LMFDB - Embedded newform 289.10.a.a.1.2

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			1.2
Root			$-21.1654$ 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)

$f(q)$	$=$	$q-28.1654 q^{2} +3.02373 q^{3} +281.287 q^{4} -762.851 q^{5} -85.1644 q^{6} -5573.11 q^{7} +6498.11 q^{8} -19673.9 q^{9} +O(q^{10})$	\(q-28.1654 q^{2} +3.02373 q^{3} +281.287 q^{4} -762.851 q^{5} -85.1644 q^{6} -5573.11 q^{7} +6498.11 q^{8} -19673.9 q^{9} +21486.0 q^{10} +47641.7 q^{11} +850.536 q^{12} -92260.9 q^{13} +156969. q^{14} -2306.65 q^{15} -327041. q^{16} +554121. q^{18} -8373.93 q^{19} -214580. q^{20} -16851.6 q^{21} -1.34184e6 q^{22} -364592. q^{23} +19648.5 q^{24} -1.37118e6 q^{25} +2.59856e6 q^{26} -119004. q^{27} -1.56764e6 q^{28} +3.50595e6 q^{29} +64967.7 q^{30} +5.20629e6 q^{31} +5.88418e6 q^{32} +144055. q^{33} +4.25145e6 q^{35} -5.53400e6 q^{36} +499530. q^{37} +235855. q^{38} -278972. q^{39} -4.95709e6 q^{40} +5.43648e6 q^{41} +474631. q^{42} -3.54411e7 q^{43} +1.34010e7 q^{44} +1.50082e7 q^{45} +1.02689e7 q^{46} +1.21753e7 q^{47} -988882. q^{48} -9.29403e6 q^{49} +3.86199e7 q^{50} -2.59518e7 q^{52} +1.04471e8 q^{53} +3.35180e6 q^{54} -3.63435e7 q^{55} -3.62147e7 q^{56} -25320.5 q^{57} -9.87464e7 q^{58} +4.16714e7 q^{59} -648832. q^{60} -5.67537e7 q^{61} -1.46637e8 q^{62} +1.09645e8 q^{63} +1.71477e6 q^{64} +7.03813e7 q^{65} -4.05737e6 q^{66} -1.74621e8 q^{67} -1.10243e6 q^{69} -1.19744e8 q^{70} -3.46330e7 q^{71} -1.27843e8 q^{72} +3.93220e8 q^{73} -1.40694e7 q^{74} -4.14609e6 q^{75} -2.35548e6 q^{76} -2.65512e8 q^{77} +7.85734e6 q^{78} -1.85772e8 q^{79} +2.49483e8 q^{80} +3.86881e8 q^{81} -1.53120e8 q^{82} +3.62239e8 q^{83} -4.74013e6 q^{84} +9.98211e8 q^{86} +1.06010e7 q^{87} +3.09581e8 q^{88} -5.04798e7 q^{89} -4.22712e8 q^{90} +5.14180e8 q^{91} -1.02555e8 q^{92} +1.57424e7 q^{93} -3.42920e8 q^{94} +6.38806e6 q^{95} +1.77922e7 q^{96} +9.67620e8 q^{97} +2.61770e8 q^{98} -9.37295e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−28.1654	−1.24474	−0.622372	−	0.782721i	$-0.713831\pi$
$2$	−28.1654	−1.24474	−0.622372	+	0.782721i	$0.713831\pi$
$3$	3.02373	0.0215525	0.0107762	−	0.999942i	$-0.496570\pi$
$3$	3.02373	0.0215525	0.0107762	+	0.999942i	$0.496570\pi$
$4$	281.287	0.549389
$5$	−762.851	−0.545852	−0.272926	−	0.962035i	$-0.587991\pi$
$5$	−762.851	−0.545852	−0.272926	+	0.962035i	$0.587991\pi$
$6$	−85.1644	−0.0268273
$7$	−5573.11	−0.877317	−0.438659	−	0.898654i	$-0.644546\pi$
$7$	−5573.11	−0.877317	−0.438659	+	0.898654i	$0.644546\pi$
$8$	6498.11	0.560896
$9$	−19673.9	−0.999535
$10$	21486.0	0.679446
$11$	47641.7	0.981115	0.490558	−	0.871409i	$-0.336793\pi$
$11$	47641.7	0.981115	0.490558	+	0.871409i	$0.336793\pi$
$12$	850.536	0.0118407
$13$	−92260.9	−0.895927	−0.447963	−	0.894052i	$-0.647851\pi$
$13$	−92260.9	−0.895927	−0.447963	+	0.894052i	$0.647851\pi$
$14$	156969.	1.09204
$15$	−2306.65	−0.0117645
$16$	−327041.	−1.24756
$17$	0	0
$17$	0	0
$18$	554121.	1.24417
$19$	−8373.93	−0.0147414	−0.00737069	−	0.999973i	$-0.502346\pi$
$19$	−8373.93	−0.0147414	−0.00737069	+	0.999973i	$0.502346\pi$
$20$	−214580.	−0.299885
$21$	−16851.6	−0.0189084
$22$	−1.34184e6	−1.22124
$23$	−364592.	−0.271664	−0.135832	−	0.990732i	$-0.543371\pi$
$23$	−364592.	−0.271664	−0.135832	+	0.990732i	$0.543371\pi$
$24$	19648.5	0.0120887
$25$	−1.37118e6	−0.702046
$26$	2.59856e6	1.11520
$27$	−119004.	−0.0430949
$28$	−1.56764e6	−0.481988
$29$	3.50595e6	0.920482	0.460241	−	0.887794i	$-0.347763\pi$
$29$	3.50595e6	0.920482	0.460241	+	0.887794i	$0.347763\pi$
$30$	64967.7	0.0146437
$31$	5.20629e6	1.01251	0.506257	−	0.862383i	$-0.331029\pi$
$31$	5.20629e6	1.01251	0.506257	+	0.862383i	$0.331029\pi$
$32$	5.88418e6	0.991999
$33$	144055.	0.0211455
$34$	0	0
$35$	4.25145e6	0.478885
$36$	−5.53400e6	−0.549134
$37$	499530.	0.0438182	0.0219091	−	0.999760i	$-0.493026\pi$
$37$	499530.	0.0438182	0.0219091	+	0.999760i	$0.493026\pi$
$38$	235855.	0.0183493
$39$	−278972.	−0.0193094
$40$	−4.95709e6	−0.306166
$41$	5.43648e6	0.300463	0.150231	−	0.988651i	$-0.451998\pi$
$41$	5.43648e6	0.300463	0.150231	+	0.988651i	$0.451998\pi$
$42$	474631.	0.0235361
$43$	−3.54411e7	−1.58088	−0.790440	−	0.612539i	$-0.790148\pi$
$43$	−3.54411e7	−1.58088	−0.790440	+	0.612539i	$0.790148\pi$
$44$	1.34010e7	0.539014
$45$	1.50082e7	0.545598
$46$	1.02689e7	0.338152
$47$	1.21753e7	0.363947	0.181973	−	0.983303i	$-0.441752\pi$
$47$	1.21753e7	0.363947	0.181973	+	0.983303i	$0.441752\pi$
$48$	−988882.	−0.0268880
$49$	−9.29403e6	−0.230315
$50$	3.86199e7	0.873868
$51$	0	0
$52$	−2.59518e7	−0.492212
$53$	1.04471e8	1.81867	0.909336	−	0.416063i	$-0.136590\pi$
$53$	1.04471e8	1.81867	0.909336	+	0.416063i	$0.136590\pi$
$54$	3.35180e6	0.0536422
$55$	−3.63435e7	−0.535543
$56$	−3.62147e7	−0.492083
$57$	−25320.5	−0.000317713 0
$58$	−9.87464e7	−1.14576
$59$	4.16714e7	0.447718	0.223859	−	0.974622i	$-0.428135\pi$
$59$	4.16714e7	0.447718	0.223859	+	0.974622i	$0.428135\pi$
$60$	−648832.	−0.00646326
$61$	−5.67537e7	−0.524819	−0.262410	−	0.964957i	$-0.584517\pi$
$61$	−5.67537e7	−0.524819	−0.262410	+	0.964957i	$0.584517\pi$
$62$	−1.46637e8	−1.26032
$63$	1.09645e8	0.876910
$64$	1.71477e6	0.0127760
$65$	7.03813e7	0.489043
$66$	−4.05737e6	−0.0263207
$67$	−1.74621e8	−1.05867	−0.529333	−	0.848414i	$-0.677558\pi$
$67$	−1.74621e8	−1.05867	−0.529333	+	0.848414i	$0.677558\pi$
$68$	0	0
$69$	−1.10243e6	−0.00585503
$70$	−1.19744e8	−0.596089
$71$	−3.46330e7	−0.161744	−0.0808719	−	0.996725i	$-0.525770\pi$
$71$	−3.46330e7	−0.161744	−0.0808719	+	0.996725i	$0.525770\pi$
$72$	−1.27843e8	−0.560635
$73$	3.93220e8	1.62063	0.810314	−	0.585996i	$-0.199297\pi$
$73$	3.93220e8	1.62063	0.810314	+	0.585996i	$0.199297\pi$
$74$	−1.40694e7	−0.0545424
$75$	−4.14609e6	−0.0151308
$76$	−2.35548e6	−0.00809875
$77$	−2.65512e8	−0.860749
$78$	7.85734e6	0.0240353
$79$	−1.85772e8	−0.536609	−0.268305	−	0.963334i	$-0.586463\pi$
