LMFDB - Embedded newform 29.10.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,Mod(1,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	29.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:	$14.9360392488$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 4803 x^{10} + 14952 x^{9} + 8248476 x^{8} - 14809944 x^{7} - 6122244486 x^{6} + \cdots + 40\!\cdots\!38 $ x^12 - 4x^11 - 4803x^10 + 14952x^9 + 8248476x^8 - 14809944x^7 - 6122244486x^6 - 1026481216x^5 + 1899055440249x^4 + 3992697832188x^3 - 174144148490503x^2 - 282853247198664*x + 4071614738753338
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$43.2474$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+44.2474 q^{2} +110.108 q^{3} +1445.83 q^{4} +350.462 q^{5} +4872.00 q^{6} -3350.56 q^{7} +41319.6 q^{8} -7559.17 q^{9} +O(q^{10})$	\(q+44.2474 q^{2} +110.108 q^{3} +1445.83 q^{4} +350.462 q^{5} +4872.00 q^{6} -3350.56 q^{7} +41319.6 q^{8} -7559.17 q^{9} +15507.0 q^{10} -63075.9 q^{11} +159198. q^{12} -4333.69 q^{13} -148253. q^{14} +38588.8 q^{15} +1.08802e6 q^{16} +67794.0 q^{17} -334473. q^{18} -340890. q^{19} +506709. q^{20} -368924. q^{21} -2.79094e6 q^{22} +1.43657e6 q^{23} +4.54963e6 q^{24} -1.83030e6 q^{25} -191755. q^{26} -2.99959e6 q^{27} -4.84434e6 q^{28} +707281. q^{29} +1.70745e6 q^{30} +8.35363e6 q^{31} +2.69864e7 q^{32} -6.94517e6 q^{33} +2.99971e6 q^{34} -1.17424e6 q^{35} -1.09293e7 q^{36} +1.62781e7 q^{37} -1.50835e7 q^{38} -477175. q^{39} +1.44810e7 q^{40} -3.36366e7 q^{41} -1.63239e7 q^{42} -3.56609e7 q^{43} -9.11971e7 q^{44} -2.64920e6 q^{45} +6.35645e7 q^{46} +1.57275e7 q^{47} +1.19800e8 q^{48} -2.91274e7 q^{49} -8.09860e7 q^{50} +7.46468e6 q^{51} -6.26579e6 q^{52} +4.17013e7 q^{53} -1.32724e8 q^{54} -2.21057e7 q^{55} -1.38444e8 q^{56} -3.75348e7 q^{57} +3.12953e7 q^{58} -5.15420e7 q^{59} +5.57929e7 q^{60} -1.02322e7 q^{61} +3.69626e8 q^{62} +2.53274e7 q^{63} +6.37010e8 q^{64} -1.51880e6 q^{65} -3.07306e8 q^{66} +2.26304e8 q^{67} +9.80188e7 q^{68} +1.58178e8 q^{69} -5.19572e7 q^{70} -2.09200e8 q^{71} -3.12342e8 q^{72} -3.09721e7 q^{73} +7.20262e8 q^{74} -2.01531e8 q^{75} -4.92870e8 q^{76} +2.11339e8 q^{77} -2.11138e7 q^{78} +1.92694e8 q^{79} +3.81310e8 q^{80} -1.81492e8 q^{81} -1.48833e9 q^{82} +7.81446e8 q^{83} -5.33402e8 q^{84} +2.37593e7 q^{85} -1.57790e9 q^{86} +7.78775e7 q^{87} -2.60627e9 q^{88} +9.13035e8 q^{89} -1.17220e8 q^{90} +1.45203e7 q^{91} +2.07704e9 q^{92} +9.19804e8 q^{93} +6.95900e8 q^{94} -1.19469e8 q^{95} +2.97142e9 q^{96} +5.03526e8 q^{97} -1.28881e9 q^{98} +4.76801e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) $ 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9} - 46678 q^{10} + 24474 q^{11} - 14210 q^{12} + 107722 q^{13} + 677768 q^{14} + 505426 q^{15} + 1656882 q^{16} + 982120 q^{17} + 2364102 q^{18} + 2084360 q^{19} + 4689410 q^{20} + 2911344 q^{21} + 2725230 q^{22} + 3004004 q^{23} + 7893170 q^{24} + 6339542 q^{25} + 6863698 q^{26} + 7881014 q^{27} + 5116944 q^{28} + 8487372 q^{29} + 10924626 q^{30} + 17872478 q^{31} + 5122946 q^{32} - 860442 q^{33} + 15662848 q^{34} - 22252312 q^{35} - 35199980 q^{36} + 452980 q^{37} - 68665276 q^{38} - 29528222 q^{39} - 61623214 q^{40} - 69039804 q^{41} - 150603216 q^{42} + 5379186 q^{43} - 58283762 q^{44} - 63687756 q^{45} - 76817844 q^{46} - 49104062 q^{47} - 99120062 q^{48} + 73113148 q^{49} - 281373726 q^{50} + 1578252 q^{51} - 49849646 q^{52} + 2253998 q^{53} - 166064634 q^{54} + 82907066 q^{55} + 119369464 q^{56} + 69024164 q^{57} + 11316496 q^{58} + 51587572 q^{59} - 107912622 q^{60} + 251179296 q^{61} + 2421010 q^{62} + 573206808 q^{63} + 460030950 q^{64} + 301434554 q^{65} + 305189958 q^{66} + 741046264 q^{67} + 503103116 q^{68} + 1480618500 q^{69} + 666826600 q^{70} + 488700124 q^{71} + 243154096 q^{72} + 1432375020 q^{73} - 208138340 q^{74} + 462882236 q^{75} - 253709644 q^{76} + 406327616 q^{77} - 1244370462 q^{78} + 400834638 q^{79} - 440320610 q^{80} + 207205984 q^{81} - 1992598260 q^{82} + 1525085236 q^{83} - 2191854376 q^{84} - 387675996 q^{85} - 3425646378 q^{86} + 171162002 q^{87} - 3147673814 q^{88} + 691159332 q^{89} - 2412410836 q^{90} + 1569278264 q^{91} - 2491626380 q^{92} + 270455138 q^{93} - 4397366402 q^{94} + 236293724 q^{95} - 1448270346 q^{96} + 2494422276 q^{97} - 3443098784 q^{98} + 2123567852 q^{99}+O(q^{100}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9 - 46678 * q^10 + 24474 * q^11 - 14210 * q^12 + 107722 * q^13 + 677768 * q^14 + 505426 * q^15 + 1656882 * q^16 + 982120 * q^17 + 2364102 * q^18 + 2084360 * q^19 + 4689410 * q^20 + 2911344 * q^21 + 2725230 * q^22 + 3004004 * q^23 + 7893170 * q^24 + 6339542 * q^25 + 6863698 * q^26 + 7881014 * q^27 + 5116944 * q^28 + 8487372 * q^29 + 10924626 * q^30 + 17872478 * q^31 + 5122946 * q^32 - 860442 * q^33 + 15662848 * q^34 - 22252312 * q^35 - 35199980 * q^36 + 452980 * q^37 - 68665276 * q^38 - 29528222 * q^39 - 61623214 * q^40 - 69039804 * q^41 - 150603216 * q^42 + 5379186 * q^43 - 58283762 * q^44 - 63687756 * q^45 - 76817844 * q^46 - 49104062 * q^47 - 99120062 * q^48 + 73113148 * q^49 - 281373726 * q^50 + 1578252 * q^51 - 49849646 * q^52 + 2253998 * q^53 - 166064634 * q^54 + 82907066 * q^55 + 119369464 * q^56 + 69024164 * q^57 + 11316496 * q^58 + 51587572 * q^59 - 107912622 * q^60 + 251179296 * q^61 + 2421010 * q^62 + 573206808 * q^63 + 460030950 * q^64 + 301434554 * q^65 + 305189958 * q^66 + 741046264 * q^67 + 503103116 * q^68 + 1480618500 * q^69 + 666826600 * q^70 + 488700124 * q^71 + 243154096 * q^72 + 1432375020 * q^73 - 208138340 * q^74 + 462882236 * q^75 - 253709644 * q^76 + 406327616 * q^77 - 1244370462 * q^78 + 400834638 * q^79 - 440320610 * q^80 + 207205984 * q^81 - 1992598260 * q^82 + 1525085236 * q^83 - 2191854376 * q^84 - 387675996 * q^85 - 3425646378 * q^86 + 171162002 * q^87 - 3147673814 * q^88 + 691159332 * q^89 - 2412410836 * q^90 + 1569278264 * q^91 - 2491626380 * q^92 + 270455138 * q^93 - 4397366402 * q^94 + 236293724 * q^95 - 1448270346 * q^96 + 2494422276 * q^97 - 3443098784 * q^98 + 2123567852 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	44.2474	1.95548	0.977738	−	0.209828i	$-0.0672903\pi$
$2$	44.2474	1.95548	0.977738	+	0.209828i	$0.0672903\pi$
$3$	110.108	0.784828	0.392414	−	0.919789i	$-0.371640\pi$
$3$	110.108	0.784828	0.392414	+	0.919789i	$0.371640\pi$
$4$	1445.83	2.82389
$5$	350.462	0.250770	0.125385	−	0.992108i	$-0.459983\pi$
$5$	350.462	0.250770	0.125385	+	0.992108i	$0.459983\pi$
$6$	4872.00	1.53471
$7$	−3350.56	−0.527443	−0.263722	−	0.964599i	$-0.584950\pi$
$7$	−3350.56	−0.527443	−0.263722	+	0.964599i	$0.584950\pi$
$8$	41319.6	3.56657
$9$	−7559.17	−0.384046
$10$	15507.0	0.490376
$11$	−63075.9	−1.29896	−0.649481	−	0.760378i	$-0.725014\pi$
$11$	−63075.9	−1.29896	−0.649481	+	0.760378i	$0.725014\pi$
$12$	159198.	2.21627
$13$	−4333.69	−0.0420836	−0.0210418	−	0.999779i	$-0.506698\pi$
