LMFDB - Embedded newform 43.10.a.a.1.12

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			1.12
Root			$-25.8680$ 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)

$f(q)$	$=$	$q+23.8680 q^{2} +64.8300 q^{3} +57.6838 q^{4} -578.837 q^{5} +1547.37 q^{6} -413.035 q^{7} -10843.6 q^{8} -15480.1 q^{9} +O(q^{10})$	\(q+23.8680 q^{2} +64.8300 q^{3} +57.6838 q^{4} -578.837 q^{5} +1547.37 q^{6} -413.035 q^{7} -10843.6 q^{8} -15480.1 q^{9} -13815.7 q^{10} +40989.1 q^{11} +3739.64 q^{12} -154895. q^{13} -9858.34 q^{14} -37526.0 q^{15} -288351. q^{16} -37046.5 q^{17} -369479. q^{18} -572136. q^{19} -33389.5 q^{20} -26777.1 q^{21} +978329. q^{22} +1.53076e6 q^{23} -702993. q^{24} -1.61807e6 q^{25} -3.69704e6 q^{26} -2.27962e6 q^{27} -23825.4 q^{28} +5.10452e6 q^{29} -895673. q^{30} -6.63330e6 q^{31} -1.33042e6 q^{32} +2.65732e6 q^{33} -884227. q^{34} +239080. q^{35} -892949. q^{36} +1.17863e7 q^{37} -1.36558e7 q^{38} -1.00418e7 q^{39} +6.27670e6 q^{40} -1.86693e7 q^{41} -639117. q^{42} -3.41880e6 q^{43} +2.36440e6 q^{44} +8.96043e6 q^{45} +3.65362e7 q^{46} -4.17423e7 q^{47} -1.86938e7 q^{48} -4.01830e7 q^{49} -3.86202e7 q^{50} -2.40172e6 q^{51} -8.93492e6 q^{52} +1.09354e8 q^{53} -5.44101e7 q^{54} -2.37260e7 q^{55} +4.47880e6 q^{56} -3.70916e7 q^{57} +1.21835e8 q^{58} +1.08726e8 q^{59} -2.16464e6 q^{60} +8.96497e7 q^{61} -1.58324e8 q^{62} +6.39381e6 q^{63} +1.15881e8 q^{64} +8.96588e7 q^{65} +6.34251e7 q^{66} -2.02489e8 q^{67} -2.13698e6 q^{68} +9.92390e7 q^{69} +5.70637e6 q^{70} +1.86518e8 q^{71} +1.67860e8 q^{72} +2.88219e8 q^{73} +2.81315e8 q^{74} -1.04900e8 q^{75} -3.30030e7 q^{76} -1.69299e7 q^{77} -2.39679e8 q^{78} +1.54282e8 q^{79} +1.66908e8 q^{80} +1.56906e8 q^{81} -4.45599e8 q^{82} +1.44177e8 q^{83} -1.54460e6 q^{84} +2.14439e7 q^{85} -8.16001e7 q^{86} +3.30926e8 q^{87} -4.44471e8 q^{88} -5.50623e8 q^{89} +2.13868e8 q^{90} +6.39770e7 q^{91} +8.82999e7 q^{92} -4.30037e8 q^{93} -9.96306e8 q^{94} +3.31174e8 q^{95} -8.62514e7 q^{96} -1.15464e9 q^{97} -9.59090e8 q^{98} -6.34514e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	23.8680	1.05483	0.527414	−	0.849608i	$-0.323162\pi$
$2$	23.8680	1.05483	0.527414	+	0.849608i	$0.323162\pi$
$3$	64.8300	0.462094	0.231047	−	0.972943i	$-0.425785\pi$
$3$	64.8300	0.462094	0.231047	+	0.972943i	$0.425785\pi$
$4$	57.6838	0.112664
$5$	−578.837	−0.414182	−0.207091	−	0.978322i	$-0.566400\pi$
$5$	−578.837	−0.414182	−0.207091	+	0.978322i	$0.566400\pi$
$6$	1547.37	0.487430
$7$	−413.035	−0.0650198	−0.0325099	−	0.999471i	$-0.510350\pi$
$7$	−413.035	−0.0650198	−0.0325099	+	0.999471i	$0.510350\pi$
$8$	−10843.6	−0.935988
$9$	−15480.1	−0.786469
$10$	−13815.7	−0.436891
$11$	40989.1	0.844114	0.422057	−	0.906569i	$-0.361308\pi$
$11$	40989.1	0.844114	0.422057	+	0.906569i	$0.361308\pi$
$12$	3739.64	0.0520612
$13$	−154895.	−1.50415	−0.752076	−	0.659076i	$-0.770947\pi$
$13$	−154895.	−1.50415	−0.752076	+	0.659076i	$0.770947\pi$
$14$	−9858.34	−0.0685848
$15$	−37526.0	−0.191391
$16$	−288351.	−1.09997
$17$	−37046.5	−0.107579	−0.0537894	−	0.998552i	$-0.517130\pi$
$17$	−37046.5	−0.107579	−0.0537894	+	0.998552i	$0.517130\pi$
$18$	−369479.	−0.829590
$19$	−572136.	−1.00718	−0.503591	−	0.863942i	$-0.667988\pi$
$19$	−572136.	−1.00718	−0.503591	+	0.863942i	$0.667988\pi$
$20$	−33389.5	−0.0466632
$21$	−26777.1	−0.0300453
$22$	978329.	0.890395
$23$	1.53076e6	1.14059	0.570297	−	0.821439i	$-0.306828\pi$
$23$	1.53076e6	1.14059	0.570297	+	0.821439i	$0.306828\pi$
$24$	−702993.	−0.432515
$25$	−1.61807e6	−0.828453
$26$	−3.69704e6	−1.58662
$27$	−2.27962e6	−0.825517
$28$	−23825.4	−0.00732537
$29$	5.10452e6	1.34018	0.670091	−	0.742279i	$-0.266255\pi$
$29$	5.10452e6	1.34018	0.670091	+	0.742279i	$0.266255\pi$
$30$	−895673.	−0.201885
$31$	−6.63330e6	−1.29004	−0.645018	−	0.764167i	$-0.723150\pi$
$31$	−6.63330e6	−1.29004	−0.645018	+	0.764167i	$0.723150\pi$
$32$	−1.33042e6	−0.224293
$33$	2.65732e6	0.390060
$34$	−884227.	−0.113477
$35$	239080.	0.0269300
$36$	−892949.	−0.0886065
$37$	1.17863e7	1.03387	0.516937	−	0.856023i	$-0.327072\pi$
$37$	1.17863e7	1.03387	0.516937	+	0.856023i	$0.327072\pi$
$38$	−1.36558e7	−1.06241
$39$	−1.00418e7	−0.695060
$40$	6.27670e6	0.387669
$41$	−1.86693e7	−1.03181	−0.515905	−	0.856646i	$-0.672544\pi$
$41$	−1.86693e7	−1.03181	−0.515905	+	0.856646i	$0.672544\pi$
$42$	−639117.	−0.0316926
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	2.36440e6	0.0951009
$45$	8.96043e6	0.325741
$46$	3.65362e7	1.20313
$47$	−4.17423e7	−1.24777	−0.623886	−	0.781515i	$-0.714447\pi$
$47$	−4.17423e7	−1.24777	−0.623886	+	0.781515i	$0.714447\pi$
$48$	−1.86938e7	−0.508290
$49$	−4.01830e7	−0.995772
$50$	−3.86202e7	−0.873876
$51$	−2.40172e6	−0.0497116
$52$	−8.93492e6	−0.169463
$53$	1.09354e8	1.90368	0.951842	−	0.306590i	$-0.0991880\pi$
$53$	1.09354e8	1.90368	0.951842	+	0.306590i	$0.0991880\pi$
$54$	−5.44101e7	−0.870779
$55$	−2.37260e7	−0.349617
$56$	4.47880e6	0.0608578
$57$	−3.70916e7	−0.465413
$58$	1.21835e8	1.41366
$59$	1.08726e8	1.16815	0.584075	−	0.811699i	$-0.301457\pi$
$59$	1.08726e8	1.16815	0.584075	+	0.811699i	$0.301457\pi$
$60$	−2.16464e6	−0.0215628
$61$	8.96497e7	0.829019	0.414510	−	0.910045i	$-0.363953\pi$
$61$	8.96497e7	0.829019	0.414510	+	0.910045i	$0.363953\pi$
$62$	−1.58324e8	−1.36077
$63$	6.39381e6	0.0511361
$64$	1.15881e8	0.863380
$65$	8.96588e7	0.622993
$66$	6.34251e7	0.411447
$67$	−2.02489e8	−1.22762	−0.613810	−	0.789454i	$-0.710364\pi$
$67$	−2.02489e8	−1.22762	−0.613810	+	0.789454i	$0.710364\pi$
$68$	−2.13698e6	−0.0121202
$69$	9.92390e7	0.527062
$70$	5.70637e6	0.0284066
$71$	1.86518e8	0.871081	0.435541	−	0.900169i	$-0.356557\pi$
$71$	1.86518e8	0.871081	0.435541	+	0.900169i	$0.356557\pi$
$72$	1.67860e8	0.736125
$73$	2.88219e8	1.18787	0.593937	−	0.804512i	$-0.297573\pi$
$73$	2.88219e8	1.18787	0.593937	+	0.804512i	$0.297573\pi$
$74$	2.81315e8	1.09056
$75$	−1.04900e8	−0.382823
$76$	−3.30030e7	−0.113473
$77$	−1.69299e7	−0.0548841
$78$	−2.39679e8	−0.733169
$79$	1.54282e8	0.445650	0.222825	−	0.974858i	$-0.428472\pi$
