LMFDB - Embedded newform 43.10.a.b.1.14

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			1.14
Root			$-34.7389$ 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)

$f(q)$	$=$	$q+37.7389 q^{2} +83.4314 q^{3} +912.221 q^{4} +1398.64 q^{5} +3148.61 q^{6} +8642.65 q^{7} +15103.9 q^{8} -12722.2 q^{9} +O(q^{10})$	\(q+37.7389 q^{2} +83.4314 q^{3} +912.221 q^{4} +1398.64 q^{5} +3148.61 q^{6} +8642.65 q^{7} +15103.9 q^{8} -12722.2 q^{9} +52783.1 q^{10} -51163.8 q^{11} +76107.9 q^{12} -25743.5 q^{13} +326164. q^{14} +116690. q^{15} +102946. q^{16} -479274. q^{17} -480121. q^{18} +1.08676e6 q^{19} +1.27587e6 q^{20} +721068. q^{21} -1.93086e6 q^{22} +2.01921e6 q^{23} +1.26014e6 q^{24} +3069.23 q^{25} -971531. q^{26} -2.70361e6 q^{27} +7.88401e6 q^{28} +178299. q^{29} +4.40377e6 q^{30} -1.50266e6 q^{31} -3.84812e6 q^{32} -4.26867e6 q^{33} -1.80872e7 q^{34} +1.20880e7 q^{35} -1.16055e7 q^{36} -1.04912e7 q^{37} +4.10131e7 q^{38} -2.14782e6 q^{39} +2.11249e7 q^{40} -2.11468e7 q^{41} +2.72123e7 q^{42} +3.41880e6 q^{43} -4.66727e7 q^{44} -1.77938e7 q^{45} +7.62026e7 q^{46} +3.87381e7 q^{47} +8.58895e6 q^{48} +3.43418e7 q^{49} +115829. q^{50} -3.99865e7 q^{51} -2.34838e7 q^{52} +7.65345e7 q^{53} -1.02031e8 q^{54} -7.15597e7 q^{55} +1.30538e8 q^{56} +9.06700e7 q^{57} +6.72882e6 q^{58} -5.14812e7 q^{59} +1.06448e8 q^{60} -1.84541e8 q^{61} -5.67085e7 q^{62} -1.09954e8 q^{63} -1.97932e8 q^{64} -3.60059e7 q^{65} -1.61095e8 q^{66} +4.03688e7 q^{67} -4.37204e8 q^{68} +1.68465e8 q^{69} +4.56186e8 q^{70} +5.56761e7 q^{71} -1.92155e8 q^{72} -4.12053e8 q^{73} -3.95925e8 q^{74} +256070. q^{75} +9.91367e8 q^{76} -4.42191e8 q^{77} -8.10562e7 q^{78} -1.49247e8 q^{79} +1.43985e8 q^{80} +2.48451e7 q^{81} -7.98056e8 q^{82} +3.20590e8 q^{83} +6.57774e8 q^{84} -6.70331e8 q^{85} +1.29022e8 q^{86} +1.48758e7 q^{87} -7.72772e8 q^{88} +8.34013e8 q^{89} -6.71517e8 q^{90} -2.22492e8 q^{91} +1.84196e9 q^{92} -1.25369e8 q^{93} +1.46193e9 q^{94} +1.51999e9 q^{95} -3.21054e8 q^{96} +2.94806e7 q^{97} +1.29602e9 q^{98} +6.50916e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	37.7389	1.66784	0.833919	−	0.551887i	$-0.186092\pi$
$2$	37.7389	1.66784	0.833919	+	0.551887i	$0.186092\pi$
$3$	83.4314	0.594681	0.297340	−	0.954772i	$-0.403900\pi$
$3$	83.4314	0.594681	0.297340	+	0.954772i	$0.403900\pi$
$4$	912.221	1.78168
$5$	1398.64	1.00079	0.500393	−	0.865799i	$-0.333189\pi$
$5$	1398.64	1.00079	0.500393	+	0.865799i	$0.333189\pi$
$6$	3148.61	0.991831
$7$	8642.65	1.36052	0.680261	−	0.732970i	$-0.261866\pi$
$7$	8642.65	1.36052	0.680261	+	0.732970i	$0.261866\pi$
$8$	15103.9	1.30372
$9$	−12722.2	−0.646355
$10$	52783.1	1.66915
$11$	−51163.8	−1.05365	−0.526824	−	0.849974i	$-0.676617\pi$
$11$	−51163.8	−1.05365	−0.526824	+	0.849974i	$0.676617\pi$
$12$	76107.9	1.05953
$13$	−25743.5	−0.249990	−0.124995	−	0.992157i	$-0.539892\pi$
$13$	−25743.5	−0.249990	−0.124995	+	0.992157i	$0.539892\pi$
$14$	326164.	2.26913
$15$	116690.	0.595148
$16$	102946.	0.392709
$17$	−479274.	−1.39176	−0.695879	−	0.718159i	$-0.744985\pi$
$17$	−479274.	−1.39176	−0.695879	+	0.718159i	$0.744985\pi$
$18$	−480121.	−1.07801
$19$	1.08676e6	1.91312	0.956562	−	0.291530i	$-0.0941642\pi$
$19$	1.08676e6	1.91312	0.956562	+	0.291530i	$0.0941642\pi$
$20$	1.27587e6	1.78308
$21$	721068.	0.809076
$22$	−1.93086e6	−1.75731
$23$	2.01921e6	1.50455	0.752273	−	0.658851i	$-0.228957\pi$
$23$	2.01921e6	1.50455	0.752273	+	0.658851i	$0.228957\pi$
$24$	1.26014e6	0.775296
$25$	3069.23	0.00157144
$26$	−971531.	−0.416943
$27$	−2.70361e6	−0.979055
$28$	7.88401e6	2.42402
$29$	178299.	0.0468122	0.0234061	−	0.999726i	$-0.492549\pi$
$29$	178299.	0.0468122	0.0234061	+	0.999726i	$0.492549\pi$
$30$	4.40377e6	0.992610
$31$	−1.50266e6	−0.292235	−0.146117	−	0.989267i	$-0.546678\pi$
$31$	−1.50266e6	−0.292235	−0.146117	+	0.989267i	$0.546678\pi$
$32$	−3.84812e6	−0.648744
$33$	−4.26867e6	−0.626584
$34$	−1.80872e7	−2.32122
$35$	1.20880e7	1.36159
$36$	−1.16055e7	−1.15160
$37$	−1.04912e7	−0.920273	−0.460137	−	0.887848i	$-0.652200\pi$
$37$	−1.04912e7	−0.920273	−0.460137	+	0.887848i	$0.652200\pi$
$38$	4.10131e7	3.19078
$39$	−2.14782e6	−0.148664
$40$	2.11249e7	1.30474
$41$	−2.11468e7	−1.16874	−0.584370	−	0.811488i	$-0.698658\pi$
$41$	−2.11468e7	−1.16874	−0.584370	+	0.811488i	$0.698658\pi$
$42$	2.72123e7	1.34941
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	−4.66727e7	−1.87727
$45$	−1.77938e7	−0.646863
$46$	7.62026e7	2.50934
$47$	3.87381e7	1.15797	0.578986	−	0.815338i	$-0.303449\pi$
$47$	3.87381e7	1.15797	0.578986	+	0.815338i	$0.303449\pi$
$48$	8.58895e6	0.233536
$49$	3.43418e7	0.851021
$50$	115829.	0.00262091
$51$	−3.99865e7	−0.827651
$52$	−2.34838e7	−0.445403
$53$	7.65345e7	1.33234	0.666171	−	0.745799i	$-0.267932\pi$
$53$	7.65345e7	1.33234	0.666171	+	0.745799i	$0.267932\pi$
$54$	−1.02031e8	−1.63291
$55$	−7.15597e7	−1.05448
$56$	1.30538e8	1.77374
$57$	9.06700e7	1.13770
$58$	6.72882e6	0.0780751
$59$	−5.14812e7	−0.553114	−0.276557	−	0.960997i	$-0.589193\pi$
$59$	−5.14812e7	−0.553114	−0.276557	+	0.960997i	$0.589193\pi$
$60$	1.06448e8	1.06036
$61$	−1.84541e8	−1.70651	−0.853256	−	0.521492i	$-0.825376\pi$
$61$	−1.84541e8	−1.70651	−0.853256	+	0.521492i	$0.825376\pi$
$62$	−5.67085e7	−0.487400
$63$	−1.09954e8	−0.879380
$64$	−1.97932e8	−1.47471
$65$	−3.60059e7	−0.250187
$66$	−1.61095e8	−1.04504
$67$	4.03688e7	0.244742	0.122371	−	0.992484i	$-0.460950\pi$
$67$	4.03688e7	0.244742	0.122371	+	0.992484i	$0.460950\pi$
$68$	−4.37204e8	−2.47967
$69$	1.68465e8	0.894725
$70$	4.56186e8	2.27091
$71$	5.56761e7	0.260020	0.130010	−	0.991513i	$-0.458499\pi$
$71$	5.56761e7	0.260020	0.130010	+	0.991513i	$0.458499\pi$
$72$	−1.92155e8	−0.842665
$73$	−4.12053e8	−1.69825	−0.849123	−	0.528196i	$-0.822869\pi$
$73$	−4.12053e8	−1.69825	−0.849123	+	0.528196i	$0.822869\pi$
$74$	−3.95925e8	−1.53487
$75$	256070.	0.000934508 0
$76$	9.91367e8	3.40858
$77$	−4.42191e8	−1.43351
$78$	−8.10562e7	−0.247948
$79$	−1.49247e8	−0.431107	−0.215553	−	0.976492i	$-0.569156\pi$
