LMFDB - Embedded newform 285.10.a.h.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,10,Mod(1,285)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("285.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	285.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:	$146.785213307$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 6356 x^{13} + 18436 x^{12} + 15858707 x^{11} - 49616078 x^{10} + \cdots + 15\!\cdots\!00 $ x^15 - 2x^14 - 6356x^13 + 18436x^12 + 15858707x^11 - 49616078x^10 - 19804799606x^9 + 51117957936x^8 + 13077899446663x^7 - 17762605232062x^6 - 4369460380063800x^5 - 1105301955330540x^4 + 617735239298795077x^3 + 844341253042208334x^2 - 21881601450607548510x + 15712212684310961400
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{6}\cdot 5^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-10.1020$ of defining polynomial
Character	$\chi$	$=$	285.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.10202 q^{2} -81.0000 q^{3} -429.153 q^{4} +625.000 q^{5} -737.264 q^{6} +6714.13 q^{7} -8566.40 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+9.10202 q^{2} -81.0000 q^{3} -429.153 q^{4} +625.000 q^{5} -737.264 q^{6} +6714.13 q^{7} -8566.40 q^{8} +6561.00 q^{9} +5688.76 q^{10} +73844.5 q^{11} +34761.4 q^{12} +48214.9 q^{13} +61112.2 q^{14} -50625.0 q^{15} +141755. q^{16} +302236. q^{17} +59718.4 q^{18} -130321. q^{19} -268221. q^{20} -543845. q^{21} +672134. q^{22} +2.35362e6 q^{23} +693878. q^{24} +390625. q^{25} +438853. q^{26} -531441. q^{27} -2.88139e6 q^{28} -2.23574e6 q^{29} -460790. q^{30} +187831. q^{31} +5.67625e6 q^{32} -5.98140e6 q^{33} +2.75096e6 q^{34} +4.19633e6 q^{35} -2.81567e6 q^{36} -4.75991e6 q^{37} -1.18618e6 q^{38} -3.90540e6 q^{39} -5.35400e6 q^{40} -9.93660e6 q^{41} -4.95009e6 q^{42} -6.79488e6 q^{43} -3.16906e7 q^{44} +4.10062e6 q^{45} +2.14227e7 q^{46} +2.32332e7 q^{47} -1.14821e7 q^{48} +4.72597e6 q^{49} +3.55548e6 q^{50} -2.44811e7 q^{51} -2.06916e7 q^{52} +6.12154e7 q^{53} -4.83719e6 q^{54} +4.61528e7 q^{55} -5.75159e7 q^{56} +1.05560e7 q^{57} -2.03497e7 q^{58} +1.19429e7 q^{59} +2.17259e7 q^{60} +11220.3 q^{61} +1.70964e6 q^{62} +4.40514e7 q^{63} -2.09132e7 q^{64} +3.01343e7 q^{65} -5.44428e7 q^{66} -1.64079e8 q^{67} -1.29705e8 q^{68} -1.90644e8 q^{69} +3.81951e7 q^{70} -2.51649e8 q^{71} -5.62041e7 q^{72} -1.11543e8 q^{73} -4.33248e7 q^{74} -3.16406e7 q^{75} +5.59277e7 q^{76} +4.95802e8 q^{77} -3.55471e7 q^{78} +3.07053e8 q^{79} +8.85968e7 q^{80} +4.30467e7 q^{81} -9.04432e7 q^{82} -2.22020e8 q^{83} +2.33393e8 q^{84} +1.88897e8 q^{85} -6.18471e7 q^{86} +1.81095e8 q^{87} -6.32581e8 q^{88} -3.96077e8 q^{89} +3.73240e7 q^{90} +3.23721e8 q^{91} -1.01007e9 q^{92} -1.52143e7 q^{93} +2.11469e8 q^{94} -8.14506e7 q^{95} -4.59776e8 q^{96} +1.27450e9 q^{97} +4.30159e7 q^{98} +4.84494e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) $ 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9} - 10625 q^{10} + 138230 q^{11} - 409455 q^{12} - 176712 q^{13} - 555994 q^{14} - 759375 q^{15} + 1695731 q^{16} - 274992 q^{17} - 111537 q^{18} - 1954815 q^{19} + 3159375 q^{20} - 109512 q^{21} - 1031106 q^{22} + 1714212 q^{23} + 291357 q^{24} + 5859375 q^{25} + 9500004 q^{26} - 7971615 q^{27} + 14545598 q^{28} + 1754340 q^{29} + 860625 q^{30} + 8442914 q^{31} + 35638859 q^{32} - 11196630 q^{33} + 47218266 q^{34} + 845000 q^{35} + 33165855 q^{36} + 2956096 q^{37} + 2215457 q^{38} + 14313672 q^{39} - 2248125 q^{40} - 38550502 q^{41} + 45035514 q^{42} + 50753570 q^{43} + 212125630 q^{44} + 61509375 q^{45} - 117130008 q^{46} - 40252876 q^{47} - 137354211 q^{48} + 110123035 q^{49} - 6640625 q^{50} + 22274352 q^{51} - 87136648 q^{52} + 65532542 q^{53} + 9034497 q^{54} + 86393750 q^{55} - 377288898 q^{56} + 158340015 q^{57} + 211630876 q^{58} + 175407418 q^{59} - 255909375 q^{60} + 151231854 q^{61} - 30983940 q^{62} + 8870472 q^{63} + 836879575 q^{64} - 110445000 q^{65} + 83519586 q^{66} + 40009476 q^{67} - 124850430 q^{68} - 138851172 q^{69} - 347496250 q^{70} + 87578500 q^{71} - 23599917 q^{72} - 360657638 q^{73} + 1373397084 q^{74} - 474609375 q^{75} - 658772655 q^{76} - 304618172 q^{77} - 769500324 q^{78} + 205798286 q^{79} + 1059831875 q^{80} + 645700815 q^{81} - 2327138772 q^{82} - 63321462 q^{83} - 1178193438 q^{84} - 171870000 q^{85} - 848405762 q^{86} - 142101540 q^{87} - 3211126502 q^{88} - 381069174 q^{89} - 69710625 q^{90} + 1476892872 q^{91} - 2382818588 q^{92} - 683876034 q^{93} - 5137318040 q^{94} - 1221759375 q^{95} - 2886747579 q^{96} - 3915268828 q^{97} - 8273557437 q^{98} + 906927030 q^{99}+O(q^{100}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9 - 10625 * q^10 + 138230 * q^11 - 409455 * q^12 - 176712 * q^13 - 555994 * q^14 - 759375 * q^15 + 1695731 * q^16 - 274992 * q^17 - 111537 * q^18 - 1954815 * q^19 + 3159375 * q^20 - 109512 * q^21 - 1031106 * q^22 + 1714212 * q^23 + 291357 * q^24 + 5859375 * q^25 + 9500004 * q^26 - 7971615 * q^27 + 14545598 * q^28 + 1754340 * q^29 + 860625 * q^30 + 8442914 * q^31 + 35638859 * q^32 - 11196630 * q^33 + 47218266 * q^34 + 845000 * q^35 + 33165855 * q^36 + 2956096 * q^37 + 2215457 * q^38 + 14313672 * q^39 - 2248125 * q^40 - 38550502 * q^41 + 45035514 * q^42 + 50753570 * q^43 + 212125630 * q^44 + 61509375 * q^45 - 117130008 * q^46 - 40252876 * q^47 - 137354211 * q^48 + 110123035 * q^49 - 6640625 * q^50 + 22274352 * q^51 - 87136648 * q^52 + 65532542 * q^53 + 9034497 * q^54 + 86393750 * q^55 - 377288898 * q^56 + 158340015 * q^57 + 211630876 * q^58 + 175407418 * q^59 - 255909375 * q^60 + 151231854 * q^61 - 30983940 * q^62 + 8870472 * q^63 + 836879575 * q^64 - 110445000 * q^65 + 83519586 * q^66 + 40009476 * q^67 - 124850430 * q^68 - 138851172 * q^69 - 347496250 * q^70 + 87578500 * q^71 - 23599917 * q^72 - 360657638 * q^73 + 1373397084 * q^74 - 474609375 * q^75 - 658772655 * q^76 - 304618172 * q^77 - 769500324 * q^78 + 205798286 * q^79 + 1059831875 * q^80 + 645700815 * q^81 - 2327138772 * q^82 - 63321462 * q^83 - 1178193438 * q^84 - 171870000 * q^85 - 848405762 * q^86 - 142101540 * q^87 - 3211126502 * q^88 - 381069174 * q^89 - 69710625 * q^90 + 1476892872 * q^91 - 2382818588 * q^92 - 683876034 * q^93 - 5137318040 * q^94 - 1221759375 * q^95 - 2886747579 * q^96 - 3915268828 * q^97 - 8273557437 * q^98 + 906927030 * 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 $

$2$	9.10202	0.402256	0.201128	−	0.979565i	$-0.435539\pi$
$2$	9.10202	0.402256	0.201128	+	0.979565i	$0.435539\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−429.153	−0.838190
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−737.264	−0.232243
$7$	6714.13	1.05694	0.528468	−	0.848953i	$-0.322767\pi$
$7$	6714.13	1.05694	0.528468	+	0.848953i	$0.322767\pi$
$8$	−8566.40	−0.739423
$9$	6561.00	0.333333
$10$	5688.76	0.179894
$11$	73844.5	1.52073	0.760363	−	0.649499i	$-0.225021\pi$
$11$	73844.5	1.52073	0.760363	+	0.649499i	$0.225021\pi$
$12$	34761.4	0.483929
