LMFDB - Embedded newform 23.14.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,14,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, 14, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 14 $
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:	$24.6631136589$
Analytic rank:	$0$
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} - 6 x^{13} - 91997 x^{12} + 766599 x^{11} + 3278769040 x^{10} - 30986318669 x^{9} + \cdots - 45\!\cdots\!18 $ x^14 - 6x^13 - 91997x^12 + 766599x^11 + 3278769040x^10 - 30986318669x^9 - 56829440072404x^8 + 496745885608086x^7 + 489413218263943745x^6 - 2739731727714726112x^5 - 1876344541617480126605x^4 + 570635039214955094451x^3 + 2228700241007939520815870x^2 - 899908554608774434140317*x - 453423216458424113690611218
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{4}\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$16.3008$ 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)

$f(q)$	$=$	$q-11.3008 q^{2} -618.076 q^{3} -8064.29 q^{4} +41118.0 q^{5} +6984.75 q^{6} -134255. q^{7} +183709. q^{8} -1.21231e6 q^{9} +O(q^{10})$	\(q-11.3008 q^{2} -618.076 q^{3} -8064.29 q^{4} +41118.0 q^{5} +6984.75 q^{6} -134255. q^{7} +183709. q^{8} -1.21231e6 q^{9} -464666. q^{10} -8.15951e6 q^{11} +4.98435e6 q^{12} -4.55315e6 q^{13} +1.51718e6 q^{14} -2.54140e7 q^{15} +6.39866e7 q^{16} +1.53466e8 q^{17} +1.37000e7 q^{18} -3.29396e7 q^{19} -3.31588e8 q^{20} +8.29796e7 q^{21} +9.22090e7 q^{22} +1.48036e8 q^{23} -1.13546e8 q^{24} +4.69987e8 q^{25} +5.14542e7 q^{26} +1.73471e9 q^{27} +1.08267e9 q^{28} +5.09147e9 q^{29} +2.87199e8 q^{30} +1.65833e9 q^{31} -2.22804e9 q^{32} +5.04320e9 q^{33} -1.73429e9 q^{34} -5.52029e9 q^{35} +9.77638e9 q^{36} +1.18455e10 q^{37} +3.72243e8 q^{38} +2.81419e9 q^{39} +7.55374e9 q^{40} +4.99822e10 q^{41} -9.37735e8 q^{42} -4.08239e10 q^{43} +6.58007e10 q^{44} -4.98476e10 q^{45} -1.67292e9 q^{46} +7.92124e10 q^{47} -3.95486e10 q^{48} -7.88647e10 q^{49} -5.31122e9 q^{50} -9.48539e10 q^{51} +3.67179e10 q^{52} -1.16861e11 q^{53} -1.96036e10 q^{54} -3.35503e11 q^{55} -2.46638e10 q^{56} +2.03592e10 q^{57} -5.75376e10 q^{58} +3.82165e11 q^{59} +2.04946e11 q^{60} +1.29194e11 q^{61} -1.87404e10 q^{62} +1.62758e11 q^{63} -4.99000e11 q^{64} -1.87216e11 q^{65} -5.69921e10 q^{66} -1.12931e12 q^{67} -1.23760e12 q^{68} -9.14974e10 q^{69} +6.23836e10 q^{70} +1.26733e12 q^{71} -2.22711e11 q^{72} +5.84981e11 q^{73} -1.33863e11 q^{74} -2.90487e11 q^{75} +2.65635e11 q^{76} +1.09545e12 q^{77} -3.18026e10 q^{78} -5.91494e11 q^{79} +2.63100e12 q^{80} +8.60623e11 q^{81} -5.64839e11 q^{82} +3.01889e12 q^{83} -6.69172e11 q^{84} +6.31023e12 q^{85} +4.61342e11 q^{86} -3.14691e12 q^{87} -1.49898e12 q^{88} +3.55769e12 q^{89} +5.63317e11 q^{90} +6.11281e11 q^{91} -1.19380e12 q^{92} -1.02497e12 q^{93} -8.95163e11 q^{94} -1.35441e12 q^{95} +1.37710e12 q^{96} -2.47290e12 q^{97} +8.91233e11 q^{98} +9.89182e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9}+O(q^{10}) $ 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9} + 3585670 q^{10} + 1070730 q^{11} - 8508331 q^{12} + 23949638 q^{13} - 119280968 q^{14} - 44834930 q^{15} + 256829072 q^{16} + 69487470 q^{17} + 92449927 q^{18} + 111438548 q^{19} + 1129282316 q^{20} + 621345174 q^{21} + 2278933028 q^{22} + 2072502446 q^{23} + 8776950724 q^{24} + 5548551686 q^{25} - 925154105 q^{26} - 2006600744 q^{27} + 10886499970 q^{28} + 6082889362 q^{29} + 33591682946 q^{30} + 15979895560 q^{31} + 39045677992 q^{32} + 48341340746 q^{33} + 26300859414 q^{34} + 71251965504 q^{35} + 134660338135 q^{36} + 52356093690 q^{37} + 96969962716 q^{38} + 35694630240 q^{39} + 30337594230 q^{40} + 116782373266 q^{41} + 47161428352 q^{42} + 551363512 q^{43} - 18191926218 q^{44} + 66956385060 q^{45} + 9474296896 q^{46} - 89763073312 q^{47} + 7373438519 q^{48} + 198965141586 q^{49} - 353559739256 q^{50} - 849385907902 q^{51} + 290946305159 q^{52} - 255252512096 q^{53} - 20138610103 q^{54} - 308239853444 q^{55} - 1741462242990 q^{56} - 373036556464 q^{57} - 2063171638367 q^{58} - 844368470500 q^{59} - 3864457510716 q^{60} - 660411924036 q^{61} - 3066592203813 q^{62} - 2044550744028 q^{63} - 149179140181 q^{64} + 25563523898 q^{65} - 3128765504558 q^{66} + 343438236966 q^{67} - 687566878740 q^{68} + 304361787784 q^{69} + 2831163146300 q^{70} + 525250335580 q^{71} - 1782771811281 q^{72} + 6080256001118 q^{73} + 1193156509458 q^{74} + 3035968085076 q^{75} + 11140697506136 q^{76} - 905513956696 q^{77} + 15392222627509 q^{78} + 2029462022780 q^{79} + 6389606776510 q^{80} + 11017226960590 q^{81} + 5032544493407 q^{82} + 1645588044714 q^{83} - 8835767120594 q^{84} + 8689341605448 q^{85} - 5028664556794 q^{86} + 14107817502696 q^{87} + 35486297142892 q^{88} + 3557834996156 q^{89} - 20611184383708 q^{90} + 20574193795614 q^{91} + 10308035022848 q^{92} + 32845521705562 q^{93} - 4653170522585 q^{94} + 35338742719324 q^{95} + 44121425602615 q^{96} + 20411381883630 q^{97} - 10415391287228 q^{98} - 9767188111540 q^{99}+O(q^{100}) \) 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9 + 3585670 * q^10 + 1070730 * q^11 - 8508331 * q^12 + 23949638 * q^13 - 119280968 * q^14 - 44834930 * q^15 + 256829072 * q^16 + 69487470 * q^17 + 92449927 * q^18 + 111438548 * q^19 + 1129282316 * q^20 + 621345174 * q^21 + 2278933028 * q^22 + 2072502446 * q^23 + 8776950724 * q^24 + 5548551686 * q^25 - 925154105 * q^26 - 2006600744 * q^27 + 10886499970 * q^28 + 6082889362 * q^29 + 33591682946 * q^30 + 15979895560 * q^31 + 39045677992 * q^32 + 48341340746 * q^33 + 26300859414 * q^34 + 71251965504 * q^35 + 134660338135 * q^36 + 52356093690 * q^37 + 96969962716 * q^38 + 35694630240 * q^39 + 30337594230 * q^40 + 116782373266 * q^41 + 47161428352 * q^42 + 551363512 * q^43 - 18191926218 * q^44 + 66956385060 * q^45 + 9474296896 * q^46 - 89763073312 * q^47 + 7373438519 * q^48 + 198965141586 * q^49 - 353559739256 * q^50 - 849385907902 * q^51 + 290946305159 * q^52 - 255252512096 * q^53 - 20138610103 * q^54 - 308239853444 * q^55 - 1741462242990 * q^56 - 373036556464 * q^57 - 2063171638367 * q^58 - 844368470500 * q^59 - 3864457510716 * q^60 - 660411924036 * q^61 - 3066592203813 * q^62 - 2044550744028 * q^63 - 149179140181 * q^64 + 25563523898 * q^65 - 3128765504558 * q^66 + 343438236966 * q^67 - 687566878740 * q^68 + 304361787784 * q^69 + 2831163146300 * q^70 + 525250335580 * q^71 - 1782771811281 * q^72 + 6080256001118 * q^73 + 1193156509458 * q^74 + 3035968085076 * q^75 + 11140697506136 * q^76 - 905513956696 * q^77 + 15392222627509 * q^78 + 2029462022780 * q^79 + 6389606776510 * q^80 + 11017226960590 * q^81 + 5032544493407 * q^82 + 1645588044714 * q^83 - 8835767120594 * q^84 + 8689341605448 * q^85 - 5028664556794 * q^86 + 14107817502696 * q^87 + 35486297142892 * q^88 + 3557834996156 * q^89 - 20611184383708 * q^90 + 20574193795614 * q^91 + 10308035022848 * q^92 + 32845521705562 * q^93 - 4653170522585 * q^94 + 35338742719324 * q^95 + 44121425602615 * q^96 + 20411381883630 * q^97 - 10415391287228 * q^98 - 9767188111540 * 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 $

$2$	−11.3008	−0.124857	−0.0624286	−	0.998049i	$-0.519885\pi$
