LMFDB - Embedded newform 23.12.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,12,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, 12, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 12 $
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:	$17.6718931529$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 16849 x^{9} - 2148 x^{8} + 97176782 x^{7} + 169360278 x^{6} - 226650696110 x^{5} + \cdots - 51\!\cdots\!56 $ x^11 - x^10 - 16849x^9 - 2148x^8 + 97176782x^7 + 169360278x^6 - 226650696110x^5 - 940430954112x^4 + 180101325169073x^3 + 1690347715497299x^2 - 9620508603737857*x - 51108001263703556
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-86.6009$ 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)

$f(q)$	$=$	$q+89.6009 q^{2} -16.7832 q^{3} +5980.32 q^{4} +2166.57 q^{5} -1503.79 q^{6} +22504.4 q^{7} +352339. q^{8} -176865. q^{9} +O(q^{10})$	\(q+89.6009 q^{2} -16.7832 q^{3} +5980.32 q^{4} +2166.57 q^{5} -1503.79 q^{6} +22504.4 q^{7} +352339. q^{8} -176865. q^{9} +194127. q^{10} -250501. q^{11} -100369. q^{12} +151577. q^{13} +2.01641e6 q^{14} -36362.1 q^{15} +1.93222e7 q^{16} +8.30365e6 q^{17} -1.58473e7 q^{18} -1.05387e7 q^{19} +1.29568e7 q^{20} -377696. q^{21} -2.24451e7 q^{22} -6.43634e6 q^{23} -5.91339e6 q^{24} -4.41341e7 q^{25} +1.35814e7 q^{26} +5.94148e6 q^{27} +1.34583e8 q^{28} +3.69958e7 q^{29} -3.25808e6 q^{30} -2.48200e8 q^{31} +1.00969e9 q^{32} +4.20422e6 q^{33} +7.44014e8 q^{34} +4.87574e7 q^{35} -1.05771e9 q^{36} -3.81208e8 q^{37} -9.44276e8 q^{38} -2.54395e6 q^{39} +7.63368e8 q^{40} -4.66200e8 q^{41} -3.38419e7 q^{42} +1.36884e9 q^{43} -1.49807e9 q^{44} -3.83192e8 q^{45} -5.76702e8 q^{46} -7.83384e8 q^{47} -3.24289e8 q^{48} -1.47088e9 q^{49} -3.95445e9 q^{50} -1.39362e8 q^{51} +9.06476e8 q^{52} -4.65719e9 q^{53} +5.32361e8 q^{54} -5.42728e8 q^{55} +7.92917e9 q^{56} +1.76873e8 q^{57} +3.31486e9 q^{58} -5.46955e8 q^{59} -2.17457e8 q^{60} +9.29943e9 q^{61} -2.22389e10 q^{62} -3.98024e9 q^{63} +5.08976e10 q^{64} +3.28402e8 q^{65} +3.76701e8 q^{66} -1.21412e10 q^{67} +4.96584e10 q^{68} +1.08023e8 q^{69} +4.36870e9 q^{70} +1.31590e10 q^{71} -6.23165e10 q^{72} -1.60260e10 q^{73} -3.41566e10 q^{74} +7.40713e8 q^{75} -6.30247e10 q^{76} -5.63736e9 q^{77} -2.27940e8 q^{78} +2.77601e10 q^{79} +4.18629e10 q^{80} +3.12314e10 q^{81} -4.17720e10 q^{82} +1.65543e10 q^{83} -2.25874e9 q^{84} +1.79905e10 q^{85} +1.22649e11 q^{86} -6.20910e8 q^{87} -8.82612e10 q^{88} +7.19803e10 q^{89} -3.43343e10 q^{90} +3.41114e9 q^{91} -3.84914e10 q^{92} +4.16559e9 q^{93} -7.01919e10 q^{94} -2.28329e10 q^{95} -1.69459e10 q^{96} +1.16439e11 q^{97} -1.31792e11 q^{98} +4.43049e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9}+O(q^{10}) $ 11 * q + 32 * q^2 - 20 * q^3 + 11264 * q^4 + 1034 * q^5 - 22385 * q^6 + 159584 * q^7 + 115497 * q^8 + 611943 * q^9	\( 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9} - 627650 q^{10} - 771396 q^{11} - 1720771 q^{12} + 3433434 q^{13} + 4585896 q^{14} + 5551840 q^{15} + 18802384 q^{16} + 29035398 q^{17} + 26169127 q^{18} + 21398428 q^{19} + 72466260 q^{20} + 61896432 q^{21} + 100463524 q^{22} - 70799773 q^{23} + 161844076 q^{24} + 233562509 q^{25} + 328796191 q^{26} + 356379712 q^{27} + 499445210 q^{28} + 226699042 q^{29} + 510413234 q^{30} + 251932328 q^{31} + 806116648 q^{32} + 221442992 q^{33} + 325378622 q^{34} - 355232072 q^{35} - 1034240009 q^{36} + 573876170 q^{37} - 770782036 q^{38} - 1199522184 q^{39} - 1009699226 q^{40} - 1733596378 q^{41} - 6499506824 q^{42} + 647370308 q^{43} - 4662321170 q^{44} - 5023123422 q^{45} - 205962976 q^{46} - 5436527248 q^{47} - 4050950401 q^{48} + 4356386219 q^{49} - 10296502416 q^{50} - 1050918064 q^{51} - 5616607137 q^{52} - 3387203910 q^{53} - 21748294807 q^{54} - 10571441512 q^{55} + 635842210 q^{56} - 4678697728 q^{57} + 1991171353 q^{58} + 15113662084 q^{59} + 19934836476 q^{60} + 23895772578 q^{61} + 7557529251 q^{62} + 56666471160 q^{63} + 32993181147 q^{64} + 3660035708 q^{65} + 33342886858 q^{66} + 46806014468 q^{67} + 40754169364 q^{68} + 128726860 q^{69} - 12274756860 q^{70} + 45541532768 q^{71} + 12763980783 q^{72} + 63786612542 q^{73} - 41720765910 q^{74} + 88573702476 q^{75} + 5581739704 q^{76} + 19147126968 q^{77} - 111443125499 q^{78} + 21847812496 q^{79} - 67715736674 q^{80} + 122793712411 q^{81} - 30216129401 q^{82} + 40153340788 q^{83} - 221098994762 q^{84} + 116854272412 q^{85} - 47307463306 q^{86} - 5595049008 q^{87} - 263050721364 q^{88} + 37300228382 q^{89} - 419483354956 q^{90} + 109416811256 q^{91} - 72498967552 q^{92} - 224700035960 q^{93} - 378035850441 q^{94} - 255722421456 q^{95} - 96864379937 q^{96} - 243602730 q^{97} - 514347061348 q^{98} + 97029276404 q^{99}+O(q^{100}) \) 11 * q + 32 * q^2 - 20 * q^3 + 11264 * q^4 + 1034 * q^5 - 22385 * q^6 + 159584 * q^7 + 115497 * q^8 + 611943 * q^9 - 627650 * q^10 - 771396 * q^11 - 1720771 * q^12 + 3433434 * q^13 + 4585896 * q^14 + 5551840 * q^15 + 18802384 * q^16 + 29035398 * q^17 + 26169127 * q^18 + 21398428 * q^19 + 72466260 * q^20 + 61896432 * q^21 + 100463524 * q^22 - 70799773 * q^23 + 161844076 * q^24 + 233562509 * q^25 + 328796191 * q^26 + 356379712 * q^27 + 499445210 * q^28 + 226699042 * q^29 + 510413234 * q^30 + 251932328 * q^31 + 806116648 * q^32 + 221442992 * q^33 + 325378622 * q^34 - 355232072 * q^35 - 1034240009 * q^36 + 573876170 * q^37 - 770782036 * q^38 - 1199522184 * q^39 - 1009699226 * q^40 - 1733596378 * q^41 - 6499506824 * q^42 + 647370308 * q^43 - 4662321170 * q^44 - 5023123422 * q^45 - 205962976 * q^46 - 5436527248 * q^47 - 4050950401 * q^48 + 4356386219 * q^49 - 10296502416 * q^50 - 1050918064 * q^51 - 5616607137 * q^52 - 3387203910 * q^53 - 21748294807 * q^54 - 10571441512 * q^55 + 635842210 * q^56 - 4678697728 * q^57 + 1991171353 * q^58 + 15113662084 * q^59 + 19934836476 * q^60 + 23895772578 * q^61 + 7557529251 * q^62 + 56666471160 * q^63 + 32993181147 * q^64 + 3660035708 * q^65 + 33342886858 * q^66 + 46806014468 * q^67 + 40754169364 * q^68 + 128726860 * q^69 - 12274756860 * q^70 + 45541532768 * q^71 + 12763980783 * q^72 + 63786612542 * q^73 - 41720765910 * q^74 + 88573702476 * q^75 + 5581739704 * q^76 + 19147126968 * q^77 - 111443125499 * q^78 + 21847812496 * q^79 - 67715736674 * q^80 + 122793712411 * q^81 - 30216129401 * q^82 + 40153340788 * q^83 - 221098994762 * q^84 + 116854272412 * q^85 - 47307463306 * q^86 - 5595049008 * q^87 - 263050721364 * q^88 + 37300228382 * q^89 - 419483354956 * q^90 + 109416811256 * q^91 - 72498967552 * q^92 - 224700035960 * q^93 - 378035850441 * q^94 - 255722421456 * q^95 - 96864379937 * q^96 - 243602730 * q^97 - 514347061348 * q^98 + 97029276404 * 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 $

$2$	89.6009	1.97992	0.989959	−	0.141354i	$-0.0451457\pi$
$2$	89.6009	1.97992	0.989959	+	0.141354i	$0.0451457\pi$
$3$	−16.7832	−0.0398758	−0.0199379	−	0.999801i	$-0.506347\pi$
$3$	−16.7832	−0.0398758	−0.0199379	+	0.999801i	$0.506347\pi$
$4$	5980.32	2.92008
$5$	2166.57	0.310055	0.155027	−	0.987910i	$-0.450453\pi$
$5$	2166.57	0.310055	0.155027	+	0.987910i	$0.450453\pi$
