LMFDB - Embedded newform 43.10.a.a.1.4

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:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} + \cdots + 52\!\cdots\!00 $ x^15 - 2x^14 - 5425x^13 + 14888x^12 + 11288030x^11 - 37600244x^10 - 11474166224x^9 + 47465836576x^8 + 5986976782464x^7 - 32493903147264x^6 - 1516975415483904x^5 + 10892588268404224x^4 + 139803541742443008x^3 - 1349125586394823680x^2 + 2103623681144094720x + 529838441422848000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$21.7142$ 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)

$f(q)$	$=$	$q-23.7142 q^{2} +2.00552 q^{3} +50.3616 q^{4} -764.097 q^{5} -47.5592 q^{6} +4079.63 q^{7} +10947.4 q^{8} -19679.0 q^{9} +O(q^{10})$	\(q-23.7142 q^{2} +2.00552 q^{3} +50.3616 q^{4} -764.097 q^{5} -47.5592 q^{6} +4079.63 q^{7} +10947.4 q^{8} -19679.0 q^{9} +18119.9 q^{10} +11874.8 q^{11} +101.001 q^{12} +108937. q^{13} -96745.1 q^{14} -1532.41 q^{15} -285393. q^{16} +190628. q^{17} +466671. q^{18} +764217. q^{19} -38481.2 q^{20} +8181.78 q^{21} -281600. q^{22} -923194. q^{23} +21955.2 q^{24} -1.36928e6 q^{25} -2.58336e6 q^{26} -78941.2 q^{27} +205457. q^{28} -3.16980e6 q^{29} +36339.9 q^{30} -1.00773e7 q^{31} +1.16280e6 q^{32} +23815.1 q^{33} -4.52058e6 q^{34} -3.11724e6 q^{35} -991065. q^{36} +6.60642e6 q^{37} -1.81228e7 q^{38} +218476. q^{39} -8.36486e6 q^{40} -2.24033e7 q^{41} -194024. q^{42} -3.41880e6 q^{43} +598032. q^{44} +1.50367e7 q^{45} +2.18928e7 q^{46} +1.96091e7 q^{47} -572361. q^{48} -2.37102e7 q^{49} +3.24713e7 q^{50} +382308. q^{51} +5.48626e6 q^{52} +2.18335e7 q^{53} +1.87203e6 q^{54} -9.07347e6 q^{55} +4.46612e7 q^{56} +1.53265e6 q^{57} +7.51692e7 q^{58} -1.05400e8 q^{59} -77174.8 q^{60} +6.39871e7 q^{61} +2.38974e8 q^{62} -8.02830e7 q^{63} +1.18546e8 q^{64} -8.32387e7 q^{65} -564754. q^{66} +6.09774e7 q^{67} +9.60032e6 q^{68} -1.85148e6 q^{69} +7.39227e7 q^{70} -3.75615e8 q^{71} -2.15433e8 q^{72} +3.38605e8 q^{73} -1.56666e8 q^{74} -2.74612e6 q^{75} +3.84872e7 q^{76} +4.84446e7 q^{77} -5.18097e6 q^{78} -6.12882e8 q^{79} +2.18068e8 q^{80} +3.87183e8 q^{81} +5.31277e8 q^{82} +3.98173e8 q^{83} +412048. q^{84} -1.45658e8 q^{85} +8.10740e7 q^{86} -6.35710e6 q^{87} +1.29997e8 q^{88} -8.15783e8 q^{89} -3.56582e8 q^{90} +4.44424e8 q^{91} -4.64936e7 q^{92} -2.02102e7 q^{93} -4.65014e8 q^{94} -5.83937e8 q^{95} +2.33202e6 q^{96} +6.93925e8 q^{97} +5.62268e8 q^{98} -2.33683e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) $ 15 * q - 32 * q^2 - 317 * q^3 + 3242 * q^4 - 4717 * q^5 + 687 * q^6 - 9680 * q^7 - 20394 * q^8 + 69516 * q^9	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9} - 36237 q^{10} - 104484 q^{11} - 266395 q^{12} - 116174 q^{13} + 416064 q^{14} + 415388 q^{15} + 996762 q^{16} - 884265 q^{17} - 588735 q^{18} - 689535 q^{19} - 3077879 q^{20} - 2070198 q^{21} - 7276218 q^{22} - 2504077 q^{23} - 11534895 q^{24} + 1315350 q^{25} - 13343414 q^{26} - 12546986 q^{27} - 28059568 q^{28} - 18406221 q^{29} - 39503820 q^{30} - 12033699 q^{31} - 18952630 q^{32} - 14197716 q^{33} - 30383125 q^{34} - 27855546 q^{35} - 18372959 q^{36} - 8722847 q^{37} - 63941843 q^{38} - 30955510 q^{39} - 39665611 q^{40} - 18689389 q^{41} - 73185310 q^{42} - 51282015 q^{43} - 68723220 q^{44} - 216992888 q^{45} - 2067521 q^{46} - 104960741 q^{47} - 145362479 q^{48} + 92663095 q^{49} - 42446347 q^{50} + 37433407 q^{51} + 149226080 q^{52} - 215907800 q^{53} + 419158122 q^{54} + 384379852 q^{55} + 430441344 q^{56} + 258744488 q^{57} + 295963139 q^{58} + 185924544 q^{59} + 973236172 q^{60} + 247538102 q^{61} + 139798853 q^{62} + 405429926 q^{63} + 848556290 q^{64} + 94294394 q^{65} + 667230492 q^{66} + 467904656 q^{67} - 88234341 q^{68} + 163914994 q^{69} + 647526126 q^{70} - 8252944 q^{71} + 889796745 q^{72} - 715627902 q^{73} + 725122989 q^{74} - 18301762 q^{75} + 346300359 q^{76} - 1236779964 q^{77} + 2058642146 q^{78} + 560681783 q^{79} - 1157214179 q^{80} - 752010645 q^{81} + 941346367 q^{82} - 1442854698 q^{83} + 1895248718 q^{84} + 699302088 q^{85} + 109401632 q^{86} - 2094576907 q^{87} - 1464507256 q^{88} - 396710008 q^{89} + 1411356270 q^{90} - 3278076852 q^{91} + 155864647 q^{92} - 1424759183 q^{93} + 4666638949 q^{94} - 3854114395 q^{95} - 952489551 q^{96} - 3063837815 q^{97} - 6161086984 q^{98} - 6576160348 q^{99}+O(q^{100}) \) 15 * q - 32 * q^2 - 317 * q^3 + 3242 * q^4 - 4717 * q^5 + 687 * q^6 - 9680 * q^7 - 20394 * q^8 + 69516 * q^9 - 36237 * q^10 - 104484 * q^11 - 266395 * q^12 - 116174 * q^13 + 416064 * q^14 + 415388 * q^15 + 996762 * q^16 - 884265 * q^17 - 588735 * q^18 - 689535 * q^19 - 3077879 * q^20 - 2070198 * q^21 - 7276218 * q^22 - 2504077 * q^23 - 11534895 * q^24 + 1315350 * q^25 - 13343414 * q^26 - 12546986 * q^27 - 28059568 * q^28 - 18406221 * q^29 - 39503820 * q^30 - 12033699 * q^31 - 18952630 * q^32 - 14197716 * q^33 - 30383125 * q^34 - 27855546 * q^35 - 18372959 * q^36 - 8722847 * q^37 - 63941843 * q^38 - 30955510 * q^39 - 39665611 * q^40 - 18689389 * q^41 - 73185310 * q^42 - 51282015 * q^43 - 68723220 * q^44 - 216992888 * q^45 - 2067521 * q^46 - 104960741 * q^47 - 145362479 * q^48 + 92663095 * q^49 - 42446347 * q^50 + 37433407 * q^51 + 149226080 * q^52 - 215907800 * q^53 + 419158122 * q^54 + 384379852 * q^55 + 430441344 * q^56 + 258744488 * q^57 + 295963139 * q^58 + 185924544 * q^59 + 973236172 * q^60 + 247538102 * q^61 + 139798853 * q^62 + 405429926 * q^63 + 848556290 * q^64 + 94294394 * q^65 + 667230492 * q^66 + 467904656 * q^67 - 88234341 * q^68 + 163914994 * q^69 + 647526126 * q^70 - 8252944 * q^71 + 889796745 * q^72 - 715627902 * q^73 + 725122989 * q^74 - 18301762 * q^75 + 346300359 * q^76 - 1236779964 * q^77 + 2058642146 * q^78 + 560681783 * q^79 - 1157214179 * q^80 - 752010645 * q^81 + 941346367 * q^82 - 1442854698 * q^83 + 1895248718 * q^84 + 699302088 * q^85 + 109401632 * q^86 - 2094576907 * q^87 - 1464507256 * q^88 - 396710008 * q^89 + 1411356270 * q^90 - 3278076852 * q^91 + 155864647 * q^92 - 1424759183 * q^93 + 4666638949 * q^94 - 3854114395 * q^95 - 952489551 * q^96 - 3063837815 * q^97 - 6161086984 * q^98 - 6576160348 * 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 $

$2$	−23.7142	−1.04803	−0.524014	−	0.851710i	$-0.675566\pi$
$2$	−23.7142	−1.04803	−0.524014	+	0.851710i	$0.675566\pi$
$3$	2.00552	0.0142949	0.00714745	−	0.999974i	$-0.497725\pi$
$3$	2.00552	0.0142949	0.00714745	+	0.999974i	$0.497725\pi$
$4$	50.3616	0.0983625
$5$	−764.097	−0.546744	−0.273372	−	0.961908i	$-0.588139\pi$
$5$	−764.097	−0.546744	−0.273372	+	0.961908i	$0.588139\pi$
$6$	−47.5592	−0.0149815
$7$	4079.63	0.642214	0.321107	−	0.947043i	$-0.395945\pi$
$7$	4079.63	0.642214	0.321107	+	0.947043i	$0.395945\pi$
$8$	10947.4	0.944941
$9$	−19679.0	−0.999796
$10$	18119.9	0.573003
$11$	11874.8	0.244544	0.122272	−	0.992497i	$-0.460982\pi$
$11$	11874.8	0.244544	0.122272	+	0.992497i	$0.460982\pi$
$12$	101.001	0.00140608
$13$	108937.	1.05787	0.528934	−	0.848663i	$-0.322592\pi$
$13$	108937.	1.05787	0.528934	+	0.848663i	$0.322592\pi$
