LMFDB - Embedded newform 177.14.a.a.1.28

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			1.28
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)

$f(q)$	$=$	$q+156.054 q^{2} +729.000 q^{3} +16160.8 q^{4} -52181.9 q^{5} +113763. q^{6} -121915. q^{7} +1.24356e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q+156.054 q^{2} +729.000 q^{3} +16160.8 q^{4} -52181.9 q^{5} +113763. q^{6} -121915. q^{7} +1.24356e6 q^{8} +531441. q^{9} -8.14319e6 q^{10} -5.92270e6 q^{11} +1.17812e7 q^{12} +3.41809e7 q^{13} -1.90252e7 q^{14} -3.80406e7 q^{15} +6.16729e7 q^{16} +1.67683e8 q^{17} +8.29334e7 q^{18} -1.20688e8 q^{19} -8.43301e8 q^{20} -8.88758e7 q^{21} -9.24260e8 q^{22} -8.89086e8 q^{23} +9.06555e8 q^{24} +1.50225e9 q^{25} +5.33406e9 q^{26} +3.87420e8 q^{27} -1.97024e9 q^{28} -1.81736e9 q^{29} -5.93639e9 q^{30} +6.89901e8 q^{31} -5.62939e8 q^{32} -4.31765e9 q^{33} +2.61675e10 q^{34} +6.36174e9 q^{35} +8.58850e9 q^{36} +1.67592e9 q^{37} -1.88338e10 q^{38} +2.49179e10 q^{39} -6.48913e10 q^{40} -3.57412e10 q^{41} -1.38694e10 q^{42} -5.31966e10 q^{43} -9.57155e10 q^{44} -2.77316e10 q^{45} -1.38745e11 q^{46} -5.93504e10 q^{47} +4.49596e10 q^{48} -8.20258e10 q^{49} +2.34432e11 q^{50} +1.22241e11 q^{51} +5.52390e11 q^{52} -2.17602e11 q^{53} +6.04584e10 q^{54} +3.09058e11 q^{55} -1.51608e11 q^{56} -8.79815e10 q^{57} -2.83606e11 q^{58} +4.21805e10 q^{59} -6.14767e11 q^{60} +6.03477e11 q^{61} +1.07662e11 q^{62} -6.47904e10 q^{63} -5.93073e11 q^{64} -1.78363e12 q^{65} -6.73786e11 q^{66} -1.22806e12 q^{67} +2.70988e12 q^{68} -6.48144e11 q^{69} +9.92774e11 q^{70} +4.34060e11 q^{71} +6.60878e11 q^{72} -1.83697e12 q^{73} +2.61533e11 q^{74} +1.09514e12 q^{75} -1.95041e12 q^{76} +7.22064e11 q^{77} +3.88853e12 q^{78} -5.33375e11 q^{79} -3.21821e12 q^{80} +2.82430e11 q^{81} -5.57755e12 q^{82} +1.78855e12 q^{83} -1.43630e12 q^{84} -8.75000e12 q^{85} -8.30153e12 q^{86} -1.32485e12 q^{87} -7.36523e12 q^{88} -7.18317e12 q^{89} -4.32763e12 q^{90} -4.16715e12 q^{91} -1.43683e13 q^{92} +5.02938e11 q^{93} -9.26186e12 q^{94} +6.29773e12 q^{95} -4.10382e11 q^{96} +5.89048e12 q^{97} -1.28004e13 q^{98} -3.14757e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	156.054	1.72417	0.862084	−	0.506766i	$-0.169159\pi$
$2$	156.054	1.72417	0.862084	+	0.506766i	$0.169159\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	16160.8	1.97275
$5$	−52181.9	−1.49353	−0.746767	−	0.665085i	$-0.768395\pi$
$5$	−52181.9	−1.49353	−0.746767	+	0.665085i	$0.768395\pi$
$6$	113763.	0.995448
$7$	−121915.	−0.391668	−0.195834	−	0.980637i	$-0.562741\pi$
$7$	−121915.	−0.391668	−0.195834	+	0.980637i	$0.562741\pi$
$8$	1.24356e6	1.67719
$9$	531441.	0.333333
$10$	−8.14319e6	−2.57510
$11$	−5.92270e6	−1.00802	−0.504008	−	0.863699i	$-0.668142\pi$
$11$	−5.92270e6	−1.00802	−0.504008	+	0.863699i	$0.668142\pi$
$12$	1.17812e7	1.13897
$13$	3.41809e7	1.96405	0.982023	−	0.188761i	$-0.0604470\pi$
$13$	3.41809e7	1.96405	0.982023	+	0.188761i	$0.0604470\pi$
$14$	−1.90252e7	−0.675302
$15$	−3.80406e7	−0.862293
$16$	6.16729e7	0.918998
$17$	1.67683e8	1.68488	0.842442	−	0.538788i	$-0.181117\pi$
$17$	1.67683e8	1.68488	0.842442	+	0.538788i	$0.181117\pi$
$18$	8.29334e7	0.574722
$19$	−1.20688e8	−0.588526	−0.294263	−	0.955725i	$-0.595074\pi$
$19$	−1.20688e8	−0.588526	−0.294263	+	0.955725i	$0.595074\pi$
$20$	−8.43301e8	−2.94637
$21$	−8.88758e7	−0.226130
$22$	−9.24260e8	−1.73799
$23$	−8.89086e8	−1.25231	−0.626156	−	0.779698i	$-0.715373\pi$
$23$	−8.89086e8	−1.25231	−0.626156	+	0.779698i	$0.715373\pi$
$24$	9.06555e8	0.968324
$25$	1.50225e9	1.23065
$26$	5.33406e9	3.38634
$27$	3.87420e8	0.192450
$28$	−1.97024e9	−0.772665
$29$	−1.81736e9	−0.567353	−0.283677	−	0.958920i	$-0.591554\pi$
$29$	−1.81736e9	−0.567353	−0.283677	+	0.958920i	$0.591554\pi$
$30$	−5.93639e9	−1.48674
$31$	6.89901e8	0.139616	0.0698081	−	0.997560i	$-0.477761\pi$
$31$	6.89901e8	0.139616	0.0698081	+	0.997560i	$0.477761\pi$
$32$	−5.62939e8	−0.0926801
$33$	−4.31765e9	−0.581978
$34$	2.61675e10	2.90502
$35$	6.36174e9	0.584970
$36$	8.58850e9	0.657584
$37$	1.67592e9	0.107384	0.0536922	−	0.998558i	$-0.482901\pi$
$37$	1.67592e9	0.107384	0.0536922	+	0.998558i	$0.482901\pi$
$38$	−1.88338e10	−1.01472
$39$	2.49179e10	1.13394
$40$	−6.48913e10	−2.50494
$41$	−3.57412e10	−1.17510	−0.587549	−	0.809189i	$-0.699907\pi$
$41$	−3.57412e10	−1.17510	−0.587549	+	0.809189i	$0.699907\pi$
$42$	−1.38694e10	−0.389886
$43$	−5.31966e10	−1.28333	−0.641666	−	0.766984i	$-0.721756\pi$
$43$	−5.31966e10	−1.28333	−0.641666	+	0.766984i	$0.721756\pi$
$44$	−9.57155e10	−1.98857
$45$	−2.77316e10	−0.497845
$46$	−1.38745e11	−2.15920
$47$	−5.93504e10	−0.803133	−0.401567	−	0.915830i	$-0.631534\pi$
$47$	−5.93504e10	−0.803133	−0.401567	+	0.915830i	$0.631534\pi$
$48$	4.49596e10	0.530584
$49$	−8.20258e10	−0.846596
$50$	2.34432e11	2.12184
$51$	1.22241e11	0.972768
$52$	5.52390e11	3.87458
$53$	−2.17602e11	−1.34856	−0.674278	−	0.738477i	$-0.735545\pi$
$53$	−2.17602e11	−1.34856	−0.674278	+	0.738477i	$0.735545\pi$
$54$	6.04584e10	0.331816
$55$	3.09058e11	1.50551
$56$	−1.51608e11	−0.656901
$57$	−8.79815e10	−0.339785
$58$	−2.83606e11	−0.978212
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−6.14767e11	−1.70109
$61$	6.03477e11	1.49974	0.749871	−	0.661584i	$-0.230116\pi$
$61$	6.03477e11	1.49974	0.749871	+	0.661584i	$0.230116\pi$
$62$	1.07662e11	0.240722
$63$	−6.47904e10	−0.130556
$64$	−5.93073e11	−1.07879
$65$	−1.78363e12	−2.93337
$66$	−6.73786e11	−1.00343
$67$	−1.22806e12	−1.65857	−0.829284	−	0.558827i	$-0.811252\pi$
$67$	−1.22806e12	−1.65857	−0.829284	+	0.558827i	$0.811252\pi$
$68$	2.70988e12	3.32386
$69$	−6.48144e11	−0.723023
$70$	9.92774e11	1.00859
$71$	4.34060e11	0.402134	0.201067	−	0.979577i	$-0.435559\pi$
$71$	4.34060e11	0.402134	0.201067	+	0.979577i	$0.435559\pi$
$72$	6.60878e11	0.559062
$73$	−1.83697e12	−1.42071	−0.710353	−	0.703846i	$-0.751465\pi$
$73$	−1.83697e12	−1.42071	−0.710353	+	0.703846i	$0.751465\pi$
$74$	2.61533e11	0.185149
$75$	1.09514e12	0.710513
$76$	−1.95041e12	−1.16102
