LMFDB - Embedded newform 23.18.a.a.1.8

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			1.8
Root			$-33.2496$ 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)

$f(q)$	$=$	$q+66.4993 q^{2} +758.112 q^{3} -126650. q^{4} -509658. q^{5} +50413.9 q^{6} +2.07983e7 q^{7} -1.71383e7 q^{8} -1.28565e8 q^{9} +O(q^{10})$	\(q+66.4993 q^{2} +758.112 q^{3} -126650. q^{4} -509658. q^{5} +50413.9 q^{6} +2.07983e7 q^{7} -1.71383e7 q^{8} -1.28565e8 q^{9} -3.38919e7 q^{10} +9.41262e8 q^{11} -9.60148e7 q^{12} +5.03964e9 q^{13} +1.38307e9 q^{14} -3.86378e8 q^{15} +1.54606e10 q^{16} -5.40559e10 q^{17} -8.54951e9 q^{18} -5.66393e10 q^{19} +6.45481e10 q^{20} +1.57675e10 q^{21} +6.25933e10 q^{22} -7.83110e10 q^{23} -1.29928e10 q^{24} -5.03188e11 q^{25} +3.35132e11 q^{26} -1.95370e11 q^{27} -2.63410e12 q^{28} +2.49988e12 q^{29} -2.56939e10 q^{30} +1.01010e12 q^{31} +3.27447e12 q^{32} +7.13583e11 q^{33} -3.59468e12 q^{34} -1.06000e13 q^{35} +1.62828e13 q^{36} -4.21504e13 q^{37} -3.76647e12 q^{38} +3.82061e12 q^{39} +8.73469e12 q^{40} -1.09910e13 q^{41} +1.04852e12 q^{42} -4.63513e13 q^{43} -1.19211e14 q^{44} +6.55244e13 q^{45} -5.20763e12 q^{46} -5.20983e13 q^{47} +1.17208e13 q^{48} +1.99939e14 q^{49} -3.34616e13 q^{50} -4.09805e13 q^{51} -6.38270e14 q^{52} -4.70316e14 q^{53} -1.29920e13 q^{54} -4.79722e14 q^{55} -3.56448e14 q^{56} -4.29389e13 q^{57} +1.66240e14 q^{58} -2.45116e14 q^{59} +4.89347e13 q^{60} -2.67127e14 q^{61} +6.71713e13 q^{62} -2.67394e15 q^{63} -1.80870e15 q^{64} -2.56849e15 q^{65} +4.74527e13 q^{66} -2.45834e15 q^{67} +6.84618e15 q^{68} -5.93685e13 q^{69} -7.04895e14 q^{70} +8.24578e15 q^{71} +2.20340e15 q^{72} -1.05486e16 q^{73} -2.80297e15 q^{74} -3.81473e14 q^{75} +7.17335e15 q^{76} +1.95767e16 q^{77} +2.54068e14 q^{78} -1.84115e16 q^{79} -7.87960e15 q^{80} +1.64548e16 q^{81} -7.30896e14 q^{82} -8.28314e15 q^{83} -1.99695e15 q^{84} +2.75501e16 q^{85} -3.08233e15 q^{86} +1.89519e15 q^{87} -1.61317e16 q^{88} +2.84699e16 q^{89} +4.35733e15 q^{90} +1.04816e17 q^{91} +9.91807e15 q^{92} +7.65773e14 q^{93} -3.46450e15 q^{94} +2.88667e16 q^{95} +2.48242e15 q^{96} +6.28188e16 q^{97} +1.32958e16 q^{98} -1.21014e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	66.4993	0.183680	0.0918400	−	0.995774i	$-0.470725\pi$
$2$	66.4993	0.183680	0.0918400	+	0.995774i	$0.470725\pi$
$3$	758.112	0.0667118	0.0333559	−	0.999444i	$-0.489381\pi$
$3$	758.112	0.0667118	0.0333559	+	0.999444i	$0.489381\pi$
$4$	−126650.	−0.966262
$5$	−509658.	−0.583491	−0.291745	−	0.956496i	$-0.594236\pi$
$5$	−509658.	−0.583491	−0.291745	+	0.956496i	$0.594236\pi$
$6$	50413.9	0.0122536
$7$	2.07983e7	1.36362	0.681812	−	0.731527i	$-0.261192\pi$
$7$	2.07983e7	1.36362	0.681812	+	0.731527i	$0.261192\pi$
$8$	−1.71383e7	−0.361163
$9$	−1.28565e8	−0.995550
$10$	−3.38919e7	−0.107176
$11$	9.41262e8	1.32395	0.661977	−	0.749524i	$-0.269718\pi$
$11$	9.41262e8	1.32395	0.661977	+	0.749524i	$0.269718\pi$
$12$	−9.60148e7	−0.0644611
$13$	5.03964e9	1.71349	0.856744	−	0.515742i	$-0.172484\pi$
$13$	5.03964e9	1.71349	0.856744	+	0.515742i	$0.172484\pi$
$14$	1.38307e9	0.250471
$15$	−3.86378e8	−0.0389257
$16$	1.54606e10	0.899923
$17$	−5.40559e10	−1.87944	−0.939718	−	0.341950i	$-0.888913\pi$
$17$	−5.40559e10	−1.87944	−0.939718	+	0.341950i	$0.888913\pi$
$18$	−8.54951e9	−0.182863
$19$	−5.66393e10	−0.765089	−0.382545	−	0.923937i	$-0.624952\pi$
$19$	−5.66393e10	−0.765089	−0.382545	+	0.923937i	$0.624952\pi$
$20$	6.45481e10	0.563805
$21$	1.57675e10	0.0909699
$22$	6.25933e10	0.243184
$23$	−7.83110e10	−0.208514
$23$	−7.83110e10	−0.208514
$24$	−1.29928e10	−0.0240939
$25$	−5.03188e11	−0.659538
$26$	3.35132e11	0.314734
$27$	−1.95370e11	−0.133127
$28$	−2.63410e12	−1.31762
$29$	2.49988e12	0.927975	0.463987	−	0.885842i	$-0.346418\pi$
$29$	2.49988e12	0.927975	0.463987	+	0.885842i	$0.346418\pi$
$30$	−2.56939e10	−0.00714988
$31$	1.01010e12	0.212712	0.106356	−	0.994328i	$-0.466082\pi$
$31$	1.01010e12	0.212712	0.106356	+	0.994328i	$0.466082\pi$
$32$	3.27447e12	0.526461
$33$	7.13583e11	0.0883234
$34$	−3.59468e12	−0.345215
$35$	−1.06000e13	−0.795663
$36$	1.62828e13	0.961961
$37$	−4.21504e13	−1.97282	−0.986409	−	0.164307i	$-0.947461\pi$
$37$	−4.21504e13	−1.97282	−0.986409	+	0.164307i	$0.947461\pi$
$38$	−3.76647e12	−0.140532
$39$	3.82061e12	0.114310
$40$	8.73469e12	0.210735
$41$	−1.09910e13	−0.214969	−0.107485	−	0.994207i	$-0.534280\pi$
$41$	−1.09910e13	−0.214969	−0.107485	+	0.994207i	$0.534280\pi$
$42$	1.04852e12	0.0167094
$43$	−4.63513e13	−0.604756	−0.302378	−	0.953188i	$-0.597780\pi$
$43$	−4.63513e13	−0.604756	−0.302378	+	0.953188i	$0.597780\pi$
$44$	−1.19211e14	−1.27929
$45$	6.55244e13	0.580894
$46$	−5.20763e12	−0.0382999
$47$	−5.20983e13	−0.319148	−0.159574	−	0.987186i	$-0.551012\pi$
$47$	−5.20983e13	−0.319148	−0.159574	+	0.987186i	$0.551012\pi$
$48$	1.17208e13	0.0600355
$49$	1.99939e14	0.859472
$50$	−3.34616e13	−0.121144
$51$	−4.09805e13	−0.125381
$52$	−6.38270e14	−1.65568
$53$	−4.70316e14	−1.03763	−0.518817	−	0.854885i	$-0.673628\pi$
$53$	−4.70316e14	−1.03763	−0.518817	+	0.854885i	$0.673628\pi$
$54$	−1.29920e13	−0.0244527
$55$	−4.79722e14	−0.772515
$56$	−3.56448e14	−0.492491
$57$	−4.29389e13	−0.0510405
$58$	1.66240e14	0.170451
$59$	−2.45116e14	−0.217335	−0.108667	−	0.994078i	$-0.534658\pi$
$59$	−2.45116e14	−0.217335	−0.108667	+	0.994078i	$0.534658\pi$
$60$	4.89347e13	0.0376125
$61$	−2.67127e14	−0.178408	−0.0892040	−	0.996013i	$-0.528432\pi$
$61$	−2.67127e14	−0.178408	−0.0892040	+	0.996013i	$0.528432\pi$
$62$	6.71713e13	0.0390710
$63$	−2.67394e15	−1.35756
$64$	−1.80870e15	−0.803223
$65$	−2.56849e15	−0.999804
$66$	4.74527e13	0.0162232
$67$	−2.45834e15	−0.739615	−0.369808	−	0.929108i	$-0.620576\pi$
$67$	−2.45834e15	−0.739615	−0.369808	+	0.929108i	$0.620576\pi$
$68$	6.84618e15	1.81603
$69$	−5.93685e13	−0.0139104
$70$	−7.04895e14	−0.146147
$71$	8.24578e15	1.51543	0.757715	−	0.652585i	$-0.226316\pi$
$71$	8.24578e15	1.51543	0.757715	+	0.652585i	$0.226316\pi$
$72$	2.20340e15	0.359556
$73$	−1.05486e16	−1.53092	−0.765459	−	0.643484i	$-0.777488\pi$
$73$	−1.05486e16	−1.53092	−0.765459	+	0.643484i	$0.777488\pi$
