LMFDB - Embedded newform 177.12.a.d.1.7

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			1.7
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)

$f(q)$	$=$	$q-44.5190 q^{2} +243.000 q^{3} -66.0554 q^{4} -2490.42 q^{5} -10818.1 q^{6} -10217.0 q^{7} +94115.7 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-44.5190 q^{2} +243.000 q^{3} -66.0554 q^{4} -2490.42 q^{5} -10818.1 q^{6} -10217.0 q^{7} +94115.7 q^{8} +59049.0 q^{9} +110871. q^{10} -935597. q^{11} -16051.5 q^{12} -1.88159e6 q^{13} +454851. q^{14} -605173. q^{15} -4.05466e6 q^{16} -7.73016e6 q^{17} -2.62880e6 q^{18} +2.90198e6 q^{19} +164506. q^{20} -2.48273e6 q^{21} +4.16519e7 q^{22} +3.68356e7 q^{23} +2.28701e7 q^{24} -4.26259e7 q^{25} +8.37664e7 q^{26} +1.43489e7 q^{27} +674888. q^{28} -1.85891e8 q^{29} +2.69417e7 q^{30} -9.30939e7 q^{31} -1.22395e7 q^{32} -2.27350e8 q^{33} +3.44139e8 q^{34} +2.54446e7 q^{35} -3.90051e6 q^{36} -2.96437e8 q^{37} -1.29193e8 q^{38} -4.57225e8 q^{39} -2.34388e8 q^{40} +3.54502e8 q^{41} +1.10529e8 q^{42} +1.17124e9 q^{43} +6.18013e7 q^{44} -1.47057e8 q^{45} -1.63989e9 q^{46} -3.82655e8 q^{47} -9.85282e8 q^{48} -1.87294e9 q^{49} +1.89766e9 q^{50} -1.87843e9 q^{51} +1.24289e8 q^{52} -1.18844e9 q^{53} -6.38800e8 q^{54} +2.33003e9 q^{55} -9.61580e8 q^{56} +7.05180e8 q^{57} +8.27570e9 q^{58} +7.14924e8 q^{59} +3.99749e7 q^{60} +3.90006e9 q^{61} +4.14445e9 q^{62} -6.03303e8 q^{63} +8.84883e9 q^{64} +4.68594e9 q^{65} +1.01214e10 q^{66} -9.49449e9 q^{67} +5.10619e8 q^{68} +8.95105e9 q^{69} -1.13277e9 q^{70} -2.28335e10 q^{71} +5.55744e9 q^{72} -1.82782e10 q^{73} +1.31971e10 q^{74} -1.03581e10 q^{75} -1.91691e8 q^{76} +9.55900e9 q^{77} +2.03552e10 q^{78} -2.69656e10 q^{79} +1.00978e10 q^{80} +3.48678e9 q^{81} -1.57821e10 q^{82} -5.51453e10 q^{83} +1.63998e8 q^{84} +1.92514e10 q^{85} -5.21423e10 q^{86} -4.51716e10 q^{87} -8.80544e10 q^{88} +2.42061e10 q^{89} +6.54683e9 q^{90} +1.92242e10 q^{91} -2.43319e9 q^{92} -2.26218e10 q^{93} +1.70354e10 q^{94} -7.22715e9 q^{95} -2.97419e9 q^{96} +3.60303e10 q^{97} +8.33815e10 q^{98} -5.52461e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−44.5190	−0.983741	−0.491871	−	0.870668i	$-0.663687\pi$
$2$	−44.5190	−0.983741	−0.491871	+	0.870668i	$0.663687\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−66.0554	−0.0322536
$5$	−2490.42	−0.356400	−0.178200	−	0.983994i	$-0.557027\pi$
$5$	−2490.42	−0.356400	−0.178200	+	0.983994i	$0.557027\pi$
$6$	−10818.1	−0.567963
$7$	−10217.0	−0.229765	−0.114883	−	0.993379i	$-0.536649\pi$
$7$	−10217.0	−0.229765	−0.114883	+	0.993379i	$0.536649\pi$
$8$	94115.7	1.01547
$9$	59049.0	0.333333
$10$	110871.	0.350606
$11$	−935597.	−1.75158	−0.875788	−	0.482695i	$-0.839658\pi$
$11$	−935597.	−1.75158	−0.875788	+	0.482695i	$0.839658\pi$
$12$	−16051.5	−0.0186216
$13$	−1.88159e6	−1.40552	−0.702758	−	0.711429i	$-0.748048\pi$
$13$	−1.88159e6	−1.40552	−0.702758	+	0.711429i	$0.748048\pi$
$14$	454851.	0.226029
$15$	−605173.	−0.205768
$16$	−4.05466e6	−0.966706
$17$	−7.73016e6	−1.32044	−0.660221	−	0.751071i	$-0.729537\pi$
$17$	−7.73016e6	−1.32044	−0.660221	+	0.751071i	$0.729537\pi$
$18$	−2.62880e6	−0.327914
$19$	2.90198e6	0.268874	0.134437	−	0.990922i	$-0.457077\pi$
$19$	2.90198e6	0.268874	0.134437	+	0.990922i	$0.457077\pi$
$20$	164506.	0.0114952
$21$	−2.48273e6	−0.132655
$22$	4.16519e7	1.72310
$23$	3.68356e7	1.19334	0.596671	−	0.802486i	$-0.296490\pi$
$23$	3.68356e7	1.19334	0.596671	+	0.802486i	$0.296490\pi$
$24$	2.28701e7	0.586282
$25$	−4.26259e7	−0.872979
$26$	8.37664e7	1.38266
$27$	1.43489e7	0.192450
$28$	674888.	0.00741075
$29$	−1.85891e8	−1.68295	−0.841473	−	0.540300i	$-0.818311\pi$
$29$	−1.85891e8	−1.68295	−0.841473	+	0.540300i	$0.818311\pi$
$30$	2.69417e7	0.202422
$31$	−9.30939e7	−0.584026	−0.292013	−	0.956414i	$-0.594325\pi$
$31$	−9.30939e7	−0.584026	−0.292013	+	0.956414i	$0.594325\pi$
$32$	−1.22395e7	−0.0644818
$33$	−2.27350e8	−1.01127
$34$	3.44139e8	1.29897
$35$	2.54446e7	0.0818883
$36$	−3.90051e6	−0.0107512
$37$	−2.96437e8	−0.702786	−0.351393	−	0.936228i	$-0.614292\pi$
$37$	−2.96437e8	−0.702786	−0.351393	+	0.936228i	$0.614292\pi$
$38$	−1.29193e8	−0.264503
$39$	−4.57225e8	−0.811475
$40$	−2.34388e8	−0.361914
$41$	3.54502e8	0.477867	0.238933	−	0.971036i	$-0.423202\pi$
$41$	3.54502e8	0.477867	0.238933	+	0.971036i	$0.423202\pi$
$42$	1.10529e8	0.130498
$43$	1.17124e9	1.21498	0.607489	−	0.794328i	$-0.292177\pi$
$43$	1.17124e9	1.21498	0.607489	+	0.794328i	$0.292177\pi$
$44$	6.18013e7	0.0564947
$45$	−1.47057e8	−0.118800
$46$	−1.63989e9	−1.17394
$47$	−3.82655e8	−0.243371	−0.121685	−	0.992569i	$-0.538830\pi$
$47$	−3.82655e8	−0.243371	−0.121685	+	0.992569i	$0.538830\pi$
$48$	−9.85282e8	−0.558128
$49$	−1.87294e9	−0.947208
$50$	1.89766e9	0.858785
$51$	−1.87843e9	−0.762358
$52$	1.24289e8	0.0453330
$53$	−1.18844e9	−0.390356	−0.195178	−	0.980768i	$-0.562528\pi$
$53$	−1.18844e9	−0.390356	−0.195178	+	0.980768i	$0.562528\pi$
$54$	−6.38800e8	−0.189321
$55$	2.33003e9	0.624262
$56$	−9.61580e8	−0.233320
$57$	7.05180e8	0.155235
$58$	8.27570e9	1.65558
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	3.99749e7	0.00663675
$61$	3.90006e9	0.591231	0.295615	−	0.955307i	$-0.404475\pi$
$61$	3.90006e9	0.591231	0.295615	+	0.955307i	$0.404475\pi$
$62$	4.14445e9	0.574530
$63$	−6.03303e8	−0.0765884
$64$	8.84883e9	1.03014
$65$	4.68594e9	0.500926
$66$	1.01214e10	0.994831
$67$	−9.49449e9	−0.859133	−0.429566	−	0.903035i	$-0.641334\pi$
$67$	−9.49449e9	−0.859133	−0.429566	+	0.903035i	$0.641334\pi$
$68$	5.10619e8	0.0425890
$69$	8.95105e9	0.688976
$70$	−1.13277e9	−0.0805569
$71$	−2.28335e10	−1.50194	−0.750969	−	0.660338i	$-0.770413\pi$
$71$	−2.28335e10	−1.50194	−0.750969	+	0.660338i	$0.770413\pi$
$72$	5.55744e9	0.338490
$73$	−1.82782e10	−1.03195	−0.515973	−	0.856605i	$-0.672569\pi$
$73$	−1.82782e10	−1.03195	−0.515973	+	0.856605i	$0.672569\pi$
$74$	1.31971e10	0.691359
$75$	−1.03581e10	−0.504015
$76$	−1.91691e8	−0.00867216
$77$	9.55900e9	0.402451
$78$	2.03552e10	0.798281
$79$	−2.69656e10	−0.985963	−0.492982	−	0.870040i	$-0.664093\pi$
