LMFDB - Embedded newform 285.10.a.h.1.4

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			1.4
Root			$31.1284$ 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)

$f(q)$	$=$	$q-32.1284 q^{2} -81.0000 q^{3} +520.237 q^{4} +625.000 q^{5} +2602.40 q^{6} +7291.16 q^{7} -264.644 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-32.1284 q^{2} -81.0000 q^{3} +520.237 q^{4} +625.000 q^{5} +2602.40 q^{6} +7291.16 q^{7} -264.644 q^{8} +6561.00 q^{9} -20080.3 q^{10} -79218.6 q^{11} -42139.2 q^{12} +148225. q^{13} -234254. q^{14} -50625.0 q^{15} -257859. q^{16} -403746. q^{17} -210795. q^{18} -130321. q^{19} +325148. q^{20} -590584. q^{21} +2.54517e6 q^{22} +1.87315e6 q^{23} +21436.1 q^{24} +390625. q^{25} -4.76224e6 q^{26} -531441. q^{27} +3.79313e6 q^{28} -4.55234e6 q^{29} +1.62650e6 q^{30} +7.02490e6 q^{31} +8.42010e6 q^{32} +6.41671e6 q^{33} +1.29717e7 q^{34} +4.55698e6 q^{35} +3.41328e6 q^{36} +6.13512e6 q^{37} +4.18701e6 q^{38} -1.20062e7 q^{39} -165402. q^{40} +8.76411e6 q^{41} +1.89746e7 q^{42} +1.06044e7 q^{43} -4.12124e7 q^{44} +4.10062e6 q^{45} -6.01815e7 q^{46} -2.81069e7 q^{47} +2.08866e7 q^{48} +1.28074e7 q^{49} -1.25502e7 q^{50} +3.27035e7 q^{51} +7.71122e7 q^{52} +7.72880e7 q^{53} +1.70744e7 q^{54} -4.95116e7 q^{55} -1.92956e6 q^{56} +1.05560e7 q^{57} +1.46260e8 q^{58} -6.20883e7 q^{59} -2.63370e7 q^{60} +5.26078e7 q^{61} -2.25699e8 q^{62} +4.78373e7 q^{63} -1.38501e8 q^{64} +9.26407e7 q^{65} -2.06159e8 q^{66} +2.09648e8 q^{67} -2.10044e8 q^{68} -1.51726e8 q^{69} -1.46409e8 q^{70} -3.12113e8 q^{71} -1.73633e6 q^{72} -2.93380e8 q^{73} -1.97112e8 q^{74} -3.16406e7 q^{75} -6.77978e7 q^{76} -5.77596e8 q^{77} +3.85742e8 q^{78} +1.63179e8 q^{79} -1.61162e8 q^{80} +4.30467e7 q^{81} -2.81577e8 q^{82} +7.23532e8 q^{83} -3.07244e8 q^{84} -2.52342e8 q^{85} -3.40704e8 q^{86} +3.68739e8 q^{87} +2.09647e7 q^{88} +3.62855e8 q^{89} -1.31747e8 q^{90} +1.08073e9 q^{91} +9.74484e8 q^{92} -5.69017e8 q^{93} +9.03032e8 q^{94} -8.14506e7 q^{95} -6.82028e8 q^{96} -3.40208e8 q^{97} -4.11483e8 q^{98} -5.19753e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−32.1284	−1.41989	−0.709945	−	0.704257i	$-0.751280\pi$
$2$	−32.1284	−1.41989	−0.709945	+	0.704257i	$0.751280\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	520.237	1.01609
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	2602.40	0.819774
$7$	7291.16	1.14777	0.573886	−	0.818935i	$-0.305435\pi$
$7$	7291.16	1.14777	0.573886	+	0.818935i	$0.305435\pi$
$8$	−264.644	−0.0228432
$9$	6561.00	0.333333
$10$	−20080.3	−0.634994
$11$	−79218.6	−1.63140	−0.815699	−	0.578476i	$-0.803648\pi$
$11$	−79218.6	−1.63140	−0.815699	+	0.578476i	$0.803648\pi$
$12$	−42139.2	−0.586639
$13$	148225.	1.43938	0.719692	−	0.694293i	$-0.244283\pi$
$13$	148225.	1.43938	0.719692	+	0.694293i	$0.244283\pi$
$14$	−234254.	−1.62971
$15$	−50625.0	−0.258199
$16$	−257859.	−0.983653
$17$	−403746.	−1.17243	−0.586217	−	0.810154i	$-0.699384\pi$
$17$	−403746.	−1.17243	−0.586217	+	0.810154i	$0.699384\pi$
$18$	−210795.	−0.473297
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	325148.	0.454408
$21$	−590584.	−0.662666
$22$	2.54517e6	2.31641
$23$	1.87315e6	1.39572	0.697860	−	0.716234i	$-0.254136\pi$
$23$	1.87315e6	1.39572	0.697860	+	0.716234i	$0.254136\pi$
$24$	21436.1	0.0131885
$25$	390625.	0.200000
$26$	−4.76224e6	−2.04377
$27$	−531441.	−0.192450
$28$	3.79313e6	1.16624
$29$	−4.55234e6	−1.19521	−0.597604	−	0.801792i	$-0.703880\pi$
$29$	−4.55234e6	−1.19521	−0.597604	+	0.801792i	$0.703880\pi$
$30$	1.62650e6	0.366614
$31$	7.02490e6	1.36619	0.683097	−	0.730327i	$-0.260633\pi$
$31$	7.02490e6	1.36619	0.683097	+	0.730327i	$0.260633\pi$
$32$	8.42010e6	1.41952
$33$	6.41671e6	0.941888
$34$	1.29717e7	1.66473
$35$	4.55698e6	0.513299
$36$	3.41328e6	0.338696
$37$	6.13512e6	0.538165	0.269082	−	0.963117i	$-0.413280\pi$
$37$	6.13512e6	0.538165	0.269082	+	0.963117i	$0.413280\pi$
$38$	4.18701e6	0.325745
$39$	−1.20062e7	−0.831029
$40$	−165402.	−0.0102158
$41$	8.76411e6	0.484373	0.242187	−	0.970230i	$-0.422135\pi$
$41$	8.76411e6	0.484373	0.242187	+	0.970230i	$0.422135\pi$
$42$	1.89746e7	0.940914
$43$	1.06044e7	0.473020	0.236510	−	0.971629i	$-0.423996\pi$
$43$	1.06044e7	0.473020	0.236510	+	0.971629i	$0.423996\pi$
$44$	−4.12124e7	−1.65764
$45$	4.10062e6	0.149071
$46$	−6.01815e7	−1.98177
$47$	−2.81069e7	−0.840181	−0.420091	−	0.907482i	$-0.638002\pi$
$47$	−2.81069e7	−0.840181	−0.420091	+	0.907482i	$0.638002\pi$
$48$	2.08866e7	0.567912
$49$	1.28074e7	0.317380
$50$	−1.25502e7	−0.283978
$51$	3.27035e7	0.676905
$52$	7.71122e7	1.46254
$53$	7.72880e7	1.34546	0.672730	−	0.739888i	$-0.265122\pi$
$53$	7.72880e7	1.34546	0.672730	+	0.739888i	$0.265122\pi$
$54$	1.70744e7	0.273258
$55$	−4.95116e7	−0.729584
$56$	−1.92956e6	−0.0262188
$57$	1.05560e7	0.132453
$58$	1.46260e8	1.69706
$59$	−6.20883e7	−0.667076	−0.333538	−	0.942737i	$-0.608243\pi$
$59$	−6.20883e7	−0.667076	−0.333538	+	0.942737i	$0.608243\pi$
$60$	−2.63370e7	−0.262353
$61$	5.26078e7	0.486481	0.243240	−	0.969966i	$-0.421790\pi$
$61$	5.26078e7	0.486481	0.243240	+	0.969966i	$0.421790\pi$
$62$	−2.25699e8	−1.93985
$63$	4.78373e7	0.382591
$64$	−1.38501e8	−1.03191
$65$	9.26407e7	0.643712
$66$	−2.06159e8	−1.33738
$67$	2.09648e8	1.27103	0.635513	−	0.772090i	$-0.280789\pi$
$67$	2.09648e8	1.27103	0.635513	+	0.772090i	$0.280789\pi$
$68$	−2.10044e8	−1.19130
$69$	−1.51726e8	−0.805819
$70$	−1.46409e8	−0.728828
$71$	−3.12113e8	−1.45764	−0.728818	−	0.684707i	$-0.759930\pi$
$71$	−3.12113e8	−1.45764	−0.728818	+	0.684707i	$0.759930\pi$
$72$	−1.73633e6	−0.00761440
$73$	−2.93380e8	−1.20914	−0.604572	−	0.796551i	$-0.706656\pi$
$73$	−2.93380e8	−1.20914	−0.604572	+	0.796551i	$0.706656\pi$
$74$	−1.97112e8	−0.764135
$75$	−3.16406e7	−0.115470
$76$	−6.77978e7	−0.233107
$77$	−5.77596e8	−1.87247
$78$	3.85742e8	1.17997
$79$	1.63179e8	0.471349	0.235674	−	0.971832i	$-0.424270\pi$
$79$	1.63179e8	0.471349	0.235674	+	0.971832i	$0.424270\pi$
$80$	−1.61162e8	−0.439903
