LMFDB - Embedded newform 177.12.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+10.5323 q^{2} +243.000 q^{3} -1937.07 q^{4} +8300.31 q^{5} +2559.34 q^{6} +46494.5 q^{7} -41971.8 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+10.5323 q^{2} +243.000 q^{3} -1937.07 q^{4} +8300.31 q^{5} +2559.34 q^{6} +46494.5 q^{7} -41971.8 q^{8} +59049.0 q^{9} +87421.0 q^{10} +529548. q^{11} -470708. q^{12} +1.93215e6 q^{13} +489692. q^{14} +2.01697e6 q^{15} +3.52506e6 q^{16} +5.64515e6 q^{17} +621920. q^{18} +2.69993e6 q^{19} -1.60783e7 q^{20} +1.12982e7 q^{21} +5.57734e6 q^{22} -1.76053e7 q^{23} -1.01992e7 q^{24} +2.00670e7 q^{25} +2.03499e7 q^{26} +1.43489e7 q^{27} -9.00631e7 q^{28} +1.24255e8 q^{29} +2.12433e7 q^{30} -1.09207e8 q^{31} +1.23085e8 q^{32} +1.28680e8 q^{33} +5.94562e7 q^{34} +3.85918e8 q^{35} -1.14382e8 q^{36} -1.90182e8 q^{37} +2.84363e7 q^{38} +4.69513e8 q^{39} -3.48379e8 q^{40} +2.79770e8 q^{41} +1.18995e8 q^{42} +5.67211e8 q^{43} -1.02577e9 q^{44} +4.90125e8 q^{45} -1.85424e8 q^{46} -1.78256e9 q^{47} +8.56591e8 q^{48} +1.84409e8 q^{49} +2.11351e8 q^{50} +1.37177e9 q^{51} -3.74272e9 q^{52} -5.80925e8 q^{53} +1.51126e8 q^{54} +4.39541e9 q^{55} -1.95146e9 q^{56} +6.56082e8 q^{57} +1.30869e9 q^{58} +7.14924e8 q^{59} -3.90702e9 q^{60} -2.90286e9 q^{61} -1.15019e9 q^{62} +2.74545e9 q^{63} -5.92297e9 q^{64} +1.60375e10 q^{65} +1.35529e9 q^{66} -5.69045e9 q^{67} -1.09351e10 q^{68} -4.27809e9 q^{69} +4.06459e9 q^{70} -4.85266e9 q^{71} -2.47839e9 q^{72} -5.37633e9 q^{73} -2.00304e9 q^{74} +4.87627e9 q^{75} -5.22995e9 q^{76} +2.46211e10 q^{77} +4.94504e9 q^{78} +1.77678e10 q^{79} +2.92591e10 q^{80} +3.48678e9 q^{81} +2.94661e9 q^{82} -1.09364e10 q^{83} -2.18853e10 q^{84} +4.68565e10 q^{85} +5.97402e9 q^{86} +3.01941e10 q^{87} -2.22261e10 q^{88} -1.49816e10 q^{89} +5.16212e9 q^{90} +8.98344e10 q^{91} +3.41028e10 q^{92} -2.65373e10 q^{93} -1.87744e10 q^{94} +2.24102e10 q^{95} +2.99097e10 q^{96} +7.14115e10 q^{97} +1.94225e9 q^{98} +3.12693e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * 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 $

$2$	10.5323	0.232732	0.116366	−	0.993206i	$-0.462875\pi$
$2$	10.5323	0.232732	0.116366	+	0.993206i	$0.462875\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1937.07	−0.945836
$5$	8300.31	1.18784	0.593922	−	0.804523i	$-0.297579\pi$
$5$	8300.31	1.18784	0.593922	+	0.804523i	$0.297579\pi$
$6$	2559.34	0.134368
$7$	46494.5	1.04559	0.522796	−	0.852458i	$-0.324889\pi$
$7$	46494.5	1.04559	0.522796	+	0.852458i	$0.324889\pi$
$8$	−41971.8	−0.452859
$9$	59049.0	0.333333
$10$	87421.0	0.276450
$11$	529548.	0.991393	0.495696	−	0.868496i	$-0.334913\pi$
$11$	529548.	0.991393	0.495696	+	0.868496i	$0.334913\pi$
$12$	−470708.	−0.546078
$13$	1.93215e6	1.44329	0.721644	−	0.692264i	$-0.243387\pi$
$13$	1.93215e6	1.44329	0.721644	+	0.692264i	$0.243387\pi$
$14$	489692.	0.243343
$15$	2.01697e6	0.685802
$16$	3.52506e6	0.840441
$17$	5.64515e6	0.964287	0.482144	−	0.876092i	$-0.339858\pi$
$17$	5.64515e6	0.964287	0.482144	+	0.876092i	$0.339858\pi$
$18$	621920.	0.0775774
$19$	2.69993e6	0.250154	0.125077	−	0.992147i	$-0.460082\pi$
$19$	2.69993e6	0.250154	0.125077	+	0.992147i	$0.460082\pi$
$20$	−1.60783e7	−1.12350
$21$	1.12982e7	0.603673
$22$	5.57734e6	0.230729
$23$	−1.76053e7	−0.570349	−0.285175	−	0.958476i	$-0.592052\pi$
$23$	−1.76053e7	−0.570349	−0.285175	+	0.958476i	$0.592052\pi$
$24$	−1.01992e7	−0.261458
$25$	2.00670e7	0.410971
$26$	2.03499e7	0.335900
$27$	1.43489e7	0.192450
$28$	−9.00631e7	−0.988958
$29$	1.24255e8	1.12493	0.562466	−	0.826820i	$-0.309853\pi$
$29$	1.24255e8	1.12493	0.562466	+	0.826820i	$0.309853\pi$
$30$	2.12433e7	0.159608
$31$	−1.09207e8	−0.685110	−0.342555	−	0.939498i	$-0.611292\pi$
$31$	−1.09207e8	−0.685110	−0.342555	+	0.939498i	$0.611292\pi$
$32$	1.23085e8	0.648457
$33$	1.28680e8	0.572381
$34$	5.94562e7	0.224421
$35$	3.85918e8	1.24200
$36$	−1.14382e8	−0.315279
$37$	−1.90182e8	−0.450878	−0.225439	−	0.974257i	$-0.572382\pi$
$37$	−1.90182e8	−0.450878	−0.225439	+	0.974257i	$0.572382\pi$
$38$	2.84363e7	0.0582189
$39$	4.69513e8	0.833283
$40$	−3.48379e8	−0.537925
$41$	2.79770e8	0.377128	0.188564	−	0.982061i	$-0.439617\pi$
$41$	2.79770e8	0.377128	0.188564	+	0.982061i	$0.439617\pi$
$42$	1.18995e8	0.140494
$43$	5.67211e8	0.588394	0.294197	−	0.955745i	$-0.404948\pi$
$43$	5.67211e8	0.588394	0.294197	+	0.955745i	$0.404948\pi$
$44$	−1.02577e9	−0.937695
$45$	4.90125e8	0.395948
$46$	−1.85424e8	−0.132739
$47$	−1.78256e9	−1.13372	−0.566860	−	0.823814i	$-0.691842\pi$
$47$	−1.78256e9	−1.13372	−0.566860	+	0.823814i	$0.691842\pi$
$48$	8.56591e8	0.485229
$49$	1.84409e8	0.0932620
$50$	2.11351e8	0.0956463
$51$	1.37177e9	0.556731
$52$	−3.74272e9	−1.36511
$53$	−5.80925e8	−0.190811	−0.0954054	−	0.995438i	$-0.530415\pi$
$53$	−5.80925e8	−0.190811	−0.0954054	+	0.995438i	$0.530415\pi$
$54$	1.51126e8	0.0447894
$55$	4.39541e9	1.17762
$56$	−1.95146e9	−0.473506
$57$	6.56082e8	0.144426
$58$	1.30869e9	0.261808
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−3.90702e9	−0.648656
$61$	−2.90286e9	−0.440060	−0.220030	−	0.975493i	$-0.570615\pi$
$61$	−2.90286e9	−0.440060	−0.220030	+	0.975493i	$0.570615\pi$
$62$	−1.15019e9	−0.159447
$63$	2.74545e9	0.348531
$64$	−5.92297e9	−0.689524
$65$	1.60375e10	1.71440
$66$	1.35529e9	0.133212
$67$	−5.69045e9	−0.514915	−0.257457	−	0.966290i	$-0.582885\pi$
$67$	−5.69045e9	−0.514915	−0.257457	+	0.966290i	$0.582885\pi$
$68$	−1.09351e10	−0.912057
$69$	−4.27809e9	−0.329291
$70$	4.06459e9	0.289053
$71$	−4.85266e9	−0.319197	−0.159599	−	0.987182i	$-0.551020\pi$
$71$	−4.85266e9	−0.319197	−0.159599	+	0.987182i	$0.551020\pi$
$72$	−2.47839e9	−0.150953
$73$	−5.37633e9	−0.303536	−0.151768	−	0.988416i	$-0.548497\pi$
$73$	−5.37633e9	−0.303536	−0.151768	+	0.988416i	$0.548497\pi$
$74$	−2.00304e9	−0.104934
$75$	4.87627e9	0.237274
$76$	−5.22995e9	−0.236604
$77$	2.46211e10	1.03659
$78$	4.94504e9	0.193932
$79$	1.77678e10	0.649658	0.324829	−	0.945773i	$-0.394693\pi$
$79$	1.77678e10	0.649658	0.324829	+	0.945773i	$0.394693\pi$
