LMFDB - Embedded newform 23.18.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,18,Mod(1,23)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 18, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	23.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:	$42.1410800892$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 327680 x^{12} - 2885829 x^{11} + 40317445636 x^{10} + 536194434472 x^{9} + \cdots + 12\!\cdots\!92 $ x^14 - 327680x^12 - 2885829x^11 + 40317445636x^10 + 536194434472x^9 - 2300019484636976x^8 - 30461644509683376x^7 + 60510672631444445504x^6 + 637677963007481584640x^5 - 633979316201323448274944x^4 - 10096979557697212773105664x^3 + 2069146574976541180680732672x^2 + 62007390478567900843052367872x + 124088176545413917176959598592
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{33}\cdot 3^{12} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-262.027$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+524.054 q^{2} +15291.9 q^{3} +143560. q^{4} -1.30350e6 q^{5} +8.01379e6 q^{6} -1.81534e7 q^{7} +6.54461e6 q^{8} +1.04702e8 q^{9} +O(q^{10})$	\(q+524.054 q^{2} +15291.9 q^{3} +143560. q^{4} -1.30350e6 q^{5} +8.01379e6 q^{6} -1.81534e7 q^{7} +6.54461e6 q^{8} +1.04702e8 q^{9} -6.83106e8 q^{10} -5.59490e8 q^{11} +2.19531e9 q^{12} +3.45529e9 q^{13} -9.51334e9 q^{14} -1.99331e10 q^{15} -1.53870e10 q^{16} -1.57446e10 q^{17} +5.48697e10 q^{18} -6.01215e10 q^{19} -1.87132e11 q^{20} -2.77600e11 q^{21} -2.93203e11 q^{22} -7.83110e10 q^{23} +1.00080e11 q^{24} +9.36184e11 q^{25} +1.81076e12 q^{26} -3.73699e11 q^{27} -2.60610e12 q^{28} +1.44599e12 q^{29} -1.04460e13 q^{30} -1.37158e12 q^{31} -8.92144e12 q^{32} -8.55568e12 q^{33} -8.25102e12 q^{34} +2.36630e13 q^{35} +1.50311e13 q^{36} +8.99170e12 q^{37} -3.15069e13 q^{38} +5.28380e13 q^{39} -8.53093e12 q^{40} +7.59867e13 q^{41} -1.45477e14 q^{42} +6.73194e13 q^{43} -8.03207e13 q^{44} -1.36480e14 q^{45} -4.10392e13 q^{46} -7.28641e13 q^{47} -2.35297e14 q^{48} +9.69140e13 q^{49} +4.90611e14 q^{50} -2.40765e14 q^{51} +4.96043e14 q^{52} -4.26060e14 q^{53} -1.95838e14 q^{54} +7.29298e14 q^{55} -1.18807e14 q^{56} -9.19373e14 q^{57} +7.57778e14 q^{58} -1.63669e15 q^{59} -2.86160e15 q^{60} -1.77675e15 q^{61} -7.18780e14 q^{62} -1.90070e15 q^{63} -2.65851e15 q^{64} -4.50398e15 q^{65} -4.48364e15 q^{66} +5.99440e15 q^{67} -2.26030e15 q^{68} -1.19752e15 q^{69} +1.24007e16 q^{70} +9.58476e15 q^{71} +6.85237e14 q^{72} -1.28308e16 q^{73} +4.71214e15 q^{74} +1.43160e16 q^{75} -8.63107e15 q^{76} +1.01566e16 q^{77} +2.76899e16 q^{78} -2.43473e16 q^{79} +2.00570e16 q^{80} -1.92359e16 q^{81} +3.98211e16 q^{82} +2.09989e16 q^{83} -3.98523e16 q^{84} +2.05232e16 q^{85} +3.52790e16 q^{86} +2.21120e16 q^{87} -3.66165e15 q^{88} +3.15326e16 q^{89} -7.15229e16 q^{90} -6.27251e16 q^{91} -1.12424e16 q^{92} -2.09740e16 q^{93} -3.81847e16 q^{94} +7.83686e16 q^{95} -1.36426e17 q^{96} -1.14203e16 q^{97} +5.07882e16 q^{98} -5.85800e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) $ 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9} - 312719540 q^{10} - 45399620 q^{11} - 8621310628 q^{12} - 10510197306 q^{13} - 12286634640 q^{14} - 16443659490 q^{15} + 65383333632 q^{16} - 35705720330 q^{17} + 27658188862 q^{18} - 84895273414 q^{19} + 331348024336 q^{20} + 185190266362 q^{21} + 270540900120 q^{22} - 1096353793934 q^{23} + 1697198124384 q^{24} + 525715171346 q^{25} + 4272672484934 q^{26} - 3706093330604 q^{27} - 9883598189096 q^{28} - 4114009788386 q^{29} - 14194804268004 q^{30} + 3718266369468 q^{31} - 29197309605632 q^{32} - 16110579243626 q^{33} - 31423174598564 q^{34} + 13804822380504 q^{35} + 51950006703548 q^{36} - 58067881808868 q^{37} - 76590705469880 q^{38} + 69866971570764 q^{39} - 129282722434320 q^{40} - 74370388815170 q^{41} - 430581394397552 q^{42} - 127444248270174 q^{43} - 563872902913048 q^{44} - 602432292081270 q^{45} - 749727107945564 q^{47} - 17\!\cdots\!72 q^{48}+ \cdots + 35\!\cdots\!38 q^{99}+O(q^{100}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9 - 312719540 * q^10 - 45399620 * q^11 - 8621310628 * q^12 - 10510197306 * q^13 - 12286634640 * q^14 - 16443659490 * q^15 + 65383333632 * q^16 - 35705720330 * q^17 + 27658188862 * q^18 - 84895273414 * q^19 + 331348024336 * q^20 + 185190266362 * q^21 + 270540900120 * q^22 - 1096353793934 * q^23 + 1697198124384 * q^24 + 525715171346 * q^25 + 4272672484934 * q^26 - 3706093330604 * q^27 - 9883598189096 * q^28 - 4114009788386 * q^29 - 14194804268004 * q^30 + 3718266369468 * q^31 - 29197309605632 * q^32 - 16110579243626 * q^33 - 31423174598564 * q^34 + 13804822380504 * q^35 + 51950006703548 * q^36 - 58067881808868 * q^37 - 76590705469880 * q^38 + 69866971570764 * q^39 - 129282722434320 * q^40 - 74370388815170 * q^41 - 430581394397552 * q^42 - 127444248270174 * q^43 - 563872902913048 * q^44 - 602432292081270 * q^45 - 749727107945564 * q^47 - 1762369490938672 * q^48 - 560241909258462 * q^49 - 1212733967351616 * q^50 - 2013927378521294 * q^51 - 3438555393950964 * q^52 - 1954645162253818 * q^53 - 2748549190422938 * q^54 - 2426218557075404 * q^55 - 1321001371084560 * q^56 - 2335835167092904 * q^57 - 340295461037046 * q^58 - 1561709417167508 * q^59 - 7486616247365616 * q^60 - 679115861109266 * q^61 - 12552327168177062 * q^62 - 10591353756704576 * q^63 - 6775416249353536 * q^64 - 6252697705990982 * q^65 - 20881430274671372 * q^66 - 7577612038827396 * q^67 + 2901964856169680 * q^68 + 833228883389840 * q^69 - 10700966230255240 * q^70 + 25039332312392368 * q^71 - 7954969753997256 * q^72 - 18720848443128734 * q^73 - 6297551300657404 * q^74 + 22553223201966436 * q^75 + 34141945529937952 * q^76 + 35092380107507048 * q^77 + 27963841408286022 * q^78 + 965348846593408 * q^79 + 36943919850262880 * q^80 + 51275234750545798 * q^81 + 106728632435914846 * q^82 + 65089411455584544 * q^83 + 189770883431502392 * q^84 + 20919534362994588 * q^85 + 86205449672049764 * q^86 + 130649890213719716 * q^87 + 164304846335490592 * q^88 - 61322357257717500 * q^89 + 237420523836214152 * q^90 + 181977537844157150 * q^91 - 61586264776507392 * q^92 - 71304974484877430 * q^93 - 14005510384703054 * q^94 + 123323286964112684 * q^95 + 566787465801380768 * q^96 - 67350702995984898 * q^97 + 134333537201072600 * q^98 + 353912447692290838 * 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 $

$2$	524.054	1.44751	0.723754	−	0.690058i	$-0.242415\pi$
$2$	524.054	1.44751	0.723754	+	0.690058i	$0.242415\pi$
$3$	15291.9	1.34565	0.672824	−	0.739803i	$-0.265081\pi$
$3$	15291.9	1.34565	0.672824	+	0.739803i	$0.265081\pi$
$4$	143560.	1.09528
$5$	−1.30350e6	−1.49234	−0.746169	−	0.665756i	$-0.768109\pi$
$5$	−1.30350e6	−1.49234	−0.746169	+	0.665756i	$0.768109\pi$
$6$	8.01379e6	1.94783
$7$	−1.81534e7	−1.19021	−0.595105	−	0.803648i	$-0.702890\pi$
$7$	−1.81534e7	−1.19021	−0.595105	+	0.803648i	$0.702890\pi$
$8$	6.54461e6	0.137917
$9$	1.04702e8	0.810766