$74$	−2.80297e15	−0.362368
$75$	−3.81473e14	−0.0439990
$76$	7.17335e15	0.739276
$77$	1.95767e16	1.80538
$78$	2.54068e14	0.0209965
$79$	−1.84115e16	−1.36539	−0.682697	−	0.730701i	$-0.739193\pi$
$79$	−1.84115e16	−1.36539	−0.682697	+	0.730701i	$0.739193\pi$
$80$	−7.87960e15	−0.525097
$81$	1.64548e16	0.986668
$82$	−7.30896e14	−0.0394855
$83$	−8.28314e15	−0.403674	−0.201837	−	0.979419i	$-0.564691\pi$
$83$	−8.28314e15	−0.403674	−0.201837	+	0.979419i	$0.564691\pi$
$84$	−1.99695e15	−0.0879007
$85$	2.75501e16	1.09663
$86$	−3.08233e15	−0.111082
$87$	1.89519e15	0.0619069
$88$	−1.61317e16	−0.478163
$89$	2.84699e16	0.766603	0.383302	−	0.923623i	$-0.374787\pi$
$89$	2.84699e16	0.766603	0.383302	+	0.923623i	$0.374787\pi$
$90$	4.35733e15	0.106699
$91$	1.04816e17	2.33655
$92$	9.91807e15	0.201479
$93$	7.65773e14	0.0141904
$94$	−3.46450e15	−0.0586211
$95$	2.88667e16	0.446422
$96$	2.48242e15	0.0351212
$97$	6.28188e16	0.813823	0.406911	−	0.913468i	$-0.366606\pi$
$97$	6.28188e16	0.813823	0.406911	+	0.913468i	$0.366606\pi$
$98$	1.32958e16	0.157868
$99$	−1.21014e17	−1.31806
$100$	6.37287e16	0.637287
$101$	1.04719e16	0.0962264	0.0481132	−	0.998842i	$-0.484679\pi$
$101$	1.04719e16	0.0962264	0.0481132	+	0.998842i	$0.484679\pi$
$102$	−2.72517e15	−0.0230299
$103$	−2.34839e17	−1.82664	−0.913322	−	0.407239i	$-0.866492\pi$
$103$	−2.34839e17	−1.82664	−0.913322	+	0.407239i	$0.866492\pi$
$104$	−8.63710e16	−0.618849
$105$	−8.03602e15	−0.0530801
$106$	−3.12757e16	−0.190593
$107$	−1.83943e17	−1.03496	−0.517478	−	0.855696i	$-0.673129\pi$
$107$	−1.83943e17	−1.03496	−0.517478	+	0.855696i	$0.673129\pi$
$108$	2.47436e16	0.128635
$109$	2.65141e17	1.27453	0.637267	−	0.770643i	$-0.280065\pi$
$109$	2.65141e17	1.27453	0.637267	+	0.770643i	$0.280065\pi$
$110$	−3.19012e16	−0.141896
$111$	−3.19547e16	−0.131610
$112$	3.21554e17	1.22716
$113$	4.87899e17	1.72649	0.863243	−	0.504788i	$-0.168429\pi$
$113$	4.87899e17	1.72649	0.863243	+	0.504788i	$0.168429\pi$
$114$	−2.85541e15	−0.00937512
$115$	3.99118e16	0.121666
$116$	−3.16609e17	−0.896666
$117$	−6.47923e17	−1.70586
$118$	−1.63000e16	−0.0399201
$119$	−1.12427e18	−2.56285
$120$	6.62187e15	0.0140585
$121$	3.80528e17	0.752854
$122$	−1.77638e16	−0.0327700
$123$	−8.33244e15	−0.0143410
$124$	−1.27930e17	−0.205536
$125$	6.45292e17	0.968325
$126$	−1.77815e17	−0.249356
$127$	−5.19836e16	−0.0681608	−0.0340804	−	0.999419i	$-0.510850\pi$
$127$	−5.19836e16	−0.0681608	−0.0340804	+	0.999419i	$0.510850\pi$
$128$	−5.49468e17	−0.673997
$129$	−3.51395e16	−0.0403444
$130$	−1.70803e17	−0.183644
$131$	−5.54693e17	−0.558788	−0.279394	−	0.960177i	$-0.590134\pi$
$131$	−5.54693e17	−0.558788	−0.279394	+	0.960177i	$0.590134\pi$
$132$	−9.03751e16	−0.0853435
$133$	−1.17800e18	−1.04329
$134$	−1.63478e17	−0.135853
$135$	9.95718e16	0.0776782
$136$	9.26428e17	0.678783
$137$	−5.67890e17	−0.390966	−0.195483	−	0.980707i	$-0.562628\pi$
$137$	−5.67890e17	−0.390966	−0.195483	+	0.980707i	$0.562628\pi$
$138$	−3.94796e15	−0.00255506
$139$	−8.76568e17	−0.533531	−0.266766	−	0.963761i	$-0.585955\pi$
$139$	−8.76568e17	−0.533531	−0.266766	+	0.963761i	$0.585955\pi$
$140$	1.34249e18	0.768818
$141$	−3.94964e16	−0.0212909
$142$	5.48339e17	0.278354
$143$	4.74362e18	2.26858
$144$	−1.98769e18	−0.895918
$145$	−1.27408e18	−0.541465
$146$	−7.01477e17	−0.281199
$147$	1.51577e17	0.0573370
$148$	5.33834e18	1.90626
$149$	−7.83727e17	−0.264291	−0.132145	−	0.991230i	$-0.542187\pi$
$149$	−7.83727e17	−0.264291	−0.132145	+	0.991230i	$0.542187\pi$
$150$	−2.53677e16	−0.00808174
$151$	7.09708e17	0.213686	0.106843	−	0.994276i	$-0.465926\pi$
$151$	7.09708e17	0.213686	0.106843	+	0.994276i	$0.465926\pi$
$152$	9.70702e17	0.276322
$153$	6.94973e18	1.87107
$154$	1.30183e18	0.331612
$155$	−5.14808e17	−0.124116
$156$	−4.83880e17	−0.110453
$157$	−5.90894e18	−1.27750	−0.638752	−	0.769412i	$-0.720549\pi$
$157$	−5.90894e18	−1.27750	−0.638752	+	0.769412i	$0.720549\pi$
$158$	−1.22435e18	−0.250796
$159$	−3.56552e17	−0.0692225
$160$	−1.66886e18	−0.307185
$161$	−1.62874e18	−0.284335
$162$	1.09424e18	0.181231
$163$	7.89832e18	1.24148	0.620741	−	0.784016i	$-0.286832\pi$
$163$	7.89832e18	1.24148	0.620741	+	0.784016i	$0.286832\pi$
$164$	1.39201e18	0.207716
$165$	−3.63683e17	−0.0515359
$166$	−5.50823e17	−0.0741469
$167$	−1.13451e19	−1.45117	−0.725585	−	0.688132i	$-0.758431\pi$
$167$	−1.13451e19	−1.45117	−0.725585	+	0.688132i	$0.758431\pi$
$168$	−2.70228e17	−0.0328550
$169$	1.67475e19	1.93604
$170$	1.83206e18	0.201430
$171$	7.28185e18	0.761684
$172$	5.87039e18	0.584352
$173$	−9.98795e18	−0.946421	−0.473211	−	0.880949i	$-0.656905\pi$
$173$	−9.98795e18	−0.946421	−0.473211	+	0.880949i	$0.656905\pi$
$174$	1.26029e17	0.0113711
$175$	−1.04655e19	−0.899363
$176$	1.45524e19	1.19146
$177$	−1.85825e17	−0.0144988
$178$	1.89323e18	0.140810
$179$	−1.85258e19	−1.31379	−0.656894	−	0.753983i	$-0.728130\pi$
$179$	−1.85258e19	−1.31379	−0.656894	+	0.753983i	$0.728130\pi$
$180$	−8.29866e18	−0.561296
$181$	−1.06473e19	−0.687021	−0.343511	−	0.939149i	$-0.611616\pi$
$181$	−1.06473e19	−0.687021	−0.343511	+	0.939149i	$0.611616\pi$
$182$	6.97019e18	0.429178
$183$	−2.02512e17	−0.0119019
$184$	1.34212e18	0.0753077
$185$	2.14823e19	1.15112
$186$	5.09234e16	0.00260650
$187$	−5.08808e19	−2.48829
$188$	6.59824e18	0.308380
$189$	−4.06336e18	−0.181535
$190$	1.91961e18	0.0819989
$191$	−2.36121e19	−0.964610	−0.482305	−	0.876003i	$-0.660200\pi$
$191$	−2.36121e19	−0.964610	−0.482305	+	0.876003i	$0.660200\pi$
$192$	−1.37120e18	−0.0535845
$193$	−1.87274e19	−0.700228	−0.350114	−	0.936707i	$-0.613857\pi$
$193$	−1.87274e19	−0.700228	−0.350114	+	0.936707i	$0.613857\pi$
$194$	4.17741e18	0.149483
$195$	−1.94721e18	−0.0666988
$196$	−2.53223e19	−0.830475
$197$	−7.80904e18	−0.245265	−0.122632	−	0.992452i	$-0.539134\pi$
$197$	−7.80904e18	−0.245265	−0.122632	+	0.992452i	$0.539134\pi$
$198$	−8.04733e18	−0.242102
$199$	−1.48058e19	−0.426758	−0.213379	−	0.976969i	$-0.568447\pi$
$199$	−1.48058e19	−0.426758	−0.213379	+	0.976969i	$0.568447\pi$
$200$	8.62380e18	0.238201
$201$	−1.86370e18	−0.0493411
$202$	6.96375e17	0.0176749
