LMFDB - Embedded newform 43.10.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,10,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	43.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:	$22.1465409550$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 6541 x^{15} + 10299 x^{14} + 17445509 x^{13} - 2347983 x^{12} + \cdots - 37\!\cdots\!40 $ x^17 - 3x^16 - 6541x^15 + 10299x^14 + 17445509x^13 - 2347983x^12 - 24275147889x^11 - 32817396993x^10 + 18668870018715x^9 + 54284997199479x^8 - 7688031373215127x^7 - 34414384567646799x^6 + 1472871456600457271x^5 + 8285298256630038219x^4 - 82173286944147552299x^3 - 301942019130667260459x^2 + 866271940633182378600x - 378136193010971707440
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$25.5994$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.5994 q^{2} -82.1072 q^{3} -1.26822 q^{4} +454.995 q^{5} +1855.57 q^{6} -6480.48 q^{7} +11599.5 q^{8} -12941.4 q^{9} +O(q^{10})$	\(q-22.5994 q^{2} -82.1072 q^{3} -1.26822 q^{4} +454.995 q^{5} +1855.57 q^{6} -6480.48 q^{7} +11599.5 q^{8} -12941.4 q^{9} -10282.6 q^{10} -74959.6 q^{11} +104.130 q^{12} -42078.1 q^{13} +146455. q^{14} -37358.3 q^{15} -261493. q^{16} -565853. q^{17} +292468. q^{18} +180221. q^{19} -577.035 q^{20} +532094. q^{21} +1.69404e6 q^{22} +634024. q^{23} -952406. q^{24} -1.74610e6 q^{25} +950939. q^{26} +2.67870e6 q^{27} +8218.70 q^{28} +445357. q^{29} +844275. q^{30} +5.98012e6 q^{31} -29385.3 q^{32} +6.15472e6 q^{33} +1.27879e7 q^{34} -2.94858e6 q^{35} +16412.6 q^{36} +8.43844e6 q^{37} -4.07289e6 q^{38} +3.45491e6 q^{39} +5.27773e6 q^{40} +2.12675e7 q^{41} -1.20250e7 q^{42} +3.41880e6 q^{43} +95065.5 q^{44} -5.88827e6 q^{45} -1.43285e7 q^{46} -5.09511e7 q^{47} +2.14705e7 q^{48} +1.64302e6 q^{49} +3.94609e7 q^{50} +4.64606e7 q^{51} +53364.5 q^{52} +2.01271e7 q^{53} -6.05369e7 q^{54} -3.41062e7 q^{55} -7.51706e7 q^{56} -1.47975e7 q^{57} -1.00648e7 q^{58} -1.42017e8 q^{59} +47378.7 q^{60} +1.00231e7 q^{61} -1.35147e8 q^{62} +8.38666e7 q^{63} +1.34549e8 q^{64} -1.91453e7 q^{65} -1.39093e8 q^{66} -2.03394e8 q^{67} +717629. q^{68} -5.20579e7 q^{69} +6.66361e7 q^{70} +3.49888e8 q^{71} -1.50114e8 q^{72} +3.32635e8 q^{73} -1.90703e8 q^{74} +1.43368e8 q^{75} -228561. q^{76} +4.85774e8 q^{77} -7.80789e7 q^{78} -6.08050e8 q^{79} -1.18978e8 q^{80} +3.47854e7 q^{81} -4.80632e8 q^{82} +4.28233e8 q^{83} -674815. q^{84} -2.57460e8 q^{85} -7.72628e7 q^{86} -3.65670e7 q^{87} -8.69496e8 q^{88} +1.15108e9 q^{89} +1.33071e8 q^{90} +2.72686e8 q^{91} -804084. q^{92} -4.91011e8 q^{93} +1.15146e9 q^{94} +8.19997e7 q^{95} +2.41274e6 q^{96} -5.10596e6 q^{97} -3.71312e7 q^{98} +9.70082e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) $ 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9} + 23763 q^{10} + 78370 q^{11} + 271339 q^{12} + 114452 q^{13} - 376208 q^{14} - 255820 q^{15} + 412586 q^{16} + 726937 q^{17} + 577055 q^{18} + 544263 q^{19} + 3642183 q^{20} + 3137394 q^{21} + 5269148 q^{22} + 5575241 q^{23} + 16215113 q^{24} + 10874708 q^{25} + 8009180 q^{26} + 8350126 q^{27} + 12534764 q^{28} + 8223345 q^{29} + 30612012 q^{30} + 13054147 q^{31} + 37111710 q^{32} + 36024808 q^{33} + 27991291 q^{34} + 17826330 q^{35} + 84105953 q^{36} + 46733879 q^{37} + 15733789 q^{38} + 8689898 q^{39} + 52241669 q^{40} + 53667013 q^{41} + 7708286 q^{42} + 58119617 q^{43} + 81727236 q^{44} + 124361968 q^{45} + 146859355 q^{46} + 122945511 q^{47} + 86356095 q^{48} + 111396073 q^{49} - 96642133 q^{50} - 187132423 q^{51} - 54447944 q^{52} - 993146 q^{53} - 219468490 q^{54} - 248155792 q^{55} - 141048116 q^{56} - 402917960 q^{57} - 466599837 q^{58} - 95519644 q^{59} - 621611940 q^{60} - 311752038 q^{61} - 212471691 q^{62} - 928966350 q^{63} - 829842590 q^{64} - 107969830 q^{65} - 978530932 q^{66} - 292438130 q^{67} - 88281129 q^{68} + 78577726 q^{69} - 1650972530 q^{70} - 13576908 q^{71} - 706943493 q^{72} - 501490738 q^{73} - 494831691 q^{74} - 641914030 q^{75} - 1248630771 q^{76} + 787365348 q^{77} - 946670550 q^{78} + 740350275 q^{79} - 27802861 q^{80} + 1582210525 q^{81} - 1600400057 q^{82} + 754109940 q^{83} - 1955423842 q^{84} + 1071609956 q^{85} + 164102448 q^{86} + 186301257 q^{87} + 1863375104 q^{88} + 1470581868 q^{89} - 698098630 q^{90} + 2895349644 q^{91} + 1041082071 q^{92} + 4540331515 q^{93} - 706582361 q^{94} + 3297255729 q^{95} + 2087289393 q^{96} + 1949310583 q^{97} + 6695989160 q^{98} + 1234191326 q^{99}+O(q^{100}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9 + 23763 * q^10 + 78370 * q^11 + 271339 * q^12 + 114452 * q^13 - 376208 * q^14 - 255820 * q^15 + 412586 * q^16 + 726937 * q^17 + 577055 * q^18 + 544263 * q^19 + 3642183 * q^20 + 3137394 * q^21 + 5269148 * q^22 + 5575241 * q^23 + 16215113 * q^24 + 10874708 * q^25 + 8009180 * q^26 + 8350126 * q^27 + 12534764 * q^28 + 8223345 * q^29 + 30612012 * q^30 + 13054147 * q^31 + 37111710 * q^32 + 36024808 * q^33 + 27991291 * q^34 + 17826330 * q^35 + 84105953 * q^36 + 46733879 * q^37 + 15733789 * q^38 + 8689898 * q^39 + 52241669 * q^40 + 53667013 * q^41 + 7708286 * q^42 + 58119617 * q^43 + 81727236 * q^44 + 124361968 * q^45 + 146859355 * q^46 + 122945511 * q^47 + 86356095 * q^48 + 111396073 * q^49 - 96642133 * q^50 - 187132423 * q^51 - 54447944 * q^52 - 993146 * q^53 - 219468490 * q^54 - 248155792 * q^55 - 141048116 * q^56 - 402917960 * q^57 - 466599837 * q^58 - 95519644 * q^59 - 621611940 * q^60 - 311752038 * q^61 - 212471691 * q^62 - 928966350 * q^63 - 829842590 * q^64 - 107969830 * q^65 - 978530932 * q^66 - 292438130 * q^67 - 88281129 * q^68 + 78577726 * q^69 - 1650972530 * q^70 - 13576908 * q^71 - 706943493 * q^72 - 501490738 * q^73 - 494831691 * q^74 - 641914030 * q^75 - 1248630771 * q^76 + 787365348 * q^77 - 946670550 * q^78 + 740350275 * q^79 - 27802861 * q^80 + 1582210525 * q^81 - 1600400057 * q^82 + 754109940 * q^83 - 1955423842 * q^84 + 1071609956 * q^85 + 164102448 * q^86 + 186301257 * q^87 + 1863375104 * q^88 + 1470581868 * q^89 - 698098630 * q^90 + 2895349644 * q^91 + 1041082071 * q^92 + 4540331515 * q^93 - 706582361 * q^94 + 3297255729 * q^95 + 2087289393 * q^96 + 1949310583 * q^97 + 6695989160 * q^98 + 1234191326 * 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 $

$2$	−22.5994	−0.998761	−0.499380	−	0.866383i	$-0.666439\pi$
$2$	−22.5994	−0.998761	−0.499380	+	0.866383i	$0.666439\pi$
$3$	−82.1072	−0.585242	−0.292621	−	0.956228i	$-0.594527\pi$
$3$	−82.1072	−0.585242	−0.292621	+	0.956228i	$0.594527\pi$
$4$	−1.26822	−0.00247700
$5$	454.995	0.325568	0.162784	−	0.986662i	$-0.447953\pi$
$5$	454.995	0.325568	0.162784	+	0.986662i	$0.447953\pi$
$6$	1855.57	0.584517
$7$	−6480.48	−1.02015	−0.510077	−	0.860129i	$-0.670383\pi$
$7$	−6480.48	−1.02015	−0.510077	+	0.860129i	$0.670383\pi$
$8$	11599.5	1.00123
$9$	−12941.4	−0.657492
$10$	−10282.6	−0.325164
$11$	−74959.6	−1.54369	−0.771845	−	0.635811i	$-0.780666\pi$
$11$	−74959.6	−1.54369	−0.771845	+	0.635811i	$0.780666\pi$
$12$	104.130	0.00144964
