LMFDB - Embedded newform 23.18.a.a.1.2

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			1.2
Root			$306.641$ 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)

$f(q)$	$=$	$q-613.281 q^{2} -4261.96 q^{3} +245042. q^{4} +1.52257e6 q^{5} +2.61378e6 q^{6} +6.06383e6 q^{7} -6.98954e7 q^{8} -1.10976e8 q^{9} +O(q^{10})$	\(q-613.281 q^{2} -4261.96 q^{3} +245042. q^{4} +1.52257e6 q^{5} +2.61378e6 q^{6} +6.06383e6 q^{7} -6.98954e7 q^{8} -1.10976e8 q^{9} -9.33761e8 q^{10} -2.09196e8 q^{11} -1.04436e9 q^{12} +1.03587e9 q^{13} -3.71883e9 q^{14} -6.48911e9 q^{15} +1.07474e10 q^{16} -1.91867e9 q^{17} +6.80594e10 q^{18} -7.16351e10 q^{19} +3.73092e11 q^{20} -2.58438e10 q^{21} +1.28296e11 q^{22} -7.83110e10 q^{23} +2.97891e11 q^{24} +1.55527e12 q^{25} -6.35280e11 q^{26} +1.02336e12 q^{27} +1.48589e12 q^{28} -4.74648e12 q^{29} +3.97965e12 q^{30} -3.74557e10 q^{31} +2.57014e12 q^{32} +8.91583e11 q^{33} +1.17668e12 q^{34} +9.23258e12 q^{35} -2.71937e13 q^{36} +1.30304e13 q^{37} +4.39325e13 q^{38} -4.41484e12 q^{39} -1.06420e14 q^{40} -4.91969e13 q^{41} +1.58495e13 q^{42} -3.37250e13 q^{43} -5.12616e13 q^{44} -1.68968e14 q^{45} +4.80266e13 q^{46} +3.72729e13 q^{47} -4.58051e13 q^{48} -1.95861e14 q^{49} -9.53816e14 q^{50} +8.17727e12 q^{51} +2.53832e14 q^{52} -3.12603e14 q^{53} -6.27610e14 q^{54} -3.18514e14 q^{55} -4.23834e14 q^{56} +3.05306e14 q^{57} +2.91093e15 q^{58} +1.91845e15 q^{59} -1.59010e15 q^{60} +1.67889e15 q^{61} +2.29709e13 q^{62} -6.72939e14 q^{63} -2.98490e15 q^{64} +1.57718e15 q^{65} -5.46791e14 q^{66} -4.85648e15 q^{67} -4.70153e14 q^{68} +3.33758e14 q^{69} -5.66217e15 q^{70} +7.72041e15 q^{71} +7.75670e15 q^{72} -8.43490e15 q^{73} -7.99129e15 q^{74} -6.62849e15 q^{75} -1.75536e16 q^{76} -1.26853e15 q^{77} +2.70754e15 q^{78} +2.28843e15 q^{79} +1.63637e16 q^{80} +9.96991e15 q^{81} +3.01715e16 q^{82} -7.94656e15 q^{83} -6.33280e15 q^{84} -2.92130e15 q^{85} +2.06829e16 q^{86} +2.02293e16 q^{87} +1.46218e16 q^{88} -3.40960e16 q^{89} +1.03625e17 q^{90} +6.28134e15 q^{91} -1.91894e16 q^{92} +1.59635e14 q^{93} -2.28587e16 q^{94} -1.09069e17 q^{95} -1.09538e16 q^{96} -4.67877e15 q^{97} +1.20118e17 q^{98} +2.32157e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−613.281	−1.69397	−0.846983	−	0.531620i	$-0.821583\pi$
$2$	−613.281	−1.69397	−0.846983	+	0.531620i	$0.821583\pi$
$3$	−4261.96	−0.375041	−0.187520	−	0.982261i	$-0.560045\pi$
$3$	−4261.96	−0.375041	−0.187520	+	0.982261i	$0.560045\pi$
$4$	245042.	1.86952
$5$	1.52257e6	1.74314	0.871568	−	0.490275i	$-0.163104\pi$
$5$	1.52257e6	1.74314	0.871568	+	0.490275i	$0.163104\pi$
$6$	2.61378e6	0.635306
$7$	6.06383e6	0.397570	0.198785	−	0.980043i	$-0.436300\pi$
$7$	6.06383e6	0.397570	0.198785	+	0.980043i	$0.436300\pi$
$8$	−6.98954e7	−1.47294
$9$	−1.10976e8	−0.859344
$10$	−9.33761e8	−2.95281
$11$	−2.09196e8	−0.294249	−0.147124	−	0.989118i	$-0.547002\pi$
$11$	−2.09196e8	−0.294249	−0.147124	+	0.989118i	$0.547002\pi$
$12$	−1.04436e9	−0.701146
$13$	1.03587e9	0.352198	0.176099	−	0.984372i	$-0.443652\pi$
$13$	1.03587e9	0.352198	0.176099	+	0.984372i	$0.443652\pi$
$14$	−3.71883e9	−0.673470
$15$	−6.48911e9	−0.653747
$16$	1.07474e10	0.625582
$17$	−1.91867e9	−0.0667088	−0.0333544	−	0.999444i	$-0.510619\pi$
$17$	−1.91867e9	−0.0667088	−0.0333544	+	0.999444i	$0.510619\pi$
$18$	6.80594e10	1.45570
$19$	−7.16351e10	−0.967655	−0.483828	−	0.875163i	$-0.660754\pi$
$19$	−7.16351e10	−0.967655	−0.483828	+	0.875163i	$0.660754\pi$
$20$	3.73092e11	3.25882
$21$	−2.58438e10	−0.149105
$22$	1.28296e11	0.498447
$23$	−7.83110e10	−0.208514
$23$	−7.83110e10	−0.208514
$24$	2.97891e11	0.552411
$25$	1.55527e12	2.03852
$26$	−6.35280e11	−0.596612
$27$	1.02336e12	0.697330
$28$	1.48589e12	0.743264
$29$	−4.74648e12	−1.76193	−0.880965	−	0.473181i	$-0.843105\pi$
$29$	−4.74648e12	−1.76193	−0.880965	+	0.473181i	$0.843105\pi$
$30$	3.97965e12	1.10742
$31$	−3.74557e10	−0.00788757	−0.00394379	−	0.999992i	$-0.501255\pi$
$31$	−3.74557e10	−0.00788757	−0.00394379	+	0.999992i	$0.501255\pi$
$32$	2.57014e12	0.413220
$33$	8.91583e11	0.110355
$34$	1.17668e12	0.113002
$35$	9.23258e12	0.693018
$36$	−2.71937e13	−1.60656
$37$	1.30304e13	0.609878	0.304939	−	0.952372i	$-0.401364\pi$
$37$	1.30304e13	0.609878	0.304939	+	0.952372i	$0.401364\pi$
$38$	4.39325e13	1.63917
$39$	−4.41484e12	−0.132089
$40$	−1.06420e14	−2.56753
$41$	−4.91969e13	−0.962222	−0.481111	−	0.876660i	$-0.659767\pi$
$41$	−4.91969e13	−0.962222	−0.481111	+	0.876660i	$0.659767\pi$
$42$	1.58495e13	0.252579
$43$	−3.37250e13	−0.440018	−0.220009	−	0.975498i	$-0.570609\pi$
$43$	−3.37250e13	−0.440018	−0.220009	+	0.975498i	$0.570609\pi$
$44$	−5.12616e13	−0.550104
$45$	−1.68968e14	−1.49795
$46$	4.80266e13	0.353216
$47$	3.72729e13	0.228329	0.114165	−	0.993462i	$-0.463581\pi$
$47$	3.72729e13	0.228329	0.114165	+	0.993462i	$0.463581\pi$
$48$	−4.58051e13	−0.234619
$49$	−1.95861e14	−0.841938
$50$	−9.53816e14	−3.45318
$51$	8.17727e12	0.0250185
$52$	2.53832e14	0.658441
$53$	−3.12603e14	−0.689681	−0.344840	−	0.938661i	$-0.612067\pi$
$53$	−3.12603e14	−0.689681	−0.344840	+	0.938661i	$0.612067\pi$
$54$	−6.27610e14	−1.18125
$55$	−3.18514e14	−0.512916
$56$	−4.23834e14	−0.585595
$57$	3.05306e14	0.362910
$58$	2.91093e15	2.98465
$59$	1.91845e15	1.70101	0.850507	−	0.525964i	$-0.176295\pi$
$59$	1.91845e15	1.70101	0.850507	+	0.525964i	$0.176295\pi$
$60$	−1.59010e15	−1.22219
$61$	1.67889e15	1.12129	0.560646	−	0.828056i	$-0.310553\pi$
$61$	1.67889e15	1.12129	0.560646	+	0.828056i	$0.310553\pi$
$62$	2.29709e13	0.0133613
$63$	−6.72939e14	−0.341649
$64$	−2.98490e15	−1.32556
$65$	1.57718e15	0.613929
$66$	−5.46791e14	−0.186938
$67$	−4.85648e15	−1.46112	−0.730560	−	0.682848i	$-0.760741\pi$
$67$	−4.85648e15	−1.46112	−0.730560	+	0.682848i	$0.760741\pi$
$68$	−4.70153e14	−0.124713
$69$	3.33758e14	0.0782014
$70$	−5.66217e15	−1.17395
$71$	7.72041e15	1.41888	0.709438	−	0.704768i	$-0.248949\pi$
$71$	7.72041e15	1.41888	0.709438	+	0.704768i	$0.248949\pi$
$72$	7.75670e15	1.26576
$73$	−8.43490e15	−1.22415	−0.612076	−	0.790799i	$-0.709666\pi$
