LMFDB - Embedded newform 177.14.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$189.798744245$
Analytic rank:	$1$
Dimension:	$30$
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)

$f(q)$	$=$	$q-112.878 q^{2} +729.000 q^{3} +4549.48 q^{4} +37606.3 q^{5} -82288.2 q^{6} -60488.5 q^{7} +411161. q^{8} +531441. q^{9} +O(q^{10})$	\(q-112.878 q^{2} +729.000 q^{3} +4549.48 q^{4} +37606.3 q^{5} -82288.2 q^{6} -60488.5 q^{7} +411161. q^{8} +531441. q^{9} -4.24493e6 q^{10} -5.38497e6 q^{11} +3.31657e6 q^{12} +1.78547e7 q^{13} +6.82784e6 q^{14} +2.74150e7 q^{15} -8.36804e7 q^{16} -7.26826e7 q^{17} -5.99881e7 q^{18} +2.05937e8 q^{19} +1.71089e8 q^{20} -4.40961e7 q^{21} +6.07846e8 q^{22} -2.11582e8 q^{23} +2.99736e8 q^{24} +1.93529e8 q^{25} -2.01541e9 q^{26} +3.87420e8 q^{27} -2.75192e8 q^{28} +4.90852e9 q^{29} -3.09455e9 q^{30} -5.76225e9 q^{31} +6.07747e9 q^{32} -3.92564e9 q^{33} +8.20427e9 q^{34} -2.27475e9 q^{35} +2.41778e9 q^{36} +5.09808e8 q^{37} -2.32458e10 q^{38} +1.30161e10 q^{39} +1.54622e10 q^{40} -4.36319e9 q^{41} +4.97749e9 q^{42} -1.35776e9 q^{43} -2.44988e10 q^{44} +1.99855e10 q^{45} +2.38830e10 q^{46} -1.26930e11 q^{47} -6.10030e10 q^{48} -9.32301e10 q^{49} -2.18452e10 q^{50} -5.29856e10 q^{51} +8.12297e10 q^{52} -2.89318e10 q^{53} -4.37313e10 q^{54} -2.02509e11 q^{55} -2.48705e10 q^{56} +1.50128e11 q^{57} -5.54065e11 q^{58} +4.21805e10 q^{59} +1.24724e11 q^{60} +2.30201e11 q^{61} +6.50432e11 q^{62} -3.21461e10 q^{63} -5.03064e8 q^{64} +6.71449e11 q^{65} +4.43119e11 q^{66} -1.70285e11 q^{67} -3.30668e11 q^{68} -1.54243e11 q^{69} +2.56769e11 q^{70} -1.48653e12 q^{71} +2.18508e11 q^{72} -1.87627e12 q^{73} -5.75462e10 q^{74} +1.41083e11 q^{75} +9.36907e11 q^{76} +3.25729e11 q^{77} -1.46923e12 q^{78} -2.52869e12 q^{79} -3.14691e12 q^{80} +2.82430e11 q^{81} +4.92509e11 q^{82} -1.34332e12 q^{83} -2.00615e11 q^{84} -2.73332e12 q^{85} +1.53261e11 q^{86} +3.57831e12 q^{87} -2.21409e12 q^{88} -1.41898e12 q^{89} -2.25593e12 q^{90} -1.08001e12 q^{91} -9.62587e11 q^{92} -4.20068e12 q^{93} +1.43276e13 q^{94} +7.74453e12 q^{95} +4.43047e12 q^{96} +1.48907e13 q^{97} +1.05236e13 q^{98} -2.86179e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) $ 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * 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 $

$2$	−112.878	−1.24714	−0.623570	−	0.781768i	$-0.714318\pi$
$2$	−112.878	−1.24714	−0.623570	+	0.781768i	$0.714318\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	4549.48	0.555357
$5$	37606.3	1.07635	0.538177	−	0.842832i	$-0.319113\pi$
$5$	37606.3	1.07635	0.538177	+	0.842832i	$0.319113\pi$
$6$	−82288.2	−0.720036
$7$	−60488.5	−0.194328	−0.0971641	−	0.995268i	$-0.530977\pi$
$7$	−60488.5	−0.194328	−0.0971641	+	0.995268i	$0.530977\pi$
$8$	411161.	0.554532
$9$	531441.	0.333333
$10$	−4.24493e6	−1.34236
$11$	−5.38497e6	−0.916497	−0.458248	−	0.888824i	$-0.651523\pi$
$11$	−5.38497e6	−0.916497	−0.458248	+	0.888824i	$0.651523\pi$
$12$	3.31657e6	0.320635
$13$	1.78547e7	1.02594	0.512969	−	0.858407i	$-0.328546\pi$
$13$	1.78547e7	1.02594	0.512969	+	0.858407i	$0.328546\pi$
$14$	6.82784e6	0.242354
$15$	2.74150e7	0.621434
$16$	−8.36804e7	−1.24694
$17$	−7.26826e7	−0.730318	−0.365159	−	0.930945i	$-0.618985\pi$
$17$	−7.26826e7	−0.730318	−0.365159	+	0.930945i	$0.618985\pi$
$18$	−5.99881e7	−0.415713
$19$	2.05937e8	1.00424	0.502119	−	0.864799i	$-0.332554\pi$
$19$	2.05937e8	1.00424	0.502119	+	0.864799i	$0.332554\pi$
$20$	1.71089e8	0.597761
$21$	−4.40961e7	−0.112195
$22$	6.07846e8	1.14300
$23$	−2.11582e8	−0.298021	−0.149011	−	0.988836i	$-0.547609\pi$
$23$	−2.11582e8	−0.298021	−0.149011	+	0.988836i	$0.547609\pi$
$24$	2.99736e8	0.320159
$25$	1.93529e8	0.158539
$26$	−2.01541e9	−1.27949
$27$	3.87420e8	0.192450
$28$	−2.75192e8	−0.107921
$29$	4.90852e9	1.53237	0.766185	−	0.642620i	$-0.222152\pi$
$29$	4.90852e9	1.53237	0.766185	+	0.642620i	$0.222152\pi$
$30$	−3.09455e9	−0.775014
$31$	−5.76225e9	−1.16611	−0.583057	−	0.812431i	$-0.698144\pi$
$31$	−5.76225e9	−1.16611	−0.583057	+	0.812431i	$0.698144\pi$
$32$	6.07747e9	1.00057
$33$	−3.92564e9	−0.529140
$34$	8.20427e9	0.910809
$35$	−2.27475e9	−0.209166
$36$	2.41778e9	0.185119
$37$	5.09808e8	0.0326659	0.0163330	−	0.999867i	$-0.494801\pi$
$37$	5.09808e8	0.0326659	0.0163330	+	0.999867i	$0.494801\pi$
$38$	−2.32458e10	−1.25242
$39$	1.30161e10	0.592326
$40$	1.54622e10	0.596873
$41$	−4.36319e9	−0.143453	−0.0717264	−	0.997424i	$-0.522851\pi$
$41$	−4.36319e9	−0.143453	−0.0717264	+	0.997424i	$0.522851\pi$
$42$	4.97749e9	0.139923
$43$	−1.35776e9	−0.0327550	−0.0163775	−	0.999866i	$-0.505213\pi$
$43$	−1.35776e9	−0.0327550	−0.0163775	+	0.999866i	$0.505213\pi$
$44$	−2.44988e10	−0.508982
$45$	1.99855e10	0.358785
$46$	2.38830e10	0.371674
$47$	−1.26930e11	−1.71762	−0.858812	−	0.512291i	$-0.828797\pi$
$47$	−1.26930e11	−1.71762	−0.858812	+	0.512291i	$0.828797\pi$
$48$	−6.10030e10	−0.719919
$49$	−9.32301e10	−0.962237
$50$	−2.18452e10	−0.197720
$51$	−5.29856e10	−0.421649
$52$	8.12297e10	0.569761
$53$	−2.89318e10	−0.179301	−0.0896504	−	0.995973i	$-0.528575\pi$
$53$	−2.89318e10	−0.179301	−0.0896504	+	0.995973i	$0.528575\pi$
$54$	−4.37313e10	−0.240012
$55$	−2.02509e11	−0.986475
$56$	−2.48705e10	−0.107761
$57$	1.50128e11	0.579797
$58$	−5.54065e11	−1.91108
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	1.24724e11	0.345117
$61$	2.30201e11	0.572088	0.286044	−	0.958216i	$-0.407660\pi$
$61$	2.30201e11	0.572088	0.286044	+	0.958216i	$0.407660\pi$
$62$	6.50432e11	1.45431
$63$	−3.21461e10	−0.0647761
$64$	−5.03064e8	−0.000915069 0
$65$	6.71449e11	1.10427
$66$	4.43119e11	0.659911
$67$	−1.70285e11	−0.229980	−0.114990	−	0.993367i	$-0.536684\pi$
$67$	−1.70285e11	−0.229980	−0.114990	+	0.993367i	$0.536684\pi$
$68$	−3.30668e11	−0.405587
$69$	−1.54243e11	−0.172063
$70$	2.56769e11	0.260859
$71$	−1.48653e12	−1.37719	−0.688594	−	0.725147i	$-0.741772\pi$
$71$	−1.48653e12	−1.37719	−0.688594	+	0.725147i	$0.741772\pi$
$72$	2.18508e11	0.184844
$73$	−1.87627e12	−1.45110	−0.725550	−	0.688170i	$-0.758414\pi$
$73$	−1.87627e12	−1.45110	−0.725550	+	0.688170i	$0.758414\pi$