$13$	48214.9	0.468205	0.234102	−	0.972212i	$-0.424785\pi$
$13$	48214.9	0.468205	0.234102	+	0.972212i	$0.424785\pi$
$14$	61112.2	0.425159
$15$	−50625.0	−0.258199
$16$	141755.	0.540752
$17$	302236.	0.877659	0.438829	−	0.898570i	$-0.355393\pi$
$17$	302236.	0.877659	0.438829	+	0.898570i	$0.355393\pi$
$18$	59718.4	0.134085
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−268221.	−0.374850
$21$	−543845.	−0.610222
$22$	672134.	0.611721
$23$	2.35362e6	1.75373	0.876863	−	0.480740i	$-0.159632\pi$
$23$	2.35362e6	1.75373	0.876863	+	0.480740i	$0.159632\pi$
$24$	693878.	0.426906
$25$	390625.	0.200000
$26$	438853.	0.188338
$27$	−531441.	−0.192450
$28$	−2.88139e6	−0.885913
$29$	−2.23574e6	−0.586988	−0.293494	−	0.955961i	$-0.594818\pi$
$29$	−2.23574e6	−0.586988	−0.293494	+	0.955961i	$0.594818\pi$
$30$	−460790.	−0.103862
$31$	187831.	0.0365292	0.0182646	−	0.999833i	$-0.494186\pi$
$31$	187831.	0.0365292	0.0182646	+	0.999833i	$0.494186\pi$
$32$	5.67625e6	0.956944
$33$	−5.98140e6	−0.877991
$34$	2.75096e6	0.353044
$35$	4.19633e6	0.472676
$36$	−2.81567e6	−0.279397
$37$	−4.75991e6	−0.417533	−0.208766	−	0.977966i	$-0.566945\pi$
$37$	−4.75991e6	−0.417533	−0.208766	+	0.977966i	$0.566945\pi$
$38$	−1.18618e6	−0.0922839
$39$	−3.90540e6	−0.270318
$40$	−5.35400e6	−0.330680
$41$	−9.93660e6	−0.549175	−0.274587	−	0.961562i	$-0.588541\pi$
$41$	−9.93660e6	−0.549175	−0.274587	+	0.961562i	$0.588541\pi$
$42$	−4.95009e6	−0.245466
$43$	−6.79488e6	−0.303091	−0.151546	−	0.988450i	$-0.548425\pi$
$43$	−6.79488e6	−0.303091	−0.151546	+	0.988450i	$0.548425\pi$
$44$	−3.16906e7	−1.27466
$45$	4.10062e6	0.149071
$46$	2.14227e7	0.705447
$47$	2.32332e7	0.694495	0.347247	−	0.937774i	$-0.387116\pi$
$47$	2.32332e7	0.694495	0.347247	+	0.937774i	$0.387116\pi$
$48$	−1.14821e7	−0.312203
$49$	4.72597e6	0.117114
$50$	3.55548e6	0.0804513
$51$	−2.44811e7	−0.506717
$52$	−2.06916e7	−0.392444
$53$	6.12154e7	1.06566	0.532831	−	0.846222i	$-0.321128\pi$
$53$	6.12154e7	1.06566	0.532831	+	0.846222i	$0.321128\pi$
$54$	−4.83719e6	−0.0774143
$55$	4.61528e7	0.680089
$56$	−5.75159e7	−0.781523
$57$	1.05560e7	0.132453
$58$	−2.03497e7	−0.236120
$59$	1.19429e7	0.128315	0.0641574	−	0.997940i	$-0.479564\pi$
$59$	1.19429e7	0.128315	0.0641574	+	0.997940i	$0.479564\pi$
$60$	2.17259e7	0.216420
$61$	11220.3	0.000103757 0	5.18786e−5	−	1.00000i	$-0.499983\pi$
$61$	11220.3	0.000103757 0	5.18786e−5		1.00000i	$0.499983\pi$
$62$	1.70964e6	0.0146941
$63$	4.40514e7	0.352312
$64$	−2.09132e7	−0.155815
$65$	3.01343e7	0.209388
$66$	−5.44428e7	−0.353178
$67$	−1.64079e8	−0.994758	−0.497379	−	0.867533i	$-0.665704\pi$
$67$	−1.64079e8	−0.994758	−0.497379	+	0.867533i	$0.665704\pi$
$68$	−1.29705e8	−0.735645
$69$	−1.90644e8	−1.01251
$70$	3.81951e7	0.190137
$71$	−2.51649e8	−1.17526	−0.587629	−	0.809131i	$-0.699938\pi$
$71$	−2.51649e8	−1.17526	−0.587629	+	0.809131i	$0.699938\pi$
$72$	−5.62041e7	−0.246474
$73$	−1.11543e8	−0.459716	−0.229858	−	0.973224i	$-0.573826\pi$
$73$	−1.11543e8	−0.459716	−0.229858	+	0.973224i	$0.573826\pi$
$74$	−4.33248e7	−0.167955
$75$	−3.16406e7	−0.115470
$76$	5.59277e7	0.192294
$77$	4.95802e8	1.60731
$78$	−3.55471e7	−0.108737
$79$	3.07053e8	0.886933	0.443467	−	0.896291i	$-0.353748\pi$
$79$	3.07053e8	0.886933	0.443467	+	0.896291i	$0.353748\pi$
$80$	8.85968e7	0.241832
$81$	4.30467e7	0.111111
$82$	−9.04432e7	−0.220909
$83$	−2.22020e8	−0.513500	−0.256750	−	0.966478i	$-0.582652\pi$
$83$	−2.22020e8	−0.513500	−0.256750	+	0.966478i	$0.582652\pi$
$84$	2.33393e8	0.511482
$85$	1.88897e8	0.392501
$86$	−6.18471e7	−0.121920
$87$	1.81095e8	0.338898
$88$	−6.32581e8	−1.12446
$89$	−3.96077e8	−0.669152	−0.334576	−	0.942369i	$-0.608593\pi$
$89$	−3.96077e8	−0.669152	−0.334576	+	0.942369i	$0.608593\pi$
$90$	3.73240e7	0.0599648
$91$	3.23721e8	0.494862
$92$	−1.01007e9	−1.46996
$93$	−1.52143e7	−0.0210901
$94$	2.11469e8	0.279365
$95$	−8.14506e7	−0.102598
$96$	−4.59776e8	−0.552492
$97$	1.27450e9	1.46173	0.730863	−	0.682524i	$-0.239118\pi$
$97$	1.27450e9	1.46173	0.730863	+	0.682524i	$0.239118\pi$
$98$	4.30159e7	0.0471098
$99$	4.84494e8	0.506909
$100$	−1.67638e8	−0.167638
$101$	1.19960e9	1.14707	0.573533	−	0.819182i	$-0.305572\pi$
$101$	1.19960e9	1.14707	0.573533	+	0.819182i	$0.305572\pi$
$102$	−2.22828e8	−0.203830
$103$	−1.98407e9	−1.73696	−0.868479	−	0.495726i	$-0.834902\pi$
$103$	−1.98407e9	−1.73696	−0.868479	+	0.495726i	$0.834902\pi$
$104$	−4.13028e8	−0.346202
$105$	−3.39903e8	−0.272900
$106$	5.57184e8	0.428669
$107$	1.26262e9	0.931203	0.465602	−	0.884994i	$-0.345838\pi$
$107$	1.26262e9	0.931203	0.465602	+	0.884994i	$0.345838\pi$
$108$	2.28070e8	0.161310
$109$	2.25160e9	1.52782	0.763909	−	0.645325i	$-0.223278\pi$
$109$	2.25160e9	1.52782	0.763909	+	0.645325i	$0.223278\pi$
$110$	4.20084e8	0.273570
$111$	3.85552e8	0.241063
$112$	9.51761e8	0.571540
$113$	1.24737e9	0.719684	0.359842	−	0.933013i	$-0.382831\pi$
$113$	1.24737e9	0.719684	0.359842	+	0.933013i	$0.382831\pi$
$114$	9.60809e7	0.0532801
$115$	1.47101e9	0.784290
$116$	9.59473e8	0.492008
$117$	3.16338e8	0.156068
$118$	1.08705e8	0.0516154
$119$	2.02925e9	0.927629
$120$	4.33674e8	0.190918
$121$	3.09506e9	1.31261
$122$	102127.	4.17370e−5 0
$123$	8.04865e8	0.317066
$124$	−8.06083e7	−0.0306184
$125$	2.44141e8	0.0894427
$126$	4.00957e8	0.141720
$127$	5.30406e8	0.180922	0.0904611	−	0.995900i	$-0.471166\pi$
$127$	5.30406e8	0.180922	0.0904611	+	0.995900i	$0.471166\pi$
$128$	−3.09659e9	−1.01962
$129$	5.50385e8	0.174990
$130$	2.74283e8	0.0842275
$131$	−7.89230e8	−0.234144	−0.117072	−	0.993123i	$-0.537351\pi$
$131$	−7.89230e8	−0.234144	−0.117072	+	0.993123i	$0.537351\pi$
$132$	2.56694e9	0.735923
$133$	−8.74992e8	−0.242478
$134$	−1.49345e9	−0.400148
$135$	−3.32151e8	−0.0860663
$136$	−2.58907e9	−0.648962
$137$	4.73758e9	1.14898	0.574492	−	0.818510i	$-0.305199\pi$
$137$	4.73758e9	1.14898	0.574492	+	0.818510i	$0.305199\pi$
$138$	−1.73524e9	−0.407290
$139$	−3.68582e9	−0.837467	−0.418733	−	0.908109i	$-0.637526\pi$
$139$	−3.68582e9	−0.837467	−0.418733	+	0.908109i	$0.637526\pi$
$140$	−1.80087e9	−0.396192
$141$	−1.88189e9	−0.400967
$142$	−2.29052e9	−0.472755
$143$	3.56040e9	0.712011
$144$	9.30054e8	0.180251
$145$	−1.39734e9	−0.262509
$146$	−1.01527e9	−0.184924
$147$	−3.82803e8	−0.0676157
$148$	2.04273e9	0.349972
$149$	2.99273e9	0.497427	0.248713	−	0.968577i	$-0.419992\pi$
$149$	2.99273e9	0.497427	0.248713	+	0.968577i	$0.419992\pi$
$150$	−2.87994e8	−0.0464486
$151$	−1.80123e9	−0.281950	−0.140975	−	0.990013i	$-0.545024\pi$
$151$	−1.80123e9	−0.281950	−0.140975	+	0.990013i	$0.545024\pi$
$152$	1.11638e9	0.169635
$153$	1.98297e9	0.292553
$154$	4.51280e9	0.646550
$155$	1.17394e8	0.0163363
$156$	1.67602e9	0.226578
$157$	2.55432e7	0.00335527	0.00167763	−	0.999999i	$-0.499466\pi$
$157$	2.55432e7	0.00335527	0.00167763	+	0.999999i	$0.499466\pi$
$158$	2.79480e9	0.356775
$159$	−4.95845e9	−0.615260
$160$	3.54766e9	0.427959
$161$	1.58025e10	1.85358
$162$	3.91812e8	0.0446951
$163$	−4.93545e8	−0.0547624	−0.0273812	−	0.999625i	$-0.508717\pi$
