LMFDB - Embedded newform 29.10.a.b.1.5

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			1.5
Root			$-11.2767$ 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)

$f(q)$	$=$	$q-10.2767 q^{2} +52.0955 q^{3} -406.390 q^{4} -2693.22 q^{5} -535.369 q^{6} +4178.53 q^{7} +9437.99 q^{8} -16969.1 q^{9} +O(q^{10})$	\(q-10.2767 q^{2} +52.0955 q^{3} -406.390 q^{4} -2693.22 q^{5} -535.369 q^{6} +4178.53 q^{7} +9437.99 q^{8} -16969.1 q^{9} +27677.4 q^{10} +65858.0 q^{11} -21171.1 q^{12} -142660. q^{13} -42941.4 q^{14} -140305. q^{15} +111080. q^{16} +316294. q^{17} +174385. q^{18} +690983. q^{19} +1.09450e6 q^{20} +217683. q^{21} -676801. q^{22} -896198. q^{23} +491677. q^{24} +5.30032e6 q^{25} +1.46607e6 q^{26} -1.90941e6 q^{27} -1.69811e6 q^{28} +707281. q^{29} +1.44187e6 q^{30} +1.64525e6 q^{31} -5.97379e6 q^{32} +3.43091e6 q^{33} -3.25045e6 q^{34} -1.12537e7 q^{35} +6.89605e6 q^{36} +1.65488e7 q^{37} -7.10101e6 q^{38} -7.43196e6 q^{39} -2.54186e7 q^{40} -2.24916e6 q^{41} -2.23706e6 q^{42} -7.29550e6 q^{43} -2.67640e7 q^{44} +4.57014e7 q^{45} +9.20993e6 q^{46} +2.83005e6 q^{47} +5.78679e6 q^{48} -2.28935e7 q^{49} -5.44696e7 q^{50} +1.64775e7 q^{51} +5.79757e7 q^{52} -4.33982e7 q^{53} +1.96224e7 q^{54} -1.77370e8 q^{55} +3.94370e7 q^{56} +3.59971e7 q^{57} -7.26850e6 q^{58} +3.65751e7 q^{59} +5.70185e7 q^{60} +1.42512e6 q^{61} -1.69077e7 q^{62} -7.09057e7 q^{63} +4.51751e6 q^{64} +3.84216e8 q^{65} -3.52583e7 q^{66} +2.66297e8 q^{67} -1.28539e8 q^{68} -4.66879e7 q^{69} +1.15651e8 q^{70} -9.49874e7 q^{71} -1.60154e8 q^{72} +1.37271e8 q^{73} -1.70067e8 q^{74} +2.76123e8 q^{75} -2.80808e8 q^{76} +2.75190e8 q^{77} +7.63759e7 q^{78} -1.58235e7 q^{79} -2.99164e8 q^{80} +2.34530e8 q^{81} +2.31139e7 q^{82} +3.47173e8 q^{83} -8.84641e7 q^{84} -8.51850e8 q^{85} +7.49735e7 q^{86} +3.68462e7 q^{87} +6.21568e8 q^{88} +6.90945e8 q^{89} -4.69659e8 q^{90} -5.96111e8 q^{91} +3.64206e8 q^{92} +8.57103e7 q^{93} -2.90835e7 q^{94} -1.86097e9 q^{95} -3.11208e8 q^{96} +1.53669e9 q^{97} +2.35269e8 q^{98} -1.11755e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.2767	−0.454169	−0.227085	−	0.973875i	$-0.572919\pi$
$2$	−10.2767	−0.454169	−0.227085	+	0.973875i	$0.572919\pi$
$3$	52.0955	0.371326	0.185663	−	0.982614i	$-0.440557\pi$
$3$	52.0955	0.371326	0.185663	+	0.982614i	$0.440557\pi$
$4$	−406.390	−0.793730
$5$	−2693.22	−1.92711	−0.963556	−	0.267506i	$-0.913801\pi$
$5$	−2693.22	−1.92711	−0.963556	+	0.267506i	$0.913801\pi$
$6$	−535.369	−0.168645
$7$	4178.53	0.657783	0.328891	−	0.944368i	$-0.393325\pi$
$7$	4178.53	0.657783	0.328891	+	0.944368i	$0.393325\pi$
$8$	9437.99	0.814657
$9$	−16969.1	−0.862117
$10$	27677.4	0.875235
$11$	65858.0	1.35626	0.678128	−	0.734944i	$-0.262792\pi$
$11$	65858.0	1.35626	0.678128	+	0.734944i	$0.262792\pi$
$12$	−21171.1	−0.294732
$13$	−142660.	−1.38535	−0.692673	−	0.721252i	$-0.743567\pi$
$13$	−142660.	−1.38535	−0.692673	+	0.721252i	$0.743567\pi$
$14$	−42941.4	−0.298745
$15$	−140305.	−0.715586
$16$	111080.	0.423738
$17$	316294.	0.918482	0.459241	−	0.888312i	$-0.348121\pi$
$17$	316294.	0.918482	0.459241	+	0.888312i	$0.348121\pi$
$18$	174385.	0.391547
$19$	690983.	1.21640	0.608199	−	0.793784i	$-0.291892\pi$
$19$	690983.	1.21640	0.608199	+	0.793784i	$0.291892\pi$
$20$	1.09450e6	1.52961
$21$	217683.	0.244252
$22$	−676801.	−0.615969
$23$	−896198.	−0.667773	−0.333886	−	0.942613i	$-0.608360\pi$
$23$	−896198.	−0.667773	−0.333886	+	0.942613i	$0.608360\pi$
$24$	491677.	0.302503
$25$	5.30032e6	2.71376
$26$	1.46607e6	0.629181
$27$	−1.90941e6	−0.691452
$28$	−1.69811e6	−0.522102
$29$	707281.	0.185695
$29$	707281.	0.185695
$30$	1.44187e6	0.324997
$31$	1.64525e6	0.319967	0.159983	−	0.987120i	$-0.448856\pi$
$31$	1.64525e6	0.319967	0.159983	+	0.987120i	$0.448856\pi$
$32$	−5.97379e6	−1.00711
$33$	3.43091e6	0.503612
$34$	−3.25045e6	−0.417146
$35$	−1.12537e7	−1.26762
$36$	6.89605e6	0.684289
$37$	1.65488e7	1.45164	0.725820	−	0.687885i	$-0.241461\pi$
$37$	1.65488e7	1.45164	0.725820	+	0.687885i	$0.241461\pi$
$38$	−7.10101e6	−0.552451
$39$	−7.43196e6	−0.514414
$40$	−2.54186e7	−1.56994
$41$	−2.24916e6	−0.124306	−0.0621532	−	0.998067i	$-0.519797\pi$
$41$	−2.24916e6	−0.124306	−0.0621532	+	0.998067i	$0.519797\pi$
$42$	−2.23706e6	−0.110932
$43$	−7.29550e6	−0.325422	−0.162711	−	0.986674i	$-0.552024\pi$
$43$	−7.29550e6	−0.325422	−0.162711	+	0.986674i	$0.552024\pi$
$44$	−2.67640e7	−1.07650
$45$	4.57014e7	1.66140
$46$	9.20993e6	0.303282
$47$	2.83005e6	0.0845966	0.0422983	−	0.999105i	$-0.486532\pi$
$47$	2.83005e6	0.0845966	0.0422983	+	0.999105i	$0.486532\pi$
$48$	5.78679e6	0.157345
$49$	−2.28935e7	−0.567322
$50$	−5.44696e7	−1.23251
$51$	1.64775e7	0.341056
$52$	5.79757e7	1.09959
$53$	−4.33982e7	−0.755492	−0.377746	−	0.925909i	$-0.623301\pi$
$53$	−4.33982e7	−0.755492	−0.377746	+	0.925909i	$0.623301\pi$
$54$	1.96224e7	0.314036
$55$	−1.77370e8	−2.61366
$56$	3.94370e7	0.535867
$57$	3.59971e7	0.451680
$58$	−7.26850e6	−0.0843371
$59$	3.65751e7	0.392962	0.196481	−	0.980508i	$-0.437049\pi$
$59$	3.65751e7	0.392962	0.196481	+	0.980508i	$0.437049\pi$
$60$	5.70185e7	0.567982
$61$	1.42512e6	0.0131786	0.00658928	−	0.999978i	$-0.497903\pi$
$61$	1.42512e6	0.0131786	0.00658928	+	0.999978i	$0.497903\pi$
$62$	−1.69077e7	−0.145319
$63$	−7.09057e7	−0.567086
$64$	4.51751e6	0.0336581
$65$	3.84216e8	2.66972
$66$	−3.52583e7	−0.228725
$67$	2.66297e8	1.61447	0.807234	−	0.590232i	$-0.200964\pi$
$67$	2.66297e8	1.61447	0.807234	+	0.590232i	$0.200964\pi$
$68$	−1.28539e8	−0.729027
$69$	−4.66879e7	−0.247961
$70$	1.15651e8	0.575715
$71$	−9.49874e7	−0.443612	−0.221806	−	0.975091i	$-0.571195\pi$
$71$	−9.49874e7	−0.443612	−0.221806	+	0.975091i	$0.571195\pi$
$72$	−1.60154e8	−0.702330
$73$	1.37271e8	0.565750	0.282875	−	0.959157i	$-0.408712\pi$
$73$	1.37271e8	0.565750	0.282875	+	0.959157i	$0.408712\pi$
$74$	−1.70067e8	−0.659290
$75$	2.76123e8	1.00769
$76$	−2.80808e8	−0.965493
$77$	2.75190e8	0.892121
$78$	7.63759e7	0.233631
$79$	−1.58235e7	−0.0457069	−0.0228534	−	0.999739i	$-0.507275\pi$