$79$	−1.49247e8	−0.431107	−0.215553	+	0.976492i	$0.569156\pi$
$80$	1.43985e8	0.393017
$81$	2.48451e7	0.0641295
$82$	−7.98056e8	−1.94927
$83$	3.20590e8	0.741477	0.370739	−	0.928737i	$-0.379105\pi$
$83$	3.20590e8	0.741477	0.370739	+	0.928737i	$0.379105\pi$
$84$	6.57774e8	1.44152
$85$	−6.70331e8	−1.39285
$86$	1.29022e8	0.254343
$87$	1.48758e7	0.0278383
$88$	−7.72772e8	−1.37366
$89$	8.34013e8	1.40902	0.704511	−	0.709693i	$-0.251166\pi$
$89$	8.34013e8	1.40902	0.704511	+	0.709693i	$0.251166\pi$
$90$	−6.71517e8	−1.07886
$91$	−2.22492e8	−0.340117
$92$	1.84196e9	2.68062
$93$	−1.25369e8	−0.173786
$94$	1.46193e9	1.93131
$95$	1.51999e9	1.91463
$96$	−3.21054e8	−0.385796
$97$	2.94806e7	0.0338115	0.0169057	−	0.999857i	$-0.494618\pi$
$97$	2.94806e7	0.0338115	0.0169057	+	0.999857i	$0.494618\pi$
$98$	1.29602e9	1.41936
$99$	6.50916e8	0.681031
$100$	2.79981e6	0.00279981
$101$	3.31828e6	0.00317298	0.00158649	−	0.999999i	$-0.499495\pi$
$101$	3.31828e6	0.00317298	0.00158649	+	0.999999i	$0.499495\pi$
$102$	−1.50904e9	−1.38039
$103$	2.49725e8	0.218622	0.109311	−	0.994008i	$-0.465136\pi$
$103$	2.49725e8	0.218622	0.109311	+	0.994008i	$0.465136\pi$
$104$	−3.88827e8	−0.325917
$105$	1.00851e9	0.809712
$106$	2.88833e9	2.22213
$107$	−3.73072e8	−0.275148	−0.137574	−	0.990492i	$-0.543930\pi$
$107$	−3.73072e8	−0.275148	−0.137574	+	0.990492i	$0.543930\pi$
$108$	−2.46629e9	−1.74437
$109$	5.02437e8	0.340928	0.170464	−	0.985364i	$-0.445473\pi$
$109$	5.02437e8	0.340928	0.170464	+	0.985364i	$0.445473\pi$
$110$	−2.70058e9	−1.75869
$111$	−8.75294e8	−0.547269
$112$	8.89728e8	0.534289
$113$	1.17931e9	0.680420	0.340210	−	0.940350i	$-0.389502\pi$
$113$	1.17931e9	0.680420	0.340210	+	0.940350i	$0.389502\pi$
$114$	3.42178e9	1.89749
$115$	2.82414e9	1.50573
$116$	1.62649e8	0.0834044
$117$	3.27514e8	0.161582
$118$	−1.94284e9	−0.922505
$119$	−4.14219e9	−1.89352
$120$	1.76248e9	0.775905
$121$	2.59786e8	0.110175
$122$	−6.96438e9	−2.84618
$123$	−1.76431e9	−0.695027
$124$	−1.37075e9	−0.520670
$125$	−2.72743e9	−0.999213
$126$	−4.14952e9	−1.46666
$127$	1.57222e9	0.536284	0.268142	−	0.963379i	$-0.413590\pi$
$127$	1.57222e9	0.536284	0.268142	+	0.963379i	$0.413590\pi$
$128$	−5.49949e9	−1.81083
$129$	2.85235e8	0.0906880
$130$	−1.35882e9	−0.417271
$131$	−9.82385e8	−0.291448	−0.145724	−	0.989325i	$-0.546551\pi$
$131$	−9.82385e8	−0.291448	−0.145724	+	0.989325i	$0.546551\pi$
$132$	−3.89397e9	−1.11637
$133$	9.39250e9	2.60285
$134$	1.52347e9	0.408191
$135$	−3.78138e9	−0.979824
$136$	−7.23890e9	−1.81446
$137$	7.08770e9	1.71895	0.859474	−	0.511180i	$-0.170792\pi$
$137$	7.08770e9	1.71895	0.859474	+	0.511180i	$0.170792\pi$
$138$	6.35769e9	1.49226
$139$	7.84732e9	1.78301	0.891507	−	0.453006i	$-0.149649\pi$
$139$	7.84732e9	1.78301	0.891507	+	0.453006i	$0.149649\pi$
$140$	1.10269e10	2.42592
$141$	3.23197e9	0.688623
$142$	2.10115e9	0.433671
$143$	1.31714e9	0.263402
$144$	−1.30970e9	−0.253829
$145$	2.49377e8	0.0468490
$146$	−1.55504e10	−2.83240
$147$	2.86518e9	0.506086
$148$	−9.57028e9	−1.63963
$149$	−7.80102e9	−1.29662	−0.648310	−	0.761376i	$-0.724524\pi$
$149$	−7.80102e9	−1.29662	−0.648310	+	0.761376i	$0.724524\pi$
$150$	9.66378e6	0.00155861
$151$	8.39488e9	1.31407	0.657034	−	0.753861i	$-0.271811\pi$
$151$	8.39488e9	1.31407	0.657034	+	0.753861i	$0.271811\pi$
$152$	1.64143e10	2.49417
$153$	6.09742e9	0.899569
$154$	−1.66878e10	−2.39086
$155$	−2.10168e9	−0.292464
$156$	−1.95929e9	−0.264873
$157$	5.73662e9	0.753543	0.376771	−	0.926306i	$-0.377034\pi$
$157$	5.73662e9	0.753543	0.376771	+	0.926306i	$0.377034\pi$
$158$	−5.63242e9	−0.719016
$159$	6.38538e9	0.792318
$160$	−5.38213e9	−0.649254
$161$	1.74513e10	2.04697
$162$	9.37626e8	0.106958
$163$	−3.22570e9	−0.357915	−0.178958	−	0.983857i	$-0.557272\pi$
$163$	−3.22570e9	−0.357915	−0.178958	+	0.983857i	$0.557272\pi$
$164$	−1.92906e10	−2.08232
$165$	−5.97033e9	−0.627076
$166$	1.20987e10	1.23666
$167$	−9.36558e9	−0.931774	−0.465887	−	0.884844i	$-0.654265\pi$
$167$	−9.36558e9	−0.931774	−0.465887	+	0.884844i	$0.654265\pi$
$168$	1.08909e10	1.05481
$169$	−9.94177e9	−0.937505
$170$	−2.52975e10	−2.32305
$171$	−1.38260e10	−1.23656
$172$	3.11870e9	0.271704
$173$	−1.27275e9	−0.108028	−0.0540139	−	0.998540i	$-0.517202\pi$
$173$	−1.27275e9	−0.108028	−0.0540139	+	0.998540i	$0.517202\pi$
$174$	5.61395e8	0.0464298
$175$	2.65263e7	0.00213798
$176$	−5.26712e9	−0.413777
$177$	−4.29515e9	−0.328926
$178$	3.14747e10	2.35002
$179$	1.15664e10	0.842093	0.421047	−	0.907039i	$-0.361663\pi$
$179$	1.15664e10	0.842093	0.421047	+	0.907039i	$0.361663\pi$
$180$	−1.62319e10	−1.15250
$181$	−1.90556e9	−0.131968	−0.0659842	−	0.997821i	$-0.521019\pi$
$181$	−1.90556e9	−0.131968	−0.0659842	+	0.997821i	$0.521019\pi$
$182$	−8.39660e9	−0.567260
$183$	−1.53965e10	−1.01483
$184$	3.04979e10	1.96151
$185$	−1.46734e10	−0.920996
$186$	−4.73127e9	−0.289847
$187$	2.45215e10	1.46642
$188$	3.53377e10	2.06314
$189$	−2.33664e10	−1.33203
$190$	5.73626e10	3.19329
$191$	3.08287e10	1.67612	0.838061	−	0.545577i	$-0.183689\pi$
$191$	3.08287e10	1.67612	0.838061	+	0.545577i	$0.183689\pi$
$192$	−1.65137e10	−0.876981
$193$	−9.66943e9	−0.501641	−0.250821	−	0.968034i	$-0.580700\pi$
$193$	−9.66943e9	−0.501641	−0.250821	+	0.968034i	$0.580700\pi$
$194$	1.11257e9	0.0563920
$195$	−3.00403e9	−0.148781
$196$	3.13273e10	1.51625
$197$	−8.48839e9	−0.401539	−0.200769	−	0.979639i	$-0.564344\pi$
$197$	−8.48839e9	−0.401539	−0.200769	+	0.979639i	$0.564344\pi$
$198$	2.45648e10	1.13585
$199$	4.42175e9	0.199873	0.0999367	−	0.994994i	$-0.468136\pi$
$199$	4.42175e9	0.199873	0.0999367	+	0.994994i	$0.468136\pi$
$200$	4.63573e7	0.00204872
$201$	3.36802e9	0.145544
$202$	1.25228e8	0.00529201
$203$	1.54098e9	0.0636890
$204$	−3.64765e10	−1.47461
$205$	−2.95768e10	−1.16966
$206$	9.42432e9	0.364626
$207$	−2.56888e10	−0.972471
$208$	−2.65020e9	−0.0981734
$209$	−5.56028e10	−2.01576
$210$	3.80602e10	1.35047
$211$	3.04741e10	1.05842	0.529212	−	0.848489i	$-0.322487\pi$
$211$	3.04741e10	1.05842	0.529212	+	0.848489i	$0.322487\pi$