$79$	1.54282e8	0.445650	0.222825	+	0.974858i	$0.428472\pi$
$80$	1.66908e8	0.455588
$81$	1.56906e8	0.405002
$82$	−4.45599e8	−1.08838
$83$	1.44177e8	0.333461	0.166730	−	0.986003i	$-0.446679\pi$
$83$	1.44177e8	0.333461	0.166730	+	0.986003i	$0.446679\pi$
$84$	−1.54460e6	−0.00338501
$85$	2.14439e7	0.0445572
$86$	−8.16001e7	−0.160860
$87$	3.30926e8	0.619291
$88$	−4.44471e8	−0.790080
$89$	−5.50623e8	−0.930248	−0.465124	−	0.885245i	$-0.653990\pi$
$89$	−5.50623e8	−0.930248	−0.465124	+	0.885245i	$0.653990\pi$
$90$	2.13868e8	0.343601
$91$	6.39770e7	0.0977997
$92$	8.82999e7	0.128503
$93$	−4.30037e8	−0.596118
$94$	−9.96306e8	−1.31619
$95$	3.31174e8	0.417157
$96$	−8.62514e7	−0.103644
$97$	−1.15464e9	−1.32427	−0.662133	−	0.749387i	$-0.730348\pi$
$97$	−1.15464e9	−1.32427	−0.662133	+	0.749387i	$0.730348\pi$
$98$	−9.59090e8	−1.05037
$99$	−6.34514e8	−0.663869
$100$	−9.33366e7	−0.0933366
$101$	−1.66204e9	−1.58926	−0.794630	−	0.607094i	$-0.792335\pi$
$101$	−1.66204e9	−1.58926	−0.794630	+	0.607094i	$0.792335\pi$
$102$	−5.73245e7	−0.0524372
$103$	−2.01491e8	−0.176396	−0.0881979	−	0.996103i	$-0.528111\pi$
$103$	−2.01491e8	−0.176396	−0.0881979	+	0.996103i	$0.528111\pi$
$104$	1.67962e9	1.40787
$105$	1.54996e7	0.0124442
$106$	2.61008e9	2.00806
$107$	−2.22025e9	−1.63748	−0.818738	−	0.574168i	$-0.805326\pi$
$107$	−2.22025e9	−1.63748	−0.818738	+	0.574168i	$0.805326\pi$
$108$	−1.31497e8	−0.0930057
$109$	−1.44526e9	−0.980679	−0.490340	−	0.871531i	$-0.663127\pi$
$109$	−1.44526e9	−0.980679	−0.490340	+	0.871531i	$0.663127\pi$
$110$	−5.66293e8	−0.368786
$111$	7.64103e8	0.477748
$112$	1.19099e8	0.0715199
$113$	1.98255e9	1.14385	0.571927	−	0.820304i	$-0.306196\pi$
$113$	1.98255e9	1.14385	0.571927	+	0.820304i	$0.306196\pi$
$114$	−8.85304e8	−0.490931
$115$	−8.86059e8	−0.472413
$116$	2.94448e8	0.150990
$117$	2.39778e9	1.18297
$118$	2.59507e9	1.23220
$119$	1.53015e7	0.00699476
$120$	4.06919e8	0.179140
$121$	−6.77844e8	−0.287472
$122$	2.13976e9	0.874473
$123$	−1.21033e9	−0.476793
$124$	−3.82634e8	−0.145340
$125$	2.06714e9	0.757312
$126$	1.52608e8	0.0539398
$127$	−5.25769e9	−1.79340	−0.896702	−	0.442635i	$-0.854044\pi$
$127$	−5.25769e9	−1.79340	−0.896702	+	0.442635i	$0.854044\pi$
$128$	3.44703e9	1.13501
$129$	−2.21641e8	−0.0704687
$130$	2.13998e9	0.657150
$131$	4.26420e8	0.126508	0.0632538	−	0.997997i	$-0.479852\pi$
$131$	4.26420e8	0.126508	0.0632538	+	0.997997i	$0.479852\pi$
$132$	1.53284e8	0.0439456
$133$	2.36312e8	0.0654868
$134$	−4.83301e9	−1.29493
$135$	1.31953e9	0.341914
$136$	4.01719e8	0.100693
$137$	2.39976e9	0.582003	0.291002	−	0.956723i	$-0.406011\pi$
$137$	2.39976e9	0.582003	0.291002	+	0.956723i	$0.406011\pi$
$138$	2.36864e9	0.555960
$139$	4.62160e8	0.105009	0.0525044	−	0.998621i	$-0.483280\pi$
$139$	4.62160e8	0.105009	0.0525044	+	0.998621i	$0.483280\pi$
$140$	1.37910e7	0.00303404
$141$	−2.70615e9	−0.576589
$142$	4.45183e9	0.918842
$143$	−6.34899e9	−1.26968
$144$	4.46369e9	0.865093
$145$	−2.95468e9	−0.555079
$146$	6.87923e9	1.25300
$147$	−2.60507e9	−0.460141
$148$	6.79876e8	0.116480
$149$	1.41734e8	0.0235578	0.0117789	−	0.999931i	$-0.496251\pi$
$149$	1.41734e8	0.0235578	0.0117789	+	0.999931i	$0.496251\pi$
$150$	−2.50375e9	−0.403813
$151$	−7.41576e9	−1.16081	−0.580403	−	0.814330i	$-0.697105\pi$
$151$	−7.41576e9	−1.16081	−0.580403	+	0.814330i	$0.697105\pi$
$152$	6.20404e9	0.942711
$153$	5.73482e8	0.0846074
$154$	−4.04084e8	−0.0578933
$155$	3.83960e9	0.534310
$156$	−5.79251e8	−0.0783080
$157$	−1.10190e10	−1.44742	−0.723709	−	0.690106i	$-0.757564\pi$
$157$	−1.10190e10	−1.44742	−0.723709	+	0.690106i	$0.757564\pi$
$158$	3.68242e9	0.470085
$159$	7.08945e9	0.879681
$160$	7.70098e8	0.0928980
$161$	−6.32256e8	−0.0741612
$162$	3.74505e9	0.427208
$163$	−1.12939e10	−1.25314	−0.626571	−	0.779364i	$-0.715542\pi$
$163$	−1.12939e10	−1.25314	−0.626571	+	0.779364i	$0.715542\pi$
$164$	−1.07691e9	−0.116247
$165$	−1.53816e9	−0.161556
$166$	3.44123e9	0.351744
$167$	2.07229e9	0.206171	0.103085	−	0.994673i	$-0.467128\pi$
$167$	2.07229e9	0.206171	0.103085	+	0.994673i	$0.467128\pi$
$168$	2.90361e8	0.0281220
$169$	1.33879e10	1.26247
$170$	5.11823e8	0.0470002
$171$	8.85671e9	0.792118
$172$	−1.97209e8	−0.0171810
$173$	−1.50835e10	−1.28025	−0.640125	−	0.768271i	$-0.721117\pi$
$173$	−1.50835e10	−1.28025	−0.640125	+	0.768271i	$0.721117\pi$
$174$	7.89856e9	0.653245
$175$	6.68321e8	0.0538659
$176$	−1.18192e10	−0.928500
$177$	7.04870e9	0.539796
$178$	−1.31423e10	−0.981253
$179$	1.57672e10	1.14793	0.573967	−	0.818878i	$-0.305404\pi$
$179$	1.57672e10	1.14793	0.573967	+	0.818878i	$0.305404\pi$
$180$	5.16872e8	0.0366992
$181$	6.68229e8	0.0462777	0.0231388	−	0.999732i	$-0.492634\pi$
$181$	6.68229e8	0.0462777	0.0231388	+	0.999732i	$0.492634\pi$
$182$	1.52701e9	0.103162
$183$	5.81199e9	0.383085
$184$	−1.65990e10	−1.06758
$185$	−6.82232e9	−0.428212
$186$	−1.02641e10	−0.628803
$187$	−1.51850e9	−0.0908088
$188$	−2.40785e9	−0.140579
$189$	9.41564e8	0.0536750
$190$	7.90447e9	0.440029
$191$	−3.50164e10	−1.90380	−0.951901	−	0.306407i	$-0.900873\pi$
$191$	−3.50164e10	−1.90380	−0.951901	+	0.306407i	$0.900873\pi$
$192$	7.51256e9	0.398963
$193$	2.42400e10	1.25755	0.628775	−	0.777587i	$-0.283557\pi$
$193$	2.42400e10	1.25755	0.628775	+	0.777587i	$0.283557\pi$
$194$	−2.75591e10	−1.39687
$195$	5.81258e9	0.287881
$196$	−2.31791e9	−0.112187
$197$	1.04603e10	0.494819	0.247409	−	0.968911i	$-0.420421\pi$
$197$	1.04603e10	0.494819	0.247409	+	0.968911i	$0.420421\pi$
$198$	−1.51446e10	−0.700268
$199$	−1.66270e10	−0.751580	−0.375790	−	0.926705i	$-0.622629\pi$
$199$	−1.66270e10	−0.751580	−0.375790	+	0.926705i	$0.622629\pi$
$200$	1.75458e10	0.775422
$201$	−1.31273e10	−0.567276
$202$	−3.96696e10	−1.67640
$203$	−2.10835e9	−0.0871384
$204$	−1.38541e8	−0.00560069
$205$	1.08065e10	0.427357
$206$	−4.80920e9	−0.186067
$207$	−2.36962e10	−0.897042
$208$	4.46640e10	1.65452
$209$	−2.34513e10	−0.850177
$210$	3.69944e8	0.0131265
$211$	2.94765e10	1.02378	0.511888	−	0.859052i	$-0.328946\pi$