$74$	−5.75462e10	−0.0407390
$75$	1.41083e11	0.0915325
$76$	9.36907e11	0.557710
$77$	3.25729e11	0.178101
$78$	−1.46923e12	−0.738713
$79$	−2.52869e12	−1.17036	−0.585180	−	0.810904i	$-0.698976\pi$
$79$	−2.52869e12	−1.17036	−0.585180	+	0.810904i	$0.698976\pi$
$80$	−3.14691e12	−1.34214
$81$	2.82430e11	0.111111
$82$	4.92509e11	0.178906
$83$	−1.34332e12	−0.450995	−0.225498	−	0.974244i	$-0.572401\pi$
$83$	−1.34332e12	−0.450995	−0.225498	+	0.974244i	$0.572401\pi$
$84$	−2.00615e11	−0.0623085
$85$	−2.73332e12	−0.786081
$86$	1.53261e11	0.0408500
$87$	3.57831e12	0.884715
$88$	−2.21409e12	−0.508227
$89$	−1.41898e12	−0.302650	−0.151325	−	0.988484i	$-0.548354\pi$
$89$	−1.41898e12	−0.302650	−0.151325	+	0.988484i	$0.548354\pi$
$90$	−2.25593e12	−0.447455
$91$	−1.08001e12	−0.199369
$92$	−9.62587e11	−0.165508
$93$	−4.20068e12	−0.673256
$94$	1.43276e13	2.14212
$95$	7.74453e12	1.08092
$96$	4.43047e12	0.577680
$97$	1.48907e13	1.81509	0.907543	−	0.419958i	$-0.137955\pi$
$97$	1.48907e13	1.81509	0.907543	+	0.419958i	$0.137955\pi$
$98$	1.05236e13	1.20004
$99$	−2.86179e12	−0.305499
$100$	8.80457e11	0.0880457
$101$	2.00384e13	1.87834	0.939169	−	0.343456i	$-0.111597\pi$
$101$	2.00384e13	1.87834	0.939169	+	0.343456i	$0.111597\pi$
$102$	5.98092e12	0.525856
$103$	−1.87483e13	−1.54710	−0.773551	−	0.633734i	$-0.781521\pi$
$103$	−1.87483e13	−1.54710	−0.773551	+	0.633734i	$0.781521\pi$
$104$	7.34116e12	0.568916
$105$	−1.65829e12	−0.120762
$106$	3.26577e12	0.223613
$107$	7.48333e11	0.0482059	0.0241030	−	0.999709i	$-0.492327\pi$
$107$	7.48333e11	0.0482059	0.0241030	+	0.999709i	$0.492327\pi$
$108$	1.76256e12	0.106878
$109$	−5.69983e12	−0.325529	−0.162765	−	0.986665i	$-0.552041\pi$
$109$	−5.69983e12	−0.325529	−0.162765	+	0.986665i	$0.552041\pi$
$110$	2.28588e13	1.23027
$111$	3.71650e11	0.0188597
$112$	5.06171e12	0.242315
$113$	3.56191e13	1.60944	0.804718	−	0.593658i	$-0.202317\pi$
$113$	3.56191e13	1.60944	0.804718	+	0.593658i	$0.202317\pi$
$114$	−1.69462e13	−0.723087
$115$	−7.95680e12	−0.320777
$116$	2.23312e13	0.851012
$117$	9.48873e12	0.341979
$118$	−4.76126e12	−0.162364
$119$	4.39646e12	0.141921
$120$	1.12720e13	0.344605
$121$	−5.52481e12	−0.160034
$122$	−2.59847e13	−0.713474
$123$	−3.18077e12	−0.0828226
$124$	−2.62152e13	−0.647609
$125$	−3.86282e13	−0.905710
$126$	3.62859e12	0.0807848
$127$	7.89356e13	1.66936	0.834678	−	0.550738i	$-0.185654\pi$
$127$	7.89356e13	1.66936	0.834678	+	0.550738i	$0.185654\pi$
$128$	−4.97298e13	−0.999429
$129$	−9.89806e11	−0.0189111
$130$	−7.57920e13	−1.37718
$131$	1.09063e14	1.88545	0.942724	−	0.333575i	$-0.108255\pi$
$131$	1.09063e14	1.88545	0.942724	+	0.333575i	$0.108255\pi$
$132$	−1.78596e13	−0.293861
$133$	−1.24568e13	−0.195152
$134$	1.92214e13	0.286817
$135$	1.45694e13	0.207145
$136$	−2.98842e13	−0.404985
$137$	−1.02328e14	−1.32224	−0.661118	−	0.750282i	$-0.729918\pi$
$137$	−1.02328e14	−1.32224	−0.661118	+	0.750282i	$0.729918\pi$
$138$	1.74107e13	0.214586
$139$	9.41040e13	1.10665	0.553327	−	0.832964i	$-0.313358\pi$
$139$	9.41040e13	1.10665	0.553327	+	0.832964i	$0.313358\pi$
$140$	−1.03489e13	−0.116162
$141$	−9.25319e13	−0.991670
$142$	1.67796e14	1.71754
$143$	−9.61471e13	−0.940269
$144$	−4.44712e13	−0.415645
$145$	1.84591e14	1.64937
$146$	2.11790e14	1.80972
$147$	−6.79648e13	−0.555548
$148$	2.31936e12	0.0181412
$149$	1.84740e14	1.38309	0.691544	−	0.722334i	$-0.256931\pi$
$149$	1.84740e14	1.38309	0.691544	+	0.722334i	$0.256931\pi$
$150$	−1.59252e13	−0.114154
$151$	−1.90572e14	−1.30831	−0.654153	−	0.756363i	$-0.726975\pi$
$151$	−1.90572e14	−1.30831	−0.654153	+	0.756363i	$0.726975\pi$
$152$	8.46733e13	0.556882
$153$	−3.86265e13	−0.243439
$154$	−3.67677e13	−0.222117
$155$	−2.16697e14	−1.25515
$156$	5.92164e13	0.328952
$157$	1.24248e13	0.0662125	0.0331063	−	0.999452i	$-0.489460\pi$
$157$	1.24248e13	0.0662125	0.0331063	+	0.999452i	$0.489460\pi$
$158$	2.85434e14	1.45960
$159$	−2.10913e13	−0.103519
$160$	2.28551e14	1.07697
$161$	1.27983e13	0.0579139
$162$	−3.18801e13	−0.138571
$163$	5.65179e13	0.236030	0.118015	−	0.993012i	$-0.462347\pi$
$163$	5.65179e13	0.236030	0.118015	+	0.993012i	$0.462347\pi$
$164$	−1.98503e13	−0.0796675
$165$	−1.47629e14	−0.569542
$166$	1.51632e14	0.562454
$167$	−2.93952e14	−1.04862	−0.524311	−	0.851527i	$-0.675677\pi$
$167$	−2.93952e14	−1.04862	−0.524311	+	0.851527i	$0.675677\pi$
$168$	−1.81306e13	−0.0622160
$169$	1.59157e13	0.0525487
$170$	3.08532e14	0.980353
$171$	1.09443e14	0.334746
$172$	−6.17710e12	−0.0181907
$173$	1.71073e14	0.485158	0.242579	−	0.970132i	$-0.422007\pi$
$173$	1.71073e14	0.485158	0.242579	+	0.970132i	$0.422007\pi$
$174$	−4.03914e14	−1.10336
$175$	−1.17063e13	−0.0308086
$176$	4.50617e14	1.14281
$177$	3.07496e13	0.0751646
$178$	1.60171e14	0.377446
$179$	−5.94981e14	−1.35194	−0.675971	−	0.736928i	$-0.736276\pi$
$179$	−5.94981e14	−1.35194	−0.675971	+	0.736928i	$0.736276\pi$
$180$	9.09238e13	0.199254
$181$	5.40767e14	1.14314	0.571570	−	0.820553i	$-0.306334\pi$
$181$	5.40767e14	1.14314	0.571570	+	0.820553i	$0.306334\pi$
$182$	1.21909e14	0.248641
$183$	1.67816e14	0.330295
$184$	−8.69941e13	−0.165262
$185$	1.91720e13	0.0351601
$186$	4.74165e14	0.839644
$187$	3.91393e14	0.669334
$188$	−5.77465e14	−0.953894
$189$	−2.34345e13	−0.0373985
$190$	−8.74188e14	−1.34805
$191$	−4.12874e14	−0.615319	−0.307660	−	0.951496i	$-0.599546\pi$
$191$	−4.12874e14	−0.615319	−0.307660	+	0.951496i	$0.599546\pi$
$192$	−3.66734e11	−0.000528315 0
$193$	−1.00065e15	−1.39366	−0.696831	−	0.717235i	$-0.745407\pi$
$193$	−1.00065e15	−1.39366	−0.696831	+	0.717235i	$0.745407\pi$
$194$	−1.68083e15	−2.26367
$195$	4.89487e14	0.637552
$196$	−4.24149e14	−0.534384
$197$	−1.03802e15	−1.26524	−0.632622	−	0.774460i	$-0.718021\pi$
$197$	−1.03802e15	−1.26524	−0.632622	+	0.774460i	$0.718021\pi$
$198$	3.23034e14	0.381000
$199$	3.01937e14	0.344645	0.172322	−	0.985041i	$-0.444873\pi$
$199$	3.01937e14	0.344645	0.172322	+	0.985041i	$0.444873\pi$
$200$	7.95715e13	0.0879150
$201$	−1.24137e14	−0.132779
$202$	−2.26190e15	−2.34255
$203$	−2.96909e14	−0.297783