$212$	6.98164e10	2.37381
$213$	4.64513e9	0.154629
$214$	−1.40793e10	−0.458901
$215$	4.78167e9	0.152618
$216$	−4.08350e10	−1.27641
$217$	−1.29869e10	−0.397592
$218$	1.89614e10	0.568613
$219$	−3.43782e10	−1.00991
$220$	−6.52783e10	−1.87874
$221$	1.23382e10	0.347926
$222$	−3.30326e10	−0.912755
$223$	−6.20504e10	−1.68025	−0.840123	−	0.542397i	$-0.817517\pi$
$223$	−6.20504e10	−1.68025	−0.840123	+	0.542397i	$0.817517\pi$
$224$	−3.32579e10	−0.882631
$225$	−3.90473e7	−0.00101571
$226$	4.45060e10	1.13483
$227$	5.50490e10	1.37605	0.688023	−	0.725689i	$-0.258479\pi$
$227$	5.50490e10	1.37605	0.688023	+	0.725689i	$0.258479\pi$
$228$	8.27111e10	2.02702
$229$	3.75095e10	0.901326	0.450663	−	0.892694i	$-0.351188\pi$
$229$	3.75095e10	0.901326	0.450663	+	0.892694i	$0.351188\pi$
$230$	1.06580e11	2.51131
$231$	−3.68926e10	−0.852482
$232$	2.69302e9	0.0610299
$233$	−4.38299e9	−0.0974245	−0.0487123	−	0.998813i	$-0.515512\pi$
$233$	−4.38299e9	−0.0974245	−0.0487123	+	0.998813i	$0.515512\pi$
$234$	1.23600e10	0.269493
$235$	5.41806e10	1.15888
$236$	−4.69623e10	−0.985474
$237$	−1.24519e10	−0.256371
$238$	−1.56322e11	−3.15808
$239$	2.42145e10	0.480049	0.240024	−	0.970767i	$-0.422845\pi$
$239$	2.42145e10	0.480049	0.240024	+	0.970767i	$0.422845\pi$
$240$	1.20129e10	0.233720
$241$	4.70535e9	0.0898494	0.0449247	−	0.998990i	$-0.485695\pi$
$241$	4.70535e9	0.0898494	0.0449247	+	0.998990i	$0.485695\pi$
$242$	9.80402e9	0.183753
$243$	5.52880e10	1.01719
$244$	−1.68343e11	−3.04046
$245$	4.80318e10	0.851689
$246$	−6.65830e10	−1.15919
$247$	−2.79771e10	−0.478262
$248$	−2.26960e10	−0.380992
$249$	2.67472e10	0.440942
$250$	−1.02930e11	−1.66652
$251$	8.58914e10	1.36590	0.682949	−	0.730466i	$-0.260697\pi$
$251$	8.58914e10	1.36590	0.682949	+	0.730466i	$0.260697\pi$
$252$	−1.00302e11	−1.56678
$253$	−1.03310e11	−1.58526
$254$	5.93336e10	0.894435
$255$	−5.59267e10	−0.828301
$256$	−1.06203e11	−1.54546
$257$	−2.26507e10	−0.323879	−0.161939	−	0.986801i	$-0.551775\pi$
$257$	−2.26507e10	−0.323879	−0.161939	+	0.986801i	$0.551775\pi$
$258$	1.07645e10	0.151253
$259$	−9.06716e10	−1.25205
$260$	−3.28454e10	−0.445753
$261$	−2.26836e9	−0.0302573
$262$	−3.70741e10	−0.486088
$263$	−1.24704e10	−0.160724	−0.0803620	−	0.996766i	$-0.525608\pi$
$263$	−1.24704e10	−0.160724	−0.0803620	+	0.996766i	$0.525608\pi$
$264$	−6.44735e10	−0.816890
$265$	1.07044e11	1.33339
$266$	3.54462e11	4.34113
$267$	6.95828e10	0.837918
$268$	3.68253e10	0.436053
$269$	−1.08677e11	−1.26547	−0.632735	−	0.774368i	$-0.718068\pi$
$269$	−1.08677e11	−1.26547	−0.632735	+	0.774368i	$0.718068\pi$
$270$	−1.42705e11	−1.63419
$271$	−1.51938e11	−1.71122	−0.855608	−	0.517625i	$-0.826816\pi$
$271$	−1.51938e11	−1.71122	−0.855608	+	0.517625i	$0.826816\pi$
$272$	−4.93394e10	−0.546555
$273$	−1.85628e10	−0.202261
$274$	2.67482e11	2.86692
$275$	−1.57033e8	−0.00165575
$276$	1.53678e11	1.59412
$277$	−1.60319e11	−1.63616	−0.818081	−	0.575103i	$-0.804962\pi$
$277$	−1.60319e11	−1.63616	−0.818081	+	0.575103i	$0.804962\pi$
$278$	2.96149e11	2.97378
$279$	1.91171e10	0.188887
$280$	1.82575e11	1.77513
$281$	5.94628e10	0.568941	0.284470	−	0.958685i	$-0.408182\pi$
$281$	5.94628e10	0.568941	0.284470	+	0.958685i	$0.408182\pi$
$282$	1.21971e11	1.14851
$283$	1.42321e11	1.31895	0.659477	−	0.751725i	$-0.270778\pi$
$283$	1.42321e11	1.31895	0.659477	+	0.751725i	$0.270778\pi$
$284$	5.07889e10	0.463272
$285$	1.26815e11	1.13859
$286$	4.97072e10	0.439311
$287$	−1.82764e11	−1.59010
$288$	4.89565e10	0.419319
$289$	1.11115e11	0.936988
$290$	9.41119e9	0.0781365
$291$	2.45961e9	0.0201070
$292$	−3.75884e11	−3.02573
$293$	2.47508e11	1.96193	0.980967	−	0.194173i	$-0.0622024\pi$
$293$	2.47508e11	1.96193	0.980967	+	0.194173i	$0.0622024\pi$
$294$	1.08129e11	0.844068
$295$	−7.20037e10	−0.553549
$296$	−1.58458e11	−1.19978
$297$	1.38327e11	1.03158
$298$	−2.94401e11	−2.16255
$299$	−5.19815e10	−0.376122
$300$	2.33592e8	0.00166500
$301$	2.95475e10	0.207478
$302$	3.16813e11	2.19165
$303$	2.76849e8	0.00188691
$304$	1.11878e11	0.751301
$305$	−2.58107e11	−1.70785
$306$	2.30110e11	1.50034
$307$	−4.13793e10	−0.265865	−0.132932	−	0.991125i	$-0.542439\pi$
$307$	−4.13793e10	−0.265865	−0.132932	+	0.991125i	$0.542439\pi$
$308$	−4.03376e11	−2.55406
$309$	2.08349e10	0.130010
$310$	−7.93148e10	−0.487783
$311$	1.57318e11	0.953578	0.476789	−	0.879018i	$-0.341801\pi$
$311$	1.57318e11	0.953578	0.476789	+	0.879018i	$0.341801\pi$
$312$	−3.24404e10	−0.193817
$313$	1.38065e11	0.813082	0.406541	−	0.913633i	$-0.366735\pi$
$313$	1.38065e11	0.813082	0.406541	+	0.913633i	$0.366735\pi$
$314$	2.16494e11	1.25679
$315$	−1.53785e11	−0.880071
$316$	−1.36147e11	−0.768095
$317$	−2.47909e10	−0.137888	−0.0689439	−	0.997621i	$-0.521963\pi$
$317$	−2.47909e10	−0.137888	−0.0689439	+	0.997621i	$0.521963\pi$
$318$	2.40977e11	1.32146
$319$	−9.12248e9	−0.0493236
$320$	−2.76836e11	−1.47587
$321$	−3.11259e10	−0.163625
$322$	6.58592e11	3.41401
$323$	−5.20856e11	−2.66260
$324$	2.26642e10	0.114258
$325$	−7.90128e7	−0.000392846 0
$326$	−1.21734e11	−0.596944
$327$	4.19191e10	0.202743
$328$	−3.19399e11	−1.52371
$329$	3.34800e11	1.57545
$330$	−2.25313e11	−1.04586
$331$	−2.04736e11	−0.937492	−0.468746	−	0.883333i	$-0.655294\pi$
$331$	−2.04736e11	−0.937492	−0.468746	+	0.883333i	$0.655294\pi$
$332$	2.92449e11	1.32108
$333$	1.33471e11	0.594823
$334$	−3.53446e11	−1.55405
$335$	5.64614e10	0.244935
$336$	7.42313e10	0.317731
$337$	1.35566e10	0.0572553	0.0286277	−	0.999590i	$-0.490886\pi$
$337$	1.35566e10	0.0572553	0.0286277	+	0.999590i	$0.490886\pi$
$338$	−3.75191e11	−1.56361
$339$	9.83919e10	0.404632
$340$	−6.11491e11	−2.48162
$341$	7.68816e10	0.307913
$342$	−5.21777e11	−2.06238
$343$	−5.19583e10	−0.202690
$344$	5.16372e10	0.198815
$345$	2.35622e11	0.895428
$346$	−4.80322e10	−0.180173
$347$	−4.70512e11	−1.74216	−0.871079	−	0.491142i	$-0.836579\pi$
$347$	−4.70512e11	−1.74216	−0.871079	+	0.491142i	$0.836579\pi$
$348$	1.35700e10	0.0495990
$349$	5.57409e10	0.201122	0.100561	−	0.994931i	$-0.467936\pi$
