LMFDB - Embedded newform 177.14.a.c.1.20

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:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+68.2207 q^{2} +729.000 q^{3} -3537.94 q^{4} -14307.6 q^{5} +49732.9 q^{6} -16077.5 q^{7} -800224. q^{8} +531441. q^{9} +O(q^{10})$	\(q+68.2207 q^{2} +729.000 q^{3} -3537.94 q^{4} -14307.6 q^{5} +49732.9 q^{6} -16077.5 q^{7} -800224. q^{8} +531441. q^{9} -976072. q^{10} -5.62969e6 q^{11} -2.57916e6 q^{12} -1.90389e7 q^{13} -1.09681e6 q^{14} -1.04302e7 q^{15} -2.56090e7 q^{16} +1.17014e8 q^{17} +3.62553e7 q^{18} +6.78180e7 q^{19} +5.06193e7 q^{20} -1.17205e7 q^{21} -3.84061e8 q^{22} -1.30559e9 q^{23} -5.83364e8 q^{24} -1.01600e9 q^{25} -1.29885e9 q^{26} +3.87420e8 q^{27} +5.68811e7 q^{28} +1.88273e8 q^{29} -7.11557e8 q^{30} -4.39205e9 q^{31} +4.80837e9 q^{32} -4.10404e9 q^{33} +7.98274e9 q^{34} +2.30029e8 q^{35} -1.88021e9 q^{36} +2.15668e10 q^{37} +4.62659e9 q^{38} -1.38794e10 q^{39} +1.14493e10 q^{40} +7.66988e9 q^{41} -7.99578e8 q^{42} +4.14186e10 q^{43} +1.99175e10 q^{44} -7.60363e9 q^{45} -8.90679e10 q^{46} -1.24725e11 q^{47} -1.86690e10 q^{48} -9.66305e10 q^{49} -6.93120e10 q^{50} +8.53029e10 q^{51} +6.73585e10 q^{52} +1.16632e11 q^{53} +2.64301e10 q^{54} +8.05471e10 q^{55} +1.28656e10 q^{56} +4.94393e10 q^{57} +1.28441e10 q^{58} -4.21805e10 q^{59} +3.69015e10 q^{60} +9.07189e10 q^{61} -2.99628e11 q^{62} -8.54422e9 q^{63} +5.37820e11 q^{64} +2.72400e11 q^{65} -2.79980e11 q^{66} +2.79779e11 q^{67} -4.13987e11 q^{68} -9.51772e11 q^{69} +1.56928e10 q^{70} +8.96606e11 q^{71} -4.25272e11 q^{72} +2.19719e9 q^{73} +1.47130e12 q^{74} -7.40661e11 q^{75} -2.39936e11 q^{76} +9.05110e10 q^{77} -9.46859e11 q^{78} -2.36194e12 q^{79} +3.66403e11 q^{80} +2.82430e11 q^{81} +5.23244e11 q^{82} +3.89435e12 q^{83} +4.14663e10 q^{84} -1.67418e12 q^{85} +2.82560e12 q^{86} +1.37251e11 q^{87} +4.50501e12 q^{88} +3.38545e12 q^{89} -5.18725e11 q^{90} +3.06097e11 q^{91} +4.61908e12 q^{92} -3.20180e12 q^{93} -8.50881e12 q^{94} -9.70311e11 q^{95} +3.50530e12 q^{96} -2.54230e12 q^{97} -6.59220e12 q^{98} -2.99185e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) $ 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * 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 $

$2$	68.2207	0.753739	0.376869	−	0.926266i	$-0.377001\pi$
$2$	68.2207	0.753739	0.376869	+	0.926266i	$0.377001\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−3537.94	−0.431878
$5$	−14307.6	−0.409507	−0.204753	−	0.978814i	$-0.565639\pi$
$5$	−14307.6	−0.409507	−0.204753	+	0.978814i	$0.565639\pi$
$6$	49732.9	0.435171
$7$	−16077.5	−0.0516512	−0.0258256	−	0.999666i	$-0.508221\pi$
$7$	−16077.5	−0.0516512	−0.0258256	+	0.999666i	$0.508221\pi$
$8$	−800224.	−1.07926
$9$	531441.	0.333333
$10$	−976072.	−0.308661
$11$	−5.62969e6	−0.958146	−0.479073	−	0.877775i	$-0.659027\pi$
$11$	−5.62969e6	−0.958146	−0.479073	+	0.877775i	$0.659027\pi$
$12$	−2.57916e6	−0.249345
$13$	−1.90389e7	−1.09398	−0.546991	−	0.837139i	$-0.684227\pi$
$13$	−1.90389e7	−1.09398	−0.546991	+	0.837139i	$0.684227\pi$
$14$	−1.09681e6	−0.0389315
$15$	−1.04302e7	−0.236429
$16$	−2.56090e7	−0.381604
$17$	1.17014e8	1.17576	0.587879	−	0.808949i	$-0.299963\pi$
$17$	1.17014e8	1.17576	0.587879	+	0.808949i	$0.299963\pi$
$18$	3.62553e7	0.251246
$19$	6.78180e7	0.330709	0.165355	−	0.986234i	$-0.447123\pi$
$19$	6.78180e7	0.330709	0.165355	+	0.986234i	$0.447123\pi$
$20$	5.06193e7	0.176857
$21$	−1.17205e7	−0.0298208
$22$	−3.84061e8	−0.722192
$23$	−1.30559e9	−1.83897	−0.919485	−	0.393126i	$-0.871394\pi$
$23$	−1.30559e9	−1.83897	−0.919485	+	0.393126i	$0.871394\pi$
$24$	−5.83364e8	−0.623112
$25$	−1.01600e9	−0.832304
$26$	−1.29885e9	−0.824577
$27$	3.87420e8	0.192450
$28$	5.68811e7	0.0223070
$29$	1.88273e8	0.0587761	0.0293881	−	0.999568i	$-0.490644\pi$
$29$	1.88273e8	0.0587761	0.0293881	+	0.999568i	$0.490644\pi$
$30$	−7.11557e8	−0.178206
$31$	−4.39205e9	−0.888824	−0.444412	−	0.895822i	$-0.646587\pi$
$31$	−4.39205e9	−0.888824	−0.444412	+	0.895822i	$0.646587\pi$
$32$	4.80837e9	0.791632
$33$	−4.10404e9	−0.553186
$34$	7.98274e9	0.886215
$35$	2.30029e8	0.0211515
$36$	−1.88021e9	−0.143959
$37$	2.15668e10	1.38189	0.690945	−	0.722907i	$-0.257194\pi$
$37$	2.15668e10	1.38189	0.690945	+	0.722907i	$0.257194\pi$
$38$	4.62659e9	0.249269
$39$	−1.38794e10	−0.631611
$40$	1.14493e10	0.441965
$41$	7.66988e9	0.252170	0.126085	−	0.992019i	$-0.459759\pi$
$41$	7.66988e9	0.252170	0.126085	+	0.992019i	$0.459759\pi$
$42$	−7.99578e8	−0.0224771
$43$	4.14186e10	0.999195	0.499598	−	0.866258i	$-0.333481\pi$
$43$	4.14186e10	0.999195	0.499598	+	0.866258i	$0.333481\pi$
$44$	1.99175e10	0.413802
$45$	−7.60363e9	−0.136502
$46$	−8.90679e10	−1.38610
$47$	−1.24725e11	−1.68778	−0.843892	−	0.536513i	$-0.819741\pi$
$47$	−1.24725e11	−1.68778	−0.843892	+	0.536513i	$0.819741\pi$
$48$	−1.86690e10	−0.220319
$49$	−9.66305e10	−0.997332
$50$	−6.93120e10	−0.627340
$51$	8.53029e10	0.678825
$52$	6.73585e10	0.472466
$53$	1.16632e11	0.722812	0.361406	−	0.932409i	$-0.382297\pi$
$53$	1.16632e11	0.722812	0.361406	+	0.932409i	$0.382297\pi$
$54$	2.64301e10	0.145057
$55$	8.05471e10	0.392367
$56$	1.28656e10	0.0557451
$57$	4.94393e10	0.190935
$58$	1.28441e10	0.0443018
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	3.69015e10	0.102108
$61$	9.07189e10	0.225452	0.112726	−	0.993626i	$-0.464042\pi$
$61$	9.07189e10	0.225452	0.112726	+	0.993626i	$0.464042\pi$
$62$	−2.99628e11	−0.669941
$63$	−8.54422e9	−0.0172171
$64$	5.37820e11	0.978288
$65$	2.72400e11	0.447993
$66$	−2.79980e11	−0.416958
$67$	2.79779e11	0.377858	0.188929	−	0.981991i	$-0.439498\pi$
$67$	2.79779e11	0.377858	0.188929	+	0.981991i	$0.439498\pi$
$68$	−4.13987e11	−0.507784
$69$	−9.51772e11	−1.06173
$70$	1.56928e10	0.0159427
$71$	8.96606e11	0.830658	0.415329	−	0.909671i	$-0.363666\pi$
$71$	8.96606e11	0.830658	0.415329	+	0.909671i	$0.363666\pi$
$72$	−4.25272e11	−0.359754
$73$	2.19719e9	0.00169930	0.000849649	−	1.00000i	$-0.499730\pi$
$73$	2.19719e9	0.00169930	0.000849649		1.00000i	$0.499730\pi$
$74$	1.47130e12	1.04158
$75$	−7.40661e11	−0.480531