$203$	5.19933e19	1.26541
$204$	5.19017e18	0.121150
$205$	5.60167e18	0.125432
$206$	−1.56166e19	−0.335518
$207$	1.00681e19	0.207586
$208$	7.79157e19	1.54201
$209$	−5.33124e19	−1.01294
$210$	−5.34389e17	−0.00974976
$211$	−3.50846e19	−0.614774	−0.307387	−	0.951585i	$-0.599455\pi$
$211$	−3.50846e19	−0.614774	−0.307387	+	0.951585i	$0.599455\pi$
$212$	5.95654e19	1.00263
$213$	6.25123e18	0.101097
$214$	−1.22321e19	−0.190101
$215$	2.36233e19	0.352870
$216$	3.34831e18	0.0480805
$217$	2.10085e19	0.290059
$218$	1.76317e19	0.234106
$219$	−7.99705e18	−0.102130
$220$	6.07567e19	0.746452
$221$	−2.72422e20	−3.22039
$222$	−2.12497e18	−0.0241742
$223$	5.09007e19	0.557356	0.278678	−	0.960385i	$-0.410104\pi$
$223$	5.09007e19	0.557356	0.278678	+	0.960385i	$0.410104\pi$
$224$	6.81035e19	0.717895
$225$	6.46926e19	0.656603
$226$	3.24450e19	0.317121
$227$	9.56627e19	0.900581	0.450290	−	0.892882i	$-0.351320\pi$
$227$	9.56627e19	0.900581	0.450290	+	0.892882i	$0.351320\pi$
$228$	5.43821e18	0.0493185
$229$	7.77741e19	0.679569	0.339784	−	0.940503i	$-0.389646\pi$
$229$	7.77741e19	0.679569	0.339784	+	0.940503i	$0.389646\pi$
$230$	2.65411e18	0.0223477
$231$	1.48413e19	0.120440
$232$	−4.28438e19	−0.335150
$233$	8.21597e19	0.619631	0.309816	−	0.950797i	$-0.399733\pi$
$233$	8.21597e19	0.619631	0.309816	+	0.950797i	$0.399733\pi$
$234$	−4.30865e19	−0.313333
$235$	2.65523e19	0.186220
$236$	3.10439e19	0.210002
$237$	−1.39580e19	−0.0910880
$238$	−7.47633e19	−0.470744
$239$	1.51233e20	0.918895	0.459447	−	0.888205i	$-0.348047\pi$
$239$	1.51233e20	0.918895	0.459447	+	0.888205i	$0.348047\pi$
$240$	−5.97362e18	−0.0350302
$241$	−3.79827e19	−0.215001	−0.107501	−	0.994205i	$-0.534285\pi$
$241$	−3.79827e19	−0.215001	−0.107501	+	0.994205i	$0.534285\pi$
$242$	2.53048e19	0.138284
$243$	3.77047e19	0.198949
$244$	3.38316e19	0.172389
$245$	−1.01901e20	−0.501494
$246$	−5.54102e17	−0.00263415
$247$	−2.85441e20	−1.31097
$248$	−1.73115e19	−0.0768238
$249$	−6.27955e18	−0.0269299
$250$	4.29115e19	0.177862
$251$	1.38946e20	0.556697	0.278348	−	0.960480i	$-0.410213\pi$
$251$	1.38946e20	0.556697	0.278348	+	0.960480i	$0.410213\pi$
$252$	3.38655e20	1.31175
$253$	−7.37112e19	−0.276063
$254$	−3.45687e18	−0.0125198
$255$	2.08860e19	0.0731585
$256$	2.00530e20	0.679423
$257$	3.96139e20	1.29842	0.649212	−	0.760607i	$-0.275099\pi$
$257$	3.96139e20	1.29842	0.649212	+	0.760607i	$0.275099\pi$
$258$	−2.33675e18	−0.00741046
$259$	−8.76658e20	−2.69018
$260$	3.25299e20	0.966073
$261$	−3.21398e20	−0.923845
$262$	−3.68867e19	−0.102638
$263$	−5.53524e20	−1.49112	−0.745560	−	0.666438i	$-0.767818\pi$
$263$	−5.53524e20	−1.49112	−0.745560	+	0.666438i	$0.767818\pi$
$264$	−1.22296e19	−0.0318991
$265$	2.39700e20	0.605450
$266$	−7.83363e19	−0.191632
$267$	2.15834e19	0.0511415
$268$	3.11348e20	0.714662
$269$	−4.67341e20	−1.03930	−0.519648	−	0.854381i	$-0.673937\pi$
$269$	−4.67341e20	−1.03930	−0.519648	+	0.854381i	$0.673937\pi$
$270$	6.62146e18	0.0142679
$271$	7.99754e20	1.67000	0.835002	−	0.550248i	$-0.185467\pi$
$271$	7.99754e20	1.67000	0.835002	+	0.550248i	$0.185467\pi$
$272$	−8.35735e20	−1.69135
$273$	7.94623e19	0.155876
$274$	−3.77643e19	−0.0718127
$275$	−4.73632e20	−0.873198
$276$	7.51901e18	0.0134411
$277$	−9.73046e20	−1.68677	−0.843384	−	0.537311i	$-0.819440\pi$
$277$	−9.73046e20	−1.68677	−0.843384	+	0.537311i	$0.819440\pi$
$278$	−5.82912e19	−0.0979991
$279$	−1.29865e20	−0.211765
$280$	1.81667e20	0.287364
$281$	4.90844e19	0.0753252	0.0376626	−	0.999291i	$-0.488009\pi$
$281$	4.90844e19	0.0753252	0.0376626	+	0.999291i	$0.488009\pi$
$282$	−2.62648e18	−0.00391072
$283$	−4.14616e20	−0.599047	−0.299524	−	0.954089i	$-0.596828\pi$
$283$	−4.14616e20	−0.599047	−0.299524	+	0.954089i	$0.596828\pi$
$284$	−1.04433e21	−1.46430
$285$	2.18842e19	0.0297817
$286$	3.15448e20	0.416693
$287$	−2.28595e20	−0.293137
$288$	−4.20984e20	−0.524118
$289$	2.09480e21	2.53228
$290$	−8.47257e19	−0.0994563
$291$	4.76237e19	0.0542916
$292$	1.33598e21	1.47927
$293$	6.19326e20	0.666108	0.333054	−	0.942908i	$-0.391921\pi$
$293$	6.19326e20	0.666108	0.333054	+	0.942908i	$0.391921\pi$
$294$	1.00797e19	0.0105317
$295$	1.24925e20	0.126813
$296$	7.22387e20	0.712509
$297$	−1.83894e20	−0.176254
$298$	−5.21173e19	−0.0485449
$299$	−3.94659e20	−0.357287
$300$	4.83135e19	0.0425146
$301$	−9.64029e20	−0.824660
$302$	4.71951e19	0.0392498
$303$	7.93889e18	0.00641944
$304$	−8.75675e20	−0.688521
$305$	1.36144e20	0.104099
$306$	4.62152e20	0.343679
$307$	−9.92693e20	−0.718023	−0.359012	−	0.933333i	$-0.616886\pi$
$307$	−9.92693e20	−0.718023	−0.359012	+	0.933333i	$0.616886\pi$
$308$	−2.47938e21	−1.74447
$309$	−1.78034e20	−0.121859
$310$	−3.42344e19	−0.0227976
$311$	2.69490e21	1.74614	0.873070	−	0.487595i	$-0.162126\pi$
$311$	2.69490e21	1.74614	0.873070	+	0.487595i	$0.162126\pi$
$312$	−6.54789e19	−0.0412845
$313$	−1.78625e19	−0.0109601	−0.00548007	−	0.999985i	$-0.501744\pi$
$313$	−1.78625e19	−0.0109601	−0.00548007	+	0.999985i	$0.501744\pi$
$314$	−3.92940e20	−0.234652
$315$	1.36280e21	0.792121
$316$	2.33181e21	1.31933
$317$	1.73922e21	0.957969	0.478985	−	0.877823i	$-0.341005\pi$
$317$	1.73922e21	0.957969	0.478985	+	0.877823i	$0.341005\pi$
$318$	−2.37105e19	−0.0127148
$319$	2.35304e21	1.22860
$320$	9.21817e20	0.468673
$321$	−1.39450e20	−0.0690439
$322$	−1.08310e20	−0.0522268
$323$	3.06169e21	1.43794
$324$	−2.08400e21	−0.953380
$325$	−2.53589e21	−1.13011
$326$	5.25233e20	0.228035
$327$	2.01006e20	0.0850265
$328$	1.88368e20	0.0776389
$329$	−1.08356e21	−0.435198
$330$	−2.41847e19	−0.00946612
$331$	−2.52855e21	−0.964570	−0.482285	−	0.876014i	$-0.660193\pi$
$331$	−2.52855e21	−0.964570	−0.482285	+	0.876014i	$0.660193\pi$
$332$	1.04906e21	0.390055
$333$	5.41909e21	1.96404
$334$	−7.54442e20	−0.266551
$335$	1.25291e21	0.431559
$336$	2.43774e20	0.0818659
$337$	−4.42758e21	−1.44981	−0.724907	−	0.688847i	$-0.758117\pi$
$337$	−4.42758e21	−1.44981	−0.724907	+	0.688847i	$0.758117\pi$
$338$	1.11370e21	0.355612
$339$	3.69882e20	0.115177
$340$	−3.48921e21	−1.05964
$341$	9.50774e20	0.281621
$342$	4.84238e20	0.139906
$343$	−6.79919e20	−0.191627
$344$	7.94384e20	0.218416