$349$	5.57409e10	0.201122	0.100561	+	0.994931i	$0.467936\pi$
$350$	1.00107e9	0.00356581
$351$	6.96005e10	0.244754
$352$	1.96884e11	0.683548
$353$	−1.22506e11	−0.419925	−0.209963	−	0.977709i	$-0.567334\pi$
$353$	−1.22506e11	−0.419925	−0.209963	+	0.977709i	$0.567334\pi$
$354$	−1.62094e11	−0.548596
$355$	7.78708e10	0.260224
$356$	7.60804e11	2.51043
$357$	−3.45589e11	−1.12604
$358$	4.36503e11	1.40447
$359$	3.71750e11	1.18121	0.590603	−	0.806962i	$-0.298890\pi$
$359$	3.71750e11	1.18121	0.590603	+	0.806962i	$0.298890\pi$
$360$	−2.68755e11	−0.843327
$361$	8.58363e11	2.66004
$362$	−7.19138e10	−0.220102
$363$	2.16743e10	0.0655187
$364$	−2.02962e11	−0.605981
$365$	−5.76314e11	−1.69958
$366$	−5.81048e11	−1.69257
$367$	7.84978e10	0.225871	0.112935	−	0.993602i	$-0.463975\pi$
$367$	7.84978e10	0.225871	0.112935	+	0.993602i	$0.463975\pi$
$368$	2.07870e11	0.590849
$369$	2.69034e11	0.755420
$370$	−5.53757e11	−1.53607
$371$	6.61461e11	1.81268
$372$	−1.14364e11	−0.309632
$373$	−4.85908e11	−1.29976	−0.649882	−	0.760035i	$-0.725182\pi$
$373$	−4.85908e11	−1.29976	−0.649882	+	0.760035i	$0.725182\pi$
$374$	9.25412e11	2.44575
$375$	−2.27553e11	−0.594213
$376$	5.85096e11	1.50967
$377$	−4.59006e9	−0.0117026
$378$	−8.81820e11	−2.22160
$379$	−6.80826e11	−1.69496	−0.847480	−	0.530827i	$-0.821881\pi$
$379$	−6.80826e11	−1.69496	−0.847480	+	0.530827i	$0.821881\pi$
$380$	1.38657e12	3.41125
$381$	1.31172e11	0.318918
$382$	1.16344e12	2.79550
$383$	−6.94418e11	−1.64902	−0.824511	−	0.565847i	$-0.808549\pi$
$383$	−6.94418e11	−1.64902	−0.824511	+	0.565847i	$0.808549\pi$
$384$	−4.58830e11	−1.07687
$385$	−6.18466e11	−1.43464
$386$	−3.64913e11	−0.836656
$387$	−4.34947e10	−0.0985682
$388$	2.68929e10	0.0602413
$389$	4.31005e11	0.954353	0.477177	−	0.878807i	$-0.341660\pi$
$389$	4.31005e11	0.954353	0.477177	+	0.878807i	$0.341660\pi$
$390$	−1.13368e11	−0.248143
$391$	−9.67753e11	−2.09396
$392$	5.18694e11	1.10949
$393$	−8.19617e10	−0.173318
$394$	−3.20342e11	−0.669701
$395$	−2.08743e11	−0.431445
$396$	5.93780e11	1.21338
$397$	1.24109e11	0.250752	0.125376	−	0.992109i	$-0.459986\pi$
$397$	1.24109e11	0.250752	0.125376	+	0.992109i	$0.459986\pi$
$398$	1.66872e11	0.333356
$399$	7.83629e11	1.54786
$400$	3.15966e8	0.000617120 0
$401$	4.64370e10	0.0896839	0.0448420	−	0.998994i	$-0.485722\pi$
$401$	4.64370e10	0.0896839	0.0448420	+	0.998994i	$0.485722\pi$
$402$	1.27105e11	0.242743
$403$	3.86837e10	0.0730559
$404$	3.02701e9	0.00565324
$405$	3.47494e10	0.0641799
$406$	5.81548e10	0.106223
$407$	5.36769e11	0.969644
$408$	−6.03951e11	−1.07902
$409$	1.08330e12	1.91424	0.957118	−	0.289700i	$-0.0935554\pi$
$409$	1.08330e12	1.91424	0.957118	+	0.289700i	$0.0935554\pi$
$410$	−1.11619e12	−1.95080
$411$	5.91336e11	1.02222
$412$	2.27804e11	0.389515
$413$	−4.44934e11	−0.752524
$414$	−9.69465e11	−1.62192
$415$	4.48389e11	0.742060
$416$	9.90641e10	0.162180
$417$	6.54713e11	1.06032
$418$	−2.09839e12	−3.36196
$419$	5.44446e11	0.862962	0.431481	−	0.902122i	$-0.357991\pi$
$419$	5.44446e11	0.862962	0.431481	+	0.902122i	$0.357991\pi$
$420$	9.19989e11	1.44265
$421$	−6.01208e11	−0.932728	−0.466364	−	0.884593i	$-0.654436\pi$
$421$	−6.01208e11	−0.932728	−0.466364	+	0.884593i	$0.654436\pi$
$422$	1.15006e12	1.76528
$423$	−4.92834e11	−0.748460
$424$	1.15597e12	1.73700
$425$	−1.47100e9	−0.00218707
$426$	1.75302e11	0.257896
$427$	−1.59493e12	−2.32175
$428$	−3.40324e11	−0.490226
$429$	1.09891e11	0.156640
$430$	1.80455e11	0.254543
$431$	4.02325e11	0.561603	0.280801	−	0.959766i	$-0.409400\pi$
$431$	4.02325e11	0.561603	0.280801	+	0.959766i	$0.409400\pi$
$432$	−2.78327e11	−0.384484
$433$	−4.08907e11	−0.559023	−0.279511	−	0.960142i	$-0.590172\pi$
$433$	−4.08907e11	−0.559023	−0.279511	+	0.960142i	$0.590172\pi$
$434$	−4.90112e11	−0.663119
$435$	2.08058e10	0.0278602
$436$	4.58334e11	0.607425
$437$	2.19440e12	2.87838
$438$	−1.29739e12	−1.68437
$439$	−1.74430e10	−0.0224146	−0.0112073	−	0.999937i	$-0.503567\pi$
$439$	−1.74430e10	−0.0224146	−0.0112073	+	0.999937i	$0.503567\pi$
$440$	−1.08083e12	−1.37474
$441$	−4.36903e11	−0.550061
$442$	4.65629e11	0.580284
$443$	−2.67394e11	−0.329864	−0.164932	−	0.986305i	$-0.552741\pi$
$443$	−2.67394e11	−0.329864	−0.164932	+	0.986305i	$0.552741\pi$
$444$	−7.98462e11	−0.975059
$445$	1.16648e12	1.41013
$446$	−2.34171e12	−2.80238
$447$	−6.50850e11	−0.771075
$448$	−1.71066e12	−2.00637
$449$	−4.89416e11	−0.568289	−0.284145	−	0.958781i	$-0.591710\pi$
$449$	−4.89416e11	−0.568289	−0.284145	+	0.958781i	$0.591710\pi$
$450$	−1.47360e9	−0.00169404
$451$	1.08195e12	1.23144
$452$	1.07580e12	1.21229
$453$	7.00396e11	0.781451
$454$	2.07749e12	2.29502
$455$	−3.11187e11	−0.340384
$456$	1.36947e12	1.48324
$457$	1.65057e12	1.77015	0.885074	−	0.465450i	$-0.154107\pi$
$457$	1.65057e12	1.77015	0.885074	+	0.465450i	$0.154107\pi$
$458$	1.41557e12	1.50327
$459$	1.29577e12	1.36261
$460$	2.57624e12	2.68273
$461$	−9.89589e11	−1.02047	−0.510235	−	0.860035i	$-0.670442\pi$
$461$	−9.89589e11	−1.02047	−0.510235	+	0.860035i	$0.670442\pi$
$462$	−1.39228e12	−1.42180
$463$	−6.93700e11	−0.701548	−0.350774	−	0.936460i	$-0.614081\pi$
$463$	−6.93700e11	−0.701548	−0.350774	+	0.936460i	$0.614081\pi$
$464$	1.83553e10	0.0183836
$465$	−1.75346e11	−0.173923
$466$	−1.65409e11	−0.162488
$467$	−7.17905e11	−0.698460	−0.349230	−	0.937037i	$-0.613557\pi$
$467$	−7.17905e11	−0.698460	−0.349230	+	0.937037i	$0.613557\pi$
$468$	2.98766e11	0.287888
$469$	3.48893e11	0.332977
$470$	2.04472e12	1.93282
$471$	4.78614e11	0.448117
$472$	−7.77567e11	−0.721105
$473$	−1.74919e11	−0.160680
$474$	−4.69921e11	−0.427585
$475$	3.33552e9	0.00300637
$476$	−3.77860e12	−3.37364
$477$	−9.73688e11	−0.861166
$478$	9.13828e11	0.800643
$479$	−6.95431e10	−0.0603593	−0.0301797	−	0.999544i	$-0.509608\pi$
$479$	−6.95431e10	−0.0603593	−0.0301797	+	0.999544i	$0.509608\pi$
$480$	−4.49039e11	−0.386099
$481$	2.70080e11	0.230059
$482$	1.77574e11	0.149854
$483$	1.45599e12	1.21729
$484$	2.36982e11	0.196296
$485$	4.12328e10	0.0338380