$80$	2.92591e10	0.998312
$81$	3.48678e9	0.111111
$82$	2.94661e9	0.0877700
$83$	−1.09364e10	−0.304751	−0.152375	−	0.988323i	$-0.548692\pi$
$83$	−1.09364e10	−0.304751	−0.152375	+	0.988323i	$0.548692\pi$
$84$	−2.18853e10	−0.570975
$85$	4.68565e10	1.14542
$86$	5.97402e9	0.136938
$87$	3.01941e10	0.649480
$88$	−2.22261e10	−0.448961
$89$	−1.49816e10	−0.284390	−0.142195	−	0.989839i	$-0.545416\pi$
$89$	−1.49816e10	−0.284390	−0.142195	+	0.989839i	$0.545416\pi$
$90$	5.16212e9	0.0921498
$91$	8.98344e10	1.50909
$92$	3.41028e10	0.539457
$93$	−2.65373e10	−0.395548
$94$	−1.87744e10	−0.263853
$95$	2.24102e10	0.297143
$96$	2.99097e10	0.374387
$97$	7.14115e10	0.844352	0.422176	−	0.906514i	$-0.361266\pi$
$97$	7.14115e10	0.844352	0.422176	+	0.906514i	$0.361266\pi$
$98$	1.94225e9	0.0217051
$99$	3.12693e10	0.330464
$100$	−3.88711e10	−0.388711
$101$	−6.72698e10	−0.636873	−0.318436	−	0.947944i	$-0.603158\pi$
$101$	−6.72698e10	−0.636873	−0.318436	+	0.947944i	$0.603158\pi$
$102$	1.44479e10	0.129569
$103$	6.47555e10	0.550391	0.275196	−	0.961388i	$-0.411257\pi$
$103$	6.47555e10	0.550391	0.275196	+	0.961388i	$0.411257\pi$
$104$	−8.10960e10	−0.653606
$105$	9.37782e10	0.717068
$106$	−6.11846e9	−0.0444079
$107$	8.20962e10	0.565864	0.282932	−	0.959140i	$-0.408693\pi$
$107$	8.20962e10	0.565864	0.282932	+	0.959140i	$0.408693\pi$
$108$	−2.77949e10	−0.182026
$109$	−3.78461e10	−0.235600	−0.117800	−	0.993037i	$-0.537584\pi$
$109$	−3.78461e10	−0.235600	−0.117800	+	0.993037i	$0.537584\pi$
$110$	4.62937e10	0.274070
$111$	−4.62142e10	−0.260315
$112$	1.63896e11	0.878758
$113$	−1.51677e11	−0.774440	−0.387220	−	0.921987i	$-0.626565\pi$
$113$	−1.51677e11	−0.774440	−0.387220	+	0.921987i	$0.626565\pi$
$114$	6.91003e9	0.0336127
$115$	−1.46130e11	−0.677486
$116$	−2.40692e11	−1.06400
$117$	1.14092e11	0.481096
$118$	7.52977e9	0.0302992
$119$	2.62468e11	1.00825
$120$	−8.46561e10	−0.310571
$121$	−4.89026e9	−0.0171400
$122$	−3.05737e10	−0.102416
$123$	6.79840e10	0.217735
$124$	2.11541e11	0.648002
$125$	−2.38726e11	−0.699674
$126$	2.89158e10	0.0811143
$127$	1.24742e11	0.335037	0.167519	−	0.985869i	$-0.446425\pi$
$127$	1.24742e11	0.335037	0.167519	+	0.985869i	$0.446425\pi$
$128$	−3.14461e11	−0.808931
$129$	1.37832e11	0.339710
$130$	1.68911e11	0.398996
$131$	4.89647e11	1.10890	0.554448	−	0.832219i	$-0.312930\pi$
$131$	4.89647e11	1.10890	0.554448	+	0.832219i	$0.312930\pi$
$132$	−2.49263e11	−0.541378
$133$	1.25532e11	0.261559
$134$	−5.99333e10	−0.119837
$135$	1.19100e11	0.228601
$136$	−2.36937e11	−0.436686
$137$	−7.97179e11	−1.41121	−0.705607	−	0.708603i	$-0.749326\pi$
$137$	−7.97179e11	−1.41121	−0.705607	+	0.708603i	$0.749326\pi$
$138$	−4.50580e10	−0.0766368
$139$	−2.50206e10	−0.0408993	−0.0204497	−	0.999791i	$-0.506510\pi$
$139$	−2.50206e10	−0.0408993	−0.0204497	+	0.999791i	$0.506510\pi$
$140$	−7.47551e11	−1.17473
$141$	−4.33162e11	−0.654554
$142$	−5.11095e10	−0.0742875
$143$	1.02317e12	1.43087
$144$	2.08152e11	0.280147
$145$	1.03136e12	1.33624
$146$	−5.66249e10	−0.0706427
$147$	4.48115e10	0.0538448
$148$	3.68396e11	0.426457
$149$	−1.00979e12	−1.12644	−0.563219	−	0.826308i	$-0.690437\pi$
$149$	−1.00979e12	−1.12644	−0.563219	+	0.826308i	$0.690437\pi$
$150$	5.13582e10	0.0552214
$151$	1.40479e12	1.45626	0.728130	−	0.685439i	$-0.240390\pi$
$151$	1.40479e12	1.45626	0.728130	+	0.685439i	$0.240390\pi$
$152$	−1.13321e11	−0.113284
$153$	3.33340e11	0.321429
$154$	2.59316e11	0.241249
$155$	−9.06450e11	−0.813803
$156$	−9.09481e11	−0.788149
$157$	1.91187e12	1.59960	0.799799	−	0.600268i	$-0.204939\pi$
$157$	1.91187e12	1.59960	0.799799	+	0.600268i	$0.204939\pi$
$158$	1.87135e11	0.151196
$159$	−1.41165e11	−0.110165
$160$	1.02164e12	0.770265
$161$	−8.18550e11	−0.596353
$162$	3.67237e10	0.0258591
$163$	4.34423e11	0.295720	0.147860	−	0.989008i	$-0.452761\pi$
$163$	4.34423e11	0.295720	0.147860	+	0.989008i	$0.452761\pi$
$164$	−5.41934e11	−0.356702
$165$	1.06809e12	0.679899
$166$	−1.15185e11	−0.0709254
$167$	−1.63621e12	−0.974764	−0.487382	−	0.873189i	$-0.662048\pi$
$167$	−1.63621e12	−0.974764	−0.487382	+	0.873189i	$0.662048\pi$
$168$	−4.74204e11	−0.273379
$169$	1.94106e12	1.08308
$170$	4.93505e11	0.266577
$171$	1.59428e11	0.0833846
$172$	−1.09873e12	−0.556524
$173$	2.15869e12	1.05910	0.529551	−	0.848278i	$-0.322361\pi$
$173$	2.15869e12	1.05910	0.529551	+	0.848278i	$0.322361\pi$
$174$	3.18012e11	0.151155
$175$	9.33003e11	0.429708
$176$	1.86669e12	0.833207
$177$	1.73727e11	0.0751646
$178$	−1.57790e11	−0.0661867
$179$	4.43277e12	1.80295	0.901476	−	0.432830i	$-0.142485\pi$
$179$	4.43277e12	1.80295	0.901476	+	0.432830i	$0.142485\pi$
$180$	−9.49407e11	−0.374501
$181$	−2.27330e12	−0.869812	−0.434906	−	0.900476i	$-0.643218\pi$
$181$	−2.27330e12	−0.869812	−0.434906	+	0.900476i	$0.643218\pi$
$182$	9.46160e11	0.351214
$183$	−7.05394e11	−0.254069
$184$	7.38928e11	0.258288
$185$	−1.57857e12	−0.535573
$186$	−2.79497e11	−0.0920569
$187$	2.98938e12	0.955987
$188$	3.45295e12	1.07231
$189$	6.67145e11	0.201224
$190$	2.36030e11	0.0691549
$191$	2.74464e12	0.781272	0.390636	−	0.920545i	$-0.372255\pi$
$191$	2.74464e12	0.781272	0.390636	+	0.920545i	$0.372255\pi$
$192$	−1.43928e12	−0.398097
$193$	4.05528e12	1.09007	0.545036	−	0.838412i	$-0.316516\pi$
$193$	4.05528e12	1.09007	0.545036	+	0.838412i	$0.316516\pi$
$194$	7.52124e11	0.196508
$195$	3.89710e12	0.989809
$196$	−3.57214e11	−0.0882105
$197$	5.80542e12	1.39402	0.697010	−	0.717061i	$-0.254513\pi$
$197$	5.80542e12	1.39402	0.697010	+	0.717061i	$0.254513\pi$
$198$	3.29336e11	0.0769097
$199$	6.61352e12	1.50224	0.751122	−	0.660163i	$-0.229513\pi$
$199$	6.61352e12	1.50224	0.751122	+	0.660163i	$0.229513\pi$
$200$	−8.42247e11	−0.186112
$201$	−1.38278e12	−0.297286
$202$	−7.08503e11	−0.148221
$203$	5.77719e12	1.17622
$204$	−2.65722e12	−0.526576
$205$	2.32217e12	0.447969
$206$	6.82022e11	0.128094
$207$	−1.03958e12	−0.190116
$208$	6.81096e12	1.21300
$209$	1.42974e12	0.248001
$210$	9.87696e11	0.166885
$211$	−1.14902e13	−1.89136	−0.945678	−	0.325104i	$-0.894601\pi$
