LMFDB - Embedded newform 285.10.a.h.1.3

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			1.3
Root			$32.1152$ 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)

$f(q)$	$=$	$q-33.1152 q^{2} -81.0000 q^{3} +584.616 q^{4} +625.000 q^{5} +2682.33 q^{6} +17.0326 q^{7} -2404.69 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-33.1152 q^{2} -81.0000 q^{3} +584.616 q^{4} +625.000 q^{5} +2682.33 q^{6} +17.0326 q^{7} -2404.69 q^{8} +6561.00 q^{9} -20697.0 q^{10} -38406.0 q^{11} -47353.9 q^{12} -79992.4 q^{13} -564.039 q^{14} -50625.0 q^{15} -219692. q^{16} -184712. q^{17} -217269. q^{18} -130321. q^{19} +365385. q^{20} -1379.64 q^{21} +1.27182e6 q^{22} -2.31309e6 q^{23} +194780. q^{24} +390625. q^{25} +2.64896e6 q^{26} -531441. q^{27} +9957.55 q^{28} -371893. q^{29} +1.67646e6 q^{30} -3.51549e6 q^{31} +8.50633e6 q^{32} +3.11089e6 q^{33} +6.11676e6 q^{34} +10645.4 q^{35} +3.83566e6 q^{36} +9.21730e6 q^{37} +4.31560e6 q^{38} +6.47939e6 q^{39} -1.50293e6 q^{40} -1.02338e6 q^{41} +45687.2 q^{42} -1.88994e7 q^{43} -2.24528e7 q^{44} +4.10062e6 q^{45} +7.65984e7 q^{46} +3.23513e7 q^{47} +1.77950e7 q^{48} -4.03533e7 q^{49} -1.29356e7 q^{50} +1.49616e7 q^{51} -4.67648e7 q^{52} -4.32331e7 q^{53} +1.75988e7 q^{54} -2.40038e7 q^{55} -40958.2 q^{56} +1.05560e7 q^{57} +1.23153e7 q^{58} +1.39320e8 q^{59} -2.95962e7 q^{60} +5.46274e7 q^{61} +1.16416e8 q^{62} +111751. q^{63} -1.69207e8 q^{64} -4.99953e7 q^{65} -1.03018e8 q^{66} -2.64972e8 q^{67} -1.07985e8 q^{68} +1.87360e8 q^{69} -352524. q^{70} -1.12609e8 q^{71} -1.57771e7 q^{72} -3.59484e7 q^{73} -3.05233e8 q^{74} -3.16406e7 q^{75} -7.61877e7 q^{76} -654156. q^{77} -2.14566e8 q^{78} +4.20019e8 q^{79} -1.37307e8 q^{80} +4.30467e7 q^{81} +3.38893e7 q^{82} -2.94218e8 q^{83} -806561. q^{84} -1.15445e8 q^{85} +6.25857e8 q^{86} +3.01234e7 q^{87} +9.23545e7 q^{88} -1.16836e9 q^{89} -1.35793e8 q^{90} -1.36248e6 q^{91} -1.35227e9 q^{92} +2.84755e8 q^{93} -1.07132e9 q^{94} -8.14506e7 q^{95} -6.89013e8 q^{96} -2.51454e8 q^{97} +1.33631e9 q^{98} -2.51982e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−33.1152	−1.46350	−0.731749	−	0.681574i	$-0.761296\pi$
$2$	−33.1152	−1.46350	−0.731749	+	0.681574i	$0.761296\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	584.616	1.14183
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	2682.33	0.844951
$7$	17.0326	0.00268127	0.00134064	−	0.999999i	$-0.499573\pi$
$7$	17.0326	0.00268127	0.00134064	+	0.999999i	$0.499573\pi$
$8$	−2404.69	−0.207565
$9$	6561.00	0.333333
$10$	−20697.0	−0.654496
$11$	−38406.0	−0.790920	−0.395460	−	0.918483i	$-0.629415\pi$
$11$	−38406.0	−0.790920	−0.395460	+	0.918483i	$0.629415\pi$
$12$	−47353.9	−0.659235
$13$	−79992.4	−0.776790	−0.388395	−	0.921493i	$-0.626970\pi$
$13$	−79992.4	−0.776790	−0.388395	+	0.921493i	$0.626970\pi$
$14$	−564.039	−0.00392404
$15$	−50625.0	−0.258199
$16$	−219692.	−0.838057
$17$	−184712.	−0.536382	−0.268191	−	0.963366i	$-0.586426\pi$
$17$	−184712.	−0.536382	−0.268191	+	0.963366i	$0.586426\pi$
$18$	−217269.	−0.487833
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	365385.	0.510641
$21$	−1379.64	−0.00154803
$22$	1.27182e6	1.15751
$23$	−2.31309e6	−1.72352	−0.861761	−	0.507314i	$-0.830638\pi$
$23$	−2.31309e6	−1.72352	−0.861761	+	0.507314i	$0.830638\pi$
$24$	194780.	0.119838
$25$	390625.	0.200000
$26$	2.64896e6	1.13683
$27$	−531441.	−0.192450
$28$	9957.55	0.00306155
$29$	−371893.	−0.0976399	−0.0488200	−	0.998808i	$-0.515546\pi$
$29$	−371893.	−0.0976399	−0.0488200	+	0.998808i	$0.515546\pi$
$30$	1.67646e6	0.377874
$31$	−3.51549e6	−0.683689	−0.341845	−	0.939756i	$-0.611052\pi$
$31$	−3.51549e6	−0.683689	−0.341845	+	0.939756i	$0.611052\pi$
$32$	8.50633e6	1.43406
$33$	3.11089e6	0.456638
$34$	6.11676e6	0.784994
$35$	10645.4	0.00119910
$36$	3.83566e6	0.380609
$37$	9.21730e6	0.808530	0.404265	−	0.914642i	$-0.367527\pi$
$37$	9.21730e6	0.808530	0.404265	+	0.914642i	$0.367527\pi$
$38$	4.31560e6	0.335750
$39$	6.47939e6	0.448480
$40$	−1.50293e6	−0.0928258
$41$	−1.02338e6	−0.0565598	−0.0282799	−	0.999600i	$-0.509003\pi$
$41$	−1.02338e6	−0.0565598	−0.0282799	+	0.999600i	$0.509003\pi$
$42$	45687.2	0.00226554
$43$	−1.88994e7	−0.843023	−0.421512	−	0.906823i	$-0.638500\pi$
$43$	−1.88994e7	−0.843023	−0.421512	+	0.906823i	$0.638500\pi$
$44$	−2.24528e7	−0.903094
$45$	4.10062e6	0.149071
$46$	7.65984e7	2.52237
$47$	3.23513e7	0.967057	0.483528	−	0.875329i	$-0.339355\pi$
$47$	3.23513e7	0.967057	0.483528	+	0.875329i	$0.339355\pi$
$48$	1.77950e7	0.483853
$49$	−4.03533e7	−0.999993
$50$	−1.29356e7	−0.292700
$51$	1.49616e7	0.309680
$52$	−4.67648e7	−0.886961
$53$	−4.32331e7	−0.752618	−0.376309	−	0.926494i	$-0.622807\pi$
$53$	−4.32331e7	−0.752618	−0.376309	+	0.926494i	$0.622807\pi$
$54$	1.75988e7	0.281650
$55$	−2.40038e7	−0.353710
$56$	−40958.2	−0.000556537 0
$57$	1.05560e7	0.132453
$58$	1.23153e7	0.142896
$59$	1.39320e8	1.49686	0.748429	−	0.663215i	$-0.230808\pi$
$59$	1.39320e8	1.49686	0.748429	+	0.663215i	$0.230808\pi$
$60$	−2.95962e7	−0.294819
$61$	5.46274e7	0.505157	0.252579	−	0.967576i	$-0.418721\pi$
$61$	5.46274e7	0.505157	0.252579	+	0.967576i	$0.418721\pi$
$62$	1.16416e8	1.00058
$63$	111751.	0.000893757 0
$64$	−1.69207e8	−1.26069
$65$	−4.99953e7	−0.347391
$66$	−1.03018e8	−0.668289
$67$	−2.64972e8	−1.60644	−0.803219	−	0.595684i	$-0.796881\pi$
$67$	−2.64972e8	−1.60644	−0.803219	+	0.595684i	$0.796881\pi$
$68$	−1.07985e8	−0.612456
$69$	1.87360e8	0.995076
$70$	−352524.	−0.00175488
$71$	−1.12609e8	−0.525910	−0.262955	−	0.964808i	$-0.584697\pi$
$71$	−1.12609e8	−0.525910	−0.262955	+	0.964808i	$0.584697\pi$
$72$	−1.57771e7	−0.0691882
$73$	−3.59484e7	−0.148159	−0.0740793	−	0.997252i	$-0.523602\pi$
$73$	−3.59484e7	−0.148159	−0.0740793	+	0.997252i	$0.523602\pi$
$74$	−3.05233e8	−1.18328
$75$	−3.16406e7	−0.115470
$76$	−7.61877e7	−0.261953
$77$	−654156.	−0.00212067
$78$	−2.14566e8	−0.656350
$79$	4.20019e8	1.21324	0.606620	−	0.794992i	$-0.292525\pi$
$79$	4.20019e8	1.21324	0.606620	+	0.794992i	$0.292525\pi$
$80$	−1.37307e8	−0.374791
