LMFDB - Embedded newform 43.10.a.b.1.2

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			1.2
Root			$39.1708$ 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)

$f(q)$	$=$	$q-36.1708 q^{2} -228.603 q^{3} +796.325 q^{4} +2349.81 q^{5} +8268.76 q^{6} +528.884 q^{7} -10284.3 q^{8} +32576.5 q^{9} +O(q^{10})$	\(q-36.1708 q^{2} -228.603 q^{3} +796.325 q^{4} +2349.81 q^{5} +8268.76 q^{6} +528.884 q^{7} -10284.3 q^{8} +32576.5 q^{9} -84994.4 q^{10} -51267.8 q^{11} -182043. q^{12} +73819.7 q^{13} -19130.1 q^{14} -537174. q^{15} -35728.9 q^{16} +454076. q^{17} -1.17832e6 q^{18} +296932. q^{19} +1.87121e6 q^{20} -120905. q^{21} +1.85440e6 q^{22} -2.55033e6 q^{23} +2.35102e6 q^{24} +3.56847e6 q^{25} -2.67012e6 q^{26} -2.94750e6 q^{27} +421163. q^{28} -1.91189e6 q^{29} +1.94300e7 q^{30} -4.32035e6 q^{31} +6.55788e6 q^{32} +1.17200e7 q^{33} -1.64243e7 q^{34} +1.24278e6 q^{35} +2.59415e7 q^{36} -857446. q^{37} -1.07403e7 q^{38} -1.68754e7 q^{39} -2.41660e7 q^{40} +2.16048e7 q^{41} +4.37321e6 q^{42} +3.41880e6 q^{43} -4.08258e7 q^{44} +7.65485e7 q^{45} +9.22473e7 q^{46} +4.95273e7 q^{47} +8.16774e6 q^{48} -4.00739e7 q^{49} -1.29074e8 q^{50} -1.03803e8 q^{51} +5.87845e7 q^{52} +1.17290e7 q^{53} +1.06613e8 q^{54} -1.20469e8 q^{55} -5.43918e6 q^{56} -6.78797e7 q^{57} +6.91544e7 q^{58} -9.89808e7 q^{59} -4.27765e8 q^{60} -5.52008e7 q^{61} +1.56270e8 q^{62} +1.72292e7 q^{63} -2.18910e8 q^{64} +1.73462e8 q^{65} -4.23921e8 q^{66} +2.34121e8 q^{67} +3.61592e8 q^{68} +5.83013e8 q^{69} -4.49521e7 q^{70} +2.83452e8 q^{71} -3.35025e8 q^{72} -2.61207e8 q^{73} +3.10145e7 q^{74} -8.15765e8 q^{75} +2.36454e8 q^{76} -2.71147e7 q^{77} +6.10397e8 q^{78} +5.71481e8 q^{79} -8.39560e7 q^{80} +3.26045e7 q^{81} -7.81463e8 q^{82} +7.94608e8 q^{83} -9.62793e7 q^{84} +1.06699e9 q^{85} -1.23661e8 q^{86} +4.37064e8 q^{87} +5.27251e8 q^{88} -1.12630e8 q^{89} -2.76882e9 q^{90} +3.90420e7 q^{91} -2.03089e9 q^{92} +9.87647e8 q^{93} -1.79144e9 q^{94} +6.97733e8 q^{95} -1.49915e9 q^{96} -6.40977e7 q^{97} +1.44950e9 q^{98} -1.67012e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−36.1708	−1.59854	−0.799269	−	0.600974i	$-0.794780\pi$
$2$	−36.1708	−1.59854	−0.799269	+	0.600974i	$0.794780\pi$
$3$	−228.603	−1.62943	−0.814717	−	0.579858i	$-0.803108\pi$
$3$	−228.603	−1.62943	−0.814717	+	0.579858i	$0.803108\pi$
$4$	796.325	1.55532
$5$	2349.81	1.68139	0.840693	−	0.541512i	$-0.182148\pi$
$5$	2349.81	1.68139	0.840693	+	0.541512i	$0.182148\pi$
$6$	8268.76	2.60471
$7$	528.884	0.0832567	0.0416283	−	0.999133i	$-0.486745\pi$
$7$	528.884	0.0832567	0.0416283	+	0.999133i	$0.486745\pi$
$8$	−10284.3	−0.887704
$9$	32576.5	1.65506
$10$	−84994.4	−2.68776
$11$	−51267.8	−1.05579	−0.527895	−	0.849310i	$-0.677018\pi$
$11$	−51267.8	−1.05579	−0.527895	+	0.849310i	$0.677018\pi$
$12$	−182043.	−2.53430
$13$	73819.7	0.716848	0.358424	−	0.933559i	$-0.383314\pi$
$13$	73819.7	0.716848	0.358424	+	0.933559i	$0.383314\pi$
$14$	−19130.1	−0.133089
$15$	−537174.	−2.73971
$16$	−35728.9	−0.136295
$17$	454076.	1.31859	0.659294	−	0.751886i	$-0.270855\pi$
$17$	454076.	1.31859	0.659294	+	0.751886i	$0.270855\pi$
$18$	−1.17832e6	−2.64567
$19$	296932.	0.522716	0.261358	−	0.965242i	$-0.415830\pi$
$19$	296932.	0.522716	0.261358	+	0.965242i	$0.415830\pi$
$20$	1.87121e6	2.61510
$21$	−120905.	−0.135661
$22$	1.85440e6	1.68772
$23$	−2.55033e6	−1.90029	−0.950146	−	0.311804i	$-0.899067\pi$
$23$	−2.55033e6	−1.90029	−0.950146	+	0.311804i	$0.899067\pi$
$24$	2.35102e6	1.44646
$25$	3.56847e6	1.82706
$26$	−2.67012e6	−1.14591
$27$	−2.94750e6	−1.06737
$28$	421163.	0.129491
$29$	−1.91189e6	−0.501962	−0.250981	−	0.967992i	$-0.580753\pi$
$29$	−1.91189e6	−0.501962	−0.250981	+	0.967992i	$0.580753\pi$
$30$	1.94300e7	4.37953
$31$	−4.32035e6	−0.840217	−0.420108	−	0.907474i	$-0.638008\pi$
$31$	−4.32035e6	−0.840217	−0.420108	+	0.907474i	$0.638008\pi$
$32$	6.55788e6	1.10558
$33$	1.17200e7	1.72034
$34$	−1.64243e7	−2.10781
$35$	1.24278e6	0.139987
$36$	2.59415e7	2.57415
$37$	−857446.	−0.0752140	−0.0376070	−	0.999293i	$-0.511974\pi$
$37$	−857446.	−0.0752140	−0.0376070	+	0.999293i	$0.511974\pi$
$38$	−1.07403e7	−0.835581
$39$	−1.68754e7	−1.16806
$40$	−2.41660e7	−1.49257
$41$	2.16048e7	1.19405	0.597026	−	0.802222i	$-0.296349\pi$
$41$	2.16048e7	1.19405	0.597026	+	0.802222i	$0.296349\pi$
$42$	4.37321e6	0.216860
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	−4.08258e7	−1.64209
$45$	7.65485e7	2.78279
$46$	9.22473e7	3.03769
$47$	4.95273e7	1.48049	0.740243	−	0.672339i	$-0.234710\pi$
$47$	4.95273e7	1.48049	0.740243	+	0.672339i	$0.234710\pi$
$48$	8.16774e6	0.222083
$49$	−4.00739e7	−0.993068
$50$	−1.29074e8	−2.92062
$51$	−1.03803e8	−2.14855
$52$	5.87845e7	1.11493
$53$	1.17290e7	0.204184	0.102092	−	0.994775i	$-0.467446\pi$
$53$	1.17290e7	0.204184	0.102092	+	0.994775i	$0.467446\pi$
$54$	1.06613e8	1.70624
$55$	−1.20469e8	−1.77519
$56$	−5.43918e6	−0.0739072
$57$	−6.78797e7	−0.851732
$58$	6.91544e7	0.802406
$59$	−9.89808e7	−1.06345	−0.531725	−	0.846917i	$-0.678456\pi$
$59$	−9.89808e7	−1.06345	−0.531725	+	0.846917i	$0.678456\pi$
$60$	−4.27765e8	−4.26113
$61$	−5.52008e7	−0.510459	−0.255230	−	0.966880i	$-0.582151\pi$
$61$	−5.52008e7	−0.510459	−0.255230	+	0.966880i	$0.582151\pi$
$62$	1.56270e8	1.34312
$63$	1.72292e7	0.137795
$64$	−2.18910e8	−1.63101
$65$	1.73462e8	1.20530
$66$	−4.23921e8	−2.75003
$67$	2.34121e8	1.41940	0.709699	−	0.704505i	$-0.248831\pi$
$67$	2.34121e8	1.41940	0.709699	+	0.704505i	$0.248831\pi$
$68$	3.61592e8	2.05083
$69$	5.83013e8	3.09640
$70$	−4.49521e7	−0.223774
$71$	2.83452e8	1.32379	0.661893	−	0.749599i	$-0.269753\pi$
$71$	2.83452e8	1.32379	0.661893	+	0.749599i	$0.269753\pi$
$72$	−3.35025e8	−1.46920
$73$	−2.61207e8	−1.07654	−0.538272	−	0.842771i	$-0.680923\pi$
$73$	−2.61207e8	−1.07654	−0.538272	+	0.842771i	$0.680923\pi$
$74$	3.10145e7	0.120232
$75$	−8.15765e8	−2.97707
$76$	2.36454e8	0.812992
$77$	−2.71147e7	−0.0879015
$78$	6.10397e8	1.86718