$14$	−96745.1	−0.673058
$15$	−1532.41	−0.00781565
$16$	−285393.	−1.08869
$17$	190628.	0.553562	0.276781	−	0.960933i	$-0.410732\pi$
$17$	190628.	0.553562	0.276781	+	0.960933i	$0.410732\pi$
$18$	466671.	1.04781
$19$	764217.	1.34532	0.672660	−	0.739951i	$-0.265152\pi$
$19$	764217.	1.34532	0.672660	+	0.739951i	$0.265152\pi$
$20$	−38481.2	−0.0537791
$21$	8181.78	0.00918039
$22$	−281600.	−0.256289
$23$	−923194.	−0.687888	−0.343944	−	0.938990i	$-0.611763\pi$
$23$	−923194.	−0.687888	−0.343944	+	0.938990i	$0.611763\pi$
$24$	21955.2	0.0135078
$25$	−1.36928e6	−0.701071
$26$	−2.58336e6	−1.10868
$27$	−78941.2	−0.0285869
$28$	205457.	0.0631698
$29$	−3.16980e6	−0.832226	−0.416113	−	0.909313i	$-0.636608\pi$
$29$	−3.16980e6	−0.832226	−0.416113	+	0.909313i	$0.636608\pi$
$30$	36339.9	0.00819102
$31$	−1.00773e7	−1.95982	−0.979909	−	0.199444i	$-0.936086\pi$
$31$	−1.00773e7	−1.95982	−0.979909	+	0.199444i	$0.936086\pi$
$32$	1.16280e6	0.196034
$33$	23815.1	0.00349574
$34$	−4.52058e6	−0.580148
$35$	−3.11724e6	−0.351126
$36$	−991065.	−0.0983424
$37$	6.60642e6	0.579506	0.289753	−	0.957101i	$-0.406427\pi$
$37$	6.60642e6	0.579506	0.289753	+	0.957101i	$0.406427\pi$
$38$	−1.81228e7	−1.40993
$39$	218476.	0.0151221
$40$	−8.36486e6	−0.516641
$41$	−2.24033e7	−1.23818	−0.619092	−	0.785318i	$-0.712499\pi$
$41$	−2.24033e7	−1.23818	−0.619092	+	0.785318i	$0.712499\pi$
$42$	−194024.	−0.00962131
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	598032.	0.0240540
$45$	1.50367e7	0.546632
$46$	2.18928e7	0.720926
$47$	1.96091e7	0.586162	0.293081	−	0.956088i	$-0.405319\pi$
$47$	1.96091e7	0.586162	0.293081	+	0.956088i	$0.405319\pi$
$48$	−572361.	−0.0155627
$49$	−2.37102e7	−0.587561
$50$	3.24713e7	0.734742
$51$	382308.	0.00791311
$52$	5.48626e6	0.104055
$53$	2.18335e7	0.380086	0.190043	−	0.981776i	$-0.439137\pi$
$53$	2.18335e7	0.380086	0.190043	+	0.981776i	$0.439137\pi$
$54$	1.87203e6	0.0299599
$55$	−9.07347e6	−0.133703
$56$	4.46612e7	0.606855
$57$	1.53265e6	0.0192312
$58$	7.51692e7	0.872196
$59$	−1.05400e8	−1.13242	−0.566210	−	0.824261i	$-0.691591\pi$
$59$	−1.05400e8	−1.13242	−0.566210	+	0.824261i	$0.691591\pi$
$60$	−77174.8	−0.000768767 0
$61$	6.39871e7	0.591709	0.295854	−	0.955233i	$-0.404396\pi$
$61$	6.39871e7	0.591709	0.295854	+	0.955233i	$0.404396\pi$
$62$	2.38974e8	2.05394
$63$	−8.02830e7	−0.642083
$64$	1.18546e8	0.883239
$65$	−8.32387e7	−0.578383
$66$	−564754.	−0.00366363
$67$	6.09774e7	0.369686	0.184843	−	0.982768i	$-0.440822\pi$
$67$	6.09774e7	0.369686	0.184843	+	0.982768i	$0.440822\pi$
$68$	9.60032e6	0.0544497
$69$	−1.85148e6	−0.00983330
$70$	7.39227e7	0.367990
$71$	−3.75615e8	−1.75420	−0.877102	−	0.480304i	$-0.840526\pi$
$71$	−3.75615e8	−1.75420	−0.877102	+	0.480304i	$0.840526\pi$
$72$	−2.15433e8	−0.944748
$73$	3.38605e8	1.39553	0.697766	−	0.716325i	$-0.254177\pi$
$73$	3.38605e8	1.39553	0.697766	+	0.716325i	$0.254177\pi$
$74$	−1.56666e8	−0.607339
$75$	−2.74612e6	−0.0100218
$76$	3.84872e7	0.132329
$77$	4.84446e7	0.157050
$78$	−5.18097e6	−0.0158484
$79$	−6.12882e8	−1.77033	−0.885166	−	0.465275i	$-0.845955\pi$
$79$	−6.12882e8	−1.77033	−0.885166	+	0.465275i	$0.845955\pi$
$80$	2.18068e8	0.595233
$81$	3.87183e8	0.999387
$82$	5.31277e8	1.29765
$83$	3.98173e8	0.920916	0.460458	−	0.887682i	$-0.347685\pi$
$83$	3.98173e8	0.920916	0.460458	+	0.887682i	$0.347685\pi$
$84$	412048.	0.000903007 0
$85$	−1.45658e8	−0.302656
$86$	8.10740e7	0.159823
$87$	−6.35710e6	−0.0118966
$88$	1.29997e8	0.231080
$89$	−8.15783e8	−1.37822	−0.689111	−	0.724655i	$-0.741999\pi$
$89$	−8.15783e8	−1.37822	−0.689111	+	0.724655i	$0.741999\pi$
$90$	−3.56582e8	−0.572885
$91$	4.44424e8	0.679378
$92$	−4.64936e7	−0.0676624
$93$	−2.02102e7	−0.0280154
$94$	−4.65014e8	−0.614314
$95$	−5.83937e8	−0.735545
$96$	2.33202e6	0.00280228
$97$	6.93925e8	0.795866	0.397933	−	0.917415i	$-0.369728\pi$
$97$	6.93925e8	0.795866	0.397933	+	0.917415i	$0.369728\pi$
$98$	5.62268e8	0.615780
$99$	−2.33683e8	−0.244494
$100$	−6.89592e7	−0.0689592
$101$	−1.18596e8	−0.113403	−0.0567014	−	0.998391i	$-0.518058\pi$
$101$	−1.18596e8	−0.113403	−0.0567014	+	0.998391i	$0.518058\pi$
$102$	−9.06611e6	−0.00829316
$103$	−1.30566e9	−1.14304	−0.571521	−	0.820587i	$-0.693647\pi$
$103$	−1.30566e9	−1.14304	−0.571521	+	0.820587i	$0.693647\pi$
$104$	1.19258e9	0.999623
$105$	−6.25168e6	−0.00501932
$106$	−5.17764e8	−0.398341
$107$	−1.24496e9	−0.918182	−0.459091	−	0.888389i	$-0.651825\pi$
$107$	−1.24496e9	−0.918182	−0.459091	+	0.888389i	$0.651825\pi$
$108$	−3.97561e6	−0.00281188
$109$	−8.52511e8	−0.578470	−0.289235	−	0.957258i	$-0.593401\pi$
$109$	−8.52511e8	−0.578470	−0.289235	+	0.957258i	$0.593401\pi$
$110$	2.15170e8	0.140125
$111$	1.32493e7	0.00828399
$112$	−1.16430e9	−0.699170
$113$	−1.50939e9	−0.870858	−0.435429	−	0.900223i	$-0.643403\pi$
$113$	−1.50939e9	−0.870858	−0.435429	+	0.900223i	$0.643403\pi$
$114$	−3.63456e7	−0.0201549
$115$	7.05410e8	0.376098
$116$	−1.59636e8	−0.0818599
$117$	−2.14377e9	−1.05765
$118$	2.49948e9	1.18681
$119$	7.77691e8	0.355505
$120$	−1.67759e7	−0.00738533
$121$	−2.21694e9	−0.940198
$122$	−1.51740e9	−0.620127
$123$	−4.49303e7	−0.0176997
$124$	−5.07508e8	−0.192773
$125$	2.53864e9	0.930050
$126$	1.90384e9	0.672921
$127$	1.49537e9	0.510071	0.255036	−	0.966932i	$-0.417913\pi$
$127$	1.49537e9	0.510071	0.255036	+	0.966932i	$0.417913\pi$
$128$	−3.40658e9	−1.12169
$129$	−6.85647e6	−0.00217995
$130$	1.97394e9	0.606161
$131$	−1.51968e8	−0.0450850	−0.0225425	−	0.999746i	$-0.507176\pi$
$131$	−1.51968e8	−0.0450850	−0.0225425	+	0.999746i	$0.507176\pi$
$132$	1.19937e6	0.000343850 0
$133$	3.11773e9	0.863984
$134$	−1.44603e9	−0.387441
$135$	6.03188e7	0.0156297
$136$	2.08687e9	0.523083
$137$	−2.01944e9	−0.489765	−0.244883	−	0.969553i	$-0.578749\pi$
$137$	−2.01944e9	−0.489765	−0.244883	+	0.969553i	$0.578749\pi$
$138$	4.39064e7	0.0103056
$139$	2.32789e9	0.528927	0.264463	−	0.964396i	$-0.414805\pi$
$139$	2.32789e9	0.528927	0.264463	+	0.964396i	$0.414805\pi$
$140$	−1.56989e8	−0.0345377
$141$	3.93265e7	0.00837913
$142$	8.90739e9	1.83845
$143$	1.29360e9	0.258696
$144$	5.61624e9	1.08846
$145$	2.42204e9	0.455014
$146$	−8.02973e9	−1.46256
$147$	−4.75513e7	−0.00839913
$148$	3.32710e8	0.0570017
$149$	−1.41126e9	−0.234568	−0.117284	−	0.993098i	$-0.537419\pi$
$149$	−1.41126e9	−0.234568	−0.117284	+	0.993098i	$0.537419\pi$
$150$	6.51219e7	0.0105031
$151$	4.13179e9	0.646758	0.323379	−	0.946269i	$-0.395181\pi$
$151$	4.13179e9	0.646758	0.323379	+	0.946269i	$0.395181\pi$
$152$	8.36617e9	1.27125
$153$	−3.75136e9	−0.553448
$154$	−1.14882e9	−0.164593
$155$	7.70003e9	1.07152
$156$	1.10028e7	0.00148745
$157$	1.22045e10	1.60314	0.801568	−	0.597904i	$-0.204000\pi$
$157$	1.22045e10	1.60314	0.801568	+	0.597904i	$0.204000\pi$
$158$	1.45340e10	1.85536
$159$	4.37875e7	0.00543330
$160$	−8.88493e8	−0.107180
$161$	−3.76629e9	−0.441772
$162$	−9.18172e9	−1.04739
$163$	−1.00930e10	−1.11990	−0.559948	−	0.828528i	$-0.689179\pi$
$163$	−1.00930e10	−1.11990	−0.559948	+	0.828528i	$0.689179\pi$
$164$	−1.12827e9	−0.121791
