LMFDB - Embedded newform 43.10.a.b.1.17

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			1.17
Root			$-37.7321$ 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)

$f(q)$	$=$	$q+40.7321 q^{2} +136.923 q^{3} +1147.10 q^{4} -1672.50 q^{5} +5577.18 q^{6} +6274.02 q^{7} +25869.0 q^{8} -934.956 q^{9} +O(q^{10})$	\(q+40.7321 q^{2} +136.923 q^{3} +1147.10 q^{4} -1672.50 q^{5} +5577.18 q^{6} +6274.02 q^{7} +25869.0 q^{8} -934.956 q^{9} -68124.5 q^{10} +59397.1 q^{11} +157065. q^{12} +129243. q^{13} +255554. q^{14} -229005. q^{15} +466380. q^{16} +344623. q^{17} -38082.7 q^{18} -805331. q^{19} -1.91853e6 q^{20} +859061. q^{21} +2.41937e6 q^{22} -1.28468e6 q^{23} +3.54207e6 q^{24} +844142. q^{25} +5.26432e6 q^{26} -2.82308e6 q^{27} +7.19693e6 q^{28} -6.23666e6 q^{29} -9.32784e6 q^{30} -4.81901e6 q^{31} +5.75173e6 q^{32} +8.13286e6 q^{33} +1.40372e7 q^{34} -1.04933e7 q^{35} -1.07249e6 q^{36} +6.69852e6 q^{37} -3.28028e7 q^{38} +1.76964e7 q^{39} -4.32659e7 q^{40} -4.77909e6 q^{41} +3.49913e7 q^{42} +3.41880e6 q^{43} +6.81344e7 q^{44} +1.56372e6 q^{45} -5.23277e7 q^{46} +3.61348e7 q^{47} +6.38584e7 q^{48} -990273. q^{49} +3.43836e7 q^{50} +4.71869e7 q^{51} +1.48254e8 q^{52} -8.20337e6 q^{53} -1.14990e8 q^{54} -9.93418e7 q^{55} +1.62302e8 q^{56} -1.10269e8 q^{57} -2.54032e8 q^{58} +1.25895e8 q^{59} -2.62692e8 q^{60} -2.69653e7 q^{61} -1.96288e8 q^{62} -5.86593e6 q^{63} -4.50700e6 q^{64} -2.16159e8 q^{65} +3.31268e8 q^{66} +1.58552e8 q^{67} +3.95317e8 q^{68} -1.75903e8 q^{69} -4.27414e8 q^{70} +1.61995e8 q^{71} -2.41863e7 q^{72} -3.96021e8 q^{73} +2.72844e8 q^{74} +1.15583e8 q^{75} -9.23796e8 q^{76} +3.72659e8 q^{77} +7.20810e8 q^{78} -1.81237e8 q^{79} -7.80023e8 q^{80} -3.68144e8 q^{81} -1.94662e8 q^{82} -7.14450e8 q^{83} +9.85429e8 q^{84} -5.76383e8 q^{85} +1.39255e8 q^{86} -8.53946e8 q^{87} +1.53654e9 q^{88} +4.22139e8 q^{89} +6.36934e7 q^{90} +8.10872e8 q^{91} -1.47366e9 q^{92} -6.59836e8 q^{93} +1.47184e9 q^{94} +1.34692e9 q^{95} +7.87547e8 q^{96} +5.61578e8 q^{97} -4.03359e7 q^{98} -5.55337e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	40.7321	1.80012	0.900060	−	0.435766i	$-0.143523\pi$
$2$	40.7321	1.80012	0.900060	+	0.435766i	$0.143523\pi$
$3$	136.923	0.975961	0.487980	−	0.872855i	$-0.337734\pi$
$3$	136.923	0.975961	0.487980	+	0.872855i	$0.337734\pi$
$4$	1147.10	2.24043
$5$	−1672.50	−1.19675	−0.598373	−	0.801218i	$-0.704186\pi$
$5$	−1672.50	−1.19675	−0.598373	+	0.801218i	$0.704186\pi$
$6$	5577.18	1.75685
$7$	6274.02	0.987654	0.493827	−	0.869560i	$-0.335598\pi$
$7$	6274.02	0.987654	0.493827	+	0.869560i	$0.335598\pi$
$8$	25869.0	2.23292
$9$	−934.956	−0.0475007
$10$	−68124.5	−2.15429
$11$	59397.1	1.22320	0.611601	−	0.791166i	$-0.290526\pi$
$11$	59397.1	1.22320	0.611601	+	0.791166i	$0.290526\pi$
$12$	157065.	2.18657
$13$	129243.	1.25505	0.627525	−	0.778596i	$-0.284068\pi$
$13$	129243.	1.25505	0.627525	+	0.778596i	$0.284068\pi$
$14$	255554.	1.77790
$15$	−229005.	−1.16798
$16$	466380.	1.77910
$17$	344623.	1.00075	0.500373	−	0.865810i	$-0.333196\pi$
$17$	344623.	1.00075	0.500373	+	0.865810i	$0.333196\pi$
$18$	−38082.7	−0.0855069
$19$	−805331.	−1.41770	−0.708848	−	0.705361i	$-0.750785\pi$
$19$	−805331.	−1.41770	−0.708848	+	0.705361i	$0.750785\pi$
$20$	−1.91853e6	−2.68123
$21$	859061.	0.963911
$22$	2.41937e6	2.20191
$23$	−1.28468e6	−0.957237	−0.478619	−	0.878023i	$-0.658862\pi$
$23$	−1.28468e6	−0.957237	−0.478619	+	0.878023i	$0.658862\pi$
$24$	3.54207e6	2.17925
$25$	844142.	0.432200
$26$	5.26432e6	2.25924
$27$	−2.82308e6	−1.02232
$28$	7.19693e6	2.21277
$29$	−6.23666e6	−1.63742	−0.818712	−	0.574204i	$-0.805312\pi$
$29$	−6.23666e6	−1.63742	−0.818712	+	0.574204i	$0.805312\pi$
$30$	−9.32784e6	−2.10250
$31$	−4.81901e6	−0.937196	−0.468598	−	0.883412i	$-0.655241\pi$
$31$	−4.81901e6	−0.937196	−0.468598	+	0.883412i	$0.655241\pi$
$32$	5.75173e6	0.969669
$33$	8.13286e6	1.19380
$34$	1.40372e7	1.80146
$35$	−1.04933e7	−1.18197
$36$	−1.07249e6	−0.106422
$37$	6.69852e6	0.587585	0.293793	−	0.955869i	$-0.405082\pi$
$37$	6.69852e6	0.587585	0.293793	+	0.955869i	$0.405082\pi$
$38$	−3.28028e7	−2.55202
$39$	1.76964e7	1.22488
$40$	−4.32659e7	−2.67224
$41$	−4.77909e6	−0.264130	−0.132065	−	0.991241i	$-0.542161\pi$
$41$	−4.77909e6	−0.264130	−0.132065	+	0.991241i	$0.542161\pi$
$42$	3.49913e7	1.73516
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	6.81344e7	2.74050
$45$	1.56372e6	0.0568462
$46$	−5.23277e7	−1.72314
$47$	3.61348e7	1.08015	0.540076	−	0.841616i	$-0.318395\pi$
$47$	3.61348e7	1.08015	0.540076	+	0.841616i	$0.318395\pi$
$48$	6.38584e7	1.73633
$49$	−990273.	−0.0245399
$50$	3.43836e7	0.778013
$51$	4.71869e7	0.976688
$52$	1.48254e8	2.81185
$53$	−8.20337e6	−0.142807	−0.0714037	−	0.997447i	$-0.522748\pi$
$53$	−8.20337e6	−0.142807	−0.0714037	+	0.997447i	$0.522748\pi$
$54$	−1.14990e8	−1.84030
$55$	−9.93418e7	−1.46386
$56$	1.62302e8	2.20536
$57$	−1.10269e8	−1.38362
$58$	−2.54032e8	−2.94756
$59$	1.25895e8	1.35262	0.676311	−	0.736617i	$-0.263578\pi$
$59$	1.25895e8	1.35262	0.676311	+	0.736617i	$0.263578\pi$
$60$	−2.62692e8	−2.61677
$61$	−2.69653e7	−0.249357	−0.124679	−	0.992197i	$-0.539790\pi$
$61$	−2.69653e7	−0.249357	−0.124679	+	0.992197i	$0.539790\pi$
$62$	−1.96288e8	−1.68706
$63$	−5.86593e6	−0.0469142
$64$	−4.50700e6	−0.0335798
$65$	−2.16159e8	−1.50198
$66$	3.31268e8	2.14898
$67$	1.58552e8	0.961247	0.480623	−	0.876927i	$-0.340410\pi$
$67$	1.58552e8	0.961247	0.480623	+	0.876927i	$0.340410\pi$
$68$	3.95317e8	2.24210
$69$	−1.75903e8	−0.934226
$70$	−4.27414e8	−2.12769
$71$	1.61995e8	0.756554	0.378277	−	0.925693i	$-0.376517\pi$
$71$	1.61995e8	0.756554	0.378277	+	0.925693i	$0.376517\pi$
$72$	−2.41863e7	−0.106065
$73$	−3.96021e8	−1.63217	−0.816085	−	0.577932i	$-0.803860\pi$
$73$	−3.96021e8	−1.63217	−0.816085	+	0.577932i	$0.803860\pi$
$74$	2.72844e8	1.05772
$75$	1.15583e8	0.421811
$76$	−9.23796e8	−3.17625
$77$	3.72659e8	1.20810
$78$	7.20810e8	2.20493
$79$	−1.81237e8	−0.523510	−0.261755	−	0.965134i	$-0.584301\pi$
$79$	−1.81237e8	−0.523510	−0.261755	+	0.965134i	$0.584301\pi$
$80$	−7.80023e8	−2.12913
$81$	−3.68144e8	−0.950243
$82$	−1.94662e8	−0.475465
$83$	−7.14450e8	−1.65242	−0.826210	−	0.563363i	$-0.809507\pi$
$83$	−7.14450e8	−1.65242	−0.826210	+	0.563363i	$0.809507\pi$
$84$	9.85429e8	2.15958
$85$	−5.76383e8	−1.19764
$86$	1.39255e8	0.274516
$87$	−8.53946e8	−1.59806
$88$	1.53654e9	2.73132
