LMFDB - Embedded newform 285.10.a.h.1.12

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			1.12
Root			$-28.5474$ 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)

$f(q)$	$=$	$q+27.5474 q^{2} -81.0000 q^{3} +246.858 q^{4} +625.000 q^{5} -2231.34 q^{6} -1319.66 q^{7} -7303.96 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+27.5474 q^{2} -81.0000 q^{3} +246.858 q^{4} +625.000 q^{5} -2231.34 q^{6} -1319.66 q^{7} -7303.96 q^{8} +6561.00 q^{9} +17217.1 q^{10} +50065.5 q^{11} -19995.5 q^{12} -18562.8 q^{13} -36353.2 q^{14} -50625.0 q^{15} -327596. q^{16} +32059.3 q^{17} +180738. q^{18} -130321. q^{19} +154286. q^{20} +106892. q^{21} +1.37917e6 q^{22} -1.36828e6 q^{23} +591621. q^{24} +390625. q^{25} -511358. q^{26} -531441. q^{27} -325769. q^{28} +2.58189e6 q^{29} -1.39459e6 q^{30} +9.87277e6 q^{31} -5.28480e6 q^{32} -4.05531e6 q^{33} +883149. q^{34} -824787. q^{35} +1.61964e6 q^{36} -1.40978e7 q^{37} -3.59000e6 q^{38} +1.50359e6 q^{39} -4.56498e6 q^{40} +6.18561e6 q^{41} +2.94461e6 q^{42} -2.30968e7 q^{43} +1.23591e7 q^{44} +4.10062e6 q^{45} -3.76925e7 q^{46} +2.84732e7 q^{47} +2.65353e7 q^{48} -3.86121e7 q^{49} +1.07607e7 q^{50} -2.59680e6 q^{51} -4.58239e6 q^{52} -3.05223e7 q^{53} -1.46398e7 q^{54} +3.12909e7 q^{55} +9.63875e6 q^{56} +1.05560e7 q^{57} +7.11243e7 q^{58} +2.45284e6 q^{59} -1.24972e7 q^{60} +2.03472e8 q^{61} +2.71969e8 q^{62} -8.65829e6 q^{63} +2.21471e7 q^{64} -1.16018e7 q^{65} -1.11713e8 q^{66} +5.42642e7 q^{67} +7.91409e6 q^{68} +1.10831e8 q^{69} -2.27207e7 q^{70} +1.26761e8 q^{71} -4.79213e7 q^{72} +3.31775e8 q^{73} -3.88357e8 q^{74} -3.16406e7 q^{75} -3.21708e7 q^{76} -6.60694e7 q^{77} +4.14200e7 q^{78} -3.42977e8 q^{79} -2.04748e8 q^{80} +4.30467e7 q^{81} +1.70397e8 q^{82} +4.85752e8 q^{83} +2.63873e7 q^{84} +2.00370e7 q^{85} -6.36256e8 q^{86} -2.09133e8 q^{87} -3.65676e8 q^{88} +1.00562e9 q^{89} +1.12961e8 q^{90} +2.44966e7 q^{91} -3.37771e8 q^{92} -7.99694e8 q^{93} +7.84362e8 q^{94} -8.14506e7 q^{95} +4.28068e8 q^{96} -3.79501e8 q^{97} -1.06366e9 q^{98} +3.28480e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	27.5474	1.21743	0.608717	−	0.793388i	$-0.291685\pi$
$2$	27.5474	1.21743	0.608717	+	0.793388i	$0.291685\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	246.858	0.482145
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−2231.34	−0.702886
$7$	−1319.66	−0.207740	−0.103870	−	0.994591i	$-0.533123\pi$
$7$	−1319.66	−0.207740	−0.103870	+	0.994591i	$0.533123\pi$
$8$	−7303.96	−0.630454
$9$	6561.00	0.333333
$10$	17217.1	0.544453
$11$	50065.5	1.03103	0.515515	−	0.856880i	$-0.327601\pi$
$11$	50065.5	1.03103	0.515515	+	0.856880i	$0.327601\pi$
$12$	−19995.5	−0.278367
$13$	−18562.8	−0.180260	−0.0901300	−	0.995930i	$-0.528728\pi$
$13$	−18562.8	−0.180260	−0.0901300	+	0.995930i	$0.528728\pi$
$14$	−36353.2	−0.252910
$15$	−50625.0	−0.258199
$16$	−327596.	−1.24968
$17$	32059.3	0.0930965	0.0465482	−	0.998916i	$-0.485178\pi$
$17$	32059.3	0.0930965	0.0465482	+	0.998916i	$0.485178\pi$
$18$	180738.	0.405811
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	154286.	0.215622
$21$	106892.	0.119939
$22$	1.37917e6	1.25521
$23$	−1.36828e6	−1.01953	−0.509765	−	0.860314i	$-0.670267\pi$
$23$	−1.36828e6	−1.01953	−0.509765	+	0.860314i	$0.670267\pi$
$24$	591621.	0.363993
$25$	390625.	0.200000
$26$	−511358.	−0.219455
$27$	−531441.	−0.192450
$28$	−325769.	−0.100161
$29$	2.58189e6	0.677870	0.338935	−	0.940810i	$-0.389933\pi$
$29$	2.58189e6	0.677870	0.338935	+	0.940810i	$0.389933\pi$
$30$	−1.39459e6	−0.314340
$31$	9.87277e6	1.92005	0.960023	−	0.279923i	$-0.0903088\pi$
$31$	9.87277e6	1.92005	0.960023	+	0.279923i	$0.0903088\pi$
$32$	−5.28480e6	−0.890950
$33$	−4.05531e6	−0.595266
$34$	883149.	0.113339
$35$	−824787.	−0.0929043
$36$	1.61964e6	0.160715
$37$	−1.40978e7	−1.23664	−0.618320	−	0.785927i	$-0.712186\pi$
$37$	−1.40978e7	−1.23664	−0.618320	+	0.785927i	$0.712186\pi$
$38$	−3.59000e6	−0.279298
$39$	1.50359e6	0.104073
$40$	−4.56498e6	−0.281948
$41$	6.18561e6	0.341865	0.170933	−	0.985283i	$-0.445322\pi$
$41$	6.18561e6	0.341865	0.170933	+	0.985283i	$0.445322\pi$
$42$	2.94461e6	0.146018
$43$	−2.30968e7	−1.03025	−0.515126	−	0.857114i	$-0.672255\pi$
$43$	−2.30968e7	−1.03025	−0.515126	+	0.857114i	$0.672255\pi$
$44$	1.23591e7	0.497106
$45$	4.10062e6	0.149071
$46$	−3.76925e7	−1.24121
$47$	2.84732e7	0.851130	0.425565	−	0.904928i	$-0.360075\pi$
$47$	2.84732e7	0.851130	0.425565	+	0.904928i	$0.360075\pi$
$48$	2.65353e7	0.721504
$49$	−3.86121e7	−0.956844
$50$	1.07607e7	0.243487
$51$	−2.59680e6	−0.0537493
$52$	−4.58239e6	−0.0869114
$53$	−3.05223e7	−0.531343	−0.265672	−	0.964064i	$-0.585594\pi$
$53$	−3.05223e7	−0.531343	−0.265672	+	0.964064i	$0.585594\pi$
$54$	−1.46398e7	−0.234295
$55$	3.12909e7	0.461091
$56$	9.63875e6	0.130971
$57$	1.05560e7	0.132453
$58$	7.11243e7	0.825262
$59$	2.45284e6	0.0263533	0.0131766	−	0.999913i	$-0.495806\pi$
$59$	2.45284e6	0.0263533	0.0131766	+	0.999913i	$0.495806\pi$
$60$	−1.24972e7	−0.124489
$61$	2.03472e8	1.88157	0.940787	−	0.338999i	$-0.110088\pi$
$61$	2.03472e8	1.88157	0.940787	+	0.338999i	$0.110088\pi$
$62$	2.71969e8	2.33753
$63$	−8.65829e6	−0.0692468
$64$	2.21471e7	0.165009
$65$	−1.16018e7	−0.0806147
$66$	−1.11713e8	−0.724697
$67$	5.42642e7	0.328985	0.164493	−	0.986378i	$-0.447401\pi$
$67$	5.42642e7	0.328985	0.164493	+	0.986378i	$0.447401\pi$
$68$	7.91409e6	0.0448860
$69$	1.10831e8	0.588625
$70$	−2.27207e7	−0.113105
$71$	1.26761e8	0.592001	0.296001	−	0.955188i	$-0.404347\pi$
$71$	1.26761e8	0.592001	0.296001	+	0.955188i	$0.404347\pi$
$72$	−4.79213e7	−0.210151
$73$	3.31775e8	1.36738	0.683692	−	0.729771i	$-0.260373\pi$
$73$	3.31775e8	1.36738	0.683692	+	0.729771i	$0.260373\pi$
$74$	−3.88357e8	−1.50553
$75$	−3.16406e7	−0.115470
$76$	−3.21708e7	−0.110612
$77$	−6.60694e7	−0.214187
$78$	4.14200e7	0.126702
$79$	−3.42977e8	−0.990701	−0.495351	−	0.868693i	$-0.664960\pi$
$79$	−3.42977e8	−0.990701	−0.495351	+	0.868693i	$0.664960\pi$
