LMFDB - Embedded newform 23.18.a.a.1.1

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			1.1
Root			$346.114$ 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)

$f(q)$	$=$	$q-692.227 q^{2} -17580.4 q^{3} +348107. q^{4} -370975. q^{5} +1.21696e7 q^{6} -1.89338e7 q^{7} -1.50237e8 q^{8} +1.79930e8 q^{9} +O(q^{10})$	\(q-692.227 q^{2} -17580.4 q^{3} +348107. q^{4} -370975. q^{5} +1.21696e7 q^{6} -1.89338e7 q^{7} -1.50237e8 q^{8} +1.79930e8 q^{9} +2.56799e8 q^{10} -7.06381e8 q^{11} -6.11985e9 q^{12} -5.49482e9 q^{13} +1.31065e10 q^{14} +6.52189e9 q^{15} +5.83713e10 q^{16} +3.24998e10 q^{17} -1.24552e11 q^{18} +5.30857e10 q^{19} -1.29139e11 q^{20} +3.32864e11 q^{21} +4.88976e11 q^{22} -7.83110e10 q^{23} +2.64123e12 q^{24} -6.25317e11 q^{25} +3.80366e12 q^{26} -8.92903e11 q^{27} -6.59099e12 q^{28} +9.57645e11 q^{29} -4.51463e12 q^{30} +7.20224e12 q^{31} -2.07143e13 q^{32} +1.24185e13 q^{33} -2.24973e13 q^{34} +7.02399e12 q^{35} +6.26348e13 q^{36} -2.15693e12 q^{37} -3.67474e13 q^{38} +9.66010e13 q^{39} +5.57343e13 q^{40} +1.31458e13 q^{41} -2.30418e14 q^{42} -2.62614e13 q^{43} -2.45896e14 q^{44} -6.67495e13 q^{45} +5.42090e13 q^{46} +3.96913e13 q^{47} -1.02619e15 q^{48} +1.25860e14 q^{49} +4.32861e14 q^{50} -5.71359e14 q^{51} -1.91278e15 q^{52} +6.70350e14 q^{53} +6.18092e14 q^{54} +2.62050e14 q^{55} +2.84457e15 q^{56} -9.33268e14 q^{57} -6.62908e14 q^{58} +1.83109e15 q^{59} +2.27031e15 q^{60} -1.19609e15 q^{61} -4.98559e15 q^{62} -3.40676e15 q^{63} +6.68816e15 q^{64} +2.03844e15 q^{65} -8.59639e15 q^{66} +3.90718e14 q^{67} +1.13134e16 q^{68} +1.37674e15 q^{69} -4.86220e15 q^{70} +9.30115e14 q^{71} -2.70322e16 q^{72} +6.13089e15 q^{73} +1.49308e15 q^{74} +1.09933e16 q^{75} +1.84795e16 q^{76} +1.33745e16 q^{77} -6.68699e16 q^{78} -1.88205e16 q^{79} -2.16543e16 q^{80} -7.53860e15 q^{81} -9.09986e15 q^{82} +2.86144e16 q^{83} +1.15872e17 q^{84} -1.20566e16 q^{85} +1.81788e16 q^{86} -1.68358e16 q^{87} +1.06125e17 q^{88} -6.45469e16 q^{89} +4.62058e16 q^{90} +1.04038e17 q^{91} -2.72606e16 q^{92} -1.26618e17 q^{93} -2.74754e16 q^{94} -1.96935e16 q^{95} +3.64165e17 q^{96} -8.58879e16 q^{97} -8.71236e16 q^{98} -1.27099e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−692.227	−1.91203	−0.956013	−	0.293325i	$-0.905238\pi$
$2$	−692.227	−1.91203	−0.956013	+	0.293325i	$0.905238\pi$
$3$	−17580.4	−1.54703	−0.773513	−	0.633780i	$-0.781502\pi$
$3$	−17580.4	−1.54703	−0.773513	+	0.633780i	$0.781502\pi$
$4$	348107.	2.65584
$5$	−370975.	−0.424717	−0.212359	−	0.977192i	$-0.568115\pi$
$5$	−370975.	−0.424717	−0.212359	+	0.977192i	$0.568115\pi$
$6$	1.21696e7	2.95795
$7$	−1.89338e7	−1.24138	−0.620691	−	0.784055i	$-0.713148\pi$
$7$	−1.89338e7	−1.24138	−0.620691	+	0.784055i	$0.713148\pi$
$8$	−1.50237e8	−3.16601
$9$	1.79930e8	1.39329
$10$	2.56799e8	0.812070
$11$	−7.06381e8	−0.993576	−0.496788	−	0.867872i	$-0.665487\pi$
$11$	−7.06381e8	−0.993576	−0.496788	+	0.867872i	$0.665487\pi$
$12$	−6.11985e9	−4.10866
$13$	−5.49482e9	−1.86825	−0.934125	−	0.356947i	$-0.883818\pi$
$13$	−5.49482e9	−1.86825	−0.934125	+	0.356947i	$0.883818\pi$
$14$	1.31065e10	2.37355
$15$	6.52189e9	0.657049
$16$	5.83713e10	3.39766
$17$	3.24998e10	1.12997	0.564983	−	0.825103i	$-0.308883\pi$
$17$	3.24998e10	1.12997	0.564983	+	0.825103i	$0.308883\pi$
$18$	−1.24552e11	−2.66401
$19$	5.30857e10	0.717088	0.358544	−	0.933513i	$-0.383273\pi$
$19$	5.30857e10	0.717088	0.358544	+	0.933513i	$0.383273\pi$
$20$	−1.29139e11	−1.12798
$21$	3.32864e11	1.92045
$22$	4.88976e11	1.89974
$23$	−7.83110e10	−0.208514
$23$	−7.83110e10	−0.208514
$24$	2.64123e12	4.89791
$25$	−6.25317e11	−0.819615
$26$	3.80366e12	3.57214
$27$	−8.92903e11	−0.608432
$28$	−6.59099e12	−3.29691
$29$	9.57645e11	0.355485	0.177743	−	0.984077i	$-0.443121\pi$
$29$	9.57645e11	0.355485	0.177743	+	0.984077i	$0.443121\pi$
$30$	−4.51463e12	−1.25629
$31$	7.20224e12	1.51668	0.758339	−	0.651860i	$-0.226011\pi$
$31$	7.20224e12	1.51668	0.758339	+	0.651860i	$0.226011\pi$
$32$	−2.07143e13	−3.33039
$33$	1.24185e13	1.53709
$34$	−2.24973e13	−2.16052
$35$	7.02399e12	0.527236
$36$	6.26348e13	3.70036
$37$	−2.15693e12	−0.100953	−0.0504767	−	0.998725i	$-0.516074\pi$
$37$	−2.15693e12	−0.100953	−0.0504767	+	0.998725i	$0.516074\pi$
$38$	−3.67474e13	−1.37109
$39$	9.66010e13	2.89023
$40$	5.57343e13	1.34466
$41$	1.31458e13	0.257113	0.128556	−	0.991702i	$-0.458966\pi$
$41$	1.31458e13	0.257113	0.128556	+	0.991702i	$0.458966\pi$
$42$	−2.30418e14	−3.67195
$43$	−2.62614e13	−0.342638	−0.171319	−	0.985216i	$-0.554803\pi$
$43$	−2.62614e13	−0.342638	−0.171319	+	0.985216i	$0.554803\pi$
$44$	−2.45896e14	−2.63878
$45$	−6.67495e13	−0.591755
$46$	5.42090e13	0.398685
$47$	3.96913e13	0.243144	0.121572	−	0.992583i	$-0.461207\pi$
$47$	3.96913e13	0.243144	0.121572	+	0.992583i	$0.461207\pi$
$48$	−1.02619e15	−5.25626
$49$	1.25860e14	0.541029
$50$	4.32861e14	1.56713
$51$	−5.71359e14	−1.74809
$52$	−1.91278e15	−4.96178
$53$	6.70350e14	1.47896	0.739481	−	0.673178i	$-0.235071\pi$
$53$	6.70350e14	1.47896	0.739481	+	0.673178i	$0.235071\pi$
$54$	6.18092e14	1.16334
$55$	2.62050e14	0.421989
$56$	2.84457e15	3.93023
$57$	−9.33268e14	−1.10935
$58$	−6.62908e14	−0.679697
$59$	1.83109e15	1.62356	0.811780	−	0.583964i	$-0.198499\pi$
$59$	1.83109e15	1.62356	0.811780	+	0.583964i	$0.198499\pi$
$60$	2.27031e15	1.74502
$61$	−1.19609e15	−0.798843	−0.399421	−	0.916768i	$-0.630789\pi$
$61$	−1.19609e15	−0.798843	−0.399421	+	0.916768i	$0.630789\pi$
$62$	−4.98559e15	−2.89993
$63$	−3.40676e15	−1.72961
$64$	6.68816e15	2.97014
$65$	2.03844e15	0.793478
$66$	−8.59639e15	−2.93895
$67$	3.90718e14	0.117551	0.0587757	−	0.998271i	$-0.481280\pi$
$67$	3.90718e14	0.117551	0.0587757	+	0.998271i	$0.481280\pi$
$68$	1.13134e16	3.00101
$69$	1.37674e15	0.322577
$70$	−4.86220e15	−1.00809
$71$	9.30115e14	0.170939	0.0854694	−	0.996341i	$-0.472761\pi$
$71$	9.30115e14	0.170939	0.0854694	+	0.996341i	$0.472761\pi$
$72$	−2.70322e16	−4.41118
$73$	6.13089e15	0.889773	0.444887	−	0.895587i	$-0.353244\pi$
