LMFDB - Embedded newform 177.12.a.d.1.12

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			1.12
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)

$f(q)$	$=$	$q-12.4112 q^{2} +243.000 q^{3} -1893.96 q^{4} -2629.42 q^{5} -3015.92 q^{6} +23296.0 q^{7} +48924.4 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-12.4112 q^{2} +243.000 q^{3} -1893.96 q^{4} -2629.42 q^{5} -3015.92 q^{6} +23296.0 q^{7} +48924.4 q^{8} +59049.0 q^{9} +32634.3 q^{10} -219870. q^{11} -460233. q^{12} +1.40491e6 q^{13} -289131. q^{14} -638950. q^{15} +3.27163e6 q^{16} -5.70617e6 q^{17} -732868. q^{18} +820391. q^{19} +4.98003e6 q^{20} +5.66094e6 q^{21} +2.72885e6 q^{22} +2.97055e7 q^{23} +1.18886e7 q^{24} -4.19143e7 q^{25} -1.74366e7 q^{26} +1.43489e7 q^{27} -4.41218e7 q^{28} +9.68327e7 q^{29} +7.93012e6 q^{30} +6.91538e7 q^{31} -1.40802e8 q^{32} -5.34284e7 q^{33} +7.08203e7 q^{34} -6.12552e7 q^{35} -1.11837e8 q^{36} -4.51038e8 q^{37} -1.01820e7 q^{38} +3.41394e8 q^{39} -1.28643e8 q^{40} +4.49616e8 q^{41} -7.02589e7 q^{42} -1.79394e9 q^{43} +4.16426e8 q^{44} -1.55265e8 q^{45} -3.68681e8 q^{46} +5.98279e8 q^{47} +7.95005e8 q^{48} -1.43462e9 q^{49} +5.20205e8 q^{50} -1.38660e9 q^{51} -2.66085e9 q^{52} -3.80930e9 q^{53} -1.78087e8 q^{54} +5.78132e8 q^{55} +1.13974e9 q^{56} +1.99355e8 q^{57} -1.20181e9 q^{58} +7.14924e8 q^{59} +1.21015e9 q^{60} +9.73343e9 q^{61} -8.58280e8 q^{62} +1.37561e9 q^{63} -4.95277e9 q^{64} -3.69412e9 q^{65} +6.63109e8 q^{66} +2.05666e10 q^{67} +1.08073e10 q^{68} +7.21845e9 q^{69} +7.60249e8 q^{70} -1.31509e10 q^{71} +2.88894e9 q^{72} +2.61072e10 q^{73} +5.59791e9 q^{74} -1.01852e10 q^{75} -1.55379e9 q^{76} -5.12210e9 q^{77} -4.23710e9 q^{78} -3.90581e10 q^{79} -8.60249e9 q^{80} +3.48678e9 q^{81} -5.58027e9 q^{82} +2.57619e10 q^{83} -1.07216e10 q^{84} +1.50039e10 q^{85} +2.22649e10 q^{86} +2.35303e10 q^{87} -1.07570e10 q^{88} +4.36938e10 q^{89} +1.92702e9 q^{90} +3.27289e10 q^{91} -5.62612e10 q^{92} +1.68044e10 q^{93} -7.42534e9 q^{94} -2.15716e9 q^{95} -3.42149e10 q^{96} -4.40290e10 q^{97} +1.78053e10 q^{98} -1.29831e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−12.4112	−0.274251	−0.137125	−	0.990554i	$-0.543786\pi$
$2$	−12.4112	−0.274251	−0.137125	+	0.990554i	$0.543786\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1893.96	−0.924786
$5$	−2629.42	−0.376293	−0.188146	−	0.982141i	$-0.560248\pi$
$5$	−2629.42	−0.376293	−0.188146	+	0.982141i	$0.560248\pi$
$6$	−3015.92	−0.158339
$7$	23296.0	0.523893	0.261947	−	0.965082i	$-0.415636\pi$
$7$	23296.0	0.523893	0.261947	+	0.965082i	$0.415636\pi$
$8$	48924.4	0.527874
$9$	59049.0	0.333333
$10$	32634.3	0.103199
$11$	−219870.	−0.411629	−0.205815	−	0.978591i	$-0.565984\pi$
$11$	−219870.	−0.411629	−0.205815	+	0.978591i	$0.565984\pi$
$12$	−460233.	−0.533926
$13$	1.40491e6	1.04945	0.524724	−	0.851272i	$-0.324168\pi$
$13$	1.40491e6	1.04945	0.524724	+	0.851272i	$0.324168\pi$
$14$	−289131.	−0.143678
$15$	−638950.	−0.217253
$16$	3.27163e6	0.780016
$17$	−5.70617e6	−0.974711	−0.487355	−	0.873204i	$-0.662038\pi$
$17$	−5.70617e6	−0.974711	−0.487355	+	0.873204i	$0.662038\pi$
$18$	−732868.	−0.0914170
$19$	820391.	0.0760109	0.0380055	−	0.999278i	$-0.487900\pi$
$19$	820391.	0.0760109	0.0380055	+	0.999278i	$0.487900\pi$
$20$	4.98003e6	0.347990
$21$	5.66094e6	0.302470
$22$	2.72885e6	0.112890
$23$	2.97055e7	0.962353	0.481176	−	0.876624i	$-0.340210\pi$
$23$	2.97055e7	0.962353	0.481176	+	0.876624i	$0.340210\pi$
$24$	1.18886e7	0.304768
$25$	−4.19143e7	−0.858404
$26$	−1.74366e7	−0.287812
$27$	1.43489e7	0.192450
$28$	−4.41218e7	−0.484489
$29$	9.68327e7	0.876664	0.438332	−	0.898813i	$-0.355569\pi$
$29$	9.68327e7	0.876664	0.438332	+	0.898813i	$0.355569\pi$
$30$	7.93012e6	0.0595817
$31$	6.91538e7	0.433837	0.216919	−	0.976190i	$-0.430399\pi$
$31$	6.91538e7	0.433837	0.216919	+	0.976190i	$0.430399\pi$
$32$	−1.40802e8	−0.741795
$33$	−5.34284e7	−0.237654
$34$	7.08203e7	0.267315
$35$	−6.12552e7	−0.197137
$36$	−1.11837e8	−0.308262
$37$	−4.51038e8	−1.06931	−0.534655	−	0.845071i	$-0.679558\pi$
$37$	−4.51038e8	−1.06931	−0.534655	+	0.845071i	$0.679558\pi$
$38$	−1.01820e7	−0.0208461
$39$	3.41394e8	0.605900
$40$	−1.28643e8	−0.198635
$41$	4.49616e8	0.606081	0.303041	−	0.952978i	$-0.401998\pi$
$41$	4.49616e8	0.606081	0.303041	+	0.952978i	$0.401998\pi$
$42$	−7.02589e7	−0.0829526
$43$	−1.79394e9	−1.86094	−0.930469	−	0.366371i	$-0.880600\pi$
$43$	−1.79394e9	−1.86094	−0.930469	+	0.366371i	$0.880600\pi$
$44$	4.16426e8	0.380669
$45$	−1.55265e8	−0.125431
$46$	−3.68681e8	−0.263926
$47$	5.98279e8	0.380509	0.190255	−	0.981735i	$-0.439069\pi$
$47$	5.98279e8	0.380509	0.190255	+	0.981735i	$0.439069\pi$
$48$	7.95005e8	0.450343
$49$	−1.43462e9	−0.725536
$50$	5.20205e8	0.235418
$51$	−1.38660e9	−0.562750
$52$	−2.66085e9	−0.970516
$53$	−3.80930e9	−1.25120	−0.625602	−	0.780143i	$-0.715146\pi$
$53$	−3.80930e9	−1.25120	−0.625602	+	0.780143i	$0.715146\pi$
$54$	−1.78087e8	−0.0527796
$55$	5.78132e8	0.154893
$56$	1.13974e9	0.276550
$57$	1.99355e8	0.0438849
$58$	−1.20181e9	−0.240426
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	1.21015e9	0.200912
$61$	9.73343e9	1.47554	0.737772	−	0.675050i	$-0.235878\pi$
$61$	9.73343e9	1.47554	0.737772	+	0.675050i	$0.235878\pi$
$62$	−8.58280e8	−0.118980
$63$	1.37561e9	0.174631
$64$	−4.95277e9	−0.576579
$65$	−3.69412e9	−0.394900
$66$	6.63109e8	0.0651769
$67$	2.05666e10	1.86102	0.930511	−	0.366265i	$-0.119364\pi$
$67$	2.05666e10	1.86102	0.930511	+	0.366265i	$0.119364\pi$
$68$	1.08073e10	0.901399
$69$	7.21845e9	0.555615
$70$	7.60249e8	0.0540650
$71$	−1.31509e10	−0.865038	−0.432519	−	0.901625i	$-0.642375\pi$
$71$	−1.31509e10	−0.865038	−0.432519	+	0.901625i	$0.642375\pi$
$72$	2.88894e9	0.175958
$73$	2.61072e10	1.47396	0.736978	−	0.675917i	$-0.236252\pi$
$73$	2.61072e10	1.47396	0.736978	+	0.675917i	$0.236252\pi$
$74$	5.59791e9	0.293259
$75$	−1.01852e10	−0.495600
$76$	−1.55379e9	−0.0702939
$77$	−5.12210e9	−0.215650
$78$	−4.23710e9	−0.166169
$79$	−3.90581e10	−1.42811	−0.714056	−	0.700089i	$-0.753144\pi$