$79$	−1.85772e8	−0.536609	−0.268305	+	0.963334i	$0.586463\pi$
$80$	2.49483e8	0.680983
$81$	3.86881e8	0.998607
$82$	−1.53120e8	−0.373999
$83$	3.62239e8	0.837807	0.418903	−	0.908031i	$-0.362415\pi$
$83$	3.62239e8	0.837807	0.418903	+	0.908031i	$0.362415\pi$
$84$	−4.74013e6	−0.0103880
$85$	0	0
$86$	9.98211e8	1.96779
$87$	1.06010e7	0.0198387
$88$	3.09581e8	0.550303
$89$	−5.04798e7	−0.0852831	−0.0426416	−	0.999090i	$-0.513577\pi$
$89$	−5.04798e7	−0.0852831	−0.0426416	+	0.999090i	$0.513577\pi$
$90$	−4.22712e8	−0.679130
$91$	5.14180e8	0.786012
$92$	−1.02555e8	−0.149249
$93$	1.57424e7	0.0218222
$94$	−3.42920e8	−0.453020
$95$	6.38806e6	0.00804661
$96$	1.77922e7	0.0213800
$97$	9.67620e8	1.10977	0.554884	−	0.831928i	$-0.312763\pi$
$97$	9.67620e8	1.10977	0.554884	+	0.831928i	$0.312763\pi$
$98$	2.61770e8	0.286683
$99$	−9.37295e8	−0.980659
$100$	−3.85696e8	−0.385696
$101$	1.60604e9	1.53572	0.767858	−	0.640621i	$-0.221323\pi$
$101$	1.60604e9	1.53572	0.767858	+	0.640621i	$0.221323\pi$
$102$	0	0
$103$	1.76819e9	1.54796	0.773982	−	0.633208i	$-0.218262\pi$
$103$	1.76819e9	1.54796	0.773982	+	0.633208i	$0.218262\pi$
$104$	−5.99522e8	−0.502522
$105$	1.28552e7	0.0103212
$106$	−2.94246e9	−2.26378
$107$	2.59627e9	1.91479	0.957397	−	0.288774i	$-0.0932477\pi$
$107$	2.59627e9	1.91479	0.957397	+	0.288774i	$0.0932477\pi$
$108$	−3.34744e7	−0.0236759
$109$	−2.64333e9	−1.79363	−0.896814	−	0.442408i	$-0.854124\pi$
$109$	−2.64333e9	−1.79363	−0.896814	+	0.442408i	$0.854124\pi$
$110$	1.02363e9	0.666614
$111$	1.51044e6	0.000944390 0
$112$	1.82263e9	1.09451
$113$	−9.53189e8	−0.549954	−0.274977	−	0.961451i	$-0.588670\pi$
$113$	−9.53189e8	−0.549954	−0.274977	+	0.961451i	$0.588670\pi$
$114$	713161.	0.000395472 0
$115$	2.78129e8	0.148288
$116$	9.86179e8	0.505702
$117$	1.81513e9	0.895511
$118$	−1.17369e9	−0.557294
$119$	0	0
$120$	−1.49889e7	−0.00659863
$121$	−8.82187e7	−0.0374133
$122$	1.59849e9	0.653266
$123$	1.64384e7	0.00647571
$124$	1.46446e9	0.556264
$125$	2.53595e9	0.929065
$126$	−3.08818e9	−1.09153
$127$	9.64764e8	0.329082	0.164541	−	0.986370i	$-0.447386\pi$
$127$	9.64764e8	0.329082	0.164541	+	0.986370i	$0.447386\pi$
$128$	−3.06100e9	−1.00790
$129$	−1.07164e8	−0.0340719
$130$	−1.98231e9	−0.608734
$131$	5.24089e9	1.55483	0.777417	−	0.628985i	$-0.216529\pi$
$131$	5.24089e9	1.55483	0.777417	+	0.628985i	$0.216529\pi$
$132$	4.05209e7	0.0116171
$133$	4.66689e7	0.0129329
$134$	4.91825e9	1.31777
$135$	9.07826e7	0.0235234
$136$	0	0
$137$	3.09452e9	0.750500	0.375250	−	0.926924i	$-0.377557\pi$
$137$	3.09452e9	0.750500	0.375250	+	0.926924i	$0.377557\pi$
$138$	3.10503e7	0.00728802
$139$	6.10981e8	0.138823	0.0694115	−	0.997588i	$-0.477888\pi$
$139$	6.10981e8	0.138823	0.0694115	+	0.997588i	$0.477888\pi$
$140$	1.19588e9	0.263094
$141$	3.68147e7	0.00784395
$142$	9.75450e8	0.201330
$143$	−4.39546e9	−0.879007
$144$	6.43415e9	1.24698
$145$	−2.67452e9	−0.502446
$146$	−1.10752e10	−2.01727
$147$	−2.81026e7	−0.00496385
$148$	1.40511e8	0.0240732
$149$	2.02582e9	0.336716	0.168358	−	0.985726i	$-0.446154\pi$
$149$	2.02582e9	0.336716	0.168358	+	0.985726i	$0.446154\pi$
$150$	1.16776e8	0.0188340
$151$	−7.09269e9	−1.11024	−0.555118	−	0.831772i	$-0.687327\pi$
$151$	−7.09269e9	−1.11024	−0.555118	+	0.831772i	$0.687327\pi$
$152$	−5.44147e7	−0.00826838
$153$	0	0
$154$	7.47825e9	1.07141
$155$	−3.97162e9	−0.552682
$156$	−7.84712e7	−0.0106084
$157$	−8.25715e9	−1.08463	−0.542315	−	0.840175i	$-0.682452\pi$
$157$	−8.25715e9	−1.08463	−0.542315	+	0.840175i	$0.682452\pi$
$158$	5.23233e9	0.667941
$159$	3.15892e8	0.0391969
$160$	−4.48875e9	−0.541484
$161$	2.03191e9	0.238335
$162$	−1.08966e10	−1.24301
$163$	6.13273e9	0.680471	0.340235	−	0.940340i	$-0.389493\pi$
$163$	6.13273e9	0.680471	0.340235	+	0.940340i	$0.389493\pi$
$164$	1.52921e9	0.165071
$165$	−1.09893e8	−0.0115423
$166$	−1.02026e10	−1.04286
$167$	1.53224e10	1.52442	0.762208	−	0.647332i	$-0.224115\pi$
$167$	1.53224e10	1.52442	0.762208	+	0.647332i	$0.224115\pi$
$168$	−1.09503e8	−0.0106056
$169$	−2.09243e9	−0.197315
$170$	0	0
$171$	1.64748e8	0.0147345
$172$	−9.96912e9	−0.868518
$173$	−1.45473e10	−1.23474	−0.617370	−	0.786673i	$-0.711802\pi$
$173$	−1.45473e10	−1.23474	−0.617370	+	0.786673i	$0.711802\pi$
$174$	−2.98582e8	−0.0246941
$175$	7.64176e9	0.615917
$176$	−1.55808e10	−1.22400
$177$	1.26003e8	0.00964942
$178$	1.42178e9	0.106156
$179$	4.64898e9	0.338469	0.169235	−	0.985576i	$-0.445870\pi$
$179$	4.64898e9	0.338469	0.169235	+	0.985576i	$0.445870\pi$
$180$	4.22162e9	0.299745
$181$	−1.08585e9	−0.0751997	−0.0375998	−	0.999293i	$-0.511971\pi$
$181$	−1.08585e9	−0.0751997	−0.0375998	+	0.999293i	$0.511971\pi$
$182$	−1.44821e10	−0.978384
$183$	−1.71608e8	−0.0113112
$184$	−2.36916e9	−0.152375
$185$	−3.81067e8	−0.0239182
$186$	−4.43391e8	−0.0271630
$187$	0	0
$188$	3.42474e9	0.199948
$189$	6.63225e8	0.0378079
$190$	−1.79922e8	−0.0100160
$191$	−3.78328e9	−0.205693	−0.102846	−	0.994697i	$-0.532795\pi$
$191$	−3.78328e9	−0.205693	−0.102846	+	0.994697i	$0.532795\pi$
$192$	5.18500e6	0.000275355 0
$193$	−3.16352e10	−1.64121	−0.820603	−	0.571499i	$-0.806362\pi$
$193$	−3.16352e10	−1.64121	−0.820603	+	0.571499i	$0.806362\pi$
$194$	−2.72534e10	−1.38138
$195$	2.12814e8	0.0105401
$196$	−2.61429e9	−0.126532
$197$	−1.24212e10	−0.587576	−0.293788	−	0.955871i	$-0.594916\pi$
$197$	−1.24212e10	−0.587576	−0.293788	+	0.955871i	$0.594916\pi$
$198$	2.63993e10	1.22067
$199$	−4.01627e10	−1.81545	−0.907724	−	0.419568i	$-0.862182\pi$
$199$	−4.01627e10	−1.81545	−0.907724	+	0.419568i	$0.862182\pi$
$200$	−8.91010e9	−0.393775
$201$	−5.28005e8	−0.0228169
$202$	−4.52347e10	−1.91157
$203$	−1.95391e10	−0.807554
$204$	0	0
$205$	−4.14722e9	−0.164008
$206$	−4.98016e10	−1.92682
$207$	7.17293e9	0.271538
$208$	3.01731e10	1.11772
$209$	−3.98948e8	−0.0144630
$210$	−3.62072e8	−0.0128472
$211$	−1.34292e10	−0.466422	−0.233211	−	0.972426i	$-0.574923\pi$
