LMFDB - Embedded newform 177.14.a.c.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.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:	$189.798744245$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+90.0430 q^{2} +729.000 q^{3} -84.2612 q^{4} -40186.9 q^{5} +65641.3 q^{6} -337958. q^{7} -745219. q^{8} +531441. q^{9} +O(q^{10})$	\(q+90.0430 q^{2} +729.000 q^{3} -84.2612 q^{4} -40186.9 q^{5} +65641.3 q^{6} -337958. q^{7} -745219. q^{8} +531441. q^{9} -3.61855e6 q^{10} -7.78053e6 q^{11} -61426.4 q^{12} +1.67004e6 q^{13} -3.04308e7 q^{14} -2.92962e7 q^{15} -6.64115e7 q^{16} -1.97130e8 q^{17} +4.78525e7 q^{18} +1.04530e8 q^{19} +3.38619e6 q^{20} -2.46372e8 q^{21} -7.00582e8 q^{22} -6.39726e8 q^{23} -5.43265e8 q^{24} +3.94283e8 q^{25} +1.50375e8 q^{26} +3.87420e8 q^{27} +2.84768e7 q^{28} -2.05934e9 q^{29} -2.63792e9 q^{30} +2.85272e9 q^{31} +1.24947e8 q^{32} -5.67201e9 q^{33} -1.77502e10 q^{34} +1.35815e10 q^{35} -4.47799e7 q^{36} -2.15628e10 q^{37} +9.41216e9 q^{38} +1.21746e9 q^{39} +2.99480e10 q^{40} +1.18090e9 q^{41} -2.21840e10 q^{42} -1.04106e10 q^{43} +6.55597e8 q^{44} -2.13570e10 q^{45} -5.76029e10 q^{46} +2.14571e10 q^{47} -4.84140e10 q^{48} +1.73268e10 q^{49} +3.55024e10 q^{50} -1.43708e11 q^{51} -1.40720e8 q^{52} +3.32881e10 q^{53} +3.48845e10 q^{54} +3.12675e11 q^{55} +2.51853e11 q^{56} +7.62021e10 q^{57} -1.85429e11 q^{58} -4.21805e10 q^{59} +2.46854e9 q^{60} -4.78046e10 q^{61} +2.56868e11 q^{62} -1.79605e11 q^{63} +5.55294e11 q^{64} -6.71137e10 q^{65} -5.10724e11 q^{66} -1.27562e12 q^{67} +1.66104e10 q^{68} -4.66360e11 q^{69} +1.22292e12 q^{70} +1.28149e12 q^{71} -3.96040e11 q^{72} -1.47258e12 q^{73} -1.94158e12 q^{74} +2.87432e11 q^{75} -8.80779e9 q^{76} +2.62950e12 q^{77} +1.09624e11 q^{78} +6.13179e11 q^{79} +2.66887e12 q^{80} +2.82430e11 q^{81} +1.06332e11 q^{82} +1.96253e11 q^{83} +2.07596e10 q^{84} +7.92206e12 q^{85} -9.37402e11 q^{86} -1.50126e12 q^{87} +5.79820e12 q^{88} +3.68905e12 q^{89} -1.92304e12 q^{90} -5.64404e11 q^{91} +5.39041e10 q^{92} +2.07964e12 q^{93} +1.93207e12 q^{94} -4.20072e12 q^{95} +9.10862e10 q^{96} +6.38735e12 q^{97} +1.56016e12 q^{98} -4.13489e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) $ 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * 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 $

$2$	90.0430	0.994844	0.497422	−	0.867509i	$-0.334280\pi$
$2$	90.0430	0.994844	0.497422	+	0.867509i	$0.334280\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−84.2612	−0.0102858
$5$	−40186.9	−1.15022	−0.575108	−	0.818078i	$-0.695040\pi$
$5$	−40186.9	−1.15022	−0.575108	+	0.818078i	$0.695040\pi$
$6$	65641.3	0.574373
$7$	−337958.	−1.08574	−0.542870	−	0.839817i	$-0.682662\pi$
$7$	−337958.	−1.08574	−0.542870	+	0.839817i	$0.682662\pi$
$8$	−745219.	−1.00508
$9$	531441.	0.333333
$10$	−3.61855e6	−1.14429
$11$	−7.78053e6	−1.32421	−0.662105	−	0.749411i	$-0.730337\pi$
$11$	−7.78053e6	−1.32421	−0.662105	+	0.749411i	$0.730337\pi$
$12$	−61426.4	−0.00593850
$13$	1.67004e6	0.0959611	0.0479805	−	0.998848i	$-0.484721\pi$
$13$	1.67004e6	0.0959611	0.0479805	+	0.998848i	$0.484721\pi$
$14$	−3.04308e7	−1.08014
$15$	−2.92962e7	−0.664077
$16$	−6.64115e7	−0.989608
$17$	−1.97130e8	−1.98078	−0.990388	−	0.138314i	$-0.955832\pi$
$17$	−1.97130e8	−1.98078	−0.990388	+	0.138314i	$0.955832\pi$
$18$	4.78525e7	0.331615
$19$	1.04530e8	0.509731	0.254865	−	0.966977i	$-0.417969\pi$
$19$	1.04530e8	0.509731	0.254865	+	0.966977i	$0.417969\pi$
$20$	3.38619e6	0.0118309
$21$	−2.46372e8	−0.626852
$22$	−7.00582e8	−1.31738
$23$	−6.39726e8	−0.901080	−0.450540	−	0.892756i	$-0.648769\pi$
$23$	−6.39726e8	−0.901080	−0.450540	+	0.892756i	$0.648769\pi$
$24$	−5.43265e8	−0.580281
$25$	3.94283e8	0.322996
$26$	1.50375e8	0.0954663
$27$	3.87420e8	0.192450
$28$	2.84768e7	0.0111677
$29$	−2.05934e9	−0.642898	−0.321449	−	0.946927i	$-0.604170\pi$
$29$	−2.05934e9	−0.642898	−0.321449	+	0.946927i	$0.604170\pi$
$30$	−2.63792e9	−0.660653
$31$	2.85272e9	0.577309	0.288655	−	0.957433i	$-0.406792\pi$
$31$	2.85272e9	0.577309	0.288655	+	0.957433i	$0.406792\pi$
$32$	1.24947e8	0.0205708
$33$	−5.67201e9	−0.764533
$34$	−1.77502e10	−1.97056
$35$	1.35815e10	1.24884
$36$	−4.47799e7	−0.00342860
$37$	−2.15628e10	−1.38163	−0.690817	−	0.723030i	$-0.742749\pi$
$37$	−2.15628e10	−1.38163	−0.690817	+	0.723030i	$0.742749\pi$
$38$	9.41216e9	0.507102
$39$	1.21746e9	0.0554032
$40$	2.99480e10	1.15605
$41$	1.18090e9	0.0388255	0.0194128	−	0.999812i	$-0.493820\pi$
$41$	1.18090e9	0.0388255	0.0194128	+	0.999812i	$0.493820\pi$
$42$	−2.21840e10	−0.623620
$43$	−1.04106e10	−0.251149	−0.125574	−	0.992084i	$-0.540077\pi$
$43$	−1.04106e10	−0.251149	−0.125574	+	0.992084i	$0.540077\pi$
$44$	6.55597e8	0.0136205
$45$	−2.13570e10	−0.383405
$46$	−5.76029e10	−0.896434
$47$	2.14571e10	0.290359	0.145180	−	0.989405i	$-0.453624\pi$
$47$	2.14571e10	0.290359	0.145180	+	0.989405i	$0.453624\pi$
$48$	−4.84140e10	−0.571351
$49$	1.73268e10	0.178832
$50$	3.55024e10	0.321331
$51$	−1.43708e11	−1.14360
$52$	−1.40720e8	−0.000987036 0
$53$	3.32881e10	0.206298	0.103149	−	0.994666i	$-0.467108\pi$
$53$	3.32881e10	0.206298	0.103149	+	0.994666i	$0.467108\pi$
$54$	3.48845e10	0.191458
$55$	3.12675e11	1.52313
$56$	2.51853e11	1.09125
$57$	7.62021e10	0.294293
$58$	−1.85429e11	−0.639583
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	2.46854e9	0.00683056
$61$	−4.78046e10	−0.118803	−0.0594013	−	0.998234i	$-0.518919\pi$
$61$	−4.78046e10	−0.118803	−0.0594013	+	0.998234i	$0.518919\pi$
$62$	2.56868e11	0.574333
$63$	−1.79605e11	−0.361913
$64$	5.55294e11	1.01007
$65$	−6.71137e10	−0.110376
$66$	−5.10724e11	−0.760591
$67$	−1.27562e12	−1.72280	−0.861402	−	0.507924i	$-0.830413\pi$
$67$	−1.27562e12	−1.72280	−0.861402	+	0.507924i	$0.830413\pi$
$68$	1.66104e10	0.0203739
$69$	−4.66360e11	−0.520239
$70$	1.22292e12	1.24240
$71$	1.28149e12	1.18723	0.593616	−	0.804748i	$-0.297700\pi$
$71$	1.28149e12	1.18723	0.593616	+	0.804748i	$0.297700\pi$
$72$	−3.96040e11	−0.335026
$73$	−1.47258e12	−1.13889	−0.569443	−	0.822031i	$-0.692841\pi$
$73$	−1.47258e12	−1.13889	−0.569443	+	0.822031i	$0.692841\pi$