$79$	−3.90581e10	−1.42811	−0.714056	+	0.700089i	$0.753144\pi$
$80$	−8.60249e9	−0.293514
$81$	3.48678e9	0.111111
$82$	−5.58027e9	−0.166218
$83$	2.57619e10	0.717875	0.358938	−	0.933362i	$-0.383139\pi$
$83$	2.57619e10	0.717875	0.358938	+	0.933362i	$0.383139\pi$
$84$	−1.07216e10	−0.279720
$85$	1.50039e10	0.366776
$86$	2.22649e10	0.510364
$87$	2.35303e10	0.506142
$88$	−1.07570e10	−0.217289
$89$	4.36938e10	0.829420	0.414710	−	0.909954i	$-0.363883\pi$
$89$	4.36938e10	0.829420	0.414710	+	0.909954i	$0.363883\pi$
$90$	1.92702e9	0.0343995
$91$	3.27289e10	0.549799
$92$	−5.62612e10	−0.889971
$93$	1.68044e10	0.250476
$94$	−7.42534e9	−0.104355
$95$	−2.15716e9	−0.0286024
$96$	−3.42149e10	−0.428275
$97$	−4.40290e10	−0.520589	−0.260294	−	0.965529i	$-0.583820\pi$
$97$	−4.40290e10	−0.520589	−0.260294	+	0.965529i	$0.583820\pi$
$98$	1.78053e10	0.198979
$99$	−1.29831e10	−0.137210
$100$	7.93840e10	0.793840
$101$	−9.64384e10	−0.913025	−0.456512	−	0.889717i	$-0.650902\pi$
$101$	−9.64384e10	−0.913025	−0.456512	+	0.889717i	$0.650902\pi$
$102$	1.72093e10	0.154335
$103$	−5.45856e10	−0.463953	−0.231976	−	0.972721i	$-0.574519\pi$
$103$	−5.45856e10	−0.463953	−0.231976	+	0.972721i	$0.574519\pi$
$104$	6.87346e10	0.553977
$105$	−1.48850e10	−0.113817
$106$	4.72779e10	0.343144
$107$	6.01740e10	0.414761	0.207381	−	0.978260i	$-0.433506\pi$
$107$	6.01740e10	0.414761	0.207381	+	0.978260i	$0.433506\pi$
$108$	−2.71763e10	−0.177975
$109$	1.50982e10	0.0939894	0.0469947	−	0.998895i	$-0.485036\pi$
$109$	1.50982e10	0.0939894	0.0469947	+	0.998895i	$0.485036\pi$
$110$	−7.17529e9	−0.0424796
$111$	−1.09602e11	−0.617366
$112$	7.62159e10	0.408645
$113$	1.65861e11	0.846863	0.423431	−	0.905928i	$-0.360826\pi$
$113$	1.65861e11	0.846863	0.423431	+	0.905928i	$0.360826\pi$
$114$	−2.47423e9	−0.0120355
$115$	−7.81085e10	−0.362126
$116$	−1.83397e11	−0.810727
$117$	8.29588e10	0.349816
$118$	−8.87305e9	−0.0357044
$119$	−1.32931e11	−0.510644
$120$	−3.12603e10	−0.114682
$121$	−2.36969e11	−0.830561
$122$	−1.20803e11	−0.404669
$123$	1.09257e11	0.349921
$124$	−1.30975e11	−0.401207
$125$	2.38600e11	0.699304
$126$	−1.70729e10	−0.0478927
$127$	4.89021e11	1.31343	0.656715	−	0.754139i	$-0.271945\pi$
$127$	4.89021e11	1.31343	0.656715	+	0.754139i	$0.271945\pi$
$128$	3.49832e11	0.899922
$129$	−4.35928e11	−1.07441
$130$	4.58483e10	0.108302
$131$	−5.90891e11	−1.33818	−0.669091	−	0.743181i	$-0.733316\pi$
$131$	−5.90891e11	−1.33818	−0.669091	+	0.743181i	$0.733316\pi$
$132$	1.01191e11	0.219779
$133$	1.91119e10	0.0398216
$134$	−2.55256e11	−0.510387
$135$	−3.77294e10	−0.0724176
$136$	−2.79171e11	−0.514525
$137$	5.20144e11	0.920789	0.460394	−	0.887714i	$-0.347708\pi$
$137$	5.20144e11	0.920789	0.460394	+	0.887714i	$0.347708\pi$
$138$	−8.95894e10	−0.152378
$139$	1.06455e10	0.0174014	0.00870072	−	0.999962i	$-0.497230\pi$
$139$	1.06455e10	0.0174014	0.00870072	+	0.999962i	$0.497230\pi$
$140$	1.16015e11	0.182310
$141$	1.45382e11	0.219687
$142$	1.63218e11	0.237237
$143$	−3.08898e11	−0.431984
$144$	1.93186e11	0.260005
$145$	−2.54614e11	−0.329882
$146$	−3.24021e11	−0.404234
$147$	−3.48613e11	−0.418888
$148$	8.54249e11	0.988883
$149$	1.50398e12	1.67771	0.838856	−	0.544353i	$-0.183225\pi$
$149$	1.50398e12	1.67771	0.838856	+	0.544353i	$0.183225\pi$
$150$	1.26410e11	0.135919
$151$	1.56843e12	1.62590	0.812949	−	0.582335i	$-0.197861\pi$
$151$	1.56843e12	1.62590	0.812949	+	0.582335i	$0.197861\pi$
$152$	4.01371e10	0.0401242
$153$	−3.36944e11	−0.324904
$154$	6.35713e10	0.0591421
$155$	−1.81835e11	−0.163250
$156$	−6.46588e11	−0.560328
$157$	1.64554e12	1.37676	0.688382	−	0.725348i	$-0.258321\pi$
$157$	1.64554e12	1.37676	0.688382	+	0.725348i	$0.258321\pi$
$158$	4.84757e11	0.391661
$159$	−9.25660e11	−0.722382
$160$	3.70228e11	0.279132
$161$	6.92021e11	0.504170
$162$	−4.32751e10	−0.0304723
$163$	−1.67635e11	−0.114113	−0.0570563	−	0.998371i	$-0.518171\pi$
$163$	−1.67635e11	−0.114113	−0.0570563	+	0.998371i	$0.518171\pi$
$164$	−8.51557e11	−0.560496
$165$	1.40486e11	0.0894275
$166$	−3.19736e11	−0.196878
$167$	2.31740e12	1.38058	0.690289	−	0.723534i	$-0.257483\pi$
$167$	2.31740e12	1.38058	0.690289	+	0.723534i	$0.257483\pi$
$168$	2.76958e11	0.159666
$169$	1.81623e11	0.101343
$170$	−1.86217e11	−0.100589
$171$	4.84433e10	0.0253370
$172$	3.39766e12	1.72097
$173$	−7.66240e10	−0.0375934	−0.0187967	−	0.999823i	$-0.505984\pi$
$173$	−7.66240e10	−0.0375934	−0.0187967	+	0.999823i	$0.505984\pi$
$174$	−2.92039e11	−0.138810
$175$	−9.76436e11	−0.449712
$176$	−7.19332e11	−0.321078
$177$	1.73727e11	0.0751646
$178$	−5.42291e11	−0.227469
$179$	4.03824e12	1.64248	0.821240	−	0.570582i	$-0.193282\pi$
$179$	4.03824e12	1.64248	0.821240	+	0.570582i	$0.193282\pi$
$180$	2.94066e11	0.115997
$181$	4.73737e12	1.81261	0.906306	−	0.422622i	$-0.138890\pi$
$181$	4.73737e12	1.81261	0.906306	+	0.422622i	$0.138890\pi$
$182$	−4.06205e11	−0.150783
$183$	2.36522e12	0.851905
$184$	1.45333e12	0.508001
$185$	1.18597e12	0.402373
$186$	−2.08562e11	−0.0686932
$187$	1.25462e12	0.401219
$188$	−1.13312e12	−0.351890
$189$	3.34273e11	0.100823
$190$	2.67729e10	0.00784422
$191$	2.61020e12	0.743002	0.371501	−	0.928433i	$-0.378843\pi$
$191$	2.61020e12	0.743002	0.371501	+	0.928433i	$0.378843\pi$
$192$	−1.20352e12	−0.332888
$193$	−2.73486e12	−0.735139	−0.367569	−	0.929996i	$-0.619810\pi$
$193$	−2.73486e12	−0.735139	−0.367569	+	0.929996i	$0.619810\pi$
$194$	5.46452e11	0.142772
$195$	−8.97670e11	−0.227996
$196$	2.71712e12	0.670966
$197$	−2.98094e12	−0.715796	−0.357898	−	0.933761i	$-0.616506\pi$
$197$	−2.98094e12	−0.715796	−0.357898	+	0.933761i	$0.616506\pi$
$198$	1.61136e11	0.0376299
$199$	2.64798e12	0.601481	0.300741	−	0.953706i	$-0.402766\pi$
$199$	2.64798e12	0.601481	0.300741	+	0.953706i	$0.402766\pi$
$200$	−2.05063e12	−0.453129
$201$	4.99769e12	1.07446
$202$	1.19691e12	0.250398
$203$	2.25582e12	0.459278
$204$	2.62617e12	0.520423
$205$	−1.18223e12	−0.228064
$206$	6.77472e11	0.127239
$207$	1.75408e12	0.320784
$208$	4.59635e12	0.818587
$209$	−1.80379e11	−0.0312883
$210$	1.84740e11	0.0312145