$13$	−4333.69	−0.0420836	−0.0210418	+	0.999779i	$0.506698\pi$
$14$	−148253.	−1.03140
$15$	38588.8	0.196812
$16$	1.08802e6	4.15046
$17$	67794.0	0.196866	0.0984331	−	0.995144i	$-0.468617\pi$
$17$	67794.0	0.196866	0.0984331	+	0.995144i	$0.468617\pi$
$18$	−334473.	−0.750992
$19$	−340890.	−0.600100	−0.300050	−	0.953924i	$-0.597003\pi$
$19$	−340890.	−0.600100	−0.300050	+	0.953924i	$0.597003\pi$
$20$	506709.	0.708148
$21$	−368924.	−0.413952
$22$	−2.79094e6	−2.54009
$23$	1.43657e6	1.07041	0.535207	−	0.844721i	$-0.320234\pi$
$23$	1.43657e6	1.07041	0.535207	+	0.844721i	$0.320234\pi$
$24$	4.54963e6	2.79915
$25$	−1.83030e6	−0.937114
$26$	−191755.	−0.0822935
$27$	−2.99959e6	−1.08624
$28$	−4.84434e6	−1.48944
$29$	707281.	0.185695
$29$	707281.	0.185695
$30$	1.70745e6	0.384860
$31$	8.35363e6	1.62460	0.812302	−	0.583237i	$-0.198214\pi$
$31$	8.35363e6	1.62460	0.812302	+	0.583237i	$0.198214\pi$
$32$	2.69864e7	4.54956
$33$	−6.94517e6	−1.01946
$34$	2.99971e6	0.384967
$35$	−1.17424e6	−0.132267
$36$	−1.09293e7	−1.08450
$37$	1.62781e7	1.42789	0.713946	−	0.700201i	$-0.246906\pi$
$37$	1.62781e7	1.42789	0.713946	+	0.700201i	$0.246906\pi$
$38$	−1.50835e7	−1.17348
$39$	−477175.	−0.0330284
$40$	1.44810e7	0.894391
$41$	−3.36366e7	−1.85903	−0.929513	−	0.368790i	$-0.879772\pi$
$41$	−3.36366e7	−1.85903	−0.929513	+	0.368790i	$0.879772\pi$
$42$	−1.63239e7	−0.809474
$43$	−3.56609e7	−1.59069	−0.795343	−	0.606159i	$-0.792709\pi$
$43$	−3.56609e7	−1.59069	−0.795343	+	0.606159i	$0.792709\pi$
$44$	−9.11971e7	−3.66812
$45$	−2.64920e6	−0.0963072
$46$	6.35645e7	2.09317
$47$	1.57275e7	0.470131	0.235065	−	0.971980i	$-0.424470\pi$
$47$	1.57275e7	0.470131	0.235065	+	0.971980i	$0.424470\pi$
$48$	1.19800e8	3.25740
$49$	−2.91274e7	−0.721804
$50$	−8.09860e7	−1.83251
$51$	7.46468e6	0.154506
$52$	−6.26579e6	−0.118839
$53$	4.17013e7	0.725952	0.362976	−	0.931799i	$-0.381761\pi$
$53$	4.17013e7	0.725952	0.362976	+	0.931799i	$0.381761\pi$
$54$	−1.32724e8	−2.12411
$55$	−2.21057e7	−0.325741
$56$	−1.38444e8	−1.88117
$57$	−3.75348e7	−0.470975
$58$	3.12953e7	0.363123
$59$	−5.15420e7	−0.553767	−0.276884	−	0.960903i	$-0.589302\pi$
$59$	−5.15420e7	−0.553767	−0.276884	+	0.960903i	$0.589302\pi$
$60$	5.57929e7	0.555774
$61$	−1.02322e7	−0.0946205	−0.0473103	−	0.998880i	$-0.515065\pi$
$61$	−1.02322e7	−0.0946205	−0.0473103	+	0.998880i	$0.515065\pi$
$62$	3.69626e8	3.17688
$63$	2.53274e7	0.202562
$64$	6.37010e8	4.74610
$65$	−1.51880e6	−0.0105533
$66$	−3.07306e8	−1.99353
$67$	2.26304e8	1.37201	0.686003	−	0.727599i	$-0.259364\pi$
$67$	2.26304e8	1.37201	0.686003	+	0.727599i	$0.259364\pi$
$68$	9.80188e7	0.555929
$69$	1.58178e8	0.840091
$70$	−5.19572e7	−0.258645
$71$	−2.09200e8	−0.977009	−0.488505	−	0.872561i	$-0.662457\pi$
$71$	−2.09200e8	−0.977009	−0.488505	+	0.872561i	$0.662457\pi$
$72$	−3.12342e8	−1.36973
$73$	−3.09721e7	−0.127649	−0.0638245	−	0.997961i	$-0.520330\pi$
$73$	−3.09721e7	−0.127649	−0.0638245	+	0.997961i	$0.520330\pi$
$74$	7.20262e8	2.79221
$75$	−2.01531e8	−0.735473
$76$	−4.92870e8	−1.69462
$77$	2.11339e8	0.685128
$78$	−2.11138e7	−0.0645862
$79$	1.92694e8	0.556603	0.278302	−	0.960494i	$-0.410228\pi$
$79$	1.92694e8	0.556603	0.278302	+	0.960494i	$0.410228\pi$
$80$	3.81310e8	1.04081
$81$	−1.81492e8	−0.468463
$82$	−1.48833e9	−3.63528
$83$	7.81446e8	1.80737	0.903686	−	0.428195i	$-0.140850\pi$
$83$	7.81446e8	1.80737	0.903686	+	0.428195i	$0.140850\pi$
$84$	−5.33402e8	−1.16896
$85$	2.37593e7	0.0493682
$86$	−1.57790e9	−3.11055
$87$	7.78775e7	0.145739
$88$	−2.60627e9	−4.63284
$89$	9.13035e8	1.54253	0.771263	−	0.636517i	$-0.219625\pi$
$89$	9.13035e8	1.54253	0.771263	+	0.636517i	$0.219625\pi$
$90$	−1.17220e8	−0.188327
$91$	1.45203e7	0.0221967
$92$	2.07704e9	3.02273
$93$	9.19804e8	1.27503
$94$	6.95900e8	0.919330
$95$	−1.19469e8	−0.150487
$96$	2.97142e9	3.57062
$97$	5.03526e8	0.577496	0.288748	−	0.957405i	$-0.406761\pi$
$97$	5.03526e8	0.577496	0.288748	+	0.957405i	$0.406761\pi$
$98$	−1.28881e9	−1.41147
$99$	4.76801e8	0.498860
$100$	−2.64631e9	−2.64631
$101$	1.04037e9	0.994818	0.497409	−	0.867516i	$-0.334285\pi$
$101$	1.04037e9	0.994818	0.497409	+	0.867516i	$0.334285\pi$
$102$	3.30293e8	0.302133
$103$	6.10435e8	0.534407	0.267203	−	0.963640i	$-0.413900\pi$
$103$	6.10435e8	0.534407	0.267203	+	0.963640i	$0.413900\pi$
$104$	−1.79066e8	−0.150094
$105$	−1.29294e8	−0.103807
$106$	1.84517e9	1.41958
$107$	−2.64291e8	−0.194919	−0.0974597	−	0.995239i	$-0.531072\pi$
$107$	−2.64291e8	−0.194919	−0.0974597	+	0.995239i	$0.531072\pi$
$108$	−4.33690e9	−3.06741
$109$	−5.40910e8	−0.367033	−0.183517	−	0.983017i	$-0.558748\pi$
$109$	−5.40910e8	−0.367033	−0.183517	+	0.983017i	$0.558748\pi$
$110$	−9.78120e8	−0.636979
$111$	1.79235e9	1.12065
$112$	−3.64547e9	−2.18913
$113$	−4.45748e8	−0.257180	−0.128590	−	0.991698i	$-0.541045\pi$
$113$	−4.45748e8	−0.257180	−0.128590	+	0.991698i	$0.541045\pi$
$114$	−1.66082e9	−0.920980
$115$	5.03464e8	0.268428
$116$	1.02261e9	0.524383
$117$	3.27591e7	0.0161620
$118$	−2.28060e9	−1.08288
$119$	−2.27148e8	−0.103836
$120$	1.59447e9	0.701943
$121$	1.62062e9	0.687300
$122$	−4.52749e8	−0.185028
$123$	−3.70367e9	−1.45901
$124$	1.20779e10	4.58770
$125$	−1.32595e9	−0.485771
$126$	1.12067e9	0.396106
$127$	−4.34445e9	−1.48190	−0.740949	−	0.671561i	$-0.765624\pi$
$127$	−4.34445e9	−1.48190	−0.740949	+	0.671561i	$0.765624\pi$
$128$	1.43690e10	4.73132
$129$	−3.92656e9	−1.24842
$130$	−6.72027e7	−0.0206368
$131$	−1.79801e9	−0.533423	−0.266712	−	0.963776i	$-0.585937\pi$
$131$	−1.79801e9	−0.533423	−0.266712	+	0.963776i	$0.585937\pi$
$132$	−1.00416e10	−2.87884
$133$	1.14217e9	0.316519
$134$	1.00134e10	2.68293
$135$	−1.05124e9	−0.272396
$136$	2.80122e9	0.702138
$137$	3.46016e9	0.839176	0.419588	−	0.907715i	$-0.362174\pi$
$137$	3.46016e9	0.839176	0.419588	+	0.907715i	$0.362174\pi$
$138$	6.99898e9	1.64278
$139$	−4.74499e9	−1.07812	−0.539062	−	0.842266i	$-0.681221\pi$
$139$	−4.74499e9	−1.07812	−0.539062	+	0.842266i	$0.681221\pi$
$140$	−1.69776e9	−0.373508
$141$	1.73173e9	0.368972
$142$	−9.25654e9	−1.91052
$143$	2.73351e8	0.0546650
$144$	−8.22452e9	−1.59397
$145$	2.47875e8	0.0465669
$146$	−1.37043e9	−0.249615
$147$	−3.20716e9	−0.566491
$148$	2.35354e10	4.03221
$149$	1.48742e7	0.00247227	0.00123614	−	0.999999i	$-0.499607\pi$
$149$	1.48742e7	0.00247227	0.00123614	+	0.999999i	$0.499607\pi$
$150$	−8.91723e9	−1.43820
$151$	−8.53258e9	−1.33562	−0.667812	−	0.744330i	$-0.732769\pi$
$151$	−8.53258e9	−1.33562	−0.667812	+	0.744330i	$0.732769\pi$
$152$	−1.40855e10	−2.14030
$153$	−5.12467e8	−0.0756056
$154$	9.35121e9	1.33975
$155$	2.92763e9	0.407403
$156$	−6.89915e8	−0.0932685
$157$	5.25376e9	0.690115	0.345058	−	0.938581i	$-0.387859\pi$
$157$	5.25376e9	0.690115	0.345058	+	0.938581i	$0.387859\pi$
$158$	8.52620e9	1.08843
$159$	4.59165e9	0.569747
$160$	9.45770e9	1.14089
$161$	−4.81331e9	−0.564583
$162$	−8.03056e9	−0.916069
$163$	6.96546e9	0.772869	0.386434	−	0.922317i	$-0.373707\pi$
