LMFDB - Embedded newform 289.10.a.a.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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 $ x^5 - 2x^4 - 1596x^3 + 5754x^2 + 488987x - 2711704
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$18.8209$ 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)

$f(q)$	$=$	$q+11.8209 q^{2} +67.6654 q^{3} -372.266 q^{4} -2390.67 q^{5} +799.867 q^{6} +11355.8 q^{7} -10452.8 q^{8} -15104.4 q^{9} +O(q^{10})$	\(q+11.8209 q^{2} +67.6654 q^{3} -372.266 q^{4} -2390.67 q^{5} +799.867 q^{6} +11355.8 q^{7} -10452.8 q^{8} -15104.4 q^{9} -28259.9 q^{10} +17740.6 q^{11} -25189.5 q^{12} -76108.0 q^{13} +134236. q^{14} -161765. q^{15} +67038.0 q^{16} -178548. q^{18} +661811. q^{19} +889964. q^{20} +768396. q^{21} +209710. q^{22} +1.64772e6 q^{23} -707295. q^{24} +3.76216e6 q^{25} -899667. q^{26} -2.35390e6 q^{27} -4.22738e6 q^{28} -1.49876e6 q^{29} -1.91222e6 q^{30} +4.40242e6 q^{31} +6.14430e6 q^{32} +1.20042e6 q^{33} -2.71480e7 q^{35} +5.62285e6 q^{36} +5.62188e6 q^{37} +7.82322e6 q^{38} -5.14988e6 q^{39} +2.49892e7 q^{40} -2.29725e7 q^{41} +9.08315e6 q^{42} -7.92989e6 q^{43} -6.60422e6 q^{44} +3.61096e7 q^{45} +1.94776e7 q^{46} -5.69337e7 q^{47} +4.53615e6 q^{48} +8.86009e7 q^{49} +4.44722e7 q^{50} +2.83324e7 q^{52} +2.56355e6 q^{53} -2.78253e7 q^{54} -4.24119e7 q^{55} -1.18700e8 q^{56} +4.47817e7 q^{57} -1.77167e7 q^{58} -6.87685e7 q^{59} +6.02197e7 q^{60} +1.09661e8 q^{61} +5.20406e7 q^{62} -1.71523e8 q^{63} +3.83079e7 q^{64} +1.81949e8 q^{65} +1.41901e7 q^{66} +1.44824e8 q^{67} +1.11494e8 q^{69} -3.20914e8 q^{70} +6.07354e7 q^{71} +1.57884e8 q^{72} +1.68554e8 q^{73} +6.64557e7 q^{74} +2.54568e8 q^{75} -2.46370e8 q^{76} +2.01459e8 q^{77} -6.08763e7 q^{78} -1.00310e8 q^{79} -1.60265e8 q^{80} +1.38022e8 q^{81} -2.71557e8 q^{82} -5.82713e8 q^{83} -2.86048e8 q^{84} -9.37386e7 q^{86} -1.01414e8 q^{87} -1.85440e8 q^{88} -1.56066e7 q^{89} +4.26848e8 q^{90} -8.64268e8 q^{91} -6.13390e8 q^{92} +2.97891e8 q^{93} -6.73009e8 q^{94} -1.58217e9 q^{95} +4.15757e8 q^{96} -1.64798e9 q^{97} +1.04734e9 q^{98} -2.67961e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 33 q^{2} + 236 q^{3} + 853 q^{4} - 1480 q^{5} - 7578 q^{6} + 13202 q^{7} - 42423 q^{8} + 10981 q^{9}+O(q^{10}) $ 5 * q - 33 * q^2 + 236 * q^3 + 853 * q^4 - 1480 * q^5 - 7578 * q^6 + 13202 * q^7 - 42423 * q^8 + 10981 * q^9	\( 5 q - 33 q^{2} + 236 q^{3} + 853 q^{4} - 1480 q^{5} - 7578 q^{6} + 13202 q^{7} - 42423 q^{8} + 10981 q^{9} + 89328 q^{10} + 68036 q^{11} + 406010 q^{12} - 158862 q^{13} + 84700 q^{14} - 687324 q^{15} + 350225 q^{16} - 1911585 q^{18} - 370992 q^{19} - 1632640 q^{20} + 1783880 q^{21} - 122290 q^{22} - 1645870 q^{23} - 9678702 q^{24} + 3270239 q^{25} + 734846 q^{26} + 2998268 q^{27} - 183372 q^{28} - 3668616 q^{29} + 17048544 q^{30} + 7262362 q^{31} - 5605919 q^{32} - 11334900 q^{33} - 26503988 q^{35} + 49782133 q^{36} + 31420708 q^{37} + 18513700 q^{38} + 42449884 q^{39} + 53930464 q^{40} + 7996938 q^{41} - 44519496 q^{42} - 56908268 q^{43} - 43323054 q^{44} - 12799536 q^{45} + 32063472 q^{46} - 16903336 q^{47} + 102794498 q^{48} - 11784059 q^{49} + 85921093 q^{50} + 173619082 q^{52} - 83362982 q^{53} - 386329164 q^{54} + 6363364 q^{55} - 317409372 q^{56} - 136615904 q^{57} - 64577488 q^{58} - 37946604 q^{59} - 223158912 q^{60} + 77685452 q^{61} - 324855300 q^{62} + 191945278 q^{63} + 131623105 q^{64} + 40321288 q^{65} + 298037676 q^{66} - 304503600 q^{67} - 333409272 q^{69} - 122787392 q^{70} + 476602922 q^{71} - 1301701911 q^{72} + 289980486 q^{73} - 262289012 q^{74} + 153685772 q^{75} - 1031276084 q^{76} - 143385648 q^{77} - 691646196 q^{78} + 828240610 q^{79} - 912750944 q^{80} + 891328609 q^{81} + 1109615654 q^{82} + 194681148 q^{83} + 1541719592 q^{84} + 1164707144 q^{86} + 158149884 q^{87} + 1017979978 q^{88} + 376848106 q^{89} + 2240087472 q^{90} - 194543664 q^{91} - 2506713088 q^{92} + 3494835920 q^{93} - 2244811104 q^{94} - 1498679864 q^{95} - 2935047582 q^{96} - 692035246 q^{97} + 871744055 q^{98} - 2027106408 q^{99}+O(q^{100}) \) 5 * q - 33 * q^2 + 236 * q^3 + 853 * q^4 - 1480 * q^5 - 7578 * q^6 + 13202 * q^7 - 42423 * q^8 + 10981 * q^9 + 89328 * q^10 + 68036 * q^11 + 406010 * q^12 - 158862 * q^13 + 84700 * q^14 - 687324 * q^15 + 350225 * q^16 - 1911585 * q^18 - 370992 * q^19 - 1632640 * q^20 + 1783880 * q^21 - 122290 * q^22 - 1645870 * q^23 - 9678702 * q^24 + 3270239 * q^25 + 734846 * q^26 + 2998268 * q^27 - 183372 * q^28 - 3668616 * q^29 + 17048544 * q^30 + 7262362 * q^31 - 5605919 * q^32 - 11334900 * q^33 - 26503988 * q^35 + 49782133 * q^36 + 31420708 * q^37 + 18513700 * q^38 + 42449884 * q^39 + 53930464 * q^40 + 7996938 * q^41 - 44519496 * q^42 - 56908268 * q^43 - 43323054 * q^44 - 12799536 * q^45 + 32063472 * q^46 - 16903336 * q^47 + 102794498 * q^48 - 11784059 * q^49 + 85921093 * q^50 + 173619082 * q^52 - 83362982 * q^53 - 386329164 * q^54 + 6363364 * q^55 - 317409372 * q^56 - 136615904 * q^57 - 64577488 * q^58 - 37946604 * q^59 - 223158912 * q^60 + 77685452 * q^61 - 324855300 * q^62 + 191945278 * q^63 + 131623105 * q^64 + 40321288 * q^65 + 298037676 * q^66 - 304503600 * q^67 - 333409272 * q^69 - 122787392 * q^70 + 476602922 * q^71 - 1301701911 * q^72 + 289980486 * q^73 - 262289012 * q^74 + 153685772 * q^75 - 1031276084 * q^76 - 143385648 * q^77 - 691646196 * q^78 + 828240610 * q^79 - 912750944 * q^80 + 891328609 * q^81 + 1109615654 * q^82 + 194681148 * q^83 + 1541719592 * q^84 + 1164707144 * q^86 + 158149884 * q^87 + 1017979978 * q^88 + 376848106 * q^89 + 2240087472 * q^90 - 194543664 * q^91 - 2506713088 * q^92 + 3494835920 * q^93 - 2244811104 * q^94 - 1498679864 * q^95 - 2935047582 * q^96 - 692035246 * q^97 + 871744055 * q^98 - 2027106408 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	11.8209	0.522416	0.261208	−	0.965283i	$-0.415879\pi$
$2$	11.8209	0.522416	0.261208	+	0.965283i	$0.415879\pi$
$3$	67.6654	0.482304	0.241152	−	0.970487i	$-0.422475\pi$
$3$	67.6654	0.482304	0.241152	+	0.970487i	$0.422475\pi$
$4$	−372.266	−0.727082
$5$	−2390.67	−1.71062	−0.855311	−	0.518115i	$-0.826634\pi$
$5$	−2390.67	−1.71062	−0.855311	+	0.518115i	$0.826634\pi$
$6$	799.867	0.251963
$7$	11355.8	1.78763	0.893814	−	0.448438i	$-0.148020\pi$
$7$	11355.8	1.78763	0.893814	+	0.448438i	$0.148020\pi$
$8$	−10452.8	−0.902255
$9$	−15104.4	−0.767383
$10$	−28259.9	−0.893656
$11$	17740.6	0.365343	0.182672	−	0.983174i	$-0.441525\pi$
$11$	17740.6	0.365343	0.182672	+	0.983174i	$0.441525\pi$
$12$	−25189.5	−0.350675
$13$	−76108.0	−0.739069	−0.369535	−	0.929217i	$-0.620483\pi$
$13$	−76108.0	−0.739069	−0.369535	+	0.929217i	$0.620483\pi$
$14$	134236.	0.933885
$15$	−161765.	−0.825040
$16$	67038.0	0.255730
$17$	0	0
$17$	0	0
$18$	−178548.	−0.400893