$163$	−4.93545e8	−0.0547624	−0.0273812	+	0.999625i	$0.508717\pi$
$164$	4.26432e9	0.460313
$165$	−3.73838e9	−0.392650
$166$	−2.02083e9	−0.206559
$167$	1.50775e10	1.50005	0.750023	−	0.661411i	$-0.230042\pi$
$167$	1.50775e10	1.50005	0.750023	+	0.661411i	$0.230042\pi$
$168$	4.65879e9	0.451213
$169$	−8.27983e9	−0.780784
$170$	1.71935e9	0.157886
$171$	−8.55036e8	−0.0764719
$172$	2.91604e9	0.254048
$173$	1.58614e10	1.34627	0.673136	−	0.739519i	$-0.264947\pi$
$173$	1.58614e10	1.34627	0.673136	+	0.739519i	$0.264947\pi$
$174$	1.64833e9	0.136324
$175$	2.62271e9	0.211387
$176$	1.04678e10	0.822336
$177$	−9.67377e8	−0.0740826
$178$	−3.60510e9	−0.269170
$179$	−1.89078e10	−1.37658	−0.688292	−	0.725433i	$-0.741639\pi$
$179$	−1.89078e10	−1.37658	−0.688292	+	0.725433i	$0.741639\pi$
$180$	−1.75980e9	−0.124950
$181$	−1.04679e10	−0.724949	−0.362474	−	0.931994i	$-0.618068\pi$
$181$	−1.04679e10	−0.724949	−0.362474	+	0.931994i	$0.618068\pi$
$182$	2.94651e9	0.199062
$183$	−908840.	−5.99043e−5 0
$184$	−2.01621e10	−1.29675
$185$	−2.97494e9	−0.186726
$186$	−1.38481e8	−0.00848363
$187$	2.23184e10	1.33468
$188$	−9.97061e9	−0.582119
$189$	−3.56817e9	−0.203407
$190$	−7.41365e8	−0.0412706
$191$	2.24819e10	1.22231	0.611157	−	0.791510i	$-0.290704\pi$
$191$	2.24819e10	1.22231	0.611157	+	0.791510i	$0.290704\pi$
$192$	1.69397e9	0.0899600
$193$	−2.49373e10	−1.29372	−0.646861	−	0.762608i	$-0.723919\pi$
$193$	−2.49373e10	−1.29372	−0.646861	+	0.762608i	$0.723919\pi$
$194$	1.16005e10	0.587989
$195$	−2.44088e9	−0.120890
$196$	−2.02816e9	−0.0981637
$197$	2.81285e10	1.33060	0.665301	−	0.746575i	$-0.268303\pi$
$197$	2.81285e10	1.33060	0.665301	+	0.746575i	$0.268303\pi$
$198$	4.40987e9	0.203907
$199$	9.44259e9	0.426827	0.213414	−	0.976962i	$-0.431542\pi$
$199$	9.44259e9	0.426827	0.213414	+	0.976962i	$0.431542\pi$
$200$	−3.34625e9	−0.147885
$201$	1.32904e10	0.574324
$202$	1.09187e10	0.461415
$203$	−1.50110e10	−0.620409
$204$	1.05061e10	0.424725
$205$	−6.21038e9	−0.245598
$206$	−1.80590e10	−0.698702
$207$	1.54421e10	0.584575
$208$	6.83469e9	0.253183
$209$	−9.62348e9	−0.348878
$210$	−3.09380e9	−0.109776
$211$	−2.64016e10	−0.916979	−0.458490	−	0.888700i	$-0.651609\pi$
$211$	−2.64016e10	−0.916979	−0.458490	+	0.888700i	$0.651609\pi$
$212$	−2.62708e10	−0.893227
$213$	2.03836e10	0.678535
$214$	1.14924e10	0.374582
$215$	−4.24680e9	−0.135547
$216$	4.55253e9	0.142302
$217$	1.26112e9	0.0386090
$218$	2.04941e10	0.614574
$219$	9.03499e9	0.265417
$220$	−1.98066e10	−0.570044
$221$	1.45723e10	0.410924
$222$	3.50931e9	0.0969690
$223$	−1.06653e10	−0.288802	−0.144401	−	0.989519i	$-0.546126\pi$
$223$	−1.06653e10	−0.288802	−0.144401	+	0.989519i	$0.546126\pi$
$224$	3.81111e10	1.01143
$225$	2.56289e9	0.0666667
$226$	1.13536e10	0.289497
$227$	7.08993e10	1.77225	0.886126	−	0.463444i	$-0.153387\pi$
$227$	7.08993e10	1.77225	0.886126	+	0.463444i	$0.153387\pi$
$228$	−4.53014e9	−0.111021
$229$	−5.41317e10	−1.30074	−0.650372	−	0.759616i	$-0.725387\pi$
$229$	−5.41317e10	−1.30074	−0.650372	+	0.759616i	$0.725387\pi$
$230$	1.33892e10	0.315486
$231$	−4.01599e10	−0.927981
$232$	1.91522e10	0.434033
$233$	−6.94395e10	−1.54349	−0.771747	−	0.635930i	$-0.780617\pi$
$233$	−6.94395e10	−1.54349	−0.771747	+	0.635930i	$0.780617\pi$
$234$	2.87931e9	0.0627794
$235$	1.45208e10	0.310588
$236$	−5.12535e9	−0.107552
$237$	−2.48713e10	−0.512071
$238$	1.84703e10	0.373145
$239$	3.81772e10	0.756857	0.378428	−	0.925631i	$-0.376465\pi$
$239$	3.81772e10	0.756857	0.378428	+	0.925631i	$0.376465\pi$
$240$	−7.17634e9	−0.139622
$241$	7.74173e10	1.47830	0.739148	−	0.673543i	$-0.235228\pi$
$241$	7.74173e10	1.47830	0.739148	+	0.673543i	$0.235228\pi$
$242$	2.81713e10	0.528004
$243$	−3.48678e9	−0.0641500
$244$	−4.81521e6	−8.69683e−5 0
$245$	2.95373e9	0.0523749
$246$	7.32590e9	0.127542
$247$	−6.28341e9	−0.107414
$248$	−1.60903e9	−0.0270105
$249$	1.79836e10	0.296469
$250$	2.22217e9	0.0359789
$251$	−9.78869e10	−1.55666	−0.778329	−	0.627857i	$-0.783932\pi$
$251$	−9.78869e10	−1.55666	−0.778329	+	0.627857i	$0.783932\pi$
$252$	−1.89048e10	−0.295304
$253$	1.73802e11	2.66694
$254$	4.82777e9	0.0727771
$255$	−1.53007e10	−0.226611
$256$	−1.74777e10	−0.254334
$257$	−1.15233e11	−1.64770	−0.823848	−	0.566811i	$-0.808177\pi$
$257$	−1.15233e11	−1.64770	−0.823848	+	0.566811i	$0.808177\pi$
$258$	5.00962e9	0.0703908
$259$	−3.19586e10	−0.441306
$260$	−1.29322e10	−0.175507
$261$	−1.46687e10	−0.195663
$262$	−7.18359e9	−0.0941858
$263$	1.36007e11	1.75291	0.876457	−	0.481480i	$-0.159901\pi$
$263$	1.36007e11	1.75291	0.876457	+	0.481480i	$0.159901\pi$
$264$	5.12391e10	0.649207
$265$	3.82596e10	0.476578
$266$	−7.96420e9	−0.0975382
$267$	3.20822e10	0.386335
$268$	7.04152e10	0.833796
$269$	3.25828e10	0.379406	0.189703	−	0.981842i	$-0.439248\pi$
$269$	3.25828e10	0.379406	0.189703	+	0.981842i	$0.439248\pi$
$270$	−3.02324e9	−0.0346207
$271$	5.73435e10	0.645836	0.322918	−	0.946427i	$-0.395336\pi$
$271$	5.73435e10	0.645836	0.322918	+	0.946427i	$0.395336\pi$
$272$	4.28434e10	0.474596
$273$	−2.62214e10	−0.285709
$274$	4.31216e10	0.462186
$275$	2.88455e10	0.304145
$276$	8.18153e10	0.848679
$277$	1.39079e11	1.41940	0.709699	−	0.704505i	$-0.248831\pi$
$277$	1.39079e11	1.41940	0.709699	+	0.704505i	$0.248831\pi$
$278$	−3.35484e10	−0.336876
$279$	1.23236e9	0.0121764
$280$	−3.59474e10	−0.349508
$281$	−9.57958e10	−0.916575	−0.458287	−	0.888804i	$-0.651537\pi$
$281$	−9.57958e10	−0.916575	−0.458287	+	0.888804i	$0.651537\pi$
$282$	−1.71290e10	−0.161291
$283$	6.26835e10	0.580917	0.290459	−	0.956888i	$-0.406192\pi$
$283$	6.26835e10	0.580917	0.290459	+	0.956888i	$0.406192\pi$
$284$	1.07996e11	0.985089
$285$	6.59750e9	0.0592349
$286$	3.24068e10	0.286411
$287$	−6.67157e10	−0.580443
$288$	3.72419e10	0.318981
$289$	−2.72414e10	−0.229715
$290$	−1.27186e10	−0.105596
$291$	−1.03234e11	−0.843928
$292$	4.78691e10	0.385329
$293$	−7.20022e10	−0.570744	−0.285372	−	0.958417i	$-0.592117\pi$
$293$	−7.20022e10	−0.570744	−0.285372	+	0.958417i	$0.592117\pi$
$294$	−3.48428e9	−0.0271989
$295$	7.46433e9	0.0573841
$296$	4.07752e10	0.308734
$297$	−3.92440e10	−0.292664
$298$	2.72399e10	0.200093
$299$	1.13480e11	0.821103
$300$	1.35787e10	0.0967858
$301$	−4.56217e10	−0.320348
$302$	−1.63948e10	−0.113416
$303$	−9.71672e10	−0.662259
$304$	−1.84736e10	−0.124057
$305$	7.01266e6	4.64016e−5 0
$306$	1.80490e10	0.117681
$307$	2.19126e11	1.40790	0.703948	−	0.710252i	$-0.251419\pi$
$307$	2.19126e11	1.40790	0.703948	+	0.710252i	$0.251419\pi$
$308$	−2.12775e11	−1.34723
$309$	1.60710e11	1.00283
$310$	1.06853e9	0.00657139
$311$	8.30389e10	0.503338	0.251669	−	0.967813i	$-0.419021\pi$
$311$	8.30389e10	0.503338	0.251669	+	0.967813i	$0.419021\pi$
$312$	3.34552e10	0.199880
$313$	−7.13234e10	−0.420032	−0.210016	−	0.977698i	$-0.567352\pi$
$313$	−7.13234e10	−0.420032	−0.210016	+	0.977698i	$0.567352\pi$
$314$	2.32495e8	0.00134968
$315$	2.75321e10	0.157559
$316$	−1.31773e11	−0.743419