$76$	−2.39936e11	−0.142826
$77$	9.05110e10	0.0494893
$78$	−9.46859e11	−0.476070
$79$	−2.36194e12	−1.09318	−0.546591	−	0.837400i	$-0.684075\pi$
$79$	−2.36194e12	−1.09318	−0.546591	+	0.837400i	$0.684075\pi$
$80$	3.66403e11	0.156269
$81$	2.82430e11	0.111111
$82$	5.23244e11	0.190070
$83$	3.89435e12	1.30746	0.653729	−	0.756729i	$-0.273204\pi$
$83$	3.89435e12	1.30746	0.653729	+	0.756729i	$0.273204\pi$
$84$	4.14663e10	0.0128789
$85$	−1.67418e12	−0.481481
$86$	2.82560e12	0.753132
$87$	1.37251e11	0.0339344
$88$	4.50501e12	1.03409
$89$	3.38545e12	0.722073	0.361036	−	0.932552i	$-0.382423\pi$
$89$	3.38545e12	0.722073	0.361036	+	0.932552i	$0.382423\pi$
$90$	−5.18725e11	−0.102887
$91$	3.06097e11	0.0565054
$92$	4.61908e12	0.794209
$93$	−3.20180e12	−0.513163
$94$	−8.50881e12	−1.27215
$95$	−9.70311e11	−0.135428
$96$	3.50530e12	0.457049
$97$	−2.54230e12	−0.309893	−0.154946	−	0.987923i	$-0.549520\pi$
$97$	−2.54230e12	−0.309893	−0.154946	+	0.987923i	$0.549520\pi$
$98$	−6.59220e12	−0.751728
$99$	−2.99185e12	−0.319382
$100$	3.59454e12	0.359454
$101$	5.35425e12	0.501891	0.250946	−	0.968001i	$-0.419258\pi$
$101$	5.35425e12	0.501891	0.250946	+	0.968001i	$0.419258\pi$
$102$	5.81942e12	0.511657
$103$	1.13168e13	0.933863	0.466932	−	0.884293i	$-0.345359\pi$
$103$	1.13168e13	0.933863	0.466932	+	0.884293i	$0.345359\pi$
$104$	1.52354e13	1.18069
$105$	1.67691e11	0.0122118
$106$	7.95673e12	0.544812
$107$	1.59125e13	1.02505	0.512525	−	0.858673i	$-0.328710\pi$
$107$	1.59125e13	1.02505	0.512525	+	0.858673i	$0.328710\pi$
$108$	−1.37067e12	−0.0831149
$109$	1.47025e13	0.839688	0.419844	−	0.907596i	$-0.362085\pi$
$109$	1.47025e13	0.839688	0.419844	+	0.907596i	$0.362085\pi$
$110$	5.49498e12	0.295742
$111$	1.57222e13	0.797835
$112$	4.11728e11	0.0197103
$113$	−1.71973e13	−0.777053	−0.388526	−	0.921438i	$-0.627016\pi$
$113$	−1.71973e13	−0.777053	−0.388526	+	0.921438i	$0.627016\pi$
$114$	3.37278e12	0.143915
$115$	1.86798e13	0.753070
$116$	−6.66098e11	−0.0253841
$117$	−1.01181e13	−0.364661
$118$	−2.87758e12	−0.0981285
$119$	−1.88128e12	−0.0607293
$120$	8.34652e12	0.255169
$121$	−2.82935e12	−0.0819562
$122$	6.18891e12	0.169932
$123$	5.59134e12	0.145590
$124$	1.55388e13	0.383863
$125$	3.20017e13	0.750341
$126$	−5.82892e11	−0.0129772
$127$	−9.22435e12	−0.195079	−0.0975397	−	0.995232i	$-0.531097\pi$
$127$	−9.22435e12	−0.195079	−0.0975397	+	0.995232i	$0.531097\pi$
$128$	−2.69978e12	−0.0542580
$129$	3.01942e13	0.576886
$130$	1.85833e13	0.337670
$131$	−3.50945e12	−0.0606702	−0.0303351	−	0.999540i	$-0.509657\pi$
$131$	−3.50945e12	−0.0606702	−0.0303351	+	0.999540i	$0.509657\pi$
$132$	1.45199e13	0.238909
$133$	−1.09034e12	−0.0170815
$134$	1.90867e13	0.284806
$135$	−5.54305e12	−0.0788096
$136$	−9.36371e13	−1.26895
$137$	−6.75736e12	−0.0873159	−0.0436579	−	0.999047i	$-0.513901\pi$
$137$	−6.75736e12	−0.0873159	−0.0436579	+	0.999047i	$0.513901\pi$
$138$	−6.49305e13	−0.800267
$139$	5.30396e13	0.623740	0.311870	−	0.950125i	$-0.399045\pi$
$139$	5.30396e13	0.623740	0.311870	+	0.950125i	$0.399045\pi$
$140$	−8.13830e11	−0.00913485
$141$	−9.09244e13	−0.974443
$142$	6.11671e13	0.626100
$143$	1.07183e14	1.04819
$144$	−1.36097e13	−0.127201
$145$	−2.69373e12	−0.0240692
$146$	1.49894e11	0.00128083
$147$	−7.04437e13	−0.575810
$148$	−7.63019e13	−0.596808
$149$	−9.35310e13	−0.700236	−0.350118	−	0.936706i	$-0.613859\pi$
$149$	−9.35310e13	−0.700236	−0.350118	+	0.936706i	$0.613859\pi$
$150$	−5.05284e13	−0.362195
$151$	1.21235e14	0.832296	0.416148	−	0.909297i	$-0.363380\pi$
$151$	1.21235e14	0.832296	0.416148	+	0.909297i	$0.363380\pi$
$152$	−5.42696e13	−0.356922
$153$	6.21858e13	0.391920
$154$	6.17472e12	0.0373021
$155$	6.28395e13	0.363979
$156$	4.91043e13	0.272778
$157$	1.43660e14	0.765574	0.382787	−	0.923837i	$-0.374964\pi$
$157$	1.43660e14	0.765574	0.382787	+	0.923837i	$0.374964\pi$
$158$	−1.61133e14	−0.823974
$159$	8.50249e13	0.417316
$160$	−6.87961e13	−0.324178
$161$	2.09905e13	0.0949849
$162$	1.92675e13	0.0837488
$163$	−6.72578e13	−0.280881	−0.140441	−	0.990089i	$-0.544852\pi$
$163$	−6.72578e13	−0.280881	−0.140441	+	0.990089i	$0.544852\pi$
$164$	−2.71356e13	−0.108907
$165$	5.87189e13	0.226533
$166$	2.65675e14	0.985482
$167$	−3.82364e13	−0.136402	−0.0682009	−	0.997672i	$-0.521726\pi$
$167$	−3.82364e13	−0.136402	−0.0682009	+	0.997672i	$0.521726\pi$
$168$	9.37900e12	0.0321845
$169$	5.96046e13	0.196796
$170$	−1.14214e14	−0.362911
$171$	3.60413e13	0.110236
$172$	−1.46537e14	−0.431530
$173$	4.20171e14	1.19159	0.595794	−	0.803137i	$-0.296838\pi$
$173$	4.20171e14	1.19159	0.595794	+	0.803137i	$0.296838\pi$
$174$	9.36335e12	0.0255777
$175$	1.63346e13	0.0429895
$176$	1.44171e14	0.365633
$177$	−3.07496e13	−0.0751646
$178$	2.30957e14	0.544254
$179$	5.91337e14	1.34366	0.671832	−	0.740704i	$-0.265508\pi$
$179$	5.91337e14	1.34366	0.671832	+	0.740704i	$0.265508\pi$
$180$	2.69012e13	0.0589522
$181$	2.38624e14	0.504433	0.252217	−	0.967671i	$-0.418840\pi$
$181$	2.38624e14	0.504433	0.252217	+	0.967671i	$0.418840\pi$
$182$	2.08821e13	0.0425903
$183$	6.61341e13	0.130165
$184$	1.04476e15	1.98473
$185$	−3.08568e14	−0.565893
$186$	−2.18429e14	−0.386791
$187$	−6.58750e14	−1.12655
$188$	4.41269e14	0.728916
$189$	−6.22874e12	−0.00994027
$190$	−6.61952e13	−0.102077
$191$	−4.91288e14	−0.732183	−0.366091	−	0.930579i	$-0.619304\pi$
$191$	−4.91288e14	−0.732183	−0.366091	+	0.930579i	$0.619304\pi$
$192$	3.92070e14	0.564815
$193$	−1.19878e15	−1.66961	−0.834806	−	0.550544i	$-0.814420\pi$
$193$	−1.19878e15	−1.66961	−0.834806	+	0.550544i	$0.814420\pi$
$194$	−1.73438e14	−0.233578
$195$	1.98580e14	0.258649
$196$	3.41873e14	0.430725
$197$	−5.83934e14	−0.711760	−0.355880	−	0.934532i	$-0.615819\pi$
$197$	−5.83934e14	−0.711760	−0.355880	+	0.934532i	$0.615819\pi$
$198$	−2.04106e14	−0.240731
$199$	1.08547e15	1.23900	0.619500	−	0.784997i	$-0.287335\pi$
$199$	1.08547e15	1.23900	0.619500	+	0.784997i	$0.287335\pi$
$200$	8.13025e14	0.898274
$201$	2.03959e14	0.218156
$202$	3.65271e14	0.378295
$203$	−3.02695e12	−0.00303585
$204$	−3.01797e14	−0.293169
$205$	−1.09737e14	−0.103265
$206$	7.72042e14	0.703889