$19$	661811.	1.16505	0.582523	−	0.812814i	$-0.302066\pi$
$19$	661811.	1.16505	0.582523	+	0.812814i	$0.302066\pi$
$20$	889964.	1.24376
$21$	768396.	0.862180
$22$	209710.	0.190861
$23$	1.64772e6	1.22774	0.613872	−	0.789405i	$-0.289611\pi$
$23$	1.64772e6	1.22774	0.613872	+	0.789405i	$0.289611\pi$
$24$	−707295.	−0.435161
$25$	3.76216e6	1.92623
$26$	−899667.	−0.386102
$27$	−2.35390e6	−0.852416
$28$	−4.22738e6	−1.29975
$29$	−1.49876e6	−0.393496	−0.196748	−	0.980454i	$-0.563038\pi$
$29$	−1.49876e6	−0.393496	−0.196748	+	0.980454i	$0.563038\pi$
$30$	−1.91222e6	−0.431014
$31$	4.40242e6	0.856177	0.428089	−	0.903737i	$-0.359187\pi$
$31$	4.40242e6	0.856177	0.428089	+	0.903737i	$0.359187\pi$
$32$	6.14430e6	1.03585
$33$	1.20042e6	0.176207
$34$	0	0
$35$	−2.71480e7	−3.05796
$36$	5.62285e6	0.557950
$37$	5.62188e6	0.493144	0.246572	−	0.969125i	$-0.420696\pi$
$37$	5.62188e6	0.493144	0.246572	+	0.969125i	$0.420696\pi$
$38$	7.82322e6	0.608638
$39$	−5.14988e6	−0.356456
$40$	2.49892e7	1.54342
$41$	−2.29725e7	−1.26964	−0.634821	−	0.772659i	$-0.718926\pi$
$41$	−2.29725e7	−1.26964	−0.634821	+	0.772659i	$0.718926\pi$
$42$	9.08315e6	0.450417
$43$	−7.92989e6	−0.353720	−0.176860	−	0.984236i	$-0.556594\pi$
$43$	−7.92989e6	−0.353720	−0.176860	+	0.984236i	$0.556594\pi$
$44$	−6.60422e6	−0.265634
$45$	3.61096e7	1.31270
$46$	1.94776e7	0.641393
$47$	−5.69337e7	−1.70188	−0.850940	−	0.525262i	$-0.823967\pi$
$47$	−5.69337e7	−1.70188	−0.850940	+	0.525262i	$0.823967\pi$
$48$	4.53615e6	0.123339
$49$	8.86009e7	2.19561
$50$	4.44722e7	1.00629
$51$	0	0
$52$	2.83324e7	0.537364
$53$	2.56355e6	0.0446272	0.0223136	−	0.999751i	$-0.492897\pi$
$53$	2.56355e6	0.0446272	0.0223136	+	0.999751i	$0.492897\pi$
$54$	−2.78253e7	−0.445316
$55$	−4.24119e7	−0.624964
$56$	−1.18700e8	−1.61290
$57$	4.47817e7	0.561906
$58$	−1.77167e7	−0.205569
$59$	−6.87685e7	−0.738849	−0.369424	−	0.929261i	$-0.620445\pi$
$59$	−6.87685e7	−0.738849	−0.369424	+	0.929261i	$0.620445\pi$
$60$	6.02197e7	0.599872
$61$	1.09661e8	1.01407	0.507036	−	0.861925i	$-0.330741\pi$
$61$	1.09661e8	1.01407	0.507036	+	0.861925i	$0.330741\pi$
$62$	5.20406e7	0.447280
$63$	−1.71523e8	−1.37179
$64$	3.83079e7	0.285416
$65$	1.81949e8	1.26427
$66$	1.41901e7	0.0920531
$67$	1.44824e8	0.878017	0.439008	−	0.898483i	$-0.355330\pi$
$67$	1.44824e8	0.878017	0.439008	+	0.898483i	$0.355330\pi$
$68$	0	0
$69$	1.11494e8	0.592147
$70$	−3.20914e8	−1.59752
$71$	6.07354e7	0.283648	0.141824	−	0.989892i	$-0.454703\pi$
$71$	6.07354e7	0.283648	0.141824	+	0.989892i	$0.454703\pi$
$72$	1.57884e8	0.692375
$73$	1.68554e8	0.694684	0.347342	−	0.937739i	$-0.387084\pi$
$73$	1.68554e8	0.694684	0.347342	+	0.937739i	$0.387084\pi$
$74$	6.64557e7	0.257626
$75$	2.54568e8	0.929027
$76$	−2.46370e8	−0.847083
$77$	2.01459e8	0.653098
$78$	−6.08763e7	−0.186218
$79$	−1.00310e8	−0.289749	−0.144875	−	0.989450i	$-0.546278\pi$
$79$	−1.00310e8	−0.289749	−0.144875	+	0.989450i	$0.546278\pi$
$80$	−1.60265e8	−0.437456
$81$	1.38022e8	0.356259
$82$	−2.71557e8	−0.663282
$83$	−5.82713e8	−1.34773	−0.673865	−	0.738854i	$-0.735367\pi$
$83$	−5.82713e8	−1.34773	−0.673865	+	0.738854i	$0.735367\pi$
$84$	−2.86048e8	−0.626876
$85$	0	0
$86$	−9.37386e7	−0.184789
$87$	−1.01414e8	−0.189785
$88$	−1.85440e8	−0.329633
$89$	−1.56066e7	−0.0263665	−0.0131832	−	0.999913i	$-0.504196\pi$
$89$	−1.56066e7	−0.0263665	−0.0131832	+	0.999913i	$0.504196\pi$
$90$	4.26848e8	0.685776
$91$	−8.64268e8	−1.32118
$92$	−6.13390e8	−0.892671
$93$	2.97891e8	0.412938
$94$	−6.73009e8	−0.889089
$95$	−1.58217e9	−1.99295
$96$	4.15757e8	0.499596
$97$	−1.64798e9	−1.89008	−0.945040	−	0.326956i	$-0.893977\pi$
$97$	−1.64798e9	−1.89008	−0.945040	+	0.326956i	$0.893977\pi$
$98$	1.04734e9	1.14702
$99$	−2.67961e8	−0.280358
$100$	−1.40052e9	−1.40052
$101$	−9.32619e8	−0.891780	−0.445890	−	0.895088i	$-0.647113\pi$
$101$	−9.32619e8	−0.891780	−0.445890	+	0.895088i	$0.647113\pi$
$102$	0	0
$103$	−1.88493e9	−1.65017	−0.825085	−	0.565009i	$-0.808873\pi$
$103$	−1.88493e9	−1.65017	−0.825085	+	0.565009i	$0.808873\pi$
$104$	7.95544e8	0.666829
$105$	−1.83698e9	−1.47486
$106$	3.03035e7	0.0233140
$107$	9.44012e7	0.0696226	0.0348113	−	0.999394i	$-0.488917\pi$
$107$	9.44012e7	0.0696226	0.0348113	+	0.999394i	$0.488917\pi$
$108$	8.76278e8	0.619776
$109$	1.72481e9	1.17037	0.585183	−	0.810901i	$-0.301023\pi$
$109$	1.72481e9	1.17037	0.585183	+	0.810901i	$0.301023\pi$
$110$	−5.01347e8	−0.326491
$111$	3.80406e8	0.237845
$112$	7.61271e8	0.457149
$113$	−1.02688e9	−0.592471	−0.296235	−	0.955115i	$-0.595731\pi$
$113$	−1.02688e9	−0.592471	−0.296235	+	0.955115i	$0.595731\pi$
$114$	5.29361e8	0.293549
$115$	−3.93915e9	−2.10021
$116$	5.57936e8	0.286104
$117$	1.14957e9	0.567149
$118$	−8.12907e8	−0.385986
$119$	0	0
$120$	1.69091e9	0.744396
$121$	−2.04322e9	−0.866524
$122$	1.29630e9	0.529767
$123$	−1.55445e9	−0.612354
$124$	−1.63887e9	−0.622511
$125$	−4.32481e9	−1.58442
$126$	−2.02756e9	−0.716647
$127$	2.57593e9	0.878653	0.439327	−	0.898327i	$-0.355217\pi$
$127$	2.57593e9	0.878653	0.439327	+	0.898327i	$0.355217\pi$
$128$	−2.69305e9	−0.886746
$129$	−5.36579e8	−0.170600
$130$	2.15080e9	0.660474
$131$	1.67438e9	0.496746	0.248373	−	0.968664i	$-0.420104\pi$
$131$	1.67438e9	0.496746	0.248373	+	0.968664i	$0.420104\pi$
$132$	−4.46877e8	−0.128117
$133$	7.51540e9	2.08267
$134$	1.71195e9	0.458690
$135$	5.62740e9	1.45816
$136$	0	0
$137$	9.77626e8	0.237099	0.118550	−	0.992948i	$-0.462176\pi$
$137$	9.77626e8	0.237099	0.118550	+	0.992948i	$0.462176\pi$
$138$	1.31796e9	0.309347
$139$	5.07318e8	0.115269	0.0576346	−	0.998338i	$-0.481644\pi$
$139$	5.07318e8	0.115269	0.0576346	+	0.998338i	$0.481644\pi$
$140$	1.01063e10	2.22338
$141$	−3.85244e9	−0.820824
$142$	7.17948e8	0.148182
$143$	−1.35020e9	−0.270014
$144$	−1.01257e9	−0.196242
$145$	3.58303e9	0.673123
$146$	1.99247e9	0.362914
$147$	5.99522e9	1.05895
$148$	−2.09283e9	−0.358556
$149$	−3.39357e9	−0.564052	−0.282026	−	0.959407i	$-0.591006\pi$
$149$	−3.39357e9	−0.564052	−0.282026	+	0.959407i	$0.591006\pi$
$150$	3.00923e9	0.485339
$151$	2.54210e9	0.397921	0.198961	−	0.980007i	$-0.436243\pi$
$151$	2.54210e9	0.397921	0.198961	+	0.980007i	$0.436243\pi$
$152$	−6.91780e9	−1.05117
$153$	0	0
$154$	2.38143e9	0.341189
$155$	−1.05247e10	−1.46460
$156$	1.91712e9	0.259173
$157$	−8.59628e9	−1.12918	−0.564588	−	0.825373i	$-0.690965\pi$
$157$	−8.59628e9	−1.12918	−0.564588	+	0.825373i	$0.690965\pi$
$158$	−1.18576e9	−0.151370
$159$	1.73464e8	0.0215239
$160$	−1.46890e10	−1.77195
$161$	1.87112e10	2.19475
$162$	1.63155e9	0.186115
$163$	−7.22903e8	−0.0802113	−0.0401057	−	0.999195i	$-0.512769\pi$
$163$	−7.22903e8	−0.0802113	−0.0401057	+	0.999195i	$0.512769\pi$
$164$	8.55189e9	0.923134
$165$	−2.86982e9	−0.301423
$166$	−6.88820e9	−0.704076
$167$	−5.77488e9	−0.574538	−0.287269	−	0.957850i	$-0.592747\pi$
$167$	−5.77488e9	−0.574538	−0.287269	+	0.957850i	$0.592747\pi$