$204$	−2.41057e14	−0.234166
$205$	−1.64083e14	−0.154406
$206$	2.11627e15	1.92945
$207$	−1.12443e14	−0.0993404
$208$	−1.49409e15	−1.27928
$209$	−1.10897e15	−0.920380
$210$	1.87185e14	0.150607
$211$	1.70594e15	1.33085	0.665424	−	0.746466i	$-0.268251\pi$
$211$	1.70594e15	1.33085	0.665424	+	0.746466i	$0.268251\pi$
$212$	−1.31625e14	−0.0995759
$213$	−1.08368e15	−0.795120
$214$	−8.44705e13	−0.0601195
$215$	−5.10602e13	−0.0352560
$216$	1.59292e14	0.106720
$217$	3.48550e14	0.226609
$218$	6.43387e14	0.405980
$219$	−1.36780e15	−0.837792
$220$	−9.21310e14	−0.547846
$221$	−1.29773e15	−0.749261
$222$	−4.19511e13	−0.0235207
$223$	1.57255e14	0.0856294	0.0428147	−	0.999083i	$-0.486367\pi$
$223$	1.57255e14	0.0856294	0.0428147	+	0.999083i	$0.486367\pi$
$224$	−3.67617e14	−0.194439
$225$	1.02849e14	0.0528463
$226$	−4.02062e15	−2.00719
$227$	−1.32918e15	−0.644784	−0.322392	−	0.946606i	$-0.604487\pi$
$227$	−1.32918e15	−0.644784	−0.322392	+	0.946606i	$0.604487\pi$
$228$	6.83005e14	0.321994
$229$	−3.49747e15	−1.60259	−0.801296	−	0.598268i	$-0.795856\pi$
$229$	−3.49747e15	−1.60259	−0.801296	+	0.598268i	$0.795856\pi$
$230$	8.98149e14	0.400053
$231$	2.37456e14	0.102827
$232$	2.01819e15	0.849749
$233$	−7.41920e14	−0.303769	−0.151884	−	0.988398i	$-0.548534\pi$
$233$	−7.41920e14	−0.303769	−0.151884	+	0.988398i	$0.548534\pi$
$234$	−1.07107e15	−0.426496
$235$	−4.77336e15	−1.84877
$236$	1.91900e14	0.0723013
$237$	−1.84341e15	−0.675707
$238$	−4.96265e14	−0.176996
$239$	−5.56819e15	−1.93254	−0.966268	−	0.257539i	$-0.917089\pi$
$239$	−5.56819e15	−1.93254	−0.966268	+	0.257539i	$0.917089\pi$
$240$	−2.29410e15	−0.774888
$241$	1.25296e15	0.411933	0.205967	−	0.978559i	$-0.433966\pi$
$241$	1.25296e15	0.411933	0.205967	+	0.978559i	$0.433966\pi$
$242$	6.23631e14	0.199585
$243$	2.05891e14	0.0641500
$244$	1.04729e15	0.317713
$245$	−3.50604e15	−1.03571
$246$	3.59039e14	0.103291
$247$	3.67695e15	1.03029
$248$	−2.36921e15	−0.646648
$249$	−9.79281e14	−0.260382
$250$	4.36028e15	1.12955
$251$	−5.16714e15	−1.30428	−0.652140	−	0.758099i	$-0.726128\pi$
$251$	−5.16714e15	−1.30428	−0.652140	+	0.758099i	$0.726128\pi$
$252$	−1.46248e14	−0.0359738
$253$	1.13936e15	0.273135
$254$	−8.91011e15	−2.08192
$255$	−1.99259e15	−0.453844
$256$	5.61753e15	1.24734
$257$	−2.18653e15	−0.473359	−0.236679	−	0.971588i	$-0.576059\pi$
$257$	−2.18653e15	−0.473359	−0.236679	+	0.971588i	$0.576059\pi$
$258$	1.11727e14	0.0235848
$259$	−3.08375e13	−0.00634791
$260$	3.05475e15	0.613265
$261$	2.60859e15	0.510790
$262$	−1.23108e16	−2.35142
$263$	4.80148e15	0.894670	0.447335	−	0.894366i	$-0.352373\pi$
$263$	4.80148e15	0.894670	0.447335	+	0.894366i	$0.352373\pi$
$264$	−1.61407e15	−0.293425
$265$	−1.08802e15	−0.192991
$266$	1.40610e15	0.243381
$267$	−1.03443e15	−0.174735
$268$	−7.74707e14	−0.127721
$269$	−1.07930e16	−1.73681	−0.868404	−	0.495858i	$-0.834854\pi$
$269$	−1.07930e16	−1.73681	−0.868404	+	0.495858i	$0.834854\pi$
$270$	−1.64457e15	−0.258338
$271$	7.90679e15	1.21255	0.606275	−	0.795255i	$-0.292663\pi$
$271$	7.90679e15	1.21255	0.606275	+	0.795255i	$0.292663\pi$
$272$	6.08211e15	0.910660
$273$	−7.87324e14	−0.115106
$274$	1.15506e16	1.64901
$275$	−1.04215e15	−0.145300
$276$	−7.01726e14	−0.0955561
$277$	−4.13424e15	−0.549892	−0.274946	−	0.961460i	$-0.588660\pi$
$277$	−4.13424e15	−0.549892	−0.274946	+	0.961460i	$0.588660\pi$
$278$	−1.06223e16	−1.38015
$279$	−3.06229e15	−0.388705
$280$	−9.35288e14	−0.115989
$281$	2.12797e15	0.257854	0.128927	−	0.991654i	$-0.458847\pi$
$281$	2.12797e15	0.257854	0.128927	+	0.991654i	$0.458847\pi$
$282$	1.04448e16	1.23675
$283$	8.05949e15	0.932601	0.466300	−	0.884626i	$-0.345587\pi$
$283$	8.05949e15	0.932601	0.466300	+	0.884626i	$0.345587\pi$
$284$	−6.76292e15	−0.764830
$285$	5.64576e15	0.624067
$286$	1.08529e16	1.17265
$287$	2.63923e14	0.0278769
$288$	3.22981e15	0.333523
$289$	−4.62182e15	−0.466635
$290$	−2.08363e16	−2.05700
$291$	1.08553e16	1.04794
$292$	−8.53606e15	−0.805878
$293$	−5.20186e15	−0.480307	−0.240153	−	0.970735i	$-0.577198\pi$
$293$	−5.20186e15	−0.480307	−0.240153	+	0.970735i	$0.577198\pi$
$294$	7.67174e15	0.692845
$295$	1.58625e15	0.140129
$296$	2.09613e14	0.0181143
$297$	−2.08625e15	−0.176380
$298$	−2.08531e16	−1.72490
$299$	−3.77773e15	−0.305751
$300$	6.41853e14	0.0508332
$301$	8.21288e13	0.00636522
$302$	2.15114e16	1.63164
$303$	1.46080e16	1.08446
$304$	−1.72329e16	−1.25222
$305$	8.65700e15	0.615770
$306$	4.36009e15	0.303603
$307$	−9.62580e15	−0.656202	−0.328101	−	0.944643i	$-0.606409\pi$
$307$	−9.62580e15	−0.656202	−0.328101	+	0.944643i	$0.606409\pi$
$308$	1.48190e15	0.0989096
$309$	−1.36675e16	−0.893220
$310$	2.44603e16	1.56535
$311$	−2.75576e16	−1.72703	−0.863514	−	0.504325i	$-0.831741\pi$
$311$	−2.75576e16	−1.72703	−0.863514	+	0.504325i	$0.831741\pi$
$312$	5.35170e15	0.328464
$313$	2.39181e16	1.43777	0.718883	−	0.695131i	$-0.244654\pi$
$313$	2.39181e16	1.43777	0.718883	+	0.695131i	$0.244654\pi$
$314$	−1.40248e15	−0.0825763
$315$	−1.20889e15	−0.0697220
$316$	−1.15042e16	−0.649967
$317$	−4.59540e15	−0.254354	−0.127177	−	0.991880i	$-0.540592\pi$
$317$	−4.59540e15	−0.254354	−0.127177	+	0.991880i	$0.540592\pi$
$318$	2.38075e15	0.129103
$319$	−2.64323e16	−1.40441
$320$	−1.89184e13	−0.000984938 0
$321$	5.45535e14	0.0278317
$322$	−1.44465e15	−0.0722267
$323$	−1.49680e16	−0.733413
$324$	1.28491e15	0.0617063
$325$	3.45541e15	0.162651
$326$	−6.37964e15	−0.294362
$327$	−4.15518e15	−0.187944
$328$	−1.79397e15	−0.0795492
$329$	7.67781e15	0.333783
$330$	1.66641e16	0.710298
$331$	−2.20324e16	−0.920831	−0.460415	−	0.887704i	$-0.652300\pi$
$331$	−2.20324e16	−0.920831	−0.460415	+	0.887704i	$0.652300\pi$
$332$	−6.11141e15	−0.250463
$333$	2.70933e14	0.0108886
$334$	3.31807e16	1.30778
$335$	−6.40377e15	−0.247539
$336$	3.68998e15	0.139900
$337$	3.26438e16	1.21397	0.606983	−	0.794715i	$-0.292380\pi$
$337$	3.26438e16	1.21397	0.606983	+	0.794715i	$0.292380\pi$
$338$	−1.79653e15	−0.0655356
$339$	2.59664e16	0.929208
$340$	−1.24352e16	−0.436556
$341$	3.10295e16	1.06874
$342$	−1.23538e16	−0.417475
$343$	1.15000e16	0.381318
