LMFDB - Embedded newform 43.10.a.b.1.6

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			1.6
Root			$23.8827$ 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)

$f(q)$	$=$	$q-20.8827 q^{2} +85.1471 q^{3} -75.9135 q^{4} +2696.38 q^{5} -1778.10 q^{6} +8355.76 q^{7} +12277.2 q^{8} -12433.0 q^{9} +O(q^{10})$	\(q-20.8827 q^{2} +85.1471 q^{3} -75.9135 q^{4} +2696.38 q^{5} -1778.10 q^{6} +8355.76 q^{7} +12277.2 q^{8} -12433.0 q^{9} -56307.6 q^{10} +10458.0 q^{11} -6463.81 q^{12} +102242. q^{13} -174491. q^{14} +229589. q^{15} -217513. q^{16} -187814. q^{17} +259634. q^{18} -820737. q^{19} -204691. q^{20} +711469. q^{21} -218391. q^{22} +430917. q^{23} +1.04537e6 q^{24} +5.31732e6 q^{25} -2.13509e6 q^{26} -2.73458e6 q^{27} -634315. q^{28} +4.30547e6 q^{29} -4.79443e6 q^{30} +6.26683e6 q^{31} -1.74367e6 q^{32} +890469. q^{33} +3.92206e6 q^{34} +2.25303e7 q^{35} +943830. q^{36} +1.13847e7 q^{37} +1.71392e7 q^{38} +8.70563e6 q^{39} +3.31040e7 q^{40} -2.93133e7 q^{41} -1.48574e7 q^{42} +3.41880e6 q^{43} -793904. q^{44} -3.35240e7 q^{45} -8.99871e6 q^{46} -2.84104e6 q^{47} -1.85206e7 q^{48} +2.94651e7 q^{49} -1.11040e8 q^{50} -1.59918e7 q^{51} -7.76156e6 q^{52} -4.60443e7 q^{53} +5.71054e7 q^{54} +2.81987e7 q^{55} +1.02585e8 q^{56} -6.98834e7 q^{57} -8.99097e7 q^{58} +1.23879e8 q^{59} -1.74289e7 q^{60} +5.81812e7 q^{61} -1.30868e8 q^{62} -1.03887e8 q^{63} +1.47779e8 q^{64} +2.75684e8 q^{65} -1.85954e7 q^{66} -2.25688e8 q^{67} +1.42576e7 q^{68} +3.66914e7 q^{69} -4.70493e8 q^{70} -2.02879e8 q^{71} -1.52642e8 q^{72} +5.53120e7 q^{73} -2.37744e8 q^{74} +4.52754e8 q^{75} +6.23050e7 q^{76} +8.73846e7 q^{77} -1.81797e8 q^{78} +3.94926e8 q^{79} -5.86498e8 q^{80} +1.18766e7 q^{81} +6.12141e8 q^{82} +1.10686e8 q^{83} -5.40100e7 q^{84} -5.06417e8 q^{85} -7.13937e7 q^{86} +3.66598e8 q^{87} +1.28395e8 q^{88} -7.87892e7 q^{89} +7.00071e8 q^{90} +8.54312e8 q^{91} -3.27124e7 q^{92} +5.33602e8 q^{93} +5.93285e7 q^{94} -2.21302e9 q^{95} -1.48468e8 q^{96} -1.11105e9 q^{97} -6.15310e8 q^{98} -1.30024e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−20.8827	−0.922893	−0.461447	−	0.887168i	$-0.652669\pi$
$2$	−20.8827	−0.922893	−0.461447	+	0.887168i	$0.652669\pi$
$3$	85.1471	0.606910	0.303455	−	0.952846i	$-0.401860\pi$
$3$	85.1471	0.606910	0.303455	+	0.952846i	$0.401860\pi$
$4$	−75.9135	−0.148268
$5$	2696.38	1.92937	0.964685	−	0.263406i	$-0.0848460\pi$
$5$	2696.38	1.92937	0.964685	+	0.263406i	$0.0848460\pi$
$6$	−1778.10	−0.560113
$7$	8355.76	1.31536	0.657680	−	0.753297i	$-0.271538\pi$
$7$	8355.76	1.31536	0.657680	+	0.753297i	$0.271538\pi$
$8$	12277.2	1.05973
$9$	−12433.0	−0.631660
$10$	−56307.6	−1.78060
$11$	10458.0	0.215368	0.107684	−	0.994185i	$-0.465656\pi$
$11$	10458.0	0.215368	0.107684	+	0.994185i	$0.465656\pi$
$12$	−6463.81	−0.0899856
$13$	102242.	0.992854	0.496427	−	0.868079i	$-0.334645\pi$
$13$	102242.	0.992854	0.496427	+	0.868079i	$0.334645\pi$
$14$	−174491.	−1.21394
$15$	229589.	1.17095
$16$	−217513.	−0.829748
$17$	−187814.	−0.545390	−0.272695	−	0.962101i	$-0.587915\pi$
$17$	−187814.	−0.545390	−0.272695	+	0.962101i	$0.587915\pi$
$18$	259634.	0.582955
$19$	−820737.	−1.44482	−0.722409	−	0.691466i	$-0.756965\pi$
$19$	−820737.	−1.44482	−0.722409	+	0.691466i	$0.756965\pi$
$20$	−204691.	−0.286065
$21$	711469.	0.798305
$22$	−218391.	−0.198762
$23$	430917.	0.321084	0.160542	−	0.987029i	$-0.448676\pi$
$23$	430917.	0.321084	0.160542	+	0.987029i	$0.448676\pi$
$24$	1.04537e6	0.643160
$25$	5.31732e6	2.72247
$26$	−2.13509e6	−0.916298
$27$	−2.73458e6	−0.990271
$28$	−634315.	−0.195026
$29$	4.30547e6	1.13039	0.565196	−	0.824957i	$-0.308800\pi$
$29$	4.30547e6	1.13039	0.565196	+	0.824957i	$0.308800\pi$
$30$	−4.79443e6	−1.08066
$31$	6.26683e6	1.21877	0.609383	−	0.792876i	$-0.291417\pi$
$31$	6.26683e6	1.21877	0.609383	+	0.792876i	$0.291417\pi$
$32$	−1.74367e6	−0.293960
$33$	890469.	0.130709
$34$	3.92206e6	0.503337
$35$	2.25303e7	2.53782
$36$	943830.	0.0936553
$37$	1.13847e7	0.998654	0.499327	−	0.866414i	$-0.333581\pi$
$37$	1.13847e7	0.998654	0.499327	+	0.866414i	$0.333581\pi$
$38$	1.71392e7	1.33341
$39$	8.70563e6	0.602573
$40$	3.31040e7	2.04461
$41$	−2.93133e7	−1.62009	−0.810043	−	0.586371i	$-0.800556\pi$
$41$	−2.93133e7	−1.62009	−0.810043	+	0.586371i	$0.800556\pi$
$42$	−1.48574e7	−0.736750
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	−793904.	−0.0319324
$45$	−3.35240e7	−1.21871
$46$	−8.99871e6	−0.296326
$47$	−2.84104e6	−0.0849253	−0.0424626	−	0.999098i	$-0.513520\pi$
$47$	−2.84104e6	−0.0849253	−0.0424626	+	0.999098i	$0.513520\pi$
$48$	−1.85206e7	−0.503582
$49$	2.94651e7	0.730173
$50$	−1.11040e8	−2.51255
$51$	−1.59918e7	−0.331003
$52$	−7.76156e6	−0.147209
$53$	−4.60443e7	−0.801556	−0.400778	−	0.916175i	$-0.631260\pi$
$53$	−4.60443e7	−0.801556	−0.400778	+	0.916175i	$0.631260\pi$
$54$	5.71054e7	0.913914
$55$	2.81987e7	0.415525
$56$	1.02585e8	1.39393
$57$	−6.98834e7	−0.876874
$58$	−8.99097e7	−1.04323
$59$	1.23879e8	1.33095	0.665477	−	0.746419i	$-0.268228\pi$
$59$	1.23879e8	1.33095	0.665477	+	0.746419i	$0.268228\pi$
$60$	−1.74289e7	−0.173615
$61$	5.81812e7	0.538020	0.269010	−	0.963137i	$-0.413304\pi$
$61$	5.81812e7	0.538020	0.269010	+	0.963137i	$0.413304\pi$
$62$	−1.30868e8	−1.12479
$63$	−1.03887e8	−0.830861
$64$	1.47779e8	1.10104
$65$	2.75684e8	1.91558
$66$	−1.85954e7	−0.120631
$67$	−2.25688e8	−1.36827	−0.684136	−	0.729354i	$-0.739821\pi$
$67$	−2.25688e8	−1.36827	−0.684136	+	0.729354i	$0.739821\pi$
$68$	1.42576e7	0.0808642
$69$	3.66914e7	0.194869
$70$	−4.70493e8	−2.34213
$71$	−2.02879e8	−0.947491	−0.473745	−	0.880662i	$-0.657098\pi$
$71$	−2.02879e8	−0.947491	−0.473745	+	0.880662i	$0.657098\pi$
$72$	−1.52642e8	−0.669389
$73$	5.53120e7	0.227964	0.113982	−	0.993483i	$-0.463639\pi$
$73$	5.53120e7	0.227964	0.113982	+	0.993483i	$0.463639\pi$
$74$	−2.37744e8	−0.921650
$75$	4.52754e8	1.65229
$76$	6.23050e7	0.214221
$77$	8.73846e7	0.283287
$78$	−1.81797e8	−0.556110
$79$	3.94926e8	1.14076	0.570379	−	0.821382i	$-0.306796\pi$