$13$	−42078.1	−0.408612	−0.204306	−	0.978907i	$-0.565494\pi$
$13$	−42078.1	−0.408612	−0.204306	+	0.978907i	$0.565494\pi$
$14$	146455.	1.01889
$15$	−37358.3	−0.190536
$16$	−261493.	−0.997517
$17$	−565853.	−1.64317	−0.821587	−	0.570083i	$-0.806911\pi$
$17$	−565853.	−1.64317	−0.821587	+	0.570083i	$0.806911\pi$
$18$	292468.	0.656677
$19$	180221.	0.317260	0.158630	−	0.987338i	$-0.449292\pi$
$19$	180221.	0.317260	0.158630	+	0.987338i	$0.449292\pi$
$20$	−577.035	−0.000806431 0
$21$	532094.	0.597037
$22$	1.69404e6	1.54178
$23$	634024.	0.472422	0.236211	−	0.971702i	$-0.424094\pi$
$23$	634024.	0.472422	0.236211	+	0.971702i	$0.424094\pi$
$24$	−952406.	−0.585965
$25$	−1.74610e6	−0.894006
$26$	950939.	0.408105
$27$	2.67870e6	0.970034
$28$	8218.70	0.00252692
$29$	445357.	0.116928	0.0584638	−	0.998290i	$-0.481380\pi$
$29$	445357.	0.116928	0.0584638	+	0.998290i	$0.481380\pi$
$30$	844275.	0.190300
$31$	5.98012e6	1.16301	0.581503	−	0.813544i	$-0.302465\pi$
$31$	5.98012e6	1.16301	0.581503	+	0.813544i	$0.302465\pi$
$32$	−29385.3	−0.00495399
$33$	6.15472e6	0.903432
$34$	1.27879e7	1.64114
$35$	−2.94858e6	−0.332129
$36$	16412.6	0.00162861
$37$	8.43844e6	0.740209	0.370105	−	0.928990i	$-0.379322\pi$
$37$	8.43844e6	0.740209	0.370105	+	0.928990i	$0.379322\pi$
$38$	−4.07289e6	−0.316866
$39$	3.45491e6	0.239137
$40$	5.27773e6	0.325970
$41$	2.12675e7	1.17541	0.587704	−	0.809076i	$-0.300032\pi$
$41$	2.12675e7	1.17541	0.587704	+	0.809076i	$0.300032\pi$
$42$	−1.20250e7	−0.596298
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	95065.5	0.00382372
$45$	−5.88827e6	−0.214058
$46$	−1.43285e7	−0.471837
$47$	−5.09511e7	−1.52305	−0.761524	−	0.648137i	$-0.775548\pi$
$47$	−5.09511e7	−1.52305	−0.761524	+	0.648137i	$0.775548\pi$
$48$	2.14705e7	0.583789
$49$	1.64302e6	0.0407155
$50$	3.94609e7	0.892898
$51$	4.64606e7	0.961655
$52$	53364.5	0.00101213
$53$	2.01271e7	0.350381	0.175190	−	0.984535i	$-0.443946\pi$
$53$	2.01271e7	0.350381	0.175190	+	0.984535i	$0.443946\pi$
$54$	−6.05369e7	−0.968832
$55$	−3.41062e7	−0.502575
$56$	−7.51706e7	−1.02141
$57$	−1.47975e7	−0.185674
$58$	−1.00648e7	−0.116783
$59$	−1.42017e8	−1.52583	−0.762917	−	0.646497i	$-0.776233\pi$
$59$	−1.42017e8	−1.52583	−0.762917	+	0.646497i	$0.776233\pi$
$60$	47378.7	0.000471957 0
$61$	1.00231e7	0.0926864	0.0463432	−	0.998926i	$-0.485243\pi$
$61$	1.00231e7	0.0926864	0.0463432	+	0.998926i	$0.485243\pi$
$62$	−1.35147e8	−1.16157
$63$	8.38666e7	0.670743
$64$	1.34549e8	1.00246
$65$	−1.91453e7	−0.133031
$66$	−1.39093e8	−0.902312
$67$	−2.03394e8	−1.23311	−0.616555	−	0.787312i	$-0.711472\pi$
$67$	−2.03394e8	−1.23311	−0.616555	+	0.787312i	$0.711472\pi$
$68$	717629.	0.00407014
$69$	−5.20579e7	−0.276481
$70$	6.66361e7	0.331718
$71$	3.49888e8	1.63405	0.817026	−	0.576600i	$-0.195621\pi$
$71$	3.49888e8	1.63405	0.817026	+	0.576600i	$0.195621\pi$
$72$	−1.50114e8	−0.658304
$73$	3.32635e8	1.37093	0.685464	−	0.728106i	$-0.259599\pi$
$73$	3.32635e8	1.37093	0.685464	+	0.728106i	$0.259599\pi$
$74$	−1.90703e8	−0.739292
$75$	1.43368e8	0.523210
$76$	−228561.	−0.000785852 0
$77$	4.85774e8	1.57480
$78$	−7.80789e7	−0.238840
$79$	−6.08050e8	−1.75638	−0.878188	−	0.478316i	$-0.841247\pi$
$79$	−6.08050e8	−1.75638	−0.878188	+	0.478316i	$0.841247\pi$
$80$	−1.18978e8	−0.324759
$81$	3.47854e7	0.0897872
$82$	−4.80632e8	−1.17395
$83$	4.28233e8	0.990442	0.495221	−	0.868767i	$-0.335087\pi$
$83$	4.28233e8	0.990442	0.495221	+	0.868767i	$0.335087\pi$
$84$	−674815.	−0.00147886
$85$	−2.57460e8	−0.534964
$86$	−7.72628e7	−0.152310
$87$	−3.65670e7	−0.0684310
$88$	−8.69496e8	−1.54560
$89$	1.15108e9	1.94470	0.972348	−	0.233536i	$-0.0750298\pi$
$89$	1.15108e9	1.94470	0.972348	+	0.233536i	$0.0750298\pi$
$90$	1.33071e8	0.213793
$91$	2.72686e8	0.416847
$92$	−804084.	−0.00117019
$93$	−4.91011e8	−0.680640
$94$	1.15146e9	1.52116
$95$	8.19997e7	0.103289
$96$	2.41274e6	0.00289928
$97$	−5.10596e6	−0.00585605	−0.00292803	−	0.999996i	$-0.500932\pi$
$97$	−5.10596e6	−0.00585605	−0.00292803	+	0.999996i	$0.500932\pi$
$98$	−3.71312e7	−0.0406651
$99$	9.70082e8	1.01496
$100$	2.21445e6	0.00221445
$101$	−8.16303e8	−0.780558	−0.390279	−	0.920697i	$-0.627621\pi$
$101$	−8.16303e8	−0.780558	−0.390279	+	0.920697i	$0.627621\pi$
$102$	−1.04998e9	−0.960463
$103$	−4.95552e8	−0.433832	−0.216916	−	0.976190i	$-0.569600\pi$
$103$	−4.95552e8	−0.433832	−0.216916	+	0.976190i	$0.569600\pi$
$104$	−4.88087e8	−0.409116
$105$	2.42100e8	0.194376
$106$	−4.54860e8	−0.349947
$107$	8.06653e8	0.594922	0.297461	−	0.954734i	$-0.403860\pi$
$107$	8.06653e8	0.594922	0.297461	+	0.954734i	$0.403860\pi$
$108$	−3.39719e6	−0.00240277
$109$	4.41605e7	0.0299650	0.0149825	−	0.999888i	$-0.495231\pi$
$109$	4.41605e7	0.0299650	0.0149825	+	0.999888i	$0.495231\pi$
$110$	7.70779e8	0.501952
$111$	−6.92857e8	−0.433202
$112$	1.69460e9	1.01762
$113$	1.80024e9	1.03867	0.519335	−	0.854571i	$-0.326180\pi$
$113$	1.80024e9	1.03867	0.519335	+	0.854571i	$0.326180\pi$
$114$	3.34413e8	0.185444
$115$	2.88477e8	0.153805
$116$	−564812.	−0.000289630 0
$117$	5.44550e8	0.268659
$118$	3.20950e9	1.52394
$119$	3.66700e9	1.67629
$120$	−4.33339e8	−0.190771
$121$	3.26099e9	1.38298
$122$	−2.26515e8	−0.0925715
$123$	−1.74621e9	−0.687898
$124$	−7.58413e6	−0.00288077
$125$	−1.68313e9	−0.616627
$126$	−1.89533e9	−0.669912
$127$	−2.21584e9	−0.755826	−0.377913	−	0.925841i	$-0.623358\pi$
$127$	−2.21584e9	−0.755826	−0.377913	+	0.925841i	$0.623358\pi$
$128$	−3.02567e9	−0.996268
$129$	−2.80708e8	−0.0892486
$130$	4.32672e8	0.132866
$131$	−4.98735e9	−1.47961	−0.739807	−	0.672819i	$-0.765083\pi$
$131$	−4.98735e9	−1.47961	−0.739807	+	0.672819i	$0.765083\pi$
$132$	−7.80556e6	−0.00223780
$133$	−1.16792e9	−0.323654
$134$	4.59658e9	1.23158
$135$	1.21879e9	0.315812
$136$	−6.56364e9	−1.64520
$137$	−6.77229e8	−0.164245	−0.0821226	−	0.996622i	$-0.526170\pi$
$137$	−6.77229e8	−0.164245	−0.0821226	+	0.996622i	$0.526170\pi$
$138$	1.17648e9	0.276139
$139$	−6.30453e9	−1.43247	−0.716236	−	0.697858i	$-0.754137\pi$
$139$	−6.30453e9	−1.43247	−0.716236	+	0.697858i	$0.754137\pi$
$140$	3.73946e6	0.000822684 0
$141$	4.18345e9	0.891351
$142$	−7.90724e9	−1.63203
$143$	3.15415e9	0.630770
$144$	3.38409e9	0.655859
$145$	2.02635e8	0.0380678
$146$	−7.51734e9	−1.36923
$147$	−1.34904e8	−0.0238284
$148$	−1.07018e7	−0.00183350
$149$	−3.26846e9	−0.543257	−0.271628	−	0.962402i	$-0.587562\pi$
$149$	−3.26846e9	−0.543257	−0.271628	+	0.962402i	$0.587562\pi$
$150$	−3.24002e9	−0.522561
$151$	−1.08473e10	−1.69796	−0.848980	−	0.528425i	$-0.822783\pi$
$151$	−1.08473e10	−1.69796	−0.848980	+	0.528425i	$0.822783\pi$
$152$	2.09048e9	0.317651
$153$	7.32294e9	1.08037
$154$	−1.09782e10	−1.57285
$155$	2.72092e9	0.378637
$156$	−4.38160e6	−0.000592342 0
$157$	1.03685e9	0.136197	0.0680983	−	0.997679i	$-0.478307\pi$
$157$	1.03685e9	0.136197	0.0680983	+	0.997679i	$0.478307\pi$
$158$	1.37416e10	1.75420
$159$	−1.65258e9	−0.205058
$160$	−1.33701e7	−0.00161286
$161$	−4.10878e9	−0.481944
$162$	−7.86128e8	−0.0896759
$163$	8.30654e9	0.921671	0.460836	−	0.887485i	$-0.347550\pi$