$81$	4.30467e7	0.111111
$82$	−2.81577e8	−0.687757
$83$	7.23532e8	1.67343	0.836713	−	0.547642i	$-0.184474\pi$
$83$	7.23532e8	1.67343	0.836713	+	0.547642i	$0.184474\pi$
$84$	−3.07244e8	−0.673327
$85$	−2.52342e8	−0.524329
$86$	−3.40704e8	−0.671637
$87$	3.68739e8	0.690053
$88$	2.09647e7	0.0372663
$89$	3.62855e8	0.613025	0.306512	−	0.951867i	$-0.400838\pi$
$89$	3.62855e8	0.613025	0.306512	+	0.951867i	$0.400838\pi$
$90$	−1.31747e8	−0.211665
$91$	1.08073e9	1.65208
$92$	9.74484e8	1.41817
$93$	−5.69017e8	−0.788773
$94$	9.03032e8	1.19297
$95$	−8.14506e7	−0.102598
$96$	−6.82028e8	−0.819562
$97$	−3.40208e8	−0.390186	−0.195093	−	0.980785i	$-0.562501\pi$
$97$	−3.40208e8	−0.390186	−0.195093	+	0.980785i	$0.562501\pi$
$98$	−4.11483e8	−0.450645
$99$	−5.19753e8	−0.543799
$100$	2.03218e8	0.203218
$101$	3.72499e8	0.356188	0.178094	−	0.984013i	$-0.443007\pi$
$101$	3.72499e8	0.356188	0.178094	+	0.984013i	$0.443007\pi$
$102$	−1.05071e9	−0.961131
$103$	−1.86027e9	−1.62858	−0.814288	−	0.580462i	$-0.802872\pi$
$103$	−1.86027e9	−1.62858	−0.814288	+	0.580462i	$0.802872\pi$
$104$	−3.92269e7	−0.0328801
$105$	−3.69115e8	−0.296353
$106$	−2.48314e9	−1.91041
$107$	−1.30461e9	−0.962171	−0.481085	−	0.876674i	$-0.659757\pi$
$107$	−1.30461e9	−0.962171	−0.481085	+	0.876674i	$0.659757\pi$
$108$	−2.76475e8	−0.195546
$109$	−2.06573e9	−1.40169	−0.700847	−	0.713311i	$-0.747195\pi$
$109$	−2.06573e9	−1.40169	−0.700847	+	0.713311i	$0.747195\pi$
$110$	1.59073e9	1.03593
$111$	−4.96945e8	−0.310710
$112$	−1.88009e9	−1.12901
$113$	2.50106e9	1.44302	0.721508	−	0.692406i	$-0.243449\pi$
$113$	2.50106e9	1.44302	0.721508	+	0.692406i	$0.243449\pi$
$114$	−3.39148e8	−0.188069
$115$	1.17072e9	0.624185
$116$	−2.36829e9	−1.21444
$117$	9.72505e8	0.479795
$118$	1.99480e9	0.947175
$119$	−2.94378e9	−1.34569
$120$	1.33976e7	0.00589809
$121$	3.91764e9	1.66146
$122$	−1.69021e9	−0.690749
$123$	−7.09893e8	−0.279653
$124$	3.65461e9	1.38817
$125$	2.44141e8	0.0894427
$126$	−1.53694e9	−0.543237
$127$	−3.84679e9	−1.31215	−0.656073	−	0.754697i	$-0.727784\pi$
$127$	−3.84679e9	−1.31215	−0.656073	+	0.754697i	$0.727784\pi$
$128$	1.38732e8	0.0456805
$129$	−8.58960e8	−0.273098
$130$	−2.97640e9	−0.914001
$131$	−2.73361e9	−0.810991	−0.405496	−	0.914097i	$-0.632901\pi$
$131$	−2.73361e9	−0.810991	−0.405496	+	0.914097i	$0.632901\pi$
$132$	3.33821e9	0.957041
$133$	−9.50192e8	−0.263317
$134$	−6.73567e9	−1.80472
$135$	−3.32151e8	−0.0860663
$136$	1.06849e8	0.0267821
$137$	6.50870e9	1.57853	0.789263	−	0.614055i	$-0.210463\pi$
$137$	6.50870e9	1.57853	0.789263	+	0.614055i	$0.210463\pi$
$138$	4.87471e9	1.14418
$139$	−4.74208e9	−1.07746	−0.538732	−	0.842477i	$-0.681096\pi$
$139$	−4.74208e9	−1.07746	−0.538732	+	0.842477i	$0.681096\pi$
$140$	2.37071e9	0.521557
$141$	2.27666e9	0.485079
$142$	1.00277e10	2.06968
$143$	−1.17422e10	−2.34821
$144$	−1.69181e9	−0.327884
$145$	−2.84521e9	−0.534513
$146$	9.42585e9	1.71685
$147$	−1.03740e9	−0.183240
$148$	3.19172e9	0.546823
$149$	−8.80321e9	−1.46320	−0.731598	−	0.681736i	$-0.761225\pi$
$149$	−8.80321e9	−1.46320	−0.731598	+	0.681736i	$0.761225\pi$
$150$	1.01656e9	0.163955
$151$	1.18413e10	1.85355	0.926775	−	0.375617i	$-0.122569\pi$
$151$	1.18413e10	1.85355	0.926775	+	0.375617i	$0.122569\pi$
$152$	3.44886e7	0.00524059
$153$	−2.64898e9	−0.390812
$154$	1.85572e10	2.65871
$155$	4.39056e9	0.610981
$156$	−6.24609e9	−0.844399
$157$	3.14790e9	0.413497	0.206749	−	0.978394i	$-0.433712\pi$
$157$	3.14790e9	0.413497	0.206749	+	0.978394i	$0.433712\pi$
$158$	−5.24269e9	−0.669263
$159$	−6.26033e9	−0.776802
$160$	5.26256e9	0.634830
$161$	1.36575e10	1.60197
$162$	−1.38302e9	−0.157766
$163$	3.35730e9	0.372517	0.186258	−	0.982501i	$-0.440364\pi$
$163$	3.35730e9	0.372517	0.186258	+	0.982501i	$0.440364\pi$
$164$	4.55941e9	0.492166
$165$	4.01044e9	0.421225
$166$	−2.32460e10	−2.37608
$167$	3.82304e9	0.380351	0.190176	−	0.981750i	$-0.439094\pi$
$167$	3.82304e9	0.380351	0.190176	+	0.981750i	$0.439094\pi$
$168$	1.56294e8	0.0151374
$169$	1.13662e10	1.07183
$170$	8.10734e9	0.744489
$171$	−8.55036e8	−0.0764719
$172$	5.51682e9	0.480630
$173$	−1.21506e10	−1.03131	−0.515655	−	0.856796i	$-0.672451\pi$
$173$	−1.21506e10	−1.03131	−0.515655	+	0.856796i	$0.672451\pi$
$174$	−1.18470e10	−0.979800
$175$	2.84811e9	0.229554
$176$	2.04272e10	1.60473
$177$	5.02915e9	0.385137
$178$	−1.16580e10	−0.870428
$179$	2.63642e10	1.91945	0.959724	−	0.280946i	$-0.0906481\pi$
$179$	2.63642e10	1.91945	0.959724	+	0.280946i	$0.0906481\pi$
$180$	2.13330e9	0.151469
$181$	2.36407e10	1.63722	0.818609	−	0.574351i	$-0.194746\pi$
$181$	2.36407e10	1.63722	0.818609	+	0.574351i	$0.194746\pi$
$182$	−3.47223e10	−2.34578
$183$	−4.26123e9	−0.280870
$184$	−4.95719e8	−0.0318827
$185$	3.83445e9	0.240675
$186$	1.82816e10	1.11997
$187$	3.19842e10	1.91271
$188$	−1.46223e10	−0.853698
$189$	−3.87482e9	−0.220889
$190$	2.61688e9	0.145678
$191$	1.19414e9	0.0649240	0.0324620	−	0.999473i	$-0.489665\pi$
$191$	1.19414e9	0.0649240	0.0324620	+	0.999473i	$0.489665\pi$
$192$	1.12186e10	0.595775
$193$	−1.39173e10	−0.722017	−0.361008	−	0.932563i	$-0.617567\pi$
$193$	−1.39173e10	−0.722017	−0.361008	+	0.932563i	$0.617567\pi$
$194$	1.09304e10	0.554021
$195$	−7.50390e9	−0.371647
$196$	6.66291e9	0.322486
$197$	−2.14918e10	−1.01666	−0.508330	−	0.861162i	$-0.669737\pi$
$197$	−2.14918e10	−1.01666	−0.508330	+	0.861162i	$0.669737\pi$
$198$	1.66989e10	0.772135
$199$	1.08704e10	0.491366	0.245683	−	0.969350i	$-0.420988\pi$
$199$	1.08704e10	0.491366	0.245683	+	0.969350i	$0.420988\pi$
$200$	−1.03376e8	−0.00456864
$201$	−1.69815e10	−0.733827
$202$	−1.19678e10	−0.505748
$203$	−3.31918e10	−1.37183
$204$	1.70136e10	0.687795
$205$	5.47757e9	0.216618
$206$	5.97675e10	2.31240
$207$	1.22898e10	0.465240
$208$	−3.82212e10	−1.41586
$209$	1.03238e10	0.374268
$210$	1.18591e10	0.420789
$211$	3.41697e10	1.18678	0.593390	−	0.804915i	$-0.297789\pi$
$211$	3.41697e10	1.18678	0.593390	+	0.804915i	$0.297789\pi$
$212$	4.02081e10	1.36711