$2$	−11.3008	−0.124857	−0.0624286	+	0.998049i	$0.519885\pi$
$3$	−618.076	−0.489501	−0.244751	−	0.969586i	$-0.578706\pi$
$3$	−618.076	−0.489501	−0.244751	+	0.969586i	$0.578706\pi$
$4$	−8064.29	−0.984411
$5$	41118.0	1.17687	0.588433	−	0.808546i	$-0.299745\pi$
$5$	41118.0	1.17687	0.588433	+	0.808546i	$0.299745\pi$
$6$	6984.75	0.0611178
$7$	−134255.	−0.431313	−0.215656	−	0.976469i	$-0.569189\pi$
$7$	−134255.	−0.431313	−0.215656	+	0.976469i	$0.569189\pi$
$8$	183709.	0.247768
$9$	−1.21231e6	−0.760389
$10$	−464666.	−0.146940
$11$	−8.15951e6	−1.38871	−0.694355	−	0.719632i	$-0.744310\pi$
$11$	−8.15951e6	−1.38871	−0.694355	+	0.719632i	$0.744310\pi$
$12$	4.98435e6	0.481870
$13$	−4.55315e6	−0.261625	−0.130813	−	0.991407i	$-0.541759\pi$
$13$	−4.55315e6	−0.261625	−0.130813	+	0.991407i	$0.541759\pi$
$14$	1.51718e6	0.0538525
$15$	−2.54140e7	−0.576077
$16$	6.39866e7	0.953475
$17$	1.53466e8	1.54204	0.771020	−	0.636811i	$-0.219747\pi$
$17$	1.53466e8	1.54204	0.771020	+	0.636811i	$0.219747\pi$
$18$	1.37000e7	0.0949401
$19$	−3.29396e7	−0.160627	−0.0803137	−	0.996770i	$-0.525592\pi$
$19$	−3.29396e7	−0.160627	−0.0803137	+	0.996770i	$0.525592\pi$
$20$	−3.31588e8	−1.15852
$21$	8.29796e7	0.211128
$22$	9.22090e7	0.173391
$23$	1.48036e8	0.208514
$23$	1.48036e8	0.208514
$24$	−1.13546e8	−0.121283
$25$	4.69987e8	0.385013
$26$	5.14542e7	0.0326658
$27$	1.73471e9	0.861712
$28$	1.08267e9	0.424589
$29$	5.09147e9	1.58948	0.794742	−	0.606948i	$-0.207606\pi$
$29$	5.09147e9	1.58948	0.794742	+	0.606948i	$0.207606\pi$
$30$	2.87199e8	0.0719274
$31$	1.65833e9	0.335598	0.167799	−	0.985821i	$-0.446334\pi$
$31$	1.65833e9	0.335598	0.167799	+	0.985821i	$0.446334\pi$
$32$	−2.22804e9	−0.366816
$33$	5.04320e9	0.679776
$34$	−1.73429e9	−0.192535
$35$	−5.52029e9	−0.507597
$36$	9.77638e9	0.748535
$37$	1.18455e10	0.758999	0.379500	−	0.925192i	$-0.376096\pi$
$37$	1.18455e10	0.758999	0.379500	+	0.925192i	$0.376096\pi$
$38$	3.72243e8	0.0200555
$39$	2.81419e9	0.128066
$40$	7.55374e9	0.291590
$41$	4.99822e10	1.64331	0.821657	−	0.569982i	$-0.193050\pi$
$41$	4.99822e10	1.64331	0.821657	+	0.569982i	$0.193050\pi$
$42$	−9.37735e8	−0.0263609
$43$	−4.08239e10	−0.984848	−0.492424	−	0.870355i	$-0.663889\pi$
$43$	−4.08239e10	−0.984848	−0.492424	+	0.870355i	$0.663889\pi$
$44$	6.58007e10	1.36706
$45$	−4.98476e10	−0.894875
$46$	−1.67292e9	−0.0260345
$47$	7.92124e10	1.07191	0.535954	−	0.844247i	$-0.319952\pi$
$47$	7.92124e10	1.07191	0.535954	+	0.844247i	$0.319952\pi$
$48$	−3.95486e10	−0.466727
$49$	−7.88647e10	−0.813969
$50$	−5.31122e9	−0.0480717
$51$	−9.48539e10	−0.754830
$52$	3.67179e10	0.257547
$53$	−1.16861e11	−0.724228	−0.362114	−	0.932134i	$-0.617945\pi$
$53$	−1.16861e11	−0.724228	−0.362114	+	0.932134i	$0.617945\pi$
$54$	−1.96036e10	−0.107591
$55$	−3.35503e11	−1.63433
$56$	−2.46638e10	−0.106866
$57$	2.03592e10	0.0786273
$58$	−5.75376e10	−0.198459
$59$	3.82165e11	1.17954	0.589771	−	0.807571i	$-0.299218\pi$
$59$	3.82165e11	1.17954	0.589771	+	0.807571i	$0.299218\pi$
$60$	2.04946e11	0.567097
$61$	1.29194e11	0.321069	0.160535	−	0.987030i	$-0.448678\pi$
$61$	1.29194e11	0.321069	0.160535	+	0.987030i	$0.448678\pi$
$62$	−1.87404e10	−0.0419018
$63$	1.62758e11	0.327965
$64$	−4.99000e11	−0.907675
$65$	−1.87216e11	−0.307898
$66$	−5.69921e10	−0.0848749
$67$	−1.12931e12	−1.52520	−0.762600	−	0.646870i	$-0.776077\pi$
$67$	−1.12931e12	−1.52520	−0.762600	+	0.646870i	$0.776077\pi$
$68$	−1.23760e12	−1.51800
$69$	−9.14974e10	−0.102068
$70$	6.23836e10	0.0633772
$71$	1.26733e12	1.17411	0.587057	−	0.809546i	$-0.300286\pi$
$71$	1.26733e12	1.17411	0.587057	+	0.809546i	$0.300286\pi$
$72$	−2.22711e11	−0.188400
$73$	5.84981e11	0.452421	0.226211	−	0.974078i	$-0.427366\pi$
$73$	5.84981e11	0.452421	0.226211	+	0.974078i	$0.427366\pi$
$74$	−1.33863e11	−0.0947666
$75$	−2.90487e11	−0.188464
$76$	2.65635e11	0.158123
$77$	1.09545e12	0.598969
$78$	−3.18026e10	−0.0159900
$79$	−5.91494e11	−0.273763	−0.136881	−	0.990587i	$-0.543708\pi$
$79$	−5.91494e11	−0.273763	−0.136881	+	0.990587i	$0.543708\pi$
$80$	2.63100e12	1.12211
$81$	8.60623e11	0.338579
$82$	−5.64839e11	−0.205180
$83$	3.01889e12	1.01354	0.506769	−	0.862082i	$-0.330840\pi$
$83$	3.01889e12	1.01354	0.506769	+	0.862082i	$0.330840\pi$
$84$	−6.69172e11	−0.207837
$85$	6.31023e12	1.81477
$86$	4.61342e11	0.122965
$87$	−3.14691e12	−0.778054
$88$	−1.49898e12	−0.344078
$89$	3.55769e12	0.758810	0.379405	−	0.925231i	$-0.376129\pi$
$89$	3.55769e12	0.758810	0.379405	+	0.925231i	$0.376129\pi$
$90$	5.63317e11	0.111732
$91$	6.11281e11	0.112842
$92$	−1.19380e12	−0.205264
$93$	−1.02497e12	−0.164276
$94$	−8.95163e11	−0.133835
$95$	−1.35441e12	−0.189037
$96$	1.37710e12	0.179557
$97$	−2.47290e12	−0.301433	−0.150717	−	0.988577i	$-0.548158\pi$
$97$	−2.47290e12	−0.301433	−0.150717	+	0.988577i	$0.548158\pi$
$98$	8.91233e11	0.101630
$99$	9.89182e12	1.05596
$100$	−3.79011e12	−0.379011
$101$	−8.00241e12	−0.750122	−0.375061	−	0.927000i	$-0.622378\pi$
$101$	−8.00241e12	−0.750122	−0.375061	+	0.927000i	$0.622378\pi$
$102$	1.07192e12	0.0942460
$103$	−7.60357e12	−0.627445	−0.313722	−	0.949515i	$-0.601576\pi$
$103$	−7.60357e12	−0.627445	−0.313722	+	0.949515i	$0.601576\pi$
$104$	−8.36454e11	−0.0648224
$105$	3.41196e12	0.248469
$106$	1.32062e12	0.0904251
$107$	−2.04243e13	−1.31568	−0.657842	−	0.753156i	$-0.728531\pi$
$107$	−2.04243e13	−1.31568	−0.657842	+	0.753156i	$0.728531\pi$
$108$	−1.39892e13	−0.848279
$109$	1.08305e13	0.618552	0.309276	−	0.950972i	$-0.399913\pi$
$109$	1.08305e13	0.618552	0.309276	+	0.950972i	$0.399913\pi$
$110$	3.79145e12	0.204058
$111$	−7.32140e12	−0.371531
$112$	−8.59051e12	−0.411246
$113$	2.75308e13	1.24397	0.621984	−	0.783030i	$-0.286327\pi$
$113$	2.75308e13	1.24397	0.621984	+	0.783030i	$0.286327\pi$
$114$	−2.30075e11	−0.00981720
$115$	6.08694e12	0.245393
$116$	−4.10591e13	−1.56470
$117$	5.51980e12	0.198937
$118$	−4.31877e12	−0.147274
$119$	−2.06036e13	−0.665101
$120$	−4.66879e12	−0.142734
$121$	3.20549e13	0.928518
$122$	−1.46000e12	−0.0400878
$123$	−3.08928e13	−0.804404
$124$	−1.33732e13	−0.330366
$125$	−3.08680e13	−0.723757
$126$	−1.83929e12	−0.0409489
$127$	5.95282e13	1.25892	0.629460	−	0.777033i	$-0.283276\pi$
$127$	5.95282e13	1.25892	0.629460	+	0.777033i	$0.283276\pi$
$128$	2.38912e13	0.480146
$129$	2.52323e13	0.482084
$130$	2.11569e12	0.0384433
$131$	−9.69261e13	−1.67563	−0.837814	−	0.545956i	$-0.816167\pi$
$131$	−9.69261e13	−1.67563	−0.837814	+	0.545956i	$0.816167\pi$
$132$	−4.06698e13	−0.669178
$133$	4.42230e12	0.0692807
$134$	1.27621e13	0.190432
$135$	7.13278e13	1.01412
$136$	2.81932e13	0.382068
$137$	1.03232e14	1.33393	0.666963	−	0.745091i	$-0.267594\pi$
$137$	1.03232e14	1.33393	0.666963	+	0.745091i	$0.267594\pi$
$138$	1.03399e12	0.0127439
$139$	4.89706e13	0.575889	0.287945	−	0.957647i	$-0.407028\pi$
$139$	4.89706e13	0.575889	0.287945	+	0.957647i	$0.407028\pi$
$140$	4.45172e13	0.499684
$141$	−4.89593e13	−0.524700
$142$	−1.43218e13	−0.146597
$143$	3.71515e13	0.363322
$144$	−7.75713e13	−0.725012
$145$	2.09351e14	1.87061
$146$	−6.61075e12	−0.0564881
$147$	4.87444e13	0.398439
$148$	−9.55254e13	−0.747167
$149$	2.37500e14	1.77809	0.889044	−	0.457822i	$-0.151370\pi$
$149$	2.37500e14	1.77809	0.889044	+	0.457822i	$0.151370\pi$
