LMFDB - Embedded newform 43.10.a.b.1.16

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			1.16
Root			$-37.0877$ 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)

$f(q)$	$=$	$q+40.0877 q^{2} +243.316 q^{3} +1095.02 q^{4} +1211.89 q^{5} +9753.98 q^{6} -12008.0 q^{7} +23372.0 q^{8} +39519.8 q^{9} +O(q^{10})$	\(q+40.0877 q^{2} +243.316 q^{3} +1095.02 q^{4} +1211.89 q^{5} +9753.98 q^{6} -12008.0 q^{7} +23372.0 q^{8} +39519.8 q^{9} +48581.8 q^{10} -5734.29 q^{11} +266437. q^{12} -119754. q^{13} -481371. q^{14} +294873. q^{15} +376277. q^{16} +18812.4 q^{17} +1.58426e6 q^{18} -801678. q^{19} +1.32705e6 q^{20} -2.92173e6 q^{21} -229874. q^{22} +1.60827e6 q^{23} +5.68678e6 q^{24} -484448. q^{25} -4.80067e6 q^{26} +4.82663e6 q^{27} -1.31490e7 q^{28} -2.51979e6 q^{29} +1.18208e7 q^{30} +8.59201e6 q^{31} +3.11761e6 q^{32} -1.39525e6 q^{33} +754145. q^{34} -1.45523e7 q^{35} +4.32751e7 q^{36} +1.09104e7 q^{37} -3.21374e7 q^{38} -2.91382e7 q^{39} +2.83242e7 q^{40} +1.47902e7 q^{41} -1.17125e8 q^{42} +3.41880e6 q^{43} -6.27917e6 q^{44} +4.78937e7 q^{45} +6.44720e7 q^{46} +3.38277e7 q^{47} +9.15542e7 q^{48} +1.03837e8 q^{49} -1.94204e7 q^{50} +4.57736e6 q^{51} -1.31133e8 q^{52} +5.59026e6 q^{53} +1.93488e8 q^{54} -6.94933e6 q^{55} -2.80649e8 q^{56} -1.95061e8 q^{57} -1.01013e8 q^{58} +3.13653e7 q^{59} +3.22892e8 q^{60} -5.16173e7 q^{61} +3.44434e8 q^{62} -4.74552e8 q^{63} -6.76760e7 q^{64} -1.45129e8 q^{65} -5.59322e7 q^{66} -1.90191e8 q^{67} +2.06000e7 q^{68} +3.91319e8 q^{69} -5.83368e8 q^{70} -3.00740e8 q^{71} +9.23656e8 q^{72} +1.72091e8 q^{73} +4.37371e8 q^{74} -1.17874e8 q^{75} -8.77854e8 q^{76} +6.88571e7 q^{77} -1.16808e9 q^{78} +2.01704e8 q^{79} +4.56006e8 q^{80} +3.96528e8 q^{81} +5.92906e8 q^{82} -5.19990e8 q^{83} -3.19936e9 q^{84} +2.27985e7 q^{85} +1.37052e8 q^{86} -6.13107e8 q^{87} -1.34022e8 q^{88} -5.19550e7 q^{89} +1.91995e9 q^{90} +1.43800e9 q^{91} +1.76109e9 q^{92} +2.09058e9 q^{93} +1.35607e9 q^{94} -9.71545e8 q^{95} +7.58565e8 q^{96} -9.48291e8 q^{97} +4.16259e9 q^{98} -2.26618e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	40.0877	1.77164	0.885821	−	0.464028i	$-0.153596\pi$
$2$	40.0877	1.77164	0.885821	+	0.464028i	$0.153596\pi$
$3$	243.316	1.73431	0.867153	−	0.498042i	$-0.165948\pi$
$3$	243.316	1.73431	0.867153	+	0.498042i	$0.165948\pi$
$4$	1095.02	2.13871
$5$	1211.89	0.867158	0.433579	−	0.901116i	$-0.357251\pi$
$5$	1211.89	0.867158	0.433579	+	0.901116i	$0.357251\pi$
$6$	9753.98	3.07257
$7$	−12008.0	−1.89029	−0.945143	−	0.326656i	$-0.894078\pi$
$7$	−12008.0	−1.89029	−0.945143	+	0.326656i	$0.894078\pi$
$8$	23372.0	2.01739
$9$	39519.8	2.00782
$10$	48581.8	1.53629
$11$	−5734.29	−0.118090	−0.0590450	−	0.998255i	$-0.518806\pi$
$11$	−5734.29	−0.118090	−0.0590450	+	0.998255i	$0.518806\pi$
$12$	266437.	3.70918
$13$	−119754.	−1.16291	−0.581455	−	0.813579i	$-0.697516\pi$
$13$	−119754.	−1.16291	−0.581455	+	0.813579i	$0.697516\pi$
$14$	−481371.	−3.34891
$15$	294873.	1.50392
$16$	376277.	1.43538
$17$	18812.4	0.0546291	0.0273145	−	0.999627i	$-0.491304\pi$
$17$	18812.4	0.0546291	0.0273145	+	0.999627i	$0.491304\pi$
$18$	1.58426e6	3.55713
$19$	−801678.	−1.41126	−0.705632	−	0.708578i	$-0.749337\pi$
$19$	−801678.	−1.41126	−0.705632	+	0.708578i	$0.749337\pi$
$20$	1.32705e6	1.85460
$21$	−2.92173e6	−3.27833
$22$	−229874.	−0.209213
$23$	1.60827e6	1.19835	0.599177	−	0.800617i	$-0.295495\pi$
$23$	1.60827e6	1.19835	0.599177	+	0.800617i	$0.295495\pi$
$24$	5.68678e6	3.49877
$25$	−484448.	−0.248037
$26$	−4.80067e6	−2.06026
$27$	4.82663e6	1.74786
$28$	−1.31490e7	−4.04278
$29$	−2.51979e6	−0.661567	−0.330784	−	0.943707i	$-0.607313\pi$
$29$	−2.51979e6	−0.661567	−0.330784	+	0.943707i	$0.607313\pi$
$30$	1.18208e7	2.66440
$31$	8.59201e6	1.67096	0.835482	−	0.549518i	$-0.185189\pi$
$31$	8.59201e6	1.67096	0.835482	+	0.549518i	$0.185189\pi$
$32$	3.11761e6	0.525589
$33$	−1.39525e6	−0.204804
$34$	754145.	0.0967831
$35$	−1.45523e7	−1.63918
$36$	4.32751e7	4.29414
$37$	1.09104e7	0.957043	0.478522	−	0.878076i	$-0.341173\pi$
$37$	1.09104e7	0.957043	0.478522	+	0.878076i	$0.341173\pi$
$38$	−3.21374e7	−2.50026
$39$	−2.91382e7	−2.01684
$40$	2.83242e7	1.74940
$41$	1.47902e7	0.817425	0.408712	−	0.912663i	$-0.365978\pi$
$41$	1.47902e7	0.817425	0.408712	+	0.912663i	$0.365978\pi$
$42$	−1.17125e8	−5.80803
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	−6.27917e6	−0.252560
$45$	4.78937e7	1.74109
$46$	6.44720e7	2.12305
$47$	3.38277e7	1.01119	0.505594	−	0.862772i	$-0.331273\pi$
$47$	3.38277e7	1.01119	0.505594	+	0.862772i	$0.331273\pi$
$48$	9.15542e7	2.48939
$49$	1.03837e8	2.57318
$50$	−1.94204e7	−0.439433
$51$	4.57736e6	0.0947435
$52$	−1.31133e8	−2.48713
$53$	5.59026e6	0.0973175	0.0486587	−	0.998815i	$-0.484505\pi$
$53$	5.59026e6	0.0973175	0.0486587	+	0.998815i	$0.484505\pi$
$54$	1.93488e8	3.09658
$55$	−6.94933e6	−0.102403
$56$	−2.80649e8	−3.81345
$57$	−1.95061e8	−2.44756
$58$	−1.01013e8	−1.17206
$59$	3.13653e7	0.336989	0.168494	−	0.985703i	$-0.446109\pi$
$59$	3.13653e7	0.336989	0.168494	+	0.985703i	$0.446109\pi$
$60$	3.22892e8	3.21645
$61$	−5.16173e7	−0.477321	−0.238661	−	0.971103i	$-0.576708\pi$
$61$	−5.16173e7	−0.477321	−0.238661	+	0.971103i	$0.576708\pi$
$62$	3.44434e8	2.96035
$63$	−4.74552e8	−3.79535
$64$	−6.76760e7	−0.504225
$65$	−1.45129e8	−1.00843
$66$	−5.59322e7	−0.362839
$67$	−1.90191e8	−1.15307	−0.576533	−	0.817074i	$-0.695595\pi$
$67$	−1.90191e8	−1.15307	−0.576533	+	0.817074i	$0.695595\pi$
$68$	2.06000e7	0.116836
$69$	3.91319e8	2.07831
$70$	−5.83368e8	−2.90403
$71$	−3.00740e8	−1.40452	−0.702260	−	0.711920i	$-0.747826\pi$
$71$	−3.00740e8	−1.40452	−0.702260	+	0.711920i	$0.747826\pi$
$72$	9.23656e8	4.05055
$73$	1.72091e8	0.709262	0.354631	−	0.935006i	$-0.384607\pi$
$73$	1.72091e8	0.709262	0.354631	+	0.935006i	$0.384607\pi$
$74$	4.37371e8	1.69554
$75$	−1.17874e8	−0.430173
$76$	−8.77854e8	−3.01829
$77$	6.88571e7	0.223224
$78$	−1.16808e9	−3.57312