$213$	2.52811e10	0.841567
$214$	4.19149e10	1.36618
$215$	6.62777e9	0.211541
$216$	1.40643e8	0.00439617
$217$	5.12197e10	1.56808
$218$	6.63685e10	1.99025
$219$	2.37638e10	0.698099
$220$	−2.57578e10	−0.741321
$221$	−5.98454e10	−1.68758
$222$	1.59661e10	0.441174
$223$	3.30933e10	0.896125	0.448063	−	0.894002i	$-0.352114\pi$
$223$	3.30933e10	0.896125	0.448063	+	0.894002i	$0.352114\pi$
$224$	6.13923e10	1.62929
$225$	2.56289e9	0.0666667
$226$	−8.03552e10	−2.04892
$227$	−3.26706e10	−0.816658	−0.408329	−	0.912835i	$-0.633888\pi$
$227$	−3.26706e10	−0.816658	−0.408329	+	0.912835i	$0.633888\pi$
$228$	5.49162e9	0.134584
$229$	2.37442e10	0.570556	0.285278	−	0.958445i	$-0.407914\pi$
$229$	2.37442e10	0.570556	0.285278	+	0.958445i	$0.407914\pi$
$230$	−3.76135e10	−0.886274
$231$	4.67852e10	1.08107
$232$	1.20475e9	0.0273024
$233$	4.15480e10	0.923524	0.461762	−	0.887004i	$-0.347217\pi$
$233$	4.15480e10	0.923524	0.461762	+	0.887004i	$0.347217\pi$
$234$	−3.12451e10	−0.681256
$235$	−1.75668e10	−0.375741
$236$	−3.23006e10	−0.677808
$237$	−1.32175e10	−0.272133
$238$	9.45791e10	1.91073
$239$	−2.27926e10	−0.451860	−0.225930	−	0.974144i	$-0.572542\pi$
$239$	−2.27926e10	−0.451860	−0.225930	+	0.974144i	$0.572542\pi$
$240$	1.30541e10	0.253978
$241$	−8.44183e9	−0.161198	−0.0805991	−	0.996747i	$-0.525683\pi$
$241$	−8.44183e9	−0.161198	−0.0805991	+	0.996747i	$0.525683\pi$
$242$	−1.25868e11	−2.35909
$243$	−3.48678e9	−0.0641500
$244$	2.73685e10	0.494307
$245$	8.00465e9	0.141937
$246$	2.28077e10	0.397077
$247$	−1.93168e10	−0.330217
$248$	−1.85910e9	−0.0312082
$249$	−5.86061e10	−0.966153
$250$	−7.84386e9	−0.126999
$251$	−2.20811e10	−0.351147	−0.175573	−	0.984466i	$-0.556178\pi$
$251$	−2.20811e10	−0.351147	−0.175573	+	0.984466i	$0.556178\pi$
$252$	2.48867e10	0.388746
$253$	−1.48389e11	−2.27698
$254$	1.23592e11	1.86310
$255$	2.04397e10	0.302721
$256$	6.64553e10	0.967052
$257$	−5.61451e10	−0.802811	−0.401405	−	0.915901i	$-0.631478\pi$
$257$	−5.61451e10	−0.802811	−0.401405	+	0.915901i	$0.631478\pi$
$258$	2.75970e10	0.387770
$259$	4.47322e10	0.617690
$260$	4.81951e10	0.654068
$261$	−2.98679e10	−0.398403
$262$	8.78268e10	1.15152
$263$	−6.01213e10	−0.774867	−0.387434	−	0.921898i	$-0.626638\pi$
$263$	−6.01213e10	−0.774867	−0.387434	+	0.921898i	$0.626638\pi$
$264$	−1.69814e9	−0.0215157
$265$	4.83050e10	0.601708
$266$	3.05282e10	0.373881
$267$	−2.93913e10	−0.353930
$268$	1.09067e11	1.29147
$269$	−1.19158e11	−1.38751	−0.693757	−	0.720209i	$-0.744046\pi$
$269$	−1.19158e11	−1.38751	−0.693757	+	0.720209i	$0.744046\pi$
$270$	1.06715e10	0.122205
$271$	1.12190e11	1.26355	0.631776	−	0.775151i	$-0.282326\pi$
$271$	1.12190e11	1.26355	0.631776	+	0.775151i	$0.282326\pi$
$272$	1.04110e11	1.15327
$273$	−8.75394e10	−0.953832
$274$	−2.09114e11	−2.24133
$275$	−3.09448e10	−0.326280
$276$	−7.89332e10	−0.818783
$277$	1.33746e11	1.36496	0.682482	−	0.730902i	$-0.260900\pi$
$277$	1.33746e11	1.36496	0.682482	+	0.730902i	$0.260900\pi$
$278$	1.52356e11	1.52988
$279$	4.60904e10	0.455398
$280$	−1.20598e9	−0.0117254
$281$	−2.70035e10	−0.258369	−0.129185	−	0.991621i	$-0.541236\pi$
$281$	−2.70035e10	−0.258369	−0.129185	+	0.991621i	$0.541236\pi$
$282$	−7.31456e10	−0.688759
$283$	1.15317e11	1.06870	0.534349	−	0.845264i	$-0.320557\pi$
$283$	1.15317e11	1.06870	0.534349	+	0.845264i	$0.320557\pi$
$284$	−1.62373e11	−1.48109
$285$	6.59750e9	0.0592349
$286$	3.77258e11	3.33420
$287$	6.39005e10	0.555950
$288$	5.52443e10	0.473174
$289$	4.44233e10	0.374603
$290$	9.14122e10	0.758950
$291$	2.75568e10	0.225274
$292$	−1.52627e11	−1.22860
$293$	−1.63123e11	−1.29304	−0.646519	−	0.762898i	$-0.723776\pi$
$293$	−1.63123e11	−1.29304	−0.646519	+	0.762898i	$0.723776\pi$
$294$	3.33301e10	0.260180
$295$	−3.88052e10	−0.298325
$296$	−1.62362e9	−0.0122934
$297$	4.21000e10	0.313963
$298$	2.82833e11	2.07758
$299$	2.77649e11	2.00898
$300$	−1.64606e10	−0.117328
$301$	7.73187e10	0.542919
$302$	−3.80444e11	−2.63184
$303$	−3.01725e10	−0.205645
$304$	3.36044e10	0.225666
$305$	3.28799e10	0.217561
$306$	8.51076e10	0.554909
$307$	−4.88233e10	−0.313693	−0.156846	−	0.987623i	$-0.550133\pi$
$307$	−4.88233e10	−0.313693	−0.156846	+	0.987623i	$0.550133\pi$
$308$	−3.00487e11	−1.90260
$309$	1.50682e11	0.940258
$310$	−1.41062e11	−0.867525
$311$	−8.38590e10	−0.508309	−0.254155	−	0.967164i	$-0.581797\pi$
$311$	−8.38590e10	−0.508309	−0.254155	+	0.967164i	$0.581797\pi$
$312$	3.17738e9	0.0189833
$313$	1.30273e10	0.0767193	0.0383596	−	0.999264i	$-0.487787\pi$
$313$	1.30273e10	0.0767193	0.0383596	+	0.999264i	$0.487787\pi$
$314$	−1.01137e11	−0.587121
$315$	2.98983e10	0.171100
$316$	8.48917e10	0.478932
$317$	−2.85804e10	−0.158965	−0.0794826	−	0.996836i	$-0.525327\pi$
$317$	−2.85804e10	−0.158965	−0.0794826	+	0.996836i	$0.525327\pi$
$318$	2.01135e11	1.10297
$319$	3.60630e11	1.94986
$320$	−8.65631e10	−0.461486
$321$	1.05673e11	0.555510
$322$	−4.38793e11	−2.27462
$323$	5.26166e10	0.268975
$324$	2.23945e10	0.112899
$325$	5.79004e10	0.287877
$326$	−1.07865e11	−0.528933
$327$	1.67324e11	0.809269
$328$	−2.31937e9	−0.0110646
$329$	−2.04932e11	−0.964337
$330$	−1.28849e11	−0.598094
$331$	3.24561e11	1.48618	0.743088	−	0.669194i	$-0.233360\pi$
$331$	3.24561e11	1.48618	0.743088	+	0.669194i	$0.233360\pi$
$332$	3.76408e11	1.70035
$333$	4.02525e10	0.179388
$334$	−1.22828e11	−0.540057
$335$	1.31030e11	0.568420
$336$	1.52287e11	0.651834
$337$	−3.95093e11	−1.66865	−0.834325	−	0.551274i	$-0.814142\pi$
$337$	−3.95093e11	−1.66865	−0.834325	+	0.551274i	$0.814142\pi$
$338$	−3.65178e11	−1.52188
$339$	−2.02586e11	−0.833126
$340$	−1.31277e11	−0.532764
$341$	−5.56503e11	−2.22881
$342$	2.74710e10	0.108582
$343$	−2.00844e11	−0.783492
$344$	−2.80640e9	−0.0108053
$345$	−9.48284e10	−0.360373
$346$	3.90379e11	1.46435
$347$	2.13747e11	0.791437	0.395719	−	0.918372i	$-0.370496\pi$
$347$	2.13747e11	0.791437	0.395719	+	0.918372i	$0.370496\pi$
$348$	1.91832e11	0.701155
$349$	−1.11084e11	−0.400809	−0.200405	−	0.979713i	$-0.564226\pi$