$211$	2.94765e10	1.02378	0.511888	+	0.859052i	$0.328946\pi$
$212$	6.30797e9	0.214476
$213$	1.20920e10	0.402522
$214$	−5.29930e10	−1.72726
$215$	1.97893e9	0.0631622
$216$	2.47194e10	0.772674
$217$	2.73978e9	0.0838779
$218$	−3.44956e10	−1.03445
$219$	1.86853e10	0.548909
$220$	−1.36860e9	−0.0393891
$221$	5.73831e9	0.161815
$222$	1.82376e10	0.503942
$223$	−3.58102e9	−0.0969694	−0.0484847	−	0.998824i	$-0.515439\pi$
$223$	−3.58102e9	−0.0969694	−0.0484847	+	0.998824i	$0.515439\pi$
$224$	5.49512e8	0.0145835
$225$	2.50479e10	0.651553
$226$	4.73196e10	1.20657
$227$	2.60470e10	0.651090	0.325545	−	0.945527i	$-0.394452\pi$
$227$	2.60470e10	0.651090	0.325545	+	0.945527i	$0.394452\pi$
$228$	−2.13958e9	−0.0524352
$229$	7.05669e9	0.169567	0.0847836	−	0.996399i	$-0.472980\pi$
$229$	7.05669e9	0.169567	0.0847836	+	0.996399i	$0.472980\pi$
$230$	−2.11485e10	−0.498315
$231$	−1.09757e9	−0.0253616
$232$	−5.53516e10	−1.25439
$233$	−6.66600e10	−1.48171	−0.740856	−	0.671664i	$-0.765580\pi$
$233$	−6.66600e10	−1.48171	−0.740856	+	0.671664i	$0.765580\pi$
$234$	5.72304e10	1.24783
$235$	2.41620e10	0.516805
$236$	6.27172e9	0.131608
$237$	1.00021e10	0.205932
$238$	3.65217e8	0.00737827
$239$	4.25444e10	0.843435	0.421717	−	0.906727i	$-0.361427\pi$
$239$	4.25444e10	0.843435	0.421717	+	0.906727i	$0.361427\pi$
$240$	1.08206e10	0.210525
$241$	1.80531e10	0.344727	0.172364	−	0.985033i	$-0.444860\pi$
$241$	1.80531e10	0.344727	0.172364	+	0.985033i	$0.444860\pi$
$242$	−1.61788e10	−0.303234
$243$	5.50420e10	1.01267
$244$	5.17133e9	0.0934003
$245$	2.32594e10	0.412431
$246$	−2.88882e10	−0.502935
$247$	8.86209e10	1.51496
$248$	7.19291e10	1.20746
$249$	9.34701e9	0.154090
$250$	4.93386e10	0.798835
$251$	−3.95656e10	−0.629196	−0.314598	−	0.949225i	$-0.601870\pi$
$251$	−3.95656e10	−0.629196	−0.314598	+	0.949225i	$0.601870\pi$
$252$	3.68819e8	0.00576118
$253$	6.27443e10	0.962791
$254$	−1.25491e11	−1.89173
$255$	1.39021e9	0.0205896
$256$	2.29428e10	0.333862
$257$	7.15316e10	1.02282	0.511410	−	0.859337i	$-0.329124\pi$
$257$	7.15316e10	1.02282	0.511410	+	0.859337i	$0.329124\pi$
$258$	−5.29014e9	−0.0743324
$259$	−4.86814e9	−0.0672224
$260$	5.17186e9	0.0701886
$261$	−7.90183e10	−1.05401
$262$	1.01778e10	0.133444
$263$	−6.08596e10	−0.784384	−0.392192	−	0.919883i	$-0.628283\pi$
$263$	−6.08596e10	−0.784384	−0.392192	+	0.919883i	$0.628283\pi$
$264$	−2.88150e10	−0.365091
$265$	−6.32983e10	−0.788471
$266$	5.64032e9	0.0690774
$267$	−3.56969e10	−0.429862
$268$	−1.16803e10	−0.138308
$269$	−5.96377e10	−0.694441	−0.347221	−	0.937783i	$-0.612875\pi$
$269$	−5.96377e10	−0.694441	−0.347221	+	0.937783i	$0.612875\pi$
$270$	3.14946e10	0.360661
$271$	7.16434e9	0.0806890	0.0403445	−	0.999186i	$-0.487154\pi$
$271$	7.16434e9	0.0806890	0.0403445	+	0.999186i	$0.487154\pi$
$272$	1.06824e10	0.118334
$273$	4.14763e9	0.0451927
$274$	5.72776e10	0.613914
$275$	−6.63233e10	−0.699309
$276$	5.72448e9	0.0593807
$277$	5.21051e10	0.531767	0.265883	−	0.964005i	$-0.414336\pi$
$277$	5.21051e10	0.531767	0.265883	+	0.964005i	$0.414336\pi$
$278$	1.10308e10	0.110766
$279$	1.02684e11	1.01457
$280$	−2.59250e9	−0.0252062
$281$	−1.92655e10	−0.184333	−0.0921663	−	0.995744i	$-0.529379\pi$
$281$	−1.92655e10	−0.184333	−0.0921663	+	0.995744i	$0.529379\pi$
$282$	−6.45905e10	−0.608202
$283$	2.24601e10	0.208148	0.104074	−	0.994570i	$-0.466812\pi$
$283$	2.24601e10	0.208148	0.104074	+	0.994570i	$0.466812\pi$
$284$	1.07591e10	0.0981392
$285$	2.14700e10	0.192766
$286$	−1.51538e11	−1.33929
$287$	7.71106e9	0.0670881
$288$	2.05950e10	0.176399
$289$	−1.17215e11	−0.988427
$290$	−7.05226e10	−0.585514
$291$	−7.48555e10	−0.611935
$292$	1.66256e10	0.133830
$293$	4.53637e10	0.359587	0.179794	−	0.983704i	$-0.442457\pi$
$293$	4.53637e10	0.359587	0.179794	+	0.983704i	$0.442457\pi$
$294$	−6.21778e10	−0.485370
$295$	−6.29346e10	−0.483827
$296$	−1.27806e11	−0.967694
$297$	−9.34396e10	−0.696830
$298$	3.38291e9	0.0248495
$299$	−2.37106e11	−1.71563
$300$	−6.05101e9	−0.0431303
$301$	1.41208e9	0.00991543
$302$	−1.77000e11	−1.22445
$303$	−1.07750e11	−0.734388
$304$	1.64976e11	1.10787
$305$	−5.18926e10	−0.343365
$306$	1.36879e10	0.0892464
$307$	2.52635e11	1.62320	0.811598	−	0.584216i	$-0.198598\pi$
$307$	2.52635e11	1.62320	0.811598	+	0.584216i	$0.198598\pi$
$308$	−9.76582e8	−0.00618344
$309$	−1.30627e10	−0.0815115
$310$	9.16437e10	0.563605
$311$	1.44034e11	0.873057	0.436529	−	0.899690i	$-0.356208\pi$
$311$	1.44034e11	0.873057	0.436529	+	0.899690i	$0.356208\pi$
$312$	1.08890e11	0.650568
$313$	1.80382e10	0.106229	0.0531147	−	0.998588i	$-0.483085\pi$
$313$	1.80382e10	0.106229	0.0531147	+	0.998588i	$0.483085\pi$
$314$	−2.63002e11	−1.52678
$315$	−3.70097e9	−0.0211796
$316$	8.89959e9	0.0502086
$317$	7.77758e9	0.0432591	0.0216296	−	0.999766i	$-0.493115\pi$
$317$	7.77758e9	0.0432591	0.0216296	+	0.999766i	$0.493115\pi$
$318$	1.69211e11	0.927913
$319$	2.09230e11	1.13127
$320$	−6.70762e10	−0.357597
$321$	−1.43939e11	−0.756668
$322$	−1.50907e10	−0.0782274
$323$	2.11956e10	0.108352
$324$	9.05095e9	0.0456290
$325$	2.50631e11	1.24612
$326$	−2.69564e11	−1.32185
$327$	−9.36963e10	−0.453166
$328$	2.02443e11	0.965761
$329$	1.72410e10	0.0811300
$330$	−3.67128e10	−0.170414
$331$	2.82639e11	1.29421	0.647106	−	0.762400i	$-0.275979\pi$
$331$	2.82639e11	1.29421	0.647106	+	0.762400i	$0.275979\pi$
$332$	8.31668e9	0.0375689
$333$	−1.82452e11	−0.813111
$334$	4.94616e10	0.217475
$335$	1.17208e11	0.508458
$336$	7.72119e9	0.0330489
$337$	1.43617e11	0.606557	0.303279	−	0.952902i	$-0.401919\pi$
$337$	1.43617e11	0.606557	0.303279	+	0.952902i	$0.401919\pi$
$338$	3.19543e11	1.33169
$339$	1.28529e11	0.528568
$340$	1.23696e9	0.00501998
$341$	−2.71893e11	−1.08894
$342$	2.11392e11	0.835549
$343$	3.32644e10	0.129765
$344$	3.70723e10	0.142737
$345$	−5.74432e10	−0.218299
$346$	−3.60014e11	−1.35044
$347$	−1.75323e10	−0.0649168	−0.0324584	−	0.999473i	$-0.510334\pi$
$347$	−1.75323e10	−0.0649168	−0.0324584	+	0.999473i	$0.510334\pi$
$348$	1.90891e10	0.0697715
