LMFDB - Embedded newform 285.10.a.h.1.7

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			1.7
Root			$5.41213$ 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)

$f(q)$	$=$	$q-6.41213 q^{2} -81.0000 q^{3} -470.885 q^{4} +625.000 q^{5} +519.382 q^{6} -7663.31 q^{7} +6302.38 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-6.41213 q^{2} -81.0000 q^{3} -470.885 q^{4} +625.000 q^{5} +519.382 q^{6} -7663.31 q^{7} +6302.38 q^{8} +6561.00 q^{9} -4007.58 q^{10} +3714.99 q^{11} +38141.7 q^{12} +140010. q^{13} +49138.1 q^{14} -50625.0 q^{15} +200681. q^{16} -29426.7 q^{17} -42070.0 q^{18} -130321. q^{19} -294303. q^{20} +620728. q^{21} -23821.0 q^{22} +543534. q^{23} -510493. q^{24} +390625. q^{25} -897763. q^{26} -531441. q^{27} +3.60854e6 q^{28} +653112. q^{29} +324614. q^{30} -6.20437e6 q^{31} -4.51361e6 q^{32} -300915. q^{33} +188688. q^{34} -4.78957e6 q^{35} -3.08947e6 q^{36} -1.43083e7 q^{37} +835635. q^{38} -1.13408e7 q^{39} +3.93899e6 q^{40} -1.40634e7 q^{41} -3.98019e6 q^{42} +3.38510e7 q^{43} -1.74933e6 q^{44} +4.10062e6 q^{45} -3.48521e6 q^{46} +4.14880e7 q^{47} -1.62552e7 q^{48} +1.83728e7 q^{49} -2.50474e6 q^{50} +2.38357e6 q^{51} -6.59286e7 q^{52} -6.45117e7 q^{53} +3.40767e6 q^{54} +2.32187e6 q^{55} -4.82971e7 q^{56} +1.05560e7 q^{57} -4.18784e6 q^{58} +7.94519e7 q^{59} +2.38385e7 q^{60} +3.29941e7 q^{61} +3.97832e7 q^{62} -5.02790e7 q^{63} -7.38069e7 q^{64} +8.75063e7 q^{65} +1.92950e6 q^{66} -1.96309e8 q^{67} +1.38566e7 q^{68} -4.40262e7 q^{69} +3.07113e7 q^{70} -3.62019e8 q^{71} +4.13499e7 q^{72} -2.73499e8 q^{73} +9.17468e7 q^{74} -3.16406e7 q^{75} +6.13662e7 q^{76} -2.84692e7 q^{77} +7.27188e7 q^{78} -2.95732e8 q^{79} +1.25426e8 q^{80} +4.30467e7 q^{81} +9.01762e7 q^{82} +2.00828e8 q^{83} -2.92291e8 q^{84} -1.83917e7 q^{85} -2.17057e8 q^{86} -5.29021e7 q^{87} +2.34133e7 q^{88} +1.00715e9 q^{89} -2.62937e7 q^{90} -1.07294e9 q^{91} -2.55942e8 q^{92} +5.02554e8 q^{93} -2.66026e8 q^{94} -8.14506e7 q^{95} +3.65603e8 q^{96} -1.03608e9 q^{97} -1.17808e8 q^{98} +2.43741e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.41213	−0.283379	−0.141689	−	0.989911i	$-0.545253\pi$
$2$	−6.41213	−0.283379	−0.141689	+	0.989911i	$0.545253\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−470.885	−0.919697
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	519.382	0.163609
$7$	−7663.31	−1.20636	−0.603178	−	0.797607i	$-0.706099\pi$
$7$	−7663.31	−1.20636	−0.603178	+	0.797607i	$0.706099\pi$
$8$	6302.38	0.544001
$9$	6561.00	0.333333
$10$	−4007.58	−0.126731
$11$	3714.99	0.0765052	0.0382526	−	0.999268i	$-0.487821\pi$
$11$	3714.99	0.0765052	0.0382526	+	0.999268i	$0.487821\pi$
$12$	38141.7	0.530987
$13$	140010.	1.35961	0.679805	−	0.733393i	$-0.262064\pi$
$13$	140010.	1.35961	0.679805	+	0.733393i	$0.262064\pi$
$14$	49138.1	0.341855
$15$	−50625.0	−0.258199
$16$	200681.	0.765538
$17$	−29426.7	−0.0854520	−0.0427260	−	0.999087i	$-0.513604\pi$
$17$	−29426.7	−0.0854520	−0.0427260	+	0.999087i	$0.513604\pi$
$18$	−42070.0	−0.0944596
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−294303.	−0.411301
$21$	620728.	0.696490
$22$	−23821.0	−0.0216799
$23$	543534.	0.404996	0.202498	−	0.979283i	$-0.435094\pi$
$23$	543534.	0.404996	0.202498	+	0.979283i	$0.435094\pi$
$24$	−510493.	−0.314079
$25$	390625.	0.200000
$26$	−897763.	−0.385285
$27$	−531441.	−0.192450
$28$	3.60854e6	1.10948
$29$	653112.	0.171473	0.0857367	−	0.996318i	$-0.472676\pi$
$29$	653112.	0.171473	0.0857367	+	0.996318i	$0.472676\pi$
$30$	324614.	0.0731681
$31$	−6.20437e6	−1.20662	−0.603309	−	0.797507i	$-0.706151\pi$
$31$	−6.20437e6	−1.20662	−0.603309	+	0.797507i	$0.706151\pi$
$32$	−4.51361e6	−0.760938
$33$	−300915.	−0.0441703
$34$	188688.	0.0242153
$35$	−4.78957e6	−0.539499
$36$	−3.08947e6	−0.306566
$37$	−1.43083e7	−1.25511	−0.627554	−	0.778573i	$-0.715944\pi$
$37$	−1.43083e7	−1.25511	−0.627554	+	0.778573i	$0.715944\pi$
$38$	835635.	0.0650115
$39$	−1.13408e7	−0.784971
$40$	3.93899e6	0.243285
$41$	−1.40634e7	−0.777253	−0.388627	−	0.921395i	$-0.627050\pi$
$41$	−1.40634e7	−0.777253	−0.388627	+	0.921395i	$0.627050\pi$
$42$	−3.98019e6	−0.197370
$43$	3.38510e7	1.50995	0.754977	−	0.655751i	$-0.227648\pi$
$43$	3.38510e7	1.50995	0.754977	+	0.655751i	$0.227648\pi$
$44$	−1.74933e6	−0.0703616
$45$	4.10062e6	0.149071
$46$	−3.48521e6	−0.114767
$47$	4.14880e7	1.24017	0.620086	−	0.784533i	$-0.287098\pi$
$47$	4.14880e7	1.24017	0.620086	+	0.784533i	$0.287098\pi$
$48$	−1.62552e7	−0.441984
$49$	1.83728e7	0.455294
$50$	−2.50474e6	−0.0566757
$51$	2.38357e6	0.0493357
$52$	−6.59286e7	−1.25043
$53$	−6.45117e7	−1.12305	−0.561523	−	0.827461i	$-0.689784\pi$
$53$	−6.45117e7	−1.12305	−0.561523	+	0.827461i	$0.689784\pi$
$54$	3.40767e6	0.0545363
$55$	2.32187e6	0.0342142
$56$	−4.82971e7	−0.656259
$57$	1.05560e7	0.132453
$58$	−4.18784e6	−0.0485919
$59$	7.94519e7	0.853631	0.426815	−	0.904339i	$-0.359635\pi$
$59$	7.94519e7	0.853631	0.426815	+	0.904339i	$0.359635\pi$
$60$	2.38385e7	0.237465
$61$	3.29941e7	0.305107	0.152554	−	0.988295i	$-0.451250\pi$
$61$	3.29941e7	0.305107	0.152554	+	0.988295i	$0.451250\pi$
$62$	3.97832e7	0.341930
$63$	−5.02790e7	−0.402119
$64$	−7.38069e7	−0.549905
$65$	8.75063e7	0.608036
$66$	1.92950e6	0.0125169
$67$	−1.96309e8	−1.19016	−0.595079	−	0.803668i	$-0.702879\pi$
$67$	−1.96309e8	−1.19016	−0.595079	+	0.803668i	$0.702879\pi$
$68$	1.38566e7	0.0785899
$69$	−4.40262e7	−0.233825
$70$	3.07113e7	0.152882
$71$	−3.62019e8	−1.69071	−0.845354	−	0.534206i	$-0.820611\pi$
$71$	−3.62019e8	−1.69071	−0.845354	+	0.534206i	$0.820611\pi$
$72$	4.13499e7	0.181334
$73$	−2.73499e8	−1.12721	−0.563603	−	0.826046i	$-0.690585\pi$
$73$	−2.73499e8	−1.12721	−0.563603	+	0.826046i	$0.690585\pi$
$74$	9.17468e7	0.355671
$75$	−3.16406e7	−0.115470
$76$	6.13662e7	0.210993
$77$	−2.84692e7	−0.0922925
$78$	7.27188e7	0.222444
$79$	−2.95732e8	−0.854232	−0.427116	−	0.904197i	$-0.640470\pi$
$79$	−2.95732e8	−0.854232	−0.427116	+	0.904197i	$0.640470\pi$
$80$	1.25426e8	0.342359
