LMFDB - Embedded newform 43.10.a.b.1.7

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			1.7
Root			$7.34621$ 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)

$f(q)$	$=$	$q-4.34621 q^{2} +171.146 q^{3} -493.110 q^{4} -694.593 q^{5} -743.834 q^{6} -7145.50 q^{7} +4368.42 q^{8} +9607.83 q^{9} +O(q^{10})$	\(q-4.34621 q^{2} +171.146 q^{3} -493.110 q^{4} -694.593 q^{5} -743.834 q^{6} -7145.50 q^{7} +4368.42 q^{8} +9607.83 q^{9} +3018.84 q^{10} +83713.7 q^{11} -84393.7 q^{12} +121236. q^{13} +31055.8 q^{14} -118877. q^{15} +233487. q^{16} -97338.7 q^{17} -41757.6 q^{18} +398730. q^{19} +342511. q^{20} -1.22292e6 q^{21} -363837. q^{22} +962418. q^{23} +747636. q^{24} -1.47067e6 q^{25} -526917. q^{26} -1.72432e6 q^{27} +3.52352e6 q^{28} +1.65065e6 q^{29} +516662. q^{30} +9.97350e6 q^{31} -3.25141e6 q^{32} +1.43272e7 q^{33} +423054. q^{34} +4.96321e6 q^{35} -4.73772e6 q^{36} +1.77531e7 q^{37} -1.73296e6 q^{38} +2.07490e7 q^{39} -3.03427e6 q^{40} -6.93555e6 q^{41} +5.31507e6 q^{42} +3.41880e6 q^{43} -4.12801e7 q^{44} -6.67353e6 q^{45} -4.18287e6 q^{46} -4.39736e7 q^{47} +3.99602e7 q^{48} +1.07045e7 q^{49} +6.39182e6 q^{50} -1.66591e7 q^{51} -5.97828e7 q^{52} +6.49389e7 q^{53} +7.49426e6 q^{54} -5.81469e7 q^{55} -3.12145e7 q^{56} +6.82409e7 q^{57} -7.17408e6 q^{58} +5.16623e7 q^{59} +5.86193e7 q^{60} -1.26928e8 q^{61} -4.33469e7 q^{62} -6.86527e7 q^{63} -1.05414e8 q^{64} -8.42097e7 q^{65} -6.22691e7 q^{66} +3.12505e8 q^{67} +4.79987e7 q^{68} +1.64714e8 q^{69} -2.15711e7 q^{70} -9.93160e7 q^{71} +4.19710e7 q^{72} -8.48349e6 q^{73} -7.71587e7 q^{74} -2.51698e8 q^{75} -1.96618e8 q^{76} -5.98176e8 q^{77} -9.01796e7 q^{78} -1.73714e8 q^{79} -1.62178e8 q^{80} -4.84221e8 q^{81} +3.01433e7 q^{82} +5.75914e8 q^{83} +6.03035e8 q^{84} +6.76108e7 q^{85} -1.48588e7 q^{86} +2.82502e8 q^{87} +3.65696e8 q^{88} +5.03769e8 q^{89} +2.90045e7 q^{90} -8.66293e8 q^{91} -4.74579e8 q^{92} +1.70692e9 q^{93} +1.91118e8 q^{94} -2.76955e8 q^{95} -5.56465e8 q^{96} +5.36212e8 q^{97} -4.65240e7 q^{98} +8.04307e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.34621	−0.192077	−0.0960385	−	0.995378i	$-0.530617\pi$
$2$	−4.34621	−0.192077	−0.0960385	+	0.995378i	$0.530617\pi$
$3$	171.146	1.21989	0.609944	−	0.792444i	$-0.291192\pi$
$3$	171.146	1.21989	0.609944	+	0.792444i	$0.291192\pi$
$4$	−493.110	−0.963106
$5$	−694.593	−0.497010	−0.248505	−	0.968631i	$-0.579939\pi$
$5$	−694.593	−0.497010	−0.248505	+	0.968631i	$0.579939\pi$
$6$	−743.834	−0.234313
$7$	−7145.50	−1.12484	−0.562421	−	0.826851i	$-0.690130\pi$
$7$	−7145.50	−1.12484	−0.562421	+	0.826851i	$0.690130\pi$
$8$	4368.42	0.377068
$9$	9607.83	0.488129
$10$	3018.84	0.0954642
$11$	83713.7	1.72397	0.861984	−	0.506935i	$-0.169222\pi$
$11$	83713.7	1.72397	0.861984	+	0.506935i	$0.169222\pi$
$12$	−84393.7	−1.17488
$13$	121236.	1.17730	0.588650	−	0.808388i	$-0.299660\pi$
$13$	121236.	1.17730	0.588650	+	0.808388i	$0.299660\pi$
$14$	31055.8	0.216056
$15$	−118877.	−0.606297
$16$	233487.	0.890680
$17$	−97338.7	−0.282661	−0.141330	−	0.989962i	$-0.545138\pi$
$17$	−97338.7	−0.282661	−0.141330	+	0.989962i	$0.545138\pi$
$18$	−41757.6	−0.0937583
$19$	398730.	0.701920	0.350960	−	0.936390i	$-0.385855\pi$
$19$	398730.	0.701920	0.350960	+	0.936390i	$0.385855\pi$
$20$	342511.	0.478674
$21$	−1.22292e6	−1.37218
$22$	−363837.	−0.331135
$23$	962418.	0.717115	0.358557	−	0.933508i	$-0.383269\pi$
$23$	962418.	0.717115	0.358557	+	0.933508i	$0.383269\pi$
$24$	747636.	0.459981
$25$	−1.47067e6	−0.752981
$26$	−526917.	−0.226132
$27$	−1.72432e6	−0.624426
$28$	3.52352e6	1.08334
$29$	1.65065e6	0.433376	0.216688	−	0.976241i	$-0.430475\pi$
$29$	1.65065e6	0.433376	0.216688	+	0.976241i	$0.430475\pi$
$30$	516662.	0.116456
$31$	9.97350e6	1.93963	0.969817	−	0.243832i	$-0.0784046\pi$
$31$	9.97350e6	1.93963	0.969817	+	0.243832i	$0.0784046\pi$
$32$	−3.25141e6	−0.548147
$33$	1.43272e7	2.10305
$34$	423054.	0.0542926
$35$	4.96321e6	0.559057
$36$	−4.73772e6	−0.470120
$37$	1.77531e7	1.55728	0.778640	−	0.627471i	$-0.215910\pi$
$37$	1.77531e7	1.55728	0.778640	+	0.627471i	$0.215910\pi$
$38$	−1.73296e6	−0.134823
$39$	2.07490e7	1.43617
$40$	−3.03427e6	−0.187406
$41$	−6.93555e6	−0.383313	−0.191656	−	0.981462i	$-0.561386\pi$
$41$	−6.93555e6	−0.383313	−0.191656	+	0.981462i	$0.561386\pi$
$42$	5.31507e6	0.263564
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	−4.12801e7	−1.66037
$45$	−6.67353e6	−0.242605
$46$	−4.18287e6	−0.137741
$47$	−4.39736e7	−1.31447	−0.657236	−	0.753685i	$-0.728275\pi$
$47$	−4.39736e7	−1.31447	−0.657236	+	0.753685i	$0.728275\pi$
$48$	3.99602e7	1.08653
$49$	1.07045e7	0.265267
$50$	6.39182e6	0.144630
$51$	−1.66591e7	−0.344815
$52$	−5.97828e7	−1.13387
$53$	6.49389e7	1.13048	0.565241	−	0.824926i	$-0.308783\pi$
$53$	6.49389e7	1.13048	0.565241	+	0.824926i	$0.308783\pi$
$54$	7.49426e6	0.119938
$55$	−5.81469e7	−0.856830
$56$	−3.12145e7	−0.424141
$57$	6.82409e7	0.856264
$58$	−7.17408e6	−0.0832415
$59$	5.16623e7	0.555060	0.277530	−	0.960717i	$-0.410484\pi$
$59$	5.16623e7	0.555060	0.277530	+	0.960717i	$0.410484\pi$
$60$	5.86193e7	0.583928
$61$	−1.26928e8	−1.17374	−0.586872	−	0.809680i	$-0.699641\pi$
$61$	−1.26928e8	−1.17374	−0.586872	+	0.809680i	$0.699641\pi$
$62$	−4.33469e7	−0.372559
$63$	−6.86527e7	−0.549067
$64$	−1.05414e8	−0.785394
$65$	−8.42097e7	−0.585130
$66$	−6.22691e7	−0.403948
$67$	3.12505e8	1.89461	0.947306	−	0.320329i	$-0.103794\pi$
$67$	3.12505e8	1.89461	0.947306	+	0.320329i	$0.103794\pi$
$68$	4.79987e7	0.272232
$69$	1.64714e8	0.874800
$70$	−2.15711e7	−0.107382
$71$	−9.93160e7	−0.463828	−0.231914	−	0.972736i	$-0.574499\pi$
$71$	−9.93160e7	−0.463828	−0.231914	+	0.972736i	$0.574499\pi$
$72$	4.19710e7	0.184057
$73$	−8.48349e6	−0.0349640	−0.0174820	−	0.999847i	$-0.505565\pi$
$73$	−8.48349e6	−0.0349640	−0.0174820	+	0.999847i	$0.505565\pi$
$74$	−7.71587e7	−0.299118
$75$	−2.51698e8	−0.918553
$76$	−1.96618e8	−0.676024
$77$	−5.98176e8	−1.93919
$78$	−9.01796e7	−0.275856
$79$	−1.73714e8	−0.501779	−0.250889	−	0.968016i	$-0.580723\pi$
$79$	−1.73714e8	−0.501779	−0.250889	+	0.968016i	$0.580723\pi$
$80$	−1.62178e8	−0.442677
$81$	−4.84221e8	−1.24986
$82$	3.01433e7	0.0736256
$83$	5.75914e8	1.33201	0.666003	−	0.745949i	$-0.268004\pi$
$83$	5.75914e8	1.33201	0.666003	+	0.745949i	$0.268004\pi$
$84$	6.03035e8	1.32156
$85$	6.76108e7	0.140485
$86$	−1.48588e7	−0.0292915
$87$	2.82502e8	0.528670
$88$	3.65696e8	0.650053