$211$	5.05129e12	0.831474	0.415737	−	0.909485i	$-0.363524\pi$
$211$	5.05129e12	0.831474	0.415737	+	0.909485i	$0.363524\pi$
$212$	7.21467e12	1.15710
$213$	−3.19567e12	−0.499430
$214$	−7.46830e11	−0.113749
$215$	4.71703e12	0.700257
$216$	7.02012e11	0.101589
$217$	1.61101e12	0.227284
$218$	−1.87386e11	−0.0257767
$219$	6.34405e12	0.850989
$220$	−1.09496e12	−0.143243
$221$	−8.01668e12	−1.02291
$222$	1.36029e12	0.169313
$223$	−1.15280e13	−1.39983	−0.699917	−	0.714224i	$-0.746780\pi$
$223$	−1.15280e13	−1.39983	−0.699917	+	0.714224i	$0.746780\pi$
$224$	−3.28013e12	−0.388621
$225$	−2.47499e12	−0.286135
$226$	−2.05853e12	−0.232253
$227$	−1.82623e12	−0.201101	−0.100550	−	0.994932i	$-0.532060\pi$
$227$	−1.82623e12	−0.201101	−0.100550	+	0.994932i	$0.532060\pi$
$228$	−3.77571e11	−0.0405842
$229$	−1.06757e12	−0.112022	−0.0560108	−	0.998430i	$-0.517838\pi$
$229$	−1.06757e12	−0.112022	−0.0560108	+	0.998430i	$0.517838\pi$
$230$	9.69418e11	0.0993135
$231$	−1.24467e12	−0.124505
$232$	4.73748e12	0.462768
$233$	1.52920e13	1.45884	0.729420	−	0.684066i	$-0.239790\pi$
$233$	1.52920e13	1.45884	0.729420	+	0.684066i	$0.239790\pi$
$234$	−1.02962e12	−0.0959374
$235$	−1.57313e12	−0.143183
$236$	−1.35404e12	−0.120397
$237$	−9.49112e12	−0.824521
$238$	1.64983e12	0.140045
$239$	−1.01553e13	−0.842372	−0.421186	−	0.906974i	$-0.638386\pi$
$239$	−1.01553e13	−0.842372	−0.421186	+	0.906974i	$0.638386\pi$
$240$	−2.09041e12	−0.169461
$241$	−1.22766e13	−0.972714	−0.486357	−	0.873760i	$-0.661674\pi$
$241$	−1.22766e13	−0.972714	−0.486357	+	0.873760i	$0.661674\pi$
$242$	2.94106e12	0.227782
$243$	8.47289e11	0.0641500
$244$	−1.84348e13	−1.36456
$245$	3.77223e12	0.273014
$246$	−1.35601e12	−0.0959662
$247$	1.15258e12	0.0797696
$248$	3.38331e12	0.229011
$249$	6.26015e12	0.414465
$250$	−2.96131e12	−0.191785
$251$	1.41141e13	0.894225	0.447112	−	0.894478i	$-0.352452\pi$
$251$	1.41141e13	0.894225	0.447112	+	0.894478i	$0.352452\pi$
$252$	−2.60535e12	−0.161496
$253$	−6.53136e12	−0.396133
$254$	−6.06933e12	−0.360209
$255$	3.64596e12	0.211759
$256$	5.80145e12	0.329774
$257$	1.81778e13	1.01137	0.505683	−	0.862719i	$-0.331240\pi$
$257$	1.81778e13	1.01137	0.505683	+	0.862719i	$0.331240\pi$
$258$	5.41038e12	0.294659
$259$	−1.05074e13	−0.560204
$260$	6.99652e12	0.365198
$261$	5.71787e12	0.292221
$262$	7.33365e12	0.366998
$263$	1.38536e13	0.678902	0.339451	−	0.940624i	$-0.389759\pi$
$263$	1.38536e13	0.678902	0.339451	+	0.940624i	$0.389759\pi$
$264$	−2.61395e12	−0.125452
$265$	1.00163e13	0.470819
$266$	−2.37201e11	−0.0109211
$267$	1.06176e13	0.478866
$268$	−3.89524e13	−1.72105
$269$	−1.54482e13	−0.668715	−0.334357	−	0.942446i	$-0.608519\pi$
$269$	−1.54482e13	−0.668715	−0.334357	+	0.942446i	$0.608519\pi$
$270$	4.68266e11	0.0198606
$271$	3.07070e13	1.27616	0.638082	−	0.769969i	$-0.279728\pi$
$271$	3.07070e13	1.27616	0.638082	+	0.769969i	$0.279728\pi$
$272$	−1.86685e13	−0.760290
$273$	7.95313e12	0.317427
$274$	−6.45559e12	−0.252527
$275$	9.21569e12	0.353344
$276$	−1.36715e13	−0.513825
$277$	1.11150e13	0.409514	0.204757	−	0.978813i	$-0.434360\pi$
$277$	1.11150e13	0.409514	0.204757	+	0.978813i	$0.434360\pi$
$278$	−1.32123e11	−0.00477236
$279$	4.08346e12	0.144612
$280$	−2.99687e12	−0.104064
$281$	3.48370e13	1.18620	0.593098	−	0.805130i	$-0.297905\pi$
$281$	3.48370e13	1.18620	0.593098	+	0.805130i	$0.297905\pi$
$282$	−1.80436e12	−0.0602494
$283$	1.58891e13	0.520324	0.260162	−	0.965565i	$-0.416224\pi$
$283$	1.58891e13	0.520324	0.260162	+	0.965565i	$0.416224\pi$
$284$	2.49073e13	0.799975
$285$	−5.24189e11	−0.0165136
$286$	3.83379e12	0.118472
$287$	1.04743e13	0.317522
$288$	−8.31421e12	−0.247265
$289$	−1.71150e12	−0.0499389
$290$	3.16006e12	0.0904704
$291$	−1.06991e13	−0.300562
$292$	−4.94461e13	−1.36309
$293$	−6.51516e13	−1.76260	−0.881299	−	0.472560i	$-0.843330\pi$
$293$	−6.51516e13	−1.76260	−0.881299	+	0.472560i	$0.843330\pi$
$294$	4.32670e12	0.114880
$295$	−1.87984e12	−0.0489891
$296$	−2.20668e13	−0.564461
$297$	−3.15489e12	−0.0792181
$298$	−1.86662e13	−0.460114
$299$	4.17337e13	1.00994
$300$	1.92903e13	0.458324
$301$	−4.17917e13	−0.974933
$302$	−1.94661e13	−0.445904
$303$	−2.34345e13	−0.527135
$304$	2.68401e12	0.0592898
$305$	−2.55933e13	−0.555236
$306$	4.18187e12	0.0891051
$307$	−6.94381e12	−0.145324	−0.0726619	−	0.997357i	$-0.523149\pi$
$307$	−6.94381e12	−0.145324	−0.0726619	+	0.997357i	$0.523149\pi$
$308$	9.70107e12	0.199430
$309$	−1.32643e13	−0.267863
$310$	2.25678e12	0.0447714
$311$	9.11794e13	1.77711	0.888555	−	0.458770i	$-0.151710\pi$
$311$	9.11794e13	1.77711	0.888555	+	0.458770i	$0.151710\pi$
$312$	1.67025e13	0.319839
$313$	4.52842e13	0.852026	0.426013	−	0.904717i	$-0.359918\pi$
$313$	4.52842e13	0.852026	0.426013	+	0.904717i	$0.359918\pi$
$314$	−2.04230e13	−0.377579
$315$	−3.61706e12	−0.0657124
$316$	7.39746e13	1.32070
$317$	5.55014e13	0.973818	0.486909	−	0.873453i	$-0.338124\pi$
$317$	5.55014e13	0.973818	0.486909	+	0.873453i	$0.338124\pi$
$318$	1.14885e13	0.198114
$319$	−2.12906e13	−0.360860
$320$	1.30229e13	0.216962
$321$	1.46223e13	0.239462
$322$	−8.58880e12	−0.138269
$323$	−4.68129e12	−0.0740887
$324$	−6.60384e12	−0.102754
$325$	−5.88859e13	−0.900851
$326$	2.08055e12	0.0312955
$327$	3.66886e12	0.0542648
$328$	2.19972e13	0.319935
$329$	1.39375e13	0.199346
$330$	−1.74360e12	−0.0245256
$331$	−1.22787e14	−1.69862	−0.849311	−	0.527892i	$-0.822982\pi$
$331$	−1.22787e14	−1.69862	−0.849311	+	0.527892i	$0.822982\pi$
$332$	−4.87921e13	−0.663881
$333$	−2.66333e13	−0.356437
$334$	−2.87617e13	−0.378625
$335$	−5.40784e13	−0.700289
$336$	1.85205e13	0.235932
$337$	1.15972e14	1.45341	0.726706	−	0.686948i	$-0.241050\pi$
$337$	1.15972e14	1.45341	0.726706	+	0.686948i	$0.241050\pi$
$338$	−2.25416e12	−0.0277934
$339$	4.03042e13	0.488936
$340$	−2.84169e13	−0.339190
$341$	−1.52048e13	−0.178580
$342$	−6.01238e11	−0.00694869
$343$	−7.94849e13	−0.903997
$344$	−8.77675e13	−0.982341
$345$	−1.89804e13	−0.209074
$346$	9.50994e11	0.0103100
$347$	8.80751e13	0.939812	0.469906	−	0.882716i	$-0.344288\pi$