$10$	−6.83106e8	−2.16017
$11$	−5.59490e8	−0.786964	−0.393482	−	0.919332i	$-0.628730\pi$
$11$	−5.59490e8	−0.786964	−0.393482	+	0.919332i	$0.628730\pi$
$12$	2.19531e9	1.47386
$13$	3.45529e9	1.17480	0.587402	−	0.809295i	$-0.300151\pi$
$13$	3.45529e9	1.17480	0.587402	+	0.809295i	$0.300151\pi$
$14$	−9.51334e9	−1.72284
$15$	−1.99331e10	−2.00816
$16$	−1.53870e10	−0.895643
$17$	−1.57446e10	−0.547414	−0.273707	−	0.961813i	$-0.588250\pi$
$17$	−1.57446e10	−0.547414	−0.273707	+	0.961813i	$0.588250\pi$
$18$	5.48697e10	1.17359
$19$	−6.01215e10	−0.812127	−0.406064	−	0.913845i	$-0.633099\pi$
$19$	−6.01215e10	−0.812127	−0.406064	+	0.913845i	$0.633099\pi$
$20$	−1.87132e11	−1.63453
$21$	−2.77600e11	−1.60160
$22$	−2.93203e11	−1.13914
$23$	−7.83110e10	−0.208514
$23$	−7.83110e10	−0.208514
$24$	1.00080e11	0.185588
$25$	9.36184e11	1.22707
$26$	1.81076e12	1.70054
$27$	−3.73699e11	−0.254642
$28$	−2.60610e12	−1.30361
$29$	1.44599e12	0.536764	0.268382	−	0.963313i	$-0.413511\pi$
$29$	1.44599e12	0.536764	0.268382	+	0.963313i	$0.413511\pi$
$30$	−1.04460e13	−2.90683
$31$	−1.37158e12	−0.288832	−0.144416	−	0.989517i	$-0.546130\pi$
$31$	−1.37158e12	−0.288832	−0.144416	+	0.989517i	$0.546130\pi$
$32$	−8.92144e12	−1.43437
$33$	−8.55568e12	−1.05898
$34$	−8.25102e12	−0.792386
$35$	2.36630e13	1.77620
$36$	1.50311e13	0.888015
$37$	8.99170e12	0.420850	0.210425	−	0.977610i	$-0.432515\pi$
$37$	8.99170e12	0.420850	0.210425	+	0.977610i	$0.432515\pi$
$38$	−3.15069e13	−1.17556
$39$	5.28380e13	1.58087
$40$	−8.53093e12	−0.205820
$41$	7.59867e13	1.48619	0.743096	−	0.669185i	$-0.233357\pi$
$41$	7.59867e13	1.48619	0.743096	+	0.669185i	$0.233357\pi$
$42$	−1.45477e14	−2.31833
$43$	6.73194e13	0.878331	0.439165	−	0.898406i	$-0.355274\pi$
$43$	6.73194e13	0.878331	0.439165	+	0.898406i	$0.355274\pi$
$44$	−8.03207e13	−0.861945
$45$	−1.36480e14	−1.20994
$46$	−4.10392e13	−0.301826
$47$	−7.28641e13	−0.446356	−0.223178	−	0.974778i	$-0.571643\pi$
$47$	−7.28641e13	−0.446356	−0.223178	+	0.974778i	$0.571643\pi$
$48$	−2.35297e14	−1.20522
$49$	9.69140e13	0.416601
$50$	4.90611e14	1.77620
$51$	−2.40765e14	−0.736626
$52$	4.96043e14	1.28674
$53$	−4.26060e14	−0.939995	−0.469998	−	0.882668i	$-0.655745\pi$
$53$	−4.26060e14	−0.939995	−0.469998	+	0.882668i	$0.655745\pi$
$54$	−1.95838e14	−0.368596
$55$	7.29298e14	1.17442
$56$	−1.18807e14	−0.164151
$57$	−9.19373e14	−1.09284
$58$	7.57778e14	0.776970
$59$	−1.63669e15	−1.45119	−0.725594	−	0.688124i	$-0.758435\pi$
$59$	−1.63669e15	−1.45119	−0.725594	+	0.688124i	$0.758435\pi$
$60$	−2.86160e15	−2.19950
$61$	−1.77675e15	−1.18665	−0.593325	−	0.804963i	$-0.702185\pi$
$61$	−1.77675e15	−1.18665	−0.593325	+	0.804963i	$0.702185\pi$
$62$	−7.18780e14	−0.418087
$63$	−1.90070e15	−0.964982
$64$	−2.65851e15	−1.18062
$65$	−4.50398e15	−1.75321
$66$	−4.48364e15	−1.53288
$67$	5.99440e15	1.80347	0.901737	−	0.432286i	$-0.142293\pi$
$67$	5.99440e15	1.80347	0.901737	+	0.432286i	$0.142293\pi$
$68$	−2.26030e15	−0.599571
$69$	−1.19752e15	−0.280587
$70$	1.24007e16	2.57106
$71$	9.58476e15	1.76151	0.880756	−	0.473571i	$-0.157035\pi$
$71$	9.58476e15	1.76151	0.880756	+	0.473571i	$0.157035\pi$
$72$	6.85237e14	0.111819
$73$	−1.28308e16	−1.86213	−0.931067	−	0.364847i	$-0.881121\pi$
$73$	−1.28308e16	−1.86213	−0.931067	+	0.364847i	$0.881121\pi$
$74$	4.71214e15	0.609184
$75$	1.43160e16	1.65121
$76$	−8.63107e15	−0.889506
$77$	1.01566e16	0.936653
$78$	2.76899e16	2.28833
$79$	−2.43473e16	−1.80559	−0.902797	−	0.430067i	$-0.858490\pi$
$79$	−2.43473e16	−1.80559	−0.902797	+	0.430067i	$0.858490\pi$
$80$	2.00570e16	1.33660
$81$	−1.92359e16	−1.15342
$82$	3.98211e16	2.15127
$83$	2.09989e16	1.02337	0.511685	−	0.859173i	$-0.329022\pi$
$83$	2.09989e16	1.02337	0.511685	+	0.859173i	$0.329022\pi$
$84$	−3.98523e16	−1.75420
$85$	2.05232e16	0.816927
$86$	3.52790e16	1.27139
$87$	2.21120e16	0.722295
$88$	−3.66165e15	−0.108536
$89$	3.15326e16	0.849072	0.424536	−	0.905411i	$-0.360437\pi$
$89$	3.15326e16	0.849072	0.424536	+	0.905411i	$0.360437\pi$
$90$	−7.15229e16	−1.75139
$91$	−6.27251e16	−1.39826
$92$	−1.12424e16	−0.228382
$93$	−2.09740e16	−0.388666
$94$	−3.81847e16	−0.646104
$95$	7.83686e16	1.21197
$96$	−1.36426e17	−1.93015
$97$	−1.14203e16	−0.147951	−0.0739757	−	0.997260i	$-0.523569\pi$
$97$	−1.14203e16	−0.147951	−0.0739757	+	0.997260i	$0.523569\pi$
$98$	5.07882e16	0.603033
$99$	−5.85800e16	−0.638044
$100$	1.34399e17	1.34399
$101$	8.07754e16	0.742245	0.371123	−	0.928584i	$-0.378973\pi$
$101$	8.07754e16	0.742245	0.371123	+	0.928584i	$0.378973\pi$
$102$	−1.26174e17	−1.06627
$103$	2.03477e17	1.58270	0.791349	−	0.611364i	$-0.209379\pi$
$103$	2.03477e17	1.58270	0.791349	+	0.611364i	$0.209379\pi$
$104$	2.26135e16	0.162026
$105$	3.61852e17	2.39013
$106$	−2.23278e17	−1.36065
$107$	−9.20901e16	−0.518144	−0.259072	−	0.965858i	$-0.583417\pi$
$107$	−9.20901e16	−0.518144	−0.259072	+	0.965858i	$0.583417\pi$
$108$	−5.36484e16	−0.278904
$109$	−3.24490e17	−1.55983	−0.779913	−	0.625888i	$-0.784737\pi$
$109$	−3.24490e17	−1.55983	−0.779913	+	0.625888i	$0.784737\pi$
$110$	3.82192e17	1.69998
$111$	1.37500e17	0.566316
$112$	2.79326e17	1.06600
$113$	−2.70970e17	−0.958858	−0.479429	−	0.877581i	$-0.659156\pi$
$113$	−2.70970e17	−0.958858	−0.479429	+	0.877581i	$0.659156\pi$
$114$	−4.81801e17	−1.58189
$115$	1.02079e17	0.311174
$116$	2.07587e17	0.587906
$117$	3.61777e17	0.952492
$118$	−8.57712e17	−2.10060
$119$	2.85817e17	0.651538
$120$	−1.30454e17	−0.276960
$121$	−1.92417e17	−0.380688
$122$	−9.31113e17	−1.71769
$123$	1.16198e18	1.99989
$124$	−1.96904e17	−0.316352
$125$	−2.25825e17	−0.338872
$126$	−9.96070e17	−1.39682
$127$	−9.52747e17	−1.24924	−0.624620	−	0.780929i	$-0.714746\pi$
$127$	−9.52747e17	−1.24924	−0.624620	+	0.780929i	$0.714746\pi$
$128$	−2.23851e17	−0.274583
$129$	1.02944e18	1.18192
$130$	−2.36033e18	−2.53778
$131$	5.78048e17	0.582315	0.291157	−	0.956675i	$-0.405960\pi$
$131$	5.78048e17	0.582315	0.291157	+	0.956675i	$0.405960\pi$
$132$	−1.22826e18	−1.15987
$133$	1.09141e18	0.966602
$134$	3.14139e18	2.61054
$135$	4.87118e17	0.380012
$136$	−1.03042e17	−0.0754979
$137$	−7.38433e17	−0.508378	−0.254189	−	0.967155i	$-0.581808\pi$
$137$	−7.38433e17	−0.508378	−0.254189	+	0.967155i	$0.581808\pi$
$138$	−6.27568e17	−0.406152
$139$	−3.06344e18	−1.86459	−0.932297	−	0.361695i	$-0.882198\pi$
$139$	−3.06344e18	−1.86459	−0.932297	+	0.361695i	$0.882198\pi$
$140$	3.39707e18	1.94543
$141$	−1.11423e18	−0.600638
$142$	5.02293e18	2.54980
$143$	−1.93320e18	−0.924529
$144$	−1.61106e18	−0.726157
$145$	−1.88486e18	−0.801033
$146$	−6.72406e18	−2.69545
$147$	1.48200e18	0.560598
$148$	1.29085e18	0.460948
$149$	6.44333e17	0.217284	0.108642	−	0.994081i	$-0.465350\pi$
$149$	6.44333e17	0.217284	0.108642	+	0.994081i	$0.465350\pi$
$150$	7.50238e18	2.39014
$151$	2.90075e18	0.873385	0.436693	−	0.899611i	$-0.356150\pi$
$151$	2.90075e18	0.873385	0.436693	+	0.899611i	$0.356150\pi$
$152$	−3.93472e17	−0.112007
$153$	−1.64850e18	−0.443825
$154$	5.32262e18	1.35581