$81$	4.30467e7	0.111111
$82$	9.01762e7	0.220257
$83$	2.00828e8	0.464486	0.232243	−	0.972658i	$-0.425393\pi$
$83$	2.00828e8	0.464486	0.232243	+	0.972658i	$0.425393\pi$
$84$	−2.92291e8	−0.640559
$85$	−1.83917e7	−0.0382153
$86$	−2.17057e8	−0.427889
$87$	−5.29021e7	−0.0990002
$88$	2.34133e7	0.0416189
$89$	1.00715e9	1.70153	0.850763	−	0.525549i	$-0.176140\pi$
$89$	1.00715e9	1.70153	0.850763	+	0.525549i	$0.176140\pi$
$90$	−2.62937e7	−0.0422436
$91$	−1.07294e9	−1.64017
$92$	−2.55942e8	−0.372474
$93$	5.02554e8	0.696641
$94$	−2.66026e8	−0.351439
$95$	−8.14506e7	−0.102598
$96$	3.65603e8	0.439328
$97$	−1.03608e9	−1.18829	−0.594143	−	0.804359i	$-0.702509\pi$
$97$	−1.03608e9	−1.18829	−0.594143	+	0.804359i	$0.702509\pi$
$98$	−1.17808e8	−0.129021
$99$	2.43741e7	0.0255017
$100$	−1.83939e8	−0.183939
$101$	8.71778e8	0.833603	0.416802	−	0.908997i	$-0.363151\pi$
$101$	8.71778e8	0.833603	0.416802	+	0.908997i	$0.363151\pi$
$102$	−1.52837e7	−0.0139807
$103$	8.04502e8	0.704303	0.352151	−	0.935943i	$-0.385450\pi$
$103$	8.04502e8	0.704303	0.352151	+	0.935943i	$0.385450\pi$
$104$	8.82397e8	0.739629
$105$	3.87955e8	0.311480
$106$	4.13657e8	0.318247
$107$	−4.78117e8	−0.352620	−0.176310	−	0.984335i	$-0.556416\pi$
$107$	−4.78117e8	−0.352620	−0.176310	+	0.984335i	$0.556416\pi$
$108$	2.50247e8	0.176996
$109$	−2.64083e9	−1.79193	−0.895967	−	0.444122i	$-0.853516\pi$
$109$	−2.64083e9	−1.79193	−0.895967	+	0.444122i	$0.853516\pi$
$110$	−1.48881e7	−0.00969557
$111$	1.15897e9	0.724637
$112$	−1.53788e9	−0.923511
$113$	9.81702e8	0.566405	0.283202	−	0.959060i	$-0.408603\pi$
$113$	9.81702e8	0.566405	0.283202	+	0.959060i	$0.408603\pi$
$114$	−6.76864e7	−0.0375344
$115$	3.39709e8	0.181120
$116$	−3.07541e8	−0.157704
$117$	9.18607e8	0.453203
$118$	−5.09455e8	−0.241901
$119$	2.25506e8	0.103085
$120$	−3.19058e8	−0.140460
$121$	−2.34415e9	−0.994147
$122$	−2.11563e8	−0.0864609
$123$	1.13913e9	0.448747
$124$	2.92154e9	1.10972
$125$	2.44141e8	0.0894427
$126$	3.22395e8	0.113952
$127$	2.27426e9	0.775754	0.387877	−	0.921711i	$-0.373208\pi$
$127$	2.27426e9	0.775754	0.387877	+	0.921711i	$0.373208\pi$
$128$	2.78423e9	0.916769
$129$	−2.74193e9	−0.871772
$130$	−5.61102e8	−0.172304
$131$	4.37731e9	1.29863	0.649316	−	0.760519i	$-0.275055\pi$
$131$	4.37731e9	1.29863	0.649316	+	0.760519i	$0.275055\pi$
$132$	1.41696e8	0.0406233
$133$	9.98691e8	0.276757
$134$	1.25876e9	0.337265
$135$	−3.32151e8	−0.0860663
$136$	−1.85459e8	−0.0464860
$137$	−1.51042e8	−0.0366316	−0.0183158	−	0.999832i	$-0.505830\pi$
$137$	−1.51042e8	−0.0366316	−0.0183158	+	0.999832i	$0.505830\pi$
$138$	2.82302e8	0.0662610
$139$	7.19747e9	1.63536	0.817679	−	0.575674i	$-0.195260\pi$
$139$	7.19747e9	1.63536	0.817679	+	0.575674i	$0.195260\pi$
$140$	2.25534e9	0.496175
$141$	−3.36053e9	−0.716014
$142$	2.32131e9	0.479111
$143$	5.20137e8	0.104017
$144$	1.31667e9	0.255179
$145$	4.08195e8	0.0766853
$146$	1.75371e9	0.319426
$147$	−1.48819e9	−0.262864
$148$	6.73757e9	1.15432
$149$	−1.93018e9	−0.320818	−0.160409	−	0.987051i	$-0.551281\pi$
$149$	−1.93018e9	−0.320818	−0.160409	+	0.987051i	$0.551281\pi$
$150$	2.02884e8	0.0327218
$151$	−2.33185e9	−0.365009	−0.182505	−	0.983205i	$-0.558420\pi$
$151$	−2.33185e9	−0.365009	−0.182505	+	0.983205i	$0.558420\pi$
$152$	−8.21333e8	−0.124802
$153$	−1.93069e8	−0.0284840
$154$	1.82548e8	0.0261537
$155$	−3.87773e9	−0.539616
$156$	5.34022e9	0.721935
$157$	−1.51864e9	−0.199483	−0.0997414	−	0.995013i	$-0.531802\pi$
$157$	−1.51864e9	−0.199483	−0.0997414	+	0.995013i	$0.531802\pi$
$158$	1.89627e9	0.242071
$159$	5.22545e9	0.648390
$160$	−2.82101e9	−0.340302
$161$	−4.16527e9	−0.488570
$162$	−2.76021e8	−0.0314865
$163$	−2.33785e9	−0.259402	−0.129701	−	0.991553i	$-0.541402\pi$
$163$	−2.33785e9	−0.259402	−0.129701	+	0.991553i	$0.541402\pi$
$164$	6.62223e9	0.714837
$165$	−1.88072e8	−0.0197536
$166$	−1.28774e9	−0.131626
$167$	1.16628e10	1.16032	0.580162	−	0.814501i	$-0.302989\pi$
$167$	1.16628e10	1.16032	0.580162	+	0.814501i	$0.302989\pi$
$168$	3.91207e9	0.378891
$169$	8.99834e9	0.848540
$170$	1.17930e8	0.0108294
$171$	−8.55036e8	−0.0764719
$172$	−1.59399e10	−1.38870
$173$	−1.18098e10	−1.00238	−0.501192	−	0.865336i	$-0.667105\pi$
$173$	−1.18098e10	−1.00238	−0.501192	+	0.865336i	$0.667105\pi$
$174$	3.39215e8	0.0280546
$175$	−2.99348e9	−0.241271
$176$	7.45530e8	0.0585677
$177$	−6.43560e9	−0.492844
$178$	−6.45797e9	−0.482176
$179$	1.80580e10	1.31472	0.657358	−	0.753578i	$-0.271674\pi$
$179$	1.80580e10	1.31472	0.657358	+	0.753578i	$0.271674\pi$
$180$	−1.93092e9	−0.137100
$181$	1.18421e10	0.820115	0.410058	−	0.912060i	$-0.365509\pi$
$181$	1.18421e10	0.820115	0.410058	+	0.912060i	$0.365509\pi$
$182$	6.87984e9	0.464790
$183$	−2.67253e9	−0.176154
$184$	3.42556e9	0.220319
$185$	−8.94271e9	−0.561301
$186$	−3.22244e9	−0.197413
$187$	−1.09320e8	−0.00653752
$188$	−1.95361e10	−1.14058
$189$	4.07260e9	0.232163
$190$	5.22272e8	0.0290740
$191$	3.60910e9	0.196223	0.0981113	−	0.995175i	$-0.468720\pi$
$191$	3.60910e9	0.196223	0.0981113	+	0.995175i	$0.468720\pi$
$192$	5.97836e9	0.317488
$193$	3.17425e9	0.164677	0.0823386	−	0.996604i	$-0.473761\pi$
$193$	3.17425e9	0.164677	0.0823386	+	0.996604i	$0.473761\pi$
$194$	6.64349e9	0.336735
$195$	−7.08801e9	−0.351050
$196$	−8.65145e9	−0.418732
$197$	−3.05926e10	−1.44717	−0.723583	−	0.690238i	$-0.757506\pi$
$197$	−3.05926e10	−1.44717	−0.723583	+	0.690238i	$0.757506\pi$
$198$	−1.56290e8	−0.00722665
$199$	−9.78742e9	−0.442415	−0.221207	−	0.975227i	$-0.571000\pi$
$199$	−9.78742e9	−0.442415	−0.221207	+	0.975227i	$0.571000\pi$
$200$	2.46187e9	0.108800
$201$	1.59011e10	0.687138
$202$	−5.58995e9	−0.236225
$203$	−5.00500e9	−0.206858
$204$	−1.12238e9	−0.0453739
$205$	−8.78962e9	−0.347598
$206$	−5.15857e9	−0.199584
$207$	3.56613e9	0.134999
$208$	2.80974e10	1.04083
$209$	−4.84142e8	−0.0175515
$210$	−2.48762e9	−0.0882667
$211$	3.63779e10	1.26348	0.631738	−	0.775182i	$-0.282342\pi$
$211$	3.63779e10	1.26348	0.631738	+	0.775182i	$0.282342\pi$
$212$	3.03776e10	1.03286