$79$	−1.58235e7	−0.0457069	−0.0228534	+	0.999739i	$0.507275\pi$
$80$	−2.99164e8	−0.816591
$81$	2.34530e8	0.605364
$82$	2.31139e7	0.0564561
$83$	3.47173e8	0.802961	0.401480	−	0.915868i	$-0.368496\pi$
$83$	3.47173e8	0.802961	0.401480	+	0.915868i	$0.368496\pi$
$84$	−8.84641e7	−0.193870
$85$	−8.51850e8	−1.77002
$86$	7.49735e7	0.147797
$87$	3.68462e7	0.0689534
$88$	6.21568e8	1.10488
$89$	6.90945e8	1.16732	0.583658	−	0.812000i	$-0.301621\pi$
$89$	6.90945e8	1.16732	0.583658	+	0.812000i	$0.301621\pi$
$90$	−4.69659e8	−0.754555
$91$	−5.96111e8	−0.911256
$92$	3.64206e8	0.530031
$93$	8.57103e7	0.118812
$94$	−2.90835e7	−0.0384212
$95$	−1.86097e9	−2.34414
$96$	−3.11208e8	−0.373964
$97$	1.53669e9	1.76243	0.881216	−	0.472714i	$-0.156726\pi$
$97$	1.53669e9	1.76243	0.881216	+	0.472714i	$0.156726\pi$
$98$	2.35269e8	0.257660
$99$	−1.11755e9	−1.16925
$100$	−2.15400e9	−2.15400
$101$	−1.09733e9	−1.04928	−0.524638	−	0.851325i	$-0.675799\pi$
$101$	−1.09733e9	−1.04928	−0.524638	+	0.851325i	$0.675799\pi$
$102$	−1.69334e8	−0.154897
$103$	1.18232e9	1.03506	0.517531	−	0.855665i	$-0.326851\pi$
$103$	1.18232e9	1.03506	0.517531	+	0.855665i	$0.326851\pi$
$104$	−1.34643e9	−1.12858
$105$	−5.86268e8	−0.470700
$106$	4.45989e8	0.343121
$107$	−1.75495e9	−1.29431	−0.647156	−	0.762358i	$-0.724042\pi$
$107$	−1.75495e9	−1.29431	−0.647156	+	0.762358i	$0.724042\pi$
$108$	7.75964e8	0.548826
$109$	2.60943e9	1.77063	0.885313	−	0.464996i	$-0.153944\pi$
$109$	2.60943e9	1.77063	0.885313	+	0.464996i	$0.153944\pi$
$110$	1.82278e9	1.18704
$111$	8.62119e8	0.539031
$112$	4.64153e8	0.278728
$113$	−8.54802e8	−0.493188	−0.246594	−	0.969119i	$-0.579311\pi$
$113$	−8.54802e8	−0.493188	−0.246594	+	0.969119i	$0.579311\pi$
$114$	−3.69931e8	−0.205139
$115$	2.41366e9	1.28687
$116$	−2.87432e8	−0.147392
$117$	2.42081e9	1.19433
$118$	−3.75870e8	−0.178471
$119$	1.32164e9	0.604162
$120$	−1.32420e9	−0.582957
$121$	1.97933e9	0.839429
$122$	−1.46455e7	−0.00598530
$123$	−1.17171e8	−0.0461581
$124$	−6.68614e8	−0.253967
$125$	−9.01473e9	−3.30261
$126$	7.28675e8	0.257553
$127$	2.84823e9	0.971536	0.485768	−	0.874088i	$-0.338540\pi$
$127$	2.84823e9	0.971536	0.485768	+	0.874088i	$0.338540\pi$
$128$	3.01216e9	0.991819
$129$	−3.80063e8	−0.120838
$130$	−3.94846e9	−1.21250
$131$	6.47204e9	1.92008	0.960042	−	0.279854i	$-0.0902861\pi$
$131$	6.47204e9	1.92008	0.960042	+	0.279854i	$0.0902861\pi$
$132$	−1.39429e9	−0.399732
$133$	2.88729e9	0.800126
$134$	−2.73664e9	−0.733241
$135$	5.14246e9	1.33251
$136$	2.98518e9	0.748248
$137$	−2.01333e9	−0.488283	−0.244142	−	0.969740i	$-0.578506\pi$
$137$	−2.01333e9	−0.488283	−0.244142	+	0.969740i	$0.578506\pi$
$138$	4.79796e8	0.112616
$139$	6.09766e9	1.38547	0.692734	−	0.721193i	$-0.256406\pi$
$139$	6.09766e9	1.38547	0.692734	+	0.721193i	$0.256406\pi$
$140$	4.57340e9	1.00615
$141$	1.47433e8	0.0314129
$142$	9.76154e8	0.201475
$143$	−9.39532e9	−1.87888
$144$	−1.88493e9	−0.365312
$145$	−1.90486e9	−0.357856
$146$	−1.41068e9	−0.256946
$147$	−1.19265e9	−0.210661
$148$	−6.72527e9	−1.15221
$149$	3.97034e9	0.659918	0.329959	−	0.943995i	$-0.392965\pi$
$149$	3.97034e9	0.659918	0.329959	+	0.943995i	$0.392965\pi$
$150$	−2.83762e9	−0.457661
$151$	−9.87553e9	−1.54584	−0.772920	−	0.634504i	$-0.781204\pi$
$151$	−9.87553e9	−1.54584	−0.772920	+	0.634504i	$0.781204\pi$
$152$	6.52149e9	0.990948
$153$	−5.36721e9	−0.791839
$154$	−2.82804e9	−0.405174
$155$	−4.43103e9	−0.616612
$156$	3.02028e9	0.408306
$157$	−4.61092e9	−0.605675	−0.302837	−	0.953042i	$-0.597934\pi$
$157$	−4.61092e9	−0.605675	−0.302837	+	0.953042i	$0.597934\pi$
$158$	1.62613e8	0.0207587
$159$	−2.26085e9	−0.280534
$160$	1.60887e10	1.94081
$161$	−3.74479e9	−0.439249
$162$	−2.41019e9	−0.274938
$163$	−1.05841e10	−1.17438	−0.587192	−	0.809448i	$-0.699767\pi$
$163$	−1.05841e10	−1.17438	−0.587192	+	0.809448i	$0.699767\pi$
$164$	9.14037e8	0.0986657
$165$	−9.24019e9	−0.970517
$166$	−3.56778e9	−0.364680
$167$	4.31140e9	0.428938	0.214469	−	0.976731i	$-0.431198\pi$
$167$	4.31140e9	0.428938	0.214469	+	0.976731i	$0.431198\pi$
$168$	2.05449e9	0.198981
$169$	9.74746e9	0.919182
$170$	8.75418e9	0.803888
$171$	−1.17253e10	−1.04868
$172$	2.96482e9	0.258297
$173$	5.56333e9	0.472201	0.236101	−	0.971729i	$-0.424130\pi$
$173$	5.56333e9	0.472201	0.236101	+	0.971729i	$0.424130\pi$
$174$	−3.78656e8	−0.0313165
$175$	2.21475e10	1.78507
$176$	7.31554e9	0.574697
$177$	1.90540e9	0.145917
$178$	−7.10061e9	−0.530159
$179$	7.09167e9	0.516309	0.258155	−	0.966104i	$-0.416886\pi$
$179$	7.09167e9	0.516309	0.258155	+	0.966104i	$0.416886\pi$
$180$	−1.85726e10	−1.31870
$181$	6.99506e9	0.484437	0.242219	−	0.970222i	$-0.422125\pi$
$181$	6.99506e9	0.484437	0.242219	+	0.970222i	$0.422125\pi$
$182$	6.12603e9	0.413864
$183$	7.42426e7	0.00489354
$184$	−8.45831e9	−0.544006
$185$	−4.45696e10	−2.79747
$186$	−8.80817e8	−0.0539607
$187$	2.08305e10	1.24570
$188$	−1.15010e9	−0.0671469
$189$	−7.97852e9	−0.454825
$190$	1.91246e10	1.06464
$191$	−2.90250e10	−1.57805	−0.789027	−	0.614359i	$-0.789415\pi$
$191$	−2.90250e10	−1.57805	−0.789027	+	0.614359i	$0.789415\pi$
$192$	2.35342e8	0.0124981
$193$	2.60292e9	0.135037	0.0675184	−	0.997718i	$-0.478492\pi$
$193$	2.60292e9	0.135037	0.0675184	+	0.997718i	$0.478492\pi$
$194$	−1.57920e10	−0.800442
$195$	2.00159e10	0.991334
$196$	9.30368e9	0.450301
$197$	6.31319e9	0.298642	0.149321	−	0.988789i	$-0.452291\pi$
$197$	6.31319e9	0.298642	0.149321	+	0.988789i	$0.452291\pi$
$198$	1.14847e10	0.531038
$199$	−2.42317e10	−1.09533	−0.547664	−	0.836698i	$-0.684483\pi$
$199$	−2.42317e10	−1.09533	−0.547664	+	0.836698i	$0.684483\pi$
$200$	5.00244e10	2.21079
$201$	1.38729e10	0.599493
$202$	1.12769e10	0.476549
$203$	2.95540e9	0.122147
$204$	−6.69629e9	−0.270706
$205$	6.05749e9	0.239552
$206$	−1.21503e10	−0.470093
$207$	1.52076e10	0.575698
$208$	−1.58468e10	−0.587024
$209$	4.55067e10	1.64975
$210$	6.02489e9	0.213777
$211$	−2.87266e10	−0.997732	−0.498866	−	0.866679i	$-0.666250\pi$
$211$	−2.87266e10	−0.997732	−0.498866	+	0.866679i	$0.666250\pi$