$163$	8.30654e9	0.921671	0.460836	+	0.887485i	$0.347550\pi$
$164$	−2.69719e7	−0.00291149
$165$	2.80036e9	0.294128
$166$	−9.67780e9	−0.989214
$167$	4.58694e9	0.456351	0.228176	−	0.973620i	$-0.426724\pi$
$167$	4.58694e9	0.456351	0.228176	+	0.973620i	$0.426724\pi$
$168$	6.17205e9	0.597775
$169$	−8.83393e9	−0.833036
$170$	5.81844e9	0.534301
$171$	−2.33232e9	−0.208596
$172$	−4.33581e6	−0.000377739 0
$173$	6.55298e8	0.0556200	0.0278100	−	0.999613i	$-0.491147\pi$
$173$	6.55298e8	0.0556200	0.0278100	+	0.999613i	$0.491147\pi$
$174$	8.26391e8	0.0683461
$175$	1.13156e10	0.912024
$176$	1.96014e10	1.53986
$177$	1.16606e10	0.892982
$178$	−2.60138e10	−1.94229
$179$	2.06382e10	1.50257	0.751283	−	0.659980i	$-0.229435\pi$
$179$	2.06382e10	1.50257	0.751283	+	0.659980i	$0.229435\pi$
$180$	7.46765e6	0.000530222 0
$181$	1.04098e10	0.720924	0.360462	−	0.932774i	$-0.382619\pi$
$181$	1.04098e10	0.720924	0.360462	+	0.932774i	$0.382619\pi$
$182$	−6.16254e9	−0.416331
$183$	−8.22965e8	−0.0542440
$184$	7.35439e9	0.473006
$185$	3.83944e9	0.240988
$186$	1.10965e10	0.679797
$187$	4.24161e10	2.53655
$188$	6.46175e7	0.00377259
$189$	−1.73593e10	−0.989585
$190$	−1.85314e9	−0.103161
$191$	−1.76436e10	−0.959260	−0.479630	−	0.877471i	$-0.659229\pi$
$191$	−1.76436e10	−0.959260	−0.479630	+	0.877471i	$0.659229\pi$
$192$	−1.10474e10	−0.586684
$193$	−5.30332e9	−0.275131	−0.137566	−	0.990493i	$-0.543928\pi$
$193$	−5.30332e9	−0.275131	−0.137566	+	0.990493i	$0.543928\pi$
$194$	1.15392e8	0.00584879
$195$	1.57197e9	0.0778552
$196$	−2.08372e6	−0.000100852 0
$197$	3.42505e10	1.62020	0.810100	−	0.586292i	$-0.199413\pi$
$197$	3.42505e10	1.62020	0.810100	+	0.586292i	$0.199413\pi$
$198$	−2.19233e10	−1.01371
$199$	−2.69788e10	−1.21950	−0.609752	−	0.792592i	$-0.708731\pi$
$199$	−2.69788e10	−1.21950	−0.609752	+	0.792592i	$0.708731\pi$
$200$	−2.02540e10	−0.895110
$201$	1.67001e10	0.721668
$202$	1.84479e10	0.779590
$203$	−2.88613e9	−0.119284
$204$	−5.89225e7	−0.00238202
$205$	9.67659e9	0.382675
$206$	1.11992e10	0.433294
$207$	−8.20516e9	−0.310614
$208$	1.10031e10	0.407597
$209$	−1.35093e10	−0.489750
$210$	−5.47131e9	−0.194135
$211$	4.01941e8	0.0139602	0.00698009	−	0.999976i	$-0.497778\pi$
$211$	4.01941e8	0.0139602	0.00698009	+	0.999976i	$0.497778\pi$
$212$	−2.55257e7	−0.000867893 0
$213$	−2.87283e10	−0.956316
$214$	−1.82299e10	−0.594185
$215$	1.55554e9	0.0496486
$216$	3.10717e10	0.971232
$217$	−3.87540e10	−1.18645
$218$	−9.98000e8	−0.0299279
$219$	−2.73117e10	−0.802325
$220$	4.32543e7	0.00124488
$221$	2.38100e10	0.671421
$222$	1.56581e10	0.432665
$223$	8.67154e9	0.234814	0.117407	−	0.993084i	$-0.462542\pi$
$223$	8.67154e9	0.234814	0.117407	+	0.993084i	$0.462542\pi$
$224$	1.90431e8	0.00505384
$225$	2.25971e10	0.587801
$226$	−4.06843e10	−1.03738
$227$	−5.94447e9	−0.148592	−0.0742962	−	0.997236i	$-0.523671\pi$
$227$	−5.94447e9	−0.148592	−0.0742962	+	0.997236i	$0.523671\pi$
$228$	1.87665e7	0.000459914 0
$229$	−3.15029e10	−0.756991	−0.378496	−	0.925603i	$-0.623558\pi$
$229$	−3.15029e10	−0.756991	−0.378496	+	0.925603i	$0.623558\pi$
$230$	−6.51941e9	−0.153615
$231$	−3.98855e10	−0.921640
$232$	5.16593e9	0.117072
$233$	4.61854e10	1.02660	0.513302	−	0.858208i	$-0.328422\pi$
$233$	4.61854e10	1.02660	0.513302	+	0.858208i	$0.328422\pi$
$234$	−1.23065e10	−0.268326
$235$	−2.31825e10	−0.495855
$236$	1.80110e8	0.00377949
$237$	4.99253e10	1.02790
$238$	−8.28719e10	−1.67421
$239$	6.69083e10	1.32645	0.663223	−	0.748422i	$-0.269188\pi$
$239$	6.69083e10	1.32645	0.663223	+	0.748422i	$0.269188\pi$
$240$	9.76894e9	0.190063
$241$	4.45942e10	0.851533	0.425767	−	0.904833i	$-0.360004\pi$
$241$	4.45942e10	0.851533	0.425767	+	0.904833i	$0.360004\pi$
$242$	−7.36963e10	−1.38126
$243$	−5.55810e10	−1.02258
$244$	−1.27115e7	−0.000229584 0
$245$	7.47565e8	0.0132557
$246$	3.94633e10	0.687046
$247$	−7.58337e9	−0.129636
$248$	6.93666e10	1.16444
$249$	−3.51610e10	−0.579648
$250$	3.80377e10	0.615863
$251$	−1.07181e11	−1.70446	−0.852231	−	0.523166i	$-0.824751\pi$
$251$	−1.07181e11	−1.70446	−0.852231	+	0.523166i	$0.824751\pi$
$252$	−1.06362e8	−0.00166143
$253$	−4.75261e10	−0.729273
$254$	5.00766e10	0.754889
$255$	2.11393e10	0.313084
$256$	−5.10651e8	−0.00743096
$257$	−5.18404e10	−0.741257	−0.370629	−	0.928781i	$-0.620858\pi$
$257$	−5.18404e10	−0.741257	−0.370629	+	0.928781i	$0.620858\pi$
$258$	6.34383e9	0.0891380
$259$	−5.46852e10	−0.755128
$260$	2.42805e7	0.000329517 0
$261$	−5.76354e9	−0.0768789
$262$	1.12711e11	1.47778
$263$	−6.17412e10	−0.795746	−0.397873	−	0.917441i	$-0.630252\pi$
$263$	−6.17412e10	−0.795746	−0.397873	+	0.917441i	$0.630252\pi$
$264$	7.13919e10	0.904547
$265$	9.15773e9	0.114073
$266$	2.63943e10	0.323253
$267$	−9.45122e10	−1.13812
$268$	2.57950e8	0.00305442
$269$	−5.32726e10	−0.620324	−0.310162	−	0.950684i	$-0.600383\pi$
$269$	−5.32726e10	−0.620324	−0.310162	+	0.950684i	$0.600383\pi$
$270$	−2.75440e10	−0.315420
$271$	1.01728e10	0.114572	0.0572859	−	0.998358i	$-0.481755\pi$
$271$	1.01728e10	0.114572	0.0572859	+	0.998358i	$0.481755\pi$
$272$	1.47967e11	1.63909
$273$	−2.23895e10	−0.243957
$274$	1.53049e10	0.164042
$275$	1.30887e11	1.38007
$276$	6.60211e7	0.000684844 0
$277$	6.91857e9	0.0706086	0.0353043	−	0.999377i	$-0.488760\pi$
$277$	6.91857e9	0.0706086	0.0353043	+	0.999377i	$0.488760\pi$
$278$	1.42479e11	1.43070
$279$	−7.73912e10	−0.764667
$280$	−3.42022e10	−0.332539
$281$	−2.20579e9	−0.0211051	−0.0105525	−	0.999944i	$-0.503359\pi$
$281$	−2.20579e9	−0.0211051	−0.0105525	+	0.999944i	$0.503359\pi$
$282$	−9.45434e10	−0.890247
$283$	1.24134e11	1.15041	0.575206	−	0.818009i	$-0.304922\pi$
$283$	1.24134e11	1.15041	0.575206	+	0.818009i	$0.304922\pi$
$284$	−4.43736e8	−0.00404755
$285$	−6.73276e9	−0.0604493
$286$	−7.12819e10	−0.629988
$287$	−1.37824e11	−1.19910
$288$	3.80287e8	0.00325721
$289$	2.01602e11	1.70002
$290$	−4.57942e9	−0.0380207
$291$	4.19236e8	0.00342721
$292$	−4.21855e8	−0.00339579
$293$	−1.48545e9	−0.0117748	−0.00588741	−	0.999983i	$-0.501874\pi$
$293$	−1.48545e9	−0.0117748	−0.00588741	+	0.999983i	$0.501874\pi$
$294$	3.04874e9	0.0237989
$295$	−6.46171e10	−0.496762
$296$	9.78820e10	0.741123
$297$	−2.00794e11	−1.49743
$298$	7.38652e10	0.542583
$299$	−2.66785e10	−0.193037
$300$	−1.81822e8	−0.00129599
$301$	−2.21555e10	−0.155572
$302$	2.45143e11	1.69586
$303$	6.70243e10	0.456815
$304$	−4.71266e10	−0.316472
$305$	4.56044e9	0.0301757
$306$	−1.65494e11	−1.07903
$307$	−1.16731e11	−0.750004	−0.375002	−	0.927024i	$-0.622358\pi$
$307$	−1.16731e11	−0.750004	−0.375002	+	0.927024i	$0.622358\pi$
$308$	−6.16070e8	−0.00390079
$309$	4.06883e10	0.253897
$310$	−6.14911e10	−0.378168
$311$	3.17765e11	1.92613	0.963063	−	0.269277i	$-0.0867846\pi$
$311$	3.17765e11	1.92613	0.963063	+	0.269277i	$0.0867846\pi$
$312$	4.00754e10	0.239432
$313$	2.02336e10	0.119158	0.0595791	−	0.998224i	$-0.481024\pi$
$313$	2.02336e10	0.119158	0.0595791	+	0.998224i	$0.481024\pi$
$314$	−2.34321e10	−0.136028
$315$	3.81588e10	0.218372
$316$	7.71144e8	0.00435054