$79$	−2.69656e10	−0.985963	−0.492982	+	0.870040i	$0.664093\pi$
$80$	1.00978e10	0.344534
$81$	3.48678e9	0.111111
$82$	−1.57821e10	−0.470097
$83$	−5.51453e10	−1.53666	−0.768332	−	0.640052i	$-0.778913\pi$
$83$	−5.51453e10	−1.53666	−0.768332	+	0.640052i	$0.778913\pi$
$84$	1.63998e8	0.00427860
$85$	1.92514e10	0.470606
$86$	−5.21423e10	−1.19522
$87$	−4.51716e10	−0.971649
$88$	−8.80544e10	−1.77867
$89$	2.42061e10	0.459494	0.229747	−	0.973250i	$-0.426210\pi$
$89$	2.42061e10	0.459494	0.229747	+	0.973250i	$0.426210\pi$
$90$	6.54683e9	0.116869
$91$	1.92242e10	0.322938
$92$	−2.43319e9	−0.0384896
$93$	−2.26218e10	−0.337187
$94$	1.70354e10	0.239414
$95$	−7.22715e9	−0.0958268
$96$	−2.97419e9	−0.0372286
$97$	3.60303e10	0.426014	0.213007	−	0.977051i	$-0.431674\pi$
$97$	3.60303e10	0.426014	0.213007	+	0.977051i	$0.431674\pi$
$98$	8.33815e10	0.931807
$99$	−5.52461e10	−0.583859
$100$	2.81567e9	0.0281567
$101$	2.80952e9	0.0265990	0.0132995	−	0.999912i	$-0.495767\pi$
$101$	2.80952e9	0.0265990	0.0132995	+	0.999912i	$0.495767\pi$
$102$	8.36258e10	0.749963
$103$	6.41454e10	0.545206	0.272603	−	0.962127i	$-0.412115\pi$
$103$	6.41454e10	0.545206	0.272603	+	0.962127i	$0.412115\pi$
$104$	−1.77087e11	−1.42726
$105$	6.18305e9	0.0472783
$106$	5.29083e10	0.384009
$107$	−3.34398e10	−0.230490	−0.115245	−	0.993337i	$-0.536765\pi$
$107$	−3.34398e10	−0.230490	−0.115245	+	0.993337i	$0.536765\pi$
$108$	−9.47823e8	−0.00620721
$109$	2.28957e10	0.142530	0.0712652	−	0.997457i	$-0.477296\pi$
$109$	2.28957e10	0.142530	0.0712652	+	0.997457i	$0.477296\pi$
$110$	−1.03731e11	−0.614113
$111$	−7.20342e10	−0.405754
$112$	4.14264e10	0.222115
$113$	−1.69298e11	−0.864412	−0.432206	−	0.901775i	$-0.642265\pi$
$113$	−1.69298e11	−0.864412	−0.432206	+	0.901775i	$0.642265\pi$
$114$	−3.13939e10	−0.152711
$115$	−9.17362e10	−0.425307
$116$	1.22791e10	0.0542811
$117$	−1.11106e11	−0.468505
$118$	−3.18277e10	−0.128072
$119$	7.89790e10	0.303392
$120$	−5.69563e10	−0.208951
$121$	5.90031e11	2.06802
$122$	−1.73627e11	−0.581618
$123$	8.61439e10	0.275897
$124$	6.14935e9	0.0188369
$125$	2.27759e11	0.667530
$126$	2.68585e10	0.0753431
$127$	−6.07077e11	−1.63051	−0.815255	−	0.579103i	$-0.803403\pi$
$127$	−6.07077e11	−1.63051	−0.815255	+	0.579103i	$0.803403\pi$
$128$	−3.68875e11	−0.948909
$129$	2.84611e11	0.701468
$130$	−2.08614e11	−0.492781
$131$	3.73200e11	0.845180	0.422590	−	0.906321i	$-0.361121\pi$
$131$	3.73200e11	0.845180	0.422590	+	0.906321i	$0.361121\pi$
$132$	1.50177e10	0.0326172
$133$	−2.96495e10	−0.0617779
$134$	4.22686e11	0.845164
$135$	−3.57348e10	−0.0685893
$136$	−7.27529e11	−1.34087
$137$	1.05238e11	0.186299	0.0931494	−	0.995652i	$-0.470307\pi$
$137$	1.05238e11	0.186299	0.0931494	+	0.995652i	$0.470307\pi$
$138$	−3.98492e11	−0.677774
$139$	−9.56452e11	−1.56344	−0.781721	−	0.623629i	$-0.785658\pi$
$139$	−9.56452e11	−1.56344	−0.781721	+	0.623629i	$0.785658\pi$
$140$	−1.68076e9	−0.00264119
$141$	−9.29851e10	−0.140510
$142$	1.01653e12	1.47752
$143$	1.76041e12	2.46187
$144$	−2.39424e11	−0.322235
$145$	4.62948e11	0.599802
$146$	8.13726e11	1.01517
$147$	−4.55124e11	−0.546871
$148$	1.95813e10	0.0226674
$149$	1.25712e12	1.40234	0.701169	−	0.712995i	$-0.252662\pi$
$149$	1.25712e12	1.40234	0.701169	+	0.712995i	$0.252662\pi$
$150$	4.61133e11	0.495820
$151$	−1.06595e12	−1.10500	−0.552501	−	0.833512i	$-0.686327\pi$
$151$	−1.06595e12	−1.10500	−0.552501	+	0.833512i	$0.686327\pi$
$152$	2.73122e11	0.273034
$153$	−4.56458e11	−0.440147
$154$	−4.25557e11	−0.395908
$155$	2.31843e11	0.208147
$156$	3.02022e10	0.0261730
$157$	1.39049e12	1.16337	0.581686	−	0.813413i	$-0.302393\pi$
$157$	1.39049e12	1.16337	0.581686	+	0.813413i	$0.302393\pi$
$158$	1.20048e12	0.969933
$159$	−2.88791e11	−0.225372
$160$	3.04814e10	0.0229813
$161$	−3.76349e11	−0.274188
$162$	−1.55228e11	−0.109305
$163$	4.36425e11	0.297083	0.148542	−	0.988906i	$-0.452542\pi$
$163$	4.36425e11	0.297083	0.148542	+	0.988906i	$0.452542\pi$
$164$	−2.34167e10	−0.0154129
$165$	5.66198e11	0.360418
$166$	2.45501e12	1.51168
$167$	−1.88865e12	−1.12515	−0.562575	−	0.826746i	$-0.690189\pi$
$167$	−1.88865e12	−1.12515	−0.562575	+	0.826746i	$0.690189\pi$
$168$	−2.33664e11	−0.134707
$169$	1.74820e12	0.975473
$170$	−8.57052e11	−0.462954
$171$	1.71359e11	0.0896247
$172$	−7.73665e10	−0.0391874
$173$	3.80723e12	1.86791	0.933955	−	0.357390i	$-0.116333\pi$
$173$	3.80723e12	1.86791	0.933955	+	0.357390i	$0.116333\pi$
$174$	2.01099e12	0.955851
$175$	4.35509e11	0.200580
$176$	3.79353e12	1.69326
$177$	1.73727e11	0.0751646
$178$	−1.07763e12	−0.452023
$179$	1.33826e12	0.544314	0.272157	−	0.962253i	$-0.412263\pi$
$179$	1.33826e12	0.544314	0.272157	+	0.962253i	$0.412263\pi$
$180$	9.71391e9	0.00383173
$181$	−4.24390e12	−1.62380	−0.811901	−	0.583795i	$-0.801567\pi$
$181$	−4.24390e12	−1.62380	−0.811901	+	0.583795i	$0.801567\pi$
$182$	−8.55841e11	−0.317688
$183$	9.47714e11	0.341347
$184$	3.46681e12	1.21180
$185$	7.38254e11	0.250473
$186$	1.00710e12	0.331705
$187$	7.23232e12	2.31286
$188$	2.52764e10	0.00784959
$189$	−1.46603e11	−0.0442183
$190$	3.21746e11	0.0942688
$191$	1.11093e12	0.316229	0.158115	−	0.987421i	$-0.449458\pi$
$191$	1.11093e12	0.316229	0.158115	+	0.987421i	$0.449458\pi$
$192$	2.15027e12	0.594751
$193$	4.08585e12	1.09829	0.549145	−	0.835727i	$-0.314953\pi$
$193$	4.08585e12	1.09829	0.549145	+	0.835727i	$0.314953\pi$
$194$	−1.60404e12	−0.419087
$195$	1.13868e12	0.289210
$196$	1.23718e11	0.0305509
$197$	3.53152e12	0.848004	0.424002	−	0.905661i	$-0.360625\pi$
$197$	3.53152e12	0.848004	0.424002	+	0.905661i	$0.360625\pi$
$198$	2.45950e12	0.574366
$199$	−5.82785e11	−0.132378	−0.0661891	−	0.997807i	$-0.521084\pi$
$199$	−5.82785e11	−0.132378	−0.0661891	+	0.997807i	$0.521084\pi$
$200$	−4.01177e12	−0.886484
$201$	−2.30716e12	−0.496020
$202$	−1.25077e11	−0.0261665
$203$	1.89925e12	0.386682
$204$	1.24080e11	0.0245888
$205$	−8.82859e11	−0.170312
$206$	−2.85569e12	−0.536342
$207$	2.17511e12	0.397781
$208$	7.62919e12	1.35872
$209$	−2.71508e12	−0.470954
$210$	−2.75263e11	−0.0465096
