LMFDB - Embedded newform 177.12.a.d.1.3

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			1.3
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)

$f(q)$	$=$	$q-76.9358 q^{2} +243.000 q^{3} +3871.11 q^{4} +1565.71 q^{5} -18695.4 q^{6} +51126.9 q^{7} -140263. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-76.9358 q^{2} +243.000 q^{3} +3871.11 q^{4} +1565.71 q^{5} -18695.4 q^{6} +51126.9 q^{7} -140263. q^{8} +59049.0 q^{9} -120459. q^{10} +913812. q^{11} +940680. q^{12} +32876.1 q^{13} -3.93349e6 q^{14} +380468. q^{15} +2.86317e6 q^{16} +6.52534e6 q^{17} -4.54298e6 q^{18} +2.05323e7 q^{19} +6.06104e6 q^{20} +1.24238e7 q^{21} -7.03049e7 q^{22} -4.51667e6 q^{23} -3.40838e7 q^{24} -4.63767e7 q^{25} -2.52935e6 q^{26} +1.43489e7 q^{27} +1.97918e8 q^{28} +1.26164e7 q^{29} -2.92716e7 q^{30} +2.56107e8 q^{31} +6.69776e7 q^{32} +2.22056e8 q^{33} -5.02032e8 q^{34} +8.00500e7 q^{35} +2.28585e8 q^{36} -2.39779e7 q^{37} -1.57967e9 q^{38} +7.98888e6 q^{39} -2.19611e8 q^{40} +6.93270e8 q^{41} -9.55838e8 q^{42} +8.57433e8 q^{43} +3.53747e9 q^{44} +9.24537e7 q^{45} +3.47494e8 q^{46} +2.59899e9 q^{47} +6.95750e8 q^{48} +6.36634e8 q^{49} +3.56803e9 q^{50} +1.58566e9 q^{51} +1.27267e8 q^{52} +3.92590e9 q^{53} -1.10394e9 q^{54} +1.43077e9 q^{55} -7.17119e9 q^{56} +4.98934e9 q^{57} -9.70650e8 q^{58} +7.14924e8 q^{59} +1.47283e9 q^{60} +1.27105e9 q^{61} -1.97038e10 q^{62} +3.01899e9 q^{63} -1.10167e10 q^{64} +5.14744e7 q^{65} -1.70841e10 q^{66} +9.16382e9 q^{67} +2.52603e10 q^{68} -1.09755e9 q^{69} -6.15870e9 q^{70} -1.96637e10 q^{71} -8.28236e9 q^{72} -3.06456e10 q^{73} +1.84475e9 q^{74} -1.12695e10 q^{75} +7.94828e10 q^{76} +4.67204e10 q^{77} -6.14631e8 q^{78} -3.72081e10 q^{79} +4.48289e9 q^{80} +3.48678e9 q^{81} -5.33373e10 q^{82} -4.45375e10 q^{83} +4.80941e10 q^{84} +1.02168e10 q^{85} -6.59672e10 q^{86} +3.06578e9 q^{87} -1.28174e11 q^{88} +2.20586e10 q^{89} -7.11299e9 q^{90} +1.68085e9 q^{91} -1.74845e10 q^{92} +6.22340e10 q^{93} -1.99955e11 q^{94} +3.21476e10 q^{95} +1.62756e10 q^{96} -8.48502e10 q^{97} -4.89799e10 q^{98} +5.39597e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−76.9358	−1.70006	−0.850028	−	0.526737i	$-0.823415\pi$
$2$	−76.9358	−1.70006	−0.850028	+	0.526737i	$0.823415\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	3871.11	1.89019
$5$	1565.71	0.224066	0.112033	−	0.993704i	$-0.464264\pi$
$5$	1565.71	0.224066	0.112033	+	0.993704i	$0.464264\pi$
$6$	−18695.4	−0.981528
$7$	51126.9	1.14977	0.574884	−	0.818235i	$-0.305047\pi$
$7$	51126.9	1.14977	0.574884	+	0.818235i	$0.305047\pi$
$8$	−140263.	−1.51338
$9$	59049.0	0.333333
$10$	−120459.	−0.380925
$11$	913812.	1.71079	0.855396	−	0.517974i	$-0.173314\pi$
$11$	913812.	1.71079	0.855396	+	0.517974i	$0.173314\pi$
$12$	940680.	1.09130
$13$	32876.1	0.0245579	0.0122790	−	0.999925i	$-0.496091\pi$
$13$	32876.1	0.0245579	0.0122790	+	0.999925i	$0.496091\pi$
$14$	−3.93349e6	−1.95467
$15$	380468.	0.129365
$16$	2.86317e6	0.682633
$17$	6.52534e6	1.11464	0.557319	−	0.830298i	$-0.311830\pi$
$17$	6.52534e6	1.11464	0.557319	+	0.830298i	$0.311830\pi$
$18$	−4.54298e6	−0.566685
$19$	2.05323e7	1.90236	0.951179	−	0.308638i	$-0.0998733\pi$
$19$	2.05323e7	1.90236	0.951179	+	0.308638i	$0.0998733\pi$
$20$	6.06104e6	0.423528
$21$	1.24238e7	0.663819
$22$	−7.03049e7	−2.90844
$23$	−4.51667e6	−0.146324	−0.0731620	−	0.997320i	$-0.523309\pi$
$23$	−4.51667e6	−0.146324	−0.0731620	+	0.997320i	$0.523309\pi$
$24$	−3.40838e7	−0.873748
$25$	−4.63767e7	−0.949794
$26$	−2.52935e6	−0.0417498
$27$	1.43489e7	0.192450
$28$	1.97918e8	2.17328
$29$	1.26164e7	0.114221	0.0571104	−	0.998368i	$-0.481811\pi$
$29$	1.26164e7	0.114221	0.0571104	+	0.998368i	$0.481811\pi$
$30$	−2.92716e7	−0.219927
$31$	2.56107e8	1.60669	0.803344	−	0.595515i	$-0.203052\pi$
$31$	2.56107e8	1.60669	0.803344	+	0.595515i	$0.203052\pi$
$32$	6.69776e7	0.352862
$33$	2.22056e8	0.987726
$34$	−5.02032e8	−1.89495
$35$	8.00500e7	0.257624
$36$	2.28585e8	0.630064
$37$	−2.39779e7	−0.0568461	−0.0284231	−	0.999596i	$-0.509049\pi$
$37$	−2.39779e7	−0.0568461	−0.0284231	+	0.999596i	$0.509049\pi$
$38$	−1.57967e9	−3.23412
$39$	7.98888e6	0.0141785
$40$	−2.19611e8	−0.339097
$41$	6.93270e8	0.934526	0.467263	−	0.884118i	$-0.345240\pi$
$41$	6.93270e8	0.934526	0.467263	+	0.884118i	$0.345240\pi$
$42$	−9.55838e8	−1.12853
$43$	8.57433e8	0.889454	0.444727	−	0.895666i	$-0.353301\pi$
$43$	8.57433e8	0.889454	0.444727	+	0.895666i	$0.353301\pi$
$44$	3.53747e9	3.23373
$45$	9.24537e7	0.0746888
$46$	3.47494e8	0.248759
$47$	2.59899e9	1.65298	0.826488	−	0.562954i	$-0.190335\pi$
$47$	2.59899e9	1.65298	0.826488	+	0.562954i	$0.190335\pi$
$48$	6.95750e8	0.394118
$49$	6.36634e8	0.321967
$50$	3.56803e9	1.61470
$51$	1.58566e9	0.643537
$52$	1.27267e8	0.0464192
$53$	3.92590e9	1.28950	0.644751	−	0.764393i	$-0.276961\pi$
$53$	3.92590e9	1.28950	0.644751	+	0.764393i	$0.276961\pi$
$54$	−1.10394e9	−0.327176
$55$	1.43077e9	0.383331
$56$	−7.17119e9	−1.74003
$57$	4.98934e9	1.09833
$58$	−9.70650e8	−0.194182
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	1.47283e9	0.244524
$61$	1.27105e9	0.192685	0.0963423	−	0.995348i	$-0.469286\pi$
$61$	1.27105e9	0.192685	0.0963423	+	0.995348i	$0.469286\pi$
$62$	−1.97038e10	−2.73146
$63$	3.01899e9	0.383256
$64$	−1.10167e10	−1.28252
$65$	5.14744e7	0.00550260
$66$	−1.70841e10	−1.67919
$67$	9.16382e9	0.829211	0.414606	−	0.910001i	$-0.363920\pi$
$67$	9.16382e9	0.829211	0.414606	+	0.910001i	$0.363920\pi$
$68$	2.52603e10	2.10688
$69$	−1.09755e9	−0.0844802
$70$	−6.15870e9	−0.437976
$71$	−1.96637e10	−1.29343	−0.646717	−	0.762730i	$-0.723859\pi$
$71$	−1.96637e10	−1.29343	−0.646717	+	0.762730i	$0.723859\pi$
$72$	−8.28236e9	−0.504459
$73$	−3.06456e10	−1.73018	−0.865092	−	0.501613i	$-0.832740\pi$
$73$	−3.06456e10	−1.73018	−0.865092	+	0.501613i	$0.832740\pi$
$74$	1.84475e9	0.0966416
$75$	−1.12695e10	−0.548364
$76$	7.94828e10	3.59582
$77$	4.67204e10	1.96701
$78$	−6.14631e8	−0.0241043
$79$	−3.72081e10	−1.36047	−0.680234	−	0.732995i	$-0.738122\pi$
