LMFDB - Embedded newform 43.10.a.b.1.11

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			1.11
Root			$-14.8584$ 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)

$f(q)$	$=$	$q+17.8584 q^{2} -263.946 q^{3} -193.078 q^{4} +542.767 q^{5} -4713.65 q^{6} -12329.9 q^{7} -12591.6 q^{8} +49984.5 q^{9} +O(q^{10})$	\(q+17.8584 q^{2} -263.946 q^{3} -193.078 q^{4} +542.767 q^{5} -4713.65 q^{6} -12329.9 q^{7} -12591.6 q^{8} +49984.5 q^{9} +9692.93 q^{10} -62214.2 q^{11} +50962.3 q^{12} -1612.70 q^{13} -220192. q^{14} -143261. q^{15} -126009. q^{16} +299545. q^{17} +892642. q^{18} +178333. q^{19} -104797. q^{20} +3.25443e6 q^{21} -1.11104e6 q^{22} +2.13660e6 q^{23} +3.32349e6 q^{24} -1.65853e6 q^{25} -28800.2 q^{26} -7.99796e6 q^{27} +2.38064e6 q^{28} +353461. q^{29} -2.55841e6 q^{30} -3.54498e6 q^{31} +4.19657e6 q^{32} +1.64212e7 q^{33} +5.34939e6 q^{34} -6.69226e6 q^{35} -9.65093e6 q^{36} -4.68076e6 q^{37} +3.18473e6 q^{38} +425665. q^{39} -6.83428e6 q^{40} -3.19964e7 q^{41} +5.81188e7 q^{42} +3.41880e6 q^{43} +1.20122e7 q^{44} +2.71299e7 q^{45} +3.81561e7 q^{46} -3.67397e7 q^{47} +3.32595e7 q^{48} +1.11673e8 q^{49} -2.96186e7 q^{50} -7.90637e7 q^{51} +311377. q^{52} +2.84403e7 q^{53} -1.42831e8 q^{54} -3.37678e7 q^{55} +1.55253e8 q^{56} -4.70702e7 q^{57} +6.31223e6 q^{58} -3.96644e7 q^{59} +2.76606e7 q^{60} +1.10955e8 q^{61} -6.33075e7 q^{62} -6.16304e8 q^{63} +1.39460e8 q^{64} -875319. q^{65} +2.93256e8 q^{66} +8.80180e7 q^{67} -5.78356e7 q^{68} -5.63946e8 q^{69} -1.19513e8 q^{70} -2.56106e8 q^{71} -6.29383e8 q^{72} +7.55335e7 q^{73} -8.35907e7 q^{74} +4.37762e8 q^{75} -3.44322e7 q^{76} +7.67095e8 q^{77} +7.60169e6 q^{78} +5.64490e7 q^{79} -6.83933e7 q^{80} +1.12719e9 q^{81} -5.71404e8 q^{82} +2.06085e8 q^{83} -6.28360e8 q^{84} +1.62583e8 q^{85} +6.10542e7 q^{86} -9.32945e7 q^{87} +7.83374e8 q^{88} +3.67011e7 q^{89} +4.84496e8 q^{90} +1.98844e7 q^{91} -4.12531e8 q^{92} +9.35683e8 q^{93} -6.56111e8 q^{94} +9.67931e7 q^{95} -1.10767e9 q^{96} +6.35358e8 q^{97} +1.99429e9 q^{98} -3.10975e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	17.8584	0.789236	0.394618	−	0.918845i	$-0.370877\pi$
$2$	17.8584	0.789236	0.394618	+	0.918845i	$0.370877\pi$
$3$	−263.946	−1.88135	−0.940675	−	0.339310i	$-0.889807\pi$
$3$	−263.946	−1.88135	−0.940675	+	0.339310i	$0.889807\pi$
$4$	−193.078	−0.377106
$5$	542.767	0.388372	0.194186	−	0.980965i	$-0.437793\pi$
$5$	542.767	0.388372	0.194186	+	0.980965i	$0.437793\pi$
$6$	−4713.65	−1.48483
$7$	−12329.9	−1.94097	−0.970484	−	0.241166i	$-0.922470\pi$
$7$	−12329.9	−1.94097	−0.970484	+	0.241166i	$0.922470\pi$
$8$	−12591.6	−1.08686
$9$	49984.5	2.53948
$10$	9692.93	0.306517
$11$	−62214.2	−1.28122	−0.640608	−	0.767868i	$-0.721318\pi$
$11$	−62214.2	−1.28122	−0.640608	+	0.767868i	$0.721318\pi$
$12$	50962.3	0.709469
$13$	−1612.70	−0.0156606	−0.00783029	−	0.999969i	$-0.502492\pi$
$13$	−1612.70	−0.0156606	−0.00783029	+	0.999969i	$0.502492\pi$
$14$	−220192.	−1.53188
$15$	−143261.	−0.730664
$16$	−126009.	−0.480685
$17$	299545.	0.869845	0.434922	−	0.900468i	$-0.356776\pi$
$17$	299545.	0.869845	0.434922	+	0.900468i	$0.356776\pi$
$18$	892642.	2.00425
$19$	178333.	0.313935	0.156968	−	0.987604i	$-0.449828\pi$
$19$	178333.	0.313935	0.156968	+	0.987604i	$0.449828\pi$
$20$	−104797.	−0.146458
$21$	3.25443e6	3.65164
$22$	−1.11104e6	−1.01118
$23$	2.13660e6	1.59202	0.796008	−	0.605286i	$-0.206941\pi$
$23$	2.13660e6	1.59202	0.796008	+	0.605286i	$0.206941\pi$
$24$	3.32349e6	2.04477
$25$	−1.65853e6	−0.849167
$26$	−28800.2	−0.0123599
$27$	−7.99796e6	−2.89629
$28$	2.38064e6	0.731951
$29$	353461.	0.0928004	0.0464002	−	0.998923i	$-0.485225\pi$
$29$	353461.	0.0928004	0.0464002	+	0.998923i	$0.485225\pi$
$30$	−2.55841e6	−0.576666
$31$	−3.54498e6	−0.689423	−0.344712	−	0.938709i	$-0.612023\pi$
$31$	−3.54498e6	−0.689423	−0.344712	+	0.938709i	$0.612023\pi$
$32$	4.19657e6	0.707488
$33$	1.64212e7	2.41042
$34$	5.34939e6	0.686513
$35$	−6.69226e6	−0.753818
$36$	−9.65093e6	−0.957652
$37$	−4.68076e6	−0.410590	−0.205295	−	0.978700i	$-0.565815\pi$
$37$	−4.68076e6	−0.410590	−0.205295	+	0.978700i	$0.565815\pi$
$38$	3.18473e6	0.247769
$39$	425665.	0.0294630
$40$	−6.83428e6	−0.422107
$41$	−3.19964e7	−1.76837	−0.884186	−	0.467135i	$-0.845286\pi$
$41$	−3.19964e7	−1.76837	−0.884186	+	0.467135i	$0.845286\pi$
$42$	5.81188e7	2.88201
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	1.20122e7	0.483155
$45$	2.71299e7	0.986262
$46$	3.81561e7	1.25648
$47$	−3.67397e7	−1.09823	−0.549117	−	0.835746i	$-0.685036\pi$
$47$	−3.67397e7	−1.09823	−0.549117	+	0.835746i	$0.685036\pi$
$48$	3.32595e7	0.904336
$49$	1.11673e8	2.76736
$50$	−2.96186e7	−0.670193
$51$	−7.90637e7	−1.63648
$52$	311377.	0.00590570
$53$	2.84403e7	0.495099	0.247549	−	0.968875i	$-0.420375\pi$
$53$	2.84403e7	0.495099	0.247549	+	0.968875i	$0.420375\pi$
$54$	−1.42831e8	−2.28586
$55$	−3.37678e7	−0.497589
$56$	1.55253e8	2.10956
$57$	−4.70702e7	−0.590622
$58$	6.31223e6	0.0732414
$59$	−3.96644e7	−0.426154	−0.213077	−	0.977035i	$-0.568349\pi$
$59$	−3.96644e7	−0.426154	−0.213077	+	0.977035i	$0.568349\pi$
$60$	2.76606e7	0.275538
$61$	1.10955e8	1.02603	0.513016	−	0.858379i	$-0.328528\pi$
$61$	1.10955e8	1.02603	0.513016	+	0.858379i	$0.328528\pi$
$62$	−6.33075e7	−0.544118
$63$	−6.16304e8	−4.92904
$64$	1.39460e8	1.03906
$65$	−875319.	−0.00608214
$66$	2.93256e8	1.90239
$67$	8.80180e7	0.533623	0.266812	−	0.963749i	$-0.414030\pi$
$67$	8.80180e7	0.533623	0.266812	+	0.963749i	$0.414030\pi$
$68$	−5.78356e7	−0.328024
$69$	−5.63946e8	−2.99514
$70$	−1.19513e8	−0.594941
$71$	−2.56106e8	−1.19607	−0.598037	−	0.801469i	$-0.704052\pi$
$71$	−2.56106e8	−1.19607	−0.598037	+	0.801469i	$0.704052\pi$
$72$	−6.29383e8	−2.76006
$73$	7.55335e7	0.311306	0.155653	−	0.987812i	$-0.450252\pi$
$73$	7.55335e7	0.311306	0.155653	+	0.987812i	$0.450252\pi$
$74$	−8.35907e7	−0.324053
$75$	4.37762e8	1.59758
$76$	−3.44322e7	−0.118387
$77$	7.67095e8	2.48680
$78$	7.60169e6	0.0232533