$77$	7.22064e11	0.394808
$78$	3.88853e12	1.95511
$79$	−5.33375e11	−0.246863	−0.123432	−	0.992353i	$-0.539390\pi$
$79$	−5.33375e11	−0.246863	−0.123432	+	0.992353i	$0.539390\pi$
$80$	−3.21821e12	−1.37256
$81$	2.82430e11	0.111111
$82$	−5.57755e12	−2.02606
$83$	1.78855e12	0.600472	0.300236	−	0.953865i	$-0.402935\pi$
$83$	1.78855e12	0.600472	0.300236	+	0.953865i	$0.402935\pi$
$84$	−1.43630e12	−0.446098
$85$	−8.75000e12	−2.51643
$86$	−8.30153e12	−2.21268
$87$	−1.32485e12	−0.327562
$88$	−7.36523e12	−1.69063
$89$	−7.18317e12	−1.53208	−0.766039	−	0.642794i	$-0.777775\pi$
$89$	−7.18317e12	−1.53208	−0.766039	+	0.642794i	$0.777775\pi$
$90$	−4.32763e12	−0.858368
$91$	−4.16715e12	−0.769255
$92$	−1.43683e13	−2.47050
$93$	5.02938e11	0.0806074
$94$	−9.26186e12	−1.38474
$95$	6.29773e12	0.878983
$96$	−4.10382e11	−0.0535089
$97$	5.89048e12	0.718017	0.359008	−	0.933334i	$-0.383115\pi$
$97$	5.89048e12	0.718017	0.359008	+	0.933334i	$0.383115\pi$
$98$	−1.28004e13	−1.45967
$99$	−3.14757e12	−0.336005
$100$	2.42776e13	2.42776
$101$	1.73063e13	1.62224	0.811122	−	0.584877i	$-0.198857\pi$
$101$	1.73063e13	1.62224	0.811122	+	0.584877i	$0.198857\pi$
$102$	1.90761e13	1.67721
$103$	−6.16348e12	−0.508609	−0.254305	−	0.967124i	$-0.581847\pi$
$103$	−6.16348e12	−0.508609	−0.254305	+	0.967124i	$0.581847\pi$
$104$	4.25060e13	3.29407
$105$	4.63771e12	0.337733
$106$	−3.39576e13	−2.32514
$107$	−2.17318e13	−1.39992	−0.699958	−	0.714184i	$-0.746798\pi$
$107$	−2.17318e13	−1.39992	−0.699958	+	0.714184i	$0.746798\pi$
$108$	6.26102e12	0.379656
$109$	−1.44799e13	−0.826978	−0.413489	−	0.910509i	$-0.635690\pi$
$109$	−1.44799e13	−0.826978	−0.413489	+	0.910509i	$0.635690\pi$
$110$	4.82297e13	2.59575
$111$	1.22174e12	0.0619984
$112$	−7.51883e12	−0.359943
$113$	−3.26791e12	−0.147659	−0.0738295	−	0.997271i	$-0.523522\pi$
$113$	−3.26791e12	−0.147659	−0.0738295	+	0.997271i	$0.523522\pi$
$114$	−1.37298e13	−0.585847
$115$	4.63942e13	1.87037
$116$	−2.93699e13	−1.11925
$117$	1.81651e13	0.654682
$118$	6.58243e12	0.224467
$119$	−2.04430e13	−0.659916
$120$	−4.73058e13	−1.44623
$121$	5.55693e11	0.0160965
$122$	9.41748e13	2.58581
$123$	−2.60553e13	−0.678443
$124$	1.11493e13	0.275428
$125$	−1.46918e13	−0.344477
$126$	−1.01108e13	−0.225101
$127$	4.17174e13	0.882253	0.441126	−	0.897445i	$-0.354579\pi$
$127$	4.17174e13	0.882253	0.441126	+	0.897445i	$0.354579\pi$
$128$	−8.79398e13	−1.76734
$129$	−3.87803e13	−0.740932
$130$	−2.78342e14	−5.05762
$131$	2.71279e13	0.468978	0.234489	−	0.972119i	$-0.424658\pi$
$131$	2.71279e13	0.468978	0.234489	+	0.972119i	$0.424658\pi$
$132$	−6.97766e13	−1.14810
$133$	1.47136e13	0.230507
$134$	−1.91643e14	−2.85965
$135$	−2.02164e13	−0.287431
$136$	2.08523e14	2.82586
$137$	−1.24745e13	−0.161191	−0.0805953	−	0.996747i	$-0.525682\pi$
$137$	−1.24745e13	−0.161191	−0.0805953	+	0.996747i	$0.525682\pi$
$138$	−1.01145e14	−1.24661
$139$	1.11015e14	1.30553	0.652763	−	0.757563i	$-0.273610\pi$
$139$	1.11015e14	1.30553	0.652763	+	0.757563i	$0.273610\pi$
$140$	1.02811e14	1.15400
$141$	−4.32665e13	−0.463689
$142$	6.77368e13	0.693346
$143$	−2.02443e14	−1.97979
$144$	3.27755e13	0.306333
$145$	9.48333e13	0.847362
$146$	−2.86667e14	−2.44953
$147$	−5.97968e13	−0.488782
$148$	2.70841e13	0.211843
$149$	−2.22205e14	−1.66358	−0.831789	−	0.555092i	$-0.812683\pi$
$149$	−2.22205e14	−1.66358	−0.831789	+	0.555092i	$0.812683\pi$
$150$	1.70901e14	1.22504
$151$	1.61844e14	1.11108	0.555541	−	0.831489i	$-0.312511\pi$
$151$	1.61844e14	1.11108	0.555541	+	0.831489i	$0.312511\pi$
$152$	−1.50083e14	−0.987067
$153$	8.91134e13	0.561628
$154$	1.12681e14	0.680715
$155$	−3.60004e13	−0.208522
$156$	4.02692e14	2.23699
$157$	3.59352e14	1.91501	0.957507	−	0.288409i	$-0.0931262\pi$
$157$	3.59352e14	1.91501	0.957507	+	0.288409i	$0.0931262\pi$
$158$	−8.32352e13	−0.425634
$159$	−1.58632e14	−0.778589
$160$	2.93752e13	0.138421
$161$	1.08393e14	0.490491
$162$	4.40742e13	0.191574
$163$	−3.60727e14	−1.50646	−0.753232	−	0.657755i	$-0.771506\pi$
$163$	−3.60727e14	−1.50646	−0.753232	+	0.657755i	$0.771506\pi$
$164$	−5.77605e14	−2.31818
$165$	2.25303e14	0.869205
$166$	2.79110e14	1.03531
$167$	−2.59242e13	−0.0924800	−0.0462400	−	0.998930i	$-0.514724\pi$
$167$	−2.59242e13	−0.0924800	−0.0462400	+	0.998930i	$0.514724\pi$
$168$	−1.10522e14	−0.379262
$169$	8.65459e14	2.85748
$170$	−1.36547e15	−4.33875
$171$	−6.41385e13	−0.196175
$172$	−8.59699e14	−2.53170
$173$	−2.28633e14	−0.648394	−0.324197	−	0.945990i	$-0.605094\pi$
$173$	−2.28633e14	−0.648394	−0.324197	+	0.945990i	$0.605094\pi$
$174$	−2.06748e14	−0.564771
$175$	−1.83147e14	−0.482005
$176$	−3.65270e14	−0.926365
$177$	3.07496e13	0.0751646
$178$	−1.12096e15	−2.64156
$179$	3.39793e14	0.772093	0.386046	−	0.922479i	$-0.373840\pi$
$179$	3.39793e14	0.772093	0.386046	+	0.922479i	$0.373840\pi$
$180$	−4.48165e14	−0.982124
$181$	6.32373e14	1.33679	0.668394	−	0.743807i	$-0.266982\pi$
$181$	6.32373e14	1.33679	0.668394	+	0.743807i	$0.266982\pi$
$182$	−6.50300e14	−1.32632
$183$	4.39934e14	0.865876
$184$	−1.10563e15	−2.10036
$185$	−8.74526e13	−0.160382
$186$	7.84853e13	0.138981
$187$	−9.93134e14	−1.69839
$188$	−9.59149e14	−1.58438
$189$	−4.72322e13	−0.0753766
$190$	9.82785e14	1.51551
$191$	1.01475e15	1.51232	0.756160	−	0.654387i	$-0.227073\pi$
$191$	1.01475e15	1.51232	0.756160	+	0.654387i	$0.227073\pi$
$192$	−4.32351e14	−0.622842
$193$	2.51827e14	0.350736	0.175368	−	0.984503i	$-0.443889\pi$
$193$	2.51827e14	0.350736	0.175368	+	0.984503i	$0.443889\pi$
$194$	9.19232e14	1.23798
$195$	−1.30026e15	−1.69358
$196$	−1.32560e15	−1.67012
$197$	8.74579e13	0.106603	0.0533014	−	0.998578i	$-0.483026\pi$
$197$	8.74579e13	0.106603	0.0533014	+	0.998578i	$0.483026\pi$
$198$	−4.91190e14	−0.579329
$199$	4.96245e14	0.566436	0.283218	−	0.959055i	$-0.408598\pi$
$199$	4.96245e14	0.566436	0.283218	+	0.959055i	$0.408598\pi$
$200$	1.86814e15	2.06402
$201$	−8.95256e14	−0.957575
$202$	2.70072e15	2.79702
$203$	2.21563e14	0.222214
$204$	1.97550e15	1.91903
$205$	1.86504e15	1.75505
$206$	−9.61835e14	−0.876927