$317$	4.20207e10	0.233720	0.116860	−	0.993148i	$-0.462717\pi$
$317$	4.20207e10	0.233720	0.116860	+	0.993148i	$0.462717\pi$
$318$	3.73473e10	0.204803
$319$	−3.33837e10	−0.180500
$320$	6.12189e10	0.326370
$321$	−6.62320e10	−0.348173
$322$	9.28558e10	0.481346
$323$	−1.01979e11	−0.521313
$324$	−4.41157e7	−0.000222403 0
$325$	7.34728e10	0.365301
$326$	−1.87723e11	−0.920529
$327$	−3.62590e9	−0.0175368
$328$	2.46693e11	1.17686
$329$	3.30188e11	1.55374
$330$	−6.32865e10	−0.293764
$331$	−8.63002e10	−0.395172	−0.197586	−	0.980286i	$-0.563310\pi$
$331$	−8.63002e10	−0.395172	−0.197586	+	0.980286i	$0.563310\pi$
$332$	−5.43096e8	−0.00245332
$333$	−1.09205e11	−0.486681
$334$	−1.03662e11	−0.455786
$335$	−9.25433e10	−0.401461
$336$	−1.39139e11	−0.595555
$337$	1.55530e11	0.656871	0.328436	−	0.944526i	$-0.393479\pi$
$337$	1.55530e11	0.656871	0.328436	+	0.944526i	$0.393479\pi$
$338$	1.99641e11	0.832004
$339$	−1.47813e11	−0.607873
$340$	3.26517e8	0.00132511
$341$	−4.48267e11	−1.79532
$342$	5.27089e10	0.208337
$343$	2.50863e11	0.978619
$344$	3.96565e10	0.152687
$345$	−2.36861e10	−0.0900134
$346$	−1.48093e10	−0.0555511
$347$	2.22736e11	0.824723	0.412361	−	0.911020i	$-0.364704\pi$
$347$	2.22736e11	0.824723	0.412361	+	0.911020i	$0.364704\pi$
$348$	4.63751e7	0.000169504 0
$349$	−4.85153e10	−0.175051	−0.0875255	−	0.996162i	$-0.527896\pi$
$349$	−4.85153e10	−0.175051	−0.0875255	+	0.996162i	$0.527896\pi$
$350$	−2.55725e11	−0.910894
$351$	−1.12715e11	−0.396367
$352$	2.20271e9	0.00764742
$353$	4.09448e11	1.40350	0.701751	−	0.712422i	$-0.252402\pi$
$353$	4.09448e11	1.40350	0.701751	+	0.712422i	$0.252402\pi$
$354$	−2.63523e11	−0.891875
$355$	1.59197e11	0.531995
$356$	−1.45983e9	−0.00481701
$357$	−3.01087e11	−0.981037
$358$	−4.66411e11	−1.50070
$359$	2.68506e11	0.853156	0.426578	−	0.904451i	$-0.359719\pi$
$359$	2.68506e11	0.853156	0.426578	+	0.904451i	$0.359719\pi$
$360$	−6.83012e10	−0.214322
$361$	−2.90208e11	−0.899346
$362$	−2.35255e11	−0.720030
$363$	−2.67750e11	−0.809376
$364$	−3.45827e8	−0.00103253
$365$	1.51347e11	0.446330
$366$	1.85985e10	0.0541767
$367$	4.20777e11	1.21075	0.605375	−	0.795940i	$-0.293023\pi$
$367$	4.20777e11	1.21075	0.605375	+	0.795940i	$0.293023\pi$
$368$	−1.65793e11	−0.471249
$369$	−2.75231e11	−0.772821
$370$	−8.67691e10	−0.240689
$371$	−1.30433e11	−0.357443
$372$	6.22712e8	0.00168595
$373$	−4.20457e11	−1.12469	−0.562344	−	0.826903i	$-0.690100\pi$
$373$	−4.20457e11	−1.12469	−0.562344	+	0.826903i	$0.690100\pi$
$374$	−9.58578e11	−2.53341
$375$	1.38197e11	0.360876
$376$	−5.91010e11	−1.52493
$377$	−1.87398e10	−0.0477780
$378$	3.92308e11	0.988358
$379$	−1.98606e11	−0.494443	−0.247221	−	0.968959i	$-0.579517\pi$
$379$	−1.98606e11	−0.494443	−0.247221	+	0.968959i	$0.579517\pi$
$380$	−1.03994e8	−0.000255848 0
$381$	1.81936e11	0.442341
$382$	3.98734e11	0.958071
$383$	4.55141e11	1.08081	0.540407	−	0.841404i	$-0.318270\pi$
$383$	4.55141e11	1.08081	0.540407	+	0.841404i	$0.318270\pi$
$384$	2.48429e11	0.583058
$385$	2.21024e11	0.512704
$386$	1.19852e11	0.274790
$387$	−4.42441e10	−0.100267
$388$	6.47551e6	1.45054e−5 0
$389$	8.23859e11	1.82423	0.912115	−	0.409934i	$-0.134448\pi$
$389$	8.23859e11	1.82423	0.912115	+	0.409934i	$0.134448\pi$
$390$	−3.55255e10	−0.0777587
$391$	−3.58764e11	−0.776272
$392$	1.90583e10	0.0407658
$393$	4.09497e11	0.865933
$394$	−7.74039e11	−1.61819
$395$	−2.76659e11	−0.571819
$396$	−1.23028e9	−0.00251406
$397$	3.77455e10	0.0762619	0.0381310	−	0.999273i	$-0.487860\pi$
$397$	3.77455e10	0.0762619	0.0381310	+	0.999273i	$0.487860\pi$
$398$	6.09703e11	1.21799
$399$	9.58946e10	0.189416
$400$	4.56594e11	0.891786
$401$	−5.61184e11	−1.08382	−0.541909	−	0.840437i	$-0.682298\pi$
$401$	−5.61184e11	−1.08382	−0.541909	+	0.840437i	$0.682298\pi$
$402$	−3.77412e11	−0.720774
$403$	−2.51632e11	−0.475218
$404$	1.03525e9	0.00193344
$405$	1.58272e10	0.0292318
$406$	6.52246e10	0.119136
$407$	−6.32542e11	−1.14265
$408$	5.38922e11	0.962842
$409$	−4.33062e8	−0.000765236 0	−0.000382618	−	1.00000i	$-0.500122\pi$
$409$	−4.33062e8	−0.000765236 0	−0.000382618		1.00000i	$0.500122\pi$
$410$	−2.18685e11	−0.382201
$411$	5.56053e10	0.0961232
$412$	6.28471e8	0.00107460
$413$	9.20340e11	1.55659
$414$	1.85432e11	0.310229
$415$	1.94844e11	0.322456
$416$	1.23648e9	0.00202426
$417$	5.17648e11	0.838343
$418$	3.05302e11	0.489143
$419$	5.53836e11	0.877846	0.438923	−	0.898525i	$-0.355360\pi$
$419$	5.53836e11	0.877846	0.438923	+	0.898525i	$0.355360\pi$
$420$	−3.07037e8	−0.000481470 0
$421$	6.16450e11	0.956376	0.478188	−	0.878258i	$-0.341294\pi$
$421$	6.16450e11	0.956376	0.478188	+	0.878258i	$0.341294\pi$
$422$	−9.08361e9	−0.0139429
$423$	6.59379e11	1.00139
$424$	2.33465e11	0.350813
$425$	9.88039e11	1.46901
$426$	6.49241e11	0.955131
$427$	−6.49542e10	−0.0945544
$428$	−1.02302e9	−0.00147362
$429$	−2.58979e11	−0.369153
$430$	−3.51541e10	−0.0495871
$431$	−1.48460e11	−0.207234	−0.103617	−	0.994617i	$-0.533042\pi$
$431$	−1.48460e11	−0.207234	−0.103617	+	0.994617i	$0.533042\pi$
$432$	−7.00461e11	−0.967625
$433$	3.10613e11	0.424643	0.212322	−	0.977200i	$-0.431898\pi$
$433$	3.10613e11	0.424643	0.212322	+	0.977200i	$0.431898\pi$
$434$	8.75817e11	1.18498
$435$	−1.66378e10	−0.0222789
$436$	−5.60054e7	−7.42234e−5 0
$437$	1.14265e11	0.149880
$438$	6.17227e11	0.801330
$439$	−9.60674e11	−1.23448	−0.617242	−	0.786773i	$-0.711750\pi$
$439$	−9.60674e11	−1.23448	−0.617242	+	0.786773i	$0.711750\pi$
$440$	−3.95616e11	−0.503196
$441$	−2.12630e10	−0.0267701
$442$	−5.38092e11	−0.670588
$443$	−3.92921e11	−0.484717	−0.242359	−	0.970187i	$-0.577921\pi$
$443$	−3.92921e11	−0.484717	−0.242359	+	0.970187i	$0.577921\pi$
$444$	8.78698e8	0.00107304
$445$	5.23737e11	0.633130
$446$	−1.95971e11	−0.234523
$447$	2.68364e11	0.317937
$448$	−8.71939e11	−1.02267
$449$	9.53341e11	1.10698	0.553490	−	0.832856i	$-0.313296\pi$
$449$	9.53341e11	1.10698	0.553490	+	0.832856i	$0.313296\pi$
$450$	−5.10679e11	−0.587073
$451$	−1.59420e12	−1.81447
$452$	−2.28311e9	−0.00257278
$453$	8.90645e11	0.993717
$454$	1.34341e11	0.148408
$455$	1.24071e11	0.135712
$456$	−1.71644e11	−0.185903
$457$	1.17113e12	1.25598	0.627988	−	0.778223i	$-0.283879\pi$
$457$	1.17113e12	1.25598	0.627988	+	0.778223i	$0.283879\pi$
$458$	7.11946e11	0.756053
$459$	−1.51575e12	−1.59394
$460$	−3.65854e8	−0.000380976 0
$461$	−1.43581e12	−1.48062	−0.740310	−	0.672266i	$-0.765321\pi$
$461$	−1.43581e12	−1.48062	−0.740310	+	0.672266i	$0.765321\pi$
$462$	9.01388e11	0.920498
$463$	−1.45941e12	−1.47592	−0.737961	−	0.674844i	$-0.764211\pi$
$463$	−1.45941e12	−1.47592	−0.737961	+	0.674844i	$0.764211\pi$
$464$	−1.16458e11	−0.116637
$465$	−2.23407e11	−0.221594
$466$	−1.04376e12	−1.02533
$467$	−2.02762e11	−0.197270	−0.0986351	−	0.995124i	$-0.531448\pi$
$467$	−2.02762e11	−0.197270	−0.0986351	+	0.995124i	$0.531448\pi$
$468$	−6.90611e8	−0.000665468 0
$469$	1.31809e12	1.25796
$470$	5.23910e11	0.495240
$471$	−8.51326e10	−0.0797080
$472$	−1.64733e12	−1.52772
$473$	−2.56272e11	−0.235410
$474$	−1.12828e12	−1.02663