$155$	1.78786e18	0.431035
$156$	7.58544e18	1.73150
$157$	4.14316e18	0.895745	0.447872	−	0.894097i	$-0.352182\pi$
$157$	4.14316e18	0.895745	0.447872	+	0.894097i	$0.352182\pi$
$158$	−1.27593e19	−2.61361
$159$	−6.51527e18	−1.26490
$160$	1.16291e19	2.14056
$161$	1.42161e18	0.248176
$162$	−1.00806e19	−1.66959
$163$	−1.10601e19	−1.73846	−0.869228	−	0.494411i	$-0.835384\pi$
$163$	−1.10601e19	−1.73846	−0.869228	+	0.494411i	$0.835384\pi$
$164$	1.09087e19	1.62780
$165$	1.11524e19	1.58035
$166$	1.10045e19	1.48134
$167$	2.41447e17	0.0308839	0.0154419	−	0.999881i	$-0.495084\pi$
$167$	2.41447e17	0.0308839	0.0154419	+	0.999881i	$0.495084\pi$
$168$	−1.81678e18	−0.220889
$169$	3.28859e18	0.380166
$170$	1.07552e19	1.18251
$171$	−6.29487e18	−0.658445
$172$	9.66440e18	0.962018
$173$	−4.21487e18	−0.399385	−0.199693	−	0.979859i	$-0.563994\pi$
$173$	−4.21487e18	−0.399385	−0.199693	+	0.979859i	$0.563994\pi$
$174$	1.15879e19	1.04553
$175$	−1.69949e19	−1.46048
$176$	8.60889e18	0.704839
$177$	−2.50281e19	−1.95279
$178$	1.65248e19	1.22904
$179$	−1.79217e19	−1.27095	−0.635476	−	0.772121i	$-0.719196\pi$
$179$	−1.79217e19	−1.27095	−0.635476	+	0.772121i	$0.719196\pi$
$180$	−1.95931e19	−1.32522
$181$	1.06182e19	0.685146	0.342573	−	0.939491i	$-0.388702\pi$
$181$	1.06182e19	0.685146	0.342573	+	0.939491i	$0.388702\pi$
$182$	−3.28713e19	−2.02400
$183$	−2.71699e19	−1.59681
$184$	−5.12515e17	−0.0287578
$185$	−1.17207e19	−0.628051
$186$	−1.09915e19	−0.562597
$187$	8.80896e18	0.430795
$188$	−1.04604e19	−0.488885
$189$	6.78389e18	0.303077
$190$	4.10694e19	1.75433
$191$	1.68829e19	0.689704	0.344852	−	0.938657i	$-0.387929\pi$
$191$	1.68829e19	0.689704	0.344852	+	0.938657i	$0.387929\pi$
$192$	−4.06537e19	−1.58869
$193$	−1.59330e19	−0.595744	−0.297872	−	0.954606i	$-0.596277\pi$
$193$	−1.59330e19	−0.595744	−0.297872	+	0.954606i	$0.596277\pi$
$194$	−5.98487e18	−0.214161
$195$	−6.88745e19	−2.35920
$196$	1.39130e19	0.456294
$197$	2.57792e19	0.809666	0.404833	−	0.914391i	$-0.367330\pi$
$197$	2.57792e19	0.809666	0.404833	+	0.914391i	$0.367330\pi$
$198$	−3.06991e19	−0.923574
$199$	−1.81428e19	−0.522942	−0.261471	−	0.965211i	$-0.584208\pi$
$199$	−1.81428e19	−0.522942	−0.261471	+	0.965211i	$0.584208\pi$
$200$	6.12696e18	0.169235
$201$	9.16658e19	2.42684
$202$	4.23307e19	1.07441
$203$	−2.62496e19	−0.638862
$204$	−3.45643e19	−0.806811
$205$	−9.90490e19	−2.21790
$206$	1.06633e20	2.29097
$207$	−8.19935e18	−0.169056
$208$	−5.31666e19	−1.05221
$209$	3.36374e19	0.639115
$210$	1.89630e20	3.45974
$211$	9.94751e19	1.74307	0.871533	−	0.490338i	$-0.163127\pi$
$211$	9.94751e19	1.74307	0.871533	+	0.490338i	$0.163127\pi$
$212$	−6.11653e19	−1.02956
$213$	1.46569e20	2.37037
$214$	−4.82602e19	−0.750018
$215$	−8.77511e19	−1.31077
$216$	−2.44572e18	−0.0351196
$217$	2.48987e19	0.343771
$218$	−1.70050e20	−2.25786
$219$	−1.96208e20	−2.50578
$220$	1.04698e20	1.28631
$221$	−5.44021e19	−0.643104
$222$	7.20576e19	0.819746
$223$	1.11884e20	1.22511	0.612555	−	0.790428i	$-0.290142\pi$
$223$	1.11884e20	1.22511	0.612555	+	0.790428i	$0.290142\pi$
$224$	1.61954e20	1.70720
$225$	9.80208e19	0.994871
$226$	−1.42003e20	−1.38795
$227$	6.31622e19	0.594618	0.297309	−	0.954781i	$-0.403911\pi$
$227$	6.31622e19	0.594618	0.297309	+	0.954781i	$0.403911\pi$
$228$	−1.31986e20	−1.19696
$229$	−6.21786e19	−0.543300	−0.271650	−	0.962396i	$-0.587569\pi$
$229$	−6.21786e19	−0.543300	−0.271650	+	0.962396i	$0.587569\pi$
$230$	5.34947e19	0.450427
$231$	1.55314e20	1.26040
$232$	9.46347e18	0.0740291
$233$	2.01576e18	0.0152025	0.00760123	−	0.999971i	$-0.497580\pi$
$233$	2.01576e18	0.0152025	0.00760123	+	0.999971i	$0.497580\pi$
$234$	1.89591e20	1.37874
$235$	9.49786e19	0.666115
$236$	−2.34963e20	−1.58946
$237$	−3.72316e20	−2.42969
$238$	1.49784e20	0.943106
$239$	−1.41034e20	−0.856924	−0.428462	−	0.903560i	$-0.640944\pi$
$239$	−1.41034e20	−0.856924	−0.428462	+	0.903560i	$0.640944\pi$
$240$	3.06711e20	1.79859
$241$	1.15021e20	0.651076	0.325538	−	0.945529i	$-0.394455\pi$
$241$	1.15021e20	0.651076	0.325538	+	0.945529i	$0.394455\pi$
$242$	−1.00837e20	−0.551048
$243$	−2.45894e20	−1.29746
$244$	−2.55071e20	−1.29971
$245$	−1.26328e20	−0.621709
$246$	6.08941e20	2.89486
$247$	−2.07737e20	−0.954091
$248$	−8.97644e18	−0.0398350
$249$	3.21113e20	1.37709
$250$	−1.18344e20	−0.490521
$251$	−4.22416e20	−1.69244	−0.846221	−	0.532832i	$-0.821128\pi$
$251$	−4.22416e20	−1.69244	−0.846221	+	0.532832i	$0.821128\pi$
$252$	−2.72866e20	−1.05693
$253$	4.38143e19	0.164093
$254$	−4.99291e20	−1.80828
$255$	3.13838e20	1.09930
$256$	2.31146e20	0.783155
$257$	1.05271e20	0.345047	0.172523	−	0.985005i	$-0.444808\pi$
$257$	1.05271e20	0.345047	0.172523	+	0.985005i	$0.444808\pi$
$258$	5.39483e20	1.71084
$259$	−1.63230e20	−0.500900
$260$	−6.46594e20	−1.92025
$261$	1.51399e20	0.435190
$262$	3.02928e20	0.842905
$263$	4.78620e20	1.28934	0.644669	−	0.764462i	$-0.276995\pi$
$263$	4.78620e20	1.28934	0.644669	+	0.764462i	$0.276995\pi$
$264$	−5.59936e19	−0.146051
$265$	5.55371e20	1.40279
$266$	5.71956e20	1.39916
$267$	4.82194e20	1.14255
$268$	8.60558e20	1.97531
$269$	−1.52954e20	−0.340148	−0.170074	−	0.985431i	$-0.554401\pi$
$269$	−1.52954e20	−0.340148	−0.170074	+	0.985431i	$0.554401\pi$
$270$	2.55276e20	0.550070
$271$	−3.83627e20	−0.801070	−0.400535	−	0.916281i	$-0.631176\pi$
$271$	−3.83627e20	−0.801070	−0.400535	+	0.916281i	$0.631176\pi$
$272$	2.42263e20	0.490287
$273$	−9.59186e20	−1.88157
$274$	−3.86979e20	−0.735881
$275$	−5.23786e20	−0.965664
$276$	−1.71917e20	−0.307321
$277$	−4.93327e20	−0.855178	−0.427589	−	0.903973i	$-0.640637\pi$
$277$	−4.93327e20	−0.855178	−0.427589	+	0.903973i	$0.640637\pi$
$278$	−1.60541e21	−2.69901
$279$	−1.43607e20	−0.234175
$280$	1.54865e20	0.244969
$281$	−2.56831e20	−0.394134	−0.197067	−	0.980390i	$-0.563142\pi$
$281$	−2.56831e20	−0.394134	−0.197067	+	0.980390i	$0.563142\pi$
$282$	−5.83917e20	−0.869428
$283$	−8.44543e20	−1.22022	−0.610108	−	0.792318i	$-0.708874\pi$
$283$	−8.44543e20	−1.22022	−0.610108	+	0.792318i	$0.708874\pi$
$284$	1.37599e21	1.92935
$285$	1.19841e21	1.63088
$286$	−1.01310e21	−1.33826
$287$	−1.37941e21	−1.76888
$288$	−9.34097e20	−1.16294
$289$	−5.79348e20	−0.700338
$290$	−9.87767e20	−1.15950
$291$	−1.74639e20	−0.199090
$292$	−1.84200e21	−2.03956
$293$	−1.38876e21	−1.49366	−0.746829	−	0.665016i	$-0.768425\pi$
$293$	−1.38876e21	−1.49366	−0.746829	+	0.665016i	$0.768425\pi$
$294$	7.76648e20	0.811469
$295$	2.13343e21	2.16566
$296$	5.88472e19	0.0580426
$297$	2.09081e20	0.200394
$298$	3.37665e20	0.314520
$299$	−2.70587e20	−0.244964
$300$	2.05522e21	1.80854
$301$	−1.22207e21	−1.04540
$302$	1.52015e21	1.26423
$303$	1.23521e21	0.998800
$304$	9.25091e20	0.727376
$305$	2.31600e21	1.77088
$306$	−8.63902e20	−0.642440
$307$	2.18877e21	1.58316	0.791578	−	0.611068i	$-0.209260\pi$
$307$	2.18877e21	1.58316	0.791578	+	0.611068i	$0.209260\pi$
$308$	1.45809e21	1.02590
$309$	3.11155e21	2.12975
$310$	9.36932e20	0.623927
$311$	1.32574e20	0.0859004	0.0429502	−	0.999077i	$-0.486324\pi$