$347$	8.80751e13	0.939812	0.469906	+	0.882716i	$0.344288\pi$
$348$	−4.45656e13	−0.468073
$349$	−1.17002e14	−1.20963	−0.604816	−	0.796365i	$-0.706753\pi$
$349$	−1.17002e14	−1.20963	−0.604816	+	0.796365i	$0.706753\pi$
$350$	1.21187e13	0.123334
$351$	2.01590e13	0.201967
$352$	3.09581e13	0.305344
$353$	−7.06831e13	−0.686364	−0.343182	−	0.939269i	$-0.611505\pi$
$353$	−7.06831e13	−0.686364	−0.343182	+	0.939269i	$0.611505\pi$
$354$	−2.15615e12	−0.0206140
$355$	3.45793e13	0.325507
$356$	−8.27544e13	−0.767037
$357$	−3.23023e13	−0.294821
$358$	−5.01193e13	−0.450452
$359$	3.49060e12	0.0308945	0.0154472	−	0.999881i	$-0.495083\pi$
$359$	3.49060e12	0.0308945	0.0154472	+	0.999881i	$0.495083\pi$
$360$	−7.59624e12	−0.0662117
$361$	−1.15817e14	−0.994222
$362$	−5.87963e13	−0.497110
$363$	−5.75834e13	−0.479525
$364$	−6.19874e13	−0.508447
$365$	−6.86469e13	−0.554639
$366$	−2.93552e13	−0.233636
$367$	2.40276e13	0.188385	0.0941927	−	0.995554i	$-0.469973\pi$
$367$	2.40276e13	0.188385	0.0941927	+	0.995554i	$0.469973\pi$
$368$	9.71854e13	0.750651
$369$	2.65494e13	0.202027
$370$	−1.47193e13	−0.110351
$371$	−8.87416e13	−0.655497
$372$	−3.18269e13	−0.231637
$373$	4.62694e13	0.331814	0.165907	−	0.986141i	$-0.446945\pi$
$373$	4.62694e13	0.331814	0.165907	+	0.986141i	$0.446945\pi$
$374$	−1.55713e13	−0.110035
$375$	5.79799e13	0.403743
$376$	2.92704e13	0.200861
$377$	1.36042e14	0.920014
$378$	−4.14872e12	−0.0276509
$379$	−1.43879e14	−0.945110	−0.472555	−	0.881301i	$-0.656668\pi$
$379$	−1.43879e14	−0.945110	−0.472555	+	0.881301i	$0.656668\pi$
$380$	4.08557e12	0.0264511
$381$	1.18832e14	0.758309
$382$	−3.23956e13	−0.203769
$383$	−1.48728e14	−0.922149	−0.461074	−	0.887362i	$-0.652536\pi$
$383$	−1.48728e14	−0.922149	−0.461074	+	0.887362i	$0.652536\pi$
$384$	8.50092e13	0.519570
$385$	1.34682e13	0.0811474
$386$	3.39428e13	0.201612
$387$	−1.05930e14	−0.620313
$388$	8.33893e13	0.481433
$389$	−1.76673e14	−1.00565	−0.502827	−	0.864387i	$-0.667707\pi$
$389$	−1.76673e14	−1.00565	−0.502827	+	0.864387i	$0.667707\pi$
$390$	1.11411e13	0.0625280
$391$	−1.69505e14	−0.938016
$392$	−7.01880e13	−0.382992
$393$	−1.43586e14	−0.772600
$394$	3.69970e13	0.196308
$395$	1.02700e14	0.537388
$396$	2.45895e13	0.126890
$397$	−6.00013e13	−0.305361	−0.152680	−	0.988276i	$-0.548790\pi$
$397$	−6.00013e13	−0.305361	−0.152680	+	0.988276i	$0.548790\pi$
$398$	−3.28645e13	−0.164957
$399$	4.64418e12	0.0229910
$400$	−1.37128e14	−0.669569
$401$	2.97986e14	1.43517	0.717583	−	0.696473i	$-0.245248\pi$
$401$	2.97986e14	1.43517	0.717583	+	0.696473i	$0.245248\pi$
$402$	−6.20272e13	−0.294672
$403$	9.71551e13	0.455290
$404$	1.82651e14	0.844353
$405$	−9.16824e12	−0.0418103
$406$	−2.79974e13	−0.125957
$407$	9.91697e13	0.440159
$408$	−6.78386e13	−0.297061
$409$	−1.83676e14	−0.793549	−0.396774	−	0.917916i	$-0.629870\pi$
$409$	−1.83676e14	−0.793549	−0.396774	+	0.917916i	$0.629870\pi$
$410$	1.46729e13	0.0625467
$411$	1.26395e14	0.531618
$412$	1.03383e14	0.429057
$413$	1.66549e13	0.0682051
$414$	−2.17702e13	−0.0879754
$415$	−6.77391e13	−0.270131
$416$	−1.97815e14	−0.778476
$417$	2.58686e12	0.0100467
$418$	2.23872e12	0.00858085
$419$	−3.37184e14	−1.27553	−0.637763	−	0.770233i	$-0.720140\pi$
$419$	−3.37184e14	−1.27553	−0.637763	+	0.770233i	$0.720140\pi$
$420$	2.81917e13	0.105257
$421$	4.41343e14	1.62639	0.813195	−	0.581991i	$-0.197726\pi$
$421$	4.41343e14	1.62639	0.813195	+	0.581991i	$0.197726\pi$
$422$	−6.26924e13	−0.228032
$423$	3.53278e13	0.126836
$424$	−1.86368e14	−0.660478
$425$	2.39170e14	0.836695
$426$	3.96620e13	0.136969
$427$	2.26750e14	0.773027
$428$	−1.13967e14	−0.383565
$429$	−7.50623e13	−0.249406
$430$	−5.85440e13	−0.192046
$431$	−4.62208e14	−1.49697	−0.748483	−	0.663154i	$-0.769218\pi$
$431$	−4.62208e14	−1.49697	−0.748483	+	0.663154i	$0.769218\pi$
$432$	4.69443e13	0.150114
$433$	−5.20774e13	−0.164424	−0.0822121	−	0.996615i	$-0.526198\pi$
$433$	−5.20774e13	−0.164424	−0.0822121	+	0.996615i	$0.526198\pi$
$434$	−1.99945e13	−0.0623329
$435$	−6.18713e13	−0.190457
$436$	−2.85954e13	−0.0869202
$437$	2.43702e13	0.0731494
$438$	−7.87371e13	−0.233384
$439$	−2.17454e14	−0.636520	−0.318260	−	0.948004i	$-0.603098\pi$
$439$	−2.17454e14	−0.636520	−0.318260	+	0.948004i	$0.603098\pi$
$440$	2.82847e13	0.0817641
$441$	−8.47130e13	−0.241845
$442$	9.94964e13	0.280534
$443$	−2.78979e14	−0.776875	−0.388438	−	0.921475i	$-0.626985\pi$
$443$	−2.78979e14	−0.776875	−0.388438	+	0.921475i	$0.626985\pi$
$444$	2.07582e14	0.570932
$445$	−1.14890e14	−0.312105
$446$	1.43076e14	0.383906
$447$	3.65467e14	0.968628
$448$	−1.15380e14	−0.302066
$449$	6.68167e14	1.72795	0.863973	−	0.503539i	$-0.167969\pi$
$449$	6.68167e14	1.72795	0.863973	+	0.503539i	$0.167969\pi$
$450$	3.07176e13	0.0784727
$451$	−9.88571e13	−0.249481
$452$	−3.14135e14	−0.783167
$453$	3.81130e14	0.938712
$454$	2.26657e13	0.0551521
$455$	−8.60583e13	−0.206885
$456$	9.75333e12	0.0231657
$457$	7.36922e13	0.172935	0.0864674	−	0.996255i	$-0.472442\pi$
$457$	7.36922e13	0.172935	0.0864674	+	0.996255i	$0.472442\pi$
$458$	1.32498e13	0.0307220
$459$	−8.18773e13	−0.187583
$460$	1.47935e14	0.334890
$461$	5.66378e13	0.126693	0.0633463	−	0.997992i	$-0.479823\pi$
$461$	5.66378e13	0.126693	0.0633463	+	0.997992i	$0.479823\pi$
$462$	1.54478e13	0.0341457
$463$	−6.02905e14	−1.31690	−0.658451	−	0.752624i	$-0.728788\pi$
$463$	−6.02905e14	−1.31690	−0.658451	+	0.752624i	$0.728788\pi$
$464$	3.16800e14	0.683812
$465$	−4.41858e13	−0.0942523
$466$	−1.89792e14	−0.400088
$467$	9.34292e14	1.94644	0.973218	−	0.229886i	$-0.0738354\pi$
$467$	9.34292e14	1.94644	0.973218	+	0.229886i	$0.0738354\pi$
$468$	−1.57121e14	−0.323505
$469$	4.79121e14	0.974976
$470$	1.95244e13	0.0392680
$471$	3.99865e14	0.794875
$472$	3.49772e13	0.0687234
$473$	3.94434e14	0.766016
$474$	1.17796e14	0.226126
$475$	−3.43861e13	−0.0652481
$476$	2.51767e14	0.472237
$477$	−2.24935e14	−0.417068
$478$	1.26039e14	0.231021
$479$	2.84742e14	0.515948	0.257974	−	0.966152i	$-0.416945\pi$
$479$	2.84742e14	0.515948	0.257974	+	0.966152i	$0.416945\pi$
$480$	8.99654e13	0.161157