$207$	−6.93842e14	−0.612990
$208$	4.87568e14	0.417468
$209$	−3.81794e14	−0.316868
$210$	1.14400e13	0.00920452
$211$	−6.59647e14	−0.514607	−0.257303	−	0.966331i	$-0.582834\pi$
$211$	−6.59647e14	−0.514607	−0.257303	+	0.966331i	$0.582834\pi$
$212$	−4.12638e14	−0.312166
$213$	6.53626e14	0.479581
$214$	1.08556e15	0.772620
$215$	−5.92599e14	−0.409177
$216$	−3.10023e14	−0.207704
$217$	7.06129e13	0.0459088
$218$	1.00301e15	0.632906
$219$	1.60175e12	0.000981090 0
$220$	−2.84971e14	−0.169455
$221$	−2.22781e15	−1.28626
$222$	1.07258e15	0.601359
$223$	3.56431e14	0.194086	0.0970429	−	0.995280i	$-0.469062\pi$
$223$	3.56431e14	0.194086	0.0970429	+	0.995280i	$0.469062\pi$
$224$	−7.73064e13	−0.0408887
$225$	−5.39942e14	−0.277435
$226$	−1.17321e15	−0.585695
$227$	1.97090e15	0.956085	0.478043	−	0.878337i	$-0.341346\pi$
$227$	1.97090e15	0.956085	0.478043	+	0.878337i	$0.341346\pi$
$228$	−1.74913e14	−0.0824606
$229$	3.65385e15	1.67425	0.837124	−	0.547014i	$-0.184236\pi$
$229$	3.65385e15	1.67425	0.837124	+	0.547014i	$0.184236\pi$
$230$	1.27435e15	0.567618
$231$	6.59825e13	0.0285727
$232$	−1.50661e14	−0.0634348
$233$	−1.47105e14	−0.0602300	−0.0301150	−	0.999546i	$-0.509587\pi$
$233$	−1.47105e14	−0.0602300	−0.0301150	+	0.999546i	$0.509587\pi$
$234$	−6.90260e14	−0.274859
$235$	1.78451e15	0.691159
$236$	1.49232e14	0.0562257
$237$	−1.72185e15	−0.631149
$238$	−1.28342e14	−0.0457740
$239$	2.23241e15	0.774798	0.387399	−	0.921912i	$-0.373374\pi$
$239$	2.23241e15	0.774798	0.387399	+	0.921912i	$0.373374\pi$
$240$	2.67108e14	0.0902222
$241$	−9.69707e13	−0.0318808	−0.0159404	−	0.999873i	$-0.505074\pi$
$241$	−9.69707e13	−0.0318808	−0.0159404	+	0.999873i	$0.505074\pi$
$242$	−1.93020e14	−0.0617736
$243$	2.05891e14	0.0641500
$244$	−3.20958e14	−0.0973676
$245$	1.38255e15	0.408414
$246$	3.81445e14	0.109737
$247$	−1.29118e15	−0.361790
$248$	3.51462e15	0.959274
$249$	2.83898e15	0.754861
$250$	2.18318e15	0.565561
$251$	−4.62528e15	−1.16751	−0.583753	−	0.811931i	$-0.698416\pi$
$251$	−4.62528e15	−1.16751	−0.583753	+	0.811931i	$0.698416\pi$
$252$	3.02289e13	0.00743566
$253$	7.35004e15	1.76200
$254$	−6.29291e14	−0.147039
$255$	−1.22048e15	−0.277983
$256$	−4.59000e15	−1.01918
$257$	−1.85280e15	−0.401110	−0.200555	−	0.979682i	$-0.564275\pi$
$257$	−1.85280e15	−0.401110	−0.200555	+	0.979682i	$0.564275\pi$
$258$	2.05987e15	0.434821
$259$	−3.46739e14	−0.0713763
$260$	−9.63737e14	−0.193478
$261$	1.00056e14	0.0195920
$262$	−2.39417e14	−0.0457295
$263$	8.13314e15	1.51546	0.757732	−	0.652566i	$-0.226307\pi$
$263$	8.13314e15	1.51546	0.757732	+	0.652566i	$0.226307\pi$
$264$	3.28415e15	0.597032
$265$	−1.66872e15	−0.295996
$266$	−7.43838e13	−0.0128750
$267$	2.46799e15	0.416889
$268$	−9.89840e14	−0.163188
$269$	−2.57796e15	−0.414845	−0.207423	−	0.978251i	$-0.566507\pi$
$269$	−2.57796e15	−0.414845	−0.207423	+	0.978251i	$0.566507\pi$
$270$	−3.78150e14	−0.0594019
$271$	9.60115e15	1.47239	0.736195	−	0.676769i	$-0.236620\pi$
$271$	9.60115e15	1.47239	0.736195	+	0.676769i	$0.236620\pi$
$272$	−2.99660e15	−0.448675
$273$	2.23145e14	0.0326234
$274$	−4.60991e14	−0.0658134
$275$	5.71974e15	0.797469
$276$	3.36731e15	0.458537
$277$	2.44482e15	0.325183	0.162592	−	0.986693i	$-0.448015\pi$
$277$	2.44482e15	0.325183	0.162592	+	0.986693i	$0.448015\pi$
$278$	3.61839e15	0.470137
$279$	−2.33411e15	−0.296275
$280$	−1.84075e14	−0.0228280
$281$	−5.47611e15	−0.663561	−0.331780	−	0.943357i	$-0.607649\pi$
$281$	−5.47611e15	−0.663561	−0.331780	+	0.943357i	$0.607649\pi$
$282$	−6.20292e15	−0.734476
$283$	−1.13967e15	−0.131877	−0.0659383	−	0.997824i	$-0.521004\pi$
$283$	−1.13967e15	−0.131877	−0.0659383	+	0.997824i	$0.521004\pi$
$284$	−3.17214e15	−0.358743
$285$	−7.07357e14	−0.0781892
$286$	7.31210e15	0.790065
$287$	−1.23312e14	−0.0130249
$288$	2.55537e15	0.263877
$289$	3.78759e15	0.382408
$290$	−1.83768e14	−0.0181419
$291$	−1.85334e15	−0.178917
$292$	−7.77353e12	−0.000733888 0
$293$	−1.25752e16	−1.16111	−0.580556	−	0.814221i	$-0.697165\pi$
$293$	−1.25752e16	−1.16111	−0.580556	+	0.814221i	$0.697165\pi$
$294$	−4.80571e15	−0.434010
$295$	6.03501e14	0.0533132
$296$	−1.72582e16	−1.49142
$297$	−2.18106e15	−0.184395
$298$	−6.38075e15	−0.527796
$299$	2.48569e16	2.01180
$300$	2.62042e15	0.207531
$301$	−6.65906e14	−0.0516096
$302$	8.27073e15	0.627334
$303$	3.90325e15	0.289767
$304$	−1.73675e15	−0.126200
$305$	−1.29797e15	−0.0923241
$306$	4.24236e15	0.295405
$307$	−3.17745e15	−0.216610	−0.108305	−	0.994118i	$-0.534542\pi$
$307$	−3.17745e15	−0.216610	−0.108305	+	0.994118i	$0.534542\pi$
$308$	−3.20223e14	−0.0213733
$309$	8.24998e15	0.539166
$310$	4.28695e15	0.274345
$311$	−7.53782e15	−0.472392	−0.236196	−	0.971705i	$-0.575901\pi$
$311$	−7.53782e15	−0.472392	−0.236196	+	0.971705i	$0.575901\pi$
$312$	1.11066e16	0.681673
$313$	1.29776e16	0.780113	0.390056	−	0.920791i	$-0.372456\pi$
$313$	1.29776e16	0.780113	0.390056	+	0.920791i	$0.372456\pi$
$314$	9.80056e15	0.577043
$315$	1.22247e14	0.00705050
$316$	8.35640e15	0.472121
$317$	3.20214e16	1.77237	0.886186	−	0.463330i	$-0.153346\pi$
$317$	3.20214e16	1.77237	0.886186	+	0.463330i	$0.153346\pi$
$318$	5.80045e15	0.314547
$319$	−1.05992e15	−0.0563161
$320$	−7.69489e15	−0.400615
$321$	1.16002e16	0.591812
$322$	1.43199e15	0.0715938
$323$	7.93562e15	0.388834
$324$	−9.99219e14	−0.0479864
$325$	1.93435e16	0.910526
$326$	−4.58837e15	−0.211711
$327$	1.07181e16	0.484794
$328$	−6.13762e15	−0.272158
$329$	2.00526e15	0.0871760
$330$	4.00584e15	0.170747
$331$	2.60836e16	1.09015	0.545073	−	0.838388i	$-0.316502\pi$
$331$	2.60836e16	1.09015	0.545073	+	0.838388i	$0.316502\pi$
$332$	−1.37780e16	−0.564661
$333$	1.14615e16	0.460630
$334$	−2.60851e15	−0.102811
$335$	−4.00295e15	−0.154735
$336$	3.00150e14	0.0113797
$337$	−1.94511e16	−0.723352	−0.361676	−	0.932304i	$-0.617795\pi$
$337$	−1.94511e16	−0.723352	−0.361676	+	0.932304i	$0.617795\pi$
$338$	4.06627e15	0.148333
$339$	−1.25368e16	−0.448632
$340$	5.92315e15	0.207941
$341$	2.47258e16	0.851623
$342$	2.45876e15	0.0830895
$343$	3.11130e15	0.103165
$344$	−3.31442e16	−1.07839
$345$	1.36175e16	0.434785
