LMFDB - Embedded newform 177.14.a.a.1.26

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			1.26
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)

$f(q)$	$=$	$q+132.796 q^{2} +729.000 q^{3} +9442.84 q^{4} +3277.42 q^{5} +96808.5 q^{6} -296432. q^{7} +166107. q^{8} +531441. q^{9} +O(q^{10})$	\(q+132.796 q^{2} +729.000 q^{3} +9442.84 q^{4} +3277.42 q^{5} +96808.5 q^{6} -296432. q^{7} +166107. q^{8} +531441. q^{9} +435229. q^{10} +9.14323e6 q^{11} +6.88383e6 q^{12} -3.48492e6 q^{13} -3.93651e7 q^{14} +2.38924e6 q^{15} -5.52973e7 q^{16} -3.85684e7 q^{17} +7.05734e7 q^{18} +2.85648e7 q^{19} +3.09482e7 q^{20} -2.16099e8 q^{21} +1.21419e9 q^{22} -7.24424e8 q^{23} +1.21092e8 q^{24} -1.20996e9 q^{25} -4.62784e8 q^{26} +3.87420e8 q^{27} -2.79916e9 q^{28} -3.17470e9 q^{29} +3.17282e8 q^{30} -4.23680e9 q^{31} -8.70403e9 q^{32} +6.66541e9 q^{33} -5.12174e9 q^{34} -9.71533e8 q^{35} +5.01831e9 q^{36} +2.66331e10 q^{37} +3.79330e9 q^{38} -2.54050e9 q^{39} +5.44404e8 q^{40} -2.67542e10 q^{41} -2.86971e10 q^{42} +7.18936e10 q^{43} +8.63381e10 q^{44} +1.74176e9 q^{45} -9.62007e10 q^{46} +7.60117e10 q^{47} -4.03118e10 q^{48} -9.01705e9 q^{49} -1.60678e11 q^{50} -2.81164e10 q^{51} -3.29075e10 q^{52} -2.54878e11 q^{53} +5.14480e10 q^{54} +2.99662e10 q^{55} -4.92396e10 q^{56} +2.08237e10 q^{57} -4.21588e11 q^{58} +4.21805e10 q^{59} +2.25612e10 q^{60} -4.30773e11 q^{61} -5.62632e11 q^{62} -1.57536e11 q^{63} -7.02867e11 q^{64} -1.14215e10 q^{65} +8.85142e11 q^{66} -1.20675e12 q^{67} -3.64195e11 q^{68} -5.28105e11 q^{69} -1.29016e11 q^{70} +6.68630e11 q^{71} +8.82763e10 q^{72} -2.42459e11 q^{73} +3.53678e12 q^{74} -8.82062e11 q^{75} +2.69733e11 q^{76} -2.71035e12 q^{77} -3.37369e11 q^{78} +4.77381e11 q^{79} -1.81233e11 q^{80} +2.82430e11 q^{81} -3.55286e12 q^{82} -2.06958e12 q^{83} -2.04059e12 q^{84} -1.26405e11 q^{85} +9.54720e12 q^{86} -2.31436e12 q^{87} +1.51876e12 q^{88} -6.68736e12 q^{89} +2.31299e11 q^{90} +1.03304e12 q^{91} -6.84062e12 q^{92} -3.08863e12 q^{93} +1.00941e13 q^{94} +9.36190e10 q^{95} -6.34524e12 q^{96} +3.13450e12 q^{97} -1.19743e12 q^{98} +4.85909e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	132.796	1.46721	0.733603	−	0.679579i	$-0.237837\pi$
$2$	132.796	1.46721	0.733603	+	0.679579i	$0.237837\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	9442.84	1.15269
$5$	3277.42	0.0938053	0.0469027	−	0.998899i	$-0.485065\pi$
$5$	3277.42	0.0938053	0.0469027	+	0.998899i	$0.485065\pi$
$6$	96808.5	0.847091
$7$	−296432.	−0.952331	−0.476165	−	0.879356i	$-0.657974\pi$
$7$	−296432.	−0.952331	−0.476165	+	0.879356i	$0.657974\pi$
$8$	166107.	0.224029
$9$	531441.	0.333333
$10$	435229.	0.137632
$11$	9.14323e6	1.55613	0.778067	−	0.628181i	$-0.216200\pi$
$11$	9.14323e6	1.55613	0.778067	+	0.628181i	$0.216200\pi$
$12$	6.88383e6	0.665506
$13$	−3.48492e6	−0.200244	−0.100122	−	0.994975i	$-0.531923\pi$
$13$	−3.48492e6	−0.200244	−0.100122	+	0.994975i	$0.531923\pi$
$14$	−3.93651e7	−1.39726
$15$	2.38924e6	0.0541585
$16$	−5.52973e7	−0.823995
$17$	−3.85684e7	−0.387538	−0.193769	−	0.981047i	$-0.562071\pi$
$17$	−3.85684e7	−0.387538	−0.193769	+	0.981047i	$0.562071\pi$
$18$	7.05734e7	0.489068
$19$	2.85648e7	0.139294	0.0696471	−	0.997572i	$-0.477813\pi$
$19$	2.85648e7	0.139294	0.0696471	+	0.997572i	$0.477813\pi$
$20$	3.09482e7	0.108129
$21$	−2.16099e8	−0.549829
$22$	1.21419e9	2.28317
$23$	−7.24424e8	−1.02038	−0.510190	−	0.860062i	$-0.670425\pi$
$23$	−7.24424e8	−1.02038	−0.510190	+	0.860062i	$0.670425\pi$
$24$	1.21092e8	0.129343
$25$	−1.20996e9	−0.991201
$26$	−4.62784e8	−0.293800
$27$	3.87420e8	0.192450
$28$	−2.79916e9	−1.09774
$29$	−3.17470e9	−0.991096	−0.495548	−	0.868580i	$-0.665033\pi$
$29$	−3.17470e9	−0.991096	−0.495548	+	0.868580i	$0.665033\pi$
$30$	3.17282e8	0.0794617
$31$	−4.23680e9	−0.857407	−0.428704	−	0.903445i	$-0.641030\pi$
$31$	−4.23680e9	−0.857407	−0.428704	+	0.903445i	$0.641030\pi$
$32$	−8.70403e9	−1.43300
$33$	6.66541e9	0.898435
$34$	−5.12174e9	−0.568597
$35$	−9.71533e8	−0.0893337
$36$	5.01831e9	0.384230
$37$	2.66331e10	1.70652	0.853259	−	0.521487i	$-0.174623\pi$
$37$	2.66331e10	1.70652	0.853259	+	0.521487i	$0.174623\pi$
$38$	3.79330e9	0.204373
$39$	−2.54050e9	−0.115611
$40$	5.44404e8	0.0210151
$41$	−2.67542e10	−0.879623	−0.439812	−	0.898090i	$-0.644955\pi$
$41$	−2.67542e10	−0.879623	−0.439812	+	0.898090i	$0.644955\pi$
$42$	−2.86971e10	−0.806711
$43$	7.18936e10	1.73438	0.867192	−	0.497974i	$-0.165923\pi$
$43$	7.18936e10	1.73438	0.867192	+	0.497974i	$0.165923\pi$
$44$	8.63381e10	1.79374
$45$	1.74176e9	0.0312684
$46$	−9.62007e10	−1.49711
$47$	7.60117e10	1.02860	0.514298	−	0.857612i	$-0.328053\pi$
$47$	7.60117e10	1.02860	0.514298	+	0.857612i	$0.328053\pi$
$48$	−4.03118e10	−0.475733
$49$	−9.01705e9	−0.0930657
$50$	−1.60678e11	−1.45429
$51$	−2.81164e10	−0.223745
$52$	−3.29075e10	−0.230820
$53$	−2.54878e11	−1.57957	−0.789787	−	0.613381i	$-0.789809\pi$
$53$	−2.54878e11	−1.57957	−0.789787	+	0.613381i	$0.789809\pi$
$54$	5.14480e10	0.282364
$55$	2.99662e10	0.145974
$56$	−4.92396e10	−0.213350
$57$	2.08237e10	0.0804215
$58$	−4.21588e11	−1.45414
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	2.25612e10	0.0624280
$61$	−4.30773e11	−1.07054	−0.535272	−	0.844680i	$-0.679791\pi$
$61$	−4.30773e11	−1.07054	−0.535272	+	0.844680i	$0.679791\pi$
$62$	−5.62632e11	−1.25799
$63$	−1.57536e11	−0.317444
$64$	−7.02867e11	−1.27851
$65$	−1.14215e10	−0.0187840
$66$	8.85142e11	1.31819
$67$	−1.20675e12	−1.62978	−0.814892	−	0.579612i	$-0.803204\pi$
$67$	−1.20675e12	−1.62978	−0.814892	+	0.579612i	$0.803204\pi$
$68$	−3.64195e11	−0.446711
$69$	−5.28105e11	−0.589116
$70$	−1.29016e11	−0.131071
$71$	6.68630e11	0.619450	0.309725	−	0.950826i	$-0.399763\pi$
$71$	6.68630e11	0.619450	0.309725	+	0.950826i	$0.399763\pi$
$72$	8.82763e10	0.0746763
$73$	−2.42459e11	−0.187517	−0.0937583	−	0.995595i	$-0.529888\pi$
$73$	−2.42459e11	−0.187517	−0.0937583	+	0.995595i	$0.529888\pi$
$74$	3.53678e12	2.50381
$75$	−8.82062e11	−0.572270
$76$	2.69733e11	0.160563
$77$	−2.71035e12	−1.48196
$78$	−3.37369e11	−0.169625