$81$	4.30467e7	0.111111
$82$	3.38893e7	0.0827752
$83$	−2.94218e8	−0.680485	−0.340242	−	0.940338i	$-0.610509\pi$
$83$	−2.94218e8	−0.680485	−0.340242	+	0.940338i	$0.610509\pi$
$84$	−806561.	−0.00176759
$85$	−1.15445e8	−0.239877
$86$	6.25857e8	1.23376
$87$	3.01234e7	0.0563724
$88$	9.23545e7	0.164167
$89$	−1.16836e9	−1.97388	−0.986939	−	0.161092i	$-0.948498\pi$
$89$	−1.16836e9	−1.97388	−0.986939	+	0.161092i	$0.948498\pi$
$90$	−1.35793e8	−0.218165
$91$	−1.36248e6	−0.00208279
$92$	−1.35227e9	−1.96797
$93$	2.84755e8	0.394728
$94$	−1.07132e9	−1.41529
$95$	−8.14506e7	−0.102598
$96$	−6.89013e8	−0.827955
$97$	−2.51454e8	−0.288394	−0.144197	−	0.989549i	$-0.546060\pi$
$97$	−2.51454e8	−0.288394	−0.144197	+	0.989549i	$0.546060\pi$
$98$	1.33631e9	1.46349
$99$	−2.51982e8	−0.263640
$100$	2.28366e8	0.228366
$101$	−9.55295e8	−0.913464	−0.456732	−	0.889604i	$-0.650980\pi$
$101$	−9.55295e8	−0.913464	−0.456732	+	0.889604i	$0.650980\pi$
$102$	−4.95458e8	−0.453216
$103$	6.25032e8	0.547186	0.273593	−	0.961846i	$-0.411788\pi$
$103$	6.25032e8	0.547186	0.273593	+	0.961846i	$0.411788\pi$
$104$	1.92357e8	0.161234
$105$	−862277.	−0.000692301 0
$106$	1.43167e9	1.10146
$107$	−1.51392e9	−1.11654	−0.558271	−	0.829658i	$-0.688535\pi$
$107$	−1.51392e9	−1.11654	−0.558271	+	0.829658i	$0.688535\pi$
$108$	−3.10689e8	−0.219745
$109$	−3.99743e8	−0.271245	−0.135622	−	0.990761i	$-0.543303\pi$
$109$	−3.99743e8	−0.271245	−0.135622	+	0.990761i	$0.543303\pi$
$110$	7.94889e8	0.517654
$111$	−7.46601e8	−0.466805
$112$	−3.74193e6	−0.00224706
$113$	−1.50113e9	−0.866095	−0.433047	−	0.901371i	$-0.642562\pi$
$113$	−1.50113e9	−0.866095	−0.433047	+	0.901371i	$0.642562\pi$
$114$	−3.49564e8	−0.193845
$115$	−1.44568e9	−0.770783
$116$	−2.17415e8	−0.111488
$117$	−5.24830e8	−0.258930
$118$	−4.61362e9	−2.19065
$119$	−3.14613e6	−0.00143818
$120$	1.21737e8	0.0535930
$121$	−8.82924e8	−0.374446
$122$	−1.80900e9	−0.739297
$123$	8.28935e7	0.0326548
$124$	−2.05521e9	−0.780656
$125$	2.44141e8	0.0894427
$126$	−3.70066e6	−0.00130801
$127$	3.83546e9	1.30828	0.654140	−	0.756374i	$-0.273031\pi$
$127$	3.83546e9	1.30828	0.654140	+	0.756374i	$0.273031\pi$
$128$	1.24807e9	0.410954
$129$	1.53085e9	0.486720
$130$	1.65560e9	0.508406
$131$	2.92086e9	0.866544	0.433272	−	0.901263i	$-0.357359\pi$
$131$	2.92086e9	0.866544	0.433272	+	0.901263i	$0.357359\pi$
$132$	1.81867e9	0.521402
$133$	−2.21971e6	−0.000615126 0
$134$	8.77461e9	2.35102
$135$	−3.32151e8	−0.0860663
$136$	4.44173e8	0.111334
$137$	−7.74194e9	−1.87762	−0.938809	−	0.344439i	$-0.888069\pi$
$137$	−7.74194e9	−1.87762	−0.938809	+	0.344439i	$0.888069\pi$
$138$	−6.20447e9	−1.45629
$139$	2.18908e9	0.497388	0.248694	−	0.968582i	$-0.419999\pi$
$139$	2.18908e9	0.497388	0.248694	+	0.968582i	$0.419999\pi$
$140$	6.22347e6	0.00136917
$141$	−2.62046e9	−0.558330
$142$	3.72907e9	0.769668
$143$	3.07219e9	0.614379
$144$	−1.44140e9	−0.279352
$145$	−2.32433e8	−0.0436659
$146$	1.19044e9	0.216830
$147$	3.26862e9	0.577346
$148$	5.38858e9	0.923202
$149$	1.66949e9	0.277490	0.138745	−	0.990328i	$-0.455693\pi$
$149$	1.66949e9	0.277490	0.138745	+	0.990328i	$0.455693\pi$
$150$	1.04779e9	0.168990
$151$	−5.64582e8	−0.0883753	−0.0441877	−	0.999023i	$-0.514070\pi$
$151$	−5.64582e8	−0.0883753	−0.0441877	+	0.999023i	$0.514070\pi$
$152$	3.13381e8	0.0476186
$153$	−1.21189e9	−0.178794
$154$	2.16625e7	0.00310360
$155$	−2.19718e9	−0.305755
$156$	3.78795e9	0.512087
$157$	7.97287e9	1.04729	0.523644	−	0.851937i	$-0.324572\pi$
$157$	7.97287e9	1.04729	0.523644	+	0.851937i	$0.324572\pi$
$158$	−1.39090e10	−1.77557
$159$	3.50188e9	0.434524
$160$	5.31646e9	0.641331
$161$	−3.93980e7	−0.00462123
$162$	−1.42550e9	−0.162611
$163$	−2.19215e9	−0.243234	−0.121617	−	0.992577i	$-0.538808\pi$
$163$	−2.19215e9	−0.243234	−0.121617	+	0.992577i	$0.538808\pi$
$164$	−5.98282e8	−0.0645816
$165$	1.94431e9	0.204215
$166$	9.74310e9	0.995888
$167$	7.36481e9	0.732719	0.366359	−	0.930473i	$-0.380604\pi$
$167$	7.36481e9	0.732719	0.366359	+	0.930473i	$0.380604\pi$
$168$	3.31761e6	0.000321317 0
$169$	−4.20571e9	−0.396597
$170$	3.82297e9	0.351060
$171$	−8.55036e8	−0.0764719
$172$	−1.10489e10	−0.962588
$173$	−2.04155e10	−1.73281	−0.866407	−	0.499339i	$-0.833576\pi$
$173$	−2.04155e10	−1.73281	−0.866407	+	0.499339i	$0.833576\pi$
$174$	−9.97541e8	−0.0825010
$175$	6.65337e6	0.000536254 0
$176$	8.43748e9	0.662836
$177$	−1.12850e10	−0.864212
$178$	3.86904e10	2.88877
$179$	−2.77278e9	−0.201872	−0.100936	−	0.994893i	$-0.532184\pi$
$179$	−2.77278e9	−0.201872	−0.100936	+	0.994893i	$0.532184\pi$
$180$	2.39729e9	0.170214
$181$	2.15283e10	1.49092	0.745462	−	0.666548i	$-0.232229\pi$
$181$	2.15283e10	1.49092	0.745462	+	0.666548i	$0.232229\pi$
$182$	4.51189e7	0.00304815
$183$	−4.42482e9	−0.291653
$184$	5.56225e9	0.357742
$185$	5.76081e9	0.361585
$186$	−9.42972e9	−0.577684
$187$	7.09404e9	0.424235
$188$	1.89131e10	1.10421
$189$	−9.05184e6	−0.000516011 0
$190$	2.69725e9	0.150152
$191$	2.92849e10	1.59218	0.796092	−	0.605176i	$-0.206897\pi$
$191$	2.92849e10	1.59218	0.796092	+	0.605176i	$0.206897\pi$
$192$	1.37057e10	0.727858
$193$	6.10880e9	0.316919	0.158460	−	0.987365i	$-0.449347\pi$
$193$	6.10880e9	0.316919	0.158460	+	0.987365i	$0.449347\pi$
$194$	8.32696e9	0.422064
$195$	4.04962e9	0.200566
$196$	−2.35912e10	−1.14182
$197$	6.69784e9	0.316838	0.158419	−	0.987372i	$-0.449360\pi$
$197$	6.69784e9	0.316838	0.158419	+	0.987372i	$0.449360\pi$
$198$	8.34443e9	0.385837
$199$	2.71119e10	1.22552	0.612761	−	0.790268i	$-0.290059\pi$
$199$	2.71119e10	1.22552	0.612761	+	0.790268i	$0.290059\pi$
$200$	−9.39331e8	−0.0415129
$201$	2.14628e10	0.927477
$202$	3.16348e10	1.33685
$203$	−6.33432e6	−0.000261799 0
$204$	8.74681e9	0.353601
$205$	−6.39610e8	−0.0252943
$206$	−2.06981e10	−0.800806
$207$	−1.51762e10	−0.574507
$208$	1.75737e10	0.650995
$209$	5.00511e9	0.181449
$210$	2.85545e7	0.00101318
$211$	−3.43404e10	−1.19271	−0.596354	−	0.802722i	$-0.703384\pi$
$211$	−3.43404e10	−1.19271	−0.596354	+	0.802722i	$0.703384\pi$
$212$	−2.52747e10	−0.859360