$165$	−1.81970e7	−0.00191127
$166$	−9.44233e9	−0.965145
$167$	−1.39128e10	−1.38417	−0.692086	−	0.721815i	$-0.743308\pi$
$167$	−1.39128e10	−1.38417	−0.692086	+	0.721815i	$0.743308\pi$
$168$	8.95690e7	0.00867493
$169$	1.26283e9	0.119085
$170$	3.45416e9	0.317192
$171$	−1.50390e10	−1.34505
$172$	−1.72176e8	−0.0150001
$173$	−2.03248e10	−1.72512	−0.862558	−	0.505958i	$-0.831139\pi$
$173$	−2.03248e10	−1.72512	−0.862558	+	0.505958i	$0.831139\pi$
$174$	1.50753e8	0.0124680
$175$	−5.58616e9	−0.450238
$176$	−3.38897e9	−0.266232
$177$	−2.11382e8	−0.0161878
$178$	1.93456e10	1.44442
$179$	−5.53330e9	−0.402852	−0.201426	−	0.979504i	$-0.564558\pi$
$179$	−5.53330e9	−0.402852	−0.201426	+	0.979504i	$0.564558\pi$
$180$	7.57270e8	0.0537681
$181$	2.15970e10	1.49569	0.747843	−	0.663875i	$-0.231089\pi$
$181$	2.15970e10	1.49569	0.747843	+	0.663875i	$0.231089\pi$
$182$	−1.05391e10	−0.712007
$183$	1.28327e8	0.00845842
$184$	−1.01065e10	−0.650014
$185$	−5.04795e9	−0.316841
$186$	4.79268e8	0.0293609
$187$	2.26366e9	0.135370
$188$	9.87546e8	0.0576564
$189$	−3.22051e8	−0.0183589
$190$	1.38476e10	0.770872
$191$	−1.65024e10	−0.897217	−0.448608	−	0.893728i	$-0.648080\pi$
$191$	−1.65024e10	−0.897217	−0.448608	+	0.893728i	$0.648080\pi$
$192$	2.37747e8	0.0126258
$193$	−3.40195e10	−1.76490	−0.882450	−	0.470407i	$-0.844107\pi$
$193$	−3.40195e10	−1.76490	−0.882450	+	0.470407i	$0.844107\pi$
$194$	−1.64559e10	−0.834090
$195$	−1.66937e8	−0.00826792
$196$	−1.19408e9	−0.0577940
$197$	−2.48463e10	−1.17534	−0.587670	−	0.809101i	$-0.699955\pi$
$197$	−2.48463e10	−1.17534	−0.587670	+	0.809101i	$0.699955\pi$
$198$	5.54160e9	0.256237
$199$	2.87975e10	1.30172	0.650858	−	0.759200i	$-0.274409\pi$
$199$	2.87975e10	1.30172	0.650858	+	0.759200i	$0.274409\pi$
$200$	−1.49900e10	−0.662471
$201$	1.22291e8	0.00528462
$202$	2.81241e9	0.118849
$203$	−1.29316e10	−0.534467
$204$	1.92536e7	0.000778354 0
$205$	1.71183e10	0.676970
$206$	3.09626e10	1.19794
$207$	1.81675e10	0.687748
$208$	−3.10899e10	−1.15169
$209$	9.07490e9	0.328991
$210$	1.48253e8	0.00526039
$211$	3.08043e10	1.06989	0.534946	−	0.844886i	$-0.320332\pi$
$211$	3.08043e10	1.06989	0.534946	+	0.844886i	$0.320332\pi$
$212$	1.09957e9	0.0373863
$213$	−7.53303e8	−0.0250762
$214$	2.95232e10	0.962281
$215$	2.61230e9	0.0833776
$216$	−8.64199e8	−0.0270129
$217$	−4.11116e10	−1.25862
$218$	2.02166e10	0.606253
$219$	6.79078e8	0.0199490
$220$	−4.56955e8	−0.0131514
$221$	2.07665e10	0.585595
$222$	−3.14196e8	−0.00868185
$223$	2.40525e10	0.651312	0.325656	−	0.945488i	$-0.394415\pi$
$223$	2.40525e10	0.651312	0.325656	+	0.945488i	$0.394415\pi$
$224$	4.74380e9	0.125895
$225$	2.69460e10	0.700928
$226$	3.57938e10	0.912683
$227$	−5.03039e9	−0.125743	−0.0628717	−	0.998022i	$-0.520026\pi$
$227$	−5.03039e9	−0.125743	−0.0628717	+	0.998022i	$0.520026\pi$
$228$	7.71869e7	0.00189163
$229$	−4.34034e9	−0.104295	−0.0521476	−	0.998639i	$-0.516607\pi$
$229$	−4.34034e9	−0.104295	−0.0521476	+	0.998639i	$0.516607\pi$
$230$	−1.67282e10	−0.394162
$231$	9.71567e7	0.00224501
$232$	−3.47010e10	−0.786405
$233$	8.25255e9	0.183437	0.0917184	−	0.995785i	$-0.470764\pi$
$233$	8.25255e9	0.183437	0.0917184	+	0.995785i	$0.470764\pi$
$234$	5.08378e10	1.10845
$235$	−1.49833e10	−0.320480
$236$	−5.30812e9	−0.111388
$237$	−1.22915e9	−0.0253067
$238$	−1.84423e10	−0.372579
$239$	−3.54632e10	−0.703052	−0.351526	−	0.936178i	$-0.614337\pi$
$239$	−3.54632e10	−0.703052	−0.351526	+	0.936178i	$0.614337\pi$
$240$	4.37340e8	0.00850880
$241$	−8.17008e9	−0.156009	−0.0780045	−	0.996953i	$-0.524855\pi$
$241$	−8.17008e9	−0.156009	−0.0780045	+	0.996953i	$0.524855\pi$
$242$	5.25728e10	0.985354
$243$	2.33030e9	0.0428730
$244$	3.22249e9	0.0582020
$245$	1.81169e10	0.321245
$246$	1.06549e9	0.0185498
$247$	8.32518e10	1.42317
$248$	−1.10320e11	−1.85191
$249$	7.98543e8	0.0131644
$250$	−6.02018e10	−0.974718
$251$	3.32427e10	0.528646	0.264323	−	0.964434i	$-0.414852\pi$
$251$	3.32427e10	0.528646	0.264323	+	0.964434i	$0.414852\pi$
$252$	−4.04318e9	−0.0631569
$253$	−1.09627e10	−0.168219
$254$	−3.54614e10	−0.534569
$255$	−2.92120e8	−0.00432644
$256$	2.00885e10	0.292326
$257$	5.99005e10	0.856508	0.428254	−	0.903658i	$-0.359129\pi$
$257$	5.99005e10	0.856508	0.428254	+	0.903658i	$0.359129\pi$
$258$	1.62596e8	0.00228465
$259$	2.69518e10	0.372167
$260$	−4.19204e9	−0.0568912
$261$	6.23785e10	0.832056
$262$	3.60380e9	0.0472503
$263$	−2.35411e10	−0.303407	−0.151703	−	0.988426i	$-0.548476\pi$
$263$	−2.35411e10	−0.303407	−0.151703	+	0.988426i	$0.548476\pi$
$264$	2.60712e8	0.00330327
$265$	−1.66829e10	−0.207810
$266$	−7.39343e10	−0.905479
$267$	−1.63607e9	−0.0197016
$268$	3.07092e9	0.0363632
$269$	−5.01380e10	−0.583824	−0.291912	−	0.956445i	$-0.594291\pi$
$269$	−5.01380e10	−0.583824	−0.291912	+	0.956445i	$0.594291\pi$
$270$	−1.43041e9	−0.0163804
$271$	−3.54796e7	−0.000399592 0	−0.000199796	−	1.00000i	$-0.500064\pi$
$271$	−3.54796e7	−0.000399592 0	−0.000199796		1.00000i	$0.500064\pi$
$272$	−5.44038e10	−0.602655
$273$	8.91301e8	0.00971164
$274$	4.78893e10	0.513288
$275$	−1.62599e10	−0.171443
$276$	−9.32438e7	−0.000967228 0
$277$	6.02234e10	0.614619	0.307310	−	0.951610i	$-0.400571\pi$
$277$	6.02234e10	0.614619	0.307310	+	0.951610i	$0.400571\pi$
$278$	−5.52039e10	−0.554330
$279$	1.98311e11	1.95942
$280$	−3.41255e10	−0.331794
$281$	−4.41869e10	−0.422781	−0.211390	−	0.977402i	$-0.567799\pi$
$281$	−4.41869e10	−0.422781	−0.211390	+	0.977402i	$0.567799\pi$
$282$	−9.32594e8	−0.00878156
$283$	4.63295e10	0.429357	0.214679	−	0.976685i	$-0.431130\pi$
$283$	4.63295e10	0.429357	0.214679	+	0.976685i	$0.431130\pi$
$284$	−1.89166e10	−0.172548
$285$	−1.17110e9	−0.0105146
$286$	−3.06767e10	−0.271120
$287$	−9.13974e10	−0.795180
$288$	−2.28827e10	−0.195993
$289$	−8.22489e10	−0.693570
$290$	−5.74366e10	−0.476868
$291$	1.39168e9	0.0113768
$292$	1.70527e10	0.137268
$293$	1.36697e11	1.08356	0.541782	−	0.840519i	$-0.317750\pi$
$293$	1.36697e11	1.08356	0.541782	+	0.840519i	$0.317750\pi$
$294$	1.12764e9	0.00880252
$295$	8.05360e10	0.619143
$296$	7.23229e10	0.547599
$297$	−9.37408e8	−0.00699076
$298$	3.34668e10	0.245833
$299$	−1.00570e11	−0.727695
$300$	−1.38299e8	−0.000985765 0
$301$	−1.39475e10	−0.0979367
$302$	−9.79819e10	−0.677821
$303$	−2.37847e8	−0.00162108
$304$	−2.18102e11	−1.46463
$305$	−4.88924e10	−0.323513
$306$	8.89603e10	0.580029
$307$	−1.70586e10	−0.109602	−0.0548012	−	0.998497i	$-0.517453\pi$
$307$	−1.70586e10	−0.109602	−0.0548012	+	0.998497i	$0.517453\pi$
$308$	2.43975e9	0.0154478
$309$	−2.61853e9	−0.0163397
$310$	−1.82600e11	−1.12298
$311$	1.68094e11	1.01890	0.509450	−	0.860500i	$-0.329849\pi$
$311$	1.68094e11	1.01890	0.509450	+	0.860500i	$0.329849\pi$
$312$	2.39174e9	0.0142895
$313$	−1.12744e11	−0.663962	−0.331981	−	0.943286i	$-0.607717\pi$
$313$	−1.12744e11	−0.663962	−0.331981	+	0.943286i	$0.607717\pi$
$314$	−2.89419e11	−1.68013
$315$	6.13440e10	0.351055
$316$	−3.08657e10	−0.174134
$317$	9.37662e10	0.521531	0.260765	−	0.965402i	$-0.416025\pi$
$317$	9.37662e10	0.521531	0.260765	+	0.965402i	$0.416025\pi$
