LMFDB - Embedded newform 23.18.a.a.1.7

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			1.7
Root			$-2.15800$ 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)

$f(q)$	$=$	$q+4.31600 q^{2} +20224.5 q^{3} -131053. q^{4} +240238. q^{5} +87288.7 q^{6} -1.90239e7 q^{7} -1.13133e6 q^{8} +2.79889e8 q^{9} +O(q^{10})$	\(q+4.31600 q^{2} +20224.5 q^{3} -131053. q^{4} +240238. q^{5} +87288.7 q^{6} -1.90239e7 q^{7} -1.13133e6 q^{8} +2.79889e8 q^{9} +1.03687e6 q^{10} +5.87229e8 q^{11} -2.65049e9 q^{12} -3.45444e9 q^{13} -8.21073e7 q^{14} +4.85869e9 q^{15} +1.71725e10 q^{16} -3.38942e10 q^{17} +1.20800e9 q^{18} -7.13630e10 q^{19} -3.14840e10 q^{20} -3.84749e11 q^{21} +2.53448e9 q^{22} -7.83110e10 q^{23} -2.28806e10 q^{24} -7.05225e11 q^{25} -1.49093e10 q^{26} +3.04882e12 q^{27} +2.49315e12 q^{28} +2.15685e12 q^{29} +2.09701e10 q^{30} -5.74356e12 q^{31} +2.22403e11 q^{32} +1.18764e13 q^{33} -1.46287e11 q^{34} -4.57028e12 q^{35} -3.66804e13 q^{36} +3.27617e13 q^{37} -3.08002e11 q^{38} -6.98642e13 q^{39} -2.71789e11 q^{40} -8.04496e13 q^{41} -1.66058e12 q^{42} -9.49109e13 q^{43} -7.69583e13 q^{44} +6.72401e13 q^{45} -3.37990e11 q^{46} -3.50567e13 q^{47} +3.47306e14 q^{48} +1.29280e14 q^{49} -3.04375e12 q^{50} -6.85493e14 q^{51} +4.52716e14 q^{52} -6.05184e14 q^{53} +1.31587e13 q^{54} +1.41075e14 q^{55} +2.15224e13 q^{56} -1.44328e15 q^{57} +9.30897e12 q^{58} +2.17590e14 q^{59} -6.36748e14 q^{60} -5.91896e14 q^{61} -2.47892e13 q^{62} -5.32460e15 q^{63} -2.24988e15 q^{64} -8.29889e14 q^{65} +5.12585e13 q^{66} +1.80844e15 q^{67} +4.44195e15 q^{68} -1.58380e15 q^{69} -1.97253e13 q^{70} +3.84385e15 q^{71} -3.16648e14 q^{72} +9.91090e15 q^{73} +1.41399e14 q^{74} -1.42628e16 q^{75} +9.35236e15 q^{76} -1.11714e16 q^{77} -3.01534e14 q^{78} +7.68104e15 q^{79} +4.12550e15 q^{80} +2.55159e16 q^{81} -3.47220e14 q^{82} -1.78791e16 q^{83} +5.04227e16 q^{84} -8.14269e15 q^{85} -4.09635e14 q^{86} +4.36212e16 q^{87} -6.64351e14 q^{88} -6.26490e16 q^{89} +2.90208e14 q^{90} +6.57171e16 q^{91} +1.02629e16 q^{92} -1.16160e17 q^{93} -1.51305e14 q^{94} -1.71441e16 q^{95} +4.49797e15 q^{96} -3.37377e16 q^{97} +5.57972e14 q^{98} +1.64359e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.31600	0.0119214	0.00596068	−	0.999982i	$-0.498103\pi$
$2$	4.31600	0.0119214	0.00596068	+	0.999982i	$0.498103\pi$
$3$	20224.5	1.77970	0.889850	−	0.456254i	$-0.150809\pi$
$3$	20224.5	1.77970	0.889850	+	0.456254i	$0.150809\pi$
$4$	−131053.	−0.999858
$5$	240238.	0.275041	0.137520	−	0.990499i	$-0.456087\pi$
$5$	240238.	0.275041	0.137520	+	0.990499i	$0.456087\pi$
$6$	87288.7	0.0212164
$7$	−1.90239e7	−1.24729	−0.623645	−	0.781708i	$-0.714349\pi$
$7$	−1.90239e7	−1.24729	−0.623645	+	0.781708i	$0.714349\pi$
$8$	−1.13133e6	−0.0238410
$9$	2.79889e8	2.16733
$10$	1.03687e6	0.00327886
$11$	5.87229e8	0.825980	0.412990	−	0.910736i	$-0.364484\pi$
$11$	5.87229e8	0.825980	0.412990	+	0.910736i	$0.364484\pi$
$12$	−2.65049e9	−1.77945
$13$	−3.45444e9	−1.17452	−0.587258	−	0.809400i	$-0.699793\pi$
$13$	−3.45444e9	−1.17452	−0.587258	+	0.809400i	$0.699793\pi$
$14$	−8.21073e7	−0.0148694
$15$	4.85869e9	0.489490
$16$	1.71725e10	0.999574
$17$	−3.38942e10	−1.17845	−0.589223	−	0.807971i	$-0.700566\pi$
$17$	−3.38942e10	−1.17845	−0.589223	+	0.807971i	$0.700566\pi$
$18$	1.20800e9	0.0258375
$19$	−7.13630e10	−0.963979	−0.481989	−	0.876177i	$-0.660086\pi$
$19$	−7.13630e10	−0.963979	−0.481989	+	0.876177i	$0.660086\pi$
$20$	−3.14840e10	−0.275002
$21$	−3.84749e11	−2.21980
$22$	2.53448e9	0.00984681
$23$	−7.83110e10	−0.208514
$23$	−7.83110e10	−0.208514
$24$	−2.28806e10	−0.0424299
$25$	−7.05225e11	−0.924353
$26$	−1.49093e10	−0.0140018
$27$	3.04882e12	2.07749
$28$	2.49315e12	1.24711
$29$	2.15685e12	0.800641	0.400320	−	0.916375i	$-0.368899\pi$
$29$	2.15685e12	0.800641	0.400320	+	0.916375i	$0.368899\pi$
$30$	2.09701e10	0.00583539
$31$	−5.74356e12	−1.20950	−0.604751	−	0.796414i	$-0.706727\pi$
$31$	−5.74356e12	−1.20950	−0.604751	+	0.796414i	$0.706727\pi$
$32$	2.22403e11	0.0357573
$33$	1.18764e13	1.47000
$34$	−1.46287e11	−0.0140487
$35$	−4.57028e12	−0.343056
$36$	−3.66804e13	−2.16702
$37$	3.27617e13	1.53339	0.766693	−	0.642014i	$-0.221901\pi$
$37$	3.27617e13	1.53339	0.766693	+	0.642014i	$0.221901\pi$
$38$	−3.08002e11	−0.0114919
$39$	−6.98642e13	−2.09029
$40$	−2.71789e11	−0.00655726
$41$	−8.04496e13	−1.57348	−0.786740	−	0.617285i	$-0.788233\pi$
$41$	−8.04496e13	−1.57348	−0.786740	+	0.617285i	$0.788233\pi$
$42$	−1.66058e12	−0.0264630
$43$	−9.49109e13	−1.23832	−0.619162	−	0.785264i	$-0.712527\pi$
$43$	−9.49109e13	−1.23832	−0.619162	+	0.785264i	$0.712527\pi$
$44$	−7.69583e13	−0.825863
$45$	6.72401e13	0.596104
$46$	−3.37990e11	−0.00248578
$47$	−3.50567e13	−0.214753	−0.107377	−	0.994218i	$-0.534245\pi$
$47$	−3.50567e13	−0.214753	−0.107377	+	0.994218i	$0.534245\pi$
$48$	3.47306e14	1.77894
$49$	1.29280e14	0.555731
$50$	−3.04375e12	−0.0110195
$51$	−6.85493e14	−2.09728
$52$	4.52716e14	1.17435
$53$	−6.05184e14	−1.33519	−0.667594	−	0.744525i	$-0.732676\pi$
$53$	−6.05184e14	−1.33519	−0.667594	+	0.744525i	$0.732676\pi$
$54$	1.31587e13	0.0247666
$55$	1.41075e14	0.227178
$56$	2.15224e13	0.0297367
$57$	−1.44328e15	−1.71559
$58$	9.30897e12	0.00954473
$59$	2.17590e14	0.192929	0.0964645	−	0.995336i	$-0.469247\pi$
$59$	2.17590e14	0.192929	0.0964645	+	0.995336i	$0.469247\pi$
$60$	−6.36748e14	−0.489420
$61$	−5.91896e14	−0.395314	−0.197657	−	0.980271i	$-0.563333\pi$
$61$	−5.91896e14	−0.395314	−0.197657	+	0.980271i	$0.563333\pi$
$62$	−2.47892e13	−0.0144189
$63$	−5.32460e15	−2.70329
$64$	−2.24988e15	−0.999147
$65$	−8.29889e14	−0.323040
$66$	5.12585e13	0.0175244
$67$	1.80844e15	0.544087	0.272044	−	0.962285i	$-0.412300\pi$
$67$	1.80844e15	0.544087	0.272044	+	0.962285i	$0.412300\pi$
$68$	4.44195e15	1.17828
$69$	−1.58380e15	−0.371093
$70$	−1.97253e13	−0.00408969
$71$	3.84385e15	0.706433	0.353216	−	0.935542i	$-0.385088\pi$
$71$	3.84385e15	0.706433	0.353216	+	0.935542i	$0.385088\pi$
$72$	−3.16648e14	−0.0516714
$73$	9.91090e15	1.43836	0.719182	−	0.694822i	$-0.244517\pi$
$73$	9.91090e15	1.43836	0.719182	+	0.694822i	$0.244517\pi$