$211$	−1.14902e13	−1.89136	−0.945678	+	0.325104i	$0.894601\pi$
$212$	1.12529e12	0.180476
$213$	−1.17920e12	−0.184288
$214$	8.64659e11	0.131695
$215$	4.70803e12	0.698920
$216$	−6.02250e11	−0.0871527
$217$	−5.07751e12	−0.716345
$218$	−3.98605e11	−0.0548317
$219$	−1.30645e12	−0.175247
$220$	−8.51423e12	−1.11383
$221$	1.09073e13	1.39174
$222$	−4.86740e11	−0.0605837
$223$	−4.24076e12	−0.514953	−0.257476	−	0.966285i	$-0.582891\pi$
$223$	−4.24076e12	−0.514953	−0.257476	+	0.966285i	$0.582891\pi$
$224$	5.72278e12	0.678021
$225$	1.18493e12	0.136990
$226$	−1.59750e12	−0.180237
$227$	−1.07805e13	−1.18712	−0.593561	−	0.804789i	$-0.702278\pi$
$227$	−1.07805e13	−1.18712	−0.593561	+	0.804789i	$0.702278\pi$
$228$	−1.27088e12	−0.136604
$229$	−1.39610e13	−1.46495	−0.732474	−	0.680795i	$-0.761635\pi$
$229$	−1.39610e13	−1.46495	−0.732474	+	0.680795i	$0.761635\pi$
$230$	−1.53908e12	−0.157673
$231$	5.98292e12	0.598477
$232$	−5.21523e12	−0.509436
$233$	−4.11516e12	−0.392581	−0.196291	−	0.980546i	$-0.562890\pi$
$233$	−4.11516e12	−0.392581	−0.196291	+	0.980546i	$0.562890\pi$
$234$	1.20164e12	0.111967
$235$	−1.47958e13	−1.34668
$236$	−1.38486e12	−0.123137
$237$	4.31758e12	0.375080
$238$	2.76438e12	0.234653
$239$	−1.46015e13	−1.21118	−0.605591	−	0.795776i	$-0.707063\pi$
$239$	−1.46015e13	−1.21118	−0.605591	+	0.795776i	$0.707063\pi$
$240$	7.10996e12	0.576376
$241$	1.53414e13	1.21554	0.607771	−	0.794112i	$-0.292064\pi$
$241$	1.53414e13	1.21554	0.607771	+	0.794112i	$0.292064\pi$
$242$	−5.15055e10	−0.00398904
$243$	8.47289e11	0.0641500
$244$	5.62304e12	0.416224
$245$	1.53065e12	0.110781
$246$	7.16025e11	0.0506740
$247$	5.21667e12	0.361044
$248$	4.58361e12	0.310258
$249$	−2.65754e12	−0.175948
$250$	−2.51433e12	−0.162837
$251$	4.24783e12	0.269129	0.134565	−	0.990905i	$-0.457036\pi$
$251$	4.24783e12	0.269129	0.134565	+	0.990905i	$0.457036\pi$
$252$	−5.31814e12	−0.329653
$253$	−9.32287e12	−0.565440
$254$	1.31382e12	0.0779740
$255$	1.13861e13	0.661310
$256$	8.81825e12	0.501259
$257$	1.06801e13	0.594214	0.297107	−	0.954844i	$-0.403978\pi$
$257$	1.06801e13	0.594214	0.297107	+	0.954844i	$0.403978\pi$
$258$	1.45169e12	0.0790614
$259$	−8.84240e12	−0.471435
$260$	−3.10657e13	−1.62154
$261$	7.33716e12	0.374978
$262$	5.15709e12	0.258076
$263$	1.08111e13	0.529800	0.264900	−	0.964276i	$-0.414661\pi$
$263$	1.08111e13	0.529800	0.264900	+	0.964276i	$0.414661\pi$
$264$	−5.40094e12	−0.259208
$265$	−4.82186e12	−0.226653
$266$	1.32213e12	0.0608732
$267$	−3.64054e12	−0.164193
$268$	1.10228e13	0.487025
$269$	−1.75753e13	−0.760789	−0.380395	−	0.924824i	$-0.624212\pi$
$269$	−1.75753e13	−0.760789	−0.380395	+	0.924824i	$0.624212\pi$
$270$	1.25440e12	0.0532027
$271$	−7.88672e12	−0.327767	−0.163884	−	0.986480i	$-0.552402\pi$
$271$	−7.88672e12	−0.327767	−0.163884	+	0.986480i	$0.552402\pi$
$272$	1.98995e13	0.810426
$273$	2.18298e13	0.871274
$274$	−8.39610e12	−0.328435
$275$	1.06264e13	0.407434
$276$	8.28697e12	0.311456
$277$	3.03489e13	1.11816	0.559081	−	0.829113i	$-0.311154\pi$
$277$	3.03489e13	1.11816	0.559081	+	0.829113i	$0.311154\pi$
$278$	−2.63524e11	−0.00951860
$279$	−6.44855e12	−0.228370
$280$	−1.61977e13	−0.562450
$281$	−1.52497e12	−0.0519252	−0.0259626	−	0.999663i	$-0.508265\pi$
$281$	−1.52497e12	−0.0519252	−0.0259626	+	0.999663i	$0.508265\pi$
$282$	−4.56218e12	−0.152336
$283$	5.83294e13	1.91013	0.955064	−	0.296401i	$-0.0957865\pi$
$283$	5.83294e13	1.91013	0.955064	+	0.296401i	$0.0957865\pi$
$284$	9.39995e12	0.301908
$285$	5.44568e12	0.171556
$286$	1.07763e13	0.333009
$287$	1.30077e13	0.394322
$288$	7.26806e12	0.216152
$289$	−2.40419e12	−0.0701504
$290$	1.08625e13	0.310987
$291$	1.73530e13	0.487487
$292$	1.04143e13	0.287095
$293$	2.59127e13	0.701037	0.350519	−	0.936556i	$-0.386005\pi$
$293$	2.59127e13	0.701037	0.350519	+	0.936556i	$0.386005\pi$
$294$	4.71966e11	0.0125314
$295$	5.93409e12	0.154644
$296$	7.98228e12	0.204184
$297$	7.59844e12	0.190794
$298$	−1.06354e13	−0.262159
$299$	−3.40162e13	−0.823179
$300$	−9.44569e12	−0.224423
$301$	2.63722e13	0.615220
$302$	1.47956e13	0.338919
$303$	−1.63466e13	−0.367699
$304$	9.51741e12	0.210239
$305$	−2.40946e13	−0.522722
$306$	3.51083e12	0.0748069
$307$	−3.59083e13	−0.751508	−0.375754	−	0.926719i	$-0.622616\pi$
$307$	−3.59083e13	−0.751508	−0.375754	+	0.926719i	$0.622616\pi$
$308$	−4.76928e13	−0.980446
$309$	1.57356e13	0.317769
$310$	−9.54697e12	−0.189398
$311$	3.43753e13	0.669985	0.334992	−	0.942221i	$-0.391266\pi$
$311$	3.43753e13	0.669985	0.334992	+	0.942221i	$0.391266\pi$
$312$	−1.97063e13	−0.377360
$313$	−9.06372e13	−1.70535	−0.852673	−	0.522445i	$-0.825020\pi$
$313$	−9.06372e13	−1.70535	−0.852673	+	0.522445i	$0.825020\pi$
$314$	2.01363e13	0.372278
$315$	2.27881e13	0.414000
$316$	−3.44175e13	−0.614470
$317$	1.24565e13	0.218559	0.109279	−	0.994011i	$-0.465146\pi$
$317$	1.24565e13	0.218559	0.109279	+	0.994011i	$0.465146\pi$
$318$	−1.48679e12	−0.0256389
$319$	6.57993e13	1.11525
$320$	−4.91624e13	−0.819046
$321$	1.99494e13	0.326702
$322$	−8.62119e12	−0.138791
$323$	1.52415e13	0.241220
$324$	−6.75415e12	−0.105093
$325$	3.87724e13	0.593150
$326$	4.57546e12	0.0688237
$327$	−9.19660e12	−0.136024
$328$	−1.17424e13	−0.170786
$329$	−8.28792e13	−1.18541
$330$	1.12494e13	0.158234
$331$	3.65138e12	0.0505130	0.0252565	−	0.999681i	$-0.491960\pi$
$331$	3.65138e12	0.0505130	0.0252565	+	0.999681i	$0.491960\pi$
$332$	2.11846e13	0.288244
$333$	−1.12300e13	−0.150293
$334$	−1.72330e13	−0.226859
$335$	−4.72325e13	−0.611638
$336$	3.98267e13	0.507351
$337$	−1.32289e14	−1.65791	−0.828954	−	0.559317i	$-0.811064\pi$
$337$	−1.32289e14	−1.65791	−0.828954	+	0.559317i	$0.811064\pi$
$338$	2.04437e13	0.252068
$339$	−3.68575e13	−0.447123
$340$	−9.07643e13	−1.08338
$341$	−5.78303e13	−0.679213
$342$	1.67914e12	0.0194063
$343$	−8.33607e13	−0.948078
$344$	−2.38069e13	−0.266460
$345$	−3.55095e13	−0.391146
$346$	2.27359e13	0.246487
$347$	−1.68357e14	−1.79646	−0.898232	−	0.439522i	$-0.855148\pi$
$347$	−1.68357e14	−1.79646	−0.898232	+	0.439522i	$0.855148\pi$