$73$	−8.43490e15	−1.22415	−0.612076	+	0.790799i	$0.709666\pi$
$74$	−7.99129e15	−1.03311
$75$	−6.62849e15	−0.764529
$76$	−1.75536e16	−1.80905
$77$	−1.26853e15	−0.116984
$78$	2.70754e15	0.223754
$79$	2.28843e15	0.169710	0.0848549	−	0.996393i	$-0.472957\pi$
$79$	2.28843e15	0.169710	0.0848549	+	0.996393i	$0.472957\pi$
$80$	1.63637e16	1.09047
$81$	9.96991e15	0.597817
$82$	3.01715e16	1.62997
$83$	−7.94656e15	−0.387272	−0.193636	−	0.981073i	$-0.562028\pi$
$83$	−7.94656e15	−0.387272	−0.193636	+	0.981073i	$0.562028\pi$
$84$	−6.33280e15	−0.278755
$85$	−2.92130e15	−0.116283
$86$	2.06829e16	0.745375
$87$	2.02293e16	0.660796
$88$	1.46218e16	0.433409
$89$	−3.40960e16	−0.918097	−0.459049	−	0.888411i	$-0.651810\pi$
$89$	−3.40960e16	−0.918097	−0.459049	+	0.888411i	$0.651810\pi$
$90$	1.03625e17	2.53748
$91$	6.28134e15	0.140023
$92$	−1.91894e16	−0.389822
$93$	1.59635e14	0.00295816
$94$	−2.28587e16	−0.386781
$95$	−1.09069e17	−1.68675
$96$	−1.09538e16	−0.154974
$97$	−4.67877e15	−0.0606139	−0.0303069	−	0.999541i	$-0.509648\pi$
$97$	−4.67877e15	−0.0606139	−0.0303069	+	0.999541i	$0.509648\pi$
$98$	1.20118e17	1.42621
$99$	2.32157e16	0.252861
$100$	3.81105e17	3.81105
$101$	1.73587e17	1.59509	0.797544	−	0.603261i	$-0.206132\pi$
$101$	1.73587e17	1.59509	0.797544	+	0.603261i	$0.206132\pi$
$102$	−5.01497e15	−0.0423805
$103$	−1.86301e17	−1.44910	−0.724552	−	0.689220i	$-0.757953\pi$
$103$	−1.86301e17	−1.44910	−0.724552	+	0.689220i	$0.757953\pi$
$104$	−7.24026e16	−0.518765
$105$	−3.93489e16	−0.259910
$106$	1.91713e17	1.16830
$107$	−2.97788e17	−1.67550	−0.837751	−	0.546052i	$-0.816130\pi$
$107$	−2.97788e17	−1.67550	−0.837751	+	0.546052i	$0.816130\pi$
$108$	2.50767e17	1.30367
$109$	−2.80045e17	−1.34618	−0.673089	−	0.739561i	$-0.735033\pi$
$109$	−2.80045e17	−1.34618	−0.673089	+	0.739561i	$0.735033\pi$
$110$	1.95339e17	0.868861
$111$	−5.55350e16	−0.228729
$112$	6.51705e16	0.248713
$113$	−3.79195e17	−1.34182	−0.670912	−	0.741537i	$-0.734097\pi$
$113$	−3.79195e17	−1.34182	−0.670912	+	0.741537i	$0.734097\pi$
$114$	−1.87238e17	−0.614757
$115$	−1.19234e17	−0.363469
$116$	−1.16308e18	−3.29396
$117$	−1.14957e17	−0.302660
$118$	−1.17655e18	−2.88146
$119$	−1.16345e16	−0.0265214
$120$	4.53559e17	0.962927
$121$	−4.61684e17	−0.913418
$122$	−1.02963e18	−1.89943
$123$	2.09675e17	0.360872
$124$	−9.17820e15	−0.0147460
$125$	1.20637e18	1.81028
$126$	4.12700e17	0.578742
$127$	9.38639e17	1.23074	0.615371	−	0.788238i	$-0.289006\pi$
$127$	9.38639e17	1.23074	0.615371	+	0.788238i	$0.289006\pi$
$128$	1.49371e18	1.83224
$129$	1.43735e17	0.165025
$130$	−9.67256e17	−1.03998
$131$	−4.58520e17	−0.461904	−0.230952	−	0.972965i	$-0.574184\pi$
$131$	−4.58520e17	−0.461904	−0.230952	+	0.972965i	$0.574184\pi$
$132$	2.18475e17	0.206311
$133$	−4.34383e17	−0.384711
$134$	2.97839e18	2.47509
$135$	1.55814e18	1.21554
$136$	1.34106e17	0.0982578
$137$	−9.77707e17	−0.673107	−0.336553	−	0.941664i	$-0.609261\pi$
$137$	−9.77707e17	−0.673107	−0.336553	+	0.941664i	$0.609261\pi$
$138$	−2.04688e17	−0.132470
$139$	−1.56548e18	−0.952844	−0.476422	−	0.879217i	$-0.658067\pi$
$139$	−1.56548e18	−0.952844	−0.476422	+	0.879217i	$0.658067\pi$
$140$	2.26237e18	1.29561
$141$	−1.58855e17	−0.0856327
$142$	−4.73478e18	−2.40353
$143$	−2.16700e17	−0.103634
$144$	−1.19270e18	−0.537591
$145$	−7.22683e18	−3.07128
$146$	5.17296e18	2.07367
$147$	8.34749e17	0.315761
$148$	3.19299e18	1.14018
$149$	3.78221e18	1.27545	0.637723	−	0.770266i	$-0.279877\pi$
$149$	3.78221e18	1.27545	0.637723	+	0.770266i	$0.279877\pi$
$150$	4.06513e18	1.29509
$151$	−3.47980e18	−1.04773	−0.523866	−	0.851801i	$-0.675511\pi$
$151$	−3.47980e18	−1.04773	−0.523866	+	0.851801i	$0.675511\pi$
$152$	5.00697e18	1.42529
$153$	2.12926e17	0.0573259
$154$	7.77963e17	0.198168
$155$	−5.70288e16	−0.0137491
$156$	−1.08182e18	−0.246942
$157$	−2.49020e18	−0.538378	−0.269189	−	0.963087i	$-0.586756\pi$
$157$	−2.49020e18	−0.538378	−0.269189	+	0.963087i	$0.586756\pi$
$158$	−1.40345e18	−0.287482
$159$	1.33230e18	0.258658
$160$	3.91321e18	0.720299
$161$	−4.74864e17	−0.0828991
$162$	−6.11435e18	−1.01268
$163$	1.10133e19	1.73110	0.865548	−	0.500826i	$-0.166970\pi$
$163$	1.10133e19	1.73110	0.865548	+	0.500826i	$0.166970\pi$
$164$	−1.20553e19	−1.79889
$165$	1.35749e18	0.192364
$166$	4.87348e18	0.656025
$167$	3.22040e18	0.411926	0.205963	−	0.978560i	$-0.433967\pi$
$167$	3.22040e18	0.411926	0.205963	+	0.978560i	$0.433967\pi$
$168$	1.80636e18	0.219622
$169$	−7.57739e18	−0.875956
$170$	1.79157e18	0.196979
$171$	7.94977e18	0.831549
$172$	−8.26403e18	−0.822622
$173$	−8.34818e18	−0.791043	−0.395521	−	0.918457i	$-0.629436\pi$
$173$	−8.34818e18	−0.791043	−0.395521	+	0.918457i	$0.629436\pi$
$174$	−1.24062e19	−1.11936
$175$	9.43088e18	0.810455
$176$	−2.24831e18	−0.184077
$177$	−8.17634e18	−0.637950
$178$	2.09104e19	1.55523
$179$	2.80979e19	1.99261	0.996306	−	0.0858745i	$-0.0273684\pi$
$179$	2.80979e19	1.99261	0.996306	+	0.0858745i	$0.0273684\pi$
$180$	−4.14042e19	−2.80045
$181$	−1.26788e19	−0.818105	−0.409052	−	0.912511i	$-0.634141\pi$
$181$	−1.26788e19	−0.818105	−0.409052	+	0.912511i	$0.634141\pi$
$182$	−3.85223e18	−0.237195
$183$	−7.15536e18	−0.420530
$184$	5.47358e18	0.307128
$185$	1.98396e19	1.06310
$186$	−9.79009e16	−0.00501102
$187$	4.01376e17	0.0196290
$188$	9.13340e18	0.426865
$189$	6.20551e18	0.277237
$190$	6.68901e19	2.85730
$191$	8.98635e18	0.367113	0.183556	−	0.983009i	$-0.441239\pi$
$191$	8.98635e18	0.367113	0.183556	+	0.983009i	$0.441239\pi$
$192$	1.27215e19	0.497140
$193$	−1.30819e18	−0.0489142	−0.0244571	−	0.999701i	$-0.507786\pi$
$193$	−1.30819e18	−0.0489142	−0.0244571	+	0.999701i	$0.507786\pi$
$194$	2.86940e18	0.102678
$195$	−6.72189e18	−0.230249
$196$	−4.79940e19	−1.57402
$197$	−3.14427e19	−0.987545	−0.493772	−	0.869591i	$-0.664382\pi$
$197$	−3.14427e19	−0.987545	−0.493772	+	0.869591i	$0.664382\pi$
$198$	−1.42377e19	−0.428338
$199$	9.58958e18	0.276407	0.138203	−	0.990404i	$-0.455867\pi$
$199$	9.58958e18	0.276407	0.138203	+	0.990404i	$0.455867\pi$
$200$	−1.08706e20	−3.00261
$201$	2.06981e19	0.547980
$202$	−1.06457e20	−2.70202