$168$	−8.03192e9	−0.777906
$169$	−4.81207e9	−0.453776
$170$	0	0
$171$	−9.99625e9	−0.894036
$172$	2.95203e9	0.257183
$173$	2.26224e9	0.192014	0.0960068	−	0.995381i	$-0.469393\pi$
$173$	2.26224e9	0.192014	0.0960068	+	0.995381i	$0.469393\pi$
$174$	−1.19881e9	−0.0991466
$175$	4.27224e10	3.44338
$176$	1.18929e9	0.0934291
$177$	−4.65325e9	−0.356350
$178$	−1.84484e8	−0.0137743
$179$	−3.69322e9	−0.268885	−0.134443	−	0.990921i	$-0.542924\pi$
$179$	−3.69322e9	−0.268885	−0.134443	+	0.990921i	$0.542924\pi$
$180$	−1.34424e10	−0.954441
$181$	−1.91251e10	−1.32449	−0.662247	−	0.749285i	$-0.730397\pi$
$181$	−1.91251e10	−1.32449	−0.662247	+	0.749285i	$0.730397\pi$
$182$	−1.02164e10	−0.690206
$183$	7.42027e9	0.489091
$184$	−1.72233e10	−1.10774
$185$	−1.34400e10	−0.843582
$186$	3.52135e9	0.215725
$187$	0	0
$188$	2.11945e10	1.23741
$189$	−2.67305e10	−1.52380
$190$	−1.87027e10	−1.04115
$191$	−4.41416e9	−0.239993	−0.119996	−	0.992774i	$-0.538288\pi$
$191$	−4.41416e9	−0.239993	−0.119996	+	0.992774i	$0.538288\pi$
$192$	2.59212e9	0.137657
$193$	5.98467e9	0.310479	0.155239	−	0.987877i	$-0.450385\pi$
$193$	5.98467e9	0.310479	0.155239	+	0.987877i	$0.450385\pi$
$194$	−1.94807e10	−0.987407
$195$	1.23116e10	0.609762
$196$	−3.29831e10	−1.59639
$197$	−2.74494e10	−1.29848	−0.649240	−	0.760584i	$-0.724913\pi$
$197$	−2.74494e10	−1.29848	−0.649240	+	0.760584i	$0.724913\pi$
$198$	−3.16754e9	−0.146463
$199$	−3.34164e10	−1.51050	−0.755250	−	0.655436i	$-0.772485\pi$
$199$	−3.34164e10	−1.51050	−0.755250	+	0.655436i	$0.772485\pi$
$200$	−3.93253e10	−1.73795
$201$	9.79955e9	0.423471
$202$	−1.10244e10	−0.465880
$203$	−1.70196e10	−0.703425
$204$	0	0
$205$	5.49197e10	2.17188
$206$	−2.22817e10	−0.862075
$207$	−2.48878e10	−0.942150
$208$	−5.10212e9	−0.189002
$209$	1.17409e10	0.425641
$210$	−2.17148e10	−0.770493
$211$	−4.50084e9	−0.156323	−0.0781615	−	0.996941i	$-0.524905\pi$
$211$	−4.50084e9	−0.156323	−0.0781615	+	0.996941i	$0.524905\pi$
$212$	−9.54321e8	−0.0324477
$213$	4.10969e9	0.136805
$214$	1.11591e9	0.0363720
$215$	1.89577e10	0.605081
$216$	2.46050e10	0.769097
$217$	4.99930e10	1.53053
$218$	2.03888e10	0.611418
$219$	1.14053e10	0.335049
$220$	1.57885e10	0.454400
$221$	0	0
$222$	4.49675e9	0.124254
$223$	−4.59996e10	−1.24561	−0.622805	−	0.782377i	$-0.714007\pi$
$223$	−4.59996e10	−1.24561	−0.622805	+	0.782377i	$0.714007\pi$
$224$	6.97736e10	1.85172
$225$	−5.68252e10	−1.47815
$226$	−1.21387e10	−0.309516
$227$	−1.68405e10	−0.420958	−0.210479	−	0.977598i	$-0.567502\pi$
$227$	−1.68405e10	−0.420958	−0.210479	+	0.977598i	$0.567502\pi$
$228$	−1.66707e10	−0.408552
$229$	4.54814e10	1.09288	0.546442	−	0.837497i	$-0.315982\pi$
$229$	4.54814e10	1.09288	0.546442	+	0.837497i	$0.315982\pi$
$230$	−4.65644e10	−1.09718
$231$	1.36318e10	0.314992
$232$	1.56663e10	0.355034
$233$	5.00961e10	1.11353	0.556766	−	0.830669i	$-0.312042\pi$
$233$	5.00961e10	1.11353	0.556766	+	0.830669i	$0.312042\pi$
$234$	1.35889e10	0.296288
$235$	1.36110e11	2.91127
$236$	2.56002e10	0.537204
$237$	−6.78751e9	−0.139747
$238$	0	0
$239$	4.75443e10	0.942558	0.471279	−	0.881984i	$-0.343792\pi$
$239$	4.75443e10	0.942558	0.471279	+	0.881984i	$0.343792\pi$
$240$	−1.08444e10	−0.210987
$241$	−8.24645e10	−1.57467	−0.787337	−	0.616523i	$-0.788541\pi$
$241$	−8.24645e10	−1.57467	−0.787337	+	0.616523i	$0.788541\pi$
$242$	−2.41527e10	−0.452686
$243$	5.56712e10	1.02424
$244$	−4.08231e10	−0.737313
$245$	−2.11815e11	−3.75586
$246$	−1.83750e10	−0.319903
$247$	−5.03691e10	−0.861049
$248$	−4.60177e10	−0.772490
$249$	−3.94295e10	−0.650016
$250$	−5.11232e10	−0.827728
$251$	−5.90523e10	−0.939085	−0.469543	−	0.882910i	$-0.655581\pi$
$251$	−5.90523e10	−0.939085	−0.469543	+	0.882910i	$0.655581\pi$
$252$	6.38520e10	0.997407
$253$	2.92315e10	0.448548
$254$	3.04499e10	0.459022
$255$	0	0
$256$	−5.14479e10	−0.748666
$257$	3.35982e10	0.480415	0.240207	−	0.970722i	$-0.422785\pi$
$257$	3.35982e10	0.480415	0.240207	+	0.970722i	$0.422785\pi$
$258$	−6.34286e9	−0.0891244
$259$	6.38410e10	0.881557
$260$	−6.77333e10	−0.919226
$261$	2.26378e10	0.301962
$262$	1.97928e10	0.259508
$263$	3.91693e9	0.0504830	0.0252415	−	0.999681i	$-0.491965\pi$
$263$	3.91693e9	0.0504830	0.0252415	+	0.999681i	$0.491965\pi$
$264$	−1.25478e10	−0.158983
$265$	−6.12859e9	−0.0763403
$266$	8.88390e10	1.08802
$267$	−1.05602e9	−0.0127167
$268$	−5.39129e10	−0.638390
$269$	−6.33897e10	−0.738131	−0.369065	−	0.929403i	$-0.620322\pi$
$269$	−6.33897e10	−0.738131	−0.369065	+	0.929403i	$0.620322\pi$
$270$	6.65210e10	0.761767
$271$	4.27576e10	0.481561	0.240781	−	0.970580i	$-0.422597\pi$
$271$	4.27576e10	0.481561	0.240781	+	0.970580i	$0.422597\pi$
$272$	0	0
$273$	−5.84811e10	−0.637211
$274$	1.15564e10	0.123864
$275$	6.67430e10	0.703734
$276$	−4.15053e10	−0.430539
$277$	1.32848e11	1.35580	0.677899	−	0.735155i	$-0.262891\pi$
$277$	1.32848e11	1.35580	0.677899	+	0.735155i	$0.262891\pi$
$278$	5.99696e9	0.0602185
$279$	−6.64958e10	−0.657015
$280$	2.83773e11	2.75905
$281$	−1.43951e11	−1.37733	−0.688663	−	0.725082i	$-0.741802\pi$
$281$	−1.43951e11	−1.37733	−0.688663	+	0.725082i	$0.741802\pi$
$282$	−4.55394e10	−0.428812
$283$	−6.72871e10	−0.623581	−0.311790	−	0.950151i	$-0.600929\pi$
$283$	−6.72871e10	−0.623581	−0.311790	+	0.950151i	$0.600929\pi$
$284$	−2.26097e10	−0.206235
$285$	−1.07058e11	−0.961209
$286$	−1.59606e10	−0.141060
$287$	−2.60872e11	−2.26965
$288$	−9.28060e10	−0.794895
$289$	0	0
$290$	4.23547e10	0.351650
$291$	−1.11511e11	−0.911593
$292$	−6.27470e10	−0.505092
$293$	8.76124e10	0.694482	0.347241	−	0.937776i	$-0.387119\pi$
$293$	8.76124e10	0.694482	0.347241	+	0.937776i	$0.387119\pi$
$294$	7.08690e10	0.553214
$295$	1.64403e11	1.26389
$296$	−5.87645e10	−0.444941
$297$	−4.17596e10	−0.311424
$298$	−4.01152e10	−0.294670
$299$	−1.25405e11	−0.907389
$300$	−9.47671e10	−0.675479
$301$	−9.00504e10	−0.632319
$302$	3.00500e10	0.207880
$303$	−6.31060e10	−0.430109
$304$	4.43665e10	0.297936
$305$	−2.62163e11	−1.73469
$306$	0	0
$307$	2.30476e11	1.48083	0.740413	−	0.672153i	$-0.234630\pi$
$307$	2.30476e11	1.48083	0.740413	+	0.672153i	$0.234630\pi$
$308$	−7.49963e10	−0.474855
$309$	−1.27545e11	−0.795884
$310$	−1.24412e11	−0.765128
$311$	−2.89033e10	−0.175197	−0.0875984	−	0.996156i	$-0.527919\pi$
$311$	−2.89033e10	−0.175197	−0.0875984	+	0.996156i	$0.527919\pi$
$312$	5.38308e10	0.321614
$313$	2.95929e11	1.74276	0.871382	−	0.490605i	$-0.163224\pi$
$313$	2.95929e11	1.74276	0.871382	+	0.490605i	$0.163224\pi$
$314$	−1.01616e11	−0.589900
$315$	4.10054e11	2.34662
$316$	3.73420e10	0.210671
$317$	3.12812e11	1.73987	0.869934	−	0.493168i	$-0.164161\pi$
$317$	3.12812e11	1.73987	0.869934	+	0.493168i	$0.164161\pi$
$318$	2.05050e9	0.0112444
$319$	−2.65888e10	−0.143761
$320$	−9.15814e10	−0.488239
$321$	6.38769e9	0.0335793
$322$	2.21184e11	1.14657