$79$	2.01704e8	0.582629	0.291315	−	0.956627i	$-0.405907\pi$
$79$	2.01704e8	0.582629	0.291315	+	0.956627i	$0.405907\pi$
$80$	4.56006e8	1.24470
$81$	3.96528e8	1.02351
$82$	5.92906e8	1.44818
$83$	−5.19990e8	−1.20266	−0.601331	−	0.799000i	$-0.705363\pi$
$83$	−5.19990e8	−1.20266	−0.601331	+	0.799000i	$0.705363\pi$
$84$	−3.19936e9	−7.01142
$85$	2.27985e7	0.0473720
$86$	1.37052e8	0.270173
$87$	−6.13107e8	−1.14736
$88$	−1.34022e8	−0.238234
$89$	−5.19550e7	−0.0877753	−0.0438876	−	0.999036i	$-0.513974\pi$
$89$	−5.19550e7	−0.0877753	−0.0438876	+	0.999036i	$0.513974\pi$
$90$	1.91995e9	3.08459
$91$	1.43800e9	2.19823
$92$	1.76109e9	2.56293
$93$	2.09058e9	2.89796
$94$	1.35607e9	1.79146
$95$	−9.71545e8	−1.22379
$96$	7.58565e8	0.911533
$97$	−9.48291e8	−1.08760	−0.543800	−	0.839215i	$-0.683015\pi$
$97$	−9.48291e8	−1.08760	−0.543800	+	0.839215i	$0.683015\pi$
$98$	4.16259e9	4.55876
$99$	−2.26618e8	−0.237103
$100$	−5.30481e8	−0.530481
$101$	2.93522e8	0.280669	0.140334	−	0.990104i	$-0.455182\pi$
$101$	2.93522e8	0.280669	0.140334	+	0.990104i	$0.455182\pi$
$102$	1.83496e8	0.167851
$103$	−7.80278e8	−0.683096	−0.341548	−	0.939864i	$-0.610951\pi$
$103$	−7.80278e8	−0.683096	−0.341548	+	0.939864i	$0.610951\pi$
$104$	−2.79889e9	−2.34604
$105$	−3.54082e9	−2.84283
$106$	2.24101e8	0.172412
$107$	5.83118e8	0.430060	0.215030	−	0.976607i	$-0.431015\pi$
$107$	5.83118e8	0.430060	0.215030	+	0.976607i	$0.431015\pi$
$108$	5.28526e9	3.73817
$109$	2.15474e9	1.46210	0.731049	−	0.682325i	$-0.239031\pi$
$109$	2.15474e9	1.46210	0.731049	+	0.682325i	$0.239031\pi$
$110$	−2.78583e8	−0.181421
$111$	2.65467e9	1.65981
$112$	−4.51831e9	−2.71328
$113$	2.13548e9	1.23209	0.616046	−	0.787710i	$-0.288734\pi$
$113$	2.13548e9	1.23209	0.616046	+	0.787710i	$0.288734\pi$
$114$	−7.81955e9	−4.33621
$115$	1.94905e9	1.03916
$116$	−2.75923e9	−1.41490
$117$	−4.73267e9	−2.33491
$118$	1.25736e9	0.597024
$119$	−2.25898e8	−0.103265
$120$	6.89175e9	3.03399
$121$	−2.32507e9	−0.986055
$122$	−2.06922e9	−0.845642
$123$	3.59871e9	1.41766
$124$	9.40843e9	3.57371
$125$	−2.95407e9	−1.08225
$126$	−1.90237e10	−6.72399
$127$	3.25039e9	1.10871	0.554356	−	0.832279i	$-0.312964\pi$
$127$	3.25039e9	1.10871	0.554356	+	0.832279i	$0.312964\pi$
$128$	−4.30919e9	−1.41890
$129$	8.31850e8	0.264479
$130$	−5.81788e9	−1.78657
$131$	−2.98794e9	−0.886445	−0.443222	−	0.896412i	$-0.646165\pi$
$131$	−2.98794e9	−0.886445	−0.443222	+	0.896412i	$0.646165\pi$
$132$	−1.52783e9	−0.438017
$133$	9.62650e9	2.66770
$134$	−7.62433e9	−2.04282
$135$	5.84934e9	1.51567
$136$	4.39682e8	0.110208
$137$	−5.85333e9	−1.41958	−0.709791	−	0.704412i	$-0.751211\pi$
$137$	−5.85333e9	−1.41958	−0.709791	+	0.704412i	$0.751211\pi$
$138$	1.56871e10	3.68202
$139$	4.98702e9	1.13312	0.566558	−	0.824022i	$-0.308275\pi$
$139$	4.98702e9	1.13312	0.566558	+	0.824022i	$0.308275\pi$
$140$	−1.59351e10	−3.50573
$141$	8.23082e9	1.75371
$142$	−1.20560e10	−2.48831
$143$	6.86706e8	0.137328
$144$	1.48704e10	2.88198
$145$	−3.05371e9	−0.573683
$146$	6.89875e9	1.25656
$147$	2.52653e10	4.46269
$148$	1.19471e10	2.04684
$149$	1.87100e9	0.310982	0.155491	−	0.987837i	$-0.450304\pi$
$149$	1.87100e9	0.310982	0.155491	+	0.987837i	$0.450304\pi$
$150$	−4.72530e9	−0.762111
$151$	−4.59148e9	−0.718715	−0.359358	−	0.933200i	$-0.617004\pi$
$151$	−4.59148e9	−0.718715	−0.359358	+	0.933200i	$0.617004\pi$
$152$	−1.87368e10	−2.84707
$153$	7.43462e8	0.109685
$154$	2.76032e9	0.395473
$155$	1.04126e10	1.44899
$156$	−3.19069e10	−4.31344
$157$	6.10934e9	0.802501	0.401251	−	0.915968i	$-0.368576\pi$
$157$	6.10934e9	0.802501	0.401251	+	0.915968i	$0.368576\pi$
$158$	8.08584e9	1.03221
$159$	1.36020e9	0.168778
$160$	3.77820e9	0.455769
$161$	−1.93121e10	−2.26523
$162$	1.58959e10	1.81329
$163$	2.08028e9	0.230822	0.115411	−	0.993318i	$-0.463181\pi$
$163$	2.08028e9	0.230822	0.115411	+	0.993318i	$0.463181\pi$
$164$	1.61956e10	1.74824
$165$	−1.69089e9	−0.177597
$166$	−2.08452e10	−2.13069
$167$	1.41667e9	0.140944	0.0704719	−	0.997514i	$-0.477549\pi$
$167$	1.41667e9	0.140944	0.0704719	+	0.997514i	$0.477549\pi$
$168$	−6.82866e10	−6.61369
$169$	3.73658e9	0.352358
$170$	9.13940e8	0.0839262
$171$	−3.16822e10	−2.83356
$172$	3.74366e9	0.326151
$173$	1.65084e9	0.140119	0.0700596	−	0.997543i	$-0.477681\pi$
$173$	1.65084e9	0.140119	0.0700596	+	0.997543i	$0.477681\pi$
$174$	−2.45780e10	−2.03271
$175$	5.81723e9	0.468862
$176$	−2.15768e9	−0.169504
$177$	7.63169e9	0.584442
$178$	−2.08275e9	−0.155506
$179$	−1.34726e10	−0.980873	−0.490437	−	0.871477i	$-0.663163\pi$
$179$	−1.34726e10	−0.980873	−0.490437	+	0.871477i	$0.663163\pi$
$180$	5.24446e10	3.72370
$181$	−6.23612e9	−0.431878	−0.215939	−	0.976407i	$-0.569281\pi$
$181$	−6.23612e9	−0.431878	−0.215939	+	0.976407i	$0.569281\pi$
$182$	5.76462e10	3.89448
$183$	−1.25593e10	−0.827821
$184$	3.75885e10	2.41755
$185$	1.32222e10	0.829908
$186$	8.38063e10	5.13415
$187$	−1.07876e8	−0.00645114
$188$	3.70420e10	2.16264
$189$	−5.79579e10	−3.30396
$190$	−3.89470e10	−2.16812
$191$	4.56785e9	0.248348	0.124174	−	0.992260i	$-0.460372\pi$
$191$	4.56785e9	0.248348	0.124174	+	0.992260i	$0.460372\pi$
$192$	−1.64667e10	−0.874481
$193$	2.47514e10	1.28408	0.642039	−	0.766672i	$-0.278089\pi$
$193$	2.47514e10	1.28408	0.642039	+	0.766672i	$0.278089\pi$
$194$	−3.80148e10	−1.92684
$195$	−3.53122e10	−1.74892
$196$	1.13704e11	5.50330
$197$	1.90435e9	0.0900843	0.0450421	−	0.998985i	$-0.485658\pi$
$197$	1.90435e9	0.0900843	0.0450421	+	0.998985i	$0.485658\pi$
$198$	−9.08460e9	−0.420061
$199$	9.63488e9	0.435519	0.217760	−	0.976002i	$-0.430125\pi$
$199$	9.63488e9	0.435519	0.217760	+	0.976002i	$0.430125\pi$
$200$	−1.13225e10	−0.500388
$201$	−4.62766e10	−1.99977
$202$	1.17666e10	0.497244
$203$	3.02576e10	1.25055
$204$	5.01231e9	0.202629
$205$	1.79241e10	0.708836
$206$	−3.12795e10	−1.21020
$207$	6.35587e10	2.40607
$208$	−4.50607e10	−1.66922
$209$	4.59705e9	0.166656
$210$	−1.41943e11	−5.03648
$211$	−2.28121e9	−0.0792307	−0.0396153	−	0.999215i	$-0.512613\pi$