$79$	−3.72081e10	−1.36047	−0.680234	+	0.732995i	$0.738122\pi$
$80$	4.48289e9	0.152955
$81$	3.48678e9	0.111111
$82$	−5.33373e10	−1.58875
$83$	−4.45375e10	−1.24107	−0.620535	−	0.784179i	$-0.713085\pi$
$83$	−4.45375e10	−1.24107	−0.620535	+	0.784179i	$0.713085\pi$
$84$	4.80941e10	1.25475
$85$	1.02168e10	0.249753
$86$	−6.59672e10	−1.51212
$87$	3.06578e9	0.0659454
$88$	−1.28174e11	−2.58907
$89$	2.20586e10	0.418728	0.209364	−	0.977838i	$-0.432861\pi$
$89$	2.20586e10	0.418728	0.209364	+	0.977838i	$0.432861\pi$
$90$	−7.11299e9	−0.126975
$91$	1.68085e9	0.0282359
$92$	−1.74845e10	−0.276580
$93$	6.22340e10	0.927622
$94$	−1.99955e11	−2.81015
$95$	3.21476e10	0.426254
$96$	1.62756e10	0.203725
$97$	−8.48502e10	−1.00325	−0.501624	−	0.865086i	$-0.667264\pi$
$97$	−8.48502e10	−1.00325	−0.501624	+	0.865086i	$0.667264\pi$
$98$	−4.89799e10	−0.547362
$99$	5.39597e10	0.570264
$100$	−1.79529e11	−1.79529
$101$	4.47202e8	0.00423386	0.00211693	−	0.999998i	$-0.499326\pi$
$101$	4.47202e8	0.00423386	0.00211693	+	0.999998i	$0.499326\pi$
$102$	−1.21994e11	−1.09405
$103$	−1.78642e11	−1.51838	−0.759189	−	0.650870i	$-0.774404\pi$
$103$	−1.78642e11	−1.51838	−0.759189	+	0.650870i	$0.774404\pi$
$104$	−4.61128e9	−0.0371653
$105$	1.94521e10	0.148739
$106$	−3.02042e11	−2.19222
$107$	2.67706e11	1.84522	0.922608	−	0.385740i	$-0.126054\pi$
$107$	2.67706e11	1.84522	0.922608	+	0.385740i	$0.126054\pi$
$108$	5.55462e10	0.363768
$109$	−1.91231e11	−1.19046	−0.595228	−	0.803557i	$-0.702938\pi$
$109$	−1.91231e11	−1.19046	−0.595228	+	0.803557i	$0.702938\pi$
$110$	−1.10077e11	−0.651684
$111$	−5.82662e9	−0.0328201
$112$	1.46385e11	0.784869
$113$	−1.46819e11	−0.749639	−0.374819	−	0.927098i	$-0.622295\pi$
$113$	−1.46819e11	−0.749639	−0.374819	+	0.927098i	$0.622295\pi$
$114$	−3.83859e11	−1.86722
$115$	−7.07180e9	−0.0327863
$116$	4.88394e10	0.215899
$117$	1.94130e9	0.00818597
$118$	−5.50033e10	−0.221328
$119$	3.33620e11	1.28158
$120$	−5.33654e10	−0.195777
$121$	5.49741e11	1.92681
$122$	−9.77888e10	−0.327575
$123$	1.68465e11	0.539549
$124$	9.91418e11	3.03695
$125$	−1.49063e11	−0.436883
$126$	−2.32269e11	−0.651557
$127$	−4.33041e11	−1.16308	−0.581538	−	0.813519i	$-0.697549\pi$
$127$	−4.33041e11	−1.16308	−0.581538	+	0.813519i	$0.697549\pi$
$128$	7.10411e11	1.82749
$129$	2.08356e11	0.513527
$130$	−3.96022e9	−0.00935473
$131$	−2.63061e11	−0.595751	−0.297875	−	0.954605i	$-0.596278\pi$
$131$	−2.63061e11	−0.595751	−0.297875	+	0.954605i	$0.596278\pi$
$132$	8.59605e11	1.86699
$133$	1.04975e12	2.18727
$134$	−7.05026e11	−1.40971
$135$	2.24662e10	0.0431216
$136$	−9.15260e11	−1.68687
$137$	−1.61673e11	−0.286202	−0.143101	−	0.989708i	$-0.545707\pi$
$137$	−1.61673e11	−0.286202	−0.143101	+	0.989708i	$0.545707\pi$
$138$	8.44410e10	0.143621
$139$	−9.90647e11	−1.61934	−0.809669	−	0.586887i	$-0.800353\pi$
$139$	−9.90647e11	−1.61934	−0.809669	+	0.586887i	$0.800353\pi$
$140$	3.09882e11	0.486959
$141$	6.31555e11	0.954346
$142$	1.51284e12	2.19891
$143$	3.00426e10	0.0420135
$144$	1.69067e11	0.227544
$145$	1.97536e10	0.0255930
$146$	2.35774e12	2.94141
$147$	1.54702e11	0.185888
$148$	−9.28210e10	−0.107450
$149$	−1.05631e12	−1.17834	−0.589168	−	0.808011i	$-0.700544\pi$
$149$	−1.05631e12	−1.17834	−0.589168	+	0.808011i	$0.700544\pi$
$150$	8.67030e11	0.932250
$151$	−8.33063e11	−0.863585	−0.431792	−	0.901973i	$-0.642119\pi$
$151$	−8.33063e11	−0.863585	−0.431792	+	0.901973i	$0.642119\pi$
$152$	−2.87991e12	−2.87898
$153$	3.85315e11	0.371546
$154$	−3.59447e12	−3.34404
$155$	4.00989e11	0.360005
$156$	3.09259e10	0.0268001
$157$	1.19086e12	0.996350	0.498175	−	0.867076i	$-0.334004\pi$
$157$	1.19086e12	0.996350	0.498175	+	0.867076i	$0.334004\pi$
$158$	2.86263e12	2.31287
$159$	9.53993e11	0.744494
$160$	1.04868e11	0.0790644
$161$	−2.30924e11	−0.168239
$162$	−2.68258e11	−0.188895
$163$	1.90143e12	1.29434	0.647170	−	0.762346i	$-0.275953\pi$
$163$	1.90143e12	1.29434	0.647170	+	0.762346i	$0.275953\pi$
$164$	2.68373e12	1.76643
$165$	3.47676e11	0.221316
$166$	3.42653e12	2.10989
$167$	1.16025e12	0.691213	0.345607	−	0.938379i	$-0.387673\pi$
$167$	1.16025e12	0.691213	0.345607	+	0.938379i	$0.387673\pi$
$168$	−1.74260e12	−1.00461
$169$	−1.79108e12	−0.999397
$170$	−7.86037e11	−0.424594
$171$	1.21241e12	0.634120
$172$	3.31922e12	1.68124
$173$	5.72770e11	0.281013	0.140507	−	0.990080i	$-0.455127\pi$
$173$	5.72770e11	0.281013	0.140507	+	0.990080i	$0.455127\pi$
$174$	−2.35868e11	−0.112111
$175$	−2.37110e12	−1.09204
$176$	2.61640e12	1.16784
$177$	1.73727e11	0.0751646
$178$	−1.69709e12	−0.711862
$179$	−2.31921e12	−0.943297	−0.471648	−	0.881787i	$-0.656341\pi$
$179$	−2.31921e12	−0.943297	−0.471648	+	0.881787i	$0.656341\pi$
$180$	3.57898e11	0.141176
$181$	3.81190e12	1.45851	0.729254	−	0.684243i	$-0.239867\pi$
$181$	3.81190e12	1.45851	0.729254	+	0.684243i	$0.239867\pi$
$182$	−1.29318e11	−0.0480026
$183$	3.08864e11	0.111246
$184$	6.33520e11	0.221443
$185$	−3.75424e10	−0.0127373
$186$	−4.78802e12	−1.57701
$187$	5.96293e12	1.90691
$188$	1.00610e13	3.12444
$189$	7.33615e11	0.221273
$190$	−2.47330e12	−0.724657
$191$	−2.53491e11	−0.0721571	−0.0360785	−	0.999349i	$-0.511487\pi$
$191$	−2.53491e11	−0.0721571	−0.0360785	+	0.999349i	$0.511487\pi$
$192$	−2.67707e12	−0.740462
$193$	−7.22905e12	−1.94319	−0.971596	−	0.236645i	$-0.923952\pi$
$193$	−7.22905e12	−1.94319	−0.971596	+	0.236645i	$0.923952\pi$
$194$	6.52801e12	1.70558
$195$	1.25083e10	0.00317693
$196$	2.46448e12	0.608580
$197$	−1.65192e12	−0.396666	−0.198333	−	0.980135i	$-0.563553\pi$
$197$	−1.65192e12	−0.396666	−0.198333	+	0.980135i	$0.563553\pi$
$198$	−4.15143e12	−0.969481
$199$	−5.73623e12	−1.30297	−0.651486	−	0.758661i	$-0.725854\pi$
$199$	−5.73623e12	−1.30297	−0.651486	+	0.758661i	$0.725854\pi$
$200$	6.50491e12	1.43740
$201$	2.22681e12	0.478745
$202$	−3.44059e10	−0.00719780
$203$	6.45036e11	0.131327
$204$	6.13826e12	1.21641
$205$	1.08546e12	0.209396
$206$	1.37440e13	2.58133
$207$	−2.66705e11	−0.0487747
$208$	9.41297e10	0.0167640
$209$	1.87627e13	3.25454