$481$	−6.33669e14	−1.12219
$482$	1.52367e14	0.266768
$483$	1.68161e14	0.291083
$484$	4.48810e14	0.768092
$485$	1.15771e14	0.195894
$486$	−1.05158e13	−0.0175932
$487$	−1.18679e15	−1.96320	−0.981602	−	0.190941i	$-0.938846\pi$
$487$	−1.18679e15	−1.96320	−0.981602	+	0.190941i	$0.938846\pi$
$488$	4.76202e14	0.778902
$489$	−4.07354e13	−0.0658829
$490$	−4.68178e13	−0.0748743
$491$	−3.24362e14	−0.512959	−0.256479	−	0.966550i	$-0.582563\pi$
$491$	−3.24362e14	−0.512959	−0.256479	+	0.966550i	$0.582563\pi$
$492$	−2.06928e14	−0.323602
$493$	−5.52544e14	−0.854493
$494$	−1.43049e13	−0.0218769
$495$	3.41381e13	0.0516310
$496$	2.26245e14	0.338400
$497$	−3.06364e14	−0.453187
$498$	−7.76958e13	−0.113668
$499$	1.00957e15	1.46078	0.730388	−	0.683033i	$-0.239339\pi$
$499$	1.00957e15	1.46078	0.730388	+	0.683033i	$0.239339\pi$
$500$	−4.51900e14	−0.646707
$501$	5.63129e14	0.797077
$502$	−1.75172e14	−0.245242
$503$	−1.07256e15	−1.48524	−0.742619	−	0.669714i	$-0.766416\pi$
$503$	−1.07256e15	−1.48524	−0.742619	+	0.669714i	$0.766416\pi$
$504$	6.73008e13	0.0921833
$505$	2.53578e14	0.343564
$506$	8.10618e13	0.108640
$507$	4.41344e13	0.0585105
$508$	−9.26187e14	−1.21464
$509$	1.40656e15	1.82478	0.912391	−	0.409319i	$-0.134234\pi$
$509$	1.40656e15	1.82478	0.912391	+	0.409319i	$0.134234\pi$
$510$	−4.52507e13	−0.0580750
$511$	6.08194e14	0.772196
$512$	−7.88459e14	−0.990363
$513$	1.17717e13	0.0146283
$514$	−2.25608e14	−0.277368
$515$	1.43529e14	0.174582
$516$	8.25631e14	0.993602
$517$	−1.31544e14	−0.156629
$518$	1.30409e14	0.153636
$519$	−1.86196e13	−0.0217045
$520$	−1.80732e14	−0.208458
$521$	−9.68497e14	−1.10533	−0.552663	−	0.833405i	$-0.686388\pi$
$521$	−9.68497e14	−1.10533	−0.552663	+	0.833405i	$0.686388\pi$
$522$	−7.09655e13	−0.0801419
$523$	5.77418e14	0.645254	0.322627	−	0.946526i	$-0.395434\pi$
$523$	5.77418e14	0.645254	0.322627	+	0.946526i	$0.395434\pi$
$524$	1.11913e15	1.23753
$525$	−2.37274e14	−0.259641
$526$	−1.71940e14	−0.186189
$527$	−3.94603e14	−0.422866
$528$	−1.74798e14	−0.185374
$529$	−7.03905e13	−0.0738767
$530$	−1.24314e14	−0.129122
$531$	4.22156e13	0.0433963
$532$	−3.61972e13	−0.0368265
$533$	6.31672e14	0.636051
$534$	−1.31777e14	−0.131329
$535$	−1.58223e14	−0.156072
$536$	1.00621e15	0.982385
$537$	9.81292e14	0.948287
$538$	1.91731e14	0.183396
$539$	3.15430e14	0.298652
$540$	7.14580e13	0.0669708
$541$	−3.42211e14	−0.317474	−0.158737	−	0.987321i	$-0.550742\pi$
$541$	−3.42211e14	−0.317474	−0.158737	+	0.987321i	$0.550742\pi$
$542$	−3.81110e14	−0.349989
$543$	1.15118e15	1.04651
$544$	8.03440e14	0.723035
$545$	−3.96995e13	−0.0353675
$546$	−9.87077e13	−0.0870546
$547$	1.11343e15	0.972148	0.486074	−	0.873918i	$-0.338429\pi$
$547$	1.11343e15	0.972148	0.486074	+	0.873918i	$0.338429\pi$
$548$	−9.85132e14	−0.851533
$549$	5.74750e14	0.491848
$550$	−1.14378e14	−0.0969049
$551$	7.94407e13	0.0666360
$552$	3.53158e14	0.293295
$553$	−9.09899e14	−0.748178
$554$	−1.37950e14	−0.112310
$555$	2.88191e14	0.232310
$556$	−2.01622e13	−0.0160926
$557$	1.77163e15	1.40013	0.700066	−	0.714078i	$-0.253154\pi$
$557$	1.77163e15	1.40013	0.700066	+	0.714078i	$0.253154\pi$
$558$	−5.06806e13	−0.0396601
$559$	−2.52033e15	−1.95296
$560$	−2.00404e14	−0.153770
$561$	3.04872e14	0.231644
$562$	−4.32369e14	−0.325315
$563$	1.13752e15	0.847542	0.423771	−	0.905769i	$-0.360706\pi$
$563$	1.13752e15	0.847542	0.423771	+	0.905769i	$0.360706\pi$
$564$	−2.75348e14	−0.203164
$565$	−4.36119e14	−0.318668
$566$	−1.97202e14	−0.142699
$567$	8.12283e13	0.0582104
$568$	−6.43400e14	−0.456631
$569$	2.22030e15	1.56061	0.780303	−	0.625402i	$-0.215065\pi$
$569$	2.22030e15	1.56061	0.780303	+	0.625402i	$0.215065\pi$
$570$	6.50580e12	0.00452886
$571$	1.21610e15	0.838437	0.419218	−	0.907885i	$-0.362304\pi$
$571$	1.21610e15	0.838437	0.419218	+	0.907885i	$0.362304\pi$
$572$	5.85042e14	0.399493
$573$	6.34278e14	0.428972
$574$	−1.29998e14	−0.0870807
$575$	−1.24509e15	−0.826088
$576$	−2.92456e14	−0.192193
$577$	−2.57058e15	−1.67326	−0.836631	−	0.547767i	$-0.815478\pi$
$577$	−2.57058e15	−1.67326	−0.836631	+	0.547767i	$0.815478\pi$
$578$	2.12417e13	0.0136958
$579$	−6.64570e14	−0.424432
$580$	4.82230e14	0.305070
$581$	6.00151e14	0.376090
$582$	1.32788e14	0.0824294
$583$	8.37551e14	0.515032
$584$	1.27728e15	0.778064
$585$	−2.18134e14	−0.131633
$586$	8.08608e14	0.483394
$587$	8.26236e14	0.489322	0.244661	−	0.969609i	$-0.421323\pi$
$587$	8.26236e14	0.489322	0.244661	+	0.969609i	$0.421323\pi$
$588$	6.60260e14	0.387382
$589$	5.67332e13	0.0329764
$590$	2.33310e13	0.0134353
$591$	−7.24369e14	−0.413265
$592$	−1.47563e15	−0.834079
$593$	2.20813e15	1.23659	0.618293	−	0.785948i	$-0.287824\pi$
$593$	2.20813e15	1.23659	0.618293	+	0.785948i	$0.287824\pi$
$594$	3.91560e13	0.0217256
$595$	3.49533e14	0.192152
$596$	−2.84848e15	−1.55153
$597$	6.43458e14	0.347265
$598$	−5.17965e14	−0.276977
$599$	2.14568e15	1.13689	0.568443	−	0.822722i	$-0.307546\pi$
$599$	2.14568e15	1.13689	0.568443	+	0.822722i	$0.307546\pi$
$600$	−4.98303e14	−0.261614
$601$	1.03034e15	0.536006	0.268003	−	0.963418i	$-0.413636\pi$
$601$	1.03034e15	0.536006	0.268003	+	0.963418i	$0.413636\pi$
$602$	5.18685e14	0.267376
$603$	1.21444e15	0.620340
$604$	−2.97056e15	−1.50361
$605$	6.23092e14	0.312534
$606$	2.90850e14	0.144567
$607$	6.29663e14	0.310149	0.155074	−	0.987903i	$-0.450438\pi$
$607$	6.29663e14	0.310149	0.155074	+	0.987903i	$0.450438\pi$
$608$	−1.15513e14	−0.0563845
$609$	5.48164e14	0.265164
$610$	3.17643e14	0.152274
$611$	8.40530e14	0.399325
$612$	6.38159e14	0.300466
$613$	4.61880e14	0.215524	0.107762	−	0.994177i	$-0.465631\pi$
$613$	4.61880e14	0.215524	0.107762	+	0.994177i	$0.465631\pi$
$614$	8.61808e13	0.0398552
$615$	−2.87282e14	−0.131673
$616$	−2.50596e14	−0.113836
$617$	2.25606e15	1.01574	0.507870	−	0.861434i	$-0.330433\pi$
$617$	2.25606e15	1.01574	0.507870	+	0.861434i	$0.330433\pi$
$618$	1.64626e14	0.0734617
$619$	3.97848e13	0.0175962	0.00879810	−	0.999961i	$-0.497199\pi$
$619$	3.97848e13	0.0175962	0.00879810	+	0.999961i	$0.497199\pi$
$620$	3.44388e14	0.150971