$349$	−1.11084e11	−0.400809	−0.200405	+	0.979713i	$0.564226\pi$
$350$	−9.15054e10	−0.325942
$351$	−7.87729e10	−0.277010
$352$	−6.67028e11	−2.31581
$353$	2.60767e11	0.893853	0.446926	−	0.894571i	$-0.352519\pi$
$353$	2.60767e11	0.893853	0.446926	+	0.894571i	$0.352519\pi$
$354$	−1.61579e11	−0.546852
$355$	−1.95071e11	−0.651875
$356$	1.88771e11	0.622887
$357$	2.38446e11	0.776933
$358$	−8.47041e11	−2.72540
$359$	1.70320e11	0.541178	0.270589	−	0.962695i	$-0.412782\pi$
$359$	1.70320e11	0.541178	0.270589	+	0.962695i	$0.412782\pi$
$360$	−1.08520e9	−0.00340526
$361$	1.69836e10	0.0526316
$362$	−7.59538e11	−2.32467
$363$	−3.17329e11	−0.959245
$364$	5.62238e11	1.67866
$365$	−1.83363e11	−0.540745
$366$	1.36907e11	0.398804
$367$	−1.28371e11	−0.369376	−0.184688	−	0.982797i	$-0.559127\pi$
$367$	−1.28371e11	−0.369376	−0.184688	+	0.982797i	$0.559127\pi$
$368$	−4.83009e11	−1.37290
$369$	5.75013e10	0.161458
$370$	−1.23195e11	−0.341732
$371$	5.63520e11	1.54428
$372$	−2.96024e11	−0.801462
$373$	5.12085e11	1.36979	0.684893	−	0.728644i	$-0.259849\pi$
$373$	5.12085e11	1.36979	0.684893	+	0.728644i	$0.259849\pi$
$374$	−1.02760e12	−2.71583
$375$	−1.97754e10	−0.0516398
$376$	7.43832e9	0.0191924
$377$	−6.74771e11	−1.72036
$378$	1.24492e11	0.313638
$379$	−4.49463e11	−1.11897	−0.559484	−	0.828841i	$-0.689001\pi$
$379$	−4.49463e11	−1.11897	−0.559484	+	0.828841i	$0.689001\pi$
$380$	−4.23736e10	−0.104248
$381$	3.11590e11	0.757568
$382$	−3.83659e10	−0.0921849
$383$	5.56817e11	1.32226	0.661131	−	0.750270i	$-0.270077\pi$
$383$	5.56817e11	1.32226	0.661131	+	0.750270i	$0.270077\pi$
$384$	−1.12373e10	−0.0263736
$385$	−3.60997e11	−0.837395
$386$	4.47142e11	1.02518
$387$	6.95757e10	0.157673
$388$	−1.76989e11	−0.396463
$389$	4.54747e11	1.00692	0.503462	−	0.864017i	$-0.332059\pi$
$389$	4.54747e11	1.00692	0.503462	+	0.864017i	$0.332059\pi$
$390$	2.41089e11	0.527699
$391$	−7.56280e11	−1.63639
$392$	−3.38941e9	−0.00724998
$393$	2.21423e11	0.468226
$394$	6.90500e11	1.44355
$395$	1.01987e11	0.210794
$396$	−2.70395e11	−0.552548
$397$	−3.54931e11	−0.717111	−0.358556	−	0.933508i	$-0.616731\pi$
$397$	−3.54931e11	−0.717111	−0.358556	+	0.933508i	$0.616731\pi$
$398$	−3.49248e11	−0.697686
$399$	7.69655e10	0.152026
$400$	−1.00726e11	−0.196731
$401$	1.16496e11	0.224990	0.112495	−	0.993652i	$-0.464116\pi$
$401$	1.16496e11	0.224990	0.112495	+	0.993652i	$0.464116\pi$
$402$	5.45589e11	1.04195
$403$	1.04127e12	1.96648
$404$	1.93788e11	0.361919
$405$	2.69042e10	0.0496904
$406$	1.06640e12	1.94784
$407$	−4.86016e11	−0.877961
$408$	−8.65477e9	−0.0154627
$409$	4.97357e11	0.878847	0.439423	−	0.898280i	$-0.355183\pi$
$409$	4.97357e11	0.878847	0.439423	+	0.898280i	$0.355183\pi$
$410$	−1.75986e11	−0.307574
$411$	−5.27205e11	−0.911362
$412$	−9.67780e11	−1.65478
$413$	−4.52696e11	−0.765651
$414$	−3.94851e11	−0.660590
$415$	4.52208e11	0.748379
$416$	1.24807e12	2.04324
$417$	3.84109e11	0.622074
$418$	−3.31689e11	−0.531420
$419$	−5.96782e11	−0.945916	−0.472958	−	0.881085i	$-0.656814\pi$
$419$	−5.96782e11	−0.945916	−0.472958	+	0.881085i	$0.656814\pi$
$420$	−1.92027e11	−0.301121
$421$	−5.70647e11	−0.885315	−0.442658	−	0.896691i	$-0.645964\pi$
$421$	−5.70647e11	−0.885315	−0.442658	+	0.896691i	$0.645964\pi$
$422$	−1.09782e12	−1.68510
$423$	−1.84410e11	−0.280060
$424$	−2.04538e10	−0.0307346
$425$	−1.57713e11	−0.234487
$426$	−8.12244e11	−1.19493
$427$	3.83572e11	0.558369
$428$	−6.78704e11	−0.977650
$429$	9.51117e11	1.35574
$430$	−2.12940e11	−0.300365
$431$	−5.48853e11	−0.766141	−0.383070	−	0.923719i	$-0.625133\pi$
$431$	−5.48853e11	−0.766141	−0.383070	+	0.923719i	$0.625133\pi$
$432$	1.37037e11	0.189304
$433$	−1.92999e11	−0.263852	−0.131926	−	0.991260i	$-0.542116\pi$
$433$	−1.92999e11	−0.263852	−0.131926	+	0.991260i	$0.542116\pi$
$434$	−1.64561e12	−2.22650
$435$	2.30462e11	0.308601
$436$	−1.07467e12	−1.42424
$437$	−2.44111e11	−0.320200
$438$	−7.63494e11	−0.991224
$439$	−9.32239e11	−1.19794	−0.598972	−	0.800770i	$-0.704424\pi$
$439$	−9.32239e11	−1.19794	−0.598972	+	0.800770i	$0.704424\pi$
$440$	1.31029e10	0.0166660
$441$	8.40296e10	0.105793
$442$	1.92274e12	2.39618
$443$	5.24666e11	0.647241	0.323621	−	0.946187i	$-0.395100\pi$
$443$	5.24666e11	0.647241	0.323621	+	0.946187i	$0.395100\pi$
$444$	−2.58529e11	−0.315708
$445$	2.26784e11	0.274153
$446$	−1.06324e12	−1.27240
$447$	7.13060e11	0.844777
$448$	−1.00983e12	−1.18440
$449$	5.78153e11	0.671327	0.335664	−	0.941982i	$-0.391039\pi$
$449$	5.78153e11	0.671327	0.335664	+	0.941982i	$0.391039\pi$
$450$	−8.23417e10	−0.0946593
$451$	−6.94280e11	−0.790206
$452$	1.30114e12	1.46623
$453$	−9.59148e11	−1.07015
$454$	1.04965e12	1.15956
$455$	6.75458e11	0.738835
$456$	−2.79358e9	−0.00302565
$457$	1.14602e12	1.22904	0.614522	−	0.788899i	$-0.289349\pi$
$457$	1.14602e12	1.22904	0.614522	+	0.788899i	$0.289349\pi$
$458$	−7.62864e11	−0.810126
$459$	2.14567e11	0.225635
$460$	6.09053e11	0.634227
$461$	−2.67687e11	−0.276040	−0.138020	−	0.990429i	$-0.544074\pi$
$461$	−2.67687e11	−0.276040	−0.138020	+	0.990429i	$0.544074\pi$
$462$	−1.50314e12	−1.53500
$463$	1.54932e12	1.56685	0.783423	−	0.621489i	$-0.213472\pi$
$463$	1.54932e12	1.56685	0.783423	+	0.621489i	$0.213472\pi$
$464$	1.17386e12	1.17567
$465$	−3.55636e11	−0.352750
$466$	−1.33487e12	−1.31130
$467$	1.28980e12	1.25487	0.627433	−	0.778670i	$-0.284106\pi$
$467$	1.28980e12	1.25487	0.627433	+	0.778670i	$0.284106\pi$
$468$	5.05933e11	0.487514
$469$	1.52858e12	1.45885
$470$	5.64395e11	0.533510
$471$	−2.54980e11	−0.238733
$472$	1.64313e10	0.0152381
$473$	−8.40069e11	−0.771684
$474$	4.24658e11	0.386399
$475$	−5.09066e10	−0.0458831
$476$	−1.53146e12	−1.36734
$477$	5.07087e11	0.448487
$478$	7.32292e11	0.641592
$479$	−1.16631e12	−1.01229	−0.506144	−	0.862449i	$-0.668930\pi$
$479$	−1.16631e12	−1.01229	−0.506144	+	0.862449i	$0.668930\pi$
$480$	−4.26268e11	−0.366519
$481$	9.09379e11	0.774626
$482$	2.71223e11	0.228884
$483$	−1.10626e12	−0.924897
$484$	2.03810e12	1.68819