$210$	−1.49657e12	−0.252865
$211$	5.59098e12	0.920310	0.460155	−	0.887839i	$-0.347794\pi$
$211$	5.59098e12	0.920310	0.460155	+	0.887839i	$0.347794\pi$
$212$	1.51976e13	2.43740
$213$	−4.77828e12	−0.746765
$214$	−2.05962e13	−3.13697
$215$	1.34249e12	0.199297
$216$	−2.01261e12	−0.291249
$217$	1.30939e13	1.84732
$218$	1.47125e13	2.02384
$219$	−7.44688e12	−0.998922
$220$	5.53866e12	0.724569
$221$	2.14527e11	0.0273732
$222$	4.48275e11	0.0557961
$223$	−9.40765e12	−1.14236	−0.571182	−	0.820823i	$-0.693515\pi$
$223$	−9.40765e12	−1.14236	−0.571182	+	0.820823i	$0.693515\pi$
$224$	3.42436e12	0.405709
$225$	−2.73850e12	−0.316598
$226$	1.12957e13	1.27443
$227$	−4.54229e12	−0.500188	−0.250094	−	0.968222i	$-0.580461\pi$
$227$	−4.54229e12	−0.500188	−0.250094	+	0.968222i	$0.580461\pi$
$228$	1.93143e13	2.07605
$229$	−7.76171e11	−0.0814446	−0.0407223	−	0.999171i	$-0.512966\pi$
$229$	−7.76171e11	−0.0814446	−0.0407223	+	0.999171i	$0.512966\pi$
$230$	5.44075e11	0.0557385
$231$	1.13531e13	1.13566
$232$	−1.76960e12	−0.172859
$233$	−1.74016e13	−1.66009	−0.830046	−	0.557695i	$-0.811686\pi$
$233$	−1.74016e13	−1.66009	−0.830046	+	0.557695i	$0.811686\pi$
$234$	−1.49355e11	−0.0139166
$235$	4.06927e12	0.370376
$236$	2.76755e12	0.246082
$237$	−9.04157e12	−0.785467
$238$	−2.56673e13	−2.17875
$239$	−7.77017e12	−0.644528	−0.322264	−	0.946650i	$-0.604444\pi$
$239$	−7.77017e12	−0.644528	−0.322264	+	0.946650i	$0.604444\pi$
$240$	1.08934e12	0.0883086
$241$	8.55732e12	0.678023	0.339011	−	0.940782i	$-0.389908\pi$
$241$	8.55732e12	0.678023	0.339011	+	0.940782i	$0.389908\pi$
$242$	−4.22948e13	−3.27569
$243$	8.47289e11	0.0641500
$244$	4.92036e12	0.364211
$245$	9.96785e11	0.0721420
$246$	−1.29610e13	−0.917263
$247$	6.75021e11	0.0467180
$248$	−3.59222e13	−2.43152
$249$	−1.08226e13	−0.716532
$250$	1.14683e13	0.742726
$251$	−3.85428e12	−0.244195	−0.122098	−	0.992518i	$-0.538962\pi$
$251$	−3.85428e12	−0.244195	−0.122098	+	0.992518i	$0.538962\pi$
$252$	1.16869e13	0.724427
$253$	−4.12739e12	−0.250330
$254$	3.33163e13	1.97730
$255$	2.48268e12	0.144195
$256$	−3.20938e13	−1.82432
$257$	1.67310e13	0.930870	0.465435	−	0.885082i	$-0.345898\pi$
$257$	1.67310e13	0.930870	0.465435	+	0.885082i	$0.345898\pi$
$258$	−1.60300e13	−0.873024
$259$	−1.22591e12	−0.0653599
$260$	1.99263e11	0.0104010
$261$	7.44984e11	0.0380736
$262$	2.02388e13	1.01281
$263$	3.61000e13	1.76909	0.884547	−	0.466451i	$-0.154468\pi$
$263$	3.61000e13	1.76909	0.884547	+	0.466451i	$0.154468\pi$
$264$	−3.11462e13	−1.49480
$265$	6.14682e12	0.288934
$266$	−8.07635e13	−3.71849
$267$	5.36023e12	0.241753
$268$	3.54742e13	1.56737
$269$	4.59887e12	0.199074	0.0995368	−	0.995034i	$-0.468264\pi$
$269$	4.59887e12	0.199074	0.0995368	+	0.995034i	$0.468264\pi$
$270$	−1.72846e12	−0.0733091
$271$	−5.83394e12	−0.242455	−0.121228	−	0.992625i	$-0.538683\pi$
$271$	−5.83394e12	−0.242455	−0.121228	+	0.992625i	$0.538683\pi$
$272$	1.86831e13	0.760888
$273$	4.08447e11	0.0163020
$274$	1.24384e13	0.486560
$275$	−4.23796e13	−1.62490
$276$	−4.24875e12	−0.159684
$277$	3.31954e13	1.22304	0.611518	−	0.791230i	$-0.290559\pi$
$277$	3.31954e13	1.22304	0.611518	+	0.791230i	$0.290559\pi$
$278$	7.62162e13	2.75297
$279$	1.51229e13	0.535563
$280$	−1.12280e13	−0.389882
$281$	−6.70673e12	−0.228363	−0.114182	−	0.993460i	$-0.536425\pi$
$281$	−6.70673e12	−0.228363	−0.114182	+	0.993460i	$0.536425\pi$
$282$	−4.85892e13	−1.62244
$283$	−4.61820e13	−1.51233	−0.756166	−	0.654379i	$-0.772930\pi$
$283$	−4.61820e13	−1.51233	−0.756166	+	0.654379i	$0.772930\pi$
$284$	−7.61204e13	−2.44484
$285$	7.81187e12	0.246098
$286$	−2.31135e12	−0.0714253
$287$	3.54448e13	1.07449
$288$	3.95496e12	0.117621
$289$	8.30812e12	0.242418
$290$	−1.51976e12	−0.0435096
$291$	−2.06186e13	−0.579225
$292$	−1.18633e14	−3.27038
$293$	−2.57384e13	−0.696321	−0.348160	−	0.937435i	$-0.613194\pi$
$293$	−2.57384e13	−0.696321	−0.348160	+	0.937435i	$0.613194\pi$
$294$	−1.19021e13	−0.316020
$295$	1.11936e12	0.0291709
$296$	3.36320e12	0.0860295
$297$	1.31122e13	0.329242
$298$	8.12684e13	2.00324
$299$	−1.48490e11	−0.00359341
$300$	−4.36256e13	−1.03651
$301$	4.38379e13	1.02267
$302$	6.40924e13	1.46814
$303$	1.08670e11	0.00244442
$304$	5.87874e13	1.29861
$305$	1.99009e12	0.0431741
$306$	−2.96445e13	−0.631649
$307$	−4.18095e13	−0.875012	−0.437506	−	0.899216i	$-0.644138\pi$
$307$	−4.18095e13	−0.875012	−0.437506	+	0.899216i	$0.644138\pi$
$308$	1.80860e14	3.71803
$309$	−4.34101e13	−0.876636
$310$	−3.08504e13	−0.612028
$311$	2.49606e13	0.486488	0.243244	−	0.969965i	$-0.421788\pi$
$311$	2.49606e13	0.486488	0.243244	+	0.969965i	$0.421788\pi$
$312$	−1.12054e12	−0.0214574
$313$	3.25889e13	0.613163	0.306582	−	0.951844i	$-0.400815\pi$
$313$	3.25889e13	0.613163	0.306582	+	0.951844i	$0.400815\pi$
$314$	−9.16196e13	−1.69385
$315$	4.72687e12	0.0858748
$316$	−1.44037e14	−2.57155
$317$	2.60297e13	0.456712	0.228356	−	0.973578i	$-0.426665\pi$
$317$	2.60297e13	0.456712	0.228356	+	0.973578i	$0.426665\pi$
$318$	−7.33962e13	−1.26568
$319$	1.15290e13	0.195408
$320$	−1.72490e13	−0.287369
$321$	6.50525e13	1.06534
$322$	1.77663e13	0.286015
$323$	1.33980e14	2.12044
$324$	1.34977e13	0.210021
$325$	−1.52468e12	−0.0233250
$326$	−1.46288e14	−2.20045
$327$	−4.64692e13	−0.687311
$328$	−9.72398e13	−1.41429
$329$	1.32878e14	1.90054
$330$	−2.67487e13	−0.376250
$331$	−1.38408e14	−1.91472	−0.957362	−	0.288890i	$-0.906714\pi$
$331$	−1.38408e14	−1.91472	−0.957362	+	0.288890i	$0.906714\pi$
$332$	−1.72410e14	−2.34586
$333$	−1.41587e12	−0.0189487
$334$	−8.92650e13	−1.17510
$335$	1.43479e13	0.185798
$336$	3.55716e13	0.453145
$337$	−1.29114e14	−1.61811	−0.809056	−	0.587731i	$-0.800021\pi$
$337$	−1.29114e14	−1.61811	−0.809056	+	0.587731i	$0.800021\pi$
$338$	1.37798e14	1.69903
$339$	−3.56771e13	−0.432804
$340$	3.95503e13	0.472081
$341$	2.34034e14	2.74871
$342$	−9.32778e13	−1.07804
$343$	−6.85455e13	−0.779581
$344$	−1.20266e14	−1.34608
$345$	−1.71845e12	−0.0189292
$346$	−4.40665e13	−0.477738
$347$	5.49638e13	0.586495	0.293248	−	0.956036i	$-0.405264\pi$
