LMFDB - Embedded newform 285.10.a.d.1.8

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:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4398 x^{10} + 11376 x^{9} + 7070146 x^{8} - 15274638 x^{7} - 5114407260 x^{6} + \cdots + 43\!\cdots\!00 $ x^12 - 3x^11 - 4398x^10 + 11376x^9 + 7070146x^8 - 15274638x^7 - 5114407260x^6 + 8284970600x^5 + 1621868619141x^4 - 1541179405015x^3 - 176385539891230x^2 + 130401229370000*x + 4344410152258400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$11.5013$ 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)

$f(q)$	$=$	\(q+8.50131 q^{2} +81.0000 q^{3} -439.728 q^{4} +625.000 q^{5} +688.606 q^{6} -8602.42 q^{7} -8090.93 q^{8} +6561.00 q^{9} +5313.32 q^{10} -2144.81 q^{11} -35617.9 q^{12} +70308.7 q^{13} -73131.8 q^{14} +50625.0 q^{15} +156357. q^{16} +263687. q^{17} +55777.1 q^{18} -130321. q^{19} -274830. q^{20} -696796. q^{21} -18233.7 q^{22} +295644. q^{23} -655366. q^{24} +390625. q^{25} +597716. q^{26} +531441. q^{27} +3.78272e6 q^{28} +1.37332e6 q^{29} +430379. q^{30} +5.69212e6 q^{31} +5.47180e6 q^{32} -173729. q^{33} +2.24168e6 q^{34} -5.37651e6 q^{35} -2.88505e6 q^{36} +2.06086e6 q^{37} -1.10790e6 q^{38} +5.69500e6 q^{39} -5.05683e6 q^{40} +4.65536e6 q^{41} -5.92368e6 q^{42} -2.99326e7 q^{43} +943131. q^{44} +4.10062e6 q^{45} +2.51336e6 q^{46} -4.23360e7 q^{47} +1.26649e7 q^{48} +3.36479e7 q^{49} +3.32082e6 q^{50} +2.13586e7 q^{51} -3.09167e7 q^{52} +1.46136e6 q^{53} +4.51795e6 q^{54} -1.34050e6 q^{55} +6.96016e7 q^{56} -1.05560e7 q^{57} +1.16750e7 q^{58} -1.52959e8 q^{59} -2.22612e7 q^{60} +3.93525e7 q^{61} +4.83905e7 q^{62} -5.64404e7 q^{63} -3.35374e7 q^{64} +4.39429e7 q^{65} -1.47693e6 q^{66} +8.09717e7 q^{67} -1.15950e8 q^{68} +2.39472e7 q^{69} -4.57074e7 q^{70} -2.70449e8 q^{71} -5.30846e7 q^{72} -2.60740e8 q^{73} +1.75200e7 q^{74} +3.16406e7 q^{75} +5.73058e7 q^{76} +1.84505e7 q^{77} +4.84150e7 q^{78} -4.52449e8 q^{79} +9.77232e7 q^{80} +4.30467e7 q^{81} +3.95767e7 q^{82} +3.90244e8 q^{83} +3.06400e8 q^{84} +1.64804e8 q^{85} -2.54466e8 q^{86} +1.11239e8 q^{87} +1.73535e7 q^{88} +2.57339e8 q^{89} +3.48607e7 q^{90} -6.04825e8 q^{91} -1.30003e8 q^{92} +4.61062e8 q^{93} -3.59911e8 q^{94} -8.14506e7 q^{95} +4.43216e8 q^{96} -6.90478e8 q^{97} +2.86052e8 q^{98} -1.40721e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 33 q^{2} + 972 q^{3} + 2751 q^{4} + 7500 q^{5} - 2673 q^{6} - 5100 q^{7} - 40215 q^{8} + 78732 q^{9} - 20625 q^{10} - 60416 q^{11} + 222831 q^{12} - 164042 q^{13} - 444762 q^{14} + 607500 q^{15}+ \cdots - 396389376 q^{99}+O(q^{100}) $ 12 * q - 33 * q^2 + 972 * q^3 + 2751 * q^4 + 7500 * q^5 - 2673 * q^6 - 5100 * q^7 - 40215 * q^8 + 78732 * q^9 - 20625 * q^10 - 60416 * q^11 + 222831 * q^12 - 164042 * q^13 - 444762 * q^14 + 607500 * q^15 + 319475 * q^16 - 552834 * q^17 - 216513 * q^18 - 1563852 * q^19 + 1719375 * q^20 - 413100 * q^21 + 708846 * q^22 - 2749174 * q^23 - 3257415 * q^24 + 4687500 * q^25 - 5159376 * q^26 + 6377292 * q^27 - 2379170 * q^28 - 3415632 * q^29 - 1670625 * q^30 - 9822574 * q^31 - 22282623 * q^32 - 4893696 * q^33 + 5214442 * q^34 - 3187500 * q^35 + 18049311 * q^36 - 24559054 * q^37 + 4300593 * q^38 - 13287402 * q^39 - 25134375 * q^40 - 35856950 * q^41 - 36025722 * q^42 - 73839462 * q^43 - 88153054 * q^44 + 49207500 * q^45 - 19966000 * q^46 - 134699358 * q^47 + 25877475 * q^48 - 64331236 * q^49 - 12890625 * q^50 - 44779554 * q^51 - 290325860 * q^52 - 74807846 * q^53 - 17537553 * q^54 - 37760000 * q^55 - 403278618 * q^56 - 126672012 * q^57 - 377474064 * q^58 - 294192102 * q^59 + 139269375 * q^60 - 184407884 * q^61 - 356900784 * q^62 - 33461100 * q^63 + 169573219 * q^64 - 102526250 * q^65 + 57416526 * q^66 - 427627864 * q^67 - 56755242 * q^68 - 222683094 * q^69 - 277976250 * q^70 - 488904216 * q^71 - 263850615 * q^72 - 184702472 * q^73 - 1424419204 * q^74 + 379687500 * q^75 - 358513071 * q^76 - 827371672 * q^77 - 417909456 * q^78 - 620531838 * q^79 + 199671875 * q^80 + 516560652 * q^81 + 100137664 * q^82 - 32273124 * q^83 - 192712770 * q^84 - 345521250 * q^85 + 1147824298 * q^86 - 276666192 * q^87 + 2717542210 * q^88 + 473499162 * q^89 - 135320625 * q^90 - 1430236924 * q^91 + 1920565904 * q^92 - 795628494 * q^93 + 2483643504 * q^94 - 977407500 * q^95 - 1804892463 * q^96 + 318965234 * q^97 + 2863543931 * q^98 - 396389376 * q^99

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 $

$2$	8.50131	0.375708	0.187854	−	0.982197i	$-0.439847\pi$
$2$	8.50131	0.375708	0.187854	+	0.982197i	$0.439847\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−439.728	−0.858843
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	688.606	0.216915
$7$	−8602.42	−1.35419	−0.677094	−	0.735896i	$-0.736761\pi$
$7$	−8602.42	−1.35419	−0.677094	+	0.735896i	$0.736761\pi$
$8$	−8090.93	−0.698383
$9$	6561.00	0.333333
$10$	5313.32	0.168022
$11$	−2144.81	−0.0441694	−0.0220847	−	0.999756i	$-0.507030\pi$
$11$	−2144.81	−0.0441694	−0.0220847	+	0.999756i	$0.507030\pi$
$12$	−35617.9	−0.495853
$13$	70308.7	0.682753	0.341377	−	0.939927i	$-0.389107\pi$
$13$	70308.7	0.682753	0.341377	+	0.939927i	$0.389107\pi$
$14$	−73131.8	−0.508780
$15$	50625.0	0.258199
$16$	156357.	0.596455
$17$	263687.	0.765717	0.382858	−	0.923807i	$-0.374940\pi$
$17$	263687.	0.765717	0.382858	+	0.923807i	$0.374940\pi$
$18$	55777.1	0.125236
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−274830.	−0.384086
$21$	−696796.	−0.781841
$22$	−18233.7	−0.0165948
$23$	295644.	0.220290	0.110145	−	0.993916i	$-0.464869\pi$
$23$	295644.	0.220290	0.110145	+	0.993916i	$0.464869\pi$
$24$	−655366.	−0.403212
$25$	390625.	0.200000
$26$	597716.	0.256516
$27$	531441.	0.192450
$28$	3.78272e6	1.16304
$29$	1.37332e6	0.360562	0.180281	−	0.983615i	$-0.442299\pi$
$29$	1.37332e6	0.360562	0.180281	+	0.983615i	$0.442299\pi$
$30$	430379.	0.0970075
$31$	5.69212e6	1.10700	0.553499	−	0.832850i	$-0.313292\pi$
$31$	5.69212e6	1.10700	0.553499	+	0.832850i	$0.313292\pi$
$32$	5.47180e6	0.922476
$33$	−173729.	−0.0255012
$34$	2.24168e6	0.287686
$35$	−5.37651e6	−0.605612
$36$	−2.88505e6	−0.286281
$37$	2.06086e6	0.180776	0.0903882	−	0.995907i	$-0.471189\pi$
$37$	2.06086e6	0.180776	0.0903882	+	0.995907i	$0.471189\pi$
$38$	−1.10790e6	−0.0861934
$39$	5.69500e6	0.394188
$40$	−5.05683e6	−0.312326
$41$	4.65536e6	0.257292	0.128646	−	0.991691i	$-0.458937\pi$
$41$	4.65536e6	0.257292	0.128646	+	0.991691i	$0.458937\pi$
$42$	−5.92368e6	−0.293744
$43$	−2.99326e7	−1.33517	−0.667585	−	0.744534i	$-0.732672\pi$
