LMFDB - Embedded newform 285.10.a.h.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:	$0$
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			1.8
Root			$0.751797$ 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)

$f(q)$	$=$	$q-1.75180 q^{2} -81.0000 q^{3} -508.931 q^{4} +625.000 q^{5} +141.896 q^{6} +2356.35 q^{7} +1788.46 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-1.75180 q^{2} -81.0000 q^{3} -508.931 q^{4} +625.000 q^{5} +141.896 q^{6} +2356.35 q^{7} +1788.46 q^{8} +6561.00 q^{9} -1094.87 q^{10} -58059.9 q^{11} +41223.4 q^{12} -35623.9 q^{13} -4127.85 q^{14} -50625.0 q^{15} +257440. q^{16} +567431. q^{17} -11493.5 q^{18} -130321. q^{19} -318082. q^{20} -190864. q^{21} +101709. q^{22} -1.17571e6 q^{23} -144866. q^{24} +390625. q^{25} +62405.9 q^{26} -531441. q^{27} -1.19922e6 q^{28} -1.92724e6 q^{29} +88684.7 q^{30} +2.50653e6 q^{31} -1.36668e6 q^{32} +4.70285e6 q^{33} -994024. q^{34} +1.47272e6 q^{35} -3.33910e6 q^{36} +8.97380e6 q^{37} +228296. q^{38} +2.88554e6 q^{39} +1.11779e6 q^{40} +1.69059e6 q^{41} +334355. q^{42} -9.56490e6 q^{43} +2.95485e7 q^{44} +4.10062e6 q^{45} +2.05961e6 q^{46} +6.17413e6 q^{47} -2.08526e7 q^{48} -3.48012e7 q^{49} -684296. q^{50} -4.59619e7 q^{51} +1.81301e7 q^{52} -7.25514e7 q^{53} +930977. q^{54} -3.62874e7 q^{55} +4.21425e6 q^{56} +1.05560e7 q^{57} +3.37612e6 q^{58} -1.64663e8 q^{59} +2.57646e7 q^{60} -9.49267e7 q^{61} -4.39092e6 q^{62} +1.54600e7 q^{63} -1.29415e8 q^{64} -2.22650e7 q^{65} -8.23844e6 q^{66} +1.74495e8 q^{67} -2.88783e8 q^{68} +9.52327e7 q^{69} -2.57990e6 q^{70} +1.58288e8 q^{71} +1.17341e7 q^{72} -5.12511e6 q^{73} -1.57203e7 q^{74} -3.16406e7 q^{75} +6.63244e7 q^{76} -1.36809e8 q^{77} -5.05488e6 q^{78} -2.90576e8 q^{79} +1.60900e8 q^{80} +4.30467e7 q^{81} -2.96156e6 q^{82} +2.26627e8 q^{83} +9.71368e7 q^{84} +3.54644e8 q^{85} +1.67558e7 q^{86} +1.56106e8 q^{87} -1.03838e8 q^{88} -8.41387e8 q^{89} -7.18346e6 q^{90} -8.39425e7 q^{91} +5.98357e8 q^{92} -2.03029e8 q^{93} -1.08158e7 q^{94} -8.14506e7 q^{95} +1.10701e8 q^{96} -1.02373e9 q^{97} +6.09647e7 q^{98} -3.80931e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.75180	−0.0774192	−0.0387096	−	0.999251i	$-0.512325\pi$
$2$	−1.75180	−0.0774192	−0.0387096	+	0.999251i	$0.512325\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−508.931	−0.994006
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	141.896	0.0446980
$7$	2356.35	0.370936	0.185468	−	0.982650i	$-0.440620\pi$
$7$	2356.35	0.370936	0.185468	+	0.982650i	$0.440620\pi$
$8$	1788.46	0.154374
$9$	6561.00	0.333333
$10$	−1094.87	−0.0346229
$11$	−58059.9	−1.19566	−0.597832	−	0.801621i	$-0.703971\pi$
$11$	−58059.9	−1.19566	−0.597832	+	0.801621i	$0.703971\pi$
$12$	41223.4	0.573890
$13$	−35623.9	−0.345937	−0.172968	−	0.984927i	$-0.555336\pi$
$13$	−35623.9	−0.345937	−0.172968	+	0.984927i	$0.555336\pi$
$14$	−4127.85	−0.0287175
$15$	−50625.0	−0.258199
$16$	257440.	0.982055
$17$	567431.	1.64776	0.823878	−	0.566767i	$-0.191806\pi$
$17$	567431.	1.64776	0.823878	+	0.566767i	$0.191806\pi$
$18$	−11493.5	−0.0258064
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−318082.	−0.444533
$21$	−190864.	−0.214160
$22$	101709.	0.0925674
$23$	−1.17571e6	−0.876044	−0.438022	−	0.898964i	$-0.644321\pi$
$23$	−1.17571e6	−0.876044	−0.438022	+	0.898964i	$0.644321\pi$
$24$	−144866.	−0.0891281
$25$	390625.	0.200000
$26$	62405.9	0.0267822
$27$	−531441.	−0.192450
$28$	−1.19922e6	−0.368712
$29$	−1.92724e6	−0.505992	−0.252996	−	0.967467i	$-0.581416\pi$
$29$	−1.92724e6	−0.505992	−0.252996	+	0.967467i	$0.581416\pi$
$30$	88684.7	0.0199896
$31$	2.50653e6	0.487466	0.243733	−	0.969842i	$-0.421628\pi$
$31$	2.50653e6	0.487466	0.243733	+	0.969842i	$0.421628\pi$
$32$	−1.36668e6	−0.230404
$33$	4.70285e6	0.690317
$34$	−994024.	−0.127568
$35$	1.47272e6	0.165887
$36$	−3.33910e6	−0.331335
$37$	8.97380e6	0.787170	0.393585	−	0.919288i	$-0.371235\pi$
$37$	8.97380e6	0.787170	0.393585	+	0.919288i	$0.371235\pi$
$38$	228296.	0.0177612
$39$	2.88554e6	0.199727
$40$	1.11779e6	0.0690383
$41$	1.69059e6	0.0934351	0.0467175	−	0.998908i	$-0.485124\pi$
$41$	1.69059e6	0.0934351	0.0467175	+	0.998908i	$0.485124\pi$
$42$	334355.	0.0165801
$43$	−9.56490e6	−0.426651	−0.213325	−	0.976981i	$-0.568429\pi$
$43$	−9.56490e6	−0.426651	−0.213325	+	0.976981i	$0.568429\pi$
$44$	2.95485e7	1.18850
$45$	4.10062e6	0.149071
$46$	2.05961e6	0.0678226
$47$	6.17413e6	0.184559	0.0922795	−	0.995733i	$-0.470585\pi$
$47$	6.17413e6	0.184559	0.0922795	+	0.995733i	$0.470585\pi$
$48$	−2.08526e7	−0.566990
$49$	−3.48012e7	−0.862407
$50$	−684296.	−0.0154838
$51$	−4.59619e7	−0.951332
$52$	1.81301e7	0.343863
$53$	−7.25514e7	−1.26300	−0.631501	−	0.775375i	$-0.717561\pi$
$53$	−7.25514e7	−1.26300	−0.631501	+	0.775375i	$0.717561\pi$
$54$	930977.	0.0148993
$55$	−3.62874e7	−0.534717
$56$	4.21425e6	0.0572630
$57$	1.05560e7	0.132453
$58$	3.37612e6	0.0391735
$59$	−1.64663e8	−1.76914	−0.884569	−	0.466409i	$-0.845547\pi$
$59$	−1.64663e8	−1.76914	−0.884569	+	0.466409i	$0.845547\pi$
$60$	2.57646e7	0.256651
$61$	−9.49267e7	−0.877817	−0.438909	−	0.898532i	$-0.644635\pi$
$61$	−9.49267e7	−0.877817	−0.438909	+	0.898532i	$0.644635\pi$
$62$	−4.39092e6	−0.0377392
$63$	1.54600e7	0.123645
$64$	−1.29415e8	−0.964217
$65$	−2.22650e7	−0.154708
$66$	−8.23844e6	−0.0534438
$67$	1.74495e8	1.05790	0.528951	−	0.848653i	$-0.322586\pi$
$67$	1.74495e8	1.05790	0.528951	+	0.848653i	$0.322586\pi$
$68$	−2.88783e8	−1.63788
$69$	9.52327e7	0.505784
$70$	−2.57990e6	−0.0128429
$71$	1.58288e8	0.739242	0.369621	−	0.929183i	$-0.379488\pi$
$71$	1.58288e8	0.739242	0.369621	+	0.929183i	$0.379488\pi$
$72$	1.17341e7	0.0514581
$73$	−5.12511e6	−0.0211228	−0.0105614	−	0.999944i	$-0.503362\pi$
$73$	−5.12511e6	−0.0211228	−0.0105614	+	0.999944i	$0.503362\pi$
$74$	−1.57203e7	−0.0609421
$75$	−3.16406e7	−0.115470
$76$	6.63244e7	0.228041
$77$	−1.36809e8	−0.443515
$78$	−5.05488e6	−0.0154627
$79$	−2.90576e8	−0.839340	−0.419670	−	0.907677i	$-0.637854\pi$
$79$	−2.90576e8	−0.839340	−0.419670	+	0.907677i	$0.637854\pi$