$347$	5.49638e13	0.586495	0.293248	+	0.956036i	$0.405264\pi$
$348$	1.18680e13	0.124650
$349$	1.07812e14	1.11462	0.557308	−	0.830306i	$-0.311834\pi$
$349$	1.07812e14	1.11462	0.557308	+	0.830306i	$0.311834\pi$
$350$	1.82422e14	1.85654
$351$	4.71736e11	0.00472617
$352$	6.12050e13	0.603673
$353$	−3.68605e12	−0.0357932	−0.0178966	−	0.999840i	$-0.505697\pi$
$353$	−3.68605e12	−0.0357932	−0.0178966	+	0.999840i	$0.505697\pi$
$354$	−1.33658e13	−0.127784
$355$	−3.07877e13	−0.289815
$356$	8.53912e13	0.791477
$357$	8.10697e13	0.739918
$358$	1.78430e14	1.60366
$359$	1.24750e14	1.10414	0.552068	−	0.833799i	$-0.313839\pi$
$359$	1.24750e14	1.10414	0.552068	+	0.833799i	$0.313839\pi$
$360$	−1.29678e13	−0.113032
$361$	3.05084e14	2.61897
$362$	−2.93271e14	−2.47955
$363$	1.33587e14	1.11244
$364$	6.50677e12	0.0533713
$365$	−4.79821e13	−0.387676
$366$	−2.37627e13	−0.189125
$367$	−1.29296e14	−1.01373	−0.506864	−	0.862026i	$-0.669196\pi$
$367$	−1.29296e14	−1.01373	−0.506864	+	0.862026i	$0.669196\pi$
$368$	−1.29320e13	−0.0998855
$369$	4.09369e13	0.311509
$370$	2.88835e12	0.0216541
$371$	2.00719e14	1.48263
$372$	2.40915e14	1.75338
$373$	9.93102e13	0.712189	0.356094	−	0.934450i	$-0.384108\pi$
$373$	9.93102e13	0.712189	0.356094	+	0.934450i	$0.384108\pi$
$374$	−4.58763e14	−3.24186
$375$	−3.62224e13	−0.252235
$376$	−3.64541e14	−2.50157
$377$	4.14776e11	0.00280502
$378$	−5.64413e13	−0.376177
$379$	8.97364e13	0.589458	0.294729	−	0.955581i	$-0.404771\pi$
$379$	8.97364e13	0.589458	0.294729	+	0.955581i	$0.404771\pi$
$380$	1.24447e14	0.805703
$381$	−1.05229e14	−0.671503
$382$	1.95025e13	0.122671
$383$	2.51798e14	1.56120	0.780600	−	0.625031i	$-0.214914\pi$
$383$	2.51798e14	1.56120	0.780600	+	0.625031i	$0.214914\pi$
$384$	1.72630e14	1.05510
$385$	7.31506e13	0.440742
$386$	5.56172e14	3.30354
$387$	5.06305e13	0.296485
$388$	−3.28465e14	−1.89633
$389$	7.40151e13	0.421306	0.210653	−	0.977561i	$-0.432441\pi$
$389$	7.40151e13	0.421306	0.210653	+	0.977561i	$0.432441\pi$
$390$	−9.62334e11	−0.00540096
$391$	−2.94728e13	−0.163098
$392$	−8.92960e13	−0.487257
$393$	−6.39239e13	−0.343957
$394$	1.27092e14	0.674354
$395$	−5.82571e13	−0.304835
$396$	2.08884e14	1.07791
$397$	−2.83014e14	−1.44033	−0.720163	−	0.693805i	$-0.755933\pi$
$397$	−2.83014e14	−1.44033	−0.720163	+	0.693805i	$0.755933\pi$
$398$	4.41322e14	2.21513
$399$	2.55090e14	1.26282
$400$	−1.32784e14	−0.648361
$401$	−1.30178e14	−0.626964	−0.313482	−	0.949594i	$-0.601496\pi$
$401$	−1.30178e14	−0.626964	−0.313482	+	0.949594i	$0.601496\pi$
$402$	−1.71321e14	−0.813894
$403$	8.41978e12	0.0394569
$404$	1.73117e12	0.00800281
$405$	5.45930e12	0.0248963
$406$	−4.96263e13	−0.223264
$407$	−2.19113e13	−0.0972519
$408$	−2.22408e14	−0.973913
$409$	1.36549e14	0.589944	0.294972	−	0.955506i	$-0.404690\pi$
$409$	1.36549e14	0.589944	0.294972	+	0.955506i	$0.404690\pi$
$410$	−8.35107e13	−0.355984
$411$	−3.92864e13	−0.165239
$412$	−6.91545e14	−2.87003
$413$	3.65519e13	0.149687
$414$	2.05192e13	0.0829197
$415$	−6.97329e13	−0.278082
$416$	2.20196e12	0.00866555
$417$	−2.40727e14	−0.934925
$418$	−1.44352e15	−5.53290
$419$	−2.52548e14	−0.955359	−0.477680	−	0.878534i	$-0.658522\pi$
$419$	−2.52548e14	−0.955359	−0.477680	+	0.878534i	$0.658522\pi$
$420$	7.53014e13	0.281146
$421$	−8.40559e13	−0.309754	−0.154877	−	0.987934i	$-0.549498\pi$
$421$	−8.40559e13	−0.309754	−0.154877	+	0.987934i	$0.549498\pi$
$422$	−4.30146e14	−1.56458
$423$	1.53468e14	0.550992
$424$	−5.50656e14	−1.95150
$425$	−3.02623e14	−1.05868
$426$	3.67621e14	1.26954
$427$	6.49846e13	0.221543
$428$	1.03632e15	3.48781
$429$	7.30034e12	0.0242565
$430$	−1.03286e14	−0.338816
$431$	−4.02522e14	−1.30366	−0.651830	−	0.758365i	$-0.725998\pi$
$431$	−4.02522e14	−1.30366	−0.651830	+	0.758365i	$0.725998\pi$
$432$	4.10833e13	0.131373
$433$	6.12432e14	1.93364	0.966818	−	0.255467i	$-0.0822291\pi$
$433$	6.12432e14	1.93364	0.966818	+	0.255467i	$0.0822291\pi$
$434$	−1.00739e15	−3.14055
$435$	4.80012e12	0.0147761
$436$	−7.40279e14	−2.25019
$437$	−9.27376e13	−0.278361
$438$	5.72931e14	1.69822
$439$	−2.46527e14	−0.721622	−0.360811	−	0.932639i	$-0.617500\pi$
$439$	−2.46527e14	−0.721622	−0.360811	+	0.932639i	$0.617500\pi$
$440$	−2.00683e14	−0.580124
$441$	3.75926e13	0.107322
$442$	−1.65048e13	−0.0465359
$443$	−2.24582e14	−0.625396	−0.312698	−	0.949853i	$-0.601233\pi$
$443$	−2.24582e14	−0.625396	−0.312698	+	0.949853i	$0.601233\pi$
$444$	−2.25555e13	−0.0620363
$445$	3.45373e13	0.0938229
$446$	7.23785e14	1.94208
$447$	−2.56684e14	−0.680312
$448$	−5.63252e14	−1.47460
$449$	−2.31424e14	−0.598486	−0.299243	−	0.954177i	$-0.596734\pi$
$449$	−2.31424e14	−0.598486	−0.299243	+	0.954177i	$0.596734\pi$
$450$	2.10688e14	0.538235
$451$	6.33519e14	1.59878
$452$	−5.68354e14	−1.41696
$453$	−2.02434e14	−0.498591
$454$	3.49465e14	0.850347
$455$	2.63173e12	0.00632671
$456$	−6.99818e14	−1.66218
$457$	−1.17751e14	−0.276329	−0.138165	−	0.990409i	$-0.544120\pi$
$457$	−1.17751e14	−0.276329	−0.138165	+	0.990409i	$0.544120\pi$
$458$	5.97153e13	0.138460
$459$	9.36314e13	0.214512
$460$	−2.73757e13	−0.0619723
$461$	8.83754e13	0.197686	0.0988431	−	0.995103i	$-0.468486\pi$
$461$	8.83754e13	0.197686	0.0988431	+	0.995103i	$0.468486\pi$
$462$	−8.73456e14	−1.93068
$463$	−5.39769e13	−0.117900	−0.0589498	−	0.998261i	$-0.518775\pi$
$463$	−5.39769e13	−0.117900	−0.0589498	+	0.998261i	$0.518775\pi$
$464$	3.61228e13	0.0779709
$465$	9.74404e13	0.207849
$466$	1.33881e15	2.82225
$467$	−2.11045e14	−0.439675	−0.219838	−	0.975536i	$-0.570553\pi$
$467$	−2.11045e14	−0.439675	−0.219838	+	0.975536i	$0.570553\pi$
$468$	7.51499e12	0.0154731
$469$	4.68518e14	0.953401
$470$	−3.13072e14	−0.629661
$471$	2.89379e14	0.575243
$472$	−1.00277e14	−0.197025
$473$	7.83533e14	1.52167
$474$	6.95620e14	1.33534
$475$	−9.52219e14	−1.80685
$476$	1.29148e15	2.42242
$477$	2.31820e14	0.429834
$478$	5.97804e14	1.09573
$479$	1.49975e14	0.271752	0.135876	−	0.990726i	$-0.456615\pi$
$479$	1.49975e14	0.271752	0.135876	+	0.990726i	$0.456615\pi$