$211$	−1.34292e10	−0.466422	−0.233211	+	0.972426i	$0.574923\pi$
$212$	2.93863e10	0.999158
$213$	−1.04721e8	−0.00348598
$214$	−7.31247e10	−2.38343
$215$	2.70363e10	0.862926
$216$	−7.73304e8	−0.0241718
$217$	−2.90153e10	−0.888296
$218$	7.44503e10	2.23261
$219$	1.18899e9	0.0349285
$220$	−1.02230e10	−0.294221
$221$	0	0
$222$	−4.25422e7	−0.00117552
$223$	−4.41977e10	−1.19682	−0.598409	−	0.801191i	$-0.704200\pi$
$223$	−4.41977e10	−1.19682	−0.598409	+	0.801191i	$0.704200\pi$
$224$	−3.27932e10	−0.870297
$225$	2.69765e10	0.701720
$226$	2.68469e10	0.684552
$227$	3.42932e10	0.857218	0.428609	−	0.903490i	$-0.359004\pi$
$227$	3.42932e10	0.857218	0.428609	+	0.903490i	$0.359004\pi$
$228$	−7.12233e6	−0.000174548 0
$229$	5.87161e10	1.41090	0.705452	−	0.708757i	$-0.250744\pi$
$229$	5.87161e10	1.41090	0.705452	+	0.708757i	$0.250744\pi$
$230$	−7.83361e9	−0.184581
$231$	−8.02837e8	−0.0185513
$232$	2.27821e10	0.516294
$233$	−8.16442e10	−1.81478	−0.907390	−	0.420290i	$-0.861928\pi$
$233$	−8.16442e10	−1.81478	−0.907390	+	0.420290i	$0.861928\pi$
$234$	−5.11237e10	−1.11468
$235$	−9.28790e9	−0.198661
$236$	1.17216e10	0.245971
$237$	−5.61724e8	−0.0115653
$238$	0	0
$239$	−6.99278e10	−1.38631	−0.693153	−	0.720790i	$-0.743779\pi$
$239$	−6.99278e10	−1.38631	−0.693153	+	0.720790i	$0.743779\pi$
$240$	7.54369e8	0.0146769
$241$	−2.20186e10	−0.420448	−0.210224	−	0.977653i	$-0.567419\pi$
$241$	−2.20186e10	−0.420448	−0.210224	+	0.977653i	$0.567419\pi$
$242$	2.48471e9	0.0465700
$243$	3.51219e9	0.0646174
$244$	−1.59641e10	−0.288330
$245$	7.08996e9	0.125718
$246$	−4.62995e8	−0.00806061
$247$	7.72586e8	0.0132072
$248$	3.38311e10	0.567915
$249$	1.09531e9	0.0180568
$250$	−7.14260e10	−1.15645
$251$	−7.51995e10	−1.19587	−0.597934	−	0.801545i	$-0.704012\pi$
$251$	−7.51995e10	−1.19587	−0.597934	+	0.801545i	$0.704012\pi$
$252$	3.08416e10	0.481764
$253$	−1.73698e10	−0.266534
$254$	−2.71729e10	−0.409623
$255$	0	0
$256$	8.53361e10	1.24180
$257$	−4.88179e10	−0.698039	−0.349020	−	0.937115i	$-0.613485\pi$
$257$	−4.88179e10	−0.698039	−0.349020	+	0.937115i	$0.613485\pi$
$258$	3.01832e9	0.0424108
$259$	−2.78394e9	−0.0384424
$260$	1.97973e10	0.268675
$261$	−6.89756e10	−0.920054
$262$	−1.47612e11	−1.93537
$263$	1.51056e10	0.194687	0.0973437	−	0.995251i	$-0.468965\pi$
$263$	1.51056e10	0.194687	0.0973437	+	0.995251i	$0.468965\pi$
$264$	9.36088e8	0.0118604
$265$	−7.96958e10	−0.992725
$266$	−1.31444e9	−0.0160981
$267$	−1.52637e8	−0.00183806
$268$	−4.91185e10	−0.581619
$269$	−7.34701e9	−0.0855511	−0.0427755	−	0.999085i	$-0.513620\pi$
$269$	−7.34701e9	−0.0855511	−0.0427755	+	0.999085i	$0.513620\pi$
$270$	−2.55692e9	−0.0292807
$271$	9.26149e10	1.04308	0.521542	−	0.853226i	$-0.325357\pi$
$271$	9.26149e10	1.04308	0.521542	+	0.853226i	$0.325357\pi$
$272$	0	0
$273$	1.55474e9	0.0169405
$274$	−8.71583e10	−0.934181
$275$	−6.53255e10	−0.688788
$276$	−3.10099e8	−0.00321669
$277$	−2.09446e10	−0.213753	−0.106877	−	0.994272i	$-0.534085\pi$
$277$	−2.09446e10	−0.213753	−0.106877	+	0.994272i	$0.534085\pi$
$278$	−1.72085e10	−0.172799
$279$	−1.02428e11	−1.01204
$280$	2.76264e10	0.268605
$281$	−7.54010e10	−0.721438	−0.360719	−	0.932675i	$-0.617469\pi$
$281$	−7.54010e10	−0.721438	−0.360719	+	0.932675i	$0.617469\pi$
$282$	−1.03690e9	−0.00976371
$283$	1.56859e11	1.45368	0.726842	−	0.686805i	$-0.240987\pi$
$283$	1.56859e11	1.45368	0.726842	+	0.686805i	$0.240987\pi$
$284$	−9.74181e9	−0.0888602
$285$	1.93158e7	0.000173424 0
$286$	1.23800e11	1.09414
$287$	−3.02981e10	−0.263601
$288$	−1.15765e11	−0.991538
$289$	0	0
$290$	7.53288e10	0.625417
$291$	2.92582e9	0.0239182
$292$	1.10608e11	0.890355
$293$	−1.90997e11	−1.51399	−0.756994	−	0.653422i	$-0.773333\pi$
$293$	−1.90997e11	−1.51399	−0.756994	+	0.653422i	$0.773333\pi$
$294$	7.91520e8	0.00617873
$295$	−3.17891e10	−0.244387
$296$	3.24600e9	0.0245774
$297$	−5.66957e9	−0.0422811
$298$	−5.70580e10	−0.419125
$299$	3.36376e10	0.243391
$300$	−1.16624e9	−0.00831271
$301$	1.97517e11	1.38693
$302$	1.99768e11	1.38196
$303$	4.85623e9	0.0330985
$304$	2.73862e9	0.0183908
$305$	4.32946e10	0.286473
$306$	0	0
$307$	7.83989e10	0.503718	0.251859	−	0.967764i	$-0.418958\pi$
$307$	7.83989e10	0.503718	0.251859	+	0.967764i	$0.418958\pi$
$308$	−7.46852e10	−0.472886
$309$	5.34652e9	0.0333624
$310$	1.11862e11	0.687948
$311$	2.81000e11	1.70328	0.851639	−	0.524130i	$-0.175609\pi$
$311$	2.81000e11	1.70328	0.851639	+	0.524130i	$0.175609\pi$
$312$	−1.81279e9	−0.0108306
$313$	8.83831e10	0.520499	0.260249	−	0.965541i	$-0.416195\pi$
$313$	8.83831e10	0.520499	0.260249	+	0.965541i	$0.416195\pi$
$314$	2.32566e11	1.35009
$315$	−8.36425e10	−0.478662
$316$	−5.22552e10	−0.294807
$317$	−2.32664e11	−1.29409	−0.647043	−	0.762454i	$-0.723994\pi$
$317$	−2.32664e11	−1.29409	−0.647043	+	0.762454i	$0.723994\pi$
$318$	−8.89721e9	−0.0487901
$319$	1.67029e11	0.903098
$320$	−1.30811e9	−0.00697382
$321$	7.85040e9	0.0412686
$322$	−5.72295e10	−0.296667
$323$	0	0
$324$	1.08825e11	0.548623
$325$	1.26507e11	0.628982
$326$	−1.72730e11	−0.847012
$327$	−7.99271e9	−0.0386571
$328$	3.53269e10	0.168528
$329$	−6.78540e10	−0.319297
$330$	3.09517e9	0.0143672
$331$	−1.08788e11	−0.498144	−0.249072	−	0.968485i	$-0.580126\pi$
$331$	−1.08788e11	−0.498144	−0.249072	+	0.968485i	$0.580126\pi$
$332$	1.01893e11	0.460282
$333$	−9.82769e9	−0.0437978
$334$	−4.31562e11	−1.89751
$335$	1.33209e11	0.577874
$336$	5.51115e9	0.0235893
$337$	−1.67127e11	−0.705849	−0.352925	−	0.935652i	$-0.614813\pi$
$337$	−1.67127e11	−0.705849	−0.352925	+	0.935652i	$0.614813\pi$
$338$	5.89339e10	0.245607
$339$	−2.88218e9	−0.0118529
$340$	0	0
$341$	2.48037e11	0.993393
$342$	−4.64017e9	−0.0183407
$343$	2.76692e11	1.07938
$344$	−2.30300e11	−0.886709
$345$	8.40988e8	0.00319598
$346$	4.09731e11	1.53694
$347$	−4.77989e11	−1.76985	−0.884923	−	0.465737i	$-0.845789\pi$
$347$	−4.77989e11	−1.76985	−0.884923	+	0.465737i	$0.845789\pi$
$348$	2.98194e9	0.0108991