$73$	6.13089e15	0.889773	0.444887	+	0.895587i	$0.353244\pi$
$74$	1.49308e15	0.193026
$75$	1.09933e16	1.26797
$76$	1.84795e16	1.90447
$77$	1.33745e16	1.23341
$78$	−6.68699e16	−5.52620
$79$	−1.88205e16	−1.39573	−0.697863	−	0.716232i	$-0.745865\pi$
$79$	−1.88205e16	−1.39573	−0.697863	+	0.716232i	$0.745865\pi$
$80$	−2.16543e16	−1.44304
$81$	−7.53860e15	−0.452031
$82$	−9.09986e15	−0.491606
$83$	2.86144e16	1.39451	0.697253	−	0.716826i	$-0.254406\pi$
$83$	2.86144e16	1.39451	0.697253	+	0.716826i	$0.254406\pi$
$84$	1.15872e17	5.10041
$85$	−1.20566e16	−0.479916
$86$	1.81788e16	0.655133
$87$	−1.68358e16	−0.549945
$88$	1.06125e17	3.14567
$89$	−6.45469e16	−1.73804	−0.869022	−	0.494774i	$-0.835251\pi$
$89$	−6.45469e16	−1.73804	−0.869022	+	0.494774i	$0.835251\pi$
$90$	4.62058e16	1.13145
$91$	1.04038e17	2.31921
$92$	−2.72606e16	−0.553781
$93$	−1.26618e17	−2.34634
$94$	−2.74754e16	−0.464897
$95$	−1.96935e16	−0.304560
$96$	3.64165e17	5.15220
$97$	−8.58879e16	−1.11268	−0.556342	−	0.830953i	$-0.687796\pi$
$97$	−8.58879e16	−1.11268	−0.556342	+	0.830953i	$0.687796\pi$
$98$	−8.71236e16	−1.03446
$99$	−1.27099e17	−1.38434
$100$	−2.17677e17	−2.17677
$101$	2.04570e16	0.187979	0.0939897	−	0.995573i	$-0.470038\pi$
$101$	2.04570e16	0.187979	0.0939897	+	0.995573i	$0.470038\pi$
$102$	3.95510e17	3.34239
$103$	7.12946e16	0.554550	0.277275	−	0.960791i	$-0.410569\pi$
$103$	7.12946e16	0.554550	0.277275	+	0.960791i	$0.410569\pi$
$104$	8.25526e17	5.91490
$105$	−1.23484e17	−0.815649
$106$	−4.64035e17	−2.82781
$107$	1.87888e17	1.05715	0.528576	−	0.848886i	$-0.322726\pi$
$107$	1.87888e17	1.05715	0.528576	+	0.848886i	$0.322726\pi$
$108$	−3.10825e17	−1.61590
$109$	7.37013e15	0.0354282	0.0177141	−	0.999843i	$-0.494361\pi$
$109$	7.37013e15	0.0354282	0.0177141	+	0.999843i	$0.494361\pi$
$110$	−1.81398e17	−0.806854
$111$	3.79196e16	0.156178
$112$	−1.10519e18	−4.21779
$113$	−5.51859e17	−1.95282	−0.976408	−	0.215935i	$-0.930720\pi$
$113$	−5.51859e17	−1.95282	−0.976408	+	0.215935i	$0.930720\pi$
$114$	6.46033e17	2.12111
$115$	2.90514e16	0.0885597
$116$	3.33362e17	0.944112
$117$	−9.88682e17	−2.60302
$118$	−1.26753e18	−3.10429
$119$	−6.15346e17	−1.40272
$120$	−9.79831e17	−2.08023
$121$	−6.47292e15	−0.0128063
$122$	8.27968e17	1.52741
$123$	−2.31108e17	−0.397760
$124$	2.50715e18	4.02806
$125$	5.15009e17	0.772822
$126$	2.35825e18	3.30705
$127$	−3.37119e17	−0.442030	−0.221015	−	0.975270i	$-0.570937\pi$
$127$	−3.37119e17	−0.442030	−0.221015	+	0.975270i	$0.570937\pi$
$128$	−1.91466e18	−2.34859
$129$	4.61685e17	0.530070
$130$	−1.41107e18	−1.51715
$131$	3.04947e17	0.307198	0.153599	−	0.988133i	$-0.450914\pi$
$131$	3.04947e17	0.307198	0.153599	+	0.988133i	$0.450914\pi$
$132$	4.32294e18	4.08227
$133$	−1.00512e18	−0.890180
$134$	−2.70466e17	−0.224761
$135$	3.31245e17	0.258412
$136$	−4.88268e18	−3.57748
$137$	1.13807e18	0.783509	0.391755	−	0.920070i	$-0.371868\pi$
$137$	1.13807e18	0.783509	0.391755	+	0.920070i	$0.371868\pi$
$138$	−9.53015e17	−0.616776
$139$	−2.09575e18	−1.27559	−0.637797	−	0.770204i	$-0.720154\pi$
$139$	−2.09575e18	−1.27559	−0.637797	+	0.770204i	$0.720154\pi$
$140$	2.44510e18	1.40026
$141$	−6.97788e17	−0.376150
$142$	−6.43851e17	−0.326839
$143$	3.88144e18	1.85625
$144$	1.05027e19	4.73392
$145$	−3.55263e17	−0.150981
$146$	−4.24397e18	−1.70127
$147$	−2.21266e18	−0.836986
$148$	−7.50841e17	−0.268116
$149$	2.74525e17	0.0925760	0.0462880	−	0.998928i	$-0.485261\pi$
$149$	2.74525e17	0.0925760	0.0462880	+	0.998928i	$0.485261\pi$
$150$	−7.60987e18	−2.42438
$151$	−1.35255e18	−0.407238	−0.203619	−	0.979050i	$-0.565270\pi$
$151$	−1.35255e18	−0.407238	−0.203619	+	0.979050i	$0.565270\pi$
$152$	−7.97545e18	−2.27031
$153$	5.84769e18	1.57437
$154$	−9.25820e18	−2.35831
$155$	−2.67185e18	−0.644159
$156$	3.36275e19	7.67600
$157$	−3.38933e18	−0.732769	−0.366384	−	0.930464i	$-0.619404\pi$
$157$	−3.38933e18	−0.732769	−0.366384	+	0.930464i	$0.619404\pi$
$158$	1.30280e19	2.66866
$159$	−1.17850e19	−2.28799
$160$	7.68449e18	1.41447
$161$	1.48273e18	0.258846
$162$	5.21842e18	0.864294
$163$	5.53606e18	0.870174	0.435087	−	0.900388i	$-0.356718\pi$
$163$	5.53606e18	0.870174	0.435087	+	0.900388i	$0.356718\pi$
$164$	4.57613e18	0.682850
$165$	−4.60694e18	−0.652828
$166$	−1.98076e19	−2.66633
$167$	1.31548e18	0.168265	0.0841326	−	0.996455i	$-0.473188\pi$
$167$	1.31548e18	0.168265	0.0841326	+	0.996455i	$0.473188\pi$
$168$	−5.00086e19	−6.08017
$169$	2.15426e19	2.49036
$170$	8.34593e18	0.917611
$171$	9.55171e18	0.999112
$172$	−9.14176e18	−0.909993
$173$	4.50184e18	0.426578	0.213289	−	0.976989i	$-0.431582\pi$
$173$	4.50184e18	0.426578	0.213289	+	0.976989i	$0.431582\pi$
$174$	1.16542e19	1.05151
$175$	1.18396e19	1.01746
$176$	−4.12324e19	−3.37583
$177$	−3.21913e19	−2.51169
$178$	4.46811e19	3.32318
$179$	1.64257e19	1.16486	0.582430	−	0.812881i	$-0.302102\pi$
$179$	1.64257e19	1.16486	0.582430	+	0.812881i	$0.302102\pi$
$180$	−2.32360e19	−1.57161
$181$	2.02404e19	1.30603	0.653013	−	0.757346i	$-0.273505\pi$
$181$	2.02404e19	1.30603	0.653013	+	0.757346i	$0.273505\pi$
$182$	−7.20180e19	−4.43439
$183$	2.10278e19	1.23583
$184$	1.17652e19	0.660159
$185$	8.00167e17	0.0428767
$186$	8.76486e19	4.48626
$187$	−2.29572e19	−1.12271
$188$	1.38168e19	0.645751
$189$	1.69061e19	0.755297
$190$	1.36324e19	0.582326
$191$	−7.04024e18	−0.287610	−0.143805	−	0.989606i	$-0.545934\pi$
$191$	−7.04024e18	−0.287610	−0.143805	+	0.989606i	$0.545934\pi$
$192$	−1.17580e20	−4.59488
$193$	−1.89457e19	−0.708393	−0.354196	−	0.935171i	$-0.615246\pi$
$193$	−1.89457e19	−0.708393	−0.354196	+	0.935171i	$0.615246\pi$
$194$	5.94539e19	2.12748
$195$	−3.58366e19	−1.22753
$196$	4.38126e19	1.43689
$197$	−1.69463e19	−0.532245	−0.266122	−	0.963939i	$-0.585743\pi$
$197$	−1.69463e19	−0.532245	−0.266122	+	0.963939i	$0.585743\pi$
$198$	8.79814e19	2.64690
$199$	5.95992e18	0.171787	0.0858933	−	0.996304i	$-0.472626\pi$
$199$	5.95992e18	0.171787	0.0858933	+	0.996304i	$0.472626\pi$
$200$	9.39459e19	2.59491
$201$	−6.86898e18	−0.181855
$202$	−1.41609e19	−0.359421
