LMFDB - Embedded newform 29.10.a.b.1.10

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			1.10
Root			$29.2132$ 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)

$f(q)$	$=$	$q+30.2132 q^{2} +241.333 q^{3} +400.835 q^{4} -389.202 q^{5} +7291.44 q^{6} +3096.10 q^{7} -3358.64 q^{8} +38558.7 q^{9} +O(q^{10})$	\(q+30.2132 q^{2} +241.333 q^{3} +400.835 q^{4} -389.202 q^{5} +7291.44 q^{6} +3096.10 q^{7} -3358.64 q^{8} +38558.7 q^{9} -11759.0 q^{10} +84724.8 q^{11} +96734.8 q^{12} -133830. q^{13} +93543.0 q^{14} -93927.4 q^{15} -306703. q^{16} +109750. q^{17} +1.16498e6 q^{18} -808289. q^{19} -156006. q^{20} +747192. q^{21} +2.55981e6 q^{22} +658181. q^{23} -810551. q^{24} -1.80165e6 q^{25} -4.04342e6 q^{26} +4.55533e6 q^{27} +1.24103e6 q^{28} +707281. q^{29} -2.83784e6 q^{30} +3.58131e6 q^{31} -7.54684e6 q^{32} +2.04469e7 q^{33} +3.31589e6 q^{34} -1.20501e6 q^{35} +1.54557e7 q^{36} -1.30043e7 q^{37} -2.44210e7 q^{38} -3.22976e7 q^{39} +1.30719e6 q^{40} +7.36654e6 q^{41} +2.25750e7 q^{42} -4.64416e6 q^{43} +3.39607e7 q^{44} -1.50071e7 q^{45} +1.98857e7 q^{46} -3.04304e7 q^{47} -7.40176e7 q^{48} -3.07678e7 q^{49} -5.44334e7 q^{50} +2.64863e7 q^{51} -5.36437e7 q^{52} -2.29856e7 q^{53} +1.37631e8 q^{54} -3.29751e7 q^{55} -1.03987e7 q^{56} -1.95067e8 q^{57} +2.13692e7 q^{58} +9.73089e7 q^{59} -3.76494e7 q^{60} +9.36027e7 q^{61} +1.08203e8 q^{62} +1.19382e8 q^{63} -7.09820e7 q^{64} +5.20868e7 q^{65} +6.17766e8 q^{66} -1.23820e7 q^{67} +4.39916e7 q^{68} +1.58841e8 q^{69} -3.64071e7 q^{70} +2.07833e8 q^{71} -1.29505e8 q^{72} +4.56510e8 q^{73} -3.92902e8 q^{74} -4.34797e8 q^{75} -3.23991e8 q^{76} +2.62317e8 q^{77} -9.75812e8 q^{78} -3.33877e8 q^{79} +1.19369e8 q^{80} +3.40402e8 q^{81} +2.22566e8 q^{82} -7.19986e8 q^{83} +2.99501e8 q^{84} -4.27148e7 q^{85} -1.40315e8 q^{86} +1.70690e8 q^{87} -2.84560e8 q^{88} +9.04939e8 q^{89} -4.53413e8 q^{90} -4.14350e8 q^{91} +2.63822e8 q^{92} +8.64290e8 q^{93} -9.19398e8 q^{94} +3.14588e8 q^{95} -1.82130e9 q^{96} +6.30607e8 q^{97} -9.29592e8 q^{98} +3.26688e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	30.2132	1.33525	0.667623	−	0.744500i	$-0.267312\pi$
$2$	30.2132	1.33525	0.667623	+	0.744500i	$0.267312\pi$
$3$	241.333	1.72017	0.860085	−	0.510151i	$-0.170410\pi$
$3$	241.333	1.72017	0.860085	+	0.510151i	$0.170410\pi$
$4$	400.835	0.782881
$5$	−389.202	−0.278490	−0.139245	−	0.990258i	$-0.544468\pi$
$5$	−389.202	−0.278490	−0.139245	+	0.990258i	$0.544468\pi$
$6$	7291.44	2.29685
$7$	3096.10	0.487387	0.243693	−	0.969852i	$-0.421641\pi$
$7$	3096.10	0.487387	0.243693	+	0.969852i	$0.421641\pi$
$8$	−3358.64	−0.289907
$9$	38558.7	1.95899
$10$	−11759.0	−0.371853
$11$	84724.8	1.74479	0.872396	−	0.488800i	$-0.162565\pi$
$11$	84724.8	1.74479	0.872396	+	0.488800i	$0.162565\pi$
$12$	96734.8	1.34669
$13$	−133830.	−1.29959	−0.649797	−	0.760108i	$-0.725146\pi$
$13$	−133830.	−1.29959	−0.649797	+	0.760108i	$0.725146\pi$
$14$	93543.0	0.650781
$15$	−93927.4	−0.479051
$16$	−306703.	−1.16998
$17$	109750.	0.318701	0.159351	−	0.987222i	$-0.449060\pi$
$17$	109750.	0.318701	0.159351	+	0.987222i	$0.449060\pi$
$18$	1.16498e6	2.61573
$19$	−808289.	−1.42290	−0.711452	−	0.702735i	$-0.751962\pi$
$19$	−808289.	−1.42290	−0.711452	+	0.702735i	$0.751962\pi$
$20$	−156006.	−0.218025
$21$	747192.	0.838388
$22$	2.55981e6	2.32973
$23$	658181.	0.490422	0.245211	−	0.969470i	$-0.421143\pi$
$23$	658181.	0.490422	0.245211	+	0.969470i	$0.421143\pi$
$24$	−810551.	−0.498689
$25$	−1.80165e6	−0.922443
$26$	−4.04342e6	−1.73528
$27$	4.55533e6	1.64962
$28$	1.24103e6	0.381566
$29$	707281.	0.185695
$29$	707281.	0.185695
$30$	−2.83784e6	−0.639650
$31$	3.58131e6	0.696490	0.348245	−	0.937404i	$-0.386778\pi$
$31$	3.58131e6	0.696490	0.348245	+	0.937404i	$0.386778\pi$
$32$	−7.54684e6	−1.27230
$33$	2.04469e7	3.00134
$34$	3.31589e6	0.425544
$35$	−1.20501e6	−0.135732
$36$	1.54557e7	1.53365
$37$	−1.30043e7	−1.14072	−0.570362	−	0.821393i	$-0.693197\pi$
$37$	−1.30043e7	−1.14072	−0.570362	+	0.821393i	$0.693197\pi$
$38$	−2.44210e7	−1.89993
$39$	−3.22976e7	−2.23552
$40$	1.30719e6	0.0807362
$41$	7.36654e6	0.407133	0.203566	−	0.979061i	$-0.434747\pi$
$41$	7.36654e6	0.407133	0.203566	+	0.979061i	$0.434747\pi$
$42$	2.25750e7	1.11945
$43$	−4.64416e6	−0.207157	−0.103578	−	0.994621i	$-0.533029\pi$
$43$	−4.64416e6	−0.207157	−0.103578	+	0.994621i	$0.533029\pi$
$44$	3.39607e7	1.36597
$45$	−1.50071e7	−0.545558
$46$	1.98857e7	0.654834
$47$	−3.04304e7	−0.909635	−0.454817	−	0.890585i	$-0.650295\pi$
$47$	−3.04304e7	−0.909635	−0.454817	+	0.890585i	$0.650295\pi$
$48$	−7.40176e7	−2.01256
$49$	−3.07678e7	−0.762454
$50$	−5.44334e7	−1.23169
$51$	2.64863e7	0.548220
$52$	−5.36437e7	−1.01743
$53$	−2.29856e7	−0.400143	−0.200072	−	0.979781i	$-0.564117\pi$
$53$	−2.29856e7	−0.400143	−0.200072	+	0.979781i	$0.564117\pi$
$54$	1.37631e8	2.20265
$55$	−3.29751e7	−0.485908
$56$	−1.03987e7	−0.141297
$57$	−1.95067e8	−2.44764
$58$	2.13692e7	0.247949
$59$	9.73089e7	1.04549	0.522743	−	0.852490i	$-0.324909\pi$
$59$	9.73089e7	1.04549	0.522743	+	0.852490i	$0.324909\pi$
$60$	−3.76494e7	−0.375040
$61$	9.36027e7	0.865574	0.432787	−	0.901496i	$-0.357530\pi$
$61$	9.36027e7	0.865574	0.432787	+	0.901496i	$0.357530\pi$
$62$	1.08203e8	0.929985
$63$	1.19382e8	0.954783
$64$	−7.09820e7	−0.528857
$65$	5.20868e7	0.361924
$66$	6.17766e8	4.00753
$67$	−1.23820e7	−0.0750678	−0.0375339	−	0.999295i	$-0.511950\pi$
$67$	−1.23820e7	−0.0750678	−0.0375339	+	0.999295i	$0.511950\pi$
$68$	4.39916e7	0.249505
$69$	1.58841e8	0.843610
$70$	−3.64071e7	−0.181236
$71$	2.07833e8	0.970626	0.485313	−	0.874341i	$-0.338706\pi$
$71$	2.07833e8	0.970626	0.485313	+	0.874341i	$0.338706\pi$
$72$	−1.29505e8	−0.567923
$73$	4.56510e8	1.88147	0.940735	−	0.339143i	$-0.110137\pi$
$73$	4.56510e8	1.88147	0.940735	+	0.339143i	$0.110137\pi$
$74$	−3.92902e8	−1.52315
$75$	−4.34797e8	−1.58676
$76$	−3.23991e8	−1.11396
$77$	2.62317e8	0.850389
$78$	−9.75812e8	−2.98497
$79$	−3.33877e8	−0.964418	−0.482209	−	0.876056i	$-0.660165\pi$