$80$	1.60900e8	0.439188
$81$	4.30467e7	0.111111
$82$	−2.96156e6	−0.00723367
$83$	2.26627e8	0.524157	0.262078	−	0.965047i	$-0.415592\pi$
$83$	2.26627e8	0.524157	0.262078	+	0.965047i	$0.415592\pi$
$84$	9.71368e7	0.212876
$85$	3.54644e8	0.736899
$86$	1.67558e7	0.0330310
$87$	1.56106e8	0.292135
$88$	−1.03838e8	−0.184580
$89$	−8.41387e8	−1.42148	−0.710740	−	0.703455i	$-0.751640\pi$
$89$	−8.41387e8	−1.42148	−0.710740	+	0.703455i	$0.751640\pi$
$90$	−7.18346e6	−0.0115410
$91$	−8.39425e7	−0.128320
$92$	5.98357e8	0.870793
$93$	−2.03029e8	−0.281439
$94$	−1.08158e7	−0.0142884
$95$	−8.14506e7	−0.102598
$96$	1.10701e8	0.133024
$97$	−1.02373e9	−1.17412	−0.587061	−	0.809543i	$-0.699715\pi$
$97$	−1.02373e9	−1.17412	−0.587061	+	0.809543i	$0.699715\pi$
$98$	6.09647e7	0.0667668
$99$	−3.80931e8	−0.398555
$100$	−1.98801e8	−0.198801
$101$	−6.45588e8	−0.617318	−0.308659	−	0.951173i	$-0.599880\pi$
$101$	−6.45588e8	−0.617318	−0.308659	+	0.951173i	$0.599880\pi$
$102$	8.05159e7	0.0736514
$103$	8.91591e8	0.780546	0.390273	−	0.920699i	$-0.372381\pi$
$103$	8.91591e8	0.780546	0.390273	+	0.920699i	$0.372381\pi$
$104$	−6.37121e7	−0.0534038
$105$	−1.19290e8	−0.0957752
$106$	1.27095e8	0.0977806
$107$	1.81900e9	1.34154	0.670772	−	0.741663i	$-0.265963\pi$
$107$	1.81900e9	1.34154	0.670772	+	0.741663i	$0.265963\pi$
$108$	2.70467e8	0.191297
$109$	8.66242e8	0.587787	0.293893	−	0.955838i	$-0.405049\pi$
$109$	8.66242e8	0.587787	0.293893	+	0.955838i	$0.405049\pi$
$110$	6.35682e7	0.0413974
$111$	−7.26878e8	−0.454473
$112$	6.06618e8	0.364279
$113$	2.42801e9	1.40087	0.700433	−	0.713718i	$-0.252990\pi$
$113$	2.42801e9	1.40087	0.700433	+	0.713718i	$0.252990\pi$
$114$	−1.84920e7	−0.0102544
$115$	−7.34820e8	−0.391779
$116$	9.80830e8	0.502959
$117$	−2.33729e8	−0.115312
$118$	2.88456e8	0.136965
$119$	1.33707e9	0.611211
$120$	−9.05410e7	−0.0398593
$121$	1.01301e9	0.429613
$122$	1.66292e8	0.0679599
$123$	−1.36938e8	−0.0539448
$124$	−1.27565e9	−0.484544
$125$	2.44141e8	0.0894427
$126$	−2.70828e7	−0.00957251
$127$	−1.63430e9	−0.557461	−0.278730	−	0.960369i	$-0.589914\pi$
$127$	−1.63430e9	−0.557461	−0.278730	+	0.960369i	$0.589914\pi$
$128$	9.26447e8	0.305053
$129$	7.74757e8	0.246327
$130$	3.90037e7	0.0119773
$131$	5.74382e9	1.70404	0.852021	−	0.523507i	$-0.175377\pi$
$131$	5.74382e9	1.70404	0.852021	+	0.523507i	$0.175377\pi$
$132$	−2.39343e9	−0.686180
$133$	−3.07082e8	−0.0850985
$134$	−3.05679e8	−0.0819019
$135$	−3.32151e8	−0.0860663
$136$	1.01483e9	0.254371
$137$	2.95005e9	0.715462	0.357731	−	0.933825i	$-0.383550\pi$
$137$	2.95005e9	0.715462	0.357731	+	0.933825i	$0.383550\pi$
$138$	−1.66828e8	−0.0391574
$139$	−1.29155e9	−0.293457	−0.146728	−	0.989177i	$-0.546874\pi$
$139$	−1.29155e9	−0.293457	−0.146728	+	0.989177i	$0.546874\pi$
$140$	−7.49512e8	−0.164893
$141$	−5.00104e8	−0.106555
$142$	−2.77289e8	−0.0572315
$143$	2.06832e9	0.413624
$144$	1.68906e9	0.327352
$145$	−1.20452e9	−0.226287
$146$	8.97816e6	0.00163531
$147$	2.81890e9	0.497911
$148$	−4.56705e9	−0.782452
$149$	4.53638e7	0.00753999	0.00377000	−	0.999993i	$-0.498800\pi$
$149$	4.53638e7	0.00753999	0.00377000	+	0.999993i	$0.498800\pi$
$150$	5.54279e7	0.00893960
$151$	7.12435e9	1.11519	0.557596	−	0.830113i	$-0.311724\pi$
$151$	7.12435e9	1.11519	0.557596	+	0.830113i	$0.311724\pi$
$152$	−2.33074e8	−0.0354159
$153$	3.72292e9	0.549252
$154$	2.39662e8	0.0343365
$155$	1.56658e9	0.218002
$156$	−1.46854e9	−0.198530
$157$	3.74317e8	0.0491689	0.0245845	−	0.999698i	$-0.492174\pi$
$157$	3.74317e8	0.0491689	0.0245845	+	0.999698i	$0.492174\pi$
$158$	5.09030e8	0.0649810
$159$	5.87666e9	0.729195
$160$	−8.54172e8	−0.103040
$161$	−2.77039e9	−0.324956
$162$	−7.54091e7	−0.00860213
$163$	1.28608e10	1.42700	0.713502	−	0.700653i	$-0.247108\pi$
$163$	1.28608e10	1.42700	0.713502	+	0.700653i	$0.247108\pi$
$164$	−8.60392e8	−0.0928751
$165$	2.93928e9	0.308719
$166$	−3.97005e8	−0.0405798
$167$	8.79645e9	0.875152	0.437576	−	0.899181i	$-0.355837\pi$
$167$	8.79645e9	0.875152	0.437576	+	0.899181i	$0.355837\pi$
$168$	−3.41354e8	−0.0330608
$169$	−9.33543e9	−0.880328
$170$	−6.21265e8	−0.0570501
$171$	−8.55036e8	−0.0764719
$172$	4.86788e9	0.424094
$173$	−4.11872e9	−0.349587	−0.174793	−	0.984605i	$-0.555926\pi$
$173$	−4.11872e9	−0.349587	−0.174793	+	0.984605i	$0.555926\pi$
$174$	−2.73466e8	−0.0226168
$175$	9.20449e8	0.0741871
$176$	−1.49469e10	−1.17421
$177$	1.33377e10	1.02141
$178$	1.47394e9	0.110050
$179$	1.22320e10	0.890548	0.445274	−	0.895394i	$-0.353106\pi$
$179$	1.22320e10	0.890548	0.445274	+	0.895394i	$0.353106\pi$
$180$	−2.08694e9	−0.148178
$181$	−6.48331e9	−0.448997	−0.224498	−	0.974474i	$-0.572074\pi$
$181$	−6.48331e9	−0.448997	−0.224498	+	0.974474i	$0.572074\pi$
$182$	1.47050e8	0.00993446
$183$	7.68906e9	0.506808
$184$	−2.10272e9	−0.135239
$185$	5.60863e9	0.352033
$186$	3.55665e8	0.0217888
$187$	−3.29450e10	−1.97016
$188$	−3.14221e9	−0.183453
$189$	−1.25226e9	−0.0713866
$190$	1.42685e8	0.00794304
$191$	−1.38010e10	−0.750344	−0.375172	−	0.926955i	$-0.622416\pi$
$191$	−1.38010e10	−0.750344	−0.375172	+	0.926955i	$0.622416\pi$
$192$	1.04826e10	0.556691
$193$	−2.88704e10	−1.49777	−0.748884	−	0.662701i	$-0.769410\pi$
$193$	−2.88704e10	−1.49777	−0.748884	+	0.662701i	$0.769410\pi$
$194$	1.79337e9	0.0908996
$195$	1.80346e9	0.0893205
$196$	1.77114e10	0.857238
$197$	2.94524e10	1.39323	0.696615	−	0.717445i	$-0.254689\pi$
$197$	2.94524e10	1.39323	0.696615	+	0.717445i	$0.254689\pi$
$198$	6.67314e8	0.0308558
$199$	2.68901e10	1.21550	0.607748	−	0.794130i	$-0.292073\pi$
$199$	2.68901e10	1.21550	0.607748	+	0.794130i	$0.292073\pi$
$200$	6.98619e8	0.0308749
$201$	−1.41341e10	−0.610780
$202$	1.13094e9	0.0477923
$203$	−4.54124e9	−0.187691
$204$	2.33915e10	0.945630
$205$	1.05662e9	0.0417854
$206$	−1.56189e9	−0.0604292
$207$	−7.71385e9	−0.292015
$208$	−9.17102e9	−0.339729
$209$	7.56643e9	0.274304
$210$	2.08972e8	0.00741484
$211$	6.75862e9	0.234740	0.117370	−	0.993088i	$-0.462554\pi$
$211$	6.75862e9	0.234740	0.117370	+	0.993088i	$0.462554\pi$
$212$	3.69236e10	1.25543