$311$	1.32574e20	0.0859004	0.0429502	+	0.999077i	$0.486324\pi$
$312$	3.45804e20	0.218030
$313$	−2.16148e21	−1.32625	−0.663123	−	0.748511i	$-0.730769\pi$
$313$	−2.16148e21	−1.32625	−0.663123	+	0.748511i	$0.730769\pi$
$314$	2.17124e21	1.29660
$315$	2.47757e21	1.44008
$316$	−3.49531e21	−1.97763
$317$	−1.14666e21	−0.631581	−0.315791	−	0.948829i	$-0.602270\pi$
$317$	−1.14666e21	−0.631581	−0.315791	+	0.948829i	$0.602270\pi$
$318$	−3.41435e21	−1.83096
$319$	−8.09019e20	−0.422414
$320$	3.46538e21	1.76188
$321$	−1.40823e21	−0.697239
$322$	7.44999e20	0.359237
$323$	9.46589e20	0.444570
$324$	−2.76151e21	−1.26332
$325$	3.23478e21	1.44157
$326$	−5.79608e21	−2.51643
$327$	−4.96207e21	−2.09898
$328$	4.97304e20	0.204972
$329$	1.32273e21	0.531258
$330$	5.84444e21	2.28757
$331$	2.48614e21	0.948391	0.474196	−	0.880419i	$-0.342739\pi$
$331$	2.48614e21	0.948391	0.474196	+	0.880419i	$0.342739\pi$
$332$	3.01461e21	1.12088
$333$	9.41454e20	0.341211
$334$	1.26531e20	0.0447047
$335$	−7.81372e21	−2.69139
$336$	4.27143e21	1.43446
$337$	3.37658e21	1.10566	0.552832	−	0.833293i	$-0.313547\pi$
$337$	3.37658e21	1.10566	0.552832	+	0.833293i	$0.313547\pi$
$338$	1.72340e21	0.550293
$339$	−4.14365e21	−1.29028
$340$	2.94631e21	0.894763
$341$	7.67384e20	0.227301
$342$	−3.29885e21	−0.953105
$343$	2.46371e21	0.694368
$344$	4.40579e20	0.121137
$345$	1.56098e21	0.418731
$346$	−2.20882e21	−0.578113
$347$	−2.17131e21	−0.554525	−0.277262	−	0.960794i	$-0.589427\pi$
$347$	−2.17131e21	−0.554525	−0.277262	+	0.960794i	$0.589427\pi$
$348$	3.17441e21	0.791114
$349$	2.57791e21	0.626977	0.313489	−	0.949592i	$-0.398502\pi$
$349$	2.57791e21	0.626977	0.313489	+	0.949592i	$0.398502\pi$
$350$	−8.90623e21	−2.11405
$351$	−1.29124e21	−0.299154
$352$	4.99146e21	1.12880
$353$	−6.43064e21	−1.41961	−0.709806	−	0.704398i	$-0.751217\pi$
$353$	−6.43064e21	−1.41961	−0.709806	+	0.704398i	$0.751217\pi$
$354$	−1.31161e22	−2.82667
$355$	−1.24938e22	−2.62877
$356$	4.52683e21	0.929971
$357$	4.37070e21	0.876740
$358$	−9.39195e21	−1.83971
$359$	7.22575e21	1.38223	0.691115	−	0.722745i	$-0.257120\pi$
$359$	7.22575e21	1.38223	0.691115	+	0.722745i	$0.257120\pi$
$360$	−8.93210e20	−0.166872
$361$	−1.86579e21	−0.340449
$362$	5.56451e21	0.991755
$363$	−2.94243e21	−0.512271
$364$	−9.00484e21	−1.53149
$365$	1.67251e22	2.77894
$366$	−1.42385e22	−2.31140
$367$	3.16314e21	0.501715	0.250858	−	0.968024i	$-0.419287\pi$
$367$	3.16314e21	0.501715	0.250858	+	0.968024i	$0.419287\pi$
$368$	1.20497e21	0.186754
$369$	7.95600e21	1.20495
$370$	−6.14229e21	−0.909109
$371$	7.73442e21	1.11879
$372$	−3.01104e21	−0.425698
$373$	−8.59939e20	−0.118835	−0.0594173	−	0.998233i	$-0.518924\pi$
$373$	−8.59939e20	−0.118835	−0.0594173	+	0.998233i	$0.518924\pi$
$374$	4.61637e21	0.623579
$375$	−3.45329e21	−0.456003
$376$	−4.76867e20	−0.0615603
$377$	4.99632e21	0.630593
$378$	3.55512e21	0.438707
$379$	−5.05576e21	−0.610032	−0.305016	−	0.952347i	$-0.598662\pi$
$379$	−5.05576e21	−0.610032	−0.305016	+	0.952347i	$0.598662\pi$
$380$	1.12506e22	1.32744
$381$	−1.45693e22	−1.68104
$382$	8.84754e21	0.998352
$383$	−3.87748e20	−0.0427918	−0.0213959	−	0.999771i	$-0.506811\pi$
$383$	−3.87748e20	−0.0427918	−0.0213959	+	0.999771i	$0.506811\pi$
$384$	−3.42310e21	−0.369492
$385$	−1.32392e22	−1.39780
$386$	−8.34973e21	−0.862344
$387$	7.04850e21	0.712121
$388$	−1.63951e21	−0.162048
$389$	3.38463e21	0.327295	0.163648	−	0.986519i	$-0.447674\pi$
$389$	3.38463e21	0.327295	0.163648	+	0.986519i	$0.447674\pi$
$390$	−3.60939e22	−3.41496
$391$	1.23298e21	0.114144
$392$	6.34265e20	0.0574565
$393$	8.83946e21	0.783590
$394$	1.35097e22	1.17200
$395$	3.17368e22	2.69456
$396$	−8.40978e21	−0.698836
$397$	−1.16256e20	−0.00945578	−0.00472789	−	0.999989i	$-0.501505\pi$
$397$	−1.16256e20	−0.00945578	−0.00472789	+	0.999989i	$0.501505\pi$
$398$	−9.50781e21	−0.756962
$399$	1.66897e22	1.30071
$400$	−1.44051e22	−1.09902
$401$	1.95106e22	1.45728	0.728642	−	0.684895i	$-0.240152\pi$
$401$	1.95106e22	1.45728	0.728642	+	0.684895i	$0.240152\pi$
$402$	4.80378e22	3.51287
$403$	−4.73919e21	−0.339321
$404$	1.15961e22	0.812966
$405$	2.50740e22	1.72130
$406$	−1.37562e22	−0.924758
$407$	−5.03077e21	−0.331194
$408$	−1.57572e21	−0.101594
$409$	−6.68346e20	−0.0422040	−0.0211020	−	0.999777i	$-0.506717\pi$
$409$	−6.68346e20	−0.0422040	−0.0211020	+	0.999777i	$0.506717\pi$
$410$	−5.19070e22	−3.21043
$411$	−1.12921e22	−0.684097
$412$	2.92112e22	1.73350
$413$	2.97114e22	1.72722
$414$	−4.29690e21	−0.244711
$415$	−2.73721e22	−1.52721
$416$	−3.08262e22	−1.68510
$417$	−4.68459e22	−2.50908
$418$	1.76278e22	0.925124
$419$	1.31071e22	0.674045	0.337023	−	0.941497i	$-0.390580\pi$
$419$	1.31071e22	0.674045	0.337023	+	0.941497i	$0.390580\pi$
$420$	5.19477e22	2.61786
$421$	8.58227e21	0.423842	0.211921	−	0.977287i	$-0.432028\pi$
$421$	8.58227e21	0.423842	0.211921	+	0.977287i	$0.432028\pi$
$422$	5.21303e22	2.52310
$423$	−7.62905e21	−0.361891
$424$	−2.78840e21	−0.129642
$425$	−1.47398e22	−0.671718
$426$	7.68103e22	3.43113
$427$	3.22540e22	1.41236
$428$	−1.32205e22	−0.567513
$429$	−2.95623e22	−1.24409
$430$	−4.59863e22	−1.89735
$431$	−3.19554e22	−1.29267	−0.646335	−	0.763054i	$-0.723699\pi$
$431$	−3.19554e22	−1.29267	−0.646335	+	0.763054i	$0.723699\pi$
$432$	5.75011e21	0.228068
$433$	−3.41309e22	−1.32740	−0.663698	−	0.748001i	$-0.731014\pi$
$433$	−3.41309e22	−1.32740	−0.663698	+	0.748001i	$0.731014\pi$
$434$	1.30483e22	0.497611
$435$	−2.88231e22	−1.07791
$436$	−4.65839e22	−1.70844
$437$	4.70817e21	0.169340
$438$	−1.02824e23	−3.62713
$439$	−8.76326e21	−0.303192	−0.151596	−	0.988443i	$-0.548441\pi$
$439$	−8.76326e21	−0.303192	−0.151596	+	0.988443i	$0.548441\pi$
$440$	4.77298e21	0.161973
$441$	1.01471e22	0.337766
$442$	−2.85096e22	−0.930899
$443$	3.59758e22	1.15234	0.576168	−	0.817331i	$-0.304547\pi$
$443$	3.59758e22	1.15234	0.576168	+	0.817331i	$0.304547\pi$
$444$	1.97396e22	0.620274
$445$	−4.11029e22	−1.26710
$446$	5.86331e22	1.77336
$447$	9.85308e21	0.292387
$448$	4.82609e22	1.40518
$449$	1.66352e22	0.475262	0.237631	−	0.971356i	$-0.423629\pi$
$449$	1.66352e22	0.475262	0.237631	+	0.971356i	$0.423629\pi$
$450$	5.13682e22	1.44008
$451$	−4.25139e22	−1.16958
$452$	−3.89006e22	−1.05022
$453$	4.43580e22	1.17527
$454$	3.31004e22	0.860714
$455$	8.17624e22	2.08668
$456$	−6.01694e21	−0.150721
$457$	−6.69709e22	−1.64664	−0.823319	−	0.567578i	$-0.807880\pi$
$457$	−6.69709e22	−1.64664	−0.823319	+	0.567578i	$0.807880\pi$
$458$	−3.25850e22	−0.786431
$459$	5.88374e21	0.139395
$460$	1.46545e22	0.340823
$461$	−1.29536e22	−0.295756	−0.147878	−	0.989006i	$-0.547244\pi$
$461$	−1.29536e22	−0.295756	−0.147878	+	0.989006i	$0.547244\pi$
$462$	8.13931e22	1.82444
$463$	1.79129e22	0.394209	0.197104	−	0.980383i	$-0.436846\pi$
$463$	1.79129e22	0.394209	0.197104	+	0.980383i	$0.436846\pi$
$464$	−2.22495e22	−0.480749
$465$	2.73397e22	0.580022
$466$	1.05637e21	0.0220057
$467$	−5.00622e22	−1.02404	−0.512020	−	0.858974i	$-0.671103\pi$