$203$	−1.81319e19	−0.441293
$204$	−1.98894e20	−4.64264
$205$	−4.87676e18	−0.109200
$206$	−4.93521e19	−1.06031
$207$	−1.40905e19	−0.290521
$208$	−3.20740e20	−6.34767
$209$	−3.74988e19	−0.712481
$210$	8.54793e19	1.55954
$211$	8.37209e19	1.46701	0.733505	−	0.679684i	$-0.237883\pi$
$211$	8.37209e19	1.46701	0.733505	+	0.679684i	$0.237883\pi$
$212$	2.33353e20	3.92789
$213$	−1.63518e19	−0.264447
$214$	−1.30061e20	−2.02130
$215$	9.74233e18	0.145524
$216$	1.34147e20	1.92630
$217$	−1.36366e20	−1.88278
$218$	−5.10180e18	−0.0677397
$219$	−1.07783e20	−1.37650
$220$	9.12213e19	1.12074
$221$	−1.78581e20	−2.11106
$222$	−2.62490e19	−0.298616
$223$	−4.15607e19	−0.455084	−0.227542	−	0.973768i	$-0.573069\pi$
$223$	−4.15607e19	−0.455084	−0.227542	+	0.973768i	$0.573069\pi$
$224$	3.92201e20	4.13429
$225$	−1.12513e20	−1.14196
$226$	3.82012e20	3.73383
$227$	−4.17824e19	−0.393345	−0.196672	−	0.980469i	$-0.563014\pi$
$227$	−4.17824e19	−0.393345	−0.196672	+	0.980469i	$0.563014\pi$
$228$	−3.24877e20	−2.94627
$229$	2.19894e20	1.92137	0.960685	−	0.277641i	$-0.0895525\pi$
$229$	2.19894e20	1.92137	0.960685	+	0.277641i	$0.0895525\pi$
$230$	−2.01102e19	−0.169328
$231$	−2.35129e20	−1.90811
$232$	−1.43874e20	−1.12547
$233$	1.75793e20	1.32580	0.662898	−	0.748710i	$-0.269326\pi$
$233$	1.75793e20	1.32580	0.662898	+	0.748710i	$0.269326\pi$
$234$	6.84393e20	4.97703
$235$	−1.47245e19	−0.103267
$236$	6.37415e20	4.31192
$237$	3.30871e20	2.15922
$238$	4.25959e20	2.68203
$239$	−3.67473e19	−0.223277	−0.111638	−	0.993749i	$-0.535610\pi$
$239$	−3.67473e19	−0.223277	−0.111638	+	0.993749i	$0.535610\pi$
$240$	3.80691e20	2.23243
$241$	−2.33567e20	−1.32211	−0.661054	−	0.750339i	$-0.729890\pi$
$241$	−2.33567e20	−1.32211	−0.661054	+	0.750339i	$0.729890\pi$
$242$	4.48073e18	0.0244860
$243$	2.47841e20	1.30774
$244$	−4.16368e20	−2.12160
$245$	−4.66909e19	−0.229784
$246$	1.59979e20	0.760527
$247$	−2.91697e20	−1.33970
$248$	−1.08204e21	−4.80182
$249$	−5.03051e20	−2.15734
$250$	−3.56503e20	−1.47766
$251$	−2.44658e19	−0.0980239	−0.0490120	−	0.998798i	$-0.515607\pi$
$251$	−2.44658e19	−0.0980239	−0.0490120	+	0.998798i	$0.515607\pi$
$252$	−1.18592e21	−4.59356
$253$	5.53174e19	0.207175
$254$	2.33363e20	0.845173
$255$	2.11960e20	0.742442
$256$	4.48750e20	1.52043
$257$	−4.70618e20	−1.54254	−0.771271	−	0.636506i	$-0.780379\pi$
$257$	−4.70618e20	−1.54254	−0.771271	+	0.636506i	$0.780379\pi$
$258$	−3.19591e20	−1.01351
$259$	4.08389e19	0.125322
$260$	7.09595e20	2.10735
$261$	1.72309e20	0.495294
$262$	−2.11093e20	−0.587371
$263$	2.03103e20	0.547132	0.273566	−	0.961853i	$-0.411797\pi$
$263$	2.03103e20	0.547132	0.273566	+	0.961853i	$0.411797\pi$
$264$	−1.86571e21	−4.86644
$265$	−2.48683e20	−0.628141
$266$	6.95769e20	1.70205
$267$	1.13476e21	2.68880
$268$	1.36012e20	0.312198
$269$	−2.57682e20	−0.573047	−0.286523	−	0.958073i	$-0.592500\pi$
$269$	−2.57682e20	−0.573047	−0.286523	+	0.958073i	$0.592500\pi$
$270$	−2.29297e20	−0.494090
$271$	1.20330e20	0.251267	0.125633	−	0.992077i	$-0.459904\pi$
$271$	1.20330e20	0.251267	0.125633	+	0.992077i	$0.459904\pi$
$272$	1.89706e21	3.83923
$273$	−1.82903e21	−3.58788
$274$	−7.87803e20	−1.49809
$275$	4.41712e20	0.814350
$276$	4.79251e20	0.856715
$277$	−7.46399e18	−0.0129388	−0.00646938	−	0.999979i	$-0.502059\pi$
$277$	−7.46399e18	−0.0129388	−0.00646938	+	0.999979i	$0.502059\pi$
$278$	1.45073e21	2.43897
$279$	1.29590e21	2.11317
$280$	−1.05526e21	−1.66924
$281$	−6.18253e20	−0.948773	−0.474386	−	0.880317i	$-0.657330\pi$
$281$	−6.18253e20	−0.948773	−0.474386	+	0.880317i	$0.657330\pi$
$282$	4.83028e20	0.719208
$283$	−1.21311e21	−1.75273	−0.876365	−	0.481648i	$-0.840038\pi$
$283$	−1.21311e21	−1.75273	−0.876365	+	0.481648i	$0.840038\pi$
$284$	3.23779e20	0.453986
$285$	3.46219e20	0.471162
$286$	−2.68684e21	−3.54919
$287$	−2.48900e20	−0.319175
$288$	−3.72712e21	−4.64021
$289$	2.28997e20	0.276821
$290$	2.45922e20	0.288679
$291$	1.50994e21	1.72135
$292$	2.13420e21	2.36310
$293$	−3.27656e20	−0.352406	−0.176203	−	0.984354i	$-0.556381\pi$
$293$	−3.27656e20	−0.352406	−0.176203	+	0.984354i	$0.556381\pi$
$294$	1.53167e21	1.60034
$295$	−6.79290e20	−0.689554
$296$	3.24051e20	0.319620
$297$	6.30730e20	0.604524
$298$	−1.90034e20	−0.177008
$299$	4.30305e20	0.389557
$300$	3.82684e21	3.36752
$301$	4.97229e20	0.425345
$302$	9.36269e20	0.778649
$303$	−3.59642e20	−0.290809
$304$	3.09868e21	2.43642
$305$	4.43721e20	0.339282
$306$	−4.04793e21	−3.01024
$307$	9.91847e20	0.717412	0.358706	−	0.933451i	$-0.383218\pi$
$307$	9.91847e20	0.717412	0.358706	+	0.933451i	$0.383218\pi$
$308$	4.65575e21	3.27574
$309$	−1.25339e21	−0.857903
$310$	1.84953e21	1.23165
$311$	7.89659e20	0.511654	0.255827	−	0.966723i	$-0.417652\pi$
$311$	7.89659e20	0.511654	0.255827	+	0.966723i	$0.417652\pi$
$312$	−1.45131e22	−9.15051
$313$	1.63680e21	1.00431	0.502156	−	0.864777i	$-0.332540\pi$
$313$	1.63680e21	1.00431	0.502156	+	0.864777i	$0.332540\pi$
$314$	2.34619e21	1.40107
$315$	1.26383e21	0.734594
$316$	−6.55152e21	−3.70683
$317$	3.18280e20	0.175310	0.0876548	−	0.996151i	$-0.472063\pi$
$317$	3.18280e20	0.175310	0.0876548	+	0.996151i	$0.472063\pi$
$318$	8.15791e21	4.37470
$319$	−6.76462e20	−0.353202
$320$	−2.48114e21	−1.26147
$321$	−3.30315e21	−1.63544
$322$	−1.02638e21	−0.494920
$323$	1.72528e21	0.810284
$324$	−2.62423e21	−1.20052
$325$	3.43600e21	1.53125
$326$	−3.83221e21	−1.66380
$327$	−1.29570e20	−0.0548084
$328$	−1.97498e21	−0.814022
$329$	−7.51508e20	−0.301834
$330$	3.18905e21	1.24822
$331$	−2.44271e21	−0.931824	−0.465912	−	0.884831i	$-0.654274\pi$
$331$	−2.44271e21	−0.931824	−0.465912	+	0.884831i	$0.654274\pi$
$332$	9.96084e21	3.70359
$333$	−3.88096e20	−0.140658
$334$	−9.10612e20	−0.321728
$335$	−1.44947e20	−0.0499261
$336$	1.94297e22	6.52503
$337$	9.64083e20	0.315690	0.157845	−	0.987464i	$-0.449545\pi$
$337$	9.64083e20	0.315690	0.157845	+	0.987464i	$0.449545\pi$
$338$	−1.49124e22	−4.76163
$339$	9.70189e21	3.02106
$340$	−4.19699e21	−1.27458
$341$	−5.08753e21	−1.50694
$342$	−6.61195e21	−1.91033
$343$	2.02158e21	0.569759
