.26268e6	−0.0480775
$56$	−1.27834e7	−0.173700
$57$	−9.67510e7	−1.21400
$58$	1.31231e7	0.152269
$59$	−5.03437e7	−0.540893	−0.270446	−	0.962735i	$-0.587171\pi$
$59$	−5.03437e7	−0.540893	−0.270446	+	0.962735i	$0.587171\pi$
$60$	3.35987e6	0.0334689
$61$	−1.53033e8	−1.41515	−0.707574	−	0.706639i	$-0.750211\pi$
$61$	−1.53033e8	−1.41515	−0.707574	+	0.706639i	$0.750211\pi$
$62$	2.25429e8	1.93752
$63$	−4.29697e7	−0.343661
$64$	7.28341e7	0.542656
$65$	1.33615e7	0.0928425
$66$	1.96696e8	1.27599
$67$	−2.44023e8	−1.47943	−0.739713	−	0.672922i	$-0.765039\pi$
$67$	−2.44023e8	−1.47943	−0.739713	+	0.672922i	$0.765039\pi$
$68$	0	0
$69$	7.94386e7	0.421901
$70$	3.45063e6	0.0171774
$71$	−3.78713e8	−1.76867	−0.884337	−	0.466850i	$-0.845389\pi$
$71$	−3.78713e8	−1.76867	−0.884337	+	0.466850i	$0.845389\pi$
$72$	2.86038e8	1.25437
$73$	1.38738e7	0.0571798	0.0285899	−	0.999591i	$-0.490898\pi$
$73$	1.38738e7	0.0571798	0.0285899	+	0.999591i	$0.490898\pi$
$74$	−4.18871e8	−1.62382
$75$	−4.37645e8	−1.59715
$76$	−6.65004e7	−0.228646
$77$	4.68858e7	0.151996
$78$	−8.05523e8	−2.46407
$79$	5.65164e8	1.63250	0.816250	−	0.577700i	$-0.196049\pi$
$79$	5.65164e8	1.63250	0.816250	+	0.577700i	$0.196049\pi$
$80$	−3.06105e7	−0.0835537
$81$	−3.62648e7	−0.0936057
$82$	−2.90325e8	−0.709124
$83$	5.68408e8	1.31465	0.657323	−	0.753609i	$-0.271689\pi$
$83$	5.68408e8	1.31465	0.657323	+	0.753609i	$0.271689\pi$
$84$	−4.82825e7	−0.105811
$85$	0	0
$86$	−6.29517e8	−1.24098
$87$	−1.14425e8	−0.214133
$88$	−3.12106e8	−0.554792
$89$	2.61194e8	0.441275	0.220637	−	0.975356i	$-0.429186\pi$
$89$	2.61194e8	0.441275	0.220637	+	0.975356i	$0.429186\pi$
$90$	−7.72106e7	−0.124047
$91$	−1.92010e8	−0.293520
$92$	5.46009e7	0.0794611
$93$	−1.96558e9	−2.72470
$94$	2.88357e8	0.380939
$95$	−4.14396e7	−0.0521987
$96$	7.82030e8	0.939730
$97$	−1.04492e9	−1.19842	−0.599212	−	0.800590i	$-0.704519\pi$
$97$	−1.04492e9	−1.19842	−0.599212	+	0.800590i	$0.704519\pi$
$98$	9.92405e8	1.08685
$99$	−1.04911e9	−1.09764
$100$	−3.00809e8	−0.300809
$101$	2.97630e7	0.0284597	0.0142299	−	0.999899i	$-0.495470\pi$
$101$	2.97630e7	0.0284597	0.0142299	+	0.999899i	$0.495470\pi$
$102$	0	0
$103$	1.60523e9	1.40530	0.702650	−	0.711536i	$-0.252000\pi$
$103$	1.60523e9	1.40530	0.702650	+	0.711536i	$0.252000\pi$
$104$	1.27816e9	1.07136
$105$	−3.00872e7	−0.0241562
$106$	9.14849e8	0.703838
$107$	2.35483e9	1.73673	0.868365	−	0.495925i	$-0.165171\pi$
$107$	2.35483e9	1.73673	0.868365	+	0.495925i	$0.165171\pi$
$108$	3.94572e8	0.279074
$109$	1.68886e9	1.14597	0.572985	−	0.819566i	$-0.305785\pi$
$109$	1.68886e9	1.14597	0.572985	+	0.819566i	$0.305785\pi$
$110$	8.42473e7	0.0548642
$111$	3.65227e9	2.28354
$112$	4.39884e8	0.264154
$113$	−2.39661e9	−1.38275	−0.691375	−	0.722496i	$-0.742995\pi$
$113$	−2.39661e9	−1.38275	−0.691375	+	0.722496i	$0.742995\pi$
$114$	2.49826e9	1.38537
$115$	3.40245e7	0.0181406
$116$	−7.86480e7	−0.0403299
$117$	4.29638e9	2.11966
$118$	1.29995e9	0.617245
$119$	0	0
$120$	2.00282e8	0.0881712
$121$	−1.21323e9	−0.514527
$122$	3.95156e9	1.61491
$123$	2.53144e9	0.997227
$124$	−1.35101e9	−0.513171
$125$	−3.75794e8	−0.137675
$126$	1.10954e9	0.392172
$127$	−4.20715e9	−1.43506	−0.717532	−	0.696526i	$-0.754728\pi$
$127$	−4.20715e9	−1.43506	−0.717532	+	0.696526i	$0.754728\pi$
$128$	−3.65909e9	−1.20484
$129$	5.48896e9	1.74516
$130$	−3.45015e8	−0.105948
$131$	−1.46332e9	−0.434129	−0.217064	−	0.976157i	$-0.569648\pi$
$131$	−1.46332e9	−0.434129	−0.217064	+	0.976157i	$0.569648\pi$
$132$	−1.17882e9	−0.337959
$133$	5.95502e8	0.165025
$134$	6.30103e9	1.68826
$135$	2.45877e8	0.0637113
$136$	0	0
$137$	−4.13890e9	−1.00379	−0.501894	−	0.864929i	$-0.667363\pi$
$137$	−4.13890e9	−1.00379	−0.501894	+	0.864929i	$0.667363\pi$
$138$	−2.05122e9	−0.481457
$139$	−1.74238e9	−0.395892	−0.197946	−	0.980213i	$-0.563427\pi$
$139$	−1.74238e9	−0.395892	−0.197946	+	0.980213i	$0.563427\pi$
$140$	−2.06800e7	−0.00454960
$141$	−2.51428e9	−0.535708
$142$	9.77895e9	2.01834
$143$	−4.68793e9	−0.937496
$144$	−9.84275e9	−1.90759
$145$	−4.90094e7	−0.00920712
$146$	−3.58243e8	−0.0652514
$147$	−8.65309e9	−1.52842
$148$	2.51033e9	0.430084
$149$	4.80220e9	0.798183	0.399092	−	0.916911i	$-0.369326\pi$
$149$	4.80220e9	0.798183	0.399092	+	0.916911i	$0.369326\pi$
$150$	1.13007e10	1.82261
$151$	−1.22756e9	−0.192152	−0.0960762	−	0.995374i	$-0.530629\pi$
$151$	−1.22756e9	−0.192152	−0.0960762	+	0.995374i	$0.530629\pi$
$152$	−3.96410e9	−0.602349
$153$	0	0
$154$	−1.21066e9	−0.173452
$155$	−8.41883e8	−0.117155
$156$	4.82758e9	0.652632
$157$	1.72654e9	0.226792	0.113396	−	0.993550i	$-0.463827\pi$
$157$	1.72654e9	0.226792	0.113396	+	0.993550i	$0.463827\pi$
$158$	−1.45934e10	−1.86294
$159$	−7.97686e9	−0.989794
$160$	3.34953e8	0.0404058
$161$	−4.88944e8	−0.0573512
$162$	9.36411e8	0.106819
$163$	2.27451e9	0.252374	0.126187	−	0.992006i	$-0.459726\pi$
$163$	2.27451e9	0.252374	0.126187	+	0.992006i	$0.459726\pi$
$164$	1.73995e9	0.187818
$165$	−7.34580e8	−0.0771545
$166$	−1.46772e10	−1.50022
$167$	1.42586e10	1.41857	0.709286	−	0.704921i	$-0.249018\pi$
$167$	1.42586e10	1.41857	0.709286	+	0.704921i	$0.249018\pi$
$168$	−2.87812e9	−0.278752
$169$	8.59384e9	0.810396
$170$	0	0
$171$	−1.33248e10	−1.19173
$172$	3.77275e9	0.328685
$173$	−6.92744e9	−0.587984	−0.293992	−	0.955808i	$-0.594984\pi$
$173$	−6.92744e9	−0.587984	−0.293992	+	0.955808i	$0.594984\pi$
$174$	2.95462e9	0.244360
$175$	2.69370e9	0.217109
$176$	1.07398e10	0.843701
$177$	−1.13347e10	−0.868020
$178$	−6.74444e9	−0.503565
$179$	−1.32700e10	−0.966120	−0.483060	−	0.875587i	$-0.660475\pi$