$79$	4.77381e11	0.220947	0.110474	−	0.993879i	$-0.464763\pi$
$79$	4.77381e11	0.220947	0.110474	+	0.993879i	$0.464763\pi$
$80$	−1.81233e11	−0.0772951
$81$	2.82430e11	0.111111
$82$	−3.55286e12	−1.29059
$83$	−2.06958e12	−0.694825	−0.347413	−	0.937712i	$-0.612940\pi$
$83$	−2.06958e12	−0.694825	−0.347413	+	0.937712i	$0.612940\pi$
$84$	−2.04059e12	−0.633782
$85$	−1.26405e11	−0.0363531
$86$	9.54720e12	2.54470
$87$	−2.31436e12	−0.572210
$88$	1.51876e12	0.348619
$89$	−6.68736e12	−1.42633	−0.713165	−	0.700997i	$-0.752739\pi$
$89$	−6.68736e12	−1.42633	−0.713165	+	0.700997i	$0.752739\pi$
$90$	2.31299e11	0.0458772
$91$	1.03304e12	0.190699
$92$	−6.84062e12	−1.17618
$93$	−3.08863e12	−0.495024
$94$	1.00941e13	1.50916
$95$	9.36190e10	0.0130665
$96$	−6.34524e12	−0.827342
$97$	3.13450e12	0.382078	0.191039	−	0.981582i	$-0.438814\pi$
$97$	3.13450e12	0.382078	0.191039	+	0.981582i	$0.438814\pi$
$98$	−1.19743e12	−0.136547
$99$	4.85909e12	0.518712
$100$	−1.14255e13	−1.14255
$101$	−7.94215e12	−0.744474	−0.372237	−	0.928138i	$-0.621409\pi$
$101$	−7.94215e12	−0.744474	−0.372237	+	0.928138i	$0.621409\pi$
$102$	−3.73375e12	−0.328280
$103$	−2.08416e13	−1.71985	−0.859923	−	0.510423i	$-0.829489\pi$
$103$	−2.08416e13	−1.71985	−0.859923	+	0.510423i	$0.829489\pi$
$104$	−5.78870e11	−0.0448605
$105$	−7.08248e11	−0.0515768
$106$	−3.38469e13	−2.31756
$107$	1.89166e13	1.21856	0.609281	−	0.792954i	$-0.291458\pi$
$107$	1.89166e13	1.21856	0.609281	+	0.792954i	$0.291458\pi$
$108$	3.65835e12	0.221835
$109$	−1.64082e13	−0.937109	−0.468554	−	0.883435i	$-0.655225\pi$
$109$	−1.64082e13	−0.937109	−0.468554	+	0.883435i	$0.655225\pi$
$110$	3.97940e12	0.214173
$111$	1.94155e13	0.985259
$112$	1.63919e13	0.784716
$113$	1.39969e13	0.632443	0.316222	−	0.948685i	$-0.397586\pi$
$113$	1.39969e13	0.632443	0.316222	+	0.948685i	$0.397586\pi$
$114$	2.76532e12	0.117995
$115$	−2.37424e12	−0.0957170
$116$	−2.99782e13	−1.14243
$117$	−1.85203e12	−0.0667481
$118$	5.60142e12	0.191014
$119$	1.14329e13	0.369064
$120$	3.96871e11	0.0121331
$121$	4.90759e13	1.42155
$122$	−5.72051e13	−1.57071
$123$	−1.95038e13	−0.507851
$124$	−4.00075e13	−0.988326
$125$	−7.96632e12	−0.186785
$126$	−2.09202e13	−0.465755
$127$	−8.70776e13	−1.84154	−0.920772	−	0.390101i	$-0.872440\pi$
$127$	−8.70776e13	−1.84154	−0.920772	+	0.390101i	$0.872440\pi$
$128$	−2.20347e13	−0.442835
$129$	5.24104e13	1.00135
$130$	−1.51674e12	−0.0275600
$131$	8.26459e13	1.42876	0.714378	−	0.699760i	$-0.246710\pi$
$131$	8.26459e13	1.42876	0.714378	+	0.699760i	$0.246710\pi$
$132$	6.29405e13	1.03562
$133$	−8.46753e12	−0.132654
$134$	−1.60252e14	−2.39123
$135$	1.26974e12	0.0180528
$136$	−6.40650e12	−0.0868196
$137$	−8.20575e13	−1.06031	−0.530157	−	0.847899i	$-0.677867\pi$
$137$	−8.20575e13	−1.06031	−0.530157	+	0.847899i	$0.677867\pi$
$138$	−7.01303e13	−0.864355
$139$	−8.14600e13	−0.957961	−0.478981	−	0.877825i	$-0.658994\pi$
$139$	−8.14600e13	−0.957961	−0.478981	+	0.877825i	$0.658994\pi$
$140$	−9.17404e12	−0.102974
$141$	5.54125e13	0.593860
$142$	8.87915e13	0.908861
$143$	−3.18634e13	−0.311607
$144$	−2.93873e13	−0.274665
$145$	−1.04048e13	−0.0929701
$146$	−3.21977e13	−0.275125
$147$	−6.57343e12	−0.0537315
$148$	2.51492e14	1.96709
$149$	−9.57664e13	−0.716972	−0.358486	−	0.933535i	$-0.616707\pi$
$149$	−9.57664e13	−0.716972	−0.358486	+	0.933535i	$0.616707\pi$
$150$	−1.17135e14	−0.839637
$151$	−1.03063e14	−0.707544	−0.353772	−	0.935332i	$-0.615101\pi$
$151$	−1.03063e14	−0.707544	−0.353772	+	0.935332i	$0.615101\pi$
$152$	4.74483e12	0.0312059
$153$	−2.04968e13	−0.129179
$154$	−3.59924e14	−2.17433
$155$	−1.38858e13	−0.0804294
$156$	−2.39896e13	−0.133264
$157$	2.47605e14	1.31951	0.659753	−	0.751482i	$-0.270661\pi$
$157$	2.47605e14	1.31951	0.659753	+	0.751482i	$0.270661\pi$
$158$	6.33944e13	0.324175
$159$	−1.85806e14	−0.911967
$160$	−2.85268e13	−0.134423
$161$	2.14742e14	0.971739
$162$	3.75056e13	0.163023
$163$	4.49313e14	1.87642	0.938208	−	0.346072i	$-0.112485\pi$
$163$	4.49313e14	1.87642	0.938208	+	0.346072i	$0.112485\pi$
$164$	−2.52636e14	−1.01393
$165$	2.18454e13	0.0842779
$166$	−2.74833e14	−1.01945
$167$	−1.95100e14	−0.695984	−0.347992	−	0.937498i	$-0.613136\pi$
$167$	−1.95100e14	−0.695984	−0.347992	+	0.937498i	$0.613136\pi$
$168$	−3.58956e13	−0.123177
$169$	−2.90730e14	−0.959902
$170$	−1.67861e13	−0.0533374
$171$	1.51805e13	0.0464314
$172$	6.78880e14	1.99921
$173$	−1.26094e14	−0.357597	−0.178798	−	0.983886i	$-0.557221\pi$
$173$	−1.26094e14	−0.357597	−0.178798	+	0.983886i	$0.557221\pi$
$174$	−3.07338e14	−0.839549
$175$	3.58671e14	0.943951
$176$	−5.05596e14	−1.28225
$177$	3.07496e13	0.0751646
$178$	−8.88057e14	−2.09272
$179$	−3.09537e13	−0.0703344	−0.0351672	−	0.999381i	$-0.511196\pi$
$179$	−3.09537e13	−0.0703344	−0.0351672	+	0.999381i	$0.511196\pi$
$180$	1.64471e13	0.0360428
$181$	−2.55327e14	−0.539741	−0.269871	−	0.962897i	$-0.586981\pi$
$181$	−2.55327e14	−0.539741	−0.269871	+	0.962897i	$0.586981\pi$
$182$	1.37184e14	0.279794
$183$	−3.14034e14	−0.618079
$184$	−1.20332e14	−0.228594
$185$	8.72880e13	0.160080
$186$	−4.10158e14	−0.726302
$187$	−3.52640e14	−0.603061
$188$	7.17767e14	1.18565
$189$	−1.14844e14	−0.183276
$190$	1.24322e13	0.0191713
$191$	8.50898e14	1.26812	0.634060	−	0.773284i	$-0.281387\pi$
$191$	8.50898e14	1.26812	0.634060	+	0.773284i	$0.281387\pi$
$192$	−5.12390e14	−0.738147
$193$	−2.10969e14	−0.293830	−0.146915	−	0.989149i	$-0.546934\pi$
$193$	−2.10969e14	−0.293830	−0.146915	+	0.989149i	$0.546934\pi$
$194$	4.16250e14	0.560586
$195$	−8.32630e12	−0.0108449
$196$	−8.51466e13	−0.107276
$197$	−6.04601e14	−0.736950	−0.368475	−	0.929638i	$-0.620120\pi$
$197$	−6.04601e14	−0.736950	−0.368475	+	0.929638i	$0.620120\pi$
$198$	6.45269e14	0.761056
$199$	1.46244e14	0.166929	0.0834647	−	0.996511i	$-0.473401\pi$
$199$	1.46244e14	0.166929	0.0834647	+	0.996511i	$0.473401\pi$
$200$	−2.00984e14	−0.222058
$201$	−8.79719e14	−0.940957
$202$	−1.05469e15	−1.09230
$203$	9.41083e14	0.943852
$204$	−2.65499e14	−0.257909
$205$	−8.76848e13	−0.0825133
$206$	−2.76769e15	−2.52337
$207$	−3.84988e14	−0.340126