$212$	1.76366e10	0.599657
$213$	−4.94842e9	−0.164724
$214$	1.80351e10	0.587836
$215$	1.96484e10	0.627125
$216$	−1.80210e10	−0.563296
$217$	6.87474e9	0.210469
$218$	−2.68163e10	−0.804164
$219$	7.15118e9	0.210077
$220$	7.20815e10	2.07454
$221$	−4.51226e10	−1.27241
$222$	−8.85971e9	−0.244811
$223$	2.88168e10	0.780322	0.390161	−	0.920747i	$-0.372419\pi$
$223$	2.88168e10	0.780322	0.390161	+	0.920747i	$0.372419\pi$
$224$	−2.49617e10	−0.662457
$225$	−8.99414e10	−2.33958
$226$	8.78452e9	0.223991
$227$	−5.50604e10	−1.37633	−0.688166	−	0.725553i	$-0.741584\pi$
$227$	−5.50604e10	−1.37633	−0.688166	+	0.725553i	$0.741584\pi$
$228$	−1.46289e10	−0.358512
$229$	4.26142e10	1.02399	0.511994	−	0.858989i	$-0.328907\pi$
$229$	4.26142e10	1.02399	0.511994	+	0.858989i	$0.328907\pi$
$230$	−2.48044e10	−0.584458
$231$	1.43362e10	0.331267
$232$	6.67531e9	0.151278
$233$	−2.55611e10	−0.568169	−0.284084	−	0.958799i	$-0.591690\pi$
$233$	−2.55611e10	−0.568169	−0.284084	+	0.958799i	$0.591690\pi$
$234$	−2.48779e10	−0.542428
$235$	−7.62194e9	−0.163027
$236$	−1.48637e10	−0.311906
$237$	−8.24336e8	−0.0169721
$238$	−1.35821e10	−0.274392
$239$	−3.20541e10	−0.635468	−0.317734	−	0.948180i	$-0.602922\pi$
$239$	−3.20541e10	−0.635468	−0.317734	+	0.948180i	$0.602922\pi$
$240$	−1.55851e10	−0.303221
$241$	4.33806e10	0.828360	0.414180	−	0.910195i	$-0.364068\pi$
$241$	4.33806e10	0.828360	0.414180	+	0.910195i	$0.364068\pi$
$242$	−2.03409e10	−0.381243
$243$	4.98009e10	0.916239
$244$	−5.79156e8	−0.0104602
$245$	6.16572e10	1.09329
$246$	1.20413e9	0.0209636
$247$	−9.85758e10	−1.68513
$248$	1.55279e10	0.260663
$249$	1.80862e10	0.298160
$250$	9.26415e10	1.49995
$251$	−3.13042e8	−0.00497819	−0.00248909	−	0.999997i	$-0.500792\pi$
$251$	−3.13042e8	−0.00497819	−0.00248909	+	0.999997i	$0.500792\pi$
$252$	2.88154e10	0.450113
$253$	−5.90218e10	−0.905670
$254$	−2.92704e10	−0.441242
$255$	−4.43776e10	−0.657253
$256$	−3.32679e10	−0.484112
$257$	−1.18004e11	−1.68732	−0.843662	−	0.536874i	$-0.819605\pi$
$257$	−1.18004e11	−1.68732	−0.843662	+	0.536874i	$0.819605\pi$
$258$	3.90578e9	0.0548807
$259$	6.91497e10	0.954864
$260$	−1.56141e11	−2.11904
$261$	−1.20019e10	−0.160091
$262$	−6.65111e10	−0.872043
$263$	7.58613e10	0.977731	0.488865	−	0.872359i	$-0.337411\pi$
$263$	7.58613e10	0.977731	0.488865	+	0.872359i	$0.337411\pi$
$264$	3.23809e10	0.410271
$265$	1.16881e11	1.45592
$266$	−2.96718e10	−0.363393
$267$	3.59951e10	0.433454
$268$	−1.08220e11	−1.28145
$269$	8.63217e10	1.00516	0.502580	−	0.864531i	$-0.332384\pi$
$269$	8.63217e10	1.00516	0.502580	+	0.864531i	$0.332384\pi$
$270$	−5.28474e10	−0.605183
$271$	1.38357e11	1.55826	0.779129	−	0.626864i	$-0.215662\pi$
$271$	1.38357e11	1.55826	0.779129	+	0.626864i	$0.215662\pi$
$272$	3.51341e10	0.389196
$273$	−3.10547e10	−0.338373
$274$	2.06903e10	0.221763
$275$	3.49068e11	3.68056
$276$	1.89735e10	0.196814
$277$	9.26208e10	0.945256	0.472628	−	0.881262i	$-0.343305\pi$
$277$	9.26208e10	0.945256	0.472628	+	0.881262i	$0.343305\pi$
$278$	−6.26637e10	−0.629237
$279$	−2.79184e10	−0.275849
$280$	−1.06212e11	−1.03268
$281$	−9.09701e10	−0.870403	−0.435201	−	0.900333i	$-0.643323\pi$
$281$	−9.09701e10	−0.870403	−0.435201	+	0.900333i	$0.643323\pi$
$282$	−1.51512e9	−0.0142668
$283$	4.47641e10	0.414850	0.207425	−	0.978251i	$-0.433492\pi$
$283$	4.47641e10	0.414850	0.207425	+	0.978251i	$0.433492\pi$
$284$	3.86019e10	0.352108
$285$	−9.69482e10	−0.870438
$286$	9.65527e10	0.853330
$287$	−9.39819e9	−0.0817666
$288$	1.01370e11	0.868243
$289$	−1.85460e10	−0.156391
$290$	1.95757e10	0.162527
$291$	8.00545e10	0.654436
$292$	−5.57854e10	−0.449053
$293$	−2.32987e8	−0.00184684	−0.000923418	−	1.00000i	$-0.500294\pi$
$293$	−2.32987e8	−0.00184684	−0.000923418		1.00000i	$0.500294\pi$
$294$	1.22565e10	0.0956758
$295$	−9.85047e10	−0.757283
$296$	1.56188e11	1.18259
$297$	−1.25750e11	−0.937785
$298$	−4.08019e10	−0.299714
$299$	1.27852e11	0.925096
$300$	−1.12214e11	−0.799834
$301$	−3.04845e10	−0.214057
$302$	1.01488e11	0.702072
$303$	−5.71658e10	−0.389623
$304$	7.67547e10	0.515435
$305$	−3.83817e9	−0.0253966
$306$	5.51571e10	0.359629
$307$	5.10014e10	0.327687	0.163844	−	0.986486i	$-0.447611\pi$
$307$	5.10014e10	0.327687	0.163844	+	0.986486i	$0.447611\pi$
$308$	−1.11834e11	−0.708104
$309$	6.15934e10	0.384345
$310$	4.55362e10	0.280046
$311$	−2.30223e11	−1.39549	−0.697745	−	0.716347i	$-0.745813\pi$
$311$	−2.30223e11	−1.39549	−0.697745	+	0.716347i	$0.745813\pi$
$312$	−7.01428e10	−0.419071
$313$	−1.75614e11	−1.03421	−0.517106	−	0.855921i	$-0.672991\pi$
$313$	−1.75614e11	−1.03421	−0.517106	+	0.855921i	$0.672991\pi$
$314$	4.73850e10	0.275079
$315$	1.90965e11	1.09284
$316$	6.43053e9	0.0362789
$317$	9.06748e10	0.504336	0.252168	−	0.967683i	$-0.418856\pi$
$317$	9.06748e10	0.504336	0.252168	+	0.967683i	$0.418856\pi$
$318$	2.32340e10	0.127410
$319$	4.65801e10	0.251850
$320$	−1.21667e10	−0.0648630
$321$	−9.14253e10	−0.480611
$322$	3.84840e10	0.199493
$323$	2.18554e11	1.11724
$324$	−9.53108e10	−0.480496
$325$	−7.56145e11	−3.75950
$326$	1.08769e11	0.533369
$327$	1.35940e11	0.657479
$328$	−2.12276e10	−0.101267
$329$	1.18254e10	0.0556462
$330$	9.49585e10	0.440779
$331$	2.30967e11	1.05760	0.528802	−	0.848745i	$-0.322641\pi$
$331$	2.30967e11	1.05760	0.528802	+	0.848745i	$0.322641\pi$
$332$	−1.41088e11	−0.637334
$333$	−2.80818e11	−1.25148
$334$	−4.43068e10	−0.194810
$335$	−7.17196e11	−3.11126
$336$	2.41803e10	0.103499
$337$	−3.72386e10	−0.157275	−0.0786373	−	0.996903i	$-0.525057\pi$
$337$	−3.72386e10	−0.157275	−0.0786373	+	0.996903i	$0.525057\pi$
$338$	−1.00171e11	−0.417464
$339$	−4.45313e10	−0.183133
$340$	3.46183e11	1.40492
$341$	1.08353e11	0.433957
$342$	1.20497e11	0.476278
$343$	−2.64280e11	−1.03096
$344$	−6.88549e10	−0.265107
$345$	1.25741e11	0.477849
$346$	−5.71725e10	−0.214459
$347$	1.42121e11	0.526229	0.263115	−	0.964765i	$-0.415250\pi$
$347$	1.42121e11	0.526229	0.263115	+	0.964765i	$0.415250\pi$
$348$	−1.49739e10	−0.0547304
$349$	1.49218e11	0.538402	0.269201	−	0.963084i	$-0.413240\pi$