$344$	3.94544e21	1.08480
$345$	−5.10736e20	−0.137004
$346$	−3.11630e21	−0.815628
$347$	−5.10464e21	−1.30366	−0.651830	−	0.758365i	$-0.725998\pi$
$347$	−5.10464e21	−1.30366	−0.651830	+	0.758365i	$0.725998\pi$
$348$	−5.86064e21	−1.46057
$349$	−3.30973e21	−0.804965	−0.402482	−	0.915428i	$-0.631853\pi$
$349$	−3.30973e21	−0.804965	−0.402482	+	0.915428i	$0.631853\pi$
$350$	−8.19573e21	−1.94540
$351$	4.90634e21	1.13670
$352$	1.46322e22	3.30900
$353$	2.38289e21	0.526040	0.263020	−	0.964790i	$-0.415281\pi$
$353$	2.38289e21	0.526040	0.263020	+	0.964790i	$0.415281\pi$
$354$	2.22837e22	4.80241
$355$	−3.45050e20	−0.0726007
$356$	−2.24692e22	−4.61597
$357$	1.08180e22	2.17004
$358$	−1.13703e22	−2.22724
$359$	3.85537e21	0.737502	0.368751	−	0.929528i	$-0.379786\pi$
$359$	3.85537e21	0.737502	0.368751	+	0.929528i	$0.379786\pi$
$360$	1.00283e22	1.87350
$361$	−2.66229e21	−0.485785
$362$	−1.40110e22	−2.49716
$363$	1.13796e20	0.0198117
$364$	3.62163e22	6.15946
$365$	−2.27441e21	−0.377902
$366$	−1.45560e22	−2.36294
$367$	2.24889e21	0.356703	0.178352	−	0.983967i	$-0.442924\pi$
$367$	2.24889e21	0.356703	0.178352	+	0.983967i	$0.442924\pi$
$368$	−4.57111e21	−0.708460
$369$	2.36532e21	0.358233
$370$	−5.53898e20	−0.0819813
$371$	−1.26923e22	−1.83596
$372$	−4.40766e22	−6.23151
$373$	1.05115e21	0.145258	0.0726292	−	0.997359i	$-0.476861\pi$
$373$	1.05115e21	0.145258	0.0726292	+	0.997359i	$0.476861\pi$
$374$	1.58916e22	2.14664
$375$	−9.05405e21	−1.19558
$376$	−5.96310e21	−0.769796
$377$	−5.26208e21	−0.664135
$378$	−1.17028e22	−1.44415
$379$	5.48375e21	0.661674	0.330837	−	0.943688i	$-0.392669\pi$
$379$	5.48375e21	0.661674	0.330837	+	0.943688i	$0.392669\pi$
$380$	−6.85544e21	−0.808862
$381$	5.92668e21	0.683832
$382$	4.87345e21	0.549918
$383$	1.23744e22	1.36564	0.682820	−	0.730587i	$-0.260753\pi$
$383$	1.23744e22	1.36564	0.682820	+	0.730587i	$0.260753\pi$
$384$	3.36605e22	3.63333
$385$	−4.96161e21	−0.523849
$386$	1.31147e22	1.35447
$387$	−4.72521e21	−0.477395
$388$	−2.98981e22	−2.95511
$389$	3.86443e21	0.373692	0.186846	−	0.982389i	$-0.440174\pi$
$389$	3.86443e21	0.373692	0.186846	+	0.982389i	$0.440174\pi$
$390$	2.48071e22	2.34707
$391$	−2.54509e21	−0.235614
$392$	−1.89088e22	−1.71290
$393$	−5.36109e21	−0.475244
$394$	1.17307e22	1.01767
$395$	6.98192e21	0.592789
$396$	−4.42440e22	−3.67659
$397$	1.43575e22	1.16777	0.583887	−	0.811835i	$-0.301531\pi$
$397$	1.43575e22	1.16777	0.583887	+	0.811835i	$0.301531\pi$
$398$	−4.12562e21	−0.328460
$399$	1.76703e22	1.37713
$400$	−3.65005e22	−2.78477
$401$	1.28272e22	0.958083	0.479042	−	0.877792i	$-0.340984\pi$
$401$	1.28272e22	0.958083	0.479042	+	0.877792i	$0.340984\pi$
$402$	4.75490e21	0.347712
$403$	−3.95750e22	−2.83353
$404$	7.12122e21	0.499244
$405$	2.79663e21	0.191985
$406$	1.25514e22	0.843763
$407$	1.52361e21	0.100305
$408$	8.58394e22	5.53446
$409$	−1.29982e22	−0.820794	−0.410397	−	0.911907i	$-0.634610\pi$
$409$	−1.29982e22	−0.820794	−0.410397	+	0.911907i	$0.634610\pi$
$410$	3.37582e21	0.208794
$411$	−2.00077e22	−1.21211
$412$	2.48181e22	1.47280
$413$	−3.46696e22	−2.01546
$414$	9.75382e21	0.555484
$415$	−1.06152e22	−0.592271
$416$	1.13821e23	6.22200
$417$	3.68440e22	1.97338
$418$	2.59577e22	1.36228
$419$	1.60134e22	0.823504	0.411752	−	0.911296i	$-0.364917\pi$
$419$	1.60134e22	0.823504	0.411752	+	0.911296i	$0.364917\pi$
$420$	−4.29857e22	−2.16623
$421$	3.57983e22	1.76793	0.883965	−	0.467553i	$-0.154864\pi$
$421$	3.57983e22	1.76793	0.883965	+	0.467553i	$0.154864\pi$
$422$	−5.79539e22	−2.80496
$423$	7.14164e21	0.338770
$424$	−1.00712e23	−4.68241
$425$	−2.03227e22	−0.926137
$426$	1.13191e22	0.505629
$427$	2.26466e22	0.991669
$428$	6.54051e22	2.80763
$429$	−6.82371e22	−2.87167
$430$	−6.74390e21	−0.278246
$431$	−2.78067e22	−1.12485	−0.562423	−	0.826850i	$-0.690131\pi$
$431$	−2.78067e22	−1.12485	−0.562423	+	0.826850i	$0.690131\pi$
$432$	−5.21199e22	−2.06724
$433$	−3.28753e22	−1.27856	−0.639282	−	0.768972i	$-0.720768\pi$
$433$	−3.28753e22	−1.27856	−0.639282	+	0.768972i	$0.720768\pi$
$434$	9.43963e22	3.59992
$435$	6.24565e21	0.233571
$436$	2.56559e21	0.0940918
$437$	−4.15720e21	−0.149523
$438$	7.46106e22	2.63191
$439$	−4.60160e22	−1.59207	−0.796033	−	0.605254i	$-0.793072\pi$
$439$	−4.60160e22	−1.59207	−0.796033	+	0.605254i	$0.793072\pi$
$440$	−3.93696e22	−1.33602
$441$	2.26459e22	0.753811
$442$	1.23618e23	4.03639
$443$	3.39451e21	0.108729	0.0543645	−	0.998521i	$-0.482687\pi$
$443$	3.39451e21	0.108729	0.0543645	+	0.998521i	$0.482687\pi$
$444$	1.32001e22	0.414783
$445$	2.39453e22	0.738177
$446$	2.87695e22	0.870132
$447$	−4.82625e21	−0.143217
$448$	−1.26633e23	−3.68708
$449$	−1.65018e22	−0.471453	−0.235726	−	0.971819i	$-0.575747\pi$
$449$	−1.65018e22	−0.471453	−0.235726	+	0.971819i	$0.575747\pi$
$450$	7.78847e22	2.18346
$451$	−9.28592e21	−0.255461
$452$	−1.92106e23	−5.18637
$453$	2.37783e22	0.630007
$454$	2.89229e22	0.752085
$455$	−3.85955e22	−0.985009
$456$	1.40212e23	3.51223
$457$	1.38382e22	0.340244	0.170122	−	0.985423i	$-0.445584\pi$
$457$	1.38382e22	0.340244	0.170122	+	0.985423i	$0.445584\pi$
$458$	−1.52216e23	−3.67371
$459$	−2.90192e22	−0.687507
$460$	1.01130e22	0.235201
$461$	5.85129e22	1.33596	0.667980	−	0.744179i	$-0.267159\pi$
$461$	5.85129e22	1.33596	0.667980	+	0.744179i	$0.267159\pi$
$462$	1.62763e23	3.64836
$463$	7.73248e22	1.70169	0.850845	−	0.525417i	$-0.176091\pi$
$463$	7.73248e22	1.70169	0.850845	+	0.525417i	$0.176091\pi$
$464$	5.58989e22	1.20782
$465$	4.69722e22	0.996532
$466$	−1.21689e23	−2.53496
$467$	3.47088e22	0.709980	0.354990	−	0.934870i	$-0.384484\pi$
$467$	3.47088e22	0.709980	0.354990	+	0.934870i	$0.384484\pi$
$468$	−3.44167e23	−6.91320
$469$	−7.39780e21	−0.145926
$470$	1.01927e22	0.197450
$471$	5.95857e22	1.13361
$472$	−2.75098e23	−5.14021
$473$	1.85505e22	0.340437
$474$	−2.29038e23	−4.12849
$475$	−3.31954e22	−0.587736
$476$	−2.14206e23	−3.72540
$477$	1.20616e23	2.06062
$478$	2.54375e22	0.426911
$479$	3.84574e22	0.634056	0.317028	−	0.948416i	$-0.397315\pi$