$480$	2.54828e13	0.0456479
$481$	−7.88297e11	−0.00139602
$482$	−6.58364e14	−1.15268
$483$	−5.61144e13	−0.0971327
$484$	2.12811e15	3.64204
$485$	−1.32851e14	−0.224794
$486$	−6.51868e13	−0.109059
$487$	4.89329e13	0.0809452	0.0404726	−	0.999181i	$-0.487114\pi$
$487$	4.89329e13	0.0809452	0.0404726	+	0.999181i	$0.487114\pi$
$488$	−1.78280e14	−0.291604
$489$	4.62047e14	0.747287
$490$	−7.66884e13	−0.122645
$491$	9.34061e14	1.47716	0.738579	−	0.674166i	$-0.235497\pi$
$491$	9.34061e14	1.47716	0.738579	+	0.674166i	$0.235497\pi$
$492$	6.52145e14	1.01985
$493$	8.23260e13	0.127315
$494$	−5.19332e13	−0.0794232
$495$	8.44853e13	0.127777
$496$	7.33277e14	1.09678
$497$	−1.00534e15	−1.48715
$498$	8.32646e14	1.21815
$499$	9.58838e14	1.38737	0.693685	−	0.720278i	$-0.255986\pi$
$499$	9.58838e14	1.38737	0.693685	+	0.720278i	$0.255986\pi$
$500$	−5.77040e14	−0.825793
$501$	2.81942e14	0.399072
$502$	2.96532e14	0.415146
$503$	−1.14612e15	−1.58710	−0.793552	−	0.608502i	$-0.791771\pi$
$503$	−1.14612e15	−1.58710	−0.793552	+	0.608502i	$0.791771\pi$
$504$	−4.23452e14	−0.580011
$505$	7.00189e11	0.000948665 0
$506$	3.17544e14	0.425575
$507$	−4.35232e14	−0.577002
$508$	−1.67635e15	−2.19844
$509$	1.03284e15	1.33994	0.669971	−	0.742388i	$-0.266307\pi$
$509$	1.03284e15	1.33994	0.669971	+	0.742388i	$0.266307\pi$
$510$	−1.91007e14	−0.245139
$511$	−1.56681e15	−1.98931
$512$	1.01424e15	1.27395
$513$	2.94616e14	0.366109
$514$	−1.28721e15	−1.58253
$515$	−2.79702e14	−0.340217
$516$	8.06570e14	0.970664
$517$	2.37499e15	2.82790
$518$	9.43166e13	0.111115
$519$	1.39183e14	0.162243
$520$	−7.21993e12	−0.00832750
$521$	−8.31000e14	−0.948404	−0.474202	−	0.880416i	$-0.657263\pi$
$521$	−8.31000e14	−0.948404	−0.474202	+	0.880416i	$0.657263\pi$
$522$	−5.73159e13	−0.0647273
$523$	1.40683e15	1.57211	0.786053	−	0.618159i	$-0.212121\pi$
$523$	1.40683e15	1.57211	0.786053	+	0.618159i	$0.212121\pi$
$524$	−1.01834e15	−1.12608
$525$	−5.76176e14	−0.630492
$526$	−2.77738e15	−3.00756
$527$	1.67118e15	1.79088
$528$	6.35785e14	0.674254
$529$	−9.32409e14	−0.978589
$530$	−4.72910e14	−0.491204
$531$	4.22156e13	0.0433963
$532$	4.06371e15	4.13436
$533$	2.27920e13	0.0229500
$534$	−4.12394e14	−0.410994
$535$	4.19150e14	0.413451
$536$	−1.28534e15	−1.25491
$537$	−5.63568e14	−0.544613
$538$	−3.53818e14	−0.338437
$539$	5.81764e14	0.550819
$540$	8.69693e13	0.0815080
$541$	−1.07327e15	−0.995693	−0.497846	−	0.867265i	$-0.665876\pi$
$541$	−1.07327e15	−0.995693	−0.497846	+	0.867265i	$0.665876\pi$
$542$	4.48839e14	0.412187
$543$	9.26291e14	0.842070
$544$	4.37051e14	0.393313
$545$	−2.99413e14	−0.266741
$546$	−3.14242e13	−0.0277143
$547$	5.35752e14	0.467771	0.233885	−	0.972264i	$-0.424856\pi$
$547$	5.35752e14	0.467771	0.233885	+	0.972264i	$0.424856\pi$
$548$	−6.25853e14	−0.540977
$549$	7.50539e13	0.0642282
$550$	3.26051e15	2.76242
$551$	2.59043e14	0.217289
$552$	1.53945e14	0.127850
$553$	−1.90233e15	−1.56422
$554$	−2.55392e15	−2.07923
$555$	−9.12280e12	−0.00735388
$556$	−3.83491e15	−3.06086
$557$	1.83578e14	0.145083	0.0725414	−	0.997365i	$-0.476889\pi$
$557$	1.83578e14	0.145083	0.0725414	+	0.997365i	$0.476889\pi$
$558$	−1.16349e15	−0.910487
$559$	2.81890e13	0.0218431
$560$	2.29197e14	0.175863
$561$	1.44899e15	1.10096
$562$	5.15988e14	0.388230
$563$	−1.07635e15	−0.801968	−0.400984	−	0.916085i	$-0.631332\pi$
$563$	−1.07635e15	−0.801968	−0.400984	+	0.916085i	$0.631332\pi$
$564$	2.44482e15	1.80390
$565$	−2.29877e14	−0.167969
$566$	3.55305e15	2.57105
$567$	1.78269e14	0.127752
$568$	2.75808e15	1.95745
$569$	7.24643e14	0.509339	0.254669	−	0.967028i	$-0.418033\pi$
$569$	7.24643e14	0.509339	0.254669	+	0.967028i	$0.418033\pi$
$570$	−6.01012e14	−0.418381
$571$	4.18065e13	0.0288234	0.0144117	−	0.999896i	$-0.495412\pi$
$571$	4.18065e13	0.0288234	0.0144117	+	0.999896i	$0.495412\pi$
$572$	1.16298e14	0.0794135
$573$	−6.15983e13	−0.0416599
$574$	−2.72697e15	−1.82669
$575$	2.09468e14	0.138978
$576$	−6.50528e14	−0.427506
$577$	−6.03500e14	−0.392835	−0.196417	−	0.980520i	$-0.562931\pi$
$577$	−6.03500e14	−0.392835	−0.196417	+	0.980520i	$0.562931\pi$
$578$	−6.39192e14	−0.412124
$579$	−1.75666e15	−1.12190
$580$	7.64683e13	0.0483757
$581$	−2.27707e15	−1.42694
$582$	1.58631e15	0.984716
$583$	3.58753e15	2.20607
$584$	4.29843e15	2.61842
$585$	3.03951e12	0.00183420
$586$	1.98020e15	1.18378
$587$	5.57063e14	0.329910	0.164955	−	0.986301i	$-0.447252\pi$
$587$	5.57063e14	0.329910	0.164955	+	0.986301i	$0.447252\pi$
$588$	5.98869e14	0.351364
$589$	5.25846e15	3.05650
$590$	−8.61192e13	−0.0495922
$591$	−4.01416e14	−0.229015
$592$	−6.86527e13	−0.0388050
$593$	1.34398e15	0.752649	0.376324	−	0.926488i	$-0.377188\pi$
$593$	1.34398e15	0.752649	0.376324	+	0.926488i	$0.377188\pi$
$594$	−1.00880e15	−0.559730
$595$	5.22353e14	0.287158
$596$	−4.08911e15	−2.22728
$597$	−1.39390e15	−0.752271
$598$	1.14242e13	0.00610900
$599$	−1.30206e14	−0.0689895	−0.0344947	−	0.999405i	$-0.510982\pi$
$599$	−1.30206e14	−0.0689895	−0.0344947	+	0.999405i	$0.510982\pi$
$600$	1.58069e15	0.829881
$601$	−8.49953e14	−0.442166	−0.221083	−	0.975255i	$-0.570959\pi$
$601$	−8.49953e14	−0.442166	−0.221083	+	0.975255i	$0.570959\pi$
$602$	−3.37270e15	−1.73859
$603$	5.41115e14	0.276404
$604$	−3.22488e15	−1.63234
$605$	8.60736e14	0.431733
$606$	−8.36062e12	−0.00415565
$607$	−1.32016e15	−0.650264	−0.325132	−	0.945669i	$-0.605409\pi$
$607$	−1.32016e15	−0.650264	−0.325132	+	0.945669i	$0.605409\pi$
$608$	1.37520e15	0.671270
$609$	1.56744e14	0.0758220
$610$	−1.53109e14	−0.0733984
$611$	8.54446e13	0.0405936
$612$	1.49160e15	0.702293
$613$	3.37466e15	1.57470	0.787349	−	0.616508i	$-0.211453\pi$
$613$	3.37466e15	1.57470	0.787349	+	0.616508i	$0.211453\pi$
$614$	3.21665e15	1.48757
$615$	2.63767e14	0.120895
$616$	−6.55312e15	−2.97683
$617$	−3.99533e15	−1.79880	−0.899402	−	0.437123i	$-0.855998\pi$
$617$	−3.99533e15	−1.79880	−0.899402	+	0.437123i	$0.855998\pi$
$618$	3.33979e15	1.49033
$619$	−3.73341e15	−1.65123	−0.825615	−	0.564234i	$-0.809172\pi$