$79$	5.64490e7	0.163055	0.0815275	−	0.996671i	$-0.474020\pi$
$79$	5.64490e7	0.163055	0.0815275	+	0.996671i	$0.474020\pi$
$80$	−6.83933e7	−0.186685
$81$	1.12719e9	2.90946
$82$	−5.71404e8	−1.39566
$83$	2.06085e8	0.476645	0.238323	−	0.971186i	$-0.423402\pi$
$83$	2.06085e8	0.476645	0.238323	+	0.971186i	$0.423402\pi$
$84$	−6.28360e8	−1.37706
$85$	1.62583e8	0.337824
$86$	6.10542e7	0.120357
$87$	−9.32945e7	−0.174590
$88$	7.83374e8	1.39251
$89$	3.67011e7	0.0620046	0.0310023	−	0.999519i	$-0.490130\pi$
$89$	3.67011e7	0.0620046	0.0310023	+	0.999519i	$0.490130\pi$
$90$	4.84496e8	0.778394
$91$	1.98844e7	0.0303967
$92$	−4.12531e8	−0.600359
$93$	9.35683e8	1.29705
$94$	−6.56111e8	−0.866766
$95$	9.67931e7	0.121924
$96$	−1.10767e9	−1.33103
$97$	6.35358e8	0.728695	0.364348	−	0.931263i	$-0.381292\pi$
$97$	6.35358e8	0.728695	0.364348	+	0.931263i	$0.381292\pi$
$98$	1.99429e9	2.18410
$99$	−3.10975e9	−3.25362
$100$	3.20226e8	0.320226
$101$	−3.94028e8	−0.376774	−0.188387	−	0.982095i	$-0.560326\pi$
$101$	−3.94028e8	−0.376774	−0.188387	+	0.982095i	$0.560326\pi$
$102$	−1.41195e9	−1.29157
$103$	1.21187e9	1.06093	0.530467	−	0.847706i	$-0.322017\pi$
$103$	1.21187e9	1.06093	0.530467	+	0.847706i	$0.322017\pi$
$104$	2.03064e7	0.0170209
$105$	1.76640e9	1.41820
$106$	5.07897e8	0.390750
$107$	1.78380e9	1.31558	0.657792	−	0.753200i	$-0.271491\pi$
$107$	1.78380e9	1.31558	0.657792	+	0.753200i	$0.271491\pi$
$108$	1.54423e9	1.09221
$109$	−2.01755e9	−1.36901	−0.684504	−	0.729010i	$-0.739981\pi$
$109$	−2.01755e9	−1.36901	−0.684504	+	0.729010i	$0.739981\pi$
$110$	−6.03038e8	−0.392715
$111$	1.23547e9	0.772463
$112$	1.55367e9	0.932993
$113$	−1.34770e9	−0.777571	−0.388786	−	0.921328i	$-0.627105\pi$
$113$	−1.34770e9	−0.777571	−0.388786	+	0.921328i	$0.627105\pi$
$114$	−8.40598e8	−0.466140
$115$	1.15967e9	0.618295
$116$	−6.82456e7	−0.0349956
$117$	−8.06099e7	−0.0397697
$118$	−7.08341e8	−0.336336
$119$	−3.69336e9	−1.68834
$120$	1.80388e9	0.794131
$121$	1.51266e9	0.641516
$122$	1.98147e9	0.809782
$123$	8.44532e9	3.32693
$124$	6.84459e8	0.259986
$125$	−1.96029e9	−0.718165
$126$	−1.10062e10	−3.89018
$127$	2.05640e9	0.701441	0.350721	−	0.936480i	$-0.385937\pi$
$127$	2.05640e9	0.701441	0.350721	+	0.936480i	$0.385937\pi$
$128$	3.41892e8	0.112575
$129$	−9.02379e8	−0.286903
$130$	−1.56318e7	−0.00480024
$131$	−2.96429e8	−0.0879426	−0.0439713	−	0.999033i	$-0.514001\pi$
$131$	−2.96429e8	−0.0879426	−0.0439713	+	0.999033i	$0.514001\pi$
$132$	−3.17058e9	−0.908983
$133$	−2.19882e9	−0.609338
$134$	1.57186e9	0.421155
$135$	−4.34103e9	−1.12484
$136$	−3.77174e9	−0.945401
$137$	3.88758e9	0.942839	0.471419	−	0.881909i	$-0.343742\pi$
$137$	3.88758e9	0.942839	0.471419	+	0.881909i	$0.343742\pi$
$138$	−1.00712e10	−2.36387
$139$	4.47607e9	1.01702	0.508511	−	0.861056i	$-0.330196\pi$
$139$	4.47607e9	1.01702	0.508511	+	0.861056i	$0.330196\pi$
$140$	1.29213e9	0.284270
$141$	9.69729e9	2.06616
$142$	−4.57364e9	−0.943985
$143$	1.00333e8	0.0200646
$144$	−6.29848e9	−1.22069
$145$	1.91847e8	0.0360411
$146$	1.34891e9	0.245694
$147$	−2.94756e10	−5.20636
$148$	9.03753e8	0.154836
$149$	5.77103e7	0.00959213	0.00479607	−	0.999988i	$-0.498473\pi$
$149$	5.77103e7	0.00959213	0.00479607	+	0.999988i	$0.498473\pi$
$150$	7.81772e9	1.26087
$151$	9.70737e9	1.51952	0.759758	−	0.650206i	$-0.225317\pi$
$151$	9.70737e9	1.51952	0.759758	+	0.650206i	$0.225317\pi$
$152$	−2.24549e9	−0.341204
$153$	1.49726e10	2.20895
$154$	1.36991e10	1.96267
$155$	−1.92410e9	−0.267753
$156$	−8.21868e7	−0.0111107
$157$	3.48104e9	0.457258	0.228629	−	0.973514i	$-0.426576\pi$
$157$	3.48104e9	0.457258	0.228629	+	0.973514i	$0.426576\pi$
$158$	1.00809e9	0.128689
$159$	−7.50669e9	−0.931454
$160$	2.27776e9	0.274769
$161$	−2.63440e10	−3.09005
$162$	2.01297e10	2.29625
$163$	−8.59453e9	−0.953626	−0.476813	−	0.879005i	$-0.658208\pi$
$163$	−8.59453e9	−0.953626	−0.476813	+	0.879005i	$0.658208\pi$
$164$	6.17781e9	0.666864
$165$	8.91288e9	0.936139
$166$	3.68035e9	0.376186
$167$	1.56830e10	1.56029	0.780146	−	0.625597i	$-0.215145\pi$
$167$	1.56830e10	1.56029	0.780146	+	0.625597i	$0.215145\pi$
$168$	−4.09783e10	−3.96883
$169$	−1.06019e10	−0.999755
$170$	2.90347e9	0.266623
$171$	8.91387e9	0.797231
$172$	−6.60097e8	−0.0575082
$173$	1.41376e10	1.19997	0.599984	−	0.800012i	$-0.295174\pi$
$173$	1.41376e10	1.19997	0.599984	+	0.800012i	$0.295174\pi$
$174$	−1.66609e9	−0.137793
$175$	2.04495e10	1.64821
$176$	7.83953e9	0.615861
$177$	1.04693e10	0.801744
$178$	6.55422e8	0.0489363
$179$	−3.13844e9	−0.228494	−0.114247	−	0.993452i	$-0.536446\pi$
$179$	−3.13844e9	−0.228494	−0.114247	+	0.993452i	$0.536446\pi$
$180$	−5.23820e9	−0.371926
$181$	9.58919e9	0.664092	0.332046	−	0.943263i	$-0.392261\pi$
$181$	9.58919e9	0.664092	0.332046	+	0.943263i	$0.392261\pi$
$182$	3.55103e8	0.0239902
$183$	−2.92860e10	−1.93033
$184$	−2.69031e10	−1.73030
$185$	−2.54056e9	−0.159462
$186$	1.67098e10	1.02368
$187$	−1.86360e10	−1.11446
$188$	7.09363e9	0.414151
$189$	9.86140e10	5.62161
$190$	1.72857e9	0.0962266
$191$	−1.32511e10	−0.720444	−0.360222	−	0.932867i	$-0.617299\pi$
$191$	−1.32511e10	−0.720444	−0.360222	+	0.932867i	$0.617299\pi$
$192$	−3.68100e10	−1.95484
$193$	2.54411e9	0.131986	0.0659930	−	0.997820i	$-0.478978\pi$
$193$	2.54411e9	0.131986	0.0659930	+	0.997820i	$0.478978\pi$
$194$	1.13465e10	0.575113
$195$	2.31037e8	0.0114426
$196$	−2.15616e10	−1.04359
$197$	−1.71149e10	−0.809612	−0.404806	−	0.914403i	$-0.632661\pi$
$197$	−1.71149e10	−0.809612	−0.404806	+	0.914403i	$0.632661\pi$
$198$	−5.55350e10	−2.56787
$199$	−4.13350e10	−1.86844	−0.934221	−	0.356695i	$-0.883903\pi$
$199$	−4.13350e10	−1.86844	−0.934221	+	0.356695i	$0.883903\pi$
$200$	2.08835e10	0.922927
$201$	−2.32320e10	−1.00393
$202$	−7.03671e9	−0.297364
$203$	−4.35813e9	−0.180123
$204$	1.52655e10	0.617128
$205$	−1.73666e10	−0.686787
$206$	2.16420e10	0.837328
$207$	1.06797e11	4.04288
$208$	2.03214e8	0.00752780
$209$	−1.10948e10	−0.402219
$210$	3.15450e10	1.11929
$211$	1.63594e9	0.0568192	0.0284096	−	0.999596i	$-0.490956\pi$