$179$	−1.32700e10	−0.966120	−0.483060	+	0.875587i	$0.660475\pi$
$180$	4.62731e8	0.0328550
$181$	−8.95066e9	−0.619871	−0.309936	−	0.950758i	$-0.600308\pi$
$181$	−8.95066e9	−0.619871	−0.309936	+	0.950758i	$0.600308\pi$
$182$	4.95799e9	0.334953
$183$	−3.44549e10	−2.27102
$184$	3.25477e9	0.209334
$185$	1.56431e9	0.0981861
$186$	5.07544e10	3.10932
$187$	0	0
$188$	−1.72815e9	−0.100896
$189$	−3.53334e9	−0.201422
$190$	1.07003e9	0.0595671
$191$	−2.10560e9	−0.114479	−0.0572394	−	0.998360i	$-0.518230\pi$
$191$	−2.10560e9	−0.114479	−0.0572394	+	0.998360i	$0.518230\pi$
$192$	1.63983e10	0.870851
$193$	−5.10730e9	−0.264962	−0.132481	−	0.991186i	$-0.542294\pi$
$193$	−5.10730e9	−0.264962	−0.132481	+	0.991186i	$0.542294\pi$
$194$	2.69815e10	1.36760
$195$	3.00830e9	0.148993
$196$	−5.94758e9	−0.287864
$197$	1.85517e10	0.877578	0.438789	−	0.898590i	$-0.355408\pi$
$197$	1.85517e10	0.877578	0.438789	+	0.898590i	$0.355408\pi$
$198$	2.70896e10	1.25259
$199$	−1.37208e10	−0.620211	−0.310105	−	0.950702i	$-0.600364\pi$
$199$	−1.37208e10	−0.620211	−0.310105	+	0.950702i	$0.600364\pi$
$200$	−1.79312e10	−0.792456
$201$	−5.49407e10	−2.37417
$202$	−7.68527e8	−0.0324771
$203$	7.04282e8	0.0291082
$204$	0	0
$205$	1.08425e9	0.0428781
$206$	−4.14494e10	−1.60367
$207$	1.09405e10	0.414163
$208$	−4.39823e10	−1.62927
$209$	1.45392e10	0.527087
$210$	7.76896e8	0.0275662
$211$	6.12032e9	0.212570	0.106285	−	0.994336i	$-0.466104\pi$
$211$	6.12032e9	0.212570	0.106285	+	0.994336i	$0.466104\pi$
$212$	−5.48278e9	−0.186419
$213$	−8.52658e10	−2.83835
$214$	−6.08053e10	−1.98189
$215$	2.35099e9	0.0750373
$216$	2.35205e10	0.735199
$217$	1.20982e10	0.370382
$218$	−4.36088e10	−1.30774
$219$	3.12363e9	0.0917617
$220$	−5.04902e8	−0.0145313
$221$	0	0
$222$	−9.43071e10	−2.60589
$223$	6.31228e9	0.170928	0.0854642	−	0.996341i	$-0.472763\pi$
$223$	6.31228e9	0.170928	0.0854642	+	0.996341i	$0.472763\pi$
$224$	−4.81339e9	−0.127742
$225$	−6.02737e10	−1.56786
$226$	6.18840e10	1.57794
$227$	−5.43032e10	−1.35740	−0.678702	−	0.734413i	$-0.737457\pi$
$227$	−5.43032e10	−1.35740	−0.678702	+	0.734413i	$0.737457\pi$
$228$	−1.49723e10	−0.366929
$229$	1.03751e10	0.249306	0.124653	−	0.992200i	$-0.460218\pi$
$229$	1.03751e10	0.249306	0.124653	+	0.992200i	$0.460218\pi$
$230$	−8.78564e8	−0.0207013
$231$	1.05562e10	0.243923
$232$	−4.68822e9	−0.106246
$233$	−5.93158e10	−1.31846	−0.659232	−	0.751939i	$-0.729119\pi$
$233$	−5.93158e10	−1.31846	−0.659232	+	0.751939i	$0.729119\pi$
$234$	−1.10939e11	−2.41887
$235$	−1.07690e9	−0.0230340
$236$	−7.79073e9	−0.163484
$237$	1.27245e11	2.61982
$238$	0	0
$239$	−6.57143e10	−1.30278	−0.651388	−	0.758745i	$-0.725813\pi$
$239$	−6.57143e10	−1.30278	−0.651388	+	0.758745i	$0.725813\pi$
$240$	−6.89184e9	−0.134086
$241$	−2.02970e10	−0.387574	−0.193787	−	0.981044i	$-0.562077\pi$
$241$	−2.02970e10	−0.387574	−0.193787	+	0.981044i	$0.562077\pi$
$242$	3.13274e10	0.587158
$243$	−5.83511e10	−1.07355
$244$	−2.36820e10	−0.427725
$245$	−3.70623e9	−0.0657180
$246$	−6.53655e10	−1.13800
$247$	−5.95420e10	−1.01786
$248$	−8.05342e10	−1.35191
$249$	1.27975e11	2.10974
$250$	9.70357e9	0.157109
$251$	−8.71654e10	−1.38616	−0.693078	−	0.720863i	$-0.743746\pi$
$251$	−8.71654e10	−1.38616	−0.693078	+	0.720863i	$0.743746\pi$
$252$	−6.64960e9	−0.103871
$253$	−1.19376e10	−0.183178
$254$	1.08635e11	1.63764
$255$	0	0
$256$	5.71921e10	0.832254
$257$	1.20306e10	0.172023	0.0860115	−	0.996294i	$-0.472588\pi$
$257$	1.20306e10	0.172023	0.0860115	+	0.996294i	$0.472588\pi$
$258$	−1.41733e11	−1.99151
$259$	−2.24797e10	−0.310414
$260$	2.06771e9	0.0280614
$261$	−1.57589e10	−0.210205
$262$	3.77851e10	0.495411
$263$	−3.51365e10	−0.452853	−0.226426	−	0.974028i	$-0.572704\pi$
$263$	−3.51365e10	−0.452853	−0.226426	+	0.974028i	$0.572704\pi$
$264$	−7.02695e10	−0.890327
$265$	−3.41659e9	−0.0425585
$266$	−1.53768e10	−0.188321
$267$	5.88069e10	0.708154
$268$	−3.77627e10	−0.447153
$269$	8.30055e10	0.966544	0.483272	−	0.875470i	$-0.339448\pi$
$269$	8.30055e10	0.966544	0.483272	+	0.875470i	$0.339448\pi$
$270$	−6.34893e9	−0.0727048
$271$	−5.57473e10	−0.627858	−0.313929	−	0.949446i	$-0.601645\pi$
$271$	−5.57473e10	−0.627858	−0.313929	+	0.949446i	$0.601645\pi$
$272$	0	0
$273$	−4.32303e10	−0.471038
$274$	1.06873e11	1.14548
$275$	6.57668e10	0.693441
$276$	1.22932e10	0.127519
$277$	−1.84969e11	−1.88773	−0.943864	−	0.330333i	$-0.892839\pi$
$277$	−1.84969e11	−1.88773	−0.943864	+	0.330333i	$0.892839\pi$
$278$	4.49910e10	0.451777
$279$	−2.70706e11	−2.67472
$280$	−1.23274e9	−0.0119856
$281$	1.35823e11	1.29956	0.649778	−	0.760124i	$-0.274862\pi$
$281$	1.35823e11	1.29956	0.649778	+	0.760124i	$0.274862\pi$
$282$	6.49225e10	0.611328
$283$	−5.85987e10	−0.543062	−0.271531	−	0.962430i	$-0.587530\pi$
$283$	−5.85987e10	−0.543062	−0.271531	+	0.962430i	$0.587530\pi$
$284$	−5.86061e10	−0.534577
$285$	−9.32997e9	−0.0837681
$286$	1.21050e11	1.06983
$287$	−1.55810e10	−0.135558
$288$	1.07703e11	0.922493
$289$	0	0
$290$	1.26550e9	0.0105068
$291$	−2.35260e11	−1.92322
$292$	2.14698e9	0.0172825
$293$	−5.48232e10	−0.434571	−0.217285	−	0.976108i	$-0.569720\pi$
$293$	−5.48232e10	−0.434571	−0.217285	+	0.976108i	$0.569720\pi$
$294$	2.23436e11	1.74418
$295$	−4.85478e9	−0.0373225
$296$	1.49641e11	1.13302
$297$	−8.62667e10	−0.643338
$298$	−1.24000e11	−0.910855
$299$	4.88876e10	0.353735
$300$	−6.77259e10	−0.482735
$301$	−3.37845e10	−0.237229
$302$	3.16974e10	0.219277
$303$	6.70103e9	0.0456720
$304$	1.36407e11	0.916023
$305$	−1.47574e10	−0.0976477
$306$	0	0