$619$	−3.73341e15	−1.65123	−0.825615	+	0.564234i	$0.809172\pi$
$620$	1.55227e15	0.680478
$621$	−6.48093e13	−0.0281601
$622$	−1.92036e15	−0.827058
$623$	1.12779e15	0.481441
$624$	2.28735e13	0.00967872
$625$	2.03110e15	0.851904
$626$	−2.50725e15	−1.04241
$627$	4.55933e15	1.87901
$628$	4.60995e15	1.88329
$629$	−1.56464e14	−0.0633628
$630$	−3.63665e14	−0.145992
$631$	2.36236e14	0.0940122	0.0470061	−	0.998895i	$-0.485032\pi$
$631$	2.36236e14	0.0940122	0.0470061	+	0.998895i	$0.485032\pi$
$632$	5.21890e15	2.05890
$633$	1.35861e15	0.531341
$634$	−2.00261e15	−0.776436
$635$	−6.78017e14	−0.260606
$636$	3.69301e15	1.40724
$637$	2.09300e13	0.00790684
$638$	−8.86992e14	−0.332205
$639$	−1.16112e15	−0.431145
$640$	1.11230e15	0.409479
$641$	−2.64828e15	−0.966597	−0.483298	−	0.875456i	$-0.660561\pi$
$641$	−2.64828e15	−0.966597	−0.483298	+	0.875456i	$0.660561\pi$
$642$	−5.00487e15	−1.81113
$643$	3.97895e15	1.42760	0.713802	−	0.700347i	$-0.246971\pi$
$643$	3.97895e15	1.42760	0.713802	+	0.700347i	$0.246971\pi$
$644$	−8.93931e14	−0.318003
$645$	3.26225e14	0.115064
$646$	−1.03079e16	−3.60487
$647$	−4.68166e15	−1.62340	−0.811701	−	0.584073i	$-0.801458\pi$
$647$	−4.68166e15	−1.62340	−0.811701	+	0.584073i	$0.801458\pi$
$648$	−4.89065e14	−0.168153
$649$	6.53307e14	0.222726
$650$	1.17303e14	0.0396537
$651$	3.18183e15	1.06655
$652$	7.36064e15	2.44655
$653$	−2.30151e15	−0.758561	−0.379281	−	0.925282i	$-0.623828\pi$
$653$	−2.30151e15	−0.758561	−0.379281	+	0.925282i	$0.623828\pi$
$654$	3.57515e15	1.16847
$655$	−4.11878e14	−0.133488
$656$	1.98495e15	0.637938
$657$	−1.80959e15	−0.576728
$658$	−1.02231e16	−3.23103
$659$	−2.06137e15	−0.646078	−0.323039	−	0.946386i	$-0.604705\pi$
$659$	−2.06137e15	−0.646078	−0.323039	+	0.946386i	$0.604705\pi$
$660$	1.34589e15	0.418330
$661$	−3.47857e15	−1.07224	−0.536121	−	0.844141i	$-0.680111\pi$
$661$	−3.47857e15	−1.07224	−0.536121	+	0.844141i	$0.680111\pi$
$662$	1.06485e16	3.25514
$663$	5.21302e13	0.0158039
$664$	6.24695e15	1.87821
$665$	1.64361e15	0.490094
$666$	1.08931e14	0.0322139
$667$	−5.69840e13	−0.0167132
$668$	4.49147e15	1.30653
$669$	−2.28606e15	−0.659544
$670$	−1.10387e15	−0.315868
$671$	1.16150e15	0.329643
$672$	8.32119e14	0.234236
$673$	−8.65934e14	−0.241770	−0.120885	−	0.992667i	$-0.538573\pi$
$673$	−8.65934e14	−0.241770	−0.120885	+	0.992667i	$0.538573\pi$
$674$	9.93348e15	2.75088
$675$	−6.65455e14	−0.182788
$676$	−6.93347e15	−1.88905
$677$	5.97805e15	1.61556	0.807778	−	0.589487i	$-0.200670\pi$
$677$	5.97805e15	1.61556	0.807778	+	0.589487i	$0.200670\pi$
$678$	2.74485e15	0.735791
$679$	−4.33813e15	−1.15350
$680$	−1.43303e15	−0.377970
$681$	−1.10378e15	−0.288784
$682$	−1.80056e16	−4.67296
$683$	−5.49833e15	−1.41552	−0.707762	−	0.706451i	$-0.750295\pi$
$683$	−5.49833e15	−1.41552	−0.707762	+	0.706451i	$0.750295\pi$
$684$	4.69338e15	1.19861
$685$	−2.53133e14	−0.0641283
$686$	5.27360e15	1.32533
$687$	−1.88610e14	−0.0470221
$688$	2.45498e15	0.607171
$689$	1.29068e14	0.0316674
$690$	1.32210e14	0.0321806
$691$	1.75970e15	0.424922	0.212461	−	0.977170i	$-0.431852\pi$
$691$	1.75970e15	0.424922	0.212461	+	0.977170i	$0.431852\pi$
$692$	2.21726e15	0.531169
$693$	2.75879e15	0.655672
$694$	−4.22868e15	−0.997075
$695$	−1.55107e15	−0.362839
$696$	−4.30014e14	−0.0998002
$697$	4.52382e15	1.04166
$698$	−8.29456e15	−1.89491
$699$	−4.22860e15	−0.958455
$700$	−9.17878e15	−2.06417
$701$	−2.42930e13	−0.00542040	−0.00271020	−	0.999996i	$-0.500863\pi$
$701$	−2.42930e13	−0.00542040	−0.00271020	+	0.999996i	$0.500863\pi$
$702$	−3.62933e13	−0.00803476
$703$	−4.92320e14	−0.108142
$704$	−1.00672e16	−2.19412
$705$	9.88832e14	0.213837
$706$	2.83589e14	0.0608504
$707$	2.28641e13	0.00486796
$708$	6.72515e14	0.142076
$709$	9.48390e14	0.198807	0.0994037	−	0.995047i	$-0.468306\pi$
$709$	9.48390e14	0.198807	0.0994037	+	0.995047i	$0.468306\pi$
$710$	2.36867e15	0.492702
$711$	−2.19710e15	−0.453489
$712$	−3.09399e15	−0.633694
$713$	−1.15675e15	−0.235097
$714$	−6.23716e15	−1.25790
$715$	4.70380e13	0.00941380
$716$	−8.97792e15	−1.78301
$717$	−1.88815e15	−0.372118
$718$	−9.59777e15	−1.87709
$719$	4.17730e14	0.0810749	0.0405375	−	0.999178i	$-0.487093\pi$
$719$	4.17730e14	0.0810749	0.0405375	+	0.999178i	$0.487093\pi$
$720$	2.64710e14	0.0509850
$721$	−9.13344e15	−1.74578
$722$	−2.34719e16	−4.45240
$723$	2.07943e15	0.391457
$724$	1.47563e16	2.75686
$725$	−5.85105e14	−0.108486
$726$	−1.02776e16	−1.89122
$727$	−1.11557e15	−0.203731	−0.101866	−	0.994798i	$-0.532481\pi$
$727$	−1.11557e15	−0.203731	−0.101866	+	0.994798i	$0.532481\pi$
$728$	−2.35761e14	−0.0427315
$729$	2.05891e14	0.0370370
$730$	3.69154e15	0.659071
$731$	5.59504e15	0.991419
$732$	1.19565e15	0.210277
$733$	−1.69075e15	−0.295126	−0.147563	−	0.989053i	$-0.547143\pi$
$733$	−1.69075e15	−0.295126	−0.147563	+	0.989053i	$0.547143\pi$
$734$	9.94749e15	1.72340
$735$	2.42219e14	0.0416512
$736$	−3.02516e14	−0.0516321
$737$	8.37401e15	1.41861
$738$	−3.14951e15	−0.529582
$739$	−2.83296e15	−0.472820	−0.236410	−	0.971653i	$-0.575971\pi$
$739$	−2.83296e15	−0.472820	−0.236410	+	0.971653i	$0.575971\pi$
$740$	−1.45331e14	−0.0240759
$741$	1.64030e14	0.0269726
$742$	−1.54425e16	−2.52055
$743$	4.85393e15	0.786421	0.393210	−	0.919448i	$-0.371364\pi$
$743$	4.85393e15	0.786421	0.393210	+	0.919448i	$0.371364\pi$
$744$	−8.72909e15	−1.40384
$745$	−1.65388e15	−0.264025
$746$	−7.64051e15	−1.21076
$747$	−2.62990e15	−0.413690
$748$	2.30832e16	3.60443
$749$	1.36870e16	2.12157
$750$	2.78679e15	0.428813
$751$	3.71833e15	0.567974	0.283987	−	0.958828i	$-0.408343\pi$
$751$	3.71833e15	0.567974	0.283987	+	0.958828i	$0.408343\pi$
$752$	7.44135e15	1.12838
$753$	−9.36589e14	−0.140986
$754$	−3.19111e13	−0.00476870
$755$	−1.30434e15	−0.193500
$756$	2.83991e15	0.418248
$757$	6.65316e15	0.972749	0.486374	−	0.873750i	$-0.338319\pi$
$757$	6.65316e15	0.972749	0.486374	+	0.873750i	$0.338319\pi$
$758$	−6.90394e15	−1.00211
$759$	−1.00296e15	−0.144528
$760$	−4.50911e15	−0.645083
$761$	−5.97347e15	−0.848421	−0.424210	−	0.905564i	$-0.639448\pi$