$80$	−2.04748e8	−0.558874
$81$	4.30467e7	0.111111
$82$	1.70397e8	0.416198
$83$	4.85752e8	1.12347	0.561737	−	0.827316i	$-0.310133\pi$
$83$	4.85752e8	1.12347	0.561737	+	0.827316i	$0.310133\pi$
$84$	2.63873e7	0.0578280
$85$	2.00370e7	0.0416340
$86$	−6.36256e8	−1.25426
$87$	−2.09133e8	−0.391369
$88$	−3.65676e8	−0.650017
$89$	1.00562e9	1.69894	0.849471	−	0.527635i	$-0.176921\pi$
$89$	1.00562e9	1.69894	0.849471	+	0.527635i	$0.176921\pi$
$90$	1.12961e8	0.181484
$91$	2.44966e7	0.0374473
$92$	−3.37771e8	−0.491561
$93$	−7.99694e8	−1.10854
$94$	7.84362e8	1.03619
$95$	−8.14506e7	−0.102598
$96$	4.28068e8	0.514390
$97$	−3.79501e8	−0.435251	−0.217625	−	0.976032i	$-0.569831\pi$
$97$	−3.79501e8	−0.435251	−0.217625	+	0.976032i	$0.569831\pi$
$98$	−1.06366e9	−1.16489
$99$	3.28480e8	0.343677
$100$	9.64290e7	0.0964290
$101$	1.53209e9	1.46500	0.732500	−	0.680767i	$-0.238353\pi$
$101$	1.53209e9	1.46500	0.732500	+	0.680767i	$0.238353\pi$
$102$	−7.15350e7	−0.0654362
$103$	1.36874e9	1.19827	0.599135	−	0.800648i	$-0.295511\pi$
$103$	1.36874e9	1.19827	0.599135	+	0.800648i	$0.295511\pi$
$104$	1.35582e8	0.113646
$105$	6.68078e7	0.0536383
$106$	−8.40808e8	−0.646875
$107$	−1.99214e9	−1.46924	−0.734619	−	0.678480i	$-0.762639\pi$
$107$	−1.99214e9	−1.46924	−0.734619	+	0.678480i	$0.762639\pi$
$108$	−1.31191e8	−0.0927888
$109$	1.80152e9	1.22242	0.611209	−	0.791469i	$-0.290683\pi$
$109$	1.80152e9	1.22242	0.611209	+	0.791469i	$0.290683\pi$
$110$	8.61983e8	0.561348
$111$	1.14192e9	0.713974
$112$	4.32316e8	0.259609
$113$	−9.20512e8	−0.531100	−0.265550	−	0.964097i	$-0.585554\pi$
$113$	−9.20512e8	−0.531100	−0.265550	+	0.964097i	$0.585554\pi$
$114$	2.90790e8	0.161253
$115$	−8.55175e8	−0.455947
$116$	6.37360e8	0.326832
$117$	−1.21791e8	−0.0600866
$118$	6.75692e7	0.0320833
$119$	−4.23073e7	−0.0193399
$120$	3.69763e8	0.162783
$121$	1.48606e8	0.0630236
$122$	5.60513e9	2.29069
$123$	−5.01034e8	−0.197376
$124$	2.43717e9	0.925740
$125$	2.44141e8	0.0894427
$126$	−2.38513e8	−0.0843034
$127$	7.87032e7	0.0268458	0.0134229	−	0.999910i	$-0.495727\pi$
$127$	7.87032e7	0.0268458	0.0134229	+	0.999910i	$0.495727\pi$
$128$	3.31591e9	1.09184
$129$	1.87084e9	0.594816
$130$	−3.19598e8	−0.0981431
$131$	5.16785e9	1.53317	0.766583	−	0.642145i	$-0.221955\pi$
$131$	5.16785e9	1.53317	0.766583	+	0.642145i	$0.221955\pi$
$132$	−1.00109e9	−0.287004
$133$	1.71979e8	0.0476589
$134$	1.49484e9	0.400518
$135$	−3.32151e8	−0.0860663
$136$	−2.34160e8	−0.0586931
$137$	−1.27849e9	−0.310066	−0.155033	−	0.987909i	$-0.549548\pi$
$137$	−1.27849e9	−0.310066	−0.155033	+	0.987909i	$0.549548\pi$
$138$	3.05309e9	0.716612
$139$	−2.67710e9	−0.608271	−0.304136	−	0.952629i	$-0.598368\pi$
$139$	−2.67710e9	−0.608271	−0.304136	+	0.952629i	$0.598368\pi$
$140$	−2.03606e8	−0.0447933
$141$	−2.30633e9	−0.491400
$142$	3.49193e9	0.720722
$143$	−9.29358e8	−0.185853
$144$	−2.14936e9	−0.416560
$145$	1.61368e9	0.303153
$146$	9.13952e9	1.66470
$147$	3.12758e9	0.552434
$148$	−3.48015e9	−0.596239
$149$	−8.18570e8	−0.136056	−0.0680280	−	0.997683i	$-0.521671\pi$
$149$	−8.18570e8	−0.136056	−0.0680280	+	0.997683i	$0.521671\pi$
$150$	−8.71616e8	−0.140577
$151$	1.24493e10	1.94871	0.974356	−	0.225011i	$-0.0722418\pi$
$151$	1.24493e10	1.94871	0.974356	+	0.225011i	$0.0722418\pi$
$152$	9.51860e8	0.144636
$153$	2.10341e8	0.0310322
$154$	−1.82004e9	−0.260758
$155$	6.17048e9	0.858670
$156$	3.71173e8	0.0501783
$157$	1.04321e10	1.37032	0.685159	−	0.728394i	$-0.259733\pi$
$157$	1.04321e10	1.37032	0.685159	+	0.728394i	$0.259733\pi$
$158$	−9.44811e9	−1.20611
$159$	2.47230e9	0.306771
$160$	−3.30300e9	−0.398445
$161$	1.80566e9	0.211797
$162$	1.18582e9	0.135270
$163$	2.01106e8	0.0223142	0.0111571	−	0.999938i	$-0.496449\pi$
$163$	2.01106e8	0.0223142	0.0111571	+	0.999938i	$0.496449\pi$
$164$	1.52697e9	0.164829
$165$	−2.53457e9	−0.266211
$166$	1.33812e10	1.36776
$167$	7.71273e8	0.0767333	0.0383667	−	0.999264i	$-0.487785\pi$
$167$	7.71273e8	0.0767333	0.0383667	+	0.999264i	$0.487785\pi$
$168$	−7.80738e8	−0.0756160
$169$	−1.02599e10	−0.967506
$170$	5.51968e8	0.0506867
$171$	−8.55036e8	−0.0764719
$172$	−5.70163e9	−0.496731
$173$	1.92165e10	1.63105	0.815526	−	0.578720i	$-0.196448\pi$
$173$	1.92165e10	1.63105	0.815526	+	0.578720i	$0.196448\pi$
$174$	−5.76107e9	−0.476465
$175$	−5.15492e8	−0.0415481
$176$	−1.64013e10	−1.28846
$177$	−1.98680e8	−0.0152151
$178$	2.77022e10	2.06835
$179$	2.41022e10	1.75476	0.877380	−	0.479796i	$-0.159289\pi$
$179$	2.41022e10	1.75476	0.877380	+	0.479796i	$0.159289\pi$
$180$	1.01227e9	0.0718739
$181$	−5.95422e9	−0.412355	−0.206178	−	0.978515i	$-0.566102\pi$
$181$	−5.95422e9	−0.412355	−0.206178	+	0.978515i	$0.566102\pi$
$182$	6.74818e8	0.0455896
$183$	−1.64813e10	−1.08633
$184$	9.99386e9	0.642766
$185$	−8.81111e9	−0.553042
$186$	−2.20295e10	−1.34957
$187$	1.60506e9	0.0959853
$188$	7.02884e9	0.410368
$189$	7.01321e8	0.0399796
$190$	−2.24375e9	−0.124906
$191$	3.53262e10	1.92064	0.960322	−	0.278892i	$-0.0899673\pi$
$191$	3.53262e10	1.92064	0.960322	+	0.278892i	$0.0899673\pi$
$192$	−1.79391e9	−0.0952678
$193$	2.46605e9	0.127936	0.0639682	−	0.997952i	$-0.479624\pi$
$193$	2.46605e9	0.127936	0.0639682	+	0.997952i	$0.479624\pi$
$194$	−1.04542e10	−0.529889
$195$	9.39744e8	0.0465429
$196$	−9.53172e9	−0.461338
$197$	−2.91701e10	−1.37988	−0.689938	−	0.723868i	$-0.742362\pi$
$197$	−2.91701e10	−1.37988	−0.689938	+	0.723868i	$0.742362\pi$
$198$	9.04876e9	0.418404
$199$	−2.44383e10	−1.10467	−0.552335	−	0.833622i	$-0.686263\pi$
$199$	−2.44383e10	−1.10467	−0.552335	+	0.833622i	$0.686263\pi$
$200$	−2.85311e9	−0.126091
$201$	−4.39540e9	−0.189940
$202$	4.22050e10	1.78354
$203$	−3.40721e9	−0.140821
$204$	−6.41041e8	−0.0259149
$205$	3.86600e9	0.152887
$206$	3.77053e10	1.45881
$207$	−8.97728e9	−0.339843
$208$	6.08112e9	0.225267
$209$	−6.52459e9	−0.236535
$210$	1.84038e9	0.0653011
$211$	1.61453e10	0.560759	0.280380	−	0.959889i	$-0.409540\pi$
$211$	1.61453e10	0.560759	0.280380	+	0.959889i	$0.409540\pi$