$475$	−3.14685e11	−0.283632
$476$	−4.65058e9	−0.00415218
$477$	−2.60473e11	−0.230372
$478$	−1.51209e12	−1.32480
$479$	7.61749e11	0.661153	0.330576	−	0.943779i	$-0.392757\pi$
$479$	7.61749e11	0.661153	0.330576	+	0.943779i	$0.392757\pi$
$480$	1.09779e9	0.000943913 0
$481$	−3.55073e11	−0.302458
$482$	−1.00780e12	−0.850478
$483$	3.37360e11	0.282054
$484$	−4.13566e9	−0.00342563
$485$	−2.32319e9	−0.00190654
$486$	1.25609e12	1.02131
$487$	7.32671e11	0.590240	0.295120	−	0.955460i	$-0.404640\pi$
$487$	7.32671e11	0.590240	0.295120	+	0.955460i	$0.404640\pi$
$488$	1.16263e11	0.0928008
$489$	−6.82027e11	−0.539401
$490$	−1.68945e10	−0.0132392
$491$	7.87321e11	0.611343	0.305672	−	0.952137i	$-0.401119\pi$
$491$	7.87321e11	0.611343	0.305672	+	0.952137i	$0.401119\pi$
$492$	2.21459e9	0.00170392
$493$	−2.52007e11	−0.192132
$494$	1.71379e11	0.129475
$495$	4.41382e11	0.330439
$496$	−1.56376e12	−1.16012
$497$	−2.26744e12	−1.66699
$498$	7.94617e11	0.578930
$499$	1.22851e12	0.887008	0.443504	−	0.896272i	$-0.353735\pi$
$499$	1.22851e12	0.887008	0.443504	+	0.896272i	$0.353735\pi$
$500$	2.13459e9	0.00152739
$501$	−3.76621e11	−0.267076
$502$	2.42223e12	1.70235
$503$	−2.39481e12	−1.66807	−0.834036	−	0.551711i	$-0.813975\pi$
$503$	−2.39481e12	−1.66807	−0.834036	+	0.551711i	$0.813975\pi$
$504$	9.72814e11	0.671571
$505$	−3.71413e11	−0.254124
$506$	1.07406e12	0.728369
$507$	7.25329e11	0.487528
$508$	2.81018e9	0.00187218
$509$	−2.59081e12	−1.71082	−0.855412	−	0.517948i	$-0.826696\pi$
$509$	−2.59081e12	−1.71082	−0.855412	+	0.517948i	$0.826696\pi$
$510$	−4.77736e11	−0.312696
$511$	−2.15563e12	−1.39856
$512$	1.56068e12	1.00369
$513$	4.82758e11	0.307753
$514$	1.17156e12	0.740339
$515$	−2.25473e11	−0.141242
$516$	3.56001e8	0.000221069 0
$517$	3.81927e12	2.35111
$518$	1.23585e12	0.754192
$519$	−5.38047e10	−0.0325512
$520$	−2.22077e11	−0.133195
$521$	1.30560e12	0.776321	0.388161	−	0.921592i	$-0.373111\pi$
$521$	1.30560e12	0.776321	0.388161	+	0.921592i	$0.373111\pi$
$522$	1.30253e11	0.0767837
$523$	4.88189e10	0.0285319	0.0142659	−	0.999898i	$-0.495459\pi$
$523$	4.88189e10	0.0285319	0.0142659	+	0.999898i	$0.495459\pi$
$524$	6.32507e9	0.00366501
$525$	−9.29092e11	−0.533755
$526$	1.39531e12	0.794760
$527$	−3.38387e12	−1.91102
$528$	−1.60942e12	−0.901189
$529$	−1.39917e12	−0.776817
$530$	−2.06959e11	−0.113931
$531$	1.83790e12	1.00322
$532$	1.48118e9	0.000801691 0
$533$	−8.94895e11	−0.480286
$534$	2.13592e12	1.13671
$535$	3.67023e11	0.193687
$536$	−2.35928e12	−1.23463
$537$	−1.69455e12	−0.879365
$538$	1.20393e12	0.619555
$539$	−1.23160e11	−0.0628521
$540$	−1.54570e9	−0.000782265 0
$541$	1.27819e12	0.641518	0.320759	−	0.947161i	$-0.396062\pi$
$541$	1.27819e12	0.641518	0.320759	+	0.947161i	$0.396062\pi$
$542$	−2.29898e11	−0.114430
$543$	−8.54720e11	−0.421915
$544$	1.66278e10	0.00814027
$545$	2.00928e10	0.00975565
$546$	5.05989e11	0.243654
$547$	2.43603e12	1.16343	0.581714	−	0.813393i	$-0.302382\pi$
$547$	2.43603e12	1.16343	0.581714	+	0.813393i	$0.302382\pi$
$548$	8.58878e8	0.000406835 0
$549$	−1.29712e11	−0.0609405
$550$	−2.95797e12	−1.37836
$551$	8.02628e10	0.0370964
$552$	−6.03848e11	−0.276823
$553$	3.94046e12	1.79177
$554$	−1.56355e11	−0.0705211
$555$	−3.15246e11	−0.141036
$556$	7.99556e9	0.00354824
$557$	3.05250e12	1.34371	0.671857	−	0.740681i	$-0.265497\pi$
$557$	3.05250e12	1.34371	0.671857	+	0.740681i	$0.265497\pi$
$558$	1.74899e12	0.763720
$559$	−1.43857e11	−0.0623127
$560$	7.71034e11	0.331305
$561$	−3.48267e12	−1.48450
$562$	4.98496e10	0.0210789
$563$	2.47415e12	1.03786	0.518930	−	0.854817i	$-0.326331\pi$
$563$	2.47415e12	1.03786	0.518930	+	0.854817i	$0.326331\pi$
$564$	−5.30556e9	−0.00220788
$565$	8.19099e11	0.338157
$566$	−2.80536e12	−1.14899
$567$	−2.25426e11	−0.0915968
$568$	4.05854e12	1.63607
$569$	2.72039e12	1.08799	0.543997	−	0.839087i	$-0.316910\pi$
$569$	2.72039e12	1.08799	0.543997	+	0.839087i	$0.316910\pi$
$570$	1.52156e11	0.0603744
$571$	−4.58163e12	−1.80367	−0.901835	−	0.432081i	$-0.857780\pi$
$571$	−4.58163e12	−1.80367	−0.901835	+	0.432081i	$0.857780\pi$
$572$	−4.00018e9	−0.00156242
$573$	1.44866e12	0.561399
$574$	3.11473e12	1.19761
$575$	−1.10707e12	−0.422348
$576$	−1.74125e12	−0.659112
$577$	−1.87534e12	−0.704349	−0.352175	−	0.935934i	$-0.614558\pi$
$577$	−1.87534e12	−0.704349	−0.352175	+	0.935934i	$0.614558\pi$
$578$	−4.55608e12	−1.69792
$579$	4.35441e11	0.161018
$580$	−2.56987e8	−9.42941e−5 0
$581$	−2.77516e12	−1.01040
$582$	−9.47448e9	−0.00342296
$583$	−1.50872e12	−0.540879
$584$	3.85841e12	1.37262
$585$	2.47767e11	0.0874666
$586$	3.35703e10	0.0117602
$587$	−3.05946e12	−1.06359	−0.531793	−	0.846874i	$-0.678482\pi$
$587$	−3.05946e12	−1.06359	−0.531793	+	0.846874i	$0.678482\pi$
$588$	1.71088e8	5.90231e−5 0
$589$	1.07774e12	0.368975
$590$	1.46031e12	0.496146
$591$	−2.81221e12	−0.948209
$592$	−2.20659e12	−0.738371
$593$	1.88690e12	0.626616	0.313308	−	0.949652i	$-0.398563\pi$
$593$	1.88690e12	0.626616	0.313308	+	0.949652i	$0.398563\pi$
$594$	4.53782e12	1.49558
$595$	1.66847e12	0.545746
$596$	4.14514e9	0.00134565
$597$	2.21515e12	0.713705
$598$	6.02918e11	0.192798
$599$	−4.20886e12	−1.33581	−0.667904	−	0.744247i	$-0.732808\pi$
$599$	−4.20886e12	−1.33581	−0.667904	+	0.744247i	$0.732808\pi$
$600$	1.66300e12	0.523856
$601$	7.27533e11	0.227467	0.113733	−	0.993511i	$-0.463719\pi$
$601$	7.27533e11	0.227467	0.113733	+	0.993511i	$0.463719\pi$
$602$	5.00700e11	0.155379
$603$	2.63221e12	0.810760
$604$	1.37569e10	0.00420585
$605$	1.48373e12	0.450252
$606$	−1.51471e12	−0.456249
$607$	−4.69381e11	−0.140338	−0.0701692	−	0.997535i	$-0.522354\pi$
$607$	−4.69381e11	−0.140338	−0.0701692	+	0.997535i	$0.522354\pi$
$608$	−5.29585e9	−0.00157170
$609$	2.36972e11	0.0698102
$610$	−1.03063e11	−0.0301383
$611$	2.14393e12	0.622335
$612$	−9.28713e9	−0.00267609
$613$	5.15798e12	1.47539	0.737696	−	0.675133i	$-0.235914\pi$
$613$	5.15798e12	1.47539	0.737696	+	0.675133i	$0.235914\pi$
$614$	2.63805e12	0.749075
$615$	−7.94518e11	−0.223957
$616$	5.63475e12	1.57675
$617$	4.49963e12	1.24995	0.624977	−	0.780643i	$-0.285109\pi$
$617$	4.49963e12	1.24995	0.624977	+	0.780643i	$0.285109\pi$
$618$	−9.19531e11	−0.253582
$619$	−8.46139e11	−0.231651	−0.115825	−	0.993270i	$-0.536951\pi$
$619$	−8.46139e11	−0.231651	−0.115825	+	0.993270i	$0.536951\pi$
$620$	−3.45074e9	−0.000937885 0
$621$	1.69836e12	0.458266
$622$	−7.18130e12	−1.92374
$623$	−7.45957e12	−1.98389
$624$	−9.03436e11	−0.238543
$625$	2.64455e12	0.693252
$626$	−4.57267e11	−0.119011
$627$	1.10921e12	0.286622
$628$	−1.31495e9	−0.000337359 0
$629$	−4.77492e12	−1.21629
$630$	−8.62366e11	−0.218102
$631$	−4.85623e11	−0.121946	−0.0609729	−	0.998139i	$-0.519420\pi$
$631$	−4.85623e11	−0.121946	−0.0609729	+	0.998139i	$0.519420\pi$
$632$	−7.05310e12	−1.75854
$633$	−3.30022e10	−0.00817008
$634$	−9.49642e11	−0.233431
$635$	−1.00820e12	−0.246072
$636$	2.09584e9	0.000507928 0
$637$	−6.91351e10	−0.0166368
$638$	7.54452e11	0.180276
$639$	−4.52804e12	−1.07438
$640$	−1.37666e12	−0.324353