$6$	−1503.79	−0.0789508
$7$	22504.4	0.506090	0.253045	−	0.967455i	$-0.418568\pi$
$7$	22504.4	0.506090	0.253045	+	0.967455i	$0.418568\pi$
$8$	352339.	3.80159
$9$	−176865.	−0.998410
$10$	194127.	0.613883
$11$	−250501.	−0.468975	−0.234487	−	0.972119i	$-0.575341\pi$
$11$	−250501.	−0.468975	−0.234487	+	0.972119i	$0.575341\pi$
$12$	−100369.	−0.116440
$13$	151577.	0.113225	0.0566127	−	0.998396i	$-0.481970\pi$
$13$	151577.	0.113225	0.0566127	+	0.998396i	$0.481970\pi$
$14$	2.01641e6	1.00202
$15$	−36362.1	−0.0123637
$16$	1.93222e7	4.60677
$17$	8.30365e6	1.41840	0.709202	−	0.705005i	$-0.249055\pi$
$17$	8.30365e6	1.41840	0.709202	+	0.705005i	$0.249055\pi$
$18$	−1.58473e7	−1.97677
$19$	−1.05387e7	−0.976432	−0.488216	−	0.872723i	$-0.662352\pi$
$19$	−1.05387e7	−0.976432	−0.488216	+	0.872723i	$0.662352\pi$
$20$	1.29568e7	0.905384
$21$	−377696.	−0.0201807
$22$	−2.24451e7	−0.928531
$23$	−6.43634e6	−0.208514
$23$	−6.43634e6	−0.208514
$24$	−5.91339e6	−0.151591
$25$	−4.41341e7	−0.903866
$26$	1.35814e7	0.224177
$27$	5.94148e6	0.0796881
$28$	1.34583e8	1.47782
$29$	3.69958e7	0.334937	0.167469	−	0.985877i	$-0.446441\pi$
$29$	3.69958e7	0.334937	0.167469	+	0.985877i	$0.446441\pi$
$30$	−3.25808e6	−0.0244791
$31$	−2.48200e8	−1.55708	−0.778541	−	0.627593i	$-0.784040\pi$
$31$	−2.48200e8	−1.55708	−0.778541	+	0.627593i	$0.784040\pi$
$32$	1.00969e9	5.31943
$33$	4.20422e6	0.0187007
$34$	7.44014e8	2.80832
$35$	4.87574e7	0.156916
$36$	−1.05771e9	−2.91543
$37$	−3.81208e8	−0.903759	−0.451879	−	0.892079i	$-0.649246\pi$
$37$	−3.81208e8	−0.903759	−0.451879	+	0.892079i	$0.649246\pi$
$38$	−9.44276e8	−1.93325
$39$	−2.54395e6	−0.00451495
$40$	7.63368e8	1.17870
$41$	−4.66200e8	−0.628437	−0.314218	−	0.949351i	$-0.601742\pi$
$41$	−4.66200e8	−0.628437	−0.314218	+	0.949351i	$0.601742\pi$
$42$	−3.38419e7	−0.0399562
$43$	1.36884e9	1.41996	0.709980	−	0.704222i	$-0.248704\pi$
$43$	1.36884e9	1.41996	0.709980	+	0.704222i	$0.248704\pi$
$44$	−1.49807e9	−1.36944
$45$	−3.83192e8	−0.309562
$46$	−5.76702e8	−0.412841
$47$	−7.83384e8	−0.498237	−0.249119	−	0.968473i	$-0.580141\pi$
$47$	−7.83384e8	−0.498237	−0.249119	+	0.968473i	$0.580141\pi$
$48$	−3.24289e8	−0.183698
$49$	−1.47088e9	−0.743873
$50$	−3.95445e9	−1.78958
$51$	−1.39362e8	−0.0565600
$52$	9.06476e8	0.330627
$53$	−4.65719e9	−1.52970	−0.764851	−	0.644207i	$-0.777187\pi$
$53$	−4.65719e9	−1.52970	−0.764851	+	0.644207i	$0.777187\pi$
$54$	5.32361e8	0.157776
$55$	−5.42728e8	−0.145408
$56$	7.92917e9	1.92395
$57$	1.76873e8	0.0389360
$58$	3.31486e9	0.663149
$59$	−5.46955e8	−0.0996014	−0.0498007	−	0.998759i	$-0.515859\pi$
$59$	−5.46955e8	−0.0996014	−0.0498007	+	0.998759i	$0.515859\pi$
$60$	−2.17457e8	−0.0361029
$61$	9.29943e9	1.40975	0.704875	−	0.709331i	$-0.251003\pi$
$61$	9.29943e9	1.40975	0.704875	+	0.709331i	$0.251003\pi$
$62$	−2.22389e10	−3.08290
$63$	−3.98024e9	−0.505285
$64$	5.08976e10	5.92526
$65$	3.28402e8	0.0351061
$66$	3.76701e8	0.0370259
$67$	−1.21412e10	−1.09863	−0.549313	−	0.835617i	$-0.685111\pi$
$67$	−1.21412e10	−1.09863	−0.549313	+	0.835617i	$0.685111\pi$
$68$	4.96584e10	4.14185
$69$	1.08023e8	0.00831467
$70$	4.36870e9	0.310680
$71$	1.31590e10	0.865569	0.432784	−	0.901497i	$-0.357531\pi$
$71$	1.31590e10	0.865569	0.432784	+	0.901497i	$0.357531\pi$
$72$	−6.23165e10	−3.79555
$73$	−1.60260e10	−0.904791	−0.452396	−	0.891817i	$-0.649431\pi$
$73$	−1.60260e10	−0.904791	−0.452396	+	0.891817i	$0.649431\pi$
$74$	−3.41566e10	−1.78937
$75$	7.40713e8	0.0360424
$76$	−6.30247e10	−2.85125
$77$	−5.63736e9	−0.237343
$78$	−2.27940e8	−0.00893924
$79$	2.77601e10	1.01501	0.507507	−	0.861647i	$-0.330567\pi$
$79$	2.77601e10	1.01501	0.507507	+	0.861647i	$0.330567\pi$
$80$	4.18629e10	1.42835
$81$	3.12314e10	0.995232
$82$	−4.17720e10	−1.24425
$83$	1.65543e10	0.461299	0.230649	−	0.973037i	$-0.425915\pi$
$83$	1.65543e10	0.461299	0.230649	+	0.973037i	$0.425915\pi$
$84$	−2.25874e9	−0.0589293
$85$	1.79905e10	0.439783
$86$	1.22649e11	2.81140
$87$	−6.20910e8	−0.0133559
$88$	−8.82612e10	−1.78285
$89$	7.19803e10	1.36637	0.683185	−	0.730245i	$-0.260594\pi$
$89$	7.19803e10	1.36637	0.683185	+	0.730245i	$0.260594\pi$
$90$	−3.43343e10	−0.612907
$91$	3.41114e9	0.0573023
$92$	−3.84914e10	−0.608878
$93$	4.16559e9	0.0620899
$94$	−7.01919e10	−0.986469
$95$	−2.28329e10	−0.302747
$96$	−1.69459e10	−0.212116
$97$	1.16439e11	1.37675	0.688375	−	0.725355i	$-0.258324\pi$
$97$	1.16439e11	1.37675	0.688375	+	0.725355i	$0.258324\pi$
$98$	−1.31792e11	−1.47281
$99$	4.43049e10	0.468229
$100$	−2.63936e11	−2.63936
$101$	1.31003e11	1.24026	0.620130	−	0.784499i	$-0.287080\pi$
$101$	1.31003e11	1.24026	0.620130	+	0.784499i	$0.287080\pi$
$102$	−1.24870e10	−0.111984
$103$	2.07529e11	1.76390	0.881950	−	0.471343i	$-0.156231\pi$
$103$	2.07529e11	1.76390	0.881950	+	0.471343i	$0.156231\pi$
$104$	5.34064e10	0.430437
$105$	−8.18307e8	−0.00625713
$106$	−4.17288e11	−3.02869
$107$	−1.88687e11	−1.30056	−0.650281	−	0.759694i	$-0.725349\pi$
$107$	−1.88687e11	−1.30056	−0.650281	+	0.759694i	$0.725349\pi$
$108$	3.55319e10	0.232695
$109$	−2.07500e10	−0.129173	−0.0645864	−	0.997912i	$-0.520573\pi$
$109$	−2.07500e10	−0.129173	−0.0645864	+	0.997912i	$0.520573\pi$
$110$	−4.86289e10	−0.287896
$111$	6.39791e9	0.0360381
$112$	4.34834e11	2.33144
$113$	1.14552e11	0.584888	0.292444	−	0.956283i	$-0.405531\pi$
$113$	1.14552e11	0.584888	0.292444	+	0.956283i	$0.405531\pi$
$114$	1.58480e10	0.0770900
$115$	−1.39448e10	−0.0646509
$116$	2.21247e11	0.978043
$117$	−2.68087e10	−0.113045
$118$	−4.90077e10	−0.197203
$119$	1.86868e11	0.717840
$120$	−1.28118e10	−0.0470017
$121$	−2.22561e11	−0.780063
$122$	8.33237e11	2.79119
$123$	7.82436e9	0.0250594
$124$	−1.48431e12	−4.54680
$125$	−2.01409e11	−0.590303
$126$	−3.56633e11	−1.00042
$127$	−3.82240e11	−1.02663	−0.513317	−	0.858199i	$-0.671583\pi$
$127$	−3.82240e11	−1.02663	−0.513317	+	0.858199i	$0.671583\pi$
$128$	2.49262e12	6.41211
$129$	−2.29736e10	−0.0566220
$130$	2.94251e10	0.0695072
$131$	5.18398e11	1.17401	0.587005	−	0.809584i	$-0.300307\pi$
$131$	5.18398e11	1.17401	0.587005	+	0.809584i	$0.300307\pi$
$132$	2.51425e10	0.0546075
$133$	−2.37167e11	−0.494162
$134$	−1.08786e12	−2.17519
$135$	1.28726e10	0.0247077
$136$	2.92570e12	5.39219
$137$	−1.03443e11	−0.183122	−0.0915609	−	0.995799i	$-0.529186\pi$
$137$	−1.03443e11	−0.183122	−0.0915609	+	0.995799i	$0.529186\pi$
$138$	9.67893e9	0.0164624
$139$	−3.99155e11	−0.652469	−0.326234	−	0.945289i	$-0.605780\pi$
$139$	−3.99155e11	−0.652469	−0.326234	+	0.945289i	$0.605780\pi$
$140$	2.91585e11	0.458206
$141$	1.31477e10	0.0198676
$142$	1.17906e12	1.71376
$143$	−3.79701e10	−0.0530999
$144$	−3.41742e12	−4.59944
$145$	8.01542e10	0.103849
$146$	−1.43594e12	−1.79141
$147$	2.46861e10	0.0296625
$148$	−2.27974e12	−2.63904
$149$	−4.75774e10	−0.0530733	−0.0265367	−	0.999648i	$-0.508448\pi$
$149$	−4.75774e10	−0.0530733	−0.0265367	+	0.999648i	$0.508448\pi$
$150$	6.63685e10	0.0713609
$151$	5.30535e11	0.549973	0.274986	−	0.961448i	$-0.411327\pi$
$151$	5.30535e11	0.549973	0.274986	+	0.961448i	$0.411327\pi$
$152$	−3.71319e12	−3.71200
$153$	−1.46863e12	−1.41615
$154$	−5.05113e11	−0.469920