$211$	−5.21749e11	−0.0858832	−0.0429416	−	0.999078i	$-0.513673\pi$
$211$	−5.21749e11	−0.0858832	−0.0429416	+	0.999078i	$0.513673\pi$
$212$	7.85030e10	0.0125904
$213$	−5.54854e12	−0.867144
$214$	1.48871e12	0.226743
$215$	−2.91688e12	−0.433018
$216$	1.35046e12	0.195427
$217$	9.51140e11	0.134189
$218$	−1.01929e12	−0.140213
$219$	−4.44159e12	−0.595794
$220$	−1.53911e11	−0.0201347
$221$	1.45450e13	1.85590
$222$	3.20689e12	0.399157
$223$	−1.56293e11	−0.0189785	−0.00948925	−	0.999955i	$-0.503021\pi$
$223$	−1.56293e11	−0.0189785	−0.00948925	+	0.999955i	$0.503021\pi$
$224$	1.25050e11	0.0148157
$225$	−2.51702e12	−0.290993
$226$	7.53699e12	0.850358
$227$	9.18590e12	1.01153	0.505766	−	0.862671i	$-0.331210\pi$
$227$	9.18590e12	1.01153	0.505766	+	0.862671i	$0.331210\pi$
$228$	−4.65810e10	−0.00500688
$229$	1.24732e13	1.30883	0.654413	−	0.756137i	$-0.272916\pi$
$229$	1.24732e13	1.30883	0.654413	+	0.756137i	$0.272916\pi$
$230$	4.08401e12	0.418392
$231$	2.32284e12	0.232355
$232$	−1.74953e13	−1.70898
$233$	−4.85840e12	−0.463485	−0.231742	−	0.972777i	$-0.574443\pi$
$233$	−4.85840e12	−0.463485	−0.231742	+	0.972777i	$0.574443\pi$
$234$	4.94632e12	0.460888
$235$	9.52972e11	0.0867375
$236$	−4.72246e10	−0.00419906
$237$	−6.55264e12	−0.569246
$238$	−3.51607e12	−0.298459
$239$	2.27996e13	1.89121	0.945604	−	0.325321i	$-0.105472\pi$
$239$	2.27996e13	1.89121	0.945604	+	0.325321i	$0.105472\pi$
$240$	2.45377e12	0.198917
$241$	6.68231e12	0.529460	0.264730	−	0.964323i	$-0.414717\pi$
$241$	6.68231e12	0.529460	0.264730	+	0.964323i	$0.414717\pi$
$242$	−2.62676e13	−2.03440
$243$	8.47289e11	0.0641500
$244$	−2.57620e11	−0.0190693
$245$	4.66441e12	0.337585
$246$	−3.83504e12	−0.271411
$247$	−5.46032e12	−0.377907
$248$	−8.76160e12	−0.593061
$249$	−1.34003e13	−0.887193
$250$	−1.01396e13	−0.656677
$251$	−7.74963e12	−0.490993	−0.245497	−	0.969397i	$-0.578951\pi$
$251$	−7.74963e12	−0.490993	−0.245497	+	0.969397i	$0.578951\pi$
$252$	3.98515e10	0.00247025
$253$	−3.44633e13	−2.09023
$254$	2.70265e13	1.60400
$255$	4.67808e12	0.271704
$256$	−1.70044e12	−0.0966591
$257$	1.22661e13	0.682453	0.341226	−	0.939981i	$-0.389158\pi$
$257$	1.22661e13	0.682453	0.341226	+	0.939981i	$0.389158\pi$
$258$	−1.26706e13	−0.690063
$259$	3.02870e12	0.161476
$260$	−3.09532e11	−0.0161567
$261$	−1.09767e13	−0.560982
$262$	−1.66145e13	−0.831438
$263$	1.37447e13	0.673561	0.336781	−	0.941583i	$-0.390662\pi$
$263$	1.37447e13	0.673561	0.336781	+	0.941583i	$0.390662\pi$
$264$	−2.13972e13	−1.02692
$265$	2.95972e12	0.139123
$266$	1.31997e12	0.0607734
$267$	5.88208e12	0.265289
$268$	6.27162e11	0.0277101
$269$	5.26687e12	0.227990	0.113995	−	0.993481i	$-0.463635\pi$
$269$	5.26687e12	0.227990	0.113995	+	0.993481i	$0.463635\pi$
$270$	1.59088e12	0.0674741
$271$	−2.16142e13	−0.898273	−0.449136	−	0.893463i	$-0.648268\pi$
$271$	−2.16142e13	−0.898273	−0.449136	+	0.893463i	$0.648268\pi$
$272$	3.13432e13	1.27648
$273$	4.67147e12	0.186449
$274$	−4.68510e12	−0.183270
$275$	3.98807e13	1.52909
$276$	−5.91265e11	−0.0222220
$277$	1.20207e13	0.442886	0.221443	−	0.975173i	$-0.428923\pi$
$277$	1.20207e13	0.442886	0.221443	+	0.975173i	$0.428923\pi$
$278$	4.25803e13	1.53802
$279$	−5.49710e12	−0.194675
$280$	2.39474e12	0.0831552
$281$	−4.23114e12	−0.144070	−0.0720348	−	0.997402i	$-0.522949\pi$
$281$	−4.23114e12	−0.144070	−0.0720348	+	0.997402i	$0.522949\pi$
$282$	4.13961e12	0.138226
$283$	−8.21411e12	−0.268989	−0.134495	−	0.990914i	$-0.542941\pi$
$283$	−8.21411e12	−0.268989	−0.134495	+	0.990914i	$0.542941\pi$
$284$	1.50828e12	0.0484429
$285$	−1.75620e12	−0.0553256
$286$	−7.83716e13	−2.42184
$287$	−3.62194e12	−0.109797
$288$	−7.22727e11	−0.0214939
$289$	2.54835e13	0.743568
$290$	−2.06100e13	−0.590050
$291$	8.75537e12	0.245959
$292$	1.20737e12	0.0332840
$293$	3.03847e12	0.0822020	0.0411010	−	0.999155i	$-0.486913\pi$
$293$	3.03847e12	0.0822020	0.0411010	+	0.999155i	$0.486913\pi$
$294$	2.02617e13	0.537979
$295$	−1.78046e12	−0.0463994
$296$	−2.78994e13	−0.713658
$297$	−1.34248e13	−0.337091
$298$	−5.59658e13	−1.37954
$299$	−6.93094e13	−1.67726
$300$	6.84208e11	0.0162563
$301$	−1.19665e13	−0.279159
$302$	4.74550e13	1.08704
$303$	6.82714e11	0.0153569
$304$	−1.17665e13	−0.259922
$305$	−9.71279e12	−0.210715
$306$	2.03211e13	0.432991
$307$	−3.88687e12	−0.0813466	−0.0406733	−	0.999172i	$-0.512950\pi$
$307$	−3.88687e12	−0.0813466	−0.0406733	+	0.999172i	$0.512950\pi$
$308$	−6.31423e11	−0.0129805
$309$	1.55873e13	0.314775
$310$	−1.03214e13	−0.204763
$311$	1.35635e13	0.264357	0.132178	−	0.991226i	$-0.457803\pi$
$311$	1.35635e13	0.264357	0.132178	+	0.991226i	$0.457803\pi$
$312$	−4.30321e13	−0.824028
$313$	−7.66164e13	−1.44154	−0.720772	−	0.693172i	$-0.756213\pi$
$313$	−7.66164e13	−1.44154	−0.720772	+	0.693172i	$0.756213\pi$
$314$	−6.19031e13	−1.14446
$315$	1.50248e12	0.0272961
$316$	1.78122e12	0.0318009
$317$	3.19725e13	0.560984	0.280492	−	0.959856i	$-0.409502\pi$
$317$	3.19725e13	0.560984	0.280492	+	0.959856i	$0.409502\pi$
$318$	1.28567e13	0.221708
$319$	1.73919e14	2.94781
$320$	−2.20373e13	−0.367142
$321$	−8.12586e12	−0.133074
$322$	1.67547e13	0.269730
$323$	−2.24327e13	−0.355033
$324$	−2.30321e11	−0.00358373
$325$	8.02043e13	1.22699
$326$	−1.94292e13	−0.292253
$327$	5.56365e12	0.0822900
$328$	3.33642e13	0.485260
$329$	3.90958e12	0.0559181
$330$	−2.52066e13	−0.354558
$331$	−4.22366e13	−0.584299	−0.292150	−	0.956373i	$-0.594371\pi$
$331$	−4.22366e13	−0.584299	−0.292150	+	0.956373i	$0.594371\pi$
$332$	3.64264e12	0.0495630
$333$	−1.75043e13	−0.234262
$334$	8.40807e13	1.10686
$335$	2.36453e13	0.306195
$336$	1.00666e13	0.128238
$337$	−1.09741e14	−1.37533	−0.687663	−	0.726030i	$-0.741363\pi$
$337$	−1.09741e14	−1.37533	−0.687663	+	0.726030i	$0.741363\pi$
$338$	−7.78284e13	−0.959613
$339$	−4.11395e13	−0.499069
$340$	−1.27166e12	−0.0151787
$341$	8.70984e13	1.02297
$342$	−7.62873e12	−0.0881675
$343$	3.93382e13	0.447400
$344$	1.10232e14	1.23377
$345$	−2.22919e13	−0.245551
$346$	−1.69494e14	−1.83754
$347$	5.58659e13	0.596121	0.298060	−	0.954547i	$-0.403660\pi$