$163$	6.96546e9	0.772869	0.386434	+	0.922317i	$0.373707\pi$
$164$	−4.86329e10	−5.24968
$165$	−2.43402e9	−0.255651
$166$	3.45770e10	3.53428
$167$	1.73216e10	1.72332	0.861658	−	0.507489i	$-0.169426\pi$
$167$	1.73216e10	1.72332	0.861658	+	0.507489i	$0.169426\pi$
$168$	−1.52438e10	−1.47639
$169$	−1.05857e10	−0.998229
$170$	1.05128e9	0.0965384
$171$	2.57685e9	0.230466
$172$	−5.15597e10	−4.49192
$173$	−1.44542e10	−1.22684	−0.613419	−	0.789758i	$-0.710206\pi$
$173$	−1.44542e10	−1.22684	−0.613419	+	0.789758i	$0.710206\pi$
$174$	3.44588e9	0.284989
$175$	6.13253e9	0.494275
$176$	−6.86277e10	−5.39129
$177$	−5.67520e9	−0.434612
$178$	4.03994e10	3.01637
$179$	−2.99463e9	−0.218024	−0.109012	−	0.994040i	$-0.534769\pi$
$179$	−2.99463e9	−0.218024	−0.109012	+	0.994040i	$0.534769\pi$
$180$	−3.83030e9	−0.271961
$181$	6.22201e9	0.430900	0.215450	−	0.976515i	$-0.430878\pi$
$181$	6.22201e9	0.430900	0.215450	+	0.976515i	$0.430878\pi$
$182$	6.42484e8	0.0434052
$183$	−1.12665e9	−0.0742608
$184$	5.93586e10	3.81771
$185$	5.70485e9	0.358073
$186$	4.06989e10	2.49330
$187$	−4.27617e9	−0.255722
$188$	2.27393e10	1.32760
$189$	1.00503e10	0.572929
$190$	−5.28620e9	−0.294274
$191$	−2.40269e9	−0.130631	−0.0653156	−	0.997865i	$-0.520805\pi$
$191$	−2.40269e9	−0.130631	−0.0653156	+	0.997865i	$0.520805\pi$
$192$	7.01401e10	3.72487
$193$	−8.28410e9	−0.429771	−0.214886	−	0.976639i	$-0.568938\pi$
$193$	−8.28410e9	−0.429771	−0.214886	+	0.976639i	$0.568938\pi$
$194$	2.22797e10	1.12928
$195$	−1.67232e8	−0.00828254
$196$	−4.21133e10	−2.03829
$197$	−1.64648e10	−0.778860	−0.389430	−	0.921056i	$-0.627328\pi$
$197$	−1.64648e10	−0.778860	−0.389430	+	0.921056i	$0.627328\pi$
$198$	2.10972e10	0.975510
$199$	3.48586e9	0.157569	0.0787845	−	0.996892i	$-0.474896\pi$
$199$	3.48586e9	0.157569	0.0787845	+	0.996892i	$0.474896\pi$
$200$	−7.56273e10	−3.34229
$201$	2.49180e10	1.07679
$202$	4.60339e10	1.94534
$203$	−2.36979e9	−0.0979438
$204$	1.07927e10	0.436308
$205$	−1.17884e10	−0.466188
$206$	2.70101e10	1.04502
$207$	−1.08593e10	−0.411088
$208$	−4.71514e9	−0.174666
$209$	2.15020e10	0.779506
$210$	−5.72092e9	−0.202992
$211$	5.93027e9	0.205970	0.102985	−	0.994683i	$-0.467161\pi$
$211$	5.93027e9	0.205970	0.102985	+	0.994683i	$0.467161\pi$
$212$	6.02930e10	2.05001
$213$	−2.30346e10	−0.766784
$214$	−1.16942e10	−0.381161
$215$	−1.24978e10	−0.398897
$216$	−1.23942e11	−3.87415
$217$	−2.79893e10	−0.856887
$218$	−2.39338e10	−0.717725
$219$	−3.41028e9	−0.100182
$220$	−3.19611e10	−0.919856
$221$	−2.93798e8	−0.00828484
$222$	7.93069e10	2.19140
$223$	6.84759e10	1.85424	0.927120	−	0.374765i	$-0.122276\pi$
$223$	6.84759e10	1.85424	0.927120	+	0.374765i	$0.122276\pi$
$224$	−9.04193e10	−2.39963
$225$	1.38356e10	0.359895
$226$	−1.97232e10	−0.502909
$227$	1.63371e10	0.408374	0.204187	−	0.978932i	$-0.434545\pi$
$227$	1.63371e10	0.408374	0.204187	+	0.978932i	$0.434545\pi$
$228$	−5.42691e10	−1.32998
$229$	−5.74230e10	−1.37983	−0.689917	−	0.723889i	$-0.742353\pi$
$229$	−5.74230e10	−1.37983	−0.689917	+	0.723889i	$0.742353\pi$
$230$	2.22770e10	0.524905
$231$	2.32702e10	0.537708
$232$	2.92246e10	0.662296
$233$	−5.53767e10	−1.23091	−0.615454	−	0.788173i	$-0.711027\pi$
$233$	−5.53767e10	−1.23091	−0.615454	+	0.788173i	$0.711027\pi$
$234$	1.44950e9	0.0316045
$235$	5.51189e9	0.117895
$236$	−7.45211e10	−1.56378
$237$	2.12172e10	0.436838
$238$	−1.00507e10	−0.203049
$239$	−4.21585e10	−0.835785	−0.417893	−	0.908496i	$-0.637231\pi$
$239$	−4.21585e10	−0.835785	−0.417893	+	0.908496i	$0.637231\pi$
$240$	4.19853e10	0.816859
$241$	4.34352e10	0.829401	0.414701	−	0.909958i	$-0.363886\pi$
$241$	4.34352e10	0.829401	0.414701	+	0.909958i	$0.363886\pi$
$242$	7.17081e10	1.34400
$243$	3.90571e10	0.718574
$244$	−1.47941e10	−0.267198
$245$	−1.02080e10	−0.181007
$246$	−1.63878e11	−2.85307
$247$	1.47731e9	0.0252544
$248$	3.45169e11	5.79427
$249$	8.60437e10	1.41848
$250$	−5.86697e10	−0.949914
$251$	−6.58863e10	−1.04776	−0.523882	−	0.851791i	$-0.675517\pi$
$251$	−6.58863e10	−1.04776	−0.523882	+	0.851791i	$0.675517\pi$
$252$	3.66192e10	0.572013
$253$	−9.06130e10	−1.39043
$254$	−1.92231e11	−2.89782
$255$	2.61609e9	0.0387456
$256$	3.09642e11	4.50589
$257$	−1.50406e10	−0.215063	−0.107531	−	0.994202i	$-0.534295\pi$
$257$	−1.50406e10	−0.215063	−0.107531	+	0.994202i	$0.534295\pi$
$258$	−1.73740e11	−2.44125
$259$	−5.45406e10	−0.753132
$260$	−2.19592e9	−0.0298014
$261$	−5.34646e9	−0.0713155
$262$	−7.95574e10	−1.04310
$263$	3.47995e10	0.448510	0.224255	−	0.974531i	$-0.428005\pi$
$263$	3.47995e10	0.448510	0.224255	+	0.974531i	$0.428005\pi$
$264$	−2.86972e11	−3.63598
$265$	1.46147e10	0.182047
$266$	5.05381e10	0.618945
$267$	1.00533e11	1.21062
$268$	3.27198e11	3.87439
$269$	−8.99860e10	−1.04783	−0.523914	−	0.851771i	$-0.675529\pi$
$269$	−8.99860e10	−1.04783	−0.523914	+	0.851771i	$0.675529\pi$
$270$	−4.65147e10	−0.532664
$271$	3.27693e10	0.369067	0.184534	−	0.982826i	$-0.440923\pi$
$271$	3.27693e10	0.369067	0.184534	+	0.982826i	$0.440923\pi$
$272$	7.37612e10	0.817086
$273$	1.59880e9	0.0174206
$274$	1.53103e11	1.64099
$275$	1.15448e11	1.21727
$276$	2.28699e11	2.37232
$277$	−1.91316e9	−0.0195250	−0.00976251	−	0.999952i	$-0.503108\pi$
$277$	−1.91316e9	−0.0195250	−0.00976251	+	0.999952i	$0.503108\pi$
$278$	−2.09953e11	−2.10825
$279$	−6.31465e10	−0.623922
$280$	−4.85193e10	−0.471741
$281$	−1.64159e11	−1.57068	−0.785338	−	0.619067i	$-0.787511\pi$
$281$	−1.64159e11	−1.57068	−0.785338	+	0.619067i	$0.787511\pi$
$282$	7.66243e10	0.721516
$283$	1.83320e11	1.69891	0.849457	−	0.527658i	$-0.176930\pi$
$283$	1.83320e11	1.69891	0.849457	+	0.527658i	$0.176930\pi$
$284$	−3.02468e11	−2.75897
$285$	−1.31545e10	−0.118107
$286$	1.20951e10	0.106896
$287$	1.12701e11	0.980531
$288$	−2.03994e11	−1.74724
$289$	−1.13992e11	−0.961244
$290$	1.09678e10	0.0910605
$291$	5.54423e10	0.453235
$292$	−4.47804e10	−0.360467
$293$	−1.90030e11	−1.50633	−0.753163	−	0.657834i	$-0.771473\pi$
$293$	−1.90030e11	−1.50633	−0.753163	+	0.657834i	$0.771473\pi$
$294$	−1.41909e11	−1.10776
$295$	−1.80635e10	−0.138868
$296$	6.72604e11	5.09268
$297$	1.89202e11	1.41098
$298$	6.58146e8	0.00483447
$299$	−6.22566e9	−0.0450469
$300$	−2.91380e11	−2.07689
$301$	1.19484e11	0.838997
$302$	−3.77545e11	−2.61178
$303$	1.14554e11	0.780761
$304$	−3.70895e11	−2.49069
$305$	−3.58600e9	−0.0237280
$306$	−2.26753e10	−0.147845
$307$	−1.18434e11	−0.760947	−0.380473	−	0.924792i	$-0.624239\pi$
$307$	−1.18434e11	−0.760947	−0.380473	+	0.924792i	$0.624239\pi$
$308$	3.05561e11	1.93473
$309$	6.72139e10	0.419417
$310$	1.29540e11	0.796667
$311$	2.66459e11	1.61513	0.807566	−	0.589778i	$-0.200785\pi$
$311$	2.66459e11	1.61513	0.807566	+	0.589778i	$0.200785\pi$
$312$	−1.97167e10	−0.117798
$313$	6.48967e10	0.382185	0.191092	−	0.981572i	$-0.438797\pi$
$313$	6.48967e10	0.382185	0.191092	+	0.981572i	$0.438797\pi$
$314$	2.32465e11	1.34950
$315$	8.87631e9	0.0507966
$316$	2.78603e11	1.57179
$317$	1.31984e11	0.734101	0.367051	−	0.930201i	$-0.380368\pi$