$207$	−4.72497e14	−0.417438
$208$	2.10804e15	1.80496
$209$	7.14799e14	0.593243
$210$	7.23732e14	0.582308
$211$	−8.21832e14	−0.641131	−0.320566	−	0.947226i	$-0.603873\pi$
$211$	−8.21832e14	−0.641131	−0.320566	+	0.947226i	$0.603873\pi$
$212$	−3.51661e15	−2.66037
$213$	3.16430e14	0.232172
$214$	−3.39133e15	−2.41369
$215$	2.77590e15	1.91670
$216$	4.81780e14	0.322775
$217$	−8.41090e13	−0.0546832
$218$	−2.25965e15	−1.42585
$219$	−1.33915e15	−0.820245
$220$	4.99462e15	2.96999
$221$	5.73154e15	3.30919
$222$	1.90658e14	0.106896
$223$	−1.83322e14	−0.0998238	−0.0499119	−	0.998754i	$-0.515894\pi$
$223$	−1.83322e14	−0.0998238	−0.0499119	+	0.998754i	$0.515894\pi$
$224$	6.86305e13	0.0362999
$225$	7.98359e14	0.410215
$226$	−5.09969e14	−0.254589
$227$	−3.16679e15	−1.53621	−0.768106	−	0.640323i	$-0.778800\pi$
$227$	−3.16679e15	−1.53621	−0.768106	+	0.640323i	$0.778800\pi$
$228$	−1.42185e15	−0.670312
$229$	3.31038e15	1.51687	0.758434	−	0.651750i	$-0.225965\pi$
$229$	3.31038e15	1.51687	0.758434	+	0.651750i	$0.225965\pi$
$230$	7.24000e15	3.22483
$231$	5.26385e14	0.227943
$232$	−2.25999e15	−0.951557
$233$	−1.14630e15	−0.469337	−0.234668	−	0.972075i	$-0.575400\pi$
$233$	−1.14630e15	−0.469337	−0.234668	+	0.972075i	$0.575400\pi$
$234$	2.83474e15	1.12878
$235$	3.09702e15	1.19951
$236$	6.81671e14	0.256830
$237$	−3.88830e14	−0.142527
$238$	−3.19020e15	−1.13780
$239$	−2.47854e15	−0.860220	−0.430110	−	0.902776i	$-0.641525\pi$
$239$	−2.47854e15	−0.860220	−0.430110	+	0.902776i	$0.641525\pi$
$240$	−2.34608e15	−0.792446
$241$	−5.39736e14	−0.177448	−0.0887239	−	0.996056i	$-0.528279\pi$
$241$	−5.39736e14	−0.177448	−0.0887239	+	0.996056i	$0.528279\pi$
$242$	8.67180e13	0.0277530
$243$	2.05891e14	0.0641500
$244$	9.75266e15	2.95862
$245$	4.28027e15	1.26442
$246$	−4.06603e15	−1.16975
$247$	−4.12522e15	−1.15589
$248$	8.57932e14	0.234162
$249$	1.30385e15	0.346683
$250$	−2.29271e15	−0.593936
$251$	3.22018e15	0.812832	0.406416	−	0.913688i	$-0.366778\pi$
$251$	3.22018e15	0.812832	0.406416	+	0.913688i	$0.366778\pi$
$252$	−1.04706e15	−0.257555
$253$	5.26579e15	1.26235
$254$	6.51016e15	1.52115
$255$	−6.37875e15	−1.45286
$256$	−8.86488e15	−1.96840
$257$	2.12569e15	0.460188	0.230094	−	0.973168i	$-0.426097\pi$
$257$	2.12569e15	0.460188	0.230094	+	0.973168i	$0.426097\pi$
$258$	−6.05182e15	−1.27749
$259$	−2.04319e14	−0.0420591
$260$	−2.88248e16	−5.78681
$261$	−9.65819e14	−0.189118
$262$	4.23341e15	0.808597
$263$	−5.97627e15	−1.11357	−0.556785	−	0.830657i	$-0.687965\pi$
$263$	−5.97627e15	−1.11357	−0.556785	+	0.830657i	$0.687965\pi$
$264$	−5.36925e15	−0.976087
$265$	1.13549e16	2.01412
$266$	2.29612e15	0.397432
$267$	−5.23653e15	−0.884546
$268$	−1.98464e16	−3.27195
$269$	−7.57554e15	−1.21906	−0.609528	−	0.792764i	$-0.708641\pi$
$269$	−7.57554e15	−1.21906	−0.609528	+	0.792764i	$0.708641\pi$
$270$	−3.15484e15	−0.495579
$271$	1.99676e15	0.306214	0.153107	−	0.988210i	$-0.451072\pi$
$271$	1.99676e15	0.306214	0.153107	+	0.988210i	$0.451072\pi$
$272$	1.03415e16	1.54841
$273$	−3.03785e15	−0.444130
$274$	−1.94669e15	−0.277920
$275$	−8.89740e15	−1.24051
$276$	−1.04745e16	−1.42635
$277$	−1.17682e16	−1.56528	−0.782639	−	0.622476i	$-0.786127\pi$
$277$	−1.17682e16	−1.56528	−0.782639	+	0.622476i	$0.786127\pi$
$278$	1.73243e16	2.25094
$279$	3.66642e14	0.0465387
$280$	7.91120e15	0.981105
$281$	9.16675e15	1.11077	0.555385	−	0.831593i	$-0.312571\pi$
$281$	9.16675e15	1.11077	0.555385	+	0.831593i	$0.312571\pi$
$282$	−6.75189e15	−0.799478
$283$	−1.59284e16	−1.84315	−0.921577	−	0.388196i	$-0.873098\pi$
$283$	−1.59284e16	−1.84315	−0.921577	+	0.388196i	$0.873098\pi$
$284$	7.01476e15	0.793311
$285$	4.59105e15	0.507481
$286$	−3.15920e16	−3.41349
$287$	4.35737e15	0.460248
$288$	−2.99169e14	−0.0308934
$289$	1.82128e16	1.83883
$290$	1.47991e16	1.46099
$291$	4.29416e15	0.414547
$292$	−2.96869e16	−2.80270
$293$	−1.20834e16	−1.11570	−0.557851	−	0.829941i	$-0.688374\pi$
$293$	−1.20834e16	−1.11570	−0.557851	+	0.829941i	$0.688374\pi$
$294$	−9.33152e15	−0.842742
$295$	−2.20106e15	−0.194442
$296$	2.08410e15	0.180104
$297$	−2.29458e15	−0.193993
$298$	−3.46759e16	−2.86829
$299$	−3.03898e16	−2.45960
$300$	1.76984e16	1.40167
$301$	6.48545e15	0.502641
$302$	2.52564e16	1.91569
$303$	1.26163e16	0.936603
$304$	−7.44318e15	−0.540854
$305$	−3.14906e16	−2.23992
$306$	1.39065e16	0.968340
$307$	5.55517e15	0.378702	0.189351	−	0.981909i	$-0.439362\pi$
$307$	5.55517e15	0.378702	0.189351	+	0.981909i	$0.439362\pi$
$308$	1.16691e16	0.778858
$309$	−4.49318e15	−0.293646
$310$	−5.61799e15	−0.359526
$311$	−1.69708e16	−1.06355	−0.531776	−	0.846885i	$-0.678475\pi$
$311$	−1.69708e16	−1.06355	−0.531776	+	0.846885i	$0.678475\pi$
$312$	3.09869e16	1.90183
$313$	−2.17358e16	−1.30658	−0.653292	−	0.757106i	$-0.726613\pi$
$313$	−2.17358e16	−1.30658	−0.653292	+	0.757106i	$0.726613\pi$
$314$	5.60782e16	3.30181
$315$	3.38089e15	0.194990
$316$	−8.61976e15	−0.487000
$317$	−1.04149e16	−0.576461	−0.288230	−	0.957561i	$-0.593067\pi$
$317$	−1.04149e16	−0.576461	−0.288230	+	0.957561i	$0.593067\pi$
$318$	−2.47551e16	−1.34242
$319$	1.07637e16	0.571901
$320$	3.09477e16	1.61122
$321$	−1.58425e16	−0.808241
$322$	1.69151e16	0.845689
$323$	−2.02373e16	−0.991597
$324$	4.56428e15	0.219195
$325$	5.13483e16	2.41704
$326$	−5.62928e16	−2.59740
$327$	−1.05559e16	−0.477456
$328$	−4.44463e16	−1.97086
$329$	7.23568e15	0.314562
$330$	3.51594e16	1.49865
$331$	−3.94837e15	−0.165020	−0.0825098	−	0.996590i	$-0.526294\pi$
$331$	−3.94837e15	−0.165020	−0.0825098	+	0.996590i	$0.526294\pi$
$332$	2.89043e16	1.18458
$333$	8.90651e14	0.0357948
$334$	−4.04557e15	−0.159451
$335$	6.40826e16	2.47713
$336$	−5.48123e15	−0.207813
$337$	1.62810e16	0.605461	0.302730	−	0.953076i	$-0.402102\pi$
$337$	1.62810e16	0.605461	0.302730	+	0.953076i	$0.402102\pi$
$338$	1.35058e17	4.92677
$339$	−2.38231e15	−0.0852510
$340$	−1.41407e17	−4.96429
$341$	−4.08608e15	−0.140735
$342$	−1.00091e16	−0.338239
$343$	2.18123e16	0.723253
$344$	−6.61531e16	−2.15239
$345$	3.38214e16	1.07986
$346$	−3.56790e16	−1.11794