$79$	−3.33877e8	−0.964418	−0.482209	+	0.876056i	$0.660165\pi$
$80$	1.19369e8	0.325828
$81$	3.40402e8	0.878638
$82$	2.22566e8	0.543622
$83$	−7.19986e8	−1.66522	−0.832612	−	0.553856i	$-0.813156\pi$
$83$	−7.19986e8	−1.66522	−0.832612	+	0.553856i	$0.813156\pi$
$84$	2.99501e8	0.656358
$85$	−4.27148e7	−0.0887551
$86$	−1.40315e8	−0.276605
$87$	1.70690e8	0.319428
$88$	−2.84560e8	−0.505827
$89$	9.04939e8	1.52885	0.764424	−	0.644714i	$-0.223024\pi$
$89$	9.04939e8	1.52885	0.764424	+	0.644714i	$0.223024\pi$
$90$	−4.53413e8	−0.728454
$91$	−4.14350e8	−0.633405
$92$	2.63822e8	0.383942
$93$	8.64290e8	1.19808
$94$	−9.19398e8	−1.21459
$95$	3.14588e8	0.396265
$96$	−1.82130e9	−2.18858
$97$	6.30607e8	0.723245	0.361623	−	0.932325i	$-0.382223\pi$
$97$	6.30607e8	0.723245	0.361623	+	0.932325i	$0.382223\pi$
$98$	−9.29592e8	−1.01806
$99$	3.26688e9	3.41802
$100$	−7.22164e8	−0.722164
$101$	1.19020e9	1.13808	0.569040	−	0.822310i	$-0.307315\pi$
$101$	1.19020e9	1.13808	0.569040	+	0.822310i	$0.307315\pi$
$102$	8.00234e8	0.732009
$103$	−2.14210e9	−1.87530	−0.937651	−	0.347577i	$-0.887004\pi$
$103$	−2.14210e9	−1.87530	−0.937651	+	0.347577i	$0.887004\pi$
$104$	4.49486e8	0.376761
$105$	−2.90808e8	−0.233483
$106$	−6.94469e8	−0.534289
$107$	1.90153e9	1.40241	0.701205	−	0.712959i	$-0.252646\pi$
$107$	1.90153e9	1.40241	0.701205	+	0.712959i	$0.252646\pi$
$108$	1.82594e9	1.29145
$109$	6.70727e8	0.455121	0.227560	−	0.973764i	$-0.426925\pi$
$109$	6.70727e8	0.455121	0.227560	+	0.973764i	$0.426925\pi$
$110$	−9.96281e8	−0.648806
$111$	−3.13838e9	−1.96224
$112$	−9.49582e8	−0.570232
$113$	−3.14760e8	−0.181605	−0.0908023	−	0.995869i	$-0.528943\pi$
$113$	−3.14760e8	−0.181605	−0.0908023	+	0.995869i	$0.528943\pi$
$114$	−5.89359e9	−3.26820
$115$	−2.56165e8	−0.136578
$116$	2.83503e8	0.145377
$117$	−5.16030e9	−2.54588
$118$	2.94001e9	1.39598
$119$	3.39796e8	0.155331
$120$	3.15468e8	0.138880
$121$	4.82035e9	2.04430
$122$	2.82804e9	1.15575
$123$	1.77779e9	0.700337
$124$	1.43552e9	0.545269
$125$	1.46136e9	0.535382
$126$	3.60690e9	1.27487
$127$	−4.08792e9	−1.39439	−0.697197	−	0.716880i	$-0.745570\pi$
$127$	−4.08792e9	−1.39439	−0.697197	+	0.716880i	$0.745570\pi$
$128$	1.71939e9	0.566147
$129$	−1.12079e9	−0.356345
$130$	1.57371e9	0.483258
$131$	3.65405e8	0.108406	0.0542031	−	0.998530i	$-0.482738\pi$
$131$	3.65405e8	0.108406	0.0542031	+	0.998530i	$0.482738\pi$
$132$	8.19584e9	2.34969
$133$	−2.50254e9	−0.693504
$134$	−3.74099e8	−0.100234
$135$	−1.77295e9	−0.459403
$136$	−3.68610e8	−0.0923936
$137$	3.18191e8	0.0771695	0.0385848	−	0.999255i	$-0.487715\pi$
$137$	3.18191e8	0.0771695	0.0385848	+	0.999255i	$0.487715\pi$
$138$	4.79909e9	1.12643
$139$	8.51901e9	1.93563	0.967815	−	0.251662i	$-0.0809772\pi$
$139$	8.51901e9	1.93563	0.967815	+	0.251662i	$0.0809772\pi$
$140$	−4.83010e8	−0.106262
$141$	−7.34386e9	−1.56473
$142$	6.27929e9	1.29602
$143$	−1.13387e10	−2.26752
$144$	−1.18261e10	−2.29197
$145$	−2.75275e8	−0.0517143
$146$	1.37926e10	2.51222
$147$	−7.42529e9	−1.31155
$148$	−5.21260e9	−0.893051
$149$	1.06374e9	0.176807	0.0884034	−	0.996085i	$-0.471824\pi$
$149$	1.06374e9	0.176807	0.0884034	+	0.996085i	$0.471824\pi$
$150$	−1.31366e10	−2.11871
$151$	5.72012e9	0.895383	0.447692	−	0.894188i	$-0.352246\pi$
$151$	5.72012e9	0.895383	0.447692	+	0.894188i	$0.352246\pi$
$152$	2.71475e9	0.412509
$153$	4.23181e9	0.624331
$154$	7.92541e9	1.13548
$155$	−1.39385e9	−0.193966
$156$	−1.29460e10	−1.75015
$157$	8.65408e9	1.13677	0.568385	−	0.822763i	$-0.307568\pi$
$157$	8.65408e9	1.13677	0.568385	+	0.822763i	$0.307568\pi$
$158$	−1.00875e10	−1.28773
$159$	−5.54720e9	−0.688314
$160$	2.93724e9	0.354324
$161$	2.03779e9	0.239025
$162$	1.02846e10	1.17320
$163$	1.67933e10	1.86334	0.931671	−	0.363304i	$-0.118351\pi$
$163$	1.67933e10	1.86334	0.931671	+	0.363304i	$0.118351\pi$
$164$	2.95277e9	0.318737
$165$	−7.95798e9	−0.835844
$166$	−2.17531e10	−2.22348
$167$	−1.27390e10	−1.26739	−0.633694	−	0.773584i	$-0.718462\pi$
$167$	−1.27390e10	−1.26739	−0.633694	+	0.773584i	$0.718462\pi$
$168$	−2.50955e9	−0.243054
$169$	7.30590e9	0.688944
$170$	−1.29055e9	−0.118510
$171$	−3.11666e10	−2.78745
$172$	−1.86154e9	−0.162179
$173$	5.78390e9	0.490923	0.245462	−	0.969406i	$-0.421060\pi$
$173$	5.78390e9	0.490923	0.245462	+	0.969406i	$0.421060\pi$
$174$	5.15710e9	0.426514
$175$	−5.57808e9	−0.449587
$176$	−2.59853e10	−2.04137
$177$	2.34839e10	1.79841
$178$	2.73411e10	2.04139
$179$	−1.27981e9	−0.0931763	−0.0465881	−	0.998914i	$-0.514835\pi$
$179$	−1.27981e9	−0.0931763	−0.0465881	+	0.998914i	$0.514835\pi$
$180$	−6.01538e9	−0.427107
$181$	−7.08541e9	−0.490695	−0.245347	−	0.969435i	$-0.578902\pi$
$181$	−7.08541e9	−0.490695	−0.245347	+	0.969435i	$0.578902\pi$
$182$	−1.25188e10	−0.845751
$183$	2.25894e10	1.48893
$184$	−2.21059e9	−0.142177
$185$	5.06131e9	0.317681
$186$	2.61129e10	1.59973
$187$	9.29853e9	0.556067
$188$	−1.21976e10	−0.712136
$189$	1.41038e10	0.804002
$190$	9.50469e9	0.529111
$191$	4.40676e8	0.0239590	0.0119795	−	0.999928i	$-0.496187\pi$
$191$	4.40676e8	0.0239590	0.0119795	+	0.999928i	$0.496187\pi$
$192$	−1.71303e10	−0.909724
$193$	−3.34830e10	−1.73707	−0.868534	−	0.495630i	$-0.834937\pi$
$193$	−3.34830e10	−1.73707	−0.868534	+	0.495630i	$0.834937\pi$
$194$	1.90526e10	0.965710
$195$	1.25703e10	0.622571
$196$	−1.23328e10	−0.596911
$197$	−3.05990e10	−1.44747	−0.723735	−	0.690078i	$-0.757576\pi$
$197$	−3.05990e10	−1.44747	−0.723735	+	0.690078i	$0.757576\pi$
$198$	9.87028e10	4.56390
$199$	−1.70193e9	−0.0769311	−0.0384656	−	0.999260i	$-0.512247\pi$
$199$	−1.70193e9	−0.0769311	−0.0384656	+	0.999260i	$0.512247\pi$
$200$	6.05108e9	0.267423
$201$	−2.98818e9	−0.129129
$202$	3.59596e10	1.51962
$203$	2.18981e9	0.0905054
$204$	1.06166e10	0.429191
$205$	−2.86707e9	−0.113382
$206$	−6.47195e10	−2.50399
$207$	2.53786e10	0.960730
$208$	4.10460e10	1.52050
$209$	−6.84821e10	−2.48267
$210$	−8.78624e9	−0.311757
$211$	−3.18947e10	−1.10777	−0.553883	−	0.832595i	$-0.686855\pi$