$307$	−1.88055e11	−1.20826	−0.604132	−	0.796884i	$-0.706480\pi$
$307$	−1.88055e11	−1.20826	−0.604132	+	0.796884i	$0.706480\pi$
$308$	7.25562e9	0.0459406
$309$	3.61411e11	2.25521
$310$	2.17387e10	0.133692
$311$	−1.81717e11	−1.10147	−0.550737	−	0.834679i	$-0.685653\pi$
$311$	−1.81717e11	−1.10147	−0.550737	+	0.834679i	$0.685653\pi$
$312$	2.87773e11	1.71931
$313$	2.21549e11	1.30473	0.652364	−	0.757905i	$-0.273777\pi$
$313$	2.21549e11	1.30473	0.652364	+	0.757905i	$0.273777\pi$
$314$	−4.45819e10	−0.258807
$315$	−4.14369e9	−0.0237132
$316$	8.74597e10	0.493419
$317$	−2.66841e11	−1.48418	−0.742089	−	0.670301i	$-0.766165\pi$
$317$	−2.66841e11	−1.48418	−0.742089	+	0.670301i	$0.766165\pi$
$318$	2.05975e11	1.12951
$319$	1.71951e10	0.0929708
$320$	7.02360e9	0.0374442
$321$	5.30181e11	2.78709
$322$	1.26253e10	0.0654469
$323$	0	0
$324$	−5.61200e9	−0.0282921
$325$	−2.69333e11	−1.33910
$326$	−5.87314e10	−0.287999
$327$	3.80239e11	1.83904
$328$	1.03718e11	0.494793
$329$	1.54754e10	0.0728215
$330$	1.89680e10	0.0880456
$331$	−3.46276e11	−1.58561	−0.792804	−	0.609476i	$-0.791380\pi$
$331$	−3.46276e11	−1.58561	−0.792804	+	0.609476i	$0.791380\pi$
$332$	8.79617e10	0.397349
$333$	5.03001e11	2.24166
$334$	−3.68177e11	−1.61882
$335$	−2.35318e10	−0.102083
$336$	9.90381e10	0.423912
$337$	−2.14440e11	−0.905671	−0.452836	−	0.891594i	$-0.649588\pi$
$337$	−2.14440e11	−0.905671	−0.452836	+	0.891594i	$0.649588\pi$
$338$	−2.21906e11	−0.924792
$339$	−5.39586e11	−2.21903
$340$	0	0
$341$	2.95377e11	1.18299
$342$	3.44067e11	1.35996
$343$	1.09181e11	0.425914
$344$	2.24894e11	0.865896
$345$	7.66048e9	0.0291119
$346$	1.78877e11	0.670984
$347$	2.25675e11	0.835603	0.417801	−	0.908538i	$-0.362801\pi$
$347$	2.25675e11	0.835603	0.417801	+	0.908538i	$0.362801\pi$
$348$	−1.77073e10	−0.0647211
$349$	3.13210e10	0.113011	0.0565055	−	0.998402i	$-0.482004\pi$
$349$	3.13210e10	0.113011	0.0565055	+	0.998402i	$0.482004\pi$
$350$	−6.95554e10	−0.247756
$351$	3.53285e11	1.24235
$352$	−1.17519e11	−0.408006
$353$	1.67054e11	0.572625	0.286312	−	0.958136i	$-0.407571\pi$
$353$	1.67054e11	0.572625	0.286312	+	0.958136i	$0.407571\pi$
$354$	2.92679e11	0.990551
$355$	−3.65204e10	−0.122041
$356$	4.04201e10	0.133374
$357$	0	0
$358$	3.42650e11	1.10250
$359$	5.25130e11	1.66856	0.834280	−	0.551341i	$-0.185884\pi$
$359$	5.25130e11	1.66856	0.834280	+	0.551341i	$0.185884\pi$
$360$	2.75834e10	0.0865540
$361$	−1.38024e11	−0.427731
$362$	2.31120e11	0.707373
$363$	−2.73154e11	−0.825709
$364$	−2.97137e10	−0.0887157
$365$	1.33789e9	0.00394551
$366$	8.89677e11	2.59160
$367$	9.23982e10	0.265868	0.132934	−	0.991125i	$-0.457560\pi$
$367$	9.23982e10	0.265868	0.132934	+	0.991125i	$0.457560\pi$
$368$	−1.11999e11	−0.318345
$369$	3.48637e11	0.978936
$370$	−4.03929e10	−0.112046
$371$	4.90975e10	0.134548
$372$	−3.04176e11	−0.823533
$373$	1.27208e11	0.340272	0.170136	−	0.985421i	$-0.445579\pi$
$373$	1.27208e11	0.340272	0.170136	+	0.985421i	$0.445579\pi$
$374$	0	0
$375$	−8.46085e10	−0.220940
$376$	−1.03015e11	−0.265801
$377$	−7.04185e10	−0.179536
$378$	9.12363e10	0.229855
$379$	−4.08652e11	−1.01737	−0.508683	−	0.860954i	$-0.669868\pi$
$379$	−4.08652e11	−1.01737	−0.508683	+	0.860954i	$0.669868\pi$
$380$	−6.41282e9	−0.0157769
$381$	−9.47223e11	−2.30298
$382$	5.43697e10	0.130639
$383$	−2.61140e11	−0.620123	−0.310062	−	0.950716i	$-0.600350\pi$
$383$	−2.61140e11	−0.620123	−0.310062	+	0.950716i	$0.600350\pi$
$384$	−8.23829e11	−1.93351
$385$	4.52133e9	0.0104880
$386$	1.31878e11	0.302364
$387$	7.55955e11	1.71316
$388$	−1.61702e11	−0.362221
$389$	3.51283e11	0.777829	0.388914	−	0.921274i	$-0.372850\pi$
$389$	3.51283e11	0.777829	0.388914	+	0.921274i	$0.372850\pi$
$390$	−7.76789e10	−0.170025
$391$	0	0
$392$	−3.54536e11	−0.758355
$393$	−3.29461e11	−0.696686
$394$	−4.79033e11	−1.00146
$395$	5.45004e10	0.112645
$396$	−1.62350e11	−0.331760
$397$	−4.17307e11	−0.843137	−0.421569	−	0.906797i	$-0.638520\pi$
$397$	−4.17307e11	−0.843137	−0.421569	+	0.906797i	$0.638520\pi$
$398$	3.54291e11	0.707760
$399$	1.34075e11	0.264831
$400$	6.17026e11	1.20513
$401$	−4.93060e11	−0.952248	−0.476124	−	0.879378i	$-0.657959\pi$
$401$	−4.93060e11	−0.952248	−0.476124	+	0.879378i	$0.657959\pi$
$402$	1.41865e12	2.70931
$403$	−1.20965e12	−2.28447
$404$	4.60585e9	0.00860189
$405$	−3.49711e9	−0.00645895
$406$	−1.81856e10	−0.0332171
$407$	−5.48842e11	−0.991454
$408$	0	0
$409$	2.79374e11	0.493663	0.246831	−	0.969058i	$-0.420611\pi$
$409$	2.79374e11	0.493663	0.246831	+	0.969058i	$0.420611\pi$
$410$	−2.79969e10	−0.0489308
$411$	−9.31857e11	−1.61087
$412$	2.48410e11	0.424748
$413$	6.97649e10	0.117995
$414$	−2.82500e11	−0.472626
$415$	5.48132e10	0.0907129
$416$	4.81272e11	0.787900
$417$	−3.92291e11	−0.635325
$418$	−3.75424e11	−0.601491
$419$	4.89354e10	0.0775640	0.0387820	−	0.999248i	$-0.487652\pi$
$419$	4.89354e10	0.0775640	0.0387820	+	0.999248i	$0.487652\pi$
$420$	−4.65601e9	−0.00730117
$421$	9.73572e11	1.51042	0.755211	−	0.655481i	$-0.227534\pi$
$421$	9.73572e11	1.51042	0.755211	+	0.655481i	$0.227534\pi$
$422$	−1.58036e11	−0.242577
$423$	−3.46274e11	−0.525882
$424$	−3.26829e11	−0.491105
$425$	0	0
$426$	2.20169e12	3.23902
$427$	2.12070e11	0.308712
$428$	3.64412e11	0.524923
$429$	−1.05547e12	−1.50449
$430$	−6.07061e10	−0.0856296
$431$	−3.60887e11	−0.503760	−0.251880	−	0.967758i	$-0.581049\pi$
$431$	−3.60887e11	−0.503760	−0.251880	+	0.967758i	$0.581049\pi$
$432$	−8.09356e11	−1.11805
$433$	1.32088e12	1.80579	0.902895	−	0.429862i	$-0.141438\pi$
$433$	1.32088e12	1.80579	0.902895	+	0.429862i	$0.141438\pi$