$212$	−7.53467e9	−0.256185
$213$	−1.02676e10	−0.341792
$214$	−5.48781e10	−1.78870
$215$	−1.44355e10	−0.460743
$216$	3.88162e9	0.121331
$217$	−1.30287e10	−0.398871
$218$	4.96272e10	1.48821
$219$	−2.68737e10	−0.789459
$220$	7.72443e9	0.222313
$221$	−5.95111e8	−0.0167816
$222$	3.14569e10	0.869216
$223$	−3.97635e10	−1.07674	−0.538372	−	0.842708i	$-0.680960\pi$
$223$	−3.97635e10	−1.07674	−0.538372	+	0.842708i	$0.680960\pi$
$224$	6.97413e9	0.185086
$225$	2.56289e9	0.0666667
$226$	−2.53577e10	−0.646579
$227$	−4.34660e10	−1.08651	−0.543255	−	0.839568i	$-0.682808\pi$
$227$	−4.34660e10	−1.08651	−0.543255	+	0.839568i	$0.682808\pi$
$228$	2.60584e9	0.0638617
$229$	−4.13939e10	−0.994665	−0.497333	−	0.867560i	$-0.665687\pi$
$229$	−4.13939e10	−0.994665	−0.497333	+	0.867560i	$0.665687\pi$
$230$	−2.35578e10	−0.555086
$231$	5.35162e9	0.123661
$232$	−1.88580e10	−0.427366
$233$	5.25068e10	1.16712	0.583558	−	0.812071i	$-0.301660\pi$
$233$	5.25068e10	1.16712	0.583558	+	0.812071i	$0.301660\pi$
$234$	−3.35502e9	−0.0731515
$235$	1.77957e10	0.380637
$236$	6.05503e8	0.0127061
$237$	2.77811e10	0.571982
$238$	−1.16546e9	−0.0235450
$239$	3.18065e9	0.0630559	0.0315279	−	0.999503i	$-0.489963\pi$
$239$	3.18065e9	0.0630559	0.0315279	+	0.999503i	$0.489963\pi$
$240$	1.65846e10	0.322666
$241$	1.62484e10	0.310265	0.155132	−	0.987894i	$-0.450420\pi$
$241$	1.62484e10	0.310265	0.155132	+	0.987894i	$0.450420\pi$
$242$	4.09372e9	0.0767271
$243$	−3.48678e9	−0.0641500
$244$	5.02288e10	0.907191
$245$	−2.41326e10	−0.427914
$246$	−1.38022e10	−0.240292
$247$	2.41913e9	0.0413545
$248$	−7.21103e10	−1.21050
$249$	−3.93459e10	−0.648638
$250$	6.72543e9	0.108891
$251$	−3.97913e10	−0.632786	−0.316393	−	0.948628i	$-0.602472\pi$
$251$	−3.97913e10	−0.632786	−0.316393	+	0.948628i	$0.602472\pi$
$252$	−2.13737e9	−0.0333870
$253$	−6.85036e10	−1.05117
$254$	2.16807e9	0.0326829
$255$	−1.62300e9	−0.0240374
$256$	8.00053e10	1.16423
$257$	2.01723e9	0.0288440	0.0144220	−	0.999896i	$-0.495409\pi$
$257$	2.01723e9	0.0288440	0.0144220	+	0.999896i	$0.495409\pi$
$258$	5.15367e10	0.724149
$259$	1.86043e10	0.256900
$260$	−2.86399e9	−0.0388680
$261$	1.69398e10	0.225957
$262$	1.42361e11	1.86653
$263$	8.63610e10	1.11305	0.556527	−	0.830829i	$-0.312133\pi$
$263$	8.63610e10	1.11305	0.556527	+	0.830829i	$0.312133\pi$
$264$	2.96198e10	0.375288
$265$	−1.90764e10	−0.237624
$266$	4.73758e9	0.0580216
$267$	−8.14552e10	−0.980885
$268$	1.33956e10	0.158619
$269$	9.14697e10	1.06510	0.532552	−	0.846397i	$-0.321233\pi$
$269$	9.14697e10	1.06510	0.532552	+	0.846397i	$0.321233\pi$
$270$	−9.14988e9	−0.104780
$271$	9.92649e10	1.11798	0.558990	−	0.829174i	$-0.311189\pi$
$271$	9.92649e10	1.11798	0.558990	+	0.829174i	$0.311189\pi$
$272$	−1.05025e10	−0.116341
$273$	−1.98423e9	−0.0216202
$274$	−3.52190e10	−0.377485
$275$	1.95568e10	0.206206
$276$	2.73595e10	0.283803
$277$	1.06737e11	1.08932	0.544658	−	0.838658i	$-0.316659\pi$
$277$	1.06737e11	1.08932	0.544658	+	0.838658i	$0.316659\pi$
$278$	−7.37470e10	−0.740530
$279$	6.47753e10	0.640015
$280$	6.02422e9	0.0585719
$281$	1.92405e10	0.184093	0.0920465	−	0.995755i	$-0.470659\pi$
$281$	1.92405e10	0.184093	0.0920465	+	0.995755i	$0.470659\pi$
$282$	−6.35333e10	−0.598247
$283$	−1.48095e10	−0.137247	−0.0686235	−	0.997643i	$-0.521861\pi$
$283$	−1.48095e10	−0.137247	−0.0686235	+	0.997643i	$0.521861\pi$
$284$	3.12920e10	0.285430
$285$	6.59750e9	0.0592349
$286$	−2.56014e10	−0.226264
$287$	−8.16290e9	−0.0710192
$288$	−3.46735e10	−0.296983
$289$	−1.17560e11	−0.991333
$290$	4.44527e10	0.369068
$291$	3.07395e10	0.251292
$292$	8.19013e10	0.659277
$293$	1.15726e11	0.917332	0.458666	−	0.888609i	$-0.348327\pi$
$293$	1.15726e11	0.917332	0.458666	+	0.888609i	$0.348327\pi$
$294$	8.61567e10	0.672552
$295$	1.53302e9	0.0117855
$296$	1.02970e11	0.779644
$297$	−2.66069e10	−0.198422
$298$	−2.25495e10	−0.165639
$299$	2.53991e10	0.183780
$300$	−7.81075e9	−0.0556733
$301$	3.04799e10	0.214025
$302$	3.42945e11	2.37243
$303$	−1.24099e11	−0.845818
$304$	4.26927e10	0.286697
$305$	1.27170e11	0.841465
$306$	5.79434e9	0.0377796
$307$	−1.54764e11	−0.994369	−0.497185	−	0.867645i	$-0.665633\pi$
$307$	−1.54764e11	−0.994369	−0.497185	+	0.867645i	$0.665633\pi$
$308$	−1.63098e10	−0.103269
$309$	−1.10868e11	−0.691821
$310$	1.69981e11	1.04537
$311$	−2.75794e11	−1.67172	−0.835858	−	0.548945i	$-0.815030\pi$
$311$	−2.75794e11	−1.67172	−0.835858	+	0.548945i	$0.815030\pi$
$312$	−1.09822e10	−0.0656133
$313$	−3.16982e11	−1.86675	−0.933374	−	0.358906i	$-0.883150\pi$
$313$	−3.16982e11	−1.86675	−0.933374	+	0.358906i	$0.883150\pi$
$314$	2.87376e11	1.66827
$315$	−5.41143e9	−0.0309681
$316$	−8.46666e10	−0.477662
$317$	3.13022e11	1.74104	0.870518	−	0.492137i	$-0.163784\pi$
$317$	3.13022e11	1.74104	0.870518	+	0.492137i	$0.163784\pi$
$318$	6.81055e10	0.373474
$319$	1.29264e11	0.698905
$320$	1.38419e10	0.0737941
$321$	1.61363e11	0.848265
$322$	4.97413e10	0.257849
$323$	−4.17799e9	−0.0213578
$324$	1.06264e10	0.0535717
$325$	−7.25111e9	−0.0360520
$326$	5.53996e9	0.0271661
$327$	−1.45923e11	−0.705763
$328$	−4.51794e10	−0.215530
$329$	−3.75749e10	−0.176814
$330$	−6.98207e10	−0.324094
$331$	−3.10022e11	−1.41960	−0.709802	−	0.704401i	$-0.751215\pi$
$331$	−3.10022e11	−1.41960	−0.709802	+	0.704401i	$0.751215\pi$
$332$	1.19912e11	0.541678
$333$	−9.24955e10	−0.412213
$334$	2.12465e10	0.0934177
$335$	3.39151e10	0.147127
$336$	−3.50176e10	−0.149885
$337$	−4.14276e11	−1.74967	−0.874833	−	0.484425i	$-0.839029\pi$
$337$	−4.14276e11	−1.74967	−0.874833	+	0.484425i	$0.839029\pi$
$338$	−2.82634e11	−1.17787
$339$	7.45614e10	0.306631
$340$	4.94631e9	0.0200736
$341$	4.94285e11	1.97962
$342$	−2.35540e10	−0.0930995
$343$	1.04208e11	0.406515
$344$	1.68698e11	0.649527
$345$	6.92692e10	0.263241
$346$	5.29365e11	1.98570
$347$	2.17610e11	0.805744	0.402872	−	0.915256i	$-0.368012\pi$
$347$	2.17610e11	0.805744	0.402872	+	0.915256i	$0.368012\pi$
$348$	−5.16262e10	−0.188696
$349$	2.23783e11	0.807444	0.403722	−	0.914882i	$-0.367716\pi$