$208$	1.92707e14	0.165000
$209$	2.61175e14	0.216760
$210$	−9.40526e13	−0.0756738
$211$	2.16811e15	1.69140	0.845700	−	0.533659i	$-0.179183\pi$
$211$	2.16811e15	1.69140	0.845700	+	0.533659i	$0.179183\pi$
$212$	−2.40678e15	−1.82076
$213$	4.87431e14	0.357640
$214$	2.51205e15	1.78788
$215$	2.35626e14	0.162694
$216$	6.43534e13	0.0431144
$217$	1.25592e15	0.816536
$218$	−2.17895e15	−1.37493
$219$	−1.76753e14	−0.108263
$220$	2.82966e14	0.168263
$221$	1.34408e14	0.0776022
$222$	2.57831e15	1.44558
$223$	1.49124e15	0.812020	0.406010	−	0.913869i	$-0.366920\pi$
$223$	1.49124e15	0.812020	0.406010	+	0.913869i	$0.366920\pi$
$224$	2.58015e15	1.36469
$225$	−6.43023e14	−0.330400
$226$	1.85873e15	0.927924
$227$	3.66877e15	1.77972	0.889862	−	0.456229i	$-0.150800\pi$
$227$	3.66877e15	1.77972	0.889862	+	0.456229i	$0.150800\pi$
$228$	1.96635e14	0.0927012
$229$	3.82282e15	1.75167	0.875836	−	0.482609i	$-0.160311\pi$
$229$	3.82282e15	1.75167	0.875836	+	0.482609i	$0.160311\pi$
$230$	−3.15291e14	−0.140436
$231$	−1.97584e15	−0.855607
$232$	−5.27341e14	−0.222034
$233$	−4.06875e15	−1.66590	−0.832948	−	0.553351i	$-0.813349\pi$
$233$	−4.06875e15	−1.66590	−0.832948	+	0.553351i	$0.813349\pi$
$234$	−2.45942e14	−0.0979332
$235$	2.49122e14	0.0964877
$236$	3.98304e14	0.150068
$237$	3.48010e14	0.127564
$238$	1.51825e15	0.541493
$239$	−4.72269e14	−0.163909	−0.0819546	−	0.996636i	$-0.526116\pi$
$239$	−4.72269e14	−0.163909	−0.0819546	+	0.996636i	$0.526116\pi$
$240$	−1.32119e14	−0.0446263
$241$	−2.15926e15	−0.709894	−0.354947	−	0.934886i	$-0.615501\pi$
$241$	−2.15926e15	−0.709894	−0.354947	+	0.934886i	$0.615501\pi$
$242$	6.51710e15	2.08571
$243$	2.05891e14	0.0641500
$244$	−4.06772e15	−1.23401
$245$	−2.95527e13	−0.00873006
$246$	−2.59003e15	−0.745121
$247$	−9.95459e13	−0.0278929
$248$	−7.03764e14	−0.192084
$249$	−1.50873e15	−0.401157
$250$	−1.05790e15	−0.274052
$251$	5.29839e15	1.33741	0.668705	−	0.743528i	$-0.266849\pi$
$251$	5.29839e15	1.33741	0.668705	+	0.743528i	$0.266849\pi$
$252$	−1.48759e15	−0.365914
$253$	−6.62357e15	−1.58785
$254$	−1.15636e16	−2.70192
$255$	−9.21492e13	−0.0209885
$256$	2.83177e15	0.628778
$257$	−7.76202e15	−1.68039	−0.840193	−	0.542287i	$-0.817559\pi$
$257$	−7.76202e15	−1.68039	−0.840193	+	0.542287i	$0.817559\pi$
$258$	6.95991e15	1.46918
$259$	−7.89491e15	−1.62517
$260$	−1.07852e14	−0.0216521
$261$	−1.68717e15	−0.330365
$262$	1.09751e16	2.09628
$263$	4.72422e15	0.880273	0.440137	−	0.897931i	$-0.354930\pi$
$263$	4.72422e15	0.880273	0.440137	+	0.897931i	$0.354930\pi$
$264$	1.10717e15	0.201275
$265$	−8.35344e14	−0.148172
$266$	−1.12446e15	−0.194631
$267$	−4.87509e15	−0.823492
$268$	−1.13951e16	−1.87864
$269$	8.59423e15	1.38298	0.691492	−	0.722384i	$-0.256954\pi$
$269$	8.59423e15	1.38298	0.691492	+	0.722384i	$0.256954\pi$
$270$	1.68617e14	0.0264872
$271$	−1.15719e16	−1.77462	−0.887308	−	0.461177i	$-0.847427\pi$
$271$	−1.15719e16	−1.77462	−0.887308	+	0.461177i	$0.847427\pi$
$272$	2.13273e15	0.319329
$273$	7.53087e14	0.110100
$274$	−1.08969e16	−1.55570
$275$	−1.10630e16	−1.54244
$276$	−4.98681e15	−0.679069
$277$	3.59234e15	0.477815	0.238907	−	0.971042i	$-0.423211\pi$
$277$	3.59234e15	0.477815	0.238907	+	0.971042i	$0.423211\pi$
$278$	−1.08176e16	−1.40553
$279$	−2.25161e15	−0.285802
$280$	−1.61379e14	−0.0200133
$281$	1.03686e16	1.25641	0.628204	−	0.778048i	$-0.283790\pi$
$281$	1.03686e16	1.25641	0.628204	+	0.778048i	$0.283790\pi$
$282$	7.35858e15	0.871314
$283$	1.07320e15	0.124185	0.0620924	−	0.998070i	$-0.480223\pi$
$283$	1.07320e15	0.124185	0.0620924	+	0.998070i	$0.480223\pi$
$284$	6.31377e15	0.714035
$285$	6.82482e13	0.00754397
$286$	−4.23134e15	−0.457192
$287$	7.93080e15	0.837692
$288$	−4.62568e15	−0.477666
$289$	−8.41706e15	−0.849815
$290$	−1.38172e15	−0.136406
$291$	2.28505e15	0.220593
$292$	−2.28950e15	−0.216149
$293$	1.79687e14	0.0165911	0.00829557	−	0.999966i	$-0.497359\pi$
$293$	1.79687e14	0.0165911	0.00829557	+	0.999966i	$0.497359\pi$
$294$	−8.72926e14	−0.0788352
$295$	1.38243e14	0.0122124
$296$	4.42396e15	0.382309
$297$	3.54227e15	0.299478
$298$	−1.27174e16	−1.05195
$299$	2.52456e15	0.204325
$300$	−8.32917e15	−0.659650
$301$	−2.13116e16	−1.65171
$302$	−1.36864e16	−1.03811
$303$	−5.78983e15	−0.429822
$304$	−1.57956e15	−0.114778
$305$	−1.41183e15	−0.100423
$306$	−2.72190e15	−0.189532
$307$	−7.84218e15	−0.534610	−0.267305	−	0.963612i	$-0.586133\pi$
$307$	−7.84218e15	−0.534610	−0.267305	+	0.963612i	$0.586133\pi$
$308$	−2.55934e16	−1.70824
$309$	−1.51935e16	−0.992954
$310$	−1.84398e15	−0.118006
$311$	9.56638e15	0.599522	0.299761	−	0.954014i	$-0.403093\pi$
$311$	9.56638e15	0.599522	0.299761	+	0.954014i	$0.403093\pi$
$312$	−4.21996e14	−0.0259002
$313$	4.96244e15	0.298303	0.149151	−	0.988814i	$-0.452346\pi$
$313$	4.96244e15	0.298303	0.149151	+	0.988814i	$0.452346\pi$
$314$	3.28810e16	1.93599
$315$	−5.16313e14	−0.0297779
$316$	4.50783e15	0.254684
$317$	2.91290e16	1.61228	0.806139	−	0.591726i	$-0.201553\pi$
$317$	2.91290e16	1.61228	0.806139	+	0.591726i	$0.201553\pi$
$318$	−2.46744e16	−1.33804
$319$	−2.90270e16	−1.54228
$320$	−2.30359e15	−0.119931
$321$	1.37902e16	0.703537
$322$	2.85170e16	1.42574
$323$	−1.10170e15	−0.0539817
$324$	2.66694e15	0.128077
$325$	4.21661e15	0.198482
$326$	5.96670e16	2.75309
$327$	−1.19616e16	−0.541040
$328$	−4.44407e15	−0.197061
$329$	−2.25323e16	−0.979563
$330$	2.90098e15	0.123653
$331$	−2.34480e15	−0.0979996	−0.0489998	−	0.998799i	$-0.515603\pi$
$331$	−2.34480e15	−0.0979996	−0.0489998	+	0.998799i	$0.515603\pi$
$332$	−1.95428e16	−0.800918
$333$	1.41539e16	0.568839
$334$	−2.59085e16	−1.02115
$335$	−3.95502e15	−0.152882
$336$	1.19497e16	0.453056
$337$	−4.95458e15	−0.184252	−0.0921260	−	0.995747i	$-0.529366\pi$
$337$	−4.95458e15	−0.184252	−0.0921260	+	0.995747i	$0.529366\pi$
$338$	−3.86079e16	−1.40837
$339$	1.02037e16	0.365141
$340$	−1.19362e15	−0.0419039
$341$	−3.87381e16	−1.33424
$342$	2.01591e15	0.0681244
$343$	3.13940e16	1.04096
$344$	1.19421e16	0.388552
$345$	−1.73082e15	−0.0552622
$346$	−1.67448e16	−0.524668
$347$	3.72121e16	1.14431	0.572153	−	0.820147i	$-0.306108\pi$