$79$	5.71481e8	1.65075	0.825373	−	0.564588i	$-0.190965\pi$
$79$	5.71481e8	1.65075	0.825373	+	0.564588i	$0.190965\pi$
$80$	−8.39560e7	−0.229164
$81$	3.26045e7	0.0841580
$82$	−7.81463e8	−1.90874
$83$	7.94608e8	1.83781	0.918907	−	0.394474i	$-0.129073\pi$
$83$	7.94608e8	1.83781	0.918907	+	0.394474i	$0.129073\pi$
$84$	−9.62793e7	−0.210997
$85$	1.06699e9	2.21705
$86$	−1.23661e8	−0.243775
$87$	4.37064e8	0.817915
$88$	5.27251e8	0.937228
$89$	−1.12630e8	−0.190282	−0.0951411	−	0.995464i	$-0.530330\pi$
$89$	−1.12630e8	−0.190282	−0.0951411	+	0.995464i	$0.530330\pi$
$90$	−2.76882e9	−4.44839
$91$	3.90420e7	0.0596824
$92$	−2.03089e9	−2.95557
$93$	9.87647e8	1.36908
$94$	−1.79144e9	−2.36661
$95$	6.97733e8	0.878887
$96$	−1.49915e9	−1.80146
$97$	−6.40977e7	−0.0735139	−0.0367569	−	0.999324i	$-0.511703\pi$
$97$	−6.40977e7	−0.0735139	−0.0367569	+	0.999324i	$0.511703\pi$
$98$	1.44950e9	1.58746
$99$	−1.67012e9	−1.74739
$100$	2.84166e9	2.84166
$101$	7.85240e8	0.750856	0.375428	−	0.926852i	$-0.377496\pi$
$101$	7.85240e8	0.750856	0.375428	+	0.926852i	$0.377496\pi$
$102$	3.75465e9	3.43454
$103$	−1.71560e9	−1.50192	−0.750962	−	0.660345i	$-0.770410\pi$
$103$	−1.71560e9	−1.50192	−0.750962	+	0.660345i	$0.770410\pi$
$104$	−7.59181e8	−0.636349
$105$	−2.84103e8	−0.228099
$106$	−4.24249e8	−0.326395
$107$	2.23217e9	1.64627	0.823135	−	0.567846i	$-0.192223\pi$
$107$	2.23217e9	1.64627	0.823135	+	0.567846i	$0.192223\pi$
$108$	−2.34717e9	−1.66011
$109$	−9.23194e8	−0.626432	−0.313216	−	0.949682i	$-0.601406\pi$
$109$	−9.23194e8	−0.626432	−0.313216	+	0.949682i	$0.601406\pi$
$110$	4.35747e9	2.83771
$111$	1.96015e8	0.122556
$112$	−1.88964e7	−0.0113474
$113$	1.91757e9	1.10636	0.553182	−	0.833060i	$-0.313413\pi$
$113$	1.91757e9	1.10636	0.553182	+	0.833060i	$0.313413\pi$
$114$	2.45526e9	1.36153
$115$	−5.99278e9	−3.19513
$116$	−1.52248e9	−0.780713
$117$	2.40479e9	1.18642
$118$	3.58021e9	1.69996
$119$	2.40154e8	0.109781
$120$	5.52444e9	2.43205
$121$	2.70437e8	0.114692
$122$	1.99666e9	0.815988
$123$	−4.93894e9	−1.94563
$124$	−3.44040e9	−1.30681
$125$	3.79576e9	1.39060
$126$	−6.23193e8	−0.220270
$127$	4.91327e9	1.67592	0.837961	−	0.545730i	$-0.183748\pi$
$127$	4.91327e9	1.67592	0.837961	+	0.545730i	$0.183748\pi$
$128$	4.56053e9	1.50165
$129$	−7.81549e8	−0.248486
$130$	−6.27426e9	−1.92671
$131$	−2.12399e9	−0.630132	−0.315066	−	0.949070i	$-0.602027\pi$
$131$	−2.12399e9	−0.630132	−0.315066	+	0.949070i	$0.602027\pi$
$132$	9.33292e9	2.67568
$133$	1.57043e8	0.0435196
$134$	−8.46835e9	−2.26896
$135$	−6.92605e9	−1.79467
$136$	−4.66984e9	−1.17051
$137$	5.24047e9	1.27095	0.635474	−	0.772122i	$-0.280805\pi$
$137$	5.24047e9	1.27095	0.635474	+	0.772122i	$0.280805\pi$
$138$	−2.10880e10	−4.94972
$139$	1.77009e8	0.0402188	0.0201094	−	0.999798i	$-0.493599\pi$
$139$	1.77009e8	0.0402188	0.0201094	+	0.999798i	$0.493599\pi$
$140$	9.89653e8	0.217724
$141$	−1.13221e10	−2.41236
$142$	−1.02527e10	−2.11612
$143$	−3.78457e9	−0.756841
$144$	−1.16392e9	−0.225576
$145$	−4.49257e9	−0.843992
$146$	9.44806e9	1.72090
$147$	9.16103e9	1.61814
$148$	−6.82805e8	−0.116982
$149$	−2.95611e9	−0.491341	−0.245670	−	0.969353i	$-0.579008\pi$
$149$	−2.95611e9	−0.491341	−0.245670	+	0.969353i	$0.579008\pi$
$150$	2.95069e10	4.75896
$151$	2.05821e9	0.322177	0.161088	−	0.986940i	$-0.448500\pi$
$151$	2.05821e9	0.322177	0.161088	+	0.986940i	$0.448500\pi$
$152$	−3.05373e9	−0.464017
$153$	1.47922e10	2.18234
$154$	9.80759e8	0.140514
$155$	−1.01520e10	−1.41273
$156$	−1.34383e10	−1.81671
$157$	−5.72168e9	−0.751580	−0.375790	−	0.926705i	$-0.622629\pi$
$157$	−5.72168e9	−0.751580	−0.375790	+	0.926705i	$0.622629\pi$
$158$	−2.06709e10	−2.63878
$159$	−2.68130e9	−0.332704
$160$	1.54098e10	1.85890
$161$	−1.34883e9	−0.158212
$162$	−1.17933e9	−0.134530
$163$	−5.28208e8	−0.0586086	−0.0293043	−	0.999571i	$-0.509329\pi$
$163$	−5.28208e8	−0.0586086	−0.0293043	+	0.999571i	$0.509329\pi$
$164$	1.72045e10	1.85714
$165$	2.75397e10	2.89256
$166$	−2.87416e10	−2.93781
$167$	5.95488e9	0.592446	0.296223	−	0.955119i	$-0.404273\pi$
$167$	5.95488e9	0.592446	0.296223	+	0.955119i	$0.404273\pi$
$168$	1.24341e9	0.120427
$169$	−5.15515e9	−0.486129
$170$	−3.85939e10	−3.54404
$171$	9.67301e9	0.865125
$172$	2.72248e9	0.237184
$173$	5.33877e9	0.453142	0.226571	−	0.973995i	$-0.427249\pi$
$173$	5.33877e9	0.453142	0.226571	+	0.973995i	$0.427249\pi$
$174$	−1.58089e10	−1.30747
$175$	1.88731e9	0.152115
$176$	1.83174e9	0.143899
$177$	2.26273e10	1.73282
$178$	4.07390e9	0.304173
$179$	2.02033e9	0.147090	0.0735451	−	0.997292i	$-0.476569\pi$
$179$	2.02033e9	0.147090	0.0735451	+	0.997292i	$0.476569\pi$
$180$	6.09575e10	4.32814
$181$	2.37778e10	1.64672	0.823358	−	0.567522i	$-0.192098\pi$
$181$	2.37778e10	1.64672	0.823358	+	0.567522i	$0.192098\pi$
$182$	−1.41218e9	−0.0954045
$183$	1.26191e10	0.831760
$184$	2.62282e10	1.68690
$185$	−2.01483e9	−0.126464
$186$	−3.57239e10	−2.18852
$187$	−2.32795e10	−1.39215
$188$	3.94398e10	2.30263
$189$	−1.55888e9	−0.0888660
$190$	−2.52376e10	−1.40493
$191$	1.62750e9	0.0884855	0.0442428	−	0.999021i	$-0.485912\pi$
$191$	1.62750e9	0.0884855	0.0442428	+	0.999021i	$0.485912\pi$
$192$	5.00437e10	2.65762
$193$	2.16242e10	1.12184	0.560921	−	0.827870i	$-0.310447\pi$
$193$	2.16242e10	1.12184	0.560921	+	0.827870i	$0.310447\pi$
$194$	2.31846e9	0.117515
$195$	−3.96540e10	−1.96395
$196$	−3.19118e10	−1.54454
$197$	1.58437e10	0.749476	0.374738	−	0.927131i	$-0.377733\pi$
$197$	1.58437e10	0.749476	0.374738	+	0.927131i	$0.377733\pi$
$198$	6.04097e10	2.79327
$199$	1.25307e10	0.566419	0.283210	−	0.959058i	$-0.408601\pi$
$199$	1.25307e10	0.566419	0.283210	+	0.959058i	$0.408601\pi$
$200$	−3.66991e10	−1.62189
$201$	−5.35209e10	−2.31282
$202$	−2.84028e10	−1.20027
$203$	−1.01117e9	−0.0417917
$204$	−8.26613e10	−3.34169
$205$	5.07672e10	2.00766
$206$	6.20545e10	2.40088
$207$	−8.30807e10	−3.14509
$208$	−2.63749e9	−0.0977026
$209$	−1.52230e10	−0.551878
$210$	1.02762e10	0.364625
$211$	3.48797e9	0.121144	0.0605720	−	0.998164i	$-0.480708\pi$