$79$	3.94926e8	1.14076	0.570379	+	0.821382i	$0.306796\pi$
$80$	−5.86498e8	−1.60089
$81$	1.18766e7	0.0306555
$82$	6.12141e8	1.49517
$83$	1.10686e8	0.256002	0.128001	−	0.991774i	$-0.459144\pi$
$83$	1.10686e8	0.256002	0.128001	+	0.991774i	$0.459144\pi$
$84$	−5.40100e7	−0.118363
$85$	−5.06417e8	−1.05226
$86$	−7.13937e7	−0.140740
$87$	3.66598e8	0.686046
$88$	1.28395e8	0.228232
$89$	−7.87892e7	−0.133110	−0.0665552	−	0.997783i	$-0.521201\pi$
$89$	−7.87892e7	−0.133110	−0.0665552	+	0.997783i	$0.521201\pi$
$90$	7.00071e8	1.12474
$91$	8.54312e8	1.30596
$92$	−3.27124e7	−0.0476066
$93$	5.33602e8	0.739681
$94$	5.93285e7	0.0783770
$95$	−2.21302e9	−2.78759
$96$	−1.48468e8	−0.178407
$97$	−1.11105e9	−1.27427	−0.637136	−	0.770751i	$-0.719881\pi$
$97$	−1.11105e9	−1.27427	−0.637136	+	0.770751i	$0.719881\pi$
$98$	−6.15310e8	−0.673871
$99$	−1.30024e8	−0.136040
$100$	−4.03656e8	−0.403656
$101$	1.20954e9	1.15657	0.578285	−	0.815834i	$-0.303722\pi$
$101$	1.20954e9	1.15657	0.578285	+	0.815834i	$0.303722\pi$
$102$	3.33952e8	0.305480
$103$	−6.32671e8	−0.553873	−0.276936	−	0.960888i	$-0.589319\pi$
$103$	−6.32671e8	−0.553873	−0.276936	+	0.960888i	$0.589319\pi$
$104$	1.25525e9	1.05216
$105$	1.91839e9	1.54023
$106$	9.61528e8	0.739751
$107$	1.69957e9	1.25346	0.626732	−	0.779235i	$-0.284392\pi$
$107$	1.69957e9	1.25346	0.626732	+	0.779235i	$0.284392\pi$
$108$	2.07592e8	0.146826
$109$	−2.27846e8	−0.154604	−0.0773022	−	0.997008i	$-0.524631\pi$
$109$	−2.27846e8	−0.154604	−0.0773022	+	0.997008i	$0.524631\pi$
$110$	−5.88865e8	−0.383486
$111$	9.69376e8	0.606093
$112$	−1.81749e9	−1.09142
$113$	3.22465e9	1.86050	0.930248	−	0.366930i	$-0.119591\pi$
$113$	3.22465e9	1.86050	0.930248	+	0.366930i	$0.119591\pi$
$114$	1.45935e9	0.809261
$115$	1.16192e9	0.619490
$116$	−3.26843e8	−0.167602
$117$	−1.27118e9	−0.627147
$118$	−2.58692e9	−1.22833
$119$	−1.56933e9	−0.717385
$120$	2.81871e9	1.24089
$121$	−2.24858e9	−0.953616
$122$	−1.21498e9	−0.496535
$123$	−2.49595e9	−0.983246
$124$	−4.75737e8	−0.180705
$125$	9.07114e9	3.32328
$126$	2.16944e9	0.766796
$127$	−9.53007e8	−0.325072	−0.162536	−	0.986703i	$-0.551967\pi$
$127$	−9.53007e8	−0.325072	−0.162536	+	0.986703i	$0.551967\pi$
$128$	−2.19327e9	−0.722184
$129$	2.91101e8	0.0925529
$130$	−5.75701e9	−1.76788
$131$	1.87242e9	0.555497	0.277748	−	0.960654i	$-0.410412\pi$
$131$	1.87242e9	0.555497	0.277748	+	0.960654i	$0.410412\pi$
$132$	−6.75986e7	−0.0193801
$133$	−6.85788e9	−1.90046
$134$	4.71298e9	1.26277
$135$	−7.37346e9	−1.91060
$136$	−2.30583e9	−0.577966
$137$	8.46701e8	0.205347	0.102673	−	0.994715i	$-0.467260\pi$
$137$	8.46701e8	0.205347	0.102673	+	0.994715i	$0.467260\pi$
$138$	−7.66214e8	−0.179843
$139$	−6.15360e9	−1.39818	−0.699089	−	0.715035i	$-0.746411\pi$
$139$	−6.15360e9	−1.39818	−0.699089	+	0.715035i	$0.746411\pi$
$140$	−1.71035e9	−0.376278
$141$	−2.41906e8	−0.0515420
$142$	4.23666e9	0.874432
$143$	1.06925e9	0.213829
$144$	2.70434e9	0.524119
$145$	1.16092e10	2.18094
$146$	−1.15506e9	−0.210386
$147$	2.50887e9	0.443149
$148$	−8.64254e8	−0.148069
$149$	−1.84833e9	−0.307213	−0.153607	−	0.988132i	$-0.549089\pi$
$149$	−1.84833e9	−0.307213	−0.153607	+	0.988132i	$0.549089\pi$
$150$	−9.45473e9	−1.52489
$151$	−3.28551e9	−0.514288	−0.257144	−	0.966373i	$-0.582782\pi$
$151$	−3.28551e9	−0.514288	−0.257144	+	0.966373i	$0.582782\pi$
$152$	−1.00764e10	−1.53111
$153$	2.33508e9	0.344501
$154$	−1.82483e9	−0.261444
$155$	1.68977e10	2.35145
$156$	−6.60874e8	−0.0893425
$157$	−1.46282e10	−1.92151	−0.960755	−	0.277397i	$-0.910528\pi$
$157$	−1.46282e10	−1.92151	−0.960755	+	0.277397i	$0.910528\pi$
$158$	−8.24711e9	−1.05280
$159$	−3.92053e9	−0.486472
$160$	−4.70158e9	−0.567158
$161$	3.60064e9	0.422341
$162$	−2.48014e8	−0.0282917
$163$	−5.38221e9	−0.597196	−0.298598	−	0.954379i	$-0.596519\pi$
$163$	−5.38221e9	−0.597196	−0.298598	+	0.954379i	$0.596519\pi$
$164$	2.22528e9	0.240208
$165$	2.40104e9	0.252186
$166$	−2.31143e9	−0.236262
$167$	−6.60141e9	−0.656769	−0.328385	−	0.944544i	$-0.606504\pi$
$167$	−6.60141e9	−0.656769	−0.328385	+	0.944544i	$0.606504\pi$
$168$	8.73485e9	0.845987
$169$	−1.51023e8	−0.0142414
$170$	1.05753e10	0.971123
$171$	1.02042e10	0.912634
$172$	−2.59533e8	−0.0226107
$173$	1.03328e9	0.0877022	0.0438511	−	0.999038i	$-0.486037\pi$
$173$	1.03328e9	0.0877022	0.0438511	+	0.999038i	$0.486037\pi$
$174$	−7.65555e9	−0.633147
$175$	4.44302e10	3.58103
$176$	−2.27476e9	−0.178702
$177$	1.05479e10	0.807768
$178$	1.64533e9	0.122847
$179$	−2.55602e10	−1.86091	−0.930457	−	0.366402i	$-0.880590\pi$
$179$	−2.55602e10	−1.86091	−0.930457	+	0.366402i	$0.880590\pi$
$180$	2.54492e9	0.180696
$181$	1.30810e10	0.905914	0.452957	−	0.891532i	$-0.350369\pi$
$181$	1.30810e10	0.905914	0.452957	+	0.891532i	$0.350369\pi$
$182$	−1.78403e10	−1.20526
$183$	4.95396e9	0.326530
$184$	5.29046e9	0.340262
$185$	3.06975e10	1.92677
$186$	−1.11430e10	−0.682646
$187$	−1.96416e9	−0.117460
$188$	2.15673e8	0.0125917
$189$	−2.28495e10	−1.30256
$190$	4.62137e10	2.57264
$191$	−4.06617e9	−0.221073	−0.110536	−	0.993872i	$-0.535257\pi$
$191$	−4.06617e9	−0.221073	−0.110536	+	0.993872i	$0.535257\pi$
$192$	1.25830e10	0.668233
$193$	−2.12864e10	−1.10432	−0.552159	−	0.833739i	$-0.686196\pi$
$193$	−2.12864e10	−1.10432	−0.552159	+	0.833739i	$0.686196\pi$
$194$	2.32018e10	1.17602
$195$	2.34737e10	1.16259
$196$	−2.23680e9	−0.108262
$197$	−3.30625e10	−1.56400	−0.782002	−	0.623276i	$-0.785801\pi$
$197$	−3.30625e10	−1.56400	−0.782002	+	0.623276i	$0.785801\pi$
$198$	2.71525e9	0.125550
$199$	2.40729e10	1.08815	0.544076	−	0.839036i	$-0.316880\pi$
$199$	2.40729e10	1.08815	0.544076	+	0.839036i	$0.316880\pi$
$200$	6.52819e10	2.88508
$201$	−1.92167e10	−0.830418
$202$	−2.52583e10	−1.06739
$203$	3.59754e10	1.48687
$204$	1.21399e9	0.0490773
$205$	−7.90398e10	−3.12574
$206$	1.32119e10	0.511165
$207$	−5.35758e9	−0.202816
$208$	−2.22391e10	−0.823818
$209$	−8.58328e9	−0.311168
$210$	−4.00611e10	−1.42146
$211$	8.21104e8	0.0285185	0.0142593	−	0.999898i	$-0.495461\pi$