$348$	−5.84881e13	−0.614302
$349$	1.68121e13	0.173813	0.0869067	−	0.996216i	$-0.472302\pi$
$349$	1.68121e13	0.173813	0.0869067	+	0.996216i	$0.472302\pi$
$350$	9.82663e12	0.100007
$351$	2.77243e13	0.277761
$352$	6.51796e13	0.642875
$353$	−1.80494e14	−1.75268	−0.876339	−	0.481695i	$-0.840021\pi$
$353$	−1.80494e14	−1.75268	−0.876339	+	0.481695i	$0.840021\pi$
$354$	1.82973e12	0.0174932
$355$	−4.02786e13	−0.379156
$356$	2.90205e13	0.268986
$357$	6.37798e13	0.582114
$358$	4.66871e13	0.419605
$359$	−1.62816e14	−1.44105	−0.720523	−	0.693431i	$-0.756098\pi$
$359$	−1.62816e14	−1.44105	−0.720523	+	0.693431i	$0.756098\pi$
$360$	−2.05714e13	−0.179308
$361$	−1.09201e14	−0.937423
$362$	−2.39430e13	−0.202433
$363$	−1.18833e12	−0.00989581
$364$	−1.74016e14	−1.42735
$365$	−4.46252e13	−0.360553
$366$	−7.42940e12	−0.0591300
$367$	−8.46944e13	−0.664035	−0.332018	−	0.943273i	$-0.607729\pi$
$367$	−8.46944e13	−0.664035	−0.332018	+	0.943273i	$0.607729\pi$
$368$	−6.20599e13	−0.479345
$369$	1.65201e13	0.125709
$370$	−1.66259e13	−0.124645
$371$	−2.70098e13	−0.199510
$372$	5.14046e13	0.374124
$373$	3.14593e13	0.225606	0.112803	−	0.993617i	$-0.464017\pi$
$373$	3.14593e13	0.225606	0.112803	+	0.993617i	$0.464017\pi$
$374$	3.14849e13	0.222489
$375$	−5.80105e13	−0.403957
$376$	7.48173e13	0.513415
$377$	2.40081e14	1.62360
$378$	7.02655e12	0.0468314
$379$	5.94402e13	0.390449	0.195225	−	0.980759i	$-0.437456\pi$
$379$	5.94402e13	0.390449	0.195225	+	0.980759i	$0.437456\pi$
$380$	−4.34102e13	−0.281049
$381$	3.03124e13	0.193434
$382$	2.89073e13	0.181827
$383$	8.25725e13	0.511967	0.255984	−	0.966681i	$-0.417601\pi$
$383$	8.25725e13	0.511967	0.255984	+	0.966681i	$0.417601\pi$
$384$	−7.64140e13	−0.467037
$385$	2.04362e14	1.23131
$386$	4.27113e13	0.253695
$387$	3.34933e13	0.196131
$388$	−1.38329e14	−0.798618
$389$	−1.16261e13	−0.0661777	−0.0330888	−	0.999452i	$-0.510534\pi$
$389$	−1.16261e13	−0.0661777	−0.0330888	+	0.999452i	$0.510534\pi$
$390$	4.10453e13	0.230361
$391$	−9.93847e13	−0.549981
$392$	−7.74000e12	−0.0422345
$393$	1.18984e14	0.640221
$394$	6.11442e13	0.324434
$395$	1.47478e14	0.771692
$396$	−6.05709e13	−0.312565
$397$	1.29965e14	0.661419	0.330710	−	0.943733i	$-0.392712\pi$
$397$	1.29965e14	0.661419	0.330710	+	0.943733i	$0.392712\pi$
$398$	6.96553e13	0.349621
$399$	3.05042e13	0.151011
$400$	7.07373e13	0.345397
$401$	−9.22351e13	−0.444224	−0.222112	−	0.975021i	$-0.571295\pi$
$401$	−9.22351e13	−0.444224	−0.222112	+	0.975021i	$0.571295\pi$
$402$	−1.45638e13	−0.0691881
$403$	−2.11004e14	−0.988811
$404$	1.30306e14	0.602377
$405$	2.89414e13	0.131983
$406$	6.08469e13	0.273745
$407$	−1.00710e14	−0.446998
$408$	−5.75757e13	−0.252121
$409$	−2.17087e14	−0.937897	−0.468949	−	0.883225i	$-0.655367\pi$
$409$	−2.17087e14	−0.937897	−0.468949	+	0.883225i	$0.655367\pi$
$410$	2.44577e13	0.104257
$411$	−1.93715e14	−0.814765
$412$	−1.25436e14	−0.520580
$413$	3.32400e13	0.136124
$414$	−1.09491e13	−0.0442462
$415$	−9.07755e13	−0.361996
$416$	2.37819e14	0.935910
$417$	−6.08001e12	−0.0236132
$418$	1.50584e13	0.0577178
$419$	2.46901e14	0.933998	0.466999	−	0.884258i	$-0.345335\pi$
$419$	2.46901e14	0.933998	0.466999	+	0.884258i	$0.345335\pi$
$420$	−1.81655e14	−0.678229
$421$	−3.49559e14	−1.28816	−0.644080	−	0.764958i	$-0.722759\pi$
$421$	−3.49559e14	−1.28816	−0.644080	+	0.764958i	$0.722759\pi$
$422$	−1.21018e14	−0.440180
$423$	−1.05258e14	−0.377907
$424$	2.43825e13	0.0864104
$425$	1.13281e14	0.396294
$426$	−1.24196e13	−0.0428899
$427$	−1.34967e14	−0.460123
$428$	−1.59026e14	−0.535214
$429$	2.48630e14	0.826111
$430$	4.95862e13	0.162661
$431$	−2.31486e14	−0.749720	−0.374860	−	0.927081i	$-0.622309\pi$
$431$	−2.31486e14	−0.749720	−0.374860	+	0.927081i	$0.622309\pi$
$432$	5.05808e13	0.161743
$433$	2.11942e14	0.669166	0.334583	−	0.942366i	$-0.391405\pi$
$433$	2.11942e14	0.669166	0.334583	+	0.942366i	$0.391405\pi$
$434$	−5.34777e13	−0.166717
$435$	2.50620e14	0.771481
$436$	7.33106e13	0.222839
$437$	−4.75331e13	−0.142675
$438$	−1.37599e13	−0.0407856
$439$	−4.37167e14	−1.27965	−0.639826	−	0.768520i	$-0.720994\pi$
$439$	−4.37167e14	−1.27965	−0.639826	+	0.768520i	$0.720994\pi$
$440$	−1.84484e14	−0.533295
$441$	1.08892e13	0.0310873
$442$	1.14878e14	0.323904
$443$	−2.32859e14	−0.648443	−0.324222	−	0.945981i	$-0.605102\pi$
$443$	−2.32859e14	−0.648443	−0.324222	+	0.945981i	$0.605102\pi$
$444$	8.95202e13	0.246215
$445$	−1.24352e14	−0.337810
$446$	−4.46648e13	−0.119846
$447$	−2.45379e14	−0.650350
$448$	−2.75385e14	−0.720960
$449$	−3.20003e12	−0.00827560	−0.00413780	−	0.999991i	$-0.501317\pi$
$449$	−3.20003e12	−0.00827560	−0.00413780	+	0.999991i	$0.501317\pi$
$450$	1.24800e13	0.0318821
$451$	1.48152e14	0.373882
$452$	2.93809e14	0.732493
$453$	3.41364e14	0.840772
$454$	−1.13543e14	−0.276282
$455$	7.45653e14	1.79256
$456$	−2.75370e13	−0.0654047
$457$	−5.70523e13	−0.133886	−0.0669429	−	0.997757i	$-0.521325\pi$
$457$	−5.70523e13	−0.133886	−0.0669429	+	0.997757i	$0.521325\pi$
$458$	−1.47041e14	−0.340941
$459$	8.10017e13	0.185577
$460$	2.83063e14	0.640790
$461$	5.13155e14	1.14787	0.573936	−	0.818900i	$-0.305416\pi$
$461$	5.13155e14	1.14787	0.573936	+	0.818900i	$0.305416\pi$
$462$	6.30137e13	0.139285
$463$	1.18238e14	0.258262	0.129131	−	0.991628i	$-0.458781\pi$
$463$	1.18238e14	0.258262	0.129131	+	0.991628i	$0.458781\pi$
$464$	4.38009e14	0.945439
$465$	−2.20267e14	−0.469850
$466$	−4.33420e13	−0.0913663
$467$	5.89495e14	1.22811	0.614055	−	0.789263i	$-0.289537\pi$
$467$	5.89495e14	1.22811	0.614055	+	0.789263i	$0.289537\pi$
$468$	−2.21004e14	−0.455038
$469$	−2.64574e14	−0.538390
$470$	−1.55833e14	−0.313417
$471$	4.64585e14	0.923528
$472$	−3.00067e13	−0.0589572
$473$	3.00366e14	0.583330
$474$	4.54739e13	0.0872933
$475$	5.41793e13	0.102806
$476$	−5.08420e14	−0.953639
$477$	−3.43031e13	−0.0636036
$478$	−1.53787e14	−0.281881
$479$	−2.41097e14	−0.436863	−0.218432	−	0.975852i	$-0.570094\pi$
$479$	−2.41097e14	−0.436863	−0.218432	+	0.975852i	$0.570094\pi$
$480$	2.48260e14	0.444713
$481$	−3.67460e14	−0.650748