$347$	5.58659e13	0.596121	0.298060	+	0.954547i	$0.403660\pi$
$348$	2.98383e12	0.0313392
$349$	−6.82666e13	−0.705778	−0.352889	−	0.935665i	$-0.614801\pi$
$349$	−6.82666e13	−0.705778	−0.352889	+	0.935665i	$0.614801\pi$
$350$	−1.93884e13	−0.197319
$351$	−2.69987e13	−0.270492
$352$	1.14512e13	0.112945
$353$	−1.69275e13	−0.164374	−0.0821868	−	0.996617i	$-0.526190\pi$
$353$	−1.69275e13	−0.164374	−0.0821868	+	0.996617i	$0.526190\pi$
$354$	−7.73414e12	−0.0739425
$355$	5.68651e13	0.535291
$356$	−1.59894e12	−0.0148203
$357$	1.91919e13	0.175163
$358$	−5.95781e13	−0.535464
$359$	2.14398e14	1.89759	0.948793	−	0.315897i	$-0.102305\pi$
$359$	2.14398e14	1.89759	0.948793	+	0.315897i	$0.102305\pi$
$360$	−1.38404e13	−0.120638
$361$	−1.08069e14	−0.927707
$362$	1.88934e14	1.59740
$363$	1.43377e14	1.19397
$364$	−1.26986e12	−0.0104159
$365$	4.55204e13	0.367786
$366$	−4.21913e13	−0.335797
$367$	−1.01526e14	−0.796001	−0.398001	−	0.917385i	$-0.630296\pi$
$367$	−1.01526e14	−0.796001	−0.398001	+	0.917385i	$0.630296\pi$
$368$	−1.49356e14	−1.15361
$369$	2.09330e13	0.159289
$370$	−3.28663e13	−0.246401
$371$	1.21423e13	0.0896902
$372$	1.49429e12	0.0108755
$373$	−1.91918e13	−0.137631	−0.0688155	−	0.997629i	$-0.521922\pi$
$373$	−1.91918e13	−0.137631	−0.0688155	+	0.997629i	$0.521922\pi$
$374$	−3.21976e14	−2.27525
$375$	5.53455e13	0.385399
$376$	−3.60138e13	−0.247136
$377$	3.49770e14	2.36541
$378$	6.52661e12	0.0434994
$379$	−2.05345e13	−0.134886	−0.0674431	−	0.997723i	$-0.521484\pi$
$379$	−2.05345e13	−0.134886	−0.0674431	+	0.997723i	$0.521484\pi$
$380$	4.77392e11	0.00309076
$381$	−1.47520e14	−0.941375
$382$	−4.94574e13	−0.311088
$383$	−1.62004e14	−1.00446	−0.502230	−	0.864734i	$-0.667487\pi$
$383$	−1.62004e14	−1.00446	−0.502230	+	0.864734i	$0.667487\pi$
$384$	−8.96366e13	−0.547853
$385$	−2.38059e13	−0.143434
$386$	−1.81898e14	−1.08043
$387$	6.91604e13	0.404993
$388$	−2.38000e12	−0.0137405
$389$	−2.51401e13	−0.143102	−0.0715509	−	0.997437i	$-0.522795\pi$
$389$	−2.51401e13	−0.143102	−0.0715509	+	0.997437i	$0.522795\pi$
$390$	−5.06931e13	−0.284508
$391$	−2.84745e14	−1.57574
$392$	−1.76273e14	−0.961862
$393$	9.06875e13	0.487965
$394$	−1.57220e14	−0.834216
$395$	6.71557e13	0.351398
$396$	3.64930e12	0.0188316
$397$	−2.69669e14	−1.37241	−0.686205	−	0.727409i	$-0.740725\pi$
$397$	−2.69669e14	−1.37241	−0.686205	+	0.727409i	$0.740725\pi$
$398$	2.59450e13	0.130226
$399$	−7.20482e12	−0.0356675
$400$	1.72834e14	0.843914
$401$	−2.06505e14	−0.994575	−0.497287	−	0.867586i	$-0.665671\pi$
$401$	−2.06505e14	−0.994575	−0.497287	+	0.867586i	$0.665671\pi$
$402$	1.02713e14	0.487956
$403$	1.75164e14	0.820857
$404$	−1.85584e11	−0.000857913 0
$405$	−8.68357e12	−0.0396000
$406$	−8.45528e13	−0.380395
$407$	2.77346e14	1.23098
$408$	−1.76790e14	−0.774152
$409$	−7.27752e12	−0.0314416	−0.0157208	−	0.999876i	$-0.505004\pi$
$409$	−7.27752e12	−0.0314416	−0.0157208	+	0.999876i	$0.505004\pi$
$410$	3.93040e13	0.167543
$411$	2.55729e13	0.107560
$412$	−4.23715e12	−0.0175849
$413$	−7.30438e12	−0.0299129
$414$	−9.68336e13	−0.391313
$415$	1.37335e14	0.547667
$416$	2.30296e13	0.0906301
$417$	−2.32418e14	−0.902653
$418$	1.20873e14	0.463297
$419$	8.22109e13	0.310994	0.155497	−	0.987836i	$-0.450302\pi$
$419$	8.22109e13	0.310994	0.155497	+	0.987836i	$0.450302\pi$
$420$	−4.08424e11	−0.00152489
$421$	1.37353e14	0.506158	0.253079	−	0.967446i	$-0.418557\pi$
$421$	1.37353e14	0.506158	0.253079	+	0.967446i	$0.418557\pi$
$422$	2.32278e13	0.0844868
$423$	−2.25954e13	−0.0811236
$424$	−1.11851e14	−0.396395
$425$	3.29505e14	1.15272
$426$	2.47016e14	0.853045
$427$	−3.98469e13	−0.135844
$428$	2.20888e12	0.00743414
$429$	4.27779e14	1.42136
$430$	1.29856e14	0.425978
$431$	−5.24678e14	−1.69929	−0.849646	−	0.527353i	$-0.823184\pi$
$431$	−5.24678e14	−1.69929	−0.849646	+	0.527353i	$0.823184\pi$
$432$	−5.81799e13	−0.186043
$433$	−2.51830e14	−0.795104	−0.397552	−	0.917580i	$-0.630140\pi$
$433$	−2.51830e14	−0.795104	−0.397552	+	0.917580i	$0.630140\pi$
$434$	−4.23438e13	−0.132007
$435$	1.12496e14	0.346296
$436$	−1.51238e12	−0.00459712
$437$	1.06896e14	0.320859
$438$	1.97735e14	0.586107
$439$	2.08832e14	0.611281	0.305641	−	0.952147i	$-0.401129\pi$
$439$	2.08832e14	0.611281	0.305641	+	0.952147i	$0.401129\pi$
$440$	2.19293e14	0.633920
$441$	−1.10595e14	−0.315736
$442$	−6.47528e14	−1.82573
$443$	−2.31456e13	−0.0644538	−0.0322269	−	0.999481i	$-0.510260\pi$
$443$	−2.31456e13	−0.0644538	−0.0322269	+	0.999481i	$0.510260\pi$
$444$	4.75825e12	0.0130870
$445$	−6.02834e13	−0.163764
$446$	6.95800e12	0.0186699
$447$	3.05480e14	0.809640
$448$	−9.04085e13	−0.236690
$449$	4.34904e14	1.12471	0.562353	−	0.826897i	$-0.309896\pi$
$449$	4.34904e14	1.12471	0.562353	+	0.826897i	$0.309896\pi$
$450$	1.12055e14	0.286262
$451$	−3.31671e14	−0.837021
$452$	1.11831e13	0.0278804
$453$	−2.59026e14	−0.637973
$454$	−4.08948e14	−0.995085
$455$	−4.78763e13	−0.115095
$456$	6.63685e13	0.157636
$457$	−2.73262e14	−0.641269	−0.320634	−	0.947203i	$-0.603896\pi$
$457$	−2.73262e14	−0.641269	−0.320634	+	0.947203i	$0.603896\pi$
$458$	−5.55294e14	−1.28755
$459$	−1.10919e14	−0.254119
$460$	6.05967e12	0.0137177
$461$	1.44656e14	0.323581	0.161790	−	0.986825i	$-0.448273\pi$
$461$	1.44656e14	0.323581	0.161790	+	0.986825i	$0.448273\pi$
$462$	−1.03410e14	−0.228577
$463$	5.13100e14	1.12074	0.560372	−	0.828241i	$-0.310658\pi$
$463$	5.13100e14	1.12074	0.560372	+	0.828241i	$0.310658\pi$
$464$	7.53726e14	1.62691
$465$	5.63379e13	0.120174
$466$	2.16291e14	0.455949
$467$	−6.21431e14	−1.29464	−0.647321	−	0.762217i	$-0.724111\pi$
$467$	−6.21431e14	−1.29464	−0.647321	+	0.762217i	$0.724111\pi$
$468$	7.33914e12	0.0151110
$469$	9.70052e13	0.197399
$470$	−4.24254e13	−0.0853272
$471$	3.37888e14	0.671673
$472$	6.72856e13	0.132203
$473$	−1.09581e15	−2.12813
$474$	2.91717e14	0.559991
$475$	−1.23699e14	−0.234721
$476$	−5.21699e12	−0.00978547
$477$	−7.01763e13	−0.130119
$478$	−1.01502e15	−1.86046
$479$	−9.93368e13	−0.179997	−0.0899984	−	0.995942i	$-0.528686\pi$
$479$	−9.93368e13	−0.179997	−0.0899984	+	0.995942i	$0.528686\pi$
