LMFDB - Embedded newform 23.18.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,18,Mod(1,23)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	23.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$42.1410800892$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 327680 x^{12} - 2885829 x^{11} + 40317445636 x^{10} + 536194434472 x^{9} + \cdots + 12\!\cdots\!92 $ x^14 - 327680x^12 - 2885829x^11 + 40317445636x^10 + 536194434472x^9 - 2300019484636976x^8 - 30461644509683376x^7 + 60510672631444445504x^6 + 637677963007481584640x^5 - 633979316201323448274944x^4 - 10096979557697212773105664x^3 + 2069146574976541180680732672x^2 + 62007390478567900843052367872x + 124088176545413917176959598592
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{33}\cdot 3^{12} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-107.083$ 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)

$f(q)$	$=$	$q+214.166 q^{2} +8587.97 q^{3} -85204.9 q^{4} +1.16203e6 q^{5} +1.83925e6 q^{6} -1.80417e6 q^{7} -4.63192e7 q^{8} -5.53869e7 q^{9} +O(q^{10})$	\(q+214.166 q^{2} +8587.97 q^{3} -85204.9 q^{4} +1.16203e6 q^{5} +1.83925e6 q^{6} -1.80417e6 q^{7} -4.63192e7 q^{8} -5.53869e7 q^{9} +2.48868e8 q^{10} -1.08503e9 q^{11} -7.31737e8 q^{12} -6.11587e8 q^{13} -3.86393e8 q^{14} +9.97950e9 q^{15} +1.24799e9 q^{16} +1.45692e10 q^{17} -1.18620e10 q^{18} -7.26361e10 q^{19} -9.90109e10 q^{20} -1.54942e10 q^{21} -2.32377e11 q^{22} -7.83110e10 q^{23} -3.97788e11 q^{24} +5.87380e11 q^{25} -1.30981e11 q^{26} -1.58471e12 q^{27} +1.53725e11 q^{28} -6.26780e11 q^{29} +2.13727e12 q^{30} +3.22919e12 q^{31} +6.33842e12 q^{32} -9.31822e12 q^{33} +3.12023e12 q^{34} -2.09651e12 q^{35} +4.71924e12 q^{36} -4.22373e13 q^{37} -1.55562e13 q^{38} -5.25229e12 q^{39} -5.38244e13 q^{40} +2.29934e13 q^{41} -3.31833e12 q^{42} +7.62596e12 q^{43} +9.24500e13 q^{44} -6.43614e13 q^{45} -1.67715e13 q^{46} -1.08707e13 q^{47} +1.07177e13 q^{48} -2.29375e14 q^{49} +1.25797e14 q^{50} +1.25120e14 q^{51} +5.21102e13 q^{52} -1.36494e13 q^{53} -3.39392e14 q^{54} -1.26084e15 q^{55} +8.35678e13 q^{56} -6.23796e14 q^{57} -1.34235e14 q^{58} -1.88245e15 q^{59} -8.50302e14 q^{60} -7.32070e14 q^{61} +6.91582e14 q^{62} +9.99277e13 q^{63} +1.19390e15 q^{64} -7.10683e14 q^{65} -1.99564e15 q^{66} -7.26956e14 q^{67} -1.24137e15 q^{68} -6.72532e14 q^{69} -4.49001e14 q^{70} +2.48016e15 q^{71} +2.56548e15 q^{72} +1.46437e15 q^{73} -9.04579e15 q^{74} +5.04440e15 q^{75} +6.18895e15 q^{76} +1.95759e15 q^{77} -1.12486e15 q^{78} +2.41598e16 q^{79} +1.45021e15 q^{80} -6.45679e15 q^{81} +4.92440e15 q^{82} +5.57979e15 q^{83} +1.32018e15 q^{84} +1.69299e16 q^{85} +1.63322e15 q^{86} -5.38276e15 q^{87} +5.02577e16 q^{88} -9.43245e13 q^{89} -1.37840e16 q^{90} +1.10341e15 q^{91} +6.67248e15 q^{92} +2.77322e16 q^{93} -2.32813e15 q^{94} -8.44055e16 q^{95} +5.44342e16 q^{96} -5.70123e16 q^{97} -4.91244e16 q^{98} +6.00966e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) $ 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9} - 312719540 q^{10} - 45399620 q^{11} - 8621310628 q^{12} - 10510197306 q^{13} - 12286634640 q^{14} - 16443659490 q^{15} + 65383333632 q^{16} - 35705720330 q^{17} + 27658188862 q^{18} - 84895273414 q^{19} + 331348024336 q^{20} + 185190266362 q^{21} + 270540900120 q^{22} - 1096353793934 q^{23} + 1697198124384 q^{24} + 525715171346 q^{25} + 4272672484934 q^{26} - 3706093330604 q^{27} - 9883598189096 q^{28} - 4114009788386 q^{29} - 14194804268004 q^{30} + 3718266369468 q^{31} - 29197309605632 q^{32} - 16110579243626 q^{33} - 31423174598564 q^{34} + 13804822380504 q^{35} + 51950006703548 q^{36} - 58067881808868 q^{37} - 76590705469880 q^{38} + 69866971570764 q^{39} - 129282722434320 q^{40} - 74370388815170 q^{41} - 430581394397552 q^{42} - 127444248270174 q^{43} - 563872902913048 q^{44} - 602432292081270 q^{45} - 749727107945564 q^{47} - 17\!\cdots\!72 q^{48}+ \cdots + 35\!\cdots\!38 q^{99}+O(q^{100}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9 - 312719540 * q^10 - 45399620 * q^11 - 8621310628 * q^12 - 10510197306 * q^13 - 12286634640 * q^14 - 16443659490 * q^15 + 65383333632 * q^16 - 35705720330 * q^17 + 27658188862 * q^18 - 84895273414 * q^19 + 331348024336 * q^20 + 185190266362 * q^21 + 270540900120 * q^22 - 1096353793934 * q^23 + 1697198124384 * q^24 + 525715171346 * q^25 + 4272672484934 * q^26 - 3706093330604 * q^27 - 9883598189096 * q^28 - 4114009788386 * q^29 - 14194804268004 * q^30 + 3718266369468 * q^31 - 29197309605632 * q^32 - 16110579243626 * q^33 - 31423174598564 * q^34 + 13804822380504 * q^35 + 51950006703548 * q^36 - 58067881808868 * q^37 - 76590705469880 * q^38 + 69866971570764 * q^39 - 129282722434320 * q^40 - 74370388815170 * q^41 - 430581394397552 * q^42 - 127444248270174 * q^43 - 563872902913048 * q^44 - 602432292081270 * q^45 - 749727107945564 * q^47 - 1762369490938672 * q^48 - 560241909258462 * q^49 - 1212733967351616 * q^50 - 2013927378521294 * q^51 - 3438555393950964 * q^52 - 1954645162253818 * q^53 - 2748549190422938 * q^54 - 2426218557075404 * q^55 - 1321001371084560 * q^56 - 2335835167092904 * q^57 - 340295461037046 * q^58 - 1561709417167508 * q^59 - 7486616247365616 * q^60 - 679115861109266 * q^61 - 12552327168177062 * q^62 - 10591353756704576 * q^63 - 6775416249353536 * q^64 - 6252697705990982 * q^65 - 20881430274671372 * q^66 - 7577612038827396 * q^67 + 2901964856169680 * q^68 + 833228883389840 * q^69 - 10700966230255240 * q^70 + 25039332312392368 * q^71 - 7954969753997256 * q^72 - 18720848443128734 * q^73 - 6297551300657404 * q^74 + 22553223201966436 * q^75 + 34141945529937952 * q^76 + 35092380107507048 * q^77 + 27963841408286022 * q^78 + 965348846593408 * q^79 + 36943919850262880 * q^80 + 51275234750545798 * q^81 + 106728632435914846 * q^82 + 65089411455584544 * q^83 + 189770883431502392 * q^84 + 20919534362994588 * q^85 + 86205449672049764 * q^86 + 130649890213719716 * q^87 + 164304846335490592 * q^88 - 61322357257717500 * q^89 + 237420523836214152 * q^90 + 181977537844157150 * q^91 - 61586264776507392 * q^92 - 71304974484877430 * q^93 - 14005510384703054 * q^94 + 123323286964112684 * q^95 + 566787465801380768 * q^96 - 67350702995984898 * q^97 + 134333537201072600 * q^98 + 353912447692290838 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	214.166	0.591556	0.295778	−	0.955257i	$-0.404421\pi$
$2$	214.166	0.591556	0.295778	+	0.955257i	$0.404421\pi$
$3$	8587.97	0.755718	0.377859	−	0.925863i	$-0.376660\pi$
$3$	8587.97	0.755718	0.377859	+	0.925863i	$0.376660\pi$
$4$	−85204.9	−0.650062
$5$	1.16203e6	1.33037	0.665186	−	0.746678i	$-0.268352\pi$
$5$	1.16203e6	1.33037	0.665186	+	0.746678i	$0.268352\pi$
$6$	1.83925e6	0.447049
$7$	−1.80417e6	−0.118289	−0.0591446	−	0.998249i	$-0.518837\pi$
$7$	−1.80417e6	−0.118289	−0.0591446	+	0.998249i	$0.518837\pi$
$8$	−4.63192e7	−0.976103
$9$	−5.53869e7	−0.428890
$10$	2.48868e8	0.786989
$11$	−1.08503e9	−1.52618	−0.763088	−	0.646295i	$-0.776318\pi$