$203$	−2.87818e19	−0.700490
$204$	2.00377e18	0.0467726
$205$	−7.49056e19	−1.67728
$206$	1.14255e20	2.45473
$207$	8.69063e18	0.179186
$208$	1.11329e19	0.220329
$209$	1.49858e19	0.284731
$210$	2.41319e19	0.440279
$211$	−5.55363e19	−0.973142	−0.486571	−	0.873641i	$-0.661752\pi$
$211$	−5.55363e19	−0.973142	−0.486571	+	0.873641i	$0.661752\pi$
$212$	−7.66007e19	−1.28937
$213$	−3.29041e19	−0.532136
$214$	1.82628e20	2.83824
$215$	−5.13486e19	−0.767011
$216$	−7.15285e19	−1.02712
$217$	−2.27125e17	−0.00313586
$218$	1.71746e20	2.28038
$219$	3.59492e19	0.459107
$220$	−7.80492e19	−0.958905
$221$	−1.98749e18	−0.0234947
$222$	3.40585e19	0.387459
$223$	−4.61691e19	−0.505545	−0.252773	−	0.967526i	$-0.581342\pi$
$223$	−4.61691e19	−0.505545	−0.252773	+	0.967526i	$0.581342\pi$
$224$	1.55849e19	0.164284
$225$	−1.72597e20	−1.75179
$226$	2.32553e20	2.27300
$227$	−3.01510e19	−0.283845	−0.141923	−	0.989878i	$-0.545328\pi$
$227$	−3.01510e19	−0.283845	−0.141923	+	0.989878i	$0.545328\pi$
$228$	7.48127e19	0.678467
$229$	−1.85617e20	−1.62187	−0.810934	−	0.585138i	$-0.801040\pi$
$229$	−1.85617e20	−1.62187	−0.810934	+	0.585138i	$0.801040\pi$
$230$	7.31237e19	0.615704
$231$	5.40640e18	0.0438739
$232$	3.31757e20	2.59521
$233$	1.84198e20	1.38919	0.694593	−	0.719403i	$-0.255584\pi$
$233$	1.84198e20	1.38919	0.694593	+	0.719403i	$0.255584\pi$
$234$	7.05008e19	0.512695
$235$	5.67504e19	0.398008
$236$	4.70100e20	3.18008
$237$	−9.75318e18	−0.0636481
$238$	7.13519e18	0.0449264
$239$	1.05522e20	0.641152	0.320576	−	0.947223i	$-0.396124\pi$
$239$	1.05522e20	0.641152	0.320576	+	0.947223i	$0.396124\pi$
$240$	−6.97412e19	−0.408973
$241$	−1.72407e20	−0.975913	−0.487957	−	0.872868i	$-0.662258\pi$
$241$	−1.72407e20	−0.975913	−0.487957	+	0.872868i	$0.662258\pi$
$242$	2.83142e20	1.54730
$243$	−1.74649e20	−0.921536
$244$	4.11398e20	2.09628
$245$	−2.98211e20	−1.46761
$246$	−1.28590e20	−0.611306
$247$	−7.42048e19	−0.340806
$248$	2.61798e18	0.0116179
$249$	3.38679e19	0.145243
$250$	−7.39846e20	−3.06656
$251$	−1.15981e20	−0.464688	−0.232344	−	0.972634i	$-0.574639\pi$
$251$	−1.15981e20	−0.464688	−0.232344	+	0.972634i	$0.574639\pi$
$252$	−1.64898e20	−0.638720
$253$	1.63823e19	0.0613551
$254$	−5.75649e20	−2.08483
$255$	1.24504e19	0.0436107
$256$	−5.24828e20	−1.77818
$257$	5.53878e20	1.81544	0.907722	−	0.419573i	$-0.137820\pi$
$257$	5.53878e20	1.81544	0.907722	+	0.419573i	$0.137820\pi$
$258$	−8.81497e19	−0.279546
$259$	7.90140e19	0.242469
$260$	3.86475e20	1.14775
$261$	5.26745e20	1.51410
$262$	2.81201e20	0.782450
$263$	−5.84613e20	−1.57487	−0.787434	−	0.616398i	$-0.788591\pi$
$263$	−5.84613e20	−1.57487	−0.787434	+	0.616398i	$0.788591\pi$
$264$	−6.23175e19	−0.162546
$265$	−4.75959e20	−1.20221
$266$	2.66399e20	0.651686
$267$	1.45316e20	0.344324
$268$	−1.19004e21	−2.73159
$269$	4.63006e20	1.02966	0.514828	−	0.857293i	$-0.327856\pi$
$269$	4.63006e20	1.02966	0.514828	+	0.857293i	$0.327856\pi$
$270$	−9.55578e20	−2.05908
$271$	−4.17155e20	−0.871080	−0.435540	−	0.900169i	$-0.643443\pi$
$271$	−4.17155e20	−0.871080	−0.435540	+	0.900169i	$0.643443\pi$
$272$	−2.06207e19	−0.0417319
$273$	−2.67708e19	−0.0525145
$274$	5.99609e20	1.14022
$275$	−3.25355e20	−0.599832
$276$	8.17846e19	0.146199
$277$	−4.05630e20	−0.703157	−0.351578	−	0.936158i	$-0.614355\pi$
$277$	−4.05630e20	−0.703157	−0.351578	+	0.936158i	$0.614355\pi$
$278$	9.60079e20	1.61408
$279$	4.15668e18	0.00677814
$280$	−6.45315e20	−1.02077
$281$	−2.99973e20	−0.460340	−0.230170	−	0.973150i	$-0.573928\pi$
$281$	−2.99973e20	−0.460340	−0.230170	+	0.973150i	$0.573928\pi$
$282$	9.74230e19	0.145059
$283$	−6.69677e20	−0.967566	−0.483783	−	0.875188i	$-0.660738\pi$
$283$	−6.69677e20	−0.967566	−0.483783	+	0.875188i	$0.660738\pi$
$284$	1.89182e21	2.65262
$285$	4.64849e20	0.632601
$286$	1.32898e20	0.175552
$287$	−2.98322e20	−0.382550
$288$	−2.85223e20	−0.355099
$289$	−8.23559e20	−0.995550
$290$	4.43208e21	5.20265
$291$	1.99407e19	0.0227327
$292$	−2.06690e21	−2.28858
$293$	−4.41257e20	−0.474588	−0.237294	−	0.971438i	$-0.576260\pi$
$293$	−4.41257e20	−0.474588	−0.237294	+	0.971438i	$0.576260\pi$
$294$	−5.11936e20	−0.534889
$295$	2.92096e21	2.96510
$296$	−9.10764e20	−0.898310
$297$	−2.14083e20	−0.205189
$298$	−2.31956e21	−2.16056
$299$	−8.11201e19	−0.0734384
$300$	−1.62426e21	−1.42930
$301$	−2.04503e20	−0.174938
$302$	2.13410e21	1.77482
$303$	−7.39819e20	−0.598223
$304$	−7.69893e20	−0.605348
$305$	2.55622e21	1.95456
$306$	−1.30583e20	−0.0971081
$307$	7.03305e20	0.508706	0.254353	−	0.967111i	$-0.418137\pi$
$307$	7.03305e20	0.508706	0.254353	+	0.967111i	$0.418137\pi$
$308$	−3.10842e20	−0.218705
$309$	7.94009e20	0.543473
$310$	3.49747e19	0.0232905
$311$	1.70302e21	1.10346	0.551731	−	0.834022i	$-0.313968\pi$
$311$	1.70302e21	1.10346	0.551731	+	0.834022i	$0.313968\pi$
$312$	3.08577e20	0.194558
$313$	1.18832e21	0.729131	0.364565	−	0.931178i	$-0.381218\pi$
$313$	1.18832e21	0.729131	0.364565	+	0.931178i	$0.381218\pi$
$314$	1.52719e21	0.911994
$315$	−1.02459e21	−0.595541
$316$	5.60760e20	0.317276
$317$	−1.02642e21	−0.565357	−0.282678	−	0.959215i	$-0.591223\pi$
$317$	−1.02642e21	−0.565357	−0.282678	+	0.959215i	$0.591223\pi$
$318$	−8.17075e20	−0.438158
$319$	9.92943e20	0.518446
$320$	−4.54471e21	−2.31064
$321$	1.26916e21	0.628382
$322$	2.91225e20	0.140428
$323$	1.37444e20	0.0645511
$324$	2.44304e21	1.11763
$325$	1.61106e21	0.717964
$326$	−6.75422e21	−2.93242
$327$	1.19354e21	0.504872
$328$	3.43864e21	1.41729
$329$	2.26016e20	0.0907767
$330$	−8.32525e20	−0.325858
$331$	1.58955e21	0.606369	0.303185	−	0.952932i	$-0.401950\pi$
$331$	1.58955e21	0.606369	0.303185	+	0.952932i	$0.401950\pi$
$332$	−1.94724e21	−0.724012
$333$	−1.44606e21	−0.524095
$334$	−1.97501e21	−0.697788
$335$	−7.39432e21	−2.54693
$336$	−2.77754e20	−0.0932774
$337$	2.19247e21	0.717925	0.358962	−	0.933352i	$-0.383131\pi$
$337$	2.19247e21	0.717925	0.358962	+	0.933352i	$0.383131\pi$
$338$	4.64707e21	1.48384
$339$	1.61611e21	0.503239
$340$	−7.15839e20	−0.217392
$341$	7.83557e18	0.00232091
$342$	−4.87544e21	−1.40862
$343$	−2.59830e21	−0.732299
