LMFDB - Embedded newform 285.10.a.h.1.1

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			1.1
Root			$43.0696$ 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)

$f(q)$	$=$	$q-44.0696 q^{2} -81.0000 q^{3} +1430.13 q^{4} +625.000 q^{5} +3569.64 q^{6} +9758.51 q^{7} -40461.6 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-44.0696 q^{2} -81.0000 q^{3} +1430.13 q^{4} +625.000 q^{5} +3569.64 q^{6} +9758.51 q^{7} -40461.6 q^{8} +6561.00 q^{9} -27543.5 q^{10} +83107.6 q^{11} -115841. q^{12} -68713.3 q^{13} -430054. q^{14} -50625.0 q^{15} +1.05090e6 q^{16} -659839. q^{17} -289141. q^{18} -130321. q^{19} +893831. q^{20} -790439. q^{21} -3.66252e6 q^{22} -1.57802e6 q^{23} +3.27739e6 q^{24} +390625. q^{25} +3.02817e6 q^{26} -531441. q^{27} +1.39559e7 q^{28} -2.82963e6 q^{29} +2.23102e6 q^{30} -1.91046e6 q^{31} -2.55965e7 q^{32} -6.73171e6 q^{33} +2.90789e7 q^{34} +6.09907e6 q^{35} +9.38308e6 q^{36} -1.68862e7 q^{37} +5.74320e6 q^{38} +5.56578e6 q^{39} -2.52885e7 q^{40} +634906. q^{41} +3.48344e7 q^{42} +3.49112e7 q^{43} +1.18855e8 q^{44} +4.10062e6 q^{45} +6.95426e7 q^{46} +1.09085e7 q^{47} -8.51230e7 q^{48} +5.48749e7 q^{49} -1.72147e7 q^{50} +5.34470e7 q^{51} -9.82689e7 q^{52} +9.61915e7 q^{53} +2.34204e7 q^{54} +5.19422e7 q^{55} -3.94845e8 q^{56} +1.05560e7 q^{57} +1.24701e8 q^{58} -1.11455e8 q^{59} -7.24003e7 q^{60} +5.62686e7 q^{61} +8.41933e7 q^{62} +6.40256e7 q^{63} +5.89964e8 q^{64} -4.29458e7 q^{65} +2.96664e8 q^{66} +1.12744e8 q^{67} -9.43656e8 q^{68} +1.27819e8 q^{69} -2.68784e8 q^{70} -1.00568e8 q^{71} -2.65469e8 q^{72} -1.07558e8 q^{73} +7.44170e8 q^{74} -3.16406e7 q^{75} -1.86376e8 q^{76} +8.11006e8 q^{77} -2.45282e8 q^{78} +9.09498e7 q^{79} +6.56813e8 q^{80} +4.30467e7 q^{81} -2.79801e7 q^{82} -7.21878e8 q^{83} -1.13043e9 q^{84} -4.12400e8 q^{85} -1.53852e9 q^{86} +2.29200e8 q^{87} -3.36267e9 q^{88} +2.98299e8 q^{89} -1.80713e8 q^{90} -6.70539e8 q^{91} -2.25677e9 q^{92} +1.54747e8 q^{93} -4.80733e8 q^{94} -8.14506e7 q^{95} +2.07331e9 q^{96} -1.31774e8 q^{97} -2.41832e9 q^{98} +5.45269e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−44.0696	−1.94762	−0.973810	−	0.227364i	$-0.926989\pi$
$2$	−44.0696	−1.94762	−0.973810	+	0.227364i	$0.926989\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	1430.13	2.79322
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	3569.64	1.12446
$7$	9758.51	1.53618	0.768091	−	0.640341i	$-0.221207\pi$
$7$	9758.51	1.53618	0.768091	+	0.640341i	$0.221207\pi$
$8$	−40461.6	−3.49252
$9$	6561.00	0.333333
$10$	−27543.5	−0.871002
$11$	83107.6	1.71149	0.855743	−	0.517400i	$-0.173100\pi$
$11$	83107.6	1.71149	0.855743	+	0.517400i	$0.173100\pi$
$12$	−115841.	−1.61267
$13$	−68713.3	−0.667261	−0.333630	−	0.942704i	$-0.608274\pi$
$13$	−68713.3	−0.667261	−0.333630	+	0.942704i	$0.608274\pi$
$14$	−430054.	−2.99190
$15$	−50625.0	−0.258199
$16$	1.05090e6	4.00887
$17$	−659839.	−1.91610	−0.958050	−	0.286601i	$-0.907474\pi$
$17$	−659839.	−1.91610	−0.958050	+	0.286601i	$0.907474\pi$
$18$	−289141.	−0.649207
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	893831.	1.24917
$21$	−790439.	−0.886915
$22$	−3.66252e6	−3.33333
$23$	−1.57802e6	−1.17581	−0.587904	−	0.808931i	$-0.700047\pi$
$23$	−1.57802e6	−1.17581	−0.587904	+	0.808931i	$0.700047\pi$
$24$	3.27739e6	2.01641
$25$	390625.	0.200000
$26$	3.02817e6	1.29957
$27$	−531441.	−0.192450
$28$	1.39559e7	4.29090
$29$	−2.82963e6	−0.742913	−0.371457	−	0.928450i	$-0.621142\pi$
$29$	−2.82963e6	−0.742913	−0.371457	+	0.928450i	$0.621142\pi$
$30$	2.23102e6	0.502873
$31$	−1.91046e6	−0.371545	−0.185772	−	0.982593i	$-0.559479\pi$
$31$	−1.91046e6	−0.371545	−0.185772	+	0.982593i	$0.559479\pi$
$32$	−2.55965e7	−4.31524
$33$	−6.73171e6	−0.988127
$34$	2.90789e7	3.73183
$35$	6.09907e6	0.687001
$36$	9.38308e6	0.931074
$37$	−1.68862e7	−1.48124	−0.740620	−	0.671925i	$-0.765468\pi$
$37$	−1.68862e7	−1.48124	−0.740620	+	0.671925i	$0.765468\pi$
$38$	5.74320e6	0.446815
$39$	5.56578e6	0.385243
$40$	−2.52885e7	−1.56190
$41$	634906.	0.0350899	0.0175450	−	0.999846i	$-0.494415\pi$
$41$	634906.	0.0350899	0.0175450	+	0.999846i	$0.494415\pi$
$42$	3.48344e7	1.72737
$43$	3.49112e7	1.55724	0.778622	−	0.627493i	$-0.215919\pi$
$43$	3.49112e7	1.55724	0.778622	+	0.627493i	$0.215919\pi$
$44$	1.18855e8	4.78056
$45$	4.10062e6	0.149071
$46$	6.95426e7	2.29003
$47$	1.09085e7	0.326080	0.163040	−	0.986619i	$-0.447870\pi$
$47$	1.09085e7	0.326080	0.163040	+	0.986619i	$0.447870\pi$
$48$	−8.51230e7	−2.31452
$49$	5.48749e7	1.35985
$50$	−1.72147e7	−0.389524
$51$	5.34470e7	1.10626
$52$	−9.82689e7	−1.86381
$53$	9.61915e7	1.67454	0.837270	−	0.546790i	$-0.184150\pi$
$53$	9.61915e7	1.67454	0.837270	+	0.546790i	$0.184150\pi$
$54$	2.34204e7	0.374820
$55$	5.19422e7	0.765400
$56$	−3.94845e8	−5.36514
$57$	1.05560e7	0.132453
$58$	1.24701e8	1.44691
$59$	−1.11455e8	−1.19747	−0.598735	−	0.800947i	$-0.704330\pi$
$59$	−1.11455e8	−1.19747	−0.598735	+	0.800947i	$0.704330\pi$
$60$	−7.24003e7	−0.721207
$61$	5.62686e7	0.520334	0.260167	−	0.965564i	$-0.416222\pi$
$61$	5.62686e7	0.520334	0.260167	+	0.965564i	$0.416222\pi$
$62$	8.41933e7	0.723627
$63$	6.40256e7	0.512060
$64$	5.89964e8	4.39558
$65$	−4.29458e7	−0.298408
$66$	2.96664e8	1.92450
$67$	1.12744e8	0.683529	0.341765	−	0.939786i	$-0.388975\pi$
$67$	1.12744e8	0.683529	0.341765	+	0.939786i	$0.388975\pi$
$68$	−9.43656e8	−5.35209
$69$	1.27819e8	0.678853
$70$	−2.68784e8	−1.33802
$71$	−1.00568e8	−0.469674	−0.234837	−	0.972035i	$-0.575456\pi$
$71$	−1.00568e8	−0.469674	−0.234837	+	0.972035i	$0.575456\pi$
$72$	−2.65469e8	−1.16417
$73$	−1.07558e8	−0.443293	−0.221647	−	0.975127i	$-0.571143\pi$
$73$	−1.07558e8	−0.443293	−0.221647	+	0.975127i	$0.571143\pi$
$74$	7.44170e8	2.88489
$75$	−3.16406e7	−0.115470
$76$	−1.86376e8	−0.640809
$77$	8.11006e8	2.62915
$78$	−2.45282e8	−0.750307
$79$	9.09498e7	0.262712	0.131356	−	0.991335i	$-0.458067\pi$
$79$	9.09498e7	0.262712	0.131356	+	0.991335i	$0.458067\pi$