$317$	1.31984e11	0.734101	0.367051	+	0.930201i	$0.380368\pi$
$318$	2.03169e11	1.11413
$319$	−4.46124e10	−0.241211
$320$	2.23248e11	1.19018
$321$	−2.91006e10	−0.152978
$322$	−2.12977e11	−1.10403
$323$	−2.31103e10	−0.118139
$324$	−2.62407e11	−1.32289
$325$	7.93196e9	0.0394371
$326$	3.08204e11	1.51133
$327$	−5.95586e10	−0.288058
$328$	−1.38985e12	−6.63035
$329$	−5.26958e10	−0.247967
$330$	−1.07699e11	−0.499919
$331$	2.93526e10	0.134407	0.0672033	−	0.997739i	$-0.478592\pi$
$331$	2.93526e10	0.134407	0.0672033	+	0.997739i	$0.478592\pi$
$332$	1.12984e12	5.10382
$333$	−1.23049e11	−0.548376
$334$	7.66437e11	3.36990
$335$	7.93111e10	0.344058
$336$	−4.01396e11	−1.71809
$337$	2.80434e11	1.18439	0.592197	−	0.805793i	$-0.298261\pi$
$337$	2.80434e11	1.18439	0.592197	+	0.805793i	$0.298261\pi$
$338$	−4.68390e11	−1.95201
$339$	−4.90806e10	−0.201842
$340$	3.43519e10	0.139410
$341$	−5.26913e11	−2.11030
$342$	1.14019e11	0.450670
$343$	2.32800e11	0.908154
$344$	−1.47350e12	−5.67330
$345$	5.54356e10	0.210670
$346$	−6.39561e11	−2.39905
$347$	−6.20482e10	−0.229745	−0.114873	−	0.993380i	$-0.536646\pi$
$347$	−6.20482e10	−0.229745	−0.114873	+	0.993380i	$0.536646\pi$
$348$	1.12598e11	0.411550
$349$	1.85652e11	0.669863	0.334932	−	0.942242i	$-0.391287\pi$
$349$	1.85652e11	0.669863	0.334932	+	0.942242i	$0.391287\pi$
$350$	2.71348e11	0.966543
$351$	1.29993e10	0.0457128
$352$	−1.70219e12	−5.90970
$353$	−1.67909e11	−0.575556	−0.287778	−	0.957697i	$-0.592917\pi$
$353$	−1.67909e11	−0.575556	−0.287778	+	0.957697i	$0.592917\pi$
$354$	−2.51113e11	−0.849874
$355$	−7.33166e10	−0.245005
$356$	1.32009e12	4.35592
$357$	−2.50109e10	−0.0814932
$358$	−1.32505e11	−0.426341
$359$	−3.91106e11	−1.24271	−0.621354	−	0.783530i	$-0.713417\pi$
$359$	−3.91106e11	−1.24271	−0.621354	+	0.783530i	$0.713417\pi$
$360$	−1.09464e11	−0.343487
$361$	−2.06482e11	−0.639880
$362$	2.75308e11	0.842616
$363$	1.78443e11	0.539412
$364$	2.09939e10	0.0626811
$365$	−1.08545e10	−0.0320106
$366$	−4.98514e10	−0.145215
$367$	−1.85042e11	−0.532442	−0.266221	−	0.963912i	$-0.585775\pi$
$367$	−1.85042e11	−0.532442	−0.266221	+	0.963912i	$0.585775\pi$
$368$	1.56302e12	4.44271
$369$	2.54265e11	0.713950
$370$	2.52425e11	0.700204
$371$	−1.39722e11	−0.382898
$372$	1.32988e12	3.60056
$373$	4.33641e11	1.15995	0.579977	−	0.814633i	$-0.303061\pi$
$373$	4.33641e11	1.15995	0.579977	+	0.814633i	$0.303061\pi$
$374$	−1.89209e11	−0.500058
$375$	−1.45998e11	−0.381246
$376$	6.49853e11	1.67676
$377$	−3.06514e9	−0.00781473
$378$	4.44699e11	1.12035
$379$	−1.69446e11	−0.421846	−0.210923	−	0.977503i	$-0.567647\pi$
$379$	−1.69446e11	−0.421846	−0.210923	+	0.977503i	$0.567647\pi$
$380$	−1.72732e11	−0.424959
$381$	−4.78360e11	−1.16304
$382$	−1.06313e11	−0.255446
$383$	2.88620e11	0.685381	0.342690	−	0.939448i	$-0.388662\pi$
$383$	2.88620e11	0.685381	0.342690	+	0.939448i	$0.388662\pi$
$384$	1.58215e12	3.71327
$385$	7.40664e10	0.171810
$386$	−3.66550e11	−0.840408
$387$	2.69567e11	0.610896
$388$	7.28013e11	1.63078
$389$	−3.69767e11	−0.818756	−0.409378	−	0.912365i	$-0.634254\pi$
$389$	−3.69767e11	−0.818756	−0.409378	+	0.912365i	$0.634254\pi$
$390$	−7.39957e9	−0.0161963
$391$	9.73910e10	0.210729
$392$	−1.20353e12	−2.57437
$393$	−1.97976e11	−0.418645
$394$	−7.28526e11	−1.52304
$395$	6.75319e10	0.139580
$396$	6.89374e11	1.40873
$397$	−2.90233e11	−0.586393	−0.293197	−	0.956052i	$-0.594719\pi$
$397$	−2.90233e11	−0.586393	−0.293197	+	0.956052i	$0.594719\pi$
$398$	1.54240e11	0.308123
$399$	1.25763e11	0.248413
$400$	−1.99140e12	−3.88946
$401$	−8.85424e11	−1.71002	−0.855011	−	0.518610i	$-0.826450\pi$
$401$	−8.85424e11	−1.71002	−0.855011	+	0.518610i	$0.826450\pi$
$402$	1.10255e12	2.10563
$403$	−3.62021e10	−0.0683692
$404$	1.50421e12	2.80926
$405$	−6.36062e10	−0.117477
$406$	−1.04857e11	−0.191527
$407$	−1.02675e12	−1.85478
$408$	3.08438e11	0.551057
$409$	−8.80009e11	−1.55501	−0.777503	−	0.628879i	$-0.783514\pi$
$409$	−8.80009e11	−1.55501	−0.777503	+	0.628879i	$0.783514\pi$
$410$	−5.21605e11	−0.911621
$411$	3.80992e11	0.658609
$412$	8.82586e11	1.50911
$413$	1.72694e11	0.292081
$414$	−4.80495e11	−0.803873
$415$	2.73867e11	0.453236
$416$	−1.16951e11	−0.191462
$417$	−5.22462e11	−0.846141
$418$	9.51405e11	1.52431
$419$	3.83043e11	0.607134	0.303567	−	0.952810i	$-0.401822\pi$
$419$	3.83043e11	0.607134	0.303567	+	0.952810i	$0.401822\pi$
$420$	−1.86937e11	−0.293139
$421$	6.43682e11	0.998623	0.499312	−	0.866422i	$-0.333586\pi$
$421$	6.43682e11	0.998623	0.499312	+	0.866422i	$0.333586\pi$
$422$	2.62399e11	0.402769
$423$	−1.18887e11	−0.180552
$424$	1.72308e12	2.58916
$425$	−1.24084e11	−0.184486
$426$	−1.01922e12	−1.49943
$427$	3.42836e10	0.0499070
$428$	−3.82120e11	−0.550431
$429$	3.00982e10	0.0429026
$430$	−5.52996e11	−0.780034
$431$	−1.03397e11	−0.144331	−0.0721657	−	0.997393i	$-0.522991\pi$
$431$	−1.03397e11	−0.144331	−0.0721657	+	0.997393i	$0.522991\pi$
$432$	−3.26361e12	−4.50839
$433$	−7.00164e11	−0.957204	−0.478602	−	0.878032i	$-0.658856\pi$
$433$	−7.00164e11	−0.957204	−0.478602	+	0.878032i	$0.658856\pi$
$434$	−1.23845e12	−1.67562
$435$	2.72931e10	0.0365470
$436$	−7.82064e11	−1.03646
$437$	−4.89713e11	−0.642355
$438$	−1.50896e11	−0.195904
$439$	1.41115e12	1.81335	0.906676	−	0.421828i	$-0.138611\pi$
$439$	1.41115e12	1.81335	0.906676	+	0.421828i	$0.138611\pi$
$440$	−9.13399e11	−1.16178
$441$	2.20179e11	0.277205
$442$	−1.29998e10	−0.0162008
$443$	−1.35265e12	−1.66867	−0.834334	−	0.551260i	$-0.814147\pi$
$443$	−1.35265e12	−1.66867	−0.834334	+	0.551260i	$0.814147\pi$
$444$	2.59144e12	3.16459
$445$	3.19984e11	0.386820
$446$	3.02988e12	3.62592
$447$	1.63778e9	0.00194031
$448$	−2.13434e12	−2.50330
$449$	−5.30480e10	−0.0615971	−0.0307986	−	0.999526i	$-0.509805\pi$
$449$	−5.30480e10	−0.0615971	−0.0307986	+	0.999526i	$0.509805\pi$
$450$	6.12187e11	0.703765
$451$	2.12166e12	2.41480
$452$	−6.44477e11	−0.726247
$453$	−9.39508e11	−1.04823
$454$	7.22873e11	0.798566
$455$	5.08881e9	0.00556628
$456$	−1.55092e12	−1.67977
$457$	6.32178e11	0.677980	0.338990	−	0.940790i	$-0.389915\pi$
$457$	6.32178e11	0.677980	0.338990	+	0.940790i	$0.389915\pi$
$458$	−2.54082e12	−2.69823
$459$	−2.03354e11	−0.213844
$460$	7.27924e11	0.758012
$461$	−4.93891e11	−0.509304	−0.254652	−	0.967033i	$-0.581961\pi$
$461$	−4.93891e11	−0.509304	−0.254652	+	0.967033i	$0.581961\pi$
$462$	1.02965e12	1.05147
$463$	1.04565e12	1.05748	0.528742	−	0.848783i	$-0.322664\pi$
$463$	1.04565e12	1.05748	0.528742	+	0.848783i	$0.322664\pi$
$464$	7.69535e11	0.770722
$465$	3.22357e11	0.319741
$466$	−2.45027e12	−2.40701
$467$	2.20041e11	0.214081	0.107041	−	0.994255i	$-0.465863\pi$
$467$	2.20041e11	0.214081	0.107041	+	0.994255i	$0.465863\pi$
$468$	4.73641e10	0.0456398
$469$	−7.58245e11	−0.723655
$470$	2.43887e11	0.230541
$471$	5.78482e11	0.541622
$472$	−2.12970e12	−1.97505
$473$	2.24934e12	2.06624
$474$	9.38805e11	0.854226
$475$	6.23932e11	0.562362