$345$	3.02577e19	0.00811658
$346$	−6.64192e20	−0.173839
$347$	4.60688e21	1.17654	0.588269	−	0.808665i	$-0.299809\pi$
$347$	4.60688e21	1.17654	0.588269	+	0.808665i	$0.299809\pi$
$348$	−2.40025e20	−0.0598183
$349$	−3.51804e21	−0.855626	−0.427813	−	0.903867i	$-0.640716\pi$
$349$	−3.51804e21	−0.855626	−0.427813	+	0.903867i	$0.640716\pi$
$350$	−6.95946e20	−0.165195
$351$	−9.84593e20	−0.228111
$352$	3.08214e21	0.697010
$353$	1.89410e21	0.418136	0.209068	−	0.977901i	$-0.432957\pi$
$353$	1.89410e21	0.418136	0.209068	+	0.977901i	$0.432957\pi$
$354$	−1.23573e19	−0.00266314
$355$	−4.20253e21	−0.884240
$356$	−3.60571e21	−0.740739
$357$	−8.52325e20	−0.170972
$358$	−1.23195e21	−0.241317
$359$	−9.23762e21	−1.76708	−0.883542	−	0.468352i	$-0.844848\pi$
$359$	−9.23762e21	−1.76708	−0.883542	+	0.468352i	$0.844848\pi$
$360$	−1.12298e21	−0.209798
$361$	−2.27238e21	−0.414639
$362$	−7.08036e20	−0.126192
$363$	2.88483e20	0.0502243
$364$	−1.32749e22	−2.25772
$365$	5.37620e21	0.893277
$366$	−1.34669e19	−0.00218615
$367$	8.35810e21	1.32570	0.662851	−	0.748751i	$-0.269346\pi$
$367$	8.35810e21	1.32570	0.662851	+	0.748751i	$0.269346\pi$
$368$	−1.21073e21	−0.187647
$369$	1.41307e21	0.214012
$370$	1.42856e21	0.211438
$371$	−9.78177e21	−1.41494
$372$	−9.69850e19	−0.0137116
$373$	2.02184e20	0.0279397	0.0139699	−	0.999902i	$-0.495553\pi$
$373$	2.02184e20	0.0279397	0.0139699	+	0.999902i	$0.495553\pi$
$374$	−3.38354e21	−0.457049
$375$	4.89204e20	0.0645988
$376$	8.92878e20	0.115264
$377$	1.25985e22	1.59007
$378$	−2.70211e20	−0.0333444
$379$	4.11476e21	0.496491	0.248246	−	0.968697i	$-0.420146\pi$
$379$	4.11476e21	0.496491	0.248246	+	0.968697i	$0.420146\pi$
$380$	−3.65596e21	−0.431361
$381$	−3.94094e19	−0.00454713
$382$	−1.57019e21	−0.177180
$383$	9.77725e21	1.07901	0.539507	−	0.841981i	$-0.318611\pi$
$383$	9.77725e21	1.07901	0.539507	+	0.841981i	$0.318611\pi$
$384$	−4.16559e20	−0.0449636
$385$	−9.97741e21	−1.05342
$386$	−1.24536e21	−0.128618
$387$	5.95918e21	0.602064
$388$	−7.95599e21	−0.786366
$389$	8.87722e21	0.858431	0.429216	−	0.903202i	$-0.358790\pi$
$389$	8.87722e21	0.858431	0.429216	+	0.903202i	$0.358790\pi$
$390$	−1.29488e20	−0.0122512
$391$	4.23317e21	0.391890
$392$	−3.42663e21	−0.310410
$393$	−4.20520e20	−0.0372778
$394$	−5.19296e20	−0.0450502
$395$	9.38356e21	0.796695
$396$	1.53264e22	1.27359
$397$	−1.44769e22	−1.17749	−0.588743	−	0.808320i	$-0.700377\pi$
$397$	−1.44769e22	−1.17749	−0.588743	+	0.808320i	$0.700377\pi$
$398$	−9.84578e20	−0.0783870
$399$	−8.93057e20	−0.0696001
$400$	−7.77957e21	−0.593534
$401$	1.37157e22	1.02445	0.512227	−	0.858850i	$-0.328821\pi$
$401$	1.37157e22	1.02445	0.512227	+	0.858850i	$0.328821\pi$
$402$	−1.23935e20	−0.00906298
$403$	5.09056e21	0.364479
$404$	−1.32627e21	−0.0929799
$405$	−8.38635e21	−0.575712
$406$	3.45752e21	0.232431
$407$	−3.96746e22	−2.61192
$408$	7.02337e20	0.0452829
$409$	7.96039e21	0.502674	0.251337	−	0.967900i	$-0.419130\pi$
$409$	7.96039e21	0.502674	0.251337	+	0.967900i	$0.419130\pi$
$410$	3.72507e20	0.0230395
$411$	−4.30524e20	−0.0260821
$412$	2.97423e22	1.76502
$413$	−5.09800e21	−0.296363
$414$	6.69521e20	0.0381295
$415$	4.22157e21	0.235540
$416$	1.65022e22	0.902085
$417$	−6.64537e20	−0.0355928
$418$	−3.54524e21	−0.186057
$419$	9.42116e21	0.484490	0.242245	−	0.970215i	$-0.422116\pi$
$419$	9.42116e21	0.484490	0.242245	+	0.970215i	$0.422116\pi$
$420$	1.01776e21	0.0512893
$421$	1.28732e22	0.635755	0.317877	−	0.948132i	$-0.397030\pi$
$421$	1.28732e22	0.635755	0.317877	+	0.948132i	$0.397030\pi$
$422$	−2.33310e21	−0.112922
$423$	6.69804e21	0.317727
$424$	8.06042e21	0.374755
$425$	2.72003e22	1.23956
$426$	4.15702e20	0.0185695
$427$	−5.55579e21	−0.243282
$428$	2.32964e22	1.00004
$429$	3.59620e21	0.151341
$430$	1.57093e21	0.0648151
$431$	−1.76582e22	−0.714314	−0.357157	−	0.934044i	$-0.616254\pi$
$431$	−1.76582e22	−0.714314	−0.357157	+	0.934044i	$0.616254\pi$
$432$	−3.02053e21	−0.119804
$433$	2.08523e22	0.810975	0.405488	−	0.914101i	$-0.367102\pi$
$433$	2.08523e22	0.810975	0.405488	+	0.914101i	$0.367102\pi$
$434$	1.39705e21	0.0532781
$435$	−9.65899e20	−0.0361221
$436$	−3.35800e22	−1.23153
$437$	4.43548e21	0.159532
$438$	−5.31798e20	−0.0187593
$439$	−1.37940e22	−0.477244	−0.238622	−	0.971113i	$-0.576696\pi$
$439$	−1.37940e22	−0.477244	−0.238622	+	0.971113i	$0.576696\pi$
$440$	8.22163e21	0.279004
$441$	−2.57053e22	−0.855647
$442$	−1.81159e22	−0.591522
$443$	5.17650e22	1.65807	0.829037	−	0.559193i	$-0.188889\pi$
$443$	5.17650e22	1.65807	0.829037	+	0.559193i	$0.188889\pi$
$444$	4.04706e21	0.127170
$445$	−1.45099e22	−0.447306
$446$	3.38486e21	0.102375
$447$	−5.94153e20	−0.0176313
$448$	−3.76178e22	−1.09529
$449$	−1.04229e22	−0.297781	−0.148890	−	0.988854i	$-0.547570\pi$
$449$	−1.04229e22	−0.297781	−0.148890	+	0.988854i	$0.547570\pi$
$450$	4.30201e21	0.120605
$451$	−1.03455e22	−0.284609
$452$	−6.17924e22	−1.66824
$453$	5.38038e20	0.0142554
$454$	6.36150e21	0.165419
$455$	−5.34204e22	−1.36336
$456$	7.35901e20	0.0184339
$457$	−2.19697e22	−0.540176	−0.270088	−	0.962836i	$-0.587053\pi$
$457$	−2.19697e22	−0.540176	−0.270088	+	0.962836i	$0.587053\pi$
$458$	5.17192e21	0.124823
$459$	1.05609e22	0.250203
$460$	−5.05483e21	−0.117561
$461$	7.01174e21	0.160091	0.0800457	−	0.996791i	$-0.474493\pi$
$461$	7.01174e21	0.160091	0.0800457	+	0.996791i	$0.474493\pi$
$462$	9.86937e20	0.0221224
$463$	−1.88616e21	−0.0415089	−0.0207544	−	0.999785i	$-0.506607\pi$
$463$	−1.88616e21	−0.0415089	−0.0207544	+	0.999785i	$0.506607\pi$
$464$	3.86496e22	0.835106
$465$	−3.90283e20	−0.00827998
$466$	5.46356e21	0.113814
$467$	−2.80070e22	−0.572892	−0.286446	−	0.958096i	$-0.592474\pi$
$467$	−2.80070e22	−0.572892	−0.286446	+	0.958096i	$0.592474\pi$
$468$	8.20594e22	1.64831
$469$	−5.11293e22	−1.00856
$470$	1.76571e21	0.0342049
$471$	−4.47964e21	−0.0852247
$472$	4.20087e21	0.0784933
$473$	−4.36287e22	−0.800669
$474$	−9.28195e20	−0.0167311
$475$	2.85002e22	0.504606
$476$	1.42389e23	2.47638
$477$	6.04663e22	1.03302
$478$	1.00569e22	0.168783
$479$	−4.50360e22	−0.742520	−0.371260	−	0.928529i	$-0.621074\pi$
