LMFDB - Embedded newform 43.10.a.b.1.10

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			1.10
Root			$-5.60390$ 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)

$f(q)$	$=$	$q+8.60390 q^{2} -44.7892 q^{3} -437.973 q^{4} -1151.27 q^{5} -385.362 q^{6} +6348.30 q^{7} -8173.47 q^{8} -17676.9 q^{9} +O(q^{10})$	\(q+8.60390 q^{2} -44.7892 q^{3} -437.973 q^{4} -1151.27 q^{5} -385.362 q^{6} +6348.30 q^{7} -8173.47 q^{8} -17676.9 q^{9} -9905.41 q^{10} -58991.0 q^{11} +19616.5 q^{12} +185716. q^{13} +54620.2 q^{14} +51564.5 q^{15} +153918. q^{16} +289976. q^{17} -152091. q^{18} -292051. q^{19} +504225. q^{20} -284335. q^{21} -507553. q^{22} +1.86734e6 q^{23} +366083. q^{24} -627703. q^{25} +1.59788e6 q^{26} +1.67332e6 q^{27} -2.78038e6 q^{28} +4.59023e6 q^{29} +443656. q^{30} -1.11840e6 q^{31} +5.50912e6 q^{32} +2.64216e6 q^{33} +2.49492e6 q^{34} -7.30861e6 q^{35} +7.74201e6 q^{36} -3.15802e6 q^{37} -2.51278e6 q^{38} -8.31808e6 q^{39} +9.40987e6 q^{40} +2.18456e7 q^{41} -2.44639e6 q^{42} +3.41880e6 q^{43} +2.58364e7 q^{44} +2.03509e7 q^{45} +1.60664e7 q^{46} -2.45304e7 q^{47} -6.89388e6 q^{48} -52690.1 q^{49} -5.40069e6 q^{50} -1.29878e7 q^{51} -8.13387e7 q^{52} -1.66515e6 q^{53} +1.43971e7 q^{54} +6.79145e7 q^{55} -5.18877e7 q^{56} +1.30807e7 q^{57} +3.94939e7 q^{58} +9.51313e7 q^{59} -2.25838e7 q^{60} -6.95792e7 q^{61} -9.62264e6 q^{62} -1.12218e8 q^{63} -3.14063e7 q^{64} -2.13810e8 q^{65} +2.27329e7 q^{66} -3.86021e7 q^{67} -1.27002e8 q^{68} -8.36366e7 q^{69} -6.28825e7 q^{70} +2.19962e8 q^{71} +1.44482e8 q^{72} -4.39764e8 q^{73} -2.71713e7 q^{74} +2.81143e7 q^{75} +1.27910e8 q^{76} -3.74492e8 q^{77} -7.15680e7 q^{78} +1.45334e8 q^{79} -1.77202e8 q^{80} +2.72988e8 q^{81} +1.87957e8 q^{82} +2.73724e8 q^{83} +1.24531e8 q^{84} -3.33840e8 q^{85} +2.94150e7 q^{86} -2.05593e8 q^{87} +4.82161e8 q^{88} -1.49139e8 q^{89} +1.75097e8 q^{90} +1.17898e9 q^{91} -8.17843e8 q^{92} +5.00924e7 q^{93} -2.11057e8 q^{94} +3.36229e8 q^{95} -2.46749e8 q^{96} +1.51871e9 q^{97} -453340. q^{98} +1.04278e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.60390	0.380242	0.190121	−	0.981761i	$-0.439112\pi$
$2$	8.60390	0.380242	0.190121	+	0.981761i	$0.439112\pi$
$3$	−44.7892	−0.319248	−0.159624	−	0.987178i	$-0.551028\pi$
$3$	−44.7892	−0.319248	−0.159624	+	0.987178i	$0.551028\pi$
$4$	−437.973	−0.855416
$5$	−1151.27	−0.823782	−0.411891	−	0.911233i	$-0.635132\pi$
$5$	−1151.27	−0.823782	−0.411891	+	0.911233i	$0.635132\pi$
$6$	−385.362	−0.121391
$7$	6348.30	0.999347	0.499673	−	0.866214i	$-0.333453\pi$
$7$	6348.30	0.999347	0.499673	+	0.866214i	$0.333453\pi$
$8$	−8173.47	−0.705508
$9$	−17676.9	−0.898081
$10$	−9905.41	−0.313237
$11$	−58991.0	−1.21484	−0.607419	−	0.794381i	$-0.707795\pi$
$11$	−58991.0	−1.21484	−0.607419	+	0.794381i	$0.707795\pi$
$12$	19616.5	0.273089
$13$	185716.	1.80345	0.901726	−	0.432307i	$-0.142300\pi$
$13$	185716.	1.80345	0.901726	+	0.432307i	$0.142300\pi$
$14$	54620.2	0.379994
$15$	51564.5	0.262990
$16$	153918.	0.587152
$17$	289976.	0.842057	0.421029	−	0.907047i	$-0.361669\pi$
$17$	289976.	0.842057	0.421029	+	0.907047i	$0.361669\pi$
$18$	−152091.	−0.341488
$19$	−292051.	−0.514123	−0.257061	−	0.966395i	$-0.582754\pi$
$19$	−292051.	−0.514123	−0.257061	+	0.966395i	$0.582754\pi$
$20$	504225.	0.704676
$21$	−284335.	−0.319039
$22$	−507553.	−0.461933
$23$	1.86734e6	1.39139	0.695693	−	0.718339i	$-0.255097\pi$
$23$	1.86734e6	1.39139	0.695693	+	0.718339i	$0.255097\pi$
$24$	366083.	0.225232
$25$	−627703.	−0.321384
$26$	1.59788e6	0.685749
$27$	1.67332e6	0.605958
$28$	−2.78038e6	−0.854857
$29$	4.59023e6	1.20516	0.602578	−	0.798060i	$-0.294140\pi$
$29$	4.59023e6	1.20516	0.602578	+	0.798060i	$0.294140\pi$
$30$	443656.	0.100000
$31$	−1.11840e6	−0.217506	−0.108753	−	0.994069i	$-0.534686\pi$
$31$	−1.11840e6	−0.217506	−0.108753	+	0.994069i	$0.534686\pi$
$32$	5.50912e6	0.928768
$33$	2.64216e6	0.387834
$34$	2.49492e6	0.320186
$35$	−7.30861e6	−0.823244
$36$	7.74201e6	0.768233
$37$	−3.15802e6	−0.277017	−0.138509	−	0.990361i	$-0.544231\pi$
$37$	−3.15802e6	−0.277017	−0.138509	+	0.990361i	$0.544231\pi$
$38$	−2.51278e6	−0.195491
$39$	−8.31808e6	−0.575748
$40$	9.40987e6	0.581184
$41$	2.18456e7	1.20736	0.603680	−	0.797227i	$-0.293701\pi$
$41$	2.18456e7	1.20736	0.603680	+	0.797227i	$0.293701\pi$
$42$	−2.44639e6	−0.121312
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	2.58364e7	1.03919
$45$	2.03509e7	0.739823
$46$	1.60664e7	0.529064
$47$	−2.45304e7	−0.733269	−0.366635	−	0.930365i	$-0.619490\pi$
$47$	−2.45304e7	−0.733269	−0.366635	+	0.930365i	$0.619490\pi$
$48$	−6.89388e6	−0.187447
$49$	−52690.1	−0.00130571
$50$	−5.40069e6	−0.122204
$51$	−1.29878e7	−0.268825
$52$	−8.13387e7	−1.54270
$53$	−1.66515e6	−0.0289876	−0.0144938	−	0.999895i	$-0.504614\pi$
$53$	−1.66515e6	−0.0289876	−0.0144938	+	0.999895i	$0.504614\pi$
$54$	1.43971e7	0.230411
$55$	6.79145e7	1.00076
$56$	−5.18877e7	−0.705047
$57$	1.30807e7	0.164133
$58$	3.94939e7	0.458251
$59$	9.51313e7	1.02209	0.511045	−	0.859554i	$-0.329258\pi$
$59$	9.51313e7	1.02209	0.511045	+	0.859554i	$0.329258\pi$
$60$	−2.25838e7	−0.224966
$61$	−6.95792e7	−0.643421	−0.321711	−	0.946838i	$-0.604258\pi$
$61$	−6.95792e7	−0.643421	−0.321711	+	0.946838i	$0.604258\pi$
$62$	−9.62264e6	−0.0827050
$63$	−1.12218e8	−0.897494
$64$	−3.14063e7	−0.233995
$65$	−2.13810e8	−1.48565
$66$	2.27329e7	0.147471
$67$	−3.86021e7	−0.234032	−0.117016	−	0.993130i	$-0.537333\pi$
$67$	−3.86021e7	−0.234032	−0.117016	+	0.993130i	$0.537333\pi$
$68$	−1.27002e8	−0.720309
$69$	−8.36366e7	−0.444197
$70$	−6.28825e7	−0.313032
$71$	2.19962e8	1.02727	0.513635	−	0.858009i	$-0.328299\pi$
$71$	2.19962e8	1.02727	0.513635	+	0.858009i	$0.328299\pi$
$72$	1.44482e8	0.633603
$73$	−4.39764e8	−1.81245	−0.906226	−	0.422793i	$-0.861050\pi$
$73$	−4.39764e8	−1.81245	−0.906226	+	0.422793i	$0.861050\pi$
$74$	−2.71713e7	−0.105334
$75$	2.81143e7	0.102601
$76$	1.27910e8	0.439789
$77$	−3.74492e8	−1.21405
$78$	−7.15680e7	−0.218924
$79$	1.45334e8	0.419803	0.209902	−	0.977722i	$-0.432686\pi$
$79$	1.45334e8	0.419803	0.209902	+	0.977722i	$0.432686\pi$
$80$	−1.77202e8	−0.483685
$81$	2.72988e8	0.704630
$82$	1.87957e8	0.459089
$83$	2.73724e8	0.633084	0.316542	−	0.948578i	$-0.397478\pi$
$83$	2.73724e8	0.633084	0.316542	+	0.948578i	$0.397478\pi$
$84$	1.24531e8	0.272911
$85$	−3.33840e8	−0.693671
$86$	2.94150e7	0.0579864
$87$	−2.05593e8	−0.384743
$88$	4.82161e8	0.857078