$211$	3.48797e9	0.121144	0.0605720	+	0.998164i	$0.480708\pi$
$212$	9.34013e9	0.317571
$213$	−6.47982e10	−2.15702
$214$	−8.07395e10	−2.63162
$215$	8.03353e9	0.256409
$216$	3.03128e10	0.947511
$217$	−2.28496e9	−0.0699536
$218$	3.33926e10	1.00137
$219$	5.97128e10	1.75416
$220$	−9.59328e10	−2.76099
$221$	3.35198e10	0.945227
$222$	−7.09001e9	−0.195911
$223$	−2.93916e10	−0.795887	−0.397943	−	0.917410i	$-0.630276\pi$
$223$	−2.93916e10	−0.795887	−0.397943	+	0.917410i	$0.630276\pi$
$224$	3.46836e9	0.0920466
$225$	1.16248e11	3.02389
$226$	−6.93600e10	−1.76856
$227$	3.58447e10	0.896002	0.448001	−	0.894033i	$-0.352136\pi$
$227$	3.58447e10	0.896002	0.448001	+	0.894033i	$0.352136\pi$
$228$	−5.40543e10	−1.32472
$229$	4.99324e10	1.19984	0.599919	−	0.800061i	$-0.295200\pi$
$229$	4.99324e10	1.19984	0.599919	+	0.800061i	$0.295200\pi$
$230$	2.16763e11	5.10753
$231$	6.19851e9	0.143230
$232$	1.96623e10	0.445594
$233$	−6.79102e9	−0.150950	−0.0754750	−	0.997148i	$-0.524047\pi$
$233$	−6.79102e9	−0.150950	−0.0754750	+	0.997148i	$0.524047\pi$
$234$	−8.69830e10	−1.89654
$235$	1.16380e11	2.48927
$236$	−7.88209e10	−1.65401
$237$	−1.30643e11	−2.68978
$238$	−8.68654e9	−0.175489
$239$	5.07213e10	1.00554	0.502771	−	0.864420i	$-0.332314\pi$
$239$	5.07213e10	1.00554	0.502771	+	0.864420i	$0.332314\pi$
$240$	1.91926e10	0.373408
$241$	−5.99306e10	−1.14438	−0.572192	−	0.820120i	$-0.693907\pi$
$241$	−5.99306e10	−1.14438	−0.572192	+	0.820120i	$0.693907\pi$
$242$	−9.78193e9	−0.183339
$243$	5.05621e10	0.930244
$244$	−4.39578e10	−0.793929
$245$	−9.41659e10	−1.66973
$246$	1.78645e11	3.11016
$247$	2.19194e10	0.374708
$248$	4.44316e10	0.745863
$249$	−1.81650e11	−2.99460
$250$	−1.37296e11	−2.22293
$251$	3.27284e10	0.520466	0.260233	−	0.965546i	$-0.416201\pi$
$251$	3.27284e10	0.520466	0.260233	+	0.965546i	$0.416201\pi$
$252$	1.37200e10	0.214315
$253$	1.30750e11	2.00631
$254$	−1.77717e11	−2.67902
$255$	−2.43918e11	−3.61254
$256$	−5.28756e10	−0.769441
$257$	1.64331e10	0.234975	0.117487	−	0.993074i	$-0.462516\pi$
$257$	1.64331e10	0.234975	0.117487	+	0.993074i	$0.462516\pi$
$258$	2.82692e10	0.397215
$259$	−4.53489e8	−0.00626207
$260$	1.38132e11	1.87463
$261$	−6.22826e10	−0.830777
$262$	7.68264e10	1.00729
$263$	−5.50775e10	−0.709861	−0.354930	−	0.934893i	$-0.615495\pi$
$263$	−5.50775e10	−0.709861	−0.354930	+	0.934893i	$0.615495\pi$
$264$	−1.20531e11	−1.52715
$265$	2.75610e10	0.343312
$266$	−5.68035e9	−0.0695677
$267$	2.57475e10	0.310052
$268$	1.86437e11	2.20762
$269$	−3.94908e10	−0.459844	−0.229922	−	0.973209i	$-0.573847\pi$
$269$	−3.94908e10	−0.459844	−0.229922	+	0.973209i	$0.573847\pi$
$270$	2.50521e11	2.86884
$271$	5.48730e10	0.618012	0.309006	−	0.951060i	$-0.400004\pi$
$271$	5.48730e10	0.618012	0.309006	+	0.951060i	$0.400004\pi$
$272$	−1.62236e10	−0.179717
$273$	−8.92514e9	−0.0972485
$274$	−1.89552e11	−2.03166
$275$	−1.82948e11	−1.92899
$276$	4.64268e11	4.81591
$277$	3.77794e9	0.0385564	0.0192782	−	0.999814i	$-0.493863\pi$
$277$	3.77794e9	0.0385564	0.0192782	+	0.999814i	$0.493863\pi$
$278$	−6.40257e9	−0.0642913
$279$	−1.40742e11	−1.39061
$280$	−1.27810e10	−0.124267
$281$	6.74050e10	0.644931	0.322466	−	0.946581i	$-0.395488\pi$
$281$	6.74050e10	0.644931	0.322466	+	0.946581i	$0.395488\pi$
$282$	4.09530e11	3.85624
$283$	−1.64810e11	−1.52737	−0.763685	−	0.645589i	$-0.776612\pi$
$283$	−1.64810e11	−1.52737	−0.763685	+	0.645589i	$0.776612\pi$
$284$	2.25720e11	2.05891
$285$	−1.59504e11	−1.43209
$286$	1.36891e11	1.20984
$287$	1.14264e10	0.0994128
$288$	2.13633e11	1.82979
$289$	8.75976e10	0.738672
$290$	1.62500e11	1.34915
$291$	1.46529e10	0.119786
$292$	−2.08006e11	−1.67437
$293$	−8.34203e10	−0.661253	−0.330626	−	0.943762i	$-0.607260\pi$
$293$	−8.34203e10	−0.661253	−0.330626	+	0.943762i	$0.607260\pi$
$294$	−3.31361e11	−2.58666
$295$	−2.32586e11	−1.78807
$296$	8.81819e9	0.0667678
$297$	1.51112e11	1.12692
$298$	1.06925e11	0.785427
$299$	−1.88264e11	−1.36222
$300$	−6.49614e11	−4.63031
$301$	1.80815e9	0.0126965
$302$	−7.44472e10	−0.515012
$303$	−1.79509e11	−1.22347
$304$	−1.06090e10	−0.0712435
$305$	−1.29711e11	−0.858279
$306$	−5.35046e11	−3.48855
$307$	2.25539e11	1.44910	0.724550	−	0.689222i	$-0.242048\pi$
$307$	2.25539e11	1.44910	0.724550	+	0.689222i	$0.242048\pi$
$308$	−2.15921e10	−0.136715
$309$	3.92191e11	2.44729
$310$	3.67205e11	2.25830
$311$	2.16366e11	1.31150	0.655749	−	0.754979i	$-0.272353\pi$
$311$	2.16366e11	1.31150	0.655749	+	0.754979i	$0.272353\pi$
$312$	1.73551e11	1.03689
$313$	1.51372e11	0.891445	0.445723	−	0.895171i	$-0.352947\pi$
$313$	1.51372e11	0.891445	0.445723	+	0.895171i	$0.352947\pi$
$314$	2.06958e11	1.20143
$315$	4.04853e10	0.231686
$316$	4.55085e11	2.56744
$317$	8.10873e10	0.451010	0.225505	−	0.974242i	$-0.427597\pi$
$317$	8.10873e10	0.451010	0.225505	+	0.974242i	$0.427597\pi$
$318$	9.69846e10	0.531840
$319$	9.80182e10	0.529967
$320$	−5.14398e11	−2.74236
$321$	−5.10282e11	−2.68249
$322$	4.87881e10	0.252908
$323$	1.34830e11	0.689247
$324$	2.59638e10	0.130893
$325$	2.63424e11	1.30972
$326$	1.91057e10	0.0936880
$327$	2.11045e11	1.02073
$328$	−2.22190e11	−1.05996
$329$	2.61942e10	0.123260
$330$	−9.96133e11	−4.62386
$331$	−5.35832e10	−0.245360	−0.122680	−	0.992446i	$-0.539149\pi$
$331$	−5.35832e10	−0.245360	−0.122680	+	0.992446i	$0.539149\pi$
$332$	6.32766e11	2.85839
$333$	−2.79326e10	−0.124484
$334$	−2.15393e11	−0.947047
$335$	5.50140e11	2.38656
$336$	4.31978e9	0.0184899
$337$	−3.54885e11	−1.49883	−0.749416	−	0.662099i	$-0.769666\pi$
$337$	−3.54885e11	−1.49883	−0.749416	+	0.662099i	$0.769666\pi$
$338$	1.86466e11	0.777095
$339$	−4.38363e11	−1.80275
$340$	8.49673e11	3.44823
$341$	2.21495e11	0.887092
$342$	−3.49880e11	−1.38294
$343$	−4.25368e10	−0.165936
$344$	−3.51598e10	−0.135374
$345$	1.36997e12	5.20625
$346$	−1.93108e11	−0.724364
$347$	−3.80899e11	−1.41035	−0.705175	−	0.709034i	$-0.749131\pi$
$347$	−3.80899e11	−1.41035	−0.705175	+	0.709034i	$0.749131\pi$
$348$	3.48045e11	1.27212