$318$	−1.03839e9	−0.00569425
$319$	−3.76406e10	−0.203516
$320$	−9.05809e10	−0.482905
$321$	−2.49680e9	−0.0131253
$322$	8.93145e10	0.462989
$323$	1.45681e11	0.744718
$324$	1.94992e10	0.0983022
$325$	−1.49166e11	−0.741641
$326$	2.39348e11	1.17368
$327$	−1.70973e9	−0.00826917
$328$	−2.45258e11	−1.17001
$329$	7.99980e10	0.376441
$330$	4.31527e8	0.00200307
$331$	−2.93005e11	−1.34168	−0.670840	−	0.741602i	$-0.734066\pi$
$331$	−2.93005e11	−1.34168	−0.670840	+	0.741602i	$0.734066\pi$
$332$	2.00526e10	0.0905836
$333$	−1.30008e11	−0.579388
$334$	3.29930e11	1.45065
$335$	−4.65927e10	−0.202123
$336$	−2.33502e9	−0.00999458
$337$	3.82436e11	1.61519	0.807596	−	0.589736i	$-0.200768\pi$
$337$	3.82436e11	1.61519	0.807596	+	0.589736i	$0.200768\pi$
$338$	−2.99470e10	−0.124804
$339$	−3.02710e9	−0.0124488
$340$	−7.33558e9	−0.0297700
$341$	−1.19665e11	−0.479263
$342$	3.56638e11	1.40965
$343$	−2.61357e11	−1.01955
$344$	−3.74269e10	−0.144102
$345$	1.41471e9	0.00537629
$346$	4.81985e11	1.80797
$347$	−9.85113e10	−0.364757	−0.182378	−	0.983228i	$-0.558380\pi$
$347$	−9.85113e10	−0.364757	−0.182378	+	0.983228i	$0.558380\pi$
$348$	−3.20154e8	−0.00117018
$349$	−2.38389e11	−0.860145	−0.430073	−	0.902794i	$-0.641512\pi$
$349$	−2.38389e11	−0.860145	−0.430073	+	0.902794i	$0.641512\pi$
$350$	1.32471e11	0.471862
$351$	−8.59964e9	−0.0302412
$352$	1.38080e10	0.0479389
$353$	1.97866e10	0.0678243	0.0339122	−	0.999425i	$-0.489203\pi$
$353$	1.97866e10	0.0678243	0.0339122	+	0.999425i	$0.489203\pi$
$354$	5.01275e9	0.0169653
$355$	2.87006e11	0.959100
$356$	−4.10841e10	−0.135566
$357$	1.55967e9	0.00508191
$358$	1.31217e11	0.422200
$359$	5.77059e10	0.183356	0.0916781	−	0.995789i	$-0.470777\pi$
$359$	5.77059e10	0.183356	0.0916781	+	0.995789i	$0.470777\pi$
$360$	1.64612e11	0.516535
$361$	2.61341e11	0.809887
$362$	−5.12156e11	−1.56752
$363$	−4.44611e9	−0.0134400
$364$	2.23819e10	0.0668253
$365$	−2.58727e11	−0.762999
$366$	−3.04318e9	−0.00886466
$367$	3.72822e11	1.07276	0.536382	−	0.843975i	$-0.319791\pi$
$367$	3.72822e11	1.07276	0.536382	+	0.843975i	$0.319791\pi$
$368$	2.63473e11	0.748895
$369$	4.40875e11	1.23793
$370$	1.19708e11	0.332059
$371$	8.90727e10	0.244097
$372$	−1.01782e9	−0.00275567
$373$	−1.51504e11	−0.405260	−0.202630	−	0.979255i	$-0.564949\pi$
$373$	−1.51504e11	−0.405260	−0.202630	+	0.979255i	$0.564949\pi$
$374$	−5.36808e10	−0.141872
$375$	5.09129e9	0.0132950
$376$	2.14668e11	0.553888
$377$	−3.45310e11	−0.880385
$378$	7.63718e9	0.0192406
$379$	3.48542e11	0.867719	0.433860	−	0.900981i	$-0.357151\pi$
$379$	3.48542e11	0.867719	0.433860	+	0.900981i	$0.357151\pi$
$380$	−2.94080e10	−0.0723501
$381$	2.99899e9	0.00729142
$382$	3.91341e11	0.940308
$383$	−1.32499e11	−0.314643	−0.157321	−	0.987547i	$-0.550286\pi$
$383$	−1.32499e11	−0.314643	−0.157321	+	0.987547i	$0.550286\pi$
$384$	−6.83196e9	−0.0160345
$385$	−3.70164e10	−0.0858660
$386$	8.06744e11	1.84966
$387$	6.72785e10	0.152467
$388$	3.49472e10	0.0782834
$389$	−7.39994e11	−1.63853	−0.819266	−	0.573413i	$-0.805619\pi$
$389$	−7.39994e11	−1.63853	−0.819266	+	0.573413i	$0.805619\pi$
$390$	3.95877e9	0.00866501
$391$	−1.75986e11	−0.380789
$392$	−2.59564e11	−0.555211
$393$	−3.04775e8	−0.000644486 0
$394$	5.89209e11	1.23179
$395$	4.68301e11	0.967918
$396$	−1.17687e10	−0.0240491
$397$	−5.46776e10	−0.110472	−0.0552360	−	0.998473i	$-0.517591\pi$
$397$	−5.46776e10	−0.110472	−0.0552360	+	0.998473i	$0.517591\pi$
$398$	−6.82909e11	−1.36423
$399$	6.25266e9	0.0123506
$400$	3.90783e11	0.763248
$401$	−3.83788e11	−0.741212	−0.370606	−	0.928790i	$-0.620850\pi$
$401$	−3.83788e11	−0.741212	−0.370606	+	0.928790i	$0.620850\pi$
$402$	−2.90004e9	−0.00553843
$403$	−1.09779e12	−2.07323
$404$	−5.97269e9	−0.0111546
$405$	−2.95846e11	−0.546408
$406$	3.06663e11	0.560137
$407$	7.84496e10	0.141715
$408$	4.18526e9	0.00747742
$409$	−7.70773e11	−1.36198	−0.680992	−	0.732291i	$-0.738451\pi$
$409$	−7.70773e11	−1.36198	−0.680992	+	0.732291i	$0.738451\pi$
$410$	−4.05947e11	−0.709483
$411$	−4.05002e9	−0.00700115
$412$	−6.57551e10	−0.112433
$413$	−4.29994e11	−0.727256
$414$	−4.30828e11	−0.720779
$415$	−3.04243e11	−0.503505
$416$	1.26672e11	0.207378
$417$	4.66863e9	0.00756096
$418$	−2.15204e11	−0.344791
$419$	1.70733e11	0.270617	0.135309	−	0.990804i	$-0.456797\pi$
$419$	1.70733e11	0.270617	0.135309	+	0.990804i	$0.456797\pi$
$420$	−3.14845e8	−0.000493713 0
$421$	−1.17127e12	−1.81714	−0.908572	−	0.417728i	$-0.862827\pi$
$421$	−1.17127e12	−1.81714	−0.908572	+	0.417728i	$0.862827\pi$
$422$	−7.30498e11	−1.12128
$423$	−3.85887e11	−0.586042
$424$	2.39020e11	0.359159
$425$	−2.61023e11	−0.388086
$426$	1.78639e10	0.0262805
$427$	2.61044e11	0.380004
$428$	−6.26983e10	−0.0903148
$429$	2.59435e9	0.00369803
$430$	−6.19484e10	−0.0873821
$431$	1.01493e12	1.41673	0.708364	−	0.705847i	$-0.249434\pi$
$431$	1.01493e12	1.41673	0.708364	+	0.705847i	$0.249434\pi$
$432$	2.25293e10	0.0311222
$433$	4.90479e11	0.670540	0.335270	−	0.942122i	$-0.391172\pi$
$433$	4.90479e11	0.670540	0.335270	+	0.942122i	$0.391172\pi$
$434$	9.74928e11	1.31907
$435$	4.85745e9	0.00650439
$436$	−4.29338e10	−0.0568998
$437$	−7.05521e11	−0.925430
$438$	−1.61038e10	−0.0209071
$439$	7.89685e11	1.01476	0.507380	−	0.861722i	$-0.330614\pi$
$439$	7.89685e11	1.01476	0.507380	+	0.861722i	$0.330614\pi$
$440$	−9.93306e10	−0.126342
$441$	4.66593e11	0.587441
$442$	−4.92459e11	−0.613720
$443$	−1.09410e12	−1.34971	−0.674857	−	0.737949i	$-0.735795\pi$
$443$	−1.09410e12	−1.34971	−0.674857	+	0.737949i	$0.735795\pi$
$444$	6.67256e8	0.000814834 0
$445$	6.23337e11	0.753535
$446$	−5.70386e11	−0.682593
$447$	−2.83031e9	−0.00335312
$448$	4.83625e11	0.567228
$449$	−5.93385e11	−0.689015	−0.344507	−	0.938784i	$-0.611954\pi$
$449$	−5.93385e11	−0.689015	−0.344507	+	0.938784i	$0.611954\pi$
$450$	−6.39003e11	−0.734592
$451$	−2.66034e11	−0.302791
$452$	−7.60151e10	−0.0856598
$453$	8.28639e9	0.00924535
$454$	1.19291e11	0.131783
$455$	−3.39583e11	−0.371445
$456$	1.67785e10	0.0181724
$457$	4.56802e11	0.489898	0.244949	−	0.969536i	$-0.421229\pi$
$457$	4.56802e11	0.489898	0.244949	+	0.969536i	$0.421229\pi$
$458$	1.02928e11	0.109304
$459$	−1.50484e10	−0.0158246
$460$	3.55256e10	0.0369940
$461$	1.69775e12	1.75073	0.875367	−	0.483460i	$-0.160620\pi$
$461$	1.69775e12	1.75073	0.875367	+	0.483460i	$0.160620\pi$
$462$	−2.30399e9	−0.00235284
$463$	3.87467e11	0.391851	0.195925	−	0.980619i	$-0.437229\pi$
$463$	3.87467e11	0.391851	0.195925	+	0.980619i	$0.437229\pi$
$464$	9.04639e11	0.906034
$465$	1.54426e10	0.0153173
$466$	−1.95702e11	−0.192247
$467$	1.51160e12	1.47066	0.735328	−	0.677711i	$-0.237028\pi$
$467$	1.51160e12	1.47066	0.735328	+	0.677711i	$0.237028\pi$
$468$	−1.07964e11	−0.104033
$469$	2.48766e11	0.237417
$470$	3.55316e11	0.335872
$471$	2.44763e10	0.0229167
$472$	−1.15385e12	−1.07007
$473$	−4.05974e10	−0.0372927
$474$	2.91482e10	0.0265222
$475$	−1.04643e12	−0.943166
$476$	3.91658e10	0.0349684
$477$	−4.29661e11	−0.380009
$478$	8.40980e11	0.736818
$479$	1.14506e12	0.993847	0.496924	−	0.867794i	$-0.334463\pi$