$344$	−5.58257e14	−0.0181637
$345$	−5.80051e15	−0.185200
$346$	−1.93105e16	−0.605059
$347$	−2.58464e16	−0.794801	−0.397400	−	0.917645i	$-0.630088\pi$
$347$	−2.58464e16	−0.794801	−0.397400	+	0.917645i	$0.630088\pi$
$348$	1.62795e16	0.491332
$349$	1.49249e16	0.442127	0.221063	−	0.975259i	$-0.429047\pi$
$349$	1.49249e16	0.442127	0.221063	+	0.975259i	$0.429047\pi$
$350$	1.32138e15	0.0384226
$351$	6.91728e15	0.197442
$352$	−3.27270e16	−0.917019
$353$	3.75129e16	1.03192	0.515958	−	0.856614i	$-0.327436\pi$
$353$	3.75129e16	1.03192	0.515958	+	0.856614i	$0.327436\pi$
$354$	−3.47096e15	−0.0937407
$355$	−5.59027e16	−1.48234
$356$	−6.45561e15	−0.168079
$357$	3.20502e15	0.0819384
$358$	6.71603e16	1.68606
$359$	3.72336e16	0.917953	0.458977	−	0.888448i	$-0.348216\pi$
$359$	3.72336e16	0.917953	0.458977	+	0.888448i	$0.348216\pi$
$360$	8.21726e15	0.198958
$361$	3.57124e14	0.00849224
$362$	−6.10408e16	−1.42566
$363$	−4.02759e15	−0.0923958
$364$	−4.91347e15	−0.110721
$365$	−7.05596e16	−1.56190
$366$	−1.89428e16	−0.411924
$367$	3.69154e16	0.788639	0.394319	−	0.918973i	$-0.370980\pi$
$367$	3.69154e16	0.788639	0.394319	+	0.918973i	$0.370980\pi$
$368$	1.77053e16	0.371613
$369$	−2.31878e15	−0.0478176
$370$	−2.16410e15	−0.0438496
$371$	1.75004e15	0.0348432
$372$	−1.91109e16	−0.373897
$373$	5.13533e16	0.987328	0.493664	−	0.869653i	$-0.335657\pi$
$373$	5.13533e16	0.987328	0.493664	+	0.869653i	$0.335657\pi$
$374$	−4.41798e16	−0.834753
$375$	−2.81600e16	−0.522912
$376$	−5.21886e16	−0.952478
$377$	8.76403e16	1.57212
$378$	2.64524e15	0.0466411
$379$	3.45756e16	0.599260	0.299630	−	0.954056i	$-0.403137\pi$
$379$	3.45756e16	0.599260	0.299630	+	0.954056i	$0.403137\pi$
$380$	3.52336e16	0.600293
$381$	5.75441e16	0.963803
$382$	4.66045e16	0.767389
$383$	−7.39616e16	−1.19733	−0.598666	−	0.800999i	$-0.704302\pi$
$383$	−7.39616e16	−1.19733	−0.598666	+	0.800999i	$0.704302\pi$
$384$	−3.62530e16	−0.577021
$385$	1.22495e16	0.191700
$386$	1.12951e17	1.73809
$387$	−7.21568e14	−0.0109183
$388$	6.77448e16	1.00802
$389$	3.29116e16	0.481589	0.240795	−	0.970576i	$-0.422592\pi$
$389$	3.29116e16	0.481589	0.240795	+	0.970576i	$0.422592\pi$
$390$	−5.52523e16	−0.795117
$391$	1.53783e16	0.217650
$392$	−3.83326e16	−0.533591
$393$	7.95070e16	1.08856
$394$	1.17170e17	1.57794
$395$	−9.50945e16	−1.25972
$396$	−1.30197e16	−0.169661
$397$	−4.79591e15	−0.0614798	−0.0307399	−	0.999527i	$-0.509786\pi$
$397$	−4.79591e15	−0.0614798	−0.0307399	+	0.999527i	$0.509786\pi$
$398$	−3.40821e16	−0.429820
$399$	−9.08103e15	−0.112671
$400$	−1.61946e16	−0.197688
$401$	−1.13071e17	−1.35804	−0.679020	−	0.734119i	$-0.737595\pi$
$401$	−1.13071e17	−1.35804	−0.679020	+	0.734119i	$0.737595\pi$
$402$	1.40124e16	0.165594
$403$	−1.02883e17	−1.19636
$404$	9.11643e16	1.04315
$405$	1.06211e16	0.119595
$406$	3.35146e16	0.371377
$407$	−2.74530e15	−0.0299382
$408$	−2.17856e16	−0.233818
$409$	−1.02879e17	−1.08674	−0.543369	−	0.839494i	$-0.682852\pi$
$409$	−1.02879e17	−1.08674	−0.543369	+	0.839494i	$0.682852\pi$
$410$	1.85214e16	0.192566
$411$	−7.45968e16	−0.763394
$412$	−8.52949e16	−0.859193
$413$	−2.55144e15	−0.0252994
$414$	1.26924e16	0.123891
$415$	−5.05173e16	−0.485431
$416$	1.08511e17	1.02652
$417$	6.86018e16	0.638927
$418$	1.25178e17	1.14784
$419$	−1.30846e17	−1.18132	−0.590661	−	0.806920i	$-0.701133\pi$
$419$	−1.30846e17	−1.18132	−0.590661	+	0.806920i	$0.701133\pi$
$420$	−7.54437e15	−0.0670660
$421$	1.95222e17	1.70881	0.854407	−	0.519605i	$-0.173921\pi$
$421$	1.95222e17	1.70881	0.854407	+	0.519605i	$0.173921\pi$
$422$	−1.92564e17	−1.65975
$423$	−6.74558e16	−0.572541
$424$	−1.18956e16	−0.0994281
$425$	−1.40662e16	−0.115784
$426$	1.22323e17	0.991625
$427$	−1.39245e16	−0.111173
$428$	3.40453e15	0.0267715
$429$	−7.00912e16	−0.542864
$430$	5.76358e15	0.0439691
$431$	−6.29681e16	−0.473171	−0.236586	−	0.971611i	$-0.576028\pi$
$431$	−6.29681e16	−0.473171	−0.236586	+	0.971611i	$0.576028\pi$
$432$	−3.24195e16	−0.239973
$433$	−7.19886e16	−0.524919	−0.262460	−	0.964943i	$-0.584534\pi$
$433$	−7.19886e16	−0.524919	−0.262460	+	0.964943i	$0.584534\pi$
$434$	−3.93437e16	−0.282613
$435$	1.34567e17	0.952267
$436$	−2.59313e16	−0.180785
$437$	−4.35725e16	−0.299284
$438$	1.54395e17	1.04484
$439$	2.01569e16	0.134402	0.0672008	−	0.997739i	$-0.478593\pi$
$439$	2.01569e16	0.134402	0.0672008	+	0.997739i	$0.478593\pi$
$440$	−8.32636e16	−0.547032
$441$	−4.95463e16	−0.320746
$442$	1.46485e17	0.934433
$443$	−1.48799e17	−0.935351	−0.467676	−	0.883900i	$-0.654908\pi$
$443$	−1.48799e17	−0.935351	−0.467676	+	0.883900i	$0.654908\pi$
$444$	1.69081e15	0.0104739
$445$	−5.33624e16	−0.325758
$446$	−1.77507e16	−0.106792
$447$	1.34675e17	0.798526
$448$	3.04296e13	0.000177824 0
$449$	1.70580e17	0.982485	0.491242	−	0.871023i	$-0.336543\pi$
$449$	1.70580e17	0.982485	0.491242	+	0.871023i	$0.336543\pi$
$450$	−1.16094e16	−0.0659067
$451$	2.34957e16	0.131474
$452$	1.62049e17	0.893811
$453$	−1.38927e17	−0.755350
$454$	1.50035e17	0.804135
$455$	−4.06150e16	−0.214591
$456$	6.17268e16	0.321516
$457$	−1.64203e17	−0.843190	−0.421595	−	0.906784i	$-0.638530\pi$
$457$	−1.64203e17	−0.843190	−0.421595	+	0.906784i	$0.638530\pi$
$458$	3.94788e17	1.99866
$459$	−2.81587e16	−0.140550
$460$	−3.61993e16	−0.178145
$461$	−2.46285e17	−1.19504	−0.597519	−	0.801855i	$-0.703847\pi$
$461$	−2.46285e17	−1.19504	−0.597519	+	0.801855i	$0.703847\pi$
$462$	−2.68036e16	−0.128239
$463$	−1.89854e17	−0.895659	−0.447829	−	0.894119i	$-0.647803\pi$
$463$	−1.89854e17	−0.895659	−0.447829	+	0.894119i	$0.647803\pi$
$464$	−4.10747e17	−1.91077
$465$	−1.57972e17	−0.724662
$466$	8.37465e16	0.378842
$467$	−3.77881e17	−1.68576	−0.842880	−	0.538102i	$-0.819141\pi$
$467$	−3.77881e17	−1.68576	−0.842880	+	0.538102i	$0.819141\pi$
$468$	4.31688e16	0.189920
$469$	1.03003e16	0.0446915
$470$	5.38808e17	2.30568
$471$	9.05765e15	0.0382278
$472$	1.73430e16	0.0721939
$473$	7.31149e15	0.0300198
$474$	2.08081e17	0.842701
$475$	3.98548e16	0.159211
$476$	2.00016e16	0.0788170
$477$	−1.53755e16	−0.0597669
$478$	6.28527e17	2.41014
$479$	−2.06918e17	−0.782738	−0.391369	−	0.920234i	$-0.627998\pi$