$349$	2.23783e11	0.807444	0.403722	+	0.914882i	$0.367716\pi$
$350$	−1.42005e10	−0.0505820
$351$	9.86505e9	0.0346910
$352$	−2.64586e11	−0.918596
$353$	9.61990e10	0.329750	0.164875	−	0.986315i	$-0.447278\pi$
$353$	9.61990e10	0.329750	0.164875	+	0.986315i	$0.447278\pi$
$354$	−5.47310e9	−0.0185233
$355$	7.92255e10	0.264751
$356$	2.48245e11	0.819137
$357$	3.42689e9	0.0111659
$358$	6.63952e11	2.13630
$359$	−5.18159e11	−1.64641	−0.823205	−	0.567744i	$-0.807816\pi$
$359$	−5.18159e11	−1.64641	−0.823205	+	0.567744i	$0.807816\pi$
$360$	−2.99508e10	−0.0939826
$361$	1.69836e10	0.0526316
$362$	−1.64023e11	−0.502015
$363$	−1.20371e10	−0.0363867
$364$	6.04719e9	0.0180550
$365$	2.07359e11	0.611512
$366$	−4.54016e11	−1.32253
$367$	3.39605e11	0.977184	0.488592	−	0.872512i	$-0.337511\pi$
$367$	3.39605e11	0.977184	0.488592	+	0.872512i	$0.337511\pi$
$368$	4.48244e11	1.27409
$369$	4.05838e10	0.113955
$370$	−2.42723e11	−0.673292
$371$	4.02790e10	0.110381
$372$	−1.97411e11	−0.534476
$373$	−5.92743e11	−1.58554	−0.792769	−	0.609522i	$-0.791362\pi$
$373$	−5.92743e11	−1.58554	−0.792769	+	0.609522i	$0.791362\pi$
$374$	4.42153e10	0.116856
$375$	−1.97754e10	−0.0516398
$376$	−2.07967e11	−0.536598
$377$	−4.79272e10	−0.122193
$378$	1.93196e10	0.0486726
$379$	−5.77352e11	−1.43736	−0.718678	−	0.695343i	$-0.755253\pi$
$379$	−5.77352e11	−1.43736	−0.718678	+	0.695343i	$0.755253\pi$
$380$	−2.01068e10	−0.0494670
$381$	−6.37496e9	−0.0154994
$382$	9.73145e11	2.33826
$383$	−2.19148e11	−0.520407	−0.260203	−	0.965554i	$-0.583790\pi$
$383$	−2.19148e11	−0.520407	−0.260203	+	0.965554i	$0.583790\pi$
$384$	−2.68589e11	−0.630372
$385$	−4.12934e10	−0.0957872
$386$	6.79333e10	0.155754
$387$	−1.51538e11	−0.343417
$388$	−9.36828e10	−0.209854
$389$	1.97665e10	0.0437679	0.0218839	−	0.999761i	$-0.493034\pi$
$389$	1.97665e10	0.0437679	0.0218839	+	0.999761i	$0.493034\pi$
$390$	2.58875e10	0.0566629
$391$	−4.38660e10	−0.0949146
$392$	2.82021e11	0.603246
$393$	−4.18596e11	−0.885174
$394$	−8.03560e11	−1.67991
$395$	−2.14360e11	−0.443055
$396$	8.10879e10	0.165702
$397$	2.63814e11	0.533016	0.266508	−	0.963833i	$-0.414130\pi$
$397$	2.63814e11	0.533016	0.266508	+	0.963833i	$0.414130\pi$
$398$	−6.73212e11	−1.34486
$399$	−1.39303e10	−0.0275159
$400$	−1.27967e11	−0.249936
$401$	2.72694e10	0.0526655	0.0263327	−	0.999653i	$-0.491617\pi$
$401$	2.72694e10	0.0526655	0.0263327	+	0.999653i	$0.491617\pi$
$402$	−1.21082e11	−0.231239
$403$	−1.83267e11	−0.346107
$404$	3.78209e11	0.706342
$405$	2.69042e10	0.0496904
$406$	−9.38599e10	−0.171440
$407$	−7.05812e11	−1.27501
$408$	1.89669e10	0.0338865
$409$	−9.77950e11	−1.72807	−0.864035	−	0.503431i	$-0.832071\pi$
$409$	−9.77950e11	−1.72807	−0.864035	+	0.503431i	$0.832071\pi$
$410$	1.06498e11	0.186130
$411$	1.03558e11	0.179017
$412$	3.37886e11	0.577740
$413$	−3.23691e9	−0.00547463
$414$	−2.47301e11	−0.413736
$415$	3.03595e11	0.502433
$416$	9.81008e10	0.160603
$417$	2.16845e11	0.351186
$418$	−1.79735e11	−0.287965
$419$	6.52847e9	0.0103478	0.00517390	−	0.999987i	$-0.498353\pi$
$419$	6.52847e9	0.0103478	0.00517390	+	0.999987i	$0.498353\pi$
$420$	1.64921e10	0.0258614
$421$	4.11617e10	0.0638592	0.0319296	−	0.999490i	$-0.489835\pi$
$421$	4.11617e10	0.0638592	0.0319296	+	0.999490i	$0.489835\pi$
$422$	4.44762e11	0.682687
$423$	1.86813e11	0.283710
$424$	2.22933e11	0.334988
$425$	1.25231e10	0.0186193
$426$	−2.82846e11	−0.416109
$427$	−2.68514e11	−0.390879
$428$	−4.91775e11	−0.708385
$429$	7.52780e10	0.107303
$430$	−3.97660e11	−0.560924
$431$	9.29056e11	1.29686	0.648432	−	0.761273i	$-0.275425\pi$
$431$	9.29056e11	1.29686	0.648432	+	0.761273i	$0.275425\pi$
$432$	1.74098e11	0.240501
$433$	−5.31386e11	−0.726465	−0.363233	−	0.931698i	$-0.618327\pi$
$433$	−5.31386e11	−0.726465	−0.363233	+	0.931698i	$0.618327\pi$
$434$	−3.58907e11	−0.485599
$435$	−1.30708e11	−0.175025
$436$	4.44720e11	0.589383
$437$	1.78316e11	0.233896
$438$	−7.40301e11	−0.961114
$439$	1.97454e11	0.253732	0.126866	−	0.991920i	$-0.459508\pi$
$439$	1.97454e11	0.253732	0.126866	+	0.991920i	$0.459508\pi$
$440$	−2.28548e11	−0.290697
$441$	−2.53334e11	−0.318948
$442$	−1.63937e10	−0.0204304
$443$	−2.34277e11	−0.289010	−0.144505	−	0.989504i	$-0.546159\pi$
$443$	−2.34277e11	−0.289010	−0.144505	+	0.989504i	$0.546159\pi$
$444$	2.81892e11	0.344239
$445$	6.28512e11	0.759790
$446$	−1.09538e12	−1.31086
$447$	6.63042e10	0.0785520
$448$	−2.92266e10	−0.0342790
$449$	−1.15248e12	−1.33821	−0.669105	−	0.743167i	$-0.733323\pi$
$449$	−1.15248e12	−1.33821	−0.669105	+	0.743167i	$0.733323\pi$
$450$	7.06009e10	0.0811623
$451$	3.09686e11	0.352473
$452$	−2.27236e11	−0.256067
$453$	−1.00839e12	−1.12509
$454$	−1.19737e12	−1.32275
$455$	1.53104e10	0.0167469
$456$	−7.71006e10	−0.0835057
$457$	−9.72558e10	−0.104302	−0.0521510	−	0.998639i	$-0.516608\pi$
$457$	−9.72558e10	−0.104302	−0.0521510	+	0.998639i	$0.516608\pi$
$458$	−1.14029e12	−1.21094
$459$	−1.70376e10	−0.0179164
$460$	−2.11107e11	−0.219833
$461$	−1.92816e12	−1.98833	−0.994166	−	0.107861i	$-0.965600\pi$
$461$	−1.92816e12	−1.98833	−0.994166	+	0.107861i	$0.965600\pi$
$462$	1.47423e11	0.150549
$463$	−1.06915e12	−1.08124	−0.540621	−	0.841266i	$-0.681811\pi$
$463$	−1.06915e12	−1.08124	−0.540621	+	0.841266i	$0.681811\pi$
$464$	−8.45818e11	−0.847122
$465$	−4.99809e11	−0.495754
$466$	1.44643e12	1.42089
$467$	5.91512e11	0.575490	0.287745	−	0.957707i	$-0.407094\pi$
$467$	5.91512e11	0.575490	0.287745	+	0.957707i	$0.407094\pi$
$468$	−3.00651e10	−0.0289705
$469$	−7.16102e10	−0.0683435
$470$	4.90226e11	0.463400
$471$	−8.44996e11	−0.791153
$472$	−1.79154e10	−0.0166145
$473$	−1.15635e12	−1.06222
$474$	7.65297e11	0.696350
$475$	−5.09066e10	−0.0458831
$476$	−1.04439e10	−0.00932463
$477$	−2.00257e11	−0.177114
$478$	8.76186e10	0.0767664
$479$	9.48329e10	0.0823093	0.0411547	−	0.999153i	$-0.486896\pi$
$479$	9.48329e10	0.0823093	0.0411547	+	0.999153i	$0.486896\pi$
$480$	2.67543e11	0.230042
$481$	2.61695e11	0.222916
$482$	4.47600e11	0.377727