$213$	9.12134e9	0.303634
$214$	5.01337e10	1.63406
$215$	−1.18121e10	−0.377012
$216$	1.27795e9	0.0399458
$217$	−5.98781e7	−0.00183316
$218$	1.32376e10	0.396966
$219$	2.91182e9	0.0855394
$220$	−1.40330e10	−0.403876
$221$	1.47755e10	0.416656
$222$	2.47238e10	0.683168
$223$	−6.20859e10	−1.68121	−0.840603	−	0.541652i	$-0.817799\pi$
$223$	−6.20859e10	−1.68121	−0.840603	+	0.541652i	$0.817799\pi$
$224$	1.44885e8	0.00384510
$225$	2.56289e9	0.0666667
$226$	4.97102e10	1.26753
$227$	−1.96434e10	−0.491021	−0.245510	−	0.969394i	$-0.578956\pi$
$227$	−1.96434e10	−0.491021	−0.245510	+	0.969394i	$0.578956\pi$
$228$	6.17121e9	0.151239
$229$	5.49131e10	1.31952	0.659761	−	0.751475i	$-0.270657\pi$
$229$	5.49131e10	1.31952	0.659761	+	0.751475i	$0.270657\pi$
$230$	4.78740e10	1.12804
$231$	5.29866e7	0.00122437
$232$	8.94287e8	0.0202666
$233$	−3.46346e10	−0.769855	−0.384928	−	0.922947i	$-0.625774\pi$
$233$	−3.46346e10	−0.769855	−0.384928	+	0.922947i	$0.625774\pi$
$234$	1.73799e10	0.378944
$235$	2.02196e10	0.432481
$236$	8.14489e10	1.70915
$237$	−3.40215e10	−0.700464
$238$	1.04185e8	0.00210478
$239$	−8.52413e9	−0.168990	−0.0844948	−	0.996424i	$-0.526928\pi$
$239$	−8.52413e9	−0.168990	−0.0844948	+	0.996424i	$0.526928\pi$
$240$	1.11219e10	0.216385
$241$	1.04020e11	1.98629	0.993144	−	0.116899i	$-0.0372955\pi$
$241$	1.04020e11	1.98629	0.993144	+	0.116899i	$0.0372955\pi$
$242$	2.92382e10	0.548001
$243$	−3.48678e9	−0.0641500
$244$	3.19361e10	0.576802
$245$	−2.52208e10	−0.447210
$246$	−2.74503e9	−0.0477903
$247$	1.04247e10	0.178208
$248$	8.45366e9	0.141910
$249$	2.38317e10	0.392878
$250$	−8.08476e9	−0.130899
$251$	−8.12749e10	−1.29248	−0.646242	−	0.763133i	$-0.723660\pi$
$251$	−8.12749e10	−1.29248	−0.646242	+	0.763133i	$0.723660\pi$
$252$	6.53315e7	0.00102052
$253$	8.88365e10	1.36317
$254$	−1.27012e11	−1.91467
$255$	9.35102e9	0.138493
$256$	4.53038e10	0.659257
$257$	−1.11919e11	−1.60032	−0.800158	−	0.599789i	$-0.795251\pi$
$257$	−1.11919e11	−1.60032	−0.800158	+	0.599789i	$0.795251\pi$
$258$	−5.06944e10	−0.712314
$259$	1.56995e8	0.00216789
$260$	−2.92280e10	−0.396661
$261$	−2.43999e9	−0.0325466
$262$	−9.67250e10	−1.26819
$263$	9.30128e10	1.19879	0.599393	−	0.800455i	$-0.295409\pi$
$263$	9.30128e10	1.19879	0.599393	+	0.800455i	$0.295409\pi$
$264$	−7.48071e9	−0.0947819
$265$	−2.70207e10	−0.336581
$266$	7.35061e7	0.000900236 0
$267$	9.46369e10	1.13962
$268$	−1.54907e11	−1.83428
$269$	1.52235e10	0.177268	0.0886341	−	0.996064i	$-0.471750\pi$
$269$	1.52235e10	0.177268	0.0886341	+	0.996064i	$0.471750\pi$
$270$	1.09992e10	0.125958
$271$	1.23934e11	1.39582	0.697911	−	0.716184i	$-0.254113\pi$
$271$	1.23934e11	1.39582	0.697911	+	0.716184i	$0.254113\pi$
$272$	4.05796e10	0.449519
$273$	1.10361e8	0.00120250
$274$	2.56376e11	2.74789
$275$	−1.50024e10	−0.158184
$276$	1.09534e11	1.13621
$277$	−7.06725e10	−0.721259	−0.360630	−	0.932709i	$-0.617438\pi$
$277$	−7.06725e10	−0.721259	−0.360630	+	0.932709i	$0.617438\pi$
$278$	−7.24918e10	−0.727926
$279$	−2.30652e10	−0.227896
$280$	−2.55988e7	−0.000248891 0
$281$	1.31055e11	1.25393	0.626966	−	0.779046i	$-0.284296\pi$
$281$	1.31055e11	1.25393	0.626966	+	0.779046i	$0.284296\pi$
$282$	8.67770e10	0.817116
$283$	2.10919e10	0.195468	0.0977341	−	0.995213i	$-0.468841\pi$
$283$	2.10919e10	0.195468	0.0977341	+	0.995213i	$0.468841\pi$
$284$	−6.58331e10	−0.600498
$285$	6.59750e9	0.0592349
$286$	−1.01736e11	−0.899142
$287$	−1.74308e7	−0.000151652 0
$288$	5.58100e10	0.478020
$289$	−8.44695e10	−0.712295
$290$	7.69707e9	0.0639050
$291$	2.03678e10	0.166504
$292$	−2.10160e10	−0.169172
$293$	−5.49153e10	−0.435300	−0.217650	−	0.976027i	$-0.569839\pi$
$293$	−5.49153e10	−0.435300	−0.217650	+	0.976027i	$0.569839\pi$
$294$	−1.08241e11	−0.844945
$295$	8.70753e10	0.669416
$296$	−2.21647e10	−0.167822
$297$	2.04105e10	0.152213
$298$	−5.52856e10	−0.406106
$299$	1.85030e11	1.33882
$300$	−1.84976e10	−0.131847
$301$	−3.21906e8	−0.00226037
$302$	1.86963e10	0.129337
$303$	7.73789e10	0.527388
$304$	2.86304e10	0.192263
$305$	3.41421e10	0.225913
$306$	4.01321e10	0.261665
$307$	7.62919e10	0.490180	0.245090	−	0.969500i	$-0.421182\pi$
$307$	7.62919e10	0.490180	0.245090	+	0.969500i	$0.421182\pi$
$308$	−3.82430e8	−0.00242144
$309$	−5.06276e10	−0.315918
$310$	7.27602e10	0.447472
$311$	−3.89402e10	−0.236035	−0.118018	−	0.993012i	$-0.537654\pi$
$311$	−3.89402e10	−0.236035	−0.118018	+	0.993012i	$0.537654\pi$
$312$	−1.55809e10	−0.0930886
$313$	2.49070e11	1.46680	0.733402	−	0.679795i	$-0.237931\pi$
$313$	2.49070e11	1.46680	0.733402	+	0.679795i	$0.237931\pi$
$314$	−2.64023e11	−1.53271
$315$	6.98445e7	0.000399700 0
$316$	2.45550e11	1.38531
$317$	−4.97240e10	−0.276567	−0.138283	−	0.990393i	$-0.544158\pi$
$317$	−4.97240e10	−0.276567	−0.138283	+	0.990393i	$0.544158\pi$
$318$	−1.15965e11	−0.635926
$319$	1.42829e10	0.0772253
$320$	−1.05754e11	−0.563797
$321$	1.22627e11	0.644636
$322$	1.30467e9	0.00676316
$323$	2.40718e10	0.123054
$324$	2.51658e10	0.126870
$325$	−3.12470e10	−0.155358
$326$	7.25933e10	0.355973
$327$	3.23792e10	0.156603
$328$	2.46090e9	0.0117398
$329$	5.51029e8	0.00259294
$330$	−6.43860e10	−0.298868
$331$	−2.77449e11	−1.27045	−0.635225	−	0.772327i	$-0.719093\pi$
$331$	−2.77449e11	−1.27045	−0.635225	+	0.772327i	$0.719093\pi$
$332$	−1.72005e11	−0.776996
$333$	6.04747e10	0.269510
$334$	−2.43887e11	−1.07233
$335$	−1.65608e11	−0.718421
$336$	3.03096e8	0.00129734
$337$	−2.64627e11	−1.11763	−0.558817	−	0.829291i	$-0.688744\pi$
$337$	−2.64627e11	−1.11763	−0.558817	+	0.829291i	$0.688744\pi$
$338$	1.39273e11	0.580419
$339$	1.21592e11	0.500040
$340$	−6.74908e10	−0.273898
$341$	1.35016e11	0.540743
$342$	2.83147e10	0.111917
$343$	−1.37465e9	−0.00536252
$344$	4.54471e10	0.174982
$345$	1.17100e11	0.445012
$346$	6.76062e11	2.53597
$347$	−3.73130e11	−1.38159	−0.690793	−	0.723053i	$-0.742738\pi$
$347$	−3.73130e11	−1.38159	−0.690793	+	0.723053i	$0.742738\pi$
$348$	1.76106e10	0.0643676
$349$	−2.59676e10	−0.0936952	−0.0468476	−	0.998902i	$-0.514918\pi$