$482$	1.61579e14	0.282896
$483$	−1.98908e14	−0.344304
$484$	9.47277e12	0.0162117
$485$	5.92737e14	1.00296
$486$	8.92387e12	0.0149298
$487$	7.11458e14	1.17690	0.588450	−	0.808533i	$-0.299738\pi$
$487$	7.11458e14	1.17690	0.588450	+	0.808533i	$0.299738\pi$
$488$	1.21838e14	0.199285
$489$	1.05565e14	0.170734
$490$	1.61213e13	0.0257822
$491$	7.98098e14	1.26214	0.631070	−	0.775726i	$-0.282616\pi$
$491$	7.98098e14	1.26214	0.631070	+	0.775726i	$0.282616\pi$
$492$	−1.31690e14	−0.205942
$493$	7.01441e14	1.08476
$494$	5.49433e13	0.0840266
$495$	2.59545e14	0.392540
$496$	−3.84961e14	−0.575794
$497$	−2.25622e14	−0.333750
$498$	−2.79900e13	−0.0409488
$499$	−3.06692e14	−0.443762	−0.221881	−	0.975074i	$-0.571220\pi$
$499$	−3.06692e14	−0.443762	−0.221881	+	0.975074i	$0.571220\pi$
$500$	4.62430e14	0.661776
$501$	−3.97600e14	−0.562780
$502$	4.47392e13	0.0626351
$503$	3.90342e14	0.540532	0.270266	−	0.962786i	$-0.412888\pi$
$503$	3.90342e14	0.540532	0.270266	+	0.962786i	$0.412888\pi$
$504$	−1.15232e14	−0.157835
$505$	−5.58360e14	−0.756505
$506$	−9.81909e13	−0.131596
$507$	4.71677e14	0.625317
$508$	−2.41635e14	−0.316890
$509$	−9.21181e14	−1.19508	−0.597540	−	0.801839i	$-0.703855\pi$
$509$	−9.21181e14	−1.19508	−0.597540	+	0.801839i	$0.703855\pi$
$510$	1.19922e14	0.153908
$511$	−2.49970e14	−0.317375
$512$	7.36892e14	0.925590
$513$	3.87410e13	0.0481421
$514$	1.12486e14	0.138293
$515$	5.37490e14	0.653779
$516$	−2.66991e14	−0.321309
$517$	−9.43952e14	−1.12396
$518$	−9.31305e13	−0.109718
$519$	5.24563e14	0.611473
$520$	−6.73122e14	−0.776381
$521$	1.79069e14	0.204368	0.102184	−	0.994765i	$-0.467417\pi$
$521$	1.79069e14	0.204368	0.102184	+	0.994765i	$0.467417\pi$
$522$	7.72769e13	0.0872694
$523$	7.02264e14	0.784768	0.392384	−	0.919802i	$-0.371650\pi$
$523$	7.02264e14	0.784768	0.392384	+	0.919802i	$0.371650\pi$
$524$	−9.48480e14	−1.04883
$525$	2.26720e14	0.248092
$526$	1.13865e14	0.123302
$527$	−6.16489e14	−0.660643
$528$	4.53606e14	0.481052
$529$	−6.42862e14	−0.674702
$530$	−5.07851e13	−0.0527496
$531$	4.22156e13	0.0433963
$532$	−2.43164e14	−0.247391
$533$	5.40558e14	0.544305
$534$	−3.83431e13	−0.0382129
$535$	6.81423e14	0.672158
$536$	2.38839e14	0.233184
$537$	1.07716e15	1.04093
$538$	−1.85107e14	−0.177060
$539$	9.76537e13	0.0924593
$540$	−2.30706e14	−0.216219
$541$	1.68340e15	1.56172	0.780859	−	0.624708i	$-0.214782\pi$
$541$	1.68340e15	1.56172	0.780859	+	0.624708i	$0.214782\pi$
$542$	−8.30651e13	−0.0762820
$543$	−5.52413e14	−0.502186
$544$	6.94834e14	0.625298
$545$	−3.14134e14	−0.279856
$546$	2.29917e14	0.202774
$547$	−2.20542e15	−1.92558	−0.962788	−	0.270257i	$-0.912891\pi$
$547$	−2.20542e15	−1.92558	−0.962788	+	0.270257i	$0.912891\pi$
$548$	1.54419e15	1.33478
$549$	−1.71411e14	−0.146687
$550$	1.11920e14	0.0948231
$551$	3.35481e14	0.281406
$552$	1.79559e14	0.149123
$553$	8.26105e14	0.679277
$554$	3.19643e14	0.260232
$555$	−3.83592e14	−0.309213
$556$	4.84667e13	0.0386841
$557$	−1.48311e14	−0.117211	−0.0586057	−	0.998281i	$-0.518665\pi$
$557$	−1.48311e14	−0.117211	−0.0586057	+	0.998281i	$0.518665\pi$
$558$	−6.79179e13	−0.0531491
$559$	1.09594e15	0.849222
$560$	1.36039e15	1.04383
$561$	7.26419e14	0.551940
$562$	−1.60614e13	−0.0120847
$563$	9.70328e14	0.722973	0.361487	−	0.932377i	$-0.382269\pi$
$563$	9.70328e14	0.722973	0.361487	+	0.932377i	$0.382269\pi$
$564$	8.39066e14	0.619100
$565$	−1.25896e15	−0.919914
$566$	6.14341e14	0.444548
$567$	1.62116e14	0.116177
$568$	2.03675e14	0.144551
$569$	−1.56308e15	−1.09866	−0.549330	−	0.835606i	$-0.685117\pi$
$569$	−1.56308e15	−1.09866	−0.549330	+	0.835606i	$0.685117\pi$
$570$	5.73553e13	0.0399266
$571$	−1.28059e15	−0.882899	−0.441450	−	0.897286i	$-0.645536\pi$
$571$	−1.28059e15	−0.882899	−0.441450	+	0.897286i	$0.645536\pi$
$572$	−1.98195e15	−1.35336
$573$	6.66948e14	0.451068
$574$	1.37001e14	0.0917716
$575$	−3.53285e14	−0.234397
$576$	−3.49745e14	−0.229841
$577$	2.00667e15	1.30620	0.653100	−	0.757272i	$-0.273468\pi$
$577$	2.00667e15	1.30620	0.653100	+	0.757272i	$0.273468\pi$
$578$	−2.53215e13	−0.0163263
$579$	9.85433e14	0.629354
$580$	−1.99782e15	−1.26387
$581$	−5.08482e14	−0.318645
$582$	1.82766e14	0.113454
$583$	−3.07628e14	−0.189169
$584$	2.25654e14	0.137459
$585$	9.46996e14	0.571467
$586$	2.72920e14	0.163154
$587$	1.66363e13	0.00985251	0.00492625	−	0.999988i	$-0.498432\pi$
$587$	1.66363e13	0.00985251	0.00492625	+	0.999988i	$0.498432\pi$
$588$	−8.68031e13	−0.0509284
$589$	−2.94850e14	−0.171383
$590$	6.24994e13	0.0359907
$591$	1.41072e15	0.804838
$592$	−6.70403e14	−0.378937
$593$	3.20402e15	1.79430	0.897148	−	0.441730i	$-0.145635\pi$
$593$	3.20402e15	1.79430	0.897148	+	0.441730i	$0.145635\pi$
$594$	8.00288e13	0.0444039
$595$	2.17857e15	1.19764
$596$	1.95604e15	1.06543
$597$	1.60708e15	0.867321
$598$	−3.58267e14	−0.191580
$599$	1.72077e15	0.911752	0.455876	−	0.890043i	$-0.349326\pi$
$599$	1.72077e15	0.911752	0.455876	+	0.890043i	$0.349326\pi$
$600$	−2.04666e14	−0.107452
$601$	−2.39539e15	−1.24614	−0.623069	−	0.782167i	$-0.714114\pi$
$601$	−2.39539e15	−1.24614	−0.623069	+	0.782167i	$0.714114\pi$
$602$	2.77759e14	0.143182
$603$	−3.36015e14	−0.171638
$604$	−2.72118e15	−1.37738
$605$	−4.05906e13	−0.0203597
$606$	−1.72166e14	−0.0855754
$607$	−3.86178e15	−1.90217	−0.951085	−	0.308929i	$-0.900029\pi$
$607$	−3.86178e15	−1.90217	−0.951085	+	0.308929i	$0.900029\pi$
$608$	3.32321e14	0.162214
$609$	1.40386e15	0.679091
$610$	−2.53771e14	−0.121654
$611$	−3.44418e15	−1.63629
$612$	−6.45704e14	−0.304019
$613$	−1.45374e15	−0.678350	−0.339175	−	0.940723i	$-0.610148\pi$
$613$	−1.45374e15	−0.678350	−0.339175	+	0.940723i	$0.610148\pi$
$614$	−3.78195e14	−0.174900
$615$	5.64288e14	0.258635
$616$	−1.03339e15	−0.469430
$617$	−7.93563e14	−0.357284	−0.178642	−	0.983914i	$-0.557170\pi$
$617$	−7.93563e14	−0.357284	−0.178642	+	0.983914i	$0.557170\pi$
$618$	1.65731e14	0.0739550
$619$	−1.29098e15	−0.570981	−0.285491	−	0.958382i	$-0.592157\pi$
$619$	−1.29098e15	−0.570981	−0.285491	+	0.958382i	$0.592157\pi$
$620$	1.75586e15	0.769724