$349$	1.49218e11	0.538402	0.269201	+	0.963084i	$0.413240\pi$
$350$	−2.27603e11	−0.810722
$351$	2.72397e11	0.957899
$352$	−3.93422e11	−1.36589
$353$	3.10372e11	1.06389	0.531944	−	0.846779i	$-0.321462\pi$
$353$	3.10372e11	1.06389	0.531944	+	0.846779i	$0.321462\pi$
$354$	−1.95811e10	−0.0662710
$355$	2.55822e11	0.854890
$356$	−2.80793e11	−0.926534
$357$	6.88517e10	0.224341
$358$	−7.28788e10	−0.234492
$359$	7.10396e9	0.0225723	0.0112861	−	0.999936i	$-0.496407\pi$
$359$	7.10396e9	0.0225723	0.0112861	+	0.999936i	$0.496407\pi$
$360$	4.31330e11	1.35347
$361$	1.54770e11	0.479626
$362$	−7.18859e10	−0.220017
$363$	1.03114e11	0.311701
$364$	2.42253e11	0.723292
$365$	−3.69700e11	−1.09026
$366$	−7.62967e8	−0.00222249
$367$	5.61208e11	1.61483	0.807414	−	0.589985i	$-0.200867\pi$
$367$	5.61208e11	1.61483	0.807414	+	0.589985i	$0.200867\pi$
$368$	−9.95501e10	−0.282961
$369$	3.81662e10	0.107167
$370$	4.58027e11	1.27053
$371$	−1.81341e11	−0.496950
$372$	−3.48318e10	−0.0943045
$373$	−1.65207e11	−0.441916	−0.220958	−	0.975283i	$-0.570918\pi$
$373$	−1.65207e11	−0.441916	−0.220958	+	0.975283i	$0.570918\pi$
$374$	−2.14068e11	−0.565757
$375$	−4.69627e11	−1.22634
$376$	2.67100e10	0.0689172
$377$	−1.00901e11	−0.257252
$378$	8.19927e10	0.206567
$379$	2.90349e11	0.722842	0.361421	−	0.932403i	$-0.382292\pi$
$379$	2.90349e11	0.722842	0.361421	+	0.932403i	$0.382292\pi$
$380$	7.56279e11	1.86061
$381$	1.48380e11	0.360756
$382$	2.98280e11	0.716703
$383$	−1.32459e11	−0.314549	−0.157274	−	0.987555i	$-0.550271\pi$
$383$	−1.32459e11	−0.314549	−0.157274	+	0.987555i	$0.550271\pi$
$384$	1.56920e11	0.368288
$385$	−7.41147e11	−1.71922
$386$	−2.67493e10	−0.0613295
$387$	1.23798e11	0.280552
$388$	−6.24494e11	−1.39890
$389$	1.39828e11	0.309613	0.154807	−	0.987945i	$-0.450525\pi$
$389$	1.39828e11	0.309613	0.154807	+	0.987945i	$0.450525\pi$
$390$	−2.05697e11	−0.450233
$391$	−2.83462e11	−0.613337
$392$	−2.16069e11	−0.462173
$393$	3.37164e11	0.712977
$394$	−6.48786e10	−0.135634
$395$	4.26163e10	0.0880823
$396$	4.54160e11	0.928070
$397$	−2.10649e11	−0.425600	−0.212800	−	0.977096i	$-0.568258\pi$
$397$	−2.10649e11	−0.425600	−0.212800	+	0.977096i	$0.568258\pi$
$398$	2.49021e11	0.497464
$399$	1.50415e11	0.297107
$400$	5.88762e11	1.14993
$401$	2.85575e11	0.551532	0.275766	−	0.961225i	$-0.411068\pi$
$401$	2.85575e11	0.551532	0.275766	+	0.961225i	$0.411068\pi$
$402$	−1.42567e11	−0.272271
$403$	−2.34712e11	−0.443264
$404$	4.45943e11	0.832842
$405$	−6.31642e11	−1.16660
$406$	−3.03716e10	−0.0554755
$407$	1.08987e12	1.96879
$408$	1.55515e11	0.277844
$409$	−2.47067e11	−0.436575	−0.218288	−	0.975884i	$-0.570047\pi$
$409$	−2.47067e11	−0.436575	−0.218288	+	0.975884i	$0.570047\pi$
$410$	−6.22509e10	−0.108797
$411$	−1.04885e11	−0.181312
$412$	−4.80481e11	−0.821560
$413$	1.52830e11	0.258484
$414$	−1.56284e11	−0.261464
$415$	−9.35014e11	−1.54740
$416$	8.52223e11	1.39519
$417$	3.17661e11	0.514460
$418$	−4.67658e11	−0.749264
$419$	−9.10363e11	−1.44295	−0.721475	−	0.692440i	$-0.756536\pi$
$419$	−9.10363e11	−1.44295	−0.721475	+	0.692440i	$0.756536\pi$
$420$	2.38253e11	0.373609
$421$	1.22024e11	0.189310	0.0946552	−	0.995510i	$-0.469825\pi$
$421$	1.22024e11	0.189310	0.0946552	+	0.995510i	$0.469825\pi$
$422$	2.95214e11	0.453139
$423$	−4.80232e10	−0.0729322
$424$	−4.09592e11	−0.615467
$425$	1.67646e12	2.49254
$426$	5.08533e10	0.0748128
$427$	5.95492e9	0.00866863
$428$	7.13196e11	1.02733
$429$	−4.89454e11	−0.697677
$430$	−2.01920e11	−0.284821
$431$	1.32737e12	1.85286	0.926432	−	0.376463i	$-0.122860\pi$
$431$	1.32737e12	1.85286	0.926432	+	0.376463i	$0.122860\pi$
$432$	−2.12098e11	−0.292995
$433$	−1.30621e12	−1.78574	−0.892870	−	0.450314i	$-0.851312\pi$
$433$	−1.30621e12	−1.78574	−0.892870	+	0.450314i	$0.851312\pi$
$434$	−7.06494e10	−0.0955883
$435$	−9.92349e10	−0.132881
$436$	−1.06045e12	−1.40540
$437$	−6.19257e11	−0.812278
$438$	−7.34903e10	−0.0954106
$439$	−1.91917e11	−0.246617	−0.123309	−	0.992368i	$-0.539351\pi$
$439$	−1.91917e11	−0.246617	−0.123309	+	0.992368i	$0.539351\pi$
$440$	−1.67402e12	−2.12923
$441$	3.88481e11	0.489098
$442$	4.63710e11	0.577892
$443$	−1.13891e12	−1.40499	−0.702497	−	0.711687i	$-0.747931\pi$
$443$	−1.13891e12	−1.40499	−0.702497	+	0.711687i	$0.747931\pi$
$444$	−3.50356e11	−0.427845
$445$	−1.86087e12	−2.24955
$446$	−2.96141e11	−0.354398
$447$	2.06837e11	0.245044
$448$	1.88766e10	0.0221397
$449$	4.02992e11	0.467937	0.233969	−	0.972244i	$-0.424829\pi$
$449$	4.02992e11	0.467937	0.233969	+	0.972244i	$0.424829\pi$
$450$	9.24298e11	1.06257
$451$	−1.48125e11	−0.168591
$452$	3.47383e11	0.391458
$453$	−5.14471e11	−0.574009
$454$	5.65838e11	0.625088
$455$	1.60546e12	1.75609
$456$	3.39741e11	0.367964
$457$	1.30712e12	1.40182	0.700911	−	0.713249i	$-0.252777\pi$
$457$	1.30712e12	1.40182	0.700911	+	0.713249i	$0.252777\pi$
$458$	−4.37932e11	−0.465064
$459$	−6.03934e11	−0.635086
$460$	−9.80887e11	−1.02143
$461$	1.64361e12	1.69490	0.847451	−	0.530873i	$-0.178136\pi$
$461$	1.64361e12	1.69490	0.847451	+	0.530873i	$0.178136\pi$
$462$	−1.47328e11	−0.150451
$463$	−7.44150e11	−0.752569	−0.376284	−	0.926504i	$-0.622798\pi$
$463$	−7.44150e11	−0.752569	−0.376284	+	0.926504i	$0.622798\pi$
$464$	7.85651e10	0.0786862
$465$	−2.30837e11	−0.228964
$466$	2.62683e11	0.258045
$467$	−6.30532e11	−0.613453	−0.306726	−	0.951798i	$-0.599234\pi$
$467$	−6.30532e11	−0.613453	−0.306726	+	0.951798i	$0.599234\pi$
$468$	−9.83793e11	−0.947976
$469$	1.11273e12	1.06197
$470$	7.83282e10	0.0740419
$471$	−2.40208e11	−0.224902
$472$	3.45195e11	0.320130
$473$	−4.80467e11	−0.441356
$474$	8.47143e9	0.00770822
$475$	3.66243e12	3.30102
$476$	−5.37103e11	−0.479542
$477$	7.36426e11	0.651323
$478$	3.29410e11	0.288610
$479$	−9.84764e11	−0.854717	−0.427359	−	0.904082i	$-0.640556\pi$
$479$	−9.84764e11	−0.854717	−0.427359	+	0.904082i	$0.640556\pi$
$480$	8.38152e11	0.720671
$481$	−2.36086e12	−2.01102
$482$	−4.45808e11	−0.376215
$483$	−1.95087e11	−0.163104
$484$	−8.04379e11	−0.666280
$485$	−4.13864e12	−3.39640