$479$	3.84574e22	0.634056	0.317028	+	0.948416i	$0.397315\pi$
$480$	−1.35096e23	−2.18823
$481$	1.18519e22	0.188606
$482$	1.61681e23	2.52790
$483$	−2.60669e22	−0.400442
$484$	−2.25327e21	−0.0340116
$485$	3.18623e22	0.472576
$486$	−1.71562e23	−2.50042
$487$	5.73682e22	0.821627	0.410814	−	0.911719i	$-0.365245\pi$
$487$	5.73682e22	0.821627	0.410814	+	0.911719i	$0.365245\pi$
$488$	1.79698e23	2.52915
$489$	−9.73261e22	−1.34618
$490$	3.23207e22	0.439353
$491$	−1.59413e22	−0.212976	−0.106488	−	0.994314i	$-0.533961\pi$
$491$	−1.59413e22	−0.212976	−0.106488	+	0.994314i	$0.533961\pi$
$492$	−8.04501e22	−1.05639
$493$	3.11233e22	0.401686
$494$	2.01920e23	2.56154
$495$	4.71506e22	0.587954
$496$	4.20404e23	5.15315
$497$	−1.76106e22	−0.212200
$498$	3.48226e23	4.12488
$499$	−1.68504e22	−0.196226	−0.0981128	−	0.995175i	$-0.531281\pi$
$499$	−1.68504e22	−0.196226	−0.0981128	+	0.995175i	$0.531281\pi$
$500$	1.79278e23	2.05249
$501$	−2.31267e22	−0.260311
$502$	1.69359e22	0.187424
$503$	9.70517e22	1.05603	0.528014	−	0.849236i	$-0.322937\pi$
$503$	9.70517e22	1.05603	0.528014	+	0.849236i	$0.322937\pi$
$504$	5.11823e23	5.47596
$505$	−7.58904e21	−0.0798381
$506$	−3.82922e22	−0.396124
$507$	−3.78728e23	−3.85265
$508$	−1.17353e23	−1.17396
$509$	−1.61979e22	−0.159352	−0.0796762	−	0.996821i	$-0.525389\pi$
$509$	−1.61979e22	−0.159352	−0.0796762	+	0.996821i	$0.525389\pi$
$510$	−1.46725e23	−1.41957
$511$	−1.16081e23	−1.10455
$512$	−5.96788e22	−0.558503
$513$	−4.74004e22	−0.436299
$514$	3.25775e23	2.94938
$515$	−2.64486e22	−0.235527
$516$	1.60716e23	1.40778
$517$	−2.80371e22	−0.241582
$518$	−2.82698e22	−0.239618
$519$	−7.91441e22	−0.659927
$520$	−3.06250e23	−2.51216
$521$	−9.76267e22	−0.787858	−0.393929	−	0.919141i	$-0.628884\pi$
$521$	−9.76267e22	−0.787858	−0.393929	+	0.919141i	$0.628884\pi$
$522$	−1.19277e23	−0.947015
$523$	−2.36090e23	−1.84422	−0.922112	−	0.386924i	$-0.873538\pi$
$523$	−2.36090e23	−1.84422	−0.922112	+	0.386924i	$0.873538\pi$
$524$	1.06154e23	0.815870
$525$	−2.08146e23	−1.57403
$526$	−1.40593e23	−1.04613
$527$	2.34072e23	1.71379
$528$	7.24881e23	5.22250
$529$	6.13261e21	0.0434783
$530$	1.72145e23	1.20102
$531$	3.29468e23	2.26209
$532$	−3.49888e23	−2.36418
$533$	−7.22336e22	−0.480350
$534$	−7.85512e23	−5.14105
$535$	−6.97019e22	−0.448991
$536$	−5.87004e22	−0.372169
$537$	−2.88770e23	−1.80207
$538$	1.78375e23	1.09568
$539$	−8.89050e22	−0.537553
$540$	1.15309e23	0.686301
$541$	2.99513e23	1.75485	0.877424	−	0.479716i	$-0.159260\pi$
$541$	2.99513e23	1.75485	0.877424	+	0.479716i	$0.159260\pi$
$542$	−8.32958e22	−0.480429
$543$	−3.55835e23	−2.02046
$544$	−6.73211e23	−3.76323
$545$	−2.73413e21	−0.0150470
$546$	1.26610e24	6.86012
$547$	−3.20248e22	−0.170842	−0.0854210	−	0.996345i	$-0.527224\pi$
$547$	−3.20248e22	−0.170842	−0.0854210	+	0.996345i	$0.527224\pi$
$548$	3.96170e23	2.08088
$549$	−2.15213e23	−1.11302
$550$	−3.05765e23	−1.55706
$551$	5.08373e22	0.254914
$552$	−2.06837e23	−1.02128
$553$	3.56344e23	1.73263
$554$	5.16678e21	0.0247393
$555$	−1.40673e22	−0.0663314
$556$	−7.29543e23	−3.38778
$557$	−1.75227e23	−0.801368	−0.400684	−	0.916216i	$-0.631228\pi$
$557$	−1.75227e23	−0.801368	−0.400684	+	0.916216i	$0.631228\pi$
$558$	−8.97056e23	−4.04044
$559$	1.44302e23	0.640134
$560$	4.09999e23	1.79137
$561$	4.03597e23	1.73686
$562$	4.27971e23	1.81408
$563$	−6.99256e22	−0.291954	−0.145977	−	0.989288i	$-0.546633\pi$
$563$	−6.99256e22	−0.291954	−0.145977	+	0.989288i	$0.546633\pi$
$564$	−2.42904e23	−0.998994
$565$	2.04726e23	0.829395
$566$	8.39746e23	3.35126
$567$	1.42735e23	0.561143
$568$	−1.39738e23	−0.541194
$569$	−4.48499e23	−1.71122	−0.855612	−	0.517617i	$-0.826819\pi$
$569$	−4.48499e23	−1.71122	−0.855612	+	0.517617i	$0.826819\pi$
$570$	−2.39662e23	−0.900873
$571$	2.92407e23	1.08288	0.541441	−	0.840739i	$-0.317879\pi$
$571$	2.92407e23	1.08288	0.541441	+	0.840739i	$0.317879\pi$
$572$	1.35115e24	4.92990
$573$	1.23770e23	0.444940
$574$	1.72295e23	0.610271
$575$	4.89692e22	0.170902
$576$	1.20340e24	4.13827
$577$	−3.26613e23	−1.10672	−0.553361	−	0.832941i	$-0.686655\pi$
$577$	−3.26613e23	−1.10672	−0.553361	+	0.832941i	$0.686655\pi$
$578$	−1.58518e23	−0.529289
$579$	3.33073e23	1.09590
$580$	−1.23669e23	−0.400981
$581$	−5.41780e23	−1.73111
$582$	−1.04522e24	−3.29127
$583$	−4.73523e23	−1.46946
$584$	−9.21088e23	−2.81703
$585$	3.66777e23	1.10555
$586$	2.26812e23	0.673809
$587$	−6.62571e23	−1.94003	−0.970016	−	0.243042i	$-0.921855\pi$
$587$	−6.62571e23	−1.94003	−0.970016	+	0.243042i	$0.921855\pi$
$588$	−7.70243e23	−2.22290
$589$	3.82336e23	1.08759
$590$	4.70223e23	1.31844
$591$	2.97922e23	0.823397
$592$	−1.25903e23	−0.343005
$593$	6.35819e23	1.70753	0.853765	−	0.520658i	$-0.174313\pi$
$593$	6.35819e23	1.70753	0.853765	+	0.520658i	$0.174313\pi$
$594$	−4.36608e23	−1.15586
$595$	2.28278e23	0.595759
$596$	9.55639e22	0.245867
$597$	−1.04778e23	−0.265758
$598$	−2.97869e23	−0.744843
$599$	1.62542e23	0.400717	0.200358	−	0.979723i	$-0.435789\pi$
$599$	1.62542e23	0.400717	0.200358	+	0.979723i	$0.435789\pi$
$600$	−1.65160e24	−4.01440
$601$	9.60329e22	0.230137	0.115069	−	0.993358i	$-0.463291\pi$
$601$	9.60329e22	0.230137	0.115069	+	0.993358i	$0.463291\pi$
$602$	−3.44195e23	−0.813270
$603$	7.03019e22	0.163783
$604$	−4.70830e23	−1.08156
$605$	2.40129e21	0.00543907
$606$	2.48954e23	0.556035
$607$	−3.14315e23	−0.692246	−0.346123	−	0.938189i	$-0.612502\pi$
$607$	−3.14315e23	−0.692246	−0.346123	+	0.938189i	$0.612502\pi$
$608$	−1.09963e24	−2.38818
$609$	3.18766e23	0.682692
$610$	−3.07156e23	−0.648716
$611$	−2.18096e23	−0.454253
$612$	2.03562e24	4.18128
$613$	1.74504e23	0.353502	0.176751	−	0.984256i	$-0.443441\pi$
$613$	1.74504e23	0.353502	0.176751	+	0.984256i	$0.443441\pi$
$614$	−6.86583e23	−1.37171
$615$	8.57353e22	0.168936
$616$	−2.00935e24	−3.90498
$617$	−6.60561e22	−0.126616	−0.0633081	−	0.997994i	$-0.520165\pi$
$617$	−6.60561e22	−0.126616	−0.0633081	+	0.997994i	$0.520165\pi$
$618$	8.67629e23	1.64033
$619$	2.73477e23	0.509977	0.254988	−	0.966944i	$-0.417928\pi$