$349$	−2.59676e10	−0.0936952	−0.0468476	+	0.998902i	$0.514918\pi$
$350$	−2.20328e8	−0.000784807 0
$351$	4.25113e10	0.149493
$352$	−3.26694e11	−1.13423
$353$	−2.07044e11	−0.709704	−0.354852	−	0.934922i	$-0.615469\pi$
$353$	−2.07044e11	−0.709704	−0.354852	+	0.934922i	$0.615469\pi$
$354$	3.73703e11	1.26477
$355$	−7.03807e10	−0.235194
$356$	−6.83040e11	−2.25383
$357$	2.54836e8	0.000830336 0
$358$	9.18212e10	0.295440
$359$	−8.82044e10	−0.280263	−0.140131	−	0.990133i	$-0.544752\pi$
$359$	−8.82044e10	−0.280263	−0.140131	+	0.990133i	$0.544752\pi$
$360$	−9.86072e9	−0.0309419
$361$	1.69836e10	0.0526316
$362$	−7.12912e11	−2.18196
$363$	7.15169e10	0.216187
$364$	−7.96529e8	−0.00237818
$365$	−2.24678e10	−0.0662585
$366$	1.46529e11	0.426833
$367$	3.16481e10	0.0910648	0.0455324	−	0.998963i	$-0.485502\pi$
$367$	3.16481e10	0.0910648	0.0455324	+	0.998963i	$0.485502\pi$
$368$	5.08166e11	1.44441
$369$	−6.71437e9	−0.0188533
$370$	−1.90770e11	−0.529180
$371$	−7.36373e8	−0.00201797
$372$	1.66472e11	0.450712
$373$	−2.33909e11	−0.625686	−0.312843	−	0.949805i	$-0.601281\pi$
$373$	−2.33909e11	−0.625686	−0.312843	+	0.949805i	$0.601281\pi$
$374$	−2.34920e11	−0.620867
$375$	−1.97754e10	−0.0516398
$376$	−7.77948e10	−0.200727
$377$	2.97486e10	0.0758457
$378$	2.99753e8	0.000755181 0
$379$	−8.71780e10	−0.217035	−0.108518	−	0.994095i	$-0.534610\pi$
$379$	−8.71780e10	−0.217035	−0.108518	+	0.994095i	$0.534610\pi$
$380$	−4.76173e10	−0.117149
$381$	−3.10672e11	−0.755336
$382$	−9.69774e11	−2.33016
$383$	−6.02315e11	−1.43031	−0.715154	−	0.698967i	$-0.753643\pi$
$383$	−6.02315e11	−1.43031	−0.715154	+	0.698967i	$0.753643\pi$
$384$	−1.01094e11	−0.237265
$385$	−4.08848e8	−0.000948392 0
$386$	−2.02294e11	−0.463811
$387$	−1.23999e11	−0.281008
$388$	−1.47004e11	−0.329296
$389$	−1.13185e11	−0.250619	−0.125310	−	0.992118i	$-0.539992\pi$
$389$	−1.13185e11	−0.250619	−0.125310	+	0.992118i	$0.539992\pi$
$390$	−1.34104e11	−0.293529
$391$	4.27254e11	0.924466
$392$	9.70371e10	0.207563
$393$	−2.36590e11	−0.500299
$394$	−2.21800e11	−0.463691
$395$	2.62512e11	0.542577
$396$	−1.47313e11	−0.301031
$397$	2.33057e11	0.470873	0.235437	−	0.971890i	$-0.424348\pi$
$397$	2.33057e11	0.470873	0.235437	+	0.971890i	$0.424348\pi$
$398$	−8.97816e11	−1.79355
$399$	1.79797e8	0.000355143 0
$400$	−8.58171e10	−0.167611
$401$	−9.42560e10	−0.182037	−0.0910184	−	0.995849i	$-0.529012\pi$
$401$	−9.42560e10	−0.182037	−0.0910184	+	0.995849i	$0.529012\pi$
$402$	−7.10743e11	−1.35736
$403$	2.81213e11	0.531083
$404$	−5.58480e11	−1.04302
$405$	2.69042e10	0.0496904
$406$	2.09762e8	0.000383142 0
$407$	−3.54000e11	−0.639482
$408$	−3.59781e10	−0.0642787
$409$	4.22209e11	0.746059	0.373029	−	0.927820i	$-0.378319\pi$
$409$	4.22209e11	0.746059	0.373029	+	0.927820i	$0.378319\pi$
$410$	2.11808e10	0.0370182
$411$	6.27097e11	1.08404
$412$	3.65404e11	0.624792
$413$	2.37299e9	0.00401348
$414$	5.02562e11	0.840791
$415$	−1.83886e11	−0.304322
$416$	−6.80442e11	−1.11396
$417$	−1.77316e11	−0.287167
$418$	−1.65745e11	−0.265551
$419$	2.62907e11	0.416715	0.208358	−	0.978053i	$-0.433188\pi$
$419$	2.62907e11	0.416715	0.208358	+	0.978053i	$0.433188\pi$
$420$	−5.04101e8	−0.000790489 0
$421$	2.42438e11	0.376124	0.188062	−	0.982157i	$-0.439779\pi$
$421$	2.42438e11	0.376124	0.188062	+	0.982157i	$0.439779\pi$
$422$	1.13719e12	1.74553
$423$	2.12257e11	0.322352
$424$	1.03962e11	0.156217
$425$	−7.21530e10	−0.107276
$426$	−3.02055e11	−0.444368
$427$	9.30449e8	0.00135446
$428$	−8.85060e11	−1.27490
$429$	−2.48848e11	−0.354712
$430$	3.91160e11	0.551756
$431$	−7.41006e10	−0.103437	−0.0517183	−	0.998662i	$-0.516470\pi$
$431$	−7.41006e10	−0.103437	−0.0517183	+	0.998662i	$0.516470\pi$
$432$	1.16753e11	0.161284
$433$	−3.50860e11	−0.479665	−0.239833	−	0.970814i	$-0.577093\pi$
$433$	−3.50860e11	−0.479665	−0.239833	+	0.970814i	$0.577093\pi$
$434$	1.98288e9	0.00268282
$435$	1.88271e10	0.0252105
$436$	−2.33696e11	−0.309715
$437$	3.01444e11	0.395403
$438$	−9.64255e10	−0.125187
$439$	4.53984e11	0.583378	0.291689	−	0.956513i	$-0.405783\pi$
$439$	4.53984e11	0.583378	0.291689	+	0.956513i	$0.405783\pi$
$440$	5.77215e10	0.0734177
$441$	−2.64758e11	−0.333331
$442$	−4.89294e11	−0.609776
$443$	9.28919e11	1.14594	0.572969	−	0.819577i	$-0.305792\pi$
$443$	9.28919e11	1.14594	0.572969	+	0.819577i	$0.305792\pi$
$444$	−4.36475e11	−0.533011
$445$	−7.30223e11	−0.882745
$446$	2.05598e12	2.46044
$447$	−1.35229e11	−0.160209
$448$	−2.88203e9	−0.00338024
$449$	−2.07633e11	−0.241095	−0.120547	−	0.992708i	$-0.538465\pi$
$449$	−2.07633e11	−0.241095	−0.120547	+	0.992708i	$0.538465\pi$
$450$	−8.48706e10	−0.0975666
$451$	3.93038e10	0.0447343
$452$	−8.77585e11	−0.988931
$453$	4.57312e10	0.0510235
$454$	6.50494e11	0.718608
$455$	−8.51551e8	−0.000931450 0
$456$	−2.53839e10	−0.0274926
$457$	5.26835e11	0.565004	0.282502	−	0.959267i	$-0.408836\pi$
$457$	5.26835e11	0.565004	0.282502	+	0.959267i	$0.408836\pi$
$458$	−1.81846e12	−1.93112
$459$	9.81633e10	0.103227
$460$	−8.45167e11	−0.880101
$461$	9.30031e11	0.959055	0.479527	−	0.877527i	$-0.340808\pi$
$461$	9.30031e11	0.959055	0.479527	+	0.877527i	$0.340808\pi$
$462$	−1.75466e9	−0.00179186
$463$	1.56207e12	1.57974	0.789871	−	0.613273i	$-0.210148\pi$
$463$	1.56207e12	1.57974	0.789871	+	0.613273i	$0.210148\pi$
$464$	8.17018e10	0.0818278
$465$	1.77972e11	0.176528
$466$	1.14693e12	1.12668
$467$	4.72113e11	0.459325	0.229662	−	0.973270i	$-0.426238\pi$
$467$	4.72113e11	0.459325	0.229662	+	0.973270i	$0.426238\pi$
$468$	−3.06824e11	−0.295654
$469$	−4.51318e9	−0.00430730
$470$	−6.69575e11	−0.632935
$471$	−6.45803e11	−0.604652
$472$	−3.35022e11	−0.310695
$473$	7.25850e11	0.666764
$474$	1.12663e12	1.02513
$475$	−5.09066e10	−0.0458831
$476$	−1.83927e9	−0.00164216
$477$	−2.83652e11	−0.250873
$478$	2.82278e11	0.247316
$479$	1.31456e12	1.14096	0.570478	−	0.821313i	$-0.306758\pi$
$479$	1.31456e12	1.14096	0.570478	+	0.821313i	$0.306758\pi$
$480$	−4.30633e11	−0.370273
$481$	−7.37314e11	−0.628058
$482$	−3.44466e12	−2.90693
$483$	3.19124e9	0.00266807
$484$	−5.16172e11	−0.427553