$89$	−1.49139e8	−0.251963	−0.125981	−	0.992033i	$-0.540208\pi$
$89$	−1.49139e8	−0.251963	−0.125981	+	0.992033i	$0.540208\pi$
$90$	1.75097e8	0.281312
$91$	1.17898e9	1.80228
$92$	−8.17843e8	−1.19021
$93$	5.00924e7	0.0694383
$94$	−2.11057e8	−0.278820
$95$	3.36229e8	0.423525
$96$	−2.46749e8	−0.296507
$97$	1.51871e9	1.74182	0.870909	−	0.491445i	$-0.163531\pi$
$97$	1.51871e9	1.74182	0.870909	+	0.491445i	$0.163531\pi$
$98$	−453340.	−0.000496486 0
$99$	1.04278e9	1.09102
$100$	2.74917e8	0.274917
$101$	1.43092e8	0.136826	0.0684130	−	0.997657i	$-0.478206\pi$
$101$	1.43092e8	0.136826	0.0684130	+	0.997657i	$0.478206\pi$
$102$	−1.11746e8	−0.102219
$103$	−1.52696e9	−1.33678	−0.668392	−	0.743810i	$-0.733017\pi$
$103$	−1.52696e9	−1.33678	−0.668392	+	0.743810i	$0.733017\pi$
$104$	−1.51795e9	−1.27235
$105$	3.27347e8	0.262819
$106$	−1.43268e7	−0.0110223
$107$	2.44993e9	1.80687	0.903435	−	0.428725i	$-0.141037\pi$
$107$	2.44993e9	1.80687	0.903435	+	0.428725i	$0.141037\pi$
$108$	−7.32869e8	−0.518346
$109$	1.88920e9	1.28191	0.640956	−	0.767578i	$-0.278538\pi$
$109$	1.88920e9	1.28191	0.640956	+	0.767578i	$0.278538\pi$
$110$	5.84330e8	0.380532
$111$	1.41445e8	0.0884371
$112$	9.77120e8	0.586768
$113$	1.62446e8	0.0937249	0.0468625	−	0.998901i	$-0.485078\pi$
$113$	1.62446e8	0.0937249	0.0468625	+	0.998901i	$0.485078\pi$
$114$	1.12545e8	0.0624101
$115$	−2.14981e9	−1.14620
$116$	−2.01039e9	−1.03091
$117$	−3.28289e9	−1.61965
$118$	8.18500e8	0.388642
$119$	1.84085e9	0.841507
$120$	−4.21461e8	−0.185542
$121$	1.12199e9	0.475832
$122$	−5.98653e8	−0.244656
$123$	−9.78447e8	−0.385447
$124$	4.89831e8	0.186058
$125$	2.97123e9	1.08853
$126$	−9.65517e8	−0.341265
$127$	2.90579e9	0.991170	0.495585	−	0.868559i	$-0.334954\pi$
$127$	2.90579e9	0.991170	0.495585	+	0.868559i	$0.334954\pi$
$128$	−3.09088e9	−1.01774
$129$	−1.53125e8	−0.0486848
$130$	−1.83960e9	−0.564908
$131$	3.75951e9	1.11535	0.557673	−	0.830060i	$-0.311694\pi$
$131$	3.75951e9	1.11535	0.557673	+	0.830060i	$0.311694\pi$
$132$	−1.15719e9	−0.331760
$133$	−1.85403e9	−0.513787
$134$	−3.32129e8	−0.0889888
$135$	−1.92644e9	−0.499177
$136$	−2.37011e9	−0.594078
$137$	4.71241e9	1.14288	0.571440	−	0.820644i	$-0.306385\pi$
$137$	4.71241e9	1.14288	0.571440	+	0.820644i	$0.306385\pi$
$138$	−7.19601e8	−0.168902
$139$	−3.32175e9	−0.754744	−0.377372	−	0.926062i	$-0.623172\pi$
$139$	−3.32175e9	−0.754744	−0.377372	+	0.926062i	$0.623172\pi$
$140$	3.20097e9	0.704216
$141$	1.09869e9	0.234094
$142$	1.89253e9	0.390611
$143$	−1.09556e10	−2.19090
$144$	−2.72080e9	−0.527310
$145$	−5.28459e9	−0.992785
$146$	−3.78369e9	−0.689171
$147$	2.35995e6	0.000416845 0
$148$	1.38313e9	0.236965
$149$	2.96493e9	0.492807	0.246403	−	0.969167i	$-0.420751\pi$
$149$	2.96493e9	0.492807	0.246403	+	0.969167i	$0.420751\pi$
$150$	2.41893e8	0.0390132
$151$	−1.03548e10	−1.62087	−0.810433	−	0.585832i	$-0.800768\pi$
$151$	−1.03548e10	−1.62087	−0.810433	+	0.585832i	$0.800768\pi$
$152$	2.38707e9	0.362718
$153$	−5.12588e9	−0.756235
$154$	−3.22210e9	−0.461631
$155$	1.28759e9	0.179177
$156$	3.64309e9	0.492504
$157$	8.12184e9	1.06686	0.533428	−	0.845845i	$-0.320903\pi$
$157$	8.12184e9	1.06686	0.533428	+	0.845845i	$0.320903\pi$
$158$	1.25044e9	0.159627
$159$	7.45808e7	0.00925422
$160$	−6.34248e9	−0.765102
$161$	1.18544e10	1.39048
$162$	2.34876e9	0.267930
$163$	1.18317e10	1.31281	0.656406	−	0.754408i	$-0.272076\pi$
$163$	1.18317e10	1.31281	0.656406	+	0.754408i	$0.272076\pi$
$164$	−9.56778e9	−1.03279
$165$	−3.04184e9	−0.319491
$166$	2.35509e9	0.240725
$167$	9.01204e9	0.896600	0.448300	−	0.893883i	$-0.352030\pi$
$167$	9.01204e9	0.896600	0.448300	+	0.893883i	$0.352030\pi$
$168$	2.32401e9	0.225085
$169$	2.38860e10	2.25244
$170$	−2.87233e9	−0.263763
$171$	5.16256e9	0.461724
$172$	−1.49734e9	−0.130450
$173$	−9.19485e9	−0.780436	−0.390218	−	0.920723i	$-0.627600\pi$
$173$	−9.19485e9	−0.780436	−0.390218	+	0.920723i	$0.627600\pi$
$174$	−1.76890e9	−0.146296
$175$	−3.98484e9	−0.321174
$176$	−9.07979e9	−0.713295
$177$	−4.26086e9	−0.326300
$178$	−1.28318e9	−0.0958070
$179$	8.67953e8	0.0631913	0.0315957	−	0.999501i	$-0.489941\pi$
$179$	8.67953e8	0.0631913	0.0315957	+	0.999501i	$0.489941\pi$
$180$	−8.91315e9	−0.632856
$181$	−3.35950e9	−0.232660	−0.116330	−	0.993211i	$-0.537113\pi$
$181$	−3.35950e9	−0.232660	−0.116330	+	0.993211i	$0.537113\pi$
$182$	1.01439e10	0.685301
$183$	3.11640e9	0.205411
$184$	−1.52626e10	−0.981634
$185$	3.63573e9	0.228202
$186$	4.30991e8	0.0264034
$187$	−1.71060e10	−1.02296
$188$	1.07436e10	0.627250
$189$	1.06227e10	0.605562
$190$	2.89288e9	0.161042
$191$	5.07564e9	0.275956	0.137978	−	0.990435i	$-0.455940\pi$
$191$	5.07564e9	0.275956	0.137978	+	0.990435i	$0.455940\pi$
$192$	1.40666e9	0.0747023
$193$	3.37053e9	0.174860	0.0874299	−	0.996171i	$-0.472135\pi$
$193$	3.37053e9	0.174860	0.0874299	+	0.996171i	$0.472135\pi$
$194$	1.30668e10	0.662313
$195$	9.57636e9	0.474291
$196$	2.30768e7	0.00111692
$197$	−2.43861e10	−1.15357	−0.576785	−	0.816896i	$-0.695693\pi$
$197$	−2.43861e10	−1.15357	−0.576785	+	0.816896i	$0.695693\pi$
$198$	8.97197e9	0.414853
$199$	3.69330e10	1.66946	0.834730	−	0.550660i	$-0.185624\pi$
$199$	3.69330e10	1.66946	0.834730	+	0.550660i	$0.185624\pi$
$200$	5.13051e9	0.226739
$201$	1.72896e9	0.0747141
$202$	1.23115e9	0.0520270
$203$	2.91401e10	1.20437
$204$	5.68830e9	0.229957
$205$	−2.51502e10	−0.994601
$206$	−1.31378e10	−0.508302
$207$	−3.30088e10	−1.24958
$208$	2.85851e10	1.05890
$209$	1.72284e10	0.624576
$210$	2.81646e9	0.0999348
$211$	2.75882e7	0.000958192 0	0.000479096	−	1.00000i	$-0.499847\pi$
$211$	2.75882e7	0.000958192 0	0.000479096		1.00000i	$0.499847\pi$
$212$	7.29291e8	0.0247964
$213$	−9.85190e9	−0.327953
$214$	2.10790e10	0.687049
$215$	−3.93596e9	−0.125626
$216$	−1.36768e10	−0.427508
$217$	−7.09997e9	−0.217364
$218$	1.62545e10	0.487437
$219$	1.96967e10	0.578621
$220$	−2.97447e10	−0.856067
$221$	5.38532e10	1.51861
$222$	1.21698e9	0.0336275
$223$	−6.45923e10	−1.74908	−0.874539	−	0.484956i	$-0.838836\pi$
$223$	−6.45923e10	−1.74908	−0.874539	+	0.484956i	$0.838836\pi$
$224$	3.49735e10	0.928161
$225$	1.10959e10	0.288629
$226$	1.39767e9	0.0356382
$227$	−5.49657e10	−1.37396	−0.686982	−	0.726674i	$-0.741065\pi$
$227$	−5.49657e10	−1.37396	−0.686982	+	0.726674i	$0.741065\pi$
$228$	−5.72900e9	−0.140402
$229$	−6.28251e10	−1.50964	−0.754820	−	0.655932i	$-0.772276\pi$
$229$	−6.28251e10	−1.50964	−0.754820	+	0.655932i	$0.772276\pi$
$230$	−1.84968e10	−0.435833
$231$	1.67732e10	0.387581