$347$	−2.81521e16	−0.865703	−0.432851	−	0.901465i	$-0.642492\pi$
$347$	−2.81521e16	−0.865703	−0.432851	+	0.901465i	$0.642492\pi$
$348$	−2.14107e16	−0.646198
$349$	−2.86410e15	−0.0848443	−0.0424221	−	0.999100i	$-0.513507\pi$
$349$	−2.86410e15	−0.0848443	−0.0424221	+	0.999100i	$0.513507\pi$
$350$	−2.85807e16	−0.831057
$351$	1.32424e16	0.377981
$352$	3.33412e15	0.0934230
$353$	4.96486e16	1.36575	0.682876	−	0.730535i	$-0.260729\pi$
$353$	4.96486e16	1.36575	0.682876	+	0.730535i	$0.260729\pi$
$354$	4.79859e15	0.129596
$355$	−2.26501e16	−0.600601
$356$	−1.16086e17	−3.02241
$357$	−1.49029e16	−0.381002
$358$	5.30260e16	1.33122
$359$	−6.95931e16	−1.71574	−0.857871	−	0.513865i	$-0.828213\pi$
$359$	−6.95931e16	−1.71574	−0.857871	+	0.513865i	$0.828213\pi$
$360$	−3.44859e16	−0.834979
$361$	−2.74874e16	−0.653638
$362$	9.86842e16	2.30485
$363$	4.05100e14	0.00929329
$364$	−6.73444e16	−1.51755
$365$	9.58568e16	2.12187
$366$	6.86534e16	1.49292
$367$	−3.45201e16	−0.737468	−0.368734	−	0.929535i	$-0.620209\pi$
$367$	−3.45201e16	−0.737468	−0.368734	+	0.929535i	$0.620209\pi$
$368$	−5.48325e16	−1.15087
$369$	−1.89943e16	−0.391699
$370$	−1.36473e16	−0.276526
$371$	2.65288e16	0.528187
$372$	8.12787e15	0.159018
$373$	2.79811e16	0.537969	0.268985	−	0.963144i	$-0.413312\pi$
$373$	2.79811e16	0.537969	0.268985	+	0.963144i	$0.413312\pi$
$374$	−1.54982e17	−2.92831
$375$	−1.07103e16	−0.198884
$376$	−7.38057e16	−1.34700
$377$	−6.21189e16	−1.11431
$378$	−7.37077e15	−0.129962
$379$	−3.70727e15	−0.0642539	−0.0321269	−	0.999484i	$-0.510228\pi$
$379$	−3.70727e15	−0.0642539	−0.0321269	+	0.999484i	$0.510228\pi$
$380$	1.01776e17	1.73402
$381$	3.04120e16	0.509369
$382$	1.58356e17	2.60749
$383$	1.18077e16	0.191150	0.0955748	−	0.995422i	$-0.469531\pi$
$383$	1.18077e16	0.191150	0.0955748	+	0.995422i	$0.469531\pi$
$384$	−6.41081e16	−1.02038
$385$	−3.76787e16	−0.589659
$386$	3.92986e16	0.604727
$387$	−2.82709e16	−0.427777
$388$	9.51948e16	1.41647
$389$	3.79654e16	0.555540	0.277770	−	0.960648i	$-0.410405\pi$
$389$	3.79654e16	0.555540	0.277770	+	0.960648i	$0.410405\pi$
$390$	−2.02911e17	−2.92002
$391$	−1.49084e17	−2.11000
$392$	−1.02004e17	−1.41990
$393$	1.97762e16	0.270765
$394$	1.36481e16	0.183801
$395$	2.78325e16	0.368699
$396$	−5.08672e16	−0.662855
$397$	−4.82488e16	−0.618512	−0.309256	−	0.950979i	$-0.600080\pi$
$397$	−4.82488e16	−0.618512	−0.309256	+	0.950979i	$0.600080\pi$
$398$	7.74409e16	0.976631
$399$	1.07262e16	0.133083
$400$	9.26483e16	1.13096
$401$	−1.17837e16	−0.141529	−0.0707644	−	0.997493i	$-0.522544\pi$
$401$	−1.17837e16	−0.141529	−0.0707644	+	0.997493i	$0.522544\pi$
$402$	−1.39708e17	−1.65102
$403$	2.35814e16	0.274213
$404$	2.79684e17	3.20028
$405$	−1.47377e16	−0.165948
$406$	3.45757e16	0.383135
$407$	−9.92596e15	−0.108245
$408$	1.52013e17	1.63151
$409$	1.59142e16	0.168106	0.0840529	−	0.996461i	$-0.473214\pi$
$409$	1.59142e16	0.168106	0.0840529	+	0.996461i	$0.473214\pi$
$410$	2.91047e17	3.02600
$411$	−9.09392e15	−0.0930635
$412$	−9.96067e16	−1.00336
$413$	−5.14242e15	−0.0509909
$414$	−7.37349e16	−0.719732
$415$	−9.33299e16	−0.896826
$416$	−1.92418e16	−0.182028
$417$	8.09299e16	0.753745
$418$	1.11547e17	1.02285
$419$	1.58884e17	1.43446	0.717231	−	0.696835i	$-0.245409\pi$
$419$	1.58884e17	1.43446	0.717231	+	0.696835i	$0.245409\pi$
$420$	7.49490e16	0.666263
$421$	−8.21674e15	−0.0719227	−0.0359614	−	0.999353i	$-0.511449\pi$
$421$	−8.21674e15	−0.0719227	−0.0359614	+	0.999353i	$0.511449\pi$
$422$	−1.28250e17	−1.10542
$423$	−3.15412e16	−0.267711
$424$	−2.70601e17	−2.26178
$425$	2.51902e17	2.07349
$426$	4.93801e16	0.400304
$427$	−7.35726e16	−0.587402
$428$	−3.51203e17	−2.76169
$429$	−1.47581e17	−1.14303
$430$	4.33190e17	3.30471
$431$	8.17701e16	0.614458	0.307229	−	0.951636i	$-0.400598\pi$
$431$	8.17701e16	0.614458	0.307229	+	0.951636i	$0.400598\pi$
$432$	2.38934e16	0.176861
$433$	6.50576e16	0.474380	0.237190	−	0.971463i	$-0.423774\pi$
$433$	6.50576e16	0.474380	0.237190	+	0.971463i	$0.423774\pi$
$434$	−1.31255e16	−0.0942830
$435$	6.91335e16	0.489224
$436$	−2.34007e17	−1.63142
$437$	1.07302e17	0.737018
$438$	−2.08980e17	−1.41424
$439$	1.58621e17	1.05765	0.528823	−	0.848732i	$-0.322634\pi$
$439$	1.58621e17	1.05765	0.528823	+	0.848732i	$0.322634\pi$
$440$	3.84332e17	2.52502
$441$	−4.35919e16	−0.282199
$442$	8.94428e17	5.70559
$443$	−3.53242e16	−0.222049	−0.111024	−	0.993818i	$-0.535413\pi$
$443$	−3.53242e16	−0.222049	−0.111024	+	0.993818i	$0.535413\pi$
$444$	1.97443e16	0.122308
$445$	3.74832e17	2.28821
$446$	−2.86082e16	−0.172113
$447$	−1.61987e17	−0.960467
$448$	7.23043e16	0.422530
$449$	5.45520e16	0.314202	0.157101	−	0.987583i	$-0.449785\pi$
$449$	5.45520e16	0.314202	0.157101	+	0.987583i	$0.449785\pi$
$450$	1.24587e17	0.707279
$451$	2.11684e17	1.18452
$452$	−5.28120e16	−0.291295
$453$	1.17984e17	0.641484
$454$	−4.94189e17	−2.64869
$455$	2.17450e17	1.14891
$456$	−1.09410e17	−0.569884
$457$	−2.14838e16	−0.110320	−0.0551602	−	0.998478i	$-0.517567\pi$
$457$	−2.14838e16	−0.110320	−0.0551602	+	0.998478i	$0.517567\pi$
$458$	5.16598e17	2.61533
$459$	6.49636e16	0.324256
$460$	7.49767e17	3.68978
$461$	−1.21905e17	−0.591516	−0.295758	−	0.955263i	$-0.595572\pi$
$461$	−1.21905e17	−0.591516	−0.295758	+	0.955263i	$0.595572\pi$
$462$	8.21443e16	0.393011
$463$	−1.41322e17	−0.666707	−0.333353	−	0.942802i	$-0.608180\pi$
$463$	−1.41322e17	−0.666707	−0.333353	+	0.942802i	$0.608180\pi$
$464$	−1.12082e17	−0.521397
$465$	−2.62443e16	−0.120390
$466$	−1.78884e17	−0.809215
$467$	7.98405e16	0.356175	0.178088	−	0.984015i	$-0.443009\pi$
$467$	7.98405e16	0.356175	0.178088	+	0.984015i	$0.443009\pi$
$468$	2.93563e17	1.29153
$469$	1.49719e17	0.649609
$470$	4.83302e17	2.06815
$471$	2.61967e17	1.10563
$472$	5.24540e16	0.218351
$473$	3.15068e17	1.29362
$474$	−6.06785e16	−0.245740
$475$	−1.81304e17	−0.724266
$476$	−3.30374e17	−1.30185
$477$	−1.15642e17	−0.449519
$478$	−3.86786e17	−1.48316
$479$	−1.87162e17	−0.708007	−0.354004	−	0.935244i	$-0.615180\pi$
$479$	−1.87162e17	−0.708007	−0.354004	+	0.935244i	$0.615180\pi$