$486$	−5.11787e11	−0.416127
$487$	−7.87334e10	−0.0634277	−0.0317138	−	0.999497i	$-0.510097\pi$
$487$	−7.87334e10	−0.0634277	−0.0317138	+	0.999497i	$0.510097\pi$
$488$	1.34503e10	0.0107360
$489$	−5.51385e11	−0.436079
$490$	−6.33631e11	−0.496540
$491$	2.43693e12	1.89224	0.946121	−	0.323813i	$-0.104965\pi$
$491$	2.43693e12	1.89224	0.946121	+	0.323813i	$0.104965\pi$
$492$	4.76172e10	0.0366371
$493$	2.23709e11	0.170558
$494$	1.01303e12	0.765335
$495$	3.00980e12	2.25328
$496$	1.82755e11	0.135582
$497$	−3.96908e11	−0.291800
$498$	−1.85866e11	−0.135415
$499$	−3.83979e11	−0.277239	−0.138620	−	0.990346i	$-0.544267\pi$
$499$	−3.83979e11	−0.277239	−0.138620	+	0.990346i	$0.544267\pi$
$500$	3.66350e12	2.62139
$501$	2.24605e11	0.159275
$502$	3.21703e9	0.00226094
$503$	6.17401e11	0.430043	0.215021	−	0.976609i	$-0.431018\pi$
$503$	6.17401e11	0.430043	0.215021	+	0.976609i	$0.431018\pi$
$504$	−6.69208e11	−0.461981
$505$	2.95534e12	2.02207
$506$	6.06548e11	0.411327
$507$	5.07799e11	0.341316
$508$	−1.15749e12	−0.771137
$509$	1.20793e12	0.797648	0.398824	−	0.917027i	$-0.369418\pi$
$509$	1.20793e12	0.797648	0.398824	+	0.917027i	$0.369418\pi$
$510$	4.56054e11	0.298504
$511$	5.73589e11	0.372140
$512$	−1.20034e12	−0.771951
$513$	−1.31937e12	−0.841081
$514$	1.21269e12	0.766331
$515$	−3.18424e12	−1.99468
$516$	1.54454e11	0.0959124
$517$	1.86381e11	0.114735
$518$	−7.10629e11	−0.433670
$519$	2.89824e11	0.175340
$520$	3.62623e12	2.17490
$521$	1.26592e12	0.752728	0.376364	−	0.926472i	$-0.377174\pi$
$521$	1.26592e12	0.752728	0.376364	+	0.926472i	$0.377174\pi$
$522$	1.23340e11	0.0727085
$523$	1.71358e12	1.00149	0.500746	−	0.865594i	$-0.333059\pi$
$523$	1.71358e12	1.00149	0.500746	+	0.865594i	$0.333059\pi$
$524$	−2.63017e12	−1.52403
$525$	1.15379e12	0.662841
$526$	−7.79602e11	−0.444055
$527$	5.20383e11	0.293884
$528$	3.81107e11	0.213400
$529$	−9.97982e11	−0.554080
$530$	−1.20115e12	−0.661233
$531$	−6.20644e11	−0.338780
$532$	−1.17337e12	−0.635085
$533$	3.20866e11	0.172207
$534$	−3.69910e11	−0.196861
$535$	4.72648e12	2.49428
$536$	2.51331e12	1.31524
$537$	3.69444e11	0.191719
$538$	−8.87101e11	−0.456512
$539$	−1.50772e12	−0.769433
$540$	−2.08984e12	−1.05765
$541$	1.37892e11	0.0692070	0.0346035	−	0.999401i	$-0.488983\pi$
$541$	1.37892e11	0.0692070	0.0346035	+	0.999401i	$0.488983\pi$
$542$	−1.42185e12	−0.707713
$543$	3.64411e11	0.179884
$544$	−1.88947e12	−0.925009
$545$	−7.02778e12	−3.41220
$546$	3.19139e11	0.153678
$547$	−1.30665e12	−0.624044	−0.312022	−	0.950075i	$-0.601006\pi$
$547$	−1.30665e12	−0.624044	−0.312022	+	0.950075i	$0.601006\pi$
$548$	8.18196e11	0.387565
$549$	−2.41830e10	−0.0113615
$550$	−3.58726e12	−1.67159
$551$	4.88719e11	0.225880
$552$	−4.40640e11	−0.202003
$553$	−6.61191e10	−0.0300652
$554$	−9.51834e11	−0.429306
$555$	−2.32188e12	−1.03877
$556$	−2.47803e12	−1.09969
$557$	−1.29273e12	−0.569060	−0.284530	−	0.958667i	$-0.591838\pi$
$557$	−1.29273e12	−0.569060	−0.284530	+	0.958667i	$0.591838\pi$
$558$	2.86908e11	0.125282
$559$	1.04078e12	0.450822
$560$	−1.25007e12	−0.537140
$561$	1.08518e12	0.462559
$562$	9.34870e11	0.395310
$563$	−3.06721e11	−0.128664	−0.0643319	−	0.997929i	$-0.520492\pi$
$563$	−3.06721e11	−0.128664	−0.0643319	+	0.997929i	$0.520492\pi$
$564$	−5.99152e10	−0.0249334
$565$	2.30217e12	0.950428
$566$	−4.60026e11	−0.188412
$567$	9.79992e11	0.398198
$568$	−8.96490e11	−0.361392
$569$	3.85500e12	1.54177	0.770884	−	0.636976i	$-0.219815\pi$
$569$	3.85500e12	1.54177	0.770884	+	0.636976i	$0.219815\pi$
$570$	9.96305e11	0.395326
$571$	3.06202e12	1.20544	0.602719	−	0.797954i	$-0.294084\pi$
$571$	3.06202e12	1.20544	0.602719	+	0.797954i	$0.294084\pi$
$572$	3.81816e12	1.49133
$573$	−1.51207e12	−0.585972
$574$	9.65822e10	0.0371359
$575$	−4.75013e12	−1.81218
$576$	−7.66580e10	−0.0290172
$577$	3.46465e12	1.30127	0.650636	−	0.759390i	$-0.274503\pi$
$577$	3.46465e12	1.30127	0.650636	+	0.759390i	$0.274503\pi$
$578$	1.90591e11	0.0710278
$579$	1.35600e11	0.0501426
$580$	7.74118e11	0.284041
$581$	1.45067e12	0.528174
$582$	−8.22694e11	−0.297225
$583$	−2.85812e12	−1.02464
$584$	1.29556e12	0.460892
$585$	−6.51978e12	−2.30161
$586$	2.39434e9	0.000838776 0
$587$	2.71766e12	0.944766	0.472383	−	0.881393i	$-0.343394\pi$
$587$	2.71766e12	0.944766	0.472383	+	0.881393i	$0.343394\pi$
$588$	4.84680e11	0.167208
$589$	1.13684e12	0.389207
$590$	1.01230e12	0.343934
$591$	3.28889e11	0.110893
$592$	1.83825e12	0.615116
$593$	1.86314e12	0.618727	0.309364	−	0.950944i	$-0.399884\pi$
$593$	1.86314e12	0.618727	0.309364	+	0.950944i	$0.399884\pi$
$594$	1.29229e12	0.425913
$595$	−3.55948e12	−1.16429
$596$	−1.61351e12	−0.523797
$597$	−1.26236e12	−0.406723
$598$	−1.31389e12	−0.420150
$599$	1.98442e12	0.629814	0.314907	−	0.949122i	$-0.398027\pi$
$599$	1.98442e12	0.629814	0.314907	+	0.949122i	$0.398027\pi$
$600$	2.60605e12	0.820921
$601$	−1.56363e12	−0.488876	−0.244438	−	0.969665i	$-0.578603\pi$
$601$	−1.56363e12	−0.488876	−0.244438	+	0.969665i	$0.578603\pi$
$602$	3.13279e11	0.0972181
$603$	−4.51880e12	−1.39186
$604$	4.01332e12	1.22698
$605$	−5.33077e12	−1.61767
$606$	5.87475e11	0.176955
$607$	−2.84779e12	−0.851451	−0.425725	−	0.904852i	$-0.639981\pi$
$607$	−2.84779e12	−0.851451	−0.425725	+	0.904852i	$0.639981\pi$
$608$	−4.12779e12	−1.22504
$609$	1.53963e11	0.0453564
$610$	3.94437e10	0.0115343
$611$	−4.03735e11	−0.117196
$612$	2.18118e12	0.628507
$613$	−2.63820e11	−0.0754633	−0.0377317	−	0.999288i	$-0.512013\pi$
$613$	−2.63820e11	−0.0754633	−0.0377317	+	0.999288i	$0.512013\pi$
$614$	−5.24125e11	−0.148825
$615$	3.15568e11	0.0889519
$616$	2.59724e12	0.726773
$617$	−1.91747e12	−0.532654	−0.266327	−	0.963883i	$-0.585810\pi$
$617$	−1.91747e12	−0.532654	−0.266327	+	0.963883i	$0.585810\pi$
$618$	−6.32975e11	−0.174557
$619$	−3.42272e12	−0.937051	−0.468525	−	0.883450i	$-0.655215\pi$
$619$	−3.42272e12	−0.937051	−0.468525	+	0.883450i	$0.655215\pi$
$620$	1.80073e12	0.489424
$621$	1.71121e12	0.461733
$622$	2.36592e12	0.633788
$623$	2.88713e12	0.767840
$624$	−8.25546e11	−0.217977