$74$	1.41399e14	0.0182801
$75$	−1.42628e16	−1.64507
$76$	9.35236e15	0.963842
$77$	−1.11714e16	−1.03024
$78$	−3.01534e14	−0.0249191
$79$	7.68104e15	0.569626	0.284813	−	0.958583i	$-0.408068\pi$
$79$	7.68104e15	0.569626	0.284813	+	0.958583i	$0.408068\pi$
$80$	4.12550e15	0.274924
$81$	2.55159e16	1.52999
$82$	−3.47220e14	−0.0187580
$83$	−1.78791e16	−0.871326	−0.435663	−	0.900110i	$-0.643486\pi$
$83$	−1.78791e16	−0.871326	−0.435663	+	0.900110i	$0.643486\pi$
$84$	5.04227e16	2.21948
$85$	−8.14269e15	−0.324121
$86$	−4.09635e14	−0.0147625
$87$	4.36212e16	1.42490
$88$	−6.64351e14	−0.0196922
$89$	−6.26490e16	−1.68694	−0.843468	−	0.537179i	$-0.819490\pi$
$89$	−6.26490e16	−1.68694	−0.843468	+	0.537179i	$0.819490\pi$
$90$	2.90208e14	0.00710637
$91$	6.57171e16	1.46496
$92$	1.02629e16	0.208485
$93$	−1.16160e17	−2.15255
$94$	−1.51305e14	−0.00256015
$95$	−1.71441e16	−0.265134
$96$	4.49797e15	0.0636373
$97$	−3.37377e16	−0.437075	−0.218538	−	0.975829i	$-0.570129\pi$
$97$	−3.37377e16	−0.437075	−0.218538	+	0.975829i	$0.570129\pi$
$98$	5.57972e14	0.00662508
$99$	1.64359e17	1.79017
$100$	9.24221e16	0.924221
$101$	1.55621e17	1.43000	0.715001	−	0.699124i	$-0.246426\pi$
$101$	1.55621e17	1.43000	0.715001	+	0.699124i	$0.246426\pi$
$102$	−2.95858e15	−0.0250024
$103$	5.51722e16	0.429145	0.214572	−	0.976708i	$-0.431164\pi$
$103$	5.51722e16	0.429145	0.214572	+	0.976708i	$0.431164\pi$
$104$	3.90812e15	0.0280017
$105$	−9.24315e16	−0.610536
$106$	−2.61197e15	−0.0159173
$107$	−7.54629e16	−0.424591	−0.212296	−	0.977205i	$-0.568094\pi$
$107$	−7.54629e16	−0.424591	−0.212296	+	0.977205i	$0.568094\pi$
$108$	−3.99558e17	−2.07720
$109$	1.97300e15	0.00948425	0.00474212	−	0.999989i	$-0.498491\pi$
$109$	1.97300e15	0.00948425	0.00474212	+	0.999989i	$0.498491\pi$
$110$	6.08878e14	0.00270827
$111$	6.62588e17	2.72897
$112$	−3.26690e17	−1.24676
$113$	1.07623e17	0.380837	0.190419	−	0.981703i	$-0.439015\pi$
$113$	1.07623e17	0.380837	0.190419	+	0.981703i	$0.439015\pi$
$114$	−6.22919e15	−0.0204522
$115$	−1.88133e16	−0.0573500
$116$	−2.82663e17	−0.800527
$117$	−9.66861e17	−2.54556
$118$	9.39119e14	0.00229998
$119$	6.44802e17	1.46986
$120$	−5.49679e15	−0.0116699
$121$	−1.60609e17	−0.317757
$122$	−2.55462e15	−0.00471268
$123$	−1.62705e18	−2.80032
$124$	7.52713e17	1.20933
$125$	−3.52709e17	−0.529276
$126$	−2.29809e16	−0.0322269
$127$	8.76691e17	1.14952	0.574758	−	0.818323i	$-0.305096\pi$
$127$	8.76691e17	1.14952	0.574758	+	0.818323i	$0.305096\pi$
$128$	−3.88612e16	−0.0476685
$129$	−1.91952e18	−2.20384
$130$	−3.58180e15	−0.00385108
$131$	−1.29990e18	−1.30950	−0.654748	−	0.755847i	$-0.727225\pi$
$131$	−1.29990e18	−1.30950	−0.654748	+	0.755847i	$0.727225\pi$
$132$	−1.55644e18	−1.46979
$133$	1.35761e18	1.20236
$134$	7.80522e15	0.00648626
$135$	7.32443e17	0.571396
$136$	3.83456e16	0.0280954
$137$	2.52219e18	1.73642	0.868208	−	0.496201i	$-0.165272\pi$
$137$	2.52219e18	1.73642	0.868208	+	0.496201i	$0.165272\pi$
$138$	−6.83567e15	−0.00442393
$139$	3.14955e18	1.91700	0.958501	−	0.285088i	$-0.0920228\pi$
$139$	3.14955e18	1.91700	0.958501	+	0.285088i	$0.0920228\pi$
$140$	5.98951e17	0.343007
$141$	−7.09003e17	−0.382196
$142$	1.65900e16	0.00842164
$143$	−2.02855e18	−0.970127
$144$	4.80641e18	2.16641
$145$	5.18159e17	0.220209
$146$	4.27754e16	0.0171473
$147$	2.61462e18	0.989035
$148$	−4.29353e18	−1.53317
$149$	2.75301e18	0.928377	0.464188	−	0.885736i	$-0.346346\pi$
$149$	2.75301e18	0.928377	0.464188	+	0.885736i	$0.346346\pi$
$150$	−6.15582e16	−0.0196115
$151$	−7.18107e17	−0.216215	−0.108107	−	0.994139i	$-0.534479\pi$
$151$	−7.18107e17	−0.216215	−0.108107	+	0.994139i	$0.534479\pi$
$152$	8.07352e16	0.0229823
$153$	−9.48662e18	−2.55408
$154$	−4.82158e16	−0.0122818
$155$	−1.37982e18	−0.332663
$156$	9.15594e18	2.08999
$157$	5.59118e18	1.20880	0.604402	−	0.796679i	$-0.293412\pi$
$157$	5.59118e18	1.20880	0.604402	+	0.796679i	$0.293412\pi$
$158$	3.31514e16	0.00679072
$159$	−1.22395e19	−2.37623
$160$	5.34296e16	0.00983472
$161$	1.48978e18	0.260078
$162$	1.10126e17	0.0182395
$163$	5.76473e18	0.906117	0.453059	−	0.891481i	$-0.350333\pi$
$163$	5.76473e18	0.906117	0.453059	+	0.891481i	$0.350333\pi$
$164$	1.05432e19	1.57326
$165$	2.85316e18	0.404309
$166$	−7.71659e16	−0.0103874
$167$	−1.14580e19	−1.46562	−0.732808	−	0.680436i	$-0.761791\pi$
$167$	−1.14580e19	−1.46562	−0.732808	+	0.680436i	$0.761791\pi$
$168$	4.35279e17	0.0529223
$169$	3.28274e18	0.379489
$170$	−3.51438e16	−0.00386396
$171$	−1.99737e19	−2.08926
$172$	1.24384e19	1.23815
$173$	1.25521e18	0.118939	0.0594694	−	0.998230i	$-0.481059\pi$
$173$	1.25521e18	0.118939	0.0594694	+	0.998230i	$0.481059\pi$
$174$	1.88269e17	0.0169867
$175$	1.34162e19	1.15294
$176$	1.00842e19	0.825628
$177$	4.40065e18	0.343356
$178$	−2.70393e17	−0.0201106
$179$	1.79259e19	1.27125	0.635626	−	0.771997i	$-0.280742\pi$
$179$	1.79259e19	1.27125	0.635626	+	0.771997i	$0.280742\pi$
$180$	−8.81204e18	−0.596019
$181$	−5.03449e16	−0.00324853	−0.00162427	−	0.999999i	$-0.500517\pi$
$181$	−5.03449e16	−0.00324853	−0.00162427	+	0.999999i	$0.500517\pi$
$182$	2.83635e17	0.0174644
$183$	−1.19708e19	−0.703540
$184$	8.85957e16	0.00497120
$185$	7.87061e18	0.421744
$186$	−5.01348e17	−0.0256613
$187$	−1.99037e19	−0.973373
$188$	4.59430e18	0.214723
$189$	−5.80006e19	−2.59124
$190$	−7.39940e16	−0.00316075
$191$	1.36302e18	0.0556825	0.0278412	−	0.999612i	$-0.491137\pi$
$191$	1.36302e18	0.0556825	0.0278412	+	0.999612i	$0.491137\pi$
$192$	−4.55026e19	−1.77818
$193$	−3.79015e19	−1.41716	−0.708581	−	0.705629i	$-0.750664\pi$
$193$	−3.79015e19	−1.41716	−0.708581	+	0.705629i	$0.750664\pi$
$194$	−1.45612e17	−0.00521053
$195$	−1.67841e19	−0.574914
$196$	−1.69426e19	−0.555652
$197$	3.61514e19	1.13544	0.567718	−	0.823223i	$-0.307827\pi$
$197$	3.61514e19	1.13544	0.567718	+	0.823223i	$0.307827\pi$
$198$	7.09373e17	0.0213413
$199$	−2.95898e19	−0.852885	−0.426443	−	0.904515i	$-0.640233\pi$
$199$	−2.95898e19	−0.852885	−0.426443	+	0.904515i	$0.640233\pi$
$200$	7.97843e17	0.0220375
$201$	3.65748e19	0.968312
$202$	6.71659e17	0.0170476
$203$	−4.10319e19	−0.998631
$204$	8.98361e19	2.09698