$80$	6.56813e8	1.79282
$81$	4.30467e7	0.111111
$82$	−2.79801e7	−0.0683418
$83$	−7.21878e8	−1.66960	−0.834799	−	0.550554i	$-0.814416\pi$
$83$	−7.21878e8	−1.66960	−0.834799	+	0.550554i	$0.814416\pi$
$84$	−1.13043e9	−2.47735
$85$	−4.12400e8	−0.856906
$86$	−1.53852e9	−3.03292
$87$	2.29200e8	0.428921
$88$	−3.36267e9	−5.97740
$89$	2.98299e8	0.503961	0.251980	−	0.967732i	$-0.418918\pi$
$89$	2.98299e8	0.503961	0.251980	+	0.967732i	$0.418918\pi$
$90$	−1.80713e8	−0.290334
$91$	−6.70539e8	−1.02503
$92$	−2.25677e9	−3.28430
$93$	1.54747e8	0.214511
$94$	−4.80733e8	−0.635081
$95$	−8.14506e7	−0.102598
$96$	2.07331e9	2.49141
$97$	−1.31774e8	−0.151133	−0.0755663	−	0.997141i	$-0.524076\pi$
$97$	−1.31774e8	−0.151133	−0.0755663	+	0.997141i	$0.524076\pi$
$98$	−2.41832e9	−2.64848
$99$	5.45269e8	0.570496
$100$	5.58645e8	0.558645
$101$	6.38345e8	0.610392	0.305196	−	0.952289i	$-0.401278\pi$
$101$	6.38345e8	0.610392	0.305196	+	0.952289i	$0.401278\pi$
$102$	−2.35539e9	−2.15458
$103$	1.45769e9	1.27613	0.638067	−	0.769981i	$-0.279734\pi$
$103$	1.45769e9	1.27613	0.638067	+	0.769981i	$0.279734\pi$
$104$	2.78025e9	2.33042
$105$	−4.94025e8	−0.396640
$106$	−4.23912e9	−3.26137
$107$	−8.98746e8	−0.662842	−0.331421	−	0.943483i	$-0.607528\pi$
$107$	−8.98746e8	−0.662842	−0.331421	+	0.943483i	$0.607528\pi$
$108$	−7.60030e8	−0.537556
$109$	2.22191e9	1.50767	0.753837	−	0.657061i	$-0.228201\pi$
$109$	2.22191e9	1.50767	0.753837	+	0.657061i	$0.228201\pi$
$110$	−2.28907e9	−1.49071
$111$	1.36779e9	0.855194
$112$	1.02552e10	6.15835
$113$	1.28566e9	0.741778	0.370889	−	0.928677i	$-0.379053\pi$
$113$	1.28566e9	0.741778	0.370889	+	0.928677i	$0.379053\pi$
$114$	−4.65199e8	−0.257969
$115$	−9.86261e8	−0.525838
$116$	−4.04674e9	−2.07512
$117$	−4.50828e8	−0.222420
$118$	4.91176e9	2.33221
$119$	−6.43905e9	−2.94348
$120$	2.04837e9	0.901764
$121$	4.54892e9	1.92919
$122$	−2.47974e9	−1.01341
$123$	−5.14274e7	−0.0202592
$124$	−2.73221e9	−1.03781
$125$	2.44141e8	0.0894427
$126$	−2.82158e9	−0.997299
$127$	2.10445e9	0.717832	0.358916	−	0.933370i	$-0.383146\pi$
$127$	2.10445e9	0.717832	0.358916	+	0.933370i	$0.383146\pi$
$128$	−1.28941e10	−4.24567
$129$	−2.82781e9	−0.899076
$130$	1.89260e9	0.581186
$131$	−2.38213e9	−0.706716	−0.353358	−	0.935488i	$-0.614960\pi$
$131$	−2.38213e9	−0.706716	−0.353358	+	0.935488i	$0.614960\pi$
$132$	−9.62723e9	−2.76006
$133$	−1.27174e9	−0.352424
$134$	−4.96859e9	−1.33125
$135$	−3.32151e8	−0.0860663
$136$	2.66982e10	6.69201
$137$	2.01716e9	0.489213	0.244607	−	0.969622i	$-0.421341\pi$
$137$	2.01716e9	0.489213	0.244607	+	0.969622i	$0.421341\pi$
$138$	−5.63295e9	−1.32215
$139$	3.02057e9	0.686313	0.343156	−	0.939278i	$-0.388504\pi$
$139$	3.02057e9	0.686313	0.343156	+	0.939278i	$0.388504\pi$
$140$	8.72246e9	1.91895
$141$	−8.83588e8	−0.188263
$142$	4.43198e9	0.914746
$143$	−5.71060e9	−1.14201
$144$	6.89496e9	1.33629
$145$	−1.76852e9	−0.332241
$146$	4.74005e9	0.863366
$147$	−4.44487e9	−0.785111
$148$	−2.41495e10	−4.13743
$149$	6.11718e9	1.01675	0.508373	−	0.861137i	$-0.330247\pi$
$149$	6.11718e9	1.01675	0.508373	+	0.861137i	$0.330247\pi$
$150$	1.39439e9	0.224892
$151$	6.56980e9	1.02839	0.514193	−	0.857675i	$-0.328092\pi$
$151$	6.56980e9	1.02839	0.514193	+	0.857675i	$0.328092\pi$
$152$	5.27300e9	0.801238
$153$	−4.32921e9	−0.638700
$154$	−3.57407e10	−5.12059
$155$	−1.19404e9	−0.166160
$156$	7.95978e9	1.07607
$157$	−8.41573e9	−1.10546	−0.552730	−	0.833360i	$-0.686414\pi$
$157$	−8.41573e9	−1.10546	−0.552730	+	0.833360i	$0.686414\pi$
$158$	−4.00812e9	−0.511663
$159$	−7.79151e9	−0.966796
$160$	−1.59978e10	−1.92983
$161$	−1.53991e10	−1.80625
$162$	−1.89705e9	−0.216402
$163$	4.90069e9	0.543768	0.271884	−	0.962330i	$-0.412353\pi$
$163$	4.90069e9	0.543768	0.271884	+	0.962330i	$0.412353\pi$
$164$	9.07999e8	0.0980139
$165$	−4.20732e9	−0.441904
$166$	3.18129e10	3.25174
$167$	2.23401e9	0.222260	0.111130	−	0.993806i	$-0.464553\pi$
$167$	2.23401e9	0.222260	0.111130	+	0.993806i	$0.464553\pi$
$168$	3.19825e10	3.09756
$169$	−5.88298e9	−0.554763
$170$	1.81743e10	1.66893
$171$	−8.55036e8	−0.0764719
$172$	4.99276e10	4.34973
$173$	1.39842e10	1.18695	0.593474	−	0.804853i	$-0.297756\pi$
$173$	1.39842e10	1.18695	0.593474	+	0.804853i	$0.297756\pi$
$174$	−1.01007e10	−0.835376
$175$	3.81192e9	0.307236
$176$	8.73379e10	6.86113
$177$	9.02783e9	0.691359
$178$	−1.31459e10	−0.981524
$179$	1.42509e10	1.03754	0.518769	−	0.854915i	$-0.326391\pi$
$179$	1.42509e10	1.03754	0.518769	+	0.854915i	$0.326391\pi$
$180$	5.86443e9	0.416389
$181$	−1.03942e10	−0.719844	−0.359922	−	0.932982i	$-0.617197\pi$
$181$	−1.03942e10	−0.719844	−0.359922	+	0.932982i	$0.617197\pi$
$182$	2.95504e10	1.99638
$183$	−4.55776e9	−0.300415
$184$	6.38492e10	4.10653
$185$	−1.05539e10	−0.662430
$186$	−6.81966e9	−0.417787
$187$	−5.48377e10	−3.27938
$188$	1.56006e10	0.910815
$189$	−5.18607e9	−0.295638
$190$	3.58950e9	0.199822
$191$	1.15049e10	0.625508	0.312754	−	0.949834i	$-0.398748\pi$
$191$	1.15049e10	0.625508	0.312754	+	0.949834i	$0.398748\pi$
$192$	−4.77871e10	−2.53779
$193$	3.11563e10	1.61636	0.808180	−	0.588935i	$-0.200453\pi$
$193$	3.11563e10	1.61636	0.808180	+	0.588935i	$0.200453\pi$
$194$	5.80724e9	0.294349
$195$	3.47861e9	0.172286
$196$	7.84783e10	3.79837
$197$	3.71917e10	1.75933	0.879665	−	0.475593i	$-0.157767\pi$
$197$	3.71917e10	1.75933	0.879665	+	0.475593i	$0.157767\pi$
$198$	−2.40298e10	−1.11111
$199$	3.42758e10	1.54935	0.774675	−	0.632360i	$-0.217914\pi$
$199$	3.42758e10	1.54935	0.774675	+	0.632360i	$0.217914\pi$
$200$	−1.58053e10	−0.698503
$201$	−9.13227e9	−0.394636
$202$	−2.81316e10	−1.18881
$203$	−2.76130e10	−1.14125
$204$	7.64362e10	3.09003
$205$	3.96816e8	0.0156927
$206$	−6.42396e10	−2.48542
$207$	−1.03534e10	−0.391936
$208$	−7.22109e10	−2.67496
$209$	−1.08307e10	−0.392642
$210$	2.17715e10	0.772504
$211$	7.67891e8	0.0266703	0.0133352	−	0.999911i	$-0.495755\pi$
$211$	7.67891e8	0.0266703	0.0133352	+	0.999911i	$0.495755\pi$