$625$	1.39265e13	3.65075
$626$	1.80473e12	0.469707
$627$	2.37070e12	0.612593
$628$	1.87383e12	0.480742
$629$	5.23429e12	1.33331
$630$	−1.96248e12	−0.496334
$631$	3.52340e12	0.884768	0.442384	−	0.896826i	$-0.354133\pi$
$631$	3.52340e12	0.884768	0.442384	+	0.896826i	$0.354133\pi$
$632$	−1.49342e11	−0.0372354
$633$	−1.49653e12	−0.370483
$634$	−9.31835e11	−0.229054
$635$	−7.67092e12	−1.87226
$636$	9.18787e11	0.222668
$637$	3.26599e12	0.785937
$638$	−4.78689e11	−0.114383
$639$	1.61185e12	0.382446
$640$	−8.11240e12	−1.91135
$641$	4.81575e12	1.12669	0.563343	−	0.826223i	$-0.309515\pi$
$641$	4.81575e12	1.12669	0.563343	+	0.826223i	$0.309515\pi$
$642$	9.39548e11	0.218279
$643$	−1.59791e12	−0.368640	−0.184320	−	0.982866i	$-0.559008\pi$
$643$	−1.59791e12	−0.368640	−0.184320	+	0.982866i	$0.559008\pi$
$644$	1.52185e12	0.348646
$645$	1.02359e12	0.232868
$646$	−2.24601e12	−0.507416
$647$	−6.09528e11	−0.136749	−0.0683746	−	0.997660i	$-0.521781\pi$
$647$	−6.09528e11	−0.136749	−0.0683746	+	0.997660i	$0.521781\pi$
$648$	2.21350e12	0.493164
$649$	2.40876e12	0.532957
$650$	7.77066e12	1.70745
$651$	3.58143e11	0.0781524
$652$	4.30127e12	0.932144
$653$	4.57188e12	0.983979	0.491989	−	0.870601i	$-0.336270\pi$
$653$	4.57188e12	0.983979	0.491989	+	0.870601i	$0.336270\pi$
$654$	−1.39701e12	−0.298607
$655$	−1.74306e13	−3.70022
$656$	−2.49838e11	−0.0526734
$657$	−2.32935e12	−0.487743
$658$	−1.21526e11	−0.0252728
$659$	−5.28674e12	−1.09195	−0.545976	−	0.837800i	$-0.683841\pi$
$659$	−5.28674e12	−1.09195	−0.545976	+	0.837800i	$0.683841\pi$
$660$	3.75512e12	0.770329
$661$	−7.03143e11	−0.143264	−0.0716320	−	0.997431i	$-0.522821\pi$
$661$	−7.03143e11	−0.143264	−0.0716320	+	0.997431i	$0.522821\pi$
$662$	−2.37357e12	−0.480332
$663$	−2.35068e12	−0.472480
$664$	3.27662e12	0.654138
$665$	−7.77612e12	−1.54193
$666$	2.88587e12	0.568385
$667$	−6.33864e11	−0.124002
$668$	−1.75211e12	−0.340461
$669$	1.50123e12	0.289753
$670$	7.37039e12	1.41304
$671$	9.38558e10	0.0178735
$672$	−1.30039e12	−0.245987
$673$	−3.10654e12	−0.583726	−0.291863	−	0.956460i	$-0.594275\pi$
$673$	−3.10654e12	−0.583726	−0.291863	+	0.956460i	$0.594275\pi$
$674$	3.82689e11	0.0714293
$675$	−1.01205e13	−1.87644
$676$	−3.96127e12	−0.729582
$677$	3.63374e12	0.664820	0.332410	−	0.943135i	$-0.392138\pi$
$677$	3.63374e12	0.664820	0.332410	+	0.943135i	$0.392138\pi$
$678$	4.57634e11	0.0831735
$679$	6.42109e12	1.15930
$680$	−8.03975e12	−1.44196
$681$	−2.86840e12	−0.511067
$682$	−1.11351e12	−0.197090
$683$	−1.41134e12	−0.248164	−0.124082	−	0.992272i	$-0.539599\pi$
$683$	−1.41134e12	−0.248164	−0.124082	+	0.992272i	$0.539599\pi$
$684$	4.76505e12	0.832368
$685$	5.42234e12	0.940977
$686$	2.71592e12	0.468229
$687$	2.22001e12	0.380233
$688$	−8.10388e11	−0.137894
$689$	6.19120e12	1.04662
$690$	−1.29220e12	−0.217024
$691$	1.02257e13	1.70624	0.853121	−	0.521713i	$-0.174707\pi$
$691$	1.02257e13	1.70624	0.853121	+	0.521713i	$0.174707\pi$
$692$	−2.26088e12	−0.374800
$693$	−4.66971e12	−0.769113
$694$	−1.46053e12	−0.238997
$695$	−1.64223e13	−2.66995
$696$	3.47754e11	0.0561734
$697$	−7.11396e11	−0.114173
$698$	−1.53347e12	−0.244526
$699$	−1.33162e12	−0.210976
$700$	−9.00054e12	−1.41686
$701$	8.23266e12	1.28768	0.643842	−	0.765159i	$-0.277340\pi$
$701$	8.23266e12	1.28768	0.643842	+	0.765159i	$0.277340\pi$
$702$	−2.79933e12	−0.435048
$703$	1.14349e13	1.76577
$704$	2.97514e11	0.0456490
$705$	−3.97069e11	−0.0605362
$706$	−3.18959e12	−0.483185
$707$	−4.58521e12	−0.690196
$708$	−7.74334e11	−0.115819
$709$	−1.25517e13	−1.86550	−0.932749	−	0.360527i	$-0.882597\pi$
$709$	−1.25517e13	−1.86550	−0.932749	+	0.360527i	$0.882597\pi$
$710$	−2.62900e12	−0.388265
$711$	2.68511e11	0.0394047
$712$	6.52113e12	0.950962
$713$	−1.47447e12	−0.213665
$714$	−7.07567e11	−0.101889
$715$	2.53037e13	3.62082
$716$	−2.88198e12	−0.409810
$717$	−1.66988e12	−0.235965
$718$	−7.30051e10	−0.0102516
$719$	−1.15370e13	−1.60995	−0.804974	−	0.593310i	$-0.797821\pi$
$719$	−1.15370e13	−1.60995	−0.804974	+	0.593310i	$0.797821\pi$
$720$	5.07654e12	0.703998
$721$	4.94034e12	0.680845
$722$	−1.59052e12	−0.217832
$723$	2.25994e12	0.307591
$724$	−2.84272e12	−0.384513
$725$	3.74881e12	0.503933
$726$	−1.05967e12	−0.141565
$727$	−8.75597e12	−1.16252	−0.581259	−	0.813719i	$-0.697440\pi$
$727$	−8.75597e12	−1.16252	−0.581259	+	0.813719i	$0.697440\pi$
$728$	−5.62609e12	−0.742361
$729$	−2.02186e12	−0.265141
$730$	3.79929e12	0.495164
$731$	−2.30752e12	−0.298894
$732$	−3.01714e10	−0.00388415
$733$	−5.50802e12	−0.704738	−0.352369	−	0.935861i	$-0.614624\pi$
$733$	−5.50802e12	−0.704738	−0.352369	+	0.935861i	$0.614624\pi$
$734$	−5.76735e12	−0.733405
$735$	3.21207e12	0.405968
$736$	5.35370e12	0.672518
$737$	1.75378e13	2.18963
$738$	−3.92221e11	−0.0486718
$739$	−9.16008e12	−1.12979	−0.564897	−	0.825161i	$-0.691084\pi$
$739$	−9.16008e12	−1.12979	−0.564897	+	0.825161i	$0.691084\pi$
$740$	1.81126e13	2.22044
$741$	−5.13536e12	−0.625733
$742$	1.86358e12	0.225699
$743$	−1.28129e13	−1.54240	−0.771200	−	0.636592i	$-0.780343\pi$
$743$	−1.28129e13	−1.54240	−0.771200	+	0.636592i	$0.780343\pi$
$744$	8.08933e11	0.0967909
$745$	−1.06930e13	−1.27174
$746$	1.69778e12	0.200705
$747$	−5.89120e12	−0.692246
$748$	−8.46530e12	−0.988747
$749$	−7.33313e12	−0.851376
$750$	4.82621e12	0.556968
$751$	−4.63907e12	−0.532171	−0.266086	−	0.963949i	$-0.585730\pi$
$751$	−4.63907e12	−0.532171	−0.266086	+	0.963949i	$0.585730\pi$
$752$	3.14363e11	0.0358468
$753$	−1.63081e10	−0.00184853
$754$	1.03693e12	0.116836
$755$	2.65970e13	2.97901
$756$	3.24239e12	0.361008
$757$	−1.95777e12	−0.216686	−0.108343	−	0.994114i	$-0.534554\pi$
$757$	−1.95777e12	−0.216686	−0.108343	+	0.994114i	$0.534554\pi$
$758$	−2.98382e12	−0.328293
$759$	−3.07477e12	−0.336298
$760$	−1.75638e13	−1.90967
$761$	1.27273e13	1.37564	0.687818	−	0.725883i	$-0.258569\pi$
$761$	1.27273e13	1.37564	0.687818	+	0.725883i	$0.258569\pi$
$762$	−1.52485e12	−0.163844
$763$	1.09036e13	1.16469
$764$	1.17955e13	1.25255
$765$	1.44551e13	1.52596
$766$	1.36124e12	0.142858