$155$	−5.37743e11	−0.482781
$156$	−1.52136e10	−0.0131840
$157$	1.37398e12	1.14956	0.574780	−	0.818308i	$-0.305088\pi$
$157$	1.37398e12	1.14956	0.574780	+	0.818308i	$0.305088\pi$
$158$	2.48733e12	2.00965
$159$	7.81628e10	0.0609981
$160$	2.18758e12	1.64931
$161$	−1.44846e11	−0.105527
$162$	2.79836e12	1.97048
$163$	−5.17491e11	−0.352266	−0.176133	−	0.984366i	$-0.556359\pi$
$163$	−5.17491e11	−0.352266	−0.176133	+	0.984366i	$0.556359\pi$
$164$	−2.78803e12	−1.83508
$165$	9.10875e9	0.00579825
$166$	1.48328e12	0.913334
$167$	−1.21163e12	−0.721824	−0.360912	−	0.932600i	$-0.617534\pi$
$167$	−1.21163e12	−0.721824	−0.360912	+	0.932600i	$0.617534\pi$
$168$	−1.33077e11	−0.0767189
$169$	−1.76918e12	−0.987180
$170$	1.61196e12	0.870734
$171$	1.86393e12	0.974879
$172$	8.18609e12	4.14639
$173$	2.22465e12	1.09146	0.545731	−	0.837960i	$-0.316252\pi$
$173$	2.22465e12	1.09146	0.545731	+	0.837960i	$0.316252\pi$
$174$	−5.56341e10	−0.0264436
$175$	−9.93210e11	−0.457438
$176$	−4.84022e12	−2.16046
$177$	9.17968e9	0.00397168
$178$	6.44950e12	2.70530
$179$	−1.95819e12	−0.796460	−0.398230	−	0.917286i	$-0.630375\pi$
$179$	−1.95819e12	−0.796460	−0.398230	+	0.917286i	$0.630375\pi$
$180$	−2.29161e12	−0.903944
$181$	4.22005e12	1.61468	0.807338	−	0.590089i	$-0.200907\pi$
$181$	4.22005e12	1.61468	0.807338	+	0.590089i	$0.200907\pi$
$182$	3.05641e11	0.113454
$183$	−1.56075e11	−0.0562149
$184$	−2.26777e12	−0.792687
$185$	−8.25915e11	−0.280215
$186$	3.73241e11	0.122933
$187$	−2.08007e12	−0.665195
$188$	−4.68488e12	−1.45489
$189$	1.33709e11	0.0403294
$190$	−2.04584e12	−0.599415
$191$	1.71982e11	0.0489552	0.0244776	−	0.999700i	$-0.492208\pi$
$191$	1.71982e11	0.0489552	0.0244776	+	0.999700i	$0.492208\pi$
$192$	−8.54228e11	−0.236275
$193$	−3.61177e12	−0.970857	−0.485429	−	0.874276i	$-0.661336\pi$
$193$	−3.61177e12	−0.970857	−0.485429	+	0.874276i	$0.661336\pi$
$194$	1.04331e13	2.72585
$195$	−5.51165e9	−0.00139988
$196$	−8.79633e12	−2.17217
$197$	−6.59945e11	−0.158469	−0.0792344	−	0.996856i	$-0.525248\pi$
$197$	−6.59945e11	−0.158469	−0.0792344	+	0.996856i	$0.525248\pi$
$198$	3.96976e12	0.927055
$199$	4.82316e12	1.09557	0.547784	−	0.836620i	$-0.315472\pi$
$199$	4.82316e12	1.09557	0.547784	+	0.836620i	$0.315472\pi$
$200$	−1.55502e13	−3.43613
$201$	2.03769e11	0.0438086
$202$	1.17380e13	2.45561
$203$	8.32568e11	0.169509
$204$	−8.33430e11	−0.165159
$205$	−1.01006e12	−0.194850
$206$	1.85948e13	3.49238
$207$	1.13837e12	0.208183
$208$	2.92879e12	0.521603
$209$	2.63995e12	0.457922
$210$	−7.33210e10	−0.0123886
$211$	−1.89050e12	−0.311188	−0.155594	−	0.987821i	$-0.549729\pi$
$211$	−1.89050e12	−0.311188	−0.155594	+	0.987821i	$0.549729\pi$
$212$	−2.78515e13	−4.46685
$213$	−2.20851e11	−0.0345152
$214$	−1.69065e13	−2.57501
$215$	2.96569e12	0.440265
$216$	2.09341e12	0.302942
$217$	−5.58558e12	−0.788024
$218$	−1.85921e12	−0.255752
$219$	2.68968e11	0.0360793
$220$	−3.24569e12	−0.424602
$221$	1.25864e12	0.160599
$222$	5.73258e11	0.0713525
$223$	−1.61714e12	−0.196368	−0.0981842	−	0.995168i	$-0.531303\pi$
$223$	−1.61714e12	−0.196368	−0.0981842	+	0.995168i	$0.531303\pi$
$224$	2.27225e13	2.69211
$225$	7.80579e12	0.902429
$226$	1.02640e13	1.15803
$227$	−1.64366e13	−1.80996	−0.904981	−	0.425453i	$-0.860115\pi$
$227$	−1.64366e13	−1.80996	−0.904981	+	0.425453i	$0.860115\pi$
$228$	1.05776e12	0.113696
$229$	−3.54753e12	−0.372246	−0.186123	−	0.982526i	$-0.559592\pi$
$229$	−3.54753e12	−0.372246	−0.186123	+	0.982526i	$0.559592\pi$
$230$	−1.24947e12	−0.128003
$231$	9.46133e10	0.00946425
$232$	1.30351e13	1.27330
$233$	8.88383e12	0.847506	0.423753	−	0.905778i	$-0.360712\pi$
$233$	8.88383e12	0.847506	0.423753	+	0.905778i	$0.360712\pi$
$234$	−2.40208e12	−0.223821
$235$	−1.69726e12	−0.154481
$236$	−3.27096e12	−0.290844
$237$	−4.65905e11	−0.0404745
$238$	1.67436e13	1.42126
$239$	−9.78394e12	−0.811569	−0.405785	−	0.913969i	$-0.633002\pi$
$239$	−9.78394e12	−0.811569	−0.405785	+	0.913969i	$0.633002\pi$
$240$	−7.02596e11	−0.0569566
$241$	−1.09599e13	−0.868387	−0.434194	−	0.900820i	$-0.642967\pi$
$241$	−1.09599e13	−0.868387	−0.434194	+	0.900820i	$0.642967\pi$
$242$	−1.99417e13	−1.54446
$243$	−1.57668e12	−0.119374
$244$	5.56135e13	4.11658
$245$	−3.18677e12	−0.230641
$246$	7.01069e11	0.0496155
$247$	−1.59742e12	−0.110557
$248$	−8.74503e13	−5.91939
$249$	−2.77836e11	−0.0183946
$250$	−1.80465e13	−1.16875
$251$	7.27212e12	0.460740	0.230370	−	0.973103i	$-0.426006\pi$
$251$	7.27212e12	0.460740	0.230370	+	0.973103i	$0.426006\pi$
$252$	−2.38031e13	−1.47547
$253$	1.61231e12	0.0977880
$254$	−3.42490e13	−2.03265
$255$	−3.01939e11	−0.0175367
$256$	1.19102e14	6.77019
$257$	2.13902e13	1.19010	0.595050	−	0.803689i	$-0.297132\pi$
$257$	2.13902e13	1.19010	0.595050	+	0.803689i	$0.297132\pi$
$258$	−2.05845e12	−0.112107
$259$	−8.57885e12	−0.457383
$260$	1.96395e12	0.102512
$261$	−6.54328e12	−0.334405
$262$	4.64489e13	2.32444
$263$	−6.96961e12	−0.341548	−0.170774	−	0.985310i	$-0.554627\pi$
$263$	−6.96961e12	−0.341548	−0.170774	+	0.985310i	$0.554627\pi$
$264$	1.48131e12	0.0710925
$265$	−1.00902e13	−0.474292
$266$	−2.12503e13	−0.978401
$267$	−1.20806e12	−0.0544851
$268$	−7.26082e13	−3.20807
$269$	7.55310e12	0.326955	0.163477	−	0.986547i	$-0.447729\pi$
$269$	7.55310e12	0.326955	0.163477	+	0.986547i	$0.447729\pi$
$270$	1.15340e12	0.0489192
$271$	−2.43252e13	−1.01094	−0.505469	−	0.862845i	$-0.668681\pi$
$271$	−2.43252e13	−1.01094	−0.505469	+	0.862845i	$0.668681\pi$
$272$	1.60445e14	6.53426
$273$	−5.72500e10	−0.00228497
$274$	−9.26862e12	−0.362566
$275$	1.10556e13	0.423890
$276$	6.46010e11	0.0242795
$277$	4.71006e13	1.73535	0.867676	−	0.497131i	$-0.165613\pi$
$277$	4.71006e13	1.73535	0.867676	+	0.497131i	$0.165613\pi$
$278$	−3.57646e13	−1.29183
$279$	4.38979e13	1.55461
$280$	1.71791e13	0.596529
$281$	8.27106e11	0.0281629	0.0140814	−	0.999901i	$-0.495518\pi$
$281$	8.27106e11	0.0281629	0.0140814	+	0.999901i	$0.495518\pi$
$282$	1.17805e12	0.0393362
$283$	2.18573e13	0.715767	0.357884	−	0.933766i	$-0.383498\pi$
$283$	2.18573e13	0.715767	0.357884	+	0.933766i	$0.383498\pi$
$284$	7.86949e13	2.52753
$285$	3.83209e11	0.0120723
$286$	−3.40215e12	−0.105133
$287$	−1.04915e13	−0.318045
$288$	−1.78580e14	−5.31097
$289$	3.46787e13	1.01187
$290$	7.18189e12	0.205612
$291$	−1.95423e12	−0.0548990
$292$	−9.58403e13	−2.64206
$293$	−1.55896e13	−0.421757	−0.210879	−	0.977512i	$-0.567633\pi$
$293$	−1.55896e13	−0.421757	−0.210879	+	0.977512i	$0.567633\pi$
$294$	2.21190e12	0.0587293
$295$	−1.18502e12	−0.0308819
$296$	−1.34314e14	−3.43572
$297$	−1.48834e12	−0.0373717
$298$	−4.26298e12	−0.105081
$299$	−9.75600e11	−0.0236091
$300$	4.42970e12	0.105246
$301$	3.08049e13	0.718627
$302$	4.75364e13	1.08890
$303$	−2.19865e12	−0.0494563
$304$	−2.03630e14	−4.49819
$305$	2.01479e13	0.437100
$306$	−1.31590e14	−2.80386
$307$	2.38546e13	0.499242	0.249621	−	0.968344i	$-0.419694\pi$
$307$	2.38546e13	0.499242	0.249621	+	0.968344i	$0.419694\pi$
$308$	−3.37132e13	−0.693061
$309$	−3.48301e12	−0.0703369
$310$	−4.81822e13	−0.955867
$311$	5.22952e13	1.01925	0.509623	−	0.860398i	$-0.329785\pi$
$311$	5.22952e13	1.01925	0.509623	+	0.860398i	$0.329785\pi$