$485$	−1.57159e11	−0.128974
$486$	1.15466e11	0.0938835
$487$	2.31114e12	1.86186	0.930928	−	0.365203i	$-0.119001\pi$
$487$	2.31114e12	1.86186	0.930928	+	0.365203i	$0.119001\pi$
$488$	−1.31362e11	−0.104853
$489$	1.77564e11	0.140431
$490$	8.35192e11	0.654492
$491$	−1.90175e12	−1.47668	−0.738342	−	0.674426i	$-0.764391\pi$
$491$	−1.90175e12	−1.47668	−0.738342	+	0.674426i	$0.764391\pi$
$492$	4.84609e10	0.0372862
$493$	6.86930e10	0.0523723
$494$	−3.45216e11	−0.260807
$495$	−1.57489e11	−0.117903
$496$	7.72325e11	0.572971
$497$	−1.91803e9	−0.00141011
$498$	−7.89191e11	−0.574976
$499$	2.26601e12	1.63610	0.818048	−	0.575150i	$-0.195056\pi$
$499$	2.26601e12	1.63610	0.818048	+	0.575150i	$0.195056\pi$
$500$	1.42728e11	0.102128
$501$	−5.96549e11	−0.423035
$502$	2.69144e12	1.89155
$503$	7.91926e11	0.551605	0.275803	−	0.961214i	$-0.411056\pi$
$503$	7.91926e11	0.551605	0.275803	+	0.961214i	$0.411056\pi$
$504$	−2.68726e8	−0.000185512 0
$505$	−5.97059e11	−0.408513
$506$	−2.94184e12	−1.99499
$507$	3.40663e11	0.228975
$508$	2.24227e12	1.49383
$509$	2.29459e12	1.51522	0.757610	−	0.652708i	$-0.226367\pi$
$509$	2.29459e12	1.51522	0.757610	+	0.652708i	$0.226367\pi$
$510$	−3.09661e11	−0.202685
$511$	−6.12296e8	−0.000397253 0
$512$	−2.13925e12	−1.37578
$513$	6.92579e10	0.0441511
$514$	3.70623e12	2.34206
$515$	3.90645e11	0.244709
$516$	8.94959e11	0.555750
$517$	−1.24249e12	−0.764864
$518$	−5.19892e9	−0.00317270
$519$	1.65365e12	1.00044
$520$	1.20223e11	0.0721062
$521$	−1.72956e12	−1.02841	−0.514205	−	0.857667i	$-0.671913\pi$
$521$	−1.72956e12	−1.02841	−0.514205	+	0.857667i	$0.671913\pi$
$522$	8.08008e10	0.0476319
$523$	9.73136e11	0.568743	0.284371	−	0.958714i	$-0.408215\pi$
$523$	9.73136e11	0.568743	0.284371	+	0.958714i	$0.408215\pi$
$524$	1.70758e12	0.989444
$525$	−5.38923e8	−0.000309607 0
$526$	−3.08014e12	−1.75442
$527$	6.49353e11	0.366719
$528$	−6.83436e11	−0.382688
$529$	3.54922e12	1.97053
$530$	8.94794e11	0.492586
$531$	9.14081e11	0.498953
$532$	−1.29768e9	−0.000702368 0
$533$	8.18624e10	0.0439351
$534$	−3.13392e12	−1.66783
$535$	−9.46199e11	−0.499333
$536$	6.37175e11	0.333440
$537$	2.24595e11	0.116551
$538$	−5.04131e11	−0.259432
$539$	1.54981e12	0.790914
$540$	−1.94181e11	−0.0982729
$541$	2.76529e12	1.38788	0.693941	−	0.720032i	$-0.255873\pi$
$541$	2.76529e12	1.38788	0.693941	+	0.720032i	$0.255873\pi$
$542$	−4.10411e12	−2.04278
$543$	−1.74379e12	−0.860785
$544$	−1.57122e12	−0.769204
$545$	−2.49839e11	−0.121304
$546$	−3.65463e9	−0.00175985
$547$	−1.66817e12	−0.796702	−0.398351	−	0.917233i	$-0.630417\pi$
$547$	−1.66817e12	−0.796702	−0.398351	+	0.917233i	$0.630417\pi$
$548$	−4.52606e12	−2.14392
$549$	3.58410e11	0.168386
$550$	4.96806e11	0.231502
$551$	4.84655e10	0.0224001
$552$	−4.50542e11	−0.206543
$553$	7.15403e9	0.00325303
$554$	2.34033e12	1.05556
$555$	−4.66626e11	−0.208761
$556$	1.27977e12	0.567931
$557$	−1.55962e12	−0.686547	−0.343273	−	0.939235i	$-0.611536\pi$
$557$	−1.55962e12	−0.686547	−0.343273	+	0.939235i	$0.611536\pi$
$558$	7.63807e11	0.333526
$559$	1.51181e12	0.654853
$560$	−2.33871e9	−0.00100492
$561$	−5.74617e11	−0.244932
$562$	−4.33990e12	−1.83513
$563$	4.46009e12	1.87092	0.935461	−	0.353430i	$-0.114985\pi$
$563$	4.46009e12	1.87092	0.935461	+	0.353430i	$0.114985\pi$
$564$	−1.53196e12	−0.637517
$565$	−9.38207e11	−0.387329
$566$	−6.98461e11	−0.286067
$567$	7.33199e8	0.000297919 0
$568$	2.70790e11	0.109160
$569$	3.73323e12	1.49307	0.746535	−	0.665346i	$-0.231716\pi$
$569$	3.73323e12	1.49307	0.746535	+	0.665346i	$0.231716\pi$
$570$	−2.18477e11	−0.0866902
$571$	−3.37208e12	−1.32750	−0.663752	−	0.747953i	$-0.731037\pi$
$571$	−3.37208e12	−1.32750	−0.663752	+	0.747953i	$0.731037\pi$
$572$	1.79605e12	0.701515
$573$	−2.37207e12	−0.919248
$574$	5.77224e8	0.000221943 0
$575$	−9.03550e11	−0.344704
$576$	−1.11016e12	−0.420229
$577$	3.49209e12	1.31158	0.655790	−	0.754944i	$-0.272336\pi$
$577$	3.49209e12	1.31158	0.655790	+	0.754944i	$0.272336\pi$
$578$	2.79722e12	1.04244
$579$	−4.94813e11	−0.182973
$580$	−1.35884e11	−0.0498589
$581$	−5.01131e9	−0.00182456
$582$	−6.74484e11	−0.243679
$583$	1.66041e12	0.595260
$584$	8.64447e10	0.0307525
$585$	−3.28019e11	−0.115797
$586$	1.81853e12	0.637062
$587$	−2.58099e11	−0.0897253	−0.0448626	−	0.998993i	$-0.514285\pi$
$587$	−2.58099e11	−0.0897253	−0.0448626	+	0.998993i	$0.514285\pi$
$588$	1.91089e12	0.659230
$589$	4.58143e11	0.156849
$590$	−2.88351e12	−0.979689
$591$	−5.42525e11	−0.182926
$592$	−2.02496e12	−0.677594
$593$	5.00345e12	1.66159	0.830794	−	0.556580i	$-0.187887\pi$
$593$	5.00345e12	1.66159	0.830794	+	0.556580i	$0.187887\pi$
$594$	−6.75899e11	−0.222763
$595$	−1.96633e9	−0.000643176 0
$596$	9.76012e11	0.316845
$597$	−2.19606e12	−0.707556
$598$	−6.12729e12	−1.95935
$599$	−1.59577e11	−0.0506467	−0.0253233	−	0.999679i	$-0.508062\pi$
$599$	−1.59577e11	−0.0506467	−0.0253233	+	0.999679i	$0.508062\pi$
$600$	7.60858e10	0.0239675
$601$	−1.39393e12	−0.435820	−0.217910	−	0.975969i	$-0.569924\pi$
$601$	−1.39393e12	−0.435820	−0.217910	+	0.975969i	$0.569924\pi$
$602$	1.06600e10	0.00330805
$603$	−1.73848e12	−0.535479
$604$	−3.30064e11	−0.100909
$605$	−5.51828e11	−0.167457
$606$	−2.56242e12	−0.771832
$607$	−1.62643e12	−0.486279	−0.243140	−	0.969991i	$-0.578177\pi$
$607$	−1.62643e12	−0.486279	−0.243140	+	0.969991i	$0.578177\pi$
$608$	−1.10855e12	−0.328996
$609$	5.13080e8	0.000151150 0
$610$	−1.13062e12	−0.330623
$611$	−2.58786e12	−0.751200
$612$	−7.08492e11	−0.204152
$613$	−4.76697e12	−1.36355	−0.681774	−	0.731563i	$-0.738791\pi$
$613$	−4.76697e12	−1.36355	−0.681774	+	0.731563i	$0.738791\pi$
$614$	−2.52642e12	−0.717378
$615$	5.18084e10	0.0146037
$616$	1.57304e9	0.000440176 0
$617$	1.05135e12	0.292054	0.146027	−	0.989281i	$-0.453351\pi$
$617$	1.05135e12	0.292054	0.146027	+	0.989281i	$0.453351\pi$
$618$	1.67654e12	0.462346
$619$	3.48165e12	0.953184	0.476592	−	0.879125i	$-0.341872\pi$
$619$	3.48165e12	0.953184	0.476592	+	0.879125i	$0.341872\pi$
$620$	−1.28451e12	−0.349120
$621$	1.22927e12	0.331692