$479$	1.14506e12	0.993847	0.496924	+	0.867794i	$0.334463\pi$
$480$	−1.78189e9	−0.00153213
$481$	7.19685e11	0.613041
$482$	1.93747e11	0.163502
$483$	−7.55338e9	−0.00631508
$484$	−1.11649e11	−0.0924803
$485$	−5.30226e11	−0.435135
$486$	−5.52612e10	−0.0449321
$487$	1.23558e12	0.995382	0.497691	−	0.867354i	$-0.334181\pi$
$487$	1.23558e12	0.995382	0.497691	+	0.867354i	$0.334181\pi$
$488$	7.00490e11	0.559130
$489$	−2.02418e10	−0.0160088
$490$	−4.29627e11	−0.336674
$491$	1.82342e12	1.41586	0.707931	−	0.706281i	$-0.249629\pi$
$491$	1.82342e12	1.41586	0.707931	+	0.706281i	$0.249629\pi$
$492$	−2.26277e9	−0.00174099
$493$	−6.04252e11	−0.460688
$494$	−1.97425e12	−1.49152
$495$	1.78557e11	0.133676
$496$	2.87598e12	2.13363
$497$	−1.53237e12	−1.12657
$498$	−1.89368e10	−0.0137967
$499$	1.34781e12	0.973145	0.486573	−	0.873640i	$-0.338247\pi$
$499$	1.34781e12	0.973145	0.486573	+	0.873640i	$0.338247\pi$
$500$	1.27850e11	0.0914821
$501$	−2.79024e10	−0.0197866
$502$	−7.88323e11	−0.554036
$503$	1.07497e12	0.748757	0.374378	−	0.927276i	$-0.377856\pi$
$503$	1.07497e12	0.748757	0.374378	+	0.927276i	$0.377856\pi$
$504$	−8.78888e11	−0.606731
$505$	9.06189e10	0.0620023
$506$	2.59972e11	0.176298
$507$	2.53264e9	0.00170230
$508$	7.53091e10	0.0501719
$509$	−8.76635e11	−0.578881	−0.289440	−	0.957196i	$-0.593469\pi$
$509$	−8.76635e11	−0.578881	−0.289440	+	0.957196i	$0.593469\pi$
$510$	6.92739e9	0.00453423
$511$	1.38138e12	0.896231
$512$	1.26779e12	0.815326
$513$	−6.03283e10	−0.0384585
$514$	−1.42049e12	−0.897644
$515$	9.97651e11	0.624951
$516$	−3.45303e8	−0.000214426 0
$517$	2.32853e11	0.143343
$518$	−6.39138e11	−0.390042
$519$	−4.07617e10	−0.0246604
$520$	−9.11245e11	−0.546537
$521$	1.32443e11	0.0787517	0.0393758	−	0.999224i	$-0.487463\pi$
$521$	1.32443e11	0.0787517	0.0393758	+	0.999224i	$0.487463\pi$
$522$	−1.47925e12	−0.872018
$523$	−3.27846e12	−1.91607	−0.958037	−	0.286643i	$-0.907461\pi$
$523$	−3.27846e12	−1.91607	−0.958037	+	0.286643i	$0.907461\pi$
$524$	−7.65337e9	−0.00443467
$525$	−1.12032e10	−0.00643611
$526$	5.58257e11	0.317979
$527$	−1.92101e12	−1.08488
$528$	−6.79665e9	−0.00380577
$529$	−9.48865e11	−0.526810
$530$	3.95622e11	0.217790
$531$	2.07417e12	1.13219
$532$	1.57014e11	0.0849836
$533$	−2.44056e12	−1.30984
$534$	3.87980e10	0.0206478
$535$	9.51272e11	0.502010
$536$	6.67542e11	0.349331
$537$	−1.10971e10	−0.00575873
$538$	1.18898e12	0.611864
$539$	−2.81553e11	−0.143685
$540$	3.03775e9	0.00153738
$541$	1.03137e12	0.517638	0.258819	−	0.965926i	$-0.416667\pi$
$541$	1.03137e12	0.517638	0.258819	+	0.965926i	$0.416667\pi$
$542$	8.41368e8	0.000418783 0
$543$	4.33133e10	0.0213807
$544$	2.21662e11	0.108517
$545$	6.51402e11	0.316275
$546$	−2.11365e10	−0.0101781
$547$	1.11547e12	0.532741	0.266371	−	0.963871i	$-0.414175\pi$
$547$	1.11547e12	0.532741	0.266371	+	0.963871i	$0.414175\pi$
$548$	−1.01702e11	−0.0481746
$549$	−1.25920e12	−0.591588
$550$	3.85589e11	0.179677
$551$	−2.42242e12	−1.11961
$552$	−2.02689e10	−0.00929189
$553$	−2.50033e12	−1.13693
$554$	−1.42815e12	−0.644138
$555$	−1.01238e10	−0.00452922
$556$	1.17236e11	0.0520266
$557$	2.62897e12	1.15728	0.578638	−	0.815585i	$-0.303584\pi$
$557$	2.62897e12	1.15728	0.578638	+	0.815585i	$0.303584\pi$
$558$	−4.70277e12	−2.05352
$559$	−3.72435e11	−0.161323
$560$	8.89637e11	0.382267
$561$	4.53981e9	0.00193511
$562$	1.04786e12	0.443086
$563$	3.88359e12	1.62909	0.814546	−	0.580099i	$-0.196986\pi$
$563$	3.88359e12	1.62909	0.814546	+	0.580099i	$0.196986\pi$
$564$	1.98054e9	0.000824192 0
$565$	1.15332e12	0.476136
$566$	−1.09867e12	−0.449979
$567$	1.57956e12	0.641820
$568$	−4.11199e12	−1.65762
$569$	−3.46357e12	−1.38522	−0.692609	−	0.721313i	$-0.743539\pi$
$569$	−3.46357e12	−1.38522	−0.692609	+	0.721313i	$0.743539\pi$
$570$	2.77716e10	0.0110195
$571$	6.88790e11	0.271159	0.135580	−	0.990766i	$-0.456710\pi$
$571$	6.88790e11	0.271159	0.135580	+	0.990766i	$0.456710\pi$
$572$	6.51480e10	0.0254460
$573$	−3.30959e10	−0.0128256
$574$	2.16741e12	0.833371
$575$	1.26411e12	0.482259
$576$	−2.33287e12	−0.883058
$577$	−1.20927e12	−0.454184	−0.227092	−	0.973873i	$-0.572922\pi$
$577$	−1.20927e12	−0.454184	−0.227092	+	0.973873i	$0.572922\pi$
$578$	1.95047e12	0.726880
$579$	−6.82268e10	−0.0252291
$580$	1.21978e11	0.0447564
$581$	1.62440e12	0.591425
$582$	−3.30025e10	−0.0119232
$583$	2.59268e11	0.0929480
$584$	3.70683e12	1.31870
$585$	1.63805e12	0.578264
$586$	−3.24166e12	−1.13561
$587$	3.86701e12	1.34432	0.672162	−	0.740404i	$-0.265366\pi$
$587$	3.86701e12	1.34432	0.672162	+	0.740404i	$0.265366\pi$
$588$	−2.39476e9	−0.000826160 0
$589$	−7.70124e12	−2.63658
$590$	−1.90984e12	−0.648879
$591$	−4.98297e10	−0.0168014
$592$	−1.88542e12	−0.630901
$593$	−1.67086e10	−0.00554872	−0.00277436	−	0.999996i	$-0.500883\pi$
$593$	−1.67086e10	−0.00554872	−0.00277436	+	0.999996i	$0.500883\pi$
$594$	2.22298e10	0.00732652
$595$	−5.94232e11	−0.194370
$596$	−7.10732e10	−0.0230727
$597$	5.77540e10	0.0186079
$598$	2.38494e12	0.762645
$599$	7.82498e11	0.248349	0.124174	−	0.992260i	$-0.460372\pi$
$599$	7.82498e11	0.248349	0.124174	+	0.992260i	$0.460372\pi$
$600$	−3.00628e10	−0.00946997
$601$	4.64544e12	1.45242	0.726210	−	0.687473i	$-0.241280\pi$
$601$	4.64544e12	1.45242	0.726210	+	0.687473i	$0.241280\pi$
$602$	3.30752e11	0.102640
$603$	−1.19997e12	−0.369610
$604$	2.08084e11	0.0636168
$605$	1.69396e12	0.514047
$606$	5.64034e9	0.00169894
$607$	−3.78070e12	−1.13038	−0.565188	−	0.824962i	$-0.691197\pi$
$607$	−3.78070e12	−1.13038	−0.565188	+	0.824962i	$0.691197\pi$
$608$	8.88632e11	0.263728
$609$	−2.59346e10	−0.00764016
$610$	1.15944e12	0.339051
$611$	2.13616e12	0.620082
$612$	−1.88925e11	−0.0544386
$613$	−4.92457e12	−1.40863	−0.704314	−	0.709889i	$-0.748745\pi$
$613$	−4.92457e12	−1.40863	−0.704314	+	0.709889i	$0.748745\pi$
$614$	4.04530e11	0.114866
$615$	3.43312e10	0.00967722
$616$	5.30341e11	0.148403
$617$	1.68798e12	0.468904	0.234452	−	0.972128i	$-0.424670\pi$
$617$	1.68798e12	0.468904	0.234452	+	0.972128i	$0.424670\pi$
$618$	6.20962e10	0.0171245
$619$	−1.50175e12	−0.411141	−0.205570	−	0.978642i	$-0.565905\pi$
$619$	−1.50175e12	−0.411141	−0.205570	+	0.978642i	$0.565905\pi$
$620$	3.87786e11	0.105397
$621$	7.28781e10	0.0196646
$622$	−3.98622e12	−1.06784
$623$	−3.32809e12	−0.885114
$624$	−6.23515e10	−0.0164633
$625$	7.34606e11	0.192573
$626$	2.67363e12	0.695851
$627$	1.81999e10	0.00470289
$628$	6.14637e11	0.157688
$629$	1.25937e12	0.320792
$630$	−1.45472e12	−0.367915
$631$	−6.62550e12	−1.66374	−0.831872	−	0.554968i	$-0.812731\pi$
$631$	−6.62550e12	−1.66374	−0.831872	+	0.554968i	$0.812731\pi$
$632$	−6.70944e12	−1.67286
$633$	6.17786e10	0.0152940
$634$	−2.22359e12	−0.546579
$635$	−1.14261e12	−0.278878
$636$	2.20521e9	0.000534433 0
$637$	−2.58293e12	−0.621562
$638$	8.92617e11	0.213291
$639$	7.39171e12	1.75385
$640$	2.60296e12	0.613278
$641$	7.46690e12	1.74694	0.873472	−	0.486875i	$-0.161863\pi$
$641$	7.46690e12	1.74694	0.873472	+	0.486875i	$0.161863\pi$
$642$	5.92094e10	0.0137557