$479$	−4.50360e22	−0.742520	−0.371260	+	0.928529i	$0.621074\pi$
$480$	−1.26518e21	−0.0204929
$481$	−2.12423e23	−3.38040
$482$	−2.52582e21	−0.0394915
$483$	−1.23477e21	−0.0189685
$484$	−4.81938e22	−0.727454
$485$	−3.20161e22	−0.474858
$486$	2.50734e21	0.0365430
$487$	−5.36601e21	−0.0768520	−0.0384260	−	0.999261i	$-0.512234\pi$
$487$	−5.36601e21	−0.0768520	−0.0384260	+	0.999261i	$0.512234\pi$
$488$	4.57811e21	0.0644344
$489$	5.98782e21	0.0828215
$490$	−6.77633e21	−0.0921145
$491$	3.27558e21	0.0437618	0.0218809	−	0.999761i	$-0.493035\pi$
$491$	3.27558e21	0.0437618	0.0218809	+	0.999761i	$0.493035\pi$
$492$	1.05530e21	0.0138571
$493$	−1.35133e23	−1.74407
$494$	−1.89817e22	−0.240799
$495$	6.16757e22	0.769077
$496$	1.56168e22	0.191425
$497$	1.71498e23	2.06648
$498$	−4.17586e20	−0.00494648
$499$	4.38603e22	0.510760	0.255380	−	0.966841i	$-0.417800\pi$
$499$	4.38603e22	0.510760	0.255380	+	0.966841i	$0.417800\pi$
$500$	−8.17262e22	−0.935656
$501$	−8.60086e21	−0.0968103
$502$	9.23980e21	0.102254
$503$	7.36027e21	0.0800877	0.0400438	−	0.999198i	$-0.487250\pi$
$503$	7.36027e21	0.0800877	0.0400438	+	0.999198i	$0.487250\pi$
$504$	4.58269e22	0.490299
$505$	−5.33710e21	−0.0561473
$506$	−4.90174e21	−0.0507074
$507$	1.26965e22	0.129157
$508$	6.58371e21	0.0658612
$509$	8.81662e22	0.867363	0.433682	−	0.901066i	$-0.357214\pi$
$509$	8.81662e22	0.867363	0.433682	+	0.901066i	$0.357214\pi$
$510$	1.38891e21	0.0134378
$511$	−2.19394e23	−2.08760
$512$	8.53551e22	0.798794
$513$	1.10656e22	0.101854
$514$	2.63430e22	0.238495
$515$	1.19688e23	1.06583
$516$	4.45041e21	0.0389832
$517$	−4.90382e22	−0.422537
$518$	−5.82971e22	−0.494133
$519$	−7.57199e21	−0.0631375
$520$	4.40197e22	0.361092
$521$	1.86562e23	1.50558	0.752790	−	0.658261i	$-0.228708\pi$
$521$	1.86562e23	1.50558	0.752790	+	0.658261i	$0.228708\pi$
$522$	−2.13728e22	−0.169692
$523$	5.43923e22	0.424886	0.212443	−	0.977173i	$-0.431858\pi$
$523$	5.43923e22	0.424886	0.212443	+	0.977173i	$0.431858\pi$
$524$	7.02518e22	0.539935
$525$	−7.93399e21	−0.0599981
$526$	−3.68090e22	−0.273889
$527$	−5.46022e22	−0.399779
$528$	1.10324e22	0.0794843
$529$	6.13261e21	0.0434783
$530$	1.59399e22	0.111209
$531$	3.15134e22	0.216368
$532$	1.49194e23	1.00810
$533$	−5.53909e22	−0.368347
$534$	1.43528e21	0.00939368
$535$	9.37483e22	0.603888
$536$	4.21318e22	0.267122
$537$	−1.40446e22	−0.0876452
$538$	−3.10778e22	−0.190898
$539$	1.88195e23	1.13790
$540$	−1.26108e22	−0.0750575
$541$	1.64770e23	0.965385	0.482692	−	0.875790i	$-0.339659\pi$
$541$	1.64770e23	0.965385	0.482692	+	0.875790i	$0.339659\pi$
$542$	5.31831e22	0.306746
$543$	−8.07182e21	−0.0458324
$544$	−1.77005e23	−0.989450
$545$	−1.35131e23	−0.743679
$546$	5.28419e21	0.0286313
$547$	2.35712e23	1.25745	0.628724	−	0.777629i	$-0.283578\pi$
$547$	2.35712e23	1.25745	0.628724	+	0.777629i	$0.283578\pi$
$548$	7.19232e22	0.377776
$549$	3.43433e22	0.177614
$550$	−3.14962e22	−0.160389
$551$	−1.41591e23	−0.709983
$552$	1.01748e21	0.00502392
$553$	−3.82928e23	−1.86189
$554$	−6.47069e22	−0.309826
$555$	1.62860e22	0.0767934
$556$	1.11017e23	0.515531
$557$	2.64644e23	1.21030	0.605151	−	0.796111i	$-0.293113\pi$
$557$	2.64644e23	1.21030	0.605151	+	0.796111i	$0.293113\pi$
$558$	−8.63590e21	−0.0388971
$559$	−2.33594e23	−1.03624
$560$	−1.63882e23	−0.716035
$561$	−3.85734e22	−0.165998
$562$	3.26408e21	0.0138357
$563$	−2.75474e23	−1.15016	−0.575082	−	0.818096i	$-0.695030\pi$
$563$	−2.75474e23	−1.15016	−0.575082	+	0.818096i	$0.695030\pi$
$564$	5.00221e21	0.0205726
$565$	−2.48662e23	−1.00739
$566$	−2.75717e22	−0.110033
$567$	3.42233e23	1.34545
$568$	−1.41319e23	−0.547318
$569$	2.76827e22	0.105622	0.0528111	−	0.998605i	$-0.483182\pi$
$569$	2.76827e22	0.105622	0.0528111	+	0.998605i	$0.483182\pi$
$570$	1.45528e21	0.00547030
$571$	2.78458e23	1.03122	0.515612	−	0.856822i	$-0.327564\pi$
$571$	2.78458e23	1.03122	0.515612	+	0.856822i	$0.327564\pi$
$572$	−6.00779e23	−2.19204
$573$	−1.79007e22	−0.0643509
$574$	−1.52014e22	−0.0538435
$575$	3.94051e22	0.137523
$576$	2.32536e23	0.799648
$577$	−4.15301e23	−1.40724	−0.703621	−	0.710575i	$-0.748435\pi$
$577$	−4.15301e23	−1.40724	−0.703621	+	0.710575i	$0.748435\pi$
$578$	1.39303e23	0.465130
$579$	−1.41974e22	−0.0467135
$580$	1.61363e23	0.523197
$581$	−1.72275e23	−0.550460
$582$	3.16694e21	0.00997229
$583$	−4.42690e23	−1.37378
$584$	1.80786e23	0.552911
$585$	3.30220e23	0.995355
$586$	4.11848e22	0.122351
$587$	−2.74147e23	−0.802711	−0.401356	−	0.915922i	$-0.631461\pi$
$587$	−2.74147e23	−0.802711	−0.401356	+	0.915922i	$0.631461\pi$
$588$	−1.91971e22	−0.0554025
$589$	−5.72116e22	−0.162744
$590$	8.30744e21	0.0232930
$591$	−5.92013e21	−0.0163620
$592$	−6.51669e23	−1.77539
$593$	2.86146e23	0.768462	0.384231	−	0.923237i	$-0.374467\pi$
$593$	2.86146e23	0.768462	0.384231	+	0.923237i	$0.374467\pi$
$594$	−1.22288e22	−0.0323743
$595$	5.72995e23	1.49540
$596$	9.92589e22	0.255374
$597$	−1.12245e22	−0.0284698
$598$	−2.62446e22	−0.0656265
$599$	3.92931e23	0.968697	0.484349	−	0.874875i	$-0.339057\pi$
$599$	3.92931e23	0.968697	0.484349	+	0.874875i	$0.339057\pi$
$600$	6.53781e21	0.0158908
$601$	−3.97447e23	−0.952458	−0.476229	−	0.879321i	$-0.657997\pi$
$601$	−3.97447e23	−0.952458	−0.476229	+	0.879321i	$0.657997\pi$
$602$	−6.41073e22	−0.151474
$603$	3.16057e23	0.736324
$604$	−8.98844e22	−0.206476
$605$	−1.93939e23	−0.439283
$606$	5.27930e20	0.00117912
$607$	5.84744e23	1.28784	0.643920	−	0.765093i	$-0.277307\pi$
$607$	5.84744e23	1.28784	0.643920	+	0.765093i	$0.277307\pi$
$608$	−1.85464e23	−0.402790
$609$	3.94168e22	0.0844178
$610$	9.05345e21	0.0191210
$611$	−2.62557e23	−0.546856
$612$	−8.80182e23	−1.80794
$613$	−2.72783e23	−0.552590	−0.276295	−	0.961073i	$-0.589107\pi$
$613$	−2.72783e23	−0.552590	−0.276295	+	0.961073i	$0.589107\pi$
$614$	−6.60134e22	−0.131887
$615$	4.24670e21	0.00836783
$616$	−3.35511e23	−0.652035
$617$	−6.86919e23	−1.31668	−0.658342	−	0.752719i	$-0.728742\pi$
$617$	−6.86919e23	−1.31668	−0.658342	+	0.752719i	$0.728742\pi$
$618$	−1.18392e22	−0.0223830
$619$	−1.68448e22	−0.0314120	−0.0157060	−	0.999877i	$-0.505000\pi$
$619$	−1.68448e22	−0.0314120	−0.0157060	+	0.999877i	$0.505000\pi$