$74$	−1.94158e12	−1.37451
$75$	2.87432e11	0.186482
$76$	−8.80779e9	−0.00524298
$77$	2.62950e12	1.43775
$78$	1.09624e11	0.0551175
$79$	6.13179e11	0.283799	0.141900	−	0.989881i	$-0.454679\pi$
$79$	6.13179e11	0.283799	0.141900	+	0.989881i	$0.454679\pi$
$80$	2.66887e12	1.13826
$81$	2.82430e11	0.111111
$82$	1.06332e11	0.0386253
$83$	1.96253e11	0.0658884	0.0329442	−	0.999457i	$-0.489512\pi$
$83$	1.96253e11	0.0658884	0.0329442	+	0.999457i	$0.489512\pi$
$84$	2.07596e10	0.00644767
$85$	7.92206e12	2.27832
$86$	−9.37402e11	−0.249854
$87$	−1.50126e12	−0.371177
$88$	5.79820e12	1.33093
$89$	3.68905e12	0.786828	0.393414	−	0.919362i	$-0.371294\pi$
$89$	3.68905e12	0.786828	0.393414	+	0.919362i	$0.371294\pi$
$90$	−1.92304e12	−0.381428
$91$	−5.64404e11	−0.104189
$92$	5.39041e10	0.00926832
$93$	2.07964e12	0.333310
$94$	1.93207e12	0.288862
$95$	−4.20072e12	−0.586300
$96$	9.10862e10	0.0118765
$97$	6.38735e12	0.778582	0.389291	−	0.921115i	$-0.372720\pi$
$97$	6.38735e12	0.778582	0.389291	+	0.921115i	$0.372720\pi$
$98$	1.56016e12	0.177910
$99$	−4.13489e12	−0.441403
$100$	−3.32227e10	−0.00332227
$101$	−2.60857e12	−0.244520	−0.122260	−	0.992498i	$-0.539014\pi$
$101$	−2.60857e12	−0.244520	−0.122260	+	0.992498i	$0.539014\pi$
$102$	−1.29399e13	−1.13771
$103$	1.11490e12	0.0920015	0.0460008	−	0.998941i	$-0.485352\pi$
$103$	1.11490e12	0.0920015	0.0460008	+	0.998941i	$0.485352\pi$
$104$	−1.24455e12	−0.0964482
$105$	9.90091e12	0.721015
$106$	2.99736e12	0.205234
$107$	1.64226e12	0.105791	0.0528955	−	0.998600i	$-0.483155\pi$
$107$	1.64226e12	0.105791	0.0528955	+	0.998600i	$0.483155\pi$
$108$	−3.26445e10	−0.00197950
$109$	−1.62793e13	−0.929746	−0.464873	−	0.885377i	$-0.653900\pi$
$109$	−1.62793e13	−0.929746	−0.464873	+	0.885377i	$0.653900\pi$
$110$	2.81542e13	1.51527
$111$	−1.57193e13	−0.797687
$112$	2.24443e13	1.07446
$113$	2.44955e13	1.10682	0.553409	−	0.832910i	$-0.313327\pi$
$113$	2.44955e13	1.10682	0.553409	+	0.832910i	$0.313327\pi$
$114$	6.86146e12	0.292776
$115$	2.57086e13	1.03644
$116$	1.73523e11	0.00661271
$117$	8.87528e11	0.0319870
$118$	−3.79806e12	−0.129518
$119$	6.66219e13	2.15061
$120$	2.18321e13	0.667449
$121$	2.60140e13	0.753532
$122$	−4.30447e12	−0.118190
$123$	8.60875e11	0.0224159
$124$	−2.40374e11	−0.00593808
$125$	3.32113e13	0.778700
$126$	−1.61722e13	−0.360047
$127$	−3.80464e13	−0.804618	−0.402309	−	0.915504i	$-0.631792\pi$
$127$	−3.80464e13	−0.804618	−0.402309	+	0.915504i	$0.631792\pi$
$128$	4.89767e13	0.984294
$129$	−7.58933e12	−0.145001
$130$	−6.04312e12	−0.109807
$131$	−3.68735e13	−0.637456	−0.318728	−	0.947846i	$-0.603256\pi$
$131$	−3.68735e13	−0.637456	−0.318728	+	0.947846i	$0.603256\pi$
$132$	4.77930e11	0.00786382
$133$	−3.53266e13	−0.553435
$134$	−1.14861e14	−1.71392
$135$	−1.55692e13	−0.221359
$136$	1.46905e14	1.99083
$137$	3.12968e13	0.404405	0.202202	−	0.979344i	$-0.435190\pi$
$137$	3.12968e13	0.404405	0.202202	+	0.979344i	$0.435190\pi$
$138$	−4.19925e13	−0.517556
$139$	−1.39096e14	−1.63575	−0.817875	−	0.575396i	$-0.804848\pi$
$139$	−1.39096e14	−1.63575	−0.817875	+	0.575396i	$0.804848\pi$
$140$	−1.14439e12	−0.0128453
$141$	1.56423e13	0.167639
$142$	1.15389e14	1.18111
$143$	−1.29938e13	−0.127073
$144$	−3.52938e13	−0.329869
$145$	8.27586e13	0.739471
$146$	−1.32595e14	−1.13301
$147$	1.26313e13	0.103248
$148$	1.81690e12	0.0142112
$149$	2.43694e14	1.82446	0.912229	−	0.409682i	$-0.134360\pi$
$149$	2.43694e14	1.82446	0.912229	+	0.409682i	$0.134360\pi$
$150$	2.58812e13	0.185520
$151$	−2.06249e14	−1.41593	−0.707965	−	0.706248i	$-0.750386\pi$
$151$	−2.06249e14	−1.41593	−0.707965	+	0.706248i	$0.750386\pi$
$152$	−7.78975e13	−0.512318
$153$	−1.04763e14	−0.660259
$154$	2.36768e14	1.43033
$155$	−1.14642e14	−0.664030
$156$	−1.02585e11	−0.000569865 0
$157$	−2.30572e14	−1.22874	−0.614368	−	0.789019i	$-0.710589\pi$
$157$	−2.30572e14	−1.22874	−0.614368	+	0.789019i	$0.710589\pi$
$158$	5.52125e13	0.282336
$159$	2.42670e13	0.119106
$160$	−5.02122e12	−0.0236608
$161$	2.16201e14	0.978339
$162$	2.54308e13	0.110538
$163$	−1.76290e14	−0.736220	−0.368110	−	0.929782i	$-0.619995\pi$
$163$	−1.76290e14	−0.736220	−0.368110	+	0.929782i	$0.619995\pi$
$164$	−9.95039e10	−0.000399351 0
$165$	2.27940e14	0.879378
$166$	1.76712e13	0.0655487
$167$	2.26529e14	0.808104	0.404052	−	0.914736i	$-0.367601\pi$
$167$	2.26529e14	0.808104	0.404052	+	0.914736i	$0.367601\pi$
$168$	1.83601e14	0.630035
$169$	−3.00086e14	−0.990791
$170$	7.13326e14	2.26657
$171$	5.55513e13	0.169910
$172$	8.77210e11	0.00258326
$173$	−3.87760e14	−1.09967	−0.549836	−	0.835273i	$-0.685310\pi$
$173$	−3.87760e14	−1.09967	−0.549836	+	0.835273i	$0.685310\pi$
$174$	−1.35178e14	−0.369263
$175$	−1.33251e14	−0.350690
$176$	5.16717e14	1.31045
$177$	−3.07496e13	−0.0751646
$178$	3.32173e14	0.782771
$179$	−3.18218e14	−0.723069	−0.361534	−	0.932359i	$-0.617747\pi$
$179$	−3.18218e14	−0.723069	−0.361534	+	0.932359i	$0.617747\pi$
$180$	1.79956e12	0.00394363
$181$	1.86455e14	0.394152	0.197076	−	0.980388i	$-0.436855\pi$
$181$	1.86455e14	0.394152	0.197076	+	0.980388i	$0.436855\pi$
$182$	−5.08206e13	−0.103652
$183$	−3.48496e13	−0.0685907
$184$	4.76736e14	0.905654
$185$	8.66540e14	1.58918
$186$	1.87257e14	0.331591
$187$	1.53378e15	2.62296
$188$	−1.80800e12	−0.00298658
$189$	−1.30932e14	−0.208951
$190$	−3.78245e14	−0.583277
$191$	9.08371e14	1.35378	0.676888	−	0.736086i	$-0.263328\pi$
$191$	9.08371e14	1.35378	0.676888	+	0.736086i	$0.263328\pi$
$192$	4.04809e14	0.583166
$193$	5.18184e14	0.721708	0.360854	−	0.932622i	$-0.382485\pi$
$193$	5.18184e14	0.721708	0.360854	+	0.932622i	$0.382485\pi$
$194$	5.75136e14	0.774568
$195$	−4.89259e13	−0.0637256
$196$	−1.45998e12	−0.00183942
$197$	−1.30902e15	−1.59557	−0.797785	−	0.602942i	$-0.793995\pi$
$197$	−1.30902e15	−1.59557	−0.797785	+	0.602942i	$0.793995\pi$
$198$	−3.72318e14	−0.439127
$199$	−1.00837e15	−1.15100	−0.575499	−	0.817802i	$-0.695192\pi$
$199$	−1.00837e15	−1.15100	−0.575499	+	0.817802i	$0.695192\pi$
$200$	−2.93827e14	−0.324636
$201$	−9.29928e14	−0.994661
$202$	−2.34884e14	−0.243259
$203$	6.95972e14	0.698020
$204$	1.21090e13	0.0117629