$150$	3.28274e12	0.0235311
$151$	−7.59317e13	−0.521283	−0.260641	−	0.965436i	$-0.583934\pi$
$151$	−7.59317e13	−0.521283	−0.260641	+	0.965436i	$0.583934\pi$
$152$	−6.05130e12	−0.0397984
$153$	−1.86048e14	−1.17255
$154$	−1.23795e13	−0.0747856
$155$	6.81871e13	0.394954
$156$	−2.26945e13	−0.126069
$157$	−2.58233e14	−1.37615	−0.688073	−	0.725642i	$-0.741543\pi$
$157$	−2.58233e14	−1.37615	−0.688073	+	0.725642i	$0.741543\pi$
$158$	6.68435e12	0.0341813
$159$	7.22288e13	0.354510
$160$	−9.16127e13	−0.431694
$161$	−1.98745e13	−0.0899349
$162$	−9.72572e12	−0.0422741
$163$	4.32795e14	1.80744	0.903718	−	0.428128i	$-0.140827\pi$
$163$	4.32795e14	1.80744	0.903718	+	0.428128i	$0.140827\pi$
$164$	−4.03071e14	−1.61770
$165$	2.07366e14	0.800005
$166$	−3.41158e13	−0.126548
$167$	3.56614e13	0.127216	0.0636079	−	0.997975i	$-0.479739\pi$
$167$	3.56614e13	0.127216	0.0636079	+	0.997975i	$0.479739\pi$
$168$	1.52441e13	0.0523108
$169$	−2.82144e14	−0.931552
$170$	−7.13106e13	−0.226588
$171$	3.99328e13	0.122139
$172$	3.29216e14	0.969495
$173$	−1.88065e14	−0.533345	−0.266672	−	0.963787i	$-0.585924\pi$
$173$	−1.88065e14	−0.533345	−0.266672	+	0.963787i	$0.585924\pi$
$174$	3.55626e13	0.0971457
$175$	−6.30979e13	−0.166061
$176$	−5.22100e14	−1.32410
$177$	−2.36207e14	−0.577387
$178$	−4.02047e13	−0.0947430
$179$	−2.10825e14	−0.479047	−0.239524	−	0.970891i	$-0.576991\pi$
$179$	−2.10825e14	−0.479047	−0.239524	+	0.970891i	$0.576991\pi$
$180$	4.01985e14	0.880925
$181$	1.59017e14	0.336149	0.168075	−	0.985774i	$-0.446245\pi$
$181$	1.59017e14	0.336149	0.168075	+	0.985774i	$0.446245\pi$
$182$	−6.90796e12	−0.0140892
$183$	−7.98518e13	−0.157164
$184$	2.71955e13	0.0516632
$185$	4.87062e14	0.893240
$186$	1.15830e13	0.0205110
$187$	−1.25221e15	−2.14145
$188$	−6.38792e14	−1.05520
$189$	−2.32893e14	−0.371668
$190$	1.53059e13	0.0236026
$191$	5.53655e14	0.825131	0.412565	−	0.910928i	$-0.364633\pi$
$191$	5.53655e14	0.825131	0.412565	+	0.910928i	$0.364633\pi$
$192$	3.08420e14	0.444308
$193$	−1.18734e15	−1.65368	−0.826840	−	0.562437i	$-0.809864\pi$
$193$	−1.18734e15	−1.65368	−0.826840	+	0.562437i	$0.809864\pi$
$194$	2.79458e13	0.0376361
$195$	1.15714e14	0.150716
$196$	6.35988e14	0.801280
$197$	5.62406e14	0.685520	0.342760	−	0.939423i	$-0.388638\pi$
$197$	5.62406e14	0.685520	0.342760	+	0.939423i	$0.388638\pi$
$198$	−1.11785e14	−0.131844
$199$	7.59378e14	0.866788	0.433394	−	0.901205i	$-0.357316\pi$
$199$	7.59378e14	0.866788	0.433394	+	0.901205i	$0.357316\pi$
$200$	8.63407e13	0.0953939
$201$	6.97999e14	0.746587
$202$	9.04336e13	0.0936582
$203$	−6.83554e14	−0.685564
$204$	7.64930e14	0.743063
$205$	2.05517e15	1.93396
$206$	8.59263e13	0.0783410
$207$	−1.79465e14	−0.158552
$208$	−2.91340e14	−0.249453
$209$	2.68771e14	0.223065
$210$	−3.85578e13	−0.0310232
$211$	−5.92215e14	−0.462002	−0.231001	−	0.972954i	$-0.574200\pi$
$211$	−5.92215e14	−0.462002	−0.231001	+	0.972954i	$0.574200\pi$
$212$	9.42398e14	0.712937
$213$	−7.83306e14	−0.574730
$214$	2.30810e14	0.164273
$215$	−1.67860e15	−1.15903
$216$	3.18682e14	0.213505
$217$	−2.22638e14	−0.144748
$218$	−1.22393e14	−0.0772307
$219$	−3.61563e14	−0.221461
$220$	2.70559e15	1.60885
$221$	−6.98755e14	−0.403437
$222$	8.27377e13	0.0463884
$223$	2.76975e14	0.150820	0.0754100	−	0.997153i	$-0.475973\pi$
$223$	2.76975e14	0.150820	0.0754100	+	0.997153i	$0.475973\pi$
$224$	2.99125e14	0.158213
$225$	−5.69767e14	−0.292759
$226$	−3.11120e14	−0.155318
$227$	3.65622e14	0.177364	0.0886818	−	0.996060i	$-0.471735\pi$
$227$	3.65622e14	0.177364	0.0886818	+	0.996060i	$0.471735\pi$
$228$	−1.64182e14	−0.0774016
$229$	3.48056e15	1.59484	0.797422	−	0.603422i	$-0.206197\pi$
$229$	3.48056e15	1.59484	0.797422	+	0.603422i	$0.206197\pi$
$230$	−6.87872e13	−0.0306392
$231$	−6.77073e14	−0.293196
$232$	9.35348e14	0.393823
$233$	−2.14008e14	−0.0876226	−0.0438113	−	0.999040i	$-0.513950\pi$
$233$	−2.14008e14	−0.0876226	−0.0438113	+	0.999040i	$0.513950\pi$
$234$	−6.23781e13	−0.0248387
$235$	3.25706e15	1.26149
$236$	−3.08189e15	−1.16115
$237$	3.65588e14	0.134007
$238$	2.32837e14	0.0830427
$239$	1.69863e15	0.589539	0.294770	−	0.955568i	$-0.404757\pi$
$239$	1.69863e15	0.589539	0.294770	+	0.955568i	$0.404757\pi$
$240$	−1.62616e15	−0.549275
$241$	−4.47230e15	−1.47035	−0.735173	−	0.677879i	$-0.762899\pi$
$241$	−4.47230e15	−1.47035	−0.735173	+	0.677879i	$0.762899\pi$
$242$	−3.62246e14	−0.115932
$243$	−3.29762e15	−1.02745
$244$	−1.04186e15	−0.316064
$245$	−3.24276e15	−0.957933
$246$	3.49113e14	0.100436
$247$	1.49979e14	0.0420242
$248$	3.04649e14	0.0831504
$249$	−1.86590e15	−0.496128
$250$	3.48832e14	0.0903664
$251$	−1.21688e15	−0.307163	−0.153581	−	0.988136i	$-0.549081\pi$
$251$	−1.21688e15	−0.307163	−0.153581	+	0.988136i	$0.549081\pi$
$252$	−1.31253e15	−0.322853
$253$	−1.20790e15	−0.289566
$254$	−6.72716e14	−0.157185
$255$	−3.90020e15	−0.888334
$256$	3.81782e15	0.847726
$257$	−3.63377e14	−0.0786669	−0.0393334	−	0.999226i	$-0.512523\pi$
$257$	−3.63377e14	−0.0786669	−0.0393334	+	0.999226i	$0.512523\pi$
$258$	−2.85144e14	−0.0601917
$259$	−1.59031e15	−0.327366
$260$	1.50977e15	0.303098
$261$	−6.17241e15	−1.20863
$262$	1.09534e15	0.209214
$263$	−4.58408e14	−0.0854161	−0.0427081	−	0.999088i	$-0.513599\pi$
$263$	−4.58408e14	−0.0854161	−0.0427081	+	0.999088i	$0.513599\pi$
$264$	9.26481e14	0.168427
$265$	−4.80508e15	−0.852319
$266$	−4.99754e13	−0.00865020
$267$	−2.19892e15	−0.371439
$268$	9.10708e15	1.50142
$269$	8.45936e15	1.36128	0.680641	−	0.732618i	$-0.261702\pi$
$269$	8.45936e15	1.36128	0.680641	+	0.732618i	$0.261702\pi$
$270$	−8.06060e14	−0.126620
$271$	8.15577e15	1.25073	0.625366	−	0.780331i	$-0.284950\pi$
$271$	8.15577e15	1.25073	0.625366	+	0.780331i	$0.284950\pi$
$272$	9.81980e15	1.47030
$273$	−3.77818e14	−0.0552365
$274$	−1.16661e15	−0.166550
$275$	−3.83486e15	−0.534672
$276$	7.37862e14	0.100477
$277$	1.11989e16	1.48956	0.744778	−	0.667312i	$-0.232555\pi$
$277$	1.11989e16	1.48956	0.744778	+	0.667312i	$0.232555\pi$
$278$	−5.53406e14	−0.0719040
$279$	−2.01040e15	−0.255185
$280$	−1.01413e15	−0.125766
$281$	−3.02860e15	−0.366987	−0.183494	−	0.983021i	$-0.558741\pi$
$281$	−3.02860e15	−0.366987	−0.183494	+	0.983021i	$0.558741\pi$
$282$	5.53279e14	0.0655126
$283$	−8.67911e15	−1.00430	−0.502150	−	0.864781i	$-0.667457\pi$
$283$	−8.67911e15	−1.00430	−0.502150	+	0.864781i	$0.667457\pi$
$284$	−1.02201e16	−1.15581
$285$	8.37128e14	0.0925338
$286$	−4.19841e14	−0.0453634
$287$	−6.71035e15	−0.708782
$288$	2.70107e15	0.278923
$289$	1.36474e16	1.37789
$290$	−2.36583e15	−0.233559
$291$	1.52844e15	0.147552
$292$	−4.71746e15	−0.445368
$293$	6.29958e15	0.581664	0.290832	−	0.956774i	$-0.406068\pi$
$293$	6.29958e15	0.581664	0.290832	+	0.956774i	$0.406068\pi$
$294$	−5.50850e14	−0.0497480
$295$	1.57139e16	1.38816
$296$	2.17612e15	0.188056
$297$	−1.41544e16	−1.19667
$298$	−2.68394e15	−0.222007
$299$	−6.74029e14	−0.0545527
$300$	2.34258e15	0.185526
$301$	5.48080e15	0.424777
$302$	8.58089e14	0.0650859
$303$	4.94610e15	0.367186
$304$	−2.10769e15	−0.153154
$305$	5.31220e15	0.377856
$306$	2.10249e15	0.146401
$307$	2.48862e16	1.69652	0.848259	−	0.529582i	$-0.177651\pi$
$307$	2.48862e16	1.69652	0.848259	+	0.529582i	$0.177651\pi$