$767$	−5.21781e12	−0.544389
$768$	−1.73311e12	−0.179763
$769$	−9.24722e11	−0.0953548	−0.0476774	−	0.998863i	$-0.515182\pi$
$769$	−9.24722e11	−0.0953548	−0.0476774	+	0.998863i	$0.515182\pi$
$770$	7.61653e12	0.780816
$771$	−6.14749e12	−0.626547
$772$	−1.05780e12	−0.107183
$773$	2.55997e12	0.257885	0.128943	−	0.991652i	$-0.458842\pi$
$773$	2.55997e12	0.257885	0.128943	+	0.991652i	$0.458842\pi$
$774$	−1.27223e12	−0.127418
$775$	8.72036e12	0.868314
$776$	1.45032e13	1.43578
$777$	3.60239e12	0.354565
$778$	−1.43696e12	−0.140617
$779$	−1.55413e12	−0.151206
$780$	−8.13427e12	−0.786852
$781$	−6.25568e12	−0.601651
$782$	2.91305e12	0.278559
$783$	−1.35049e12	−0.128399
$784$	−2.54302e12	−0.240396
$785$	1.24182e13	1.16720
$786$	−3.46493e12	−0.323812
$787$	9.59617e12	0.891686	0.445843	−	0.895111i	$-0.352904\pi$
$787$	9.59617e12	0.891686	0.445843	+	0.895111i	$0.352904\pi$
$788$	−2.56562e12	−0.237041
$789$	3.95203e12	0.363056
$790$	−4.37954e11	−0.0400043
$791$	−3.57182e12	−0.324410
$792$	−1.05474e13	−0.952539
$793$	−2.03309e11	−0.0182569
$794$	2.16477e12	0.193294
$795$	6.08897e12	0.540620
$796$	9.84751e12	0.869396
$797$	4.93542e12	0.433273	0.216637	−	0.976252i	$-0.430491\pi$
$797$	4.93542e12	0.433273	0.216637	+	0.976252i	$0.430491\pi$
$798$	−1.54577e12	−0.134937
$799$	8.95126e11	0.0777005
$800$	−3.16630e13	−2.73305
$801$	−1.17247e13	−1.00636
$802$	−2.93476e12	−0.250489
$803$	9.04036e12	0.767301
$804$	−5.63779e12	−0.475836
$805$	1.00856e13	0.846483
$806$	2.41206e12	0.201317
$807$	4.49698e12	0.373241
$808$	−1.03566e13	−0.854800
$809$	−4.79972e12	−0.393956	−0.196978	−	0.980408i	$-0.563113\pi$
$809$	−4.79972e12	−0.393956	−0.196978	+	0.980408i	$0.563113\pi$
$810$	6.49118e12	0.529836
$811$	5.88642e12	0.477813	0.238906	−	0.971043i	$-0.423211\pi$
$811$	5.88642e12	0.477813	0.238906	+	0.971043i	$0.423211\pi$
$812$	−1.20104e12	−0.0969519
$813$	7.20778e12	0.578621
$814$	−1.12003e13	−0.894166
$815$	2.85053e13	2.26317
$816$	1.83033e12	0.144518
$817$	−5.04107e12	−0.395843
$818$	2.53902e12	0.198279
$819$	1.01154e13	0.785610
$820$	−2.46170e12	−0.190140
$821$	−1.46987e13	−1.12911	−0.564553	−	0.825397i	$-0.690951\pi$
$821$	−1.46987e13	−1.12911	−0.564553	+	0.825397i	$0.690951\pi$
$822$	1.07787e12	0.0823463
$823$	−1.14020e13	−0.866330	−0.433165	−	0.901315i	$-0.642603\pi$
$823$	−1.14020e13	−0.866330	−0.433165	+	0.901315i	$0.642603\pi$
$824$	1.11587e13	0.843220
$825$	1.81849e13	1.36668
$826$	−1.57058e12	−0.117395
$827$	−6.43586e12	−0.478445	−0.239223	−	0.970965i	$-0.576893\pi$
$827$	−6.43586e12	−0.478445	−0.239223	+	0.970965i	$0.576893\pi$
$828$	−6.18023e12	−0.456949
$829$	8.65507e12	0.636466	0.318233	−	0.948013i	$-0.396911\pi$
$829$	8.65507e12	0.636466	0.318233	+	0.948013i	$0.396911\pi$
$830$	9.60883e12	0.702779
$831$	4.82513e12	0.350998
$832$	−6.44470e11	−0.0466281
$833$	−7.24107e12	−0.521075
$834$	−3.26450e12	−0.233652
$835$	−1.16116e13	−0.826611
$836$	−1.84935e13	−1.30945
$837$	−3.14146e12	−0.221242
$838$	9.35551e12	0.655344
$839$	−4.40978e12	−0.307248	−0.153624	−	0.988129i	$-0.549094\pi$
$839$	−4.40978e12	−0.307248	−0.153624	+	0.988129i	$0.549094\pi$
$840$	−5.53319e12	−0.383459
$841$	5.00246e11	0.0344828
$842$	−1.25400e12	−0.0859790
$843$	−4.73914e12	−0.323203
$844$	1.16742e13	0.791930
$845$	−2.62521e13	−1.77137
$846$	4.93519e11	0.0331236
$847$	8.27069e12	0.552162
$848$	−4.82069e12	−0.320131
$849$	2.33201e12	0.154044
$850$	−1.72284e13	−1.13204
$851$	−1.48310e13	−0.969365
$852$	2.01099e12	0.130747
$853$	−1.72411e13	−1.11505	−0.557524	−	0.830161i	$-0.688248\pi$
$853$	−1.72411e13	−1.11505	−0.557524	+	0.830161i	$0.688248\pi$
$854$	−6.11968e10	−0.00393703
$855$	3.15789e13	2.02092
$856$	−1.65632e13	−1.05442
$857$	−3.09577e12	−0.196045	−0.0980224	−	0.995184i	$-0.531252\pi$
$857$	−3.09577e12	−0.196045	−0.0980224	+	0.995184i	$0.531252\pi$
$858$	5.02996e12	0.316863
$859$	−4.24866e12	−0.266246	−0.133123	−	0.991100i	$-0.542501\pi$
$859$	−4.24866e12	−0.266246	−0.133123	+	0.991100i	$0.542501\pi$
$860$	−7.98492e12	−0.497768
$861$	−4.89604e11	−0.0303620
$862$	−1.36409e13	−0.841514
$863$	−2.14514e13	−1.31646	−0.658229	−	0.752818i	$-0.728694\pi$
$863$	−2.14514e13	−1.31646	−0.658229	+	0.752818i	$0.728694\pi$
$864$	1.14064e13	0.696365
$865$	−1.49833e13	−0.909985
$866$	1.34235e13	0.811028
$867$	−9.66165e11	−0.0580718
$868$	−2.79382e12	−0.167055
$869$	−1.04211e12	−0.0619902
$870$	1.01981e12	0.0603504
$871$	−3.79900e13	−2.23659
$872$	2.46278e13	1.44245
$873$	−2.60761e13	−1.51942
$874$	6.36391e12	0.368912
$875$	−3.76683e13	−2.17240
$876$	−2.90617e12	−0.166745
$877$	2.57017e13	1.46711	0.733557	−	0.679628i	$-0.237859\pi$
$877$	2.57017e13	1.46711	0.733557	+	0.679628i	$0.237859\pi$
$878$	1.97227e12	0.112006
$879$	−1.21376e10	−0.000685777 0
$880$	−1.97024e13	−1.10751
$881$	3.38112e13	1.89090	0.945451	−	0.325765i	$-0.105622\pi$
$881$	3.38112e13	1.89090	0.945451	+	0.325765i	$0.105622\pi$
$882$	−3.99229e12	−0.222133
$883$	1.81714e13	1.00593	0.502963	−	0.864308i	$-0.332243\pi$
$883$	1.81714e13	1.00593	0.502963	+	0.864308i	$0.332243\pi$
$884$	1.83374e13	1.00995
$885$	−5.13166e12	−0.281198
$886$	1.17043e13	0.638105
$887$	1.26898e13	0.688333	0.344167	−	0.938909i	$-0.388161\pi$
$887$	1.26898e13	0.688333	0.344167	+	0.938909i	$0.388161\pi$
$888$	8.13667e12	0.439125
$889$	1.19014e13	0.639059
$890$	1.91235e13	1.02168
$891$	1.54457e13	0.821028
$892$	−1.17109e13	−0.619365
$893$	1.95551e12	0.102903
$894$	−2.12560e12	−0.111292
$895$	−1.90994e13	−0.994986
$896$	1.25864e13	0.652402
$897$	6.66051e12	0.343512
$898$	−4.14141e12	−0.212523
$899$	1.16366e12	0.0594163
$900$	3.65513e13	1.85700
$901$	−1.37266e13	−0.693906
$902$	1.52224e12	0.0765689
$903$	−1.58811e12	−0.0794849
$904$	−8.06761e12	−0.401779
$905$	−1.88392e13	−0.933565
$906$	5.28705e12	0.260697
$907$	−2.37782e13	−1.16667	−0.583333	−	0.812233i	$-0.698252\pi$
$907$	−2.37782e13	−1.16667	−0.583333	+	0.812233i	$0.698252\pi$
$908$	2.23760e13	1.09244
$909$	1.86206e13	0.904599
$910$	−1.64988e13	−0.797563
$911$	−2.62430e13	−1.26235	−0.631175	−	0.775640i	$-0.717427\pi$