$467$	−5.00622e22	−1.02404	−0.512020	+	0.858974i	$0.671103\pi$
$468$	5.19369e22	1.04324
$469$	−1.08818e23	−2.14651
$470$	4.97739e22	0.964206
$471$	6.33568e22	1.20536
$472$	−1.07115e22	−0.200144
$473$	−3.76645e22	−0.691215
$474$	−1.95114e23	−3.51700
$475$	−5.62848e22	−0.996541
$476$	4.10321e22	0.713616
$477$	−4.46095e22	−0.762117
$478$	−7.39095e22	−1.24040
$479$	1.66519e22	0.274544	0.137272	−	0.990533i	$-0.456167\pi$
$479$	1.66519e22	0.274544	0.137272	+	0.990533i	$0.456167\pi$
$480$	1.77832e23	2.88044
$481$	3.10689e22	0.494417
$482$	6.02772e22	0.942438
$483$	2.17391e22	0.333957
$484$	−2.76235e22	−0.416959
$485$	1.48864e22	0.220794
$486$	−1.28862e23	−1.87808
$487$	9.33406e22	1.33682	0.668412	−	0.743791i	$-0.266974\pi$
$487$	9.33406e22	1.33682	0.668412	+	0.743791i	$0.266974\pi$
$488$	−1.16281e22	−0.163660
$489$	−1.69130e23	−2.33935
$490$	−6.62026e22	−0.899929
$491$	−3.93214e21	−0.0525335	−0.0262668	−	0.999655i	$-0.508362\pi$
$491$	−3.93214e21	−0.0525335	−0.0262668	+	0.999655i	$0.508362\pi$
$492$	1.66815e23	2.19044
$493$	−2.27666e22	−0.293832
$494$	−1.08865e23	−1.38105
$495$	7.63593e22	0.952178
$496$	2.11045e22	0.258690
$497$	−1.73996e23	−2.09657
$498$	1.68281e23	1.99336
$499$	−7.63906e22	−0.889581	−0.444790	−	0.895635i	$-0.646722\pi$
$499$	−7.63906e22	−0.889581	−0.444790	+	0.895635i	$0.646722\pi$
$500$	−3.24195e22	−0.371160
$501$	3.69219e21	0.0415588
$502$	−2.21369e23	−2.44982
$503$	5.38972e22	0.586460	0.293230	−	0.956042i	$-0.405270\pi$
$503$	5.38972e22	0.586460	0.293230	+	0.956042i	$0.405270\pi$
$504$	−1.24394e22	−0.133088
$505$	−1.05291e23	−1.10768
$506$	2.29610e22	0.237526
$507$	5.02889e22	0.511569
$508$	−1.36777e23	−1.36827
$509$	−4.56095e22	−0.448698	−0.224349	−	0.974509i	$-0.572026\pi$
$509$	−4.56095e22	−0.448698	−0.224349	+	0.974509i	$0.572026\pi$
$510$	1.64468e23	1.59124
$511$	2.32923e23	2.21633
$512$	1.50474e23	1.40821
$513$	2.24673e22	0.206802
$514$	5.51678e22	0.499458
$515$	−2.65233e23	−2.36192
$516$	1.47787e23	1.29454
$517$	4.07668e22	0.351266
$518$	−8.55411e22	−0.725057
$519$	−6.44534e22	−0.537432
$520$	−2.94768e22	−0.241798
$521$	2.66581e22	0.215134	0.107567	−	0.994198i	$-0.465694\pi$
$521$	2.66581e22	0.215134	0.107567	+	0.994198i	$0.465694\pi$
$522$	7.93413e22	0.629941
$523$	4.11122e22	0.321149	0.160575	−	0.987024i	$-0.448665\pi$
$523$	4.11122e22	0.321149	0.160575	+	0.987024i	$0.448665\pi$
$524$	8.29848e22	0.637797
$525$	−2.59884e23	−1.96529
$526$	2.50822e23	1.86633
$527$	2.15949e22	0.158111
$528$	1.31646e23	0.948464
$529$	6.13261e21	0.0434783
$530$	2.91044e23	2.03055
$531$	−1.71365e23	−1.17657
$532$	1.56683e23	1.05870
$533$	2.62556e23	1.74599
$534$	2.52695e23	1.65385
$535$	1.20040e23	0.773247
$536$	3.92310e22	0.248730
$537$	−2.74057e23	−1.71025
$538$	−8.01563e22	−0.492367
$539$	−5.42225e22	−0.327850
$540$	6.99309e22	0.416219
$541$	2.80103e23	1.64112	0.820561	−	0.571558i	$-0.193661\pi$
$541$	2.80103e23	1.64112	0.820561	+	0.571558i	$0.193661\pi$
$542$	−2.01041e23	−1.15956
$543$	1.62373e23	0.921965
$544$	1.40465e23	0.785193
$545$	4.22974e23	2.32779
$546$	−5.02665e23	−2.72359
$547$	1.24918e23	0.666397	0.333198	−	0.942857i	$-0.391872\pi$
$547$	1.24918e23	0.666397	0.333198	+	0.942857i	$0.391872\pi$
$548$	−1.06010e23	−0.556816
$549$	−1.86030e23	−0.962096
$550$	−2.74492e23	−1.39781
$551$	−8.69353e22	−0.435921
$552$	−7.83734e21	−0.0386978
$553$	4.41985e23	2.14904
$554$	−2.58530e23	−1.23788
$555$	−1.79232e23	−0.845135
$556$	−4.39789e23	−2.04225
$557$	2.27956e23	1.04252	0.521258	−	0.853399i	$-0.325463\pi$
$557$	2.27956e23	1.04252	0.521258	+	0.853399i	$0.325463\pi$
$558$	−7.52580e22	−0.338971
$559$	2.32608e23	1.03187
$560$	−3.64103e23	−1.59084
$561$	1.34706e23	0.579698
$562$	−1.34593e23	−0.570513
$563$	1.26285e23	0.527269	0.263634	−	0.964623i	$-0.415079\pi$
$563$	1.26285e23	0.527269	0.263634	+	0.964623i	$0.415079\pi$
$564$	−1.59960e23	−0.657866
$565$	3.53210e23	1.43094
$566$	−4.42586e23	−1.76627
$567$	3.49196e23	1.37282
$568$	6.27286e22	0.242943
$569$	1.76663e23	0.674050	0.337025	−	0.941496i	$-0.390579\pi$
$569$	1.76663e23	0.674050	0.337025	+	0.941496i	$0.390579\pi$
$570$	6.28029e23	2.36072
$571$	−2.72382e23	−1.00872	−0.504361	−	0.863493i	$-0.668272\pi$
$571$	−2.72382e23	−1.00872	−0.504361	+	0.863493i	$0.668272\pi$
$572$	−2.77531e23	−1.01262
$573$	2.58171e23	0.928098
$574$	−7.22887e23	−2.56047
$575$	−7.33135e22	−0.255863
$576$	−2.78353e23	−0.957203
$577$	−3.59663e23	−1.21871	−0.609357	−	0.792896i	$-0.708572\pi$
$577$	−3.59663e23	−1.21871	−0.609357	+	0.792896i	$0.708572\pi$
$578$	−3.03609e23	−1.01374
$579$	−2.43646e23	−0.801661
$580$	−2.70591e23	−0.877355
$581$	−3.81200e23	−1.21803
$582$	−9.15201e22	−0.288185
$583$	2.38376e23	0.739743
$584$	−8.39730e22	−0.256821
$585$	−4.71578e23	−1.42144
$586$	−7.27783e23	−2.16208
$587$	2.35640e23	0.689963	0.344981	−	0.938610i	$-0.387885\pi$
$587$	2.35640e23	0.689963	0.344981	+	0.938610i	$0.387885\pi$
$588$	2.12757e23	0.614011
$589$	8.24612e22	0.234568
$590$	1.11803e24	3.13481
$591$	3.94213e23	1.08953
$592$	−1.38356e23	−0.376931
$593$	−3.68070e23	−0.988473	−0.494237	−	0.869327i	$-0.664552\pi$
$593$	−3.68070e23	−0.988473	−0.494237	+	0.869327i	$0.664552\pi$
$594$	1.09570e23	0.290072
$595$	−3.72564e23	−0.972315
$596$	9.25007e22	0.237986
$597$	−2.77438e23	−0.703695
$598$	−1.41802e23	−0.354587
$599$	−5.33659e23	−1.31564	−0.657818	−	0.753177i	$-0.728521\pi$
$599$	−5.33659e23	−1.31564	−0.657818	+	0.753177i	$0.728521\pi$
$600$	9.36930e22	0.227731
$601$	−3.48013e23	−0.833994	−0.416997	−	0.908908i	$-0.636917\pi$
$601$	−3.48013e23	−0.833994	−0.416997	+	0.908908i	$0.636917\pi$
$602$	−6.40432e23	−1.51322
$603$	6.27628e23	1.46220
$604$	4.16433e23	0.956601
$605$	2.50817e23	0.568115
$606$	6.47317e23	1.44577
$607$	−9.85331e22	−0.217009	−0.108505	−	0.994096i	$-0.534606\pi$
$607$	−9.85331e22	−0.217009	−0.108505	+	0.994096i	$0.534606\pi$
$608$	5.36371e23	1.16489
$609$	−4.01407e23	−0.859683
$610$	1.21371e24	2.56337
$611$	−2.51766e23	−0.524381
$612$	−2.36659e23	−0.486112
$613$	3.89599e23	0.789231	0.394615	−	0.918846i	$-0.370878\pi$
$613$	3.89599e23	0.789231	0.394615	+	0.918846i	$0.370878\pi$
$614$	1.14703e24	2.29163
$615$	−1.51465e24	−2.98451
$616$	6.64713e22	0.129181
$617$	7.97034e23	1.52775	0.763876	−	0.645363i	$-0.223294\pi$
$617$	7.97034e23	1.52775	0.763876	+	0.645363i	$0.223294\pi$
$618$	1.63062e24	3.08284
$619$	2.42274e22	0.0451790	0.0225895	−	0.999745i	$-0.492809\pi$
$619$	2.42274e22	0.0451790	0.0225895	+	0.999745i	$0.492809\pi$
$620$	2.56665e23	0.472104
$621$	2.92647e22	0.0530965
$622$	6.94760e22	0.124342
$623$	−5.72423e23	−1.01057
$624$	−8.13019e23	−1.41590
$625$	−4.19888e23	−0.721362
$626$	−1.13273e24	−1.91975
$627$	5.14380e23	0.860023
$628$	5.94793e23	0.981091
$629$	−1.41571e23	−0.230379
$630$	1.29838e24	2.08453
$631$	−4.90558e23	−0.777035	−0.388517	−	0.921441i	$-0.627013\pi$
$631$	−4.90558e23	−0.777035	−0.388517	+	0.921441i	$0.627013\pi$
$632$	−1.59344e23	−0.249023