$641$	−2.06674e12	−0.483533	−0.241766	−	0.970335i	$-0.577727\pi$
$641$	−2.06674e12	−0.483533	−0.241766	+	0.970335i	$0.577727\pi$
$642$	1.49680e12	0.347742
$643$	−4.04930e11	−0.0934181	−0.0467090	−	0.998909i	$-0.514873\pi$
$643$	−4.04930e11	−0.0934181	−0.0467090	+	0.998909i	$0.514873\pi$
$644$	5.21085e9	0.00119377
$645$	−1.27721e11	−0.0290564
$646$	2.30466e12	0.520667
$647$	−3.25515e12	−0.730301	−0.365150	−	0.930949i	$-0.618982\pi$
$647$	−3.25515e12	−0.730301	−0.365150	+	0.930949i	$0.618982\pi$
$648$	4.03495e11	0.0898980
$649$	1.06455e13	2.35541
$650$	−1.66044e12	−0.364849
$651$	3.18198e12	0.694358
$652$	−1.05346e10	−0.00228298
$653$	5.44264e12	1.17139	0.585694	−	0.810532i	$-0.300822\pi$
$653$	5.44264e12	1.17139	0.585694	+	0.810532i	$0.300822\pi$
$654$	8.19430e10	0.0175151
$655$	−2.26922e12	−0.481715
$656$	−5.56130e12	−1.17249
$657$	−4.30476e12	−0.901374
$658$	−7.46204e12	−1.55182
$659$	−4.54335e12	−0.938408	−0.469204	−	0.883090i	$-0.655459\pi$
$659$	−4.54335e12	−0.938408	−0.469204	+	0.883090i	$0.655459\pi$
$660$	−3.55149e9	−0.000728556 0
$661$	−1.75368e12	−0.357309	−0.178654	−	0.983912i	$-0.557174\pi$
$661$	−1.75368e12	−0.357309	−0.178654	+	0.983912i	$0.557174\pi$
$662$	1.95033e12	0.394682
$663$	−1.95497e12	−0.392944
$664$	4.96731e12	0.991665
$665$	−5.31397e11	−0.105371
$666$	2.46797e12	0.486078
$667$	2.82367e11	0.0552392
$668$	−5.81727e9	−0.00113038
$669$	−7.11996e11	−0.137423
$670$	2.09142e12	0.400963
$671$	−7.51324e11	−0.143079
$672$	−1.56357e10	−0.00295772
$673$	−2.92530e11	−0.0549672	−0.0274836	−	0.999622i	$-0.508749\pi$
$673$	−2.92530e11	−0.0549672	−0.0274836	+	0.999622i	$0.508749\pi$
$674$	−3.51489e12	−0.656057
$675$	−4.67729e12	−0.867216
$676$	1.12034e10	0.00206343
$677$	4.66330e12	0.853187	0.426593	−	0.904444i	$-0.359714\pi$
$677$	4.66330e12	0.853187	0.426593	+	0.904444i	$0.359714\pi$
$678$	3.34047e12	0.607120
$679$	3.30891e10	0.00597408
$680$	−2.98642e12	−0.535625
$681$	4.88084e11	0.0869626
$682$	1.01306e13	1.79310
$683$	3.96568e12	0.697308	0.348654	−	0.937252i	$-0.386639\pi$
$683$	3.96568e12	0.697308	0.348654	+	0.937252i	$0.386639\pi$
$684$	2.95790e9	0.000516691 0
$685$	−3.08135e11	−0.0534729
$686$	−5.66935e12	−0.977406
$687$	2.58661e12	0.443023
$688$	−8.93993e11	−0.152120
$689$	−8.46911e11	−0.143170
$690$	5.35290e11	0.0899018
$691$	5.14648e12	0.858735	0.429368	−	0.903130i	$-0.358737\pi$
$691$	5.14648e12	0.858735	0.429368	+	0.903130i	$0.358737\pi$
$692$	−8.31065e8	−0.000137771 0
$693$	−6.28660e12	−1.03542
$694$	−5.03370e12	−0.823701
$695$	−2.86853e12	−0.466367
$696$	−4.24160e11	−0.0685154
$697$	−1.20343e13	−1.93140
$698$	1.09642e12	0.174834
$699$	−3.79215e12	−0.600812
$700$	−1.43507e10	−0.00225908
$701$	−1.08512e13	−1.69725	−0.848627	−	0.528991i	$-0.822570\pi$
$701$	−1.08512e13	−1.69725	−0.848627	+	0.528991i	$0.822570\pi$
$702$	2.54728e12	0.395876
$703$	1.52079e12	0.234838
$704$	−1.00857e13	−1.54749
$705$	1.90345e12	0.290195
$706$	−9.25328e12	−1.40176
$707$	5.29003e12	0.796290
$708$	−1.47883e10	−0.00221192
$709$	4.85075e12	0.720943	0.360471	−	0.932770i	$-0.382616\pi$
$709$	4.85075e12	0.720943	0.360471	+	0.932770i	$0.382616\pi$
$710$	−3.59775e12	−0.531335
$711$	7.86902e12	1.15480
$712$	1.33520e13	1.94710
$713$	3.79154e12	0.549430
$714$	6.80438e12	0.979821
$715$	1.43512e12	0.205358
$716$	−2.61739e10	−0.00372186
$717$	−5.49366e12	−0.776292
$718$	−6.06806e12	−0.852099
$719$	3.20970e12	0.447903	0.223952	−	0.974600i	$-0.428104\pi$
$719$	3.20970e12	0.447903	0.223952	+	0.974600i	$0.428104\pi$
$720$	1.53974e12	0.213526
$721$	3.21141e12	0.442576
$722$	6.55852e12	0.898232
$723$	−3.66150e12	−0.498353
$724$	−1.32020e10	−0.00178573
$725$	−7.77640e11	−0.104534
$726$	6.05099e12	0.808373
$727$	6.24701e12	0.829407	0.414703	−	0.909957i	$-0.363885\pi$
$727$	6.24701e12	0.829407	0.414703	+	0.909957i	$0.363885\pi$
$728$	3.16304e12	0.417362
$729$	3.87891e12	0.508670
$730$	−3.42035e12	−0.445777
$731$	−1.93454e12	−0.250582
$732$	1.04370e9	0.000134362 0
$733$	−9.66280e12	−1.23633	−0.618166	−	0.786048i	$-0.712124\pi$
$733$	−9.66280e12	−1.23633	−0.618166	+	0.786048i	$0.712124\pi$
$734$	−9.50929e12	−1.20925
$735$	−6.13804e10	−0.00775777
$736$	−1.86310e10	−0.00234037
$737$	1.52463e13	1.90354
$738$	6.22005e12	0.771864
$739$	1.53357e13	1.89149	0.945745	−	0.324909i	$-0.105334\pi$
$739$	1.53357e13	1.89149	0.945745	+	0.324909i	$0.105334\pi$
$740$	−4.86928e9	−0.000596928 0
$741$	6.22649e11	0.0758685
$742$	2.94771e12	0.357000
$743$	6.56971e12	0.790854	0.395427	−	0.918497i	$-0.370597\pi$
$743$	6.56971e12	0.790854	0.395427	+	0.918497i	$0.370597\pi$
$744$	−5.69550e12	−0.681481
$745$	−1.48713e12	−0.176867
$746$	9.50207e12	1.12329
$747$	−5.54194e12	−0.651207
$748$	−5.37931e10	−0.00628304
$749$	−5.22750e12	−0.606912
$750$	−3.12317e12	−0.360429
$751$	−1.15081e12	−0.132016	−0.0660078	−	0.997819i	$-0.521026\pi$
$751$	−1.15081e12	−0.132016	−0.0660078	+	0.997819i	$0.521026\pi$
$752$	1.33234e13	1.51927
$753$	8.80035e12	0.997522
$754$	4.23507e11	0.0477188
$755$	−4.93548e12	−0.552801
$756$	2.20154e10	0.00245120
$757$	6.33702e12	0.701380	0.350690	−	0.936492i	$-0.385947\pi$
$757$	6.33702e12	0.701380	0.350690	+	0.936492i	$0.385947\pi$
$758$	4.48837e12	0.493830
$759$	3.90224e12	0.426801
$760$	9.51159e11	0.103417
$761$	−4.41074e12	−0.476739	−0.238369	−	0.971175i	$-0.576613\pi$
$761$	−4.41074e12	−0.476739	−0.238369	+	0.971175i	$0.576613\pi$
$762$	−4.11165e12	−0.441793
$763$	−2.86181e11	−0.0305690
$764$	2.23760e10	0.00237609
$765$	3.33190e12	0.351735
$766$	−1.02859e13	−1.07948
$767$	5.97581e12	0.623473
$768$	4.19281e10	0.00434891
$769$	9.95807e12	1.02685	0.513425	−	0.858135i	$-0.328377\pi$
$769$	9.95807e12	1.02685	0.513425	+	0.858135i	$0.328377\pi$
$770$	−4.99502e12	−0.512069
$771$	4.25647e12	0.433815
$772$	6.72580e9	0.000681500 0
$773$	5.87337e12	0.591670	0.295835	−	0.955239i	$-0.404402\pi$
$773$	5.87337e12	0.591670	0.295835	+	0.955239i	$0.404402\pi$
$774$	9.99889e11	0.100142
$775$	−1.04419e13	−1.03973
$776$	−5.92268e10	−0.00586328
$777$	4.49004e12	0.441933
$778$	−1.86187e13	−1.82197
$779$	3.83285e12	0.372910
$780$	−1.99361e9	−0.000192847 0
$781$	−2.62274e13	−2.52247
$782$	8.10785e12	0.775310
$783$	1.19298e12	0.113424
$784$	−4.29638e11	−0.0406144
$785$	4.71760e11	0.0443412
$786$	−9.25438e12	−0.864860
$787$	7.22169e11	0.0671046	0.0335523	−	0.999437i	$-0.489318\pi$
$787$	7.22169e11	0.0671046	0.0335523	+	0.999437i	$0.489318\pi$
$788$	−4.34373e10	−0.00401324
$789$	5.06940e12	0.465704
$790$	6.25233e12	0.571110
$791$	−1.16664e13	−1.05960
$792$	1.12525e13	1.01622
$793$	−4.21751e11	−0.0378727
$794$	−8.53025e11	−0.0761674
$795$	−7.51916e11	−0.0667601
$796$	3.42151e10	0.00302071
$797$	1.59164e13	1.39728	0.698640	−	0.715473i	$-0.253789\pi$
$797$	1.59164e13	1.39728	0.698640	+	0.715473i	$0.253789\pi$
$798$	−2.16716e12	−0.189181
$799$	2.88309e13	2.50263
$800$	5.13098e10	0.00442890
$801$	−1.48966e13	−1.27862
$802$	1.26824e13	1.08247
$803$	−2.49341e13	−2.11629
$804$	−2.11795e10	−0.00178757
$805$	−1.86947e12	−0.156905