$622$	1.28951e12	0.345437
$623$	−1.99002e10	−0.00529250
$624$	−1.42347e12	−0.375852
$625$	1.52588e11	0.0400000
$626$	−8.24800e12	−2.14667
$627$	−4.05414e11	−0.104760
$628$	4.66107e12	1.19582
$629$	−1.70254e12	−0.433681
$630$	−2.31291e9	−0.000584961 0
$631$	1.59019e12	0.399316	0.199658	−	0.979866i	$-0.436017\pi$
$631$	1.59019e12	0.399316	0.199658	+	0.979866i	$0.436017\pi$
$632$	−1.01001e12	−0.251826
$633$	2.78157e12	0.688610
$634$	1.64662e12	0.404755
$635$	2.39716e12	0.585081
$636$	2.04725e12	0.496152
$637$	3.22796e12	0.776785
$638$	−4.72982e11	−0.113019
$639$	−7.38829e11	−0.175303
$640$	7.80043e11	0.183784
$641$	1.00116e12	0.234230	0.117115	−	0.993118i	$-0.462635\pi$
$641$	1.00116e12	0.234230	0.117115	+	0.993118i	$0.462635\pi$
$642$	−4.06083e12	−0.943424
$643$	1.37759e12	0.317812	0.158906	−	0.987294i	$-0.449203\pi$
$643$	1.37759e12	0.317812	0.158906	+	0.987294i	$0.449203\pi$
$644$	−2.30327e10	−0.00527665
$645$	9.56781e11	0.217668
$646$	−7.97142e11	−0.180090
$647$	−2.38096e12	−0.534175	−0.267087	−	0.963672i	$-0.586061\pi$
$647$	−2.38096e12	−0.534175	−0.267087	+	0.963672i	$0.586061\pi$
$648$	−1.03514e11	−0.0230627
$649$	−5.35075e12	−1.18389
$650$	1.03475e12	0.227366
$651$	4.85013e9	0.00105837
$652$	−1.28156e12	−0.277732
$653$	1.79434e12	0.386185	0.193093	−	0.981181i	$-0.438148\pi$
$653$	1.79434e12	0.386185	0.193093	+	0.981181i	$0.438148\pi$
$654$	−1.07224e12	−0.229189
$655$	1.82554e12	0.387530
$656$	2.24827e11	0.0474004
$657$	−2.35858e11	−0.0493862
$658$	−1.82474e10	−0.00379477
$659$	3.35077e12	0.692085	0.346043	−	0.938219i	$-0.387525\pi$
$659$	3.35077e12	0.692085	0.346043	+	0.938219i	$0.387525\pi$
$660$	1.13667e12	0.233178
$661$	1.87117e12	0.381247	0.190624	−	0.981663i	$-0.438949\pi$
$661$	1.87117e12	0.381247	0.190624	+	0.981663i	$0.438949\pi$
$662$	9.18779e12	1.85930
$663$	−1.19682e12	−0.240557
$664$	7.07503e11	0.141245
$665$	−1.38732e9	−0.000275093 0
$666$	−2.00263e12	−0.394427
$667$	8.60222e11	0.168285
$668$	4.30558e12	0.836639
$669$	5.02895e12	0.970644
$670$	5.48413e12	1.05141
$671$	−2.09802e12	−0.399539
$672$	−1.17357e10	−0.00221997
$673$	−5.21762e12	−0.980404	−0.490202	−	0.871609i	$-0.663077\pi$
$673$	−5.21762e12	−0.980404	−0.490202	+	0.871609i	$0.663077\pi$
$674$	8.76317e12	1.63565
$675$	−2.07594e11	−0.0384900
$676$	−2.45872e12	−0.452845
$677$	−4.24827e12	−0.777255	−0.388627	−	0.921395i	$-0.627051\pi$
$677$	−4.24827e12	−0.777255	−0.388627	+	0.921395i	$0.627051\pi$
$678$	−4.02653e12	−0.731808
$679$	−4.28293e9	−0.000773263 0
$680$	2.77608e11	0.0497900
$681$	1.59111e12	0.283491
$682$	−4.47109e12	−0.791377
$683$	4.48987e12	0.789479	0.394740	−	0.918793i	$-0.370835\pi$
$683$	4.48987e12	0.789479	0.394740	+	0.918793i	$0.370835\pi$
$684$	−4.99868e11	−0.0873178
$685$	−4.83871e12	−0.839696
$686$	4.55219e10	0.00784804
$687$	−4.44796e12	−0.761826
$688$	4.15204e12	0.706502
$689$	3.45832e12	0.584626
$690$	−3.87779e12	−0.651274
$691$	−4.14341e12	−0.691364	−0.345682	−	0.938352i	$-0.612352\pi$
$691$	−4.14341e12	−0.691364	−0.345682	+	0.938352i	$0.612352\pi$
$692$	−1.19352e13	−1.97857
$693$	−4.29192e9	−0.000706890 0
$694$	1.23563e13	2.02195
$695$	1.36818e12	0.222439
$696$	−7.24372e10	−0.0117009
$697$	1.89030e11	0.0303377
$698$	8.59922e11	0.137123
$699$	2.80541e12	0.444476
$700$	3.88967e9	0.000612310 0
$701$	6.06995e12	0.949410	0.474705	−	0.880145i	$-0.342555\pi$
$701$	6.06995e12	0.949410	0.474705	+	0.880145i	$0.342555\pi$
$702$	−1.40777e12	−0.218783
$703$	−1.20121e12	−0.185489
$704$	6.49855e12	0.997103
$705$	−1.63779e12	−0.249693
$706$	6.85632e12	1.03865
$707$	−1.62712e10	−0.00244924
$708$	−6.59736e12	−0.986781
$709$	3.98033e12	0.591576	0.295788	−	0.955254i	$-0.404418\pi$
$709$	3.98033e12	0.591576	0.295788	+	0.955254i	$0.404418\pi$
$710$	2.33067e12	0.344206
$711$	2.75574e12	0.404413
$712$	2.80953e12	0.409708
$713$	8.13165e12	1.17835
$714$	−8.43895e9	−0.00121520
$715$	1.92012e12	0.274759
$716$	−1.62101e12	−0.230504
$717$	6.90455e11	0.0975661
$718$	2.92090e12	0.410164
$719$	1.28152e12	0.178832	0.0894158	−	0.995994i	$-0.471500\pi$
$719$	1.28152e12	0.178832	0.0894158	+	0.995994i	$0.471500\pi$
$720$	−9.00873e11	−0.124930
$721$	1.06460e10	0.00146715
$722$	−5.62414e11	−0.0770262
$723$	−8.42566e12	−1.14678
$724$	1.25858e13	1.70238
$725$	−1.45271e11	−0.0195280
$726$	−2.36829e12	−0.316389
$727$	5.34292e12	0.709371	0.354686	−	0.934986i	$-0.384588\pi$
$727$	5.34292e12	0.709371	0.354686	+	0.934986i	$0.384588\pi$
$728$	3.27634e9	0.000432313 0
$729$	2.82430e11	0.0370370
$730$	7.44024e11	0.0969693
$731$	3.49094e12	0.452182
$732$	−2.58682e12	−0.333017
$733$	−9.41048e12	−1.20405	−0.602024	−	0.798478i	$-0.705639\pi$
$733$	−9.41048e12	−1.20405	−0.602024	+	0.798478i	$0.705639\pi$
$734$	−1.04803e12	−0.133273
$735$	2.04289e12	0.258197
$736$	−1.96759e13	−2.47163
$737$	1.01765e13	1.27056
$738$	2.22348e11	0.0275917
$739$	−1.39316e12	−0.171831	−0.0859157	−	0.996302i	$-0.527382\pi$
$739$	−1.39316e12	−0.171831	−0.0859157	+	0.996302i	$0.527382\pi$
$740$	3.36786e12	0.412868
$741$	−8.44400e11	−0.102888
$742$	2.43851e10	0.00295330
$743$	1.50796e13	1.81526	0.907630	−	0.419771i	$-0.137890\pi$
$743$	1.50796e13	1.81526	0.907630	+	0.419771i	$0.137890\pi$
$744$	−6.84747e11	−0.0819317
$745$	1.04343e12	0.124097
$746$	7.74593e12	0.915691
$747$	−1.93037e12	−0.226828
$748$	4.14729e12	0.484403
$749$	−2.57860e10	−0.00299375
$750$	6.54866e11	0.0755747
$751$	−3.73380e12	−0.428323	−0.214162	−	0.976798i	$-0.568702\pi$
$751$	−3.73380e12	−0.428323	−0.214162	+	0.976798i	$0.568702\pi$
$752$	−7.10732e12	−0.810449
$753$	6.58327e12	0.746216
$754$	−9.85132e11	−0.111000
$755$	−3.52864e11	−0.0395226
$756$	−5.29185e9	−0.000589196 0
$757$	3.93471e11	0.0435493	0.0217747	−	0.999763i	$-0.493068\pi$
$757$	3.93471e11	0.0435493	0.0217747	+	0.999763i	$0.493068\pi$
$758$	2.88692e12	0.317631
$759$	−7.19576e12	−0.787025
$760$	1.95863e11	0.0212957
$761$	7.63945e12	0.825717	0.412858	−	0.910795i	$-0.364530\pi$
$761$	7.63945e12	0.825717	0.412858	+	0.910795i	$0.364530\pi$
$762$	1.02880e13	1.10543