$346$	2.86643e16	0.898146
$347$	3.17367e16	0.975933	0.487966	−	0.872862i	$-0.337739\pi$
$347$	3.17367e16	0.975933	0.487966	+	0.872862i	$0.337739\pi$
$348$	−4.85586e14	−0.0146555
$349$	1.90370e16	0.563939	0.281970	−	0.959423i	$-0.409012\pi$
$349$	1.90370e16	0.563939	0.281970	+	0.959423i	$0.409012\pi$
$350$	1.11436e15	0.0324028
$351$	−7.37606e15	−0.210537
$352$	−2.70696e16	−0.758499
$353$	−5.22879e16	−1.43835	−0.719177	−	0.694827i	$-0.755481\pi$
$353$	−5.22879e16	−1.43835	−0.719177	+	0.694827i	$0.755481\pi$
$354$	−2.09776e15	−0.0566545
$355$	−1.28283e16	−0.340160
$356$	−1.19775e16	−0.311847
$357$	−1.37145e15	−0.0350621
$358$	4.03414e16	1.01277
$359$	−1.28083e16	−0.315774	−0.157887	−	0.987457i	$-0.550468\pi$
$359$	−1.28083e16	−0.315774	−0.157887	+	0.987457i	$0.550468\pi$
$360$	6.08461e15	0.147322
$361$	−3.74537e16	−0.890631
$362$	1.62791e16	0.380211
$363$	−2.06260e15	−0.0473175
$364$	−1.08295e15	−0.0244034
$365$	−3.14365e13	−0.000695873 0
$366$	4.51171e15	0.0981102
$367$	−2.23147e15	−0.0476718	−0.0238359	−	0.999716i	$-0.507588\pi$
$367$	−2.23147e15	−0.0476718	−0.0238359	+	0.999716i	$0.507588\pi$
$368$	3.34348e16	0.701758
$369$	4.07609e15	0.0840567
$370$	−2.10507e16	−0.426536
$371$	−1.87515e15	−0.0373341
$372$	1.13278e16	0.221623
$373$	3.49809e16	0.672548	0.336274	−	0.941764i	$-0.390833\pi$
$373$	3.49809e16	0.672548	0.336274	+	0.941764i	$0.390833\pi$
$374$	−4.49403e16	−0.849123
$375$	2.33293e16	0.433209
$376$	9.98079e16	1.82156
$377$	−3.58451e15	−0.0643000
$378$	−4.24928e14	−0.00749237
$379$	4.02456e16	0.697530	0.348765	−	0.937210i	$-0.386601\pi$
$379$	4.02456e16	0.697530	0.348765	+	0.937210i	$0.386601\pi$
$380$	3.43290e15	0.0584882
$381$	−6.72455e15	−0.112629
$382$	−3.35160e16	−0.551875
$383$	−7.55162e16	−1.22250	−0.611249	−	0.791438i	$-0.709333\pi$
$383$	−7.55162e16	−1.22250	−0.611249	+	0.791438i	$0.709333\pi$
$384$	−1.96814e15	−0.0313259
$385$	−1.29499e15	−0.0202662
$386$	−8.17813e16	−1.25845
$387$	2.20115e16	0.333065
$388$	8.99452e15	0.133836
$389$	1.02590e17	1.50117	0.750586	−	0.660772i	$-0.229771\pi$
$389$	1.02590e17	1.50117	0.750586	+	0.660772i	$0.229771\pi$
$390$	1.35473e16	0.194954
$391$	−1.52771e17	−2.16218
$392$	7.73261e16	1.07638
$393$	−2.55839e15	−0.0350280
$394$	−3.98364e16	−0.536481
$395$	3.37936e16	0.447665
$396$	1.05850e16	0.137934
$397$	−7.63990e16	−0.979376	−0.489688	−	0.871898i	$-0.662889\pi$
$397$	−7.63990e16	−0.979376	−0.489688	+	0.871898i	$0.662889\pi$
$398$	7.40512e16	0.933882
$399$	−7.94858e14	−0.00986202
$400$	2.60187e16	0.317611
$401$	−3.11585e16	−0.374229	−0.187115	−	0.982338i	$-0.559914\pi$
$401$	−3.11585e16	−0.374229	−0.187115	+	0.982338i	$0.559914\pi$
$402$	1.39142e16	0.164433
$403$	8.36197e16	0.972357
$404$	−1.89430e16	−0.216756
$405$	−4.04088e15	−0.0455007
$406$	−2.06500e14	−0.00228824
$407$	−1.21414e17	−1.32405
$408$	−6.82614e16	−0.732630
$409$	2.97554e16	0.314314	0.157157	−	0.987574i	$-0.449767\pi$
$409$	2.97554e16	0.314314	0.157157	+	0.987574i	$0.449767\pi$
$410$	−7.48636e15	−0.0778351
$411$	−4.92611e15	−0.0504118
$412$	−4.00383e16	−0.403315
$413$	6.78156e14	0.00672441
$414$	−4.73343e16	−0.462034
$415$	−5.57187e16	−0.535412
$416$	−9.15461e16	−0.866031
$417$	3.86658e16	0.360117
$418$	−2.60462e16	−0.238836
$419$	4.42811e16	0.399786	0.199893	−	0.979818i	$-0.435941\pi$
$419$	4.42811e16	0.399786	0.199893	+	0.979818i	$0.435941\pi$
$420$	−5.93282e14	−0.00527401
$421$	−1.57089e16	−0.137503	−0.0687516	−	0.997634i	$-0.521902\pi$
$421$	−1.57089e16	−0.137503	−0.0687516	+	0.997634i	$0.521902\pi$
$422$	−4.50015e16	−0.387879
$423$	−6.62839e16	−0.562595
$424$	−9.33319e16	−0.780104
$425$	−1.18885e17	−0.978589
$426$	4.45908e16	0.361479
$427$	−1.45853e15	−0.0116449
$428$	−5.62976e16	−0.442696
$429$	7.81364e16	0.605175
$430$	−4.04275e16	−0.308413
$431$	−4.64195e16	−0.348818	−0.174409	−	0.984673i	$-0.555801\pi$
$431$	−4.64195e16	−0.348818	−0.174409	+	0.984673i	$0.555801\pi$
$432$	−9.92146e15	−0.0734398
$433$	−1.74150e17	−1.26985	−0.634923	−	0.772575i	$-0.718968\pi$
$433$	−1.74150e17	−1.26985	−0.634923	+	0.772575i	$0.718968\pi$
$434$	4.81726e15	0.0346032
$435$	−1.96373e15	−0.0138964
$436$	−5.20165e16	−0.362643
$437$	−8.85422e16	−0.608164
$438$	1.09273e14	0.000739486 0
$439$	9.81827e16	0.654660	0.327330	−	0.944910i	$-0.393851\pi$
$439$	9.81827e16	0.654660	0.327330	+	0.944910i	$0.393851\pi$
$440$	−6.44558e16	−0.423467
$441$	−5.13534e16	−0.332444
$442$	−1.51983e17	−0.969503
$443$	−6.64375e16	−0.417628	−0.208814	−	0.977955i	$-0.566960\pi$
$443$	−6.64375e16	−0.417628	−0.208814	+	0.977955i	$0.566960\pi$
$444$	−5.56241e16	−0.344567
$445$	−4.84375e16	−0.295694
$446$	2.43160e16	0.146290
$447$	−6.81841e16	−0.404282
$448$	−8.64677e15	−0.0505297
$449$	−2.30121e17	−1.32542	−0.662712	−	0.748874i	$-0.730595\pi$
$449$	−2.30121e17	−1.32542	−0.662712	+	0.748874i	$0.730595\pi$
$450$	−3.68352e16	−0.209113
$451$	−4.31790e16	−0.241616
$452$	6.08430e16	0.335592
$453$	8.83803e16	0.480526
$454$	1.34456e17	0.720639
$455$	−4.37951e15	−0.0231393
$456$	−3.95625e16	−0.206069
$457$	−3.07539e17	−1.57923	−0.789613	−	0.613605i	$-0.789719\pi$
$457$	−3.07539e17	−1.57923	−0.789613	+	0.613605i	$0.789719\pi$
$458$	2.49268e17	1.26195
$459$	4.53334e16	0.226275
$460$	−6.60879e16	−0.325234
$461$	−1.50288e17	−0.729235	−0.364617	−	0.931157i	$-0.618800\pi$
$461$	−1.50288e17	−0.729235	−0.364617	+	0.931157i	$0.618800\pi$
$462$	4.50137e15	0.0215363
$463$	−1.70959e17	−0.806522	−0.403261	−	0.915085i	$-0.632123\pi$
$463$	−1.70959e17	−0.806522	−0.403261	+	0.915085i	$0.632123\pi$
$464$	−4.82149e15	−0.0224292
$465$	4.58100e16	0.210144
$466$	−1.00356e16	−0.0453977
$467$	−2.26436e17	−1.01015	−0.505074	−	0.863076i	$-0.668535\pi$
$467$	−2.26436e17	−1.01015	−0.505074	+	0.863076i	$0.668535\pi$
$468$	3.57971e16	0.157489
$469$	−4.49813e15	−0.0195168
$470$	1.21740e17	0.520953
$471$	1.04728e17	0.442004
$472$	3.37539e16	0.140508
$473$	−2.33174e17	−0.957375
$474$	−1.17466e17	−0.475722
$475$	−6.89028e16	−0.275251
$476$	6.65586e15	0.0262276
$477$	6.19831e16	0.240937
$478$	1.52297e17	0.583995
$479$	1.64646e17	0.622831	0.311415	−	0.950274i	$-0.399197\pi$