$211$	8.21104e8	0.0285185	0.0142593	+	0.999898i	$0.495461\pi$
$212$	3.49538e9	0.118846
$213$	−1.72746e10	−0.575041
$214$	−3.54916e10	−1.15681
$215$	9.21837e9	0.294226
$216$	−3.35730e10	−1.04942
$217$	5.23641e10	1.60312
$218$	4.75803e9	0.142683
$219$	4.70965e9	0.138354
$220$	−2.14066e9	−0.0616093
$221$	−1.92025e10	−0.541493
$222$	−2.02432e10	−0.559359
$223$	1.21345e10	0.328588	0.164294	−	0.986411i	$-0.447465\pi$
$223$	1.21345e10	0.328588	0.164294	+	0.986411i	$0.447465\pi$
$224$	−1.45697e10	−0.386664
$225$	−6.61101e10	−1.71968
$226$	−6.73392e10	−1.71704
$227$	1.70887e10	0.427162	0.213581	−	0.976925i	$-0.431487\pi$
$227$	1.70887e10	0.427162	0.213581	+	0.976925i	$0.431487\pi$
$228$	5.30509e9	0.130013
$229$	7.20213e10	1.73062	0.865309	−	0.501239i	$-0.167122\pi$
$229$	7.20213e10	1.73062	0.865309	+	0.501239i	$0.167122\pi$
$230$	−2.42639e10	−0.571723
$231$	7.44055e9	0.171930
$232$	5.28591e10	1.19791
$233$	1.38200e10	0.307190	0.153595	−	0.988134i	$-0.450915\pi$
$233$	1.38200e10	0.307190	0.153595	+	0.988134i	$0.450915\pi$
$234$	2.65455e10	0.578789
$235$	−7.66051e9	−0.163852
$236$	−9.40406e9	−0.197338
$237$	3.36268e10	0.692337
$238$	3.27718e10	0.662069
$239$	−2.87930e10	−0.570817	−0.285409	−	0.958406i	$-0.592129\pi$
$239$	−2.87930e10	−0.570817	−0.285409	+	0.958406i	$0.592129\pi$
$240$	−4.99386e10	−0.971596
$241$	−3.23422e10	−0.617579	−0.308790	−	0.951130i	$-0.599924\pi$
$241$	−3.23422e10	−0.617579	−0.308790	+	0.951130i	$0.599924\pi$
$242$	4.69563e10	0.880086
$243$	5.48360e10	1.00888
$244$	−4.41674e9	−0.0797714
$245$	7.94490e10	1.40877
$246$	5.21220e10	0.907431
$247$	−8.39140e10	−1.43449
$248$	7.69392e10	1.29156
$249$	9.42462e9	0.155370
$250$	−1.89430e11	−3.06703
$251$	−1.20048e11	−1.90907	−0.954535	−	0.298099i	$-0.903647\pi$
$251$	−1.20048e11	−1.90907	−0.954535	+	0.298099i	$0.903647\pi$
$252$	7.88642e9	0.123191
$253$	4.50654e9	0.0691514
$254$	1.99013e10	0.300007
$255$	−4.31199e10	−0.638627
$256$	−2.98616e10	−0.434544
$257$	−4.39632e10	−0.628622	−0.314311	−	0.949320i	$-0.601774\pi$
$257$	−4.39632e10	−0.628622	−0.314311	+	0.949320i	$0.601774\pi$
$258$	−6.07897e9	−0.0854164
$259$	9.51280e10	1.31359
$260$	−2.09281e10	−0.284020
$261$	−5.35297e10	−0.714024
$262$	−3.91011e10	−0.512664
$263$	2.36332e10	0.304594	0.152297	−	0.988335i	$-0.451333\pi$
$263$	2.36332e10	0.304594	0.152297	+	0.988335i	$0.451333\pi$
$264$	1.09325e10	0.138516
$265$	−1.24153e11	−1.54650
$266$	1.43211e11	1.75392
$267$	−6.70867e9	−0.0807860
$268$	1.71328e10	0.202872
$269$	3.94031e10	0.458823	0.229411	−	0.973330i	$-0.426320\pi$
$269$	3.94031e10	0.458823	0.229411	+	0.973330i	$0.426320\pi$
$270$	1.53978e11	1.76328
$271$	−2.98192e10	−0.335841	−0.167921	−	0.985801i	$-0.553705\pi$
$271$	−2.98192e10	−0.335841	−0.167921	+	0.985801i	$0.553705\pi$
$272$	4.08520e10	0.452536
$273$	7.27421e10	0.792600
$274$	−1.76814e10	−0.189513
$275$	5.56086e10	0.586334
$276$	−2.78537e9	−0.0288929
$277$	−5.01538e10	−0.511853	−0.255926	−	0.966696i	$-0.582380\pi$
$277$	−5.01538e10	−0.511853	−0.255926	+	0.966696i	$0.582380\pi$
$278$	1.28504e11	1.29037
$279$	−7.79153e10	−0.769846
$280$	2.76609e11	2.68940
$281$	1.43075e11	1.36894	0.684472	−	0.729039i	$-0.260033\pi$
$281$	1.43075e11	1.36894	0.684472	+	0.729039i	$0.260033\pi$
$282$	5.05165e9	0.0475677
$283$	−1.66984e11	−1.54752	−0.773758	−	0.633481i	$-0.781625\pi$
$283$	−1.66984e11	−1.54752	−0.773758	+	0.633481i	$0.781625\pi$
$284$	1.54013e10	0.140483
$285$	−1.88432e11	−1.69181
$286$	−2.23288e10	−0.197342
$287$	−2.44935e11	−2.13100
$288$	2.16790e10	0.185683
$289$	−8.33139e10	−0.702550
$290$	−2.42430e11	−2.01278
$291$	−9.46030e10	−0.773369
$292$	−4.19892e9	−0.0337999
$293$	−6.40649e10	−0.507827	−0.253914	−	0.967227i	$-0.581718\pi$
$293$	−6.40649e10	−0.507827	−0.253914	+	0.967227i	$0.581718\pi$
$294$	−5.23919e10	−0.408979
$295$	3.34024e11	2.56790
$296$	1.39773e11	1.05830
$297$	−2.85983e10	−0.213273
$298$	3.85980e10	0.283525
$299$	4.40580e10	0.318789
$300$	−3.43702e10	−0.244983
$301$	2.85667e10	0.200591
$302$	6.86103e10	0.474633
$303$	1.02988e11	0.701934
$304$	1.78521e11	1.19883
$305$	1.56878e11	1.03804
$306$	−4.87628e10	−0.317938
$307$	5.43772e10	0.349377	0.174689	−	0.984624i	$-0.444108\pi$
$307$	5.43772e10	0.349377	0.174689	+	0.984624i	$0.444108\pi$
$308$	−6.63367e9	−0.0420025
$309$	−5.38701e10	−0.336151
$310$	−3.52870e11	−2.17014
$311$	−2.58516e11	−1.56699	−0.783495	−	0.621398i	$-0.786565\pi$
$311$	−2.58516e11	−1.56699	−0.783495	+	0.621398i	$0.786565\pi$
$312$	1.06881e11	0.638564
$313$	2.79589e11	1.64653	0.823267	−	0.567654i	$-0.192149\pi$
$313$	2.79589e11	1.64653	0.823267	+	0.567654i	$0.192149\pi$
$314$	3.05476e11	1.77335
$315$	−2.80118e11	−1.60304
$316$	−2.99802e10	−0.169138
$317$	−1.31158e11	−0.729507	−0.364754	−	0.931104i	$-0.618847\pi$
$317$	−1.31158e11	−0.729507	−0.364754	+	0.931104i	$0.618847\pi$
$318$	8.18713e10	0.448962
$319$	4.50266e10	0.243451
$320$	3.98469e11	2.12432
$321$	1.44713e11	0.760740
$322$	−7.51911e10	−0.389776
$323$	1.54146e11	0.787989
$324$	−9.01590e8	−0.00454524
$325$	5.43655e11	2.70301
$326$	1.12395e11	0.551148
$327$	−1.94004e10	−0.0938309
$328$	−3.59886e11	−1.71685
$329$	−2.37390e10	−0.111707
$330$	−5.01402e10	−0.232741
$331$	−1.45694e11	−0.667140	−0.333570	−	0.942725i	$-0.608253\pi$
$331$	−1.45694e11	−0.667140	−0.333570	+	0.942725i	$0.608253\pi$
$332$	−8.40258e9	−0.0379570
$333$	−1.41546e11	−0.630810
$334$	1.37855e11	0.606128
$335$	−6.08541e11	−2.63990
$336$	−1.54754e11	−0.662392
$337$	2.78008e11	1.17415	0.587073	−	0.809534i	$-0.300280\pi$
$337$	2.78008e11	1.17415	0.587073	+	0.809534i	$0.300280\pi$
$338$	3.15376e9	0.0131433
$339$	2.74569e11	1.12915
$340$	3.84438e10	0.156017
$341$	6.55386e10	0.262484
$342$	−2.13091e11	−0.842264
$343$	−9.09817e10	−0.354920
$344$	4.19733e10	0.161607
$345$	9.89337e10	0.375974
$346$	−2.15777e10	−0.0809398
$347$	7.86382e10	0.291173	0.145586	−	0.989346i	$-0.453493\pi$
$347$	7.86382e10	0.291173	0.145586	+	0.989346i	$0.453493\pi$
$348$	−2.78297e10	−0.101719