$349$	−4.80098e11	−1.73227	−0.866134	−	0.499811i	$-0.833403\pi$
$349$	−4.80098e11	−1.73227	−0.866134	+	0.499811i	$0.833403\pi$
$350$	−2.15233e11	−0.766659
$351$	1.09795e10	0.0386099
$352$	2.80332e11	0.973265
$353$	−2.98926e11	−1.02466	−0.512328	−	0.858790i	$-0.671217\pi$
$353$	−2.98926e11	−1.02466	−0.512328	+	0.858790i	$0.671217\pi$
$354$	−3.54892e9	−0.0120111
$355$	2.64198e10	0.0882881
$356$	−1.41993e10	−0.0468536
$357$	0	0
$358$	−1.30940e11	−0.421308
$359$	3.68878e11	1.17208	0.586041	−	0.810282i	$-0.300686\pi$
$359$	3.68878e11	1.17208	0.586041	+	0.810282i	$0.300686\pi$
$360$	9.75251e10	0.306024
$361$	−3.22618e11	−0.999783
$362$	3.05833e10	0.0936044
$363$	−2.66749e8	−0.000806350 0
$364$	1.44632e11	0.431826
$365$	−2.99969e11	−0.884622
$366$	4.83339e9	0.0140795
$367$	6.01112e11	1.72965	0.864825	−	0.502074i	$-0.167429\pi$
$367$	6.01112e11	1.72965	0.864825	+	0.502074i	$0.167429\pi$
$368$	1.19236e11	0.338917
$369$	−1.06957e11	−0.300323
$370$	1.07329e10	0.0297721
$371$	−5.82229e11	−1.59555
$372$	4.42814e9	0.0119889
$373$	3.28495e11	0.878697	0.439349	−	0.898317i	$-0.355209\pi$
$373$	3.28495e11	0.878697	0.439349	+	0.898317i	$0.355209\pi$
$374$	0	0
$375$	7.66803e9	0.0200236
$376$	7.91161e10	0.204136
$377$	−3.23462e11	−0.824684
$378$	−1.86800e10	−0.0470612
$379$	−1.10170e11	−0.274276	−0.137138	−	0.990552i	$-0.543790\pi$
$379$	−1.10170e11	−0.274276	−0.137138	+	0.990552i	$0.543790\pi$
$380$	1.79688e9	0.00442072
$381$	2.91718e9	0.00709253
$382$	1.06557e11	0.256035
$383$	4.46966e11	1.06140	0.530702	−	0.847559i	$-0.321928\pi$
$383$	4.46966e11	1.06140	0.530702	+	0.847559i	$0.321928\pi$
$384$	−9.25562e9	−0.0217228
$385$	2.02546e11	0.469841
$386$	8.91017e11	2.04288
$387$	6.97263e11	1.58015
$388$	2.72179e11	0.609694
$389$	5.35885e11	1.18658	0.593292	−	0.804987i	$-0.297828\pi$
$389$	5.35885e11	1.18658	0.593292	+	0.804987i	$0.297828\pi$
$390$	−5.99398e9	−0.0131197
$391$	0	0
$392$	−6.03936e10	−0.129183
$393$	1.58470e10	0.0335105
$394$	3.49846e11	0.731382
$395$	1.41716e11	0.292909
$396$	−2.63649e11	−0.538763
$397$	5.15293e11	1.04111	0.520555	−	0.853828i	$-0.325725\pi$
$397$	5.15293e11	1.04111	0.520555	+	0.853828i	$0.325725\pi$
$398$	1.13120e12	2.25977
$399$	1.41114e8	0.000278735 0
$400$	4.48433e11	0.875845
$401$	4.93193e11	0.952504	0.476252	−	0.879309i	$-0.341995\pi$
$401$	4.93193e11	0.952504	0.476252	+	0.879309i	$0.341995\pi$
$402$	1.48714e10	0.0284012
$403$	−4.80337e11	−0.907138
$404$	4.51759e11	0.843705
$405$	−2.95132e11	−0.545091
$406$	5.50325e11	1.00520
$407$	2.37985e10	0.0429907
$408$	0	0
$409$	−2.86274e11	−0.505857	−0.252928	−	0.967485i	$-0.581394\pi$
$409$	−2.86274e11	−0.505857	−0.252928	+	0.967485i	$0.581394\pi$
$410$	1.16808e11	0.204148
$411$	9.35699e9	0.0161751
$412$	4.97368e11	0.850434
$413$	−2.32239e11	−0.392790
$414$	−2.02028e11	−0.337995
$415$	−2.76334e11	−0.457318
$416$	−5.42880e11	−0.888758
$417$	1.84744e9	0.00299198
$418$	1.12365e10	0.0180027
$419$	1.66697e11	0.264219	0.132110	−	0.991235i	$-0.457825\pi$
$419$	1.66697e11	0.264219	0.132110	+	0.991235i	$0.457825\pi$
$420$	3.61601e9	0.00567033
$421$	−5.15187e11	−0.799274	−0.399637	−	0.916674i	$-0.630864\pi$
$421$	−5.15187e11	−0.799274	−0.399637	+	0.916674i	$0.630864\pi$
$422$	3.78238e11	0.580576
$423$	−2.39534e11	−0.363777
$424$	6.78864e11	1.02009
$425$	0	0
$426$	2.94950e9	0.00433915
$427$	3.16295e11	0.460433
$428$	7.30296e11	1.05197
$429$	−1.32907e10	−0.0189448
$430$	−7.61486e11	−1.07412
$431$	−5.42449e10	−0.0757202	−0.0378601	−	0.999283i	$-0.512054\pi$
$431$	−5.42449e10	−0.0757202	−0.0378601	+	0.999283i	$0.512054\pi$
$432$	3.89193e10	0.0537635
$433$	−2.49025e11	−0.340445	−0.170222	−	0.985406i	$-0.554449\pi$
$433$	−2.49025e11	−0.340445	−0.170222	+	0.985406i	$0.554449\pi$
$434$	8.17225e11	1.10570
$435$	−8.08702e9	−0.0108290
$436$	−7.43535e11	−0.985399
$437$	3.05307e9	0.00400470
$438$	−3.34884e10	−0.0434771
$439$	−2.46288e11	−0.316485	−0.158242	−	0.987400i	$-0.550583\pi$
$439$	−2.46288e11	−0.316485	−0.158242	+	0.987400i	$0.550583\pi$
$440$	−2.36164e11	−0.300384
$441$	1.82849e11	0.230208
$442$	0	0
$443$	−1.20603e12	−1.48779	−0.743895	−	0.668297i	$-0.767024\pi$
$443$	−1.20603e12	−1.48779	−0.743895	+	0.668297i	$0.767024\pi$
$444$	4.24868e8	0.000518837 0
$445$	3.85086e10	0.0465519
$446$	1.24484e12	1.48973
$447$	6.12554e9	0.00725706
$448$	−9.55660e9	−0.0112086
$449$	1.43303e12	1.66398	0.831988	−	0.554794i	$-0.187203\pi$
$449$	1.43303e12	1.66398	0.831988	+	0.554794i	$0.187203\pi$
$450$	−7.59802e11	−0.873462
$451$	2.59003e11	0.294788
$452$	−2.68120e11	−0.302138
$453$	−2.14464e10	−0.0239283
$454$	−9.65879e11	−1.06702
$455$	−3.92243e11	−0.429046
$456$	−1.64535e8	−0.000178204 0
$457$	−1.45072e12	−1.55582	−0.777911	−	0.628375i	$-0.783721\pi$
$457$	−1.45072e12	−1.55582	−0.777911	+	0.628375i	$0.783721\pi$
$458$	−1.65376e12	−1.75622
$459$	0	0
$460$	7.82342e10	0.0814679
$461$	4.79650e11	0.494619	0.247309	−	0.968937i	$-0.420454\pi$
$461$	4.79650e11	0.494619	0.247309	+	0.968937i	$0.420454\pi$
$462$	2.26122e10	0.0230916
$463$	−1.02183e11	−0.103339	−0.0516697	−	0.998664i	$-0.516454\pi$
$463$	−1.02183e11	−0.103339	−0.0516697	+	0.998664i	$0.516454\pi$
$464$	−1.14659e12	−1.14836
$465$	−1.20091e10	−0.0119117
$466$	2.29954e12	2.25894
$467$	−9.48806e11	−0.923106	−0.461553	−	0.887113i	$-0.652708\pi$
$467$	−9.48806e11	−0.923106	−0.461553	+	0.887113i	$0.652708\pi$
$468$	5.10572e11	0.491984
$469$	9.73180e11	0.928785
$470$	2.61597e11	0.247282
$471$	−2.49674e10	−0.0233765
$472$	2.70785e11	0.251123
$473$	−1.68847e12	−1.55103
$474$	1.58211e10	0.0143958
$475$	1.14822e10	0.0103491
$476$	0	0
$477$	−2.05535e12	−1.81783
$478$	1.96954e12	1.72560
$479$	−1.54645e12	−1.34223	−0.671114	−	0.741354i	$-0.734184\pi$
$479$	−1.54645e12	−1.34223	−0.671114	+	0.741354i	$0.734184\pi$
$480$	−1.35728e10	−0.0116703
$481$	−4.60871e10	−0.0392579
$482$	6.20161e11	0.523350
$483$	6.14395e9	0.00513672