$434$	−3.12393e11	−0.422666
$435$	−1.10343e10	−0.0147755
$436$	2.61352e11	0.346367
$437$	−1.51621e11	−0.198880
$438$	−8.06570e10	−0.104715
$439$	−4.29288e11	−0.551643	−0.275822	−	0.961209i	$-0.588950\pi$
$439$	−4.29288e11	−0.551643	−0.275822	+	0.961209i	$0.588950\pi$
$440$	−3.00973e10	−0.0382816
$441$	−1.19173e12	−1.50039
$442$	0	0
$443$	−9.88207e11	−1.21908	−0.609538	−	0.792757i	$-0.708645\pi$
$443$	−9.88207e11	−1.21908	−0.609538	+	0.792757i	$0.708645\pi$
$444$	5.65191e11	0.690195
$445$	2.51877e10	0.0304487
$446$	−1.62993e11	−0.195057
$447$	1.08120e12	1.28092
$448$	−1.00932e11	−0.118379
$449$	5.27610e11	0.612639	0.306319	−	0.951929i	$-0.400902\pi$
$449$	5.27610e11	0.612639	0.306319	+	0.951929i	$0.400902\pi$
$450$	1.55636e12	1.78918
$451$	−3.80410e11	−0.432970
$452$	−3.70877e11	−0.417933
$453$	−2.76380e11	−0.308365
$454$	1.40219e12	1.54902
$455$	−1.85161e10	−0.0202534
$456$	−8.92501e11	−0.966645
$457$	−1.13024e11	−0.121213	−0.0606064	−	0.998162i	$-0.519303\pi$
$457$	−1.13024e11	−0.121213	−0.0606064	+	0.998162i	$0.519303\pi$
$458$	−2.67901e11	−0.284498
$459$	0	0
$460$	5.26532e9	0.00548295
$461$	−1.11660e12	−1.15145	−0.575725	−	0.817643i	$-0.695280\pi$
$461$	−1.11660e12	−1.15145	−0.575725	+	0.817643i	$0.695280\pi$
$462$	−2.72576e11	−0.278355
$463$	−3.92248e11	−0.396685	−0.198343	−	0.980133i	$-0.563556\pi$
$463$	−3.92248e11	−0.396685	−0.198343	+	0.980133i	$0.563556\pi$
$464$	1.61325e11	0.161573
$465$	−1.89547e11	−0.188009
$466$	1.53162e12	1.50458
$467$	−1.59510e11	−0.155189	−0.0775946	−	0.996985i	$-0.524724\pi$
$467$	−1.59510e11	−0.155189	−0.0775946	+	0.996985i	$0.524724\pi$
$468$	6.64868e11	0.640662
$469$	3.38160e11	0.322734
$470$	2.78071e10	0.0262855
$471$	3.88724e11	0.363955
$472$	−4.64406e11	−0.430684
$473$	−8.24850e11	−0.757705
$474$	−3.28565e12	−2.98964
$475$	8.35312e11	0.752883
$476$	0	0
$477$	−1.09860e12	−0.971640
$478$	1.69684e12	1.48668
$479$	4.37040e11	0.379325	0.189662	−	0.981849i	$-0.439261\pi$
$479$	4.37040e11	0.379325	0.189662	+	0.981849i	$0.439261\pi$
$480$	7.54134e10	0.0648429
$481$	2.24766e12	1.91460
$482$	5.24099e11	0.442284
$483$	−1.10084e11	−0.0920367
$484$	−1.87748e11	−0.155515
$485$	−1.00765e11	−0.0826933
$486$	1.50672e12	1.22509
$487$	−1.05048e12	−0.846270	−0.423135	−	0.906067i	$-0.639070\pi$
$487$	−1.05048e12	−0.846270	−0.423135	+	0.906067i	$0.639070\pi$
$488$	−1.41169e12	−1.12681
$489$	5.12097e11	0.405007
$490$	9.57004e10	0.0749948
$491$	−1.77945e12	−1.38172	−0.690859	−	0.722990i	$-0.742767\pi$
$491$	−1.77945e12	−1.38172	−0.690859	+	0.722990i	$0.742767\pi$
$492$	3.91742e11	0.301410
$493$	0	0
$494$	1.53746e12	1.16154
$495$	−1.01168e11	−0.0757393
$496$	2.77123e12	2.05592
$497$	5.24810e11	0.385832
$498$	−3.30451e12	−2.40755
$499$	1.14978e12	0.830162	0.415081	−	0.909785i	$-0.363753\pi$
$499$	1.14978e12	0.830162	0.415081	+	0.909785i	$0.363753\pi$
$500$	−5.81544e10	−0.0416119
$501$	3.21026e12	2.27651
$502$	2.25074e12	1.58183
$503$	1.33344e12	0.928788	0.464394	−	0.885629i	$-0.346272\pi$
$503$	1.33344e12	0.928788	0.464394	+	0.885629i	$0.346272\pi$
$504$	−3.96383e11	−0.273639
$505$	2.87013e9	0.00196377
$506$	3.08247e11	0.209036
$507$	1.93487e12	1.30052
$508$	−6.51059e11	−0.433744
$509$	−2.18589e12	−1.44344	−0.721721	−	0.692185i	$-0.756648\pi$
$509$	−2.18589e12	−1.44344	−0.721721	+	0.692185i	$0.756648\pi$
$510$	0	0
$511$	−1.92259e10	−0.0124737
$512$	3.96666e11	0.255100
$513$	−1.09568e12	−0.698484
$514$	−3.10647e11	−0.196306
$515$	1.54797e11	0.0969681
$516$	8.49421e11	0.527472
$517$	3.77832e11	0.232590
$518$	5.80459e11	0.354232
$519$	−1.55969e12	−0.943592
$520$	1.23256e11	0.0739256
$521$	−9.81356e11	−0.583521	−0.291761	−	0.956491i	$-0.594241\pi$
$521$	−9.81356e11	−0.583521	−0.291761	+	0.956491i	$0.594241\pi$
$522$	4.06918e11	0.239878
$523$	1.01562e11	0.0593572	0.0296786	−	0.999559i	$-0.490552\pi$
$523$	1.01562e11	0.0593572	0.0296786	+	0.999559i	$0.490552\pi$
$524$	−2.26450e11	−0.131214
$525$	6.06476e11	0.348415
$526$	9.07277e11	0.516778
$527$	0	0
$528$	2.41802e12	1.35396
$529$	−1.67666e12	−0.930883
$530$	8.82214e10	0.0485660
$531$	−1.56105e12	−0.852099
$532$	9.21544e10	0.0498785
$533$	1.55788e12	0.836107
$534$	−1.51848e12	−0.808117
$535$	2.27083e11	0.119837
$536$	−2.25104e12	−1.17799
$537$	−2.98768e12	−1.55042
$538$	−2.14333e12	−1.10298
$539$	1.30034e12	0.663601
$540$	3.80497e10	0.0192566
$541$	2.29392e12	1.15131	0.575653	−	0.817694i	$-0.304748\pi$
$541$	2.29392e12	1.15131	0.575653	+	0.817694i	$0.304748\pi$
$542$	1.43948e12	0.716487
$543$	−2.01521e12	−0.994765
$544$	0	0
$545$	1.62861e11	0.0790739
$546$	1.11627e12	0.537531
$547$	4.31625e10	0.0206140	0.0103070	−	0.999947i	$-0.496719\pi$
$547$	4.31625e10	0.0206140	0.0103070	+	0.999947i	$0.496719\pi$
$548$	−6.40498e11	−0.303393
$549$	−4.74522e12	−2.22937
$550$	−1.69820e12	−0.791328
$551$	2.18397e11	0.100940
$552$	7.32798e11	0.335938
$553$	−7.83189e11	−0.356126
$554$	4.77618e12	2.15420
$555$	3.52198e11	0.157568
$556$	−2.69635e11	−0.119658
$557$	−1.26017e12	−0.554730	−0.277365	−	0.960765i	$-0.589461\pi$
$557$	−1.26017e12	−0.554730	−0.277365	+	0.960765i	$0.589461\pi$
$558$	6.99003e12	3.05229
$559$	3.37798e12	1.46320
$560$	4.24192e10	0.0182271
$561$	0	0
$562$	−3.50716e12	−1.48300
$563$	−1.57680e12	−0.661436	−0.330718	−	0.943730i	$-0.607291\pi$
$563$	−1.57680e12	−0.661436	−0.330718	+	0.943730i	$0.607291\pi$
$564$	−3.89087e11	−0.161916
$565$	−2.31111e11	−0.0954121
$566$	1.51311e12	0.619721
$567$	5.02547e10	0.0204199
$568$	−3.49352e12	−1.40830
$569$	−4.44023e12	−1.77583	−0.887913	−	0.460012i	$-0.847845\pi$