$619$	2.73477e23	0.509977	0.254988	+	0.966944i	$0.417928\pi$
$620$	−9.30090e23	−1.71079
$621$	6.99241e22	0.126867
$622$	−5.46623e23	−0.978295
$623$	1.22212e24	2.15758
$624$	5.63873e24	9.82001
$625$	2.86023e23	0.491384
$626$	−1.13304e24	−1.92027
$627$	6.59243e23	1.10223
$628$	−1.17985e24	−1.94612
$629$	−7.00998e22	−0.114074
$630$	−8.74854e23	−1.40456
$631$	5.78984e23	0.917101	0.458550	−	0.888668i	$-0.348369\pi$
$631$	5.78984e23	0.917101	0.458550	+	0.888668i	$0.348369\pi$
$632$	2.82753e24	4.41888
$633$	−1.47185e24	−2.26950
$634$	−2.20322e23	−0.335196
$635$	1.25063e23	0.187738
$636$	−4.10244e24	−6.07655
$637$	−6.91577e23	−1.01078
$638$	4.68265e23	0.675330
$639$	1.67355e23	0.238168
$640$	7.10292e23	0.997487
$641$	−9.20075e23	−1.27506	−0.637529	−	0.770426i	$-0.720043\pi$
$641$	−9.20075e23	−1.27506	−0.637529	+	0.770426i	$0.720043\pi$
$642$	2.28653e24	3.12701
$643$	2.48861e23	0.335864	0.167932	−	0.985799i	$-0.446291\pi$
$643$	2.48861e23	0.335864	0.167932	+	0.985799i	$0.446291\pi$
$644$	5.16147e23	0.687454
$645$	−1.71274e23	−0.225130
$646$	−1.19428e24	−1.54928
$647$	1.02988e24	1.31857	0.659283	−	0.751895i	$-0.270860\pi$
$647$	1.02988e24	1.31857	0.659283	+	0.751895i	$0.270860\pi$
$648$	1.13258e24	1.43113
$649$	−1.29345e24	−1.61313
$650$	−2.37849e24	−2.92778
$651$	2.39737e24	2.91271
$652$	1.92714e24	2.31105
$653$	−4.57617e23	−0.541677	−0.270838	−	0.962625i	$-0.587301\pi$
$653$	−4.57617e23	−0.541677	−0.270838	+	0.962625i	$0.587301\pi$
$654$	8.96917e22	0.104795
$655$	−1.13128e23	−0.130472
$656$	7.67335e23	0.873580
$657$	1.10313e24	1.23971
$658$	5.20214e23	0.577115
$659$	1.05243e24	1.15257	0.576284	−	0.817249i	$-0.304502\pi$
$659$	1.05243e24	1.15257	0.576284	+	0.817249i	$0.304502\pi$
$660$	−1.60371e24	−1.73381
$661$	−1.19964e24	−1.28038	−0.640190	−	0.768217i	$-0.721144\pi$
$661$	−1.19964e24	−1.28038	−0.640190	+	0.768217i	$0.721144\pi$
$662$	1.69091e24	1.78167
$663$	3.13952e24	3.26586
$664$	−4.29894e24	−4.41502
$665$	3.72874e23	0.378075
$666$	2.68651e23	0.268941
$667$	−7.49941e22	−0.0741238
$668$	4.57927e23	0.446886
$669$	7.30653e23	0.704027
$670$	1.00336e23	0.0954601
$671$	8.44897e23	0.793711
$672$	−6.89505e24	−6.39585
$673$	2.55086e23	0.233646	0.116823	−	0.993153i	$-0.462729\pi$
$673$	2.55086e23	0.233646	0.116823	+	0.993153i	$0.462729\pi$
$674$	−6.67365e23	−0.603607
$675$	5.58347e23	0.498680
$676$	7.49913e24	6.61399
$677$	−1.37820e24	−1.20035	−0.600177	−	0.799867i	$-0.704903\pi$
$677$	−1.37820e24	−1.20035	−0.600177	+	0.799867i	$0.704903\pi$
$678$	−6.71591e24	−5.77634
$679$	1.62619e24	1.38127
$680$	1.81135e24	1.51942
$681$	7.34550e23	0.608515
$682$	3.52173e24	2.88130
$683$	−1.06422e24	−0.859913	−0.429957	−	0.902850i	$-0.641471\pi$
$683$	−1.06422e24	−0.859913	−0.429957	+	0.902850i	$0.641471\pi$
$684$	3.32501e24	2.65348
$685$	−4.22196e23	−0.332770
$686$	−1.39939e24	−1.08939
$687$	−3.86581e24	−2.97241
$688$	−1.53291e24	−1.16417
$689$	−3.68345e24	−2.76307
$690$	3.53545e23	0.261956
$691$	−1.36371e23	−0.0998063	−0.0499031	−	0.998754i	$-0.515891\pi$
$691$	−1.36371e23	−0.0998063	−0.0499031	+	0.998754i	$0.515891\pi$
$692$	1.56712e24	1.13292
$693$	2.40647e24	1.71850
$694$	3.53357e24	2.49263
$695$	7.77470e23	0.541767
$696$	2.52936e24	1.74113
$697$	4.27235e23	0.290528
$698$	2.29109e24	1.53911
$699$	−3.09051e24	−2.05104
$700$	4.12146e24	2.70220
$701$	−1.61292e24	−1.04474	−0.522371	−	0.852718i	$-0.674952\pi$
$701$	−1.61292e24	−1.04474	−0.522371	+	0.852718i	$0.674952\pi$
$702$	−3.39630e24	−2.17341
$703$	−1.14502e23	−0.0723925
$704$	−4.72439e24	−2.95106
$705$	2.58862e23	0.159757
$706$	−1.64950e24	−1.00580
$707$	−3.87330e23	−0.233354
$708$	−1.12060e25	−6.67065
$709$	1.37853e23	0.0810817	0.0405409	−	0.999178i	$-0.487092\pi$
$709$	1.37853e23	0.0810817	0.0405409	+	0.999178i	$0.487092\pi$
$710$	2.38853e23	0.138814
$711$	−3.38636e24	−1.94465
$712$	9.69735e24	5.50267
$713$	−5.64015e23	−0.316249
$714$	−7.48853e24	−4.14918
$715$	−1.43992e24	−0.788381
$716$	5.71790e24	3.09368
$717$	6.46033e23	0.345415
$718$	−2.66879e24	−1.41012
$719$	−2.65619e24	−1.38696	−0.693480	−	0.720475i	$-0.743924\pi$
$719$	−2.65619e24	−1.38696	−0.693480	+	0.720475i	$0.743924\pi$
$720$	−3.89626e24	−2.01058
$721$	−1.34988e24	−0.688408
$722$	1.84291e24	0.928834
$723$	4.10620e24	2.04534
$724$	7.04583e24	3.46860
$725$	−5.98831e23	−0.291361
$726$	−7.87730e22	−0.0378805
$727$	−1.71767e24	−0.816387	−0.408194	−	0.912895i	$-0.633841\pi$
$727$	−1.71767e24	−0.816387	−0.408194	+	0.912895i	$0.633841\pi$
$728$	−1.56304e25	−7.34265
$729$	−3.38361e24	−1.57107
$730$	1.57441e24	0.722558
$731$	−8.53490e23	−0.387169
$732$	7.31990e24	3.28217
$733$	−6.78684e23	−0.300804	−0.150402	−	0.988625i	$-0.548057\pi$
$733$	−6.78684e23	−0.300804	−0.150402	+	0.988625i	$0.548057\pi$
$734$	−1.55674e24	−0.682026
$735$	8.20844e23	0.355482
$736$	1.62216e24	0.694435
$737$	−2.75996e23	−0.116796
$738$	−1.63734e24	−0.684950
$739$	−2.93737e23	−0.121473	−0.0607366	−	0.998154i	$-0.519345\pi$
$739$	−2.93737e23	−0.121473	−0.0607366	+	0.998154i	$0.519345\pi$
$740$	2.78543e23	0.113874
$741$	5.12814e24	2.07255
$742$	8.78596e24	3.51040
$743$	−3.25964e24	−1.28755	−0.643776	−	0.765214i	$-0.722633\pi$
$743$	−3.25964e24	−1.28755	−0.643776	+	0.765214i	$0.722633\pi$
$744$	1.90228e25	7.42855
$745$	−1.01842e23	−0.0393186
$746$	−7.27637e23	−0.277738
$747$	5.14858e24	1.94295
$748$	−7.99157e24	−2.98173
$749$	−3.55745e24	−1.31233
$750$	6.26746e24	2.28597
$751$	1.06260e24	0.383205	0.191603	−	0.981473i	$-0.438631\pi$
$751$	1.06260e24	0.383205	0.191603	+	0.981473i	$0.438631\pi$
$752$	2.31683e24	0.826119
$753$	4.30118e23	0.151646
$754$	3.64256e24	1.26984
$755$	5.01761e23	0.172961
$756$	5.88512e24	2.00595
$757$	−3.56934e21	−0.00120302	−0.000601511	−	1.00000i	$-0.500191\pi$
$757$	−3.56934e21	−0.00120302	−0.000601511		1.00000i	$0.500191\pi$
$758$	−3.79600e24	−1.26514
$759$	−9.72501e23	−0.320505
$760$	2.95870e24	0.964239
$761$	1.98650e24	0.640204	0.320102	−	0.947383i	$-0.396283\pi$
$761$	1.98650e24	0.640204	0.320102	+	0.947383i	$0.396283\pi$
$762$	−4.10261e24	−1.30750