$643$	4.63171e12	1.06854	0.534271	−	0.845313i	$-0.320586\pi$
$643$	4.63171e12	1.06854	0.534271	+	0.845313i	$0.320586\pi$
$644$	−1.89677e11	−0.0434538
$645$	5.23901e9	0.00119188
$646$	−3.45470e12	−0.780485
$647$	−2.14353e12	−0.480906	−0.240453	−	0.970661i	$-0.577296\pi$
$647$	−2.14353e12	−0.480906	−0.240453	+	0.970661i	$0.577296\pi$
$648$	4.23864e12	0.944362
$649$	−1.25160e12	−0.276927
$650$	3.53734e12	0.777261
$651$	−8.24502e10	−0.0179919
$652$	−5.08302e11	−0.110156
$653$	8.17170e12	1.75874	0.879372	−	0.476135i	$-0.157962\pi$
$653$	8.17170e12	1.75874	0.879372	+	0.476135i	$0.157962\pi$
$654$	4.05448e10	0.00866633
$655$	1.16119e11	0.0246499
$656$	6.39375e12	1.34800
$657$	−6.66339e12	−1.39525
$658$	−1.89708e12	−0.394521
$659$	3.65558e12	0.755044	0.377522	−	0.926001i	$-0.376776\pi$
$659$	3.65558e12	0.755044	0.377522	+	0.926001i	$0.376776\pi$
$660$	−9.16432e8	−0.000187998 0
$661$	−3.52150e12	−0.717499	−0.358750	−	0.933434i	$-0.616797\pi$
$661$	−3.52150e12	−0.717499	−0.358750	+	0.933434i	$0.616797\pi$
$662$	6.94837e12	1.40612
$663$	4.16476e10	0.00837103
$664$	4.35894e12	0.870211
$665$	−2.38225e12	−0.472378
$666$	3.08302e12	0.607215
$667$	2.92634e12	0.572479
$668$	−7.00671e11	−0.136151
$669$	4.82379e10	0.00931045
$670$	1.10491e12	0.211831
$671$	7.59831e11	0.144699
$672$	9.51378e9	0.00179966
$673$	−5.32239e12	−1.00009	−0.500045	−	0.866000i	$-0.666683\pi$
$673$	−5.32239e12	−1.00009	−0.500045	+	0.866000i	$0.666683\pi$
$674$	−9.06915e12	−1.69277
$675$	1.08093e11	0.0200415
$676$	6.35983e10	0.0117135
$677$	−9.87601e11	−0.180689	−0.0903447	−	0.995911i	$-0.528797\pi$
$677$	−9.87601e11	−0.180689	−0.0903447	+	0.995911i	$0.528797\pi$
$678$	7.17852e10	0.0130467
$679$	2.83096e12	0.511116
$680$	−1.59457e12	−0.285992
$681$	−1.00885e10	−0.00179749
$682$	2.83776e12	0.502281
$683$	8.97820e11	0.157869	0.0789343	−	0.996880i	$-0.474848\pi$
$683$	8.97820e11	0.157869	0.0789343	+	0.996880i	$0.474848\pi$
$684$	−7.57389e11	−0.132302
$685$	1.54305e12	0.267776
$686$	6.19786e12	1.06852
$687$	−8.70463e9	−0.00149089
$688$	9.75701e11	0.166023
$689$	2.37848e12	0.402081
$690$	−3.35488e10	−0.00563450
$691$	3.95252e12	0.659512	0.329756	−	0.944066i	$-0.393034\pi$
$691$	3.95252e12	0.659512	0.329756	+	0.944066i	$0.393034\pi$
$692$	−1.02359e12	−0.169687
$693$	−9.53341e11	−0.157018
$694$	2.33611e12	0.382275
$695$	−1.77873e12	−0.289187
$696$	−6.95936e10	−0.0112416
$697$	−4.27070e12	−0.685412
$698$	5.65320e12	0.901456
$699$	1.65506e10	0.00262221
$700$	−2.81328e11	−0.0442866
$701$	−1.15110e13	−1.80046	−0.900230	−	0.435415i	$-0.856601\pi$
$701$	−1.15110e13	−1.80046	−0.900230	+	0.435415i	$0.856601\pi$
$702$	2.03933e11	0.0316936
$703$	5.04874e12	0.779622
$704$	1.40771e12	0.215991
$705$	−3.00492e10	−0.00458123
$706$	−4.69223e11	−0.0710818
$707$	−4.83828e11	−0.0728289
$708$	−1.06455e10	−0.00159228
$709$	1.05617e12	0.156974	0.0784869	−	0.996915i	$-0.474991\pi$
$709$	1.05617e12	0.156974	0.0784869	+	0.996915i	$0.474991\pi$
$710$	−6.80611e12	−1.00516
$711$	1.20609e13	1.76997
$712$	−8.93067e12	−1.30234
$713$	9.30329e12	1.34814
$714$	−3.69864e10	−0.00532599
$715$	−9.88439e11	−0.141440
$716$	−2.78666e11	−0.0396255
$717$	−7.11222e10	−0.0100501
$718$	−1.36845e12	−0.192162
$719$	8.18317e12	1.14194	0.570968	−	0.820973i	$-0.306568\pi$
$719$	8.18317e12	1.14194	0.570968	+	0.820973i	$0.306568\pi$
$720$	−4.29135e12	−0.595111
$721$	−5.32661e12	−0.734078
$722$	−6.19748e12	−0.848784
$723$	−1.63853e10	−0.00223013
$724$	1.08766e12	0.147120
$725$	4.34035e12	0.583450
$726$	1.05436e11	0.0140855
$727$	−9.27117e12	−1.23092	−0.615460	−	0.788168i	$-0.711030\pi$
$727$	−9.27117e12	−1.23092	−0.615460	+	0.788168i	$0.711030\pi$
$728$	4.86527e12	0.641972
$729$	−7.61625e12	−0.998774
$730$	6.13549e12	0.799644
$731$	−6.51718e11	−0.0844173
$732$	6.46277e9	0.000831992 0
$733$	−4.24321e12	−0.542909	−0.271454	−	0.962451i	$-0.587505\pi$
$733$	−4.24321e12	−0.542909	−0.271454	+	0.962451i	$0.587505\pi$
$734$	−8.84116e12	−1.12429
$735$	3.63338e10	0.00459217
$736$	−1.07349e12	−0.134849
$737$	7.24092e11	0.0904045
$738$	−1.04550e13	−1.29739
$739$	2.15623e12	0.265947	0.132974	−	0.991120i	$-0.457547\pi$
$739$	2.15623e12	0.265947	0.132974	+	0.991120i	$0.457547\pi$
$740$	−2.54223e11	−0.0311653
$741$	1.66963e11	0.0203441
$742$	−2.11229e12	−0.255820
$743$	−8.84199e12	−1.06439	−0.532194	−	0.846622i	$-0.678632\pi$
$743$	−8.84199e12	−1.06439	−0.532194	+	0.846622i	$0.678632\pi$
$744$	−2.21248e11	−0.0264729
$745$	1.07834e12	0.128248
$746$	3.59278e12	0.424724
$747$	−7.83563e12	−0.920728
$748$	1.14001e11	0.0133154
$749$	−5.07899e12	−0.589670
$750$	−1.20736e11	−0.0139335
$751$	−2.48740e12	−0.285342	−0.142671	−	0.989770i	$-0.545569\pi$
$751$	−2.48740e12	−0.285342	−0.142671	+	0.989770i	$0.545569\pi$
$752$	−5.59630e12	−0.638147
$753$	6.66689e10	0.00755694
$754$	8.18873e12	0.922668
$755$	−3.15709e12	−0.353611
$756$	−1.62190e10	−0.00180583
$757$	4.59030e12	0.508054	0.254027	−	0.967197i	$-0.418245\pi$
$757$	4.59030e12	0.508054	0.254027	+	0.967197i	$0.418245\pi$
$758$	−8.26539e12	−0.909394
$759$	−2.19859e10	−0.00240468
$760$	−6.39257e12	−0.695047
$761$	−1.26409e13	−1.36631	−0.683153	−	0.730275i	$-0.739392\pi$
$761$	−1.26409e13	−1.36631	−0.683153	+	0.730275i	$0.739392\pi$
$762$	−7.11185e10	−0.00764161
$763$	−3.47793e12	−0.371502
$764$	−8.31089e11	−0.0882525
$765$	2.86640e12	0.302594
$766$	3.14210e12	0.329755
$767$	−1.14820e13	−1.19795
$768$	4.02879e10	0.00417878
$769$	7.97884e11	0.0822757	0.0411378	−	0.999153i	$-0.486902\pi$
$769$	7.97884e11	0.0822757	0.0411378	+	0.999153i	$0.486902\pi$
$770$	8.77814e11	0.0899900
$771$	1.20132e11	0.0122437
$772$	−1.71328e12	−0.173600
$773$	1.55667e13	1.56816	0.784079	−	0.620662i	$-0.213136\pi$
$773$	1.55667e13	1.56816	0.784079	+	0.620662i	$0.213136\pi$
$774$	−1.59545e12	−0.159790
$775$	1.37986e13	1.37397
$776$	7.59665e12	0.752046
$777$	5.40523e10	0.00532010
$778$	1.75483e13	1.71723
$779$	−1.71210e13	−1.66576
$780$	−8.40721e9	−0.000813254 0
$781$	−4.46033e12	−0.428981
$782$	4.17337e12	0.399077
$783$	2.50228e11	0.0237908
$784$	6.76672e12	0.639670
$785$	−9.32540e12	−0.876504
$786$	7.22749e9	0.000675439 0
$787$	−1.64141e13	−1.52521	−0.762607	−	0.646862i	$-0.776081\pi$
$787$	−1.64141e13	−1.52521	−0.762607	+	0.646862i	$0.776081\pi$
$788$	−1.25130e12	−0.115609
$789$	−4.72121e10	−0.00433717
$790$	−1.11054e13	−1.01440
$791$	−6.15774e12	−0.559277
$792$	−2.55822e12	−0.231033
$793$	6.97058e12	0.625950
$794$	1.29663e12	0.115778
$795$	−3.34579e10	−0.00297062
$796$	1.45029e12	0.128040
$797$	−2.56157e12	−0.224877	−0.112438	−	0.993659i	$-0.535866\pi$
$797$	−2.56157e12	−0.224877	−0.112438	+	0.993659i	$0.535866\pi$
$798$	−1.48277e11	−0.0129437
$799$	3.73804e12	0.324477
$800$	−1.59220e12	−0.137433
$801$	1.60538e13	1.37794
$802$	9.10122e12	0.776810
$803$	4.02085e12	0.341270
$804$	6.15880e9	0.000519809 0
$805$	2.87782e12	0.241536
$806$	2.60332e13	2.17280
$807$	−1.00553e11	−0.00834571
$808$	−1.29831e12	−0.107159
$809$	−2.05067e13	−1.68317	−0.841584	−	0.540126i	$-0.818377\pi$
$809$	−2.05067e13	−1.68317	−0.841584	+	0.540126i	$0.818377\pi$