$211$	−3.18947e10	−1.10777	−0.553883	+	0.832595i	$0.686855\pi$
$212$	−9.21346e9	−0.313265
$213$	5.01570e10	1.66964
$214$	5.74511e10	1.87256
$215$	1.80752e9	0.0576911
$216$	−1.52997e10	−0.478235
$217$	1.10881e10	0.339460
$218$	2.02648e10	0.607698
$219$	1.10171e11	3.23645
$220$	−1.32176e10	−0.380408
$221$	−1.46878e10	−0.414182
$222$	−9.48203e10	−2.62007
$223$	−3.96950e9	−0.107489	−0.0537444	−	0.998555i	$-0.517116\pi$
$223$	−3.96950e9	−0.107489	−0.0537444	+	0.998555i	$0.517116\pi$
$224$	−2.33658e10	−0.620103
$225$	−6.94692e10	−1.80705
$226$	−9.50990e9	−0.242487
$227$	−8.67347e9	−0.216809	−0.108404	−	0.994107i	$-0.534574\pi$
$227$	−8.67347e9	−0.216809	−0.108404	+	0.994107i	$0.534574\pi$
$228$	−7.81897e10	−1.91621
$229$	−5.00356e10	−1.20232	−0.601159	−	0.799129i	$-0.705294\pi$
$229$	−5.00356e10	−1.20232	−0.601159	+	0.799129i	$0.705294\pi$
$230$	−7.73957e9	−0.182365
$231$	6.33057e10	1.46281
$232$	−2.37550e9	−0.0538343
$233$	−9.48039e9	−0.210729	−0.105365	−	0.994434i	$-0.533601\pi$
$233$	−9.48039e9	−0.210729	−0.105365	+	0.994434i	$0.533601\pi$
$234$	−1.55909e11	−3.39938
$235$	1.18436e10	0.253324
$236$	3.90048e10	0.818492
$237$	−8.05757e10	−1.65896
$238$	1.02663e10	0.207405
$239$	−4.77201e10	−0.946042	−0.473021	−	0.881051i	$-0.656837\pi$
$239$	−4.77201e10	−0.946042	−0.473021	+	0.881051i	$0.656837\pi$
$240$	2.88078e10	0.560479
$241$	−4.29245e8	−0.00819650	−0.00409825	−	0.999992i	$-0.501305\pi$
$241$	−4.29245e8	−0.00819650	−0.00409825	+	0.999992i	$0.501305\pi$
$242$	1.45638e11	2.72964
$243$	−7.51226e9	−0.138211
$244$	3.75193e10	0.677642
$245$	1.19749e10	0.212336
$246$	5.37126e10	0.935123
$247$	1.08173e11	1.84920
$248$	−1.20283e10	−0.201917
$249$	−1.73757e11	−2.86447
$250$	4.41524e10	0.714866
$251$	7.97428e10	1.26812	0.634059	−	0.773285i	$-0.281388\pi$
$251$	7.97428e10	1.26812	0.634059	+	0.773285i	$0.281388\pi$
$252$	4.78523e10	0.747482
$253$	5.57643e10	0.855685
$254$	−1.23509e11	−1.86186
$255$	−1.03085e10	−0.152674
$256$	8.82910e10	1.28480
$257$	5.58224e10	0.798195	0.399098	−	0.916908i	$-0.369323\pi$
$257$	5.58224e10	0.798195	0.399098	+	0.916908i	$0.369323\pi$
$258$	−3.38626e10	−0.475808
$259$	−4.02627e10	−0.555974
$260$	2.08782e10	0.283344
$261$	2.72718e10	0.363774
$262$	1.10401e10	0.144749
$263$	−1.09064e11	−1.40565	−0.702827	−	0.711361i	$-0.748079\pi$
$263$	−1.09064e11	−1.40565	−0.702827	+	0.711361i	$0.748079\pi$
$264$	−6.86738e10	−0.870109
$265$	8.94606e9	0.111436
$266$	−7.56097e10	−0.925999
$267$	2.18392e11	2.62988
$268$	−4.96313e9	−0.0587692
$269$	1.80299e10	0.209946	0.104973	−	0.994475i	$-0.466524\pi$
$269$	1.80299e10	0.209946	0.104973	+	0.994475i	$0.466524\pi$
$270$	−5.35663e10	−0.613415
$271$	−3.29703e10	−0.371331	−0.185666	−	0.982613i	$-0.559444\pi$
$271$	−3.29703e10	−0.371331	−0.185666	+	0.982613i	$0.559444\pi$
$272$	−3.36606e10	−0.372873
$273$	−9.99965e10	−1.08956
$274$	9.61357e9	0.103040
$275$	−1.52644e11	−1.60947
$276$	6.36690e10	0.660446
$277$	1.59065e11	1.62336	0.811679	−	0.584103i	$-0.198554\pi$
$277$	1.59065e11	1.62336	0.811679	+	0.584103i	$0.198554\pi$
$278$	2.57386e11	2.58454
$279$	1.38091e11	1.36441
$280$	4.04719e9	0.0393498
$281$	1.31498e11	1.25817	0.629086	−	0.777336i	$-0.283429\pi$
$281$	1.31498e11	1.25817	0.629086	+	0.777336i	$0.283429\pi$
$282$	−2.21881e11	−2.08929
$283$	−3.39703e10	−0.314819	−0.157410	−	0.987533i	$-0.550314\pi$
$283$	−3.39703e10	−0.314819	−0.157410	+	0.987533i	$0.550314\pi$
$284$	8.33068e10	0.759885
$285$	7.59204e10	0.681643
$286$	−3.42578e11	−3.02770
$287$	2.28075e10	0.198431
$288$	−2.90996e11	−2.49242
$289$	−1.06543e11	−0.898430
$290$	−8.31693e9	−0.0690514
$291$	1.52186e11	1.24411
$292$	1.82985e11	1.47297
$293$	−1.54483e11	−1.22455	−0.612277	−	0.790644i	$-0.709746\pi$
$293$	−1.54483e11	−1.22455	−0.612277	+	0.790644i	$0.709746\pi$
$294$	−2.24341e11	−1.75124
$295$	−3.78728e10	−0.291158
$296$	4.36769e10	0.330704
$297$	3.85950e11	2.87824
$298$	3.21391e10	0.236080
$299$	−8.80842e10	−0.637350
$300$	−1.74282e11	−1.24224
$301$	−1.43788e10	−0.100965
$302$	1.72823e11	1.19556
$303$	2.87234e11	1.95769
$304$	2.47904e11	1.66477
$305$	−3.64304e10	−0.241054
$306$	1.27856e11	0.833635
$307$	−1.29947e11	−0.834920	−0.417460	−	0.908695i	$-0.637080\pi$
$307$	−1.29947e11	−0.834920	−0.417460	+	0.908695i	$0.637080\pi$
$308$	1.05146e11	0.665753
$309$	−5.16959e11	−3.22584
$310$	−4.21128e10	−0.258992
$311$	1.88586e11	1.14311	0.571554	−	0.820564i	$-0.306341\pi$
$311$	1.88586e11	1.14311	0.571554	+	0.820564i	$0.306341\pi$
$312$	1.08476e11	0.648093
$313$	2.64175e10	0.155576	0.0777878	−	0.996970i	$-0.475214\pi$
$313$	2.64175e10	0.155576	0.0777878	+	0.996970i	$0.475214\pi$
$314$	2.61467e11	1.51787
$315$	−4.64636e10	−0.265898
$316$	−1.33830e11	−0.755025
$317$	−2.78105e11	−1.54683	−0.773415	−	0.633900i	$-0.781453\pi$
$317$	−2.78105e11	−1.54683	−0.773415	+	0.633900i	$0.781453\pi$
$318$	−1.67598e11	−0.919069
$319$	5.99243e10	0.324000
$320$	2.76263e10	0.147282
$321$	4.58901e11	2.41239
$322$	6.15682e10	0.319157
$323$	−8.87095e10	−0.453481
$324$	1.36445e11	0.687869
$325$	2.41114e11	1.19880
$326$	5.07379e11	2.48802
$327$	1.61869e11	0.782885
$328$	−2.47415e10	−0.118031
$329$	−9.42155e10	−0.443344
$330$	−2.40436e11	−1.11606
$331$	1.07164e11	0.490709	0.245355	−	0.969433i	$-0.421096\pi$
$331$	1.07164e11	0.490709	0.245355	+	0.969433i	$0.421096\pi$
$332$	−2.88596e11	−1.30367
$333$	−5.01431e11	−2.23466
$334$	−3.84884e11	−1.69227
$335$	4.81909e9	0.0209056
$336$	−2.29166e11	−0.980896
$337$	−3.40814e11	−1.43940	−0.719702	−	0.694283i	$-0.755722\pi$
$337$	−3.40814e11	−1.43940	−0.719702	+	0.694283i	$0.755722\pi$
$338$	2.20734e11	0.919909
$339$	−7.59621e10	−0.312391
$340$	−1.71216e10	−0.0694847
$341$	3.03426e11	1.21523
$342$	−9.41641e11	−3.72193
$343$	−2.20199e11	−0.858997
$344$	1.55981e10	0.0600561
$345$	−6.18212e10	−0.234937
$346$	1.74750e11	0.655503
$347$	−1.19858e11	−0.443797	−0.221898	−	0.975070i	$-0.571225\pi$
$347$	−1.19858e11	−0.443797	−0.221898	+	0.975070i	$0.571225\pi$
$348$	6.84187e10	0.250074