$347$	3.72121e16	1.14431	0.572153	+	0.820147i	$0.306108\pi$
$348$	−2.18541e16	−0.659581
$349$	−5.71815e16	−1.69391	−0.846954	−	0.531666i	$-0.821566\pi$
$349$	−5.71815e16	−1.69391	−0.846954	+	0.531666i	$0.821566\pi$
$350$	4.76302e16	1.38497
$351$	−1.35013e15	−0.0385371
$352$	−7.95829e16	−2.22994
$353$	1.22107e16	0.335896	0.167948	−	0.985796i	$-0.446286\pi$
$353$	1.22107e16	0.335896	0.167948	+	0.985796i	$0.446286\pi$
$354$	4.08343e15	0.110282
$355$	2.19138e15	0.0581077
$356$	−6.31477e16	−1.64412
$357$	8.33459e15	0.213079
$358$	−4.11053e15	−0.103195
$359$	−3.01276e13	−0.000742764 0	−0.000371382	−	1.00000i	$-0.500118\pi$
$359$	−3.01276e13	−0.000742764 0	−0.000371382		1.00000i	$0.500118\pi$
$360$	2.89319e14	0.00700503
$361$	−4.12370e16	−0.980597
$362$	−3.39064e16	−0.791911
$363$	3.57763e16	0.820735
$364$	9.75484e15	0.219817
$365$	−7.94641e14	−0.0175901
$366$	−4.17025e16	−0.906849
$367$	−1.56082e16	−0.333445	−0.166722	−	0.986004i	$-0.553318\pi$
$367$	−1.56082e16	−0.333445	−0.166722	+	0.986004i	$0.553318\pi$
$368$	4.00587e16	0.840787
$369$	−1.42183e16	−0.293208
$370$	1.15915e16	0.234871
$371$	7.55541e16	1.50428
$372$	−2.91654e16	−0.570610
$373$	5.51883e16	1.06106	0.530530	−	0.847666i	$-0.321993\pi$
$373$	5.51883e16	1.06106	0.530530	+	0.847666i	$0.321993\pi$
$374$	−4.68292e16	−0.884813
$375$	−5.80744e15	−0.107840
$376$	1.26261e16	0.230435
$377$	1.10636e16	0.198461
$378$	−1.52508e16	−0.268904
$379$	−1.00024e17	−1.73360	−0.866801	−	0.498655i	$-0.833827\pi$
$379$	−1.00024e17	−1.73360	−0.866801	+	0.498655i	$0.833827\pi$
$380$	8.84029e14	0.0150617
$381$	−6.34796e16	−1.06322
$382$	1.12996e17	1.86059
$383$	−4.18380e16	−0.677297	−0.338648	−	0.940913i	$-0.609970\pi$
$383$	−4.18380e16	−0.677297	−0.338648	+	0.940913i	$0.609970\pi$
$384$	−1.60633e16	−0.255671
$385$	−8.88295e15	−0.139015
$386$	−2.80159e16	−0.431108
$387$	3.82072e16	0.578128
$388$	2.95986e16	0.440418
$389$	1.99542e16	0.291986	0.145993	−	0.989286i	$-0.453362\pi$
$389$	1.99542e16	0.291986	0.145993	+	0.989286i	$0.453362\pi$
$390$	−1.10570e15	−0.0159118
$391$	2.79399e16	0.395435
$392$	−1.49780e15	−0.0208494
$393$	6.02489e16	0.824893
$394$	−8.02887e16	−1.08126
$395$	1.56458e15	0.0207260
$396$	4.58836e16	0.597914
$397$	−1.04995e15	−0.0134595	−0.00672976	−	0.999977i	$-0.502142\pi$
$397$	−1.04995e15	−0.0134595	−0.00672976	+	0.999977i	$0.502142\pi$
$398$	1.94206e16	0.244920
$399$	−6.17283e15	−0.0765879
$400$	6.69077e16	0.816744
$401$	7.08401e16	0.850826	0.425413	−	0.904999i	$-0.360129\pi$
$401$	7.08401e16	0.850826	0.425413	+	0.904999i	$0.360129\pi$
$402$	−1.16823e17	−1.38058
$403$	1.47649e16	0.171691
$404$	−7.49965e16	−0.858148
$405$	9.25641e14	0.0104228
$406$	1.24972e17	1.38482
$407$	2.43513e17	2.65557
$408$	−4.67034e15	−0.0501253
$409$	1.41645e17	1.49624	0.748118	−	0.663566i	$-0.230958\pi$
$409$	1.41645e17	1.49624	0.748118	+	0.663566i	$0.230958\pi$
$410$	−1.16442e16	−0.121064
$411$	−5.98199e16	−0.612173
$412$	−1.96804e17	−1.98245
$413$	−1.25037e16	−0.123983
$414$	−5.11250e16	−0.499035
$415$	−6.78290e15	−0.0651783
$416$	3.03328e16	0.286950
$417$	−5.93843e16	−0.553079
$418$	3.46830e16	0.318032
$419$	1.73885e17	1.56990	0.784949	−	0.619560i	$-0.212689\pi$
$419$	1.73885e17	1.56990	0.784949	+	0.619560i	$0.212689\pi$
$420$	−6.68787e15	−0.0594521
$421$	−1.68885e17	−1.47828	−0.739140	−	0.673552i	$-0.764768\pi$
$421$	−1.68885e17	−1.47828	−0.739140	+	0.673552i	$0.764768\pi$
$422$	2.87918e17	2.48163
$423$	4.03957e16	0.342865
$424$	−4.23372e16	−0.353870
$425$	4.66663e16	0.384127
$426$	6.47290e16	0.524731
$427$	1.27695e17	1.01951
$428$	1.78626e17	1.40463
$429$	−2.32284e16	−0.179907
$430$	3.12902e16	0.238706
$431$	1.52159e17	1.14339	0.571696	−	0.820465i	$-0.306286\pi$
$431$	1.52159e17	1.14339	0.571696	+	0.820465i	$0.306286\pi$
$432$	−2.14233e16	−0.158578
$433$	−5.23343e16	−0.381606	−0.190803	−	0.981628i	$-0.561109\pi$
$433$	−5.23343e16	−0.381606	−0.190803	+	0.981628i	$0.561109\pi$
$434$	1.66782e17	1.19803
$435$	−7.58513e15	−0.0536763
$436$	−1.54941e17	−1.08020
$437$	−2.06930e16	−0.142133
$438$	−2.34721e16	−0.158844
$439$	1.72056e17	1.14723	0.573616	−	0.819124i	$-0.305540\pi$
$439$	1.72056e17	1.14723	0.573616	+	0.819124i	$0.305540\pi$
$440$	4.97761e15	0.0327023
$441$	−4.79203e15	−0.0310219
$442$	1.78488e16	0.113858
$443$	−2.29805e17	−1.44456	−0.722280	−	0.691601i	$-0.756906\pi$
$443$	−2.29805e17	−1.44456	−0.722280	+	0.691601i	$0.756906\pi$
$444$	1.83338e17	1.13570
$445$	−2.19173e16	−0.133797
$446$	1.98031e17	1.19140
$447$	−6.98137e16	−0.413944
$448$	2.08352e17	1.21756
$449$	1.56059e17	0.898852	0.449426	−	0.893318i	$-0.351629\pi$
$449$	1.56059e17	0.898852	0.449426	+	0.893318i	$0.351629\pi$
$450$	−8.53911e16	−0.484765
$451$	−2.44620e17	−1.36881
$452$	1.32170e17	0.729012
$453$	−7.51330e16	−0.408501
$454$	4.87199e17	2.61122
$455$	3.38571e15	0.0178886
$456$	3.45898e15	0.0180167
$457$	3.56412e17	1.83019	0.915097	−	0.403234i	$-0.132114\pi$
$457$	3.56412e17	1.83019	0.915097	+	0.403234i	$0.132114\pi$
$458$	5.07656e17	2.57006
$459$	−1.49422e16	−0.0745816
$460$	−2.24196e16	−0.110332
$461$	−2.42553e17	−1.17693	−0.588465	−	0.808523i	$-0.700267\pi$
$461$	−2.42553e17	−1.17693	−0.588465	+	0.808523i	$0.700267\pi$
$462$	−2.62384e17	−1.25535
$463$	8.80260e16	0.415274	0.207637	−	0.978206i	$-0.433423\pi$
$463$	8.80260e16	0.415274	0.207637	+	0.978206i	$0.433423\pi$
$464$	1.75553e17	0.816658
$465$	−1.01227e16	−0.0464359
$466$	−5.40315e17	−2.44421
$467$	−9.09789e16	−0.405864	−0.202932	−	0.979193i	$-0.565047\pi$
$467$	−9.09789e16	−0.405864	−0.202932	+	0.979193i	$0.565047\pi$
$468$	−1.74884e16	−0.0769400
$469$	3.57719e17	1.55209
$470$	3.30825e16	0.141567
$471$	1.80504e17	0.761817
$472$	7.00650e15	0.0291661
$473$	6.57339e17	2.69893
$474$	4.62145e16	0.187163
$475$	−3.45623e16	−0.138068
$476$	1.07959e17	0.425417
$477$	−1.35453e17	−0.526525
$478$	−6.27156e16	−0.240488
$479$	−1.63047e17	−0.616782	−0.308391	−	0.951260i	$-0.599791\pi$
$479$	−1.63047e17	−0.616782	−0.308391	+	0.951260i	$0.599791\pi$
$480$	−2.07960e16	−0.0776090