$479$	1.64646e17	0.622831	0.311415	+	0.950274i	$0.399197\pi$
$480$	−5.01524e16	−0.187165
$481$	−4.10607e17	−1.51176
$482$	−6.61540e15	−0.0240298
$483$	1.53021e16	0.0548395
$484$	1.00101e16	0.0353951
$485$	3.63742e16	0.126903
$486$	1.40460e16	0.0483524
$487$	8.54260e16	0.290170	0.145085	−	0.989419i	$-0.453654\pi$
$487$	8.54260e16	0.290170	0.145085	+	0.989419i	$0.453654\pi$
$488$	−7.25955e16	−0.243322
$489$	−4.90309e16	−0.162167
$490$	9.43184e16	0.307838
$491$	−3.83545e17	−1.23534	−0.617670	−	0.786437i	$-0.711923\pi$
$491$	−3.83545e17	−1.23534	−0.617670	+	0.786437i	$0.711923\pi$
$492$	−1.97818e16	−0.0628772
$493$	2.20305e16	0.0691065
$494$	−8.80852e16	−0.272695
$495$	4.28060e16	0.130789
$496$	1.12476e17	0.339179
$497$	−1.44151e16	−0.0429045
$498$	1.93677e17	0.568968
$499$	4.84648e17	1.40531	0.702656	−	0.711530i	$-0.251997\pi$
$499$	4.84648e17	1.40531	0.702656	+	0.711530i	$0.251997\pi$
$500$	−1.13220e17	−0.324055
$501$	−2.78743e16	−0.0787516
$502$	−3.15540e17	−0.879995
$503$	2.36855e17	0.652063	0.326032	−	0.945359i	$-0.394288\pi$
$503$	2.36855e17	0.652063	0.326032	+	0.945359i	$0.394288\pi$
$504$	6.83729e15	0.0185817
$505$	−7.66063e16	−0.205528
$506$	5.01424e17	1.32809
$507$	4.34518e16	0.113620
$508$	3.26352e16	0.0842504
$509$	−2.52726e17	−0.644147	−0.322073	−	0.946715i	$-0.604380\pi$
$509$	−2.52726e17	−0.644147	−0.322073	+	0.946715i	$0.604380\pi$
$510$	−8.32618e16	−0.209527
$511$	−3.53252e13	−8.77707e−5 0
$512$	−2.91016e17	−0.713941
$513$	2.62741e16	0.0636450
$514$	−1.26399e17	−0.302332
$515$	−1.61917e17	−0.382423
$516$	−1.06825e17	−0.249144
$517$	7.02162e17	1.61714
$518$	−2.36547e16	−0.0537991
$519$	3.06304e17	0.687964
$520$	−2.17981e17	−0.483501
$521$	−6.03304e17	−1.32157	−0.660786	−	0.750574i	$-0.729777\pi$
$521$	−6.03304e17	−1.32157	−0.660786	+	0.750574i	$0.729777\pi$
$522$	6.82588e15	0.0147673
$523$	−1.80923e17	−0.386574	−0.193287	−	0.981142i	$-0.561915\pi$
$523$	−1.80923e17	−0.386574	−0.193287	+	0.981142i	$0.561915\pi$
$524$	1.24162e16	0.0262021
$525$	1.19080e16	0.0248200
$526$	5.54848e17	1.14226
$527$	−5.13929e17	−1.04504
$528$	1.05101e17	0.211098
$529$	1.20052e18	2.38181
$530$	−1.13841e17	−0.223104
$531$	−2.24165e16	−0.0433963
$532$	3.85756e15	0.00737713
$533$	−1.46026e17	−0.275869
$534$	1.68368e17	0.314225
$535$	−2.27670e17	−0.419764
$536$	−2.23886e17	−0.407808
$537$	4.31085e17	0.775764
$538$	−1.75870e17	−0.312685
$539$	5.43999e17	0.955590
$540$	1.96110e16	0.0340361
$541$	4.78906e17	0.821236	0.410618	−	0.911807i	$-0.365313\pi$
$541$	4.78906e17	0.821236	0.410618	+	0.911807i	$0.365313\pi$
$542$	6.54997e17	1.10980
$543$	1.73957e17	0.291235
$544$	5.62645e17	0.930768
$545$	−2.10357e17	−0.343858
$546$	1.52231e16	0.0245895
$547$	−3.24068e17	−0.517272	−0.258636	−	0.965975i	$-0.583273\pi$
$547$	−3.24068e17	−0.517272	−0.258636	+	0.965975i	$0.583273\pi$
$548$	2.39071e16	0.0377098
$549$	4.82118e16	0.0751507
$550$	3.90205e17	0.601084
$551$	1.27683e16	0.0194378
$552$	7.61631e17	1.14588
$553$	3.79740e16	0.0564641
$554$	1.66787e17	0.245103
$555$	−2.24946e17	−0.326719
$556$	−1.87651e17	−0.269379
$557$	−4.01406e16	−0.0569541	−0.0284771	−	0.999594i	$-0.509066\pi$
$557$	−4.01406e16	−0.0569541	−0.0284771	+	0.999594i	$0.509066\pi$
$558$	−1.59235e17	−0.223314
$559$	−7.88564e17	−1.09310
$560$	−5.89083e15	−0.00807150
$561$	−4.80228e17	−0.650413
$562$	−3.73584e17	−0.500152
$563$	1.07562e18	1.42349	0.711746	−	0.702437i	$-0.247905\pi$
$563$	1.07562e18	1.42349	0.711746	+	0.702437i	$0.247905\pi$
$564$	3.21685e17	0.420840
$565$	2.46052e17	0.318208
$566$	−7.77492e16	−0.0994006
$567$	−4.54075e15	−0.00573902
$568$	−7.17486e17	−0.896498
$569$	−8.84728e17	−1.09290	−0.546449	−	0.837492i	$-0.684021\pi$
$569$	−8.84728e17	−1.09290	−0.546449	+	0.837492i	$0.684021\pi$
$570$	−4.82563e16	−0.0589342
$571$	−4.11167e17	−0.496460	−0.248230	−	0.968701i	$-0.579849\pi$
$571$	−4.11167e17	−0.496460	−0.248230	+	0.968701i	$0.579849\pi$
$572$	−3.79207e17	−0.452692
$573$	−3.58149e17	−0.422726
$574$	−8.41244e15	−0.00981736
$575$	1.32647e18	1.53058
$576$	2.85819e17	0.326096
$577$	−8.47435e17	−0.956012	−0.478006	−	0.878357i	$-0.658640\pi$
$577$	−8.47435e17	−0.956012	−0.478006	+	0.878357i	$0.658640\pi$
$578$	2.58392e17	0.288236
$579$	−8.73908e17	−0.963951
$580$	9.53025e15	0.0103949
$581$	−6.26113e16	−0.0675317
$582$	−1.26436e17	−0.134856
$583$	−6.56603e17	−0.692559
$584$	−1.75825e15	−0.00183399
$585$	1.44765e17	0.149331
$586$	−8.57885e17	−0.875175
$587$	1.57040e18	1.58440	0.792198	−	0.610264i	$-0.208937\pi$
$587$	1.57040e18	1.58440	0.792198	+	0.610264i	$0.208937\pi$
$588$	2.49225e17	0.248679
$589$	−2.97860e17	−0.293942
$590$	4.11712e16	0.0401842
$591$	−4.25688e17	−0.410935
$592$	−5.52304e17	−0.527335
$593$	7.08580e17	0.669165	0.334582	−	0.942366i	$-0.391405\pi$
$593$	7.08580e17	0.669165	0.334582	+	0.942366i	$0.391405\pi$
$594$	−1.48793e17	−0.138986
$595$	2.69165e16	0.0248690
$596$	3.30907e17	0.302416
$597$	7.91305e17	0.715337
$598$	1.69576e18	1.51637
$599$	1.29626e18	1.14662	0.573308	−	0.819340i	$-0.305660\pi$
$599$	1.29626e18	1.14662	0.573308	+	0.819340i	$0.305660\pi$
$600$	5.92695e17	0.518619
$601$	−1.79436e18	−1.55319	−0.776597	−	0.629998i	$-0.783056\pi$
$601$	−1.79436e18	−1.55319	−0.776597	+	0.629998i	$0.783056\pi$
$602$	−4.54285e16	−0.0389002
$603$	1.48686e17	0.125953
$604$	−4.28922e17	−0.359450
$605$	4.04811e16	0.0335616
$606$	2.66282e17	0.218409
$607$	−1.09671e18	−0.889948	−0.444974	−	0.895543i	$-0.646787\pi$
$607$	−1.09671e18	−0.889948	−0.444974	+	0.895543i	$0.646787\pi$
$608$	3.26094e17	0.261800
$609$	−2.20665e15	−0.00175275
$610$	−8.85482e16	−0.0695882
$611$	2.37462e18	1.84641
$612$	−2.20010e17	−0.169261
$613$	1.12867e17	0.0859163	0.0429582	−	0.999077i	$-0.486322\pi$
$613$	1.12867e17	0.0859163	0.0429582	+	0.999077i	$0.486322\pi$
$614$	−2.16768e17	−0.163268
$615$	−7.99985e16	−0.0596202
$616$	−7.24291e16	−0.0534120
$617$	1.11045e18	0.810299	0.405149	−	0.914250i	$-0.367219\pi$
$617$	1.11045e18	0.810299	0.405149	+	0.914250i	$0.367219\pi$
$618$	5.62819e17	0.406391
$619$	−2.37317e18	−1.69567	−0.847833	−	0.530263i	$-0.822093\pi$