$308$	−8.83405e15	−0.589631
$309$	4.69958e15	0.307135
$310$	−7.70568e14	−0.0493128
$311$	−1.21434e16	−0.761023	−0.380512	−	0.924776i	$-0.624252\pi$
$311$	−1.21434e16	−0.761023	−0.380512	+	0.924776i	$0.624252\pi$
$312$	5.16992e14	0.0317307
$313$	1.22438e16	0.736000	0.368000	−	0.929826i	$-0.380043\pi$
$313$	1.22438e16	0.736000	0.368000	+	0.929826i	$0.380043\pi$
$314$	2.91824e15	0.171822
$315$	6.69227e15	0.385971
$316$	4.76998e15	0.269495
$317$	1.44737e16	0.801115	0.400557	−	0.916272i	$-0.368817\pi$
$317$	1.44737e16	0.801115	0.400557	+	0.916272i	$0.368817\pi$
$318$	−8.16242e14	−0.0442632
$319$	−4.15439e16	−2.20733
$320$	−2.05179e16	−1.06821
$321$	1.26237e16	0.644029
$322$	2.24598e14	0.0112290
$323$	−5.05512e15	−0.247694
$324$	−6.94032e15	−0.333301
$325$	−2.13992e15	−0.100729
$326$	−4.89093e15	−0.225672
$327$	−6.69407e15	−0.302782
$328$	9.18218e15	0.407161
$329$	−1.06346e16	−0.462327
$330$	−2.34340e15	−0.0998864
$331$	3.91975e16	1.63823	0.819117	−	0.573627i	$-0.194464\pi$
$331$	3.91975e16	1.63823	0.819117	+	0.573627i	$0.194464\pi$
$332$	−2.43452e16	−0.997737
$333$	−1.43603e16	−0.577134
$334$	−4.03002e14	−0.0158838
$335$	−4.64349e16	−1.79496
$336$	5.30959e15	0.201305
$337$	1.23789e15	0.0460349	0.0230175	−	0.999735i	$-0.492673\pi$
$337$	1.23789e15	0.0460349	0.0230175	+	0.999735i	$0.492673\pi$
$338$	3.18845e15	0.116311
$339$	−1.70161e16	−0.608924
$340$	−5.08876e16	−1.78648
$341$	−1.35311e16	−0.466048
$342$	−4.51273e14	−0.0152500
$343$	2.35958e16	0.782388
$344$	−7.49971e15	−0.244014
$345$	−3.76219e15	−0.120120
$346$	2.12528e15	0.0665920
$347$	1.95546e16	0.601322	0.300661	−	0.953731i	$-0.402793\pi$
$347$	1.95546e16	0.601322	0.300661	+	0.953731i	$0.402793\pi$
$348$	2.53776e16	0.765925
$349$	−2.94540e16	−0.872528	−0.436264	−	0.899819i	$-0.643699\pi$
$349$	−2.94540e16	−0.872528	−0.436264	+	0.899819i	$0.643699\pi$
$350$	7.13056e14	0.0207339
$351$	−7.89839e15	−0.225446
$352$	1.81797e16	0.509402
$353$	1.64601e16	0.452791	0.226396	−	0.974035i	$-0.427306\pi$
$353$	1.64601e16	0.452791	0.226396	+	0.974035i	$0.427306\pi$
$354$	2.66933e15	0.0720910
$355$	5.21101e16	1.38177
$356$	−2.86903e16	−0.746981
$357$	1.27346e16	0.325568
$358$	2.38249e15	0.0598125
$359$	5.84559e16	1.44117	0.720584	−	0.693368i	$-0.243874\pi$
$359$	5.84559e16	1.44117	0.720584	+	0.693368i	$0.243874\pi$
$360$	−9.15744e15	−0.221722
$361$	−4.09680e16	−0.974199
$362$	−1.79701e15	−0.0419707
$363$	−1.98124e16	−0.454510
$364$	−4.92955e15	−0.111083
$365$	2.40532e16	0.532439
$366$	9.02389e14	0.0196230
$367$	−4.01402e15	−0.0857531	−0.0428765	−	0.999080i	$-0.513652\pi$
$367$	−4.01402e15	−0.0857531	−0.0428765	+	0.999080i	$0.513652\pi$
$368$	9.47232e15	0.198813
$369$	−6.05937e16	−1.24956
$370$	−5.50419e15	−0.111528
$371$	1.56891e16	0.312369
$372$	8.26567e15	0.161715
$373$	6.74765e16	1.29731	0.648657	−	0.761081i	$-0.275331\pi$
$373$	6.74765e16	1.29731	0.648657	+	0.761081i	$0.275331\pi$
$374$	1.41510e16	0.267375
$375$	1.90787e16	0.354280
$376$	1.45520e16	0.265584
$377$	−2.31822e16	−0.415849
$378$	2.63187e15	0.0464054
$379$	3.63717e16	0.630389	0.315195	−	0.949027i	$-0.397930\pi$
$379$	3.63717e16	0.630389	0.315195	+	0.949027i	$0.397930\pi$
$380$	1.09224e16	0.186090
$381$	−3.67929e16	−0.616243
$382$	−6.25674e15	−0.103024
$383$	−6.06278e16	−0.981476	−0.490738	−	0.871307i	$-0.663273\pi$
$383$	−6.06278e16	−0.981476	−0.490738	+	0.871307i	$0.663273\pi$
$384$	−1.47666e16	−0.235032
$385$	4.50428e16	0.704906
$386$	1.34178e16	0.206474
$387$	4.94910e16	0.748867
$388$	1.99422e16	0.296734
$389$	3.85555e16	0.564175	0.282088	−	0.959389i	$-0.408973\pi$
$389$	3.85555e16	0.564175	0.282088	+	0.959389i	$0.408973\pi$
$390$	−1.30766e15	−0.0188180
$391$	2.27185e16	0.321537
$392$	−1.44881e16	−0.201676
$393$	5.99077e16	0.820222
$394$	−6.35564e15	−0.0855921
$395$	−2.43210e16	−0.322182
$396$	−7.97705e16	−1.03950
$397$	6.23061e16	0.798715	0.399358	−	0.916795i	$-0.369233\pi$
$397$	6.23061e16	0.798715	0.399358	+	0.916795i	$0.369233\pi$
$398$	−8.58157e15	−0.108225
$399$	−2.73332e15	−0.0339130
$400$	3.00729e16	0.367100
$401$	5.88325e16	0.706608	0.353304	−	0.935509i	$-0.385058\pi$
$401$	5.88325e16	0.706608	0.353304	+	0.935509i	$0.385058\pi$
$402$	−7.88794e15	−0.0932169
$403$	−7.55060e15	−0.0878009
$404$	6.45338e16	0.738428
$405$	3.53871e16	0.398462
$406$	7.72470e15	0.0855977
$407$	−9.66533e16	−1.05403
$408$	−1.74255e16	−0.187023
$409$	−8.97110e16	−0.947642	−0.473821	−	0.880621i	$-0.657126\pi$
$409$	−8.97110e16	−0.947642	−0.473821	+	0.880621i	$0.657126\pi$
$410$	−2.32250e16	−0.241469
$411$	−6.38054e16	−0.652958
$412$	6.13174e16	0.617663
$413$	−5.13075e16	−0.508751
$414$	2.02809e15	0.0197964
$415$	1.24131e17	1.19280
$416$	1.01446e16	0.0959685
$417$	−3.02675e16	−0.281898
$418$	−3.03733e15	−0.0278513
$419$	−1.61398e17	−1.45716	−0.728578	−	0.684963i	$-0.759818\pi$
$419$	−1.61398e17	−1.45716	−0.728578	+	0.684963i	$0.759818\pi$
$420$	−2.75150e16	−0.244596
$421$	5.94583e16	0.520450	0.260225	−	0.965548i	$-0.416203\pi$
$421$	5.94583e16	0.520450	0.260225	+	0.965548i	$0.416203\pi$
$422$	6.69250e15	0.0576843
$423$	−9.60296e16	−0.815066
$424$	−2.14683e16	−0.179441
$425$	7.21272e16	0.593705
$426$	8.85198e15	0.0717593
$427$	−1.73449e16	−0.138481
$428$	1.64707e17	1.29517
$429$	−2.29624e16	−0.177847
$430$	1.89695e16	0.144714
$431$	−8.08686e16	−0.607684	−0.303842	−	0.952722i	$-0.598270\pi$
$431$	−8.08686e16	−0.607684	−0.303842	+	0.952722i	$0.598270\pi$
$432$	1.10998e17	0.821621
$433$	−1.86473e17	−1.35970	−0.679851	−	0.733350i	$-0.737956\pi$
$433$	−1.86473e17	−1.35970	−0.679851	+	0.733350i	$0.737956\pi$
$434$	2.51599e15	0.0180728
$435$	−1.29395e17	−0.915665
$436$	−8.73403e16	−0.608909
$437$	−4.87624e15	−0.0334931
$438$	4.08595e15	0.0276510
$439$	−1.08558e17	−0.723843	−0.361921	−	0.932209i	$-0.617879\pi$
$439$	−1.08558e17	−0.723843	−0.361921	+	0.932209i	$0.617879\pi$
$440$	−6.16349e16	−0.404934
$441$	9.56080e16	0.618933
$442$	7.89649e15	0.0503720
$443$	−2.04656e17	−1.28647	−0.643237	−	0.765667i	$-0.722409\pi$
$443$	−2.04656e17	−1.28647	−0.643237	+	0.765667i	$0.722409\pi$
$444$	5.90419e16	0.365739
$445$	1.46285e17	0.893018
$446$	−3.13004e15	−0.0188310
$447$	−1.46793e17	−0.870376
$448$	6.69931e16	0.391492
$449$	1.03977e17	0.598877	0.299438	−	0.954116i	$-0.403201\pi$
$449$	1.03977e17	0.598877	0.299438	+	0.954116i	$0.403201\pi$
$450$	6.43882e15	0.0365532
$451$	−4.07831e17	−2.28209
$452$	−2.22017e17	−1.22458
$453$	4.69316e16	0.255168
$454$	−4.13182e15	−0.0221451
$455$	2.51347e16	0.132800
$456$	3.74016e15	0.0194813
$457$	2.63211e16	0.135160	0.0675802	−	0.997714i	$-0.478472\pi$
$457$	2.63211e16	0.135160	0.0675802	+	0.997714i	$0.478472\pi$
$458$	−3.93331e16	−0.199128
$459$	2.66220e17	1.32879
$460$	−4.90869e16	−0.241568
$461$	2.86701e17	1.39115	0.695573	−	0.718455i	$-0.255150\pi$
$461$	2.86701e17	1.39115	0.695573	+	0.718455i	$0.255150\pi$
$462$	7.65146e15	0.0366076
$463$	−8.20006e16	−0.386848	−0.193424	−	0.981115i	$-0.561959\pi$
$463$	−8.20006e16	−0.386848	−0.193424	+	0.981115i	$0.561959\pi$
$464$	3.25786e17	1.51553
$465$	−4.21448e16	−0.193330
$466$	2.41846e15	0.0109403
$467$	−8.48415e16	−0.378485	−0.189243	−	0.981930i	$-0.560603\pi$
$467$	−8.48415e16	−0.378485	−0.189243	+	0.981930i	$0.560603\pi$