$89$	4.22139e8	0.713182	0.356591	−	0.934261i	$-0.383939\pi$
$89$	4.22139e8	0.713182	0.356591	+	0.934261i	$0.383939\pi$
$90$	6.36934e7	0.102330
$91$	8.10872e8	1.23956
$92$	−1.47366e9	−2.14462
$93$	−6.59836e8	−0.914666
$94$	1.47184e9	1.94440
$95$	1.34692e9	1.69662
$96$	7.87547e8	0.946359
$97$	5.61578e8	0.644077	0.322038	−	0.946727i	$-0.395632\pi$
$97$	5.61578e8	0.644077	0.322038	+	0.946727i	$0.395632\pi$
$98$	−4.03359e7	−0.0441747
$99$	−5.55337e7	−0.0581029
$100$	9.68315e8	0.968315
$101$	1.75619e9	1.67929	0.839645	−	0.543136i	$-0.182763\pi$
$101$	1.75619e9	1.67929	0.839645	+	0.543136i	$0.182763\pi$
$102$	1.92202e9	1.75816
$103$	2.00937e9	1.75911	0.879553	−	0.475801i	$-0.157842\pi$
$103$	2.00937e9	1.75911	0.879553	+	0.475801i	$0.157842\pi$
$104$	3.34338e9	2.80243
$105$	−1.43678e9	−1.15356
$106$	−3.34140e8	−0.257070
$107$	−9.31131e8	−0.686726	−0.343363	−	0.939203i	$-0.611566\pi$
$107$	−9.31131e8	−0.686726	−0.343363	+	0.939203i	$0.611566\pi$
$108$	−3.23836e9	−2.29044
$109$	−1.60701e9	−1.09044	−0.545218	−	0.838294i	$-0.683553\pi$
$109$	−1.60701e9	−1.09044	−0.545218	+	0.838294i	$0.683553\pi$
$110$	−4.04640e9	−2.63513
$111$	9.17184e8	0.573460
$112$	2.92608e9	1.75714
$113$	1.77403e9	1.02355	0.511775	−	0.859120i	$-0.328988\pi$
$113$	1.77403e9	1.02355	0.511775	+	0.859120i	$0.328988\pi$
$114$	−4.49147e9	−2.49067
$115$	2.14863e9	1.14557
$116$	−7.15408e9	−3.66854
$117$	−1.20836e8	−0.0596157
$118$	5.12798e9	2.43488
$119$	2.16217e9	0.988390
$120$	−5.92412e9	−2.60800
$121$	1.17007e9	0.496223
$122$	−1.09835e9	−0.448873
$123$	−6.54369e8	−0.257780
$124$	−5.52789e9	−2.09972
$125$	1.85478e9	0.679512
$126$	−2.38931e8	−0.0844512
$127$	−8.96218e8	−0.305701	−0.152851	−	0.988249i	$-0.548845\pi$
$127$	−8.96218e8	−0.305701	−0.152851	+	0.988249i	$0.548845\pi$
$128$	−3.12847e9	−1.03012
$129$	4.68114e8	0.148833
$130$	−8.80460e9	−2.70374
$131$	−5.56037e8	−0.164961	−0.0824807	−	0.996593i	$-0.526284\pi$
$131$	−5.56037e8	−0.164961	−0.0824807	+	0.996593i	$0.526284\pi$
$132$	9.32921e9	2.67462
$133$	−5.05266e9	−1.40019
$134$	6.45814e9	1.73036
$135$	4.72161e9	1.22346
$136$	8.91503e9	2.23459
$137$	−1.25468e9	−0.304292	−0.152146	−	0.988358i	$-0.548618\pi$
$137$	−1.25468e9	−0.304292	−0.152146	+	0.988358i	$0.548618\pi$
$138$	−7.16489e9	−1.68172
$139$	2.04724e9	0.465160	0.232580	−	0.972577i	$-0.425283\pi$
$139$	2.04724e9	0.465160	0.232580	+	0.972577i	$0.425283\pi$
$140$	−1.20369e10	−2.64812
$141$	4.94770e9	1.05419
$142$	6.59840e9	1.36189
$143$	7.67665e9	1.53518
$144$	−4.36045e8	−0.0845085
$145$	1.04308e10	1.95958
$146$	−1.61308e10	−2.93810
$147$	−1.35592e8	−0.0239500
$148$	7.68387e9	1.31644
$149$	4.04734e9	0.672715	0.336358	−	0.941734i	$-0.390805\pi$
$149$	4.04734e9	0.672715	0.336358	+	0.941734i	$0.390805\pi$
$150$	4.70793e9	0.759310
$151$	−5.03500e9	−0.788139	−0.394070	−	0.919081i	$-0.628933\pi$
$151$	−5.03500e9	−0.788139	−0.394070	+	0.919081i	$0.628933\pi$
$152$	−2.08331e10	−3.16561
$153$	−3.22207e8	−0.0475361
$154$	1.51792e10	2.17472
$155$	8.05981e9	1.12159
$156$	2.02995e10	2.74426
$157$	−1.00123e10	−1.31518	−0.657592	−	0.753374i	$-0.728425\pi$
$157$	−1.00123e10	−1.31518	−0.657592	+	0.753374i	$0.728425\pi$
$158$	−7.38215e9	−0.942380
$159$	−1.12323e9	−0.139374
$160$	−9.61979e9	−1.16045
$161$	−8.06011e9	−0.945419
$162$	−1.49952e10	−1.71055
$163$	1.47083e10	1.63199	0.815995	−	0.578059i	$-0.196190\pi$
$163$	1.47083e10	1.63199	0.815995	+	0.578059i	$0.196190\pi$
$164$	−5.48209e9	−0.591765
$165$	−1.36022e10	−1.42867
$166$	−2.91010e10	−2.97455
$167$	9.40172e9	0.935370	0.467685	−	0.883895i	$-0.345088\pi$
$167$	9.40172e9	0.935370	0.467685	+	0.883895i	$0.345088\pi$
$168$	2.22230e10	2.15234
$169$	6.09920e9	0.575152
$170$	−2.34772e10	−2.15589
$171$	7.52949e8	0.0673415
$172$	3.92171e9	0.341663
$173$	2.74975e9	0.233392	0.116696	−	0.993168i	$-0.462770\pi$
$173$	2.74975e9	0.233392	0.116696	+	0.993168i	$0.462770\pi$
$174$	−3.47830e10	−2.87670
$175$	5.29616e9	0.426864
$176$	2.77016e10	2.17620
$177$	1.72381e10	1.32010
$178$	1.71946e10	1.28381
$179$	−2.63971e10	−1.92184	−0.960920	−	0.276826i	$-0.910717\pi$
$179$	−2.63971e10	−1.92184	−0.960920	+	0.276826i	$0.910717\pi$
$180$	1.79374e9	0.127360
$181$	1.02862e10	0.712360	0.356180	−	0.934417i	$-0.384079\pi$
$181$	1.02862e10	0.712360	0.356180	+	0.934417i	$0.384079\pi$
$182$	3.30285e10	2.23135
$183$	−3.69219e9	−0.243363
$184$	−3.32333e10	−2.13744
$185$	−1.12033e10	−0.703190
$186$	−2.68765e10	−1.64651
$187$	2.04696e10	1.22411
$188$	4.14502e10	2.42001
$189$	−1.77121e10	−1.00970
$190$	5.48628e10	3.05412
$191$	1.46774e9	0.0797990	0.0398995	−	0.999204i	$-0.487296\pi$
$191$	1.46774e9	0.0797990	0.0398995	+	0.999204i	$0.487296\pi$
$192$	−6.17114e8	−0.0327725
$193$	−2.00489e10	−1.04012	−0.520060	−	0.854130i	$-0.674090\pi$
$193$	−2.00489e10	−1.04012	−0.520060	+	0.854130i	$0.674090\pi$
$194$	2.28742e10	1.15941
$195$	−2.95972e10	−1.46587
$196$	−1.13594e9	−0.0549799
$197$	−5.45542e9	−0.258066	−0.129033	−	0.991640i	$-0.541187\pi$
$197$	−5.45542e9	−0.258066	−0.129033	+	0.991640i	$0.541187\pi$
$198$	−2.26200e9	−0.104592
$199$	−3.63668e10	−1.64386	−0.821932	−	0.569585i	$-0.807104\pi$
$199$	−3.63668e10	−1.64386	−0.821932	+	0.569585i	$0.807104\pi$
$200$	2.18371e10	0.965071
$201$	2.17095e10	0.938139
$202$	7.15333e10	3.02292
$203$	−3.91290e10	−1.61721
$204$	5.41282e10	2.18820
$205$	7.99304e9	0.316096
$206$	8.18457e10	3.16660
$207$	1.20112e9	0.0454694
$208$	6.02763e10	2.23286
$209$	−4.78343e10	−1.73413
$210$	−5.85231e10	−2.07654
$211$	3.74610e9	0.130109	0.0650547	−	0.997882i	$-0.479278\pi$
$211$	3.74610e9	0.130109	0.0650547	+	0.997882i	$0.479278\pi$
$212$	−9.41009e9	−0.319950
$213$	2.21810e10	0.738367
$214$	−3.79269e10	−1.23619
$215$	−5.71796e9	−0.182502
$216$	−7.30302e10	−2.28276
$217$	−3.02346e10	−0.925625
$218$	−6.54569e10	−1.96291
$219$	−5.42246e10	−1.59293
$220$	−1.13955e11	−3.27968
$221$	4.45400e10	1.25599
$222$	3.73588e10	1.03230
$223$	6.47547e10	1.75347	0.876737	−	0.480970i	$-0.159715\pi$
$223$	6.47547e10	1.75347	0.876737	+	0.480970i	$0.159715\pi$
$224$	3.60865e10	0.957697
$225$	−7.89235e8	−0.0205298
$226$	7.22600e10	1.84251
$227$	3.57945e10	0.894747	0.447374	−	0.894347i	$-0.352359\pi$
$227$	3.57945e10	0.894747	0.447374	+	0.894347i	$0.352359\pi$
$228$	−1.26489e11	−3.09990
$229$	−6.85479e9	−0.164716	−0.0823578	−	0.996603i	$-0.526245\pi$
$229$	−6.85479e9	−0.164716	−0.0823578	+	0.996603i	$0.526245\pi$
$230$	8.75182e10	2.06216