$619$	−2.37317e18	−1.69567	−0.847833	+	0.530263i	$0.822093\pi$
$620$	−2.22322e17	−0.157194
$621$	−5.05811e17	−0.353910
$622$	−5.14235e17	−0.356061
$623$	−5.44294e16	−0.0372959
$624$	3.55437e17	0.241025
$625$	7.82363e17	0.525035
$626$	8.85343e17	0.588001
$627$	−2.78328e17	−0.182944
$628$	−5.08259e17	−0.330634
$629$	2.52360e18	1.62477
$630$	8.33977e15	0.00531423
$631$	−1.04868e18	−0.661379	−0.330690	−	0.943740i	$-0.607281\pi$
$631$	−1.04868e18	−0.661379	−0.330690	+	0.943740i	$0.607281\pi$
$632$	1.89008e18	1.17983
$633$	−4.80882e17	−0.297108
$634$	2.18452e18	1.33591
$635$	1.31978e17	0.0798863
$636$	−3.00813e17	−0.180229
$637$	1.83974e18	1.09106
$638$	−7.23083e16	−0.0424476
$639$	4.76493e17	0.276886
$640$	3.86273e16	0.0222190
$641$	3.54450e16	0.0201826	0.0100913	−	0.999949i	$-0.496788\pi$
$641$	3.54450e16	0.0201826	0.0100913	+	0.999949i	$0.496788\pi$
$642$	7.91376e17	0.446072
$643$	−1.18886e18	−0.663376	−0.331688	−	0.943389i	$-0.607618\pi$
$643$	−1.18886e18	−0.663376	−0.331688	+	0.943389i	$0.607618\pi$
$644$	−7.42631e16	−0.0410218
$645$	−4.32005e17	−0.236238
$646$	5.41374e17	0.293080
$647$	1.24743e18	0.668559	0.334279	−	0.942474i	$-0.391507\pi$
$647$	1.24743e18	0.668559	0.334279	+	0.942474i	$0.391507\pi$
$648$	−2.26007e17	−0.119918
$649$	2.37463e17	0.124740
$650$	1.31962e18	0.686299
$651$	5.14768e16	0.0265055
$652$	2.37954e17	0.121306
$653$	−2.11743e18	−1.06875	−0.534373	−	0.845249i	$-0.679452\pi$
$653$	−2.11743e18	−1.06875	−0.534373	+	0.845249i	$0.679452\pi$
$654$	7.31196e17	0.365408
$655$	5.02117e16	0.0248449
$656$	−1.96418e17	−0.0962292
$657$	1.16768e15	0.000566432 0
$658$	1.36800e17	0.0657080
$659$	4.39330e17	0.208947	0.104473	−	0.994528i	$-0.466684\pi$
$659$	4.39330e17	0.208947	0.104473	+	0.994528i	$0.466684\pi$
$660$	−2.07744e17	−0.0978346
$661$	−3.23741e17	−0.150969	−0.0754845	−	0.997147i	$-0.524050\pi$
$661$	−3.23741e17	−0.150969	−0.0754845	+	0.997147i	$0.524050\pi$
$662$	1.77944e18	0.821686
$663$	−1.62407e18	−0.742622
$664$	−3.11635e18	−1.41109
$665$	1.56001e16	0.00699500
$666$	7.81908e17	0.347195
$667$	−2.45806e17	−0.108087
$668$	1.35278e17	0.0589088
$669$	2.59838e17	0.112055
$670$	−2.73084e17	−0.116630
$671$	−5.10719e17	−0.216016
$672$	−5.63564e16	−0.0236071
$673$	2.95687e18	1.22669	0.613345	−	0.789815i	$-0.289824\pi$
$673$	2.95687e18	1.22669	0.613345	+	0.789815i	$0.289824\pi$
$674$	−1.32697e18	−0.545218
$675$	−3.93618e17	−0.160177
$676$	−2.10878e17	−0.0849918
$677$	−4.20450e18	−1.67837	−0.839185	−	0.543846i	$-0.816968\pi$
$677$	−4.20450e18	−1.67837	−0.839185	+	0.543846i	$0.816968\pi$
$678$	−8.55271e17	−0.338151
$679$	4.08738e16	0.0160063
$680$	1.33972e18	0.519644
$681$	1.43679e18	0.551996
$682$	1.68681e18	0.641902
$683$	3.06840e18	1.15658	0.578292	−	0.815830i	$-0.303720\pi$
$683$	3.06840e18	1.15658	0.578292	+	0.815830i	$0.303720\pi$
$684$	−1.27512e17	−0.0476086
$685$	9.66814e16	0.0357564
$686$	2.12255e17	0.0777591
$687$	2.66365e18	0.966627
$688$	−1.06069e18	−0.381297
$689$	−2.22055e18	−0.790743
$690$	9.28998e17	0.327715
$691$	−5.62560e18	−1.96590	−0.982949	−	0.183876i	$-0.941136\pi$
$691$	−5.62560e18	−1.96590	−0.982949	+	0.183876i	$0.941136\pi$
$692$	−1.48654e18	−0.514620
$693$	4.81013e16	0.0164964
$694$	2.16510e18	0.735598
$695$	−7.58867e17	−0.255426
$696$	−1.09832e17	−0.0366241
$697$	8.97480e17	0.296491
$698$	1.29871e18	0.425063
$699$	−1.07239e17	−0.0347738
$700$	−5.77910e16	−0.0185662
$701$	4.11353e18	1.30933	0.654663	−	0.755921i	$-0.272810\pi$
$701$	4.11353e18	1.30933	0.654663	+	0.755921i	$0.272810\pi$
$702$	−5.03200e17	−0.158690
$703$	1.46261e18	0.457004
$704$	−3.02776e18	−0.937343
$705$	1.30091e18	0.399041
$706$	−3.56712e18	−1.08414
$707$	−8.60827e16	−0.0259233
$708$	1.08790e17	0.0324619
$709$	−1.08476e18	−0.320727	−0.160363	−	0.987058i	$-0.551267\pi$
$709$	−1.08476e18	−0.320727	−0.160363	+	0.987058i	$0.551267\pi$
$710$	−8.75152e17	−0.256392
$711$	−1.25523e18	−0.364394
$712$	−2.70912e18	−0.779306
$713$	5.73419e18	1.63452
$714$	−9.35615e16	−0.0264277
$715$	−1.53353e18	−0.429242
$716$	−2.09212e18	−0.580298
$717$	1.62743e18	0.447330
$718$	−8.73789e17	−0.238011
$719$	5.12406e16	0.0138317	0.00691586	−	0.999976i	$-0.497799\pi$
$719$	5.12406e16	0.0138317	0.00691586	+	0.999976i	$0.497799\pi$
$720$	1.94722e17	0.0520898
$721$	−1.81946e17	−0.0482351
$722$	−2.55512e18	−0.671304
$723$	−7.06916e16	−0.0184064
$724$	−8.44238e17	−0.217853
$725$	−1.91285e17	−0.0489196
$726$	−1.40712e17	−0.0356650
$727$	−5.49897e18	−1.38136	−0.690682	−	0.723159i	$-0.742689\pi$
$727$	−5.49897e18	−1.38136	−0.690682	+	0.723159i	$0.742689\pi$
$728$	−2.44946e17	−0.0609841
$729$	1.50095e17	0.0370370
$730$	−2.14462e15	−0.000524507 0
$731$	4.84654e18	1.17481
$732$	−2.33979e17	−0.0562152
$733$	7.36959e17	0.175496	0.0877480	−	0.996143i	$-0.472033\pi$
$733$	7.36959e17	0.175496	0.0877480	+	0.996143i	$0.472033\pi$
$734$	−1.52232e17	−0.0359321
$735$	1.00788e18	0.235798
$736$	−6.27774e18	−1.45579
$737$	−1.57507e18	−0.362043
$738$	2.78073e17	0.0633568
$739$	−9.89430e17	−0.223458	−0.111729	−	0.993739i	$-0.535639\pi$
$739$	−9.89430e17	−0.223458	−0.111729	+	0.993739i	$0.535639\pi$
$740$	1.09170e18	0.244397
$741$	−9.41270e17	−0.208880
$742$	−1.27924e17	−0.0281401
$743$	7.55374e18	1.64716	0.823578	−	0.567203i	$-0.191975\pi$
$743$	7.55374e18	1.64716	0.823578	+	0.567203i	$0.191975\pi$
$744$	2.56216e18	0.553837
$745$	1.33820e18	0.286751
$746$	2.38642e18	0.506926
$747$	2.06962e18	0.435819
$748$	2.33062e18	0.486531
$749$	−2.55833e17	−0.0529450
$750$	1.59154e18	0.326527
$751$	2.68314e17	0.0545737	0.0272869	−	0.999628i	$-0.491313\pi$
$751$	2.68314e17	0.0545737	0.0272869	+	0.999628i	$0.491313\pi$
$752$	3.19408e18	0.644066
$753$	−3.37183e18	−0.674060
$754$	−2.44538e17	−0.0484654
$755$	−1.73458e18	−0.340831
$756$	2.20369e16	0.00429298
$757$	6.12937e18	1.18384	0.591919	−	0.805997i	$-0.298371\pi$
$757$	6.12937e18	1.18384	0.591919	+	0.805997i	$0.298371\pi$
$758$	2.74558e18	0.525756
$759$	5.35818e18	1.01729
$760$	7.76466e17	0.146162
$761$	8.37915e18	1.56387	0.781933	−	0.623362i	$-0.214234\pi$