$468$	−4.45133e16	−0.195836
$469$	1.51615e17	0.657838
$470$	−3.68073e16	−0.157506
$471$	1.59608e17	0.673625
$472$	7.02072e16	0.292253
$473$	3.33103e17	1.36767
$474$	−4.13144e15	−0.0167318
$475$	−1.54812e16	−0.0618437
$476$	1.66153e17	0.654733
$477$	1.41671e17	0.550694
$478$	−1.91959e16	−0.0736083
$479$	−4.62575e16	−0.174985	−0.0874926	−	0.996165i	$-0.527885\pi$
$479$	−4.62575e16	−0.174985	−0.0874926	+	0.996165i	$0.527885\pi$
$480$	5.66236e16	0.211315
$481$	−5.39342e16	−0.198573
$482$	5.05405e16	0.183583
$483$	1.22840e16	0.0440233
$484$	−2.58500e17	−0.914043
$485$	−1.01681e17	−0.354746
$486$	3.72657e16	0.128284
$487$	−2.88369e17	−0.979512	−0.489756	−	0.871860i	$-0.662914\pi$
$487$	−2.88369e17	−0.979512	−0.489756	+	0.871860i	$0.662914\pi$
$488$	2.37341e16	0.0795508
$489$	−2.67500e17	−0.884742
$490$	3.66457e16	0.119605
$491$	−4.55954e17	−1.46856	−0.734279	−	0.678848i	$-0.762480\pi$
$491$	−4.55954e17	−1.46856	−0.734279	+	0.678848i	$0.762480\pi$
$492$	2.49129e17	0.791864
$493$	7.81369e17	2.45105
$494$	−1.69488e15	−0.00524703
$495$	4.06732e17	1.24272
$496$	1.06111e17	0.319984
$497$	−1.70145e17	−0.506410
$498$	2.10862e16	0.0619452
$499$	−2.41981e17	−0.701662	−0.350831	−	0.936439i	$-0.614101\pi$
$499$	−2.41981e17	−0.701662	−0.350831	+	0.936439i	$0.614101\pi$
$500$	2.48928e17	0.712474
$501$	−2.20414e16	−0.0622723
$502$	1.37517e16	0.0383515
$503$	5.05502e17	1.39165	0.695826	−	0.718210i	$-0.255038\pi$
$503$	5.05502e17	1.39165	0.695826	+	0.718210i	$0.255038\pi$
$504$	2.99000e16	0.0812593
$505$	−3.29043e17	−0.882793
$506$	1.36502e16	0.0361545
$507$	1.74386e17	0.455996
$508$	−4.80053e17	−1.23930
$509$	3.56634e17	0.908985	0.454493	−	0.890751i	$-0.349821\pi$
$509$	3.56634e17	0.908985	0.454493	+	0.890751i	$0.349821\pi$
$510$	4.40754e16	0.110915
$511$	−7.85365e16	−0.195135
$512$	−2.38861e17	−0.585991
$513$	−5.71406e16	−0.138415
$514$	4.10645e15	0.00982213
$515$	−3.12643e17	−0.738418
$516$	−2.03480e17	−0.474569
$517$	−6.46335e17	−1.48857
$518$	1.79718e16	0.0408740
$519$	1.16238e17	0.261073
$520$	−3.43933e16	−0.0762873
$521$	2.00446e17	0.439088	0.219544	−	0.975603i	$-0.429543\pi$
$521$	2.00446e17	0.439088	0.219544	+	0.975603i	$0.429543\pi$
$522$	6.97531e16	0.150906
$523$	−1.59492e17	−0.340783	−0.170392	−	0.985376i	$-0.554503\pi$
$523$	−1.59492e17	−0.340783	−0.170392	+	0.985376i	$0.554503\pi$
$524$	7.81641e17	1.64951
$525$	3.89993e16	0.0812871
$526$	5.18037e15	0.0106648
$527$	2.54497e17	0.517505
$528$	3.22697e17	0.648149
$529$	2.19146e16	0.0434783
$530$	5.43012e16	0.106418
$531$	−4.63301e17	−0.896910
$532$	−3.56627e16	−0.0682006
$533$	−2.27576e17	−0.429933
$534$	2.48496e16	0.0463768
$535$	−8.39804e17	−1.54838
$536$	−2.07464e17	−0.377896
$537$	1.30306e17	0.234494
$538$	−9.55975e16	−0.169966
$539$	6.43497e17	1.13037
$540$	−5.75208e17	−0.998310
$541$	−5.08047e17	−0.871207	−0.435603	−	0.900139i	$-0.643465\pi$
$541$	−5.08047e17	−0.871207	−0.435603	+	0.900139i	$0.643465\pi$
$542$	−9.21666e16	−0.156163
$543$	−9.82844e16	−0.164545
$544$	−3.41930e17	−0.565645
$545$	4.45328e17	0.727952
$546$	4.26965e15	0.00689668
$547$	−2.09048e17	−0.333678	−0.166839	−	0.985984i	$-0.553356\pi$
$547$	−2.09048e17	−0.333678	−0.166839	+	0.985984i	$0.553356\pi$
$548$	−8.32495e17	−1.31313
$549$	−1.56623e17	−0.244137
$550$	4.33370e16	0.0667577
$551$	−1.67711e17	−0.255315
$552$	−1.68089e16	−0.0252892
$553$	7.94108e16	0.118077
$554$	−1.26556e17	−0.185982
$555$	−3.01041e17	−0.437242
$556$	−3.94913e17	−0.566912
$557$	8.60562e17	1.22102	0.610511	−	0.792008i	$-0.290964\pi$
$557$	8.60562e17	1.22102	0.610511	+	0.792008i	$0.290964\pi$
$558$	2.27191e16	0.0318617
$559$	1.85877e17	0.257661
$560$	−3.53224e17	−0.483981
$561$	7.73962e17	1.04824
$562$	3.42256e16	0.0458210
$563$	−7.32648e17	−0.969596	−0.484798	−	0.874626i	$-0.661107\pi$
$563$	−7.32648e17	−0.969596	−0.484798	+	0.874626i	$0.661107\pi$
$564$	3.94822e17	0.516520
$565$	1.13201e18	1.46398
$566$	9.80808e16	0.125394
$567$	−1.15543e17	−0.146034
$568$	2.32820e17	0.290908
$569$	1.05554e17	0.130390	0.0651950	−	0.997873i	$-0.479233\pi$
$569$	1.05554e17	0.130390	0.0651950	+	0.997873i	$0.479233\pi$
$570$	−9.46021e15	−0.0115535
$571$	−5.77761e17	−0.697611	−0.348806	−	0.937195i	$-0.613413\pi$
$571$	−5.77761e17	−0.697611	−0.348806	+	0.937195i	$0.613413\pi$
$572$	−2.99600e17	−0.357658
$573$	−3.42201e17	−0.403902
$574$	7.58323e16	0.0884966
$575$	6.95749e16	0.0802808
$576$	6.04940e17	0.690186
$577$	1.49342e18	1.68476	0.842382	−	0.538880i	$-0.181152\pi$
$577$	1.49342e18	1.68476	0.842382	+	0.538880i	$0.181152\pi$
$578$	−1.54226e17	−0.172039
$579$	7.33865e17	0.809478
$580$	−1.68827e18	−1.84145
$581$	−4.05300e17	−0.437152
$582$	−1.72726e16	−0.0184229
$583$	9.53526e17	1.00574
$584$	1.07466e17	0.112096
$585$	2.26963e17	0.234122
$586$	−7.11902e16	−0.0726249
$587$	8.83767e17	0.891642	0.445821	−	0.895122i	$-0.352912\pi$
$587$	8.83767e17	0.891642	0.445821	+	0.895122i	$0.352912\pi$
$588$	−3.93089e17	−0.392228
$589$	−5.46246e16	−0.0539062
$590$	−1.77579e17	−0.173322
$591$	−3.47610e17	−0.335563
$592$	7.57952e17	0.723687
$593$	−1.35317e18	−1.27790	−0.638951	−	0.769247i	$-0.720631\pi$
$593$	−1.35317e18	−1.27790	−0.638951	+	0.769247i	$0.720631\pi$
$594$	1.59956e17	0.149413
$595$	−8.47179e17	−0.782735
$596$	−1.91527e18	−1.75037
$597$	−4.69353e17	−0.424294
$598$	7.61706e15	0.00681130
$599$	1.88165e18	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$599$	1.88165e18	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$600$	−5.33651e16	−0.0466955
$601$	−7.68050e16	−0.0664822	−0.0332411	−	0.999447i	$-0.510583\pi$
$601$	−7.68050e16	−0.0664822	−0.0332411	+	0.999447i	$0.510583\pi$
$602$	−6.19373e16	−0.0530366
$603$	1.36907e18	1.15974
$604$	6.12336e17	0.513156
$605$	1.31804e18	1.09274
$606$	−5.58948e16	−0.0458458
$607$	1.33354e18	1.08213	0.541066	−	0.840980i	$-0.318021\pi$
$607$	1.33354e18	1.08213	0.541066	+	0.840980i	$0.318021\pi$
$608$	7.33908e16	0.0589208
$609$	4.22488e17	0.335585
$610$	−6.00321e16	−0.0471780
$611$	−3.60666e17	−0.280438
$612$	1.50035e18	1.15427
$613$	−1.19001e17	−0.0905851	−0.0452925	−	0.998974i	$-0.514422\pi$
$613$	−1.19001e17	−0.0905851	−0.0452925	+	0.998974i	$0.514422\pi$
$614$	−2.81233e17	−0.211823
$615$	−1.27025e18	−0.946676
$616$	2.01245e17	0.148405
$617$	1.65182e18	1.20534	0.602669	−	0.797991i	$-0.294104\pi$
$617$	1.65182e18	1.20534	0.602669	+	0.797991i	$0.294104\pi$
$618$	−5.31090e16	−0.0383480
$619$	−7.73799e17	−0.552890	−0.276445	−	0.961030i	$-0.589156\pi$
$619$	−7.73799e17	−0.552890	−0.276445	+	0.961030i	$0.589156\pi$
$620$	−5.49880e17	−0.388796
$621$	2.56799e17	0.179679
$622$	1.37230e17	0.0950193
$623$	−4.77637e17	−0.327285
$624$	1.80071e17	0.122108
$625$	−1.84294e18	−1.23678
$626$	−1.38365e17	−0.0918950
$627$	−1.66121e17	−0.109191
$628$	2.08247e18	1.35469
$629$	1.81788e18	1.17041
$630$	−7.56279e16	−0.0481913
$631$	1.02264e18	0.644957	0.322479	−	0.946577i	$-0.395484\pi$
$631$	1.02264e18	0.644957	0.322479	+	0.946577i	$0.395484\pi$
$632$	−1.08663e17	−0.0678296
$633$	3.66034e17	0.226150
$634$	−1.63564e17	−0.100025
$635$	2.44768e18	1.48158
$636$	−5.82474e17	−0.348984
$637$	3.59082e17	0.212955
$638$	4.69479e17	0.275602
$639$	−1.53639e18	−0.892783