$213$	−1.28214e10	−0.426802
$214$	−3.18651e9	−0.103861
$215$	−5.97806e9	−0.190804
$216$	−9.50463e8	−0.0297094
$217$	5.90625e9	0.180819
$218$	−1.51748e9	−0.0455060
$219$	4.15134e8	0.0121952
$220$	1.84678e10	0.531512
$221$	−2.02141e10	−0.570020
$222$	1.27334e9	0.0351849
$223$	4.99132e10	1.35159	0.675793	−	0.737091i	$-0.263801\pi$
$223$	4.99132e10	1.35159	0.675793	+	0.737091i	$0.263801\pi$
$224$	−3.22037e9	−0.0854652
$225$	2.56289e9	0.0666667
$226$	−4.25337e9	−0.108454
$227$	7.06331e10	1.76560	0.882800	−	0.469750i	$-0.155656\pi$
$227$	7.06331e10	1.76560	0.882800	+	0.469750i	$0.155656\pi$
$228$	−5.37228e9	−0.131659
$229$	6.54968e10	1.57384	0.786920	−	0.617055i	$-0.211674\pi$
$229$	6.54968e10	1.57384	0.786920	+	0.617055i	$0.211674\pi$
$230$	1.28726e9	0.0303312
$231$	1.10816e10	0.256063
$232$	−3.44679e9	−0.0781122
$233$	6.88175e9	0.152967	0.0764835	−	0.997071i	$-0.475631\pi$
$233$	6.88175e9	0.152967	0.0764835	+	0.997071i	$0.475631\pi$
$234$	4.09445e8	0.00892739
$235$	3.85883e9	0.0825373
$236$	8.38021e10	1.75853
$237$	2.35367e10	0.484593
$238$	−2.34227e9	−0.0473195
$239$	6.39302e10	1.26741	0.633703	−	0.773576i	$-0.281534\pi$
$239$	6.39302e10	1.26741	0.633703	+	0.773576i	$0.281534\pi$
$240$	−1.30329e10	−0.253565
$241$	−8.45832e10	−1.61513	−0.807564	−	0.589779i	$-0.799215\pi$
$241$	−8.45832e10	−1.61513	−0.807564	+	0.589779i	$0.799215\pi$
$242$	−1.77458e9	−0.0332603
$243$	−3.48678e9	−0.0641500
$244$	4.83112e10	0.872556
$245$	−2.17508e10	−0.385680
$246$	2.39887e8	0.00417636
$247$	4.64255e9	0.0793634
$248$	4.48283e9	0.0752523
$249$	−1.83568e10	−0.302622
$250$	−4.27685e8	−0.00692458
$251$	6.90916e8	0.0109874	0.00549368	−	0.999985i	$-0.498251\pi$
$251$	6.90916e8	0.0109874	0.00549368	+	0.999985i	$0.498251\pi$
$252$	−7.86808e9	−0.122904
$253$	6.82618e10	1.04745
$254$	2.86296e9	0.0431582
$255$	−2.87262e10	−0.425449
$256$	6.46375e10	0.940600
$257$	−3.93519e10	−0.562687	−0.281343	−	0.959607i	$-0.590780\pi$
$257$	−3.93519e10	−0.562687	−0.281343	+	0.959607i	$0.590780\pi$
$258$	−1.35722e9	−0.0190704
$259$	2.11454e10	0.291990
$260$	1.13313e10	0.153780
$261$	−1.26446e10	−0.168664
$262$	−1.00620e10	−0.131926
$263$	−1.07320e11	−1.38318	−0.691591	−	0.722289i	$-0.743090\pi$
$263$	−1.07320e11	−1.38318	−0.691591	+	0.722289i	$0.743090\pi$
$264$	8.41088e9	0.106567
$265$	−4.53446e10	−0.564832
$266$	5.37945e8	0.00658826
$267$	6.81523e10	0.820692
$268$	−8.88057e10	−1.05156
$269$	−1.43277e11	−1.66836	−0.834182	−	0.551490i	$-0.814059\pi$
$269$	−1.43277e11	−1.66836	−0.834182	+	0.551490i	$0.814059\pi$
$270$	5.81860e8	0.00666318
$271$	8.69948e10	0.979786	0.489893	−	0.871783i	$-0.337036\pi$
$271$	8.69948e10	0.979786	0.489893	+	0.871783i	$0.337036\pi$
$272$	1.46079e11	1.61819
$273$	6.79934e9	0.0740858
$274$	−5.16789e9	−0.0553905
$275$	−2.26797e10	−0.239133
$276$	−4.84669e10	−0.502753
$277$	5.49940e10	0.561250	0.280625	−	0.959818i	$-0.409458\pi$
$277$	5.49940e10	0.561250	0.280625	+	0.959818i	$0.409458\pi$
$278$	2.26253e9	0.0227192
$279$	1.64453e10	0.162489
$280$	2.63390e9	0.0256088
$281$	−2.33120e9	−0.0223050	−0.0111525	−	0.999938i	$-0.503550\pi$
$281$	−2.33120e9	−0.0223050	−0.0111525	+	0.999938i	$0.503550\pi$
$282$	8.76081e8	0.00824942
$283$	1.44127e11	1.33570	0.667848	−	0.744298i	$-0.267216\pi$
$283$	1.44127e11	1.33570	0.667848	+	0.744298i	$0.267216\pi$
$284$	−8.05579e10	−0.734811
$285$	6.59750e9	0.0592349
$286$	−3.62328e9	−0.0320225
$287$	3.98361e9	0.0346584
$288$	−8.96676e9	−0.0768014
$289$	2.03390e11	1.71510
$290$	2.11008e9	0.0175189
$291$	8.29222e10	0.677880
$292$	2.60833e9	0.0209962
$293$	2.02740e11	1.60707	0.803534	−	0.595258i	$-0.202950\pi$
$293$	2.02740e11	1.60707	0.803534	+	0.595258i	$0.202950\pi$
$294$	−4.93814e9	−0.0385479
$295$	−1.02914e11	−0.791183
$296$	1.60493e10	0.121519
$297$	3.08554e10	0.230106
$298$	−7.94681e7	−0.000583740 0
$299$	4.18835e10	0.303056
$300$	1.61029e10	0.114778
$301$	−2.25383e10	−0.158260
$302$	−1.24804e10	−0.0863372
$303$	5.22926e10	0.356409
$304$	−3.35498e10	−0.225299
$305$	−5.93292e10	−0.392572
$306$	−6.52179e9	−0.0425227
$307$	8.27391e10	0.531604	0.265802	−	0.964028i	$-0.414363\pi$
$307$	8.27391e10	0.531604	0.265802	+	0.964028i	$0.414363\pi$
$308$	6.96266e10	0.440856
$309$	−7.22189e10	−0.450648
$310$	−2.74433e9	−0.0168775
$311$	−1.59406e11	−0.966234	−0.483117	−	0.875556i	$-0.660495\pi$
$311$	−1.59406e11	−0.966234	−0.483117	+	0.875556i	$0.660495\pi$
$312$	5.16068e9	0.0308327
$313$	−4.50058e10	−0.265045	−0.132522	−	0.991180i	$-0.542308\pi$
$313$	−4.50058e10	−0.265045	−0.132522	+	0.991180i	$0.542308\pi$
$314$	−6.55727e8	−0.00380662
$315$	9.66251e9	0.0552958
$316$	1.47883e11	0.834309
$317$	−9.80488e10	−0.545350	−0.272675	−	0.962106i	$-0.587908\pi$
$317$	−9.80488e10	−0.545350	−0.272675	+	0.962106i	$0.587908\pi$
$318$	−1.02947e10	−0.0564537
$319$	1.11895e11	0.604997
$320$	−8.08844e10	−0.431211
$321$	−1.47339e11	−0.774541
$322$	4.85316e9	0.0251578
$323$	−7.39482e10	−0.378021
$324$	−2.19078e10	−0.110445
$325$	−1.39156e10	−0.0691874
$326$	−2.25296e10	−0.110478
$327$	−7.01656e10	−0.339359
$328$	3.02355e9	0.0144240
$329$	1.45484e10	0.0684595
$330$	−5.14903e9	−0.0239008
$331$	−7.56927e10	−0.346600	−0.173300	−	0.984869i	$-0.555443\pi$
$331$	−7.56927e10	−0.346600	−0.173300	+	0.984869i	$0.555443\pi$
$332$	−1.15338e11	−0.521015
$333$	5.88771e10	0.262390
$334$	−1.54096e10	−0.0677536
$335$	1.09059e11	0.473108
$336$	−4.91361e10	−0.210317
$337$	3.05022e9	0.0128824	0.00644121	−	0.999979i	$-0.497950\pi$
$337$	3.05022e9	0.0128824	0.00644121	+	0.999979i	$0.497950\pi$
$338$	1.63538e10	0.0681543
$339$	−1.96668e11	−0.808791
$340$	−1.80490e11	−0.732482
$341$	−1.45529e11	−0.582846
$342$	1.49785e9	0.00592039
$343$	−1.77091e11	−0.690833
$344$	−1.71065e10	−0.0658639
$345$	5.95204e10	0.226194
$346$	7.21516e9	0.0270647
$347$	1.64908e11	0.610605	0.305302	−	0.952255i	$-0.401242\pi$
$347$	1.64908e11	0.610605	0.305302	+	0.952255i	$0.401242\pi$
$348$	−7.94472e10	−0.290384
$349$	3.32107e11	1.19830	0.599148	−	0.800639i	$-0.295506\pi$