$911$	−2.62430e13	−1.26235	−0.631175	+	0.775640i	$0.717427\pi$
$912$	3.99858e12	0.191394
$913$	2.28641e13	1.08902
$914$	−1.34328e13	−0.636664
$915$	−1.99952e11	−0.00943040
$916$	−1.73180e13	−0.812770
$917$	2.70436e13	1.26300
$918$	6.20644e12	0.288436
$919$	1.56739e13	0.724865	0.362432	−	0.932010i	$-0.381946\pi$
$919$	1.56739e13	0.724865	0.362432	+	0.932010i	$0.381946\pi$
$920$	2.27801e13	1.04836
$921$	2.65695e12	0.121679
$922$	−1.68909e13	−0.769773
$923$	1.35509e13	0.614556
$924$	−5.82607e12	−0.262937
$925$	8.77139e13	3.93941
$926$	7.64739e12	0.341794
$927$	−2.00628e13	−0.892344
$928$	−4.22515e12	−0.187015
$929$	−9.25096e12	−0.407489	−0.203745	−	0.979024i	$-0.565311\pi$
$929$	−9.25096e12	−0.407489	−0.203745	+	0.979024i	$0.565311\pi$
$930$	2.37223e12	0.103988
$931$	−1.58190e13	−0.690090
$932$	1.03878e13	0.450973
$933$	−1.19936e13	−0.518181
$934$	6.47977e12	0.278611
$935$	−5.61011e13	−2.40060
$936$	2.28476e13	0.972970
$937$	−1.73230e13	−0.734169	−0.367084	−	0.930188i	$-0.619644\pi$
$937$	−1.73230e13	−0.734169	−0.367084	+	0.930188i	$0.619644\pi$
$938$	−1.14352e13	−0.482313
$939$	−9.14870e12	−0.384029
$940$	3.09748e12	0.129400
$941$	−8.53838e12	−0.354995	−0.177498	−	0.984121i	$-0.556800\pi$
$941$	−8.53838e12	−0.354995	−0.177498	+	0.984121i	$0.556800\pi$
$942$	2.46854e12	0.102144
$943$	2.01569e12	0.0830084
$944$	4.06277e12	0.166513
$945$	2.14879e13	0.876499
$946$	4.93761e12	0.200450
$947$	−4.58870e12	−0.185402	−0.0927011	−	0.995694i	$-0.529550\pi$
$947$	−4.58870e12	−0.185402	−0.0927011	+	0.995694i	$0.529550\pi$
$948$	3.35002e11	0.0134713
$949$	−1.95831e13	−0.783759
$950$	−3.76376e13	−1.49922
$951$	4.72375e12	0.187273
$952$	1.24737e13	0.492185
$953$	6.71852e11	0.0263849	0.0131925	−	0.999913i	$-0.495801\pi$
$953$	6.71852e11	0.0263849	0.0131925	+	0.999913i	$0.495801\pi$
$954$	−7.56801e12	−0.295811
$955$	7.81707e13	3.04109
$956$	1.30265e13	0.504390
$957$	2.42662e12	0.0935184
$958$	1.01201e13	0.388186
$959$	−8.41275e12	−0.321184
$960$	−6.33829e11	−0.0240853
$961$	−2.37328e13	−0.897621
$962$	2.42618e13	0.913345
$963$	2.97799e13	1.11585
$964$	−1.76294e13	−0.657494
$965$	−7.01023e12	−0.260231
$966$	2.00484e12	0.0740770
$967$	−1.96863e13	−0.724009	−0.362004	−	0.932176i	$-0.617907\pi$
$967$	−1.96863e13	−0.724009	−0.362004	+	0.932176i	$0.617907\pi$
$968$	1.86809e13	0.683846
$969$	1.13857e13	0.414860
$970$	4.25314e13	1.54254
$971$	2.70947e13	0.978133	0.489066	−	0.872247i	$-0.337338\pi$
$971$	2.70947e13	0.978133	0.489066	+	0.872247i	$0.337338\pi$
$972$	−2.02386e13	−0.727246
$973$	2.54793e13	0.911337
$974$	8.09118e11	0.0288069
$975$	−3.93918e13	−1.39600
$976$	1.58303e11	0.00558426
$977$	−3.64953e13	−1.28148	−0.640740	−	0.767758i	$-0.721372\pi$
$977$	−3.64953e13	−1.28148	−0.640740	+	0.767758i	$0.721372\pi$
$978$	5.66640e12	0.198053
$979$	4.55042e13	1.58318
$980$	−2.50569e13	−0.867780
$981$	−4.42796e13	−1.52649
$982$	−2.50436e13	−0.859398
$983$	−3.01528e13	−1.03000	−0.515000	−	0.857190i	$-0.672208\pi$
$983$	−3.01528e13	−1.03000	−0.515000	+	0.857190i	$0.672208\pi$
$984$	−1.10586e12	−0.0376030
$985$	−1.70028e13	−0.575516
$986$	−2.29898e12	−0.0774621
$987$	6.16052e11	0.0206629
$988$	4.00602e13	1.33754
$989$	6.53821e12	0.217308
$990$	−3.09308e13	−1.02337
$991$	2.96732e13	0.977312	0.488656	−	0.872476i	$-0.337487\pi$
$991$	2.96732e13	0.977312	0.488656	+	0.872476i	$0.337487\pi$
$992$	−9.82839e12	−0.322240
$993$	1.20323e13	0.392716
$994$	4.07889e12	0.132527
$995$	6.52612e13	2.11082
$996$	−7.35003e12	−0.236659
$997$	−5.09963e13	−1.63460	−0.817299	−	0.576214i	$-0.804529\pi$
$997$	−5.09963e13	−1.63460	−0.817299	+	0.576214i	$0.804529\pi$
$998$	3.94603e12	0.125914
$999$	−3.15984e13	−1.00374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.b.1.5	✓	12
3.2	odd	2		261.10.a.e.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.b.1.5	✓	12	1.1	even	1	trivial
261.10.a.e.1.8		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)

\(f(q)\)	\(=\)	\(q-10.2767 q^{2} +52.0955 q^{3} -406.390 q^{4} -2693.22 q^{5} -535.369 q^{6} +4178.53 q^{7} +9437.99 q^{8} -16969.1 q^{9} +O(q^{10})\)	\(q-10.2767 q^{2} +52.0955 q^{3} -406.390 q^{4} -2693.22 q^{5} -535.369 q^{6} +4178.53 q^{7} +9437.99 q^{8} -16969.1 q^{9} +27677.4 q^{10} +65858.0 q^{11} -21171.1 q^{12} -142660. q^{13} -42941.4 q^{14} -140305. q^{15} +111080. q^{16} +316294. q^{17} +174385. q^{18} +690983. q^{19} +1.09450e6 q^{20} +217683. q^{21} -676801. q^{22} -896198. q^{23} +491677. q^{24} +5.30032e6 q^{25} +1.46607e6 q^{26} -1.90941e6 q^{27} -1.69811e6 q^{28} +707281. q^{29} +1.44187e6 q^{30} +1.64525e6 q^{31} -5.97379e6 q^{32} +3.43091e6 q^{33} -3.25045e6 q^{34} -1.12537e7 q^{35} +6.89605e6 q^{36} +1.65488e7 q^{37} -7.10101e6 q^{38} -7.43196e6 q^{39} -2.54186e7 q^{40} -2.24916e6 q^{41} -2.23706e6 q^{42} -7.29550e6 q^{43} -2.67640e7 q^{44} +4.57014e7 q^{45} +9.20993e6 q^{46} +2.83005e6 q^{47} +5.78679e6 q^{48} -2.28935e7 q^{49} -5.44696e7 q^{50} +1.64775e7 q^{51} +5.79757e7 q^{52} -4.33982e7 q^{53} +1.96224e7 q^{54} -1.77370e8 q^{55} +3.94370e7 q^{56} +3.59971e7 q^{57} -7.26850e6 q^{58} +3.65751e7 q^{59} +5.70185e7 q^{60} +1.42512e6 q^{61} -1.69077e7 q^{62} -7.09057e7 q^{63} +4.51751e6 q^{64} +3.84216e8 q^{65} -3.52583e7 q^{66} +2.66297e8 q^{67} -1.28539e8 q^{68} -4.66879e7 q^{69} +1.15651e8 q^{70} -9.49874e7 q^{71} -1.60154e8 q^{72} +1.37271e8 q^{73} -1.70067e8 q^{74} +2.76123e8 q^{75} -2.80808e8 q^{76} +2.75190e8 q^{77} +7.63759e7 q^{78} -1.58235e7 q^{79} -2.99164e8 q^{80} +2.34530e8 q^{81} +2.31139e7 q^{82} +3.47173e8 q^{83} -8.84641e7 q^{84} -8.51850e8 q^{85} +7.49735e7 q^{86} +3.68462e7 q^{87} +6.21568e8 q^{88} +6.90945e8 q^{89} -4.69659e8 q^{90} -5.96111e8 q^{91} +3.64206e8 q^{92} +8.57103e7 q^{93} -2.90835e7 q^{94} -1.86097e9 q^{95} -3.11208e8 q^{96} +1.53669e9 q^{97} +2.35269e8 q^{98} -1.11755e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) \) 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

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