$620$	6.52004e22	0.119928
$621$	1.52996e22	0.0277588
$622$	1.79209e23	0.320731
$623$	5.92126e23	1.04536
$624$	5.90688e22	0.102870
$625$	5.50233e22	0.0945294
$626$	−1.18785e21	−0.00201316
$627$	−4.04168e22	−0.0675753
$628$	7.48366e23	1.23440
$629$	2.27848e24	3.70779
$630$	9.06251e22	0.145497
$631$	−5.00967e23	−0.793523	−0.396761	−	0.917922i	$-0.629866\pi$
$631$	−5.00967e23	−0.793523	−0.396761	+	0.917922i	$0.629866\pi$
$632$	3.15542e23	0.493130
$633$	−2.65981e22	−0.0410127
$634$	1.15657e23	0.175960
$635$	2.64939e22	0.0397712
$636$	4.51573e22	0.0668870
$637$	1.00762e24	1.47270
$638$	1.56476e23	0.225669
$639$	−1.06012e24	−1.50869
$640$	2.80041e23	0.393271
$641$	3.05764e23	0.423734	0.211867	−	0.977298i	$-0.432046\pi$
$641$	3.05764e23	0.423734	0.211867	+	0.977298i	$0.432046\pi$
$642$	−9.27331e21	−0.0126820
$643$	6.50731e23	0.878230	0.439115	−	0.898431i	$-0.355292\pi$
$643$	6.50731e23	0.878230	0.439115	+	0.898431i	$0.355292\pi$
$644$	2.06279e23	0.274742
$645$	1.79091e22	0.0235406
$646$	2.03600e23	0.264120
$647$	−1.31545e24	−1.68418	−0.842090	−	0.539338i	$-0.818675\pi$
$647$	−1.31545e24	−1.68418	−0.842090	+	0.539338i	$0.818675\pi$
$648$	−2.82008e23	−0.356348
$649$	−2.30718e23	−0.287741
$650$	−1.68635e23	−0.207579
$651$	1.59268e22	0.0193504
$652$	−1.00032e24	−1.19960
$653$	−5.24966e23	−0.621397	−0.310699	−	0.950508i	$-0.600563\pi$
$653$	−5.24966e23	−0.621397	−0.310699	+	0.950508i	$0.600563\pi$
$654$	1.33668e22	0.0156177
$655$	2.82704e23	0.326048
$656$	−1.69928e23	−0.193456
$657$	1.35619e24	1.52411
$658$	−7.20558e22	−0.0799372
$659$	−9.74796e21	−0.0106755	−0.00533774	−	0.999986i	$-0.501699\pi$
$659$	−9.74796e21	−0.0106755	−0.00533774	+	0.999986i	$0.501699\pi$
$660$	4.60604e22	0.0497971
$661$	1.11856e24	1.19384	0.596919	−	0.802302i	$-0.296391\pi$
$661$	1.11856e24	1.19384	0.596919	+	0.802302i	$0.296391\pi$
$662$	−1.68147e23	−0.177172
$663$	−2.06527e23	−0.214838
$664$	1.41959e23	0.145792
$665$	6.00378e23	0.608753
$666$	3.60365e23	0.360755
$667$	−1.95768e23	−0.193496
$668$	1.43686e24	1.40221
$669$	3.85885e22	0.0371822
$670$	8.33178e22	0.0792688
$671$	−2.51437e23	−0.236204
$672$	5.16301e22	0.0478921
$673$	−4.00946e23	−0.367247	−0.183624	−	0.982997i	$-0.558783\pi$
$673$	−4.00946e23	−0.367247	−0.183624	+	0.982997i	$0.558783\pi$
$674$	−2.94431e23	−0.266302
$675$	9.83077e22	0.0878022
$676$	−2.12107e24	−1.87072
$677$	1.81924e23	0.158448	0.0792241	−	0.996857i	$-0.474756\pi$
$677$	1.81924e23	0.158448	0.0792241	+	0.996857i	$0.474756\pi$
$678$	2.45969e22	0.0211557
$679$	1.30653e24	1.10975
$680$	−4.72162e23	−0.396064
$681$	7.25230e22	0.0600794
$682$	6.32258e22	0.0517282
$683$	2.36839e23	0.191372	0.0956859	−	0.995412i	$-0.469496\pi$
$683$	2.36839e23	0.191372	0.0956859	+	0.995412i	$0.469496\pi$
$684$	−9.22245e23	−0.735986
$685$	2.89430e23	0.228125
$686$	−4.52141e22	−0.0351981
$687$	5.89615e22	0.0453353
$688$	−7.16617e23	−0.544234
$689$	−2.37022e24	−1.77797
$690$	2.01211e21	0.00149085
$691$	−1.12632e24	−0.824327	−0.412163	−	0.911110i	$-0.635227\pi$
$691$	−1.12632e24	−0.824327	−0.412163	+	0.911110i	$0.635227\pi$
$692$	1.26497e24	0.914490
$693$	−2.51688e24	−1.79734
$694$	3.06354e23	0.216107
$695$	4.46750e23	0.311311
$696$	−3.24804e22	−0.0223585
$697$	5.94131e23	0.404021
$698$	−2.33947e23	−0.157162
$699$	6.22863e22	0.0413367
$700$	1.32545e24	0.869020
$701$	−1.45499e24	−0.942447	−0.471224	−	0.882014i	$-0.656188\pi$
$701$	−1.45499e24	−0.942447	−0.471224	+	0.882014i	$0.656188\pi$
$702$	−6.54748e22	−0.0418995
$703$	2.38737e24	1.50938
$704$	−1.70246e24	−1.06343
$705$	2.01297e22	0.0124231
$706$	1.25956e23	0.0768033
$707$	2.17798e23	0.131217
$708$	2.35347e22	0.0140096
$709$	−2.65147e24	−1.55953	−0.779765	−	0.626072i	$-0.784662\pi$
$709$	−2.65147e24	−1.55953	−0.779765	+	0.626072i	$0.784662\pi$
$710$	−2.79465e23	−0.162417
$711$	2.36708e24	1.35932
$712$	−4.87926e23	−0.276869
$713$	−7.91023e22	−0.0443535
$714$	−5.66790e22	−0.0314042
$715$	−2.41763e24	−1.32369
$716$	2.34628e24	1.26946
$717$	1.14652e23	0.0613011
$718$	−6.14295e23	−0.324578
$719$	1.05725e24	0.552057	0.276028	−	0.961149i	$-0.410982\pi$
$719$	1.05725e24	0.552057	0.276028	+	0.961149i	$0.410982\pi$
$720$	1.01304e24	0.522760
$721$	−4.88426e24	−2.49086
$722$	−1.51112e23	−0.0761609
$723$	−2.87952e22	−0.0143431
$724$	1.34847e24	0.663842
$725$	−1.25791e24	−0.612035
$726$	1.91839e22	0.00922520
$727$	3.68332e24	1.75064	0.875321	−	0.483542i	$-0.160650\pi$
$727$	3.68332e24	1.75064	0.875321	+	0.483542i	$0.160650\pi$
$728$	−1.79637e24	−0.843877
$729$	−2.09640e24	−0.973396
$730$	3.57514e23	0.164077
$731$	2.50556e24	1.13660
$732$	2.56482e22	0.0115004
$733$	1.89359e24	0.839269	0.419635	−	0.907693i	$-0.362158\pi$
$733$	1.89359e24	0.839269	0.419635	+	0.907693i	$0.362158\pi$
$734$	5.55808e23	0.243505
$735$	−7.72523e22	−0.0334556
$736$	−2.56427e23	−0.109775
$737$	−2.31394e24	−0.979217
$738$	9.39680e22	0.0393098
$739$	−1.77641e24	−0.734623	−0.367311	−	0.930098i	$-0.619722\pi$
$739$	−1.77641e24	−0.734623	−0.367311	+	0.930098i	$0.619722\pi$
$740$	−2.72073e24	−1.11228
$741$	−2.16397e23	−0.0874572
$742$	−6.50481e23	−0.259897
$743$	3.27470e24	1.29350	0.646751	−	0.762701i	$-0.276127\pi$
$743$	3.27470e24	1.29350	0.646751	+	0.762701i	$0.276127\pi$
$744$	−1.31241e22	−0.00512505
$745$	3.99433e23	0.154211
$746$	1.34451e22	0.00513198
$747$	1.06493e24	0.401878
$748$	6.44405e24	2.40434
$749$	−3.82571e24	−1.41129
$750$	3.25317e22	0.0118655
$751$	−1.98559e24	−0.716060	−0.358030	−	0.933710i	$-0.616551\pi$
$751$	−1.98559e24	−0.716060	−0.358030	+	0.933710i	$0.616551\pi$
$752$	−8.05469e23	−0.287209
$753$	1.05337e23	0.0371383
$754$	8.37791e23	0.292065
$755$	−3.61709e23	−0.124684
$756$	5.14624e23	0.175410
$757$	−1.57240e24	−0.529966	−0.264983	−	0.964253i	$-0.585366\pi$
$757$	−1.57240e24	−0.529966	−0.264983	+	0.964253i	$0.585366\pi$
$758$	2.73629e23	0.0911956
$759$	−5.58813e22	−0.0184167
$760$	−4.94726e23	−0.161231
$761$	−1.04832e24	−0.337851	−0.168925	−	0.985629i	$-0.554030\pi$
$761$	−1.04832e24	−0.337851	−0.168925	+	0.985629i	$0.554030\pi$
$762$	−2.62070e21	−0.000835218 0
$763$	5.51448e24	1.73799