$43$	−2.99326e7	−1.33517	−0.667585	+	0.744534i	$0.732672\pi$
$44$	943131.	0.0379346
$45$	4.10062e6	0.149071
$46$	2.51336e6	0.0827647
$47$	−4.23360e7	−1.26552	−0.632760	−	0.774348i	$-0.718078\pi$
$47$	−4.23360e7	−1.26552	−0.632760	+	0.774348i	$0.718078\pi$
$48$	1.26649e7	0.344363
$49$	3.36479e7	0.833827
$50$	3.32082e6	0.0751417
$51$	2.13586e7	0.442087
$52$	−3.09167e7	−0.586378
$53$	1.46136e6	0.0254400	0.0127200	−	0.999919i	$-0.495951\pi$
$53$	1.46136e6	0.0254400	0.0127200	+	0.999919i	$0.495951\pi$
$54$	4.51795e6	0.0723051
$55$	−1.34050e6	−0.0197531
$56$	6.96016e7	0.945743
$57$	−1.05560e7	−0.132453
$58$	1.16750e7	0.135466
$59$	−1.52959e8	−1.64339	−0.821695	−	0.569928i	$-0.806971\pi$
$59$	−1.52959e8	−1.64339	−0.821695	+	0.569928i	$0.806971\pi$
$60$	−2.22612e7	−0.221752
$61$	3.93525e7	0.363905	0.181952	−	0.983307i	$-0.441758\pi$
$61$	3.93525e7	0.363905	0.181952	+	0.983307i	$0.441758\pi$
$62$	4.83905e7	0.415908
$63$	−5.64404e7	−0.451396
$64$	−3.35374e7	−0.249873
$65$	4.39429e7	0.305337
$66$	−1.47693e6	−0.00958101
$67$	8.09717e7	0.490904	0.245452	−	0.969409i	$-0.421064\pi$
$67$	8.09717e7	0.490904	0.245452	+	0.969409i	$0.421064\pi$
$68$	−1.15950e8	−0.657630
$69$	2.39472e7	0.127184
$70$	−4.57074e7	−0.227533
$71$	−2.70449e8	−1.26306	−0.631529	−	0.775352i	$-0.717572\pi$
$71$	−2.70449e8	−1.26306	−0.631529	+	0.775352i	$0.717572\pi$
$72$	−5.30846e7	−0.232794
$73$	−2.60740e8	−1.07462	−0.537310	−	0.843385i	$-0.680559\pi$
$73$	−2.60740e8	−1.07462	−0.537310	+	0.843385i	$0.680559\pi$
$74$	1.75200e7	0.0679192
$75$	3.16406e7	0.115470
$76$	5.73058e7	0.197032
$77$	1.84505e7	0.0598137
$78$	4.84150e7	0.148100
$79$	−4.52449e8	−1.30691	−0.653457	−	0.756963i	$-0.726682\pi$
$79$	−4.52449e8	−1.30691	−0.653457	+	0.756963i	$0.726682\pi$
$80$	9.77232e7	0.266743
$81$	4.30467e7	0.111111
$82$	3.95767e7	0.0966667
$83$	3.90244e8	0.902578	0.451289	−	0.892378i	$-0.350964\pi$
$83$	3.90244e8	0.902578	0.451289	+	0.892378i	$0.350964\pi$
$84$	3.06400e8	0.671479
$85$	1.64804e8	0.342439
$86$	−2.54466e8	−0.501634
$87$	1.11239e8	0.208171
$88$	1.73535e7	0.0308471
$89$	2.57339e8	0.434760	0.217380	−	0.976087i	$-0.430249\pi$
$89$	2.57339e8	0.434760	0.217380	+	0.976087i	$0.430249\pi$
$90$	3.48607e7	0.0560073
$91$	−6.04825e8	−0.924577
$92$	−1.30003e8	−0.189194
$93$	4.61062e8	0.639125
$94$	−3.59911e8	−0.475467
$95$	−8.14506e7	−0.102598
$96$	4.43216e8	0.532592
$97$	−6.90478e8	−0.791912	−0.395956	−	0.918269i	$-0.629587\pi$
$97$	−6.90478e8	−0.791912	−0.395956	+	0.918269i	$0.629587\pi$
$98$	2.86052e8	0.313276
$99$	−1.40721e7	−0.0147231
$100$	−1.71769e8	−0.171769
$101$	8.09329e8	0.773889	0.386945	−	0.922103i	$-0.373530\pi$
$101$	8.09329e8	0.773889	0.386945	+	0.922103i	$0.373530\pi$
$102$	1.81576e8	0.166096
$103$	−4.61235e8	−0.403789	−0.201895	−	0.979407i	$-0.564710\pi$
$103$	−4.61235e8	−0.403789	−0.201895	+	0.979407i	$0.564710\pi$
$104$	−5.68863e8	−0.476823
$105$	−4.35497e8	−0.349650
$106$	1.24235e7	0.00955801
$107$	2.07157e9	1.52782	0.763910	−	0.645323i	$-0.223277\pi$
$107$	2.07157e9	1.52782	0.763910	+	0.645323i	$0.223277\pi$
$108$	−2.33689e8	−0.165284
$109$	−1.48763e9	−1.00943	−0.504716	−	0.863286i	$-0.668403\pi$
$109$	−1.48763e9	−1.00943	−0.504716	+	0.863286i	$0.668403\pi$
$110$	−1.13960e7	−0.00742142
$111$	1.66930e8	0.104371
$112$	−1.34505e9	−0.807712
$113$	−1.80621e9	−1.04212	−0.521058	−	0.853521i	$-0.674462\pi$
$113$	−1.80621e9	−1.04212	−0.521058	+	0.853521i	$0.674462\pi$
$114$	−8.97398e7	−0.0497638
$115$	1.84778e8	0.0985165
$116$	−6.03886e8	−0.309666
$117$	4.61295e8	0.227584
$118$	−1.30035e9	−0.617435
$119$	−2.26834e9	−1.03692
$120$	−4.09604e8	−0.180322
$121$	−2.35335e9	−0.998049
$122$	3.34548e8	0.136722
$123$	3.77084e8	0.148547
$124$	−2.50298e9	−0.950737
$125$	2.44141e8	0.0894427
$126$	−4.79818e8	−0.169593
$127$	5.96178e7	0.0203357	0.0101679	−	0.999948i	$-0.496763\pi$
$127$	5.96178e7	0.0203357	0.0101679	+	0.999948i	$0.496763\pi$
$128$	−3.08667e9	−1.01636
$129$	−2.42454e9	−0.770860
$130$	3.73572e8	0.114718
$131$	−1.77693e9	−0.527170	−0.263585	−	0.964636i	$-0.584905\pi$
$131$	−1.77693e9	−0.527170	−0.263585	+	0.964636i	$0.584905\pi$
$132$	7.63936e7	0.0219015
$133$	1.12108e9	0.310672
$134$	6.88365e8	0.184437
$135$	3.32151e8	0.0860663
$136$	−2.13347e9	−0.534763
$137$	5.67513e9	1.37636	0.688182	−	0.725538i	$-0.258409\pi$
$137$	5.67513e9	1.37636	0.688182	+	0.725538i	$0.258409\pi$
$138$	2.03582e8	0.0477842
$139$	−3.44001e9	−0.781615	−0.390808	−	0.920472i	$-0.627804\pi$
$139$	−3.44001e9	−0.781615	−0.390808	+	0.920472i	$0.627804\pi$
$140$	2.36420e9	0.520125
$141$	−3.42921e9	−0.730649
$142$	−2.29917e9	−0.474541
$143$	−1.50799e8	−0.0301568
$144$	1.02586e9	0.198818
$145$	8.58323e8	0.161248
$146$	−2.21663e9	−0.403744
$147$	2.72548e9	0.481411
$148$	−9.06219e8	−0.155259
$149$	2.87682e9	0.478162	0.239081	−	0.971000i	$-0.423154\pi$
$149$	2.87682e9	0.478162	0.239081	+	0.971000i	$0.423154\pi$
$150$	2.68987e8	0.0433831
$151$	1.91829e9	0.300274	0.150137	−	0.988665i	$-0.452029\pi$
$151$	1.91829e9	0.300274	0.150137	+	0.988665i	$0.452029\pi$
$152$	1.05442e9	0.160220
$153$	1.73005e9	0.255239
$154$	1.56854e8	0.0224725
$155$	3.55758e9	0.495064
$156$	−2.50425e9	−0.338546
$157$	−8.04093e9	−1.05623	−0.528114	−	0.849173i	$-0.677101\pi$
$157$	−8.04093e9	−1.05623	−0.528114	+	0.849173i	$0.677101\pi$
$158$	−3.84641e9	−0.491019
$159$	1.18370e8	0.0146878
$160$	3.41987e9	0.412544
$161$	−2.54325e9	−0.298314
$162$	3.65954e8	0.0417454
$163$	1.11263e9	0.123455	0.0617273	−	0.998093i	$-0.480339\pi$
$163$	1.11263e9	0.123455	0.0617273	+	0.998093i	$0.480339\pi$
$164$	−2.04709e9	−0.220973
$165$	−1.08581e8	−0.0114045
$166$	3.31759e9	0.339106
$167$	2.76400e9	0.274988	0.137494	−	0.990503i	$-0.456095\pi$
$167$	2.76400e9	0.274988	0.137494	+	0.990503i	$0.456095\pi$
$168$	5.63773e9	0.546025
$169$	−5.66119e9	−0.533848
$170$	1.40105e9	0.128657
$171$	−8.55036e8	−0.0764719
$172$	1.31622e10	1.14670
$173$	3.79638e9	0.322227	0.161114	−	0.986936i	$-0.448491\pi$
$173$	3.79638e9	0.322227	0.161114	+	0.986936i	$0.448491\pi$
$174$	9.45675e8	0.0782114
$175$	−3.36032e9	−0.270838
$176$	−3.35356e8	−0.0263450
$177$	−1.23897e10	−0.948811
$178$	2.18772e9	0.163343
$179$	1.07013e10	0.779107	0.389554	−	0.921004i	$-0.372629\pi$
$179$	1.07013e10	0.779107	0.389554	+	0.921004i	$0.372629\pi$
$180$	−1.80316e9	−0.128029
$181$	2.07548e10	1.43736	0.718679	−	0.695342i	$-0.244747\pi$
$181$	2.07548e10	1.43736	0.718679	+	0.695342i	$0.244747\pi$
$182$	−5.14180e9	−0.347371
$183$	3.18755e9	0.210101
$184$	−2.39204e9	−0.153847
$185$	1.28804e9	0.0808456
$186$	3.91963e9	0.240125