$323$	0	0
$324$	−5.13809e10	−0.259029
$325$	−2.86331e11	−1.42362
$326$	−8.54537e9	−0.0419037
$327$	1.16710e11	0.564473
$328$	2.40128e11	1.14554
$329$	−6.46529e11	−3.04233
$330$	−3.39239e10	−0.157468
$331$	8.91016e9	0.0408000	0.0204000	−	0.999792i	$-0.493506\pi$
$331$	8.91016e9	0.0408000	0.0204000	+	0.999792i	$0.493506\pi$
$332$	2.16924e11	0.979910
$333$	−8.49150e10	−0.378430
$334$	−6.82644e10	−0.300148
$335$	−3.46225e11	−1.50195
$336$	5.15117e10	0.220485
$337$	−2.90899e10	−0.122859	−0.0614296	−	0.998111i	$-0.519566\pi$
$337$	−2.90899e10	−0.122859	−0.0614296	+	0.998111i	$0.519566\pi$
$338$	−5.68831e10	−0.237060
$339$	−6.94843e10	−0.285751
$340$	0	0
$341$	7.81015e10	0.312799
$342$	−1.18165e11	−0.467058
$343$	5.47888e11	2.13731
$344$	8.28899e10	0.319145
$345$	−2.66544e11	−1.01294
$346$	2.67418e10	0.100311
$347$	−1.09628e11	−0.405918	−0.202959	−	0.979187i	$-0.565056\pi$
$347$	−1.09628e11	−0.405918	−0.202959	+	0.979187i	$0.565056\pi$
$348$	3.77530e10	0.137989
$349$	−6.35598e10	−0.229334	−0.114667	−	0.993404i	$-0.536580\pi$
$349$	−6.35598e10	−0.229334	−0.114667	+	0.993404i	$0.536580\pi$
$350$	5.05018e11	1.79887
$351$	1.79151e11	0.629995
$352$	1.09004e11	0.378442
$353$	7.79401e10	0.267162	0.133581	−	0.991038i	$-0.457352\pi$
$353$	7.79401e10	0.267162	0.133581	+	0.991038i	$0.457352\pi$
$354$	−5.50057e10	−0.186163
$355$	−1.45198e11	−0.485214
$356$	5.80979e9	0.0191706
$357$	0	0
$358$	−4.36573e10	−0.140470
$359$	3.06852e11	0.974998	0.487499	−	0.873124i	$-0.337909\pi$
$359$	3.06852e11	0.974998	0.487499	+	0.873124i	$0.337909\pi$
$360$	−3.77447e11	−1.18439
$361$	1.15306e11	0.357331
$362$	−2.26076e11	−0.691937
$363$	−1.38255e11	−0.417928
$364$	3.21738e11	0.960607
$365$	−4.02957e11	−1.18834
$366$	8.77144e10	0.255509
$367$	2.13117e11	0.613225	0.306613	−	0.951834i	$-0.400804\pi$
$367$	2.13117e11	0.613225	0.306613	+	0.951834i	$0.400804\pi$
$368$	1.10460e11	0.313971
$369$	3.46986e11	0.974302
$370$	−1.58874e11	−0.440701
$371$	2.91112e10	0.0797769
$372$	−1.10895e11	−0.300240
$373$	2.27081e11	0.607423	0.303712	−	0.952764i	$-0.401774\pi$
$373$	2.27081e11	0.607423	0.303712	+	0.952764i	$0.401774\pi$
$374$	0	0
$375$	−2.92640e11	−0.764175
$376$	5.95119e11	1.53553
$377$	1.14067e11	0.290821
$378$	−3.15979e11	−0.796059
$379$	−3.53633e11	−0.880391	−0.440196	−	0.897902i	$-0.645091\pi$
$379$	−3.53633e11	−0.880391	−0.440196	+	0.897902i	$0.645091\pi$
$380$	5.88988e11	1.44904
$381$	1.74301e11	0.423778
$382$	−5.21794e10	−0.125376
$383$	−6.69512e11	−1.58988	−0.794939	−	0.606689i	$-0.792497\pi$
$383$	−6.69512e11	−1.58988	−0.794939	+	0.606689i	$0.792497\pi$
$384$	−1.82226e11	−0.427681
$385$	−4.81621e11	−1.11720
$386$	7.07443e10	0.162199
$387$	1.19776e11	0.271438
$388$	6.13488e11	1.37424
$389$	6.62054e11	1.46595	0.732976	−	0.680254i	$-0.238131\pi$
$389$	6.62054e11	1.46595	0.732976	+	0.680254i	$0.238131\pi$
$390$	1.45535e11	0.318549
$391$	0	0
$392$	−9.26131e11	−1.98100
$393$	1.13298e11	0.239583
$394$	−3.24477e11	−0.678346
$395$	2.39808e11	0.495651
$396$	9.97527e10	0.203843
$397$	6.61102e11	1.33571	0.667854	−	0.744293i	$-0.267213\pi$
$397$	6.61102e11	1.33571	0.667854	+	0.744293i	$0.267213\pi$
$398$	−3.95013e11	−0.789110
$399$	5.08533e11	1.00448
$400$	2.52208e11	0.492593
$401$	−6.56727e11	−1.26834	−0.634169	−	0.773195i	$-0.718658\pi$
$401$	−6.56727e11	−1.26834	−0.634169	+	0.773195i	$0.718658\pi$
$402$	1.15840e11	0.221228
$403$	−3.35059e11	−0.632774
$404$	3.47182e11	0.648397
$405$	−3.29964e11	−0.609424
$406$	−2.01187e11	−0.367480
$407$	9.97354e10	0.180167
$408$	0	0
$409$	−4.36145e11	−0.770684	−0.385342	−	0.922774i	$-0.625917\pi$
$409$	−4.36145e11	−0.770684	−0.385342	+	0.922774i	$0.625917\pi$
$410$	6.49201e11	1.13462
$411$	6.61515e10	0.114354
$412$	7.01697e11	1.19981
$413$	−7.80923e11	−1.32079
$414$	−2.94197e11	−0.492194
$415$	1.39307e12	2.30546
$416$	−4.67631e11	−0.765566
$417$	3.43279e10	0.0555948
$418$	1.38789e11	0.222362
$419$	−6.66344e11	−1.05617	−0.528087	−	0.849190i	$-0.677091\pi$
$419$	−6.66344e11	−1.05617	−0.528087	+	0.849190i	$0.677091\pi$
$420$	6.83844e11	1.07235
$421$	−4.68417e11	−0.726713	−0.363357	−	0.931650i	$-0.618369\pi$
$421$	−4.68417e11	−0.726713	−0.363357	+	0.931650i	$0.618369\pi$
$422$	−5.32041e10	−0.0816656
$423$	8.59949e11	1.30599
$424$	−2.67964e10	−0.0402651
$425$	0	0
$426$	4.85803e10	0.0714688
$427$	1.24529e12	1.81278
$428$	−3.51423e10	−0.0506213
$429$	−9.13619e10	−0.130229
$430$	2.24098e11	0.316104
$431$	3.43298e11	0.479207	0.239604	−	0.970871i	$-0.422982\pi$
$431$	3.43298e11	0.479207	0.239604	+	0.970871i	$0.422982\pi$
$432$	−1.57801e11	−0.217988
$433$	−1.30884e12	−1.78933	−0.894666	−	0.446735i	$-0.852587\pi$
$433$	−1.30884e12	−1.78933	−0.894666	+	0.446735i	$0.852587\pi$
$434$	5.90964e11	0.799571
$435$	2.42447e11	0.324650
$436$	−6.42088e11	−0.850952
$437$	1.09048e12	1.43038
$438$	1.34821e11	0.175035
$439$	−5.48226e11	−0.704481	−0.352241	−	0.935909i	$-0.614580\pi$
$439$	−5.48226e11	−0.704481	−0.352241	+	0.935909i	$0.614580\pi$
$440$	4.43324e11	0.563877
$441$	−1.33826e12	−1.68488
$442$	0	0
$443$	−1.00051e10	−0.0123426	−0.00617130	−	0.999981i	$-0.501964\pi$
$443$	−1.00051e10	−0.0123426	−0.00617130	+	0.999981i	$0.501964\pi$
$444$	−1.41612e11	−0.172933
$445$	3.73101e10	0.0451031
$446$	−5.43758e11	−0.650727
$447$	−2.29628e11	−0.272045
$448$	4.35017e11	0.510218
$449$	8.97323e10	0.104193	0.0520967	−	0.998642i	$-0.483410\pi$
$449$	8.97323e10	0.104193	0.0520967	+	0.998642i	$0.483410\pi$
$450$	−6.71726e11	−0.772211
$451$	−4.07546e11	−0.463855
$452$	3.82272e11	0.430775
$453$	1.72012e11	0.191919
$454$	−1.99071e11	−0.219915
$455$	2.06618e12	2.26004
$456$	−4.68096e11	−0.506983
$457$	−1.13166e12	−1.21365	−0.606823	−	0.794837i	$-0.707556\pi$
$457$	−1.13166e12	−1.21365	−0.606823	+	0.794837i	$0.707556\pi$
$458$	5.37632e11	0.570940
$459$	0	0
$460$	1.46641e12	1.52702
$461$	−1.76123e12	−1.81620	−0.908098	−	0.418757i	$-0.862466\pi$
$461$	−1.76123e12	−1.81620	−0.908098	+	0.418757i	$0.862466\pi$
$462$	1.61140e11	0.164557
$463$	−6.00361e11	−0.607152	−0.303576	−	0.952807i	$-0.598181\pi$
$463$	−6.00361e11	−0.607152	−0.303576	+	0.952807i	$0.598181\pi$
$464$	−1.00474e11	−0.100629
$465$	−7.12159e11	−0.706380
$466$	5.92182e11	0.581727
$467$	−7.30949e11	−0.711150	−0.355575	−	0.934648i	$-0.615715\pi$
$467$	−7.30949e11	−0.711150	−0.355575	+	0.934648i	$0.615715\pi$
$468$	−4.27944e11	−0.412364
$469$	1.64459e12	1.56957
$470$	1.60894e12	1.52090
$471$	−5.81671e11	−0.544607
$472$	7.18826e11	0.666630
$473$	−1.40681e11	−0.129229
$474$	−8.02347e10	−0.0730062
$475$	2.48984e12	2.24414
$476$	0	0
$477$	−3.87208e10	−0.0342462
$478$	5.62018e11	0.492407
$479$	1.76035e12	1.52788	0.763938	−	0.645289i	$-0.223263\pi$
$479$	1.76035e12	1.52788	0.763938	+	0.645289i	$0.223263\pi$
$480$	−9.93936e11	−0.854619
$481$	−4.27870e11	−0.364467