$621$	−2.52617e14	−0.109764
$622$	3.62050e14	0.155927
$623$	−6.96563e14	−0.297356
$624$	1.65506e15	0.700325
$625$	−2.96133e15	−1.24207
$626$	−9.54615e14	−0.396889
$627$	3.47427e14	0.143183
$628$	−3.70343e15	−1.51296
$629$	−1.07360e15	−0.434776
$630$	2.40010e14	0.0963511
$631$	6.53217e14	0.259954	0.129977	−	0.991517i	$-0.458510\pi$
$631$	6.53217e14	0.259954	0.129977	+	0.991517i	$0.458510\pi$
$632$	−7.45747e14	−0.294203
$633$	−2.79211e15	−1.09198
$634$	1.31195e14	0.0508657
$635$	1.03540e15	0.397972
$636$	2.73446e14	0.104198
$637$	3.56307e14	0.134604
$638$	6.93015e14	0.259555
$639$	−2.86545e14	−0.106399
$640$	−2.61012e15	−0.960883
$641$	2.04218e15	0.745374	0.372687	−	0.927957i	$-0.378436\pi$
$641$	2.04218e15	0.745374	0.372687	+	0.927957i	$0.378436\pi$
$642$	2.10112e14	0.0760341
$643$	2.99974e15	1.07628	0.538138	−	0.842857i	$-0.319128\pi$
$643$	2.99974e15	1.07628	0.538138	+	0.842857i	$0.319128\pi$
$644$	1.58559e15	0.564052
$645$	1.14405e15	0.403522
$646$	1.60527e14	0.0561397
$647$	−1.39460e14	−0.0483589	−0.0241795	−	0.999708i	$-0.507697\pi$
$647$	−1.39460e14	−0.0483589	−0.0241795	+	0.999708i	$0.507697\pi$
$648$	−1.46347e14	−0.0503177
$649$	3.78587e14	0.129068
$650$	4.08362e14	0.138045
$651$	−1.23384e15	−0.413582
$652$	−8.41509e14	−0.279703
$653$	5.44858e14	0.179581	0.0897906	−	0.995961i	$-0.471380\pi$
$653$	5.44858e14	0.179581	0.0897906	+	0.995961i	$0.471380\pi$
$654$	−9.68610e13	−0.0316571
$655$	4.06422e15	1.31719
$656$	9.86206e14	0.316954
$657$	−3.17467e14	−0.101179
$658$	−8.72906e14	−0.275883
$659$	5.06140e15	1.58636	0.793179	−	0.608989i	$-0.208425\pi$
$659$	5.06140e15	1.58636	0.793179	+	0.608989i	$0.208425\pi$
$660$	−2.06896e15	−0.643073
$661$	1.64713e15	0.507713	0.253857	−	0.967242i	$-0.418301\pi$
$661$	1.64713e15	0.507713	0.253857	+	0.967242i	$0.418301\pi$
$662$	3.84573e13	0.0117560
$663$	2.65047e15	0.803524
$664$	4.59021e14	0.138009
$665$	1.04195e15	0.310691
$666$	−1.18278e14	−0.0349780
$667$	−2.18756e15	−0.641605
$668$	3.16946e15	0.921967
$669$	−1.03051e15	−0.297308
$670$	−4.97465e14	−0.142348
$671$	−1.53720e15	−0.436272
$672$	1.39064e15	0.391456
$673$	−1.65542e15	−0.462194	−0.231097	−	0.972931i	$-0.574232\pi$
$673$	−1.65542e15	−0.462194	−0.231097	+	0.972931i	$0.574232\pi$
$674$	−1.39331e15	−0.385849
$675$	2.87939e14	0.0790915
$676$	−3.75996e15	−1.02442
$677$	−2.03395e15	−0.549671	−0.274835	−	0.961491i	$-0.588623\pi$
$677$	−2.03395e15	−0.549671	−0.274835	+	0.961491i	$0.588623\pi$
$678$	−3.88193e14	−0.104060
$679$	3.32024e15	0.882847
$680$	−1.96665e15	−0.518714
$681$	−2.61965e15	−0.685385
$682$	−6.09084e14	−0.158075
$683$	4.24192e15	1.09207	0.546033	−	0.837764i	$-0.316137\pi$
$683$	4.24192e15	1.09207	0.546033	+	0.837764i	$0.316137\pi$
$684$	−3.08823e14	−0.0788681
$685$	−6.61683e15	−1.67630
$686$	−8.77977e14	−0.220648
$687$	−3.39253e15	−0.845788
$688$	1.99946e15	0.494510
$689$	−1.12244e15	−0.275395
$690$	−3.73995e14	−0.0910324
$691$	1.35658e15	0.327579	0.163789	−	0.986495i	$-0.447628\pi$
$691$	1.35658e15	0.327579	0.163789	+	0.986495i	$0.447628\pi$
$692$	−4.18155e15	−1.00174
$693$	1.45385e15	0.345531
$694$	−1.77318e15	−0.418095
$695$	−2.07679e14	−0.0485820
$696$	−1.26730e15	−0.294123
$697$	1.57934e15	0.363660
$698$	1.77070e14	0.0404520
$699$	−9.99984e14	−0.226657
$700$	−1.80729e15	−0.406433
$701$	1.74735e15	0.389881	0.194940	−	0.980815i	$-0.437549\pi$
$701$	1.74735e15	0.389881	0.194940	+	0.980815i	$0.437549\pi$
$702$	2.91999e14	0.0646440
$703$	−5.13477e14	−0.112789
$704$	−3.13650e15	−0.683589
$705$	−3.59538e15	−0.777507
$706$	−1.90101e15	−0.407905
$707$	−3.12767e15	−0.665909
$708$	−3.36521e14	−0.0710934
$709$	2.11534e15	0.443430	0.221715	−	0.975112i	$-0.428835\pi$
$709$	2.11534e15	0.443430	0.221715	+	0.975112i	$0.428835\pi$
$710$	−4.24224e14	−0.0882419
$711$	1.04917e15	0.216553
$712$	6.28806e14	0.128788
$713$	1.92262e15	0.390752
$714$	6.71746e14	0.135477
$715$	8.49261e15	1.69964
$716$	−8.58660e15	−1.70530
$717$	−3.54817e15	−0.699276
$718$	−1.71482e15	−0.335378
$719$	−6.69755e14	−0.129989	−0.0649945	−	0.997886i	$-0.520703\pi$
$719$	−6.69755e14	−0.129989	−0.0649945	+	0.997886i	$0.520703\pi$
$720$	1.72772e15	0.332771
$721$	3.01077e15	0.575485
$722$	−1.15013e15	−0.218169
$723$	3.72795e15	0.701794
$724$	4.40355e15	0.822699
$725$	2.49343e15	0.462315
$726$	−1.25158e13	−0.00230308
$727$	4.65915e15	0.850879	0.425439	−	0.904987i	$-0.360120\pi$
$727$	4.65915e15	0.850879	0.425439	+	0.904987i	$0.360120\pi$
$728$	−3.77052e15	−0.683405
$729$	2.05891e14	0.0370370
$730$	−4.70004e14	−0.0839124
$731$	3.20199e15	0.567381
$732$	1.36640e15	0.240307
$733$	6.21756e15	1.08530	0.542648	−	0.839961i	$-0.317422\pi$
$733$	6.21756e15	1.08530	0.542648	+	0.839961i	$0.317422\pi$
$734$	−8.92023e14	−0.154542
$735$	3.71949e14	0.0639592
$736$	−2.16695e15	−0.369847
$737$	−3.01337e15	−0.510483
$738$	1.73994e14	0.0292567
$739$	7.78238e14	0.129888	0.0649439	−	0.997889i	$-0.479313\pi$
$739$	7.78238e14	0.129888	0.0649439	+	0.997889i	$0.479313\pi$
$740$	3.05780e15	0.506564
$741$	1.26765e15	0.208449
$742$	−2.84475e14	−0.0464325
$743$	−1.05630e16	−1.71139	−0.855696	−	0.517479i	$-0.826871\pi$
$743$	−1.05630e16	−1.71139	−0.855696	+	0.517479i	$0.826871\pi$
$744$	1.11382e15	0.179128
$745$	−8.38158e15	−1.33803
$746$	3.31337e14	0.0525058
$747$	−6.45783e14	−0.101584
$748$	−5.79064e15	−0.904207
$749$	3.81702e15	0.591663
$750$	−6.10982e14	−0.0940138
$751$	−9.17216e14	−0.140105	−0.0700523	−	0.997543i	$-0.522317\pi$
$751$	−9.17216e14	−0.140105	−0.0700523	+	0.997543i	$0.522317\pi$
$752$	−6.28364e15	−0.952825
$753$	1.03222e15	0.155382
$754$	2.52859e15	0.377865
$755$	1.16602e16	1.72981
$756$	−1.29231e15	−0.190325
$757$	−7.57673e15	−1.10778	−0.553891	−	0.832589i	$-0.686858\pi$
$757$	−7.57673e15	−1.10778	−0.553891	+	0.832589i	$0.686858\pi$
$758$	6.26039e14	0.0908701
$759$	−2.26546e15	−0.326457
$760$	−9.40597e14	−0.134564
$761$	4.74339e15	0.673711	0.336855	−	0.941556i	$-0.390637\pi$
$761$	4.74339e15	0.673711	0.336855	+	0.941556i	$0.390637\pi$
$762$	3.19258e14	0.0450183
$763$	−1.75963e15	−0.246341