$621$	4.26242e14	0.185205
$622$	−1.13164e15	−0.487374
$623$	1.01789e15	0.434528
$624$	1.11691e15	0.472612
$625$	1.41921e15	0.595261
$626$	−5.62030e14	−0.233669
$627$	−4.38322e13	−0.0180643
$628$	−3.11658e15	−1.27321
$629$	2.57370e15	1.04227
$630$	4.48919e13	0.0180217
$631$	−3.85979e15	−1.53604	−0.768018	−	0.640428i	$-0.778757\pi$
$631$	−3.85979e15	−1.53604	−0.768018	+	0.640428i	$0.778757\pi$
$632$	−1.91089e15	−0.753864
$633$	1.22746e15	0.480052
$634$	−6.88837e14	−0.267070
$635$	−1.28584e15	−0.494234
$636$	1.75316e15	0.668050
$637$	−2.01552e15	−0.761413
$638$	2.64241e14	0.0989663
$639$	−7.76548e14	−0.288346
$640$	−9.19857e14	−0.338634
$641$	3.34095e15	1.21941	0.609707	−	0.792627i	$-0.291287\pi$
$641$	3.34095e15	1.21941	0.609707	+	0.792627i	$0.291287\pi$
$642$	−1.81480e14	−0.0656728
$643$	−2.23408e15	−0.801563	−0.400781	−	0.916174i	$-0.631261\pi$
$643$	−2.23408e15	−0.801563	−0.400781	+	0.916174i	$0.631261\pi$
$644$	−1.31066e15	−0.466250
$645$	1.14624e15	0.404294
$646$	5.81004e13	0.0203189
$647$	−5.72708e15	−1.98591	−0.992956	−	0.118486i	$-0.962196\pi$
$647$	−5.72708e15	−1.98591	−0.992956	+	0.118486i	$0.962196\pi$
$648$	1.70589e14	0.0586527
$649$	−1.57190e14	−0.0535896
$650$	7.30844e14	0.247059
$651$	3.91475e14	0.131223
$652$	3.17495e14	0.105530
$653$	−5.26368e15	−1.73487	−0.867435	−	0.497551i	$-0.834233\pi$
$653$	−5.26368e15	−1.73487	−0.867435	+	0.497551i	$0.834233\pi$
$654$	−4.55349e13	−0.0148822
$655$	1.55370e15	0.503548
$656$	1.47098e15	0.472753
$657$	1.54160e15	0.491319
$658$	−1.72981e14	−0.0546709
$659$	−3.25334e13	−0.0101967	−0.00509835	−	0.999987i	$-0.501623\pi$
$659$	−3.25334e13	−0.0101967	−0.00509835	+	0.999987i	$0.501623\pi$
$660$	−2.66075e14	−0.0827014
$661$	3.05435e15	0.941479	0.470739	−	0.882272i	$-0.343987\pi$
$661$	3.05435e15	0.941479	0.470739	+	0.882272i	$0.343987\pi$
$662$	1.52393e15	0.465849
$663$	−1.94805e15	−0.590577
$664$	1.26039e15	0.378948
$665$	−5.02532e13	−0.0149846
$666$	3.30551e14	0.0977530
$667$	2.87647e15	0.843660
$668$	−4.38908e15	−1.27674
$669$	−2.80130e15	−0.808194
$670$	6.71176e14	0.192055
$671$	−2.14009e15	−0.607377
$672$	−7.97071e14	−0.224371
$673$	7.74289e14	0.216182	0.108091	−	0.994141i	$-0.465526\pi$
$673$	7.74289e14	0.216182	0.108091	+	0.994141i	$0.465526\pi$
$674$	−1.43935e15	−0.398600
$675$	−6.01424e14	−0.165200
$676$	−3.43987e14	−0.0937208
$677$	−7.12871e14	−0.192652	−0.0963260	−	0.995350i	$-0.530709\pi$
$677$	−7.12871e14	−0.192652	−0.0963260	+	0.995350i	$0.530709\pi$
$678$	−5.00223e14	−0.134091
$679$	−1.02570e15	−0.272733
$680$	7.34059e14	0.193612
$681$	−4.43774e14	−0.116106
$682$	1.88710e14	0.0489757
$683$	3.21628e15	0.828018	0.414009	−	0.910273i	$-0.364128\pi$
$683$	3.21628e15	0.828018	0.414009	+	0.910273i	$0.364128\pi$
$684$	−9.17498e13	−0.0234313
$685$	−1.36768e15	−0.346486
$686$	9.86501e14	0.247922
$687$	−2.59420e14	−0.0646757
$688$	−5.86911e15	−1.45156
$689$	−5.35174e15	−1.31307
$690$	2.35569e14	0.0573387
$691$	−5.82369e15	−1.40627	−0.703135	−	0.711056i	$-0.748217\pi$
$691$	−5.82369e15	−1.40627	−0.703135	+	0.711056i	$0.748217\pi$
$692$	1.45123e14	0.0347658
$693$	−3.02455e14	−0.0718833
$694$	−1.09312e15	−0.257744
$695$	−2.79916e13	−0.00654804
$696$	1.15121e15	0.267179
$697$	−2.56559e15	−0.590754
$698$	1.45213e15	0.331743
$699$	3.71597e15	0.842262
$700$	1.84933e15	0.415888
$701$	−5.89396e15	−1.31510	−0.657549	−	0.753412i	$-0.728407\pi$
$701$	−5.89396e15	−1.31510	−0.657549	+	0.753412i	$0.728407\pi$
$702$	−2.50197e14	−0.0553895
$703$	−3.70027e14	−0.0812792
$704$	1.08897e15	0.237337
$705$	−3.82270e14	−0.0826667
$706$	8.77260e14	0.188236
$707$	−2.24663e15	−0.478328
$708$	−3.29032e14	−0.0695112
$709$	−4.66229e14	−0.0977339	−0.0488669	−	0.998805i	$-0.515561\pi$
$709$	−4.66229e14	−0.0977339	−0.0488669	+	0.998805i	$0.515561\pi$
$710$	−4.29170e14	−0.0892706
$711$	−2.30634e15	−0.476037
$712$	2.13769e15	0.437830
$713$	2.05425e15	0.417504
$714$	4.00909e14	0.0808548
$715$	8.12225e14	0.162552
$716$	−7.64827e15	−1.51894
$717$	−2.46774e15	−0.486344
$718$	−4.33225e13	−0.00847284
$719$	7.59546e15	1.47416	0.737081	−	0.675805i	$-0.236204\pi$
$719$	7.59546e15	1.47416	0.737081	+	0.675805i	$0.236204\pi$
$720$	−5.07969e14	−0.0978382
$721$	−1.27163e15	−0.243062
$722$	1.43743e15	0.272666
$723$	−2.98322e15	−0.561596
$724$	−8.97240e15	−1.67628
$725$	−4.05867e15	−0.752531
$726$	7.14678e14	0.131510
$727$	6.98199e15	1.27509	0.637543	−	0.770414i	$-0.279951\pi$
$727$	6.98199e15	1.27509	0.637543	+	0.770414i	$0.279951\pi$
$728$	1.60124e15	0.290225
$729$	2.05891e14	0.0370370
$730$	8.51989e14	0.152110
$731$	1.02365e16	1.81388
$732$	−4.47965e15	−0.787831
$733$	−1.14815e15	−0.200413	−0.100207	−	0.994967i	$-0.531950\pi$
$733$	−1.14815e15	−0.200413	−0.100207	+	0.994967i	$0.531950\pi$
$734$	−2.98211e14	−0.0516649
$735$	9.16652e14	0.157625
$736$	−4.18260e15	−0.713868
$737$	−4.52198e15	−0.766051
$738$	−3.29509e14	−0.0554061
$739$	8.01991e15	1.33852	0.669261	−	0.743028i	$-0.266611\pi$
$739$	8.01991e15	1.33852	0.669261	+	0.743028i	$0.266611\pi$
$740$	−2.24618e15	−0.372109
$741$	2.80077e14	0.0460550
$742$	1.10139e15	0.179771
$743$	−4.20001e15	−0.680474	−0.340237	−	0.940340i	$-0.610507\pi$
$743$	−4.20001e15	−0.680474	−0.340237	+	0.940340i	$0.610507\pi$
$744$	8.22144e14	0.132220
$745$	−3.95460e15	−0.631311
$746$	−5.74257e14	−0.0910003
$747$	1.52122e15	0.239292
$748$	−2.37620e15	−0.371042
$749$	1.40182e15	0.217291
$750$	−7.19598e14	−0.110727
$751$	6.91910e15	1.05689	0.528445	−	0.848967i	$-0.322775\pi$
$751$	6.91910e15	1.05689	0.528445	+	0.848967i	$0.322775\pi$
$752$	1.95734e15	0.296804
$753$	3.42972e15	0.516281
$754$	−1.68844e15	−0.252315
$755$	−4.12408e15	−0.611813
$756$	−6.33100e14	−0.0932400
$757$	−1.00977e16	−1.47636	−0.738182	−	0.674601i	$-0.764316\pi$
$757$	−1.00977e16	−1.47636	−0.738182	+	0.674601i	$0.764316\pi$
$758$	1.78571e15	0.259197
$759$	−1.58712e15	−0.228707
$760$	−1.05538e14	−0.0150985
$761$	3.19854e14	0.0454293	0.0227146	−	0.999742i	$-0.492769\pi$
$761$	3.19854e14	0.0454293	0.0227146	+	0.999742i	$0.492769\pi$