$479$	−2.06918e17	−0.782738	−0.391369	+	0.920234i	$0.627998\pi$
$480$	1.66614e17	0.621788
$481$	9.10247e15	0.0335132
$482$	−1.41432e17	−0.513738
$483$	9.32994e15	0.0334366
$484$	−2.51350e16	−0.0888760
$485$	5.59982e17	1.95368
$486$	−2.32406e16	−0.0800040
$487$	2.82990e17	0.961241	0.480620	−	0.876929i	$-0.340412\pi$
$487$	2.82990e17	0.961241	0.480620	+	0.876929i	$0.340412\pi$
$488$	9.46496e16	0.317241
$489$	4.12015e16	0.136272
$490$	3.95755e17	1.29167
$491$	5.16102e17	1.66229	0.831144	−	0.556057i	$-0.187687\pi$
$491$	5.16102e17	1.66229	0.831144	+	0.556057i	$0.187687\pi$
$492$	−1.44708e16	−0.0459961
$493$	−3.56764e17	−1.11912
$494$	−4.15047e17	−1.28491
$495$	−1.07621e17	−0.328825
$496$	4.82187e17	1.45407
$497$	8.99177e16	0.267626
$498$	1.10539e17	0.324733
$499$	−4.45068e17	−1.29054	−0.645272	−	0.763953i	$-0.723256\pi$
$499$	−4.45068e17	−1.29054	−0.645272	+	0.763953i	$0.723256\pi$
$500$	−1.75738e17	−0.502992
$501$	−2.14291e17	−0.605422
$502$	5.83257e17	1.62662
$503$	−5.08695e16	−0.140044	−0.0700221	−	0.997545i	$-0.522307\pi$
$503$	−5.08695e16	−0.140044	−0.0700221	+	0.997545i	$0.522307\pi$
$504$	−1.32172e16	−0.0359204
$505$	7.53569e17	2.02176
$506$	−1.28609e17	−0.340638
$507$	1.16025e16	0.0303390
$508$	3.59116e17	0.927088
$509$	−5.39326e17	−1.37463	−0.687315	−	0.726359i	$-0.741211\pi$
$509$	−5.39326e17	−1.37463	−0.687315	+	0.726359i	$0.741211\pi$
$510$	2.24920e17	0.566007
$511$	1.13493e17	0.281989
$512$	−2.26710e17	−0.556181
$513$	7.97843e16	0.193266
$514$	2.46812e17	0.590345
$515$	−7.05052e17	−1.66523
$516$	−4.50310e15	−0.0105024
$517$	6.83514e17	1.57420
$518$	3.48088e15	0.00791673
$519$	1.24713e17	0.280106
$520$	2.76074e17	0.612355
$521$	−1.85031e17	−0.405321	−0.202660	−	0.979249i	$-0.564959\pi$
$521$	−1.85031e17	−0.405321	−0.202660	+	0.979249i	$0.564959\pi$
$522$	−2.94453e17	−0.637027
$523$	5.78358e16	0.123577	0.0617883	−	0.998089i	$-0.480320\pi$
$523$	5.78358e16	0.123577	0.0617883	+	0.998089i	$0.480320\pi$
$524$	4.96181e17	1.04710
$525$	−8.53388e15	−0.0177873
$526$	−5.41983e17	−1.11578
$527$	4.18815e17	0.851634
$528$	3.28500e17	0.659803
$529$	−4.59270e17	−0.911183
$530$	1.22813e17	0.240687
$531$	2.24165e16	0.0433963
$532$	−5.66722e16	−0.108379
$533$	−7.79036e16	−0.147174
$534$	1.16765e17	0.217919
$535$	2.81420e16	0.0518867
$536$	−7.00144e16	−0.127531
$537$	−4.33741e17	−0.780544
$538$	1.21829e18	2.16604
$539$	5.02042e17	0.881886
$540$	6.62834e16	0.115039
$541$	−9.84842e17	−1.68882	−0.844412	−	0.535695i	$-0.820050\pi$
$541$	−9.84842e17	−1.68882	−0.844412	+	0.535695i	$0.820050\pi$
$542$	−8.92504e17	−1.51222
$543$	3.94219e17	0.659992
$544$	−4.41726e17	−0.730735
$545$	−2.14349e17	−0.350385
$546$	8.88717e16	0.143553
$547$	−5.30697e17	−0.847089	−0.423545	−	0.905875i	$-0.639214\pi$
$547$	−5.30697e17	−0.847089	−0.423545	+	0.905875i	$0.639214\pi$
$548$	−4.65538e17	−0.734313
$549$	1.22338e17	0.190696
$550$	1.17636e17	0.181210
$551$	1.01085e18	1.53886
$552$	−6.34187e16	−0.0954143
$553$	1.52957e17	0.227434
$554$	4.66666e17	0.685792
$555$	1.39764e16	0.0202997
$556$	4.28124e17	0.614587
$557$	2.55005e17	0.361818	0.180909	−	0.983500i	$-0.442096\pi$
$557$	2.55005e17	0.361818	0.180909	+	0.983500i	$0.442096\pi$
$558$	3.45666e17	0.484769
$559$	−2.42424e16	−0.0336046
$560$	1.90352e17	0.260817
$561$	2.85326e17	0.386440
$562$	−2.40201e17	−0.321580
$563$	2.29203e17	0.303331	0.151665	−	0.988432i	$-0.451536\pi$
$563$	2.29203e17	0.303331	0.151665	+	0.988432i	$0.451536\pi$
$564$	−4.20972e17	−0.550731
$565$	1.33950e18	1.73232
$566$	−9.09740e17	−1.16308
$567$	−1.70837e16	−0.0215920
$568$	−6.11201e17	−0.763695
$569$	3.00295e17	0.370953	0.185477	−	0.982649i	$-0.440617\pi$
$569$	3.00295e17	0.370953	0.185477	+	0.982649i	$0.440617\pi$
$570$	−6.37283e17	−0.778298
$571$	−2.35916e17	−0.284854	−0.142427	−	0.989805i	$-0.545491\pi$
$571$	−2.35916e17	−0.284854	−0.142427	+	0.989805i	$0.545491\pi$
$572$	−4.37419e17	−0.522184
$573$	−3.00985e17	−0.355255
$574$	−2.97912e16	−0.0347664
$575$	−4.09472e16	−0.0472480
$576$	−2.67349e14	−0.000305023 0
$577$	4.01859e17	0.453348	0.226674	−	0.973971i	$-0.427215\pi$
$577$	4.01859e17	0.453348	0.226674	+	0.973971i	$0.427215\pi$
$578$	5.21703e17	0.581959
$579$	−7.29470e17	−0.804631
$580$	8.39795e17	0.915991
$581$	8.12555e16	0.0876411
$582$	−1.22532e18	−1.30693
$583$	1.55797e17	0.164329
$584$	−7.71449e17	−0.804681
$585$	3.56836e17	0.368091
$586$	5.87176e17	0.599010
$587$	−3.28742e17	−0.331671	−0.165836	−	0.986153i	$-0.553032\pi$
$587$	−3.28742e17	−0.331671	−0.165836	+	0.986153i	$0.553032\pi$
$588$	−3.09205e17	−0.308527
$589$	−1.18666e18	−1.17105
$590$	−1.79053e17	−0.174761
$591$	−7.56715e17	−0.730489
$592$	−4.26609e16	−0.0407323
$593$	−3.60972e17	−0.340893	−0.170447	−	0.985367i	$-0.554521\pi$
$593$	−3.60972e17	−0.340893	−0.170447	+	0.985367i	$0.554521\pi$
$594$	2.35492e17	0.219970
$595$	1.65335e17	0.152758
$596$	8.40471e17	0.768107
$597$	2.20112e17	0.198981
$598$	4.26423e17	0.381315
$599$	−5.53752e17	−0.489825	−0.244912	−	0.969545i	$-0.578759\pi$
$599$	−5.53752e17	−0.489825	−0.244912	+	0.969545i	$0.578759\pi$
$600$	5.80077e16	0.0507577
$601$	3.16392e17	0.273868	0.136934	−	0.990580i	$-0.456275\pi$
$601$	3.16392e17	0.273868	0.136934	+	0.990580i	$0.456275\pi$
$602$	−9.27055e15	−0.00793831
$603$	−9.04962e16	−0.0766598
$604$	−8.67004e17	−0.726576
$605$	−2.07768e17	−0.172253
$606$	−1.64892e18	−1.35247
$607$	−1.18964e18	−0.965360	−0.482680	−	0.875797i	$-0.660337\pi$
$607$	−1.18964e18	−0.965360	−0.482680	+	0.875797i	$0.660337\pi$
$608$	1.25158e18	1.00481
$609$	−2.16447e17	−0.171925
$610$	−9.77186e17	−0.767951
$611$	−2.26630e18	−1.76218
$612$	−1.75731e17	−0.135196
$613$	5.22634e17	0.397836	0.198918	−	0.980016i	$-0.436257\pi$
$613$	5.22634e17	0.397836	0.198918	+	0.980016i	$0.436257\pi$
$614$	1.08654e18	0.818375
$615$	−1.19617e17	−0.0891464
$616$	1.33927e17	0.0987628
$617$	4.74752e16	0.0346428	0.0173214	−	0.999850i	$-0.494486\pi$
$617$	4.74752e16	0.0346428	0.0173214	+	0.999850i	$0.494486\pi$
$618$	1.54276e18	1.11397
$619$	−2.02115e18	−1.44414	−0.722070	−	0.691820i	$-0.756809\pi$