$213$	2.93235e10	0.976131
$214$	3.06575e9	0.0999250
$215$	2.11569e10	0.675272
$216$	−3.34934e9	−0.104693
$217$	4.75460e10	1.45561
$218$	1.69334e10	0.507796
$219$	2.21534e10	0.650793
$220$	−1.09333e9	−0.0314667
$221$	−4.12004e9	−0.116181
$222$	−7.43149e9	−0.205347
$223$	1.95194e10	0.528561	0.264281	−	0.964446i	$-0.414865\pi$
$223$	1.95194e10	0.528561	0.264281	+	0.964446i	$0.414865\pi$
$224$	3.45892e10	0.917962
$225$	2.56289e9	0.0666667
$226$	−6.29480e9	−0.160507
$227$	4.92901e10	1.23209	0.616047	−	0.787710i	$-0.288733\pi$
$227$	4.92901e10	1.23209	0.616047	+	0.787710i	$0.288733\pi$
$228$	−4.97066e9	−0.121817
$229$	4.61647e10	1.10930	0.554651	−	0.832083i	$-0.312852\pi$
$229$	4.61647e10	1.10930	0.554651	+	0.832083i	$0.312852\pi$
$230$	−2.17825e9	−0.0513255
$231$	2.30600e9	0.0532851
$232$	4.11616e9	0.0932817
$233$	7.63034e10	1.69606	0.848032	−	0.529946i	$-0.177788\pi$
$233$	7.63034e10	1.69606	0.848032	+	0.529946i	$0.177788\pi$
$234$	−5.89022e9	−0.128428
$235$	2.59300e10	0.554622
$236$	−3.74127e10	−0.785081
$237$	2.39543e10	0.493191
$238$	−1.44598e9	−0.0292122
$239$	3.06912e10	0.608447	0.304223	−	0.952601i	$-0.401603\pi$
$239$	3.06912e10	0.608447	0.304223	+	0.952601i	$0.401603\pi$
$240$	−1.01595e10	−0.197661
$241$	−3.25607e10	−0.621752	−0.310876	−	0.950450i	$-0.600622\pi$
$241$	−3.25607e10	−0.621752	−0.310876	+	0.950450i	$0.600622\pi$
$242$	1.50310e10	0.281720
$243$	−3.48678e9	−0.0641500
$244$	−1.55364e10	−0.280606
$245$	1.14830e10	0.203614
$246$	−7.30428e9	−0.127165
$247$	−1.82463e10	−0.311916
$248$	−3.91023e10	−0.656402
$249$	−1.62671e10	−0.268171
$250$	−1.56546e9	−0.0253462
$251$	2.11051e10	0.335626	0.167813	−	0.985819i	$-0.446330\pi$
$251$	2.11051e10	0.335626	0.167813	+	0.985819i	$0.446330\pi$
$252$	2.36756e10	0.369827
$253$	2.01922e9	0.0309843
$254$	−1.45829e10	−0.219832
$255$	1.48973e9	0.0220636
$256$	1.99363e10	0.290112
$257$	1.18323e11	1.69189	0.845944	−	0.533272i	$-0.179038\pi$
$257$	1.18323e11	1.69189	0.845944	+	0.533272i	$0.179038\pi$
$258$	1.75816e10	0.247042
$259$	1.09649e11	1.51411
$260$	−4.12054e10	−0.559209
$261$	4.28507e9	0.0571578
$262$	−2.80678e10	−0.368005
$263$	−7.49327e10	−0.965763	−0.482881	−	0.875686i	$-0.660410\pi$
$263$	−7.49327e10	−0.965763	−0.482881	+	0.875686i	$0.660410\pi$
$264$	−1.89648e9	−0.0240287
$265$	−4.03198e10	−0.502241
$266$	−6.40373e9	−0.0784270
$267$	−8.15791e10	−0.982377
$268$	9.24390e10	1.09458
$269$	−9.65323e10	−1.12405	−0.562027	−	0.827119i	$-0.689978\pi$
$269$	−9.65323e10	−1.12405	−0.562027	+	0.827119i	$0.689978\pi$
$270$	2.12979e9	0.0243894
$271$	7.15254e10	0.805561	0.402781	−	0.915297i	$-0.368044\pi$
$271$	7.15254e10	0.805561	0.402781	+	0.915297i	$0.368044\pi$
$272$	−5.90540e9	−0.0654168
$273$	8.69083e10	0.946955
$274$	9.68502e8	0.0103806
$275$	1.45117e9	0.0153010
$276$	2.07313e10	0.215048
$277$	7.09793e10	0.724390	0.362195	−	0.932102i	$-0.382027\pi$
$277$	7.09793e10	0.724390	0.362195	+	0.932102i	$0.382027\pi$
$278$	−4.61511e10	−0.463426
$279$	−4.07069e10	−0.402206
$280$	−3.01857e10	−0.293488
$281$	−8.31014e10	−0.795115	−0.397557	−	0.917577i	$-0.630142\pi$
$281$	−8.31014e10	−0.795115	−0.397557	+	0.917577i	$0.630142\pi$
$282$	2.15481e10	0.202903
$283$	−1.48804e11	−1.37904	−0.689519	−	0.724268i	$-0.742178\pi$
$283$	−1.48804e11	−1.37904	−0.689519	+	0.724268i	$0.742178\pi$
$284$	1.70469e11	1.55494
$285$	6.59750e9	0.0592349
$286$	−3.33518e9	−0.0294763
$287$	1.07772e11	0.937644
$288$	−2.96138e10	−0.253646
$289$	−1.17722e11	−0.992698
$290$	−2.61740e9	−0.0217310
$291$	8.39226e10	0.686057
$292$	1.28787e11	1.03669
$293$	−1.44391e11	−1.14455	−0.572275	−	0.820062i	$-0.693939\pi$
$293$	−1.44391e11	−1.14455	−0.572275	+	0.820062i	$0.693939\pi$
$294$	9.54249e9	0.0744901
$295$	4.96574e10	0.381755
$296$	−9.01766e10	−0.682780
$297$	−1.97430e9	−0.0147234
$298$	1.23766e10	0.0909131
$299$	7.61002e10	0.550637
$300$	1.48991e10	0.106197
$301$	−2.59411e11	−1.82154
$302$	1.49521e10	0.103436
$303$	−7.06140e10	−0.481281
$304$	−2.61530e10	−0.175627
$305$	2.06213e10	0.136448
$306$	1.23798e9	0.00807176
$307$	2.59884e11	1.66977	0.834886	−	0.550423i	$-0.185533\pi$
$307$	2.59884e11	1.66977	0.834886	+	0.550423i	$0.185533\pi$
$308$	1.34057e10	0.0848811
$309$	−6.51646e10	−0.406629
$310$	2.48645e10	0.152916
$311$	−8.90718e9	−0.0539906	−0.0269953	−	0.999636i	$-0.508594\pi$
$311$	−8.90718e9	−0.0539906	−0.0269953	+	0.999636i	$0.508594\pi$
$312$	−7.14742e10	−0.427025
$313$	1.29555e11	0.762967	0.381483	−	0.924376i	$-0.375413\pi$
$313$	1.29555e11	0.762967	0.381483	+	0.924376i	$0.375413\pi$
$314$	9.73769e9	0.0565292
$315$	−3.14244e10	−0.179833
$316$	1.39255e11	0.785634
$317$	1.75658e10	0.0977017	0.0488508	−	0.998806i	$-0.484444\pi$
$317$	1.75658e10	0.0977017	0.0488508	+	0.998806i	$0.484444\pi$
$318$	−3.35063e10	−0.183740
$319$	2.42631e9	0.0131186
$320$	−4.61293e10	−0.245925
$321$	3.87275e10	0.203585
$322$	2.67082e10	0.138450
$323$	3.83492e9	0.0196040
$324$	−2.02700e10	−0.102189
$325$	5.46915e10	0.271922
$326$	1.49906e10	0.0735089
$327$	2.13908e11	1.03457
$328$	−8.86328e10	−0.422827
$329$	−3.17936e11	−1.49609
$330$	1.20594e9	0.00559774
$331$	1.03775e11	0.475191	0.237595	−	0.971364i	$-0.423641\pi$
$331$	1.03775e11	0.475191	0.237595	+	0.971364i	$0.423641\pi$
$332$	−9.45669e10	−0.427187
$333$	−9.38770e10	−0.418369
$334$	−7.47834e10	−0.328811
$335$	−1.22693e11	−0.532254
$336$	1.24569e11	0.533190
$337$	1.52153e11	0.642608	0.321304	−	0.946976i	$-0.395879\pi$
$337$	1.52153e11	0.642608	0.321304	+	0.946976i	$0.395879\pi$
$338$	−5.76985e10	−0.240458
$339$	−7.95179e10	−0.327014
$340$	8.66038e9	0.0351465
$341$	−2.30492e10	−0.0923126
$342$	5.48260e9	0.0216705
$343$	1.68446e11	0.657109
$344$	2.13342e11	0.821417
$345$	−2.75164e10	−0.104570
$346$	7.57257e10	0.284054
$347$	−6.05703e10	−0.224273	−0.112137	−	0.993693i	$-0.535769\pi$
$347$	−6.05703e10	−0.224273	−0.112137	+	0.993693i	$0.535769\pi$
$348$	2.49108e10	0.0910502
$349$	−1.54026e11	−0.555751	−0.277876	−	0.960617i	$-0.589630\pi$
$349$	−1.54026e11	−0.555751	−0.277876	+	0.960617i	$0.589630\pi$