$211$	1.63594e9	0.0568192	0.0284096	+	0.999596i	$0.490956\pi$
$212$	−5.49120e9	−0.186705
$213$	6.75983e10	2.25023
$214$	3.18557e10	1.03831
$215$	1.85561e9	0.0592262
$216$	1.00707e11	3.14787
$217$	4.37092e10	1.33815
$218$	−3.60302e10	−1.08047
$219$	−1.99368e10	−0.585675
$220$	6.51983e9	0.187644
$221$	−4.83075e8	−0.0136223
$222$	2.20634e10	0.609656
$223$	−1.03055e10	−0.279059	−0.139529	−	0.990218i	$-0.544559\pi$
$223$	−1.03055e10	−0.279059	−0.139529	+	0.990218i	$0.544559\pi$
$224$	−5.17432e10	−1.37321
$225$	−8.29008e10	−2.15644
$226$	−2.40677e10	−0.613687
$227$	3.19747e10	0.799263	0.399632	−	0.916676i	$-0.369138\pi$
$227$	3.19747e10	0.799263	0.399632	+	0.916676i	$0.369138\pi$
$228$	9.08824e9	0.222727
$229$	4.65306e10	1.11810	0.559048	−	0.829135i	$-0.311167\pi$
$229$	4.65306e10	1.11810	0.559048	+	0.829135i	$0.311167\pi$
$230$	2.07099e10	0.487981
$231$	−2.02472e11	−4.67854
$232$	−4.45062e9	−0.100861
$233$	−7.78222e10	−1.72982	−0.864912	−	0.501924i	$-0.832626\pi$
$233$	−7.78222e10	−1.72982	−0.864912	+	0.501924i	$0.832626\pi$
$234$	−1.43956e9	−0.0313877
$235$	−1.99411e10	−0.426524
$236$	7.65833e9	0.160705
$237$	−1.48995e10	−0.306763
$238$	−6.59574e10	−1.33250
$239$	−8.97205e10	−1.77869	−0.889347	−	0.457233i	$-0.848840\pi$
$239$	−8.97205e10	−1.77869	−0.889347	+	0.457233i	$0.848840\pi$
$240$	1.80521e10	0.351219
$241$	3.18390e8	0.00607971	0.00303986	−	0.999995i	$-0.499032\pi$
$241$	3.18390e8	0.00607971	0.00303986	+	0.999995i	$0.499032\pi$
$242$	2.70137e10	0.506308
$243$	−1.40092e11	−2.57742
$244$	−2.14229e10	−0.386923
$245$	6.06123e10	1.07476
$246$	1.50820e11	2.62573
$247$	−2.87597e8	−0.00491641
$248$	4.46368e10	0.749308
$249$	−5.43954e10	−0.896737
$250$	−3.50075e10	−0.566802
$251$	5.74998e10	0.914396	0.457198	−	0.889365i	$-0.348853\pi$
$251$	5.74998e10	0.914396	0.457198	+	0.889365i	$0.348853\pi$
$252$	1.18995e11	1.85877
$253$	−1.32927e11	−2.03972
$254$	3.67240e10	0.553603
$255$	−4.29131e10	−0.635564
$256$	−6.52980e10	−0.950211
$257$	2.98098e9	0.0426246	0.0213123	−	0.999773i	$-0.493216\pi$
$257$	2.98098e9	0.0426246	0.0213123	+	0.999773i	$0.493216\pi$
$258$	−1.61150e10	−0.226434
$259$	5.77133e10	0.796942
$260$	1.69005e8	0.00229361
$261$	1.76675e10	0.235664
$262$	−5.29373e9	−0.0694075
$263$	3.90444e10	0.503220	0.251610	−	0.967829i	$-0.419040\pi$
$263$	3.90444e10	0.503220	0.251610	+	0.967829i	$0.419040\pi$
$264$	−2.06768e11	−2.61979
$265$	1.54364e10	0.192283
$266$	−3.92674e10	−0.480912
$267$	−9.68710e9	−0.116652
$268$	−1.69944e10	−0.201233
$269$	8.79555e10	1.02418	0.512092	−	0.858931i	$-0.328871\pi$
$269$	8.79555e10	1.02418	0.512092	+	0.858931i	$0.328871\pi$
$270$	−7.75237e10	−0.887764
$271$	1.39932e11	1.57600	0.787999	−	0.615677i	$-0.211117\pi$
$271$	1.39932e11	1.57600	0.787999	+	0.615677i	$0.211117\pi$
$272$	−3.77452e10	−0.418121
$273$	−5.24841e9	−0.0571868
$274$	6.94260e10	0.744122
$275$	1.03184e11	1.08797
$276$	1.08886e11	1.12949
$277$	−1.30837e11	−1.33528	−0.667641	−	0.744483i	$-0.732696\pi$
$277$	−1.30837e11	−1.33528	−0.667641	+	0.744483i	$0.732696\pi$
$278$	7.99353e10	0.802670
$279$	−1.77194e11	−1.75077
$280$	8.42660e10	0.819296
$281$	5.07202e10	0.485292	0.242646	−	0.970115i	$-0.421985\pi$
$281$	5.07202e10	0.485292	0.242646	+	0.970115i	$0.421985\pi$
$282$	1.73178e11	1.63069
$283$	1.50237e11	1.39231	0.696156	−	0.717891i	$-0.254892\pi$
$283$	1.50237e11	1.39231	0.696156	+	0.717891i	$0.254892\pi$
$284$	4.94486e10	0.451047
$285$	−2.55482e10	−0.229381
$286$	1.79178e9	0.0158357
$287$	3.94512e11	3.43235
$288$	2.09763e11	1.79665
$289$	−2.88607e10	−0.243370
$290$	3.42607e9	0.0284449
$291$	−1.67700e11	−1.37093
$292$	−1.45839e10	−0.117395
$293$	7.70103e9	0.0610442	0.0305221	−	0.999534i	$-0.490283\pi$
$293$	7.70103e9	0.0610442	0.0305221	+	0.999534i	$0.490283\pi$
$294$	−5.26386e11	−4.10905
$295$	−2.15285e10	−0.165506
$296$	5.89380e10	0.446255
$297$	4.97587e11	3.71078
$298$	1.03061e9	0.00757046
$299$	−3.44569e9	−0.0249319
$300$	−8.45224e10	−0.602457
$301$	−4.21535e10	−0.295995
$302$	1.73358e11	1.19926
$303$	1.04002e11	0.708844
$304$	−2.24715e10	−0.150904
$305$	6.02225e10	0.398483
$306$	2.67386e11	1.74338
$307$	−1.58304e11	−1.01711	−0.508555	−	0.861030i	$-0.669820\pi$
$307$	−1.58304e11	−1.01711	−0.508555	+	0.861030i	$0.669820\pi$
$308$	−1.48109e11	−0.937788
$309$	−3.19868e11	−1.99599
$310$	−3.43612e10	−0.211320
$311$	−1.37182e10	−0.0831528	−0.0415764	−	0.999135i	$-0.513238\pi$
$311$	−1.37182e10	−0.0831528	−0.0415764	+	0.999135i	$0.513238\pi$
$312$	−5.35979e9	−0.0320223
$313$	−6.35309e10	−0.374141	−0.187071	−	0.982346i	$-0.559899\pi$
$313$	−6.35309e10	−0.374141	−0.187071	+	0.982346i	$0.559899\pi$
$314$	6.21658e10	0.360884
$315$	−3.34509e11	−1.91430
$316$	−1.08991e10	−0.0614890
$317$	8.45007e10	0.469995	0.234998	−	0.971996i	$-0.424492\pi$
$317$	8.45007e10	0.469995	0.234998	+	0.971996i	$0.424492\pi$
$318$	−1.34057e11	−0.735137
$319$	−2.19903e10	−0.118897
$320$	7.56944e10	0.403542
$321$	−4.70826e11	−2.47507
$322$	−4.70461e11	−2.43878
$323$	5.34187e10	0.273075
$324$	−2.17635e11	−1.09718
$325$	2.67471e9	0.0132985
$326$	−1.53484e11	−0.752636
$327$	5.32525e11	2.57558
$328$	4.02884e11	1.92198
$329$	4.52996e11	2.13164
$330$	1.59170e11	0.738835
$331$	−3.02866e11	−1.38683	−0.693417	−	0.720537i	$-0.743895\pi$
$331$	−3.02866e11	−1.38683	−0.693417	+	0.720537i	$0.743895\pi$
$332$	−3.97906e10	−0.179746
$333$	−2.33965e11	−1.04268
$334$	2.80074e11	1.23144
$335$	4.77733e10	0.207245
$336$	−4.10086e11	−1.75529
$337$	4.25162e11	1.79564	0.897821	−	0.440360i	$-0.145149\pi$
$337$	4.25162e11	1.79564	0.897821	+	0.440360i	$0.145149\pi$
$338$	−1.89333e11	−0.789043
$339$	3.55720e11	1.46288
$340$	−3.13913e10	−0.127395
$341$	2.20548e11	0.883300
$342$	1.59187e11	0.629203
$343$	−8.79358e11	−3.43038
$344$	−4.30480e10	−0.165745
$345$	−3.06091e11	−1.16323
$346$	2.52475e11	0.947058
$347$	2.27802e11	0.843481	0.421740	−	0.906717i	$-0.361419\pi$
$347$	2.27802e11	0.843481	0.421740	+	0.906717i	$0.361419\pi$