$89$	5.03769e8	0.851093	0.425546	−	0.904937i	$-0.360082\pi$
$89$	5.03769e8	0.851093	0.425546	+	0.904937i	$0.360082\pi$
$90$	2.90045e7	0.0465988
$91$	−8.66293e8	−1.32428
$92$	−4.74579e8	−0.690658
$93$	1.70692e9	2.36614
$94$	1.91118e8	0.252480
$95$	−2.76955e8	−0.348861
$96$	−5.56465e8	−0.668678
$97$	5.36212e8	0.614983	0.307492	−	0.951551i	$-0.400510\pi$
$97$	5.36212e8	0.614983	0.307492	+	0.951551i	$0.400510\pi$
$98$	−4.65240e7	−0.0509518
$99$	8.04307e8	0.841518
$100$	7.25201e8	0.725201
$101$	4.29369e8	0.410567	0.205284	−	0.978703i	$-0.434188\pi$
$101$	4.29369e8	0.410567	0.205284	+	0.978703i	$0.434188\pi$
$102$	7.24039e7	0.0662310
$103$	4.21579e8	0.369072	0.184536	−	0.982826i	$-0.440922\pi$
$103$	4.21579e8	0.369072	0.184536	+	0.982826i	$0.440922\pi$
$104$	5.29610e8	0.443922
$105$	8.49432e8	0.681988
$106$	−2.82238e8	−0.217140
$107$	−8.25086e8	−0.608516	−0.304258	−	0.952590i	$-0.598409\pi$
$107$	−8.25086e8	−0.608516	−0.304258	+	0.952590i	$0.598409\pi$
$108$	8.50281e8	0.601389
$109$	−1.92773e9	−1.30806	−0.654029	−	0.756470i	$-0.726922\pi$
$109$	−1.92773e9	−1.30806	−0.654029	+	0.756470i	$0.726922\pi$
$110$	2.52718e8	0.164577
$111$	3.03837e9	1.89971
$112$	−1.66838e9	−1.00187
$113$	−3.26679e9	−1.88481	−0.942406	−	0.334472i	$-0.891442\pi$
$113$	−3.26679e9	−1.88481	−0.942406	+	0.334472i	$0.891442\pi$
$114$	−2.96589e8	−0.164469
$115$	−6.68489e8	−0.356413
$116$	−8.13954e8	−0.417387
$117$	1.16482e9	0.574674
$118$	−2.24535e8	−0.106614
$119$	6.95533e8	0.317948
$120$	−5.19302e8	−0.228615
$121$	4.65003e9	1.97207
$122$	5.51656e8	0.225449
$123$	−1.18699e9	−0.467599
$124$	−4.91804e9	−1.86807
$125$	2.37814e9	0.871249
$126$	2.98379e8	0.105463
$127$	3.09572e9	1.05596	0.527978	−	0.849258i	$-0.322950\pi$
$127$	3.09572e9	1.05596	0.527978	+	0.849258i	$0.322950\pi$
$128$	2.12287e9	0.699003
$129$	5.85113e8	0.186031
$130$	3.65993e8	0.112390
$131$	4.26451e8	0.126517	0.0632584	−	0.997997i	$-0.479851\pi$
$131$	4.26451e8	0.126517	0.0632584	+	0.997997i	$0.479851\pi$
$132$	−7.06491e9	−2.02546
$133$	−2.84912e9	−0.789548
$134$	−1.35821e9	−0.363912
$135$	1.19770e9	0.310346
$136$	−4.25216e8	−0.106582
$137$	−4.71666e9	−1.14391	−0.571955	−	0.820285i	$-0.693815\pi$
$137$	−4.71666e9	−1.14391	−0.571955	+	0.820285i	$0.693815\pi$
$138$	−7.15880e8	−0.168029
$139$	1.58241e9	0.359545	0.179773	−	0.983708i	$-0.442464\pi$
$139$	1.58241e9	0.359545	0.179773	+	0.983708i	$0.442464\pi$
$140$	−2.44741e9	−0.538432
$141$	−7.52589e9	−1.60351
$142$	4.31648e8	0.0890906
$143$	1.01491e10	2.02963
$144$	2.24330e9	0.434767
$145$	−1.14653e9	−0.215392
$146$	3.68710e7	0.00671579
$147$	1.83203e9	0.323597
$148$	−8.75424e9	−1.49983
$149$	−2.48703e7	−0.00413373	−0.00206687	−	0.999998i	$-0.500658\pi$
$149$	−2.48703e7	−0.00413373	−0.00206687	+	0.999998i	$0.500658\pi$
$150$	1.09393e9	0.176433
$151$	6.75466e9	1.05732	0.528661	−	0.848833i	$-0.322694\pi$
$151$	6.75466e9	1.05732	0.528661	+	0.848833i	$0.322694\pi$
$152$	1.74182e9	0.264671
$153$	−9.35214e8	−0.137975
$154$	2.59980e9	0.372474
$155$	−6.92752e9	−0.964018
$156$	−1.02316e10	−1.38319
$157$	−1.21950e10	−1.60189	−0.800945	−	0.598738i	$-0.795669\pi$
$157$	−1.21950e10	−1.60189	−0.800945	+	0.598738i	$0.795669\pi$
$158$	7.54996e8	0.0963802
$159$	1.11140e10	1.37906
$160$	2.25841e9	0.272434
$161$	−6.87696e9	−0.806640
$162$	2.10452e9	0.240069
$163$	−3.45700e9	−0.383579	−0.191790	−	0.981436i	$-0.561429\pi$
$163$	−3.45700e9	−0.383579	−0.191790	+	0.981436i	$0.561429\pi$
$164$	3.41999e9	0.369171
$165$	−9.95159e9	−1.04524
$166$	−2.50304e9	−0.255848
$167$	3.64179e9	0.362319	0.181159	−	0.983454i	$-0.442015\pi$
$167$	3.64179e9	0.362319	0.181159	+	0.983454i	$0.442015\pi$
$168$	−5.34223e9	−0.517405
$169$	4.09371e9	0.386035
$170$	−2.93850e8	−0.0269840
$171$	3.83093e9	0.342627
$172$	−1.68585e9	−0.146872
$173$	1.86480e10	1.58279	0.791396	−	0.611303i	$-0.209354\pi$
$173$	1.86480e10	1.58279	0.791396	+	0.611303i	$0.209354\pi$
$174$	−1.22781e9	−0.101545
$175$	1.05086e10	0.846984
$176$	1.95460e10	1.53550
$177$	8.84178e9	0.677111
$178$	−2.18949e9	−0.163475
$179$	1.33732e10	0.973634	0.486817	−	0.873504i	$-0.338158\pi$
$179$	1.33732e10	0.973634	0.486817	+	0.873504i	$0.338158\pi$
$180$	3.29079e9	0.233654
$181$	−1.11415e10	−0.771593	−0.385797	−	0.922584i	$-0.626073\pi$
$181$	−1.11415e10	−0.771593	−0.385797	+	0.922584i	$0.626073\pi$
$182$	3.76509e9	0.254363
$183$	−2.17232e10	−1.43184
$184$	4.20425e9	0.270401
$185$	−1.23312e10	−0.773984
$186$	−7.41863e9	−0.454481
$187$	−8.14858e9	−0.487298
$188$	2.16838e10	1.26598
$189$	1.23211e10	0.702380
$190$	1.20370e9	0.0670082
$191$	3.08053e10	1.67485	0.837423	−	0.546556i	$-0.184061\pi$
$191$	3.08053e10	1.67485	0.837423	+	0.546556i	$0.184061\pi$
$192$	−1.80411e10	−0.958093
$193$	−1.14247e9	−0.0592705	−0.0296352	−	0.999561i	$-0.509435\pi$
$193$	−1.14247e9	−0.0592705	−0.0296352	+	0.999561i	$0.509435\pi$
$194$	−2.33049e9	−0.118124
$195$	−1.44121e10	−0.713793
$196$	−5.27850e9	−0.255481
$197$	1.25402e10	0.593206	0.296603	−	0.955001i	$-0.404146\pi$
$197$	1.25402e10	0.593206	0.296603	+	0.955001i	$0.404146\pi$
$198$	−3.49569e9	−0.161636
$199$	1.80497e10	0.815887	0.407944	−	0.913007i	$-0.366246\pi$
$199$	1.80497e10	0.815887	0.407944	+	0.913007i	$0.366246\pi$
$200$	−6.42448e9	−0.283925
$201$	5.34839e10	2.31122
$202$	−1.86613e9	−0.0788606
$203$	−1.17947e10	−0.487479
$204$	8.21478e9	0.332093
$205$	4.81738e9	0.190510
$206$	−1.83227e9	−0.0708903
$207$	9.24676e9	0.350044
$208$	2.83070e10	1.04860
$209$	3.33791e10	1.21009
$210$	−3.69181e9	−0.130994
$211$	−5.22140e10	−1.81349	−0.906747	−	0.421675i	$-0.861442\pi$
$211$	−5.22140e10	−1.81349	−0.906747	+	0.421675i	$0.861442\pi$
$212$	−3.20221e10	−1.08877
$213$	−1.69975e10	−0.565818
$214$	3.58600e9	0.116882
$215$	−2.37467e9	−0.0757933
$216$	−7.53255e9	−0.235451
$217$	−7.12656e10	−2.18178
$218$	8.37831e9	0.251248
$219$	−1.45191e9	−0.0426522
$220$	2.86728e10	0.825218
$221$	−1.18010e10	−0.332776
$222$	−1.32054e10	−0.364890
$223$	4.64921e8	0.0125895	0.00629473	−	0.999980i	$-0.497996\pi$
$223$	4.64921e8	0.0125895	0.00629473	+	0.999980i	$0.497996\pi$
$224$	2.32329e10	0.616578
$225$	−1.41299e10	−0.367552
$226$	1.41981e10	0.362029
$227$	1.84970e10	0.462364	0.231182	−	0.972911i	$-0.425741\pi$
$227$	1.84970e10	0.462364	0.231182	+	0.972911i	$0.425741\pi$
$228$	−3.36503e10	−0.824673
$229$	2.01961e10	0.485298	0.242649	−	0.970114i	$-0.421984\pi$
$229$	2.01961e10	0.485298	0.242649	+	0.970114i	$0.421984\pi$
$230$	2.90539e9	0.0684588