$480$	7.40698e12	0.0132683
$481$	5.57772e14	0.987776
$482$	−2.97490e14	−0.520851
$483$	−9.14529e13	−0.158303
$484$	−3.89747e13	−0.0667012
$485$	−8.97308e13	−0.151831
$486$	−3.77205e13	−0.0631070
$487$	−1.00443e15	−1.66154	−0.830769	−	0.556617i	$-0.812099\pi$
$487$	−1.00443e15	−1.66154	−0.830769	+	0.556617i	$0.812099\pi$
$488$	3.67057e14	0.600377
$489$	1.06051e14	0.171521
$490$	−2.07655e14	−0.332096
$491$	−4.27357e14	−0.675837	−0.337919	−	0.941175i	$-0.609723\pi$
$491$	−4.27357e14	−0.675837	−0.337919	+	0.941175i	$0.609723\pi$
$492$	−5.69027e12	−0.00889866
$493$	1.43697e15	2.22223
$494$	2.43088e14	0.371762
$495$	1.37586e14	0.208087
$496$	3.77464e14	0.564581
$497$	2.33290e14	0.345093
$498$	5.96569e14	0.872768
$499$	1.08268e15	1.56656	0.783281	−	0.621668i	$-0.213545\pi$
$499$	1.08268e15	1.56656	0.783281	+	0.621668i	$0.213545\pi$
$500$	−1.50447e13	−0.0215303
$501$	−4.58941e14	−0.649605
$502$	3.45006e14	0.483010
$503$	−6.22606e14	−0.862163	−0.431082	−	0.902313i	$-0.641868\pi$
$503$	−6.22606e14	−0.862163	−0.431082	+	0.902313i	$0.641868\pi$
$504$	−5.67803e13	−0.0777732
$505$	−6.99690e12	−0.00947988
$506$	1.53427e15	2.05624
$507$	4.24814e14	0.563190
$508$	4.01007e13	0.0525898
$509$	−7.08898e14	−0.919679	−0.459839	−	0.888002i	$-0.652093\pi$
$509$	−7.08898e14	−0.919679	−0.459839	+	0.888002i	$0.652093\pi$
$510$	−2.08264e14	−0.267287
$511$	1.86748e14	0.237105
$512$	8.31158e14	1.04400
$513$	4.16402e13	0.0517449
$514$	−5.46073e14	−0.671357
$515$	−1.59749e14	−0.194312
$516$	−1.88001e13	−0.0226249
$517$	3.58011e14	0.426283
$518$	−1.34835e14	−0.158850
$519$	9.25158e14	1.07844
$520$	4.41021e14	0.508675
$521$	1.57927e15	1.80239	0.901196	−	0.433411i	$-0.142690\pi$
$521$	1.57927e15	1.80239	0.901196	+	0.433411i	$0.142690\pi$
$522$	4.88672e14	0.551861
$523$	−4.13879e14	−0.462503	−0.231251	−	0.972894i	$-0.574282\pi$
$523$	−4.13879e14	−0.462503	−0.231251	+	0.972894i	$0.574282\pi$
$524$	−2.46519e13	−0.0272601
$525$	1.05829e14	0.115805
$526$	−6.11899e14	−0.662610
$527$	7.19631e14	0.771172
$528$	9.21827e14	0.977604
$529$	4.04053e14	0.424064
$530$	−1.31764e14	−0.136861
$531$	4.22156e13	0.0433963
$532$	1.95851e12	0.00199256
$533$	−6.67025e14	−0.671649
$534$	−2.61865e14	−0.260976
$535$	8.32791e13	0.0821467
$536$	−8.93581e14	−0.872424
$537$	3.25197e14	0.314260
$538$	−2.34476e14	−0.224283
$539$	1.75232e15	1.65911
$540$	2.36048e12	0.00221225
$541$	7.77033e14	0.720866	0.360433	−	0.932785i	$-0.382629\pi$
$541$	7.77033e14	0.720866	0.360433	+	0.932785i	$0.382629\pi$
$542$	9.62244e14	0.883668
$543$	−1.03127e15	−0.937503
$544$	9.46129e13	0.0851445
$545$	−5.70199e13	−0.0507979
$546$	−2.07969e14	−0.183417
$547$	−1.27966e15	−1.11729	−0.558643	−	0.829408i	$-0.688678\pi$
$547$	−1.27966e15	−1.11729	−0.558643	+	0.829408i	$0.688678\pi$
$548$	−6.95155e12	−0.00600881
$549$	2.30294e14	0.197077
$550$	−1.77545e15	−1.50423
$551$	−5.39452e14	−0.452500
$552$	8.42435e14	0.699635
$553$	2.75507e14	0.226540
$554$	−5.35151e14	−0.435685
$555$	1.79396e14	0.144611
$556$	6.31788e13	0.0504266
$557$	−3.96428e14	−0.313300	−0.156650	−	0.987654i	$-0.550070\pi$
$557$	−3.96428e14	−0.313300	−0.156650	+	0.987654i	$0.550070\pi$
$558$	2.44726e14	0.191510
$559$	−2.20378e15	−1.70767
$560$	−1.03169e14	−0.0791620
$561$	1.75745e15	1.33533
$562$	1.88366e14	0.141727
$563$	1.36730e15	1.01875	0.509374	−	0.860545i	$-0.329877\pi$
$563$	1.36730e15	1.01875	0.509374	+	0.860545i	$0.329877\pi$
$564$	6.14217e12	0.00453196
$565$	4.21624e14	0.308077
$566$	3.65684e14	0.264616
$567$	−3.56245e13	−0.0255295
$568$	−2.14899e15	−1.52517
$569$	2.17587e15	1.52938	0.764690	−	0.644399i	$-0.222892\pi$
$569$	2.17587e15	1.52938	0.764690	+	0.644399i	$0.222892\pi$
$570$	7.81842e13	0.0544261
$571$	−1.13698e15	−0.783890	−0.391945	−	0.919989i	$-0.628198\pi$
$571$	−1.13698e15	−0.783890	−0.391945	+	0.919989i	$0.628198\pi$
$572$	−1.16284e14	−0.0794041
$573$	2.69955e14	0.182575
$574$	1.61245e14	0.108012
$575$	−1.57015e15	−1.04176
$576$	5.22515e14	0.343380
$577$	−2.14346e14	−0.139524	−0.0697619	−	0.997564i	$-0.522224\pi$
$577$	−2.14346e14	−0.139524	−0.0697619	+	0.997564i	$0.522224\pi$
$578$	−1.13450e15	−0.731478
$579$	9.92861e14	0.634098
$580$	−3.05802e13	−0.0193458
$581$	5.63419e14	0.353072
$582$	−3.89781e14	−0.241960
$583$	1.11190e15	0.683738
$584$	−1.72026e15	−1.04791
$585$	2.76700e14	0.166975
$586$	−1.35270e14	−0.0808655
$587$	8.32831e14	0.493228	0.246614	−	0.969114i	$-0.420682\pi$
$587$	8.32831e14	0.493228	0.246614	+	0.969114i	$0.420682\pi$
$588$	3.00634e13	0.0176386
$589$	−2.70156e14	−0.157029
$590$	7.92645e13	0.0456450
$591$	8.58160e14	0.489595
$592$	1.20195e15	0.679387
$593$	−1.61872e14	−0.0906507	−0.0453254	−	0.998972i	$-0.514432\pi$
$593$	−1.61872e14	−0.0906507	−0.0453254	+	0.998972i	$0.514432\pi$
$594$	5.97659e14	0.331610
$595$	−1.96691e14	−0.108129
$596$	−8.30396e13	−0.0452304
$597$	−1.41617e14	−0.0764286
$598$	3.08559e15	1.64999
$599$	2.58065e15	1.36735	0.683677	−	0.729785i	$-0.260380\pi$
$599$	2.58065e15	1.36735	0.683677	+	0.729785i	$0.260380\pi$
$600$	−9.74860e14	−0.511812
$601$	2.85968e15	1.48767	0.743836	−	0.668362i	$-0.233004\pi$
$601$	2.85968e15	1.48767	0.743836	+	0.668362i	$0.233004\pi$
$602$	5.32738e14	0.274621
$603$	−5.60640e14	−0.286378
$604$	7.04117e13	0.0356403
$605$	−1.46943e15	−0.737043
$606$	−3.03938e13	−0.0151072
$607$	−1.92232e15	−0.946864	−0.473432	−	0.880830i	$-0.656985\pi$
$607$	−1.92232e15	−0.946864	−0.473432	+	0.880830i	$0.656985\pi$
$608$	−3.55186e13	−0.0173375
$609$	4.61518e14	0.223251
$610$	4.32404e14	0.207289
$611$	7.19997e14	0.342062
$612$	3.01515e13	0.0141963
$613$	−1.12928e15	−0.526948	−0.263474	−	0.964667i	$-0.584868\pi$
$613$	−1.12928e15	−0.526948	−0.263474	+	0.964667i	$0.584868\pi$
$614$	1.73040e14	0.0800240
$615$	−2.14535e14	−0.0983296
$616$	8.99652e14	0.408677
$617$	3.52040e15	1.58498	0.792490	−	0.609884i	$-0.208784\pi$
$617$	3.52040e15	1.58498	0.792490	+	0.609884i	$0.208784\pi$
$618$	−6.93933e14	−0.309657
$619$	7.60941e14	0.336552	0.168276	−	0.985740i	$-0.446180\pi$
$619$	7.60941e14	0.336552	0.168276	+	0.985740i	$0.446180\pi$