$344$	2.35722e21	0.648118
$345$	5.08169e20	0.136316
$346$	5.11978e21	1.34000
$347$	−2.60924e21	−0.666367	−0.333184	−	0.942862i	$-0.608123\pi$
$347$	−2.60924e21	−0.666367	−0.333184	+	0.942862i	$0.608123\pi$
$348$	4.95702e21	1.23537
$349$	4.51062e21	1.09703	0.548517	−	0.836139i	$-0.315192\pi$
$349$	4.51062e21	1.09703	0.548517	+	0.836139i	$0.315192\pi$
$350$	−5.78378e21	−1.37288
$351$	1.06007e21	0.245598
$352$	−5.37662e20	−0.121590
$353$	−4.65886e20	−0.102848	−0.0514239	−	0.998677i	$-0.516376\pi$
$353$	−4.65886e20	−0.102848	−0.0514239	+	0.998677i	$0.516376\pi$
$354$	5.01440e21	1.08066
$355$	1.17548e22	2.47329
$356$	−8.35494e21	−1.71640
$357$	4.95856e19	0.00994662
$358$	−1.72319e22	−3.37542
$359$	6.52053e21	1.24733	0.623664	−	0.781693i	$-0.285644\pi$
$359$	6.52053e21	1.24733	0.623664	+	0.781693i	$0.285644\pi$
$360$	1.18101e22	2.20639
$361$	−3.48793e20	−0.0636438
$362$	7.77564e21	1.38584
$363$	1.96768e21	0.342569
$364$	1.53919e21	0.261777
$365$	−1.28427e22	−2.13386
$366$	4.38825e21	0.712364
$367$	5.36545e21	0.851029	0.425515	−	0.904952i	$-0.360093\pi$
$367$	5.36545e21	0.851029	0.425515	+	0.904952i	$0.360093\pi$
$368$	−8.41641e20	−0.130443
$369$	5.45967e21	0.826880
$370$	−1.21673e22	−1.80085
$371$	−1.89557e21	−0.274196
$372$	3.91171e19	0.00553034
$373$	−8.21770e21	−1.13560	−0.567800	−	0.823167i	$-0.692205\pi$
$373$	−8.21770e21	−1.13560	−0.567800	+	0.823167i	$0.692205\pi$
$374$	−2.46157e20	−0.0332508
$375$	−5.14151e21	−0.678930
$376$	−2.60520e21	−0.336314
$377$	−4.91674e21	−0.620549
$378$	−3.80572e21	−0.469631
$379$	−4.95056e20	−0.0597339	−0.0298670	−	0.999554i	$-0.509508\pi$
$379$	−4.95056e20	−0.0597339	−0.0298670	+	0.999554i	$0.509508\pi$
$380$	−2.67265e22	−3.15342
$381$	−4.00044e21	−0.461578
$382$	−5.51116e21	−0.621877
$383$	−2.32028e20	−0.0256066	−0.0128033	−	0.999918i	$-0.504076\pi$
$383$	−2.32028e20	−0.0256066	−0.0128033	+	0.999918i	$0.504076\pi$
$384$	−6.36613e21	−0.687164
$385$	−1.93141e21	−0.203920
$386$	8.02290e20	0.0828589
$387$	3.74266e21	0.378127
$388$	−1.14649e21	−0.113319
$389$	−5.81023e21	−0.561852	−0.280926	−	0.959729i	$-0.590642\pi$
$389$	−5.81023e21	−0.561852	−0.280926	+	0.959729i	$0.590642\pi$
$390$	4.12241e21	0.390033
$391$	1.50253e20	0.0139098
$392$	1.36897e22	1.24012
$393$	1.95419e21	0.173233
$394$	1.92832e22	1.67287
$395$	3.48428e21	0.295827
$396$	5.68880e21	0.472729
$397$	−1.35450e22	−1.10169	−0.550844	−	0.834608i	$-0.685694\pi$
$397$	−1.35450e22	−1.10169	−0.550844	+	0.834608i	$0.685694\pi$
$398$	−5.88111e21	−0.468223
$399$	1.85132e21	0.144282
$400$	1.67151e22	1.27526
$401$	−1.46899e22	−1.09721	−0.548607	−	0.836080i	$-0.684842\pi$
$401$	−1.46899e22	−1.09721	−0.548607	+	0.836080i	$0.684842\pi$
$402$	−1.26938e22	−0.928259
$403$	−3.87993e19	−0.00277799
$404$	4.25359e22	2.98205
$405$	1.51798e22	1.04208
$406$	1.76514e22	1.18661
$407$	−2.72590e21	−0.179456
$408$	−5.71554e20	−0.0368507
$409$	−1.80044e21	−0.113692	−0.0568462	−	0.998383i	$-0.518104\pi$
$409$	−1.80044e21	−0.113692	−0.0568462	+	0.998383i	$0.518104\pi$
$410$	4.59382e22	2.84126
$411$	4.16695e21	0.252442
$412$	−4.56516e22	−2.70913
$413$	1.16331e22	0.676272
$414$	−5.32980e21	−0.303534
$415$	−1.20992e22	−0.675067
$416$	2.66233e21	0.145536
$417$	6.67201e21	0.357355
$418$	−9.19048e21	−0.482325
$419$	2.89294e22	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$419$	2.89294e22	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$420$	−9.64211e21	−0.485907
$421$	−2.21817e22	−1.09546	−0.547731	−	0.836655i	$-0.684508\pi$
$421$	−2.21817e22	−1.09546	−0.547731	+	0.836655i	$0.684508\pi$
$422$	3.40594e22	1.64847
$423$	−4.13639e21	−0.196213
$424$	2.18495e22	1.01586
$425$	−2.98404e21	−0.135987
$426$	2.01794e22	0.901421
$427$	1.01805e22	0.445792
$428$	−7.29704e22	−3.13238
$429$	9.23565e20	0.0388670
$430$	3.14911e22	1.29929
$431$	−1.44700e22	−0.585344	−0.292672	−	0.956213i	$-0.594544\pi$
$431$	−1.44700e22	−0.585344	−0.292672	+	0.956213i	$0.594544\pi$
$432$	1.09985e22	0.436237
$433$	4.40999e22	1.71511	0.857553	−	0.514396i	$-0.171984\pi$
$433$	4.40999e22	1.71511	0.857553	+	0.514396i	$0.171984\pi$
$434$	1.39291e20	0.00531204
$435$	3.08004e22	1.15186
$436$	−6.86227e22	−2.51671
$437$	5.60982e21	0.201770
$438$	−2.20470e22	−0.777712
$439$	2.00732e22	0.694495	0.347248	−	0.937774i	$-0.387116\pi$
$439$	2.00732e22	0.694495	0.347248	+	0.937774i	$0.387116\pi$
$440$	2.22627e22	0.755491
$441$	2.17358e22	0.723515
$442$	1.21889e21	0.0397993
$443$	−4.30307e22	−1.37831	−0.689154	−	0.724615i	$-0.742018\pi$
$443$	−4.30307e22	−1.37831	−0.689154	+	0.724615i	$0.742018\pi$
$444$	−1.36084e22	−0.427613
$445$	−5.19135e22	−1.60037
$446$	2.83146e22	0.856377
$447$	−1.61196e22	−0.478344
$448$	−1.80999e22	−0.527004
$449$	−2.51095e22	−0.717372	−0.358686	−	0.933458i	$-0.616775\pi$
$449$	−2.51095e22	−0.717372	−0.358686	+	0.933458i	$0.616775\pi$
$450$	1.05851e23	2.96747
$451$	1.02918e22	0.283133
$452$	−9.29185e22	−2.50857
$453$	1.48308e22	0.392942
$454$	1.84910e22	0.480824
$455$	9.56376e21	0.244080
$456$	−2.13395e22	−0.534543
$457$	2.12087e22	0.521467	0.260734	−	0.965411i	$-0.416036\pi$
$457$	2.12087e22	0.521467	0.260734	+	0.965411i	$0.416036\pi$
$458$	1.13835e23	2.74739
$459$	−1.96349e21	−0.0465181
$460$	−2.92172e22	−0.679512
$461$	6.21668e22	1.41939	0.709693	−	0.704511i	$-0.248834\pi$
$461$	6.21668e22	1.41939	0.709693	+	0.704511i	$0.248834\pi$
$462$	−3.31565e21	−0.0743210
$463$	−5.80845e22	−1.27827	−0.639134	−	0.769095i	$-0.720707\pi$
$463$	−5.80845e22	−1.27827	−0.639134	+	0.769095i	$0.720707\pi$
$464$	−5.10124e22	−1.10223
$465$	2.43054e20	0.00515648
$466$	−1.12965e23	−2.35323
$467$	−6.60135e22	−1.35033	−0.675164	−	0.737668i	$-0.735927\pi$
$467$	−6.60135e22	−1.35033	−0.675164	+	0.737668i	$0.735927\pi$
$468$	−2.81692e22	−0.565828
$469$	−2.94489e22	−0.580898
$470$	−3.48040e22	−0.674212
$471$	1.06131e22	0.201914
$472$	−1.34091e23	−2.50548
$473$	7.05512e21	0.129475
$474$	5.98144e21	0.107818
$475$	−1.11412e23	−1.97259
$476$	−2.85093e21	−0.0495823
$477$	3.46914e22	0.592673
$478$	−6.47147e22	−1.08609