$11$	−1.08503e9	−1.52618	−0.763088	+	0.646295i	$0.776318\pi$
$12$	−7.31737e8	−0.491264
$13$	−6.11587e8	−0.207941	−0.103970	−	0.994580i	$-0.533155\pi$
$13$	−6.11587e8	−0.207941	−0.103970	+	0.994580i	$0.533155\pi$
$14$	−3.86393e8	−0.0699746
$15$	9.97950e9	1.00539
$16$	1.24799e9	0.0726427
$17$	1.45692e10	0.506547	0.253273	−	0.967395i	$-0.418493\pi$
$17$	1.45692e10	0.506547	0.253273	+	0.967395i	$0.418493\pi$
$18$	−1.18620e10	−0.253712
$19$	−7.26361e10	−0.981176	−0.490588	−	0.871392i	$-0.663218\pi$
$19$	−7.26361e10	−0.981176	−0.490588	+	0.871392i	$0.663218\pi$
$20$	−9.90109e10	−0.864824
$21$	−1.54942e10	−0.0893933
$22$	−2.32377e11	−0.902817
$23$	−7.83110e10	−0.208514
$23$	−7.83110e10	−0.208514
$24$	−3.97788e11	−0.737659
$25$	5.87380e11	0.769890
$26$	−1.30981e11	−0.123008
$27$	−1.58471e12	−1.07984
$28$	1.53725e11	0.0768953
$29$	−6.26780e11	−0.232665	−0.116333	−	0.993210i	$-0.537114\pi$
$29$	−6.26780e11	−0.232665	−0.116333	+	0.993210i	$0.537114\pi$
$30$	2.13727e12	0.594742
$31$	3.22919e12	0.680016	0.340008	−	0.940423i	$-0.389570\pi$
$31$	3.22919e12	0.680016	0.340008	+	0.940423i	$0.389570\pi$
$32$	6.33842e12	1.01908
$33$	−9.31822e12	−1.15336
$34$	3.12023e12	0.299651
$35$	−2.09651e12	−0.157369
$36$	4.71924e12	0.278805
$37$	−4.22373e13	−1.97688	−0.988442	−	0.151600i	$-0.951558\pi$
$37$	−4.22373e13	−1.97688	−0.988442	+	0.151600i	$0.951558\pi$
$38$	−1.55562e13	−0.580420
$39$	−5.25229e12	−0.157145
$40$	−5.38244e13	−1.29858
$41$	2.29934e13	0.449718	0.224859	−	0.974391i	$-0.427808\pi$
$41$	2.29934e13	0.449718	0.224859	+	0.974391i	$0.427808\pi$
$42$	−3.31833e12	−0.0528811
$43$	7.62596e12	0.0994976	0.0497488	−	0.998762i	$-0.484158\pi$
$43$	7.62596e12	0.0994976	0.0497488	+	0.998762i	$0.484158\pi$
$44$	9.24500e13	0.992109
$45$	−6.43614e13	−0.570584
$46$	−1.67715e13	−0.123348
$47$	−1.08707e13	−0.0665923	−0.0332962	−	0.999446i	$-0.510600\pi$
$47$	−1.08707e13	−0.0665923	−0.0332962	+	0.999446i	$0.510600\pi$
$48$	1.07177e13	0.0548974
$49$	−2.29375e14	−0.986008
$50$	1.25797e14	0.455433
$51$	1.25120e14	0.382807
$52$	5.21102e13	0.135174
$53$	−1.36494e13	−0.0301140	−0.0150570	−	0.999887i	$-0.504793\pi$
$53$	−1.36494e13	−0.0301140	−0.0150570	+	0.999887i	$0.504793\pi$
$54$	−3.39392e14	−0.638784
$55$	−1.26084e15	−2.03038
$56$	8.35678e13	0.115463
$57$	−6.23796e14	−0.741492
$58$	−1.34235e14	−0.137635
$59$	−1.88245e15	−1.66910	−0.834548	−	0.550935i	$-0.814271\pi$
$59$	−1.88245e15	−1.66910	−0.834548	+	0.550935i	$0.814271\pi$
$60$	−8.50302e14	−0.653564
$61$	−7.32070e14	−0.488933	−0.244466	−	0.969658i	$-0.578613\pi$
$61$	−7.32070e14	−0.488933	−0.244466	+	0.969658i	$0.578613\pi$
$62$	6.91582e14	0.402267
$63$	9.99277e13	0.0507331
$64$	1.19390e15	0.530197
$65$	−7.10683e14	−0.276639
$66$	−1.99564e15	−0.682276
$67$	−7.26956e14	−0.218712	−0.109356	−	0.994003i	$-0.534879\pi$
$67$	−7.26956e14	−0.218712	−0.109356	+	0.994003i	$0.534879\pi$
$68$	−1.24137e15	−0.329287
$69$	−6.72532e14	−0.157578
$70$	−4.49001e14	−0.0930923
$71$	2.48016e15	0.455809	0.227905	−	0.973683i	$-0.426813\pi$
$71$	2.48016e15	0.455809	0.227905	+	0.973683i	$0.426813\pi$
$72$	2.56548e15	0.418641
$73$	1.46437e15	0.212523	0.106261	−	0.994338i	$-0.466112\pi$
$73$	1.46437e15	0.212523	0.106261	+	0.994338i	$0.466112\pi$
$74$	−9.04579e15	−1.16944
$75$	5.04440e15	0.581820
$76$	6.18895e15	0.637825
$77$	1.95759e15	0.180530
$78$	−1.12486e15	−0.0929597
$79$	2.41598e16	1.79169	0.895846	−	0.444364i	$-0.146570\pi$
$79$	2.41598e16	1.79169	0.895846	+	0.444364i	$0.146570\pi$
$80$	1.45021e15	0.0966418
$81$	−6.45679e15	−0.387163
$82$	4.92440e15	0.266033
$83$	5.57979e15	0.271928	0.135964	−	0.990714i	$-0.456587\pi$
$83$	5.57979e15	0.271928	0.135964	+	0.990714i	$0.456587\pi$
$84$	1.32018e15	0.0581112
$85$	1.69299e16	0.673896
$86$	1.63322e15	0.0588583
$87$	−5.38276e15	−0.175829
$88$	5.02577e16	1.48970
$89$	−9.43245e13	−0.00253986	−0.00126993	−	0.999999i	$-0.500404\pi$
$89$	−9.43245e13	−0.00253986	−0.00126993	+	0.999999i	$0.500404\pi$
$90$	−1.37840e16	−0.337532
$91$	1.10341e15	0.0245971
$92$	6.67248e15	0.135547
$93$	2.77322e16	0.513900
$94$	−2.32813e15	−0.0393931
$95$	−8.44055e16	−1.30533
$96$	5.44342e16	0.770134
$97$	−5.70123e16	−0.738600	−0.369300	−	0.929310i	$-0.620402\pi$
$97$	−5.70123e16	−0.738600	−0.369300	+	0.929310i	$0.620402\pi$
$98$	−4.91244e16	−0.583278
$99$	6.00966e16	0.654562
$100$	−5.00476e16	−0.500476
$101$	−1.00864e17	−0.926839	−0.463420	−	0.886139i	$-0.653378\pi$
$101$	−1.00864e17	−0.926839	−0.463420	+	0.886139i	$0.653378\pi$
$102$	2.67964e16	0.226451
$103$	1.71765e17	1.33604	0.668020	−	0.744144i	$-0.267142\pi$
$103$	1.71765e17	1.33604	0.668020	+	0.744144i	$0.267142\pi$
$104$	2.83282e16	0.202972
$105$	−1.80048e16	−0.118926
$106$	−2.92323e15	−0.0178141
$107$	3.50565e17	1.97245	0.986225	−	0.165409i	$-0.0528944\pi$
$107$	3.50565e17	1.97245	0.986225	+	0.165409i	$0.0528944\pi$
$108$	1.35025e17	0.701962
$109$	2.98881e17	1.43672	0.718361	−	0.695671i	$-0.244893\pi$
$109$	2.98881e17	1.43672	0.718361	+	0.695671i	$0.244893\pi$
$110$	−2.70029e17	−1.20108
$111$	−3.62732e17	−1.49397
$112$	−2.25159e15	−0.00859284
$113$	−4.27591e17	−1.51308	−0.756539	−	0.653948i	$-0.773111\pi$
$113$	−4.27591e17	−1.51308	−0.756539	+	0.653948i	$0.773111\pi$
$114$	−1.33596e17	−0.438634
$115$	−9.09999e16	−0.277402
$116$	5.34047e16	0.151247
$117$	3.38739e16	0.0891837
$118$	−4.03157e17	−0.987363
$119$	−2.62854e16	−0.0599190
$120$	−4.62242e17	−0.981361
$121$	6.71846e17	1.32921
$122$	−1.56785e17	−0.289231
$123$	1.97466e17	0.339860
$124$	−2.75143e17	−0.442053
$125$	−2.04006e17	−0.306132
$126$	2.14011e16	0.0300114
$127$	−2.90888e16	−0.0381412	−0.0190706	−	0.999818i	$-0.506071\pi$
$127$	−2.90888e16	−0.0381412	−0.0190706	+	0.999818i	$0.506071\pi$
$128$	−5.75097e17	−0.705434
$129$	6.54915e16	0.0751921
$130$	−1.52204e17	−0.163647
$131$	−5.55003e17	−0.559100	−0.279550	−	0.960131i	$-0.590185\pi$
$131$	−5.55003e17	−0.559100	−0.279550	+	0.960131i	$0.590185\pi$
$132$	7.93958e17	0.749754
$133$	1.31048e17	0.116063
$134$	−1.55689e17	−0.129380
$135$	−1.84149e18	−1.43659
$136$	−6.74833e17	−0.494442
$137$	1.13084e17	0.0778529	0.0389264	−	0.999242i	$-0.487606\pi$
$137$	1.13084e17	0.0778529	0.0389264	+	0.999242i	$0.487606\pi$
$138$	−1.44034e17	−0.0932162
$139$	2.04594e18	1.24528	0.622640	−	0.782509i	$-0.286060\pi$
$139$	2.04594e18	1.24528	0.622640	+	0.782509i	$0.286060\pi$
$140$	1.78633e17	0.102299
$141$	−9.33569e16	−0.0503250
$142$	5.31165e17	0.269637
$143$	6.63591e17	0.317354
$144$	−6.91224e16	−0.0311557
$145$	−7.28338e17	−0.309532
$146$	3.13618e17	0.125719
$147$	−1.96987e18	−0.745144
$148$	3.59882e18	1.28510
$149$	2.06868e18	0.697605	0.348802	−	0.937196i	$-0.386588\pi$
$149$	2.06868e18	0.697605	0.348802	+	0.937196i	$0.386588\pi$
$150$	1.08034e18	0.344179
$151$	−3.08727e17	−0.0929545	−0.0464772	−	0.998919i	$-0.514799\pi$
$151$	−3.08727e17	−0.0929545	−0.0464772	+	0.998919i	$0.514799\pi$
$152$	3.36444e18	0.957729
$153$	−8.06943e17	−0.217253
$154$	4.19248e17	0.106794
$155$	3.75242e18	0.904674
$156$	4.47521e17	0.102154