$620$	−1.53145e13	−0.00671349
$621$	5.28551e14	0.229659
$622$	−6.03835e14	−0.260058
$623$	−2.47314e14	−0.105576
$624$	1.85389e15	0.784458
$625$	1.51413e15	0.635071
$626$	3.41089e15	1.41811
$627$	−6.59765e14	−0.271905
$628$	−9.18491e13	−0.0375230
$629$	2.29151e15	0.927988
$630$	−6.68890e13	−0.0268523
$631$	−1.58045e15	−0.628955	−0.314477	−	0.949265i	$-0.601829\pi$
$631$	−1.58045e15	−0.628955	−0.314477	+	0.949265i	$0.601829\pi$
$632$	−2.53788e15	−1.00122
$633$	−1.26785e14	−0.0495847
$634$	−1.42338e15	−0.551863
$635$	1.51188e15	0.581114
$636$	1.90762e13	0.00726906
$637$	3.52410e15	1.33132
$638$	−7.74272e15	−2.89988
$639$	−1.34830e15	−0.500646
$640$	9.18655e14	0.338191
$641$	1.11628e15	0.407430	0.203715	−	0.979030i	$-0.434698\pi$
$641$	1.11628e15	0.407430	0.203715	+	0.979030i	$0.434698\pi$
$642$	3.61756e14	0.130910
$643$	−1.23857e15	−0.444385	−0.222192	−	0.975003i	$-0.571321\pi$
$643$	−1.23857e15	−0.444385	−0.222192	+	0.975003i	$0.571321\pi$
$644$	2.48599e13	0.00884356
$645$	−7.08801e14	−0.250003
$646$	9.98684e14	0.349260
$647$	4.33083e15	1.50175	0.750874	−	0.660445i	$-0.229632\pi$
$647$	4.33083e15	1.50175	0.750874	+	0.660445i	$0.229632\pi$
$648$	3.28161e14	0.112830
$649$	−6.68881e14	−0.228036
$650$	−3.57062e15	−1.20704
$651$	2.31127e14	0.0774739
$652$	−2.88283e13	−0.00958201
$653$	−5.76545e15	−1.90025	−0.950125	−	0.311871i	$-0.899044\pi$
$653$	−5.76545e15	−1.90025	−0.950125	+	0.311871i	$0.899044\pi$
$654$	−2.47688e14	−0.0809520
$655$	−9.29425e14	−0.301222
$656$	−1.43738e15	−0.461957
$657$	−1.07931e15	−0.343982
$658$	−1.74051e14	−0.0550090
$659$	3.43713e15	1.07727	0.538637	−	0.842538i	$-0.318939\pi$
$659$	3.43713e15	1.07727	0.538637	+	0.842538i	$0.318939\pi$
$660$	−3.74004e13	−0.0116248
$661$	−3.24130e15	−0.999105	−0.499552	−	0.866284i	$-0.666502\pi$
$661$	−3.24130e15	−0.999105	−0.499552	+	0.866284i	$0.666502\pi$
$662$	1.88033e15	0.574799
$663$	3.53443e15	1.07151
$664$	−5.19004e15	−1.56044
$665$	7.38397e13	0.0220177
$666$	7.79275e14	0.230453
$667$	−6.84742e15	−2.00833
$668$	1.24755e14	0.0362901
$669$	−3.79791e13	−0.0109572
$670$	−1.05267e15	−0.301217
$671$	−3.64888e15	−1.03559
$672$	3.03873e13	0.00855383
$673$	8.79248e14	0.245487	0.122744	−	0.992438i	$-0.460831\pi$
$673$	8.79248e14	0.245487	0.122744	+	0.992438i	$0.460831\pi$
$674$	4.88558e15	1.35296
$675$	−6.11635e14	−0.168005
$676$	−1.15478e14	−0.0314625
$677$	−2.78076e15	−0.751495	−0.375748	−	0.926722i	$-0.622614\pi$
$677$	−2.78076e15	−0.751495	−0.375748	+	0.926722i	$0.622614\pi$
$678$	1.83149e15	0.490954
$679$	−3.68122e14	−0.0978831
$680$	1.81186e15	0.477886
$681$	2.23217e15	0.584008
$682$	−3.87754e15	−1.00633
$683$	−2.68994e15	−0.692516	−0.346258	−	0.938139i	$-0.612548\pi$
$683$	−2.68994e15	−0.692516	−0.346258	+	0.938139i	$0.612548\pi$
$684$	−1.13192e13	−0.00289072
$685$	−2.62087e14	−0.0663969
$686$	−1.75130e15	−0.440126
$687$	3.03098e15	0.755651
$688$	−4.74897e15	−1.17453
$689$	2.23616e15	0.548651
$690$	9.92414e14	0.241559
$691$	1.62328e15	0.391979	0.195990	−	0.980606i	$-0.437208\pi$
$691$	1.62328e15	0.391979	0.195990	+	0.980606i	$0.437208\pi$
$692$	−2.51488e14	−0.0602469
$693$	5.64449e14	0.134150
$694$	−2.48709e15	−0.586429
$695$	2.38197e15	0.557211
$696$	−4.25135e15	−0.986680
$697$	−2.74035e15	−0.630996
$698$	3.03916e15	0.694303
$699$	−1.18059e15	−0.267593
$700$	−2.87677e13	−0.00646943
$701$	−4.75356e15	−1.06064	−0.530322	−	0.847796i	$-0.677929\pi$
$701$	−4.75356e15	−1.06064	−0.530322	+	0.847796i	$0.677929\pi$
$702$	1.20196e15	0.266094
$703$	−8.60253e14	−0.188961
$704$	−8.27894e15	−1.80437
$705$	2.31572e14	0.0500779
$706$	7.53596e14	0.161701
$707$	−2.87049e13	−0.00611152
$708$	−1.14756e13	−0.00242433
$709$	3.22804e15	0.676681	0.338340	−	0.941024i	$-0.390134\pi$
$709$	3.22804e15	0.676681	0.338340	+	0.941024i	$0.390134\pi$
$710$	−2.53158e15	−0.526588
$711$	−1.59229e15	−0.328654
$712$	2.27817e15	0.466602
$713$	−3.42917e15	−0.696942
$714$	−8.54405e14	−0.172315
$715$	−4.38416e15	−0.877410
$716$	−8.83994e13	−0.0175561
$717$	5.54031e15	1.09189
$718$	−9.54480e15	−1.86673
$719$	3.05161e14	0.0592270	0.0296135	−	0.999561i	$-0.490572\pi$
$719$	3.05161e14	0.0592270	0.0296135	+	0.999561i	$0.490572\pi$
$720$	5.96266e14	0.114845
$721$	−6.55374e14	−0.125269
$722$	4.81112e15	0.912623
$723$	1.62380e15	0.305684
$724$	2.80333e14	0.0523735
$725$	7.92379e15	1.46918
$726$	−6.38303e15	−1.17456
$727$	−7.96110e15	−1.45390	−0.726949	−	0.686691i	$-0.759062\pi$
$727$	−7.96110e15	−1.45390	−0.726949	+	0.686691i	$0.759062\pi$
$728$	1.80930e15	0.327934
$729$	2.05891e14	0.0370370
$730$	−2.02652e15	−0.361806
$731$	−9.05385e15	−1.60431
$732$	−6.26016e13	−0.0110097
$733$	−3.48049e15	−0.607531	−0.303765	−	0.952747i	$-0.598244\pi$
$733$	−3.48049e15	−0.607531	−0.303765	+	0.952747i	$0.598244\pi$
$734$	4.51984e15	0.783059
$735$	1.13345e15	0.194905
$736$	−4.50848e14	−0.0769488
$737$	8.88302e15	1.50484
$738$	−9.31915e14	−0.156699
$739$	4.41230e15	0.736412	0.368206	−	0.929744i	$-0.379972\pi$
$739$	4.41230e15	0.736412	0.368206	+	0.929744i	$0.379972\pi$
$740$	−4.87656e13	−0.00807866
$741$	−1.32686e15	−0.218185
$742$	−5.40564e14	−0.0882319
$743$	4.00429e14	0.0648765	0.0324382	−	0.999474i	$-0.489673\pi$
$743$	4.00429e14	0.0648765	0.0324382	+	0.999474i	$0.489673\pi$
$744$	−2.12907e15	−0.342404
$745$	−3.13076e15	−0.499793
$746$	8.54399e14	0.135393
$747$	−3.25627e15	−0.512221
$748$	−4.77734e14	−0.0745980
$749$	3.41654e14	0.0529586
$750$	−2.46393e15	−0.379133
$751$	−5.50767e15	−0.841294	−0.420647	−	0.907224i	$-0.638197\pi$
$751$	−5.50767e15	−0.841294	−0.420647	+	0.907224i	$0.638197\pi$
$752$	1.55153e15	0.235268
$753$	−1.88316e15	−0.283475
$754$	−1.55714e16	−2.32695
$755$	2.65466e15	0.393823
$756$	9.68390e12	0.00142620
$757$	−6.23781e15	−0.912021	−0.456010	−	0.889974i	$-0.650722\pi$
$757$	−6.23781e15	−0.912021	−0.456010	+	0.889974i	$0.650722\pi$
$758$	9.14174e14	0.132693
$759$	−8.37458e15	−1.20679
$760$	−6.80188e14	−0.0973093
$761$	−1.20166e16	−1.70673	−0.853367	−	0.521311i	$-0.825443\pi$