$349$	−4.96247e11	−1.79054	−0.895269	−	0.445525i	$-0.853017\pi$
$349$	−4.96247e11	−1.79054	−0.895269	+	0.445525i	$0.853017\pi$
$350$	−1.68531e11	−0.600309
$351$	−6.09639e11	−2.14383
$352$	−6.39405e11	−2.21990
$353$	8.50042e10	0.291376	0.145688	−	0.989331i	$-0.453460\pi$
$353$	8.50042e10	0.291376	0.145688	+	0.989331i	$0.453460\pi$
$354$	7.09522e11	2.40133
$355$	−8.08890e10	−0.270310
$356$	3.62731e11	1.19691
$357$	8.20041e10	0.267195
$358$	−3.86670e10	−0.124413
$359$	6.38356e10	0.202833	0.101416	−	0.994844i	$-0.467663\pi$
$359$	6.38356e10	0.202833	0.101416	+	0.994844i	$0.467663\pi$
$360$	5.04035e10	0.158161
$361$	3.30643e11	1.02465
$362$	−2.14073e11	−0.655198
$363$	1.16331e12	3.51654
$364$	−1.66086e11	−0.495881
$365$	−1.77675e11	−0.523971
$366$	6.82499e11	1.98809
$367$	3.26692e11	0.940029	0.470014	−	0.882659i	$-0.344249\pi$
$367$	3.26692e11	0.940029	0.470014	+	0.882659i	$0.344249\pi$
$368$	−2.01866e11	−0.573783
$369$	2.84044e11	0.797567
$370$	1.52918e11	0.424182
$371$	−7.11658e10	−0.195024
$372$	3.46438e11	0.937955
$373$	2.14481e11	0.573719	0.286860	−	0.957973i	$-0.407389\pi$
$373$	2.14481e11	0.573719	0.286860	+	0.957973i	$0.407389\pi$
$374$	2.80938e11	0.742486
$375$	3.52676e11	0.920948
$376$	1.02205e11	0.263709
$377$	−9.46552e10	−0.241328
$378$	4.26119e11	1.07354
$379$	−2.90045e11	−0.722087	−0.361043	−	0.932549i	$-0.617579\pi$
$379$	−2.90045e11	−0.722087	−0.361043	+	0.932549i	$0.617579\pi$
$380$	1.26098e11	0.310228
$381$	−9.86550e11	−2.39859
$382$	1.33142e10	0.0319912
$383$	3.59850e11	0.854528	0.427264	−	0.904127i	$-0.359477\pi$
$383$	3.59850e11	0.854528	0.427264	+	0.904127i	$0.359477\pi$
$384$	4.14946e11	0.973870
$385$	−1.02094e11	−0.236825
$386$	−1.01163e12	−2.31941
$387$	−1.79073e11	−0.405817
$388$	2.52769e11	0.566215
$389$	4.51980e10	0.100080	0.0500399	−	0.998747i	$-0.484065\pi$
$389$	4.51980e10	0.100080	0.0500399	+	0.998747i	$0.484065\pi$
$390$	3.79788e11	0.831286
$391$	7.22352e10	0.156298
$392$	1.03338e11	0.221041
$393$	8.81845e10	0.186477
$394$	−9.24493e11	−1.93273
$395$	1.29946e11	0.268581
$396$	1.30948e12	2.67591
$397$	6.26989e11	1.26678	0.633392	−	0.773831i	$-0.281662\pi$
$397$	6.26989e11	1.26678	0.633392	+	0.773831i	$0.281662\pi$
$398$	−5.14206e10	−0.102722
$399$	−6.03947e11	−1.19295
$400$	5.52570e11	1.07924
$401$	−2.11724e11	−0.408903	−0.204452	−	0.978877i	$-0.565541\pi$
$401$	−2.11724e11	−0.408903	−0.204452	+	0.978877i	$0.565541\pi$
$402$	−9.02825e10	−0.172419
$403$	−4.79286e11	−0.905154
$404$	4.77073e11	0.890982
$405$	−1.32485e11	−0.244692
$406$	6.61612e10	0.120847
$407$	−1.10179e12	−1.99033
$408$	−8.89578e10	−0.158933
$409$	−4.69154e11	−0.829011	−0.414505	−	0.910047i	$-0.636045\pi$
$409$	−4.69154e11	−0.829011	−0.414505	+	0.910047i	$0.636045\pi$
$410$	−8.66233e10	−0.151394
$411$	7.67901e10	0.132745
$412$	−8.58627e11	−1.46814
$413$	3.01278e11	0.509556
$414$	7.66768e11	1.28281
$415$	2.80220e11	0.463749
$416$	1.00999e12	1.65348
$417$	2.05592e12	3.32961
$418$	−2.06906e12	−3.31498
$419$	−2.27531e11	−0.360643	−0.180322	−	0.983608i	$-0.557714\pi$
$419$	−2.27531e11	−0.360643	−0.180322	+	0.983608i	$0.557714\pi$
$420$	−1.16566e11	−0.182789
$421$	−1.18879e11	−0.184431	−0.0922156	−	0.995739i	$-0.529395\pi$
$421$	−1.18879e11	−0.184431	−0.0922156	+	0.995739i	$0.529395\pi$
$422$	−9.63641e11	−1.47914
$423$	−1.17336e12	−1.78196
$424$	7.72005e10	0.116004
$425$	−1.97730e11	−0.293984
$426$	1.51540e12	2.22938
$427$	2.89803e11	0.421869
$428$	7.62199e11	1.09792
$429$	−2.73641e12	−3.90052
$430$	5.46108e10	0.0770318
$431$	1.55102e11	0.216506	0.108253	−	0.994123i	$-0.465474\pi$
$431$	1.55102e11	0.216506	0.108253	+	0.994123i	$0.465474\pi$
$432$	−1.39713e12	−1.93002
$433$	−1.54737e11	−0.211543	−0.105771	−	0.994390i	$-0.533731\pi$
$433$	−1.54737e11	−0.211543	−0.105771	+	0.994390i	$0.533731\pi$
$434$	3.35007e11	0.453262
$435$	−6.64330e10	−0.0889575
$436$	2.68851e11	0.356306
$437$	−5.32000e11	−0.697823
$438$	3.32861e12	4.32145
$439$	1.07126e12	1.37659	0.688294	−	0.725432i	$-0.258360\pi$
$439$	1.07126e12	1.37659	0.688294	+	0.725432i	$0.258360\pi$
$440$	1.10751e11	0.140868
$441$	−1.18637e12	−1.49364
$442$	−4.43764e11	−0.553035
$443$	−1.38181e12	−1.70463	−0.852315	−	0.523028i	$-0.824802\pi$
$443$	−1.38181e12	−1.70463	−0.852315	+	0.523028i	$0.824802\pi$
$444$	−1.25797e12	−1.53620
$445$	−3.52204e11	−0.425769
$446$	−1.19931e11	−0.143524
$447$	2.56717e11	0.304138
$448$	−2.19767e11	−0.257758
$449$	9.89189e11	1.14861	0.574303	−	0.818643i	$-0.305273\pi$
$449$	9.89189e11	1.14861	0.574303	+	0.818643i	$0.305273\pi$
$450$	−2.09888e12	−2.41286
$451$	6.24129e11	0.710362
$452$	−1.26167e11	−0.142175
$453$	1.38046e12	1.54021
$454$	−2.62053e11	−0.289493
$455$	1.61266e11	0.176397
$456$	6.55159e11	0.709586
$457$	1.24933e12	1.33984	0.669921	−	0.742432i	$-0.266328\pi$
$457$	1.24933e12	1.33984	0.669921	+	0.742432i	$0.266328\pi$
$458$	−1.51173e12	−1.60539
$459$	4.99947e11	0.525735
$460$	−1.02680e11	−0.106924
$461$	−1.44175e12	−1.48674	−0.743370	−	0.668881i	$-0.766774\pi$
$461$	−1.44175e12	−1.48674	−0.743370	+	0.668881i	$0.766774\pi$
$462$	1.91266e12	1.95321
$463$	−2.10394e11	−0.212774	−0.106387	−	0.994325i	$-0.533928\pi$
$463$	−2.10394e11	−0.212774	−0.106387	+	0.994325i	$0.533928\pi$
$464$	−2.16925e11	−0.217259
$465$	−3.36383e11	−0.333654
$466$	−2.86433e11	−0.281375
$467$	6.37764e11	0.620489	0.310244	−	0.950657i	$-0.399589\pi$
$467$	6.37764e11	0.620489	0.310244	+	0.950657i	$0.399589\pi$
$468$	−2.06843e12	−1.99313
$469$	−3.83358e10	−0.0365870
$470$	3.57832e11	0.338250
$471$	2.08852e12	1.95544
$472$	−3.26825e11	−0.303094
$473$	−3.93476e11	−0.361445
$474$	−2.43445e12	−2.21512
$475$	1.45625e12	1.31255
$476$	1.36202e11	0.121605
$477$	−8.86297e11	−0.783874
$478$	−1.44177e12	−1.26320
$479$	−3.52297e11	−0.305773	−0.152887	−	0.988244i	$-0.548857\pi$
$479$	−3.52297e11	−0.305773	−0.152887	+	0.988244i	$0.548857\pi$
$480$	7.08854e11	0.609497
$481$	1.74037e12	1.48248
$482$	−1.29688e10	−0.0109443
$483$	4.91787e11	0.411164
$484$	1.93217e12	1.60044
$485$	−2.45433e11	−0.201417