$231$	−1.02375e11	−2.36560
$232$	7.21074e9	0.163412
$233$	−6.57898e10	−1.46237	−0.731185	−	0.682180i	$-0.761032\pi$
$233$	−6.57898e10	−1.46237	−0.731185	+	0.682180i	$0.761032\pi$
$234$	−5.06254e9	−0.110382
$235$	3.05437e10	0.653306
$236$	−2.54752e10	−0.534582
$237$	−2.97304e10	−0.612114
$238$	−3.02293e9	−0.0610706
$239$	−1.64809e10	−0.326731	−0.163365	−	0.986566i	$-0.552235\pi$
$239$	−1.64809e10	−0.326731	−0.163365	+	0.986566i	$0.552235\pi$
$240$	−2.77561e10	−0.540017
$241$	−3.16670e9	−0.0604687	−0.0302344	−	0.999543i	$-0.509625\pi$
$241$	−3.16670e9	−0.0604687	−0.0302344	+	0.999543i	$0.509625\pi$
$242$	−2.02100e10	−0.378789
$243$	−4.89325e10	−0.900263
$244$	6.25896e10	1.13044
$245$	−7.43527e9	−0.131841
$246$	5.15890e9	0.0898150
$247$	4.83405e10	0.826370
$248$	4.35684e10	0.731374
$249$	9.85651e10	1.62490
$250$	−1.03359e10	−0.167347
$251$	−2.27075e10	−0.361108	−0.180554	−	0.983565i	$-0.557789\pi$
$251$	−2.27075e10	−0.361108	−0.180554	+	0.983565i	$0.557789\pi$
$252$	3.38534e10	0.528810
$253$	8.05676e10	1.23628
$254$	−1.34547e10	−0.202825
$255$	1.15713e10	0.171376
$256$	4.47454e10	0.651132
$257$	2.37082e9	0.0339000	0.0169500	−	0.999856i	$-0.494604\pi$
$257$	2.37082e9	0.0339000	0.0169500	+	0.999856i	$0.494604\pi$
$258$	−2.54302e9	−0.0357323
$259$	−1.26855e11	−1.75169
$260$	4.15247e10	0.563542
$261$	1.58592e10	0.211543
$262$	−1.85344e9	−0.0243010
$263$	1.04738e11	1.34991	0.674955	−	0.737859i	$-0.264163\pi$
$263$	1.04738e11	1.34991	0.674955	+	0.737859i	$0.264163\pi$
$264$	6.25873e10	0.792992
$265$	−4.51061e10	−0.561861
$266$	1.23829e10	0.151654
$267$	8.62179e10	1.03824
$268$	−1.54100e11	−1.82471
$269$	−6.90062e10	−0.803532	−0.401766	−	0.915742i	$-0.631603\pi$
$269$	−6.90062e10	−0.803532	−0.401766	+	0.915742i	$0.631603\pi$
$270$	−5.20545e9	−0.0596104
$271$	−3.50481e10	−0.394732	−0.197366	−	0.980330i	$-0.563239\pi$
$271$	−3.50481e10	−0.394732	−0.197366	+	0.980330i	$0.563239\pi$
$272$	−2.27273e10	−0.251760
$273$	−1.48262e11	−1.61547
$274$	2.04996e10	0.219719
$275$	−1.23115e11	−1.29812
$276$	−8.12221e10	−0.842526
$277$	−5.00752e10	−0.511051	−0.255525	−	0.966802i	$-0.582248\pi$
$277$	−5.00752e10	−0.511051	−0.255525	+	0.966802i	$0.582248\pi$
$278$	−6.87750e9	−0.0690603
$279$	9.58237e10	0.946791
$280$	2.16814e10	0.210802
$281$	1.98549e11	1.89972	0.949860	−	0.312676i	$-0.101225\pi$
$281$	1.98549e11	1.89972	0.949860	+	0.312676i	$0.101225\pi$
$282$	3.27091e10	0.307997
$283$	2.30869e10	0.213957	0.106978	−	0.994261i	$-0.465882\pi$
$283$	2.30869e10	0.213957	0.106978	+	0.994261i	$0.465882\pi$
$284$	4.89738e10	0.446715
$285$	−4.73996e10	−0.425572
$286$	−4.41102e10	−0.389845
$287$	4.95579e10	0.431166
$288$	−3.12390e10	−0.267566
$289$	−1.09113e11	−0.920103
$290$	4.98306e9	0.0413719
$291$	9.17703e10	0.750211
$292$	4.18330e9	0.0336741
$293$	1.64416e11	1.30329	0.651643	−	0.758526i	$-0.274080\pi$
$293$	1.64416e11	1.30329	0.651643	+	0.758526i	$0.274080\pi$
$294$	−7.96238e9	−0.0621555
$295$	−3.58843e10	−0.275870
$296$	7.75530e10	0.587200
$297$	−1.44349e11	−1.07649
$298$	1.08091e8	0.000793995 0
$299$	1.16680e11	0.844259
$300$	1.24115e11	0.884664
$301$	−2.44290e10	−0.171537
$302$	−2.93571e10	−0.203087
$303$	7.34846e10	0.500847
$304$	9.30980e10	0.625186
$305$	8.81633e10	0.583363
$306$	4.06463e9	0.0265018
$307$	−2.21864e11	−1.42549	−0.712744	−	0.701424i	$-0.752548\pi$
$307$	−2.21864e11	−1.42549	−0.712744	+	0.701424i	$0.752548\pi$
$308$	2.94967e11	1.86765
$309$	7.21514e10	0.450227
$310$	3.01084e10	0.185166
$311$	−4.46997e10	−0.270946	−0.135473	−	0.990781i	$-0.543255\pi$
$311$	−4.46997e10	−0.270946	−0.135473	+	0.990781i	$0.543255\pi$
$312$	9.06405e10	0.541535
$313$	−1.44243e11	−0.849464	−0.424732	−	0.905319i	$-0.639632\pi$
$313$	−1.44243e11	−0.849464	−0.424732	+	0.905319i	$0.639632\pi$
$314$	5.30019e10	0.307686
$315$	4.76857e10	0.272892
$316$	8.56601e10	0.483266
$317$	9.81965e10	0.546172	0.273086	−	0.961990i	$-0.411956\pi$
$317$	9.81965e10	0.546172	0.273086	+	0.961990i	$0.411956\pi$
$318$	−4.83038e10	−0.264886
$319$	1.38182e11	0.747126
$320$	7.32196e10	0.390349
$321$	−1.41210e11	−0.742322
$322$	2.98887e10	0.154937
$323$	−3.88119e10	−0.198405
$324$	2.38774e11	1.20375
$325$	−1.78298e11	−0.886485
$326$	1.50248e10	0.0736768
$327$	−3.29922e11	−1.59568
$328$	−3.02974e10	−0.144535
$329$	3.14213e11	1.47857
$330$	4.32517e10	0.200766
$331$	−1.20008e11	−0.549522	−0.274761	−	0.961513i	$-0.588599\pi$
$331$	−1.20008e11	−0.549522	−0.274761	+	0.961513i	$0.588599\pi$
$332$	−2.83989e11	−1.28286
$333$	1.70569e11	0.760153
$334$	−1.58280e10	−0.0695931
$335$	−2.17064e11	−0.941641
$336$	−2.85535e11	−1.22217
$337$	−6.01762e10	−0.254150	−0.127075	−	0.991893i	$-0.540559\pi$
$337$	−6.01762e10	−0.254150	−0.127075	+	0.991893i	$0.540559\pi$
$338$	−1.77921e10	−0.0741485
$339$	−5.59096e11	−2.29926
$340$	−3.33396e10	−0.135302
$341$	8.34918e11	3.34387
$342$	−1.66500e10	−0.0658108
$343$	2.11858e11	0.826457
$344$	1.49348e10	0.0575023
$345$	−1.14409e11	−0.434784
$346$	−8.10479e10	−0.304018
$347$	−3.82323e11	−1.41562	−0.707812	−	0.706401i	$-0.750318\pi$
$347$	−3.82323e11	−1.41562	−0.707812	+	0.706401i	$0.750318\pi$
$348$	−1.39305e11	−0.509166
$349$	−1.22118e11	−0.440621	−0.220311	−	0.975430i	$-0.570707\pi$
$349$	−1.22118e11	−0.440621	−0.220311	+	0.975430i	$0.570707\pi$
$350$	−4.56727e10	−0.162686
$351$	−2.09050e11	−0.735137
$352$	−2.72188e11	−0.944988
$353$	−2.60358e11	−0.892452	−0.446226	−	0.894920i	$-0.647232\pi$
$353$	−2.60358e11	−0.892452	−0.446226	+	0.894920i	$0.647232\pi$
$354$	−3.84282e10	−0.130058
$355$	6.89841e10	0.230527
$356$	−2.48414e11	−0.819693
$357$	1.19038e11	0.387862
$358$	−5.81226e10	−0.187013
$359$	−5.17873e11	−1.64550	−0.822750	−	0.568403i	$-0.807561\pi$
$359$	−5.17873e11	−1.64550	−0.822750	+	0.568403i	$0.807561\pi$
$360$	−2.91528e10	−0.0914784
$361$	−1.63702e11	−0.507309
$362$	4.84231e10	0.148205
$363$	7.95833e11	2.40570
$364$	4.27178e11	1.27542
$365$	5.89257e9	0.0173775
$366$	9.44135e10	0.275023
$367$	6.03365e10	0.173613	0.0868066	−	0.996225i	$-0.472334\pi$
$367$	6.03365e10	0.173613	0.0868066	+	0.996225i	$0.472334\pi$
$368$	2.24712e11	0.638720
$369$	−6.66356e10	−0.187106
$370$	5.35939e10	0.148664
$371$	−4.64021e11	−1.27161
$372$	−8.41701e11	−2.27884
$373$	2.77329e11	0.741832	0.370916	−	0.928667i	$-0.379044\pi$
$373$	2.77329e11	0.741832	0.370916	+	0.928667i	$0.379044\pi$
$374$	3.54154e10	0.0935988
$375$	4.07008e11	1.06283
$376$	−1.92095e11	−0.495645
$377$	2.00119e11	0.510213