$350$	1.91946e10	0.0683711
$351$	−7.44071e10	−0.261657
$352$	−1.67680e10	−0.0582158
$353$	−1.68508e11	−0.577610	−0.288805	−	0.957388i	$-0.593258\pi$
$353$	−1.68508e11	−0.577610	−0.288805	+	0.957388i	$0.593258\pi$
$354$	4.12659e10	0.139661
$355$	−2.26262e11	−0.756108
$356$	−4.74251e11	−1.56489
$357$	−1.82660e10	−0.0595164
$358$	−1.15790e11	−0.372562
$359$	1.77806e11	0.564964	0.282482	−	0.959273i	$-0.408842\pi$
$359$	1.77806e11	0.564964	0.282482	+	0.959273i	$0.408842\pi$
$360$	2.58437e10	0.0810949
$361$	1.69836e10	0.0526316
$362$	−7.59330e10	−0.232403
$363$	1.89876e11	0.573971
$364$	5.05232e11	1.50846
$365$	−1.70937e11	−0.504102
$366$	1.71366e10	0.0499182
$367$	1.67690e11	0.482514	0.241257	−	0.970461i	$-0.422440\pi$
$367$	1.67690e11	0.482514	0.241257	+	0.970461i	$0.422440\pi$
$368$	1.09077e11	0.310040
$369$	−9.22699e10	−0.259084
$370$	5.73418e10	0.159061
$371$	4.94374e11	1.35479
$372$	−2.36645e11	−0.640699
$373$	−4.60723e11	−1.23239	−0.616197	−	0.787592i	$-0.711328\pi$
$373$	−4.60723e11	−1.23239	−0.616197	+	0.787592i	$0.711328\pi$
$374$	7.00975e8	0.00185259
$375$	−1.97754e10	−0.0516398
$376$	2.61473e11	0.674655
$377$	9.14423e10	0.233137
$378$	−2.61140e10	−0.0657901
$379$	1.55061e10	0.0386034	0.0193017	−	0.999814i	$-0.493856\pi$
$379$	1.55061e10	0.0386034	0.0193017	+	0.999814i	$0.493856\pi$
$380$	3.83538e10	0.0943589
$381$	−1.84215e11	−0.447882
$382$	−2.31420e10	−0.0556053
$383$	−6.69455e11	−1.58974	−0.794872	−	0.606777i	$-0.792462\pi$
$383$	−6.69455e11	−1.58974	−0.794872	+	0.606777i	$0.792462\pi$
$384$	−2.25523e11	−0.529297
$385$	−1.77932e10	−0.0412745
$386$	−2.03537e10	−0.0466660
$387$	2.22097e11	0.503318
$388$	4.87875e11	1.09286
$389$	5.47042e11	1.21129	0.605644	−	0.795735i	$-0.292915\pi$
$389$	5.47042e11	1.21129	0.605644	+	0.795735i	$0.292915\pi$
$390$	4.54492e10	0.0994800
$391$	−1.59944e10	−0.0346078
$392$	1.15792e11	0.247680
$393$	−3.54562e11	−0.749765
$394$	1.96164e11	0.410096
$395$	−1.84832e11	−0.382024
$396$	−1.14774e10	−0.0234539
$397$	−3.07228e11	−0.620731	−0.310365	−	0.950617i	$-0.600451\pi$
$397$	−3.07228e11	−0.620731	−0.310365	+	0.950617i	$0.600451\pi$
$398$	6.27582e10	0.125371
$399$	−8.08939e10	−0.159786
$400$	7.83911e10	0.153108
$401$	−3.15152e11	−0.608654	−0.304327	−	0.952568i	$-0.598432\pi$
$401$	−3.15152e11	−0.608654	−0.304327	+	0.952568i	$0.598432\pi$
$402$	−1.01960e11	−0.194720
$403$	−8.68674e11	−1.64053
$404$	−4.10507e11	−0.766662
$405$	2.69042e10	0.0496904
$406$	3.20927e10	0.0586191
$407$	−5.31554e10	−0.0960223
$408$	1.50221e10	0.0268387
$409$	2.54256e11	0.449279	0.224639	−	0.974442i	$-0.427880\pi$
$409$	2.54256e11	0.449279	0.224639	+	0.974442i	$0.427880\pi$
$410$	5.63602e10	0.0985019
$411$	1.22344e10	0.0211493
$412$	−3.78827e11	−0.647745
$413$	−6.08864e11	−1.02978
$414$	−2.28664e10	−0.0382558
$415$	1.25518e11	0.207725
$416$	−6.31952e11	−1.03458
$417$	−5.82995e11	−0.944175
$418$	3.10438e9	0.00497372
$419$	−4.42107e11	−0.700751	−0.350376	−	0.936609i	$-0.613946\pi$
$419$	−4.42107e11	−0.700751	−0.350376	+	0.936609i	$0.613946\pi$
$420$	−1.82682e11	−0.286467
$421$	4.54833e11	0.705640	0.352820	−	0.935691i	$-0.385223\pi$
$421$	4.54833e11	0.705640	0.352820	+	0.935691i	$0.385223\pi$
$422$	−2.33260e11	−0.358042
$423$	2.72203e11	0.413391
$424$	−4.06578e11	−0.610938
$425$	−1.14948e10	−0.0170904
$426$	−1.88026e11	−0.276615
$427$	−2.52844e11	−0.368068
$428$	2.25138e11	0.324303
$429$	−4.21311e10	−0.0600544
$430$	−1.35661e11	−0.191358
$431$	−4.64761e11	−0.648757	−0.324379	−	0.945927i	$-0.605155\pi$
$431$	−4.64761e11	−0.648757	−0.324379	+	0.945927i	$0.605155\pi$
$432$	−1.06650e11	−0.147328
$433$	3.49673e10	0.0478043	0.0239022	−	0.999714i	$-0.492391\pi$
$433$	3.49673e10	0.0478043	0.0239022	+	0.999714i	$0.492391\pi$
$434$	−3.04871e11	−0.412489
$435$	−3.30638e10	−0.0442743
$436$	1.24353e12	1.64803
$437$	−7.08339e10	−0.0929126
$438$	−1.42051e11	−0.184421
$439$	4.57704e11	0.588159	0.294079	−	0.955781i	$-0.404987\pi$
$439$	4.57704e11	0.588159	0.294079	+	0.955781i	$0.404987\pi$
$440$	1.46333e10	0.0186125
$441$	1.20544e11	0.151765
$442$	2.64182e10	0.0329233
$443$	1.24741e12	1.53884	0.769421	−	0.638742i	$-0.220545\pi$
$443$	1.24741e12	1.53884	0.769421	+	0.638742i	$0.220545\pi$
$444$	−5.45743e11	−0.666446
$445$	6.29468e11	0.760946
$446$	−1.25161e11	−0.149783
$447$	1.56344e11	0.185225
$448$	5.65606e11	0.663380
$449$	−3.13180e11	−0.363651	−0.181826	−	0.983331i	$-0.558201\pi$
$449$	−3.13180e11	−0.363651	−0.181826	+	0.983331i	$0.558201\pi$
$450$	−1.64336e10	−0.0188919
$451$	−5.22454e10	−0.0594639
$452$	−4.62269e11	−0.520920
$453$	1.88880e11	0.210738
$454$	−3.16055e11	−0.349149
$455$	−6.70588e11	−0.733508
$456$	6.65279e10	0.0720547
$457$	−1.46629e12	−1.57252	−0.786259	−	0.617897i	$-0.787985\pi$
$457$	−1.46629e12	−1.57252	−0.786259	+	0.617897i	$0.787985\pi$
$458$	−2.96014e11	−0.314353
$459$	1.56386e10	0.0164452
$460$	−1.59964e11	−0.166575
$461$	−8.71723e10	−0.0898927	−0.0449464	−	0.998989i	$-0.514312\pi$
$461$	−8.71723e10	−0.0898927	−0.0449464	+	0.998989i	$0.514312\pi$
$462$	−1.47864e10	−0.0150999
$463$	−2.70929e11	−0.273994	−0.136997	−	0.990571i	$-0.543745\pi$
$463$	−2.70929e11	−0.273994	−0.136997	+	0.990571i	$0.543745\pi$
$464$	1.31067e11	0.131269
$465$	3.14096e11	0.311548
$466$	−4.89267e11	−0.480628
$467$	−1.12023e12	−1.08988	−0.544941	−	0.838474i	$-0.683448\pi$
$467$	−1.12023e12	−1.08988	−0.544941	+	0.838474i	$0.683448\pi$
$468$	−4.32558e11	−0.416810
$469$	1.50438e12	1.43575
$470$	−1.66267e11	−0.157168
$471$	1.23010e11	0.115171
$472$	5.00736e11	0.464376
$473$	1.25756e11	0.115519
$474$	−1.53598e11	−0.139760
$475$	−5.09066e10	−0.0458831
$476$	−1.06187e11	−0.0948074
$477$	−4.23261e11	−0.374348
$478$	−1.96796e11	−0.172421
$479$	1.75231e12	1.52090	0.760451	−	0.649395i	$-0.224978\pi$
$479$	1.75231e12	1.52090	0.760451	+	0.649395i	$0.224978\pi$
$480$	2.28502e11	0.196473
$481$	−2.00331e12	−1.70646
$482$	2.08783e11	0.176191
$483$	3.37387e11	0.282076
$484$	1.10382e12	0.914313