$231$	5.10257e10	1.17906
$232$	−1.61336e11	−3.65625
$233$	7.97262e10	1.77215	0.886073	−	0.463545i	$-0.153423\pi$
$233$	7.97262e10	1.77215	0.886073	+	0.463545i	$0.153423\pi$
$234$	−4.92191e9	−0.107315
$235$	−6.04355e10	−1.29267
$236$	1.44415e11	3.03045
$237$	−2.48156e10	−0.510925
$238$	8.80696e10	1.77922
$239$	8.14161e10	1.61406	0.807030	−	0.590511i	$-0.201074\pi$
$239$	8.14161e10	1.61406	0.807030	+	0.590511i	$0.201074\pi$
$240$	−1.06803e11	−2.07795
$241$	−4.20240e10	−0.802456	−0.401228	−	0.915978i	$-0.631416\pi$
$241$	−4.20240e10	−0.802456	−0.401228	+	0.915978i	$0.631416\pi$
$242$	4.76592e10	0.893260
$243$	5.15922e9	0.0949197
$244$	−3.09320e10	−0.558667
$245$	1.65623e9	0.0293680
$246$	−2.66538e10	−0.464036
$247$	−1.04083e11	−1.77928
$248$	−1.24663e11	−2.09269
$249$	−9.78250e10	−1.61270
$250$	7.55489e10	1.22320
$251$	5.15405e10	0.819629	0.409814	−	0.912169i	$-0.365593\pi$
$251$	5.15405e10	0.819629	0.409814	+	0.912169i	$0.365593\pi$
$252$	−6.72881e9	−0.105108
$253$	−7.63063e10	−1.17089
$254$	−3.65048e10	−0.550299
$255$	−7.89203e10	−1.16885
$256$	−1.25121e11	−1.82075
$257$	2.95867e10	0.423056	0.211528	−	0.977372i	$-0.432156\pi$
$257$	2.95867e10	0.423056	0.211528	+	0.977372i	$0.432156\pi$
$258$	1.90673e10	0.267917
$259$	4.20266e10	0.580331
$260$	−2.47956e11	−3.36507
$261$	5.83101e9	0.0777788
$262$	−2.26485e10	−0.296950
$263$	−1.51451e11	−1.95196	−0.975982	−	0.217853i	$-0.930095\pi$
$263$	−1.51451e11	−1.95196	−0.975982	+	0.217853i	$0.930095\pi$
$264$	2.10389e11	2.66566
$265$	1.37202e10	0.170904
$266$	−2.05805e11	−2.52052
$267$	5.78007e10	0.696037
$268$	1.81875e11	2.15361
$269$	1.22693e11	1.42867	0.714336	−	0.699803i	$-0.246729\pi$
$269$	1.22693e11	1.42867	0.714336	+	0.699803i	$0.246729\pi$
$270$	1.92321e11	2.20237
$271$	9.32570e10	1.05032	0.525158	−	0.851005i	$-0.324006\pi$
$271$	9.32570e10	1.05032	0.525158	+	0.851005i	$0.324006\pi$
$272$	1.60725e11	1.78043
$273$	1.11027e11	1.20976
$274$	−5.11057e10	−0.547762
$275$	5.01396e10	0.528668
$276$	−2.01778e11	−2.09307
$277$	−1.36939e11	−1.39755	−0.698775	−	0.715342i	$-0.746271\pi$
$277$	−1.36939e11	−1.39755	−0.698775	+	0.715342i	$0.746271\pi$
$278$	8.33883e10	0.837343
$279$	4.50556e9	0.0445174
$280$	−2.71451e11	−2.63925
$281$	5.38417e10	0.515158	0.257579	−	0.966257i	$-0.417075\pi$
$281$	5.38417e10	0.515158	0.257579	+	0.966257i	$0.417075\pi$
$282$	2.01530e11	1.89766
$283$	3.73425e10	0.346070	0.173035	−	0.984916i	$-0.444643\pi$
$283$	3.73425e10	0.346070	0.173035	+	0.984916i	$0.444643\pi$
$284$	1.85825e11	1.69501
$285$	1.84425e11	1.65584
$286$	3.12686e11	2.76351
$287$	−2.99841e10	−0.260869
$288$	−5.37761e9	−0.0460599
$289$	1.76921e8	0.00149190
$290$	4.24870e11	3.52748
$291$	7.68933e10	0.628593
$292$	−4.54276e11	−3.65676
$293$	−2.07387e11	−1.64391	−0.821955	−	0.569552i	$-0.807117\pi$
$293$	−2.07387e11	−1.64391	−0.821955	+	0.569552i	$0.807117\pi$
$294$	−5.52293e9	−0.0431128
$295$	−2.10561e11	−1.61874
$296$	1.73284e11	1.31203
$297$	−1.67683e11	−1.25050
$298$	1.64856e11	1.21097
$299$	−1.66036e11	−1.20138
$300$	1.32585e11	0.945038
$301$	2.14496e10	0.150616
$302$	−2.05086e11	−1.41874
$303$	2.40464e11	1.63892
$304$	−3.75591e11	−2.52222
$305$	4.50996e10	0.298417
$306$	−1.31242e10	−0.0855707
$307$	1.83205e11	1.17711	0.588553	−	0.808459i	$-0.299698\pi$
$307$	1.83205e11	1.17711	0.588553	+	0.808459i	$0.299698\pi$
$308$	4.27477e11	2.70666
$309$	2.75130e11	1.71682
$310$	3.28293e11	2.01899
$311$	2.49561e11	1.51270	0.756352	−	0.654165i	$-0.226980\pi$
$311$	2.49561e11	1.51270	0.756352	+	0.654165i	$0.226980\pi$
$312$	4.57787e11	2.73506
$313$	−2.17457e11	−1.28063	−0.640317	−	0.768111i	$-0.721197\pi$
$313$	−2.17457e11	−1.28063	−0.640317	+	0.768111i	$0.721197\pi$
$314$	−4.07822e11	−2.36749
$315$	9.81079e9	0.0561444
$316$	−2.07897e11	−1.17289
$317$	−7.74502e10	−0.430780	−0.215390	−	0.976528i	$-0.569102\pi$
$317$	−7.74502e10	−0.430780	−0.215390	+	0.976528i	$0.569102\pi$
$318$	−4.57516e10	−0.250891
$319$	−3.70440e11	−2.00290
$320$	7.53797e9	0.0401864
$321$	−1.27494e11	−0.670218
$322$	−3.28305e11	−1.70187
$323$	−2.77535e11	−1.41875
$324$	−4.22298e11	−2.12895
$325$	1.09099e11	0.542433
$326$	5.99098e11	2.93778
$327$	−2.20038e11	−1.06422
$328$	−1.23630e11	−0.589782
$329$	2.26710e11	1.06682
$330$	−5.54047e11	−2.57178
$331$	1.90937e11	0.874306	0.437153	−	0.899387i	$-0.355987\pi$
$331$	1.90937e11	0.874306	0.437153	+	0.899387i	$0.355987\pi$
$332$	−8.19546e11	−3.70213
$333$	−6.26282e9	−0.0279107
$334$	3.82952e11	1.68378
$335$	−2.65179e11	−1.15037
$336$	4.00649e11	1.71489
$337$	1.82392e11	0.770321	0.385161	−	0.922850i	$-0.374146\pi$
$337$	1.82392e11	0.770321	0.385161	+	0.922850i	$0.374146\pi$
$338$	2.48433e11	1.03534
$339$	2.42907e11	0.998944
$340$	−6.61169e11	−2.68323
$341$	−2.86235e11	−1.14638
$342$	3.06692e10	0.121223
$343$	−2.59392e11	−1.01189
$344$	8.84408e10	0.340518
$345$	2.94198e11	1.11803
$346$	1.12003e11	0.420133
$347$	−2.55019e11	−0.944255	−0.472128	−	0.881530i	$-0.656514\pi$
$347$	−2.55019e11	−0.944255	−0.472128	+	0.881530i	$0.656514\pi$
$348$	−9.79562e11	−3.58035
$349$	4.21693e11	1.52154	0.760768	−	0.649024i	$-0.224822\pi$
$349$	4.21693e11	1.52154	0.760768	+	0.649024i	$0.224822\pi$
$350$	2.15724e11	0.768407
$351$	−3.64863e11	−1.28306
$352$	3.41636e11	1.18610
$353$	−1.47488e11	−0.505557	−0.252779	−	0.967524i	$-0.581344\pi$
$353$	−1.47488e11	−0.505557	−0.252779	+	0.967524i	$0.581344\pi$
$354$	7.02141e11	2.37635
$355$	−2.70938e11	−0.905402
$356$	4.84236e11	1.59783
$357$	2.96052e11	0.964630
$358$	−1.07521e12	−3.45954
$359$	−1.64579e11	−0.522937	−0.261469	−	0.965212i	$-0.584207\pi$
$359$	−1.64579e11	−0.522937	−0.261469	+	0.965212i	$0.584207\pi$
$360$	4.04517e10	0.126933
$361$	3.25870e11	1.00986
$362$	4.18976e11	1.28233
$363$	1.60210e11	0.484294
$364$	9.30152e11	2.77714
$365$	6.62346e11	1.95329
$366$	−1.50390e11	−0.438082
$367$	−3.78138e10	−0.108806	−0.0544030	−	0.998519i	$-0.517326\pi$
$367$	−3.78138e10	−0.108806	−0.0544030	+	0.998519i	$0.517326\pi$
$368$	−5.99150e11	−1.70302
$369$	4.46823e9	0.0125463
$370$	−4.56333e11	−1.26583
$371$	−5.14681e10	−0.141044
$372$	−7.56898e11	−2.04925
$373$	−1.33593e11	−0.357350	−0.178675	−	0.983908i	$-0.557181\pi$
$373$	−1.33593e11	−0.357350	−0.178675	+	0.983908i	$0.557181\pi$
$374$	8.33768e11	2.20355
$375$	2.53963e11	0.663177
$376$	9.34769e11	2.41190
$377$	−8.06044e11	−2.05505
$378$	−7.21449e11	−1.81758