$157$	−7.05579e18	−1.52545	−0.762726	−	0.646722i	$-0.776139\pi$
$157$	−7.05579e18	−1.52545	−0.762726	+	0.646722i	$0.776139\pi$
$158$	5.17421e18	1.05989
$159$	−1.17220e17	−0.0227577
$160$	7.36545e18	1.35575
$161$	1.41287e17	0.0246650
$162$	−1.38282e18	−0.229028
$163$	4.10235e18	0.644819	0.322410	−	0.946600i	$-0.395507\pi$
$163$	4.10235e18	0.644819	0.322410	+	0.946600i	$0.395507\pi$
$164$	−1.95915e18	−0.292345
$165$	−1.08281e19	−1.53440
$166$	1.19500e18	0.160860
$167$	8.86196e18	1.13355	0.566774	−	0.823873i	$-0.308191\pi$
$167$	8.86196e18	1.13355	0.566774	+	0.823873i	$0.308191\pi$
$168$	7.17678e17	0.0872571
$169$	−8.27638e18	−0.956761
$170$	3.62580e18	0.398647
$171$	4.02309e18	0.420817
$172$	−6.49769e17	−0.0646796
$173$	−1.25061e18	−0.118503	−0.0592517	−	0.998243i	$-0.518871\pi$
$173$	−1.25061e18	−0.118503	−0.0592517	+	0.998243i	$0.518871\pi$
$174$	−1.15280e18	−0.104013
$175$	−1.05974e18	−0.0910697
$176$	−1.35411e18	−0.110865
$177$	−1.61664e19	−1.26137
$178$	−2.02011e16	−0.00150247
$179$	1.55419e19	1.10218	0.551090	−	0.834446i	$-0.314212\pi$
$179$	1.55419e19	1.10218	0.551090	+	0.834446i	$0.314212\pi$
$180$	5.48391e18	0.370915
$181$	1.96439e19	1.26754	0.633769	−	0.773523i	$-0.281507\pi$
$181$	1.96439e19	1.26754	0.633769	+	0.773523i	$0.281507\pi$
$182$	2.36313e17	0.0145506
$183$	−6.28700e18	−0.369495
$184$	3.62730e18	0.203532
$185$	−4.90811e19	−2.62999
$186$	5.93929e18	0.304001
$187$	−1.58080e19	−0.773079
$188$	9.26234e17	0.0432891
$189$	2.85910e18	0.127733
$190$	−1.80768e19	−0.772175
$191$	−2.25790e19	−0.922402	−0.461201	−	0.887296i	$-0.652581\pi$
$191$	−2.25790e19	−0.922402	−0.461201	+	0.887296i	$0.652581\pi$
$192$	1.02532e19	0.400680
$193$	2.97327e18	0.111172	0.0555862	−	0.998454i	$-0.482297\pi$
$193$	2.97327e18	0.111172	0.0555862	+	0.998454i	$0.482297\pi$
$194$	−1.22101e19	−0.436923
$195$	−6.10333e18	−0.209061
$196$	1.95439e19	0.640966
$197$	−4.18262e19	−1.31367	−0.656835	−	0.754035i	$-0.728105\pi$
$197$	−4.18262e19	−1.31367	−0.656835	+	0.754035i	$0.728105\pi$
$198$	1.28706e19	0.387209
$199$	−5.03466e19	−1.45117	−0.725587	−	0.688131i	$-0.758432\pi$
$199$	−5.03466e19	−1.45117	−0.725587	+	0.688131i	$0.758432\pi$
$200$	−2.72069e19	−0.751492
$201$	−6.24307e18	−0.165284
$202$	−2.16016e19	−0.548277
$203$	1.13082e18	0.0275218
$204$	−1.06608e19	−0.248848
$205$	2.67191e19	0.598292
$206$	3.67863e19	0.790341
$207$	4.33741e18	0.0894298
$208$	−7.63255e17	−0.0151054
$209$	7.88124e19	1.49745
$210$	−3.85601e18	−0.0703516
$211$	3.35844e19	0.588487	0.294244	−	0.955730i	$-0.404932\pi$
$211$	3.35844e19	0.588487	0.294244	+	0.955730i	$0.404932\pi$
$212$	1.16299e18	0.0195759
$213$	2.12995e19	0.344463
$214$	7.50790e19	1.16681
$215$	8.86161e18	0.132369
$216$	7.34026e19	1.05403
$217$	−5.82602e18	−0.0804386
$218$	6.40101e19	0.849901
$219$	1.25759e19	0.160607
$220$	1.07430e20	1.31987
$221$	−8.91032e18	−0.105332
$222$	−7.76849e19	−0.883765
$223$	−8.39879e19	−0.919656	−0.459828	−	0.888008i	$-0.652089\pi$
$223$	−8.39879e19	−0.919656	−0.459828	+	0.888008i	$0.652089\pi$
$224$	−1.14356e19	−0.120546
$225$	−3.25332e19	−0.330198
$226$	−9.15754e19	−0.895070
$227$	−6.27242e19	−0.590494	−0.295247	−	0.955421i	$-0.595402\pi$
$227$	−6.27242e19	−0.590494	−0.295247	+	0.955421i	$0.595402\pi$
$228$	5.31505e19	0.482016
$229$	−5.16522e19	−0.451323	−0.225661	−	0.974206i	$-0.572454\pi$
$229$	−5.16522e19	−0.451323	−0.225661	+	0.974206i	$0.572454\pi$
$230$	−1.94891e19	−0.164099
$231$	1.68117e19	0.136430
$232$	2.90319e19	0.227105
$233$	−1.41414e20	−1.06651	−0.533256	−	0.845954i	$-0.679032\pi$
$233$	−1.41414e20	−1.06651	−0.533256	+	0.845954i	$0.679032\pi$
$234$	7.25464e18	0.0527571
$235$	−1.26321e19	−0.0885926
$236$	1.60394e20	1.08502
$237$	2.07484e20	1.35401
$238$	−5.62943e18	−0.0354454
$239$	−3.07611e20	−1.86905	−0.934523	−	0.355903i	$-0.884173\pi$
$239$	−3.07611e20	−1.86905	−0.934523	+	0.355903i	$0.884173\pi$
$240$	1.24543e19	0.0730339
$241$	2.69315e20	1.52446	0.762228	−	0.647309i	$-0.224106\pi$
$241$	2.69315e20	1.52446	0.762228	+	0.647309i	$0.224106\pi$
$242$	1.43887e20	0.786302
$243$	1.49199e20	0.787252
$244$	6.23760e19	0.317837
$245$	−2.66542e20	−1.31176
$246$	4.22906e19	0.201046
$247$	4.44233e19	0.204026
$248$	−1.49573e20	−0.663766
$249$	4.79190e19	0.205501
$250$	−4.36912e19	−0.181094
$251$	4.94823e19	0.198255	0.0991274	−	0.995075i	$-0.468395\pi$
$251$	4.94823e19	0.198255	0.0991274	+	0.995075i	$0.468395\pi$
$252$	−8.51433e18	−0.0329796
$253$	8.49699e19	0.318230
$254$	−6.22983e18	−0.0225626
$255$	1.45393e20	0.509275
$256$	−2.79653e20	−0.947501
$257$	3.33145e20	1.09195	0.545973	−	0.837803i	$-0.316160\pi$
$257$	3.33145e20	1.09195	0.545973	+	0.837803i	$0.316160\pi$
$258$	1.40260e19	0.0444803
$259$	7.62034e19	0.233844
$260$	6.05537e19	0.179832
$261$	3.47154e19	0.0997879
$262$	−1.18863e20	−0.330739
$263$	−5.76097e20	−1.55193	−0.775964	−	0.630777i	$-0.782736\pi$
$263$	−5.76097e20	−1.55193	−0.775964	+	0.630777i	$0.782736\pi$
$264$	4.31612e20	1.12580
$265$	−1.58610e19	−0.0400628
$266$	2.80661e19	0.0686574
$267$	−8.10056e17	−0.00191942
$268$	6.19402e19	0.142176
$269$	−4.95933e20	−1.10288	−0.551441	−	0.834214i	$-0.685922\pi$
$269$	−4.95933e20	−1.10288	−0.551441	+	0.834214i	$0.685922\pi$
$270$	−3.94384e20	−0.849821
$271$	−7.07966e20	−1.47834	−0.739168	−	0.673521i	$-0.764781\pi$
$271$	−7.07966e20	−1.47834	−0.739168	+	0.673521i	$0.764781\pi$
$272$	1.81822e19	0.0367969
$273$	9.47604e18	0.0185885
$274$	2.42186e19	0.0460543
$275$	−6.37325e20	−1.17499
$276$	5.73031e19	0.102436
$277$	2.51091e20	0.435264	0.217632	−	0.976031i	$-0.430167\pi$
$277$	2.51091e20	0.435264	0.217632	+	0.976031i	$0.430167\pi$
$278$	4.38170e20	0.736652
$279$	−1.78855e20	−0.291652
$280$	9.71085e19	0.153608
$281$	−8.01534e20	−1.23004	−0.615019	−	0.788513i	$-0.710851\pi$
$281$	−8.01534e20	−1.23004	−0.615019	+	0.788513i	$0.710851\pi$
$282$	−1.99939e19	−0.0297700
$283$	1.19210e21	1.72237	0.861187	−	0.508288i	$-0.169721\pi$
$283$	1.19210e21	1.72237	0.861187	+	0.508288i	$0.169721\pi$
$284$	−2.11322e20	−0.296304
$285$	−7.24872e20	−0.986461
$286$	1.42119e20	0.187733
$287$	−4.14841e19	−0.0531968
$288$	−3.51066e20	−0.437071
$289$	−6.14979e20	−0.743410
$290$	−1.55985e20	−0.183105
$291$	−4.89620e20	−0.558173
$292$	−1.24771e20	−0.138153
$293$	1.62853e21	1.75154	0.875769	−	0.482730i	$-0.160355\pi$
$293$	1.62853e21	1.75154	0.875769	+	0.482730i	$0.160355\pi$
$294$	−4.21879e20	−0.440794
$295$	−2.18747e21	−2.22052
$296$	1.95639e21	1.92964
$297$	1.71946e21	1.64802
$298$	4.43040e20	0.412672
$299$	4.78940e19	0.0433586
$300$	−4.29808e20	−0.378219
$301$	−1.37586e19	−0.0117695
$302$	−6.61188e19	−0.0549877
$303$	−8.66217e20	−0.700429
$304$	−9.06492e19	−0.0712752
$305$	−8.50689e20	−0.650462
$306$	−1.72820e20	−0.128517
$307$	3.79148e20	0.274241	0.137121	−	0.990554i	$-0.456215\pi$
$307$	3.79148e20	0.274241	0.137121	+	0.990554i	$0.456215\pi$
$308$	−1.66796e20	−0.117356
$309$	1.47512e21	1.00967
$310$	8.03641e20	0.535165
$311$	1.71011e21	1.10805	0.554027	−	0.832499i	$-0.313090\pi$