$232$	−3.75181e10	−0.850247
$233$	1.22811e10	0.272983	0.136492	−	0.990641i	$-0.456417\pi$
$233$	1.22811e10	0.272983	0.136492	+	0.990641i	$0.456417\pi$
$234$	−2.82457e10	−0.615858
$235$	2.82411e10	0.604054
$236$	−4.16649e10	−0.874312
$237$	−6.50940e9	−0.134021
$238$	1.58385e10	0.319977
$239$	−9.78735e10	−1.94033	−0.970163	−	0.242455i	$-0.922047\pi$
$239$	−9.78735e10	−1.94033	−0.970163	+	0.242455i	$0.922047\pi$
$240$	7.93672e9	0.154415
$241$	2.50358e10	0.478063	0.239032	−	0.971012i	$-0.423170\pi$
$241$	2.50358e10	0.478063	0.239032	+	0.971012i	$0.423170\pi$
$242$	9.65348e9	0.180932
$243$	−4.51629e10	−0.830909
$244$	3.04738e10	0.550393
$245$	6.06605e7	0.00107562
$246$	−8.41846e9	−0.146563
$247$	−5.42385e10	−0.927196
$248$	9.14125e9	0.153452
$249$	−1.22599e10	−0.202111
$250$	2.55642e10	0.413906
$251$	−2.38314e10	−0.378981	−0.189490	−	0.981883i	$-0.560684\pi$
$251$	−2.38314e10	−0.378981	−0.189490	+	0.981883i	$0.560684\pi$
$252$	4.91486e10	0.767731
$253$	−1.10156e11	−1.69031
$254$	2.50012e10	0.376885
$255$	1.49524e10	0.221453
$256$	−1.05137e10	−0.152994
$257$	1.32282e11	1.89148	0.945740	−	0.324925i	$-0.105339\pi$
$257$	1.32282e11	1.89148	0.945740	+	0.324925i	$0.105339\pi$
$258$	−1.31748e9	−0.0185120
$259$	−2.00480e10	−0.276836
$260$	9.36428e10	1.27085
$261$	−8.11411e10	−1.08233
$262$	3.23464e10	0.424102
$263$	−8.95345e10	−1.15396	−0.576978	−	0.816759i	$-0.695768\pi$
$263$	−8.95345e10	−1.15396	−0.576978	+	0.816759i	$0.695768\pi$
$264$	−2.15956e10	−0.273620
$265$	1.91704e9	0.0238794
$266$	−1.59519e10	−0.195364
$267$	6.67982e9	0.0804386
$268$	1.69067e10	0.200194
$269$	7.62239e10	0.887576	0.443788	−	0.896132i	$-0.353634\pi$
$269$	7.62239e10	0.887576	0.443788	+	0.896132i	$0.353634\pi$
$270$	−1.65749e10	−0.189808
$271$	7.42396e9	0.0836130	0.0418065	−	0.999126i	$-0.486689\pi$
$271$	7.42396e9	0.0836130	0.0418065	+	0.999126i	$0.486689\pi$
$272$	4.46326e10	0.494415
$273$	−5.28057e10	−0.575372
$274$	4.05451e10	0.434572
$275$	3.70288e10	0.390429
$276$	3.66306e10	0.379973
$277$	1.31886e11	1.34599	0.672993	−	0.739649i	$-0.265009\pi$
$277$	1.31886e11	1.34599	0.672993	+	0.739649i	$0.265009\pi$
$278$	−2.85800e10	−0.286986
$279$	1.97700e10	0.195338
$280$	5.97367e10	0.580805
$281$	−9.94483e9	−0.0951522	−0.0475761	−	0.998868i	$-0.515150\pi$
$281$	−9.94483e9	−0.0951522	−0.0475761	+	0.998868i	$0.515150\pi$
$282$	9.45306e9	0.0890126
$283$	1.06717e9	0.00988997	0.00494499	−	0.999988i	$-0.498426\pi$
$283$	1.06717e9	0.00988997	0.00494499	+	0.999988i	$0.498426\pi$
$284$	−9.63372e10	−0.878742
$285$	−1.50594e10	−0.135209
$286$	−9.42608e10	−0.833074
$287$	1.38682e11	1.20657
$288$	−9.73843e10	−0.834109
$289$	−3.45019e10	−0.290940
$290$	−4.54681e10	−0.377499
$291$	−6.80219e10	−0.556071
$292$	1.92605e11	1.55040
$293$	1.46143e11	1.15844	0.579222	−	0.815170i	$-0.303356\pi$
$293$	1.46143e11	1.15844	0.579222	+	0.815170i	$0.303356\pi$
$294$	2.03048e7	0.000158502 0
$295$	−1.09522e11	−0.841980
$296$	2.58120e10	0.195438
$297$	−9.87109e10	−0.736141
$298$	2.55100e10	0.187386
$299$	3.46795e11	2.50930
$300$	−1.23133e10	−0.0877665
$301$	2.17036e10	0.152399
$302$	−8.90920e10	−0.616322
$303$	−6.40897e9	−0.0436814
$304$	−4.49519e10	−0.301868
$305$	8.01045e10	0.530039
$306$	−4.41026e10	−0.287553
$307$	3.59311e10	0.230860	0.115430	−	0.993316i	$-0.463175\pi$
$307$	3.59311e10	0.230860	0.115430	+	0.993316i	$0.463175\pi$
$308$	1.64018e11	1.03851
$309$	6.83914e10	0.426765
$310$	1.10783e10	0.0681309
$311$	1.71949e11	1.04226	0.521132	−	0.853476i	$-0.325510\pi$
$311$	1.71949e11	1.04226	0.521132	+	0.853476i	$0.325510\pi$
$312$	6.79876e10	0.406195
$313$	−1.32043e11	−0.777618	−0.388809	−	0.921318i	$-0.627113\pi$
$313$	−1.32043e11	−0.777618	−0.388809	+	0.921318i	$0.627113\pi$
$314$	6.98795e10	0.405664
$315$	1.29194e11	0.739340
$316$	−6.36524e10	−0.359106
$317$	8.32715e10	0.463159	0.231579	−	0.972816i	$-0.425611\pi$
$317$	8.32715e10	0.463159	0.231579	+	0.972816i	$0.425611\pi$
$318$	6.41686e8	0.00351885
$319$	−2.70782e11	−1.46407
$320$	3.61571e10	0.192761
$321$	−1.09730e11	−0.576839
$322$	1.01994e11	0.528719
$323$	−8.46876e10	−0.432921
$324$	−1.19561e11	−0.602752
$325$	−1.16575e11	−0.579600
$326$	1.01799e11	0.499187
$327$	−8.46157e10	−0.409247
$328$	−1.78554e11	−0.851801
$329$	−1.55726e11	−0.732790
$330$	−2.61717e10	−0.121484
$331$	−1.89586e11	−0.868119	−0.434060	−	0.900884i	$-0.642919\pi$
$331$	−1.89586e11	−0.868119	−0.434060	+	0.900884i	$0.642919\pi$
$332$	−1.19884e11	−0.541550
$333$	5.58240e10	0.248784
$334$	7.75387e10	0.340925
$335$	4.44415e10	0.192791
$336$	−4.37644e10	−0.187324
$337$	−4.34848e11	−1.83655	−0.918276	−	0.395940i	$-0.870419\pi$
$337$	−4.34848e11	−1.83655	−0.918276	+	0.395940i	$0.870419\pi$
$338$	2.05513e11	0.856474
$339$	−7.27581e9	−0.0299215
$340$	1.46213e11	0.593377
$341$	6.59758e10	0.264235
$342$	4.44181e10	0.175567
$343$	−2.56511e11	−1.00065
$344$	−2.79435e10	−0.107589
$345$	9.62883e10	0.365921
$346$	−7.91116e10	−0.296755
$347$	2.46052e11	0.911056	0.455528	−	0.890221i	$-0.349450\pi$
$347$	2.46052e11	0.911056	0.455528	+	0.890221i	$0.349450\pi$
$348$	9.00440e10	0.329115
$349$	4.08648e11	1.47447	0.737233	−	0.675638i	$-0.236132\pi$
$349$	4.08648e11	1.47447	0.737233	+	0.675638i	$0.236132\pi$
$350$	−3.42852e10	−0.122124
$351$	3.10763e11	1.09282
$352$	−3.24988e11	−1.12830
$353$	−2.93838e11	−1.00721	−0.503607	−	0.863933i	$-0.667994\pi$
$353$	−2.93838e11	−1.00721	−0.503607	+	0.863933i	$0.667994\pi$
$354$	−3.66600e10	−0.124073
$355$	−2.53235e11	−0.846246
$356$	6.53189e10	0.215533
$357$	−8.24503e10	−0.268649
$358$	7.46778e9	0.0240280
$359$	−2.90096e11	−0.921759	−0.460879	−	0.887463i	$-0.652466\pi$
$359$	−2.90096e11	−0.921759	−0.460879	+	0.887463i	$0.652466\pi$
$360$	−1.66338e11	−0.521951
$361$	−2.37394e11	−0.735678
$362$	−2.89048e10	−0.0884671
$363$	−5.02530e10	−0.151908
$364$	−5.16362e11	−1.54169
$365$	5.06287e11	1.49307
$366$	2.68132e10	0.0781058
$367$	−8.34753e10	−0.240193	−0.120097	−	0.992762i	$-0.538320\pi$
$367$	−8.34753e10	−0.240193	−0.120097	+	0.992762i	$0.538320\pi$
$368$	2.87418e11	0.816955
$369$	−3.86163e11	−1.08431
$370$	3.12815e10	0.0867719
$371$	−1.05709e10	−0.0289687
$372$	−2.19391e10	−0.0593986
$373$	3.60523e11	0.964370	0.482185	−	0.876069i	$-0.339843\pi$
$373$	3.60523e11	0.964370	0.482185	+	0.876069i	$0.339843\pi$
$374$	−1.47178e11	−0.388974
$375$	−1.33079e11	−0.347511
$376$	2.00498e11	0.517327
$377$	8.52480e11	2.17344
$378$	9.13971e10	0.230260