$761$	8.37915e18	1.56387	0.781933	+	0.623362i	$0.214234\pi$
$762$	−4.58753e17	−0.0848930
$763$	−2.36378e17	−0.0433709
$764$	1.73815e18	0.316213
$765$	−8.89728e17	−0.160494
$766$	−5.15177e18	−0.921445
$767$	8.03071e17	0.142424
$768$	−3.34611e18	−0.588426
$769$	−6.77570e18	−1.18150	−0.590749	−	0.806856i	$-0.701167\pi$
$769$	−6.77570e18	−1.18150	−0.590749	+	0.806856i	$0.701167\pi$
$770$	−8.83453e16	−0.0152754
$771$	−1.35069e18	−0.231581
$772$	4.24120e18	0.721068
$773$	5.04035e18	0.849755	0.424877	−	0.905251i	$-0.360317\pi$
$773$	5.04035e18	0.849755	0.424877	+	0.905251i	$0.360317\pi$
$774$	1.50164e18	0.251044
$775$	4.46230e18	0.739772
$776$	2.03441e18	0.334455
$777$	−2.52772e17	−0.0412091
$778$	6.99873e18	1.13149
$779$	5.20156e17	0.0833950
$780$	−7.02564e17	−0.111705
$781$	−5.04761e18	−0.795892
$782$	−1.04222e19	−1.62972
$783$	7.29408e16	0.0113115
$784$	2.47461e18	0.380586
$785$	−2.05542e18	−0.313508
$786$	−1.74535e17	−0.0264019
$787$	−5.19452e18	−0.779308	−0.389654	−	0.920961i	$-0.627405\pi$
$787$	−5.19452e18	−0.779308	−0.389654	+	0.920961i	$0.627405\pi$
$788$	2.06593e18	0.307393
$789$	5.92906e18	0.874954
$790$	2.30542e18	0.337423
$791$	2.76489e17	0.0401357
$792$	2.39415e18	0.344697
$793$	−1.72719e18	−0.246640
$794$	−5.21199e18	−0.738194
$795$	−1.21650e18	−0.170894
$796$	−3.84031e18	−0.535096
$797$	4.77261e18	0.659595	0.329797	−	0.944052i	$-0.393020\pi$
$797$	4.77261e18	0.659595	0.329797	+	0.944052i	$0.393020\pi$
$798$	−5.42258e16	−0.00743339
$799$	−1.45945e19	−1.98443
$800$	−4.88529e18	−0.658879
$801$	1.79917e18	0.240691
$802$	−2.12565e18	−0.282071
$803$	−1.23695e16	−0.00162817
$804$	−7.21594e17	−0.0942168
$805$	−3.00323e17	−0.0388969
$806$	5.70459e18	0.732904
$807$	−1.87933e18	−0.239511
$808$	−4.28460e18	−0.541672
$809$	−8.09008e18	−1.01458	−0.507291	−	0.861775i	$-0.669353\pi$
$809$	−8.09008e18	−1.01458	−0.507291	+	0.861775i	$0.669353\pi$
$810$	−2.75672e17	−0.0342957
$811$	−1.96586e18	−0.242615	−0.121307	−	0.992615i	$-0.538709\pi$
$811$	−1.96586e18	−0.242615	−0.121307	+	0.992615i	$0.538709\pi$
$812$	1.07092e16	0.00131112
$813$	6.99924e18	0.850085
$814$	−8.28295e18	−0.997990
$815$	9.62295e17	0.115023
$816$	−2.18452e18	−0.259042
$817$	2.80893e18	0.330443
$818$	2.02993e18	0.236911
$819$	1.62673e17	0.0188351
$820$	3.88244e17	0.0445980
$821$	1.11006e19	1.26507	0.632535	−	0.774531i	$-0.282014\pi$
$821$	1.11006e19	1.26507	0.632535	+	0.774531i	$0.282014\pi$
$822$	−3.36063e17	−0.0379974
$823$	−2.15363e18	−0.241587	−0.120793	−	0.992678i	$-0.538544\pi$
$823$	−2.15363e18	−0.241587	−0.120793	+	0.992678i	$0.538544\pi$
$824$	−9.05601e18	−1.00788
$825$	4.16969e18	0.460419
$826$	4.62642e16	0.00506845
$827$	8.03212e18	0.873060	0.436530	−	0.899690i	$-0.356207\pi$
$827$	8.03212e18	0.873060	0.436530	+	0.899690i	$0.356207\pi$
$828$	2.45477e18	0.264736
$829$	9.02831e18	0.966055	0.483028	−	0.875605i	$-0.339537\pi$
$829$	9.02831e18	0.966055	0.483028	+	0.875605i	$0.339537\pi$
$830$	−3.80117e18	−0.403561
$831$	1.78227e18	0.187745
$832$	−1.02395e19	−1.07023
$833$	−1.13071e19	−1.17262
$834$	2.63781e18	0.271434
$835$	5.47070e17	0.0558574
$836$	1.35076e18	0.136848
$837$	−1.70157e18	−0.171054
$838$	3.02089e18	0.301334
$839$	1.37081e19	1.35683	0.678414	−	0.734680i	$-0.262668\pi$
$839$	1.37081e19	1.35683	0.678414	+	0.734680i	$0.262668\pi$
$840$	−1.34191e17	−0.0131797
$841$	−1.02252e19	−0.996545
$842$	−1.07167e18	−0.103642
$843$	−3.99208e18	−0.383107
$844$	2.33379e18	0.222247
$845$	−8.52797e17	−0.0805893
$846$	−4.52193e18	−0.424050
$847$	4.54888e16	0.00423313
$848$	−2.98684e18	−0.275828
$849$	−8.30821e17	−0.0761390
$850$	−8.11044e18	−0.737601
$851$	−2.81573e19	−2.54125
$852$	−2.31249e18	−0.207120
$853$	9.37089e18	0.832937	0.416469	−	0.909150i	$-0.363268\pi$
$853$	9.37089e18	0.832937	0.416469	+	0.909150i	$0.363268\pi$
$854$	−9.95019e16	−0.00877718
$855$	−5.15663e17	−0.0451426
$856$	−1.27336e19	−1.10630
$857$	5.26665e18	0.454108	0.227054	−	0.973882i	$-0.427091\pi$
$857$	5.26665e18	0.454108	0.227054	+	0.973882i	$0.427091\pi$
$858$	5.33052e18	0.456144
$859$	8.04270e18	0.683040	0.341520	−	0.939874i	$-0.389058\pi$
$859$	8.04270e18	0.683040	0.341520	+	0.939874i	$0.389058\pi$
$860$	2.09658e18	0.176714
$861$	−8.98946e16	−0.00751991
$862$	−3.16677e18	−0.262917
$863$	1.47717e19	1.21720	0.608598	−	0.793479i	$-0.291732\pi$
$863$	1.47717e19	1.21720	0.608598	+	0.793479i	$0.291732\pi$
$864$	1.86286e18	0.152350
$865$	−6.01162e18	−0.487963
$866$	−1.18806e19	−0.957133
$867$	2.76116e18	0.220784
$868$	−2.49824e17	−0.0198270
$869$	1.32970e19	1.04743
$870$	−1.33967e17	−0.0104742
$871$	−5.32668e18	−0.413369
$872$	−1.17653e19	−0.906244
$873$	−1.35108e18	−0.103298
$874$	−6.04041e18	−0.458397
$875$	−5.14507e17	−0.0387560
$876$	−5.66691e15	−0.000423711 0
$877$	2.26858e19	1.68367	0.841836	−	0.539734i	$-0.181475\pi$
$877$	2.26858e19	1.68367	0.841836	+	0.539734i	$0.181475\pi$
$878$	6.69809e18	0.493443
$879$	−9.16729e18	−0.670368
$880$	−2.06273e18	−0.149729
$881$	2.47327e19	1.78209	0.891044	−	0.453918i	$-0.149974\pi$
$881$	2.47327e19	1.78209	0.891044	+	0.453918i	$0.149974\pi$
$882$	−3.50336e18	−0.250576
$883$	−1.62910e19	−1.15665	−0.578327	−	0.815805i	$-0.696294\pi$
$883$	−1.62910e19	−1.15665	−0.578327	+	0.815805i	$0.696294\pi$
$884$	7.88186e18	0.555506
$885$	4.39952e17	0.0307804
$886$	−4.53241e18	−0.314782
$887$	−7.01228e18	−0.483454	−0.241727	−	0.970344i	$-0.577714\pi$
$887$	−7.01228e18	−0.483454	−0.241727	+	0.970344i	$0.577714\pi$
$888$	−1.25813e19	−0.861073
$889$	1.48304e17	0.0100761
$890$	−3.30444e18	−0.222876
$891$	−1.58999e18	−0.106461
$892$	−1.26103e18	−0.0838213
$893$	−8.45859e18	−0.558166
$894$	−4.65156e18	−0.304723
$895$	−8.46060e18	−0.550239
$896$	4.34056e16	0.00280249
$897$	1.81207e19	1.16151
$898$	−1.56990e19	−0.999024
$899$	−8.26903e17	−0.0522416
$900$	1.91028e18	0.119818
$901$	1.36476e19	0.849853
$902$	−2.94570e18	−0.182115
$903$	−4.85445e17	−0.0297968
$904$	1.37617e19	0.838643
$905$	−3.41413e18	−0.206569
$906$	6.02936e18	0.362191
$907$	2.17609e19	1.29786	0.648931	−	0.760847i	$-0.275216\pi$
$907$	2.17609e19	1.29786	0.648931	+	0.760847i	$0.275216\pi$