$349$	3.32107e11	1.19830	0.599148	+	0.800639i	$0.295506\pi$
$350$	−1.61244e9	−0.00574351
$351$	1.89320e10	0.0665756
$352$	7.93491e10	0.275486
$353$	−3.81617e11	−1.30810	−0.654050	−	0.756451i	$-0.726931\pi$
$353$	−3.81617e11	−1.30810	−0.654050	+	0.756451i	$0.726931\pi$
$354$	−2.33649e10	−0.0790769
$355$	9.89303e10	0.330599
$356$	4.28208e11	1.41296
$357$	−1.08302e11	−0.352883
$358$	−2.14279e10	−0.0689455
$359$	−5.57645e11	−1.77187	−0.885937	−	0.463806i	$-0.846483\pi$
$359$	−5.57645e11	−1.77187	−0.885937	+	0.463806i	$0.846483\pi$
$360$	7.33382e9	0.0230128
$361$	1.69836e10	0.0526316
$362$	1.13574e10	0.0347610
$363$	−8.20535e10	−0.248037
$364$	4.27209e10	0.127551
$365$	−3.20320e9	−0.00944638
$366$	−1.34697e10	−0.0392367
$367$	4.59178e11	1.32125	0.660623	−	0.750718i	$-0.270292\pi$
$367$	4.59178e11	1.32125	0.660623	+	0.750718i	$0.270292\pi$
$368$	−3.02675e11	−0.860323
$369$	1.10919e10	0.0311450
$370$	−9.82517e9	−0.0272541
$371$	−1.70956e11	−0.468493
$372$	1.03328e11	0.279752
$373$	2.11696e10	0.0566268	0.0283134	−	0.999599i	$-0.490986\pi$
$373$	2.11696e10	0.0566268	0.0283134	+	0.999599i	$0.490986\pi$
$374$	5.77129e10	0.152528
$375$	−1.97754e10	−0.0516398
$376$	1.10422e10	0.0284912
$377$	6.86557e10	0.175041
$378$	2.19371e9	0.00552669
$379$	4.37116e11	1.08823	0.544115	−	0.839011i	$-0.316866\pi$
$379$	4.37116e11	1.08823	0.544115	+	0.839011i	$0.316866\pi$
$380$	4.14528e10	0.101983
$381$	1.32378e11	0.321850
$382$	2.41766e10	0.0580911
$383$	2.85588e11	0.678180	0.339090	−	0.940754i	$-0.389881\pi$
$383$	2.85588e11	0.678180	0.339090	+	0.940754i	$0.389881\pi$
$384$	−7.50422e10	−0.176123
$385$	−8.55059e10	−0.198346
$386$	5.05750e10	0.115956
$387$	−6.27553e10	−0.142217
$388$	5.21009e11	1.16708
$389$	−9.80733e10	−0.217159	−0.108579	−	0.994088i	$-0.534630\pi$
$389$	−9.80733e10	−0.217159	−0.108579	+	0.994088i	$0.534630\pi$
$390$	−3.15930e9	−0.00691512
$391$	−6.67136e11	−1.44351
$392$	−6.22407e10	−0.133134
$393$	−4.65250e11	−0.983829
$394$	−5.15946e10	−0.107863
$395$	−1.81610e11	−0.375364
$396$	1.93868e11	0.396166
$397$	3.16692e10	0.0639853	0.0319927	−	0.999488i	$-0.489815\pi$
$397$	3.16692e10	0.0639853	0.0319927	+	0.999488i	$0.489815\pi$
$398$	−4.71060e10	−0.0941028
$399$	2.48736e10	0.0491316
$400$	1.00562e11	0.196411
$401$	−1.46868e11	−0.283646	−0.141823	−	0.989892i	$-0.545296\pi$
$401$	−1.46868e11	−0.283646	−0.141823	+	0.989892i	$0.545296\pi$
$402$	2.47600e10	0.0472861
$403$	−8.92923e10	−0.168633
$404$	3.28560e11	0.613618
$405$	2.69042e10	0.0496904
$406$	7.95533e9	0.0145308
$407$	−5.21018e11	−0.941192
$408$	−8.22012e10	−0.146861
$409$	1.81133e11	0.320069	0.160035	−	0.987111i	$-0.448839\pi$
$409$	1.81133e11	0.320069	0.160035	+	0.987111i	$0.448839\pi$
$410$	−1.85098e9	−0.00323500
$411$	−2.38954e11	−0.413072
$412$	−4.53759e11	−0.775867
$413$	−3.88003e11	−0.656236
$414$	1.35131e10	0.0226075
$415$	1.41642e11	0.234410
$416$	4.86864e10	0.0797053
$417$	1.04616e11	0.169427
$418$	−1.32548e10	−0.0212364
$419$	8.42722e11	1.33574	0.667869	−	0.744279i	$-0.267207\pi$
$419$	8.42722e11	1.33574	0.667869	+	0.744279i	$0.267207\pi$
$420$	6.07105e10	0.0952011
$421$	7.81778e9	0.0121287	0.00606435	−	0.999982i	$-0.498070\pi$
$421$	7.81778e9	0.0121287	0.00606435	+	0.999982i	$0.498070\pi$
$422$	−1.18397e10	−0.0181734
$423$	4.05084e10	0.0615197
$424$	−1.29755e11	−0.194975
$425$	2.21653e11	0.329551
$426$	2.24604e10	0.0330426
$427$	−2.23681e11	−0.325614
$428$	−9.25745e11	−1.33350
$429$	−1.67534e11	−0.238806
$430$	1.04724e10	0.0147719
$431$	7.35734e11	1.02701	0.513503	−	0.858088i	$-0.328347\pi$
$431$	7.35734e11	1.02701	0.513503	+	0.858088i	$0.328347\pi$
$432$	−1.36814e11	−0.188997
$433$	−1.04750e11	−0.143205	−0.0716024	−	0.997433i	$-0.522811\pi$
$433$	−1.04750e11	−0.143205	−0.0716024	+	0.997433i	$0.522811\pi$
$434$	−1.03466e10	−0.0139988
$435$	9.75663e10	0.130647
$436$	−4.40858e11	−0.584264
$437$	1.53220e11	0.200978
$438$	−7.27231e8	−0.000944145 0
$439$	−9.52578e11	−1.22408	−0.612041	−	0.790826i	$-0.709651\pi$
$439$	−9.52578e11	−1.22408	−0.612041	+	0.790826i	$0.709651\pi$
$440$	−6.48988e10	−0.0825467
$441$	−2.28331e11	−0.287469
$442$	3.54110e10	0.0441305
$443$	−7.65967e11	−0.944916	−0.472458	−	0.881353i	$-0.656633\pi$
$443$	−7.65967e11	−0.944916	−0.472458	+	0.881353i	$0.656633\pi$
$444$	3.69931e11	0.451749
$445$	−5.25867e11	−0.635705
$446$	−8.74379e10	−0.104639
$447$	−3.67446e9	−0.00435322
$448$	−3.04947e11	−0.357662
$449$	8.80490e11	1.02239	0.511194	−	0.859465i	$-0.329203\pi$
$449$	8.80490e11	1.02239	0.511194	+	0.859465i	$0.329203\pi$
$450$	−4.48966e9	−0.00516128
$451$	−9.81553e10	−0.111717
$452$	−1.23569e12	−1.39247
$453$	−5.77073e11	−0.643856
$454$	−1.23735e11	−0.136691
$455$	−5.24640e10	−0.0573866
$456$	1.88790e10	0.0204474
$457$	−8.66223e11	−0.928980	−0.464490	−	0.885578i	$-0.653762\pi$
$457$	−8.66223e11	−0.928980	−0.464490	+	0.885578i	$0.653762\pi$
$458$	−1.14737e11	−0.121845
$459$	−3.01556e11	−0.317111
$460$	3.73973e11	0.389431
$461$	1.50066e12	1.54749	0.773747	−	0.633495i	$-0.218380\pi$
$461$	1.50066e12	1.54749	0.773747	+	0.633495i	$0.218380\pi$
$462$	−1.94126e10	−0.0198242
$463$	−1.21900e12	−1.23279	−0.616393	−	0.787438i	$-0.711407\pi$
$463$	−1.21900e12	−1.23279	−0.616393	+	0.787438i	$0.711407\pi$
$464$	−4.96147e11	−0.496912
$465$	−1.26893e11	−0.125863
$466$	−1.20554e10	−0.0118426
$467$	−1.56205e12	−1.51974	−0.759870	−	0.650075i	$-0.774737\pi$
$467$	−1.56205e12	−1.51974	−0.759870	+	0.650075i	$0.774737\pi$
$468$	1.18952e11	0.114621
$469$	4.11170e11	0.392413
$470$	−6.75988e9	−0.00638997
$471$	−3.03196e10	−0.0283877
$472$	−2.94494e11	−0.273110
$473$	5.55337e11	0.510131
$474$	−4.12314e10	−0.0375168
$475$	−5.09066e10	−0.0458831
$476$	−6.80475e11	−0.607548
$477$	−4.76009e11	−0.421001
$478$	−1.11993e11	−0.0981216
$479$	−7.50341e11	−0.651251	−0.325626	−	0.945499i	$-0.605575\pi$
$479$	−7.50341e11	−0.651251	−0.325626	+	0.945499i	$0.605575\pi$
$480$	6.91879e10	0.0594901
$481$	−3.19682e11	−0.272311
$482$	1.48172e11	0.125042
$483$	2.24402e11	0.187613
$484$	−5.15550e11	−0.427038
$485$	−6.39832e11	−0.525083