$205$	−4.74566e13	−0.0446577
$206$	1.00389e14	0.0915272
$207$	−3.39977e14	−0.300360
$208$	−1.10910e14	−0.0949639
$209$	−8.13296e14	−0.674990
$210$	8.91507e14	0.717298
$211$	5.64751e14	0.440576	0.220288	−	0.975435i	$-0.429300\pi$
$211$	5.64751e14	0.440576	0.220288	+	0.975435i	$0.429300\pi$
$212$	−2.80489e12	−0.00212194
$213$	9.34206e14	0.685449
$214$	1.47874e14	0.105245
$215$	4.18370e14	0.288875
$216$	−2.88713e14	−0.193427
$217$	−9.64102e14	−0.626808
$218$	−1.46584e15	−0.924953
$219$	−1.07351e15	−0.657536
$220$	−2.63464e13	−0.0156666
$221$	−3.29216e14	−0.190078
$222$	−1.41541e15	−0.793574
$223$	−3.29010e15	−1.79154	−0.895772	−	0.444514i	$-0.853376\pi$
$223$	−3.29010e15	−1.79154	−0.895772	+	0.444514i	$0.853376\pi$
$224$	−4.22268e13	−0.0223345
$225$	2.09538e14	0.107665
$226$	2.20564e15	1.10111
$227$	−1.76555e15	−0.856471	−0.428236	−	0.903667i	$-0.640865\pi$
$227$	−1.76555e15	−0.856471	−0.428236	+	0.903667i	$0.640865\pi$
$228$	−6.42088e12	−0.00302704
$229$	−4.02071e15	−1.84235	−0.921174	−	0.389151i	$-0.872768\pi$
$229$	−4.02071e15	−1.84235	−0.921174	+	0.389151i	$0.872768\pi$
$230$	2.31488e15	1.03109
$231$	1.91690e15	0.830084
$232$	1.53466e15	0.646161
$233$	9.91908e14	0.406123	0.203062	−	0.979166i	$-0.434911\pi$
$233$	9.91908e14	0.406123	0.203062	+	0.979166i	$0.434911\pi$
$234$	7.99157e13	0.0318221
$235$	−8.62296e14	−0.333976
$236$	3.55418e12	0.00133910
$237$	4.47008e14	0.163852
$238$	5.99883e15	2.13952
$239$	−3.64903e15	−1.26646	−0.633230	−	0.773964i	$-0.718271\pi$
$239$	−3.64903e15	−1.26646	−0.633230	+	0.773964i	$0.718271\pi$
$240$	1.94561e15	0.657177
$241$	2.03441e15	0.668847	0.334423	−	0.942423i	$-0.391458\pi$
$241$	2.03441e15	0.668847	0.334423	+	0.942423i	$0.391458\pi$
$242$	2.34237e15	0.749646
$243$	2.05891e14	0.0641500
$244$	4.02807e12	0.00122198
$245$	−6.96311e14	−0.205695
$246$	7.75157e13	0.0223003
$247$	1.74569e14	0.0489143
$248$	−2.12590e15	−0.580240
$249$	1.43069e14	0.0380407
$250$	2.99044e15	0.774685
$251$	5.44688e13	0.0137489	0.00687446	−	0.999976i	$-0.497812\pi$
$251$	5.44688e13	0.0137489	0.00687446	+	0.999976i	$0.497812\pi$
$252$	1.51337e13	0.00372257
$253$	4.97741e15	1.19322
$254$	−3.42581e15	−0.800469
$255$	5.77518e15	1.31539
$256$	−1.38954e14	−0.0308541
$257$	5.97427e15	1.29336	0.646680	−	0.762761i	$-0.276157\pi$
$257$	5.97427e15	1.29336	0.646680	+	0.762761i	$0.276157\pi$
$258$	−6.83366e14	−0.144253
$259$	7.28731e15	1.50010
$260$	5.65508e12	0.00113530
$261$	−1.09442e15	−0.214299
$262$	−3.32020e15	−0.634169
$263$	4.52791e15	0.843695	0.421847	−	0.906667i	$-0.361382\pi$
$263$	4.52791e15	0.843695	0.421847	+	0.906667i	$0.361382\pi$
$264$	4.22689e15	0.768414
$265$	−1.33774e15	−0.237287
$266$	−3.18092e15	−0.550582
$267$	2.68932e15	0.454275
$268$	1.07485e14	0.0177204
$269$	−4.51311e15	−0.726249	−0.363125	−	0.931741i	$-0.618290\pi$
$269$	−4.51311e15	−0.726249	−0.363125	+	0.931741i	$0.618290\pi$
$270$	−1.40190e15	−0.220218
$271$	−1.18934e16	−1.82393	−0.911963	−	0.410272i	$-0.865434\pi$
$271$	−1.18934e16	−1.82393	−0.911963	+	0.410272i	$0.865434\pi$
$272$	1.30917e16	1.96019
$273$	−4.11451e14	−0.0601534
$274$	2.81806e15	0.402320
$275$	−3.06773e15	−0.427715
$276$	3.92961e13	0.00535107
$277$	1.29850e15	0.172712	0.0863560	−	0.996264i	$-0.472478\pi$
$277$	1.29850e15	0.172712	0.0863560	+	0.996264i	$0.472478\pi$
$278$	−1.25246e16	−1.62732
$279$	1.51605e15	0.192436
$280$	−1.01212e16	−1.25518
$281$	1.46747e16	1.77819	0.889093	−	0.457727i	$-0.151336\pi$
$281$	1.46747e16	1.77819	0.889093	+	0.457727i	$0.151336\pi$
$282$	1.40848e15	0.166775
$283$	6.12284e15	0.708502	0.354251	−	0.935150i	$-0.384736\pi$
$283$	6.12284e15	0.708502	0.354251	+	0.935150i	$0.384736\pi$
$284$	−1.07980e14	−0.0122116
$285$	−3.06232e15	−0.338501
$286$	−1.17000e15	−0.126417
$287$	−3.99094e14	−0.0421544
$288$	6.64019e13	0.00685692
$289$	2.89558e16	2.92348
$290$	7.45183e15	0.735658
$291$	4.65638e15	0.449515
$292$	1.24081e14	0.0117143
$293$	−1.20455e16	−1.11221	−0.556103	−	0.831114i	$-0.687704\pi$
$293$	−1.20455e16	−1.11221	−0.556103	+	0.831114i	$0.687704\pi$
$294$	1.13736e15	0.102716
$295$	1.69510e15	0.149745
$296$	1.60690e16	1.38865
$297$	−3.01434e15	−0.254844
$298$	2.19429e16	1.81505
$299$	−1.06837e15	−0.0864686
$300$	−2.42194e13	−0.00191811
$301$	3.51835e15	0.272682
$302$	−1.85713e16	−1.40863
$303$	−1.90165e15	−0.141174
$304$	−6.94197e15	−0.504434
$305$	1.92112e15	0.136649
$306$	−9.43319e15	−0.656855
$307$	2.19355e16	1.49537	0.747684	−	0.664054i	$-0.231166\pi$
$307$	2.19355e16	1.49537	0.747684	+	0.664054i	$0.231166\pi$
$308$	−2.21564e14	−0.0147884
$309$	8.12764e14	0.0531171
$310$	−1.03227e16	−0.660607
$311$	4.21104e15	0.263904	0.131952	−	0.991256i	$-0.457875\pi$
$311$	4.21104e15	0.263904	0.131952	+	0.991256i	$0.457875\pi$
$312$	−9.07274e14	−0.0556844
$313$	1.16220e16	0.698620	0.349310	−	0.937007i	$-0.386416\pi$
$313$	1.16220e16	0.698620	0.349310	+	0.937007i	$0.386416\pi$
$314$	−2.07614e16	−1.22240
$315$	7.21776e15	0.416278
$316$	−5.16672e13	−0.00291910
$317$	1.51358e16	0.837762	0.418881	−	0.908041i	$-0.362423\pi$
$317$	1.51358e16	0.837762	0.418881	+	0.908041i	$0.362423\pi$
$318$	2.18507e15	0.118492
$319$	1.60228e16	0.851331
$320$	−2.23155e16	−1.16180
$321$	1.19721e15	0.0610784
$322$	1.94674e16	0.973294
$323$	−2.06060e16	−1.00966
$324$	−2.37978e13	−0.00114287
$325$	6.58468e14	0.0309951
$326$	−1.58736e16	−0.732424
$327$	−1.18676e16	−0.536789
$328$	−8.80028e14	−0.0390226
$329$	−7.25162e15	−0.315255
$330$	2.05244e16	0.874844
$331$	−1.16691e16	−0.487705	−0.243852	−	0.969812i	$-0.578411\pi$
$331$	−1.16691e16	−0.487705	−0.243852	+	0.969812i	$0.578411\pi$
$332$	−1.65365e13	−0.000677715 0
$333$	−1.14593e16	−0.460545
$334$	2.03974e16	0.803937
$335$	5.12633e16	1.98160
$336$	1.63619e16	0.620338
$337$	3.56912e16	1.32729	0.663646	−	0.748047i	$-0.269008\pi$
$337$	3.56912e16	1.32729	0.663646	+	0.748047i	$0.269008\pi$
$338$	−2.70206e16	−0.985683
$339$	1.78572e16	0.639021
$340$	−6.67522e14	−0.0234343
$341$	−2.21957e16	−0.764479
$342$	5.00201e15	0.169034
$343$	2.68887e16	0.891575
$344$	7.75818e15	0.252424
$345$	1.87416e16	0.598387
$346$	−3.49150e16	−1.09400