$485$	−2.12630e11	−0.174497
$486$	1.12025e11	0.0910860
$487$	−1.43639e11	−0.115715	−0.0578577	−	0.998325i	$-0.518427\pi$
$487$	−1.43639e11	−0.115715	−0.0578577	+	0.998325i	$0.518427\pi$
$488$	−1.39223e10	−0.0111128
$489$	−2.71941e11	−0.215073
$490$	−2.57177e11	−0.201535
$491$	5.03616e11	0.391050	0.195525	−	0.980699i	$-0.437359\pi$
$491$	5.03616e11	0.391050	0.195525	+	0.980699i	$0.437359\pi$
$492$	−3.69312e11	−0.284152
$493$	1.83799e12	1.40130
$494$	6.20620e11	0.468872
$495$	−3.24846e11	−0.243195
$496$	−1.81143e12	−1.34386
$497$	−2.27567e12	−1.67303
$498$	1.88292e12	1.37183
$499$	2.68964e12	1.94197	0.970984	−	0.239145i	$-0.0768672\pi$
$499$	2.68964e12	1.94197	0.970984	+	0.239145i	$0.0768672\pi$
$500$	1.27011e11	0.0908817
$501$	−3.09667e11	−0.219596
$502$	7.09431e11	0.498590
$503$	1.57010e12	1.09363	0.546816	−	0.837253i	$-0.315840\pi$
$503$	1.57010e12	1.09363	0.546816	+	0.837253i	$0.315840\pi$
$504$	−1.26598e10	−0.00873959
$505$	2.32812e11	0.159292
$506$	4.76750e12	3.23306
$507$	−9.20662e11	−0.618820
$508$	−2.00124e12	−1.33326
$509$	2.31469e12	1.52849	0.764245	−	0.644926i	$-0.223112\pi$
$509$	2.31469e12	1.52849	0.764245	+	0.644926i	$0.223112\pi$
$510$	−6.56695e11	−0.429831
$511$	−2.13908e12	−1.38782
$512$	−2.20614e12	−1.41879
$513$	6.92579e10	0.0441511
$514$	1.80386e12	1.13990
$515$	−1.16267e12	−0.728321
$516$	−4.46863e11	−0.277492
$517$	2.22659e12	1.37067
$518$	−1.43717e12	−0.877053
$519$	9.84197e11	0.595428
$520$	−2.45168e10	−0.0147044
$521$	5.91477e11	0.351697	0.175848	−	0.984417i	$-0.443733\pi$
$521$	5.91477e11	0.351697	0.175848	+	0.984417i	$0.443733\pi$
$522$	9.59609e11	0.565688
$523$	6.33830e11	0.370438	0.185219	−	0.982697i	$-0.440701\pi$
$523$	6.33830e11	0.370438	0.185219	+	0.982697i	$0.440701\pi$
$524$	−1.42213e12	−0.824039
$525$	−2.30697e11	−0.132533
$526$	1.93160e12	1.10023
$527$	−2.83628e12	−1.60177
$528$	−1.65460e12	−0.926491
$529$	1.70756e12	0.948035
$530$	−1.55197e12	−0.854359
$531$	−4.07361e11	−0.222359
$532$	−4.94325e11	−0.267553
$533$	1.29906e12	0.697200
$534$	9.44295e11	0.502542
$535$	−8.15378e11	−0.430296
$536$	−5.54821e10	−0.0290343
$537$	−2.13550e12	−1.10819
$538$	3.82836e12	1.97012
$539$	−1.01459e12	−0.517774
$540$	−1.72797e11	−0.0874509
$541$	8.68493e11	0.435892	0.217946	−	0.975961i	$-0.430064\pi$
$541$	8.68493e11	0.435892	0.217946	+	0.975961i	$0.430064\pi$
$542$	−3.60450e12	−1.79410
$543$	−1.91490e12	−0.945248
$544$	−3.39959e12	−1.66430
$545$	−1.29108e12	−0.626857
$546$	2.81251e12	1.35434
$547$	8.04749e11	0.384341	0.192171	−	0.981362i	$-0.438447\pi$
$547$	8.04749e11	0.384341	0.192171	+	0.981362i	$0.438447\pi$
$548$	3.38607e12	1.60392
$549$	3.45160e11	0.162160
$550$	9.94207e11	0.463281
$551$	5.93265e11	0.274199
$552$	4.01532e10	0.0184075
$553$	1.18976e12	0.541001
$554$	−4.29705e12	−1.93810
$555$	−3.10590e11	−0.138954
$556$	−2.46701e12	−1.09480
$557$	9.18654e11	0.404393	0.202197	−	0.979345i	$-0.435192\pi$
$557$	9.18654e11	0.404393	0.202197	+	0.979345i	$0.435192\pi$
$558$	−1.48081e12	−0.646615
$559$	1.57184e12	0.680858
$560$	−1.17506e12	−0.504908
$561$	−2.59072e12	−1.10430
$562$	8.67579e11	0.366856
$563$	4.47734e12	1.87816	0.939080	−	0.343698i	$-0.111680\pi$
$563$	4.47734e12	1.87816	0.939080	+	0.343698i	$0.111680\pi$
$564$	1.18440e12	0.492883
$565$	1.56316e12	0.645336
$566$	−3.70496e12	−1.51743
$567$	3.13861e11	0.127530
$568$	8.25987e10	0.0332971
$569$	4.39599e12	1.75813	0.879066	−	0.476699i	$-0.158167\pi$
$569$	4.39599e12	1.75813	0.879066	+	0.476699i	$0.158167\pi$
$570$	−2.11967e11	−0.0841070
$571$	4.03732e12	1.58939	0.794696	−	0.607008i	$-0.207630\pi$
$571$	4.03732e12	1.58939	0.794696	+	0.607008i	$0.207630\pi$
$572$	−6.10872e12	−2.38599
$573$	−9.67253e10	−0.0374839
$574$	−2.05302e12	−0.789388
$575$	7.31701e11	0.279144
$576$	−9.08705e11	−0.343971
$577$	−4.81971e11	−0.181021	−0.0905107	−	0.995895i	$-0.528850\pi$
$577$	−4.81971e11	−0.181021	−0.0905107	+	0.995895i	$0.528850\pi$
$578$	−1.42725e12	−0.531895
$579$	1.12730e12	0.416857
$580$	−1.48018e12	−0.543112
$581$	5.27539e12	1.92071
$582$	−8.85359e11	−0.319864
$583$	−6.12265e12	−2.19498
$584$	7.76412e10	0.0276207
$585$	6.07816e11	0.214571
$586$	5.24089e12	1.83597
$587$	1.72004e12	0.597954	0.298977	−	0.954260i	$-0.403355\pi$
$587$	1.72004e12	0.597954	0.298977	+	0.954260i	$0.403355\pi$
$588$	−5.39695e11	−0.186188
$589$	−9.15492e11	−0.313426
$590$	1.24675e12	0.423589
$591$	1.74084e12	0.586969
$592$	−1.58199e12	−0.529368
$593$	2.08897e12	0.693723	0.346861	−	0.937916i	$-0.387247\pi$
$593$	2.08897e12	0.693723	0.346861	+	0.937916i	$0.387247\pi$
$594$	−1.35261e12	−0.445793
$595$	−1.83986e12	−0.601810
$596$	−4.57976e12	−1.48674
$597$	−8.80500e11	−0.283690
$598$	−8.92042e12	−2.85253
$599$	5.70633e12	1.81107	0.905537	−	0.424266i	$-0.139468\pi$
$599$	5.70633e12	1.81107	0.905537	+	0.424266i	$0.139468\pi$
$600$	8.37349e9	0.00263770
$601$	−5.16223e12	−1.61400	−0.806998	−	0.590554i	$-0.798909\pi$
$601$	−5.16223e12	−1.61400	−0.806998	+	0.590554i	$0.798909\pi$
$602$	−2.48413e12	−0.770886
$603$	1.37550e12	0.423675
$604$	6.16030e12	1.88337
$605$	2.44852e12	0.743028
$606$	9.69394e11	0.291994
$607$	−1.81411e12	−0.542393	−0.271196	−	0.962524i	$-0.587419\pi$
$607$	−1.81411e12	−0.542393	−0.271196	+	0.962524i	$0.587419\pi$
$608$	−1.09732e12	−0.325661
$609$	2.68854e12	0.792024
$610$	−1.05638e12	−0.308912
$611$	−4.16615e12	−1.20934
$612$	−1.37810e12	−0.397099
$613$	6.03843e12	1.72724	0.863618	−	0.504147i	$-0.168193\pi$
$613$	6.03843e12	1.72724	0.863618	+	0.504147i	$0.168193\pi$
$614$	1.56862e12	0.445409
$615$	−4.43683e11	−0.125065
$616$	1.52857e11	0.0427733
$617$	1.72649e12	0.479601	0.239800	−	0.970822i	$-0.422918\pi$
$617$	1.72649e12	0.479601	0.239800	+	0.970822i	$0.422918\pi$
$618$	−4.84117e12	−1.33506
$619$	−4.44023e12	−1.21562	−0.607810	−	0.794083i	$-0.707952\pi$
$619$	−4.44023e12	−1.21562	−0.607810	+	0.794083i	$0.707952\pi$
$620$	2.28413e12	0.620810
$621$	−9.95471e11	−0.268606
$622$	2.69426e12	0.721743