$479$	−7.05252e22	−1.16277	−0.581383	−	0.813630i	$-0.697488\pi$
$479$	−7.05252e22	−1.16277	−0.581383	+	0.813630i	$0.697488\pi$
$480$	−1.66779e22	−0.270142
$481$	1.34978e22	0.214798
$482$	1.05734e23	1.65316
$483$	2.02385e21	0.0310905
$484$	−1.13132e23	−1.70765
$485$	−7.12374e21	−0.105658
$486$	1.07109e23	1.56105
$487$	1.11660e23	1.59919	0.799595	−	0.600539i	$-0.205047\pi$
$487$	1.11660e23	1.59919	0.799595	+	0.600539i	$0.205047\pi$
$488$	−1.17347e23	−1.65159
$489$	−4.69381e22	−0.649232
$490$	1.82887e23	2.48608
$491$	6.32673e22	0.845253	0.422626	−	0.906304i	$-0.361108\pi$
$491$	6.32673e22	0.845253	0.422626	+	0.906304i	$0.361108\pi$
$492$	5.13792e22	0.674658
$493$	9.10691e21	0.117536
$494$	4.55084e22	0.577314
$495$	3.53474e22	0.440771
$496$	−4.02552e20	−0.00493433
$497$	4.68152e22	0.564102
$498$	−2.07706e22	−0.246036
$499$	1.26525e22	0.147341	0.0736703	−	0.997283i	$-0.476529\pi$
$499$	1.26525e22	0.147341	0.0736703	+	0.997283i	$0.476529\pi$
$500$	2.95612e23	3.38436
$501$	−1.37252e22	−0.154489
$502$	7.11291e22	0.787165
$503$	3.68865e22	0.401365	0.200683	−	0.979656i	$-0.435684\pi$
$503$	3.68865e22	0.401365	0.200683	+	0.979656i	$0.435684\pi$
$504$	4.70353e22	0.503228
$505$	2.64297e23	2.78045
$506$	−1.00470e22	−0.103933
$507$	3.22945e22	0.328519
$508$	2.30005e23	2.30089
$509$	−1.01752e23	−1.00101	−0.500506	−	0.865733i	$-0.666853\pi$
$509$	−1.01752e23	−1.00101	−0.500506	+	0.865733i	$0.666853\pi$
$510$	−7.63562e21	−0.0738750
$511$	−5.11478e22	−0.486686
$512$	1.26083e23	1.17995
$513$	−7.33089e22	−0.674775
$514$	−3.39683e23	−3.07530
$515$	−2.83656e23	−2.52599
$516$	3.52210e22	0.308517
$517$	−7.79732e21	−0.0671855
$518$	−4.84578e22	−0.410734
$519$	3.55796e22	0.296673
$520$	−1.10238e23	−0.904278
$521$	5.20093e22	0.419721	0.209860	−	0.977731i	$-0.432699\pi$
$521$	5.20093e22	0.419721	0.209860	+	0.977731i	$0.432699\pi$
$522$	−3.23043e23	−2.56484
$523$	1.84967e23	1.44487	0.722436	−	0.691437i	$-0.243022\pi$
$523$	1.84967e23	1.44487	0.722436	+	0.691437i	$0.243022\pi$
$524$	−1.12356e23	−0.863539
$525$	−4.01940e22	−0.303954
$526$	3.58532e23	2.66777
$527$	7.18649e19	0.000526171 0
$528$	9.58222e21	0.0690363
$529$	6.13261e21	0.0434783
$530$	2.91896e23	2.03650
$531$	−2.12901e23	−1.46176
$532$	−1.06442e23	−0.719224
$533$	−5.09617e22	−0.338893
$534$	−8.91194e22	−0.583273
$535$	−4.53402e23	−2.92063
$536$	3.39446e23	2.15214
$537$	−1.19752e23	−0.747311
$538$	−2.83953e23	−1.74420
$539$	4.09732e22	0.247739
$540$	3.81809e23	2.27248
$541$	1.11457e23	0.653027	0.326513	−	0.945193i	$-0.394126\pi$
$541$	1.11457e23	0.653027	0.326513	+	0.945193i	$0.394126\pi$
$542$	2.55833e23	1.47558
$543$	5.40363e22	0.306823
$544$	−4.93124e21	−0.0275655
$545$	−4.26387e23	−2.34657
$546$	1.64180e22	0.0889578
$547$	−5.78957e22	−0.308855	−0.154427	−	0.988004i	$-0.549353\pi$
$547$	−5.78957e22	−0.308855	−0.154427	+	0.988004i	$0.549353\pi$
$548$	−2.39579e23	−1.25839
$549$	−1.86316e23	−0.963576
$550$	1.99534e23	1.01610
$551$	3.40015e23	1.70494
$552$	−2.33282e22	−0.115186
$553$	1.38766e22	0.0674715
$554$	2.48765e23	1.19112
$555$	−8.45557e22	−0.398706
$556$	−3.83608e23	−1.78136
$557$	2.11556e23	0.967513	0.483757	−	0.875203i	$-0.339272\pi$
$557$	2.11556e23	0.967513	0.483757	+	0.875203i	$0.339272\pi$
$558$	−2.54921e21	−0.0114819
$559$	−3.49348e22	−0.154974
$560$	9.92264e22	0.433540
$561$	−1.71065e21	−0.00736168
$562$	1.83968e23	0.779800
$563$	4.00058e23	1.67033	0.835164	−	0.550001i	$-0.185373\pi$
$563$	4.00058e23	1.67033	0.835164	+	0.550001i	$0.185373\pi$
$564$	−3.89262e22	−0.160092
$565$	−5.77349e23	−2.33898
$566$	4.10700e23	1.63902
$567$	6.04558e22	0.237674
$568$	−5.39621e23	−2.08991
$569$	3.56066e23	1.35855	0.679275	−	0.733883i	$-0.262294\pi$
$569$	3.56066e23	1.35855	0.679275	+	0.733883i	$0.262294\pi$
$570$	−2.85083e23	−1.07161
$571$	2.80172e23	1.03757	0.518785	−	0.854905i	$-0.326385\pi$
$571$	2.80172e23	1.03757	0.518785	+	0.854905i	$0.326385\pi$
$572$	−5.31004e22	−0.193746
$573$	−3.82994e22	−0.137682
$574$	1.82955e23	0.648027
$575$	−1.21795e23	−0.425061
$576$	3.31252e23	1.13912
$577$	2.03538e23	0.689687	0.344843	−	0.938660i	$-0.387932\pi$
$577$	2.03538e23	0.689687	0.344843	+	0.938660i	$0.387932\pi$
$578$	5.05073e23	1.68643
$579$	5.57546e21	0.0183448
$580$	−1.77087e24	−5.74182
$581$	−4.81866e22	−0.153968
$582$	−1.22293e22	−0.0385084
$583$	6.53952e22	0.202938
$584$	5.89561e23	1.80310
$585$	−1.75029e23	−0.527577
$586$	2.70615e23	0.803936
$587$	−1.96525e23	−0.575431	−0.287716	−	0.957716i	$-0.592896\pi$
$587$	−1.96525e23	−0.575431	−0.287716	+	0.957716i	$0.592896\pi$
$588$	2.04548e23	0.590322
$589$	2.68314e21	0.00763245
$590$	−1.79137e24	−5.02277
$591$	1.34007e23	0.370370
$592$	1.40043e23	0.381529
$593$	1.23442e23	0.331511	0.165756	−	0.986167i	$-0.446994\pi$
$593$	1.23442e23	0.331511	0.165756	+	0.986167i	$0.446994\pi$
$594$	1.31293e23	0.347582
$595$	−1.77142e22	−0.0462304
$596$	9.26798e23	2.38447
$597$	−4.08704e22	−0.103664
$598$	4.97494e22	0.124402
$599$	1.67555e23	0.413076	0.206538	−	0.978439i	$-0.433780\pi$
$599$	1.67555e23	0.413076	0.206538	+	0.978439i	$0.433780\pi$
$600$	4.63301e23	1.12610
$601$	−1.86375e23	−0.446636	−0.223318	−	0.974746i	$-0.571689\pi$
$601$	−1.86375e23	−0.446636	−0.223318	+	0.974746i	$0.571689\pi$
$602$	1.25418e23	0.296339
$603$	5.38953e23	1.25561
$604$	−8.52696e23	−1.95876
$605$	−7.02945e23	−1.59221
$606$	4.53717e23	1.01337
$607$	1.62734e23	0.358405	0.179203	−	0.983812i	$-0.442648\pi$
$607$	1.62734e23	0.358405	0.179203	+	0.983812i	$0.442648\pi$
$608$	−1.84112e23	−0.399855
$609$	1.22667e23	0.262712
$610$	−1.56768e24	−3.31096
$611$	3.86099e22	0.0804171
$612$	5.21756e22	0.107172
$613$	−5.26562e23	−1.06668	−0.533342	−	0.845900i	$-0.679064\pi$
$613$	−5.26562e23	−1.06668	−0.533342	+	0.845900i	$0.679064\pi$
$614$	−4.31323e23	−0.861731
$615$	3.19244e23	0.629050
$616$	8.86641e22	0.172311
$617$	7.26070e23	1.39173	0.695864	−	0.718174i	$-0.255022\pi$
$617$	7.26070e23	1.39173	0.695864	+	0.718174i	$0.255022\pi$
$618$	−4.86950e23	−0.920625
$619$	8.82521e23	1.64571	0.822857	−	0.568249i	$-0.192379\pi$
$619$	8.82521e23	1.64571	0.822857	+	0.568249i	$0.192379\pi$