$633$	1.52116e24	2.34555
$634$	−6.00909e23	−0.914219
$635$	1.24191e24	1.86429
$636$	−9.35335e23	−1.38542
$637$	3.34866e23	0.489424
$638$	−4.23970e23	−0.611447
$639$	1.00355e24	1.42817
$640$	2.91790e23	0.409771
$641$	−1.40315e23	−0.194452	−0.0972259	−	0.995262i	$-0.530997\pi$
$641$	−1.40315e23	−0.194452	−0.0972259	+	0.995262i	$0.530997\pi$
$642$	−7.37990e23	−1.00926
$643$	−4.35244e23	−0.587408	−0.293704	−	0.955896i	$-0.594888\pi$
$643$	−4.35244e23	−0.587408	−0.293704	+	0.955896i	$0.594888\pi$
$644$	2.04087e23	0.271822
$645$	−1.34188e24	−1.76383
$646$	4.96064e23	0.643518
$647$	4.96531e23	0.635712	0.317856	−	0.948139i	$-0.397037\pi$
$647$	4.96531e23	0.635712	0.317856	+	0.948139i	$0.397037\pi$
$648$	−1.25891e23	−0.159077
$649$	9.15711e23	1.14203
$650$	1.69520e24	2.08669
$651$	3.80749e23	0.462594
$652$	−1.58779e24	−1.90410
$653$	−1.92470e23	−0.227824	−0.113912	−	0.993491i	$-0.536338\pi$
$653$	−1.92470e23	−0.227824	−0.113912	+	0.993491i	$0.536338\pi$
$654$	−2.60039e24	−3.03828
$655$	−7.53488e23	−0.869011
$656$	−1.16921e24	−1.33110
$657$	−1.34342e24	−1.50976
$658$	6.93181e23	0.769000
$659$	−7.21499e23	−0.790151	−0.395075	−	0.918649i	$-0.629282\pi$
$659$	−7.21499e23	−0.790151	−0.395075	+	0.918649i	$0.629282\pi$
$660$	1.60104e24	1.73093
$661$	−6.07289e23	−0.648161	−0.324081	−	0.946030i	$-0.605055\pi$
$661$	−6.07289e23	−0.648161	−0.324081	+	0.946030i	$0.605055\pi$
$662$	1.30287e24	1.37280
$663$	−8.31913e23	−0.865392
$664$	1.37430e23	0.141141
$665$	−1.42265e24	−1.44250
$666$	4.93372e23	0.493906
$667$	−1.13237e23	−0.111923
$668$	3.46623e22	0.0338265
$669$	1.71092e24	1.64857
$670$	−4.09481e24	−3.89581
$671$	9.94075e23	0.933851
$672$	2.47659e24	2.29729
$673$	1.42497e24	1.30520	0.652601	−	0.757702i	$-0.273678\pi$
$673$	1.42497e24	1.30520	0.652601	+	0.757702i	$0.273678\pi$
$674$	1.76951e24	1.60046
$675$	−3.49851e23	−0.312465
$676$	4.72112e23	0.416388
$677$	1.80897e24	1.57553	0.787766	−	0.615975i	$-0.211238\pi$
$677$	1.80897e24	1.57553	0.787766	+	0.615975i	$0.211238\pi$
$678$	−2.17149e24	−1.86770
$679$	2.07317e23	0.176093
$680$	1.34316e23	0.112668
$681$	9.65871e23	0.800145
$682$	4.02150e23	0.329019
$683$	−3.87521e23	−0.313126	−0.156563	−	0.987668i	$-0.550041\pi$
$683$	−3.87521e23	−0.313126	−0.156563	+	0.987668i	$0.550041\pi$
$684$	−9.03694e23	−0.721182
$685$	9.62551e23	0.758672
$686$	1.29112e24	1.00510
$687$	−9.50830e23	−0.731090
$688$	−1.03584e24	−0.786671
$689$	−1.47216e24	−1.10431
$690$	8.18037e23	0.606116
$691$	1.32822e24	0.972093	0.486046	−	0.873933i	$-0.338439\pi$
$691$	1.32822e24	0.972093	0.486046	+	0.873933i	$0.338439\pi$
$692$	−6.05088e23	−0.437438
$693$	1.06342e24	0.759406
$694$	−1.13788e24	−0.802679
$695$	3.99321e24	2.78260
$696$	1.44715e23	0.0996170
$697$	−1.19638e24	−0.813562
$698$	1.35096e24	0.907555
$699$	3.08248e22	0.0204571
$700$	−2.43979e24	−1.59963
$701$	−9.28365e23	−0.601334	−0.300667	−	0.953729i	$-0.597209\pi$
$701$	−9.28365e23	−0.601334	−0.300667	+	0.953729i	$0.597209\pi$
$702$	−6.76678e23	−0.433028
$703$	−5.40595e23	−0.341784
$704$	1.48741e24	0.929102
$705$	1.45240e24	0.896355
$706$	−3.37000e24	−2.05490
$707$	−1.46634e24	−0.883428
$708$	−3.59304e24	−2.13885
$709$	−5.39646e23	−0.317407	−0.158703	−	0.987326i	$-0.550731\pi$
$709$	−5.39646e23	−0.317407	−0.158703	+	0.987326i	$0.550731\pi$
$710$	−6.54741e24	−3.80517
$711$	−2.54922e24	−1.46391
$712$	2.06369e23	0.117102
$713$	1.07409e23	0.0602257
$714$	2.29048e24	1.26909
$715$	2.51993e24	1.37971
$716$	−2.57285e24	−1.39205
$717$	−2.15668e24	−1.15312
$718$	3.78668e24	2.00079
$719$	2.87270e24	1.50001	0.750006	−	0.661431i	$-0.230051\pi$
$719$	2.87270e24	1.50001	0.750006	+	0.661431i	$0.230051\pi$
$720$	2.10002e24	1.08367
$721$	−3.69379e24	−1.88374
$722$	−9.77776e23	−0.492803
$723$	1.75889e24	0.876119
$724$	1.52435e24	0.750427
$725$	1.35372e24	0.658649
$726$	−1.54199e24	−0.741517
$727$	−2.86324e24	−1.36086	−0.680432	−	0.732811i	$-0.738208\pi$
$727$	−2.86324e24	−1.36086	−0.680432	+	0.732811i	$0.738208\pi$
$728$	−4.10511e23	−0.192845
$729$	−1.27606e24	−0.592499
$730$	8.76484e24	4.02253
$731$	−1.05992e24	−0.480811
$732$	−3.90052e24	−1.74896
$733$	1.42544e24	0.631780	0.315890	−	0.948796i	$-0.397697\pi$
$733$	1.42544e24	0.631780	0.315890	+	0.948796i	$0.397697\pi$
$734$	1.65766e24	0.726237
$735$	−1.93179e24	−0.836601
$736$	6.98647e23	0.299086
$737$	−3.35381e24	−1.41927
$738$	4.16937e24	1.74418
$739$	3.93128e24	1.62576	0.812880	−	0.582431i	$-0.197898\pi$
$739$	3.93128e24	1.62576	0.812880	+	0.582431i	$0.197898\pi$
$740$	−1.68263e24	−0.687891
$741$	−3.17670e24	−1.28387
$742$	4.05325e24	1.61946
$743$	3.04650e24	1.20336	0.601681	−	0.798737i	$-0.294498\pi$
$743$	3.04650e24	1.20336	0.601681	+	0.798737i	$0.294498\pi$
$744$	−1.37267e23	−0.0536038
$745$	−8.39890e23	−0.324261
$746$	−4.50654e23	−0.172014
$747$	2.19864e24	0.829714
$748$	1.26462e24	0.471841
$749$	1.67174e24	0.616701
$750$	−1.80971e24	−0.660068
$751$	2.72854e24	0.983992	0.491996	−	0.870598i	$-0.336268\pi$
$751$	2.72854e24	0.983992	0.491996	+	0.870598i	$0.336268\pi$
$752$	1.12116e24	0.399776
$753$	−6.45955e24	−2.27743
$754$	2.61834e24	0.912788
$755$	−3.78114e24	−1.30339
$756$	9.73898e23	0.331954
$757$	−1.94273e24	−0.654784	−0.327392	−	0.944889i	$-0.606170\pi$
$757$	−1.94273e24	−0.654784	−0.327392	+	0.944889i	$0.606170\pi$
$758$	−2.64949e24	−0.883027
$759$	6.70004e23	0.220812
$760$	5.12892e23	0.167152
$761$	5.15562e24	1.66154	0.830772	−	0.556613i	$-0.187900\pi$
$761$	5.15562e24	1.66154	0.830772	+	0.556613i	$0.187900\pi$
$762$	−7.63511e24	−2.43331
$763$	5.89058e24	1.85652
$764$	2.42371e24	0.755419
$765$	2.14883e24	0.662337
$766$	−2.03201e23	−0.0619415
$767$	−5.65522e24	−1.70486
$768$	3.53467e24	1.05385
$769$	8.67845e23	0.255899	0.127949	−	0.991781i	$-0.459160\pi$
$769$	8.67845e23	0.255899	0.127949	+	0.991781i	$0.459160\pi$
$770$	−6.93806e24	−2.02333
$771$	1.60980e24	0.464311
$772$	−2.28734e24	−0.652506
$773$	1.93074e24	0.544750	0.272375	−	0.962191i	$-0.412191\pi$
$773$	1.93074e24	0.544750	0.272375	+	0.962191i	$0.412191\pi$
$774$	3.69380e24	1.03080
$775$	−1.28405e24	−0.354419
$776$	−7.47417e22	−0.0204051
$777$	−2.49609e24	−0.674035
$778$	1.77373e24	0.473762
$779$	−4.56844e24	−1.20698
$780$	−9.88765e24	−2.58398
$781$	−5.36258e24	−1.38625
$782$	6.46146e23	0.165224
$783$	−5.40366e23	−0.136683
$784$	−1.49122e24	−0.373125
$785$	−5.40062e24	−1.33675
$786$	4.63235e24	1.13425
$787$	−8.11626e24	−1.96594	−0.982971	−	0.183761i	$-0.941173\pi$
$787$	−8.11626e24	−1.96594	−0.982971	+	0.183761i	$0.941173\pi$
$788$	3.70087e24	0.886811
$789$	7.31901e24	1.73499
$790$	1.66318e25	3.90039
$791$	4.91901e24	1.14124
$792$	−3.83384e23	−0.0879974
$793$	−6.13918e24	−1.39408
$794$	−6.09246e22	−0.0136873
$795$	8.49268e24	1.88766
$796$	−2.60459e24	−0.572767
$797$	3.06633e24	0.667149	0.333575	−	0.942724i	$-0.391745\pi$
$797$	3.06633e24	0.667149	0.333575	+	0.942724i	$0.391745\pi$
$798$	8.74630e24	1.88278
$799$	1.14722e24	0.244342
$800$	−8.35211e24	−1.76008