$640$	9.82359e17	0.565068
$641$	−2.48292e18	−1.41379	−0.706895	−	0.707319i	$-0.749905\pi$
$641$	−2.48292e18	−1.41379	−0.706895	+	0.707319i	$0.749905\pi$
$642$	−1.42658e17	−0.0804117
$643$	−1.97926e18	−1.10441	−0.552206	−	0.833708i	$-0.686214\pi$
$643$	−1.97926e18	−1.10441	−0.552206	+	0.833708i	$0.686214\pi$
$644$	1.60274e17	0.0885329
$645$	1.03750e18	0.567348
$646$	5.71269e16	0.0309264
$647$	−3.37606e18	−1.80939	−0.904695	−	0.426060i	$-0.859901\pi$
$647$	−3.37606e18	−1.80939	−0.904695	+	0.426060i	$0.859901\pi$
$648$	1.58104e17	0.0838892
$649$	−3.11828e18	−1.63804
$650$	2.41828e16	0.0125768
$651$	1.37607e17	0.0708541
$652$	−3.49019e18	−1.77926
$653$	1.76937e18	0.893064	0.446532	−	0.894768i	$-0.352659\pi$
$653$	1.76937e18	0.893064	0.446532	+	0.894768i	$0.352659\pi$
$654$	7.56483e16	0.0378045
$655$	−3.98541e18	−1.97199
$656$	3.19819e18	1.56686
$657$	−7.09175e17	−0.344016
$658$	1.20180e17	0.0577249
$659$	−3.80605e18	−1.81017	−0.905085	−	0.425231i	$-0.860193\pi$
$659$	−3.80605e18	−1.81017	−0.905085	+	0.425231i	$0.860193\pi$
$660$	−1.67226e18	−0.787533
$661$	−2.62837e17	−0.122568	−0.0612840	−	0.998120i	$-0.519520\pi$
$661$	−2.62837e17	−0.122568	−0.0612840	+	0.998120i	$0.519520\pi$
$662$	−4.42962e17	−0.204545
$663$	4.31884e17	0.197483
$664$	5.54597e17	0.251122
$665$	1.81836e17	0.0815341
$666$	1.62283e17	0.0720594
$667$	7.53720e17	0.331430
$668$	−2.87584e17	−0.125233
$669$	−1.71192e17	−0.0738265
$670$	5.24752e17	0.224113
$671$	−1.05416e18	−0.445872
$672$	−1.84882e17	−0.0774453
$673$	1.19959e18	0.497662	0.248831	−	0.968547i	$-0.419954\pi$
$673$	1.19959e18	0.497662	0.248831	+	0.968547i	$0.419954\pi$
$674$	−1.39891e16	−0.00574780
$675$	8.15290e17	0.331770
$676$	2.27529e18	0.917030
$677$	2.34186e18	0.934836	0.467418	−	0.884036i	$-0.345184\pi$
$677$	2.34186e18	0.934836	0.467418	+	0.884036i	$0.345184\pi$
$678$	1.92296e17	0.0760286
$679$	3.31999e17	0.130012
$680$	1.15925e18	0.449643
$681$	−2.25982e17	−0.0868197
$682$	1.52913e17	0.0581895
$683$	−2.53576e18	−0.955814	−0.477907	−	0.878410i	$-0.658604\pi$
$683$	−2.53576e18	−0.955814	−0.477907	+	0.878410i	$0.658604\pi$
$684$	−3.22030e17	−0.120235
$685$	4.24470e18	1.56985
$686$	−2.66651e17	−0.0976869
$687$	−2.15125e18	−0.780678
$688$	−2.61218e18	−0.939028
$689$	5.32084e17	0.189476
$690$	4.25157e16	0.0149979
$691$	−1.28939e18	−0.450585	−0.225292	−	0.974291i	$-0.572334\pi$
$691$	−1.28939e18	−0.450585	−0.225292	+	0.974291i	$0.572334\pi$
$692$	1.51661e18	0.525030
$693$	−1.32802e18	−0.455449
$694$	−2.20982e17	−0.0750795
$695$	2.01357e18	0.677744
$696$	−5.78116e17	−0.192777
$697$	7.67059e18	2.53405
$698$	3.32854e17	0.108941
$699$	1.32273e17	0.0428914
$700$	5.08840e17	0.163472
$701$	−6.08439e18	−1.93664	−0.968322	−	0.249704i	$-0.919667\pi$
$701$	−6.08439e18	−1.93664	−0.968322	+	0.249704i	$0.919667\pi$
$702$	8.92580e16	0.0281485
$703$	−3.90185e17	−0.121916
$704$	4.07160e18	1.26050
$705$	−2.01311e18	−0.617501
$706$	−1.86013e17	−0.0565343
$707$	1.07436e18	0.323537
$708$	1.90484e18	0.568386
$709$	−6.65163e18	−1.96665	−0.983326	−	0.181851i	$-0.941791\pi$
$709$	−6.65163e18	−1.96665	−0.983326	+	0.181851i	$0.941791\pi$
$710$	−5.88885e17	−0.172525
$711$	7.17071e17	0.208166
$712$	6.53580e17	0.188009
$713$	2.45492e17	0.0699770
$714$	−1.43911e17	−0.0406495
$715$	1.52759e18	0.427581
$716$	1.70016e18	0.471579
$717$	−1.04988e18	−0.288580
$718$	−6.60598e17	−0.179940
$719$	−5.62596e18	−1.51865	−0.759327	−	0.650710i	$-0.774471\pi$
$719$	−5.62596e18	−1.51865	−0.759327	+	0.650710i	$0.774471\pi$
$720$	−3.18958e18	−0.853241
$721$	1.02081e18	0.270625
$722$	4.62970e17	0.121636
$723$	2.76422e18	0.719736
$724$	−1.28236e18	−0.330909
$725$	2.39292e18	0.611972
$726$	2.23896e17	0.0567489
$727$	6.88159e18	1.72868	0.864341	−	0.502907i	$-0.167736\pi$
$727$	6.88159e18	1.72868	0.864341	+	0.502907i	$0.167736\pi$
$728$	1.12298e17	0.0279587
$729$	6.66067e17	0.164357
$730$	−2.71821e17	−0.0664789
$731$	−6.26509e18	−1.51867
$732$	6.43948e17	0.154714
$733$	3.01909e18	0.718952	0.359476	−	0.933154i	$-0.382955\pi$
$733$	3.01909e18	0.718952	0.359476	+	0.933154i	$0.382955\pi$
$734$	4.53616e16	0.0107069
$735$	2.00427e18	0.468909
$736$	−3.29830e17	−0.0764865
$737$	9.21462e18	2.11806
$738$	6.84757e17	0.156016
$739$	2.48785e18	0.561869	0.280934	−	0.959727i	$-0.409356\pi$
$739$	2.48785e18	0.561869	0.280934	+	0.959727i	$0.409356\pi$
$740$	−3.92781e18	−0.879315
$741$	−9.26983e16	−0.0205709
$742$	−1.77299e17	−0.0390015
$743$	7.65305e17	0.166881	0.0834406	−	0.996513i	$-0.473409\pi$
$743$	7.65305e17	0.166881	0.0834406	+	0.996513i	$0.473409\pi$
$744$	−1.88297e17	−0.0407022
$745$	9.76553e18	2.09257
$746$	−7.62537e17	−0.161979
$747$	−3.65982e18	−0.770682
$748$	1.00982e19	2.10806
$749$	2.74205e18	0.567471
$750$	−2.15605e17	−0.0442344
$751$	−3.55017e18	−0.722087	−0.361043	−	0.932549i	$-0.617579\pi$
$751$	−3.55017e18	−0.722087	−0.361043	+	0.932549i	$0.617579\pi$
$752$	5.06854e18	1.02204
$753$	7.52125e17	0.150357
$754$	2.61977e17	0.0519218
$755$	−3.12216e18	−0.613480
$756$	1.87812e18	0.365873
$757$	−8.69168e18	−1.67873	−0.839364	−	0.543570i	$-0.817072\pi$
$757$	−8.69168e18	−1.67873	−0.839364	+	0.543570i	$0.817072\pi$
$758$	−4.11029e17	−0.0787087
$759$	7.46575e17	0.141743
$760$	−2.48817e17	−0.0468373
$761$	−7.07461e18	−1.32039	−0.660195	−	0.751094i	$-0.729526\pi$
$761$	−7.07461e18	−1.32039	−0.660195	+	0.751094i	$0.729526\pi$
$762$	4.15789e17	0.0769425
$763$	−1.45404e18	−0.266789
$764$	−4.46484e18	−0.812267
$765$	−7.64993e18	−1.37993
$766$	6.85142e17	0.122544
$767$	−1.74005e18	−0.308598
$768$	−2.35970e18	−0.414963
$769$	7.71470e18	1.34523	0.672617	−	0.739991i	$-0.265170\pi$
$769$	7.71470e18	1.34523	0.672617	+	0.739991i	$0.265170\pi$
$770$	−5.09020e17	−0.0880126
$771$	2.24595e17	0.0385075
$772$	9.57503e18	1.62790
$773$	−1.05577e19	−1.77992	−0.889961	−	0.456037i	$-0.849269\pi$
$773$	−1.05577e19	−1.77992	−0.889961	+	0.456037i	$0.849269\pi$
$774$	−5.59287e17	−0.0935015
$775$	7.79391e17	0.129210
$776$	−4.54295e17	−0.0746855
$777$	9.82933e17	0.160246
$778$	−4.35708e17	−0.0704414
$779$	−1.64639e18	−0.263961
$780$	−9.33151e17	−0.148367
$781$	−1.03408e19	−1.63050
$782$	−2.56737e17	−0.0401463
$783$	8.83222e18	1.36968
$784$	−5.04628e18	−0.776099
$785$	−1.06180e19	−1.61954
$786$	−6.77005e17	−0.102411
$787$	5.06227e18	0.759468	0.379734	−	0.925096i	$-0.376016\pi$
$787$	5.06227e18	0.759468	0.379734	+	0.925096i	$0.376016\pi$
$788$	−4.53541e18	−0.674833
$789$	2.83331e17	0.0418113
$790$	2.74847e17	0.0402267
$791$	−3.69614e18	−0.536539
$792$	1.81722e18	0.261633
$793$	−5.88240e17	−0.0839999
$794$	−7.04108e17	−0.0997254
$795$	2.96990e18	0.417211
$796$	−6.12384e18	−0.853275
$797$	2.96351e18	0.409569	0.204784	−	0.978807i	$-0.434351\pi$
$797$	2.96351e18	0.409569	0.204784	+	0.978807i	$0.434351\pi$
$798$	3.08886e16	0.00423428
$799$	1.21564e19	1.65292
$800$	−1.04715e18	−0.141229
$801$	−4.31301e18	−0.576991
$802$	−6.64853e17	−0.0882252
$803$	−4.77316e18	−0.628283
$804$	−5.62887e18	−0.734948
$805$	−8.17200e17	−0.105841
$806$	8.53278e16	0.0109626
$807$	−5.22853e18	−0.666349
$808$	−1.47011e18	−0.185856
$809$	1.12142e19	1.40638	0.703189	−	0.711003i	$-0.251759\pi$
$809$	1.12142e19	1.40638	0.703189	+	0.711003i	$0.251759\pi$