$481$	−9.28142e16	−0.341721
$482$	−2.86741e17	−1.04156
$483$	1.56547e17	0.561034
$484$	4.63416e17	1.63861
$485$	1.02731e16	0.0358409
$486$	2.73416e16	0.0941213
$487$	5.00624e17	1.70049	0.850244	−	0.526389i	$-0.176454\pi$
$487$	5.00624e17	1.70049	0.850244	+	0.526389i	$0.176454\pi$
$488$	−7.15546e16	−0.239833
$489$	3.27549e17	1.08335
$490$	−3.92448e15	−0.0128088
$491$	−2.43281e17	−0.783571	−0.391786	−	0.920057i	$-0.628143\pi$
$491$	−2.43281e17	−0.783571	−0.391786	+	0.920057i	$0.628143\pi$
$492$	−1.84171e17	−0.585395
$493$	1.22443e17	0.384087
$494$	−1.32193e16	−0.0409246
$495$	1.59253e16	0.0486579
$496$	2.34284e17	0.706499
$497$	−1.98203e17	−0.589922
$498$	−2.00353e17	−0.588580
$499$	−1.64054e17	−0.475701	−0.237850	−	0.971302i	$-0.576443\pi$
$499$	−1.64054e17	−0.475701	−0.237850	+	0.971302i	$0.576443\pi$
$500$	−7.52247e16	−0.215306
$501$	−1.42228e17	−0.401827
$502$	7.03606e17	1.96226
$503$	−4.62875e17	−1.27430	−0.637150	−	0.770740i	$-0.719887\pi$
$503$	−4.62875e17	−1.27430	−0.637150	+	0.770740i	$0.719887\pi$
$504$	−2.61679e16	−0.0711165
$505$	−2.60298e16	−0.0698356
$506$	−8.79585e17	−2.32970
$507$	−2.11943e17	−0.554200
$508$	−8.22260e17	−2.12273
$509$	2.93175e17	0.747242	0.373621	−	0.927581i	$-0.378116\pi$
$509$	2.93175e17	0.747242	0.373621	+	0.927581i	$0.378116\pi$
$510$	−1.22371e16	−0.0307944
$511$	7.18726e16	0.178578
$512$	5.56556e17	1.36538
$513$	1.10666e16	0.0268072
$514$	−1.03077e18	−2.46547
$515$	−6.83068e16	−0.161331
$516$	4.94903e17	1.15424
$517$	6.94992e17	1.60063
$518$	−1.04841e18	−2.38446
$519$	−9.19222e16	−0.206458
$520$	−1.89720e15	−0.00420816
$521$	3.81809e17	0.836374	0.418187	−	0.908361i	$-0.362666\pi$
$521$	3.81809e17	0.836374	0.418187	+	0.908361i	$0.362666\pi$
$522$	−2.24049e17	−0.484714
$523$	3.63828e17	0.777384	0.388692	−	0.921368i	$-0.372927\pi$
$523$	3.63828e17	0.777384	0.388692	+	0.921368i	$0.372927\pi$
$524$	7.80413e17	1.64691
$525$	2.61471e17	0.544990
$526$	6.27358e17	1.29154
$527$	1.63407e17	0.332278
$528$	−3.68580e17	−0.740305
$529$	2.07533e16	0.0411742
$530$	−1.10931e17	−0.217399
$531$	2.24165e16	0.0433963
$532$	−7.99575e16	−0.152909
$533$	9.32361e16	0.176140
$534$	−6.47393e17	−1.20823
$535$	6.19976e16	0.114308
$536$	−2.00450e17	−0.365119
$537$	−2.25652e16	−0.0406076
$538$	1.14128e18	2.02912
$539$	−8.24449e16	−0.144823
$540$	1.19900e16	0.0208093
$541$	−2.11790e17	−0.363181	−0.181591	−	0.983374i	$-0.558125\pi$
$541$	−2.11790e17	−0.363181	−0.181591	+	0.983374i	$0.558125\pi$
$542$	−1.53671e18	−2.60373
$543$	−1.86133e17	−0.311620
$544$	3.35701e17	0.555340
$545$	−5.37768e16	−0.0879058
$546$	1.00007e17	0.161539
$547$	−1.02072e18	−1.62926	−0.814629	−	0.579983i	$-0.803059\pi$
$547$	−1.02072e18	−1.62926	−0.814629	+	0.579983i	$0.803059\pi$
$548$	−7.74856e17	−1.22221
$549$	−2.28931e17	−0.356848
$550$	−1.46912e18	−2.26308
$551$	−9.06847e16	−0.138054
$552$	−8.77221e16	−0.131979
$553$	−1.41511e17	−0.210415
$554$	4.77050e17	0.701052
$555$	6.36330e16	0.0924225
$556$	−7.69214e17	−1.10423
$557$	−1.35287e17	−0.191954	−0.0959771	−	0.995384i	$-0.530598\pi$
$557$	−1.35287e17	−0.191954	−0.0959771	+	0.995384i	$0.530598\pi$
$558$	−2.99005e17	−0.419331
$559$	−2.50543e17	−0.347301
$560$	5.37232e16	0.0736105
$561$	−2.57074e17	−0.348177
$562$	1.37692e18	1.84341
$563$	6.57878e17	0.870644	0.435322	−	0.900275i	$-0.356635\pi$
$563$	6.57878e17	0.870644	0.435322	+	0.900275i	$0.356635\pi$
$564$	5.23252e17	0.684537
$565$	4.58737e16	0.0593265
$566$	1.42517e17	0.182205
$567$	−8.37212e16	−0.105815
$568$	1.11064e17	0.138775
$569$	−2.58560e17	−0.319398	−0.159699	−	0.987166i	$-0.551052\pi$
$569$	−2.58560e17	−0.319398	−0.159699	+	0.987166i	$0.551052\pi$
$570$	9.06311e15	0.0110685
$571$	4.96473e17	0.599460	0.299730	−	0.954024i	$-0.403103\pi$
$571$	4.96473e17	0.599460	0.299730	+	0.954024i	$0.403103\pi$
$572$	−3.00881e17	−0.359187
$573$	6.20304e17	0.732150
$574$	1.05318e18	1.22907
$575$	8.76525e17	1.01140
$576$	−3.73532e17	−0.426169
$577$	2.24527e17	0.253295	0.126647	−	0.991948i	$-0.459578\pi$
$577$	2.24527e17	0.253295	0.126647	+	0.991948i	$0.459578\pi$
$578$	−1.11775e18	−1.24685
$579$	−1.53796e17	−0.169643
$580$	−9.82512e16	−0.107166
$581$	6.13491e17	0.661703
$582$	3.03446e17	0.323655
$583$	−2.33041e18	−2.45803
$584$	−4.02742e16	−0.0420091
$585$	−6.06987e15	−0.00626133
$586$	2.38617e16	0.0243426
$587$	−1.19786e18	−1.20853	−0.604267	−	0.796782i	$-0.706534\pi$
$587$	−1.19786e18	−1.20853	−0.604267	+	0.796782i	$0.706534\pi$
$588$	−6.20718e16	−0.0619358
$589$	−1.21023e17	−0.119432
$590$	1.83582e16	0.0179181
$591$	−4.40754e17	−0.425478
$592$	−1.47274e18	−1.40616
$593$	4.49893e17	0.424868	0.212434	−	0.977175i	$-0.431861\pi$
$593$	4.49893e17	0.424868	0.212434	+	0.977175i	$0.431861\pi$
$594$	4.70401e17	0.439396
$595$	3.74705e16	0.0346202
$596$	−9.04307e17	−0.826448
$597$	1.06612e17	0.0963767
$598$	3.35251e17	0.299787
$599$	−1.21623e18	−1.07582	−0.537912	−	0.843001i	$-0.680787\pi$
$599$	−1.21623e18	−1.07582	−0.537912	+	0.843001i	$0.680787\pi$
$600$	−1.46517e17	−0.128205
$601$	−1.74005e18	−1.50618	−0.753090	−	0.657918i	$-0.771437\pi$
$601$	−1.74005e18	−1.50618	−0.753090	+	0.657918i	$0.771437\pi$
$602$	−2.83010e18	−2.42339
$603$	−6.41315e17	−0.543262
$604$	−9.73209e17	−0.815579
$605$	1.60843e17	0.133349
$606$	−7.68868e17	−0.630637
$607$	−2.51327e17	−0.203945	−0.101973	−	0.994787i	$-0.532515\pi$
$607$	−2.51327e17	−0.203945	−0.101973	+	0.994787i	$0.532515\pi$
$608$	−2.48629e17	−0.199608
$609$	6.86050e17	0.544933
$610$	−1.87485e17	−0.147341
$611$	−2.64894e17	−0.205970
$612$	−1.93548e17	−0.148904
$613$	−1.43577e18	−1.09293	−0.546463	−	0.837483i	$-0.684026\pi$
$613$	−1.43577e18	−1.09293	−0.546463	+	0.837483i	$0.684026\pi$
$614$	−1.04141e18	−0.784383
$615$	−6.39222e16	−0.0476391
$616$	−4.50208e17	−0.332001
$617$	−7.11480e17	−0.519169	−0.259585	−	0.965720i	$-0.583586\pi$
$617$	−7.11480e17	−0.519169	−0.259585	+	0.965720i	$0.583586\pi$
$618$	−2.01765e18	−1.45687
$619$	2.70201e18	1.93063	0.965313	−	0.261096i	$-0.0840839\pi$
$619$	2.70201e18	1.93063	0.965313	+	0.261096i	$0.0840839\pi$
$620$	−1.31121e17	−0.0927102