$482$	−9.74807e11	−0.822634
$483$	1.26610e12	1.05854
$484$	7.60621e11	0.630034
$485$	3.93978e12	3.23321
$486$	6.58085e11	0.535080
$487$	−2.40112e12	−1.93434	−0.967171	−	0.254126i	$-0.918212\pi$
$487$	−2.40112e12	−1.93434	−0.967171	+	0.254126i	$0.918212\pi$
$488$	−1.14627e12	−0.914951
$489$	−4.89155e10	−0.0386862
$490$	−2.50385e12	−1.96212
$491$	−3.93654e11	−0.305666	−0.152833	−	0.988252i	$-0.548840\pi$
$491$	−3.93654e11	−0.305666	−0.152833	+	0.988252i	$0.548840\pi$
$492$	5.78667e11	0.445231
$493$	0	0
$494$	−5.95409e11	−0.449826
$495$	6.40605e11	0.479587
$496$	2.95129e11	0.218950
$497$	6.89700e11	0.507057
$498$	−4.66093e11	−0.339579
$499$	1.16585e12	0.841763	0.420881	−	0.907116i	$-0.361721\pi$
$499$	1.16585e12	0.841763	0.420881	+	0.907116i	$0.361721\pi$
$500$	1.60998e12	1.15201
$501$	−3.90760e11	−0.277102
$502$	−6.98053e11	−0.490593
$503$	1.06497e12	0.741794	0.370897	−	0.928674i	$-0.379050\pi$
$503$	1.06497e12	0.741794	0.370897	+	0.928674i	$0.379050\pi$
$504$	1.79290e12	1.23771
$505$	2.22958e12	1.52550
$506$	3.45544e11	0.234329
$507$	−3.25611e11	−0.218858
$508$	−9.58931e11	−0.638853
$509$	−1.27920e12	−0.844711	−0.422355	−	0.906430i	$-0.638797\pi$
$509$	−1.27920e12	−0.844711	−0.422355	+	0.906430i	$0.638797\pi$
$510$	0	0
$511$	1.91407e12	1.24184
$512$	7.70679e11	0.495631
$513$	−1.55784e12	−0.993103
$514$	3.97161e11	0.250976
$515$	4.50625e12	2.82282
$516$	1.99750e11	0.124041
$517$	−1.01004e12	−0.621771
$518$	7.54659e11	0.460540
$519$	1.53076e11	0.0926089
$520$	−1.90188e12	−1.14069
$521$	−1.01572e12	−0.603955	−0.301977	−	0.953315i	$-0.597647\pi$
$521$	−1.01572e12	−0.603955	−0.301977	+	0.953315i	$0.597647\pi$
$522$	2.67600e11	0.157750
$523$	−7.26782e10	−0.0424763	−0.0212381	−	0.999774i	$-0.506761\pi$
$523$	−7.26782e10	−0.0424763	−0.0212381	+	0.999774i	$0.506761\pi$
$524$	−6.23316e11	−0.361175
$525$	2.89083e12	1.66076
$526$	4.63017e10	0.0263731
$527$	0	0
$528$	8.04740e10	0.0450612
$529$	9.13829e11	0.507358
$530$	−7.24456e10	−0.0398814
$531$	1.03871e12	0.566980
$532$	−2.79773e12	−1.51427
$533$	1.74839e12	0.938354
$534$	−1.24832e10	−0.00664339
$535$	−2.25682e11	−0.119098
$536$	−1.51382e12	−0.792195
$537$	−2.49903e11	−0.129684
$538$	−7.49324e11	−0.385611
$539$	1.57183e12	0.802153
$540$	−2.09489e12	−1.06020
$541$	4.64227e11	0.232993	0.116496	−	0.993191i	$-0.462834\pi$
$541$	4.64227e11	0.232993	0.116496	+	0.993191i	$0.462834\pi$
$542$	5.05434e11	0.251575
$543$	−1.29411e12	−0.638809
$544$	0	0
$545$	−4.12345e12	−2.00205
$546$	−6.91300e11	−0.332889
$547$	2.64589e12	1.26366	0.631828	−	0.775109i	$-0.282305\pi$
$547$	2.64589e12	1.26366	0.631828	+	0.775109i	$0.282305\pi$
$548$	−3.63937e11	−0.172391
$549$	−1.65637e12	−0.778181
$550$	7.88964e11	0.367642
$551$	−9.91894e11	−0.458441
$552$	−1.16542e12	−0.534267
$553$	−1.13910e12	−0.517964
$554$	1.57038e12	0.708291
$555$	−9.09425e11	−0.406863
$556$	−1.88857e11	−0.0838101
$557$	−1.89427e11	−0.0833862	−0.0416931	−	0.999130i	$-0.513275\pi$
$557$	−1.89427e11	−0.0833862	−0.0416931	+	0.999130i	$0.513275\pi$
$558$	−7.86042e11	−0.343235
$559$	6.03528e11	0.261423
$560$	−1.81994e12	−0.782009
$561$	0	0
$562$	−1.70163e12	−0.719537
$563$	3.50385e12	1.46980	0.734900	−	0.678175i	$-0.237229\pi$
$563$	3.50385e12	1.46980	0.734900	+	0.678175i	$0.237229\pi$
$564$	1.43413e12	0.596806
$565$	2.45493e12	1.01349
$566$	−7.95395e11	−0.325769
$567$	1.56735e12	0.636858
$568$	−6.34857e11	−0.255923
$569$	4.15736e12	1.66270	0.831348	−	0.555752i	$-0.187570\pi$
$569$	4.15736e12	1.66270	0.831348	+	0.555752i	$0.187570\pi$
$570$	−1.26553e12	−0.502151
$571$	−3.38832e12	−1.33390	−0.666948	−	0.745104i	$-0.732400\pi$
$571$	−3.38832e12	−1.33390	−0.666948	+	0.745104i	$0.732400\pi$
$572$	5.02634e11	0.196322
$573$	−2.98686e11	−0.115749
$574$	−3.08375e12	−1.18570
$575$	6.19899e12	2.36492
$576$	−5.78617e11	−0.219023
$577$	−7.93761e11	−0.298125	−0.149062	−	0.988828i	$-0.547626\pi$
$577$	−7.93761e11	−0.298125	−0.149062	+	0.988828i	$0.547626\pi$
$578$	0	0
$579$	4.04955e11	0.149745
$580$	−1.33384e12	−0.489415
$581$	−6.61718e12	−2.40924
$582$	−1.31817e12	−0.476231
$583$	4.54789e10	0.0163043
$584$	−1.76187e12	−0.626782
$585$	−2.74823e12	−0.970178
$586$	1.03566e12	0.362809
$587$	3.50948e12	1.22003	0.610016	−	0.792389i	$-0.291163\pi$
$587$	3.50948e12	1.22003	0.610016	+	0.792389i	$0.291163\pi$
$588$	−2.23181e12	−0.769946
$589$	2.91357e12	0.997485
$590$	1.94339e12	0.660277
$591$	−1.85738e12	−0.626262
$592$	3.76879e11	0.126111
$593$	1.01035e12	0.335527	0.167763	−	0.985827i	$-0.446346\pi$
$593$	1.01035e12	0.335527	0.167763	+	0.985827i	$0.446346\pi$
$594$	−4.93637e11	−0.162693
$595$	0	0
$596$	1.26331e12	0.410112
$597$	−2.26114e12	−0.728521
$598$	−1.48240e12	−0.474034
$599$	1.26453e12	0.401337	0.200669	−	0.979659i	$-0.435689\pi$
$599$	1.26453e12	0.401337	0.200669	+	0.979659i	$0.435689\pi$
$600$	−2.66096e12	−0.838220
$601$	−4.11286e12	−1.28591	−0.642953	−	0.765906i	$-0.722291\pi$
$601$	−4.11286e12	−1.28591	−0.642953	+	0.765906i	$0.722291\pi$
$602$	−1.06448e12	−0.330334
$603$	−2.18747e12	−0.673775
$604$	−9.46338e11	−0.289321
$605$	4.88466e12	1.48230
$606$	−7.45971e11	−0.224696
$607$	−2.94970e12	−0.881919	−0.440959	−	0.897527i	$-0.645362\pi$
$607$	−2.94970e12	−0.881919	−0.440959	+	0.897527i	$0.645362\pi$
$608$	4.06637e12	1.20681
$609$	−1.15164e12	−0.339265
$610$	−3.09901e12	−0.906232
$611$	4.33311e12	1.25781
$612$	0	0
$613$	−1.04819e12	−0.299825	−0.149912	−	0.988699i	$-0.547899\pi$
$613$	−1.04819e12	−0.299825	−0.149912	+	0.988699i	$0.547899\pi$
$614$	2.72444e12	0.773606
$615$	3.71616e12	1.04751
$616$	−2.10582e12	−0.589261
$617$	2.24197e12	0.622797	0.311398	−	0.950279i	$-0.399203\pi$
$617$	2.24197e12	0.622797	0.311398	+	0.950279i	$0.399203\pi$
$618$	−1.50770e12	−0.415782
$619$	4.31403e12	1.18107	0.590534	−	0.807013i	$-0.298917\pi$
$619$	4.31403e12	1.18107	0.590534	+	0.807013i	$0.298917\pi$
$620$	3.91799e12	1.06488
$621$	−3.87857e12	−1.04655
$622$	−3.41664e11	−0.0915256
$623$	−1.77225e11	−0.0471335
$624$	−3.45237e11	−0.0911564
$625$	2.99120e12	0.784124
$626$	3.49816e12	0.910448
$627$	7.94454e11	0.205289
$628$	3.20010e12	0.821004
$629$	0	0
$630$	4.84721e12	1.22591
$631$	−5.04376e12	−1.26655	−0.633275	−	0.773927i	$-0.718290\pi$
$631$	−5.04376e12	−1.26655	−0.633275	+	0.773927i	$0.718290\pi$
$632$	1.04852e12	0.261428
$633$	−3.04552e11	−0.0753953
$634$	3.69772e12	0.908934
$635$	−6.15819e12	−1.50304
$636$	−6.45745e10	−0.0156496
$637$	−6.74324e12	−1.62271
$638$	−3.14305e11	−0.0751031
$639$	−9.17371e11	−0.217666
$640$	6.43818e12	1.51689
$641$	−4.31567e12	−1.00969	−0.504844	−	0.863210i	$-0.668450\pi$
$641$	−4.31567e12	−1.00969	−0.504844	+	0.863210i	$0.668450\pi$
$642$	7.55084e10	0.0175423
$643$	4.67632e12	1.07883	0.539417	−	0.842039i	$-0.318645\pi$
$643$	4.67632e12	1.07883	0.539417	+	0.842039i	$0.318645\pi$