$378$	−5.35502e10	−0.134911
$379$	−6.36812e11	−1.58538	−0.792692	−	0.609622i	$-0.791321\pi$
$379$	−6.36812e11	−1.58538	−0.792692	+	0.609622i	$0.791321\pi$
$380$	1.36569e11	0.335990
$381$	5.29820e11	1.28815
$382$	−1.33886e11	−0.321699
$383$	3.29899e11	0.783405	0.391702	−	0.920092i	$-0.371886\pi$
$383$	3.29899e11	0.783405	0.391702	+	0.920092i	$0.371886\pi$
$384$	3.63320e11	0.852706
$385$	4.15488e11	0.963797
$386$	4.96543e9	0.0113845
$387$	3.28473e10	0.0744389
$388$	−2.64412e11	−0.592294
$389$	2.06910e11	0.458151	0.229075	−	0.973409i	$-0.426430\pi$
$389$	2.06910e11	0.458151	0.229075	+	0.973409i	$0.426430\pi$
$390$	6.26381e10	0.137103
$391$	−9.36806e10	−0.202700
$392$	4.67617e10	0.100024
$393$	7.29852e10	0.154336
$394$	−5.45022e10	−0.113941
$395$	1.20660e11	0.249389
$396$	−3.96612e11	−0.810472
$397$	−2.89546e11	−0.585006	−0.292503	−	0.956265i	$-0.594488\pi$
$397$	−2.89546e11	−0.585006	−0.292503	+	0.956265i	$0.594488\pi$
$398$	−7.84476e10	−0.156713
$399$	−4.87615e11	−0.963161
$400$	−3.43381e11	−0.670665
$401$	1.02129e12	1.97243	0.986214	−	0.165476i	$-0.0529162\pi$
$401$	1.02129e12	1.97243	0.986214	+	0.165476i	$0.0529162\pi$
$402$	−2.32452e11	−0.443932
$403$	1.20915e12	2.28353
$404$	−2.11726e11	−0.395420
$405$	3.36336e11	0.621192
$406$	5.12623e10	0.0936335
$407$	1.48618e12	2.68470
$408$	−7.27739e10	−0.130018
$409$	1.37283e11	0.242585	0.121292	−	0.992617i	$-0.461296\pi$
$409$	1.37283e11	0.242585	0.121292	+	0.992617i	$0.461296\pi$
$410$	−2.09373e10	−0.0365927
$411$	−8.07235e11	−1.39544
$412$	−2.07885e11	−0.355456
$413$	−3.69153e11	−0.624354
$414$	−4.01883e10	−0.0672354
$415$	−4.00025e11	−0.662020
$416$	−3.94189e11	−0.645333
$417$	2.70823e11	0.438605
$418$	−1.45073e11	−0.232430
$419$	−6.55005e11	−1.03820	−0.519100	−	0.854713i	$-0.673733\pi$
$419$	−6.55005e11	−1.03820	−0.519100	+	0.854713i	$0.673733\pi$
$420$	−4.18864e11	−0.656827
$421$	−7.09415e11	−1.10060	−0.550301	−	0.834966i	$-0.685487\pi$
$421$	−7.09415e11	−1.10060	−0.550301	+	0.834966i	$0.685487\pi$
$422$	2.26933e11	0.348330
$423$	−4.22491e11	−0.641631
$424$	2.83680e11	0.426268
$425$	1.43153e11	0.212838
$426$	7.38746e10	0.108681
$427$	9.06964e11	1.32028
$428$	4.06859e11	0.586066
$429$	1.73698e12	2.47592
$430$	1.03208e10	0.0145582
$431$	−1.30197e12	−1.81742	−0.908708	−	0.417433i	$-0.862930\pi$
$431$	−1.30197e12	−1.81742	−0.908708	+	0.417433i	$0.862930\pi$
$432$	−4.02606e11	−0.556164
$433$	1.16707e11	0.159552	0.0797761	−	0.996813i	$-0.474579\pi$
$433$	1.16707e11	0.159552	0.0797761	+	0.996813i	$0.474579\pi$
$434$	3.09735e11	0.419070
$435$	−1.96224e11	−0.262754
$436$	9.50583e11	1.25980
$437$	3.83745e11	0.503357
$438$	6.31031e9	0.00819251
$439$	1.26701e12	1.62814	0.814068	−	0.580770i	$-0.197248\pi$
$439$	1.26701e12	1.62814	0.814068	+	0.580770i	$0.197248\pi$
$440$	−2.54010e11	−0.323083
$441$	1.02847e11	0.129485
$442$	5.12895e10	0.0639187
$443$	−2.71096e11	−0.334431	−0.167216	−	0.985920i	$-0.553478\pi$
$443$	−2.71096e11	−0.334431	−0.167216	+	0.985920i	$0.553478\pi$
$444$	−1.49825e12	−1.82962
$445$	−3.49915e11	−0.423002
$446$	−2.02064e9	−0.00241815
$447$	−4.25644e9	−0.00504269
$448$	7.53234e11	0.883443
$449$	3.06988e11	0.356462	0.178231	−	0.983989i	$-0.442963\pi$
$449$	3.06988e11	0.356462	0.178231	+	0.983989i	$0.442963\pi$
$450$	6.14115e10	0.0705982
$451$	−5.80600e11	−0.660819
$452$	1.61089e12	1.81527
$453$	1.15603e12	1.28981
$454$	−8.03916e10	−0.0888095
$455$	6.01720e11	0.658178
$456$	2.98105e11	0.322869
$457$	6.36194e11	0.682286	0.341143	−	0.940011i	$-0.389186\pi$
$457$	6.36194e11	0.682286	0.341143	+	0.940011i	$0.389186\pi$
$458$	−8.77766e10	−0.0932147
$459$	1.67843e11	0.176501
$460$	3.29639e11	0.343264
$461$	−1.61558e12	−1.66600	−0.832998	−	0.553276i	$-0.813377\pi$
$461$	−1.61558e12	−1.66600	−0.832998	+	0.553276i	$0.813377\pi$
$462$	4.44944e11	0.454377
$463$	6.19847e10	0.0626859	0.0313429	−	0.999509i	$-0.490022\pi$
$463$	6.19847e10	0.0626859	0.0313429	+	0.999509i	$0.490022\pi$
$464$	3.85405e11	0.385999
$465$	−1.18561e12	−1.17599
$466$	2.85936e11	0.280888
$467$	3.95766e10	0.0385046	0.0192523	−	0.999815i	$-0.493871\pi$
$467$	3.95766e10	0.0385046	0.0192523	+	0.999815i	$0.493871\pi$
$468$	−5.74383e11	−0.553472
$469$	−2.23300e12	−2.13114
$470$	−1.32749e11	−0.125485
$471$	−2.08712e12	−1.95413
$472$	2.25683e11	0.209295
$473$	2.86200e11	0.262903
$474$	1.29214e11	0.117573
$475$	−5.86398e11	−0.528532
$476$	−3.42975e11	−0.306218
$477$	6.23922e11	0.551820
$478$	7.16294e10	0.0627575
$479$	−1.19317e12	−1.03560	−0.517802	−	0.855500i	$-0.673250\pi$
$479$	−1.19317e12	−1.03560	−0.517802	+	0.855500i	$0.673250\pi$
$480$	3.86516e11	0.332340
$481$	2.15232e12	1.83339
$482$	1.37631e10	0.0116147
$483$	−1.17696e12	−0.984011
$484$	−2.29298e12	−1.89931
$485$	−3.72449e11	−0.305653
$486$	2.12671e11	0.172920
$487$	1.38316e12	1.11427	0.557137	−	0.830421i	$-0.311900\pi$
$487$	1.38316e12	1.11427	0.557137	+	0.830421i	$0.311900\pi$
$488$	−5.54475e11	−0.442581
$489$	−5.91651e11	−0.467924
$490$	3.23152e10	0.0253236
$491$	4.25145e11	0.330119	0.165059	−	0.986284i	$-0.447218\pi$
$491$	4.25145e11	0.330119	0.165059	+	0.986284i	$0.447218\pi$
$492$	5.85316e11	0.450348
$493$	−1.60672e11	−0.122498
$494$	−2.10098e11	−0.158727
$495$	−5.58666e11	−0.418243
$496$	2.32868e12	1.72759
$497$	7.09662e11	0.521732
$498$	−4.28384e11	−0.312106
$499$	−1.46467e12	−1.05752	−0.528758	−	0.848773i	$-0.677342\pi$
$499$	−1.46467e12	−1.05752	−0.528758	+	0.848773i	$0.677342\pi$
$500$	−1.17269e12	−0.839106
$501$	6.23276e11	0.441988
$502$	9.86915e10	0.0693606
$503$	−2.53323e12	−1.76449	−0.882244	−	0.470793i	$-0.843968\pi$
$503$	−2.53323e12	−1.76449	−0.882244	+	0.470793i	$0.843968\pi$
$504$	−2.99904e11	−0.207035
$505$	−2.98236e11	−0.204056
$506$	−3.50163e11	−0.237462
$507$	7.00621e11	0.470920
$508$	−1.52653e12	−1.01700
$509$	9.78046e11	0.645846	0.322923	−	0.946425i	$-0.395334\pi$
$509$	9.78046e11	0.645846	0.322923	+	0.946425i	$0.395334\pi$
$510$	−5.02912e10	−0.0329175
$511$	6.06187e10	0.0393290
$512$	−1.28138e12	−0.824070
$513$	−6.87538e11	−0.438297
$514$	−1.03041e10	−0.00651141
$515$	−2.92825e11	−0.183432
$516$	−2.88525e11	−0.179168
$517$	−3.68119e12	−2.26611
$518$	5.51337e11	0.336460
$519$	3.19152e12	1.93083
$520$	−3.67863e11	−0.220634
$521$	1.71468e12	1.01956	0.509780	−	0.860305i	$-0.329727\pi$
$521$	1.71468e12	1.01956	0.509780	+	0.860305i	$0.329727\pi$
$522$	−6.89273e10	−0.0406326
$523$	−2.34031e12	−1.36778	−0.683891	−	0.729585i	$-0.739713\pi$