$347$	−1.04389e16	−0.321007	−0.160504	−	0.987035i	$-0.551312\pi$
$347$	−1.04389e16	−0.321007	−0.160504	+	0.987035i	$0.551312\pi$
$348$	1.26498e14	0.00381785
$349$	−3.10397e15	−0.0919502	−0.0459751	−	0.998943i	$-0.514639\pi$
$349$	−3.10397e15	−0.0919502	−0.0459751	+	0.998943i	$0.514639\pi$
$350$	−1.19983e16	−0.348882
$351$	6.47008e14	0.0184677
$352$	−9.72153e14	−0.0272400
$353$	−3.89779e16	−1.07222	−0.536108	−	0.844149i	$-0.680106\pi$
$353$	−3.89779e16	−1.07222	−0.536108	+	0.844149i	$0.680106\pi$
$354$	−2.76879e15	−0.0747770
$355$	−5.14991e16	−1.36557
$356$	−3.10844e14	−0.00809314
$357$	4.85673e16	1.24165
$358$	−2.86533e16	−0.719340
$359$	3.91903e16	0.966194	0.483097	−	0.875567i	$-0.339512\pi$
$359$	3.91903e16	0.966194	0.483097	+	0.875567i	$0.339512\pi$
$360$	1.59156e16	0.385352
$361$	−3.11265e16	−0.740175
$362$	1.67890e16	0.392119
$363$	1.89642e16	0.435052
$364$	4.75574e13	0.00107166
$365$	5.91784e16	1.30996
$366$	−3.13796e15	−0.0682370
$367$	6.31226e16	1.34851	0.674257	−	0.738497i	$-0.264464\pi$
$367$	6.31226e16	1.34851	0.674257	+	0.738497i	$0.264464\pi$
$368$	4.24852e16	0.891716
$369$	6.27578e14	0.0129418
$370$	7.80259e16	1.58098
$371$	−1.12500e16	−0.223986
$372$	−1.75233e14	−0.00342835
$373$	−7.24571e16	−1.39307	−0.696536	−	0.717522i	$-0.745276\pi$
$373$	−7.24571e16	−1.39307	−0.696536	+	0.717522i	$0.745276\pi$
$374$	1.38106e17	2.60944
$375$	2.42110e16	0.449583
$376$	−1.59903e16	−0.291833
$377$	−3.43919e15	−0.0616932
$378$	−1.17895e16	−0.207873
$379$	−1.08205e16	−0.187540	−0.0937698	−	0.995594i	$-0.529892\pi$
$379$	−1.08205e16	−0.187540	−0.0937698	+	0.995594i	$0.529892\pi$
$380$	3.53958e14	0.00603056
$381$	−2.77358e16	−0.464546
$382$	8.17925e16	1.34679
$383$	−5.34764e16	−0.865706	−0.432853	−	0.901465i	$-0.642493\pi$
$383$	−5.34764e16	−0.865706	−0.432853	+	0.901465i	$0.642493\pi$
$384$	3.57040e16	0.568283
$385$	−1.05671e17	−1.65372
$386$	4.66588e16	0.717986
$387$	−5.53262e15	−0.0837162
$388$	−5.38206e14	−0.00800833
$389$	−8.84206e16	−1.29384	−0.646921	−	0.762557i	$-0.723944\pi$
$389$	−8.84206e16	−1.29384	−0.646921	+	0.762557i	$0.723944\pi$
$390$	−4.40543e15	−0.0633970
$391$	1.26109e17	1.78484
$392$	−1.29123e16	−0.179739
$393$	−2.68807e16	−0.368036
$394$	−1.17868e17	−1.58734
$395$	−2.46418e16	−0.326430
$396$	3.48411e14	0.00454018
$397$	−5.88699e16	−0.754667	−0.377333	−	0.926077i	$-0.623159\pi$
$397$	−5.88699e16	−0.754667	−0.377333	+	0.926077i	$0.623159\pi$
$398$	−9.07966e16	−1.14506
$399$	−2.57531e16	−0.319526
$400$	−2.61849e16	−0.319640
$401$	−9.98337e16	−1.19905	−0.599527	−	0.800354i	$-0.704645\pi$
$401$	−9.98337e16	−1.19905	−0.599527	+	0.800354i	$0.704645\pi$
$402$	−8.37335e16	−0.989532
$403$	4.76416e15	0.0553992
$404$	2.19802e14	0.00251508
$405$	−1.13500e16	−0.127802
$406$	6.26674e16	0.694421
$407$	1.67770e17	1.82957
$408$	1.07094e17	1.14941
$409$	−2.49098e16	−0.263129	−0.131564	−	0.991308i	$-0.542000\pi$
$409$	−2.49098e16	−0.263129	−0.131564	+	0.991308i	$0.542000\pi$
$410$	−4.27313e15	−0.0444275
$411$	2.28154e16	0.233483
$412$	−9.39430e13	−0.000946308 0
$413$	1.42553e16	0.141351
$414$	−3.06125e16	−0.298811
$415$	−7.88681e15	−0.0757859
$416$	2.08666e14	0.00197399
$417$	−1.01401e17	−0.944401
$418$	−7.32316e16	−0.671510
$419$	−8.75012e16	−0.789992	−0.394996	−	0.918683i	$-0.629254\pi$
$419$	−8.75012e16	−0.789992	−0.394996	+	0.918683i	$0.629254\pi$
$420$	−8.34262e14	−0.00741621
$421$	−1.44750e17	−1.26703	−0.633513	−	0.773732i	$-0.718388\pi$
$421$	−1.44750e17	−1.26703	−0.633513	+	0.773732i	$0.718388\pi$
$422$	5.08519e16	0.438304
$423$	1.14032e16	0.0967865
$424$	−2.48069e16	−0.207345
$425$	−7.77251e16	−0.639784
$426$	8.41187e16	0.681915
$427$	1.61560e16	0.128989
$428$	−1.38379e14	−0.00108814
$429$	−9.47248e15	−0.0733654
$430$	3.76713e16	0.287386
$431$	2.22187e16	0.166962	0.0834808	−	0.996509i	$-0.473396\pi$
$431$	2.22187e16	0.166962	0.0834808	+	0.996509i	$0.473396\pi$
$432$	−2.57292e16	−0.190450
$433$	−1.18469e17	−0.863838	−0.431919	−	0.901912i	$-0.642163\pi$
$433$	−1.18469e17	−0.863838	−0.431919	+	0.901912i	$0.642163\pi$
$434$	−8.68106e16	−0.623576
$435$	6.03310e16	0.426934
$436$	1.37172e15	0.00956318
$437$	−6.68703e16	−0.459308
$438$	−9.66620e16	−0.654145
$439$	−6.63349e16	−0.442306	−0.221153	−	0.975239i	$-0.570982\pi$
$439$	−6.63349e16	−0.442306	−0.221153	+	0.975239i	$0.570982\pi$
$440$	−2.33012e17	−1.53086
$441$	9.20818e15	0.0596105
$442$	−2.96436e16	−0.189097
$443$	−6.72329e16	−0.422627	−0.211314	−	0.977418i	$-0.567774\pi$
$443$	−6.72329e16	−0.422627	−0.211314	+	0.977418i	$0.567774\pi$
$444$	1.32452e15	0.00820484
$445$	−1.48251e17	−0.905021
$446$	−2.96250e17	−1.78231
$447$	1.77653e17	1.05335
$448$	−1.87666e17	−1.09668
$449$	−1.81710e17	−1.04659	−0.523297	−	0.852150i	$-0.675298\pi$
$449$	−1.81710e17	−1.04659	−0.523297	+	0.852150i	$0.675298\pi$
$450$	1.88674e16	0.107110
$451$	−9.18801e15	−0.0514131
$452$	−2.06402e15	−0.0113845
$453$	−1.50355e17	−0.817487
$454$	−1.58976e17	−0.852055
$455$	2.26816e16	0.119840
$456$	−5.67872e16	−0.295787
$457$	−6.94341e16	−0.356548	−0.178274	−	0.983981i	$-0.557051\pi$
$457$	−6.94341e16	−0.356548	−0.178274	+	0.983981i	$0.557051\pi$
$458$	−3.62036e17	−1.83285
$459$	−7.63724e16	−0.381201
$460$	−2.16624e15	−0.0106606
$461$	−6.05089e16	−0.293605	−0.146803	−	0.989166i	$-0.546898\pi$
$461$	−6.05089e16	−0.293605	−0.146803	+	0.989166i	$0.546898\pi$
$462$	1.72604e17	0.825804
$463$	−2.32747e17	−1.09801	−0.549006	−	0.835818i	$-0.684994\pi$
$463$	−2.32747e17	−1.09801	−0.549006	+	0.835818i	$0.684994\pi$
$464$	1.36764e17	0.636217
$465$	−8.35741e16	−0.383378
$466$	8.93143e16	0.404029
$467$	9.13814e16	0.407660	0.203830	−	0.979006i	$-0.434661\pi$
$467$	9.13814e16	0.407660	0.203830	+	0.979006i	$0.434661\pi$
$468$	−7.47842e13	−0.000329012 0
$469$	4.31107e17	1.87052
$470$	−7.76437e16	−0.332254
$471$	−1.68087e17	−0.709411
$472$	3.14337e16	0.130850
$473$	8.10000e16	0.332574
$474$	4.02499e16	0.163007
$475$	4.12142e16	0.164641
$476$	−5.61364e15	−0.0221207
$477$	1.76906e16	0.0687661
$478$	−3.28570e17	−1.25993
$479$	−3.46435e17	−1.31051	−0.655256	−	0.755407i	$-0.727439\pi$