$483$	−1.46259e11	−0.122281
$484$	3.66847e10	0.0303865
$485$	−2.37188e11	−0.194650
$486$	−9.60518e10	−0.0780984
$487$	4.72490e11	0.380638	0.190319	−	0.981722i	$-0.439048\pi$
$487$	4.72490e11	0.380638	0.190319	+	0.981722i	$0.439048\pi$
$488$	−1.48615e12	−1.18625
$489$	−1.62896e10	−0.0128831
$490$	−6.64789e11	−0.520956
$491$	−2.25196e11	−0.174861	−0.0874307	−	0.996171i	$-0.527866\pi$
$491$	−2.25196e11	−0.174861	−0.0874307	+	0.996171i	$0.527866\pi$
$492$	−1.23684e11	−0.0951639
$493$	8.27734e10	0.0631073
$494$	6.66406e10	0.0503463
$495$	2.05300e11	0.153697
$496$	−3.23428e12	−2.39944
$497$	−1.67281e11	−0.122983
$498$	−1.08388e12	−0.789674
$499$	1.32909e12	0.959627	0.479813	−	0.877371i	$-0.340704\pi$
$499$	1.32909e12	0.959627	0.479813	+	0.877371i	$0.340704\pi$
$500$	6.02681e10	0.0431244
$501$	−6.24731e10	−0.0443020
$502$	−1.09615e12	−0.770375
$503$	1.54733e12	1.07777	0.538885	−	0.842379i	$-0.318846\pi$
$503$	1.54733e12	1.07777	0.538885	+	0.842379i	$0.318846\pi$
$504$	6.32398e10	0.0436569
$505$	9.57555e11	0.655168
$506$	−1.88709e12	−1.27972
$507$	8.31054e11	0.558590
$508$	1.94285e10	0.0129435
$509$	−1.47488e12	−0.973928	−0.486964	−	0.873422i	$-0.661896\pi$
$509$	−1.47488e12	−0.973928	−0.486964	+	0.873422i	$0.661896\pi$
$510$	−4.47094e10	−0.0292640
$511$	−4.37830e11	−0.284061
$512$	5.06191e11	0.325537
$513$	6.92579e10	0.0441511
$514$	5.55693e10	0.0351157
$515$	8.55465e11	0.535882
$516$	4.61832e11	0.286788
$517$	1.42552e12	0.877541
$518$	5.12499e11	0.312759
$519$	−1.55654e12	−0.941688
$520$	8.47389e10	0.0508239
$521$	−4.37468e10	−0.0260121	−0.0130061	−	0.999915i	$-0.504140\pi$
$521$	−4.37468e10	−0.0260121	−0.0130061	+	0.999915i	$0.504140\pi$
$522$	4.66646e11	0.275087
$523$	1.88419e12	1.10120	0.550601	−	0.834769i	$-0.314399\pi$
$523$	1.88419e12	1.10120	0.550601	+	0.834769i	$0.314399\pi$
$524$	1.27573e12	0.739208
$525$	4.17549e10	0.0239878
$526$	2.37902e12	1.35507
$527$	3.16514e11	0.178749
$528$	1.32850e12	0.743892
$529$	7.10365e10	0.0394395
$530$	−5.25505e11	−0.289291
$531$	1.60931e10	0.00878442
$532$	4.24545e10	0.0229785
$533$	−1.14822e11	−0.0616246
$534$	−2.24388e12	−1.19416
$535$	−1.24509e12	−0.657063
$536$	−3.96343e11	−0.207410
$537$	−1.95228e12	−1.01311
$538$	2.51975e12	1.29669
$539$	−1.93313e12	−0.986535
$540$	−8.19941e10	−0.0414964
$541$	−1.85676e12	−0.931899	−0.465950	−	0.884811i	$-0.654287\pi$
$541$	−1.85676e12	−0.931899	−0.465950	+	0.884811i	$0.654287\pi$
$542$	2.73449e12	1.36107
$543$	4.82292e11	0.238073
$544$	−1.69427e11	−0.0829443
$545$	1.12595e12	0.546682
$546$	−5.46603e10	−0.0263211
$547$	2.83450e12	1.35374	0.676868	−	0.736104i	$-0.263337\pi$
$547$	2.83450e12	1.35374	0.676868	+	0.736104i	$0.263337\pi$
$548$	−3.15606e11	−0.149497
$549$	1.33498e12	0.627191
$550$	5.38740e11	0.251042
$551$	−3.36474e11	−0.155514
$552$	−8.09503e11	−0.371101
$553$	4.52613e11	0.205809
$554$	2.94031e12	1.32617
$555$	7.13700e11	0.319299
$556$	−6.60863e11	−0.293275
$557$	−1.81103e12	−0.797218	−0.398609	−	0.917121i	$-0.630507\pi$
$557$	−1.81103e12	−0.797218	−0.398609	+	0.917121i	$0.630507\pi$
$558$	1.78439e12	0.779176
$559$	4.28742e11	0.185713
$560$	2.70197e11	0.116101
$561$	−1.30010e11	−0.0554171
$562$	5.30024e11	0.224121
$563$	−6.01090e11	−0.252146	−0.126073	−	0.992021i	$-0.540237\pi$
$563$	−6.01090e11	−0.252146	−0.126073	+	0.992021i	$0.540237\pi$
$564$	−5.69336e11	−0.236926
$565$	−5.75320e11	−0.237515
$566$	−4.07964e11	−0.167089
$567$	−5.68070e10	−0.0230823
$568$	−9.25856e11	−0.373230
$569$	2.86845e12	1.14721	0.573605	−	0.819132i	$-0.305545\pi$
$569$	2.86845e12	1.14721	0.573605	+	0.819132i	$0.305545\pi$
$570$	1.81744e11	0.0721146
$571$	4.07751e12	1.60521	0.802605	−	0.596510i	$-0.203447\pi$
$571$	4.07751e12	1.60521	0.802605	+	0.596510i	$0.203447\pi$
$572$	−2.29420e11	−0.0896083
$573$	−2.86142e12	−1.10888
$574$	−2.24866e11	−0.0864612
$575$	−5.34484e11	−0.203906
$576$	1.45307e11	0.0550029
$577$	4.03404e12	1.51513	0.757564	−	0.652761i	$-0.226389\pi$
$577$	4.03404e12	1.51513	0.757564	+	0.652761i	$0.226389\pi$
$578$	−3.23847e12	−1.20688
$579$	−1.99750e11	−0.0738641
$580$	3.98350e11	0.146164
$581$	−6.41028e11	−0.233391
$582$	8.46794e11	0.305932
$583$	−1.52811e12	−0.547831
$584$	−2.42327e12	−0.862073
$585$	−7.61192e10	−0.0268716
$586$	3.18795e12	1.11679
$587$	−2.38576e12	−0.829382	−0.414691	−	0.909962i	$-0.636110\pi$
$587$	−2.38576e12	−0.829382	−0.414691	+	0.909962i	$0.636110\pi$
$588$	7.72069e11	0.266353
$589$	−1.28663e12	−0.440489
$590$	4.22307e10	0.0143481
$591$	2.36278e12	0.796672
$592$	4.61838e12	1.54540
$593$	5.79734e11	0.192523	0.0962614	−	0.995356i	$-0.469312\pi$
$593$	5.79734e11	0.192523	0.0962614	+	0.995356i	$0.469312\pi$
$594$	−7.32949e11	−0.241566
$595$	−2.64421e10	−0.00864907
$596$	−2.02071e11	−0.0655987
$597$	1.97950e12	0.637782
$598$	6.99680e11	0.223740
$599$	−2.98994e12	−0.948948	−0.474474	−	0.880270i	$-0.657362\pi$
$599$	−2.98994e12	−0.948948	−0.474474	+	0.880270i	$0.657362\pi$
$600$	2.31102e11	0.0727986
$601$	6.58051e11	0.205743	0.102871	−	0.994695i	$-0.467197\pi$
$601$	6.58051e11	0.205743	0.102871	+	0.994695i	$0.467197\pi$
$602$	8.39642e11	0.260561
$603$	3.56027e11	0.109662
$604$	3.07321e12	0.939562
$605$	9.28790e10	0.0281850
$606$	−3.41861e12	−1.02973
$607$	4.24840e12	1.27021	0.635107	−	0.772425i	$-0.280956\pi$
$607$	4.24840e12	1.27021	0.635107	+	0.772425i	$0.280956\pi$
$608$	6.88720e11	0.204398
$609$	2.75984e11	0.0813030
$610$	3.50321e12	1.02443
$611$	−5.28543e11	−0.153425
$612$	5.19244e10	0.0149620
$613$	2.46446e12	0.704935	0.352467	−	0.935824i	$-0.385343\pi$
$613$	2.46446e12	0.704935	0.352467	+	0.935824i	$0.385343\pi$
$614$	−4.26335e12	−1.21058
$615$	−3.13146e11	−0.0882692
$616$	4.82569e11	0.135035
$617$	5.98845e12	1.66353	0.831766	−	0.555126i	$-0.187330\pi$
$617$	5.98845e12	1.66353	0.831766	+	0.555126i	$0.187330\pi$
$618$	−3.05413e12	−0.842247
$619$	1.42181e12	0.389255	0.194628	−	0.980877i	$-0.437650\pi$
$619$	1.42181e12	0.389255	0.194628	+	0.980877i	$0.437650\pi$