$212$	1.37566e11	4.67736
$213$	8.14599e9	0.271166
$214$	3.96074e10	1.29096
$215$	2.18195e10	0.696421
$216$	2.15030e10	0.672135
$217$	−1.86433e10	−0.570760
$218$	−9.79188e10	−2.93638
$219$	8.71222e9	0.255935
$220$	7.42842e10	2.13793
$221$	4.53397e10	1.27854
$222$	−6.02778e10	−1.66559
$223$	1.05024e10	0.284391	0.142195	−	0.989839i	$-0.454584\pi$
$223$	1.05024e10	0.284391	0.142195	+	0.989839i	$0.454584\pi$
$224$	−2.49783e11	−6.62899
$225$	2.56289e9	0.0666667
$226$	−5.66587e10	−1.44470
$227$	−9.24552e9	−0.231108	−0.115554	−	0.993301i	$-0.536864\pi$
$227$	−9.24552e9	−0.231108	−0.115554	+	0.993301i	$0.536864\pi$
$228$	1.50965e10	0.369971
$229$	3.66715e10	0.881189	0.440594	−	0.897706i	$-0.354768\pi$
$229$	3.66715e10	0.881189	0.440594	+	0.897706i	$0.354768\pi$
$230$	4.34641e10	1.02413
$231$	−6.56915e10	−1.51794
$232$	1.14491e11	2.59464
$233$	2.72947e10	0.606704	0.303352	−	0.952879i	$-0.401894\pi$
$233$	2.72947e10	0.606704	0.303352	+	0.952879i	$0.401894\pi$
$234$	1.98678e10	0.433190
$235$	6.81781e9	0.145828
$236$	−1.59395e11	−3.34480
$237$	−7.36693e9	−0.151677
$238$	2.83766e11	5.73277
$239$	1.93984e10	0.384571	0.192285	−	0.981339i	$-0.438410\pi$
$239$	1.93984e10	0.384571	0.192285	+	0.981339i	$0.438410\pi$
$240$	−5.32019e10	−1.03509
$241$	−6.57530e10	−1.25556	−0.627782	−	0.778390i	$-0.716037\pi$
$241$	−6.57530e10	−1.25556	−0.627782	+	0.778390i	$0.716037\pi$
$242$	−2.00469e11	−3.75732
$243$	−3.48678e9	−0.0641500
$244$	8.04715e10	1.45341
$245$	3.42968e10	0.608144
$246$	2.26639e9	0.0394572
$247$	8.95478e9	0.153080
$248$	7.73004e10	1.29763
$249$	5.84721e10	0.963943
$250$	−1.07592e10	−0.174200
$251$	−1.50667e10	−0.239600	−0.119800	−	0.992798i	$-0.538225\pi$
$251$	−1.50667e10	−0.239600	−0.119800	+	0.992798i	$0.538225\pi$
$252$	9.15649e10	1.43030
$253$	−1.31145e11	−2.01238
$254$	−9.27425e10	−1.39806
$255$	3.34044e10	0.494735
$256$	2.66176e11	3.87338
$257$	9.16595e9	0.131063	0.0655313	−	0.997851i	$-0.479126\pi$
$257$	9.16595e9	0.131063	0.0655313	+	0.997851i	$0.479126\pi$
$258$	1.24620e11	1.75106
$259$	−1.64785e11	−2.27545
$260$	−6.14181e10	−0.833520
$261$	−1.85652e10	−0.247638
$262$	1.04980e11	1.37641
$263$	−8.74404e10	−1.12697	−0.563484	−	0.826127i	$-0.690539\pi$
$263$	−8.74404e10	−1.12697	−0.563484	+	0.826127i	$0.690539\pi$
$264$	2.72376e11	3.45105
$265$	6.01197e10	0.748877
$266$	5.60450e10	0.686388
$267$	−2.41622e10	−0.290962
$268$	1.61239e11	1.90925
$269$	6.76776e10	0.788060	0.394030	−	0.919097i	$-0.371081\pi$
$269$	6.76776e10	0.788060	0.394030	+	0.919097i	$0.371081\pi$
$270$	1.46377e10	0.167624
$271$	−5.83870e10	−0.657589	−0.328794	−	0.944402i	$-0.606642\pi$
$271$	−5.83870e10	−0.657589	−0.328794	+	0.944402i	$0.606642\pi$
$272$	−6.93426e11	−7.68140
$273$	5.43137e10	0.591803
$274$	−8.88955e10	−0.952801
$275$	3.24639e10	0.342297
$276$	1.82798e11	1.89619
$277$	−8.27440e10	−0.844457	−0.422228	−	0.906489i	$-0.638752\pi$
$277$	−8.27440e10	−0.844457	−0.422228	+	0.906489i	$0.638752\pi$
$278$	−1.33115e11	−1.33668
$279$	−1.25345e10	−0.123848
$280$	−2.46778e11	−2.39936
$281$	8.85508e10	0.847254	0.423627	−	0.905837i	$-0.360757\pi$
$281$	8.85508e10	0.847254	0.423627	+	0.905837i	$0.360757\pi$
$282$	3.89394e10	0.366664
$283$	−7.43966e10	−0.689468	−0.344734	−	0.938700i	$-0.612031\pi$
$283$	−7.43966e10	−0.689468	−0.344734	+	0.938700i	$0.612031\pi$
$284$	−1.43825e11	−1.31190
$285$	6.59750e9	0.0592349
$286$	2.51664e11	2.22420
$287$	6.19574e9	0.0539045
$288$	−1.67938e11	−1.43841
$289$	3.16800e11	2.67144
$290$	7.79378e10	0.647079
$291$	1.06737e10	0.0872564
$292$	−1.53822e11	−1.23822
$293$	1.79888e10	0.142593	0.0712963	−	0.997455i	$-0.477286\pi$
$293$	1.79888e10	0.142593	0.0712963	+	0.997455i	$0.477286\pi$
$294$	1.95884e11	1.52910
$295$	−6.96592e10	−0.535524
$296$	6.83245e11	5.17325
$297$	−4.41668e10	−0.329376
$298$	−2.69581e11	−1.98024
$299$	1.08431e11	0.784571
$300$	−4.52502e10	−0.322534
$301$	3.40681e11	2.39221
$302$	−2.89529e11	−2.00290
$303$	−5.17059e10	−0.352410
$304$	−1.36955e11	−0.919698
$305$	3.51679e10	0.232700
$306$	1.90786e11	1.24394
$307$	−7.90208e10	−0.507714	−0.253857	−	0.967242i	$-0.581699\pi$
$307$	−7.90208e10	−0.507714	−0.253857	+	0.967242i	$0.581699\pi$
$308$	1.15984e12	7.34381
$309$	−1.18073e11	−0.736776
$310$	5.26208e10	0.323616
$311$	−2.38546e11	−1.44594	−0.722971	−	0.690879i	$-0.757224\pi$
$311$	−2.38546e11	−1.44594	−0.722971	+	0.690879i	$0.757224\pi$
$312$	−2.25200e11	−1.34547
$313$	2.01412e11	1.18614	0.593070	−	0.805151i	$-0.297916\pi$
$313$	2.01412e11	1.18614	0.593070	+	0.805151i	$0.297916\pi$
$314$	3.70878e11	2.15302
$315$	4.00160e10	0.229000
$316$	1.30070e11	0.733813
$317$	−1.00180e11	−0.557202	−0.278601	−	0.960407i	$-0.589871\pi$
$317$	−1.00180e11	−0.557202	−0.278601	+	0.960407i	$0.589871\pi$
$318$	3.43369e11	1.88295
$319$	−2.35163e11	−1.27149
$320$	3.68728e11	1.96576
$321$	7.27984e10	0.382692
$322$	6.78632e11	3.51790
$323$	8.59909e10	0.439583
$324$	6.15624e10	0.310358
$325$	−2.68411e10	−0.133452
$326$	−2.15972e11	−1.05905
$327$	−1.79975e11	−0.870456
$328$	−2.56893e10	−0.122552
$329$	1.06451e11	0.500918
$330$	1.85415e11	0.860661
$331$	2.46688e11	1.12959	0.564797	−	0.825230i	$-0.308954\pi$
$331$	2.46688e11	1.12959	0.564797	+	0.825230i	$0.308954\pi$
$332$	−1.03238e12	−4.66356
$333$	−1.10791e11	−0.493746
$334$	−9.84519e10	−0.432878
$335$	7.04650e10	0.305684
$336$	−8.30674e11	−3.55553
$337$	4.02837e11	1.70135	0.850676	−	0.525690i	$-0.176193\pi$
$337$	4.02837e11	1.70135	0.850676	+	0.525690i	$0.176193\pi$
$338$	2.59261e11	1.08047
$339$	−1.04139e11	−0.428266
$340$	−5.89785e11	−2.39353
$341$	−1.58774e11	−0.635894
$342$	3.76811e10	0.148938
$343$	1.41707e11	0.552798
$344$	−1.41256e12	−5.43870
$345$	7.98871e10	0.303592
$346$	−6.16280e11	−2.31172
$347$	−4.17462e11	−1.54573	−0.772866	−	0.634569i	$-0.781178\pi$
$347$	−4.17462e11	−1.54573	−0.772866	+	0.634569i	$0.781178\pi$
$348$	3.27786e11	1.19807
$349$	−2.31672e10	−0.0835910	−0.0417955	−	0.999126i	$-0.513308\pi$