$762$	−1.47485e15	−0.207967
$763$	3.51728e14	0.0492404
$764$	−4.94362e15	−0.687118
$765$	8.85968e14	0.122259
$766$	1.84590e15	0.252900
$767$	1.00441e15	0.136627
$768$	1.40975e15	0.190395
$769$	−2.19159e14	−0.0293876	−0.0146938	−	0.999892i	$-0.504677\pi$
$769$	−2.19159e14	−0.0293876	−0.0146938	+	0.999892i	$0.504677\pi$
$770$	−1.67156e14	−0.0222548
$771$	4.41720e15	0.583913
$772$	5.17971e15	0.679846
$773$	1.29588e16	1.68879	0.844396	−	0.535720i	$-0.179960\pi$
$773$	1.29588e16	1.68879	0.844396	+	0.535720i	$0.179960\pi$
$774$	1.31472e15	0.170121
$775$	−2.89853e15	−0.372407
$776$	−2.15409e15	−0.274805
$777$	−2.55330e15	−0.323434
$778$	2.19272e15	0.275801
$779$	3.68861e14	0.0460688
$780$	1.70015e15	0.210847
$781$	2.89149e15	0.356075
$782$	2.10376e15	0.257252
$783$	1.38944e15	0.168714
$784$	−4.69354e15	−0.565930
$785$	−4.32681e15	−0.518066
$786$	1.78208e15	0.211886
$787$	−1.52401e16	−1.79939	−0.899696	−	0.436517i	$-0.856212\pi$
$787$	−1.52401e16	−1.79939	−0.899696	+	0.436517i	$0.856212\pi$
$788$	5.64579e15	0.661959
$789$	3.36643e15	0.391964
$790$	−1.27463e15	−0.147379
$791$	3.86390e15	0.443666
$792$	−6.35191e14	−0.0724295
$793$	1.36746e16	1.54851
$794$	7.44687e14	0.0837454
$795$	2.43395e15	0.271827
$796$	−5.01517e15	−0.556242
$797$	−1.44420e16	−1.59077	−0.795384	−	0.606106i	$-0.792731\pi$
$797$	−1.44420e16	−1.59077	−0.795384	+	0.606106i	$0.792731\pi$
$798$	−5.76398e13	−0.00630531
$799$	−3.41388e15	−0.370887
$800$	5.90161e15	0.636759
$801$	2.58007e15	0.276473
$802$	−3.69836e15	−0.393595
$803$	−5.74019e15	−0.606723
$804$	−9.46543e15	−0.993647
$805$	−1.81962e15	−0.189716
$806$	−1.20581e15	−0.124864
$807$	−3.75392e15	−0.386083
$808$	−4.71819e15	−0.481962
$809$	−2.52611e15	−0.256293	−0.128146	−	0.991755i	$-0.540903\pi$
$809$	−2.52611e15	−0.256293	−0.128146	+	0.991755i	$0.540903\pi$
$810$	1.13789e14	0.0114665
$811$	−1.71297e16	−1.71450	−0.857248	−	0.514905i	$-0.827827\pi$
$811$	−1.71297e16	−1.71450	−0.857248	+	0.514905i	$0.827827\pi$
$812$	−4.27243e15	−0.424734
$813$	7.46180e15	0.736793
$814$	−1.23081e15	−0.120714
$815$	4.40784e14	0.0429397
$816$	−4.53644e15	−0.438954
$817$	−1.47173e15	−0.141452
$818$	2.27963e15	0.217631
$819$	1.93261e15	0.183266
$820$	2.23910e15	0.210910
$821$	1.56247e16	1.46192	0.730960	−	0.682420i	$-0.239073\pi$
$821$	1.56247e16	1.46192	0.730960	+	0.682420i	$0.239073\pi$
$822$	−1.56871e15	−0.145797
$823$	−1.41870e15	−0.130976	−0.0654881	−	0.997853i	$-0.520860\pi$
$823$	−1.41870e15	−0.130976	−0.0654881	+	0.997853i	$0.520860\pi$
$824$	−2.67057e15	−0.244909
$825$	2.23941e15	0.204003
$826$	−2.06707e14	−0.0187053
$827$	1.58941e16	1.42874	0.714372	−	0.699766i	$-0.246713\pi$
$827$	1.58941e16	1.42874	0.714372	+	0.699766i	$0.246713\pi$
$828$	−3.32217e15	−0.296657
$829$	9.82076e15	0.871154	0.435577	−	0.900151i	$-0.356544\pi$
$829$	9.82076e15	0.871154	0.435577	+	0.900151i	$0.356544\pi$
$830$	8.40722e14	0.0740837
$831$	2.70094e15	0.236433
$832$	−6.95822e15	−0.605090
$833$	8.18620e15	0.707188
$834$	−3.21060e13	−0.00275532
$835$	−6.09344e15	−0.519502
$836$	3.41632e14	0.0289350
$837$	9.92281e14	0.0834920
$838$	4.18485e15	0.349814
$839$	−1.39823e16	−1.16115	−0.580576	−	0.814206i	$-0.697173\pi$
$839$	−1.39823e16	−1.16115	−0.580576	+	0.814206i	$0.697173\pi$
$840$	−7.28240e14	−0.0600812
$841$	−2.82394e15	−0.231461
$842$	−5.47759e15	−0.446039
$843$	8.46540e15	0.684851
$844$	−9.56695e15	−0.768936
$845$	−4.77564e14	−0.0381347
$846$	−4.38459e14	−0.0347850
$847$	−5.52044e15	−0.435126
$848$	−1.24626e16	−0.975959
$849$	3.86105e15	0.300409
$850$	−2.96838e15	−0.229464
$851$	−1.33983e16	−1.02905
$852$	6.05248e15	0.461866
$853$	2.98160e15	0.226063	0.113032	−	0.993591i	$-0.463944\pi$
$853$	2.98160e15	0.226063	0.113032	+	0.993591i	$0.463944\pi$
$854$	−2.81424e15	−0.212003
$855$	−1.27378e14	−0.00953412
$856$	2.94398e15	0.218942
$857$	1.96566e16	1.45249	0.726247	−	0.687434i	$-0.241263\pi$
$857$	1.96566e16	1.45249	0.726247	+	0.687434i	$0.241263\pi$
$858$	9.31612e14	0.0683998
$859$	2.47331e15	0.180433	0.0902164	−	0.995922i	$-0.471244\pi$
$859$	2.47331e15	0.180433	0.0902164	+	0.995922i	$0.471244\pi$
$860$	−8.93389e15	−0.647588
$861$	2.54525e15	0.183321
$862$	5.73654e15	0.410544
$863$	2.05179e16	1.45906	0.729530	−	0.683949i	$-0.239739\pi$
$863$	2.05179e16	1.45906	0.729530	+	0.683949i	$0.239739\pi$
$864$	−2.02035e15	−0.142758
$865$	2.01477e14	0.0141461
$866$	6.46341e14	0.0450935
$867$	−4.15895e14	−0.0288322
$868$	−3.05119e15	−0.210189
$869$	8.58771e15	0.587853
$870$	7.67895e14	0.0522331
$871$	2.88943e16	1.95305
$872$	7.38670e14	0.0496146
$873$	−2.59987e15	−0.173530
$874$	−3.02462e14	−0.0200613
$875$	5.55844e15	0.366361
$876$	−1.20154e16	−0.786983
$877$	−1.47558e16	−0.960428	−0.480214	−	0.877151i	$-0.659441\pi$
$877$	−1.47558e16	−0.960428	−0.480214	+	0.877151i	$0.659441\pi$
$878$	2.69886e15	0.174566
$879$	−1.58318e16	−1.01764
$880$	1.89143e15	0.120819
$881$	1.32702e16	0.842385	0.421192	−	0.906971i	$-0.361612\pi$
$881$	1.32702e16	0.842385	0.421192	+	0.906971i	$0.361612\pi$
$882$	1.05139e15	0.0663263
$883$	1.33127e16	0.834608	0.417304	−	0.908767i	$-0.362975\pi$
$883$	1.33127e16	0.834608	0.417304	+	0.908767i	$0.362975\pi$
$884$	1.51833e16	0.945973
$885$	−4.56801e14	−0.0282839
$886$	3.46246e15	0.213059
$887$	2.10196e16	1.28542	0.642709	−	0.766111i	$-0.277811\pi$
$887$	2.10196e16	1.28542	0.642709	+	0.766111i	$0.277811\pi$
$888$	−5.36222e15	−0.325892
$889$	1.13922e16	0.688097
$890$	1.42591e15	0.0855950
$891$	−7.66639e14	−0.0457366
$892$	2.18336e16	1.29455
$893$	4.90823e14	0.0289229
$894$	−4.53588e15	−0.265647
$895$	−1.06182e16	−0.618053
$896$	8.14970e15	0.471463
$897$	1.01413e16	0.583089
$898$	−8.29274e15	−0.473890
$899$	6.69635e15	0.380329
$900$	4.68755e15	0.264613
$901$	2.17365e16	1.21956
$902$	1.22693e15	0.0684203
$903$	−1.01554e16	−0.562878
$904$	8.11465e15	0.447037
$905$	−1.24566e16	−0.682073
$906$	−4.73027e15	−0.257443
$907$	1.91783e16	1.03745	0.518727	−	0.854940i	$-0.326406\pi$
$907$	1.91783e16	1.03745	0.518727	+	0.854940i	$0.326406\pi$
$908$	3.45882e15	0.185975