$205$	−1.93271e19	−0.432771
$206$	2.38123e17	0.00511599
$207$	−2.19184e19	−0.451919
$208$	−5.93215e19	−1.17402
$209$	−4.19064e19	−0.796227
$210$	−3.98934e17	−0.00727842
$211$	4.06948e19	0.713079	0.356540	−	0.934280i	$-0.383956\pi$
$211$	4.06948e19	0.713079	0.356540	+	0.934280i	$0.383956\pi$
$212$	7.93114e19	1.33500
$213$	7.77399e19	1.25724
$214$	−3.25697e17	−0.00506171
$215$	−2.28012e19	−0.340589
$216$	−3.44923e18	−0.0495296
$217$	1.09265e20	1.50860
$218$	8.51548e15	0.000113065 0
$219$	2.00443e20	2.55986
$220$	−1.84883e19	−0.227146
$221$	1.17085e20	1.38410
$222$	2.85973e18	0.0325330
$223$	4.61143e19	0.504945	0.252473	−	0.967604i	$-0.418756\pi$
$223$	4.61143e19	0.504945	0.252473	+	0.967604i	$0.418756\pi$
$224$	−4.23097e18	−0.0445997
$225$	−1.97385e20	−2.00338
$226$	4.64501e17	0.00454010
$227$	−1.39591e20	−1.31413	−0.657064	−	0.753835i	$-0.728202\pi$
$227$	−1.39591e20	−1.31413	−0.657064	+	0.753835i	$0.728202\pi$
$228$	1.89147e20	1.71535
$229$	−1.43781e20	−1.25632	−0.628161	−	0.778083i	$-0.716192\pi$
$229$	−1.43781e20	−1.25632	−0.628161	+	0.778083i	$0.716192\pi$
$230$	−8.11981e16	−0.000683690 0
$231$	−2.25936e20	−1.83351
$232$	−2.44012e18	−0.0190881
$233$	1.68420e19	0.127019	0.0635096	−	0.997981i	$-0.479771\pi$
$233$	1.68420e19	0.127019	0.0635096	+	0.997981i	$0.479771\pi$
$234$	−4.17297e18	−0.0303466
$235$	−8.42196e18	−0.0590658
$236$	−2.85160e19	−0.192902
$237$	1.55345e20	1.01376
$238$	2.78296e18	0.0175228
$239$	−1.91100e20	−1.16112	−0.580562	−	0.814216i	$-0.697167\pi$
$239$	−1.91100e20	−1.16112	−0.580562	+	0.814216i	$0.697167\pi$
$240$	8.34361e19	0.489281
$241$	7.43777e19	0.421015	0.210508	−	0.977592i	$-0.432488\pi$
$241$	7.43777e19	0.421015	0.210508	+	0.977592i	$0.432488\pi$
$242$	−6.93189e17	−0.00378810
$243$	1.22320e20	0.645421
$244$	7.75700e19	0.395258
$245$	3.10580e19	0.152849
$246$	−7.02234e18	−0.0333836
$247$	2.46519e20	1.13221
$248$	6.49787e18	0.0288358
$249$	−3.61594e20	−1.55070
$250$	−1.52229e18	−0.00630969
$251$	1.49958e20	0.600820	0.300410	−	0.953810i	$-0.402877\pi$
$251$	1.49958e20	0.600820	0.300410	+	0.953810i	$0.402877\pi$
$252$	6.97807e20	2.70290
$253$	−4.59865e19	−0.172229
$254$	3.78379e18	0.0137038
$255$	−1.64682e20	−0.576837
$256$	2.94729e20	0.998579
$257$	−3.41126e20	−1.11811	−0.559053	−	0.829132i	$-0.688835\pi$
$257$	−3.41126e20	−1.11811	−0.559053	+	0.829132i	$0.688835\pi$
$258$	−8.28465e18	−0.0262728
$259$	−6.23257e20	−1.91258
$260$	1.08760e20	0.322994
$261$	6.03680e20	1.73525
$262$	−5.61036e18	−0.0156110
$263$	−2.28629e20	−0.615897	−0.307948	−	0.951403i	$-0.599642\pi$
$263$	−2.28629e20	−0.615897	−0.307948	+	0.951403i	$0.599642\pi$
$264$	−1.34361e19	−0.0350462
$265$	−1.45388e20	−0.367231
$266$	5.85942e18	0.0143338
$267$	−1.26704e21	−3.00224
$268$	−2.37002e20	−0.544010
$269$	8.93737e19	0.198754	0.0993768	−	0.995050i	$-0.468315\pi$
$269$	8.93737e19	0.198754	0.0993768	+	0.995050i	$0.468315\pi$
$270$	3.16122e18	0.00681182
$271$	7.31820e19	0.152815	0.0764074	−	0.997077i	$-0.475655\pi$
$271$	7.31820e19	0.152815	0.0764074	+	0.997077i	$0.475655\pi$
$272$	−5.82050e20	−1.17794
$273$	1.32909e21	2.60719
$274$	1.08858e19	0.0207004
$275$	−4.14128e20	−0.763497
$276$	2.07562e20	0.371040
$277$	3.56447e20	0.617898	0.308949	−	0.951079i	$-0.400023\pi$
$277$	3.56447e20	0.617898	0.308949	+	0.951079i	$0.400023\pi$
$278$	1.35934e19	0.0228533
$279$	−1.60756e21	−2.62139
$280$	5.17050e18	0.00817880
$281$	2.97394e20	0.456382	0.228191	−	0.973616i	$-0.426719\pi$
$281$	2.97394e20	0.456382	0.228191	+	0.973616i	$0.426719\pi$
$282$	−3.06006e18	−0.00455630
$283$	−1.05388e21	−1.52267	−0.761334	−	0.648360i	$-0.775455\pi$
$283$	−1.05388e21	−1.52267	−0.761334	+	0.648360i	$0.775455\pi$
$284$	−5.03750e20	−0.706332
$285$	−3.46731e20	−0.471858
$286$	−8.75520e18	−0.0115652
$287$	1.53047e21	1.96258
$288$	6.22481e19	0.0774979
$289$	3.21577e20	0.388735
$290$	2.23637e18	0.00262519
$291$	−6.82328e20	−0.777862
$292$	−1.29886e21	−1.43816
$293$	−1.78596e21	−1.92086	−0.960431	−	0.278518i	$-0.910157\pi$
$293$	−1.78596e21	−1.92086	−0.960431	+	0.278518i	$0.910157\pi$
$294$	1.12847e19	0.0117906
$295$	5.22735e19	0.0530634
$296$	−3.70643e19	−0.0365575
$297$	1.79036e21	1.71597
$298$	1.18820e19	0.0110675
$299$	2.70521e20	0.244904
$300$	1.86919e21	1.64484
$301$	1.80558e21	1.54455
$302$	−3.09935e18	−0.00257757
$303$	3.14735e21	2.54497
$304$	−1.22548e21	−0.963568
$305$	−1.42196e20	−0.108727
$306$	−4.09442e19	−0.0304481
$307$	6.03385e20	0.436434	0.218217	−	0.975900i	$-0.429976\pi$
$307$	6.03385e20	0.436434	0.218217	+	0.975900i	$0.429976\pi$
$308$	1.46405e21	1.03009
$309$	1.11583e21	0.763749
$310$	−5.95531e18	−0.00396579
$311$	−7.59899e20	−0.492371	−0.246185	−	0.969223i	$-0.579177\pi$
$311$	−7.59899e20	−0.492371	−0.246185	+	0.969223i	$0.579177\pi$
$312$	7.90396e19	0.0498346
$313$	−2.12226e21	−1.30218	−0.651091	−	0.758999i	$-0.725689\pi$
$313$	−2.12226e21	−1.30218	−0.651091	+	0.758999i	$0.725689\pi$
$314$	2.41315e19	0.0144106
$315$	−1.27917e21	−0.743514
$316$	−1.00663e21	−0.569545
$317$	1.85129e21	1.01970	0.509848	−	0.860264i	$-0.329702\pi$
$317$	1.85129e21	1.01970	0.509848	+	0.860264i	$0.329702\pi$
$318$	−5.28257e19	−0.0283279
$319$	1.26657e21	0.661313
$320$	−5.40507e20	−0.274806
$321$	−1.52620e21	−0.755645
$322$	6.42990e18	0.00310048
$323$	2.41879e21	1.13600
$324$	−3.34394e21	−1.52977
$325$	2.43616e21	1.08567
$326$	2.48805e19	0.0108022
$327$	3.99030e19	0.0168791
$328$	9.10152e19	0.0375134
$329$	6.66917e20	0.267859
$330$	1.23142e19	0.00481991
$331$	−2.94129e21	−1.12202	−0.561009	−	0.827810i	$-0.689587\pi$
$331$	−2.94129e21	−1.12202	−0.561009	+	0.827810i	$0.689587\pi$
$332$	2.34311e21	0.871202
$333$	9.16964e21	3.32335
$334$	−4.94528e19	−0.0174721
$335$	4.34457e20	0.149646
$336$	−6.60713e21	−2.21885
$337$	−2.30795e21	−0.755740	−0.377870	−	0.925859i	$-0.623343\pi$
$337$	−2.30795e21	−0.755740	−0.377870	+	0.925859i	$0.623343\pi$
$338$	1.41683e19	0.00452403
$339$	2.17662e21	0.677776
$340$	1.06713e21	0.324075
$341$	−3.37278e21	−0.999025
$342$	−8.62065e19	−0.0249068
$343$	1.96613e21	0.554132
$344$	1.07376e20	0.0295229
$345$	−3.80489e20	−0.102066