$349$	1.88143e11	0.678849	0.339425	−	0.940633i	$-0.389768\pi$
$349$	1.88143e11	0.678849	0.339425	+	0.940633i	$0.389768\pi$
$350$	−6.82654e10	−0.243161
$351$	−2.17583e11	−0.765145
$352$	−3.36208e11	−1.16726
$353$	−3.86343e11	−1.32430	−0.662151	−	0.749371i	$-0.730356\pi$
$353$	−3.86343e11	−1.32430	−0.662151	+	0.749371i	$0.730356\pi$
$354$	−8.18449e11	−2.76998
$355$	6.66059e11	2.22579
$356$	−8.96899e10	−0.295950
$357$	−5.48999e10	−0.178881
$358$	−7.30769e10	−0.235129
$359$	2.59033e11	0.823058	0.411529	−	0.911397i	$-0.364995\pi$
$359$	2.59033e11	0.823058	0.411529	+	0.911397i	$0.364995\pi$
$360$	−7.87245e11	−2.47029
$361$	−2.34519e11	−0.726768
$362$	−8.60063e11	−2.63234
$363$	−6.18229e10	−0.186883
$364$	3.10901e10	0.0928253
$365$	−6.13787e11	−1.81009
$366$	−4.56442e11	−1.32960
$367$	−2.42405e11	−0.697501	−0.348750	−	0.937216i	$-0.613394\pi$
$367$	−2.42405e11	−0.697501	−0.348750	+	0.937216i	$0.613394\pi$
$368$	9.11203e10	0.259000
$369$	7.03810e11	1.97623
$370$	7.28781e10	0.202157
$371$	6.20330e9	0.0169997
$372$	7.86488e11	2.12936
$373$	−1.03316e11	−0.276362	−0.138181	−	0.990407i	$-0.544125\pi$
$373$	−1.03316e11	−0.276362	−0.138181	+	0.990407i	$0.544125\pi$
$374$	8.42037e11	2.22541
$375$	−8.67723e11	−2.26590
$376$	−5.09352e11	−1.31423
$377$	−1.41135e11	−0.359831
$378$	5.63860e10	0.142056
$379$	5.08681e11	1.26639	0.633197	−	0.773991i	$-0.281742\pi$
$379$	5.08681e11	1.26639	0.633197	+	0.773991i	$0.281742\pi$
$380$	5.55623e11	1.36695
$381$	−1.12319e12	−2.73081
$382$	−5.88681e10	−0.141447
$383$	3.90685e11	0.927752	0.463876	−	0.885900i	$-0.346458\pi$
$383$	3.90685e11	0.927752	0.463876	+	0.885900i	$0.346458\pi$
$384$	−1.04255e12	−2.44685
$385$	−6.37143e10	−0.147796
$386$	−7.82163e11	−1.79331
$387$	1.11373e11	0.252394
$388$	−5.10426e10	−0.114338
$389$	−2.38021e11	−0.527037	−0.263519	−	0.964654i	$-0.584883\pi$
$389$	−2.38021e11	−0.527037	−0.263519	+	0.964654i	$0.584883\pi$
$390$	1.43432e12	3.13946
$391$	−1.15804e12	−2.50570
$392$	4.12130e11	0.881550
$393$	4.85551e11	1.02676
$394$	−5.73078e11	−1.19807
$395$	1.34287e12	2.77554
$396$	−1.32996e12	−2.71776
$397$	2.97558e11	0.601194	0.300597	−	0.953751i	$-0.402814\pi$
$397$	2.97558e11	0.601194	0.300597	+	0.953751i	$0.402814\pi$
$398$	−4.53247e11	−0.905443
$399$	−3.59004e10	−0.0709123
$400$	−1.27497e11	−0.249018
$401$	−2.48500e11	−0.479929	−0.239964	−	0.970782i	$-0.577136\pi$
$401$	−2.48500e11	−0.479929	−0.239964	+	0.970782i	$0.577136\pi$
$402$	1.93589e12	3.69713
$403$	−3.18927e11	−0.602308
$404$	6.25307e11	1.16782
$405$	7.66144e10	0.141502
$406$	3.65746e10	0.0668056
$407$	4.39593e10	0.0794102
$408$	1.06754e12	1.90728
$409$	5.62016e11	0.993101	0.496551	−	0.868008i	$-0.334600\pi$
$409$	5.62016e11	0.993101	0.496551	+	0.868008i	$0.334600\pi$
$410$	−1.83629e12	−3.20932
$411$	−1.19799e12	−2.07093
$412$	−1.36617e12	−2.33598
$413$	−5.23493e10	−0.0885393
$414$	3.00509e12	5.02755
$415$	1.86718e12	3.09007
$416$	4.84101e11	0.792530
$417$	−4.04649e10	−0.0655340
$418$	5.50629e11	0.882198
$419$	−5.37065e11	−0.851263	−0.425632	−	0.904897i	$-0.639948\pi$
$419$	−5.37065e11	−0.851263	−0.425632	+	0.904897i	$0.639948\pi$
$420$	−2.26238e11	−0.354767
$421$	−8.17247e11	−1.26790	−0.633948	−	0.773375i	$-0.718567\pi$
$421$	−8.17247e11	−1.26790	−0.633948	+	0.773375i	$0.718567\pi$
$422$	−1.26163e11	−0.193653
$423$	1.61343e12	2.45029
$424$	−1.20624e11	−0.181255
$425$	1.62036e12	2.40914
$426$	2.34380e12	3.44808
$427$	−2.91948e10	−0.0424991
$428$	1.77754e12	2.56048
$429$	8.65166e11	1.23322
$430$	−2.90579e11	−0.409879
$431$	−4.88218e10	−0.0681501	−0.0340750	−	0.999419i	$-0.510849\pi$
$431$	−4.88218e10	−0.0681501	−0.0340750	+	0.999419i	$0.510849\pi$
$432$	1.05311e11	0.145477
$433$	1.40564e11	0.192167	0.0960836	−	0.995373i	$-0.469368\pi$
$433$	1.40564e11	0.192167	0.0960836	+	0.995373i	$0.469368\pi$
$434$	8.26489e10	0.111824
$435$	1.02702e12	1.37523
$436$	−7.35162e11	−0.974303
$437$	−7.57274e11	−0.993314
$438$	−2.15986e12	−2.80409
$439$	−9.63262e11	−1.23781	−0.618905	−	0.785466i	$-0.712423\pi$
$439$	−9.63262e11	−1.23781	−0.618905	+	0.785466i	$0.712423\pi$
$440$	1.23894e12	1.57584
$441$	−1.30547e12	−1.64359
$442$	−1.21244e12	−1.51098
$443$	3.39921e11	0.419336	0.209668	−	0.977773i	$-0.432762\pi$
$443$	3.39921e11	0.419336	0.209668	+	0.977773i	$0.432762\pi$
$444$	1.56092e11	0.190615
$445$	−2.64658e11	−0.319938
$446$	1.06312e12	1.27225
$447$	6.75777e11	0.800608
$448$	−1.15778e11	−0.135792
$449$	1.07172e12	1.24444	0.622221	−	0.782842i	$-0.286231\pi$
$449$	1.07172e12	1.24444	0.622221	+	0.782842i	$0.286231\pi$
$450$	−4.20479e12	−4.83380
$451$	−1.10763e12	−1.26067
$452$	1.52701e12	1.72075
$453$	−4.70515e11	−0.524966
$454$	−1.29653e12	−1.43229
$455$	9.17413e10	0.100349
$456$	6.98092e11	0.756085
$457$	−1.93460e11	−0.207476	−0.103738	−	0.994605i	$-0.533080\pi$
$457$	−1.93460e11	−0.207476	−0.103738	+	0.994605i	$0.533080\pi$
$458$	−1.80609e12	−1.91799
$459$	−1.33839e12	−1.40743
$460$	−4.77220e12	−4.96945
$461$	5.63423e11	0.581006	0.290503	−	0.956874i	$-0.406177\pi$
$461$	5.63423e11	0.581006	0.290503	+	0.956874i	$0.406177\pi$
$462$	−2.24205e11	−0.228958
$463$	−1.39473e12	−1.41051	−0.705256	−	0.708953i	$-0.749168\pi$
$463$	−1.39473e12	−1.41051	−0.705256	+	0.708953i	$0.749168\pi$
$464$	6.83095e10	0.0684148
$465$	2.32078e12	2.30195
$466$	2.45636e11	0.241299
$467$	3.48083e11	0.338654	0.169327	−	0.985560i	$-0.445841\pi$
$467$	3.48083e11	0.338654	0.169327	+	0.985560i	$0.445841\pi$
$468$	1.91499e12	1.84527
$469$	1.23823e11	0.118174
$470$	−4.20954e12	−3.97919
$471$	1.30800e12	1.22465
$472$	1.01794e12	0.944028
$473$	−1.75274e11	−0.161006
$474$	4.72544e12	4.29972
$475$	1.05959e12	0.955033
$476$	1.91240e11	0.170745
$477$	3.82091e11	0.337936
$478$	−1.83463e12	−1.60740
$479$	−3.81601e10	−0.0331207	−0.0165603	−	0.999863i	$-0.505272\pi$
$479$	−3.81601e10	−0.0331207	−0.0165603	+	0.999863i	$0.505272\pi$
$480$	−3.52272e12	−3.02896
$481$	−6.32964e10	−0.0539170
$482$	2.16773e12	1.82934
$483$	3.08346e11	0.257796