$476$	−3.28417e11	−0.293221
$477$	−3.15227e11	−0.278798
$478$	−1.86540e12	−1.63436
$479$	−8.54397e11	−0.741566	−0.370783	−	0.928719i	$-0.620911\pi$
$479$	−8.54397e11	−0.741566	−0.370783	+	0.928719i	$0.620911\pi$
$480$	1.04137e12	0.895406
$481$	−7.05442e10	−0.0600908
$482$	1.92189e12	1.62187
$483$	−5.29986e11	−0.443100
$484$	2.34314e12	1.94086
$485$	1.76467e11	0.144819
$486$	1.72817e12	1.40516
$487$	1.81995e12	1.46616	0.733078	−	0.680145i	$-0.238083\pi$
$487$	1.81995e12	1.46616	0.733078	+	0.680145i	$0.238083\pi$
$488$	−4.22791e11	−0.337471
$489$	7.66955e11	0.606569
$490$	−4.51679e11	−0.353955
$491$	3.34455e11	0.259699	0.129850	−	0.991534i	$-0.458551\pi$
$491$	3.34455e11	0.259699	0.129850	+	0.991534i	$0.458551\pi$
$492$	−5.35489e12	−4.12010
$493$	4.79494e10	0.0365572
$494$	6.53672e10	0.0493843
$495$	1.67101e11	0.125099
$496$	9.08891e12	6.74286
$497$	7.00936e11	0.515317
$498$	3.80721e12	2.77380
$499$	9.44828e11	0.682182	0.341091	−	0.940030i	$-0.389204\pi$
$499$	9.44828e11	0.682182	0.341091	+	0.940030i	$0.389204\pi$
$500$	−1.91710e12	−1.37176
$501$	1.90726e12	1.35251
$502$	−2.91530e12	−2.04888
$503$	3.99494e11	0.278263	0.139131	−	0.990274i	$-0.455569\pi$
$503$	3.99494e11	0.278263	0.139131	+	0.990274i	$0.455569\pi$
$504$	1.04652e12	0.722453
$505$	3.64612e11	0.249471
$506$	−4.00939e12	−2.71895
$507$	−1.16558e12	−0.783438
$508$	−6.28135e12	−4.18472
$509$	−2.44294e12	−1.61318	−0.806590	−	0.591111i	$-0.798689\pi$
$509$	−2.44294e12	−1.61318	−0.806590	+	0.591111i	$0.798689\pi$
$510$	1.15755e11	0.0757660
$511$	1.03774e11	0.0673276
$512$	6.34393e12	4.07985
$513$	1.02253e12	0.651851
$514$	−6.65506e11	−0.420551
$515$	2.13934e11	0.134013
$516$	−5.67715e12	−3.52539
$517$	−9.92024e11	−0.610682
$518$	−2.41328e12	−1.47273
$519$	−1.59153e12	−0.962856
$520$	−6.27560e10	−0.0376392
$521$	−4.55376e11	−0.270770	−0.135385	−	0.990793i	$-0.543227\pi$
$521$	−4.55376e11	−0.270770	−0.135385	+	0.990793i	$0.543227\pi$
$522$	−2.36567e11	−0.139456
$523$	−1.56326e12	−0.913638	−0.456819	−	0.889560i	$-0.651011\pi$
$523$	−1.56326e12	−0.913638	−0.456819	+	0.889560i	$0.651011\pi$
$524$	−2.59962e12	−1.50633
$525$	6.75242e11	0.387920
$526$	1.53979e12	0.877051
$527$	5.66326e11	0.319830
$528$	−7.55648e12	−4.23123
$529$	2.62585e11	0.145787
$530$	6.46663e11	0.355989
$531$	3.89615e11	0.212672
$532$	1.65139e12	0.893814
$533$	1.45771e11	0.0782345
$534$	4.44831e12	2.36733
$535$	−9.26240e10	−0.0488800
$536$	9.35080e12	4.89336
$537$	−3.29734e11	−0.171111
$538$	−3.98165e12	−2.04900
$539$	1.83723e12	0.937595
$540$	−1.51992e12	−0.769217
$541$	−1.39101e12	−0.698140	−0.349070	−	0.937097i	$-0.613502\pi$
$541$	−1.39101e12	−0.698140	−0.349070	+	0.937097i	$0.613502\pi$
$542$	1.44996e12	0.721703
$543$	6.85094e11	0.338183
$544$	1.82951e12	0.895655
$545$	−1.89568e11	−0.0920411
$546$	7.07428e10	0.0340656
$547$	1.19134e12	0.568973	0.284487	−	0.958680i	$-0.408177\pi$
$547$	1.19134e12	0.568973	0.284487	+	0.958680i	$0.408177\pi$
$548$	5.00280e12	2.36974
$549$	7.73470e10	0.0363386
$550$	5.10827e12	2.38035
$551$	−2.41105e11	−0.111436
$552$	6.53587e12	2.99625
$553$	−6.45632e11	−0.293577
$554$	−8.46522e10	−0.0381807
$555$	6.28151e11	0.281026
$556$	−6.86045e12	−3.04450
$557$	−2.80986e11	−0.123691	−0.0618453	−	0.998086i	$-0.519699\pi$
$557$	−2.80986e11	−0.123691	−0.0618453	+	0.998086i	$0.519699\pi$
$558$	−2.79407e12	−1.22007
$559$	1.54543e11	0.0669418
$560$	−1.27760e12	−0.548970
$561$	−4.70841e11	−0.200697
$562$	−7.26362e12	−3.07142
$563$	2.20890e12	0.926593	0.463296	−	0.886203i	$-0.346667\pi$
$563$	2.20890e12	0.926593	0.463296	+	0.886203i	$0.346667\pi$
$564$	2.50378e12	1.04194
$565$	−1.56218e11	−0.0644931
$566$	8.11144e12	3.32219
$567$	6.08100e11	0.247088
$568$	−8.64405e12	−3.48458
$569$	−7.42228e11	−0.296847	−0.148423	−	0.988924i	$-0.547420\pi$
$569$	−7.42228e11	−0.296847	−0.148423	+	0.988924i	$0.547420\pi$
$570$	−5.82054e11	−0.230955
$571$	−2.27202e12	−0.894435	−0.447217	−	0.894425i	$-0.647585\pi$
$571$	−2.27202e12	−0.894435	−0.447217	+	0.894425i	$0.647585\pi$
$572$	3.95220e11	0.154368
$573$	−2.64556e11	−0.102523
$574$	4.98675e12	1.91740
$575$	−2.62936e12	−1.00310
$576$	−4.81527e12	−1.82272
$577$	1.56283e12	0.586977	0.293489	−	0.955963i	$-0.405184\pi$
$577$	1.56283e12	0.586977	0.293489	+	0.955963i	$0.405184\pi$
$578$	−5.04384e12	−1.87969
$579$	−9.12148e11	−0.337296
$580$	3.58386e11	0.131500
$581$	−2.61828e12	−0.953287
$582$	2.45318e12	0.886290
$583$	−2.63034e12	−0.942983
$584$	−1.27975e12	−0.455269
$585$	1.14808e10	0.00405296
$586$	−8.40835e12	−2.94559
$587$	−9.65519e11	−0.335652	−0.167826	−	0.985817i	$-0.553675\pi$
$587$	−9.65519e11	−0.335652	−0.167826	+	0.985817i	$0.553675\pi$
$588$	−4.63702e12	−1.59971
$589$	−2.84767e12	−0.974925
$590$	−7.99264e11	−0.271554
$591$	−1.81291e12	−0.611271
$592$	1.77109e13	5.92641
$593$	2.74883e12	0.912856	0.456428	−	0.889760i	$-0.349129\pi$
$593$	2.74883e12	0.912856	0.456428	+	0.889760i	$0.349129\pi$
$594$	8.37168e12	2.75914
$595$	−7.96067e10	−0.0260389
$596$	2.15056e10	0.00698142
$597$	3.83822e11	0.123665
$598$	−2.75469e11	−0.0880881
$599$	−5.45190e11	−0.173032	−0.0865162	−	0.996250i	$-0.527573\pi$
$599$	−5.45190e11	−0.173032	−0.0865162	+	0.996250i	$0.527573\pi$
$600$	−8.32719e12	−2.62312
$601$	5.51571e12	1.72451	0.862256	−	0.506472i	$-0.169051\pi$
$601$	5.51571e12	1.72451	0.862256	+	0.506472i	$0.169051\pi$
$602$	5.28686e12	1.64064
$603$	−1.71067e12	−0.526913
$604$	−1.23367e13	−3.77166
$605$	5.67965e11	0.172354
$606$	5.06871e12	1.52676
$607$	2.25446e12	0.674053	0.337027	−	0.941495i	$-0.390579\pi$
$607$	2.25446e12	0.674053	0.337027	+	0.941495i	$0.390579\pi$
$608$	−9.19939e12	−2.73019
$609$	−2.60933e11	−0.0768690
$610$	−1.58671e11	−0.0463996
$611$	−6.81580e10	−0.0197848
$612$	−7.40940e11	−0.213502
$613$	−5.31692e11	−0.152086	−0.0760428	−	0.997105i	$-0.524229\pi$
$613$	−5.31692e11	−0.152086	−0.0760428	+	0.997105i	$0.524229\pi$
$614$	−5.24040e12	−1.48801
$615$	−1.29800e12	−0.365878
$616$	8.73246e12	2.44356
$617$	−5.79860e12	−1.61079	−0.805397	−	0.592736i	$-0.798048\pi$
$617$	−5.79860e12	−1.61079	−0.805397	+	0.592736i	$0.798048\pi$
$618$	2.97404e12	0.820160
$619$	−3.65029e12	−0.999354	−0.499677	−	0.866212i	$-0.666548\pi$
$619$	−3.65029e12	−0.999354	−0.499677	+	0.866212i	$0.666548\pi$
$620$	4.23286e12	1.15046
$621$	−4.30912e12	−1.16272
$622$	1.17901e13	3.15835
$623$	−3.05918e12	−0.813595
$624$	−5.19176e11	−0.137083
$625$	3.11011e12	0.815297
$626$	2.87151e12	0.747353
$627$	2.36754e12	0.611778
$628$	7.59605e12	1.94881
$629$	1.10356e12	0.281104
$630$	3.92753e11	0.0993316
$631$	−2.42441e12	−0.608799	−0.304400	−	0.952544i	$-0.598456\pi$
$631$	−2.42441e12	−0.608799	−0.304400	+	0.952544i	$0.598456\pi$
$632$	7.96203e12	1.98517
$633$	6.52972e11	0.161651
$634$	5.83996e12	1.43552
$635$	−1.52257e12	−0.371616
$636$	6.63876e12	1.60890
$637$	1.26229e11	0.0303761
$638$	−1.97398e12	−0.471683
$639$	1.58138e12	0.375216
$640$	5.03580e12	1.18647