$486$	−2.26969e11	−0.184546
$487$	7.39402e10	0.0595662	0.0297831	−	0.999556i	$-0.490518\pi$
$487$	7.39402e10	0.0595662	0.0297831	+	0.999556i	$0.490518\pi$
$488$	−3.14378e11	−0.250936
$489$	4.05279e12	3.20526
$490$	3.61799e11	0.283521
$491$	3.02110e11	0.234584	0.117292	−	0.993097i	$-0.462579\pi$
$491$	3.02110e11	0.234584	0.117292	+	0.993097i	$0.462579\pi$
$492$	7.12601e11	0.548281
$493$	7.76239e10	0.0591813
$494$	3.26825e12	2.46913
$495$	−1.27148e12	−0.951886
$496$	−1.09840e12	−0.814878
$497$	6.43471e11	0.473070
$498$	−5.24974e12	−3.82477
$499$	1.50534e12	1.08688	0.543442	−	0.839446i	$-0.317121\pi$
$499$	1.50534e12	1.08688	0.543442	+	0.839446i	$0.317121\pi$
$500$	5.85766e11	0.419140
$501$	−3.07433e12	−2.18012
$502$	2.40928e12	1.69325
$503$	2.08010e12	1.44887	0.724433	−	0.689345i	$-0.242101\pi$
$503$	2.08010e12	1.44887	0.724433	+	0.689345i	$0.242101\pi$
$504$	−4.00960e11	−0.276798
$505$	−4.63227e11	−0.316944
$506$	1.68482e12	1.14255
$507$	1.76316e12	1.18510
$508$	−1.63858e12	−1.09164
$509$	−8.30153e11	−0.548186	−0.274093	−	0.961703i	$-0.588378\pi$
$509$	−8.30153e11	−0.548186	−0.274093	+	0.961703i	$0.588378\pi$
$510$	−3.11453e11	−0.203857
$511$	1.41340e12	0.917003
$512$	1.78722e12	1.14938
$513$	−3.68203e12	−2.34725
$514$	1.68657e12	1.06579
$515$	8.33708e11	0.522254
$516$	−4.49252e11	−0.278976
$517$	−2.57821e12	−1.58712
$518$	−1.21646e12	−0.742362
$519$	1.39585e12	0.844472
$520$	−1.74941e11	−0.104924
$521$	−2.58561e11	−0.153742	−0.0768711	−	0.997041i	$-0.524493\pi$
$521$	−2.58561e11	−0.153742	−0.0768711	+	0.997041i	$0.524493\pi$
$522$	8.23969e11	0.485728
$523$	1.65048e12	0.964612	0.482306	−	0.876003i	$-0.339799\pi$
$523$	1.65048e12	0.964612	0.482306	+	0.876003i	$0.339799\pi$
$524$	1.46467e11	0.0848692
$525$	−1.34618e12	−0.773365
$526$	−3.29515e12	−1.87689
$527$	3.93048e11	0.221972
$528$	−6.27113e12	−3.51150
$529$	−1.36795e12	−0.759486
$530$	2.70289e11	0.148794
$531$	3.75210e12	2.04809
$532$	−1.00311e12	−0.542932
$533$	−9.85862e11	−0.529107
$534$	6.59831e12	3.51153
$535$	−7.40078e11	−0.390558
$536$	4.15866e10	0.0217627
$537$	−3.08860e11	−0.160279
$538$	5.44739e11	0.280329
$539$	−2.60680e12	−1.33032
$540$	−7.10659e11	−0.359658
$541$	1.37096e12	0.688076	0.344038	−	0.938956i	$-0.388205\pi$
$541$	1.37096e12	0.688076	0.344038	+	0.938956i	$0.388205\pi$
$542$	−9.96137e11	−0.495818
$543$	−1.70994e12	−0.844079
$544$	−8.28264e11	−0.405484
$545$	−2.61048e11	−0.126747
$546$	−3.02121e12	−1.45484
$547$	−2.31426e12	−1.10527	−0.552635	−	0.833423i	$-0.686378\pi$
$547$	−2.31426e12	−1.10527	−0.552635	+	0.833423i	$0.686378\pi$
$548$	1.27542e11	0.0604146
$549$	3.60920e12	1.69565
$550$	−4.61187e12	−2.14904
$551$	−5.71687e11	−0.264227
$552$	−5.33489e11	−0.244568
$553$	−1.03372e12	−0.470044
$554$	4.80584e12	2.16758
$555$	1.22146e12	0.546465
$556$	3.41472e12	1.51537
$557$	3.80342e12	1.67427	0.837137	−	0.546994i	$-0.184228\pi$
$557$	3.80342e12	1.67427	0.837137	+	0.546994i	$0.184228\pi$
$558$	4.17216e12	1.82183
$559$	6.21527e11	0.269220
$560$	3.69579e11	0.158804
$561$	2.24404e12	0.956530
$562$	3.97296e12	1.67997
$563$	2.22013e12	0.931301	0.465651	−	0.884969i	$-0.345820\pi$
$563$	2.22013e12	0.931301	0.465651	+	0.884969i	$0.345820\pi$
$564$	−2.94368e12	−1.22500
$565$	1.22505e11	0.0505751
$566$	−1.02635e12	−0.420361
$567$	1.05392e12	0.428236
$568$	−6.98036e11	−0.281391
$569$	−1.58728e12	−0.634818	−0.317409	−	0.948289i	$-0.602813\pi$
$569$	−1.58728e12	−0.634818	−0.317409	+	0.948289i	$0.602813\pi$
$570$	2.29380e12	0.910161
$571$	8.84382e11	0.348159	0.174079	−	0.984732i	$-0.444305\pi$
$571$	8.84382e11	0.348159	0.174079	+	0.984732i	$0.444305\pi$
$572$	−4.54495e12	−1.77520
$573$	1.06350e11	0.0412136
$574$	6.89088e11	0.264954
$575$	−1.18581e12	−0.452387
$576$	−2.73697e12	−1.03602
$577$	1.86383e12	0.700028	0.350014	−	0.936744i	$-0.386177\pi$
$577$	1.86383e12	0.700028	0.350014	+	0.936744i	$0.386177\pi$
$578$	−3.21900e12	−1.19962
$579$	−8.08056e12	−2.98805
$580$	−1.10340e11	−0.0404862
$581$	−2.22915e12	−0.811608
$582$	4.59803e12	1.66119
$583$	−1.94746e12	−0.698167
$584$	−1.53325e12	−0.545451
$585$	2.00840e12	0.709004
$586$	−4.66743e12	−1.63508
$587$	−1.54798e12	−0.538140	−0.269070	−	0.963121i	$-0.586716\pi$
$587$	−1.54798e12	−0.538140	−0.269070	+	0.963121i	$0.586716\pi$
$588$	−2.97632e12	−1.02679
$589$	−2.89474e12	−0.991038
$590$	−1.14426e12	−0.388767
$591$	−7.38456e12	−2.48989
$592$	3.98847e12	1.33462
$593$	3.37155e11	0.111965	0.0559827	−	0.998432i	$-0.482171\pi$
$593$	3.37155e11	0.111965	0.0559827	+	0.998432i	$0.482171\pi$
$594$	1.16608e13	3.84316
$595$	−1.32249e11	−0.0432581
$596$	4.26386e11	0.138419
$597$	−4.10732e11	−0.132335
$598$	−2.66130e12	−0.851018
$599$	−2.13840e12	−0.678685	−0.339342	−	0.940663i	$-0.610204\pi$
$599$	−2.13840e12	−0.678685	−0.339342	+	0.940663i	$0.610204\pi$
$600$	1.46033e12	0.460012
$601$	−2.13267e12	−0.666788	−0.333394	−	0.942788i	$-0.608194\pi$
$601$	−2.13267e12	−0.666788	−0.333394	+	0.942788i	$0.608194\pi$
$602$	−4.34428e11	−0.134814
$603$	−4.77433e11	−0.147057
$604$	2.29283e12	0.700979
$605$	−1.87609e12	−0.569318
$606$	8.67825e12	2.61400
$607$	−4.43246e12	−1.32524	−0.662622	−	0.748954i	$-0.730556\pi$
$607$	−4.43246e12	−1.32524	−0.662622	+	0.748954i	$0.730556\pi$
$608$	6.10002e12	1.81036
$609$	5.28474e11	0.155685
$610$	−1.10068e12	−0.321866
$611$	4.07249e12	1.18216
$612$	1.69626e12	0.488777
$613$	3.90610e12	1.11730	0.558652	−	0.829402i	$-0.311319\pi$
$613$	3.90610e12	1.11730	0.558652	+	0.829402i	$0.311319\pi$
$614$	−3.92612e12	−1.11482
$615$	−6.91919e11	−0.195037
$616$	−8.81027e11	−0.246533
$617$	1.23858e12	0.344066	0.172033	−	0.985091i	$-0.444967\pi$
$617$	1.23858e12	0.344066	0.172033	+	0.985091i	$0.444967\pi$
$618$	−1.56190e13	−4.30729
$619$	−1.31339e11	−0.0359571	−0.0179785	−	0.999838i	$-0.505723\pi$
$619$	−1.31339e11	−0.0359571	−0.0179785	+	0.999838i	$0.505723\pi$
$620$	−5.58706e11	−0.151852
$621$	2.99823e12	0.809009
$622$	5.69777e12	1.52633
$623$	2.80178e12	0.745140
$624$	9.90575e12	2.61551