$480$	2.14146e16	0.0799173
$481$	5.72844e16	0.210908
$482$	−8.42279e16	−0.305950
$483$	7.90182e16	0.283185
$484$	8.98044e15	0.0317543
$485$	−3.07377e17	−1.07238
$486$	3.21301e16	0.110605
$487$	−5.37748e16	−0.182659	−0.0913295	−	0.995821i	$-0.529112\pi$
$487$	−5.37748e16	−0.182659	−0.0913295	+	0.995821i	$0.529112\pi$
$488$	7.50459e17	2.51535
$489$	−2.62970e17	−0.869757
$490$	6.67952e17	2.18007
$491$	2.78706e17	0.897669	0.448835	−	0.893615i	$-0.351839\pi$
$491$	2.78706e17	0.897669	0.448835	+	0.893615i	$0.351839\pi$
$492$	−4.21074e17	−1.33840
$493$	−3.04739e17	−0.955924
$494$	−6.43756e17	−1.99295
$495$	1.64246e17	0.501836
$496$	4.25482e16	0.128307
$497$	−5.29183e16	−0.157503
$498$	2.03471e17	0.597739
$499$	−3.89004e17	−1.12798	−0.563989	−	0.825782i	$-0.690734\pi$
$499$	−3.89004e17	−1.12798	−0.563989	+	0.825782i	$0.690734\pi$
$500$	−2.37431e17	−0.679567
$501$	−1.88987e16	−0.0533934
$502$	5.02521e17	1.40146
$503$	−3.67578e17	−1.01195	−0.505973	−	0.862549i	$-0.668867\pi$
$503$	−3.67578e17	−1.01195	−0.505973	+	0.862549i	$0.668867\pi$
$504$	−8.05707e16	−0.218967
$505$	−9.03078e17	−2.42288
$506$	8.21747e17	2.17650
$507$	6.30920e17	1.64977
$508$	6.74186e17	1.74047
$509$	1.60850e17	0.409973	0.204987	−	0.978765i	$-0.434285\pi$
$509$	1.60850e17	0.409973	0.204987	+	0.978765i	$0.434285\pi$
$510$	−9.95428e17	−2.50498
$511$	2.23954e17	0.556445
$512$	−6.62995e17	−1.62651
$513$	−4.67570e16	−0.113262
$514$	3.31723e17	0.793441
$515$	3.21622e17	0.759625
$516$	−6.26721e17	−1.46168
$517$	3.51515e17	0.809571
$518$	−3.18847e16	−0.0725169
$519$	−1.66673e17	−0.374351
$520$	−2.21804e18	−4.91981
$521$	1.12922e17	0.247362	0.123681	−	0.992322i	$-0.460530\pi$
$521$	1.12922e17	0.247362	0.123681	+	0.992322i	$0.460530\pi$
$522$	−1.50720e17	−0.326071
$523$	5.70815e17	1.21965	0.609824	−	0.792537i	$-0.291240\pi$
$523$	5.70815e17	1.21965	0.609824	+	0.792537i	$0.291240\pi$
$524$	4.38408e17	0.925178
$525$	−1.33514e17	−0.278286
$526$	−9.32619e17	−1.91998
$527$	1.15684e17	0.235237
$528$	−2.66282e17	−0.534837
$529$	2.86437e17	0.568287
$530$	1.77197e18	3.47267
$531$	2.24165e16	0.0433963
$532$	2.37784e17	0.454733
$533$	−1.22167e18	−2.30795
$534$	−8.17180e17	−1.52510
$535$	1.13401e18	2.09082
$536$	−1.52717e18	−2.78173
$537$	2.47709e17	0.445768
$538$	−1.18219e18	−2.10186
$539$	4.85815e17	0.853382
$540$	−3.26712e17	−0.567030
$541$	8.44721e17	1.44854	0.724271	−	0.689515i	$-0.242176\pi$
$541$	8.44721e17	1.44854	0.724271	+	0.689515i	$0.242176\pi$
$542$	3.11602e17	0.527965
$543$	4.61000e17	0.771795
$544$	−9.43950e16	−0.156155
$545$	7.55591e17	1.23512
$546$	−4.74069e17	−0.765753
$547$	9.00693e17	1.43767	0.718835	−	0.695181i	$-0.244676\pi$
$547$	9.00693e17	1.43767	0.718835	+	0.695181i	$0.244676\pi$
$548$	−2.01598e17	−0.317989
$549$	3.20712e17	0.499914
$550$	−1.38847e18	−2.13885
$551$	2.19333e17	0.333902
$552$	−8.06005e17	−1.21264
$553$	6.50262e16	0.0966886
$554$	−1.83647e18	−2.69880
$555$	−6.37530e16	−0.0925968
$556$	1.79409e18	2.57548
$557$	−1.16770e18	−1.65682	−0.828408	−	0.560126i	$-0.810753\pi$
$557$	−1.16770e18	−1.65682	−0.828408	+	0.560126i	$0.810753\pi$
$558$	5.72158e16	0.0802405
$559$	−1.81831e18	−2.52052
$560$	3.92347e17	0.537587
$561$	−7.23994e17	−0.980566
$562$	1.43051e18	1.91515
$563$	−2.08258e17	−0.275611	−0.137806	−	0.990459i	$-0.544005\pi$
$563$	−2.08258e17	−0.275611	−0.137806	+	0.990459i	$0.544005\pi$
$564$	−6.99220e17	−0.914744
$565$	1.70526e17	0.220534
$566$	−2.48569e18	−3.17790
$567$	−3.44323e16	−0.0435187
$568$	5.39780e17	0.674454
$569$	1.07782e18	1.33143	0.665715	−	0.746206i	$-0.268127\pi$
$569$	1.07782e18	1.33143	0.665715	+	0.746206i	$0.268127\pi$
$570$	7.16450e17	0.874982
$571$	−8.67398e17	−1.04733	−0.523665	−	0.851924i	$-0.675436\pi$
$571$	−8.67398e17	−1.04733	−0.523665	+	0.851924i	$0.675436\pi$
$572$	−3.27164e18	−3.90564
$573$	7.39755e17	0.873138
$574$	6.79984e17	0.793545
$575$	−1.33563e18	−1.54115
$576$	−3.15184e17	−0.359598
$577$	1.09198e17	0.123189	0.0615946	−	0.998101i	$-0.480381\pi$
$577$	1.09198e17	0.123189	0.0615946	+	0.998101i	$0.480381\pi$
$578$	2.84218e18	3.17045
$579$	1.83582e17	0.202497
$580$	1.53258e18	1.67163
$581$	−2.18050e17	−0.235186
$582$	6.70120e17	0.714748
$583$	1.28879e18	1.35937
$584$	−2.28438e18	−2.38279
$585$	−9.47892e17	−0.977790
$586$	−1.88565e18	−1.92366
$587$	1.00380e18	1.01274	0.506370	−	0.862316i	$-0.330987\pi$
$587$	1.00380e18	1.01274	0.506370	+	0.862316i	$0.330987\pi$
$588$	−9.66364e17	−0.964246
$589$	−8.32627e16	−0.0821677
$590$	−3.43484e17	−0.335250
$591$	6.37568e16	0.0615471
$592$	1.03359e17	0.0986861
$593$	7.26251e17	0.685853	0.342927	−	0.939362i	$-0.388582\pi$
$593$	7.26251e17	0.685853	0.342927	+	0.939362i	$0.388582\pi$
$594$	−3.58077e17	−0.334476
$595$	1.06675e18	0.985607
$596$	−3.59101e18	−3.28183
$597$	3.61763e17	0.327032
$598$	−4.74244e18	−4.24076
$599$	5.81628e17	0.514483	0.257241	−	0.966347i	$-0.417186\pi$
$599$	5.81628e17	0.514483	0.257241	+	0.966347i	$0.417186\pi$
$600$	1.36187e18	1.19166
$601$	1.88165e18	1.62875	0.814376	−	0.580338i	$-0.197080\pi$
$601$	1.88165e18	1.62875	0.814376	+	0.580338i	$0.197080\pi$
$602$	1.01208e18	0.866636
$603$	−6.52642e17	−0.552856
$604$	2.61552e18	2.19189
$605$	−2.89972e16	−0.0240406
$606$	1.96882e18	1.61486
$607$	2.03103e18	1.64813	0.824064	−	0.566497i	$-0.191702\pi$
$607$	2.03103e18	1.64813	0.824064	+	0.566497i	$0.191702\pi$
$608$	6.79399e16	0.0545446
$609$	1.61519e17	0.128296
$610$	−4.91423e18	−3.86199
$611$	−2.02865e18	−1.57739
$612$	1.44014e18	1.10795
$613$	−1.20805e18	−0.919583	−0.459792	−	0.888027i	$-0.652076\pi$
$613$	−1.20805e18	−0.919583	−0.459792	+	0.888027i	$0.652076\pi$
$614$	8.66905e17	0.652946
$615$	1.35962e18	1.01328
$616$	8.97929e17	0.662167
$617$	1.07093e18	0.781458	0.390729	−	0.920506i	$-0.372223\pi$
$617$	1.07093e18	0.781458	0.390729	+	0.920506i	$0.372223\pi$
$618$	−7.01177e17	−0.506294
$619$	−7.77646e17	−0.555639	−0.277820	−	0.960633i	$-0.589612\pi$
$619$	−7.77646e17	−0.555639	−0.277820	+	0.960633i	$0.589612\pi$
$620$	−5.81794e17	−0.411361