$523$	−2.34031e12	−1.36778	−0.683891	+	0.729585i	$0.739713\pi$
$524$	−2.10287e11	−0.121849
$525$	1.79851e12	1.03323
$526$	−4.55214e11	−0.259287
$527$	−9.70808e11	−0.548259
$528$	3.34522e12	1.87315
$529$	−8.74904e11	−0.485747
$530$	1.96040e11	0.107921
$531$	4.96363e11	0.270941
$532$	1.40493e12	0.760419
$533$	−8.40839e11	−0.451274
$534$	−3.74721e11	−0.199422
$535$	5.73099e11	0.302439
$536$	1.36515e12	0.714397
$537$	2.28876e12	1.18773
$538$	2.99915e11	0.154340
$539$	8.96113e11	0.457313
$540$	−5.90599e11	−0.298896
$541$	1.91353e11	0.0960392	0.0480196	−	0.998846i	$-0.484709\pi$
$541$	1.91353e11	0.0960392	0.0480196	+	0.998846i	$0.484709\pi$
$542$	1.52326e11	0.0758190
$543$	−1.90681e12	−0.941258
$544$	3.16488e11	0.154940
$545$	1.33899e12	0.650117
$546$	6.44378e11	0.310294
$547$	4.21467e11	0.201289	0.100645	−	0.994922i	$-0.467909\pi$
$547$	4.21467e11	0.201289	0.100645	+	0.994922i	$0.467909\pi$
$548$	2.32583e12	1.10171
$549$	−1.21950e12	−0.572938
$550$	5.35083e11	0.249338
$551$	6.58164e11	0.304195
$552$	7.19538e11	0.329859
$553$	1.24127e12	0.564421
$554$	2.17637e11	0.0981611
$555$	−2.11043e12	−0.944174
$556$	−7.80305e11	−0.346280
$557$	2.16316e12	0.952227	0.476114	−	0.879384i	$-0.342045\pi$
$557$	2.16316e12	0.952227	0.476114	+	0.879384i	$0.342045\pi$
$558$	−4.16470e11	−0.181857
$559$	4.14482e11	0.179537
$560$	1.15884e12	0.497941
$561$	−1.39459e12	−0.594450
$562$	−8.62935e11	−0.364892
$563$	−3.11330e12	−1.30597	−0.652985	−	0.757371i	$-0.726484\pi$
$563$	−3.11330e12	−1.30597	−0.652985	+	0.757371i	$0.726484\pi$
$564$	3.71109e12	1.54435
$565$	2.26909e12	0.936770
$566$	−1.00340e11	−0.0410962
$567$	3.46000e12	1.40589
$568$	−4.33854e11	−0.174894
$569$	−4.55671e12	−1.82241	−0.911205	−	0.411952i	$-0.864847\pi$
$569$	−4.55671e12	−1.82241	−0.911205	+	0.411952i	$0.864847\pi$
$570$	2.06009e11	0.0817426
$571$	4.51825e11	0.177872	0.0889360	−	0.996037i	$-0.471653\pi$
$571$	4.51825e11	0.177872	0.0889360	+	0.996037i	$0.471653\pi$
$572$	−5.00464e12	−1.95475
$573$	5.27219e12	2.04313
$574$	−2.15389e11	−0.0828171
$575$	−1.41540e12	−0.539974
$576$	−1.01280e12	−0.383373
$577$	−2.70242e12	−1.01499	−0.507494	−	0.861655i	$-0.669428\pi$
$577$	−2.70242e12	−1.01499	−0.507494	+	0.861655i	$0.669428\pi$
$578$	4.74228e11	0.176731
$579$	−1.95529e11	−0.0723034
$580$	5.65366e11	0.207446
$581$	−4.11519e12	−1.49829
$582$	−3.98853e11	−0.144098
$583$	5.43628e12	1.94892
$584$	−3.70594e10	−0.0131838
$585$	−8.09073e11	−0.285619
$586$	−7.14586e11	−0.250331
$587$	8.20194e11	0.285131	0.142566	−	0.989785i	$-0.454465\pi$
$587$	8.20194e11	0.285131	0.142566	+	0.989785i	$0.454465\pi$
$588$	−9.03393e11	−0.311658
$589$	3.97673e12	1.36147
$590$	1.55960e11	0.0529884
$591$	2.14620e12	0.723645
$592$	4.14511e12	1.38704
$593$	−4.20732e12	−1.39720	−0.698601	−	0.715512i	$-0.746194\pi$
$593$	−4.20732e12	−1.39720	−0.698601	+	0.715512i	$0.746194\pi$
$594$	6.27372e11	0.206769
$595$	−4.83112e11	−0.158024
$596$	1.22638e10	0.00398122
$597$	3.08912e12	0.995292
$598$	−5.07115e11	−0.162163
$599$	2.53068e12	0.803188	0.401594	−	0.915818i	$-0.368456\pi$
$599$	2.53068e12	0.803188	0.401594	+	0.915818i	$0.368456\pi$
$600$	−1.09952e12	−0.346357
$601$	−3.48816e12	−1.09059	−0.545294	−	0.838245i	$-0.683582\pi$
$601$	−3.48816e12	−1.09059	−0.545294	+	0.838245i	$0.683582\pi$
$602$	1.06174e11	0.0329483
$603$	3.00250e12	0.924814
$604$	−3.33079e12	−1.01831
$605$	−3.22988e12	−0.980137
$606$	−3.19379e11	−0.0962011
$607$	3.83875e12	1.14773	0.573866	−	0.818949i	$-0.305443\pi$
$607$	3.83875e12	1.14773	0.573866	+	0.818949i	$0.305443\pi$
$608$	−1.29643e12	−0.384755
$609$	−2.01862e12	−0.594670
$610$	−3.83176e11	−0.112051
$611$	−5.33119e12	−1.54753
$612$	4.61164e11	0.132884
$613$	4.06569e12	1.16295	0.581477	−	0.813563i	$-0.302475\pi$
$613$	4.06569e12	1.16295	0.581477	+	0.813563i	$0.302475\pi$
$614$	9.64266e11	0.273804
$615$	8.24473e11	0.232401
$616$	−2.61308e12	−0.731206
$617$	2.74046e12	0.761272	0.380636	−	0.924725i	$-0.375705\pi$
$617$	2.74046e12	0.761272	0.380636	+	0.924725i	$0.375705\pi$
$618$	−3.13585e11	−0.0864782
$619$	−4.39332e11	−0.120278	−0.0601388	−	0.998190i	$-0.519154\pi$
$619$	−4.39332e11	−0.120278	−0.0601388	+	0.998190i	$0.519154\pi$
$620$	3.41603e12	0.928452
$621$	−1.65952e12	−0.447785
$622$	1.94274e11	0.0520425
$623$	−3.59968e12	−0.957344
$624$	4.84462e12	1.27917
$625$	1.22056e12	0.319961
$626$	6.26910e11	0.163163
$627$	5.71269e12	1.47617
$628$	6.01347e12	1.54279
$629$	−1.72806e12	−0.440182
$630$	−2.07252e11	−0.0524163
$631$	−3.98165e12	−0.999840	−0.499920	−	0.866072i	$-0.666637\pi$
$631$	−3.98165e12	−0.999840	−0.499920	+	0.866072i	$0.666637\pi$
$632$	−7.58854e11	−0.189205
$633$	−8.93620e12	−2.21226
$634$	−4.26782e11	−0.104907
$635$	−2.15027e12	−0.524820
$636$	−5.48044e12	−1.32818
$637$	1.29777e12	0.312299
$638$	−6.00568e11	−0.143506
$639$	−9.54211e11	−0.226407
$640$	−1.47453e12	−0.347412
$641$	2.71199e12	0.634494	0.317247	−	0.948343i	$-0.397242\pi$
$641$	2.71199e12	0.634494	0.317247	+	0.948343i	$0.397242\pi$
$642$	6.13728e11	0.142583
$643$	−3.76666e12	−0.868976	−0.434488	−	0.900678i	$-0.643071\pi$
$643$	−3.76666e12	−0.868976	−0.434488	+	0.900678i	$0.643071\pi$
$644$	3.39110e12	0.776880
$645$	−4.06415e11	−0.0924594
$646$	1.68684e11	0.0381091
$647$	−4.40950e12	−0.989281	−0.494641	−	0.869098i	$-0.664700\pi$
$647$	−4.40950e12	−0.989281	−0.494641	+	0.869098i	$0.664700\pi$
$648$	−2.11528e12	−0.471281
$649$	4.32484e12	0.956906
$650$	7.74920e11	0.170273
$651$	−1.21968e13	−2.66153
$652$	1.70468e12	0.369428
$653$	2.30958e12	0.497077	0.248539	−	0.968622i	$-0.420050\pi$
$653$	2.30958e12	0.497077	0.248539	+	0.968622i	$0.420050\pi$
$654$	1.43391e12	0.306494
$655$	−2.96209e11	−0.0628801
$656$	−1.61936e12	−0.341409
$657$	−8.15079e10	−0.0170669
$658$	−1.36563e12	−0.284000
$659$	4.07987e12	0.842678	0.421339	−	0.906903i	$-0.361560\pi$
$659$	4.07987e12	0.842678	0.421339	+	0.906903i	$0.361560\pi$
$660$	4.90723e12	1.00667
$661$	−2.46484e12	−0.502207	−0.251103	−	0.967960i	$-0.580793\pi$
$661$	−2.46484e12	−0.502207	−0.251103	+	0.967960i	$0.580793\pi$
$662$	5.21581e11	0.105551
$663$	−2.01969e12	−0.405950
$664$	2.51583e12	0.502256
$665$	1.97898e12	0.392413
$666$	−7.41328e11	−0.146008
$667$	1.58862e12	0.310780
$668$	−1.79580e12	−0.348951
$669$	7.95692e10	0.0153578
$670$	9.43404e11	0.180868
$671$	−1.06256e13	−2.02350
$672$	3.97622e12	0.752157
$673$	1.87410e12	0.352148	0.176074	−	0.984377i	$-0.443660\pi$