$569$	−4.44023e12	−1.77583	−0.887913	+	0.460012i	$0.847845\pi$
$570$	2.40914e11	0.0955928
$571$	−2.59026e11	−0.101972	−0.0509860	−	0.998699i	$-0.516236\pi$
$571$	−2.59026e11	−0.101972	−0.0509860	+	0.998699i	$0.516236\pi$
$572$	−7.25461e11	−0.283356
$573$	−4.74067e11	−0.183715
$574$	4.02324e11	0.154694
$575$	−6.85842e11	−0.261649
$576$	2.25842e12	0.854878
$577$	2.66713e12	1.00173	0.500867	−	0.865524i	$-0.333015\pi$
$577$	2.66713e12	1.00173	0.500867	+	0.865524i	$0.333015\pi$
$578$	0	0
$579$	−1.14989e12	−0.425209
$580$	−7.58425e9	−0.00278283
$581$	−7.87685e11	−0.286787
$582$	6.07477e12	2.19471
$583$	1.19872e12	0.429743
$584$	1.27982e11	0.0455293
$585$	4.14312e11	0.146260
$586$	1.41562e12	0.495915
$587$	4.82084e12	1.67591	0.837956	−	0.545738i	$-0.183751\pi$
$587$	4.82084e12	1.67591	0.837956	+	0.545738i	$0.183751\pi$
$588$	−1.33907e12	−0.461962
$589$	3.75162e12	1.28440
$590$	1.25358e11	0.0425910
$591$	4.17684e12	1.40833
$592$	−5.14925e12	−1.72304
$593$	−2.49924e12	−0.829968	−0.414984	−	0.909829i	$-0.636213\pi$
$593$	−2.49924e12	−0.829968	−0.414984	+	0.909829i	$0.636213\pi$
$594$	2.22754e12	0.734152
$595$	0	0
$596$	7.43145e11	0.241249
$597$	−3.08918e12	−0.995310
$598$	−1.26235e12	−0.403669
$599$	−3.23334e12	−1.02620	−0.513098	−	0.858330i	$-0.671502\pi$
$599$	−3.23334e12	−1.02620	−0.513098	+	0.858330i	$0.671502\pi$
$600$	−4.03715e12	−1.27173
$601$	5.50244e12	1.72036	0.860181	−	0.509988i	$-0.170350\pi$
$601$	5.50244e12	1.72036	0.860181	+	0.509988i	$0.170350\pi$
$602$	8.72367e11	0.270717
$603$	−7.56660e12	−2.33063
$604$	−1.89966e11	−0.0580776
$605$	−1.16995e11	−0.0355032
$606$	−1.73031e11	−0.0521191
$607$	3.65674e12	1.09331	0.546657	−	0.837357i	$-0.315900\pi$
$607$	3.65674e12	1.09331	0.546657	+	0.837357i	$0.315900\pi$
$608$	−1.49262e12	−0.442980
$609$	1.58566e11	0.0467125
$610$	3.81060e11	0.111432
$611$	−1.54732e12	−0.449155
$612$	0	0
$613$	1.17726e12	0.336743	0.168372	−	0.985724i	$-0.446149\pi$
$613$	1.17726e12	0.336743	0.168372	+	0.985724i	$0.446149\pi$
$614$	4.85586e12	1.37882
$615$	2.44114e11	0.0688104
$616$	4.32508e11	0.121027
$617$	3.74523e12	1.04039	0.520194	−	0.854048i	$-0.325859\pi$
$617$	3.74523e12	1.04039	0.520194	+	0.854048i	$0.325859\pi$
$618$	−9.33217e12	−2.57356
$619$	6.72874e12	1.84215	0.921077	−	0.389381i	$-0.127311\pi$
$619$	6.72874e12	1.84215	0.921077	+	0.389381i	$0.127311\pi$
$620$	−1.30282e11	−0.0354097
$621$	8.99623e11	0.242744
$622$	4.69221e12	1.25696
$623$	−3.61956e11	−0.0962631
$624$	−9.90244e12	−2.61464
$625$	3.76030e12	0.985739
$626$	−5.72073e12	−1.48891
$627$	3.27345e12	0.845865
$628$	2.67184e11	0.0685475
$629$	0	0
$630$	1.06996e11	0.0270605
$631$	4.61439e12	1.15873	0.579365	−	0.815068i	$-0.303300\pi$
$631$	4.61439e12	1.15873	0.579365	+	0.815068i	$0.303300\pi$
$632$	5.21348e12	1.29987
$633$	1.37797e12	0.341131
$634$	6.89024e12	1.69369
$635$	−4.05707e11	−0.0990218
$636$	−1.23443e12	−0.299163
$637$	−5.32524e12	−1.28148
$638$	−4.44003e11	−0.106095
$639$	−1.17430e13	−2.78629
$640$	−3.52856e11	−0.0831357
$641$	7.42031e12	1.73605	0.868023	−	0.496524i	$-0.165391\pi$
$641$	7.42031e12	1.73605	0.868023	+	0.496524i	$0.165391\pi$
$642$	−1.36901e13	−3.18052
$643$	−6.05336e12	−1.39652	−0.698260	−	0.715845i	$-0.746042\pi$
$643$	−6.05336e12	−1.39652	−0.698260	+	0.715845i	$0.746042\pi$
$644$	−7.56644e10	−0.0173343
$645$	5.29316e11	0.120419
$646$	0	0
$647$	−4.28077e12	−0.960402	−0.480201	−	0.877159i	$-0.659436\pi$
$647$	−4.28077e12	−0.960402	−0.480201	+	0.877159i	$0.659436\pi$
$648$	−3.34532e11	−0.0745333
$649$	1.70331e12	0.376872
$650$	6.95458e12	1.52813
$651$	2.72385e12	0.594387
$652$	3.51983e11	0.0762793
$653$	−2.02322e12	−0.435445	−0.217723	−	0.976011i	$-0.569863\pi$
$653$	−2.02322e12	−0.435445	−0.217723	+	0.976011i	$0.569863\pi$
$654$	−9.81835e12	−2.09864
$655$	−1.41112e11	−0.0299556
$656$	−3.56902e12	−0.752457
$657$	4.30196e11	0.0900787
$658$	−3.99598e11	−0.0831011
$659$	−2.09148e12	−0.431985	−0.215993	−	0.976395i	$-0.569299\pi$
$659$	−2.09148e12	−0.431985	−0.215993	+	0.976395i	$0.569299\pi$
$660$	−1.13677e11	−0.0233198
$661$	3.66578e12	0.746895	0.373448	−	0.927651i	$-0.378176\pi$
$661$	3.66578e12	0.746895	0.373448	+	0.927651i	$0.378176\pi$
$662$	8.94136e12	1.80943
$663$	0	0
$664$	5.24341e12	1.04678
$665$	5.74259e10	0.0113870
$666$	−1.29882e13	−2.55809
$667$	−1.79317e11	−0.0350797
$668$	2.20652e12	0.428760
$669$	1.42118e12	0.274305
$670$	6.07626e11	0.116493
$671$	5.17769e12	0.986017
$672$	−1.08372e12	−0.205000
$673$	4.12814e12	0.775686	0.387843	−	0.921725i	$-0.373220\pi$
$673$	4.12814e12	0.775686	0.387843	+	0.921725i	$0.373220\pi$
$674$	5.53716e12	1.03352
$675$	−4.95622e12	−0.918933
$676$	1.32990e12	0.244940
$677$	−3.86753e12	−0.707594	−0.353797	−	0.935322i	$-0.615110\pi$
$677$	−3.86753e12	−0.707594	−0.353797	+	0.935322i	$0.615110\pi$
$678$	1.39329e13	2.53226
$679$	1.44802e12	0.261434
$680$	0	0
$681$	−1.22262e13	−2.17835
$682$	−7.62708e12	−1.34998
$683$	6.60671e12	1.16170	0.580848	−	0.814012i	$-0.302721\pi$
$683$	6.60671e12	1.16170	0.580848	+	0.814012i	$0.302721\pi$
$684$	−2.06203e12	−0.360199
$685$	−3.99126e11	−0.0692631
$686$	−2.81921e12	−0.486037
$687$	2.33591e12	0.400084
$688$	−7.73876e12	−1.31681
$689$	−4.90907e12	−0.829875
$690$	−1.97805e11	−0.0332213
$691$	8.12202e12	1.35523	0.677615	−	0.735417i	$-0.263014\pi$
$691$	8.12202e12	1.35523	0.677615	+	0.735417i	$0.263014\pi$
$692$	−1.07203e12	−0.177717
$693$	1.45382e12	0.239449
$694$	−5.82726e12	−0.953557
$695$	−1.68023e11	−0.0273172
$696$	−1.05553e12	−0.170503