$908$	−6.97293e18	−0.412912
$909$	2.84547e18	0.167297
$910$	−2.98773e17	−0.0174410
$911$	5.88291e18	0.340975	0.170487	−	0.985360i	$-0.445466\pi$
$911$	5.88291e18	0.340975	0.170487	+	0.985360i	$0.445466\pi$
$912$	−1.26609e18	−0.0728617
$913$	−2.19240e19	−1.25274
$914$	−2.09805e19	−1.19032
$915$	−9.46218e17	−0.0533033
$916$	−1.29271e19	−0.723070
$917$	5.64230e16	0.00313369
$918$	3.09268e18	0.170552
$919$	−2.07394e18	−0.113565	−0.0567827	−	0.998387i	$-0.518084\pi$
$919$	−2.07394e18	−0.113565	−0.0567827	+	0.998387i	$0.518084\pi$
$920$	−1.49480e19	−0.812760
$921$	−2.31636e18	−0.125060
$922$	−1.02527e19	−0.549652
$923$	−1.70704e19	−0.908725
$924$	−2.33442e17	−0.0123399
$925$	−2.19118e19	−1.15015
$926$	−1.16630e19	−0.607907
$927$	6.01423e18	0.311288
$928$	9.05286e17	0.0465290
$929$	−2.07666e19	−1.05989	−0.529947	−	0.848031i	$-0.677788\pi$
$929$	−2.07666e19	−1.05989	−0.529947	+	0.848031i	$0.677788\pi$
$930$	3.12519e18	0.158393
$931$	−6.55329e18	−0.329827
$932$	5.20448e17	0.0260120
$933$	−5.49507e18	−0.272736
$934$	−1.54476e19	−0.761388
$935$	9.42511e18	0.461329
$936$	8.09671e18	0.393564
$937$	−1.34263e19	−0.648108	−0.324054	−	0.946039i	$-0.605046\pi$
$937$	−1.34263e19	−0.648108	−0.324054	+	0.946039i	$0.605046\pi$
$938$	−3.06865e17	−0.0147106
$939$	9.46070e18	0.450398
$940$	−6.31349e18	−0.298496
$941$	1.06489e19	0.500004	0.250002	−	0.968245i	$-0.419569\pi$
$941$	1.06489e19	0.500004	0.250002	+	0.968245i	$0.419569\pi$
$942$	7.14461e18	0.333156
$943$	−1.00137e19	−0.463733
$944$	1.08020e18	0.0496806
$945$	8.91181e16	0.00407061
$946$	−1.59073e19	−0.721611
$947$	−3.41478e19	−1.53846	−0.769232	−	0.638969i	$-0.779361\pi$
$947$	−3.41478e19	−1.53846	−0.769232	+	0.638969i	$0.779361\pi$
$948$	6.09181e18	0.272579
$949$	−4.18321e16	−0.00185900
$950$	−4.70060e18	−0.207467
$951$	2.33436e19	1.02328
$952$	1.50545e18	0.0655428
$953$	1.27884e19	0.552985	0.276493	−	0.961016i	$-0.410828\pi$
$953$	1.27884e19	0.552985	0.276493	+	0.961016i	$0.410828\pi$
$954$	4.22853e18	0.181604
$955$	7.02914e18	0.299834
$956$	−7.89815e18	−0.334618
$957$	−7.72680e17	−0.0325141
$958$	1.12322e19	0.469452
$959$	1.08641e17	0.00450997
$960$	−5.60958e18	−0.231295
$961$	−5.12748e18	−0.209992
$962$	−2.80119e19	−1.13947
$963$	8.45657e18	0.341683
$964$	3.43077e17	0.0137686
$965$	1.71516e19	0.683717
$966$	1.04392e18	0.0413347
$967$	3.66407e19	1.44109	0.720545	−	0.693408i	$-0.243892\pi$
$967$	3.66407e19	1.44109	0.720545	+	0.693408i	$0.243892\pi$
$968$	2.26412e18	0.0884522
$969$	5.78507e18	0.224494
$970$	2.48147e18	0.0956518
$971$	2.18984e19	0.838468	0.419234	−	0.907878i	$-0.362299\pi$
$971$	2.18984e19	0.838468	0.419234	+	0.907878i	$0.362299\pi$
$972$	−7.28431e17	−0.0277050
$973$	−8.52741e17	−0.0322169
$974$	5.82782e18	0.218712
$975$	1.41014e19	0.525692
$976$	−2.32322e18	−0.0860334
$977$	3.15469e19	1.16049	0.580246	−	0.814441i	$-0.302956\pi$
$977$	3.15469e19	1.16049	0.580246	+	0.814441i	$0.302956\pi$
$978$	−3.34492e18	−0.122232
$979$	−1.90590e19	−0.691851
$980$	−4.89137e18	−0.176385
$981$	7.81350e18	0.279896
$982$	−2.61657e19	−0.931124
$983$	−1.64360e19	−0.581029	−0.290514	−	0.956871i	$-0.593826\pi$
$983$	−1.64360e19	−0.581029	−0.290514	+	0.956871i	$0.593826\pi$
$984$	−4.47433e18	−0.157130
$985$	8.35468e18	0.291470
$986$	1.50293e18	0.0520883
$987$	1.46183e18	0.0503311
$988$	4.56812e18	0.156249
$989$	−5.40755e19	−1.83749
$990$	2.92026e18	0.0985808
$991$	2.50355e19	0.839610	0.419805	−	0.907614i	$-0.362098\pi$
$991$	2.50355e19	0.839610	0.419805	+	0.907614i	$0.362098\pi$
$992$	−2.11186e19	−0.703621
$993$	1.90149e19	0.629396
$994$	−9.83411e17	−0.0323388
$995$	−1.55304e19	−0.507378
$996$	−1.00442e19	−0.326007
$997$	−4.00653e19	−1.29196	−0.645981	−	0.763354i	$-0.723551\pi$
$997$	−4.00653e19	−1.29196	−0.645981	+	0.763354i	$0.723551\pi$
$998$	3.30630e19	1.05924
$999$	8.35540e18	0.265945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.20	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.20	✓	31	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)

\(f(q)\)	\(=\)	\(q+68.2207 q^{2} +729.000 q^{3} -3537.94 q^{4} -14307.6 q^{5} +49732.9 q^{6} -16077.5 q^{7} -800224. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+68.2207 q^{2} +729.000 q^{3} -3537.94 q^{4} -14307.6 q^{5} +49732.9 q^{6} -16077.5 q^{7} -800224. q^{8} +531441. q^{9} -976072. q^{10} -5.62969e6 q^{11} -2.57916e6 q^{12} -1.90389e7 q^{13} -1.09681e6 q^{14} -1.04302e7 q^{15} -2.56090e7 q^{16} +1.17014e8 q^{17} +3.62553e7 q^{18} +6.78180e7 q^{19} +5.06193e7 q^{20} -1.17205e7 q^{21} -3.84061e8 q^{22} -1.30559e9 q^{23} -5.83364e8 q^{24} -1.01600e9 q^{25} -1.29885e9 q^{26} +3.87420e8 q^{27} +5.68811e7 q^{28} +1.88273e8 q^{29} -7.11557e8 q^{30} -4.39205e9 q^{31} +4.80837e9 q^{32} -4.10404e9 q^{33} +7.98274e9 q^{34} +2.30029e8 q^{35} -1.88021e9 q^{36} +2.15668e10 q^{37} +4.62659e9 q^{38} -1.38794e10 q^{39} +1.14493e10 q^{40} +7.66988e9 q^{41} -7.99578e8 q^{42} +4.14186e10 q^{43} +1.99175e10 q^{44} -7.60363e9 q^{45} -8.90679e10 q^{46} -1.24725e11 q^{47} -1.86690e10 q^{48} -9.66305e10 q^{49} -6.93120e10 q^{50} +8.53029e10 q^{51} +6.73585e10 q^{52} +1.16632e11 q^{53} +2.64301e10 q^{54} +8.05471e10 q^{55} +1.28656e10 q^{56} +4.94393e10 q^{57} +1.28441e10 q^{58} -4.21805e10 q^{59} +3.69015e10 q^{60} +9.07189e10 q^{61} -2.99628e11 q^{62} -8.54422e9 q^{63} +5.37820e11 q^{64} +2.72400e11 q^{65} -2.79980e11 q^{66} +2.79779e11 q^{67} -4.13987e11 q^{68} -9.51772e11 q^{69} +1.56928e10 q^{70} +8.96606e11 q^{71} -4.25272e11 q^{72} +2.19719e9 q^{73} +1.47130e12 q^{74} -7.40661e11 q^{75} -2.39936e11 q^{76} +9.05110e10 q^{77} -9.46859e11 q^{78} -2.36194e12 q^{79} +3.66403e11 q^{80} +2.82430e11 q^{81} +5.23244e11 q^{82} +3.89435e12 q^{83} +4.14663e10 q^{84} -1.67418e12 q^{85} +2.82560e12 q^{86} +1.37251e11 q^{87} +4.50501e12 q^{88} +3.38545e12 q^{89} -5.18725e11 q^{90} +3.06097e11 q^{91} +4.61908e12 q^{92} -3.20180e12 q^{93} -8.50881e12 q^{94} -9.70311e11 q^{95} +3.50530e12 q^{96} -2.54230e12 q^{97} -6.59220e12 q^{98} -2.99185e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more