$311$	1.71011e21	1.10805	0.554027	+	0.832499i	$0.313090\pi$
$312$	2.43282e20	0.153389
$313$	5.67527e20	0.348225	0.174112	−	0.984726i	$-0.444294\pi$
$313$	5.67527e20	0.348225	0.174112	+	0.984726i	$0.444294\pi$
$314$	−1.51111e21	−0.902389
$315$	1.16119e20	0.0674939
$316$	−2.05854e21	−1.16471
$317$	3.01713e21	1.66184	0.830921	−	0.556390i	$-0.187814\pi$
$317$	3.01713e21	1.66184	0.830921	+	0.556390i	$0.187814\pi$
$318$	−2.51046e19	−0.0134624
$319$	6.80075e20	0.355088
$320$	1.38735e21	0.705360
$321$	3.01064e21	1.49062
$322$	3.02588e19	0.0145907
$323$	−1.05825e21	−0.497012
$324$	5.50150e20	0.251680
$325$	−3.59234e20	−0.160092
$326$	8.78584e20	0.381446
$327$	2.56678e21	1.08576
$328$	−1.06503e21	−0.438971
$329$	1.96126e19	0.00787715
$330$	−2.31900e21	−0.907680
$331$	2.21569e21	0.845221	0.422610	−	0.906311i	$-0.361114\pi$
$331$	2.21569e21	0.845221	0.422610	+	0.906311i	$0.361114\pi$
$332$	−4.75425e20	−0.176770
$333$	2.33939e21	0.847866
$334$	1.89793e21	0.670557
$335$	−8.44746e20	−0.290968
$336$	−1.93366e19	−0.00649377
$337$	4.52116e20	0.148046	0.0740228	−	0.997257i	$-0.476416\pi$
$337$	4.52116e20	0.148046	0.0740228	+	0.997257i	$0.476416\pi$
$338$	−1.77252e21	−0.565977
$339$	−3.67214e21	−1.14346
$340$	−1.44251e21	−0.438074
$341$	−3.50377e21	−1.03782
$342$	8.61609e20	0.248936
$343$	8.33539e20	0.234923
$344$	−3.53228e20	−0.0971199
$345$	−7.81504e20	−0.209638
$346$	−2.67839e20	−0.0701014
$347$	−5.10091e21	−1.30271	−0.651354	−	0.758774i	$-0.725799\pi$
$347$	−5.10091e21	−1.30271	−0.651354	+	0.758774i	$0.725799\pi$
$348$	4.58638e20	0.114300
$349$	−2.99941e21	−0.729491	−0.364746	−	0.931107i	$-0.618844\pi$
$349$	−2.99941e21	−0.729491	−0.364746	+	0.931107i	$0.618844\pi$
$350$	−2.26959e20	−0.0538728
$351$	9.69189e20	0.224542
$352$	−6.87739e21	−1.55529
$353$	5.99097e21	1.32255	0.661275	−	0.750143i	$-0.270015\pi$
$353$	5.99097e21	1.32255	0.661275	+	0.750143i	$0.270015\pi$
$354$	−3.46230e21	−0.746168
$355$	2.88202e21	0.606396
$356$	8.03691e18	0.00165107
$357$	−2.25738e20	−0.0452819
$358$	3.32854e21	0.652001
$359$	−6.74602e21	−1.29046	−0.645230	−	0.763988i	$-0.723239\pi$
$359$	−6.74602e21	−1.29046	−0.645230	+	0.763988i	$0.723239\pi$
$360$	2.98117e21	0.556948
$361$	−2.04386e20	−0.0372941
$362$	4.20707e21	0.749819
$363$	5.76979e21	1.00451
$364$	−9.40159e19	−0.0159897
$365$	1.70164e21	0.282734
$366$	−1.34646e21	−0.218577
$367$	−4.24165e21	−0.672780	−0.336390	−	0.941723i	$-0.609206\pi$
$367$	−4.24165e21	−0.672780	−0.336390	+	0.941723i	$0.609206\pi$
$368$	−9.77314e19	−0.0151470
$369$	−1.27353e21	−0.192880
$370$	−1.05115e22	−1.55579
$371$	2.46259e19	0.00356216
$372$	−2.36292e21	−0.334067
$373$	−7.72910e21	−1.06808	−0.534040	−	0.845459i	$-0.679327\pi$
$373$	−7.72910e21	−1.06808	−0.534040	+	0.845459i	$0.679327\pi$
$374$	−3.38554e21	−0.457319
$375$	−1.75200e21	−0.231349
$376$	5.03520e20	0.0650010
$377$	3.83330e20	0.0483806
$378$	6.12322e20	0.0755613
$379$	5.80704e21	0.700683	0.350341	−	0.936622i	$-0.386066\pi$
$379$	5.80704e21	0.700683	0.350341	+	0.936622i	$0.386066\pi$
$380$	7.19176e21	0.848545
$381$	−2.49814e20	−0.0288240
$382$	−4.83565e21	−0.545652
$383$	4.17406e21	0.460648	0.230324	−	0.973114i	$-0.426021\pi$
$383$	4.17406e21	0.460648	0.230324	+	0.973114i	$0.426021\pi$
$384$	−4.93892e21	−0.533110
$385$	2.27478e21	0.240172
$386$	6.36773e20	0.0657647
$387$	−4.22378e20	−0.0426735
$388$	4.85773e21	0.480135
$389$	−2.96559e21	−0.286773	−0.143387	−	0.989667i	$-0.545799\pi$
$389$	−2.96559e21	−0.286773	−0.143387	+	0.989667i	$0.545799\pi$
$390$	−1.30713e21	−0.123671
$391$	−1.14093e21	−0.105622
$392$	1.06245e22	0.962445
$393$	−4.76635e21	−0.422522
$394$	−8.95776e21	−0.777108
$395$	2.80745e22	2.38362
$396$	−5.12052e21	−0.425506
$397$	−1.36988e22	−1.11420	−0.557101	−	0.830444i	$-0.688087\pi$
$397$	−1.36988e22	−1.11420	−0.557101	+	0.830444i	$0.688087\pi$
$398$	−1.07825e22	−0.858450
$399$	1.12544e21	0.0877105
$400$	7.33045e20	0.0559269
$401$	5.73022e21	0.428001	0.214000	−	0.976834i	$-0.431351\pi$
$401$	5.73022e21	0.428001	0.214000	+	0.976834i	$0.431351\pi$
$402$	−1.33705e21	−0.0977749
$403$	−1.97493e21	−0.141403
$404$	8.59411e21	0.602503
$405$	−7.50300e21	−0.515071
$406$	2.42183e20	0.0162807
$407$	4.58288e22	3.01707
$408$	−5.79544e21	−0.373659
$409$	1.27634e22	0.805969	0.402985	−	0.915207i	$-0.367973\pi$
$409$	1.27634e22	0.805969	0.402985	+	0.915207i	$0.367973\pi$
$410$	5.72231e21	0.353923
$411$	9.71158e20	0.0588348
$412$	−1.46353e22	−0.868508
$413$	3.39627e21	0.197436
$414$	9.28925e20	0.0529027
$415$	6.48389e21	0.361765
$416$	−3.87649e21	−0.211907
$417$	1.75705e22	0.941080
$418$	1.68789e22	0.885823
$419$	−2.64098e21	−0.135815	−0.0679073	−	0.997692i	$-0.521632\pi$
$419$	−2.64098e21	−0.135815	−0.0679073	+	0.997692i	$0.521632\pi$
$420$	1.53409e21	0.0773095
$421$	−6.11457e21	−0.301973	−0.150986	−	0.988536i	$-0.548245\pi$
$421$	−6.11457e21	−0.301973	−0.150986	+	0.988536i	$0.548245\pi$
$422$	7.19264e21	0.348123
$423$	6.02093e20	0.0285608
$424$	6.32228e20	0.0293943
$425$	8.55765e21	0.389986
$426$	4.56163e21	0.203769
$427$	1.32078e21	0.0578355
$428$	−2.98698e22	−1.28221
$429$	5.69890e21	0.239830
$430$	1.89785e21	0.0783035
$431$	−2.07481e22	−0.839309	−0.419655	−	0.907684i	$-0.637849\pi$
$431$	−2.07481e22	−0.839309	−0.419655	+	0.907684i	$0.637849\pi$
$432$	−1.97771e21	−0.0784423
$433$	−4.74336e22	−1.84476	−0.922379	−	0.386287i	$-0.873757\pi$
$433$	−4.74336e22	−1.84476	−0.922379	+	0.386287i	$0.873757\pi$
$434$	−1.24774e21	−0.0475839
$435$	−6.25495e21	−0.233919
$436$	−2.54661e22	−0.933958
$437$	5.68820e21	0.204589
$438$	2.69334e21	0.0950082
$439$	−3.08266e22	−1.06654	−0.533270	−	0.845945i	$-0.679037\pi$
$439$	−3.08266e22	−1.06654	−0.533270	+	0.845945i	$0.679037\pi$
$440$	5.84011e22	1.98186
$441$	1.27044e22	0.422889
$442$	−1.90829e21	−0.0623096
$443$	3.75372e22	1.20235	0.601173	−	0.799119i	$-0.294700\pi$
$443$	3.75372e22	1.20235	0.601173	+	0.799119i	$0.294700\pi$
$444$	3.09066e22	0.971171
$445$	−1.09608e20	−0.00337896
$446$	−1.79874e22	−0.544028
$447$	1.77657e22	0.527192
$448$	−2.15400e21	−0.0627166
$449$	−5.47501e22	−1.56420	−0.782098	−	0.623155i	$-0.785851\pi$
$449$	−5.47501e22	−1.56420	−0.782098	+	0.623155i	$0.785851\pi$
$450$	−6.96750e21	−0.195331
$451$	−2.49485e22	−0.686348
$452$	3.64328e22	0.983595
$453$	−2.65134e21	−0.0702474
$454$	−1.34334e22	−0.349310
$455$	1.28220e21	0.0327234
$456$	2.88937e22	0.723773
$457$	−3.06514e22	−0.753637	−0.376818	−	0.926287i	$-0.622982\pi$
$457$	−3.06514e22	−0.753637	−0.376818	+	0.926287i	$0.622982\pi$
$458$	−1.10621e22	−0.266982
$459$	−2.30880e22	−0.546989
$460$	7.75364e21	0.180328
$461$	−2.96805e22	−0.677663	−0.338832	−	0.940847i	$-0.610032\pi$
$461$	−2.96805e22	−0.677663	−0.338832	+	0.940847i	$0.610032\pi$
$462$	3.60049e21	0.0807058
$463$	4.04620e22	0.890449	0.445224	−	0.895419i	$-0.353124\pi$
$463$	4.04620e22	0.890449	0.445224	+	0.895419i	$0.353124\pi$
$464$	−7.82216e20	−0.0169014
$465$	3.22257e22	0.683679
$466$	−3.02860e22	−0.630901
$467$	−6.11370e22	−1.25058	−0.625289	−	0.780393i	$-0.715019\pi$