$317$	1.22647e10	0.0682165	0.0341083	−	0.999418i	$-0.489141\pi$
$317$	1.22647e10	0.0682165	0.0341083	+	0.999418i	$0.489141\pi$
$318$	−4.51319e10	−0.247492
$319$	−1.65097e11	−0.892648
$320$	−1.30707e10	−0.0696827
$321$	−1.02272e11	−0.537630
$322$	1.43835e11	0.745613
$323$	−3.93877e10	−0.201349
$324$	−1.84736e10	−0.0931322
$325$	1.88339e10	0.0936409
$326$	−4.49226e9	−0.0220285
$327$	−1.82379e11	−0.882086
$328$	8.51209e10	0.406073
$329$	1.55991e11	0.734037
$330$	−3.40268e10	−0.157946
$331$	−1.70317e11	−0.779889	−0.389944	−	0.920838i	$-0.627506\pi$
$331$	−1.70317e11	−0.779889	−0.389944	+	0.920838i	$0.627506\pi$
$332$	9.52805e10	0.430410
$333$	−3.12297e10	−0.139178
$334$	1.37236e11	0.603403
$335$	−1.02550e11	−0.444869
$336$	−7.70927e10	−0.329979
$337$	9.72564e10	0.410756	0.205378	−	0.978683i	$-0.434158\pi$
$337$	9.72564e10	0.410756	0.205378	+	0.978683i	$0.434158\pi$
$338$	−7.53632e10	−0.314075
$339$	−1.01037e11	−0.415510
$340$	−8.10659e10	−0.328990
$341$	1.38703e10	0.0555508
$342$	−7.78256e9	−0.0307613
$343$	−2.39209e11	−0.933154
$344$	5.82076e10	0.224113
$345$	−1.19152e11	−0.452810
$346$	1.44370e11	0.541546
$347$	−1.28565e10	−0.0476037	−0.0238019	−	0.999717i	$-0.507577\pi$
$347$	−1.28565e10	−0.0476037	−0.0238019	+	0.999717i	$0.507577\pi$
$348$	−7.77173e10	−0.284061
$349$	2.08670e11	0.752915	0.376458	−	0.926434i	$-0.377142\pi$
$349$	2.08670e11	0.752915	0.376458	+	0.926434i	$0.377142\pi$
$350$	2.38719e10	0.0850318
$351$	−2.56234e10	−0.0901060
$352$	4.19160e11	1.45525
$353$	2.05435e11	0.704187	0.352094	−	0.935965i	$-0.385470\pi$
$353$	2.05435e11	0.704187	0.352094	+	0.935965i	$0.385470\pi$
$354$	−8.80509e9	−0.0298002
$355$	−1.57281e11	−0.525591
$356$	1.69978e11	0.560876
$357$	−1.64369e11	−0.535567
$358$	−1.72099e11	−0.553740
$359$	4.80510e11	1.52678	0.763391	−	0.645936i	$-0.223533\pi$
$359$	4.80510e11	1.52678	0.763391	+	0.645936i	$0.223533\pi$
$360$	−3.51276e10	−0.110227
$361$	1.69836e10	0.0526316
$362$	−9.52794e10	−0.291615
$363$	−2.50700e11	−0.757834
$364$	−1.38926e11	−0.414789
$365$	−6.97144e10	−0.205591
$366$	−8.27228e6	−2.40969e−5 0
$367$	−5.21160e11	−1.49959	−0.749797	−	0.661668i	$-0.769849\pi$
$367$	−5.21160e11	−1.49959	−0.749797	+	0.661668i	$0.769849\pi$
$368$	3.33638e11	0.948331
$369$	−6.51940e10	−0.183058
$370$	−2.70780e10	−0.0751119
$371$	4.11008e11	1.12634
$372$	6.52927e9	0.0176775
$373$	−4.18600e10	−0.111972	−0.0559860	−	0.998432i	$-0.517830\pi$
$373$	−4.18600e10	−0.111972	−0.0559860	+	0.998432i	$0.517830\pi$
$374$	2.03143e11	0.536883
$375$	−1.97754e10	−0.0516398
$376$	−1.99025e11	−0.513526
$377$	−1.07796e11	−0.274831
$378$	−3.24775e10	−0.0818219
$379$	−1.73975e11	−0.433123	−0.216561	−	0.976269i	$-0.569484\pi$
$379$	−1.73975e11	−0.433123	−0.216561	+	0.976269i	$0.569484\pi$
$380$	3.49548e10	0.0859965
$381$	−4.29629e10	−0.104455
$382$	2.04631e11	0.491683
$383$	−5.69818e11	−1.35314	−0.676568	−	0.736380i	$-0.736533\pi$
$383$	−5.69818e11	−1.35314	−0.676568	+	0.736380i	$0.736533\pi$
$384$	2.50824e11	0.588679
$385$	3.09876e11	0.718811
$386$	−2.26979e11	−0.520408
$387$	−4.45812e10	−0.101030
$388$	−5.46955e11	−1.22520
$389$	−3.80391e11	−0.842281	−0.421141	−	0.906995i	$-0.638370\pi$
$389$	−3.80391e11	−0.842281	−0.421141	+	0.906995i	$0.638370\pi$
$390$	−2.22169e10	−0.0486287
$391$	7.11349e11	1.53917
$392$	−4.04845e10	−0.0865967
$393$	6.39276e10	0.135183
$394$	2.56026e11	0.535243
$395$	1.91908e11	0.396649
$396$	−2.07922e11	−0.424886
$397$	7.20671e10	0.145606	0.0728031	−	0.997346i	$-0.476806\pi$
$397$	7.20671e10	0.145606	0.0728031	+	0.997346i	$0.476806\pi$
$398$	8.59466e10	0.171694
$399$	7.08744e10	0.139995
$400$	5.53730e10	0.108150
$401$	4.17281e11	0.805896	0.402948	−	0.915223i	$-0.367986\pi$
$401$	4.17281e11	0.805896	0.402948	+	0.915223i	$0.367986\pi$
$402$	1.20970e11	0.231025
$403$	9.05624e9	0.0171031
$404$	−5.14810e11	−0.961460
$405$	2.69042e10	0.0496904
$406$	−1.36631e11	−0.249564
$407$	−3.51493e11	−0.634953
$408$	2.09715e11	0.374678
$409$	−7.33241e10	−0.129566	−0.0647831	−	0.997899i	$-0.520636\pi$
$409$	−7.33241e10	−0.129566	−0.0647831	+	0.997899i	$0.520636\pi$
$410$	−5.65270e10	−0.0987935
$411$	−3.83744e11	−0.663367
$412$	8.51470e11	1.45590
$413$	8.01864e10	0.135621
$414$	1.40555e11	0.235149
$415$	−1.38762e11	−0.229644
$416$	2.73680e11	0.448046
$417$	2.98551e11	0.483512
$418$	−8.75932e10	−0.140339
$419$	−6.46164e11	−1.02419	−0.512094	−	0.858929i	$-0.671130\pi$
$419$	−6.46164e11	−1.02419	−0.512094	+	0.858929i	$0.671130\pi$
$420$	1.45870e11	0.228742
$421$	3.56296e11	0.552766	0.276383	−	0.961048i	$-0.410864\pi$
$421$	3.56296e11	0.552766	0.276383	+	0.961048i	$0.410864\pi$
$422$	−2.40308e11	−0.368861
$423$	1.52433e11	0.231498
$424$	−5.24395e11	−0.787975
$425$	1.18061e11	0.175532
$426$	1.85532e11	0.272945
$427$	7.53343e7	0.000109665 0
$428$	−5.41856e11	−0.780525
$429$	−2.88392e11	−0.411080
$430$	−3.86544e10	−0.0545245
$431$	5.09663e11	0.711436	0.355718	−	0.934593i	$-0.384236\pi$
$431$	5.09663e11	0.711436	0.355718	+	0.934593i	$0.384236\pi$
$432$	−7.53344e10	−0.104068
$433$	−7.97045e11	−1.08965	−0.544825	−	0.838550i	$-0.683404\pi$
$433$	−7.97045e11	−1.08965	−0.544825	+	0.838550i	$0.683404\pi$
$434$	1.14788e10	0.0155307
$435$	1.13184e11	0.151560
$436$	−9.66280e11	−1.28060
$437$	−3.06727e11	−0.402332
$438$	8.22366e10	0.106766
$439$	−6.82610e11	−0.877167	−0.438583	−	0.898691i	$-0.644520\pi$
$439$	−6.82610e11	−0.877167	−0.438583	+	0.898691i	$0.644520\pi$
$440$	−3.95363e11	−0.502874
$441$	3.10071e10	0.0390380
$442$	1.32637e11	0.165297
$443$	−6.88984e11	−0.849948	−0.424974	−	0.905206i	$-0.639717\pi$
$443$	−6.88984e11	−0.849948	−0.424974	+	0.905206i	$0.639717\pi$
$444$	−1.65461e11	−0.202056
$445$	−2.47548e11	−0.299254
$446$	−9.70756e10	−0.116173
$447$	−2.42411e11	−0.287190
$448$	−1.40414e11	−0.164687
$449$	−9.59035e11	−1.11359	−0.556796	−	0.830650i	$-0.687969\pi$
$449$	−9.59035e11	−1.11359	−0.556796	+	0.830650i	$0.687969\pi$
$450$	2.33275e10	0.0268171
$451$	−7.33763e11	−0.835144
$452$	−5.35312e11	−0.603232
$453$	1.45899e11	0.162784
$454$	6.45327e11	0.712900
$455$	2.02326e11	0.221309
$456$	−9.04269e10	−0.0979390
$457$	1.28438e12	1.37743	0.688717	−	0.725031i	$-0.258174\pi$
$457$	1.28438e12	1.37743	0.688717	+	0.725031i	$0.258174\pi$
$458$	−4.92707e11	−0.523232
$459$	−1.60621e11	−0.168906
$460$	−6.31291e11	−0.657384
$461$	9.19279e11	0.947967	0.473983	−	0.880534i	$-0.342816\pi$
$461$	9.19279e11	0.947967	0.473983	+	0.880534i	$0.342816\pi$
$462$	−3.65536e11	−0.373286
$463$	1.40861e12	1.42454	0.712270	−	0.701905i	$-0.247667\pi$
$463$	1.40861e12	1.42454	0.712270	+	0.701905i	$0.247667\pi$
$464$	−3.16927e11	−0.317415
$465$	−9.50894e9	−0.00943179
$466$	−6.32040e11	−0.620880
$467$	−6.08957e11	−0.592462	−0.296231	−	0.955116i	$-0.595730\pi$
$467$	−6.08957e11	−0.592462	−0.296231	+	0.955116i	$0.595730\pi$
$468$	−1.35757e11	−0.130815
$469$	−1.10165e12	−1.05140
$470$	1.32168e11	0.124936
$471$	−2.06900e9	−0.00193716
$472$	−1.02308e11	−0.0948790
$473$	−5.01764e11	−0.460919