$619$	−2.02115e18	−1.44414	−0.722070	+	0.691820i	$0.756809\pi$
$620$	−9.85858e17	−0.697057
$621$	−8.19711e16	−0.0573542
$622$	3.11065e18	2.15384
$623$	8.58318e16	0.0588134
$624$	−1.08919e18	−0.738592
$625$	−1.68890e18	−1.13340
$626$	−2.69983e18	−1.79309
$627$	−8.08436e17	−0.531382
$628$	5.65262e16	0.0367716
$629$	−3.70541e16	−0.0238565
$630$	1.36458e17	0.0869531
$631$	3.30428e17	0.208394	0.104197	−	0.994557i	$-0.466773\pi$
$631$	3.30428e17	0.208394	0.104197	+	0.994557i	$0.466773\pi$
$632$	−1.03970e18	−0.649002
$633$	1.24363e18	0.768365
$634$	5.18721e17	0.317215
$635$	2.96848e18	1.79682
$636$	−9.59544e16	−0.0574902
$637$	−1.66460e18	−0.987195
$638$	2.98362e18	1.75150
$639$	−7.90001e17	−0.459062
$640$	−1.87015e18	−1.07574
$641$	1.91323e18	1.08941	0.544704	−	0.838629i	$-0.316642\pi$
$641$	1.91323e18	1.08941	0.544704	+	0.838629i	$0.316642\pi$
$642$	−6.15790e16	−0.0347100
$643$	2.29819e18	1.28237	0.641186	−	0.767386i	$-0.278443\pi$
$643$	2.29819e18	1.28237	0.641186	+	0.767386i	$0.278443\pi$
$644$	5.82255e16	0.0321629
$645$	−3.72229e16	−0.0203550
$646$	1.68956e18	0.914668
$647$	1.04365e18	0.559344	0.279672	−	0.960096i	$-0.409774\pi$
$647$	1.04365e18	0.559344	0.279672	+	0.960096i	$0.409774\pi$
$648$	1.16124e17	0.0616147
$649$	−2.27141e17	−0.119318
$650$	−3.90040e17	−0.202849
$651$	2.54093e17	0.130833
$652$	2.57127e17	0.131081
$653$	−2.93783e18	−1.48283	−0.741413	−	0.671049i	$-0.765844\pi$
$653$	−2.93783e18	−1.48283	−0.741413	+	0.671049i	$0.765844\pi$
$654$	4.69029e17	0.234393
$655$	4.10146e18	2.02941
$656$	3.65114e17	0.178877
$657$	−9.97128e17	−0.483700
$658$	−8.66657e17	−0.416274
$659$	3.86883e18	1.84003	0.920014	−	0.391886i	$-0.128177\pi$
$659$	3.86883e18	1.84003	0.920014	+	0.391886i	$0.128177\pi$
$660$	−6.71635e17	−0.316299
$661$	−3.25119e18	−1.51612	−0.758059	−	0.652186i	$-0.773852\pi$
$661$	−3.25119e18	−1.51612	−0.758059	+	0.652186i	$0.773852\pi$
$662$	2.48698e18	1.14840
$663$	−9.46042e17	−0.432586
$664$	−5.52321e17	−0.250091
$665$	−4.68455e17	−0.210052
$666$	−3.05824e16	−0.0135797
$667$	−1.03855e18	−0.456679
$668$	−1.33733e18	−0.582359
$669$	1.14639e17	0.0494382
$670$	7.22846e17	0.308716
$671$	−1.23962e18	−0.524317
$672$	−2.67993e17	−0.112259
$673$	−1.43947e18	−0.597179	−0.298590	−	0.954382i	$-0.596516\pi$
$673$	−1.43947e18	−0.597179	−0.298590	+	0.954382i	$0.596516\pi$
$674$	−3.68477e18	−1.51398
$675$	7.49771e16	0.0305108
$676$	7.24082e16	0.0291833
$677$	4.50455e18	1.79815	0.899073	−	0.437799i	$-0.144242\pi$
$677$	4.50455e18	1.79815	0.899073	+	0.437799i	$0.144242\pi$
$678$	−2.93103e18	−1.15885
$679$	−9.00714e17	−0.352723
$680$	−1.12383e18	−0.435907
$681$	−9.68969e17	−0.372266
$682$	−3.50256e18	−1.33287
$683$	−3.11602e18	−1.17453	−0.587267	−	0.809393i	$-0.699796\pi$
$683$	−3.11602e18	−1.17453	−0.587267	+	0.809393i	$0.699796\pi$
$684$	4.97911e17	0.185903
$685$	−3.84816e18	−1.42320
$686$	−1.29810e18	−0.475557
$687$	−2.54965e18	−0.925257
$688$	1.13618e17	0.0408434
$689$	−5.16569e17	−0.183952
$690$	6.54751e17	0.230971
$691$	−2.28134e18	−0.797227	−0.398613	−	0.917119i	$-0.630508\pi$
$691$	−2.28134e18	−0.797227	−0.398613	+	0.917119i	$0.630508\pi$
$692$	7.78295e17	0.269436
$693$	1.73106e17	0.0593670
$694$	2.91749e18	0.991228
$695$	3.53890e18	1.19115
$696$	1.47126e18	0.490603
$697$	3.17128e17	0.104766
$698$	−1.68470e18	−0.551394
$699$	−5.40859e17	−0.175381
$700$	−5.32575e16	−0.0171098
$701$	2.07987e18	0.662016	0.331008	−	0.943628i	$-0.392611\pi$
$701$	2.07987e18	0.662016	0.331008	+	0.943628i	$0.392611\pi$
$702$	−7.80810e17	−0.246238
$703$	1.04988e17	0.0328043
$704$	2.70899e15	0.000838657 0
$705$	−3.47978e18	−1.06739
$706$	−4.23438e18	−1.28694
$707$	−1.21209e18	−0.365014
$708$	1.39895e17	0.0417432
$709$	−4.44743e18	−1.31495	−0.657474	−	0.753477i	$-0.728375\pi$
$709$	−4.44743e18	−1.31495	−0.657474	+	0.753477i	$0.728375\pi$
$710$	6.31019e18	1.84869
$711$	−1.34385e18	−0.390120
$712$	−5.83428e17	−0.167829
$713$	1.21919e18	0.347527
$714$	−3.61777e17	−0.102189
$715$	−3.61573e18	−1.01206
$716$	−2.70685e18	−0.750810
$717$	−4.05921e18	−1.11575
$718$	−4.20286e18	−1.14482
$719$	−4.13508e18	−1.11621	−0.558105	−	0.829770i	$-0.688471\pi$
$719$	−4.13508e18	−1.11621	−0.558105	+	0.829770i	$0.688471\pi$
$720$	−1.67240e18	−0.447382
$721$	1.13405e18	0.300646
$722$	−4.03115e16	−0.0105910
$723$	9.13409e17	0.237830
$724$	2.46021e18	0.634851
$725$	9.49942e17	0.242940
$726$	4.54627e17	0.115230
$727$	2.82326e18	0.709214	0.354607	−	0.935016i	$-0.384615\pi$
$727$	2.82326e18	0.709214	0.354607	+	0.935016i	$0.384615\pi$
$728$	−4.44056e17	−0.110556
$729$	1.50095e17	0.0370370
$730$	7.96464e18	1.94790
$731$	9.86853e16	0.0239216
$732$	7.63478e17	0.183432
$733$	−1.09963e18	−0.261862	−0.130931	−	0.991391i	$-0.541797\pi$
$733$	−1.09963e18	−0.261862	−0.130931	+	0.991391i	$0.541797\pi$
$734$	−4.16694e18	−0.983543
$735$	−2.55590e18	−0.597966
$736$	−1.28588e18	−0.298191
$737$	9.16977e17	0.210775
$738$	2.61740e17	0.0596352
$739$	−3.16812e18	−0.715506	−0.357753	−	0.933816i	$-0.616457\pi$
$739$	−3.16812e18	−0.715506	−0.357753	+	0.933816i	$0.616457\pi$
$740$	8.72225e16	0.0195264
$741$	2.68050e18	0.594835
$742$	−1.97542e17	−0.0434543
$743$	−6.30790e18	−1.37549	−0.687745	−	0.725952i	$-0.741399\pi$
$743$	−6.30790e18	−1.37549	−0.687745	+	0.725952i	$0.741399\pi$
$744$	−1.72715e18	−0.373342
$745$	6.94738e18	1.48869
$746$	−5.79667e18	−1.23134
$747$	−7.13896e17	−0.150332
$748$	1.78064e18	0.371719
$749$	−4.52656e16	−0.00936777
$750$	3.17864e18	0.652144
$751$	1.38416e18	0.281531	0.140765	−	0.990043i	$-0.455044\pi$
$751$	1.38416e18	0.281531	0.140765	+	0.990043i	$0.455044\pi$
$752$	1.06216e19	2.14177
$753$	−3.76684e18	−0.753026
$754$	−9.89267e18	−1.96065
$755$	−7.16671e18	−1.40820
$756$	−1.06615e17	−0.0207695
$757$	1.50601e18	0.290873	0.145436	−	0.989368i	$-0.453541\pi$
$757$	1.50601e18	0.290873	0.145436	+	0.989368i	$0.453541\pi$
$758$	−3.90283e18	−0.747360
$759$	8.30594e17	0.157695
$760$	3.18425e18	0.599402
$761$	−5.30144e17	−0.0989450	−0.0494725	−	0.998775i	$-0.515754\pi$
$761$	−5.30144e17	−0.0989450	−0.0494725	+	0.998775i	$0.515754\pi$