$349$	−3.23877e10	−0.116860	−0.0584300	−	0.998292i	$-0.518609\pi$
$349$	−3.23877e10	−0.116860	−0.0584300	+	0.998292i	$0.518609\pi$
$350$	−9.27823e11	−3.30490
$351$	−2.79590e11	−0.983194
$352$	−1.82353e10	−0.0633098
$353$	3.97210e11	1.36155	0.680776	−	0.732492i	$-0.261643\pi$
$353$	3.97210e11	1.36155	0.680776	+	0.732492i	$0.261643\pi$
$354$	−2.20269e11	−0.745484
$355$	−5.47039e11	−1.82806
$356$	5.98116e9	0.0197361
$357$	−1.33624e11	−0.435388
$358$	5.33766e11	1.71742
$359$	1.34152e10	0.0426257	0.0213128	−	0.999773i	$-0.493215\pi$
$359$	1.34152e10	0.0426257	0.0213128	+	0.999773i	$0.493215\pi$
$360$	−4.11581e11	−1.29150
$361$	3.50922e11	1.08750
$362$	−2.73166e11	−0.836061
$363$	−1.91460e11	−0.578759
$364$	−6.48537e10	−0.193633
$365$	1.49142e11	0.439827
$366$	−1.03452e11	−0.301352
$367$	−2.93949e11	−0.845813	−0.422906	−	0.906173i	$-0.638990\pi$
$367$	−2.93949e11	−0.845813	−0.422906	+	0.906173i	$0.638990\pi$
$368$	−9.37303e10	−0.266419
$369$	3.64452e11	1.02334
$370$	−6.41046e11	−1.77820
$371$	−3.84735e11	−1.05434
$372$	−4.05076e10	−0.109671
$373$	−3.62064e11	−0.968490	−0.484245	−	0.874932i	$-0.660906\pi$
$373$	−3.62064e11	−0.968490	−0.484245	+	0.874932i	$0.660906\pi$
$374$	4.10169e10	0.108403
$375$	7.72381e11	2.01693
$376$	−3.48801e10	−0.0899978
$377$	4.40201e11	1.12231
$378$	4.77159e11	1.20213
$379$	−9.16319e10	−0.228124	−0.114062	−	0.993474i	$-0.536386\pi$
$379$	−9.16319e10	−0.228124	−0.114062	+	0.993474i	$0.536386\pi$
$380$	1.67998e11	0.413311
$381$	−8.11458e10	−0.197289
$382$	8.49125e10	0.204026
$383$	−4.95294e11	−1.17617	−0.588083	−	0.808801i	$-0.700117\pi$
$383$	−4.95294e11	−1.17617	−0.588083	+	0.808801i	$0.700117\pi$
$384$	−1.86751e11	−0.438300
$385$	2.35622e11	0.546566
$386$	4.44517e11	1.01917
$387$	−4.25059e10	−0.0963273
$388$	8.43440e10	0.188934
$389$	3.36311e11	0.744678	0.372339	−	0.928097i	$-0.378556\pi$
$389$	3.36311e11	0.744678	0.372339	+	0.928097i	$0.378556\pi$
$390$	−4.90193e11	−1.07294
$391$	−8.09322e10	−0.175116
$392$	3.61749e11	0.773785
$393$	1.59431e11	0.337136
$394$	6.90434e11	1.44341
$395$	1.06487e12	2.20094
$396$	9.87059e9	0.0201704
$397$	−7.57886e11	−1.53125	−0.765626	−	0.643286i	$-0.777570\pi$
$397$	−7.57886e11	−1.53125	−0.765626	+	0.643286i	$0.777570\pi$
$398$	−5.02707e11	−1.00425
$399$	−5.83929e11	−1.15341
$400$	−1.15659e12	−2.25896
$401$	6.25247e11	1.20754	0.603771	−	0.797158i	$-0.293664\pi$
$401$	6.25247e11	1.20754	0.603771	+	0.797158i	$0.293664\pi$
$402$	4.01297e11	0.766387
$403$	6.40735e11	1.21006
$404$	−9.18200e10	−0.171483
$405$	3.20237e10	0.0591457
$406$	−7.51264e11	−1.37222
$407$	1.19062e11	0.215078
$408$	−1.96335e11	−0.350773
$409$	−7.41239e11	−1.30979	−0.654897	−	0.755718i	$-0.727288\pi$
$409$	−7.41239e11	−1.30979	−0.654897	+	0.755718i	$0.727288\pi$
$410$	1.65056e12	2.88473
$411$	7.20942e10	0.124627
$412$	4.80282e10	0.0821219
$413$	1.03510e12	1.75068
$414$	1.11881e11	0.187178
$415$	2.98452e11	0.493922
$416$	−1.78276e11	−0.291860
$417$	−5.23961e11	−0.848568
$418$	1.79242e11	0.287175
$419$	7.96088e11	1.26182	0.630911	−	0.775856i	$-0.282681\pi$
$419$	7.96088e11	1.26182	0.630911	+	0.775856i	$0.282681\pi$
$420$	−1.45631e11	−0.228367
$421$	2.32370e10	0.0360504	0.0180252	−	0.999838i	$-0.494262\pi$
$421$	2.32370e10	0.0360504	0.0180252	+	0.999838i	$0.494262\pi$
$422$	−1.71469e10	−0.0263195
$423$	3.53226e10	0.0536439
$424$	−5.65295e11	−0.849433
$425$	−9.98666e11	−1.48481
$426$	3.60739e11	0.530702
$427$	4.86148e11	0.707690
$428$	−1.29020e11	−0.185849
$429$	9.10436e10	0.129775
$430$	−1.92504e11	−0.271539
$431$	1.44971e11	0.202364	0.101182	−	0.994868i	$-0.467738\pi$
$431$	1.44971e11	0.202364	0.101182	+	0.994868i	$0.467738\pi$
$432$	5.94808e11	0.821675
$433$	1.44846e12	1.98022	0.990108	−	0.140310i	$-0.0448099\pi$
$433$	1.44846e12	1.98022	0.990108	+	0.140310i	$0.0448099\pi$
$434$	−1.09350e12	−1.47950
$435$	9.88486e11	1.32364
$436$	1.72966e10	0.0229229
$437$	−3.53670e11	−0.463908
$438$	−9.83502e10	−0.127686
$439$	−8.50535e11	−1.09295	−0.546477	−	0.837474i	$-0.684031\pi$
$439$	−8.50535e11	−1.09295	−0.546477	+	0.837474i	$0.684031\pi$
$440$	3.46202e11	0.440344
$441$	−3.66339e11	−0.461221
$442$	4.01000e11	0.499740
$443$	2.05793e11	0.253871	0.126936	−	0.991911i	$-0.459486\pi$
$443$	2.05793e11	0.253871	0.126936	+	0.991911i	$0.459486\pi$
$444$	−7.35887e10	−0.0898644
$445$	−2.12445e11	−0.256819
$446$	−2.53402e11	−0.303251
$447$	−1.57380e11	−0.186451
$448$	1.23481e12	1.44827
$449$	1.00629e11	0.116846	0.0584232	−	0.998292i	$-0.481393\pi$
$449$	1.00629e11	0.116846	0.0584232	+	0.998292i	$0.481393\pi$
$450$	1.38056e12	1.58708
$451$	−3.06559e11	−0.348915
$452$	−2.44794e11	−0.275853
$453$	−2.79752e11	−0.312127
$454$	−3.56858e11	−0.394225
$455$	2.30355e12	2.51968
$456$	−8.57973e11	−0.929249
$457$	2.05253e11	0.220123	0.110062	−	0.993925i	$-0.464895\pi$
$457$	2.05253e11	0.220123	0.110062	+	0.993925i	$0.464895\pi$
$458$	−1.50400e12	−1.59717
$459$	5.13592e11	0.540084
$460$	−8.82050e10	−0.0918508
$461$	1.68413e11	0.173669	0.0868345	−	0.996223i	$-0.472325\pi$
$461$	1.68413e11	0.173669	0.0868345	+	0.996223i	$0.472325\pi$
$462$	−1.55379e11	−0.158673
$463$	4.59394e11	0.464592	0.232296	−	0.972645i	$-0.425376\pi$
$463$	4.59394e11	0.464592	0.232296	+	0.972645i	$0.425376\pi$
$464$	−9.36497e11	−0.937941
$465$	1.43879e12	1.42712
$466$	−2.88599e11	−0.283503
$467$	−3.62831e11	−0.353003	−0.176501	−	0.984300i	$-0.556478\pi$
$467$	−3.62831e11	−0.353003	−0.176501	+	0.984300i	$0.556478\pi$
$468$	9.64993e10	0.0929861
$469$	−1.88580e12	−1.79977
$470$	1.59972e11	0.151218
$471$	−1.24555e12	−1.16618
$472$	1.52089e12	1.41045
$473$	3.57539e10	0.0328434
$474$	−7.02217e11	−0.638953
$475$	−4.36412e12	−3.93347
$476$	1.19133e11	0.106366
$477$	5.72467e11	0.506312
$478$	6.01276e11	0.526803
$479$	−1.80224e11	−0.156424	−0.0782121	−	0.996937i	$-0.524921\pi$
$479$	−1.80224e11	−0.156424	−0.0782121	+	0.996937i	$0.524921\pi$
$480$	−4.00326e11	−0.344214
$481$	1.16400e12	0.991517
$482$	6.75392e11	0.569960