$484$	2.15356e11	0.178383
$485$	−1.50617e11	−0.123605
$486$	−1.82887e12	−1.48703
$487$	−1.36216e12	−1.09736	−0.548679	−	0.836033i	$-0.684869\pi$
$487$	−1.36216e12	−1.09736	−0.548679	+	0.836033i	$0.684869\pi$
$488$	5.67699e11	0.453137
$489$	1.20750e11	0.0954988
$490$	3.40606e12	2.66913
$491$	−2.31224e12	−1.79542	−0.897711	−	0.440585i	$-0.854771\pi$
$491$	−2.31224e12	−1.79542	−0.897711	+	0.440585i	$0.854771\pi$
$492$	−3.93300e12	−3.02608
$493$	−8.68143e11	−0.661881
$494$	−7.92843e11	−0.598985
$495$	−3.92447e12	−2.93804
$496$	1.54361e11	0.114517
$497$	1.49913e11	0.110214
$498$	6.57042e12	4.78698
$499$	2.49495e12	1.80140	0.900699	−	0.434443i	$-0.143055\pi$
$499$	2.49495e12	1.80140	0.900699	+	0.434443i	$0.143055\pi$
$500$	3.02266e12	2.16284
$501$	−1.36131e12	−0.965352
$502$	−1.18381e12	−0.831985
$503$	−9.42957e11	−0.656804	−0.328402	−	0.944538i	$-0.606510\pi$
$503$	−9.42957e11	−0.656804	−0.328402	+	0.944538i	$0.606510\pi$
$504$	−1.77189e11	−0.122321
$505$	1.84516e12	1.26248
$506$	−4.72931e12	−3.20716
$507$	1.17849e12	0.792115
$508$	3.91256e12	2.60660
$509$	−1.06970e12	−0.706370	−0.353185	−	0.935553i	$-0.614901\pi$
$509$	−1.06970e12	−0.706370	−0.353185	+	0.935553i	$0.614901\pi$
$510$	8.82271e12	5.77479
$511$	−1.38148e11	−0.0896295
$512$	−4.22437e11	−0.271674
$513$	−8.75206e11	−0.557933
$514$	−5.94399e11	−0.375616
$515$	−4.03133e12	−2.52531
$516$	−6.22367e11	−0.386477
$517$	−2.53916e12	−1.56308
$518$	1.64030e10	0.0100102
$519$	−1.22046e12	−0.738365
$520$	−1.78393e12	−1.06995
$521$	3.14899e12	1.87241	0.936206	−	0.351453i	$-0.114312\pi$
$521$	3.14899e12	1.87241	0.936206	+	0.351453i	$0.114312\pi$
$522$	2.25281e12	1.32803
$523$	1.04032e11	0.0608007	0.0304004	−	0.999538i	$-0.490322\pi$
$523$	1.04032e11	0.0608007	0.0304004	+	0.999538i	$0.490322\pi$
$524$	−1.69139e12	−0.980059
$525$	−4.31445e11	−0.247861
$526$	1.99220e12	1.13474
$527$	−1.96177e12	−1.10790
$528$	−4.18742e11	−0.234473
$529$	4.70301e12	2.61111
$530$	−9.96903e11	−0.548796
$531$	−3.22445e12	−1.76007
$532$	1.25057e11	0.0676870
$533$	1.59486e12	0.855954
$534$	−9.31308e11	−0.495630
$535$	5.24518e12	2.76801
$536$	−2.40776e12	−1.26001
$537$	−4.61855e11	−0.239674
$538$	1.42841e12	0.735077
$539$	2.05450e12	1.04847
$540$	−5.51539e12	−2.79129
$541$	6.60907e11	0.331706	0.165853	−	0.986151i	$-0.446962\pi$
$541$	6.60907e11	0.331706	0.165853	+	0.986151i	$0.446962\pi$
$542$	−1.98480e12	−0.987916
$543$	−5.43569e12	−2.68322
$544$	2.97778e12	1.45780
$545$	−2.16933e12	−1.05327
$546$	3.22829e11	0.155455
$547$	−4.07016e11	−0.194388	−0.0971939	−	0.995265i	$-0.530987\pi$
$547$	−4.07016e11	−0.194388	−0.0971939	+	0.995265i	$0.530987\pi$
$548$	4.17312e12	1.97674
$549$	−1.79825e12	−0.844840
$550$	6.61736e12	3.08356
$551$	−5.67700e11	−0.262384
$552$	−5.99586e12	−2.74869
$553$	3.02247e11	0.137436
$554$	−1.36651e11	−0.0616338
$555$	4.60598e11	0.206064
$556$	1.40957e11	0.0625533
$557$	1.82751e12	0.804475	0.402237	−	0.915535i	$-0.368233\pi$
$557$	1.82751e12	0.804475	0.402237	+	0.915535i	$0.368233\pi$
$558$	5.09074e12	2.22294
$559$	2.52375e11	0.109318
$560$	−4.44029e10	−0.0190794
$561$	5.32177e12	2.26842
$562$	−2.43809e12	−1.03095
$563$	3.84288e12	1.61201	0.806007	−	0.591907i	$-0.201625\pi$
$563$	3.84288e12	1.61201	0.806007	+	0.591907i	$0.201625\pi$
$564$	−9.01608e12	−3.75199
$565$	4.50592e12	1.86023
$566$	5.96130e12	2.44156
$567$	1.72440e10	0.00700671
$568$	−2.91510e12	−1.17513
$569$	3.08220e12	1.23270	0.616348	−	0.787474i	$-0.288611\pi$
$569$	3.08220e12	1.23270	0.616348	+	0.787474i	$0.288611\pi$
$570$	5.76939e12	2.28925
$571$	−3.63014e12	−1.42909	−0.714547	−	0.699588i	$-0.753367\pi$
$571$	−3.63014e12	−1.42909	−0.714547	+	0.699588i	$0.753367\pi$
$572$	−3.01375e12	−1.17713
$573$	−3.72053e11	−0.144181
$574$	−4.13303e11	−0.158915
$575$	−9.10077e12	−3.47195
$576$	−7.13134e12	−2.69942
$577$	1.64327e12	0.617188	0.308594	−	0.951194i	$-0.400142\pi$
$577$	1.64327e12	0.617188	0.308594	+	0.951194i	$0.400142\pi$
$578$	−3.16847e12	−1.18080
$579$	−4.94336e12	−1.82797
$580$	−3.57754e12	−1.31268
$581$	4.20255e11	0.153010
$582$	−5.30008e11	−0.191483
$583$	−6.01322e11	−0.215575
$584$	2.68632e12	0.955653
$585$	5.65079e12	1.99484
$586$	3.01738e12	1.05704
$587$	−1.06565e12	−0.370461	−0.185231	−	0.982695i	$-0.559303\pi$
$587$	−1.06565e12	−0.370461	−0.185231	+	0.982695i	$0.559303\pi$
$588$	7.29515e12	2.51673
$589$	−1.28285e12	−0.439195
$590$	8.41281e12	2.85830
$591$	−3.62192e12	−1.22122
$592$	3.06356e10	0.0102513
$593$	−5.78864e12	−1.92234	−0.961171	−	0.275952i	$-0.911007\pi$
$593$	−5.78864e12	−1.92234	−0.961171	+	0.275952i	$0.911007\pi$
$594$	−5.46582e12	−1.80143
$595$	5.64315e11	0.184584
$596$	−2.35403e12	−0.764193
$597$	−2.86457e12	−0.922944
$598$	6.80967e12	2.17756
$599$	−4.91063e11	−0.155854	−0.0779268	−	0.996959i	$-0.524830\pi$
$599$	−4.91063e11	−0.155854	−0.0779268	+	0.996959i	$0.524830\pi$
$600$	8.38954e12	2.64276
$601$	−1.81755e11	−0.0568267	−0.0284133	−	0.999596i	$-0.509045\pi$
$601$	−1.81755e11	−0.0568267	−0.0284133	+	0.999596i	$0.509045\pi$
$602$	−6.54021e10	−0.0202959
$603$	7.62685e12	2.34919
$604$	1.63901e12	0.501089
$605$	6.35476e11	0.192841
$606$	6.49296e12	1.95576
$607$	−2.59649e12	−0.776313	−0.388156	−	0.921594i	$-0.626888\pi$
$607$	−2.59649e12	−0.776313	−0.388156	+	0.921594i	$0.626888\pi$
$608$	1.94724e12	0.577902
$609$	2.31156e11	0.0680969
$610$	4.69176e12	1.37199
$611$	3.65609e12	1.06128
$612$	1.17794e13	3.39424
$613$	4.01894e12	1.14958	0.574790	−	0.818301i	$-0.305084\pi$
$613$	4.01894e12	1.14958	0.574790	+	0.818301i	$0.305084\pi$
$614$	−8.15791e12	−2.31644
$615$	−1.16056e13	−3.27136
$616$	2.78854e11	0.0780305
$617$	3.56949e12	0.991570	0.495785	−	0.868445i	$-0.334880\pi$
$617$	3.56949e12	0.991570	0.495785	+	0.868445i	$0.334880\pi$
$618$	−1.41859e13	−3.91208
$619$	−3.00576e12	−0.822900	−0.411450	−	0.911432i	$-0.634977\pi$
$619$	−3.00576e12	−0.822900	−0.411450	+	0.911432i	$0.634977\pi$
$620$	−8.08429e12	−2.19725
$621$	7.51708e12	2.02832