$644$	−6.96554e12	−1.59576
$645$	1.28278e12	0.291833
$646$	0	0
$647$	−2.41143e11	−0.0541010	−0.0270505	−	0.999634i	$-0.508611\pi$
$647$	−2.41143e11	−0.0541010	−0.0270505	+	0.999634i	$0.508611\pi$
$648$	−1.44272e12	−0.321436
$649$	−1.21999e12	−0.269933
$650$	−3.38469e12	−0.743719
$651$	3.38280e12	0.738179
$652$	2.69112e11	0.0583202
$653$	−5.60932e12	−1.20726	−0.603631	−	0.797264i	$-0.706280\pi$
$653$	−5.60932e12	−1.20726	−0.603631	+	0.797264i	$0.706280\pi$
$654$	1.37962e12	0.294890
$655$	−4.00289e12	−0.849744
$656$	−1.54003e12	−0.324685
$657$	−2.54591e12	−0.533088
$658$	−7.64256e12	−1.58936
$659$	−5.89433e12	−1.21745	−0.608724	−	0.793382i	$-0.708318\pi$
$659$	−5.89433e12	−1.21745	−0.608724	+	0.793382i	$0.708318\pi$
$660$	1.06833e12	0.219159
$661$	−6.88972e11	−0.140377	−0.0701883	−	0.997534i	$-0.522360\pi$
$661$	−6.88972e11	−0.140377	−0.0701883	+	0.997534i	$0.522360\pi$
$662$	1.05326e11	0.0213145
$663$	0	0
$664$	6.09100e12	1.21600
$665$	−1.79668e13	−3.56266
$666$	−1.00377e12	−0.197698
$667$	−2.46953e12	−0.483113
$668$	2.14979e12	0.417736
$669$	−3.11258e12	−0.600763
$670$	−4.09270e12	−0.784645
$671$	1.94546e12	0.370484
$672$	4.72126e12	0.893091
$673$	−5.91814e12	−1.11203	−0.556016	−	0.831171i	$-0.687671\pi$
$673$	−5.91814e12	−1.11203	−0.556016	+	0.831171i	$0.687671\pi$
$674$	−3.43869e11	−0.0641836
$675$	−8.85577e12	−1.64195
$676$	1.79137e12	0.329933
$677$	−9.75918e12	−1.78552	−0.892759	−	0.450534i	$-0.851234\pi$
$677$	−9.75918e12	−1.78552	−0.892759	+	0.450534i	$0.851234\pi$
$678$	−8.21368e11	−0.149281
$679$	−1.87142e13	−3.37876
$680$	0	0
$681$	−1.13952e12	−0.203030
$682$	9.23232e11	0.163411
$683$	1.05702e12	0.185862	0.0929310	−	0.995673i	$-0.470376\pi$
$683$	1.05702e12	0.185862	0.0929310	+	0.995673i	$0.470376\pi$
$684$	3.72126e12	0.650037
$685$	−2.33718e12	−0.405587
$686$	6.47654e12	1.11657
$687$	3.07752e12	0.527103
$688$	−5.31604e11	−0.0904566
$689$	−1.95107e11	−0.0329826
$690$	−3.15080e12	−0.529175
$691$	1.03154e12	0.172122	0.0860608	−	0.996290i	$-0.472572\pi$
$691$	1.03154e12	0.172122	0.0860608	+	0.996290i	$0.472572\pi$
$692$	−8.42156e11	−0.139610
$693$	−3.04291e12	−0.501176
$694$	−1.29590e12	−0.212058
$695$	−1.21283e12	−0.197182
$696$	1.06006e12	0.171234
$697$	0	0
$698$	−7.51336e11	−0.119808
$699$	3.38978e12	0.537061
$700$	−1.59041e13	−2.50362
$701$	5.14597e12	0.804889	0.402444	−	0.915444i	$-0.368161\pi$
$701$	5.14597e12	0.804889	0.402444	+	0.915444i	$0.368161\pi$
$702$	2.11773e12	0.329119
$703$	3.72062e12	0.574535
$704$	6.79605e11	0.104275
$705$	9.20991e12	1.40412
$706$	9.21324e11	0.139570
$707$	−1.05906e13	−1.59417
$708$	1.73225e12	0.259096
$709$	1.28349e13	1.90759	0.953795	−	0.300458i	$-0.0971395\pi$
$709$	1.28349e13	1.90759	0.953795	+	0.300458i	$0.0971395\pi$
$710$	−1.71638e12	−0.253483
$711$	1.51512e12	0.222348
$712$	1.63133e11	0.0237893
$713$	7.25395e12	1.05117
$714$	0	0
$715$	3.22788e12	0.461892
$716$	1.37486e12	0.195501
$717$	3.21711e12	0.454600
$718$	3.62727e12	0.509354
$719$	6.51717e12	0.909451	0.454725	−	0.890632i	$-0.349737\pi$
$719$	6.51717e12	0.909451	0.454725	+	0.890632i	$0.349737\pi$
$720$	2.42071e12	0.335697
$721$	−2.14050e13	−2.94989
$722$	1.36303e12	0.186675
$723$	−5.58000e12	−0.759472
$724$	7.11962e12	0.963016
$725$	−5.63857e12	−0.757963
$726$	−1.63430e12	−0.218332
$727$	−4.75481e12	−0.631290	−0.315645	−	0.948877i	$-0.602221\pi$
$727$	−4.75481e12	−0.631290	−0.315645	+	0.948877i	$0.602221\pi$
$728$	9.03406e12	1.19204
$729$	1.05033e12	0.137737
$730$	−4.76333e12	−0.620808
$731$	0	0
$732$	−2.76231e12	−0.355609
$733$	−4.70068e12	−0.601441	−0.300721	−	0.953712i	$-0.597227\pi$
$733$	−4.70068e12	−0.601441	−0.300721	+	0.953712i	$0.597227\pi$
$734$	2.51923e12	0.320358
$735$	−1.43326e13	−1.81147
$736$	1.01241e13	1.27176
$737$	2.56926e12	0.320778
$738$	4.10170e12	0.508991
$739$	7.68600e12	0.947983	0.473992	−	0.880529i	$-0.342813\pi$
$739$	7.68600e12	0.947983	0.473992	+	0.880529i	$0.342813\pi$
$740$	5.00326e12	0.613353
$741$	−3.40825e12	−0.415288
$742$	3.44121e11	0.0416767
$743$	−1.54208e13	−1.85634	−0.928170	−	0.372156i	$-0.878618\pi$
$743$	−1.54208e13	−1.85634	−0.928170	+	0.372156i	$0.878618\pi$
$744$	−3.11381e12	−0.372575
$745$	8.11290e12	0.964879
$746$	2.68431e12	0.317328
$747$	8.80152e12	1.03423
$748$	0	0
$749$	1.07200e12	0.124459
$750$	−3.45927e12	−0.399217
$751$	6.56715e12	0.753351	0.376676	−	0.926345i	$-0.377067\pi$
$751$	6.56715e12	0.753351	0.376676	+	0.926345i	$0.377067\pi$
$752$	−3.81672e12	−0.435221
$753$	−3.99580e12	−0.452925
$754$	1.34838e12	0.151929
$755$	−6.07732e12	−0.680693
$756$	9.95085e12	1.10793
$757$	−1.40433e13	−1.55431	−0.777156	−	0.629308i	$-0.783338\pi$
$757$	−1.40433e13	−1.55431	−0.777156	+	0.629308i	$0.783338\pi$
$758$	−4.18026e12	−0.459930
$759$	1.97796e12	0.216337
$760$	1.65382e13	1.79815
$761$	−9.41842e12	−1.01800	−0.508999	−	0.860767i	$-0.669984\pi$
$761$	−9.41842e12	−1.01800	−0.508999	+	0.860767i	$0.669984\pi$
$762$	2.06040e12	0.221388
$763$	1.95866e13	2.09218
$764$	1.64324e12	0.174494
$765$	0	0
$766$	−7.91425e12	−0.830578
$767$	5.23384e12	0.546061
$768$	−3.48125e12	−0.361085
$769$	1.32235e13	1.36358	0.681788	−	0.731550i	$-0.261203\pi$
$769$	1.32235e13	1.36358	0.681788	+	0.731550i	$0.261203\pi$
$770$	−5.69321e12	−0.583645
$771$	2.27343e12	0.231706
$772$	−2.22789e12	−0.225744
$773$	−1.14561e13	−1.15406	−0.577031	−	0.816722i	$-0.695789\pi$
$773$	−1.14561e13	−1.15406	−0.577031	+	0.816722i	$0.695789\pi$
$774$	1.41587e12	0.141804
$775$	1.65626e13	1.64919
$776$	1.72261e13	1.70533
$777$	4.31983e12	0.425179
$778$	7.82608e12	0.765837
$779$	−1.52035e13	−1.47919
$780$	−4.58320e12	−0.443347
$781$	1.07748e12	0.103629
$782$	0	0
$783$	3.52793e12	0.335422
$784$	5.93962e12	0.561483
$785$	2.05508e13	1.93159
$786$	1.33929e12	0.125162
$787$	−4.46778e12	−0.415151	−0.207575	−	0.978219i	$-0.566557\pi$
$787$	−4.46778e12	−0.415151	−0.207575	+	0.978219i	$0.566557\pi$
$788$	1.02185e13	0.944101
$789$	2.65041e11	0.0243482
$790$	2.83475e12	0.258936
$791$	−1.16611e13	−1.05912
$792$	2.80095e12	0.252954
$793$	−8.34610e12	−0.749470
$794$	7.81484e12	0.697795
$795$	−4.14694e11	−0.0368193
$796$	1.24398e13	1.09826
$797$	−1.13816e13	−0.999177	−0.499589	−	0.866263i	$-0.666515\pi$
$797$	−1.13816e13	−0.999177	−0.499589	+	0.866263i	$0.666515\pi$
$798$	6.01133e12	0.524756
$799$	0	0
$800$	2.31159e13	1.99529
$801$	2.35728e11	0.0202332
$802$	−7.76311e12	−0.662600
$803$	2.99026e12	0.253798
$804$	−3.64804e12	−0.307898
$805$	−4.47323e13	−3.75439
$806$	−3.96071e12	−0.330571
$807$	−4.28929e12	−0.356003
$808$	9.74851e12	0.804613
$809$	1.94386e13	1.59550	0.797748	−	0.602991i	$-0.206024\pi$
$809$	1.94386e13	1.59550	0.797748	+	0.602991i	$0.206024\pi$
$810$	−3.90048e12	−0.318373
$811$	−1.02059e12	−0.0828431	−0.0414216	−	0.999142i	$-0.513189\pi$
$811$	−1.02059e12	−0.0828431	−0.0414216	+	0.999142i	$0.513189\pi$