$697$	0	0
$698$	−8.08755e11	−0.128964
$699$	−1.33547e13	−2.11586
$700$	4.16852e11	0.0656207
$701$	6.09018e12	0.952574	0.476287	−	0.879290i	$-0.341982\pi$
$701$	6.09018e12	0.952574	0.476287	+	0.879290i	$0.341982\pi$
$702$	−9.12236e12	−1.41772
$703$	−6.97091e12	−1.07644
$704$	−2.46425e12	−0.378101
$705$	−2.42459e11	−0.0369647
$706$	−4.31358e12	−0.653457
$707$	−4.12448e10	−0.00620843
$708$	−1.75405e12	−0.262357
$709$	1.24847e12	0.185553	0.0927767	−	0.995687i	$-0.470426\pi$
$709$	1.24847e12	0.185553	0.0927767	+	0.995687i	$0.470426\pi$
$710$	9.43011e11	0.139269
$711$	1.75245e13	2.57177
$712$	2.40944e12	0.351364
$713$	−3.08031e12	−0.446366
$714$	0	0
$715$	−4.52071e11	−0.0646888
$716$	−2.05354e12	−0.292007
$717$	−1.47953e13	−2.09068
$718$	−1.35596e13	−1.90409
$719$	4.85534e12	0.677547	0.338774	−	0.940868i	$-0.389988\pi$
$719$	4.85534e12	0.677547	0.338774	+	0.940868i	$0.389988\pi$
$720$	−9.49164e11	−0.131627
$721$	−2.22448e12	−0.306563
$722$	3.56398e12	0.488110
$723$	−4.56979e12	−0.621976
$724$	−1.38512e12	−0.187355
$725$	9.87898e11	0.132798
$726$	7.05324e12	0.942267
$727$	3.36183e12	0.446345	0.223173	−	0.974779i	$-0.428359\pi$
$727$	3.36183e12	0.446345	0.223173	+	0.974779i	$0.428359\pi$
$728$	−1.77124e12	−0.233715
$729$	−1.24237e13	−1.62921
$730$	−3.45464e10	−0.00450246
$731$	0	0
$732$	−5.33192e12	−0.686410
$733$	1.02897e13	1.31654	0.658271	−	0.752781i	$-0.271288\pi$
$733$	1.02897e13	1.31654	0.658271	+	0.752781i	$0.271288\pi$
$734$	−2.38586e12	−0.303398
$735$	−8.34442e11	−0.105464
$736$	1.22554e12	0.153949
$737$	8.25619e12	1.03080
$738$	−9.00233e12	−1.11712
$739$	1.10714e12	0.136553	0.0682766	−	0.997666i	$-0.478250\pi$
$739$	1.10714e12	0.136553	0.0682766	+	0.997666i	$0.478250\pi$
$740$	2.42078e11	0.0296765
$741$	−1.34056e13	−1.63345
$742$	−1.26777e12	−0.153541
$743$	−5.80468e12	−0.698761	−0.349380	−	0.936981i	$-0.613608\pi$
$743$	−5.80468e12	−0.698761	−0.349380	+	0.936981i	$0.613608\pi$
$744$	−1.81320e13	−2.16953
$745$	4.63090e11	0.0550760
$746$	−3.28471e12	−0.388305
$747$	1.76251e13	2.07104
$748$	0	0
$749$	−3.26326e12	−0.378864
$750$	2.18472e12	0.252128
$751$	8.01566e12	0.919517	0.459758	−	0.888044i	$-0.347936\pi$
$751$	8.01566e12	0.919517	0.459758	+	0.888044i	$0.347936\pi$
$752$	3.54483e12	0.404218
$753$	−1.96249e13	−2.22449
$754$	1.81831e12	0.204879
$755$	−1.18377e11	−0.0132588
$756$	−5.46788e11	−0.0608794
$757$	4.40521e12	0.487568	0.243784	−	0.969829i	$-0.421611\pi$
$757$	4.40521e12	0.487568	0.243784	+	0.969829i	$0.421611\pi$
$758$	1.05520e13	1.16098
$759$	−2.68770e12	−0.293963
$760$	−3.82269e11	−0.0415631
$761$	−1.23860e13	−1.33875	−0.669377	−	0.742923i	$-0.733439\pi$
$761$	−1.23860e13	−1.33875	−0.669377	+	0.742923i	$0.733439\pi$
$762$	2.44587e13	2.62807
$763$	−2.34037e12	−0.249991
$764$	−3.25843e11	−0.0346009
$765$	0	0
$766$	6.74302e12	0.707660
$767$	−6.97553e12	−0.727776
$768$	1.28766e13	1.33560
$769$	−1.34212e13	−1.38396	−0.691978	−	0.721919i	$-0.743260\pi$
$769$	−1.34212e13	−1.38396	−0.691978	+	0.721919i	$0.743260\pi$
$770$	−1.16748e11	−0.0119685
$771$	2.70863e12	0.276061
$772$	−7.90359e11	−0.0800842
$773$	−3.10743e12	−0.313036	−0.156518	−	0.987675i	$-0.550027\pi$
$773$	−3.10743e12	−0.313036	−0.156518	+	0.987675i	$0.550027\pi$
$774$	−1.95199e13	−1.95499
$775$	1.69701e13	1.68977
$776$	−9.63910e12	−0.954243
$777$	−5.06121e12	−0.498150
$778$	−9.07066e12	−0.887628
$779$	−4.83163e12	−0.470084
$780$	4.65537e11	0.0450327
$781$	1.28133e13	1.23234
$782$	0	0
$783$	−1.29583e12	−0.123203
$784$	1.21998e13	1.15327
$785$	1.66495e11	0.0156491
$786$	8.50718e12	0.795031
$787$	4.60263e12	0.427681	0.213840	−	0.976869i	$-0.431403\pi$
$787$	4.60263e12	0.427681	0.213840	+	0.976869i	$0.431403\pi$
$788$	2.87089e12	0.265246
$789$	−7.91084e12	−0.726735
$790$	−1.40728e12	−0.128546
$791$	3.32115e12	0.301644
$792$	−9.67772e12	−0.873997
$793$	−2.12040e13	−1.90410
$794$	1.07755e13	0.962155
$795$	−7.69231e11	−0.0682975
$796$	−2.12330e12	−0.187457
$797$	−1.39540e13	−1.22500	−0.612502	−	0.790469i	$-0.709837\pi$
$797$	−1.39540e13	−1.22500	−0.612502	+	0.790469i	$0.709837\pi$
$798$	−3.46202e12	−0.302215
$799$	0	0
$800$	−6.75175e12	−0.582789
$801$	8.09906e12	0.695165
$802$	1.27316e13	1.08667
$803$	−4.69402e11	−0.0398405
$804$	−8.50212e12	−0.717588
$805$	−4.71502e10	−0.00395733
$806$	3.12349e13	2.60695
$807$	1.86884e13	1.55110
$808$	2.74556e11	0.0226610
$809$	2.10896e13	1.73101	0.865507	−	0.500896i	$-0.166996\pi$
$809$	2.10896e13	1.73101	0.865507	+	0.500896i	$0.166996\pi$
$810$	9.03008e10	0.00737070
$811$	3.64082e12	0.295533	0.147766	−	0.989022i	$-0.452792\pi$
$811$	3.64082e12	0.295533	0.147766	+	0.989022i	$0.452792\pi$
$812$	1.08988e11	0.00879787
$813$	−1.25513e13	−1.00758
$814$	1.41719e13	1.13141
$815$	2.19338e11	0.0174142
$816$	0	0
$817$	−1.04765e13	−0.822655
$818$	−7.21385e12	−0.563349
$819$	−5.95380e12	−0.462399
$820$	1.67788e11	0.0129598
$821$	1.79752e13	1.38080	0.690399	−	0.723429i	$-0.257435\pi$
$821$	1.79752e13	1.38080	0.690399	+	0.723429i	$0.257435\pi$
$822$	2.40620e13	1.83826
$823$	4.92718e12	0.374368	0.187184	−	0.982325i	$-0.440064\pi$
$823$	4.92718e12	0.374368	0.187184	+	0.982325i	$0.440064\pi$
$824$	1.48078e13	1.11897
$825$	1.48071e13	1.11283
$826$	−1.80144e12	−0.134651
$827$	−5.12459e12	−0.380964	−0.190482	−	0.981691i	$-0.561005\pi$
$827$	−5.12459e12	−0.380964	−0.190482	+	0.981691i	$0.561005\pi$
$828$	1.69305e12	0.125180
$829$	1.91602e13	1.40898	0.704490	−	0.709714i	$-0.251176\pi$
$829$	1.91602e13	1.40898	0.704490	+	0.709714i	$0.251176\pi$