$622$	−7.82613e12	−2.09648
$623$	−5.95680e10	−0.0158423
$624$	6.02940e11	0.159200
$625$	1.94963e12	0.511083
$626$	−5.47523e12	−1.42501
$627$	3.48004e12	0.899250
$628$	−4.55632e12	−1.16895
$629$	−3.89346e11	−0.0991763
$630$	−1.46438e12	−0.370358
$631$	−6.37980e12	−1.60205	−0.801023	−	0.598633i	$-0.795711\pi$
$631$	−6.37980e12	−1.60205	−0.801023	+	0.598633i	$0.795711\pi$
$632$	−5.87726e12	−1.46537
$633$	−7.97363e11	−0.197396
$634$	−2.93299e12	−0.720956
$635$	1.15452e13	2.81787
$636$	−2.13518e12	−0.517462
$637$	−2.95824e12	−0.711879
$638$	−3.54539e12	−0.847172
$639$	9.23389e12	2.19094
$640$	1.07164e13	2.52486
$641$	−3.60654e12	−0.843781	−0.421890	−	0.906647i	$-0.638633\pi$
$641$	−3.60654e12	−0.843781	−0.421890	+	0.906647i	$0.638633\pi$
$642$	1.84573e13	4.28806
$643$	3.16326e12	0.729769	0.364885	−	0.931053i	$-0.381108\pi$
$643$	3.16326e12	0.729769	0.364885	+	0.931053i	$0.381108\pi$
$644$	−1.07410e12	−0.246071
$645$	−1.83649e12	−0.417802
$646$	−4.87690e12	−1.10179
$647$	−3.30146e11	−0.0740690	−0.0370345	−	0.999314i	$-0.511791\pi$
$647$	−3.30146e11	−0.0740690	−0.0370345	+	0.999314i	$0.511791\pi$
$648$	−3.35313e11	−0.0747073
$649$	5.07453e12	1.12278
$650$	−9.52823e12	−2.09364
$651$	5.22350e11	0.113985
$652$	−4.20626e11	−0.0911552
$653$	−2.25424e12	−0.485166	−0.242583	−	0.970131i	$-0.577995\pi$
$653$	−2.25424e12	−0.485166	−0.242583	+	0.970131i	$0.577995\pi$
$654$	−7.63367e12	−1.63167
$655$	−4.99097e12	−1.05950
$656$	−7.71916e11	−0.162743
$657$	−8.50921e12	−1.78174
$658$	−9.47464e11	−0.197036
$659$	1.22496e12	0.253010	0.126505	−	0.991966i	$-0.459624\pi$
$659$	1.22496e12	0.253010	0.126505	+	0.991966i	$0.459624\pi$
$660$	2.19306e13	4.49886
$661$	6.99081e12	1.42436	0.712182	−	0.701995i	$-0.247707\pi$
$661$	6.99081e12	1.42436	0.712182	+	0.701995i	$0.247707\pi$
$662$	1.93815e12	0.392217
$663$	−7.66274e12	−1.54019
$664$	−8.17195e12	−1.63143
$665$	3.69020e11	0.0731732
$666$	1.01034e12	0.198992
$667$	4.87594e12	0.953876
$668$	4.74202e12	0.921445
$669$	6.71902e12	1.29685
$670$	−1.98990e13	−3.81500
$671$	2.83002e12	0.538938
$672$	−7.92878e11	−0.149984
$673$	−1.90115e12	−0.357230	−0.178615	−	0.983919i	$-0.557162\pi$
$673$	−1.90115e12	−0.357230	−0.178615	+	0.983919i	$0.557162\pi$
$674$	1.28365e13	2.39594
$675$	−1.05181e13	−1.95015
$676$	−4.10518e12	−0.756087
$677$	−6.40867e12	−1.17252	−0.586258	−	0.810124i	$-0.699400\pi$
$677$	−6.40867e12	−1.17252	−0.586258	+	0.810124i	$0.699400\pi$
$678$	1.58559e13	2.88176
$679$	−3.39002e10	−0.00612052
$680$	−1.09732e13	−1.96809
$681$	−8.19423e12	−1.45998
$682$	−8.01164e12	−1.41805
$683$	−5.34161e12	−0.939246	−0.469623	−	0.882867i	$-0.655610\pi$
$683$	−5.34161e12	−0.939246	−0.469623	+	0.882867i	$0.655610\pi$
$684$	7.70286e12	1.34555
$685$	1.23141e13	2.13696
$686$	1.53859e12	0.265255
$687$	−1.14147e13	−1.95506
$688$	−1.22150e11	−0.0207848
$689$	8.65834e11	0.146369
$690$	−4.95528e13	−8.32238
$691$	4.33054e12	0.722589	0.361294	−	0.932452i	$-0.382335\pi$
$691$	4.33054e12	0.722589	0.361294	+	0.932452i	$0.382335\pi$
$692$	4.25140e12	0.704781
$693$	−8.83302e11	−0.145482
$694$	1.37774e13	2.25450
$695$	4.15938e11	0.0676234
$696$	−4.49488e12	−0.726066
$697$	9.81024e12	1.57446
$698$	−6.80528e12	−1.08517
$699$	1.55245e12	0.245963
$700$	1.50291e12	0.236587
$701$	6.93122e12	1.08412	0.542061	−	0.840339i	$-0.317644\pi$
$701$	6.93122e12	1.08412	0.542061	+	0.840339i	$0.317644\pi$
$702$	7.87016e12	1.22311
$703$	−2.54603e11	−0.0393156
$704$	1.12231e13	1.72200
$705$	−2.66048e13	−4.05610
$706$	1.39743e13	2.11694
$707$	4.15301e11	0.0625137
$708$	1.80187e13	2.69510
$709$	−2.03150e11	−0.0301932	−0.0150966	−	0.999886i	$-0.504806\pi$
$709$	−2.03150e11	−0.0301932	−0.0150966	+	0.999886i	$0.504806\pi$
$710$	−2.40919e13	−3.55801
$711$	1.86169e13	2.73208
$712$	1.15831e12	0.168914
$713$	1.10183e13	1.59666
$714$	1.98577e12	0.285948
$715$	−8.89302e12	−1.27254
$716$	1.60884e12	0.228773
$717$	−1.15951e13	−1.63846
$718$	−9.36943e12	−1.31569
$719$	−5.15802e12	−0.719785	−0.359893	−	0.932994i	$-0.617187\pi$
$719$	−5.15802e12	−0.719785	−0.359893	+	0.932994i	$0.617187\pi$
$720$	−2.73499e12	−0.379280
$721$	−9.07352e11	−0.125045
$722$	8.48274e12	1.16177
$723$	1.37003e13	1.86470
$724$	1.89349e13	2.56117
$725$	−6.82252e12	−0.917115
$726$	2.23618e12	0.298739
$727$	7.87772e12	1.04591	0.522957	−	0.852359i	$-0.324829\pi$
$727$	7.87772e12	1.04591	0.522957	+	0.852359i	$0.324829\pi$
$728$	−4.01518e11	−0.0529803
$729$	−1.22004e13	−1.59993
$730$	2.22011e13	2.89349
$731$	1.55240e12	0.201083
$732$	1.00489e13	1.29366
$733$	1.47487e13	1.88706	0.943532	−	0.331283i	$-0.107481\pi$
$733$	1.47487e13	1.88706	0.943532	+	0.331283i	$0.107481\pi$
$734$	8.76798e12	1.11498
$735$	2.15267e13	2.72072
$736$	−1.67247e13	−2.10092
$737$	−1.20029e13	−1.49859
$738$	−2.54573e13	−3.15907
$739$	5.00325e12	0.617095	0.308547	−	0.951209i	$-0.400157\pi$
$739$	5.00325e12	0.617095	0.308547	+	0.951209i	$0.400157\pi$
$740$	−1.60446e12	−0.196692
$741$	−5.01086e12	−0.610562
$742$	−2.24378e11	−0.0271746
$743$	−5.49188e12	−0.661107	−0.330553	−	0.943787i	$-0.607235\pi$
$743$	−5.49188e12	−0.661107	−0.330553	+	0.943787i	$0.607235\pi$
$744$	−1.01572e13	−1.21534
$745$	−6.94630e12	−0.826133
$746$	3.73702e12	0.441774
$747$	2.58855e13	3.04169
$748$	−1.85380e13	−2.16524
$749$	1.18056e12	0.137063
$750$	3.13862e13	3.62212
$751$	−3.02382e12	−0.346877	−0.173439	−	0.984845i	$-0.555488\pi$
$751$	−3.02382e12	−0.346877	−0.173439	+	0.984845i	$0.555488\pi$
$752$	−1.76955e12	−0.201783
$753$	−7.48182e12	−0.848066
$754$	5.10496e12	0.575203
$755$	4.83641e12	0.541704
$756$	−1.24138e12	−0.138215
$757$	1.13566e13	1.25695	0.628473	−	0.777831i	$-0.283680\pi$
$757$	1.13566e13	1.25695	0.628473	+	0.777831i	$0.283680\pi$
$758$	−1.83994e13	−2.02438
$759$	−2.98898e13	−3.26915
$760$	−7.17567e12	−0.780192
$761$	−3.56778e12	−0.385626	−0.192813	−	0.981235i	$-0.561761\pi$
$761$	−3.56778e12	−0.385626	−0.192813	+	0.981235i	$0.561761\pi$
$762$	4.06266e13	4.36529