$620$	1.52323e12	0.414004
$621$	7.27160e11	0.196208
$622$	−7.59740e12	−2.03520
$623$	−1.32708e12	−0.352939
$624$	−4.92571e11	−0.130058
$625$	1.52588e11	0.0400000
$626$	−8.73204e12	−2.27264
$627$	5.28491e11	0.136563
$628$	2.57524e12	0.660692
$629$	−4.51964e11	−0.115127
$630$	−1.49071e11	−0.0377016
$631$	−3.80034e12	−0.954313	−0.477156	−	0.878818i	$-0.658332\pi$
$631$	−3.80034e12	−0.954313	−0.477156	+	0.878818i	$0.658332\pi$
$632$	2.50509e12	0.624592
$633$	−1.30777e12	−0.323754
$634$	8.62292e12	2.11960
$635$	4.91895e10	0.0120058
$636$	6.10308e11	0.147908
$637$	7.16750e11	0.172481
$638$	3.56087e12	0.850870
$639$	8.31678e11	0.197334
$640$	2.07244e12	0.488284
$641$	−2.56410e12	−0.599892	−0.299946	−	0.953956i	$-0.596969\pi$
$641$	−2.56410e12	−0.599892	−0.299946	+	0.953956i	$0.596969\pi$
$642$	4.44513e12	1.03271
$643$	−1.76871e12	−0.408044	−0.204022	−	0.978966i	$-0.565401\pi$
$643$	−1.76871e12	−0.408044	−0.204022	+	0.978966i	$0.565401\pi$
$644$	4.45743e11	0.102117
$645$	1.16927e12	0.266010
$646$	−1.15093e11	−0.0260017
$647$	3.55382e12	0.797309	0.398655	−	0.917101i	$-0.369477\pi$
$647$	3.55382e12	0.797309	0.398655	+	0.917101i	$0.369477\pi$
$648$	−3.14412e11	−0.0700505
$649$	1.22802e11	0.0271710
$650$	−1.99749e11	−0.0438909
$651$	1.05532e12	0.230288
$652$	4.96448e10	0.0107587
$653$	−6.38549e12	−1.37431	−0.687156	−	0.726510i	$-0.741141\pi$
$653$	−6.38549e12	−1.37431	−0.687156	+	0.726510i	$0.741141\pi$
$654$	−4.01980e12	−0.859220
$655$	3.22991e12	0.685653
$656$	−2.02638e12	−0.427223
$657$	2.17677e12	0.455794
$658$	−1.03509e12	−0.215259
$659$	−4.11478e12	−0.849889	−0.424945	−	0.905219i	$-0.639706\pi$
$659$	−4.11478e12	−0.849889	−0.424945	+	0.905219i	$0.639706\pi$
$660$	−6.25678e11	−0.128352
$661$	4.87343e12	0.992951	0.496476	−	0.868051i	$-0.334627\pi$
$661$	4.87343e12	0.992951	0.496476	+	0.868051i	$0.334627\pi$
$662$	−8.54030e12	−1.72827
$663$	4.82040e10	0.00968884
$664$	−3.54792e12	−0.708299
$665$	1.07487e11	0.0213137
$666$	−2.54801e12	−0.501842
$667$	−3.53275e12	−0.691108
$668$	1.90395e11	0.0369966
$669$	3.22084e12	0.621658
$670$	9.34272e11	0.179117
$671$	1.01869e13	1.93996
$672$	−5.64905e11	−0.106860
$673$	6.29501e12	1.18285	0.591423	−	0.806361i	$-0.298566\pi$
$673$	6.29501e12	1.18285	0.591423	+	0.806361i	$0.298566\pi$
$674$	−1.14122e13	−2.13010
$675$	−2.07594e11	−0.0384900
$676$	−2.53275e12	−0.466478
$677$	2.20875e12	0.404108	0.202054	−	0.979374i	$-0.435238\pi$
$677$	2.20875e12	0.404108	0.202054	+	0.979374i	$0.435238\pi$
$678$	2.05397e12	0.373303
$679$	5.00812e11	0.0904192
$680$	−1.46350e11	−0.0262483
$681$	3.52075e12	0.627296
$682$	1.36163e13	2.41006
$683$	1.06996e13	1.88138	0.940688	−	0.339274i	$-0.110181\pi$
$683$	1.06996e13	1.88138	0.940688	+	0.339274i	$0.110181\pi$
$684$	−2.11073e11	−0.0368705
$685$	−7.99056e11	−0.138666
$686$	2.87065e12	0.494906
$687$	3.35291e12	0.574270
$688$	7.56642e12	1.28749
$689$	5.66580e11	0.0957799
$690$	1.90818e12	0.320479
$691$	5.88997e12	0.982793	0.491396	−	0.870936i	$-0.336487\pi$
$691$	5.88997e12	0.982793	0.491396	+	0.870936i	$0.336487\pi$
$692$	4.74376e12	0.786404
$693$	−4.33482e11	−0.0713955
$694$	5.99460e12	0.980940
$695$	−1.67319e12	−0.272027
$696$	1.52750e12	0.246740
$697$	1.98306e11	0.0318265
$698$	6.16463e12	0.983010
$699$	−4.25305e12	−0.673835
$700$	−1.27253e11	−0.0200322
$701$	−1.07320e13	−1.67861	−0.839305	−	0.543661i	$-0.817038\pi$
$701$	−1.07320e13	−1.67861	−0.839305	+	0.543661i	$0.817038\pi$
$702$	2.71756e11	0.0422340
$703$	1.83724e12	0.283704
$704$	1.10881e12	0.170129
$705$	−1.44146e12	−0.219761
$706$	2.65003e12	0.401448
$707$	−2.02184e12	−0.304340
$708$	−4.90457e10	−0.00733586
$709$	7.06857e12	1.05057	0.525283	−	0.850927i	$-0.323959\pi$
$709$	7.06857e12	1.05057	0.525283	+	0.850927i	$0.323959\pi$
$710$	2.18246e12	0.322317
$711$	−2.25027e12	−0.330234
$712$	−7.34501e12	−1.07111
$713$	−1.35087e13	−1.95754
$714$	9.44019e10	0.0135937
$715$	−5.80848e11	−0.0831162
$716$	5.94982e12	0.846049
$717$	−2.57633e11	−0.0364053
$718$	−1.42739e13	−2.00439
$719$	5.67130e12	0.791412	0.395706	−	0.918377i	$-0.370500\pi$
$719$	5.67130e12	0.791412	0.395706	+	0.918377i	$0.370500\pi$
$720$	−1.34335e12	−0.186291
$721$	−1.80628e12	−0.248929
$722$	4.67853e11	0.0640755
$723$	−1.31612e12	−0.179132
$724$	−1.46985e12	−0.198815
$725$	1.00855e12	0.135574
$726$	−3.31591e11	−0.0442984
$727$	1.22356e13	1.62450	0.812252	−	0.583307i	$-0.198241\pi$
$727$	1.22356e13	1.62450	0.812252	+	0.583307i	$0.198241\pi$
$728$	−1.78922e11	−0.0236088
$729$	2.82430e11	0.0370370
$730$	5.71220e12	0.744476
$731$	−7.40466e11	−0.0959129
$732$	−4.06854e12	−0.523767
$733$	−7.93868e12	−1.01573	−0.507867	−	0.861435i	$-0.669566\pi$
$733$	−7.93868e12	−1.01573	−0.507867	+	0.861435i	$0.669566\pi$
$734$	9.35522e12	1.18966
$735$	1.95474e12	0.247056
$736$	7.23108e12	0.908349
$737$	2.71676e12	0.339194
$738$	1.11798e12	0.138733
$739$	−6.25783e12	−0.771834	−0.385917	−	0.922534i	$-0.626115\pi$
$739$	−6.25783e12	−0.771834	−0.385917	+	0.922534i	$0.626115\pi$
$740$	−2.17510e12	−0.266646
$741$	−1.95949e11	−0.0238760
$742$	1.10958e12	0.134382
$743$	1.48294e13	1.78514	0.892572	−	0.450906i	$-0.148899\pi$
$743$	1.48294e13	1.78514	0.892572	+	0.450906i	$0.148899\pi$
$744$	5.84094e12	0.698883
$745$	−5.11606e11	−0.0608461
$746$	−1.63285e13	−1.93029
$747$	3.18702e12	0.374492
$748$	3.96223e11	0.0462788
$749$	2.62894e12	0.305220
$750$	−5.44760e11	−0.0628680
$751$	8.61490e12	0.988258	0.494129	−	0.869389i	$-0.335487\pi$
$751$	8.61490e12	0.988258	0.494129	+	0.869389i	$0.335487\pi$
$752$	−9.32771e12	−1.06364
$753$	3.22310e12	0.365339
$754$	−1.32027e12	−0.148762
$755$	7.78080e12	0.871491
$756$	1.73127e11	0.0192760
$757$	2.67843e12	0.296448	0.148224	−	0.988954i	$-0.452644\pi$
$757$	2.67843e12	0.296448	0.148224	+	0.988954i	$0.452644\pi$
$758$	−1.59045e13	−1.74989
$759$	5.54879e12	0.606891
$760$	5.94912e11	0.0646832
$761$	−1.74929e13	−1.89073	−0.945367	−	0.326009i	$-0.894296\pi$
$761$	−1.74929e13	−1.89073	−0.945367	+	0.326009i	$0.894296\pi$