$812$	6.33582e12	0.511447
$813$	2.89321e12	0.232259
$814$	1.17896e12	0.0941219
$815$	1.72822e12	0.137211
$816$	0	0
$817$	−5.24809e12	−0.412099
$818$	−5.15564e12	−0.402618
$819$	1.30542e13	1.01385
$820$	−2.04447e13	−1.57913
$821$	−2.88205e12	−0.221390	−0.110695	−	0.993854i	$-0.535308\pi$
$821$	−2.88205e12	−0.221390	−0.110695	+	0.993854i	$0.535308\pi$
$822$	7.81971e11	0.0597403
$823$	−1.16904e13	−0.888237	−0.444118	−	0.895968i	$-0.646483\pi$
$823$	−1.16904e13	−0.888237	−0.444118	+	0.895968i	$0.646483\pi$
$824$	1.97029e13	1.48887
$825$	4.51619e12	0.339414
$826$	−9.23122e12	−0.690000
$827$	−5.81279e12	−0.432126	−0.216063	−	0.976379i	$-0.569322\pi$
$827$	−5.81279e12	−0.432126	−0.216063	+	0.976379i	$0.569322\pi$
$828$	9.26488e12	0.685020
$829$	6.40775e12	0.471205	0.235603	−	0.971849i	$-0.424294\pi$
$829$	6.40775e12	0.471205	0.235603	+	0.971849i	$0.424294\pi$
$830$	1.64674e13	1.20441
$831$	8.98920e12	0.653907
$832$	−2.91554e12	−0.210942
$833$	0	0
$834$	4.05787e11	0.0290436
$835$	1.38058e13	0.982817
$836$	−4.37074e12	−0.309476
$837$	−1.03629e13	−0.729819
$838$	−7.87680e12	−0.551762
$839$	3.65270e12	0.254498	0.127249	−	0.991871i	$-0.459385\pi$
$839$	3.65270e12	0.254498	0.127249	+	0.991871i	$0.459385\pi$
$840$	1.92016e13	1.33070
$841$	−1.22609e13	−0.845161
$842$	−5.53712e12	−0.379647
$843$	−9.74051e12	−0.664290
$844$	1.67551e12	0.113660
$845$	1.15041e13	0.776240
$846$	1.01654e13	0.682272
$847$	−2.32024e13	−1.54902
$848$	1.71855e11	0.0114125
$849$	−4.55301e12	−0.300756
$850$	0	0
$851$	9.26328e12	0.605455
$852$	−1.52990e12	−0.0994681
$853$	−2.63808e13	−1.70615	−0.853076	−	0.521787i	$-0.825266\pi$
$853$	−2.63808e13	−1.70615	−0.853076	+	0.521787i	$0.825266\pi$
$854$	1.47205e13	0.947027
$855$	2.38977e13	1.52936
$856$	−9.86760e11	−0.0628173
$857$	2.49098e13	1.57745	0.788726	−	0.614745i	$-0.210741\pi$
$857$	2.49098e13	1.57745	0.788726	+	0.614745i	$0.210741\pi$
$858$	−1.07998e12	−0.0680336
$859$	2.76464e13	1.73248	0.866242	−	0.499625i	$-0.166529\pi$
$859$	2.76464e13	1.73248	0.866242	+	0.499625i	$0.166529\pi$
$860$	−7.05731e12	−0.439943
$861$	−1.76520e13	−1.09466
$862$	4.05810e12	0.250346
$863$	6.15764e12	0.377890	0.188945	−	0.981988i	$-0.439493\pi$
$863$	6.15764e12	0.377890	0.188945	+	0.981988i	$0.439493\pi$
$864$	−1.44631e13	−0.882977
$865$	−5.40827e12	−0.328463
$866$	−1.54717e13	−0.934776
$867$	0	0
$868$	−1.86107e13	−1.11282
$869$	−1.77956e12	−0.105858
$870$	2.86595e12	0.169602
$871$	−1.10222e13	−0.648915
$872$	−1.80292e13	−1.05597
$873$	2.48918e13	1.45041
$874$	1.28905e13	0.747252
$875$	−4.91117e13	−2.83236
$876$	−4.24580e12	−0.243608
$877$	−1.26417e11	−0.00721619	−0.00360809	−	0.999993i	$-0.501148\pi$
$877$	−1.26417e11	−0.00721619	−0.00360809	+	0.999993i	$0.501148\pi$
$878$	−6.48054e12	−0.368032
$879$	5.92833e12	0.334952
$880$	−2.84320e12	−0.159822
$881$	−1.81563e13	−1.01540	−0.507699	−	0.861535i	$-0.669504\pi$
$881$	−1.81563e13	−1.01540	−0.507699	+	0.861535i	$0.669504\pi$
$882$	−1.58195e13	−0.880206
$883$	−3.40979e13	−1.88758	−0.943788	−	0.330553i	$-0.892765\pi$
$883$	−3.40979e13	−1.88758	−0.943788	+	0.330553i	$0.892765\pi$
$884$	0	0
$885$	1.11244e13	0.609580
$886$	−1.18270e11	−0.00644797
$887$	−1.64233e13	−0.890851	−0.445426	−	0.895319i	$-0.646948\pi$
$887$	−1.64233e13	−0.890851	−0.445426	+	0.895319i	$0.646948\pi$
$888$	−3.97633e12	−0.214597
$889$	2.92518e13	1.57071
$890$	4.41039e11	0.0235626
$891$	2.44859e12	0.130157
$892$	1.71241e13	0.905661
$893$	−3.76794e13	−1.98277
$894$	−2.71441e12	−0.142120
$895$	8.82926e12	0.459961
$896$	−3.05818e13	−1.58517
$897$	−8.48556e12	−0.437637
$898$	1.06072e12	0.0544323
$899$	−6.59816e12	−0.336902
$900$	2.11541e13	1.07474
$901$	0	0
$902$	−4.81757e12	−0.242325
$903$	−6.09330e12	−0.304970
$904$	1.07338e13	0.534560
$905$	4.57217e13	2.26571
$906$	2.03335e12	0.100262
$907$	3.95675e12	0.194136	0.0970679	−	0.995278i	$-0.469054\pi$
$907$	3.95675e12	0.194136	0.0970679	+	0.995278i	$0.469054\pi$
$908$	6.26915e12	0.306071
$909$	1.40866e13	0.684337
$910$	2.44241e13	1.18068
$911$	−9.23006e12	−0.443989	−0.221994	−	0.975048i	$-0.571257\pi$
$911$	−9.23006e12	−0.443989	−0.221994	+	0.975048i	$0.571257\pi$
$912$	3.00207e12	0.143696
$913$	−1.03377e13	−0.492384
$914$	−1.33772e13	−0.634028
$915$	−1.77394e13	−0.836650
$916$	−1.69312e13	−0.794616
$917$	1.90140e13	0.887997
$918$	0	0
$919$	−3.01409e13	−1.39391	−0.696957	−	0.717113i	$-0.745463\pi$
$919$	−3.01409e13	−1.39391	−0.696957	+	0.717113i	$0.745463\pi$
$920$	4.11753e13	1.89492
$921$	1.55953e13	0.714208
$922$	−2.08194e13	−0.948810
$923$	−4.62245e12	−0.209635
$924$	−5.07465e12	−0.229025
$925$	2.11504e13	0.949907
$926$	−7.09682e12	−0.317186
$927$	2.84708e13	1.26631
$928$	−9.20882e12	−0.407604
$929$	−3.04484e13	−1.34120	−0.670601	−	0.741818i	$-0.733964\pi$
$929$	−3.04484e13	−1.34120	−0.670601	+	0.741818i	$0.733964\pi$
$930$	−8.41837e12	−0.369024
$931$	5.86371e13	2.55799
$932$	−1.86491e13	−0.809629
$933$	−1.95576e12	−0.0844981
$934$	−8.64049e12	−0.371516
$935$	0	0
$936$	−1.20162e13	−0.511713
$937$	2.04000e13	0.864572	0.432286	−	0.901736i	$-0.357707\pi$
$937$	2.04000e13	0.864572	0.432286	+	0.901736i	$0.357707\pi$
$938$	1.94406e13	0.819967
$939$	2.00242e13	0.840543
$940$	−5.06689e13	−2.11673
$941$	2.55881e13	1.06386	0.531930	−	0.846789i	$-0.321467\pi$
$941$	2.55881e13	1.06386	0.531930	+	0.846789i	$0.321467\pi$
$942$	−6.87588e12	−0.284511
$943$	−3.78523e13	−1.55880
$944$	−4.61010e12	−0.188945
$945$	6.39037e13	2.60665
$946$	−1.66298e12	−0.0675113
$947$	−8.56722e12	−0.346151	−0.173075	−	0.984909i	$-0.555370\pi$
$947$	−8.56722e12	−0.346151	−0.173075	+	0.984909i	$0.555370\pi$
$948$	2.52676e12	0.101608
$949$	−1.28283e13	−0.513420
$950$	2.94322e13	1.17238
$951$	2.11665e13	0.839146
$952$	0	0
$953$	−3.84991e13	−1.51193	−0.755966	−	0.654611i	$-0.772832\pi$
$953$	−3.84991e13	−1.51193	−0.755966	+	0.654611i	$0.772832\pi$
$954$	−4.57716e11	−0.0178907
$955$	1.05528e13	0.410537
$956$	−1.76991e13	−0.685317
$957$	−1.79915e12	−0.0693366
$958$	2.08089e13	0.798187
$959$	1.11017e13	0.423845
$960$	−6.19689e12	−0.235480
$961$	−7.05834e12	−0.266961
$962$	−5.05781e12	−0.190404
$963$	−1.42587e12	−0.0534272
$964$	3.06987e13	1.14492
$965$	−1.43073e13	−0.531112
$966$	1.49665e13	0.552997
$967$	4.31991e13	1.58875	0.794375	−	0.607428i	$-0.207799\pi$
$967$	4.31991e13	1.58875	0.794375	+	0.607428i	$0.207799\pi$
$968$	2.13574e13	0.781826
$969$	0	0
$970$	4.65718e13	1.68908
$971$	−1.97835e13	−0.714196	−0.357098	−	0.934067i	$-0.616234\pi$
$971$	−1.97835e13	−0.714196	−0.357098	+	0.934067i	$0.616234\pi$
$972$	−2.07245e13	−0.744707
$973$	5.76100e12	0.206058
$974$	−2.83834e13	−1.01053
$975$	−1.93747e13	−0.686616
$976$	7.35146e12	0.259328
$977$	−2.56325e13	−0.900047	−0.450024	−	0.893017i	$-0.648584\pi$
$977$	−2.56325e13	−0.900047	−0.450024	+	0.893017i	$0.648584\pi$