$485$	−6.47551e11	−0.531418
$486$	2.23577e10	0.0181788
$487$	−2.13072e12	−1.71651	−0.858256	−	0.513221i	$-0.828452\pi$
$487$	−2.13072e12	−1.71651	−0.858256	+	0.513221i	$0.828452\pi$
$488$	2.07942e11	0.165979
$489$	1.89366e11	0.149766
$490$	−7.36303e10	−0.0576998
$491$	1.15336e12	0.895570	0.447785	−	0.894141i	$-0.352213\pi$
$491$	1.15336e12	0.895570	0.447785	+	0.894141i	$0.352213\pi$
$492$	−5.36401e11	−0.412711
$493$	−1.92190e10	−0.0146527
$494$	1.16997e11	0.0883903
$495$	1.52338e10	0.0114047
$496$	−1.24510e12	−0.923712
$497$	2.77426e12	2.03960
$498$	1.04307e11	0.0759941
$499$	3.30316e11	0.238494	0.119247	−	0.992865i	$-0.461952\pi$
$499$	3.30316e11	0.238494	0.119247	+	0.992865i	$0.461952\pi$
$500$	−1.14962e11	−0.0822602
$501$	−9.44687e11	−0.669913
$502$	−1.35329e11	−0.0951093
$503$	8.53940e11	0.594800	0.297400	−	0.954753i	$-0.403880\pi$
$503$	8.53940e11	0.594800	0.297400	+	0.954753i	$0.403880\pi$
$504$	−3.16877e11	−0.218753
$505$	5.44861e11	0.372799
$506$	−1.29475e10	−0.00878030
$507$	−7.28865e11	−0.489905
$508$	−1.07092e12	−0.713458
$509$	−2.38099e12	−1.57227	−0.786137	−	0.618052i	$-0.787922\pi$
$509$	−2.38099e12	−1.57227	−0.786137	+	0.618052i	$0.787922\pi$
$510$	−9.55233e9	−0.00625236
$511$	2.09591e12	1.35981
$512$	−1.55336e12	−0.998981
$513$	6.92579e10	0.0441511
$514$	−7.58704e11	−0.479445
$515$	5.02813e11	0.314974
$516$	1.29113e12	0.801766
$517$	1.54128e11	0.0948797
$518$	−7.03085e11	−0.429066
$519$	9.56591e11	0.578726
$520$	5.51498e11	0.330772
$521$	7.51808e11	0.447031	0.223515	−	0.974700i	$-0.428247\pi$
$521$	7.51808e11	0.447031	0.223515	+	0.974700i	$0.428247\pi$
$522$	−2.74764e10	−0.0161973
$523$	−1.25482e12	−0.733370	−0.366685	−	0.930345i	$-0.619507\pi$
$523$	−1.25482e12	−0.733370	−0.366685	+	0.930345i	$0.619507\pi$
$524$	−2.06121e12	−1.19435
$525$	2.42472e11	0.139298
$526$	4.80478e11	0.273677
$527$	1.82574e11	0.103108
$528$	−6.03879e10	−0.0338141
$529$	−1.50572e12	−0.835978
$530$	2.58536e11	0.142324
$531$	5.21284e11	0.284544
$532$	−4.70268e11	−0.254532
$533$	−1.96902e12	−1.05676
$534$	5.23095e11	0.278385
$535$	−2.98823e11	−0.157696
$536$	−1.23722e12	−0.647447
$537$	−1.46270e12	−0.759052
$538$	6.18977e11	0.318533
$539$	6.82547e10	0.0348324
$540$	1.56405e11	0.0791549
$541$	3.07388e12	1.54276	0.771381	−	0.636374i	$-0.219566\pi$
$541$	3.07388e12	1.54276	0.771381	+	0.636374i	$0.219566\pi$
$542$	−4.58630e11	−0.228279
$543$	−9.59209e11	−0.473494
$544$	1.32821e11	0.0650237
$545$	−1.65052e12	−0.801377
$546$	−5.57267e11	−0.268347
$547$	−9.41163e11	−0.449492	−0.224746	−	0.974417i	$-0.572155\pi$
$547$	−9.41163e11	−0.449492	−0.224746	+	0.974417i	$0.572155\pi$
$548$	7.11235e10	0.0336900
$549$	2.16475e11	0.101702
$550$	−9.30508e9	−0.00433599
$551$	−8.51142e10	−0.0393387
$552$	−2.77470e11	−0.127201
$553$	2.26628e12	1.03051
$554$	−4.55128e11	−0.205277
$555$	7.24359e11	0.324068
$556$	−3.38918e12	−1.50403
$557$	2.31315e12	1.01825	0.509127	−	0.860692i	$-0.329968\pi$
$557$	2.31315e12	1.01825	0.509127	+	0.860692i	$0.329968\pi$
$558$	2.61018e11	0.113977
$559$	4.73949e12	2.05295
$560$	−9.61177e11	−0.413007
$561$	8.85494e9	0.00377444
$562$	5.32857e11	0.225319
$563$	1.13510e12	0.476152	0.238076	−	0.971247i	$-0.423483\pi$
$563$	1.13510e12	0.476152	0.238076	+	0.971247i	$0.423483\pi$
$564$	1.58242e12	0.658516
$565$	6.13564e11	0.253304
$566$	9.54151e11	0.390790
$567$	−3.29880e11	−0.134040
$568$	−2.28158e12	−0.919747
$569$	3.41521e12	1.36588	0.682939	−	0.730476i	$-0.260702\pi$
$569$	3.41521e12	1.36588	0.682939	+	0.730476i	$0.260702\pi$
$570$	−4.23040e10	−0.0167859
$571$	−8.45690e10	−0.0332927	−0.0166463	−	0.999861i	$-0.505299\pi$
$571$	−8.45690e10	−0.0332927	−0.0166463	+	0.999861i	$0.505299\pi$
$572$	−2.44924e11	−0.0956643
$573$	−2.92337e11	−0.113289
$574$	−6.91049e11	−0.265708
$575$	2.12318e11	0.0809993
$576$	−4.84247e11	−0.183302
$577$	4.19306e12	1.57485	0.787426	−	0.616409i	$-0.211413\pi$
$577$	4.19306e12	1.57485	0.787426	+	0.616409i	$0.211413\pi$
$578$	7.54848e11	0.281309
$579$	−2.57114e11	−0.0950764
$580$	−1.92213e11	−0.0705272
$581$	−1.53901e12	−0.560336
$582$	−5.38122e11	−0.194414
$583$	−2.39661e11	−0.0859188
$584$	−1.72370e12	−0.613201
$585$	5.74129e11	0.202679
$586$	9.25852e11	0.324341
$587$	−7.53756e11	−0.262035	−0.131018	−	0.991380i	$-0.541824\pi$
$587$	−7.53756e11	−0.262035	−0.131018	+	0.991380i	$0.541824\pi$
$588$	7.00767e11	0.241755
$589$	8.08559e11	0.276817
$590$	−3.18410e11	−0.108181
$591$	2.47800e12	0.835521
$592$	−2.87141e12	−0.960833
$593$	1.64013e12	0.544668	0.272334	−	0.962203i	$-0.412204\pi$
$593$	1.64013e12	0.544668	0.272334	+	0.962203i	$0.412204\pi$
$594$	1.26595e10	0.00417231
$595$	1.40941e11	0.0461012
$596$	9.08891e11	0.295056
$597$	7.92781e11	0.255428
$598$	−4.87964e11	−0.156039
$599$	4.87701e12	1.54786	0.773932	−	0.633269i	$-0.218287\pi$
$599$	4.87701e12	1.54786	0.773932	+	0.633269i	$0.218287\pi$
$600$	−1.99411e11	−0.0628158
$601$	5.04535e12	1.57745	0.788727	−	0.614744i	$-0.210741\pi$
$601$	5.04535e12	1.57745	0.788727	+	0.614744i	$0.210741\pi$
$602$	1.66338e12	0.516186
$603$	−1.28799e12	−0.396719
$604$	1.09803e12	0.335698
$605$	−1.46509e12	−0.444596
$606$	4.52786e11	0.136385
$607$	1.16776e12	0.349144	0.174572	−	0.984644i	$-0.444146\pi$
$607$	1.16776e12	0.349144	0.174572	+	0.984644i	$0.444146\pi$
$608$	5.88219e11	0.174571
$609$	4.05405e11	0.119430
$610$	−1.32227e11	−0.0386665
$611$	5.80874e12	1.68615
$612$	9.09132e10	0.0261966
$613$	−1.32333e12	−0.378527	−0.189264	−	0.981926i	$-0.560610\pi$
$613$	−1.32333e12	−0.378527	−0.189264	+	0.981926i	$0.560610\pi$
$614$	−1.66641e12	−0.473178
$615$	7.11959e11	0.200686
$616$	−1.79424e11	−0.0502072
$617$	−3.75725e12	−1.04373	−0.521864	−	0.853029i	$-0.674763\pi$
$617$	−3.75725e12	−1.04373	−0.521864	+	0.853029i	$0.674763\pi$
$618$	4.17844e11	0.115230
$619$	1.15710e12	0.316783	0.158392	−	0.987376i	$-0.449369\pi$
$619$	1.15710e12	0.316783	0.158392	+	0.987376i	$0.449369\pi$
$620$	1.82596e12	0.496283
$621$	−2.88856e11	−0.0779416
$622$	5.71140e10	0.0152998