$346$	5.41746e18	0.00141791
$347$	−7.05967e21	−1.80295	−0.901476	−	0.432829i	$-0.857515\pi$
$347$	−7.05967e21	−1.80295	−0.901476	+	0.432829i	$0.857515\pi$
$348$	−5.71671e21	−1.42470
$349$	1.67590e21	0.407598	0.203799	−	0.979013i	$-0.434671\pi$
$349$	1.67590e21	0.407598	0.203799	+	0.979013i	$0.434671\pi$
$350$	5.79041e19	0.0137446
$351$	−1.05320e22	−2.44005
$352$	1.30601e20	0.0295348
$353$	1.92219e21	0.424338	0.212169	−	0.977233i	$-0.431947\pi$
$353$	1.92219e21	0.424338	0.212169	+	0.977233i	$0.431947\pi$
$354$	1.89932e19	0.00409327
$355$	9.23440e20	0.194298
$356$	8.21036e21	1.68670
$357$	1.30408e22	2.61591
$358$	7.73683e19	0.0151550
$359$	5.42750e20	0.103824	0.0519119	−	0.998652i	$-0.483468\pi$
$359$	5.42750e20	0.103824	0.0519119	+	0.998652i	$0.483468\pi$
$360$	−7.60709e19	−0.0142117
$361$	−3.87709e20	−0.0707449
$362$	−2.17288e17	−3.87269e−5 0
$363$	−3.24824e21	−0.565512
$364$	−8.61245e21	−1.46475
$365$	2.38098e21	0.395609
$366$	−5.16659e19	−0.00838715
$367$	5.38885e21	0.854741	0.427371	−	0.904076i	$-0.359440\pi$
$367$	5.38885e21	0.854741	0.427371	+	0.904076i	$0.359440\pi$
$368$	−1.34480e21	−0.208426
$369$	−2.25170e22	−3.41025
$370$	3.39695e19	0.00502776
$371$	1.15130e22	1.66537
$372$	1.52232e22	2.15224
$373$	−9.34062e21	−1.29077	−0.645387	−	0.763855i	$-0.723304\pi$
$373$	−9.34062e21	−1.29077	−0.645387	+	0.763855i	$0.723304\pi$
$374$	−8.59041e19	−0.0116039
$375$	−7.13336e21	−0.941951
$376$	3.96608e19	0.00511993
$377$	−7.45072e21	−0.940366
$378$	−2.50330e20	−0.0308911
$379$	−1.19164e22	−1.43785	−0.718923	−	0.695089i	$-0.755365\pi$
$379$	−1.19164e22	−1.43785	−0.718923	+	0.695089i	$0.755365\pi$
$380$	2.24680e21	0.265096
$381$	1.77306e22	2.04579
$382$	5.88279e18	0.000663811 0
$383$	1.05183e21	0.116079	0.0580397	−	0.998314i	$-0.481515\pi$
$383$	1.05183e21	0.116079	0.0580397	+	0.998314i	$0.481515\pi$
$384$	−7.85948e20	−0.0848356
$385$	−2.68380e21	−0.283357
$386$	−1.63583e20	−0.0168945
$387$	−2.65645e22	−2.68385
$388$	4.42144e21	0.437013
$389$	1.01149e22	0.978119	0.489060	−	0.872250i	$-0.337340\pi$
$389$	1.01149e22	0.978119	0.489060	+	0.872250i	$0.337340\pi$
$390$	−7.24399e19	−0.00685376
$391$	2.65429e21	0.245723
$392$	−1.46259e20	−0.0132492
$393$	−2.62898e22	−2.33051
$394$	1.56029e20	0.0135359
$395$	1.84528e21	0.156670
$396$	−2.15398e22	−1.78992
$397$	1.96196e22	1.59577	0.797887	−	0.602807i	$-0.205951\pi$
$397$	1.96196e22	1.59577	0.797887	+	0.602807i	$0.205951\pi$
$398$	−1.27709e20	−0.0101676
$399$	2.74569e22	2.13984
$400$	−1.21105e22	−0.923958
$401$	1.70086e22	1.27040	0.635200	−	0.772348i	$-0.280918\pi$
$401$	1.70086e22	1.27040	0.635200	+	0.772348i	$0.280918\pi$
$402$	1.57857e20	0.0115436
$403$	1.98408e22	1.42058
$404$	−2.03947e22	−1.42980
$405$	6.12989e21	0.420809
$406$	−1.77093e20	−0.0119050
$407$	1.92386e22	1.26655
$408$	7.75519e20	0.0500013
$409$	−1.55251e22	−0.980360	−0.490180	−	0.871621i	$-0.663069\pi$
$409$	−1.55251e22	−0.980360	−0.490180	+	0.871621i	$0.663069\pi$
$410$	−8.34155e19	−0.00515922
$411$	5.10100e22	3.09030
$412$	−7.23050e21	−0.429084
$413$	−4.13943e21	−0.240638
$414$	−9.45997e19	−0.00538750
$415$	−4.29523e21	−0.239650
$416$	−7.68276e20	−0.0419976
$417$	6.36980e22	3.41169
$418$	−1.80868e20	−0.00949211
$419$	−1.43614e22	−0.738548	−0.369274	−	0.929321i	$-0.620394\pi$
$419$	−1.43614e22	−0.738548	−0.369274	+	0.929321i	$0.620394\pi$
$420$	1.21135e22	0.610449
$421$	−2.15055e22	−1.06207	−0.531034	−	0.847350i	$-0.678196\pi$
$421$	−2.15055e22	−1.06207	−0.531034	+	0.847350i	$0.678196\pi$
$422$	1.75639e20	0.00850088
$423$	−9.81199e21	−0.465440
$424$	6.84664e20	0.0318323
$425$	2.39030e22	1.08930
$426$	3.35525e20	0.0149880
$427$	1.12602e22	0.493071
$428$	9.88966e21	0.424531
$429$	−4.10263e22	−1.72653
$430$	−9.84100e19	−0.00406029
$431$	7.54466e21	0.305199	0.152600	−	0.988288i	$-0.451236\pi$
$431$	7.54466e21	0.305199	0.152600	+	0.988288i	$0.451236\pi$
$432$	5.23560e22	2.07661
$433$	−4.32427e22	−1.68177	−0.840883	−	0.541217i	$-0.817964\pi$
$433$	−4.32427e22	−1.68177	−0.840883	+	0.541217i	$0.817964\pi$
$434$	4.71588e20	0.0179846
$435$	1.04795e22	0.391905
$436$	−2.58569e20	−0.00948290
$437$	5.58851e21	0.201003
$438$	8.65110e20	0.0305170
$439$	−4.65668e22	−1.61112	−0.805561	−	0.592513i	$-0.798136\pi$
$439$	−4.65668e22	−1.61112	−0.805561	+	0.592513i	$0.798136\pi$
$440$	−1.59602e20	−0.00541616
$441$	3.61841e22	1.20445
$442$	5.05340e20	0.0165004
$443$	−5.97066e22	−1.91245	−0.956227	−	0.292627i	$-0.905470\pi$
$443$	−5.97066e22	−1.91245	−0.956227	+	0.292627i	$0.905470\pi$
$444$	−8.68344e22	−2.72858
$445$	−1.50507e22	−0.463977
$446$	1.99029e20	0.00601964
$447$	5.56782e22	1.65223
$448$	4.28016e22	1.24623
$449$	−5.57825e21	−0.159369	−0.0796845	−	0.996820i	$-0.525391\pi$
$449$	−5.57825e21	−0.159369	−0.0796845	+	0.996820i	$0.525391\pi$
$450$	−8.51912e20	−0.0238830
$451$	−4.72423e22	−1.29966
$452$	−1.41044e22	−0.380783
$453$	−1.45233e22	−0.384797
$454$	−6.02474e20	−0.0156662
$455$	1.57878e22	0.402924
$456$	1.63283e21	0.0409015
$457$	−5.03800e22	−1.23871	−0.619356	−	0.785110i	$-0.712606\pi$
$457$	−5.03800e22	−1.23871	−0.619356	+	0.785110i	$0.712606\pi$
$458$	−6.20560e20	−0.0149771
$459$	−1.03337e23	−2.44821
$460$	2.46555e21	0.0573418
$461$	−3.41226e21	−0.0779084	−0.0389542	−	0.999241i	$-0.512403\pi$
$461$	−3.41226e21	−0.0779084	−0.0389542	+	0.999241i	$0.512403\pi$
$462$	−9.75138e20	−0.0218579
$463$	4.34928e22	0.957147	0.478574	−	0.878047i	$-0.341154\pi$
$463$	4.34928e22	0.957147	0.478574	+	0.878047i	$0.341154\pi$
$464$	3.70387e22	0.800299
$465$	−2.79062e22	−0.592039
$466$	7.26902e19	0.00151424
$467$	7.51038e22	1.53627	0.768136	−	0.640287i	$-0.221184\pi$
$467$	7.51038e22	1.53627	0.768136	+	0.640287i	$0.221184\pi$
$468$	1.26710e23	2.54520
$469$	−3.44037e22	−0.678635
$470$	−3.63491e19	−0.000704146 0
$471$	1.13079e23	2.15131
$472$	−2.46167e20	−0.00459963
$473$	−5.57344e22	−1.02283
$474$	6.70469e20	0.0120854
$475$	5.03270e22	0.891056
$476$	−8.45034e22	−1.46965
$477$	−1.69384e23	−2.89379
$478$	−8.24786e20	−0.0138422
$479$	−3.27814e22	−0.540475	−0.270238	−	0.962794i	$-0.587102\pi$