$379$	2.11360e11	0.526196	0.263098	−	0.964769i	$-0.415256\pi$
$379$	2.11360e11	0.526196	0.263098	+	0.964769i	$0.415256\pi$
$380$	1.54505e12	3.80117
$381$	−1.22713e11	−0.298352
$382$	5.97839e10	0.143648
$383$	9.07858e10	0.215587	0.107794	−	0.994173i	$-0.465621\pi$
$383$	9.07858e10	0.215587	0.107794	+	0.994173i	$0.465621\pi$
$384$	−4.28360e11	−1.00535
$385$	−6.23273e11	−1.44579
$386$	−8.16634e11	−1.87234
$387$	−3.19643e9	−0.00724378
$388$	6.44187e11	1.44301
$389$	4.01199e11	0.888354	0.444177	−	0.895939i	$-0.353496\pi$
$389$	4.01199e11	0.888354	0.444177	+	0.895939i	$0.353496\pi$
$390$	−1.20556e12	−2.63874
$391$	−4.42730e11	−0.957951
$392$	−2.56173e10	−0.0547957
$393$	−7.61345e10	−0.160996
$394$	−2.22211e11	−0.464549
$395$	3.03119e11	0.626508
$396$	−6.37027e10	−0.130176
$397$	4.71822e11	0.953281	0.476641	−	0.879098i	$-0.341854\pi$
$397$	4.71822e11	0.953281	0.476641	+	0.879098i	$0.341854\pi$
$398$	−1.48129e12	−2.95915
$399$	−6.91828e11	−1.36653
$400$	3.93691e11	0.768928
$401$	4.96582e10	0.0959050	0.0479525	−	0.998850i	$-0.484730\pi$
$401$	4.96582e10	0.0959050	0.0479525	+	0.998850i	$0.484730\pi$
$402$	8.84272e11	1.68876
$403$	−6.22822e11	−1.17623
$404$	2.01453e12	3.76233
$405$	6.15721e11	1.13720
$406$	−1.59380e12	−2.91117
$407$	3.97872e11	0.718735
$408$	1.22068e12	2.18087
$409$	−5.83420e11	−1.03092	−0.515461	−	0.856913i	$-0.672379\pi$
$409$	−5.83420e11	−1.03092	−0.515461	+	0.856913i	$0.672379\pi$
$410$	3.25573e11	0.569011
$411$	−1.71795e11	−0.296977
$412$	2.30495e12	3.94115
$413$	7.89871e11	1.33592
$414$	4.89240e10	0.0818504
$415$	1.19492e12	1.97753
$416$	7.43370e11	1.21698
$417$	2.80315e11	0.453978
$418$	−1.94839e12	−3.12164
$419$	5.27009e10	0.0835324	0.0417662	−	0.999127i	$-0.486702\pi$
$419$	5.27009e10	0.0835324	0.0417662	+	0.999127i	$0.486702\pi$
$420$	−1.64813e12	−2.58446
$421$	−5.70311e10	−0.0884795	−0.0442397	−	0.999021i	$-0.514087\pi$
$421$	−5.70311e10	−0.0884795	−0.0442397	+	0.999021i	$0.514087\pi$
$422$	1.52586e11	0.234213
$423$	−3.37844e10	−0.0513080
$424$	−2.12213e11	−0.318878
$425$	2.90910e11	0.432523
$426$	9.03476e11	1.32915
$427$	−1.69181e11	−0.246278
$428$	−1.06810e12	−1.53856
$429$	1.05111e12	1.49828
$430$	−2.32904e11	−0.328525
$431$	−4.15265e11	−0.579665	−0.289833	−	0.957077i	$-0.593600\pi$
$431$	−4.15265e11	−0.579665	−0.289833	+	0.957077i	$0.593600\pi$
$432$	−1.31663e12	−1.81881
$433$	−1.36287e12	−1.86320	−0.931602	−	0.363481i	$-0.881588\pi$
$433$	−1.36287e12	−1.86320	−0.931602	+	0.363481i	$0.881588\pi$
$434$	−1.23152e12	−1.66624
$435$	1.42823e12	1.91247
$436$	−1.84341e12	−2.44305
$437$	1.03459e12	1.35707
$438$	−2.20868e12	−2.86747
$439$	5.58658e10	0.0717886	0.0358943	−	0.999356i	$-0.488572\pi$
$439$	5.58658e10	0.0717886	0.0358943	+	0.999356i	$0.488572\pi$
$440$	−2.56987e12	−3.26869
$441$	9.25861e8	0.00116566
$442$	1.81421e12	2.26093
$443$	−2.60675e11	−0.321575	−0.160787	−	0.986989i	$-0.551403\pi$
$443$	−2.60675e11	−0.321575	−0.160787	+	0.986989i	$0.551403\pi$
$444$	1.05210e12	1.28480
$445$	−7.06028e11	−0.853497
$446$	2.63759e12	3.15646
$447$	5.54175e11	0.656543
$448$	−2.82770e10	−0.0331652
$449$	6.07819e11	0.705775	0.352887	−	0.935666i	$-0.385200\pi$
$449$	6.07819e11	0.705775	0.352887	+	0.935666i	$0.385200\pi$
$450$	−3.21472e10	−0.0369561
$451$	−2.83864e11	−0.323084
$452$	2.03499e12	2.29319
$453$	−6.89409e11	−0.769193
$454$	1.45799e12	1.61065
$455$	−1.35619e12	−1.48343
$456$	−2.85254e12	−3.08951
$457$	7.95343e11	0.852966	0.426483	−	0.904496i	$-0.359752\pi$
$457$	7.95343e11	0.852966	0.426483	+	0.904496i	$0.359752\pi$
$458$	−2.79210e11	−0.296508
$459$	−9.72898e11	−1.02308
$460$	2.46470e12	2.56657
$461$	−3.51250e10	−0.0362212	−0.0181106	−	0.999836i	$-0.505765\pi$
$461$	−3.51250e10	−0.0362212	−0.0181106	+	0.999836i	$0.505765\pi$
$462$	2.07838e12	2.12245
$463$	1.00851e12	1.01992	0.509959	−	0.860199i	$-0.329661\pi$
$463$	1.00851e12	1.01992	0.509959	+	0.860199i	$0.329661\pi$
$464$	−2.90866e12	−2.91314
$465$	1.10358e12	1.09462
$466$	3.24741e12	3.19008
$467$	−5.82637e11	−0.566855	−0.283427	−	0.958994i	$-0.591472\pi$
$467$	−5.82637e11	−0.566855	−0.283427	+	0.958994i	$0.591472\pi$
$468$	−1.38611e11	−0.133565
$469$	9.94758e11	0.949379
$470$	−2.46166e12	−2.32696
$471$	−1.37092e12	−1.28357
$472$	3.25679e12	3.02030
$473$	2.03067e11	0.186537
$474$	−1.01079e12	−0.919726
$475$	−6.79813e11	−0.612729
$476$	2.48023e12	2.21442
$477$	7.66979e9	0.00678345
$478$	3.31624e12	2.90550
$479$	1.57329e12	1.36552	0.682760	−	0.730642i	$-0.260779\pi$
$479$	1.57329e12	1.36552	0.682760	+	0.730642i	$0.260779\pi$
$480$	−1.31717e12	−1.13255
$481$	8.65735e11	0.737449
$482$	−1.71173e12	−1.44452
$483$	−1.10362e12	−0.922692
$484$	1.34218e12	1.11175
$485$	−9.39241e11	−0.770796
$486$	2.10146e11	0.170867
$487$	1.20326e12	0.969350	0.484675	−	0.874694i	$-0.338938\pi$
$487$	1.20326e12	0.969350	0.484675	+	0.874694i	$0.338938\pi$
$488$	−6.97565e11	−0.556795
$489$	2.01391e12	1.59276
$490$	6.74618e10	0.0528659
$491$	−9.12134e11	−0.708259	−0.354129	−	0.935196i	$-0.615223\pi$
$491$	−9.12134e11	−0.708259	−0.354129	+	0.935196i	$0.615223\pi$
$492$	−7.50627e11	−0.577539
$493$	−2.14930e12	−1.63865
$494$	−4.23952e12	−3.20292
$495$	9.28802e10	0.0695344
$496$	−2.24749e12	−1.66737
$497$	1.01636e12	0.747213
$498$	−3.98461e12	−2.90305
$499$	−1.10261e10	−0.00796103	−0.00398052	−	0.999992i	$-0.501267\pi$
$499$	−1.10261e10	−0.00796103	−0.00398052	+	0.999992i	$0.501267\pi$
$500$	2.12762e12	1.52240
$501$	1.28732e12	0.912884
$502$	2.09935e12	1.47543
$503$	9.04880e11	0.630282	0.315141	−	0.949045i	$-0.397948\pi$
$503$	9.04880e11	0.630282	0.315141	+	0.949045i	$0.397948\pi$
$504$	−1.51746e11	−0.104756
$505$	−2.93724e12	−2.00968
$506$	−3.10811e12	−2.10775
$507$	8.35123e11	0.561326
$508$	−1.02805e12	−0.684902
$509$	−8.20613e10	−0.0541886	−0.0270943	−	0.999633i	$-0.508625\pi$
$509$	−8.20613e10	−0.0541886	−0.0270943	+	0.999633i	$0.508625\pi$
$510$	−3.21459e12	−2.10407
$511$	−2.48464e12	−1.61202
$512$	−3.49467e12	−2.24746
$513$	2.27352e12	1.44934
$514$	1.20513e12	0.761551
$515$	−3.36067e12	−2.10520
$516$	5.36974e11	0.333449
$517$	2.14630e12	1.32124
$518$	1.71183e12	1.04467
$519$	3.76505e11	0.227781
$520$	−5.59181e12	−3.35380
$521$	−4.56535e11	−0.271459	−0.135730	−	0.990746i	$-0.543338\pi$
$521$	−4.56535e11	−0.271459	−0.135730	+	0.990746i	$0.543338\pi$
$522$	2.37509e11	0.140011
$523$	−6.15826e11	−0.359916	−0.179958	−	0.983674i	$-0.557596\pi$