$467$	−6.11370e22	−1.25058	−0.625289	+	0.780393i	$0.715019\pi$
$468$	−2.88622e21	−0.0579749
$469$	1.31155e21	0.0258712
$470$	−2.70536e21	−0.0524074
$471$	−6.05949e22	−1.15281
$472$	8.71935e22	1.62921
$473$	−8.27440e21	−0.151851
$474$	4.44360e22	0.800975
$475$	−4.26650e22	−0.755398
$476$	2.23964e21	0.0389511
$477$	7.55997e20	0.0129156
$478$	−6.58798e22	−1.10564
$479$	−9.50545e22	−1.56719	−0.783593	−	0.621274i	$-0.786615\pi$
$479$	−9.50545e22	−1.56719	−0.783593	+	0.621274i	$0.786615\pi$
$480$	6.32543e22	1.02456
$481$	2.58318e22	0.411075
$482$	5.76780e22	0.901800
$483$	1.21337e21	0.0186398
$484$	−5.72446e22	−0.864070
$485$	−6.62502e22	−0.982612
$486$	3.19534e22	0.465703
$487$	1.20367e21	0.0172390	0.00861952	−	0.999963i	$-0.497256\pi$
$487$	1.20367e21	0.0172390	0.00861952	+	0.999963i	$0.497256\pi$
$488$	3.39089e22	0.477249
$489$	3.52308e22	0.487302
$490$	−5.70842e22	−0.775977
$491$	5.62439e22	0.751420	0.375710	−	0.926737i	$-0.377399\pi$
$491$	5.62439e22	0.751420	0.375710	+	0.926737i	$0.377399\pi$
$492$	−1.68251e22	−0.220930
$493$	−9.13167e21	−0.117856
$494$	9.51395e21	0.120693
$495$	6.98341e22	0.870810
$496$	4.03000e21	0.0493982
$497$	−4.47464e21	−0.0539173
$498$	1.02626e22	0.121565
$499$	−1.56085e23	−1.81763	−0.908816	−	0.417196i	$-0.863013\pi$
$499$	−1.56085e23	−1.81763	−0.908816	+	0.417196i	$0.863013\pi$
$500$	1.73823e22	0.199005
$501$	7.61063e22	0.856643
$502$	1.05974e22	0.117279
$503$	−5.28942e21	−0.0575546	−0.0287773	−	0.999586i	$-0.509161\pi$
$503$	−5.28942e21	−0.0575546	−0.0287773	+	0.999586i	$0.509161\pi$
$504$	−4.62857e21	−0.0495207
$505$	−1.17207e23	−1.23304
$506$	1.81977e22	0.188250
$507$	−7.10773e22	−0.723041
$508$	2.47851e21	0.0247941
$509$	−1.15621e23	−1.13746	−0.568728	−	0.822526i	$-0.692564\pi$
$509$	−1.15621e23	−1.13746	−0.568728	+	0.822526i	$0.692564\pi$
$510$	3.11383e22	0.301265
$511$	−2.64197e21	−0.0251392
$512$	1.54870e22	0.144935
$513$	1.15107e23	1.05951
$514$	7.13482e22	0.645947
$515$	1.99597e23	1.77743
$516$	−5.58020e21	−0.0488795
$517$	1.17950e22	0.101632
$518$	1.63202e22	0.138332
$519$	−1.07402e22	−0.0895552
$520$	3.29183e22	0.270028
$521$	−5.03957e22	−0.406699	−0.203349	−	0.979106i	$-0.565183\pi$
$521$	−5.03957e22	−0.406699	−0.203349	+	0.979106i	$0.565183\pi$
$522$	7.43486e21	0.0590301
$523$	−1.17717e23	−0.919549	−0.459775	−	0.888036i	$-0.652070\pi$
$523$	−1.17717e23	−0.919549	−0.459775	+	0.888036i	$0.652070\pi$
$524$	4.72890e22	0.363450
$525$	−9.10097e21	−0.0688230
$526$	−1.23380e23	−0.918052
$527$	4.70467e22	0.344460
$528$	−1.16291e22	−0.0837830
$529$	6.13261e21	0.0434783
$530$	−3.39689e21	−0.0236994
$531$	1.04263e23	0.715859
$532$	−1.11659e22	−0.0754478
$533$	−1.40624e22	−0.0935147
$534$	−1.73486e20	−0.00113544
$535$	4.07367e23	2.62409
$536$	3.36720e22	0.213485
$537$	1.33473e23	0.832938
$538$	−1.06212e23	−0.652416
$539$	2.48880e23	1.50482
$540$	1.56904e23	0.933870
$541$	7.25784e22	0.425237	0.212618	−	0.977135i	$-0.431801\pi$
$541$	7.25784e22	0.425237	0.212618	+	0.977135i	$0.431801\pi$
$542$	−1.51622e23	−0.874518
$543$	1.68702e23	0.957901
$544$	9.23457e22	0.516210
$545$	3.47309e23	1.91137
$546$	2.02945e21	0.0109961
$547$	−1.09472e23	−0.583998	−0.291999	−	0.956419i	$-0.594320\pi$
$547$	−1.09472e23	−0.583998	−0.291999	+	0.956419i	$0.594320\pi$
$548$	−9.63527e21	−0.0506092
$549$	4.05471e22	0.209698
$550$	−1.36493e23	−0.695070
$551$	4.55268e22	0.228286
$552$	3.11511e22	0.153813
$553$	−4.35885e22	−0.211938
$554$	5.37751e22	0.257483
$555$	−4.21507e23	−1.98753
$556$	−1.74324e23	−0.809509
$557$	−1.90354e23	−0.870547	−0.435274	−	0.900298i	$-0.643348\pi$
$557$	−1.90354e23	−0.870547	−0.435274	+	0.900298i	$0.643348\pi$
$558$	−3.83046e22	−0.172528
$559$	−4.66393e21	−0.0206896
$560$	−2.61643e21	−0.0114317
$561$	−1.35759e23	−0.584230
$562$	−1.71661e23	−0.727635
$563$	1.29154e22	0.0539245	0.0269623	−	0.999636i	$-0.491417\pi$
$563$	1.29154e22	0.0539245	0.0269623	+	0.999636i	$0.491417\pi$
$564$	7.95447e21	0.0327144
$565$	−4.96874e23	−2.01296
$566$	2.55307e23	1.01888
$567$	1.16492e22	0.0457972
$568$	−1.14879e23	−0.444917
$569$	−3.72032e23	−1.41947	−0.709735	−	0.704468i	$-0.751185\pi$
$569$	−3.72032e23	−1.41947	−0.709735	+	0.704468i	$0.751185\pi$
$570$	−1.55243e23	−0.583546
$571$	−2.13141e23	−0.789331	−0.394666	−	0.918825i	$-0.629140\pi$
$571$	−2.13141e23	−0.789331	−0.394666	+	0.918825i	$0.629140\pi$
$572$	−5.65412e22	−0.206300
$573$	−1.93907e23	−0.697076
$574$	−8.88448e21	−0.0314688
$575$	−4.59983e22	−0.160533
$576$	−6.61263e22	−0.227396
$577$	3.91118e23	1.32530	0.662649	−	0.748930i	$-0.269432\pi$
$577$	3.91118e23	1.32530	0.662649	+	0.748930i	$0.269432\pi$
$578$	−1.31708e23	−0.439768
$579$	2.55344e22	0.0840151
$580$	6.20580e22	0.201215
$581$	−1.00669e22	−0.0321661
$582$	−1.04860e23	−0.330190
$583$	1.48100e22	0.0459592
$584$	−6.78283e22	−0.207444
$585$	3.93626e22	0.118648
$586$	3.48775e23	1.03613
$587$	4.13327e23	1.21023	0.605117	−	0.796136i	$-0.293126\pi$
$587$	4.13327e23	1.21023	0.605117	+	0.796136i	$0.293126\pi$
$588$	1.67843e23	0.484390
$589$	−2.34556e23	−0.667215
$590$	−4.68481e23	−1.31356
$591$	−3.59203e23	−0.992764
$592$	−5.27118e22	−0.143606
$593$	4.87408e23	1.30896	0.654482	−	0.756078i	$-0.272887\pi$
$593$	4.87408e23	1.30896	0.654482	+	0.756078i	$0.272887\pi$
$594$	3.68251e23	0.974897
$595$	−3.05444e22	−0.0797146
$596$	−1.76261e23	−0.453486
$597$	−4.32375e23	−1.09668
$598$	1.02573e22	0.0256490
$599$	4.48733e23	1.10627	0.553134	−	0.833092i	$-0.313432\pi$
$599$	4.48733e23	1.10627	0.553134	+	0.833092i	$0.313432\pi$
$600$	−2.33652e23	−0.567916
$601$	−3.76800e23	−0.902980	−0.451490	−	0.892276i	$-0.649107\pi$
$601$	−3.76800e23	−0.902980	−0.451490	+	0.892276i	$0.649107\pi$
$602$	−2.94661e21	−0.00696231
$603$	4.02639e22	0.0938033
$604$	2.63050e22	0.0604262
$605$	7.80706e23	1.76835
$606$	−1.85514e23	−0.414343
$607$	8.94890e22	0.197091	0.0985453	−	0.995133i	$-0.468581\pi$
$607$	8.94890e22	0.197091	0.0985453	+	0.995133i	$0.468581\pi$
$608$	−4.60398e23	−0.999892
$609$	9.71144e21	0.0207987
$610$	−1.82189e23	−0.384785
$611$	6.64835e21	0.0138473
$612$	6.87555e22	0.141228
$613$	7.69680e23	1.55918	0.779589	−	0.626291i	$-0.215428\pi$
$613$	7.69680e23	1.55918	0.779589	+	0.626291i	$0.215428\pi$
$614$	8.12007e22	0.162229
$615$	2.29462e23	0.452140
$616$	−9.06737e22	−0.176216
$617$	−2.30229e23	−0.441302	−0.220651	−	0.975353i	$-0.570818\pi$
$617$	−2.30229e23	−0.441302	−0.220651	+	0.975353i	$0.570818\pi$
$618$	3.15920e23	0.597275
$619$	1.24631e23	0.232410	0.116205	−	0.993225i	$-0.462927\pi$
$619$	1.24631e23	0.232410	0.116205	+	0.993225i	$0.462927\pi$
$620$	−3.19725e23	−0.588094
$621$	1.24100e23	0.225162
$622$	3.66247e23	0.655475
$623$	1.70178e20	0.000300438 0
$624$	−6.55481e21	−0.0114154
$625$	−6.85197e23	−1.17716
$626$	1.21545e23	0.205994
$627$	6.76839e23	1.13165
$628$	6.01188e23	0.991638
$629$	−6.15363e23	−1.00138
$630$	2.48688e22	0.0399264
$631$	−6.37007e23	−1.00901	−0.504504	−	0.863409i	$-0.668325\pi$
$631$	−6.37007e23	−1.00901	−0.504504	+	0.863409i	$0.668325\pi$