$623$	−7.71810e12	−2.05265
$624$	−2.27589e12	−0.600926
$625$	1.52588e11	0.0400000
$626$	−8.30725e11	−0.216209
$627$	3.92155e10	0.0101334
$628$	7.15103e11	0.183464
$629$	4.21048e11	0.107251
$630$	2.01497e11	0.0509608
$631$	6.07532e12	1.52559	0.762793	−	0.646643i	$-0.223827\pi$
$631$	6.07532e12	1.52559	0.762793	+	0.646643i	$0.223827\pi$
$632$	−1.86381e12	−0.464703
$633$	−2.94661e12	−0.729468
$634$	−1.12634e11	−0.0276866
$635$	1.42142e12	0.346928
$636$	−2.46058e12	−0.596322
$637$	2.57237e12	0.619022
$638$	−1.55578e10	−0.00371754
$639$	−2.37521e12	−0.563569
$640$	1.74014e12	0.409992
$641$	−2.93024e12	−0.685555	−0.342778	−	0.939417i	$-0.611368\pi$
$641$	−2.93024e12	−0.685555	−0.342778	+	0.939417i	$0.611368\pi$
$642$	−2.48325e11	−0.0576917
$643$	3.91581e12	0.903383	0.451691	−	0.892174i	$-0.350821\pi$
$643$	3.91581e12	0.903383	0.451691	+	0.892174i	$0.350821\pi$
$644$	1.96136e12	0.449336
$645$	−1.71371e12	−0.389868
$646$	−2.45900e10	−0.00555536
$647$	6.29965e12	1.41334	0.706671	−	0.707543i	$-0.250196\pi$
$647$	6.29965e12	1.41334	0.706671	+	0.707543i	$0.250196\pi$
$648$	2.71297e11	0.0604446
$649$	2.95163e11	0.0653072
$650$	−3.50689e11	−0.0770569
$651$	−3.85123e12	−0.840397
$652$	1.10086e12	0.238571
$653$	−6.86506e12	−1.47753	−0.738763	−	0.673965i	$-0.764590\pi$
$653$	−6.86506e12	−1.47753	−0.738763	+	0.673965i	$0.764590\pi$
$654$	−1.37160e12	−0.293176
$655$	2.73582e12	0.580766
$656$	−2.82226e12	−0.595017
$657$	−1.79443e12	−0.375735
$658$	2.03864e12	0.423960
$659$	5.67110e12	1.17134	0.585670	−	0.810550i	$-0.300832\pi$
$659$	5.67110e12	1.17134	0.585670	+	0.810550i	$0.300832\pi$
$660$	8.85600e10	0.0181673
$661$	8.49879e11	0.173161	0.0865806	−	0.996245i	$-0.472406\pi$
$661$	8.49879e11	0.173161	0.0865806	+	0.996245i	$0.472406\pi$
$662$	−6.65420e11	−0.134659
$663$	3.33723e11	0.0670773
$664$	1.26570e12	0.252681
$665$	6.24182e11	0.123769
$666$	6.01951e11	0.118557
$667$	3.54989e11	0.0694461
$668$	−5.49184e12	−1.06715
$669$	−1.58107e12	−0.305165
$670$	7.86725e11	0.150830
$671$	1.22573e11	0.0233423
$672$	−2.80173e12	−0.529986
$673$	9.43446e12	1.77276	0.886378	−	0.462962i	$-0.153213\pi$
$673$	9.43446e12	1.77276	0.886378	+	0.462962i	$0.153213\pi$
$674$	−9.75625e11	−0.182101
$675$	−2.07594e11	−0.0384900
$676$	−4.23718e12	−0.780399
$677$	−5.95829e12	−1.09012	−0.545058	−	0.838399i	$-0.683492\pi$
$677$	−5.95829e12	−1.09012	−0.545058	+	0.838399i	$0.683492\pi$
$678$	5.09879e11	0.0926688
$679$	7.93982e12	1.43350
$680$	−1.15912e11	−0.0207892
$681$	−3.99250e12	−0.711350
$682$	1.47794e11	0.0261594
$683$	−4.27586e12	−0.751848	−0.375924	−	0.926650i	$-0.622675\pi$
$683$	−4.27586e12	−0.751848	−0.375924	+	0.926650i	$0.622675\pi$
$684$	4.02623e11	0.0703310
$685$	−9.44014e10	−0.0163822
$686$	−1.08010e12	−0.186211
$687$	−3.73934e12	−0.640456
$688$	6.79326e12	1.15593
$689$	−9.03230e12	−1.52690
$690$	1.76439e11	0.0296328
$691$	2.63866e12	0.440284	0.220142	−	0.975468i	$-0.429348\pi$
$691$	2.63866e12	0.440284	0.220142	+	0.975468i	$0.429348\pi$
$692$	5.56104e12	0.921888
$693$	−1.86786e11	−0.0307642
$694$	3.88385e11	0.0635542
$695$	4.49842e12	0.731355
$696$	−3.33409e11	−0.0538562
$697$	4.13840e11	0.0664178
$698$	9.87637e11	0.157488
$699$	−6.18057e12	−0.979223
$700$	1.40958e12	0.221896
$701$	6.86502e12	1.07377	0.536884	−	0.843656i	$-0.319601\pi$
$701$	6.86502e12	1.07377	0.536884	+	0.843656i	$0.319601\pi$
$702$	4.77108e11	0.0741480
$703$	1.86468e12	0.287942
$704$	−2.74192e11	−0.0420706
$705$	−2.10033e12	−0.320211
$706$	1.08050e12	0.163682
$707$	−6.68070e12	−1.00562
$708$	3.03043e12	0.453267
$709$	6.47288e12	0.962031	0.481016	−	0.876712i	$-0.340268\pi$
$709$	6.47288e12	0.962031	0.481016	+	0.876712i	$0.340268\pi$
$710$	1.45082e12	0.214265
$711$	−1.94029e12	−0.284744
$712$	6.34744e12	0.925632
$713$	−3.37228e12	−0.488676
$714$	1.17124e11	0.0168657
$715$	3.25086e11	0.0465179
$716$	−8.50325e12	−1.20914
$717$	−2.48598e12	−0.351287
$718$	−1.14011e12	−0.160099
$719$	1.14013e13	1.59102	0.795508	−	0.605944i	$-0.207204\pi$
$719$	1.14013e13	1.59102	0.795508	+	0.605944i	$0.207204\pi$
$720$	8.22919e11	0.114120
$721$	−6.16515e12	−0.849640
$722$	−1.08901e11	−0.0149147
$723$	2.63742e12	0.358969
$724$	−5.57626e12	−0.754257
$725$	2.55122e11	0.0342947
$726$	−1.21751e12	−0.162651
$727$	−7.60440e12	−1.00963	−0.504813	−	0.863229i	$-0.668438\pi$
$727$	−7.60440e12	−1.00963	−0.504813	+	0.863229i	$0.668438\pi$
$728$	−6.76209e12	−0.892256
$729$	2.82430e11	0.0370370
$730$	1.09607e12	0.142852
$731$	−9.96125e11	−0.129029
$732$	1.25845e12	0.162008
$733$	6.68325e12	0.855105	0.427553	−	0.903990i	$-0.359376\pi$
$733$	6.68325e12	0.855105	0.427553	+	0.903990i	$0.359376\pi$
$734$	−1.07525e12	−0.136734
$735$	−9.30121e11	−0.117556
$736$	−2.45330e12	−0.308177
$737$	−7.29288e11	−0.0910532
$738$	5.91646e11	0.0734190
$739$	−3.91666e12	−0.483076	−0.241538	−	0.970391i	$-0.577652\pi$
$739$	−3.91666e12	−0.483076	−0.241538	+	0.970391i	$0.577652\pi$
$740$	4.21098e12	0.516227
$741$	1.47795e12	0.180085
$742$	−3.16999e12	−0.383919
$743$	−6.29435e11	−0.0757707	−0.0378854	−	0.999282i	$-0.512062\pi$
$743$	−6.29435e11	−0.0757707	−0.0378854	+	0.999282i	$0.512062\pi$
$744$	3.16729e12	0.378974
$745$	−1.20636e12	−0.143474
$746$	2.95421e12	0.349234
$747$	1.31763e12	0.154829
$748$	5.14772e10	0.00601254
$749$	3.66396e12	0.425385
$750$	1.26802e11	0.0146336
$751$	−1.11542e12	−0.127955	−0.0639776	−	0.997951i	$-0.520379\pi$
$751$	−1.11542e12	−0.127955	−0.0639776	+	0.997951i	$0.520379\pi$
$752$	8.32587e12	0.949400
$753$	−1.70951e12	−0.193774
$754$	−5.86340e11	−0.0660661
$755$	−1.45740e12	−0.163237
$756$	−1.91772e12	−0.213520
$757$	8.27028e12	0.915354	0.457677	−	0.889119i	$-0.348682\pi$
$757$	8.27028e12	0.915354	0.457677	+	0.889119i	$0.348682\pi$
$758$	−9.94270e10	−0.0109394
$759$	−1.63557e11	−0.0178888
$760$	−5.13333e11	−0.0558133
$761$	6.37906e12	0.689486	0.344743	−	0.938697i	$-0.387966\pi$
$761$	6.37906e12	0.689486	0.344743	+	0.938697i	$0.387966\pi$
$762$	1.18121e12	0.126920