$673$	1.87410e12	0.352148	0.176074	+	0.984377i	$0.443660\pi$
$674$	2.61538e11	0.0488164
$675$	2.53590e12	0.470181
$676$	−2.01865e12	−0.371793
$677$	−2.73473e12	−0.500340	−0.250170	−	0.968202i	$-0.580486\pi$
$677$	−2.73473e12	−0.500340	−0.250170	+	0.968202i	$0.580486\pi$
$678$	2.42995e12	0.441635
$679$	−3.83150e12	−0.691759
$680$	2.95352e11	0.0529724
$681$	3.16568e12	0.564033
$682$	−3.62873e12	−0.642281
$683$	−3.59575e12	−0.632261	−0.316130	−	0.948716i	$-0.602384\pi$
$683$	−3.59575e12	−0.632261	−0.316130	+	0.948716i	$0.602384\pi$
$684$	−1.88907e12	−0.329986
$685$	3.27615e12	0.568535
$686$	−9.20777e11	−0.158743
$687$	3.45648e12	0.592010
$688$	7.98244e11	0.135827
$689$	7.87295e12	1.33092
$690$	4.97245e11	0.0835121
$691$	4.85692e11	0.0810420	0.0405210	−	0.999179i	$-0.487098\pi$
$691$	4.85692e11	0.0810420	0.0405210	+	0.999179i	$0.487098\pi$
$692$	−9.19551e12	−1.52440
$693$	−5.74717e12	−0.946574
$694$	1.66166e12	0.271909
$695$	−1.09913e12	−0.178697
$696$	1.23409e12	0.199344
$697$	6.75097e11	0.108347
$698$	5.30750e11	0.0846332
$699$	−1.12596e13	−1.78393
$700$	−5.18192e12	−0.815736
$701$	4.91473e12	0.768721	0.384360	−	0.923183i	$-0.374422\pi$
$701$	4.91473e12	0.768721	0.384360	+	0.923183i	$0.374422\pi$
$702$	9.08575e11	0.141203
$703$	7.07869e12	1.09309
$704$	−8.82458e12	−1.35399
$705$	5.22743e12	0.796960
$706$	1.13157e12	0.171419
$707$	−3.06805e12	−0.461823
$708$	−4.35997e12	−0.652130
$709$	3.90213e12	0.579954	0.289977	−	0.957034i	$-0.406352\pi$
$709$	3.90213e12	0.579954	0.289977	+	0.957034i	$0.406352\pi$
$710$	−2.99819e11	−0.0442789
$711$	−1.66901e12	−0.244933
$712$	2.20068e12	0.320919
$713$	9.59868e12	1.39094
$714$	−5.17362e11	−0.0744993
$715$	−7.04951e12	−1.00875
$716$	−6.59445e12	−0.937713
$717$	−2.82063e12	−0.398575
$718$	2.25078e12	0.316063
$719$	7.78412e12	1.08625	0.543124	−	0.839652i	$-0.317241\pi$
$719$	7.78412e12	1.08625	0.543124	+	0.839652i	$0.317241\pi$
$720$	−1.55818e12	−0.216083
$721$	−3.01239e12	−0.415147
$722$	7.11484e11	0.0974423
$723$	−5.41968e11	−0.0737651
$724$	5.49397e12	0.743126
$725$	−2.42756e12	−0.326324
$726$	−3.45885e12	−0.462080
$727$	1.21940e13	1.61898	0.809489	−	0.587135i	$-0.199744\pi$
$727$	1.21940e13	1.61898	0.809489	+	0.587135i	$0.199744\pi$
$728$	−3.78433e12	−0.499341
$729$	1.15634e12	0.151639
$730$	−2.56103e10	−0.00333781
$731$	−3.32782e11	−0.0431054
$732$	1.07119e13	1.37901
$733$	4.49897e12	0.575632	0.287816	−	0.957686i	$-0.407071\pi$
$733$	4.49897e12	0.575632	0.287816	+	0.957686i	$0.407071\pi$
$734$	−2.62235e11	−0.0333471
$735$	−1.27251e12	−0.160831
$736$	−3.12922e12	−0.393084
$737$	2.61609e13	3.26625
$738$	2.89612e11	0.0359387
$739$	−5.39033e12	−0.664837	−0.332418	−	0.943132i	$-0.607865\pi$
$739$	−5.39033e12	−0.664837	−0.332418	+	0.943132i	$0.607865\pi$
$740$	6.08063e12	0.745429
$741$	8.27326e12	1.00808
$742$	2.01673e12	0.244248
$743$	−1.18733e13	−1.42930	−0.714649	−	0.699484i	$-0.753413\pi$
$743$	−1.18733e13	−1.42930	−0.714649	+	0.699484i	$0.753413\pi$
$744$	7.45655e12	0.892194
$745$	1.72747e10	0.00205451
$746$	−1.20533e12	−0.142489
$747$	5.53328e12	0.650190
$748$	4.01815e12	0.469320
$749$	5.89565e12	0.684484
$750$	−1.76894e12	−0.204145
$751$	3.41014e12	0.391194	0.195597	−	0.980684i	$-0.437336\pi$
$751$	3.41014e12	0.391194	0.195597	+	0.980684i	$0.437336\pi$
$752$	−1.02672e13	−1.17077
$753$	−3.88629e12	−0.440512
$754$	−8.69758e11	−0.0980003
$755$	−4.69173e12	−0.525499
$756$	−6.07568e12	−0.676467
$757$	7.13321e12	0.789503	0.394751	−	0.918788i	$-0.370831\pi$
$757$	7.13321e12	0.789503	0.394751	+	0.918788i	$0.370831\pi$
$758$	2.76771e12	0.304516
$759$	1.37888e13	1.50813
$760$	−1.20985e12	−0.131544
$761$	1.23812e13	1.33823	0.669115	−	0.743159i	$-0.266673\pi$
$761$	1.23812e13	1.33823	0.669115	+	0.743159i	$0.266673\pi$
$762$	−2.30271e12	−0.247424
$763$	1.37746e13	1.47136
$764$	−1.51904e13	−1.61305
$765$	6.49593e11	0.0685748
$766$	−1.43381e12	−0.150474
$767$	6.26334e12	0.653472
$768$	7.65798e12	0.794308
$769$	1.49705e12	0.154372	0.0771860	−	0.997017i	$-0.475406\pi$
$769$	1.49705e12	0.154372	0.0771860	+	0.997017i	$0.475406\pi$
$770$	−1.80580e12	−0.185123
$771$	4.05756e11	0.0413542
$772$	5.63366e11	0.0570838
$773$	−4.99913e11	−0.0503602	−0.0251801	−	0.999683i	$-0.508016\pi$
$773$	−4.99913e11	−0.0503602	−0.0251801	+	0.999683i	$0.508016\pi$
$774$	−1.42761e11	−0.0142980
$775$	−1.46677e13	−1.46051
$776$	2.34240e12	0.231890
$777$	−2.17106e13	−2.13687
$778$	−8.99274e11	−0.0880002
$779$	−2.76541e12	−0.269055
$780$	7.10677e12	0.687459
$781$	−8.31411e12	−0.799624
$782$	4.07155e11	0.0389340
$783$	−2.84625e12	−0.270611
$784$	2.49936e12	0.236269
$785$	8.47054e12	0.796155
$786$	−3.17209e11	−0.0296445
$787$	−1.61703e13	−1.50256	−0.751282	−	0.659981i	$-0.770564\pi$
$787$	−1.61703e13	−1.50256	−0.751282	+	0.659981i	$0.770564\pi$
$788$	−6.18369e12	−0.571320
$789$	1.79255e13	1.64674
$790$	−5.24415e11	−0.0479019
$791$	2.33428e13	2.12011
$792$	3.51355e12	0.317309
$793$	−1.53883e13	−1.38185
$794$	1.25843e12	0.112366
$795$	−7.71971e12	−0.685408
$796$	−8.90048e12	−0.785786
$797$	1.12948e12	0.0991553	0.0495777	−	0.998770i	$-0.484212\pi$
$797$	1.12948e12	0.0991553	0.0495777	+	0.998770i	$0.484212\pi$
$798$	2.11928e12	0.185001
$799$	4.28033e12	0.371550
$800$	4.78174e12	0.412744
$801$	4.84013e12	0.415443
$802$	−4.43875e12	−0.378858
$803$	−7.10184e11	−0.0602769
$804$	−2.63735e13	−2.22595
$805$	4.77668e12	0.400908
$806$	−5.25521e12	−0.438614
$807$	−1.18101e13	−0.980219
$808$	1.87566e12	0.154812
$809$	−1.05575e13	−0.866547	−0.433273	−	0.901263i	$-0.642642\pi$
$809$	−1.05575e13	−0.866547	−0.433273	+	0.901263i	$0.642642\pi$
$810$	−1.46179e12	−0.119317
$811$	−1.58721e12	−0.128837	−0.0644184	−	0.997923i	$-0.520519\pi$
$811$	−1.58721e12	−0.128837	−0.0644184	+	0.997923i	$0.520519\pi$
$812$	5.81610e12	0.469494
$813$	−5.99833e12	−0.481529
$814$	−6.45924e12	−0.515669
$815$	2.40121e12	0.190643
$816$	−3.88967e12	−0.307120
$817$	1.36318e12	0.107042
$818$	−5.96662e11	−0.0465949
$819$	−8.32319e12	−0.646417
$820$	−2.37550e12	−0.183482
$821$	9.46150e12	0.726801	0.363401	−	0.931633i	$-0.381616\pi$
$821$	9.46150e12	0.726801	0.363401	+	0.931633i	$0.381616\pi$
$822$	3.50841e12	0.268032
$823$	−2.15068e13	−1.63409	−0.817044	−	0.576575i	$-0.804389\pi$
$823$	−2.15068e13	−1.63409	−0.817044	+	0.576575i	$0.804389\pi$
$824$	1.84163e12	0.139165
$825$	−2.10706e13	−1.58356
$826$	1.60441e12	0.119924
$827$	1.83034e13	1.36068	0.680342	−	0.732895i	$-0.261831\pi$