$486$	2.08651e12	1.69651
$487$	−1.01111e12	−0.814552	−0.407276	−	0.913305i	$-0.633521\pi$
$487$	−1.01111e12	−0.814552	−0.407276	+	0.913305i	$0.633521\pi$
$488$	−2.78729e12	−2.22481
$489$	−2.69125e11	−0.212845
$490$	1.81266e12	1.42048
$491$	7.05807e11	0.548049	0.274024	−	0.961723i	$-0.411645\pi$
$491$	7.05807e11	0.548049	0.274024	+	0.961723i	$0.411645\pi$
$492$	−1.60944e12	−1.23832
$493$	−8.54542e10	−0.0651512
$494$	−1.05582e12	−0.797664
$495$	9.10397e11	0.681566
$496$	−1.54693e11	−0.114763
$497$	4.81189e11	0.353763
$498$	1.00941e12	0.735420
$499$	−3.46682e11	−0.250311	−0.125155	−	0.992137i	$-0.539943\pi$
$499$	−3.46682e11	−0.250311	−0.125155	+	0.992137i	$0.539943\pi$
$500$	−2.48802e12	−1.78028
$501$	−7.81384e11	−0.554108
$502$	3.24144e12	2.27809
$503$	2.73079e12	1.90209	0.951047	−	0.309046i	$-0.100010\pi$
$503$	2.73079e12	1.90209	0.951047	+	0.309046i	$0.100010\pi$
$504$	−1.66073e12	−1.14646
$505$	4.64108e9	0.00317547
$506$	−3.89881e12	−2.64396
$507$	−8.29456e11	−0.557516
$508$	1.43421e12	0.955488
$509$	7.90210e11	0.521810	0.260905	−	0.965365i	$-0.415979\pi$
$509$	7.90210e11	0.521810	0.260905	+	0.965365i	$0.415979\pi$
$510$	−2.11061e12	−1.38147
$511$	−3.56123e12	−2.31050
$512$	−1.19225e12	−0.766749
$513$	−2.93818e12	−1.87305
$514$	−8.54811e11	−0.540177
$515$	3.49275e11	0.218794
$516$	2.60198e11	0.161577
$517$	−1.98199e12	−1.22009
$518$	−3.42184e12	−2.08822
$519$	−1.06187e11	−0.0642421
$520$	−5.43830e11	−0.326173
$521$	4.72018e11	0.280666	0.140333	−	0.990104i	$-0.455183\pi$
$521$	4.72018e11	0.280666	0.140333	+	0.990104i	$0.455183\pi$
$522$	−8.56054e10	−0.0504642
$523$	−2.37926e12	−1.39054	−0.695271	−	0.718748i	$-0.744716\pi$
$523$	−2.37926e12	−1.39054	−0.695271	+	0.718748i	$0.744716\pi$
$524$	−8.96152e11	−0.519267
$525$	2.21312e9	0.00127142
$526$	−4.70620e11	−0.268062
$527$	7.20184e11	0.406720
$528$	−4.39443e11	−0.246065
$529$	2.27605e12	1.26366
$530$	4.03973e12	2.22388
$531$	6.54955e11	0.357508
$532$	8.56803e12	4.63745
$533$	5.44394e11	0.292173
$534$	2.62598e12	1.39751
$535$	−5.21794e11	−0.275364
$536$	6.09726e11	0.319075
$537$	9.65002e11	0.500777
$538$	−4.10134e12	−2.11060
$539$	−1.75705e12	−0.896676
$540$	−3.44945e12	−1.74574
$541$	−2.77941e12	−1.39497	−0.697485	−	0.716599i	$-0.745698\pi$
$541$	−2.77941e12	−1.39497	−0.697485	+	0.716599i	$0.745698\pi$
$542$	−5.73397e12	−2.85403
$543$	−1.58984e11	−0.0784790
$544$	1.84430e12	0.902894
$545$	7.02729e11	0.341196
$546$	−7.00540e11	−0.337339
$547$	−4.21677e11	−0.201390	−0.100695	−	0.994917i	$-0.532107\pi$
$547$	−4.21677e11	−0.201390	−0.100695	+	0.994917i	$0.532107\pi$
$548$	6.46555e12	3.06262
$549$	2.34777e12	1.10301
$550$	−5.92626e9	−0.00276152
$551$	1.93769e11	0.0895575
$552$	2.54448e12	1.16647
$553$	−1.28989e12	−0.586530
$554$	−6.05026e12	−2.72885
$555$	−1.22422e12	−0.547699
$556$	7.15849e12	3.17677
$557$	2.80141e12	1.23319	0.616593	−	0.787282i	$-0.288512\pi$
$557$	2.80141e12	1.23319	0.616593	+	0.787282i	$0.288512\pi$
$558$	7.21457e11	0.315034
$559$	−8.80120e10	−0.0381232
$560$	1.24441e12	0.534709
$561$	2.04586e12	0.872053
$562$	2.24406e12	0.948901
$563$	−7.13670e11	−0.299371	−0.149685	−	0.988734i	$-0.547826\pi$
$563$	−7.13670e11	−0.299371	−0.149685	+	0.988734i	$0.547826\pi$
$564$	2.94827e12	1.22691
$565$	1.64944e12	0.680954
$566$	5.37103e12	2.19980
$567$	2.14727e11	0.0872497
$568$	8.40926e11	0.338993
$569$	−4.23069e12	−1.69202	−0.846011	−	0.533166i	$-0.821002\pi$
$569$	−4.23069e12	−1.69202	−0.846011	+	0.533166i	$0.821002\pi$
$570$	4.78584e12	1.89899
$571$	−1.92606e12	−0.758243	−0.379122	−	0.925347i	$-0.623774\pi$
$571$	−1.92606e12	−0.758243	−0.379122	+	0.925347i	$0.623774\pi$
$572$	1.20152e12	0.469298
$573$	2.57208e12	0.996757
$574$	−6.89732e12	−2.65202
$575$	6.19741e9	0.00236431
$576$	2.51813e12	0.953185
$577$	3.78940e12	1.42324	0.711622	−	0.702563i	$-0.247961\pi$
$577$	3.78940e12	1.42324	0.711622	+	0.702563i	$0.247961\pi$
$578$	4.19337e12	1.56274
$579$	−8.06734e11	−0.298316
$580$	2.27487e11	0.0834700
$581$	2.77074e12	1.00880
$582$	9.28229e10	0.0335353
$583$	−3.91580e12	−1.40382
$584$	−6.22361e12	−2.21403
$585$	4.58075e11	0.161709
$586$	9.34066e12	3.27219
$587$	−4.53425e12	−1.57628	−0.788141	−	0.615494i	$-0.788956\pi$
$587$	−4.53425e12	−1.57628	−0.788141	+	0.615494i	$0.788956\pi$
$588$	2.61368e12	0.901684
$589$	−1.63303e12	−0.559081
$590$	−2.71734e12	−0.923229
$591$	−7.08198e11	−0.238787
$592$	−1.08003e12	−0.361399
$593$	1.52410e12	0.506136	0.253068	−	0.967448i	$-0.418560\pi$
$593$	1.52410e12	0.506136	0.253068	+	0.967448i	$0.418560\pi$
$594$	5.22030e12	1.72051
$595$	−5.79344e12	−1.89500
$596$	−7.11625e12	−2.31017
$597$	3.68913e11	0.118861
$598$	−1.96172e12	−0.627310
$599$	−2.17979e12	−0.691820	−0.345910	−	0.938268i	$-0.612430\pi$
$599$	−2.17979e12	−0.691820	−0.345910	+	0.938268i	$0.612430\pi$
$600$	3.86765e9	0.00121833
$601$	3.40504e11	0.106460	0.0532301	−	0.998582i	$-0.483048\pi$
$601$	3.40504e11	0.106460	0.0532301	+	0.998582i	$0.483048\pi$
$602$	1.11509e12	0.346039
$603$	−5.13580e11	−0.158190
$604$	7.65798e12	2.34125
$605$	3.63347e11	0.110261
$606$	1.04480e10	0.00314706
$607$	3.10276e12	0.927682	0.463841	−	0.885918i	$-0.346471\pi$
$607$	3.10276e12	0.927682	0.463841	+	0.885918i	$0.346471\pi$
$608$	−4.18199e12	−1.24113
$609$	1.28566e11	0.0378746
$610$	−9.74066e12	−2.84842
$611$	−9.97255e11	−0.289482
$612$	5.56219e12	1.60275
$613$	−1.22233e12	−0.349636	−0.174818	−	0.984601i	$-0.555934\pi$
$613$	−1.22233e12	−0.349636	−0.174818	+	0.984601i	$0.555934\pi$
$614$	−1.56161e12	−0.443419
$615$	−2.46763e12	−0.695572
$616$	−6.67880e12	−1.86890
$617$	−2.76189e12	−0.767225	−0.383613	−	0.923494i	$-0.625320\pi$
$617$	−2.76189e12	−0.767225	−0.383613	+	0.923494i	$0.625320\pi$
$618$	7.86284e11	0.216836
$619$	−1.57795e12	−0.432001	−0.216001	−	0.976393i	$-0.569301\pi$
$619$	−1.57795e12	−0.432001	−0.216001	+	0.976393i	$0.569301\pi$
$620$	−1.91719e12	−0.521078
$621$	−5.45915e12	−1.47303
$622$	5.93699e12	1.59041
$623$	7.20808e12	1.91701