$762$	−1.75613e11	−0.0188695
$763$	−2.37739e12	−0.253946
$764$	8.72057e12	0.926029
$765$	1.31463e11	0.0138780
$766$	−6.03695e12	−0.633561
$767$	−4.55316e10	−0.00475044
$768$	−6.48043e12	−0.672169
$769$	3.89757e12	0.401907	0.200953	−	0.979601i	$-0.435596\pi$
$769$	3.89757e12	0.401907	0.200953	+	0.979601i	$0.435596\pi$
$770$	−1.13752e12	−0.116615
$771$	−1.63395e11	−0.0166531
$772$	6.08765e11	0.0616839
$773$	−7.28811e11	−0.0734188	−0.0367094	−	0.999326i	$-0.511688\pi$
$773$	−7.28811e11	−0.0734188	−0.0367094	+	0.999326i	$0.511688\pi$
$774$	−4.17448e12	−0.418088
$775$	3.85655e12	0.384009
$776$	2.77186e12	0.274406
$777$	−1.50695e12	−0.148321
$778$	5.44514e11	0.0532845
$779$	−8.06115e11	−0.0784293
$780$	2.31983e11	0.0224404
$781$	6.34634e12	0.610371
$782$	−1.20839e12	−0.115552
$783$	−1.37212e12	−0.130456
$784$	1.26492e13	1.19575
$785$	6.52003e12	0.612825
$786$	−1.15312e13	−1.07764
$787$	−1.08845e13	−1.01140	−0.505699	−	0.862710i	$-0.668765\pi$
$787$	−1.08845e13	−1.01140	−0.505699	+	0.862710i	$0.668765\pi$
$788$	−7.20088e12	−0.665301
$789$	−6.99524e12	−0.642623
$790$	−5.90507e12	−0.539390
$791$	1.21476e12	0.110331
$792$	−2.39920e12	−0.216672
$793$	−3.77702e12	−0.339172
$794$	7.26738e12	0.648912
$795$	1.54519e12	0.137192
$796$	−6.03280e12	−0.532611
$797$	−1.13763e13	−0.998710	−0.499355	−	0.866398i	$-0.666430\pi$
$797$	−1.13763e13	−0.998710	−0.499355	+	0.866398i	$0.666430\pi$
$798$	−3.83744e11	−0.0334988
$799$	9.12829e11	0.0792372
$800$	−2.06437e12	−0.178190
$801$	6.59787e12	0.566314
$802$	7.51201e11	0.0641167
$803$	1.66105e13	1.40981
$804$	−1.08504e12	−0.0915785
$805$	1.12854e12	0.0947186
$806$	−5.04852e12	−0.421363
$807$	−7.40905e12	−0.614938
$808$	−1.11903e13	−0.923615
$809$	1.01146e13	0.830191	0.415096	−	0.909778i	$-0.363748\pi$
$809$	1.01146e13	0.830191	0.415096	+	0.909778i	$0.363748\pi$
$810$	7.41140e11	0.0604948
$811$	4.69805e11	0.0381350	0.0190675	−	0.999818i	$-0.493930\pi$
$811$	4.69805e11	0.0381350	0.0190675	+	0.999818i	$0.493930\pi$
$812$	−8.41099e11	−0.0678961
$813$	−8.04046e12	−0.645466
$814$	−1.94433e13	−1.55224
$815$	1.25692e11	0.00997922
$816$	8.50702e11	0.0671695
$817$	3.01000e12	0.236356
$818$	−2.69399e13	−2.10381
$819$	1.60722e11	0.0124824
$820$	9.54355e11	0.0737136
$821$	−4.95067e11	−0.0380294	−0.0190147	−	0.999819i	$-0.506053\pi$
$821$	−4.95067e11	−0.0380294	−0.0190147	+	0.999819i	$0.506053\pi$
$822$	2.85274e12	0.217941
$823$	6.93184e12	0.526683	0.263342	−	0.964703i	$-0.415175\pi$
$823$	6.93184e12	0.526683	0.263342	+	0.964703i	$0.415175\pi$
$824$	−9.99725e12	−0.755454
$825$	−1.58410e12	−0.119053
$826$	−8.91683e10	−0.00666500
$827$	−2.30832e13	−1.71602	−0.858008	−	0.513636i	$-0.828298\pi$
$827$	−2.30832e13	−1.71602	−0.858008	+	0.513636i	$0.828298\pi$
$828$	−2.21612e12	−0.163854
$829$	1.92635e13	1.41658	0.708288	−	0.705924i	$-0.249468\pi$
$829$	1.92635e13	1.41658	0.708288	+	0.705924i	$0.249468\pi$
$830$	8.36325e12	0.611679
$831$	−8.64566e12	−0.628917
$832$	−4.11113e11	−0.0297445
$833$	−1.23788e12	−0.0890788
$834$	5.97351e12	0.427545
$835$	4.82046e11	0.0343162
$836$	−1.61065e12	−0.114044
$837$	−5.24680e12	−0.369513
$838$	1.79842e11	0.0125978
$839$	−1.60655e13	−1.11935	−0.559674	−	0.828713i	$-0.689074\pi$
$839$	−1.60655e13	−1.11935	−0.559674	+	0.828713i	$0.689074\pi$
$840$	−4.87961e11	−0.0338165
$841$	−7.84100e12	−0.540492
$842$	1.13390e12	0.0777443
$843$	−1.55848e12	−0.106286
$844$	3.98561e12	0.270367
$845$	−6.41245e12	−0.432682
$846$	5.14620e12	0.345398
$847$	−1.96110e11	−0.0130926
$848$	9.99898e12	0.664010
$849$	1.19957e12	0.0792395
$850$	3.44980e11	0.0226678
$851$	1.92897e13	1.26079
$852$	−2.53465e12	−0.164793
$853$	−1.84899e12	−0.119581	−0.0597906	−	0.998211i	$-0.519043\pi$
$853$	−1.84899e12	−0.119581	−0.0597906	+	0.998211i	$0.519043\pi$
$854$	−7.39687e12	−0.475869
$855$	−5.34398e11	−0.0341993
$856$	1.45505e13	0.926287
$857$	−3.75898e11	−0.0238044	−0.0119022	−	0.999929i	$-0.503789\pi$
$857$	−3.75898e11	−0.0238044	−0.0119022	+	0.999929i	$0.503789\pi$
$858$	2.07371e12	0.130634
$859$	1.72280e13	1.07960	0.539802	−	0.841792i	$-0.318499\pi$
$859$	1.72280e13	1.07960	0.539802	+	0.841792i	$0.318499\pi$
$860$	−3.56352e12	−0.222145
$861$	6.61195e11	0.0410030
$862$	2.55931e13	1.57885
$863$	−2.08298e13	−1.27831	−0.639157	−	0.769076i	$-0.720717\pi$
$863$	−2.08298e13	−1.27831	−0.639157	+	0.769076i	$0.720717\pi$
$864$	2.80856e12	0.171463
$865$	1.20103e13	0.729429
$866$	−1.46383e13	−0.884424
$867$	9.52237e12	0.572346
$868$	−3.21624e12	−0.192314
$869$	−1.71713e13	−1.02144
$870$	−3.60067e12	−0.213082
$871$	−1.00730e12	−0.0593029
$872$	−1.31582e13	−0.770679
$873$	−2.48990e12	−0.145084
$874$	4.91213e12	0.284753
$875$	−3.22183e11	−0.0185809
$876$	−6.63401e12	−0.380634
$877$	−2.46003e12	−0.140425	−0.0702123	−	0.997532i	$-0.522368\pi$
$877$	−2.46003e12	−0.140425	−0.0702123	+	0.997532i	$0.522368\pi$
$878$	5.43933e12	0.308902
$879$	−9.37380e12	−0.529622
$880$	−1.02508e13	−0.576217
$881$	2.14787e13	1.20120	0.600602	−	0.799548i	$-0.294928\pi$
$881$	2.14787e13	1.20120	0.600602	+	0.799548i	$0.294928\pi$
$882$	−6.97869e12	−0.388298
$883$	−1.08514e13	−0.600708	−0.300354	−	0.953828i	$-0.597105\pi$
$883$	−1.08514e13	−0.600708	−0.300354	+	0.953828i	$0.597105\pi$
$884$	−1.46908e11	−0.00809115
$885$	−1.24175e11	−0.00680438
$886$	−6.45372e12	−0.351851
$887$	8.57667e12	0.465224	0.232612	−	0.972570i	$-0.425273\pi$
$887$	8.57667e12	0.465224	0.232612	+	0.972570i	$0.425273\pi$
$888$	−8.34054e12	−0.450128
$889$	−1.03861e11	−0.00557695
$890$	1.73139e13	0.924994
$891$	2.15516e12	0.114559
$892$	−9.81594e12	−0.519146
$893$	−3.71065e12	−0.195263
$894$	1.82651e12	0.0956318
$895$	1.50639e13	0.784752
$896$	−4.37587e12	−0.226819
$897$	−2.05733e12	−0.106106
$898$	−3.17478e13	−1.62918
$899$	2.54904e13	1.30154
$900$	6.32671e11	0.0321430
$901$	−9.78521e11	−0.0494662
$902$	8.53103e12	0.429113
$903$	−2.46887e12	−0.123567
$904$	6.72338e12	0.334834
$905$	−3.72139e12	−0.184411