$621$	−2.80657e17	−0.196372
$622$	1.27038e18	0.879622
$623$	1.98235e18	1.35834
$624$	1.40483e17	0.0952630
$625$	1.45089e18	0.973679
$626$	6.58994e17	0.437671
$627$	1.90396e17	0.125147
$628$	2.33809e18	1.52098
$629$	−1.02720e18	−0.661340
$630$	−6.85644e16	−0.0436903
$631$	2.58875e18	1.63268	0.816338	−	0.577575i	$-0.196001\pi$
$631$	2.58875e18	1.63268	0.816338	+	0.577575i	$0.196001\pi$
$632$	7.92964e16	0.0494986
$633$	1.58056e18	0.976530
$634$	3.86822e18	2.36554
$635$	−2.85390e17	−0.172747
$636$	−1.75454e18	−1.05122
$637$	3.14236e16	0.0186359
$638$	−3.85468e18	−2.26284
$639$	3.55337e17	0.206483
$640$	−7.22169e16	−0.0415402
$641$	1.47806e18	0.841617	0.420808	−	0.907150i	$-0.361746\pi$
$641$	1.47806e18	0.841617	0.420808	+	0.907150i	$0.361746\pi$
$642$	1.83128e18	1.03223
$643$	2.44980e18	1.36697	0.683487	−	0.729963i	$-0.260463\pi$
$643$	2.44980e18	1.36697	0.683487	+	0.729963i	$0.260463\pi$
$644$	2.02778e18	1.12011
$645$	1.71771e17	0.0939316
$646$	−1.46302e17	−0.0792023
$647$	−1.72269e18	−0.923270	−0.461635	−	0.887070i	$-0.652737\pi$
$647$	−1.72269e18	−0.923270	−0.461635	+	0.887070i	$0.652737\pi$
$648$	4.69136e16	0.0248921
$649$	3.85666e17	0.202591
$650$	5.59950e17	0.291214
$651$	9.15569e17	0.471427
$652$	4.24279e18	2.16293
$653$	−3.90745e17	−0.197223	−0.0986114	−	0.995126i	$-0.531440\pi$
$653$	−3.90745e17	−0.197223	−0.0986114	+	0.995126i	$0.531440\pi$
$654$	−1.58846e18	−0.793817
$655$	2.70866e17	0.134025
$656$	1.47944e18	0.724805
$657$	−1.28853e17	−0.0625056
$658$	−2.99221e18	−1.43722
$659$	1.27372e18	0.605787	0.302893	−	0.953024i	$-0.402047\pi$
$659$	1.27372e18	0.605787	0.302893	+	0.953024i	$0.402047\pi$
$660$	2.06282e17	0.0971464
$661$	−1.99395e18	−0.929832	−0.464916	−	0.885355i	$-0.653916\pi$
$661$	−1.99395e18	−0.929832	−0.464916	+	0.885355i	$0.653916\pi$
$662$	−3.11381e17	−0.143786
$663$	9.79832e16	0.0448037
$664$	−3.43773e17	−0.155661
$665$	−2.77517e16	−0.0124437
$666$	1.87959e18	0.834604
$667$	2.29983e18	1.01129
$668$	−1.84229e18	−0.802254
$669$	1.08712e18	0.468820
$670$	−5.25212e17	−0.224310
$671$	−3.93866e18	−1.66591
$672$	1.88093e18	0.787903
$673$	1.92835e18	0.799995	0.399998	−	0.916516i	$-0.369011\pi$
$673$	1.92835e18	0.799995	0.399998	+	0.916516i	$0.369011\pi$
$674$	−6.57949e17	−0.270335
$675$	−4.68764e17	−0.190757
$676$	−2.74532e18	−1.10647
$677$	4.89704e18	1.95482	0.977411	−	0.211347i	$-0.0677849\pi$
$677$	4.89704e18	1.95482	0.977411	+	0.211347i	$0.0677849\pi$
$678$	1.35502e18	0.535737
$679$	−9.29166e17	−0.363864
$680$	−2.09968e16	−0.00814414
$681$	2.67454e18	1.02752
$682$	−5.14427e18	−1.95761
$683$	3.31543e18	1.24970	0.624850	−	0.780745i	$-0.285160\pi$
$683$	3.31543e18	1.24970	0.624850	+	0.780745i	$0.285160\pi$
$684$	1.43347e17	0.0535210
$685$	−2.68937e17	−0.0994631
$686$	4.16900e18	1.52730
$687$	2.78683e18	1.01133
$688$	−3.97552e18	−1.42912
$689$	8.88230e17	0.316301
$690$	−2.29847e17	−0.0810810
$691$	−5.55368e18	−1.94077	−0.970385	−	0.241565i	$-0.922339\pi$
$691$	−5.55368e18	−1.94077	−0.970385	+	0.241565i	$0.922339\pi$
$692$	−1.19068e18	−0.412198
$693$	−1.44039e18	−0.493985
$694$	4.94163e18	1.67893
$695$	−2.66979e17	−0.0898619
$696$	−3.84432e17	−0.128191
$697$	1.03187e18	0.340887
$698$	−7.59348e18	−2.48531
$699$	−2.96612e18	−0.961806
$700$	3.38688e18	1.08808
$701$	−9.71425e17	−0.309202	−0.154601	−	0.987977i	$-0.549409\pi$
$701$	−9.71425e17	−0.309202	−0.154601	+	0.987977i	$0.549409\pi$
$702$	−1.79292e17	−0.0565418
$703$	7.60770e17	0.237708
$704$	−6.42647e18	−1.98953
$705$	1.81610e17	0.0557072
$706$	1.62154e18	0.492829
$707$	2.35431e18	0.708985
$708$	2.90364e17	0.0866416
$709$	5.57260e18	1.64762	0.823810	−	0.566866i	$-0.191844\pi$
$709$	5.57260e18	1.64762	0.823810	+	0.566866i	$0.191844\pi$
$710$	2.91007e17	0.0852559
$711$	2.53700e17	0.0736491
$712$	−1.11082e18	−0.319539
$713$	3.06924e18	0.874881
$714$	1.10680e18	0.312631
$715$	−1.04430e17	−0.0292304
$716$	−2.92291e17	−0.0810738
$717$	−3.44284e17	−0.0946330
$718$	−4.00084e15	−0.00108979
$719$	−5.92454e18	−1.59925	−0.799626	−	0.600498i	$-0.794969\pi$
$719$	−5.92454e18	−1.59925	−0.799626	+	0.600498i	$0.794969\pi$
$720$	−9.63145e16	−0.0257650
$721$	6.17813e18	1.63786
$722$	−5.47612e18	−1.43874
$723$	−1.57410e18	−0.409858
$724$	−2.41101e18	−0.622155
$725$	3.84127e18	0.982375
$726$	4.75097e18	1.20419
$727$	1.86694e18	0.468983	0.234492	−	0.972118i	$-0.424657\pi$
$727$	1.86694e18	0.468983	0.234492	+	0.972118i	$0.424657\pi$
$728$	1.71596e17	0.0427221
$729$	1.50095e17	0.0370370
$730$	−1.05525e17	−0.0258082
$731$	−2.77282e18	−0.672139
$732$	−2.96537e18	−0.712454
$733$	−6.19237e18	−1.47462	−0.737312	−	0.675552i	$-0.763905\pi$
$733$	−6.19237e18	−1.47462	−0.737312	+	0.675552i	$0.763905\pi$
$734$	−2.07271e18	−0.489232
$735$	−2.15439e16	−0.00504030
$736$	6.30541e18	1.46220
$737$	−1.10336e19	−2.53616
$738$	−1.88813e18	−0.430196
$739$	−4.59785e18	−1.03840	−0.519201	−	0.854652i	$-0.673770\pi$
$739$	−4.59785e18	−1.03840	−0.519201	+	0.854652i	$0.673770\pi$
$740$	8.24247e17	0.184523
$741$	−7.25690e16	−0.0161040
$742$	1.00333e19	2.20708
$743$	−7.98411e18	−1.74100	−0.870501	−	0.492167i	$-0.836205\pi$
$743$	−7.98411e18	−1.74100	−0.870501	+	0.492167i	$0.836205\pi$
$744$	−5.13044e17	−0.110900
$745$	−3.13867e17	−0.0672558
$746$	7.32881e18	1.55679
$747$	−1.09986e18	−0.231608
$748$	−3.32992e18	−0.695142
$749$	−5.60748e18	−1.16047
$750$	−7.71207e17	−0.158224
$751$	−5.05379e18	−1.02792	−0.513958	−	0.857816i	$-0.671821\pi$
$751$	−5.05379e18	−1.02792	−0.513958	+	0.857816i	$0.671821\pi$
$752$	−4.20325e18	−0.847557
$753$	3.86253e18	0.772154
$754$	1.46920e18	0.291184
$755$	−3.37782e17	−0.0663714
$756$	−1.08445e18	−0.211261
$757$	2.12068e18	0.409592	0.204796	−	0.978805i	$-0.434347\pi$
$757$	2.12068e18	0.409592	0.204796	+	0.978805i	$0.434347\pi$
$758$	−1.32828e19	−2.54355
$759$	−4.82858e18	−0.916744
$760$	1.55508e16	0.00292728
$761$	1.52694e18	0.284985	0.142492	−	0.989796i	$-0.454488\pi$
$761$	1.52694e18	0.284985	0.142492	+	0.989796i	$0.454488\pi$
$762$	−8.42985e18	−1.55996
$763$	4.86393e18	0.892438
$764$	8.03489e18	1.46175