$312$	−8.96332e11	−0.0171640
$313$	7.51422e13	1.41381	0.706904	−	0.707310i	$-0.250091\pi$
$313$	7.51422e13	1.41381	0.706904	+	0.707310i	$0.250091\pi$
$314$	1.23110e14	2.27603
$315$	−8.62349e12	−0.156666
$316$	1.66014e14	2.96392
$317$	−2.01025e13	−0.352716	−0.176358	−	0.984326i	$-0.556432\pi$
$317$	−2.01025e13	−0.352716	−0.176358	+	0.984326i	$0.556432\pi$
$318$	7.00346e12	0.120771
$319$	−9.26748e12	−0.157077
$320$	1.10273e14	1.83716
$321$	3.16678e12	0.0518609
$322$	−1.29783e13	−0.208935
$323$	−8.75096e13	−1.38497
$324$	1.86774e14	2.90615
$325$	−6.68970e12	−0.102341
$326$	−4.63677e13	−0.697459
$327$	3.48252e11	0.00515087
$328$	−1.64261e14	−2.38906
$329$	−1.76296e13	−0.252153
$330$	8.16152e11	0.0114801
$331$	3.25189e13	0.449865	0.224932	−	0.974374i	$-0.427784\pi$
$331$	3.25189e13	0.449865	0.224932	+	0.974374i	$0.427784\pi$
$332$	9.90002e13	1.34703
$333$	6.74225e13	0.902322
$334$	−1.08564e14	−1.42915
$335$	−2.63048e13	−0.340634
$336$	−7.29792e12	−0.0929679
$337$	−3.39796e13	−0.425847	−0.212924	−	0.977069i	$-0.568299\pi$
$337$	−3.39796e13	−0.425847	−0.212924	+	0.977069i	$0.568299\pi$
$338$	−1.58520e14	−1.95454
$339$	−1.92256e12	−0.0233229
$340$	1.07589e14	1.28420
$341$	6.21742e13	0.730232
$342$	1.67010e14	1.93018
$343$	−7.75997e13	−0.882557
$344$	4.82295e14	5.39811
$345$	2.34039e11	0.00257800
$346$	1.99331e14	2.16101
$347$	−1.21068e14	−1.29187	−0.645933	−	0.763394i	$-0.723532\pi$
$347$	−1.21068e14	−1.29187	−0.645933	+	0.763394i	$0.723532\pi$
$348$	−3.71324e12	−0.0390002
$349$	−9.82590e13	−1.01586	−0.507928	−	0.861399i	$-0.669589\pi$
$349$	−9.82590e13	−1.01586	−0.507928	+	0.861399i	$0.669589\pi$
$350$	−8.89925e13	−0.905689
$351$	9.00589e11	0.00902272
$352$	−2.52929e14	−2.49468
$353$	−1.05012e14	−1.01971	−0.509855	−	0.860260i	$-0.670301\pi$
$353$	−1.05012e14	−1.01971	−0.509855	+	0.860260i	$0.670301\pi$
$354$	8.22508e11	0.00786361
$355$	2.85099e13	0.268374
$356$	4.30465e14	3.98991
$357$	−3.13626e12	−0.0286244
$358$	−1.75456e14	−1.57693
$359$	−1.63805e14	−1.44980	−0.724899	−	0.688855i	$-0.758114\pi$
$359$	−1.63805e14	−1.44980	−0.724899	+	0.688855i	$0.758114\pi$
$360$	−1.35013e14	−1.17683
$361$	−5.42626e12	−0.0465812
$362$	3.78120e14	3.19693
$363$	3.73530e12	0.0311056
$364$	2.03997e13	0.167327
$365$	−3.47214e13	−0.280535
$366$	−1.39844e13	−0.111301
$367$	−9.76925e13	−0.765946	−0.382973	−	0.923760i	$-0.625100\pi$
$367$	−9.76925e13	−0.765946	−0.382973	+	0.923760i	$0.625100\pi$
$368$	−1.24364e14	−0.960577
$369$	8.24547e13	0.627437
$370$	−7.40027e13	−0.554802
$371$	−1.04807e14	−0.774167
$372$	2.49116e13	0.181307
$373$	1.83937e14	1.31908	0.659538	−	0.751671i	$-0.270752\pi$
$373$	1.83937e14	1.31908	0.659538	+	0.751671i	$0.270752\pi$
$374$	−1.86376e14	−1.31703
$375$	3.38031e12	0.0235388
$376$	−2.76017e14	−1.89410
$377$	5.60771e12	0.0379234
$378$	1.19805e13	0.0798488
$379$	3.71501e13	0.244031	0.122015	−	0.992528i	$-0.461064\pi$
$379$	3.71501e13	0.244031	0.122015	+	0.992528i	$0.461064\pi$
$380$	−1.36548e14	−0.884045
$381$	6.41523e12	0.0409378
$382$	1.54097e13	0.0969273
$383$	−2.50201e14	−1.55130	−0.775651	−	0.631162i	$-0.782578\pi$
$383$	−2.50201e14	−1.55130	−0.775651	+	0.631162i	$0.782578\pi$
$384$	−4.18342e13	−0.255688
$385$	−1.22138e13	−0.0735894
$386$	−3.23618e14	−1.92222
$387$	−2.42100e14	−1.41770
$388$	6.96344e14	4.02022
$389$	1.24860e14	0.710724	0.355362	−	0.934729i	$-0.384358\pi$
$389$	1.24860e14	0.710724	0.355362	+	0.934729i	$0.384358\pi$
$390$	−4.93849e11	−0.00277165
$391$	−5.34451e13	−0.295758
$392$	−5.18248e14	−2.82790
$393$	−8.70041e12	−0.0468145
$394$	−5.91317e13	−0.313755
$395$	6.01444e13	0.314710
$396$	2.64957e14	1.36726
$397$	−1.14795e14	−0.584216	−0.292108	−	0.956385i	$-0.594357\pi$
$397$	−1.14795e14	−0.584216	−0.292108	+	0.956385i	$0.594357\pi$
$398$	4.32159e14	2.16914
$399$	3.98043e12	0.0197051
$400$	−8.52767e14	−4.16390
$401$	1.54425e14	0.743745	0.371873	−	0.928284i	$-0.378716\pi$
$401$	1.54425e14	0.743745	0.371873	+	0.928284i	$0.378716\pi$
$402$	1.82578e13	0.0867374
$403$	−3.76213e13	−0.176301
$404$	7.83438e14	3.62165
$405$	6.76652e13	0.308577
$406$	7.45988e13	0.335613
$407$	9.54929e13	0.423840
$408$	−4.91027e13	−0.215018
$409$	3.16609e14	1.36787	0.683934	−	0.729543i	$-0.260267\pi$
$409$	3.16609e14	1.36787	0.683934	+	0.729543i	$0.260267\pi$
$410$	−9.05020e13	−0.385787
$411$	1.73612e12	0.00730212
$412$	1.24109e15	5.15072
$413$	−1.23089e13	−0.0504073
$414$	1.01999e14	0.412185
$415$	3.58662e13	0.143028
$416$	1.53046e14	0.602295
$417$	6.69911e12	0.0260177
$418$	2.36542e14	0.906647
$419$	−5.11349e14	−1.93437	−0.967186	−	0.254068i	$-0.918231\pi$
$419$	−5.11349e14	−1.93437	−0.967186	+	0.254068i	$0.918231\pi$
$420$	−4.89374e12	−0.0182713
$421$	8.97090e13	0.330586	0.165293	−	0.986245i	$-0.447143\pi$
$421$	8.97090e13	0.330586	0.165293	+	0.986245i	$0.447143\pi$
$422$	−1.69391e14	−0.616128
$423$	1.38553e14	0.497445
$424$	−1.64091e15	−5.81530
$425$	−3.66474e14	−1.28205
$426$	−1.97884e13	−0.0683373
$427$	2.09278e14	0.713461
$428$	−1.12841e15	−3.79774
$429$	6.37261e11	0.00211740
$430$	2.65728e14	0.871689
$431$	−1.56171e14	−0.505797	−0.252898	−	0.967493i	$-0.581384\pi$
$431$	−1.56171e14	−0.505797	−0.252898	+	0.967493i	$0.581384\pi$
$432$	1.14802e14	0.367105
$433$	2.89251e14	0.913253	0.456626	−	0.889659i	$-0.349058\pi$
$433$	2.89251e14	0.913253	0.456626	+	0.889659i	$0.349058\pi$
$434$	−5.00472e14	−1.56022
$435$	−1.34525e12	−0.00414106
$436$	−1.24091e14	−0.377195
$437$	6.78306e13	0.203600
$438$	2.40997e13	0.0714340
$439$	3.56339e14	1.04306	0.521528	−	0.853234i	$-0.325362\pi$
$439$	3.56339e14	1.04306	0.521528	+	0.853234i	$0.325362\pi$
$440$	−1.91224e14	−0.552781
$441$	2.60148e14	0.742690
$442$	1.12775e14	0.317974
$443$	−4.18015e13	−0.116405	−0.0582024	−	0.998305i	$-0.518537\pi$
$443$	−4.18015e13	−0.116405	−0.0582024	+	0.998305i	$0.518537\pi$
$444$	3.82615e13	0.105234
$445$	1.55951e14	0.423650
$446$	−1.44897e14	−0.388793
$447$	7.98503e11	0.00211634
$448$	1.14542e15	2.99872
$449$	1.04701e14	0.270767	0.135383	−	0.990793i	$-0.456773\pi$
$449$	1.04701e14	0.270767	0.135383	+	0.990793i	$0.456773\pi$
$450$	6.99405e14	1.78674
$451$	1.16784e14	0.294721
$452$	6.85059e14	1.70792
$453$	−8.90411e12	−0.0219306
$454$	−1.47273e15	−3.58357
$455$	7.39048e12	0.0177668
$456$	6.23194e13	0.148019
$457$	2.20460e14	0.517358	0.258679	−	0.965963i	$-0.416713\pi$
$457$	2.20460e14	0.517358	0.258679	+	0.965963i	$0.416713\pi$
$458$	−3.17861e14	−0.737017
$459$	4.93359e13	0.113030
$460$	−8.33944e13	−0.188786
$461$	1.07967e14	0.241511	0.120755	−	0.992682i	$-0.461468\pi$
$461$	1.07967e14	0.241511	0.120755	+	0.992682i	$0.461468\pi$
$462$	8.47743e12	0.0187384
$463$	3.25660e14	0.711327	0.355663	−	0.934614i	$-0.384255\pi$
$463$	3.25660e14	0.711327	0.355663	+	0.934614i	$0.384255\pi$
$464$	7.14840e14	1.54298
$465$	9.02507e12	0.0192513
$466$	7.95999e14	1.67799
$467$	9.49459e13	0.197803	0.0989016	−	0.995097i	$-0.468467\pi$
$467$	9.49459e13	0.197803	0.0989016	+	0.995097i	$0.468467\pi$
$468$	−1.60324e14	−0.330101
$469$	−2.73230e14	−0.556004
$470$	−1.52076e14	−0.305860
$471$	−2.30598e13	−0.0458396
$472$	−1.92714e14	−0.378644