$620$	−1.39744e22	−0.0257042
$621$	−8.01407e22	−0.145403
$622$	−1.04443e24	−1.86923
$623$	−2.06752e23	−0.365008
$624$	−4.74482e22	−0.0826324
$625$	6.50207e23	1.11705
$626$	−7.28772e23	−1.23512
$627$	−6.38687e22	−0.106786
$628$	−6.10203e23	−1.00651
$629$	−2.50010e22	−0.0406842
$630$	6.28364e23	1.00883
$631$	1.16127e24	1.83943	0.919714	−	0.392589i	$-0.128421\pi$
$631$	1.16127e24	1.83943	0.919714	+	0.392589i	$0.128421\pi$
$632$	−1.59950e23	−0.249971
$633$	2.36693e23	0.364968
$634$	6.29486e23	0.957695
$635$	1.42914e24	2.14535
$636$	3.26469e23	0.483567
$637$	−2.02886e23	−0.296529
$638$	−6.08953e23	−0.878229
$639$	−8.56779e23	−1.21930
$640$	2.27427e24	3.19384
$641$	−2.58056e23	−0.357620	−0.178810	−	0.983884i	$-0.557225\pi$
$641$	−2.58056e23	−0.357620	−0.178810	+	0.983884i	$0.557225\pi$
$642$	−7.78352e23	−1.06446
$643$	−7.15881e23	−0.966157	−0.483078	−	0.875577i	$-0.660481\pi$
$643$	−7.15881e23	−0.966157	−0.483078	+	0.875577i	$0.660481\pi$
$644$	−1.16362e23	−0.154981
$645$	2.18845e23	0.287660
$646$	−8.42917e22	−0.109347
$647$	1.43254e24	1.83409	0.917045	−	0.398785i	$-0.130568\pi$
$647$	1.43254e24	1.83409	0.917045	+	0.398785i	$0.130568\pi$
$648$	−6.96850e23	−0.880546
$649$	−4.01331e23	−0.500521
$650$	−9.88031e23	−1.21621
$651$	9.67997e20	0.00117608
$652$	2.69871e24	3.23632
$653$	8.79416e23	1.04096	0.520478	−	0.853875i	$-0.325754\pi$
$653$	8.79416e23	1.04096	0.520478	+	0.853875i	$0.325754\pi$
$654$	−7.31976e23	−0.855235
$655$	−6.98126e23	−0.805162
$656$	−5.28740e23	−0.601949
$657$	9.36070e23	1.05197
$658$	−1.38611e23	−0.153773
$659$	3.32364e23	0.363988	0.181994	−	0.983300i	$-0.441745\pi$
$659$	3.32364e23	0.363988	0.181994	+	0.983300i	$0.441745\pi$
$660$	3.32642e23	0.359629
$661$	−1.81974e23	−0.194222	−0.0971108	−	0.995274i	$-0.530960\pi$
$661$	−1.81974e23	−0.194222	−0.0971108	+	0.995274i	$0.530960\pi$
$662$	−9.74843e23	−1.02717
$663$	8.47060e21	0.00881149
$664$	5.55428e23	0.570426
$665$	−6.61377e23	−0.670603
$666$	8.86840e23	0.887799
$667$	3.71701e23	0.367388
$668$	7.89131e23	0.770104
$669$	1.96771e23	0.189600
$670$	4.53480e24	4.31441
$671$	−3.51216e23	−0.329939
$672$	−6.64221e22	−0.0616132
$673$	−1.19063e24	−1.09056	−0.545280	−	0.838254i	$-0.683576\pi$
$673$	−1.19063e24	−1.09056	−0.545280	+	0.838254i	$0.683576\pi$
$674$	−1.34460e24	−1.21614
$675$	1.59161e24	1.42152
$676$	−1.85677e24	−1.63762
$677$	2.23827e23	0.194943	0.0974716	−	0.995238i	$-0.468924\pi$
$677$	2.23827e23	0.194943	0.0974716	+	0.995238i	$0.468924\pi$
$678$	−9.91132e23	−0.852470
$679$	−2.83713e22	−0.0240983
$680$	2.04185e23	0.171277
$681$	1.28502e23	0.106454
$682$	−4.80540e21	−0.00393154
$683$	−1.70037e24	−1.37394	−0.686970	−	0.726686i	$-0.741060\pi$
$683$	−1.70037e24	−1.37394	−0.686970	+	0.726686i	$0.741060\pi$
$684$	1.94803e24	1.55460
$685$	−1.48862e24	−1.17332
$686$	1.59349e24	1.24049
$687$	7.91090e23	0.608267
$688$	−3.62457e23	−0.275267
$689$	−3.23816e23	−0.242904
$690$	−3.11650e23	−0.230914
$691$	4.27404e22	0.0312806	0.0156403	−	0.999878i	$-0.495021\pi$
$691$	4.27404e22	0.0312806	0.0156403	+	0.999878i	$0.495021\pi$
$692$	−2.04565e24	−1.47887
$693$	1.40776e23	0.100530
$694$	1.60020e24	1.12880
$695$	−2.38355e24	−1.66094
$696$	−1.41393e24	−0.973309
$697$	9.43925e22	0.0641887
$698$	−2.76628e24	−1.85834
$699$	−7.85046e23	−0.521002
$700$	2.31096e24	1.51516
$701$	−7.77091e23	−0.503348	−0.251674	−	0.967812i	$-0.580981\pi$
$701$	−7.77091e23	−0.503348	−0.251674	+	0.967812i	$0.580981\pi$
$702$	−6.50123e23	−0.416035
$703$	−9.33434e23	−0.590151
$704$	6.24429e23	0.390045
$705$	−2.41868e23	−0.149269
$706$	2.85719e23	0.174220
$707$	1.05260e24	0.634159
$708$	−2.00354e24	−1.19266
$709$	1.80685e24	1.06275	0.531373	−	0.847138i	$-0.321676\pi$
$709$	1.80685e24	1.06275	0.531373	+	0.847138i	$0.321676\pi$
$710$	−7.20902e24	−4.18967
$711$	−2.53960e23	−0.145839
$712$	2.38315e24	1.35230
$713$	2.93319e21	0.00164467
$714$	−3.04099e22	−0.0168492
$715$	−3.29940e23	−0.180648
$716$	6.88515e24	3.72523
$717$	−4.49730e23	−0.240458
$718$	−3.99892e24	−2.11293
$719$	1.37138e24	0.716080	0.358040	−	0.933706i	$-0.383445\pi$
$719$	1.37138e24	0.716080	0.358040	+	0.933706i	$0.383445\pi$
$720$	−1.81597e24	−0.937093
$721$	−1.12970e24	−0.576120
$722$	2.13908e23	0.107810
$723$	7.34793e23	0.366007
$724$	−3.10682e24	−1.52946
$725$	−7.38205e24	−3.59173
$726$	−1.20674e24	−0.580300
$727$	3.54526e23	0.168502	0.0842512	−	0.996445i	$-0.473150\pi$
$727$	3.54526e23	0.168502	0.0842512	+	0.996445i	$0.473150\pi$
$728$	−4.39037e23	−0.206245
$729$	−5.43169e23	−0.252204
$730$	7.87618e24	3.61469
$731$	6.47070e22	0.0293531
$732$	−1.75336e24	−0.786189
$733$	−3.48858e24	−1.54620	−0.773098	−	0.634287i	$-0.781294\pi$
$733$	−3.48858e24	−1.54620	−0.773098	+	0.634287i	$0.781294\pi$
$734$	−3.29053e24	−1.44161
$735$	1.27096e24	0.550414
$736$	−2.01270e23	−0.0861624
$737$	1.01596e24	0.429933
$738$	−3.34831e24	−1.40071
$739$	2.44937e24	1.01292	0.506462	−	0.862262i	$-0.330953\pi$
$739$	2.44937e24	1.01292	0.506462	+	0.862262i	$0.330953\pi$
$740$	4.86153e24	1.98748
$741$	3.16258e23	0.127816
$742$	1.16252e24	0.464479
$743$	−2.93291e24	−1.15849	−0.579246	−	0.815153i	$-0.696653\pi$
$743$	−2.93291e24	−1.15849	−0.579246	+	0.815153i	$0.696653\pi$
$744$	−1.11577e22	−0.00435718
$745$	5.75866e24	2.22327
$746$	5.03976e24	1.92367
$747$	8.81877e23	0.332800
$748$	9.83539e22	0.0366968
$749$	−1.80573e24	−0.666129
$750$	3.15319e24	1.15008
$751$	3.88104e24	1.39962	0.699808	−	0.714331i	$-0.253269\pi$
$751$	3.88104e24	1.39962	0.699808	+	0.714331i	$0.253269\pi$
$752$	4.00587e23	0.142839
$753$	4.94307e23	0.174277
$754$	3.01534e24	1.05119
$755$	−5.29823e24	−1.82634
$756$	1.52061e24	0.518301
$757$	−5.68213e23	−0.191512	−0.0957560	−	0.995405i	$-0.530527\pi$
$757$	−5.68213e23	−0.191512	−0.0957560	+	0.995405i	$0.530527\pi$
$758$	3.03609e23	0.101187
$759$	−6.98207e22	−0.0230107
$760$	7.62344e24	2.48448
$761$	5.73056e24	1.84683	0.923416	−	0.383800i	$-0.125385\pi$
$761$	5.73056e24	1.84683	0.923416	+	0.383800i	$0.125385\pi$
$762$	2.45339e24	0.781898
$763$	−1.69814e24	−0.535200