$379$	4.53176e11	1.12821	0.564106	−	0.825703i	$-0.309221\pi$
$379$	4.53176e11	1.12821	0.564106	+	0.825703i	$0.309221\pi$
$380$	−1.47259e11	−0.362290
$381$	−1.30148e11	−0.316429
$382$	4.36703e10	0.104930
$383$	−6.03671e11	−1.43353	−0.716763	−	0.697317i	$-0.754377\pi$
$383$	−6.03671e11	−1.43353	−0.716763	+	0.697317i	$0.754377\pi$
$384$	1.38438e11	0.324912
$385$	4.31142e11	1.00011
$386$	2.89997e10	0.0664891
$387$	−6.04339e10	−0.136956
$388$	−6.65155e11	−1.48998
$389$	−2.72491e11	−0.603364	−0.301682	−	0.953409i	$-0.597548\pi$
$389$	−2.72491e11	−0.603364	−0.301682	+	0.953409i	$0.597548\pi$
$390$	8.23941e10	0.180345
$391$	5.41483e11	1.17163
$392$	4.30661e8	0.000921188 0
$393$	−1.68385e11	−0.356072
$394$	−2.09816e11	−0.438636
$395$	−1.67319e11	−0.345826
$396$	−4.56709e11	−0.933278
$397$	−1.26137e11	−0.254851	−0.127425	−	0.991848i	$-0.540671\pi$
$397$	−1.26137e11	−0.254851	−0.127425	+	0.991848i	$0.540671\pi$
$398$	3.17768e11	0.634799
$399$	8.30403e10	0.164025
$400$	−9.66149e10	−0.188701
$401$	1.95516e11	0.377602	0.188801	−	0.982015i	$-0.439540\pi$
$401$	1.95516e11	0.377602	0.188801	+	0.982015i	$0.439540\pi$
$402$	1.48758e10	0.0284095
$403$	−2.07706e11	−0.392262
$404$	−6.26703e10	−0.117043
$405$	−3.14283e11	−0.580462
$406$	2.50719e11	0.457952
$407$	1.86294e11	0.336531
$408$	1.06155e11	0.189658
$409$	2.50036e11	0.441822	0.220911	−	0.975294i	$-0.429097\pi$
$409$	2.50036e11	0.441822	0.220911	+	0.975294i	$0.429097\pi$
$410$	−2.16390e11	−0.378189
$411$	−2.11065e11	−0.364862
$412$	6.68768e11	1.14351
$413$	6.03922e11	1.02142
$414$	−2.84005e11	−0.475142
$415$	−3.15130e11	−0.521523
$416$	1.02313e12	1.67499
$417$	1.48778e11	0.240950
$418$	1.48231e11	0.237490
$419$	−3.87240e11	−0.613786	−0.306893	−	0.951744i	$-0.599289\pi$
$419$	−3.87240e11	−0.613786	−0.306893	+	0.951744i	$0.599289\pi$
$420$	−1.43369e11	−0.224819
$421$	1.25266e12	1.94341	0.971706	−	0.236192i	$-0.0758996\pi$
$421$	1.25266e12	1.94341	0.971706	+	0.236192i	$0.0758996\pi$
$422$	2.37366e8	0.000364345 0
$423$	4.33621e11	0.658535
$424$	1.36101e10	0.0204510
$425$	−1.82019e11	−0.270623
$426$	−8.47648e10	−0.124702
$427$	−4.41710e11	−0.643001
$428$	−1.07300e12	−1.54563
$429$	4.90692e11	0.699441
$430$	−3.38646e10	−0.0477682
$431$	1.01918e12	1.42267	0.711334	−	0.702855i	$-0.248092\pi$
$431$	1.01918e12	1.42267	0.711334	+	0.702855i	$0.248092\pi$
$432$	2.57555e11	0.355789
$433$	5.14679e11	0.703624	0.351812	−	0.936071i	$-0.385566\pi$
$433$	5.14679e11	0.703624	0.351812	+	0.936071i	$0.385566\pi$
$434$	−6.10874e10	−0.0826510
$435$	2.36693e11	0.316944
$436$	−8.27417e11	−1.09657
$437$	−5.45357e11	−0.715344
$438$	1.69468e11	0.220016
$439$	1.35144e12	1.73663	0.868315	−	0.496013i	$-0.165203\pi$
$439$	1.35144e12	1.73663	0.868315	+	0.496013i	$0.165203\pi$
$440$	−5.55098e11	−0.706045
$441$	9.31399e8	0.00117263
$442$	4.63348e11	0.577440
$443$	4.45190e10	0.0549198	0.0274599	−	0.999623i	$-0.491258\pi$
$443$	4.45190e10	0.0549198	0.0274599	+	0.999623i	$0.491258\pi$
$444$	−6.19491e10	−0.0756504
$445$	1.71699e11	0.207562
$446$	−5.55746e11	−0.665073
$447$	−1.32797e11	−0.157327
$448$	−1.99376e11	−0.233842
$449$	−9.56261e11	−1.11037	−0.555185	−	0.831727i	$-0.687353\pi$
$449$	−9.56261e11	−1.11037	−0.555185	+	0.831727i	$0.687353\pi$
$450$	9.54676e10	0.109749
$451$	−1.28869e12	−1.46675
$452$	−7.11468e10	−0.0801738
$453$	4.63785e11	0.517458
$454$	−4.72920e11	−0.522439
$455$	−1.35733e12	−1.48468
$456$	−1.06915e11	−0.115797
$457$	1.33435e12	1.43103	0.715513	−	0.698600i	$-0.246193\pi$
$457$	1.33435e12	1.43103	0.715513	+	0.698600i	$0.246193\pi$
$458$	−5.40541e11	−0.574029
$459$	4.85223e11	0.510251
$460$	9.41559e11	0.980476
$461$	1.58615e12	1.63565	0.817824	−	0.575469i	$-0.195180\pi$
$461$	1.58615e12	1.63565	0.817824	+	0.575469i	$0.195180\pi$
$462$	1.44315e11	0.147375
$463$	6.02126e11	0.608938	0.304469	−	0.952522i	$-0.401521\pi$
$463$	6.02126e11	0.608938	0.304469	+	0.952522i	$0.401521\pi$
$464$	7.06520e11	0.707609
$465$	−5.76699e10	−0.0572020
$466$	1.05665e11	0.103800
$467$	−8.90786e11	−0.866657	−0.433329	−	0.901236i	$-0.642661\pi$
$467$	−8.90786e11	−0.866657	−0.433329	+	0.901236i	$0.642661\pi$
$468$	1.43782e12	1.38547
$469$	−2.45058e11	−0.233879
$470$	2.42983e11	0.229687
$471$	−3.63771e11	−0.340591
$472$	−7.77553e11	−0.721093
$473$	−2.01678e11	−0.185261
$474$	−5.60063e10	−0.0509606
$475$	1.83321e11	0.165231
$476$	−8.06244e11	−0.719838
$477$	2.94347e10	0.0260332
$478$	−8.42094e11	−0.737794
$479$	−2.74907e11	−0.238603	−0.119302	−	0.992858i	$-0.538066\pi$
$479$	−2.74907e11	−0.238603	−0.119302	+	0.992858i	$0.538066\pi$
$480$	2.84075e11	0.244257
$481$	−5.86495e11	−0.499587
$482$	2.15406e11	0.181780
$483$	−5.30950e11	−0.443907
$484$	−4.91400e11	−0.407035
$485$	−1.74845e12	−1.43488
$486$	−3.88577e11	−0.315947
$487$	−1.45675e12	−1.17356	−0.586780	−	0.809746i	$-0.699605\pi$
$487$	−1.45675e12	−1.17356	−0.586780	+	0.809746i	$0.699605\pi$
$488$	5.68704e11	0.453938
$489$	−5.29932e11	−0.419112
$490$	5.21917e8	0.000408996 0
$491$	1.19785e12	0.930114	0.465057	−	0.885281i	$-0.346034\pi$
$491$	1.19785e12	0.930114	0.465057	+	0.885281i	$0.346034\pi$
$492$	4.28533e11	0.329717
$493$	1.33105e12	1.01481
$494$	−4.66663e11	−0.352559
$495$	−1.20052e12	−0.898765
$496$	−1.72143e11	−0.127709
$497$	1.39638e12	1.02660
$498$	−1.05483e11	−0.0768510
$499$	−5.12897e11	−0.370321	−0.185160	−	0.982708i	$-0.559280\pi$
$499$	−5.12897e11	−0.370321	−0.185160	+	0.982708i	$0.559280\pi$
$500$	−1.30132e12	−0.931147
$501$	−4.03642e11	−0.286237
$502$	−2.05043e11	−0.144104
$503$	−6.04557e11	−0.421096	−0.210548	−	0.977583i	$-0.567525\pi$
$503$	−6.04557e11	−0.421096	−0.210548	+	0.977583i	$0.567525\pi$
$504$	9.17215e11	0.633189
$505$	−1.64737e11	−0.112715
$506$	−9.47772e11	−0.642727
$507$	−1.06984e12	−0.719087
$508$	−1.27266e12	−0.847862
$509$	−2.32317e11	−0.153409	−0.0767044	−	0.997054i	$-0.524440\pi$
$509$	−2.32317e11	−0.153409	−0.0767044	+	0.997054i	$0.524440\pi$
$510$	1.28649e11	0.0842058
$511$	−2.79175e12	−1.81127
$512$	1.49207e12	0.959568
$513$	−4.88695e11	−0.311537
$514$	1.13814e12	0.719221
$515$	1.75795e12	1.10122
$516$	6.70648e10	0.0416458
$517$	1.44707e12	0.890804
$518$	−1.72491e11	−0.105265
$519$	4.11830e11	0.249152
$520$	1.74757e12	1.04814
$521$	5.47762e11	0.325703	0.162852	−	0.986651i	$-0.447931\pi$
$521$	5.47762e11	0.325703	0.162852	+	0.986651i	$0.447931\pi$
$522$	−6.98130e11	−0.411547
$523$	8.12576e11	0.474905	0.237452	−	0.971399i	$-0.423688\pi$
$523$	8.12576e11	0.474905	0.237452	+	0.971399i	$0.423688\pi$