$484$	−2.48148e10	−0.0205545
$485$	−7.38150e11	−0.605768
$486$	−9.89220e10	−0.0804321
$487$	8.16740e11	0.657966	0.328983	−	0.944336i	$-0.393294\pi$
$487$	8.16740e11	0.657966	0.328983	+	0.944336i	$0.393294\pi$
$488$	−3.68792e11	−0.294369
$489$	1.85437e10	0.0146658
$490$	−1.99691e11	−0.156486
$491$	2.36995e11	0.184023	0.0920116	−	0.995758i	$-0.470670\pi$
$491$	2.36995e11	0.184023	0.0920116	+	0.995758i	$0.470670\pi$
$492$	4.62392e9	0.00355768
$493$	0	0
$494$	−2.17602e10	−0.0164396
$495$	7.15017e11	0.535294
$496$	−1.70267e12	−1.26317
$497$	1.93014e11	0.141901
$498$	−3.08499e10	−0.0224761
$499$	−1.95695e12	−1.41295	−0.706477	−	0.707736i	$-0.749717\pi$
$499$	−1.95695e12	−1.41295	−0.706477	+	0.707736i	$0.749717\pi$
$500$	7.13330e11	0.510418
$501$	4.63309e10	0.0328549
$502$	2.11802e12	1.48855
$503$	−1.25952e12	−0.877302	−0.438651	−	0.898658i	$-0.644544\pi$
$503$	−1.25952e12	−0.877302	−0.438651	+	0.898658i	$0.644544\pi$
$504$	7.12483e11	0.491855
$505$	−1.22517e12	−0.838273
$506$	4.89226e11	0.331766
$507$	−6.32693e9	−0.00425263
$508$	2.71376e11	0.180794
$509$	8.63543e11	0.570235	0.285118	−	0.958493i	$-0.407967\pi$
$509$	8.63543e11	0.570235	0.285118	+	0.958493i	$0.407967\pi$
$510$	0	0
$511$	−2.19146e12	−1.42180
$512$	−8.36291e11	−0.537827
$513$	9.96535e8	0.000635279 0
$514$	1.37497e12	0.868881
$515$	−1.34886e12	−0.844958
$516$	−3.01439e10	−0.0187187
$517$	5.80049e11	0.357073
$518$	7.84106e10	0.0478510
$519$	−4.39872e10	−0.0266117
$520$	4.57345e11	0.274302
$521$	−8.44577e11	−0.502192	−0.251096	−	0.967962i	$-0.580791\pi$
$521$	−8.44577e11	−0.502192	−0.251096	+	0.967962i	$0.580791\pi$
$522$	1.94272e12	1.14523
$523$	9.06283e11	0.529671	0.264835	−	0.964294i	$-0.414682\pi$
$523$	9.06283e11	0.529671	0.264835	+	0.964294i	$0.414682\pi$
$524$	1.47419e12	0.854209
$525$	2.31066e10	0.0132745
$526$	−4.25455e11	−0.242336
$527$	0	0
$528$	−4.71120e10	−0.0263802
$529$	−1.66823e12	−0.926199
$530$	2.24466e12	1.23569
$531$	−8.19837e11	−0.447510
$532$	1.31273e10	0.00710517
$533$	−5.01575e11	−0.269193
$534$	4.29908e9	0.00228792
$535$	−1.98056e12	−1.04519
$536$	−1.13470e12	−0.593801
$537$	1.40573e10	0.00729485
$538$	2.06931e11	0.106489
$539$	−4.42783e11	−0.225965
$540$	2.55360e10	0.0129235
$541$	−1.55099e12	−0.778435	−0.389217	−	0.921146i	$-0.627255\pi$
$541$	−1.55099e12	−0.778435	−0.389217	+	0.921146i	$0.627255\pi$
$542$	−2.60853e12	−1.29837
$543$	−3.28331e9	−0.00162074
$544$	0	0
$545$	2.01647e12	0.979054
$546$	−4.37898e10	−0.0210866
$547$	2.93476e12	1.40162	0.700808	−	0.713350i	$-0.252823\pi$
$547$	2.93476e12	1.40162	0.700808	+	0.713350i	$0.252823\pi$
$548$	8.70449e11	0.412317
$549$	1.11656e12	0.524576
$550$	1.83992e12	0.857365
$551$	−2.93586e10	−0.0135692
$552$	−7.16370e9	−0.00328406
$553$	1.03533e12	0.470776
$554$	5.89912e11	0.266068
$555$	−1.15224e9	−0.000515497 0
$556$	1.71861e11	0.0762678
$557$	−2.35783e12	−1.03792	−0.518961	−	0.854798i	$-0.673681\pi$
$557$	−2.35783e12	−1.03792	−0.518961	+	0.854798i	$0.673681\pi$
$558$	2.88492e12	1.25974
$559$	3.26983e12	1.41635
$560$	−1.39040e12	−0.597438
$561$	0	0
$562$	2.12370e12	0.898006
$563$	2.31243e12	0.970020	0.485010	−	0.874509i	$-0.338816\pi$
$563$	2.31243e12	0.970020	0.485010	+	0.874509i	$0.338816\pi$
$564$	1.03555e10	0.00430938
$565$	7.27141e11	0.300193
$566$	−4.41798e12	−1.80946
$567$	−2.15613e12	−0.876095
$568$	−2.25049e11	−0.0907214
$569$	−8.35674e11	−0.334220	−0.167110	−	0.985938i	$-0.553443\pi$
$569$	−8.35674e11	−0.334220	−0.167110	+	0.985938i	$0.553443\pi$
$570$	−5.44035e8	−0.000215869 0
$571$	2.79849e12	1.10169	0.550846	−	0.834607i	$-0.314305\pi$
$571$	2.79849e12	1.10169	0.550846	+	0.834607i	$0.314305\pi$
$572$	−1.23639e12	−0.482917
$573$	−1.14396e10	−0.00443318
$574$	8.53357e11	0.328116
$575$	4.99923e11	0.190721
$576$	−3.37361e10	−0.0127701
$577$	4.23010e12	1.58876	0.794382	−	0.607419i	$-0.207795\pi$
$577$	4.23010e12	1.58876	0.794382	+	0.607419i	$0.207795\pi$
$578$	0	0
$579$	−9.56563e10	−0.0353720
$580$	−7.52308e11	−0.276038
$581$	−2.01880e12	−0.735022
$582$	−8.24068e10	−0.0297721
$583$	4.97717e12	1.78433
$584$	2.55519e12	0.909003
$585$	−1.38467e12	−0.488816
$586$	5.37950e12	1.88453
$587$	−9.29095e11	−0.322990	−0.161495	−	0.986874i	$-0.551632\pi$
$587$	−9.29095e11	−0.322990	−0.161495	+	0.986874i	$0.551632\pi$
$588$	−7.90490e9	−0.00272708
$589$	−4.35971e10	−0.0149259
$590$	8.95350e11	0.304200
$591$	−3.75582e10	−0.0126637
$592$	−1.63367e11	−0.0546658
$593$	3.56436e12	1.18368	0.591841	−	0.806055i	$-0.298401\pi$
$593$	3.56436e12	1.18368	0.591841	+	0.806055i	$0.298401\pi$
$594$	1.59685e11	0.0526291
$595$	0	0
$596$	5.69838e11	0.184988
$597$	−1.21441e11	−0.0391274
$598$	−9.47415e11	−0.302960
$599$	−5.69493e12	−1.80746	−0.903728	−	0.428106i	$-0.859181\pi$
$599$	−5.69493e12	−1.80746	−0.903728	+	0.428106i	$0.859181\pi$
$600$	−2.69417e10	−0.00848682
$601$	3.23003e12	1.00989	0.504943	−	0.863153i	$-0.331514\pi$
$601$	3.23003e12	1.00989	0.504943	+	0.863153i	$0.331514\pi$
$602$	−5.56314e12	−1.72638
$603$	3.43546e12	1.05817
$604$	−1.99508e12	−0.609951
$605$	6.72977e10	0.0204221
$606$	−1.36778e11	−0.0411991
$607$	1.62163e12	0.484846	0.242423	−	0.970171i	$-0.422058\pi$
$607$	1.62163e12	0.484846	0.242423	+	0.970171i	$0.422058\pi$
$608$	−4.92737e10	−0.0146234
$609$	−5.90808e10	−0.0174048
$610$	−1.21941e12	−0.356586
$611$	−1.12330e12	−0.326070
$612$	0	0
$613$	3.22227e12	0.921700	0.460850	−	0.887478i	$-0.347545\pi$
$613$	3.22227e12	0.921700	0.460850	+	0.887478i	$0.347545\pi$
$614$	−2.20813e12	−0.627000
$615$	−1.25401e10	−0.00353478
$616$	−1.72533e12	−0.482790
$617$	3.76562e12	1.04605	0.523026	−	0.852317i	$-0.324803\pi$
$617$	3.76562e12	1.04605	0.523026	+	0.852317i	$0.324803\pi$
$618$	−1.50587e11	−0.0415277
$619$	−3.75883e12	−1.02907	−0.514535	−	0.857470i	$-0.672035\pi$
$619$	−3.75883e12	−1.02907	−0.514535	+	0.857470i	$0.672035\pi$
$620$	−1.11717e12	−0.303637
$621$	4.33881e10	0.0117073