$764$	2.99047e24	0.932065
$765$	−3.54199e24	−1.09175
$766$	6.50180e23	0.198193
$767$	−1.23530e24	−0.372400
$768$	1.52024e23	0.0453255
$769$	−3.30749e24	−0.975269	−0.487634	−	0.873048i	$-0.662140\pi$
$769$	−3.30749e24	−0.975269	−0.487634	+	0.873048i	$0.662140\pi$
$770$	−6.63491e23	−0.193492
$771$	3.00318e23	0.0866202
$772$	2.37182e24	0.676604
$773$	3.68725e24	1.04034	0.520172	−	0.854061i	$-0.325868\pi$
$773$	3.68725e24	1.04034	0.520172	+	0.854061i	$0.325868\pi$
$774$	3.96281e23	0.110587
$775$	−5.08273e23	−0.140292
$776$	−1.07661e24	−0.293923
$777$	−6.64605e23	−0.179467
$778$	5.90329e23	0.157677
$779$	6.22524e23	0.164470
$780$	2.46613e23	0.0644485
$781$	7.76145e24	2.00636
$782$	2.81503e23	0.0719823
$783$	−4.88401e23	−0.123538
$784$	3.09118e24	0.773459
$785$	3.01154e24	0.745412
$786$	−2.79643e22	−0.00684718
$787$	−2.47293e24	−0.598999	−0.299500	−	0.954096i	$-0.596820\pi$
$787$	−2.47293e24	−0.598999	−0.299500	+	0.954096i	$0.596820\pi$
$788$	9.89014e23	0.236990
$789$	−4.19633e23	−0.0994754
$790$	6.24000e23	0.146337
$791$	1.01475e25	2.35428
$792$	2.07397e24	0.476035
$793$	−1.34622e24	−0.305700
$794$	−9.62703e23	−0.216281
$795$	1.81720e23	0.0403907
$796$	1.87516e24	0.412360
$797$	−9.59921e23	−0.208853	−0.104426	−	0.994533i	$-0.533301\pi$
$797$	−9.59921e23	−0.208853	−0.104426	+	0.994533i	$0.533301\pi$
$798$	−5.93877e22	−0.0127841
$799$	2.81622e24	0.599818
$800$	−1.64767e24	−0.347221
$801$	−3.66024e24	−0.763191
$802$	9.12088e23	0.188172
$803$	−9.92904e24	−2.02687
$804$	2.36037e23	0.0476764
$805$	8.30099e23	0.165907
$806$	3.38519e23	0.0669476
$807$	−3.54297e23	−0.0693333
$808$	−1.79471e23	−0.0347534
$809$	−1.96003e23	−0.0375578	−0.0187789	−	0.999824i	$-0.505978\pi$
$809$	−1.96003e23	−0.0375578	−0.0187789	+	0.999824i	$0.505978\pi$
$810$	−5.57686e23	−0.105747
$811$	−6.85491e22	−0.0128625	−0.00643124	−	0.999979i	$-0.502047\pi$
$811$	−6.85491e22	−0.0128625	−0.00643124	+	0.999979i	$0.502047\pi$
$812$	−6.58494e24	−1.22272
$813$	6.06303e23	0.111409
$814$	−2.63833e24	−0.479758
$815$	−4.02545e24	−0.724393
$816$	−6.33581e23	−0.112833
$817$	2.62530e24	0.462692
$818$	5.29360e23	0.0923312
$819$	−1.34757e25	−2.32616
$820$	−7.09451e23	−0.121201
$821$	1.87170e24	0.316461	0.158230	−	0.987402i	$-0.449421\pi$
$821$	1.87170e24	0.316461	0.158230	+	0.987402i	$0.449421\pi$
$822$	−2.86296e22	−0.00479076
$823$	1.05917e25	1.75416	0.877078	−	0.480347i	$-0.159489\pi$
$823$	1.05917e25	1.75416	0.877078	+	0.480347i	$0.159489\pi$
$824$	4.02475e24	0.659716
$825$	−3.59066e23	−0.0582527
$826$	−3.39013e23	−0.0544360
$827$	−6.22510e24	−0.989349	−0.494674	−	0.869078i	$-0.664713\pi$
$827$	−6.22510e24	−0.989349	−0.494674	+	0.869078i	$0.664713\pi$
$828$	−1.27512e24	−0.200583
$829$	1.19184e25	1.85568	0.927842	−	0.372973i	$-0.121662\pi$
$829$	1.19184e25	1.85568	0.927842	+	0.372973i	$0.121662\pi$
$830$	2.80731e23	0.0432641
$831$	−7.37678e23	−0.112527
$832$	−9.11518e24	−1.37631
$833$	−1.08079e25	−1.61532
$834$	−4.41912e22	−0.00653770
$835$	5.78213e24	0.846745
$836$	6.75201e24	0.978767
$837$	−1.97344e23	−0.0283177
$838$	6.26501e23	0.0889913
$839$	−8.44978e24	−1.18814	−0.594072	−	0.804412i	$-0.702480\pi$
$839$	−8.44978e24	−1.18814	−0.594072	+	0.804412i	$0.702480\pi$
$840$	1.37724e23	0.0191706
$841$	−1.00775e24	−0.138863
$842$	8.56060e23	0.116775
$843$	3.72115e22	0.00502508
$844$	4.44346e24	0.594032
$845$	−8.53553e24	−1.12966
$846$	4.45415e23	0.0583602
$847$	7.91434e24	1.02661
$848$	−7.27134e24	−0.933791
$849$	−3.14325e23	−0.0399635
$850$	1.80880e24	0.227683
$851$	3.30084e24	0.411361
$852$	−7.91717e23	−0.0976863
$853$	−1.06048e25	−1.29549	−0.647745	−	0.761857i	$-0.724288\pi$
$853$	−1.06048e25	−1.29549	−0.647745	+	0.761857i	$0.724288\pi$
$854$	−3.69456e23	−0.0446860
$855$	−3.71126e24	−0.444436
$856$	3.15248e24	0.373788
$857$	8.00999e24	0.940362	0.470181	−	0.882570i	$-0.344189\pi$
$857$	8.00999e24	0.940362	0.470181	+	0.882570i	$0.344189\pi$
$858$	2.39145e23	0.0277983
$859$	7.99852e24	0.920594	0.460297	−	0.887765i	$-0.347743\pi$
$859$	7.99852e24	0.920594	0.460297	+	0.887765i	$0.347743\pi$
$860$	−2.99189e24	−0.340964
$861$	−1.73301e23	−0.0195557
$862$	−1.17426e24	−0.131205
$863$	−8.10681e24	−0.896929	−0.448464	−	0.893801i	$-0.648029\pi$
$863$	−8.10681e24	−0.896929	−0.448464	+	0.893801i	$0.648029\pi$
$864$	−6.39733e23	−0.0700861
$865$	5.09044e24	0.552228
$866$	1.38667e24	0.148960
$867$	1.58810e24	0.168933
$868$	−2.66072e24	−0.280273
$869$	−1.73300e25	−1.80772
$870$	−6.42316e22	−0.00663491
$871$	−1.23891e25	−1.26732
$872$	−4.54407e24	−0.460314
$873$	−8.07633e24	−0.810201
$874$	2.94956e23	0.0293029
$875$	1.34210e25	1.32043
$876$	1.01283e24	0.0986847
$877$	−6.48714e24	−0.625975	−0.312987	−	0.949757i	$-0.601330\pi$
$877$	−6.48714e24	−0.625975	−0.312987	+	0.949757i	$0.601330\pi$
$878$	−9.17288e23	−0.0876602
$879$	4.69519e23	0.0444373
$880$	−7.41677e24	−0.695204
$881$	−9.64395e24	−0.895282	−0.447641	−	0.894213i	$-0.647736\pi$
$881$	−9.64395e24	−0.895282	−0.447641	+	0.894213i	$0.647736\pi$
$882$	−1.70938e24	−0.157165
$883$	1.29044e23	0.0117509	0.00587546	−	0.999983i	$-0.498130\pi$
$883$	1.29044e23	0.0117509	0.00587546	+	0.999983i	$0.498130\pi$
$884$	3.45023e25	3.11174
$885$	9.47074e22	0.00845992
$886$	3.44233e24	0.304555
$887$	6.97849e24	0.611520	0.305760	−	0.952109i	$-0.401089\pi$
$887$	6.97849e24	0.611520	0.305760	+	0.952109i	$0.401089\pi$
$888$	5.47651e23	0.0475328
$889$	−1.08117e24	−0.0929457
$890$	−9.64899e23	−0.0821612
$891$	1.54883e25	1.30630
$892$	−6.44657e24	−0.538552
$893$	2.95081e24	0.244176
$894$	−3.95108e22	−0.00323852
$895$	9.44180e24	0.766583
$896$	−1.14280e25	−0.919079
$897$	−2.99196e23	−0.0238353
$898$	−6.93118e23	−0.0546964
$899$	2.52514e24	0.197391
$900$	−8.19330e24	−0.634450
$901$	2.54233e25	1.95017
$902$	−6.87965e23	−0.0522770
$903$	−7.30842e23	−0.0550146
$904$	−8.36177e24	−0.623543
$905$	5.42647e24	0.400871
$906$	3.57792e22	0.00261843
$907$	1.17129e25	0.849188	0.424594	−	0.905384i	$-0.360417\pi$
$907$	1.17129e25	0.849188	0.424594	+	0.905384i	$0.360417\pi$
$908$	−1.21157e25	−0.870197
$909$	−1.34633e24	−0.0957982
$910$	−3.55242e24	−0.250422