$211$	−2.28121e9	−0.0792307	−0.0396153	+	0.999215i	$0.512613\pi$
$212$	6.12146e9	0.208134
$213$	−7.31749e10	−2.43587
$214$	2.33758e10	0.761913
$215$	4.14321e9	0.132240
$216$	1.12808e11	3.52612
$217$	−1.03172e11	−3.15860
$218$	8.63787e10	2.59031
$219$	4.18727e10	1.23008
$220$	−7.60967e9	−0.219010
$221$	−2.25286e9	−0.0635286
$222$	1.06420e11	2.94058
$223$	−2.84926e10	−0.771542	−0.385771	−	0.922595i	$-0.626065\pi$
$223$	−2.84926e10	−0.771542	−0.385771	+	0.922595i	$0.626065\pi$
$224$	−3.74361e10	−0.993515
$225$	−1.91453e10	−0.498013
$226$	8.56065e10	2.18282
$227$	−6.29356e10	−1.57319	−0.786593	−	0.617472i	$-0.788157\pi$
$227$	−6.29356e10	−1.57319	−0.786593	+	0.617472i	$0.788157\pi$
$228$	−2.13596e11	−5.23464
$229$	6.04875e10	1.45347	0.726735	−	0.686918i	$-0.241037\pi$
$229$	6.04875e10	1.45347	0.726735	+	0.686918i	$0.241037\pi$
$230$	7.81329e10	1.84102
$231$	1.67541e10	0.387138
$232$	−5.88925e10	−1.33464
$233$	−8.98004e9	−0.199607	−0.0998037	−	0.995007i	$-0.531821\pi$
$233$	−8.98004e9	−0.199607	−0.0998037	+	0.995007i	$0.531821\pi$
$234$	−1.89722e11	−4.13662
$235$	4.09954e10	0.876859
$236$	3.43457e10	0.720723
$237$	4.90779e10	1.01046
$238$	−9.05573e9	−0.182948
$239$	1.71812e10	0.340615	0.170307	−	0.985391i	$-0.445524\pi$
$239$	1.71812e10	0.340615	0.170307	+	0.985391i	$0.445524\pi$
$240$	1.10954e11	2.15869
$241$	3.98739e10	0.761398	0.380699	−	0.924699i	$-0.375683\pi$
$241$	3.98739e10	0.761398	0.380699	+	0.924699i	$0.375683\pi$
$242$	−9.32065e10	−1.74694
$243$	1.47923e9	0.0272149
$244$	−5.65220e10	−1.02085
$245$	1.25839e11	2.23136
$246$	1.44264e11	2.51159
$247$	9.60043e10	1.64117
$248$	2.00812e11	3.37099
$249$	−1.26522e11	−2.08578
$250$	−1.18422e11	−1.91735
$251$	−6.81662e10	−1.08402	−0.542010	−	0.840372i	$-0.682337\pi$
$251$	−6.81662e10	−1.08402	−0.542010	+	0.840372i	$0.682337\pi$
$252$	−5.19645e11	−8.11716
$253$	−9.22232e9	−0.141513
$254$	1.30301e11	1.96424
$255$	5.54726e9	0.0821575
$256$	−1.38095e11	−2.00955
$257$	2.33077e10	0.333273	0.166637	−	0.986018i	$-0.446709\pi$
$257$	2.33077e10	0.333273	0.166637	+	0.986018i	$0.446709\pi$
$258$	3.33469e10	0.468562
$259$	−1.31011e11	−1.80909
$260$	−1.58919e11	−2.15673
$261$	−9.95818e10	−1.32830
$262$	−1.19780e11	−1.57046
$263$	−8.48825e10	−1.09400	−0.547000	−	0.837132i	$-0.684230\pi$
$263$	−8.48825e10	−1.09400	−0.547000	+	0.837132i	$0.684230\pi$
$264$	−3.26097e10	−0.413170
$265$	6.77478e9	0.0843896
$266$	3.85904e11	4.72620
$267$	−1.26415e10	−0.152229
$268$	−2.08263e11	−2.46608
$269$	1.38545e11	1.61326	0.806630	−	0.591056i	$-0.201289\pi$
$269$	1.38545e11	1.61326	0.806630	+	0.591056i	$0.201289\pi$
$270$	2.34486e11	2.68522
$271$	1.94415e10	0.218962	0.109481	−	0.993989i	$-0.465081\pi$
$271$	1.94415e10	0.218962	0.109481	+	0.993989i	$0.465081\pi$
$272$	7.07866e9	0.0784135
$273$	3.49890e11	3.81241
$274$	−2.34647e11	−2.51499
$275$	2.77797e9	0.0292907
$276$	4.28503e11	4.44491
$277$	7.79557e10	0.795589	0.397795	−	0.917475i	$-0.369776\pi$
$277$	7.79557e10	0.795589	0.397795	+	0.917475i	$0.369776\pi$
$278$	1.99918e11	2.00748
$279$	3.39555e11	3.35499
$280$	−3.40116e11	−3.30686
$281$	−1.32827e11	−1.27089	−0.635444	−	0.772147i	$-0.719183\pi$
$281$	−1.32827e11	−1.27089	−0.635444	+	0.772147i	$0.719183\pi$
$282$	3.29955e11	3.10694
$283$	−7.55950e10	−0.700574	−0.350287	−	0.936642i	$-0.613916\pi$
$283$	−7.55950e10	−0.700574	−0.350287	+	0.936642i	$0.613916\pi$
$284$	−3.29316e11	−3.00387
$285$	−2.36393e11	−2.12242
$286$	2.75284e10	0.243296
$287$	−1.77600e11	−1.54517
$288$	1.23207e11	1.05529
$289$	−1.18234e11	−0.997016
$290$	−1.22416e11	−1.01636
$291$	−2.30735e11	−1.88623
$292$	1.88444e11	1.51691
$293$	1.46338e11	1.15999	0.579993	−	0.814621i	$-0.303055\pi$
$293$	1.46338e11	1.15999	0.579993	+	0.814621i	$0.303055\pi$
$294$	1.01283e12	7.90628
$295$	3.80113e10	0.292223
$296$	2.54997e11	1.93073
$297$	−2.76773e10	−0.206405
$298$	7.50039e10	0.550948
$299$	−1.92598e11	−1.39358
$300$	−1.29075e11	−0.920016
$301$	−4.10528e10	−0.288266
$302$	−1.84062e11	−1.27331
$303$	7.14186e10	0.486765
$304$	−3.01653e11	−2.02570
$305$	−6.25545e10	−0.413913
$306$	2.98037e10	0.194323
$307$	−1.35518e10	−0.0870713	−0.0435356	−	0.999052i	$-0.513862\pi$
$307$	−1.35518e10	−0.0870713	−0.0435356	+	0.999052i	$0.513862\pi$
$308$	7.54000e10	0.477412
$309$	−1.89854e11	−1.18470
$310$	4.17416e11	2.56709
$311$	2.52262e11	1.52908	0.764539	−	0.644578i	$-0.222967\pi$
$311$	2.52262e11	1.52908	0.764539	+	0.644578i	$0.222967\pi$
$312$	−6.81016e11	−4.06876
$313$	−4.78704e10	−0.281914	−0.140957	−	0.990016i	$-0.545018\pi$
$313$	−4.78704e10	−0.281914	−0.140957	+	0.990016i	$0.545018\pi$
$314$	2.44909e11	1.42174
$315$	−5.75105e11	−3.29117
$316$	2.20870e11	1.24608
$317$	3.39930e11	1.89070	0.945350	−	0.326058i	$-0.105721\pi$
$317$	3.39930e11	1.89070	0.945350	+	0.326058i	$0.105721\pi$
$318$	5.45273e10	0.299014
$319$	1.44492e10	0.0781244
$320$	−8.20158e10	−0.437243
$321$	1.41882e11	0.745856
$322$	−7.74176e11	−4.01318
$323$	−1.50815e10	−0.0770961
$324$	4.34206e11	2.18899
$325$	5.80147e10	0.288445
$326$	8.33935e10	0.408934
$327$	5.24284e11	2.53572
$328$	3.45677e11	1.64907
$329$	−4.06201e11	−1.91143
$330$	−6.77837e10	−0.314639
$331$	1.59873e11	0.732065	0.366032	−	0.930602i	$-0.380716\pi$
$331$	1.59873e11	0.732065	0.366032	+	0.930602i	$0.380716\pi$
$332$	−5.69400e11	−2.57215
$333$	4.31176e11	1.92157
$334$	5.67912e10	0.249702
$335$	−2.30491e11	−0.999890
$336$	−1.09938e12	−4.70566
$337$	2.60458e11	1.10003	0.550014	−	0.835156i	$-0.314622\pi$
$337$	2.60458e11	1.10003	0.550014	+	0.835156i	$0.314622\pi$
$338$	1.49791e11	0.624252
$339$	5.19598e11	2.13682
$340$	2.49649e10	0.101315
$341$	−4.92691e10	−0.197324
$342$	−1.27006e12	−5.02005
$343$	−7.62309e11	−2.97377
$344$	7.99041e10	0.307649
$345$	4.74236e11	1.80222
$346$	6.61783e10	0.248241
$347$	2.64978e11	0.981130	0.490565	−	0.871405i	$-0.336790\pi$
$347$	2.64978e11	0.981130	0.490565	+	0.871405i	$0.336790\pi$
$348$	−6.71365e11	−2.45387