$761$	−5.97347e15	−0.848421	−0.424210	+	0.905564i	$0.639448\pi$
$762$	8.09587e15	1.14159
$763$	−9.77707e15	−1.36875
$764$	−9.81292e14	−0.136391
$765$	6.03291e14	0.0832509
$766$	−1.93722e16	−2.65413
$767$	2.35039e13	0.00319717
$768$	−7.79878e15	−1.05327
$769$	−3.70785e15	−0.497195	−0.248598	−	0.968607i	$-0.579970\pi$
$769$	−3.70785e15	−0.497195	−0.248598	+	0.968607i	$0.579970\pi$
$770$	−5.62790e15	−0.749286
$771$	4.06563e15	0.537438
$772$	−2.79845e16	−3.67301
$773$	3.54842e15	0.462432	0.231216	−	0.972902i	$-0.425730\pi$
$773$	3.54842e15	0.462432	0.231216	+	0.972902i	$0.425730\pi$
$774$	−3.89530e15	−0.504041
$775$	−1.18774e16	−1.52602
$776$	1.19013e16	1.51829
$777$	−2.97897e14	−0.0377355
$778$	−5.69441e15	−0.716244
$779$	1.42344e16	1.77780
$780$	4.84210e13	0.00600500
$781$	−1.79689e16	−2.21280
$782$	2.26751e15	0.277276
$783$	1.81031e14	0.0219818
$784$	1.82279e15	0.219785
$785$	1.86454e15	0.223249
$786$	4.91803e15	0.584746
$787$	8.76529e15	1.03492	0.517458	−	0.855709i	$-0.326878\pi$
$787$	8.76529e15	1.03492	0.517458	+	0.855709i	$0.326878\pi$
$788$	−6.39477e15	−0.749774
$789$	8.77231e15	1.02139
$790$	4.48206e15	0.518237
$791$	−7.50642e15	−0.861911
$792$	−7.56853e15	−0.863024
$793$	4.17870e13	0.00473193
$794$	2.17739e16	2.44863
$795$	1.49368e15	0.166816
$796$	−2.22056e16	−2.46287
$797$	7.06335e15	0.778019	0.389009	−	0.921234i	$-0.372817\pi$
$797$	7.06335e15	0.778019	0.389009	+	0.921234i	$0.372817\pi$
$798$	−1.96255e16	−2.14687
$799$	1.69593e16	1.84247
$800$	−3.10620e15	−0.335146
$801$	1.30254e15	0.139576
$802$	1.00153e16	1.06587
$803$	−2.80043e16	−2.95999
$804$	8.62023e15	0.904921
$805$	−3.61559e14	−0.0376966
$806$	−6.47783e14	−0.0670790
$807$	1.11753e15	0.114935
$808$	−6.27257e13	−0.00640742
$809$	−9.88415e15	−1.00282	−0.501409	−	0.865210i	$-0.667185\pi$
$809$	−9.88415e15	−1.00282	−0.501409	+	0.865210i	$0.667185\pi$
$810$	−4.20015e14	−0.0423250
$811$	−1.34709e16	−1.34828	−0.674141	−	0.738603i	$-0.735486\pi$
$811$	−1.34709e16	−1.34828	−0.674141	+	0.738603i	$0.735486\pi$
$812$	2.49701e15	0.248234
$813$	−1.41765e15	−0.139981
$814$	1.68576e15	0.165334
$815$	2.97709e15	0.290018
$816$	4.54000e15	0.439299
$817$	1.76051e16	1.69206
$818$	−1.05055e16	−1.00294
$819$	9.92526e13	0.00941197
$820$	4.20194e15	0.395798
$821$	2.04293e16	1.91147	0.955733	−	0.294235i	$-0.0950649\pi$
$821$	2.04293e16	1.91147	0.955733	+	0.294235i	$0.0950649\pi$
$822$	3.02253e15	0.280916
$823$	1.35924e16	1.25486	0.627431	−	0.778672i	$-0.284106\pi$
$823$	1.35924e16	1.25486	0.627431	+	0.778672i	$0.284106\pi$
$824$	2.50568e16	2.29788
$825$	−1.02982e16	−0.938137
$826$	−2.81215e15	−0.254476
$827$	9.45269e14	0.0849718	0.0424859	−	0.999097i	$-0.486472\pi$
$827$	9.45269e14	0.0849718	0.0424859	+	0.999097i	$0.486472\pi$
$828$	−1.03245e15	−0.0921935
$829$	1.79154e16	1.58919	0.794595	−	0.607140i	$-0.207683\pi$
$829$	1.79154e16	1.58919	0.794595	+	0.607140i	$0.207683\pi$
$830$	5.36495e15	0.472755
$831$	8.06649e15	0.706121
$832$	−3.62187e14	−0.0314960
$833$	4.15425e15	0.358877
$834$	1.85205e16	1.58943
$835$	1.81662e15	0.154878
$836$	7.26324e16	6.15171
$837$	3.67485e15	0.309207
$838$	1.94300e16	1.62416
$839$	1.21669e15	0.101039	0.0505197	−	0.998723i	$-0.483912\pi$
$839$	1.21669e15	0.101039	0.0505197	+	0.998723i	$0.483912\pi$
$840$	−2.72841e15	−0.225099
$841$	−1.20413e16	−0.986954
$842$	6.46691e15	0.526599
$843$	−1.62974e15	−0.131846
$844$	2.16433e16	1.73956
$845$	−2.80431e15	−0.223931
$846$	−1.18072e16	−0.936718
$847$	2.81066e16	2.21539
$848$	1.12405e16	0.880256
$849$	−1.12222e16	−0.873146
$850$	2.32826e16	1.79981
$851$	1.08300e14	0.00831795
$852$	−1.84973e16	−1.41153
$853$	5.65881e15	0.429048	0.214524	−	0.976719i	$-0.431180\pi$
$853$	5.65881e15	0.429048	0.214524	+	0.976719i	$0.431180\pi$
$854$	−4.99964e15	−0.376635
$855$	1.89828e15	0.142085
$856$	−3.75491e16	−2.79250
$857$	−2.30030e16	−1.69977	−0.849885	−	0.526969i	$-0.823329\pi$
$857$	−2.30030e16	−1.69977	−0.849885	+	0.526969i	$0.823329\pi$
$858$	−5.61657e14	−0.0412374
$859$	−1.57086e16	−1.14597	−0.572986	−	0.819565i	$-0.694215\pi$
$859$	−1.57086e16	−1.14597	−0.572986	+	0.819565i	$0.694215\pi$
$860$	5.19694e15	0.376709
$861$	8.61308e15	0.620356
$862$	3.09683e16	2.21629
$863$	−2.37841e16	−1.69132	−0.845662	−	0.533718i	$-0.820794\pi$
$863$	−2.37841e16	−1.69132	−0.845662	+	0.533718i	$0.820794\pi$
$864$	9.61055e14	0.0679083
$865$	8.96792e14	0.0629656
$866$	−4.71180e16	−3.28729
$867$	2.01887e15	0.139960
$868$	5.06882e16	3.49179
$869$	−3.40012e16	−2.32748
$870$	−3.69301e14	−0.0251203
$871$	3.01270e14	0.0203637
$872$	2.68226e16	1.80161
$873$	−5.01032e15	−0.334416
$874$	7.13484e15	0.473229
$875$	−7.62114e15	−0.502314
$876$	−2.88277e16	−1.88815
$877$	9.34304e15	0.608121	0.304061	−	0.952653i	$-0.401657\pi$
$877$	9.34304e15	0.608121	0.304061	+	0.952653i	$0.401657\pi$
$878$	1.89668e16	1.22680
$879$	−6.25443e15	−0.402021
$880$	4.09652e15	0.261674
$881$	2.21334e16	1.40502	0.702509	−	0.711675i	$-0.252063\pi$
$881$	2.21334e16	1.40502	0.702509	+	0.711675i	$0.252063\pi$
$882$	−2.89222e15	−0.182454
$883$	8.12953e15	0.509661	0.254831	−	0.966986i	$-0.417980\pi$
$883$	8.12953e15	0.509661	0.254831	+	0.966986i	$0.417980\pi$
$884$	8.30460e14	0.0517406
$885$	2.72006e14	0.0168419
$886$	1.72784e16	1.06321
$887$	4.28272e15	0.261903	0.130951	−	0.991389i	$-0.458197\pi$
$887$	4.28272e15	0.261903	0.130951	+	0.991389i	$0.458197\pi$
$888$	8.17256e14	0.0496692
$889$	−2.21400e16	−1.33727
$890$	−2.65716e15	−0.159504
$891$	3.18627e15	0.190088
$892$	−3.64181e16	−2.15929
$893$	5.33632e16	3.14455
$894$	1.97482e16	1.15657
$895$	−3.63121e15	−0.211361
$896$	3.63211e16	2.10119
$897$	−3.60832e13	−0.00207466
$898$	1.78048e16	1.01746
$899$	3.23114e15	0.183517
$900$	−1.06010e16	−0.598431
$901$	2.56178e16	1.43733
$902$	−4.87403e16	−2.71801
$903$	1.06526e16	0.590437
$904$	2.05933e16	1.13449
$905$	5.96833e15	0.326803
$906$	1.55744e16	0.847632
$907$	2.31261e16	1.25101	0.625507	−	0.780219i	$-0.284892\pi$
$907$	2.31261e16	1.25101	0.625507	+	0.780219i	$0.284892\pi$