$625$	2.95008e12	0.773345
$626$	7.98155e11	0.207732
$627$	−1.65270e13	−4.27062
$628$	3.46886e12	0.889956
$629$	−1.42722e12	−0.363550
$630$	−1.40381e12	−0.355039
$631$	3.31226e12	0.831749	0.415875	−	0.909422i	$-0.363476\pi$
$631$	3.31226e12	0.831749	0.415875	+	0.909422i	$0.363476\pi$
$632$	1.12137e12	0.279591
$633$	−7.69726e12	−1.90555
$634$	−8.40244e12	−2.06540
$635$	1.59103e12	0.388325
$636$	−2.22351e12	−0.538868
$637$	4.11764e12	0.990881
$638$	1.81050e12	0.432619
$639$	8.01377e12	1.90144
$640$	−6.69190e11	−0.157666
$641$	4.93505e11	0.115460	0.0577299	−	0.998332i	$-0.481614\pi$
$641$	4.93505e11	0.115460	0.0577299	+	0.998332i	$0.481614\pi$
$642$	1.38649e13	3.22113
$643$	2.74194e12	0.632570	0.316285	−	0.948664i	$-0.397564\pi$
$643$	2.74194e12	0.632570	0.316285	+	0.948664i	$0.397564\pi$
$644$	8.16820e11	0.187128
$645$	4.36214e11	0.0992385
$646$	−2.68020e12	−0.605508
$647$	−1.90763e12	−0.427981	−0.213991	−	0.976836i	$-0.568646\pi$
$647$	−1.90763e12	−0.427981	−0.213991	+	0.976836i	$0.568646\pi$
$648$	−1.14329e12	−0.254723
$649$	8.24448e12	1.82416
$650$	7.28482e12	1.60069
$651$	2.67593e12	0.583929
$652$	6.73136e12	1.45878
$653$	−6.44143e12	−1.38635	−0.693176	−	0.720769i	$-0.743789\pi$
$653$	−6.44143e12	−1.38635	−0.693176	+	0.720769i	$0.743789\pi$
$654$	4.89057e12	1.04534
$655$	−1.42217e11	−0.0301901
$656$	−2.25934e12	−0.476336
$657$	1.76024e13	3.68577
$658$	−2.84655e12	−0.591973
$659$	−2.68480e12	−0.554532	−0.277266	−	0.960793i	$-0.589428\pi$
$659$	−2.68480e12	−0.554532	−0.277266	+	0.960793i	$0.589428\pi$
$660$	−3.18984e12	−0.654367
$661$	6.55222e12	1.33500	0.667501	−	0.744609i	$-0.267364\pi$
$661$	6.55222e12	1.33500	0.667501	+	0.744609i	$0.267364\pi$
$662$	3.23777e12	0.655218
$663$	−3.54465e12	−0.712463
$664$	2.41817e12	0.482760
$665$	9.73995e11	0.193134
$666$	−1.51498e13	−2.98382
$667$	4.65519e11	0.0910691
$668$	−5.10622e12	−0.992215
$669$	−9.57971e11	−0.184899
$670$	1.45600e11	0.0279142
$671$	7.93048e12	1.51025
$672$	−5.63893e12	−1.06668
$673$	−3.53072e12	−0.663431	−0.331715	−	0.943380i	$-0.607627\pi$
$673$	−3.53072e12	−0.663431	−0.331715	+	0.943380i	$0.607627\pi$
$674$	−1.02971e13	−1.92196
$675$	−8.20710e12	−1.52168
$676$	2.92846e12	0.539361
$677$	−6.34562e10	−0.0116098	−0.00580490	−	0.999983i	$-0.501848\pi$
$677$	−6.34562e10	−0.0116098	−0.00580490	+	0.999983i	$0.501848\pi$
$678$	−2.29506e12	−0.417119
$679$	1.95242e12	0.352500
$680$	1.43464e11	0.0257307
$681$	−2.09320e12	−0.372948
$682$	9.16747e12	1.62263
$683$	3.02638e12	0.532146	0.266073	−	0.963953i	$-0.414274\pi$
$683$	3.02638e12	0.532146	0.266073	+	0.963953i	$0.414274\pi$
$684$	−1.24927e13	−2.18224
$685$	−1.23841e11	−0.0214910
$686$	−6.65290e12	−1.14697
$687$	−1.20752e13	−2.06819
$688$	1.42438e12	0.242369
$689$	3.07616e12	0.520023
$690$	−1.86781e12	−0.313699
$691$	−4.28021e12	−0.714190	−0.357095	−	0.934068i	$-0.616233\pi$
$691$	−4.28021e12	−0.714190	−0.357095	+	0.934068i	$0.616233\pi$
$692$	2.31839e12	0.384335
$693$	1.01146e13	1.66590
$694$	−3.62129e12	−0.592578
$695$	−3.31561e12	−0.539054
$696$	−5.73287e11	−0.0926042
$697$	8.08476e11	0.129754
$698$	−1.49932e13	−2.39081
$699$	−2.28793e12	−0.362490
$700$	−2.23589e12	−0.351973
$701$	−1.14774e13	−1.79520	−0.897599	−	0.440814i	$-0.854690\pi$
$701$	−1.14774e13	−1.79520	−0.897599	+	0.440814i	$0.854690\pi$
$702$	−1.84191e13	−2.86254
$703$	1.05113e13	1.62314
$704$	−6.01394e12	−0.922746
$705$	2.85825e12	0.435761
$706$	2.56825e12	0.389059
$707$	3.68497e12	0.554685
$708$	9.41316e12	1.40795
$709$	5.31997e12	0.790680	0.395340	−	0.918535i	$-0.370627\pi$
$709$	5.31997e12	0.790680	0.395340	+	0.918535i	$0.370627\pi$
$710$	−2.44391e12	−0.360930
$711$	−1.28739e13	−1.88928
$712$	−3.03936e12	−0.443223
$713$	2.35715e12	0.341574
$714$	2.47760e12	0.356771
$715$	4.41305e12	0.631483
$716$	−5.12991e11	−0.0729460
$717$	−1.15164e13	−1.62735
$718$	1.92868e12	0.270831
$719$	8.10784e11	0.113142	0.0565711	−	0.998399i	$-0.481983\pi$
$719$	8.10784e11	0.113142	0.0565711	+	0.998399i	$0.481983\pi$
$720$	4.60273e12	0.638291
$721$	−6.63214e12	−0.913998
$722$	9.98978e12	1.36816
$723$	−1.03591e11	−0.0140994
$724$	−2.84008e12	−0.384156
$725$	−1.27427e12	−0.171293
$726$	3.51473e13	4.69545
$727$	5.48591e12	0.728356	0.364178	−	0.931329i	$-0.381350\pi$
$727$	5.48591e12	0.728356	0.364178	+	0.931329i	$0.381350\pi$
$728$	1.39165e12	0.183628
$729$	−8.51310e12	−1.11638
$730$	−5.36811e12	−0.699630
$731$	−5.09695e11	−0.0660211
$732$	9.05465e12	1.16566
$733$	−8.11749e12	−1.03861	−0.519307	−	0.854588i	$-0.673810\pi$
$733$	−8.11749e12	−1.03861	−0.519307	+	0.854588i	$0.673810\pi$
$734$	9.87040e12	1.25517
$735$	2.88994e12	0.365254
$736$	−4.96718e12	−0.623965
$737$	−1.04906e12	−0.130978
$738$	8.58187e12	1.06495
$739$	−3.75427e12	−0.463047	−0.231523	−	0.972829i	$-0.574371\pi$
$739$	−3.75427e12	−0.463047	−0.231523	+	0.972829i	$0.574371\pi$
$740$	2.02875e12	0.248706
$741$	2.61058e13	3.18093
$742$	−2.15015e12	−0.260406
$743$	−1.43144e13	−1.72315	−0.861574	−	0.507632i	$-0.830521\pi$
$743$	−1.43144e13	−1.72315	−0.861574	+	0.507632i	$0.830521\pi$
$744$	−2.90284e12	−0.347332
$745$	−4.14011e11	−0.0492390
$746$	6.48015e12	0.766056
$747$	−2.77617e13	−3.26215
$748$	3.72718e12	0.435335
$749$	5.88731e12	0.683516
$750$	1.06555e13	1.22969
$751$	−1.39679e13	−1.60233	−0.801166	−	0.598442i	$-0.795787\pi$
$751$	−1.39679e13	−1.60233	−0.801166	+	0.598442i	$0.795787\pi$
$752$	9.33308e12	1.06425
$753$	1.92446e13	2.18138
$754$	−2.85983e12	−0.322233
$755$	−2.22628e12	−0.249356
$756$	5.65329e12	0.629438
$757$	8.30530e12	0.919229	0.459615	−	0.888119i	$-0.347988\pi$
$757$	8.30530e12	0.919229	0.459615	+	0.888119i	$0.347988\pi$
$758$	−8.76318e12	−0.964163
$759$	1.34578e13	1.47192
$760$	−1.05659e12	−0.114880
$761$	1.48448e13	1.60451	0.802255	−	0.596982i	$-0.203634\pi$
$761$	1.48448e13	1.60451	0.802255	+	0.596982i	$0.203634\pi$
$762$	−2.98068e13	−3.20271
$763$	2.07664e12	0.221820
$764$	1.76639e11	0.0187571
$765$	−1.64703e12	−0.173870
$766$	1.08722e13	1.14101