$473$	−3.42895e14	−0.665925
$474$	−4.17455e13	−0.0801362
$475$	4.65115e14	0.882563
$476$	1.11753e15	2.09615
$477$	8.23696e14	1.52727
$478$	−8.76650e14	−1.60684
$479$	−5.80096e14	−1.05113	−0.525563	−	0.850755i	$-0.676145\pi$
$479$	−5.80096e14	−1.05113	−0.525563	+	0.850755i	$0.676145\pi$
$480$	−3.67146e13	−0.0657677
$481$	−5.77823e13	−0.102329
$482$	−9.82018e14	−1.71934
$483$	2.43098e12	0.00420797
$484$	−1.33099e15	−2.27784
$485$	2.52275e14	0.426868
$486$	−1.41272e14	−0.236350
$487$	−8.44061e14	−1.39625	−0.698127	−	0.715974i	$-0.745983\pi$
$487$	−8.44061e14	−1.39625	−0.698127	+	0.715974i	$0.745983\pi$
$488$	3.27655e15	5.35930
$489$	8.68519e12	0.0140469
$490$	−2.85537e14	−0.456651
$491$	−4.11357e14	−0.650535	−0.325267	−	0.945622i	$-0.605454\pi$
$491$	−4.11357e14	−0.650535	−0.325267	+	0.945622i	$0.605454\pi$
$492$	4.67921e13	0.0731753
$493$	3.07200e14	0.475077
$494$	−1.43130e14	−0.218894
$495$	9.59898e13	0.145177
$496$	−4.79576e15	−7.17312
$497$	2.96135e14	0.438056
$498$	−2.48943e13	−0.0364199
$499$	−3.30126e14	−0.477668	−0.238834	−	0.971060i	$-0.576765\pi$
$499$	−3.30126e14	−0.477668	−0.238834	+	0.971060i	$0.576765\pi$
$500$	−1.20449e15	−1.72373
$501$	2.03352e13	0.0287833
$502$	6.51589e14	0.912227
$503$	5.58700e14	0.773668	0.386834	−	0.922149i	$-0.373569\pi$
$503$	5.58700e14	0.773668	0.386834	+	0.922149i	$0.373569\pi$
$504$	−1.40239e15	−1.92089
$505$	2.83827e14	0.384549
$506$	1.44464e14	0.193612
$507$	2.96927e13	0.0393646
$508$	−2.28591e15	−2.99785
$509$	−4.62678e14	−0.600248	−0.300124	−	0.953900i	$-0.597028\pi$
$509$	−4.62678e14	−0.600248	−0.300124	+	0.953900i	$0.597028\pi$
$510$	−2.70540e13	−0.0347212
$511$	−3.60654e14	−0.457906
$512$	5.56680e15	6.99231
$513$	−6.26154e13	−0.0778100
$514$	1.91658e15	2.35630
$515$	4.49627e14	0.546906
$516$	−1.37389e14	−0.165340
$517$	1.96238e14	0.233661
$518$	−7.68672e14	−0.905582
$519$	−3.73369e13	−0.0435229
$520$	1.15709e14	0.133459
$521$	−1.30826e14	−0.149309	−0.0746546	−	0.997209i	$-0.523785\pi$
$521$	−1.30826e14	−0.149309	−0.0746546	+	0.997209i	$0.523785\pi$
$522$	−5.86283e14	−0.662094
$523$	−6.72181e14	−0.751151	−0.375575	−	0.926792i	$-0.622555\pi$
$523$	−6.72181e14	−0.751151	−0.375575	+	0.926792i	$0.622555\pi$
$524$	3.10019e15	3.42820
$525$	1.66693e13	0.0182407
$526$	−6.24483e14	−0.676237
$527$	−2.06096e15	−2.20857
$528$	8.12346e13	0.0861499
$529$	4.14265e13	0.0434783
$530$	−9.04086e14	−0.939058
$531$	9.67374e13	0.0994431
$532$	−1.41833e15	−1.44299
$533$	−7.06651e13	−0.0711550
$534$	−1.08244e14	−0.107876
$535$	−4.08804e14	−0.403246
$536$	−4.27781e15	−4.17653
$537$	3.28648e13	0.0317595
$538$	6.76764e14	0.647344
$539$	3.68457e14	0.348858
$540$	7.69825e13	0.0721483
$541$	1.58041e15	1.46617	0.733086	−	0.680136i	$-0.238079\pi$
$541$	1.58041e15	1.46617	0.733086	+	0.680136i	$0.238079\pi$
$542$	−2.17955e15	−2.00157
$543$	−7.08262e13	−0.0643865
$544$	8.38415e15	7.54510
$545$	−4.49563e13	−0.0400507
$546$	−5.12965e12	−0.00452406
$547$	1.17991e15	1.03019	0.515096	−	0.857133i	$-0.327756\pi$
$547$	1.17991e15	1.03019	0.515096	+	0.857133i	$0.327756\pi$
$548$	−6.18625e14	−0.534729
$549$	−1.64475e15	−1.40751
$550$	9.90593e14	0.839268
$551$	−3.89888e14	−0.327044
$552$	3.80606e13	0.0316090
$553$	6.24724e14	0.513689
$554$	4.22025e15	3.43585
$555$	1.38615e13	0.0111738
$556$	−2.38707e15	−1.90526
$557$	−3.29975e14	−0.260782	−0.130391	−	0.991463i	$-0.541623\pi$
$557$	−3.29975e14	−0.260782	−0.130391	+	0.991463i	$0.541623\pi$
$558$	3.93329e15	3.07799
$559$	2.07484e14	0.160776
$560$	9.42099e14	0.722874
$561$	3.49103e13	0.0265252
$562$	7.41094e13	0.0557601
$563$	−1.08401e15	−0.807675	−0.403838	−	0.914831i	$-0.632324\pi$
$563$	−1.08401e15	−0.807675	−0.403838	+	0.914831i	$0.632324\pi$
$564$	7.86275e13	0.0580149
$565$	2.48186e14	0.181347
$566$	1.95844e15	1.41716
$567$	7.02844e14	0.503677
$568$	4.63642e15	3.29054
$569$	4.60614e14	0.323757	0.161879	−	0.986811i	$-0.448245\pi$
$569$	4.60614e14	0.323757	0.161879	+	0.986811i	$0.448245\pi$
$570$	3.43359e13	0.0239021
$571$	−1.26309e15	−0.870835	−0.435418	−	0.900229i	$-0.643399\pi$
$571$	−1.26309e15	−0.870835	−0.435418	+	0.900229i	$0.643399\pi$
$572$	−2.27073e14	−0.155056
$573$	−2.88641e12	−0.00195213
$574$	−9.40052e14	−0.629704
$575$	2.84062e14	0.188469
$576$	−9.00203e15	−5.91584
$577$	−2.66039e15	−1.73172	−0.865860	−	0.500287i	$-0.833228\pi$
$577$	−2.66039e15	−1.73172	−0.865860	+	0.500287i	$0.833228\pi$
$578$	3.10724e15	2.00342
$579$	6.06173e13	0.0387137
$580$	4.79347e14	0.303247
$581$	3.72545e14	0.233459
$582$	−1.75101e14	−0.108696
$583$	1.16663e15	0.717391
$584$	−5.64657e15	−3.43965
$585$	−5.80830e13	−0.0350503
$586$	−1.39684e15	−0.835045
$587$	−1.96642e15	−1.16457	−0.582287	−	0.812983i	$-0.697842\pi$
$587$	−1.96642e15	−1.16457	−0.582287	+	0.812983i	$0.697842\pi$
$588$	1.47631e14	0.0866168
$589$	2.61570e15	1.52038
$590$	−1.06179e14	−0.0611437
$591$	1.10760e13	0.00631906
$592$	−7.36577e15	−4.16341
$593$	−1.18678e15	−0.664616	−0.332308	−	0.943171i	$-0.607827\pi$
$593$	−1.18678e15	−0.664616	−0.332308	+	0.943171i	$0.607827\pi$
$594$	−1.33357e14	−0.0739929
$595$	4.04864e14	0.222570
$596$	−2.84528e14	−0.154978
$597$	−8.09482e13	−0.0436866
$598$	−8.74146e13	−0.0467442
$599$	1.05984e15	0.561554	0.280777	−	0.959773i	$-0.409408\pi$
$599$	1.05984e15	0.561554	0.280777	+	0.959773i	$0.409408\pi$
$600$	2.60982e14	0.137018
$601$	−4.37669e14	−0.227686	−0.113843	−	0.993499i	$-0.536316\pi$
$601$	−4.37669e14	−0.227686	−0.113843	+	0.993499i	$0.536316\pi$
$602$	2.76014e15	1.42282
$603$	2.14736e15	1.09688
$604$	3.17277e15	1.60596
$605$	−4.82195e14	−0.241862
$606$	−1.97001e14	−0.0979195
$607$	3.30956e15	1.63017	0.815083	−	0.579344i	$-0.196691\pi$
$607$	3.30956e15	1.63017	0.815083	+	0.579344i	$0.196691\pi$
$608$	−1.06409e16	−5.19406
$609$	−1.39732e13	−0.00675928
$610$	1.80527e15	0.865422
$611$	−1.18743e14	−0.0564132
$612$	−8.78286e15	−4.13526
$613$	−3.35399e15	−1.56505	−0.782527	−	0.622617i	$-0.786070\pi$
$613$	−3.35399e15	−1.56505	−0.782527	+	0.622617i	$0.786070\pi$
$614$	2.13739e15	0.988457
$615$	1.69520e13	0.00776979
$616$	−1.98626e15	−0.902283
$617$	1.60439e15	0.722342	0.361171	−	0.932500i	$-0.382377\pi$
$617$	1.60439e15	0.722342	0.361171	+	0.932500i	$0.382377\pi$
$618$	−3.12081e14	−0.139261
$619$	2.27180e15	1.00478	0.502391	−	0.864640i	$-0.332454\pi$
$619$	2.27180e15	1.00478	0.502391	+	0.864640i	$0.332454\pi$
$620$	−3.21587e15	−1.40976
$621$	−3.82414e13	−0.0166161
$622$	4.68569e15	2.01803
$623$	1.61987e15	0.691507
$624$	−4.91546e13	−0.0207993
$625$	1.71862e15	0.720840
$626$	6.73281e15	2.79922
$627$	−4.43069e13	−0.0182600
$628$	8.21682e15	3.35680
$629$	−3.16542e15	−1.28190
$630$	−7.72672e14	−0.310186
$631$	−9.59560e14	−0.381866	−0.190933	−	0.981603i	$-0.561151\pi$
$631$	−9.59560e14	−0.381866	−0.190933	+	0.981603i	$0.561151\pi$
$632$	9.78097e15	3.85867
$633$	3.17288e13	0.0124089
$634$	−1.80120e15	−0.698348
$635$	−8.28151e14	−0.318313
$636$	4.67438e14	0.178119
$637$	−2.22951e14	−0.0842253
$638$	−8.30375e14	−0.311000
$639$	−2.32737e15	−0.864192
$640$	5.40044e15	1.98811
$641$	3.71091e15	1.35444	0.677222	−	0.735779i	$-0.263184\pi$