$483$	3.06584e11	0.256323
$484$	1.70697e11	0.141391
$485$	−2.99582e12	−2.45854
$486$	−1.14512e12	−0.931084
$487$	−1.77463e12	−1.42964	−0.714820	−	0.699308i	$-0.753492\pi$
$487$	−1.77463e12	−1.42964	−0.714820	+	0.699308i	$0.753492\pi$
$488$	7.14303e11	0.570155
$489$	−4.58280e11	−0.362444
$490$	−1.65911e12	−1.30015
$491$	−1.30536e12	−1.01360	−0.506798	−	0.862065i	$-0.669171\pi$
$491$	−1.30536e12	−1.01360	−0.506798	+	0.862065i	$0.669171\pi$
$492$	1.89476e11	0.145784
$493$	−8.08626e11	−0.616505
$494$	1.75235e12	1.32388
$495$	−3.50594e11	−0.262471
$496$	−1.36312e12	−1.01127
$497$	−1.69521e12	−1.24629
$498$	−1.96811e11	−0.143390
$499$	8.24032e11	0.594965	0.297483	−	0.954727i	$-0.403853\pi$
$499$	8.24032e11	0.594965	0.297483	+	0.954727i	$0.403853\pi$
$500$	−6.88621e11	−0.492737
$501$	−5.62091e11	−0.398600
$502$	2.50692e12	1.76187
$503$	1.69785e12	1.18261	0.591306	−	0.806447i	$-0.298612\pi$
$503$	1.69785e12	1.18261	0.591306	+	0.806447i	$0.298612\pi$
$504$	−1.27544e12	−0.880488
$505$	3.26136e12	2.23145
$506$	−9.41086e10	−0.0638193
$507$	−1.28591e10	−0.00864323
$508$	7.23461e10	0.0481979
$509$	1.97053e12	1.30122	0.650612	−	0.759410i	$-0.274512\pi$
$509$	1.97053e12	1.30122	0.650612	+	0.759410i	$0.274512\pi$
$510$	9.00459e11	0.589384
$511$	4.62174e11	0.299855
$512$	1.74655e12	1.12322
$513$	2.24437e12	1.43076
$514$	9.18069e11	0.580151
$515$	−1.70592e12	−1.06863
$516$	−2.20985e10	−0.0137227
$517$	−2.97116e10	−0.0182902
$518$	−1.98653e12	−1.21230
$519$	8.79808e10	0.0532273
$520$	3.38463e12	2.03000
$521$	−2.62819e12	−1.56274	−0.781370	−	0.624068i	$-0.785479\pi$
$521$	−2.62819e12	−1.56274	−0.781370	+	0.624068i	$0.785479\pi$
$522$	1.11784e12	0.658968
$523$	−2.09980e12	−1.22721	−0.613607	−	0.789612i	$-0.710282\pi$
$523$	−2.09980e12	−1.22721	−0.613607	+	0.789612i	$0.710282\pi$
$524$	−1.42142e11	−0.0823627
$525$	3.78311e12	2.17336
$526$	−4.93524e11	−0.281108
$527$	−1.17700e12	−0.664703
$528$	−1.93689e11	−0.108456
$529$	−1.61546e12	−0.896905
$530$	2.59264e12	1.42725
$531$	−1.54018e12	−0.840710
$532$	5.20606e11	0.281778
$533$	−2.99706e12	−1.60851
$534$	1.40095e11	0.0745568
$535$	4.58268e12	2.41840
$536$	−2.77082e12	−1.45000
$537$	−2.17638e12	−1.12941
$538$	−8.22842e11	−0.423444
$539$	3.08146e11	0.157256
$540$	5.59745e11	0.283282
$541$	1.64248e11	0.0824350	0.0412175	−	0.999150i	$-0.486876\pi$
$541$	1.64248e11	0.0824350	0.0412175	+	0.999150i	$0.486876\pi$
$542$	6.22705e11	0.309946
$543$	1.11381e12	0.549808
$544$	3.27485e11	0.160323
$545$	−6.14358e11	−0.298289
$546$	−1.51905e12	−0.731485
$547$	−4.07195e12	−1.94473	−0.972364	−	0.233468i	$-0.924993\pi$
$547$	−4.07195e12	−1.94473	−0.972364	+	0.233468i	$0.924993\pi$
$548$	−6.42760e10	−0.0304464
$549$	−7.23365e11	−0.339846
$550$	−1.16126e12	−0.541123
$551$	−3.53366e12	−1.63321
$552$	4.50468e11	0.206508
$553$	3.29990e12	1.50051
$554$	1.04735e12	0.472385
$555$	2.61380e12	1.16938
$556$	4.67141e11	0.207306
$557$	2.26836e12	0.998535	0.499268	−	0.866448i	$-0.333602\pi$
$557$	2.26836e12	0.998535	0.499268	+	0.866448i	$0.333602\pi$
$558$	1.62708e12	0.710485
$559$	3.49546e11	0.151409
$560$	−4.90064e12	−2.10575
$561$	−1.67242e11	−0.0712875
$562$	−2.98779e12	−1.26339
$563$	−1.01128e12	−0.424212	−0.212106	−	0.977247i	$-0.568032\pi$
$563$	−1.01128e12	−0.424212	−0.212106	+	0.977247i	$0.568032\pi$
$564$	1.83639e10	0.00764205
$565$	8.69486e12	3.58959
$566$	3.48707e12	1.42819
$567$	9.92376e10	0.0403230
$568$	−2.49079e12	−1.00408
$569$	4.78027e12	1.91182	0.955910	−	0.293661i	$-0.0948735\pi$
$569$	4.78027e12	1.91182	0.955910	+	0.293661i	$0.0948735\pi$
$570$	3.93496e12	1.56136
$571$	−1.26457e12	−0.497831	−0.248916	−	0.968525i	$-0.580074\pi$
$571$	−1.26457e12	−0.497831	−0.248916	+	0.968525i	$0.580074\pi$
$572$	−8.11705e10	−0.0317042
$573$	−3.46222e11	−0.134171
$574$	5.11490e12	1.96668
$575$	2.29133e12	0.874141
$576$	−1.83734e12	−0.695485
$577$	8.87274e11	0.333247	0.166624	−	0.986021i	$-0.446713\pi$
$577$	8.87274e11	0.333247	0.166624	+	0.986021i	$0.446713\pi$
$578$	1.73982e12	0.648378
$579$	−1.81248e12	−0.670222
$580$	−8.81291e11	−0.323365
$581$	9.24868e11	0.336734
$582$	1.97557e12	0.713737
$583$	−4.81531e11	−0.172630
$584$	6.79077e11	0.241580
$585$	−3.42757e12	−1.21000
$586$	1.33785e12	0.468670
$587$	−2.01339e12	−0.699934	−0.349967	−	0.936762i	$-0.613807\pi$
$587$	−2.01339e12	−0.699934	−0.349967	+	0.936762i	$0.613807\pi$
$588$	−1.90457e11	−0.0657050
$589$	−5.14342e12	−1.76089
$590$	−6.97531e12	−2.36990
$591$	−2.81518e12	−0.949209
$592$	−2.47633e12	−0.828631
$593$	3.49061e12	1.15919	0.579596	−	0.814904i	$-0.303210\pi$
$593$	3.49061e12	1.15919	0.579596	+	0.814904i	$0.303210\pi$
$594$	5.97209e11	0.196828
$595$	−4.23150e12	−1.38410
$596$	1.40313e11	0.0455501
$597$	2.04974e12	0.660410
$598$	−9.20048e11	−0.294209
$599$	1.89679e12	0.602004	0.301002	−	0.953624i	$-0.402679\pi$
$599$	1.89679e12	0.602004	0.301002	+	0.953624i	$0.402679\pi$
$600$	5.55856e12	1.75098
$601$	1.53261e12	0.479178	0.239589	−	0.970874i	$-0.422987\pi$
$601$	1.53261e12	0.479178	0.239589	+	0.970874i	$0.422987\pi$
$602$	−5.96549e11	−0.185124
$603$	2.80598e12	0.864284
$604$	2.49414e11	0.0762527
$605$	−6.06301e12	−1.83988
$606$	−2.15067e12	−0.647810
$607$	2.35146e12	0.703054	0.351527	−	0.936178i	$-0.385662\pi$
$607$	2.35146e12	0.703054	0.351527	+	0.936178i	$0.385662\pi$
$608$	1.43109e12	0.424719
$609$	3.06320e12	0.902398
$610$	−3.27604e12	−0.957999
$611$	−2.90474e11	−0.0843184
$612$	−1.77264e11	−0.0510787
$613$	−2.52180e12	−0.721337	−0.360668	−	0.932694i	$-0.617451\pi$
$613$	−2.52180e12	−0.721337	−0.360668	+	0.932694i	$0.617451\pi$
$614$	−1.13554e12	−0.322438
$615$	−6.73001e12	−1.89704
$616$	1.07284e12	0.300208
$617$	2.76603e12	0.768375	0.384188	−	0.923255i	$-0.374482\pi$
$617$	2.76603e12	0.768375	0.384188	+	0.923255i	$0.374482\pi$
$618$	1.12495e12	0.310231
$619$	−5.77530e12	−1.58113	−0.790563	−	0.612381i	$-0.790212\pi$
$619$	−5.77530e12	−1.58113	−0.790563	+	0.612381i	$0.790212\pi$
$620$	−1.28276e12	−0.348646
$621$	−1.17838e12	−0.317960