$763$	2.02375e13	2.16171
$764$	−1.69947e12	−0.180465
$765$	−1.20668e11	−0.0127384
$766$	4.29263e12	0.450500
$767$	1.11241e13	1.16060
$768$	−1.61484e12	−0.167496
$769$	9.45187e12	0.974651	0.487326	−	0.873220i	$-0.337972\pi$
$769$	9.45187e12	0.974651	0.487326	+	0.873220i	$0.337972\pi$
$770$	1.14092e11	0.0116963
$771$	−9.58419e12	−0.976811
$772$	−1.49471e12	−0.151453
$773$	9.55983e12	0.963036	0.481518	−	0.876436i	$-0.340086\pi$
$773$	9.55983e12	0.963036	0.481518	+	0.876436i	$0.340086\pi$
$774$	−1.42411e12	−0.142630
$775$	−2.42358e12	−0.241324
$776$	−6.52978e12	−0.646429
$777$	−8.88159e12	−0.874170
$778$	−3.50770e12	−0.343253
$779$	1.83275e12	0.178314
$780$	3.33764e12	0.322859
$781$	−1.34490e12	−0.129348
$782$	1.02558e11	0.00980710
$783$	−3.47091e11	−0.0330001
$784$	3.68707e12	0.348545
$785$	−9.49148e11	−0.0892114
$786$	2.27350e12	0.212468
$787$	9.28420e12	0.862697	0.431349	−	0.902185i	$-0.358038\pi$
$787$	9.28420e12	0.862697	0.431349	+	0.902185i	$0.358038\pi$
$788$	1.44056e13	1.33095
$789$	6.06955e12	0.557584
$790$	1.18517e12	0.108257
$791$	−7.52309e12	−0.683286
$792$	1.53615e11	0.0138730
$793$	4.61951e12	0.414827
$794$	1.96998e12	0.175902
$795$	3.26591e12	0.289969
$796$	4.60875e12	0.406887
$797$	1.07459e13	0.943368	0.471684	−	0.881768i	$-0.343646\pi$
$797$	1.07459e13	0.943368	0.471684	+	0.881768i	$0.343646\pi$
$798$	5.18702e11	0.0452799
$799$	−1.22086e12	−0.105975
$800$	−1.76313e12	−0.152188
$801$	6.60790e12	0.567175
$802$	2.02080e12	0.172480
$803$	−1.01605e12	−0.0862372
$804$	−7.48756e12	−0.631958
$805$	−2.60329e12	−0.218495
$806$	5.57005e12	0.464891
$807$	7.81912e12	0.648973
$808$	5.49427e12	0.453481
$809$	5.05042e12	0.414533	0.207267	−	0.978285i	$-0.433543\pi$
$809$	5.05042e12	0.414533	0.207267	+	0.978285i	$0.433543\pi$
$810$	−1.72513e11	−0.0140812
$811$	−1.06064e13	−0.860945	−0.430473	−	0.902604i	$-0.641653\pi$
$811$	−1.06064e13	−0.860945	−0.430473	+	0.902604i	$0.641653\pi$
$812$	2.35678e12	0.190247
$813$	−5.79356e12	−0.465091
$814$	3.40839e11	0.0272107
$815$	−1.46116e12	−0.116008
$816$	4.78337e11	0.0377684
$817$	−4.41150e12	−0.346407
$818$	−1.63032e12	−0.127316
$819$	−7.03957e12	−0.546724
$820$	4.13890e12	0.319685
$821$	−9.46900e12	−0.727377	−0.363689	−	0.931521i	$-0.618483\pi$
$821$	−9.46900e12	−0.727377	−0.363689	+	0.931521i	$0.618483\pi$
$822$	−7.84487e10	−0.00599325
$823$	2.36475e12	0.179675	0.0898373	−	0.995956i	$-0.471365\pi$
$823$	2.36475e12	0.179675	0.0898373	+	0.995956i	$0.471365\pi$
$824$	5.07028e12	0.383141
$825$	−1.17545e11	−0.00883406
$826$	3.90412e12	0.291818
$827$	5.78008e12	0.429694	0.214847	−	0.976648i	$-0.431075\pi$
$827$	5.78008e12	0.429694	0.214847	+	0.976648i	$0.431075\pi$
$828$	−1.67923e12	−0.124158
$829$	2.52841e13	1.85931	0.929655	−	0.368430i	$-0.120105\pi$
$829$	2.52841e13	1.85931	0.929655	+	0.368430i	$0.120105\pi$
$830$	−8.04835e11	−0.0588647
$831$	−5.74932e12	−0.418227
$832$	−1.03337e13	−0.747656
$833$	−5.40651e11	−0.0389058
$834$	3.73824e12	0.267559
$835$	7.28925e12	0.518912
$836$	2.27975e11	0.0161421
$837$	3.29726e12	0.232214
$838$	2.83484e12	0.198578
$839$	2.54151e13	1.77077	0.885385	−	0.464858i	$-0.153895\pi$
$839$	2.54151e13	1.77077	0.885385	+	0.464858i	$0.153895\pi$
$840$	2.44504e12	0.169445
$841$	−1.40806e13	−0.970597
$842$	−2.91645e12	−0.199963
$843$	6.73121e12	0.459060
$844$	−1.71298e13	−1.16201
$845$	5.62396e12	0.379478
$846$	−1.74540e12	−0.117146
$847$	1.79639e13	1.19929
$848$	−1.29463e13	−0.859734
$849$	1.20531e13	0.796188
$850$	7.37063e10	0.00484305
$851$	−7.77706e12	−0.508314
$852$	−1.38080e13	−0.897744
$853$	−9.95854e12	−0.644058	−0.322029	−	0.946730i	$-0.604365\pi$
$853$	−9.95854e12	−0.644058	−0.322029	+	0.946730i	$0.604365\pi$
$854$	1.62127e12	0.104303
$855$	−5.34398e11	−0.0341993
$856$	−3.01327e12	−0.191826
$857$	−3.04083e13	−1.92565	−0.962827	−	0.270120i	$-0.912937\pi$
$857$	−3.04083e13	−1.92565	−0.962827	+	0.270120i	$0.912937\pi$
$858$	2.70150e11	0.0170181
$859$	1.98580e13	1.24442	0.622209	−	0.782851i	$-0.286236\pi$
$859$	1.98580e13	1.24442	0.622209	+	0.782851i	$0.286236\pi$
$860$	−9.96245e12	−0.621045
$861$	−8.72954e12	−0.541349
$862$	2.98011e12	0.183844
$863$	−2.58816e13	−1.58833	−0.794167	−	0.607700i	$-0.792093\pi$
$863$	−2.58816e13	−1.58833	−0.794167	+	0.607700i	$0.792093\pi$
$864$	2.39872e12	0.146443
$865$	−7.38110e12	−0.448279
$866$	−2.24215e11	−0.0135467
$867$	9.53548e12	0.573134
$868$	−2.23887e13	−1.33872
$869$	−1.09864e12	−0.0653532
$870$	2.12009e11	0.0125464
$871$	−2.74853e13	−1.61815
$872$	−1.66435e13	−0.974814
$873$	−6.79773e12	−0.396095
$874$	4.54196e11	0.0263294
$875$	−1.87093e12	−0.107900
$876$	−1.04317e13	−0.598532
$877$	−8.70251e12	−0.496760	−0.248380	−	0.968663i	$-0.579898\pi$
$877$	−8.70251e12	−0.496760	−0.248380	+	0.968663i	$0.579898\pi$
$878$	−2.93486e12	−0.166672
$879$	1.16956e13	0.660807
$880$	4.65956e11	0.0261923
$881$	2.28612e13	1.27852	0.639260	−	0.768991i	$-0.279241\pi$
$881$	2.28612e13	1.27852	0.639260	+	0.768991i	$0.279241\pi$
$882$	−7.72941e11	−0.0430069
$883$	−1.35938e13	−0.752521	−0.376261	−	0.926514i	$-0.622790\pi$
$883$	−1.35938e13	−0.752521	−0.376261	+	0.926514i	$0.622790\pi$
$884$	1.94006e12	0.106852
$885$	−4.02225e12	−0.220407
$886$	−7.99858e12	−0.436075
$887$	3.64841e12	0.197901	0.0989503	−	0.995092i	$-0.468452\pi$
$887$	3.64841e12	0.197901	0.0989503	+	0.995092i	$0.468452\pi$
$888$	7.30430e12	0.394203
$889$	−1.74284e13	−0.935836
$890$	−4.03623e12	−0.215636
$891$	1.59918e11	0.00850058
$892$	−9.19140e12	−0.486116
$893$	−5.40676e12	−0.284515
$894$	−1.00250e12	−0.0524887
$895$	1.12863e13	0.587959
$896$	−2.13364e13	−1.10595
$897$	−6.16412e12	−0.317911
$898$	2.00815e12	0.103051
$899$	−4.05215e12	−0.206903
$900$	−1.20683e12	−0.0613131
$901$	1.89837e12	0.0959664
$902$	3.35004e11	0.0168508
$903$	2.10123e13	1.05167
$904$	6.18706e12	0.308125
$905$	7.40131e12	0.366767
$906$	−1.21112e12	−0.0597187
$907$	5.50332e12	0.270018	0.135009	−	0.990844i	$-0.456894\pi$
$907$	5.50332e12	0.270018	0.135009	+	0.990844i	$0.456894\pi$