$524$	−1.64656e12	−0.954085
$525$	1.78478e11	0.102534
$526$	−7.70346e11	−0.438783
$527$	−3.24310e11	−0.183152
$528$	4.06677e11	0.227718
$529$	1.68580e12	0.935956
$530$	1.64940e10	0.00907998
$531$	−1.68163e12	−0.917920
$532$	8.12013e11	0.439502
$533$	4.05708e12	2.17742
$534$	5.74725e10	0.0305861
$535$	−2.82053e12	−1.48847
$536$	3.15514e11	0.165111
$537$	−3.88749e10	−0.0201737
$538$	6.55823e11	0.337494
$539$	3.10824e9	0.00158623
$540$	8.43730e11	0.427004
$541$	−3.22713e12	−1.61968	−0.809839	−	0.586653i	$-0.800445\pi$
$541$	−3.22713e12	−1.61968	−0.809839	+	0.586653i	$0.800445\pi$
$542$	6.38751e10	0.0317932
$543$	1.50469e11	0.0742761
$544$	1.59751e12	0.782075
$545$	−2.17498e12	−1.05602
$546$	−4.54335e11	−0.218781
$547$	3.63148e11	0.173437	0.0867184	−	0.996233i	$-0.472362\pi$
$547$	3.63148e11	0.173437	0.0867184	+	0.996233i	$0.472362\pi$
$548$	−2.06391e12	−0.977638
$549$	1.22995e12	0.577844
$550$	3.18592e11	0.148458
$551$	−1.34058e12	−0.619598
$552$	6.83602e11	0.313384
$553$	9.22625e11	0.419529
$554$	1.13474e12	0.511801
$555$	−1.62841e11	−0.0728528
$556$	1.45483e12	0.645620
$557$	−1.99821e12	−0.879616	−0.439808	−	0.898092i	$-0.644954\pi$
$557$	−1.99821e12	−0.879616	−0.439808	+	0.898092i	$0.644954\pi$
$558$	1.70099e11	0.0742758
$559$	6.34927e11	0.275024
$560$	−1.12493e12	−0.483369
$561$	7.66162e11	0.326579
$562$	−8.55643e10	−0.0361809
$563$	−2.17908e12	−0.914082	−0.457041	−	0.889446i	$-0.651091\pi$
$563$	−2.17908e12	−0.914082	−0.457041	+	0.889446i	$0.651091\pi$
$564$	−4.81199e11	−0.200248
$565$	−1.87019e11	−0.0772089
$566$	9.18184e9	0.00376059
$567$	1.73301e12	0.704170
$568$	−1.79785e12	−0.724746
$569$	4.02160e12	1.60840	0.804199	−	0.594360i	$-0.202594\pi$
$569$	4.02160e12	1.60840	0.804199	+	0.594360i	$0.202594\pi$
$570$	−1.29570e11	−0.0514123
$571$	1.03577e12	0.407757	0.203879	−	0.978996i	$-0.434645\pi$
$571$	1.03577e12	0.407757	0.203879	+	0.978996i	$0.434645\pi$
$572$	4.79825e12	1.87413
$573$	−2.27334e11	−0.0880984
$574$	1.19321e12	0.458789
$575$	−1.17213e12	−0.447169
$576$	5.55166e11	0.210146
$577$	1.88421e12	0.707680	0.353840	−	0.935306i	$-0.384876\pi$
$577$	1.88421e12	0.707680	0.353840	+	0.935306i	$0.384876\pi$
$578$	−2.96851e11	−0.110628
$579$	−1.50963e11	−0.0558236
$580$	2.31451e12	0.849244
$581$	1.73768e12	0.632671
$582$	−5.85254e11	−0.211442
$583$	9.82289e10	0.0352152
$584$	3.59440e12	1.27870
$585$	3.77950e12	1.33424
$586$	1.25740e12	0.440490
$587$	−4.30653e11	−0.149712	−0.0748559	−	0.997194i	$-0.523850\pi$
$587$	−4.30653e11	−0.149712	−0.0748559	+	0.997194i	$0.523850\pi$
$588$	−1.03359e9	−0.000356575 0
$589$	3.26631e11	0.111825
$590$	−9.42315e11	−0.320156
$591$	1.09223e12	0.368275
$592$	−4.86077e11	−0.162651
$593$	−4.69669e12	−1.55972	−0.779859	−	0.625955i	$-0.784709\pi$
$593$	−4.69669e12	−1.55972	−0.779859	+	0.625955i	$0.784709\pi$
$594$	−8.49299e11	−0.279912
$595$	−2.11932e12	−0.693218
$596$	−1.29856e12	−0.421555
$597$	−1.65420e12	−0.532971
$598$	2.98379e12	0.954142
$599$	1.91656e12	0.608279	0.304139	−	0.952628i	$-0.401631\pi$
$599$	1.91656e12	0.608279	0.304139	+	0.952628i	$0.401631\pi$
$600$	−2.29791e11	−0.0723858
$601$	−4.23012e12	−1.32257	−0.661284	−	0.750136i	$-0.729988\pi$
$601$	−4.23012e12	−1.32257	−0.661284	+	0.750136i	$0.729988\pi$
$602$	1.86735e11	0.0579485
$603$	6.82367e11	0.210179
$604$	4.53514e12	1.38651
$605$	−1.29171e12	−0.391982
$606$	−5.51421e10	−0.0166095
$607$	−2.51983e12	−0.753392	−0.376696	−	0.926337i	$-0.622940\pi$
$607$	−2.51983e12	−0.753392	−0.376696	+	0.926337i	$0.622940\pi$
$608$	−1.60894e12	−0.477501
$609$	−1.30516e12	−0.384492
$610$	6.89211e11	0.201543
$611$	−4.55568e12	−1.32242
$612$	2.24500e12	0.646896
$613$	4.31238e12	1.23352	0.616758	−	0.787152i	$-0.288446\pi$
$613$	4.31238e12	1.23352	0.616758	+	0.787152i	$0.288446\pi$
$614$	3.09148e11	0.0877827
$615$	1.12646e12	0.317524
$616$	3.06090e12	0.856518
$617$	−7.93927e11	−0.220545	−0.110273	−	0.993901i	$-0.535172\pi$
$617$	−7.93927e11	−0.220545	−0.110273	+	0.993901i	$0.535172\pi$
$618$	5.88433e11	0.162274
$619$	1.75602e12	0.480754	0.240377	−	0.970680i	$-0.422729\pi$
$619$	1.75602e12	0.480754	0.240377	+	0.970680i	$0.422729\pi$
$620$	−5.63928e11	−0.153271
$621$	3.12466e12	0.843121
$622$	1.47943e12	0.396313
$623$	−9.46780e11	−0.251798
$624$	−1.28031e12	−0.338052
$625$	−2.19471e12	−0.575329
$626$	−1.13609e12	−0.295683
$627$	−7.71644e11	−0.199394
$628$	−3.55715e12	−0.912606
$629$	−9.15748e11	−0.233264
$630$	1.11157e12	0.281128
$631$	−6.57762e12	−1.65172	−0.825860	−	0.563875i	$-0.809310\pi$
$631$	−6.57762e12	−1.65172	−0.825860	+	0.563875i	$0.809310\pi$
$632$	−1.18789e12	−0.296175
$633$	−1.23565e9	−0.000305901 0
$634$	7.16460e11	0.176113
$635$	−3.34535e12	−0.816508
$636$	−3.26643e10	−0.00791620
$637$	−9.78540e9	−0.00235479
$638$	−2.32978e12	−0.556701
$639$	−3.88824e12	−0.922571
$640$	3.55844e12	0.838398
$641$	−2.42777e12	−0.567997	−0.283998	−	0.958825i	$-0.591661\pi$
$641$	−2.42777e12	−0.567997	−0.283998	+	0.958825i	$0.591661\pi$
$642$	−9.44110e11	−0.219339
$643$	1.34647e12	0.310633	0.155316	−	0.987865i	$-0.450360\pi$
$643$	1.34647e12	0.310633	0.155316	+	0.987865i	$0.450360\pi$
$644$	−5.19192e12	−1.18944
$645$	1.76289e11	0.0401057
$646$	−7.28644e11	−0.164615
$647$	3.75333e12	0.842068	0.421034	−	0.907045i	$-0.361667\pi$
$647$	3.75333e12	0.842068	0.421034	+	0.907045i	$0.361667\pi$
$648$	−2.23126e12	−0.497122
$649$	−5.61189e12	−1.24167
$650$	−1.00300e12	−0.220389
$651$	3.18002e11	0.0693929
$652$	−5.18196e12	−1.12300
$653$	−1.63246e12	−0.351344	−0.175672	−	0.984449i	$-0.556210\pi$
$653$	−1.63246e12	−0.351344	−0.175672	+	0.984449i	$0.556210\pi$
$654$	−7.28025e11	−0.155613
$655$	−4.32821e12	−0.918802
$656$	3.36244e12	0.708903
$657$	7.77367e12	1.62773
$658$	−1.33985e12	−0.278638
$659$	−2.92418e12	−0.603976	−0.301988	−	0.953312i	$-0.597650\pi$
$659$	−2.92418e12	−0.603976	−0.301988	+	0.953312i	$0.597650\pi$
$660$	1.33224e12	0.273297
$661$	3.02483e12	0.616303	0.308151	−	0.951337i	$-0.400290\pi$
$661$	3.02483e12	0.616303	0.308151	+	0.951337i	$0.400290\pi$
$662$	−1.63118e12	−0.330096
$663$	−2.41204e12	−0.484813
$664$	−2.23728e12	−0.446646
$665$	2.13448e12	0.423248
$666$	4.80304e11	0.0945981
$667$	8.57151e12	1.67684
$668$	−3.94703e12	−0.766966
$669$	2.89304e12	0.558389
$670$	3.82370e11	0.0733073
$671$	4.10455e12	0.781653
$672$	−1.56644e12	−0.296313
$673$	6.85188e12	1.28749	0.643743	−	0.765242i	$-0.277381\pi$