$622$	5.39851e12	1.44616
$623$	−6.58344e11	−0.175088
$624$	−1.89359e12	−0.499983
$625$	1.40738e13	3.68936
$626$	−5.83857e12	−1.51958
$627$	−7.30841e11	−0.188851
$628$	1.11048e12	0.284899
$629$	−2.13821e12	−0.544656
$630$	5.84962e12	1.47943
$631$	3.07089e12	0.771139	0.385569	−	0.922679i	$-0.374005\pi$
$631$	3.07089e12	0.771139	0.385569	+	0.922679i	$0.374005\pi$
$632$	4.84859e12	1.20889
$633$	6.99146e10	0.0173082
$634$	2.73894e12	0.673257
$635$	−2.56967e12	−0.627184
$636$	2.97621e11	0.0721285
$637$	3.01258e12	0.724955
$638$	−9.40277e11	−0.224679
$639$	2.52239e12	0.598492
$640$	−5.91389e12	−1.39336
$641$	−3.26258e12	−0.763308	−0.381654	−	0.924305i	$-0.624645\pi$
$641$	−3.26258e12	−0.763308	−0.381654	+	0.924305i	$0.624645\pi$
$642$	−3.02200e12	−0.702081
$643$	−1.05886e12	−0.244280	−0.122140	−	0.992513i	$-0.538976\pi$
$643$	−1.05886e12	−0.244280	−0.122140	+	0.992513i	$0.538976\pi$
$644$	−2.73337e11	−0.0626199
$645$	7.84918e11	0.178569
$646$	−3.21898e12	−0.727230
$647$	2.54612e12	0.571228	0.285614	−	0.958345i	$-0.407803\pi$
$647$	2.54612e12	0.571228	0.285614	+	0.958345i	$0.407803\pi$
$648$	1.45811e11	0.0324865
$649$	1.29553e12	0.286645
$650$	−1.13530e13	−2.49459
$651$	4.45865e12	0.972947
$652$	4.08582e11	0.0885453
$653$	2.38472e12	0.513250	0.256625	−	0.966511i	$-0.417389\pi$
$653$	2.38472e12	0.513250	0.256625	+	0.966511i	$0.417389\pi$
$654$	4.05132e11	0.0865959
$655$	5.04874e12	1.07176
$656$	6.37605e12	1.34426
$657$	−6.87692e11	−0.143996
$658$	4.95735e11	0.103094
$659$	−1.21203e11	−0.0250339	−0.0125170	−	0.999922i	$-0.503984\pi$
$659$	−1.21203e11	−0.0250339	−0.0125170	+	0.999922i	$0.503984\pi$
$660$	−1.82271e11	−0.0373913
$661$	−5.30566e12	−1.08102	−0.540508	−	0.841339i	$-0.681768\pi$
$661$	−5.30566e12	−1.08102	−0.540508	+	0.841339i	$0.681768\pi$
$662$	3.04249e12	0.615699
$663$	−1.63504e12	−0.328637
$664$	1.35892e12	0.271292
$665$	−1.84914e13	−3.66668
$666$	2.95586e12	0.582170
$667$	1.85530e12	0.362951
$668$	5.01136e11	0.0973782
$669$	1.03322e12	0.199423
$670$	1.27080e13	2.43635
$671$	6.08460e11	0.115873
$672$	−1.24056e12	−0.234670
$673$	2.24004e12	0.420909	0.210454	−	0.977604i	$-0.432506\pi$
$673$	2.24004e12	0.420909	0.210454	+	0.977604i	$0.432506\pi$
$674$	−5.80555e12	−1.08361
$675$	−1.45406e13	−2.69598
$676$	1.14646e10	0.00211155
$677$	1.60331e12	0.293338	0.146669	−	0.989186i	$-0.453145\pi$
$677$	1.60331e12	0.293338	0.146669	+	0.989186i	$0.453145\pi$
$678$	−5.73374e12	−1.04209
$679$	−9.28370e12	−1.67613
$680$	−6.21738e12	−1.11511
$681$	1.45505e12	0.259249
$682$	−1.36862e12	−0.242244
$683$	−2.68317e12	−0.471797	−0.235898	−	0.971778i	$-0.575803\pi$
$683$	−2.68317e12	−0.471797	−0.235898	+	0.971778i	$0.575803\pi$
$684$	−7.74637e11	−0.135315
$685$	2.28303e12	0.396190
$686$	1.89994e12	0.327553
$687$	6.13240e12	1.05033
$688$	−7.43635e11	−0.126535
$689$	−4.70767e12	−0.795828
$690$	−2.06600e12	−0.346984
$691$	2.43554e12	0.406391	0.203195	−	0.979138i	$-0.434867\pi$
$691$	2.43554e12	0.406391	0.203195	+	0.979138i	$0.434867\pi$
$692$	−7.84399e10	−0.0130035
$693$	−1.08645e12	−0.178941
$694$	−1.64218e12	−0.268721
$695$	−1.65924e13	−2.69760
$696$	4.50080e12	0.727023
$697$	5.50545e12	0.883579
$698$	6.76343e11	0.107849
$699$	1.17673e12	0.186436
$700$	−3.37285e12	−0.530953
$701$	−2.61161e12	−0.408487	−0.204243	−	0.978920i	$-0.565473\pi$
$701$	−2.61161e12	−0.408487	−0.204243	+	0.978920i	$0.565473\pi$
$702$	5.83859e12	0.907383
$703$	−9.34387e12	−1.44287
$704$	1.54548e12	0.237130
$705$	−6.52270e11	−0.0994436
$706$	−8.29481e12	−1.25657
$707$	1.01066e13	1.52131
$708$	−8.00729e11	−0.119767
$709$	−2.58382e12	−0.384020	−0.192010	−	0.981393i	$-0.561501\pi$
$709$	−2.58382e12	−0.384020	−0.192010	+	0.981393i	$0.561501\pi$
$710$	1.14236e13	1.68710
$711$	−4.91010e12	−0.720572
$712$	−9.67312e11	−0.141061
$713$	2.70048e12	0.391326
$714$	2.79042e12	0.401816
$715$	2.88310e12	0.412556
$716$	1.94037e12	0.275915
$717$	−2.45164e12	−0.346435
$718$	−2.80145e11	−0.0393389
$719$	1.05754e13	1.47577	0.737883	−	0.674929i	$-0.235826\pi$
$719$	1.05754e13	1.47577	0.737883	+	0.674929i	$0.235826\pi$
$720$	7.29192e12	1.01122
$721$	−5.28644e12	−0.728542
$722$	−7.32819e12	−1.00364
$723$	−2.75384e12	−0.374815
$724$	−9.93023e11	−0.134318
$725$	2.28935e13	3.07746
$726$	3.99820e12	0.534133
$727$	1.12948e13	1.49960	0.749800	−	0.661664i	$-0.230150\pi$
$727$	1.12948e13	1.49960	0.749800	+	0.661664i	$0.230150\pi$
$728$	1.04886e13	1.38396
$729$	4.43536e12	0.581641
$730$	−3.11448e12	−0.405913
$731$	−6.42098e11	−0.0831712
$732$	−3.76072e11	−0.0484140
$733$	5.68869e12	0.727854	0.363927	−	0.931428i	$-0.381436\pi$
$733$	5.68869e12	0.727854	0.363927	+	0.931428i	$0.381436\pi$
$734$	6.13844e12	0.780595
$735$	6.76485e12	0.854998
$736$	−7.51377e11	−0.0943860
$737$	−2.36025e12	−0.294683
$738$	−7.61073e12	−0.944437
$739$	1.01166e13	1.24778	0.623888	−	0.781514i	$-0.285552\pi$
$739$	1.01166e13	1.24778	0.623888	+	0.781514i	$0.285552\pi$
$740$	−2.33035e12	−0.285680
$741$	−7.14504e12	−0.870608
$742$	8.03429e12	0.973039
$743$	−1.34326e13	−1.61700	−0.808500	−	0.588496i	$-0.799720\pi$
$743$	−1.34326e13	−1.61700	−0.808500	+	0.588496i	$0.799720\pi$
$744$	6.55115e12	0.783861
$745$	−4.98378e12	−0.592728
$746$	7.56086e12	0.893813
$747$	−1.37616e12	−0.161706
$748$	1.49106e11	0.0174156
$749$	1.42012e13	1.64876
$750$	−1.61294e13	−1.86141
$751$	1.50224e13	1.72330	0.861650	−	0.507503i	$-0.169431\pi$
$751$	1.50224e13	1.72330	0.861650	+	0.507503i	$0.169431\pi$
$752$	6.17964e11	0.0704666
$753$	−1.02217e13	−1.15863
$754$	−9.19257e12	−1.03578
$755$	−8.85897e12	−0.992252
$756$	1.73459e12	0.193129
$757$	1.68594e13	1.86599	0.932996	−	0.359886i	$-0.117184\pi$
$757$	1.68594e13	1.86599	0.932996	+	0.359886i	$0.117184\pi$
$758$	1.91352e12	0.210534
$759$	3.83719e11	0.0419686
$760$	−2.71697e13	−2.95409
$761$	−7.67185e12	−0.829219	−0.414609	−	0.909999i	$-0.636082\pi$
$761$	−7.67185e12	−0.829219	−0.414609	+	0.909999i	$0.636082\pi$
$762$	1.69454e12	0.182077
$763$	−1.90382e12	−0.203360