$763$	−4.88262e11	−0.0521546
$764$	1.29602e12	0.137623
$765$	3.47589e13	3.66935
$766$	−1.41314e13	−1.48305
$767$	−7.30673e12	−0.762332
$768$	1.20875e13	1.25375
$769$	−6.93809e12	−0.715437	−0.357718	−	0.933830i	$-0.616445\pi$
$769$	−6.93809e12	−0.715437	−0.357718	+	0.933830i	$0.616445\pi$
$770$	2.30460e12	0.236258
$771$	−3.75667e12	−0.382876
$772$	1.72199e13	1.74482
$773$	1.84198e11	0.0185557	0.00927785	−	0.999957i	$-0.497047\pi$
$773$	1.84198e11	0.0185557	0.00927785	+	0.999957i	$0.497047\pi$
$774$	−4.02843e12	−0.403461
$775$	−1.54171e13	−1.53512
$776$	6.59197e11	0.0652585
$777$	1.03669e11	0.0102036
$778$	8.60939e12	0.842489
$779$	6.41517e12	0.624151
$780$	−3.15775e13	−3.05458
$781$	−1.45320e13	−1.39764
$782$	4.18873e13	4.00546
$783$	5.63528e12	0.535781
$784$	1.43179e12	0.135350
$785$	−1.34449e13	−1.26370
$786$	−1.75628e13	−1.64131
$787$	−1.09203e13	−1.01473	−0.507364	−	0.861732i	$-0.669380\pi$
$787$	−1.09203e13	−1.01473	−0.507364	+	0.861732i	$0.669380\pi$
$788$	1.26167e13	1.16568
$789$	1.25909e13	1.15667
$790$	−4.85727e13	−4.43680
$791$	1.01417e12	0.0921122
$792$	1.71760e13	1.55117
$793$	−4.07491e12	−0.365922
$794$	−1.07629e13	−0.961031
$795$	−6.30054e12	−0.559404
$796$	9.97855e12	0.880965
$797$	3.77160e12	0.331103	0.165551	−	0.986201i	$-0.447060\pi$
$797$	3.77160e12	0.331103	0.165551	+	0.986201i	$0.447060\pi$
$798$	1.29855e12	0.113356
$799$	2.24892e13	1.95215
$800$	2.34016e13	2.01995
$801$	−3.66908e12	−0.314928
$802$	8.98844e12	0.767185
$803$	1.33915e13	1.13660
$804$	−4.26200e13	−3.59718
$805$	−3.16948e12	−0.266015
$806$	1.15358e13	0.962812
$807$	9.02772e12	0.749285
$808$	−8.07561e12	−0.666537
$809$	−1.00154e13	−0.822057	−0.411029	−	0.911622i	$-0.634830\pi$
$809$	−1.00154e13	−0.822057	−0.411029	+	0.911622i	$0.634830\pi$
$810$	−2.77120e12	−0.226196
$811$	−1.38525e13	−1.12443	−0.562216	−	0.826990i	$-0.690051\pi$
$811$	−1.38525e13	−1.12443	−0.562216	+	0.826990i	$0.690051\pi$
$812$	−8.05217e11	−0.0649996
$813$	−1.25442e13	−1.00701
$814$	−1.59004e12	−0.126940
$815$	−1.24119e12	−0.0985436
$816$	3.70878e12	0.292836
$817$	1.01515e12	0.0797135
$818$	−2.03285e13	−1.58751
$819$	1.27185e12	0.0987778
$820$	4.04272e13	3.12256
$821$	2.22943e12	0.171258	0.0856289	−	0.996327i	$-0.472710\pi$
$821$	2.22943e12	0.171258	0.0856289	+	0.996327i	$0.472710\pi$
$822$	4.33322e13	3.31046
$823$	4.25244e12	0.323102	0.161551	−	0.986864i	$-0.448350\pi$
$823$	4.25244e12	0.323102	0.161551	+	0.986864i	$0.448350\pi$
$824$	1.76437e13	1.33326
$825$	4.18225e13	3.14316
$826$	1.89352e12	0.141533
$827$	2.58942e12	0.192498	0.0962492	−	0.995357i	$-0.469315\pi$
$827$	2.58942e12	0.192498	0.0962492	+	0.995357i	$0.469315\pi$
$828$	−6.61592e13	−4.89164
$829$	8.43532e10	0.00620306	0.00310153	−	0.999995i	$-0.499013\pi$
$829$	8.43532e10	0.00620306	0.00310153	+	0.999995i	$0.499013\pi$
$830$	−6.75372e13	−4.93960
$831$	−8.63650e11	−0.0628251
$832$	−1.61599e13	−1.16919
$833$	−1.81966e13	−1.30945
$834$	1.46365e12	0.104759
$835$	1.39928e13	0.996130
$836$	−1.21225e13	−0.858349
$837$	1.27342e13	0.896825
$838$	1.94261e13	1.36078
$839$	1.11555e13	0.777252	0.388626	−	0.921396i	$-0.372950\pi$
$839$	1.11555e13	0.777252	0.388626	+	0.921396i	$0.372950\pi$
$840$	2.92178e12	0.202484
$841$	−1.08518e13	−0.748034
$842$	2.95605e13	2.02678
$843$	−1.54090e13	−1.05087
$844$	2.77756e12	0.188418
$845$	−1.21136e13	−0.817370
$846$	−5.83589e13	−3.91688
$847$	1.43030e11	0.00954886
$848$	−4.19065e11	−0.0278292
$849$	3.76761e13	2.48875
$850$	−5.86097e13	−3.85109
$851$	2.18677e12	0.142929
$852$	−5.16004e13	−3.35486
$853$	−1.86064e13	−1.20335	−0.601676	−	0.798741i	$-0.705500\pi$
$853$	−1.86064e13	−1.20335	−0.601676	+	0.798741i	$0.705500\pi$
$854$	1.05600e12	0.0679365
$855$	2.27297e13	1.45461
$856$	−2.29563e13	−1.46140
$857$	−2.14280e13	−1.35696	−0.678482	−	0.734617i	$-0.737362\pi$
$857$	−2.14280e13	−1.35696	−0.678482	+	0.734617i	$0.737362\pi$
$858$	−3.12937e13	−1.97135
$859$	−1.26356e13	−0.791823	−0.395912	−	0.918289i	$-0.629571\pi$
$859$	−1.26356e13	−0.791823	−0.395912	+	0.918289i	$0.629571\pi$
$860$	6.39730e12	0.398799
$861$	−2.61212e12	−0.161987
$862$	1.76592e12	0.108940
$863$	1.21317e13	0.744517	0.372258	−	0.928129i	$-0.378583\pi$
$863$	1.21317e13	0.744517	0.372258	+	0.928129i	$0.378583\pi$
$864$	−1.93293e13	−1.18006
$865$	1.25451e13	0.761906
$866$	−5.08432e12	−0.307186
$867$	−2.00251e13	−1.20362
$868$	−1.81957e12	−0.108800
$869$	−2.92986e13	−1.74284
$870$	−3.71480e13	−2.19836
$871$	1.72828e13	1.01749
$872$	9.49436e12	0.556086
$873$	−2.08808e12	−0.121670
$874$	2.73912e13	1.58785
$875$	2.00751e12	0.115777
$876$	4.75508e13	2.72828
$877$	−1.09225e13	−0.623482	−0.311741	−	0.950167i	$-0.600912\pi$
$877$	−1.09225e13	−0.623482	−0.311741	+	0.950167i	$0.600912\pi$
$878$	3.48419e13	1.97869
$879$	1.90702e13	1.07747
$880$	4.30424e12	0.241949
$881$	−3.48175e13	−1.94718	−0.973589	−	0.228306i	$-0.926681\pi$
$881$	−3.48175e13	−1.94718	−0.973589	+	0.228306i	$0.926681\pi$
$882$	4.72198e13	2.62733
$883$	8.15631e12	0.451513	0.225757	−	0.974184i	$-0.427515\pi$
$883$	8.15631e12	0.451513	0.225757	+	0.974184i	$0.427515\pi$
$884$	2.66926e13	1.47013
$885$	5.31699e13	2.91354
$886$	−1.22952e13	−0.670324
$887$	3.66947e13	1.99043	0.995214	−	0.0977191i	$-0.0311547\pi$
$887$	3.66947e13	1.99043	0.995214	+	0.0977191i	$0.0311547\pi$
$888$	−2.01587e12	−0.108794
$889$	2.59855e12	0.139532
$890$	9.57289e12	0.511432
$891$	−1.67156e12	−0.0888531
$892$	−2.34053e13	−1.23786
$893$	1.47062e13	0.773874
$894$	−2.44434e13	−1.27980
$895$	4.74739e12	0.247315
$896$	2.41199e12	0.125023
$897$	4.30379e13	2.21965
$898$	−3.87651e13	−1.98929
$899$	8.26002e12	0.421757
$900$	9.25715e13	4.70312
$901$	5.32588e12	0.269234
$902$	4.00639e13	2.01523
$903$	−4.13349e11	−0.0206882
$904$	−1.97208e13	−0.982124
$905$	5.58734e13	2.76877
$906$	1.70189e13	0.839178
$907$	−7.60400e12	−0.373086	−0.186543	−	0.982447i	$-0.559728\pi$
$907$	−7.60400e12	−0.373086	−0.186543	+	0.982447i	$0.559728\pi$
$908$	2.85441e13	1.39357