$486$	6.10814e9	0.00496644
$487$	2.26945e12	1.82827	0.914135	−	0.405410i	$-0.132871\pi$
$487$	2.26945e12	1.82827	0.914135	+	0.405410i	$0.132871\pi$
$488$	−1.69773e11	−0.135513
$489$	−1.04173e12	−0.823881
$490$	3.81029e10	0.0298590
$491$	−9.86468e11	−0.765978	−0.382989	−	0.923753i	$-0.625105\pi$
$491$	−9.86468e11	−0.765978	−0.382989	+	0.923753i	$0.625105\pi$
$492$	6.96918e10	0.0536214
$493$	−1.09357e12	−0.833752
$494$	−8.13280e9	−0.00614425
$495$	−2.38082e11	−0.178239
$496$	6.45279e11	0.478718
$497$	3.72983e11	0.274211
$498$	3.21574e10	0.0234287
$499$	5.57068e11	0.402213	0.201106	−	0.979569i	$-0.435546\pi$
$499$	5.57068e11	0.402213	0.201106	+	0.979569i	$0.435546\pi$
$500$	−1.24251e11	−0.0889066
$501$	−7.12513e11	−0.505269
$502$	−1.21034e9	−0.000850633 0
$503$	−2.37491e11	−0.165421	−0.0827107	−	0.996574i	$-0.526358\pi$
$503$	−2.37491e11	−0.165421	−0.0827107	+	0.996574i	$0.526358\pi$
$504$	2.76497e10	0.0190877
$505$	−4.03492e11	−0.276073
$506$	−1.19581e11	−0.0810931
$507$	7.56170e11	0.508257
$508$	8.31745e11	0.554119
$509$	−2.86375e10	−0.0189106	−0.00945529	−	0.999955i	$-0.503010\pi$
$509$	−2.86375e10	−0.0189106	−0.00945529	+	0.999955i	$0.503010\pi$
$510$	5.03225e10	0.0329379
$511$	−1.20766e10	−0.00783518
$512$	−5.87573e11	−0.377874
$513$	6.92579e10	0.0441511
$514$	6.89365e10	0.0435628
$515$	5.57245e11	0.349071
$516$	−3.94298e11	−0.244851
$517$	−3.58469e11	−0.220671
$518$	−3.70425e10	−0.0226056
$519$	3.33616e11	0.201834
$520$	−3.98201e10	−0.0238829
$521$	1.63234e12	0.970604	0.485302	−	0.874347i	$-0.338710\pi$
$521$	1.63234e12	0.970604	0.485302	+	0.874347i	$0.338710\pi$
$522$	2.21507e10	0.0130578
$523$	1.88974e12	1.10444	0.552222	−	0.833697i	$-0.313780\pi$
$523$	1.88974e12	1.10444	0.552222	+	0.833697i	$0.313780\pi$
$524$	−2.92321e12	−1.69383
$525$	−7.45564e10	−0.0428320
$526$	1.88003e11	0.107085
$527$	1.42228e12	0.803225
$528$	1.21070e12	0.677929
$529$	−4.18853e11	−0.232547
$530$	7.94345e10	0.0437288
$531$	−1.08035e12	−0.589713
$532$	1.56284e11	0.0845884
$533$	−6.02253e10	−0.0323226
$534$	−1.19389e11	−0.0635373
$535$	1.13687e12	0.599957
$536$	3.12077e11	0.163313
$537$	−9.90788e11	−0.514158
$538$	2.50992e11	0.129163
$539$	2.02056e12	1.03115
$540$	1.69042e11	0.0855504
$541$	1.97521e12	0.991349	0.495674	−	0.868508i	$-0.334921\pi$
$541$	1.97521e12	0.991349	0.495674	+	0.868508i	$0.334921\pi$
$542$	−1.52397e11	−0.0758543
$543$	5.25148e11	0.259228
$544$	−7.75494e11	−0.379650
$545$	5.41401e11	0.262866
$546$	−1.19111e10	−0.00573566
$547$	2.07818e12	0.992522	0.496261	−	0.868173i	$-0.334706\pi$
$547$	2.07818e12	0.992522	0.496261	+	0.868173i	$0.334706\pi$
$548$	−1.50137e12	−0.711174
$549$	−6.22814e11	−0.292606
$550$	3.97301e10	0.0185135
$551$	2.51159e11	0.116083
$552$	1.70320e11	0.0780801
$553$	−6.84699e11	−0.311341
$554$	−9.63383e10	−0.0434515
$555$	−4.54299e11	−0.203247
$556$	6.57310e11	0.291698
$557$	−2.52229e12	−1.11032	−0.555158	−	0.831745i	$-0.687342\pi$
$557$	−2.52229e12	−1.11032	−0.555158	+	0.831745i	$0.687342\pi$
$558$	−2.88088e10	−0.0125797
$559$	3.40740e11	0.147594
$560$	3.79136e11	0.162911
$561$	2.66854e12	1.13747
$562$	4.08379e9	0.00172683
$563$	−4.08264e12	−1.71259	−0.856295	−	0.516486i	$-0.827240\pi$
$563$	−4.08264e12	−1.71259	−0.856295	+	0.516486i	$0.827240\pi$
$564$	2.54519e11	0.105916
$565$	1.51750e12	0.626486
$566$	−2.52482e11	−0.103408
$567$	1.01433e11	0.0412151
$568$	2.83093e11	0.114120
$569$	7.72902e11	0.309114	0.154557	−	0.987984i	$-0.450605\pi$
$569$	7.72902e11	0.309114	0.154557	+	0.987984i	$0.450605\pi$
$570$	−1.15575e10	−0.00458592
$571$	3.13559e12	1.23440	0.617202	−	0.786805i	$-0.288266\pi$
$571$	3.13559e12	1.23440	0.617202	+	0.786805i	$0.288266\pi$
$572$	−1.05263e12	−0.411145
$573$	1.11788e12	0.433211
$574$	−6.97848e9	−0.00268323
$575$	−4.59263e11	−0.175209
$576$	−8.49092e11	−0.321406
$577$	−1.45919e12	−0.548051	−0.274025	−	0.961722i	$-0.588355\pi$
$577$	−1.45919e12	−0.548051	−0.274025	+	0.961722i	$0.588355\pi$
$578$	−3.56298e11	−0.132782
$579$	2.33850e12	0.864737
$580$	6.13019e11	0.224930
$581$	5.34013e11	0.194428
$582$	−1.45263e11	−0.0524809
$583$	4.21233e12	1.51013
$584$	−9.16608e9	−0.00326081
$585$	−1.46080e11	−0.0515692
$586$	−3.55159e11	−0.124418
$587$	2.87039e12	0.997861	0.498930	−	0.866642i	$-0.333726\pi$
$587$	2.87039e12	0.997861	0.498930	+	0.866642i	$0.333726\pi$
$588$	−1.43463e12	−0.494926
$589$	−3.26653e11	−0.111832
$590$	1.80285e11	0.0612527
$591$	−2.38564e12	−0.804381
$592$	2.31021e12	0.773044
$593$	9.23971e10	0.0306840	0.0153420	−	0.999882i	$-0.495116\pi$
$593$	9.23971e10	0.0306840	0.0153420	+	0.999882i	$0.495116\pi$
$594$	−5.40524e10	−0.0178146
$595$	8.35666e11	0.273342
$596$	−2.30870e10	−0.00749480
$597$	−2.17810e12	−0.701767
$598$	−7.33714e10	−0.0234623
$599$	−3.35276e12	−1.06410	−0.532049	−	0.846714i	$-0.678578\pi$
$599$	−3.35276e12	−1.06410	−0.532049	+	0.846714i	$0.678578\pi$
$600$	−5.65881e10	−0.0178256
$601$	3.50482e12	1.09580	0.547899	−	0.836545i	$-0.315428\pi$
$601$	3.50482e12	1.09580	0.547899	+	0.836545i	$0.315428\pi$
$602$	3.94824e10	0.0122524
$603$	1.14486e12	0.352634
$604$	−3.62581e12	−1.10851
$605$	6.33129e11	0.192129
$606$	−9.16060e10	−0.0275929
$607$	−1.85938e12	−0.555928	−0.277964	−	0.960591i	$-0.589660\pi$
$607$	−1.85938e12	−0.555928	−0.277964	+	0.960591i	$0.589660\pi$
$608$	1.78107e11	0.0528584
$609$	3.67840e11	0.108363
$610$	1.03933e11	0.0303926
$611$	−2.19947e11	−0.0638457
$612$	−1.89471e12	−0.545960
$613$	−8.50969e11	−0.243412	−0.121706	−	0.992566i	$-0.538836\pi$
$613$	−8.50969e11	−0.243412	−0.121706	+	0.992566i	$0.538836\pi$
$614$	−1.44942e11	−0.0411564
$615$	−8.55859e10	−0.0241248
$616$	−2.44679e11	−0.0684673
$617$	6.08736e12	1.69101	0.845504	−	0.533970i	$-0.179300\pi$
$617$	6.08736e12	1.69101	0.845504	+	0.533970i	$0.179300\pi$
$618$	1.26513e11	0.0348888
$619$	6.82662e12	1.86895	0.934475	−	0.356028i	$-0.115869\pi$
$619$	6.82662e12	1.86895	0.934475	+	0.356028i	$0.115869\pi$
$620$	−7.97281e11	−0.216695
$621$	6.24822e11	0.168595
$622$	2.79247e11	0.0748051