$349$	−2.31672e10	−0.0835910	−0.0417955	+	0.999126i	$0.513308\pi$
$350$	−1.67990e11	−0.598379
$351$	3.65171e10	0.128414
$352$	−2.12726e12	−7.38548
$353$	−3.81093e11	−1.30631	−0.653153	−	0.757226i	$-0.726554\pi$
$353$	−3.81093e11	−1.30631	−0.653153	+	0.757226i	$0.726554\pi$
$354$	−3.97853e11	−1.34650
$355$	−6.28549e10	−0.210045
$356$	4.26606e11	1.40767
$357$	5.21563e11	1.69942
$358$	−6.28032e11	−2.02073
$359$	6.93513e10	0.220358	0.110179	−	0.993912i	$-0.464858\pi$
$359$	6.93513e10	0.220358	0.110179	+	0.993912i	$0.464858\pi$
$360$	−1.65918e11	−0.520634
$361$	1.69836e10	0.0526316
$362$	4.58069e11	1.40198
$363$	−3.68463e11	−1.11382
$364$	−9.58959e11	−2.86315
$365$	−6.72239e10	−0.198247
$366$	2.00859e11	0.585094
$367$	4.80006e11	1.38118	0.690588	−	0.723248i	$-0.257352\pi$
$367$	4.80006e11	1.38118	0.690588	+	0.723248i	$0.257352\pi$
$368$	−1.65834e12	−4.71366
$369$	4.16562e9	0.0116966
$370$	4.65106e11	1.29016
$371$	9.38686e11	2.57240
$372$	2.21309e11	0.599178
$373$	−1.22775e11	−0.328412	−0.164206	−	0.986426i	$-0.552506\pi$
$373$	−1.22775e11	−0.328412	−0.164206	+	0.986426i	$0.552506\pi$
$374$	2.41667e12	6.38699
$375$	−1.97754e10	−0.0516398
$376$	−4.41376e11	−1.13884
$377$	1.94433e11	0.495717
$378$	2.28548e11	0.575791
$379$	6.43989e11	1.60325	0.801626	−	0.597826i	$-0.203969\pi$
$379$	6.43989e11	1.60325	0.801626	+	0.597826i	$0.203969\pi$
$380$	−1.16485e11	−0.286579
$381$	−1.70461e11	−0.414440
$382$	−5.07017e11	−1.21825
$383$	−2.36644e11	−0.561953	−0.280977	−	0.959715i	$-0.590658\pi$
$383$	−2.36644e11	−0.561953	−0.280977	+	0.959715i	$0.590658\pi$
$384$	1.04442e12	2.45124
$385$	5.06879e11	1.17579
$386$	−1.37305e12	−3.14806
$387$	2.29052e11	0.519082
$388$	−1.88454e11	−0.422147
$389$	5.07462e11	1.12365	0.561824	−	0.827257i	$-0.310100\pi$
$389$	5.07462e11	1.12365	0.561824	+	0.827257i	$0.310100\pi$
$390$	−1.53301e11	−0.335548
$391$	1.04124e12	2.25297
$392$	−2.22033e12	−4.74931
$393$	1.92953e11	0.408023
$394$	−1.63902e12	−3.42651
$395$	5.68436e10	0.117488
$396$	7.79805e11	1.59352
$397$	6.20976e7	0.000125464 0	6.27318e−5	−	1.00000i	$-0.499980\pi$
$397$	6.20976e7	0.000125464 0	6.27318e−5		1.00000i	$0.499980\pi$
$398$	−1.51052e12	−3.01754
$399$	1.03011e11	0.203472
$400$	4.10508e11	0.801774
$401$	1.33552e11	0.257929	0.128964	−	0.991649i	$-0.458835\pi$
$401$	1.33552e11	0.257929	0.128964	+	0.991649i	$0.458835\pi$
$402$	4.02455e11	0.768600
$403$	1.31274e11	0.247917
$404$	9.12916e11	1.70496
$405$	2.69042e10	0.0496904
$406$	1.21689e12	2.22272
$407$	−1.40337e12	−2.53512
$408$	−2.16255e12	−3.86363
$409$	−9.15255e11	−1.61729	−0.808644	−	0.588299i	$-0.799798\pi$
$409$	−9.15255e11	−1.61729	−0.808644	+	0.588299i	$0.799798\pi$
$410$	−1.74875e10	−0.0305634
$411$	−1.63390e11	−0.282447
$412$	2.08468e12	3.56453
$413$	−1.08763e12	−1.83953
$414$	4.56269e11	0.763343
$415$	−4.51173e11	−0.746667
$416$	1.75882e12	2.87939
$417$	−2.44666e11	−0.396243
$418$	4.77303e11	0.764717
$419$	1.07655e12	1.70636	0.853179	−	0.521618i	$-0.174671\pi$
$419$	1.07655e12	1.70636	0.853179	+	0.521618i	$0.174671\pi$
$420$	−7.06520e11	−1.10790
$421$	−6.95477e11	−1.07898	−0.539490	−	0.841992i	$-0.681383\pi$
$421$	−6.95477e11	−1.07898	−0.539490	+	0.841992i	$0.681383\pi$
$422$	−3.38406e10	−0.0519437
$423$	7.15707e10	0.108693
$424$	−3.89207e12	−5.84836
$425$	−2.57750e11	−0.383220
$426$	−3.58991e11	−0.528129
$427$	5.49098e11	0.799327
$428$	−1.28532e12	−1.85146
$429$	4.62558e11	0.659339
$430$	−9.61577e11	−1.35636
$431$	5.03589e11	0.702956	0.351478	−	0.936196i	$-0.385679\pi$
$431$	5.03589e11	0.702956	0.351478	+	0.936196i	$0.385679\pi$
$432$	−5.58492e11	−0.771508
$433$	1.27865e12	1.74805	0.874027	−	0.485878i	$-0.161500\pi$
$433$	1.27865e12	1.74805	0.874027	+	0.485878i	$0.161500\pi$
$434$	8.21602e11	1.11162
$435$	1.43250e11	0.191819
$436$	3.17762e12	4.21127
$437$	2.05649e11	0.269749
$438$	−3.83944e11	−0.498465
$439$	−1.03893e12	−1.33505	−0.667524	−	0.744589i	$-0.732646\pi$
$439$	−1.03893e12	−1.33505	−0.667524	+	0.744589i	$0.732646\pi$
$440$	−2.10167e12	−2.67317
$441$	3.60035e11	0.453284
$442$	−1.99810e12	−2.49011
$443$	4.21624e11	0.520125	0.260063	−	0.965592i	$-0.416257\pi$
$443$	4.21624e11	0.520125	0.260063	+	0.965592i	$0.416257\pi$
$444$	1.95611e12	2.38875
$445$	1.86437e11	0.225378
$446$	−4.62835e11	−0.553885
$447$	−4.95491e11	−0.587019
$448$	5.75717e12	6.75240
$449$	−3.73705e11	−0.433931	−0.216965	−	0.976179i	$-0.569616\pi$
$449$	−3.73705e11	−0.433931	−0.216965	+	0.976179i	$0.569616\pi$
$450$	−1.12946e11	−0.129841
$451$	5.27655e10	0.0600559
$452$	1.83867e12	2.07195
$453$	−5.32154e11	−0.593739
$454$	4.07446e11	0.450110
$455$	−4.19087e11	−0.458409
$456$	−4.27113e11	−0.462595
$457$	−4.18561e11	−0.448886	−0.224443	−	0.974487i	$-0.572056\pi$
$457$	−4.18561e11	−0.448886	−0.224443	+	0.974487i	$0.572056\pi$
$458$	−1.61610e12	−1.71622
$459$	3.50666e11	0.368754
$460$	−1.41048e12	−1.46878
$461$	6.17190e11	0.636451	0.318225	−	0.948015i	$-0.396913\pi$
$461$	6.17190e11	0.636451	0.318225	+	0.948015i	$0.396913\pi$
$462$	2.89500e12	2.95638
$463$	−2.24614e11	−0.227155	−0.113578	−	0.993529i	$-0.536231\pi$
$463$	−2.24614e11	−0.227155	−0.113578	+	0.993529i	$0.536231\pi$
$464$	−2.97366e12	−2.97824
$465$	9.67172e10	0.0959324
$466$	−1.20287e12	−1.18163
$467$	−1.72081e12	−1.67419	−0.837097	−	0.547055i	$-0.815749\pi$
$467$	−1.72081e12	−1.67419	−0.837097	+	0.547055i	$0.815749\pi$
$468$	−6.44743e11	−0.621269
$469$	1.10021e12	1.05002
$470$	−3.00458e11	−0.284017
$471$	6.81674e11	0.638238
$472$	4.50964e12	4.18218
$473$	2.90139e12	2.66520
$474$	3.24658e11	0.295409
$475$	−5.09066e10	−0.0458831
$476$	−9.20868e12	−8.22179
$477$	6.31113e11	0.558180
$478$	−8.54881e11	−0.748997
$479$	1.97449e12	1.71374	0.856872	−	0.515530i	$-0.172405\pi$
$479$	1.97449e12	1.71374	0.856872	+	0.515530i	$0.172405\pi$
$480$	1.29582e12	1.11419
$481$	1.16031e12	0.988373
$482$	2.89771e12	2.44536
$483$	1.24733e12	1.04284
$484$	6.50555e12	5.38865