$623$	2.64563e12	0.703613
$624$	3.09591e12	0.817444
$625$	1.52588e11	0.0400000
$626$	−4.18546e11	−0.108933
$627$	−8.36232e11	−0.216084
$628$	1.63766e12	0.420150
$629$	−2.47703e12	−0.630963
$630$	−9.60587e11	−0.242943
$631$	−2.22856e12	−0.559619	−0.279810	−	0.960055i	$-0.590271\pi$
$631$	−2.22856e12	−0.559619	−0.279810	+	0.960055i	$0.590271\pi$
$632$	−4.31843e10	−0.0107671
$633$	−2.76775e12	−0.685188
$634$	9.18245e11	0.225713
$635$	−2.40425e12	−0.586810
$636$	−3.25686e12	−0.789299
$637$	1.89839e12	0.456832
$638$	−1.15865e13	−2.76859
$639$	−2.04777e12	−0.485879
$640$	8.67072e10	0.0204289
$641$	−3.78005e12	−0.884375	−0.442188	−	0.896923i	$-0.645798\pi$
$641$	−3.78005e12	−0.884375	−0.442188	+	0.896923i	$0.645798\pi$
$642$	−3.39511e12	−0.788763
$643$	1.02799e12	0.237158	0.118579	−	0.992945i	$-0.462166\pi$
$643$	1.02799e12	0.237158	0.118579	+	0.992945i	$0.462166\pi$
$644$	7.10512e12	1.62774
$645$	−5.36850e11	−0.122133
$646$	−1.69049e12	−0.381915
$647$	2.67859e12	0.600949	0.300474	−	0.953790i	$-0.402855\pi$
$647$	2.67859e12	0.600949	0.300474	+	0.953790i	$0.402855\pi$
$648$	−1.13920e10	−0.00253813
$649$	4.91854e12	1.08827
$650$	−1.86025e12	−0.408754
$651$	−4.14879e12	−0.905331
$652$	1.74659e12	0.378510
$653$	6.41202e12	1.38002	0.690011	−	0.723799i	$-0.257606\pi$
$653$	6.41202e12	1.38002	0.690011	+	0.723799i	$0.257606\pi$
$654$	−5.37585e12	−1.14907
$655$	−1.70851e12	−0.362686
$656$	−2.25990e12	−0.476455
$657$	−1.92487e12	−0.403048
$658$	6.58415e12	1.36925
$659$	1.90060e11	0.0392560	0.0196280	−	0.999807i	$-0.493752\pi$
$659$	1.90060e11	0.0392560	0.0196280	+	0.999807i	$0.493752\pi$
$660$	2.08638e12	0.428002
$661$	2.25692e12	0.459843	0.229922	−	0.973209i	$-0.426153\pi$
$661$	2.25692e12	0.459843	0.229922	+	0.973209i	$0.426153\pi$
$662$	−1.04276e13	−2.11021
$663$	4.84748e12	0.974327
$664$	−1.91478e11	−0.0382264
$665$	−5.93870e11	−0.117759
$666$	−1.29325e12	−0.254712
$667$	−8.52723e12	−1.66818
$668$	1.98889e12	0.386471
$669$	−2.68056e12	−0.517378
$670$	−4.20979e12	−0.807094
$671$	−4.16751e12	−0.793644
$672$	−4.97278e12	−0.940670
$673$	−5.47515e12	−1.02879	−0.514396	−	0.857553i	$-0.671984\pi$
$673$	−5.47515e12	−1.02879	−0.514396	+	0.857553i	$0.671984\pi$
$674$	1.26937e13	2.36930
$675$	−2.07594e11	−0.0384900
$676$	5.91311e12	1.08907
$677$	9.09947e12	1.66482	0.832409	−	0.554161i	$-0.186961\pi$
$677$	9.09947e12	1.66482	0.832409	+	0.554161i	$0.186961\pi$
$678$	6.50877e12	1.18295
$679$	−2.48051e12	−0.447845
$680$	6.67806e10	0.0119773
$681$	2.64632e12	0.471498
$682$	1.78796e13	3.16466
$683$	5.38356e12	0.946622	0.473311	−	0.880895i	$-0.343059\pi$
$683$	5.38356e12	0.946622	0.473311	+	0.880895i	$0.343059\pi$
$684$	−4.44821e11	−0.0777022
$685$	4.06794e12	0.705938
$686$	6.45279e12	1.11247
$687$	−1.92328e12	−0.329410
$688$	−2.73445e12	−0.465288
$689$	1.14560e13	1.93663
$690$	3.04669e12	0.511691
$691$	5.45592e12	0.910368	0.455184	−	0.890397i	$-0.349573\pi$
$691$	5.45592e12	0.910368	0.455184	+	0.890397i	$0.349573\pi$
$692$	−6.32118e12	−1.04790
$693$	−3.78960e12	−0.624158
$694$	−6.86734e12	−1.12375
$695$	−2.96380e12	−0.481856
$696$	−9.75845e10	−0.0157630
$697$	−3.53848e12	−0.567896
$698$	3.56896e12	0.569105
$699$	−3.36538e12	−0.533197
$700$	1.48169e12	0.233247
$701$	−6.20862e12	−0.971099	−0.485550	−	0.874209i	$-0.661381\pi$
$701$	−6.20862e12	−0.971099	−0.485550	+	0.874209i	$0.661381\pi$
$702$	2.53085e12	0.393323
$703$	−7.99535e11	−0.123463
$704$	1.09719e13	1.68346
$705$	1.42291e12	0.216934
$706$	−8.37803e12	−1.26917
$707$	2.71595e12	0.408823
$708$	2.61635e12	0.391333
$709$	4.28672e12	0.637114	0.318557	−	0.947904i	$-0.396802\pi$
$709$	4.28672e12	0.637114	0.318557	+	0.947904i	$0.396802\pi$
$710$	6.26731e12	0.925591
$711$	1.07062e12	0.157116
$712$	−9.60273e10	−0.0140034
$713$	1.31587e13	1.90683
$714$	−7.66091e12	−1.10316
$715$	−7.33887e12	−1.05015
$716$	1.37156e13	1.95033
$717$	1.84620e12	0.260882
$718$	−5.47211e12	−0.768414
$719$	7.85422e12	1.09603	0.548016	−	0.836468i	$-0.315383\pi$
$719$	7.85422e12	1.09603	0.548016	+	0.836468i	$0.315383\pi$
$720$	−1.05738e12	−0.146634
$721$	−1.35635e13	−1.86923
$722$	−5.45655e11	−0.0747311
$723$	6.83788e11	0.0930678
$724$	1.22988e13	1.66356
$725$	−1.77826e12	−0.239042
$726$	1.01953e13	1.36202
$727$	4.11305e12	0.546084	0.273042	−	0.962002i	$-0.411970\pi$
$727$	4.11305e12	0.546084	0.273042	+	0.962002i	$0.411970\pi$
$728$	−2.86009e11	−0.0377389
$729$	2.82430e11	0.0370370
$730$	5.89116e12	0.767799
$731$	−4.28150e12	−0.554585
$732$	−2.21685e12	−0.285388
$733$	9.99915e11	0.127937	0.0639683	−	0.997952i	$-0.479624\pi$
$733$	9.99915e11	0.127937	0.0639683	+	0.997952i	$0.479624\pi$
$734$	4.12435e12	0.524473
$735$	−6.48377e11	−0.0819473
$736$	1.57721e13	1.98126
$737$	−1.66080e13	−2.07355
$738$	−1.84743e12	−0.229252
$739$	1.22724e13	1.51366	0.756831	−	0.653610i	$-0.226746\pi$
$739$	1.22724e13	1.51366	0.756831	+	0.653610i	$0.226746\pi$
$740$	1.99482e12	0.244547
$741$	1.56466e12	0.190651
$742$	−1.81050e13	−2.19271
$743$	−4.36651e12	−0.525636	−0.262818	−	0.964845i	$-0.584652\pi$
$743$	−4.36651e12	−0.525636	−0.262818	+	0.964845i	$0.584652\pi$
$744$	1.50587e11	0.0180181
$745$	−5.50201e12	−0.654362
$746$	−1.64525e13	−1.94494
$747$	4.74710e12	0.557809
$748$	1.66394e13	1.94348
$749$	−9.51209e12	−1.10435
$750$	6.35353e11	0.0733228
$751$	9.65504e12	1.10758	0.553789	−	0.832657i	$-0.313181\pi$
$751$	9.65504e12	1.10758	0.553789	+	0.832657i	$0.313181\pi$
$752$	7.24762e12	0.826447
$753$	1.78857e12	0.202735
$754$	2.16793e13	2.44273
$755$	7.40083e12	0.828933
$756$	−2.01583e12	−0.224442
$757$	3.74109e12	0.414063	0.207032	−	0.978334i	$-0.433620\pi$
$757$	3.74109e12	0.414063	0.207032	+	0.978334i	$0.433620\pi$
$758$	1.44406e13	1.58881
$759$	1.20195e13	1.31461
$760$	2.15554e10	0.00234366
$761$	2.99119e12	0.323305	0.161652	−	0.986848i	$-0.448318\pi$
$761$	2.99119e12	0.323305	0.161652	+	0.986848i	$0.448318\pi$
$762$	−1.00109e13	−1.07566
$763$	−1.50615e13	−1.60883
$764$	6.21236e11	0.0659685