$623$	−1.98260e12	−0.527277
$624$	7.42852e11	0.196143
$625$	1.52588e11	0.0400000
$626$	7.88410e10	0.0205195
$627$	−6.12880e11	−0.158370
$628$	−1.90501e11	−0.0488742
$629$	5.09201e12	1.29706
$630$	−1.69267e10	−0.00428096
$631$	−3.66188e12	−0.919543	−0.459771	−	0.888037i	$-0.652069\pi$
$631$	−3.66188e12	−0.919543	−0.459771	+	0.888037i	$0.652069\pi$
$632$	−5.19685e11	−0.129573
$633$	−5.47449e11	−0.135527
$634$	1.71762e11	0.0422206
$635$	−1.02144e12	−0.249304
$636$	−2.99082e12	−0.724824
$637$	1.23976e12	0.298338
$638$	−1.96017e11	−0.0468384
$639$	1.03853e12	0.246414
$640$	5.79029e11	0.136424
$641$	1.90725e12	0.446217	0.223109	−	0.974794i	$-0.428380\pi$
$641$	1.90725e12	0.446217	0.223109	+	0.974794i	$0.428380\pi$
$642$	2.58108e11	0.0599644
$643$	5.31123e12	1.22531	0.612655	−	0.790351i	$-0.290102\pi$
$643$	5.31123e12	1.22531	0.612655	+	0.790351i	$0.290102\pi$
$644$	1.40994e12	0.323008
$645$	4.84223e11	0.110161
$646$	1.29542e11	0.0292661
$647$	−6.23349e12	−1.39850	−0.699249	−	0.714878i	$-0.746482\pi$
$647$	−6.23349e12	−1.39850	−0.699249	+	0.714878i	$0.746482\pi$
$648$	7.69875e10	0.0171527
$649$	9.56031e12	2.11530
$650$	2.43773e10	0.00535643
$651$	−4.78406e11	−0.104396
$652$	−6.54529e12	−1.41845
$653$	2.85345e12	0.614132	0.307066	−	0.951688i	$-0.400653\pi$
$653$	2.85345e12	0.614132	0.307066	+	0.951688i	$0.400653\pi$
$654$	1.22916e11	0.0262729
$655$	3.58989e12	0.762071
$656$	4.35224e11	0.0917584
$657$	−3.36259e10	−0.00704092
$658$	−2.54858e10	−0.00530008
$659$	−1.25192e12	−0.258579	−0.129290	−	0.991607i	$-0.541270\pi$
$659$	−1.25192e12	−0.258579	−0.129290	+	0.991607i	$0.541270\pi$
$660$	−1.49589e12	−0.306869
$661$	−1.04559e12	−0.213036	−0.106518	−	0.994311i	$-0.533970\pi$
$661$	−1.04559e12	−0.213036	−0.106518	+	0.994311i	$0.533970\pi$
$662$	1.32598e11	0.0268335
$663$	1.63734e12	0.329101
$664$	4.05315e11	0.0809163
$665$	−1.91926e11	−0.0380572
$666$	−1.03141e11	−0.0203140
$667$	2.26587e12	0.443271
$668$	−4.47679e12	−0.869907
$669$	−4.04297e12	−0.780339
$670$	−1.91049e11	−0.0366276
$671$	5.51144e12	1.04958
$672$	2.60850e11	0.0493433
$673$	−6.02090e12	−1.13134	−0.565670	−	0.824632i	$-0.691382\pi$
$673$	−6.02090e12	−1.13134	−0.565670	+	0.824632i	$0.691382\pi$
$674$	−5.34337e9	−0.000997346 0
$675$	−2.07594e11	−0.0384900
$676$	4.75109e12	0.875051
$677$	−2.46156e12	−0.450361	−0.225181	−	0.974317i	$-0.572297\pi$
$677$	−2.46156e12	−0.450361	−0.225181	+	0.974317i	$0.572297\pi$
$678$	3.44523e11	0.0626159
$679$	−2.41227e12	−0.435524
$680$	6.34269e11	0.113758
$681$	−5.72128e12	−1.01937
$682$	2.54937e11	0.0451235
$683$	5.07863e12	0.893004	0.446502	−	0.894783i	$-0.352670\pi$
$683$	5.07863e12	0.893004	0.446502	+	0.894783i	$0.352670\pi$
$684$	4.35155e11	0.0760136
$685$	1.84378e12	0.319964
$686$	3.10228e11	0.0534837
$687$	−5.30524e12	−0.908657
$688$	−2.46239e12	−0.418994
$689$	2.58456e12	0.436919
$690$	−1.04268e11	−0.0175117
$691$	8.74918e11	0.145988	0.0729938	−	0.997332i	$-0.476745\pi$
$691$	8.74918e11	0.145988	0.0729938	+	0.997332i	$0.476745\pi$
$692$	2.09614e12	0.347491
$693$	−8.97607e11	−0.147838
$694$	−2.88886e11	−0.0472725
$695$	−8.07218e11	−0.131238
$696$	2.79190e11	0.0450981
$697$	9.59291e11	0.153958
$698$	−5.81784e11	−0.0927711
$699$	−5.57422e11	−0.0883155
$700$	−4.68445e11	−0.0737425
$701$	−2.83110e12	−0.442817	−0.221408	−	0.975181i	$-0.571065\pi$
$701$	−2.83110e12	−0.442817	−0.221408	+	0.975181i	$0.571065\pi$
$702$	−3.31651e10	−0.00515423
$703$	−1.16947e12	−0.180589
$704$	7.51382e12	1.15288
$705$	−3.12565e11	−0.0476529
$706$	6.68515e11	0.101272
$707$	−1.52123e12	−0.228985
$708$	−6.78797e12	−1.01529
$709$	8.42005e12	1.25143	0.625715	−	0.780052i	$-0.284807\pi$
$709$	8.42005e12	1.25143	0.625715	+	0.780052i	$0.284807\pi$
$710$	−1.73306e11	−0.0255947
$711$	−1.90647e12	−0.279780
$712$	−1.50479e12	−0.219440
$713$	−2.94695e12	−0.427042
$714$	1.89724e11	0.0273199
$715$	1.29270e12	0.184978
$716$	−6.22522e12	−0.885210
$717$	−5.17835e12	−0.731737
$718$	9.76880e11	0.137177
$719$	−6.19860e12	−0.864995	−0.432498	−	0.901635i	$-0.642368\pi$
$719$	−6.19860e12	−0.864995	−0.432498	+	0.901635i	$0.642368\pi$
$720$	1.05566e12	0.146396
$721$	2.10090e12	0.289532
$722$	−2.97517e10	−0.00407469
$723$	6.85124e12	0.932495
$724$	3.29956e12	0.446306
$725$	−7.52826e11	−0.101198
$726$	1.43741e11	0.0192029
$727$	1.23433e12	0.163880	0.0819400	−	0.996637i	$-0.473888\pi$
$727$	1.23433e12	0.163880	0.0819400	+	0.996637i	$0.473888\pi$
$728$	−1.50128e11	−0.0198094
$729$	2.82430e11	0.0370370
$730$	5.61135e9	0.000731331 0
$731$	−5.42742e12	−0.703016
$732$	−3.91320e12	−0.503770
$733$	1.44420e13	1.84782	0.923911	−	0.382608i	$-0.124974\pi$
$733$	1.44420e13	1.84782	0.923911	+	0.382608i	$0.124974\pi$
$734$	−8.04386e11	−0.102290
$735$	1.76181e12	0.222672
$736$	1.60682e12	0.201844
$737$	−1.01311e13	−1.26490
$738$	−1.94308e10	−0.00241122
$739$	1.34207e13	1.65529	0.827646	−	0.561250i	$-0.189679\pi$
$739$	1.34207e13	1.65529	0.827646	+	0.561250i	$0.189679\pi$
$740$	−2.85441e12	−0.349923
$741$	−3.76046e11	−0.0458205
$742$	2.99481e11	0.0362703
$743$	2.23655e11	0.0269234	0.0134617	−	0.999909i	$-0.495715\pi$
$743$	2.23655e11	0.0269234	0.0134617	+	0.999909i	$0.495715\pi$
$744$	−3.63109e11	−0.0434469
$745$	2.83523e10	0.00337199
$746$	−3.70848e10	−0.00438400
$747$	1.48690e12	0.174719
$748$	1.67667e13	1.95835
$749$	4.28620e12	0.497627
$750$	3.46425e10	0.00399791
$751$	−6.03105e11	−0.0691852	−0.0345926	−	0.999401i	$-0.511013\pi$
$751$	−6.03105e11	−0.0691852	−0.0345926	+	0.999401i	$0.511013\pi$
$752$	1.58947e12	0.181247
$753$	−5.59642e10	−0.00634356
$754$	−1.20271e11	−0.0135516
$755$	4.45272e12	0.498729
$756$	6.37315e11	0.0709587
$757$	4.20225e12	0.465104	0.232552	−	0.972584i	$-0.425292\pi$
$757$	4.20225e12	0.465104	0.232552	+	0.972584i	$0.425292\pi$
$758$	−7.65739e11	−0.0842498
$759$	−5.52920e12	−0.604748
$760$	−1.45671e11	−0.0158385
$761$	−7.62991e11	−0.0824685	−0.0412343	−	0.999150i	$-0.513129\pi$
$761$	−7.62991e11	−0.0824685	−0.0412343	+	0.999150i	$0.513129\pi$
$762$	−2.31899e11	−0.0249174