$187$	−5.65557e8	−0.0338212
$188$	1.86163e10	1.08688
$189$	−4.57168e9	−0.260614
$190$	−6.92437e8	−0.0385469
$191$	−1.39914e10	−0.760695	−0.380348	−	0.924844i	$-0.624196\pi$
$191$	−1.39914e10	−0.760695	−0.380348	+	0.924844i	$0.624196\pi$
$192$	−2.71653e9	−0.144264
$193$	−2.41922e10	−1.25507	−0.627535	−	0.778588i	$-0.715936\pi$
$193$	−2.41922e10	−1.25507	−0.627535	+	0.778588i	$0.715936\pi$
$194$	−5.86997e9	−0.297528
$195$	3.55938e9	0.176286
$196$	−1.47959e10	−0.716127
$197$	6.24104e9	0.295229	0.147615	−	0.989045i	$-0.452840\pi$
$197$	6.24104e9	0.295229	0.147615	+	0.989045i	$0.452840\pi$
$198$	−1.19631e8	−0.00553160
$199$	−3.55762e10	−1.60813	−0.804064	−	0.594543i	$-0.797333\pi$
$199$	−3.55762e10	−1.60813	−0.804064	+	0.594543i	$0.797333\pi$
$200$	−3.16052e9	−0.139677
$201$	6.55871e9	0.283424
$202$	6.88035e9	0.290757
$203$	−1.18138e10	−0.488269
$204$	−9.39198e9	−0.379683
$205$	2.90960e9	0.115064
$206$	−3.92110e9	−0.151707
$207$	1.93972e9	0.0734299
$208$	1.09933e10	0.407232
$209$	2.79513e8	0.0101331
$210$	−3.70230e9	−0.131366
$211$	−1.51159e10	−0.525003	−0.262501	−	0.964932i	$-0.584547\pi$
$211$	−1.51159e10	−0.525003	−0.262501	+	0.964932i	$0.584547\pi$
$212$	−6.42602e8	−0.0218489
$213$	−2.19064e10	−0.729227
$214$	1.76110e10	0.574015
$215$	−1.87079e10	−0.597106
$216$	−4.29985e9	−0.134404
$217$	−4.89660e10	−1.49908
$218$	−1.26468e10	−0.379252
$219$	−2.11199e10	−0.620432
$220$	5.89457e8	0.0169649
$221$	1.85395e10	0.522796
$222$	1.41912e9	0.0392132
$223$	−2.92879e10	−0.793080	−0.396540	−	0.918018i	$-0.629789\pi$
$223$	−2.92879e10	−0.793080	−0.396540	+	0.918018i	$0.629789\pi$
$224$	−4.70707e10	−1.24921
$225$	2.56289e9	0.0666667
$226$	−1.53552e10	−0.391531
$227$	−6.62027e10	−1.65485	−0.827426	−	0.561574i	$-0.810196\pi$
$227$	−6.62027e10	−1.65485	−0.827426	+	0.561574i	$0.810196\pi$
$228$	4.64177e9	0.113757
$229$	−2.98555e10	−0.717406	−0.358703	−	0.933452i	$-0.616781\pi$
$229$	−2.98555e10	−0.717406	−0.358703	+	0.933452i	$0.616781\pi$
$230$	1.57085e9	0.0370135
$231$	1.49449e9	0.0345334
$232$	−1.11114e10	−0.251810
$233$	−1.62148e10	−0.360421	−0.180211	−	0.983628i	$-0.557678\pi$
$233$	−1.62148e10	−0.360421	−0.180211	+	0.983628i	$0.557678\pi$
$234$	3.92161e9	0.0855054
$235$	−2.64600e10	−0.565958
$236$	6.72602e10	1.41141
$237$	−3.66483e10	−0.754548
$238$	−1.92839e10	−0.389581
$239$	−8.99004e10	−1.78226	−0.891130	−	0.453749i	$-0.850086\pi$
$239$	−8.99004e10	−1.78226	−0.891130	+	0.453749i	$0.850086\pi$
$240$	7.91558e9	0.154004
$241$	9.07409e10	1.73271	0.866356	−	0.499426i	$-0.166456\pi$
$241$	9.07409e10	1.73271	0.866356	+	0.499426i	$0.166456\pi$
$242$	−2.00065e10	−0.374975
$243$	3.48678e9	0.0641500
$244$	−1.73044e10	−0.312537
$245$	2.10300e10	0.372899
$246$	3.20571e9	0.0558105
$247$	−9.16270e9	−0.156634
$248$	−4.60546e10	−0.773108
$249$	3.16098e10	0.521104
$250$	2.07552e9	0.0336044
$251$	−1.91156e10	−0.303987	−0.151994	−	0.988381i	$-0.548569\pi$
$251$	−1.91156e10	−0.303987	−0.151994	+	0.988381i	$0.548569\pi$
$252$	2.48184e10	0.387679
$253$	−6.34100e8	−0.00973005
$254$	5.06830e8	0.00764030
$255$	1.33491e10	0.197707
$256$	−9.06964e9	−0.131981
$257$	4.66528e10	0.667081	0.333541	−	0.942736i	$-0.391757\pi$
$257$	4.66528e10	0.667081	0.333541	+	0.942736i	$0.391757\pi$
$258$	−2.06118e10	−0.289619
$259$	−1.77284e10	−0.244805
$260$	−1.93229e10	−0.262236
$261$	9.01034e9	0.120187
$262$	−1.51063e10	−0.198062
$263$	−3.87982e10	−0.500047	−0.250023	−	0.968240i	$-0.580438\pi$
$263$	−3.87982e10	−0.500047	−0.250023	+	0.968240i	$0.580438\pi$
$264$	1.40563e9	0.0178096
$265$	9.13352e8	0.0113771
$266$	9.53061e9	0.116722
$267$	2.08444e10	0.251009
$268$	−3.56055e10	−0.421609
$269$	3.81888e10	0.444683	0.222342	−	0.974969i	$-0.428630\pi$
$269$	3.81888e10	0.444683	0.222342	+	0.974969i	$0.428630\pi$
$270$	2.82372e9	0.0323358
$271$	1.12956e11	1.27218	0.636088	−	0.771617i	$-0.280552\pi$
$271$	1.12956e11	1.27218	0.636088	+	0.771617i	$0.280552\pi$
$272$	4.12293e10	0.456715
$273$	−4.89908e10	−0.533805
$274$	4.82460e10	0.517111
$275$	−8.37815e8	−0.00883387
$276$	−1.05302e10	−0.109231
$277$	−1.75341e11	−1.78947	−0.894737	−	0.446594i	$-0.852637\pi$
$277$	−1.75341e11	−1.78947	−0.894737	+	0.446594i	$0.852637\pi$
$278$	−2.92446e10	−0.293659
$279$	3.73460e10	0.368999
$280$	4.35010e10	0.422949
$281$	−7.22309e10	−0.691105	−0.345553	−	0.938399i	$-0.612309\pi$
$281$	−7.22309e10	−0.691105	−0.345553	+	0.938399i	$0.612309\pi$
$282$	−2.91528e10	−0.274511
$283$	−8.68728e10	−0.805090	−0.402545	−	0.915400i	$-0.631874\pi$
$283$	−8.68728e10	−0.805090	−0.402545	+	0.915400i	$0.631874\pi$
$284$	1.18924e11	1.08477
$285$	−6.59750e9	−0.0592349
$286$	−1.28199e9	−0.0113302
$287$	−4.00473e10	−0.348422
$288$	3.59005e10	0.307492
$289$	−4.90572e10	−0.413678
$290$	7.29688e9	0.0605823
$291$	−5.59287e10	−0.457211
$292$	1.14655e11	0.922930
$293$	−1.30875e11	−1.03742	−0.518708	−	0.854951i	$-0.673587\pi$
$293$	−1.30875e11	−1.03742	−0.518708	+	0.854951i	$0.673587\pi$
$294$	2.31702e10	0.180870
$295$	−9.55993e10	−0.734946
$296$	−1.66743e10	−0.126251
$297$	−1.13984e9	−0.00850040
$298$	2.44568e10	0.179650
$299$	2.07863e10	0.150403
$300$	−1.39133e10	−0.0991707
$301$	2.57493e11	1.80807
$302$	1.63080e10	0.112815
$303$	6.55556e10	0.446805
$304$	−2.03766e10	−0.136836
$305$	2.45953e10	0.162743
$306$	1.47077e10	0.0958954
$307$	−1.56180e11	−1.00346	−0.501732	−	0.865023i	$-0.667304\pi$
$307$	−1.56180e11	−1.00346	−0.501732	+	0.865023i	$0.667304\pi$
$308$	−8.11321e9	−0.0513706
$309$	−3.73600e10	−0.233128
$310$	3.02441e10	0.186000
$311$	2.89274e10	0.175343	0.0876713	−	0.996149i	$-0.472057\pi$
$311$	2.89274e10	0.175343	0.0876713	+	0.996149i	$0.472057\pi$
$312$	−4.60779e10	−0.275294
$313$	9.15012e10	0.538862	0.269431	−	0.963020i	$-0.413164\pi$
$313$	9.15012e10	0.538862	0.269431	+	0.963020i	$0.413164\pi$
$314$	−6.83585e10	−0.396834
$315$	−3.52753e10	−0.201871
$316$	1.98954e11	1.12244
$317$	−5.26556e10	−0.292872	−0.146436	−	0.989220i	$-0.546780\pi$
$317$	−5.26556e10	−0.292872	−0.146436	+	0.989220i	$0.546780\pi$
$318$	1.00630e9	0.00551832
$319$	−2.94550e9	−0.0159258
$320$	−2.09608e10	−0.111746
$321$	1.67797e11	0.882087
$322$	−2.16210e10	−0.112079
$323$	−3.43639e10	−0.175667
$324$	−1.89288e10	−0.0954270
$325$	2.74643e10	0.136551
$326$	9.45882e9	0.0463829
$327$	−1.20498e11	−0.582795
$328$	−3.76662e10	−0.179688
$329$	3.64192e11	1.71375
$330$	−9.23080e8	−0.00428476
$331$	−1.18390e11	−0.542111	−0.271056	−	0.962564i	$-0.587373\pi$
$331$	−1.18390e11	−0.542111	−0.271056	+	0.962564i	$0.587373\pi$
$332$	−1.71601e11	−0.775173