$624$	−2.21110e11	−0.0583818
$625$	−3.82068e12	−1.00157
$626$	5.21042e12	1.35609
$627$	−4.63902e12	−1.19873
$628$	5.23307e12	1.34257
$629$	5.02815e12	1.28080
$630$	−5.80369e12	−1.46782
$631$	5.14266e12	1.29138	0.645692	−	0.763598i	$-0.276569\pi$
$631$	5.14266e12	1.29138	0.645692	+	0.763598i	$0.276569\pi$
$632$	−2.25422e12	−0.562042
$633$	2.54250e12	0.629425
$634$	−9.35581e11	−0.229975
$635$	2.19896e12	0.536706
$636$	5.82488e12	1.41166
$637$	−8.84078e11	−0.212747
$638$	−3.44272e11	−0.0822637
$639$	−7.08323e11	−0.168065
$640$	−7.69181e12	−1.81225
$641$	−1.84647e12	−0.431998	−0.215999	−	0.976394i	$-0.569301\pi$
$641$	−1.84647e12	−0.431998	−0.215999	+	0.976394i	$0.569301\pi$
$642$	−1.17466e12	−0.272900
$643$	−6.69123e12	−1.54368	−0.771838	−	0.635819i	$-0.780663\pi$
$643$	−6.69123e12	−1.54368	−0.771838	+	0.635819i	$0.780663\pi$
$644$	1.59194e13	3.64705
$645$	3.98942e11	0.0907592
$646$	−1.96565e13	−4.44079
$647$	−4.10932e12	−0.921936	−0.460968	−	0.887417i	$-0.652498\pi$
$647$	−4.10932e12	−0.921936	−0.460968	+	0.887417i	$0.652498\pi$
$648$	3.75258e11	0.0836069
$649$	2.63397e12	0.582788
$650$	−2.98185e9	−0.000655203 0
$651$	−1.08352e12	−0.236440
$652$	−2.94255e12	−0.637691
$653$	−6.67467e12	−1.43655	−0.718274	−	0.695760i	$-0.755068\pi$
$653$	−6.67467e12	−1.43655	−0.718274	+	0.695760i	$0.755068\pi$
$654$	1.58198e12	0.338143
$655$	−1.37400e12	−0.291677
$656$	−2.17699e12	−0.458974
$657$	5.24223e12	1.09767
$658$	1.26350e13	2.62759
$659$	−2.66508e12	−0.550461	−0.275230	−	0.961378i	$-0.588754\pi$
$659$	−2.66508e12	−0.550461	−0.275230	+	0.961378i	$0.588754\pi$
$660$	−5.44626e12	−1.11725
$661$	3.01763e11	0.0614835	0.0307418	−	0.999527i	$-0.490213\pi$
$661$	3.01763e11	0.0614835	0.0307418	+	0.999527i	$0.490213\pi$
$662$	−7.72649e12	−1.56359
$663$	1.02939e12	0.206905
$664$	4.84215e12	0.966678
$665$	1.31367e13	2.60489
$666$	5.03704e12	0.992068
$667$	3.60024e11	0.0704311
$668$	−8.54348e12	−1.66013
$669$	−5.17695e12	−0.999209
$670$	2.13079e12	0.408511
$671$	9.44183e12	1.79806
$672$	−2.77475e12	−0.524883
$673$	−1.03659e13	−1.94777	−0.973886	−	0.227036i	$-0.927096\pi$
$673$	−1.03659e13	−1.94777	−0.973886	+	0.227036i	$0.927096\pi$
$674$	5.11610e11	0.0954926
$675$	−8.29800e9	−0.00153853
$676$	−9.06909e12	−1.67034
$677$	−9.71577e12	−1.77758	−0.888788	−	0.458318i	$-0.848452\pi$
$677$	−9.71577e12	−1.77758	−0.888788	+	0.458318i	$0.848452\pi$
$678$	3.71320e12	0.674861
$679$	2.54791e11	0.0460013
$680$	−1.01246e13	−1.81588
$681$	4.59281e12	0.818308
$682$	2.90142e12	0.513548
$683$	9.24732e12	1.62601	0.813004	−	0.582258i	$-0.197831\pi$
$683$	9.24732e12	1.62601	0.813004	+	0.582258i	$0.197831\pi$
$684$	−1.26124e13	−2.20315
$685$	9.91314e12	1.72030
$686$	−1.96085e12	−0.338053
$687$	3.12947e12	0.536001
$688$	3.51953e11	0.0598875
$689$	−1.97027e12	−0.333073
$690$	8.89212e12	1.49343
$691$	−6.98474e12	−1.16547	−0.582733	−	0.812664i	$-0.698016\pi$
$691$	−6.98474e12	−1.16547	−0.582733	+	0.812664i	$0.698016\pi$
$692$	−1.16103e12	−0.192471
$693$	5.62564e12	0.926557
$694$	−1.77566e13	−2.90564
$695$	1.09756e13	1.78442
$696$	2.24682e11	0.0362933
$697$	1.01351e13	1.62660
$698$	2.10360e12	0.335439
$699$	−3.65679e11	−0.0579365
$700$	2.41978e10	0.00380921
$701$	2.04978e12	0.320609	0.160305	−	0.987068i	$-0.448752\pi$
$701$	2.04978e12	0.320609	0.160305	+	0.987068i	$0.448752\pi$
$702$	2.62664e12	0.408210
$703$	−1.14014e13	−1.76060
$704$	1.01270e13	1.55382
$705$	4.52037e12	0.689164
$706$	−4.62325e12	−0.700367
$707$	2.86787e10	0.00431691
$708$	−3.91813e12	−0.586042
$709$	3.58382e12	0.532646	0.266323	−	0.963884i	$-0.414191\pi$
$709$	3.58382e12	0.532646	0.266323	+	0.963884i	$0.414191\pi$
$710$	2.93876e12	0.434011
$711$	1.89876e12	0.278648
$712$	1.25968e13	1.83697
$713$	−3.03417e12	−0.439681
$714$	−1.30421e13	−1.87805
$715$	1.84220e12	0.263609
$716$	1.05511e13	1.50034
$717$	2.02025e12	0.285476
$718$	1.40294e13	1.97006
$719$	−8.48246e12	−1.18370	−0.591850	−	0.806048i	$-0.701602\pi$
$719$	−8.48246e12	−1.18370	−0.591850	+	0.806048i	$0.701602\pi$
$720$	−1.83180e12	−0.254029
$721$	2.15828e12	0.297440
$722$	3.23936e13	4.43652
$723$	3.92574e11	0.0534317
$724$	−1.73830e12	−0.235126
$725$	5.47242e8	7.35628e−5 0
$726$	8.17963e11	0.109274
$727$	1.42815e12	0.189614	0.0948070	−	0.995496i	$-0.469777\pi$
$727$	1.42815e12	0.189614	0.0948070	+	0.995496i	$0.469777\pi$
$728$	−3.36050e12	−0.443417
$729$	4.12373e12	0.540775
$730$	−2.17494e13	−2.83462
$731$	−1.63854e12	−0.212241
$732$	−1.40450e13	−1.80810
$733$	7.55608e12	0.966782	0.483391	−	0.875404i	$-0.339405\pi$
$733$	7.55608e12	0.966782	0.483391	+	0.875404i	$0.339405\pi$
$734$	2.96242e12	0.376716
$735$	4.00736e12	0.506483
$736$	−7.77015e12	−0.976066
$737$	−2.06542e12	−0.257872
$738$	1.01530e13	1.25992
$739$	3.08275e12	0.380223	0.190111	−	0.981763i	$-0.439115\pi$
$739$	3.08275e12	0.380223	0.190111	+	0.981763i	$0.439115\pi$
$740$	−1.33854e13	−1.64092
$741$	−2.33417e12	−0.284413
$742$	2.49628e13	3.02326
$743$	1.19084e13	1.43352	0.716758	−	0.697322i	$-0.245625\pi$
$743$	1.19084e13	1.43352	0.716758	+	0.697322i	$0.245625\pi$
$744$	−1.89355e12	−0.226569
$745$	−1.09108e13	−1.29764
$746$	−1.83376e13	−2.16780
$747$	−4.07861e12	−0.479258
$748$	2.23690e13	2.61270
$749$	−3.22433e12	−0.374344
$750$	−8.58759e12	−0.991050
$751$	1.41878e13	1.62755	0.813776	−	0.581179i	$-0.197408\pi$
$751$	1.41878e13	1.62755	0.813776	+	0.581179i	$0.197408\pi$
$752$	3.98794e12	0.454746
$753$	7.16604e12	0.812273
$754$	−1.73224e11	−0.0195180
$755$	1.17414e13	1.31510
$756$	−2.13153e13	−2.37325
$757$	1.41017e12	0.156077	0.0780385	−	0.996950i	$-0.475134\pi$
$757$	1.41017e12	0.156077	0.0780385	+	0.996950i	$0.475134\pi$
$758$	−2.56936e13	−2.82692
$759$	−8.61932e12	−0.942725
$760$	2.29577e13	2.49613
$761$	−1.44034e13	−1.55681	−0.778403	−	0.627765i	$-0.783970\pi$
$761$	−1.44034e13	−1.55681	−0.778403	+	0.627765i	$0.783970\pi$
$762$	4.95028e12	0.531903
$763$	4.34239e12	0.463840
$764$	2.81226e13	2.98632
$765$	8.52809e12	0.900276
$766$	−2.62065e13	−2.75030
$767$	1.32531e12	0.138273