$485$	−8.23590e10	−0.0675885
$486$	1.53661e11	0.124940
$487$	4.83448e11	0.389466	0.194733	−	0.980856i	$-0.437616\pi$
$487$	4.83448e11	0.389466	0.194733	+	0.980856i	$0.437616\pi$
$488$	−2.27672e12	−1.81727
$489$	−3.96956e11	−0.313944
$490$	−1.51145e12	−1.18443
$491$	−1.62883e12	−1.26477	−0.632383	−	0.774656i	$-0.717923\pi$
$491$	−1.62883e12	−1.26477	−0.632383	+	0.774656i	$0.717923\pi$
$492$	−7.35479e10	−0.0565884
$493$	1.86710e12	1.42350
$494$	−3.94634e11	−0.298142
$495$	3.40793e11	0.255133
$496$	−2.00771e12	−1.48947
$497$	−9.81392e11	−0.721504
$498$	−2.57684e12	−1.87739
$499$	4.01893e11	0.290174	0.145087	−	0.989419i	$-0.453654\pi$
$499$	4.01893e11	0.290174	0.145087	+	0.989419i	$0.453654\pi$
$500$	3.49153e11	0.249833
$501$	−1.80955e11	−0.128322
$502$	6.63983e11	0.466649
$503$	2.23256e12	1.55506	0.777530	−	0.628846i	$-0.216472\pi$
$503$	2.23256e12	1.55506	0.777530	+	0.628846i	$0.216472\pi$
$504$	−2.59058e12	−1.78838
$505$	3.98966e11	0.272976
$506$	5.77952e12	3.91935
$507$	4.76522e11	0.320293
$508$	3.00964e12	2.00506
$509$	1.43367e11	0.0946717	0.0473358	−	0.998879i	$-0.484927\pi$
$509$	1.43367e11	0.0946717	0.0473358	+	0.998879i	$0.484927\pi$
$510$	−1.47212e12	−0.963555
$511$	−1.04961e12	−0.680978
$512$	−5.12851e12	−3.29819
$513$	6.92579e10	0.0441511
$514$	−4.03940e11	−0.255260
$515$	9.11053e11	0.570705
$516$	−4.04413e12	−2.51132
$517$	9.06579e11	0.558082
$518$	7.26199e12	4.43171
$519$	−1.13272e12	−0.685285
$520$	1.73766e12	1.04220
$521$	−1.34420e12	−0.799270	−0.399635	−	0.916674i	$-0.630863\pi$
$521$	−1.34420e12	−0.799270	−0.399635	+	0.916674i	$0.630863\pi$
$522$	8.18160e11	0.482304
$523$	−7.53431e10	−0.0440338	−0.0220169	−	0.999758i	$-0.507009\pi$
$523$	−7.53431e10	−0.0440338	−0.0220169	+	0.999758i	$0.507009\pi$
$524$	−3.40676e12	−1.97401
$525$	−3.08765e11	−0.177383
$526$	3.85347e12	2.19490
$527$	1.26060e12	0.711916
$528$	−7.07437e12	−3.96128
$529$	6.88987e11	0.382526
$530$	−2.64945e12	−1.45853
$531$	−7.31254e11	−0.399156
$532$	−1.81875e12	−0.984399
$533$	−4.36265e10	−0.0234141
$534$	1.06482e12	0.566683
$535$	−5.61716e11	−0.296432
$536$	−4.56181e12	−2.38724
$537$	−1.15432e12	−0.599023
$538$	−2.98252e12	−1.53484
$539$	4.56052e12	2.32737
$540$	−4.75019e11	−0.240402
$541$	−2.50299e12	−1.25624	−0.628118	−	0.778118i	$-0.716174\pi$
$541$	−2.50299e12	−1.25624	−0.628118	+	0.778118i	$0.716174\pi$
$542$	2.57309e12	1.28073
$543$	8.41931e11	0.415602
$544$	1.68896e13	8.26843
$545$	1.38870e12	0.674253
$546$	−2.39358e12	−1.15261
$547$	2.91493e12	1.39215	0.696074	−	0.717970i	$-0.254929\pi$
$547$	2.91493e12	1.39215	0.696074	+	0.717970i	$0.254929\pi$
$548$	2.88480e12	1.36648
$549$	3.69179e11	0.173445
$550$	−1.43067e12	−0.666665
$551$	3.68760e11	0.170436
$552$	−5.17178e12	−2.37091
$553$	8.87535e11	0.403573
$554$	3.64650e12	1.64468
$555$	8.54866e11	0.382454
$556$	4.31981e12	1.91702
$557$	2.75181e12	1.21135	0.605676	−	0.795712i	$-0.292903\pi$
$557$	2.75181e12	1.21135	0.605676	+	0.795712i	$0.292903\pi$
$558$	5.52392e11	0.241209
$559$	−2.39886e12	−1.03909
$560$	6.40952e12	2.75410
$561$	4.44185e12	1.89335
$562$	−3.90240e12	−1.65013
$563$	−1.38035e12	−0.579032	−0.289516	−	0.957173i	$-0.593494\pi$
$563$	−1.38035e12	−0.579032	−0.289516	+	0.957173i	$0.593494\pi$
$564$	−1.26365e12	−0.525859
$565$	8.03539e11	0.331733
$566$	3.27863e12	1.34282
$567$	4.20072e11	0.170687
$568$	4.06914e12	1.64034
$569$	−2.78819e12	−1.11511	−0.557555	−	0.830140i	$-0.688261\pi$
$569$	−2.78819e12	−1.11511	−0.557555	+	0.830140i	$0.688261\pi$
$570$	−2.90749e11	−0.115367
$571$	−4.21419e12	−1.65902	−0.829510	−	0.558491i	$-0.811380\pi$
$571$	−4.21419e12	−1.65902	−0.829510	+	0.558491i	$0.811380\pi$
$572$	−8.16689e12	−3.18988
$573$	−9.31898e11	−0.361137
$574$	−2.73044e11	−0.104985
$575$	−6.16413e11	−0.235162
$576$	3.87076e12	1.46519
$577$	3.24484e12	1.21872	0.609358	−	0.792895i	$-0.291427\pi$
$577$	3.24484e12	1.21872	0.609358	+	0.792895i	$0.291427\pi$
$578$	−1.39613e13	−5.20295
$579$	−2.52366e12	−0.933206
$580$	−2.52921e12	−0.928023
$581$	−7.04445e12	−2.56481
$582$	−4.70387e11	−0.169942
$583$	7.99425e12	2.86595
$584$	4.35198e12	1.54821
$585$	−2.81767e11	−0.0994694
$586$	−7.92757e11	−0.277716
$587$	−5.37315e11	−0.186792	−0.0933959	−	0.995629i	$-0.529772\pi$
$587$	−5.37315e11	−0.186792	−0.0933959	+	0.995629i	$0.529772\pi$
$588$	−6.35674e12	−2.19299
$589$	2.48973e11	0.0852382
$590$	3.06985e12	1.04300
$591$	−3.01252e12	−1.01575
$592$	−1.77458e13	−5.93810
$593$	5.74122e12	1.90659	0.953296	−	0.302038i	$-0.0976670\pi$
$593$	5.74122e12	1.90659	0.953296	+	0.302038i	$0.0976670\pi$
$594$	1.94641e12	0.641499
$595$	−4.02441e12	−1.31636
$596$	8.74836e12	2.84000
$597$	−2.77634e12	−0.894517
$598$	−4.77850e12	−1.52805
$599$	3.28237e12	1.04176	0.520880	−	0.853630i	$-0.325604\pi$
$599$	3.28237e12	1.04176	0.520880	+	0.853630i	$0.325604\pi$
$600$	1.28023e12	0.403281
$601$	9.39268e11	0.293666	0.146833	−	0.989161i	$-0.453092\pi$
$601$	9.39268e11	0.293666	0.146833	+	0.989161i	$0.453092\pi$
$602$	−1.50137e13	−4.65912
$603$	7.39714e11	0.227843
$604$	9.39567e12	2.87251
$605$	2.84308e12	0.862759
$606$	2.27866e12	0.686361
$607$	−4.30843e12	−1.28816	−0.644080	−	0.764958i	$-0.722760\pi$
$607$	−4.30843e12	−1.28816	−0.644080	+	0.764958i	$0.722760\pi$
$608$	3.33576e12	0.989984
$609$	2.23665e12	0.658901
$610$	−1.54984e12	−0.453212
$611$	−7.49559e11	−0.217581
$612$	−6.19133e12	−1.78403
$613$	−4.56018e12	−1.30440	−0.652198	−	0.758048i	$-0.726153\pi$
$613$	−4.56018e12	−1.30440	−0.652198	+	0.758048i	$0.726153\pi$
$614$	3.48242e12	0.988833
$615$	−3.21421e10	−0.00906018
$616$	−3.28146e13	−9.18236
$617$	2.46376e12	0.684408	0.342204	−	0.939626i	$-0.388827\pi$
$617$	2.46376e12	0.684408	0.342204	+	0.939626i	$0.388827\pi$
$618$	5.20341e12	1.43496
$619$	−2.58119e12	−0.706663	−0.353332	−	0.935498i	$-0.614951\pi$
$619$	−2.58119e12	−0.706663	−0.353332	+	0.935498i	$0.614951\pi$
$620$	−1.70763e12	−0.464121
$621$	8.38623e11	0.226284