$641$	2.24768e11	0.0525863	0.0262932	−	0.999654i	$-0.491630\pi$
$641$	2.24768e11	0.0525863	0.0262932	+	0.999654i	$0.491630\pi$
$642$	−1.28763e12	−0.299145
$643$	5.04676e12	1.16429	0.582147	−	0.813083i	$-0.302213\pi$
$643$	5.04676e12	1.16429	0.582147	+	0.813083i	$0.302213\pi$
$644$	−6.95924e12	−1.59432
$645$	−1.37611e12	−0.313066
$646$	−1.02257e12	−0.231019
$647$	−3.08595e12	−0.692341	−0.346171	−	0.938172i	$-0.612518\pi$
$647$	−3.08595e12	−0.692341	−0.346171	+	0.938172i	$0.612518\pi$
$648$	−7.49919e12	−1.67081
$649$	3.25106e12	0.719322
$650$	3.50968e11	0.0771184
$651$	−3.08186e12	−0.672509
$652$	1.00709e13	2.18250
$653$	2.84334e12	0.611955	0.305977	−	0.952039i	$-0.401017\pi$
$653$	2.84334e12	0.611955	0.305977	+	0.952039i	$0.401017\pi$
$654$	−2.63531e12	−0.563290
$655$	−6.30135e11	−0.133767
$656$	−3.65973e13	−7.71581
$657$	2.34123e11	0.0490230
$658$	−2.33165e12	−0.484894
$659$	−3.22353e12	−0.665805	−0.332903	−	0.942961i	$-0.608028\pi$
$659$	−3.22353e12	−0.665805	−0.332903	+	0.942961i	$0.608028\pi$
$660$	−3.51918e12	−0.721929
$661$	1.28652e12	0.262126	0.131063	−	0.991374i	$-0.458161\pi$
$661$	1.28652e12	0.262126	0.131063	+	0.991374i	$0.458161\pi$
$662$	1.29878e12	0.262829
$663$	−3.23496e10	−0.00650217
$664$	3.22891e13	6.44613
$665$	4.00288e11	0.0793735
$666$	−5.44459e12	−1.07234
$667$	1.01606e12	0.198771
$668$	2.50442e13	4.86645
$669$	7.53976e12	1.45526
$670$	3.50931e12	0.672798
$671$	6.45406e11	0.122908
$672$	−9.95592e12	−1.88330
$673$	5.98764e12	1.12509	0.562546	−	0.826766i	$-0.309822\pi$
$673$	5.98764e12	1.12509	0.562546	+	0.826766i	$0.309822\pi$
$674$	1.24085e13	2.31606
$675$	5.49015e12	1.01793
$676$	−1.53052e13	−2.81889
$677$	6.67435e12	1.22113	0.610563	−	0.791968i	$-0.290943\pi$
$677$	6.67435e12	1.22113	0.610563	+	0.791968i	$0.290943\pi$
$678$	−2.17169e12	−0.394697
$679$	−1.68709e12	−0.304596
$680$	9.81723e11	0.176075
$681$	1.79885e12	0.320503
$682$	−2.33145e13	−4.12664
$683$	8.24878e11	0.145043	0.0725215	−	0.997367i	$-0.476895\pi$
$683$	8.24878e11	0.145043	0.0725215	+	0.997367i	$0.476895\pi$
$684$	3.72569e12	0.650809
$685$	1.21265e12	0.210441
$686$	1.03008e13	1.77587
$687$	−6.32275e12	−1.08293
$688$	−3.87998e13	−6.60209
$689$	−1.80720e11	−0.0305507
$690$	2.45288e12	0.411960
$691$	5.19393e12	0.866653	0.433326	−	0.901237i	$-0.357340\pi$
$691$	5.19393e12	0.866653	0.433326	+	0.901237i	$0.357340\pi$
$692$	−2.08984e13	−3.46445
$693$	−1.59755e12	−0.263121
$694$	−2.74547e12	−0.449261
$695$	−1.66294e12	−0.270361
$696$	3.21787e12	0.519788
$697$	−2.28036e12	−0.365979
$698$	8.21464e12	1.30990
$699$	−6.09743e12	−0.966050
$700$	8.86660e12	1.39578
$701$	1.08332e13	1.69443	0.847217	−	0.531247i	$-0.178276\pi$
$701$	1.08332e13	1.69443	0.847217	+	0.531247i	$0.178276\pi$
$702$	5.75185e11	0.0893903
$703$	−5.54904e12	−0.856878
$704$	−4.01800e13	−6.16499
$705$	6.06904e11	0.0925272
$706$	−7.42953e12	−1.12549
$707$	−3.48583e12	−0.524710
$708$	−8.20539e12	−1.22730
$709$	−1.13223e13	−1.68278	−0.841390	−	0.540429i	$-0.818262\pi$
$709$	−1.13223e13	−1.68278	−0.841390	+	0.540429i	$0.818262\pi$
$710$	−3.24407e12	−0.479102
$711$	−1.45661e12	−0.213761
$712$	3.77263e13	5.50153
$713$	1.20006e13	1.73900
$714$	−1.10666e12	−0.159358
$715$	9.57993e10	0.0137084
$716$	−4.32973e12	−0.615676
$717$	−4.64200e12	−0.655947
$718$	−1.73054e13	−2.43009
$719$	8.39153e12	1.17101	0.585506	−	0.810668i	$-0.300896\pi$
$719$	8.39153e12	1.17101	0.585506	+	0.810668i	$0.300896\pi$
$720$	−2.88238e12	−0.399720
$721$	−2.04530e12	−0.281869
$722$	−9.13627e12	−1.25127
$723$	4.78257e12	0.650937
$724$	8.99597e12	1.21682
$725$	−1.29454e12	−0.174018
$726$	7.89565e12	1.05481
$727$	−1.53275e12	−0.203501	−0.101750	−	0.994810i	$-0.532444\pi$
$727$	−1.53275e12	−0.203501	−0.101750	+	0.994810i	$0.532444\pi$
$728$	5.99972e11	0.0791662
$729$	7.87282e12	1.03242
$730$	−4.80285e11	−0.0625959
$731$	−2.41760e12	−0.313153
$732$	−1.62895e12	−0.209704
$733$	4.25074e12	0.543871	0.271936	−	0.962315i	$-0.412336\pi$
$733$	4.25074e12	0.543871	0.271936	+	0.962315i	$0.412336\pi$
$734$	−8.18762e12	−1.04118
$735$	−1.12399e12	−0.142059
$736$	3.87678e13	4.86991
$737$	−1.42743e13	−1.78218
$738$	1.12506e13	1.39611
$739$	−1.21973e13	−1.50440	−0.752199	−	0.658936i	$-0.771007\pi$
$739$	−1.21973e13	−1.50440	−0.752199	+	0.658936i	$0.771007\pi$
$740$	8.24825e12	1.01116
$741$	1.62664e11	0.0198203
$742$	−6.18235e12	−0.748749
$743$	−4.61370e12	−0.555392	−0.277696	−	0.960669i	$-0.589571\pi$
$743$	−4.61370e12	−0.555392	−0.277696	+	0.960669i	$0.589571\pi$
$744$	3.80059e13	4.54751
$745$	5.21286e9	0.000619973 0
$746$	1.91875e13	2.26826
$747$	−5.90708e12	−0.694113
$748$	−6.18262e12	−0.722130
$749$	8.85522e11	0.102809
$750$	−6.46002e12	−0.745518
$751$	1.26510e13	1.45126	0.725628	−	0.688087i	$-0.241549\pi$
$751$	1.26510e13	1.45126	0.725628	+	0.688087i	$0.241549\pi$
$752$	1.71118e13	1.95126
$753$	−7.25463e12	−0.822314
$754$	−1.35624e11	−0.0152815
$755$	−2.99035e12	−0.334935
$756$	1.45310e13	1.61789
$757$	1.18561e12	0.131223	0.0656117	−	0.997845i	$-0.479100\pi$
$757$	1.18561e12	0.131223	0.0656117	+	0.997845i	$0.479100\pi$
$758$	−7.49752e12	−0.824910
$759$	−9.97724e12	−1.09125
$760$	−4.93642e12	−0.536724
$761$	−1.50688e11	−0.0162873	−0.00814363	−	0.999967i	$-0.502592\pi$
$761$	−1.50688e11	−0.0162873	−0.00814363	+	0.999967i	$0.502592\pi$
$762$	−2.11662e13	−2.27429
$763$	1.81235e12	0.193589
$764$	−3.47388e12	−0.368888
$765$	−1.79600e11	−0.0189597
$766$	1.27707e13	1.34025
$767$	2.23367e11	0.0233045
$768$	3.40942e13	3.53635
$769$	−3.30448e12	−0.340750	−0.170375	−	0.985379i	$-0.554498\pi$
$769$	−3.30448e12	−0.340750	−0.170375	+	0.985379i	$0.554498\pi$
$770$	3.27725e12	0.335970
$771$	−1.65609e12	−0.168787
$772$	−1.19774e13	−1.21363
$773$	1.66358e13	1.67586	0.837928	−	0.545781i	$-0.183767\pi$
$773$	1.66358e13	1.67586	0.837928	+	0.545781i	$0.183767\pi$
$774$	1.19276e13	1.19459
$775$	−1.52897e13	−1.52244
$776$	2.08055e13	2.05968
$777$	−6.00537e12	−0.591079
$778$	−1.63612e13	−1.60106
$779$	1.14664e13	1.11560
$780$	−2.41789e11	−0.0233890
$781$	1.31955e13	1.26910
$782$	4.30930e12	0.412075
$783$	−2.12155e12	−0.201709
$784$	−3.16911e13	−2.99582
$785$	1.84124e12	0.173061
$786$	−8.75992e12	−0.818651
$787$	−1.20035e13	−1.11538	−0.557690	−	0.830050i	$-0.688312\pi$
$787$	−1.20035e13	−1.11538	−0.557690	+	0.830050i	$0.688312\pi$
$788$	−2.38054e13	−2.19941
$789$	3.83171e12	0.352003
$790$	2.98811e12	0.272945
$791$	1.49351e12	0.135648
$792$	1.97012e13	1.77922
$793$	4.43433e10	0.00398197
$794$	−1.28420e13	−1.14668
$795$	1.60920e12	0.142876
$796$	5.03996e12	0.444957
$797$	1.30587e12	0.114640	0.0573200	−	0.998356i	$-0.481744\pi$
$797$	1.30587e12	0.114640	0.0573200	+	0.998356i	$0.481744\pi$
$798$	5.56467e12	0.485765
$799$	1.06623e12	0.0925529
$800$	−4.93932e13	−4.26346
$801$	−6.90179e12	−0.592400
$802$	−3.91777e13	−3.34391
$803$	1.95359e12	0.165811
$804$	3.60272e13	3.04073
$805$	−1.68688e12	−0.141581
$806$	−1.60185e12	−0.133694