$641$	3.71091e15	1.35444	0.677222	+	0.735779i	$0.263184\pi$
$642$	2.83746e14	0.102680
$643$	−4.35822e15	−1.56368	−0.781842	−	0.623476i	$-0.785720\pi$
$643$	−4.35822e15	−1.56368	−0.781842	+	0.623476i	$0.785720\pi$
$644$	−8.66224e14	−0.308147
$645$	−4.97739e13	−0.0175559
$646$	−7.84094e15	−2.74214
$647$	6.03044e14	0.209110	0.104555	−	0.994519i	$-0.466658\pi$
$647$	6.03044e14	0.209110	0.104555	+	0.994519i	$0.466658\pi$
$648$	1.10041e16	3.78347
$649$	1.37013e14	0.0467105
$650$	−5.99403e14	−0.202626
$651$	9.37441e13	0.0314231
$652$	−3.09476e15	−1.02864
$653$	−2.45722e15	−0.809882	−0.404941	−	0.914343i	$-0.632708\pi$
$653$	−2.45722e15	−0.809882	−0.404941	+	0.914343i	$0.632708\pi$
$654$	3.12036e13	0.0101983
$655$	1.12315e15	0.364007
$656$	−9.00801e15	−2.89506
$657$	2.83444e15	0.903353
$658$	−1.57962e15	−0.499242
$659$	−3.61194e15	−1.13206	−0.566032	−	0.824384i	$-0.691522\pi$
$659$	−3.61194e15	−1.13206	−0.566032	+	0.824384i	$0.691522\pi$
$660$	5.44732e13	0.0169313
$661$	−1.61818e15	−0.498792	−0.249396	−	0.968402i	$-0.580232\pi$
$661$	−1.61818e15	−0.498792	−0.249396	+	0.968402i	$0.580232\pi$
$662$	2.91372e15	0.890695
$663$	−2.11241e13	−0.00640403
$664$	5.83274e15	1.75367
$665$	−5.13839e14	−0.153217
$666$	6.04111e15	1.78652
$667$	−2.38118e14	−0.0698393
$668$	−7.24596e15	−2.10778
$669$	2.71409e13	0.00783034
$670$	−2.35693e15	−0.674428
$671$	−2.32951e15	−0.661137
$672$	−3.81358e14	−0.107350
$673$	−5.84149e15	−1.63095	−0.815475	−	0.578793i	$-0.803524\pi$
$673$	−5.84149e15	−1.63095	−0.815475	+	0.578793i	$0.803524\pi$
$674$	−3.04460e15	−0.843143
$675$	−2.62222e14	−0.0720274
$676$	−1.05803e16	−2.88264
$677$	−1.27866e15	−0.345556	−0.172778	−	0.984961i	$-0.555274\pi$
$677$	−1.27866e15	−0.345556	−0.172778	+	0.984961i	$0.555274\pi$
$678$	−1.72263e14	−0.0461774
$679$	2.62040e15	0.696760
$680$	6.33874e15	1.67188
$681$	2.75859e14	0.0721736
$682$	5.57086e15	1.44580
$683$	2.02471e15	0.521254	0.260627	−	0.965440i	$-0.416071\pi$
$683$	2.02471e15	0.521254	0.260627	+	0.965440i	$0.416071\pi$
$684$	1.11469e16	2.84672
$685$	−2.24118e14	−0.0567778
$686$	−6.95300e15	−1.74739
$687$	5.95390e13	0.0148436
$688$	2.64490e16	6.54142
$689$	−7.05922e14	−0.173201
$690$	2.09701e13	0.00510424
$691$	4.01949e15	0.970604	0.485302	−	0.874347i	$-0.338710\pi$
$691$	4.01949e15	0.970604	0.485302	+	0.874347i	$0.338710\pi$
$692$	1.33041e16	3.18715
$693$	9.97054e14	0.236966
$694$	−1.08478e16	−2.55779
$695$	−8.64798e14	−0.202301
$696$	−2.18771e14	−0.0507737
$697$	−3.87117e15	−0.891377
$698$	−8.80409e15	−2.01131
$699$	−1.49100e14	−0.0337950
$700$	−5.93971e15	−1.33575
$701$	−2.25740e15	−0.503686	−0.251843	−	0.967768i	$-0.581037\pi$
$701$	−2.25740e15	−0.503686	−0.251843	+	0.967768i	$0.581037\pi$
$702$	8.06936e13	0.0178643
$703$	4.01743e15	0.882459
$704$	−1.27499e16	−2.77880
$705$	2.84855e13	0.00616005
$706$	−9.40914e15	−2.01894
$707$	2.94813e15	0.627683
$708$	5.48974e13	0.0115976
$709$	−2.89681e15	−0.607248	−0.303624	−	0.952792i	$-0.598197\pi$
$709$	−2.89681e15	−0.607248	−0.303624	+	0.952792i	$0.598197\pi$
$710$	2.55451e15	0.531358
$711$	−4.90980e15	−1.01340
$712$	2.53615e16	5.19439
$713$	1.59750e15	0.324674
$714$	−2.81012e14	−0.0566740
$715$	−8.22650e13	−0.0164639
$716$	−1.17106e16	−2.32572
$717$	1.64206e14	0.0323619
$718$	−1.46771e16	−2.87048
$719$	−1.17716e15	−0.228468	−0.114234	−	0.993454i	$-0.536441\pi$
$719$	−1.17716e15	−0.228468	−0.114234	+	0.993454i	$0.536441\pi$
$720$	−7.40410e15	−1.42608
$721$	4.67031e15	0.892692
$722$	−4.86197e14	−0.0922270
$723$	1.83943e14	0.0346276
$724$	2.52372e16	4.71498
$725$	−1.63278e15	−0.302739
$726$	3.34686e14	0.0615866
$727$	1.80042e15	0.328803	0.164401	−	0.986394i	$-0.447431\pi$
$727$	1.80042e15	0.328803	0.164401	+	0.986394i	$0.447431\pi$
$728$	1.20188e15	0.217840
$729$	−5.50609e15	−0.990472
$730$	−3.11107e15	−0.555436
$731$	1.13664e16	2.01408
$732$	−9.33376e14	−0.164152
$733$	5.20293e14	0.0908189	0.0454095	−	0.998968i	$-0.485541\pi$
$733$	5.20293e14	0.0908189	0.0454095	+	0.998968i	$0.485541\pi$
$734$	−8.75333e15	−1.51651
$735$	5.34843e13	0.00919700
$736$	−6.49874e15	−1.10918
$737$	3.04138e15	0.515228
$738$	7.38801e15	1.24227
$739$	−4.57140e14	−0.0762965	−0.0381483	−	0.999272i	$-0.512146\pi$
$739$	−4.57140e14	−0.0762965	−0.0381483	+	0.999272i	$0.512146\pi$
$740$	−4.93923e15	−0.818248
$741$	2.68099e13	0.00440854
$742$	−9.39082e15	−1.53279
$743$	5.40001e15	0.874896	0.437448	−	0.899244i	$-0.355882\pi$
$743$	5.40001e15	0.874896	0.437448	+	0.899244i	$0.355882\pi$
$744$	1.46770e15	0.236040
$745$	−1.03080e14	−0.0164556
$746$	1.64809e16	2.61166
$747$	−2.92789e15	−0.460565
$748$	−1.24395e16	−1.94242
$749$	−4.24628e15	−0.658202
$750$	3.02878e14	0.0466049
$751$	7.96592e15	1.21679	0.608396	−	0.793634i	$-0.291813\pi$
$751$	7.96592e15	1.21679	0.608396	+	0.793634i	$0.291813\pi$
$752$	−1.51367e16	−2.29526
$753$	−1.22050e14	−0.0183724
$754$	5.02455e14	0.0750853
$755$	1.14944e15	0.170522
$756$	7.99623e14	0.117765
$757$	4.07764e15	0.596186	0.298093	−	0.954537i	$-0.403649\pi$
$757$	4.07764e15	0.596186	0.298093	+	0.954537i	$0.403649\pi$
$758$	3.32868e15	0.483161
$759$	−2.70598e13	−0.00389937
$760$	−8.04490e15	−1.15092
$761$	9.46468e15	1.34428	0.672141	−	0.740423i	$-0.265375\pi$
$761$	9.46468e15	1.34428	0.672141	+	0.740423i	$0.265375\pi$
$762$	5.74810e14	0.0810535
$763$	−4.66965e14	−0.0653731
$764$	1.02851e15	0.142953
$765$	−3.18189e15	−0.439084
$766$	−2.24182e16	−3.07145
$767$	−8.29057e13	−0.0112774
$768$	−1.99893e15	−0.269967
$769$	2.03906e14	0.0273422	0.0136711	−	0.999907i	$-0.495648\pi$
$769$	2.03906e14	0.0273422	0.0136711	+	0.999907i	$0.495648\pi$
$770$	−1.09436e15	−0.145701
$771$	−3.58998e14	−0.0474562
$772$	−2.15995e16	−2.83498
$773$	1.10426e15	0.143908	0.0719538	−	0.997408i	$-0.477077\pi$
$773$	1.10426e15	0.143908	0.0719538	+	0.997408i	$0.477077\pi$
$774$	−2.16924e16	−2.80693
$775$	1.09541e16	1.40739
$776$	4.10261e16	5.23385
$777$	1.43981e14	0.0182385
$778$	1.11876e16	1.40718
$779$	4.91314e15	0.613625
$780$	−3.29614e13	−0.00408776
$781$	−3.29634e15	−0.405930
$782$	−4.78873e15	−0.585576
$783$	2.19810e14	0.0266905
$784$	−2.84206e16	−3.42685
$785$	2.97682e15	0.356426
$786$	−7.79564e14	−0.0926889
$787$	3.94353e15	0.465612	0.232806	−	0.972523i	$-0.425209\pi$
$787$	3.94353e15	0.465612	0.232806	+	0.972523i	$0.425209\pi$
$788$	−3.94668e15	−0.462741
$789$	1.16973e14	0.0136195
$790$	5.38899e15	0.623100
$791$	2.57793e15	0.296006
$792$	1.56103e16	1.78002
$793$	1.40958e15	0.159620
$794$	−1.02857e16	−1.15670
$795$	1.69346e14	0.0189127
$796$	2.88440e16	3.19914
$797$	−7.80081e15	−0.859249	−0.429624	−	0.903008i	$-0.641354\pi$
$797$	−7.80081e15	−0.859249	−0.429624	+	0.903008i	$0.641354\pi$
$798$	3.56650e14	0.0390145
$799$	−6.50495e15	−0.706702
$800$	−4.45619e16	−4.80805
$801$	−1.27308e16	−1.36420
$802$	1.38366e16	1.47255
$803$	4.01452e15	0.424324
$804$	1.21860e15	0.127924
$805$	−3.13819e14	−0.0327192
$806$	−3.37090e15	−0.349062
$807$	−1.26766e14	−0.0130376
$808$	4.61573e16	4.71496
$809$	5.51345e15	0.559380	0.279690	−	0.960090i	$-0.409768\pi$
$809$	5.51345e15	0.559380	0.279690	+	0.960090i	$0.409768\pi$
$810$	6.06286e15	0.610956