$765$	−1.65561e12	−0.174776
$766$	−1.78897e13	−1.87747
$767$	−9.20304e12	−0.960179
$768$	−5.38288e12	−0.558328
$769$	−7.17150e12	−0.739505	−0.369753	−	0.929130i	$-0.620558\pi$
$769$	−7.17150e12	−0.739505	−0.369753	+	0.929130i	$0.620558\pi$
$770$	1.15983e13	1.18901
$771$	4.54776e12	0.463503
$772$	−7.24030e12	−0.733633
$773$	−1.17084e11	−0.0117948	−0.00589738	−	0.999983i	$-0.501877\pi$
$773$	−1.17084e11	−0.0117948	−0.00589738	+	0.999983i	$0.501877\pi$
$774$	−2.23536e12	−0.223879
$775$	2.74410e12	0.273239
$776$	9.00339e10	0.00891309
$777$	−3.62330e12	−0.356624
$778$	−1.46103e13	−1.42972
$779$	−1.14215e12	−0.111123
$780$	−3.90381e12	−0.377627
$781$	2.47251e13	2.37799
$782$	2.42981e13	2.32349
$783$	2.41930e12	0.230018
$784$	−3.30251e12	−0.312192
$785$	1.96744e12	0.184922
$786$	−7.11397e12	−0.664830
$787$	−5.87418e12	−0.545834	−0.272917	−	0.962038i	$-0.587989\pi$
$787$	−5.87418e12	−0.545834	−0.272917	+	0.962038i	$0.587989\pi$
$788$	−1.11809e13	−1.03302
$789$	4.86982e12	0.447370
$790$	−3.27668e12	−0.299304
$791$	1.82356e13	1.65625
$792$	1.37549e11	0.0124221
$793$	7.79779e12	0.700233
$794$	1.14034e13	1.01822
$795$	−3.91271e12	−0.347396
$796$	5.65517e12	0.499271
$797$	−1.06044e13	−0.930945	−0.465472	−	0.885062i	$-0.654116\pi$
$797$	−1.06044e13	−0.930945	−0.465472	+	0.885062i	$0.654116\pi$
$798$	−2.47278e12	−0.215860
$799$	1.13481e13	0.985058
$800$	3.28910e12	0.283905
$801$	2.38069e12	0.204342
$802$	−3.74285e12	−0.319461
$803$	2.32412e13	1.97259
$804$	−8.83440e12	−0.745633
$805$	8.53592e12	0.716422
$806$	−3.34543e13	−2.79218
$807$	9.65179e12	0.801082
$808$	−9.85797e10	−0.00813647
$809$	−1.95948e13	−1.60832	−0.804160	−	0.594413i	$-0.797385\pi$
$809$	−1.95948e13	−1.60832	−0.804160	+	0.594413i	$0.797385\pi$
$810$	−8.64390e11	−0.0705549
$811$	−1.45321e13	−1.17960	−0.589800	−	0.807549i	$-0.700793\pi$
$811$	−1.45321e13	−1.17960	−0.589800	+	0.807549i	$0.700793\pi$
$812$	−1.72676e13	−1.39390
$813$	−9.08740e12	−0.729512
$814$	1.56149e13	1.24661
$815$	2.09831e12	0.166595
$816$	−8.43288e12	−0.665840
$817$	−1.38198e12	−0.108518
$818$	−1.59793e13	−1.24787
$819$	7.09069e12	0.550695
$820$	2.84963e12	0.220103
$821$	1.16117e13	0.891973	0.445987	−	0.895040i	$-0.352853\pi$
$821$	1.16117e13	0.891973	0.445987	+	0.895040i	$0.352853\pi$
$822$	1.69383e13	1.29403
$823$	1.72550e13	1.31104	0.655520	−	0.755178i	$-0.272450\pi$
$823$	1.72550e13	1.31104	0.655520	+	0.755178i	$0.272450\pi$
$824$	4.92308e11	0.0372018
$825$	2.50653e12	0.188378
$826$	1.45444e13	1.08714
$827$	−2.50781e13	−1.86432	−0.932159	−	0.362049i	$-0.882077\pi$
$827$	−2.50781e13	−1.86432	−0.932159	+	0.362049i	$0.882077\pi$
$828$	6.39359e12	0.472725
$829$	−1.64035e13	−1.20626	−0.603129	−	0.797644i	$-0.706080\pi$
$829$	−1.64035e13	−1.20626	−0.603129	+	0.797644i	$0.706080\pi$
$830$	−1.45287e13	−1.06262
$831$	−1.08334e13	−0.788063
$832$	−2.05293e13	−1.48532
$833$	−5.17096e12	−0.372108
$834$	−1.23408e13	−0.883276
$835$	2.38940e12	0.170098
$836$	5.37085e12	0.380290
$837$	−3.73332e12	−0.262924
$838$	1.91737e13	1.34310
$839$	−1.32313e12	−0.0921876	−0.0460938	−	0.998937i	$-0.514677\pi$
$839$	−1.32313e12	−0.0921876	−0.0460938	+	0.998937i	$0.514677\pi$
$840$	9.76840e10	0.00676966
$841$	6.21662e12	0.428521
$842$	1.83340e13	1.25705
$843$	2.18728e12	0.149170
$844$	1.77763e13	1.20587
$845$	7.10387e12	0.479336
$846$	5.92479e12	0.397655
$847$	2.85641e13	1.90698
$848$	−1.99294e13	−1.32347
$849$	−9.34070e12	−0.617013
$850$	5.06709e12	0.332946
$851$	1.14920e13	0.751127
$852$	1.31522e13	0.855106
$853$	−1.19507e12	−0.0772896	−0.0386448	−	0.999253i	$-0.512304\pi$
$853$	−1.19507e12	−0.0772896	−0.0386448	+	0.999253i	$0.512304\pi$
$854$	−1.23236e13	−0.792823
$855$	−5.34398e11	−0.0341993
$856$	3.45256e11	0.0219790
$857$	7.41160e12	0.469351	0.234676	−	0.972074i	$-0.424597\pi$
$857$	7.41160e12	0.469351	0.234676	+	0.972074i	$0.424597\pi$
$858$	−3.05579e13	−1.92500
$859$	2.45050e13	1.53563	0.767814	−	0.640673i	$-0.221344\pi$
$859$	2.45050e13	1.53563	0.767814	+	0.640673i	$0.221344\pi$
$860$	3.44801e12	0.214944
$861$	−5.17594e12	−0.320978
$862$	1.76338e13	1.08784
$863$	1.16324e13	0.713875	0.356937	−	0.934128i	$-0.383821\pi$
$863$	1.16324e13	0.713875	0.356937	+	0.934128i	$0.383821\pi$
$864$	−4.47479e12	−0.273187
$865$	−7.59411e12	−0.461216
$866$	6.20076e12	0.374641
$867$	−3.59829e12	−0.216277
$868$	2.66464e13	1.59331
$869$	−1.29268e13	−0.768957
$870$	−7.40439e12	−0.438180
$871$	3.10751e13	1.82949
$872$	5.46681e11	0.0320192
$873$	−2.23210e12	−0.130062
$874$	7.84292e12	0.454649
$875$	1.78007e12	0.102660
$876$	1.23628e13	0.709330
$877$	−8.79318e12	−0.501935	−0.250968	−	0.967995i	$-0.580749\pi$
$877$	−8.79318e12	−0.501935	−0.250968	+	0.967995i	$0.580749\pi$
$878$	2.99514e13	1.70095
$879$	1.32130e13	0.746536
$880$	1.27670e13	0.717657
$881$	−2.69534e13	−1.50738	−0.753689	−	0.657231i	$-0.771728\pi$
$881$	−2.69534e13	−1.50738	−0.753689	+	0.657231i	$0.771728\pi$
$882$	−2.69974e12	−0.150215
$883$	−1.08823e13	−0.602419	−0.301210	−	0.953558i	$-0.597390\pi$
$883$	−1.08823e13	−0.602419	−0.301210	+	0.953558i	$0.597390\pi$
$884$	−3.11338e13	−1.71473
$885$	3.14322e12	0.172238
$886$	−1.68567e13	−0.919012
$887$	−3.10625e13	−1.68493	−0.842463	−	0.538755i	$-0.818895\pi$
$887$	−3.10625e13	−1.68493	−0.842463	+	0.538755i	$0.818895\pi$
$888$	1.31513e11	0.00709760
$889$	−2.80476e13	−1.50604
$890$	−7.28623e12	−0.389267
$891$	−3.41010e12	−0.181266
$892$	1.72164e13	0.910542
$893$	3.66292e12	0.192751
$894$	−2.29095e13	−1.19949
$895$	1.64776e13	0.858403
$896$	1.01151e12	0.0524307
$897$	−2.24895e13	−1.15988
$898$	−1.85752e13	−0.953211
$899$	−3.19797e13	−1.63289
$900$	1.33331e12	0.0677392
$901$	−3.12048e13	−1.57746
$902$	2.23061e13	1.12201
$903$	−6.26281e12	−0.313455
$904$	−6.61890e11	−0.0329631
$905$	1.47754e13	0.732186
$906$	3.08159e13	1.51949
$907$	−1.72933e13	−0.848489	−0.424244	−	0.905548i	$-0.639460\pi$
$907$	−1.72933e13	−0.848489	−0.424244	+	0.905548i	$0.639460\pi$
$908$	−1.69964e13	−0.829796