$474$	−2.26379e11	−0.205984
$475$	−5.09066e10	−0.0458831
$476$	−8.70860e11	−0.777530
$477$	4.01634e11	0.355220
$478$	3.47490e11	0.304450
$479$	−2.06118e12	−1.78898	−0.894491	−	0.447085i	$-0.852462\pi$
$479$	−2.06118e12	−1.78898	−0.894491	+	0.447085i	$0.852462\pi$
$480$	−2.87360e11	−0.247082
$481$	−2.29498e11	−0.195491
$482$	7.04654e11	0.594654
$483$	−1.28001e12	−1.07016
$484$	−1.32825e12	−1.10021
$485$	7.96561e11	0.653704
$486$	−3.17368e10	−0.0258048
$487$	−1.18779e12	−0.956884	−0.478442	−	0.878119i	$-0.658798\pi$
$487$	−1.18779e12	−0.956884	−0.478442	+	0.878119i	$0.658798\pi$
$488$	−9.61171e7	−7.67205e−5 0
$489$	3.99771e10	0.0316171
$490$	2.68849e10	0.0210681
$491$	1.01285e12	0.786460	0.393230	−	0.919440i	$-0.371358\pi$
$491$	1.01285e12	0.786460	0.393230	+	0.919440i	$0.371358\pi$
$492$	−3.45410e11	−0.265762
$493$	−6.75720e11	−0.515176
$494$	−5.71917e10	−0.0432078
$495$	3.02808e11	0.226696
$496$	2.66260e10	0.0197532
$497$	−1.68961e12	−1.24217
$498$	1.63687e11	0.119257
$499$	1.10300e12	0.796382	0.398191	−	0.917303i	$-0.369638\pi$
$499$	1.10300e12	0.796382	0.398191	+	0.917303i	$0.369638\pi$
$500$	−1.04774e11	−0.0749700
$501$	−1.22128e12	−0.866052
$502$	−8.90969e11	−0.626175
$503$	−2.17428e12	−1.51447	−0.757233	−	0.653144i	$-0.773449\pi$
$503$	−2.17428e12	−1.51447	−0.757233	+	0.653144i	$0.773449\pi$
$504$	−3.77362e11	−0.260508
$505$	7.49747e11	0.512984
$506$	1.58195e12	1.07279
$507$	6.70666e11	0.450786
$508$	−2.27626e11	−0.151647
$509$	6.36726e11	0.420458	0.210229	−	0.977652i	$-0.432579\pi$
$509$	6.36726e11	0.420458	0.210229	+	0.977652i	$0.432579\pi$
$510$	−1.39267e11	−0.0911555
$511$	−7.48915e11	−0.485890
$512$	1.42637e12	0.917315
$513$	6.92579e10	0.0441511
$514$	−1.04885e12	−0.662796
$515$	−1.24004e12	−0.776791
$516$	−2.36199e11	−0.146675
$517$	1.71564e12	1.05614
$518$	−2.90888e11	−0.177518
$519$	−1.28477e12	−0.777271
$520$	−2.58142e11	−0.154826
$521$	−2.37643e12	−1.41304	−0.706521	−	0.707692i	$-0.749736\pi$
$521$	−2.37643e12	−1.41304	−0.706521	+	0.707692i	$0.749736\pi$
$522$	−1.33514e11	−0.0787066
$523$	−2.16146e12	−1.26325	−0.631626	−	0.775273i	$-0.717612\pi$
$523$	−2.16146e12	−1.26325	−0.631626	+	0.775273i	$0.717612\pi$
$524$	3.38700e11	0.196257
$525$	−2.12439e11	−0.122044
$526$	1.23794e12	0.705121
$527$	5.67692e10	0.0320601
$528$	−8.47893e11	−0.474776
$529$	3.73839e12	2.07555
$530$	3.48240e11	0.191707
$531$	7.83576e10	0.0427716
$532$	3.75506e11	0.203242
$533$	−4.79092e11	−0.257126
$534$	2.92013e11	0.155406
$535$	7.89135e11	0.416447
$536$	1.40557e12	0.735547
$537$	1.53153e12	0.794772
$538$	2.96570e11	0.152618
$539$	3.48987e11	0.178098
$540$	1.42544e11	0.0721399
$541$	2.68093e12	1.34554	0.672771	−	0.739851i	$-0.265104\pi$
$541$	2.68093e12	1.34554	0.672771	+	0.739851i	$0.265104\pi$
$542$	5.21941e11	0.259792
$543$	8.47903e11	0.418549
$544$	1.71557e12	0.839871
$545$	1.40725e12	0.683261
$546$	−2.38668e11	−0.114928
$547$	6.88362e11	0.328756	0.164378	−	0.986397i	$-0.447438\pi$
$547$	6.88362e11	0.328756	0.164378	+	0.986397i	$0.447438\pi$
$548$	−2.03315e12	−0.963067
$549$	7.36161e7	3.45857e−5 0
$550$	2.62552e11	0.122344
$551$	2.91363e11	0.134664
$552$	1.63313e12	0.748677
$553$	2.06159e12	0.937432
$554$	1.26590e12	0.570962
$555$	2.40970e11	0.107807
$556$	1.58178e12	0.701956
$557$	2.15568e12	0.948932	0.474466	−	0.880274i	$-0.342641\pi$
$557$	2.15568e12	0.948932	0.474466	+	0.880274i	$0.342641\pi$
$558$	1.12170e10	0.00489803
$559$	−3.27614e11	−0.141909
$560$	5.94851e11	0.255601
$561$	−1.80779e12	−0.770577
$562$	−8.71935e11	−0.368698
$563$	3.41510e12	1.43257	0.716285	−	0.697807i	$-0.245841\pi$
$563$	3.41510e12	1.43257	0.716285	+	0.697807i	$0.245841\pi$
$564$	8.07620e11	0.336086
$565$	7.79605e11	0.321852
$566$	5.70547e11	0.233678
$567$	2.89021e11	0.117437
$568$	2.15573e12	0.869013
$569$	−1.10361e12	−0.441378	−0.220689	−	0.975344i	$-0.570831\pi$
$569$	−1.10361e12	−0.441378	−0.220689	+	0.975344i	$0.570831\pi$
$570$	6.00506e10	0.0238276
$571$	2.26641e12	0.892227	0.446114	−	0.894976i	$-0.352808\pi$
$571$	2.26641e12	0.892227	0.446114	+	0.894976i	$0.352808\pi$
$572$	−1.52796e12	−0.596800
$573$	−1.82103e12	−0.705703
$574$	−6.07247e11	−0.233487
$575$	9.19384e11	0.350745
$576$	−1.37211e11	−0.0519384
$577$	−1.29552e12	−0.486579	−0.243290	−	0.969954i	$-0.578227\pi$
$577$	−1.29552e12	−0.486579	−0.243290	+	0.969954i	$0.578227\pi$
$578$	−2.47952e11	−0.0924042
$579$	2.01992e12	0.746930
$580$	5.99671e11	0.220033
$581$	−1.49067e12	−0.542736
$582$	−9.39641e11	−0.339475
$583$	4.52042e12	1.62058
$584$	9.55522e11	0.339925
$585$	1.97711e11	0.0697958
$586$	−6.55365e11	−0.229585
$587$	3.07246e12	1.06811	0.534053	−	0.845451i	$-0.320668\pi$
$587$	3.07246e12	1.06811	0.534053	+	0.845451i	$0.320668\pi$
$588$	1.64281e11	0.0566748
$589$	−2.44783e10	−0.00838036
$590$	6.79405e10	0.0230831
$591$	−2.27841e12	−0.768224
$592$	−6.74740e11	−0.225782
$593$	−5.63854e12	−1.87249	−0.936247	−	0.351341i	$-0.885726\pi$
$593$	−5.63854e12	−1.87249	−0.936247	+	0.351341i	$0.885726\pi$
$594$	−3.57199e11	−0.117726
$595$	1.26828e12	0.414848
$596$	−1.28434e12	−0.416938
$597$	−7.64849e11	−0.246429
$598$	1.03289e12	0.330294
$599$	−3.28316e12	−1.04201	−0.521004	−	0.853554i	$-0.674442\pi$
$599$	−3.28316e12	−1.04201	−0.521004	+	0.853554i	$0.674442\pi$
$600$	2.71046e11	0.0853813
$601$	1.38459e11	0.0432898	0.0216449	−	0.999766i	$-0.493110\pi$
$601$	1.38459e11	0.0432898	0.0216449	+	0.999766i	$0.493110\pi$
$602$	−4.15250e11	−0.128862
$603$	−1.07652e12	−0.331586
$604$	7.73003e11	0.236328
$605$	1.93441e12	0.587015
$606$	−8.84418e11	−0.266398
$607$	−8.17186e11	−0.244327	−0.122164	−	0.992510i	$-0.538983\pi$
$607$	−8.17186e11	−0.244327	−0.122164	+	0.992510i	$0.538983\pi$
$608$	−7.39735e11	−0.219538
$609$	1.21589e12	0.358193
$610$	6.38294e7	1.86654e−5 0
$611$	1.12019e12	0.325166
$612$	−8.50998e11	−0.245215
$613$	7.82596e11	0.223854	0.111927	−	0.993716i	$-0.464298\pi$
$613$	7.82596e11	0.223854	0.111927	+	0.993716i	$0.464298\pi$
$614$	1.99449e12	0.566335
$615$	5.03041e11	0.141796
$616$	−4.24723e12	−1.18848
$617$	−4.18412e12	−1.16231	−0.581154	−	0.813794i	$-0.697399\pi$
$617$	−4.18412e12	−1.16231	−0.581154	+	0.813794i	$0.697399\pi$
$618$	1.46278e12	0.403396
$619$	3.59757e12	0.984921	0.492461	−	0.870335i	$-0.336098\pi$
$619$	3.59757e12	0.984921	0.492461	+	0.870335i	$0.336098\pi$
$620$	−5.03802e10	−0.0136929
$621$	−1.25081e12	−0.337505
$622$	7.55822e11	0.202471
$623$	−2.65931e12	−0.707251
$624$	−5.53610e11	−0.146175
$625$	1.52588e11	0.0400000
$626$	−6.49187e11	−0.168961
$627$	7.79502e11	0.201425
$628$	−1.09619e10	−0.00281235
$629$	−1.43861e12	−0.366451
$630$	2.50598e11	0.0633790
$631$	3.77704e12	0.948462	0.474231	−	0.880401i	$-0.342726\pi$
$631$	3.77704e12	0.948462	0.474231	+	0.880401i	$0.342726\pi$
$632$	−2.63033e12	−0.655819
$633$	2.13853e12	0.529418
$634$	1.11633e11	0.0274405
$635$	3.31504e11	0.0809109
$636$	2.12793e12	0.515705
$637$	2.27862e11	0.0548333
$638$	−1.50271e12	−0.359073
$639$	−1.65107e12	−0.391753