$767$	−1.30228e13	−1.35871
$768$	2.13075e13	2.21008
$769$	−1.74698e12	−0.180144	−0.0900722	−	0.995935i	$-0.528710\pi$
$769$	−1.74698e12	−0.180144	−0.0900722	+	0.995935i	$0.528710\pi$
$770$	−3.08459e12	−0.316220
$771$	1.34718e13	1.37303
$772$	−1.34212e13	−1.35992
$773$	9.48097e11	0.0955091	0.0477546	−	0.998859i	$-0.484793\pi$
$773$	9.48097e11	0.0955091	0.0477546	+	0.998859i	$0.484793\pi$
$774$	−5.41035e12	−0.541865
$775$	−6.45226e12	−0.642472
$776$	−2.11798e12	−0.209674
$777$	−9.71673e12	−0.956369
$778$	1.36557e12	0.133631
$779$	−5.95429e12	−0.579310
$780$	5.03861e12	0.487399
$781$	1.76086e13	1.69354
$782$	2.18245e12	0.208696
$783$	3.22190e12	0.306326
$784$	9.43656e12	0.892055
$785$	−3.36819e12	−0.316579
$786$	2.66433e12	0.248993
$787$	1.13926e12	0.105861	0.0529307	−	0.998598i	$-0.483144\pi$
$787$	1.13926e12	0.105861	0.0529307	+	0.998598i	$0.483144\pi$
$788$	−1.22652e13	−1.13320
$789$	−2.63206e13	−2.41796
$790$	3.92607e12	0.358622
$791$	−9.74529e11	−0.0885117
$792$	−1.09723e13	−0.990908
$793$	−1.25268e13	−1.12489
$794$	1.89433e13	1.69147
$795$	2.15898e12	0.191689
$796$	−6.82192e11	−0.0602280
$797$	−2.72611e12	−0.239321	−0.119661	−	0.992815i	$-0.538181\pi$
$797$	−2.72611e12	−0.239321	−0.119661	+	0.992815i	$0.538181\pi$
$798$	−1.82471e13	−1.59288
$799$	−3.33973e12	−0.289902
$800$	1.35967e13	1.17363
$801$	3.48933e13	2.99499
$802$	−6.39685e12	−0.545986
$803$	3.86777e13	3.28277
$804$	−1.19777e12	−0.101093
$805$	−7.93113e11	−0.0665662
$806$	−1.44808e13	−1.20860
$807$	4.35120e12	0.361142
$808$	−3.99744e12	−0.329937
$809$	−1.07204e13	−0.879917	−0.439959	−	0.898018i	$-0.645007\pi$
$809$	−1.07204e13	−0.879917	−0.439959	+	0.898018i	$0.645007\pi$
$810$	−4.00280e12	−0.326724
$811$	−6.81148e8	−5.52902e−5 0	−2.76451e−5	−	1.00000i	$-0.500009\pi$
$811$	−6.81148e8	−5.52902e−5 0	−2.76451e−5		1.00000i	$0.500009\pi$
$812$	8.77754e11	0.0708550
$813$	−7.95683e12	−0.638753
$814$	−3.32886e13	−2.65757
$815$	−6.53600e12	−0.518923
$816$	−8.12341e12	−0.641405
$817$	3.75382e12	0.294764
$818$	−1.41746e13	−1.10693
$819$	−1.59768e13	−1.24083
$820$	−1.14922e12	−0.0887650
$821$	1.15717e13	0.888899	0.444450	−	0.895804i	$-0.353399\pi$
$821$	1.15717e13	0.888899	0.444450	+	0.895804i	$0.353399\pi$
$822$	2.32007e12	0.177247
$823$	−1.15736e13	−0.879363	−0.439682	−	0.898154i	$-0.644909\pi$
$823$	−1.15736e13	−0.879363	−0.439682	+	0.898154i	$0.644909\pi$
$824$	7.19453e12	0.543663
$825$	−3.68381e13	−2.76856
$826$	9.10256e12	0.680383
$827$	3.29309e12	0.244810	0.122405	−	0.992480i	$-0.460939\pi$
$827$	3.29309e12	0.244810	0.122405	+	0.992480i	$0.460939\pi$
$828$	1.01726e13	0.752137
$829$	5.77412e12	0.424610	0.212305	−	0.977203i	$-0.431903\pi$
$829$	5.77412e12	0.424610	0.212305	+	0.977203i	$0.431903\pi$
$830$	8.46633e12	0.619219
$831$	3.83876e13	2.79245
$832$	9.49951e12	0.687300
$833$	−3.37676e12	−0.242995
$834$	6.21158e13	4.44585
$835$	4.95803e12	0.352955
$836$	−2.74501e13	−1.94364
$837$	1.63141e13	1.14894
$838$	−6.87443e12	−0.481547
$839$	1.33204e13	0.928084	0.464042	−	0.885813i	$-0.346399\pi$
$839$	1.33204e13	0.928084	0.464042	+	0.885813i	$0.346399\pi$
$840$	9.76721e11	0.0676883
$841$	5.00246e11	0.0344828
$842$	−3.59170e12	−0.246261
$843$	3.17348e13	2.16427
$844$	−1.27845e13	−0.867249
$845$	−2.84347e12	−0.191864
$846$	−3.54508e13	−2.37936
$847$	1.49243e13	0.996364
$848$	7.04976e12	0.468159
$849$	−8.19817e12	−0.541542
$850$	−5.97406e12	−0.392540
$851$	−8.55921e12	−0.559436
$852$	2.01047e13	1.30713
$853$	−1.86296e13	−1.20485	−0.602425	−	0.798176i	$-0.705799\pi$
$853$	−1.86296e13	−1.20485	−0.602425	+	0.798176i	$0.705799\pi$
$854$	8.75588e12	0.563299
$855$	1.21301e13	0.776277
$856$	−6.38654e12	−0.406568
$857$	9.55082e12	0.604821	0.302411	−	0.953178i	$-0.402209\pi$
$857$	9.55082e12	0.604821	0.302411	+	0.953178i	$0.402209\pi$
$858$	−8.26755e13	−5.20816
$859$	−2.30005e12	−0.144135	−0.0720673	−	0.997400i	$-0.522960\pi$
$859$	−2.30005e12	−0.144135	−0.0720673	+	0.997400i	$0.522960\pi$
$860$	7.24516e11	0.0451653
$861$	5.50421e12	0.341335
$862$	4.68612e12	0.289088
$863$	−1.51572e13	−0.930186	−0.465093	−	0.885262i	$-0.653979\pi$
$863$	−1.51572e13	−0.930186	−0.465093	+	0.885262i	$0.653979\pi$
$864$	−3.43784e13	−2.09881
$865$	−2.25111e12	−0.136717
$866$	−4.67509e12	−0.282462
$867$	−2.57123e13	−1.54545
$868$	4.44450e12	0.265757
$869$	−2.82877e13	−1.68271
$870$	−2.00715e12	−0.118780
$871$	1.65708e12	0.0975576
$872$	−2.25273e12	−0.131943
$873$	2.43154e13	1.41683
$874$	−1.60734e13	−0.931766
$875$	4.52453e12	0.260938
$876$	4.41604e13	2.53375
$877$	−1.17770e13	−0.672261	−0.336130	−	0.941815i	$-0.609118\pi$
$877$	−1.17770e13	−0.672261	−0.336130	+	0.941815i	$0.609118\pi$
$878$	3.23661e13	1.83808
$879$	−3.72820e13	−2.10644
$880$	1.01135e13	0.568501
$881$	3.20883e13	1.79455	0.897275	−	0.441472i	$-0.145544\pi$
$881$	3.20883e13	1.79455	0.897275	+	0.441472i	$0.145544\pi$
$882$	−3.58439e13	−1.99437
$883$	1.12261e13	0.621447	0.310724	−	0.950500i	$-0.399429\pi$
$883$	1.12261e13	0.621447	0.310724	+	0.950500i	$0.399429\pi$
$884$	−5.88738e12	−0.324255
$885$	−9.13996e12	−0.500841
$886$	−4.17487e13	−2.27610
$887$	1.29150e13	0.700550	0.350275	−	0.936647i	$-0.386088\pi$
$887$	1.29150e13	0.700550	0.350275	+	0.936647i	$0.386088\pi$
$888$	1.05407e13	0.568866
$889$	−1.26566e13	−0.679609
$890$	−1.06412e13	−0.568507
$891$	2.88405e13	1.53304
$892$	−1.59111e12	−0.0841510
$893$	2.45965e13	1.29432
$894$	7.75622e12	0.406099
$895$	4.98103e11	0.0259487
$896$	5.32340e12	0.275933
$897$	−2.12576e13	−1.09635
$898$	2.98865e13	1.53367
$899$	2.53300e12	0.129335
$900$	−2.78457e13	−1.41471
$901$	−2.52267e12	−0.127526
$902$	1.88569e13	0.948508
$903$	−3.47008e12	−0.173678
$904$	1.05717e12	0.0526484
$905$	2.75766e12	0.136654
$906$	4.17079e13	2.05656
$907$	3.58672e13	1.75981	0.879904	−	0.475152i	$-0.157607\pi$
$907$	3.58672e13	1.75981	0.879904	+	0.475152i	$0.157607\pi$
$908$	−3.47663e12	−0.169735
$909$	4.58925e13	2.22948
$910$	4.87235e12	0.235533
$911$	2.08642e13	1.00362	0.501809	−	0.864978i	$-0.332668\pi$