$807$	−9.90820e12	−0.822364
$808$	4.29879e13	3.54809
$809$	−1.55372e13	−1.27528	−0.637640	−	0.770335i	$-0.720089\pi$
$809$	−1.55372e13	−1.27528	−0.637640	+	0.770335i	$0.720089\pi$
$810$	−2.81441e12	−0.229723
$811$	8.52088e12	0.691657	0.345828	−	0.938298i	$-0.387598\pi$
$811$	8.52088e12	0.691657	0.345828	+	0.938298i	$0.387598\pi$
$812$	−3.42631e12	−0.276582
$813$	3.60817e12	0.289654
$814$	−4.54312e13	−3.62697
$815$	2.44113e12	0.193813
$816$	8.12172e12	0.641272
$817$	1.21565e13	0.954571
$818$	−3.89381e13	−3.04078
$819$	−1.09761e11	−0.00852455
$820$	−1.70440e13	−1.31646
$821$	−1.60424e11	−0.0123232	−0.00616161	−	0.999981i	$-0.501961\pi$
$821$	−1.60424e11	−0.0123232	−0.00616161	+	0.999981i	$0.501961\pi$
$822$	1.68579e13	1.28789
$823$	1.96539e13	1.49331	0.746655	−	0.665212i	$-0.231659\pi$
$823$	1.96539e13	1.49331	0.746655	+	0.665212i	$0.231659\pi$
$824$	2.52229e13	1.90600
$825$	1.27118e13	0.955351
$826$	7.64128e12	0.571157
$827$	4.63515e12	0.344579	0.172290	−	0.985046i	$-0.444883\pi$
$827$	4.63515e12	0.344579	0.172290	+	0.985046i	$0.444883\pi$
$828$	−1.57007e13	−1.16087
$829$	1.54359e13	1.13511	0.567555	−	0.823336i	$-0.307889\pi$
$829$	1.54359e13	1.13511	0.567555	+	0.823336i	$0.307889\pi$
$830$	1.21179e13	0.886292
$831$	−2.10654e11	−0.0153238
$832$	−2.76060e12	−0.199733
$833$	−1.97466e12	−0.142099
$834$	−2.31176e13	−1.65461
$835$	6.07058e12	0.432157
$836$	3.10882e13	2.20124
$837$	−2.50575e13	−1.76471
$838$	1.69487e13	1.18724
$839$	−5.56415e12	−0.387677	−0.193838	−	0.981033i	$-0.562094\pi$
$839$	−5.56415e12	−0.387677	−0.193838	+	0.981033i	$0.562094\pi$
$840$	−5.34237e12	−0.370235
$841$	5.00246e11	0.0344828
$842$	2.84812e13	1.95278
$843$	−1.80753e13	−1.23271
$844$	8.57417e12	0.581636
$845$	−3.70989e12	−0.250326
$846$	−5.26042e12	−0.353065
$847$	−5.42997e12	−0.362512
$848$	4.53717e13	3.01304
$849$	2.01851e13	1.33335
$850$	−5.49037e12	−0.360758
$851$	2.33846e13	1.52844
$852$	−3.33042e13	−2.16531
$853$	2.78118e13	1.79870	0.899350	−	0.437229i	$-0.144040\pi$
$853$	2.78118e13	1.79870	0.899350	+	0.437229i	$0.144040\pi$
$854$	1.51696e12	0.0975919
$855$	9.03088e11	0.0577940
$856$	−1.09204e13	−0.695195
$857$	9.47409e12	0.599962	0.299981	−	0.953945i	$-0.403020\pi$
$857$	9.47409e12	0.599962	0.299981	+	0.953945i	$0.403020\pi$
$858$	1.33177e12	0.0838950
$859$	1.60764e13	1.00744	0.503720	−	0.863867i	$-0.331964\pi$
$859$	1.60764e13	1.00744	0.503720	+	0.863867i	$0.331964\pi$
$860$	−1.80697e13	−1.12644
$861$	1.24094e13	0.769547
$862$	−4.57505e12	−0.282237
$863$	2.57634e12	0.158108	0.0790540	−	0.996870i	$-0.474810\pi$
$863$	2.57634e12	0.158108	0.0790540	+	0.996870i	$0.474810\pi$
$864$	−8.09480e13	−4.94190
$865$	−5.06566e12	−0.307655
$866$	−3.09804e13	−1.87179
$867$	−1.25514e13	−0.754411
$868$	−4.04678e13	−2.41975
$869$	−1.21543e13	−0.723006
$870$	1.20765e12	0.0714668
$871$	−9.80732e11	−0.0577389
$872$	−2.23502e13	−1.30905
$873$	−3.80623e12	−0.221785
$874$	−2.16685e13	−1.25611
$875$	4.44266e12	0.256217
$876$	−4.93069e12	−0.282904
$877$	−1.23955e13	−0.707567	−0.353783	−	0.935327i	$-0.615105\pi$
$877$	−1.23955e13	−0.707567	−0.353783	+	0.935327i	$0.615105\pi$
$878$	6.24396e13	3.54597
$879$	−2.09239e13	−1.18221
$880$	−2.40514e13	−1.35198
$881$	−2.17490e13	−1.21632	−0.608160	−	0.793814i	$-0.708092\pi$
$881$	−2.17490e13	−1.21632	−0.608160	+	0.793814i	$0.708092\pi$
$882$	9.74233e12	0.542069
$883$	−4.54933e12	−0.251840	−0.125920	−	0.992040i	$-0.540188\pi$
$883$	−4.54933e12	−0.251840	−0.125920	+	0.992040i	$0.540188\pi$
$884$	−4.24783e11	−0.0233955
$885$	−1.98894e12	−0.108988
$886$	−5.98514e13	−3.26304
$887$	2.27427e13	1.23363	0.616817	−	0.787107i	$-0.288422\pi$
$887$	2.27427e13	1.23363	0.616817	+	0.787107i	$0.288422\pi$
$888$	7.40592e13	3.99688
$889$	1.45563e13	0.781618
$890$	1.41585e13	0.756417
$891$	1.14478e13	0.608516
$892$	9.90046e13	5.23617
$893$	−5.36134e12	−0.282125
$894$	7.24673e10	0.00379423
$895$	−1.04951e12	−0.0546740
$896$	−4.81442e13	−2.49550
$897$	−6.85496e11	−0.0353540
$898$	−2.34724e12	−0.120452
$899$	5.90837e12	0.301682
$900$	2.00039e13	1.01630
$901$	2.82710e12	0.142915
$902$	9.38779e13	4.72209
$903$	1.31562e13	0.658468
$904$	−1.84181e13	−0.917251
$905$	2.18058e12	0.108057
$906$	−4.15708e13	−2.04980
$907$	2.79140e13	1.36959	0.684794	−	0.728737i	$-0.259892\pi$
$907$	2.79140e13	1.36959	0.684794	+	0.728737i	$0.259892\pi$
$908$	2.36207e13	1.15320
$909$	−7.86437e12	−0.382055
$910$	2.25167e11	0.0108847
$911$	−3.61488e12	−0.173885	−0.0869423	−	0.996213i	$-0.527710\pi$
$911$	−3.61488e12	−0.173885	−0.0869423	+	0.996213i	$0.527710\pi$
$912$	−4.08386e13	−1.95476
$913$	−4.92904e13	−2.34771
$914$	2.79722e13	1.32577
$915$	−3.94849e11	−0.0186224
$916$	−8.30240e13	−3.89650
$917$	6.02434e12	0.281350
$918$	−8.99789e12	−0.418166
$919$	2.16963e13	1.00338	0.501690	−	0.865047i	$-0.332712\pi$
$919$	2.16963e13	1.00338	0.501690	+	0.865047i	$0.332712\pi$
$920$	2.08029e13	0.957369
$921$	−1.30406e13	−0.597212
$922$	−2.18534e13	−0.995931
$923$	9.06607e11	0.0411161
$924$	3.36448e13	1.51843
$925$	−2.97938e13	−1.33810
$926$	4.62674e13	2.06788
$927$	−4.61438e12	−0.205236
$928$	1.90869e13	0.844832
$929$	1.72184e13	0.758440	0.379220	−	0.925307i	$-0.376192\pi$
$929$	1.72184e13	0.758440	0.379220	+	0.925307i	$0.376192\pi$
$930$	1.42634e13	0.625246
$931$	9.92924e12	0.433154
$932$	−8.00654e13	−3.47595
$933$	2.93393e13	1.26760
$934$	9.73625e12	0.418631
$935$	−1.49864e12	−0.0641274
$936$	1.35359e12	0.0576430
$937$	−4.90082e12	−0.207702	−0.103851	−	0.994593i	$-0.533116\pi$
$937$	−4.90082e12	−0.207702	−0.103851	+	0.994593i	$0.533116\pi$
$938$	−3.35504e13	−1.41509
$939$	7.14567e12	0.299949
$940$	7.96926e12	0.332922
$941$	−7.81574e12	−0.324950	−0.162475	−	0.986713i	$-0.551948\pi$
$941$	−7.81574e12	−0.324950	−0.162475	+	0.986713i	$0.551948\pi$
$942$	2.55963e13	1.05913
$943$	−4.83214e13	−1.98993
$944$	−5.60787e13	−2.29839
$945$	3.52225e12	0.143674
$946$	9.95276e13	4.04049
$947$	−9.61939e12	−0.388662	−0.194331	−	0.980936i	$-0.562254\pi$
$947$	−9.61939e12	−0.388662	−0.194331	+	0.980936i	$0.562254\pi$
$948$	3.06765e13	1.23358
$949$	1.34223e11	0.00537193
$950$	2.76074e13	1.09969
$951$	1.45326e13	0.576143
$952$	−9.38566e12	−0.370338
$953$	−4.26189e13	−1.67373	−0.836863	−	0.547412i	$-0.815613\pi$
$953$	−4.26189e13	−1.67373	−0.836863	+	0.547412i	$0.815613\pi$
$954$	−1.39480e13	−0.545184
$955$	−8.42051e11	−0.0327585
$956$	−6.09541e13	−2.36016
$957$	−4.91219e12	−0.189309
$958$	−3.78048e13	−1.45012
$959$	−1.15935e13	−0.442618
$960$	2.45815e13	0.934086
$961$	4.33435e13	1.63934
$962$	−3.12139e12	−0.117506
$963$	1.99782e12	0.0748580
$964$	6.27999e13	2.34214
$965$	−2.90326e12	−0.107774
$966$	−2.34505e13	−0.866472
$967$	−1.22704e13	−0.451275	−0.225637	−	0.974211i	$-0.572446\pi$
$967$	−1.22704e13	−0.451275	−0.225637	+	0.974211i	$0.572446\pi$
$968$	6.69633e13	2.45131
$969$	−2.54464e12	−0.0927191
$970$	7.80819e12	0.283190
$971$	−2.57355e13	−0.929064	−0.464532	−	0.885556i	$-0.653777\pi$