$349$	−2.77581e11	−1.00156	−0.500779	−	0.865575i	$-0.666953\pi$
$349$	−2.77581e11	−1.00156	−0.500779	+	0.865575i	$0.666953\pi$
$350$	2.33199e11	0.830655
$351$	−5.78009e11	−2.03260
$352$	−1.78773e10	−0.0620668
$353$	1.25275e11	0.429416	0.214708	−	0.976678i	$-0.431120\pi$
$353$	1.25275e11	0.429416	0.214708	+	0.976678i	$0.431120\pi$
$354$	3.05937e11	1.03542
$355$	−3.64463e11	−1.21794
$356$	−5.68918e10	−0.187726
$357$	−5.49647e10	−0.179092
$358$	−5.40085e11	−1.73776
$359$	−1.63338e11	−0.518995	−0.259497	−	0.965744i	$-0.583557\pi$
$359$	−1.63338e11	−0.518995	−0.259497	+	0.965744i	$0.583557\pi$
$360$	1.11937e12	3.51247
$361$	3.19999e11	0.991668
$362$	−2.49992e11	−0.765133
$363$	−5.65726e11	−1.71012
$364$	1.57464e12	4.70139
$365$	2.08556e11	0.615042
$366$	−5.03474e11	−1.46660
$367$	−1.22512e11	−0.352518	−0.176259	−	0.984344i	$-0.556400\pi$
$367$	−1.22512e11	−0.352518	−0.176259	+	0.984344i	$0.556400\pi$
$368$	6.05156e11	1.72009
$369$	5.84508e11	1.64124
$370$	5.30046e11	1.47030
$371$	−6.71276e10	−0.183958
$372$	2.28923e12	6.19791
$373$	−6.93580e11	−1.85527	−0.927635	−	0.373488i	$-0.878162\pi$
$373$	−6.93580e11	−1.85527	−0.927635	+	0.373488i	$0.878162\pi$
$374$	−4.32449e9	−0.0114291
$375$	−7.18773e11	−1.87694
$376$	7.90619e11	2.03996
$377$	3.01756e11	0.769343
$378$	−2.32340e12	−5.85343
$379$	−1.72410e11	−0.429225	−0.214612	−	0.976699i	$-0.568849\pi$
$379$	−1.72410e11	−0.429225	−0.214612	+	0.976699i	$0.568849\pi$
$380$	−1.06386e12	−2.61733
$381$	7.90874e11	1.92285
$382$	1.83114e11	0.439984
$383$	−2.20410e11	−0.523403	−0.261701	−	0.965149i	$-0.584284\pi$
$383$	−2.20410e11	−0.523403	−0.261701	+	0.965149i	$0.584284\pi$
$384$	−1.04850e12	−2.46080
$385$	8.34472e10	0.193570
$386$	9.92225e11	2.27493
$387$	1.35110e11	0.306189
$388$	−1.03840e12	−2.32606
$389$	1.81915e11	0.402806	0.201403	−	0.979508i	$-0.435450\pi$
$389$	1.81915e11	0.402806	0.201403	+	0.979508i	$0.435450\pi$
$390$	−1.41559e12	−3.09846
$391$	3.02555e10	0.0654649
$392$	2.42688e12	5.19112
$393$	−7.27015e11	−1.53737
$394$	7.63410e10	0.159597
$395$	2.44443e11	0.505232
$396$	−2.48152e11	−0.507095
$397$	8.88950e10	0.179606	0.0898028	−	0.995960i	$-0.471376\pi$
$397$	8.88950e10	0.179606	0.0898028	+	0.995960i	$0.471376\pi$
$398$	3.86240e11	0.771584
$399$	2.34229e12	4.62660
$400$	−1.82286e11	−0.356028
$401$	2.32437e11	0.448906	0.224453	−	0.974485i	$-0.427940\pi$
$401$	2.32437e11	0.448906	0.224453	+	0.974485i	$0.427940\pi$
$402$	−1.85512e12	−3.54287
$403$	−1.02893e12	−1.94318
$404$	3.21413e11	0.600270
$405$	4.80548e11	0.887543
$406$	1.21295e12	2.21553
$407$	−6.25632e10	−0.113017
$408$	1.06982e11	0.191135
$409$	5.61292e11	0.991823	0.495911	−	0.868373i	$-0.334834\pi$
$409$	5.61292e11	0.991823	0.495911	+	0.868373i	$0.334834\pi$
$410$	7.18537e11	1.25580
$411$	−1.42421e12	−2.46199
$412$	−8.54421e11	−1.46095
$413$	−3.76633e11	−0.637006
$414$	2.54792e12	4.26270
$415$	−6.30170e11	−1.04290
$416$	−3.73347e11	−0.611213
$417$	1.21342e12	1.96517
$418$	1.84285e11	0.295255
$419$	1.75016e11	0.277405	0.138703	−	0.990334i	$-0.455707\pi$
$419$	1.75016e11	0.277405	0.138703	+	0.990334i	$0.455707\pi$
$420$	−3.87727e12	−6.08001
$421$	−1.05177e12	−1.63175	−0.815873	−	0.578231i	$-0.803743\pi$
$421$	−1.05177e12	−1.63175	−0.815873	+	0.578231i	$0.803743\pi$
$422$	−9.14482e10	−0.140368
$423$	1.33686e12	2.03028
$424$	1.30655e11	0.196327
$425$	−9.11362e9	−0.0135500
$426$	−2.93341e12	−4.31548
$427$	6.19818e11	0.902274
$428$	6.38527e11	0.919776
$429$	1.67087e11	0.238168
$430$	1.66092e11	0.234282
$431$	−8.28981e11	−1.15717	−0.578585	−	0.815622i	$-0.696395\pi$
$431$	−8.28981e11	−1.15717	−0.578585	+	0.815622i	$0.696395\pi$
$432$	1.81615e12	2.50885
$433$	−6.12135e11	−0.836858	−0.418429	−	0.908249i	$-0.637419\pi$
$433$	−6.12135e11	−0.836858	−0.418429	+	0.908249i	$0.637419\pi$
$434$	−4.13594e12	−5.59591
$435$	−7.43018e11	−0.994942
$436$	2.35949e12	3.12701
$437$	−1.28932e12	−1.69119
$438$	1.67858e12	2.17925
$439$	−3.74982e11	−0.481860	−0.240930	−	0.970543i	$-0.577452\pi$
$439$	−3.74982e11	−0.481860	−0.240930	+	0.970543i	$0.577452\pi$
$440$	−1.62420e11	−0.206586
$441$	4.10363e12	5.16648
$442$	−9.03120e10	−0.112550
$443$	1.37938e12	1.70164	0.850818	−	0.525460i	$-0.176107\pi$
$443$	1.37938e12	1.70164	0.850818	+	0.525460i	$0.176107\pi$
$444$	2.90692e12	3.54985
$445$	−6.29637e10	−0.0761150
$446$	−1.14220e12	−1.36690
$447$	4.55244e11	0.539337
$448$	8.12650e11	0.953131
$449$	−1.70030e12	−1.97431	−0.987157	−	0.159753i	$-0.948930\pi$
$449$	−1.70030e12	−1.97431	−0.987157	+	0.159753i	$0.948930\pi$
$450$	−7.67491e11	−0.882301
$451$	−8.48115e10	−0.0965296
$452$	2.33840e12	2.63509
$453$	−1.11718e12	−1.24647
$454$	−2.52294e12	−2.78712
$455$	1.74270e12	1.90621
$456$	−4.55896e12	−4.93770
$457$	−2.36115e11	−0.253221	−0.126611	−	0.991953i	$-0.540410\pi$
$457$	−2.36115e11	−0.253221	−0.126611	+	0.991953i	$0.540410\pi$
$458$	2.42480e12	2.57503
$459$	9.08003e10	0.0954839
$460$	2.13425e12	2.22247
$461$	−9.49030e11	−0.978646	−0.489323	−	0.872103i	$-0.662756\pi$
$461$	−9.49030e11	−0.978646	−0.489323	+	0.872103i	$0.662756\pi$
$462$	6.71631e11	0.685870
$463$	−9.79060e11	−0.990136	−0.495068	−	0.868854i	$-0.664857\pi$
$463$	−9.79060e11	−0.990136	−0.495068	+	0.868854i	$0.664857\pi$
$464$	−9.48139e11	−0.949601
$465$	2.53355e12	2.51299
$466$	−3.59989e11	−0.353633
$467$	−2.91441e11	−0.283547	−0.141774	−	0.989899i	$-0.545280\pi$
$467$	−2.91441e11	−0.283547	−0.141774	+	0.989899i	$0.545280\pi$
$468$	−5.18237e12	−4.99370
$469$	2.28381e12	2.17962
$470$	1.64341e12	1.55348
$471$	1.48650e12	1.39178
$472$	7.33069e11	0.679839
$473$	−1.96044e10	−0.0180085
$474$	1.96742e12	1.79017
$475$	3.88371e11	0.350046
$476$	−2.47363e11	−0.220853
$477$	2.20926e11	0.195396
$478$	6.88755e11	0.603447
$479$	1.54610e12	1.34193	0.670964	−	0.741490i	$-0.265881\pi$
$479$	1.54610e12	1.34193	0.670964	+	0.741490i	$0.265881\pi$
$480$	9.19297e11	0.790443
$481$	−1.30656e12	−1.11295
$482$	1.59845e12	1.34892
$483$	−4.69895e12	−3.92860