$763$	−6.80867e9	−0.000727280 0
$764$	1.71204e13	1.81800
$765$	−7.57433e11	−0.0799591
$766$	1.99458e13	2.09325
$767$	−1.11446e13	−1.16275
$768$	−3.66961e12	−0.380622
$769$	3.42360e12	0.353033	0.176516	−	0.984298i	$-0.443517\pi$
$769$	3.42360e12	0.353033	0.176516	+	0.984298i	$0.443517\pi$
$770$	1.35391e10	0.00138797
$771$	9.06546e12	0.923943
$772$	3.57130e12	0.361867
$773$	−1.88667e12	−0.190059	−0.0950293	−	0.995474i	$-0.530294\pi$
$773$	−1.88667e12	−0.190059	−0.0950293	+	0.995474i	$0.530294\pi$
$774$	4.10625e12	0.411255
$775$	−1.37324e12	−0.136738
$776$	6.04669e11	0.0598604
$777$	−1.27166e10	−0.00125163
$778$	3.74813e12	0.366781
$779$	1.33367e11	0.0129757
$780$	2.36747e12	0.229012
$781$	4.32487e12	0.415952
$782$	−1.41486e13	−1.35295
$783$	1.97639e11	0.0187908
$784$	8.86529e12	0.838051
$785$	4.98305e12	0.468362
$786$	7.83472e12	0.732187
$787$	−1.12024e11	−0.0104094	−0.00520469	−	0.999986i	$-0.501657\pi$
$787$	−1.12024e11	−0.0104094	−0.00520469	+	0.999986i	$0.501657\pi$
$788$	3.91566e12	0.361774
$789$	−7.53404e12	−0.692120
$790$	−8.69312e12	−0.794061
$791$	−2.55682e10	−0.00232223
$792$	6.05938e11	0.0547223
$793$	−4.36978e12	−0.392401
$794$	−7.71771e12	−0.689122
$795$	2.18867e12	0.194325
$796$	1.58501e13	1.39934
$797$	−1.56209e13	−1.37134	−0.685668	−	0.727914i	$-0.740490\pi$
$797$	−1.56209e13	−1.37134	−0.685668	+	0.727914i	$0.740490\pi$
$798$	−5.95400e9	−0.000519751 0
$799$	−5.97567e12	−0.518712
$800$	3.32279e12	0.286812
$801$	−7.66559e12	−0.657960
$802$	3.12130e12	0.266411
$803$	1.38064e12	0.117182
$804$	1.25475e13	1.05902
$805$	−2.46237e10	−0.00206668
$806$	−9.31242e12	−0.777240
$807$	−1.23311e12	−0.102346
$808$	2.29718e12	0.189603
$809$	−1.10907e13	−0.910317	−0.455158	−	0.890411i	$-0.650417\pi$
$809$	−1.10907e13	−0.910317	−0.455158	+	0.890411i	$0.650417\pi$
$810$	−8.90938e11	−0.0727218
$811$	1.33620e13	1.08462	0.542309	−	0.840179i	$-0.317550\pi$
$811$	1.33620e13	1.08462	0.542309	+	0.840179i	$0.317550\pi$
$812$	−3.70315e9	−0.000298929 0
$813$	−1.00387e13	−0.805878
$814$	1.17228e13	0.935881
$815$	−1.37009e12	−0.108778
$816$	−3.28695e12	−0.259530
$817$	2.46299e12	0.193403
$818$	−1.39815e13	−1.09186
$819$	−8.93925e9	−0.000694262 0
$820$	−3.73926e11	−0.0288818
$821$	2.87412e12	0.220780	0.110390	−	0.993888i	$-0.464790\pi$
$821$	2.87412e12	0.220780	0.110390	+	0.993888i	$0.464790\pi$
$822$	−2.07664e13	−1.58650
$823$	1.70469e13	1.29523	0.647613	−	0.761969i	$-0.275767\pi$
$823$	1.70469e13	1.29523	0.647613	+	0.761969i	$0.275767\pi$
$824$	−1.50301e12	−0.113577
$825$	1.21519e12	0.0913275
$826$	−7.85822e10	−0.00587373
$827$	1.64480e13	1.22275	0.611376	−	0.791341i	$-0.290616\pi$
$827$	1.64480e13	1.22275	0.611376	+	0.791341i	$0.290616\pi$
$828$	−8.87223e12	−0.655989
$829$	7.33681e12	0.539526	0.269763	−	0.962927i	$-0.413055\pi$
$829$	7.33681e12	0.539526	0.269763	+	0.962927i	$0.413055\pi$
$830$	6.08944e12	0.445375
$831$	5.72447e12	0.416419
$832$	1.35352e13	0.979290
$833$	7.45373e12	0.536378
$834$	5.87184e12	0.420268
$835$	4.60301e12	0.327682
$836$	2.92607e12	0.207184
$837$	1.86828e12	0.131576
$838$	−8.70623e12	−0.609862
$839$	−4.79559e12	−0.334128	−0.167064	−	0.985946i	$-0.553429\pi$
$839$	−4.79559e12	−0.334128	−0.167064	+	0.985946i	$0.553429\pi$
$840$	2.07351e9	0.000143697 0
$841$	−1.43688e13	−0.990466
$842$	−8.02837e12	−0.550457
$843$	−1.06154e13	−0.723958
$844$	−2.00759e13	−1.36187
$845$	−2.62857e12	−0.177363
$846$	−7.02894e12	−0.471762
$847$	−1.50385e10	−0.00100399
$848$	9.49794e12	0.630737
$849$	−1.70844e12	−0.112854
$850$	2.38936e12	0.156999
$851$	−2.13204e13	−1.39352
$852$	5.33248e12	0.346698
$853$	1.40453e13	0.908367	0.454183	−	0.890908i	$-0.349931\pi$
$853$	1.40453e13	0.908367	0.454183	+	0.890908i	$0.349931\pi$
$854$	−3.08120e10	−0.00198225
$855$	−5.34398e11	−0.0341993
$856$	3.64050e12	0.231755
$857$	2.65416e13	1.68079	0.840394	−	0.541976i	$-0.182324\pi$
$857$	2.65416e13	1.68079	0.840394	+	0.541976i	$0.182324\pi$
$858$	8.24063e12	0.519120
$859$	1.49667e13	0.937903	0.468951	−	0.883224i	$-0.344632\pi$
$859$	1.49667e13	0.937903	0.468951	+	0.883224i	$0.344632\pi$
$860$	−6.90555e12	−0.430482
$861$	1.41189e9	8.75565e−5 0
$862$	2.45385e12	0.151379
$863$	−1.24632e13	−0.764858	−0.382429	−	0.923985i	$-0.624912\pi$
$863$	−1.24632e13	−0.764858	−0.382429	+	0.923985i	$0.624912\pi$
$864$	−4.52061e12	−0.275985
$865$	−1.27597e13	−0.774938
$866$	1.16188e13	0.701989
$867$	6.84203e12	0.411243
$868$	−3.50057e10	−0.00209315
$869$	−1.61313e13	−0.959575
$870$	−6.23463e11	−0.0368955
$871$	2.11958e13	1.24787
$872$	9.61256e11	0.0563008
$873$	−1.64979e12	−0.0961314
$874$	−9.98237e12	−0.578672
$875$	4.15836e9	0.000239820 0
$876$	1.70230e12	0.0976713
$877$	−6.70365e12	−0.382660	−0.191330	−	0.981526i	$-0.561280\pi$
$877$	−6.70365e12	−0.382660	−0.191330	+	0.981526i	$0.561280\pi$
$878$	−1.50337e13	−0.853772
$879$	4.44814e12	0.251321
$880$	5.27343e12	0.296429
$881$	−2.22555e13	−1.24464	−0.622322	−	0.782761i	$-0.713811\pi$
$881$	−2.22555e13	−1.24464	−0.622322	+	0.782761i	$0.713811\pi$
$882$	8.76752e12	0.487829
$883$	−3.00571e13	−1.66389	−0.831944	−	0.554859i	$-0.812772\pi$
$883$	−3.00571e13	−1.66389	−0.831944	+	0.554859i	$0.812772\pi$
$884$	8.63801e12	0.475750
$885$	−7.05310e12	−0.386487
$886$	−3.07613e13	−1.67708
$887$	−2.69460e13	−1.46163	−0.730816	−	0.682574i	$-0.760860\pi$
$887$	−2.69460e13	−1.46163	−0.730816	+	0.682574i	$0.760860\pi$
$888$	1.79534e12	0.0968922
$889$	6.53280e10	0.00350785
$890$	2.41815e13	1.29190
$891$	−1.65325e12	−0.0878800
$892$	−3.62964e13	−1.91965
$893$	−4.21606e12	−0.221858
$894$	4.47813e12	0.234465
$895$	−1.73299e12	−0.0902801
$896$	2.12579e10	0.00110188
$897$	−1.49874e13	−0.772966
$898$	6.87581e12	0.352842
$899$	1.30739e12	0.0667554
$900$	1.49831e12	0.0761219
$901$	7.98565e12	0.403691
$902$	−1.30155e12	−0.0654686
$903$	2.60744e10	0.00130503
$904$	3.60975e12	0.179771
$905$	1.34552e13	0.666761
$906$	−1.51440e12	−0.0746728
$907$	−9.12004e12	−0.447470	−0.223735	−	0.974650i	$-0.571825\pi$
$907$	−9.12004e12	−0.447470	−0.223735	+	0.974650i	$0.571825\pi$