$762$	−6.49547e18	−1.20200
$763$	3.44775e17	0.0632595
$764$	−1.87836e18	−0.341722
$765$	−1.45260e18	−0.262027
$766$	8.34866e18	1.49324
$767$	7.53121e17	0.133566
$768$	4.09518e18	0.720154
$769$	8.41617e18	1.46755	0.733776	−	0.679391i	$-0.237756\pi$
$769$	8.41617e18	1.46755	0.733776	+	0.679391i	$0.237756\pi$
$770$	−1.38270e18	−0.239077
$771$	−1.59398e18	−0.273294
$772$	−4.55242e18	−0.773980
$773$	−5.35077e18	−0.902090	−0.451045	−	0.892501i	$-0.648949\pi$
$773$	−5.35077e18	−0.902090	−0.451045	+	0.892501i	$0.648949\pi$
$774$	8.14493e16	0.0136167
$775$	−1.11516e18	−0.184874
$776$	6.12245e18	1.00652
$777$	−2.24806e16	−0.00366497
$778$	−3.71500e18	−0.600609
$779$	−8.98543e17	−0.144061
$780$	2.22691e18	0.354069
$781$	8.00489e18	1.26219
$782$	−1.73587e18	−0.271440
$783$	1.90166e18	0.294905
$784$	7.80154e18	1.19985
$785$	4.67249e17	0.0712682
$786$	−8.97460e18	−1.35759
$787$	1.03442e19	1.55189	0.775947	−	0.630798i	$-0.217272\pi$
$787$	1.03442e19	1.55189	0.775947	+	0.630798i	$0.217272\pi$
$788$	−4.72245e18	−0.702662
$789$	3.50028e18	0.516538
$790$	1.07341e19	1.57105
$791$	−2.15455e18	−0.312759
$792$	−1.17666e18	−0.169409
$793$	4.11017e18	0.586927
$794$	5.41353e17	0.0766739
$795$	−7.93164e17	−0.111424
$796$	1.37366e18	0.191401
$797$	2.65964e18	0.367573	0.183786	−	0.982966i	$-0.441165\pi$
$797$	2.65964e18	0.367573	0.183786	+	0.982966i	$0.441165\pi$
$798$	1.02505e18	0.140516
$799$	9.22559e18	1.25441
$800$	1.17617e18	0.158629
$801$	−7.54102e17	−0.100883
$802$	1.27632e19	1.69367
$803$	1.01037e19	1.32993
$804$	−5.64761e17	−0.0737396
$805$	4.81295e17	0.0623359
$806$	1.16133e19	1.49203
$807$	−7.86808e18	−1.00275
$808$	8.23900e18	1.04160
$809$	−6.86795e18	−0.861314	−0.430657	−	0.902516i	$-0.641718\pi$
$809$	−6.86795e18	−0.861314	−0.430657	+	0.902516i	$0.641718\pi$
$810$	−1.19889e18	−0.149152
$811$	3.89506e18	0.480705	0.240352	−	0.970686i	$-0.422737\pi$
$811$	3.89506e18	0.480705	0.240352	+	0.970686i	$0.422737\pi$
$812$	−1.35078e18	−0.165376
$813$	5.76405e18	0.700067
$814$	3.09884e17	0.0373371
$815$	2.12543e18	0.254052
$816$	4.43386e18	0.525770
$817$	−2.79613e17	−0.0328938
$818$	1.16128e19	1.35531
$819$	−5.73959e17	−0.0664562
$820$	−7.46495e17	−0.0857505
$821$	3.11330e18	0.354806	0.177403	−	0.984138i	$-0.443230\pi$
$821$	3.11330e18	0.354806	0.177403	+	0.984138i	$0.443230\pi$
$822$	8.42035e18	0.952058
$823$	−1.17761e19	−1.32100	−0.660501	−	0.750825i	$-0.729656\pi$
$823$	−1.17761e19	−1.32100	−0.660501	+	0.750825i	$0.729656\pi$
$824$	−7.70855e18	−0.857918
$825$	−7.59726e17	−0.0838892
$826$	2.88002e17	0.0315518
$827$	−6.06239e18	−0.658958	−0.329479	−	0.944163i	$-0.606873\pi$
$827$	−6.06239e18	−0.658958	−0.329479	+	0.944163i	$0.606873\pi$
$828$	−5.11558e17	−0.0551694
$829$	9.26464e18	0.991343	0.495672	−	0.868510i	$-0.334922\pi$
$829$	9.26464e18	0.991343	0.495672	+	0.868510i	$0.334922\pi$
$830$	5.70230e18	0.605400
$831$	−3.01386e18	−0.317480
$832$	−8.98207e15	−0.000938804 0
$833$	6.77621e18	0.702739
$834$	−7.74364e18	−0.796831
$835$	−1.10544e19	−1.12869
$836$	−5.04522e18	−0.511139
$837$	−2.23241e18	−0.224419
$838$	1.47696e19	1.47327
$839$	1.26271e19	1.24983	0.624917	−	0.780691i	$-0.285133\pi$
$839$	1.26271e19	1.24983	0.624917	+	0.780691i	$0.285133\pi$
$840$	−6.81825e17	−0.0669665
$841$	1.38330e19	1.34816
$842$	−2.20363e19	−2.13113
$843$	1.55129e18	0.148872
$844$	7.76115e18	0.739095
$845$	5.98530e17	0.0565610
$846$	7.61428e18	0.714039
$847$	3.34188e17	0.0310991
$848$	2.42103e18	0.223577
$849$	5.87537e18	0.538437
$850$	1.58777e18	0.144399
$851$	−1.07866e17	−0.00973514
$852$	−4.93017e18	−0.441575
$853$	1.35794e18	0.120702	0.0603508	−	0.998177i	$-0.480778\pi$
$853$	1.35794e18	0.120702	0.0603508	+	0.998177i	$0.480778\pi$
$854$	1.57177e18	0.138648
$855$	4.11576e18	0.360305
$856$	3.07685e17	0.0267317
$857$	1.32280e18	0.114056	0.0570280	−	0.998373i	$-0.481838\pi$
$857$	1.32280e18	0.114056	0.0570280	+	0.998373i	$0.481838\pi$
$858$	7.91177e18	0.677027
$859$	4.68816e18	0.398150	0.199075	−	0.979984i	$-0.436206\pi$
$859$	4.68816e18	0.398150	0.199075	+	0.979984i	$0.436206\pi$
$860$	−2.32298e17	−0.0195796
$861$	1.92400e17	0.0160948
$862$	7.10772e18	0.590111
$863$	1.90241e19	1.56759	0.783797	−	0.621017i	$-0.213280\pi$
$863$	1.90241e19	1.56759	0.783797	+	0.621017i	$0.213280\pi$
$864$	2.35453e18	0.192560
$865$	6.43343e18	0.522202
$866$	8.12595e18	0.654648
$867$	−3.36931e18	−0.269412
$868$	1.58572e18	0.125849
$869$	1.36169e19	1.07263
$870$	−1.51897e19	−1.18761
$871$	−3.04038e18	−0.235945
$872$	−2.34355e18	−0.180516
$873$	7.91350e18	0.605029
$874$	4.91839e18	0.373249
$875$	2.33656e18	0.176005
$876$	−6.22279e18	−0.465274
$877$	1.15848e19	0.859785	0.429893	−	0.902880i	$-0.358551\pi$
$877$	1.15848e19	0.859785	0.429893	+	0.902880i	$0.358551\pi$
$878$	−2.27527e18	−0.167617
$879$	−3.79215e18	−0.277305
$880$	1.69460e19	1.23007
$881$	−2.59103e19	−1.86693	−0.933465	−	0.358667i	$-0.883231\pi$
$881$	−2.59103e19	−1.86693	−0.933465	+	0.358667i	$0.883231\pi$
$882$	5.59270e18	0.400014
$883$	−3.41825e18	−0.242694	−0.121347	−	0.992610i	$-0.538721\pi$
$883$	−3.41825e18	−0.242694	−0.121347	+	0.992610i	$0.538721\pi$
$884$	−5.90398e18	−0.416107
$885$	1.15638e18	0.0809038
$886$	1.67961e19	1.16651
$887$	−5.83477e18	−0.402272	−0.201136	−	0.979563i	$-0.564463\pi$
$887$	−5.83477e18	−0.402272	−0.201136	+	0.979563i	$0.564463\pi$
$888$	1.52808e17	0.0104583
$889$	−4.77470e18	−0.324403
$890$	6.02345e18	0.406266
$891$	−1.52087e18	−0.101833
$892$	7.15429e17	0.0475549
$893$	−2.61396e19	−1.72490
$894$	−1.52019e19	−0.995874
$895$	−2.23750e19	−1.45517
$896$	3.00808e18	0.194217
$897$	−2.75397e18	−0.176526
$898$	−1.92547e19	−1.22530
$899$	−2.82841e19	−1.78692
$900$	4.67911e17	0.0293486
$901$	2.10284e18	0.130947
$902$	−2.65215e18	−0.163966
$903$	5.98719e16	0.00367496
$904$	1.46452e19	0.892484
$905$	2.03362e19	1.23042
$906$	1.56818e19	0.942027
$907$	8.30355e18	0.495241	0.247620	−	0.968857i	$-0.420351\pi$
$907$	8.30355e18	0.495241	0.247620	+	0.968857i	$0.420351\pi$
$908$	−6.04706e18	−0.358085
$909$	1.06492e19	0.626113