$806$	5.68672e12	0.474629
$807$	4.37406e12	0.363040
$808$	−9.46874e12	−0.781521
$809$	−2.10502e13	−1.72778	−0.863891	−	0.503679i	$-0.831979\pi$
$809$	−2.10502e13	−1.72778	−0.863891	+	0.503679i	$0.831979\pi$
$810$	−3.57684e11	−0.0291956
$811$	1.41236e13	1.14644	0.573220	−	0.819402i	$-0.305694\pi$
$811$	1.41236e13	1.14644	0.573220	+	0.819402i	$0.305694\pi$
$812$	3.66025e9	0.000295467 0
$813$	−8.35258e11	−0.0670522
$814$	1.42950e13	1.14124
$815$	3.77943e12	0.300066
$816$	−1.21491e13	−0.959267
$817$	6.16141e11	0.0483816
$818$	9.78694e9	0.000764288 0
$819$	−3.52894e12	−0.274074
$820$	−1.22721e10	−0.000947886 0
$821$	2.57886e13	1.98100	0.990498	−	0.137525i	$-0.0439148\pi$
$821$	2.57886e13	1.98100	0.990498	+	0.137525i	$0.0439148\pi$
$822$	−1.25665e12	−0.0960041
$823$	−2.37305e13	−1.80305	−0.901524	−	0.432729i	$-0.857551\pi$
$823$	−2.37305e13	−1.80305	−0.901524	+	0.432729i	$0.857551\pi$
$824$	−5.74817e12	−0.434367
$825$	−1.07468e13	−0.807673
$826$	−2.07991e13	−1.55466
$827$	1.13747e13	0.845601	0.422800	−	0.906223i	$-0.361047\pi$
$827$	1.13747e13	0.845601	0.422800	+	0.906223i	$0.361047\pi$
$828$	1.04060e10	0.000769390 0
$829$	−2.50069e13	−1.83893	−0.919465	−	0.393172i	$-0.871378\pi$
$829$	−2.50069e13	−1.83893	−0.919465	+	0.393172i	$0.871378\pi$
$830$	−4.40335e12	−0.322056
$831$	−5.68065e11	−0.0413231
$832$	−5.66155e12	−0.409619
$833$	−9.29708e11	−0.0669027
$834$	−1.16985e13	−0.837304
$835$	2.08703e12	0.148573
$836$	1.71328e10	0.00121311
$837$	1.60189e13	1.12816
$838$	−1.25164e13	−0.876758
$839$	−3.34277e12	−0.232904	−0.116452	−	0.993196i	$-0.537152\pi$
$839$	−3.34277e12	−0.232904	−0.116452	+	0.993196i	$0.537152\pi$
$840$	2.80825e12	0.194616
$841$	−1.43088e13	−0.986328
$842$	−1.39314e13	−0.955191
$843$	1.81112e11	0.0123516
$844$	−5.09751e8	−3.45794e−5 0
$845$	−4.01939e12	−0.271210
$846$	−1.49016e13	−1.00015
$847$	−2.11328e13	−1.41085
$848$	−5.26310e12	−0.349511
$849$	−1.01923e13	−0.673269
$850$	−2.23291e13	−1.46719
$851$	5.35017e12	0.349691
$852$	3.64339e10	0.00236880
$853$	−1.21621e13	−0.786573	−0.393286	−	0.919416i	$-0.628662\pi$
$853$	−1.21621e13	−0.786573	−0.393286	+	0.919416i	$0.628662\pi$
$854$	1.46792e12	0.0944373
$855$	−1.06119e12	−0.0679120
$856$	9.35681e12	0.595657
$857$	1.63637e13	1.03626	0.518130	−	0.855302i	$-0.326628\pi$
$857$	1.63637e13	1.03626	0.518130	+	0.855302i	$0.326628\pi$
$858$	5.85276e12	0.368695
$859$	1.60705e13	1.00707	0.503536	−	0.863974i	$-0.332032\pi$
$859$	1.60705e13	1.00707	0.503536	+	0.863974i	$0.332032\pi$
$860$	−1.97277e9	−0.000122980 0
$861$	1.13163e13	0.701763
$862$	3.35511e12	0.206978
$863$	1.16801e13	0.716801	0.358400	−	0.933568i	$-0.383322\pi$
$863$	1.16801e13	0.716801	0.358400	+	0.933568i	$0.383322\pi$
$864$	−7.87143e10	−0.00480554
$865$	2.98157e11	0.0181081
$866$	−7.01967e12	−0.424117
$867$	−1.65530e13	−0.994925
$868$	4.91488e10	0.00293883
$869$	4.55792e13	2.71130
$870$	3.76003e11	0.0222513
$871$	8.55844e12	0.503864
$872$	5.12242e11	0.0300020
$873$	6.60784e10	0.00385030
$874$	−2.58231e12	−0.149695
$875$	1.09075e13	0.629055
$876$	3.46374e10	0.00198736
$877$	9.59713e12	0.547827	0.273913	−	0.961754i	$-0.411682\pi$
$877$	9.59713e12	0.547827	0.273913	+	0.961754i	$0.411682\pi$
$878$	2.17106e13	1.23295
$879$	1.21966e11	0.00689112
$880$	8.91853e12	0.501327
$881$	−2.72521e13	−1.52408	−0.762040	−	0.647530i	$-0.775802\pi$
$881$	−2.72521e13	−1.52408	−0.762040	+	0.647530i	$0.775802\pi$
$882$	4.80530e11	0.0267370
$883$	5.70516e12	0.315824	0.157912	−	0.987453i	$-0.449524\pi$
$883$	5.70516e12	0.315824	0.157912	+	0.987453i	$0.449524\pi$
$884$	−3.01965e10	−0.00166311
$885$	5.30553e12	0.290726
$886$	8.87977e12	0.484117
$887$	3.56571e12	0.193415	0.0967074	−	0.995313i	$-0.469169\pi$
$887$	3.56571e12	0.193415	0.0967074	+	0.995313i	$0.469169\pi$
$888$	−8.03682e12	−0.433736
$889$	1.43597e13	0.771059
$890$	−1.18361e13	−0.632345
$891$	−2.60750e12	−0.138604
$892$	−1.09975e10	−0.000581635 0
$893$	−9.18248e12	−0.483201
$894$	−6.06486e12	−0.317543
$895$	9.39028e12	0.489187
$896$	1.96078e13	1.01635
$897$	2.19050e12	0.112974
$898$	−2.15449e13	−1.10561
$899$	2.66329e12	0.135988
$900$	−2.86581e10	−0.00145598
$901$	−1.13890e13	−0.575737
$902$	3.60280e13	1.81222
$903$	1.81912e12	0.0910473
$904$	2.08820e13	1.03995
$905$	4.73641e12	0.234709
$906$	−2.01280e13	−0.992486
$907$	−4.80969e12	−0.235985	−0.117992	−	0.993015i	$-0.537646\pi$
$907$	−4.80969e12	−0.235985	−0.117992	+	0.993015i	$0.537646\pi$
$908$	7.53892e9	0.000368064 0
$909$	1.05641e13	0.513210
$910$	−2.80392e12	−0.135544
$911$	2.32435e13	1.11807	0.559036	−	0.829144i	$-0.311172\pi$
$911$	2.32435e13	1.11807	0.559036	+	0.829144i	$0.311172\pi$
$912$	3.86943e12	0.185213
$913$	−3.21002e13	−1.52893
$914$	−2.64668e13	−1.25442
$915$	−3.74445e11	−0.0176601
$916$	3.99527e10	0.00187507
$917$	3.23204e13	1.50944
$918$	3.42550e13	1.59196
$919$	−1.28689e13	−0.595143	−0.297572	−	0.954699i	$-0.596177\pi$
$919$	−1.28689e13	−0.595143	−0.297572	+	0.954699i	$0.596177\pi$
$920$	3.34621e12	0.153995
$921$	9.58446e12	0.438934
$922$	3.24485e13	1.47878
$923$	−1.47226e13	−0.667693
$924$	5.05838e10	0.00228290
$925$	−1.47344e13	−0.661751
$926$	3.29818e13	1.47409
$927$	6.41314e12	0.285241
$928$	−1.30869e10	−0.000579258 0
$929$	1.37766e13	0.606835	0.303417	−	0.952858i	$-0.401872\pi$
$929$	1.37766e13	0.606835	0.303417	+	0.952858i	$0.401872\pi$
$930$	5.04886e12	0.221320
$931$	2.96107e11	0.0129174
$932$	−5.85734e10	−0.00254290
$933$	−2.60908e13	−1.12725
$934$	4.58230e12	0.197026
$935$	1.92991e13	0.825819
$936$	6.31653e12	0.268991
$937$	−4.51728e13	−1.91447	−0.957235	−	0.289312i	$-0.906573\pi$
$937$	−4.51728e13	−1.91447	−0.957235	+	0.289312i	$0.906573\pi$
$938$	−2.97881e13	−1.25640
$939$	−1.66133e12	−0.0697364
$940$	2.94006e10	0.00122823
$941$	−3.42835e13	−1.42538	−0.712691	−	0.701478i	$-0.752524\pi$
$941$	−3.42835e13	−1.42538	−0.712691	+	0.701478i	$0.752524\pi$
$942$	1.92394e12	0.0796092
$943$	1.34841e13	0.555289
$944$	3.71365e13	1.52204
$945$	−7.89837e12	−0.322177
$946$	5.79158e12	0.235119
$947$	−1.37682e13	−0.556291	−0.278146	−	0.960539i	$-0.589720\pi$
$947$	−1.37682e13	−0.556291	−0.278146	+	0.960539i	$0.589720\pi$
$948$	−6.33164e10	−0.00254612
$949$	−1.39966e13	−0.560177
$950$	7.11169e12	0.283280
$951$	−3.45020e12	−0.136783
$952$	4.25355e13	1.67836
$953$	−1.36645e13	−0.536631	−0.268315	−	0.963331i	$-0.586467\pi$
$953$	−1.36645e13	−0.536631	−0.268315	+	0.963331i	$0.586467\pi$
$954$	5.88654e12	0.230087
$955$	−8.02773e12	−0.312304
$956$	−8.48548e10	−0.00328561
$957$	2.74105e12	0.105636
$958$	−1.72150e13	−0.660333
$959$	4.38877e12	0.167556
$960$	−5.02651e12	−0.191005
$961$	9.32219e12	0.352584
$962$	8.02444e12	0.302083
$963$	−1.04392e13	−0.391156
$964$	−5.65554e10	−0.00210925
$965$	−2.41298e12	−0.0895738
$966$	−7.62413e12	−0.281704
$967$	−4.12683e13	−1.51774	−0.758870	−	0.651242i	$-0.774248\pi$
$967$	−4.12683e13	−1.51774	−0.758870	+	0.651242i	$0.774248\pi$
$968$	3.78260e13	1.38468
$969$	8.37319e12	0.305094
$970$	5.25025e10	0.00190418