$810$	−3.99902e17	−0.0497509
$811$	−1.08510e19	−1.33917	−0.669585	−	0.742735i	$-0.733528\pi$
$811$	−1.08510e19	−1.33917	−0.669585	+	0.742735i	$0.733528\pi$
$812$	5.51238e18	0.674877
$813$	−5.04088e18	−0.612235
$814$	1.09226e18	0.131603
$815$	1.77957e19	2.12711
$816$	−6.06938e18	−0.719712
$817$	1.34472e18	0.158194
$818$	1.01381e18	0.118320
$819$	−7.41059e17	−0.0858040
$820$	−1.65735e19	−1.90381
$821$	3.81296e18	0.434542	0.217271	−	0.976111i	$-0.430284\pi$
$821$	3.81296e18	0.434542	0.217271	+	0.976111i	$0.430284\pi$
$822$	7.21051e17	0.0815266
$823$	7.55639e18	0.847647	0.423824	−	0.905745i	$-0.360688\pi$
$823$	7.55639e18	0.847647	0.423824	+	0.905745i	$0.360688\pi$
$824$	−1.39684e18	−0.155461
$825$	2.37024e18	0.261722
$826$	5.79815e17	0.0635213
$827$	8.92962e18	0.970615	0.485307	−	0.874344i	$-0.338708\pi$
$827$	8.92962e18	0.970615	0.485307	+	0.874344i	$0.338708\pi$
$828$	1.44726e18	0.156080
$829$	1.65583e19	1.77179	0.885895	−	0.463886i	$-0.153545\pi$
$829$	1.65583e19	1.77179	0.885895	+	0.463886i	$0.153545\pi$
$830$	−1.40278e18	−0.148929
$831$	−6.92177e18	−0.729139
$832$	2.27202e18	0.237471
$833$	−1.21031e19	−1.25517
$834$	3.42047e17	0.0351971
$835$	1.46632e18	0.149716
$836$	−2.16745e18	−0.219588
$837$	2.87672e18	0.289189
$838$	1.82392e18	0.181937
$839$	−7.09742e18	−0.702502	−0.351251	−	0.936281i	$-0.614244\pi$
$839$	−7.09742e18	−0.702502	−0.351251	+	0.936281i	$0.614244\pi$
$840$	6.26807e17	0.0615628
$841$	1.56624e19	1.52646
$842$	−6.71926e17	−0.0649820
$843$	1.87191e18	0.179641
$844$	4.77580e18	0.454799
$845$	−1.16012e19	−1.09631
$846$	1.08521e18	0.101767
$847$	−4.30353e18	−0.400481
$848$	−7.47752e18	−0.690533
$849$	5.36435e18	0.491606
$850$	−8.15094e17	−0.0741284
$851$	1.75356e18	0.158262
$852$	6.31681e18	0.565771
$853$	−1.03027e19	−0.915762	−0.457881	−	0.889014i	$-0.651391\pi$
$853$	−1.03027e19	−0.915762	−0.457881	+	0.889014i	$0.651391\pi$
$854$	1.96011e17	0.0172904
$855$	1.64196e18	0.143742
$856$	−3.75212e18	−0.325985
$857$	−1.31204e19	−1.13128	−0.565642	−	0.824651i	$-0.691372\pi$
$857$	−1.31204e19	−1.13128	−0.565642	+	0.824651i	$0.691372\pi$
$858$	2.59494e17	0.0222054
$859$	1.15025e19	0.976870	0.488435	−	0.872600i	$-0.337568\pi$
$859$	1.15025e19	0.976870	0.488435	+	0.872600i	$0.337568\pi$
$860$	1.35367e19	1.14097
$861$	4.14751e18	0.346950
$862$	9.13880e17	0.0758738
$863$	2.32597e19	1.91661	0.958306	−	0.285745i	$-0.0922410\pi$
$863$	2.32597e19	1.91661	0.958306	+	0.285745i	$0.0922410\pi$
$864$	−3.86501e18	−0.316090
$865$	−7.73285e18	−0.627675
$866$	2.10729e18	0.169769
$867$	−8.43511e18	−0.674476
$868$	1.79542e18	0.142491
$869$	4.82630e18	0.380177
$870$	1.46226e18	0.114327
$871$	5.14191e18	0.399031
$872$	1.98966e18	0.153257
$873$	2.99791e18	0.229206
$874$	5.51054e16	0.00418186
$875$	4.14417e18	0.312166
$876$	2.91575e18	0.218008
$877$	1.36401e19	1.01233	0.506163	−	0.862438i	$-0.331063\pi$
$877$	1.36401e19	1.01233	0.506163	+	0.862438i	$0.331063\pi$
$878$	1.22680e18	0.0903771
$879$	−3.89362e18	−0.284725
$880$	−2.14677e19	−1.55829
$881$	6.96163e18	0.501611	0.250806	−	0.968037i	$-0.419305\pi$
$881$	6.96163e18	0.501611	0.250806	+	0.968037i	$0.419305\pi$
$882$	−1.08045e18	−0.0772783
$883$	1.28816e19	0.914588	0.457294	−	0.889316i	$-0.348819\pi$
$883$	1.28816e19	0.914588	0.457294	+	0.889316i	$0.348819\pi$
$884$	5.63497e18	0.397147
$885$	−9.71237e18	−0.679507
$886$	2.31278e18	0.160626
$887$	9.38205e18	0.646836	0.323418	−	0.946256i	$-0.395168\pi$
$887$	9.38205e18	0.646836	0.323418	+	0.946256i	$0.395168\pi$
$888$	−1.34501e18	−0.0920535
$889$	−7.99194e18	−0.542989
$890$	−1.65314e18	−0.111500
$891$	−7.02227e18	−0.470189
$892$	−2.23361e18	−0.148469
$893$	−2.60923e18	−0.172178
$894$	1.65888e18	0.108673
$895$	−8.66872e18	−0.563774
$896$	−3.20751e18	−0.207093
$897$	4.16601e17	0.0267036
$898$	−1.17503e18	−0.0747741
$899$	8.44332e18	0.533427
$900$	4.59477e18	0.288196
$901$	−1.79342e19	−1.11679
$902$	4.60881e18	0.284935
$903$	−3.38755e18	−0.207929
$904$	5.05766e18	0.308216
$905$	6.53845e18	0.395602
$906$	−5.30364e17	−0.0318596
$907$	1.73629e18	0.103556	0.0517779	−	0.998659i	$-0.483511\pi$
$907$	1.73629e18	0.103556	0.0517779	+	0.998659i	$0.483511\pi$
$908$	−2.94849e18	−0.174599
$909$	9.70136e18	0.570384
$910$	−2.84042e17	−0.0165811
$911$	1.91216e19	1.10829	0.554146	−	0.832419i	$-0.313045\pi$
$911$	1.91216e19	1.10829	0.554146	+	0.832419i	$0.313045\pi$
$912$	1.30271e18	0.0749692
$913$	−2.46327e19	−1.40751
$914$	−2.97450e17	−0.0168758
$915$	−3.28335e18	−0.184961
$916$	−2.80682e19	−1.56998
$917$	1.30128e19	0.722720
$918$	−3.00849e18	−0.165910
$919$	1.59117e19	0.871298	0.435649	−	0.900117i	$-0.356519\pi$
$919$	1.59117e19	0.871298	0.435649	+	0.900117i	$0.356519\pi$
$920$	1.11823e18	0.0608007
$921$	−1.53815e19	−0.830447
$922$	−3.23995e18	−0.173695
$923$	−5.77034e18	−0.307178
$924$	5.46012e18	0.288625
$925$	5.56721e18	0.292225
$926$	9.26672e17	0.0483008
$927$	9.21784e18	0.477102
$928$	−1.13440e19	−0.583049
$929$	1.39882e19	0.713939	0.356969	−	0.934116i	$-0.383810\pi$
$929$	1.39882e19	0.713939	0.356969	+	0.934116i	$0.383810\pi$
$930$	4.76270e17	0.0241387
$931$	2.59777e18	0.130746
$932$	1.72582e18	0.0862566
$933$	7.50555e18	0.372522
$934$	9.58776e17	0.0472566
$935$	−5.14884e19	−2.52020
$936$	1.01404e18	0.0492902
$937$	6.82024e18	0.329224	0.164612	−	0.986358i	$-0.447363\pi$
$937$	6.82024e18	0.329224	0.164612	+	0.986358i	$0.447363\pi$
$938$	−1.71337e18	−0.0821359
$939$	−7.56760e18	−0.360273
$940$	−2.62659e19	−1.24183
$941$	−4.13987e19	−1.94381	−0.971906	−	0.235371i	$-0.924369\pi$
$941$	−4.13987e19	−1.94381	−0.971906	+	0.235371i	$0.924369\pi$
$942$	−1.80369e18	−0.0841070
$943$	7.39916e18	0.342655
$944$	2.44535e19	1.12466
$945$	−9.57609e18	−0.437403
$946$	−3.76433e18	−0.170763
$947$	−1.29217e19	−0.582165	−0.291082	−	0.956698i	$-0.594015\pi$
$947$	−1.29217e19	−0.582165	−0.291082	+	0.956698i	$0.594015\pi$
$948$	−2.94821e18	−0.131918
$949$	−2.66350e18	−0.118365
$950$	1.74949e17	0.00772163
$951$	−8.94585e18	−0.392147
$952$	−3.78506e18	−0.164791
$953$	1.39194e19	0.601891	0.300946	−	0.953641i	$-0.402698\pi$
$953$	1.39194e19	0.601891	0.300946	+	0.953641i	$0.402698\pi$
$954$	−1.60099e18	−0.0687582
$955$	2.27652e19	0.971068
$956$	−1.36983e19	−0.580349
$957$	2.56773e19	1.08049
$958$	5.22746e17	0.0218482
$959$	−1.38594e19	−0.575339
$960$	1.26816e19	0.522891
$961$	−2.16675e19	−0.887374
$962$	6.09499e17	0.0247933
$963$	2.47604e19	1.00043
$964$	3.60659e19	1.44742
$965$	−4.88209e19	−1.94616
$966$	−1.38819e17	−0.00549662
$967$	−4.83819e18	−0.190288	−0.0951438	−	0.995464i	$-0.530331\pi$
$967$	−4.83819e18	−0.190288	−0.0951438	+	0.995464i	$0.530331\pi$
$968$	5.88878e18	0.230057
$969$	3.12445e18	0.121246
$970$	1.14907e18	0.0442927
$971$	−3.54722e19	−1.35820	−0.679099	−	0.734047i	$-0.737629\pi$
$971$	−3.54722e19	−1.35820	−0.679099	+	0.734047i	$0.737629\pi$
$972$	2.65930e19	1.01143
$973$	−6.57453e18	−0.248388
$974$	3.25879e18	0.122299
$975$	1.32263e18	0.0493070
$976$	8.26670e18	0.306132
$977$	−2.40507e19	−0.884734	−0.442367	−	0.896834i	$-0.645861\pi$
$977$	−2.40507e19	−0.884734	−0.442367	+	0.896834i	$0.645861\pi$
$978$	3.02297e18	0.110466
$979$	−2.90290e19	−1.05377
$980$	2.61505e19	0.942999