$479$	−3.27814e22	−0.540475	−0.270238	+	0.962794i	$0.587102\pi$
$480$	1.08059e21	0.0175028
$481$	−1.13173e23	−1.80099
$482$	3.21014e20	0.00501908
$483$	3.01301e22	0.462860
$484$	2.10484e22	0.317712
$485$	−8.10509e21	−0.120213
$486$	5.27931e20	0.00769429
$487$	1.05838e23	1.51581	0.757907	−	0.652362i	$-0.226222\pi$
$487$	1.05838e23	1.51581	0.757907	+	0.652362i	$0.226222\pi$
$488$	6.69631e20	0.00942469
$489$	1.16589e23	1.61262
$490$	1.34046e20	0.00182217
$491$	7.67445e22	1.02531	0.512655	−	0.858595i	$-0.328662\pi$
$491$	7.67445e22	1.02531	0.512655	+	0.858595i	$0.328662\pi$
$492$	2.13230e23	2.79992
$493$	−7.31048e22	−0.943511
$494$	1.06398e21	0.0134975
$495$	3.94853e22	0.492370
$496$	−9.86315e22	−1.20899
$497$	−7.31252e22	−0.881126
$498$	−1.56064e21	−0.0184864
$499$	−7.57426e22	−0.882035	−0.441018	−	0.897498i	$-0.645382\pi$
$499$	−7.57426e22	−0.882035	−0.441018	+	0.897498i	$0.645382\pi$
$500$	4.62237e22	0.529200
$501$	−2.31733e23	−2.60836
$502$	6.47220e20	0.00716259
$503$	−1.24383e23	−1.35342	−0.676709	−	0.736250i	$-0.736595\pi$
$503$	−1.24383e23	−1.35342	−0.676709	+	0.736250i	$0.736595\pi$
$504$	6.02389e21	0.0644492
$505$	3.73861e22	0.393309
$506$	−1.98477e20	−0.00205320
$507$	6.63917e22	0.675377
$508$	−1.14893e23	−1.14935
$509$	9.07146e22	0.892434	0.446217	−	0.894925i	$-0.352771\pi$
$509$	9.07146e22	0.892434	0.446217	+	0.894925i	$0.352771\pi$
$510$	−7.10765e20	−0.00687669
$511$	−1.88545e23	−1.79406
$512$	6.36566e21	0.0595729
$513$	−2.17573e23	−2.00266
$514$	−1.47230e21	−0.0133293
$515$	1.32545e22	0.118032
$516$	2.51560e23	2.20353
$517$	−2.05863e22	−0.177382
$518$	−2.68997e21	−0.0228005
$519$	2.53859e22	0.211675
$520$	9.38879e20	0.00770161
$521$	1.86139e23	1.50216	0.751081	−	0.660210i	$-0.229533\pi$
$521$	1.86139e23	1.50216	0.751081	+	0.660210i	$0.229533\pi$
$522$	2.60548e21	0.0206866
$523$	−1.16410e23	−0.909342	−0.454671	−	0.890660i	$-0.650243\pi$
$523$	−1.16410e23	−0.909342	−0.454671	+	0.890660i	$0.650243\pi$
$524$	1.70356e23	1.30931
$525$	2.71335e23	2.05188
$526$	−9.86762e20	−0.00734233
$527$	1.94673e23	1.42533
$528$	2.03948e23	1.46937
$529$	6.13261e21	0.0434783
$530$	−6.27495e20	−0.00437790
$531$	6.09012e22	0.418141
$532$	−1.77919e23	−1.20219
$533$	2.77908e23	1.84808
$534$	−5.46855e21	−0.0357908
$535$	−1.81291e22	−0.116780
$536$	−2.04595e21	−0.0129716
$537$	3.62543e23	2.26244
$538$	3.85736e20	0.00236941
$539$	7.59170e22	0.459023
$540$	−9.59892e22	−0.571315
$541$	2.62695e22	0.153913	0.0769564	−	0.997034i	$-0.475480\pi$
$541$	2.62695e22	0.153913	0.0769564	+	0.997034i	$0.475480\pi$
$542$	3.15853e20	0.00182176
$543$	−1.01820e21	−0.00578141
$544$	−7.53816e21	−0.0421381
$545$	4.73991e20	0.00260855
$546$	5.73636e21	0.0310813
$547$	−1.00625e23	−0.536804	−0.268402	−	0.963307i	$-0.586496\pi$
$547$	−1.00625e23	−0.536804	−0.268402	+	0.963307i	$0.586496\pi$
$548$	−3.30542e23	−1.73617
$549$	−1.65665e23	−0.856775
$550$	−1.78738e21	−0.00910192
$551$	−1.53919e23	−0.771800
$552$	1.79180e21	0.00884724
$553$	−1.46124e23	−0.710489
$554$	1.53842e21	0.00736619
$555$	1.59179e23	0.750577
$556$	−4.12759e23	−1.91673
$557$	2.24439e23	1.02643	0.513214	−	0.858261i	$-0.328455\pi$
$557$	2.24439e23	1.02643	0.513214	+	0.858261i	$0.328455\pi$
$558$	−6.93822e21	−0.0312505
$559$	3.27864e23	1.45443
$560$	−7.84833e22	−0.342909
$561$	−4.02541e23	−1.73231
$562$	1.28355e21	0.00544069
$563$	−8.62079e22	−0.359936	−0.179968	−	0.983672i	$-0.557599\pi$
$563$	−8.62079e22	−0.359936	−0.179968	+	0.983672i	$0.557599\pi$
$564$	9.29173e22	0.382141
$565$	2.58552e22	0.104746
$566$	−4.54853e21	−0.0181523
$567$	−4.85412e23	−1.90834
$568$	−4.34867e21	−0.0168421
$569$	2.31891e23	0.884767	0.442383	−	0.896826i	$-0.354133\pi$
$569$	2.31891e23	0.884767	0.442383	+	0.896826i	$0.354133\pi$
$570$	−1.49649e21	−0.00562519
$571$	1.08559e23	0.402031	0.201015	−	0.979588i	$-0.435576\pi$
$571$	1.08559e23	0.402031	0.201015	+	0.979588i	$0.435576\pi$
$572$	2.65848e23	0.969989
$573$	2.75664e22	0.0990981
$574$	6.60550e21	0.0233967
$575$	5.52269e22	0.192741
$576$	−6.29717e23	−2.16548
$577$	−5.24134e22	−0.177602	−0.0888011	−	0.996049i	$-0.528304\pi$
$577$	−5.24134e22	−0.177602	−0.0888011	+	0.996049i	$0.528304\pi$
$578$	1.38792e21	0.00463425
$579$	−7.66539e23	−2.52212
$580$	−6.79064e22	−0.220178
$581$	3.40130e23	1.08680
$582$	−2.94492e21	−0.00927318
$583$	−3.55381e23	−1.10284
$584$	−1.12125e22	−0.0342921
$585$	−2.32277e23	−0.700134
$586$	−7.70818e21	−0.0228993
$587$	−4.10440e23	−1.20178	−0.600892	−	0.799330i	$-0.705188\pi$
$587$	−4.10440e23	−1.20178	−0.600892	+	0.799330i	$0.705188\pi$
$588$	−3.42655e23	−0.988894
$589$	4.09878e23	1.16593
$590$	2.25612e20	0.000632588 0
$591$	7.31143e23	2.02073
$592$	5.62602e23	1.53273
$593$	−3.26402e23	−0.876573	−0.438286	−	0.898835i	$-0.644414\pi$
$593$	−3.26402e23	−0.876573	−0.438286	+	0.898835i	$0.644414\pi$
$594$	7.72716e21	0.0204567
$595$	1.54906e23	0.404272
$596$	−3.60791e23	−0.928245
$597$	−5.98438e23	−1.51788
$598$	1.16757e21	0.00291959
$599$	7.79857e23	1.92259	0.961295	−	0.275521i	$-0.0888502\pi$
$599$	7.79857e23	1.92259	0.961295	+	0.275521i	$0.0888502\pi$
$600$	1.61360e22	0.0392202
$601$	8.06587e23	1.93294	0.966470	−	0.256781i	$-0.0826620\pi$
$601$	8.06587e23	1.93294	0.966470	+	0.256781i	$0.0826620\pi$
$602$	7.79287e21	0.0184131
$603$	5.06163e23	1.17922
$604$	9.41103e22	0.216184
$605$	−3.85845e22	−0.0873962
$606$	1.35840e22	0.0303395
$607$	2.33783e23	0.514885	0.257442	−	0.966294i	$-0.417120\pi$
$607$	2.33783e23	0.514885	0.257442	+	0.966294i	$0.417120\pi$
$608$	−1.58713e22	−0.0344693
$609$	−8.29848e23	−1.77726
$610$	−6.13718e20	−0.00129618
$611$	1.21101e23	0.252231
$612$	1.24325e24	2.55372
$613$	−1.30393e23	−0.264143	−0.132072	−	0.991240i	$-0.542163\pi$
$613$	−1.30393e23	−0.264143	−0.132072	+	0.991240i	$0.542163\pi$
$614$	2.60421e21	0.00520289
$615$	−3.90880e23	−0.770202
$616$	1.26386e22	0.0245619
$617$	−4.33493e23	−0.830919	−0.415459	−	0.909612i	$-0.636379\pi$
$617$	−4.33493e23	−0.830919	−0.415459	+	0.909612i	$0.636379\pi$
$618$	4.81591e21	0.00910493
$619$	−2.14473e23	−0.399946	−0.199973	−	0.979801i	$-0.564086\pi$
$619$	−2.14473e23	−0.399946	−0.199973	+	0.979801i	$0.564086\pi$