$764$	−5.31657e15	−0.738955
$765$	2.76683e15	0.381807
$766$	8.69676e14	0.119151
$767$	1.38134e15	0.187900
$768$	2.14283e15	0.289402
$769$	−3.00905e15	−0.403492	−0.201746	−	0.979438i	$-0.564662\pi$
$769$	−3.00905e15	−0.403492	−0.201746	+	0.979438i	$0.564662\pi$
$770$	2.15240e15	0.286565
$771$	2.59526e15	0.343070
$772$	−7.85536e15	−1.03103
$773$	6.36741e15	0.829805	0.414902	−	0.909866i	$-0.363816\pi$
$773$	6.36741e15	0.829805	0.414902	+	0.909866i	$0.363816\pi$
$774$	3.52760e14	0.0456461
$775$	−2.19145e15	−0.281561
$776$	−2.99727e15	−0.382372
$777$	−2.14870e15	−0.272183
$778$	−1.22449e14	−0.0154017
$779$	7.55357e14	0.0943401
$780$	−7.54897e15	−0.936197
$781$	−2.56972e15	−0.316450
$782$	−1.04675e15	−0.127998
$783$	1.78293e15	0.216493
$784$	6.50055e14	0.0783812
$785$	1.58691e16	1.90007
$786$	1.25317e15	0.149000
$787$	−6.42132e15	−0.758164	−0.379082	−	0.925363i	$-0.623760\pi$
$787$	−6.42132e15	−0.758164	−0.379082	+	0.925363i	$0.623760\pi$
$788$	−1.12455e16	−1.31851
$789$	2.62709e15	0.305880
$790$	1.55328e15	0.179598
$791$	−7.05214e15	−0.809749
$792$	−1.31243e15	−0.149654
$793$	−5.60876e15	−0.635133
$794$	1.36882e15	0.153934
$795$	−1.17171e15	−0.130858
$796$	−1.28109e16	−1.42088
$797$	−1.29411e16	−1.42544	−0.712721	−	0.701448i	$-0.752537\pi$
$797$	−1.29411e16	−1.42544	−0.712721	+	0.701448i	$0.752537\pi$
$798$	3.21278e14	0.0351451
$799$	−1.00628e16	−1.09323
$800$	2.46995e15	0.266497
$801$	−8.84650e14	−0.0947966
$802$	−9.71445e14	−0.103385
$803$	−2.84703e15	−0.300923
$804$	2.67854e15	0.281184
$805$	−6.79422e15	−0.708373
$806$	−2.22235e15	−0.230128
$807$	−4.27079e15	−0.439242
$808$	2.82344e15	0.288413
$809$	2.18983e15	0.222174	0.111087	−	0.993811i	$-0.464567\pi$
$809$	2.18983e15	0.222174	0.111087	+	0.993811i	$0.464567\pi$
$810$	3.04818e14	0.0307166
$811$	7.41175e15	0.741833	0.370917	−	0.928666i	$-0.379044\pi$
$811$	7.41175e15	0.741833	0.370917	+	0.928666i	$0.379044\pi$
$812$	−1.11908e16	−1.11251
$813$	−1.91647e15	−0.189236
$814$	−1.06071e15	−0.104031
$815$	3.60585e15	0.351270
$816$	4.83558e15	0.467900
$817$	1.53143e15	0.147189
$818$	−2.28642e15	−0.218279
$819$	5.30463e15	0.503030
$820$	−4.49822e15	−0.423705
$821$	6.34847e15	0.593994	0.296997	−	0.954878i	$-0.404015\pi$
$821$	6.34847e15	0.593994	0.296997	+	0.954878i	$0.404015\pi$
$822$	−2.04025e15	−0.189622
$823$	1.90319e16	1.75704	0.878521	−	0.477704i	$-0.158531\pi$
$823$	1.90319e16	1.75704	0.878521	+	0.477704i	$0.158531\pi$
$824$	−2.71790e15	−0.249250
$825$	2.58222e15	0.235232
$826$	3.50093e14	0.0316806
$827$	9.51689e15	0.855489	0.427745	−	0.903900i	$-0.359308\pi$
$827$	9.51689e15	0.855489	0.427745	+	0.903900i	$0.359308\pi$
$828$	2.01373e15	0.179819
$829$	−4.20099e15	−0.372650	−0.186325	−	0.982488i	$-0.559658\pi$
$829$	−4.20099e15	−0.372650	−0.186325	+	0.982488i	$0.559658\pi$
$830$	−9.56071e14	−0.0842482
$831$	7.37479e15	0.645571
$832$	−1.14441e16	−0.995182
$833$	1.04102e15	0.0899313
$834$	−6.40362e13	−0.00549557
$835$	−1.35811e16	−1.15787
$836$	−2.76951e15	−0.234568
$837$	−1.56700e15	−0.131849
$838$	2.60043e15	0.217371
$839$	3.02779e15	0.251440	0.125720	−	0.992066i	$-0.459876\pi$
$839$	3.02779e15	0.251440	0.125720	+	0.992066i	$0.459876\pi$
$840$	−3.93604e15	−0.324731
$841$	3.23892e15	0.265474
$842$	−3.68165e15	−0.299796
$843$	−3.70569e14	−0.0299790
$844$	2.22573e16	1.78891
$845$	1.61114e16	1.28653
$846$	−1.10861e15	−0.0879512
$847$	−2.27370e14	−0.0179215
$848$	−2.04780e15	−0.160365
$849$	1.41740e16	1.10281
$850$	1.19311e15	0.0922305
$851$	3.34821e15	0.257158
$852$	2.28419e15	0.174307
$853$	−2.17603e16	−1.64985	−0.824926	−	0.565241i	$-0.808783\pi$
$853$	−2.17603e16	−1.64985	−0.824926	+	0.565241i	$0.808783\pi$
$854$	−1.42151e15	−0.107085
$855$	1.32330e15	0.0990478
$856$	−3.44573e15	−0.256257
$857$	1.58468e15	0.117097	0.0585485	−	0.998285i	$-0.481353\pi$
$857$	1.58468e15	0.117097	0.0585485	+	0.998285i	$0.481353\pi$
$858$	2.61864e15	0.192263
$859$	2.23915e16	1.63351	0.816754	−	0.576986i	$-0.195771\pi$
$859$	2.23915e16	1.63351	0.816754	+	0.576986i	$0.195771\pi$
$860$	−9.11979e15	−0.661063
$861$	3.16088e15	0.227662
$862$	−2.43807e15	−0.174484
$863$	1.84795e16	1.31411	0.657055	−	0.753843i	$-0.271802\pi$
$863$	1.84795e16	1.31411	0.657055	+	0.753843i	$0.271802\pi$
$864$	1.76614e15	0.124796
$865$	1.79178e16	1.25805
$866$	2.23223e15	0.155737
$867$	−5.84217e14	−0.0405013
$868$	9.83550e15	0.677545
$869$	9.40891e15	0.644066
$870$	2.63960e15	0.179549
$871$	−1.09948e16	−0.743170
$872$	1.58847e15	0.106694
$873$	4.21678e15	0.281451
$874$	−5.00631e14	−0.0332051
$875$	−1.10995e16	−0.731573
$876$	2.53068e15	0.165754
$877$	2.40887e16	1.56789	0.783945	−	0.620830i	$-0.213204\pi$
$877$	2.40887e16	1.56789	0.783945	+	0.620830i	$0.213204\pi$
$878$	−4.60435e15	−0.297817
$879$	6.29679e15	0.404744
$880$	1.54941e16	0.989719
$881$	1.85528e16	1.17772	0.588860	−	0.808235i	$-0.299577\pi$
$881$	1.85528e16	1.17772	0.588860	+	0.808235i	$0.299577\pi$
$882$	1.14688e14	0.00723503
$883$	−2.24230e16	−1.40575	−0.702877	−	0.711311i	$-0.748102\pi$
$883$	−2.24230e16	−1.40575	−0.702877	+	0.711311i	$0.748102\pi$
$884$	−2.11282e16	−1.31636
$885$	1.44198e15	0.0892838
$886$	−2.45253e15	−0.150914
$887$	−1.76236e16	−1.07774	−0.538870	−	0.842389i	$-0.681149\pi$
$887$	−1.76236e16	−1.07774	−0.538870	+	0.842389i	$0.681149\pi$
$888$	1.93969e15	0.117886
$889$	5.79983e15	0.350312
$890$	−1.30971e15	−0.0786194
$891$	1.84642e15	0.110155
$892$	8.21466e15	0.487061
$893$	−4.81278e15	−0.283604
$894$	−2.58440e15	−0.151357
$895$	3.67934e16	2.14162
$896$	−1.46207e16	−0.845812
$897$	−8.26593e15	−0.475262
$898$	−3.37036e13	−0.00192600
$899$	−1.35695e16	−0.770703
$900$	−2.29530e15	−0.129570
$901$	−3.27941e15	−0.183996
$902$	1.56037e15	0.0870145
$903$	6.40844e15	0.355197
$904$	6.36616e15	0.350712
$905$	−1.88691e16	−1.03320
$906$	3.59534e15	0.195675
$907$	−2.58341e16	−1.39750	−0.698752	−	0.715364i	$-0.746261\pi$
$907$	−2.58341e16	−1.39750	−0.698752	+	0.715364i	$0.746261\pi$
$908$	2.08825e16	1.12282
$909$	−3.97222e15	−0.212291
$910$	7.85342e15	0.417187