$479$	−3.46435e17	−1.31051	−0.655256	+	0.755407i	$0.727439\pi$
$480$	−3.66047e15	−0.0136606
$481$	−3.60107e16	−0.132583
$482$	1.83184e17	0.665398
$483$	1.57610e17	0.564844
$484$	−2.19197e15	−0.00775067
$485$	−2.56688e17	−0.895537
$486$	1.85391e16	0.0638193
$487$	−2.06802e16	−0.0702452	−0.0351226	−	0.999383i	$-0.511182\pi$
$487$	−2.06802e16	−0.0702452	−0.0351226	+	0.999383i	$0.511182\pi$
$488$	3.56249e16	0.119406
$489$	−1.28515e17	−0.425057
$490$	−6.26979e16	−0.204634
$491$	−1.31817e17	−0.424564	−0.212282	−	0.977208i	$-0.568090\pi$
$491$	−1.31817e17	−0.424564	−0.212282	+	0.977208i	$0.568090\pi$
$492$	−7.25383e13	−0.000230565 0
$493$	4.05959e17	1.27344
$494$	1.57187e16	0.0486621
$495$	1.66168e17	0.507709
$496$	−1.89454e17	−0.571310
$497$	−4.33090e17	−1.28903
$498$	1.28823e16	0.0378446
$499$	2.84304e17	0.824384	0.412192	−	0.911097i	$-0.364763\pi$
$499$	2.84304e17	0.824384	0.412192	+	0.911097i	$0.364763\pi$
$500$	−2.79842e15	−0.00800955
$501$	1.65140e17	0.466559
$502$	4.90453e15	0.0136780
$503$	−1.72043e17	−0.473635	−0.236818	−	0.971554i	$-0.576104\pi$
$503$	−1.72043e17	−0.473635	−0.236818	+	0.971554i	$0.576104\pi$
$504$	1.33845e17	0.363751
$505$	1.04830e17	0.281251
$506$	4.48181e17	1.18707
$507$	−2.18763e17	−0.572034
$508$	3.20584e15	0.00827613
$509$	5.88521e17	1.50002	0.750009	−	0.661428i	$-0.230049\pi$
$509$	5.88521e17	1.50002	0.750009	+	0.661428i	$0.230049\pi$
$510$	5.20014e17	1.30861
$511$	4.97670e17	1.23653
$512$	−4.13729e17	−1.01499
$513$	4.04969e16	0.0980977
$514$	5.37941e17	1.28669
$515$	−4.48045e16	−0.105822
$516$	6.39486e14	0.00149145
$517$	−1.66948e17	−0.384497
$518$	6.56171e17	1.49236
$519$	−2.82677e17	−0.634895
$520$	5.00144e16	0.110936
$521$	−4.75534e17	−1.04169	−0.520843	−	0.853653i	$-0.674382\pi$
$521$	−4.75534e17	−1.04169	−0.520843	+	0.853653i	$0.674382\pi$
$522$	−9.85448e16	−0.213194
$523$	3.63277e17	0.776205	0.388103	−	0.921616i	$-0.373131\pi$
$523$	3.63277e17	0.776205	0.388103	+	0.921616i	$0.373131\pi$
$524$	3.10700e15	0.00655674
$525$	−9.71400e16	−0.202471
$526$	4.07706e17	0.839345
$527$	−5.62358e17	−1.14352
$528$	3.76687e17	0.756588
$529$	−9.47866e16	−0.188055
$530$	−1.20454e17	−0.236064
$531$	−2.24165e16	−0.0433963
$532$	2.97667e15	0.00569252
$533$	1.97215e15	0.00372574
$534$	2.42154e17	0.451933
$535$	−6.59975e16	−0.121682
$536$	9.50618e17	1.73155
$537$	−2.31981e17	−0.417464
$538$	−4.06373e17	−0.722504
$539$	−1.34812e17	−0.236811
$540$	1.31188e15	0.00227685
$541$	6.51983e17	1.11803	0.559016	−	0.829157i	$-0.311179\pi$
$541$	6.51983e17	1.11803	0.559016	+	0.829157i	$0.311179\pi$
$542$	−1.07092e18	−1.81452
$543$	1.35926e17	0.227564
$544$	−2.46308e16	−0.0407461
$545$	6.54216e17	1.06941
$546$	−3.70482e16	−0.0598433
$547$	−9.94054e17	−1.58669	−0.793345	−	0.608772i	$-0.791662\pi$
$547$	−9.94054e17	−1.58669	−0.793345	+	0.608772i	$0.791662\pi$
$548$	−2.63711e15	−0.00415962
$549$	−2.54053e16	−0.0396009
$550$	−2.76227e17	−0.425509
$551$	−2.15262e17	−0.327705
$552$	3.47541e17	0.522880
$553$	−2.07229e17	−0.308132
$554$	1.16921e17	0.171821
$555$	6.31708e17	0.917512
$556$	1.17204e16	0.0168250
$557$	−4.27281e16	−0.0606254	−0.0303127	−	0.999540i	$-0.509650\pi$
$557$	−4.27281e16	−0.0606254	−0.0303127	+	0.999540i	$0.509650\pi$
$558$	1.36510e17	0.191444
$559$	−1.73861e16	−0.0241005
$560$	−9.01967e17	−1.23586
$561$	1.11813e18	1.51437
$562$	1.32135e18	1.76902
$563$	−1.33391e17	−0.176531	−0.0882656	−	0.996097i	$-0.528132\pi$
$563$	−1.33391e17	−0.176531	−0.0882656	+	0.996097i	$0.528132\pi$
$564$	−1.31804e15	−0.00172430
$565$	−9.84396e17	−1.27308
$566$	5.51319e17	0.704849
$567$	−9.54494e16	−0.120638
$568$	−9.54990e17	−1.19326
$569$	−7.10016e17	−0.877079	−0.438539	−	0.898712i	$-0.644504\pi$
$569$	−7.10016e17	−0.877079	−0.438539	+	0.898712i	$0.644504\pi$
$570$	−2.75741e17	−0.336755
$571$	2.02183e17	0.244124	0.122062	−	0.992522i	$-0.461049\pi$
$571$	2.02183e17	0.244124	0.122062	+	0.992522i	$0.461049\pi$
$572$	1.09487e15	0.00130704
$573$	6.62203e17	0.781603
$574$	−3.59356e16	−0.0419371
$575$	−2.52233e17	−0.291045
$576$	2.95106e17	0.336691
$577$	−1.35801e18	−1.53201	−0.766005	−	0.642835i	$-0.777758\pi$
$577$	−1.35801e18	−1.53201	−0.766005	+	0.642835i	$0.777758\pi$
$578$	2.60727e18	2.90840
$579$	3.77756e17	0.416678
$580$	−6.97334e15	−0.00760604
$581$	−6.63254e16	−0.0715377
$582$	4.19274e17	0.447197
$583$	−2.58999e17	−0.273182
$584$	1.09739e18	1.14467
$585$	−3.56670e16	−0.0367920
$586$	−1.08461e18	−1.10647
$587$	1.41805e18	1.43068	0.715341	−	0.698775i	$-0.246271\pi$
$587$	1.41805e18	1.43068	0.715341	+	0.698775i	$0.246271\pi$
$588$	−1.06432e15	−0.00106199
$589$	2.98194e17	0.294272
$590$	1.52632e17	0.148973
$591$	−9.54275e17	−0.921203
$592$	1.43202e18	1.36728
$593$	2.00275e17	0.189135	0.0945675	−	0.995518i	$-0.469853\pi$
$593$	2.00275e17	0.189135	0.0945675	+	0.995518i	$0.469853\pi$
$594$	−2.71420e17	−0.253530
$595$	−2.67732e18	−2.47366
$596$	−2.05339e16	−0.0187660
$597$	−7.35102e17	−0.664529
$598$	−9.61991e16	−0.0860228
$599$	1.13243e18	1.00170	0.500850	−	0.865534i	$-0.333021\pi$
$599$	1.13243e18	1.00170	0.500850	+	0.865534i	$0.333021\pi$
$600$	−2.14200e17	−0.187429
$601$	2.69570e17	0.233339	0.116670	−	0.993171i	$-0.462778\pi$
$601$	2.69570e17	0.233339	0.116670	+	0.993171i	$0.462778\pi$
$602$	3.16803e17	0.271276
$603$	−6.77918e17	−0.574268
$604$	1.73788e16	0.0145640
$605$	−1.04542e18	−0.866724
$606$	−1.71230e17	−0.140446
$607$	7.11002e17	0.576958	0.288479	−	0.957486i	$-0.406850\pi$
$607$	7.11002e17	0.576958	0.288479	+	0.957486i	$0.406850\pi$
$608$	1.30606e16	0.0104855
$609$	5.07364e17	0.403002
$610$	1.72983e17	0.135944
$611$	3.58343e16	0.0278632
$612$	8.82747e15	0.00679129
$613$	1.49381e18	1.13711	0.568556	−	0.822645i	$-0.307502\pi$
$613$	1.49381e18	1.13711	0.568556	+	0.822645i	$0.307502\pi$
$614$	1.97514e18	1.48766
$615$	−3.45959e16	−0.0257831
$616$	−1.95955e18	−1.44505
$617$	1.80348e18	1.31600	0.658002	−	0.753017i	$-0.271402\pi$
$617$	1.80348e18	1.31600	0.658002	+	0.753017i	$0.271402\pi$
$618$	7.31837e16	0.0528432
$619$	−1.76812e17	−0.126334	−0.0631672	−	0.998003i	$-0.520120\pi$