$811$	8.00639e15	0.801350	0.400675	−	0.916220i	$-0.368776\pi$
$811$	8.00639e15	0.801350	0.400675	+	0.916220i	$0.368776\pi$
$812$	4.97902e15	0.494978
$813$	4.08255e14	0.0403119
$814$	8.55625e15	0.839168
$815$	−1.12118e15	−0.109222
$816$	−2.69278e15	−0.260559
$817$	−1.44258e16	−1.38649
$818$	2.83684e16	2.70827
$819$	−6.03312e14	−0.0572111
$820$	−6.04046e15	−0.568976
$821$	−4.09187e15	−0.382855	−0.191428	−	0.981507i	$-0.561312\pi$
$821$	−4.09187e15	−0.382855	−0.191428	+	0.981507i	$0.561312\pi$
$822$	1.55558e14	0.0144576
$823$	6.63185e14	0.0612259	0.0306130	−	0.999531i	$-0.490254\pi$
$823$	6.63185e14	0.0612259	0.0306130	+	0.999531i	$0.490254\pi$
$824$	7.31205e16	6.70563
$825$	−1.85549e14	−0.0169029
$826$	−1.10289e15	−0.0998023
$827$	6.79705e15	0.610999	0.305499	−	0.952192i	$-0.401177\pi$
$827$	6.79705e15	0.610999	0.305499	+	0.952192i	$0.401177\pi$
$828$	6.80779e15	0.607910
$829$	1.47380e16	1.30734	0.653671	−	0.756779i	$-0.273228\pi$
$829$	1.47380e16	1.30734	0.653671	+	0.756779i	$0.273228\pi$
$830$	3.21364e15	0.283184
$831$	−7.90500e14	−0.0691985
$832$	7.71490e15	0.670891
$833$	−1.22137e16	−1.05511
$834$	6.00246e14	0.0515129
$835$	−2.62510e15	−0.223805
$836$	1.57877e16	1.33717
$837$	−1.47467e15	−0.124081
$838$	−4.58173e16	−3.82990
$839$	−3.21304e15	−0.266825	−0.133412	−	0.991061i	$-0.542593\pi$
$839$	−3.21304e15	−0.266825	−0.133412	+	0.991061i	$0.542593\pi$
$840$	−2.88321e14	−0.0237871
$841$	−1.08318e16	−0.887817
$842$	8.03800e15	0.654533
$843$	−1.38815e13	−0.00112302
$844$	−1.13058e16	−0.908694
$845$	−3.83307e15	−0.306080
$846$	1.24145e16	0.984901
$847$	−5.00860e15	−0.394782
$848$	−8.99871e16	−7.04698
$849$	−3.66837e14	−0.0285418
$850$	−3.28364e16	−2.53835
$851$	2.45359e15	0.188447
$852$	−1.32076e15	−0.100787
$853$	2.12296e16	1.60961	0.804807	−	0.593537i	$-0.202269\pi$
$853$	2.12296e16	1.60961	0.804807	+	0.593537i	$0.202269\pi$
$854$	1.87515e16	1.41259
$855$	4.03834e15	0.302266
$856$	−6.64818e16	−4.94421
$857$	−3.67267e15	−0.271386	−0.135693	−	0.990751i	$-0.543326\pi$
$857$	−3.67267e15	−0.271386	−0.135693	+	0.990751i	$0.543326\pi$
$858$	5.70992e13	0.00419227
$859$	−1.65599e16	−1.20808	−0.604039	−	0.796955i	$-0.706443\pi$
$859$	−1.65599e16	−1.20808	−0.604039	+	0.796955i	$0.706443\pi$
$860$	1.77358e16	1.28561
$861$	1.76082e14	0.0126823
$862$	−1.39931e16	−1.00144
$863$	−8.16477e15	−0.580610	−0.290305	−	0.956934i	$-0.593757\pi$
$863$	−8.16477e15	−0.580610	−0.290305	+	0.956934i	$0.593757\pi$
$864$	5.99907e15	0.423895
$865$	4.81987e15	0.338413
$866$	2.59171e16	1.80817
$867$	−5.82021e14	−0.0403491
$868$	−3.34035e16	−2.30109
$869$	−6.95393e15	−0.476016
$870$	−1.20535e14	−0.00819896
$871$	−1.84032e15	−0.124392
$872$	−7.31101e15	−0.491063
$873$	−2.05941e16	−1.37456
$874$	6.07768e15	0.403111
$875$	−4.53259e15	−0.298746
$876$	1.60851e15	0.105354
$877$	2.23663e16	1.45578	0.727890	−	0.685694i	$-0.240501\pi$
$877$	2.23663e16	1.45578	0.727890	+	0.685694i	$0.240501\pi$
$878$	3.19282e16	2.06517
$879$	2.61644e14	0.0168179
$880$	−1.04867e16	−0.669860
$881$	−4.90482e15	−0.311355	−0.155677	−	0.987808i	$-0.549756\pi$
$881$	−4.90482e15	−0.311355	−0.155677	+	0.987808i	$0.549756\pi$
$882$	2.33095e16	1.47047
$883$	−1.83055e16	−1.14762	−0.573810	−	0.818988i	$-0.694535\pi$
$883$	−1.83055e16	−1.14762	−0.573810	+	0.818988i	$0.694535\pi$
$884$	7.52706e15	0.468963
$885$	1.98885e13	0.00123144
$886$	−3.74545e15	−0.230472
$887$	3.19105e15	0.195143	0.0975717	−	0.995228i	$-0.468892\pi$
$887$	3.19105e15	0.195143	0.0975717	+	0.995228i	$0.468892\pi$
$888$	2.25423e15	0.137002
$889$	−8.60207e15	−0.519569
$890$	1.39733e16	0.838792
$891$	−7.82350e15	−0.466739
$892$	−9.67102e15	−0.573410
$893$	8.25584e15	0.486495
$894$	7.15466e13	0.00419018
$895$	−4.24257e15	−0.246946
$896$	5.60948e16	3.24511
$897$	1.63737e13	0.000941433 0
$898$	9.38128e15	0.536096
$899$	−9.18235e15	−0.521525
$900$	4.66811e16	2.63516
$901$	−3.86717e16	−2.16974
$902$	1.04639e16	0.583523
$903$	−5.17006e14	−0.0286558
$904$	4.03613e16	2.22351
$905$	9.14305e15	0.500638
$906$	−7.97816e14	−0.0434208
$907$	2.05145e16	1.10974	0.554869	−	0.831938i	$-0.312768\pi$
$907$	2.05145e16	1.10974	0.554869	+	0.831938i	$0.312768\pi$
$908$	−9.82959e16	−5.28522
$909$	−2.31698e16	−1.23829
$910$	6.62194e14	0.0351769
$911$	1.71443e16	0.905250	0.452625	−	0.891701i	$-0.350488\pi$
$911$	1.71443e16	0.905250	0.452625	+	0.891701i	$0.350488\pi$
$912$	3.41758e15	0.179369
$913$	−4.14687e15	−0.216337
$914$	1.97534e16	1.02433
$915$	−3.38147e14	−0.0174297
$916$	−2.12153e16	−1.08699
$917$	1.16662e16	0.594154
$918$	4.42054e15	0.223790
$919$	−2.70085e16	−1.35914	−0.679571	−	0.733610i	$-0.737834\pi$
$919$	−2.70085e16	−1.35914	−0.679571	+	0.733610i	$0.737834\pi$
$920$	−4.91330e15	−0.245776
$921$	−4.00357e14	−0.0199076
$922$	9.67395e15	0.478171
$923$	1.99460e15	0.0980044
$924$	5.65817e14	0.0276363
$925$	1.68243e16	0.816877
$926$	2.91794e16	1.40837
$927$	−3.67047e16	−1.76109
$928$	3.73545e16	1.78168
$929$	2.56969e16	1.21841	0.609205	−	0.793013i	$-0.291489\pi$
$929$	2.56969e16	1.21841	0.609205	+	0.793013i	$0.291489\pi$
$930$	8.08654e14	0.0381159
$931$	1.55011e16	0.726341
$932$	5.31281e16	2.47478
$933$	−8.77683e14	−0.0406433
$934$	8.50723e15	0.391634
$935$	−4.50663e15	−0.206247
$936$	−9.44573e15	−0.429753
$937$	2.02944e16	0.917926	0.458963	−	0.888455i	$-0.348221\pi$
$937$	2.02944e16	0.917926	0.458963	+	0.888455i	$0.348221\pi$
$938$	−2.44816e16	−1.10084
$939$	−1.26113e15	−0.0563767
$940$	−1.01501e16	−0.451096
$941$	−2.59252e16	−1.14546	−0.572729	−	0.819745i	$-0.694115\pi$
$941$	−2.59252e16	−1.14546	−0.572729	+	0.819745i	$0.694115\pi$
$942$	−2.06618e15	−0.0907586
$943$	3.00063e15	0.131038
$944$	−1.05684e16	−0.458841
$945$	2.89691e14	0.0125043
$946$	−3.07237e16	−1.31848
$947$	−1.85239e16	−0.790329	−0.395164	−	0.918610i	$-0.629312\pi$
$947$	−1.85239e16	−0.790329	−0.395164	+	0.918610i	$0.629312\pi$
$948$	−2.78626e15	−0.118189
$949$	−2.42916e15	−0.102445
$950$	4.16747e16	1.74740
$951$	3.37386e14	0.0140648
$952$	6.58410e16	2.72894
$953$	−3.66433e16	−1.51003	−0.755013	−	0.655710i	$-0.772369\pi$
$953$	−3.66433e16	−1.51003	−0.755013	+	0.655710i	$0.772369\pi$
$954$	7.38039e16	3.02387
$955$	3.72611e14	0.0151788
$956$	−5.85111e16	−2.36984
$957$	1.55538e14	0.00626357
$958$	−5.19771e16	−2.08114
$959$	−2.32793e15	−0.0926761
$960$	−1.85075e15	−0.0732580
$961$	3.61945e16	1.42451
$962$	−5.17734e15	−0.202602
$963$	3.33722e16	1.29849
$964$	−6.55437e16	−2.53576
$965$	−7.82518e15	−0.301019
$966$	2.17818e14	0.00833144
$967$	4.01876e16	1.52843	0.764217	−	0.644959i	$-0.223125\pi$
$967$	4.01876e16	1.52843	0.764217	+	0.644959i	$0.223125\pi$
$968$	−7.84169e16	−2.96548
$969$	1.46870e15	0.0552269
$970$	2.26040e16	0.845164
$971$	5.07821e16	1.88801	0.944007	−	0.329926i	$-0.107024\pi$
$971$	5.07821e16	1.88801	0.944007	+	0.329926i	$0.107024\pi$
$972$	−9.42904e15	−0.348581
$973$	−8.98272e15	−0.330208
$974$	−7.56286e16	−2.76447
$975$	1.12275e14	0.00408091
$976$	1.79685e17	6.49439
$977$	5.52473e16	1.98560	0.992798	−	0.119803i	$-0.0382261\pi$
$977$	5.52473e16	1.98560	0.992798	+	0.119803i	$0.0382261\pi$
$978$	7.78200e14	0.0278117
$979$	−1.80311e16	−0.640793