$830$	−1.41536e12	−0.103518
$831$	−4.16450e13	−3.02941
$832$	1.00918e13	0.730149
$833$	0	0
$834$	1.01295e13	0.725008
$835$	1.37499e12	0.0978839
$836$	2.24995e12	0.159311
$837$	−2.22598e13	−1.56768
$838$	−1.26359e12	−0.0885130
$839$	−9.27849e12	−0.646470	−0.323235	−	0.946319i	$-0.604770\pi$
$839$	−9.27849e12	−0.646470	−0.323235	+	0.946319i	$0.604770\pi$
$840$	−2.77546e11	−0.0192343
$841$	−1.42489e13	−0.982196
$842$	−2.51391e13	−1.72364
$843$	3.05800e13	2.08552
$844$	9.47124e11	0.0642489
$845$	8.28729e11	0.0559187
$846$	8.94132e12	0.600116
$847$	1.68126e12	0.112243
$848$	1.12464e13	0.746848
$849$	−1.31933e13	−0.871501
$850$	0	0
$851$	5.72354e12	0.374095
$852$	−1.31949e13	−0.857886
$853$	1.45073e13	0.938244	0.469122	−	0.883133i	$-0.344571\pi$
$853$	1.45073e13	0.938244	0.469122	+	0.883133i	$0.344571\pi$
$854$	−5.47596e12	−0.352289
$855$	−1.28495e12	−0.0822317
$856$	2.17226e13	1.38287
$857$	−6.75756e12	−0.427933	−0.213967	−	0.976841i	$-0.568638\pi$
$857$	−6.75756e12	−0.427933	−0.213967	+	0.976841i	$0.568638\pi$
$858$	2.72538e13	1.71686
$859$	6.20315e11	0.0388726	0.0194363	−	0.999811i	$-0.493813\pi$
$859$	6.20315e11	0.0388726	0.0194363	+	0.999811i	$0.493813\pi$
$860$	3.63817e11	0.0226799
$861$	−3.50800e12	−0.217543
$862$	9.31866e12	0.574871
$863$	1.36639e12	0.0838542	0.0419271	−	0.999121i	$-0.486650\pi$
$863$	1.36639e12	0.0838542	0.0419271	+	0.999121i	$0.486650\pi$
$864$	8.85631e12	0.540681
$865$	−6.68033e11	−0.0405719
$866$	−3.41071e13	−2.06070
$867$	0	0
$868$	1.87220e12	0.111947
$869$	−1.91216e13	−1.13746
$870$	2.84922e11	0.0168612
$871$	−3.38113e13	−1.99058
$872$	1.55792e13	0.912476
$873$	−3.24007e13	−1.88795
$874$	3.91507e12	0.226954
$875$	5.20765e11	0.0300335
$876$	4.83385e11	0.0277348
$877$	−1.47910e13	−0.844304	−0.422152	−	0.906525i	$-0.638725\pi$
$877$	−1.47910e13	−0.844304	−0.422152	+	0.906525i	$0.638725\pi$
$878$	1.10849e13	0.629514
$879$	−1.23432e13	−0.697396
$880$	1.03567e12	0.0582168
$881$	1.90695e12	0.106647	0.0533234	−	0.998577i	$-0.483019\pi$
$881$	1.90695e12	0.106647	0.0533234	+	0.998577i	$0.483019\pi$
$882$	3.07723e13	1.71218
$883$	9.34392e12	0.517256	0.258628	−	0.965977i	$-0.416730\pi$
$883$	9.34392e12	0.517256	0.258628	+	0.965977i	$0.416730\pi$
$884$	0	0
$885$	−1.09304e12	−0.0598949
$886$	2.55170e13	1.39116
$887$	6.67058e12	0.361832	0.180916	−	0.983499i	$-0.442094\pi$
$887$	6.67058e12	0.361832	0.180916	+	0.983499i	$0.442094\pi$
$888$	3.36911e13	1.81826
$889$	5.83015e12	0.313056
$890$	−6.50385e11	−0.0347469
$891$	1.22697e12	0.0652206
$892$	9.76830e11	0.0516627
$893$	4.79889e12	0.252528
$894$	−2.79182e13	−1.46173
$895$	−1.27966e12	−0.0666639
$896$	5.07066e12	0.262832
$897$	1.10069e13	0.567672
$898$	−1.36237e13	−0.699119
$899$	4.43692e12	0.226550
$900$	−9.32740e12	−0.473881
$901$	0	0
$902$	9.82277e12	0.494088
$903$	−7.60645e12	−0.380704
$904$	−2.21080e13	−1.10101
$905$	−8.63138e11	−0.0427722
$906$	7.13655e12	0.351893
$907$	−2.25953e13	−1.10863	−0.554313	−	0.832308i	$-0.687019\pi$
$907$	−2.25953e13	−1.10863	−0.554313	+	0.832308i	$0.687019\pi$
$908$	−8.40347e12	−0.410272
$909$	9.22885e11	0.0448343
$910$	4.78113e11	0.0231124
$911$	−2.70620e13	−1.30175	−0.650873	−	0.759186i	$-0.725597\pi$
$911$	−2.70620e13	−1.30175	−0.650873	+	0.759186i	$0.725597\pi$
$912$	3.07115e13	1.47003
$913$	−1.92314e13	−0.915992
$914$	2.91846e12	0.138323
$915$	−3.32258e12	−0.156704
$916$	1.60555e12	0.0753521
$917$	2.02783e12	0.0947042
$918$	0	0
$919$	1.59897e13	0.739468	0.369734	−	0.929138i	$-0.379449\pi$
$919$	1.59897e13	0.739468	0.369734	+	0.929138i	$0.379449\pi$
$920$	3.13866e11	0.0144444
$921$	−4.23398e13	−1.93901
$922$	2.88324e13	1.31399
$923$	−5.24738e13	−2.37977
$924$	1.63357e12	0.0737250
$925$	−3.15323e13	−1.41618
$926$	1.01284e13	0.452682
$927$	4.97745e13	2.21385
$928$	−1.76528e12	−0.0781354
$929$	−9.00625e12	−0.396710	−0.198355	−	0.980130i	$-0.563560\pi$
$929$	−9.00625e12	−0.396710	−0.198355	+	0.980130i	$0.563560\pi$
$930$	4.89438e12	0.214548
$931$	1.65157e13	0.720485
$932$	−9.17916e12	−0.398503
$933$	−4.09129e13	−1.76764
$934$	4.11879e12	0.177096
$935$	0	0
$936$	3.96329e13	1.68777
$937$	4.00157e13	1.69591	0.847954	−	0.530071i	$-0.177835\pi$
$937$	4.00157e13	1.69591	0.847954	+	0.530071i	$0.177835\pi$
$938$	−8.73180e12	−0.368291
$939$	4.98809e13	2.09382
$940$	−1.66651e11	−0.00696196
$941$	2.42260e13	1.00723	0.503615	−	0.863928i	$-0.332003\pi$
$941$	2.42260e13	1.00723	0.503615	+	0.863928i	$0.332003\pi$
$942$	−1.00374e13	−0.415331
$943$	3.96707e12	0.163368
$944$	1.59805e13	0.654964
$945$	−3.40730e11	−0.0138985
$946$	2.12989e13	0.864663
$947$	−3.52100e13	−1.42263	−0.711313	−	0.702875i	$-0.751899\pi$
$947$	−3.52100e13	−1.42263	−0.711313	+	0.702875i	$0.751899\pi$
$948$	1.96912e13	0.791835
$949$	1.92233e12	0.0769360
$950$	−2.15690e13	−0.859160
$951$	−6.00782e13	−2.38180
$952$	0	0
$953$	9.99226e12	0.392415	0.196208	−	0.980562i	$-0.437137\pi$
$953$	9.99226e12	0.392415	0.196208	+	0.980562i	$0.437137\pi$
$954$	2.83674e13	1.10880
$955$	−2.03049e11	−0.00789923
$956$	−1.01693e13	−0.393761
$957$	3.87141e12	0.149199
$958$	−1.12850e13	−0.432870
$959$	5.73557e12	0.218974
$960$	1.58134e12	0.0600902
$961$	4.97778e13	1.88270
$962$	−5.80379e13	−2.18486
$963$	7.30180e13	2.73597
$964$	−3.14097e12	−0.117143
$965$	−4.92511e11	−0.0182828
$966$	2.84253e12	0.105029
$967$	−3.17277e12	−0.116686	−0.0583431	−	0.998297i	$-0.518582\pi$
$967$	−3.17277e12	−0.116686	−0.0583431	+	0.998297i	$0.518582\pi$
$968$	−1.11917e13	−0.409691
$969$	0	0
$970$	2.60190e12	0.0943664