$763$	−1.39545e23	−0.0439800
$764$	−2.45075e24	−0.763847
$765$	−2.16935e24	−0.668662
$766$	−8.56593e24	−2.61114
$767$	−1.00615e25	−3.03321
$768$	−7.88921e24	−2.35214
$769$	2.16962e24	0.639749	0.319875	−	0.947460i	$-0.396359\pi$
$769$	2.16962e24	0.639749	0.319875	+	0.947460i	$0.396359\pi$
$770$	3.43456e24	1.00161
$771$	8.27365e24	2.38635
$772$	−6.59513e24	−1.88138
$773$	2.12329e24	0.599077	0.299539	−	0.954084i	$-0.403167\pi$
$773$	2.12329e24	0.599077	0.299539	+	0.954084i	$0.403167\pi$
$774$	3.27092e24	0.912791
$775$	−4.50368e24	−1.24309
$776$	1.29036e25	3.52277
$777$	−7.17965e23	−0.193876
$778$	−2.67506e24	−0.714508
$779$	6.97853e23	0.184372
$780$	−1.24750e25	−3.26013
$781$	−6.57015e23	−0.169841
$782$	1.76178e24	0.450500
$783$	−8.55084e23	−0.216289
$784$	7.34660e24	1.83823
$785$	1.25736e24	0.311220
$786$	3.71109e24	0.908679
$787$	4.92878e24	1.19386	0.596931	−	0.802292i	$-0.296386\pi$
$787$	4.92878e24	1.19386	0.596931	+	0.802292i	$0.296386\pi$
$788$	−5.89911e24	−1.41356
$789$	−3.57062e24	−0.846427
$790$	−4.83308e24	−1.13343
$791$	1.04488e25	2.42419
$792$	1.90950e25	4.38284
$793$	6.57231e24	1.49244
$794$	−9.93864e24	−2.23282
$795$	4.37195e24	0.971750
$796$	2.07469e24	0.456238
$797$	−1.80444e24	−0.392596	−0.196298	−	0.980544i	$-0.562892\pi$
$797$	−1.80444e24	−0.392596	−0.196298	+	0.980544i	$0.562892\pi$
$798$	−1.22319e25	−2.63311
$799$	1.28996e24	0.274744
$800$	1.29530e25	2.72964
$801$	−1.16139e25	−2.42160
$802$	−8.87931e24	−1.83188
$803$	−4.33074e24	−0.884057
$804$	−2.39114e24	−0.482979
$805$	−5.50055e23	−0.109936
$806$	2.73949e25	5.41779
$807$	4.53015e24	0.886519
$808$	−3.07340e24	−0.595145
$809$	−4.73159e23	−0.0906661	−0.0453330	−	0.998972i	$-0.514435\pi$
$809$	−4.73159e23	−0.0906661	−0.0453330	+	0.998972i	$0.514435\pi$
$810$	−1.93591e24	−0.367081
$811$	−8.56377e24	−1.60689	−0.803447	−	0.595376i	$-0.797003\pi$
$811$	−8.56377e24	−1.60689	−0.803447	+	0.595376i	$0.797003\pi$
$812$	−6.31183e24	−1.17200
$813$	−2.11545e24	−0.388717
$814$	−1.05469e24	−0.191786
$815$	−2.05374e24	−0.369578
$816$	−3.33510e25	−5.93939
$817$	−1.39411e24	−0.245702
$818$	8.99769e24	1.56938
$819$	1.87195e25	3.23134
$820$	−1.69763e24	−0.290018
$821$	3.73634e24	0.631728	0.315864	−	0.948805i	$-0.397706\pi$
$821$	3.73634e24	0.631728	0.315864	+	0.948805i	$0.397706\pi$
$822$	1.38499e25	2.31759
$823$	3.46676e23	0.0574149	0.0287074	−	0.999588i	$-0.490861\pi$
$823$	3.46676e23	0.0574149	0.0287074	+	0.999588i	$0.490861\pi$
$824$	−1.07111e25	−1.75571
$825$	−7.76547e24	−1.25982
$826$	2.39992e25	3.85361
$827$	−3.80802e24	−0.605205	−0.302602	−	0.953117i	$-0.597855\pi$
$827$	−3.80802e24	−0.605205	−0.302602	+	0.953117i	$0.597855\pi$
$828$	−4.90499e24	−0.771579
$829$	−6.43973e24	−1.00266	−0.501331	−	0.865256i	$-0.667156\pi$
$829$	−6.43973e24	−1.00266	−0.501331	+	0.865256i	$0.667156\pi$
$830$	7.34814e24	1.13244
$831$	1.31220e23	0.0200166
$832$	−3.67502e25	−5.54896
$833$	4.09042e24	0.611344
$834$	−2.55044e25	−3.77315
$835$	−4.88011e23	−0.0714652
$836$	−1.30536e25	−1.89224
$837$	−6.43090e24	−0.922796
$838$	−1.10849e25	−1.57456
$839$	−4.81384e24	−0.676886	−0.338443	−	0.940987i	$-0.609900\pi$
$839$	−4.81384e24	−0.676886	−0.338443	+	0.940987i	$0.609900\pi$
$840$	1.85520e25	2.58235
$841$	−6.34006e24	−0.873630
$842$	−2.47806e25	−3.38033
$843$	1.08691e25	1.46778
$844$	2.91438e25	3.89615
$845$	−7.99178e24	−1.05770
$846$	−4.94364e24	−0.647737
$847$	1.22557e23	0.0158975
$848$	3.91292e25	5.02500
$849$	2.13269e25	2.71152
$850$	1.40679e25	1.77080
$851$	1.68911e23	0.0210502
$852$	−5.69216e24	−0.702329
$853$	−6.85686e24	−0.837642	−0.418821	−	0.908069i	$-0.637557\pi$
$853$	−6.85686e24	−0.837642	−0.418821	+	0.908069i	$0.637557\pi$
$854$	−1.56766e25	−1.89610
$855$	−3.54345e24	−0.424340
$856$	−2.82278e25	−3.34696
$857$	1.09512e25	1.28566	0.642830	−	0.766009i	$-0.277760\pi$
$857$	1.09512e25	1.28566	0.642830	+	0.766009i	$0.277760\pi$
$858$	4.72356e25	5.49070
$859$	−4.94757e23	−0.0569443	−0.0284721	−	0.999595i	$-0.509064\pi$
$859$	−4.94757e23	−0.0569443	−0.0284721	+	0.999595i	$0.509064\pi$
$860$	3.39137e24	0.386490
$861$	4.37576e24	0.493772
$862$	1.92486e25	2.15073
$863$	5.59944e24	0.619516	0.309758	−	0.950815i	$-0.399752\pi$
$863$	5.59944e24	0.619516	0.309758	+	0.950815i	$0.399752\pi$
$864$	1.84958e25	2.02632
$865$	−1.67007e24	−0.181175
$866$	2.27572e25	2.44465
$867$	−4.02586e24	−0.428249
$868$	−4.74699e25	−5.00036
$869$	1.32944e25	1.38676
$870$	−4.32341e24	−0.446594
$871$	−2.14693e24	−0.219615
$872$	−1.10727e24	−0.112166
$873$	−1.54538e25	−1.55029
$874$	2.87772e24	0.285892
$875$	−9.75109e24	−0.959367
$876$	−3.75201e25	−3.65577
$877$	1.09392e25	1.05557	0.527787	−	0.849377i	$-0.323022\pi$
$877$	1.09392e25	1.05557	0.527787	+	0.849377i	$0.323022\pi$
$878$	3.18536e25	3.04407
$879$	5.76032e24	0.545181
$880$	1.52962e25	1.43377
$881$	−7.47389e24	−0.693828	−0.346914	−	0.937897i	$-0.612770\pi$
$881$	−7.47389e24	−0.693828	−0.346914	+	0.937897i	$0.612770\pi$
$882$	−1.56761e25	−1.44131
$883$	5.88234e24	0.535654	0.267827	−	0.963467i	$-0.413694\pi$
$883$	5.88234e24	0.535654	0.267827	+	0.963467i	$0.413694\pi$
$884$	−6.21651e25	−5.60663
$885$	1.19422e25	1.06676
$886$	−2.34977e24	−0.207893
$887$	3.75564e24	0.329104	0.164552	−	0.986368i	$-0.447382\pi$
$887$	3.75564e24	0.329104	0.164552	+	0.986368i	$0.447382\pi$
$888$	−5.69694e24	−0.494461
$889$	6.38296e24	0.548728
$890$	−1.65756e25	−1.41141
$891$	5.32512e24	0.449127
$892$	−1.44676e25	−1.20863
$893$	2.10704e24	0.174355
$894$	3.34086e24	0.273835
$895$	−6.09353e24	−0.494736
$896$	3.62519e25	2.91550
$897$	−7.56492e24	−0.602655
$898$	1.14230e25	0.901430
$899$	6.89719e24	0.539156
$900$	−3.91666e25	−3.03287
$901$	2.17863e25	1.67118
$902$	6.42797e24	0.488448
$903$	−8.74148e24	−0.658020
$904$	8.29097e25	6.18264
$905$	−7.50870e24	−0.554692
$906$	−1.64600e25	−1.20459
$907$	2.12366e25	1.53965	0.769827	−	0.638253i	$-0.220343\pi$
$907$	2.12366e25	1.53965	0.769827	+	0.638253i	$0.220343\pi$
$908$	−1.45447e25	−1.04466
$909$	3.68083e24	0.261910