$980$	−1.90579e16	−0.673490
$981$	3.66995e15	0.128968
$982$	−3.68579e16	−1.28801
$983$	−1.90494e16	−0.661967	−0.330983	−	0.943637i	$-0.607380\pi$
$983$	−1.90494e16	−0.661967	−0.330983	+	0.943637i	$0.607380\pi$
$984$	2.75682e15	0.0952656
$985$	−1.42982e15	−0.0491340
$986$	2.75254e16	0.940613
$987$	2.95881e14	0.0100548
$988$	−9.55308e15	−0.322835
$989$	−8.81032e15	−0.296082
$990$	8.60077e15	0.287438
$991$	1.71599e16	0.570310	0.285155	−	0.958481i	$-0.407955\pi$
$991$	1.71599e16	0.570310	0.285155	+	0.958481i	$0.407955\pi$
$992$	−2.50606e17	−8.28279
$993$	−5.45773e14	−0.0179387
$994$	2.65339e16	0.867314
$995$	1.04497e16	0.339686
$996$	−1.66154e15	−0.0537138
$997$	−1.65738e16	−0.532844	−0.266422	−	0.963857i	$-0.585841\pi$
$997$	−1.65738e16	−0.532844	−0.266422	+	0.963857i	$0.585841\pi$
$998$	−2.95795e16	−0.945743
$999$	−2.26494e15	−0.0720189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.12.a.b.1.11	✓	11
3.2	odd	2		207.12.a.d.1.1		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.12.a.b.1.11	✓	11	1.1	even	1	trivial
207.12.a.d.1.1		11	3.2	odd	2

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q+89.6009 q^{2} -16.7832 q^{3} +5980.32 q^{4} +2166.57 q^{5} -1503.79 q^{6} +22504.4 q^{7} +352339. q^{8} -176865. q^{9} +O(q^{10})\)	\(q+89.6009 q^{2} -16.7832 q^{3} +5980.32 q^{4} +2166.57 q^{5} -1503.79 q^{6} +22504.4 q^{7} +352339. q^{8} -176865. q^{9} +194127. q^{10} -250501. q^{11} -100369. q^{12} +151577. q^{13} +2.01641e6 q^{14} -36362.1 q^{15} +1.93222e7 q^{16} +8.30365e6 q^{17} -1.58473e7 q^{18} -1.05387e7 q^{19} +1.29568e7 q^{20} -377696. q^{21} -2.24451e7 q^{22} -6.43634e6 q^{23} -5.91339e6 q^{24} -4.41341e7 q^{25} +1.35814e7 q^{26} +5.94148e6 q^{27} +1.34583e8 q^{28} +3.69958e7 q^{29} -3.25808e6 q^{30} -2.48200e8 q^{31} +1.00969e9 q^{32} +4.20422e6 q^{33} +7.44014e8 q^{34} +4.87574e7 q^{35} -1.05771e9 q^{36} -3.81208e8 q^{37} -9.44276e8 q^{38} -2.54395e6 q^{39} +7.63368e8 q^{40} -4.66200e8 q^{41} -3.38419e7 q^{42} +1.36884e9 q^{43} -1.49807e9 q^{44} -3.83192e8 q^{45} -5.76702e8 q^{46} -7.83384e8 q^{47} -3.24289e8 q^{48} -1.47088e9 q^{49} -3.95445e9 q^{50} -1.39362e8 q^{51} +9.06476e8 q^{52} -4.65719e9 q^{53} +5.32361e8 q^{54} -5.42728e8 q^{55} +7.92917e9 q^{56} +1.76873e8 q^{57} +3.31486e9 q^{58} -5.46955e8 q^{59} -2.17457e8 q^{60} +9.29943e9 q^{61} -2.22389e10 q^{62} -3.98024e9 q^{63} +5.08976e10 q^{64} +3.28402e8 q^{65} +3.76701e8 q^{66} -1.21412e10 q^{67} +4.96584e10 q^{68} +1.08023e8 q^{69} +4.36870e9 q^{70} +1.31590e10 q^{71} -6.23165e10 q^{72} -1.60260e10 q^{73} -3.41566e10 q^{74} +7.40713e8 q^{75} -6.30247e10 q^{76} -5.63736e9 q^{77} -2.27940e8 q^{78} +2.77601e10 q^{79} +4.18629e10 q^{80} +3.12314e10 q^{81} -4.17720e10 q^{82} +1.65543e10 q^{83} -2.25874e9 q^{84} +1.79905e10 q^{85} +1.22649e11 q^{86} -6.20910e8 q^{87} -8.82612e10 q^{88} +7.19803e10 q^{89} -3.43343e10 q^{90} +3.41114e9 q^{91} -3.84914e10 q^{92} +4.16559e9 q^{93} -7.01919e10 q^{94} -2.28329e10 q^{95} -1.69459e10 q^{96} +1.16439e11 q^{97} -1.31792e11 q^{98} +4.43049e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9}+O(q^{10}) \) 11 * q + 32 * q^2 - 20 * q^3 + 11264 * q^4 + 1034 * q^5 - 22385 * q^6 + 159584 * q^7 + 115497 * q^8 + 611943 * q^9	\( 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9} - 627650 q^{10} - 771396 q^{11} - 1720771 q^{12} + 3433434 q^{13} + 4585896 q^{14} + 5551840 q^{15} + 18802384 q^{16} + 29035398 q^{17} + 26169127 q^{18} + 21398428 q^{19} + 72466260 q^{20} + 61896432 q^{21} + 100463524 q^{22} - 70799773 q^{23} + 161844076 q^{24} + 233562509 q^{25} + 328796191 q^{26} + 356379712 q^{27} + 499445210 q^{28} + 226699042 q^{29} + 510413234 q^{30} + 251932328 q^{31} + 806116648 q^{32} + 221442992 q^{33} + 325378622 q^{34} - 355232072 q^{35} - 1034240009 q^{36} + 573876170 q^{37} - 770782036 q^{38} - 1199522184 q^{39} - 1009699226 q^{40} - 1733596378 q^{41} - 6499506824 q^{42} + 647370308 q^{43} - 4662321170 q^{44} - 5023123422 q^{45} - 205962976 q^{46} - 5436527248 q^{47} - 4050950401 q^{48} + 4356386219 q^{49} - 10296502416 q^{50} - 1050918064 q^{51} - 5616607137 q^{52} - 3387203910 q^{53} - 21748294807 q^{54} - 10571441512 q^{55} + 635842210 q^{56} - 4678697728 q^{57} + 1991171353 q^{58} + 15113662084 q^{59} + 19934836476 q^{60} + 23895772578 q^{61} + 7557529251 q^{62} + 56666471160 q^{63} + 32993181147 q^{64} + 3660035708 q^{65} + 33342886858 q^{66} + 46806014468 q^{67} + 40754169364 q^{68} + 128726860 q^{69} - 12274756860 q^{70} + 45541532768 q^{71} + 12763980783 q^{72} + 63786612542 q^{73} - 41720765910 q^{74} + 88573702476 q^{75} + 5581739704 q^{76} + 19147126968 q^{77} - 111443125499 q^{78} + 21847812496 q^{79} - 67715736674 q^{80} + 122793712411 q^{81} - 30216129401 q^{82} + 40153340788 q^{83} - 221098994762 q^{84} + 116854272412 q^{85} - 47307463306 q^{86} - 5595049008 q^{87} - 263050721364 q^{88} + 37300228382 q^{89} - 419483354956 q^{90} + 109416811256 q^{91} - 72498967552 q^{92} - 224700035960 q^{93} - 378035850441 q^{94} - 255722421456 q^{95} - 96864379937 q^{96} - 243602730 q^{97} - 514347061348 q^{98} + 97029276404 q^{99}+O(q^{100}) \) 11 * q + 32 * q^2 - 20 * q^3 + 11264 * q^4 + 1034 * q^5 - 22385 * q^6 + 159584 * q^7 + 115497 * q^8 + 611943 * q^9 - 627650 * q^10 - 771396 * q^11 - 1720771 * q^12 + 3433434 * q^13 + 4585896 * q^14 + 5551840 * q^15 + 18802384 * q^16 + 29035398 * q^17 + 26169127 * q^18 + 21398428 * q^19 + 72466260 * q^20 + 61896432 * q^21 + 100463524 * q^22 - 70799773 * q^23 + 161844076 * q^24 + 233562509 * q^25 + 328796191 * q^26 + 356379712 * q^27 + 499445210 * q^28 + 226699042 * q^29 + 510413234 * q^30 + 251932328 * q^31 + 806116648 * q^32 + 221442992 * q^33 + 325378622 * q^34 - 355232072 * q^35 - 1034240009 * q^36 + 573876170 * q^37 - 770782036 * q^38 - 1199522184 * q^39 - 1009699226 * q^40 - 1733596378 * q^41 - 6499506824 * q^42 + 647370308 * q^43 - 4662321170 * q^44 - 5023123422 * q^45 - 205962976 * q^46 - 5436527248 * q^47 - 4050950401 * q^48 + 4356386219 * q^49 - 10296502416 * q^50 - 1050918064 * q^51 - 5616607137 * q^52 - 3387203910 * q^53 - 21748294807 * q^54 - 10571441512 * q^55 + 635842210 * q^56 - 4678697728 * q^57 + 1991171353 * q^58 + 15113662084 * q^59 + 19934836476 * q^60 + 23895772578 * q^61 + 7557529251 * q^62 + 56666471160 * q^63 + 32993181147 * q^64 + 3660035708 * q^65 + 33342886858 * q^66 + 46806014468 * q^67 + 40754169364 * q^68 + 128726860 * q^69 - 12274756860 * q^70 + 45541532768 * q^71 + 12763980783 * q^72 + 63786612542 * q^73 - 41720765910 * q^74 + 88573702476 * q^75 + 5581739704 * q^76 + 19147126968 * q^77 - 111443125499 * q^78 + 21847812496 * q^79 - 67715736674 * q^80 + 122793712411 * q^81 - 30216129401 * q^82 + 40153340788 * q^83 - 221098994762 * q^84 + 116854272412 * q^85 - 47307463306 * q^86 - 5595049008 * q^87 - 263050721364 * q^88 + 37300228382 * q^89 - 419483354956 * q^90 + 109416811256 * q^91 - 72498967552 * q^92 - 224700035960 * q^93 - 378035850441 * q^94 - 255722421456 * q^95 - 96864379937 * q^96 - 243602730 * q^97 - 514347061348 * q^98 + 97029276404 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more