$640$	−1.93537e12	−0.455989
$641$	7.15759e11	0.167458	0.0837289	−	0.996489i	$-0.473317\pi$
$641$	7.15759e11	0.167458	0.0837289	+	0.996489i	$0.473317\pi$
$642$	−9.30881e11	−0.216265
$643$	7.72725e11	0.178269	0.0891345	−	0.996020i	$-0.471590\pi$
$643$	7.72725e11	0.178269	0.0891345	+	0.996020i	$0.471590\pi$
$644$	−6.78171e12	−1.55365
$645$	3.43991e11	0.0782578
$646$	−3.58507e11	−0.0809938
$647$	8.14391e12	1.82711	0.913553	−	0.406720i	$-0.133328\pi$
$647$	8.14391e12	1.82711	0.913553	+	0.406720i	$0.133328\pi$
$648$	−3.68755e11	−0.0821582
$649$	8.81919e11	0.195132
$650$	1.71427e11	0.0376677
$651$	−1.02151e11	−0.0222909
$652$	2.11806e11	0.0459013
$653$	6.54498e12	1.40864	0.704318	−	0.709885i	$-0.251253\pi$
$653$	6.54498e12	1.40864	0.704318	+	0.709885i	$0.251253\pi$
$654$	−1.66002e12	−0.354824
$655$	−4.93269e11	−0.104712
$656$	−1.40856e12	−0.296967
$657$	−7.31834e11	−0.153239
$658$	1.41983e12	0.295271
$659$	6.27993e12	1.29709	0.648545	−	0.761176i	$-0.275378\pi$
$659$	6.27993e12	1.29709	0.648545	+	0.761176i	$0.275378\pi$
$660$	1.60434e12	0.329115
$661$	4.81592e12	0.981235	0.490617	−	0.871375i	$-0.336771\pi$
$661$	4.81592e12	0.981235	0.490617	+	0.871375i	$0.336771\pi$
$662$	−1.55023e12	−0.313715
$663$	−1.18035e12	−0.237247
$664$	1.90191e12	0.379694
$665$	−5.46870e11	−0.108439
$666$	−2.84254e11	−0.0559851
$667$	−5.26208e12	−1.02942
$668$	−6.47055e12	−1.25732
$669$	8.63888e11	0.166740
$670$	−9.33409e11	−0.178951
$671$	8.28553e8	0.000157786 0
$672$	−3.08700e12	−0.583949
$673$	7.99063e12	1.50146	0.750729	−	0.660610i	$-0.229702\pi$
$673$	7.99063e12	1.50146	0.750729	+	0.660610i	$0.229702\pi$
$674$	8.85230e11	0.165229
$675$	−2.07594e11	−0.0384900
$676$	3.55331e12	0.654446
$677$	−1.65437e12	−0.302680	−0.151340	−	0.988482i	$-0.548359\pi$
$677$	−1.65437e12	−0.302680	−0.151340	+	0.988482i	$0.548359\pi$
$678$	−9.19640e11	−0.167141
$679$	8.55714e12	1.54495
$680$	−1.61817e12	−0.290224
$681$	−5.74284e12	−1.02321
$682$	1.26248e11	0.0223457
$683$	1.38265e12	0.243120	0.121560	−	0.992584i	$-0.461210\pi$
$683$	1.38265e12	0.243120	0.121560	+	0.992584i	$0.461210\pi$
$684$	3.66941e11	0.0640980
$685$	2.96099e12	0.513842
$686$	−2.17728e12	−0.375367
$687$	4.38466e12	0.750985
$688$	−9.63207e11	−0.163897
$689$	2.95149e12	0.498948
$690$	−1.08453e12	−0.182146
$691$	1.04232e13	1.73921	0.869604	−	0.493749i	$-0.164374\pi$
$691$	1.04232e13	1.73921	0.869604	+	0.493749i	$0.164374\pi$
$692$	−6.80695e12	−1.12843
$693$	3.25295e12	0.535770
$694$	−1.17020e11	−0.0191489
$695$	−2.30364e12	−0.374526
$696$	−1.55133e12	−0.250589
$697$	−3.00320e12	−0.481988
$698$	1.89932e12	0.302865
$699$	5.62460e12	0.891137
$700$	−1.12554e12	−0.177183
$701$	5.06089e11	0.0791581	0.0395791	−	0.999216i	$-0.487398\pi$
$701$	5.06089e11	0.0791581	0.0395791	+	0.999216i	$0.487398\pi$
$702$	−2.33224e11	−0.0362457
$703$	6.20316e11	0.0957886
$704$	−1.54432e12	−0.236952
$705$	−1.17618e12	−0.179318
$706$	1.86987e12	0.283264
$707$	8.05424e12	1.21238
$708$	4.15153e11	0.0620953
$709$	2.76713e12	0.411265	0.205632	−	0.978629i	$-0.434075\pi$
$709$	2.76713e12	0.411265	0.205632	+	0.978629i	$0.434075\pi$
$710$	−1.43157e12	−0.211422
$711$	2.01457e12	0.295644
$712$	3.39295e12	0.494786
$713$	4.42083e11	0.0640621
$714$	−1.49609e12	−0.215435
$715$	2.22525e12	0.318421
$716$	8.11435e12	1.15384
$717$	−3.09235e12	−0.436971
$718$	4.37361e12	0.614158
$719$	−1.71873e12	−0.239843	−0.119922	−	0.992783i	$-0.538264\pi$
$719$	−1.71873e12	−0.239843	−0.119922	+	0.992783i	$0.538264\pi$
$720$	5.81284e11	0.0806106
$721$	−1.33213e13	−1.83585
$722$	1.54585e11	0.0211714
$723$	−6.27081e12	−0.853495
$724$	4.49235e12	0.607645
$725$	−8.73334e11	−0.117398
$726$	−2.28187e12	−0.304843
$727$	1.26842e13	1.68406	0.842030	−	0.539430i	$-0.181360\pi$
$727$	1.26842e13	1.68406	0.842030	+	0.539430i	$0.181360\pi$
$728$	−2.77312e12	−0.365913
$729$	2.82430e11	0.0370370
$730$	−6.34542e11	−0.0827004
$731$	−2.05366e12	−0.266011
$732$	3.90032e8	5.02111e−5 0
$733$	5.97034e12	0.763891	0.381945	−	0.924185i	$-0.375254\pi$
$733$	5.97034e12	0.763891	0.381945	+	0.924185i	$0.375254\pi$
$734$	−4.74361e12	−0.603221
$735$	−2.39252e11	−0.0302387
$736$	1.33598e13	1.67822
$737$	−1.21164e13	−1.51275
$738$	−5.93398e11	−0.0736363
$739$	3.12083e12	0.384920	0.192460	−	0.981305i	$-0.438353\pi$
$739$	3.12083e12	0.384920	0.192460	+	0.981305i	$0.438353\pi$
$740$	1.27671e12	0.156512
$741$	5.08956e11	0.0620152
$742$	3.74101e12	0.453076
$743$	−2.65382e12	−0.319464	−0.159732	−	0.987160i	$-0.551063\pi$
$743$	−2.65382e12	−0.319464	−0.159732	+	0.987160i	$0.551063\pi$
$744$	1.30332e11	0.0155945
$745$	1.87046e12	0.222456
$746$	−3.81010e11	−0.0450414
$747$	−1.45667e12	−0.171167
$748$	−9.57803e12	−1.11871
$749$	8.47737e12	0.984222
$750$	−1.79996e11	−0.0207724
$751$	−1.03430e13	−1.18650	−0.593248	−	0.805020i	$-0.702155\pi$
$751$	−1.03430e13	−1.18650	−0.593248	+	0.805020i	$0.702155\pi$
$752$	3.29342e12	0.375550
$753$	7.92884e12	0.898736
$754$	−9.81159e11	−0.110552
$755$	−1.12577e12	−0.126092
$756$	1.53129e12	0.170494
$757$	−1.77921e13	−1.96922	−0.984612	−	0.174755i	$-0.944087\pi$
$757$	−1.77921e13	−1.96922	−0.984612	+	0.174755i	$0.944087\pi$
$758$	−1.58353e12	−0.174226
$759$	−1.40780e13	−1.53976
$760$	6.97738e11	0.0758632
$761$	9.71641e12	1.05021	0.525103	−	0.851038i	$-0.324027\pi$
$761$	9.71641e12	1.05021	0.525103	+	0.851038i	$0.324027\pi$
$762$	−3.91049e11	−0.0420179
$763$	1.51175e13	1.61480
$764$	−9.64818e12	−1.02453
$765$	1.23936e12	0.130834
$766$	−5.18649e12	−0.544307
$767$	5.75827e11	0.0600776
$768$	1.41569e12	0.146840
$769$	1.59058e13	1.64017	0.820083	−	0.572244i	$-0.193927\pi$
$769$	1.59058e13	1.64017	0.820083	+	0.572244i	$0.193927\pi$
$770$	2.82050e12	0.289146
$771$	9.33385e12	0.951297
$772$	1.07019e13	1.08438
$773$	−2.98616e12	−0.300819	−0.150409	−	0.988624i	$-0.548059\pi$
$773$	−2.98616e12	−0.300819	−0.150409	+	0.988624i	$0.548059\pi$
$774$	−4.05779e11	−0.0406401
$775$	7.33715e10	0.00730583
$776$	−1.09178e13	−1.08083
$777$	2.58865e12	0.254788
$778$	−3.46233e12	−0.338813
$779$	1.29495e12	0.125989
$780$	1.04751e12	0.101329
$781$	−1.85829e13	−1.78724
$782$	6.47472e12	0.619142
$783$	1.18816e12	0.112966
$784$	6.69929e11	0.0633296
$785$	1.59645e10	0.00150052
$786$	5.81870e11	0.0543782
$787$	7.99268e12	0.742688	0.371344	−	0.928495i	$-0.378897\pi$
$787$	7.99268e12	0.742688	0.371344	+	0.928495i	$0.378897\pi$
$788$	−1.20714e13	−1.11530
$789$	−1.10166e13	−1.01205
$790$	1.74675e12	0.159554
$791$	8.37500e12	0.760660
$792$	−4.15036e12	−0.374820
$793$	5.40983e8	4.85796e−5 0
$794$	6.55956e11	0.0585710
$795$	−3.09903e12	−0.275153
$796$	−4.05232e12	−0.357762
$797$	−4.03790e12	−0.354481	−0.177240	−	0.984168i	$-0.556717\pi$
$797$	−4.03790e12	−0.354481	−0.177240	+	0.984168i	$0.556717\pi$
$798$	6.45100e11	0.0563137
$799$	7.02191e12	0.609530
$800$	2.21729e12	0.191389
$801$	−2.59866e12	−0.223051
$802$	3.79810e12	0.324177
$803$	−8.23684e12	−0.699102
$804$	−5.70363e12	−0.481392
$805$	9.87659e12	0.828945