$908$	−1.75837e16	−0.945451
$909$	2.64069e13	0.00141129
$910$	−2.02474e14	−0.0107558
$911$	2.70095e16	1.42615	0.713075	−	0.701088i	$-0.247302\pi$
$911$	2.70095e16	1.42615	0.713075	+	0.701088i	$0.247302\pi$
$912$	1.42853e16	0.749754
$913$	−4.06989e16	−2.12321
$914$	9.05929e15	0.469775
$915$	4.83592e14	0.0249266
$916$	−3.00465e15	−0.153946
$917$	−1.34495e16	−0.684976
$918$	−7.20361e15	−0.364683
$919$	−1.76645e16	−0.888926	−0.444463	−	0.895797i	$-0.646605\pi$
$919$	−1.76645e16	−0.888926	−0.444463	+	0.895797i	$0.646605\pi$
$920$	9.91909e14	0.0496180
$921$	−1.01597e16	−0.505188
$922$	−6.79923e15	−0.336078
$923$	−6.46465e14	−0.0317640
$924$	4.39490e16	2.14661
$925$	1.11201e15	0.0539921
$926$	4.15275e15	0.200436
$927$	−1.05487e16	−0.506126
$928$	8.45014e14	0.0403042
$929$	−5.81360e15	−0.275651	−0.137825	−	0.990457i	$-0.544011\pi$
$929$	−5.81360e15	−0.275651	−0.137825	+	0.990457i	$0.544011\pi$
$930$	−7.49665e15	−0.353355
$931$	1.30716e16	0.612497
$932$	−6.73637e16	−3.13789
$933$	6.06542e15	0.280874
$934$	1.62369e16	0.747472
$935$	9.33623e15	0.427275
$936$	−2.72292e14	−0.0123884
$937$	3.33891e16	1.51021	0.755104	−	0.655606i	$-0.227587\pi$
$937$	3.33891e16	1.51021	0.755104	+	0.655606i	$0.227587\pi$
$938$	−3.60458e16	−1.62084
$939$	7.91910e15	0.354010
$940$	1.57526e16	0.700082
$941$	1.60096e15	0.0707357	0.0353678	−	0.999374i	$-0.488740\pi$
$941$	1.60096e15	0.0707357	0.0353678	+	0.999374i	$0.488740\pi$
$942$	−2.22636e16	−0.977946
$943$	−3.13127e15	−0.136744
$944$	2.04695e15	0.0888712
$945$	1.14863e15	0.0495798
$946$	−6.02817e16	−2.58693
$947$	−2.59697e16	−1.10801	−0.554003	−	0.832515i	$-0.686900\pi$
$947$	−2.59697e16	−1.10801	−0.554003	+	0.832515i	$0.686900\pi$
$948$	−3.50009e16	−1.48468
$949$	−1.00751e15	−0.0424897
$950$	7.32597e16	3.07175
$951$	6.32521e15	0.263683
$952$	−4.67944e16	−1.93951
$953$	1.89690e16	0.781687	0.390843	−	0.920457i	$-0.372183\pi$
$953$	1.89690e16	0.781687	0.390843	+	0.920457i	$0.372183\pi$
$954$	−1.78353e16	−0.730741
$955$	−3.96893e14	−0.0161680
$956$	−3.00792e16	−1.21828
$957$	2.80155e15	0.112819
$958$	−1.15384e16	−0.461994
$959$	−8.26582e15	−0.329066
$960$	−4.19151e15	−0.165913
$961$	4.01822e16	1.58145
$962$	6.06483e13	0.00237332
$963$	1.58078e16	0.615072
$964$	3.31264e16	1.28159
$965$	−1.13186e16	−0.435404
$966$	4.31721e15	0.165131
$967$	1.04059e16	0.395761	0.197880	−	0.980226i	$-0.436594\pi$
$967$	1.04059e16	0.395761	0.197880	+	0.980226i	$0.436594\pi$
$968$	−7.71081e16	−2.91599
$969$	3.25572e16	1.22424
$970$	1.02210e16	0.382162
$971$	−2.97243e16	−1.10511	−0.552556	−	0.833476i	$-0.686347\pi$
$971$	−2.97243e16	−1.10511	−0.552556	+	0.833476i	$0.686347\pi$
$972$	3.27995e15	0.121256
$973$	−5.06487e16	−1.86186
$974$	−3.76469e15	−0.137611
$975$	−3.70498e14	−0.0134667
$976$	3.63922e15	0.131533
$977$	−4.20362e15	−0.151079	−0.0755394	−	0.997143i	$-0.524068\pi$
$977$	−4.20362e15	−0.151079	−0.0755394	+	0.997143i	$0.524068\pi$
$978$	−3.55479e16	−1.27043
$979$	2.01574e16	0.716357
$980$	3.85867e15	0.136362
$981$	−1.12920e16	−0.396819
$982$	−7.18627e16	−2.51125
$983$	−5.44435e15	−0.189192	−0.0945958	−	0.995516i	$-0.530156\pi$
$983$	−5.44435e15	−0.189192	−0.0945958	+	0.995516i	$0.530156\pi$
$984$	−2.36293e16	−0.816540
$985$	−2.58643e15	−0.0888794
$986$	−6.33382e15	−0.216442
$987$	3.22895e16	1.09728
$988$	2.61308e15	0.0883059
$989$	−3.87274e15	−0.130148
$990$	−6.49994e15	−0.217228
$991$	3.98861e16	1.32561	0.662805	−	0.748792i	$-0.269366\pi$
$991$	3.98861e16	1.32561	0.662805	+	0.748792i	$0.269366\pi$
$992$	1.71534e16	0.566939
$993$	−3.36331e16	−1.10547
$994$	7.73469e16	2.52824
$995$	−8.98128e15	−0.291952
$996$	−4.18956e16	−1.35438
$997$	−5.81768e16	−1.87036	−0.935182	−	0.354168i	$-0.884764\pi$
$997$	−5.81768e16	−1.87036	−0.935182	+	0.354168i	$0.884764\pi$
$998$	−7.37690e16	−2.35861
$999$	−3.44056e14	−0.0109400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-76.9358 q^{2} +243.000 q^{3} +3871.11 q^{4} +1565.71 q^{5} -18695.4 q^{6} +51126.9 q^{7} -140263. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-76.9358 q^{2} +243.000 q^{3} +3871.11 q^{4} +1565.71 q^{5} -18695.4 q^{6} +51126.9 q^{7} -140263. q^{8} +59049.0 q^{9} -120459. q^{10} +913812. q^{11} +940680. q^{12} +32876.1 q^{13} -3.93349e6 q^{14} +380468. q^{15} +2.86317e6 q^{16} +6.52534e6 q^{17} -4.54298e6 q^{18} +2.05323e7 q^{19} +6.06104e6 q^{20} +1.24238e7 q^{21} -7.03049e7 q^{22} -4.51667e6 q^{23} -3.40838e7 q^{24} -4.63767e7 q^{25} -2.52935e6 q^{26} +1.43489e7 q^{27} +1.97918e8 q^{28} +1.26164e7 q^{29} -2.92716e7 q^{30} +2.56107e8 q^{31} +6.69776e7 q^{32} +2.22056e8 q^{33} -5.02032e8 q^{34} +8.00500e7 q^{35} +2.28585e8 q^{36} -2.39779e7 q^{37} -1.57967e9 q^{38} +7.98888e6 q^{39} -2.19611e8 q^{40} +6.93270e8 q^{41} -9.55838e8 q^{42} +8.57433e8 q^{43} +3.53747e9 q^{44} +9.24537e7 q^{45} +3.47494e8 q^{46} +2.59899e9 q^{47} +6.95750e8 q^{48} +6.36634e8 q^{49} +3.56803e9 q^{50} +1.58566e9 q^{51} +1.27267e8 q^{52} +3.92590e9 q^{53} -1.10394e9 q^{54} +1.43077e9 q^{55} -7.17119e9 q^{56} +4.98934e9 q^{57} -9.70650e8 q^{58} +7.14924e8 q^{59} +1.47283e9 q^{60} +1.27105e9 q^{61} -1.97038e10 q^{62} +3.01899e9 q^{63} -1.10167e10 q^{64} +5.14744e7 q^{65} -1.70841e10 q^{66} +9.16382e9 q^{67} +2.52603e10 q^{68} -1.09755e9 q^{69} -6.15870e9 q^{70} -1.96637e10 q^{71} -8.28236e9 q^{72} -3.06456e10 q^{73} +1.84475e9 q^{74} -1.12695e10 q^{75} +7.94828e10 q^{76} +4.67204e10 q^{77} -6.14631e8 q^{78} -3.72081e10 q^{79} +4.48289e9 q^{80} +3.48678e9 q^{81} -5.33373e10 q^{82} -4.45375e10 q^{83} +4.80941e10 q^{84} +1.02168e10 q^{85} -6.59672e10 q^{86} +3.06578e9 q^{87} -1.28174e11 q^{88} +2.20586e10 q^{89} -7.11299e9 q^{90} +1.68085e9 q^{91} -1.74845e10 q^{92} +6.22340e10 q^{93} -1.99955e11 q^{94} +3.21476e10 q^{95} +1.62756e10 q^{96} -8.48502e10 q^{97} -4.89799e10 q^{98} +5.39597e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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

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