$349$	6.51688e10	0.235139	0.117570	−	0.993065i	$-0.462490\pi$
$349$	6.51688e10	0.235139	0.117570	+	0.993065i	$0.462490\pi$
$350$	1.59515e10	0.0568193
$351$	3.53102e11	1.24170
$352$	−5.45328e10	−0.189328
$353$	2.83965e11	0.973372	0.486686	−	0.873577i	$-0.338206\pi$
$353$	2.83965e11	0.973372	0.486686	+	0.873577i	$0.338206\pi$
$354$	1.68239e11	0.569392
$355$	−1.07964e11	−0.360786
$356$	−3.17620e10	−0.104805
$357$	9.91997e8	0.00323224
$358$	3.76333e11	1.21087
$359$	−7.02188e10	−0.223115	−0.111557	−	0.993758i	$-0.535584\pi$
$359$	−7.02188e10	−0.223115	−0.111557	+	0.993758i	$0.535584\pi$
$360$	−9.71637e10	−0.304890
$361$	4.65223e9	0.0144171
$362$	1.59493e10	0.0488150
$363$	−4.39447e10	−0.132839
$364$	3.69043e9	0.0110185
$365$	−1.66832e11	−0.491996
$366$	1.38721e11	0.404089
$367$	−3.53552e11	−1.01732	−0.508658	−	0.860969i	$-0.669858\pi$
$367$	−3.53552e11	−1.01732	−0.508658	+	0.860969i	$0.669858\pi$
$368$	−4.41395e11	−1.25462
$369$	2.89001e11	0.811486
$370$	−1.62835e11	−0.451691
$371$	−4.51672e10	−0.123777
$372$	−2.48061e10	−0.0671608
$373$	6.13570e11	1.64125	0.820624	−	0.571468i	$-0.193626\pi$
$373$	6.13570e11	1.64125	0.820624	+	0.571468i	$0.193626\pi$
$374$	−3.62437e10	−0.0957877
$375$	1.34013e11	0.349950
$376$	4.52638e11	1.16790
$377$	−7.90664e11	−2.01584
$378$	2.24733e10	0.0566179
$379$	−2.66556e11	−0.663609	−0.331804	−	0.943348i	$-0.607657\pi$
$379$	−2.66556e11	−0.663609	−0.331804	+	0.943348i	$0.607657\pi$
$380$	1.91033e10	0.0469984
$381$	−3.40856e11	−0.828721
$382$	−8.35774e11	−2.00818
$383$	−2.18172e11	−0.518090	−0.259045	−	0.965865i	$-0.583408\pi$
$383$	−2.18172e11	−0.518090	−0.259045	+	0.965865i	$0.583408\pi$
$384$	2.23471e11	0.524482
$385$	9.79966e9	0.0227320
$386$	5.78562e11	1.32650
$387$	5.29233e10	0.119935
$388$	−6.66042e10	−0.149197
$389$	8.62682e10	0.191019	0.0955097	−	0.995428i	$-0.469552\pi$
$389$	8.62682e10	0.191019	0.0955097	+	0.995428i	$0.469552\pi$
$390$	1.38735e11	0.303665
$391$	−5.67092e10	−0.122704
$392$	4.35730e11	0.932031
$393$	2.76448e10	0.0584584
$394$	2.49667e11	0.521949
$395$	−8.93043e10	−0.184580
$396$	−3.66011e10	−0.0747939
$397$	−9.38797e11	−1.89677	−0.948384	−	0.317124i	$-0.897283\pi$
$397$	−9.38797e11	−1.89677	−0.948384	+	0.317124i	$0.897283\pi$
$398$	−3.96854e11	−0.792789
$399$	1.53201e10	0.0302611
$400$	4.66572e11	0.911274
$401$	−4.13612e11	−0.798810	−0.399405	−	0.916775i	$-0.630783\pi$
$401$	−4.13612e11	−0.798810	−0.399405	+	0.916775i	$0.630783\pi$
$402$	−3.13324e11	−0.598379
$403$	1.02746e12	1.94041
$404$	−9.58727e10	−0.179052
$405$	−9.08231e10	−0.167745
$406$	−5.03221e10	−0.0919161
$407$	4.83107e11	0.872708
$408$	2.60434e10	0.0465294
$409$	9.59930e10	0.169623	0.0848115	−	0.996397i	$-0.472971\pi$
$409$	9.59930e10	0.169623	0.0848115	+	0.996397i	$0.472971\pi$
$410$	2.57929e11	0.450788
$411$	1.55577e11	0.268940
$412$	−1.16228e10	−0.0198734
$413$	−4.49076e10	−0.0759530
$414$	−5.65583e11	−0.946225
$415$	−8.34550e10	−0.138113
$416$	2.06076e11	0.337370
$417$	2.99618e10	0.0485239
$418$	−5.59738e11	−0.896791
$419$	−6.82383e10	−0.108160	−0.0540798	−	0.998537i	$-0.517223\pi$
$419$	−6.82383e10	−0.108160	−0.0540798	+	0.998537i	$0.517223\pi$
$420$	8.94073e8	0.00140201
$421$	−3.11922e11	−0.483923	−0.241961	−	0.970286i	$-0.577791\pi$
$421$	−3.11922e11	−0.483923	−0.241961	+	0.970286i	$0.577791\pi$
$422$	7.03546e11	1.07991
$423$	6.46173e11	0.981335
$424$	−1.18580e12	−1.78182
$425$	5.99439e10	0.0891241
$426$	2.88612e11	0.424591
$427$	−3.70285e10	−0.0539027
$428$	−1.28072e11	−0.184484
$429$	−4.11605e11	−0.586710
$430$	4.72332e10	0.0666253
$431$	−1.57117e11	−0.219318	−0.109659	−	0.993969i	$-0.534976\pi$
$431$	−1.57117e11	−0.219318	−0.109659	+	0.993969i	$0.534976\pi$
$432$	6.57331e11	0.908044
$433$	−1.09449e12	−1.49629	−0.748143	−	0.663537i	$-0.769054\pi$
$433$	−1.09449e12	−1.49629	−0.748143	+	0.663537i	$0.769054\pi$
$434$	6.53933e10	0.0884768
$435$	−1.91552e11	−0.256499
$436$	−8.33681e10	−0.110487
$437$	−8.75802e11	−1.14879
$438$	4.45981e11	0.579005
$439$	−7.01115e11	−0.900947	−0.450473	−	0.892790i	$-0.648745\pi$
$439$	−7.01115e11	−0.900947	−0.450473	+	0.892790i	$0.648745\pi$
$440$	2.57276e11	0.327237
$441$	6.22036e11	0.783144
$442$	1.36962e11	0.170687
$443$	4.23032e11	0.521863	0.260932	−	0.965357i	$-0.415970\pi$
$443$	4.23032e11	0.521863	0.260932	+	0.965357i	$0.415970\pi$
$444$	4.40763e10	0.0538248
$445$	3.18721e11	0.385292
$446$	−8.54720e10	−0.102286
$447$	9.18860e9	0.0108859
$448$	−4.78629e10	−0.0561368
$449$	−1.04536e11	−0.121383	−0.0606916	−	0.998157i	$-0.519331\pi$
$449$	−1.04536e11	−0.121383	−0.0606916	+	0.998157i	$0.519331\pi$
$450$	5.97844e11	0.687277
$451$	−7.65235e11	−0.870965
$452$	1.14361e11	0.128871
$453$	−4.80764e11	−0.536402
$454$	6.21690e11	0.686788
$455$	−3.70322e10	−0.0405069
$456$	4.02208e11	0.435621
$457$	5.68647e11	0.609845	0.304923	−	0.952377i	$-0.401369\pi$
$457$	5.68647e11	0.609845	0.304923	+	0.952377i	$0.401369\pi$
$458$	1.68430e11	0.178864
$459$	8.44520e10	0.0888082
$460$	−5.11112e10	−0.0532238
$461$	−1.55226e12	−1.60070	−0.800349	−	0.599535i	$-0.795352\pi$
$461$	−1.55226e12	−1.60070	−0.800349	+	0.599535i	$0.795352\pi$
$462$	−2.61968e10	−0.0267522
$463$	1.18555e12	1.19897	0.599483	−	0.800387i	$-0.295373\pi$
$463$	1.18555e12	1.19897	0.599483	+	0.800387i	$0.295373\pi$
$464$	−1.47189e12	−1.47416
$465$	2.48921e11	0.246901
$466$	−1.59104e12	−1.56295
$467$	7.96561e11	0.774985	0.387492	−	0.921873i	$-0.373341\pi$
$467$	7.96561e11	0.774985	0.387492	+	0.921873i	$0.373341\pi$
$468$	1.38313e11	0.133278
$469$	8.36349e10	0.0798196
$470$	5.76699e11	0.545141
$471$	−7.14362e11	−0.668843
$472$	−1.17898e12	−1.09338
$473$	−1.40133e11	−0.128726
$474$	2.38731e11	0.217223
$475$	9.25758e11	0.834404
$476$	8.82648e8	0.000788055 0
$477$	−1.69281e12	−1.49719
$478$	1.01545e12	0.889679
$479$	−1.33615e12	−1.15970	−0.579848	−	0.814725i	$-0.696888\pi$
$479$	−1.33615e12	−1.15970	−0.579848	+	0.814725i	$0.696888\pi$
$480$	4.99255e10	0.0429276
$481$	−1.82563e12	−1.55510
$482$	4.30893e11	0.363628