$673$	6.85188e12	1.28749	0.643743	+	0.765242i	$0.277381\pi$
$674$	−3.74139e12	−0.698335
$675$	−1.05035e12	−0.194745
$676$	−1.04614e13	−1.92677
$677$	−4.82723e12	−0.883180	−0.441590	−	0.897217i	$-0.645585\pi$
$677$	−4.82723e12	−0.883180	−0.441590	+	0.897217i	$0.645585\pi$
$678$	−6.26004e10	−0.0113774
$679$	9.64124e12	1.74068
$680$	2.72864e12	0.489390
$681$	2.46187e12	0.438635
$682$	5.67649e11	0.100473
$683$	−7.16850e12	−1.26048	−0.630239	−	0.776401i	$-0.717043\pi$
$683$	−7.16850e12	−1.26048	−0.630239	+	0.776401i	$0.717043\pi$
$684$	−2.26106e12	−0.394966
$685$	−5.42526e12	−0.941484
$686$	−2.20700e12	−0.380490
$687$	2.81389e12	0.481949
$688$	5.26216e11	0.0895398
$689$	−3.09245e11	−0.0522777
$690$	8.28455e11	0.139139
$691$	−4.29369e12	−0.716439	−0.358219	−	0.933637i	$-0.616616\pi$
$691$	−4.29369e12	−0.716439	−0.358219	+	0.933637i	$0.616616\pi$
$692$	4.02709e12	0.667597
$693$	6.61988e12	1.09031
$694$	2.11701e12	0.346422
$695$	3.82423e12	0.621745
$696$	1.68041e12	0.271439
$697$	6.33469e12	1.01667
$698$	3.51597e12	0.560655
$699$	−5.50061e11	−0.0871492
$700$	1.74525e12	0.274737
$701$	−4.69682e12	−0.734637	−0.367318	−	0.930095i	$-0.619724\pi$
$701$	−4.69682e12	−0.734637	−0.367318	+	0.930095i	$0.619724\pi$
$702$	2.67377e12	0.415535
$703$	9.22301e11	0.142421
$704$	1.85269e12	0.284266
$705$	−1.26489e12	−0.192843
$706$	−2.52815e12	−0.382985
$707$	9.08390e11	0.136737
$708$	1.86614e12	0.279122
$709$	8.90549e12	1.32358	0.661790	−	0.749690i	$-0.269797\pi$
$709$	8.90549e12	1.32358	0.661790	+	0.749690i	$0.269797\pi$
$710$	−2.17881e12	−0.321778
$711$	−2.56906e12	−0.377017
$712$	1.21898e12	0.177762
$713$	−2.08844e12	−0.302635
$714$	−7.09395e11	−0.102152
$715$	1.26128e13	1.80483
$716$	−3.80140e11	−0.0540548
$717$	4.38368e12	0.619444
$718$	−2.49596e12	−0.350492
$719$	1.14062e12	0.159170	0.0795850	−	0.996828i	$-0.474640\pi$
$719$	1.14062e12	0.159170	0.0795850	+	0.996828i	$0.474640\pi$
$720$	3.13238e12	0.434388
$721$	−9.69362e12	−1.33591
$722$	−2.04252e12	−0.279736
$723$	−1.12134e12	−0.152621
$724$	1.47137e12	0.199021
$725$	−2.88130e12	−0.387317
$726$	−4.32372e11	−0.0577620
$727$	−7.18983e12	−0.954583	−0.477292	−	0.878745i	$-0.658381\pi$
$727$	−7.18983e12	−0.954583	−0.477292	+	0.878745i	$0.658381\pi$
$728$	−9.63638e12	−1.27152
$729$	−3.35042e12	−0.439364
$730$	4.35604e12	0.567727
$731$	9.91369e11	0.128412
$732$	−1.36490e12	−0.175712
$733$	−7.48589e12	−0.957801	−0.478901	−	0.877869i	$-0.658965\pi$
$733$	−7.48589e12	−0.957801	−0.478901	+	0.877869i	$0.658965\pi$
$734$	−7.18213e11	−0.0913316
$735$	−2.71694e9	−0.000343389 0
$736$	1.02874e13	1.29227
$737$	2.27718e12	0.284311
$738$	−3.32251e12	−0.412299
$739$	−1.18021e13	−1.45566	−0.727829	−	0.685759i	$-0.759471\pi$
$739$	−1.18021e13	−1.45566	−0.727829	+	0.685759i	$0.759471\pi$
$740$	−1.59235e12	−0.195207
$741$	2.42930e12	0.296005
$742$	−9.09508e10	−0.0110151
$743$	1.55030e12	0.186623	0.0933117	−	0.995637i	$-0.470255\pi$
$743$	1.55030e12	0.186623	0.0933117	+	0.995637i	$0.470255\pi$
$744$	−4.09429e11	−0.0489892
$745$	−3.41344e12	−0.405965
$746$	3.10191e12	0.366694
$747$	−4.83860e12	−0.568561
$748$	7.49194e12	0.875059
$749$	1.55529e13	1.80569
$750$	−1.14500e12	−0.132138
$751$	−1.50756e13	−1.72939	−0.864697	−	0.502294i	$-0.832489\pi$
$751$	−1.50756e13	−1.72939	−0.864697	+	0.502294i	$0.832489\pi$
$752$	−3.77567e12	−0.430540
$753$	1.06739e12	0.120989
$754$	7.33465e12	0.826435
$755$	1.19212e13	1.33524
$756$	−4.65247e12	−0.518007
$757$	5.90095e12	0.653116	0.326558	−	0.945177i	$-0.394111\pi$
$757$	5.90095e12	0.653116	0.326558	+	0.945177i	$0.394111\pi$
$758$	3.89908e12	0.428994
$759$	4.93380e12	0.539627
$760$	−2.74816e12	−0.298800
$761$	1.49313e13	1.61386	0.806931	−	0.590646i	$-0.201127\pi$
$761$	1.49313e13	1.61386	0.806931	+	0.590646i	$0.201127\pi$
$762$	−1.11978e12	−0.120320
$763$	1.19932e13	1.28107
$764$	−2.22299e12	−0.236057
$765$	5.90127e12	0.622973
$766$	−5.19392e12	−0.545087
$767$	1.76674e13	1.84329
$768$	4.70898e11	0.0488429
$769$	1.15271e13	1.18864	0.594321	−	0.804228i	$-0.297421\pi$
$769$	1.15271e13	1.18864	0.594321	+	0.804228i	$0.297421\pi$
$770$	3.70950e12	0.380283
$771$	−5.92480e12	−0.603850
$772$	−1.47620e12	−0.149578
$773$	5.75890e12	0.580139	0.290069	−	0.957006i	$-0.406322\pi$
$773$	5.75890e12	0.580139	0.290069	+	0.957006i	$0.406322\pi$
$774$	−5.19967e11	−0.0520765
$775$	7.02025e11	0.0699029
$776$	−1.24132e13	−1.22887
$777$	8.97935e11	0.0883793
$778$	−2.34449e12	−0.229424
$779$	−6.38002e12	−0.620731
$780$	−4.19418e12	−0.405716
$781$	−1.29757e13	−1.24797
$782$	4.65887e12	0.445502
$783$	7.68092e12	0.730274
$784$	−8.10997e9	−0.000766650 0
$785$	−9.35043e12	−0.878857
$786$	−1.44877e12	−0.135394
$787$	4.64905e12	0.431994	0.215997	−	0.976394i	$-0.430700\pi$
$787$	4.64905e12	0.431994	0.215997	+	0.976394i	$0.430700\pi$
$788$	1.06804e13	0.986782
$789$	4.01018e12	0.368398
$790$	−1.43960e12	−0.131498
$791$	1.03125e12	0.0936637
$792$	−8.52313e12	−0.769725
$793$	−1.29220e13	−1.16038
$794$	−1.08527e12	−0.0969050
$795$	−8.58626e10	−0.00762346
$796$	−1.61757e13	−1.42808
$797$	−4.45228e12	−0.390859	−0.195430	−	0.980718i	$-0.562610\pi$
$797$	−4.45228e12	−0.390859	−0.195430	+	0.980718i	$0.562610\pi$
$798$	7.14471e11	0.0623694
$799$	−7.11321e12	−0.617454
$800$	−3.45809e12	−0.298491
$801$	2.63632e12	0.226283
$802$	1.68220e12	0.143580
$803$	2.59421e13	2.20184
$804$	−7.57237e11	−0.0639116
$805$	−1.36476e13	−1.14545
$806$	−1.78708e12	−0.149155
$807$	−3.41401e12	−0.283357
$808$	−1.16956e12	−0.0965318
$809$	1.58047e13	1.29723	0.648615	−	0.761117i	$-0.275349\pi$
$809$	1.58047e13	1.29723	0.648615	+	0.761117i	$0.275349\pi$
$810$	−2.70406e12	−0.220716
$811$	−4.29079e12	−0.348292	−0.174146	−	0.984720i	$-0.555716\pi$
$811$	−4.29079e12	−0.348292	−0.174146	+	0.984720i	$0.555716\pi$
$812$	−1.27626e13	−1.03024
$813$	−3.32513e11	−0.0266933
$814$	1.60286e12	0.127963
$815$	−1.36215e13	−1.08147
$816$	−1.99906e12	−0.157841
$817$	−9.98463e11	−0.0784030
$818$	2.15128e12	0.167999
$819$	−2.08408e13	−1.61859
$820$	1.10151e13	0.850797
$821$	−1.15783e13	−0.889406	−0.444703	−	0.895678i	$-0.646691\pi$
$821$	−1.15783e13	−0.889406	−0.444703	+	0.895678i	$0.646691\pi$
$822$	−1.81598e12	−0.138736
$823$	4.12270e12	0.313244	0.156622	−	0.987659i	$-0.449940\pi$
$823$	4.12270e12	0.313244	0.156622	+	0.987659i	$0.449940\pi$
$824$	1.24806e13	0.943111
$825$	−1.65849e12	−0.124644
$826$	5.19609e12	0.388388
$827$	2.77973e12	0.206646	0.103323	−	0.994648i	$-0.467052\pi$