$801$	3.30154e24	0.688399
$802$	1.02246e25	2.10943
$803$	7.17874e24	1.46543
$804$	1.31596e25	2.65807
$805$	−1.85307e24	−0.370363
$806$	−2.48359e24	−0.491170
$807$	−2.33897e24	−0.457719
$808$	5.28644e23	0.102369
$809$	−7.79280e24	−1.49324	−0.746622	−	0.665248i	$-0.768326\pi$
$809$	−7.79280e24	−1.49324	−0.746622	+	0.665248i	$0.768326\pi$
$810$	1.31401e25	2.49160
$811$	−2.32125e24	−0.435556	−0.217778	−	0.975998i	$-0.569881\pi$
$811$	−2.32125e24	−0.435556	−0.217778	+	0.975998i	$0.569881\pi$
$812$	−3.76841e24	−0.699732
$813$	−5.86639e24	−1.07796
$814$	−2.63640e24	−0.479406
$815$	1.44169e25	2.59437
$816$	3.70466e24	0.659754
$817$	−4.04734e24	−0.713316
$818$	−3.50249e23	−0.0610906
$819$	−6.56747e24	−1.13367
$820$	−1.42195e25	−2.42922
$821$	4.94756e24	0.836517	0.418258	−	0.908328i	$-0.362641\pi$
$821$	4.94756e24	0.836517	0.418258	+	0.908328i	$0.362641\pi$
$822$	−5.91765e24	−0.990236
$823$	1.09739e25	1.81746	0.908729	−	0.417387i	$-0.137054\pi$
$823$	1.09739e25	1.81746	0.908729	+	0.417387i	$0.137054\pi$
$824$	1.33168e24	0.218282
$825$	−8.00969e24	−1.29944
$826$	1.55704e25	2.50016
$827$	−4.19184e23	−0.0666205	−0.0333103	−	0.999445i	$-0.510605\pi$
$827$	−4.19184e23	−0.0666205	−0.0333103	+	0.999445i	$0.510605\pi$
$828$	−1.17710e24	−0.185164
$829$	−1.12207e25	−1.74706	−0.873529	−	0.486772i	$-0.838174\pi$
$829$	−1.12207e25	−1.74706	−0.873529	+	0.486772i	$0.838174\pi$
$830$	−1.43445e25	−2.21065
$831$	−7.54391e24	−1.15077
$832$	−9.18591e24	−1.38699
$833$	−1.52587e24	−0.228053
$834$	−2.45498e25	−3.63192
$835$	−3.14727e23	−0.0460892
$836$	4.82900e24	0.700009
$837$	5.12557e23	0.0735488
$838$	6.86885e24	0.975686
$839$	2.74415e24	0.385861	0.192931	−	0.981212i	$-0.438201\pi$
$839$	2.74415e24	0.385861	0.192931	+	0.981212i	$0.438201\pi$
$840$	2.36818e24	0.329641
$841$	−5.16625e24	−0.711885
$842$	4.49757e24	0.613515
$843$	−3.92744e24	−0.530366
$844$	1.42807e25	1.90914
$845$	−4.28669e24	−0.567336
$846$	−3.99803e24	−0.523839
$847$	3.49302e24	0.453098
$848$	6.55579e24	0.841900
$849$	−1.29147e25	−1.64198
$850$	−7.72447e24	−0.972317
$851$	−7.04149e23	−0.0877533
$852$	2.10416e25	2.59622
$853$	−4.52238e24	−0.552460	−0.276230	−	0.961092i	$-0.589085\pi$
$853$	−4.52238e24	−0.552460	−0.276230	+	0.961092i	$0.589085\pi$
$854$	1.69028e25	2.04441
$855$	8.20539e24	0.982624
$856$	−6.02694e23	−0.0714611
$857$	−6.58054e24	−0.772546	−0.386273	−	0.922384i	$-0.626238\pi$
$857$	−6.58054e24	−0.772546	−0.386273	+	0.922384i	$0.626238\pi$
$858$	−1.54923e25	−1.80083
$859$	−9.56361e23	−0.110073	−0.0550364	−	0.998484i	$-0.517527\pi$
$859$	−9.56361e23	−0.110073	−0.0550364	+	0.998484i	$0.517527\pi$
$860$	−1.25976e25	−1.43566
$861$	−2.10939e25	−2.38029
$862$	−1.67463e25	−1.87115
$863$	1.49049e25	1.64906	0.824529	−	0.565820i	$-0.191440\pi$
$863$	1.49049e25	1.64906	0.824529	+	0.565820i	$0.191440\pi$
$864$	3.33393e24	0.365250
$865$	5.49410e24	0.596018
$866$	−1.78864e25	−1.92142
$867$	−8.85934e24	−0.942408
$868$	3.57447e24	0.376525
$869$	1.36221e25	1.42094
$870$	−1.51049e25	−1.56028
$871$	2.07124e25	2.11873
$872$	−2.12366e24	−0.215127
$873$	−1.19574e24	−0.119954
$874$	2.46734e24	0.245121
$875$	4.09948e24	0.403330
$876$	−2.81677e25	−2.74452
$877$	8.40590e24	0.811125	0.405562	−	0.914067i	$-0.367076\pi$
$877$	8.40590e24	0.811125	0.405562	+	0.914067i	$0.367076\pi$
$878$	−4.59242e24	−0.438872
$879$	−2.12367e25	−2.00994
$880$	−1.12217e25	−1.05186
$881$	−1.27421e25	−1.18289	−0.591446	−	0.806345i	$-0.701443\pi$
$881$	−1.27421e25	−1.18289	−0.591446	+	0.806345i	$0.701443\pi$
$882$	5.31765e24	0.488919
$883$	3.18563e24	0.290087	0.145044	−	0.989425i	$-0.453668\pi$
$883$	3.18563e24	0.290087	0.145044	+	0.989425i	$0.453668\pi$
$884$	−7.80999e24	−0.704379
$885$	3.26242e25	2.91422
$886$	1.88533e25	1.66802
$887$	−2.52965e24	−0.221671	−0.110836	−	0.993839i	$-0.535353\pi$
$887$	−2.52965e24	−0.221671	−0.110836	+	0.993839i	$0.535353\pi$
$888$	8.99887e23	0.0781048
$889$	1.72956e25	1.48686
$890$	−2.15401e25	−1.83414
$891$	1.07623e25	0.907703
$892$	1.60621e25	1.34184
$893$	4.38070e24	0.362498
$894$	5.16354e24	0.423233
$895$	2.33610e25	1.89669
$896$	4.06364e24	0.326811
$897$	−4.13779e24	−0.329635
$898$	8.71772e24	0.687945
$899$	−1.98329e24	−0.155035
$900$	1.40719e25	1.08966
$901$	6.70814e24	0.514567
$902$	−2.22795e25	−1.69298
$903$	−1.86878e25	−1.40674
$904$	−1.77339e24	−0.132243
$905$	−1.38409e25	−1.02247
$906$	2.32460e25	1.70121
$907$	8.47187e24	0.614211	0.307105	−	0.951676i	$-0.400640\pi$
$907$	8.47187e24	0.614211	0.307105	+	0.951676i	$0.400640\pi$
$908$	9.06760e24	0.651272
$909$	8.45738e24	0.601787
$910$	4.28479e25	3.02049
$911$	1.51883e25	1.06072	0.530362	−	0.847771i	$-0.322056\pi$
$911$	1.51883e25	1.06072	0.530362	+	0.847771i	$0.322056\pi$
$912$	1.41464e25	0.978791
$913$	−1.17487e25	−0.805355
$914$	−3.50964e25	−2.38352
$915$	3.54161e25	2.38299
$916$	−8.92639e24	−0.595065
$917$	−1.04935e25	−0.693077
$918$	3.08340e24	0.201775
$919$	−1.89943e25	−1.23152	−0.615760	−	0.787934i	$-0.711151\pi$
$919$	−1.89943e25	−1.23152	−0.615760	+	0.787934i	$0.711151\pi$
$920$	6.68066e23	0.0429163
$921$	3.34705e25	2.13037
$922$	−6.78840e24	−0.428109
$923$	3.31181e25	2.06943
$924$	2.22970e25	1.38049
$925$	8.41789e24	0.516414
$926$	9.38730e24	0.570620
$927$	2.13045e25	1.28320
$928$	−1.29003e25	−0.769917
$929$	−1.31747e25	−0.779125	−0.389563	−	0.921000i	$-0.627374\pi$
$929$	−1.31747e25	−0.779125	−0.389563	+	0.921000i	$0.627374\pi$
$930$	1.43275e25	0.839586
$931$	−5.82662e24	−0.338333
$932$	2.89384e23	0.0166509
$933$	2.02731e24	0.115592
$934$	−2.62353e25	−1.48231
$935$	−1.14825e25	−0.642892
$936$	2.36769e24	0.131365
$937$	2.02324e25	1.11240	0.556199	−	0.831049i	$-0.312259\pi$
$937$	2.02324e25	1.11240	0.556199	+	0.831049i	$0.312259\pi$
$938$	−5.70267e25	−3.10709
$939$	−3.30531e25	−1.78466
$940$	1.36352e25	0.729582
$941$	−2.54277e25	−1.34833	−0.674164	−	0.738582i	$-0.735496\pi$
$941$	−2.54277e25	−1.34833	−0.674164	+	0.738582i	$0.735496\pi$
$942$	3.32024e25	1.74476
$943$	−5.95060e24	−0.309892
$944$	2.51837e25	1.29975
$945$	−8.84283e24	−0.452294
$946$	−1.97382e25	−1.00054
$947$	−1.24100e25	−0.623442	−0.311721	−	0.950174i	$-0.600905\pi$
$947$	−1.24100e25	−0.623442	−0.311721	+	0.950174i	$0.600905\pi$
$948$	−5.34499e25	−2.66119
$949$	−4.43343e25	−2.18764
$950$	−2.94962e25	−1.44250
$951$	−1.75346e25	−0.849885
$952$	1.87057e24	0.0898584
$953$	4.05223e25	1.92932	0.964660	−	0.263499i	$-0.0848765\pi$
$953$	4.05223e25	1.92932	0.964660	+	0.263499i	$0.0848765\pi$
$954$	−2.33778e25	−1.10317
$955$	−2.20069e25	−1.02927
$956$	−2.02469e25	−0.938571
$957$	−1.23715e25	−0.568420
$958$	8.72650e24	0.397405
$959$	1.34050e25	0.605076
$960$	5.29923e25	2.37087
$961$	−2.06689e25	−0.916576
$962$	1.62818e25	0.715672
$963$	−9.64206e24	−0.420094
$964$	1.65125e25	0.713110
$965$	2.07687e25	0.889051
$966$	1.13925e25	0.483406
$967$	−3.21865e25	−1.35378	−0.676891	−	0.736084i	$-0.736673\pi$
$967$	−3.21865e25	−1.35378	−0.676891	+	0.736084i	$0.736673\pi$
$968$	−1.25930e24	−0.0525035