$971$	1.00786e13	0.363841	0.181921	−	0.983313i	$-0.441769\pi$
$971$	1.00786e13	0.363841	0.181921	+	0.983313i	$0.441769\pi$
$972$	7.04891e10	0.00253293
$973$	4.08564e13	1.46134
$974$	−1.65579e13	−0.589509
$975$	−6.03264e12	−0.213790
$976$	−2.62096e12	−0.0924562
$977$	−1.91473e13	−0.672328	−0.336164	−	0.941803i	$-0.609130\pi$
$977$	−1.91473e13	−0.672328	−0.336164	+	0.941803i	$0.609130\pi$
$978$	1.54134e13	0.538732
$979$	−8.62847e13	−3.00201
$980$	−9.48080e8	−3.28343e−5 0
$981$	−5.71499e11	−0.0197018
$982$	−1.77930e13	−0.610586
$983$	−1.52587e12	−0.0521228	−0.0260614	−	0.999660i	$-0.508297\pi$
$983$	−1.52587e12	−0.0521228	−0.0260614	+	0.999660i	$0.508297\pi$
$984$	−2.02553e13	−0.688748
$985$	1.55838e13	0.527485
$986$	5.69519e12	0.191894
$987$	−2.71108e13	−0.909316
$988$	9.61741e9	0.000321108 0
$989$	2.16760e12	0.0720437
$990$	−9.97496e12	−0.330030
$991$	−3.05103e11	−0.0100488	−0.00502441	−	0.999987i	$-0.501599\pi$
$991$	−3.05103e11	−0.0100488	−0.00502441	+	0.999987i	$0.501599\pi$
$992$	−1.75728e11	−0.00576152
$993$	7.08587e12	0.231271
$994$	5.12427e13	1.66492
$995$	−1.22752e13	−0.397031
$996$	4.45921e10	0.00143579
$997$	−1.60848e13	−0.515571	−0.257785	−	0.966202i	$-0.582993\pi$
$997$	−1.60848e13	−0.515571	−0.257785	+	0.966202i	$0.582993\pi$
$998$	−2.77636e13	−0.885908
$999$	2.26040e13	0.718028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.b.1.5	✓	17
3.2	odd	2		387.10.a.e.1.13		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.5	✓	17	1.1	even	1	trivial
387.10.a.e.1.13		17	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-22.5994 q^{2} -82.1072 q^{3} -1.26822 q^{4} +454.995 q^{5} +1855.57 q^{6} -6480.48 q^{7} +11599.5 q^{8} -12941.4 q^{9} +O(q^{10})\)	\(q-22.5994 q^{2} -82.1072 q^{3} -1.26822 q^{4} +454.995 q^{5} +1855.57 q^{6} -6480.48 q^{7} +11599.5 q^{8} -12941.4 q^{9} -10282.6 q^{10} -74959.6 q^{11} +104.130 q^{12} -42078.1 q^{13} +146455. q^{14} -37358.3 q^{15} -261493. q^{16} -565853. q^{17} +292468. q^{18} +180221. q^{19} -577.035 q^{20} +532094. q^{21} +1.69404e6 q^{22} +634024. q^{23} -952406. q^{24} -1.74610e6 q^{25} +950939. q^{26} +2.67870e6 q^{27} +8218.70 q^{28} +445357. q^{29} +844275. q^{30} +5.98012e6 q^{31} -29385.3 q^{32} +6.15472e6 q^{33} +1.27879e7 q^{34} -2.94858e6 q^{35} +16412.6 q^{36} +8.43844e6 q^{37} -4.07289e6 q^{38} +3.45491e6 q^{39} +5.27773e6 q^{40} +2.12675e7 q^{41} -1.20250e7 q^{42} +3.41880e6 q^{43} +95065.5 q^{44} -5.88827e6 q^{45} -1.43285e7 q^{46} -5.09511e7 q^{47} +2.14705e7 q^{48} +1.64302e6 q^{49} +3.94609e7 q^{50} +4.64606e7 q^{51} +53364.5 q^{52} +2.01271e7 q^{53} -6.05369e7 q^{54} -3.41062e7 q^{55} -7.51706e7 q^{56} -1.47975e7 q^{57} -1.00648e7 q^{58} -1.42017e8 q^{59} +47378.7 q^{60} +1.00231e7 q^{61} -1.35147e8 q^{62} +8.38666e7 q^{63} +1.34549e8 q^{64} -1.91453e7 q^{65} -1.39093e8 q^{66} -2.03394e8 q^{67} +717629. q^{68} -5.20579e7 q^{69} +6.66361e7 q^{70} +3.49888e8 q^{71} -1.50114e8 q^{72} +3.32635e8 q^{73} -1.90703e8 q^{74} +1.43368e8 q^{75} -228561. q^{76} +4.85774e8 q^{77} -7.80789e7 q^{78} -6.08050e8 q^{79} -1.18978e8 q^{80} +3.47854e7 q^{81} -4.80632e8 q^{82} +4.28233e8 q^{83} -674815. q^{84} -2.57460e8 q^{85} -7.72628e7 q^{86} -3.65670e7 q^{87} -8.69496e8 q^{88} +1.15108e9 q^{89} +1.33071e8 q^{90} +2.72686e8 q^{91} -804084. q^{92} -4.91011e8 q^{93} +1.15146e9 q^{94} +8.19997e7 q^{95} +2.41274e6 q^{96} -5.10596e6 q^{97} -3.71312e7 q^{98} +9.70082e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9} + 23763 q^{10} + 78370 q^{11} + 271339 q^{12} + 114452 q^{13} - 376208 q^{14} - 255820 q^{15} + 412586 q^{16} + 726937 q^{17} + 577055 q^{18} + 544263 q^{19} + 3642183 q^{20} + 3137394 q^{21} + 5269148 q^{22} + 5575241 q^{23} + 16215113 q^{24} + 10874708 q^{25} + 8009180 q^{26} + 8350126 q^{27} + 12534764 q^{28} + 8223345 q^{29} + 30612012 q^{30} + 13054147 q^{31} + 37111710 q^{32} + 36024808 q^{33} + 27991291 q^{34} + 17826330 q^{35} + 84105953 q^{36} + 46733879 q^{37} + 15733789 q^{38} + 8689898 q^{39} + 52241669 q^{40} + 53667013 q^{41} + 7708286 q^{42} + 58119617 q^{43} + 81727236 q^{44} + 124361968 q^{45} + 146859355 q^{46} + 122945511 q^{47} + 86356095 q^{48} + 111396073 q^{49} - 96642133 q^{50} - 187132423 q^{51} - 54447944 q^{52} - 993146 q^{53} - 219468490 q^{54} - 248155792 q^{55} - 141048116 q^{56} - 402917960 q^{57} - 466599837 q^{58} - 95519644 q^{59} - 621611940 q^{60} - 311752038 q^{61} - 212471691 q^{62} - 928966350 q^{63} - 829842590 q^{64} - 107969830 q^{65} - 978530932 q^{66} - 292438130 q^{67} - 88281129 q^{68} + 78577726 q^{69} - 1650972530 q^{70} - 13576908 q^{71} - 706943493 q^{72} - 501490738 q^{73} - 494831691 q^{74} - 641914030 q^{75} - 1248630771 q^{76} + 787365348 q^{77} - 946670550 q^{78} + 740350275 q^{79} - 27802861 q^{80} + 1582210525 q^{81} - 1600400057 q^{82} + 754109940 q^{83} - 1955423842 q^{84} + 1071609956 q^{85} + 164102448 q^{86} + 186301257 q^{87} + 1863375104 q^{88} + 1470581868 q^{89} - 698098630 q^{90} + 2895349644 q^{91} + 1041082071 q^{92} + 4540331515 q^{93} - 706582361 q^{94} + 3297255729 q^{95} + 2087289393 q^{96} + 1949310583 q^{97} + 6695989160 q^{98} + 1234191326 q^{99}+O(q^{100}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9 + 23763 * q^10 + 78370 * q^11 + 271339 * q^12 + 114452 * q^13 - 376208 * q^14 - 255820 * q^15 + 412586 * q^16 + 726937 * q^17 + 577055 * q^18 + 544263 * q^19 + 3642183 * q^20 + 3137394 * q^21 + 5269148 * q^22 + 5575241 * q^23 + 16215113 * q^24 + 10874708 * q^25 + 8009180 * q^26 + 8350126 * q^27 + 12534764 * q^28 + 8223345 * q^29 + 30612012 * q^30 + 13054147 * q^31 + 37111710 * q^32 + 36024808 * q^33 + 27991291 * q^34 + 17826330 * q^35 + 84105953 * q^36 + 46733879 * q^37 + 15733789 * q^38 + 8689898 * q^39 + 52241669 * q^40 + 53667013 * q^41 + 7708286 * q^42 + 58119617 * q^43 + 81727236 * q^44 + 124361968 * q^45 + 146859355 * q^46 + 122945511 * q^47 + 86356095 * q^48 + 111396073 * q^49 - 96642133 * q^50 - 187132423 * q^51 - 54447944 * q^52 - 993146 * q^53 - 219468490 * q^54 - 248155792 * q^55 - 141048116 * q^56 - 402917960 * q^57 - 466599837 * q^58 - 95519644 * q^59 - 621611940 * q^60 - 311752038 * q^61 - 212471691 * q^62 - 928966350 * q^63 - 829842590 * q^64 - 107969830 * q^65 - 978530932 * q^66 - 292438130 * q^67 - 88281129 * q^68 + 78577726 * q^69 - 1650972530 * q^70 - 13576908 * q^71 - 706943493 * q^72 - 501490738 * q^73 - 494831691 * q^74 - 641914030 * q^75 - 1248630771 * q^76 + 787365348 * q^77 - 946670550 * q^78 + 740350275 * q^79 - 27802861 * q^80 + 1582210525 * q^81 - 1600400057 * q^82 + 754109940 * q^83 - 1955423842 * q^84 + 1071609956 * q^85 + 164102448 * q^86 + 186301257 * q^87 + 1863375104 * q^88 + 1470581868 * q^89 - 698098630 * q^90 + 2895349644 * q^91 + 1041082071 * q^92 + 4540331515 * q^93 - 706582361 * q^94 + 3297255729 * q^95 + 2087289393 * q^96 + 1949310583 * q^97 + 6695989160 * q^98 + 1234191326 * q^99

Introduction

L-functions

Modular forms

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