$484$	−2.54600e12	−2.10889
$485$	−1.14922e12	−0.943120
$486$	5.92988e10	0.0482151
$487$	3.66859e11	0.295541	0.147771	−	0.989022i	$-0.452790\pi$
$487$	3.66859e11	0.295541	0.147771	+	0.989022i	$0.452790\pi$
$488$	−1.20640e12	−0.962944
$489$	5.06166e11	0.400316
$490$	5.04461e12	3.95316
$491$	−1.65416e12	−1.28443	−0.642215	−	0.766525i	$-0.721984\pi$
$491$	−1.65416e12	−1.28443	−0.642215	+	0.766525i	$0.721984\pi$
$492$	3.94066e12	3.03198
$493$	−4.74033e10	−0.0361408
$494$	3.84859e12	2.90757
$495$	−2.74636e11	−0.205606
$496$	3.23297e12	2.39847
$497$	3.61127e12	2.65495
$498$	−5.07197e12	−3.69526
$499$	−4.77065e11	−0.344449	−0.172224	−	0.985058i	$-0.555095\pi$
$499$	−4.77065e11	−0.344449	−0.172224	+	0.985058i	$0.555095\pi$
$500$	−3.23477e12	−2.31461
$501$	3.44700e11	0.244440
$502$	−2.73262e12	−1.92050
$503$	−1.24662e12	−0.868318	−0.434159	−	0.900836i	$-0.642954\pi$
$503$	−1.24662e12	−0.868318	−0.434159	+	0.900836i	$0.642954\pi$
$504$	−1.10912e13	−7.65670
$505$	3.55716e11	0.243384
$506$	−3.69701e11	−0.250711
$507$	9.09170e11	0.611096
$508$	3.55925e12	2.37122
$509$	−1.07766e12	−0.711627	−0.355814	−	0.934557i	$-0.615796\pi$
$509$	−1.07766e12	−0.711627	−0.355814	+	0.934557i	$0.615796\pi$
$510$	2.22377e11	0.145554
$511$	−2.06647e12	−1.34071
$512$	−3.32961e12	−2.14131
$513$	−3.86940e12	−2.46669
$514$	9.34351e11	0.590440
$515$	−9.45611e11	−0.592352
$516$	9.10894e11	0.565645
$517$	−1.93978e11	−0.119411
$518$	−5.25193e12	−3.20505
$519$	4.01676e11	0.243009
$520$	−3.39195e12	−2.03439
$521$	9.12978e11	0.542863	0.271432	−	0.962458i	$-0.412503\pi$
$521$	9.12978e11	0.542863	0.271432	+	0.962458i	$0.412503\pi$
$522$	−3.99200e12	−2.35328
$523$	2.83520e12	1.65701	0.828507	−	0.559979i	$-0.189191\pi$
$523$	2.83520e12	1.65701	0.828507	+	0.559979i	$0.189191\pi$
$524$	−3.27186e12	−1.89585
$525$	1.41543e12	0.813150
$526$	−3.40274e12	−1.93818
$527$	1.61636e11	0.0912832
$528$	−5.24999e11	−0.293972
$529$	7.85395e11	0.436051
$530$	2.71585e11	0.149508
$531$	1.23955e12	0.676612
$532$	1.05412e13	5.70544
$533$	−1.77119e12	−0.950591
$534$	−5.06768e11	−0.269696
$535$	7.06675e11	0.372930
$536$	−4.44514e12	−2.32618
$537$	−3.27810e12	−1.70113
$538$	5.55393e12	2.85812
$539$	−5.95433e11	−0.303867
$540$	6.40515e12	3.24158
$541$	−6.54090e11	−0.328284	−0.164142	−	0.986437i	$-0.552486\pi$
$541$	−6.54090e11	−0.328284	−0.164142	+	0.986437i	$0.552486\pi$
$542$	7.79364e11	0.387921
$543$	−1.51735e12	−0.749008
$544$	5.86496e10	0.0287125
$545$	2.61131e12	1.26787
$546$	1.40263e13	6.75422
$547$	−1.59844e12	−0.763401	−0.381701	−	0.924286i	$-0.624661\pi$
$547$	−1.59844e12	−0.763401	−0.381701	+	0.924286i	$0.624661\pi$
$548$	−6.40953e12	−3.03608
$549$	−2.03991e12	−0.958373
$550$	1.11362e11	0.0518926
$551$	2.02006e12	0.933646
$552$	9.14590e12	4.19277
$553$	−2.42205e12	−1.10134
$554$	3.12506e12	1.40950
$555$	3.21717e12	1.43931
$556$	5.46089e12	2.42341
$557$	−1.69039e10	−0.00744114	−0.00372057	−	0.999993i	$-0.501184\pi$
$557$	−1.69039e10	−0.00744114	−0.00372057	+	0.999993i	$0.501184\pi$
$558$	1.36120e13	5.94383
$559$	−4.09416e11	−0.177342
$560$	−5.47570e12	−2.35284
$561$	−2.62479e10	−0.0111882
$562$	−5.32471e12	−2.25156
$563$	6.21804e11	0.260835	0.130417	−	0.991459i	$-0.458368\pi$
$563$	6.21804e11	0.260835	0.130417	+	0.991459i	$0.458368\pi$
$564$	9.01293e12	3.75068
$565$	2.58797e12	1.06842
$566$	−3.03043e12	−1.24117
$567$	−4.76149e12	−1.93472
$568$	−7.02888e12	−2.83347
$569$	1.56325e12	0.625205	0.312602	−	0.949884i	$-0.398799\pi$
$569$	1.56325e12	0.625205	0.312602	+	0.949884i	$0.398799\pi$
$570$	−9.47643e12	−3.76018
$571$	2.33020e12	0.917339	0.458670	−	0.888607i	$-0.348326\pi$
$571$	2.33020e12	0.917339	0.458670	+	0.888607i	$0.348326\pi$
$572$	7.51958e11	0.293705
$573$	1.11143e12	0.430712
$574$	−7.11959e12	−2.73748
$575$	−7.79125e11	−0.297236
$576$	−2.67454e12	−1.01239
$577$	−3.01072e12	−1.13078	−0.565392	−	0.824822i	$-0.691275\pi$
$577$	−3.01072e12	−1.13078	−0.565392	+	0.824822i	$0.691275\pi$
$578$	−4.73972e12	−1.76635
$579$	6.02241e12	2.22698
$580$	−3.34388e12	−1.22694
$581$	6.24401e12	2.27338
$582$	−9.24962e12	−3.34172
$583$	−3.20562e10	−0.0114922
$584$	4.02211e12	1.43086
$585$	−5.73547e12	−2.02473
$586$	5.86635e12	2.05508
$587$	−6.22809e11	−0.216513	−0.108256	−	0.994123i	$-0.534527\pi$
$587$	−6.22809e11	−0.216513	−0.108256	+	0.994123i	$0.534527\pi$
$588$	2.76660e13	9.54441
$589$	−6.88802e12	−2.35817
$590$	1.52378e12	0.517714
$591$	4.63360e11	0.156234
$592$	4.10532e12	1.37372
$593$	3.51751e11	0.116813	0.0584063	−	0.998293i	$-0.481398\pi$
$593$	3.51751e11	0.116813	0.0584063	+	0.998293i	$0.481398\pi$
$594$	−1.10952e12	−0.365675
$595$	−2.73764e11	−0.0895467
$596$	2.04878e12	0.665101
$597$	2.34432e12	0.755324
$598$	−7.72079e12	−2.46892
$599$	−3.60750e12	−1.14495	−0.572474	−	0.819923i	$-0.694016\pi$
$599$	−3.60750e12	−1.14495	−0.572474	+	0.819923i	$0.694016\pi$
$600$	−2.75495e12	−0.867827
$601$	−4.18356e12	−1.30801	−0.654005	−	0.756490i	$-0.726913\pi$
$601$	−4.18356e12	−1.30801	−0.654005	+	0.756490i	$0.726913\pi$
$602$	−1.64571e12	−0.510704
$603$	−7.51633e12	−2.31514
$604$	−5.02777e12	−1.53713
$605$	−2.81772e12	−0.855065
$606$	2.86301e12	0.862374
$607$	3.43998e12	1.02851	0.514253	−	0.857638i	$-0.328069\pi$
$607$	3.43998e12	1.02851	0.514253	+	0.857638i	$0.328069\pi$
$608$	−2.49932e12	−0.741746
$609$	7.36216e12	2.16884
$610$	−2.50766e12	−0.733305
$611$	−4.05101e12	−1.17592
$612$	8.14107e11	0.234585
$613$	5.53640e12	1.58363	0.791817	−	0.610758i	$-0.209135\pi$
$613$	5.53640e12	1.58363	0.791817	+	0.610758i	$0.209135\pi$
$614$	−5.43261e11	−0.154259
$615$	4.36123e12	1.22934
$616$	1.60933e12	0.450330
$617$	−9.28785e11	−0.258007	−0.129004	−	0.991644i	$-0.541178\pi$
$617$	−9.28785e11	−0.258007	−0.129004	+	0.991644i	$0.541178\pi$
$618$	−7.61082e12	−2.09886
$619$	−4.22185e12	−1.15583	−0.577916	−	0.816096i	$-0.696134\pi$
$619$	−4.22185e12	−1.15583	−0.577916	+	0.816096i	$0.696134\pi$
$620$	1.14020e13	3.09897
$621$	7.76254e12	2.09455