$764$	2.20203e24	0.686325
$765$	3.24193e23	0.0999268
$766$	1.42298e23	0.0433766
$767$	1.98726e24	0.599094
$768$	2.23679e24	0.666892
$769$	−3.46644e24	−1.02214	−0.511069	−	0.859540i	$-0.670750\pi$
$769$	−3.46644e24	−1.02214	−0.511069	+	0.859540i	$0.670750\pi$
$770$	1.18450e24	0.345433
$771$	−2.36061e24	−0.680865
$772$	−3.20562e23	−0.0914460
$773$	−5.20948e24	−1.46984	−0.734918	−	0.678156i	$-0.762779\pi$
$773$	−5.20948e24	−1.46984	−0.734918	+	0.678156i	$0.762779\pi$
$774$	−2.29530e24	−0.640534
$775$	−5.82536e22	−0.0160790
$776$	3.27025e23	0.0892803
$777$	−3.36754e23	−0.0909357
$778$	3.56331e24	0.951758
$779$	3.52423e24	0.931099
$780$	−1.64714e24	−0.430454
$781$	−1.61508e24	−0.417503
$782$	−9.21471e22	−0.0235626
$783$	−4.85738e24	−1.22865
$784$	−2.10500e24	−0.526702
$785$	−3.79150e24	−0.938466
$786$	−1.19847e24	−0.293451
$787$	−4.25641e24	−1.03100	−0.515499	−	0.856890i	$-0.672394\pi$
$787$	−4.25641e24	−1.03100	−0.515499	+	0.856890i	$0.672394\pi$
$788$	−7.70477e24	−1.84623
$789$	2.49159e24	0.590640
$790$	−2.13684e24	−0.501121
$791$	−2.29937e24	−0.533469
$792$	−1.62267e24	−0.372448
$793$	1.73911e24	0.394917
$794$	8.30687e24	1.86622
$795$	2.02852e24	0.450877
$796$	2.34985e24	0.516748
$797$	3.23858e24	0.704627	0.352314	−	0.935882i	$-0.385395\pi$
$797$	3.23858e24	0.704627	0.352314	+	0.935882i	$0.385395\pi$
$798$	−1.13538e24	−0.244409
$799$	−7.15142e22	−0.0152316
$800$	3.99725e24	0.842358
$801$	3.78384e24	0.788962
$802$	9.00903e24	1.85864
$803$	1.76454e24	0.360206
$804$	5.07190e24	1.02446
$805$	−7.23012e23	−0.144504
$806$	2.37949e22	0.00470582
$807$	−1.97331e24	−0.386163
$808$	−1.21329e25	−2.34946
$809$	−9.33357e24	−1.78849	−0.894243	−	0.447582i	$-0.852285\pi$
$809$	−9.33357e24	−1.78849	−0.894243	+	0.447582i	$0.852285\pi$
$810$	−9.30951e24	−1.76524
$811$	8.12182e23	0.152397	0.0761984	−	0.997093i	$-0.475722\pi$
$811$	8.12182e23	0.152397	0.0761984	+	0.997093i	$0.475722\pi$
$812$	−7.05275e24	−1.30958
$813$	1.77790e24	0.326691
$814$	1.67174e24	0.303992
$815$	1.67684e25	3.01754
$816$	8.78846e22	0.0156512
$817$	2.41590e24	0.425785
$818$	1.10418e24	0.192591
$819$	−6.97078e23	−0.120328
$820$	−1.83550e25	−3.13571
$821$	−8.65986e24	−1.46418	−0.732089	−	0.681209i	$-0.761455\pi$
$821$	−8.65986e24	−1.46418	−0.732089	+	0.681209i	$0.761455\pi$
$822$	−2.55551e24	−0.427629
$823$	−2.18728e23	−0.0362248	−0.0181124	−	0.999836i	$-0.505766\pi$
$823$	−2.18728e23	−0.0362248	−0.0181124	+	0.999836i	$0.505766\pi$
$824$	1.30216e25	2.13444
$825$	1.38665e24	0.224962
$826$	−7.13438e24	−1.14558
$827$	−5.51147e24	−0.875932	−0.437966	−	0.898991i	$-0.644301\pi$
$827$	−5.51147e24	−0.875932	−0.437966	+	0.898991i	$0.644301\pi$
$828$	2.12957e24	0.334991
$829$	−7.84616e23	−0.122164	−0.0610821	−	0.998133i	$-0.519455\pi$
$829$	−7.84616e23	−0.122164	−0.0610821	+	0.998133i	$0.519455\pi$
$830$	7.42019e24	1.14354
$831$	1.72878e24	0.263712
$832$	−3.09198e24	−0.466861
$833$	3.75791e23	0.0561647
$834$	−4.09182e24	−0.605348
$835$	4.90327e24	0.718043
$836$	3.67213e24	0.532311
$837$	−3.83308e22	−0.00550024
$838$	−1.77418e25	−2.52014
$839$	4.11108e24	0.578068	0.289034	−	0.957319i	$-0.406666\pi$
$839$	4.11108e24	0.578068	0.289034	+	0.957319i	$0.406666\pi$
$840$	2.75030e24	0.382831
$841$	1.52719e25	2.10440
$842$	1.36036e25	1.85567
$843$	1.27847e24	0.172646
$844$	−1.36087e25	−1.81931
$845$	−1.15371e25	−1.52691
$846$	2.53677e24	0.332378
$847$	−2.79957e24	−0.363147
$848$	−3.35968e24	−0.431452
$849$	2.85413e24	0.362877
$850$	1.83005e24	0.230358
$851$	−1.02042e24	−0.127168
$852$	−8.06287e24	−0.994839
$853$	4.34649e24	0.530973	0.265486	−	0.964115i	$-0.414467\pi$
$853$	4.34649e24	0.530973	0.265486	+	0.964115i	$0.414467\pi$
$854$	−6.24351e24	−0.755156
$855$	1.21041e25	1.44950
$856$	2.08140e25	2.46791
$857$	−1.27176e25	−1.49302	−0.746512	−	0.665372i	$-0.768273\pi$
$857$	−1.27176e25	−1.49302	−0.746512	+	0.665372i	$0.768273\pi$
$858$	−5.66405e23	−0.0658393
$859$	9.31193e24	1.07176	0.535880	−	0.844294i	$-0.319980\pi$
$859$	9.31193e24	1.07176	0.535880	+	0.844294i	$0.319980\pi$
$860$	−1.25825e25	−1.43394
$861$	1.27143e24	0.143472
$862$	8.87417e24	0.991553
$863$	1.35964e24	0.150429	0.0752146	−	0.997167i	$-0.476036\pi$
$863$	1.35964e24	0.150429	0.0752146	+	0.997167i	$0.476036\pi$
$864$	2.63019e24	0.288151
$865$	−1.27107e25	−1.37889
$866$	−2.70457e25	−2.90533
$867$	3.50997e24	0.373372
$868$	−5.56550e22	−0.00586255
$869$	−4.78729e23	−0.0499369
$870$	−1.88893e25	−1.95120
$871$	−5.03069e24	−0.514604
$872$	1.95739e25	1.98283
$873$	5.19231e23	0.0520882
$874$	−3.44040e24	−0.341791
$875$	7.31524e24	0.719714
$876$	8.80905e24	0.858310
$877$	−1.80106e25	−1.73793	−0.868965	−	0.494874i	$-0.835214\pi$
$877$	−1.80106e25	−1.73793	−0.868965	+	0.494874i	$0.835214\pi$
$878$	−1.23105e25	−1.17645
$879$	1.88062e24	0.177990
$880$	−3.42321e24	−0.320871
$881$	2.01002e25	1.86597	0.932984	−	0.359918i	$-0.117195\pi$
$881$	2.01002e25	1.86597	0.932984	+	0.359918i	$0.117195\pi$
$882$	−1.33301e25	−1.22561
$883$	2.10036e25	1.91262	0.956308	−	0.292361i	$-0.0944408\pi$
$883$	2.10036e25	1.91262	0.956308	+	0.292361i	$0.0944408\pi$
$884$	−4.87018e23	−0.0439239
$885$	−1.24490e25	−1.11203
$886$	2.63899e25	2.33481
$887$	2.05468e24	0.180050	0.0900249	−	0.995940i	$-0.471305\pi$
$887$	2.05468e24	0.180050	0.0900249	+	0.995940i	$0.471305\pi$
$888$	3.88164e24	0.336903
$889$	5.69174e24	0.489306
$890$	3.18375e25	2.71097
$891$	−2.08566e24	−0.175907
$892$	−1.13134e25	−0.945127
$893$	−2.67005e24	−0.220944
$894$	9.88585e24	0.810299
$895$	4.27809e25	3.47339
$896$	9.05761e24	0.728443
$897$	3.45730e23	0.0275424
$898$	1.53992e25	1.21520
$899$	1.77783e23	0.0138974
$900$	−4.22935e25	−3.27501
$901$	5.99780e23	0.0460078
$902$	−6.31175e24	−0.479617
$903$	8.71582e23	0.0656088
$904$	2.65040e25	1.97642
$905$	−1.93042e25	−1.42607
$906$	−9.09543e24	−0.665631
$907$	−9.11097e24	−0.660545	−0.330273	−	0.943886i	$-0.607141\pi$
$907$	−9.11097e24	−0.660545	−0.330273	+	0.943886i	$0.607141\pi$
$908$	−7.38825e24	−0.530654
$909$	−1.92639e25	−1.37073
$910$	−5.86527e24	−0.413463