$483$	−4.09892e10	−0.0342695
$484$	−3.91006e10	−0.0323877
$485$	6.68350e11	0.548487
$486$	1.31375e12	1.06819
$487$	1.33606e12	1.07633	0.538165	−	0.842839i	$-0.319118\pi$
$487$	1.33606e12	1.07633	0.538165	+	0.842839i	$0.319118\pi$
$488$	−9.72129e11	−0.775952
$489$	−7.32185e11	−0.579070
$490$	5.55157e11	0.435044
$491$	1.45714e12	1.13145	0.565725	−	0.824594i	$-0.308596\pi$
$491$	1.45714e12	1.13145	0.565725	+	0.824594i	$0.308596\pi$
$492$	−6.98163e10	−0.0537173
$493$	−1.89105e11	−0.144175
$494$	2.11521e12	1.59802
$495$	3.67280e11	0.274963
$496$	1.91272e12	1.41900
$497$	−7.70386e10	−0.0566376
$498$	2.23095e11	0.162539
$499$	−9.98947e11	−0.721257	−0.360628	−	0.932710i	$-0.617438\pi$
$499$	−9.98947e11	−0.721257	−0.360628	+	0.932710i	$0.617438\pi$
$500$	1.19241e11	0.0853216
$501$	1.34347e11	0.0952704
$502$	−9.44354e11	−0.663694
$503$	2.25381e12	1.56986	0.784930	−	0.619584i	$-0.212699\pi$
$503$	2.25381e12	1.56986	0.784930	+	0.619584i	$0.212699\pi$
$504$	−6.93322e10	−0.0478627
$505$	9.62049e11	0.658243
$506$	1.49758e12	1.01558
$507$	8.67937e11	0.583381
$508$	−3.03283e11	−0.202051
$509$	2.45200e12	1.61916	0.809581	−	0.587008i	$-0.199694\pi$
$509$	2.45200e12	1.61916	0.809581	+	0.587008i	$0.199694\pi$
$510$	3.31815e10	0.0217185
$511$	−1.19045e11	−0.0772353
$512$	−1.21728e12	−0.782844
$513$	1.30425e12	0.831446
$514$	1.70732e12	1.07890
$515$	1.16630e11	0.0730600
$516$	−1.27851e10	−0.00793926
$517$	−1.71098e12	−1.05326
$518$	−1.16193e11	−0.0709081
$519$	−9.77864e11	−0.591596
$520$	−9.72228e11	−0.583113
$521$	2.99007e12	1.77791	0.888957	−	0.457990i	$-0.151430\pi$
$521$	2.99007e12	1.77791	0.888957	+	0.457990i	$0.151430\pi$
$522$	−1.88601e12	−1.11180
$523$	1.07354e12	0.627425	0.313713	−	0.949518i	$-0.398427\pi$
$523$	1.07354e12	0.627425	0.313713	+	0.949518i	$0.398427\pi$
$524$	2.45975e10	0.0142528
$525$	4.33273e10	0.0248911
$526$	−1.45260e12	−0.827390
$527$	2.45740e11	0.138781
$528$	−7.66241e11	−0.429055
$529$	5.42065e11	0.300954
$530$	−1.51081e12	−0.831702
$531$	−1.68308e12	−0.918714
$532$	1.36314e10	0.00737799
$533$	2.89177e12	1.55200
$534$	−8.52015e11	−0.453431
$535$	1.28516e12	0.678213
$536$	2.19571e12	1.14904
$537$	1.02219e12	0.530454
$538$	−1.42344e12	−0.732517
$539$	−1.64706e12	−0.840545
$540$	7.61155e10	0.0385213
$541$	−2.99583e12	−1.50359	−0.751796	−	0.659395i	$-0.770812\pi$
$541$	−2.99583e12	−1.50359	−0.751796	+	0.659395i	$0.770812\pi$
$542$	1.70999e11	0.0851131
$543$	4.33213e10	0.0213846
$544$	4.92875e10	0.0241291
$545$	8.36570e11	0.406180
$546$	9.89958e10	0.0476705
$547$	−2.38362e11	−0.113840	−0.0569199	−	0.998379i	$-0.518128\pi$
$547$	−2.38362e11	−0.113840	−0.0569199	+	0.998379i	$0.518128\pi$
$548$	1.38427e11	0.0655706
$549$	−1.38778e12	−0.651998
$550$	−1.58301e12	−0.737651
$551$	−2.92048e12	−1.34981
$552$	−1.07611e12	−0.493323
$553$	−6.37240e10	−0.0289761
$554$	1.24365e12	0.560923
$555$	−4.42291e11	−0.197874
$556$	2.66591e10	0.0118307
$557$	−3.97940e12	−1.75174	−0.875870	−	0.482548i	$-0.839711\pi$
$557$	−3.97940e12	−1.75174	−0.875870	+	0.482548i	$0.839711\pi$
$558$	2.45086e12	1.07020
$559$	5.29554e11	0.229381
$560$	−6.89389e10	−0.0296222
$561$	−9.84444e10	−0.0419622
$562$	−4.59830e11	−0.194439
$563$	9.04378e11	0.379369	0.189685	−	0.981845i	$-0.439253\pi$
$563$	9.04378e11	0.379369	0.189685	+	0.981845i	$0.439253\pi$
$564$	−1.56101e11	−0.0649606
$565$	−1.14757e12	−0.473764
$566$	5.36078e11	0.219560
$567$	−6.48078e10	−0.0263332
$568$	−2.02254e12	−0.815322
$569$	−1.36290e12	−0.545079	−0.272539	−	0.962145i	$-0.587864\pi$
$569$	−1.36290e12	−0.545079	−0.272539	+	0.962145i	$0.587864\pi$
$570$	5.12447e11	0.203335
$571$	2.48489e12	0.978240	0.489120	−	0.872217i	$-0.337318\pi$
$571$	2.48489e12	0.978240	0.489120	+	0.872217i	$0.337318\pi$
$572$	−3.66234e11	−0.143046
$573$	−2.27011e12	−0.879735
$574$	1.84048e11	0.0707664
$575$	−2.47688e12	−0.944929
$576$	−1.79384e12	−0.679022
$577$	−1.75235e12	−0.658156	−0.329078	−	0.944303i	$-0.606738\pi$
$577$	−1.75235e12	−0.658156	−0.329078	+	0.944303i	$0.606738\pi$
$578$	−2.79770e12	−1.04262
$579$	1.57148e12	0.581107
$580$	−1.70437e11	−0.0625373
$581$	−5.95502e10	−0.0216816
$582$	−1.78666e12	−0.645487
$583$	4.48233e12	1.60693
$584$	−3.12535e12	−1.11184
$585$	−1.38792e12	−0.489964
$586$	1.08274e12	0.379303
$587$	2.44179e12	0.848862	0.424431	−	0.905460i	$-0.360474\pi$
$587$	2.44179e12	0.848862	0.424431	+	0.905460i	$0.360474\pi$
$588$	−1.50270e11	−0.0518411
$589$	3.79515e12	1.29930
$590$	−1.50213e12	−0.510355
$591$	6.78141e11	0.228653
$592$	−3.39857e12	−1.13723
$593$	4.50598e12	1.49638	0.748192	−	0.663482i	$-0.230922\pi$
$593$	4.50598e12	1.49638	0.748192	+	0.663482i	$0.230922\pi$
$594$	−2.23022e12	−0.735036
$595$	−8.85707e9	−0.00289710
$596$	8.17574e9	0.00265411
$597$	−1.07793e12	−0.347301
$598$	−5.65926e12	−1.80969
$599$	−7.19552e11	−0.228371	−0.114186	−	0.993459i	$-0.536426\pi$
$599$	−7.19552e11	−0.228371	−0.114186	+	0.993459i	$0.536426\pi$
$600$	1.13749e12	0.358318
$601$	2.18823e12	0.684160	0.342080	−	0.939671i	$-0.388869\pi$
$601$	2.18823e12	0.684160	0.342080	+	0.939671i	$0.388869\pi$
$602$	3.37037e10	0.0104591
$603$	3.13454e12	0.965485
$604$	−4.27769e11	−0.130781
$605$	3.92361e11	0.119066
$606$	−2.57178e12	−0.774653
$607$	−4.88532e12	−1.46064	−0.730321	−	0.683104i	$-0.760630\pi$
$607$	−4.88532e12	−1.46064	−0.730321	+	0.683104i	$0.760630\pi$
$608$	7.61184e11	0.225904
$609$	−1.36684e11	−0.0402662
$610$	−1.23857e12	−0.362191
$611$	6.46566e12	1.87684
$612$	3.30806e10	0.00953218
$613$	6.65380e11	0.190326	0.0951629	−	0.995462i	$-0.469663\pi$
$613$	6.65380e11	0.190326	0.0951629	+	0.995462i	$0.469663\pi$
$614$	6.02991e12	1.71219
$615$	7.00582e11	0.197479
$616$	1.83582e11	0.0513709
$617$	−5.62159e12	−1.56162	−0.780812	−	0.624767i	$-0.785194\pi$
$617$	−5.62159e12	−1.56162	−0.780812	+	0.624767i	$0.785194\pi$
$618$	−3.11780e11	−0.0859807
$619$	4.24453e12	1.16204	0.581020	−	0.813889i	$-0.302654\pi$
$619$	4.24453e12	1.16204	0.581020	+	0.813889i	$0.302654\pi$
$620$	2.21482e11	0.0601973
$621$	−3.48955e12	−0.941580