$619$	−1.76812e17	−0.126334	−0.0631672	+	0.998003i	$0.520120\pi$
$620$	9.65988e15	0.00683008
$621$	−2.47843e17	−0.173413
$622$	3.79174e17	0.262544
$623$	−1.24675e18	−0.854290
$624$	−8.08533e16	−0.0548274
$625$	−1.81596e18	−1.21867
$626$	1.04648e18	0.695018
$627$	−5.92893e17	−0.389706
$628$	1.94283e16	0.0126385
$629$	4.25067e18	2.73671
$630$	6.49909e17	0.414132
$631$	−2.04609e18	−1.29043	−0.645214	−	0.764002i	$-0.723232\pi$
$631$	−2.04609e18	−1.29043	−0.645214	+	0.764002i	$0.723232\pi$
$632$	−4.56953e17	−0.285240
$633$	4.11703e17	0.254367
$634$	1.36287e18	0.833442
$635$	1.52897e18	0.925484
$636$	−2.04477e15	−0.00122510
$637$	2.89365e16	0.0171609
$638$	1.44274e18	0.846942
$639$	6.81036e17	0.395744
$640$	−1.96822e18	−1.13215
$641$	1.60226e18	0.912341	0.456170	−	0.889892i	$-0.349221\pi$
$641$	1.60226e18	0.912341	0.456170	+	0.889892i	$0.349221\pi$
$642$	1.07800e17	0.0607635
$643$	−1.62233e18	−0.905249	−0.452624	−	0.891701i	$-0.649512\pi$
$643$	−1.62233e18	−0.905249	−0.452624	+	0.891701i	$0.649512\pi$
$644$	−1.82173e16	−0.0100630
$645$	3.04992e17	0.166782
$646$	−1.85542e18	−1.00446
$647$	2.57046e18	1.37763	0.688815	−	0.724937i	$-0.258131\pi$
$647$	2.57046e18	1.37763	0.688815	+	0.724937i	$0.258131\pi$
$648$	−2.10472e17	−0.111675
$649$	3.28187e17	0.172397
$650$	5.92904e16	0.0308353
$651$	−7.02830e17	−0.361888
$652$	1.48544e16	0.00757260
$653$	2.12874e18	1.07445	0.537226	−	0.843438i	$-0.319472\pi$
$653$	2.12874e18	1.07445	0.537226	+	0.843438i	$0.319472\pi$
$654$	−1.06860e18	−0.534022
$655$	1.48183e18	0.733212
$656$	−7.84252e16	−0.0384221
$657$	−7.82589e17	−0.379628
$658$	−6.52958e17	−0.313629
$659$	−3.05469e18	−1.45282	−0.726410	−	0.687262i	$-0.758812\pi$
$659$	−3.05469e18	−1.45282	−0.726410	+	0.687262i	$0.758812\pi$
$660$	−1.92065e16	−0.00904510
$661$	−1.48526e17	−0.0692617	−0.0346309	−	0.999400i	$-0.511026\pi$
$661$	−1.48526e17	−0.0692617	−0.0346309	+	0.999400i	$0.511026\pi$
$662$	−1.05072e18	−0.485190
$663$	−2.39998e17	−0.109741
$664$	−1.46252e17	−0.0662229
$665$	1.41967e18	0.636570
$666$	−1.03183e18	−0.458170
$667$	1.31742e18	0.579302
$668$	−1.90876e16	−0.00831199
$669$	−2.39848e18	−1.03435
$670$	4.61590e18	1.97138
$671$	3.71945e17	0.157320
$672$	−3.07834e16	−0.0128948
$673$	−1.36938e18	−0.568102	−0.284051	−	0.958809i	$-0.591678\pi$
$673$	−1.36938e18	−0.568102	−0.284051	+	0.958809i	$0.591678\pi$
$674$	3.21374e18	1.32045
$675$	1.52753e17	0.0621607
$676$	2.52856e16	0.0101911
$677$	−2.11562e18	−0.844524	−0.422262	−	0.906474i	$-0.638764\pi$
$677$	−2.11562e18	−0.844524	−0.422262	+	0.906474i	$0.638764\pi$
$678$	1.60792e18	0.635726
$679$	−2.15866e18	−0.845338
$680$	−5.90367e18	−2.28989
$681$	−1.28709e18	−0.494484
$682$	−1.99857e18	−0.760537
$683$	1.05313e18	0.396962	0.198481	−	0.980105i	$-0.436399\pi$
$683$	1.05313e18	0.396962	0.198481	+	0.980105i	$0.436399\pi$
$684$	−4.68082e15	−0.00174766
$685$	−1.25772e18	−0.465153
$686$	2.42114e18	0.886978
$687$	−2.93109e18	−1.06368
$688$	6.91384e17	0.248539
$689$	5.55924e16	0.0197966
$690$	1.68755e18	0.595301
$691$	−2.23892e17	−0.0782405	−0.0391202	−	0.999235i	$-0.512456\pi$
$691$	−2.23892e17	−0.0782405	−0.0391202	+	0.999235i	$0.512456\pi$
$692$	3.26731e16	0.0113110
$693$	1.39742e18	0.479249
$694$	−9.39953e17	−0.319352
$695$	5.58982e18	1.88147
$696$	1.11877e18	0.373061
$697$	−2.32791e17	−0.0769047
$698$	−2.79491e17	−0.0914760
$699$	7.23101e17	0.234475
$700$	1.12279e16	0.00360712
$701$	2.42492e18	0.771846	0.385923	−	0.922531i	$-0.373883\pi$
$701$	2.42492e18	0.771846	0.385923	+	0.922531i	$0.373883\pi$
$702$	5.82585e16	0.0183725
$703$	−2.25395e18	−0.704261
$704$	−4.32048e18	−1.33755
$705$	−6.28614e17	−0.192821
$706$	−3.50968e18	−1.06669
$707$	8.81590e17	0.265485
$708$	2.59100e15	0.000773127 0
$709$	1.81057e18	0.535323	0.267661	−	0.963513i	$-0.413749\pi$
$709$	1.81057e18	0.535323	0.267661	+	0.963513i	$0.413749\pi$
$710$	−4.63713e18	−1.35853
$711$	3.25869e17	0.0945998
$712$	−2.74915e18	−0.790822
$713$	−1.82496e18	−0.520202
$714$	4.37315e18	1.23525
$715$	5.22180e17	0.146161
$716$	2.68134e16	0.00743733
$717$	−2.66015e18	−0.731191
$718$	3.52881e18	0.961212
$719$	−5.10683e18	−1.37852	−0.689261	−	0.724513i	$-0.742065\pi$
$719$	−5.10683e18	−1.37852	−0.689261	+	0.724513i	$0.742065\pi$
$720$	1.41835e18	0.379421
$721$	−3.76791e17	−0.0998898
$722$	−2.80273e18	−0.736358
$723$	1.48308e18	0.386159
$724$	−1.57109e16	−0.00405416
$725$	−8.11963e17	−0.207654
$726$	1.70759e18	0.432809
$727$	6.95525e18	1.74718	0.873592	−	0.486658i	$-0.161784\pi$
$727$	6.95525e18	1.74718	0.873592	+	0.486658i	$0.161784\pi$
$728$	4.20605e17	0.104718
$729$	1.50095e17	0.0370370
$730$	5.32860e18	1.30321
$731$	2.05225e18	0.497470
$732$	2.93647e15	0.000705510 0
$733$	2.80649e18	0.668325	0.334163	−	0.942515i	$-0.391547\pi$
$733$	2.80649e18	0.668325	0.334163	+	0.942515i	$0.391547\pi$
$734$	5.68374e18	1.34156
$735$	−5.07611e17	−0.118758
$736$	−7.99318e16	−0.0185359
$737$	9.92502e18	2.28135
$738$	5.65090e16	0.0128751
$739$	−7.52822e18	−1.70021	−0.850107	−	0.526611i	$-0.823463\pi$
$739$	−7.52822e18	−1.70021	−0.850107	+	0.526611i	$0.823463\pi$
$740$	−7.30157e16	−0.0163459
$741$	1.27261e17	0.0282407
$742$	−1.01298e18	−0.222831
$743$	6.27241e18	1.36775	0.683876	−	0.729599i	$-0.260293\pi$
$743$	6.27241e18	1.36775	0.683876	+	0.729599i	$0.260293\pi$
$744$	−1.54978e18	−0.335002
$745$	−9.79329e18	−2.09852
$746$	−6.52426e18	−1.38589
$747$	1.04297e17	0.0219628
$748$	−1.29238e17	−0.0269793
$749$	−5.55017e17	−0.114861
$750$	2.18003e18	0.447265
$751$	−2.46805e18	−0.501989	−0.250995	−	0.967989i	$-0.580758\pi$
$751$	−2.46805e18	−0.501989	−0.250995	+	0.967989i	$0.580758\pi$
$752$	−1.42500e18	−0.287342
$753$	3.97078e16	0.00793795
$754$	−3.09675e17	−0.0613751
$755$	8.28850e18	1.62862
$756$	1.10325e16	0.00214922
$757$	8.84362e18	1.70808	0.854038	−	0.520211i	$-0.174147\pi$
$757$	8.84362e18	1.70808	0.854038	+	0.520211i	$0.174147\pi$
$758$	−9.74311e17	−0.186573
$759$	3.62853e18	0.688905
$760$	3.13046e18	0.589277
$761$	2.29194e17	0.0427762	0.0213881	−	0.999771i	$-0.493191\pi$
$761$	2.29194e17	0.0427762	0.0213881	+	0.999771i	$0.493191\pi$
$762$	−2.49742e18	−0.462151