$906$	−2.77785e13	−1.36972
$907$	−2.30212e13	−1.12952	−0.564761	−	0.825255i	$-0.691031\pi$
$907$	−2.30212e13	−1.12952	−0.564761	+	0.825255i	$0.691031\pi$
$908$	−1.07299e13	−0.523855
$909$	1.00520e13	0.488333
$910$	4.21761e11	0.0203883
$911$	−2.29352e13	−1.10324	−0.551620	−	0.834095i	$-0.685990\pi$
$911$	−2.29352e13	−1.10324	−0.551620	+	0.834095i	$0.685990\pi$
$912$	−3.45811e12	−0.165524
$913$	2.43194e13	1.15834
$914$	−2.67914e12	−0.126981
$915$	−1.03008e13	−0.485820
$916$	−1.02184e13	−0.479573
$917$	−6.81980e12	−0.318500
$918$	−4.69341e11	−0.0218121
$919$	−6.40818e12	−0.296357	−0.148179	−	0.988961i	$-0.547341\pi$
$919$	−6.40818e12	−0.296357	−0.148179	+	0.988961i	$0.547341\pi$
$920$	6.24616e12	0.287454
$921$	1.25359e13	0.574099
$922$	−5.31158e13	−2.42066
$923$	−2.35304e12	−0.106714
$924$	1.32109e12	0.0596224
$925$	−5.50695e12	−0.247328
$926$	−2.94522e13	−1.31634
$927$	8.98033e12	0.399423
$928$	−1.36448e13	−0.603948
$929$	1.54448e13	0.680317	0.340159	−	0.940368i	$-0.389519\pi$
$929$	1.54448e13	0.680317	0.340159	+	0.940368i	$0.389519\pi$
$930$	−1.37684e13	−0.603547
$931$	5.03197e12	0.219515
$932$	1.29617e13	0.562719
$933$	2.23393e13	0.965166
$934$	1.62946e13	0.700621
$935$	1.00316e12	0.0429259
$936$	8.89555e11	0.0378819
$937$	−1.31601e13	−0.557737	−0.278868	−	0.960329i	$-0.589959\pi$
$937$	−1.31601e13	−0.557737	−0.278868	+	0.960329i	$0.589959\pi$
$938$	−1.97267e12	−0.0832037
$939$	2.56756e13	1.07777
$940$	4.39303e12	0.183522
$941$	2.34164e13	0.973569	0.486784	−	0.873522i	$-0.338170\pi$
$941$	2.34164e13	0.973569	0.486784	+	0.873522i	$0.338170\pi$
$942$	−2.32774e13	−0.963177
$943$	−8.46364e12	−0.348542
$944$	−8.03540e11	−0.0329332
$945$	4.38326e11	0.0178794
$946$	−3.18545e13	−1.29318
$947$	2.63169e13	1.06331	0.531655	−	0.846961i	$-0.321570\pi$
$947$	2.63169e13	1.06331	0.531655	+	0.846961i	$0.321570\pi$
$948$	6.85800e12	0.275778
$949$	−6.15868e12	−0.246484
$950$	−1.40234e12	−0.0558597
$951$	−2.53547e13	−1.00519
$952$	3.09011e11	0.0121929
$953$	3.50206e13	1.37533	0.687663	−	0.726030i	$-0.258636\pi$
$953$	3.50206e13	1.37533	0.687663	+	0.726030i	$0.258636\pi$
$954$	−5.51654e12	−0.215625
$955$	2.20789e13	0.858938
$956$	7.85170e11	0.0304021
$957$	−1.04703e13	−0.403513
$958$	2.61240e12	0.100206
$959$	1.68717e12	0.0644133
$960$	−1.12120e12	−0.0426051
$961$	7.10320e13	2.68657
$962$	7.20901e12	0.271386
$963$	−1.30704e13	−0.489746
$964$	4.01104e12	0.149593
$965$	1.54128e12	0.0572149
$966$	−4.02905e12	−0.148869
$967$	4.39674e13	1.61701	0.808503	−	0.588492i	$-0.200278\pi$
$967$	4.39674e13	1.61701	0.808503	+	0.588492i	$0.200278\pi$
$968$	−1.08542e12	−0.0397335
$969$	3.38418e11	0.0123309
$970$	−6.53390e12	−0.236974
$971$	6.89918e12	0.249064	0.124532	−	0.992216i	$-0.460257\pi$
$971$	6.89918e12	0.249064	0.124532	+	0.992216i	$0.460257\pi$
$972$	−8.60741e11	−0.0309296
$973$	3.53286e12	0.126363
$974$	1.30159e13	0.463402
$975$	5.87340e11	0.0208146
$976$	−6.66568e13	−2.35137
$977$	−1.33531e13	−0.468875	−0.234437	−	0.972131i	$-0.575325\pi$
$977$	−1.33531e13	−0.468875	−0.234437	+	0.972131i	$0.575325\pi$
$978$	−4.48736e11	−0.0156843
$979$	5.03469e13	1.75166
$980$	−5.95732e12	−0.206316
$981$	1.18198e13	0.407473
$982$	−6.20356e12	−0.212882
$983$	1.03447e13	0.353366	0.176683	−	0.984268i	$-0.443463\pi$
$983$	1.03447e13	0.353366	0.176683	+	0.984268i	$0.443463\pi$
$984$	3.65953e12	0.124437
$985$	−1.82313e13	−0.617100
$986$	2.28019e12	0.0768290
$987$	3.04357e12	0.102084
$988$	5.97181e11	0.0199388
$989$	3.16029e13	1.05037
$990$	5.65547e12	0.187116
$991$	−5.94249e12	−0.195721	−0.0978604	−	0.995200i	$-0.531200\pi$
$991$	−5.94249e12	−0.195721	−0.0978604	+	0.995200i	$0.531200\pi$
$992$	−5.21756e13	−1.71066
$993$	2.51118e13	0.819608
$994$	−4.60816e12	−0.149723
$995$	−1.52740e13	−0.494024
$996$	−9.71287e12	−0.312738
$997$	−2.36160e13	−0.756969	−0.378484	−	0.925608i	$-0.623555\pi$
$997$	−2.36160e13	−0.756969	−0.378484	+	0.925608i	$0.623555\pi$
$998$	3.66130e13	1.16828
$999$	7.49214e12	0.237991

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+27.5474 q^{2} -81.0000 q^{3} +246.858 q^{4} +625.000 q^{5} -2231.34 q^{6} -1319.66 q^{7} -7303.96 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+27.5474 q^{2} -81.0000 q^{3} +246.858 q^{4} +625.000 q^{5} -2231.34 q^{6} -1319.66 q^{7} -7303.96 q^{8} +6561.00 q^{9} +17217.1 q^{10} +50065.5 q^{11} -19995.5 q^{12} -18562.8 q^{13} -36353.2 q^{14} -50625.0 q^{15} -327596. q^{16} +32059.3 q^{17} +180738. q^{18} -130321. q^{19} +154286. q^{20} +106892. q^{21} +1.37917e6 q^{22} -1.36828e6 q^{23} +591621. q^{24} +390625. q^{25} -511358. q^{26} -531441. q^{27} -325769. q^{28} +2.58189e6 q^{29} -1.39459e6 q^{30} +9.87277e6 q^{31} -5.28480e6 q^{32} -4.05531e6 q^{33} +883149. q^{34} -824787. q^{35} +1.61964e6 q^{36} -1.40978e7 q^{37} -3.59000e6 q^{38} +1.50359e6 q^{39} -4.56498e6 q^{40} +6.18561e6 q^{41} +2.94461e6 q^{42} -2.30968e7 q^{43} +1.23591e7 q^{44} +4.10062e6 q^{45} -3.76925e7 q^{46} +2.84732e7 q^{47} +2.65353e7 q^{48} -3.86121e7 q^{49} +1.07607e7 q^{50} -2.59680e6 q^{51} -4.58239e6 q^{52} -3.05223e7 q^{53} -1.46398e7 q^{54} +3.12909e7 q^{55} +9.63875e6 q^{56} +1.05560e7 q^{57} +7.11243e7 q^{58} +2.45284e6 q^{59} -1.24972e7 q^{60} +2.03472e8 q^{61} +2.71969e8 q^{62} -8.65829e6 q^{63} +2.21471e7 q^{64} -1.16018e7 q^{65} -1.11713e8 q^{66} +5.42642e7 q^{67} +7.91409e6 q^{68} +1.10831e8 q^{69} -2.27207e7 q^{70} +1.26761e8 q^{71} -4.79213e7 q^{72} +3.31775e8 q^{73} -3.88357e8 q^{74} -3.16406e7 q^{75} -3.21708e7 q^{76} -6.60694e7 q^{77} +4.14200e7 q^{78} -3.42977e8 q^{79} -2.04748e8 q^{80} +4.30467e7 q^{81} +1.70397e8 q^{82} +4.85752e8 q^{83} +2.63873e7 q^{84} +2.00370e7 q^{85} -6.36256e8 q^{86} -2.09133e8 q^{87} -3.65676e8 q^{88} +1.00562e9 q^{89} +1.12961e8 q^{90} +2.44966e7 q^{91} -3.37771e8 q^{92} -7.99694e8 q^{93} +7.84362e8 q^{94} -8.14506e7 q^{95} +4.28068e8 q^{96} -3.79501e8 q^{97} -1.06366e9 q^{98} +3.28480e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more