$978$	−5.78226e11	−0.0202103
$979$	−2.76870e11	−0.00963281
$980$	7.88516e13	2.73082
$981$	−2.60522e13	−0.898119
$982$	−4.65335e12	−0.159685
$983$	3.03713e13	1.03746	0.518732	−	0.854937i	$-0.326404\pi$
$983$	3.03713e13	1.03746	0.518732	+	0.854937i	$0.326404\pi$
$984$	1.62484e13	0.552499
$985$	6.56224e13	2.22121
$986$	0	0
$987$	−4.37476e13	−1.46733
$988$	1.87507e13	0.626053
$989$	−1.30662e13	−0.434278
$990$	7.57254e12	0.250544
$991$	1.54521e13	0.508929	0.254465	−	0.967082i	$-0.418101\pi$
$991$	1.54521e13	0.508929	0.254465	+	0.967082i	$0.418101\pi$
$992$	2.70498e13	0.886873
$993$	6.02910e11	0.0196780
$994$	8.15289e12	0.264894
$995$	7.98875e13	2.58390
$996$	1.46783e13	0.472615
$997$	7.77458e12	0.249201	0.124600	−	0.992207i	$-0.460235\pi$
$997$	7.77458e12	0.249201	0.124600	+	0.992207i	$0.460235\pi$
$998$	1.37814e13	0.439750
$999$	−1.32333e13	−0.420364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.a.1.4		5
17.16	even	2		17.10.a.a.1.4	✓	5
51.50	odd	2		153.10.a.c.1.2		5
68.67	odd	2		272.10.a.f.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.a.1.4	✓	5	17.16	even	2
153.10.a.c.1.2		5	51.50	odd	2
272.10.a.f.1.3		5	68.67	odd	2
289.10.a.a.1.4		5	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)

\(f(q)\)	\(=\)	\(q+11.8209 q^{2} +67.6654 q^{3} -372.266 q^{4} -2390.67 q^{5} +799.867 q^{6} +11355.8 q^{7} -10452.8 q^{8} -15104.4 q^{9} +O(q^{10})\)	\(q+11.8209 q^{2} +67.6654 q^{3} -372.266 q^{4} -2390.67 q^{5} +799.867 q^{6} +11355.8 q^{7} -10452.8 q^{8} -15104.4 q^{9} -28259.9 q^{10} +17740.6 q^{11} -25189.5 q^{12} -76108.0 q^{13} +134236. q^{14} -161765. q^{15} +67038.0 q^{16} -178548. q^{18} +661811. q^{19} +889964. q^{20} +768396. q^{21} +209710. q^{22} +1.64772e6 q^{23} -707295. q^{24} +3.76216e6 q^{25} -899667. q^{26} -2.35390e6 q^{27} -4.22738e6 q^{28} -1.49876e6 q^{29} -1.91222e6 q^{30} +4.40242e6 q^{31} +6.14430e6 q^{32} +1.20042e6 q^{33} -2.71480e7 q^{35} +5.62285e6 q^{36} +5.62188e6 q^{37} +7.82322e6 q^{38} -5.14988e6 q^{39} +2.49892e7 q^{40} -2.29725e7 q^{41} +9.08315e6 q^{42} -7.92989e6 q^{43} -6.60422e6 q^{44} +3.61096e7 q^{45} +1.94776e7 q^{46} -5.69337e7 q^{47} +4.53615e6 q^{48} +8.86009e7 q^{49} +4.44722e7 q^{50} +2.83324e7 q^{52} +2.56355e6 q^{53} -2.78253e7 q^{54} -4.24119e7 q^{55} -1.18700e8 q^{56} +4.47817e7 q^{57} -1.77167e7 q^{58} -6.87685e7 q^{59} +6.02197e7 q^{60} +1.09661e8 q^{61} +5.20406e7 q^{62} -1.71523e8 q^{63} +3.83079e7 q^{64} +1.81949e8 q^{65} +1.41901e7 q^{66} +1.44824e8 q^{67} +1.11494e8 q^{69} -3.20914e8 q^{70} +6.07354e7 q^{71} +1.57884e8 q^{72} +1.68554e8 q^{73} +6.64557e7 q^{74} +2.54568e8 q^{75} -2.46370e8 q^{76} +2.01459e8 q^{77} -6.08763e7 q^{78} -1.00310e8 q^{79} -1.60265e8 q^{80} +1.38022e8 q^{81} -2.71557e8 q^{82} -5.82713e8 q^{83} -2.86048e8 q^{84} -9.37386e7 q^{86} -1.01414e8 q^{87} -1.85440e8 q^{88} -1.56066e7 q^{89} +4.26848e8 q^{90} -8.64268e8 q^{91} -6.13390e8 q^{92} +2.97891e8 q^{93} -6.73009e8 q^{94} -1.58217e9 q^{95} +4.15757e8 q^{96} -1.64798e9 q^{97} +1.04734e9 q^{98} -2.67961e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 33 q^{2} + 236 q^{3} + 853 q^{4} - 1480 q^{5} - 7578 q^{6} + 13202 q^{7} - 42423 q^{8} + 10981 q^{9}+O(q^{10}) \) 5 * q - 33 * q^2 + 236 * q^3 + 853 * q^4 - 1480 * q^5 - 7578 * q^6 + 13202 * q^7 - 42423 * q^8 + 10981 * q^9	\( 5 q - 33 q^{2} + 236 q^{3} + 853 q^{4} - 1480 q^{5} - 7578 q^{6} + 13202 q^{7} - 42423 q^{8} + 10981 q^{9} + 89328 q^{10} + 68036 q^{11} + 406010 q^{12} - 158862 q^{13} + 84700 q^{14} - 687324 q^{15} + 350225 q^{16} - 1911585 q^{18} - 370992 q^{19} - 1632640 q^{20} + 1783880 q^{21} - 122290 q^{22} - 1645870 q^{23} - 9678702 q^{24} + 3270239 q^{25} + 734846 q^{26} + 2998268 q^{27} - 183372 q^{28} - 3668616 q^{29} + 17048544 q^{30} + 7262362 q^{31} - 5605919 q^{32} - 11334900 q^{33} - 26503988 q^{35} + 49782133 q^{36} + 31420708 q^{37} + 18513700 q^{38} + 42449884 q^{39} + 53930464 q^{40} + 7996938 q^{41} - 44519496 q^{42} - 56908268 q^{43} - 43323054 q^{44} - 12799536 q^{45} + 32063472 q^{46} - 16903336 q^{47} + 102794498 q^{48} - 11784059 q^{49} + 85921093 q^{50} + 173619082 q^{52} - 83362982 q^{53} - 386329164 q^{54} + 6363364 q^{55} - 317409372 q^{56} - 136615904 q^{57} - 64577488 q^{58} - 37946604 q^{59} - 223158912 q^{60} + 77685452 q^{61} - 324855300 q^{62} + 191945278 q^{63} + 131623105 q^{64} + 40321288 q^{65} + 298037676 q^{66} - 304503600 q^{67} - 333409272 q^{69} - 122787392 q^{70} + 476602922 q^{71} - 1301701911 q^{72} + 289980486 q^{73} - 262289012 q^{74} + 153685772 q^{75} - 1031276084 q^{76} - 143385648 q^{77} - 691646196 q^{78} + 828240610 q^{79} - 912750944 q^{80} + 891328609 q^{81} + 1109615654 q^{82} + 194681148 q^{83} + 1541719592 q^{84} + 1164707144 q^{86} + 158149884 q^{87} + 1017979978 q^{88} + 376848106 q^{89} + 2240087472 q^{90} - 194543664 q^{91} - 2506713088 q^{92} + 3494835920 q^{93} - 2244811104 q^{94} - 1498679864 q^{95} - 2935047582 q^{96} - 692035246 q^{97} + 871744055 q^{98} - 2027106408 q^{99}+O(q^{100}) \) 5 * q - 33 * q^2 + 236 * q^3 + 853 * q^4 - 1480 * q^5 - 7578 * q^6 + 13202 * q^7 - 42423 * q^8 + 10981 * q^9 + 89328 * q^10 + 68036 * q^11 + 406010 * q^12 - 158862 * q^13 + 84700 * q^14 - 687324 * q^15 + 350225 * q^16 - 1911585 * q^18 - 370992 * q^19 - 1632640 * q^20 + 1783880 * q^21 - 122290 * q^22 - 1645870 * q^23 - 9678702 * q^24 + 3270239 * q^25 + 734846 * q^26 + 2998268 * q^27 - 183372 * q^28 - 3668616 * q^29 + 17048544 * q^30 + 7262362 * q^31 - 5605919 * q^32 - 11334900 * q^33 - 26503988 * q^35 + 49782133 * q^36 + 31420708 * q^37 + 18513700 * q^38 + 42449884 * q^39 + 53930464 * q^40 + 7996938 * q^41 - 44519496 * q^42 - 56908268 * q^43 - 43323054 * q^44 - 12799536 * q^45 + 32063472 * q^46 - 16903336 * q^47 + 102794498 * q^48 - 11784059 * q^49 + 85921093 * q^50 + 173619082 * q^52 - 83362982 * q^53 - 386329164 * q^54 + 6363364 * q^55 - 317409372 * q^56 - 136615904 * q^57 - 64577488 * q^58 - 37946604 * q^59 - 223158912 * q^60 + 77685452 * q^61 - 324855300 * q^62 + 191945278 * q^63 + 131623105 * q^64 + 40321288 * q^65 + 298037676 * q^66 - 304503600 * q^67 - 333409272 * q^69 - 122787392 * q^70 + 476602922 * q^71 - 1301701911 * q^72 + 289980486 * q^73 - 262289012 * q^74 + 153685772 * q^75 - 1031276084 * q^76 - 143385648 * q^77 - 691646196 * q^78 + 828240610 * q^79 - 912750944 * q^80 + 891328609 * q^81 + 1109615654 * q^82 + 194681148 * q^83 + 1541719592 * q^84 + 1164707144 * q^86 + 158149884 * q^87 + 1017979978 * q^88 + 376848106 * q^89 + 2240087472 * q^90 - 194543664 * q^91 - 2506713088 * q^92 + 3494835920 * q^93 - 2244811104 * q^94 - 1498679864 * q^95 - 2935047582 * q^96 - 692035246 * q^97 + 871744055 * q^98 - 2027106408 * q^99

Introduction

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