$768$	−8.86069e12	−0.919056
$769$	−9.24623e12	−0.953446	−0.476723	−	0.879053i	$-0.658176\pi$
$769$	−9.24623e12	−0.953446	−0.476723	+	0.879053i	$0.658176\pi$
$770$	−2.33402e13	−2.39274
$771$	−1.88978e12	−0.192604
$772$	−8.82066e12	−0.893765
$773$	1.62461e12	0.163660	0.0818299	−	0.996646i	$-0.473924\pi$
$773$	1.62461e12	0.163660	0.0818299	+	0.996646i	$0.473924\pi$
$774$	−1.64144e12	−0.164396
$775$	−4.61199e9	−0.000459231 0
$776$	4.45272e11	0.0440806
$777$	−7.56486e12	−0.744571
$778$	1.62656e13	1.59171
$779$	−2.29815e13	−2.23594
$780$	−2.74034e12	−0.265081
$781$	−2.84860e12	−0.273969
$782$	−3.65219e13	−3.49239
$783$	−4.82052e11	−0.0458317
$784$	3.53536e12	0.334203
$785$	8.02347e12	0.754134
$786$	−3.09314e12	−0.289067
$787$	8.84267e12	0.821670	0.410835	−	0.911710i	$-0.365237\pi$
$787$	8.84267e12	0.821670	0.410835	+	0.911710i	$0.365237\pi$
$788$	−7.74329e12	−0.715414
$789$	−1.04043e12	−0.0955795
$790$	−7.87773e12	−0.719581
$791$	1.01924e13	0.925726
$792$	9.83137e12	0.887872
$793$	4.75075e12	0.426611
$794$	4.68372e12	0.418214
$795$	8.93085e12	0.792941
$796$	4.03361e12	0.356111
$797$	5.37773e12	0.472103	0.236051	−	0.971741i	$-0.424147\pi$
$797$	5.37773e12	0.472103	0.236051	+	0.971741i	$0.424147\pi$
$798$	2.95733e13	2.58158
$799$	−1.85661e13	−1.61161
$800$	−1.18107e10	−0.00101947
$801$	−1.06105e13	−0.910728
$802$	1.75248e12	0.149578
$803$	2.10822e13	1.78935
$804$	3.07238e12	0.259312
$805$	2.44081e13	2.04858
$806$	1.45988e12	0.121845
$807$	−9.06707e12	−0.752551
$808$	5.01190e10	0.00413667
$809$	1.80417e13	1.48084	0.740422	−	0.672143i	$-0.234626\pi$
$809$	1.80417e13	1.48084	0.740422	+	0.672143i	$0.234626\pi$
$810$	1.31140e12	0.107042
$811$	5.02430e12	0.407833	0.203916	−	0.978988i	$-0.434633\pi$
$811$	5.02430e12	0.407833	0.203916	+	0.978988i	$0.434633\pi$
$812$	1.40571e12	0.113474
$813$	−1.26764e13	−1.01763
$814$	2.02570e13	1.61721
$815$	−4.51160e12	−0.358196
$816$	−4.11646e12	−0.325026
$817$	3.71542e12	0.291749
$818$	4.08826e13	3.19263
$819$	2.83059e12	0.219836
$820$	−2.69806e13	−2.08396
$821$	4.18829e12	0.321731	0.160865	−	0.986976i	$-0.448571\pi$
$821$	4.18829e12	0.321731	0.160865	+	0.986976i	$0.448571\pi$
$822$	2.23164e13	1.70490
$823$	−1.76745e13	−1.34291	−0.671455	−	0.741045i	$-0.734330\pi$
$823$	−1.76745e13	−1.34291	−0.671455	+	0.741045i	$0.734330\pi$
$824$	3.77181e12	0.285021
$825$	−1.31015e10	−0.000984642 0
$826$	−1.67913e13	−1.25509
$827$	−1.00101e13	−0.744154	−0.372077	−	0.928202i	$-0.621354\pi$
$827$	−1.00101e13	−0.744154	−0.372077	+	0.928202i	$0.621354\pi$
$828$	−2.34338e13	−1.73263
$829$	1.72640e13	1.26954	0.634770	−	0.772701i	$-0.281095\pi$
$829$	1.72640e13	1.26954	0.634770	+	0.772701i	$0.281095\pi$
$830$	1.69217e13	1.23764
$831$	−1.33756e13	−0.972994
$832$	5.09547e12	0.368663
$833$	−1.64591e13	−1.18441
$834$	2.47081e13	1.76845
$835$	−1.30991e13	−0.932506
$836$	−5.07221e13	−3.59144
$837$	4.06260e12	0.286114
$838$	2.05468e13	1.43928
$839$	1.34185e13	0.934923	0.467461	−	0.884013i	$-0.345169\pi$
$839$	1.34185e13	0.934923	0.467461	+	0.884013i	$0.345169\pi$
$840$	1.52325e13	1.05564
$841$	−1.44754e13	−0.997809
$842$	−2.26889e13	−1.55564
$843$	4.96107e12	0.338338
$844$	2.77991e13	1.88578
$845$	−1.39050e13	−0.938241
$846$	−1.85990e13	−1.24831
$847$	2.24524e12	0.149895
$848$	7.87894e12	0.523223
$849$	1.18740e13	0.784356
$850$	−5.55139e10	−0.00364768
$851$	−2.11839e13	−1.38459
$852$	4.23739e12	0.275499
$853$	2.11635e11	0.0136873	0.00684364	−	0.999977i	$-0.497822\pi$
$853$	2.11635e11	0.0136873	0.00684364	+	0.999977i	$0.497822\pi$
$854$	−6.01907e13	−3.87230
$855$	−1.93376e13	−1.23753
$856$	−5.63484e12	−0.358715
$857$	−2.67976e12	−0.169700	−0.0848500	−	0.996394i	$-0.527041\pi$
$857$	−2.67976e12	−0.169700	−0.0848500	+	0.996394i	$0.527041\pi$
$858$	4.14714e12	0.261250
$859$	1.26864e13	0.795003	0.397502	−	0.917601i	$-0.369877\pi$
$859$	1.26864e13	0.795003	0.397502	+	0.917601i	$0.369877\pi$
$860$	4.36194e12	0.271917
$861$	−1.52483e13	−0.945599
$862$	1.51833e13	0.936662
$863$	−1.47740e13	−0.906669	−0.453334	−	0.891341i	$-0.649766\pi$
$863$	−1.47740e13	−0.906669	−0.453334	+	0.891341i	$0.649766\pi$
$864$	1.04038e13	0.635156
$865$	−1.78012e12	−0.108113
$866$	−1.54317e13	−0.932359
$867$	9.27051e12	0.557209
$868$	−1.18470e13	−0.708382
$869$	7.63606e12	0.454235
$870$	7.85189e11	0.0464662
$871$	−1.03924e12	−0.0611832
$872$	7.58876e12	0.444474
$873$	−3.75059e11	−0.0218542
$874$	8.28140e13	4.80068
$875$	−2.35722e13	−1.35945
$876$	−3.13605e13	−1.79935
$877$	−2.15391e13	−1.22950	−0.614750	−	0.788722i	$-0.710743\pi$
$877$	−2.15391e13	−1.22950	−0.614750	+	0.788722i	$0.710743\pi$
$878$	−6.58280e11	−0.0373839
$879$	2.06499e13	1.16672
$880$	−7.36681e12	−0.414102
$881$	−7.44645e12	−0.416445	−0.208222	−	0.978082i	$-0.566768\pi$
$881$	−7.44645e12	−0.416445	−0.208222	+	0.978082i	$0.566768\pi$
$882$	−1.64882e13	−0.917413
$883$	−3.18129e13	−1.76109	−0.880543	−	0.473967i	$-0.842822\pi$
$883$	−3.18129e13	−1.76109	−0.880543	+	0.473967i	$0.842822\pi$
$884$	1.12552e13	0.619893
$885$	−6.00737e12	−0.329185
$886$	−1.00912e13	−0.550160
$887$	−5.30190e11	−0.0287591	−0.0143796	−	0.999897i	$-0.504577\pi$
$887$	−5.30190e11	−0.0287591	−0.0143796	+	0.999897i	$0.504577\pi$
$888$	−1.32203e13	−0.713484
$889$	1.35881e13	0.729627
$890$	4.40218e13	2.35187
$891$	−1.27117e12	−0.0675700
$892$	−5.66037e13	−2.99366
$893$	4.20991e13	2.21534
$894$	−2.45623e13	−1.28603
$895$	1.61773e13	0.842755
$896$	−4.75302e13	−2.46367
$897$	−4.33689e12	−0.223672
$898$	−1.84700e13	−0.947815
$899$	−2.67923e11	−0.0136802
$900$	−3.56198e10	−0.00180967
$901$	−3.66810e13	−1.85430
$902$	4.08316e13	2.05384
$903$	2.46519e12	0.123383
$904$	1.78122e13	0.887076
$905$	−2.66520e12	−0.132072
$906$	2.64322e13	1.30333
$907$	−1.14272e13	−0.560668	−0.280334	−	0.959903i	$-0.590445\pi$
$907$	−1.14272e13	−0.560668	−0.280334	+	0.959903i	$0.590445\pi$
$908$	5.02168e13	2.45168
$909$	−4.22159e10	−0.00205087
$910$	−1.17438e13	−0.567706
$911$	1.64218e13	0.789928	0.394964	−	0.918697i	$-0.370757\pi$