$632$	−1.11906e24	−1.74888
$633$	2.88422e23	0.444730
$634$	6.46166e23	0.983072
$635$	−3.38021e22	−0.0507419
$636$	9.98776e21	0.0147939
$637$	1.40283e23	0.205031
$638$	1.45649e23	0.210054
$639$	−1.37368e23	−0.195492
$640$	−6.68282e23	−0.938490
$641$	1.70637e23	0.236473	0.118236	−	0.992985i	$-0.462276\pi$
$641$	1.70637e23	0.236473	0.118236	+	0.992985i	$0.462276\pi$
$642$	6.44776e23	0.881782
$643$	3.81462e23	0.514822	0.257411	−	0.966302i	$-0.417130\pi$
$643$	3.81462e23	0.514822	0.257411	+	0.966302i	$0.417130\pi$
$644$	−1.20383e22	−0.0160338
$645$	7.61032e22	0.100033
$646$	−2.26641e23	−0.294010
$647$	2.43491e23	0.311742	0.155871	−	0.987777i	$-0.450182\pi$
$647$	2.43491e23	0.311742	0.155871	+	0.987777i	$0.450182\pi$
$648$	2.99073e23	0.377911
$649$	2.04252e24	2.54733
$650$	−7.69356e22	−0.0947030
$651$	−5.00337e22	−0.0607889
$652$	−3.49540e23	−0.419172
$653$	3.19453e23	0.378133	0.189066	−	0.981964i	$-0.439454\pi$
$653$	3.19453e23	0.378133	0.189066	+	0.981964i	$0.439454\pi$
$654$	5.49717e23	0.642285
$655$	−6.44932e23	−0.743811
$656$	2.86956e22	0.0326687
$657$	−8.11068e22	−0.0911490
$658$	4.20035e21	0.00465977
$659$	1.17216e24	1.28369	0.641846	−	0.766834i	$-0.278169\pi$
$659$	1.17216e24	1.28369	0.641846	+	0.766834i	$0.278169\pi$
$660$	9.22605e23	0.997452
$661$	−1.00976e24	−1.07772	−0.538859	−	0.842396i	$-0.681145\pi$
$661$	−1.00976e24	−1.07772	−0.538859	+	0.842396i	$0.681145\pi$
$662$	4.74524e23	0.499995
$663$	−7.65216e22	−0.0796011
$664$	−2.58451e23	−0.265430
$665$	1.52282e23	0.154406
$666$	5.01018e23	0.501560
$667$	4.90837e22	0.0485141
$668$	−7.55083e23	−0.736877
$669$	−7.21286e23	−0.695001
$670$	−1.80916e23	−0.172124
$671$	7.94319e23	0.746197
$672$	−9.82088e22	−0.0910985
$673$	−1.07312e24	−0.982926	−0.491463	−	0.870899i	$-0.663538\pi$
$673$	−1.07312e24	−0.982926	−0.491463	+	0.870899i	$0.663538\pi$
$674$	9.68278e22	0.0875772
$675$	−9.30828e23	−0.831357
$676$	7.05188e23	0.621954
$677$	−1.22686e24	−1.06854	−0.534269	−	0.845314i	$-0.679413\pi$
$677$	−1.22686e24	−1.06854	−0.534269	+	0.845314i	$0.679413\pi$
$678$	−7.86447e23	−0.676421
$679$	1.02860e23	0.0873684
$680$	−7.84178e23	−0.657792
$681$	−5.38674e23	−0.446247
$682$	−7.50389e23	−0.613930
$683$	1.15706e24	0.934931	0.467466	−	0.884011i	$-0.345167\pi$
$683$	1.15706e24	0.934931	0.467466	+	0.884011i	$0.345167\pi$
$684$	−3.42787e23	−0.273557
$685$	1.31407e23	0.103573
$686$	1.78516e23	0.138970
$687$	−4.43588e23	−0.341073
$688$	9.51713e21	0.00722777
$689$	8.34778e21	0.00626192
$690$	−1.67372e23	−0.124012
$691$	−6.38776e23	−0.467504	−0.233752	−	0.972296i	$-0.575100\pi$
$691$	−6.38776e23	−0.467504	−0.233752	+	0.972296i	$0.575100\pi$
$692$	1.06558e23	0.0770346
$693$	−1.08425e23	−0.0774276
$694$	−1.09244e24	−0.770624
$695$	2.37745e24	1.65669
$696$	2.49325e23	0.171628
$697$	3.34995e23	0.227803
$698$	−6.42372e23	−0.431535
$699$	−1.21446e24	−0.805982
$700$	9.02947e22	0.0592010
$701$	−1.14041e24	−0.738682	−0.369341	−	0.929294i	$-0.620417\pi$
$701$	−1.14041e24	−0.738682	−0.369341	+	0.929294i	$0.620417\pi$
$702$	2.07567e23	0.132829
$703$	3.06795e24	1.93967
$704$	−1.29542e24	−0.809174
$705$	−1.08484e23	−0.0669510
$706$	1.28306e24	0.782362
$707$	1.81976e23	0.109635
$708$	1.37746e24	0.819966
$709$	7.49981e23	0.441121	0.220560	−	0.975373i	$-0.429211\pi$
$709$	7.49981e23	0.441121	0.220560	+	0.975373i	$0.429211\pi$
$710$	6.17231e23	0.358717
$711$	−1.33814e24	−0.768439
$712$	4.36903e21	0.00247916
$713$	−2.52881e23	−0.141793
$714$	−4.83454e22	−0.0267868
$715$	7.71114e23	0.422199
$716$	−1.32424e24	−0.716486
$717$	−2.64176e24	−1.41247
$718$	−1.44477e24	−0.763379
$719$	−2.18102e24	−1.13884	−0.569422	−	0.822045i	$-0.692833\pi$
$719$	−2.18102e24	−1.13884	−0.569422	+	0.822045i	$0.692833\pi$
$720$	−8.03225e22	−0.0414487
$721$	−3.09895e23	−0.158039
$722$	−4.37726e22	−0.0220616
$723$	2.31286e24	1.15206
$724$	−1.67376e24	−0.823978
$725$	−3.68158e23	−0.179127
$726$	1.23569e24	0.594223
$727$	−3.72182e24	−1.76894	−0.884471	−	0.466596i	$-0.845480\pi$
$727$	−3.72182e24	−1.76894	−0.884471	+	0.466596i	$0.845480\pi$
$728$	−5.11090e22	−0.0240094
$729$	2.11515e24	0.982104
$730$	3.64434e23	0.167253
$731$	1.11104e23	0.0504002
$732$	5.35683e23	0.240195
$733$	1.32578e24	0.587608	0.293804	−	0.955866i	$-0.405079\pi$
$733$	1.32578e24	0.587608	0.293804	+	0.955866i	$0.405079\pi$
$734$	−9.08416e23	−0.397987
$735$	−2.28905e24	−0.991319
$736$	−4.96368e23	−0.212492
$737$	7.88770e23	0.333792
$738$	−2.72748e23	−0.114099
$739$	−2.41955e24	−1.00059	−0.500296	−	0.865854i	$-0.666776\pi$
$739$	−2.41955e24	−1.00059	−0.500296	+	0.865854i	$0.666776\pi$
$740$	4.18195e24	1.70966
$741$	3.81506e23	0.154186
$742$	5.27402e21	0.00210721
$743$	−6.58347e23	−0.260046	−0.130023	−	0.991511i	$-0.541505\pi$
$743$	−6.58347e23	−0.260046	−0.130023	+	0.991511i	$0.541505\pi$
$744$	−1.28453e24	−0.501620
$745$	2.40387e24	0.928074
$746$	−1.65531e24	−0.631829
$747$	−3.09047e23	−0.116627
$748$	1.34692e24	0.502550
$749$	−6.32480e23	−0.233320
$750$	−3.75219e23	−0.136856
$751$	3.07463e24	1.10880	0.554400	−	0.832250i	$-0.312948\pi$
$751$	3.07463e24	1.10880	0.554400	+	0.832250i	$0.312948\pi$
$752$	−1.35665e22	−0.00483744
$753$	4.24953e23	0.149825
$754$	8.20963e22	0.0286198
$755$	−3.58751e23	−0.123664
$756$	−2.43609e23	−0.0830345
$757$	−5.12790e24	−1.72832	−0.864162	−	0.503214i	$-0.832151\pi$
$757$	−5.12790e24	−1.72832	−0.864162	+	0.503214i	$0.832151\pi$
$758$	1.24367e24	0.414493
$759$	7.29719e23	0.240492
$760$	3.90959e24	1.27414
$761$	7.88950e23	0.254261	0.127131	−	0.991886i	$-0.459423\pi$
$761$	7.88950e23	0.254261	0.127131	+	0.991886i	$0.459423\pi$
$762$	−5.35016e22	−0.0170510
$763$	−5.39233e23	−0.169949
$764$	1.92384e24	0.599619
$765$	−9.37694e23	−0.289027
$766$	8.93942e23	0.272499
$767$	1.15128e24	0.347073
$768$	−2.40165e24	−0.716044
$769$	3.68265e24	1.08589	0.542946	−	0.839768i	$-0.317309\pi$
$769$	3.68265e24	1.08589	0.542946	+	0.839768i	$0.317309\pi$
$770$	4.87180e23	0.142075
$771$	2.86104e24	0.825203
$772$	−2.53337e23	−0.0722690
$773$	3.11513e24	0.878923	0.439462	−	0.898261i	$-0.355169\pi$
$773$	3.11513e24	0.878923	0.439462	+	0.898261i	$0.355169\pi$
$774$	−9.04591e22	−0.0252438
$775$	1.89676e24	0.523538
$776$	2.64076e24	0.720949
$777$	6.54432e23	0.176720
$778$	−6.35127e23	−0.169642
$779$	−1.67015e24	−0.441252
$780$	5.20034e23	0.135902
$781$	−2.69105e24	−0.695645
$782$	−2.44348e23	−0.0624815
$783$	9.93266e23	0.251241
$784$	−2.86259e23	−0.0716262
$785$	−8.19905e24	−2.02942
$786$	−1.02079e24	−0.249945
$787$	1.96026e24	0.474819	0.237409	−	0.971410i	$-0.423702\pi$
$787$	1.96026e24	0.474819	0.237409	+	0.971410i	$0.423702\pi$
$788$	3.56380e24	0.853966
$789$	−4.94750e24	−1.17282
$790$	6.01260e24	1.41004
$791$	7.71448e23	0.178981
$792$	−2.78362e24	−0.638920
$793$	4.47724e23	0.101669
$794$	−2.93382e24	−0.659113
$795$	−1.36214e23	−0.0302762
$796$	4.28978e24	0.943353
$797$	1.34462e24	0.292553	0.146276	−	0.989244i	$-0.453271\pi$
$797$	1.34462e24	0.292553	0.146276	+	0.989244i	$0.453271\pi$
$798$	2.41030e23	0.0518857
$799$	−1.58377e23	−0.0337321