$333$	1.35213e10	0.0602588
$334$	2.34977e10	0.103315
$335$	5.06073e10	0.219539
$336$	−1.08949e11	−0.466333
$337$	5.53843e10	0.233912	0.116956	−	0.993137i	$-0.462686\pi$
$337$	5.53843e10	0.233912	0.116956	+	0.993137i	$0.462686\pi$
$338$	−4.81275e10	−0.200571
$339$	−1.46303e11	−0.601666
$340$	−7.24690e10	−0.294101
$341$	−1.22085e10	−0.0488954
$342$	−7.26893e9	−0.0287311
$343$	5.76849e10	0.225029
$344$	2.42183e11	0.932459
$345$	1.49670e10	0.0568785
$346$	3.22742e10	0.121063
$347$	1.58194e11	0.585744	0.292872	−	0.956152i	$-0.405389\pi$
$347$	1.58194e11	0.585744	0.292872	+	0.956152i	$0.405389\pi$
$348$	−4.89147e10	−0.178786
$349$	−3.34223e11	−1.20593	−0.602964	−	0.797768i	$-0.706014\pi$
$349$	−3.34223e11	−1.20593	−0.602964	+	0.797768i	$0.706014\pi$
$350$	−2.85671e10	−0.101756
$351$	3.73649e10	0.131396
$352$	−1.17360e10	−0.0407452
$353$	2.89176e11	0.991233	0.495616	−	0.868542i	$-0.334942\pi$
$353$	2.89176e11	0.991233	0.495616	+	0.868542i	$0.334942\pi$
$354$	−1.05328e11	−0.356476
$355$	−1.69031e11	−0.564857
$356$	−1.13159e11	−0.373391
$357$	−1.83736e11	−0.598669
$358$	9.09749e10	0.292717
$359$	5.54463e11	1.76176	0.880882	−	0.473336i	$-0.156950\pi$
$359$	5.54463e11	1.76176	0.880882	+	0.473336i	$0.156950\pi$
$360$	−3.31779e10	−0.104109
$361$	1.69836e10	0.0526316
$362$	1.76443e11	0.540027
$363$	−1.90621e11	−0.576224
$364$	2.65958e11	0.794067
$365$	−1.62963e11	−0.480585
$366$	2.70984e10	0.0789365
$367$	−1.93025e11	−0.555414	−0.277707	−	0.960666i	$-0.589574\pi$
$367$	−1.93025e11	−0.555414	−0.277707	+	0.960666i	$0.589574\pi$
$368$	4.62260e10	0.131393
$369$	3.05438e10	0.0857639
$370$	1.09500e10	0.0303744
$371$	−1.25712e10	−0.0344505
$372$	−2.02742e11	−0.548908
$373$	2.11386e11	0.565441	0.282720	−	0.959202i	$-0.408763\pi$
$373$	2.11386e11	0.565441	0.282720	+	0.959202i	$0.408763\pi$
$374$	−4.80798e9	−0.0127069
$375$	1.97754e10	0.0516398
$376$	3.42538e11	0.883818
$377$	9.65562e10	0.246175
$378$	−3.88652e10	−0.0979148
$379$	3.57260e11	0.889422	0.444711	−	0.895674i	$-0.353306\pi$
$379$	3.57260e11	0.889422	0.444711	+	0.895674i	$0.353306\pi$
$380$	3.58161e10	0.0881155
$381$	4.82905e9	0.0117408
$382$	−1.18945e11	−0.285800
$383$	−5.89233e11	−1.39924	−0.699621	−	0.714515i	$-0.746648\pi$
$383$	−5.89233e11	−1.39924	−0.699621	+	0.714515i	$0.746648\pi$
$384$	−2.50020e11	−0.586793
$385$	1.15316e10	0.0267495
$386$	−2.05666e11	−0.471541
$387$	−1.96388e11	−0.445056
$388$	3.03622e11	0.680128
$389$	−6.40517e11	−1.41827	−0.709133	−	0.705075i	$-0.750913\pi$
$389$	−6.40517e11	−1.41827	−0.709133	+	0.705075i	$0.750913\pi$
$390$	3.02594e10	0.0662322
$391$	7.79574e10	0.168679
$392$	−2.72243e11	−0.582331
$393$	−1.43932e11	−0.304362
$394$	5.30570e10	0.110920
$395$	−2.82780e11	−0.584470
$396$	6.18788e9	0.0126449
$397$	5.48741e11	1.10869	0.554345	−	0.832287i	$-0.312969\pi$
$397$	5.48741e11	1.10869	0.554345	+	0.832287i	$0.312969\pi$
$398$	−3.02444e11	−0.604187
$399$	9.08071e10	0.179367
$400$	6.10770e10	0.119291
$401$	2.21962e11	0.428676	0.214338	−	0.976760i	$-0.431241\pi$
$401$	2.21962e11	0.428676	0.214338	+	0.976760i	$0.431241\pi$
$402$	5.57576e10	0.106485
$403$	4.00205e11	0.755806
$404$	−3.55884e11	−0.664649
$405$	2.69042e10	0.0496904
$406$	−1.00433e11	−0.183447
$407$	−4.42016e9	−0.00798478
$408$	−1.72811e11	−0.308746
$409$	−9.17718e10	−0.162164	−0.0810820	−	0.996707i	$-0.525838\pi$
$409$	−9.17718e10	−0.162164	−0.0810820	+	0.996707i	$0.525838\pi$
$410$	2.47354e10	0.0432306
$411$	4.59685e11	0.794644
$412$	2.02818e11	0.346792
$413$	1.31582e12	2.22546
$414$	1.64902e10	0.0275882
$415$	2.43903e11	0.403645
$416$	3.84715e11	0.629824
$417$	−2.78641e11	−0.451266
$418$	2.37623e9	0.00380711
$419$	8.34752e11	1.32311	0.661553	−	0.749899i	$-0.269898\pi$
$419$	8.34752e11	1.32311	0.661553	+	0.749899i	$0.269898\pi$
$420$	1.91500e11	0.300295
$421$	−3.68245e11	−0.571304	−0.285652	−	0.958333i	$-0.592210\pi$
$421$	−3.68245e11	−0.571304	−0.285652	+	0.958333i	$0.592210\pi$
$422$	−1.28505e11	−0.197248
$423$	−2.77766e11	−0.421840
$424$	−1.18238e10	−0.0177668
$425$	1.03003e11	0.153143
$426$	−1.86233e11	−0.273977
$427$	−3.38526e11	−0.492796
$428$	−9.10926e11	−1.31216
$429$	−1.22147e10	−0.0174110
$430$	−1.59041e11	−0.224338
$431$	−5.03089e11	−0.702259	−0.351129	−	0.936327i	$-0.614202\pi$
$431$	−5.03089e11	−0.702259	−0.351129	+	0.936327i	$0.614202\pi$
$432$	8.30945e10	0.114788
$433$	8.95533e11	1.22430	0.612148	−	0.790743i	$-0.290306\pi$
$433$	8.95533e11	1.22430	0.612148	+	0.790743i	$0.290306\pi$
$434$	−4.16275e11	−0.563218
$435$	6.95242e10	0.0930967
$436$	6.54154e11	0.866943
$437$	−3.85286e10	−0.0505379
$438$	−1.79547e11	−0.233102
$439$	4.16326e11	0.534987	0.267494	−	0.963560i	$-0.413805\pi$
$439$	4.16326e11	0.534987	0.267494	+	0.963560i	$0.413805\pi$
$440$	1.08459e10	0.0137953
$441$	2.20764e11	0.277942
$442$	1.57610e11	0.196419
$443$	8.58126e11	1.05861	0.529303	−	0.848433i	$-0.322453\pi$
$443$	8.58126e11	1.05861	0.529303	+	0.848433i	$0.322453\pi$
$444$	−7.34037e10	−0.0896386
$445$	1.60837e11	0.194431
$446$	−2.48986e11	−0.297967
$447$	2.33023e11	0.276067
$448$	2.88502e11	0.338375
$449$	8.93036e11	1.03696	0.518478	−	0.855091i	$-0.326499\pi$
$449$	8.93036e11	1.03696	0.518478	+	0.855091i	$0.326499\pi$
$450$	2.17879e10	0.0250472
$451$	−9.98485e9	−0.0113644
$452$	7.94242e11	0.895014
$453$	1.55381e11	0.173363
$454$	−5.62810e11	−0.621742
$455$	−3.78015e11	−0.413483
$456$	8.54079e10	0.0925031
$457$	9.88248e11	1.05985	0.529924	−	0.848045i	$-0.322221\pi$
$457$	9.88248e11	1.05985	0.529924	+	0.848045i	$0.322221\pi$
$458$	−2.53811e11	−0.269535
$459$	1.40134e11	0.147362
$460$	−8.12518e10	−0.0846102
$461$	5.23638e11	0.539979	0.269989	−	0.962863i	$-0.412980\pi$
$461$	5.23638e11	0.539979	0.269989	+	0.962863i	$0.412980\pi$
$462$	1.27051e10	0.0129745
$463$	−2.36334e11	−0.239008	−0.119504	−	0.992834i	$-0.538130\pi$
$463$	−2.36334e11	−0.239008	−0.119504	+	0.992834i	$0.538130\pi$
$464$	2.14728e11	0.215059
$465$	2.88164e11	0.285825
$466$	−1.37847e11	−0.135413
$467$	−3.42883e11	−0.333595	−0.166798	−	0.985991i	$-0.553343\pi$
$467$	−3.42883e11	−0.333595	−0.166798	+	0.985991i	$0.553343\pi$
$468$	−2.02844e11	−0.195459
$469$	−6.96552e11	−0.664777
$470$	−2.24945e11	−0.212635
$471$	−6.51316e11	−0.609814
$472$	1.23758e12	1.14772
$473$	6.41996e10	0.0589736
$474$	−3.11559e11	−0.283490
$475$	−5.09066e10	−0.0458831
$476$	9.97453e11	0.890556
$477$	9.58800e9	0.00847999
$478$	−7.64271e11	−0.669610
$479$	−9.37114e11	−0.813359	−0.406680	−	0.913571i	$-0.633313\pi$
$479$	−9.37114e11	−0.813359	−0.406680	+	0.913571i	$0.633313\pi$