$909$	−5.69459e15	−0.304342
$910$	1.06808e15	0.0567385
$911$	−1.43002e16	−0.755077	−0.377538	−	0.925994i	$-0.623229\pi$
$911$	−1.43002e16	−0.755077	−0.377538	+	0.925994i	$0.623229\pi$
$912$	6.52215e14	0.0342310
$913$	−5.66428e15	−0.295498
$914$	−9.14607e14	−0.0474275
$915$	−6.21918e15	−0.320566
$916$	2.02194e15	0.103596
$917$	−1.37654e16	−0.701065
$918$	1.01619e15	0.0514448
$919$	−1.10785e16	−0.557501	−0.278750	−	0.960364i	$-0.589920\pi$
$919$	−1.10785e16	−0.557501	−0.278750	+	0.960364i	$0.589920\pi$
$920$	−3.82141e15	−0.191157
$921$	−1.68735e15	−0.0839027
$922$	−7.02942e14	−0.0347456
$923$	−1.84759e16	−0.907813
$924$	2.35736e15	0.115141
$925$	1.89049e16	0.917899
$926$	7.48276e15	0.361161
$927$	−3.22323e15	−0.154651
$928$	−1.36342e16	−0.650304
$929$	3.91778e16	1.85761	0.928803	−	0.370575i	$-0.120839\pi$
$929$	3.91778e16	1.85761	0.928803	+	0.370575i	$0.120839\pi$
$930$	5.48398e14	0.0258488
$931$	−1.17695e15	−0.0551487
$932$	−2.89626e16	−1.34912
$933$	2.21566e16	1.02602
$934$	−1.15957e16	−0.533811
$935$	−3.29892e15	−0.150976
$936$	4.05871e15	0.184659
$937$	−5.36663e15	−0.242736	−0.121368	−	0.992608i	$-0.538728\pi$
$937$	−5.36663e15	−0.242736	−0.121368	+	0.992608i	$0.538728\pi$
$938$	−5.94645e15	−0.267388
$939$	1.10041e16	0.491917
$940$	2.97945e15	0.132414
$941$	3.20147e16	1.41451	0.707255	−	0.706959i	$-0.249933\pi$
$941$	3.20147e16	1.41451	0.707255	+	0.706959i	$0.249933\pi$
$942$	−4.96280e15	−0.217995
$943$	1.33561e16	0.583264
$944$	2.33897e15	0.101549
$945$	−8.78945e14	−0.0379391
$946$	−4.89539e15	−0.210081
$947$	3.95764e16	1.68854	0.844271	−	0.535917i	$-0.180034\pi$
$947$	3.95764e16	1.68854	0.844271	+	0.535917i	$0.180034\pi$
$948$	1.79758e16	0.762506
$949$	3.66784e16	1.54684
$950$	4.26772e14	0.0178943
$951$	1.34868e16	0.562234
$952$	−6.50358e15	−0.269556
$953$	−3.58692e15	−0.147812	−0.0739061	−	0.997265i	$-0.523547\pi$
$953$	−3.58692e15	−0.147812	−0.0739061	+	0.997265i	$0.523547\pi$
$954$	2.79171e15	0.114381
$955$	−6.86332e15	−0.279586
$956$	1.92337e16	0.779014
$957$	−5.17362e15	−0.208343
$958$	−3.53398e15	−0.141499
$959$	1.21173e16	0.482395
$960$	3.16458e15	0.125263
$961$	−2.06262e16	−0.811785
$962$	7.86458e15	0.307760
$963$	3.55321e15	0.138254
$964$	2.32515e16	0.899552
$965$	7.19110e15	0.276627
$966$	−2.08708e15	−0.0798297
$967$	6.50498e15	0.247400	0.123700	−	0.992320i	$-0.460524\pi$
$967$	6.50498e15	0.247400	0.123700	+	0.992320i	$0.460524\pi$
$968$	−1.15936e16	−0.438432
$969$	−1.13755e15	−0.0427751
$970$	−1.43685e15	−0.0537240
$971$	−9.73203e14	−0.0361824	−0.0180912	−	0.999836i	$-0.505759\pi$
$971$	−9.73203e14	−0.0361824	−0.0180912	+	0.999836i	$0.505759\pi$
$972$	−1.60473e15	−0.0593251
$973$	2.47998e14	0.00911650
$974$	1.47295e16	0.538410
$975$	−1.43093e16	−0.520107
$976$	3.18442e16	1.15095
$977$	−1.99885e16	−0.718389	−0.359195	−	0.933263i	$-0.616949\pi$
$977$	−1.99885e16	−0.718389	−0.359195	+	0.933263i	$0.616949\pi$
$978$	5.05574e14	0.0180685
$979$	−9.60695e15	−0.341414
$980$	−7.14446e15	−0.252479
$981$	8.91533e14	0.0313298
$982$	4.02572e15	0.140679
$983$	−4.23850e16	−1.47288	−0.736440	−	0.676503i	$-0.763495\pi$
$983$	−4.23850e16	−1.47288	−0.736440	+	0.676503i	$0.763495\pi$
$984$	5.34532e15	0.184714
$985$	7.83817e15	0.269349
$986$	6.85772e15	0.234346
$987$	3.38682e15	0.115093
$988$	−2.18294e15	−0.0737699
$989$	−5.32900e16	−1.79088
$990$	−4.23694e14	−0.0141599
$991$	5.09195e16	1.69231	0.846154	−	0.532938i	$-0.178912\pi$
$991$	5.09195e16	1.69231	0.846154	+	0.532938i	$0.178912\pi$
$992$	−9.73699e15	−0.321818
$993$	−2.98371e16	−0.980700
$994$	3.80234e15	0.124287
$995$	−6.96265e15	−0.226333
$996$	−1.18565e16	−0.383292
$997$	−3.39819e15	−0.109251	−0.0546253	−	0.998507i	$-0.517396\pi$
$997$	−3.39819e15	−0.109251	−0.0546253	+	0.998507i	$0.517396\pi$
$998$	−1.25300e16	−0.400619
$999$	−6.47190e15	−0.205789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.12	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-12.4112 q^{2} +243.000 q^{3} -1893.96 q^{4} -2629.42 q^{5} -3015.92 q^{6} +23296.0 q^{7} +48924.4 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-12.4112 q^{2} +243.000 q^{3} -1893.96 q^{4} -2629.42 q^{5} -3015.92 q^{6} +23296.0 q^{7} +48924.4 q^{8} +59049.0 q^{9} +32634.3 q^{10} -219870. q^{11} -460233. q^{12} +1.40491e6 q^{13} -289131. q^{14} -638950. q^{15} +3.27163e6 q^{16} -5.70617e6 q^{17} -732868. q^{18} +820391. q^{19} +4.98003e6 q^{20} +5.66094e6 q^{21} +2.72885e6 q^{22} +2.97055e7 q^{23} +1.18886e7 q^{24} -4.19143e7 q^{25} -1.74366e7 q^{26} +1.43489e7 q^{27} -4.41218e7 q^{28} +9.68327e7 q^{29} +7.93012e6 q^{30} +6.91538e7 q^{31} -1.40802e8 q^{32} -5.34284e7 q^{33} +7.08203e7 q^{34} -6.12552e7 q^{35} -1.11837e8 q^{36} -4.51038e8 q^{37} -1.01820e7 q^{38} +3.41394e8 q^{39} -1.28643e8 q^{40} +4.49616e8 q^{41} -7.02589e7 q^{42} -1.79394e9 q^{43} +4.16426e8 q^{44} -1.55265e8 q^{45} -3.68681e8 q^{46} +5.98279e8 q^{47} +7.95005e8 q^{48} -1.43462e9 q^{49} +5.20205e8 q^{50} -1.38660e9 q^{51} -2.66085e9 q^{52} -3.80930e9 q^{53} -1.78087e8 q^{54} +5.78132e8 q^{55} +1.13974e9 q^{56} +1.99355e8 q^{57} -1.20181e9 q^{58} +7.14924e8 q^{59} +1.21015e9 q^{60} +9.73343e9 q^{61} -8.58280e8 q^{62} +1.37561e9 q^{63} -4.95277e9 q^{64} -3.69412e9 q^{65} +6.63109e8 q^{66} +2.05666e10 q^{67} +1.08073e10 q^{68} +7.21845e9 q^{69} +7.60249e8 q^{70} -1.31509e10 q^{71} +2.88894e9 q^{72} +2.61072e10 q^{73} +5.59791e9 q^{74} -1.01852e10 q^{75} -1.55379e9 q^{76} -5.12210e9 q^{77} -4.23710e9 q^{78} -3.90581e10 q^{79} -8.60249e9 q^{80} +3.48678e9 q^{81} -5.58027e9 q^{82} +2.57619e10 q^{83} -1.07216e10 q^{84} +1.50039e10 q^{85} +2.22649e10 q^{86} +2.35303e10 q^{87} -1.07570e10 q^{88} +4.36938e10 q^{89} +1.92702e9 q^{90} +3.27289e10 q^{91} -5.62612e10 q^{92} +1.68044e10 q^{93} -7.42534e9 q^{94} -2.15716e9 q^{95} -3.42149e10 q^{96} -4.40290e10 q^{97} +1.78053e10 q^{98} -1.29831e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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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