$806$	8.24301e10	0.00687984
$807$	−2.63921e12	−0.219050
$808$	−1.02762e13	−0.848168
$809$	1.81646e10	0.00149093	0.000745464	−	1.00000i	$-0.499763\pi$
$809$	1.81646e10	0.00149093	0.000745464		1.00000i	$0.499763\pi$
$810$	2.44883e11	0.0199883
$811$	−7.94110e12	−0.644595	−0.322298	−	0.946638i	$-0.604455\pi$
$811$	−7.94110e12	−0.644595	−0.322298	+	0.946638i	$0.604455\pi$
$812$	6.44203e12	0.520021
$813$	−4.64482e12	−0.372873
$814$	−3.19929e12	−0.255414
$815$	−3.08466e11	−0.0244905
$816$	−3.47032e12	−0.274008
$817$	8.85515e11	0.0695339
$818$	−6.67397e11	−0.0521188
$819$	2.12393e12	0.164954
$820$	2.66520e12	0.205858
$821$	−2.38451e13	−1.83171	−0.915853	−	0.401514i	$-0.868484\pi$
$821$	−2.38451e13	−1.83171	−0.915853	+	0.401514i	$0.868484\pi$
$822$	−3.49285e12	−0.266843
$823$	−8.19985e11	−0.0623027	−0.0311513	−	0.999515i	$-0.509917\pi$
$823$	−8.19985e11	−0.0623027	−0.0311513	+	0.999515i	$0.509917\pi$
$824$	1.69963e13	1.28435
$825$	−2.33648e12	−0.175598
$826$	7.29858e11	0.0545542
$827$	2.12676e13	1.58104	0.790520	−	0.612436i	$-0.209810\pi$
$827$	2.12676e13	1.58104	0.790520	+	0.612436i	$0.209810\pi$
$828$	−6.62704e12	−0.489985
$829$	2.38648e13	1.75494	0.877471	−	0.479629i	$-0.159229\pi$
$829$	2.38648e13	1.75494	0.877471	+	0.479629i	$0.159229\pi$
$830$	−1.26302e12	−0.0923758
$831$	−1.12654e13	−0.819489
$832$	−1.00833e12	−0.0729534
$833$	1.42836e12	0.102786
$834$	2.71742e12	0.194496
$835$	9.42343e12	0.670841
$836$	4.12995e12	0.292426
$837$	−9.98211e10	−0.00703004
$838$	−5.88140e12	−0.411986
$839$	1.56706e13	1.09184	0.545918	−	0.837839i	$-0.316181\pi$
$839$	1.56706e13	1.09184	0.545918	+	0.837839i	$0.316181\pi$
$840$	2.91174e12	0.201788
$841$	−9.50863e12	−0.655445
$842$	3.24301e12	0.222354
$843$	7.75946e12	0.529185
$844$	1.13303e13	0.768603
$845$	−5.17489e12	−0.349177
$846$	1.38745e12	0.0931216
$847$	2.07806e13	1.38734
$848$	8.67758e12	0.576259
$849$	−5.07736e12	−0.335393
$850$	1.07459e12	0.0706088
$851$	−1.12030e13	−0.732238
$852$	−8.74768e12	−0.568741
$853$	2.17264e12	0.140513	0.0702565	−	0.997529i	$-0.477618\pi$
$853$	2.17264e12	0.140513	0.0702565	+	0.997529i	$0.477618\pi$
$854$	6.85694e8	4.41133e−5 0
$855$	−5.34398e11	−0.0341993
$856$	−1.08161e13	−0.688553
$857$	1.93131e13	1.22303	0.611517	−	0.791231i	$-0.290560\pi$
$857$	1.93131e13	1.22303	0.611517	+	0.791231i	$0.290560\pi$
$858$	−2.62495e12	−0.165359
$859$	−2.47882e13	−1.55337	−0.776687	−	0.629887i	$-0.783101\pi$
$859$	−2.47882e13	−1.55337	−0.776687	+	0.629887i	$0.783101\pi$
$860$	1.82253e12	0.113614
$861$	5.40397e12	0.335119
$862$	4.63897e12	0.286179
$863$	−1.89315e13	−1.16181	−0.580907	−	0.813970i	$-0.697302\pi$
$863$	−1.89315e13	−1.16181	−0.580907	+	0.813970i	$0.697302\pi$
$864$	−3.01659e12	−0.184164
$865$	9.91335e12	0.602071
$866$	−7.25472e12	−0.438319
$867$	2.20655e12	0.132626
$868$	−5.41215e11	−0.0323617
$869$	2.26741e13	1.34878
$870$	1.03020e12	0.0609659
$871$	−7.91106e12	−0.465750
$872$	−1.92881e13	−1.12970
$873$	8.36198e12	0.487242
$874$	−2.79183e12	−0.161841
$875$	1.63919e12	0.0945352
$876$	−3.87739e12	−0.222470
$877$	1.98006e13	1.13026	0.565131	−	0.825001i	$-0.308826\pi$
$877$	1.98006e13	1.13026	0.565131	+	0.825001i	$0.308826\pi$
$878$	−6.21313e12	−0.352846
$879$	5.83218e12	0.329519
$880$	6.54239e12	0.367760
$881$	−1.46871e13	−0.821379	−0.410689	−	0.911775i	$-0.634712\pi$
$881$	−1.46871e13	−0.821379	−0.410689	+	0.911775i	$0.634712\pi$
$882$	2.82227e11	0.0157033
$883$	−1.32350e13	−0.732659	−0.366330	−	0.930485i	$-0.619386\pi$
$883$	−1.32350e13	−0.732659	−0.366330	+	0.930485i	$0.619386\pi$
$884$	−6.25373e12	−0.344432
$885$	−6.04611e11	−0.0331307
$886$	−6.27115e12	−0.341897
$887$	−2.36475e13	−1.28271	−0.641355	−	0.767245i	$-0.721627\pi$
$887$	−2.36475e13	−1.28271	−0.641355	+	0.767245i	$0.721627\pi$
$888$	−3.30279e12	−0.178247
$889$	3.56122e12	0.191223
$890$	−2.25319e12	−0.120377
$891$	3.17876e12	0.168970
$892$	4.57704e12	0.242071
$893$	−3.02778e12	−0.159328
$894$	−2.20643e12	−0.115524
$895$	−1.18174e13	−0.615627
$896$	−2.07909e13	−1.07768
$897$	−9.19185e12	−0.474064
$898$	−8.72915e12	−0.447949
$899$	−4.19940e11	−0.0214422
$900$	−1.09987e12	−0.0558793
$901$	1.85015e13	0.935287
$902$	−6.67873e12	−0.335942
$903$	3.69536e12	0.184953
$904$	−1.06855e13	−0.532151
$905$	−6.54246e12	−0.324207
$906$	1.32798e12	0.0654809
$907$	−1.44762e13	−0.710268	−0.355134	−	0.934815i	$-0.615565\pi$
$907$	−1.44762e13	−0.710268	−0.355134	+	0.934815i	$0.615565\pi$
$908$	−3.04267e13	−1.48548
$909$	7.87055e12	0.382356
$910$	1.84157e12	0.0890230
$911$	−1.48193e13	−0.712846	−0.356423	−	0.934325i	$-0.616004\pi$
$911$	−1.48193e13	−0.712846	−0.356423	+	0.934325i	$0.616004\pi$
$912$	1.49637e12	0.0716244
$913$	−1.63949e13	−0.780892
$914$	1.16905e13	0.554081
$915$	−5.68025e8	−2.67900e−5 0
$916$	2.32308e13	1.09027
$917$	−5.29899e12	−0.247475
$918$	−1.46197e12	−0.0679433
$919$	3.46419e13	1.60207	0.801036	−	0.598617i	$-0.204283\pi$
$919$	3.46419e13	1.60207	0.801036	+	0.598617i	$0.204283\pi$
$920$	−1.26013e13	−0.579923
$921$	−1.77492e13	−0.812849
$922$	8.36730e12	0.381326
$923$	−1.21332e13	−0.550261
$924$	1.72348e13	0.777824
$925$	−1.85934e12	−0.0835066
$926$	1.28212e13	0.573030
$927$	−1.30175e13	−0.578986
$928$	−1.26906e13	−0.561715
$929$	−5.53709e12	−0.243900	−0.121950	−	0.992536i	$-0.538915\pi$
$929$	−5.53709e12	−0.243900	−0.121950	+	0.992536i	$0.538915\pi$
$930$	−8.65506e10	−0.00379400
$931$	−6.15893e11	−0.0268678
$932$	2.98002e13	1.29374
$933$	−6.72615e12	−0.290602
$934$	−5.54274e12	−0.238322
$935$	1.39490e13	0.596886
$936$	−2.70987e12	−0.115401
$937$	−1.21162e13	−0.513496	−0.256748	−	0.966478i	$-0.582651\pi$
$937$	−1.21162e13	−0.513496	−0.256748	+	0.966478i	$0.582651\pi$
$938$	−1.00272e13	−0.422930
$939$	5.77720e12	0.242506
$940$	−6.23163e12	−0.260331
$941$	1.74126e13	0.723954	0.361977	−	0.932187i	$-0.382102\pi$
$941$	1.74126e13	0.723954	0.361977	+	0.932187i	$0.382102\pi$
$942$	−1.88321e10	−0.000779236 0
$943$	−2.33870e13	−0.963102
$944$	1.69297e12	0.0693865
$945$	−2.23010e12	−0.0909666
$946$	−4.56707e12	−0.185407
$947$	−2.11907e13	−0.856189	−0.428094	−	0.903734i	$-0.640815\pi$
$947$	−2.11907e13	−0.856189	−0.428094	+	0.903734i	$0.640815\pi$
$948$	1.06736e13	0.429213
$949$	−5.37803e12	−0.215241
$950$	−4.63353e11	−0.0184568
$951$	−9.93439e11	−0.0393848
$952$	−1.73834e13	−0.685911
$953$	−3.52382e13	−1.38387	−0.691935	−	0.721959i	$-0.743242\pi$
$953$	−3.52382e13	−1.38387	−0.691935	+	0.721959i	$0.743242\pi$
$954$	3.65568e12	0.142890
$955$	1.40512e13	0.546635
$956$	−1.63839e13	−0.634390
$957$	1.33728e13	0.515371
$958$	−1.87609e13	−0.719629
$959$	3.18088e13	1.21440
$960$	1.05873e12	0.0402313
$961$	−2.64043e13	−0.998666
$962$	−2.08890e12	−0.0786374
$963$	8.28403e12	0.310401
$964$	−3.32239e13	−1.23909
$965$	−1.55858e13	−0.578570
$966$	−1.16506e13	−0.430480
$967$	−2.32572e13	−0.855337	−0.427669	−	0.903936i	$-0.640665\pi$
$967$	−2.32572e13	−0.855337	−0.427669	+	0.903936i	$0.640665\pi$
$968$	−2.65135e13	−0.970572