$827$	2.77973e12	0.206646	0.103323	+	0.994648i	$0.467052\pi$
$828$	1.44570e13	1.06891
$829$	−7.92882e12	−0.583060	−0.291530	−	0.956562i	$-0.594164\pi$
$829$	−7.92882e12	−0.583060	−0.291530	+	0.956562i	$0.594164\pi$
$830$	−2.71135e12	−0.198305
$831$	−5.90708e12	−0.429703
$832$	−5.83266e12	−0.421999
$833$	−1.52788e10	−0.00109948
$834$	1.28007e12	0.0916195
$835$	−1.03753e13	−0.738603
$836$	−7.54555e12	−0.534272
$837$	−1.87145e12	−0.131799
$838$	−3.33178e12	−0.233388
$839$	9.02760e12	0.628990	0.314495	−	0.949259i	$-0.398165\pi$
$839$	9.02760e12	0.628990	0.314495	+	0.949259i	$0.398165\pi$
$840$	−2.67556e12	−0.185421
$841$	6.56304e12	0.452400
$842$	1.07778e13	0.738968
$843$	4.45421e11	0.0303771
$844$	−1.20829e10	−0.000819653 0
$845$	−2.74993e13	−1.85552
$846$	3.73084e12	0.250403
$847$	7.12272e12	0.475522
$848$	−2.56297e11	−0.0170201
$849$	−4.77977e10	−0.00315735
$850$	−1.56607e12	−0.102902
$851$	−5.89708e12	−0.385438
$852$	4.31487e12	0.280536
$853$	8.30953e12	0.537410	0.268705	−	0.963222i	$-0.413404\pi$
$853$	8.30953e12	0.537410	0.268705	+	0.963222i	$0.413404\pi$
$854$	−3.80043e12	−0.244496
$855$	−5.94350e12	−0.380360
$856$	−2.00245e13	−1.27476
$857$	2.85889e13	1.81044	0.905219	−	0.424945i	$-0.139706\pi$
$857$	2.85889e13	1.81044	0.905219	+	0.424945i	$0.139706\pi$
$858$	4.22186e12	0.265957
$859$	1.74265e13	1.09204	0.546021	−	0.837771i	$-0.316142\pi$
$859$	1.74265e13	1.09204	0.546021	+	0.837771i	$0.316142\pi$
$860$	1.72384e12	0.107462
$861$	−6.21148e12	−0.385195
$862$	8.76893e12	0.540958
$863$	−2.90310e13	−1.78161	−0.890807	−	0.454381i	$-0.849860\pi$
$863$	−2.90310e13	−1.78161	−0.890807	+	0.454381i	$0.849860\pi$
$864$	9.21852e12	0.562794
$865$	1.05858e13	0.642909
$866$	4.42825e12	0.267548
$867$	1.54531e12	0.0928819
$868$	3.10959e12	0.185937
$869$	−8.57341e12	−0.509993
$870$	2.03648e12	0.120516
$871$	−7.16905e12	−0.422065
$872$	−1.54413e13	−0.904399
$873$	−2.68462e13	−1.56429
$874$	−4.69220e12	−0.272004
$875$	1.88623e13	1.08782
$876$	−8.62661e12	−0.494962
$877$	2.58557e13	1.47590	0.737952	−	0.674853i	$-0.235793\pi$
$877$	2.58557e13	1.47590	0.737952	+	0.674853i	$0.235793\pi$
$878$	1.16277e13	0.660341
$879$	−6.54565e12	−0.369831
$880$	1.04533e13	0.587599
$881$	−8.44939e12	−0.472535	−0.236267	−	0.971688i	$-0.575924\pi$
$881$	−8.44939e12	−0.472535	−0.236267	+	0.971688i	$0.575924\pi$
$882$	8.01366e9	0.000445885 0
$883$	−1.55878e13	−0.862905	−0.431452	−	0.902136i	$-0.641999\pi$
$883$	−1.55878e13	−0.862905	−0.431452	+	0.902136i	$0.641999\pi$
$884$	−2.35862e13	−1.29904
$885$	4.90539e12	0.268800
$886$	3.83037e11	0.0208828
$887$	−2.19029e12	−0.118808	−0.0594041	−	0.998234i	$-0.518920\pi$
$887$	−2.19029e12	−0.118808	−0.0594041	+	0.998234i	$0.518920\pi$
$888$	−1.15610e12	−0.0623930
$889$	1.84469e13	0.990523
$890$	1.47728e12	0.0789240
$891$	−1.61038e13	−0.856012
$892$	2.82897e13	1.49619
$893$	7.16410e12	0.376990
$894$	−1.14257e12	−0.0598225
$895$	−9.99248e11	−0.0520558
$896$	−1.96219e13	−1.01708
$897$	−1.55327e13	−0.801088
$898$	−8.22758e12	−0.422210
$899$	−5.13373e12	−0.262129
$900$	−4.85968e12	−0.246897
$901$	−4.82853e11	−0.0244092
$902$	−1.10878e13	−0.557719
$903$	−9.72086e11	−0.0486530
$904$	−1.32774e12	−0.0661236
$905$	3.86769e12	0.191661
$906$	3.99036e12	0.196759
$907$	8.82876e12	0.433178	0.216589	−	0.976263i	$-0.430507\pi$
$907$	8.82876e12	0.433178	0.216589	+	0.976263i	$0.430507\pi$
$908$	2.40735e13	1.17531
$909$	−2.52942e12	−0.122881
$910$	−1.16783e13	−0.564539
$911$	−2.10890e13	−1.01443	−0.507217	−	0.861819i	$-0.669326\pi$
$911$	−2.10890e13	−1.01443	−0.507217	+	0.861819i	$0.669326\pi$
$912$	2.01336e12	0.0963707
$913$	−1.61472e13	−0.769095
$914$	1.14806e13	0.544137
$915$	−3.58781e12	−0.169214
$916$	2.75157e13	1.29137
$917$	2.38665e13	1.11462
$918$	4.17481e12	0.194019
$919$	−2.88293e13	−1.33326	−0.666628	−	0.745390i	$-0.732263\pi$
$919$	−2.88293e13	−1.33326	−0.666628	+	0.745390i	$0.732263\pi$
$920$	1.75714e13	0.808652
$921$	−1.60933e12	−0.0737014
$922$	1.36471e13	0.621942
$923$	4.08504e13	1.85263
$924$	−7.34621e12	−0.331543
$925$	1.98229e12	0.0890288
$926$	5.18064e12	0.231544
$927$	2.69920e13	1.20054
$928$	2.52881e13	1.11931
$929$	1.72191e13	0.758473	0.379237	−	0.925300i	$-0.376187\pi$
$929$	1.72191e13	0.758473	0.379237	+	0.925300i	$0.376187\pi$
$930$	−4.96186e11	−0.0217506
$931$	1.53882e10	0.000671295 0
$932$	−5.37879e12	−0.233514
$933$	−7.70145e12	−0.332740
$934$	−7.66424e12	−0.329540
$935$	1.96936e13	0.842698
$936$	2.68326e13	1.14267
$937$	−6.25976e12	−0.265295	−0.132648	−	0.991163i	$-0.542348\pi$
$937$	−6.25976e12	−0.265295	−0.132648	+	0.991163i	$0.542348\pi$
$938$	−2.10846e12	−0.0889307
$939$	5.91411e12	0.248253
$940$	−1.23688e13	−0.516717
$941$	−3.28356e13	−1.36518	−0.682592	−	0.730800i	$-0.739147\pi$
$941$	−3.28356e13	−1.36518	−0.682592	+	0.730800i	$0.739147\pi$
$942$	−3.12985e12	−0.129507
$943$	4.07931e13	1.67990
$944$	1.46425e13	0.600122
$945$	−1.22296e13	−0.498851
$946$	−1.73522e12	−0.0704441
$947$	3.05752e13	1.23536	0.617682	−	0.786428i	$-0.288072\pi$
$947$	3.05752e13	1.23536	0.617682	+	0.786428i	$0.288072\pi$
$948$	2.85094e12	0.114644
$949$	−8.16713e13	−3.26867
$950$	1.57728e12	0.0628277
$951$	−3.72967e12	−0.147862
$952$	−1.50462e13	−0.593690
$953$	3.90162e13	1.53224	0.766120	−	0.642698i	$-0.222185\pi$
$953$	3.90162e13	1.53224	0.766120	+	0.642698i	$0.222185\pi$
$954$	2.53254e11	0.00989893
$955$	−5.84343e12	−0.227328
$956$	4.28659e13	1.65978
$957$	1.21281e13	0.467401
$958$	−2.36528e12	−0.0907271
$959$	2.99158e13	1.14213
$960$	−1.61945e12	−0.0615384
$961$	−2.51888e13	−0.952691
$962$	−5.04614e12	−0.189964
$963$	−4.33073e13	−1.62272
$964$	−1.09650e13	−0.408943
$965$	−3.88039e12	−0.144046
$966$	−4.56824e12	−0.168792
$967$	3.08732e13	1.13544	0.567718	−	0.823223i	$-0.307826\pi$
$967$	3.08732e13	1.13544	0.567718	+	0.823223i	$0.307826\pi$
$968$	−9.17054e12	−0.335703
$969$	3.79309e12	0.138209
$970$	−1.50435e13	−0.545601
$971$	4.60961e13	1.66409	0.832047	−	0.554705i	$-0.187169\pi$
$971$	4.60961e13	1.66409	0.832047	+	0.554705i	$0.187169\pi$
$972$	1.97801e13	0.710773
$973$	−2.10874e13	−0.754251
$974$	−1.25338e13	−0.446237
$975$	5.22128e12	0.185036
$976$	−1.07095e13	−0.377786
$977$	−1.27438e13	−0.447478	−0.223739	−	0.974649i	$-0.571826\pi$
$977$	−1.27438e13	−0.447478	−0.223739	+	0.974649i	$0.571826\pi$
$978$	−4.55948e12	−0.159364
$979$	8.79786e12	0.306094
$980$	−2.65677e10	−0.000920102 0
$981$	−3.33952e13	−1.15126
$982$	1.03062e13	0.353669