$911$	−2.62183e25	−1.83104	−0.915521	−	0.402269i	$-0.868222\pi$
$911$	−2.62183e25	−1.83104	−0.915521	+	0.402269i	$0.868222\pi$
$912$	3.28125e24	0.227030
$913$	1.66239e24	0.113954
$914$	−1.30069e25	−0.883348
$915$	−1.08945e25	−0.733041
$916$	−4.54838e25	−3.03211
$917$	−2.78038e24	−0.183639
$918$	1.20417e24	0.0788000
$919$	−2.96483e25	−1.92229	−0.961143	−	0.276051i	$-0.910974\pi$
$919$	−2.96483e25	−1.92229	−0.961143	+	0.276051i	$0.910974\pi$
$920$	8.33388e24	0.535366
$921$	−2.99745e24	−0.190786
$922$	−3.81257e25	−2.40439
$923$	7.99735e24	0.499726
$924$	1.32479e24	0.0820232
$925$	2.02657e25	1.24325
$926$	3.56221e25	2.16534
$927$	2.06750e25	1.24528
$928$	−1.21991e25	−0.728065
$929$	−1.57083e25	−0.928959	−0.464479	−	0.885584i	$-0.653759\pi$
$929$	−1.57083e25	−0.928959	−0.464479	+	0.885584i	$0.653759\pi$
$930$	−1.49061e23	−0.00873489
$931$	1.40305e25	0.814706
$932$	4.51363e25	2.59711
$933$	−7.25821e24	−0.413843
$934$	4.04848e25	2.28741
$935$	6.11122e23	0.0342160
$936$	8.03494e24	0.445798
$937$	1.14203e25	0.627903	0.313951	−	0.949439i	$-0.398347\pi$
$937$	1.14203e25	0.627903	0.313951	+	0.949439i	$0.398347\pi$
$938$	1.80604e25	0.984021
$939$	−5.06456e24	−0.273454
$940$	1.39062e25	0.744084
$941$	−2.46617e25	−1.30771	−0.653855	−	0.756620i	$-0.726849\pi$
$941$	−2.46617e25	−1.30771	−0.653855	+	0.756620i	$0.726849\pi$
$942$	−6.50883e24	−0.342035
$943$	3.85266e24	0.200637
$944$	2.06184e25	1.06412
$945$	9.44829e24	0.483262
$946$	−4.32677e24	−0.219326
$947$	−7.11449e23	−0.0357412	−0.0178706	−	0.999840i	$-0.505689\pi$
$947$	−7.11449e23	−0.0357412	−0.0178706	+	0.999840i	$0.505689\pi$
$948$	−2.38993e24	−0.118991
$949$	−8.73747e24	−0.431145
$950$	6.83268e25	3.34149
$951$	4.37457e24	0.212032
$952$	8.13195e23	0.0390643
$953$	−3.12976e24	−0.149012	−0.0745061	−	0.997221i	$-0.523738\pi$
$953$	−3.12976e24	−0.149012	−0.0745061	+	0.997221i	$0.523738\pi$
$954$	−2.12756e25	−1.00397
$955$	1.36823e25	0.639927
$956$	2.58573e25	1.19865
$957$	−4.23188e24	−0.194438
$958$	4.32518e25	1.96969
$959$	−5.92865e24	−0.267607
$960$	1.93694e25	0.866583
$961$	−2.25487e25	−0.999938
$962$	−8.27795e24	−0.363860
$963$	3.30473e25	1.43983
$964$	−4.22470e25	−1.82449
$965$	−1.99181e24	−0.0852640
$966$	−1.24119e24	−0.0526663
$967$	2.24052e25	0.942377	0.471188	−	0.882033i	$-0.343825\pi$
$967$	2.24052e25	0.942377	0.471188	+	0.882033i	$0.343825\pi$
$968$	3.22696e25	1.34540
$969$	−5.85780e23	−0.0242093
$970$	4.36885e24	0.178981
$971$	3.61762e25	1.46913	0.734563	−	0.678540i	$-0.237387\pi$
$971$	3.61762e25	1.46913	0.734563	+	0.678540i	$0.237387\pi$
$972$	−4.27962e25	−1.72283
$973$	−9.49280e24	−0.378822
$974$	−6.84788e25	−2.70897
$975$	−6.86626e24	−0.269266
$976$	1.80437e25	0.701460
$977$	7.45875e24	0.287450	0.143725	−	0.989618i	$-0.454092\pi$
$977$	7.45875e24	0.287450	0.143725	+	0.989618i	$0.454092\pi$
$978$	2.87862e25	1.09978
$979$	7.13274e24	0.270149
$980$	−7.30740e25	−2.74373
$981$	3.10782e25	1.15683
$982$	−3.88006e25	−1.43183
$983$	−2.40299e25	−0.879117	−0.439558	−	0.898214i	$-0.644865\pi$
$983$	−2.40299e25	−0.879117	−0.439558	+	0.898214i	$0.644865\pi$
$984$	−1.46553e25	−0.531542
$985$	−4.78736e25	−1.72142
$986$	−5.58509e24	−0.199102
$987$	−9.63272e23	−0.0340450
$988$	−1.81833e25	−0.637144
$989$	2.64104e24	0.0917501
$990$	−2.16779e25	−0.746651
$991$	−1.88786e25	−0.644681	−0.322340	−	0.946624i	$-0.604470\pi$
$991$	−1.88786e25	−0.644681	−0.322340	+	0.946624i	$0.604470\pi$
$992$	−9.62663e22	−0.00325931
$993$	−6.77461e24	−0.227413
$994$	−2.87109e25	−0.955570
$995$	1.46008e25	0.481814
$996$	8.29905e24	0.271534
$997$	4.04271e25	1.31148	0.655742	−	0.754985i	$-0.272356\pi$
$997$	4.04271e25	1.31148	0.655742	+	0.754985i	$0.272356\pi$
$998$	−7.75955e24	−0.249590
$999$	1.33348e25	0.425286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.18.a.a.1.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.18.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-613.281 q^{2} -4261.96 q^{3} +245042. q^{4} +1.52257e6 q^{5} +2.61378e6 q^{6} +6.06383e6 q^{7} -6.98954e7 q^{8} -1.10976e8 q^{9} +O(q^{10})\)	\(q-613.281 q^{2} -4261.96 q^{3} +245042. q^{4} +1.52257e6 q^{5} +2.61378e6 q^{6} +6.06383e6 q^{7} -6.98954e7 q^{8} -1.10976e8 q^{9} -9.33761e8 q^{10} -2.09196e8 q^{11} -1.04436e9 q^{12} +1.03587e9 q^{13} -3.71883e9 q^{14} -6.48911e9 q^{15} +1.07474e10 q^{16} -1.91867e9 q^{17} +6.80594e10 q^{18} -7.16351e10 q^{19} +3.73092e11 q^{20} -2.58438e10 q^{21} +1.28296e11 q^{22} -7.83110e10 q^{23} +2.97891e11 q^{24} +1.55527e12 q^{25} -6.35280e11 q^{26} +1.02336e12 q^{27} +1.48589e12 q^{28} -4.74648e12 q^{29} +3.97965e12 q^{30} -3.74557e10 q^{31} +2.57014e12 q^{32} +8.91583e11 q^{33} +1.17668e12 q^{34} +9.23258e12 q^{35} -2.71937e13 q^{36} +1.30304e13 q^{37} +4.39325e13 q^{38} -4.41484e12 q^{39} -1.06420e14 q^{40} -4.91969e13 q^{41} +1.58495e13 q^{42} -3.37250e13 q^{43} -5.12616e13 q^{44} -1.68968e14 q^{45} +4.80266e13 q^{46} +3.72729e13 q^{47} -4.58051e13 q^{48} -1.95861e14 q^{49} -9.53816e14 q^{50} +8.17727e12 q^{51} +2.53832e14 q^{52} -3.12603e14 q^{53} -6.27610e14 q^{54} -3.18514e14 q^{55} -4.23834e14 q^{56} +3.05306e14 q^{57} +2.91093e15 q^{58} +1.91845e15 q^{59} -1.59010e15 q^{60} +1.67889e15 q^{61} +2.29709e13 q^{62} -6.72939e14 q^{63} -2.98490e15 q^{64} +1.57718e15 q^{65} -5.46791e14 q^{66} -4.85648e15 q^{67} -4.70153e14 q^{68} +3.33758e14 q^{69} -5.66217e15 q^{70} +7.72041e15 q^{71} +7.75670e15 q^{72} -8.43490e15 q^{73} -7.99129e15 q^{74} -6.62849e15 q^{75} -1.75536e16 q^{76} -1.26853e15 q^{77} +2.70754e15 q^{78} +2.28843e15 q^{79} +1.63637e16 q^{80} +9.96991e15 q^{81} +3.01715e16 q^{82} -7.94656e15 q^{83} -6.33280e15 q^{84} -2.92130e15 q^{85} +2.06829e16 q^{86} +2.02293e16 q^{87} +1.46218e16 q^{88} -3.40960e16 q^{89} +1.03625e17 q^{90} +6.28134e15 q^{91} -1.91894e16 q^{92} +1.59635e14 q^{93} -2.28587e16 q^{94} -1.09069e17 q^{95} -1.09538e16 q^{96} -4.67877e15 q^{97} +1.20118e17 q^{98} +2.32157e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) \) 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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