$971$	−2.57355e13	−0.929064	−0.464532	+	0.885556i	$0.653777\pi$
$972$	5.64700e13	2.02917
$973$	1.58984e13	0.568649
$974$	8.05282e13	2.86703
$975$	8.73374e11	0.0309514
$976$	−1.11328e13	−0.392719
$977$	−4.60134e13	−1.61569	−0.807847	−	0.589392i	$-0.799367\pi$
$977$	−4.60134e13	−1.61569	−0.807847	+	0.589392i	$0.799367\pi$
$978$	3.39358e13	1.18613
$979$	−5.75905e13	−2.00368
$980$	−1.47591e13	−0.511144
$981$	4.08883e12	0.140957
$982$	1.47988e13	0.507836
$983$	2.08511e13	0.712260	0.356130	−	0.934436i	$-0.384096\pi$
$983$	2.08511e13	0.712260	0.356130	+	0.934436i	$0.384096\pi$
$984$	−1.53034e14	−5.20368
$985$	−5.77030e12	−0.195315
$986$	2.12164e12	0.0714867
$987$	−5.80224e12	−0.194612
$988$	2.13595e12	0.0713155
$989$	−5.12295e13	−1.70269
$990$	7.39377e12	0.244629
$991$	3.88754e13	1.28039	0.640197	−	0.768211i	$-0.278853\pi$
$991$	3.88754e13	1.28039	0.640197	+	0.768211i	$0.278853\pi$
$992$	2.25434e14	7.39124
$993$	3.23196e12	0.105486
$994$	3.10146e13	1.00769
$995$	1.22166e12	0.0395136
$996$	1.24405e14	4.00562
$997$	−3.98756e13	−1.27814	−0.639071	−	0.769148i	$-0.720681\pi$
$997$	−3.98756e13	−1.27814	−0.639071	+	0.769148i	$0.720681\pi$
$998$	4.18062e13	1.33399
$999$	−4.88275e13	−1.55103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.b.1.12	✓	12
3.2	odd	2		261.10.a.e.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.b.1.12	✓	12	1.1	even	1	trivial
261.10.a.e.1.1		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+44.2474 q^{2} +110.108 q^{3} +1445.83 q^{4} +350.462 q^{5} +4872.00 q^{6} -3350.56 q^{7} +41319.6 q^{8} -7559.17 q^{9} +O(q^{10})\)	\(q+44.2474 q^{2} +110.108 q^{3} +1445.83 q^{4} +350.462 q^{5} +4872.00 q^{6} -3350.56 q^{7} +41319.6 q^{8} -7559.17 q^{9} +15507.0 q^{10} -63075.9 q^{11} +159198. q^{12} -4333.69 q^{13} -148253. q^{14} +38588.8 q^{15} +1.08802e6 q^{16} +67794.0 q^{17} -334473. q^{18} -340890. q^{19} +506709. q^{20} -368924. q^{21} -2.79094e6 q^{22} +1.43657e6 q^{23} +4.54963e6 q^{24} -1.83030e6 q^{25} -191755. q^{26} -2.99959e6 q^{27} -4.84434e6 q^{28} +707281. q^{29} +1.70745e6 q^{30} +8.35363e6 q^{31} +2.69864e7 q^{32} -6.94517e6 q^{33} +2.99971e6 q^{34} -1.17424e6 q^{35} -1.09293e7 q^{36} +1.62781e7 q^{37} -1.50835e7 q^{38} -477175. q^{39} +1.44810e7 q^{40} -3.36366e7 q^{41} -1.63239e7 q^{42} -3.56609e7 q^{43} -9.11971e7 q^{44} -2.64920e6 q^{45} +6.35645e7 q^{46} +1.57275e7 q^{47} +1.19800e8 q^{48} -2.91274e7 q^{49} -8.09860e7 q^{50} +7.46468e6 q^{51} -6.26579e6 q^{52} +4.17013e7 q^{53} -1.32724e8 q^{54} -2.21057e7 q^{55} -1.38444e8 q^{56} -3.75348e7 q^{57} +3.12953e7 q^{58} -5.15420e7 q^{59} +5.57929e7 q^{60} -1.02322e7 q^{61} +3.69626e8 q^{62} +2.53274e7 q^{63} +6.37010e8 q^{64} -1.51880e6 q^{65} -3.07306e8 q^{66} +2.26304e8 q^{67} +9.80188e7 q^{68} +1.58178e8 q^{69} -5.19572e7 q^{70} -2.09200e8 q^{71} -3.12342e8 q^{72} -3.09721e7 q^{73} +7.20262e8 q^{74} -2.01531e8 q^{75} -4.92870e8 q^{76} +2.11339e8 q^{77} -2.11138e7 q^{78} +1.92694e8 q^{79} +3.81310e8 q^{80} -1.81492e8 q^{81} -1.48833e9 q^{82} +7.81446e8 q^{83} -5.33402e8 q^{84} +2.37593e7 q^{85} -1.57790e9 q^{86} +7.78775e7 q^{87} -2.60627e9 q^{88} +9.13035e8 q^{89} -1.17220e8 q^{90} +1.45203e7 q^{91} +2.07704e9 q^{92} +9.19804e8 q^{93} +6.95900e8 q^{94} -1.19469e8 q^{95} +2.97142e9 q^{96} +5.03526e8 q^{97} -1.28881e9 q^{98} +4.76801e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9} - 46678 q^{10} + 24474 q^{11} - 14210 q^{12} + 107722 q^{13} + 677768 q^{14} + 505426 q^{15} + 1656882 q^{16} + 982120 q^{17} + 2364102 q^{18} + 2084360 q^{19} + 4689410 q^{20} + 2911344 q^{21} + 2725230 q^{22} + 3004004 q^{23} + 7893170 q^{24} + 6339542 q^{25} + 6863698 q^{26} + 7881014 q^{27} + 5116944 q^{28} + 8487372 q^{29} + 10924626 q^{30} + 17872478 q^{31} + 5122946 q^{32} - 860442 q^{33} + 15662848 q^{34} - 22252312 q^{35} - 35199980 q^{36} + 452980 q^{37} - 68665276 q^{38} - 29528222 q^{39} - 61623214 q^{40} - 69039804 q^{41} - 150603216 q^{42} + 5379186 q^{43} - 58283762 q^{44} - 63687756 q^{45} - 76817844 q^{46} - 49104062 q^{47} - 99120062 q^{48} + 73113148 q^{49} - 281373726 q^{50} + 1578252 q^{51} - 49849646 q^{52} + 2253998 q^{53} - 166064634 q^{54} + 82907066 q^{55} + 119369464 q^{56} + 69024164 q^{57} + 11316496 q^{58} + 51587572 q^{59} - 107912622 q^{60} + 251179296 q^{61} + 2421010 q^{62} + 573206808 q^{63} + 460030950 q^{64} + 301434554 q^{65} + 305189958 q^{66} + 741046264 q^{67} + 503103116 q^{68} + 1480618500 q^{69} + 666826600 q^{70} + 488700124 q^{71} + 243154096 q^{72} + 1432375020 q^{73} - 208138340 q^{74} + 462882236 q^{75} - 253709644 q^{76} + 406327616 q^{77} - 1244370462 q^{78} + 400834638 q^{79} - 440320610 q^{80} + 207205984 q^{81} - 1992598260 q^{82} + 1525085236 q^{83} - 2191854376 q^{84} - 387675996 q^{85} - 3425646378 q^{86} + 171162002 q^{87} - 3147673814 q^{88} + 691159332 q^{89} - 2412410836 q^{90} + 1569278264 q^{91} - 2491626380 q^{92} + 270455138 q^{93} - 4397366402 q^{94} + 236293724 q^{95} - 1448270346 q^{96} + 2494422276 q^{97} - 3443098784 q^{98} + 2123567852 q^{99}+O(q^{100}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9 - 46678 * q^10 + 24474 * q^11 - 14210 * q^12 + 107722 * q^13 + 677768 * q^14 + 505426 * q^15 + 1656882 * q^16 + 982120 * q^17 + 2364102 * q^18 + 2084360 * q^19 + 4689410 * q^20 + 2911344 * q^21 + 2725230 * q^22 + 3004004 * q^23 + 7893170 * q^24 + 6339542 * q^25 + 6863698 * q^26 + 7881014 * q^27 + 5116944 * q^28 + 8487372 * q^29 + 10924626 * q^30 + 17872478 * q^31 + 5122946 * q^32 - 860442 * q^33 + 15662848 * q^34 - 22252312 * q^35 - 35199980 * q^36 + 452980 * q^37 - 68665276 * q^38 - 29528222 * q^39 - 61623214 * q^40 - 69039804 * q^41 - 150603216 * q^42 + 5379186 * q^43 - 58283762 * q^44 - 63687756 * q^45 - 76817844 * q^46 - 49104062 * q^47 - 99120062 * q^48 + 73113148 * q^49 - 281373726 * q^50 + 1578252 * q^51 - 49849646 * q^52 + 2253998 * q^53 - 166064634 * q^54 + 82907066 * q^55 + 119369464 * q^56 + 69024164 * q^57 + 11316496 * q^58 + 51587572 * q^59 - 107912622 * q^60 + 251179296 * q^61 + 2421010 * q^62 + 573206808 * q^63 + 460030950 * q^64 + 301434554 * q^65 + 305189958 * q^66 + 741046264 * q^67 + 503103116 * q^68 + 1480618500 * q^69 + 666826600 * q^70 + 488700124 * q^71 + 243154096 * q^72 + 1432375020 * q^73 - 208138340 * q^74 + 462882236 * q^75 - 253709644 * q^76 + 406327616 * q^77 - 1244370462 * q^78 + 400834638 * q^79 - 440320610 * q^80 + 207205984 * q^81 - 1992598260 * q^82 + 1525085236 * q^83 - 2191854376 * q^84 - 387675996 * q^85 - 3425646378 * q^86 + 171162002 * q^87 - 3147673814 * q^88 + 691159332 * q^89 - 2412410836 * q^90 + 1569278264 * q^91 - 2491626380 * q^92 + 270455138 * q^93 - 4397366402 * q^94 + 236293724 * q^95 - 1448270346 * q^96 + 2494422276 * q^97 - 3443098784 * q^98 + 2123567852 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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