$763$	2.04117e12	0.218031
$764$	7.02376e12	0.745847
$765$	2.32682e12	0.245633
$766$	−5.00292e11	−0.0525042
$767$	5.86594e12	0.612010
$768$	−5.23564e12	−0.543056
$769$	1.43120e13	1.47582	0.737909	−	0.674900i	$-0.235813\pi$
$769$	1.43120e13	1.47582	0.737909	+	0.674900i	$0.235813\pi$
$770$	1.49789e11	0.0153558
$771$	3.18750e12	0.324867
$772$	1.46930e13	1.48879
$773$	−2.10625e12	−0.212179	−0.106090	−	0.994357i	$-0.533833\pi$
$773$	−2.10625e12	−0.212179	−0.106090	+	0.994357i	$0.533833\pi$
$774$	1.09935e11	0.0110103
$775$	9.79112e11	0.0974932
$776$	−1.83091e12	−0.181254
$777$	−1.71278e12	−0.168580
$778$	1.71804e11	0.0168123
$779$	−2.20319e11	−0.0214355
$780$	−9.17838e11	−0.0887852
$781$	−9.19021e12	−0.883885
$782$	1.16869e12	0.111755
$783$	1.02421e12	0.0973782
$784$	−8.95922e12	−0.846931
$785$	2.33948e11	0.0219890
$786$	8.15023e11	0.0761673
$787$	1.73423e13	1.61146	0.805730	−	0.592283i	$-0.201773\pi$
$787$	1.73423e13	1.61146	0.805730	+	0.592283i	$0.201773\pi$
$788$	−1.49892e13	−1.38488
$789$	8.69291e12	0.798580
$790$	3.18144e11	0.0290604
$791$	5.72123e12	0.519631
$792$	−6.81281e11	−0.0615266
$793$	3.38166e12	0.303669
$794$	−5.54781e10	−0.00495369
$795$	3.67291e12	0.326106
$796$	−1.36852e13	−1.20821
$797$	8.59161e12	0.754245	0.377122	−	0.926163i	$-0.376914\pi$
$797$	8.59161e12	0.754245	0.377122	+	0.926163i	$0.376914\pi$
$798$	−4.35735e10	−0.00380373
$799$	3.50339e12	0.304108
$800$	−5.33858e11	−0.0460809
$801$	−5.52034e12	−0.473827
$802$	2.57282e11	0.0219596
$803$	2.97564e11	0.0252557
$804$	7.19326e12	0.607119
$805$	−1.73149e12	−0.145325
$806$	1.56422e11	0.0130554
$807$	1.16054e13	0.963230
$808$	−1.15461e12	−0.0952981
$809$	6.28613e12	0.515959	0.257979	−	0.966150i	$-0.416943\pi$
$809$	6.28613e12	0.515959	0.257979	+	0.966150i	$0.416943\pi$
$810$	−4.71307e10	−0.00384699
$811$	2.78577e12	0.226126	0.113063	−	0.993588i	$-0.463934\pi$
$811$	2.78577e12	0.226126	0.113063	+	0.993588i	$0.463934\pi$
$812$	2.31118e12	0.186566
$813$	−7.04658e12	−0.565680
$814$	9.12718e11	0.0728663
$815$	8.03803e12	0.638176
$816$	−1.18324e13	−0.934261
$817$	1.24651e12	0.0978804
$818$	−3.17309e11	−0.0247795
$819$	−5.50746e11	−0.0427734
$820$	−5.37745e11	−0.0415350
$821$	9.14280e11	0.0702320	0.0351160	−	0.999383i	$-0.488820\pi$
$821$	9.14280e11	0.0702320	0.0351160	+	0.999383i	$0.488820\pi$
$822$	4.18599e11	0.0319797
$823$	−1.61379e13	−1.22616	−0.613081	−	0.790020i	$-0.710070\pi$
$823$	−1.61379e13	−1.22616	−0.613081	+	0.790020i	$0.710070\pi$
$824$	1.59458e12	0.120496
$825$	1.83705e12	0.138063
$826$	6.79703e11	0.0508053
$827$	−5.31430e12	−0.395067	−0.197534	−	0.980296i	$-0.563293\pi$
$827$	−5.31430e12	−0.395067	−0.197534	+	0.980296i	$0.563293\pi$
$828$	3.92582e12	0.290264
$829$	−1.54164e13	−1.13367	−0.566836	−	0.823831i	$-0.691833\pi$
$829$	−1.54164e13	−1.13367	−0.566836	+	0.823831i	$0.691833\pi$
$830$	−2.48128e11	−0.0181478
$831$	−4.45451e12	−0.324038
$832$	4.61027e12	0.333558
$833$	−1.97473e13	−1.42104
$834$	−1.83265e11	−0.0131169
$835$	5.49778e12	0.391380
$836$	−3.85079e12	−0.272660
$837$	−1.33207e12	−0.0938129
$838$	−1.47628e12	−0.103412
$839$	−1.15781e13	−0.806692	−0.403346	−	0.915048i	$-0.632153\pi$
$839$	−1.15781e13	−0.806692	−0.403346	+	0.915048i	$0.632153\pi$
$840$	−2.13346e11	−0.0147852
$841$	−1.07929e13	−0.743972
$842$	−1.36952e10	−0.000938994 0
$843$	1.88827e11	0.0128778
$844$	−3.43967e12	−0.233333
$845$	−5.83465e12	−0.393695
$846$	−7.09625e10	−0.00476280
$847$	2.38700e12	0.159359
$848$	−1.86776e13	−1.24034
$849$	−1.16743e13	−0.771164
$850$	−3.88291e11	−0.0255136
$851$	−1.05506e13	−0.689596
$852$	6.52519e12	0.424243
$853$	1.83106e13	1.18422	0.592108	−	0.805859i	$-0.298296\pi$
$853$	1.83106e13	1.18422	0.592108	+	0.805859i	$0.298296\pi$
$854$	3.91843e11	0.0252088
$855$	−5.34398e11	−0.0341993
$856$	3.25321e12	0.207100
$857$	7.14208e12	0.452284	0.226142	−	0.974094i	$-0.427389\pi$
$857$	7.14208e12	0.452284	0.226142	+	0.974094i	$0.427389\pi$
$858$	2.93486e11	0.0184882
$859$	1.28128e13	0.802925	0.401463	−	0.915875i	$-0.368502\pi$
$859$	1.28128e13	0.802925	0.401463	+	0.915875i	$0.368502\pi$
$860$	3.04242e12	0.189660
$861$	−3.22673e11	−0.0200100
$862$	−1.28886e12	−0.0795100
$863$	6.68648e12	0.410345	0.205172	−	0.978726i	$-0.434225\pi$
$863$	6.68648e12	0.410345	0.205172	+	0.978726i	$0.434225\pi$
$864$	7.26307e11	0.0443413
$865$	−2.57420e12	−0.156340
$866$	1.83500e11	0.0110868
$867$	−1.64746e13	−0.990214
$868$	−3.00588e12	−0.179735
$869$	1.68708e13	1.00357
$870$	−1.70916e11	−0.0101146
$871$	−6.21618e12	−0.365967
$872$	1.54924e12	0.0907392
$873$	−6.71670e12	−0.391374
$874$	−2.68410e11	−0.0155596
$875$	5.75281e11	0.0331775
$876$	−2.11275e11	−0.0121221
$877$	1.15846e13	0.661275	0.330637	−	0.943758i	$-0.392736\pi$
$877$	1.15846e13	0.661275	0.330637	+	0.943758i	$0.392736\pi$
$878$	1.66872e12	0.0947674
$879$	−1.64219e13	−0.927842
$880$	−9.34183e12	−0.525122
$881$	2.93410e13	1.64090	0.820452	−	0.571715i	$-0.193722\pi$
$881$	2.93410e13	1.64090	0.820452	+	0.571715i	$0.193722\pi$
$882$	3.99989e11	0.0222556
$883$	1.46420e13	0.810544	0.405272	−	0.914196i	$-0.367177\pi$
$883$	1.46420e13	0.810544	0.405272	+	0.914196i	$0.367177\pi$
$884$	1.02876e13	0.566603
$885$	8.33606e12	0.456789
$886$	1.34182e12	0.0731547
$887$	1.03872e13	0.563434	0.281717	−	0.959497i	$-0.409096\pi$
$887$	1.03872e13	0.563434	0.281717	+	0.959497i	$0.409096\pi$
$888$	−1.30000e12	−0.0701590
$889$	−3.85098e12	−0.206782
$890$	9.21211e11	0.0492158
$891$	−2.49929e12	−0.132852
$892$	−2.54024e13	−1.34349
$893$	−8.04618e11	−0.0423407
$894$	6.43691e9	0.000337022 0
$895$	7.64497e12	0.398265
$896$	2.18303e12	0.113155
$897$	−3.39256e12	−0.174969
$898$	−1.54244e12	−0.0791525
$899$	−4.83066e12	−0.246654
$900$	−1.30434e12	−0.0662671
$901$	−4.11679e13	−2.08112
$902$	1.71948e11	0.00864904
$903$	1.82560e12	0.0913714
$904$	4.34240e12	0.216258
$905$	−4.05207e12	−0.200797
$906$	1.01091e12	0.0498468
$907$	−1.98457e12	−0.0973720	−0.0486860	−	0.998814i	$-0.515503\pi$
$907$	−1.98457e12	−0.0973720	−0.0486860	+	0.998814i	$0.515503\pi$