$827$	1.83034e13	1.36068	0.680342	+	0.732895i	$0.261831\pi$
$828$	−4.55967e12	−0.337130
$829$	9.41251e12	0.692165	0.346083	−	0.938204i	$-0.387512\pi$
$829$	9.41251e12	0.692165	0.346083	+	0.938204i	$0.387512\pi$
$830$	1.73859e12	0.127159
$831$	−8.57016e12	−0.623425
$832$	−1.27800e13	−0.924644
$833$	−1.04196e12	−0.0749807
$834$	−1.17705e12	−0.0842459
$835$	−2.52956e12	−0.180076
$836$	−1.64596e13	−1.16544
$837$	−1.71975e13	−1.21116
$838$	2.84679e12	0.199415
$839$	2.00576e13	1.39749	0.698746	−	0.715370i	$-0.253742\pi$
$839$	2.00576e13	1.39749	0.698746	+	0.715370i	$0.253742\pi$
$840$	3.71067e12	0.257156
$841$	−1.17825e13	−0.812185
$842$	3.08326e12	0.211401
$843$	3.39808e13	2.31745
$844$	2.57473e13	1.74659
$845$	−2.84346e12	−0.191863
$846$	1.83623e12	0.123243
$847$	−3.32268e13	−2.21826
$848$	1.51624e13	1.00690
$849$	3.95122e12	0.261003
$850$	−6.22172e11	−0.0408813
$851$	1.70859e13	1.11675
$852$	8.38164e12	0.544943
$853$	−1.73610e12	−0.112280	−0.0561401	−	0.998423i	$-0.517879\pi$
$853$	−1.73610e12	−0.112280	−0.0561401	+	0.998423i	$0.517879\pi$
$854$	−3.94185e12	−0.253595
$855$	−2.66094e12	−0.170289
$856$	−3.60432e12	−0.229452
$857$	−1.20533e13	−0.763296	−0.381648	−	0.924308i	$-0.624643\pi$
$857$	−1.20533e13	−0.763296	−0.381648	+	0.924308i	$0.624643\pi$
$858$	−7.54927e12	−0.475567
$859$	2.99312e12	0.187566	0.0937830	−	0.995593i	$-0.470104\pi$
$859$	2.99312e12	0.187566	0.0937830	+	0.995593i	$0.470104\pi$
$860$	1.17098e12	0.0729970
$861$	8.48162e12	0.525975
$862$	5.65864e12	0.349084
$863$	2.62429e13	1.61051	0.805256	−	0.592928i	$-0.202028\pi$
$863$	2.62429e13	1.61051	0.805256	+	0.592928i	$0.202028\pi$
$864$	5.60648e12	0.342277
$865$	−1.29527e13	−0.786664
$866$	−5.07234e11	−0.0306463
$867$	−1.86742e13	−1.12242
$868$	3.51418e13	2.10129
$869$	−1.45422e13	−0.865051
$870$	8.52829e11	0.0504691
$871$	3.78869e13	2.23053
$872$	−8.42113e12	−0.493226
$873$	5.15183e12	0.300191
$874$	−1.66783e12	−0.0966833
$875$	−1.69930e13	−0.980017
$876$	7.15953e11	0.0410786
$877$	−2.08051e13	−1.18760	−0.593801	−	0.804612i	$-0.702373\pi$
$877$	−2.08051e13	−1.18760	−0.593801	+	0.804612i	$0.702373\pi$
$878$	−5.50670e12	−0.312728
$879$	2.81391e13	1.58986
$880$	−1.35765e13	−0.763161
$881$	−1.13138e13	−0.632728	−0.316364	−	0.948638i	$-0.602462\pi$
$881$	−1.13138e13	−0.632728	−0.316364	+	0.948638i	$0.602462\pi$
$882$	−4.46995e11	−0.0248710
$883$	−1.51853e13	−0.840620	−0.420310	−	0.907381i	$-0.638079\pi$
$883$	−1.51853e13	−0.840620	−0.420310	+	0.907381i	$0.638079\pi$
$884$	5.81918e12	0.320499
$885$	−6.14144e12	−0.336531
$886$	1.17824e12	0.0642366
$887$	2.72566e13	1.47848	0.739239	−	0.673443i	$-0.235185\pi$
$887$	2.72566e13	1.47848	0.739239	+	0.673443i	$0.235185\pi$
$888$	1.32729e13	0.716318
$889$	−2.21205e13	−1.18778
$890$	1.52080e12	0.0812489
$891$	−4.05359e13	−2.15472
$892$	−2.29258e11	−0.0121250
$893$	−1.75336e13	−0.922654
$894$	1.84994e10	0.000968585 0
$895$	−9.28891e12	−0.483906
$896$	−1.51690e13	−0.786267
$897$	1.99693e13	1.02990
$898$	−1.33423e12	−0.0684681
$899$	1.64628e13	0.840591
$900$	6.96761e12	0.353991
$901$	−6.32107e12	−0.319543
$902$	2.52341e12	0.126928
$903$	−4.18092e12	−0.209256
$904$	−1.42707e13	−0.710701
$905$	7.73877e12	0.383490
$906$	−5.02435e12	−0.247744
$907$	2.59502e13	1.27323	0.636617	−	0.771180i	$-0.280333\pi$
$907$	2.59502e13	1.27323	0.636617	+	0.771180i	$0.280333\pi$
$908$	−9.12105e12	−0.445306
$909$	4.12531e12	0.200410
$910$	−2.61520e12	−0.126421
$911$	−3.68983e13	−1.77490	−0.887449	−	0.460906i	$-0.847524\pi$
$911$	−3.68983e13	−1.77490	−0.887449	+	0.460906i	$0.847524\pi$
$912$	1.59333e13	0.762658
$913$	4.82119e13	2.29634
$914$	−2.76503e12	−0.131052
$915$	1.50888e13	0.711637
$916$	−9.95893e12	−0.467394
$917$	−3.04720e12	−0.142311
$918$	−7.29481e11	−0.0339017
$919$	−2.70247e13	−1.24980	−0.624901	−	0.780704i	$-0.714861\pi$
$919$	−2.70247e13	−1.24980	−0.624901	+	0.780704i	$0.714861\pi$
$920$	−2.92024e12	−0.134392
$921$	−3.79710e13	−1.73894
$922$	7.02164e12	0.320000
$923$	−1.20407e13	−0.546064
$924$	5.04823e13	2.27832
$925$	−2.61089e13	−1.17260
$926$	−2.69398e11	−0.0120405
$927$	4.05046e12	0.180155
$928$	−5.36695e12	−0.237554
$929$	1.23795e13	0.545295	0.272647	−	0.962114i	$-0.412101\pi$
$929$	1.23795e13	0.545295	0.272647	+	0.962114i	$0.412101\pi$
$930$	5.15293e12	0.225882
$931$	4.26820e12	0.186197
$932$	3.24416e13	1.40842
$933$	−7.65016e12	−0.330524
$934$	−1.72008e11	−0.00739585
$935$	5.65994e12	0.242192
$936$	5.08841e12	0.216691
$937$	4.48371e13	1.90024	0.950122	−	0.311877i	$-0.100958\pi$
$937$	4.48371e13	1.90024	0.950122	+	0.311877i	$0.100958\pi$
$938$	9.70510e12	0.409343
$939$	−2.46866e13	−1.03625
$940$	−1.50614e13	−0.629203
$941$	1.28377e13	0.533743	0.266872	−	0.963732i	$-0.414010\pi$
$941$	1.28377e13	0.533743	0.266872	+	0.963732i	$0.414010\pi$
$942$	9.07105e12	0.375343
$943$	−6.67490e12	−0.274879
$944$	1.20625e13	0.494381
$945$	−8.55816e12	−0.349090
$946$	−1.24389e12	−0.0504976
$947$	1.85595e13	0.749881	0.374940	−	0.927049i	$-0.377663\pi$
$947$	1.85595e13	0.749881	0.374940	+	0.927049i	$0.377663\pi$
$948$	1.46603e13	0.589531
$949$	−1.02851e12	−0.0411632
$950$	2.54861e12	0.101519
$951$	1.68059e13	0.666269
$952$	3.03838e12	0.119888
$953$	−1.83614e13	−0.721086	−0.360543	−	0.932743i	$-0.617409\pi$
$953$	−1.83614e13	−0.721086	−0.360543	+	0.932743i	$0.617409\pi$
$954$	−2.71170e12	−0.105992
$955$	−2.13971e13	−0.832415
$956$	8.12690e12	0.314677
$957$	2.36493e13	0.911411
$958$	5.18578e12	0.198916
$959$	3.37028e13	1.28672
$960$	1.25312e13	0.476182
$961$	7.30311e13	2.76218
$962$	−9.35442e12	−0.352151
$963$	−7.92729e12	−0.297034
$964$	1.56153e12	0.0582378
$965$	7.93554e11	0.0294580
$966$	5.11532e12	0.189006
$967$	3.52191e13	1.29527	0.647633	−	0.761952i	$-0.275759\pi$
$967$	3.52191e13	1.29527	0.647633	+	0.761952i	$0.275759\pi$
$968$	2.03133e13	0.743603
$969$	−6.64248e12	−0.242032
$970$	1.61874e12	0.0587089
$971$	−1.76981e13	−0.638912	−0.319456	−	0.947601i	$-0.603500\pi$
$971$	−1.76981e13	−0.638912	−0.319456	+	0.947601i	$0.603500\pi$
$972$	2.41291e13	0.867049
$973$	−1.13071e13	−0.404431
$974$	−6.01150e12	−0.214026
$975$	−3.05149e13	−1.08141
$976$	−2.96360e13	−1.04543
$977$	−6.68753e12	−0.234823	−0.117411	−	0.993083i	$-0.537460\pi$
$977$	−6.68753e12	−0.234823	−0.117411	+	0.993083i	$0.537460\pi$
$978$	2.57144e12	0.0898775
$979$	4.21724e13	1.46726
$980$	3.66641e12	0.126977
$981$	−1.85213e13	−0.638500
$982$	−1.84777e12	−0.0634082