$348$	1.80132e10	0.0658390
$349$	−1.66392e11	−0.600369	−0.300184	−	0.953881i	$-0.597048\pi$
$349$	−1.66392e11	−0.600369	−0.300184	+	0.953881i	$0.597048\pi$
$350$	3.65195e11	1.30082
$351$	1.28983e10	0.0453576
$352$	−2.61086e11	−0.906446
$353$	−1.16576e11	−0.399597	−0.199799	−	0.979837i	$-0.564029\pi$
$353$	−1.16576e11	−0.399597	−0.199799	+	0.979837i	$0.564029\pi$
$354$	1.86964e11	0.632766
$355$	−1.39006e11	−0.464522
$356$	−7.08618e9	−0.0233823
$357$	9.74847e11	3.17636
$358$	−5.60474e10	−0.180336
$359$	5.13617e11	1.63198	0.815989	−	0.578067i	$-0.196193\pi$
$359$	5.13617e11	1.63198	0.815989	+	0.578067i	$0.196193\pi$
$360$	−3.41608e11	−1.07193
$361$	−2.90885e11	−0.901445
$362$	1.71247e11	0.524125
$363$	−3.99261e11	−1.20692
$364$	−3.83925e9	−0.0114628
$365$	4.09971e10	0.120902
$366$	−5.23001e11	−1.52348
$367$	1.13487e11	0.326550	0.163275	−	0.986581i	$-0.447794\pi$
$367$	1.13487e11	0.326550	0.163275	+	0.986581i	$0.447794\pi$
$368$	−2.69230e11	−0.765257
$369$	−1.59932e12	−4.49074
$370$	−4.53703e10	−0.125853
$371$	−3.50665e11	−0.960971
$372$	−1.80660e11	−0.489124
$373$	−3.83069e11	−1.02468	−0.512339	−	0.858783i	$-0.671221\pi$
$373$	−3.83069e11	−1.02468	−0.512339	+	0.858783i	$0.671221\pi$
$374$	−3.32808e11	−0.879572
$375$	5.17410e11	1.35112
$376$	4.62609e11	1.19363
$377$	−5.70025e8	−0.00145331
$378$	1.76109e12	4.43678
$379$	3.39826e11	0.846020	0.423010	−	0.906125i	$-0.360974\pi$
$379$	3.39826e11	0.846020	0.423010	+	0.906125i	$0.360974\pi$
$380$	−1.86887e10	−0.0459782
$381$	−5.42779e11	−1.31966
$382$	−2.36642e11	−0.568600
$383$	2.56152e11	0.608279	0.304140	−	0.952627i	$-0.401631\pi$
$383$	2.56152e11	0.608279	0.304140	+	0.952627i	$0.401631\pi$
$384$	−9.02410e10	−0.211794
$385$	4.16354e11	0.965804
$386$	4.54337e10	0.104168
$387$	1.70887e11	0.387266
$388$	−1.22674e11	−0.274796
$389$	−1.09872e11	−0.243284	−0.121642	−	0.992574i	$-0.538816\pi$
$389$	−1.09872e11	−0.243284	−0.121642	+	0.992574i	$0.538816\pi$
$390$	4.12595e9	0.00903093
$391$	6.40007e11	1.38481
$392$	−1.40613e12	−3.00773
$393$	7.82411e10	0.165451
$394$	−3.05645e11	−0.638975
$395$	3.06386e10	0.0633260
$396$	6.00425e11	1.22696
$397$	1.29718e11	0.262085	0.131042	−	0.991377i	$-0.458168\pi$
$397$	1.29718e11	0.262085	0.131042	+	0.991377i	$0.458168\pi$
$398$	−7.38177e11	−1.47464
$399$	5.80371e11	1.14638
$400$	2.08989e11	0.408182
$401$	−2.09370e11	−0.404357	−0.202179	−	0.979349i	$-0.564802\pi$
$401$	−2.09370e11	−0.404357	−0.202179	+	0.979349i	$0.564802\pi$
$402$	−4.14886e11	−0.792340
$403$	5.71698e9	0.0107968
$404$	7.60784e10	0.142084
$405$	6.11799e11	1.12995
$406$	−7.78292e10	−0.142159
$407$	2.91210e11	0.526055
$408$	9.95535e11	1.77863
$409$	4.47429e11	0.790623	0.395311	−	0.918547i	$-0.370637\pi$
$409$	4.47429e11	0.790623	0.395311	+	0.918547i	$0.370637\pi$
$410$	−3.10139e11	−0.542037
$411$	−1.02611e12	−1.77381
$412$	−2.33986e11	−0.400085
$413$	4.89058e11	0.827151
$414$	1.90722e12	3.19079
$415$	1.11856e11	0.185116
$416$	−6.76780e9	−0.0110797
$417$	−1.18144e12	−1.91337
$418$	−1.98136e11	−0.317446
$419$	−3.30875e10	−0.0524447	−0.0262223	−	0.999656i	$-0.508348\pi$
$419$	−3.30875e10	−0.0524447	−0.0262223	+	0.999656i	$0.508348\pi$
$420$	−3.41053e11	−0.534810
$421$	6.72742e11	1.04371	0.521854	−	0.853035i	$-0.325241\pi$
$421$	6.72742e11	1.04371	0.521854	+	0.853035i	$0.325241\pi$
$422$	2.92151e10	0.0448438
$423$	−1.83641e12	−2.78894
$424$	−3.58107e11	−0.538104
$425$	−4.96804e11	−0.738643
$426$	1.20720e12	1.77596
$427$	−1.36806e12	−1.99150
$428$	−3.44413e11	−0.496115
$429$	−2.64824e10	−0.0377485
$430$	3.31382e10	0.0467435
$431$	3.03216e11	0.423257	0.211629	−	0.977350i	$-0.432123\pi$
$431$	3.03216e11	0.423257	0.211629	+	0.977350i	$0.432123\pi$
$432$	1.00781e12	1.39220
$433$	9.04290e11	1.23627	0.618134	−	0.786073i	$-0.287889\pi$
$433$	9.04290e11	1.23627	0.618134	+	0.786073i	$0.287889\pi$
$434$	7.80576e11	1.05611
$435$	−5.06372e10	−0.0678059
$436$	3.89546e11	0.516261
$437$	3.81025e11	0.499790
$438$	−3.56038e11	−0.462236
$439$	−5.18533e11	−0.666325	−0.333163	−	0.942869i	$-0.608116\pi$
$439$	−5.18533e11	−0.666325	−0.333163	+	0.942869i	$0.608116\pi$
$440$	4.25189e11	0.540811
$441$	5.58191e12	7.02763
$442$	−8.62694e9	−0.0107512
$443$	5.83805e10	0.0720196	0.0360098	−	0.999351i	$-0.488535\pi$
$443$	5.83805e10	0.0720196	0.0360098	+	0.999351i	$0.488535\pi$
$444$	−2.38542e11	−0.291301
$445$	1.99201e10	0.0240809
$446$	−1.84039e11	−0.220243
$447$	−1.52324e10	−0.0180462
$448$	−1.71953e12	−2.01678
$449$	5.60165e10	0.0650440	0.0325220	−	0.999471i	$-0.489646\pi$
$449$	5.60165e10	0.0650440	0.0325220	+	0.999471i	$0.489646\pi$
$450$	−1.48047e12	−1.70194
$451$	1.99063e12	2.26567
$452$	2.60212e11	0.293227
$453$	−2.56222e12	−2.85874
$454$	5.71016e11	0.630807
$455$	1.07926e10	0.0118052
$456$	5.92687e11	0.641924
$457$	4.66456e11	0.500251	0.250125	−	0.968213i	$-0.419528\pi$
$457$	4.66456e11	0.500251	0.250125	+	0.968213i	$0.419528\pi$
$458$	8.30962e11	0.882442
$459$	−2.39575e12	−2.51932
$460$	−2.23908e11	−0.233163
$461$	5.12024e11	0.528003	0.264002	−	0.964522i	$-0.414958\pi$
$461$	5.12024e11	0.528003	0.264002	+	0.964522i	$0.414958\pi$
$462$	−3.61582e12	−3.69247
$463$	7.61896e11	0.770515	0.385257	−	0.922809i	$-0.374113\pi$
$463$	7.61896e11	0.770515	0.385257	+	0.922809i	$0.374113\pi$
$464$	−4.45391e10	−0.0446077
$465$	5.07858e11	0.503737
$466$	−1.38978e12	−1.36524
$467$	−4.59638e11	−0.447188	−0.223594	−	0.974682i	$-0.571779\pi$
$467$	−4.59638e11	−0.447188	−0.223594	+	0.974682i	$0.571779\pi$
$468$	1.55640e10	0.0149974
$469$	−1.08525e12	−1.03575
$470$	−3.56115e11	−0.336628
$471$	−9.18807e11	−0.860261
$472$	4.99436e11	0.463171
$473$	−2.12698e11	−0.195384
$474$	−2.66080e11	−0.242109
$475$	−2.95770e11	−0.266583
$476$	7.13108e11	0.636684
$477$	1.42157e12	1.25729
$478$	−1.60226e12	−1.40381
$479$	−1.47088e12	−1.27663	−0.638317	−	0.769773i	$-0.720369\pi$
$479$	−1.47088e12	−1.27663	−0.638317	+	0.769773i	$0.720369\pi$
$480$	−6.01205e11	−0.516936
$481$	7.54865e9	0.00643008