$765$	−6.71768e16	−0.0121177
$766$	−5.55593e18	−0.993733
$767$	−1.46996e17	−0.0260696
$768$	2.06436e18	0.363025
$769$	5.81098e18	1.01328	0.506639	−	0.862158i	$-0.330888\pi$
$769$	5.81098e18	1.01328	0.506639	+	0.862158i	$0.330888\pi$
$770$	−1.17962e18	−0.203964
$771$	−5.65851e18	−0.970172
$772$	−1.99214e18	−0.338695
$773$	−6.26176e17	−0.105567	−0.0527837	−	0.998606i	$-0.516809\pi$
$773$	−6.26176e17	−0.105567	−0.0527837	+	0.998606i	$0.516809\pi$
$774$	5.07377e18	0.848232
$775$	5.12637e18	0.849863
$776$	5.20663e17	0.0855965
$777$	−5.75539e18	−0.938292
$778$	2.64984e18	0.428403
$779$	−7.64228e17	−0.122526
$780$	−7.86240e16	−0.0125009
$781$	6.11343e18	0.963948
$782$	3.71031e18	0.580185
$783$	−1.22994e18	−0.190737
$784$	4.98619e17	0.0766857
$785$	8.11506e17	0.123777
$786$	8.00083e18	1.21029
$787$	2.26575e18	0.339920	0.169960	−	0.985451i	$-0.445636\pi$
$787$	2.26575e18	0.339920	0.169960	+	0.985451i	$0.445636\pi$
$788$	−5.70915e18	−0.849476
$789$	3.44395e18	0.508226
$790$	2.07770e17	0.0304093
$791$	−4.14913e18	−0.602295
$792$	8.07130e17	0.116206
$793$	1.50121e18	0.214371
$794$	−1.39429e17	−0.0197479
$795$	−6.08966e17	−0.0855474
$796$	1.38096e18	0.192418
$797$	−1.35306e19	−1.86998	−0.934991	−	0.354671i	$-0.884593\pi$
$797$	−1.35306e19	−1.86998	−0.934991	+	0.354671i	$0.884593\pi$
$798$	−8.19728e17	−0.112370
$799$	−2.93165e18	−0.398619
$800$	1.05315e19	1.42039
$801$	−3.55394e18	−0.475443
$802$	9.40730e18	1.24834
$803$	−2.21686e18	−0.291801
$804$	−8.30705e18	−1.08463
$805$	7.03802e17	0.0911543
$806$	1.96072e18	0.251906
$807$	6.26519e18	0.798466
$808$	−1.31925e18	−0.166784
$809$	−1.48044e19	−1.85663	−0.928316	−	0.371792i	$-0.878743\pi$
$809$	−1.48044e19	−1.85663	−0.928316	+	0.371792i	$0.878743\pi$
$810$	1.22922e17	0.0152924
$811$	−3.69728e18	−0.456296	−0.228148	−	0.973626i	$-0.573267\pi$
$811$	−3.69728e18	−0.456296	−0.228148	+	0.973626i	$0.573267\pi$
$812$	8.88650e18	1.08797
$813$	−8.43592e18	−1.02458
$814$	3.23376e19	3.89627
$815$	1.47259e18	0.176018
$816$	1.55476e18	0.184365
$817$	2.05363e18	0.241589
$818$	1.88099e19	2.19528
$819$	5.49000e17	0.0635663
$820$	−8.27994e17	−0.0951124
$821$	−5.35507e18	−0.610288	−0.305144	−	0.952306i	$-0.598705\pi$
$821$	−5.35507e18	−0.610288	−0.305144	+	0.952306i	$0.598705\pi$
$822$	−7.94386e18	−0.898183
$823$	−5.20121e18	−0.583452	−0.291726	−	0.956502i	$-0.594230\pi$
$823$	−5.20121e18	−0.583452	−0.291726	+	0.956502i	$0.594230\pi$
$824$	−3.46195e18	−0.385295
$825$	−8.06490e18	−0.890529
$826$	−1.66044e18	−0.181908
$827$	1.78558e18	0.194086	0.0970429	−	0.995280i	$-0.469062\pi$
$827$	1.78558e18	0.194086	0.0970429	+	0.995280i	$0.469062\pi$
$828$	−3.63539e18	−0.392061
$829$	−1.17882e19	−1.26137	−0.630685	−	0.776039i	$-0.717226\pi$
$829$	−1.17882e19	−1.26137	−0.630685	+	0.776039i	$0.717226\pi$
$830$	−9.00744e17	−0.0956299
$831$	2.61882e18	0.275866
$832$	2.44943e18	0.256014
$833$	3.47773e17	0.0360665
$834$	−7.88601e18	−0.811481
$835$	−6.39424e17	−0.0652870
$836$	2.46623e18	0.249858
$837$	−1.64142e18	−0.165008
$838$	2.30913e19	2.30336
$839$	5.72612e18	0.566771	0.283385	−	0.959006i	$-0.408542\pi$
$839$	5.72612e18	0.566771	0.283385	+	0.959006i	$0.408542\pi$
$840$	−1.17645e17	−0.0115547
$841$	−1.81903e17	−0.0177282
$842$	−2.24273e19	−2.16894
$843$	7.55874e18	0.725388
$844$	2.04732e19	1.94966
$845$	−9.52847e17	−0.0900439
$846$	5.36440e18	0.503053
$847$	−1.45477e19	−1.35379
$848$	1.40941e19	1.30156
$849$	7.82362e17	0.0716981
$850$	6.19711e18	0.563594
$851$	−1.92937e19	−1.74130
$852$	4.60274e18	0.412248
$853$	−2.20710e19	−1.96180	−0.980899	−	0.194518i	$-0.937686\pi$
$853$	−2.20710e19	−1.96180	−0.980899	+	0.194518i	$0.937686\pi$
$854$	1.69574e19	1.49583
$855$	4.97530e16	0.00435551
$856$	3.14218e18	0.272993
$857$	−4.23577e17	−0.0365222	−0.0182611	−	0.999833i	$-0.505813\pi$
$857$	−4.23577e17	−0.0365222	−0.0182611	+	0.999833i	$0.505813\pi$
$858$	−3.08464e18	−0.263960
$859$	2.07535e19	1.76253	0.881263	−	0.472626i	$-0.156694\pi$
$859$	2.07535e19	1.76253	0.881263	+	0.472626i	$0.156694\pi$
$860$	2.22498e18	0.187536
$861$	5.78155e18	0.483642
$862$	2.02061e19	1.67759
$863$	1.59791e19	1.31669	0.658343	−	0.752718i	$-0.271258\pi$
$863$	1.59791e19	1.31669	0.658343	+	0.752718i	$0.271258\pi$
$864$	−3.37212e18	−0.275781
$865$	−4.13262e17	−0.0335445
$866$	−6.94980e18	−0.559894
$867$	−6.13603e18	−0.490641
$868$	1.18595e19	0.941213
$869$	4.36480e18	0.343824
$870$	−1.00728e18	−0.0787542
$871$	4.20541e18	0.326355
$872$	−2.72553e18	−0.209939
$873$	1.66580e18	0.127359
$874$	−2.74796e18	−0.208538
$875$	2.36147e18	0.177881
$876$	−1.66905e18	−0.124794
$877$	1.05162e19	0.780478	0.390239	−	0.920714i	$-0.372392\pi$
$877$	1.05162e19	0.780478	0.390239	+	0.920714i	$0.372392\pi$
$878$	2.28484e19	1.68323
$879$	1.30992e17	0.00957890
$880$	−1.65705e18	−0.120282
$881$	−1.06384e19	−0.766538	−0.383269	−	0.923637i	$-0.625202\pi$
$881$	−1.06384e19	−0.766538	−0.383269	+	0.923637i	$0.625202\pi$
$882$	−6.36363e17	−0.0455155
$883$	−1.69853e19	−1.20595	−0.602973	−	0.797762i	$-0.706017\pi$
$883$	−1.69853e19	−1.20595	−0.602973	+	0.797762i	$0.706017\pi$
$884$	1.26919e18	0.0894514
$885$	1.00779e17	0.00705084
$886$	−3.05173e19	−2.11947
$887$	−9.89263e18	−0.682038	−0.341019	−	0.940056i	$-0.610772\pi$
$887$	−9.89263e18	−0.682038	−0.341019	+	0.940056i	$0.610772\pi$
$888$	3.22507e18	0.220726
$889$	2.58126e19	1.75376
$890$	−2.91054e18	−0.196308
$891$	2.58232e18	0.172904
$892$	1.40816e19	0.936008
$893$	2.17126e18	0.143277
$894$	−9.27100e18	−0.607341
$895$	−1.01448e17	−0.00659774
$896$	6.53178e18	0.421725
$897$	1.84040e18	0.117967
$898$	2.07241e19	1.31880
$899$	1.34506e19	0.849773
$900$	−6.07197e18	−0.380849
$901$	9.83026e18	0.612144
$902$	−3.24846e19	−2.00833
$903$	−1.55361e19	−0.953613
$904$	2.32499e18	0.141686
$905$	−8.36814e17	−0.0506306
$906$	−9.97739e18	−0.599354
$907$	2.97940e18	0.177697	0.0888486	−	0.996045i	$-0.471681\pi$
$907$	2.97940e18	0.177697	0.0888486	+	0.996045i	$0.471681\pi$
$908$	3.46437e19	2.05147
$909$	−4.22079e18	−0.248158
$910$	4.49610e17	0.0262462
$911$	6.63263e18	0.384429	0.192214	−	0.981353i	$-0.438433\pi$