$909$	2.55804e13	1.24271
$910$	−3.31835e12	−0.160412
$911$	−1.11686e13	−0.537239	−0.268620	−	0.963246i	$-0.586567\pi$
$911$	−1.11686e13	−0.537239	−0.268620	+	0.963246i	$0.586567\pi$
$912$	2.42526e12	0.116087
$913$	−4.07378e13	−1.94035
$914$	6.99758e12	0.331658
$915$	2.96524e13	1.39851
$916$	3.97624e13	1.86613
$917$	−1.12334e12	−0.0524627
$918$	4.84106e13	2.24982
$919$	8.62422e11	0.0398841	0.0199421	−	0.999801i	$-0.493652\pi$
$919$	8.62422e11	0.0398841	0.0199421	+	0.999801i	$0.493652\pi$
$920$	6.16313e13	2.83632
$921$	−5.15589e13	−2.36121
$922$	−2.03795e13	−0.928760
$923$	2.09244e13	0.948953
$924$	4.93603e12	0.222769
$925$	−3.05977e12	−0.137420
$926$	5.04486e13	2.25476
$927$	−5.58882e13	−2.48577
$928$	−1.25379e13	−0.554958
$929$	−8.17576e12	−0.360128	−0.180064	−	0.983655i	$-0.557631\pi$
$929$	−8.17576e12	−0.360128	−0.180064	+	0.983655i	$0.557631\pi$
$930$	−8.39444e13	−3.67975
$931$	−1.18992e13	−0.519093
$932$	−5.40786e12	−0.234776
$933$	−4.94620e13	−2.13700
$934$	−1.25904e13	−0.541352
$935$	−5.47023e13	−2.34074
$936$	−2.47314e13	−1.05319
$937$	−2.67767e13	−1.13483	−0.567413	−	0.823433i	$-0.692056\pi$
$937$	−2.67767e13	−1.13483	−0.567413	+	0.823433i	$0.692056\pi$
$938$	−4.47877e12	−0.188906
$939$	−3.46040e13	−1.45255
$940$	9.26761e13	3.87162
$941$	1.41767e13	0.589416	0.294708	−	0.955587i	$-0.404778\pi$
$941$	1.41767e13	0.589416	0.294708	+	0.955587i	$0.404778\pi$
$942$	−4.73112e13	−1.95765
$943$	−5.50994e13	−2.26905
$944$	3.53647e12	0.144943
$945$	−3.66308e12	−0.149418
$946$	6.33981e12	0.257375
$947$	−1.84266e13	−0.744509	−0.372254	−	0.928131i	$-0.621415\pi$
$947$	−1.84266e13	−0.744509	−0.372254	+	0.928131i	$0.621415\pi$
$948$	−1.04034e14	−4.18348
$949$	−1.92822e13	−0.771719
$950$	−3.83263e13	−1.52666
$951$	−1.85368e13	−0.734891
$952$	−2.46980e12	−0.0974531
$953$	2.11720e13	0.831463	0.415732	−	0.909487i	$-0.363526\pi$
$953$	2.11720e13	0.831463	0.415732	+	0.909487i	$0.363526\pi$
$954$	−1.38205e13	−0.540203
$955$	3.82432e12	0.148778
$956$	4.03906e13	1.56394
$957$	−2.24073e13	−0.863546
$958$	1.38028e12	0.0529447
$959$	2.77160e12	0.105815
$960$	1.17593e14	4.46849
$961$	−7.77420e12	−0.294036
$962$	2.28948e12	0.0861884
$963$	7.27164e13	2.72467
$964$	−4.77242e13	−1.77989
$965$	5.08126e13	1.88625
$966$	−1.11531e13	−0.412097
$967$	−1.57986e13	−0.581033	−0.290516	−	0.956870i	$-0.593827\pi$
$967$	−1.57986e13	−0.581033	−0.290516	+	0.956870i	$0.593827\pi$
$968$	−2.78125e12	−0.101812
$969$	−3.08226e13	−1.12308
$970$	5.44794e12	0.197588
$971$	2.13533e13	0.770867	0.385433	−	0.922736i	$-0.374052\pi$
$971$	2.13533e13	0.770867	0.385433	+	0.922736i	$0.374052\pi$
$972$	4.02639e13	1.44683
$973$	9.36173e10	0.00334849
$974$	4.92705e13	1.75417
$975$	−6.02195e13	−2.13411
$976$	1.97226e12	0.0695729
$977$	−1.46807e13	−0.515491	−0.257745	−	0.966213i	$-0.582980\pi$
$977$	−1.46807e13	−0.515491	−0.257745	+	0.966213i	$0.582980\pi$
$978$	−4.36763e12	−0.152658
$979$	5.77428e12	0.200898
$980$	−7.49867e13	−2.59697
$981$	−3.00744e13	−1.03678
$982$	8.36356e13	2.87005
$983$	−2.00985e13	−0.686550	−0.343275	−	0.939235i	$-0.611536\pi$
$983$	−2.00985e13	−0.686550	−0.343275	+	0.939235i	$0.611536\pi$
$984$	5.07933e13	1.72714
$985$	3.72296e13	1.26016
$986$	3.14014e13	1.05804
$987$	−5.98808e12	−0.200845
$988$	1.74550e13	0.582792
$989$	−8.71906e12	−0.289792
$990$	1.41951e14	4.69657
$991$	−4.17873e13	−1.37630	−0.688150	−	0.725569i	$-0.741577\pi$
$991$	−4.17873e13	−1.37630	−0.688150	+	0.725569i	$0.741577\pi$
$992$	−2.83323e13	−0.928923
$993$	1.22493e13	0.399797
$994$	−5.42248e12	−0.176181
$995$	2.94449e13	0.952370
$996$	−1.44653e14	−4.65757
$997$	4.41289e13	1.41447	0.707236	−	0.706977i	$-0.249942\pi$
$997$	4.41289e13	1.41447	0.707236	+	0.706977i	$0.249942\pi$
$998$	−9.02444e13	−2.87960
$999$	2.52732e12	0.0802815

Twists

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

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

\(f(q)\)	\(=\)	\(q-36.1708 q^{2} -228.603 q^{3} +796.325 q^{4} +2349.81 q^{5} +8268.76 q^{6} +528.884 q^{7} -10284.3 q^{8} +32576.5 q^{9} +O(q^{10})\)	\(q-36.1708 q^{2} -228.603 q^{3} +796.325 q^{4} +2349.81 q^{5} +8268.76 q^{6} +528.884 q^{7} -10284.3 q^{8} +32576.5 q^{9} -84994.4 q^{10} -51267.8 q^{11} -182043. q^{12} +73819.7 q^{13} -19130.1 q^{14} -537174. q^{15} -35728.9 q^{16} +454076. q^{17} -1.17832e6 q^{18} +296932. q^{19} +1.87121e6 q^{20} -120905. q^{21} +1.85440e6 q^{22} -2.55033e6 q^{23} +2.35102e6 q^{24} +3.56847e6 q^{25} -2.67012e6 q^{26} -2.94750e6 q^{27} +421163. q^{28} -1.91189e6 q^{29} +1.94300e7 q^{30} -4.32035e6 q^{31} +6.55788e6 q^{32} +1.17200e7 q^{33} -1.64243e7 q^{34} +1.24278e6 q^{35} +2.59415e7 q^{36} -857446. q^{37} -1.07403e7 q^{38} -1.68754e7 q^{39} -2.41660e7 q^{40} +2.16048e7 q^{41} +4.37321e6 q^{42} +3.41880e6 q^{43} -4.08258e7 q^{44} +7.65485e7 q^{45} +9.22473e7 q^{46} +4.95273e7 q^{47} +8.16774e6 q^{48} -4.00739e7 q^{49} -1.29074e8 q^{50} -1.03803e8 q^{51} +5.87845e7 q^{52} +1.17290e7 q^{53} +1.06613e8 q^{54} -1.20469e8 q^{55} -5.43918e6 q^{56} -6.78797e7 q^{57} +6.91544e7 q^{58} -9.89808e7 q^{59} -4.27765e8 q^{60} -5.52008e7 q^{61} +1.56270e8 q^{62} +1.72292e7 q^{63} -2.18910e8 q^{64} +1.73462e8 q^{65} -4.23921e8 q^{66} +2.34121e8 q^{67} +3.61592e8 q^{68} +5.83013e8 q^{69} -4.49521e7 q^{70} +2.83452e8 q^{71} -3.35025e8 q^{72} -2.61207e8 q^{73} +3.10145e7 q^{74} -8.15765e8 q^{75} +2.36454e8 q^{76} -2.71147e7 q^{77} +6.10397e8 q^{78} +5.71481e8 q^{79} -8.39560e7 q^{80} +3.26045e7 q^{81} -7.81463e8 q^{82} +7.94608e8 q^{83} -9.62793e7 q^{84} +1.06699e9 q^{85} -1.23661e8 q^{86} +4.37064e8 q^{87} +5.27251e8 q^{88} -1.12630e8 q^{89} -2.76882e9 q^{90} +3.90420e7 q^{91} -2.03089e9 q^{92} +9.87647e8 q^{93} -1.79144e9 q^{94} +6.97733e8 q^{95} -1.49915e9 q^{96} -6.40977e7 q^{97} +1.44950e9 q^{98} -1.67012e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 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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