$763$	5.50174e18	1.00946
$764$	−7.65405e16	−0.0139246
$765$	4.21011e18	0.759440
$766$	−4.81518e18	−0.861242
$767$	−7.04432e16	−0.0124931
$768$	−1.01298e17	−0.0178136
$769$	−4.43569e18	−0.773464	−0.386732	−	0.922192i	$-0.626396\pi$
$769$	−4.43569e18	−0.773464	−0.386732	+	0.922192i	$0.626396\pi$
$770$	−9.51495e18	−1.64519
$771$	4.35524e18	0.746722
$772$	−4.36628e16	−0.00742333
$773$	2.16975e18	0.365799	0.182900	−	0.983132i	$-0.441452\pi$
$773$	2.16975e18	0.365799	0.182900	+	0.983132i	$0.441452\pi$
$774$	−4.98174e17	−0.0832846
$775$	1.12478e18	0.186469
$776$	−4.75998e18	−0.782535
$777$	5.31245e18	0.866081
$778$	−7.96166e18	−1.28717
$779$	1.23439e17	0.0197906
$780$	4.12255e15	0.000655468 0
$781$	−9.97067e18	−1.57214
$782$	1.13553e19	1.77564
$783$	−7.97832e17	−0.123726
$784$	−1.15070e18	−0.176973
$785$	9.26597e18	1.41331
$786$	−2.42042e18	−0.366138
$787$	−8.26718e18	−1.24029	−0.620143	−	0.784489i	$-0.712925\pi$
$787$	−8.26718e18	−1.24029	−0.620143	+	0.784489i	$0.712925\pi$
$788$	1.10300e17	0.0164117
$789$	3.30085e18	0.487107
$790$	−2.21882e18	−0.324747
$791$	−8.27845e18	−1.20172
$792$	3.08140e18	0.443644
$793$	−7.98356e16	−0.0114004
$794$	−5.30082e18	−0.750776
$795$	−9.75215e17	−0.136998
$796$	8.49664e16	0.0118389
$797$	1.30803e19	1.80776	0.903878	−	0.427791i	$-0.140708\pi$
$797$	1.30803e19	1.80776	0.903878	+	0.427791i	$0.140708\pi$
$798$	−2.31889e18	−0.317878
$799$	−4.22986e18	−0.575137
$800$	4.92643e16	0.00664428
$801$	1.96051e18	0.262276
$802$	−8.98933e18	−1.19287
$803$	1.14574e19	1.50812
$804$	7.83569e16	0.0102309
$805$	−8.68844e18	−1.12530
$806$	4.28979e17	0.0551136
$807$	−3.29005e18	−0.419300
$808$	1.94396e18	0.245761
$809$	3.30186e18	0.414088	0.207044	−	0.978332i	$-0.433616\pi$
$809$	3.30186e18	0.414088	0.207044	+	0.978332i	$0.433616\pi$
$810$	−1.02198e18	−0.127143
$811$	−9.15328e18	−1.12964	−0.564821	−	0.825213i	$-0.691055\pi$
$811$	−9.15328e18	−1.12964	−0.564821	+	0.825213i	$0.691055\pi$
$812$	−5.86435e16	−0.00717969
$813$	−8.67032e18	−1.05304
$814$	1.51065e19	1.82014
$815$	7.08453e18	0.846812
$816$	9.54387e18	1.13172
$817$	−1.08822e18	−0.128018
$818$	−2.24295e18	−0.261772
$819$	−2.99947e17	−0.0347296
$820$	3.99875e15	0.000459340 0
$821$	1.19209e19	1.35855	0.679277	−	0.733882i	$-0.262293\pi$
$821$	1.19209e19	1.35855	0.679277	+	0.733882i	$0.262293\pi$
$822$	2.05436e18	0.232279
$823$	2.15576e18	0.241825	0.120913	−	0.992663i	$-0.461418\pi$
$823$	2.15576e18	0.241825	0.120913	+	0.992663i	$0.461418\pi$
$824$	−8.30847e17	−0.0924686
$825$	−2.23637e18	−0.246941
$826$	1.28359e18	0.140622
$827$	−3.85072e18	−0.418559	−0.209279	−	0.977856i	$-0.567112\pi$
$827$	−3.85072e18	−0.418559	−0.209279	+	0.977856i	$0.567112\pi$
$828$	2.86468e16	0.00308944
$829$	−1.14612e19	−1.22638	−0.613189	−	0.789936i	$-0.710114\pi$
$829$	−1.14612e19	−1.22638	−0.613189	+	0.789936i	$0.710114\pi$
$830$	−7.10152e17	−0.0753952
$831$	9.46604e17	0.0997153
$832$	9.27363e17	0.0969277
$833$	−3.41564e18	−0.354226
$834$	−9.13042e18	−0.939531
$835$	−9.10351e18	−0.929494
$836$	6.85293e16	0.00694281
$837$	1.10520e18	0.111103
$838$	−7.87887e18	−0.785919
$839$	−6.88425e18	−0.681402	−0.340701	−	0.940172i	$-0.610664\pi$
$839$	−6.88425e18	−0.681402	−0.340701	+	0.940172i	$0.610664\pi$
$840$	−7.37835e18	−0.724676
$841$	−6.01973e18	−0.586683
$842$	−1.30337e19	−1.26049
$843$	1.06978e19	1.02664
$844$	−4.75866e16	−0.00453167
$845$	1.20595e19	1.13962
$846$	1.02678e18	0.0962874
$847$	−8.79163e18	−0.818140
$848$	−2.21071e18	−0.204154
$849$	4.46355e18	0.409054
$850$	−6.99860e18	−0.636485
$851$	1.37943e19	1.24496
$852$	−7.87173e16	−0.00705038
$853$	−6.74773e17	−0.0599776	−0.0299888	−	0.999550i	$-0.509547\pi$
$853$	−6.74773e17	−0.0599776	−0.0299888	+	0.999550i	$0.509547\pi$
$854$	1.45473e18	0.128324
$855$	−2.23243e18	−0.195433
$856$	−1.22385e18	−0.106328
$857$	1.22185e19	1.05352	0.526758	−	0.850016i	$-0.323408\pi$
$857$	1.22185e19	1.05352	0.526758	+	0.850016i	$0.323408\pi$
$858$	−8.52930e17	−0.0729871
$859$	−6.17866e18	−0.524733	−0.262367	−	0.964968i	$-0.584503\pi$
$859$	−6.17866e18	−0.524733	−0.262367	+	0.964968i	$0.584503\pi$
$860$	−3.52523e16	−0.00297131
$861$	−2.90940e17	−0.0243379
$862$	2.00064e18	0.166101
$863$	−7.21154e18	−0.594234	−0.297117	−	0.954841i	$-0.596025\pi$
$863$	−7.21154e18	−0.594234	−0.297117	+	0.954841i	$0.596025\pi$
$864$	4.84070e16	0.00395884
$865$	1.55828e19	1.26486
$866$	−1.06673e19	−0.859384
$867$	2.11088e19	1.68787
$868$	8.12364e16	0.00644722
$869$	−4.77086e18	−0.375810
$870$	5.43239e18	0.424732
$871$	−2.13034e18	−0.165322
$872$	1.21317e19	0.934466
$873$	3.39450e18	0.259527
$874$	−6.02120e18	−0.456940
$875$	−1.12240e19	−0.845466
$876$	9.04552e16	0.00676327
$877$	1.76805e19	1.31219	0.656096	−	0.754678i	$-0.272207\pi$
$877$	1.76805e19	1.31219	0.656096	+	0.754678i	$0.272207\pi$
$878$	−5.97299e18	−0.440025
$879$	−8.78116e18	−0.642132
$880$	−2.07652e19	−1.50730
$881$	−1.50776e19	−1.08640	−0.543199	−	0.839604i	$-0.682787\pi$
$881$	−1.50776e19	−1.08640	−0.543199	+	0.839604i	$0.682787\pi$
$882$	8.29132e17	0.0593032
$883$	2.17243e19	1.54241	0.771206	−	0.636585i	$-0.219654\pi$
$883$	2.17243e19	1.54241	0.771206	+	0.636585i	$0.219654\pi$
$884$	2.77401e16	0.00195510
$885$	1.23573e18	0.0864555
$886$	−6.05385e18	−0.420448
$887$	2.06467e18	0.142346	0.0711732	−	0.997464i	$-0.477326\pi$
$887$	2.06467e18	0.142346	0.0711732	+	0.997464i	$0.477326\pi$
$888$	1.17143e19	0.801736
$889$	1.28581e19	0.873606
$890$	−1.33490e19	−0.900355
$891$	−2.19745e18	−0.147134
$892$	2.77228e17	0.0184274
$893$	2.24291e18	0.148005
$894$	1.59964e19	1.04792
$895$	1.27882e19	0.831685
$896$	−1.65521e19	−1.06869
$897$	−7.78841e17	−0.0499227
$898$	−1.63617e19	−1.04120
$899$	−5.87474e18	−0.371151
$900$	−1.76559e16	−0.00110742
$901$	−6.56209e18	−0.408631
$902$	−8.27316e17	−0.0511480
$903$	2.56488e18	0.157433
$904$	−1.82545e19	−1.11244
$905$	−7.49304e18	−0.453359
$906$	−1.35385e19	−0.813272
$907$	3.35016e18	0.199810	0.0999051	−	0.994997i	$-0.468146\pi$
$907$	3.35016e18	0.199810	0.0999051	+	0.994997i	$0.468146\pi$
$908$	1.48768e17	0.00880948
$909$	−1.38630e18	−0.0815067