$761$	−1.20166e16	−1.70673	−0.853367	+	0.521311i	$0.825443\pi$
$762$	6.56743e15	0.926069
$763$	−2.33925e14	−0.0327485
$764$	−7.33828e13	−0.0101995
$765$	1.13677e15	0.156869
$766$	7.21226e15	0.988128
$767$	−1.34519e15	−0.182983
$768$	−4.13208e14	−0.0558062
$769$	−7.44470e15	−0.998280	−0.499140	−	0.866521i	$-0.666351\pi$
$769$	−7.44470e15	−0.998280	−0.499140	+	0.866521i	$0.666351\pi$
$770$	1.05982e15	0.141102
$771$	2.98065e15	0.394014
$772$	−2.69892e14	−0.0354238
$773$	−1.34774e16	−1.75638	−0.878192	−	0.478308i	$-0.841250\pi$
$773$	−1.34774e16	−1.75638	−0.878192	+	0.478308i	$0.841250\pi$
$774$	−3.07895e15	−0.398408
$775$	3.96821e15	0.509842
$776$	3.39102e15	0.432604
$777$	7.35973e14	0.0932280
$778$	1.11921e15	0.140775
$779$	1.02876e15	0.128486
$780$	−7.52163e13	−0.00932806
$781$	2.13630e16	2.63076
$782$	1.26766e16	1.55012
$783$	−2.66734e15	−0.323883
$784$	7.59413e15	0.915672
$785$	−3.46290e15	−0.414626
$786$	−4.03732e15	−0.480031
$787$	6.17125e14	0.0728638	0.0364319	−	0.999336i	$-0.488401\pi$
$787$	6.17125e14	0.0728638	0.0364319	+	0.999336i	$0.488401\pi$
$788$	−2.33276e14	−0.0273512
$789$	3.33995e15	0.388881
$790$	−2.98971e15	−0.345684
$791$	1.72972e15	0.198612
$792$	−5.19952e15	−0.592891
$793$	−7.33829e15	−0.830984
$794$	1.20054e16	1.35010
$795$	7.19213e14	0.0803227
$796$	3.84961e13	0.00426968
$797$	−8.57078e15	−0.944060	−0.472030	−	0.881582i	$-0.656479\pi$
$797$	−8.57078e15	−0.944060	−0.472030	+	0.881582i	$0.656479\pi$
$798$	3.20752e14	0.0350876
$799$	2.95798e15	0.321357
$800$	5.21718e14	0.0562912
$801$	1.42935e15	0.153165
$802$	9.19342e15	0.978404
$803$	1.71010e16	1.80753
$804$	1.52400e14	0.0159985
$805$	9.37269e14	0.0977208
$806$	−7.79814e15	−0.807511
$807$	1.27985e15	0.131630
$808$	2.64420e14	0.0270105
$809$	−1.94459e16	−1.97293	−0.986463	−	0.163981i	$-0.947566\pi$
$809$	−1.94459e16	−1.97293	−0.986463	+	0.163981i	$0.947566\pi$
$810$	3.86584e14	0.0389562
$811$	1.86366e16	1.86531	0.932657	−	0.360765i	$-0.117484\pi$
$811$	1.86366e16	1.86531	0.932657	+	0.360765i	$0.117484\pi$
$812$	−1.25456e14	−0.0124719
$813$	−5.25225e15	−0.518618
$814$	−1.23472e16	−1.21097
$815$	−1.08688e15	−0.105881
$816$	7.61639e15	0.736976
$817$	3.39890e15	0.326676
$818$	3.23988e14	0.0309304
$819$	1.13517e15	0.107646
$820$	5.83176e13	0.00549317
$821$	1.20101e16	1.12373	0.561863	−	0.827230i	$-0.310085\pi$
$821$	1.20101e16	1.12373	0.561863	+	0.827230i	$0.310085\pi$
$822$	−1.13848e15	−0.105811
$823$	9.51460e15	0.878398	0.439199	−	0.898390i	$-0.355262\pi$
$823$	9.51460e15	0.878398	0.439199	+	0.898390i	$0.355262\pi$
$824$	6.03709e15	0.553641
$825$	9.69101e15	0.882820
$826$	3.25184e14	0.0294265
$827$	6.13526e15	0.551509	0.275755	−	0.961228i	$-0.411072\pi$
$827$	6.13526e15	0.551509	0.275755	+	0.961228i	$0.411072\pi$
$828$	−1.43678e14	−0.0128299
$829$	−2.74031e15	−0.243080	−0.121540	−	0.992587i	$-0.538783\pi$
$829$	−2.74031e15	−0.243080	−0.121540	+	0.992587i	$0.538783\pi$
$830$	−6.11402e15	−0.538763
$831$	2.92103e15	0.255700
$832$	−1.66498e16	−1.44788
$833$	1.44781e16	1.25073
$834$	1.03470e16	0.887977
$835$	4.70353e15	0.401004
$836$	1.79346e14	0.0151900
$837$	−1.33580e15	−0.112396
$838$	−3.65995e15	−0.305938
$839$	−1.56360e16	−1.29848	−0.649240	−	0.760584i	$-0.724913\pi$
$839$	−1.56360e16	−1.29848	−0.649240	+	0.760584i	$0.724913\pi$
$840$	5.81922e14	0.0480097
$841$	2.23550e16	1.83230
$842$	−6.11481e15	−0.497928
$843$	−1.02817e15	−0.0831786
$844$	3.44643e13	0.00277004
$845$	−4.35377e15	−0.347659
$846$	1.00592e15	0.0798046
$847$	−6.02834e15	−0.475159
$848$	4.81873e15	0.377359
$849$	−1.99603e15	−0.155301
$850$	−1.46693e16	−1.13398
$851$	−1.09194e16	−0.838664
$852$	3.66511e14	0.0279685
$853$	−1.36871e16	−1.03775	−0.518875	−	0.854850i	$-0.673649\pi$
$853$	−1.36871e16	−1.03775	−0.518875	+	0.854850i	$0.673649\pi$
$854$	1.77394e15	0.133635
$855$	−4.26756e14	−0.0319423
$856$	−3.14721e15	−0.234056
$857$	1.05025e16	0.776065	0.388033	−	0.921646i	$-0.373155\pi$
$857$	1.05025e16	0.776065	0.388033	+	0.921646i	$0.373155\pi$
$858$	−1.90443e16	−1.39825
$859$	−2.49090e16	−1.81716	−0.908580	−	0.417710i	$-0.862833\pi$
$859$	−2.49090e16	−1.81716	−0.908580	+	0.417710i	$0.862833\pi$
$860$	1.92675e14	0.0139664
$861$	−8.80132e14	−0.0633914
$862$	2.33582e16	1.67166
$863$	1.65938e16	1.18001	0.590005	−	0.807400i	$-0.299126\pi$
$863$	1.65938e16	1.18001	0.590005	+	0.807400i	$0.299126\pi$
$864$	−1.75623e14	−0.0124095
$865$	−9.48162e15	−0.665724
$866$	1.12112e16	0.782176
$867$	6.19248e15	0.429299
$868$	−6.28279e13	−0.00432807
$869$	2.52289e16	1.72699
$870$	−5.00823e15	−0.340665
$871$	1.78647e16	1.20752
$872$	2.15484e15	0.144735
$873$	2.12756e15	0.142005
$874$	−4.75891e15	−0.315642
$875$	−2.32702e15	−0.153375
$876$	2.93391e14	0.0192165
$877$	8.89740e15	0.579116	0.289558	−	0.957161i	$-0.406492\pi$
$877$	8.89740e15	0.579116	0.289558	+	0.957161i	$0.406492\pi$
$878$	−9.29698e15	−0.601343
$879$	7.38347e14	0.0474594
$880$	−9.44749e15	−0.603478
$881$	2.46827e16	1.56684	0.783421	−	0.621491i	$-0.213473\pi$
$881$	2.46827e16	1.56684	0.783421	+	0.621491i	$0.213473\pi$
$882$	4.92359e15	0.310602
$883$	−5.66978e15	−0.355453	−0.177727	−	0.984080i	$-0.556874\pi$
$883$	−5.66978e15	−0.355453	−0.177727	+	0.984080i	$0.556874\pi$
$884$	−9.60773e14	−0.0598595
$885$	−4.32653e14	−0.0267887
$886$	1.03042e15	0.0634059
$887$	2.27269e16	1.38983	0.694913	−	0.719094i	$-0.255443\pi$
$887$	2.27269e16	1.38983	0.694913	+	0.719094i	$0.255443\pi$
$888$	−6.77955e15	−0.412031
$889$	6.20250e15	0.374634
$890$	2.68376e15	0.161101
$891$	−3.26223e15	−0.194620
$892$	1.03240e13	0.000612125 0
$893$	−1.11045e15	−0.0654361
$894$	−1.35997e16	−0.796476
$895$	−3.33284e15	−0.193994
$896$	3.76879e15	0.218026
$897$	−1.68422e16	−0.968367
$898$	−1.93615e16	−1.10642
$899$	1.73053e16	0.982883
$900$	1.66263e14	0.00938557
$901$	9.18685e15	0.515442
$902$	1.47657e16	0.823411
$903$	−2.90787e15	−0.161173
$904$	−1.59336e16	−0.877785
$905$	1.05691e16	0.578723
$906$	1.15316e16	0.627601
$907$	1.22135e16	0.660692	0.330346	−	0.943860i	$-0.392835\pi$
$907$	1.22135e16	0.660692	0.330346	+	0.943860i	$0.392835\pi$