$983$	−1.67865e13	−0.573416	−0.286708	−	0.958018i	$-0.592561\pi$
$983$	−1.67865e13	−0.573416	−0.286708	+	0.958018i	$0.592561\pi$
$984$	−5.18526e12	−0.176316
$985$	−8.71031e12	−0.294829
$986$	6.98315e11	0.0235291
$987$	5.37762e13	1.80369
$988$	−2.38372e13	−0.795882
$989$	3.29032e12	0.109359
$990$	2.42808e12	0.0803349
$991$	−1.20190e13	−0.395856	−0.197928	−	0.980217i	$-0.563421\pi$
$991$	−1.20190e13	−0.395856	−0.197928	+	0.980217i	$0.563421\pi$
$992$	−3.24279e13	−1.06320
$993$	−2.05389e13	−0.670356
$994$	−3.08434e12	−0.100213
$995$	−1.25372e13	−0.405504
$996$	−4.86035e13	−1.56495
$997$	−2.34150e13	−0.750528	−0.375264	−	0.926918i	$-0.622448\pi$
$997$	−2.34150e13	−0.750528	−0.375264	+	0.926918i	$0.622448\pi$
$998$	6.36575e12	0.203125
$999$	−3.06121e13	−0.972406

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.b.1.7	✓	17
3.2	odd	2		387.10.a.e.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.7	✓	17	1.1	even	1	trivial
387.10.a.e.1.11		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)

\(f(q)\)	\(=\)	\(q-4.34621 q^{2} +171.146 q^{3} -493.110 q^{4} -694.593 q^{5} -743.834 q^{6} -7145.50 q^{7} +4368.42 q^{8} +9607.83 q^{9} +O(q^{10})\)	\(q-4.34621 q^{2} +171.146 q^{3} -493.110 q^{4} -694.593 q^{5} -743.834 q^{6} -7145.50 q^{7} +4368.42 q^{8} +9607.83 q^{9} +3018.84 q^{10} +83713.7 q^{11} -84393.7 q^{12} +121236. q^{13} +31055.8 q^{14} -118877. q^{15} +233487. q^{16} -97338.7 q^{17} -41757.6 q^{18} +398730. q^{19} +342511. q^{20} -1.22292e6 q^{21} -363837. q^{22} +962418. q^{23} +747636. q^{24} -1.47067e6 q^{25} -526917. q^{26} -1.72432e6 q^{27} +3.52352e6 q^{28} +1.65065e6 q^{29} +516662. q^{30} +9.97350e6 q^{31} -3.25141e6 q^{32} +1.43272e7 q^{33} +423054. q^{34} +4.96321e6 q^{35} -4.73772e6 q^{36} +1.77531e7 q^{37} -1.73296e6 q^{38} +2.07490e7 q^{39} -3.03427e6 q^{40} -6.93555e6 q^{41} +5.31507e6 q^{42} +3.41880e6 q^{43} -4.12801e7 q^{44} -6.67353e6 q^{45} -4.18287e6 q^{46} -4.39736e7 q^{47} +3.99602e7 q^{48} +1.07045e7 q^{49} +6.39182e6 q^{50} -1.66591e7 q^{51} -5.97828e7 q^{52} +6.49389e7 q^{53} +7.49426e6 q^{54} -5.81469e7 q^{55} -3.12145e7 q^{56} +6.82409e7 q^{57} -7.17408e6 q^{58} +5.16623e7 q^{59} +5.86193e7 q^{60} -1.26928e8 q^{61} -4.33469e7 q^{62} -6.86527e7 q^{63} -1.05414e8 q^{64} -8.42097e7 q^{65} -6.22691e7 q^{66} +3.12505e8 q^{67} +4.79987e7 q^{68} +1.64714e8 q^{69} -2.15711e7 q^{70} -9.93160e7 q^{71} +4.19710e7 q^{72} -8.48349e6 q^{73} -7.71587e7 q^{74} -2.51698e8 q^{75} -1.96618e8 q^{76} -5.98176e8 q^{77} -9.01796e7 q^{78} -1.73714e8 q^{79} -1.62178e8 q^{80} -4.84221e8 q^{81} +3.01433e7 q^{82} +5.75914e8 q^{83} +6.03035e8 q^{84} +6.76108e7 q^{85} -1.48588e7 q^{86} +2.82502e8 q^{87} +3.65696e8 q^{88} +5.03769e8 q^{89} +2.90045e7 q^{90} -8.66293e8 q^{91} -4.74579e8 q^{92} +1.70692e9 q^{93} +1.91118e8 q^{94} -2.76955e8 q^{95} -5.56465e8 q^{96} +5.36212e8 q^{97} -4.65240e7 q^{98} +8.04307e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9} + 23763 q^{10} + 78370 q^{11} + 271339 q^{12} + 114452 q^{13} - 376208 q^{14} - 255820 q^{15} + 412586 q^{16} + 726937 q^{17} + 577055 q^{18} + 544263 q^{19} + 3642183 q^{20} + 3137394 q^{21} + 5269148 q^{22} + 5575241 q^{23} + 16215113 q^{24} + 10874708 q^{25} + 8009180 q^{26} + 8350126 q^{27} + 12534764 q^{28} + 8223345 q^{29} + 30612012 q^{30} + 13054147 q^{31} + 37111710 q^{32} + 36024808 q^{33} + 27991291 q^{34} + 17826330 q^{35} + 84105953 q^{36} + 46733879 q^{37} + 15733789 q^{38} + 8689898 q^{39} + 52241669 q^{40} + 53667013 q^{41} + 7708286 q^{42} + 58119617 q^{43} + 81727236 q^{44} + 124361968 q^{45} + 146859355 q^{46} + 122945511 q^{47} + 86356095 q^{48} + 111396073 q^{49} - 96642133 q^{50} - 187132423 q^{51} - 54447944 q^{52} - 993146 q^{53} - 219468490 q^{54} - 248155792 q^{55} - 141048116 q^{56} - 402917960 q^{57} - 466599837 q^{58} - 95519644 q^{59} - 621611940 q^{60} - 311752038 q^{61} - 212471691 q^{62} - 928966350 q^{63} - 829842590 q^{64} - 107969830 q^{65} - 978530932 q^{66} - 292438130 q^{67} - 88281129 q^{68} + 78577726 q^{69} - 1650972530 q^{70} - 13576908 q^{71} - 706943493 q^{72} - 501490738 q^{73} - 494831691 q^{74} - 641914030 q^{75} - 1248630771 q^{76} + 787365348 q^{77} - 946670550 q^{78} + 740350275 q^{79} - 27802861 q^{80} + 1582210525 q^{81} - 1600400057 q^{82} + 754109940 q^{83} - 1955423842 q^{84} + 1071609956 q^{85} + 164102448 q^{86} + 186301257 q^{87} + 1863375104 q^{88} + 1470581868 q^{89} - 698098630 q^{90} + 2895349644 q^{91} + 1041082071 q^{92} + 4540331515 q^{93} - 706582361 q^{94} + 3297255729 q^{95} + 2087289393 q^{96} + 1949310583 q^{97} + 6695989160 q^{98} + 1234191326 q^{99}+O(q^{100}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9 + 23763 * q^10 + 78370 * q^11 + 271339 * q^12 + 114452 * q^13 - 376208 * q^14 - 255820 * q^15 + 412586 * q^16 + 726937 * q^17 + 577055 * q^18 + 544263 * q^19 + 3642183 * q^20 + 3137394 * q^21 + 5269148 * q^22 + 5575241 * q^23 + 16215113 * q^24 + 10874708 * q^25 + 8009180 * q^26 + 8350126 * q^27 + 12534764 * q^28 + 8223345 * q^29 + 30612012 * q^30 + 13054147 * q^31 + 37111710 * q^32 + 36024808 * q^33 + 27991291 * q^34 + 17826330 * q^35 + 84105953 * q^36 + 46733879 * q^37 + 15733789 * q^38 + 8689898 * q^39 + 52241669 * q^40 + 53667013 * q^41 + 7708286 * q^42 + 58119617 * q^43 + 81727236 * q^44 + 124361968 * q^45 + 146859355 * q^46 + 122945511 * q^47 + 86356095 * q^48 + 111396073 * q^49 - 96642133 * q^50 - 187132423 * q^51 - 54447944 * q^52 - 993146 * q^53 - 219468490 * q^54 - 248155792 * q^55 - 141048116 * q^56 - 402917960 * q^57 - 466599837 * q^58 - 95519644 * q^59 - 621611940 * q^60 - 311752038 * q^61 - 212471691 * q^62 - 928966350 * q^63 - 829842590 * q^64 - 107969830 * q^65 - 978530932 * q^66 - 292438130 * q^67 - 88281129 * q^68 + 78577726 * q^69 - 1650972530 * q^70 - 13576908 * q^71 - 706943493 * q^72 - 501490738 * q^73 - 494831691 * q^74 - 641914030 * q^75 - 1248630771 * q^76 + 787365348 * q^77 - 946670550 * q^78 + 740350275 * q^79 - 27802861 * q^80 + 1582210525 * q^81 - 1600400057 * q^82 + 754109940 * q^83 - 1955423842 * q^84 + 1071609956 * q^85 + 164102448 * q^86 + 186301257 * q^87 + 1863375104 * q^88 + 1470581868 * q^89 - 698098630 * q^90 + 2895349644 * q^91 + 1041082071 * q^92 + 4540331515 * q^93 - 706582361 * q^94 + 3297255729 * q^95 + 2087289393 * q^96 + 1949310583 * q^97 + 6695989160 * q^98 + 1234191326 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more