$622$	1.01126e13	2.70898
$623$	6.23873e11	0.165920
$624$	−1.09640e13	−2.89493
$625$	−2.63382e12	−0.690440
$626$	−1.91901e12	−0.499451
$627$	1.11854e12	0.289033
$628$	6.68985e12	1.71632
$629$	2.05250e11	0.0522824
$630$	−2.30546e13	−5.83076
$631$	−3.64511e12	−0.915333	−0.457666	−	0.889124i	$-0.651315\pi$
$631$	−3.64511e12	−0.915333	−0.457666	+	0.889124i	$0.651315\pi$
$632$	4.71422e12	1.17539
$633$	−5.55054e11	−0.137410
$634$	1.36270e13	3.34964
$635$	3.93912e12	0.961429
$636$	1.48945e12	0.360968
$637$	−1.24350e13	−2.99238
$638$	5.79236e11	0.138408
$639$	−1.18852e13	−2.82002
$640$	−5.22226e12	−1.23041
$641$	3.05338e10	0.00714365	0.00357183	−	0.999994i	$-0.498863\pi$
$641$	3.05338e10	0.00714365	0.00357183	+	0.999994i	$0.498863\pi$
$642$	5.68772e12	1.32139
$643$	1.59990e12	0.369099	0.184550	−	0.982823i	$-0.440917\pi$
$643$	1.59990e12	0.369099	0.184550	+	0.982823i	$0.440917\pi$
$644$	−2.11471e13	−4.84468
$645$	1.00811e12	0.229345
$646$	−6.04581e11	−0.136587
$647$	2.22495e12	0.499172	0.249586	−	0.968353i	$-0.419705\pi$
$647$	2.22495e12	0.499172	0.249586	+	0.968353i	$0.419705\pi$
$648$	9.26763e12	2.06482
$649$	−1.79858e11	−0.0397950
$650$	2.32567e12	0.511021
$651$	−2.51035e13	−5.47798
$652$	2.27795e12	0.493662
$653$	3.33259e12	0.717254	0.358627	−	0.933481i	$-0.383245\pi$
$653$	3.33259e12	0.717254	0.358627	+	0.933481i	$0.383245\pi$
$654$	2.10173e13	4.49239
$655$	−3.62106e12	−0.768687
$656$	5.56522e12	1.17332
$657$	6.80103e12	1.42407
$658$	−1.62837e13	−3.38638
$659$	4.35014e12	0.898502	0.449251	−	0.893405i	$-0.351691\pi$
$659$	4.35014e12	0.898502	0.449251	+	0.893405i	$0.351691\pi$
$660$	−1.85156e12	−0.379830
$661$	3.50558e12	0.714254	0.357127	−	0.934056i	$-0.383756\pi$
$661$	3.50558e12	0.714254	0.357127	+	0.934056i	$0.383756\pi$
$662$	6.40894e12	1.29696
$663$	−5.48158e11	−0.110178
$664$	−1.21532e13	−2.42624
$665$	1.16663e13	2.31331
$666$	1.72848e13	3.40433
$667$	−4.05252e12	−0.792791
$668$	1.55129e12	0.301438
$669$	−6.93271e12	−1.33809
$670$	−9.23984e12	−1.77145
$671$	2.95989e11	0.0563668
$672$	−9.10881e12	−1.72306
$673$	1.58840e12	0.298463	0.149232	−	0.988802i	$-0.452320\pi$
$673$	1.58840e12	0.298463	0.149232	+	0.988802i	$0.452320\pi$
$674$	1.04412e13	1.94885
$675$	−2.33825e12	−0.433535
$676$	4.09163e12	0.753592
$677$	8.62297e12	1.57764	0.788820	−	0.614624i	$-0.210692\pi$
$677$	8.62297e12	1.57764	0.788820	+	0.614624i	$0.210692\pi$
$678$	2.08295e13	3.78568
$679$	1.13870e13	2.05587
$680$	5.32847e11	0.0955679
$681$	−1.53133e13	−2.72839
$682$	−1.97508e12	−0.349587
$683$	−2.61885e12	−0.460487	−0.230244	−	0.973133i	$-0.573952\pi$
$683$	−2.61885e12	−0.460487	−0.230244	+	0.973133i	$0.573952\pi$
$684$	−3.46926e13	−6.06017
$685$	−7.09360e12	−1.23100
$686$	−3.05592e13	−5.26845
$687$	1.47176e13	2.52076
$688$	1.28641e12	0.218894
$689$	−6.69458e11	−0.113171
$690$	1.90110e13	3.19289
$691$	6.28716e11	0.104907	0.0524534	−	0.998623i	$-0.483296\pi$
$691$	6.28716e11	0.104907	0.0524534	+	0.998623i	$0.483296\pi$
$692$	1.80770e12	0.299675
$693$	2.72122e12	0.448192
$694$	1.06223e13	1.73821
$695$	6.04372e12	0.982591
$696$	−1.43295e13	−2.31467
$697$	2.78240e11	0.0446551
$698$	−1.11276e13	−1.77440
$699$	−2.18499e12	−0.346180
$700$	6.36999e12	1.00276
$701$	7.04665e12	1.10218	0.551089	−	0.834447i	$-0.314212\pi$
$701$	7.04665e12	1.10218	0.551089	+	0.834447i	$0.314212\pi$
$702$	−2.31710e13	−3.60104
$703$	−8.74660e12	−1.35064
$704$	3.88074e11	0.0595439
$705$	9.97485e12	1.52074
$706$	5.02199e12	0.760772
$707$	−3.52459e12	−0.530545
$708$	8.35687e12	1.24995
$709$	3.23092e12	0.480196	0.240098	−	0.970749i	$-0.422820\pi$
$709$	3.23092e12	0.480196	0.240098	+	0.970749i	$0.422820\pi$
$710$	−1.46105e13	−2.15775
$711$	7.97130e12	1.16981
$712$	−1.21429e12	−0.177077
$713$	1.38183e13	2.00241
$714$	−2.20341e12	−0.317287
$715$	8.32212e11	0.119085
$716$	−1.47528e13	−2.09781
$717$	4.18047e12	0.590730
$718$	−6.54785e12	−0.919472
$719$	1.51642e12	0.211611	0.105806	−	0.994387i	$-0.466258\pi$
$719$	1.51642e12	0.211611	0.105806	+	0.994387i	$0.466258\pi$
$720$	1.80213e13	2.49913
$721$	9.36954e12	1.29125
$722$	1.28280e13	1.75688
$723$	9.70197e12	1.32050
$724$	−6.82868e12	−0.923663
$725$	1.22071e12	0.164093
$726$	−2.26787e13	−3.02972
$727$	−7.56557e12	−1.00447	−0.502235	−	0.864731i	$-0.667489\pi$
$727$	−7.56557e12	−1.00447	−0.502235	+	0.864731i	$0.667489\pi$
$728$	3.36090e13	4.43470
$729$	−7.44494e12	−0.976309
$730$	8.36052e12	1.08963
$731$	6.43158e10	0.00833085
$732$	−1.37527e13	−1.77047
$733$	7.72260e12	0.988088	0.494044	−	0.869437i	$-0.335518\pi$
$733$	7.72260e12	0.988088	0.494044	+	0.869437i	$0.335518\pi$
$734$	−4.91122e12	−0.624536
$735$	3.06188e13	3.86985
$736$	5.01397e12	0.629842
$737$	1.09061e12	0.136165
$738$	2.34315e13	2.90769
$739$	1.02598e13	1.26543	0.632716	−	0.774384i	$-0.281940\pi$
$739$	1.02598e13	1.26543	0.632716	+	0.774384i	$0.281940\pi$
$740$	1.44785e13	1.77493
$741$	2.33594e13	2.84630
$742$	−2.69099e12	−0.325908
$743$	−7.09011e12	−0.853500	−0.426750	−	0.904370i	$-0.640342\pi$
$743$	−7.09011e12	−0.853500	−0.426750	+	0.904370i	$0.640342\pi$
$744$	4.88609e13	5.84632
$745$	2.26744e12	0.269670
$746$	−2.78040e13	−3.28687
$747$	−2.05499e13	−2.41472
$748$	−1.18126e11	−0.0137971
$749$	−7.00205e12	−0.812938
$750$	−2.88140e13	−3.32527
$751$	−2.03257e12	−0.233166	−0.116583	−	0.993181i	$-0.537194\pi$
$751$	−2.03257e12	−0.233166	−0.116583	+	0.993181i	$0.537194\pi$
$752$	1.27286e13	1.45144
$753$	−1.65860e13	−1.88002
$754$	1.20967e13	1.36300
$755$	−5.56437e12	−0.623239
$756$	−6.34651e13	−7.06622
$757$	1.25312e13	1.38695	0.693477	−	0.720478i	$-0.256078\pi$
$757$	1.25312e13	1.38695	0.693477	+	0.720478i	$0.256078\pi$
$758$	−6.91150e12	−0.760433
$759$	−2.24394e12	−0.245428
$760$	−2.27069e13	−2.46886
$761$	1.63323e13	1.76529	0.882646	−	0.470039i	$-0.155760\pi$
$761$	1.63323e13	1.76529	0.882646	+	0.470039i	$0.155760\pi$
$762$	3.17043e13	3.40660
$763$	−2.58741e13	−2.76378
$764$	5.00189e12	0.531146
$765$	9.00994e11	0.0951143