$911$	−7.39276e14	−0.0390351	−0.0195176	−	0.999810i	$-0.506213\pi$
$911$	−7.39276e14	−0.0390351	−0.0195176	+	0.999810i	$0.506213\pi$
$912$	2.31273e15	0.121382
$913$	−5.79135e15	−0.302128
$914$	−6.00890e14	−0.0311595
$915$	−5.85499e15	−0.301794
$916$	2.70435e16	1.38560
$917$	2.27659e16	1.15945
$918$	8.53131e14	0.0431898
$919$	6.32240e15	0.318161	0.159080	−	0.987266i	$-0.449147\pi$
$919$	6.32240e15	0.318161	0.159080	+	0.987266i	$0.449147\pi$
$920$	6.13333e15	0.306805
$921$	−8.72571e15	−0.433883
$922$	5.40469e15	0.267147
$923$	−9.37608e15	−0.460693
$924$	−1.15893e16	−0.566061
$925$	−3.81637e15	−0.185298
$926$	1.24531e15	0.0601059
$927$	3.82375e15	0.183464
$928$	1.52940e16	0.729470
$929$	1.11302e15	0.0527735	0.0263868	−	0.999652i	$-0.491600\pi$
$929$	1.11302e15	0.0527735	0.0263868	+	0.999652i	$0.491600\pi$
$930$	−2.31991e15	−0.109349
$931$	4.97892e14	0.0233298
$932$	7.97136e15	0.371317
$933$	8.35321e15	0.386816
$934$	6.20872e15	0.285821
$935$	2.48128e16	1.13556
$936$	−4.78864e15	−0.217869
$937$	−2.97929e15	−0.134755	−0.0673774	−	0.997728i	$-0.521463\pi$
$937$	−2.97929e15	−0.134755	−0.0673774	+	0.997728i	$0.521463\pi$
$938$	−2.78657e15	−0.125301
$939$	−2.20248e16	−0.984582
$940$	2.86605e16	1.27374
$941$	−7.29885e15	−0.322487	−0.161243	−	0.986915i	$-0.551550\pi$
$941$	−7.29885e15	−0.322487	−0.161243	+	0.986915i	$0.551550\pi$
$942$	4.89313e15	0.214935
$943$	−4.92543e15	−0.215095
$944$	2.52015e15	0.109416
$945$	5.53751e15	0.239023
$946$	3.16353e15	0.135760
$947$	−1.47142e16	−0.627784	−0.313892	−	0.949459i	$-0.601633\pi$
$947$	−1.47142e16	−0.627784	−0.313892	+	0.949459i	$0.601633\pi$
$948$	−8.36345e15	−0.354764
$949$	−1.03879e16	−0.438090
$950$	5.70631e14	0.0239263
$951$	3.02692e15	0.126185
$952$	−1.10163e16	−0.456595
$953$	−2.56522e16	−1.05709	−0.528547	−	0.848904i	$-0.677263\pi$
$953$	−2.56522e16	−1.05709	−0.528547	+	0.848904i	$0.677263\pi$
$954$	−3.61289e14	−0.0148026
$955$	2.27814e16	0.928028
$956$	2.82842e16	1.14558
$957$	1.59892e16	0.643890
$958$	−2.53929e15	−0.101672
$959$	−3.70644e16	−1.47555
$960$	−1.19465e16	−0.472877
$961$	−1.34824e16	−0.530624
$962$	−3.87019e15	−0.151450
$963$	4.84770e15	0.188621
$964$	−2.97173e16	−1.14970
$965$	3.36601e16	1.29484
$966$	−2.09495e15	−0.0801308
$967$	−2.49894e16	−0.950409	−0.475205	−	0.879875i	$-0.657626\pi$
$967$	−2.49894e16	−0.950409	−0.475205	+	0.879875i	$0.657626\pi$
$968$	2.05253e14	0.00776202
$969$	3.70368e15	0.139268
$970$	6.24286e15	0.233421
$971$	5.05666e16	1.88000	0.940000	−	0.341174i	$-0.110825\pi$
$971$	5.05666e16	1.88000	0.940000	+	0.341174i	$0.110825\pi$
$972$	−1.64126e15	−0.0606754
$973$	−1.16332e15	−0.0427640
$974$	7.49326e15	0.273903
$975$	9.42170e15	0.342455
$976$	−1.02328e16	−0.369844
$977$	6.57844e15	0.236430	0.118215	−	0.992988i	$-0.462283\pi$
$977$	6.57844e15	0.236430	0.118215	+	0.992988i	$0.462283\pi$
$978$	1.11184e15	0.0397354
$979$	−7.93350e15	−0.281942
$980$	−2.96499e15	−0.104780
$981$	−2.23477e15	−0.0785333
$982$	8.40577e15	0.293741
$983$	9.91690e15	0.344613	0.172306	−	0.985043i	$-0.444878\pi$
$983$	9.91690e15	0.344613	0.172306	+	0.985043i	$0.444878\pi$
$984$	−2.85341e15	−0.0986033
$985$	4.81867e16	1.65588
$986$	7.38776e15	0.252458
$987$	−2.01396e16	−0.684396
$988$	−1.01051e16	−0.341488
$989$	−9.98594e15	−0.335590
$990$	2.73359e15	0.0913567
$991$	−2.18032e15	−0.0724630	−0.0362315	−	0.999343i	$-0.511535\pi$
$991$	−2.18032e15	−0.0724630	−0.0362315	+	0.999343i	$0.511535\pi$
$992$	−1.34417e16	−0.444264
$993$	8.87286e14	0.0291637
$994$	−2.37631e15	−0.0776744
$995$	5.48942e16	1.78443
$996$	5.14785e15	0.166418
$997$	1.94934e16	0.626707	0.313354	−	0.949636i	$-0.398547\pi$
$997$	1.94934e16	0.626707	0.313354	+	0.949636i	$0.398547\pi$
$998$	−3.23017e15	−0.103278
$999$	−2.72890e15	−0.0867716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.15	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.15	✓	28	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+10.5323 q^{2} +243.000 q^{3} -1937.07 q^{4} +8300.31 q^{5} +2559.34 q^{6} +46494.5 q^{7} -41971.8 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+10.5323 q^{2} +243.000 q^{3} -1937.07 q^{4} +8300.31 q^{5} +2559.34 q^{6} +46494.5 q^{7} -41971.8 q^{8} +59049.0 q^{9} +87421.0 q^{10} +529548. q^{11} -470708. q^{12} +1.93215e6 q^{13} +489692. q^{14} +2.01697e6 q^{15} +3.52506e6 q^{16} +5.64515e6 q^{17} +621920. q^{18} +2.69993e6 q^{19} -1.60783e7 q^{20} +1.12982e7 q^{21} +5.57734e6 q^{22} -1.76053e7 q^{23} -1.01992e7 q^{24} +2.00670e7 q^{25} +2.03499e7 q^{26} +1.43489e7 q^{27} -9.00631e7 q^{28} +1.24255e8 q^{29} +2.12433e7 q^{30} -1.09207e8 q^{31} +1.23085e8 q^{32} +1.28680e8 q^{33} +5.94562e7 q^{34} +3.85918e8 q^{35} -1.14382e8 q^{36} -1.90182e8 q^{37} +2.84363e7 q^{38} +4.69513e8 q^{39} -3.48379e8 q^{40} +2.79770e8 q^{41} +1.18995e8 q^{42} +5.67211e8 q^{43} -1.02577e9 q^{44} +4.90125e8 q^{45} -1.85424e8 q^{46} -1.78256e9 q^{47} +8.56591e8 q^{48} +1.84409e8 q^{49} +2.11351e8 q^{50} +1.37177e9 q^{51} -3.74272e9 q^{52} -5.80925e8 q^{53} +1.51126e8 q^{54} +4.39541e9 q^{55} -1.95146e9 q^{56} +6.56082e8 q^{57} +1.30869e9 q^{58} +7.14924e8 q^{59} -3.90702e9 q^{60} -2.90286e9 q^{61} -1.15019e9 q^{62} +2.74545e9 q^{63} -5.92297e9 q^{64} +1.60375e10 q^{65} +1.35529e9 q^{66} -5.69045e9 q^{67} -1.09351e10 q^{68} -4.27809e9 q^{69} +4.06459e9 q^{70} -4.85266e9 q^{71} -2.47839e9 q^{72} -5.37633e9 q^{73} -2.00304e9 q^{74} +4.87627e9 q^{75} -5.22995e9 q^{76} +2.46211e10 q^{77} +4.94504e9 q^{78} +1.77678e10 q^{79} +2.92591e10 q^{80} +3.48678e9 q^{81} +2.94661e9 q^{82} -1.09364e10 q^{83} -2.18853e10 q^{84} +4.68565e10 q^{85} +5.97402e9 q^{86} +3.01941e10 q^{87} -2.22261e10 q^{88} -1.49816e10 q^{89} +5.16212e9 q^{90} +8.98344e10 q^{91} +3.41028e10 q^{92} -2.65373e10 q^{93} -1.87744e10 q^{94} +2.24102e10 q^{95} +2.99097e10 q^{96} +7.14115e10 q^{97} +1.94225e9 q^{98} +3.12693e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Introduction

L-functions

Modular forms

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