$622$	−7.91448e12	−2.12014
$623$	2.81330e11	0.0748203
$624$	9.12351e10	0.0240897
$625$	7.43541e11	0.194915
$626$	−2.48934e12	−0.647888
$627$	−1.20631e9	−0.000311713 0
$628$	−2.32263e12	−0.595884
$629$	0	0
$630$	2.35582e12	0.595812
$631$	−5.72141e12	−1.43672	−0.718358	−	0.695673i	$-0.755106\pi$
$631$	−5.72141e12	−1.43672	−0.718358	+	0.695673i	$0.755106\pi$
$632$	−1.20717e12	−0.300982
$633$	−4.06062e10	−0.0100525
$634$	6.55307e12	1.61081
$635$	−7.35971e11	−0.179630
$636$	8.88563e10	0.0215343
$637$	8.57475e11	0.206345
$638$	−4.70444e12	−1.12413
$639$	6.81365e11	0.161669
$640$	2.33508e12	0.550165
$641$	2.45043e12	0.573299	0.286650	−	0.958035i	$-0.407458\pi$
$641$	2.45043e12	0.573299	0.286650	+	0.958035i	$0.407458\pi$
$642$	−2.21109e11	−0.0513688
$643$	−5.20042e12	−1.19975	−0.599873	−	0.800095i	$-0.704782\pi$
$643$	−5.20042e12	−1.19975	−0.599873	+	0.800095i	$0.704782\pi$
$644$	5.71551e11	0.130939
$645$	8.17503e10	0.0185982
$646$	0	0
$647$	9.06811e11	0.203445	0.101723	−	0.994813i	$-0.467565\pi$
$647$	9.06811e11	0.203445	0.101723	+	0.994813i	$0.467565\pi$
$648$	2.51399e12	0.560114
$649$	1.98530e12	0.439262
$650$	−3.56310e12	−0.782922
$651$	−8.77342e10	−0.0191450
$652$	1.72506e12	0.373843
$653$	−5.74944e12	−1.23742	−0.618708	−	0.785621i	$-0.712344\pi$
$653$	−5.74944e12	−1.23742	−0.618708	+	0.785621i	$0.712344\pi$
$654$	2.25118e11	0.0481182
$655$	−3.99802e12	−0.848709
$656$	−1.77795e12	−0.374845
$657$	−7.73616e12	−1.61987
$658$	1.91113e12	0.397443
$659$	−1.14504e12	−0.236503	−0.118252	−	0.992984i	$-0.537729\pi$
$659$	−1.14504e12	−0.236503	−0.118252	+	0.992984i	$0.537729\pi$
$660$	−3.09114e10	−0.00634120
$661$	−2.18103e12	−0.444380	−0.222190	−	0.975003i	$-0.571321\pi$
$661$	−2.18103e12	−0.444380	−0.222190	+	0.975003i	$0.571321\pi$
$662$	3.06405e12	0.620062
$663$	0	0
$664$	2.35387e12	0.469922
$665$	−3.56014e10	−0.00705943
$666$	2.76800e11	0.0545171
$667$	−1.27824e12	−0.250062
$668$	4.31000e12	0.837497
$669$	−1.33642e11	−0.0257944
$670$	−3.75189e12	−0.719306
$671$	−2.70384e12	−0.514908
$672$	−9.91577e10	−0.0187571
$673$	5.45288e12	1.02461	0.512304	−	0.858804i	$-0.328792\pi$
$673$	5.45288e12	1.02461	0.512304	+	0.858804i	$0.328792\pi$
$674$	4.70719e12	0.878602
$675$	1.63177e11	0.0302546
$676$	−5.88573e11	−0.108403
$677$	4.84898e12	0.887159	0.443579	−	0.896235i	$-0.353708\pi$
$677$	4.84898e12	0.887159	0.443579	+	0.896235i	$0.353708\pi$
$678$	8.11777e10	0.0147538
$679$	−5.39266e12	−0.973618
$680$	0	0
$681$	1.03693e11	0.0184752
$682$	−6.98604e12	−1.23652
$683$	1.30756e11	0.0229916	0.0114958	−	0.999934i	$-0.496341\pi$
$683$	1.30756e11	0.0229916	0.0114958	+	0.999934i	$0.496341\pi$
$684$	4.63414e10	0.00809499
$685$	−2.36066e12	−0.409662
$686$	−7.79312e12	−1.34355
$687$	1.77542e11	0.0304085
$688$	1.15907e13	1.97224
$689$	−9.63859e12	−1.62940
$690$	−2.36867e10	−0.00397818
$691$	−3.22565e12	−0.538227	−0.269113	−	0.963108i	$-0.586731\pi$
$691$	−3.22565e12	−0.538227	−0.269113	+	0.963108i	$0.586731\pi$
$692$	−4.09198e12	−0.678353
$693$	5.22365e12	0.860349
$694$	1.34627e13	2.20301
$695$	−4.66088e11	−0.0757767
$696$	6.88868e10	0.0111274
$697$	0	0
$698$	1.35221e13	2.15623
$699$	−2.46870e11	−0.0391130
$700$	2.14953e12	0.338378
$701$	8.43820e12	1.31983	0.659916	−	0.751339i	$-0.270592\pi$
$701$	8.43820e12	1.31983	0.659916	+	0.751339i	$0.270592\pi$
$702$	−3.09240e11	−0.0480595
$703$	−4.18303e9	−0.000645940 0
$704$	8.16945e10	0.0125348
$705$	−2.80841e10	−0.00428163
$706$	8.41936e12	1.27543
$707$	−8.95065e12	−1.34731
$708$	3.54430e10	0.00530128
$709$	−5.72297e12	−0.850576	−0.425288	−	0.905058i	$-0.639827\pi$
$709$	−5.72297e12	−0.850576	−0.425288	+	0.905058i	$0.639827\pi$
$710$	−7.44123e11	−0.109896
$711$	3.65485e12	0.536360
$712$	−3.28024e11	−0.0478349
$713$	−1.89817e12	−0.275064
$714$	0	0
$715$	3.35308e12	0.479808
$716$	1.30770e12	0.185951
$717$	−2.11443e11	−0.0298783
$718$	−1.03896e13	−1.45894
$719$	6.14814e12	0.857954	0.428977	−	0.903316i	$-0.358874\pi$
$719$	6.14814e12	0.857954	0.428977	+	0.903316i	$0.358874\pi$
$720$	−4.90830e12	−0.680667
$721$	−9.85431e12	−1.35805
$722$	9.08664e12	1.24447
$723$	−6.65782e10	−0.00906170
$724$	−3.05435e11	−0.0413138
$725$	−4.80731e12	−0.646220
$726$	7.51309e9	0.00100370
$727$	−9.21269e12	−1.22316	−0.611578	−	0.791184i	$-0.709465\pi$
$727$	−9.21269e12	−1.22316	−0.611578	+	0.791184i	$0.709465\pi$
$728$	3.34120e12	0.440871
$729$	−7.60435e12	−0.997214
$730$	8.44872e12	1.10113
$731$	0	0
$732$	−4.82710e10	−0.00621422
$733$	−8.69962e12	−1.11310	−0.556548	−	0.830816i	$-0.687874\pi$
$733$	−8.69962e12	−1.11310	−0.556548	+	0.830816i	$0.687874\pi$
$734$	−1.69305e13	−2.15297
$735$	2.14381e10	0.00270953
$736$	−2.14533e12	−0.269490
$737$	−8.31921e12	−1.03867
$738$	3.01247e12	0.373826
$739$	−8.74888e12	−1.07908	−0.539539	−	0.841961i	$-0.681401\pi$
$739$	−8.74888e12	−1.07908	−0.539539	+	0.841961i	$0.681401\pi$
$740$	−1.07189e11	−0.0131404
$741$	2.33609e9	0.000284648 0
$742$	1.63987e13	1.98605
$743$	4.65215e11	0.0560021	0.0280010	−	0.999608i	$-0.491086\pi$
$743$	4.65215e11	0.0560021	0.0280010	+	0.999608i	$0.491086\pi$
$744$	1.02296e11	0.0122400
$745$	−1.54540e12	−0.183797
$746$	−9.25219e12	−1.09375
$747$	−7.12664e12	−0.837418
$748$	0	0
$749$	−1.44693e13	−1.67988
$750$	−2.15973e11	−0.0249243
$751$	8.93867e12	1.02540	0.512700	−	0.858568i	$-0.328645\pi$
$751$	8.93867e12	1.02540	0.512700	+	0.858568i	$0.328645\pi$
$752$	−3.98180e12	−0.454045
$753$	−2.27383e11	−0.0257739
$754$	9.11043e12	1.02652
$755$	5.41067e12	0.606024
$756$	1.86557e11	0.0207712
$757$	6.47580e12	0.716741	0.358371	−	0.933579i	$-0.383332\pi$
$757$	6.47580e12	0.716741	0.358371	+	0.933579i	$0.383332\pi$
$758$	3.10298e12	0.341403
$759$	−5.25215e10	−0.00574446
$760$	4.15103e10	0.00451331
$761$	1.50384e12	0.162544	0.0812720	−	0.996692i	$-0.474102\pi$
$761$	1.50384e12	0.162544	0.0812720	+	0.996692i	$0.474102\pi$
$762$	−8.21635e10	−0.00882839