$766$	−8.83571e12	−0.927282
$767$	−3.75613e12	−0.391888
$768$	−3.36008e13	−3.48517
$769$	8.23142e12	0.848802	0.424401	−	0.905474i	$-0.360485\pi$
$769$	8.23142e12	0.848802	0.424401	+	0.905474i	$0.360485\pi$
$770$	3.34521e12	0.342937
$771$	5.67114e12	0.577997
$772$	2.71033e13	2.74627
$773$	1.97064e12	0.198518	0.0992589	−	0.995062i	$-0.468353\pi$
$773$	1.97064e12	0.198518	0.0992589	+	0.995062i	$0.468353\pi$
$774$	5.41626e12	0.542457
$775$	−4.16238e12	−0.414461
$776$	−2.21634e13	−2.19411
$777$	−3.18771e13	−3.13751
$778$	7.29256e12	0.713628
$779$	−1.18570e13	−1.15360
$780$	−3.86677e13	−3.74044
$781$	1.72453e12	0.165860
$782$	1.21287e12	0.115980
$783$	−1.21621e13	−1.15633
$784$	3.90715e13	3.69350
$785$	7.40384e12	0.695895
$786$	−2.91444e13	−2.72366
$787$	1.35249e13	1.25675	0.628374	−	0.777911i	$-0.283721\pi$
$787$	1.35249e13	1.25675	0.628374	+	0.777911i	$0.283721\pi$
$788$	2.08530e12	0.192664
$789$	−2.06533e13	−1.89733
$790$	9.79915e12	0.895089
$791$	−2.56428e13	−2.32901
$792$	−5.29651e12	−0.478329
$793$	6.18139e12	0.555081
$794$	3.56359e12	0.318197
$795$	1.64842e12	0.146357
$796$	1.05504e13	0.931451
$797$	1.02564e13	0.900397	0.450199	−	0.892928i	$-0.351353\pi$
$797$	1.02564e13	0.900397	0.450199	+	0.892928i	$0.351353\pi$
$798$	9.38968e13	8.19667
$799$	6.36379e11	0.0552402
$800$	−1.51032e12	−0.130366
$801$	−2.05325e12	−0.176237
$802$	9.31786e12	0.795301
$803$	−9.86823e11	−0.0837566
$804$	−5.06739e13	−4.27693
$805$	−2.34041e13	−1.96431
$806$	−4.12474e13	−3.44262
$807$	3.37102e13	2.79789
$808$	6.86018e12	0.566219
$809$	1.62448e13	1.33336	0.666679	−	0.745345i	$-0.267715\pi$
$809$	1.62448e13	1.33336	0.666679	+	0.745345i	$0.267715\pi$
$810$	1.92641e13	1.57241
$811$	−1.59962e13	−1.29845	−0.649223	−	0.760598i	$-0.724906\pi$
$811$	−1.59962e13	−1.29845	−0.649223	+	0.760598i	$0.724906\pi$
$812$	3.31327e13	2.67457
$813$	4.73043e12	0.379746
$814$	−2.50801e12	−0.200226
$815$	2.52107e12	0.200159
$816$	1.72235e12	0.135993
$817$	−2.74078e12	−0.215216
$818$	2.25009e13	1.75715
$819$	5.68296e13	4.41364
$820$	1.96273e13	1.51600
$821$	−1.81884e13	−1.39717	−0.698587	−	0.715525i	$-0.746188\pi$
$821$	−1.81884e13	−1.39717	−0.698587	+	0.715525i	$0.746188\pi$
$822$	−5.70933e13	−4.36176
$823$	6.06641e12	0.460927	0.230463	−	0.973081i	$-0.425976\pi$
$823$	6.06641e12	0.460927	0.230463	+	0.973081i	$0.425976\pi$
$824$	−1.82366e13	−1.37807
$825$	6.75925e11	0.0507990
$826$	−1.50983e13	−1.12855
$827$	−1.56740e13	−1.16522	−0.582608	−	0.812753i	$-0.697968\pi$
$827$	−1.56740e13	−1.16522	−0.582608	+	0.812753i	$0.697968\pi$
$828$	6.95982e13	5.14590
$829$	1.82187e13	1.33974	0.669872	−	0.742477i	$-0.266349\pi$
$829$	1.82187e13	1.33974	0.669872	+	0.742477i	$0.266349\pi$
$830$	−2.52621e13	−1.84764
$831$	1.89679e13	1.37979
$832$	8.10449e12	0.586368
$833$	1.95343e12	0.140571
$834$	4.86433e13	3.48158
$835$	1.71685e12	0.122221
$836$	5.03387e12	0.356430
$837$	4.14704e13	2.92061
$838$	7.01598e12	0.491463
$839$	−2.01462e13	−1.40367	−0.701835	−	0.712340i	$-0.747635\pi$
$839$	−2.01462e13	−1.40367	−0.701835	+	0.712340i	$0.747635\pi$
$840$	−8.27558e13	−5.73511
$841$	−8.15779e12	−0.562329
$842$	−4.21631e13	−2.89087
$843$	−3.23189e13	−2.20411
$844$	−2.49797e12	−0.169452
$845$	4.52832e12	0.305550
$846$	5.35918e13	3.59692
$847$	2.79193e13	1.86393
$848$	2.10349e12	0.139688
$849$	−1.83935e13	−1.21501
$850$	−3.65344e11	−0.0240058
$851$	1.75469e13	1.14688
$852$	−8.01280e13	−5.20962
$853$	−1.98693e13	−1.28503	−0.642515	−	0.766273i	$-0.722109\pi$
$853$	−1.98693e13	−1.28503	−0.642515	+	0.766273i	$0.722109\pi$
$854$	2.48470e13	1.59851
$855$	−3.83953e13	−2.45714
$856$	1.36286e13	0.867600
$857$	−1.99512e13	−1.26344	−0.631722	−	0.775195i	$-0.717652\pi$
$857$	−1.99512e13	−1.26344	−0.631722	+	0.775195i	$0.717652\pi$
$858$	6.69812e12	0.421949
$859$	6.03196e12	0.377998	0.188999	−	0.981977i	$-0.439476\pi$
$859$	6.03196e12	0.377998	0.188999	+	0.981977i	$0.439476\pi$
$860$	4.53690e12	0.282824
$861$	−4.32131e13	−2.67979
$862$	−3.32319e13	−2.05009
$863$	3.90405e12	0.239589	0.119794	−	0.992799i	$-0.461776\pi$
$863$	3.90405e12	0.239589	0.119794	+	0.992799i	$0.461776\pi$
$864$	1.50475e13	0.918657
$865$	2.00064e12	0.121505
$866$	−2.45391e13	−1.48261
$867$	−2.87683e13	−1.72913
$868$	−1.12976e14	−6.75534
$869$	−1.15663e12	−0.0688027
$870$	−2.97859e13	−1.76268
$871$	2.27762e13	1.34091
$872$	5.03606e13	2.94962
$873$	−3.74763e13	−2.18370
$874$	−5.16857e13	−2.99619
$875$	3.54723e13	2.04575
$876$	4.58515e13	2.63078
$877$	1.67814e13	0.957921	0.478961	−	0.877836i	$-0.341014\pi$
$877$	1.67814e13	0.957921	0.478961	+	0.877836i	$0.341014\pi$
$878$	−1.50322e13	−0.853682
$879$	3.56064e13	2.01177
$880$	−2.61487e12	−0.146987
$881$	1.12851e13	0.631121	0.315561	−	0.948905i	$-0.397807\pi$
$881$	1.12851e13	0.631121	0.315561	+	0.948905i	$0.397807\pi$
$882$	1.64505e14	9.15315
$883$	−5.24886e12	−0.290564	−0.145282	−	0.989390i	$-0.546409\pi$
$883$	−5.24886e12	−0.290564	−0.145282	+	0.989390i	$0.546409\pi$
$884$	−2.46693e12	−0.135870
$885$	9.24877e12	0.506803
$886$	5.52961e13	3.01469
$887$	2.48373e13	1.34725	0.673624	−	0.739074i	$-0.264737\pi$
$887$	2.48373e13	1.34725	0.673624	+	0.739074i	$0.264737\pi$
$888$	6.20448e13	3.34848
$889$	−3.90306e13	−2.09579
$890$	−2.52407e12	−0.134849
$891$	−2.27381e12	−0.120866
$892$	−3.12000e13	−1.65011
$893$	−2.71189e13	−1.42705
$894$	1.82497e13	0.955512
$895$	−1.63273e13	−0.850572
$896$	5.17445e13	2.68212
$897$	−4.68622e13	−2.41689
$898$	−6.81609e13	−3.49778
$899$	−2.16501e13	−1.10545
$900$	−2.09645e13	−1.06511
$901$	1.05166e11	0.00531636
$902$	−3.39990e12	−0.171016
$903$	−9.98882e12	−0.499941
$904$	4.99104e13	2.48561
$905$	−7.55749e12	−0.374506
$906$	−4.47853e13	−2.20830
$907$	−2.98028e13	−1.46226	−0.731130	−	0.682239i	$-0.761007\pi$
$907$	−2.98028e13	−1.46226	−0.731130	+	0.682239i	$0.761007\pi$
$908$	−6.89158e13	−3.36459
$909$	1.15999e13	0.563531
$910$	6.98608e13	3.37713
$911$	−2.45032e13	−1.17866	−0.589331	−	0.807891i	$-0.700609\pi$