$480$	2.77010e11	0.238182
$481$	1.44897e11	0.123426
$482$	7.71417e11	0.650995
$483$	−2.06004e11	−0.172232
$484$	1.03483e12	0.857168
$485$	−4.31549e11	−0.354154
$486$	2.96422e10	0.0241017
$487$	7.19365e11	0.579520	0.289760	−	0.957099i	$-0.406424\pi$
$487$	7.19365e11	0.579520	0.289760	+	0.957099i	$0.406424\pi$
$488$	−3.18398e11	−0.254145
$489$	9.01231e10	0.0712765
$490$	1.78782e11	0.140101
$491$	−3.72813e11	−0.289484	−0.144742	−	0.989469i	$-0.546235\pi$
$491$	−3.72813e11	−0.289484	−0.144742	+	0.989469i	$0.546235\pi$
$492$	−1.65814e11	−0.127579
$493$	3.62126e11	0.276088
$494$	−7.78949e10	−0.0588489
$495$	−8.79505e9	−0.00658438
$496$	8.90003e11	0.660274
$497$	2.32652e12	1.71042
$498$	2.68725e11	0.195783
$499$	1.06787e11	0.0771022	0.0385511	−	0.999257i	$-0.487726\pi$
$499$	1.06787e11	0.0771022	0.0385511	+	0.999257i	$0.487726\pi$
$500$	−1.07355e11	−0.0768173
$501$	2.23884e11	0.158765
$502$	−1.62507e11	−0.114211
$503$	4.25008e11	0.296034	0.148017	−	0.988985i	$-0.452711\pi$
$503$	4.25008e11	0.296034	0.148017	+	0.988985i	$0.452711\pi$
$504$	4.56656e11	0.315248
$505$	5.05830e11	0.346094
$506$	−5.39068e9	−0.00365566
$507$	−4.58556e11	−0.308217
$508$	−2.62156e10	−0.0174652
$509$	1.79395e12	1.18462	0.592310	−	0.805710i	$-0.298216\pi$
$509$	1.79395e12	1.18462	0.592310	+	0.805710i	$0.298216\pi$
$510$	1.13485e11	0.0742802
$511$	2.24299e12	1.45524
$512$	1.50327e12	0.966769
$513$	−6.92579e10	−0.0441511
$514$	3.96610e11	0.250628
$515$	−2.88272e11	−0.180580
$516$	1.06614e12	0.662048
$517$	9.08025e10	0.0558972
$518$	−1.50715e11	−0.0919754
$519$	3.07507e11	0.186038
$520$	−3.55539e11	−0.213242
$521$	−6.85487e11	−0.407596	−0.203798	−	0.979013i	$-0.565329\pi$
$521$	−6.85487e11	−0.407596	−0.203798	+	0.979013i	$0.565329\pi$
$522$	7.65997e10	0.0451554
$523$	−2.20856e12	−1.29078	−0.645390	−	0.763853i	$-0.723305\pi$
$523$	−2.20856e12	−1.29078	−0.645390	+	0.763853i	$0.723305\pi$
$524$	7.81368e11	0.452756
$525$	−2.72186e11	−0.156368
$526$	−3.29836e11	−0.187872
$527$	1.50094e12	0.847646
$528$	−2.71638e10	−0.0152103
$529$	−1.71375e12	−0.951472
$530$	7.76469e9	0.00427447
$531$	−1.00356e12	−0.547796
$532$	−4.92968e11	−0.266819
$533$	3.27312e11	0.175667
$534$	1.77205e11	0.0943062
$535$	1.29473e12	0.683262
$536$	−6.55136e11	−0.342839
$537$	8.66804e11	0.449818
$538$	3.24655e11	0.167071
$539$	−7.21684e10	−0.0368296
$540$	−1.46056e11	−0.0739175
$541$	−4.05993e11	−0.203765	−0.101883	−	0.994796i	$-0.532487\pi$
$541$	−4.05993e11	−0.203765	−0.101883	+	0.994796i	$0.532487\pi$
$542$	9.60273e11	0.477967
$543$	1.68114e12	0.829859
$544$	1.44284e12	0.706355
$545$	−9.29771e11	−0.451431
$546$	−4.16486e11	−0.200555
$547$	−6.34987e11	−0.303265	−0.151632	−	0.988437i	$-0.548453\pi$
$547$	−6.34987e11	−0.303265	−0.151632	+	0.988437i	$0.548453\pi$
$548$	−2.49551e12	−1.18208
$549$	2.58192e11	0.121302
$550$	−7.12253e9	−0.00331896
$551$	−1.78972e11	−0.0827186
$552$	−1.93755e11	−0.0888233
$553$	3.89215e12	1.76981
$554$	−1.49063e12	−0.672320
$555$	1.04331e11	0.0466763
$556$	1.51267e12	0.671285
$557$	−1.86712e11	−0.0821909	−0.0410955	−	0.999155i	$-0.513085\pi$
$557$	−1.86712e11	−0.0821909	−0.0410955	+	0.999155i	$0.513085\pi$
$558$	3.17490e11	0.138636
$559$	−2.10452e12	−0.911591
$560$	−8.40655e11	−0.361220
$561$	−4.58101e10	−0.0195267
$562$	−6.14057e11	−0.259654
$563$	6.11205e11	0.256389	0.128194	−	0.991749i	$-0.459082\pi$
$563$	6.11205e11	0.256389	0.128194	+	0.991749i	$0.459082\pi$
$564$	1.50792e12	0.627513
$565$	−1.12888e12	−0.466048
$566$	−7.38532e11	−0.302479
$567$	−3.70306e11	−0.150465
$568$	2.18819e12	0.882098
$569$	−2.16442e12	−0.865638	−0.432819	−	0.901481i	$-0.642481\pi$
$569$	−2.16442e12	−0.865638	−0.432819	+	0.901481i	$0.642481\pi$
$570$	−5.60874e10	−0.0222550
$571$	7.99521e11	0.314751	0.157376	−	0.987539i	$-0.449697\pi$
$571$	7.99521e11	0.314751	0.157376	+	0.987539i	$0.449697\pi$
$572$	6.63103e10	0.0258999
$573$	−1.13330e12	−0.439188
$574$	−3.40455e11	−0.130905
$575$	1.15486e11	0.0440579
$576$	−2.20039e11	−0.0832909
$577$	−2.52485e12	−0.948296	−0.474148	−	0.880445i	$-0.657244\pi$
$577$	−2.52485e12	−0.948296	−0.474148	+	0.880445i	$0.657244\pi$
$578$	−4.17051e11	−0.155422
$579$	−1.95957e12	−0.724615
$580$	−3.77429e11	−0.138487
$581$	−3.35704e12	−1.22226
$582$	−4.75467e11	−0.171778
$583$	−3.13434e9	−0.00112367
$584$	2.10963e12	0.750496
$585$	2.88310e11	0.101779
$586$	−1.11261e12	−0.389766
$587$	−3.03439e12	−1.05487	−0.527436	−	0.849595i	$-0.676846\pi$
$587$	−3.03439e12	−1.05487	−0.527436	+	0.849595i	$0.676846\pi$
$588$	−1.19847e12	−0.413456
$589$	−7.41803e11	−0.253963
$590$	−8.12719e11	−0.276125
$591$	5.05524e11	0.170451
$592$	3.22231e11	0.107825
$593$	3.40070e12	1.12933	0.564667	−	0.825319i	$-0.309005\pi$
$593$	3.40070e12	1.12933	0.564667	+	0.825319i	$0.309005\pi$
$594$	−9.69012e9	−0.00319367
$595$	−1.41771e12	−0.463727
$596$	−1.26502e12	−0.410666
$597$	−2.88167e12	−0.928453
$598$	1.76711e11	0.0565079
$599$	−4.61319e12	−1.46413	−0.732066	−	0.681234i	$-0.761444\pi$
$599$	−4.61319e12	−1.46413	−0.732066	+	0.681234i	$0.761444\pi$
$600$	−2.56002e11	−0.0806423
$601$	−5.97933e11	−0.186947	−0.0934733	−	0.995622i	$-0.529797\pi$
$601$	−5.97933e11	−0.186947	−0.0934733	+	0.995622i	$0.529797\pi$
$602$	2.18902e12	0.679308
$603$	5.31255e11	0.163635
$604$	−8.43524e11	−0.257888
$605$	−1.47084e12	−0.446341
$606$	5.57309e11	0.167868
$607$	−5.36203e12	−1.60317	−0.801586	−	0.597880i	$-0.796010\pi$
$607$	−5.36203e12	−1.60317	−0.801586	+	0.597880i	$0.796010\pi$
$608$	−7.13090e11	−0.211631
$609$	−9.56922e11	−0.281902
$610$	2.09092e11	0.0611440
$611$	−2.97659e12	−0.864039
$612$	−7.60750e11	−0.219210
$613$	4.13132e12	1.18173	0.590864	−	0.806772i	$-0.298787\pi$
$613$	4.13132e12	1.18173	0.590864	+	0.806772i	$0.298787\pi$
$614$	−1.32773e12	−0.377010
$615$	2.35678e11	0.0664324
$616$	−1.49282e11	−0.0417728
$617$	−4.64600e12	−1.29061	−0.645307	−	0.763923i	$-0.723271\pi$
$617$	−4.64600e12	−1.29061	−0.645307	+	0.763923i	$0.723271\pi$
$618$	−3.17609e11	−0.0875881
$619$	6.83793e12	1.87205	0.936023	−	0.351939i	$-0.114478\pi$
$619$	6.83793e12	1.87205	0.936023	+	0.351939i	$0.114478\pi$
$620$	−1.56436e12	−0.425182
$621$	1.57117e11	0.0423948
$622$	2.45921e11	0.0658777
$623$	−2.21373e12	−0.588748
$624$	8.90454e11	0.235115
$625$	1.52588e11	0.0400000
$626$	7.77880e11	0.202455
$627$	2.26406e10	0.00585038
$628$	3.53582e12	0.907135
$629$	5.43422e11	0.138423
$630$	−2.99886e11	−0.0758445
$631$	−3.00641e12	−0.754947	−0.377473	−	0.926020i	$-0.623207\pi$