$622$	3.43781e12	0.920926
$623$	2.27426e11	0.0604846
$624$	2.89557e12	0.764545
$625$	1.96376e12	0.514788
$626$	4.30538e11	0.112054
$627$	−1.52035e12	−0.392862
$628$	−6.35618e11	−0.163071
$629$	−4.36639e11	−0.111223
$630$	−8.83350e10	−0.0223409
$631$	4.66852e12	1.17232	0.586161	−	0.810194i	$-0.300638\pi$
$631$	4.66852e12	1.17232	0.586161	+	0.810194i	$0.300638\pi$
$632$	−1.67298e12	−0.417123
$633$	1.91096e12	0.473081
$634$	1.85636e11	0.0456310
$635$	3.04334e12	0.742795
$636$	4.08946e11	0.0991081
$637$	6.22414e12	1.49779
$638$	4.99390e12	1.19329
$639$	−2.88732e12	−0.685078
$640$	−1.99527e12	−0.470101
$641$	−3.61791e12	−0.846440	−0.423220	−	0.906027i	$-0.639100\pi$
$641$	−3.61791e12	−0.846440	−0.423220	+	0.906027i	$0.639100\pi$
$642$	−3.43554e12	−0.798155
$643$	−8.06383e12	−1.86034	−0.930169	−	0.367132i	$-0.880340\pi$
$643$	−8.06383e12	−1.86034	−0.930169	+	0.367132i	$0.880340\pi$
$644$	−3.64709e10	−0.00835527
$645$	1.28294e11	0.0291869
$646$	5.05899e11	0.114292
$647$	5.05529e12	1.13417	0.567083	−	0.823661i	$-0.308072\pi$
$647$	5.05529e12	1.13417	0.567083	+	0.823661i	$0.308072\pi$
$648$	−1.70144e12	−0.379077
$649$	4.45657e12	0.986052
$650$	5.98207e12	1.31444
$651$	1.77620e11	0.0387595
$652$	−6.51476e11	−0.141184
$653$	−1.57457e11	−0.0338886	−0.0169443	−	0.999856i	$-0.505394\pi$
$653$	−1.57457e11	−0.0338886	−0.0169443	+	0.999856i	$0.505394\pi$
$654$	−2.23635e12	−0.478013
$655$	−2.46827e11	−0.0523971
$656$	5.38329e12	1.13496
$657$	−4.46165e12	−0.934226
$658$	4.11509e11	0.0855782
$659$	6.64168e11	0.137181	0.0685904	−	0.997645i	$-0.478150\pi$
$659$	6.64168e11	0.137181	0.0685904	+	0.997645i	$0.478150\pi$
$660$	−8.87266e10	−0.0182015
$661$	6.99786e12	1.42580	0.712900	−	0.701265i	$-0.247381\pi$
$661$	6.99786e12	1.42580	0.712900	+	0.701265i	$0.247381\pi$
$662$	6.74603e12	1.36517
$663$	3.72015e11	0.0747737
$664$	−1.56341e12	−0.312115
$665$	−1.36786e11	−0.0271235
$666$	−4.35477e12	−0.857692
$667$	7.81378e12	1.52860
$668$	1.19538e11	0.0232280
$669$	−2.32158e11	−0.0448090
$670$	2.79752e12	0.536336
$671$	3.67466e12	0.699787
$672$	3.56248e10	0.00673894
$673$	−9.28905e12	−1.74543	−0.872717	−	0.488226i	$-0.837644\pi$
$673$	−9.28905e12	−1.74543	−0.872717	+	0.488226i	$0.837644\pi$
$674$	3.42786e12	0.639814
$675$	3.68860e12	0.683902
$676$	7.72264e11	0.142235
$677$	−7.12215e12	−1.30305	−0.651526	−	0.758626i	$-0.725871\pi$
$677$	−7.12215e12	−1.30305	−0.651526	+	0.758626i	$0.725871\pi$
$678$	3.06773e12	0.557549
$679$	4.76908e11	0.0861035
$680$	−2.32530e11	−0.0417050
$681$	1.68863e12	0.300865
$682$	−6.48955e12	−1.14864
$683$	−8.49722e12	−1.49411	−0.747057	−	0.664760i	$-0.768534\pi$
$683$	−8.49722e12	−1.49411	−0.747057	+	0.664760i	$0.768534\pi$
$684$	5.10888e11	0.0892429
$685$	−1.38907e12	−0.241055
$686$	7.93958e11	0.136880
$687$	4.57486e11	0.0783560
$688$	9.85814e11	0.167744
$689$	−1.69384e13	−2.86343
$690$	−1.37106e12	−0.230269
$691$	−1.99151e12	−0.332300	−0.166150	−	0.986100i	$-0.553134\pi$
$691$	−1.99151e12	−0.332300	−0.166150	+	0.986100i	$0.553134\pi$
$692$	−8.70073e11	−0.144238
$693$	2.62076e11	0.0431647
$694$	−4.18462e11	−0.0684761
$695$	−2.67515e11	−0.0434927
$696$	−3.58844e12	−0.579648
$697$	6.91630e11	0.111001
$698$	1.55545e12	0.248032
$699$	−4.32157e12	−0.684690
$700$	3.85513e10	0.00606873
$701$	5.43004e12	0.849321	0.424661	−	0.905353i	$-0.360393\pi$
$701$	5.43004e12	0.849321	0.424661	+	0.905353i	$0.360393\pi$
$702$	8.42785e12	1.30978
$703$	−6.74334e12	−1.04130
$704$	4.74985e12	0.728791
$705$	1.56642e12	0.238813
$706$	6.77769e12	1.02674
$707$	6.86480e11	0.103333
$708$	4.06596e11	0.0608153
$709$	1.00333e13	1.49120	0.745599	−	0.666395i	$-0.232163\pi$
$709$	1.00333e13	1.49120	0.745599	+	0.666395i	$0.232163\pi$
$710$	−2.57688e12	−0.380568
$711$	−2.38830e12	−0.350490
$712$	5.97075e12	0.870701
$713$	−1.01540e13	−1.47141
$714$	2.36770e10	0.00340946
$715$	3.67503e12	0.525877
$716$	9.09514e11	0.129330
$717$	2.75815e12	0.389746
$718$	−1.67599e12	−0.235348
$719$	−6.12483e12	−0.854701	−0.427351	−	0.904086i	$-0.640553\pi$
$719$	−6.12483e12	−0.854701	−0.427351	+	0.904086i	$0.640553\pi$
$720$	−2.58375e12	−0.358306
$721$	8.32229e10	0.0114692
$722$	1.11040e11	0.0152076
$723$	1.17038e12	0.159297
$724$	3.85460e10	0.00521381
$725$	−8.25949e12	−1.11028
$726$	−1.04887e12	−0.140123
$727$	−9.66565e12	−1.28329	−0.641647	−	0.767000i	$-0.721749\pi$
$727$	−9.66565e12	−1.28329	−0.641647	+	0.767000i	$0.721749\pi$
$728$	−6.93743e11	−0.0915393
$729$	4.79991e11	0.0629447
$730$	−3.98195e12	−0.518971
$731$	1.26655e11	0.0164056
$732$	3.35258e11	0.0431598
$733$	−6.58742e12	−0.842845	−0.421423	−	0.906864i	$-0.638469\pi$
$733$	−6.58742e12	−0.842845	−0.421423	+	0.906864i	$0.638469\pi$
$734$	−8.43859e12	−1.07309
$735$	1.50791e12	0.190582
$736$	−2.03656e12	−0.255827
$737$	−8.29982e12	−1.03625
$738$	6.89790e12	0.855979
$739$	−1.58773e13	−1.95829	−0.979147	−	0.203152i	$-0.934882\pi$
$739$	−1.58773e13	−1.95829	−0.979147	+	0.203152i	$0.934882\pi$
$740$	−3.93537e11	−0.0482440
$741$	5.74530e12	0.700052
$742$	−1.07805e12	−0.130564
$743$	9.03557e12	1.08769	0.543846	−	0.839185i	$-0.316968\pi$
$743$	9.03557e12	1.08769	0.543846	+	0.839185i	$0.316968\pi$
$744$	4.66316e12	0.557959
$745$	−8.20407e10	−0.00975722
$746$	1.46447e13	1.73124
$747$	−2.23187e12	−0.262257
$748$	−8.75929e10	−0.0102308
$749$	9.17041e11	0.106468
$750$	3.19862e12	0.369137
$751$	1.57604e13	1.80795	0.903976	−	0.427583i	$-0.140635\pi$
$751$	1.57604e13	1.80795	0.903976	+	0.427583i	$0.140635\pi$
$752$	1.20364e13	1.37251
$753$	−2.56504e12	−0.290748
$754$	−1.88716e13	−2.12636
$755$	4.29252e12	0.480785
$756$	5.43130e10	0.00604722
$757$	−1.06961e12	−0.118384	−0.0591919	−	0.998247i	$-0.518852\pi$
$757$	−1.06961e12	−0.118384	−0.0591919	+	0.998247i	$0.518852\pi$
$758$	−6.36217e12	−0.699994
$759$	4.06771e12	0.444900
$760$	−3.59113e12	−0.390454
$761$	3.35960e12	0.363125	0.181562	−	0.983379i	$-0.441885\pi$
$761$	3.35960e12	0.363125	0.181562	+	0.983379i	$0.441885\pi$
$762$	−8.13557e12	−0.874159