$523$	−6.15826e11	−0.359916	−0.179958	+	0.983674i	$0.557596\pi$
$524$	−6.37830e11	−0.369585
$525$	7.25169e11	0.416603
$526$	−6.16892e12	−3.51377
$527$	−1.66074e12	−0.937895
$528$	3.79301e12	2.12388
$529$	−1.50750e11	−0.0836965
$530$	5.58850e11	0.307648
$531$	−1.17707e11	−0.0642504
$532$	−5.79591e12	−3.13704
$533$	−6.17662e11	−0.331496
$534$	2.35434e12	1.25295
$535$	1.55732e12	0.821837
$536$	4.10157e12	2.14639
$537$	−3.61438e12	−1.87564
$538$	4.99752e12	2.57178
$539$	−5.88193e10	−0.0300172
$540$	5.41617e12	2.74107
$541$	2.10898e12	1.05849	0.529243	−	0.848470i	$-0.322476\pi$
$541$	2.10898e12	1.05849	0.529243	+	0.848470i	$0.322476\pi$
$542$	3.79855e12	1.89069
$543$	1.40842e12	0.695236
$544$	1.98218e12	0.970392
$545$	2.68773e12	1.30497
$546$	4.52238e12	2.17771
$547$	−1.89301e12	−0.904088	−0.452044	−	0.891996i	$-0.649305\pi$
$547$	−1.89301e12	−0.904088	−0.452044	+	0.891996i	$0.649305\pi$
$548$	−1.43924e12	−0.681745
$549$	2.52114e10	0.0118446
$550$	2.04229e12	0.951666
$551$	5.02258e12	2.32137
$552$	−4.55042e12	−2.08606
$553$	−1.13708e12	−0.517046
$554$	−5.57779e12	−2.51576
$555$	−1.53399e12	−0.686286
$556$	2.34839e12	1.04216
$557$	1.26554e12	0.557092	0.278546	−	0.960423i	$-0.410148\pi$
$557$	1.26554e12	0.557092	0.278546	+	0.960423i	$0.410148\pi$
$558$	1.83521e11	0.0801367
$559$	4.41855e11	0.191393
$560$	−4.89388e12	−2.10284
$561$	2.80277e12	1.19469
$562$	2.19308e12	0.927346
$563$	−2.21290e12	−0.928271	−0.464135	−	0.885764i	$-0.653635\pi$
$563$	−2.21290e12	−0.928271	−0.464135	+	0.885764i	$0.653635\pi$
$564$	5.67551e12	2.36183
$565$	−2.96708e12	−1.22493
$566$	1.52104e12	0.622968
$567$	−2.30974e12	−0.938511
$568$	4.19065e12	1.68933
$569$	1.08353e12	0.433346	0.216673	−	0.976244i	$-0.430479\pi$
$569$	1.08353e12	0.433346	0.216673	+	0.976244i	$0.430479\pi$
$570$	7.51200e12	2.98070
$571$	1.57967e12	0.621877	0.310939	−	0.950430i	$-0.399357\pi$
$571$	1.57967e12	0.621877	0.310939	+	0.950430i	$0.399357\pi$
$572$	8.80589e12	3.43947
$573$	2.00968e11	0.0778807
$574$	−1.22131e12	−0.469595
$575$	−1.08445e12	−0.413718
$576$	4.21385e9	0.00159506
$577$	−2.78907e12	−1.04753	−0.523767	−	0.851862i	$-0.675474\pi$
$577$	−2.78907e12	−1.04753	−0.523767	+	0.851862i	$0.675474\pi$
$578$	7.20637e9	0.00268560
$579$	−2.74517e12	−1.01512
$580$	1.19652e13	4.39031
$581$	−4.48247e12	−1.63202
$582$	3.13202e12	1.13154
$583$	−4.87256e11	−0.174682
$584$	−1.02447e13	−3.64451
$585$	2.02099e11	0.0713449
$586$	−8.44732e12	−2.95924
$587$	8.39866e11	0.291970	0.145985	−	0.989287i	$-0.453365\pi$
$587$	8.39866e11	0.291970	0.145985	+	0.989287i	$0.453365\pi$
$588$	−1.55537e11	−0.0536582
$589$	3.88090e12	1.32866
$590$	−8.57657e12	−2.91393
$591$	−7.46975e11	−0.251862
$592$	3.12406e12	1.04537
$593$	4.86701e12	1.61628	0.808138	−	0.588993i	$-0.200475\pi$
$593$	4.86701e12	1.61628	0.808138	+	0.588993i	$0.200475\pi$
$594$	−6.83007e12	−2.25106
$595$	−3.61624e12	−1.18285
$596$	4.64270e12	1.50717
$597$	−4.97947e12	−1.60435
$598$	−6.76297e12	−2.16263
$599$	1.39620e12	0.443127	0.221564	−	0.975146i	$-0.428884\pi$
$599$	1.39620e12	0.443127	0.221564	+	0.975146i	$0.428884\pi$
$600$	2.99001e12	0.941871
$601$	−3.81417e11	−0.119252	−0.0596259	−	0.998221i	$-0.518991\pi$
$601$	−3.81417e11	−0.119252	−0.0596259	+	0.998221i	$0.518991\pi$
$602$	8.73688e11	0.271126
$603$	−1.48239e11	−0.0456599
$604$	−5.77565e12	−1.76577
$605$	−1.95694e12	−0.593852
$606$	9.79459e12	2.95025
$607$	−4.60054e12	−1.37550	−0.687749	−	0.725948i	$-0.741401\pi$
$607$	−4.60054e12	−1.37550	−0.687749	+	0.725948i	$0.741401\pi$
$608$	−4.63205e12	−1.37470
$609$	−5.35767e12	−1.57833
$610$	1.83700e12	0.537186
$611$	4.67016e12	1.35565
$612$	−3.69604e11	−0.106501
$613$	−5.49882e12	−1.57289	−0.786444	−	0.617662i	$-0.788080\pi$
$613$	−5.49882e12	−1.57289	−0.786444	+	0.617662i	$0.788080\pi$
$614$	7.46233e12	2.11893
$615$	1.09443e12	0.308498
$616$	9.64029e12	2.69760
$617$	−6.38926e12	−1.77487	−0.887437	−	0.460930i	$-0.847516\pi$
$617$	−6.38926e12	−1.77487	−0.887437	+	0.460930i	$0.847516\pi$
$618$	1.12066e13	3.09048
$619$	3.30315e11	0.0904316	0.0452158	−	0.998977i	$-0.485602\pi$
$619$	3.30315e11	0.0904316	0.0452158	+	0.998977i	$0.485602\pi$
$620$	9.24542e12	2.51283
$621$	3.62676e12	0.978602
$622$	1.01651e13	2.72305
$623$	2.64851e12	0.704376
$624$	8.25324e12	2.17918
$625$	−4.75084e12	−1.24540
$626$	−8.85749e12	−2.30529
$627$	−6.54964e12	−1.69244
$628$	−1.14851e13	−2.94658
$629$	2.30846e12	0.588023
$630$	3.99614e11	0.101067
$631$	2.01956e12	0.507137	0.253568	−	0.967317i	$-0.418396\pi$
$631$	2.01956e12	0.507137	0.253568	+	0.967317i	$0.418396\pi$
$632$	−4.68841e12	−1.16896
$633$	5.12930e11	0.126982
$634$	−3.15470e12	−0.775456
$635$	1.49893e12	0.365846
$636$	−1.28846e12	−0.312259
$637$	−1.27986e11	−0.0307988
$638$	−1.50888e13	−3.60546
$639$	−1.51458e11	−0.0359368
$640$	5.23237e12	1.23279
$641$	−5.34027e12	−1.24940	−0.624701	−	0.780864i	$-0.714779\pi$
$641$	−5.34027e12	−1.24940	−0.624701	+	0.780864i	$0.714779\pi$
$642$	−5.19308e12	−1.20647
$643$	−5.49997e12	−1.26885	−0.634426	−	0.772983i	$-0.718764\pi$
$643$	−5.49997e12	−1.26885	−0.634426	+	0.772983i	$0.718764\pi$
$644$	−9.24576e12	−2.11815
$645$	−7.82922e11	−0.178115
$646$	−1.13046e13	−2.55393
$647$	4.45549e12	0.999601	0.499800	−	0.866141i	$-0.333407\pi$
$647$	4.45549e12	0.999601	0.499800	+	0.866141i	$0.333407\pi$
$648$	−9.52349e12	−2.12182
$649$	7.47783e12	1.65453
$650$	4.44383e12	0.976445
$651$	−4.13982e12	−0.903374
$652$	1.68719e13	3.65636
$653$	2.09830e12	0.451605	0.225803	−	0.974173i	$-0.427500\pi$
$653$	2.09830e12	0.451605	0.225803	+	0.974173i	$0.427500\pi$
$654$	−8.96259e12	−1.91573
$655$	9.29973e11	0.197417
$656$	−2.22887e12	−0.469914
$657$	3.70262e11	0.0775292
$658$	9.23438e12	1.92040
$659$	−4.54833e12	−0.939437	−0.469719	−	0.882816i	$-0.655645\pi$
$659$	−4.54833e12	−0.939437	−0.469719	+	0.882816i	$0.655645\pi$
$660$	−1.56031e13	−3.20084
$661$	3.46859e11	0.0706718	0.0353359	−	0.999375i	$-0.488750\pi$
$661$	3.46859e11	0.0706718	0.0353359	+	0.999375i	$0.488750\pi$
$662$	7.77725e12	1.57386
$663$	6.09857e12	1.22579
$664$	−1.84821e13	−3.68973
$665$	8.45060e12	1.67568
$666$	−2.55097e11	−0.0502426
$667$	8.01212e12	1.56740
$668$	1.07847e13	2.09563
$669$	8.86644e12	1.71132
$670$	−1.08013e13	−2.07080
$671$	−1.60166e12	−0.305014
$672$	4.94109e12	0.934675
$673$	−7.44467e12	−1.39887	−0.699436	−	0.714696i	$-0.746565\pi$
$673$	−7.44467e12	−1.39887	−0.699436	+	0.714696i	$0.746565\pi$