$622$	1.05126e13	2.81614
$623$	2.91095e12	0.774175
$624$	5.84908e12	1.54439
$625$	1.52588e11	0.0400000
$626$	−8.87615e12	−2.31015
$627$	8.77284e11	0.226692
$628$	−1.20356e13	−3.08780
$629$	1.11422e13	2.83820
$630$	−1.76349e12	−0.446006
$631$	−1.98347e12	−0.498075	−0.249037	−	0.968494i	$-0.580114\pi$
$631$	−1.98347e12	−0.498075	−0.249037	+	0.968494i	$0.580114\pi$
$632$	−3.67998e12	−0.917526
$633$	−6.21991e10	−0.0153981
$634$	4.41487e12	1.08522
$635$	1.31528e12	0.321024
$636$	−1.11429e13	−2.70048
$637$	−3.77064e12	−0.907376
$638$	1.03636e13	2.47637
$639$	−6.59825e11	−0.156558
$640$	−8.05882e12	−1.89872
$641$	−8.50685e12	−1.99025	−0.995125	−	0.0986171i	$-0.968558\pi$
$641$	−8.50685e12	−1.99025	−0.995125	+	0.0986171i	$0.968558\pi$
$642$	−3.20820e12	−0.745338
$643$	−3.12664e11	−0.0721321	−0.0360661	−	0.999349i	$-0.511483\pi$
$643$	−3.12664e11	−0.0721321	−0.0360661	+	0.999349i	$0.511483\pi$
$644$	−2.20227e13	−5.04527
$645$	−1.76738e12	−0.402079
$646$	−3.78959e12	−0.856141
$647$	3.49352e12	0.783779	0.391889	−	0.920012i	$-0.371822\pi$
$647$	3.49352e12	0.783779	0.391889	+	0.920012i	$0.371822\pi$
$648$	−1.74174e12	−0.388057
$649$	−9.26273e12	−2.04945
$650$	1.18288e12	0.259914
$651$	1.51010e12	0.329528
$652$	7.00863e12	1.51886
$653$	4.99413e12	1.07486	0.537429	−	0.843309i	$-0.319396\pi$
$653$	4.99413e12	1.07486	0.537429	+	0.843309i	$0.319396\pi$
$654$	7.93142e12	1.69532
$655$	−1.48883e12	−0.316053
$656$	6.67224e11	0.140671
$657$	−7.05690e11	−0.147764
$658$	−4.69124e12	−0.975599
$659$	5.22410e12	1.07901	0.539507	−	0.841981i	$-0.318611\pi$
$659$	5.22410e12	1.07901	0.539507	+	0.841981i	$0.318611\pi$
$660$	−6.01702e12	−1.23434
$661$	3.22164e12	0.656404	0.328202	−	0.944608i	$-0.393557\pi$
$661$	3.22164e12	0.656404	0.328202	+	0.944608i	$0.393557\pi$
$662$	−1.08715e13	−2.20002
$663$	−3.67252e12	−0.738165
$664$	2.92083e13	5.83110
$665$	−7.94837e11	−0.157609
$666$	4.88250e12	0.961630
$667$	4.46520e12	0.873524
$668$	3.19492e12	0.620821
$669$	−8.50692e11	−0.164193
$670$	−3.10537e12	−0.595355
$671$	4.67635e12	0.890545
$672$	2.02325e13	3.82725
$673$	3.58337e12	0.673324	0.336662	−	0.941626i	$-0.390702\pi$
$673$	3.58337e12	0.673324	0.336662	+	0.941626i	$0.390702\pi$
$674$	−1.77529e13	−3.31359
$675$	−2.07594e11	−0.0384900
$676$	−8.41343e12	−1.54958
$677$	1.53251e11	0.0280384	0.0140192	−	0.999902i	$-0.495537\pi$
$677$	1.53251e11	0.0280384	0.0140192	+	0.999902i	$0.495537\pi$
$678$	4.58935e12	0.834099
$679$	−1.28592e12	−0.232167
$680$	1.66864e13	2.99276
$681$	7.48887e11	0.133430
$682$	6.99710e12	1.23848
$683$	2.55365e12	0.449022	0.224511	−	0.974472i	$-0.427921\pi$
$683$	2.55365e12	0.449022	0.224511	+	0.974472i	$0.427921\pi$
$684$	−1.22281e12	−0.213603
$685$	1.26073e12	0.218783
$686$	−6.24496e12	−1.07664
$687$	−2.97039e12	−0.508754
$688$	3.66882e13	6.24279
$689$	−6.60964e12	−1.11735
$690$	−3.52059e12	−0.591283
$691$	6.21812e12	1.03755	0.518773	−	0.854912i	$-0.326389\pi$
$691$	6.21812e12	1.03755	0.518773	+	0.854912i	$0.326389\pi$
$692$	1.99993e13	3.31541
$693$	5.32101e12	0.876385
$694$	1.83974e13	3.01050
$695$	1.88786e12	0.306928
$696$	−9.27380e12	−1.49801
$697$	−4.18936e11	−0.0672358
$698$	1.02097e12	0.162803
$699$	−2.21087e12	−0.350281
$700$	5.45154e12	0.858179
$701$	9.91610e12	1.55099	0.775496	−	0.631352i	$-0.217500\pi$
$701$	9.91610e12	1.55099	0.775496	+	0.631352i	$0.217500\pi$
$702$	−1.60929e12	−0.250102
$703$	2.20063e12	0.339820
$704$	4.90305e13	7.52297
$705$	−5.52243e11	−0.0841936
$706$	1.67946e13	2.54419
$707$	6.22930e12	0.937673
$708$	1.29110e13	1.93112
$709$	−1.02416e13	−1.52215	−0.761077	−	0.648662i	$-0.775329\pi$
$709$	−1.02416e13	−1.52215	−0.761077	+	0.648662i	$0.775329\pi$
$710$	2.76999e12	0.409087
$711$	5.96722e11	0.0875706
$712$	−1.20697e13	−1.76009
$713$	3.01474e12	0.436865
$714$	−2.29851e13	−3.30982
$715$	−3.56912e12	−0.510722
$716$	2.03806e13	2.89807
$717$	−1.57127e12	−0.222032
$718$	−3.05629e12	−0.429175
$719$	7.10262e12	0.991148	0.495574	−	0.868566i	$-0.334958\pi$
$719$	7.10262e12	0.991148	0.495574	+	0.868566i	$0.334958\pi$
$720$	4.30935e12	0.597607
$721$	1.42248e13	1.96037
$722$	−7.48459e11	−0.102506
$723$	5.32599e12	0.724900
$724$	−1.48651e13	−2.01068
$725$	−1.10532e12	−0.148583
$726$	1.62380e13	2.16929
$727$	−2.62998e11	−0.0349179	−0.0174589	−	0.999848i	$-0.505558\pi$
$727$	−2.62998e11	−0.0349179	−0.0174589	+	0.999848i	$0.505558\pi$
$728$	2.71311e13	3.57995
$729$	2.82430e11	0.0370370
$730$	2.96253e12	0.386109
$731$	−2.30358e13	−2.98384
$732$	−6.51819e12	−0.839126
$733$	−4.85321e12	−0.620956	−0.310478	−	0.950580i	$-0.600489\pi$
$733$	−4.85321e12	−0.620956	−0.310478	+	0.950580i	$0.600489\pi$
$734$	−2.11537e13	−2.69001
$735$	−2.77804e12	−0.351112
$736$	4.03917e13	5.07390
$737$	9.36989e12	1.16985
$738$	−1.83577e11	−0.0227806
$739$	−1.32813e13	−1.63809	−0.819047	−	0.573726i	$-0.805497\pi$
$739$	−1.32813e13	−1.63809	−0.819047	+	0.573726i	$0.805497\pi$
$740$	−1.50934e13	−1.85032
$741$	−7.25338e11	−0.0883809
$742$	−4.13675e13	−5.01005
$743$	5.32672e12	0.641224	0.320612	−	0.947211i	$-0.396111\pi$
$743$	5.32672e12	0.641224	0.320612	+	0.947211i	$0.396111\pi$
$744$	−6.26133e12	−0.749184
$745$	3.82323e12	0.454703
$746$	5.41063e12	0.639622
$747$	−4.73624e12	−0.556533
$748$	−7.84250e13	−9.16004
$749$	−8.77042e12	−1.01824
$750$	8.71494e11	0.100575
$751$	−3.71999e12	−0.426738	−0.213369	−	0.976972i	$-0.568444\pi$
$751$	−3.71999e12	−0.426738	−0.213369	+	0.976972i	$0.568444\pi$
$752$	1.14638e13	1.30721
$753$	1.22040e12	0.138333
$754$	−8.56859e12	−0.965468
$755$	4.10613e12	0.459908
$756$	−7.41676e12	−0.825783
$757$	−7.96330e12	−0.881376	−0.440688	−	0.897660i	$-0.645266\pi$
$757$	−7.96330e12	−0.881376	−0.440688	+	0.897660i	$0.645266\pi$
$758$	−2.83803e13	−3.12253
$759$	1.06228e13	1.16185
$760$	3.29563e12	0.358325
$761$	−6.92944e12	−0.748975	−0.374488	−	0.927232i	$-0.622181\pi$
$761$	−6.92944e12	−0.748975	−0.374488	+	0.927232i	$0.622181\pi$
$762$	7.51214e12	0.807172