$800$	3.72306e24	0.784576
$801$	5.22434e21	0.00108932
$802$	1.22722e24	0.253186
$803$	−1.58888e24	−0.324347
$804$	5.31941e23	0.107445
$805$	1.64180e23	0.0328136
$806$	−4.22963e23	−0.0836477
$807$	−4.25906e24	−0.833468
$808$	4.67193e24	0.904691
$809$	−3.12783e24	−0.599351	−0.299676	−	0.954041i	$-0.596878\pi$
$809$	−3.12783e24	−0.599351	−0.299676	+	0.954041i	$0.596878\pi$
$810$	−1.60689e24	−0.304693
$811$	3.49598e24	0.655981	0.327991	−	0.944681i	$-0.393629\pi$
$811$	3.49598e24	0.655981	0.327991	+	0.944681i	$0.393629\pi$
$812$	−9.63514e22	−0.0178909
$813$	−6.07999e24	−1.11721
$814$	9.81496e24	1.78477
$815$	4.76706e24	0.857850
$816$	1.56148e23	0.0278081
$817$	−5.53920e23	−0.0976246
$818$	2.73349e24	0.476775
$819$	−6.11145e22	−0.0105495
$820$	−2.27660e24	−0.388927
$821$	−1.08219e25	−1.82972	−0.914862	−	0.403767i	$-0.867701\pi$
$821$	−1.08219e25	−1.82972	−0.914862	+	0.403767i	$0.867701\pi$
$822$	2.07989e23	0.0348041
$823$	2.41902e24	0.400627	0.200314	−	0.979732i	$-0.435804\pi$
$823$	2.41902e24	0.400627	0.200314	+	0.979732i	$0.435804\pi$
$824$	−7.95603e24	−1.30411
$825$	−5.47333e24	−0.887959
$826$	7.27365e23	0.116794
$827$	1.49230e24	0.237170	0.118585	−	0.992944i	$-0.462164\pi$
$827$	1.49230e24	0.237170	0.118585	+	0.992944i	$0.462164\pi$
$828$	−3.69568e23	−0.0581349
$829$	3.70442e24	0.576776	0.288388	−	0.957514i	$-0.406881\pi$
$829$	3.70442e24	0.576776	0.288388	+	0.957514i	$0.406881\pi$
$830$	1.38863e24	0.214004
$831$	2.15636e24	0.328937
$832$	−7.30172e23	−0.110250
$833$	−3.34182e24	−0.499459
$834$	3.76299e24	0.556701
$835$	1.02979e25	1.50804
$836$	−6.71521e24	−0.973433
$837$	−5.11734e24	−0.734307
$838$	−5.65609e23	−0.0803419
$839$	6.44404e24	0.906111	0.453056	−	0.891482i	$-0.350334\pi$
$839$	6.44404e24	0.906111	0.453056	+	0.891482i	$0.350334\pi$
$840$	8.33965e23	0.116084
$841$	−6.86430e24	−0.945867
$842$	−1.30953e24	−0.178634
$843$	−6.88355e24	−0.929561
$844$	−2.86156e24	−0.382553
$845$	−9.61742e24	−1.27285
$846$	1.28948e23	0.0168953
$847$	−1.21213e24	−0.157231
$848$	−1.70343e22	−0.00218756
$849$	1.02377e25	1.30163
$850$	1.83276e24	0.230698
$851$	3.30764e24	0.412209
$852$	−1.81482e24	−0.223923
$853$	4.84828e24	0.592272	0.296136	−	0.955146i	$-0.404302\pi$
$853$	4.84828e24	0.592272	0.296136	+	0.955146i	$0.404302\pi$
$854$	2.82867e23	0.0342129
$855$	4.67496e24	0.559843
$856$	−1.62379e25	−1.92532
$857$	−1.51457e25	−1.77808	−0.889041	−	0.457828i	$-0.848627\pi$
$857$	−1.51457e25	−1.77808	−0.889041	+	0.457828i	$0.848627\pi$
$858$	1.22051e24	0.141873
$859$	7.72643e24	0.889277	0.444638	−	0.895710i	$-0.353332\pi$
$859$	7.72643e24	0.889277	0.444638	+	0.895710i	$0.353332\pi$
$860$	−7.55053e23	−0.0860479
$861$	−3.56264e23	−0.0402018
$862$	−4.44354e24	−0.496498
$863$	1.25270e25	1.38598	0.692989	−	0.720949i	$-0.256294\pi$
$863$	1.25270e25	1.38598	0.692989	+	0.720949i	$0.256294\pi$
$864$	−1.00446e25	−1.10044
$865$	−1.45325e24	−0.157654
$866$	−1.01587e25	−1.09128
$867$	−5.28142e24	−0.561809
$868$	4.96406e23	0.0522900
$869$	−2.62142e25	−2.73444
$870$	−1.33960e24	−0.138376
$871$	4.44596e23	0.0454791
$872$	−1.38439e25	−1.40239
$873$	3.15774e24	0.316778
$874$	1.21822e24	0.121026
$875$	3.68063e23	0.0362121
$876$	−1.07153e24	−0.104405
$877$	1.68202e25	1.62306	0.811531	−	0.584309i	$-0.198634\pi$
$877$	1.68202e25	1.62306	0.811531	+	0.584309i	$0.198634\pi$
$878$	−6.60201e24	−0.630918
$879$	1.39857e25	1.32367
$880$	−1.57352e24	−0.147492
$881$	7.00447e24	0.650249	0.325125	−	0.945671i	$-0.394594\pi$
$881$	7.00447e24	0.650249	0.325125	+	0.945671i	$0.394594\pi$
$882$	2.72085e24	0.250162
$883$	−1.04115e24	−0.0948083	−0.0474042	−	0.998876i	$-0.515095\pi$
$883$	−1.04115e24	−0.0948083	−0.0474042	+	0.998876i	$0.515095\pi$
$884$	7.59204e23	0.0684722
$885$	−1.87859e25	−1.67809
$886$	8.03918e24	0.711255
$887$	−1.80802e24	−0.158436	−0.0792178	−	0.996857i	$-0.525242\pi$
$887$	−1.80802e24	−0.158436	−0.0792178	+	0.996857i	$0.525242\pi$
$888$	1.68015e25	1.45827
$889$	5.24812e22	0.00451169
$890$	−2.34743e22	−0.00199884
$891$	7.00582e24	0.590879
$892$	7.15619e24	0.597834
$893$	7.89602e23	0.0653388
$894$	3.80482e24	0.311864
$895$	1.80602e25	1.46631
$896$	1.03758e24	0.0834453
$897$	4.11312e23	0.0327669
$898$	−1.17256e25	−0.925309
$899$	−2.02399e24	−0.158216
$900$	2.77199e24	0.214649
$901$	−1.98860e23	−0.0152541
$902$	−5.34313e24	−0.406013
$903$	−1.18158e23	−0.00889442
$904$	1.98056e25	1.47692
$905$	2.28269e25	1.68630
$906$	−5.67826e23	−0.0415552
$907$	2.09316e25	1.51754	0.758772	−	0.651357i	$-0.225800\pi$
$907$	2.09316e25	1.51754	0.758772	+	0.651357i	$0.225800\pi$
$908$	5.34441e24	0.383858
$909$	5.58655e24	0.397512
$910$	2.74603e23	0.0193577
$911$	2.50047e25	1.74629	0.873143	−	0.487463i	$-0.162078\pi$
$911$	2.50047e25	1.74629	0.873143	+	0.487463i	$0.162078\pi$
$912$	−7.78493e23	−0.0538640
$913$	−6.05424e24	−0.415010
$914$	−6.56448e24	−0.445818
$915$	−7.30569e24	−0.491566
$916$	4.40102e24	0.293388
$917$	1.00132e24	0.0661355
$918$	−4.94466e24	−0.323574
$919$	−2.00283e25	−1.29856	−0.649280	−	0.760550i	$-0.724930\pi$
$919$	−2.00283e25	−1.29856	−0.649280	+	0.760550i	$0.724930\pi$
$920$	4.21504e24	0.270773
$921$	3.25611e24	0.207249
$922$	−6.35656e24	−0.400875
$923$	−1.51683e24	−0.0947813
$924$	−1.43244e24	−0.0886879
$925$	−2.48093e25	−1.52198
$926$	8.66558e24	0.526750
$927$	−9.51356e24	−0.573014
$928$	−3.97279e24	−0.237104
$929$	2.45906e25	1.45424	0.727119	−	0.686511i	$-0.240859\pi$
$929$	2.45906e25	1.45424	0.727119	+	0.686511i	$0.240859\pi$
$930$	6.90165e24	0.404434
$931$	1.66609e25	0.967447
$932$	1.20491e25	0.693299
$933$	1.46864e25	0.837376
$934$	−1.30935e25	−0.739787
$935$	−1.83694e25	−1.02848
$936$	−1.56901e24	−0.0870525
$937$	−1.56446e25	−0.860156	−0.430078	−	0.902792i	$-0.641514\pi$
$937$	−1.56446e25	−0.860156	−0.430078	+	0.902792i	$0.641514\pi$
$938$	2.80890e23	0.0153043
$939$	4.87390e24	0.263160
$940$	1.07631e24	0.0575907
$941$	8.85617e24	0.469606	0.234803	−	0.972043i	$-0.424555\pi$
$941$	8.85617e24	0.469606	0.234803	+	0.972043i	$0.424555\pi$
$942$	−1.29774e25	−0.681952
$943$	−1.80063e24	−0.0937727
$944$	−2.34928e24	−0.121248
$945$	3.32237e24	0.169933
$946$	−1.77210e24	−0.0898281
$947$	2.92548e25	1.46968	0.734840	−	0.678241i	$-0.237257\pi$
$947$	2.92548e25	1.46968	0.734840	+	0.678241i	$0.237257\pi$
$948$	−1.76786e25	−0.880194
$949$	−8.95587e23	−0.0441922
$950$	−9.13738e24	−0.446860
$951$	2.59110e25	1.25588
$952$	1.21752e24	0.0584872
$953$	−1.22488e25	−0.583181	−0.291591	−	0.956543i	$-0.594185\pi$
$953$	−1.22488e25	−0.583181	−0.291591	+	0.956543i	$0.594185\pi$
$954$	1.61909e23	0.00764028
$955$	−2.62375e25	−1.22714
$956$	2.62100e25	1.21500
$957$	5.84047e24	0.268347
$958$	−2.03574e25	−0.927078
$959$	−2.04022e23	−0.00920915
$960$	1.19145e25	0.533053
$961$	−1.21225e25	−0.537578
$962$	5.53228e24	0.243173
$963$	−1.94167e25	−0.845964
$964$	−2.29469e25	−0.990991
$965$	3.45504e24	0.147901
$966$	2.59862e23	0.0110265
$967$	2.96647e25	1.24771	0.623856	−	0.781539i	$-0.285565\pi$
$967$	2.96647e25	1.24771	0.623856	+	0.781539i	$0.285565\pi$