$763$	5.96944e11	0.0637636
$764$	−2.01988e12	−0.214489
$765$	−3.31953e11	−0.0350429
$766$	−5.20734e12	−0.546496
$767$	−1.68411e13	−1.75708
$768$	1.48738e12	0.154276
$769$	−8.70807e12	−0.897952	−0.448976	−	0.893544i	$-0.648211\pi$
$769$	−8.70807e12	−0.897952	−0.448976	+	0.893544i	$0.648211\pi$
$770$	2.33899e11	0.0239784
$771$	4.63739e12	0.472639
$772$	1.39826e12	0.141680
$773$	−5.58286e12	−0.562405	−0.281202	−	0.959649i	$-0.590733\pi$
$773$	−5.58286e12	−0.562405	−0.281202	+	0.959649i	$0.590733\pi$
$774$	1.26318e12	0.126511
$775$	1.07332e13	1.06873
$776$	1.25205e13	1.23950
$777$	−3.15601e11	−0.0310631
$778$	2.05905e12	0.201493
$779$	1.06814e13	1.03922
$780$	3.35292e11	0.0324337
$781$	7.64521e12	0.735292
$782$	−1.35354e12	−0.129431
$783$	−1.16364e13	−1.10634
$784$	1.15868e13	1.09532
$785$	6.37820e12	0.599494
$786$	6.59827e11	0.0616636
$787$	1.08054e13	1.00405	0.502025	−	0.864853i	$-0.332588\pi$
$787$	1.08054e13	1.00405	0.502025	+	0.864853i	$0.332588\pi$
$788$	6.03390e11	0.0557481
$789$	−3.94553e12	−0.362459
$790$	−2.13152e12	−0.194701
$791$	−8.18862e11	−0.0743732
$792$	6.88044e12	0.621374
$793$	−1.38863e13	−1.24697
$794$	−2.24072e13	−2.00077
$795$	−4.10363e12	−0.364348
$796$	−9.59109e11	−0.0846758
$797$	−1.72340e13	−1.51294	−0.756472	−	0.654026i	$-0.773079\pi$
$797$	−1.72340e13	−1.51294	−0.756472	+	0.654026i	$0.773079\pi$
$798$	3.65662e11	0.0319203
$799$	1.54640e12	0.134234
$800$	2.15272e12	0.185816
$801$	8.52367e12	0.731612
$802$	−9.87211e12	−0.842608
$803$	1.18138e13	1.00270
$804$	−7.57235e11	−0.0639114
$805$	3.65973e11	0.0307162
$806$	2.45235e13	2.04680
$807$	−3.86631e12	−0.320897
$808$	1.80226e13	1.48753
$809$	8.74791e12	0.718019	0.359009	−	0.933334i	$-0.383115\pi$
$809$	8.74791e12	0.718019	0.359009	+	0.933334i	$0.383115\pi$
$810$	−2.16777e12	−0.176942
$811$	−1.63936e13	−1.33070	−0.665349	−	0.746532i	$-0.731717\pi$
$811$	−1.63936e13	−1.33070	−0.665349	+	0.746532i	$0.731717\pi$
$812$	−1.21617e11	−0.00981733
$813$	4.64464e11	0.0372859
$814$	1.15308e13	0.920557
$815$	6.53734e12	0.519029
$816$	6.92539e11	0.0546813
$817$	1.95602e12	0.153594
$818$	2.29117e12	0.178923
$819$	−9.90368e11	−0.0769164
$820$	6.23357e11	0.0481476
$821$	−6.80456e12	−0.522704	−0.261352	−	0.965244i	$-0.584168\pi$
$821$	−6.80456e12	−0.522704	−0.261352	+	0.965244i	$0.584168\pi$
$822$	3.71331e12	0.283686
$823$	−1.21597e13	−0.923900	−0.461950	−	0.886906i	$-0.652850\pi$
$823$	−1.21597e13	−0.923900	−0.461950	+	0.886906i	$0.652850\pi$
$824$	2.18490e12	0.165104
$825$	−4.29974e12	−0.323147
$826$	−1.07186e12	−0.0801174
$827$	−6.47949e10	−0.00481688	−0.00240844	−	0.999997i	$-0.500767\pi$
$827$	−6.47949e10	−0.00481688	−0.00240844	+	0.999997i	$0.500767\pi$
$828$	−1.36689e12	−0.101064
$829$	−1.16602e13	−0.857452	−0.428726	−	0.903434i	$-0.641037\pi$
$829$	−1.16602e13	−0.857452	−0.428726	+	0.903434i	$0.641037\pi$
$830$	−1.99191e12	−0.145686
$831$	3.37797e12	0.245726
$832$	−1.79494e13	−1.29865
$833$	1.48864e12	0.107124
$834$	7.15130e11	0.0511844
$835$	−1.19952e12	−0.0853923
$836$	−1.35276e12	−0.0957840
$837$	1.51214e13	1.06495
$838$	−1.62872e12	−0.114090
$839$	−3.85423e12	−0.268540	−0.134270	−	0.990945i	$-0.542869\pi$
$839$	−3.85423e12	−0.268540	−0.134270	+	0.990945i	$0.542869\pi$
$840$	−1.68072e11	−0.0116476
$841$	1.15490e13	0.796089
$842$	−7.44496e12	−0.510456
$843$	−1.24898e12	−0.0851791
$844$	1.70032e12	0.115342
$845$	−7.74941e12	−0.522893
$846$	1.54229e13	1.03514
$847$	2.79973e11	0.0186914
$848$	−3.15324e13	−2.09400
$849$	1.45609e12	0.0961839
$850$	1.43074e12	0.0940106
$851$	1.80419e13	1.17923
$852$	6.97511e11	0.0453495
$853$	1.14995e13	0.743717	0.371858	−	0.928289i	$-0.378721\pi$
$853$	1.14995e13	0.743717	0.371858	+	0.928289i	$0.378721\pi$
$854$	−8.83798e11	−0.0568581
$855$	−5.12659e12	−0.328081
$856$	2.40756e13	1.53266
$857$	4.75467e12	0.301097	0.150549	−	0.988603i	$-0.451896\pi$
$857$	4.75467e12	0.301097	0.150549	+	0.988603i	$0.451896\pi$
$858$	−9.82422e12	−0.618878
$859$	2.09739e13	1.31434	0.657172	−	0.753741i	$-0.271753\pi$
$859$	2.09739e13	1.31434	0.657172	+	0.753741i	$0.271753\pi$
$860$	1.14152e11	0.00711608
$861$	4.99908e11	0.0310010
$862$	−3.75007e12	−0.231343
$863$	−7.42352e12	−0.455576	−0.227788	−	0.973711i	$-0.573149\pi$
$863$	−7.42352e12	−0.455576	−0.227788	+	0.973711i	$0.573149\pi$
$864$	3.03286e12	0.185157
$865$	8.73089e12	0.530256
$866$	−2.61232e13	−1.57833
$867$	−7.59908e12	−0.456746
$868$	1.58041e11	0.00944999
$869$	6.32389e12	0.376180
$870$	−4.57198e12	−0.270562
$871$	3.13644e13	1.84653
$872$	1.56719e13	0.917904
$873$	1.78740e13	1.04149
$874$	−2.09037e13	−1.21177
$875$	−8.53802e11	−0.0492403
$876$	1.07784e12	0.0618421
$877$	8.71674e12	0.497572	0.248786	−	0.968558i	$-0.419968\pi$
$877$	8.71674e12	0.497572	0.248786	+	0.968558i	$0.419968\pi$
$878$	−1.67343e13	−0.950345
$879$	2.94093e12	0.166163
$880$	6.84140e12	0.384568
$881$	7.91000e12	0.442369	0.221185	−	0.975232i	$-0.429008\pi$
$881$	7.91000e12	0.442369	0.221185	+	0.975232i	$0.429008\pi$
$882$	1.48468e13	0.826083
$883$	−1.42391e12	−0.0788244	−0.0394122	−	0.999223i	$-0.512549\pi$
$883$	−1.42391e12	−0.0788244	−0.0394122	+	0.999223i	$0.512549\pi$
$884$	3.31007e11	0.0182307
$885$	−4.08005e12	−0.223574
$886$	1.00970e13	0.550476
$887$	2.10969e13	1.14436	0.572179	−	0.820129i	$-0.306098\pi$
$887$	2.10969e13	1.14436	0.572179	+	0.820129i	$0.306098\pi$
$888$	−8.28566e12	−0.447166
$889$	2.17161e12	0.116607
$890$	7.60724e12	0.406417
$891$	6.43144e12	0.341868
$892$	−2.06567e11	−0.0109249
$893$	2.38823e13	1.25674
$894$	2.19314e11	0.0114828
$895$	−9.12666e12	−0.475454
$896$	−1.42374e12	−0.0737982
$897$	−1.53716e13	−0.792781
$898$	−2.49508e12	−0.128038
$899$	−3.38598e13	−1.72888
$900$	1.44486e12	0.0734063
$901$	−4.05120e12	−0.204796
$902$	−1.82647e13	−0.918718
$903$	9.15455e10	0.00458186
$904$	−2.14980e13	−1.07063
$905$	−3.86795e11	−0.0191674
$906$	−1.14749e13	−0.565812
$907$	−7.10519e12	−0.348613	−0.174306	−	0.984691i	$-0.555768\pi$
$907$	−7.10519e12	−0.348613	−0.174306	+	0.984691i	$0.555768\pi$