$620$	1.80830e23	0.332615
$621$	−2.38756e23	−0.433188
$622$	−3.27972e21	−0.00586973
$623$	1.19183e24	2.10410
$624$	−1.19975e24	−2.08940
$625$	4.53310e23	0.778780
$626$	−9.15967e21	−0.0155238
$627$	−8.47535e23	−1.41704
$628$	−7.32743e23	−1.20863
$629$	−1.11043e24	−1.80701
$630$	−5.52090e21	−0.00886371
$631$	−9.15056e23	−1.44943	−0.724717	−	0.689047i	$-0.758029\pi$
$631$	−9.15056e23	−1.44943	−0.724717	+	0.689047i	$0.758029\pi$
$632$	−8.68981e21	−0.0135805
$633$	8.23031e23	1.26907
$634$	7.99016e21	0.0121562
$635$	2.10615e23	0.316164
$636$	1.60403e24	2.37590
$637$	−4.46590e23	−0.652716
$638$	5.46649e21	0.00788375
$639$	1.07585e24	1.53107
$640$	−9.33595e21	−0.0131108
$641$	4.87776e23	0.675970	0.337985	−	0.941151i	$-0.390255\pi$
$641$	4.87776e23	0.675970	0.337985	+	0.941151i	$0.390255\pi$
$642$	−6.58706e21	−0.00900832
$643$	4.36986e23	0.589759	0.294880	−	0.955534i	$-0.404720\pi$
$643$	4.36986e23	0.589759	0.294880	+	0.955534i	$0.404720\pi$
$644$	−1.95241e23	−0.260041
$645$	−4.61143e23	−0.606147
$646$	1.04395e22	0.0135426
$647$	−8.68315e23	−1.11171	−0.555854	−	0.831280i	$-0.687609\pi$
$647$	−8.68315e23	−1.11171	−0.555854	+	0.831280i	$0.687609\pi$
$648$	−2.88669e22	−0.0364765
$649$	1.27775e23	0.159356
$650$	1.05144e22	0.0129426
$651$	2.20983e24	2.68485
$652$	−7.55487e23	−0.905988
$653$	7.22758e23	0.855521	0.427761	−	0.903892i	$-0.359303\pi$
$653$	7.22758e23	0.855521	0.427761	+	0.903892i	$0.359303\pi$
$654$	1.72221e20	0.000201222 0
$655$	−3.12286e23	−0.360165
$656$	−1.38152e24	−1.57281
$657$	2.77396e24	3.11741
$658$	2.87841e21	0.00319325
$659$	−1.24198e24	−1.36016	−0.680078	−	0.733139i	$-0.738054\pi$
$659$	−1.24198e24	−1.36016	−0.680078	+	0.733139i	$0.738054\pi$
$660$	−3.73917e23	−0.404251
$661$	1.50430e22	0.0160555	0.00802774	−	0.999968i	$-0.497445\pi$
$661$	1.50430e22	0.0160555	0.00802774	+	0.999968i	$0.497445\pi$
$662$	−1.26946e22	−0.0133760
$663$	2.36799e24	2.46329
$664$	2.02271e22	0.0207733
$665$	3.26149e23	0.330698
$666$	3.95761e22	0.0396189
$667$	−1.68905e23	−0.166945
$668$	1.50161e24	1.46541
$669$	9.32637e23	0.898651
$670$	1.87511e21	0.00178399
$671$	−3.47579e23	−0.326521
$672$	−8.55692e22	−0.0793741
$673$	−3.73045e23	−0.341690	−0.170845	−	0.985298i	$-0.554650\pi$
$673$	−3.73045e23	−0.341690	−0.170845	+	0.985298i	$0.554650\pi$
$674$	−9.96110e21	−0.00900945
$675$	−2.15010e24	−1.92034
$676$	−4.30214e23	−0.379435
$677$	−1.11471e24	−0.970863	−0.485432	−	0.874275i	$-0.661338\pi$
$677$	−1.11471e24	−0.970863	−0.485432	+	0.874275i	$0.661338\pi$
$678$	9.39430e21	0.00808001
$679$	6.41825e23	0.545159
$680$	9.21208e21	0.00772737
$681$	−2.82315e24	−2.33875
$682$	−1.45569e22	−0.0119097
$683$	1.07912e24	0.871955	0.435977	−	0.899958i	$-0.356403\pi$
$683$	1.07912e24	0.871955	0.435977	+	0.899958i	$0.356403\pi$
$684$	2.61763e24	2.08896
$685$	6.05927e23	0.477585
$686$	8.48582e21	0.00660600
$687$	−2.90790e24	−2.23588
$688$	−1.62986e24	−1.23780
$689$	2.09057e24	1.56820
$690$	−1.64219e21	−0.00121676
$691$	9.96609e23	0.729393	0.364696	−	0.931127i	$-0.381173\pi$
$691$	9.96609e23	0.729393	0.364696	+	0.931127i	$0.381173\pi$
$692$	−1.64499e23	−0.118922
$693$	−3.12676e24	−2.23286
$694$	−3.04695e22	−0.0214936
$695$	7.56643e23	0.527254
$696$	−4.93501e22	−0.0339711
$697$	2.72677e24	1.85426
$698$	7.23317e21	0.00485912
$699$	3.40621e23	0.226056
$700$	−1.75823e24	−1.15277
$701$	−6.32354e23	−0.409597	−0.204799	−	0.978804i	$-0.565654\pi$
$701$	−6.32354e23	−0.409597	−0.204799	+	0.978804i	$0.565654\pi$
$702$	−4.54559e22	−0.0290887
$703$	−2.33797e24	−1.47815
$704$	−1.32119e24	−0.825276
$705$	−1.70330e23	−0.105119
$706$	8.29617e21	0.00505868
$707$	−2.96053e24	−1.78363
$708$	−5.76720e23	−0.343307
$709$	3.03342e24	1.78418	0.892091	−	0.451856i	$-0.149238\pi$
$709$	3.03342e24	1.78418	0.892091	+	0.451856i	$0.149238\pi$
$710$	3.98556e21	0.00231629
$711$	2.14984e24	1.23457
$712$	7.08768e22	0.0402183
$713$	4.49784e23	0.252199
$714$	5.62839e22	0.0311853
$715$	−4.87335e23	−0.266825
$716$	−2.34926e24	−1.27107
$717$	−3.86490e24	−2.06645
$718$	2.34251e21	0.00123772
$719$	−9.78810e23	−0.511096	−0.255548	−	0.966796i	$-0.582256\pi$
$719$	−9.78810e23	−0.511096	−0.255548	+	0.966796i	$0.582256\pi$
$720$	1.15468e24	0.595850
$721$	−1.04959e24	−0.535268
$722$	−1.67335e21	−0.000843375 0
$723$	1.50425e24	0.749281
$724$	6.59786e21	0.00324807
$725$	−1.52107e24	−0.740074
$726$	−1.40194e22	−0.00674167
$727$	3.28742e23	0.156247	0.0781236	−	0.996944i	$-0.475107\pi$
$727$	3.28742e23	0.156247	0.0781236	+	0.996944i	$0.475107\pi$
$728$	−7.43478e22	−0.0349262
$729$	−8.21272e23	−0.381332
$730$	1.02763e22	0.00471620
$731$	3.21693e24	1.45930
$732$	1.56881e24	0.703440
$733$	−3.56120e24	−1.57838	−0.789191	−	0.614148i	$-0.789500\pi$
$733$	−3.56120e24	−1.57838	−0.789191	+	0.614148i	$0.789500\pi$
$734$	2.32583e22	0.0101897
$735$	6.28132e23	0.272025
$736$	−1.74166e22	−0.00745592
$737$	1.06197e24	0.449405
$738$	−9.71831e22	−0.0406548
$739$	−4.65321e23	−0.192431	−0.0962154	−	0.995361i	$-0.530674\pi$
$739$	−4.65321e23	−0.192431	−0.0962154	+	0.995361i	$0.530674\pi$
$740$	−1.03147e24	−0.421684
$741$	4.98572e24	2.01499
$742$	4.96900e22	0.0198534
$743$	−1.46328e24	−0.577992	−0.288996	−	0.957330i	$-0.593321\pi$
$743$	−1.46328e24	−0.577992	−0.288996	+	0.957330i	$0.593321\pi$
$744$	1.31416e23	0.0513190
$745$	6.61378e23	0.255342
$746$	−4.03141e22	−0.0153878
$747$	−5.00415e24	−1.88845
$748$	2.60844e24	0.973234
$749$	1.43560e24	0.529588
$750$	−3.07875e22	−0.0112293
$751$	1.10952e24	0.400124	0.200062	−	0.979783i	$-0.435886\pi$
$751$	1.10952e24	0.400124	0.200062	+	0.979783i	$0.435886\pi$
$752$	−6.02013e23	−0.214661
$753$	3.03283e24	1.06928
$754$	−3.21573e22	−0.0112104
$755$	−1.72517e23	−0.0594678
$756$	7.60118e24	2.59087
$757$	−1.88966e24	−0.636897	−0.318448	−	0.947940i	$-0.603162\pi$
$757$	−1.88966e24	−0.636897	−0.318448	+	0.947940i	$0.603162\pi$
$758$	−5.14312e22	−0.0171411
$759$	−9.30052e23	−0.306515
$760$	1.93957e22	0.00632106
$761$	3.01022e24	0.970128	0.485064	−	0.874479i	$-0.338796\pi$
$761$	3.01022e24	0.970128	0.485064	+	0.874479i	$0.338796\pi$
$762$	7.65253e22	0.0243886