$763$	1.47316e13	1.57358
$764$	−1.06419e12	−0.113005
$765$	0	0
$766$	−1.25890e13	−1.32118
$767$	−3.84464e12	−0.401122
$768$	2.58033e11	0.0267639
$769$	1.49083e13	1.53731	0.768653	−	0.639666i	$-0.220927\pi$
$769$	1.49083e13	1.53731	0.768653	+	0.639666i	$0.220927\pi$
$770$	−5.70479e12	−0.584832
$771$	−1.47612e11	−0.0150445
$772$	−8.89858e12	−0.901660
$773$	−2.45775e11	−0.0247588	−0.0123794	−	0.999923i	$-0.503941\pi$
$773$	−2.45775e11	−0.0247588	−0.0123794	+	0.999923i	$0.503941\pi$
$774$	−1.96387e13	−1.96688
$775$	−7.13878e12	−0.710831
$776$	6.28770e12	0.622464
$777$	−8.41787e9	−0.000828529 0
$778$	−1.50934e13	−1.47699
$779$	−4.55247e10	−0.00442924
$780$	5.98618e10	0.00579061
$781$	−1.64997e12	−0.158689
$782$	0	0
$783$	−4.17224e11	−0.0396681
$784$	3.03952e12	0.287332
$785$	6.29898e12	0.592047
$786$	−4.46337e11	−0.0417120
$787$	−8.04995e12	−0.748009	−0.374004	−	0.927427i	$-0.622016\pi$
$787$	−8.04995e12	−0.748009	−0.374004	+	0.927427i	$0.622016\pi$
$788$	−3.49391e12	−0.322808
$789$	4.56753e10	0.00419600
$790$	−3.99149e12	−0.364597
$791$	5.31223e12	0.482484
$792$	−6.09065e12	−0.550048
$793$	5.23615e12	0.470200
$794$	−1.45134e13	−1.29592
$795$	−2.40978e11	−0.0213957
$796$	−1.12972e13	−0.997387
$797$	2.27278e12	0.199524	0.0997618	−	0.995011i	$-0.468192\pi$
$797$	2.27278e12	0.199524	0.0997618	+	0.995011i	$0.468192\pi$
$798$	−3.97452e9	−0.000346954 0
$799$	0	0
$800$	−8.06829e12	−0.696429
$801$	9.93133e11	0.0852435
$802$	−1.38909e13	−1.18562
$803$	1.87337e13	1.59002
$804$	−1.48521e11	−0.0125353
$805$	−1.55005e12	−0.130096
$806$	1.35289e13	1.12916
$807$	−2.22154e10	−0.00184384
$808$	1.04362e13	0.861376
$809$	−2.47519e12	−0.203161	−0.101581	−	0.994827i	$-0.532390\pi$
$809$	−2.47519e12	−0.203161	−0.101581	+	0.994827i	$0.532390\pi$
$810$	8.31250e12	0.678499
$811$	−2.45293e13	−1.99110	−0.995548	−	0.0942611i	$-0.969951\pi$
$811$	−2.45293e13	−1.99110	−0.995548	+	0.0942611i	$0.969951\pi$
$812$	−5.49609e12	−0.443661
$813$	2.80042e11	0.0224810
$814$	−6.70292e11	−0.0535124
$815$	−4.67836e12	−0.371436
$816$	0	0
$817$	2.96781e11	0.0233044
$818$	8.06302e12	0.629662
$819$	−1.01159e13	−0.785647
$820$	−1.16656e12	−0.0901042
$821$	8.21852e12	0.631319	0.315660	−	0.948872i	$-0.397774\pi$
$821$	8.21852e12	0.631319	0.315660	+	0.948872i	$0.397774\pi$
$822$	−2.63543e11	−0.0201339
$823$	−1.55798e12	−0.118376	−0.0591878	−	0.998247i	$-0.518851\pi$
$823$	−1.55798e12	−0.118376	−0.0591878	+	0.998247i	$0.518851\pi$
$824$	1.14899e13	0.868246
$825$	−1.97527e11	−0.0148451
$826$	6.54110e12	0.488923
$827$	−1.18962e13	−0.884367	−0.442184	−	0.896924i	$-0.645796\pi$
$827$	−1.18962e13	−0.884367	−0.442184	+	0.896924i	$0.645796\pi$
$828$	2.01765e12	0.149180
$829$	−8.80333e12	−0.647368	−0.323684	−	0.946165i	$-0.604922\pi$
$829$	−8.80333e12	−0.647368	−0.323684	+	0.946165i	$0.604922\pi$
$830$	7.78305e12	0.569244
$831$	−6.33308e10	−0.00460691
$832$	−1.58206e11	−0.0114464
$833$	0	0
$834$	−5.20338e10	−0.00372425
$835$	−1.16887e13	−0.832105
$836$	−1.12219e11	−0.00794581
$837$	−6.19572e11	−0.0436342
$838$	−4.69508e12	−0.328886
$839$	6.42832e12	0.447887	0.223944	−	0.974602i	$-0.428107\pi$
$839$	6.42832e12	0.447887	0.223944	+	0.974602i	$0.428107\pi$
$840$	8.35348e10	0.00578909
$841$	−2.21544e12	−0.152714
$842$	1.45104e13	0.994892
$843$	−2.27992e11	−0.0155488
$844$	−3.77746e12	−0.256247
$845$	1.59621e12	0.107705
$846$	6.74656e12	0.452810
$847$	4.91653e11	0.0328234
$848$	−3.41663e13	−2.26890
$849$	4.74298e11	0.0313305
$850$	0	0
$851$	−1.82125e11	−0.0119038
$852$	−2.94566e10	−0.00191516
$853$	1.34906e13	0.872492	0.436246	−	0.899827i	$-0.356308\pi$
$853$	1.34906e13	0.872492	0.436246	+	0.899827i	$0.356308\pi$
$854$	−8.90855e12	−0.573121
$855$	−1.25678e11	−0.00804287
$856$	1.68708e13	1.07400
$857$	2.46136e13	1.55870	0.779348	−	0.626592i	$-0.215551\pi$
$857$	2.46136e13	1.55870	0.779348	+	0.626592i	$0.215551\pi$
$858$	3.74337e11	0.0235814
$859$	2.45934e13	1.54117	0.770583	−	0.637340i	$-0.219965\pi$
$859$	2.45934e13	1.54117	0.770583	+	0.637340i	$0.219965\pi$
$860$	7.60495e12	0.474082
$861$	−9.16133e10	−0.00568125
$862$	1.52783e12	0.0942523
$863$	1.57068e12	0.0963918	0.0481959	−	0.998838i	$-0.484653\pi$
$863$	1.57068e12	0.0963918	0.0481959	+	0.998838i	$0.484653\pi$
$864$	−7.00244e11	−0.0427501
$865$	1.10974e13	0.673985
$866$	7.01386e12	0.423767
$867$	0	0
$868$	−8.16162e12	−0.488020
$869$	−8.85048e12	−0.526475
$870$	2.27774e11	0.0134793
$871$	1.61106e13	0.948487
$872$	−1.71767e13	−1.00604
$873$	−1.90368e13	−1.10925
$874$	−8.59908e10	−0.00498483
$875$	−1.41331e13	−0.815084
$876$	3.34448e11	0.0191893
$877$	2.26638e12	0.129370	0.0646852	−	0.997906i	$-0.479396\pi$
$877$	2.26638e12	0.129370	0.0646852	+	0.997906i	$0.479396\pi$
$878$	6.93678e12	0.393942
$879$	−5.77523e11	−0.0326302
$880$	1.18858e13	0.668123
$881$	2.20342e13	1.23227	0.616134	−	0.787641i	$-0.288698\pi$
$881$	2.20342e13	1.23227	0.616134	+	0.787641i	$0.288698\pi$
$882$	−5.15002e12	−0.286550
$883$	7.71424e12	0.427041	0.213521	−	0.976939i	$-0.431507\pi$
$883$	7.71424e12	0.427041	0.213521	+	0.976939i	$0.431507\pi$
$884$	0	0
$885$	−9.61215e10	−0.00526715
$886$	3.39683e13	1.85192
$887$	3.10912e13	1.68648	0.843239	−	0.537539i	$-0.180646\pi$
$887$	3.10912e13	1.68648	0.843239	+	0.537539i	$0.180646\pi$
$888$	9.81503e9	0.000529704 0
$889$	−5.37674e12	−0.288709
$890$	−1.08461e12	−0.0579452
$891$	1.84316e13	0.979748
$892$	−1.24322e13	−0.657518
$893$	−1.01955e11	−0.00536508
$894$	−1.72528e11	−0.00903318
$895$	−3.54648e12	−0.184754
$896$	1.70593e13	0.884249
$897$	1.01711e11	0.00524568
$898$	−4.03618e13	−2.07122
$899$	1.82530e13	0.932000
$900$	7.58813e12	0.385517
$901$	0	0
$902$	−7.29491e12	−0.366936
$903$	5.97238e11	0.0298918
$904$	−6.19393e12	−0.308467
$905$	8.28341e11	0.0410479
$906$	6.04045e11	0.0297846
$907$	9.61906e12	0.471954	0.235977	−	0.971759i	$-0.424171\pi$
$907$	9.61906e12	0.471954	0.235977	+	0.971759i	$0.424171\pi$