$810$	7.01573e12	0.572651
$811$	2.03393e13	1.65098	0.825491	−	0.564415i	$-0.190898\pi$
$811$	2.03393e13	1.65098	0.825491	+	0.564415i	$0.190898\pi$
$812$	−6.51258e11	−0.0525716
$813$	−7.11550e7	−5.71213e−6 0
$814$	−1.86037e12	−0.148521
$815$	7.71207e12	0.612296
$816$	−1.09108e11	−0.00861490
$817$	−2.61271e12	−0.205159
$818$	1.82782e13	1.42740
$819$	−8.74581e12	−0.679239
$820$	8.62107e11	0.0665885
$821$	7.12024e12	0.546954	0.273477	−	0.961879i	$-0.411826\pi$
$821$	7.12024e12	0.546954	0.273477	+	0.961879i	$0.411826\pi$
$822$	9.60429e10	0.00733740
$823$	1.59854e13	1.21458	0.607289	−	0.794481i	$-0.292257\pi$
$823$	1.59854e13	1.21458	0.607289	+	0.794481i	$0.292257\pi$
$824$	−1.42935e13	−1.08011
$825$	−3.26095e10	−0.00245076
$826$	1.01969e13	0.762184
$827$	−9.14084e11	−0.0679534	−0.0339767	−	0.999423i	$-0.510817\pi$
$827$	−9.14084e11	−0.0679534	−0.0339767	+	0.999423i	$0.510817\pi$
$828$	9.14946e11	0.0676486
$829$	−1.85974e13	−1.36759	−0.683797	−	0.729672i	$-0.739673\pi$
$829$	−1.85974e13	−1.36759	−0.683797	+	0.729672i	$0.739673\pi$
$830$	7.21486e12	0.527687
$831$	1.20779e11	0.00878592
$832$	1.29141e13	0.934350
$833$	−4.51982e12	−0.325251
$834$	−1.10713e11	−0.00792409
$835$	1.06307e13	0.756787
$836$	4.57027e11	0.0323603
$837$	7.95513e11	0.0560251
$838$	−4.04880e12	−0.283614
$839$	1.49886e13	1.04432	0.522159	−	0.852848i	$-0.325127\pi$
$839$	1.49886e13	1.04432	0.522159	+	0.852848i	$0.325127\pi$
$840$	−6.84394e10	−0.00474296
$841$	−4.45949e12	−0.307400
$842$	2.77758e13	1.90442
$843$	−8.86177e10	−0.00604361
$844$	1.55135e12	0.105237
$845$	−9.64927e11	−0.0651088
$846$	9.15099e12	0.614188
$847$	−9.04429e12	−0.603808
$848$	−6.23113e12	−0.413795
$849$	9.29148e10	0.00613762
$850$	6.18994e12	0.406725
$851$	−6.09901e12	−0.398636
$852$	−3.79375e10	−0.00246656
$853$	2.59861e13	1.68062	0.840310	−	0.542106i	$-0.182373\pi$
$853$	2.59861e13	1.68062	0.840310	+	0.542106i	$0.182373\pi$
$854$	−6.19044e12	−0.398255
$855$	1.14913e13	0.735395
$856$	−1.36291e13	−0.867628
$857$	1.59617e13	1.01080	0.505400	−	0.862885i	$-0.331345\pi$
$857$	1.59617e13	1.01080	0.505400	+	0.862885i	$0.331345\pi$
$858$	−6.15228e10	−0.00387564
$859$	−2.03909e13	−1.27781	−0.638905	−	0.769286i	$-0.720612\pi$
$859$	−2.03909e13	−1.27781	−0.638905	+	0.769286i	$0.720612\pi$
$860$	1.31560e11	0.00820123
$861$	−1.83299e11	−0.0113670
$862$	−2.40681e13	−1.48477
$863$	−3.06757e13	−1.88255	−0.941273	−	0.337646i	$-0.890369\pi$
$863$	−3.06757e13	−1.88255	−0.941273	+	0.337646i	$0.890369\pi$
$864$	−9.17929e10	−0.00560399
$865$	1.55301e13	0.943196
$866$	−1.16313e13	−0.702745
$867$	−1.64952e11	−0.00991451
$868$	−2.07045e12	−0.123801
$869$	−7.27782e12	−0.432925
$870$	−1.15190e11	−0.00681678
$871$	6.64272e12	0.391079
$872$	−9.33275e12	−0.546620
$873$	−1.36557e13	−0.795703
$874$	1.67308e13	0.969877
$875$	1.03567e13	0.597291
$876$	3.41995e10	0.00196224
$877$	−1.24011e13	−0.707885	−0.353943	−	0.935267i	$-0.615159\pi$
$877$	−1.24011e13	−0.707885	−0.353943	+	0.935267i	$0.615159\pi$
$878$	−1.87267e13	−1.06350
$879$	2.74149e11	0.0154895
$880$	2.58950e12	0.145561
$881$	−2.11899e13	−1.18505	−0.592526	−	0.805552i	$-0.701869\pi$
$881$	−2.11899e13	−1.18505	−0.592526	+	0.805552i	$0.701869\pi$
$882$	−1.10649e13	−0.615654
$883$	3.32814e13	1.84238	0.921188	−	0.389118i	$-0.127220\pi$
$883$	3.32814e13	1.84238	0.921188	+	0.389118i	$0.127220\pi$
$884$	1.04583e12	0.0576006
$885$	1.61516e11	0.00885059
$886$	2.59458e13	1.41454
$887$	−2.83029e13	−1.53523	−0.767616	−	0.640910i	$-0.778557\pi$
$887$	−2.83029e13	−1.53523	−0.767616	+	0.640910i	$0.778557\pi$
$888$	1.45045e11	0.00782788
$889$	6.10055e12	0.327575
$890$	−1.47819e13	−0.789725
$891$	4.59770e12	0.244394
$892$	1.21133e12	0.0640647
$893$	1.49856e13	0.788575
$894$	6.71183e10	0.00351417
$895$	4.22798e12	0.220257
$896$	−1.38976e13	−0.720367
$897$	−2.01696e11	−0.0104023
$898$	1.40716e13	0.722106
$899$	3.19430e13	1.63101
$900$	1.35705e12	0.0689451
$901$	4.16207e12	0.210401
$902$	6.30878e12	0.317334
$903$	−2.79719e10	−0.00140000
$904$	−1.65238e13	−0.822910
$905$	−1.65022e13	−0.817757
$906$	−1.96505e11	−0.00968938
$907$	−1.55925e13	−0.765039	−0.382519	−	0.923947i	$-0.624943\pi$
$907$	−1.55925e13	−0.765039	−0.382519	+	0.923947i	$0.624943\pi$
$908$	−2.53338e11	−0.0123684
$909$	2.33385e12	0.113380
$910$	8.05293e12	0.389285
$911$	−8.70057e12	−0.418519	−0.209259	−	0.977860i	$-0.567105\pi$
$911$	−8.70057e12	−0.418519	−0.209259	+	0.977860i	$0.567105\pi$
$912$	−4.37408e11	−0.0209368
$913$	4.72820e12	0.225205
$914$	−1.08327e13	−0.513426
$915$	−9.80546e10	−0.00462459
$916$	−2.18586e11	−0.0102587
$917$	−6.19975e11	−0.0289542
$918$	3.56860e11	0.0165846
$919$	−3.60733e13	−1.66827	−0.834135	−	0.551560i	$-0.814033\pi$
$919$	−3.60733e13	−1.66827	−0.834135	+	0.551560i	$0.814033\pi$
$920$	7.72239e12	0.355391
$921$	−3.42113e10	−0.00156676
$922$	−4.02608e13	−1.83482
$923$	−4.09184e13	−1.85572
$924$	4.89297e9	0.000220825 0
$925$	−9.04604e12	−0.406275
$926$	−9.18847e12	−0.410671
$927$	2.56941e13	1.14281
$928$	−3.68585e12	−0.163144
$929$	1.24731e13	0.549418	0.274709	−	0.961527i	$-0.411418\pi$
$929$	1.24731e13	0.549418	0.274709	+	0.961527i	$0.411418\pi$
$930$	−3.66207e11	−0.0160529
$931$	−1.81198e13	−0.790458
$932$	4.15612e11	0.0180433
$933$	3.37117e11	0.0145651
$934$	−3.58464e13	−1.54129
$935$	−1.72966e12	−0.0740129
$936$	−2.34687e13	−0.999419
$937$	2.42282e13	1.02682	0.513408	−	0.858145i	$-0.328383\pi$
$937$	2.42282e13	1.02682	0.513408	+	0.858145i	$0.328383\pi$
$938$	−5.89927e12	−0.248820
$939$	−2.26110e11	−0.00949128
$940$	−7.54582e11	−0.0315232
$941$	−1.17034e13	−0.486586	−0.243293	−	0.969953i	$-0.578228\pi$
$941$	−1.17034e13	−0.486586	−0.243293	+	0.969953i	$0.578228\pi$
$942$	−5.80435e11	−0.0240173
$943$	2.06826e13	0.851733
$944$	3.00805e13	1.23285
$945$	2.46078e11	0.0100376
$946$	9.62734e11	0.0390838
$947$	−3.01213e13	−1.21702	−0.608512	−	0.793545i	$-0.708233\pi$
$947$	−3.01213e13	−1.21702	−0.608512	+	0.793545i	$0.708233\pi$
$948$	−6.19018e10	−0.00248923
$949$	3.68867e13	1.47629
$950$	2.48152e13	0.988464
$951$	1.88050e11	0.00745523
$952$	8.51367e12	0.335931
$953$	−1.01806e13	−0.399813	−0.199906	−	0.979815i	$-0.564064\pi$
$953$	−1.01806e13	−0.399813	−0.199906	+	0.979815i	$0.564064\pi$
$954$	1.01891e13	0.398260
$955$	1.26095e13	0.490548
$956$	−1.78598e12	−0.0691540
$957$	−7.54891e10	−0.00290925
$958$	−2.71542e13	−1.04158
$959$	−8.23857e12	−0.314534
$960$	−1.81662e11	−0.00690308
$961$	7.51120e13	2.84089
$962$	−1.70667e13	−0.642484
$963$	2.44996e13	0.917995
$964$	−4.11458e11	−0.0153454
$965$	2.59942e13	0.964947
$966$	1.79122e11	0.00661838
$967$	9.47914e11	0.0348618	0.0174309	−	0.999848i	$-0.494451\pi$
$967$	9.47914e11	0.0348618	0.0174309	+	0.999848i	$0.494451\pi$
$968$	−2.42696e13	−0.888432
$969$	2.92166e11	0.0106457
$970$	1.25739e13	0.456033
$971$	2.66136e13	0.960764	0.480382	−	0.877059i	$-0.340498\pi$
$971$	2.66136e13	0.960764	0.480382	+	0.877059i	$0.340498\pi$
$972$	1.17358e11	0.00421710
$973$	9.49693e12	0.339684
$974$	−2.93007e13	−1.04319