$631$	−3.00641e12	−0.754947	−0.377473	+	0.926020i	$0.623207\pi$
$632$	3.66073e12	0.912727
$633$	−1.22438e12	−0.303111
$634$	−4.47641e11	−0.110034
$635$	3.72612e10	0.00909441
$636$	−5.20507e10	−0.0126145
$637$	2.36574e12	0.569299
$638$	−2.50406e10	−0.00598346
$639$	−1.77442e12	−0.421019
$640$	−1.92917e12	−0.454528
$641$	−5.29420e12	−1.23862	−0.619311	−	0.785145i	$-0.712588\pi$
$641$	−5.29420e12	−1.23862	−0.619311	+	0.785145i	$0.712588\pi$
$642$	1.42649e12	0.331408
$643$	−9.52256e11	−0.219687	−0.109843	−	0.993949i	$-0.535035\pi$
$643$	−9.52256e11	−0.219687	−0.109843	+	0.993949i	$0.535035\pi$
$644$	1.11834e12	0.256205
$645$	−1.51534e12	−0.344739
$646$	−2.92138e11	−0.0659997
$647$	−2.22683e12	−0.499595	−0.249797	−	0.968298i	$-0.580364\pi$
$647$	−2.22683e12	−0.499595	−0.249797	+	0.968298i	$0.580364\pi$
$648$	−3.48288e11	−0.0775981
$649$	3.28067e11	0.0725875
$650$	2.33483e11	0.0513032
$651$	−3.96624e12	−0.865496
$652$	−4.89255e11	−0.106028
$653$	−8.67231e12	−1.86649	−0.933244	−	0.359242i	$-0.883035\pi$
$653$	−8.67231e12	−1.86649	−0.933244	+	0.359242i	$0.883035\pi$
$654$	−1.02439e12	−0.218961
$655$	−1.11058e12	−0.235758
$656$	7.27898e11	0.153463
$657$	−1.71072e12	−0.358207
$658$	3.09611e12	0.643872
$659$	−3.26232e12	−0.673817	−0.336909	−	0.941537i	$-0.609381\pi$
$659$	−3.26232e12	−0.673817	−0.336909	+	0.941537i	$0.609381\pi$
$660$	4.77460e10	0.00979466
$661$	9.63423e12	1.96296	0.981478	−	0.191575i	$-0.0613595\pi$
$661$	9.63423e12	1.96296	0.981478	+	0.191575i	$0.0613595\pi$
$662$	−1.00647e12	−0.203676
$663$	1.50170e12	0.301836
$664$	−3.15744e12	−0.630345
$665$	7.00672e11	0.138937
$666$	1.14949e11	0.0226397
$667$	4.06013e11	0.0794281
$668$	−1.21541e12	−0.236172
$669$	−2.37232e12	−0.457885
$670$	4.30228e11	0.0824826
$671$	−8.44035e10	−0.0160734
$672$	−3.81272e12	−0.721230
$673$	6.68101e12	1.25538	0.627689	−	0.778464i	$-0.284001\pi$
$673$	6.68101e12	1.25538	0.627689	+	0.778464i	$0.284001\pi$
$674$	4.70839e11	0.0878827
$675$	2.07594e11	0.0384900
$676$	2.48938e12	0.458492
$677$	−1.83095e12	−0.334987	−0.167494	−	0.985873i	$-0.553567\pi$
$677$	−1.83095e12	−0.334987	−0.167494	+	0.985873i	$0.553567\pi$
$678$	−1.24377e12	−0.226051
$679$	5.93978e12	1.07240
$680$	−1.33342e12	−0.239153
$681$	−5.36242e12	−0.955430
$682$	−1.03788e11	−0.0183704
$683$	−1.57939e12	−0.277712	−0.138856	−	0.990313i	$-0.544343\pi$
$683$	−1.57939e12	−0.277712	−0.138856	+	0.990313i	$0.544343\pi$
$684$	3.75983e11	0.0656774
$685$	3.54695e12	0.615528
$686$	4.90397e11	0.0845453
$687$	−2.41830e12	−0.414195
$688$	−4.68017e12	−0.796368
$689$	1.02746e11	0.0173692
$690$	1.27239e11	0.0213697
$691$	−3.29925e12	−0.550509	−0.275255	−	0.961371i	$-0.588762\pi$
$691$	−3.29925e12	−0.550509	−0.275255	+	0.961371i	$0.588762\pi$
$692$	−1.66937e12	−0.276743
$693$	1.21054e11	0.0199379
$694$	1.34486e12	0.220069
$695$	−2.15001e12	−0.349549
$696$	−9.00025e11	−0.145383
$697$	1.22756e12	0.197013
$698$	−2.84133e12	−0.453078
$699$	−1.31340e12	−0.208089
$700$	1.47763e12	0.232607
$701$	5.89829e12	0.922561	0.461280	−	0.887254i	$-0.347390\pi$
$701$	5.89829e12	0.922561	0.461280	+	0.887254i	$0.347390\pi$
$702$	3.17651e11	0.0493666
$703$	−2.68574e11	−0.0414729
$704$	7.19311e10	0.0110367
$705$	−2.14326e12	−0.326756
$706$	2.45837e12	0.372415
$707$	−6.96218e12	−1.04799
$708$	5.44808e12	0.814880
$709$	1.10767e13	1.64628	0.823138	−	0.567842i	$-0.192222\pi$
$709$	1.10767e13	1.64628	0.823138	+	0.567842i	$0.192222\pi$
$710$	−1.43698e12	−0.212221
$711$	−2.96852e12	−0.435638
$712$	−2.08211e12	−0.303629
$713$	1.68284e12	0.243860
$714$	−1.56199e12	−0.224925
$715$	−9.42491e10	−0.0134865
$716$	−4.70565e12	−0.669131
$717$	−7.28193e12	−1.02899
$718$	4.71366e12	0.661910
$719$	4.32684e12	0.603797	0.301898	−	0.953340i	$-0.402380\pi$
$719$	4.32684e12	0.603797	0.301898	+	0.953340i	$0.402380\pi$
$720$	6.41162e11	0.0889142
$721$	3.96774e12	0.546807
$722$	1.44383e11	0.0197741
$723$	7.35002e12	1.00038
$724$	−9.12646e12	−1.23446
$725$	5.36452e11	0.0721124
$726$	−1.62053e12	−0.216492
$727$	3.86448e12	0.513081	0.256541	−	0.966533i	$-0.417417\pi$
$727$	3.86448e12	0.513081	0.256541	+	0.966533i	$0.417417\pi$
$728$	4.89359e12	0.645709
$729$	2.82430e11	0.0370370
$730$	−1.38540e12	−0.180560
$731$	−7.89282e12	−1.02236
$732$	−1.40165e12	−0.180443
$733$	4.95097e12	0.633465	0.316732	−	0.948515i	$-0.397414\pi$
$733$	4.95097e12	0.633465	0.316732	+	0.948515i	$0.397414\pi$
$734$	−1.64097e12	−0.208674
$735$	1.70343e12	0.215293
$736$	1.61770e12	0.203212
$737$	−1.73669e11	−0.0216829
$738$	2.59662e11	0.0322222
$739$	5.28526e11	0.0651878	0.0325939	−	0.999469i	$-0.489623\pi$
$739$	5.28526e11	0.0651878	0.0325939	+	0.999469i	$0.489623\pi$
$740$	−5.66387e11	−0.0694337
$741$	−7.42179e11	−0.0904329
$742$	−1.06872e11	−0.0129434
$743$	1.87009e11	0.0225119	0.0112560	−	0.999937i	$-0.496417\pi$
$743$	1.87009e11	0.0225119	0.0112560	+	0.999937i	$0.496417\pi$
$744$	−3.73042e12	−0.446354
$745$	1.79802e12	0.213841
$746$	1.79706e12	0.212441
$747$	2.56039e12	0.300859
$748$	2.48691e11	0.0290471
$749$	−1.78205e13	−2.06896
$750$	1.68117e11	0.0194015
$751$	−3.65018e12	−0.418730	−0.209365	−	0.977838i	$-0.567140\pi$
$751$	−3.65018e12	−0.418730	−0.209365	+	0.977838i	$0.567140\pi$
$752$	−6.61953e12	−0.754826
$753$	−1.54836e12	−0.175507
$754$	8.20854e11	0.0924900
$755$	1.19893e12	0.134286
$756$	2.01029e12	0.223826
$757$	1.00306e13	1.11019	0.555095	−	0.831787i	$-0.312682\pi$
$757$	1.00306e13	1.11019	0.555095	+	0.831787i	$0.312682\pi$
$758$	3.03718e12	0.334163
$759$	−5.13621e10	−0.00561765
$760$	6.59012e11	0.0716526
$761$	3.29762e12	0.356426	0.178213	−	0.983992i	$-0.442968\pi$
$761$	3.29762e12	0.356426	0.178213	+	0.983992i	$0.442968\pi$
$762$	4.10532e10	0.00441113
$763$	1.27972e13	1.36696
$764$	6.15240e12	0.653318
$765$	1.08128e12	0.114146
$766$	−5.00925e12	−0.525707
$767$	−1.07543e13	−1.12203
$768$	−7.34640e11	−0.0761990
$769$	−1.76109e12	−0.181599	−0.0907994	−	0.995869i	$-0.528942\pi$
$769$	−1.76109e12	−0.181599	−0.0907994	+	0.995869i	$0.528942\pi$
$770$	9.80335e10	0.0100500
$771$	3.77888e12	0.385139
$772$	1.06380e13	1.07791
$773$	1.71547e12	0.172813	0.0864063	−	0.996260i	$-0.472462\pi$
$773$	1.71547e12	0.172813	0.0864063	+	0.996260i	$0.472462\pi$
$774$	−1.66955e12	−0.167211
$775$	2.22348e12	0.221399
$776$	5.58661e12	0.553058
$777$	−1.43600e12	−0.141338
$778$	−5.44524e12	−0.532854
$779$	−6.06691e11	−0.0590268
$780$	−1.56516e12	−0.151402
$781$	5.80061e11	0.0557885
$782$	6.62740e11	0.0633743
$783$	7.29837e11	0.0693902
$784$	5.26109e12	0.497340
$785$	−5.02558e12	−0.472360
$786$	−1.22361e12	−0.114351