$621$	−3.44450e17	−0.241008
$622$	−2.64835e18	−1.83374
$623$	8.75733e17	0.600067
$624$	1.53676e18	1.04209
$625$	−1.06716e18	−0.716157
$626$	−3.39196e18	−2.25277
$627$	5.21088e17	0.342509
$628$	5.80741e18	3.77785
$629$	2.81022e17	0.180930
$630$	5.27601e17	0.336196
$631$	−2.56691e17	−0.161890	−0.0809450	−	0.996719i	$-0.525794\pi$
$631$	−2.56691e17	−0.161890	−0.0809450	+	0.996719i	$0.525794\pi$
$632$	−6.63283e17	−0.414036
$633$	−5.99116e17	−0.370157
$634$	−1.62528e18	−0.993914
$635$	−2.17689e18	−1.31767
$636$	−2.56361e18	−1.53596
$637$	−2.80372e18	−1.66275
$638$	1.67971e18	0.986053
$639$	2.30678e17	0.134045
$640$	4.58887e18	2.63959
$641$	2.18790e18	1.24581	0.622904	−	0.782298i	$-0.285953\pi$
$641$	2.18790e18	1.24581	0.622904	+	0.782298i	$0.285953\pi$
$642$	−2.47228e18	−1.39354
$643$	1.14952e18	0.641423	0.320712	−	0.947177i	$-0.396078\pi$
$643$	1.14952e18	0.641423	0.320712	+	0.947177i	$0.396078\pi$
$644$	1.75171e18	0.967618
$645$	2.02363e18	1.10661
$646$	−3.15810e18	−1.70968
$647$	9.03192e17	0.484064	0.242032	−	0.970268i	$-0.422186\pi$
$647$	9.03192e17	0.484064	0.242032	+	0.970268i	$0.422186\pi$
$648$	3.51218e17	0.186354
$649$	−2.49823e17	−0.131233
$650$	8.01310e18	4.16739
$651$	−6.13155e16	−0.0315714
$652$	−5.82963e18	−2.97188
$653$	2.93827e18	1.48305	0.741525	−	0.670925i	$-0.234103\pi$
$653$	2.93827e18	1.48305	0.741525	+	0.670925i	$0.234103\pi$
$654$	−1.64728e18	−0.823214
$655$	−1.41559e18	−0.700435
$656$	−2.20426e18	−1.07991
$657$	−9.76243e17	−0.473569
$658$	1.12916e18	0.542357
$659$	3.68865e18	1.75433	0.877166	−	0.480187i	$-0.159431\pi$
$659$	3.68865e18	1.75433	0.877166	+	0.480187i	$0.159431\pi$
$660$	3.64108e18	1.71473
$661$	1.16940e18	0.545321	0.272661	−	0.962110i	$-0.412096\pi$
$661$	1.16940e18	0.545321	0.272661	+	0.962110i	$0.412096\pi$
$662$	−6.16158e17	−0.284521
$663$	4.17829e18	1.91056
$664$	2.22416e18	1.00710
$665$	−7.67785e17	−0.344270
$666$	1.38989e17	0.0617162
$667$	1.61579e18	0.710504
$668$	−4.18955e17	−0.182440
$669$	−1.33642e17	−0.0576333
$670$	1.00003e19	4.27099
$671$	−3.57421e18	−1.51176
$672$	5.00316e16	0.0209577
$673$	−1.79187e18	−0.743376	−0.371688	−	0.928358i	$-0.621221\pi$
$673$	−1.79187e18	−0.743376	−0.371688	+	0.928358i	$0.621221\pi$
$674$	2.54071e18	1.04392
$675$	5.82003e17	0.236838
$676$	1.39865e19	5.63710
$677$	−3.73814e18	−1.49221	−0.746103	−	0.665830i	$-0.768078\pi$
$677$	−3.73814e18	−1.49221	−0.746103	+	0.665830i	$0.768078\pi$
$678$	−3.71768e17	−0.146987
$679$	−7.18136e17	−0.281224
$680$	−1.08811e19	−4.22053
$681$	−2.30859e18	−0.886932
$682$	−6.37648e17	−0.242651
$683$	6.08746e16	0.0229457	0.0114729	−	0.999934i	$-0.496348\pi$
$683$	6.08746e16	0.0229457	0.0114729	+	0.999934i	$0.496348\pi$
$684$	−1.03653e18	−0.387005
$685$	6.50944e17	0.240744
$686$	3.40390e18	1.24701
$687$	2.41327e18	0.875764
$688$	−3.28079e18	−1.17938
$689$	−7.43782e18	−2.64863
$690$	5.27796e18	1.86186
$691$	4.72192e18	1.65011	0.825053	−	0.565056i	$-0.191145\pi$
$691$	4.72192e18	1.65011	0.825053	+	0.565056i	$0.191145\pi$
$692$	−3.69489e18	−1.27912
$693$	3.83734e17	0.131603
$694$	−4.39324e18	−1.49262
$695$	−5.79298e18	−1.94985
$696$	−1.64753e18	−0.549382
$697$	−5.99317e18	−1.97990
$698$	−4.46953e17	−0.146286
$699$	−8.35653e17	−0.270972
$700$	−2.95979e18	−0.950876
$701$	−4.09170e18	−1.30238	−0.651189	−	0.758916i	$-0.725729\pi$
$701$	−4.09170e18	−1.30238	−0.651189	+	0.758916i	$0.725729\pi$
$702$	2.06652e18	0.651702
$703$	−2.02263e17	−0.0631985
$704$	3.51260e18	1.08744
$705$	2.25773e18	0.692536
$706$	7.74786e18	2.35478
$707$	−2.10989e18	−0.635382
$708$	4.96938e17	0.148281
$709$	6.64331e16	0.0196419	0.00982097	−	0.999952i	$-0.496874\pi$
$709$	6.64331e16	0.0196419	0.00982097	+	0.999952i	$0.496874\pi$
$710$	−3.53464e18	−1.03554
$711$	−2.83457e17	−0.0822878
$712$	−8.93269e18	−2.56958
$713$	−6.13381e17	−0.174843
$714$	−2.32566e18	−0.656912
$715$	1.05639e19	2.95689
$716$	5.49132e18	1.52315
$717$	−1.80686e18	−0.496648
$718$	−1.08603e19	−2.95823
$719$	−4.43140e18	−1.19620	−0.598100	−	0.801422i	$-0.704077\pi$
$719$	−4.43140e18	−1.19620	−0.598100	+	0.801422i	$0.704077\pi$
$720$	−1.71029e18	−0.457519
$721$	7.51418e17	0.199206
$722$	−4.28951e18	−1.12698
$723$	−3.93468e17	−0.102450
$724$	1.02196e19	2.63715
$725$	−2.73013e18	−0.698211
$726$	6.32175e16	0.0160232
$727$	−7.11576e18	−1.78751	−0.893754	−	0.448558i	$-0.851938\pi$
$727$	−7.11576e18	−1.78751	−0.893754	+	0.448558i	$0.851938\pi$
$728$	−5.18210e18	−1.29018
$729$	1.50095e17	0.0370370
$730$	1.49588e19	3.65846
$731$	−8.92014e18	−2.16226
$732$	7.10969e18	1.70816
$733$	2.40874e18	0.573607	0.286804	−	0.957989i	$-0.407407\pi$
$733$	2.40874e18	0.573607	0.286804	+	0.957989i	$0.407407\pi$
$734$	−5.38700e18	−1.27152
$735$	3.12032e18	0.730013
$736$	5.00501e17	0.116064
$737$	7.27344e18	1.67186
$738$	−2.96414e18	−0.675355
$739$	−3.13387e18	−0.707769	−0.353885	−	0.935289i	$-0.615139\pi$
$739$	−3.13387e18	−0.707769	−0.353885	+	0.935289i	$0.615139\pi$
$740$	−1.41330e18	−0.316395
$741$	−3.00729e18	−0.667354
$742$	4.13992e18	0.910683
$743$	1.71490e18	0.373949	0.186974	−	0.982365i	$-0.440132\pi$
$743$	1.71490e18	0.373949	0.186974	+	0.982365i	$0.440132\pi$
$744$	6.25433e17	0.135194
$745$	1.15951e19	2.48461
$746$	4.36656e18	0.927549
$747$	9.50508e17	0.200157
$748$	−1.60498e19	−3.35050
$749$	2.64943e18	0.548303
$750$	−1.67139e18	−0.342909
$751$	−6.66396e18	−1.35542	−0.677709	−	0.735330i	$-0.737027\pi$
$751$	−6.66396e18	−1.35542	−0.677709	+	0.735330i	$0.737027\pi$
$752$	−3.66031e18	−0.738078
$753$	2.34751e18	0.469289
$754$	−9.69390e18	−1.92125
$755$	−8.44533e18	−1.65944
$756$	−7.63310e17	−0.148699
$757$	8.31558e17	0.160609	0.0803044	−	0.996770i	$-0.474411\pi$
$757$	8.31558e17	0.160609	0.0803044	+	0.996770i	$0.474411\pi$
$758$	−5.78533e17	−0.110784
$759$	3.83876e18	0.728819
$760$	7.83160e18	1.47422
$761$	6.37753e18	1.19029	0.595144	−	0.803619i	$-0.297095\pi$
$761$	6.37753e18	1.19029	0.595144	+	0.803619i	$0.297095\pi$
$762$	4.74590e18	0.878237
$763$	1.76531e18	0.323901
$764$	1.63992e19	2.98343