$911$	2.08642e13	1.00362	0.501809	+	0.864978i	$0.332668\pi$
$912$	5.98276e13	2.86368
$913$	−6.10007e13	−2.90547
$914$	3.77462e13	1.78902
$915$	−8.79186e12	−0.414654
$916$	−2.00560e13	−0.941272
$917$	1.13133e12	0.0528358
$918$	1.51050e13	0.701985
$919$	−6.99733e12	−0.323603	−0.161802	−	0.986823i	$-0.551730\pi$
$919$	−6.99733e12	−0.323603	−0.161802	+	0.986823i	$0.551730\pi$
$920$	8.60367e11	0.0395948
$921$	−3.13606e13	−1.43620
$922$	−4.35597e13	−1.98516
$923$	−2.78142e13	−1.26142
$924$	2.53751e13	1.14521
$925$	2.34292e13	1.05225
$926$	−6.35666e12	−0.284105
$927$	−8.25964e13	−3.67369
$928$	−5.33773e12	−0.236260
$929$	−3.65569e13	−1.61027	−0.805135	−	0.593091i	$-0.797907\pi$
$929$	−3.65569e13	−1.61027	−0.805135	+	0.593091i	$0.797907\pi$
$930$	−1.01632e13	−0.445510
$931$	2.48693e13	1.08490
$932$	−3.80008e12	−0.164976
$933$	4.55120e13	1.96634
$934$	1.92689e13	0.828505
$935$	−3.61901e12	−0.154859
$936$	1.73316e13	0.738069
$937$	−3.40797e12	−0.144433	−0.0722167	−	0.997389i	$-0.523007\pi$
$937$	−3.40797e12	−0.144433	−0.0722167	+	0.997389i	$0.523007\pi$
$938$	−1.15825e12	−0.0488527
$939$	6.37541e12	0.267617
$940$	4.74732e12	0.198323
$941$	3.06145e12	0.127284	0.0636421	−	0.997973i	$-0.479728\pi$
$941$	3.06145e12	0.127284	0.0636421	+	0.997973i	$0.479728\pi$
$942$	6.31007e13	2.61099
$943$	4.84851e12	0.199667
$944$	−2.98449e13	−1.22320
$945$	−5.48921e12	−0.223907
$946$	−1.18881e13	−0.482618
$947$	3.26454e13	1.31901	0.659503	−	0.751702i	$-0.270767\pi$
$947$	3.26454e13	1.31901	0.659503	+	0.751702i	$0.270767\pi$
$948$	−3.22976e13	−1.29877
$949$	−6.10946e13	−2.44515
$950$	4.39980e13	1.75257
$951$	−6.71160e13	−2.66081
$952$	−1.14125e12	−0.0450314
$953$	−2.17685e12	−0.0854892	−0.0427446	−	0.999086i	$-0.513610\pi$
$953$	−2.17685e12	−0.0854892	−0.0427446	+	0.999086i	$0.513610\pi$
$954$	−2.67778e13	−1.04667
$955$	−1.71512e11	−0.00667236
$956$	−1.91279e13	−0.740639
$957$	1.44617e13	0.557335
$958$	−1.06440e13	−0.408283
$959$	9.85152e11	0.0376114
$960$	6.66715e12	0.253349
$961$	−1.36138e13	−0.514902
$962$	5.25820e13	1.97947
$963$	7.33204e13	2.74730
$964$	−1.72056e11	−0.00641689
$965$	1.30317e13	0.483756
$966$	1.48584e13	0.549005
$967$	−4.20350e13	−1.54594	−0.772969	−	0.634444i	$-0.781229\pi$
$967$	−4.20350e13	−1.54594	−0.772969	+	0.634444i	$0.781229\pi$
$968$	−1.61898e13	−0.592656
$969$	−2.14086e13	−0.780064
$970$	−7.41532e12	−0.268941
$971$	−4.78952e13	−1.72904	−0.864521	−	0.502596i	$-0.832378\pi$
$971$	−4.78952e13	−1.72904	−0.864521	+	0.502596i	$0.832378\pi$
$972$	−3.01118e12	−0.108203
$973$	2.63757e13	0.943401
$974$	2.23397e12	0.0795356
$975$	5.81888e13	2.06214
$976$	−2.87082e13	−1.01270
$977$	1.18536e13	0.416221	0.208111	−	0.978105i	$-0.433269\pi$
$977$	1.18536e13	0.416221	0.208111	+	0.978105i	$0.433269\pi$
$978$	1.22448e14	4.27982
$979$	7.66708e13	2.66752
$980$	4.79995e12	0.166234
$981$	2.58624e13	0.891575
$982$	9.12769e12	0.313227
$983$	−4.34817e13	−1.48531	−0.742653	−	0.669676i	$-0.766433\pi$
$983$	−4.34817e13	−1.48531	−0.742653	+	0.669676i	$0.766433\pi$
$984$	−5.97095e12	−0.203033
$985$	1.19092e13	0.403106
$986$	2.34526e12	0.0790216
$987$	−2.27373e13	−0.762627
$988$	4.33596e13	1.44770
$989$	−3.05670e12	−0.101594
$990$	−3.84153e13	−1.27100
$991$	−1.37923e13	−0.454261	−0.227130	−	0.973864i	$-0.572934\pi$
$991$	−1.37923e13	−0.454261	−0.227130	+	0.973864i	$0.572934\pi$
$992$	−2.70276e13	−0.886145
$993$	2.58623e13	0.844103
$994$	1.94413e13	0.631665
$995$	6.62393e11	0.0214246
$996$	−6.96478e13	−2.24254
$997$	1.44002e13	0.461574	0.230787	−	0.973004i	$-0.425870\pi$
$997$	1.44002e13	0.461574	0.230787	+	0.973004i	$0.425870\pi$
$998$	4.54812e13	1.45126
$999$	−5.92391e13	−1.88176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.b.1.10	✓	12
3.2	odd	2		261.10.a.e.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.b.1.10	✓	12	1.1	even	1	trivial
261.10.a.e.1.3		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)

\(f(q)\)	\(=\)	\(q+30.2132 q^{2} +241.333 q^{3} +400.835 q^{4} -389.202 q^{5} +7291.44 q^{6} +3096.10 q^{7} -3358.64 q^{8} +38558.7 q^{9} +O(q^{10})\)	\(q+30.2132 q^{2} +241.333 q^{3} +400.835 q^{4} -389.202 q^{5} +7291.44 q^{6} +3096.10 q^{7} -3358.64 q^{8} +38558.7 q^{9} -11759.0 q^{10} +84724.8 q^{11} +96734.8 q^{12} -133830. q^{13} +93543.0 q^{14} -93927.4 q^{15} -306703. q^{16} +109750. q^{17} +1.16498e6 q^{18} -808289. q^{19} -156006. q^{20} +747192. q^{21} +2.55981e6 q^{22} +658181. q^{23} -810551. q^{24} -1.80165e6 q^{25} -4.04342e6 q^{26} +4.55533e6 q^{27} +1.24103e6 q^{28} +707281. q^{29} -2.83784e6 q^{30} +3.58131e6 q^{31} -7.54684e6 q^{32} +2.04469e7 q^{33} +3.31589e6 q^{34} -1.20501e6 q^{35} +1.54557e7 q^{36} -1.30043e7 q^{37} -2.44210e7 q^{38} -3.22976e7 q^{39} +1.30719e6 q^{40} +7.36654e6 q^{41} +2.25750e7 q^{42} -4.64416e6 q^{43} +3.39607e7 q^{44} -1.50071e7 q^{45} +1.98857e7 q^{46} -3.04304e7 q^{47} -7.40176e7 q^{48} -3.07678e7 q^{49} -5.44334e7 q^{50} +2.64863e7 q^{51} -5.36437e7 q^{52} -2.29856e7 q^{53} +1.37631e8 q^{54} -3.29751e7 q^{55} -1.03987e7 q^{56} -1.95067e8 q^{57} +2.13692e7 q^{58} +9.73089e7 q^{59} -3.76494e7 q^{60} +9.36027e7 q^{61} +1.08203e8 q^{62} +1.19382e8 q^{63} -7.09820e7 q^{64} +5.20868e7 q^{65} +6.17766e8 q^{66} -1.23820e7 q^{67} +4.39916e7 q^{68} +1.58841e8 q^{69} -3.64071e7 q^{70} +2.07833e8 q^{71} -1.29505e8 q^{72} +4.56510e8 q^{73} -3.92902e8 q^{74} -4.34797e8 q^{75} -3.23991e8 q^{76} +2.62317e8 q^{77} -9.75812e8 q^{78} -3.33877e8 q^{79} +1.19369e8 q^{80} +3.40402e8 q^{81} +2.22566e8 q^{82} -7.19986e8 q^{83} +2.99501e8 q^{84} -4.27148e7 q^{85} -1.40315e8 q^{86} +1.70690e8 q^{87} -2.84560e8 q^{88} +9.04939e8 q^{89} -4.53413e8 q^{90} -4.14350e8 q^{91} +2.63822e8 q^{92} +8.64290e8 q^{93} -9.19398e8 q^{94} +3.14588e8 q^{95} -1.82130e9 q^{96} +6.30607e8 q^{97} -9.29592e8 q^{98} +3.26688e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) \) 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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