$971$	−2.55138e13	−0.921061	−0.460531	−	0.887644i	$-0.652341\pi$
$971$	−2.55138e13	−0.921061	−0.460531	+	0.887644i	$0.652341\pi$
$972$	−9.02989e12	−0.324477
$973$	2.41455e12	0.0863630
$974$	2.71251e13	0.965730
$975$	−6.06392e13	−2.14898
$976$	4.85772e13	1.71359
$977$	4.02976e12	0.141499	0.0707496	−	0.997494i	$-0.477461\pi$
$977$	4.02976e12	0.141499	0.0707496	+	0.997494i	$0.477461\pi$
$978$	−1.32231e13	−0.462178
$979$	−8.83718e12	−0.307462
$980$	−5.73541e11	−0.0198631
$981$	5.23676e13	1.80531
$982$	4.59481e13	1.57676
$983$	9.84380e12	0.336258	0.168129	−	0.985765i	$-0.446228\pi$
$983$	9.84380e12	0.336258	0.168129	+	0.985765i	$0.446228\pi$
$984$	2.33518e13	0.794040
$985$	1.78899e12	0.0605544
$986$	0	0
$987$	3.48422e12	0.116863
$988$	−9.21417e12	−0.307645
$989$	8.60186e12	0.285897
$990$	2.61232e12	0.0864307
$991$	7.10324e12	0.233951	0.116976	−	0.993135i	$-0.462680\pi$
$991$	7.10324e12	0.233951	0.116976	+	0.993135i	$0.462680\pi$
$992$	−3.03240e13	−0.994222
$993$	−7.79626e13	−2.54457
$994$	−1.35514e13	−0.440297
$995$	−1.32313e12	−0.0427956
$996$	1.98042e13	0.637663
$997$	−3.04471e13	−0.975928	−0.487964	−	0.872864i	$-0.662260\pi$
$997$	−3.04471e13	−0.975928	−0.487964	+	0.872864i	$0.662260\pi$
$998$	−2.96891e13	−0.947348
$999$	4.13611e13	1.31385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.c.1.4		12
17.4	even	4		17.10.b.a.16.9	✓	12
17.13	even	4		17.10.b.a.16.10	yes	12
17.16	even	2	inner	289.10.a.c.1.3		12
51.38	odd	4		153.10.d.b.118.4		12
51.47	odd	4		153.10.d.b.118.3		12
68.47	odd	4		272.10.b.c.33.1		12
68.55	odd	4		272.10.b.c.33.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.9	✓	12	17.4	even	4
17.10.b.a.16.10	yes	12	17.13	even	4
153.10.d.b.118.3		12	51.47	odd	4
153.10.d.b.118.4		12	51.38	odd	4
272.10.b.c.33.1		12	68.47	odd	4
272.10.b.c.33.12		12	68.55	odd	4
289.10.a.c.1.3		12	17.16	even	2	inner
289.10.a.c.1.4		12	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)

\(f(q)\)	\(=\)	\(q-25.8215 q^{2} +225.146 q^{3} +154.751 q^{4} +96.4328 q^{5} -5813.61 q^{6} -1385.77 q^{7} +9224.72 q^{8} +31007.8 q^{9} +O(q^{10})\)	\(q-25.8215 q^{2} +225.146 q^{3} +154.751 q^{4} +96.4328 q^{5} -5813.61 q^{6} -1385.77 q^{7} +9224.72 q^{8} +31007.8 q^{9} -2490.04 q^{10} -33833.7 q^{11} +34841.5 q^{12} +138558. q^{13} +35782.8 q^{14} +21711.5 q^{15} -317429. q^{16} -800668. q^{18} -429726. q^{19} +14923.1 q^{20} -312001. q^{21} +873638. q^{22} +352831. q^{23} +2.07691e6 q^{24} -1.94383e6 q^{25} -3.57778e6 q^{26} +2.54973e6 q^{27} -214449. q^{28} -508224. q^{29} -560623. q^{30} -8.73026e6 q^{31} +3.47343e6 q^{32} -7.61753e6 q^{33} -133634. q^{35} +4.79848e6 q^{36} +1.62218e7 q^{37} +1.10962e7 q^{38} +3.11958e7 q^{39} +889565. q^{40} +1.12435e7 q^{41} +8.05635e6 q^{42} +2.43795e7 q^{43} -5.23579e6 q^{44} +2.99017e6 q^{45} -9.11064e6 q^{46} -1.11673e7 q^{47} -7.14678e7 q^{48} -3.84332e7 q^{49} +5.01925e7 q^{50} +2.14420e7 q^{52} -3.54297e7 q^{53} -6.58378e7 q^{54} -3.26268e6 q^{55} -1.27834e7 q^{56} -9.67510e7 q^{57} +1.31231e7 q^{58} -5.03437e7 q^{59} +3.35987e6 q^{60} -1.53033e8 q^{61} +2.25429e8 q^{62} -4.29697e7 q^{63} +7.28341e7 q^{64} +1.33615e7 q^{65} +1.96696e8 q^{66} -2.44023e8 q^{67} +7.94386e7 q^{69} +3.45063e6 q^{70} -3.78713e8 q^{71} +2.86038e8 q^{72} +1.38738e7 q^{73} -4.18871e8 q^{74} -4.37645e8 q^{75} -6.65004e7 q^{76} +4.68858e7 q^{77} -8.05523e8 q^{78} +5.65164e8 q^{79} -3.06105e7 q^{80} -3.62648e7 q^{81} -2.90325e8 q^{82} +5.68408e8 q^{83} -4.82825e7 q^{84} -6.29517e8 q^{86} -1.14425e8 q^{87} -3.12106e8 q^{88} +2.61194e8 q^{89} -7.72106e7 q^{90} -1.92010e8 q^{91} +5.46009e7 q^{92} -1.96558e9 q^{93} +2.88357e8 q^{94} -4.14396e7 q^{95} +7.82030e8 q^{96} -1.04492e9 q^{97} +9.92405e8 q^{98} -1.04911e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9}+O(q^{10}) \) 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9	\( 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9} - 63204 q^{13} + 243480 q^{15} + 38978 q^{16} + 547706 q^{18} - 1110672 q^{19} - 172580 q^{21} + 4441796 q^{25} - 1336332 q^{26} - 500496 q^{30} + 1934850 q^{32} - 6557404 q^{33} + 3519864 q^{35} - 30244102 q^{36} + 28748136 q^{38} + 11901296 q^{42} - 10004616 q^{43} - 112552440 q^{47} - 121354720 q^{49} - 164889018 q^{50} - 59093180 q^{52} - 76804272 q^{53} + 300732568 q^{55} - 11618904 q^{59} - 101609232 q^{60} - 260062974 q^{64} - 18429632 q^{66} - 304208752 q^{67} - 211308236 q^{69} - 460311456 q^{70} + 493218954 q^{72} - 416024248 q^{76} - 138357828 q^{77} - 363335792 q^{81} + 845042136 q^{83} + 958037984 q^{84} + 127952904 q^{86} - 610860648 q^{87} - 938223804 q^{89} - 1635779524 q^{93} + 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) \) 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9 - 63204 * q^13 + 243480 * q^15 + 38978 * q^16 + 547706 * q^18 - 1110672 * q^19 - 172580 * q^21 + 4441796 * q^25 - 1336332 * q^26 - 500496 * q^30 + 1934850 * q^32 - 6557404 * q^33 + 3519864 * q^35 - 30244102 * q^36 + 28748136 * q^38 + 11901296 * q^42 - 10004616 * q^43 - 112552440 * q^47 - 121354720 * q^49 - 164889018 * q^50 - 59093180 * q^52 - 76804272 * q^53 + 300732568 * q^55 - 11618904 * q^59 - 101609232 * q^60 - 260062974 * q^64 - 18429632 * q^66 - 304208752 * q^67 - 211308236 * q^69 - 460311456 * q^70 + 493218954 * q^72 - 416024248 * q^76 - 138357828 * q^77 - 363335792 * q^81 + 845042136 * q^83 + 958037984 * q^84 + 127952904 * q^86 - 610860648 * q^87 - 938223804 * q^89 - 1635779524 * q^93 + 238629952 * q^94 - 152046078 * q^98

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