$787$	−2.08698e13	−1.93924	−0.969619	−	0.244618i	$-0.921337\pi$
$787$	−2.08698e13	−1.93924	−0.969619	+	0.244618i	$0.921337\pi$
$788$	−2.74436e12	−0.253555
$789$	−3.14265e12	−0.288702
$790$	−2.40400e12	−0.219590
$791$	1.55378e13	1.41122
$792$	1.13856e11	0.0102824
$793$	2.76682e12	0.248457
$794$	4.66502e12	0.416544
$795$	7.39815e10	0.00656857
$796$	1.56438e13	1.38113
$797$	−9.92675e12	−0.871454	−0.435727	−	0.900079i	$-0.643509\pi$
$797$	−9.92675e12	−0.871454	−0.435727	+	0.900079i	$0.643509\pi$
$798$	7.71979e11	0.0673896
$799$	−1.11634e13	−0.969030
$800$	2.13742e12	0.184495
$801$	1.68840e12	0.144920
$802$	1.88697e12	0.161057
$803$	5.59237e11	0.0474653
$804$	−2.88404e12	−0.243416
$805$	−1.58953e12	−0.133410
$806$	3.40227e12	0.283963
$807$	3.09329e12	0.256738
$808$	−6.54822e12	−0.540471
$809$	−1.97003e13	−1.61698	−0.808490	−	0.588510i	$-0.799715\pi$
$809$	−1.97003e13	−1.61698	−0.808490	+	0.588510i	$0.799715\pi$
$810$	2.28721e11	0.0186691
$811$	−1.49518e13	−1.21366	−0.606832	−	0.794830i	$-0.707560\pi$
$811$	−1.49518e13	−1.21366	−0.606832	+	0.794830i	$0.707560\pi$
$812$	5.19488e12	0.419347
$813$	9.14943e12	0.734491
$814$	−3.75771e10	−0.00299995
$815$	6.95394e11	0.0552105
$816$	3.33957e12	0.263685
$817$	3.90085e12	0.306309
$818$	−7.80180e11	−0.0609264
$819$	−3.96825e12	−0.308192
$820$	−1.27943e12	−0.0988222
$821$	5.64204e11	0.0433403	0.0216701	−	0.999765i	$-0.493102\pi$
$821$	5.64204e11	0.0433403	0.0216701	+	0.999765i	$0.493102\pi$
$822$	3.90793e12	0.298554
$823$	2.11916e13	1.61015	0.805073	−	0.593175i	$-0.202126\pi$
$823$	2.11916e13	1.61015	0.805073	+	0.593175i	$0.202126\pi$
$824$	3.73182e12	0.282000
$825$	−6.78630e10	−0.00510024
$826$	1.11862e13	0.836124
$827$	2.90210e12	0.215743	0.107872	−	0.994165i	$-0.465596\pi$
$827$	2.90210e12	0.215743	0.107872	+	0.994165i	$0.465596\pi$
$828$	−8.52949e11	−0.0630647
$829$	−1.48771e13	−1.09401	−0.547006	−	0.837128i	$-0.684233\pi$
$829$	−1.48771e13	−1.09401	−0.547006	+	0.837128i	$0.684233\pi$
$830$	2.07349e12	0.151653
$831$	−1.42026e13	−1.03315
$832$	−2.35797e12	−0.170601
$833$	8.87251e12	0.638475
$834$	−2.36881e12	−0.169544
$835$	1.72750e12	0.122979
$836$	−1.22910e11	−0.00870278
$837$	3.02503e12	0.213042
$838$	7.09649e12	0.497102
$839$	−1.09689e13	−0.764248	−0.382124	−	0.924111i	$-0.624807\pi$
$839$	−1.09689e13	−0.764248	−0.382124	+	0.924111i	$0.624807\pi$
$840$	3.52358e12	0.244190
$841$	−1.26211e13	−0.869995
$842$	−3.13056e12	−0.214644
$843$	−5.85070e12	−0.399010
$844$	6.64686e12	0.450895
$845$	−3.53824e12	−0.238744
$846$	−2.36138e12	−0.158489
$847$	2.02445e13	1.35155
$848$	2.28494e11	0.0151738
$849$	−7.03669e12	−0.464819
$850$	8.75657e11	0.0575372
$851$	6.09282e11	0.0398231
$852$	9.63285e12	0.626291
$853$	−1.82093e13	−1.17767	−0.588835	−	0.808254i	$-0.700413\pi$
$853$	−1.82093e13	−1.17767	−0.588835	+	0.808254i	$0.700413\pi$
$854$	−2.87792e12	−0.185148
$855$	−5.34398e11	−0.0341993
$856$	−1.67609e13	−1.06700
$857$	−3.77462e12	−0.239034	−0.119517	−	0.992832i	$-0.538135\pi$
$857$	−3.77462e12	−0.239034	−0.119517	+	0.992832i	$0.538135\pi$
$858$	−1.03841e11	−0.00654147
$859$	−7.89410e12	−0.494690	−0.247345	−	0.968927i	$-0.579558\pi$
$859$	−7.89410e12	−0.494690	−0.247345	+	0.968927i	$0.579558\pi$
$860$	8.22637e12	0.512820
$861$	−3.24383e12	−0.201161
$862$	−4.27692e12	−0.263845
$863$	−6.96799e12	−0.427621	−0.213810	−	0.976875i	$-0.568587\pi$
$863$	−6.96799e12	−0.427621	−0.213810	+	0.976875i	$0.568587\pi$
$864$	2.90794e12	0.177531
$865$	2.37274e12	0.144104
$866$	7.61321e12	0.459978
$867$	−3.97364e12	−0.238837
$868$	2.15317e13	1.28748
$869$	9.70415e11	0.0577256
$870$	5.91047e11	0.0349772
$871$	5.69301e12	0.335166
$872$	1.20363e13	0.704970
$873$	−4.53023e12	−0.263971
$874$	−3.27544e11	−0.0189875
$875$	−2.10020e12	−0.121122
$876$	9.28702e12	0.532854
$877$	−2.60614e13	−1.48765	−0.743824	−	0.668375i	$-0.766990\pi$
$877$	−2.60614e13	−1.48765	−0.743824	+	0.668375i	$0.766990\pi$
$878$	3.53932e12	0.200999
$879$	−1.06009e13	−0.598953
$880$	−2.09597e11	−0.0117819
$881$	1.73552e13	0.970593	0.485296	−	0.874350i	$-0.338712\pi$
$881$	1.73552e13	0.970593	0.485296	+	0.874350i	$0.338712\pi$
$882$	1.87678e12	0.104425
$883$	−3.13519e12	−0.173556	−0.0867782	−	0.996228i	$-0.527657\pi$
$883$	−3.13519e12	−0.173556	−0.0867782	+	0.996228i	$0.527657\pi$
$884$	−8.15231e12	−0.448999
$885$	−7.74354e12	−0.424321
$886$	7.29520e12	0.397727
$887$	2.15561e13	1.16927	0.584633	−	0.811298i	$-0.301238\pi$
$887$	2.15561e13	1.16927	0.584633	+	0.811298i	$0.301238\pi$
$888$	−1.35062e12	−0.0728911
$889$	−5.12857e11	−0.0275384
$890$	1.36732e12	0.0730493
$891$	−9.23269e10	−0.00490771
$892$	1.28787e13	0.681131
$893$	5.51727e12	0.290330
$894$	1.98100e12	0.103721
$895$	6.68830e12	0.348427
$896$	2.65528e13	1.37634
$897$	1.68369e12	0.0868355
$898$	7.59198e12	0.389593
$899$	7.81709e12	0.399141
$900$	−1.12697e12	−0.0572562
$901$	3.85342e11	0.0194798
$902$	−8.48843e10	−0.00426971
$903$	2.08569e13	1.04389
$904$	1.46139e13	0.727796
$905$	1.29717e13	0.642806
$906$	1.32094e12	0.0651340
$907$	1.84546e13	0.905467	0.452734	−	0.891646i	$-0.350449\pi$
$907$	1.84546e13	0.905467	0.452734	+	0.891646i	$0.350449\pi$
$908$	2.91112e13	1.42126
$909$	5.31001e12	0.257963
$910$	−3.21363e12	−0.155349
$911$	1.94952e13	0.937766	0.468883	−	0.883260i	$-0.344657\pi$
$911$	1.94952e13	0.937766	0.468883	+	0.883260i	$0.344657\pi$
$912$	−1.65051e12	−0.0790024
$913$	−8.36998e11	−0.0398663
$914$	8.40141e12	0.398194
$915$	1.99222e12	0.0939598
$916$	1.31283e13	0.616139
$917$	1.52859e13	0.713888
$918$	1.19132e12	0.0553652
$919$	1.25306e13	0.579498	0.289749	−	0.957103i	$-0.406428\pi$
$919$	1.25306e13	0.579498	0.289749	+	0.957103i	$0.406428\pi$
$920$	−1.49502e12	−0.0688023
$921$	−1.26506e13	−0.579351
$922$	4.45161e12	0.202875
$923$	−1.90149e13	−0.862357
$924$	−6.57170e11	−0.0296588
$925$	8.05025e11	0.0361553
$926$	−2.00915e12	−0.0897974
$927$	−3.02616e12	−0.134596
$928$	7.51452e12	0.332610
$929$	−3.45751e13	−1.52298	−0.761488	−	0.648179i	$-0.775531\pi$
$929$	−3.45751e13	−1.52298	−0.761488	+	0.648179i	$0.775531\pi$
$930$	2.44977e12	0.107387
$931$	−4.38503e12	−0.191293
$932$	7.13010e12	0.309545
$933$	2.34312e12	0.101234
$934$	−2.91496e12	−0.125335
$935$	−3.53473e11	−0.0151253
$936$	−3.73231e12	−0.158941
$937$	5.46318e12	0.231535	0.115768	−	0.993276i	$-0.463067\pi$
$937$	5.46318e12	0.231535	0.115768	+	0.993276i	$0.463067\pi$
$938$	−5.92161e12	−0.249762
$939$	7.41160e12	0.311112
$940$	1.16352e13	0.486069
$941$	−3.27531e12	−0.136176	−0.0680879	−	0.997679i	$-0.521690\pi$