$983$	1.90652e13	0.651255	0.325627	−	0.945498i	$-0.394424\pi$
$983$	1.90652e13	0.651255	0.325627	+	0.945498i	$0.394424\pi$
$984$	7.99731e12	0.271936
$985$	2.80750e13	0.950290
$986$	1.14523e13	0.385874
$987$	6.97485e12	0.233942
$988$	2.37550e13	0.793138
$989$	6.38406e12	0.212184
$990$	−1.03292e13	−0.341749
$991$	1.83651e13	0.604868	0.302434	−	0.953170i	$-0.402201\pi$
$991$	1.83651e13	0.604868	0.302434	+	0.953170i	$0.402201\pi$
$992$	−6.16142e12	−0.202013
$993$	8.49139e12	0.277145
$994$	1.20143e13	0.390356
$995$	−4.25199e13	−1.37527
$996$	5.36950e12	0.172889
$997$	−7.79594e12	−0.249885	−0.124943	−	0.992164i	$-0.539875\pi$
$997$	−7.79594e12	−0.249885	−0.124943	+	0.992164i	$0.539875\pi$
$998$	−4.41292e12	−0.140812
$999$	−5.28438e12	−0.167861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.b.1.10	✓	17
3.2	odd	2		387.10.a.e.1.8		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.10	✓	17	1.1	even	1	trivial
387.10.a.e.1.8		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)

\(f(q)\)	\(=\)	\(q+8.60390 q^{2} -44.7892 q^{3} -437.973 q^{4} -1151.27 q^{5} -385.362 q^{6} +6348.30 q^{7} -8173.47 q^{8} -17676.9 q^{9} +O(q^{10})\)	\(q+8.60390 q^{2} -44.7892 q^{3} -437.973 q^{4} -1151.27 q^{5} -385.362 q^{6} +6348.30 q^{7} -8173.47 q^{8} -17676.9 q^{9} -9905.41 q^{10} -58991.0 q^{11} +19616.5 q^{12} +185716. q^{13} +54620.2 q^{14} +51564.5 q^{15} +153918. q^{16} +289976. q^{17} -152091. q^{18} -292051. q^{19} +504225. q^{20} -284335. q^{21} -507553. q^{22} +1.86734e6 q^{23} +366083. q^{24} -627703. q^{25} +1.59788e6 q^{26} +1.67332e6 q^{27} -2.78038e6 q^{28} +4.59023e6 q^{29} +443656. q^{30} -1.11840e6 q^{31} +5.50912e6 q^{32} +2.64216e6 q^{33} +2.49492e6 q^{34} -7.30861e6 q^{35} +7.74201e6 q^{36} -3.15802e6 q^{37} -2.51278e6 q^{38} -8.31808e6 q^{39} +9.40987e6 q^{40} +2.18456e7 q^{41} -2.44639e6 q^{42} +3.41880e6 q^{43} +2.58364e7 q^{44} +2.03509e7 q^{45} +1.60664e7 q^{46} -2.45304e7 q^{47} -6.89388e6 q^{48} -52690.1 q^{49} -5.40069e6 q^{50} -1.29878e7 q^{51} -8.13387e7 q^{52} -1.66515e6 q^{53} +1.43971e7 q^{54} +6.79145e7 q^{55} -5.18877e7 q^{56} +1.30807e7 q^{57} +3.94939e7 q^{58} +9.51313e7 q^{59} -2.25838e7 q^{60} -6.95792e7 q^{61} -9.62264e6 q^{62} -1.12218e8 q^{63} -3.14063e7 q^{64} -2.13810e8 q^{65} +2.27329e7 q^{66} -3.86021e7 q^{67} -1.27002e8 q^{68} -8.36366e7 q^{69} -6.28825e7 q^{70} +2.19962e8 q^{71} +1.44482e8 q^{72} -4.39764e8 q^{73} -2.71713e7 q^{74} +2.81143e7 q^{75} +1.27910e8 q^{76} -3.74492e8 q^{77} -7.15680e7 q^{78} +1.45334e8 q^{79} -1.77202e8 q^{80} +2.72988e8 q^{81} +1.87957e8 q^{82} +2.73724e8 q^{83} +1.24531e8 q^{84} -3.33840e8 q^{85} +2.94150e7 q^{86} -2.05593e8 q^{87} +4.82161e8 q^{88} -1.49139e8 q^{89} +1.75097e8 q^{90} +1.17898e9 q^{91} -8.17843e8 q^{92} +5.00924e7 q^{93} -2.11057e8 q^{94} +3.36229e8 q^{95} -2.46749e8 q^{96} +1.51871e9 q^{97} -453340. q^{98} +1.04278e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9} + 23763 q^{10} + 78370 q^{11} + 271339 q^{12} + 114452 q^{13} - 376208 q^{14} - 255820 q^{15} + 412586 q^{16} + 726937 q^{17} + 577055 q^{18} + 544263 q^{19} + 3642183 q^{20} + 3137394 q^{21} + 5269148 q^{22} + 5575241 q^{23} + 16215113 q^{24} + 10874708 q^{25} + 8009180 q^{26} + 8350126 q^{27} + 12534764 q^{28} + 8223345 q^{29} + 30612012 q^{30} + 13054147 q^{31} + 37111710 q^{32} + 36024808 q^{33} + 27991291 q^{34} + 17826330 q^{35} + 84105953 q^{36} + 46733879 q^{37} + 15733789 q^{38} + 8689898 q^{39} + 52241669 q^{40} + 53667013 q^{41} + 7708286 q^{42} + 58119617 q^{43} + 81727236 q^{44} + 124361968 q^{45} + 146859355 q^{46} + 122945511 q^{47} + 86356095 q^{48} + 111396073 q^{49} - 96642133 q^{50} - 187132423 q^{51} - 54447944 q^{52} - 993146 q^{53} - 219468490 q^{54} - 248155792 q^{55} - 141048116 q^{56} - 402917960 q^{57} - 466599837 q^{58} - 95519644 q^{59} - 621611940 q^{60} - 311752038 q^{61} - 212471691 q^{62} - 928966350 q^{63} - 829842590 q^{64} - 107969830 q^{65} - 978530932 q^{66} - 292438130 q^{67} - 88281129 q^{68} + 78577726 q^{69} - 1650972530 q^{70} - 13576908 q^{71} - 706943493 q^{72} - 501490738 q^{73} - 494831691 q^{74} - 641914030 q^{75} - 1248630771 q^{76} + 787365348 q^{77} - 946670550 q^{78} + 740350275 q^{79} - 27802861 q^{80} + 1582210525 q^{81} - 1600400057 q^{82} + 754109940 q^{83} - 1955423842 q^{84} + 1071609956 q^{85} + 164102448 q^{86} + 186301257 q^{87} + 1863375104 q^{88} + 1470581868 q^{89} - 698098630 q^{90} + 2895349644 q^{91} + 1041082071 q^{92} + 4540331515 q^{93} - 706582361 q^{94} + 3297255729 q^{95} + 2087289393 q^{96} + 1949310583 q^{97} + 6695989160 q^{98} + 1234191326 q^{99}+O(q^{100}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9 + 23763 * q^10 + 78370 * q^11 + 271339 * q^12 + 114452 * q^13 - 376208 * q^14 - 255820 * q^15 + 412586 * q^16 + 726937 * q^17 + 577055 * q^18 + 544263 * q^19 + 3642183 * q^20 + 3137394 * q^21 + 5269148 * q^22 + 5575241 * q^23 + 16215113 * q^24 + 10874708 * q^25 + 8009180 * q^26 + 8350126 * q^27 + 12534764 * q^28 + 8223345 * q^29 + 30612012 * q^30 + 13054147 * q^31 + 37111710 * q^32 + 36024808 * q^33 + 27991291 * q^34 + 17826330 * q^35 + 84105953 * q^36 + 46733879 * q^37 + 15733789 * q^38 + 8689898 * q^39 + 52241669 * q^40 + 53667013 * q^41 + 7708286 * q^42 + 58119617 * q^43 + 81727236 * q^44 + 124361968 * q^45 + 146859355 * q^46 + 122945511 * q^47 + 86356095 * q^48 + 111396073 * q^49 - 96642133 * q^50 - 187132423 * q^51 - 54447944 * q^52 - 993146 * q^53 - 219468490 * q^54 - 248155792 * q^55 - 141048116 * q^56 - 402917960 * q^57 - 466599837 * q^58 - 95519644 * q^59 - 621611940 * q^60 - 311752038 * q^61 - 212471691 * q^62 - 928966350 * q^63 - 829842590 * q^64 - 107969830 * q^65 - 978530932 * q^66 - 292438130 * q^67 - 88281129 * q^68 + 78577726 * q^69 - 1650972530 * q^70 - 13576908 * q^71 - 706943493 * q^72 - 501490738 * q^73 - 494831691 * q^74 - 641914030 * q^75 - 1248630771 * q^76 + 787365348 * q^77 - 946670550 * q^78 + 740350275 * q^79 - 27802861 * q^80 + 1582210525 * q^81 - 1600400057 * q^82 + 754109940 * q^83 - 1955423842 * q^84 + 1071609956 * q^85 + 164102448 * q^86 + 186301257 * q^87 + 1863375104 * q^88 + 1470581868 * q^89 - 698098630 * q^90 + 2895349644 * q^91 + 1041082071 * q^92 + 4540331515 * q^93 - 706582361 * q^94 + 3297255729 * q^95 + 2087289393 * q^96 + 1949310583 * q^97 + 6695989160 * q^98 + 1234191326 * q^99

Introduction

L-functions

Modular forms

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