$482$	5.68593e9	0.00479833
$483$	6.95340e12	5.81347
$484$	−2.92062e11	−0.241920
$485$	3.44851e11	0.283005
$486$	−2.50182e12	−2.03419
$487$	−2.00769e12	−1.61740	−0.808699	−	0.588223i	$-0.799828\pi$
$487$	−2.00769e12	−1.61740	−0.808699	+	0.588223i	$0.799828\pi$
$488$	−1.39709e12	−1.11516
$489$	2.26849e12	1.79410
$490$	1.08244e12	0.848243
$491$	−6.70747e10	−0.0520826	−0.0260413	−	0.999661i	$-0.508290\pi$
$491$	−6.70747e10	−0.0520826	−0.0260413	+	0.999661i	$0.508290\pi$
$492$	−1.63061e12	−1.25460
$493$	1.05877e11	0.0807220
$494$	−5.13601e9	−0.00388021
$495$	−1.68787e12	−1.26362
$496$	4.46698e11	0.331395
$497$	3.15777e12	2.32154
$498$	−9.71413e11	−0.707737
$499$	6.22530e11	0.449477	0.224739	−	0.974419i	$-0.427847\pi$
$499$	6.22530e11	0.449477	0.224739	+	0.974419i	$0.427847\pi$
$500$	3.78489e11	0.270825
$501$	−4.13947e12	−2.93546
$502$	1.02685e12	0.721674
$503$	−7.04840e11	−0.490947	−0.245473	−	0.969403i	$-0.578943\pi$
$503$	−7.04840e11	−0.490947	−0.245473	+	0.969403i	$0.578943\pi$
$504$	7.76022e12	5.35719
$505$	−2.13865e11	−0.146329
$506$	−2.37385e12	−1.60982
$507$	2.79833e12	1.88089
$508$	−3.97047e11	−0.264518
$509$	3.83439e11	0.253201	0.126601	−	0.991954i	$-0.459593\pi$
$509$	3.83439e11	0.253201	0.126601	+	0.991954i	$0.459593\pi$
$510$	−7.66359e11	−0.501610
$511$	−9.31321e11	−0.604234
$512$	−1.34117e12	−0.862517
$513$	−1.42630e12	−0.909248
$514$	5.32355e10	0.0336409
$515$	6.57763e11	0.412037
$516$	1.74230e11	0.108193
$517$	2.28573e12	1.40708
$518$	1.03067e12	0.628975
$519$	−3.73157e12	−2.25756
$520$	1.10216e10	0.00661044
$521$	−2.71418e12	−1.61387	−0.806937	−	0.590638i	$-0.798876\pi$
$521$	−2.71418e12	−1.61387	−0.806937	+	0.590638i	$0.798876\pi$
$522$	3.15514e11	0.185995
$523$	2.13908e12	1.25017	0.625086	−	0.780556i	$-0.285064\pi$
$523$	2.13908e12	1.25017	0.625086	+	0.780556i	$0.285064\pi$
$524$	5.72339e10	0.0331637
$525$	−5.39756e12	−3.10085
$526$	6.97270e11	0.397160
$527$	−1.06188e12	−0.599691
$528$	−2.06921e12	−1.15865
$529$	2.76389e12	1.53451
$530$	2.75669e11	0.151756
$531$	−1.98260e12	−1.08221
$532$	4.24546e11	0.229785
$533$	5.16005e10	0.0276937
$534$	−1.72996e11	−0.0920662
$535$	9.68186e11	0.510936
$536$	−1.10828e12	−0.579975
$537$	8.28379e11	0.429877
$538$	1.57074e12	0.808323
$539$	−6.94763e12	−3.54558
$540$	8.38159e11	0.424184
$541$	9.70124e11	0.486900	0.243450	−	0.969913i	$-0.421721\pi$
$541$	9.70124e11	0.486900	0.243450	+	0.969913i	$0.421721\pi$
$542$	2.49896e12	1.24383
$543$	−2.53103e12	−1.24939
$544$	1.25706e12	0.615405
$545$	−1.09506e12	−0.531684
$546$	−9.37281e10	−0.0451339
$547$	−3.62322e12	−1.73042	−0.865211	−	0.501408i	$-0.832816\pi$
$547$	−3.62322e12	−1.73042	−0.865211	+	0.501408i	$0.832816\pi$
$548$	−7.50609e11	−0.355550
$549$	5.54601e12	2.60558
$550$	1.84270e12	0.858663
$551$	6.30336e10	0.0291333
$552$	7.10096e12	3.25530
$553$	−6.96010e11	−0.316484
$554$	−2.33654e12	−1.05385
$555$	6.70571e11	0.300003
$556$	−8.64232e11	−0.383525
$557$	2.48740e12	1.09496	0.547478	−	0.836820i	$-0.315588\pi$
$557$	2.48740e12	1.09496	0.547478	+	0.836820i	$0.315588\pi$
$558$	−3.16440e12	−1.38177
$559$	−5.51349e9	−0.00238822
$560$	8.43282e11	0.362349
$561$	4.91888e12	2.09669
$562$	9.05781e11	0.383010
$563$	−3.90454e11	−0.163788	−0.0818940	−	0.996641i	$-0.526097\pi$
$563$	−3.90454e11	−0.163788	−0.0818940	+	0.996641i	$0.526097\pi$
$564$	−1.87234e12	−0.779162
$565$	−7.31487e11	−0.301987
$566$	2.68298e12	1.09886
$567$	−1.38981e13	−5.64717
$568$	3.22478e12	1.29997
$569$	1.28781e12	0.515046	0.257523	−	0.966272i	$-0.417094\pi$
$569$	1.28781e12	0.515046	0.257523	+	0.966272i	$0.417094\pi$
$570$	−4.56249e11	−0.181036
$571$	2.12561e12	0.836797	0.418399	−	0.908264i	$-0.362592\pi$
$571$	2.12561e12	0.836797	0.418399	+	0.908264i	$0.362592\pi$
$572$	−1.93721e10	−0.00756649
$573$	3.49756e12	1.35541
$574$	7.04535e12	2.70894
$575$	−3.54361e12	−1.35189
$576$	6.97085e12	2.63867
$577$	−1.77876e12	−0.668077	−0.334038	−	0.942560i	$-0.608411\pi$
$577$	−1.77876e12	−0.668077	−0.334038	+	0.942560i	$0.608411\pi$
$578$	−5.15406e11	−0.192076
$579$	−6.71508e11	−0.248312
$580$	−3.70414e10	−0.0135913
$581$	−2.54101e12	−0.925154
$582$	−2.99486e12	−1.08199
$583$	−1.76939e12	−0.634329
$584$	−9.51085e11	−0.338346
$585$	−4.37524e10	−0.0154454
$586$	1.37528e11	0.0481783
$587$	4.15189e12	1.44336	0.721680	−	0.692227i	$-0.243370\pi$
$587$	4.15189e12	1.44336	0.721680	+	0.692227i	$0.243370\pi$
$588$	5.69110e12	1.96335
$589$	−6.32186e11	−0.216434
$590$	−3.84464e11	−0.130624
$591$	4.51742e12	1.52316
$592$	5.89816e11	0.197364
$593$	2.72790e12	0.905904	0.452952	−	0.891535i	$-0.350371\pi$
$593$	2.72790e12	0.905904	0.452952	+	0.891535i	$0.350371\pi$
$594$	8.88609e12	2.92868
$595$	−2.00463e12	−0.655705
$596$	−1.11426e10	−0.00361725
$597$	1.09102e13	3.51519
$598$	−6.15343e10	−0.0196772
$599$	2.46904e12	0.783623	0.391812	−	0.920045i	$-0.371848\pi$
$599$	2.46904e12	0.783623	0.391812	+	0.920045i	$0.371848\pi$
$600$	−5.51211e12	−1.73635
$601$	−1.80063e12	−0.562976	−0.281488	−	0.959565i	$-0.590828\pi$
$601$	−1.80063e12	−0.562976	−0.281488	+	0.959565i	$0.590828\pi$
$602$	−7.52793e11	−0.233610
$603$	4.39954e12	1.35512
$604$	−1.87428e12	−0.573019
$605$	8.21022e11	0.249147
$606$	1.85731e12	0.559445
$607$	−3.83396e12	−1.14630	−0.573150	−	0.819451i	$-0.694279\pi$
$607$	−3.83396e12	−1.14630	−0.573150	+	0.819451i	$0.694279\pi$
$608$	7.48385e11	0.222105
$609$	1.15031e12	0.338874
$610$	1.07548e12	0.314497
$611$	5.92500e10	0.0171990
$612$	−2.89089e12	−0.833009
$613$	−6.16914e12	−1.76463	−0.882313	−	0.470664i	$-0.844014\pi$
$613$	−6.16914e12	−1.76463	−0.882313	+	0.470664i	$0.844014\pi$
$614$	−2.82704e12	−0.802740
$615$	4.58384e12	1.29209
$616$	−9.65892e12	−2.70281
$617$	3.63257e11	0.100909	0.0504546	−	0.998726i	$-0.483933\pi$
$617$	3.63257e11	0.100909	0.0504546	+	0.998726i	$0.483933\pi$
$618$	−5.71233e12	−1.57531
$619$	4.53686e12	1.24208	0.621038	−	0.783781i	$-0.286711\pi$
$619$	4.53686e12	1.24208	0.621038	+	0.783781i	$0.286711\pi$