$674$	7.42922e12	1.38667
$675$	−2.38308e12	−0.441847
$676$	6.99639e12	1.28859
$677$	6.81814e12	1.24743	0.623716	−	0.781651i	$-0.285622\pi$
$677$	6.81814e12	1.24743	0.623716	+	0.781651i	$0.285622\pi$
$678$	9.89410e12	1.79822
$679$	3.52335e12	0.636125
$680$	−1.49104e13	−2.67424
$681$	4.90111e12	0.873238
$682$	−1.16590e13	−2.06362
$683$	−6.19460e11	−0.108923	−0.0544615	−	0.998516i	$-0.517344\pi$
$683$	−6.19460e11	−0.108923	−0.0544615	+	0.998516i	$0.517344\pi$
$684$	8.63708e11	0.150874
$685$	2.09846e12	0.364160
$686$	−1.05656e13	−1.82152
$687$	−9.38582e11	−0.160756
$688$	1.59446e12	0.271310
$689$	−1.06023e12	−0.179231
$690$	1.19833e13	2.01259
$691$	−4.18682e12	−0.698607	−0.349303	−	0.937010i	$-0.613582\pi$
$691$	−4.18682e12	−0.698607	−0.349303	+	0.937010i	$0.613582\pi$
$692$	3.15424e12	0.522898
$693$	−3.48419e11	−0.0573856
$694$	−1.03874e13	−1.69977
$695$	−3.42401e12	−0.556678
$696$	−2.20907e13	−3.56835
$697$	−1.64698e12	−0.264327
$698$	1.71764e13	2.73895
$699$	1.09164e13	1.72955
$700$	6.07523e12	0.956360
$701$	1.02585e13	1.60454	0.802271	−	0.596961i	$-0.203625\pi$
$701$	1.02585e13	1.60454	0.802271	+	0.596961i	$0.203625\pi$
$702$	−1.48616e13	−2.30967
$703$	−5.39452e12	−0.833018
$704$	−2.67703e11	−0.0410748
$705$	−8.27504e12	−1.26159
$706$	−6.00749e12	−0.910064
$707$	1.10184e13	1.65856
$708$	1.97738e13	2.95760
$709$	2.48568e11	0.0369434	0.0184717	−	0.999829i	$-0.494120\pi$
$709$	2.48568e11	0.0369434	0.0184717	+	0.999829i	$0.494120\pi$
$710$	−1.10358e13	−1.62983
$711$	1.69448e11	0.0248671
$712$	1.09203e13	1.59248
$713$	6.19089e12	0.897119
$714$	1.20588e13	1.73645
$715$	−1.28392e13	−1.83722
$716$	−3.02801e13	−4.30575
$717$	1.11478e13	1.57526
$718$	−6.70365e12	−0.941350
$719$	8.72683e12	1.21780	0.608901	−	0.793246i	$-0.291611\pi$
$719$	8.72683e12	1.21780	0.608901	+	0.793246i	$0.291611\pi$
$720$	7.29287e11	0.101135
$721$	1.26068e13	1.73739
$722$	1.32734e13	1.81787
$723$	−5.75408e12	−0.783165
$724$	1.17993e13	1.59599
$725$	−5.26463e12	−0.707696
$726$	6.52567e12	0.871787
$727$	−8.47088e12	−1.12467	−0.562333	−	0.826911i	$-0.690096\pi$
$727$	−8.47088e12	−1.12467	−0.562333	+	0.826911i	$0.690096\pi$
$728$	2.09764e13	2.76783
$729$	7.95259e12	1.04288
$730$	2.69787e13	3.51616
$731$	1.17820e12	0.152612
$732$	−4.23531e12	−0.545237
$733$	1.21968e13	1.56055	0.780273	−	0.625439i	$-0.215080\pi$
$733$	1.21968e13	1.56055	0.780273	+	0.625439i	$0.215080\pi$
$734$	−1.54023e12	−0.195864
$735$	2.26777e11	0.0286620
$736$	−7.38913e12	−0.928204
$737$	9.41752e12	1.17580
$738$	1.82000e11	0.0225849
$739$	−1.08186e13	−1.33435	−0.667174	−	0.744902i	$-0.732496\pi$
$739$	−1.08186e13	−1.33435	−0.667174	+	0.744902i	$0.732496\pi$
$740$	−1.28513e13	−1.57545
$741$	−1.42514e13	−1.73651
$742$	−2.09640e12	−0.253897
$743$	−1.11954e13	−1.34769	−0.673844	−	0.738874i	$-0.735358\pi$
$743$	−1.11954e13	−1.34769	−0.673844	+	0.738874i	$0.735358\pi$
$744$	−1.70693e13	−2.04238
$745$	−6.76918e12	−0.805069
$746$	−5.44152e12	−0.643273
$747$	6.67979e11	0.0784910
$748$	2.34807e13	2.74254
$749$	−5.84193e12	−0.678248
$750$	1.03444e13	1.19380
$751$	−7.76369e12	−0.890611	−0.445306	−	0.895379i	$-0.646905\pi$
$751$	−7.76369e12	−0.890611	−0.445306	+	0.895379i	$0.646905\pi$
$752$	1.68526e13	1.92170
$753$	7.05711e12	0.799925
$754$	−3.28318e13	−3.69934
$755$	8.42105e12	0.943202
$756$	−2.03175e13	−2.26216
$757$	4.10000e12	0.453788	0.226894	−	0.973920i	$-0.427143\pi$
$757$	4.10000e12	0.453788	0.226894	+	0.973920i	$0.427143\pi$
$758$	8.60915e12	0.947215
$759$	−1.04481e13	−1.14275
$760$	3.48434e13	3.78843
$761$	−5.30444e12	−0.573335	−0.286668	−	0.958030i	$-0.592548\pi$
$761$	−5.30444e12	−0.573335	−0.286668	+	0.958030i	$0.592548\pi$
$762$	−4.99837e12	−0.537070
$763$	−1.00824e13	−1.07697
$764$	1.68364e12	0.178784
$765$	5.38892e11	0.0568886
$766$	3.69789e12	0.388083
$767$	1.62711e13	1.69761
$768$	−1.71320e13	−1.77698
$769$	−7.00449e12	−0.722284	−0.361142	−	0.932511i	$-0.617613\pi$
$769$	−7.00449e12	−0.722284	−0.361142	+	0.932511i	$0.617613\pi$
$770$	−2.53872e13	−2.60259
$771$	4.05112e12	0.412886
$772$	−2.29981e13	−2.33032
$773$	8.08955e12	0.814923	0.407461	−	0.913222i	$-0.366414\pi$
$773$	8.08955e12	0.814923	0.407461	+	0.913222i	$0.366414\pi$
$774$	−1.30197e11	−0.0130397
$775$	−4.06793e12	−0.405056
$776$	1.45274e13	1.43817
$777$	5.75443e12	0.566380
$778$	1.63416e13	1.59914
$779$	3.84875e12	0.374456
$780$	−3.39510e13	−3.28418
$781$	9.62205e12	0.925418
$782$	−1.80333e13	−1.72443
$783$	1.76066e13	1.67397
$784$	−4.61844e11	−0.0436589
$785$	1.67456e13	1.57394
$786$	−3.10111e12	−0.289812
$787$	−6.01513e12	−0.558931	−0.279466	−	0.960156i	$-0.590157\pi$
$787$	−6.01513e12	−0.558931	−0.279466	+	0.960156i	$0.590157\pi$
$788$	−6.25792e12	−0.578178
$789$	−2.07372e13	−1.90504
$790$	1.23467e13	1.12779
$791$	1.11303e13	1.01091
$792$	−1.43660e12	−0.129739
$793$	−3.48508e12	−0.312956
$794$	1.92183e13	1.71602
$795$	1.87861e12	0.166796
$796$	−4.17164e13	−3.68296
$797$	8.83051e12	0.775217	0.387609	−	0.921824i	$-0.373301\pi$
$797$	8.83051e12	0.775217	0.387609	+	0.921824i	$0.373301\pi$
$798$	−2.81796e13	−2.45992
$799$	1.24529e13	1.08096
$800$	4.85527e12	0.419091
$801$	−3.94681e11	−0.0338766
$802$	2.02268e12	0.172641
$803$	−2.35225e13	−1.99647
$804$	2.49030e13	2.10184
$805$	1.34806e13	1.13143
$806$	−2.53688e13	−2.11735
$807$	1.67995e13	1.39433
$808$	4.54308e13	3.74973
$809$	−7.44156e11	−0.0610795	−0.0305397	−	0.999534i	$-0.509723\pi$
$809$	−7.44156e11	−0.0610795	−0.0305397	+	0.999534i	$0.509723\pi$
$810$	2.50796e13	2.04709
$811$	2.23511e12	0.181429	0.0907143	−	0.995877i	$-0.471085\pi$
$811$	2.23511e12	0.181429	0.0907143	+	0.995877i	$0.471085\pi$
$812$	−4.48849e13	−3.62325
$813$	1.27691e13	1.02507
$814$	1.62062e13	1.29381
$815$	−2.45996e13	−1.95308
$816$	2.20071e13	1.73763
$817$	−2.75327e12	−0.216197
$818$	−2.37639e13	−1.85578
$819$	−7.58129e11	−0.0588797
$820$	9.16882e12	0.708192
$821$	−1.88122e13	−1.44509	−0.722546	−	0.691322i	$-0.757028\pi$
$821$	−1.88122e13	−1.44509	−0.722546	+	0.691322i	$0.757028\pi$
$822$	−6.99757e12	−0.534594
$823$	2.44627e11	0.0185869	0.00929343	−	0.999957i	$-0.497042\pi$
$823$	2.44627e11	0.0185869	0.00929343	+	0.999957i	$0.497042\pi$
$824$	5.19802e13	3.92795
$825$	6.86528e12	0.515960
$826$	3.21731e13	2.40482
$827$	−1.92446e13	−1.43065	−0.715327	−	0.698790i	$-0.753722\pi$
$827$	−1.92446e13	−1.43065	−0.715327	+	0.698790i	$0.753722\pi$