$910$	2.67169e25	1.88336
$911$	−8.81393e24	−0.615550	−0.307775	−	0.951459i	$-0.599584\pi$
$911$	−8.81393e24	−0.615550	−0.307775	+	0.951459i	$0.599584\pi$
$912$	−5.44760e25	−3.76920
$913$	−2.02126e25	−1.38555
$914$	−9.57916e24	−0.650556
$915$	−7.80078e24	−0.524879
$916$	7.65464e25	5.10286
$917$	−5.77382e24	−0.381350
$918$	2.00879e25	1.31453
$919$	1.89492e24	0.122860	0.0614299	−	0.998111i	$-0.480434\pi$
$919$	1.89492e24	0.122860	0.0614299	+	0.998111i	$0.480434\pi$
$920$	−4.36461e24	−0.280381
$921$	−1.74370e25	−1.10985
$922$	−4.05042e25	−2.55439
$923$	−5.11081e24	−0.319356
$924$	−8.18499e25	−5.06765
$925$	1.34876e24	0.0827430
$926$	−5.35263e25	−3.25367
$927$	1.28280e25	0.772649
$928$	−1.98369e25	−1.18390
$929$	−2.10867e25	−1.24703	−0.623513	−	0.781813i	$-0.714295\pi$
$929$	−2.10867e25	−1.24703	−0.623513	+	0.781813i	$0.714295\pi$
$930$	−3.25155e25	−1.90539
$931$	6.68136e24	0.387965
$932$	6.11947e25	3.52110
$933$	−1.38825e25	−0.791542
$934$	−2.40264e25	−1.35750
$935$	8.51657e24	0.476833
$936$	1.48537e26	8.24118
$937$	−1.40900e25	−0.774683	−0.387341	−	0.921936i	$-0.626607\pi$
$937$	−1.40900e25	−0.774683	−0.387341	+	0.921936i	$0.626607\pi$
$938$	5.12096e24	0.279015
$939$	−2.87756e25	−1.55370
$940$	−5.12569e24	−0.274262
$941$	8.92038e24	0.473011	0.236506	−	0.971630i	$-0.423998\pi$
$941$	8.92038e24	0.473011	0.236506	+	0.971630i	$0.423998\pi$
$942$	−4.12469e25	−2.16750
$943$	−1.02946e24	−0.0536117
$944$	1.06883e26	5.51629
$945$	−6.27174e24	−0.320788
$946$	−1.28412e25	−0.650925
$947$	1.86810e25	0.938479	0.469240	−	0.883071i	$-0.344528\pi$
$947$	1.86810e25	0.938479	0.469240	+	0.883071i	$0.344528\pi$
$948$	1.15178e26	5.73456
$949$	−3.36881e25	−1.66232
$950$	2.29788e25	1.12377
$951$	−5.59549e24	−0.271209
$952$	9.24479e25	4.44102
$953$	4.00497e25	1.90682	0.953411	−	0.301675i	$-0.0975458\pi$
$953$	4.00497e25	1.90682	0.953411	+	0.301675i	$0.0975458\pi$
$954$	−8.34937e25	−3.93997
$955$	2.61176e24	0.122153
$956$	−1.27920e25	−0.592988
$957$	1.18925e25	0.546412
$958$	−2.66212e25	−1.21233
$959$	−2.15480e25	−0.972634
$960$	4.36194e25	1.95153
$961$	2.93222e25	1.30031
$962$	−8.20423e24	−0.360620
$963$	3.38067e25	1.47292
$964$	−8.13062e25	−3.51131
$965$	7.02840e24	0.300867
$966$	1.80442e25	0.765655
$967$	2.98469e25	1.25538	0.627689	−	0.778464i	$-0.284001\pi$
$967$	2.98469e25	1.25538	0.627689	+	0.778464i	$0.284001\pi$
$968$	9.72474e23	0.0405450
$969$	−3.03310e25	−1.25353
$970$	−2.20559e25	−0.903578
$971$	1.28722e25	0.522745	0.261372	−	0.965238i	$-0.415825\pi$
$971$	1.28722e25	0.522745	0.261372	+	0.965238i	$0.415825\pi$
$972$	8.62751e25	3.47314
$973$	3.96805e25	1.58350
$974$	−3.97118e25	−1.57097
$975$	−6.04063e25	−2.36888
$976$	−6.98174e25	−2.71419
$977$	−2.69175e25	−1.03736	−0.518681	−	0.854968i	$-0.673577\pi$
$977$	−2.69175e25	−1.03736	−0.518681	+	0.854968i	$0.673577\pi$
$978$	6.73718e25	2.57394
$979$	4.55947e25	1.72688
$980$	−1.62534e25	−0.610271
$981$	1.32611e24	0.0493619
$982$	1.10350e25	0.407216
$983$	−2.07900e25	−0.760588	−0.380294	−	0.924866i	$-0.624177\pi$
$983$	−2.07900e25	−0.760588	−0.380294	+	0.924866i	$0.624177\pi$
$984$	3.47210e25	1.25931
$985$	6.28665e24	0.226054
$986$	−2.15444e25	−0.768033
$987$	1.32118e25	0.466946
$988$	−1.01541e26	−3.55803
$989$	2.05656e24	0.0714450
$990$	−3.26389e25	−1.12418
$991$	3.33625e25	1.13929	0.569643	−	0.821892i	$-0.307082\pi$
$991$	3.33625e25	1.13929	0.569643	+	0.821892i	$0.307082\pi$
$992$	−1.49189e26	−5.05113
$993$	4.29438e25	1.44156
$994$	1.21906e25	0.405732
$995$	−2.21098e24	−0.0729607
$996$	−1.75115e26	−5.72955
$997$	−3.54734e25	−1.15078	−0.575391	−	0.817878i	$-0.695150\pi$
$997$	−3.54734e25	−1.15078	−0.575391	+	0.817878i	$0.695150\pi$
$998$	1.16643e25	0.375188
$999$	1.92593e24	0.0614233

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.18.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-692.227 q^{2} -17580.4 q^{3} +348107. q^{4} -370975. q^{5} +1.21696e7 q^{6} -1.89338e7 q^{7} -1.50237e8 q^{8} +1.79930e8 q^{9} +O(q^{10})\)	\(q-692.227 q^{2} -17580.4 q^{3} +348107. q^{4} -370975. q^{5} +1.21696e7 q^{6} -1.89338e7 q^{7} -1.50237e8 q^{8} +1.79930e8 q^{9} +2.56799e8 q^{10} -7.06381e8 q^{11} -6.11985e9 q^{12} -5.49482e9 q^{13} +1.31065e10 q^{14} +6.52189e9 q^{15} +5.83713e10 q^{16} +3.24998e10 q^{17} -1.24552e11 q^{18} +5.30857e10 q^{19} -1.29139e11 q^{20} +3.32864e11 q^{21} +4.88976e11 q^{22} -7.83110e10 q^{23} +2.64123e12 q^{24} -6.25317e11 q^{25} +3.80366e12 q^{26} -8.92903e11 q^{27} -6.59099e12 q^{28} +9.57645e11 q^{29} -4.51463e12 q^{30} +7.20224e12 q^{31} -2.07143e13 q^{32} +1.24185e13 q^{33} -2.24973e13 q^{34} +7.02399e12 q^{35} +6.26348e13 q^{36} -2.15693e12 q^{37} -3.67474e13 q^{38} +9.66010e13 q^{39} +5.57343e13 q^{40} +1.31458e13 q^{41} -2.30418e14 q^{42} -2.62614e13 q^{43} -2.45896e14 q^{44} -6.67495e13 q^{45} +5.42090e13 q^{46} +3.96913e13 q^{47} -1.02619e15 q^{48} +1.25860e14 q^{49} +4.32861e14 q^{50} -5.71359e14 q^{51} -1.91278e15 q^{52} +6.70350e14 q^{53} +6.18092e14 q^{54} +2.62050e14 q^{55} +2.84457e15 q^{56} -9.33268e14 q^{57} -6.62908e14 q^{58} +1.83109e15 q^{59} +2.27031e15 q^{60} -1.19609e15 q^{61} -4.98559e15 q^{62} -3.40676e15 q^{63} +6.68816e15 q^{64} +2.03844e15 q^{65} -8.59639e15 q^{66} +3.90718e14 q^{67} +1.13134e16 q^{68} +1.37674e15 q^{69} -4.86220e15 q^{70} +9.30115e14 q^{71} -2.70322e16 q^{72} +6.13089e15 q^{73} +1.49308e15 q^{74} +1.09933e16 q^{75} +1.84795e16 q^{76} +1.33745e16 q^{77} -6.68699e16 q^{78} -1.88205e16 q^{79} -2.16543e16 q^{80} -7.53860e15 q^{81} -9.09986e15 q^{82} +2.86144e16 q^{83} +1.15872e17 q^{84} -1.20566e16 q^{85} +1.81788e16 q^{86} -1.68358e16 q^{87} +1.06125e17 q^{88} -6.45469e16 q^{89} +4.62058e16 q^{90} +1.04038e17 q^{91} -2.72606e16 q^{92} -1.26618e17 q^{93} -2.74754e16 q^{94} -1.96935e16 q^{95} +3.64165e17 q^{96} -8.58879e16 q^{97} -8.71236e16 q^{98} -1.27099e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) \) 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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