$764$	3.08677e11	0.0327781
$765$	6.29626e12	0.664671
$766$	1.03431e13	1.08548
$767$	1.26656e13	1.32144
$768$	−2.54263e12	−0.263729
$769$	1.04252e13	1.07502	0.537509	−	0.843258i	$-0.319366\pi$
$769$	1.04252e13	1.07502	0.537509	+	0.843258i	$0.319366\pi$
$770$	−4.92042e12	−0.504422
$771$	−3.74334e12	−0.381517
$772$	1.61592e12	0.163736
$773$	8.06883e12	0.812836	0.406418	−	0.913687i	$-0.366778\pi$
$773$	8.06883e12	0.812836	0.406418	+	0.913687i	$0.366778\pi$
$774$	8.87637e11	0.0888998
$775$	3.33227e13	3.31805
$776$	−1.36406e13	−1.35038
$777$	8.09988e12	0.797230
$778$	−7.02309e12	−0.687258
$779$	2.40585e13	2.34073
$780$	−1.78197e12	−0.172375
$781$	−2.12171e12	−0.204060
$782$	1.69008e12	0.161613
$783$	−1.17736e13	−1.11939
$784$	−6.40906e12	−0.605859
$785$	−3.94432e13	−3.70730
$786$	−3.32934e12	−0.311141
$787$	−1.72826e13	−1.60591	−0.802956	−	0.596038i	$-0.796741\pi$
$787$	−1.72826e13	−1.60591	−0.802956	+	0.596038i	$0.796741\pi$
$788$	2.50989e12	0.231892
$789$	2.01230e12	0.184861
$790$	−2.22373e13	−2.03124
$791$	2.69444e13	2.44722
$792$	−1.59633e12	−0.144165
$793$	5.94858e12	0.534175
$794$	1.58267e13	1.41318
$795$	−1.05712e13	−0.938585
$796$	−1.82746e12	−0.161339
$797$	4.58362e12	0.402389	0.201194	−	0.979551i	$-0.435518\pi$
$797$	4.58362e12	0.402389	0.201194	+	0.979551i	$0.435518\pi$
$798$	1.21940e13	1.06447
$799$	5.33587e11	0.0463174
$800$	−9.27164e12	−0.800298
$801$	9.79585e11	0.0840806
$802$	−1.30568e13	−1.11443
$803$	5.78453e11	0.0490963
$804$	1.45881e12	0.123125
$805$	9.70868e12	0.814852
$806$	−1.33803e13	−1.11675
$807$	3.35506e12	0.278464
$808$	1.48497e13	1.22565
$809$	−1.20544e13	−0.989410	−0.494705	−	0.869061i	$-0.664724\pi$
$809$	−1.20544e13	−0.989410	−0.494705	+	0.869061i	$0.664724\pi$
$810$	−6.68740e11	−0.0545852
$811$	−1.28365e13	−1.04196	−0.520982	−	0.853568i	$-0.674434\pi$
$811$	−1.28365e13	−1.04196	−0.520982	+	0.853568i	$0.674434\pi$
$812$	−2.73102e12	−0.220456
$813$	−2.53902e12	−0.203825
$814$	−2.48633e12	−0.198494
$815$	−1.45125e13	−1.15221
$816$	3.47843e12	0.274649
$817$	−2.80594e12	−0.220333
$818$	1.54791e13	1.20880
$819$	−1.06216e13	−0.824924
$820$	6.00018e12	0.463449
$821$	−3.69539e12	−0.283868	−0.141934	−	0.989876i	$-0.545332\pi$
$821$	−3.69539e12	−0.283868	−0.141934	+	0.989876i	$0.545332\pi$
$822$	−1.50552e12	−0.115017
$823$	−1.43444e13	−1.08989	−0.544947	−	0.838471i	$-0.683450\pi$
$823$	−1.43444e13	−1.08989	−0.544947	+	0.838471i	$0.683450\pi$
$824$	−7.76743e12	−0.586955
$825$	4.73491e12	0.355852
$826$	−2.16157e13	−1.61569
$827$	2.09275e12	0.155576	0.0777880	−	0.996970i	$-0.475214\pi$
$827$	2.09275e12	0.155576	0.0777880	+	0.996970i	$0.475214\pi$
$828$	4.06713e11	0.0300712
$829$	4.14252e12	0.304628	0.152314	−	0.988332i	$-0.451328\pi$
$829$	4.14252e12	0.304628	0.152314	+	0.988332i	$0.451328\pi$
$830$	−6.23248e12	−0.455837
$831$	−4.27045e12	−0.310648
$832$	1.51093e13	1.09317
$833$	−5.53395e12	−0.398229
$834$	1.09417e13	0.783137
$835$	−1.77999e13	−1.26715
$836$	6.51587e11	0.0461364
$837$	−1.71372e13	−1.20691
$838$	−1.66244e13	−1.16453
$839$	−1.12598e13	−0.784517	−0.392259	−	0.919855i	$-0.628306\pi$
$839$	−1.12598e13	−0.784517	−0.392259	+	0.919855i	$0.628306\pi$
$840$	2.35524e13	1.63222
$841$	4.02989e12	0.277787
$842$	−4.85250e11	−0.0332707
$843$	1.21824e13	0.830825
$844$	−6.23328e10	−0.00422840
$845$	−4.07214e11	−0.0274769
$846$	−7.37630e11	−0.0495076
$847$	−1.87886e13	−1.25435
$848$	1.00152e13	0.665090
$849$	−1.42182e13	−0.939203
$850$	2.08548e13	1.37032
$851$	4.90588e12	0.320652
$852$	1.31137e12	0.0852605
$853$	−3.02496e12	−0.195636	−0.0978180	−	0.995204i	$-0.531186\pi$
$853$	−3.02496e12	−0.195636	−0.0978180	+	0.995204i	$0.531186\pi$
$854$	−1.01521e13	−0.653122
$855$	2.75144e13	1.76081
$856$	2.08660e13	1.32833
$857$	−9.38926e12	−0.594590	−0.297295	−	0.954786i	$-0.596085\pi$
$857$	−9.38926e12	−0.594590	−0.297295	+	0.954786i	$0.596085\pi$
$858$	−1.90123e12	−0.119769
$859$	−8.16218e12	−0.511489	−0.255745	−	0.966744i	$-0.582321\pi$
$859$	−8.16218e12	−0.511489	−0.255745	+	0.966744i	$0.582321\pi$
$860$	−6.99799e11	−0.0436245
$861$	−2.08555e13	−1.29332
$862$	−3.02738e12	−0.186760
$863$	−3.43684e12	−0.210917	−0.105458	−	0.994424i	$-0.533631\pi$
$863$	−3.43684e12	−0.210917	−0.105458	+	0.994424i	$0.533631\pi$
$864$	4.76820e12	0.291100
$865$	2.78611e12	0.169210
$866$	−3.02478e13	−1.82753
$867$	−7.09393e12	−0.426384
$868$	−3.97514e12	−0.237692
$869$	4.13014e12	0.245683
$870$	−2.06422e13	−1.22158
$871$	−2.30749e13	−1.35849
$872$	−2.79731e12	−0.163839
$873$	1.38137e13	0.804908
$874$	7.38558e12	0.428137
$875$	7.57962e13	4.37131
$876$	−3.57526e11	−0.0205135
$877$	−4.77680e12	−0.272671	−0.136336	−	0.990663i	$-0.543533\pi$
$877$	−4.77680e12	−0.272671	−0.136336	+	0.990663i	$0.543533\pi$
$878$	1.77614e13	1.00868
$879$	−5.45494e12	−0.308205
$880$	−6.13361e12	−0.344781
$881$	5.58463e12	0.312322	0.156161	−	0.987732i	$-0.450088\pi$
$881$	5.58463e12	0.312322	0.156161	+	0.987732i	$0.450088\pi$
$882$	7.65014e12	0.425658
$883$	−3.41836e12	−0.189232	−0.0946160	−	0.995514i	$-0.530162\pi$
$883$	−3.41836e12	−0.189232	−0.0946160	+	0.995514i	$0.530162\pi$
$884$	1.45773e12	0.0802863
$885$	2.84411e13	1.55848
$886$	−4.29751e12	−0.234296
$887$	2.19538e12	0.119084	0.0595419	−	0.998226i	$-0.481036\pi$
$887$	2.19538e12	0.119084	0.0595419	+	0.998226i	$0.481036\pi$
$888$	1.19012e13	0.642294
$889$	−7.96310e12	−0.427587
$890$	4.43643e12	0.237017
$891$	1.24205e11	0.00660222
$892$	−9.21175e11	−0.0487192
$893$	2.33175e12	0.122702
$894$	3.28651e12	0.172074
$895$	−6.89200e13	−3.59039
$896$	−1.83265e13	−0.949932
$897$	3.75141e12	0.193476
$898$	−2.10141e12	−0.107837
$899$	2.69816e13	1.37768
$900$	5.01865e12	0.254974
$901$	8.64775e12	0.437161
$902$	6.40178e12	0.322011
$903$	2.43237e12	0.121740
$904$	3.95897e13	1.97162
$905$	3.52713e13	1.74784
$906$	5.84197e12	0.288059
$907$	4.78607e12	0.234826	0.117413	−	0.993083i	$-0.462540\pi$
$907$	4.78607e12	0.234826	0.117413	+	0.993083i	$0.462540\pi$
$908$	−1.29726e12	−0.0633346