$911$	6.63263e18	0.384429	0.192214	+	0.981353i	$0.438433\pi$
$912$	−1.15150e18	−0.0662669
$913$	−1.89227e19	−1.08124
$914$	4.73302e19	2.68527
$915$	−1.02922e18	−0.0579791
$916$	3.60983e19	2.01914
$917$	−2.44989e19	−1.36065
$918$	−1.98427e18	−0.109427
$919$	−7.46279e18	−0.408649	−0.204325	−	0.978903i	$-0.565500\pi$
$919$	−7.46279e18	−0.408649	−0.204325	+	0.978903i	$0.565500\pi$
$920$	−3.94379e17	−0.0214434
$921$	−5.71695e18	−0.308657
$922$	−3.22101e19	−1.72680
$923$	−2.33012e18	−0.124041
$924$	−1.86576e19	−0.986251
$925$	−3.22251e19	−1.69150
$926$	1.16895e19	0.609292
$927$	−1.10761e19	−0.573282
$928$	2.76327e19	1.42024
$929$	−3.43293e19	−1.75212	−0.876059	−	0.482204i	$-0.839836\pi$
$929$	−3.43293e19	−1.75212	−0.876059	+	0.482204i	$0.839836\pi$
$930$	−1.34426e18	−0.0681310
$931$	−2.57570e17	−0.0129635
$932$	−3.84206e19	−1.92026
$933$	6.97389e18	0.346134
$934$	−1.20817e19	−0.595486
$935$	−1.15575e18	−0.0565703
$936$	−3.07635e17	−0.0149535
$937$	−1.72224e19	−0.831353	−0.415676	−	0.909513i	$-0.636455\pi$
$937$	−1.72224e19	−0.831353	−0.415676	+	0.909513i	$0.636455\pi$
$938$	4.75037e19	2.27724
$939$	3.61762e18	0.172225
$940$	2.35242e18	0.111220
$941$	8.65054e18	0.406173	0.203086	−	0.979161i	$-0.434903\pi$
$941$	8.65054e18	0.406173	0.203086	+	0.979161i	$0.434903\pi$
$942$	2.39702e19	1.11774
$943$	1.93814e19	0.897549
$944$	−2.33247e18	−0.107275
$945$	−3.76392e17	−0.0171923
$946$	8.72922e19	3.95989
$947$	1.25519e19	0.565502	0.282751	−	0.959193i	$-0.408753\pi$
$947$	1.25519e19	0.565502	0.282751	+	0.959193i	$0.408753\pi$
$948$	3.28621e18	0.147042
$949$	8.44949e17	0.0375492
$950$	−4.58975e18	−0.202575
$951$	2.12350e19	0.930849
$952$	1.89909e18	0.0826810
$953$	2.13965e18	0.0925206	0.0462603	−	0.998929i	$-0.485270\pi$
$953$	2.13965e18	0.0925206	0.0462603	+	0.998929i	$0.485270\pi$
$954$	−1.79876e19	−0.772520
$955$	2.78875e18	0.118956
$956$	−4.45956e18	−0.188937
$957$	−2.11607e19	−0.890435
$958$	−2.16520e19	−0.904946
$959$	2.43245e19	1.00977
$960$	−1.67932e18	−0.0692421
$961$	−6.46705e18	−0.264852
$962$	−1.23254e19	−0.501374
$963$	1.00530e19	0.406187
$964$	−2.03895e19	−0.818288
$965$	−6.91434e17	−0.0275628
$966$	2.07889e19	0.823152
$967$	−2.35896e19	−0.927787	−0.463893	−	0.885891i	$-0.653548\pi$
$967$	−2.35896e19	−0.927787	−0.463893	+	0.885891i	$0.653548\pi$
$968$	8.15187e18	0.318469
$969$	−8.03139e17	−0.0311664
$970$	1.36423e18	0.0525860
$971$	4.95150e18	0.189589	0.0947943	−	0.995497i	$-0.469781\pi$
$971$	4.95150e18	0.189589	0.0947943	+	0.995497i	$0.469781\pi$
$972$	1.94420e18	0.0739452
$973$	2.41473e19	0.912296
$974$	6.64810e19	2.49496
$975$	3.07391e18	0.114594
$976$	2.38206e19	0.882123
$977$	−3.13735e19	−1.15411	−0.577057	−	0.816704i	$-0.695799\pi$
$977$	−3.13735e19	−1.15411	−0.577057	+	0.816704i	$0.695799\pi$
$978$	4.34973e19	1.58950
$979$	−6.11441e19	−2.21956
$980$	−2.79061e17	−0.0100631
$981$	−8.72002e18	−0.312370
$982$	−3.23068e19	−1.14966
$983$	4.03527e19	1.42651	0.713256	−	0.700904i	$-0.247220\pi$
$983$	4.03527e19	1.42651	0.713256	+	0.700904i	$0.247220\pi$
$984$	−3.23972e18	−0.113773
$985$	−1.98153e18	−0.0691299
$986$	1.62600e19	0.563534
$987$	−1.64261e19	−0.565551
$988$	−9.39997e17	−0.0321519
$989$	−5.20814e19	−1.76973
$990$	2.11482e18	0.0713911
$991$	1.85886e19	0.623403	0.311701	−	0.950180i	$-0.399101\pi$
$991$	1.85886e19	0.623403	0.311701	+	0.950180i	$0.399101\pi$
$992$	3.68773e19	1.22866
$993$	−1.70936e18	−0.0565801
$994$	−2.63207e19	−0.865536
$995$	4.79303e17	0.0156589
$996$	−1.42467e19	−0.462410
$997$	−1.41749e19	−0.457090	−0.228545	−	0.973533i	$-0.573397\pi$
$997$	−1.41749e19	−0.457090	−0.228545	+	0.973533i	$0.573397\pi$
$998$	−2.17858e19	−0.697951
$999$	1.03182e19	0.328420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.26	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.26	✓	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)

\(f(q)\)	\(=\)	\(q+132.796 q^{2} +729.000 q^{3} +9442.84 q^{4} +3277.42 q^{5} +96808.5 q^{6} -296432. q^{7} +166107. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+132.796 q^{2} +729.000 q^{3} +9442.84 q^{4} +3277.42 q^{5} +96808.5 q^{6} -296432. q^{7} +166107. q^{8} +531441. q^{9} +435229. q^{10} +9.14323e6 q^{11} +6.88383e6 q^{12} -3.48492e6 q^{13} -3.93651e7 q^{14} +2.38924e6 q^{15} -5.52973e7 q^{16} -3.85684e7 q^{17} +7.05734e7 q^{18} +2.85648e7 q^{19} +3.09482e7 q^{20} -2.16099e8 q^{21} +1.21419e9 q^{22} -7.24424e8 q^{23} +1.21092e8 q^{24} -1.20996e9 q^{25} -4.62784e8 q^{26} +3.87420e8 q^{27} -2.79916e9 q^{28} -3.17470e9 q^{29} +3.17282e8 q^{30} -4.23680e9 q^{31} -8.70403e9 q^{32} +6.66541e9 q^{33} -5.12174e9 q^{34} -9.71533e8 q^{35} +5.01831e9 q^{36} +2.66331e10 q^{37} +3.79330e9 q^{38} -2.54050e9 q^{39} +5.44404e8 q^{40} -2.67542e10 q^{41} -2.86971e10 q^{42} +7.18936e10 q^{43} +8.63381e10 q^{44} +1.74176e9 q^{45} -9.62007e10 q^{46} +7.60117e10 q^{47} -4.03118e10 q^{48} -9.01705e9 q^{49} -1.60678e11 q^{50} -2.81164e10 q^{51} -3.29075e10 q^{52} -2.54878e11 q^{53} +5.14480e10 q^{54} +2.99662e10 q^{55} -4.92396e10 q^{56} +2.08237e10 q^{57} -4.21588e11 q^{58} +4.21805e10 q^{59} +2.25612e10 q^{60} -4.30773e11 q^{61} -5.62632e11 q^{62} -1.57536e11 q^{63} -7.02867e11 q^{64} -1.14215e10 q^{65} +8.85142e11 q^{66} -1.20675e12 q^{67} -3.64195e11 q^{68} -5.28105e11 q^{69} -1.29016e11 q^{70} +6.68630e11 q^{71} +8.82763e10 q^{72} -2.42459e11 q^{73} +3.53678e12 q^{74} -8.82062e11 q^{75} +2.69733e11 q^{76} -2.71035e12 q^{77} -3.37369e11 q^{78} +4.77381e11 q^{79} -1.81233e11 q^{80} +2.82430e11 q^{81} -3.55286e12 q^{82} -2.06958e12 q^{83} -2.04059e12 q^{84} -1.26405e11 q^{85} +9.54720e12 q^{86} -2.31436e12 q^{87} +1.51876e12 q^{88} -6.68736e12 q^{89} +2.31299e11 q^{90} +1.03304e12 q^{91} -6.84062e12 q^{92} -3.08863e12 q^{93} +1.00941e13 q^{94} +9.36190e10 q^{95} -6.34524e12 q^{96} +3.13450e12 q^{97} -1.19743e12 q^{98} +4.85909e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 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

Modular forms

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