$941$	−3.27531e12	−0.136176	−0.0680879	+	0.997679i	$0.521690\pi$
$942$	−5.53704e12	−0.229112
$943$	1.37633e12	0.0566787
$944$	−2.39162e13	−0.980208
$945$	−2.85730e12	−0.116550
$946$	5.45781e11	0.0221569
$947$	−2.09027e13	−0.844555	−0.422278	−	0.906467i	$-0.638769\pi$
$947$	−2.09027e13	−0.844555	−0.422278	+	0.906467i	$0.638769\pi$
$948$	1.61153e13	0.648038
$949$	−1.83323e13	−0.733700
$950$	−4.32773e11	−0.0172387
$951$	−4.26510e12	−0.169090
$952$	1.83530e13	0.724171
$953$	−2.97285e13	−1.16750	−0.583748	−	0.811935i	$-0.698414\pi$
$953$	−2.97285e13	−1.16750	−0.583748	+	0.811935i	$0.698414\pi$
$954$	8.15106e10	0.00318600
$955$	−8.74462e12	−0.340193
$956$	3.95317e13	1.53068
$957$	−2.38586e11	−0.00919476
$958$	−7.96669e12	−0.305586
$959$	−4.88198e13	−1.86386
$960$	−1.69783e12	−0.0645169
$961$	5.96061e12	0.225442
$962$	1.23181e12	0.0463721
$963$	1.35916e13	0.509273
$964$	−3.99013e13	−1.48813
$965$	−1.51202e13	−0.561285
$966$	−1.75130e12	−0.0647088
$967$	6.55213e12	0.240970	0.120485	−	0.992715i	$-0.461555\pi$
$967$	6.55213e12	0.240970	0.120485	+	0.992715i	$0.461555\pi$
$968$	1.90408e13	0.697021
$969$	−2.78348e12	−0.101422
$970$	−3.66873e12	−0.133059
$971$	4.42665e13	1.59804	0.799021	−	0.601302i	$-0.205351\pi$
$971$	4.42665e13	1.59804	0.799021	+	0.601302i	$0.205351\pi$
$972$	−1.53324e12	−0.0550948
$973$	2.95924e13	1.05845
$974$	6.11554e12	0.217731
$975$	2.22461e12	0.0788376
$976$	6.15304e12	0.217053
$977$	−2.13009e13	−0.747948	−0.373974	−	0.927439i	$-0.622005\pi$
$977$	−2.13009e13	−0.747948	−0.373974	+	0.927439i	$0.622005\pi$
$978$	7.66165e11	0.0267792
$979$	−5.51942e11	−0.0192031
$980$	−9.24746e12	−0.320262
$981$	−9.76036e12	−0.336477
$982$	−3.16940e12	−0.108762
$983$	1.38841e13	0.474272	0.237136	−	0.971476i	$-0.423791\pi$
$983$	1.38841e13	0.474272	0.237136	+	0.971476i	$0.423791\pi$
$984$	−3.05096e12	−0.103743
$985$	3.90065e12	0.132030
$986$	3.07854e12	0.103729
$987$	2.94995e13	0.989436
$988$	4.02909e12	0.134524
$989$	−8.84939e12	−0.294124
$990$	−7.47695e10	−0.00247381
$991$	−1.55882e13	−0.513409	−0.256705	−	0.966490i	$-0.582637\pi$
$991$	−1.55882e13	−0.513409	−0.256705	+	0.966490i	$0.582637\pi$
$992$	3.11461e13	1.02118
$993$	−9.58958e12	−0.312988
$994$	1.97784e13	0.642619
$995$	−2.22351e13	−0.719177
$996$	−1.38997e13	−0.447547
$997$	−2.00048e13	−0.641219	−0.320610	−	0.947211i	$-0.603888\pi$
$997$	−2.00048e13	−0.641219	−0.320610	+	0.947211i	$0.603888\pi$
$998$	9.07832e11	0.0289680
$999$	1.09523e12	0.0347904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.d.1.8	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.d.1.8	✓	12	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)

\(f(q)\)	\(=\)	\(q+8.50131 q^{2} +81.0000 q^{3} -439.728 q^{4} +625.000 q^{5} +688.606 q^{6} -8602.42 q^{7} -8090.93 q^{8} +6561.00 q^{9} +5313.32 q^{10} -2144.81 q^{11} -35617.9 q^{12} +70308.7 q^{13} -73131.8 q^{14} +50625.0 q^{15} +156357. q^{16} +263687. q^{17} +55777.1 q^{18} -130321. q^{19} -274830. q^{20} -696796. q^{21} -18233.7 q^{22} +295644. q^{23} -655366. q^{24} +390625. q^{25} +597716. q^{26} +531441. q^{27} +3.78272e6 q^{28} +1.37332e6 q^{29} +430379. q^{30} +5.69212e6 q^{31} +5.47180e6 q^{32} -173729. q^{33} +2.24168e6 q^{34} -5.37651e6 q^{35} -2.88505e6 q^{36} +2.06086e6 q^{37} -1.10790e6 q^{38} +5.69500e6 q^{39} -5.05683e6 q^{40} +4.65536e6 q^{41} -5.92368e6 q^{42} -2.99326e7 q^{43} +943131. q^{44} +4.10062e6 q^{45} +2.51336e6 q^{46} -4.23360e7 q^{47} +1.26649e7 q^{48} +3.36479e7 q^{49} +3.32082e6 q^{50} +2.13586e7 q^{51} -3.09167e7 q^{52} +1.46136e6 q^{53} +4.51795e6 q^{54} -1.34050e6 q^{55} +6.96016e7 q^{56} -1.05560e7 q^{57} +1.16750e7 q^{58} -1.52959e8 q^{59} -2.22612e7 q^{60} +3.93525e7 q^{61} +4.83905e7 q^{62} -5.64404e7 q^{63} -3.35374e7 q^{64} +4.39429e7 q^{65} -1.47693e6 q^{66} +8.09717e7 q^{67} -1.15950e8 q^{68} +2.39472e7 q^{69} -4.57074e7 q^{70} -2.70449e8 q^{71} -5.30846e7 q^{72} -2.60740e8 q^{73} +1.75200e7 q^{74} +3.16406e7 q^{75} +5.73058e7 q^{76} +1.84505e7 q^{77} +4.84150e7 q^{78} -4.52449e8 q^{79} +9.77232e7 q^{80} +4.30467e7 q^{81} +3.95767e7 q^{82} +3.90244e8 q^{83} +3.06400e8 q^{84} +1.64804e8 q^{85} -2.54466e8 q^{86} +1.11239e8 q^{87} +1.73535e7 q^{88} +2.57339e8 q^{89} +3.48607e7 q^{90} -6.04825e8 q^{91} -1.30003e8 q^{92} +4.61062e8 q^{93} -3.59911e8 q^{94} -8.14506e7 q^{95} +4.43216e8 q^{96} -6.90478e8 q^{97} +2.86052e8 q^{98} -1.40721e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 33 q^{2} + 972 q^{3} + 2751 q^{4} + 7500 q^{5} - 2673 q^{6} - 5100 q^{7} - 40215 q^{8} + 78732 q^{9} - 20625 q^{10} - 60416 q^{11} + 222831 q^{12} - 164042 q^{13} - 444762 q^{14} + 607500 q^{15}+ \cdots - 396389376 q^{99}+O(q^{100}) \) 12 * q - 33 * q^2 + 972 * q^3 + 2751 * q^4 + 7500 * q^5 - 2673 * q^6 - 5100 * q^7 - 40215 * q^8 + 78732 * q^9 - 20625 * q^10 - 60416 * q^11 + 222831 * q^12 - 164042 * q^13 - 444762 * q^14 + 607500 * q^15 + 319475 * q^16 - 552834 * q^17 - 216513 * q^18 - 1563852 * q^19 + 1719375 * q^20 - 413100 * q^21 + 708846 * q^22 - 2749174 * q^23 - 3257415 * q^24 + 4687500 * q^25 - 5159376 * q^26 + 6377292 * q^27 - 2379170 * q^28 - 3415632 * q^29 - 1670625 * q^30 - 9822574 * q^31 - 22282623 * q^32 - 4893696 * q^33 + 5214442 * q^34 - 3187500 * q^35 + 18049311 * q^36 - 24559054 * q^37 + 4300593 * q^38 - 13287402 * q^39 - 25134375 * q^40 - 35856950 * q^41 - 36025722 * q^42 - 73839462 * q^43 - 88153054 * q^44 + 49207500 * q^45 - 19966000 * q^46 - 134699358 * q^47 + 25877475 * q^48 - 64331236 * q^49 - 12890625 * q^50 - 44779554 * q^51 - 290325860 * q^52 - 74807846 * q^53 - 17537553 * q^54 - 37760000 * q^55 - 403278618 * q^56 - 126672012 * q^57 - 377474064 * q^58 - 294192102 * q^59 + 139269375 * q^60 - 184407884 * q^61 - 356900784 * q^62 - 33461100 * q^63 + 169573219 * q^64 - 102526250 * q^65 + 57416526 * q^66 - 427627864 * q^67 - 56755242 * q^68 - 222683094 * q^69 - 277976250 * q^70 - 488904216 * q^71 - 263850615 * q^72 - 184702472 * q^73 - 1424419204 * q^74 + 379687500 * q^75 - 358513071 * q^76 - 827371672 * q^77 - 417909456 * q^78 - 620531838 * q^79 + 199671875 * q^80 + 516560652 * q^81 + 100137664 * q^82 - 32273124 * q^83 - 192712770 * q^84 - 345521250 * q^85 + 1147824298 * q^86 - 276666192 * q^87 + 2717542210 * q^88 + 473499162 * q^89 - 135320625 * q^90 - 1430236924 * q^91 + 1920565904 * q^92 - 795628494 * q^93 + 2483643504 * q^94 - 977407500 * q^95 - 1804892463 * q^96 + 318965234 * q^97 + 2863543931 * q^98 - 396389376 * q^99

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