$620$	3.71501e11	0.100971
$621$	−1.70884e13	−4.61094
$622$	−2.44986e11	−0.0656272
$623$	−4.52521e11	−0.120349
$624$	−5.36375e10	−0.0141624
$625$	2.17534e12	0.570251
$626$	−1.13456e12	−0.295286
$627$	2.92844e12	0.756714
$628$	−6.72114e11	−0.172435
$629$	−1.40210e12	−0.357150
$630$	−5.97379e12	−1.51084
$631$	−1.55409e12	−0.390251	−0.195125	−	0.980778i	$-0.562511\pi$
$631$	−1.55409e12	−0.390251	−0.195125	+	0.980778i	$0.562511\pi$
$632$	−7.10780e11	−0.177218
$633$	−4.31799e11	−0.106897
$634$	1.50905e12	0.370937
$635$	1.11615e12	0.272420
$636$	1.44938e12	0.351257
$637$	−1.80094e11	−0.0433384
$638$	−3.92710e11	−0.0938381
$639$	−1.28014e13	−3.03740
$640$	1.85567e11	0.0437212
$641$	5.21346e12	1.21973	0.609866	−	0.792504i	$-0.291223\pi$
$641$	5.21346e12	1.21973	0.609866	+	0.792504i	$0.291223\pi$
$642$	−8.40819e12	−1.95342
$643$	5.32568e12	1.22864	0.614321	−	0.789056i	$-0.289430\pi$
$643$	5.32568e12	1.22864	0.614321	+	0.789056i	$0.289430\pi$
$644$	5.08646e12	1.16528
$645$	−4.89781e11	−0.111425
$646$	9.53971e11	0.215521
$647$	−5.93392e11	−0.133129	−0.0665644	−	0.997782i	$-0.521204\pi$
$647$	−5.93392e11	−0.133129	−0.0665644	+	0.997782i	$0.521204\pi$
$648$	−1.41930e13	−3.16218
$649$	2.46769e12	0.545995
$650$	4.77659e10	0.0104956
$651$	−1.15369e13	−2.51752
$652$	1.65942e12	0.359618
$653$	5.02049e12	1.08053	0.540265	−	0.841495i	$-0.318324\pi$
$653$	5.02049e12	1.08053	0.540265	+	0.841495i	$0.318324\pi$
$654$	9.51003e12	2.03274
$655$	−1.60892e11	−0.0341545
$656$	4.03182e12	0.850029
$657$	3.77551e12	0.790553
$658$	8.08978e12	1.68236
$659$	7.32459e11	0.151286	0.0756430	−	0.997135i	$-0.475899\pi$
$659$	7.32459e11	0.151286	0.0756430	+	0.997135i	$0.475899\pi$
$660$	−1.72088e12	−0.353024
$661$	−8.14141e12	−1.65880	−0.829398	−	0.558657i	$-0.811317\pi$
$661$	−8.14141e12	−1.65880	−0.829398	+	0.558657i	$0.811317\pi$
$662$	−5.40869e12	−1.09454
$663$	1.27506e11	0.0256283
$664$	−2.59493e12	−0.518048
$665$	−1.19345e12	−0.236650
$666$	−4.17824e12	−0.822923
$667$	7.55203e11	0.147740
$668$	−3.02805e12	−0.588396
$669$	2.72009e12	0.525007
$670$	8.53153e11	0.163565
$671$	−6.90295e12	−1.31457
$672$	1.36574e13	2.58349
$673$	−7.58901e12	−1.42599	−0.712997	−	0.701167i	$-0.752663\pi$
$673$	−7.58901e12	−1.42599	−0.712997	+	0.701167i	$0.752663\pi$
$674$	7.59270e12	1.41719
$675$	1.32649e13	2.45944
$676$	2.04700e12	0.377014
$677$	2.34458e12	0.428960	0.214480	−	0.976728i	$-0.431194\pi$
$677$	2.34458e12	0.428960	0.214480	+	0.976728i	$0.431194\pi$
$678$	6.35258e12	1.15456
$679$	−7.83391e12	−1.41437
$680$	−2.04717e12	−0.367168
$681$	−8.43959e12	−1.50369
$682$	3.93863e12	0.697133
$683$	−7.68157e12	−1.35069	−0.675347	−	0.737500i	$-0.736006\pi$
$683$	−7.68157e12	−1.35069	−0.675347	+	0.737500i	$0.736006\pi$
$684$	−1.72108e12	−0.300641
$685$	2.11005e12	0.366172
$686$	−1.57039e13	−2.70738
$687$	−1.22816e13	−2.10353
$688$	−4.30798e11	−0.0733037
$689$	−4.58655e10	−0.00775354
$690$	−5.46629e12	−0.918062
$691$	1.02677e13	1.71325	0.856627	−	0.515937i	$-0.172556\pi$
$691$	1.02677e13	1.71325	0.856627	+	0.515937i	$0.172556\pi$
$692$	−2.72967e12	−0.452515
$693$	3.83429e13	6.31517
$694$	4.06818e12	0.665706
$695$	2.42946e12	0.394983
$696$	1.17472e12	0.189755
$697$	−9.58436e12	−1.53821
$698$	−2.97149e12	−0.473833
$699$	2.05409e13	3.25440
$700$	−3.94836e12	−0.621549
$701$	9.20972e12	1.44051	0.720253	−	0.693711i	$-0.244026\pi$
$701$	9.20972e12	1.44051	0.720253	+	0.693711i	$0.244026\pi$
$702$	2.30343e11	0.0357979
$703$	−8.34732e11	−0.128899
$704$	−8.67641e12	−1.33126
$705$	5.26337e12	0.802440
$706$	−2.08185e12	−0.315376
$707$	4.85833e12	0.731307
$708$	−2.02139e12	−0.302343
$709$	−2.94952e12	−0.438372	−0.219186	−	0.975683i	$-0.570340\pi$
$709$	−2.94952e12	−0.438372	−0.219186	+	0.975683i	$0.570340\pi$
$710$	−2.48242e12	−0.366617
$711$	2.82157e12	0.414074
$712$	−4.62124e11	−0.0673904
$713$	−7.57419e12	−1.09757
$714$	1.74092e13	2.50690
$715$	5.44573e10	0.00779254
$716$	6.05965e11	0.0861666
$717$	2.36814e13	3.34634
$718$	9.17236e12	1.28802
$719$	−1.00384e13	−1.40083	−0.700414	−	0.713737i	$-0.747001\pi$
$719$	−1.00384e13	−1.40083	−0.700414	+	0.713737i	$0.747001\pi$
$720$	−3.41860e12	−0.474081
$721$	−1.49422e13	−2.05924
$722$	−5.19474e12	−0.711453
$723$	−8.40378e10	−0.0114381
$724$	−1.85147e12	−0.250433
$725$	−5.86225e11	−0.0788030
$726$	−7.13015e12	−0.952541
$727$	4.11260e11	0.0546024	0.0273012	−	0.999627i	$-0.491309\pi$
$727$	4.11260e11	0.0546024	0.0273012	+	0.999627i	$0.491309\pi$
$728$	−2.50376e11	−0.0330370
$729$	1.47904e13	1.93957
$730$	7.32142e11	0.0954206
$731$	1.02408e12	0.132650
$732$	5.65450e12	0.727938
$733$	9.13015e12	1.16818	0.584090	−	0.811689i	$-0.301451\pi$
$733$	9.13015e12	1.16818	0.584090	+	0.811689i	$0.301451\pi$
$734$	2.02669e12	0.257725
$735$	−1.59984e13	−2.02201
$736$	8.96637e12	1.12633
$737$	−5.47597e12	−0.683687
$738$	−2.85613e13	−3.54425
$739$	−1.12794e13	−1.39119	−0.695596	−	0.718433i	$-0.744859\pi$
$739$	−1.12794e13	−1.39119	−0.695596	+	0.718433i	$0.744859\pi$
$740$	4.90527e11	0.0601340
$741$	7.59101e10	0.00924948
$742$	−6.26231e12	−0.758433
$743$	6.58448e12	0.792633	0.396316	−	0.918114i	$-0.370288\pi$
$743$	6.58448e12	0.792633	0.396316	+	0.918114i	$0.370288\pi$
$744$	−1.17817e13	−1.40971
$745$	3.13232e10	0.00372532
$746$	−6.84099e12	−0.808713
$747$	1.03011e13	1.21043
$748$	3.59820e12	0.420270
$749$	−2.19940e13	−2.55351
$750$	9.24010e12	1.06635
$751$	−3.88685e12	−0.445880	−0.222940	−	0.974832i	$-0.571565\pi$
$751$	−3.88685e12	−0.445880	−0.222940	+	0.974832i	$0.571565\pi$
$752$	4.62951e12	0.527904
$753$	−1.51768e13	−1.72030
$754$	−1.01797e10	−0.00114700
$755$	5.26884e12	0.590138
$756$	−1.90402e13	−2.11994
$757$	−1.39930e10	−0.00154875	−0.000774374	−	1.00000i	$-0.500246\pi$
$757$	−1.39930e10	−0.00154875	−0.000774374		1.00000i	$0.500246\pi$
$758$	6.06874e12	0.667709
$759$	3.50855e13	3.83742
$760$	−1.21878e12	−0.132514
$761$	−7.78034e11	−0.0840945	−0.0420472	−	0.999116i	$-0.513388\pi$