$908$	1.50249e12	0.0733541
$909$	2.57285e13	1.24990
$910$	−8.83887e11	−0.0427278
$911$	−2.23287e13	−1.07407	−0.537034	−	0.843561i	$-0.680455\pi$
$911$	−2.23287e13	−1.07407	−0.537034	+	0.843561i	$0.680455\pi$
$912$	1.06954e13	0.511941
$913$	5.90969e12	0.281479
$914$	1.35725e13	0.643283
$915$	−3.36420e12	−0.158667
$916$	4.07057e11	0.0191040
$917$	−1.76126e11	−0.00822550
$918$	2.01570e12	0.0936774
$919$	−2.55522e13	−1.18170	−0.590852	−	0.806780i	$-0.701208\pi$
$919$	−2.55522e13	−1.18170	−0.590852	+	0.806780i	$0.701208\pi$
$920$	9.60810e12	0.442173
$921$	1.63783e13	0.750070
$922$	−3.70493e13	−1.68846
$923$	−2.88907e13	−1.31024
$924$	−6.33118e10	−0.00285733
$925$	−1.90710e13	−0.856517
$926$	2.82969e13	1.26470
$927$	3.11910e12	0.138730
$928$	−6.79117e12	−0.300593
$929$	4.00707e13	1.76505	0.882523	−	0.470270i	$-0.155843\pi$
$929$	4.00707e13	1.76505	0.882523	+	0.470270i	$0.155843\pi$
$930$	5.94126e12	0.260439
$931$	2.29902e13	1.00292
$932$	−3.84520e12	−0.166935
$933$	9.33771e12	0.403435
$934$	1.90124e13	0.817476
$935$	8.78964e11	0.0376114
$936$	−2.60007e13	−1.10724
$937$	5.88813e12	0.249545	0.124773	−	0.992185i	$-0.460180\pi$
$937$	5.88813e12	0.249545	0.124773	+	0.992185i	$0.460180\pi$
$938$	1.99620e12	0.0841961
$939$	1.16942e12	0.0490880
$940$	1.39375e12	0.0582251
$941$	−1.42277e13	−0.591537	−0.295768	−	0.955260i	$-0.595576\pi$
$941$	−1.42277e13	−0.591537	−0.295768	+	0.955260i	$0.595576\pi$
$942$	−1.70504e13	−0.705515
$943$	−2.85781e13	−1.17688
$944$	−3.13512e13	−1.28493
$945$	−5.45012e11	−0.0222312
$946$	−3.34471e12	−0.135784
$947$	−8.76631e12	−0.354195	−0.177097	−	0.984193i	$-0.556671\pi$
$947$	−8.76631e12	−0.354195	−0.177097	+	0.984193i	$0.556671\pi$
$948$	5.76961e11	0.0232011
$949$	−4.46437e13	−1.78674
$950$	2.20960e13	0.880153
$951$	5.04221e11	0.0199898
$952$	−1.65924e11	−0.00654701
$953$	−4.63164e13	−1.81893	−0.909467	−	0.415775i	$-0.863510\pi$
$953$	−4.63164e13	−1.81893	−0.909467	+	0.415775i	$0.863510\pi$
$954$	−4.04041e13	−1.57928
$955$	2.02688e13	0.788520
$956$	2.45412e12	0.0950244
$957$	1.35644e13	0.522752
$958$	−3.18912e13	−1.22328
$959$	−9.91185e11	−0.0378417
$960$	−4.34855e12	−0.165243
$961$	1.75610e13	0.664193
$962$	−4.35742e13	−1.64037
$963$	3.43696e13	1.28782
$964$	1.04137e12	0.0388382
$965$	−1.40310e13	−0.520854
$966$	−9.78332e11	−0.0361484
$967$	−2.72329e12	−0.100155	−0.0500777	−	0.998745i	$-0.515947\pi$
$967$	−2.72329e12	−0.100155	−0.0500777	+	0.998745i	$0.515947\pi$
$968$	7.35030e12	0.269070
$969$	1.37411e12	0.0500686
$970$	1.59522e13	0.578560
$971$	−4.44982e13	−1.60641	−0.803203	−	0.595705i	$-0.796873\pi$
$971$	−4.44982e13	−1.60641	−0.803203	+	0.595705i	$0.796873\pi$
$972$	3.17503e12	0.114091
$973$	−1.90888e11	−0.00682765
$974$	3.18891e13	1.13534
$975$	1.62484e13	0.575825
$976$	−2.58506e13	−0.911897
$977$	−8.92268e12	−0.313307	−0.156653	−	0.987654i	$-0.550071\pi$
$977$	−8.92268e12	−0.313307	−0.156653	+	0.987654i	$0.550071\pi$
$978$	−1.74758e13	−0.610820
$979$	−2.25695e13	−0.785235
$980$	1.34169e12	0.0464660
$981$	2.23727e13	0.771274
$982$	3.47792e13	1.19349
$983$	−2.04743e13	−0.699389	−0.349694	−	0.936864i	$-0.613715\pi$
$983$	−2.04743e13	−0.699389	−0.349694	+	0.936864i	$0.613715\pi$
$984$	1.31244e13	0.446273
$985$	−6.05481e12	−0.204945
$986$	−4.51356e12	−0.152080
$987$	1.11774e12	0.0374897
$988$	5.11199e12	0.170680
$989$	−5.23335e12	−0.173939
$990$	8.76625e12	0.290038
$991$	4.30681e13	1.41848	0.709241	−	0.704966i	$-0.249038\pi$
$991$	4.30681e13	1.41848	0.709241	+	0.704966i	$0.249038\pi$
$992$	8.82509e12	0.289346
$993$	1.83235e13	0.598048
$994$	−1.83876e12	−0.0597429
$995$	9.62433e12	0.311291
$996$	5.39171e11	0.0173604
$997$	1.53746e13	0.492806	0.246403	−	0.969167i	$-0.420751\pi$
$997$	1.53746e13	0.492806	0.246403	+	0.969167i	$0.420751\pi$
$998$	−2.38429e13	−0.760802
$999$	−2.68682e13	−0.853481

Twists

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

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

\(f(q)\)	\(=\)	\(q+23.8680 q^{2} +64.8300 q^{3} +57.6838 q^{4} -578.837 q^{5} +1547.37 q^{6} -413.035 q^{7} -10843.6 q^{8} -15480.1 q^{9} +O(q^{10})\)	\(q+23.8680 q^{2} +64.8300 q^{3} +57.6838 q^{4} -578.837 q^{5} +1547.37 q^{6} -413.035 q^{7} -10843.6 q^{8} -15480.1 q^{9} -13815.7 q^{10} +40989.1 q^{11} +3739.64 q^{12} -154895. q^{13} -9858.34 q^{14} -37526.0 q^{15} -288351. q^{16} -37046.5 q^{17} -369479. q^{18} -572136. q^{19} -33389.5 q^{20} -26777.1 q^{21} +978329. q^{22} +1.53076e6 q^{23} -702993. q^{24} -1.61807e6 q^{25} -3.69704e6 q^{26} -2.27962e6 q^{27} -23825.4 q^{28} +5.10452e6 q^{29} -895673. q^{30} -6.63330e6 q^{31} -1.33042e6 q^{32} +2.65732e6 q^{33} -884227. q^{34} +239080. q^{35} -892949. q^{36} +1.17863e7 q^{37} -1.36558e7 q^{38} -1.00418e7 q^{39} +6.27670e6 q^{40} -1.86693e7 q^{41} -639117. q^{42} -3.41880e6 q^{43} +2.36440e6 q^{44} +8.96043e6 q^{45} +3.65362e7 q^{46} -4.17423e7 q^{47} -1.86938e7 q^{48} -4.01830e7 q^{49} -3.86202e7 q^{50} -2.40172e6 q^{51} -8.93492e6 q^{52} +1.09354e8 q^{53} -5.44101e7 q^{54} -2.37260e7 q^{55} +4.47880e6 q^{56} -3.70916e7 q^{57} +1.21835e8 q^{58} +1.08726e8 q^{59} -2.16464e6 q^{60} +8.96497e7 q^{61} -1.58324e8 q^{62} +6.39381e6 q^{63} +1.15881e8 q^{64} +8.96588e7 q^{65} +6.34251e7 q^{66} -2.02489e8 q^{67} -2.13698e6 q^{68} +9.92390e7 q^{69} +5.70637e6 q^{70} +1.86518e8 q^{71} +1.67860e8 q^{72} +2.88219e8 q^{73} +2.81315e8 q^{74} -1.04900e8 q^{75} -3.30030e7 q^{76} -1.69299e7 q^{77} -2.39679e8 q^{78} +1.54282e8 q^{79} +1.66908e8 q^{80} +1.56906e8 q^{81} -4.45599e8 q^{82} +1.44177e8 q^{83} -1.54460e6 q^{84} +2.14439e7 q^{85} -8.16001e7 q^{86} +3.30926e8 q^{87} -4.44471e8 q^{88} -5.50623e8 q^{89} +2.13868e8 q^{90} +6.39770e7 q^{91} +8.82999e7 q^{92} -4.30037e8 q^{93} -9.96306e8 q^{94} +3.31174e8 q^{95} -8.62514e7 q^{96} -1.15464e9 q^{97} -9.59090e8 q^{98} -6.34514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) \) 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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