$908$	−1.14838e13	−0.560661
$909$	−6.26769e12	−0.304488
$910$	2.81993e10	0.00136318
$911$	1.96010e13	0.942855	0.471427	−	0.881905i	$-0.343739\pi$
$911$	1.96010e13	0.942855	0.471427	+	0.881905i	$0.343739\pi$
$912$	−2.31907e12	−0.111003
$913$	1.12998e13	0.538209
$914$	−1.74462e13	−0.826883
$915$	−2.76551e12	−0.130431
$916$	3.21031e13	1.50667
$917$	4.97500e10	0.00232344
$918$	−3.25070e12	−0.151072
$919$	6.11131e12	0.282628	0.141314	−	0.989965i	$-0.454867\pi$
$919$	6.11131e12	0.282628	0.141314	+	0.989965i	$0.454867\pi$
$920$	3.47641e12	0.159987
$921$	−6.17964e12	−0.283006
$922$	−3.07982e13	−1.40358
$923$	9.00788e12	0.408521
$924$	3.09768e10	0.00139802
$925$	3.60051e12	0.161706
$926$	−5.17283e13	−2.31195
$927$	4.10084e12	0.182395
$928$	−3.16345e12	−0.140021
$929$	−3.35624e13	−1.47837	−0.739183	−	0.673504i	$-0.764788\pi$
$929$	−3.35624e13	−1.47837	−0.739183	+	0.673504i	$0.764788\pi$
$930$	−5.89357e12	−0.258348
$931$	5.25888e12	0.229414
$932$	−2.02480e13	−0.879042
$933$	3.15416e12	0.136275
$934$	−1.56341e13	−0.672221
$935$	4.43377e12	0.189724
$936$	1.26205e12	0.0537448
$937$	−1.78191e13	−0.755194	−0.377597	−	0.925970i	$-0.623249\pi$
$937$	−1.78191e13	−0.755194	−0.377597	+	0.925970i	$0.623249\pi$
$938$	1.49455e11	0.00630372
$939$	−2.01747e13	−0.846860
$940$	1.18207e13	0.493819
$941$	−3.04959e13	−1.26791	−0.633954	−	0.773370i	$-0.718569\pi$
$941$	−3.04959e13	−1.26791	−0.633954	+	0.773370i	$0.718569\pi$
$942$	2.13859e13	0.884908
$943$	2.36716e12	0.0974821
$944$	−3.06075e13	−1.25445
$945$	−5.65740e9	−0.000230767 0
$946$	−2.40367e13	−0.975808
$947$	2.14194e13	0.865430	0.432715	−	0.901531i	$-0.357556\pi$
$947$	2.14194e13	0.865430	0.432715	+	0.901531i	$0.357556\pi$
$948$	−1.98895e13	−0.799810
$949$	2.87560e12	0.115088
$950$	1.68578e12	0.0671499
$951$	4.02765e12	0.159676
$952$	7.56545e9	0.000298516 0
$953$	−4.05601e13	−1.59287	−0.796435	−	0.604724i	$-0.793283\pi$
$953$	−4.05601e13	−1.59287	−0.796435	+	0.604724i	$0.793283\pi$
$954$	9.39319e12	0.367152
$955$	1.83030e13	0.712046
$956$	−4.98334e12	−0.192957
$957$	−1.15692e12	−0.0445861
$958$	−4.35317e13	−1.66979
$959$	−1.31866e11	−0.00503440
$960$	8.56608e12	0.325508
$961$	−1.40809e13	−0.532569
$962$	2.44163e13	0.919162
$963$	−9.93282e12	−0.372181
$964$	6.08120e13	2.26800
$965$	3.81800e12	0.141731
$966$	−1.05678e11	−0.00390471
$967$	2.00201e12	0.0736288	0.0368144	−	0.999322i	$-0.488279\pi$
$967$	2.00201e12	0.0736288	0.0368144	+	0.999322i	$0.488279\pi$
$968$	2.12316e12	0.0777218
$969$	−1.94982e12	−0.0710455
$970$	5.20435e12	0.188753
$971$	−5.10256e13	−1.84205	−0.921026	−	0.389502i	$-0.872647\pi$
$971$	−5.10256e13	−1.84205	−0.921026	+	0.389502i	$0.872647\pi$
$972$	−2.03843e12	−0.0732483
$973$	3.72858e10	0.00133363
$974$	−7.65339e13	−2.72482
$975$	2.53101e12	0.0896960
$976$	−1.20012e13	−0.423350
$977$	−5.47823e13	−1.92360	−0.961800	−	0.273753i	$-0.911735\pi$
$977$	−5.47823e13	−1.92360	−0.961800	+	0.273753i	$0.911735\pi$
$978$	−5.88006e12	−0.205521
$979$	4.48720e13	1.56118
$980$	−1.47445e13	−0.510637
$981$	−2.62271e12	−0.0904149
$982$	6.29769e13	2.16112
$983$	3.88250e13	1.32624	0.663118	−	0.748515i	$-0.269233\pi$
$983$	3.88250e13	1.32624	0.663118	+	0.748515i	$0.269233\pi$
$984$	−1.99333e11	−0.00677799
$985$	4.18615e12	0.141694
$986$	−2.27478e12	−0.0766467
$987$	−4.46333e10	−0.00149704
$988$	6.09444e12	0.203483
$989$	4.37160e13	1.45297
$990$	5.21527e12	0.172551
$991$	−3.30103e13	−1.08722	−0.543610	−	0.839338i	$-0.682943\pi$
$991$	−3.30103e13	−1.08722	−0.543610	+	0.839338i	$0.682943\pi$
$992$	−2.99040e13	−0.980452
$993$	2.24734e13	0.733495
$994$	6.35159e10	0.00206369
$995$	1.69449e13	0.548070
$996$	1.39324e13	0.448599
$997$	6.02031e13	1.92971	0.964853	−	0.262791i	$-0.0846431\pi$
$997$	6.02031e13	1.92971	0.964853	+	0.262791i	$0.0846431\pi$
$998$	−7.50393e13	−2.39442
$999$	−4.89845e12	−0.155602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.3	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-33.1152 q^{2} -81.0000 q^{3} +584.616 q^{4} +625.000 q^{5} +2682.33 q^{6} +17.0326 q^{7} -2404.69 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-33.1152 q^{2} -81.0000 q^{3} +584.616 q^{4} +625.000 q^{5} +2682.33 q^{6} +17.0326 q^{7} -2404.69 q^{8} +6561.00 q^{9} -20697.0 q^{10} -38406.0 q^{11} -47353.9 q^{12} -79992.4 q^{13} -564.039 q^{14} -50625.0 q^{15} -219692. q^{16} -184712. q^{17} -217269. q^{18} -130321. q^{19} +365385. q^{20} -1379.64 q^{21} +1.27182e6 q^{22} -2.31309e6 q^{23} +194780. q^{24} +390625. q^{25} +2.64896e6 q^{26} -531441. q^{27} +9957.55 q^{28} -371893. q^{29} +1.67646e6 q^{30} -3.51549e6 q^{31} +8.50633e6 q^{32} +3.11089e6 q^{33} +6.11676e6 q^{34} +10645.4 q^{35} +3.83566e6 q^{36} +9.21730e6 q^{37} +4.31560e6 q^{38} +6.47939e6 q^{39} -1.50293e6 q^{40} -1.02338e6 q^{41} +45687.2 q^{42} -1.88994e7 q^{43} -2.24528e7 q^{44} +4.10062e6 q^{45} +7.65984e7 q^{46} +3.23513e7 q^{47} +1.77950e7 q^{48} -4.03533e7 q^{49} -1.29356e7 q^{50} +1.49616e7 q^{51} -4.67648e7 q^{52} -4.32331e7 q^{53} +1.75988e7 q^{54} -2.40038e7 q^{55} -40958.2 q^{56} +1.05560e7 q^{57} +1.23153e7 q^{58} +1.39320e8 q^{59} -2.95962e7 q^{60} +5.46274e7 q^{61} +1.16416e8 q^{62} +111751. q^{63} -1.69207e8 q^{64} -4.99953e7 q^{65} -1.03018e8 q^{66} -2.64972e8 q^{67} -1.07985e8 q^{68} +1.87360e8 q^{69} -352524. q^{70} -1.12609e8 q^{71} -1.57771e7 q^{72} -3.59484e7 q^{73} -3.05233e8 q^{74} -3.16406e7 q^{75} -7.61877e7 q^{76} -654156. q^{77} -2.14566e8 q^{78} +4.20019e8 q^{79} -1.37307e8 q^{80} +4.30467e7 q^{81} +3.38893e7 q^{82} -2.94218e8 q^{83} -806561. q^{84} -1.15445e8 q^{85} +6.25857e8 q^{86} +3.01234e7 q^{87} +9.23545e7 q^{88} -1.16836e9 q^{89} -1.35793e8 q^{90} -1.36248e6 q^{91} -1.35227e9 q^{92} +2.84755e8 q^{93} -1.07132e9 q^{94} -8.14506e7 q^{95} -6.89013e8 q^{96} -2.51454e8 q^{97} +1.33631e9 q^{98} -2.51982e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 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

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