$761$	−7.78034e11	−0.0840945	−0.0420472	+	0.999116i	$0.513388\pi$
$762$	−9.69315e12	−1.04152
$763$	2.48762e13	2.65720
$764$	2.55849e12	0.271684
$765$	8.12663e12	0.857895
$766$	4.57446e12	0.480076
$767$	6.39667e10	0.00667382
$768$	1.72352e13	1.78768
$769$	−1.51538e13	−1.56262	−0.781310	−	0.624144i	$-0.785448\pi$
$769$	−1.51538e13	−1.56262	−0.781310	+	0.624144i	$0.785448\pi$
$770$	7.43540e12	0.762248
$771$	−7.86819e11	−0.0801918
$772$	−4.91213e11	−0.0497728
$773$	−7.36906e12	−0.742343	−0.371171	−	0.928564i	$-0.621044\pi$
$773$	−7.36906e12	−0.742343	−0.371171	+	0.928564i	$0.621044\pi$
$774$	3.05177e12	0.305645
$775$	5.87945e12	0.585435
$776$	−8.00015e12	−0.791991
$777$	−1.52332e13	−1.49933
$778$	−1.96213e12	−0.192009
$779$	−5.70601e12	−0.555154
$780$	−4.46082e10	−0.00431509
$781$	1.59335e13	1.53243
$782$	1.14295e13	1.09294
$783$	−2.82696e12	−0.268777
$784$	−1.40717e13	−1.33023
$785$	1.88939e12	0.177586
$786$	1.39726e12	0.130580
$787$	2.97932e12	0.276842	0.138421	−	0.990374i	$-0.455797\pi$
$787$	2.97932e12	0.276842	0.138421	+	0.990374i	$0.455797\pi$
$788$	3.30452e12	0.305310
$789$	−1.03056e13	−0.946734
$790$	5.47156e11	0.0499792
$791$	1.66170e13	1.50924
$792$	3.91565e13	3.53623
$793$	−1.78936e11	−0.0160683
$794$	2.31655e12	0.206847
$795$	−4.07438e12	−0.361751
$796$	7.98090e12	0.704601
$797$	5.65430e12	0.496382	0.248191	−	0.968711i	$-0.420164\pi$
$797$	5.65430e12	0.496382	0.248191	+	0.968711i	$0.420164\pi$
$798$	1.03645e13	0.904763
$799$	−1.10052e13	−0.955293
$800$	−6.96013e12	−0.600776
$801$	1.83448e12	0.157459
$802$	−3.73901e12	−0.319133
$803$	−4.69926e12	−0.398850
$804$	4.48560e12	0.378589
$805$	−1.42987e13	−1.20009
$806$	1.02096e11	0.00852120
$807$	−2.32155e13	−1.92685
$808$	4.96143e12	0.409502
$809$	−3.58080e12	−0.293908	−0.146954	−	0.989143i	$-0.546947\pi$
$809$	−3.58080e12	−0.293908	−0.146954	+	0.989143i	$0.546947\pi$
$810$	1.09257e13	0.891801
$811$	−9.34503e12	−0.758554	−0.379277	−	0.925283i	$-0.623827\pi$
$811$	−9.34503e12	−0.758554	−0.379277	+	0.925283i	$0.623827\pi$
$812$	8.41461e11	0.0679254
$813$	−3.69345e13	−2.96500
$814$	5.20053e12	0.415181
$815$	−4.66483e12	−0.370362
$816$	9.96270e12	0.786632
$817$	6.09684e11	0.0478747
$818$	7.99035e12	0.623988
$819$	9.93912e11	0.0771917
$820$	3.35311e12	0.258992
$821$	2.46186e13	1.89112	0.945560	−	0.325449i	$-0.105515\pi$
$821$	2.46186e13	1.89112	0.945560	+	0.325449i	$0.105515\pi$
$822$	−1.83247e13	−1.39995
$823$	−3.14911e12	−0.239270	−0.119635	−	0.992818i	$-0.538172\pi$
$823$	−3.14911e12	−0.239270	−0.119635	+	0.992818i	$0.538172\pi$
$824$	−1.52593e13	−1.15309
$825$	−2.72350e13	−2.04685
$826$	8.73378e12	0.652818
$827$	−2.95396e12	−0.219598	−0.109799	−	0.993954i	$-0.535021\pi$
$827$	−2.95396e12	−0.219598	−0.109799	+	0.993954i	$0.535021\pi$
$828$	−2.06201e13	−1.52460
$829$	1.06626e13	0.784092	0.392046	−	0.919946i	$-0.371767\pi$
$829$	1.06626e13	0.784092	0.392046	+	0.919946i	$0.371767\pi$
$830$	1.99757e12	0.146100
$831$	3.45340e13	2.51213
$832$	−2.24907e11	−0.0162723
$833$	3.34510e13	2.40717
$834$	−2.10986e13	−1.51010
$835$	8.51223e12	0.605974
$836$	2.14217e12	0.151679
$837$	2.83526e13	1.99677
$838$	−5.90889e11	−0.0413912
$839$	2.20297e13	1.53490	0.767450	−	0.641108i	$-0.221525\pi$
$839$	2.20297e13	1.53490	0.767450	+	0.641108i	$0.221525\pi$
$840$	−2.22417e13	−1.54138
$841$	−1.43822e13	−0.991388
$842$	1.20141e13	0.823732
$843$	−1.33874e13	−0.913003
$844$	−3.15864e11	−0.0214269
$845$	−5.75436e12	−0.388277
$846$	−3.27954e13	−2.20113
$847$	−1.86510e13	−1.24516
$848$	−3.58372e12	−0.237986
$849$	−3.96543e13	−2.61943
$850$	−8.87211e12	−0.582964
$851$	−1.00009e13	−0.653666
$852$	−1.30518e13	−0.848577
$853$	1.55188e13	1.00367	0.501833	−	0.864965i	$-0.332659\pi$
$853$	1.55188e13	1.00367	0.501833	+	0.864965i	$0.332659\pi$
$854$	−2.44313e13	−1.57176
$855$	4.83816e12	0.309622
$856$	−2.24608e13	−1.42986
$857$	3.00703e13	1.90425	0.952124	−	0.305711i	$-0.0988940\pi$
$857$	3.00703e13	1.90425	0.952124	+	0.305711i	$0.0988940\pi$
$858$	−4.72933e11	−0.0297925
$859$	2.46295e13	1.54343	0.771714	−	0.635970i	$-0.219400\pi$
$859$	2.46295e13	1.54343	0.771714	+	0.635970i	$0.219400\pi$
$860$	−3.58279e11	−0.0223346
$861$	−1.04130e14	−6.45746
$862$	5.41495e12	0.334050
$863$	3.46510e12	0.212651	0.106326	−	0.994331i	$-0.466091\pi$
$863$	3.46510e12	0.212651	0.106326	+	0.994331i	$0.466091\pi$
$864$	−3.35640e13	−2.04909
$865$	7.67344e12	0.466034
$866$	1.61492e13	0.975707
$867$	7.61768e12	0.457864
$868$	−8.43930e12	−0.504624
$869$	−3.51193e12	−0.208909
$870$	−9.04297e11	−0.0535149
$871$	−1.41946e11	−0.00835686
$872$	2.54041e13	1.48792
$873$	3.17581e13	1.85050
$874$	6.80449e12	0.394452
$875$	2.41701e13	1.39394
$876$	3.84936e12	0.220862
$877$	1.30687e13	0.745992	0.372996	−	0.927833i	$-0.378331\pi$
$877$	1.30687e13	0.745992	0.372996	+	0.927833i	$0.378331\pi$
$878$	−9.26016e12	−0.525888
$879$	−2.03266e12	−0.114846
$880$	4.25503e12	0.239183
$881$	1.41012e13	0.788615	0.394307	−	0.918979i	$-0.370985\pi$
$881$	1.41012e13	0.788615	0.394307	+	0.918979i	$0.370985\pi$
$882$	9.96838e13	5.54646
$883$	3.48937e13	1.93163	0.965815	−	0.259232i	$-0.0834693\pi$
$883$	3.48937e13	1.93163	0.965815	+	0.259232i	$0.0834693\pi$
$884$	9.32714e10	0.00513705
$885$	5.68236e12	0.311375
$886$	1.04258e12	0.0568405
$887$	−8.10987e12	−0.439903	−0.219952	−	0.975511i	$-0.570590\pi$
$887$	−8.10987e12	−0.439903	−0.219952	+	0.975511i	$0.570590\pi$
$888$	−1.55565e13	−0.839561
$889$	−2.53552e13	−1.36147
$890$	3.55741e11	0.0190055
$891$	−7.01269e13	−3.72765
$892$	1.98976e12	0.105235
$893$	−6.55189e12	−0.344774
$894$	−2.72026e11	−0.0142427
$895$	−1.70344e12	−0.0887408
$896$	−4.21549e12	−0.218505
$897$	9.09475e11	0.0469056
$898$	1.00036e12	0.0513351
$899$	−1.25301e12	−0.0639788
$900$	1.60063e13	0.813207
$901$	8.51913e12	0.430659
$902$	3.55494e13	1.78815
$903$	1.11262e13	0.556870
$904$	1.69696e13	0.845113
$905$	5.20469e12	0.257915
$906$	−4.57571e13	−2.25622
$907$	−3.06563e13	−1.50413	−0.752067	−	0.659087i	$-0.770943\pi$