$911$	1.64218e13	0.789928	0.394964	+	0.918697i	$0.370757\pi$
$912$	9.33414e12	0.446784
$913$	−1.64026e13	−0.781256
$914$	6.22904e13	2.95232
$915$	−2.15342e13	−1.01563
$916$	3.42170e13	1.60588
$917$	−8.49041e12	−0.396521
$918$	4.89009e13	2.27261
$919$	−5.80211e12	−0.268328	−0.134164	−	0.990959i	$-0.542835\pi$
$919$	−5.80211e12	−0.268328	−0.134164	+	0.990959i	$0.542835\pi$
$920$	4.26556e13	1.96305
$921$	−3.45233e12	−0.158104
$922$	−3.73459e13	−1.70198
$923$	−1.43330e12	−0.0650024
$924$	−3.36542e13	−1.51885
$925$	−3.21998e10	−0.00144616
$926$	−2.61794e13	−1.17007
$927$	−3.17705e12	−0.141307
$928$	−6.86117e11	−0.0303691
$929$	9.00946e11	0.0396851	0.0198426	−	0.999803i	$-0.493683\pi$
$929$	9.00946e11	0.0396851	0.0198426	+	0.999803i	$0.493683\pi$
$930$	−6.61734e12	−0.290075
$931$	3.73213e13	1.62811
$932$	−3.99825e12	−0.173580
$933$	1.31252e13	0.567074
$934$	−2.70929e13	−1.16492
$935$	3.42967e13	1.46757
$936$	4.94674e12	0.210658
$937$	2.94534e13	1.24827	0.624134	−	0.781318i	$-0.285452\pi$
$937$	2.94534e13	1.24827	0.624134	+	0.781318i	$0.285452\pi$
$938$	1.31668e13	0.555352
$939$	1.15190e13	0.483524
$940$	4.94247e13	2.06476
$941$	−5.00902e12	−0.208257	−0.104128	−	0.994564i	$-0.533205\pi$
$941$	−5.00902e12	−0.208257	−0.104128	+	0.994564i	$0.533205\pi$
$942$	1.80624e13	0.747387
$943$	−4.26998e13	−1.75842
$944$	−5.29980e12	−0.217213
$945$	−3.26811e13	−1.33307
$946$	−6.60124e12	−0.267988
$947$	3.78708e13	1.53013	0.765067	−	0.643951i	$-0.222706\pi$
$947$	3.78708e13	1.53013	0.765067	+	0.643951i	$0.222706\pi$
$948$	−1.13589e13	−0.456771
$949$	1.06077e13	0.424545
$950$	1.25879e11	0.00501413
$951$	−2.06834e12	−0.0819993
$952$	−6.25632e13	−2.46861
$953$	−4.10676e13	−1.61280	−0.806401	−	0.591368i	$-0.798588\pi$
$953$	−4.10676e13	−1.61280	−0.806401	+	0.591368i	$0.798588\pi$
$954$	−3.67459e13	−1.43629
$955$	4.31183e13	1.67744
$956$	2.20890e13	0.855294
$957$	−7.61101e11	−0.0293318
$958$	−2.62448e12	−0.100670
$959$	6.12565e13	2.33867
$960$	−2.30968e13	−0.877669
$961$	−2.41816e13	−0.914599
$962$	1.01925e13	0.383702
$963$	4.74630e12	0.177843
$964$	4.29232e12	0.160083
$965$	−1.35241e13	−0.502035
$966$	5.49472e13	2.03025
$967$	−3.17333e13	−1.16707	−0.583533	−	0.812089i	$-0.698330\pi$
$967$	−3.17333e13	−1.16707	−0.583533	+	0.812089i	$0.698330\pi$
$968$	3.92378e12	0.143637
$969$	−4.34558e13	−1.58340
$970$	1.55608e12	0.0564363
$971$	5.14959e13	1.85903	0.929515	−	0.368784i	$-0.120226\pi$
$971$	5.14959e13	1.85903	0.929515	+	0.368784i	$0.120226\pi$
$972$	5.04349e13	1.81231
$973$	6.78216e13	2.42583
$974$	−3.81582e13	−1.35854
$975$	−6.59214e9	−0.000233618 0
$976$	−1.89978e13	−0.670162
$977$	−5.52878e12	−0.194135	−0.0970675	−	0.995278i	$-0.530946\pi$
$977$	−5.52878e12	−0.194135	−0.0970675	+	0.995278i	$0.530946\pi$
$978$	−1.01565e13	−0.354991
$979$	−4.26713e13	−1.48461
$980$	4.38156e13	1.51744
$981$	−6.39211e12	−0.220361
$982$	2.66363e13	0.914056
$983$	−1.78778e13	−0.610695	−0.305348	−	0.952241i	$-0.598773\pi$
$983$	−1.78778e13	−0.610695	−0.305348	+	0.952241i	$0.598773\pi$
$984$	−2.66479e13	−0.906119
$985$	−1.18722e13	−0.401854
$986$	−3.22495e12	−0.108662
$987$	2.79328e13	0.936887
$988$	−2.55213e13	−0.852111
$989$	6.90327e12	0.229441
$990$	3.43574e13	1.13674
$991$	3.13616e13	1.03292	0.516461	−	0.856311i	$-0.327249\pi$
$991$	3.13616e13	1.03292	0.516461	+	0.856311i	$0.327249\pi$
$992$	5.78240e12	0.189586
$993$	−1.70814e13	−0.557509
$994$	1.81595e13	0.590018
$995$	6.18443e12	0.200030
$996$	2.43994e13	0.785619
$997$	−2.88495e13	−0.924718	−0.462359	−	0.886693i	$-0.652997\pi$
$997$	−2.88495e13	−0.924718	−0.462359	+	0.886693i	$0.652997\pi$
$998$	−1.30834e13	−0.417477
$999$	2.83641e13	0.900999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.b.1.14	✓	17
3.2	odd	2		387.10.a.e.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.14	✓	17	1.1	even	1	trivial
387.10.a.e.1.4		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)

\(f(q)\)	\(=\)	\(q+37.7389 q^{2} +83.4314 q^{3} +912.221 q^{4} +1398.64 q^{5} +3148.61 q^{6} +8642.65 q^{7} +15103.9 q^{8} -12722.2 q^{9} +O(q^{10})\)	\(q+37.7389 q^{2} +83.4314 q^{3} +912.221 q^{4} +1398.64 q^{5} +3148.61 q^{6} +8642.65 q^{7} +15103.9 q^{8} -12722.2 q^{9} +52783.1 q^{10} -51163.8 q^{11} +76107.9 q^{12} -25743.5 q^{13} +326164. q^{14} +116690. q^{15} +102946. q^{16} -479274. q^{17} -480121. q^{18} +1.08676e6 q^{19} +1.27587e6 q^{20} +721068. q^{21} -1.93086e6 q^{22} +2.01921e6 q^{23} +1.26014e6 q^{24} +3069.23 q^{25} -971531. q^{26} -2.70361e6 q^{27} +7.88401e6 q^{28} +178299. q^{29} +4.40377e6 q^{30} -1.50266e6 q^{31} -3.84812e6 q^{32} -4.26867e6 q^{33} -1.80872e7 q^{34} +1.20880e7 q^{35} -1.16055e7 q^{36} -1.04912e7 q^{37} +4.10131e7 q^{38} -2.14782e6 q^{39} +2.11249e7 q^{40} -2.11468e7 q^{41} +2.72123e7 q^{42} +3.41880e6 q^{43} -4.66727e7 q^{44} -1.77938e7 q^{45} +7.62026e7 q^{46} +3.87381e7 q^{47} +8.58895e6 q^{48} +3.43418e7 q^{49} +115829. q^{50} -3.99865e7 q^{51} -2.34838e7 q^{52} +7.65345e7 q^{53} -1.02031e8 q^{54} -7.15597e7 q^{55} +1.30538e8 q^{56} +9.06700e7 q^{57} +6.72882e6 q^{58} -5.14812e7 q^{59} +1.06448e8 q^{60} -1.84541e8 q^{61} -5.67085e7 q^{62} -1.09954e8 q^{63} -1.97932e8 q^{64} -3.60059e7 q^{65} -1.61095e8 q^{66} +4.03688e7 q^{67} -4.37204e8 q^{68} +1.68465e8 q^{69} +4.56186e8 q^{70} +5.56761e7 q^{71} -1.92155e8 q^{72} -4.12053e8 q^{73} -3.95925e8 q^{74} +256070. q^{75} +9.91367e8 q^{76} -4.42191e8 q^{77} -8.10562e7 q^{78} -1.49247e8 q^{79} +1.43985e8 q^{80} +2.48451e7 q^{81} -7.98056e8 q^{82} +3.20590e8 q^{83} +6.57774e8 q^{84} -6.70331e8 q^{85} +1.29022e8 q^{86} +1.48758e7 q^{87} -7.72772e8 q^{88} +8.34013e8 q^{89} -6.71517e8 q^{90} -2.22492e8 q^{91} +1.84196e9 q^{92} -1.25369e8 q^{93} +1.46193e9 q^{94} +1.51999e9 q^{95} -3.21054e8 q^{96} +2.94806e7 q^{97} +1.29602e9 q^{98} +6.50916e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 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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