$910$	4.58455e18	0.267625
$911$	4.71643e18	0.273366	0.136683	−	0.990615i	$-0.456356\pi$
$911$	4.71643e18	0.273366	0.136683	+	0.990615i	$0.456356\pi$
$912$	−1.25628e19	−0.722969
$913$	7.23374e18	0.413336
$914$	1.85349e19	1.05158
$915$	6.31095e18	0.355515
$916$	−1.59117e19	−0.890010
$917$	−6.59707e18	−0.366396
$918$	3.17850e18	0.175285
$919$	−1.67823e19	−0.918968	−0.459484	−	0.888186i	$-0.651966\pi$
$919$	−1.67823e19	−0.918968	−0.459484	+	0.888186i	$0.651966\pi$
$920$	−3.27152e18	−0.177881
$921$	−7.01721e18	−0.378858
$922$	2.78002e19	1.49038
$923$	−2.65415e19	−1.41291
$924$	1.08030e18	0.0571055
$925$	9.86626e16	0.00517882
$926$	2.14303e19	1.11701
$927$	−9.96359e18	−0.515701
$928$	2.98314e19	1.53324
$929$	−4.47502e18	−0.228398	−0.114199	−	0.993458i	$-0.536430\pi$
$929$	−4.47502e18	−0.228398	−0.114199	+	0.993458i	$0.536430\pi$
$930$	1.78316e19	0.903755
$931$	−1.91996e19	−0.966314
$932$	−3.37535e18	−0.168700
$933$	−2.00895e19	−0.997100
$934$	4.26545e19	2.10238
$935$	1.47188e19	0.720441
$936$	3.90139e18	0.189639
$937$	2.18745e19	1.05592	0.527959	−	0.849270i	$-0.322957\pi$
$937$	2.18745e19	1.05592	0.527959	+	0.849270i	$0.322957\pi$
$938$	−1.16268e18	−0.0557365
$939$	1.74363e19	0.830095
$940$	−2.17163e19	−1.02673
$941$	3.27197e19	1.53630	0.768151	−	0.640269i	$-0.221177\pi$
$941$	3.27197e19	1.53630	0.768151	+	0.640269i	$0.221177\pi$
$942$	−1.02241e18	−0.0476754
$943$	9.23172e17	0.0427520
$944$	−3.52969e18	−0.162337
$945$	−8.81284e17	−0.0402540
$946$	−8.25307e17	−0.0374389
$947$	−3.33673e19	−1.50330	−0.751652	−	0.659560i	$-0.770743\pi$
$947$	−3.33673e19	−1.50330	−0.751652	+	0.659560i	$0.770743\pi$
$948$	−8.38658e18	−0.375259
$949$	−3.35003e19	−1.48874
$950$	−4.49874e18	−0.198558
$951$	−3.35005e18	−0.146851
$952$	1.80765e18	0.0787000
$953$	1.58341e18	0.0684682	0.0342341	−	0.999414i	$-0.489101\pi$
$953$	1.58341e18	0.0684682	0.0342341	+	0.999414i	$0.489101\pi$
$954$	1.73556e18	0.0745377
$955$	−1.55267e19	−0.662302
$956$	−2.53324e19	−1.07325
$957$	−1.92691e19	−0.810838
$958$	2.33565e19	0.976183
$959$	6.18965e18	0.256948
$960$	−1.37915e16	−0.000568654 0
$961$	8.78595e18	0.359821
$962$	−1.02747e18	−0.0417957
$963$	3.97695e17	0.0160686
$964$	5.70033e18	0.228770
$965$	−3.76305e19	−1.50008
$966$	−1.05315e18	−0.0417001
$967$	1.74059e19	0.684579	0.342290	−	0.939595i	$-0.388798\pi$
$967$	1.74059e19	0.684579	0.342290	+	0.939595i	$0.388798\pi$
$968$	−2.27159e18	−0.0887441
$969$	−1.09117e19	−0.423436
$970$	−6.32097e19	−2.43651
$971$	4.41500e18	0.169046	0.0845231	−	0.996422i	$-0.473063\pi$
$971$	4.41500e18	0.169046	0.0845231	+	0.996422i	$0.473063\pi$
$972$	9.36698e17	0.0356261
$973$	−5.69221e18	−0.215054
$974$	−3.19433e19	−1.19880
$975$	2.51899e18	0.0939067
$976$	−1.92633e19	−0.713357
$977$	−3.40810e19	−1.25371	−0.626856	−	0.779135i	$-0.715658\pi$
$977$	−3.40810e19	−1.25371	−0.626856	+	0.779135i	$0.715658\pi$
$978$	−4.65075e18	−0.169950
$979$	7.64115e18	0.277377
$980$	−1.59507e19	−0.575187
$981$	−3.02912e18	−0.108510
$982$	−5.82567e19	−2.07310
$983$	−1.48223e19	−0.523983	−0.261992	−	0.965070i	$-0.584379\pi$
$983$	−1.48223e19	−0.523983	−0.261992	+	0.965070i	$0.584379\pi$
$984$	−1.30781e18	−0.0459278
$985$	−3.90360e19	−1.36185
$986$	4.02709e19	1.39570
$987$	5.59712e18	0.192710
$988$	1.67282e19	0.572176
$989$	2.87277e17	0.00976168
$990$	1.21481e19	0.410091
$991$	3.49904e18	0.117347	0.0586733	−	0.998277i	$-0.481313\pi$
$991$	3.49904e18	0.117347	0.0586733	+	0.998277i	$0.481313\pi$
$992$	−3.50199e19	−1.16678
$993$	−1.60616e19	−0.531642
$994$	−1.01498e19	−0.333767
$995$	1.13547e19	0.370960
$996$	−4.45522e18	−0.144605
$997$	8.94587e18	0.288472	0.144236	−	0.989543i	$-0.453928\pi$
$997$	8.94587e18	0.288472	0.144236	+	0.989543i	$0.453928\pi$
$998$	5.02385e19	1.60949
$999$	1.97510e17	0.00628656

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.7	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.7	✓	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-112.878 q^{2} +729.000 q^{3} +4549.48 q^{4} +37606.3 q^{5} -82288.2 q^{6} -60488.5 q^{7} +411161. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-112.878 q^{2} +729.000 q^{3} +4549.48 q^{4} +37606.3 q^{5} -82288.2 q^{6} -60488.5 q^{7} +411161. q^{8} +531441. q^{9} -4.24493e6 q^{10} -5.38497e6 q^{11} +3.31657e6 q^{12} +1.78547e7 q^{13} +6.82784e6 q^{14} +2.74150e7 q^{15} -8.36804e7 q^{16} -7.26826e7 q^{17} -5.99881e7 q^{18} +2.05937e8 q^{19} +1.71089e8 q^{20} -4.40961e7 q^{21} +6.07846e8 q^{22} -2.11582e8 q^{23} +2.99736e8 q^{24} +1.93529e8 q^{25} -2.01541e9 q^{26} +3.87420e8 q^{27} -2.75192e8 q^{28} +4.90852e9 q^{29} -3.09455e9 q^{30} -5.76225e9 q^{31} +6.07747e9 q^{32} -3.92564e9 q^{33} +8.20427e9 q^{34} -2.27475e9 q^{35} +2.41778e9 q^{36} +5.09808e8 q^{37} -2.32458e10 q^{38} +1.30161e10 q^{39} +1.54622e10 q^{40} -4.36319e9 q^{41} +4.97749e9 q^{42} -1.35776e9 q^{43} -2.44988e10 q^{44} +1.99855e10 q^{45} +2.38830e10 q^{46} -1.26930e11 q^{47} -6.10030e10 q^{48} -9.32301e10 q^{49} -2.18452e10 q^{50} -5.29856e10 q^{51} +8.12297e10 q^{52} -2.89318e10 q^{53} -4.37313e10 q^{54} -2.02509e11 q^{55} -2.48705e10 q^{56} +1.50128e11 q^{57} -5.54065e11 q^{58} +4.21805e10 q^{59} +1.24724e11 q^{60} +2.30201e11 q^{61} +6.50432e11 q^{62} -3.21461e10 q^{63} -5.03064e8 q^{64} +6.71449e11 q^{65} +4.43119e11 q^{66} -1.70285e11 q^{67} -3.30668e11 q^{68} -1.54243e11 q^{69} +2.56769e11 q^{70} -1.48653e12 q^{71} +2.18508e11 q^{72} -1.87627e12 q^{73} -5.75462e10 q^{74} +1.41083e11 q^{75} +9.36907e11 q^{76} +3.25729e11 q^{77} -1.46923e12 q^{78} -2.52869e12 q^{79} -3.14691e12 q^{80} +2.82430e11 q^{81} +4.92509e11 q^{82} -1.34332e12 q^{83} -2.00615e11 q^{84} -2.73332e12 q^{85} +1.53261e11 q^{86} +3.57831e12 q^{87} -2.21409e12 q^{88} -1.41898e12 q^{89} -2.25593e12 q^{90} -1.08001e12 q^{91} -9.62587e11 q^{92} -4.20068e12 q^{93} +1.43276e13 q^{94} +7.74453e12 q^{95} +4.43047e12 q^{96} +1.48907e13 q^{97} +1.05236e13 q^{98} -2.86179e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * q^99

Introduction

L-functions

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