$908$	−6.06778e14	−0.0326256
$909$	1.65899e14	0.00886632
$910$	2.13141e15	0.113224
$911$	3.02855e16	1.59913	0.799565	−	0.600579i	$-0.205063\pi$
$911$	3.02855e16	1.59913	0.799565	+	0.600579i	$0.205063\pi$
$912$	−2.85927e15	−0.150066
$913$	5.15938e16	2.69158
$914$	1.21654e16	0.630842
$915$	−2.36021e15	−0.121656
$916$	−8.23921e14	−0.0422144
$917$	−3.81298e15	−0.194193
$918$	4.93802e15	0.249988
$919$	8.27134e15	0.416237	0.208118	−	0.978104i	$-0.433266\pi$
$919$	8.27134e15	0.416237	0.208118	+	0.978104i	$0.433266\pi$
$920$	−8.63382e15	−0.431887
$921$	−9.44510e14	−0.0469655
$922$	−6.43996e15	−0.318320
$923$	4.29632e16	2.11100
$924$	−1.53436e14	−0.00749430
$925$	1.26359e16	0.613517
$926$	−2.28427e16	−1.10252
$927$	3.78772e15	0.181735
$928$	2.27521e15	0.108519
$929$	−2.33636e16	−1.10778	−0.553889	−	0.832590i	$-0.686857\pi$
$929$	−2.33636e16	−1.10778	−0.553889	+	0.832590i	$0.686857\pi$
$930$	−2.50811e15	−0.118220
$931$	−5.43523e15	−0.254680
$932$	3.20923e14	0.0149491
$933$	3.29594e15	0.152626
$934$	2.76655e16	1.27359
$935$	−1.80115e16	−0.824303
$936$	−1.04568e16	−0.475753
$937$	2.78969e16	1.26179	0.630897	−	0.775866i	$-0.282687\pi$
$937$	2.78969e16	1.26179	0.630897	+	0.775866i	$0.282687\pi$
$938$	−4.31858e15	−0.194189
$939$	−1.86178e16	−0.832276
$940$	−6.29489e13	−0.00279760
$941$	−4.19435e16	−1.85320	−0.926599	−	0.376052i	$-0.877281\pi$
$941$	−4.19435e16	−1.85320	−0.926599	+	0.376052i	$0.877281\pi$
$942$	−1.50425e16	−0.660752
$943$	1.30583e16	0.570258
$944$	−2.89877e15	−0.125854
$945$	3.65103e14	0.0157594
$946$	4.87842e16	2.09353
$947$	−3.38432e16	−1.44393	−0.721966	−	0.691928i	$-0.756761\pi$
$947$	−3.38432e16	−1.44393	−0.721966	+	0.691928i	$0.756761\pi$
$948$	4.32837e14	0.0183602
$949$	3.43919e16	1.45042
$950$	5.50698e15	0.230905
$951$	7.76932e15	0.323884
$952$	7.43317e15	0.308085
$953$	1.35827e16	0.559724	0.279862	−	0.960040i	$-0.409711\pi$
$953$	1.35827e16	0.559724	0.279862	+	0.960040i	$0.409711\pi$
$954$	3.12418e15	0.128003
$955$	−2.76668e15	−0.112704
$956$	−1.50604e15	−0.0609983
$957$	4.22624e16	1.70192
$958$	4.42238e15	0.177070
$959$	−1.07522e15	−0.0428049
$960$	−5.35507e15	−0.211970
$961$	−1.67420e16	−0.658914
$962$	−2.48315e16	−0.971716
$963$	−1.97458e15	−0.0768300
$964$	−4.41403e14	−0.0170770
$965$	−1.01755e16	−0.391431
$966$	4.07139e15	0.155729
$967$	−2.15462e16	−0.819455	−0.409728	−	0.912208i	$-0.634376\pi$
$967$	−2.15462e16	−0.819455	−0.409728	+	0.912208i	$0.634376\pi$
$968$	5.55312e16	2.10001
$969$	−5.45116e15	−0.204978
$970$	3.99473e15	0.149363
$971$	−3.86429e16	−1.43669	−0.718347	−	0.695685i	$-0.755101\pi$
$971$	−3.86429e16	−1.43669	−0.718347	+	0.695685i	$0.755101\pi$
$972$	−5.59680e13	−0.00206907
$973$	9.77206e15	0.359224
$974$	4.47162e16	1.63452
$975$	1.94897e16	0.708400
$976$	−1.58134e16	−0.571546
$977$	−4.19060e16	−1.50611	−0.753055	−	0.657958i	$-0.771420\pi$
$977$	−4.19060e16	−1.50611	−0.753055	+	0.657958i	$0.771420\pi$
$978$	−4.72131e15	−0.168732
$979$	−2.26472e16	−0.804839
$980$	−3.08110e14	−0.0108883
$981$	1.35197e15	0.0475101
$982$	1.90255e16	0.664849
$983$	6.34482e15	0.220483	0.110241	−	0.993905i	$-0.464838\pi$
$983$	6.34482e15	0.220483	0.110241	+	0.993905i	$0.464838\pi$
$984$	8.10749e15	0.280165
$985$	−8.79499e15	−0.302229
$986$	−6.39725e16	−2.18610
$987$	9.50028e14	0.0322844
$988$	3.60683e14	0.0121889
$989$	4.31432e16	1.44988
$990$	−6.12520e15	−0.204704
$991$	−5.24907e16	−1.74452	−0.872262	−	0.489039i	$-0.837348\pi$
$991$	−5.24907e16	−1.74452	−0.872262	+	0.489039i	$0.837348\pi$
$992$	1.13942e15	0.0376590
$993$	−1.02635e16	−0.337345
$994$	−1.03858e16	−0.339482
$995$	1.45138e15	0.0471796
$996$	8.85162e14	0.0286152
$997$	−1.01187e16	−0.325313	−0.162656	−	0.986683i	$-0.552006\pi$
$997$	−1.01187e16	−0.325313	−0.162656	+	0.986683i	$0.552006\pi$
$998$	−4.81999e16	−1.54109
$999$	−4.25355e15	−0.135251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.7	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-44.5190 q^{2} +243.000 q^{3} -66.0554 q^{4} -2490.42 q^{5} -10818.1 q^{6} -10217.0 q^{7} +94115.7 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-44.5190 q^{2} +243.000 q^{3} -66.0554 q^{4} -2490.42 q^{5} -10818.1 q^{6} -10217.0 q^{7} +94115.7 q^{8} +59049.0 q^{9} +110871. q^{10} -935597. q^{11} -16051.5 q^{12} -1.88159e6 q^{13} +454851. q^{14} -605173. q^{15} -4.05466e6 q^{16} -7.73016e6 q^{17} -2.62880e6 q^{18} +2.90198e6 q^{19} +164506. q^{20} -2.48273e6 q^{21} +4.16519e7 q^{22} +3.68356e7 q^{23} +2.28701e7 q^{24} -4.26259e7 q^{25} +8.37664e7 q^{26} +1.43489e7 q^{27} +674888. q^{28} -1.85891e8 q^{29} +2.69417e7 q^{30} -9.30939e7 q^{31} -1.22395e7 q^{32} -2.27350e8 q^{33} +3.44139e8 q^{34} +2.54446e7 q^{35} -3.90051e6 q^{36} -2.96437e8 q^{37} -1.29193e8 q^{38} -4.57225e8 q^{39} -2.34388e8 q^{40} +3.54502e8 q^{41} +1.10529e8 q^{42} +1.17124e9 q^{43} +6.18013e7 q^{44} -1.47057e8 q^{45} -1.63989e9 q^{46} -3.82655e8 q^{47} -9.85282e8 q^{48} -1.87294e9 q^{49} +1.89766e9 q^{50} -1.87843e9 q^{51} +1.24289e8 q^{52} -1.18844e9 q^{53} -6.38800e8 q^{54} +2.33003e9 q^{55} -9.61580e8 q^{56} +7.05180e8 q^{57} +8.27570e9 q^{58} +7.14924e8 q^{59} +3.99749e7 q^{60} +3.90006e9 q^{61} +4.14445e9 q^{62} -6.03303e8 q^{63} +8.84883e9 q^{64} +4.68594e9 q^{65} +1.01214e10 q^{66} -9.49449e9 q^{67} +5.10619e8 q^{68} +8.95105e9 q^{69} -1.13277e9 q^{70} -2.28335e10 q^{71} +5.55744e9 q^{72} -1.82782e10 q^{73} +1.31971e10 q^{74} -1.03581e10 q^{75} -1.91691e8 q^{76} +9.55900e9 q^{77} +2.03552e10 q^{78} -2.69656e10 q^{79} +1.00978e10 q^{80} +3.48678e9 q^{81} -1.57821e10 q^{82} -5.51453e10 q^{83} +1.63998e8 q^{84} +1.92514e10 q^{85} -5.21423e10 q^{86} -4.51716e10 q^{87} -8.80544e10 q^{88} +2.42061e10 q^{89} +6.54683e9 q^{90} +1.92242e10 q^{91} -2.43319e9 q^{92} -2.26218e10 q^{93} +1.70354e10 q^{94} -7.22715e9 q^{95} -2.97419e9 q^{96} +3.60303e10 q^{97} +8.33815e10 q^{98} -5.52461e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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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