$908$	−3.59474e13	−1.75502
$909$	−4.23570e12	−0.205773
$910$	9.19063e10	0.00444282
$911$	−7.84441e12	−0.377336	−0.188668	−	0.982041i	$-0.560417\pi$
$911$	−7.84441e12	−0.377336	−0.188668	+	0.982041i	$0.560417\pi$
$912$	2.71753e12	0.130076
$913$	−1.31580e13	−0.626715
$914$	1.51745e12	0.0719209
$915$	4.80567e12	0.226652
$916$	−3.33334e13	−1.56441
$917$	1.35345e13	0.632090
$918$	5.28265e11	0.0245505
$919$	1.67705e13	0.775577	0.387789	−	0.921748i	$-0.373239\pi$
$919$	1.67705e13	0.775577	0.387789	+	0.921748i	$0.373239\pi$
$920$	−1.31420e12	−0.0604806
$921$	−6.70187e12	−0.306922
$922$	−2.62886e12	−0.119806
$923$	−5.63886e12	−0.255731
$924$	−5.63975e12	−0.254528
$925$	3.50539e12	0.157434
$926$	2.13543e12	0.0954414
$927$	5.84973e12	0.260182
$928$	2.63391e12	0.116583
$929$	2.22554e13	0.980314	0.490157	−	0.871634i	$-0.336939\pi$
$929$	2.22554e13	0.980314	0.490157	+	0.871634i	$0.336939\pi$
$930$	2.22290e11	0.00974423
$931$	4.53533e12	0.197850
$932$	−3.50234e12	−0.152050
$933$	1.29119e13	0.557856
$934$	2.73640e12	0.117657
$935$	−2.05906e13	−0.881084
$936$	−4.18015e11	−0.0178013
$937$	−3.38299e13	−1.43375	−0.716874	−	0.697202i	$-0.754428\pi$
$937$	−3.38299e13	−1.43375	−0.716874	+	0.697202i	$0.754428\pi$
$938$	−7.20287e11	−0.0303803
$939$	3.64547e12	0.153024
$940$	−1.96388e12	−0.0820426
$941$	−2.83560e13	−1.17894	−0.589471	−	0.807790i	$-0.700664\pi$
$941$	−2.83560e13	−1.17894	−0.589471	+	0.807790i	$0.700664\pi$
$942$	5.31139e10	0.00219775
$943$	−1.98764e12	−0.0818532
$944$	−4.23908e13	−1.73739
$945$	−7.82663e11	−0.0319251
$946$	−9.72838e11	−0.0394939
$947$	−2.46660e13	−0.996606	−0.498303	−	0.867003i	$-0.666043\pi$
$947$	−2.46660e13	−0.996606	−0.498303	+	0.867003i	$0.666043\pi$
$948$	−1.19785e13	−0.481689
$949$	1.82577e11	0.00730714
$950$	8.91781e10	0.00355224
$951$	7.94195e12	0.314858
$952$	2.39129e12	0.0943554
$953$	−3.26739e12	−0.128317	−0.0641583	−	0.997940i	$-0.520436\pi$
$953$	−3.26739e12	−0.128317	−0.0641583	+	0.997940i	$0.520436\pi$
$954$	8.33872e11	0.0325935
$955$	−8.62563e12	−0.335564
$956$	−3.25361e13	−1.25981
$957$	−9.06350e12	−0.349295
$958$	1.31444e12	0.0504194
$959$	6.95135e12	0.265390
$960$	6.55164e12	0.248960
$961$	−2.01570e13	−0.762377
$962$	5.60018e11	0.0210821
$963$	1.19344e13	0.447182
$964$	4.30470e13	1.60545
$965$	−1.80440e13	−0.669822
$966$	−3.93106e11	−0.0145249
$967$	−3.32399e13	−1.22248	−0.611239	−	0.791446i	$-0.709328\pi$
$967$	−3.32399e13	−1.22248	−0.611239	+	0.791446i	$0.709328\pi$
$968$	1.81172e12	0.0663213
$969$	5.98980e12	0.218251
$970$	1.12086e12	0.0406515
$971$	−3.55720e13	−1.28417	−0.642083	−	0.766635i	$-0.721930\pi$
$971$	−3.55720e13	−1.28417	−0.642083	+	0.766635i	$0.721930\pi$
$972$	1.77453e12	0.0637655
$973$	−3.04334e12	−0.108854
$974$	−3.97562e12	−0.141543
$975$	1.12716e12	0.0399453
$976$	−2.44379e13	−0.862065
$977$	−8.55177e12	−0.300283	−0.150141	−	0.988665i	$-0.547973\pi$
$977$	−8.55177e12	−0.300283	−0.150141	+	0.988665i	$0.547973\pi$
$978$	1.82490e12	0.0637842
$979$	4.88508e13	1.69961
$980$	1.10696e13	0.383368
$981$	5.68341e12	0.195929
$982$	1.72809e12	0.0593014
$983$	−5.17654e13	−1.76827	−0.884135	−	0.467231i	$-0.845252\pi$
$983$	−5.17654e13	−1.76827	−0.884135	+	0.467231i	$0.845252\pi$
$984$	−2.44908e11	−0.00832769
$985$	1.84077e13	0.623071
$986$	1.91572e12	0.0645484
$987$	−1.17842e12	−0.0395251
$988$	−2.36274e12	−0.0788877
$989$	1.12456e13	0.373765
$990$	4.17071e11	0.0137991
$991$	3.06829e13	1.01057	0.505284	−	0.862953i	$-0.331388\pi$
$991$	3.06829e13	1.01057	0.505284	+	0.862953i	$0.331388\pi$
$992$	−3.42561e12	−0.112314
$993$	6.13111e12	0.200109
$994$	−6.53390e11	−0.0212292
$995$	1.68063e13	0.543586
$996$	9.34236e12	0.300808
$997$	−3.08781e13	−0.989743	−0.494872	−	0.868966i	$-0.664785\pi$
$997$	−3.08781e13	−0.989743	−0.494872	+	0.868966i	$0.664785\pi$
$998$	−9.75871e11	−0.0311390
$999$	−4.76905e12	−0.151491

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.8	✓	15

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

\(f(q)\)	\(=\)	\(q-1.75180 q^{2} -81.0000 q^{3} -508.931 q^{4} +625.000 q^{5} +141.896 q^{6} +2356.35 q^{7} +1788.46 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-1.75180 q^{2} -81.0000 q^{3} -508.931 q^{4} +625.000 q^{5} +141.896 q^{6} +2356.35 q^{7} +1788.46 q^{8} +6561.00 q^{9} -1094.87 q^{10} -58059.9 q^{11} +41223.4 q^{12} -35623.9 q^{13} -4127.85 q^{14} -50625.0 q^{15} +257440. q^{16} +567431. q^{17} -11493.5 q^{18} -130321. q^{19} -318082. q^{20} -190864. q^{21} +101709. q^{22} -1.17571e6 q^{23} -144866. q^{24} +390625. q^{25} +62405.9 q^{26} -531441. q^{27} -1.19922e6 q^{28} -1.92724e6 q^{29} +88684.7 q^{30} +2.50653e6 q^{31} -1.36668e6 q^{32} +4.70285e6 q^{33} -994024. q^{34} +1.47272e6 q^{35} -3.33910e6 q^{36} +8.97380e6 q^{37} +228296. q^{38} +2.88554e6 q^{39} +1.11779e6 q^{40} +1.69059e6 q^{41} +334355. q^{42} -9.56490e6 q^{43} +2.95485e7 q^{44} +4.10062e6 q^{45} +2.05961e6 q^{46} +6.17413e6 q^{47} -2.08526e7 q^{48} -3.48012e7 q^{49} -684296. q^{50} -4.59619e7 q^{51} +1.81301e7 q^{52} -7.25514e7 q^{53} +930977. q^{54} -3.62874e7 q^{55} +4.21425e6 q^{56} +1.05560e7 q^{57} +3.37612e6 q^{58} -1.64663e8 q^{59} +2.57646e7 q^{60} -9.49267e7 q^{61} -4.39092e6 q^{62} +1.54600e7 q^{63} -1.29415e8 q^{64} -2.22650e7 q^{65} -8.23844e6 q^{66} +1.74495e8 q^{67} -2.88783e8 q^{68} +9.52327e7 q^{69} -2.57990e6 q^{70} +1.58288e8 q^{71} +1.17341e7 q^{72} -5.12511e6 q^{73} -1.57203e7 q^{74} -3.16406e7 q^{75} +6.63244e7 q^{76} -1.36809e8 q^{77} -5.05488e6 q^{78} -2.90576e8 q^{79} +1.60900e8 q^{80} +4.30467e7 q^{81} -2.96156e6 q^{82} +2.26627e8 q^{83} +9.71368e7 q^{84} +3.54644e8 q^{85} +1.67558e7 q^{86} +1.56106e8 q^{87} -1.03838e8 q^{88} -8.41387e8 q^{89} -7.18346e6 q^{90} -8.39425e7 q^{91} +5.98357e8 q^{92} -2.03029e8 q^{93} -1.08158e7 q^{94} -8.14506e7 q^{95} +1.10701e8 q^{96} -1.02373e9 q^{97} +6.09647e7 q^{98} -3.80931e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 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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