$763$	2.16826e13	2.31606
$764$	1.64535e13	1.74718
$765$	−2.70575e12	−0.285635
$766$	1.04288e13	1.09447
$767$	7.65842e12	0.799024
$768$	−2.15603e13	−2.23630
$769$	−4.93485e12	−0.508868	−0.254434	−	0.967090i	$-0.581889\pi$
$769$	−4.93485e12	−0.508868	−0.254434	+	0.967090i	$0.581889\pi$
$770$	−2.23380e13	−2.29000
$771$	−7.42442e11	−0.0756690
$772$	4.45576e13	4.51486
$773$	−6.28021e12	−0.632654	−0.316327	−	0.948650i	$-0.602450\pi$
$773$	−6.28021e12	−0.632654	−0.316327	+	0.948650i	$0.602450\pi$
$774$	−1.00943e13	−1.01097
$775$	−7.46274e11	−0.0743089
$776$	5.33181e12	0.527833
$777$	1.33475e13	1.31373
$778$	−2.23636e13	−2.18844
$779$	−8.27416e10	−0.00805018
$780$	4.97487e12	0.481233
$781$	−8.35795e12	−0.803841
$782$	−4.58870e13	−4.38792
$783$	1.50378e12	0.142974
$784$	5.76682e13	5.45147
$785$	−5.25983e12	−0.494377
$786$	−8.50335e12	−0.794673
$787$	8.58465e12	0.797694	0.398847	−	0.917018i	$-0.369410\pi$
$787$	8.58465e12	0.797694	0.398847	+	0.917018i	$0.369410\pi$
$788$	5.31889e13	4.91420
$789$	7.08268e12	0.650655
$790$	−2.50508e12	−0.228823
$791$	1.25462e13	1.13951
$792$	−2.20625e13	−1.99247
$793$	−3.86640e12	−0.347198
$794$	−2.73662e9	−0.000244355 0
$795$	−4.86970e12	−0.432364
$796$	4.90189e13	4.32768
$797$	2.12794e12	0.186808	0.0934042	−	0.995628i	$-0.470225\pi$
$797$	2.12794e12	0.186808	0.0934042	+	0.995628i	$0.470225\pi$
$798$	−4.53965e12	−0.396286
$799$	−7.19786e12	−0.624802
$800$	−9.99862e12	−0.863048
$801$	1.95714e12	0.167987
$802$	−5.88557e12	−0.502347
$803$	−8.93891e12	−0.758690
$804$	−1.30603e13	−1.10231
$805$	−9.62444e12	−0.807782
$806$	−5.78520e12	−0.482848
$807$	−5.48188e12	−0.454987
$808$	−2.58285e13	−2.13181
$809$	9.93643e10	0.00815571	0.00407786	−	0.999992i	$-0.498702\pi$
$809$	9.93643e10	0.00815571	0.00407786	+	0.999992i	$0.498702\pi$
$810$	−1.18566e12	−0.0967780
$811$	−1.11695e13	−0.906648	−0.453324	−	0.891346i	$-0.649762\pi$
$811$	−1.11695e13	−0.906648	−0.453324	+	0.891346i	$0.649762\pi$
$812$	−3.94901e13	−3.18776
$813$	4.72935e12	0.379659
$814$	6.18462e13	4.93745
$815$	3.06293e12	0.243180
$816$	5.61675e13	4.43486
$817$	−4.54966e12	−0.357256
$818$	4.03349e13	3.14986
$819$	−4.39941e12	−0.341678
$820$	5.67499e11	0.0438332
$821$	7.51912e12	0.577594	0.288797	−	0.957390i	$-0.406745\pi$
$821$	7.51912e12	0.577594	0.288797	+	0.957390i	$0.406745\pi$
$822$	7.20053e12	0.550100
$823$	−1.69757e13	−1.28982	−0.644909	−	0.764259i	$-0.723105\pi$
$823$	−1.69757e13	−1.28982	−0.644909	+	0.764259i	$0.723105\pi$
$824$	−5.89803e13	−4.45692
$825$	−2.62958e12	−0.197625
$826$	4.79315e13	3.58270
$827$	−7.37899e11	−0.0548558	−0.0274279	−	0.999624i	$-0.508732\pi$
$827$	−7.37899e11	−0.0548558	−0.0274279	+	0.999624i	$0.508732\pi$
$828$	−1.48067e13	−1.09477
$829$	−2.54814e12	−0.187382	−0.0936910	−	0.995601i	$-0.529867\pi$
$829$	−2.54814e12	−0.187382	−0.0936910	+	0.995601i	$0.529867\pi$
$830$	1.98830e13	1.45422
$831$	6.70226e12	0.487547
$832$	−4.05384e13	−2.93300
$833$	−3.62087e13	−2.60561
$834$	1.07823e13	0.771730
$835$	1.39626e12	0.0993976
$836$	−1.54893e13	−1.09674
$837$	1.01530e12	0.0715038
$838$	−4.74430e13	−3.32334
$839$	5.11715e12	0.356533	0.178266	−	0.983982i	$-0.442951\pi$
$839$	5.11715e12	0.356533	0.178266	+	0.983982i	$0.442951\pi$
$840$	1.99890e13	1.38527
$841$	−6.50036e12	−0.448080
$842$	3.06494e13	2.10144
$843$	−7.17261e12	−0.489163
$844$	1.09818e12	0.0744962
$845$	−3.67686e12	−0.248098
$846$	−3.15409e12	−0.211694
$847$	4.43907e13	2.96358
$848$	1.01088e14	6.71301
$849$	6.02613e12	0.398065
$850$	1.13589e13	0.746367
$851$	2.66468e13	1.74165
$852$	1.16498e13	0.757428
$853$	−1.35299e13	−0.875030	−0.437515	−	0.899211i	$-0.644141\pi$
$853$	−1.35299e13	−0.875030	−0.437515	+	0.899211i	$0.644141\pi$
$854$	−2.41985e13	−1.55679
$855$	−5.34398e11	−0.0341993
$856$	3.63647e13	2.31498
$857$	−1.35882e13	−0.860498	−0.430249	−	0.902710i	$-0.641574\pi$
$857$	−1.35882e13	−0.860498	−0.430249	+	0.902710i	$0.641574\pi$
$858$	−2.03848e13	−1.28414
$859$	5.82107e12	0.364782	0.182391	−	0.983226i	$-0.441616\pi$
$859$	5.82107e12	0.364782	0.182391	+	0.983226i	$0.441616\pi$
$860$	3.12047e13	1.94526
$861$	−5.01855e11	−0.0311218
$862$	−2.21930e13	−1.36909
$863$	1.30995e13	0.803910	0.401955	−	0.915659i	$-0.368331\pi$
$863$	1.30995e13	0.803910	0.401955	+	0.915659i	$0.368331\pi$
$864$	1.36030e13	0.830468
$865$	8.74015e12	0.530819
$866$	−5.63494e13	−3.40454
$867$	−2.56608e13	−1.54236
$868$	−2.66623e13	−1.59426
$869$	7.55862e12	0.449628
$870$	−6.31297e12	−0.373591
$871$	−7.74701e12	−0.456092
$872$	−8.99022e13	−5.26558
$873$	−8.64572e11	−0.0503775
$874$	−9.06286e12	−0.525368
$875$	2.38245e12	0.137400
$876$	1.24596e13	0.714885
$877$	2.33967e13	1.33554	0.667770	−	0.744368i	$-0.267249\pi$
$877$	2.33967e13	1.33554	0.667770	+	0.744368i	$0.267249\pi$
$878$	4.57853e13	2.60016
$879$	−1.45709e12	−0.0823259
$880$	5.45862e13	3.06839
$881$	−1.53702e13	−0.859583	−0.429791	−	0.902928i	$-0.641413\pi$
$881$	−1.53702e13	−0.859583	−0.429791	+	0.902928i	$0.641413\pi$
$882$	−1.58666e13	−0.882825
$883$	2.05085e13	1.13530	0.567650	−	0.823270i	$-0.307853\pi$
$883$	2.05085e13	1.13530	0.567650	+	0.823270i	$0.307853\pi$
$884$	6.48417e13	3.57124
$885$	5.64239e12	0.309185
$886$	−1.85808e13	−1.01301
$887$	−2.57846e13	−1.39863	−0.699316	−	0.714812i	$-0.746512\pi$
$887$	−2.57846e13	−1.39863	−0.699316	+	0.714812i	$0.746512\pi$
$888$	−5.53428e13	−2.98678
$889$	2.05363e13	1.10272
$890$	−8.21620e12	−0.438951
$891$	3.57751e12	0.190165
$892$	1.50197e13	0.794366
$893$	−1.42161e12	−0.0748080
$894$	2.18361e13	1.14329
$895$	8.90682e12	0.464001
$896$	−1.25827e14	−6.52212
$897$	−8.78289e12	−0.452972
$898$	1.64690e13	0.845132
$899$	5.40590e12	0.276025
$900$	3.66527e12	0.186215
$901$	−6.34710e13	−3.20859
$902$	−2.32536e12	−0.116966
$903$	−2.75952e13	−1.38114
$904$	−5.20200e13	−2.59067
$905$	−6.49638e12	−0.321924
$906$	2.34518e13	1.15638
$907$	−2.96929e13	−1.45687	−0.728434	−	0.685115i	$-0.759752\pi$