$911$	−2.45032e13	−1.17866	−0.589331	+	0.807891i	$0.700609\pi$
$912$	−7.33970e13	−3.51319
$913$	2.98177e12	0.142022
$914$	−9.46528e12	−0.448617
$915$	−1.52205e13	−0.717851
$916$	6.62351e13	3.10856
$917$	3.58791e13	1.67563
$918$	3.63997e12	0.169163
$919$	9.32464e12	0.431233	0.215617	−	0.976478i	$-0.430824\pi$
$919$	9.32464e12	0.431233	0.215617	+	0.976478i	$0.430824\pi$
$920$	4.55532e13	2.09640
$921$	−3.29738e12	−0.151008
$922$	−3.80444e13	−1.73381
$923$	3.60148e13	1.63333
$924$	1.83461e13	0.827978
$925$	−5.28550e12	−0.237382
$926$	−3.92482e13	−1.75417
$927$	−3.08364e13	−1.37153
$928$	−7.85573e12	−0.347713
$929$	2.59394e13	1.14259	0.571293	−	0.820747i	$-0.306442\pi$
$929$	2.59394e13	1.14259	0.571293	+	0.820747i	$0.306442\pi$
$930$	1.01564e14	4.45212
$931$	−8.32440e13	−3.63144
$932$	−9.83333e12	−0.426903
$933$	6.13794e13	2.65189
$934$	−1.16832e13	−0.502344
$935$	−1.30734e11	−0.00559416
$936$	−1.10612e14	−4.71042
$937$	9.62775e12	0.408034	0.204017	−	0.978967i	$-0.434600\pi$
$937$	9.62775e12	0.408034	0.204017	+	0.978967i	$0.434600\pi$
$938$	9.15525e13	3.86151
$939$	−1.16476e13	−0.488926
$940$	4.48908e13	1.87535
$941$	−1.88478e12	−0.0783623	−0.0391811	−	0.999232i	$-0.512475\pi$
$941$	−1.88478e12	−0.0783623	−0.0391811	+	0.999232i	$0.512475\pi$
$942$	5.95904e13	2.46574
$943$	2.37868e13	0.979564
$944$	1.18020e13	0.483708
$945$	−7.02386e13	−2.86505
$946$	−7.85895e11	−0.0319047
$947$	2.73247e12	0.110403	0.0552015	−	0.998475i	$-0.482420\pi$
$947$	2.73247e12	0.110403	0.0552015	+	0.998475i	$0.482420\pi$
$948$	5.37413e13	2.16108
$949$	−2.06087e13	−0.824807
$950$	1.55689e13	0.620157
$951$	8.27104e13	3.27905
$952$	−5.27968e12	−0.208325
$953$	−4.31364e13	−1.69405	−0.847025	−	0.531554i	$-0.821608\pi$
$953$	−4.31364e13	−1.69405	−0.847025	+	0.531554i	$0.821608\pi$
$954$	8.85642e12	0.346171
$955$	5.53573e12	0.215357
$956$	1.88138e13	0.728477
$957$	3.51573e12	0.135492
$958$	6.19797e13	2.37741
$959$	7.02866e13	2.68342
$960$	−1.99558e13	−0.758313
$961$	4.73830e13	1.79212
$962$	−5.23770e13	−1.97176
$963$	2.30447e13	0.863482
$964$	4.36627e13	1.62841
$965$	2.99959e13	1.11350
$966$	−1.88370e14	−6.96008
$967$	−3.43896e13	−1.26476	−0.632380	−	0.774658i	$-0.717922\pi$
$967$	−3.43896e13	−1.26476	−0.632380	+	0.774658i	$0.717922\pi$
$968$	−5.43413e13	−1.98926
$969$	−3.66957e12	−0.133708
$970$	−4.60697e13	−1.67087
$971$	−2.85177e13	−1.02950	−0.514752	−	0.857339i	$-0.672116\pi$
$971$	−2.85177e13	−1.02950	−0.514752	+	0.857339i	$0.672116\pi$
$972$	1.61979e12	0.0582049
$973$	−5.98839e13	−2.14191
$974$	1.47065e13	0.523593
$975$	1.41159e13	0.500252
$976$	−1.94224e13	−0.685138
$977$	−1.33713e13	−0.469513	−0.234756	−	0.972054i	$-0.575429\pi$
$977$	−1.33713e13	−0.469513	−0.234756	+	0.972054i	$0.575429\pi$
$978$	2.02910e13	0.709217
$979$	2.97925e11	0.0103654
$980$	1.37797e14	4.77223
$981$	8.51551e13	2.93562
$982$	−6.63113e13	−2.27555
$983$	5.05444e13	1.72656	0.863281	−	0.504724i	$-0.168406\pi$
$983$	5.05444e13	1.72656	0.863281	+	0.504724i	$0.168406\pi$
$984$	8.41088e13	2.85998
$985$	2.30786e12	0.0781173
$986$	−1.90029e12	−0.0640285
$987$	−9.88353e13	−3.31501
$988$	1.05127e14	3.51000
$989$	5.49837e12	0.182747
$990$	−1.10095e13	−0.364259
$991$	5.77318e13	1.90144	0.950722	−	0.310045i	$-0.100344\pi$
$991$	5.77318e13	1.90144	0.950722	+	0.310045i	$0.100344\pi$
$992$	2.67865e13	0.878241
$993$	3.88997e13	1.26962
$994$	1.44767e14	4.70361
$995$	1.16764e13	0.377664
$996$	−1.38544e14	−4.46089
$997$	1.01914e13	0.326667	0.163333	−	0.986571i	$-0.447775\pi$
$997$	1.01914e13	0.326667	0.163333	+	0.986571i	$0.447775\pi$
$998$	−1.91244e13	−0.610240
$999$	5.26602e13	1.67278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.b.1.16	✓	17
3.2	odd	2		387.10.a.e.1.2		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.16	✓	17	1.1	even	1	trivial
387.10.a.e.1.2		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)

\(f(q)\)	\(=\)	\(q+40.0877 q^{2} +243.316 q^{3} +1095.02 q^{4} +1211.89 q^{5} +9753.98 q^{6} -12008.0 q^{7} +23372.0 q^{8} +39519.8 q^{9} +O(q^{10})\)	\(q+40.0877 q^{2} +243.316 q^{3} +1095.02 q^{4} +1211.89 q^{5} +9753.98 q^{6} -12008.0 q^{7} +23372.0 q^{8} +39519.8 q^{9} +48581.8 q^{10} -5734.29 q^{11} +266437. q^{12} -119754. q^{13} -481371. q^{14} +294873. q^{15} +376277. q^{16} +18812.4 q^{17} +1.58426e6 q^{18} -801678. q^{19} +1.32705e6 q^{20} -2.92173e6 q^{21} -229874. q^{22} +1.60827e6 q^{23} +5.68678e6 q^{24} -484448. q^{25} -4.80067e6 q^{26} +4.82663e6 q^{27} -1.31490e7 q^{28} -2.51979e6 q^{29} +1.18208e7 q^{30} +8.59201e6 q^{31} +3.11761e6 q^{32} -1.39525e6 q^{33} +754145. q^{34} -1.45523e7 q^{35} +4.32751e7 q^{36} +1.09104e7 q^{37} -3.21374e7 q^{38} -2.91382e7 q^{39} +2.83242e7 q^{40} +1.47902e7 q^{41} -1.17125e8 q^{42} +3.41880e6 q^{43} -6.27917e6 q^{44} +4.78937e7 q^{45} +6.44720e7 q^{46} +3.38277e7 q^{47} +9.15542e7 q^{48} +1.03837e8 q^{49} -1.94204e7 q^{50} +4.57736e6 q^{51} -1.31133e8 q^{52} +5.59026e6 q^{53} +1.93488e8 q^{54} -6.94933e6 q^{55} -2.80649e8 q^{56} -1.95061e8 q^{57} -1.01013e8 q^{58} +3.13653e7 q^{59} +3.22892e8 q^{60} -5.16173e7 q^{61} +3.44434e8 q^{62} -4.74552e8 q^{63} -6.76760e7 q^{64} -1.45129e8 q^{65} -5.59322e7 q^{66} -1.90191e8 q^{67} +2.06000e7 q^{68} +3.91319e8 q^{69} -5.83368e8 q^{70} -3.00740e8 q^{71} +9.23656e8 q^{72} +1.72091e8 q^{73} +4.37371e8 q^{74} -1.17874e8 q^{75} -8.77854e8 q^{76} +6.88571e7 q^{77} -1.16808e9 q^{78} +2.01704e8 q^{79} +4.56006e8 q^{80} +3.96528e8 q^{81} +5.92906e8 q^{82} -5.19990e8 q^{83} -3.19936e9 q^{84} +2.27985e7 q^{85} +1.37052e8 q^{86} -6.13107e8 q^{87} -1.34022e8 q^{88} -5.19550e7 q^{89} +1.91995e9 q^{90} +1.43800e9 q^{91} +1.76109e9 q^{92} +2.09058e9 q^{93} +1.35607e9 q^{94} -9.71545e8 q^{95} +7.58565e8 q^{96} -9.48291e8 q^{97} +4.16259e9 q^{98} -2.26618e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 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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