$981$	−1.31299e19	−0.470340
$982$	5.15264e18	0.183360
$983$	2.28023e19	0.806084	0.403042	−	0.915181i	$-0.367953\pi$
$983$	2.28023e19	0.806084	0.403042	+	0.915181i	$0.367953\pi$
$984$	−5.67529e18	−0.199306
$985$	2.31250e19	0.806764
$986$	−8.83009e18	−0.306031
$987$	6.57302e18	0.226310
$988$	−1.20947e18	−0.0413691
$989$	−6.04340e18	−0.205355
$990$	−4.59639e18	−0.155163
$991$	6.53950e18	0.219314	0.109657	−	0.993970i	$-0.465025\pi$
$991$	6.53950e18	0.219314	0.109657	+	0.993970i	$0.465025\pi$
$992$	−3.69482e18	−0.123103
$993$	−2.42270e19	−0.801917
$994$	1.92277e18	0.0632290
$995$	3.12241e19	1.02009
$996$	1.50472e19	0.488393
$997$	3.92165e19	1.26459	0.632295	−	0.774727i	$-0.282113\pi$
$997$	3.92165e19	1.26459	0.632295	+	0.774727i	$0.282113\pi$
$998$	2.73458e18	0.0876076
$999$	2.05485e19	0.654039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.14.a.b.1.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.14.a.b.1.7	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q-11.3008 q^{2} -618.076 q^{3} -8064.29 q^{4} +41118.0 q^{5} +6984.75 q^{6} -134255. q^{7} +183709. q^{8} -1.21231e6 q^{9} +O(q^{10})\)	\(q-11.3008 q^{2} -618.076 q^{3} -8064.29 q^{4} +41118.0 q^{5} +6984.75 q^{6} -134255. q^{7} +183709. q^{8} -1.21231e6 q^{9} -464666. q^{10} -8.15951e6 q^{11} +4.98435e6 q^{12} -4.55315e6 q^{13} +1.51718e6 q^{14} -2.54140e7 q^{15} +6.39866e7 q^{16} +1.53466e8 q^{17} +1.37000e7 q^{18} -3.29396e7 q^{19} -3.31588e8 q^{20} +8.29796e7 q^{21} +9.22090e7 q^{22} +1.48036e8 q^{23} -1.13546e8 q^{24} +4.69987e8 q^{25} +5.14542e7 q^{26} +1.73471e9 q^{27} +1.08267e9 q^{28} +5.09147e9 q^{29} +2.87199e8 q^{30} +1.65833e9 q^{31} -2.22804e9 q^{32} +5.04320e9 q^{33} -1.73429e9 q^{34} -5.52029e9 q^{35} +9.77638e9 q^{36} +1.18455e10 q^{37} +3.72243e8 q^{38} +2.81419e9 q^{39} +7.55374e9 q^{40} +4.99822e10 q^{41} -9.37735e8 q^{42} -4.08239e10 q^{43} +6.58007e10 q^{44} -4.98476e10 q^{45} -1.67292e9 q^{46} +7.92124e10 q^{47} -3.95486e10 q^{48} -7.88647e10 q^{49} -5.31122e9 q^{50} -9.48539e10 q^{51} +3.67179e10 q^{52} -1.16861e11 q^{53} -1.96036e10 q^{54} -3.35503e11 q^{55} -2.46638e10 q^{56} +2.03592e10 q^{57} -5.75376e10 q^{58} +3.82165e11 q^{59} +2.04946e11 q^{60} +1.29194e11 q^{61} -1.87404e10 q^{62} +1.62758e11 q^{63} -4.99000e11 q^{64} -1.87216e11 q^{65} -5.69921e10 q^{66} -1.12931e12 q^{67} -1.23760e12 q^{68} -9.14974e10 q^{69} +6.23836e10 q^{70} +1.26733e12 q^{71} -2.22711e11 q^{72} +5.84981e11 q^{73} -1.33863e11 q^{74} -2.90487e11 q^{75} +2.65635e11 q^{76} +1.09545e12 q^{77} -3.18026e10 q^{78} -5.91494e11 q^{79} +2.63100e12 q^{80} +8.60623e11 q^{81} -5.64839e11 q^{82} +3.01889e12 q^{83} -6.69172e11 q^{84} +6.31023e12 q^{85} +4.61342e11 q^{86} -3.14691e12 q^{87} -1.49898e12 q^{88} +3.55769e12 q^{89} +5.63317e11 q^{90} +6.11281e11 q^{91} -1.19380e12 q^{92} -1.02497e12 q^{93} -8.95163e11 q^{94} -1.35441e12 q^{95} +1.37710e12 q^{96} -2.47290e12 q^{97} +8.91233e11 q^{98} +9.89182e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9}+O(q^{10}) \) 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9} + 3585670 q^{10} + 1070730 q^{11} - 8508331 q^{12} + 23949638 q^{13} - 119280968 q^{14} - 44834930 q^{15} + 256829072 q^{16} + 69487470 q^{17} + 92449927 q^{18} + 111438548 q^{19} + 1129282316 q^{20} + 621345174 q^{21} + 2278933028 q^{22} + 2072502446 q^{23} + 8776950724 q^{24} + 5548551686 q^{25} - 925154105 q^{26} - 2006600744 q^{27} + 10886499970 q^{28} + 6082889362 q^{29} + 33591682946 q^{30} + 15979895560 q^{31} + 39045677992 q^{32} + 48341340746 q^{33} + 26300859414 q^{34} + 71251965504 q^{35} + 134660338135 q^{36} + 52356093690 q^{37} + 96969962716 q^{38} + 35694630240 q^{39} + 30337594230 q^{40} + 116782373266 q^{41} + 47161428352 q^{42} + 551363512 q^{43} - 18191926218 q^{44} + 66956385060 q^{45} + 9474296896 q^{46} - 89763073312 q^{47} + 7373438519 q^{48} + 198965141586 q^{49} - 353559739256 q^{50} - 849385907902 q^{51} + 290946305159 q^{52} - 255252512096 q^{53} - 20138610103 q^{54} - 308239853444 q^{55} - 1741462242990 q^{56} - 373036556464 q^{57} - 2063171638367 q^{58} - 844368470500 q^{59} - 3864457510716 q^{60} - 660411924036 q^{61} - 3066592203813 q^{62} - 2044550744028 q^{63} - 149179140181 q^{64} + 25563523898 q^{65} - 3128765504558 q^{66} + 343438236966 q^{67} - 687566878740 q^{68} + 304361787784 q^{69} + 2831163146300 q^{70} + 525250335580 q^{71} - 1782771811281 q^{72} + 6080256001118 q^{73} + 1193156509458 q^{74} + 3035968085076 q^{75} + 11140697506136 q^{76} - 905513956696 q^{77} + 15392222627509 q^{78} + 2029462022780 q^{79} + 6389606776510 q^{80} + 11017226960590 q^{81} + 5032544493407 q^{82} + 1645588044714 q^{83} - 8835767120594 q^{84} + 8689341605448 q^{85} - 5028664556794 q^{86} + 14107817502696 q^{87} + 35486297142892 q^{88} + 3557834996156 q^{89} - 20611184383708 q^{90} + 20574193795614 q^{91} + 10308035022848 q^{92} + 32845521705562 q^{93} - 4653170522585 q^{94} + 35338742719324 q^{95} + 44121425602615 q^{96} + 20411381883630 q^{97} - 10415391287228 q^{98} - 9767188111540 q^{99}+O(q^{100}) \) 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9 + 3585670 * q^10 + 1070730 * q^11 - 8508331 * q^12 + 23949638 * q^13 - 119280968 * q^14 - 44834930 * q^15 + 256829072 * q^16 + 69487470 * q^17 + 92449927 * q^18 + 111438548 * q^19 + 1129282316 * q^20 + 621345174 * q^21 + 2278933028 * q^22 + 2072502446 * q^23 + 8776950724 * q^24 + 5548551686 * q^25 - 925154105 * q^26 - 2006600744 * q^27 + 10886499970 * q^28 + 6082889362 * q^29 + 33591682946 * q^30 + 15979895560 * q^31 + 39045677992 * q^32 + 48341340746 * q^33 + 26300859414 * q^34 + 71251965504 * q^35 + 134660338135 * q^36 + 52356093690 * q^37 + 96969962716 * q^38 + 35694630240 * q^39 + 30337594230 * q^40 + 116782373266 * q^41 + 47161428352 * q^42 + 551363512 * q^43 - 18191926218 * q^44 + 66956385060 * q^45 + 9474296896 * q^46 - 89763073312 * q^47 + 7373438519 * q^48 + 198965141586 * q^49 - 353559739256 * q^50 - 849385907902 * q^51 + 290946305159 * q^52 - 255252512096 * q^53 - 20138610103 * q^54 - 308239853444 * q^55 - 1741462242990 * q^56 - 373036556464 * q^57 - 2063171638367 * q^58 - 844368470500 * q^59 - 3864457510716 * q^60 - 660411924036 * q^61 - 3066592203813 * q^62 - 2044550744028 * q^63 - 149179140181 * q^64 + 25563523898 * q^65 - 3128765504558 * q^66 + 343438236966 * q^67 - 687566878740 * q^68 + 304361787784 * q^69 + 2831163146300 * q^70 + 525250335580 * q^71 - 1782771811281 * q^72 + 6080256001118 * q^73 + 1193156509458 * q^74 + 3035968085076 * q^75 + 11140697506136 * q^76 - 905513956696 * q^77 + 15392222627509 * q^78 + 2029462022780 * q^79 + 6389606776510 * q^80 + 11017226960590 * q^81 + 5032544493407 * q^82 + 1645588044714 * q^83 - 8835767120594 * q^84 + 8689341605448 * q^85 - 5028664556794 * q^86 + 14107817502696 * q^87 + 35486297142892 * q^88 + 3557834996156 * q^89 - 20611184383708 * q^90 + 20574193795614 * q^91 + 10308035022848 * q^92 + 32845521705562 * q^93 - 4653170522585 * q^94 + 35338742719324 * q^95 + 44121425602615 * q^96 + 20411381883630 * q^97 - 10415391287228 * q^98 - 9767188111540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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