$763$	−3.75343e22	−0.0118296
$764$	−1.78628e23	−0.0556746
$765$	−2.27905e24	−0.702476
$766$	4.53968e21	0.00138382
$767$	−7.51653e23	−0.226598
$768$	5.96073e24	1.77717
$769$	2.39087e24	0.704989	0.352494	−	0.935814i	$-0.385334\pi$
$769$	2.39087e24	0.704989	0.352494	+	0.935814i	$0.385334\pi$
$770$	−1.15833e22	−0.00337800
$771$	−6.89909e24	−1.98989
$772$	4.96712e24	1.41696
$773$	−3.99220e24	−1.12638	−0.563192	−	0.826326i	$-0.690427\pi$
$773$	−3.99220e24	−1.12638	−0.563192	+	0.826326i	$0.690427\pi$
$774$	−1.14652e23	−0.0319952
$775$	4.05050e24	1.11801
$776$	3.81686e22	0.0104203
$777$	−1.26050e25	−3.40381
$778$	4.36560e22	0.0116605
$779$	5.74112e24	1.51680
$780$	2.19961e24	0.574832
$781$	2.25722e24	0.583499
$782$	1.14559e22	0.00292935
$783$	6.57586e24	1.66333
$784$	2.22007e24	0.555495
$785$	1.34321e24	0.332471
$786$	−1.13467e23	−0.0277828
$787$	3.01514e24	0.730336	0.365168	−	0.930942i	$-0.381011\pi$
$787$	3.01514e24	0.730336	0.365168	+	0.930942i	$0.381011\pi$
$788$	−4.73776e24	−1.13527
$789$	−4.62391e24	−1.09611
$790$	7.96422e21	0.00186773
$791$	−2.04742e24	−0.475014
$792$	−1.85945e23	−0.0426795
$793$	2.04467e24	0.464303
$794$	8.46782e22	0.0190238
$795$	−2.94040e24	−0.653561
$796$	3.87784e24	0.852764
$797$	−4.14721e24	−0.902320	−0.451160	−	0.892443i	$-0.648990\pi$
$797$	−4.14721e24	−0.902320	−0.451160	+	0.892443i	$0.648990\pi$
$798$	1.18504e23	0.0255098
$799$	1.18822e24	0.253075
$800$	−1.56844e23	−0.0330524
$801$	−1.75348e25	−3.65615
$802$	7.34088e22	0.0151449
$803$	5.81997e24	1.18806
$804$	−4.79325e24	−0.968174
$805$	3.57903e23	0.0715320
$806$	8.56327e22	0.0169353
$807$	1.80754e24	0.353722
$808$	−1.76059e23	−0.0340927
$809$	−3.74505e24	−0.717621	−0.358810	−	0.933410i	$-0.616818\pi$
$809$	−3.74505e24	−0.717621	−0.358810	+	0.933410i	$0.616818\pi$
$810$	2.64566e22	0.00501661
$811$	5.12265e24	0.961208	0.480604	−	0.876938i	$-0.340417\pi$
$811$	5.12265e24	0.961208	0.480604	+	0.876938i	$0.340417\pi$
$812$	5.37736e24	0.998489
$813$	1.48007e24	0.271964
$814$	8.30337e22	0.0150990
$815$	1.38491e24	0.249219
$816$	−1.17717e25	−2.09638
$817$	6.77312e24	1.19372
$818$	−6.70061e22	−0.0116872
$819$	1.83935e25	3.17506
$820$	2.53288e24	0.432710
$821$	−1.43914e24	−0.243325	−0.121662	−	0.992572i	$-0.538822\pi$
$821$	−1.43914e24	−0.243325	−0.121662	+	0.992572i	$0.538822\pi$
$822$	2.20159e23	0.0368406
$823$	8.65088e24	1.43272	0.716361	−	0.697730i	$-0.245807\pi$
$823$	8.65088e24	1.43272	0.716361	+	0.697730i	$0.245807\pi$
$824$	−6.24181e22	−0.0102313
$825$	−8.37553e24	−1.35879
$826$	−1.78658e22	−0.00286874
$827$	−9.97464e24	−1.58526	−0.792630	−	0.609703i	$-0.791289\pi$
$827$	−9.97464e24	−1.58526	−0.792630	+	0.609703i	$0.791289\pi$
$828$	2.87248e24	0.451855
$829$	−8.54005e24	−1.32968	−0.664839	−	0.746986i	$-0.731500\pi$
$829$	−8.54005e24	−1.32968	−0.664839	+	0.746986i	$0.731500\pi$
$830$	−1.85382e22	−0.00285696
$831$	7.20895e24	1.09967
$832$	7.77208e24	1.17352
$833$	−4.38185e24	−0.654899
$834$	2.74920e23	0.0406720
$835$	−2.75266e24	−0.403104
$836$	5.49198e24	0.796114
$837$	−1.75111e25	−2.51273
$838$	−6.19839e22	−0.00880450
$839$	9.64253e24	1.35586	0.677929	−	0.735127i	$-0.262878\pi$
$839$	9.64253e24	1.35586	0.677929	+	0.735127i	$0.262878\pi$
$840$	1.04571e23	0.0145558
$841$	−2.60513e24	−0.358975
$842$	−9.28178e22	−0.0126613
$843$	6.01463e24	0.812222
$844$	−5.33319e24	−0.712978
$845$	7.88640e23	0.104375
$846$	−4.23485e22	−0.00554869
$847$	3.05542e24	0.396335
$848$	−1.03925e25	−1.33462
$849$	−2.13141e25	−2.70989
$850$	1.03165e23	0.0129859
$851$	−2.56560e24	−0.319733
$852$	−1.01881e25	−1.25706
$853$	−2.16354e24	−0.264301	−0.132150	−	0.991230i	$-0.542188\pi$
$853$	−2.16354e24	−0.264301	−0.132150	+	0.991230i	$0.542188\pi$
$854$	4.85990e22	0.00587808
$855$	−4.79846e24	−0.574632
$856$	8.53735e22	0.0101227
$857$	−1.04065e25	−1.22171	−0.610854	−	0.791743i	$-0.709174\pi$
$857$	−1.04065e25	−1.22171	−0.610854	+	0.791743i	$0.709174\pi$
$858$	−1.77069e23	−0.0205826
$859$	1.18346e25	1.36211	0.681053	−	0.732234i	$-0.261522\pi$
$859$	1.18346e25	1.36211	0.681053	+	0.732234i	$0.261522\pi$
$860$	2.98818e24	0.340541
$861$	3.09529e25	3.49281
$862$	3.25627e22	0.00363839
$863$	9.28446e24	1.02722	0.513612	−	0.858023i	$-0.328307\pi$
$863$	9.28446e24	1.02722	0.513612	+	0.858023i	$0.328307\pi$
$864$	6.78065e23	0.0742856
$865$	3.01549e23	0.0327130
$866$	−1.86635e23	−0.0200489
$867$	6.50372e24	0.691831
$868$	−1.43196e25	−1.50839
$869$	4.51053e24	0.470500
$870$	4.52294e22	0.00467205
$871$	−6.24715e24	−0.639040
$872$	−2.23212e21	−0.000226114 0
$873$	−9.44282e24	−0.947285
$874$	2.41200e22	0.00239624
$875$	6.70992e24	0.660160
$876$	−2.62687e25	−2.55949
$877$	1.47767e24	0.142587	0.0712937	−	0.997455i	$-0.477287\pi$
$877$	1.47767e24	0.142587	0.0712937	+	0.997455i	$0.477287\pi$
$878$	−2.00982e23	−0.0192068
$879$	−3.61200e25	−3.41856
$880$	2.42261e24	0.227081
$881$	−1.45302e24	−0.134889	−0.0674443	−	0.997723i	$-0.521484\pi$
$881$	−1.45302e24	−0.134889	−0.0674443	+	0.997723i	$0.521484\pi$
$882$	1.56170e23	0.0143587
$883$	2.04535e25	1.86252	0.931261	−	0.364352i	$-0.118710\pi$
$883$	2.04535e25	1.86252	0.931261	+	0.364352i	$0.118710\pi$
$884$	−1.53444e25	−1.38391
$885$	1.05720e24	0.0944368
$886$	−2.57693e23	−0.0227991
$887$	−2.90629e23	−0.0254676	−0.0127338	−	0.999919i	$-0.504053\pi$
$887$	−2.90629e23	−0.0254676	−0.0127338	+	0.999919i	$0.504053\pi$
$888$	−7.49607e23	−0.0650614
$889$	−1.66781e25	−1.43378
$890$	−6.49587e22	−0.00553123
$891$	1.49836e25	1.26374
$892$	−6.04343e24	−0.504873
$893$	2.50175e24	0.207017
$894$	2.40307e23	0.0196969
$895$	4.30650e24	0.349646
$896$	7.39294e23	0.0594564
$897$	5.47114e24	0.435855
$898$	−2.40757e22	−0.00189990
$899$	−1.23880e25	−0.968377
$900$	2.58680e25	2.00309
$901$	2.05122e25	1.57345
$902$	−2.03898e23	−0.0154937
$903$	3.65169e25	2.74883
$904$	−1.21758e23	−0.00907955
$905$	−1.20948e22	−0.000893479 0
$906$	−6.26826e22	−0.00458730
$907$	6.50604e24	0.471688	0.235844	−	0.971791i	$-0.424215\pi$
$907$	6.50604e24	0.471688	0.235844	+	0.971791i	$0.424215\pi$
$908$	1.82939e25	1.31394
$909$	4.35566e25	3.09928
$910$	6.81399e22	0.00480341