$969$	3.19040e12	0.116249
$970$	7.25031e12	0.262957
$971$	1.17934e12	0.0425749	0.0212874	−	0.999773i	$-0.493223\pi$
$971$	1.17934e12	0.0425749	0.0212874	+	0.999773i	$0.493223\pi$
$972$	1.49636e12	0.0537699
$973$	−2.47471e13	−0.885149
$974$	−1.08113e13	−0.384913
$975$	−1.52555e12	−0.0540636
$976$	1.59053e9	5.61069e−5 0
$977$	1.86181e13	0.653747	0.326874	−	0.945068i	$-0.394005\pi$
$977$	1.86181e13	0.653747	0.326874	+	0.945068i	$0.394005\pi$
$978$	3.63873e11	0.0127182
$979$	−2.92481e13	−1.01760
$980$	−1.26760e12	−0.0439001
$981$	1.47727e13	0.509272
$982$	9.21894e12	0.316358
$983$	3.31516e13	1.13244	0.566219	−	0.824255i	$-0.308406\pi$
$983$	3.31516e13	1.13244	0.566219	+	0.824255i	$0.308406\pi$
$984$	−6.89479e12	−0.234446
$985$	1.75803e13	0.595064
$986$	−6.15041e12	−0.207233
$987$	−1.26353e13	−0.423796
$988$	2.69654e12	0.0900329
$989$	−1.59926e13	−0.531539
$990$	2.75617e12	0.0911901
$991$	−5.96892e11	−0.0196591	−0.00982957	−	0.999952i	$-0.503129\pi$
$991$	−5.96892e11	−0.0196591	−0.00982957	+	0.999952i	$0.503129\pi$
$992$	1.06618e12	0.0349564
$993$	1.37957e13	0.450269
$994$	−1.53788e13	−0.499672
$995$	5.90162e12	0.190883
$996$	−7.71772e12	−0.248498
$997$	−1.01387e13	−0.324979	−0.162490	−	0.986710i	$-0.551952\pi$
$997$	−1.01387e13	−0.324979	−0.162490	+	0.986710i	$0.551952\pi$
$998$	1.00395e13	0.320350
$999$	2.52961e12	0.0803542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.9	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.9	✓	15	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	285.a (trivial)

\(f(q)\)	\(=\)	\(q+9.10202 q^{2} -81.0000 q^{3} -429.153 q^{4} +625.000 q^{5} -737.264 q^{6} +6714.13 q^{7} -8566.40 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+9.10202 q^{2} -81.0000 q^{3} -429.153 q^{4} +625.000 q^{5} -737.264 q^{6} +6714.13 q^{7} -8566.40 q^{8} +6561.00 q^{9} +5688.76 q^{10} +73844.5 q^{11} +34761.4 q^{12} +48214.9 q^{13} +61112.2 q^{14} -50625.0 q^{15} +141755. q^{16} +302236. q^{17} +59718.4 q^{18} -130321. q^{19} -268221. q^{20} -543845. q^{21} +672134. q^{22} +2.35362e6 q^{23} +693878. q^{24} +390625. q^{25} +438853. q^{26} -531441. q^{27} -2.88139e6 q^{28} -2.23574e6 q^{29} -460790. q^{30} +187831. q^{31} +5.67625e6 q^{32} -5.98140e6 q^{33} +2.75096e6 q^{34} +4.19633e6 q^{35} -2.81567e6 q^{36} -4.75991e6 q^{37} -1.18618e6 q^{38} -3.90540e6 q^{39} -5.35400e6 q^{40} -9.93660e6 q^{41} -4.95009e6 q^{42} -6.79488e6 q^{43} -3.16906e7 q^{44} +4.10062e6 q^{45} +2.14227e7 q^{46} +2.32332e7 q^{47} -1.14821e7 q^{48} +4.72597e6 q^{49} +3.55548e6 q^{50} -2.44811e7 q^{51} -2.06916e7 q^{52} +6.12154e7 q^{53} -4.83719e6 q^{54} +4.61528e7 q^{55} -5.75159e7 q^{56} +1.05560e7 q^{57} -2.03497e7 q^{58} +1.19429e7 q^{59} +2.17259e7 q^{60} +11220.3 q^{61} +1.70964e6 q^{62} +4.40514e7 q^{63} -2.09132e7 q^{64} +3.01343e7 q^{65} -5.44428e7 q^{66} -1.64079e8 q^{67} -1.29705e8 q^{68} -1.90644e8 q^{69} +3.81951e7 q^{70} -2.51649e8 q^{71} -5.62041e7 q^{72} -1.11543e8 q^{73} -4.33248e7 q^{74} -3.16406e7 q^{75} +5.59277e7 q^{76} +4.95802e8 q^{77} -3.55471e7 q^{78} +3.07053e8 q^{79} +8.85968e7 q^{80} +4.30467e7 q^{81} -9.04432e7 q^{82} -2.22020e8 q^{83} +2.33393e8 q^{84} +1.88897e8 q^{85} -6.18471e7 q^{86} +1.81095e8 q^{87} -6.32581e8 q^{88} -3.96077e8 q^{89} +3.73240e7 q^{90} +3.23721e8 q^{91} -1.01007e9 q^{92} -1.52143e7 q^{93} +2.11469e8 q^{94} -8.14506e7 q^{95} -4.59776e8 q^{96} +1.27450e9 q^{97} +4.30159e7 q^{98} +4.84494e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9} - 10625 q^{10} + 138230 q^{11} - 409455 q^{12} - 176712 q^{13} - 555994 q^{14} - 759375 q^{15} + 1695731 q^{16} - 274992 q^{17} - 111537 q^{18} - 1954815 q^{19} + 3159375 q^{20} - 109512 q^{21} - 1031106 q^{22} + 1714212 q^{23} + 291357 q^{24} + 5859375 q^{25} + 9500004 q^{26} - 7971615 q^{27} + 14545598 q^{28} + 1754340 q^{29} + 860625 q^{30} + 8442914 q^{31} + 35638859 q^{32} - 11196630 q^{33} + 47218266 q^{34} + 845000 q^{35} + 33165855 q^{36} + 2956096 q^{37} + 2215457 q^{38} + 14313672 q^{39} - 2248125 q^{40} - 38550502 q^{41} + 45035514 q^{42} + 50753570 q^{43} + 212125630 q^{44} + 61509375 q^{45} - 117130008 q^{46} - 40252876 q^{47} - 137354211 q^{48} + 110123035 q^{49} - 6640625 q^{50} + 22274352 q^{51} - 87136648 q^{52} + 65532542 q^{53} + 9034497 q^{54} + 86393750 q^{55} - 377288898 q^{56} + 158340015 q^{57} + 211630876 q^{58} + 175407418 q^{59} - 255909375 q^{60} + 151231854 q^{61} - 30983940 q^{62} + 8870472 q^{63} + 836879575 q^{64} - 110445000 q^{65} + 83519586 q^{66} + 40009476 q^{67} - 124850430 q^{68} - 138851172 q^{69} - 347496250 q^{70} + 87578500 q^{71} - 23599917 q^{72} - 360657638 q^{73} + 1373397084 q^{74} - 474609375 q^{75} - 658772655 q^{76} - 304618172 q^{77} - 769500324 q^{78} + 205798286 q^{79} + 1059831875 q^{80} + 645700815 q^{81} - 2327138772 q^{82} - 63321462 q^{83} - 1178193438 q^{84} - 171870000 q^{85} - 848405762 q^{86} - 142101540 q^{87} - 3211126502 q^{88} - 381069174 q^{89} - 69710625 q^{90} + 1476892872 q^{91} - 2382818588 q^{92} - 683876034 q^{93} - 5137318040 q^{94} - 1221759375 q^{95} - 2886747579 q^{96} - 3915268828 q^{97} - 8273557437 q^{98} + 906927030 q^{99}+O(q^{100}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9 - 10625 * q^10 + 138230 * q^11 - 409455 * q^12 - 176712 * q^13 - 555994 * q^14 - 759375 * q^15 + 1695731 * q^16 - 274992 * q^17 - 111537 * q^18 - 1954815 * q^19 + 3159375 * q^20 - 109512 * q^21 - 1031106 * q^22 + 1714212 * q^23 + 291357 * q^24 + 5859375 * q^25 + 9500004 * q^26 - 7971615 * q^27 + 14545598 * q^28 + 1754340 * q^29 + 860625 * q^30 + 8442914 * q^31 + 35638859 * q^32 - 11196630 * q^33 + 47218266 * q^34 + 845000 * q^35 + 33165855 * q^36 + 2956096 * q^37 + 2215457 * q^38 + 14313672 * q^39 - 2248125 * q^40 - 38550502 * q^41 + 45035514 * q^42 + 50753570 * q^43 + 212125630 * q^44 + 61509375 * q^45 - 117130008 * q^46 - 40252876 * q^47 - 137354211 * q^48 + 110123035 * q^49 - 6640625 * q^50 + 22274352 * q^51 - 87136648 * q^52 + 65532542 * q^53 + 9034497 * q^54 + 86393750 * q^55 - 377288898 * q^56 + 158340015 * q^57 + 211630876 * q^58 + 175407418 * q^59 - 255909375 * q^60 + 151231854 * q^61 - 30983940 * q^62 + 8870472 * q^63 + 836879575 * q^64 - 110445000 * q^65 + 83519586 * q^66 + 40009476 * q^67 - 124850430 * q^68 - 138851172 * q^69 - 347496250 * q^70 + 87578500 * q^71 - 23599917 * q^72 - 360657638 * q^73 + 1373397084 * q^74 - 474609375 * q^75 - 658772655 * q^76 - 304618172 * q^77 - 769500324 * q^78 + 205798286 * q^79 + 1059831875 * q^80 + 645700815 * q^81 - 2327138772 * q^82 - 63321462 * q^83 - 1178193438 * q^84 - 171870000 * q^85 - 848405762 * q^86 - 142101540 * q^87 - 3211126502 * q^88 - 381069174 * q^89 - 69710625 * q^90 + 1476892872 * q^91 - 2382818588 * q^92 - 683876034 * q^93 - 5137318040 * q^94 - 1221759375 * q^95 - 2886747579 * q^96 - 3915268828 * q^97 - 8273557437 * q^98 + 906927030 * q^99

Introduction

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