$907$	−2.96929e13	−1.45687	−0.728434	+	0.685115i	$0.759752\pi$
$908$	−1.32223e13	−0.645536
$909$	4.18818e12	0.203464
$910$	1.84690e13	0.892806
$911$	−1.24331e13	−0.598063	−0.299032	−	0.954243i	$-0.596664\pi$
$911$	−1.24331e13	−0.598063	−0.299032	+	0.954243i	$0.596664\pi$
$912$	1.10933e13	0.530988
$913$	−5.99935e13	−2.85750
$914$	1.84458e13	0.874259
$915$	−2.84860e12	−0.134350
$916$	5.24450e13	2.46136
$917$	−2.32461e13	−1.08564
$918$	−1.54537e13	−0.718192
$919$	−2.39965e13	−1.10976	−0.554880	−	0.831931i	$-0.687236\pi$
$919$	−2.39965e13	−1.10976	−0.554880	+	0.831931i	$0.687236\pi$
$920$	3.99057e13	1.83650
$921$	6.40069e12	0.293129
$922$	−2.71993e13	−1.23956
$923$	6.91034e12	0.313395
$924$	−9.39474e13	−4.23995
$925$	−6.59619e12	−0.296248
$926$	9.89865e12	0.442412
$927$	9.56387e12	0.425378
$928$	7.24284e13	3.20585
$929$	2.41460e13	1.06359	0.531795	−	0.846873i	$-0.321518\pi$
$929$	2.41460e13	1.06359	0.531795	+	0.846873i	$0.321518\pi$
$930$	−4.26229e12	−0.186840
$931$	−7.15136e12	−0.311972
$932$	3.90350e13	1.69466
$933$	1.93222e13	0.834814
$934$	7.58352e13	3.26069
$935$	−3.42735e13	−1.46658
$936$	1.82412e13	0.776806
$937$	4.35824e13	1.84707	0.923535	−	0.383514i	$-0.125286\pi$
$937$	4.35824e13	1.84707	0.923535	+	0.383514i	$0.125286\pi$
$938$	−4.84860e13	−2.04505
$939$	−1.63144e13	−0.684819
$940$	9.75036e12	0.407329
$941$	4.07354e12	0.169363	0.0846814	−	0.996408i	$-0.473013\pi$
$941$	4.07354e12	0.169363	0.0846814	+	0.996408i	$0.473013\pi$
$942$	−3.00411e13	−1.24304
$943$	−1.00189e12	−0.0412590
$944$	−1.17128e14	−4.80050
$945$	−3.24130e12	−0.132213
$946$	−1.27863e14	−5.19080
$947$	2.11050e12	0.0852729	0.0426365	−	0.999091i	$-0.486424\pi$
$947$	2.11050e12	0.0852729	0.0426365	+	0.999091i	$0.486424\pi$
$948$	−1.05357e13	−0.423667
$949$	7.39068e12	0.295792
$950$	2.24344e12	0.0893629
$951$	8.11454e12	0.321700
$952$	2.60535e14	10.2801
$953$	−9.09273e10	−0.00357089	−0.00178544	−	0.999998i	$-0.500568\pi$
$953$	−9.09273e10	−0.00357089	−0.00178544	+	0.999998i	$0.500568\pi$
$954$	−2.78129e13	−1.08712
$955$	7.19057e12	0.279736
$956$	2.77423e13	1.07419
$957$	1.90482e13	0.734093
$958$	−8.70151e13	−3.33772
$959$	1.96845e13	0.751520
$960$	−2.98669e13	−1.13493
$961$	−2.27898e13	−0.861955
$962$	−5.11344e13	−1.92497
$963$	−5.89667e12	−0.220947
$964$	−9.40353e13	−3.50707
$965$	1.94727e13	0.722858
$966$	−5.49692e13	−2.03106
$967$	−5.07933e13	−1.86805	−0.934023	−	0.357212i	$-0.883727\pi$
$967$	−5.07933e13	−1.86805	−0.934023	+	0.357212i	$0.883727\pi$
$968$	−1.84057e14	−6.73772
$969$	−6.96527e12	−0.253794
$970$	3.62953e12	0.131637
$971$	4.16593e13	1.50392	0.751961	−	0.659207i	$-0.229108\pi$
$971$	4.16593e13	1.50392	0.751961	+	0.659207i	$0.229108\pi$
$972$	−4.98656e12	−0.179185
$973$	2.94763e13	1.05430
$974$	−2.13054e13	−0.758532
$975$	2.17413e12	0.0770486
$976$	5.91328e13	2.08595
$977$	3.99517e13	1.40285	0.701423	−	0.712745i	$-0.252548\pi$
$977$	3.99517e13	1.40285	0.701423	+	0.712745i	$0.252548\pi$
$978$	1.74937e13	0.611444
$979$	2.47909e13	0.862522
$980$	4.90489e13	1.69868
$981$	1.45780e13	0.502558
$982$	7.17821e13	2.46328
$983$	1.13120e13	0.386411	0.193205	−	0.981158i	$-0.438112\pi$
$983$	1.13120e13	0.386411	0.193205	+	0.981158i	$0.438112\pi$
$984$	2.08084e12	0.0707555
$985$	2.32448e13	0.786797
$986$	−8.22823e13	−2.77243
$987$	−8.62251e12	−0.289205
$988$	1.28065e13	0.427587
$989$	−5.50905e13	−1.83102
$990$	−1.50186e13	−0.496903
$991$	2.77307e13	0.913333	0.456666	−	0.889638i	$-0.349043\pi$
$991$	2.77307e13	0.913333	0.456666	+	0.889638i	$0.349043\pi$
$992$	4.89011e13	1.60330
$993$	−1.99818e13	−0.652172
$994$	4.32496e13	1.40522
$995$	2.14224e13	0.692890
$996$	8.36227e13	2.69251
$997$	−3.77438e13	−1.20981	−0.604906	−	0.796297i	$-0.706789\pi$
$997$	−3.77438e13	−1.20981	−0.604906	+	0.796297i	$0.706789\pi$
$998$	−1.77113e13	−0.565149
$999$	8.97404e12	0.285065

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-44.0696 q^{2} -81.0000 q^{3} +1430.13 q^{4} +625.000 q^{5} +3569.64 q^{6} +9758.51 q^{7} -40461.6 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-44.0696 q^{2} -81.0000 q^{3} +1430.13 q^{4} +625.000 q^{5} +3569.64 q^{6} +9758.51 q^{7} -40461.6 q^{8} +6561.00 q^{9} -27543.5 q^{10} +83107.6 q^{11} -115841. q^{12} -68713.3 q^{13} -430054. q^{14} -50625.0 q^{15} +1.05090e6 q^{16} -659839. q^{17} -289141. q^{18} -130321. q^{19} +893831. q^{20} -790439. q^{21} -3.66252e6 q^{22} -1.57802e6 q^{23} +3.27739e6 q^{24} +390625. q^{25} +3.02817e6 q^{26} -531441. q^{27} +1.39559e7 q^{28} -2.82963e6 q^{29} +2.23102e6 q^{30} -1.91046e6 q^{31} -2.55965e7 q^{32} -6.73171e6 q^{33} +2.90789e7 q^{34} +6.09907e6 q^{35} +9.38308e6 q^{36} -1.68862e7 q^{37} +5.74320e6 q^{38} +5.56578e6 q^{39} -2.52885e7 q^{40} +634906. q^{41} +3.48344e7 q^{42} +3.49112e7 q^{43} +1.18855e8 q^{44} +4.10062e6 q^{45} +6.95426e7 q^{46} +1.09085e7 q^{47} -8.51230e7 q^{48} +5.48749e7 q^{49} -1.72147e7 q^{50} +5.34470e7 q^{51} -9.82689e7 q^{52} +9.61915e7 q^{53} +2.34204e7 q^{54} +5.19422e7 q^{55} -3.94845e8 q^{56} +1.05560e7 q^{57} +1.24701e8 q^{58} -1.11455e8 q^{59} -7.24003e7 q^{60} +5.62686e7 q^{61} +8.41933e7 q^{62} +6.40256e7 q^{63} +5.89964e8 q^{64} -4.29458e7 q^{65} +2.96664e8 q^{66} +1.12744e8 q^{67} -9.43656e8 q^{68} +1.27819e8 q^{69} -2.68784e8 q^{70} -1.00568e8 q^{71} -2.65469e8 q^{72} -1.07558e8 q^{73} +7.44170e8 q^{74} -3.16406e7 q^{75} -1.86376e8 q^{76} +8.11006e8 q^{77} -2.45282e8 q^{78} +9.09498e7 q^{79} +6.56813e8 q^{80} +4.30467e7 q^{81} -2.79801e7 q^{82} -7.21878e8 q^{83} -1.13043e9 q^{84} -4.12400e8 q^{85} -1.53852e9 q^{86} +2.29200e8 q^{87} -3.36267e9 q^{88} +2.98299e8 q^{89} -1.80713e8 q^{90} -6.70539e8 q^{91} -2.25677e9 q^{92} +1.54747e8 q^{93} -4.80733e8 q^{94} -8.14506e7 q^{95} +2.07331e9 q^{96} -1.31774e8 q^{97} -2.41832e9 q^{98} +5.45269e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 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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