$975$	−2.99155e11	−0.0106017
$976$	−1.82615e13	−0.644186
$977$	−2.65754e13	−0.933155	−0.466578	−	0.884480i	$-0.654513\pi$
$977$	−2.65754e13	−0.933155	−0.466578	+	0.884480i	$0.654513\pi$
$978$	4.80017e11	0.0167777
$979$	−9.68722e12	−0.337037
$980$	9.12397e11	0.0315985
$981$	1.67765e13	0.578352
$982$	−4.32410e13	−1.48386
$983$	2.71576e12	0.0927687	0.0463843	−	0.998924i	$-0.485230\pi$
$983$	2.71576e12	0.0927687	0.0463843	+	0.998924i	$0.485230\pi$
$984$	−4.91869e11	−0.0167252
$985$	1.89850e13	0.642609
$986$	1.43293e13	0.482814
$987$	1.60437e11	0.00538119
$988$	4.19269e12	0.139987
$989$	3.15622e12	0.104902
$990$	−4.23432e12	−0.140096
$991$	6.39401e12	0.210592	0.105296	−	0.994441i	$-0.466421\pi$
$991$	6.39401e12	0.210592	0.105296	+	0.994441i	$0.466421\pi$
$992$	−1.17179e13	−0.384190
$993$	−5.87627e11	−0.0191792
$994$	3.63389e13	1.18068
$995$	−2.20041e13	−0.711705
$996$	4.02159e10	0.00129488
$997$	1.78534e13	0.572259	0.286130	−	0.958191i	$-0.407631\pi$
$997$	1.78534e13	0.572259	0.286130	+	0.958191i	$0.407631\pi$
$998$	−3.19623e13	−1.01988
$999$	−5.21519e11	−0.0165663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.a.1.4	✓	15
3.2	odd	2		387.10.a.c.1.12		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.4	✓	15	1.1	even	1	trivial
387.10.a.c.1.12		15	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)

\(f(q)\)	\(=\)	\(q-23.7142 q^{2} +2.00552 q^{3} +50.3616 q^{4} -764.097 q^{5} -47.5592 q^{6} +4079.63 q^{7} +10947.4 q^{8} -19679.0 q^{9} +O(q^{10})\)	\(q-23.7142 q^{2} +2.00552 q^{3} +50.3616 q^{4} -764.097 q^{5} -47.5592 q^{6} +4079.63 q^{7} +10947.4 q^{8} -19679.0 q^{9} +18119.9 q^{10} +11874.8 q^{11} +101.001 q^{12} +108937. q^{13} -96745.1 q^{14} -1532.41 q^{15} -285393. q^{16} +190628. q^{17} +466671. q^{18} +764217. q^{19} -38481.2 q^{20} +8181.78 q^{21} -281600. q^{22} -923194. q^{23} +21955.2 q^{24} -1.36928e6 q^{25} -2.58336e6 q^{26} -78941.2 q^{27} +205457. q^{28} -3.16980e6 q^{29} +36339.9 q^{30} -1.00773e7 q^{31} +1.16280e6 q^{32} +23815.1 q^{33} -4.52058e6 q^{34} -3.11724e6 q^{35} -991065. q^{36} +6.60642e6 q^{37} -1.81228e7 q^{38} +218476. q^{39} -8.36486e6 q^{40} -2.24033e7 q^{41} -194024. q^{42} -3.41880e6 q^{43} +598032. q^{44} +1.50367e7 q^{45} +2.18928e7 q^{46} +1.96091e7 q^{47} -572361. q^{48} -2.37102e7 q^{49} +3.24713e7 q^{50} +382308. q^{51} +5.48626e6 q^{52} +2.18335e7 q^{53} +1.87203e6 q^{54} -9.07347e6 q^{55} +4.46612e7 q^{56} +1.53265e6 q^{57} +7.51692e7 q^{58} -1.05400e8 q^{59} -77174.8 q^{60} +6.39871e7 q^{61} +2.38974e8 q^{62} -8.02830e7 q^{63} +1.18546e8 q^{64} -8.32387e7 q^{65} -564754. q^{66} +6.09774e7 q^{67} +9.60032e6 q^{68} -1.85148e6 q^{69} +7.39227e7 q^{70} -3.75615e8 q^{71} -2.15433e8 q^{72} +3.38605e8 q^{73} -1.56666e8 q^{74} -2.74612e6 q^{75} +3.84872e7 q^{76} +4.84446e7 q^{77} -5.18097e6 q^{78} -6.12882e8 q^{79} +2.18068e8 q^{80} +3.87183e8 q^{81} +5.31277e8 q^{82} +3.98173e8 q^{83} +412048. q^{84} -1.45658e8 q^{85} +8.10740e7 q^{86} -6.35710e6 q^{87} +1.29997e8 q^{88} -8.15783e8 q^{89} -3.56582e8 q^{90} +4.44424e8 q^{91} -4.64936e7 q^{92} -2.02102e7 q^{93} -4.65014e8 q^{94} -5.83937e8 q^{95} +2.33202e6 q^{96} +6.93925e8 q^{97} +5.62268e8 q^{98} -2.33683e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) \) 15 * q - 32 * q^2 - 317 * q^3 + 3242 * q^4 - 4717 * q^5 + 687 * q^6 - 9680 * q^7 - 20394 * q^8 + 69516 * q^9	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9} - 36237 q^{10} - 104484 q^{11} - 266395 q^{12} - 116174 q^{13} + 416064 q^{14} + 415388 q^{15} + 996762 q^{16} - 884265 q^{17} - 588735 q^{18} - 689535 q^{19} - 3077879 q^{20} - 2070198 q^{21} - 7276218 q^{22} - 2504077 q^{23} - 11534895 q^{24} + 1315350 q^{25} - 13343414 q^{26} - 12546986 q^{27} - 28059568 q^{28} - 18406221 q^{29} - 39503820 q^{30} - 12033699 q^{31} - 18952630 q^{32} - 14197716 q^{33} - 30383125 q^{34} - 27855546 q^{35} - 18372959 q^{36} - 8722847 q^{37} - 63941843 q^{38} - 30955510 q^{39} - 39665611 q^{40} - 18689389 q^{41} - 73185310 q^{42} - 51282015 q^{43} - 68723220 q^{44} - 216992888 q^{45} - 2067521 q^{46} - 104960741 q^{47} - 145362479 q^{48} + 92663095 q^{49} - 42446347 q^{50} + 37433407 q^{51} + 149226080 q^{52} - 215907800 q^{53} + 419158122 q^{54} + 384379852 q^{55} + 430441344 q^{56} + 258744488 q^{57} + 295963139 q^{58} + 185924544 q^{59} + 973236172 q^{60} + 247538102 q^{61} + 139798853 q^{62} + 405429926 q^{63} + 848556290 q^{64} + 94294394 q^{65} + 667230492 q^{66} + 467904656 q^{67} - 88234341 q^{68} + 163914994 q^{69} + 647526126 q^{70} - 8252944 q^{71} + 889796745 q^{72} - 715627902 q^{73} + 725122989 q^{74} - 18301762 q^{75} + 346300359 q^{76} - 1236779964 q^{77} + 2058642146 q^{78} + 560681783 q^{79} - 1157214179 q^{80} - 752010645 q^{81} + 941346367 q^{82} - 1442854698 q^{83} + 1895248718 q^{84} + 699302088 q^{85} + 109401632 q^{86} - 2094576907 q^{87} - 1464507256 q^{88} - 396710008 q^{89} + 1411356270 q^{90} - 3278076852 q^{91} + 155864647 q^{92} - 1424759183 q^{93} + 4666638949 q^{94} - 3854114395 q^{95} - 952489551 q^{96} - 3063837815 q^{97} - 6161086984 q^{98} - 6576160348 q^{99}+O(q^{100}) \) 15 * q - 32 * q^2 - 317 * q^3 + 3242 * q^4 - 4717 * q^5 + 687 * q^6 - 9680 * q^7 - 20394 * q^8 + 69516 * q^9 - 36237 * q^10 - 104484 * q^11 - 266395 * q^12 - 116174 * q^13 + 416064 * q^14 + 415388 * q^15 + 996762 * q^16 - 884265 * q^17 - 588735 * q^18 - 689535 * q^19 - 3077879 * q^20 - 2070198 * q^21 - 7276218 * q^22 - 2504077 * q^23 - 11534895 * q^24 + 1315350 * q^25 - 13343414 * q^26 - 12546986 * q^27 - 28059568 * q^28 - 18406221 * q^29 - 39503820 * q^30 - 12033699 * q^31 - 18952630 * q^32 - 14197716 * q^33 - 30383125 * q^34 - 27855546 * q^35 - 18372959 * q^36 - 8722847 * q^37 - 63941843 * q^38 - 30955510 * q^39 - 39665611 * q^40 - 18689389 * q^41 - 73185310 * q^42 - 51282015 * q^43 - 68723220 * q^44 - 216992888 * q^45 - 2067521 * q^46 - 104960741 * q^47 - 145362479 * q^48 + 92663095 * q^49 - 42446347 * q^50 + 37433407 * q^51 + 149226080 * q^52 - 215907800 * q^53 + 419158122 * q^54 + 384379852 * q^55 + 430441344 * q^56 + 258744488 * q^57 + 295963139 * q^58 + 185924544 * q^59 + 973236172 * q^60 + 247538102 * q^61 + 139798853 * q^62 + 405429926 * q^63 + 848556290 * q^64 + 94294394 * q^65 + 667230492 * q^66 + 467904656 * q^67 - 88234341 * q^68 + 163914994 * q^69 + 647526126 * q^70 - 8252944 * q^71 + 889796745 * q^72 - 715627902 * q^73 + 725122989 * q^74 - 18301762 * q^75 + 346300359 * q^76 - 1236779964 * q^77 + 2058642146 * q^78 + 560681783 * q^79 - 1157214179 * q^80 - 752010645 * q^81 + 941346367 * q^82 - 1442854698 * q^83 + 1895248718 * q^84 + 699302088 * q^85 + 109401632 * q^86 - 2094576907 * q^87 - 1464507256 * q^88 - 396710008 * q^89 + 1411356270 * q^90 - 3278076852 * q^91 + 155864647 * q^92 - 1424759183 * q^93 + 4666638949 * q^94 - 3854114395 * q^95 - 952489551 * q^96 - 3063837815 * q^97 - 6161086984 * q^98 - 6576160348 * q^99

Introduction

L-functions

Modular forms

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