$911$	−2.51874e25	−1.75905	−0.879524	−	0.475855i	$-0.842139\pi$
$911$	−2.51874e25	−1.75905	−0.879524	+	0.475855i	$0.842139\pi$
$912$	−2.47848e25	−1.71486
$913$	−1.04991e25	−0.719698
$914$	−2.17440e23	−0.0147671
$915$	−2.87584e24	−0.193502
$916$	1.88430e25	1.25614
$917$	2.47292e25	1.63332
$918$	−4.46004e23	−0.0291861
$919$	2.94366e25	1.90856	0.954281	−	0.298912i	$-0.0966238\pi$
$919$	2.94366e25	1.90856	0.954281	+	0.298912i	$0.0966238\pi$
$920$	2.12841e22	0.00136728
$921$	1.22031e25	0.776721
$922$	−1.47273e22	−0.000928774 0
$923$	−1.32784e25	−0.829717
$924$	2.96097e25	1.83325
$925$	−2.31044e25	−1.41739
$926$	1.87715e23	0.0114105
$927$	1.54421e25	0.930098
$928$	4.79690e23	0.0286288
$929$	1.72980e25	1.02297	0.511484	−	0.859293i	$-0.329096\pi$
$929$	1.72980e25	1.02297	0.511484	+	0.859293i	$0.329096\pi$
$930$	−1.20443e23	−0.00705792
$931$	−9.22582e24	−0.535713
$932$	−2.20721e24	−0.127001
$933$	−1.53686e25	−0.876272
$934$	3.24147e23	0.0183145
$935$	−4.78162e24	−0.267717
$936$	1.09384e24	0.0606889
$937$	−2.50472e25	−1.37713	−0.688563	−	0.725177i	$-0.741758\pi$
$937$	−2.50472e25	−1.37713	−0.688563	+	0.725177i	$0.741758\pi$
$938$	−1.48486e23	−0.00809025
$939$	−4.29216e25	−2.31749
$940$	1.10373e24	0.0590575
$941$	−3.22496e25	−1.71007	−0.855033	−	0.518573i	$-0.826464\pi$
$941$	−3.22496e25	−1.71007	−0.855033	+	0.518573i	$0.826464\pi$
$942$	4.88047e23	0.0256465
$943$	6.30009e24	0.328093
$944$	3.73658e24	0.192847
$945$	−1.39340e25	−0.712696
$946$	−2.40549e23	−0.0121935
$947$	1.84322e25	0.925984	0.462992	−	0.886363i	$-0.346776\pi$
$947$	1.84322e25	0.925984	0.462992	+	0.886363i	$0.346776\pi$
$948$	−2.03585e25	−1.01362
$949$	−3.42366e25	−1.68938
$950$	2.17211e23	0.0106226
$951$	3.74414e25	1.81475
$952$	−7.29485e23	−0.0350431
$953$	3.55817e24	0.169409	0.0847046	−	0.996406i	$-0.473005\pi$
$953$	3.55817e24	0.169409	0.0847046	+	0.996406i	$0.473005\pi$
$954$	−7.31063e23	−0.0344980
$955$	3.27450e23	0.0153150
$956$	2.50443e25	1.16096
$957$	2.56156e25	1.17694
$958$	−1.41484e23	−0.00644320
$959$	−4.79821e25	−2.16581
$960$	−1.09315e25	−0.489073
$961$	1.04384e25	0.462896
$962$	−4.88455e23	−0.0214702
$963$	−2.11212e25	−0.920229
$964$	−9.74745e24	−0.420956
$965$	−9.10540e24	−0.389778
$966$	1.30041e23	0.00551793
$967$	1.43065e25	0.601739	0.300869	−	0.953665i	$-0.402723\pi$
$967$	1.43065e25	0.601739	0.300869	+	0.953665i	$0.402723\pi$
$968$	1.81702e23	0.00757566
$969$	4.89188e25	2.02173
$970$	−3.49815e22	−0.00143311
$971$	1.06702e25	0.433321	0.216661	−	0.976247i	$-0.430483\pi$
$971$	1.06702e25	0.433321	0.216661	+	0.976247i	$0.430483\pi$
$972$	−1.60304e25	−0.645329
$973$	−5.99169e25	−2.39106
$974$	4.56797e23	0.0180706
$975$	4.92700e25	1.93216
$976$	−1.01644e25	−0.395145
$977$	2.24347e25	0.864602	0.432301	−	0.901729i	$-0.357702\pi$
$977$	2.24347e25	0.864602	0.432301	+	0.901729i	$0.357702\pi$
$978$	5.03196e23	0.0192246
$979$	−3.67893e25	−1.39338
$980$	−4.07026e24	−0.152827
$981$	5.52223e23	0.0205555
$982$	3.31229e23	0.0122231
$983$	−1.99259e25	−0.728977	−0.364488	−	0.931208i	$-0.618756\pi$
$983$	−1.99259e25	−0.728977	−0.364488	+	0.931208i	$0.618756\pi$
$984$	1.84073e24	0.0667625
$985$	8.68495e24	0.312291
$986$	−3.15520e23	−0.0112479
$987$	1.34880e25	0.476709
$988$	−3.23072e25	−1.13205
$989$	7.43256e24	0.258208
$990$	1.70418e23	0.00586972
$991$	−2.51023e25	−0.857211	−0.428605	−	0.903492i	$-0.640995\pi$
$991$	−2.51023e25	−0.857211	−0.428605	+	0.903492i	$0.640995\pi$
$992$	−1.27738e24	−0.0432486
$993$	−5.94860e25	−1.99685
$994$	−3.15608e23	−0.0105042
$995$	−7.10860e24	−0.234578
$996$	4.73882e25	1.55048
$997$	2.36990e25	0.768814	0.384407	−	0.923164i	$-0.374406\pi$
$997$	2.36990e25	0.768814	0.384407	+	0.923164i	$0.374406\pi$
$998$	−3.26905e23	−0.0105151
$999$	9.98845e25	3.18560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.18.a.a.1.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.18.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+4.31600 q^{2} +20224.5 q^{3} -131053. q^{4} +240238. q^{5} +87288.7 q^{6} -1.90239e7 q^{7} -1.13133e6 q^{8} +2.79889e8 q^{9} +O(q^{10})\)	\(q+4.31600 q^{2} +20224.5 q^{3} -131053. q^{4} +240238. q^{5} +87288.7 q^{6} -1.90239e7 q^{7} -1.13133e6 q^{8} +2.79889e8 q^{9} +1.03687e6 q^{10} +5.87229e8 q^{11} -2.65049e9 q^{12} -3.45444e9 q^{13} -8.21073e7 q^{14} +4.85869e9 q^{15} +1.71725e10 q^{16} -3.38942e10 q^{17} +1.20800e9 q^{18} -7.13630e10 q^{19} -3.14840e10 q^{20} -3.84749e11 q^{21} +2.53448e9 q^{22} -7.83110e10 q^{23} -2.28806e10 q^{24} -7.05225e11 q^{25} -1.49093e10 q^{26} +3.04882e12 q^{27} +2.49315e12 q^{28} +2.15685e12 q^{29} +2.09701e10 q^{30} -5.74356e12 q^{31} +2.22403e11 q^{32} +1.18764e13 q^{33} -1.46287e11 q^{34} -4.57028e12 q^{35} -3.66804e13 q^{36} +3.27617e13 q^{37} -3.08002e11 q^{38} -6.98642e13 q^{39} -2.71789e11 q^{40} -8.04496e13 q^{41} -1.66058e12 q^{42} -9.49109e13 q^{43} -7.69583e13 q^{44} +6.72401e13 q^{45} -3.37990e11 q^{46} -3.50567e13 q^{47} +3.47306e14 q^{48} +1.29280e14 q^{49} -3.04375e12 q^{50} -6.85493e14 q^{51} +4.52716e14 q^{52} -6.05184e14 q^{53} +1.31587e13 q^{54} +1.41075e14 q^{55} +2.15224e13 q^{56} -1.44328e15 q^{57} +9.30897e12 q^{58} +2.17590e14 q^{59} -6.36748e14 q^{60} -5.91896e14 q^{61} -2.47892e13 q^{62} -5.32460e15 q^{63} -2.24988e15 q^{64} -8.29889e14 q^{65} +5.12585e13 q^{66} +1.80844e15 q^{67} +4.44195e15 q^{68} -1.58380e15 q^{69} -1.97253e13 q^{70} +3.84385e15 q^{71} -3.16648e14 q^{72} +9.91090e15 q^{73} +1.41399e14 q^{74} -1.42628e16 q^{75} +9.35236e15 q^{76} -1.11714e16 q^{77} -3.01534e14 q^{78} +7.68104e15 q^{79} +4.12550e15 q^{80} +2.55159e16 q^{81} -3.47220e14 q^{82} -1.78791e16 q^{83} +5.04227e16 q^{84} -8.14269e15 q^{85} -4.09635e14 q^{86} +4.36212e16 q^{87} -6.64351e14 q^{88} -6.26490e16 q^{89} +2.90208e14 q^{90} +6.57171e16 q^{91} +1.02629e16 q^{92} -1.16160e17 q^{93} -1.51305e14 q^{94} -1.71441e16 q^{95} +4.49797e15 q^{96} -3.37377e16 q^{97} +5.57972e14 q^{98} +1.64359e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) \) 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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