$828$	1.37780e12	0.101871
$829$	−1.12352e13	−0.826204	−0.413102	−	0.910685i	$-0.635555\pi$
$829$	−1.12352e13	−0.826204	−0.413102	+	0.910685i	$0.635555\pi$
$830$	4.86715e13	3.55978
$831$	−1.87501e13	−1.36395
$832$	−5.82497e11	−0.0421443
$833$	−3.41270e11	−0.0245582
$834$	1.14178e13	0.817214
$835$	−1.57244e13	−1.11940
$836$	−5.48708e13	−3.88520
$837$	1.36045e13	0.958114
$838$	2.14662e12	0.150368
$839$	2.33933e13	1.62991	0.814955	−	0.579524i	$-0.196762\pi$
$839$	2.33933e13	1.62991	0.814955	+	0.579524i	$0.196762\pi$
$840$	−3.71681e13	−2.57581
$841$	2.43888e13	1.68116
$842$	−2.32300e12	−0.159274
$843$	7.37220e12	0.502774
$844$	4.29716e12	0.291501
$845$	−1.02009e13	−0.688311
$846$	−1.37611e12	−0.0923605
$847$	7.34103e12	0.490096
$848$	−3.82589e12	−0.254069
$849$	5.11306e12	0.337751
$850$	1.18494e13	0.778593
$851$	−8.60545e12	−0.562459
$852$	2.54438e13	1.65426
$853$	−1.41030e13	−0.912098	−0.456049	−	0.889955i	$-0.650736\pi$
$853$	−1.41030e13	−0.912098	−0.456049	+	0.889955i	$0.650736\pi$
$854$	−6.89109e12	−0.443331
$855$	−1.25931e12	−0.0805907
$856$	−2.40874e13	−1.53341
$857$	−1.95183e13	−1.23603	−0.618013	−	0.786168i	$-0.712062\pi$
$857$	−1.95183e13	−1.23603	−0.618013	+	0.786168i	$0.712062\pi$
$858$	4.28140e13	2.69708
$859$	−3.27802e12	−0.205420	−0.102710	−	0.994711i	$-0.532751\pi$
$859$	−3.27802e12	−0.205420	−0.102710	+	0.994711i	$0.532751\pi$
$860$	−6.55907e12	−0.408883
$861$	−4.10553e12	−0.254598
$862$	−1.69146e13	−1.04347
$863$	−1.21741e13	−0.747115	−0.373558	−	0.927607i	$-0.621862\pi$
$863$	−1.21741e13	−0.747115	−0.373558	+	0.927607i	$0.621862\pi$
$864$	−1.62376e13	−0.991312
$865$	−4.59896e12	−0.279310
$866$	−5.55127e13	−3.35399
$867$	2.42247e10	0.00145604
$868$	−3.46821e13	−2.07380
$869$	−1.07649e13	−0.640358
$870$	5.81746e13	3.44268
$871$	2.04917e13	1.20641
$872$	−4.15717e13	−2.43486
$873$	−5.25051e11	−0.0305941
$874$	4.21411e13	2.44289
$875$	1.16369e13	0.671122
$876$	−6.22011e13	−3.56886
$877$	−2.57000e13	−1.46702	−0.733509	−	0.679680i	$-0.762119\pi$
$877$	−2.57000e13	−1.46702	−0.733509	+	0.679680i	$0.762119\pi$
$878$	2.27553e12	0.129228
$879$	−2.83962e13	−1.60439
$880$	−4.63311e13	−2.60436
$881$	3.11564e13	1.74243	0.871216	−	0.490900i	$-0.163332\pi$
$881$	3.11564e13	1.74243	0.871216	+	0.490900i	$0.163332\pi$
$882$	3.77122e10	0.00209833
$883$	−1.15326e13	−0.638417	−0.319209	−	0.947684i	$-0.603417\pi$
$883$	−1.15326e13	−0.638417	−0.319209	+	0.947684i	$0.603417\pi$
$884$	5.10919e13	2.81395
$885$	−2.88307e13	−1.57983
$886$	−1.06178e13	−0.578873
$887$	2.05494e13	1.11466	0.557332	−	0.830290i	$-0.311825\pi$
$887$	2.05494e13	1.11466	0.557332	+	0.830290i	$0.311825\pi$
$888$	2.37266e13	1.28049
$889$	−5.62289e12	−0.301927
$890$	−2.87580e13	−1.53640
$891$	−2.18667e13	−1.16234
$892$	7.42802e13	3.92854
$893$	−2.91005e13	−1.53133
$894$	2.25727e13	1.18186
$895$	4.41492e13	2.29995
$896$	−1.96281e13	−1.01740
$897$	−2.27342e13	−1.17250
$898$	2.47577e13	1.27048
$899$	3.00546e13	1.53459
$900$	−9.05332e11	−0.0459956
$901$	−2.82707e12	−0.142914
$902$	−1.15624e13	−0.581590
$903$	2.93696e12	0.146995
$904$	4.58924e13	2.28551
$905$	−1.72036e13	−0.852514
$906$	−2.80811e13	−1.38464
$907$	2.27787e13	1.11762	0.558811	−	0.829295i	$-0.311258\pi$
$907$	2.27787e13	1.11762	0.558811	+	0.829295i	$0.311258\pi$
$908$	4.10599e13	2.00462
$909$	−1.64196e12	−0.0797674
$910$	−5.52402e13	−2.67036
$911$	−3.01085e13	−1.44829	−0.724145	−	0.689647i	$-0.757766\pi$
$911$	−3.01085e13	−1.44829	−0.724145	+	0.689647i	$0.757766\pi$
$912$	−5.14272e13	−2.46159
$913$	−4.24362e13	−2.02124
$914$	3.23960e13	1.53544
$915$	6.17520e12	0.291243
$916$	−7.86313e12	−0.369034
$917$	−3.48858e12	−0.162925
$918$	−3.96282e13	−1.84167
$919$	5.99186e12	0.277103	0.138552	−	0.990355i	$-0.455755\pi$
$919$	5.99186e12	0.277103	0.138552	+	0.990355i	$0.455755\pi$
$920$	5.55829e13	2.55797
$921$	2.50851e13	1.14881
$922$	−1.43072e12	−0.0652025
$923$	2.09367e13	0.949513
$924$	5.85316e13	2.64160
$925$	5.65450e12	0.253955
$926$	4.10787e13	1.83598
$927$	−1.87867e12	−0.0835587
$928$	−3.58716e13	−1.58776
$929$	−3.97732e12	−0.175194	−0.0875971	−	0.996156i	$-0.527919\pi$
$929$	−3.97732e12	−0.175194	−0.0875971	+	0.996156i	$0.527919\pi$
$930$	4.49510e13	1.97045
$931$	7.97497e11	0.0347901
$932$	9.14540e13	3.97037
$933$	3.41707e13	1.47634
$934$	−2.37320e13	−1.02041
$935$	−3.42354e13	−1.46495
$936$	−3.12591e12	−0.133117
$937$	5.35424e12	0.226918	0.113459	−	0.993543i	$-0.463807\pi$
$937$	5.35424e12	0.226918	0.113459	+	0.993543i	$0.463807\pi$
$938$	4.05185e13	1.70900
$939$	−2.97750e13	−1.24985
$940$	−6.93256e13	−2.89613
$941$	−2.04376e13	−0.849722	−0.424861	−	0.905259i	$-0.639677\pi$
$941$	−2.04376e13	−0.849722	−0.424861	+	0.905259i	$0.639677\pi$
$942$	−5.58405e13	−2.31058
$943$	6.13960e12	0.252835
$944$	5.87152e13	2.40645
$945$	2.96235e13	1.20835
$946$	8.27133e12	0.335788
$947$	2.67628e13	1.08132	0.540662	−	0.841240i	$-0.318174\pi$
$947$	2.67628e13	1.08132	0.540662	+	0.841240i	$0.318174\pi$
$948$	−2.84660e13	−1.14469
$949$	−5.11829e13	−2.04846
$950$	−2.76902e13	−1.10299
$951$	−1.06047e13	−0.420424
$952$	5.59331e13	2.20700
$953$	1.73936e13	0.683079	0.341539	−	0.939867i	$-0.389052\pi$
$953$	1.73936e13	0.683079	0.341539	+	0.939867i	$0.389052\pi$
$954$	3.12406e11	0.0122110
$955$	−2.45479e12	−0.0954992
$956$	9.33924e13	3.61619
$957$	−5.07219e13	−1.95475
$958$	6.40832e13	2.45810
$959$	−7.87189e12	−0.300535
$960$	1.03213e12	0.0392204
$961$	−3.21675e12	−0.121664
$962$	3.52632e13	1.32750
$963$	8.70566e11	0.0326200
$964$	−4.82058e13	−1.79785
$965$	3.35319e13	1.24476
$966$	−4.49526e13	−1.66096
$967$	−1.28440e13	−0.472368	−0.236184	−	0.971708i	$-0.575897\pi$
$967$	−1.28440e13	−0.472368	−0.236184	+	0.971708i	$0.575897\pi$
$968$	3.02684e13	1.10803
$969$	−3.80011e13	−1.38465
$970$	−3.82572e13	−1.38752
$971$	1.51680e13	0.547573	0.273786	−	0.961791i	$-0.411724\pi$
$971$	1.51680e13	0.547573	0.273786	+	0.961791i	$0.411724\pi$
$972$	5.91815e12	0.212661
$973$	1.28444e13	0.459417
$974$	4.90114e13	1.74495
$975$	1.49382e13	0.529394
$976$	−1.25761e13	−0.443631
$977$	−1.26105e13	−0.442799	−0.221399	−	0.975183i	$-0.571062\pi$
$977$	−1.26105e13	−0.442799	−0.221399	+	0.975183i	$0.571062\pi$
$978$	8.20306e13	2.86716
$979$	2.50738e13	0.872365
$980$	1.89987e12	0.0657970
$981$	1.50249e12	0.0517964
$982$	−3.71531e13	−1.27495
$983$	7.30841e12	0.249650	0.124825	−	0.992179i	$-0.460163\pi$