$765$	−4.65011e18	−0.838810
$766$	1.84264e18	0.329574
$767$	1.44177e18	0.255697
$768$	−6.46249e18	−1.13646
$769$	−4.71388e18	−0.821972	−0.410986	−	0.911642i	$-0.634815\pi$
$769$	−4.71388e18	−0.821972	−0.410986	+	0.911642i	$0.634815\pi$
$770$	−5.87991e18	−1.01667
$771$	1.54963e18	0.265690
$772$	4.06972e18	0.691914
$773$	1.81675e18	0.306286	0.153143	−	0.988204i	$-0.451060\pi$
$773$	1.81675e18	0.306286	0.153143	+	0.988204i	$0.451060\pi$
$774$	−4.41177e18	−0.737560
$775$	1.03641e18	0.171818
$776$	7.32516e18	1.20425
$777$	−1.48948e17	−0.0242828
$778$	5.92464e18	0.957844
$779$	4.31353e18	0.691575
$780$	−2.10133e19	−3.34102
$781$	−2.57081e18	−0.405358
$782$	−2.32651e19	−3.63799
$783$	−7.04082e17	−0.109187
$784$	−5.05877e18	−0.778020
$785$	−1.87517e19	−2.86014
$786$	3.08616e18	0.466844
$787$	−6.87045e17	−0.103074	−0.0515371	−	0.998671i	$-0.516412\pi$
$787$	−6.87045e17	−0.103074	−0.0515371	+	0.998671i	$0.516412\pi$
$788$	1.41339e18	0.210301
$789$	−4.35670e18	−0.642920
$790$	4.34337e18	0.635698
$791$	3.98406e17	0.0578334
$792$	−3.91419e18	−0.563544
$793$	2.06274e19	2.94556
$794$	−7.52940e18	−1.06642
$795$	8.27771e18	1.16285
$796$	8.01971e18	1.11744
$797$	2.69793e18	0.372865	0.186432	−	0.982468i	$-0.440307\pi$
$797$	2.69793e18	0.372865	0.186432	+	0.982468i	$0.440307\pi$
$798$	1.67387e18	0.229458
$799$	−9.95203e18	−1.35319
$800$	−8.45676e17	−0.114056
$801$	−3.81743e18	−0.510693
$802$	−1.83890e18	−0.244019
$803$	1.08798e19	1.43209
$804$	−1.44680e19	−1.88906
$805$	−5.65614e18	−0.732566
$806$	3.67997e18	0.472788
$807$	−5.52257e18	−0.703823
$808$	2.15214e19	2.72081
$809$	1.12567e19	1.41170	0.705852	−	0.708359i	$-0.250564\pi$
$809$	1.12567e19	1.41170	0.705852	+	0.708359i	$0.250564\pi$
$810$	−2.29988e18	−0.286123
$811$	9.38613e18	1.15838	0.579190	−	0.815193i	$-0.303369\pi$
$811$	9.38613e18	1.15838	0.579190	+	0.815193i	$0.303369\pi$
$812$	3.58062e18	0.438374
$813$	1.45564e18	0.176793
$814$	−1.54898e18	−0.186633
$815$	1.88234e19	2.24996
$816$	7.53894e18	0.893972
$817$	6.42019e18	0.755274
$818$	2.48347e18	0.289843
$819$	−2.21460e18	−0.256418
$820$	3.01406e19	3.46227
$821$	−4.28452e18	−0.488283	−0.244142	−	0.969740i	$-0.578506\pi$
$821$	−4.28452e18	−0.488283	−0.244142	+	0.969740i	$0.578506\pi$
$822$	−1.41914e18	−0.160457
$823$	−5.70804e18	−0.640307	−0.320153	−	0.947366i	$-0.603734\pi$
$823$	−5.70804e18	−0.640307	−0.320153	+	0.947366i	$0.603734\pi$
$824$	−7.66465e18	−0.853033
$825$	−6.48620e18	−0.716209
$826$	−8.02495e17	−0.0879168
$827$	−9.61559e18	−1.04518	−0.522589	−	0.852585i	$-0.675034\pi$
$827$	−9.61559e18	−1.04518	−0.522589	+	0.852585i	$0.675034\pi$
$828$	−7.63592e18	−0.823501
$829$	8.86663e18	0.948755	0.474378	−	0.880321i	$-0.342673\pi$
$829$	8.86663e18	0.948755	0.474378	+	0.880321i	$0.342673\pi$
$830$	−1.45645e19	−1.54628
$831$	−8.57901e18	−0.903713
$832$	−2.02718e19	−2.11880
$833$	−1.37543e19	−1.42642
$834$	1.26294e19	1.29958
$835$	1.35277e18	0.138122
$836$	1.15517e19	1.17032
$837$	2.67282e17	0.0268691
$838$	2.47945e19	2.47325
$839$	−5.68168e18	−0.562372	−0.281186	−	0.959653i	$-0.590728\pi$
$839$	−5.68168e18	−0.562372	−0.281186	+	0.959653i	$0.590728\pi$
$840$	5.76727e18	0.566441
$841$	−6.95784e18	−0.678110
$842$	−1.28225e18	−0.124007
$843$	6.68256e18	0.641304
$844$	−1.32814e19	−1.26479
$845$	−4.51613e19	−4.26774
$846$	−4.92213e18	−0.461579
$847$	−6.77471e16	−0.00630447
$848$	−1.34201e19	−1.23932
$849$	−1.16118e19	−1.06415
$850$	3.93102e19	3.57505
$851$	−1.49003e18	−0.134479
$852$	5.11376e18	0.458018
$853$	3.35213e18	0.297956	0.148978	−	0.988840i	$-0.452402\pi$
$853$	3.35213e18	0.297956	0.148978	+	0.988840i	$0.452402\pi$
$854$	−1.14813e19	−1.01278
$855$	3.34687e18	0.292994
$856$	−2.70248e19	−2.34792
$857$	−1.23086e19	−1.06129	−0.530644	−	0.847595i	$-0.678050\pi$
$857$	−1.23086e19	−1.06129	−0.530644	+	0.847595i	$0.678050\pi$
$858$	−2.30306e19	−1.97078
$859$	1.27859e19	1.08586	0.542931	−	0.839777i	$-0.317315\pi$
$859$	1.27859e19	1.08586	0.542931	+	0.839777i	$0.317315\pi$
$860$	4.48608e19	3.78117
$861$	3.17652e18	0.265725
$862$	1.27605e19	1.05943
$863$	2.31148e18	0.190467	0.0952337	−	0.995455i	$-0.469640\pi$
$863$	2.31148e18	0.190467	0.0952337	+	0.995455i	$0.469640\pi$
$864$	−2.18094e17	−0.0178363
$865$	1.19305e19	0.968399
$866$	1.01525e19	0.817911
$867$	1.32772e19	1.06165
$868$	−1.35927e18	−0.107876
$869$	3.15902e18	0.248842
$870$	1.07885e19	0.843505
$871$	−4.19762e19	−3.25751
$872$	−1.80066e19	−1.38700
$873$	3.13044e18	0.239339
$874$	1.67449e19	1.27074
$875$	1.79115e18	0.134921
$876$	−2.16418e19	−1.61814
$877$	−2.57822e19	−1.91347	−0.956737	−	0.290956i	$-0.906027\pi$
$877$	−2.57822e19	−1.91347	−0.956737	+	0.290956i	$0.906027\pi$
$878$	2.47533e19	1.82356
$879$	−8.80877e18	−0.644151
$880$	1.90605e19	1.38356
$881$	−4.40218e17	−0.0317194	−0.0158597	−	0.999874i	$-0.505049\pi$
$881$	−4.40218e17	−0.0317194	−0.0158597	+	0.999874i	$0.505049\pi$
$882$	−6.80268e18	−0.486558
$883$	2.58745e19	1.83708	0.918538	−	0.395334i	$-0.129371\pi$
$883$	2.58745e19	1.83708	0.918538	+	0.395334i	$0.129371\pi$
$884$	9.26262e19	6.52821
$885$	−1.60457e18	−0.112261
$886$	−5.51248e18	−0.382849
$887$	1.20459e19	0.830493	0.415247	−	0.909709i	$-0.363695\pi$
$887$	1.20459e19	0.830493	0.415247	+	0.909709i	$0.363695\pi$
$888$	1.51931e18	0.103983
$889$	−5.08596e18	−0.345550
$890$	5.84939e19	3.94526
$891$	−1.67275e18	−0.112002
$892$	−2.96263e18	−0.196928
$893$	7.16288e18	0.472665
$894$	−2.52788e19	−1.65601
$895$	−1.77311e19	−1.15315
$896$	1.07211e19	0.692212
$897$	−2.21541e19	−1.42005
$898$	8.51305e18	0.541737
$899$	−1.25380e18	−0.0792117
$900$	1.29021e19	0.809253
$901$	−3.64880e19	−2.27216
$902$	3.30341e19	2.04230
$903$	4.72789e18	0.290200
$904$	−4.06384e18	−0.247652
$905$	−3.29985e19	−1.99654
$906$	1.84119e19	1.10603
$907$	−1.25571e18	−0.0748934	−0.0374467	−	0.999299i	$-0.511922\pi$
$907$	−1.25571e18	−0.0748934	−0.0374467	+	0.999299i	$0.511922\pi$
$908$	−5.11778e19	−3.03056
$909$	9.19729e18	0.540748
$910$	3.39339e19	1.98091
$911$	−3.26755e19	−1.89388	−0.946939	−	0.321412i	$-0.895843\pi$