$907$	−3.06563e13	−1.50413	−0.752067	+	0.659087i	$0.770943\pi$
$908$	−6.17362e12	−0.301407
$909$	−1.96953e13	−0.956809
$910$	1.92738e11	0.00931712
$911$	1.17678e13	0.566060	0.283030	−	0.959111i	$-0.408660\pi$
$911$	1.17678e13	0.566060	0.283030	+	0.959111i	$0.408660\pi$
$912$	5.93125e12	0.283903
$913$	−1.28214e13	−0.610686
$914$	8.33015e12	0.394816
$915$	−1.58955e13	−0.749685
$916$	−8.98406e12	−0.421641
$917$	3.65493e12	0.170694
$918$	−4.27842e13	−1.98834
$919$	2.31130e13	1.06890	0.534449	−	0.845201i	$-0.320519\pi$
$919$	2.31130e13	1.06890	0.534449	+	0.845201i	$0.320519\pi$
$920$	−1.46021e13	−0.672001
$921$	4.17836e13	1.91354
$922$	9.14392e12	0.416719
$923$	4.13022e11	0.0187312
$924$	3.90929e13	1.76431
$925$	7.76317e12	0.348659
$926$	1.36062e13	0.608118
$927$	6.05747e13	2.69422
$928$	1.48332e12	0.0656552
$929$	−2.42929e13	−1.07006	−0.535030	−	0.844833i	$-0.679700\pi$
$929$	−2.42929e13	−1.07006	−0.535030	+	0.844833i	$0.679700\pi$
$930$	9.06951e12	0.397567
$931$	1.99149e13	0.868770
$932$	1.50258e13	0.652327
$933$	3.62088e12	0.156439
$934$	−8.20840e12	−0.352937
$935$	−1.01150e13	−0.432825
$936$	1.01500e12	0.0432242
$937$	2.26661e13	0.960615	0.480308	−	0.877100i	$-0.340525\pi$
$937$	2.26661e13	0.960615	0.480308	+	0.877100i	$0.340525\pi$
$938$	−1.93809e13	−0.817448
$939$	1.67687e13	0.703891
$940$	3.85019e12	0.160845
$941$	−6.91129e12	−0.287346	−0.143673	−	0.989625i	$-0.545891\pi$
$941$	−6.91129e12	−0.287346	−0.143673	+	0.989625i	$0.545891\pi$
$942$	−1.64084e13	−0.678949
$943$	−6.83634e13	−2.81528
$944$	4.99805e12	0.204846
$945$	5.35244e13	2.18328
$946$	−3.79844e12	−0.154204
$947$	−2.55740e13	−1.03329	−0.516647	−	0.856198i	$-0.672820\pi$
$947$	−2.55740e13	−1.03329	−0.516647	+	0.856198i	$0.672820\pi$
$948$	2.87677e12	0.115682
$949$	−1.21813e11	−0.00487523
$950$	−5.28197e12	−0.210397
$951$	−2.23036e13	−0.884226
$952$	4.65051e13	1.83499
$953$	−1.19246e13	−0.468304	−0.234152	−	0.972200i	$-0.575231\pi$
$953$	−1.19246e13	−0.468304	−0.234152	+	0.972200i	$0.575231\pi$
$954$	2.53870e13	0.992300
$955$	−7.19223e12	−0.279800
$956$	1.73231e13	0.670756
$957$	5.80424e12	0.223688
$958$	−2.62675e13	−1.00757
$959$	−4.79335e13	−1.83002
$960$	−1.99792e13	−0.759204
$961$	−1.38728e13	−0.524696
$962$	1.34807e11	0.00507485
$963$	8.91622e13	3.34089
$964$	−6.14743e10	−0.00229270
$965$	1.38086e12	0.0512597
$966$	1.24176e14	4.58820
$967$	1.25487e13	0.461508	0.230754	−	0.973012i	$-0.425881\pi$
$967$	1.25487e13	0.461508	0.230754	+	0.973012i	$0.425881\pi$
$968$	−1.90468e13	−0.697239
$969$	−1.40996e13	−0.513749
$970$	6.15849e12	0.223358
$971$	4.66392e13	1.68370	0.841850	−	0.539712i	$-0.181467\pi$
$971$	4.66392e13	1.68370	0.841850	+	0.539712i	$0.181467\pi$
$972$	2.70488e13	0.971962
$973$	−5.51895e13	−1.97401
$974$	−3.58541e13	−1.27651
$975$	−7.05978e11	−0.0250190
$976$	−1.39812e13	−0.493198
$977$	4.30950e13	1.51322	0.756608	−	0.653869i	$-0.226855\pi$
$977$	4.30950e13	1.51322	0.756608	+	0.653869i	$0.226855\pi$
$978$	4.05116e13	1.41597
$979$	−2.28333e12	−0.0794413
$980$	−1.17029e13	−0.405300
$981$	−1.00846e14	−3.47656
$982$	−1.19785e12	−0.0411054
$983$	3.37522e13	1.15295	0.576476	−	0.817114i	$-0.304428\pi$
$983$	3.37522e13	1.15295	0.576476	+	0.817114i	$0.304428\pi$
$984$	−1.06340e14	−3.61591
$985$	−9.28942e12	−0.314431
$986$	1.89080e12	0.0637087
$987$	−1.19567e14	−4.01035
$988$	5.55288e10	0.00185401
$989$	7.30460e12	0.242780
$990$	−3.01426e13	−0.997291
$991$	−2.60751e13	−0.858805	−0.429403	−	0.903113i	$-0.641276\pi$
$991$	−2.60751e13	−0.858805	−0.429403	+	0.903113i	$0.641276\pi$
$992$	−1.48767e13	−0.487759
$993$	7.99402e13	2.60912
$994$	5.63926e13	1.83224
$995$	−2.24353e13	−0.725651
$996$	1.05026e13	0.338165
$997$	4.12660e13	1.32271	0.661354	−	0.750074i	$-0.269982\pi$
$997$	4.12660e13	1.32271	0.661354	+	0.750074i	$0.269982\pi$
$998$	1.11174e13	0.354744
$999$	3.74365e13	1.18919

Twists

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

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

\(f(q)\)	\(=\)	\(q+17.8584 q^{2} -263.946 q^{3} -193.078 q^{4} +542.767 q^{5} -4713.65 q^{6} -12329.9 q^{7} -12591.6 q^{8} +49984.5 q^{9} +O(q^{10})\)	\(q+17.8584 q^{2} -263.946 q^{3} -193.078 q^{4} +542.767 q^{5} -4713.65 q^{6} -12329.9 q^{7} -12591.6 q^{8} +49984.5 q^{9} +9692.93 q^{10} -62214.2 q^{11} +50962.3 q^{12} -1612.70 q^{13} -220192. q^{14} -143261. q^{15} -126009. q^{16} +299545. q^{17} +892642. q^{18} +178333. q^{19} -104797. q^{20} +3.25443e6 q^{21} -1.11104e6 q^{22} +2.13660e6 q^{23} +3.32349e6 q^{24} -1.65853e6 q^{25} -28800.2 q^{26} -7.99796e6 q^{27} +2.38064e6 q^{28} +353461. q^{29} -2.55841e6 q^{30} -3.54498e6 q^{31} +4.19657e6 q^{32} +1.64212e7 q^{33} +5.34939e6 q^{34} -6.69226e6 q^{35} -9.65093e6 q^{36} -4.68076e6 q^{37} +3.18473e6 q^{38} +425665. q^{39} -6.83428e6 q^{40} -3.19964e7 q^{41} +5.81188e7 q^{42} +3.41880e6 q^{43} +1.20122e7 q^{44} +2.71299e7 q^{45} +3.81561e7 q^{46} -3.67397e7 q^{47} +3.32595e7 q^{48} +1.11673e8 q^{49} -2.96186e7 q^{50} -7.90637e7 q^{51} +311377. q^{52} +2.84403e7 q^{53} -1.42831e8 q^{54} -3.37678e7 q^{55} +1.55253e8 q^{56} -4.70702e7 q^{57} +6.31223e6 q^{58} -3.96644e7 q^{59} +2.76606e7 q^{60} +1.10955e8 q^{61} -6.33075e7 q^{62} -6.16304e8 q^{63} +1.39460e8 q^{64} -875319. q^{65} +2.93256e8 q^{66} +8.80180e7 q^{67} -5.78356e7 q^{68} -5.63946e8 q^{69} -1.19513e8 q^{70} -2.56106e8 q^{71} -6.29383e8 q^{72} +7.55335e7 q^{73} -8.35907e7 q^{74} +4.37762e8 q^{75} -3.44322e7 q^{76} +7.67095e8 q^{77} +7.60169e6 q^{78} +5.64490e7 q^{79} -6.83933e7 q^{80} +1.12719e9 q^{81} -5.71404e8 q^{82} +2.06085e8 q^{83} -6.28360e8 q^{84} +1.62583e8 q^{85} +6.10542e7 q^{86} -9.32945e7 q^{87} +7.83374e8 q^{88} +3.67011e7 q^{89} +4.84496e8 q^{90} +1.98844e7 q^{91} -4.12531e8 q^{92} +9.35683e8 q^{93} -6.56111e8 q^{94} +9.67931e7 q^{95} -1.10767e9 q^{96} +6.35358e8 q^{97} +1.99429e9 q^{98} -3.10975e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 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