$909$	−1.50381e13	−0.730560
$910$	−4.81042e13	−2.32540
$911$	3.94324e13	1.89680	0.948398	−	0.317084i	$-0.102704\pi$
$911$	3.94324e13	1.89680	0.948398	+	0.317084i	$0.102704\pi$
$912$	1.52006e13	0.727584
$913$	1.15756e12	0.0551347
$914$	−4.28623e12	−0.203150
$915$	1.33577e13	0.629996
$916$	−5.46738e12	−0.256596
$917$	1.56455e13	0.730678
$918$	−1.07252e13	−0.498440
$919$	−2.73748e13	−1.26599	−0.632996	−	0.774155i	$-0.718175\pi$
$919$	−2.73748e13	−1.26599	−0.632996	+	0.774155i	$0.718175\pi$
$920$	1.42651e13	0.656491
$921$	4.63006e12	0.212040
$922$	−3.51692e12	−0.160278
$923$	−2.07428e13	−0.940720
$924$	−5.64838e11	−0.0254918
$925$	6.05362e13	2.71880
$926$	−9.59339e12	−0.428768
$927$	7.86598e12	0.349860
$928$	−7.50730e12	−0.332291
$929$	1.28298e13	0.565129	0.282565	−	0.959248i	$-0.408815\pi$
$929$	1.28298e13	0.565129	0.282565	+	0.959248i	$0.408815\pi$
$930$	−3.00458e13	−1.31708
$931$	−2.41831e13	−1.05497
$932$	−1.04912e12	−0.0455465
$933$	−2.20119e13	−0.951021
$934$	7.57688e12	0.325784
$935$	−5.29611e12	−0.226623
$936$	−1.56065e13	−0.664605
$937$	4.02808e12	0.170714	0.0853571	−	0.996350i	$-0.472797\pi$
$937$	4.02808e12	0.170714	0.0853571	+	0.996350i	$0.472797\pi$
$938$	3.93805e13	1.66100
$939$	2.38062e13	0.999298
$940$	5.81536e11	0.0242941
$941$	−1.56034e13	−0.648734	−0.324367	−	0.945931i	$-0.605151\pi$
$941$	−1.56034e13	−0.648734	−0.324367	+	0.945931i	$0.605151\pi$
$942$	2.60104e13	1.07626
$943$	−1.26316e13	−0.520184
$944$	−2.69453e13	−1.10436
$945$	−6.16109e13	−2.51313
$946$	−7.46637e11	−0.0303109
$947$	6.83849e12	0.276303	0.138151	−	0.990411i	$-0.455884\pi$
$947$	6.83849e12	0.276303	0.138151	+	0.990411i	$0.455884\pi$
$948$	−2.55272e12	−0.102652
$949$	5.65522e12	0.226335
$950$	9.11346e13	3.63017
$951$	−1.11678e13	−0.442745
$952$	−1.92670e13	−0.760233
$953$	1.38307e11	0.00543158	0.00271579	−	0.999996i	$-0.499136\pi$
$953$	1.38307e11	0.00543158	0.00271579	+	0.999996i	$0.499136\pi$
$954$	−1.19546e13	−0.467271
$955$	−1.09639e13	−0.426531
$956$	2.18578e12	0.0846342
$957$	3.83389e12	0.147753
$958$	3.76357e12	0.144363
$959$	7.07483e12	0.270105
$960$	3.39285e13	1.28927
$961$	1.28335e13	0.485389
$962$	−2.43074e13	−0.915064
$963$	−2.11307e13	−0.791764
$964$	2.45521e12	0.0915676
$965$	−5.73962e13	−2.13064
$966$	−6.40230e12	−0.236559
$967$	1.57600e13	0.579610	0.289805	−	0.957086i	$-0.406410\pi$
$967$	1.57600e13	0.579610	0.289805	+	0.957086i	$0.406410\pi$
$968$	−2.76063e13	−1.01057
$969$	1.31251e13	0.478238
$970$	6.25608e13	2.26897
$971$	−1.45177e12	−0.0524097	−0.0262048	−	0.999657i	$-0.508342\pi$
$971$	−1.45177e12	−0.0524097	−0.0262048	+	0.999657i	$0.508342\pi$
$972$	−4.16279e12	−0.149584
$973$	−5.14180e13	−1.83911
$974$	3.70590e13	1.31941
$975$	4.62906e13	1.64048
$976$	−1.26552e13	−0.446421
$977$	3.18143e13	1.11711	0.558556	−	0.829467i	$-0.311355\pi$
$977$	3.18143e13	1.11711	0.558556	+	0.829467i	$0.311355\pi$
$978$	9.57011e12	0.334497
$979$	−8.23979e11	−0.0286678
$980$	−6.03125e12	−0.208877
$981$	2.83280e12	0.0976574
$982$	2.72595e13	0.935441
$983$	2.05768e13	0.702889	0.351445	−	0.936209i	$-0.385691\pi$
$983$	2.05768e13	0.702889	0.351445	+	0.936209i	$0.385691\pi$
$984$	−3.06432e13	−1.04197
$985$	−8.91489e13	−3.01754
$986$	1.68863e13	0.568968
$987$	−2.02131e12	−0.0677963
$988$	6.37020e12	0.212690
$989$	1.47322e12	0.0489649
$990$	7.32135e12	0.242233
$991$	−5.40029e13	−1.77863	−0.889314	−	0.457296i	$-0.848818\pi$
$991$	−5.40029e13	−1.77863	−0.889314	+	0.457296i	$0.848818\pi$
$992$	−1.09273e13	−0.358269
$993$	−1.24055e13	−0.404894
$994$	3.54005e13	1.15019
$995$	6.49096e13	2.09945
$996$	−7.15456e11	−0.0230365
$997$	−1.33255e13	−0.427124	−0.213562	−	0.976930i	$-0.568506\pi$
$997$	−1.33255e13	−0.427124	−0.213562	+	0.976930i	$0.568506\pi$
$998$	−1.72080e13	−0.549089
$999$	−3.11325e13	−0.988937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.b.1.6	✓	17
3.2	odd	2		387.10.a.e.1.12		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.6	✓	17	1.1	even	1	trivial
387.10.a.e.1.12		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)

\(f(q)\)	\(=\)	\(q-20.8827 q^{2} +85.1471 q^{3} -75.9135 q^{4} +2696.38 q^{5} -1778.10 q^{6} +8355.76 q^{7} +12277.2 q^{8} -12433.0 q^{9} +O(q^{10})\)	\(q-20.8827 q^{2} +85.1471 q^{3} -75.9135 q^{4} +2696.38 q^{5} -1778.10 q^{6} +8355.76 q^{7} +12277.2 q^{8} -12433.0 q^{9} -56307.6 q^{10} +10458.0 q^{11} -6463.81 q^{12} +102242. q^{13} -174491. q^{14} +229589. q^{15} -217513. q^{16} -187814. q^{17} +259634. q^{18} -820737. q^{19} -204691. q^{20} +711469. q^{21} -218391. q^{22} +430917. q^{23} +1.04537e6 q^{24} +5.31732e6 q^{25} -2.13509e6 q^{26} -2.73458e6 q^{27} -634315. q^{28} +4.30547e6 q^{29} -4.79443e6 q^{30} +6.26683e6 q^{31} -1.74367e6 q^{32} +890469. q^{33} +3.92206e6 q^{34} +2.25303e7 q^{35} +943830. q^{36} +1.13847e7 q^{37} +1.71392e7 q^{38} +8.70563e6 q^{39} +3.31040e7 q^{40} -2.93133e7 q^{41} -1.48574e7 q^{42} +3.41880e6 q^{43} -793904. q^{44} -3.35240e7 q^{45} -8.99871e6 q^{46} -2.84104e6 q^{47} -1.85206e7 q^{48} +2.94651e7 q^{49} -1.11040e8 q^{50} -1.59918e7 q^{51} -7.76156e6 q^{52} -4.60443e7 q^{53} +5.71054e7 q^{54} +2.81987e7 q^{55} +1.02585e8 q^{56} -6.98834e7 q^{57} -8.99097e7 q^{58} +1.23879e8 q^{59} -1.74289e7 q^{60} +5.81812e7 q^{61} -1.30868e8 q^{62} -1.03887e8 q^{63} +1.47779e8 q^{64} +2.75684e8 q^{65} -1.85954e7 q^{66} -2.25688e8 q^{67} +1.42576e7 q^{68} +3.66914e7 q^{69} -4.70493e8 q^{70} -2.02879e8 q^{71} -1.52642e8 q^{72} +5.53120e7 q^{73} -2.37744e8 q^{74} +4.52754e8 q^{75} +6.23050e7 q^{76} +8.73846e7 q^{77} -1.81797e8 q^{78} +3.94926e8 q^{79} -5.86498e8 q^{80} +1.18766e7 q^{81} +6.12141e8 q^{82} +1.10686e8 q^{83} -5.40100e7 q^{84} -5.06417e8 q^{85} -7.13937e7 q^{86} +3.66598e8 q^{87} +1.28395e8 q^{88} -7.87892e7 q^{89} +7.00071e8 q^{90} +8.54312e8 q^{91} -3.27124e7 q^{92} +5.33602e8 q^{93} +5.93285e7 q^{94} -2.21302e9 q^{95} -1.48468e8 q^{96} -1.11105e9 q^{97} -6.15310e8 q^{98} -1.30024e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more