$968$	−3.11193e25	−1.29745
$969$	−9.08821e24	−0.375601
$970$	−1.41885e25	−0.581270
$971$	−2.45367e25	−0.996444	−0.498222	−	0.867049i	$-0.666014\pi$
$971$	−2.45367e25	−0.996444	−0.498222	+	0.867049i	$0.666014\pi$
$972$	−1.27125e25	−0.511763
$973$	−3.69123e24	−0.147303
$974$	2.57786e23	0.0101978
$975$	−3.08509e24	−0.120984
$976$	−9.13617e23	−0.0355174
$977$	−9.53766e24	−0.367568	−0.183784	−	0.982967i	$-0.558835\pi$
$977$	−9.53766e24	−0.367568	−0.183784	+	0.982967i	$0.558835\pi$
$978$	7.54525e24	0.288266
$979$	1.02345e23	0.00387627
$980$	2.27107e25	0.852724
$981$	−1.65541e25	−0.616196
$982$	1.20455e25	0.444506
$983$	4.22312e25	1.54500	0.772500	−	0.635014i	$-0.219006\pi$
$983$	4.22312e25	1.54500	0.772500	+	0.635014i	$0.219006\pi$
$984$	−9.14648e24	−0.331738
$985$	−4.86034e25	−1.74767
$986$	−1.95569e24	−0.0697183
$987$	1.68432e23	0.00595291
$988$	−3.78508e24	−0.132630
$989$	−5.97196e23	−0.0207467
$990$	1.49561e25	0.515133
$991$	2.05994e25	0.703444	0.351722	−	0.936104i	$-0.385596\pi$
$991$	2.05994e25	0.703444	0.351722	+	0.936104i	$0.385596\pi$
$992$	2.04680e25	0.692988
$993$	1.90282e25	0.638749
$994$	−9.58315e23	−0.0318951
$995$	−5.85044e25	−1.93060
$996$	−4.08294e24	−0.133588
$997$	−3.53138e24	−0.114561	−0.0572803	−	0.998358i	$-0.518243\pi$
$997$	−3.53138e24	−0.114561	−0.0572803	+	0.998358i	$0.518243\pi$
$998$	−3.34281e25	−1.07523
$999$	6.69340e25	2.13471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.18.a.a.1.10	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.18.a.a.1.10	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q+214.166 q^{2} +8587.97 q^{3} -85204.9 q^{4} +1.16203e6 q^{5} +1.83925e6 q^{6} -1.80417e6 q^{7} -4.63192e7 q^{8} -5.53869e7 q^{9} +O(q^{10})\)	\(q+214.166 q^{2} +8587.97 q^{3} -85204.9 q^{4} +1.16203e6 q^{5} +1.83925e6 q^{6} -1.80417e6 q^{7} -4.63192e7 q^{8} -5.53869e7 q^{9} +2.48868e8 q^{10} -1.08503e9 q^{11} -7.31737e8 q^{12} -6.11587e8 q^{13} -3.86393e8 q^{14} +9.97950e9 q^{15} +1.24799e9 q^{16} +1.45692e10 q^{17} -1.18620e10 q^{18} -7.26361e10 q^{19} -9.90109e10 q^{20} -1.54942e10 q^{21} -2.32377e11 q^{22} -7.83110e10 q^{23} -3.97788e11 q^{24} +5.87380e11 q^{25} -1.30981e11 q^{26} -1.58471e12 q^{27} +1.53725e11 q^{28} -6.26780e11 q^{29} +2.13727e12 q^{30} +3.22919e12 q^{31} +6.33842e12 q^{32} -9.31822e12 q^{33} +3.12023e12 q^{34} -2.09651e12 q^{35} +4.71924e12 q^{36} -4.22373e13 q^{37} -1.55562e13 q^{38} -5.25229e12 q^{39} -5.38244e13 q^{40} +2.29934e13 q^{41} -3.31833e12 q^{42} +7.62596e12 q^{43} +9.24500e13 q^{44} -6.43614e13 q^{45} -1.67715e13 q^{46} -1.08707e13 q^{47} +1.07177e13 q^{48} -2.29375e14 q^{49} +1.25797e14 q^{50} +1.25120e14 q^{51} +5.21102e13 q^{52} -1.36494e13 q^{53} -3.39392e14 q^{54} -1.26084e15 q^{55} +8.35678e13 q^{56} -6.23796e14 q^{57} -1.34235e14 q^{58} -1.88245e15 q^{59} -8.50302e14 q^{60} -7.32070e14 q^{61} +6.91582e14 q^{62} +9.99277e13 q^{63} +1.19390e15 q^{64} -7.10683e14 q^{65} -1.99564e15 q^{66} -7.26956e14 q^{67} -1.24137e15 q^{68} -6.72532e14 q^{69} -4.49001e14 q^{70} +2.48016e15 q^{71} +2.56548e15 q^{72} +1.46437e15 q^{73} -9.04579e15 q^{74} +5.04440e15 q^{75} +6.18895e15 q^{76} +1.95759e15 q^{77} -1.12486e15 q^{78} +2.41598e16 q^{79} +1.45021e15 q^{80} -6.45679e15 q^{81} +4.92440e15 q^{82} +5.57979e15 q^{83} +1.32018e15 q^{84} +1.69299e16 q^{85} +1.63322e15 q^{86} -5.38276e15 q^{87} +5.02577e16 q^{88} -9.43245e13 q^{89} -1.37840e16 q^{90} +1.10341e15 q^{91} +6.67248e15 q^{92} +2.77322e16 q^{93} -2.32813e15 q^{94} -8.44055e16 q^{95} +5.44342e16 q^{96} -5.70123e16 q^{97} -4.91244e16 q^{98} +6.00966e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9} - 312719540 q^{10} - 45399620 q^{11} - 8621310628 q^{12} - 10510197306 q^{13} - 12286634640 q^{14} - 16443659490 q^{15} + 65383333632 q^{16} - 35705720330 q^{17} + 27658188862 q^{18} - 84895273414 q^{19} + 331348024336 q^{20} + 185190266362 q^{21} + 270540900120 q^{22} - 1096353793934 q^{23} + 1697198124384 q^{24} + 525715171346 q^{25} + 4272672484934 q^{26} - 3706093330604 q^{27} - 9883598189096 q^{28} - 4114009788386 q^{29} - 14194804268004 q^{30} + 3718266369468 q^{31} - 29197309605632 q^{32} - 16110579243626 q^{33} - 31423174598564 q^{34} + 13804822380504 q^{35} + 51950006703548 q^{36} - 58067881808868 q^{37} - 76590705469880 q^{38} + 69866971570764 q^{39} - 129282722434320 q^{40} - 74370388815170 q^{41} - 430581394397552 q^{42} - 127444248270174 q^{43} - 563872902913048 q^{44} - 602432292081270 q^{45} - 749727107945564 q^{47} - 17\!\cdots\!72 q^{48}+ \cdots + 35\!\cdots\!38 q^{99}+O(q^{100}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9 - 312719540 * q^10 - 45399620 * q^11 - 8621310628 * q^12 - 10510197306 * q^13 - 12286634640 * q^14 - 16443659490 * q^15 + 65383333632 * q^16 - 35705720330 * q^17 + 27658188862 * q^18 - 84895273414 * q^19 + 331348024336 * q^20 + 185190266362 * q^21 + 270540900120 * q^22 - 1096353793934 * q^23 + 1697198124384 * q^24 + 525715171346 * q^25 + 4272672484934 * q^26 - 3706093330604 * q^27 - 9883598189096 * q^28 - 4114009788386 * q^29 - 14194804268004 * q^30 + 3718266369468 * q^31 - 29197309605632 * q^32 - 16110579243626 * q^33 - 31423174598564 * q^34 + 13804822380504 * q^35 + 51950006703548 * q^36 - 58067881808868 * q^37 - 76590705469880 * q^38 + 69866971570764 * q^39 - 129282722434320 * q^40 - 74370388815170 * q^41 - 430581394397552 * q^42 - 127444248270174 * q^43 - 563872902913048 * q^44 - 602432292081270 * q^45 - 749727107945564 * q^47 - 1762369490938672 * q^48 - 560241909258462 * q^49 - 1212733967351616 * q^50 - 2013927378521294 * q^51 - 3438555393950964 * q^52 - 1954645162253818 * q^53 - 2748549190422938 * q^54 - 2426218557075404 * q^55 - 1321001371084560 * q^56 - 2335835167092904 * q^57 - 340295461037046 * q^58 - 1561709417167508 * q^59 - 7486616247365616 * q^60 - 679115861109266 * q^61 - 12552327168177062 * q^62 - 10591353756704576 * q^63 - 6775416249353536 * q^64 - 6252697705990982 * q^65 - 20881430274671372 * q^66 - 7577612038827396 * q^67 + 2901964856169680 * q^68 + 833228883389840 * q^69 - 10700966230255240 * q^70 + 25039332312392368 * q^71 - 7954969753997256 * q^72 - 18720848443128734 * q^73 - 6297551300657404 * q^74 + 22553223201966436 * q^75 + 34141945529937952 * q^76 + 35092380107507048 * q^77 + 27963841408286022 * q^78 + 965348846593408 * q^79 + 36943919850262880 * q^80 + 51275234750545798 * q^81 + 106728632435914846 * q^82 + 65089411455584544 * q^83 + 189770883431502392 * q^84 + 20919534362994588 * q^85 + 86205449672049764 * q^86 + 130649890213719716 * q^87 + 164304846335490592 * q^88 - 61322357257717500 * q^89 + 237420523836214152 * q^90 + 181977537844157150 * q^91 - 61586264776507392 * q^92 - 71304974484877430 * q^93 - 14005510384703054 * q^94 + 123323286964112684 * q^95 + 566787465801380768 * q^96 - 67350702995984898 * q^97 + 134333537201072600 * q^98 + 353912447692290838 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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