$911$	1.88071e25	1.31345	0.656727	−	0.754128i	$-0.271940\pi$
$911$	1.88071e25	1.31345	0.656727	+	0.754128i	$0.271940\pi$
$912$	−6.63860e23	−0.0459325
$913$	−7.79661e24	−0.534446
$914$	−1.46097e24	−0.0992196
$915$	1.03212e23	0.00694466
$916$	−9.85008e24	−0.656641
$917$	−1.15367e25	−0.761977
$918$	7.02292e23	0.0459574
$919$	−1.40667e25	−0.912035	−0.456018	−	0.889971i	$-0.650725\pi$
$919$	−1.40667e25	−0.912035	−0.456018	+	0.889971i	$0.650725\pi$
$920$	−6.84022e23	−0.0439414
$921$	−7.52572e23	−0.0479007
$922$	4.66276e23	0.0294056
$923$	4.15558e25	2.59667
$924$	−1.87965e24	−0.116376
$925$	2.12096e25	1.30115
$926$	−1.25429e23	−0.00762436
$927$	3.01922e25	1.81851
$928$	8.18578e24	0.488543
$929$	3.29233e25	1.94702	0.973510	−	0.228645i	$-0.0734293\pi$
$929$	3.29233e25	1.94702	0.973510	+	0.228645i	$0.0734293\pi$
$930$	−2.59535e22	−0.00152087
$931$	−1.13244e25	−0.657573
$932$	−1.04055e25	−0.598726
$933$	2.04304e24	0.116488
$934$	−1.86245e24	−0.105229
$935$	2.59318e25	1.45189
$936$	1.11043e25	0.616094
$937$	1.43915e24	0.0791262	0.0395631	−	0.999217i	$-0.487403\pi$
$937$	1.43915e24	0.0791262	0.0395631	+	0.999217i	$0.487403\pi$
$938$	−3.40006e24	−0.185252
$939$	−1.35418e22	−0.000731171 0
$940$	−3.36285e24	−0.179937
$941$	−2.85337e25	−1.51303	−0.756513	−	0.653979i	$-0.773099\pi$
$941$	−2.85337e25	−1.51303	−0.756513	+	0.653979i	$0.773099\pi$
$942$	−2.97893e23	−0.0156541
$943$	8.60719e23	0.0448242
$944$	−3.78963e24	−0.195585
$945$	2.07093e24	0.105924
$946$	−2.90128e24	−0.147067
$947$	−2.54154e25	−1.27680	−0.638400	−	0.769705i	$-0.720403\pi$
$947$	−2.54154e25	−1.27680	−0.638400	+	0.769705i	$0.720403\pi$
$948$	1.76777e24	0.0880148
$949$	−5.31613e25	−2.62321
$950$	1.89524e24	0.0926860
$951$	1.31853e24	0.0639079
$952$	1.92681e25	0.925605
$953$	5.83926e24	0.278015	0.139008	−	0.990291i	$-0.455609\pi$
$953$	5.83926e24	0.278015	0.139008	+	0.990291i	$0.455609\pi$
$954$	4.02097e24	0.189745
$955$	1.20341e25	0.562841
$956$	−1.91537e25	−0.887893
$957$	1.78387e24	0.0819619
$958$	−2.99486e24	−0.136386
$959$	−1.18112e25	−0.533131
$960$	6.98841e23	0.0312660
$961$	−2.15298e25	−0.954754
$962$	−1.41260e25	−0.620912
$963$	2.36488e25	1.03035
$964$	4.81051e24	0.207748
$965$	9.54456e24	0.408577
$966$	−8.21110e22	−0.00348414
$967$	5.69559e24	0.239560	0.119780	−	0.992800i	$-0.461781\pi$
$967$	5.69559e24	0.239560	0.119780	+	0.992800i	$0.461781\pi$
$968$	−6.52161e24	−0.271903
$969$	2.32110e24	0.0959273
$970$	−2.12905e24	−0.0872220
$971$	−1.97624e25	−0.802558	−0.401279	−	0.915956i	$-0.631434\pi$
$971$	−1.97624e25	−0.802558	−0.401279	+	0.915956i	$0.631434\pi$
$972$	−4.77530e24	−0.192237
$973$	−1.82311e25	−0.727536
$974$	−3.56836e23	−0.0141162
$975$	−1.92249e24	−0.0753918
$976$	−4.12993e24	−0.160553
$977$	−4.39669e25	−1.69443	−0.847213	−	0.531254i	$-0.821721\pi$
$977$	−4.39669e25	−1.69443	−0.847213	+	0.531254i	$0.821721\pi$
$978$	3.98186e23	0.0152127
$979$	2.67976e25	1.01495
$980$	1.29057e25	0.484575
$981$	−3.40879e25	−1.26886
$982$	2.17824e23	0.00803817
$983$	−1.00184e25	−0.366518	−0.183259	−	0.983065i	$-0.558665\pi$
$983$	−1.00184e25	−0.366518	−0.183259	+	0.983065i	$0.558665\pi$
$984$	1.42804e23	0.00517943
$985$	3.97994e24	0.143110
$986$	−8.98627e24	−0.320351
$987$	−8.21458e23	−0.0290328
$988$	3.61511e25	1.26674
$989$	3.62982e24	0.126100
$990$	4.10139e24	0.141264
$991$	−1.04112e25	−0.355530	−0.177765	−	0.984073i	$-0.556887\pi$
$991$	−1.04112e25	−0.355530	−0.177765	+	0.984073i	$0.556887\pi$
$992$	3.30756e24	0.111985
$993$	−1.91693e24	−0.0643482
$994$	1.14045e25	0.379571
$995$	7.54592e24	0.249009
$996$	7.95304e23	0.0260213
$997$	−2.04793e25	−0.664365	−0.332182	−	0.943215i	$-0.607785\pi$
$997$	−2.04793e25	−0.664365	−0.332182	+	0.943215i	$0.607785\pi$
$998$	2.91668e24	0.0938164
$999$	8.23492e24	0.262635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.18.a.a.1.8	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.18.a.a.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+66.4993 q^{2} +758.112 q^{3} -126650. q^{4} -509658. q^{5} +50413.9 q^{6} +2.07983e7 q^{7} -1.71383e7 q^{8} -1.28565e8 q^{9} +O(q^{10})\)	\(q+66.4993 q^{2} +758.112 q^{3} -126650. q^{4} -509658. q^{5} +50413.9 q^{6} +2.07983e7 q^{7} -1.71383e7 q^{8} -1.28565e8 q^{9} -3.38919e7 q^{10} +9.41262e8 q^{11} -9.60148e7 q^{12} +5.03964e9 q^{13} +1.38307e9 q^{14} -3.86378e8 q^{15} +1.54606e10 q^{16} -5.40559e10 q^{17} -8.54951e9 q^{18} -5.66393e10 q^{19} +6.45481e10 q^{20} +1.57675e10 q^{21} +6.25933e10 q^{22} -7.83110e10 q^{23} -1.29928e10 q^{24} -5.03188e11 q^{25} +3.35132e11 q^{26} -1.95370e11 q^{27} -2.63410e12 q^{28} +2.49988e12 q^{29} -2.56939e10 q^{30} +1.01010e12 q^{31} +3.27447e12 q^{32} +7.13583e11 q^{33} -3.59468e12 q^{34} -1.06000e13 q^{35} +1.62828e13 q^{36} -4.21504e13 q^{37} -3.76647e12 q^{38} +3.82061e12 q^{39} +8.73469e12 q^{40} -1.09910e13 q^{41} +1.04852e12 q^{42} -4.63513e13 q^{43} -1.19211e14 q^{44} +6.55244e13 q^{45} -5.20763e12 q^{46} -5.20983e13 q^{47} +1.17208e13 q^{48} +1.99939e14 q^{49} -3.34616e13 q^{50} -4.09805e13 q^{51} -6.38270e14 q^{52} -4.70316e14 q^{53} -1.29920e13 q^{54} -4.79722e14 q^{55} -3.56448e14 q^{56} -4.29389e13 q^{57} +1.66240e14 q^{58} -2.45116e14 q^{59} +4.89347e13 q^{60} -2.67127e14 q^{61} +6.71713e13 q^{62} -2.67394e15 q^{63} -1.80870e15 q^{64} -2.56849e15 q^{65} +4.74527e13 q^{66} -2.45834e15 q^{67} +6.84618e15 q^{68} -5.93685e13 q^{69} -7.04895e14 q^{70} +8.24578e15 q^{71} +2.20340e15 q^{72} -1.05486e16 q^{73} -2.80297e15 q^{74} -3.81473e14 q^{75} +7.17335e15 q^{76} +1.95767e16 q^{77} +2.54068e14 q^{78} -1.84115e16 q^{79} -7.87960e15 q^{80} +1.64548e16 q^{81} -7.30896e14 q^{82} -8.28314e15 q^{83} -1.99695e15 q^{84} +2.75501e16 q^{85} -3.08233e15 q^{86} +1.89519e15 q^{87} -1.61317e16 q^{88} +2.84699e16 q^{89} +4.35733e15 q^{90} +1.04816e17 q^{91} +9.91807e15 q^{92} +7.65773e14 q^{93} -3.46450e15 q^{94} +2.88667e16 q^{95} +2.48242e15 q^{96} +6.28188e16 q^{97} +1.32958e16 q^{98} -1.21014e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) \) 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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