$969$	1.44752e25	0.598234
$970$	7.80130e24	0.319600
$971$	−7.52369e24	−0.305540	−0.152770	−	0.988262i	$-0.548819\pi$
$971$	−7.52369e24	−0.305540	−0.152770	+	0.988262i	$0.548819\pi$
$972$	−3.53006e25	−1.42108
$973$	5.56118e25	2.21926
$974$	4.89155e25	1.93506
$975$	4.94660e25	1.93985
$976$	2.73389e25	1.06281
$977$	3.36116e25	1.29534	0.647672	−	0.761920i	$-0.275743\pi$
$977$	3.36116e25	1.29534	0.647672	+	0.761920i	$0.275743\pi$
$978$	−8.86332e25	−3.38623
$979$	−1.76422e25	−0.668189
$980$	−1.81357e25	−0.680945
$981$	−3.39749e25	−1.26465
$982$	−2.06065e24	−0.0760427
$983$	4.36395e24	0.159652	0.0798261	−	0.996809i	$-0.474563\pi$
$983$	4.36395e24	0.159652	0.0798261	+	0.996809i	$0.474563\pi$
$984$	7.60473e24	0.275820
$985$	−3.36033e25	−1.20830
$986$	−1.19309e25	−0.425324
$987$	2.02270e25	0.714886
$988$	−2.98228e25	−1.04500
$989$	−5.27185e24	−0.183145
$990$	4.00164e25	1.37828
$991$	−4.13883e24	−0.141336	−0.0706678	−	0.997500i	$-0.522513\pi$
$991$	−4.13883e24	−0.141336	−0.0706678	+	0.997500i	$0.522513\pi$
$992$	1.22364e25	0.414291
$993$	3.80178e25	1.27620
$994$	−9.11831e25	−3.03480
$995$	2.36492e25	0.780406
$996$	4.60992e25	1.50830
$997$	4.44107e24	0.144072	0.0720358	−	0.997402i	$-0.477050\pi$
$997$	4.44107e24	0.144072	0.0720358	+	0.997402i	$0.477050\pi$
$998$	−4.00328e25	−1.28767
$999$	−3.36019e24	−0.107166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.18.a.a.1.12	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.18.a.a.1.12	✓	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q+524.054 q^{2} +15291.9 q^{3} +143560. q^{4} -1.30350e6 q^{5} +8.01379e6 q^{6} -1.81534e7 q^{7} +6.54461e6 q^{8} +1.04702e8 q^{9} +O(q^{10})\)	\(q+524.054 q^{2} +15291.9 q^{3} +143560. q^{4} -1.30350e6 q^{5} +8.01379e6 q^{6} -1.81534e7 q^{7} +6.54461e6 q^{8} +1.04702e8 q^{9} -6.83106e8 q^{10} -5.59490e8 q^{11} +2.19531e9 q^{12} +3.45529e9 q^{13} -9.51334e9 q^{14} -1.99331e10 q^{15} -1.53870e10 q^{16} -1.57446e10 q^{17} +5.48697e10 q^{18} -6.01215e10 q^{19} -1.87132e11 q^{20} -2.77600e11 q^{21} -2.93203e11 q^{22} -7.83110e10 q^{23} +1.00080e11 q^{24} +9.36184e11 q^{25} +1.81076e12 q^{26} -3.73699e11 q^{27} -2.60610e12 q^{28} +1.44599e12 q^{29} -1.04460e13 q^{30} -1.37158e12 q^{31} -8.92144e12 q^{32} -8.55568e12 q^{33} -8.25102e12 q^{34} +2.36630e13 q^{35} +1.50311e13 q^{36} +8.99170e12 q^{37} -3.15069e13 q^{38} +5.28380e13 q^{39} -8.53093e12 q^{40} +7.59867e13 q^{41} -1.45477e14 q^{42} +6.73194e13 q^{43} -8.03207e13 q^{44} -1.36480e14 q^{45} -4.10392e13 q^{46} -7.28641e13 q^{47} -2.35297e14 q^{48} +9.69140e13 q^{49} +4.90611e14 q^{50} -2.40765e14 q^{51} +4.96043e14 q^{52} -4.26060e14 q^{53} -1.95838e14 q^{54} +7.29298e14 q^{55} -1.18807e14 q^{56} -9.19373e14 q^{57} +7.57778e14 q^{58} -1.63669e15 q^{59} -2.86160e15 q^{60} -1.77675e15 q^{61} -7.18780e14 q^{62} -1.90070e15 q^{63} -2.65851e15 q^{64} -4.50398e15 q^{65} -4.48364e15 q^{66} +5.99440e15 q^{67} -2.26030e15 q^{68} -1.19752e15 q^{69} +1.24007e16 q^{70} +9.58476e15 q^{71} +6.85237e14 q^{72} -1.28308e16 q^{73} +4.71214e15 q^{74} +1.43160e16 q^{75} -8.63107e15 q^{76} +1.01566e16 q^{77} +2.76899e16 q^{78} -2.43473e16 q^{79} +2.00570e16 q^{80} -1.92359e16 q^{81} +3.98211e16 q^{82} +2.09989e16 q^{83} -3.98523e16 q^{84} +2.05232e16 q^{85} +3.52790e16 q^{86} +2.21120e16 q^{87} -3.66165e15 q^{88} +3.15326e16 q^{89} -7.15229e16 q^{90} -6.27251e16 q^{91} -1.12424e16 q^{92} -2.09740e16 q^{93} -3.81847e16 q^{94} +7.83686e16 q^{95} -1.36426e17 q^{96} -1.14203e16 q^{97} +5.07882e16 q^{98} -5.85800e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9} - 312719540 q^{10} - 45399620 q^{11} - 8621310628 q^{12} - 10510197306 q^{13} - 12286634640 q^{14} - 16443659490 q^{15} + 65383333632 q^{16} - 35705720330 q^{17} + 27658188862 q^{18} - 84895273414 q^{19} + 331348024336 q^{20} + 185190266362 q^{21} + 270540900120 q^{22} - 1096353793934 q^{23} + 1697198124384 q^{24} + 525715171346 q^{25} + 4272672484934 q^{26} - 3706093330604 q^{27} - 9883598189096 q^{28} - 4114009788386 q^{29} - 14194804268004 q^{30} + 3718266369468 q^{31} - 29197309605632 q^{32} - 16110579243626 q^{33} - 31423174598564 q^{34} + 13804822380504 q^{35} + 51950006703548 q^{36} - 58067881808868 q^{37} - 76590705469880 q^{38} + 69866971570764 q^{39} - 129282722434320 q^{40} - 74370388815170 q^{41} - 430581394397552 q^{42} - 127444248270174 q^{43} - 563872902913048 q^{44} - 602432292081270 q^{45} - 749727107945564 q^{47} - 17\!\cdots\!72 q^{48}+ \cdots + 35\!\cdots\!38 q^{99}+O(q^{100}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9 - 312719540 * q^10 - 45399620 * q^11 - 8621310628 * q^12 - 10510197306 * q^13 - 12286634640 * q^14 - 16443659490 * q^15 + 65383333632 * q^16 - 35705720330 * q^17 + 27658188862 * q^18 - 84895273414 * q^19 + 331348024336 * q^20 + 185190266362 * q^21 + 270540900120 * q^22 - 1096353793934 * q^23 + 1697198124384 * q^24 + 525715171346 * q^25 + 4272672484934 * q^26 - 3706093330604 * q^27 - 9883598189096 * q^28 - 4114009788386 * q^29 - 14194804268004 * q^30 + 3718266369468 * q^31 - 29197309605632 * q^32 - 16110579243626 * q^33 - 31423174598564 * q^34 + 13804822380504 * q^35 + 51950006703548 * q^36 - 58067881808868 * q^37 - 76590705469880 * q^38 + 69866971570764 * q^39 - 129282722434320 * q^40 - 74370388815170 * q^41 - 430581394397552 * q^42 - 127444248270174 * q^43 - 563872902913048 * q^44 - 602432292081270 * q^45 - 749727107945564 * q^47 - 1762369490938672 * q^48 - 560241909258462 * q^49 - 1212733967351616 * q^50 - 2013927378521294 * q^51 - 3438555393950964 * q^52 - 1954645162253818 * q^53 - 2748549190422938 * q^54 - 2426218557075404 * q^55 - 1321001371084560 * q^56 - 2335835167092904 * q^57 - 340295461037046 * q^58 - 1561709417167508 * q^59 - 7486616247365616 * q^60 - 679115861109266 * q^61 - 12552327168177062 * q^62 - 10591353756704576 * q^63 - 6775416249353536 * q^64 - 6252697705990982 * q^65 - 20881430274671372 * q^66 - 7577612038827396 * q^67 + 2901964856169680 * q^68 + 833228883389840 * q^69 - 10700966230255240 * q^70 + 25039332312392368 * q^71 - 7954969753997256 * q^72 - 18720848443128734 * q^73 - 6297551300657404 * q^74 + 22553223201966436 * q^75 + 34141945529937952 * q^76 + 35092380107507048 * q^77 + 27963841408286022 * q^78 + 965348846593408 * q^79 + 36943919850262880 * q^80 + 51275234750545798 * q^81 + 106728632435914846 * q^82 + 65089411455584544 * q^83 + 189770883431502392 * q^84 + 20919534362994588 * q^85 + 86205449672049764 * q^86 + 130649890213719716 * q^87 + 164304846335490592 * q^88 - 61322357257717500 * q^89 + 237420523836214152 * q^90 + 181977537844157150 * q^91 - 61586264776507392 * q^92 - 71304974484877430 * q^93 - 14005510384703054 * q^94 + 123323286964112684 * q^95 + 566787465801380768 * q^96 - 67350702995984898 * q^97 + 134333537201072600 * q^98 + 353912447692290838 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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