$911$	−3.26755e19	−1.89388	−0.946939	+	0.321412i	$0.895843\pi$
$912$	−5.42608e18	−0.312262
$913$	−1.05930e19	−0.605286
$914$	−3.35263e18	−0.190211
$915$	−2.29566e19	−1.29322
$916$	5.34984e19	2.99240
$917$	−3.30729e18	−0.183684
$918$	1.01378e19	0.559071
$919$	−5.47597e17	−0.0299854	−0.0149927	−	0.999888i	$-0.504773\pi$
$919$	−5.47597e17	−0.0299854	−0.0149927	+	0.999888i	$0.504773\pi$
$920$	5.76940e19	3.13696
$921$	4.04972e18	0.218644
$922$	−1.90238e19	−1.01987
$923$	1.48366e19	0.789810
$924$	8.50679e18	0.449674
$925$	2.51765e18	0.132152
$926$	−2.20539e19	−1.14951
$927$	−3.27553e18	−0.169536
$928$	1.02306e18	0.0525823
$929$	−7.36175e17	−0.0375733	−0.0187866	−	0.999824i	$-0.505980\pi$
$929$	−7.36175e17	−0.0375733	−0.0187866	+	0.999824i	$0.505980\pi$
$930$	−4.09552e18	−0.207572
$931$	9.89953e18	0.498243
$932$	−1.85251e19	−0.925885
$933$	−1.23717e19	−0.614042
$934$	1.24594e19	0.614105
$935$	5.18237e19	2.53660
$936$	2.25894e19	1.09802
$937$	6.57814e18	0.317538	0.158769	−	0.987316i	$-0.449247\pi$
$937$	6.57814e18	0.317538	0.158769	+	0.987316i	$0.449247\pi$
$938$	2.33641e19	1.12003
$939$	−1.58454e19	−0.754357
$940$	5.00503e19	2.36633
$941$	−9.89905e18	−0.464794	−0.232397	−	0.972621i	$-0.574657\pi$
$941$	−9.89905e18	−0.464794	−0.232397	+	0.972621i	$0.574657\pi$
$942$	4.08810e19	1.90630
$943$	3.17770e19	1.47159
$944$	2.60140e18	0.119643
$945$	2.46467e18	0.112578
$946$	4.91675e19	2.23042
$947$	9.70943e18	0.437440	0.218720	−	0.975788i	$-0.429812\pi$
$947$	9.70943e18	0.437440	0.218720	+	0.975788i	$0.429812\pi$
$948$	−6.28380e18	−0.281170
$949$	−6.27894e19	−2.79033
$950$	−2.82931e19	−1.24876
$951$	−7.59246e18	−0.332820
$952$	−2.54220e19	−1.10680
$953$	1.46901e19	0.635214	0.317607	−	0.948222i	$-0.397121\pi$
$953$	1.46901e19	0.635214	0.317607	+	0.948222i	$0.397121\pi$
$954$	−1.80464e19	−0.775046
$955$	−5.29518e19	−2.25870
$956$	−4.00552e19	−1.69700
$957$	7.84672e18	0.330187
$958$	−2.92074e19	−1.22072
$959$	1.52083e18	0.0631333
$960$	2.25609e19	0.930236
$961$	−2.39416e19	−0.980507
$962$	8.93944e18	0.363641
$963$	−1.15492e19	−0.466638
$964$	−8.72256e18	−0.350061
$965$	−1.31408e19	−0.523836
$966$	1.23311e19	0.488259
$967$	1.51359e19	0.595300	0.297650	−	0.954675i	$-0.403797\pi$
$967$	1.51359e19	0.595300	0.297650	+	0.954675i	$0.403797\pi$
$968$	6.91037e17	0.0269968
$969$	−1.47530e19	−0.572499
$970$	−4.79673e19	−1.84897
$971$	−4.05159e19	−1.55132	−0.775658	−	0.631153i	$-0.782582\pi$
$971$	−4.05159e19	−1.55132	−0.775658	+	0.631153i	$0.782582\pi$
$972$	3.32736e18	0.126552
$973$	−1.35343e19	−0.511333
$974$	−8.39177e18	−0.314935
$975$	3.74329e19	1.39548
$976$	3.72182e19	1.37826
$977$	1.58056e18	0.0581430	0.0290715	−	0.999577i	$-0.490745\pi$
$977$	1.58056e18	0.0581430	0.0290715	+	0.999577i	$0.490745\pi$
$978$	−4.10374e19	−1.49961
$979$	4.25438e19	1.54436
$980$	6.91725e19	2.49439
$981$	−7.69522e18	−0.275659
$982$	4.34931e19	1.54773
$983$	−4.97288e19	−1.75797	−0.878983	−	0.476853i	$-0.841777\pi$
$983$	−4.97288e19	−1.75797	−0.878983	+	0.476853i	$0.841777\pi$
$984$	−3.24013e19	−1.13788
$985$	−4.56372e18	−0.159215
$986$	−4.75557e19	−1.64817
$987$	5.27481e18	0.181612
$988$	−6.66668e19	−2.28029
$989$	4.72964e19	1.60713
$990$	2.56312e19	0.865248
$991$	3.01373e18	0.101071	0.0505353	−	0.998722i	$-0.483907\pi$
$991$	3.01373e18	0.101071	0.0505353	+	0.998722i	$0.483907\pi$
$992$	−3.88372e17	−0.0129396
$993$	−2.87836e18	−0.0952741
$994$	−8.25810e18	−0.271562
$995$	−2.58950e19	−0.845992
$996$	2.10713e19	0.683919
$997$	−5.51272e19	−1.77765	−0.888827	−	0.458244i	$-0.848479\pi$
$997$	−5.51272e19	−1.77765	−0.888827	+	0.458244i	$0.848479\pi$
$998$	−6.07056e19	−1.94482
$999$	6.49285e17	0.0206661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.28	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.28	✓	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)

\(f(q)\)	\(=\)	\(q+156.054 q^{2} +729.000 q^{3} +16160.8 q^{4} -52181.9 q^{5} +113763. q^{6} -121915. q^{7} +1.24356e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q+156.054 q^{2} +729.000 q^{3} +16160.8 q^{4} -52181.9 q^{5} +113763. q^{6} -121915. q^{7} +1.24356e6 q^{8} +531441. q^{9} -8.14319e6 q^{10} -5.92270e6 q^{11} +1.17812e7 q^{12} +3.41809e7 q^{13} -1.90252e7 q^{14} -3.80406e7 q^{15} +6.16729e7 q^{16} +1.67683e8 q^{17} +8.29334e7 q^{18} -1.20688e8 q^{19} -8.43301e8 q^{20} -8.88758e7 q^{21} -9.24260e8 q^{22} -8.89086e8 q^{23} +9.06555e8 q^{24} +1.50225e9 q^{25} +5.33406e9 q^{26} +3.87420e8 q^{27} -1.97024e9 q^{28} -1.81736e9 q^{29} -5.93639e9 q^{30} +6.89901e8 q^{31} -5.62939e8 q^{32} -4.31765e9 q^{33} +2.61675e10 q^{34} +6.36174e9 q^{35} +8.58850e9 q^{36} +1.67592e9 q^{37} -1.88338e10 q^{38} +2.49179e10 q^{39} -6.48913e10 q^{40} -3.57412e10 q^{41} -1.38694e10 q^{42} -5.31966e10 q^{43} -9.57155e10 q^{44} -2.77316e10 q^{45} -1.38745e11 q^{46} -5.93504e10 q^{47} +4.49596e10 q^{48} -8.20258e10 q^{49} +2.34432e11 q^{50} +1.22241e11 q^{51} +5.52390e11 q^{52} -2.17602e11 q^{53} +6.04584e10 q^{54} +3.09058e11 q^{55} -1.51608e11 q^{56} -8.79815e10 q^{57} -2.83606e11 q^{58} +4.21805e10 q^{59} -6.14767e11 q^{60} +6.03477e11 q^{61} +1.07662e11 q^{62} -6.47904e10 q^{63} -5.93073e11 q^{64} -1.78363e12 q^{65} -6.73786e11 q^{66} -1.22806e12 q^{67} +2.70988e12 q^{68} -6.48144e11 q^{69} +9.92774e11 q^{70} +4.34060e11 q^{71} +6.60878e11 q^{72} -1.83697e12 q^{73} +2.61533e11 q^{74} +1.09514e12 q^{75} -1.95041e12 q^{76} +7.22064e11 q^{77} +3.88853e12 q^{78} -5.33375e11 q^{79} -3.21821e12 q^{80} +2.82430e11 q^{81} -5.57755e12 q^{82} +1.78855e12 q^{83} -1.43630e12 q^{84} -8.75000e12 q^{85} -8.30153e12 q^{86} -1.32485e12 q^{87} -7.36523e12 q^{88} -7.18317e12 q^{89} -4.32763e12 q^{90} -4.16715e12 q^{91} -1.43683e13 q^{92} +5.02938e11 q^{93} -9.26186e12 q^{94} +6.29773e12 q^{95} -4.10382e11 q^{96} +5.89048e12 q^{97} -1.28004e13 q^{98} -3.14757e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 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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