$908$	−2.32100e13	−1.13315
$909$	5.71973e12	0.277868
$910$	4.29990e12	0.207860
$911$	−7.69595e12	−0.370194	−0.185097	−	0.982720i	$-0.559260\pi$
$911$	−7.69595e12	−0.370194	−0.185097	+	0.982720i	$0.559260\pi$
$912$	2.11839e12	0.101398
$913$	7.46075e11	0.0355356
$914$	9.40201e12	0.445618
$915$	−1.67033e12	−0.0787783
$916$	−2.17382e13	−1.02022
$917$	−3.35447e13	−1.56661
$918$	−1.00277e11	−0.00466023
$919$	2.58741e13	1.19659	0.598295	−	0.801276i	$-0.295845\pi$
$919$	2.58741e13	1.19659	0.598295	+	0.801276i	$0.295845\pi$
$920$	2.14097e12	0.0985294
$921$	−2.10506e13	−0.964043
$922$	5.58960e11	0.0254737
$923$	−5.06863e13	−2.29870
$924$	−1.08586e12	−0.0490061
$925$	−5.58919e12	−0.251022
$926$	1.73723e12	0.0776440
$927$	5.27833e12	0.234768
$928$	−2.94790e12	−0.130481
$929$	−9.64147e12	−0.424690	−0.212345	−	0.977195i	$-0.568110\pi$
$929$	−9.64147e12	−0.424690	−0.212345	+	0.977195i	$0.568110\pi$
$930$	−2.01402e12	−0.0882859
$931$	−2.39436e12	−0.104452
$932$	−3.59301e13	−1.55986
$933$	7.21482e11	0.0311715
$934$	7.18303e12	0.308849
$935$	−6.83251e10	−0.00292367
$936$	5.78941e12	0.246543
$937$	4.04477e13	1.71422	0.857109	−	0.515136i	$-0.172259\pi$
$937$	4.04477e13	1.71422	0.857109	+	0.515136i	$0.172259\pi$
$938$	−9.64628e12	−0.406862
$939$	−1.04940e13	−0.440499
$940$	−1.22100e13	−0.510084
$941$	3.16912e13	1.31761	0.658803	−	0.752316i	$-0.271063\pi$
$941$	3.16912e13	1.31761	0.658803	+	0.752316i	$0.271063\pi$
$942$	−7.88753e11	−0.0326371
$943$	−7.64393e12	−0.314785
$944$	1.59445e13	0.653487
$945$	2.54537e12	0.103827
$946$	−8.06366e11	−0.0327357
$947$	−3.27669e13	−1.32392	−0.661958	−	0.749541i	$-0.730274\pi$
$947$	−3.27669e13	−1.32392	−0.661958	+	0.749541i	$0.730274\pi$
$948$	−1.12797e13	−0.453586
$949$	−3.82927e13	−1.53256
$950$	3.26420e11	0.0130023
$951$	−1.42283e12	−0.0564081
$952$	1.42123e12	0.0560786
$953$	−7.92564e12	−0.311255	−0.155627	−	0.987816i	$-0.549740\pi$
$953$	−7.92564e12	−0.311255	−0.155627	+	0.987816i	$0.549740\pi$
$954$	2.71401e12	0.106082
$955$	2.25569e12	0.0877534
$956$	−1.44520e13	−0.559587
$957$	−1.96531e11	−0.00757404
$958$	−1.12360e13	−0.430991
$959$	1.15748e12	0.0441907
$960$	3.73648e12	0.141985
$961$	1.20546e13	0.455928
$962$	1.28455e13	0.483574
$963$	−3.13692e12	−0.117540
$964$	1.53323e13	0.571823
$965$	1.98391e12	0.0736459
$966$	−2.16337e12	−0.0799343
$967$	−1.06196e13	−0.390560	−0.195280	−	0.980748i	$-0.562562\pi$
$967$	−1.06196e13	−0.390560	−0.195280	+	0.980748i	$0.562562\pi$
$968$	−1.47737e13	−0.540817
$969$	−3.10629e11	−0.0113184
$970$	4.15218e12	0.150592
$971$	3.86349e13	1.39474	0.697370	−	0.716711i	$-0.254353\pi$
$971$	3.86349e13	1.39474	0.697370	+	0.716711i	$0.254353\pi$
$972$	1.64187e12	0.0589986
$973$	−5.51564e13	−1.97282
$974$	1.36625e13	0.486423
$975$	−4.43001e12	−0.156994
$976$	6.62130e12	0.233571
$977$	−7.02829e12	−0.246788	−0.123394	−	0.992358i	$-0.539378\pi$
$977$	−7.02829e12	−0.246788	−0.123394	+	0.992358i	$0.539378\pi$
$978$	−1.21424e12	−0.0424404
$979$	3.74155e12	0.130176
$980$	−5.40716e12	−0.187263
$981$	−1.73265e13	−0.597311
$982$	−7.39551e12	−0.253785
$983$	1.99085e13	0.680061	0.340031	−	0.940414i	$-0.389563\pi$
$983$	1.99085e13	0.680061	0.340031	+	0.940414i	$0.389563\pi$
$984$	7.17926e12	0.244119
$985$	−1.91204e13	−0.647192
$986$	1.23234e11	0.00415228
$987$	2.57528e13	0.863768
$988$	8.59188e12	0.286868
$989$	1.83992e13	0.611526
$990$	−9.76811e10	−0.00323186
$991$	−4.60084e13	−1.51533	−0.757663	−	0.652646i	$-0.773659\pi$
$991$	−4.60084e13	−1.51533	−0.757663	+	0.652646i	$0.773659\pi$
$992$	2.80041e13	0.918162
$993$	−8.40580e12	−0.274352
$994$	−1.77889e13	−0.577978
$995$	−6.11714e12	−0.197854
$996$	7.65992e12	0.246636
$997$	2.86397e13	0.917994	0.458997	−	0.888438i	$-0.348209\pi$
$997$	2.86397e13	0.917994	0.458997	+	0.888438i	$0.348209\pi$
$998$	−2.11803e12	−0.0675840
$999$	7.60403e12	0.241546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.7	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-6.41213 q^{2} -81.0000 q^{3} -470.885 q^{4} +625.000 q^{5} +519.382 q^{6} -7663.31 q^{7} +6302.38 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-6.41213 q^{2} -81.0000 q^{3} -470.885 q^{4} +625.000 q^{5} +519.382 q^{6} -7663.31 q^{7} +6302.38 q^{8} +6561.00 q^{9} -4007.58 q^{10} +3714.99 q^{11} +38141.7 q^{12} +140010. q^{13} +49138.1 q^{14} -50625.0 q^{15} +200681. q^{16} -29426.7 q^{17} -42070.0 q^{18} -130321. q^{19} -294303. q^{20} +620728. q^{21} -23821.0 q^{22} +543534. q^{23} -510493. q^{24} +390625. q^{25} -897763. q^{26} -531441. q^{27} +3.60854e6 q^{28} +653112. q^{29} +324614. q^{30} -6.20437e6 q^{31} -4.51361e6 q^{32} -300915. q^{33} +188688. q^{34} -4.78957e6 q^{35} -3.08947e6 q^{36} -1.43083e7 q^{37} +835635. q^{38} -1.13408e7 q^{39} +3.93899e6 q^{40} -1.40634e7 q^{41} -3.98019e6 q^{42} +3.38510e7 q^{43} -1.74933e6 q^{44} +4.10062e6 q^{45} -3.48521e6 q^{46} +4.14880e7 q^{47} -1.62552e7 q^{48} +1.83728e7 q^{49} -2.50474e6 q^{50} +2.38357e6 q^{51} -6.59286e7 q^{52} -6.45117e7 q^{53} +3.40767e6 q^{54} +2.32187e6 q^{55} -4.82971e7 q^{56} +1.05560e7 q^{57} -4.18784e6 q^{58} +7.94519e7 q^{59} +2.38385e7 q^{60} +3.29941e7 q^{61} +3.97832e7 q^{62} -5.02790e7 q^{63} -7.38069e7 q^{64} +8.75063e7 q^{65} +1.92950e6 q^{66} -1.96309e8 q^{67} +1.38566e7 q^{68} -4.40262e7 q^{69} +3.07113e7 q^{70} -3.62019e8 q^{71} +4.13499e7 q^{72} -2.73499e8 q^{73} +9.17468e7 q^{74} -3.16406e7 q^{75} +6.13662e7 q^{76} -2.84692e7 q^{77} +7.27188e7 q^{78} -2.95732e8 q^{79} +1.25426e8 q^{80} +4.30467e7 q^{81} +9.01762e7 q^{82} +2.00828e8 q^{83} -2.92291e8 q^{84} -1.83917e7 q^{85} -2.17057e8 q^{86} -5.29021e7 q^{87} +2.34133e7 q^{88} +1.00715e9 q^{89} -2.62937e7 q^{90} -1.07294e9 q^{91} -2.55942e8 q^{92} +5.02554e8 q^{93} -2.66026e8 q^{94} -8.14506e7 q^{95} +3.65603e8 q^{96} -1.03608e9 q^{97} -1.17808e8 q^{98} +2.43741e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 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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