$983$	7.30841e12	0.249650	0.124825	+	0.992179i	$0.460163\pi$
$984$	−1.69279e13	−0.575604
$985$	9.12421e12	0.308839
$986$	−8.75453e13	−2.94976
$987$	3.10420e13	1.04117
$988$	−1.19394e14	−3.98636
$989$	−4.39206e12	−0.145977
$990$	3.78320e12	0.125170
$991$	1.27120e13	0.418680	0.209340	−	0.977843i	$-0.432868\pi$
$991$	1.27120e13	0.418680	0.209340	+	0.977843i	$0.432868\pi$
$992$	−2.77177e13	−0.908770
$993$	2.61437e13	0.853289
$994$	4.13985e13	1.34507
$995$	6.08236e13	1.96729
$996$	−1.12215e14	−3.61314
$997$	2.51374e13	0.805735	0.402867	−	0.915258i	$-0.368014\pi$
$997$	2.51374e13	0.805735	0.402867	+	0.915258i	$0.368014\pi$
$998$	−4.49116e11	−0.0143308
$999$	−1.89105e13	−0.600700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.b.1.17	✓	17
3.2	odd	2		387.10.a.e.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.17	✓	17	1.1	even	1	trivial
387.10.a.e.1.1		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)

\(f(q)\)	\(=\)	\(q+40.7321 q^{2} +136.923 q^{3} +1147.10 q^{4} -1672.50 q^{5} +5577.18 q^{6} +6274.02 q^{7} +25869.0 q^{8} -934.956 q^{9} +O(q^{10})\)	\(q+40.7321 q^{2} +136.923 q^{3} +1147.10 q^{4} -1672.50 q^{5} +5577.18 q^{6} +6274.02 q^{7} +25869.0 q^{8} -934.956 q^{9} -68124.5 q^{10} +59397.1 q^{11} +157065. q^{12} +129243. q^{13} +255554. q^{14} -229005. q^{15} +466380. q^{16} +344623. q^{17} -38082.7 q^{18} -805331. q^{19} -1.91853e6 q^{20} +859061. q^{21} +2.41937e6 q^{22} -1.28468e6 q^{23} +3.54207e6 q^{24} +844142. q^{25} +5.26432e6 q^{26} -2.82308e6 q^{27} +7.19693e6 q^{28} -6.23666e6 q^{29} -9.32784e6 q^{30} -4.81901e6 q^{31} +5.75173e6 q^{32} +8.13286e6 q^{33} +1.40372e7 q^{34} -1.04933e7 q^{35} -1.07249e6 q^{36} +6.69852e6 q^{37} -3.28028e7 q^{38} +1.76964e7 q^{39} -4.32659e7 q^{40} -4.77909e6 q^{41} +3.49913e7 q^{42} +3.41880e6 q^{43} +6.81344e7 q^{44} +1.56372e6 q^{45} -5.23277e7 q^{46} +3.61348e7 q^{47} +6.38584e7 q^{48} -990273. q^{49} +3.43836e7 q^{50} +4.71869e7 q^{51} +1.48254e8 q^{52} -8.20337e6 q^{53} -1.14990e8 q^{54} -9.93418e7 q^{55} +1.62302e8 q^{56} -1.10269e8 q^{57} -2.54032e8 q^{58} +1.25895e8 q^{59} -2.62692e8 q^{60} -2.69653e7 q^{61} -1.96288e8 q^{62} -5.86593e6 q^{63} -4.50700e6 q^{64} -2.16159e8 q^{65} +3.31268e8 q^{66} +1.58552e8 q^{67} +3.95317e8 q^{68} -1.75903e8 q^{69} -4.27414e8 q^{70} +1.61995e8 q^{71} -2.41863e7 q^{72} -3.96021e8 q^{73} +2.72844e8 q^{74} +1.15583e8 q^{75} -9.23796e8 q^{76} +3.72659e8 q^{77} +7.20810e8 q^{78} -1.81237e8 q^{79} -7.80023e8 q^{80} -3.68144e8 q^{81} -1.94662e8 q^{82} -7.14450e8 q^{83} +9.85429e8 q^{84} -5.76383e8 q^{85} +1.39255e8 q^{86} -8.53946e8 q^{87} +1.53654e9 q^{88} +4.22139e8 q^{89} +6.36934e7 q^{90} +8.10872e8 q^{91} -1.47366e9 q^{92} -6.59836e8 q^{93} +1.47184e9 q^{94} +1.34692e9 q^{95} +7.87547e8 q^{96} +5.61578e8 q^{97} -4.03359e7 q^{98} -5.55337e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9} + 23763 q^{10} + 78370 q^{11} + 271339 q^{12} + 114452 q^{13} - 376208 q^{14} - 255820 q^{15} + 412586 q^{16} + 726937 q^{17} + 577055 q^{18} + 544263 q^{19} + 3642183 q^{20} + 3137394 q^{21} + 5269148 q^{22} + 5575241 q^{23} + 16215113 q^{24} + 10874708 q^{25} + 8009180 q^{26} + 8350126 q^{27} + 12534764 q^{28} + 8223345 q^{29} + 30612012 q^{30} + 13054147 q^{31} + 37111710 q^{32} + 36024808 q^{33} + 27991291 q^{34} + 17826330 q^{35} + 84105953 q^{36} + 46733879 q^{37} + 15733789 q^{38} + 8689898 q^{39} + 52241669 q^{40} + 53667013 q^{41} + 7708286 q^{42} + 58119617 q^{43} + 81727236 q^{44} + 124361968 q^{45} + 146859355 q^{46} + 122945511 q^{47} + 86356095 q^{48} + 111396073 q^{49} - 96642133 q^{50} - 187132423 q^{51} - 54447944 q^{52} - 993146 q^{53} - 219468490 q^{54} - 248155792 q^{55} - 141048116 q^{56} - 402917960 q^{57} - 466599837 q^{58} - 95519644 q^{59} - 621611940 q^{60} - 311752038 q^{61} - 212471691 q^{62} - 928966350 q^{63} - 829842590 q^{64} - 107969830 q^{65} - 978530932 q^{66} - 292438130 q^{67} - 88281129 q^{68} + 78577726 q^{69} - 1650972530 q^{70} - 13576908 q^{71} - 706943493 q^{72} - 501490738 q^{73} - 494831691 q^{74} - 641914030 q^{75} - 1248630771 q^{76} + 787365348 q^{77} - 946670550 q^{78} + 740350275 q^{79} - 27802861 q^{80} + 1582210525 q^{81} - 1600400057 q^{82} + 754109940 q^{83} - 1955423842 q^{84} + 1071609956 q^{85} + 164102448 q^{86} + 186301257 q^{87} + 1863375104 q^{88} + 1470581868 q^{89} - 698098630 q^{90} + 2895349644 q^{91} + 1041082071 q^{92} + 4540331515 q^{93} - 706582361 q^{94} + 3297255729 q^{95} + 2087289393 q^{96} + 1949310583 q^{97} + 6695989160 q^{98} + 1234191326 q^{99}+O(q^{100}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9 + 23763 * q^10 + 78370 * q^11 + 271339 * q^12 + 114452 * q^13 - 376208 * q^14 - 255820 * q^15 + 412586 * q^16 + 726937 * q^17 + 577055 * q^18 + 544263 * q^19 + 3642183 * q^20 + 3137394 * q^21 + 5269148 * q^22 + 5575241 * q^23 + 16215113 * q^24 + 10874708 * q^25 + 8009180 * q^26 + 8350126 * q^27 + 12534764 * q^28 + 8223345 * q^29 + 30612012 * q^30 + 13054147 * q^31 + 37111710 * q^32 + 36024808 * q^33 + 27991291 * q^34 + 17826330 * q^35 + 84105953 * q^36 + 46733879 * q^37 + 15733789 * q^38 + 8689898 * q^39 + 52241669 * q^40 + 53667013 * q^41 + 7708286 * q^42 + 58119617 * q^43 + 81727236 * q^44 + 124361968 * q^45 + 146859355 * q^46 + 122945511 * q^47 + 86356095 * q^48 + 111396073 * q^49 - 96642133 * q^50 - 187132423 * q^51 - 54447944 * q^52 - 993146 * q^53 - 219468490 * q^54 - 248155792 * q^55 - 141048116 * q^56 - 402917960 * q^57 - 466599837 * q^58 - 95519644 * q^59 - 621611940 * q^60 - 311752038 * q^61 - 212471691 * q^62 - 928966350 * q^63 - 829842590 * q^64 - 107969830 * q^65 - 978530932 * q^66 - 292438130 * q^67 - 88281129 * q^68 + 78577726 * q^69 - 1650972530 * q^70 - 13576908 * q^71 - 706943493 * q^72 - 501490738 * q^73 - 494831691 * q^74 - 641914030 * q^75 - 1248630771 * q^76 + 787365348 * q^77 - 946670550 * q^78 + 740350275 * q^79 - 27802861 * q^80 + 1582210525 * q^81 - 1600400057 * q^82 + 754109940 * q^83 - 1955423842 * q^84 + 1071609956 * q^85 + 164102448 * q^86 + 186301257 * q^87 + 1863375104 * q^88 + 1470581868 * q^89 - 698098630 * q^90 + 2895349644 * q^91 + 1041082071 * q^92 + 4540331515 * q^93 - 706582361 * q^94 + 3297255729 * q^95 + 2087289393 * q^96 + 1949310583 * q^97 + 6695989160 * q^98 + 1234191326 * q^99

Introduction

L-functions

Modular forms

Varieties

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