$910$	2.04232e18	0.119222
$911$	−3.05496e19	−1.77066	−0.885331	−	0.464961i	$-0.846068\pi$
$911$	−3.05496e19	−1.77066	−0.885331	+	0.464961i	$0.846068\pi$
$912$	−5.06069e18	−0.291235
$913$	−1.52695e18	−0.0872501
$914$	−6.25206e18	−0.354709
$915$	1.40050e18	0.0788941
$916$	3.38789e17	0.0189500
$917$	1.24617e19	0.692112
$918$	−6.87679e18	−0.379235
$919$	9.79355e18	0.536277	0.268139	−	0.963380i	$-0.413592\pi$
$919$	9.79355e18	0.536277	0.268139	+	0.963380i	$0.413592\pi$
$920$	−1.91585e19	−1.04170
$921$	1.59910e19	0.863352
$922$	−5.44841e18	−0.292091
$923$	2.14014e18	0.113928
$924$	−1.61520e17	−0.00853807
$925$	−8.50182e18	−0.446263
$926$	−2.09572e19	−1.09235
$927$	5.92505e17	0.0306672
$928$	−2.57308e17	−0.0132249
$929$	−2.50341e19	−1.27770	−0.638851	−	0.769330i	$-0.720590\pi$
$929$	−2.50341e19	−1.27770	−0.638851	+	0.769330i	$0.720590\pi$
$930$	−7.52526e18	−0.381401
$931$	1.81117e18	0.0911560
$932$	−8.35793e16	−0.00417730
$933$	3.06985e18	0.152365
$934$	8.22826e18	0.405558
$935$	−6.16378e19	−3.01697
$936$	−6.61403e17	−0.0321494
$937$	2.00303e19	0.966896	0.483448	−	0.875373i	$-0.339384\pi$
$937$	2.00303e19	0.966896	0.483448	+	0.875373i	$0.339384\pi$
$938$	3.88182e19	1.86087
$939$	8.47240e18	0.403348
$940$	7.26581e16	0.00343521
$941$	2.28491e19	1.07284	0.536421	−	0.843951i	$-0.319776\pi$
$941$	2.28491e19	1.07284	0.536421	+	0.843951i	$0.319776\pi$
$942$	−1.51351e19	−0.705754
$943$	−7.55451e17	−0.0349849
$944$	2.80127e18	0.128836
$945$	5.26175e18	0.240338
$946$	7.29348e18	0.330859
$947$	3.11282e19	1.40242	0.701211	−	0.712954i	$-0.252643\pi$
$947$	3.11282e19	1.40242	0.701211	+	0.712954i	$0.252643\pi$
$948$	−3.76654e16	−0.00168534
$949$	−2.45927e18	−0.109289
$950$	3.71105e18	0.163792
$951$	1.10340e19	0.483682
$952$	−4.96479e19	−2.16153
$953$	−3.23635e19	−1.39943	−0.699716	−	0.714421i	$-0.746690\pi$
$953$	−3.23635e19	−1.39943	−0.699716	+	0.714421i	$0.746690\pi$
$954$	1.59292e18	0.0684115
$955$	−3.65046e19	−1.55713
$956$	3.07472e17	0.0130265
$957$	1.16806e19	0.491516
$958$	−3.11941e19	−1.30376
$959$	−1.05770e19	−0.439079
$960$	−1.62680e19	−0.670767
$961$	−1.62795e19	−0.666714
$962$	−3.24251e18	−0.131900
$963$	8.72766e17	0.0352636
$964$	−1.71421e17	−0.00687962
$965$	−2.08242e19	−0.830119
$966$	1.41917e19	0.561932
$967$	−8.69480e17	−0.0341970	−0.0170985	−	0.999854i	$-0.505443\pi$
$967$	−8.69480e17	−0.0341970	−0.0170985	+	0.999854i	$0.505443\pi$
$968$	−1.93861e19	−0.757357
$969$	−1.50217e19	−0.582929
$970$	−2.31129e19	−0.890920
$971$	−2.09768e19	−0.803184	−0.401592	−	0.915819i	$-0.631543\pi$
$971$	−2.09768e19	−0.803184	−0.401592	+	0.915819i	$0.631543\pi$
$972$	−1.73486e16	−0.000659834 0
$973$	4.70085e19	1.77600
$974$	−1.86211e18	−0.0698830
$975$	4.80023e17	0.0178950
$976$	3.17478e18	0.117568
$977$	1.99240e19	0.732930	0.366465	−	0.930432i	$-0.380568\pi$
$977$	1.99240e19	0.732930	0.366465	+	0.930432i	$0.380568\pi$
$978$	−1.15719e19	−0.422865
$979$	−2.87028e19	−1.04192
$980$	5.86720e16	0.00211574
$981$	−8.65151e18	−0.309915
$982$	−1.18692e19	−0.422375
$983$	5.26331e19	1.86063	0.930317	−	0.366757i	$-0.119532\pi$
$983$	5.26331e19	1.86063	0.930317	+	0.366757i	$0.119532\pi$
$984$	−6.41540e17	−0.0225297
$985$	5.26054e19	1.83525
$986$	3.65538e19	1.26687
$987$	−5.28643e18	−0.182012
$988$	−1.47094e16	−0.000503122 0
$989$	6.65994e18	0.226305
$990$	1.49623e19	0.505091
$991$	−2.11493e19	−0.709280	−0.354640	−	0.935003i	$-0.615397\pi$
$991$	−2.11493e19	−0.709280	−0.354640	+	0.935003i	$0.615397\pi$
$992$	3.56439e17	0.0118757
$993$	−8.50680e18	−0.281576
$994$	−3.89967e19	−1.28238
$995$	4.05232e19	1.32390
$996$	−1.20551e16	−0.000391279 0
$997$	5.05032e18	0.162855	0.0814274	−	0.996679i	$-0.474052\pi$
$997$	5.05032e18	0.162855	0.0814274	+	0.996679i	$0.474052\pi$
$998$	2.55996e19	0.820133
$999$	−8.35385e18	−0.265896

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.22	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.22	✓	31	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+90.0430 q^{2} +729.000 q^{3} -84.2612 q^{4} -40186.9 q^{5} +65641.3 q^{6} -337958. q^{7} -745219. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+90.0430 q^{2} +729.000 q^{3} -84.2612 q^{4} -40186.9 q^{5} +65641.3 q^{6} -337958. q^{7} -745219. q^{8} +531441. q^{9} -3.61855e6 q^{10} -7.78053e6 q^{11} -61426.4 q^{12} +1.67004e6 q^{13} -3.04308e7 q^{14} -2.92962e7 q^{15} -6.64115e7 q^{16} -1.97130e8 q^{17} +4.78525e7 q^{18} +1.04530e8 q^{19} +3.38619e6 q^{20} -2.46372e8 q^{21} -7.00582e8 q^{22} -6.39726e8 q^{23} -5.43265e8 q^{24} +3.94283e8 q^{25} +1.50375e8 q^{26} +3.87420e8 q^{27} +2.84768e7 q^{28} -2.05934e9 q^{29} -2.63792e9 q^{30} +2.85272e9 q^{31} +1.24947e8 q^{32} -5.67201e9 q^{33} -1.77502e10 q^{34} +1.35815e10 q^{35} -4.47799e7 q^{36} -2.15628e10 q^{37} +9.41216e9 q^{38} +1.21746e9 q^{39} +2.99480e10 q^{40} +1.18090e9 q^{41} -2.21840e10 q^{42} -1.04106e10 q^{43} +6.55597e8 q^{44} -2.13570e10 q^{45} -5.76029e10 q^{46} +2.14571e10 q^{47} -4.84140e10 q^{48} +1.73268e10 q^{49} +3.55024e10 q^{50} -1.43708e11 q^{51} -1.40720e8 q^{52} +3.32881e10 q^{53} +3.48845e10 q^{54} +3.12675e11 q^{55} +2.51853e11 q^{56} +7.62021e10 q^{57} -1.85429e11 q^{58} -4.21805e10 q^{59} +2.46854e9 q^{60} -4.78046e10 q^{61} +2.56868e11 q^{62} -1.79605e11 q^{63} +5.55294e11 q^{64} -6.71137e10 q^{65} -5.10724e11 q^{66} -1.27562e12 q^{67} +1.66104e10 q^{68} -4.66360e11 q^{69} +1.22292e12 q^{70} +1.28149e12 q^{71} -3.96040e11 q^{72} -1.47258e12 q^{73} -1.94158e12 q^{74} +2.87432e11 q^{75} -8.80779e9 q^{76} +2.62950e12 q^{77} +1.09624e11 q^{78} +6.13179e11 q^{79} +2.66887e12 q^{80} +2.82430e11 q^{81} +1.06332e11 q^{82} +1.96253e11 q^{83} +2.07596e10 q^{84} +7.92206e12 q^{85} -9.37402e11 q^{86} -1.50126e12 q^{87} +5.79820e12 q^{88} +3.68905e12 q^{89} -1.92304e12 q^{90} -5.64404e11 q^{91} +5.39041e10 q^{92} +2.07964e12 q^{93} +1.93207e12 q^{94} -4.20072e12 q^{95} +9.10862e10 q^{96} +6.38735e12 q^{97} +1.56016e12 q^{98} -4.13489e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * q^99

Introduction

L-functions

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