$908$	9.64623e12	0.470946
$909$	−3.15970e13	−1.53500
$910$	1.10477e13	0.534052
$911$	1.52076e13	0.731525	0.365762	−	0.930708i	$-0.380808\pi$
$911$	1.52076e13	0.731525	0.365762	+	0.930708i	$0.380808\pi$
$912$	8.28083e9	0.000396367 0
$913$	1.72577e13	0.821985
$914$	4.08600e13	1.93660
$915$	1.30911e11	0.00617421
$916$	1.65161e13	0.775135
$917$	−2.92081e13	−1.36408
$918$	0	0
$919$	1.96701e13	0.909675	0.454838	−	0.890574i	$-0.349697\pi$
$919$	1.96701e13	0.909675	0.454838	+	0.890574i	$0.349697\pi$
$920$	1.80732e12	0.0831742
$921$	2.37057e11	0.0108564
$922$	−1.35095e13	−0.615674
$923$	3.19527e12	0.144911
$924$	−2.25828e11	−0.0101919
$925$	−6.84948e11	−0.0307624
$926$	2.87803e12	0.128631
$927$	−3.47871e13	−1.54724
$928$	2.06297e13	0.913116
$929$	−3.18903e13	−1.40471	−0.702357	−	0.711825i	$-0.747869\pi$
$929$	−3.18903e13	−1.40471	−0.702357	+	0.711825i	$0.747869\pi$
$930$	3.38241e11	0.0148270
$931$	7.78276e10	0.00339516
$932$	−2.29655e13	−0.997020
$933$	8.49669e11	0.0367098
$934$	2.67235e13	1.14903
$935$	0	0
$936$	1.17949e13	0.502288
$937$	−2.61645e13	−1.10888	−0.554439	−	0.832224i	$-0.687067\pi$
$937$	−2.61645e13	−1.10888	−0.554439	+	0.832224i	$0.687067\pi$
$938$	−2.74099e13	−1.15610
$939$	2.67246e11	0.0112180
$940$	−2.61257e12	−0.109142
$941$	−3.93723e13	−1.63696	−0.818479	−	0.574536i	$-0.805183\pi$
$941$	−3.93723e13	−1.63696	−0.818479	+	0.574536i	$0.805183\pi$
$942$	7.03215e11	0.0290977
$943$	−1.98210e12	−0.0816249
$944$	−1.36282e13	−0.558555
$945$	−5.05942e11	−0.0206375
$946$	4.75564e13	1.93063
$947$	2.26031e13	0.913258	0.456629	−	0.889657i	$-0.349057\pi$
$947$	2.26031e13	0.913258	0.456629	+	0.889657i	$0.349057\pi$
$948$	−1.58006e11	−0.00635382
$949$	−3.62789e13	−1.45196
$950$	−3.23400e11	−0.0128820
$951$	−7.03513e11	−0.0278907
$952$	0	0
$953$	−3.27556e13	−1.28637	−0.643187	−	0.765709i	$-0.722388\pi$
$953$	−3.27556e13	−1.28637	−0.643187	+	0.765709i	$0.722388\pi$
$954$	5.78896e13	2.26273
$955$	2.88608e12	0.112278
$956$	−1.96698e13	−0.761621
$957$	5.05052e11	0.0194640
$958$	4.35563e13	1.67073
$959$	−1.72461e13	−0.658427
$960$	−3.95538e9	−0.000150303 0
$961$	6.65864e11	0.0251843
$962$	1.29806e12	0.0488660
$963$	−5.10786e13	−1.91390
$964$	−6.19354e12	−0.230989
$965$	2.41329e13	0.895854
$966$	−1.73047e11	−0.00639390
$967$	2.07251e13	0.762217	0.381108	−	0.924530i	$-0.375543\pi$
$967$	2.07251e13	0.762217	0.381108	+	0.924530i	$0.375543\pi$
$968$	−5.73255e11	−0.0209850
$969$	0	0
$970$	2.07902e13	0.754027
$971$	5.19068e13	1.87386	0.936932	−	0.349512i	$-0.113652\pi$
$971$	5.19068e13	1.87386	0.936932	+	0.349512i	$0.113652\pi$
$972$	9.87933e11	0.0355001
$973$	−3.40507e12	−0.121792
$974$	−2.30038e13	−0.819000
$975$	3.82522e11	0.0135561
$976$	1.85608e13	0.654744
$977$	2.18772e12	0.0768185	0.0384093	−	0.999262i	$-0.487771\pi$
$977$	2.18772e12	0.0768185	0.0384093	+	0.999262i	$0.487771\pi$
$978$	−5.22290e11	−0.0182552
$979$	−2.40494e12	−0.0836725
$980$	1.99431e12	0.0690679
$981$	5.20045e13	1.79279
$982$	−6.67505e12	−0.229062
$983$	1.84743e13	0.631068	0.315534	−	0.948914i	$-0.397816\pi$
$983$	1.84743e13	0.631068	0.315534	+	0.948914i	$0.397816\pi$
$984$	1.06819e11	0.00363220
$985$	9.47549e12	0.320729
$986$	0	0
$987$	−2.05172e11	−0.00688163
$988$	2.17319e11	0.00725589
$989$	1.29215e13	0.429468
$990$	−2.01387e13	−0.666305
$991$	3.55303e13	1.17022	0.585110	−	0.810954i	$-0.301051\pi$
$991$	3.55303e13	1.17022	0.585110	+	0.810954i	$0.301051\pi$
$992$	3.06348e13	1.00441
$993$	−3.28945e11	−0.0107362
$994$	−5.43629e12	−0.176630
$995$	3.06381e13	0.990965
$996$	3.08097e11	0.00992021
$997$	−5.54350e13	−1.77687	−0.888435	−	0.459003i	$-0.848207\pi$
$997$	−5.54350e13	−1.77687	−0.888435	+	0.459003i	$0.848207\pi$
$998$	5.51183e13	1.75877
$999$	−5.94463e10	−0.00188834

Twists

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

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

\(f(q)\)	\(=\)	\(q-28.1654 q^{2} +3.02373 q^{3} +281.287 q^{4} -762.851 q^{5} -85.1644 q^{6} -5573.11 q^{7} +6498.11 q^{8} -19673.9 q^{9} +O(q^{10})\)	\(q-28.1654 q^{2} +3.02373 q^{3} +281.287 q^{4} -762.851 q^{5} -85.1644 q^{6} -5573.11 q^{7} +6498.11 q^{8} -19673.9 q^{9} +21486.0 q^{10} +47641.7 q^{11} +850.536 q^{12} -92260.9 q^{13} +156969. q^{14} -2306.65 q^{15} -327041. q^{16} +554121. q^{18} -8373.93 q^{19} -214580. q^{20} -16851.6 q^{21} -1.34184e6 q^{22} -364592. q^{23} +19648.5 q^{24} -1.37118e6 q^{25} +2.59856e6 q^{26} -119004. q^{27} -1.56764e6 q^{28} +3.50595e6 q^{29} +64967.7 q^{30} +5.20629e6 q^{31} +5.88418e6 q^{32} +144055. q^{33} +4.25145e6 q^{35} -5.53400e6 q^{36} +499530. q^{37} +235855. q^{38} -278972. q^{39} -4.95709e6 q^{40} +5.43648e6 q^{41} +474631. q^{42} -3.54411e7 q^{43} +1.34010e7 q^{44} +1.50082e7 q^{45} +1.02689e7 q^{46} +1.21753e7 q^{47} -988882. q^{48} -9.29403e6 q^{49} +3.86199e7 q^{50} -2.59518e7 q^{52} +1.04471e8 q^{53} +3.35180e6 q^{54} -3.63435e7 q^{55} -3.62147e7 q^{56} -25320.5 q^{57} -9.87464e7 q^{58} +4.16714e7 q^{59} -648832. q^{60} -5.67537e7 q^{61} -1.46637e8 q^{62} +1.09645e8 q^{63} +1.71477e6 q^{64} +7.03813e7 q^{65} -4.05737e6 q^{66} -1.74621e8 q^{67} -1.10243e6 q^{69} -1.19744e8 q^{70} -3.46330e7 q^{71} -1.27843e8 q^{72} +3.93220e8 q^{73} -1.40694e7 q^{74} -4.14609e6 q^{75} -2.35548e6 q^{76} -2.65512e8 q^{77} +7.85734e6 q^{78} -1.85772e8 q^{79} +2.49483e8 q^{80} +3.86881e8 q^{81} -1.53120e8 q^{82} +3.62239e8 q^{83} -4.74013e6 q^{84} +9.98211e8 q^{86} +1.06010e7 q^{87} +3.09581e8 q^{88} -5.04798e7 q^{89} -4.22712e8 q^{90} +5.14180e8 q^{91} -1.02555e8 q^{92} +1.57424e7 q^{93} -3.42920e8 q^{94} +6.38806e6 q^{95} +1.77922e7 q^{96} +9.67620e8 q^{97} +2.61770e8 q^{98} -9.37295e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 33 q^{2} + 236 q^{3} + 853 q^{4} - 1480 q^{5} - 7578 q^{6} + 13202 q^{7} - 42423 q^{8} + 10981 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more