$909$	2.44397e12	0.118729
$910$	−2.17014e13	−1.04906
$911$	−2.52104e13	−1.21268	−0.606341	−	0.795205i	$-0.707363\pi$
$911$	−2.52104e13	−1.21268	−0.606341	+	0.795205i	$0.707363\pi$
$912$	−2.72196e12	−0.130288
$913$	−5.73172e13	−2.73002
$914$	−3.68197e13	−1.74511
$915$	−2.66327e12	−0.125609
$916$	1.23526e13	0.579735
$917$	−1.99312e13	−0.930833
$918$	−6.89372e12	−0.320377
$919$	−8.20069e12	−0.379255	−0.189627	−	0.981856i	$-0.560728\pi$
$919$	−8.20069e12	−0.379255	−0.189627	+	0.981856i	$0.560728\pi$
$920$	−3.09824e11	−0.0142584
$921$	3.95469e12	0.181111
$922$	8.60036e12	0.391947
$923$	−4.62630e13	−2.09810
$924$	2.43394e13	1.09847
$925$	2.39653e12	0.107633
$926$	−4.97772e13	−2.22475
$927$	−1.22052e13	−0.542858
$928$	−3.83311e13	−1.69662
$929$	2.89615e12	0.127571	0.0637853	−	0.997964i	$-0.479683\pi$
$929$	2.89615e12	0.127571	0.0637853	+	0.997964i	$0.479683\pi$
$930$	1.14260e13	0.500866
$931$	−1.66908e12	−0.0728121
$932$	2.16148e13	0.938381
$933$	6.79258e12	0.293473
$934$	−4.14394e13	−1.78177
$935$	1.99901e13	0.855389
$936$	−2.57367e11	−0.0109600
$937$	3.68236e13	1.56062	0.780311	−	0.625392i	$-0.215061\pi$
$937$	3.68236e13	1.56062	0.780311	+	0.625392i	$0.215061\pi$
$938$	−4.91108e13	−2.07140
$939$	−1.05521e12	−0.0442939
$940$	−9.13892e12	−0.381785
$941$	4.57947e13	1.90398	0.951989	−	0.306133i	$-0.0990351\pi$
$941$	4.57947e13	1.90398	0.951989	+	0.306133i	$0.0990351\pi$
$942$	8.19211e12	0.338974
$943$	1.64165e13	0.676050
$944$	1.60100e13	0.656172
$945$	−2.42176e12	−0.0987845
$946$	2.69901e13	1.09571
$947$	2.16342e13	0.874109	0.437054	−	0.899435i	$-0.356022\pi$
$947$	2.16342e13	0.874109	0.437054	+	0.899435i	$0.356022\pi$
$948$	−6.87623e12	−0.276511
$949$	−4.34863e13	−1.74042
$950$	1.63555e12	0.0651490
$951$	2.31501e12	0.0917786
$952$	7.79053e11	0.0307398
$953$	3.40827e13	1.33849	0.669246	−	0.743041i	$-0.266617\pi$
$953$	3.40827e13	1.33849	0.669246	+	0.743041i	$0.266617\pi$
$954$	−1.62919e13	−0.636802
$955$	7.46337e11	0.0290349
$956$	−1.18576e13	−0.459130
$957$	−2.92110e13	−1.12575
$958$	3.74718e13	1.43734
$959$	4.74560e13	1.81179
$960$	7.01161e12	0.266439
$961$	2.29096e13	0.866487
$962$	−2.92169e13	−1.09988
$963$	−8.55952e12	−0.320724
$964$	−4.39175e12	−0.163791
$965$	−8.69832e12	−0.322896
$966$	3.55423e13	1.31325
$967$	5.85724e12	0.215414	0.107707	−	0.994183i	$-0.465649\pi$
$967$	5.85724e12	0.215414	0.107707	+	0.994183i	$0.465649\pi$
$968$	−1.03678e12	−0.0379531
$969$	−4.26195e12	−0.155293
$970$	6.83147e12	0.247766
$971$	−4.23372e12	−0.152840	−0.0764198	−	0.997076i	$-0.524349\pi$
$971$	−4.23372e12	−0.152840	−0.0764198	+	0.997076i	$0.524349\pi$
$972$	−1.81395e12	−0.0651821
$973$	−3.45753e13	−1.23668
$974$	4.61489e12	0.164303
$975$	−4.68994e12	−0.166206
$976$	−1.35654e13	−0.478528
$977$	1.15007e13	0.403832	0.201916	−	0.979403i	$-0.435283\pi$
$977$	1.15007e13	0.403832	0.201916	+	0.979403i	$0.435283\pi$
$978$	8.73705e12	0.305380
$979$	−2.87449e13	−1.00009
$980$	4.16432e12	0.144220
$981$	−1.35532e13	−0.467231
$982$	−1.61804e13	−0.555248
$983$	1.65487e13	0.565292	0.282646	−	0.959224i	$-0.408788\pi$
$983$	1.65487e13	0.565292	0.282646	+	0.959224i	$0.408788\pi$
$984$	1.87869e11	0.00638817
$985$	−1.34324e13	−0.454664
$986$	−5.90518e13	−1.98970
$987$	1.65995e13	0.556760
$988$	−1.00493e13	−0.335530
$989$	1.98638e13	0.660204
$990$	1.04368e13	0.345309
$991$	−1.49310e12	−0.0491765	−0.0245883	−	0.999698i	$-0.507827\pi$
$991$	−1.49310e12	−0.0491765	−0.0245883	+	0.999698i	$0.507827\pi$
$992$	5.91504e13	1.93934
$993$	−2.62894e13	−0.858044
$994$	7.31136e13	2.37552
$995$	6.79398e12	0.219746
$996$	−3.04891e13	−0.981697
$997$	2.32477e13	0.745165	0.372582	−	0.927999i	$-0.378472\pi$
$997$	2.32477e13	0.745165	0.372582	+	0.927999i	$0.378472\pi$
$998$	−8.64140e13	−2.75738
$999$	−3.26045e12	−0.103570

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.4	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-32.1284 q^{2} -81.0000 q^{3} +520.237 q^{4} +625.000 q^{5} +2602.40 q^{6} +7291.16 q^{7} -264.644 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-32.1284 q^{2} -81.0000 q^{3} +520.237 q^{4} +625.000 q^{5} +2602.40 q^{6} +7291.16 q^{7} -264.644 q^{8} +6561.00 q^{9} -20080.3 q^{10} -79218.6 q^{11} -42139.2 q^{12} +148225. q^{13} -234254. q^{14} -50625.0 q^{15} -257859. q^{16} -403746. q^{17} -210795. q^{18} -130321. q^{19} +325148. q^{20} -590584. q^{21} +2.54517e6 q^{22} +1.87315e6 q^{23} +21436.1 q^{24} +390625. q^{25} -4.76224e6 q^{26} -531441. q^{27} +3.79313e6 q^{28} -4.55234e6 q^{29} +1.62650e6 q^{30} +7.02490e6 q^{31} +8.42010e6 q^{32} +6.41671e6 q^{33} +1.29717e7 q^{34} +4.55698e6 q^{35} +3.41328e6 q^{36} +6.13512e6 q^{37} +4.18701e6 q^{38} -1.20062e7 q^{39} -165402. q^{40} +8.76411e6 q^{41} +1.89746e7 q^{42} +1.06044e7 q^{43} -4.12124e7 q^{44} +4.10062e6 q^{45} -6.01815e7 q^{46} -2.81069e7 q^{47} +2.08866e7 q^{48} +1.28074e7 q^{49} -1.25502e7 q^{50} +3.27035e7 q^{51} +7.71122e7 q^{52} +7.72880e7 q^{53} +1.70744e7 q^{54} -4.95116e7 q^{55} -1.92956e6 q^{56} +1.05560e7 q^{57} +1.46260e8 q^{58} -6.20883e7 q^{59} -2.63370e7 q^{60} +5.26078e7 q^{61} -2.25699e8 q^{62} +4.78373e7 q^{63} -1.38501e8 q^{64} +9.26407e7 q^{65} -2.06159e8 q^{66} +2.09648e8 q^{67} -2.10044e8 q^{68} -1.51726e8 q^{69} -1.46409e8 q^{70} -3.12113e8 q^{71} -1.73633e6 q^{72} -2.93380e8 q^{73} -1.97112e8 q^{74} -3.16406e7 q^{75} -6.77978e7 q^{76} -5.77596e8 q^{77} +3.85742e8 q^{78} +1.63179e8 q^{79} -1.61162e8 q^{80} +4.30467e7 q^{81} -2.81577e8 q^{82} +7.23532e8 q^{83} -3.07244e8 q^{84} -2.52342e8 q^{85} -3.40704e8 q^{86} +3.68739e8 q^{87} +2.09647e7 q^{88} +3.62855e8 q^{89} -1.31747e8 q^{90} +1.08073e9 q^{91} +9.74484e8 q^{92} -5.69017e8 q^{93} +9.03032e8 q^{94} -8.14506e7 q^{95} -6.82028e8 q^{96} -3.40208e8 q^{97} -4.11483e8 q^{98} -5.19753e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 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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